LMFDB - Embedded newform 820.2.bq.a.49.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(49,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 10, 19])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bq (of order $20$, degree $8$, 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:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	820.49
Dual form			820.2.bq.a.569.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.10870 + 2.10870i) q^{3} +(2.22522 + 0.220000i) q^{5} +(0.00805431 - 0.0508529i) q^{7} -5.89321i q^{9} +(-5.62726 + 2.86723i) q^{11} +(3.05328 - 0.483592i) q^{13} +(-5.15623 + 4.22840i) q^{15} +(-6.63399 + 3.38019i) q^{17} +(0.631767 - 3.98882i) q^{19} +(0.0902493 + 0.124218i) q^{21} +(-2.59996 + 3.57853i) q^{23} +(4.90320 + 0.979095i) q^{25} +(6.10090 + 6.10090i) q^{27} +(-0.283661 + 0.556716i) q^{29} +(-1.37734 + 4.23901i) q^{31} +(5.82007 - 17.9123i) q^{33} +(0.0291102 - 0.111387i) q^{35} +(-2.16768 + 0.704323i) q^{37} +(-5.41869 + 7.45818i) q^{39} +(-6.09149 + 1.97327i) q^{41} +(-8.19297 - 5.95254i) q^{43} +(1.29650 - 13.1137i) q^{45} +(-1.23381 - 7.78997i) q^{47} +(6.65487 + 2.16230i) q^{49} +(6.86129 - 21.1169i) q^{51} +(-7.91252 - 4.03163i) q^{53} +(-13.1527 + 5.14223i) q^{55} +(7.07901 + 9.74342i) q^{57} +(2.96443 + 2.15378i) q^{59} +(-7.25056 - 9.97954i) q^{61} +(-0.299687 - 0.0474657i) q^{63} +(6.90060 - 0.404377i) q^{65} +(2.07903 - 4.08033i) q^{67} +(-2.06352 - 13.0286i) q^{69} +(-0.617012 + 0.314384i) q^{71} -1.63367 q^{73} +(-12.4040 + 8.27475i) q^{75} +(0.100484 + 0.309256i) q^{77} +(9.28790 + 9.28790i) q^{79} -8.05027 q^{81} -8.68291i q^{83} +(-15.5057 + 6.06218i) q^{85} +(-0.575791 - 1.77210i) q^{87} +(-2.87604 - 0.455520i) q^{89} -0.159163i q^{91} +(-6.03439 - 11.8432i) q^{93} +(2.28336 - 8.73701i) q^{95} +(-5.23384 + 10.2720i) q^{97} +(16.8972 + 33.1626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) $ 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.10870	+	2.10870i	−1.21746	+	1.21746i	−0.248937	+	0.968520i	$0.580081\pi$
$3$	−2.10870	+	2.10870i	−1.21746	+	1.21746i	−0.968520	+	0.248937i	$0.919919\pi$
$4$		0			0
$5$	2.22522	+	0.220000i	0.995148	+	0.0983868i
$5$	2.22522	+	0.220000i	0.995148	+	0.0983868i
$6$		0			0
$7$	0.00805431	−	0.0508529i	0.00304424	−	0.0192206i	−0.986119	−	0.166037i	$-0.946903\pi$
$7$	0.00805431	−	0.0508529i	0.00304424	−	0.0192206i	0.989164	+	0.146817i	$0.0469028\pi$
$8$		0			0
$9$		−	5.89321i		−	1.96440i
$10$		0			0
$11$	−5.62726	+	2.86723i	−1.69668	+	0.864504i	−0.709541	+	0.704664i	$0.751098\pi$
$11$	−5.62726	+	2.86723i	−1.69668	+	0.864504i	−0.987143	+	0.159840i	$0.948902\pi$
$12$		0			0
$13$	3.05328	−	0.483592i	0.846827	−	0.134124i	0.282082	−	0.959390i	$-0.408975\pi$
$13$	3.05328	−	0.483592i	0.846827	−	0.134124i	0.564744	+	0.825266i	$0.308975\pi$
$14$		0			0
$15$	−5.15623	+	4.22840i	−1.33133	+	1.09177i
$16$		0			0
$17$	−6.63399	+	3.38019i	−1.60898	+	0.819816i	−0.609341	+	0.792908i	$0.708566\pi$
$17$	−6.63399	+	3.38019i	−1.60898	+	0.819816i	−0.999638	+	0.0269079i	$0.991434\pi$
$18$		0			0
$19$	0.631767	−	3.98882i	0.144937	−	0.915098i	−0.802847	−	0.596185i	$-0.796682\pi$
$19$	0.631767	−	3.98882i	0.144937	−	0.915098i	0.947784	−	0.318913i	$-0.103318\pi$
$20$		0			0
$21$	0.0902493	+	0.124218i	0.0196940	+	0.0271065i
$22$		0			0
$23$	−2.59996	+	3.57853i	−0.542129	+	0.746176i	−0.988918	−	0.148463i	$-0.952567\pi$
$23$	−2.59996	+	3.57853i	−0.542129	+	0.746176i	0.446789	+	0.894639i	$0.352567\pi$
$24$		0			0
$25$	4.90320	+	0.979095i	0.980640	+	0.195819i
$26$		0			0
$27$	6.10090	+	6.10090i	1.17412	+	1.17412i
$28$		0			0
$29$	−0.283661	+	0.556716i	−0.0526745	+	0.103380i	−0.915843	−	0.401536i	$-0.868476\pi$
$29$	−0.283661	+	0.556716i	−0.0526745	+	0.103380i	0.863169	+	0.504916i	$0.168476\pi$
$30$		0			0
$31$	−1.37734	+	4.23901i	−0.247377	+	0.761348i	0.747860	+	0.663857i	$0.231082\pi$
$31$	−1.37734	+	4.23901i	−0.247377	+	0.761348i	−0.995236	+	0.0974908i	$0.968918\pi$
$32$		0			0
$33$	5.82007	−	17.9123i	1.01314	−	3.11814i
$34$		0			0
$35$	0.0291102	−	0.111387i	0.00492053	−	0.0188278i
$36$		0			0
$37$	−2.16768	+	0.704323i	−0.356365	+	0.115790i	−0.481728	−	0.876321i	$-0.659991\pi$
$37$	−2.16768	+	0.704323i	−0.356365	+	0.115790i	0.125363	+	0.992111i	$0.459991\pi$
$38$		0			0
$39$	−5.41869	+	7.45818i	−0.867685	+	1.19427i
$40$		0			0
$41$	−6.09149	+	1.97327i	−0.951331	+	0.308172i
$41$	−6.09149	+	1.97327i	−0.951331	+	0.308172i
$42$		0			0
$43$	−8.19297	−	5.95254i	−1.24942	−	0.907754i	−0.251229	−	0.967928i	$-0.580835\pi$
$43$	−8.19297	−	5.95254i	−1.24942	−	0.907754i	−0.998188	+	0.0601734i	$0.980835\pi$
$44$		0			0
$45$	1.29650	−	13.1137i	0.193271	−	1.95487i
$46$		0			0
$47$	−1.23381	−	7.78997i	−0.179970	−	1.13628i	−0.897910	−	0.440179i	$-0.854915\pi$
$47$	−1.23381	−	7.78997i	−0.179970	−	1.13628i	0.717940	−	0.696104i	$-0.245085\pi$
$48$		0			0
$49$	6.65487	+	2.16230i	0.950696	+	0.308900i
$50$		0			0
$51$	6.86129	−	21.1169i	0.960772	−	2.95695i
$52$		0			0
$53$	−7.91252	−	4.03163i	−1.08687	−	0.553787i	−0.183660	−	0.982990i	$-0.558795\pi$
$53$	−7.91252	−	4.03163i	−1.08687	−	0.553787i	−0.903208	+	0.429203i	$0.858795\pi$
$54$		0			0
$55$	−13.1527	+	5.14223i	−1.77351	+	0.693378i
$56$		0			0
$57$	7.07901	+	9.74342i	0.937638	+	1.29055i
$58$		0			0
$59$	2.96443	+	2.15378i	0.385935	+	0.280398i	0.763788	−	0.645467i	$-0.223337\pi$
$59$	2.96443	+	2.15378i	0.385935	+	0.280398i	−0.377852	+	0.925866i	$0.623337\pi$
$60$		0			0
$61$	−7.25056	−	9.97954i	−0.928339	−	1.27775i	−0.960504	−	0.278266i	$-0.910240\pi$
$61$	−7.25056	−	9.97954i	−0.928339	−	1.27775i	0.0321649	−	0.999483i	$-0.489760\pi$
$62$		0			0
$63$	−0.299687	−	0.0474657i	−0.0377570	−	0.00598012i
$64$		0			0
$65$	6.90060	−	0.404377i	0.855914	−	0.0501568i
$66$		0			0
$67$	2.07903	−	4.08033i	0.253994	−	0.498492i	−0.728438	−	0.685112i	$-0.759753\pi$
$67$	2.07903	−	4.08033i	0.253994	−	0.498492i	0.982432	+	0.186620i	$0.0597533\pi$
$68$		0			0
$69$	−2.06352	−	13.0286i	−0.248419	−	1.56846i
$70$		0			0
$71$	−0.617012	+	0.314384i	−0.0732259	+	0.0373105i	−0.490220	−	0.871599i	$-0.663084\pi$
$71$	−0.617012	+	0.314384i	−0.0732259	+	0.0373105i	0.416994	+	0.908909i	$0.363084\pi$
$72$		0			0
$73$	−1.63367			−0.191206			−0.0956030	−	0.995420i	$-0.530478\pi$
$73$	−1.63367			−0.191206			−0.0956030	+	0.995420i	$0.530478\pi$
$74$		0			0
$75$	−12.4040	+	8.27475i	−1.43229	+	0.955486i
$76$		0			0
$77$	0.100484	+	0.309256i	0.0114512	+	0.0352430i
$78$		0			0
$79$	9.28790	+	9.28790i	1.04497	+	1.04497i	0.998940	+	0.0460302i	$0.0146570\pi$
$79$	9.28790	+	9.28790i	1.04497	+	1.04497i	0.0460302	+	0.998940i	$0.485343\pi$
$80$		0			0
$81$	−8.05027			−0.894474
