LMFDB - Embedded newform 820.2.y.a.137.15

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			137.15
Character	$\chi$	$=$	820.137
Dual form			820.2.y.a.413.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03876 + 0.430268i) q^{3} +(-2.16617 - 0.554719i) q^{5} +(-0.831762 + 2.00805i) q^{7} +(-1.22743 - 1.22743i) q^{9} +(2.50692 - 1.03840i) q^{11} +(-5.26176 - 2.17949i) q^{13} +(-2.01145 - 1.50825i) q^{15} +(-5.37817 + 2.22771i) q^{17} +(1.89850 + 0.786385i) q^{19} +(-1.72800 + 1.72800i) q^{21} +(-3.33290 - 3.33290i) q^{23} +(4.38457 + 2.40323i) q^{25} +(-2.03768 - 4.91941i) q^{27} +(-3.07658 + 1.27436i) q^{29} -0.621917i q^{31} +3.05088 q^{33} +(2.91564 - 3.88838i) q^{35} +(-5.98810 - 5.98810i) q^{37} +(-4.52794 - 4.52794i) q^{39} +(-6.40010 + 0.196764i) q^{41} +1.18311 q^{43} +(1.97794 + 3.33970i) q^{45} +(-2.97225 + 1.23115i) q^{47} +(1.60931 + 1.60931i) q^{49} -6.54513 q^{51} +(3.00715 - 7.25990i) q^{53} +(-6.00644 + 0.858714i) q^{55} +(1.63373 + 1.63373i) q^{57} +8.81470i q^{59} +(1.18680 + 1.18680i) q^{61} +(3.48567 - 1.44381i) q^{63} +(10.1889 + 7.63995i) q^{65} +(-4.71010 + 1.95099i) q^{67} +(-2.02804 - 4.89613i) q^{69} +(-3.30477 - 7.97843i) q^{71} +7.49459 q^{73} +(3.52048 + 4.38292i) q^{75} +5.89773i q^{77} +(2.70912 + 6.54039i) q^{79} -0.779283i q^{81} +(-3.55448 + 3.55448i) q^{83} +(12.8858 - 1.84222i) q^{85} -3.74415 q^{87} +(5.23829 - 2.16977i) q^{89} +(8.75307 - 8.75307i) q^{91} +(0.267591 - 0.646022i) q^{93} +(-3.67625 - 2.75658i) q^{95} +(-0.940462 - 2.27048i) q^{97} +(-4.35164 - 1.80251i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	1.03876	+	0.430268i	0.599728	+	0.248415i	0.661829	−	0.749654i	$-0.269780\pi$
$3$	1.03876	+	0.430268i	0.599728	+	0.248415i	−0.0621016	+	0.998070i	$0.519780\pi$
$4$		0			0
$5$	−2.16617	−	0.554719i	−0.968740	−	0.248078i
$5$	−2.16617	−	0.554719i	−0.968740	−	0.248078i
$6$		0			0
$7$	−0.831762	+	2.00805i	−0.314377	+	0.758972i	0.685156	+	0.728396i	$0.259734\pi$
$7$	−0.831762	+	2.00805i	−0.314377	+	0.758972i	−0.999532	+	0.0305756i	$0.990266\pi$
$8$		0			0
$9$	−1.22743	−	1.22743i	−0.409143	−	0.409143i
$10$		0			0
$11$	2.50692	−	1.03840i	0.755866	−	0.313090i	0.0287333	−	0.999587i	$-0.490853\pi$
$11$	2.50692	−	1.03840i	0.755866	−	0.313090i	0.727132	+	0.686497i	$0.240853\pi$
$12$		0			0
$13$	−5.26176	−	2.17949i	−1.45935	−	0.604483i	−0.494949	−	0.868922i	$-0.664813\pi$
$13$	−5.26176	−	2.17949i	−1.45935	−	0.604483i	−0.964402	+	0.264439i	$0.914813\pi$
$14$		0			0
$15$	−2.01145	−	1.50825i	−0.519354	−	0.389429i
$16$		0			0
$17$	−5.37817	+	2.22771i	−1.30440	+	0.540299i	−0.923244	−	0.384213i	$-0.874473\pi$
$17$	−5.37817	+	2.22771i	−1.30440	+	0.540299i	−0.381153	+	0.924512i	$0.624473\pi$
$18$		0			0
$19$	1.89850	+	0.786385i	0.435546	+	0.180409i	0.589673	−	0.807642i	$-0.299257\pi$
$19$	1.89850	+	0.786385i	0.435546	+	0.180409i	−0.154127	+	0.988051i	$0.549257\pi$
$20$		0			0
$21$	−1.72800	+	1.72800i	−0.377081	+	0.377081i
$22$		0			0
$23$	−3.33290	−	3.33290i	−0.694959	−	0.694959i	0.268360	−	0.963319i	$-0.413518\pi$
$23$	−3.33290	−	3.33290i	−0.694959	−	0.694959i	−0.963319	+	0.268360i	$0.913518\pi$
$24$		0			0
$25$	4.38457	+	2.40323i	0.876915	+	0.480646i
$26$		0			0
$27$	−2.03768	−	4.91941i	−0.392153	−	0.946740i
$28$		0			0
$29$	−3.07658	+	1.27436i	−0.571307	+	0.236643i	−0.649586	−	0.760288i	$-0.725058\pi$
$29$	−3.07658	+	1.27436i	−0.571307	+	0.236643i	0.0782784	+	0.996932i	$0.475058\pi$
$30$		0			0
$31$		−	0.621917i		−	0.111700i	−0.998439	−	0.0558498i	$-0.982213\pi$
$31$		−	0.621917i		−	0.111700i	0.998439	−	0.0558498i	$-0.0177868\pi$
$32$		0			0
$33$	3.05088			0.531090
$34$		0			0
$35$	2.91564	−	3.88838i	0.492833	−	0.657257i
$36$		0			0
$37$	−5.98810	−	5.98810i	−0.984438	−	0.984438i	0.0154426	−	0.999881i	$-0.495084\pi$
$37$	−5.98810	−	5.98810i	−0.984438	−	0.984438i	−0.999881	+	0.0154426i	$0.995084\pi$
$38$		0			0
$39$	−4.52794	−	4.52794i	−0.725051	−	0.725051i
$40$		0			0
$41$	−6.40010	+	0.196764i	−0.999528	+	0.0307294i
$41$	−6.40010	+	0.196764i	−0.999528	+	0.0307294i
$42$		0			0
$43$	1.18311			0.180422			0.0902110	−	0.995923i	$-0.471246\pi$
$43$	1.18311			0.180422			0.0902110	+	0.995923i	$0.471246\pi$
$44$		0			0
$45$	1.97794	+	3.33970i	0.294854	+	0.497853i
$46$		0			0
$47$	−2.97225	+	1.23115i	−0.433548	+	0.179581i	−0.588774	−	0.808298i	$-0.700389\pi$
$47$	−2.97225	+	1.23115i	−0.433548	+	0.179581i	0.155226	+	0.987879i	$0.450389\pi$
$48$		0			0
$49$	1.60931	+	1.60931i	0.229901	+	0.229901i
$50$		0			0
$51$	−6.54513			−0.916502
$52$		0			0
$53$	3.00715	−	7.25990i	0.413064	−	0.997224i	−0.571247	−	0.820778i	$-0.693540\pi$
$53$	3.00715	−	7.25990i	0.413064	−	0.997224i	0.984310	−	0.176445i	$-0.0564599\pi$
$54$		0			0
$55$	−6.00644	+	0.858714i	−0.809908	+	0.115789i
$56$		0			0
$57$	1.63373	+	1.63373i	0.216393	+	0.216393i
$58$		0			0
$59$			8.81470i			1.14758i	0.819004	+	0.573788i	$0.194527\pi$
$59$			8.81470i			1.14758i	−0.819004	+	0.573788i	$0.805473\pi$
$60$		0			0
$61$	1.18680	+	1.18680i	0.151954	+	0.151954i	0.778990	−	0.627036i	$-0.215732\pi$
$61$	1.18680	+	1.18680i	0.151954	+	0.151954i	−0.627036	+	0.778990i	$0.715732\pi$
$62$		0			0
$63$	3.48567	−	1.44381i	0.439154	−	0.181903i
$64$		0			0
$65$	10.1889	+	7.63995i	1.26377	+	0.947620i
$66$		0			0
$67$	−4.71010	+	1.95099i	−0.575430	+	0.238351i	−0.651368	−	0.758762i	$-0.725805\pi$
$67$	−4.71010	+	1.95099i	−0.575430	+	0.238351i	0.0759385	+	0.997113i	$0.475805\pi$
$68$		0			0
$69$	−2.02804	−	4.89613i	−0.244148	−	0.589424i
$70$		0			0
$71$	−3.30477	−	7.97843i	−0.392204	−	0.946865i	−0.989459	−	0.144813i	$-0.953742\pi$
$71$	−3.30477	−	7.97843i	−0.392204	−	0.946865i	0.597255	−	0.802052i	$-0.296258\pi$
$72$		0			0
$73$	7.49459			0.877176			0.438588	−	0.898688i	$-0.355479\pi$
$73$	7.49459			0.877176			0.438588	+	0.898688i	$0.355479\pi$
$74$		0			0
$75$	3.52048	+	4.38292i	0.406510	+	0.506096i
$76$		0			0
$77$			5.89773i			0.672109i
$78$		0			0
$79$	2.70912	+	6.54039i	0.304799	+	0.735851i	0.999857	+	0.0168971i	$0.00537876\pi$
$79$	2.70912	+	6.54039i	0.304799	+	0.735851i	−0.695058	+	0.718954i	$0.744621\pi$
$80$		0			0
$81$		−	0.779283i		−	0.0865870i
$82$		0			0
$83$	−3.55448	+	3.55448i	−0.390154	+	0.390154i	−0.874742	−	0.484588i	$-0.838970\pi$
$83$	−3.55448	+	3.55448i	−0.390154	+	0.390154i	0.484588	+	0.874742i	$0.338970\pi$
$84$		0			0
$85$	12.8858	−	1.84222i	1.39766	−	0.199817i
$86$		0			0
$87$	−3.74415			−0.401415
$88$		0			0
