LMFDB - Embedded newform 820.2.x.a.577.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] 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("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (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			577.4
Character	$\chi$	$=$	820.577
Dual form			820.2.x.a.793.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.953612 - 2.30222i) q^{3} +(-2.02890 + 0.939983i) q^{5} +(-4.39370 + 1.81993i) q^{7} +(-2.26953 + 2.26953i) q^{9} +(3.08755 + 1.27890i) q^{11} +(-0.711343 - 1.71733i) q^{13} +(4.09883 + 3.77460i) q^{15} +(1.70342 - 4.11242i) q^{17} +(0.225557 - 0.0934287i) q^{19} +(8.37976 + 8.37976i) q^{21} +(3.37958 + 3.37958i) q^{23} +(3.23286 - 3.81426i) q^{25} +(0.482549 + 0.199878i) q^{27} +(4.05714 + 1.68052i) q^{29} +9.60705i q^{31} -8.32780i q^{33} +(7.20366 - 7.82245i) q^{35} +(8.12274 + 8.12274i) q^{37} +(-3.27534 + 3.27534i) q^{39} +(-4.10553 - 4.91372i) q^{41} +1.26633i q^{43} +(2.47133 - 6.73797i) q^{45} +(3.13238 - 7.56224i) q^{47} +(11.0427 - 11.0427i) q^{49} -11.0921 q^{51} +(-5.64909 + 2.33993i) q^{53} +(-7.46647 + 0.307474i) q^{55} +(-0.430187 - 0.430187i) q^{57} +11.0740i q^{59} +(8.54979 - 8.54979i) q^{61} +(5.84124 - 14.1020i) q^{63} +(3.05751 + 2.81565i) q^{65} +(-0.281260 + 0.679022i) q^{67} +(4.55774 - 11.0034i) q^{69} +(-0.438426 + 1.05846i) q^{71} -2.84077i q^{73} +(-11.8642 - 3.80545i) q^{75} -15.8933 q^{77} +(-2.27767 + 5.49878i) q^{79} +8.32726i q^{81} +(-8.13593 + 8.13593i) q^{83} +(0.409536 + 9.94486i) q^{85} -10.9430i q^{87} +(14.3912 + 5.96104i) q^{89} +(6.25085 + 6.25085i) q^{91} +(22.1176 - 9.16139i) q^{93} +(-0.369811 + 0.401577i) q^{95} +(-4.89398 - 2.02715i) q^{97} +(-9.90980 + 4.10477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.953612	−	2.30222i	−0.550568	−	1.32919i	−0.917053	−	0.398765i	$-0.869439\pi$
$3$	−0.953612	−	2.30222i	−0.550568	−	1.32919i	0.366485	−	0.930424i	$-0.380561\pi$
$4$		0			0
$5$	−2.02890	+	0.939983i	−0.907351	+	0.420373i
$5$	−2.02890	+	0.939983i	−0.907351	+	0.420373i
$6$		0			0
$7$	−4.39370	+	1.81993i	−1.66066	+	0.687868i	−0.998128	−	0.0611643i	$-0.980519\pi$
$7$	−4.39370	+	1.81993i	−1.66066	+	0.687868i	−0.662533	+	0.749033i	$0.730519\pi$
$8$		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
$13$	−0.711343	−	1.71733i	−0.197291	−	0.476303i	0.794012	−	0.607902i	$-0.207989\pi$
$13$	−0.711343	−	1.71733i	−0.197291	−	0.476303i	−0.991303	+	0.131599i	$0.957989\pi$
$14$		0			0
$15$	4.09883	+	3.77460i	1.05831	+	0.974597i
$16$		0			0
$17$	1.70342	−	4.11242i	0.413140	−	0.997408i	−0.571150	−	0.820846i	$-0.693502\pi$
$17$	1.70342	−	4.11242i	0.413140	−	0.997408i	0.984290	−	0.176562i	$-0.0564975\pi$
$18$		0			0
$19$	0.225557	−	0.0934287i	0.0517463	−	0.0214340i	−0.356660	−	0.934234i	$-0.616085\pi$
$19$	0.225557	−	0.0934287i	0.0517463	−	0.0214340i	0.408406	+	0.912800i	$0.366085\pi$
$20$		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	$-0.0839605\pi$
$23$	3.37958	+	3.37958i	0.704692	+	0.704692i	−0.260722	+	0.965414i	$0.583961\pi$
$24$		0			0
$25$	3.23286	−	3.81426i	0.646573	−	0.762852i
$26$		0			0
$27$	0.482549	+	0.199878i	0.0928666	+	0.0384666i
$28$		0			0
$29$	4.05714	+	1.68052i	0.753391	+	0.312065i	0.726124	−	0.687563i	$-0.241320\pi$
$29$	4.05714	+	1.68052i	0.753391	+	0.312065i	0.0272669	+	0.999628i	$0.491320\pi$
$30$		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
$33$		−	8.32780i		−	1.44968i
$34$		0			0
$35$	7.20366	−	7.82245i	1.21764	−	1.32224i
$36$		0			0
$37$	8.12274	+	8.12274i	1.33537	+	1.33537i	0.900487	+	0.434882i	$0.143210\pi$
$37$	8.12274	+	8.12274i	1.33537	+	1.33537i	0.434882	+	0.900487i	$0.356790\pi$
$38$		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
$43$			1.26633i			0.193113i	0.995327	+	0.0965566i	$0.0307829\pi$
$43$			1.26633i			0.193113i	−0.995327	+	0.0965566i	$0.969217\pi$
$44$		0			0
$45$	2.47133	−	6.73797i	0.368404	−	1.00444i
$46$		0			0
$47$	3.13238	−	7.56224i	0.456905	−	1.10307i	−0.512739	−	0.858545i	$-0.671369\pi$
$47$	3.13238	−	7.56224i	0.456905	−	1.10307i	0.969644	−	0.244522i	$-0.0786310\pi$
$48$		0			0
$49$	11.0427	−	11.0427i	1.57753	−	1.57753i
$50$		0			0
$51$	−11.0921			−1.55320
$52$		0			0
$53$	−5.64909	+	2.33993i	−0.775963	+	0.321414i	−0.735285	−	0.677758i	$-0.762952\pi$
$53$	−5.64909	+	2.33993i	−0.775963	+	0.321414i	−0.0406777	+	0.999172i	$0.512952\pi$
$54$		0			0
$55$	−7.46647	+	0.307474i	−1.00678	+	0.0414598i
$56$		0			0
$57$	−0.430187	−	0.430187i	−0.0569797	−	0.0569797i
$58$		0			0
$59$			11.0740i			1.44171i	0.693085	+	0.720855i	$0.256251\pi$
$59$			11.0740i			1.44171i	−0.693085	+	0.720855i	$0.743749\pi$
$60$		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
$63$	5.84124	−	14.1020i	0.735928	−	1.77669i
$64$		0			0
$65$	3.05751	+	2.81565i	0.379237	+	0.349238i
$66$		0			0
$67$	−0.281260	+	0.679022i	−0.0343614	+	0.0829557i	−0.940129	−	0.340820i	$-0.889295\pi$
$67$	−0.281260	+	0.679022i	−0.0343614	+	0.0829557i	0.905767	+	0.423775i	$0.139295\pi$
$68$		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
$73$		−	2.84077i		−	0.332487i	−0.986085	−	0.166243i	$-0.946836\pi$
