LMFDB - Embedded newform 820.2.y.a.413.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (of order $8$, degree $4$, 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:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			413.18
Character	$\chi$	$=$	820.413
Dual form			820.2.y.a.137.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.30222 - 0.953612i) q^{3} +(0.939983 - 2.02890i) q^{5} +(1.81993 + 4.39370i) q^{7} +(2.26953 - 2.26953i) q^{9} +(3.08755 + 1.27890i) q^{11} +(1.71733 - 0.711343i) q^{13} +(0.229267 - 5.56736i) q^{15} +(-4.11242 - 1.70342i) q^{17} +(-0.225557 + 0.0934287i) q^{19} +(8.37976 + 8.37976i) q^{21} +(-3.37958 + 3.37958i) q^{23} +(-3.23286 - 3.81426i) q^{25} +(0.199878 - 0.482549i) q^{27} +(-4.05714 - 1.68052i) q^{29} +9.60705i q^{31} +8.32780 q^{33} +(10.6251 + 0.437547i) q^{35} +(8.12274 - 8.12274i) q^{37} +(3.27534 - 3.27534i) q^{39} +(-4.10553 - 4.91372i) q^{41} -1.26633 q^{43} +(-2.47133 - 6.73797i) q^{45} +(-7.56224 - 3.13238i) q^{47} +(-11.0427 + 11.0427i) q^{49} -11.0921 q^{51} +(-2.33993 - 5.64909i) q^{53} +(5.49701 - 5.06218i) q^{55} +(-0.430187 + 0.430187i) q^{57} -11.0740i q^{59} +(8.54979 - 8.54979i) q^{61} +(14.1020 + 5.84124i) q^{63} +(0.171021 - 4.15295i) q^{65} +(0.679022 + 0.281260i) q^{67} +(-4.55774 + 11.0034i) q^{69} +(-0.438426 + 1.05846i) q^{71} +2.84077 q^{73} +(-11.0801 - 5.69838i) q^{75} +15.8933i q^{77} +(2.27767 - 5.49878i) q^{79} +8.32726i q^{81} +(-8.13593 - 8.13593i) q^{83} +(-7.32167 + 6.74250i) q^{85} -10.9430 q^{87} +(-14.3912 - 5.96104i) q^{89} +(6.25085 + 6.25085i) q^{91} +(9.16139 + 22.1176i) q^{93} +(-0.0224622 + 0.545454i) q^{95} +(-2.02715 + 4.89398i) q^{97} +(9.90980 - 4.10477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	2.30222	−	0.953612i	1.32919	−	0.550568i	0.398765	−	0.917053i	$-0.369439\pi$
$3$	2.30222	−	0.953612i	1.32919	−	0.550568i	0.930424	+	0.366485i	$0.119439\pi$
$4$		0			0
$5$	0.939983	−	2.02890i	0.420373	−	0.907351i
$5$	0.939983	−	2.02890i	0.420373	−	0.907351i
$6$		0			0
$7$	1.81993	+	4.39370i	0.687868	+	1.66066i	0.749033	+	0.662533i	$0.230519\pi$
$7$	1.81993	+	4.39370i	0.687868	+	1.66066i	−0.0611643	+	0.998128i	$0.519481\pi$
$8$		0			0
$9$	2.26953	−	2.26953i	0.756510	−	0.756510i
$10$		0			0
$11$	3.08755	+	1.27890i	0.930931	+	0.385604i	0.796031	−	0.605255i	$-0.206929\pi$
$11$	3.08755	+	1.27890i	0.930931	+	0.385604i	0.134899	+	0.990859i	$0.456929\pi$
$12$		0			0
$13$	1.71733	−	0.711343i	0.476303	−	0.197291i	−0.131599	−	0.991303i	$-0.542011\pi$
$13$	1.71733	−	0.711343i	0.476303	−	0.197291i	0.607902	+	0.794012i	$0.292011\pi$
$14$		0			0
$15$	0.229267	−	5.56736i	0.0591966	−	1.43748i
$16$		0			0
$17$	−4.11242	−	1.70342i	−0.997408	−	0.413140i	−0.176562	−	0.984290i	$-0.556498\pi$
$17$	−4.11242	−	1.70342i	−0.997408	−	0.413140i	−0.820846	+	0.571150i	$0.806498\pi$
$18$		0			0
$19$	−0.225557	+	0.0934287i	−0.0517463	+	0.0214340i	−0.408406	−	0.912800i	$-0.633915\pi$
$19$	−0.225557	+	0.0934287i	−0.0517463	+	0.0214340i	0.356660	+	0.934234i	$0.383915\pi$
$20$		0			0
$21$	8.37976	+	8.37976i	1.82861	+	1.82861i
$22$		0			0
$23$	−3.37958	+	3.37958i	−0.704692	+	0.704692i	−0.965414	−	0.260722i	$-0.916039\pi$
$23$	−3.37958	+	3.37958i	−0.704692	+	0.704692i	0.260722	+	0.965414i	$0.416039\pi$
$24$		0			0
$25$	−3.23286	−	3.81426i	−0.646573	−	0.762852i
$26$		0			0
$27$	0.199878	−	0.482549i	0.0384666	−	0.0928666i
$28$		0			0
$29$	−4.05714	−	1.68052i	−0.753391	−	0.312065i	−0.0272669	−	0.999628i	$-0.508680\pi$
$29$	−4.05714	−	1.68052i	−0.753391	−	0.312065i	−0.726124	+	0.687563i	$0.758680\pi$
$30$		0			0
$31$			9.60705i			1.72548i	0.505651	+	0.862738i	$0.331252\pi$
$31$			9.60705i			1.72548i	−0.505651	+	0.862738i	$0.668748\pi$
$32$		0			0
$33$	8.32780			1.44968
$34$		0			0
$35$	10.6251	+	0.437547i	1.79596	+	0.0739590i
$36$		0			0
$37$	8.12274	−	8.12274i	1.33537	−	1.33537i	0.434882	−	0.900487i	$-0.356790\pi$
$37$	8.12274	−	8.12274i	1.33537	−	1.33537i	0.900487	−	0.434882i	$-0.143210\pi$
$38$		0			0
$39$	3.27534	−	3.27534i	0.524474	−	0.524474i
$40$		0			0
$41$	−4.10553	−	4.91372i	−0.641176	−	0.767394i
$41$	−4.10553	−	4.91372i	−0.641176	−	0.767394i
$42$		0			0
$43$	−1.26633			−0.193113			−0.0965566	−	0.995327i	$-0.530783\pi$
$43$	−1.26633			−0.193113			−0.0965566	+	0.995327i	$0.530783\pi$
$44$		0			0
$45$	−2.47133	−	6.73797i	−0.368404	−	1.00444i
$46$		0			0
$47$	−7.56224	−	3.13238i	−1.10307	−	0.456905i	−0.244522	−	0.969644i	$-0.578631\pi$
$47$	−7.56224	−	3.13238i	−1.10307	−	0.456905i	−0.858545	+	0.512739i	$0.828631\pi$
$48$		0			0
$49$	−11.0427	+	11.0427i	−1.57753	+	1.57753i
$50$		0			0
$51$	−11.0921			−1.55320
$52$		0			0
$53$	−2.33993	−	5.64909i	−0.321414	−	0.775963i	−0.999172	−	0.0406777i	$-0.987048\pi$
$53$	−2.33993	−	5.64909i	−0.321414	−	0.775963i	0.677758	−	0.735285i	$-0.262952\pi$
$54$		0			0
$55$	5.49701	−	5.06218i	0.741217	−	0.682584i
$56$		0			0
$57$	−0.430187	+	0.430187i	−0.0569797	+	0.0569797i
$58$		0			0
$59$		−	11.0740i		−	1.44171i	−0.693085	−	0.720855i	$-0.743749\pi$
$59$		−	11.0740i		−	1.44171i	0.693085	−	0.720855i	$-0.256251\pi$
$60$		0			0
$61$	8.54979	−	8.54979i	1.09469	−	1.09469i	0.0996673	−	0.995021i	$-0.468222\pi$
$61$	8.54979	−	8.54979i	1.09469	−	1.09469i	0.995021	−	0.0996673i	$-0.0317778\pi$
$62$		0			0
$63$	14.1020	+	5.84124i	1.77669	+	0.735928i
$64$		0			0
$65$	0.171021	−	4.15295i	0.0212126	−	0.515110i
$66$		0			0
$67$	0.679022	+	0.281260i	0.0829557	+	0.0343614i	0.423775	−	0.905767i	$-0.360705\pi$
$67$	0.679022	+	0.281260i	0.0829557	+	0.0343614i	−0.340820	+	0.940129i	$0.610705\pi$
$68$		0			0
$69$	−4.55774	+	11.0034i	−0.548688	+	1.32465i
$70$		0			0
$71$	−0.438426	+	1.05846i	−0.0520316	+	0.125616i	−0.947758	−	0.318990i	$-0.896656\pi$
$71$	−0.438426	+	1.05846i	−0.0520316	+	0.125616i	0.895726	+	0.444606i	$0.146656\pi$
$72$		0			0
$73$	2.84077			0.332487			0.166243	−	0.986085i	$-0.446836\pi$
$73$	2.84077			0.332487			0.166243	+	0.986085i	$0.446836\pi$
$74$		0			0
$75$	−11.0801	−	5.69838i	−1.27942	−	0.657992i
$76$		0			0
$77$			15.8933i			1.81121i
$78$		0			0
$79$	2.27767	−	5.49878i	0.256258	−	0.618661i	−0.742427	−	0.669927i	$-0.766326\pi$
$79$	2.27767	−	5.49878i	0.256258	−	0.618661i	0.998685	+	0.0512659i	$0.0163256\pi$
$80$		0			0
$81$			8.32726i			0.925251i
$82$		0			0
$83$	−8.13593	−	8.13593i	−0.893034	−	0.893034i	0.101774	−	0.994808i	$-0.467548\pi$
$83$	−8.13593	−	8.13593i	−0.893034	−	0.893034i	−0.994808	+	0.101774i	$0.967548\pi$