$82$		0			0
$83$		−	8.68291i		−	0.953073i	−0.879155	−	0.476537i	$-0.841892\pi$
$83$		−	8.68291i		−	0.953073i	0.879155	−	0.476537i	$-0.158108\pi$
$84$		0			0
$85$	−15.5057	+	6.06218i	−1.68183	+	0.657536i
$86$		0			0
$87$	−0.575791	−	1.77210i	−0.0617312	−	0.189989i
$88$		0			0
$89$	−2.87604	−	0.455520i	−0.304860	−	0.0482851i	0.00213029	−	0.999998i	$-0.499322\pi$
$89$	−2.87604	−	0.455520i	−0.304860	−	0.0482851i	−0.306990	+	0.951713i	$0.599322\pi$
$90$		0			0
$91$		−	0.159163i		−	0.0166848i
$92$		0			0
$93$	−6.03439	−	11.8432i	−0.625737	−	1.22808i
$94$		0			0
$95$	2.28336	−	8.73701i	0.234268	−	0.896399i
$96$		0			0
$97$	−5.23384	+	10.2720i	−0.531416	+	1.04296i	0.456753	+	0.889594i	$0.349012\pi$
$97$	−5.23384	+	10.2720i	−0.531416	+	1.04296i	−0.988169	+	0.153369i	$0.950988\pi$
$98$		0			0
$99$	16.8972	+	33.1626i	1.69823	+	3.33297i
$100$		0			0
$101$	−1.94664	+	12.2906i	−0.193698	+	1.22296i	0.678793	+	0.734330i	$0.262504\pi$
$101$	−1.94664	+	12.2906i	−0.193698	+	1.22296i	−0.872491	+	0.488631i	$0.837496\pi$
$102$		0			0
$103$	−1.11678	+	0.811387i	−0.110039	+	0.0799483i	−0.641444	−	0.767170i	$-0.721664\pi$
$103$	−1.11678	+	0.811387i	−0.110039	+	0.0799483i	0.531405	+	0.847118i	$0.321664\pi$
$104$		0			0
$105$	0.173497	+	0.296266i	0.0169315	+	0.0289126i
$106$		0			0
$107$	6.82901	+	9.39932i	0.660185	+	0.908667i	0.999488	−	0.0320107i	$-0.0101911\pi$
$107$	6.82901	+	9.39932i	0.660185	+	0.908667i	−0.339303	+	0.940677i	$0.610191\pi$
$108$		0			0
$109$	−11.4794	+	11.4794i	−1.09953	+	1.09953i	−0.105067	+	0.994465i	$0.533506\pi$
$109$	−11.4794	+	11.4794i	−1.09953	+	1.09953i	−0.994465	+	0.105067i	$0.966494\pi$
$110$		0			0
$111$	3.08578	−	6.05619i	0.292890	−	0.574828i
$112$		0			0
$113$	12.6324	+	4.10451i	1.18835	+	0.386120i	0.835464	−	0.549545i	$-0.185199\pi$
$113$	12.6324	+	4.10451i	1.18835	+	0.386120i	0.352891	+	0.935665i	$0.385199\pi$
$114$		0			0
$115$	−6.57275	+	7.39103i	−0.612912	+	0.689217i
$116$		0			0
$117$	−2.84991	−	17.9936i	−0.263474	−	1.66351i
$118$		0			0
$119$	0.118460	+	0.364583i	0.0108592	+	0.0334213i
$120$		0			0
$121$	16.9794	−	23.3702i	1.54359	−	2.12456i
$122$		0			0
$123$	8.68408	−	17.0061i	0.783017	−	1.53339i
$124$		0			0
$125$	10.6953	+	3.25740i	0.956616	+	0.291351i
$126$		0			0
$127$	2.10690	−	0.684572i	0.186957	−	0.0607459i	−0.214042	−	0.976824i	$-0.568663\pi$
$127$	2.10690	−	0.684572i	0.186957	−	0.0607459i	0.400999	+	0.916078i	$0.368663\pi$
$128$		0			0
$129$	29.8286	−	4.72439i	2.62626	−	0.415959i
$130$		0			0
$131$	0.771163	+	0.250566i	0.0673768	+	0.0218921i	0.342511	−	0.939514i	$-0.388722\pi$
$131$	0.771163	+	0.250566i	0.0673768	+	0.0218921i	−0.275135	+	0.961406i	$0.588722\pi$
$132$		0			0
$133$	−0.197755	−	0.0642544i	−0.0171475	−	0.00557156i
$134$		0			0
$135$	12.2336	+	14.9180i	1.05290	+	1.28394i
$136$		0			0
$137$	−1.25227	−	1.25227i	−0.106989	−	0.106989i	0.651586	−	0.758575i	$-0.274104\pi$
$137$	−1.25227	−	1.25227i	−0.106989	−	0.106989i	−0.758575	+	0.651586i	$0.774104\pi$
$138$		0			0
$139$	−4.13279	+	3.00265i	−0.350539	+	0.254682i	−0.749095	−	0.662462i	$-0.769511\pi$
$139$	−4.13279	+	3.00265i	−0.350539	+	0.254682i	0.398556	+	0.917144i	$0.369511\pi$
$140$		0			0
$141$	19.0284	+	13.8249i	1.60248	+	1.16427i
$142$		0			0
$143$	−15.7950	+	11.4758i	−1.32085	+	0.959651i
$144$		0			0
$145$	−0.753685	+	1.17641i	−0.0625902	+	0.0976955i
$146$		0			0
$147$	−18.5928	+	9.47348i	−1.53350	+	0.781359i
$148$		0			0
$149$	10.5477	+	5.37435i	0.864105	+	0.440284i	0.829098	−	0.559103i	$-0.188855\pi$
$149$	10.5477	+	5.37435i	0.864105	+	0.440284i	0.0350073	+	0.999387i	$0.488855\pi$
$150$		0			0
$151$	1.73463	+	10.9520i	0.141162	+	0.891261i	0.952024	+	0.306024i	$0.0989986\pi$
$151$	1.73463	+	10.9520i	0.141162	+	0.891261i	−0.810862	+	0.585237i	$0.801001\pi$
$152$		0			0
$153$	19.9201	+	39.0955i	1.61045	+	3.16068i
$154$		0			0
$155$	−3.99746	+	9.12970i	−0.321083	+	0.733315i
$156$		0			0
$157$	−1.55054	+	9.78969i	−0.123746	+	0.781303i	0.845276	+	0.534330i	$0.179436\pi$
$157$	−1.55054	+	9.78969i	−0.123746	+	0.781303i	−0.969022	+	0.246973i	$0.920564\pi$
$158$		0			0
$159$	25.1866	−	8.18362i	1.99743	−	0.649004i
$160$		0			0
$161$	0.161038	+	0.161038i	0.0126916	+	0.0126916i
$162$		0			0
$163$			9.29229i			0.727829i	0.931432	+	0.363914i	$0.118560\pi$
$163$			9.29229i			0.727829i	−0.931432	+	0.363914i	$0.881440\pi$
$164$		0			0
$165$	16.8916	−	38.5784i	1.31501	−	3.00333i
$166$		0			0
$167$	−1.54377	+	1.54377i	−0.119460	+	0.119460i	−0.764310	−	0.644849i	$-0.776920\pi$
$167$	−1.54377	+	1.54377i	−0.119460	+	0.119460i	0.644849	+	0.764310i	$0.276920\pi$
$168$		0			0
$169$	−3.27510	+	1.06414i	−0.251930	+	0.0818572i
$170$		0			0
$171$	−23.5069	−	3.72313i	−1.79762	−	0.284715i
$172$		0			0
$173$	−14.5470			−1.10599			−0.552993	−	0.833186i	$-0.686515\pi$
$173$	−14.5470			−1.10599			−0.552993	+	0.833186i	$0.686515\pi$
$174$		0			0
$175$	0.0892817	−	0.241456i	0.00674906	−	0.0182524i
$176$		0			0
$177$	−10.7927	+	1.70940i	−0.811233	+	0.128487i
$178$		0			0
$179$	−13.9986	−	7.13264i	−1.04630	−	0.533118i	−0.155655	−	0.987811i	$-0.549749\pi$
$179$	−13.9986	−	7.13264i	−1.04630	−	0.533118i	−0.890648	+	0.454693i	$0.849749\pi$
$180$		0			0
$181$	3.73206	+	7.32458i	0.277402	+	0.544432i	0.987106	−	0.160068i	$-0.0511713\pi$
$181$	3.73206	+	7.32458i	0.277402	+	0.544432i	−0.709704	+	0.704500i	$0.751171\pi$
$182$		0			0
$183$	36.3331	+	5.75459i	2.68582	+	0.425392i
$184$		0			0
$185$	−4.97852	+	1.09038i	−0.366028	+	0.0801666i
$186$		0			0
$187$	27.6394	−	38.0424i	2.02120	−	2.78194i
$188$		0			0
$189$	0.359387	−	0.261110i	0.0261416	−	0.0189930i
$190$		0			0
$191$	−14.4951	+	14.4951i	−1.04883	+	1.04883i	−0.0500871	+	0.998745i	$0.515950\pi$
$191$	−14.4951	+	14.4951i	−1.04883	+	1.04883i	−0.998745	+	0.0500871i	$0.984050\pi$
$192$		0			0
$193$	−4.35034	−	2.21661i	−0.313144	−	0.159555i	0.290354	−	0.956919i	$-0.406227\pi$
$193$	−4.35034	−	2.21661i	−0.313144	−	0.159555i	−0.603498	+	0.797364i	$0.706227\pi$
$194$		0			0
$195$	−13.6986	+	15.4040i	−0.980975	+	1.10310i
$196$		0			0
$197$	5.57469	−	17.1571i	0.397181	−	1.22240i	−0.530070	−	0.847954i	$-0.677834\pi$
$197$	5.57469	−	17.1571i	0.397181	−	1.22240i	0.927250	−	0.374442i	$-0.122166\pi$
$198$		0			0
$199$	2.21552	−	0.350904i	0.157054	−	0.0248749i	−0.0774123	−	0.996999i	$-0.524666\pi$
$199$	2.21552	−	0.350904i	0.157054	−	0.0248749i	0.234466	+	0.972124i	$0.424666\pi$
$200$		0			0
$201$	4.22013	+	12.9882i	0.297665	+	0.916120i
$202$		0			0
$203$	0.0260259	+	0.0189090i	0.00182666	+	0.00132715i
$204$		0			0
$205$	−13.9890	+	3.05082i	−0.977035	+	0.213079i
$206$		0			0
$207$	21.0890	+	15.3221i	1.46579	+	1.06496i
$208$		0			0