$73$		−	2.84077i		−	0.332487i	0.986085	−	0.166243i	$-0.0531637\pi$
$74$		0			0
$75$	−11.8642	−	3.80545i	−1.36996	−	0.439415i
$76$		0			0
$77$	−15.8933			−1.81121
$78$		0			0
$79$	−2.27767	+	5.49878i	−0.256258	+	0.618661i	−0.998685	−	0.0512659i	$-0.983674\pi$
$79$	−2.27767	+	5.49878i	−0.256258	+	0.618661i	0.742427	+	0.669927i	$0.233674\pi$
$80$		0			0
$81$			8.32726i			0.925251i
$82$		0			0
$83$	−8.13593	+	8.13593i	−0.893034	+	0.893034i	−0.994808	−	0.101774i	$-0.967548\pi$
$83$	−8.13593	+	8.13593i	−0.893034	+	0.893034i	0.101774	+	0.994808i	$0.467548\pi$
$84$		0			0
$85$	0.409536	+	9.94486i	0.0444204	+	1.07867i
$86$		0			0
$87$		−	10.9430i		−	1.17321i
$88$		0			0
$89$	14.3912	+	5.96104i	1.52547	+	0.631869i	0.978678	−	0.205402i	$-0.0658502\pi$
$89$	14.3912	+	5.96104i	1.52547	+	0.631869i	0.546788	+	0.837271i	$0.315850\pi$
$90$		0			0
$91$	6.25085	+	6.25085i	0.655267	+	0.655267i
$92$		0			0
$93$	22.1176	−	9.16139i	2.29348	−	0.949992i
$94$		0			0
$95$	−0.369811	+	0.401577i	−0.0379418	+	0.0412009i
$96$		0			0
$97$	−4.89398	−	2.02715i	−0.496908	−	0.205826i	0.120132	−	0.992758i	$-0.461668\pi$
$97$	−4.89398	−	2.02715i	−0.496908	−	0.205826i	−0.617040	+	0.786932i	$0.711668\pi$
$98$		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
$103$	7.95360			0.783692			0.391846	−	0.920031i	$-0.371837\pi$
$103$	7.95360			0.783692			0.391846	+	0.920031i	$0.371837\pi$
$104$		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	$-0.811924\pi$
$107$	−2.82796	+	2.82796i	−0.273389	+	0.273389i	0.557074	+	0.830463i	$0.311924\pi$
$108$		0			0
$109$	−0.490710	−	1.18468i	−0.0470014	−	0.113472i	0.898635	−	0.438697i	$-0.144560\pi$
$109$	−0.490710	−	1.18468i	−0.0470014	−	0.113472i	−0.945637	+	0.325225i	$0.894560\pi$
$110$		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	$-0.138762\pi$
$113$	5.14733	+	5.14733i	0.484220	+	0.484220i	−0.422257	+	0.906476i	$0.638762\pi$
$114$		0			0
$115$	−10.0336	−	3.68009i	−0.935637	−	0.343170i
$116$		0			0
$117$	5.51196	+	2.28313i	0.509581	+	0.211075i
$118$		0			0
$119$			21.1688i			1.94054i
$120$		0			0
$121$	0.119181	+	0.119181i	0.0108347	+	0.0108347i
$122$		0			0
$123$	−7.39740	+	14.1376i	−0.667001	+	1.27475i
$124$		0			0
$125$	−2.97382	+	10.7776i	−0.265986	+	0.963977i
$126$		0			0
$127$	7.67074	−	7.67074i	0.680668	−	0.680668i	−0.279483	−	0.960151i	$-0.590163\pi$
$127$	7.67074	−	7.67074i	0.680668	−	0.680668i	0.960151	+	0.279483i	$0.0901629\pi$
$128$		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
$135$	−1.16693	+	0.0480548i	−0.100433	+	0.00413590i
$136$		0			0
$137$	−5.26448	+	12.7096i	−0.449775	+	1.08585i	0.522631	+	0.852559i	$0.324951\pi$
$137$	−5.26448	+	12.7096i	−0.449775	+	1.08585i	−0.972406	+	0.233294i	$0.925049\pi$
$138$		0			0
$139$		−	4.87550i		−	0.413534i	−0.978390	−	0.206767i	$-0.933706\pi$
$139$		−	4.87550i		−	0.413534i	0.978390	−	0.206767i	$-0.0662943\pi$
$140$		0			0
$141$	−20.3970			−1.71774
$142$		0			0
$143$		−	6.21209i		−	0.519481i
$144$		0			0
$145$	−9.81118	+	0.404031i	−0.814774	+	0.0335530i
$146$		0			0
$147$	−35.9531	−	14.8923i	−2.96536	−	1.22829i
$148$		0			0
$149$	−17.3040	+	7.16754i	−1.41760	+	0.587188i	−0.954256	−	0.298992i	$-0.903350\pi$
$149$	−17.3040	+	7.16754i	−1.41760	+	0.587188i	−0.463341	+	0.886180i	$0.653350\pi$
$150$		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
$153$	5.46730	+	13.1992i	0.442005	+	1.06709i
$154$		0			0
$155$	−9.03046	−	19.4917i	−0.725344	−	1.56561i
$156$		0			0
$157$	−0.446451	−	1.07783i	−0.0356306	−	0.0860200i	0.905063	−	0.425279i	$-0.139824\pi$
$157$	−0.446451	−	1.07783i	−0.0356306	−	0.0860200i	−0.940693	+	0.339259i	$0.889824\pi$
$158$		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	$-0.0301929\pi$
$163$	11.5006	+	11.5006i	0.900793	+	0.900793i	−0.0947116	+	0.995505i	$0.530193\pi$
$164$		0			0
$165$	7.82799	+	16.8963i	0.609408	+	1.31537i
$166$		0			0
$167$	−14.0189	+	5.80682i	−1.08482	+	0.449345i	−0.852196	−	0.523222i	$-0.824730\pi$
$167$	−14.0189	+	5.80682i	−1.08482	+	0.449345i	−0.232620	+	0.972568i	$0.574730\pi$
$168$		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
$173$	5.40142			0.410662			0.205331	−	0.978693i	$-0.434173\pi$
$173$	5.40142			0.410662			0.205331	+	0.978693i	$0.434173\pi$
$174$		0			0
$175$	−7.26254	+	22.6423i	−0.548996	+	1.71160i
$176$		0			0
$177$	25.4948	−	10.5603i	1.91631	−	0.793760i
$178$		0			0
$179$	−3.76050	−	9.07864i	−0.281073	−	0.678569i	0.718789	−	0.695229i	$-0.244697\pi$
$179$	−3.76050	−	9.07864i	−0.281073	−	0.678569i	−0.999861	+	0.0166593i	$0.994697\pi$
$180$		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
$183$	−27.8367	−	11.5303i	−2.05775	−	0.852347i
$184$		0			0
$185$	−24.1154	−	8.84498i	−1.77300	−	0.650296i
$186$		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
$193$	5.26274	+	12.7054i	0.378820	+	0.914553i	0.992188	+	0.124755i	$0.0398145\pi$
$193$	5.26274	+	12.7054i	0.378820	+	0.914553i	−0.613367	+	0.789798i	$0.710186\pi$
$194$		0			0
$195$	3.56657	−	9.72410i	0.255408	−	0.696357i
$196$		0			0
$197$	5.84936			0.416750			0.208375	−	0.978049i	$-0.433183\pi$