$84$		0			0
$85$	−7.32167	+	6.74250i	−0.794146	+	0.731326i
$86$		0			0
$87$	−10.9430			−1.17321
$88$		0			0
$89$	−14.3912	−	5.96104i	−1.52547	−	0.631869i	−0.546788	−	0.837271i	$-0.684150\pi$
$89$	−14.3912	−	5.96104i	−1.52547	−	0.631869i	−0.978678	+	0.205402i	$0.934150\pi$
$90$		0			0
$91$	6.25085	+	6.25085i	0.655267	+	0.655267i
$92$		0			0
$93$	9.16139	+	22.1176i	0.949992	+	2.29348i
$94$		0			0
$95$	−0.0224622	+	0.545454i	−0.00230457	+	0.0559624i
$96$		0			0
$97$	−2.02715	+	4.89398i	−0.205826	+	0.496908i	−0.992758	−	0.120132i	$-0.961668\pi$
$97$	−2.02715	+	4.89398i	−0.205826	+	0.496908i	0.786932	+	0.617040i	$0.211668\pi$
$98$		0			0
$99$	9.90980	−	4.10477i	0.995972	−	0.412545i
$100$		0			0
$101$	3.86628	+	9.33402i	0.384709	+	0.928770i	0.991041	+	0.133558i	$0.0426403\pi$
$101$	3.86628	+	9.33402i	0.384709	+	0.928770i	−0.606332	+	0.795212i	$0.707360\pi$
$102$		0			0
$103$			7.95360i			0.783692i	0.920031	+	0.391846i	$0.128163\pi$
$103$			7.95360i			0.783692i	−0.920031	+	0.391846i	$0.871837\pi$
$104$		0			0
$105$	24.8785	−	9.12486i	2.42789	−	0.890495i
$106$		0			0
$107$	2.82796	+	2.82796i	0.273389	+	0.273389i	0.830463	−	0.557074i	$-0.188076\pi$
$107$	2.82796	+	2.82796i	0.273389	+	0.273389i	−0.557074	+	0.830463i	$0.688076\pi$
$108$		0			0
$109$	0.490710	+	1.18468i	0.0470014	+	0.113472i	0.945637	−	0.325225i	$-0.105440\pi$
$109$	0.490710	+	1.18468i	0.0470014	+	0.113472i	−0.898635	+	0.438697i	$0.855440\pi$
$110$		0			0
$111$	10.9544	−	26.4463i	1.03975	−	2.51017i
$112$		0			0
$113$	−5.14733	+	5.14733i	−0.484220	+	0.484220i	−0.906476	−	0.422257i	$-0.861238\pi$
$113$	−5.14733	+	5.14733i	−0.484220	+	0.484220i	0.422257	+	0.906476i	$0.361238\pi$
$114$		0			0
$115$	3.68009	+	10.0336i	0.343170	+	0.935637i
$116$		0			0
$117$	2.28313	−	5.51196i	0.211075	−	0.509581i
$118$		0			0
$119$		−	21.1688i		−	1.94054i
$120$		0			0
$121$	0.119181	+	0.119181i	0.0108347	+	0.0108347i
$122$		0			0
$123$	−14.1376	−	7.39740i	−1.27475	−	0.667001i
$124$		0			0
$125$	−10.7776	+	2.97382i	−0.963977	+	0.265986i
$126$		0			0
$127$	−7.67074	−	7.67074i	−0.680668	−	0.680668i	0.279483	−	0.960151i	$-0.409837\pi$
$127$	−7.67074	−	7.67074i	−0.680668	−	0.680668i	−0.960151	+	0.279483i	$0.909837\pi$
$128$		0			0
$129$	−2.91537	+	1.20759i	−0.256684	+	0.106322i
$130$		0			0
$131$	12.2673	+	12.2673i	1.07180	+	1.07180i	0.997215	+	0.0745802i	$0.0237617\pi$
$131$	12.2673	+	12.2673i	1.07180	+	1.07180i	0.0745802	+	0.997215i	$0.476238\pi$
$132$		0			0
$133$	−0.820995	−	0.820995i	−0.0711893	−	0.0711893i
$134$		0			0
$135$	−0.791161	−	0.859120i	−0.0680923	−	0.0739413i
$136$		0			0
$137$	12.7096	+	5.26448i	1.08585	+	0.449775i	0.852559	−	0.522631i	$-0.175049\pi$
$137$	12.7096	+	5.26448i	1.08585	+	0.449775i	0.233294	+	0.972406i	$0.425049\pi$
$138$		0			0
$139$			4.87550i			0.413534i	0.978390	+	0.206767i	$0.0662943\pi$
$139$			4.87550i			0.413534i	−0.978390	+	0.206767i	$0.933706\pi$
$140$		0			0
$141$	−20.3970			−1.71774
$142$		0			0
$143$	6.21209			0.519481
$144$		0			0
$145$	−7.22325	+	6.65186i	−0.599858	+	0.552407i
$146$		0			0
$147$	−14.8923	+	35.9531i	−1.22829	+	2.96536i
$148$		0			0
$149$	17.3040	−	7.16754i	1.41760	−	0.587188i	0.463341	−	0.886180i	$-0.346650\pi$
$149$	17.3040	−	7.16754i	1.41760	−	0.587188i	0.954256	+	0.298992i	$0.0966504\pi$
$150$		0			0
$151$	4.79800	+	1.98740i	0.390456	+	0.161732i	0.569270	−	0.822151i	$-0.307226\pi$
$151$	4.79800	+	1.98740i	0.390456	+	0.161732i	−0.178814	+	0.983883i	$0.557226\pi$
$152$		0			0
$153$	−13.1992	+	5.46730i	−1.06709	+	0.442005i
$154$		0			0
$155$	19.4917	+	9.03046i	1.56561	+	0.725344i
$156$		0			0
$157$	−1.07783	+	0.446451i	−0.0860200	+	0.0356306i	−0.425279	−	0.905063i	$-0.639824\pi$
$157$	−1.07783	+	0.446451i	−0.0860200	+	0.0356306i	0.339259	+	0.940693i	$0.389824\pi$
$158$		0			0
$159$	−10.7741	−	10.7741i	−0.854440	−	0.854440i
$160$		0			0
$161$	−20.9995	−	8.69826i	−1.65499	−	0.685519i
$162$		0			0
$163$	−11.5006	+	11.5006i	−0.900793	+	0.900793i	−0.995505	−	0.0947116i	$-0.969807\pi$
$163$	−11.5006	+	11.5006i	−0.900793	+	0.900793i	0.0947116	+	0.995505i	$0.469807\pi$
$164$		0			0
$165$	7.82799	−	16.8963i	0.609408	−	1.31537i
$166$		0			0
$167$	5.80682	+	14.0189i	0.449345	+	1.08482i	0.972568	+	0.232620i	$0.0747297\pi$
$167$	5.80682	+	14.0189i	0.449345	+	1.08482i	−0.523222	+	0.852196i	$0.675270\pi$
$168$		0			0
$169$	−6.74916	+	6.74916i	−0.519166	+	0.519166i
$170$		0			0
$171$	−0.299869	+	0.723948i	−0.0229316	+	0.0553617i
$172$		0			0
$173$			5.40142i			0.410662i	0.978693	+	0.205331i	$0.0658272\pi$
$173$			5.40142i			0.410662i	−0.978693	+	0.205331i	$0.934173\pi$
$174$		0			0
$175$	10.8751	−	21.1459i	0.822082	−	1.59848i
$176$		0			0
$177$	−10.5603	−	25.4948i	−0.793760	−	1.91631i
$178$		0			0
$179$	3.76050	+	9.07864i	0.281073	+	0.678569i	0.999861	−	0.0166593i	$-0.00530307\pi$
$179$	3.76050	+	9.07864i	0.281073	+	0.678569i	−0.718789	+	0.695229i	$0.755303\pi$
$180$		0			0
$181$	4.83941	+	11.6834i	0.359711	+	0.868418i	0.995340	+	0.0964240i	$0.0307405\pi$
$181$	4.83941	+	11.6834i	0.359711	+	0.868418i	−0.635630	+	0.771994i	$0.719260\pi$
$182$		0			0
$183$	11.5303	−	27.8367i	0.852347	−	2.05775i
$184$		0			0
$185$	−8.84498	−	24.1154i	−0.650296	−	1.77300i
$186$		0			0
$187$	−10.5188	−	10.5188i	−0.769209	−	0.769209i
$188$		0			0
$189$	2.48394			0.180680
$190$		0			0
$191$	1.74315	−	0.722037i	0.126130	−	0.0522448i	−0.318726	−	0.947847i	$-0.603255\pi$
$191$	1.74315	−	0.722037i	0.126130	−	0.0522448i	0.444856	+	0.895602i	$0.353255\pi$
$192$		0			0
$193$	−12.7054	+	5.26274i	−0.914553	+	0.378820i	−0.789798	−	0.613367i	$-0.789814\pi$
$193$	−12.7054	+	5.26274i	−0.914553	+	0.378820i	−0.124755	+	0.992188i	$0.539814\pi$
$194$		0			0
$195$	−3.56657	−	9.72410i	−0.255408	−	0.696357i
$196$		0			0
$197$		−	5.84936i		−	0.416750i	−0.978049	−	0.208375i	$-0.933183\pi$
$197$		−	5.84936i		−	0.416750i	0.978049	−	0.208375i	$-0.0668174\pi$
$198$		0			0
$199$	5.41583	+	13.0750i	0.383918	+	0.926860i	0.991200	+	0.132374i	$0.0422599\pi$
$199$	5.41583	+	13.0750i	0.383918	+	0.926860i	−0.607282	+	0.794487i	$0.707740\pi$
$200$		0			0
$201$	1.83147			0.129182
$202$		0			0
$203$		−	20.8843i		−	1.46579i
$204$		0			0
$205$	−13.8286	+	3.71089i	−0.965829	+	0.259180i
$206$		0			0
$207$			15.3401i			1.06621i
$208$		0			0
$209$	−0.815904			−0.0564373
$210$		0			0
$211$	−4.23485	−	10.2238i	−0.291539	−	0.703837i	0.708459	−	0.705752i	$-0.249391\pi$