$209$	7.88176	+	24.2576i	0.545193	+	1.67793i
$210$		0			0
$211$	9.38792	−	1.48690i	0.646291	−	0.102362i	0.175321	−	0.984511i	$-0.443904\pi$
$211$	9.38792	−	1.48690i	0.646291	−	0.102362i	0.470971	+	0.882149i	$0.343904\pi$
$212$		0			0
$213$	0.638153	−	1.96403i	0.0437255	−	0.134573i
$214$		0			0
$215$	−16.9216	−	15.0482i	−1.15404	−	1.02628i
$216$		0			0
$217$	0.204472	+	0.104184i	0.0138805	+	0.00707246i
$218$		0			0
$219$	3.44491	−	3.44491i	0.232785	−	0.232785i
$220$		0			0
$221$	−18.6208	+	13.5288i	−1.25257	+	0.910045i
$222$		0			0
$223$	−7.88686	+	10.8553i	−0.528143	+	0.726927i	−0.986846	−	0.161663i	$-0.948314\pi$
$223$	−7.88686	+	10.8553i	−0.528143	+	0.726927i	0.458703	+	0.888590i	$0.348314\pi$
$224$		0			0
$225$	5.77001	−	28.8956i	0.384667	−	1.92637i
$226$		0			0
$227$	26.1741	+	4.14557i	1.73724	+	0.275151i	0.943081	−	0.332564i	$-0.107914\pi$
$227$	26.1741	+	4.14557i	1.73724	+	0.275151i	0.794155	+	0.607715i	$0.207914\pi$
$228$		0			0
$229$	−4.47326	−	8.77926i	−0.295601	−	0.580150i	0.694665	−	0.719333i	$-0.255552\pi$
$229$	−4.47326	−	8.77926i	−0.295601	−	0.580150i	−0.990267	+	0.139183i	$0.955552\pi$
$230$		0			0
$231$	−0.864017	−	0.440239i	−0.0568482	−	0.0289656i
$232$		0			0
$233$	−21.3278	+	3.37800i	−1.39723	+	0.221300i	−0.809198	−	0.587536i	$-0.800098\pi$
$233$	−21.3278	+	3.37800i	−1.39723	+	0.221300i	−0.588035	+	0.808836i	$0.700098\pi$
$234$		0			0
$235$	−1.03171	−	17.6058i	−0.0673011	−	1.14848i
$236$		0			0
$237$	−39.1707			−2.54441
$238$		0			0
$239$	−1.82523	−	0.289088i	−0.118064	−	0.0186995i	0.0971227	−	0.995272i	$-0.469036\pi$
$239$	−1.82523	−	0.289088i	−0.118064	−	0.0186995i	−0.215187	+	0.976573i	$0.569036\pi$
$240$		0			0
$241$	13.9719	−	4.53973i	0.900006	−	0.292430i	0.177767	−	0.984073i	$-0.443113\pi$
$241$	13.9719	−	4.53973i	0.900006	−	0.292430i	0.722240	+	0.691643i	$0.243113\pi$
$242$		0			0
$243$	−1.32711	+	1.32711i	−0.0851344	+	0.0851344i
$244$		0			0
$245$	14.3328	+	6.27566i	0.915692	+	0.400937i
$246$		0			0
$247$		−	12.4845i		−	0.794369i
$248$		0			0
$249$	18.3096	+	18.3096i	1.16033	+	1.16033i
$250$		0			0
$251$	−12.1552	+	3.94947i	−0.767231	+	0.249288i	−0.666379	−	0.745613i	$-0.732157\pi$
$251$	−12.1552	+	3.94947i	−0.767231	+	0.249288i	−0.100852	+	0.994901i	$0.532157\pi$
$252$		0			0
$253$	4.37015	−	27.5920i	0.274749	−	1.73470i
$254$		0			0
$255$	19.9136	−	45.4802i	1.24704	−	2.84808i
$256$		0			0
$257$	12.0630	+	23.6749i	0.752469	+	1.47680i	0.874888	+	0.484324i	$0.160935\pi$
$257$	12.0630	+	23.6749i	0.752469	+	1.47680i	−0.122420	+	0.992478i	$0.539065\pi$
$258$		0			0
$259$	0.0183577	+	0.115906i	0.00114069	+	0.00720204i
$260$		0			0
$261$	3.28084	+	1.67167i	0.203079	+	0.103474i
$262$		0			0
$263$	17.1319	−	8.72915i	1.05640	−	0.538262i	0.162583	−	0.986695i	$-0.448018\pi$
$263$	17.1319	−	8.72915i	1.05640	−	0.538262i	0.893817	+	0.448433i	$0.148018\pi$
$264$		0			0
$265$	−16.7201	−	10.7120i	−1.02711	−	0.658034i
$266$		0			0
$267$	7.02526	−	5.10415i	0.429939	−	0.312369i
$268$		0			0
$269$	−18.1872	−	13.2138i	−1.10889	−	0.805658i	−0.126405	−	0.991979i	$-0.540344\pi$
$269$	−18.1872	−	13.2138i	−1.10889	−	0.805658i	−0.982489	+	0.186320i	$0.940344\pi$
$270$		0			0
$271$	6.90176	−	5.01442i	0.419252	−	0.304604i	−0.358085	−	0.933689i	$-0.616570\pi$
$271$	6.90176	−	5.01442i	0.419252	−	0.304604i	0.777337	+	0.629085i	$0.216570\pi$
$272$		0			0
$273$	0.335627	+	0.335627i	0.0203130	+	0.0203130i
$274$		0			0
$275$	−30.3989	+	8.54900i	−1.83312	+	0.515524i
$276$		0			0
$277$	−5.72931	−	1.86157i	−0.344241	−	0.111851i	0.131794	−	0.991277i	$-0.457926\pi$
$277$	−5.72931	−	1.86157i	−0.344241	−	0.111851i	−0.476035	+	0.879426i	$0.657926\pi$
$278$		0			0
$279$	24.9813	+	8.11693i	1.49559	+	0.485948i
$280$		0			0
$281$	−26.4784	+	4.19376i	−1.57957	+	0.250179i	−0.883722	−	0.468013i	$-0.844970\pi$
$281$	−26.4784	+	4.19376i	−1.57957	+	0.250179i	−0.695845	+	0.718192i	$0.744970\pi$
$282$		0			0
$283$	7.41877	−	2.41051i	0.441000	−	0.143290i	−0.0800968	−	0.996787i	$-0.525523\pi$
$283$	7.41877	−	2.41051i	0.441000	−	0.143290i	0.521097	+	0.853497i	$0.325523\pi$
$284$		0			0
$285$	13.6088	+	23.2386i	0.806116	+	1.37654i
$286$		0			0
$287$	0.0512836	+	0.325663i	0.00302718	+	0.0192233i
$288$		0			0
$289$	22.5918	−	31.0950i	1.32893	−	1.82912i
$290$		0			0
$291$	−10.6239	−	32.6971i	−0.622786	−	1.91674i
$292$		0			0
$293$	0.00246306	+	0.0155512i	0.000143894	+	0.000908509i	0.987760	−	0.155980i	$-0.0498536\pi$
$293$	0.00246306	+	0.0155512i	0.000143894	+	0.000908509i	−0.987616	+	0.156889i	$0.949854\pi$
$294$		0			0
$295$	6.12267	+	5.44481i	0.356475	+	0.317009i
$296$		0			0
$297$	−51.8241	−	16.8387i	−3.00714	−	0.977078i
$298$		0			0
$299$	−6.20784	+	12.1836i	−0.359009	+	0.704594i
$300$		0			0
$301$	−0.368693	+	0.368693i	−0.0212511	+	0.0212511i
$302$		0			0
$303$	−21.8123	−	30.0220i	−1.25308	−	1.72472i
$304$		0			0
$305$	−13.9386	−	23.8018i	−0.798121	−	1.36289i
$306$		0			0
$307$	2.07917	−	1.51061i	0.118665	−	0.0862149i	−0.526870	−	0.849946i	$-0.676635\pi$
$307$	2.07917	−	1.51061i	0.118665	−	0.0862149i	0.645535	+	0.763731i	$0.276635\pi$
$308$		0			0
$309$	0.643978	−	4.06592i	0.0366346	−	0.231302i
$310$		0			0
$311$	11.2746	+	22.1276i	0.639322	+	1.25474i	0.952353	+	0.304997i	$0.0986554\pi$
$311$	11.2746	+	22.1276i	0.639322	+	1.25474i	−0.313032	+	0.949743i	$0.601345\pi$
$312$		0			0
$313$	−11.1982	+	21.9777i	−0.632961	+	1.24226i	0.322341	+	0.946624i	$0.395530\pi$
$313$	−11.1982	+	21.9777i	−0.632961	+	1.24226i	−0.955302	+	0.295632i	$0.904470\pi$
$314$		0			0
$315$	−0.656426	−	0.171553i	−0.0369854	−	0.00966590i
$316$		0			0
$317$	0.902336	+	1.77093i	0.0506802	+	0.0994655i	0.914958	−	0.403550i	$-0.132224\pi$
$317$	0.902336	+	1.77093i	0.0506802	+	0.0994655i	−0.864277	+	0.503016i	$0.832224\pi$
$318$		0			0
$319$		−	3.94611i		−	0.220940i
$320$		0			0
$321$	−34.2206	−	5.42001i	−1.91001	−	0.302516i
$322$		0			0
$323$	9.29182	+	28.5973i	0.517011	+	1.59120i
$324$		0			0
$325$	15.4443	+	0.618301i	0.856696	+	0.0342972i
$326$		0			0
$327$		−	48.4134i		−	2.67726i
$328$		0			0
$329$	−0.406080			−0.0223879
$330$		0			0
$331$	−3.55291	−	3.55291i	−0.195286	−	0.195286i	0.602690	−	0.797976i	$-0.294096\pi$
$331$	−3.55291	−	3.55291i	−0.195286	−	0.195286i	−0.797976	+	0.602690i	$0.794096\pi$
$332$		0			0
$333$	4.15072	+	12.7746i	0.227458	+	0.700044i
$334$		0			0
$335$	5.52398	−	8.62225i	0.301807	−	0.471084i
$336$		0			0
$337$	13.8510			0.754513			0.377257	−	0.926109i	$-0.376867\pi$
$337$	13.8510			0.754513			0.377257	+	0.926109i	$0.376867\pi$
$338$		0			0
$339$	−35.2930	+	17.9827i	−1.91686	+	0.976687i
$340$		0			0
$341$	−4.40359	−	27.8032i	−0.238468	−	1.50563i
$342$		0			0