$89$	5.23829	−	2.16977i	0.555258	−	0.229995i	−0.0873672	−	0.996176i	$-0.527845\pi$
$89$	5.23829	−	2.16977i	0.555258	−	0.229995i	0.642625	+	0.766181i	$0.277845\pi$
$90$		0			0
$91$	8.75307	−	8.75307i	0.917571	−	0.917571i
$92$		0			0
$93$	0.267591	−	0.646022i	0.0277479	−	0.0669894i
$94$		0			0
$95$	−3.67625	−	2.75658i	−0.377175	−	0.282819i
$96$		0			0
$97$	−0.940462	−	2.27048i	−0.0954895	−	0.230532i	0.868916	−	0.494959i	$-0.164817\pi$
$97$	−0.940462	−	2.27048i	−0.0954895	−	0.230532i	−0.964406	+	0.264427i	$0.914817\pi$
$98$		0			0
$99$	−4.35164	−	1.80251i	−0.437356	−	0.181159i
$100$		0			0
$101$	−1.19361	+	2.88164i	−0.118769	+	0.286734i	−0.972073	−	0.234681i	$-0.924596\pi$
$101$	−1.19361	+	2.88164i	−0.118769	+	0.286734i	0.853303	+	0.521415i	$0.174596\pi$
$102$		0			0
$103$			12.0325i			1.18559i	0.805352	+	0.592797i	$0.201976\pi$
$103$			12.0325i			1.18559i	−0.805352	+	0.592797i	$0.798024\pi$
$104$		0			0
$105$	4.70170	−	2.78459i	0.458839	−	0.271748i
$106$		0			0
$107$	8.01953	−	8.01953i	0.775277	−	0.775277i	−0.203746	−	0.979024i	$-0.565312\pi$
$107$	8.01953	−	8.01953i	0.775277	−	0.775277i	0.979024	+	0.203746i	$0.0653118\pi$
$108$		0			0
$109$	1.36093	−	3.28558i	0.130353	−	0.314701i	−0.845205	−	0.534443i	$-0.820521\pi$
$109$	1.36093	−	3.28558i	0.130353	−	0.314701i	0.975558	+	0.219742i	$0.0705215\pi$
$110$		0			0
$111$	−3.64371	−	8.79669i	−0.345845	−	0.834945i
$112$		0			0
$113$	−8.29575	−	8.29575i	−0.780398	−	0.780398i	0.199500	−	0.979898i	$-0.436068\pi$
$113$	−8.29575	−	8.29575i	−0.780398	−	0.780398i	−0.979898	+	0.199500i	$0.936068\pi$
$114$		0			0
$115$	5.37081	+	9.06846i	0.500830	+	0.845638i
$116$		0			0
$117$	3.78327	+	9.13363i	0.349764	+	0.844404i
$118$		0			0
$119$		−	12.6526i		−	1.15986i
$120$		0			0
$121$	−2.57179	+	2.57179i	−0.233799	+	0.233799i
$122$		0			0
$123$	−6.73282	−	2.54937i	−0.607078	−	0.229869i
$124$		0			0
$125$	−8.16461	−	7.63801i	−0.730264	−	0.683165i
$126$		0			0
$127$	−10.3049	+	10.3049i	−0.914413	+	0.914413i	−0.996616	−	0.0822030i	$-0.973804\pi$
$127$	−10.3049	+	10.3049i	−0.914413	+	0.914413i	0.0822030	+	0.996616i	$0.473804\pi$
$128$		0			0
$129$	1.22896	+	0.509053i	0.108204	+	0.0448196i
$130$		0			0
$131$	10.3813	−	10.3813i	0.907018	−	0.907018i	−0.0890122	−	0.996031i	$-0.528371\pi$
$131$	10.3813	−	10.3813i	0.907018	−	0.907018i	0.996031	+	0.0890122i	$0.0283710\pi$
$132$		0			0
$133$	−3.15820	+	3.15820i	−0.273851	+	0.273851i
$134$		0			0
$135$	1.68508	+	11.7866i	0.145028	+	1.01443i
$136$		0			0
$137$	−13.2489	+	5.48788i	−1.13193	+	0.468861i	−0.868437	−	0.495799i	$-0.834875\pi$
$137$	−13.2489	+	5.48788i	−1.13193	+	0.468861i	−0.263495	+	0.964661i	$0.584875\pi$
$138$		0			0
$139$			20.4283i			1.73270i	0.499434	+	0.866352i	$0.333541\pi$
$139$			20.4283i			1.73270i	−0.499434	+	0.866352i	$0.666459\pi$
$140$		0			0
$141$	−3.61718			−0.304622
$142$		0			0
$143$	−15.4540			−1.29233
$144$		0			0
$145$	7.37132	−	1.05384i	0.612154	−	0.0875170i
$146$		0			0
$147$	0.979248	+	2.36411i	0.0807670	+	0.194989i
$148$		0			0
$149$	11.1470	+	4.61725i	0.913200	+	0.378260i	0.789281	−	0.614032i	$-0.210454\pi$
$149$	11.1470	+	4.61725i	0.913200	+	0.378260i	0.123919	+	0.992292i	$0.460454\pi$
$150$		0			0
$151$	11.3515	−	4.70196i	0.923775	−	0.382640i	0.130461	−	0.991453i	$-0.458354\pi$
$151$	11.3515	−	4.70196i	0.923775	−	0.382640i	0.793314	+	0.608813i	$0.208354\pi$
$152$		0			0
$153$	9.33568	+	3.86697i	0.754745	+	0.312626i
$154$		0			0
$155$	−0.344990	+	1.34718i	−0.0277102	+	0.108208i
$156$		0			0
$157$	14.0446	+	5.81748i	1.12088	+	0.464285i	0.864673	−	0.502335i	$-0.167526\pi$
$157$	14.0446	+	5.81748i	1.12088	+	0.464285i	0.256211	+	0.966621i	$0.417526\pi$
$158$		0			0
$159$	6.24741	−	6.24741i	0.495451	−	0.495451i
$160$		0			0
$161$	9.46483	−	3.92046i	0.745933	−	0.308975i
$162$		0			0
$163$	−8.96554	−	8.96554i	−0.702235	−	0.702235i	0.262654	−	0.964890i	$-0.415402\pi$
$163$	−8.96554	−	8.96554i	−0.702235	−	0.702235i	−0.964890	+	0.262654i	$0.915402\pi$
$164$		0			0
$165$	−6.60872	−	1.69238i	−0.514488	−	0.131752i
$166$		0			0
$167$	3.96088	−	9.56242i	0.306502	−	0.739962i	−0.693311	−	0.720638i	$-0.743849\pi$
$167$	3.96088	−	9.56242i	0.306502	−	0.739962i	0.999813	−	0.0193234i	$-0.00615123\pi$
$168$		0			0
$169$	13.7436	+	13.7436i	1.05720	+	1.05720i
$170$		0			0
$171$	−1.36504	−	3.29551i	−0.104388	−	0.252014i
$172$		0			0
$173$		−	12.6879i		−	0.964647i	−0.875993	−	0.482323i	$-0.839793\pi$
$173$		−	12.6879i		−	0.964647i	0.875993	−	0.482323i	$-0.160207\pi$
$174$		0			0
$175$	−8.47273	+	6.80553i	−0.640478	+	0.514450i
$176$		0			0
$177$	−3.79269	+	9.15635i	−0.285076	+	0.688234i
$178$		0			0
$179$	−1.39329	+	3.36369i	−0.104139	+	0.251414i	−0.967357	−	0.253417i	$-0.918445\pi$
$179$	−1.39329	+	3.36369i	−0.104139	+	0.251414i	0.863218	+	0.504832i	$0.168445\pi$
$180$		0			0
$181$	−1.90455	+	4.59800i	−0.141564	+	0.341767i	−0.978721	−	0.205197i	$-0.934216\pi$
$181$	−1.90455	+	4.59800i	−0.141564	+	0.341767i	0.837156	+	0.546964i	$0.184216\pi$
$182$		0			0
$183$	0.722156	+	1.74344i	0.0533833	+	0.128879i
$184$		0			0
$185$	9.64953	+	16.2930i	0.709447	+	1.19788i
$186$		0			0
$187$	−11.1694	+	11.1694i	−0.816787	+	0.816787i
$188$		0			0
$189$	11.5733			0.841833
$190$		0			0
$191$	−25.1815	−	10.4305i	−1.82207	−	0.754725i	−0.974627	−	0.223836i	$-0.928142\pi$
$191$	−25.1815	−	10.4305i	−1.82207	−	0.754725i	−0.847441	−	0.530889i	$-0.821858\pi$
$192$		0			0
$193$	12.4676	+	5.16424i	0.897436	+	0.371730i	0.783234	−	0.621728i	$-0.213569\pi$
$193$	12.4676	+	5.16424i	0.897436	+	0.371730i	0.114202	+	0.993458i	$0.463569\pi$
$194$		0			0
$195$	7.29654	+	12.3200i	0.522516	+	0.882255i
$196$		0			0
$197$			4.11316i			0.293050i	0.989207	+	0.146525i	$0.0468089\pi$
$197$			4.11316i			0.293050i	−0.989207	+	0.146525i	$0.953191\pi$
$198$		0			0
$199$	5.74541	−	13.8706i	0.407281	−	0.983263i	−0.578569	−	0.815633i	$-0.696389\pi$
$199$	5.74541	−	13.8706i	0.407281	−	0.983263i	0.985850	−	0.167630i	$-0.0536113\pi$
$200$		0			0
$201$	−5.73210			−0.404311
$202$		0			0
$203$		−	7.23791i		−	0.508001i
$204$		0			0
$205$	13.9728	+	3.12404i	0.975906	+	0.218192i
$206$		0			0
$207$			8.18182i			0.568676i
$208$		0			0
$209$	5.57598			0.385698
$210$		0			0
$211$	5.40225	−	13.0422i	0.371906	−	0.897861i	−0.621521	−	0.783397i	$-0.713485\pi$
$211$	5.40225	−	13.0422i	0.371906	−	0.897861i	0.993427	−	0.114464i	$-0.0365149\pi$
$212$		0			0
$213$		−	9.70960i		−	0.665291i
$214$		0			0
$215$	−2.56281	−	0.656292i	−0.174782	−	0.0447587i