$211$	−4.23485	−	10.2238i	−0.291539	−	0.703837i	−0.999998	+	0.00191443i	$0.999391\pi$
$212$		0			0
$213$			2.85489i			0.195614i
$214$		0			0
$215$	−1.19033	+	2.56925i	−0.0811796	+	0.175222i
$216$		0			0
$217$	−42.2104	+	17.4841i	−2.86543	+	1.18690i
$218$		0			0
$219$	6.54008	−	2.70899i	0.441937	−	0.183056i
$220$		0			0
$221$	−8.27411			−0.556577
$222$		0			0
$223$	5.58256	+	5.58256i	0.373836	+	0.373836i	0.868872	−	0.495036i	$-0.164845\pi$
$223$	5.58256	+	5.58256i	0.373836	+	0.373836i	−0.495036	+	0.868872i	$0.664845\pi$
$224$		0			0
$225$	−15.9937	−	1.31950i	−1.06624	−	0.0879665i
$226$		0			0
$227$	−0.394646	+	0.952759i	−0.0261935	+	0.0632368i	−0.936435	−	0.350841i	$-0.885896\pi$
$227$	−0.394646	+	0.952759i	−0.0261935	+	0.0632368i	0.910242	+	0.414078i	$0.135896\pi$
$228$		0			0
$229$	3.96815	+	9.57997i	0.262223	+	0.633062i	0.999075	−	0.0429914i	$-0.0136888\pi$
$229$	3.96815	+	9.57997i	0.262223	+	0.633062i	−0.736853	+	0.676053i	$0.763689\pi$
$230$		0			0
$231$	15.1560	+	36.5898i	0.997191	+	2.40743i
$232$		0			0
$233$	5.12878	+	12.3820i	0.335998	+	0.811170i	0.998092	+	0.0617495i	$0.0196680\pi$
$233$	5.12878	+	12.3820i	0.335998	+	0.811170i	−0.662094	+	0.749421i	$0.730332\pi$
$234$		0			0
$235$	−13.4637	+	12.3986i	−0.878273	+	0.808798i
$236$		0			0
$237$		−	14.8314i		−	0.963404i
$238$		0			0
$239$	4.12752	−	9.96472i	0.266987	−	0.644564i	−0.732352	−	0.680927i	$-0.761577\pi$
$239$	4.12752	−	9.96472i	0.266987	−	0.644564i	0.999339	+	0.0363628i	$0.0115772\pi$
$240$		0			0
$241$	16.0789	−	16.0789i	1.03573	−	1.03573i	0.0363924	−	0.999338i	$-0.488413\pi$
$241$	16.0789	−	16.0789i	1.03573	−	1.03573i	0.999338	−	0.0363924i	$-0.0115866\pi$
$242$		0			0
$243$	8.54061	+	20.6189i	0.547880	+	1.32270i
$244$		0			0
$245$	12.0245	+	32.7844i	0.768220	+	2.09452i
$246$		0			0
$247$	−0.320897	+	0.320897i	−0.0204182	+	0.0204182i
$248$		0			0
$249$	−26.4892	−	10.9722i	−1.67869	−	0.695335i
$250$		0			0
$251$	−5.71142	−	5.71142i	−0.360502	−	0.360502i	0.503496	−	0.863998i	$-0.332047\pi$
$251$	−5.71142	−	5.71142i	−0.360502	−	0.360502i	−0.863998	+	0.503496i	$0.832047\pi$
$252$		0			0
$253$	−14.7568	+	6.11246i	−0.927752	+	0.384287i
$254$		0			0
$255$	−10.4264	+	22.5047i	−0.652925	+	1.40930i
$256$		0			0
$257$	−15.9445	+	6.60442i	−0.994589	+	0.411972i	−0.819810	−	0.572635i	$-0.805921\pi$
$257$	−15.9445	+	6.60442i	−0.994589	+	0.411972i	−0.174779	+	0.984608i	$0.555921\pi$
$258$		0			0
$259$	50.4716	+	20.9060i	3.13615	+	1.29904i
$260$		0			0
$261$	−13.0218	+	5.39380i	−0.806029	+	0.333868i
$262$		0			0
$263$	−1.89306	+	4.57025i	−0.116731	+	0.281813i	−0.971436	−	0.237300i	$-0.923738\pi$
$263$	−1.89306	+	4.57025i	−0.116731	+	0.281813i	0.854706	+	0.519113i	$0.173738\pi$
$264$		0			0
$265$	−13.6609	−	0.562567i	−0.839185	−	0.0345582i
$266$		0			0
$267$	−38.8163			−2.37552
$268$		0			0
$269$	29.2245			1.78185			0.890926	−	0.454149i	$-0.150057\pi$
$269$	29.2245			1.78185			0.890926	+	0.454149i	$0.150057\pi$
$270$		0			0
$271$		−	8.57120i		−	0.520663i	−0.965519	−	0.260332i	$-0.916168\pi$
$271$		−	8.57120i		−	0.520663i	0.965519	−	0.260332i	$-0.0838319\pi$
$272$		0			0
$273$	20.3517	+	8.42996i	1.23174	+	0.510205i
$274$		0			0
$275$	−5.10355	−	15.9112i	−0.307756	−	0.959484i
$276$		0			0
$277$	−22.5943	−	22.5943i	−1.35756	−	1.35756i	−0.876916	−	0.480645i	$-0.840403\pi$
$277$	−22.5943	−	22.5943i	−1.35756	−	1.35756i	−0.480645	−	0.876916i	$-0.659597\pi$
$278$		0			0
$279$	21.8035	+	21.8035i	1.30534	+	1.30534i
$280$		0			0
$281$	12.5253	−	5.18815i	0.747197	−	0.309499i	0.0236000	−	0.999721i	$-0.492487\pi$
$281$	12.5253	−	5.18815i	0.747197	−	0.309499i	0.723598	+	0.690222i	$0.242487\pi$
$282$		0			0
$283$	−20.4032	−	20.4032i	−1.21285	−	1.21285i	−0.970086	−	0.242760i	$-0.921947\pi$
$283$	−20.4032	−	20.4032i	−1.21285	−	1.21285i	−0.242760	−	0.970086i	$-0.578053\pi$
$284$		0			0
$285$	0.468438	+	1.27718i	0.0277479	+	0.0756534i
$286$		0			0
$287$	14.1176	−	26.9811i	0.833337	−	1.59264i
$288$		0			0
$289$	1.98952	+	1.98952i	0.117031	+	0.117031i
$290$		0			0
$291$			13.2001i			0.773806i
$292$		0			0
$293$	−0.267450	+	0.645681i	−0.0156246	+	0.0377211i	−0.931499	−	0.363743i	$-0.881499\pi$
$293$	−0.267450	+	0.645681i	−0.0156246	+	0.0377211i	0.915875	+	0.401464i	$0.131499\pi$
$294$		0			0
$295$	−22.4680	−	10.4094i	−1.30814	−	0.606056i
$296$		0			0
$297$	1.23427	−	1.23427i	0.0716195	−	0.0716195i
$298$		0			0
$299$	−3.39983	+	8.20792i	−0.196617	+	0.474676i
$300$		0			0
$301$	−2.30463	−	5.56386i	−0.132836	−	0.320696i
$302$		0			0
$303$	17.8021	+	17.8021i	1.02270	+	1.02270i
$304$		0			0
$305$	−9.31000	−	25.3833i	−0.533089	−	1.45344i
$306$		0			0
$307$			2.63739i			0.150524i	0.997164	+	0.0752618i	$0.0239792\pi$
$307$			2.63739i			0.150524i	−0.997164	+	0.0752618i	$0.976021\pi$
$308$		0			0
$309$	7.58465	+	18.3110i	0.431475	+	1.04167i
$310$		0			0
$311$	20.1237	−	8.33552i	1.14111	−	0.472664i	0.269568	−	0.962981i	$-0.413119\pi$
$311$	20.1237	−	8.33552i	1.14111	−	0.472664i	0.871544	+	0.490317i	$0.163119\pi$
$312$		0			0
$313$	−10.1585	+	24.5247i	−0.574191	+	1.38622i	0.323767	+	0.946137i	$0.395051\pi$
$313$	−10.1585	+	24.5247i	−0.574191	+	1.38622i	−0.897957	+	0.440082i	$0.854949\pi$
$314$		0			0
$315$	25.1069	−	23.1209i	1.41462	−	1.30271i
$316$		0			0
$317$	5.57451	+	13.4580i	0.313095	+	0.755879i	0.999587	+	0.0287414i	$0.00914992\pi$
$317$	5.57451	+	13.4580i	0.313095	+	0.755879i	−0.686491	+	0.727138i	$0.740850\pi$
$318$		0			0
$319$	−10.3774	−	10.3774i	−0.581022	−	0.581022i
$320$		0			0
$321$	9.20735	+	3.81381i	0.513904	+	0.212866i
$322$		0			0
$323$	1.08673			0.0604674
$324$		0			0
$325$	−8.26516	−	4.25069i	−0.458469	−	0.235786i
$326$		0			0
$327$	2.25944	+	2.25944i	0.124948	+	0.124948i
$328$		0			0
$329$		−	38.9269i		−	2.14611i
$330$		0			0
$331$	7.96851	−	19.2377i	0.437989	−	1.05740i	−0.538654	−	0.842527i	$-0.681067\pi$
$331$	7.96851	−	19.2377i	0.437989	−	1.05740i	0.976642	−	0.214871i	$-0.0689331\pi$
$332$		0			0
$333$		−	36.8696i		−	2.02044i
$334$		0			0
$335$	1.20892	−	1.11329i	0.0660502	−	0.0608254i
$336$		0			0
$337$	31.4036			1.71066			0.855331	−	0.518081i	$-0.173353\pi$
$337$	31.4036			1.71066			0.855331	+	0.518081i	$0.173353\pi$
$338$		0			0
$339$	−6.94174	+	16.7588i	−0.377023	+	0.910215i
$340$		0			0
$341$	−12.2865	+	29.6622i	−0.665351	+	1.60630i
$342$		0			0
$343$	−37.8592	−	15.6818i	−2.04420	−	0.846736i
$344$		0			0
$345$	18.0405	+	19.5902i	0.971269	+	1.05470i
$346$		0			0