$197$	5.84936			0.416750			0.208375	+	0.978049i	$0.433183\pi$
$198$		0			0
$199$	−5.41583	−	13.0750i	−0.383918	−	0.926860i	−0.991200	−	0.132374i	$-0.957740\pi$
$199$	−5.41583	−	13.0750i	−0.383918	−	0.926860i	0.607282	−	0.794487i	$-0.292260\pi$
$200$		0			0
$201$	1.83147			0.129182
$202$		0			0
$203$	−20.8843			−1.46579
$204$		0			0
$205$	12.9485	+	6.11032i	0.904363	+	0.426763i
$206$		0			0
$207$	−15.3401			−1.06621
$208$		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
$213$	2.85489			0.195614
$214$		0			0
$215$	−1.19033	−	2.56925i	−0.0811796	−	0.175222i
$216$		0			0
$217$	−17.4841	−	42.2104i	−1.18690	−	2.86543i
$218$		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	−0.495036	−	0.868872i	$-0.664845\pi$
$223$	5.58256	−	5.58256i	0.373836	−	0.373836i	0.868872	+	0.495036i	$0.164845\pi$
$224$		0			0
$225$	1.31950	+	15.9937i	0.0879665	+	1.06624i
$226$		0			0
$227$	−0.952759	−	0.394646i	−0.0632368	−	0.0261935i	0.350841	−	0.936435i	$-0.385896\pi$
$227$	−0.952759	−	0.394646i	−0.0632368	−	0.0261935i	−0.414078	+	0.910242i	$0.635896\pi$
$228$		0			0
$229$	−3.96815	−	9.57997i	−0.262223	−	0.633062i	0.736853	−	0.676053i	$-0.236311\pi$
$229$	−3.96815	−	9.57997i	−0.262223	−	0.633062i	−0.999075	+	0.0429914i	$0.986311\pi$
$230$		0			0
$231$	15.1560	+	36.5898i	0.997191	+	2.40743i
$232$		0			0
$233$	12.3820	−	5.12878i	0.811170	−	0.335998i	0.0617495	−	0.998092i	$-0.480332\pi$
$233$	12.3820	−	5.12878i	0.811170	−	0.335998i	0.749421	+	0.662094i	$0.230332\pi$
$234$		0			0
$235$	0.753088	+	18.2874i	0.0491261	+	1.19294i
$236$		0			0
$237$	14.8314			0.963404
$238$		0			0
$239$	−4.12752	+	9.96472i	−0.266987	+	0.644564i	−0.999339	−	0.0363628i	$-0.988423\pi$
$239$	−4.12752	+	9.96472i	−0.266987	+	0.644564i	0.732352	+	0.680927i	$0.238423\pi$
$240$		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
$243$	20.6189	−	8.54061i	1.32270	−	0.547880i
$244$		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
$253$	6.11246	+	14.7568i	0.384287	+	0.927752i
$254$		0			0
$255$	22.5047	−	10.4264i	1.40930	−	0.652925i
$256$		0			0
$257$	−6.60442	−	15.9445i	−0.411972	−	0.994589i	−0.984608	−	0.174779i	$-0.944079\pi$
$257$	−6.60442	−	15.9445i	−0.411972	−	0.994589i	0.572635	−	0.819810i	$-0.305921\pi$
$258$		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
$263$	4.57025	+	1.89306i	0.281813	+	0.116731i	0.519113	−	0.854706i	$-0.326262\pi$
$263$	4.57025	+	1.89306i	0.281813	+	0.116731i	−0.237300	+	0.971436i	$0.576262\pi$
$264$		0			0
$265$	9.26195	−	10.0575i	0.568957	−	0.617830i
$266$		0			0
$267$		−	38.8163i		−	2.37552i
$268$		0			0
$269$	−29.2245			−1.78185			−0.890926	−	0.454149i	$-0.849943\pi$
$269$	−29.2245			−1.78185			−0.890926	+	0.454149i	$0.849943\pi$
$270$		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
$273$	8.42996	−	20.3517i	0.510205	−	1.23174i
$274$		0			0
$275$	14.8597	−	7.64219i	0.896074	−	0.460841i
$276$		0			0
$277$	22.5943	−	22.5943i	1.35756	−	1.35756i	0.480645	−	0.876916i	$-0.340403\pi$
$277$	22.5943	−	22.5943i	1.35756	−	1.35756i	0.876916	−	0.480645i	$-0.159597\pi$
$278$		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	−0.242760	+	0.970086i	$0.578053\pi$
$283$	−20.4032	+	20.4032i	−1.21285	+	1.21285i	−0.970086	+	0.242760i	$0.921947\pi$
$284$		0			0
$285$	1.27718	+	0.468438i	0.0756534	+	0.0277479i
$286$		0			0
$287$	26.9811	+	14.1176i	1.59264	+	0.833337i
$288$		0			0
$289$	−1.98952	−	1.98952i	−0.117031	−	0.117031i
$290$		0			0
$291$			13.2001i			0.773806i
$292$		0			0
$293$	0.645681	+	0.267450i	0.0377211	+	0.0156246i	0.401464	−	0.915875i	$-0.368501\pi$
$293$	0.645681	+	0.267450i	0.0377211	+	0.0156246i	−0.363743	+	0.931499i	$0.618501\pi$
$294$		0			0
$295$	−10.4094	−	22.4680i	−0.606056	−	1.30814i
$296$		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
$307$	−2.63739			−0.150524			−0.0752618	−	0.997164i	$-0.523979\pi$
$307$	−2.63739			−0.150524			−0.0752618	+	0.997164i	$0.523979\pi$
$308$		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
$313$	24.5247	+	10.1585i	1.38622	+	0.574191i	0.946137	−	0.323767i	$-0.104949\pi$
$313$	24.5247	+	10.1585i	1.38622	+	0.574191i	0.440082	+	0.897957i	$0.354949\pi$
$314$		0			0
$315$	1.40435	+	34.1022i	0.0791263	+	1.92144i
$316$		0			0
$317$	−13.4580	+	5.57451i	−0.755879	+	0.313095i	−0.727138	−	0.686491i	$-0.759150\pi$
$317$	−13.4580	+	5.57451i	−0.755879	+	0.313095i	−0.0287414	+	0.999587i	$0.509150\pi$
$318$		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
$323$		−	1.08673i		−	0.0604674i
$324$		0			0
$325$	−8.85004	−	2.83866i	−0.490912	−	0.157461i
$326$		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
$333$	−36.8696			−2.02044
$334$		0			0
$335$	−0.0676206	−	1.64205i	−0.00369451	−	0.0897146i
$336$		0			0
$337$			31.4036i			1.71066i	0.518081	+	0.855331i	$0.326647\pi$
$337$			31.4036i			1.71066i	−0.518081	+	0.855331i	$0.673353\pi$
$338$		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
$343$	−15.6818	+	37.8592i	−0.846736	+	2.04420i
$344$		0			0
$345$	1.09577	+	26.6089i	0.0589944	+	1.43258i
$346$		0			0
$347$	6.36649	−	15.3701i	0.341771	−	0.825108i	−0.655766	−	0.754964i	$-0.727654\pi$