$343$	0.327181	−	0.642130i	0.0176661	−	0.0346717i
$344$		0			0
$345$	−1.72551	−	29.4454i	−0.0928983	−	1.58529i
$346$		0			0
$347$	16.2530	+	2.57422i	0.872505	+	0.138191i	0.576600	−	0.817026i	$-0.304379\pi$
$347$	16.2530	+	2.57422i	0.872505	+	0.138191i	0.295905	+	0.955218i	$0.404379\pi$
$348$		0			0
$349$	14.9832	+	20.6226i	0.802032	+	1.10390i	0.992504	+	0.122209i	$0.0389979\pi$
$349$	14.9832	+	20.6226i	0.802032	+	1.10390i	−0.190473	+	0.981692i	$0.561002\pi$
$350$		0			0
$351$	21.5781	+	15.6774i	1.15175	+	0.836797i
$352$		0			0
$353$	18.8121	+	25.8926i	1.00127	+	1.37813i	0.924545	+	0.381074i	$0.124446\pi$
$353$	18.8121	+	25.8926i	1.00127	+	1.37813i	0.0767228	+	0.997052i	$0.475554\pi$
$354$		0			0
$355$	−1.44215	+	0.563830i	−0.0765415	+	0.0299250i
$356$		0			0
$357$	−1.01859	−	0.518998i	−0.0539096	−	0.0274683i
$358$		0			0
$359$	−2.33890	+	7.19839i	−0.123442	+	0.379917i	−0.993614	−	0.112832i	$-0.964008\pi$
$359$	−2.33890	+	7.19839i	−0.123442	+	0.379917i	0.870172	+	0.492749i	$0.164008\pi$
$360$		0			0
$361$	2.55851	+	0.831311i	0.134659	+	0.0437532i
$362$		0			0
$363$	13.4762	+	85.0851i	0.707315	+	4.46581i
$364$		0			0
$365$	−3.63526	−	0.359406i	−0.190278	−	0.0188122i
$366$		0			0
$367$	1.41570	+	1.02857i	0.0738990	+	0.0536907i	0.624121	−	0.781327i	$-0.285457\pi$
$367$	1.41570	+	1.02857i	0.0738990	+	0.0536907i	−0.550222	+	0.835018i	$0.685457\pi$
$368$		0			0
$369$	11.6289	+	35.8984i	0.605375	+	1.86880i
$370$		0			0
$371$	−0.268750	+	0.369903i	−0.0139528	+	0.0192044i
$372$		0			0
$373$	−0.939532	+	0.305273i	−0.0486471	+	0.0158064i	−0.333239	−	0.942842i	$-0.608142\pi$
$373$	−0.939532	+	0.305273i	−0.0486471	+	0.0158064i	0.284592	+	0.958649i	$0.408142\pi$
$374$		0			0
$375$	−29.4220	+	15.6843i	−1.51935	+	0.809932i
$376$		0			0
$377$	−0.596873	+	1.83698i	−0.0307405	+	0.0946095i
$378$		0			0
$379$	0.135167	−	0.416002i	0.00694307	−	0.0213686i	−0.947525	−	0.319682i	$-0.896424\pi$
$379$	0.135167	−	0.416002i	0.00694307	−	0.0213686i	0.954468	+	0.298313i	$0.0964240\pi$
$380$		0			0
$381$	−2.99925	+	5.88636i	−0.153656	+	0.301567i
$382$		0			0
$383$	13.2357	+	13.2357i	0.676313	+	0.676313i	0.959164	−	0.282851i	$-0.0912802\pi$
$383$	13.2357	+	13.2357i	0.676313	+	0.676313i	−0.282851	+	0.959164i	$0.591280\pi$
$384$		0			0
$385$	0.155562	+	0.710270i	0.00792815	+	0.0361987i
$386$		0			0
$387$	−35.0796	+	48.2829i	−1.78319	+	2.45436i
$388$		0			0
$389$	13.5531	+	18.6542i	0.687169	+	0.945807i	0.999992	−	0.00400462i	$-0.00127471\pi$
$389$	13.5531	+	18.6542i	0.687169	+	0.945807i	−0.312823	+	0.949811i	$0.601275\pi$
$390$		0			0
$391$	5.15198	−	32.5283i	0.260547	−	1.64503i
$392$		0			0
$393$	−2.15452	+	1.09778i	−0.108681	+	0.0553757i
$394$		0			0
$395$	18.6243	+	22.7109i	0.937089	+	1.14271i
$396$		0			0
$397$	1.15916	−	0.183594i	0.0581768	−	0.00921430i	−0.127278	−	0.991867i	$-0.540624\pi$
$397$	1.15916	−	0.183594i	0.0581768	−	0.00921430i	0.185455	+	0.982653i	$0.440624\pi$
$398$		0			0
$399$	0.552498	−	0.281512i	0.0276595	−	0.0140932i
$400$		0			0
$401$		−	0.578760i		−	0.0289019i	−0.999896	−	0.0144509i	$-0.995400\pi$
$401$		−	0.578760i		−	0.0289019i	0.999896	−	0.0144509i	$-0.00460004\pi$
$402$		0			0
$403$	−2.15544	+	13.6089i	−0.107370	+	0.677909i
$404$		0			0
$405$	−17.9136	−	1.77106i	−0.890135	−	0.0880045i
$406$		0			0
$407$	10.1787	−	10.1787i	0.504538	−	0.504538i
$408$		0			0
$409$	−3.24161			−0.160287			−0.0801436	−	0.996783i	$-0.525538\pi$
$409$	−3.24161			−0.160287			−0.0801436	+	0.996783i	$0.525538\pi$
$410$		0			0
$411$	5.28133			0.260509
$412$		0			0
$413$	0.133402	−	0.133402i	0.00656431	−	0.00656431i
$414$		0			0
$415$	1.91024	−	19.3214i	0.0937699	−	0.948449i
$416$		0			0
$417$	2.38313	−	15.0465i	0.116702	−	0.736830i
$418$		0			0
$419$		−	4.77016i		−	0.233038i	−0.993188	−	0.116519i	$-0.962826\pi$
$419$		−	4.77016i		−	0.233038i	0.993188	−	0.116519i	$-0.0371736\pi$
$420$		0			0
$421$	30.9021	−	15.7454i	1.50608	−	0.767385i	0.510372	−	0.859954i	$-0.329508\pi$
$421$	30.9021	−	15.7454i	1.50608	−	0.767385i	0.995706	+	0.0925683i	$0.0295077\pi$
$422$		0			0
$423$	−45.9079	+	7.27109i	−2.23212	+	0.353533i
$424$		0			0
$425$	−35.8373	+	10.0784i	−1.73837	+	0.488876i
$426$		0			0
$427$	−0.565887	+	0.288334i	−0.0273852	+	0.0139535i
$428$		0			0
$429$	9.10803	−	57.5058i	0.439740	−	2.77641i
$430$		0			0
$431$	−8.68513	−	11.9541i	−0.418348	−	0.575806i	0.546882	−	0.837210i	$-0.315815\pi$
$431$	−8.68513	−	11.9541i	−0.418348	−	0.575806i	−0.965230	+	0.261403i	$0.915815\pi$
$432$		0			0
$433$	−1.07310	+	1.47700i	−0.0515701	+	0.0709801i	−0.834023	−	0.551729i	$-0.813968\pi$
$433$	−1.07310	+	1.47700i	−0.0515701	+	0.0709801i	0.782453	+	0.622709i	$0.213968\pi$
$434$		0			0
$435$	−0.891398	−	4.06999i	−0.0427393	−	0.195141i
$436$		0			0
$437$	12.6316	+	12.6316i	0.604250	+	0.604250i
$438$		0			0
$439$	0.455977	−	0.894904i	0.0217626	−	0.0427115i	−0.879869	−	0.475216i	$-0.842370\pi$
$439$	0.455977	−	0.894904i	0.0217626	−	0.0427115i	0.901632	+	0.432504i	$0.142370\pi$
$440$		0			0
$441$	12.7429	−	39.2186i	0.606804	−	1.86755i
$442$		0			0
$443$	6.43525	−	19.8056i	0.305748	−	0.940995i	−0.673649	−	0.739051i	$-0.735274\pi$
$443$	6.43525	−	19.8056i	0.305748	−	0.940995i	0.979397	−	0.201944i	$-0.0647258\pi$
$444$		0			0
$445$	−6.29961	−	1.64636i	−0.298630	−	0.0780450i
$446$		0			0
$447$	−33.5749	+	10.9091i	−1.58804	+	0.515985i
$448$		0			0
$449$	8.82587	−	12.1478i	0.416519	−	0.573289i	−0.548275	−	0.836298i	$-0.684715\pi$
$449$	8.82587	−	12.1478i	0.416519	−	0.573289i	0.964793	+	0.263010i	$0.0847151\pi$
$450$		0			0
$451$	28.6206	−	28.5698i	1.34769	−	1.34530i
$452$		0			0
$453$	−26.7522	−	19.4366i	−1.25693	−	0.913213i
$454$		0			0
$455$	0.0350158	−	0.354173i	0.00164157	−	0.0166039i
$456$		0			0
$457$	−5.10990	−	32.2626i	−0.239031	−	1.50918i	−0.756791	−	0.653657i	$-0.773234\pi$
$457$	−5.10990	−	32.2626i	−0.239031	−	1.50918i	0.517760	−	0.855526i	$-0.326766\pi$
$458$		0			0
$459$	−61.0955	−	19.8511i	−2.85169	−	0.926571i
$460$		0			0
$461$	−10.1649	+	31.2842i	−0.473424	+	1.45705i	0.374646	+	0.927168i	$0.377764\pi$
$461$	−10.1649	+	31.2842i	−0.473424	+	1.45705i	−0.848071	+	0.529883i	$0.822236\pi$
$462$		0			0
$463$	−31.1971	−	15.8957i	−1.44985	−	0.738736i	−0.460966	−	0.887418i	$-0.652497\pi$
$463$	−31.1971	−	15.8957i	−1.44985	−	0.738736i	−0.988885	+	0.148682i	$0.952497\pi$
$464$		0			0
$465$	−10.8224	−	27.6812i	−0.501875	−	1.28368i
$466$		0			0
$467$	3.45304	+	4.75270i	0.159787	+	0.219929i	0.881403	−	0.472366i	$-0.156600\pi$
$467$	3.45304	+	4.75270i	0.159787	+	0.219929i	−0.721615	+	0.692294i	$0.756600\pi$
$468$		0			0
$469$	−0.190752	−	0.138589i	−0.00880809	−	0.00639945i
$470$		0			0