$347$	−15.3701	−	6.36649i	−0.825108	−	0.341771i	−0.0701440	−	0.997537i	$-0.522346\pi$
$347$	−15.3701	−	6.36649i	−0.825108	−	0.341771i	−0.754964	+	0.655766i	$0.772346\pi$
$348$		0			0
$349$	15.0669	−	15.0669i	0.806514	−	0.806514i	−0.177591	−	0.984104i	$-0.556830\pi$
$349$	15.0669	−	15.0669i	0.806514	−	0.806514i	0.984104	+	0.177591i	$0.0568302\pi$
$350$		0			0
$351$		−	0.970880i		−	0.0518217i
$352$		0			0
$353$	10.7011	−	10.7011i	0.569560	−	0.569560i	−0.362445	−	0.932005i	$-0.618058\pi$
$353$	10.7011	−	10.7011i	0.569560	−	0.569560i	0.932005	+	0.362445i	$0.118058\pi$
$354$		0			0
$355$	1.73539	+	1.88445i	0.0921047	+	0.100016i
$356$		0			0
$357$	−20.1868	−	48.7353i	−1.06840	−	2.57935i
$358$		0			0
$359$	9.40023			0.496125			0.248063	−	0.968744i	$-0.420206\pi$
$359$	9.40023			0.496125			0.248063	+	0.968744i	$0.420206\pi$
$360$		0			0
$361$	−13.3929	+	13.3929i	−0.704889	+	0.704889i
$362$		0			0
$363$	0.388034	+	0.160729i	0.0203665	+	0.00843608i
$364$		0			0
$365$	2.67027	−	5.76363i	0.139768	−	0.301682i
$366$		0			0
$367$	10.9077			0.569377			0.284688	−	0.958620i	$-0.408110\pi$
$367$	10.9077			0.569377			0.284688	+	0.958620i	$0.408110\pi$
$368$		0			0
$369$	−20.4695	−	1.83422i	−1.06560	−	0.0954856i
$370$		0			0
$371$	20.5619	−	20.5619i	1.06752	−	1.06752i
$372$		0			0
$373$	13.7142	−	13.7142i	0.710097	−	0.710097i	−0.256459	−	0.966555i	$-0.582556\pi$
$373$	13.7142	−	13.7142i	0.710097	−	0.710097i	0.966555	+	0.256459i	$0.0825558\pi$
$374$		0			0
$375$	−21.9765	+	17.1240i	−1.13486	+	0.884281i
$376$		0			0
$377$	−8.16289			−0.420410
$378$		0			0
$379$		−	21.9556i		−	1.12778i	−0.825849	−	0.563891i	$-0.809304\pi$
$379$		−	21.9556i		−	1.12778i	0.825849	−	0.563891i	$-0.190696\pi$
$380$		0			0
$381$	−24.9747	−	10.3448i	−1.27949	−	0.529982i
$382$		0			0
$383$	−8.29014	+	20.0142i	−0.423606	+	1.02268i	0.557669	+	0.830064i	$0.311696\pi$
$383$	−8.29014	+	20.0142i	−0.423606	+	1.02268i	−0.981275	+	0.192612i	$0.938304\pi$
$384$		0			0
$385$	32.2458	+	14.9394i	1.64340	+	0.761382i
$386$		0			0
$387$	−2.87397	+	2.87397i	−0.146092	+	0.146092i
$388$		0			0
$389$	−7.74110	−	7.74110i	−0.392490	−	0.392490i	0.483084	−	0.875574i	$-0.339516\pi$
$389$	−7.74110	−	7.74110i	−0.392490	−	0.392490i	−0.875574	+	0.483084i	$0.839516\pi$
$390$		0			0
$391$	19.6551	−	8.14141i	0.994002	−	0.411729i
$392$		0			0
$393$	39.9401	+	16.5438i	2.01471	+	0.834522i
$394$		0			0
$395$	−9.01549	−	9.78991i	−0.453619	−	0.492584i
$396$		0			0
$397$	35.4233	−	14.6728i	1.77785	−	0.736408i	0.784652	−	0.619937i	$-0.212842\pi$
$397$	35.4233	−	14.6728i	1.77785	−	0.736408i	0.993194	−	0.116471i	$-0.0371581\pi$
$398$		0			0
$399$	−2.67302	−	1.10720i	−0.133819	−	0.0554294i
$400$		0			0
$401$	0.208693	−	0.208693i	0.0104216	−	0.0104216i	−0.701877	−	0.712298i	$-0.747654\pi$
$401$	0.208693	−	0.208693i	0.0104216	−	0.0104216i	0.712298	+	0.701877i	$0.247654\pi$
$402$		0			0
$403$	6.83391	+	16.4985i	0.340421	+	0.821849i
$404$		0			0
$405$	16.8952	+	7.82748i	0.839528	+	0.388951i
$406$		0			0
$407$	35.4675	−	14.6911i	1.75806	−	0.728213i
$408$		0			0
$409$	−4.00115			−0.197844			−0.0989221	−	0.995095i	$-0.531539\pi$
$409$	−4.00115			−0.197844			−0.0989221	+	0.995095i	$0.531539\pi$
$410$		0			0
$411$	34.2806			1.69094
$412$		0			0
$413$	48.6557	−	20.1539i	2.39419	−	0.991707i
$414$		0			0
$415$	−24.1546	+	8.85934i	−1.18570	+	0.434888i
$416$		0			0
$417$	4.64933	+	11.2245i	0.227679	+	0.549665i
$418$		0			0
$419$	26.6694	−	26.6694i	1.30288	−	1.30288i	0.376445	−	0.926439i	$-0.377147\pi$
$419$	26.6694	−	26.6694i	1.30288	−	1.30288i	0.926439	−	0.376445i	$-0.122853\pi$
$420$		0			0
$421$	3.13599	+	1.29897i	0.152839	+	0.0633078i	0.457791	−	0.889060i	$-0.348641\pi$
$421$	3.13599	+	1.29897i	0.152839	+	0.0633078i	−0.304953	+	0.952367i	$0.598641\pi$
$422$		0			0
$423$	−24.2718	+	10.0537i	−1.18013	+	0.488828i
$424$		0			0
$425$	6.79760	+	21.1928i	0.329732	+	1.02800i
$426$		0			0
$427$	53.1252	+	22.0052i	2.57091	+	1.06490i
$428$		0			0
$429$	14.3016	−	5.92392i	0.690489	−	0.286010i
$430$		0			0
$431$	−2.36464	−	2.36464i	−0.113901	−	0.113901i	0.647859	−	0.761760i	$-0.275664\pi$
$431$	−2.36464	−	2.36464i	−0.113901	−	0.113901i	−0.761760	+	0.647859i	$0.775664\pi$
$432$		0			0
$433$	−4.26329	+	4.26329i	−0.204881	+	0.204881i	−0.802087	−	0.597207i	$-0.796277\pi$
$433$	−4.26329	+	4.26329i	−0.204881	+	0.204881i	0.597207	+	0.802087i	$0.296277\pi$
$434$		0			0
$435$	−10.2862	+	22.2022i	−0.493187	+	1.06452i
$436$		0			0
$437$	0.446538	−	1.07804i	0.0213608	−	0.0515696i
$438$		0			0
$439$	3.49173	+	1.44632i	0.166651	+	0.0690291i	0.464449	−	0.885600i	$-0.346252\pi$
$439$	3.49173	+	1.44632i	0.166651	+	0.0690291i	−0.297798	+	0.954629i	$0.596252\pi$
$440$		0			0
$441$			50.1234i			2.38683i
$442$		0			0
$443$	−7.32910			−0.348216			−0.174108	−	0.984727i	$-0.555704\pi$
$443$	−7.32910			−0.348216			−0.174108	+	0.984727i	$0.555704\pi$
$444$		0			0
$445$	−25.6218	+	23.5951i	−1.21459	+	1.11851i
$446$		0			0
$447$	33.0025	−	33.0025i	1.56097	−	1.56097i
$448$		0			0
$449$	−19.9406	+	19.9406i	−0.941055	+	0.941055i	−0.998357	−	0.0573016i	$-0.981750\pi$
$449$	−19.9406	+	19.9406i	−0.941055	+	0.941055i	0.0573016	+	0.998357i	$0.481750\pi$
$450$		0			0
$451$	−6.39184	−	20.4219i	−0.300980	−	0.961631i
$452$		0			0
$453$	12.9413			0.608034
$454$		0			0
$455$	18.5580	−	6.80666i	0.870015	−	0.319101i
$456$		0			0
$457$	−9.07504	−	3.75901i	−0.424513	−	0.175839i	0.160191	−	0.987086i	$-0.448789\pi$
$457$	−9.07504	−	3.75901i	−0.424513	−	0.175839i	−0.584703	+	0.811247i	$0.698789\pi$
$458$		0			0
$459$	−1.64397	+	1.64397i	−0.0767337	+	0.0767337i
$460$		0			0
$461$	−12.3439			−0.574912			−0.287456	−	0.957794i	$-0.592809\pi$
$461$	−12.3439			−0.574912			−0.287456	+	0.957794i	$0.592809\pi$
$462$		0			0
$463$	7.25484	+	17.5147i	0.337161	+	0.813979i	0.997986	+	0.0634385i	$0.0202067\pi$
$463$	7.25484	+	17.5147i	0.337161	+	0.813979i	−0.660825	+	0.750540i	$0.729793\pi$
$464$		0			0
$465$	53.4858	+	2.20258i	2.48035	+	0.102142i
$466$		0			0
$467$	−15.0928	+	15.0928i	−0.698412	+	0.698412i	−0.964068	−	0.265656i	$-0.914411\pi$
$467$	−15.0928	+	15.0928i	−0.698412	+	0.698412i	0.265656	+	0.964068i	$0.414411\pi$
$468$		0			0
$469$			3.49529i			0.161397i
$470$		0			0
$471$	−2.05566	+	2.05566i	−0.0947197	+	0.0947197i
$472$		0			0
$473$	−3.90985	−	1.61951i	−0.179775	−	0.0744653i
$474$		0			0
$475$	1.08556	+	0.558291i	0.0498088	+	0.0256161i
$476$		0			0
$477$	−18.1313	−	7.51025i	−0.830177	−	0.343871i
$478$		0			0