$216$		0			0
$217$	1.24884	+	0.517287i	0.0847769	+	0.0351158i
$218$		0			0
$219$	7.78508	+	3.22469i	0.526067	+	0.217904i
$220$		0			0
$221$	33.1539			2.23017
$222$		0			0
$223$	−6.45521	+	6.45521i	−0.432273	+	0.432273i	−0.889401	−	0.457128i	$-0.848878\pi$
$223$	−6.45521	+	6.45521i	−0.432273	+	0.432273i	0.457128	+	0.889401i	$0.348878\pi$
$224$		0			0
$225$	−2.43196	−	8.33156i	−0.162131	−	0.555437i
$226$		0			0
$227$	4.34434	+	10.4882i	0.288344	+	0.696125i	0.999979	−	0.00642463i	$-0.00204504\pi$
$227$	4.34434	+	10.4882i	0.288344	+	0.696125i	−0.711635	+	0.702549i	$0.752045\pi$
$228$		0			0
$229$	−7.40283	+	17.8720i	−0.489192	+	1.18102i	0.465935	+	0.884819i	$0.345718\pi$
$229$	−7.40283	+	17.8720i	−0.489192	+	1.18102i	−0.955127	+	0.296196i	$0.904282\pi$
$230$		0			0
$231$	−2.53761	+	6.12632i	−0.166962	+	0.403083i
$232$		0			0
$233$	6.10950	−	14.7496i	0.400246	−	0.966281i	−0.587359	−	0.809326i	$-0.699832\pi$
$233$	6.10950	−	14.7496i	0.400246	−	0.966281i	0.987606	−	0.156954i	$-0.0501675\pi$
$234$		0			0
$235$	7.12135	−	1.01811i	0.464545	−	0.0664140i
$236$		0			0
$237$			7.95953i			0.517027i
$238$		0			0
$239$	−9.91259	−	23.9311i	−0.641192	−	1.54797i	−0.825073	−	0.565026i	$-0.808866\pi$
$239$	−9.91259	−	23.9311i	−0.641192	−	1.54797i	0.183881	−	0.982948i	$-0.441134\pi$
$240$		0			0
$241$	−6.89778	−	6.89778i	−0.444325	−	0.444325i	0.449137	−	0.893463i	$-0.351731\pi$
$241$	−6.89778	−	6.89778i	−0.444325	−	0.444325i	−0.893463	+	0.449137i	$0.851731\pi$
$242$		0			0
$243$	−5.77775	+	13.9487i	−0.370643	+	0.894812i
$244$		0			0
$245$	−2.59331	−	4.37874i	−0.165681	−	0.279747i
$246$		0			0
$247$	−8.27554	−	8.27554i	−0.526560	−	0.526560i
$248$		0			0
$249$	−5.22162	+	2.16287i	−0.330907	+	0.137066i
$250$		0			0
$251$	11.0694	−	11.0694i	0.698695	−	0.698695i	−0.265434	−	0.964129i	$-0.585515\pi$
$251$	11.0694	−	11.0694i	0.698695	−	0.698695i	0.964129	+	0.265434i	$0.0855153\pi$
$252$		0			0
$253$	−11.8162	−	4.89444i	−0.742880	−	0.307711i
$254$		0			0
$255$	14.1779	+	3.63071i	0.887852	+	0.227364i
$256$		0			0
$257$	18.4730	+	7.65178i	1.15232	+	0.477305i	0.875310	−	0.483563i	$-0.160658\pi$
$257$	18.4730	+	7.65178i	1.15232	+	0.477305i	0.277007	+	0.960868i	$0.410658\pi$
$258$		0			0
$259$	17.0051	−	7.04374i	1.05665	−	0.437677i
$260$		0			0
$261$	5.34049	+	2.21210i	0.330568	+	0.136926i
$262$		0			0
$263$	−6.92505	−	16.7186i	−0.427017	−	1.03091i	−0.980228	−	0.197869i	$-0.936598\pi$
$263$	−6.92505	−	16.7186i	−0.427017	−	1.03091i	0.553212	−	0.833041i	$-0.313402\pi$
$264$		0			0
$265$	−10.5412	+	14.0580i	−0.647541	+	0.863578i
$266$		0			0
$267$	6.37491			0.390138
$268$		0			0
$269$	1.77062			0.107957			0.0539784	−	0.998542i	$-0.482810\pi$
$269$	1.77062			0.107957			0.0539784	+	0.998542i	$0.482810\pi$
$270$		0			0
$271$			30.8588i			1.87454i	0.348603	+	0.937270i	$0.386656\pi$
$271$			30.8588i			1.87454i	−0.348603	+	0.937270i	$0.613344\pi$
$272$		0			0
$273$	12.8585	−	5.32617i	0.778232	−	0.322354i
$274$		0			0
$275$	13.4873	+	1.47177i	0.813315	+	0.0887510i
$276$		0			0
$277$	6.82061	−	6.82061i	0.409811	−	0.409811i	−0.471862	−	0.881673i	$-0.656418\pi$
$277$	6.82061	−	6.82061i	0.409811	−	0.409811i	0.881673	+	0.471862i	$0.156418\pi$
$278$		0			0
$279$	−0.763360	+	0.763360i	−0.0457012	+	0.0457012i
$280$		0			0
$281$	0.132254	+	0.0547814i	0.00788961	+	0.00326798i	0.386625	−	0.922237i	$-0.373641\pi$
$281$	0.132254	+	0.0547814i	0.00788961	+	0.00326798i	−0.378735	+	0.925505i	$0.623641\pi$
$282$		0			0
$283$	−0.213132	+	0.213132i	−0.0126694	+	0.0126694i	−0.713413	−	0.700744i	$-0.752852\pi$
$283$	−0.213132	+	0.213132i	−0.0126694	+	0.0126694i	0.700744	+	0.713413i	$0.252852\pi$
$284$		0			0
$285$	−2.63267	−	4.44519i	−0.155946	−	0.263311i
$286$		0			0
$287$	4.92825	−	13.0154i	0.290905	−	0.768274i
$288$		0			0
$289$	11.9412	−	11.9412i	0.702422	−	0.702422i
$290$		0			0
$291$		−	2.76313i		−	0.161977i
$292$		0			0
$293$	9.69488	+	23.4055i	0.566381	+	1.36737i	0.904585	+	0.426292i	$0.140181\pi$
$293$	9.69488	+	23.4055i	0.566381	+	1.36737i	−0.338204	+	0.941073i	$0.609819\pi$
$294$		0			0
$295$	4.88969	−	19.0941i	0.284689	−	1.11170i
$296$		0			0
$297$	−10.2166	−	10.2166i	−0.592829	−	0.592829i
$298$		0			0
$299$	10.2729	+	24.8010i	0.594098	+	1.43428i
$300$		0			0
$301$	−0.984063	+	2.37574i	−0.0567204	+	0.136935i
$302$		0			0
$303$	−2.47976	+	2.47976i	−0.142458	+	0.142458i
$304$		0			0
$305$	−1.91246	−	3.22914i	−0.109507	−	0.184900i
$306$		0			0
$307$		−	17.2768i		−	0.986040i	−0.870018	−	0.493020i	$-0.835893\pi$
$307$		−	17.2768i		−	0.986040i	0.870018	−	0.493020i	$-0.164107\pi$
$308$		0			0
$309$	−5.17718	+	12.4988i	−0.294520	+	0.711034i
$310$		0			0
$311$	−9.32071	−	3.86076i	−0.528529	−	0.218924i	0.102430	−	0.994740i	$-0.467338\pi$
$311$	−9.32071	−	3.86076i	−0.528529	−	0.218924i	−0.630959	+	0.775816i	$0.717338\pi$
$312$		0			0
$313$	−2.57322	−	6.21231i	−0.145447	−	0.351140i	0.834320	−	0.551280i	$-0.185860\pi$
$313$	−2.57322	−	6.21231i	−0.145447	−	0.351140i	−0.979767	+	0.200140i	$0.935860\pi$
$314$		0			0
$315$	−8.35147	+	1.19397i	−0.470552	+	0.0672727i
$316$		0			0
$317$	−13.3110	+	32.1356i	−0.747621	+	1.80492i	−0.176020	+	0.984387i	$0.556322\pi$
$317$	−13.3110	+	32.1356i	−0.747621	+	1.80492i	−0.571602	+	0.820531i	$0.693678\pi$
$318$		0			0
$319$	−6.38946	+	6.38946i	−0.357741	+	0.357741i
$320$		0			0
$321$	11.7809	−	4.87981i	0.657546	−	0.272365i
$322$		0			0
$323$	−11.9623			−0.665600
$324$		0			0
$325$	−17.8328	−	22.2014i	−0.989184	−	1.23151i
$326$		0			0
$327$	2.82736	−	2.82736i	0.156353	−	0.156353i
$328$		0			0
$329$		−	6.99246i		−	0.385507i
$330$		0			0
$331$	−5.20365	−	12.5627i	−0.286018	−	0.690509i	0.713935	−	0.700212i	$-0.246911\pi$
$331$	−5.20365	−	12.5627i	−0.286018	−	0.690509i	−0.999953	+	0.00970317i	$0.996911\pi$
$332$		0			0
$333$			14.7000i			0.805553i
$334$		0			0
$335$	11.2851	−	1.61338i	0.616572	−	0.0881485i
$336$		0			0
$337$	−34.6505			−1.88753			−0.943766	−	0.330614i	$-0.892744\pi$
$337$	−34.6505			−1.88753			−0.943766	+	0.330614i	$0.892744\pi$
$338$		0			0
$339$	−5.04789	−	12.1867i	−0.274164	−	0.661889i
$340$		0			0
$341$	−0.645800	−	1.55910i	−0.0349720	−	0.0844299i
$342$		0			0
$343$	−18.6265	+	7.71534i	−1.00574	+	0.416589i
$344$		0			0
$345$	1.67711	+	11.7308i	0.0902923	+	0.631567i
$346$		0			0
$347$	−11.9483	+	4.94914i	−0.641418	+	0.265684i	−0.679596	−	0.733587i	$-0.737845\pi$
$347$	−11.9483	+	4.94914i	−0.641418	+	0.265684i	0.0381777	+	0.999271i	$0.487845\pi$