$347$	6.36649	−	15.3701i	0.341771	−	0.825108i	0.997537	−	0.0701440i	$-0.0223459\pi$
$348$		0			0
$349$	−15.0669	+	15.0669i	−0.806514	+	0.806514i	−0.984104	−	0.177591i	$-0.943170\pi$
$349$	−15.0669	+	15.0669i	−0.806514	+	0.806514i	0.177591	+	0.984104i	$0.443170\pi$
$350$		0			0
$351$		−	0.970880i		−	0.0518217i
$352$		0			0
$353$	−10.7011	−	10.7011i	−0.569560	−	0.569560i	0.362445	−	0.932005i	$-0.381942\pi$
$353$	−10.7011	−	10.7011i	−0.569560	−	0.569560i	−0.932005	+	0.362445i	$0.881942\pi$
$354$		0			0
$355$	−0.105407	−	2.55961i	−0.00559440	−	0.135850i
$356$		0			0
$357$	48.7353	−	20.1868i	2.57935	−	1.06840i
$358$		0			0
$359$	−9.40023			−0.496125			−0.248063	−	0.968744i	$-0.579794\pi$
$359$	−9.40023			−0.496125			−0.248063	+	0.968744i	$0.579794\pi$
$360$		0			0
$361$	−13.3929	+	13.3929i	−0.704889	+	0.704889i
$362$		0			0
$363$	0.160729	−	0.388034i	0.00843608	−	0.0203665i
$364$		0			0
$365$	2.67027	+	5.76363i	0.139768	+	0.301682i
$366$		0			0
$367$			10.9077i			0.569377i	0.958620	+	0.284688i	$0.0918901\pi$
$367$			10.9077i			0.569377i	−0.958620	+	0.284688i	$0.908110\pi$
$368$		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	$-0.417444\pi$
$373$	−13.7142	−	13.7142i	−0.710097	−	0.710097i	−0.966555	+	0.256459i	$0.917444\pi$
$374$		0			0
$375$	27.6483	−	3.43125i	1.42775	−	0.177189i
$376$		0			0
$377$		−	8.16289i		−	0.420410i
$378$		0			0
$379$			21.9556i			1.12778i	0.825849	+	0.563891i	$0.190696\pi$
$379$			21.9556i			1.12778i	−0.825849	+	0.563891i	$0.809304\pi$
$380$		0			0
$381$	−24.9747	−	10.3448i	−1.27949	−	0.529982i
$382$		0			0
$383$	20.0142	+	8.29014i	1.02268	+	0.423606i	0.830064	−	0.557669i	$-0.188304\pi$
$383$	20.0142	+	8.29014i	1.02268	+	0.423606i	0.192612	+	0.981275i	$0.438304\pi$
$384$		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	0.875574	−	0.483084i	$-0.160484\pi$
$389$	7.74110	+	7.74110i	0.392490	+	0.392490i	−0.483084	+	0.875574i	$0.660484\pi$
$390$		0			0
$391$	19.6551	−	8.14141i	0.994002	−	0.411729i
$392$		0			0
$393$	16.5438	−	39.9401i	0.834522	−	2.01471i
$394$		0			0
$395$	−0.547597	−	13.2974i	−0.0275526	−	0.669066i
$396$		0			0
$397$	14.6728	+	35.4233i	0.736408	+	1.77785i	0.619937	+	0.784652i	$0.287158\pi$
$397$	14.6728	+	35.4233i	0.736408	+	1.77785i	0.116471	+	0.993194i	$0.462842\pi$
$398$		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
$403$	16.4985	−	6.83391i	0.821849	−	0.340421i
$404$		0			0
$405$	−7.82748	−	16.8952i	−0.388951	−	0.839528i
$406$		0			0
$407$	14.6911	+	35.4675i	0.728213	+	1.75806i
$408$		0			0
$409$	4.00115			0.197844			0.0989221	−	0.995095i	$-0.468461\pi$
$409$	4.00115			0.197844			0.0989221	+	0.995095i	$0.468461\pi$
$410$		0			0
$411$	34.2806			1.69094
$412$		0			0
$413$	−20.1539	−	48.6557i	−0.991707	−	2.39419i
$414$		0			0
$415$	8.85934	−	24.1546i	0.434888	−	1.18570i
$416$		0			0
$417$	−11.2245	+	4.64933i	−0.549665	+	0.227679i
$418$		0			0
$419$	−26.6694	+	26.6694i	−1.30288	+	1.30288i	−0.376445	+	0.926439i	$0.622853\pi$
$419$	−26.6694	+	26.6694i	−1.30288	+	1.30288i	−0.926439	+	0.376445i	$0.877147\pi$
$420$		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
$423$	10.0537	+	24.2718i	0.488828	+	1.18013i
$424$		0			0
$425$	−10.1789	−	19.7922i	−0.493750	−	0.960061i
$426$		0			0
$427$	−22.0052	+	53.1252i	−1.06490	+	2.57091i
$428$		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	$-0.203723\pi$
$433$	4.26329	+	4.26329i	0.204881	+	0.204881i	−0.597207	+	0.802087i	$0.703723\pi$
$434$		0			0
$435$	10.2862	+	22.2022i	0.493187	+	1.06452i
$436$		0			0
$437$	1.07804	+	0.446538i	0.0515696	+	0.0213608i
$438$		0			0
$439$	−3.49173	−	1.44632i	−0.166651	−	0.0690291i	0.297798	−	0.954629i	$-0.403748\pi$
$439$	−3.49173	−	1.44632i	−0.166651	−	0.0690291i	−0.464449	+	0.885600i	$0.653748\pi$
$440$		0			0
$441$			50.1234i			2.38683i
$442$		0			0
$443$			7.32910i			0.348216i	0.984727	+	0.174108i	$0.0557042\pi$
$443$			7.32910i			0.348216i	−0.984727	+	0.174108i	$0.944296\pi$
$444$		0			0
$445$	−34.8016	+	1.43315i	−1.64975	+	0.0679380i
$446$		0			0
$447$	33.0025	+	33.0025i	1.56097	+	1.56097i
$448$		0			0
$449$	19.9406	−	19.9406i	0.941055	−	0.941055i	−0.0573016	−	0.998357i	$-0.518250\pi$
$449$	19.9406	−	19.9406i	0.941055	−	0.941055i	0.998357	+	0.0573016i	$0.0182497\pi$
$450$		0			0
$451$	−6.39184	−	20.4219i	−0.300980	−	0.961631i
$452$		0			0
$453$		−	12.9413i		−	0.608034i
$454$		0			0
$455$	−18.5580	−	6.80666i	−0.870015	−	0.319101i
$456$		0			0
$457$	3.75901	−	9.07504i	0.175839	−	0.424513i	−0.811247	−	0.584703i	$-0.801211\pi$
$457$	3.75901	−	9.07504i	0.175839	−	0.424513i	0.987086	+	0.160191i	$0.0512109\pi$
$458$		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
$463$	17.5147	−	7.25484i	0.813979	−	0.337161i	0.0634385	−	0.997986i	$-0.479793\pi$
$463$	17.5147	−	7.25484i	0.813979	−	0.337161i	0.750540	+	0.660825i	$0.229793\pi$
$464$		0			0
$465$	−36.2627	+	39.3777i	−1.68164	+	1.82610i
$466$		0			0
$467$	−15.0928	−	15.0928i	−0.698412	−	0.698412i	0.265656	−	0.964068i	$-0.414411\pi$
$467$	−15.0928	−	15.0928i	−0.698412	−	0.698412i	−0.964068	+	0.265656i	$0.914411\pi$