$479$	1.81043	−	4.37077i	0.0827208	−	0.199706i	−0.877107	−	0.480295i	$-0.840530\pi$
$479$	1.81043	−	4.37077i	0.0827208	−	0.199706i	0.959828	+	0.280589i	$0.0905297\pi$
$480$		0			0
$481$	8.17140	−	19.7275i	0.372584	−	0.899497i
$482$		0			0
$483$	−56.6402			−2.57722
$484$		0			0
$485$	8.02390	+	8.71315i	0.364347	+	0.395644i
$486$		0			0
$487$			19.5733i			0.886949i	0.896287	+	0.443475i	$0.146254\pi$
$487$			19.5733i			0.886949i	−0.896287	+	0.443475i	$0.853746\pi$
$488$		0			0
$489$	−15.5098	+	37.4439i	−0.701376	+	1.69327i
$490$		0			0
$491$			10.9209i			0.492852i	0.969162	+	0.246426i	$0.0792562\pi$
$491$			10.9209i			0.492852i	−0.969162	+	0.246426i	$0.920744\pi$
$492$		0			0
$493$	13.8220	+	13.8220i	0.622512	+	0.622512i
$494$		0			0
$495$	0.986870	−	23.9644i	0.0443565	−	1.07712i
$496$		0			0
$497$	−5.44843			−0.244396
$498$		0			0
$499$	−5.39314	−	2.23391i	−0.241430	−	0.100004i	0.258688	−	0.965961i	$-0.416710\pi$
$499$	−5.39314	−	2.23391i	−0.241430	−	0.100004i	−0.500118	+	0.865957i	$0.666710\pi$
$500$		0			0
$501$	26.7372	+	26.7372i	1.19453	+	1.19453i
$502$		0			0
$503$	−7.33405	−	17.7060i	−0.327009	−	0.789470i	−0.998812	−	0.0487394i	$-0.984480\pi$
$503$	−7.33405	−	17.7060i	−0.327009	−	0.789470i	0.671802	−	0.740730i	$-0.265520\pi$
$504$		0			0
$505$	22.5720	+	0.929531i	1.00444	+	0.0413636i
$506$		0			0
$507$	−9.10199	+	21.9741i	−0.404233	+	0.975906i
$508$		0			0
$509$	21.3754	−	8.85398i	0.947448	−	0.392446i	0.145177	−	0.989406i	$-0.453625\pi$
$509$	21.3754	−	8.85398i	0.947448	−	0.392446i	0.802271	+	0.596960i	$0.203625\pi$
$510$		0			0
$511$	5.16999	+	12.4815i	0.228707	+	0.552147i
$512$		0			0
$513$			0.127517i			0.00563000i
$514$		0			0
$515$	16.1371	+	7.47625i	0.711084	+	0.329443i
$516$		0			0
$517$	−19.3428	−	19.3428i	−0.850694	−	0.850694i
$518$		0			0
$519$	5.15086	+	12.4353i	0.226098	+	0.545848i
$520$		0			0
$521$	12.1538	−	29.3420i	0.532469	−	1.28549i	−0.397414	−	0.917640i	$-0.630092\pi$
$521$	12.1538	−	29.3420i	0.532469	−	1.28549i	0.929883	−	0.367855i	$-0.119908\pi$
$522$		0			0
$523$	−9.73398	+	9.73398i	−0.425637	+	0.425637i	−0.887139	−	0.461502i	$-0.847311\pi$
$523$	−9.73398	+	9.73398i	−0.425637	+	0.425637i	0.461502	+	0.887139i	$0.347311\pi$
$524$		0			0
$525$	4.87196	−	59.0532i	0.212630	−	2.57729i
$526$		0			0
$527$	16.3648	−	39.5082i	0.712863	−	1.72100i
$528$		0			0
$529$			0.156816i			0.00681808i
$530$		0			0
$531$	−25.1328	−	25.1328i	−1.09067	−	1.09067i
$532$		0			0
$533$	−10.5459	−	5.51806i	−0.456794	−	0.239014i
$534$		0			0
$535$	8.39587	−	3.07941i	0.362985	−	0.133134i
$536$		0			0
$537$	17.3150	+	17.3150i	0.747197	+	0.747197i
$538$		0			0
$539$	−48.2173	+	19.9723i	−2.07687	+	0.860266i
$540$		0			0
$541$	−20.2942	−	20.2942i	−0.872515	−	0.872515i	0.120231	−	0.992746i	$-0.461636\pi$
$541$	−20.2942	−	20.2942i	−0.872515	−	0.872515i	−0.992746	+	0.120231i	$0.961636\pi$
$542$		0			0
$543$	22.2828	+	22.2828i	0.956246	+	0.956246i
$544$		0			0
$545$	2.86485	+	0.117976i	0.122717	+	0.00505356i
$546$		0			0
$547$	−17.5051	−	7.25087i	−0.748466	−	0.310025i	−0.0243503	−	0.999703i	$-0.507752\pi$
$547$	−17.5051	−	7.25087i	−0.748466	−	0.310025i	−0.724115	+	0.689679i	$0.757752\pi$
$548$		0			0
$549$		−	38.8080i		−	1.65629i
$550$		0			0
$551$	1.07212			0.0456740
$552$		0			0
$553$	28.3051			1.20366
$554$		0			0
$555$	−43.3599	−	47.0844i	−1.84052	−	1.99862i
$556$		0			0
$557$	−2.52918	+	6.10597i	−0.107165	+	0.258718i	−0.968361	−	0.249554i	$-0.919716\pi$
$557$	−2.52918	+	6.10597i	−0.107165	+	0.258718i	0.861196	+	0.508273i	$0.169716\pi$
$558$		0			0
$559$	−2.17471	+	0.900794i	−0.0919804	+	0.0380995i
$560$		0			0
$561$	−34.2474	−	14.1857i	−1.44593	−	0.598922i
$562$		0			0
$563$	1.62944	−	0.674938i	0.0686729	−	0.0284452i	−0.348083	−	0.937464i	$-0.613167\pi$
$563$	1.62944	−	0.674938i	0.0686729	−	0.0284452i	0.416755	+	0.909019i	$0.363167\pi$
$564$		0			0
$565$	5.60501	+	15.2818i	0.235804	+	0.642910i
$566$		0			0
$567$	−36.5875	+	15.1550i	−1.53653	+	0.636451i
$568$		0			0
$569$	8.06645	+	8.06645i	0.338163	+	0.338163i	0.855676	−	0.517513i	$-0.173142\pi$
$569$	8.06645	+	8.06645i	0.338163	+	0.338163i	−0.517513	+	0.855676i	$0.673142\pi$
$570$		0			0
$571$	10.8371	+	4.48887i	0.453518	+	0.187853i	0.597737	−	0.801692i	$-0.296067\pi$
$571$	10.8371	+	4.48887i	0.453518	+	0.187853i	−0.144218	+	0.989546i	$0.546067\pi$
$572$		0			0
$573$	3.32458	−	3.32458i	0.138886	−	0.138886i
$574$		0			0
$575$	23.8164	+	1.96488i	0.993211	+	0.0819411i
$576$		0			0
$577$	9.04546	+	21.8377i	0.376567	+	0.909114i	0.992604	+	0.121397i	$0.0387373\pi$
$577$	9.04546	+	21.8377i	0.376567	+	0.909114i	−0.616037	+	0.787717i	$0.711263\pi$
$578$		0			0
$579$	−24.2320	+	24.2320i	−1.00705	+	1.00705i
$580$		0			0
$581$	20.9400	−	50.5536i	0.868737	−	2.09732i
$582$		0			0
$583$		−	20.4344i		−	0.846306i
$584$		0			0
$585$	−9.03711	−	9.81339i	−0.373639	−	0.405734i
$586$		0			0
$587$	3.39139	+	8.18754i	0.139978	+	0.337936i	0.978286	−	0.207261i	$-0.0664549\pi$
$587$	3.39139	+	8.18754i	0.139978	+	0.337936i	−0.838308	+	0.545197i	$0.816455\pi$
$588$		0			0
$589$	−0.897574	−	2.16694i	−0.0369839	−	0.0892870i
$590$		0			0
$591$	−5.57802	−	13.4665i	−0.229449	−	0.553939i
$592$		0			0
$593$	−4.72677	+	11.4114i	−0.194105	+	0.468611i	−0.990727	−	0.135866i	$-0.956618\pi$
$593$	−4.72677	+	11.4114i	−0.194105	+	0.468611i	0.796622	+	0.604478i	$0.206618\pi$
$594$		0			0
$595$	−42.9494	−	19.8983i	−1.76075	−	0.815751i
$596$		0			0
$597$	24.9369	+	24.9369i	1.02060	+	1.02060i
$598$		0			0
$599$	−26.7136			−1.09149			−0.545743	−	0.837952i	$-0.683753\pi$
$599$	−26.7136			−1.09149			−0.545743	+	0.837952i	$0.683753\pi$
$600$		0			0
$601$	41.2837	−	17.1003i	1.68400	−	0.697535i	0.684493	−	0.729019i	$-0.260024\pi$
$601$	41.2837	−	17.1003i	1.68400	−	0.697535i	0.999504	+	0.0314847i	$0.0100236\pi$
$602$		0			0
$603$	2.17939	−	0.902733i	0.0887516	−	0.0367621i
$604$		0			0
$605$	0.353835	−	0.129778i	0.0143854	−	0.00527624i
$606$		0			0
$607$			38.1886i			1.55003i	0.631945	+	0.775013i	$0.282257\pi$
$607$			38.1886i			1.55003i	−0.631945	+	0.775013i	$0.717743\pi$
$608$		0			0
$609$	−19.9155	−	48.0802i	−0.807015	−	1.94831i
$610$		0			0
$611$	−15.2151			−0.615537
$612$		0			0
$613$			41.6975i			1.68415i	0.539363	+	0.842073i	$0.318665\pi$
$613$			41.6975i			1.68415i	−0.539363	+	0.842073i	$0.681335\pi$
$614$		0			0
$615$	−28.2977	+	21.7304i	−1.14107	+	0.876253i
$616$		0			0
$617$		−	2.37669i		−	0.0956817i	−0.998855	−	0.0478409i	$-0.984766\pi$