$348$		0			0
$349$	−19.4416	−	19.4416i	−1.04069	−	1.04069i	−0.999136	−	0.0415505i	$-0.986770\pi$
$349$	−19.4416	−	19.4416i	−1.04069	−	1.04069i	−0.0415505	−	0.999136i	$-0.513230\pi$
$350$		0			0
$351$			30.3259i			1.61868i
$352$		0			0
$353$	−11.7595	−	11.7595i	−0.625894	−	0.625894i	0.321138	−	0.947032i	$-0.395935\pi$
$353$	−11.7595	−	11.7595i	−0.625894	−	0.625894i	−0.947032	+	0.321138i	$0.895935\pi$
$354$		0			0
$355$	2.73291	+	19.1158i	0.145048	+	1.01456i
$356$		0			0
$357$	5.44399	−	13.1430i	0.288127	−	0.695599i
$358$		0			0
$359$	−23.6992			−1.25080			−0.625398	−	0.780306i	$-0.715063\pi$
$359$	−23.6992			−1.25080			−0.625398	+	0.780306i	$0.715063\pi$
$360$		0			0
$361$	−10.4491	−	10.4491i	−0.549954	−	0.549954i
$362$		0			0
$363$	−3.77803	+	1.56491i	−0.198295	+	0.0821365i
$364$		0			0
$365$	−16.2346	−	4.15740i	−0.849755	−	0.217608i
$366$		0			0
$367$	−33.0947			−1.72753			−0.863764	−	0.503896i	$-0.831899\pi$
$367$	−33.0947			−1.72753			−0.863764	+	0.503896i	$0.831899\pi$
$368$		0			0
$369$	8.09719	+	7.61416i	0.421523	+	0.396378i
$370$		0			0
$371$	12.0770	+	12.0770i	0.627007	+	0.627007i
$372$		0			0
$373$	2.30216	+	2.30216i	0.119201	+	0.119201i	0.764191	−	0.644990i	$-0.223138\pi$
$373$	2.30216	+	2.30216i	0.119201	+	0.119201i	−0.644990	+	0.764191i	$0.723138\pi$
$374$		0			0
$375$	−5.19467	−	11.4470i	−0.268251	−	0.591122i
$376$		0			0
$377$	18.9657			0.976785
$378$		0			0
$379$		−	11.6146i		−	0.596603i	−0.954472	−	0.298302i	$-0.903580\pi$
$379$		−	11.6146i		−	0.596603i	0.954472	−	0.298302i	$-0.0964201\pi$
$380$		0			0
$381$	−15.1382	+	6.27044i	−0.775553	+	0.321245i
$382$		0			0
$383$	5.85484	+	14.1348i	0.299168	+	0.722256i	0.999960	+	0.00889041i	$0.00282994\pi$
$383$	5.85484	+	14.1348i	0.299168	+	0.722256i	−0.700792	+	0.713365i	$0.747170\pi$
$384$		0			0
$385$	3.27159	−	12.7755i	0.166735	−	0.651099i
$386$		0			0
$387$	−1.45218	−	1.45218i	−0.0738185	−	0.0738185i
$388$		0			0
$389$	−3.48627	+	3.48627i	−0.176761	+	0.176761i	−0.789942	−	0.613181i	$-0.789889\pi$
$389$	−3.48627	+	3.48627i	−0.176761	+	0.176761i	0.613181	+	0.789942i	$0.289889\pi$
$390$		0			0
$391$	25.3497	+	10.5002i	1.28199	+	0.531017i
$392$		0			0
$393$	15.2504	−	6.31693i	0.769282	−	0.318647i
$394$		0			0
$395$	−2.24032	−	15.6704i	−0.112723	−	0.788462i
$396$		0			0
$397$	1.20155	+	0.497697i	0.0603039	+	0.0249787i	0.412632	−	0.910898i	$-0.364610\pi$
$397$	1.20155	+	0.497697i	0.0603039	+	0.0249787i	−0.352328	+	0.935877i	$0.614610\pi$
$398$		0			0
$399$	−4.63948	+	1.92174i	−0.232265	+	0.0962072i
$400$		0			0
$401$	−19.2845	−	19.2845i	−0.963020	−	0.963020i	0.0363204	−	0.999340i	$-0.488436\pi$
$401$	−19.2845	−	19.2845i	−0.963020	−	0.963020i	−0.999340	+	0.0363204i	$0.988436\pi$
$402$		0			0
$403$	−1.35547	+	3.27238i	−0.0675205	+	0.163009i
$404$		0			0
$405$	−0.432283	+	1.68806i	−0.0214803	+	0.0838803i
$406$		0			0
$407$	−21.2298	−	8.79366i	−1.05232	−	0.435885i
$408$		0			0
$409$	−26.8639			−1.32833			−0.664166	−	0.747585i	$-0.731213\pi$
$409$	−26.8639			−1.32833			−0.664166	+	0.747585i	$0.731213\pi$
$410$		0			0
$411$	−16.1237			−0.795323
$412$		0			0
$413$	−17.7004	−	7.33174i	−0.870979	−	0.360771i
$414$		0			0
$415$	9.67133	−	5.72786i	0.474747	−	0.281169i
$416$		0			0
$417$	−8.78964	+	21.2201i	−0.430430	+	1.03915i
$418$		0			0
$419$	−11.5058	−	11.5058i	−0.562096	−	0.562096i	0.367806	−	0.929903i	$-0.380109\pi$
$419$	−11.5058	−	11.5058i	−0.562096	−	0.562096i	−0.929903	+	0.367806i	$0.880109\pi$
$420$		0			0
$421$	9.81749	−	4.06654i	0.478475	−	0.198191i	−0.130393	−	0.991462i	$-0.541624\pi$
$421$	9.81749	−	4.06654i	0.478475	−	0.198191i	0.608868	+	0.793272i	$0.291624\pi$
$422$		0			0
$423$	5.15938	+	2.13709i	0.250858	+	0.103909i
$424$		0			0
$425$	−28.9347	−	3.15742i	−1.40354	−	0.153158i
$426$		0			0
$427$	−3.37028	+	1.39602i	−0.163099	+	0.0675580i
$428$		0			0
$429$	−16.0530	−	6.64938i	−0.775047	−	0.321035i
$430$		0			0
$431$	24.4412	−	24.4412i	1.17729	−	1.17729i	0.196859	−	0.980432i	$-0.436926\pi$
$431$	24.4412	−	24.4412i	1.17729	−	1.17729i	0.980432	−	0.196859i	$-0.0630740\pi$
$432$		0			0
$433$	−14.8364	−	14.8364i	−0.712990	−	0.712990i	0.254170	−	0.967160i	$-0.418198\pi$
$433$	−14.8364	−	14.8364i	−0.712990	−	0.712990i	−0.967160	+	0.254170i	$0.918198\pi$
$434$		0			0
$435$	8.11046	+	2.07695i	0.388867	+	0.0995822i
$436$		0			0
$437$	−3.70658	−	8.94847i	−0.177310	−	0.428063i
$438$		0			0
$439$	38.4633	−	15.9320i	1.83575	−	0.760394i	0.874325	−	0.485341i	$-0.161305\pi$
$439$	38.4633	−	15.9320i	1.83575	−	0.760394i	0.961429	−	0.275053i	$-0.0886954\pi$
$440$		0			0
$441$		−	3.95062i		−	0.188125i
$442$		0			0
$443$	−6.02751			−0.286376			−0.143188	−	0.989696i	$-0.545735\pi$
$443$	−6.02751			−0.286376			−0.143188	+	0.989696i	$0.545735\pi$
$444$		0			0
$445$	−12.5506	+	1.79431i	−0.594957	+	0.0850584i
$446$		0			0
$447$	9.59242	+	9.59242i	0.453706	+	0.453706i
$448$		0			0
$449$	8.30143	+	8.30143i	0.391769	+	0.391769i	0.875317	−	0.483549i	$-0.160652\pi$
$449$	8.30143	+	8.30143i	0.391769	+	0.391769i	−0.483549	+	0.875317i	$0.660652\pi$
$450$		0			0
$451$	−15.8402	+	7.13915i	−0.745888	+	0.336169i
$452$		0			0
$453$	13.8146			0.649067
$454$		0			0
$455$	−23.8161	+	14.1051i	−1.11652	+	0.661259i
$456$		0			0
$457$	27.2373	−	11.2820i	1.27411	−	0.527752i	0.359895	−	0.932993i	$-0.382812\pi$
$457$	27.2373	−	11.2820i	1.27411	−	0.527752i	0.914210	+	0.405241i	$0.132812\pi$
$458$		0			0
$459$	21.9180	+	21.9180i	1.02305	+	1.02305i
$460$		0			0
$461$	−20.5490			−0.957062			−0.478531	−	0.878071i	$-0.658831\pi$
$461$	−20.5490			−0.957062			−0.478531	+	0.878071i	$0.658831\pi$
$462$		0			0
$463$	7.25850	−	17.5236i	0.337331	−	0.814389i	−0.660639	−	0.750704i	$-0.729715\pi$
$463$	7.25850	−	17.5236i	0.337331	−	0.814389i	0.997970	−	0.0636854i	$-0.0202854\pi$
$464$		0			0
$465$	−0.938009	+	1.25096i	−0.0434991	+	0.0580117i
$466$		0			0
$467$	−14.9200	−	14.9200i	−0.690416	−	0.690416i	0.271908	−	0.962323i	$-0.412345\pi$
$467$	−14.9200	−	14.9200i	−0.690416	−	0.690416i	−0.962323	+	0.271908i	$0.912345\pi$
$468$		0			0
$469$		−	11.0809i		−	0.511667i
$470$		0			0
$471$	12.0859	+	12.0859i	0.556890	+	0.556890i
$472$		0			0
$473$	2.96596	−	1.22854i	0.136375	−	0.0564883i
$474$		0			0
$475$	6.43425	+	8.01050i	0.295224	+	0.367547i
$476$		0			0
$477$	−12.6021	+	5.21995i	−0.577010	+	0.239005i
$478$		0			0
$479$	−14.3985	−	34.7611i	−0.657885	−	1.58828i	−0.801064	−	0.598578i	$-0.795732\pi$