$471$	−17.3739	−	23.9131i	−0.800547	−	1.10186i
$472$		0			0
$473$	63.1714	+	10.0054i	2.90462	+	0.460047i
$474$		0			0
$475$	7.00311	−	18.9394i	0.321325	−	0.869001i
$476$		0			0
$477$	−23.7592	+	46.6301i	−1.08786	+	2.13505i
$478$		0			0
$479$	0.00125562	+	0.00792765i	5.73706e−5	+	0.000362223i	0.987717	−	0.156253i	$-0.0499416\pi$
$479$	0.00125562	+	0.00792765i	5.73706e−5	+	0.000362223i	−0.987660	+	0.156616i	$0.949942\pi$
$480$		0			0
$481$	−6.27793	+	3.19877i	−0.286249	+	0.145851i
$482$		0			0
$483$	−0.679161			−0.0309029
$484$		0			0
$485$	−13.9063	+	21.7060i	−0.631452	+	0.985619i
$486$		0			0
$487$	13.5451	+	41.6876i	0.613787	+	1.88904i	0.418192	+	0.908359i	$0.362664\pi$
$487$	13.5451	+	41.6876i	0.613787	+	1.88904i	0.195596	+	0.980685i	$0.437336\pi$
$488$		0			0
$489$	−19.5946	−	19.5946i	−0.886100	−	0.886100i
$490$		0			0
$491$	−24.0194			−1.08398			−0.541990	−	0.840385i	$-0.682329\pi$
$491$	−24.0194			−1.08398			−0.541990	+	0.840385i	$0.682329\pi$
$492$		0			0
$493$		−	4.65208i		−	0.209519i
$494$		0			0
$495$	30.3042	+	77.5115i	1.36207	+	3.48388i
$496$		0			0
$497$	0.0110177	+	0.0339090i	0.000494212	+	0.00152103i
$498$		0			0
$499$	−3.05233	−	0.483442i	−0.136641	−	0.0216418i	0.0877391	−	0.996143i	$-0.472036\pi$
$499$	−3.05233	−	0.483442i	−0.136641	−	0.0216418i	−0.224380	+	0.974502i	$0.572036\pi$
$500$		0			0
$501$		−	6.51067i		−	0.290875i
$502$		0			0
$503$	−16.1762	−	31.7476i	−0.721261	−	1.41556i	−0.901873	−	0.432001i	$-0.857808\pi$
$503$	−16.1762	−	31.7476i	−0.721261	−	1.41556i	0.180612	−	0.983554i	$-0.442192\pi$
$504$		0			0
$505$	−7.03563	+	26.9210i	−0.313081	+	1.19797i
$506$		0			0
$507$	4.66223	−	9.15014i	0.207057	−	0.406372i
$508$		0			0
$509$	−6.39424	−	12.5494i	−0.283420	−	0.556242i	0.704778	−	0.709428i	$-0.251047\pi$
$509$	−6.39424	−	12.5494i	−0.283420	−	0.556242i	−0.988197	+	0.153186i	$0.951047\pi$
$510$		0			0
$511$	−0.0131580	+	0.0830766i	−0.000582078	+	0.00367509i
$512$		0			0
$513$	28.1897	−	20.4810i	1.24461	−	0.904260i
$514$		0			0
$515$	−2.66358	+	1.55982i	−0.117371	+	0.0687340i
$516$		0			0
$517$	29.2786	+	40.2986i	1.28767	+	1.77233i
$518$		0			0
$519$	30.6752	−	30.6752i	1.34649	−	1.34649i
$520$		0			0
$521$	14.1654	−	27.8011i	0.620596	−	1.21799i	−0.340101	−	0.940389i	$-0.610461\pi$
$521$	14.1654	−	27.8011i	0.620596	−	1.21799i	0.960697	−	0.277599i	$-0.0895386\pi$
$522$		0			0
$523$	−5.56778	−	1.80908i	−0.243462	−	0.0791055i	0.184744	−	0.982787i	$-0.440854\pi$
$523$	−5.56778	−	1.80908i	−0.243462	−	0.0791055i	−0.428206	+	0.903681i	$0.640854\pi$
$524$		0			0
$525$	0.320890	+	0.697426i	0.0140048	+	0.0304382i
$526$		0			0
$527$	−5.19140	−	32.7772i	−0.226141	−	1.42780i
$528$		0			0
$529$	1.06126	+	3.26622i	0.0461418	+	0.142010i
$530$		0			0
$531$	12.6927	−	17.4700i	0.550815	−	0.758132i
$532$		0			0
$533$	−17.6447	+	8.97072i	−0.764279	+	0.388565i
$534$		0			0
$535$	13.1282	+	22.4179i	0.567581	+	0.969211i
$536$		0			0
$537$	44.5594	−	14.4782i	1.92288	−	0.624781i
$538$		0			0
$539$	−43.6486	+	6.91325i	−1.88008	+	0.297775i
$540$		0			0
$541$	−11.8447	−	3.84858i	−0.509244	−	0.165464i	0.0431142	−	0.999070i	$-0.486272\pi$
$541$	−11.8447	−	3.84858i	−0.509244	−	0.165464i	−0.552359	+	0.833607i	$0.686272\pi$
$542$		0			0
$543$	−23.3151	−	7.57554i	−1.00055	−	0.325098i
$544$		0			0
$545$	−28.0698	+	23.0188i	−1.20238	+	0.986018i
$546$		0			0
$547$	−22.8227	−	22.8227i	−0.975826	−	0.975826i	0.0238884	−	0.999715i	$-0.492395\pi$
$547$	−22.8227	−	22.8227i	−0.975826	−	0.975826i	−0.999715	+	0.0238884i	$0.992395\pi$
$548$		0			0
$549$	−58.8115	+	42.7290i	−2.51001	+	1.82363i
$550$		0			0
$551$	2.04143	+	1.48319i	0.0869680	+	0.0631859i
$552$		0			0
$553$	0.547124	−	0.397509i	0.0232661	−	0.0169038i
$554$		0			0
$555$	8.19891	−	12.7975i	0.348024	−	0.543223i
$556$		0			0
$557$	8.28583	−	4.22184i	0.351082	−	0.178885i	−0.269552	−	0.962986i	$-0.586876\pi$
$557$	8.28583	−	4.22184i	0.351082	−	0.178885i	0.620633	+	0.784101i	$0.286876\pi$
$558$		0			0
$559$	−27.8940	−	14.2127i	−1.17979	−	0.601134i
$560$		0			0
$561$	21.9367	+	138.503i	0.926170	+	5.84761i
$562$		0			0
$563$	−8.06495	−	15.8284i	−0.339897	−	0.667086i	0.656273	−	0.754524i	$-0.272132\pi$
$563$	−8.06495	−	15.8284i	−0.339897	−	0.667086i	−0.996170	+	0.0874380i	$0.972132\pi$
$564$		0			0
$565$	27.2068	+	11.9126i	1.14460	+	0.501165i
$566$		0			0
$567$	−0.0648394	+	0.409380i	−0.00272300	+	0.0171923i
$568$		0			0
$569$	−10.8104	+	3.51252i	−0.453197	+	0.147253i	−0.526716	−	0.850041i	$-0.676577\pi$
$569$	−10.8104	+	3.51252i	−0.453197	+	0.147253i	0.0735192	+	0.997294i	$0.476577\pi$
$570$		0			0
$571$	−22.0859	−	22.0859i	−0.924266	−	0.924266i	0.0730616	−	0.997327i	$-0.476723\pi$
$571$	−22.0859	−	22.0859i	−0.924266	−	0.924266i	−0.997327	+	0.0730616i	$0.976723\pi$
$572$		0			0
$573$		−	61.1317i		−	2.55382i
$574$		0			0
$575$	−16.2518	+	15.0007i	−0.677748	+	0.625571i
$576$		0			0
$577$	−10.2713	+	10.2713i	−0.427601	+	0.427601i	−0.887810	−	0.460209i	$-0.847774\pi$
$577$	−10.2713	+	10.2713i	−0.427601	+	0.427601i	0.460209	+	0.887810i	$0.347774\pi$
$578$		0			0
$579$	13.8477	−	4.49939i	0.575491	−	0.186988i
$580$		0			0
$581$	−0.441551	−	0.0699349i	−0.0183186	−	0.00290139i
$582$		0			0
$583$	56.0855			2.32282
$584$		0			0
$585$	−2.38308	−	40.6667i	−0.0985282	−	1.68136i
$586$		0			0
$587$	19.9909	−	3.16625i	0.825114	−	0.130685i	0.270423	−	0.962742i	$-0.412836\pi$
$587$	19.9909	−	3.16625i	0.825114	−	0.130685i	0.554691	+	0.832056i	$0.312836\pi$
$588$		0			0
$589$	16.0385	+	8.17201i	0.660854	+	0.336722i
$590$		0			0
$591$	24.4239	+	47.9346i	1.00466	+	1.97176i
$592$		0			0
$593$	17.6259	+	2.79167i	0.723809	+	0.114640i	0.507459	−	0.861676i	$-0.330585\pi$
$593$	17.6259	+	2.79167i	0.723809	+	0.114640i	0.216350	+	0.976316i	$0.430585\pi$
$594$		0			0
$595$	0.183392	+	0.837338i	0.00751833	+	0.0343275i
$596$		0			0
$597$	−3.93191	+	5.41181i	−0.160922	+	0.221491i
$598$		0			0
$599$	33.6513	−	24.4491i	1.37496	−	0.998964i	0.377624	−	0.925959i	$-0.376741\pi$
$599$	33.6513	−	24.4491i	1.37496	−	0.998964i	0.997332	−	0.0730047i	$-0.0232588\pi$
$600$		0			0
$601$	−4.58020	+	4.58020i	−0.186830	+	0.186830i	−0.794324	−	0.607494i	$-0.792175\pi$
$601$	−4.58020	+	4.58020i	−0.186830	+	0.186830i	0.607494	+	0.794324i	$0.292175\pi$
$602$		0			0
$603$	−24.0462	−	12.2522i	−0.979239	−	0.498947i
$604$		0			0
$605$	42.9244	−	48.2683i	1.74512	−	1.96239i
$606$		0			0
$607$	−2.09145	+	6.43682i	−0.0848893	+	0.261262i	−0.984487	−	0.175457i	$-0.943860\pi$
$607$	−2.09145	+	6.43682i	−0.0848893	+	0.261262i	0.899598	+	0.436719i	$0.143860\pi$
$608$		0			0
$609$	−0.0947541	+	0.0150076i	−0.00383963	+	0.000608138i
$610$		0			0
$611$	−7.53432	−	23.1883i	−0.304806	−	0.938097i