$468$		0			0
$469$		−	3.49529i		−	0.161397i
$470$		0			0
$471$	−2.05566	+	2.05566i	−0.0947197	+	0.0947197i
$472$		0			0
$473$	−1.61951	+	3.90985i	−0.0744653	+	0.179775i
$474$		0			0
$475$	0.372833	−	1.16238i	0.0171068	−	0.0533334i
$476$		0			0
$477$	7.51025	−	18.1313i	0.343871	−	0.830177i
$478$		0			0
$479$	−1.81043	+	4.37077i	−0.0827208	+	0.199706i	−0.959828	−	0.280589i	$-0.909470\pi$
$479$	−1.81043	+	4.37077i	−0.0827208	+	0.199706i	0.877107	+	0.480295i	$0.159470\pi$
$480$		0			0
$481$	8.17140	−	19.7275i	0.372584	−	0.899497i
$482$		0			0
$483$			56.6402i			2.57722i
$484$		0			0
$485$	11.8349	−	0.487368i	0.537394	−	0.0221303i
$486$		0			0
$487$	−19.5733			−0.886949			−0.443475	−	0.896287i	$-0.646254\pi$
$487$	−19.5733			−0.886949			−0.443475	+	0.896287i	$0.646254\pi$
$488$		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
$495$	16.2476	−	17.6432i	0.730274	−	0.793003i
$496$		0			0
$497$		−	5.44843i		−	0.244396i
$498$		0			0
$499$	5.39314	+	2.23391i	0.241430	+	0.100004i	0.500118	−	0.865957i	$-0.333290\pi$
$499$	5.39314	+	2.23391i	0.241430	+	0.100004i	−0.258688	+	0.965961i	$0.583290\pi$
$500$		0			0
$501$	26.7372	+	26.7372i	1.19453	+	1.19453i
$502$		0			0
$503$	−17.7060	+	7.33405i	−0.789470	+	0.327009i	−0.740730	−	0.671802i	$-0.765520\pi$
$503$	−17.7060	+	7.33405i	−0.789470	+	0.327009i	−0.0487394	+	0.998812i	$0.515520\pi$
$504$		0			0
$505$	−16.6181	−	15.3035i	−0.739496	−	0.680999i
$506$		0			0
$507$	−21.9741	−	9.10199i	−0.975906	−	0.404233i
$508$		0			0
$509$	−21.3754	+	8.85398i	−0.947448	+	0.392446i	−0.802271	−	0.596960i	$-0.796375\pi$
$509$	−21.3754	+	8.85398i	−0.947448	+	0.392446i	−0.145177	+	0.989406i	$0.546375\pi$
$510$		0			0
$511$	5.16999	+	12.4815i	0.228707	+	0.552147i
$512$		0			0
$513$	0.127517			0.00563000
$514$		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	$-0.152689\pi$
$523$	9.73398	+	9.73398i	0.425637	+	0.425637i	−0.461502	+	0.887139i	$0.652689\pi$
$524$		0			0
$525$	59.0532	−	4.87196i	2.57729	−	0.212630i
$526$		0			0
$527$	39.5082	+	16.3648i	1.72100	+	0.712863i
$528$		0			0
$529$		−	0.156816i		−	0.00681808i
$530$		0			0
$531$	−25.1328	−	25.1328i	−1.09067	−	1.09067i
$532$		0			0
$533$	−5.51806	+	10.5459i	−0.239014	+	0.456794i
$534$		0			0
$535$	3.07941	−	8.39587i	0.133134	−	0.362985i
$536$		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
$545$	2.10918	+	1.94233i	0.0903472	+	0.0832004i
$546$		0			0
$547$	7.25087	−	17.5051i	0.310025	−	0.748466i	−0.689679	−	0.724115i	$-0.742248\pi$
$547$	7.25087	−	17.5051i	0.310025	−	0.748466i	0.999703	−	0.0243503i	$-0.00775171\pi$
$548$		0			0
$549$			38.8080i			1.65629i
$550$		0			0
$551$	1.07212			0.0456740
$552$		0			0
$553$		−	28.3051i		−	1.20366i
$554$		0			0
$555$	2.63366	+	63.9538i	0.111793	+	2.71469i
$556$		0			0
$557$	−6.10597	−	2.52918i	−0.258718	−	0.107165i	0.249554	−	0.968361i	$-0.419716\pi$
$557$	−6.10597	−	2.52918i	−0.258718	−	0.107165i	−0.508273	+	0.861196i	$0.669716\pi$
$558$		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
$563$	−0.674938	−	1.62944i	−0.0284452	−	0.0686729i	0.909019	−	0.416755i	$-0.136833\pi$
$563$	−0.674938	−	1.62944i	−0.0284452	−	0.0686729i	−0.937464	+	0.348083i	$0.886833\pi$
$564$		0			0
$565$	−15.2818	−	5.60501i	−0.642910	−	0.235804i
$566$		0			0
$567$	−15.1550	−	36.5875i	−0.636451	−	1.53653i
$568$		0			0
$569$	−8.06645	−	8.06645i	−0.338163	−	0.338163i	0.517513	−	0.855676i	$-0.326858\pi$
$569$	−8.06645	−	8.06645i	−0.338163	−	0.338163i	−0.855676	+	0.517513i	$0.826858\pi$
$570$		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
$577$	−21.8377	+	9.04546i	−0.909114	+	0.376567i	−0.787717	−	0.616037i	$-0.788737\pi$
$577$	−21.8377	+	9.04546i	−0.909114	+	0.376567i	−0.121397	+	0.992604i	$0.538737\pi$
$578$		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
$583$	−20.4344			−0.846306
$584$		0			0
$585$	−13.3293	+	0.548910i	−0.551099	+	0.0226946i
$586$		0			0
$587$	−8.18754	+	3.39139i	−0.337936	+	0.139978i	−0.545197	−	0.838308i	$-0.683545\pi$
$587$	−8.18754	+	3.39139i	−0.337936	+	0.139978i	0.207261	+	0.978286i	$0.433545\pi$
$588$		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
$593$	11.4114	+	4.72677i	0.468611	+	0.194105i	0.604478	−	0.796622i	$-0.293382\pi$
$593$	11.4114	+	4.72677i	0.468611	+	0.194105i	−0.135866	+	0.990727i	$0.543382\pi$
$594$		0			0
$595$	−19.8983	−	42.9494i	−0.815751	−	1.76075i
$596$		0			0
$597$	−24.9369	+	24.9369i	−1.02060	+	1.02060i
$598$		0			0
$599$	26.7136			1.09149			0.545743	−	0.837952i	$-0.316247\pi$
$599$	26.7136			1.09149			0.545743	+	0.837952i	$0.316247\pi$
$600$		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
$603$	−0.902733	−	2.17939i	−0.0367621	−	0.0887516i
$604$		0			0
$605$	−0.353835	−	0.129778i	−0.0143854	−	0.00527624i
$606$		0			0
$607$	−38.1886			−1.55003			−0.775013	−	0.631945i	$-0.782257\pi$
$607$	−38.1886			−1.55003			−0.775013	+	0.631945i	$0.782257\pi$
$608$		0			0
$609$	19.9155	+	48.0802i	0.807015	+	1.94831i
$610$		0			0
$611$	−15.2151			−0.615537
$612$		0			0
$613$	41.6975			1.68415			0.842073	−	0.539363i	$-0.181335\pi$