$617$		−	2.37669i		−	0.0956817i	0.998855	−	0.0478409i	$-0.0152340\pi$
$618$		0			0
$619$	−31.9132			−1.28270			−0.641350	−	0.767248i	$-0.721625\pi$
$619$	−31.9132			−1.28270			−0.641350	+	0.767248i	$0.721625\pi$
$620$		0			0
$621$	0.955309	+	2.30632i	0.0383352	+	0.0925494i
$622$		0			0
$623$		−	74.0793i		−	2.96792i
$624$		0			0
$625$	−4.09718	+	24.6620i	−0.163887	+	0.986479i
$626$		0			0
$627$	−1.87839	+	0.778056i	−0.0750158	+	0.0310726i
$628$		0			0
$629$	−47.2405	+	19.5677i	−1.88360	+	0.780213i
$630$		0			0
$631$	−22.1295			−0.880963			−0.440482	−	0.897762i	$-0.645192\pi$
$631$	−22.1295			−0.880963			−0.440482	+	0.897762i	$0.645192\pi$
$632$		0			0
$633$	−19.4991	−	19.4991i	−0.775021	−	0.775021i
$634$		0			0
$635$	−22.7735	+	8.35280i	−0.903740	+	0.331471i
$636$		0			0
$637$	−11.1088	+	26.8191i	−0.440148	+	1.06261i
$638$		0			0
$639$	1.40717	+	3.39722i	0.0556670	+	0.134392i
$640$		0			0
$641$	−1.62824	−	3.93092i	−0.0643117	−	0.155262i	0.888456	−	0.458961i	$-0.151778\pi$
$641$	−1.62824	−	3.93092i	−0.0643117	−	0.155262i	−0.952768	+	0.303699i	$0.901778\pi$
$642$		0			0
$643$	18.1657	+	43.8558i	0.716385	+	1.72951i	0.683394	+	0.730050i	$0.260503\pi$
$643$	18.1657	+	43.8558i	0.716385	+	1.72951i	0.0329904	+	0.999456i	$0.489497\pi$
$644$		0			0
$645$	−0.290328	+	7.05010i	−0.0114316	+	0.277597i
$646$		0			0
$647$		−	17.5227i		−	0.688890i	−0.938806	−	0.344445i	$-0.888067\pi$
$647$		−	17.5227i		−	0.688890i	0.938806	−	0.344445i	$-0.111933\pi$
$648$		0			0
$649$	14.1626	−	34.1915i	0.555930	−	1.34213i
$650$		0			0
$651$	−80.5047	+	80.5047i	−3.15523	+	3.15523i
$652$		0			0
$653$	−11.4075	−	27.5402i	−0.446411	−	1.07773i	−0.973657	−	0.228019i	$-0.926775\pi$
$653$	−11.4075	−	27.5402i	−0.446411	−	1.07773i	0.527246	−	0.849713i	$-0.323225\pi$
$654$		0			0
$655$	36.4200	−	13.3580i	1.42305	−	0.521941i
$656$		0			0
$657$	6.44721	−	6.44721i	0.251530	−	0.251530i
$658$		0			0
$659$	−35.5800	−	14.7377i	−1.38600	−	0.574101i	−0.439922	−	0.898036i	$-0.644994\pi$
$659$	−35.5800	−	14.7377i	−1.38600	−	0.574101i	−0.946079	+	0.323935i	$0.894994\pi$
$660$		0			0
$661$	3.17147	+	3.17147i	0.123356	+	0.123356i	0.766090	−	0.642734i	$-0.222200\pi$
$661$	3.17147	+	3.17147i	0.123356	+	0.123356i	−0.642734	+	0.766090i	$0.722200\pi$
$662$		0			0
$663$	−19.0488	+	7.89029i	−0.739796	+	0.306433i
$664$		0			0
$665$	−2.43744	+	0.893995i	−0.0945198	+	0.0346676i
$666$		0			0
$667$	19.3909	−	8.03197i	0.750819	−	0.310999i
$668$		0			0
$669$	18.1759	+	7.52870i	0.702721	+	0.291076i
$670$		0			0
$671$	37.3322	−	15.4635i	1.44120	−	0.596963i
$672$		0			0
$673$	13.5097	−	32.6154i	0.520763	−	1.25723i	−0.416668	−	0.909059i	$-0.636802\pi$
$673$	13.5097	−	32.6154i	0.520763	−	1.25723i	0.937430	−	0.348173i	$-0.113198\pi$
$674$		0			0
$675$	−2.48675	+	0.797627i	−0.0957149	+	0.0307007i
$676$		0			0
$677$	16.9700			0.652208			0.326104	−	0.945334i	$-0.394264\pi$
$677$	16.9700			0.652208			0.326104	+	0.945334i	$0.394264\pi$
$678$		0			0
$679$	−25.1919			−0.966778
$680$		0			0
$681$			2.56980i			0.0984750i
$682$		0			0
$683$	−46.0203	−	19.0623i	−1.76092	−	0.729397i	−0.996398	−	0.0847987i	$-0.972975\pi$
$683$	−46.0203	−	19.0623i	−1.76092	−	0.729397i	−0.764522	−	0.644598i	$-0.777025\pi$
$684$		0			0
$685$	22.6279	−	20.8379i	0.864567	−	0.796177i
$686$		0			0
$687$	18.2711	+	18.2711i	0.697087	+	0.697087i
$688$		0			0
$689$	−8.03689	−	8.03689i	−0.306181	−	0.306181i
$690$		0			0
$691$	33.1211	−	13.7192i	1.25999	−	0.521903i	0.350081	−	0.936720i	$-0.386154\pi$
$691$	33.1211	−	13.7192i	1.25999	−	0.521903i	0.909905	+	0.414816i	$0.136154\pi$
$692$		0			0
$693$	36.0702	+	36.0702i	1.37020	+	1.37020i
$694$		0			0
$695$	9.89189	+	4.58288i	0.375221	+	0.173839i
$696$		0			0
$697$	8.51352	+	27.2007i	0.322472	+	1.03030i
$698$		0			0
$699$	23.6152	+	23.6152i	0.893209	+	0.893209i
$700$		0			0
$701$			25.3713i			0.958261i	0.877744	+	0.479130i	$0.159048\pi$
$701$			25.3713i			0.958261i	−0.877744	+	0.479130i	$0.840952\pi$
$702$		0			0
$703$	−1.07324	+	2.59104i	−0.0404781	+	0.0977228i
$704$		0			0
$705$	−19.1729	+	41.3835i	−0.722092	+	1.55859i
$706$		0			0
$707$	−33.9745	+	33.9745i	−1.27774	+	1.27774i
$708$		0			0
$709$	−9.08944	+	21.9439i	−0.341361	+	0.824119i	0.656217	+	0.754572i	$0.272155\pi$
$709$	−9.08944	+	21.9439i	−0.341361	+	0.824119i	−0.997579	+	0.0695471i	$0.977845\pi$
$710$		0			0
$711$	−7.31040	−	17.6489i	−0.274162	−	0.661885i
$712$		0			0
$713$	−32.4678	−	32.4678i	−1.21593	−	1.21593i
$714$		0			0
$715$	5.83926	−	12.6037i	0.218376	−	0.471352i
$716$		0			0
$717$		−	26.8770i		−	1.00374i
$718$		0			0
$719$	11.8403	+	28.5850i	0.441568	+	1.06604i	0.975399	+	0.220448i	$0.0707520\pi$
$719$	11.8403	+	28.5850i	0.441568	+	1.06604i	−0.533831	+	0.845591i	$0.679248\pi$
$720$		0			0
$721$	−34.9457	+	14.4750i	−1.30145	+	0.539077i
$722$		0			0
$723$	21.6841	−	52.3501i	0.806441	−	1.94692i
$724$		0			0
$725$	6.70623	+	20.9079i	0.249063	+	0.776499i
$726$		0			0
$727$	5.89145	+	14.2232i	0.218502	+	0.527510i	0.994681	−	0.103002i	$-0.0328449\pi$
$727$	5.89145	+	14.2232i	0.218502	+	0.527510i	−0.776179	+	0.630512i	$0.782845\pi$
$728$		0			0
$729$	21.6600	+	21.6600i	0.802221	+	0.802221i
$730$		0			0
$731$	5.20767	+	2.15709i	0.192613	+	0.0797828i
$732$		0			0
$733$	−34.7888			−1.28495			−0.642476	−	0.766306i	$-0.722093\pi$
$733$	−34.7888			−1.28495			−0.642476	+	0.766306i	$0.722093\pi$
$734$		0			0
$735$	58.9468	+	64.0102i	2.17428	+	2.36105i
$736$		0			0
$737$	1.73681	+	1.73681i	0.0639762	+	0.0639762i
$738$		0			0
$739$		−	19.2080i		−	0.706578i	−0.935514	−	0.353289i	$-0.885063\pi$
$739$		−	19.2080i		−	0.706578i	0.935514	−	0.353289i	$-0.114937\pi$
$740$		0			0
$741$	−0.432765	+	1.04479i	−0.0158980	+	0.0383812i
$742$		0			0
$743$		−	20.0415i		−	0.735253i	−0.929973	−	0.367627i	$-0.880170\pi$
$743$		−	20.0415i		−	0.735253i	0.929973	−	0.367627i	$-0.119830\pi$
$744$		0			0
$745$	1.72322	−	41.8454i	0.0631339	−	1.53310i
$746$		0			0
$747$	−36.9295			−1.35118
$748$		0			0
$749$	−7.27850	+	17.5719i	−0.265951	+	0.642062i
$750$		0			0
$751$	−6.08557	+	14.6919i	−0.222066	+	0.536114i	−0.995170	−	0.0981648i	$-0.968703\pi$
$751$	−6.08557	+	14.6919i	−0.222066	+	0.536114i	0.773105	+	0.634279i	$0.218703\pi$
$752$		0			0
$753$	−18.5954	−	7.70249i	−0.677656	−	0.280694i
$754$		0			0
$755$	8.54227	−	7.86654i	0.310885	−	0.286293i
$756$		0			0
$757$	−14.6011	−	6.04798i	−0.530687	−	0.219818i	0.101217	−	0.994864i	$-0.467726\pi$