$612$		0			0
$613$	1.10815	+	0.805118i	0.0447578	+	0.0325184i	0.609939	−	0.792448i	$-0.291194\pi$
$613$	1.10815	+	0.805118i	0.0447578	+	0.0325184i	−0.565181	+	0.824967i	$0.691194\pi$
$614$		0			0
$615$	23.0653	−	35.9319i	0.930084	−	1.44891i
$616$		0			0
$617$	−10.7501	−	7.81038i	−0.432781	−	0.314434i	0.349979	−	0.936758i	$-0.386189\pi$
$617$	−10.7501	−	7.81038i	−0.432781	−	0.314434i	−0.782760	+	0.622324i	$0.786189\pi$
$618$		0			0
$619$	−4.04288	−	12.4427i	−0.162497	−	0.500115i	0.836346	−	0.548202i	$-0.184687\pi$
$619$	−4.04288	−	12.4427i	−0.162497	−	0.500115i	−0.998843	+	0.0480872i	$0.984687\pi$
$620$		0			0
$621$	−37.6943	+	5.97020i	−1.51262	+	0.239576i
$622$		0			0
$623$	−0.0463291	+	0.142586i	−0.00185614	+	0.00571260i
$624$		0			0
$625$	23.0827	+	9.60140i	0.923310	+	0.384056i
$626$		0			0
$627$	−67.7721	−	34.5316i	−2.70656	−	1.37906i
$628$		0			0
$629$	11.9997	−	11.9997i	0.478457	−	0.478457i
$630$		0			0
$631$	−15.3021	+	11.1177i	−0.609169	+	0.442587i	−0.849121	−	0.528198i	$-0.822868\pi$
$631$	−15.3021	+	11.1177i	−0.609169	+	0.442587i	0.239953	+	0.970785i	$0.422868\pi$
$632$		0			0
$633$	−16.6609	+	22.9317i	−0.662210	+	0.911454i
$634$		0			0
$635$	4.83891	−	1.05981i	0.192026	−	0.0420571i
$636$		0			0
$637$	21.3648	+	3.38386i	0.846506	+	0.134073i
$638$		0			0
$639$	1.85273	+	3.63618i	0.0732928	+	0.143845i
$640$		0			0
$641$	9.72005	+	4.95261i	0.383919	+	0.195616i	0.635289	−	0.772275i	$-0.280881\pi$
$641$	9.72005	+	4.95261i	0.383919	+	0.195616i	−0.251370	+	0.967891i	$0.580881\pi$
$642$		0			0
$643$	−25.4586	+	4.03224i	−1.00399	+	0.159016i	−0.636716	−	0.771098i	$-0.719708\pi$
$643$	−25.4586	+	4.03224i	−1.00399	+	0.159016i	−0.367271	+	0.930114i	$0.619708\pi$
$644$		0			0
$645$	67.4146	−	3.95051i	2.65445	−	0.155551i
$646$		0			0
$647$	7.61274			0.299288			0.149644	−	0.988740i	$-0.452187\pi$
$647$	7.61274			0.299288			0.149644	+	0.988740i	$0.452187\pi$
$648$		0			0
$649$	−22.8570	−	3.62019i	−0.897216	−	0.142105i
$650$		0			0
$651$	−0.650862	+	0.211478i	−0.0255093	+	0.00828848i
$652$		0			0
$653$	20.7787	−	20.7787i	0.813135	−	0.813135i	−0.171968	−	0.985103i	$-0.555012\pi$
$653$	20.7787	−	20.7787i	0.813135	−	0.813135i	0.985103	+	0.171968i	$0.0550125\pi$
$654$		0			0
$655$	1.66088	+	0.727220i	0.0648960	+	0.0284148i
$656$		0			0
$657$			9.62753i			0.375606i
$658$		0			0
$659$	7.09405	+	7.09405i	0.276345	+	0.276345i	0.831648	−	0.555303i	$-0.187398\pi$
$659$	7.09405	+	7.09405i	0.276345	+	0.276345i	−0.555303	+	0.831648i	$0.687398\pi$
$660$		0			0
$661$	−43.5526	+	14.1511i	−1.69400	+	0.550413i	−0.987544	−	0.157345i	$-0.949706\pi$
$661$	−43.5526	+	14.1511i	−1.69400	+	0.550413i	−0.706454	+	0.707759i	$0.749706\pi$
$662$		0			0
$663$	10.7375	−	67.7937i	0.417009	−	2.63289i
$664$		0			0
$665$	−0.425912	−	0.186486i	−0.0165161	−	0.00723162i
$666$		0			0
$667$	−1.25472	−	2.46253i	−0.0485830	−	0.0953495i
$668$		0			0
$669$	−6.25961	−	39.5216i	−0.242010	−	1.52799i
$670$		0			0
$671$	69.4145	+	35.3685i	2.67972	+	1.36538i
$672$		0			0
$673$	19.0545	−	9.70876i	0.734498	−	0.374245i	−0.0463844	−	0.998924i	$-0.514770\pi$
$673$	19.0545	−	9.70876i	0.734498	−	0.374245i	0.780882	+	0.624678i	$0.214770\pi$
$674$		0			0
$675$	23.9406	+	35.8873i	0.921473	+	1.38130i
$676$		0			0
$677$	2.03551	−	1.47889i	0.0782311	−	0.0568382i	−0.547982	−	0.836490i	$-0.684604\pi$
$677$	2.03551	−	1.47889i	0.0782311	−	0.0568382i	0.626213	+	0.779652i	$0.284604\pi$
$678$		0			0
$679$	0.480206	+	0.348890i	0.0184286	+	0.0133892i
$680$		0			0
$681$	−63.9350	+	46.4515i	−2.44999	+	1.78002i
$682$		0			0
$683$	−35.6140	−	35.6140i	−1.36273	−	1.36273i	−0.870418	−	0.492314i	$-0.836151\pi$
$683$	−35.6140	−	35.6140i	−1.36273	−	1.36273i	−0.492314	−	0.870418i	$-0.663849\pi$
$684$		0			0
$685$	−2.51108	−	3.06208i	−0.0959435	−	0.116996i
$686$		0			0
$687$	27.9456	+	9.08006i	1.06619	+	0.346426i
$688$		0			0
$689$	−26.1088	−	8.48326i	−0.994665	−	0.323186i
$690$		0			0
$691$	10.2166	−	1.61815i	0.388657	−	0.0615572i	0.0409517	−	0.999161i	$-0.486961\pi$
$691$	10.2166	−	1.61815i	0.388657	−	0.0615572i	0.347705	+	0.937604i	$0.386961\pi$
$692$		0			0
$693$	1.82251	−	0.592170i	0.0692315	−	0.0224947i
$694$		0			0
$695$	−9.85696	+	5.77234i	−0.373896	+	0.218957i
$696$		0			0
$697$	33.7409	−	33.6810i	1.27803	−	1.27576i
$698$		0			0
$699$	37.8508	−	52.0971i	1.43165	−	1.97049i
$700$		0			0
$701$	9.38897	+	28.8963i	0.354617	+	1.09140i	0.956232	+	0.292611i	$0.0945242\pi$
$701$	9.38897	+	28.8963i	0.354617	+	1.09140i	−0.601615	+	0.798786i	$0.705476\pi$
$702$		0			0
$703$	1.43995	+	9.09147i	0.0543086	+	0.342891i
$704$		0			0
$705$	39.3009	+	34.9498i	1.48016	+	1.31629i
$706$		0			0
$707$	0.609334	+	0.197985i	0.0229164	+	0.00744598i
$708$		0			0
$709$	1.61832	−	3.17613i	0.0607772	−	0.119282i	−0.858620	−	0.512613i	$-0.828677\pi$
$709$	1.61832	−	3.17613i	0.0607772	−	0.119282i	0.919397	+	0.393331i	$0.128677\pi$
$710$		0			0
$711$	54.7355	−	54.7355i	2.05274	−	2.05274i
$712$		0			0
$713$	−11.5884	−	15.9501i	−0.433989	−	0.597335i
$714$		0			0
$715$	−37.6721	+	22.0612i	−1.40886	+	0.825041i
$716$		0			0
$717$	4.45845	−	3.23925i	0.166504	−	0.120972i
$718$		0			0
$719$	−6.20859	+	39.1995i	−0.231541	+	1.46189i	0.548492	+	0.836156i	$0.315202\pi$
$719$	−6.20859	+	39.1995i	−0.231541	+	1.46189i	−0.780033	+	0.625738i	$0.784798\pi$
$720$		0			0
$721$	0.0322665	+	0.0633266i	0.00120167	+	0.00235841i
$722$		0			0
$723$	−19.8895	+	39.0353i	−0.739698	+	1.45174i
$724$		0			0
$725$	−1.93592	+	2.45196i	−0.0718984	+	0.0910635i
$726$		0			0
$727$	−1.44845	−	2.84274i	−0.0537199	−	0.105431i	0.862586	−	0.505911i	$-0.168844\pi$
$727$	−1.44845	−	2.84274i	−0.0537199	−	0.105431i	−0.916306	+	0.400480i	$0.868844\pi$
$728$		0			0
$729$		−	29.7478i		−	1.10177i
$730$		0			0
$731$	74.4728	+	11.7953i	2.75448	+	0.436266i
$732$		0			0
$733$	−2.15147	−	6.62156i	−0.0794665	−	0.244573i	0.903429	−	0.428738i	$-0.141042\pi$
$733$	−2.15147	−	6.62156i	−0.0794665	−	0.244573i	−0.982895	+	0.184165i	$0.941042\pi$
$734$		0			0
$735$	−43.4571	+	16.9902i	−1.60294	+	0.626692i
$736$		0			0
$737$			28.9222i			1.06536i
$738$		0			0
$739$	−35.6236			−1.31044			−0.655218	−	0.755440i	$-0.727423\pi$
$739$	−35.6236			−1.31044			−0.655218	+	0.755440i	$0.727423\pi$
$740$		0			0
$741$	26.3260	+	26.3260i	0.967110	+	0.967110i
$742$		0			0
$743$	4.81322	+	14.8136i	0.176580	+	0.543457i	0.999702	−	0.0244071i	$-0.00776981\pi$
$743$	4.81322	+	14.8136i	0.176580	+	0.543457i	−0.823122	+	0.567864i	$0.807770\pi$
$744$		0			0
$745$	22.2887	+	14.2796i	0.816595	+	0.523164i
$746$		0			0
$747$	−51.1702			−1.87222
$748$		0			0
$749$	0.532986	−	0.271570i	0.0194749	−	0.00992295i
$750$		0			0