$479$	−14.3985	−	34.7611i	−0.657885	−	1.58828i	0.143179	−	0.989697i	$-0.454268\pi$
$480$		0			0
$481$	18.4570	+	44.5590i	0.841565	+	2.03172i
$482$		0			0
$483$	11.5185			0.524111
$484$		0			0
$485$	0.777722	+	5.43993i	0.0353145	+	0.247014i
$486$		0			0
$487$			37.8251i			1.71402i	0.515299	+	0.857011i	$0.327681\pi$
$487$			37.8251i			1.71402i	−0.515299	+	0.857011i	$0.672319\pi$
$488$		0			0
$489$	−5.45545	−	13.1706i	−0.246704	−	0.595596i
$490$		0			0
$491$		−	8.37581i		−	0.377995i	−0.981978	−	0.188997i	$-0.939476\pi$
$491$		−	8.37581i		−	0.377995i	0.981978	−	0.188997i	$-0.0605238\pi$
$492$		0			0
$493$	13.7075	−	13.7075i	0.617354	−	0.617354i
$494$		0			0
$495$	8.42650	+	6.31847i	0.378743	+	0.283994i
$496$		0			0
$497$	18.7699			0.841944
$498$		0			0
$499$	33.6886	−	13.9543i	1.50811	−	0.624679i	0.532942	−	0.846151i	$-0.321086\pi$
$499$	33.6886	−	13.9543i	1.50811	−	0.624679i	0.975167	+	0.221472i	$0.0710862\pi$
$500$		0			0
$501$	8.22881	−	8.22881i	0.367636	−	0.367636i
$502$		0			0
$503$	−4.86280	+	11.7398i	−0.216821	+	0.523453i	−0.994443	−	0.105280i	$-0.966426\pi$
$503$	−4.86280	+	11.7398i	−0.216821	+	0.523453i	0.777621	+	0.628733i	$0.216426\pi$
$504$		0			0
$505$	4.18407	−	5.58000i	0.186189	−	0.248307i
$506$		0			0
$507$	8.36285	+	20.1897i	0.371407	+	0.896656i
$508$		0			0
$509$	−28.7402	−	11.9046i	−1.27389	−	0.527661i	−0.359743	−	0.933052i	$-0.617136\pi$
$509$	−28.7402	−	11.9046i	−1.27389	−	0.527661i	−0.914144	+	0.405390i	$0.867136\pi$
$510$		0			0
$511$	−6.23372	+	15.0495i	−0.275764	+	0.665752i
$512$		0			0
$513$		−	10.9419i		−	0.483097i
$514$		0			0
$515$	6.67464	−	26.0643i	0.294120	−	1.14853i
$516$		0			0
$517$	−6.17279	+	6.17279i	−0.271479	+	0.271479i
$518$		0			0
$519$	5.45922	−	13.1797i	0.239633	−	0.578526i
$520$		0			0
$521$	−13.0518	−	31.5099i	−0.571811	−	1.38047i	−0.900012	−	0.435866i	$-0.856442\pi$
$521$	−13.0518	−	31.5099i	−0.571811	−	1.38047i	0.328201	−	0.944608i	$-0.393558\pi$
$522$		0			0
$523$	10.0376	+	10.0376i	0.438912	+	0.438912i	0.891646	−	0.452734i	$-0.149551\pi$
$523$	10.0376	+	10.0376i	0.438912	+	0.438912i	−0.452734	+	0.891646i	$0.649551\pi$
$524$		0			0
$525$	−11.7293	+	3.42376i	−0.511910	+	0.149425i
$526$		0			0
$527$	1.38545	+	3.34478i	0.0603512	+	0.145701i
$528$		0			0
$529$		−	0.783497i		−	0.0340651i
$530$		0			0
$531$	10.8194	−	10.8194i	0.469524	−	0.469524i
$532$		0			0
$533$	34.1047	+	12.9137i	1.47724	+	0.559353i
$534$		0			0
$535$	−21.8202	+	12.9231i	−0.943372	+	0.558713i
$536$		0			0
$537$	−2.89458	+	2.89458i	−0.124910	+	0.124910i
$538$		0			0
$539$	5.70551	+	2.36330i	0.245754	+	0.101795i
$540$		0			0
$541$	−23.6898	+	23.6898i	−1.01850	+	1.01850i	−0.0186788	+	0.999826i	$0.505946\pi$
$541$	−23.6898	+	23.6898i	−1.01850	+	1.01850i	−0.999826	+	0.0186788i	$0.994054\pi$
$542$		0			0
$543$	−3.95674	+	3.95674i	−0.169800	+	0.169800i
$544$		0			0
$545$	−4.77058	+	6.36218i	−0.204349	+	0.272526i
$546$		0			0
$547$	7.79536	−	3.22894i	0.333306	−	0.138060i	−0.209753	−	0.977754i	$-0.567266\pi$
$547$	7.79536	−	3.22894i	0.333306	−	0.138060i	0.543059	+	0.839695i	$0.317266\pi$
$548$		0			0
$549$		−	2.91342i		−	0.124342i
$550$		0			0
$551$	−6.84304			−0.291523
$552$		0			0
$553$	−15.3868			−0.654312
$554$		0			0
$555$	3.01319	+	21.0763i	0.127903	+	0.894641i
$556$		0			0
$557$	−4.97936	−	12.0212i	−0.210982	−	0.509356i	0.782592	−	0.622534i	$-0.213897\pi$
$557$	−4.97936	−	12.0212i	−0.210982	−	0.509356i	−0.993575	+	0.113178i	$0.963897\pi$
$558$		0			0
$559$	−6.22523	−	2.57857i	−0.263299	−	0.109062i
$560$		0			0
$561$	−16.4081	+	6.79647i	−0.692752	+	0.286947i
$562$		0			0
$563$	2.10267	+	0.870954i	0.0886170	+	0.0367063i	0.426552	−	0.904463i	$-0.359728\pi$
$563$	2.10267	+	0.870954i	0.0886170	+	0.0367063i	−0.337935	+	0.941170i	$0.609728\pi$
$564$		0			0
$565$	13.3682	+	22.5718i	0.562403	+	0.949603i
$566$		0			0
$567$	1.56484	+	0.648178i	0.0657171	+	0.0272209i
$568$		0			0
$569$	−31.4978	+	31.4978i	−1.32046	+	1.32046i	−0.407052	+	0.913405i	$0.633443\pi$
$569$	−31.4978	+	31.4978i	−1.32046	+	1.32046i	−0.913405	+	0.407052i	$0.866557\pi$
$570$		0			0
$571$	−11.1776	+	4.62991i	−0.467768	+	0.193756i	−0.604102	−	0.796907i	$-0.706468\pi$
$571$	−11.1776	+	4.62991i	−0.467768	+	0.193756i	0.136334	+	0.990663i	$0.456468\pi$
$572$		0			0
$573$	−21.6696	−	21.6696i	−0.905260	−	0.905260i
$574$		0			0
$575$	−6.60362	−	22.6231i	−0.275390	−	0.943449i
$576$		0			0
$577$	14.2781	−	34.4704i	0.594405	−	1.43502i	−0.284804	−	0.958586i	$-0.591929\pi$
$577$	14.2781	−	34.4704i	0.594405	−	1.43502i	0.879209	−	0.476436i	$-0.158071\pi$
$578$		0			0
$579$	10.7288	+	10.7288i	0.445874	+	0.445874i
$580$		0			0
$581$	−4.18109	−	10.0940i	−0.173461	−	0.418772i
$582$		0			0
$583$		−	21.3226i		−	0.883093i
$584$		0			0
$585$	−3.12861	−	21.8836i	−0.129352	−	0.904777i
$586$		0			0
$587$	−2.69862	+	6.51505i	−0.111384	+	0.268905i	−0.969736	−	0.244157i	$-0.921489\pi$
$587$	−2.69862	+	6.51505i	−0.111384	+	0.268905i	0.858352	+	0.513062i	$0.171489\pi$
$588$		0			0
$589$	0.489066	−	1.18071i	0.0201516	−	0.0486503i
$590$		0			0
$591$	−1.76976	+	4.27258i	−0.0727982	+	0.175750i
$592$		0			0
$593$	10.0274	+	24.2082i	0.411774	+	0.994111i	0.984661	+	0.174477i	$0.0558234\pi$
$593$	10.0274	+	24.2082i	0.411774	+	0.994111i	−0.572887	+	0.819634i	$0.694177\pi$
$594$		0			0
$595$	−7.01862	+	27.4076i	−0.287735	+	1.12360i
$596$		0			0
$597$	11.9362	−	11.9362i	0.488516	−	0.488516i
$598$		0			0
$599$	−35.9384			−1.46840			−0.734201	−	0.678932i	$-0.762443\pi$
$599$	−35.9384			−1.46840			−0.734201	+	0.678932i	$0.762443\pi$
$600$		0			0
$601$	−22.1706	−	9.18338i	−0.904360	−	0.374598i	−0.118465	−	0.992958i	$-0.537797\pi$
$601$	−22.1706	−	9.18338i	−0.904360	−	0.374598i	−0.785895	+	0.618360i	$0.787797\pi$
$602$		0			0
$603$	8.17601	+	3.38662i	0.332953	+	0.137914i
$604$		0			0
$605$	6.99755	−	4.14431i	0.284491	−	0.168490i
$606$		0			0
$607$		−	40.7307i		−	1.65321i	−0.562785	−	0.826603i	$-0.690270\pi$
$607$		−	40.7307i		−	1.65321i	0.562785	−	0.826603i	$-0.309730\pi$
$608$		0			0
$609$	3.11424	−	7.51844i	0.126195	−	0.304663i
$610$		0			0
$611$	18.3226			0.741252
$612$		0			0
$613$			25.8321i			1.04335i	0.853145	+	0.521674i	$0.174692\pi$
$613$			25.8321i			1.04335i	−0.853145	+	0.521674i	$0.825308\pi$
$614$		0			0
$615$	13.1702	+	9.25719i	0.531076	+	0.373286i
$616$		0			0
$617$			0.825032i			0.0332145i	0.999862	+	0.0166073i	$0.00528650\pi$
$617$			0.825032i			0.0332145i	−0.999862	+	0.0166073i	$0.994713\pi$