$613$	41.6975			1.68415			0.842073	+	0.539363i	$0.181335\pi$
$614$		0			0
$615$	1.71945	−	35.6372i	0.0693351	−	1.43703i
$616$		0			0
$617$	2.37669			0.0956817			0.0478409	−	0.998855i	$-0.484766\pi$
$617$	2.37669			0.0956817			0.0478409	+	0.998855i	$0.484766\pi$
$618$		0			0
$619$	31.9132			1.28270			0.641350	−	0.767248i	$-0.278375\pi$
$619$	31.9132			1.28270			0.641350	+	0.767248i	$0.278375\pi$
$620$		0			0
$621$	0.955309	+	2.30632i	0.0383352	+	0.0925494i
$622$		0			0
$623$	−74.0793			−2.96792
$624$		0			0
$625$	−4.09718	−	24.6620i	−0.163887	−	0.986479i
$626$		0			0
$627$	−0.778056	−	1.87839i	−0.0310726	−	0.0750158i
$628$		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
$635$	−8.35280	+	22.7735i	−0.331471	+	0.903740i
$636$		0			0
$637$	−26.8191	−	11.1088i	−1.06261	−	0.440148i
$638$		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
$643$	43.8558	−	18.1657i	1.72951	−	0.716385i	0.730050	−	0.683394i	$-0.239497\pi$
$643$	43.8558	−	18.1657i	1.72951	−	0.716385i	0.999456	−	0.0329904i	$-0.0105031\pi$
$644$		0			0
$645$	−4.77988	+	5.19047i	−0.188208	+	0.204374i
$646$		0			0
$647$	17.5227			0.688890			0.344445	−	0.938806i	$-0.388067\pi$
$647$	17.5227			0.688890			0.344445	+	0.938806i	$0.388067\pi$
$648$		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
$653$	−27.5402	+	11.4075i	−1.07773	+	0.446411i	−0.849713	−	0.527246i	$-0.823225\pi$
$653$	−27.5402	+	11.4075i	−1.07773	+	0.446411i	−0.228019	+	0.973657i	$0.573225\pi$
$654$		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	0.946079	−	0.323935i	$-0.105006\pi$
$659$	35.5800	+	14.7377i	1.38600	+	0.574101i	0.439922	+	0.898036i	$0.355006\pi$
$660$		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
$663$	7.89029	+	19.0488i	0.306433	+	0.739796i
$664$		0			0
$665$	0.893995	−	2.43744i	0.0346676	−	0.0945198i
$666$		0			0
$667$	8.03197	+	19.3909i	0.310999	+	0.750819i
$668$		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
$673$	−32.6154	−	13.5097i	−1.25723	−	0.520763i	−0.348173	−	0.937430i	$-0.613198\pi$
$673$	−32.6154	−	13.5097i	−1.25723	−	0.520763i	−0.909059	+	0.416668i	$0.863198\pi$
$674$		0			0
$675$	2.32240	−	1.19439i	0.0893893	−	0.0459720i
$676$		0			0
$677$			16.9700i			0.652208i	0.945334	+	0.326104i	$0.105736\pi$
$677$			16.9700i			0.652208i	−0.945334	+	0.326104i	$0.894264\pi$
$678$		0			0
$679$	25.1919			0.966778
$680$		0			0
$681$			2.56980i			0.0984750i
$682$		0			0
$683$	−19.0623	+	46.0203i	−0.729397	+	1.76092i	−0.0847987	+	0.996398i	$0.527025\pi$
$683$	−19.0623	+	46.0203i	−0.729397	+	1.76092i	−0.644598	+	0.764522i	$0.722975\pi$
$684$		0			0
$685$	−1.26569	−	30.7350i	−0.0483594	−	1.17432i
$686$		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
$695$	4.58288	+	9.89189i	0.173839	+	0.375221i
$696$		0			0
$697$	−27.2007	+	8.51352i	−1.03030	+	0.322472i
$698$		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
$703$	2.59104	+	1.07324i	0.0977228	+	0.0404781i
$704$		0			0
$705$	41.3835	−	19.1729i	1.55859	−	0.722092i
$706$		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	$-0.727845\pi$
$709$	9.08944	−	21.9439i	0.341361	−	0.824119i	0.997579	−	0.0695471i	$-0.0221554\pi$
$710$		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
$717$	26.8770			1.00374
$718$		0			0
$719$	−11.8403	−	28.5850i	−0.441568	−	1.06604i	−0.975399	−	0.220448i	$-0.929248\pi$
$719$	−11.8403	−	28.5850i	−0.441568	−	1.06604i	0.533831	−	0.845591i	$-0.320752\pi$
$720$		0			0
$721$	−34.9457	+	14.4750i	−1.30145	+	0.539077i
$722$		0			0
$723$	−52.3501	−	21.6841i	−1.94692	−	0.806441i
$724$		0			0
$725$	19.5261	−	10.0421i	0.725182	−	0.372954i
$726$		0			0
$727$	−14.2232	+	5.89145i	−0.527510	+	0.218502i	−0.630512	−	0.776179i	$-0.717155\pi$
$727$	−14.2232	+	5.89145i	−0.527510	+	0.218502i	0.103002	+	0.994681i	$0.467155\pi$
$728$		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
$733$			34.7888i			1.28495i	0.766306	+	0.642476i	$0.222093\pi$
$733$			34.7888i			1.28495i	−0.766306	+	0.642476i	$0.777907\pi$
$734$		0			0
$735$	86.9437	−	3.58040i	3.20697	−	0.132065i
$736$		0			0
$737$	−1.73681	+	1.73681i	−0.0639762	+	0.0639762i
$738$		0			0
$739$			19.2080i			0.706578i	0.935514	+	0.353289i	$0.114937\pi$
$739$			19.2080i			0.706578i	−0.935514	+	0.353289i	$0.885063\pi$
$740$		0			0
$741$	−0.432765	+	1.04479i	−0.0158980	+	0.0383812i
$742$		0			0
$743$	−20.0415			−0.735253			−0.367627	−	0.929973i	$-0.619830\pi$
$743$	−20.0415			−0.735253			−0.367627	+	0.929973i	$0.619830\pi$
$744$		0			0
$745$	28.3707	−	30.8077i	1.03942	−	1.12871i
$746$		0			0
$747$		−	36.9295i		−	1.35118i
$748$		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
$753$	−7.70249	+	18.5954i	−0.280694	+	0.677656i
$754$		0			0
$755$	−11.6028	+	0.477810i	−0.422269	+	0.0173893i
$756$		0			0
$757$	6.04798	−	14.6011i	0.219818	−	0.530687i	−0.775047	−	0.631904i	$-0.782274\pi$
$757$	6.04798	−	14.6011i	0.219818	−	0.530687i	0.994864	+	0.101217i	$0.0322737\pi$
$758$		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
$765$	−23.4996	−	21.6407i	−0.849631	−	0.782422i
$766$		0			0
$767$	19.0178	−	7.87741i	0.686691	−	0.284437i
$768$		0			0