$751$	1.52475	+	9.62690i	0.0556390	+	0.351291i	0.999764	+	0.0217044i	$0.00690925\pi$
$751$	1.52475	+	9.62690i	0.0556390	+	0.351291i	−0.944125	+	0.329586i	$0.893091\pi$
$752$		0			0
$753$	17.3034	−	33.9599i	0.630573	−	1.23757i
$754$		0			0
$755$	1.45049	+	24.7522i	0.0527886	+	0.900825i
$756$		0			0
$757$	49.9564	+	7.91232i	1.81570	+	0.287578i	0.969464	−	0.245234i	$-0.0788648\pi$
$757$	49.9564	+	7.91232i	1.81570	+	0.287578i	0.846234	+	0.532812i	$0.178865\pi$
$758$		0			0
$759$	48.9679	+	67.3986i	1.77742	+	2.44641i
$760$		0			0
$761$	1.18527	+	0.861146i	0.0429658	+	0.0312165i	0.609061	−	0.793123i	$-0.291546\pi$
$761$	1.18527	+	0.861146i	0.0429658	+	0.0312165i	−0.566095	+	0.824340i	$0.691546\pi$
$762$		0			0
$763$	0.491304	+	0.676223i	0.0177864	+	0.0244809i
$764$		0			0
$765$	35.7257	+	91.3785i	1.29167	+	3.30379i
$766$		0			0
$767$	10.0928	+	5.14252i	0.364429	+	0.185686i
$768$		0			0
$769$	0.0267024	−	0.0821815i	0.000962913	−	0.00296354i	−0.950574	−	0.310498i	$-0.899504\pi$
$769$	0.0267024	−	0.0821815i	0.000962913	−	0.00296354i	0.951537	+	0.307535i	$0.0995041\pi$
$770$		0			0
$771$	−75.3605	−	24.4861i	−2.71404	−	0.881846i
$772$		0			0
$773$	−0.543888	−	3.43398i	−0.0195623	−	0.123512i	0.975975	−	0.217884i	$-0.0699155\pi$
$773$	−0.543888	−	3.43398i	−0.0195623	−	0.123512i	−0.995537	+	0.0943726i	$0.969915\pi$
$774$		0			0
$775$	−10.9037	+	19.4362i	−0.391674	+	0.698167i
$776$		0			0
$777$	−0.283121	−	0.205700i	−0.0101569	−	0.00737943i
$778$		0			0
$779$	4.02260	+	25.5445i	0.144125	+	0.915227i
$780$		0			0
$781$	2.57068	−	3.53824i	0.0919862	−	0.126608i
$782$		0			0
$783$	−5.12706	+	1.66588i	−0.183226	+	0.0595337i
$784$		0			0
$785$	−5.60401	+	21.4431i	−0.200016	+	0.765337i
$786$		0			0
$787$	−11.0264	+	33.9359i	−0.393050	+	1.20968i	0.537420	+	0.843315i	$0.319399\pi$
$787$	−11.0264	+	33.9359i	−0.393050	+	1.20968i	−0.930470	+	0.366369i	$0.880601\pi$
$788$		0			0
$789$	−17.7189	+	54.5332i	−0.630809	+	1.94143i
$790$		0			0
$791$	0.310472	−	0.609335i	0.0110391	−	0.0216654i
$792$		0			0
$793$	−26.9640	−	26.9640i	−0.957519	−	0.957519i
$794$		0			0
$795$	57.8461	−	12.6693i	2.05159	−	0.449334i
$796$		0			0
$797$	11.7238	−	16.1364i	0.415277	−	0.571579i	−0.549219	−	0.835679i	$-0.685075\pi$
$797$	11.7238	−	16.1364i	0.415277	−	0.571579i	0.964495	+	0.264099i	$0.0850747\pi$
$798$		0			0
$799$	34.5166	+	47.5081i	1.22111	+	1.68071i
$800$		0			0
$801$	−2.68448	+	16.9491i	−0.0948513	+	0.598868i
$802$		0			0
$803$	9.19307	−	4.68410i	0.324416	−	0.165298i
$804$		0			0
$805$	0.322917	+	0.393773i	0.0113813	+	0.0138787i
$806$		0			0
$807$	66.2152	−	10.4875i	2.33088	−	0.369176i
$808$		0			0
$809$	9.22423	−	4.69998i	0.324307	−	0.165243i	−0.284256	−	0.958748i	$-0.591746\pi$
$809$	9.22423	−	4.69998i	0.324307	−	0.165243i	0.608562	+	0.793506i	$0.291746\pi$
$810$		0			0
$811$		−	15.0239i		−	0.527561i	−0.964583	−	0.263781i	$-0.915030\pi$
$811$		−	15.0239i		−	0.527561i	0.964583	−	0.263781i	$-0.0849695\pi$
$812$		0			0
$813$	−3.97982	+	25.1276i	−0.139578	+	0.881263i
$814$		0			0
$815$	−2.04430	+	20.6774i	−0.0716088	+	0.724297i
$816$		0			0
$817$	−28.9197	+	28.9197i	−1.01177	+	1.01177i
$818$		0			0
$819$	−0.937981			−0.0327757
$820$		0			0
$821$	−37.8471			−1.32087			−0.660436	−	0.750883i	$-0.729628\pi$
$821$	−37.8471			−1.32087			−0.660436	+	0.750883i	$0.729628\pi$
$822$		0			0
$823$	24.3907	−	24.3907i	0.850205	−	0.850205i	−0.139953	−	0.990158i	$-0.544695\pi$
$823$	24.3907	−	24.3907i	0.850205	−	0.850205i	0.990158	+	0.139953i	$0.0446952\pi$
$824$		0			0
$825$	46.0748	−	82.1293i	1.60412	−	2.85938i
$826$		0			0
$827$	−2.57498	+	16.2578i	−0.0895409	+	0.565339i	0.901605	+	0.432561i	$0.142390\pi$
$827$	−2.57498	+	16.2578i	−0.0895409	+	0.565339i	−0.991146	+	0.132779i	$0.957610\pi$
$828$		0			0
$829$		−	6.17858i		−	0.214591i	−0.994227	−	0.107296i	$-0.965781\pi$
$829$		−	6.17858i		−	0.214591i	0.994227	−	0.107296i	$-0.0342191\pi$
$830$		0			0
$831$	16.0069	−	8.15591i	0.555272	−	0.282925i
$832$		0			0
$833$	−51.4574	+	8.15005i	−1.78289	+	0.282382i
$834$		0			0
$835$	−3.77485	+	3.09559i	−0.130634	+	0.107127i
$836$		0			0
$837$	−34.2647	+	17.4588i	−1.18436	+	0.603463i
$838$		0			0
$839$	6.57741	−	41.5281i	0.227077	−	1.43371i	−0.565908	−	0.824468i	$-0.691474\pi$
$839$	6.57741	−	41.5281i	0.227077	−	1.43371i	0.792985	−	0.609241i	$-0.208526\pi$
$840$		0			0
$841$	16.8163	+	23.1457i	0.579873	+	0.798126i
$842$		0			0
$843$	46.9915	−	64.6782i	1.61847	−	2.22764i
$844$		0			0
$845$	−7.52192	+	1.64743i	−0.258762	+	0.0566734i
$846$		0			0
$847$	−1.05168	−	1.05168i	−0.0361363	−	0.0361363i
$848$		0			0
$849$	−10.5609	+	20.7270i	−0.362450	+	0.711348i
$850$		0			0
$851$	3.11544	−	9.58834i	0.106796	−	0.328684i
$852$		0			0
$853$	−15.2573	+	46.9570i	−0.522399	+	1.60778i	0.247005	+	0.969014i	$0.420554\pi$
$853$	−15.2573	+	46.9570i	−0.522399	+	1.60778i	−0.769403	+	0.638763i	$0.779446\pi$
$854$		0			0
$855$	−51.4890	−	13.4563i	−1.76089	−	0.460196i
$856$		0			0
$857$	−45.1206	+	14.6606i	−1.54129	+	0.500796i	−0.951732	−	0.306929i	$-0.900699\pi$
$857$	−45.1206	+	14.6606i	−1.54129	+	0.500796i	−0.589559	+	0.807725i	$0.700699\pi$
$858$		0			0
$859$	−29.0780	+	40.0224i	−0.992129	+	1.36555i	−0.0620964	+	0.998070i	$0.519779\pi$
$859$	−29.0780	+	40.0224i	−0.992129	+	1.36555i	−0.930032	+	0.367478i	$0.880221\pi$
$860$		0			0
$861$	−0.794867	−	0.578583i	−0.0270890	−	0.0197181i
$862$		0			0
$863$	27.9466	+	20.3044i	0.951312	+	0.691169i	0.951117	−	0.308831i	$-0.0999378\pi$
$863$	27.9466	+	20.3044i	0.951312	+	0.691169i	0.000195367		1.00000i	$0.499938\pi$
$864$		0			0
$865$	−32.3702	−	3.20033i	−1.10062	−	0.108815i
$866$		0			0
$867$	17.9306	+	113.209i	0.608954	+	3.84479i
$868$		0			0
$869$	−78.8960	−	25.6349i	−2.67637	−	0.869604i
$870$		0			0
$871$	4.37465	−	13.4638i	0.148229	−	0.456203i
$872$		0			0
$873$	60.5350	+	30.8441i	2.04880	+	1.04392i
$874$		0			0
$875$	0.251792	−	0.517651i	0.00851211	−	0.0174998i
$876$		0			0
$877$	−17.7940	−	24.4913i	−0.600861	−	0.827014i	0.394926	−	0.918713i	$-0.370770\pi$
$877$	−17.7940	−	24.4913i	−0.600861	−	0.827014i	−0.995787	+	0.0916991i	$0.970770\pi$
$878$		0			0
$879$	−0.0379865	−	0.0275988i	−0.00128125	−	0.000930886i
$880$		0			0
$881$	3.63692	+	5.00579i	0.122531	+	0.168649i	0.865876	−	0.500259i	$-0.166762\pi$
$881$	3.63692	+	5.00579i	0.122531	+	0.168649i	−0.743345	+	0.668908i	$0.766762\pi$
$882$		0			0
$883$	−4.51338	−	0.714849i	−0.151887	−	0.0240566i	0.0800277	−	0.996793i	$-0.474499\pi$
$883$	−4.51338	−	0.714849i	−0.151887	−	0.0240566i	−0.231915	+	0.972736i	$0.574499\pi$
$884$		0			0
$885$	−24.3923	+	1.42940i	−0.819938	+	0.0480486i
$886$		0			0