$618$		0			0
$619$	21.3405			0.857746			0.428873	−	0.903365i	$-0.358911\pi$
$619$	21.3405			0.857746			0.428873	+	0.903365i	$0.358911\pi$
$620$		0			0
$621$	−9.60450	+	23.1873i	−0.385415	+	0.930475i
$622$		0			0
$623$			12.3235i			0.493730i
$624$		0			0
$625$	13.4490	+	21.0743i	0.537958	+	0.842971i
$626$		0			0
$627$	5.79210	+	2.39917i	0.231314	+	0.0958134i
$628$		0			0
$629$	45.5448	+	18.8653i	1.81599	+	0.752207i
$630$		0			0
$631$	16.6854			0.664235			0.332118	−	0.943238i	$-0.392237\pi$
$631$	16.6854			0.664235			0.332118	+	0.943238i	$0.392237\pi$
$632$		0			0
$633$	11.2233	−	11.2233i	0.446085	−	0.446085i
$634$		0			0
$635$	28.0385	−	16.6058i	1.11267	−	0.658982i
$636$		0			0
$637$	−4.96031	−	11.9753i	−0.196535	−	0.474477i
$638$		0			0
$639$	−5.73659	+	13.8493i	−0.226936	+	0.547872i
$640$		0			0
$641$	−0.711342	+	1.71733i	−0.0280963	+	0.0678305i	−0.937305	−	0.348510i	$-0.886688\pi$
$641$	−0.711342	+	1.71733i	−0.0280963	+	0.0678305i	0.909209	+	0.416341i	$0.136688\pi$
$642$		0			0
$643$	−8.85532	+	21.3786i	−0.349220	+	0.843091i	0.647493	+	0.762072i	$0.275818\pi$
$643$	−8.85532	+	21.3786i	−0.349220	+	0.843091i	−0.996713	+	0.0810194i	$0.974182\pi$
$644$		0			0
$645$	−2.37976	−	1.78442i	−0.0937029	−	0.0702616i
$646$		0			0
$647$		−	25.1848i		−	0.990119i	−0.868859	−	0.495059i	$-0.835146\pi$
$647$		−	25.1848i		−	0.990119i	0.868859	−	0.495059i	$-0.164854\pi$
$648$		0			0
$649$	9.15320	+	22.0978i	0.359295	+	0.867414i
$650$		0			0
$651$	1.07467	+	1.07467i	0.0421198	+	0.0421198i
$652$		0			0
$653$	12.7870	−	30.8705i	0.500393	−	1.20805i	−0.448878	−	0.893593i	$-0.648176\pi$
$653$	12.7870	−	30.8705i	0.500393	−	1.20805i	0.949270	−	0.314461i	$-0.101824\pi$
$654$		0			0
$655$	−28.2464	+	16.7289i	−1.10368	+	0.653654i
$656$		0			0
$657$	−9.19909	−	9.19909i	−0.358891	−	0.358891i
$658$		0			0
$659$	−14.4922	+	6.00286i	−0.564535	+	0.233838i	−0.646653	−	0.762784i	$-0.723832\pi$
$659$	−14.4922	+	6.00286i	−0.564535	+	0.233838i	0.0821174	+	0.996623i	$0.473832\pi$
$660$		0			0
$661$	8.01755	−	8.01755i	0.311847	−	0.311847i	−0.533778	−	0.845625i	$-0.679228\pi$
$661$	8.01755	−	8.01755i	0.311847	−	0.311847i	0.845625	+	0.533778i	$0.179228\pi$
$662$		0			0
$663$	34.4389	+	14.2651i	1.33750	+	0.554010i
$664$		0			0
$665$	8.59311	−	5.08928i	0.333227	−	0.197354i
$666$		0			0
$667$	14.5013	+	6.00663i	0.561492	+	0.232578i
$668$		0			0
$669$	−9.48288	+	3.92794i	−0.366629	+	0.151863i
$670$		0			0
$671$	4.20758	+	1.74284i	0.162432	+	0.0672815i
$672$		0			0
$673$	16.3745	+	39.5315i	0.631190	+	1.52383i	0.838128	+	0.545473i	$0.183650\pi$
$673$	16.3745	+	39.5315i	0.631190	+	1.52383i	−0.206938	+	0.978354i	$0.566350\pi$
$674$		0			0
$675$	2.88809	−	26.4665i	0.111163	−	1.01870i
$676$		0			0
$677$	41.2364			1.58484			0.792422	−	0.609973i	$-0.208820\pi$
$677$	41.2364			1.58484			0.792422	+	0.609973i	$0.208820\pi$
$678$		0			0
$679$	5.34147			0.204987
$680$		0			0
$681$			12.7639i			0.489115i
$682$		0			0
$683$	3.32742	−	1.37826i	0.127320	−	0.0527377i	−0.318114	−	0.948053i	$-0.603049\pi$
$683$	3.32742	−	1.37826i	0.127320	−	0.0527377i	0.445434	+	0.895315i	$0.353049\pi$
$684$		0			0
$685$	31.7436	−	4.53825i	1.21286	−	0.173397i
$686$		0			0
$687$	−15.3795	+	15.3795i	−0.586765	+	0.586765i
$688$		0			0
$689$	−31.6458	+	31.6458i	−1.20561	+	1.20561i
$690$		0			0
$691$	−9.26807	−	3.83896i	−0.352574	−	0.146041i	0.199365	−	0.979925i	$-0.436112\pi$
$691$	−9.26807	−	3.83896i	−0.352574	−	0.146041i	−0.551939	+	0.833884i	$0.686112\pi$
$692$		0			0
$693$	7.23906	−	7.23906i	0.274989	−	0.274989i
$694$		0			0
$695$	11.3320	−	44.2511i	0.429846	−	1.67854i
$696$		0			0
$697$	33.9825	−	15.3158i	1.28718	−	0.580127i
$698$		0			0
$699$	12.6926	−	12.6926i	0.480078	−	0.480078i
$700$		0			0
$701$		−	10.1320i		−	0.382682i	−0.981524	−	0.191341i	$-0.938716\pi$
$701$		−	10.1320i		−	0.382682i	0.981524	−	0.191341i	$-0.0612837\pi$
$702$		0			0
$703$	−6.65947	−	16.0774i	−0.251167	−	0.606370i
$704$		0			0
$705$	7.83542	+	2.00652i	0.295099	+	0.0755699i
$706$		0			0
$707$	−4.79368	−	4.79368i	−0.180285	−	0.180285i
$708$		0			0
$709$	14.0966	+	34.0322i	0.529409	+	1.27811i	0.931911	+	0.362688i	$0.118141\pi$
$709$	14.0966	+	34.0322i	0.529409	+	1.27811i	−0.402501	+	0.915419i	$0.631859\pi$
$710$		0			0
$711$	4.70262	−	11.3531i	0.176362	−	0.425775i
$712$		0			0
$713$	−2.07279	+	2.07279i	−0.0776267	+	0.0776267i
$714$		0			0
$715$	33.4760	+	8.57265i	1.25193	+	0.320599i
$716$		0			0
$717$		−	29.1237i		−	1.08765i
$718$		0			0
$719$	−12.9679	+	31.3072i	−0.483620	+	1.16756i	0.474257	+	0.880386i	$0.342717\pi$
$719$	−12.9679	+	31.3072i	−0.483620	+	1.16756i	−0.957878	+	0.287177i	$0.907283\pi$
$720$		0			0
$721$	−24.1618	−	10.0081i	−0.899832	−	0.372723i
$722$		0			0
$723$	−4.19724	−	10.1330i	−0.156097	−	0.376851i
$724$		0			0
$725$	−16.5521	−	1.80621i	−0.614730	−	0.0670808i
$726$		0			0
$727$	−1.57524	+	3.80296i	−0.0584223	+	0.141044i	−0.950395	−	0.311045i	$-0.899321\pi$
$727$	−1.57524	+	3.80296i	−0.0584223	+	0.141044i	0.891973	+	0.452089i	$0.149321\pi$
$728$		0			0
$729$	−13.6565	+	13.6565i	−0.505796	+	0.505796i
$730$		0			0
$731$	−6.36294	+	2.63562i	−0.235342	+	0.0974818i
$732$		0			0
$733$	−43.8232			−1.61865			−0.809324	−	0.587363i	$-0.800166\pi$
$733$	−43.8232			−1.61865			−0.809324	+	0.587363i	$0.800166\pi$
$734$		0			0
$735$	−0.809797	−	5.66428i	−0.0298698	−	0.208930i
$736$		0			0
$737$	−9.78194	+	9.78194i	−0.360322	+	0.360322i
$738$		0			0
$739$			27.0236i			0.994078i	0.867728	+	0.497039i	$0.165579\pi$
$739$			27.0236i			0.994078i	−0.867728	+	0.497039i	$0.834421\pi$
$740$		0			0
$741$	−5.03559	−	12.1570i	−0.184987	−	0.446599i
$742$		0			0
$743$			23.6339i			0.867042i	0.901143	+	0.433521i	$0.142729\pi$
$743$			23.6339i			0.867042i	−0.901143	+	0.433521i	$0.857271\pi$
$744$		0			0
$745$	−21.5851	−	16.1852i	−0.790815	−	0.592980i
$746$		0			0
$747$	8.72574			0.319258
$748$		0			0
$749$	9.43329	+	22.7740i	0.344685	+	0.832143i
$750$		0			0
$751$	−2.31970	−	5.60026i	−0.0846472	−	0.204356i	0.875888	−	0.482514i	$-0.160276\pi$
$751$	−2.31970	−	5.60026i	−0.0846472	−	0.204356i	−0.960535	+	0.278158i	$0.910276\pi$
$752$		0			0
$753$	16.2613	−	6.73564i	0.592593	−	0.245460i
$754$		0			0
$755$	−27.1976	+	3.88832i	−0.989822	+	0.141511i
$756$		0			0
$757$	19.6311	−	8.13149i	0.713506	−	0.295544i	0.00375148	−	0.999993i	$-0.498806\pi$
$757$	19.6311	−	8.13149i	0.713506	−	0.295544i	0.709755	+	0.704449i	$0.248806\pi$
$758$		0			0