$769$	−11.7855			−0.424995			−0.212498	−	0.977162i	$-0.568160\pi$
$769$	−11.7855			−0.424995			−0.212498	+	0.977162i	$0.568160\pi$
$770$		0			0
$771$	−30.4097	+	30.4097i	−1.09518	+	1.09518i
$772$		0			0
$773$	−7.04199	+	17.0009i	−0.253283	+	0.611478i	−0.998465	−	0.0553821i	$-0.982362\pi$
$773$	−7.04199	+	17.0009i	−0.253283	+	0.611478i	0.745183	+	0.666860i	$0.232362\pi$
$774$		0			0
$775$	36.6438	+	31.0583i	1.31628	+	1.11565i
$776$		0			0
$777$			136.133i			4.88375i
$778$		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
$785$	1.91894	+	1.76715i	0.0684900	+	0.0630722i
$786$		0			0
$787$			12.7861i			0.455774i	0.973688	+	0.227887i	$0.0731817\pi$
$787$			12.7861i			0.455774i	−0.973688	+	0.227887i	$0.926818\pi$
$788$		0			0
$789$		−	12.3270i		−	0.438851i
$790$		0			0
$791$	−31.9835	−	13.2480i	−1.13720	−	0.471045i
$792$		0			0
$793$	−20.7647	−	8.60101i	−0.737375	−	0.305431i
$794$		0			0
$795$	−31.9870	−	11.7321i	−1.13446	−	0.416094i
$796$		0			0
$797$	6.16140	+	6.16140i	0.218248	+	0.218248i	0.807760	−	0.589512i	$-0.200680\pi$
$797$	6.16140	+	6.16140i	0.218248	+	0.218248i	−0.589512	+	0.807760i	$0.700680\pi$
$798$		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
$803$	3.63307	−	8.77100i	0.128208	−	0.309522i
$804$		0			0
$805$	50.7820	−	2.09124i	1.78983	−	0.0737065i
$806$		0			0
$807$	27.8689	+	67.2814i	0.981030	+	2.36842i
$808$		0			0
$809$	−28.4639	−	11.7901i	−1.00074	−	0.414520i	−0.178671	−	0.983909i	$-0.557180\pi$
$809$	−28.4639	−	11.7901i	−1.00074	−	0.414520i	−0.822068	+	0.569389i	$0.807180\pi$
$810$		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
$813$	−19.7328	+	8.17359i	−0.692060	+	0.286660i
$814$		0			0
$815$	−34.1438	−	12.5231i	−1.19601	−	0.438667i
$816$		0			0
$817$	0.118311	+	0.285629i	0.00413919	+	0.00999290i
$818$		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
$823$	18.3237	+	44.2374i	0.638725	+	1.54202i	0.828379	+	0.560168i	$0.189263\pi$
$823$	18.3237	+	44.2374i	0.638725	+	1.54202i	−0.189654	+	0.981851i	$0.560737\pi$
$824$		0			0
$825$	−31.7644	−	26.9226i	−1.10589	−	0.937326i
$826$		0			0
$827$	11.6697	−	4.83377i	0.405797	−	0.168087i	−0.170442	−	0.985368i	$-0.554520\pi$
$827$	11.6697	−	4.83377i	0.405797	−	0.168087i	0.576239	+	0.817281i	$0.304520\pi$
$828$		0			0
$829$	−32.4596	+	32.4596i	−1.12737	+	1.12737i	−0.136767	+	0.990603i	$0.543671\pi$
$829$	−32.4596	+	32.4596i	−1.12737	+	1.12737i	−0.990603	+	0.136767i	$0.956329\pi$
$830$		0			0
$831$	−73.5633	−	30.4709i	−2.55188	−	1.05702i
$832$		0			0
$833$	−26.6018	−	64.2224i	−0.921697	−	2.22517i
$834$		0			0
$835$	22.9846	−	24.9590i	0.795416	−	0.863742i
$836$		0			0
$837$	−1.92024	+	4.63587i	−0.0663732	+	0.160239i
$838$		0			0
$839$	2.36426	−	0.979310i	0.0816234	−	0.0338095i	−0.341498	−	0.939882i	$-0.610934\pi$
$839$	2.36426	−	0.979310i	0.0816234	−	0.0338095i	0.423122	+	0.906073i	$0.360934\pi$
$840$		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
$847$	−0.740547	−	0.306745i	−0.0254455	−	0.0105399i
$848$		0			0
$849$	66.4296	+	27.5160i	2.27986	+	0.944347i
$850$		0			0
$851$			54.9029i			1.88205i
$852$		0			0
$853$		−	26.7825i		−	0.917015i	−0.888690	−	0.458508i	$-0.848384\pi$
$853$		−	26.7825i		−	0.917015i	0.888690	−	0.458508i	$-0.151616\pi$
$854$		0			0
$855$	−0.0720945	−	1.75069i	−0.00246558	−	0.0598723i
$856$		0			0
$857$	11.1900	+	11.1900i	0.382243	+	0.382243i	0.871910	−	0.489666i	$-0.162881\pi$
$857$	11.1900	+	11.1900i	0.382243	+	0.382243i	−0.489666	+	0.871910i	$0.662881\pi$
$858$		0			0
$859$	9.92550	−	9.92550i	0.338654	−	0.338654i	−0.517207	−	0.855860i	$-0.673028\pi$
$859$	9.92550	−	9.92550i	0.338654	−	0.338654i	0.855860	+	0.517207i	$0.173028\pi$
$860$		0			0
$861$	6.77246	−	75.5791i	0.230805	−	2.57573i
$862$		0			0
$863$		−	9.99669i		−	0.340291i	−0.985419	−	0.170146i	$-0.945576\pi$
$863$		−	9.99669i		−	0.340291i	0.985419	−	0.170146i	$-0.0544238\pi$
$864$		0			0
$865$	−10.9589	+	5.07724i	−0.372615	+	0.172631i
$866$		0			0
$867$	−2.68309	+	6.47755i	−0.0911225	+	0.219989i
$868$		0			0
$869$	−14.0648	+	14.0648i	−0.477116	+	0.477116i
$870$		0			0
$871$	1.36618			0.0462913
$872$		0			0
$873$	15.7077	−	6.50635i	0.531626	−	0.220207i
$874$		0			0
$875$	−6.54840	−	52.7656i	−0.221376	−	1.78380i
$876$		0			0
$877$	4.12554	+	4.12554i	0.139310	+	0.139310i	0.773322	−	0.634013i	$-0.218593\pi$
$877$	4.12554	+	4.12554i	0.139310	+	0.139310i	−0.634013	+	0.773322i	$0.718593\pi$
$878$		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
$883$	−5.64045	+	13.6173i	−0.189816	+	0.458257i	−0.989924	−	0.141599i	$-0.954776\pi$
$883$	−5.64045	+	13.6173i	−0.189816	+	0.458257i	0.800108	+	0.599856i	$0.204776\pi$
$884$		0			0
$885$	−41.7999	+	45.3904i	−1.40509	+	1.52578i
$886$		0			0
$887$	−6.25396	+	15.0984i	−0.209987	+	0.506954i	−0.993421	−	0.114522i	$-0.963467\pi$
$887$	−6.25396	+	15.0984i	−0.209987	+	0.506954i	0.783434	+	0.621476i	$0.213467\pi$
$888$		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
$893$		−	1.99837i		−	0.0668729i
$894$		0			0
$895$	16.1634	+	14.8848i	0.540284	+	0.497545i
$896$		0			0
$897$	−22.1386			−0.739186
$898$		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