$757$	−14.6011	−	6.04798i	−0.530687	−	0.219818i	−0.631904	+	0.775047i	$0.717726\pi$
$758$		0			0
$759$	−28.1445	+	28.1445i	−1.02158	+	1.02158i
$760$		0			0
$761$			34.5906i			1.25391i	0.779056	+	0.626954i	$0.215699\pi$
$761$			34.5906i			1.25391i	−0.779056	+	0.626954i	$0.784301\pi$
$762$		0			0
$763$	−4.31206	+	4.31206i	−0.156107	+	0.156107i
$764$		0			0
$765$	−1.31445	+	31.9190i	−0.0475240	+	1.15404i
$766$		0			0
$767$	−7.87741	−	19.0178i	−0.284437	−	0.686691i
$768$		0			0
$769$	11.7855			0.424995			0.212498	−	0.977162i	$-0.431840\pi$
$769$	11.7855			0.424995			0.212498	+	0.977162i	$0.431840\pi$
$770$		0			0
$771$	−30.4097	+	30.4097i	−1.09518	+	1.09518i
$772$		0			0
$773$	−17.0009	−	7.04199i	−0.611478	−	0.253283i	0.0553821	−	0.998465i	$-0.482362\pi$
$773$	−17.0009	−	7.04199i	−0.611478	−	0.253283i	−0.666860	+	0.745183i	$0.732362\pi$
$774$		0			0
$775$	36.6438	−	31.0583i	1.31628	−	1.11565i
$776$		0			0
$777$	136.133			4.88375
$778$		0			0
$779$	1.38511	+	0.724749i	0.0496268	+	0.0259668i
$780$		0			0
$781$	−2.70733	+	2.70733i	−0.0968757	+	0.0968757i
$782$		0			0
$783$	−1.62187	+	1.62187i	−0.0579608	+	0.0579608i
$784$		0			0
$785$	−0.107336	+	2.60646i	−0.00383098	+	0.0930285i
$786$		0			0
$787$	12.7861			0.455774			0.227887	−	0.973688i	$-0.426818\pi$
$787$	12.7861			0.455774			0.227887	+	0.973688i	$0.426818\pi$
$788$		0			0
$789$			12.3270i			0.438851i
$790$		0			0
$791$	−31.9835	−	13.2480i	−1.13720	−	0.471045i
$792$		0			0
$793$	8.60101	−	20.7647i	0.305431	−	0.737375i
$794$		0			0
$795$	−31.9870	+	11.7321i	−1.13446	+	0.416094i
$796$		0			0
$797$	6.16140	−	6.16140i	0.218248	−	0.218248i	−0.589512	−	0.807760i	$-0.700680\pi$
$797$	6.16140	−	6.16140i	0.218248	−	0.218248i	0.807760	+	0.589512i	$0.200680\pi$
$798$		0			0
$799$	25.7633	+	25.7633i	0.911441	+	0.911441i
$800$		0			0
$801$	−46.1901	+	19.1326i	−1.63205	+	0.676016i
$802$		0			0
$803$	8.77100	+	3.63307i	0.309522	+	0.128208i
$804$		0			0
$805$	−37.3870	+	34.4296i	−1.31772	+	1.21348i
$806$		0			0
$807$	67.2814	−	27.8689i	2.36842	−	0.981030i
$808$		0			0
$809$	28.4639	+	11.7901i	1.00074	+	0.414520i	0.822068	−	0.569389i	$-0.192820\pi$
$809$	28.4639	+	11.7901i	1.00074	+	0.414520i	0.178671	+	0.983909i	$0.442820\pi$
$810$		0			0
$811$	−3.05810	+	3.05810i	−0.107384	+	0.107384i	−0.758758	−	0.651373i	$-0.774193\pi$
$811$	−3.05810	+	3.05810i	−0.107384	+	0.107384i	0.651373	+	0.758758i	$0.274193\pi$
$812$		0			0
$813$	−8.17359	−	19.7328i	−0.286660	−	0.692060i
$814$		0			0
$815$	12.5231	+	34.1438i	0.438667	+	1.19601i
$816$		0			0
$817$	0.285629	−	0.118311i	0.00999290	−	0.00413919i
$818$		0			0
$819$	28.3730			0.991433
$820$		0			0
$821$	−47.4549			−1.65619			−0.828093	−	0.560591i	$-0.810574\pi$
$821$	−47.4549			−1.65619			−0.828093	+	0.560591i	$0.810574\pi$
$822$		0			0
$823$	−44.2374	+	18.3237i	−1.54202	+	0.638725i	−0.981851	−	0.189654i	$-0.939263\pi$
$823$	−44.2374	+	18.3237i	−1.54202	+	0.638725i	−0.560168	+	0.828379i	$0.689263\pi$
$824$		0			0
$825$	−26.9226	−	31.7644i	−0.937326	−	1.10589i
$826$		0			0
$827$	−4.83377	−	11.6697i	−0.168087	−	0.405797i	0.817281	−	0.576239i	$-0.195480\pi$
$827$	−4.83377	−	11.6697i	−0.168087	−	0.405797i	−0.985368	+	0.170442i	$0.945480\pi$
$828$		0			0
$829$	32.4596	−	32.4596i	1.12737	−	1.12737i	0.136767	−	0.990603i	$-0.456329\pi$
$829$	32.4596	−	32.4596i	1.12737	−	1.12737i	0.990603	−	0.136767i	$-0.0436711\pi$
$830$		0			0
$831$	−73.5633	−	30.4709i	−2.55188	−	1.05702i
$832$		0			0
$833$	64.2224	−	26.6018i	2.22517	−	0.921697i
$834$		0			0
$835$	33.9013	+	1.39608i	1.17320	+	0.0483132i
$836$		0			0
$837$	4.63587	+	1.92024i	0.160239	+	0.0663732i
$838$		0			0
$839$	−2.36426	+	0.979310i	−0.0816234	+	0.0338095i	−0.423122	−	0.906073i	$-0.639066\pi$
$839$	−2.36426	+	0.979310i	−0.0816234	+	0.0338095i	0.341498	+	0.939882i	$0.389066\pi$
$840$		0			0
$841$	−6.86989	−	6.86989i	−0.236893	−	0.236893i
$842$		0			0
$843$	23.8886	−	23.8886i	0.822766	−	0.822766i
$844$		0			0
$845$	7.34927	+	20.0375i	0.252823	+	0.689309i
$846$		0			0
$847$	−0.306745	+	0.740547i	−0.0105399	+	0.0254455i
$848$		0			0
$849$	−66.4296	−	27.5160i	−2.27986	−	0.944347i
$850$		0			0
$851$			54.9029i			1.88205i
$852$		0			0
$853$	26.7825			0.917015			0.458508	−	0.888690i	$-0.348384\pi$
$853$	26.7825			0.917015			0.458508	+	0.888690i	$0.348384\pi$
$854$		0			0
$855$	1.18695	+	1.28890i	0.0405927	+	0.0440795i
$856$		0			0
$857$	11.1900	−	11.1900i	0.382243	−	0.382243i	−0.489666	−	0.871910i	$-0.662881\pi$
$857$	11.1900	−	11.1900i	0.382243	−	0.382243i	0.871910	+	0.489666i	$0.162881\pi$
$858$		0			0
$859$	−9.92550	+	9.92550i	−0.338654	+	0.338654i	−0.855860	−	0.517207i	$-0.826972\pi$
$859$	−9.92550	+	9.92550i	−0.338654	+	0.338654i	0.517207	+	0.855860i	$0.326972\pi$
$860$		0			0
$861$	6.77246	−	75.5791i	0.230805	−	2.57573i
$862$		0			0
$863$	9.99669			0.340291			0.170146	−	0.985419i	$-0.445576\pi$
$863$	9.99669			0.340291			0.170146	+	0.985419i	$0.445576\pi$
$864$		0			0
$865$	10.9589	+	5.07724i	0.372615	+	0.172631i
$866$		0			0
$867$	6.47755	+	2.68309i	0.219989	+	0.0911225i
$868$		0			0
$869$	14.0648	−	14.0648i	0.477116	−	0.477116i
$870$		0			0
$871$	1.36618			0.0462913
$872$		0			0
$873$	6.50635	+	15.7077i	0.220207	+	0.531626i
$874$		0			0
$875$	−32.6805	−	41.9413i	−1.10480	−	1.41788i
$876$		0			0
$877$	4.12554	−	4.12554i	0.139310	−	0.139310i	−0.634013	−	0.773322i	$-0.718593\pi$
$877$	4.12554	−	4.12554i	0.139310	−	0.139310i	0.773322	+	0.634013i	$0.218593\pi$
$878$		0			0
$879$			1.74155i			0.0587409i
$880$		0			0
$881$	15.9100	−	15.9100i	0.536022	−	0.536022i	−0.386336	−	0.922358i	$-0.626259\pi$
$881$	15.9100	−	15.9100i	0.536022	−	0.536022i	0.922358	+	0.386336i	$0.126259\pi$
$882$		0			0
$883$	−13.6173	−	5.64045i	−0.458257	−	0.189816i	0.141599	−	0.989924i	$-0.454776\pi$
$883$	−13.6173	−	5.64045i	−0.458257	−	0.189816i	−0.599856	+	0.800108i	$0.704776\pi$
$884$		0			0
$885$	−61.6528	−	2.53891i	−2.07244	−	0.0853444i
$886$		0			0
$887$	15.0984	+	6.25396i	0.506954	+	0.209987i	0.621476	−	0.783434i	$-0.286533\pi$
$887$	15.0984	+	6.25396i	0.506954	+	0.209987i	−0.114522	+	0.993421i	$0.536533\pi$
$888$		0			0
$889$	19.7427	−	47.6631i	0.662149	−	1.59857i
$890$		0			0
$891$	−10.6498	+	25.7108i	−0.356781	+	0.861345i
$892$		0			0
$893$	1.99837			0.0668729
$894$		0			0
$895$	21.9544	+	0.904099i	0.733856	+	0.0302207i
$896$		0			0
$897$			22.1386i			0.739186i
$898$		0			0
$899$	16.1448	−	38.9771i	0.538461	−	1.29996i