$759$	−10.1683	−	10.1683i	−0.369086	−	0.369086i
$760$		0			0
$761$			26.4750i			0.959717i	0.877346	+	0.479859i	$0.159312\pi$
$761$			26.4750i			0.959717i	−0.877346	+	0.479859i	$0.840688\pi$
$762$		0			0
$763$	5.46564	+	5.46564i	0.197869	+	0.197869i
$764$		0			0
$765$	−18.0776	−	13.5552i	−0.653596	−	0.490089i
$766$		0			0
$767$	19.2116	−	46.3809i	0.693691	−	1.67472i
$768$		0			0
$769$	−24.2999			−0.876276			−0.438138	−	0.898908i	$-0.644362\pi$
$769$	−24.2999			−0.876276			−0.438138	+	0.898908i	$0.644362\pi$
$770$		0			0
$771$	15.8967	+	15.8967i	0.572506	+	0.572506i
$772$		0			0
$773$	4.68354	−	1.93999i	0.168455	−	0.0697765i	−0.296862	−	0.954920i	$-0.595940\pi$
$773$	4.68354	−	1.93999i	0.168455	−	0.0697765i	0.465317	+	0.885144i	$0.345940\pi$
$774$		0			0
$775$	1.49461	−	2.72684i	0.0536880	−	0.0979511i
$776$		0			0
$777$	20.6949			0.742425
$778$		0			0
$779$	−12.3053	−	4.65938i	−0.440884	−	0.166940i
$780$		0			0
$781$	−16.5696	−	16.5696i	−0.592908	−	0.592908i
$782$		0			0
$783$	12.5382	+	12.5382i	0.448079	+	0.448079i
$784$		0			0
$785$	−27.1960	−	20.3925i	−0.970666	−	0.727839i
$786$		0			0
$787$	45.1170			1.60825			0.804123	−	0.594462i	$-0.202635\pi$
$787$	45.1170			1.60825			0.804123	+	0.594462i	$0.202635\pi$
$788$		0			0
$789$		−	20.3462i		−	0.724343i
$790$		0			0
$791$	23.5584	−	9.75820i	0.837639	−	0.346962i
$792$		0			0
$793$	−3.65803	−	8.83127i	−0.129901	−	0.313608i
$794$		0			0
$795$	−16.9985	+	10.0674i	−0.602874	+	0.357053i
$796$		0			0
$797$	12.0953	+	12.0953i	0.428438	+	0.428438i	0.888096	−	0.459658i	$-0.152028\pi$
$797$	12.0953	+	12.0953i	0.428438	+	0.428438i	−0.459658	+	0.888096i	$0.652028\pi$
$798$		0			0
$799$	13.2426	−	13.2426i	0.468491	−	0.468491i
$800$		0			0
$801$	−9.09288	−	3.76639i	−0.321281	−	0.133079i
$802$		0			0
$803$	18.7884	−	7.78240i	0.663027	−	0.274635i
$804$		0			0
$805$	−22.6772	+	3.24205i	−0.799265	+	0.114267i
$806$		0			0
$807$	1.83925	+	0.761843i	0.0647447	+	0.0268181i
$808$		0			0
$809$	−2.84269	+	1.17748i	−0.0999436	+	0.0413980i	−0.432095	−	0.901828i	$-0.642225\pi$
$809$	−2.84269	+	1.17748i	−0.0999436	+	0.0413980i	0.332151	+	0.943226i	$0.392225\pi$
$810$		0			0
$811$	29.1811	+	29.1811i	1.02469	+	1.02469i	0.999687	+	0.0250005i	$0.00795872\pi$
$811$	29.1811	+	29.1811i	1.02469	+	1.02469i	0.0250005	+	0.999687i	$0.492041\pi$
$812$		0			0
$813$	−13.2776	+	32.0549i	−0.465665	+	1.12421i
$814$		0			0
$815$	14.4475	+	24.3942i	0.506074	+	0.854493i
$816$		0			0
$817$	2.24613	+	0.930377i	0.0785821	+	0.0325498i
$818$		0			0
$819$	−21.4876			−0.750837
$820$		0			0
$821$	41.6708			1.45432			0.727160	−	0.686468i	$-0.240840\pi$
$821$	41.6708			1.45432			0.727160	+	0.686468i	$0.240840\pi$
$822$		0			0
$823$	16.2209	+	6.71893i	0.565426	+	0.234207i	0.647039	−	0.762457i	$-0.276007\pi$
$823$	16.2209	+	6.71893i	0.565426	+	0.234207i	−0.0816128	+	0.996664i	$0.526007\pi$
$824$		0			0
$825$	13.3768	+	7.33197i	0.465721	+	0.255266i
$826$		0			0
$827$	0.143818	−	0.347207i	0.00500103	−	0.0120736i	−0.921359	−	0.388712i	$-0.872920\pi$
$827$	0.143818	−	0.347207i	0.00500103	−	0.0120736i	0.926360	+	0.376638i	$0.122920\pi$
$828$		0			0
$829$	18.8898	+	18.8898i	0.656069	+	0.656069i	0.954448	−	0.298378i	$-0.0964457\pi$
$829$	18.8898	+	18.8898i	0.656069	+	0.656069i	−0.298378	+	0.954448i	$0.596446\pi$
$830$		0			0
$831$	10.0197	−	4.15028i	0.347578	−	0.143972i
$832$		0			0
$833$	−12.2402	−	5.07005i	−0.424097	−	0.175667i
$834$		0			0
$835$	−13.8844	+	18.5166i	−0.480489	+	0.640794i
$836$		0			0
$837$	−3.05946	+	1.26727i	−0.105751	+	0.0438033i
$838$		0			0
$839$	38.4240	+	15.9158i	1.32654	+	0.549473i	0.929668	−	0.368399i	$-0.120094\pi$
$839$	38.4240	+	15.9158i	1.32654	+	0.549473i	0.396877	+	0.917872i	$0.370094\pi$
$840$		0			0
$841$	−12.6647	+	12.6647i	−0.436715	+	0.436715i
$842$		0			0
$843$	0.113809	+	0.113809i	0.00391980	+	0.00391980i
$844$		0			0
$845$	−22.1471	−	37.3948i	−0.761883	−	1.28642i
$846$		0			0
$847$	−3.02517	−	7.30340i	−0.103946	−	0.250948i
$848$		0			0
$849$	−0.313096	+	0.129689i	−0.0107454	+	0.00445091i
$850$		0			0
$851$			39.9156i			1.36829i
$852$		0			0
$853$	2.04008			0.0698510			0.0349255	−	0.999390i	$-0.488881\pi$
$853$	2.04008			0.0698510			0.0349255	+	0.999390i	$0.488881\pi$
$854$		0			0
$855$	1.12883	+	7.89585i	0.0386053	+	0.270032i
$856$		0			0
$857$	9.53949	+	9.53949i	0.325863	+	0.325863i	0.851011	−	0.525148i	$-0.175990\pi$
$857$	9.53949	+	9.53949i	0.325863	+	0.325863i	−0.525148	+	0.851011i	$0.675990\pi$
$858$		0			0
$859$	−21.3343	−	21.3343i	−0.727917	−	0.727917i	0.242288	−	0.970204i	$-0.422102\pi$
$859$	−21.3343	−	21.3343i	−0.727917	−	0.727917i	−0.970204	+	0.242288i	$0.922102\pi$
$860$		0			0
$861$	10.7194	−	11.3994i	0.365315	−	0.388490i
$862$		0			0
$863$	12.4016			0.422156			0.211078	−	0.977469i	$-0.432303\pi$
$863$	12.4016			0.422156			0.211078	+	0.977469i	$0.432303\pi$
$864$		0			0
$865$	−7.03825	+	27.4842i	−0.239308	+	0.934492i
$866$		0			0
$867$	17.5419	−	7.26609i	0.595754	−	0.246770i
$868$		0			0
$869$	13.5831	+	13.5831i	0.460775	+	0.460775i
$870$		0			0
$871$	29.0356			0.983833
$872$		0			0
$873$	−1.63250	+	3.94120i	−0.0552518	+	0.133390i
$874$		0			0
$875$	22.1285	−	10.0419i	0.748081	−	0.339479i
$876$		0			0
$877$	19.3682	+	19.3682i	0.654017	+	0.654017i	0.953958	−	0.299941i	$-0.0969670\pi$
$877$	19.3682	+	19.3682i	0.654017	+	0.654017i	−0.299941	+	0.953958i	$0.596967\pi$
$878$		0			0
$879$			28.4841i			0.960745i
$880$		0			0
$881$	2.14389	+	2.14389i	0.0722294	+	0.0722294i	0.742299	−	0.670069i	$-0.233736\pi$
$881$	2.14389	+	2.14389i	0.0722294	+	0.0722294i	−0.670069	+	0.742299i	$0.733736\pi$
$882$		0			0
$883$	−25.2865	+	10.4740i	−0.850959	+	0.352479i	−0.765165	−	0.643834i	$-0.777343\pi$
$883$	−25.2865	+	10.4740i	−0.850959	+	0.352479i	−0.0857942	+	0.996313i	$0.527343\pi$
$884$		0			0
$885$	13.2948	−	17.7303i	0.446900	−	0.595999i
$886$		0			0
$887$	−3.00057	+	1.24288i	−0.100749	+	0.0417317i	−0.432489	−	0.901639i	$-0.642365\pi$
$887$	−3.00057	+	1.24288i	−0.100749	+	0.0417317i	0.331739	+	0.943371i	$0.392365\pi$
$888$		0			0
$889$	−12.1216	−	29.2640i	−0.406544	−	0.981483i
$890$		0			0
$891$	−0.809209	−	1.95360i	−0.0271095	−	0.0654481i
$892$		0			0
$893$	−6.61098			−0.221228
$894$		0			0
$895$	4.88400	−	6.51344i	0.163254	−	0.217720i
$896$		0			0
$897$			30.1824i			1.00776i
$898$		0			0
$899$	0.792549	+	1.91338i	0.0264330	+	0.0638149i
$900$		0			0
$901$			45.7440i			1.52395i
$902$		0			0