$905$	−20.8008	−	19.1554i	−0.691443	−	0.636748i
$906$		0			0
$907$			6.16728i			0.204781i	0.994744	+	0.102391i	$0.0326492\pi$
$907$			6.16728i			0.204781i	−0.994744	+	0.102391i	$0.967351\pi$
$908$		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
$913$	−35.5251	+	14.7150i	−1.17571	+	0.486995i
$914$		0			0
$915$	67.3161	−	2.77212i	2.22540	−	0.0916436i
$916$		0			0
$917$	−76.2241	−	31.5731i	−2.51714	−	1.04263i
$918$		0			0
$919$	40.4109	−	16.7387i	1.33303	−	0.552160i	0.401514	−	0.915853i	$-0.368484\pi$
$919$	40.4109	−	16.7387i	1.33303	−	0.552160i	0.931519	+	0.363693i	$0.118484\pi$
$920$		0			0
$921$	2.51504	+	6.07185i	0.0828734	+	0.200074i
$922$		0			0
$923$	2.12959			0.0700964
$924$		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	0.883641	−	0.468165i	$-0.155085\pi$
$929$	−2.20155	−	5.31502i	−0.0722306	−	0.174380i	−0.955871	+	0.293785i	$0.905085\pi$
$930$		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
$935$	−11.4541	+	31.2290i	−0.374588	+	1.02130i
$936$		0			0
$937$	10.6542	+	4.41312i	0.348058	+	0.144170i	0.549862	−	0.835256i	$-0.314680\pi$
$937$	10.6542	+	4.41312i	0.348058	+	0.144170i	−0.201804	+	0.979426i	$0.564680\pi$
$938$		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
$943$	2.73135	−	30.4813i	0.0889452	−	0.992608i
$944$		0			0
$945$	5.03966	−	2.33486i	0.163940	−	0.0759529i
$946$		0			0
$947$	−6.07026	+	6.07026i	−0.197257	+	0.197257i	−0.798823	−	0.601566i	$-0.794544\pi$
$947$	−6.07026	+	6.07026i	−0.197257	+	0.197257i	0.601566	+	0.798823i	$0.294544\pi$
$948$		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	0.284350	−	0.958721i	$-0.408222\pi$
$953$	38.3744	−	38.3744i	1.24307	−	1.24307i	0.958721	−	0.284350i	$-0.0917777\pi$
$954$		0			0
$955$	−2.85798	+	3.10347i	−0.0924820	+	0.100426i
$956$		0			0
$957$	13.9950	−	33.7870i	0.452395	−	1.09218i
$958$		0			0
$959$		−	65.4230i		−	2.11262i
$960$		0			0
$961$	−61.2953			−1.97727
$962$		0			0
$963$		−	12.8363i		−	0.413643i
$964$		0			0
$965$	−22.6204	−	20.8310i	−0.728176	−	0.670575i
$966$		0			0
$967$	−31.8034	−	13.1734i	−1.02273	−	0.423628i	−0.192646	−	0.981268i	$-0.561707\pi$
$967$	−31.8034	−	13.1734i	−1.02273	−	0.423628i	−0.830083	+	0.557640i	$0.811707\pi$
$968$		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
$973$	8.87306	+	21.4215i	0.284457	+	0.686740i
$974$		0			0
$975$	1.90427	+	23.0817i	0.0609855	+	0.739207i
$976$		0			0
$977$	8.13749	+	19.6456i	0.260341	+	0.628520i	0.998960	−	0.0456044i	$-0.0145214\pi$
$977$	8.13749	+	19.6456i	0.260341	+	0.628520i	−0.738618	+	0.674124i	$0.764521\pi$
$978$		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	$-0.425443\pi$
$983$	−23.2199	−	23.2199i	−0.740601	−	0.740601i	−0.972694	+	0.232093i	$0.925443\pi$
$984$		0			0
$985$	−11.8678	+	5.49830i	−0.378139	+	0.175190i
$986$		0			0
$987$	89.6184	−	37.1212i	2.85258	−	1.18158i
$988$		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
$993$	−51.8883			−1.64662
$994$		0			0
$995$	23.2784	+	21.4370i	0.737976	+	0.679599i
$996$		0			0
$997$	55.1118	−	22.8281i	1.74541	−	0.722972i	0.747109	−	0.664702i	$-0.231441\pi$
$997$	55.1118	−	22.8281i	1.74541	−	0.722972i	0.998301	−	0.0582703i	$-0.0185585\pi$
$998$		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.x.a.577.4	✓	84
5.3	odd	4		820.2.y.a.413.18	yes	84
41.14	odd	8		820.2.y.a.137.18	yes	84
205.178	even	8	inner	820.2.x.a.793.4	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.4	✓	84	1.1	even	1	trivial
820.2.x.a.793.4	yes	84	205.178	even	8	inner
820.2.y.a.137.18	yes	84	41.14	odd	8
820.2.y.a.413.18	yes	84	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.953612 - 2.30222i) q^{3} +(-2.02890 + 0.939983i) q^{5} +(-4.39370 + 1.81993i) q^{7} +(-2.26953 + 2.26953i) q^{9} +(3.08755 + 1.27890i) q^{11} +(-0.711343 - 1.71733i) q^{13} +(4.09883 + 3.77460i) q^{15} +(1.70342 - 4.11242i) q^{17} +(0.225557 - 0.0934287i) q^{19} +(8.37976 + 8.37976i) q^{21} +(3.37958 + 3.37958i) q^{23} +(3.23286 - 3.81426i) q^{25} +(0.482549 + 0.199878i) q^{27} +(4.05714 + 1.68052i) q^{29} +9.60705i q^{31} -8.32780i q^{33} +(7.20366 - 7.82245i) q^{35} +(8.12274 + 8.12274i) q^{37} +(-3.27534 + 3.27534i) q^{39} +(-4.10553 - 4.91372i) q^{41} +1.26633i q^{43} +(2.47133 - 6.73797i) q^{45} +(3.13238 - 7.56224i) q^{47} +(11.0427 - 11.0427i) q^{49} -11.0921 q^{51} +(-5.64909 + 2.33993i) q^{53} +(-7.46647 + 0.307474i) q^{55} +(-0.430187 - 0.430187i) q^{57} +11.0740i q^{59} +(8.54979 - 8.54979i) q^{61} +(5.84124 - 14.1020i) q^{63} +(3.05751 + 2.81565i) q^{65} +(-0.281260 + 0.679022i) q^{67} +(4.55774 - 11.0034i) q^{69} +(-0.438426 + 1.05846i) q^{71} -2.84077i q^{73} +(-11.8642 - 3.80545i) q^{75} -15.8933 q^{77} +(-2.27767 + 5.49878i) q^{79} +8.32726i q^{81} +(-8.13593 + 8.13593i) q^{83} +(0.409536 + 9.94486i) q^{85} -10.9430i q^{87} +(14.3912 + 5.96104i) q^{89} +(6.25085 + 6.25085i) q^{91} +(22.1176 - 9.16139i) q^{93} +(-0.369811 + 0.401577i) q^{95} +(-4.89398 - 2.02715i) q^{97} +(-9.90980 + 4.10477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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