$900$		0			0
$901$			27.2173i			0.906740i
$902$		0			0
$903$	−10.6115	−	10.6115i	−0.353129	−	0.353129i
$904$		0			0
$905$	28.2533	+	1.16349i	0.939173	+	0.0386758i
$906$		0			0
$907$	6.16728			0.204781			0.102391	−	0.994744i	$-0.467351\pi$
$907$	6.16728			0.204781			0.102391	+	0.994744i	$0.467351\pi$
$908$		0			0
$909$	29.9585	+	12.4092i	0.993660	+	0.411587i
$910$		0			0
$911$	12.0258	+	12.0258i	0.398433	+	0.398433i	0.877680	−	0.479247i	$-0.159090\pi$
$911$	12.0258	+	12.0258i	0.398433	+	0.398433i	−0.479247	+	0.877680i	$0.659090\pi$
$912$		0			0
$913$	−14.7150	−	35.5251i	−0.486995	−	1.17571i
$914$		0			0
$915$	−45.6395	−	49.5599i	−1.50880	−	1.63840i
$916$		0			0
$917$	−31.5731	+	76.2241i	−1.04263	+	2.51714i
$918$		0			0
$919$	−40.4109	+	16.7387i	−1.33303	+	0.552160i	−0.931519	−	0.363693i	$-0.881516\pi$
$919$	−40.4109	+	16.7387i	−1.33303	+	0.552160i	−0.401514	+	0.915853i	$0.631516\pi$
$920$		0			0
$921$	2.51504	+	6.07185i	0.0828734	+	0.200074i
$922$		0			0
$923$			2.12959i			0.0700964i
$924$		0			0
$925$	−57.2419	−	4.72253i	−1.88210	−	0.155276i
$926$		0			0
$927$	18.0509	+	18.0509i	0.592871	+	0.592871i
$928$		0			0
$929$	2.20155	+	5.31502i	0.0722306	+	0.174380i	0.955871	−	0.293785i	$-0.0949151\pi$
$929$	2.20155	+	5.31502i	0.0722306	+	0.174380i	−0.883641	+	0.468165i	$0.844915\pi$
$930$		0			0
$931$	1.45905	−	3.52246i	0.0478184	−	0.115444i
$932$		0			0
$933$	38.3804	−	38.3804i	1.25652	−	1.25652i
$934$		0			0
$935$	−31.2290	+	11.4541i	−1.02130	+	0.374588i
$936$		0			0
$937$	4.41312	−	10.6542i	0.144170	−	0.348058i	−0.835256	−	0.549862i	$-0.814680\pi$
$937$	4.41312	−	10.6542i	0.144170	−	0.348058i	0.979426	+	0.201804i	$0.0646804\pi$
$938$		0			0
$939$			66.1486i			2.15868i
$940$		0			0
$941$	41.3204	+	41.3204i	1.34701	+	1.34701i	0.888894	+	0.458114i	$0.151475\pi$
$941$	41.3204	+	41.3204i	1.34701	+	1.34701i	0.458114	+	0.888894i	$0.348525\pi$
$942$		0			0
$943$	30.4813	+	2.73135i	0.992608	+	0.0889452i
$944$		0			0
$945$	2.33486	−	5.03966i	0.0759529	−	0.163940i
$946$		0			0
$947$	6.07026	+	6.07026i	0.197257	+	0.197257i	0.798823	−	0.601566i	$-0.205456\pi$
$947$	6.07026	+	6.07026i	0.197257	+	0.197257i	−0.601566	+	0.798823i	$0.705456\pi$
$948$		0			0
$949$	4.87855	−	2.02076i	0.158364	−	0.0655967i
$950$		0			0
$951$	25.6675	+	25.6675i	0.832326	+	0.832326i
$952$		0			0
$953$	38.3744	+	38.3744i	1.24307	+	1.24307i	0.958721	+	0.284350i	$0.0917777\pi$
$953$	38.3744	+	38.3744i	1.24307	+	1.24307i	0.284350	+	0.958721i	$0.408222\pi$
$954$		0			0
$955$	0.173592	−	4.21538i	0.00561731	−	0.136407i
$956$		0			0
$957$	−33.7870	−	13.9950i	−1.09218	−	0.452395i
$958$		0			0
$959$			65.4230i			2.11262i
$960$		0			0
$961$	−61.2953			−1.97727
$962$		0			0
$963$	12.8363			0.413643
$964$		0			0
$965$	−1.26527	+	30.7248i	−0.0407304	+	0.989066i
$966$		0			0
$967$	−13.1734	+	31.8034i	−0.423628	+	1.02273i	0.557640	+	0.830083i	$0.311707\pi$
$967$	−13.1734	+	31.8034i	−0.423628	+	1.02273i	−0.981268	+	0.192646i	$0.938293\pi$
$968$		0			0
$969$	2.50190	−	1.03632i	0.0803726	−	0.0332914i
$970$		0			0
$971$	−7.42464	−	3.07539i	−0.238268	−	0.0986938i	0.260354	−	0.965513i	$-0.416161\pi$
$971$	−7.42464	−	3.07539i	−0.238268	−	0.0986938i	−0.498622	+	0.866819i	$0.666161\pi$
$972$		0			0
$973$	−21.4215	+	8.87306i	−0.686740	+	0.284457i
$974$		0			0
$975$	−23.0817	−	1.90427i	−0.739207	−	0.0609855i
$976$		0			0
$977$	19.6456	−	8.13749i	0.628520	−	0.260341i	−0.0456044	−	0.998960i	$-0.514521\pi$
$977$	19.6456	−	8.13749i	0.628520	−	0.260341i	0.674124	+	0.738618i	$0.264521\pi$
$978$		0			0
$979$	−36.8100	−	36.8100i	−1.17645	−	1.17645i
$980$		0			0
$981$	3.80234	+	1.57498i	0.121399	+	0.0502853i
$982$		0			0
$983$	23.2199	−	23.2199i	0.740601	−	0.740601i	−0.232093	−	0.972694i	$-0.574557\pi$
$983$	23.2199	−	23.2199i	0.740601	−	0.740601i	0.972694	+	0.232093i	$0.0745574\pi$
$984$		0			0
$985$	−11.8678	−	5.49830i	−0.378139	−	0.175190i
$986$		0			0
$987$	−37.1212	−	89.6184i	−1.18158	−	2.85258i
$988$		0			0
$989$	4.27966	−	4.27966i	0.136085	−	0.136085i
$990$		0			0
$991$	16.8885	−	40.7723i	0.536479	−	1.29518i	−0.390686	−	0.920524i	$-0.627762\pi$
$991$	16.8885	−	40.7723i	0.536479	−	1.29518i	0.927165	−	0.374652i	$-0.122238\pi$
$992$		0			0
$993$		−	51.8883i		−	1.64662i
$994$		0			0
$995$	31.6186	+	1.30208i	1.00238	+	0.0412786i
$996$		0			0
$997$	−22.8281	−	55.1118i	−0.722972	−	1.74541i	−0.664702	−	0.747109i	$-0.731441\pi$
$997$	−22.8281	−	55.1118i	−0.722972	−	1.74541i	−0.0582703	−	0.998301i	$-0.518559\pi$
$998$		0			0
$999$	−2.29606	−	5.54318i	−0.0726441	−	0.175378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.y.a.413.18	yes	84
5.2	odd	4		820.2.x.a.577.4	✓	84
41.14	odd	8		820.2.x.a.793.4	yes	84
205.137	even	8	inner	820.2.y.a.137.18	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.4	✓	84	5.2	odd	4
820.2.x.a.793.4	yes	84	41.14	odd	8
820.2.y.a.137.18	yes	84	205.137	even	8	inner
820.2.y.a.413.18	yes	84	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.30222 - 0.953612i) q^{3} +(0.939983 - 2.02890i) q^{5} +(1.81993 + 4.39370i) q^{7} +(2.26953 - 2.26953i) q^{9} +(3.08755 + 1.27890i) q^{11} +(1.71733 - 0.711343i) q^{13} +(0.229267 - 5.56736i) q^{15} +(-4.11242 - 1.70342i) q^{17} +(-0.225557 + 0.0934287i) q^{19} +(8.37976 + 8.37976i) q^{21} +(-3.37958 + 3.37958i) q^{23} +(-3.23286 - 3.81426i) q^{25} +(0.199878 - 0.482549i) q^{27} +(-4.05714 - 1.68052i) q^{29} +9.60705i q^{31} +8.32780 q^{33} +(10.6251 + 0.437547i) q^{35} +(8.12274 - 8.12274i) q^{37} +(3.27534 - 3.27534i) q^{39} +(-4.10553 - 4.91372i) q^{41} -1.26633 q^{43} +(-2.47133 - 6.73797i) q^{45} +(-7.56224 - 3.13238i) q^{47} +(-11.0427 + 11.0427i) q^{49} -11.0921 q^{51} +(-2.33993 - 5.64909i) q^{53} +(5.49701 - 5.06218i) q^{55} +(-0.430187 + 0.430187i) q^{57} -11.0740i q^{59} +(8.54979 - 8.54979i) q^{61} +(14.1020 + 5.84124i) q^{63} +(0.171021 - 4.15295i) q^{65} +(0.679022 + 0.281260i) q^{67} +(-4.55774 + 11.0034i) q^{69} +(-0.438426 + 1.05846i) q^{71} +2.84077 q^{73} +(-11.0801 - 5.69838i) q^{75} +15.8933i q^{77} +(2.27767 - 5.49878i) q^{79} +8.32726i q^{81} +(-8.13593 - 8.13593i) q^{83} +(-7.32167 + 6.74250i) q^{85} -10.9430 q^{87} +(-14.3912 - 5.96104i) q^{89} +(6.25085 + 6.25085i) q^{91} +(9.16139 + 22.1176i) q^{93} +(-0.0224622 + 0.545454i) q^{95} +(-2.02715 + 4.89398i) q^{97} +(9.90980 - 4.10477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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