$903$	−2.04441	+	2.04441i	−0.0680337	+	0.0680337i
$904$		0			0
$905$	6.67618	−	8.90355i	0.221924	−	0.295964i
$906$		0			0
$907$	36.3930			1.20841			0.604205	−	0.796829i	$-0.293491\pi$
$907$	36.3930			1.20841			0.604205	+	0.796829i	$0.293491\pi$
$908$		0			0
$909$	5.00209	−	2.07193i	0.165909	−	0.0687217i
$910$		0			0
$911$	−32.8215	+	32.8215i	−1.08743	+	1.08743i	−0.0916328	+	0.995793i	$0.529209\pi$
$911$	−32.8215	+	32.8215i	−1.08743	+	1.08743i	−0.995793	+	0.0916328i	$0.970791\pi$
$912$		0			0
$913$	−5.21982	+	12.6018i	−0.172751	+	0.417058i
$914$		0			0
$915$	−0.597192	−	4.17717i	−0.0197426	−	0.138093i
$916$		0			0
$917$	12.2114	+	29.4810i	0.403256	+	0.973547i
$918$		0			0
$919$	−34.1045	−	14.1265i	−1.12500	−	0.465992i	−0.258924	−	0.965898i	$-0.583368\pi$
$919$	−34.1045	−	14.1265i	−1.12500	−	0.465992i	−0.866080	+	0.499906i	$0.833368\pi$
$920$		0			0
$921$	7.43366	−	17.9464i	0.244948	−	0.591356i
$922$		0			0
$923$			49.1833i			1.61889i
$924$		0			0
$925$	−11.8645	−	40.6461i	−0.390102	−	1.33643i
$926$		0			0
$927$	14.7690	−	14.7690i	0.485078	−	0.485078i
$928$		0			0
$929$	13.1581	−	31.7665i	0.431704	−	1.04222i	−0.547034	−	0.837110i	$-0.684243\pi$
$929$	13.1581	−	31.7665i	0.431704	−	1.04222i	0.978738	−	0.205115i	$-0.0657567\pi$
$930$		0			0
$931$	1.78973	+	4.32080i	0.0586562	+	0.141609i
$932$		0			0
$933$	−8.02081	−	8.02081i	−0.262590	−	0.262590i
$934$		0			0
$935$	30.3907	−	17.9989i	0.993881	−	0.588627i
$936$		0			0
$937$	−15.2024	−	36.7017i	−0.496639	−	1.19899i	−0.951283	−	0.308320i	$-0.900233\pi$
$937$	−15.2024	−	36.7017i	−0.496639	−	1.19899i	0.454643	−	0.890674i	$-0.349767\pi$
$938$		0			0
$939$		−	7.56027i		−	0.246720i
$940$		0			0
$941$	−1.59990	+	1.59990i	−0.0521552	+	0.0521552i	−0.732703	−	0.680548i	$-0.761742\pi$
$941$	−1.59990	+	1.59990i	−0.0521552	+	0.0521552i	0.680548	+	0.732703i	$0.261742\pi$
$942$		0			0
$943$	21.9867	+	20.6751i	0.715986	+	0.673275i
$944$		0			0
$945$	−25.0697	−	6.41993i	−0.815517	−	0.208840i
$946$		0			0
$947$	−19.3581	+	19.3581i	−0.629055	+	0.629055i	−0.947830	−	0.318775i	$-0.896728\pi$
$947$	−19.3581	+	19.3581i	−0.629055	+	0.629055i	0.318775	+	0.947830i	$0.396728\pi$
$948$		0			0
$949$	−39.4348	−	16.3344i	−1.28011	−	0.530238i
$950$		0			0
$951$	−27.6539	+	27.6539i	−0.896739	+	0.896739i
$952$		0			0
$953$	6.30344	−	6.30344i	0.204189	−	0.204189i	−0.597603	−	0.801792i	$-0.703880\pi$
$953$	6.30344	−	6.30344i	0.204189	−	0.204189i	0.801792	+	0.597603i	$0.203880\pi$
$954$		0			0
$955$	48.7613	+	36.5629i	1.57788	+	1.18315i
$956$		0			0
$957$	−9.38629	+	3.88793i	−0.303416	+	0.125679i
$958$		0			0
$959$		−	31.1691i		−	1.00650i
$960$		0			0
$961$	30.6132			0.987523
$962$		0			0
$963$	−19.6868			−0.634399
$964$		0			0
$965$	−24.1422	−	18.1026i	−0.777164	−	0.582744i
$966$		0			0
$967$	−23.2040	−	56.0195i	−0.746191	−	1.80147i	−0.578605	−	0.815608i	$-0.696403\pi$
$967$	−23.2040	−	56.0195i	−0.746191	−	1.80147i	−0.167587	−	0.985857i	$-0.553597\pi$
$968$		0			0
$969$	−12.4259	−	5.14699i	−0.399179	−	0.165345i
$970$		0			0
$971$	−13.8350	+	5.73065i	−0.443987	+	0.183905i	−0.593465	−	0.804860i	$-0.702241\pi$
$971$	−13.8350	+	5.73065i	−0.443987	+	0.183905i	0.149478	+	0.988765i	$0.452241\pi$
$972$		0			0
$973$	−41.0210	−	16.9915i	−1.31507	−	0.544722i
$974$		0			0
$975$	−8.97139	−	30.7348i	−0.287315	−	0.984300i
$976$		0			0
$977$	16.1182	+	6.67639i	0.515668	+	0.213597i	0.625313	−	0.780374i	$-0.284971\pi$
$977$	16.1182	+	6.67639i	0.515668	+	0.213597i	−0.109645	+	0.993971i	$0.534971\pi$
$978$		0			0
$979$	10.8789	−	10.8789i	0.347691	−	0.347691i
$980$		0			0
$981$	−5.70326	+	2.36237i	−0.182091	+	0.0754246i
$982$		0			0
$983$	25.4730	+	25.4730i	0.812464	+	0.812464i	0.985003	−	0.172539i	$-0.0551971\pi$
$983$	25.4730	+	25.4730i	0.812464	+	0.812464i	−0.172539	+	0.985003i	$0.555197\pi$
$984$		0			0
$985$	2.28165	−	8.90979i	0.0726993	−	0.283889i
$986$		0			0
$987$	3.00863	−	7.26348i	0.0957659	−	0.231199i
$988$		0			0
$989$	−3.94318	−	3.94318i	−0.125386	−	0.125386i
$990$		0			0
$991$	−3.86199	−	9.32368i	−0.122680	−	0.296176i	0.850594	−	0.525824i	$-0.176243\pi$
$991$	−3.86199	−	9.32368i	−0.122680	−	0.296176i	−0.973274	+	0.229647i	$0.926243\pi$
$992$		0			0
$993$		−	15.2886i		−	0.485169i
$994$		0			0
$995$	−20.1398	+	26.8590i	−0.638475	+	0.851489i
$996$		0			0
$997$	8.94394	−	21.5926i	0.283257	−	0.683844i	−0.716650	−	0.697433i	$-0.754326\pi$
$997$	8.94394	−	21.5926i	0.283257	−	0.683844i	0.999908	+	0.0135890i	$0.00432565\pi$
$998$		0			0
$999$	−17.2560	+	41.6598i	−0.545957	+	1.31806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.y.a.137.15	yes	84
5.3	odd	4		820.2.x.a.793.7	yes	84
41.3	odd	8		820.2.x.a.577.7	✓	84
205.3	even	8	inner	820.2.y.a.413.15	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.577.7	✓	84	41.3	odd	8
820.2.x.a.793.7	yes	84	5.3	odd	4
820.2.y.a.137.15	yes	84	1.1	even	1	trivial
820.2.y.a.413.15	yes	84	205.3	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.03876 + 0.430268i) q^{3} +(-2.16617 - 0.554719i) q^{5} +(-0.831762 + 2.00805i) q^{7} +(-1.22743 - 1.22743i) q^{9} +(2.50692 - 1.03840i) q^{11} +(-5.26176 - 2.17949i) q^{13} +(-2.01145 - 1.50825i) q^{15} +(-5.37817 + 2.22771i) q^{17} +(1.89850 + 0.786385i) q^{19} +(-1.72800 + 1.72800i) q^{21} +(-3.33290 - 3.33290i) q^{23} +(4.38457 + 2.40323i) q^{25} +(-2.03768 - 4.91941i) q^{27} +(-3.07658 + 1.27436i) q^{29} -0.621917i q^{31} +3.05088 q^{33} +(2.91564 - 3.88838i) q^{35} +(-5.98810 - 5.98810i) q^{37} +(-4.52794 - 4.52794i) q^{39} +(-6.40010 + 0.196764i) q^{41} +1.18311 q^{43} +(1.97794 + 3.33970i) q^{45} +(-2.97225 + 1.23115i) q^{47} +(1.60931 + 1.60931i) q^{49} -6.54513 q^{51} +(3.00715 - 7.25990i) q^{53} +(-6.00644 + 0.858714i) q^{55} +(1.63373 + 1.63373i) q^{57} +8.81470i q^{59} +(1.18680 + 1.18680i) q^{61} +(3.48567 - 1.44381i) q^{63} +(10.1889 + 7.63995i) q^{65} +(-4.71010 + 1.95099i) q^{67} +(-2.02804 - 4.89613i) q^{69} +(-3.30477 - 7.97843i) q^{71} +7.49459 q^{73} +(3.52048 + 4.38292i) q^{75} +5.89773i q^{77} +(2.70912 + 6.54039i) q^{79} -0.779283i q^{81} +(-3.55448 + 3.55448i) q^{83} +(12.8858 - 1.84222i) q^{85} -3.74415 q^{87} +(5.23829 - 2.16977i) q^{89} +(8.75307 - 8.75307i) q^{91} +(0.267591 - 0.646022i) q^{93} +(-3.67625 - 2.75658i) q^{95} +(-0.940462 - 2.27048i) q^{97} +(-4.35164 - 1.80251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 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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