$887$	10.9827	−	21.5547i	0.368762	−	0.723737i	−0.629832	−	0.776731i	$-0.716876\pi$
$887$	10.9827	−	21.5547i	0.368762	−	0.723737i	0.998595	+	0.0529941i	$0.0168765\pi$
$888$		0			0
$889$	−0.0178429	−	0.112656i	−0.000598431	−	0.00377835i
$890$		0			0
$891$	45.3010	−	23.0820i	1.51764	−	0.773276i
$892$		0			0
$893$	−31.8523			−1.06590
$894$		0			0
$895$	−29.5808	−	18.9514i	−0.988775	−	0.633474i
$896$		0			0
$897$	−12.6010	−	38.7819i	−0.420736	−	1.29489i
$898$		0			0
$899$	−1.96923	−	1.96923i	−0.0656774	−	0.0656774i
$900$		0			0
$901$	66.1193			2.20275
$902$		0			0
$903$		−	1.55492i		−	0.0517446i
$904$		0			0
$905$	6.69325	+	17.1199i	0.222491	+	0.569083i
$906$		0			0
$907$	−12.5948	−	38.7629i	−0.418204	−	1.28710i	−0.909353	−	0.416025i	$-0.863423\pi$
$907$	−12.5948	−	38.7629i	−0.418204	−	1.28710i	0.491149	−	0.871075i	$-0.336577\pi$
$908$		0			0
$909$	72.4311	+	11.4720i	2.40239	+	0.380501i
$910$		0			0
$911$		−	40.5150i		−	1.34232i	−0.741312	−	0.671161i	$-0.765796\pi$
$911$		−	40.5150i		−	1.34232i	0.741312	−	0.671161i	$-0.234204\pi$
$912$		0			0
$913$	24.8959	+	48.8610i	0.823935	+	1.61706i
$914$		0			0
$915$	79.5830	+	20.7985i	2.63093	+	0.687577i
$916$		0			0
$917$	0.0189532	−	0.0371978i	0.000625890	−	0.00122838i
$918$		0			0
$919$	−11.2619	−	22.1027i	−0.371496	−	0.729102i	0.627268	−	0.778803i	$-0.284173\pi$
$919$	−11.2619	−	22.1027i	−0.371496	−	0.729102i	−0.998764	+	0.0497014i	$0.984173\pi$
$920$		0			0
$921$	−1.19893	+	7.56976i	−0.0395062	+	0.249432i
$922$		0			0
$923$	−1.73188	+	1.25828i	−0.0570054	+	0.0414169i
$924$		0			0
$925$	−11.3182	+	1.33107i	−0.372140	+	0.0437653i
$926$		0			0
$927$	4.78167	+	6.58141i	0.157051	+	0.216162i
$928$		0			0
$929$	−12.7798	+	12.7798i	−0.419293	+	0.419293i	−0.884960	−	0.465667i	$-0.845814\pi$
$929$	−12.7798	+	12.7798i	−0.419293	+	0.419293i	0.465667	+	0.884960i	$0.345814\pi$
$930$		0			0
$931$	12.8294	−	25.1790i	0.420465	−	0.825209i
$932$		0			0
$933$	−70.4350	−	22.8857i	−2.30594	−	0.749245i
$934$		0			0
$935$	69.8731	−	78.5721i	2.28510	−	2.56958i
$936$		0			0
$937$	0.536066	+	3.38459i	0.0175125	+	0.110570i	0.994896	−	0.100904i	$-0.0321736\pi$
$937$	0.536066	+	3.38459i	0.0175125	+	0.110570i	−0.977384	+	0.211474i	$0.932174\pi$
$938$		0			0
$939$	−22.7308	−	69.9581i	−0.741790	−	2.28299i
$940$		0			0
$941$	25.1844	−	34.6634i	0.820989	−	1.12999i	−0.168545	−	0.985694i	$-0.553907\pi$
$941$	25.1844	−	34.6634i	0.820989	−	1.12999i	0.989534	−	0.144301i	$-0.0460933\pi$
$942$		0			0
$943$	8.77621	−	26.9290i	0.285793	−	0.876929i
$944$		0			0
$945$	0.857159	−	0.501962i	0.0278834	−	0.0163288i
$946$		0			0
$947$	8.39813	−	2.72872i	0.272903	−	0.0886715i	−0.169369	−	0.985553i	$-0.554173\pi$
$947$	8.39813	−	2.72872i	0.272903	−	0.0886715i	0.442271	+	0.896881i	$0.354173\pi$
$948$		0			0
$949$	−4.98803	+	0.790027i	−0.161918	+	0.0256454i
$950$		0			0
$951$	−5.63712	−	1.83161i	−0.182796	−	0.0593940i
$952$		0			0
$953$	−41.0164	−	13.3270i	−1.32865	−	0.431705i	−0.443193	−	0.896426i	$-0.646154\pi$
$953$	−41.0164	−	13.3270i	−1.32865	−	0.431705i	−0.885457	+	0.464721i	$0.846154\pi$
$954$		0			0
$955$	−35.4438	+	29.0660i	−1.14693	+	0.940552i
$956$		0			0
$957$	8.32115	+	8.32115i	0.268985	+	0.268985i
$958$		0			0
$959$	−0.0737679	+	0.0535955i	−0.00238209	+	0.00173069i
$960$		0			0
$961$	9.00741	+	6.54427i	0.290562	+	0.211105i
$962$		0			0
$963$	55.3921	−	40.2447i	1.78499	−	1.29687i
$964$		0			0
$965$	−9.19280	−	5.88951i	−0.295927	−	0.189590i
$966$		0			0
$967$	−39.1239	+	19.9346i	−1.25814	+	0.641054i	−0.950581	−	0.310475i	$-0.899512\pi$
$967$	−39.1239	+	19.9346i	−1.25814	+	0.641054i	−0.307558	+	0.951529i	$0.599512\pi$
$968$		0			0
$969$	−79.8967	−	40.7094i	−2.56665	−	1.30777i
$970$		0			0
$971$	0.681475	+	4.30266i	0.0218696	+	0.138079i	0.996207	−	0.0870123i	$-0.0277319\pi$
$971$	0.681475	+	4.30266i	0.0218696	+	0.138079i	−0.974338	+	0.225091i	$0.927732\pi$
$972$		0			0
$973$	0.119407	+	0.234349i	0.00382800	+	0.00751288i
$974$		0			0
$975$	−33.8712	+	31.2636i	−1.08475	+	1.00124i
$976$		0			0
$977$	5.87042	−	37.0643i	0.187811	−	1.18579i	−0.696032	−	0.718011i	$-0.745053\pi$
$977$	5.87042	−	37.0643i	0.187811	−	1.18579i	0.883843	−	0.467783i	$-0.154947\pi$
$978$		0			0
$979$	17.4903	−	5.68296i	0.558994	−	0.181628i
$980$		0			0
$981$	67.6508	+	67.6508i	2.15992	+	2.15992i
$982$		0			0
$983$			55.9962i			1.78600i	0.450056	+	0.893000i	$0.351404\pi$
$983$			55.9962i			1.78600i	−0.450056	+	0.893000i	$0.648596\pi$
$984$		0			0
$985$	16.1795	−	36.9520i	0.515521	−	1.17739i
$986$		0			0
$987$	0.856300	−	0.856300i	0.0272563	−	0.0272563i
$988$		0			0
$989$	42.6028	−	13.8425i	1.35469	−	0.440165i
$990$		0			0
$991$	−18.0480	−	2.85853i	−0.573315	−	0.0908041i	−0.136956	−	0.990577i	$-0.543732\pi$
$991$	−18.0480	−	2.85853i	−0.573315	−	0.0908041i	−0.436358	+	0.899773i	$0.643732\pi$
$992$		0			0
$993$	14.9840			0.475504
$994$		0			0
$995$	5.00721	−	0.293424i	0.158739	−	0.00930218i
$996$		0			0
$997$	58.6477	−	9.28889i	1.85739	−	0.294182i	0.875442	−	0.483322i	$-0.160570\pi$
$997$	58.6477	−	9.28889i	1.85739	−	0.294182i	0.981950	+	0.189140i	$0.0605701\pi$
$998$		0			0
$999$	−17.5218	−	8.92781i	−0.554366	−	0.282464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bq.a.49.3	✓	176
5.4	even	2	inner	820.2.bq.a.49.20	yes	176
41.36	even	20	inner	820.2.bq.a.569.20	yes	176
205.159	even	20	inner	820.2.bq.a.569.3	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bq.a.49.3	✓	176	1.1	even	1	trivial
820.2.bq.a.49.20	yes	176	5.4	even	2	inner
820.2.bq.a.569.3	yes	176	205.159	even	20	inner
820.2.bq.a.569.20	yes	176	41.36	even	20	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.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10870 + 2.10870i) q^{3} +(2.22522 + 0.220000i) q^{5} +(0.00805431 - 0.0508529i) q^{7} -5.89321i q^{9} +(-5.62726 + 2.86723i) q^{11} +(3.05328 - 0.483592i) q^{13} +(-5.15623 + 4.22840i) q^{15} +(-6.63399 + 3.38019i) q^{17} +(0.631767 - 3.98882i) q^{19} +(0.0902493 + 0.124218i) q^{21} +(-2.59996 + 3.57853i) q^{23} +(4.90320 + 0.979095i) q^{25} +(6.10090 + 6.10090i) q^{27} +(-0.283661 + 0.556716i) q^{29} +(-1.37734 + 4.23901i) q^{31} +(5.82007 - 17.9123i) q^{33} +(0.0291102 - 0.111387i) q^{35} +(-2.16768 + 0.704323i) q^{37} +(-5.41869 + 7.45818i) q^{39} +(-6.09149 + 1.97327i) q^{41} +(-8.19297 - 5.95254i) q^{43} +(1.29650 - 13.1137i) q^{45} +(-1.23381 - 7.78997i) q^{47} +(6.65487 + 2.16230i) q^{49} +(6.86129 - 21.1169i) q^{51} +(-7.91252 - 4.03163i) q^{53} +(-13.1527 + 5.14223i) q^{55} +(7.07901 + 9.74342i) q^{57} +(2.96443 + 2.15378i) q^{59} +(-7.25056 - 9.97954i) q^{61} +(-0.299687 - 0.0474657i) q^{63} +(6.90060 - 0.404377i) q^{65} +(2.07903 - 4.08033i) q^{67} +(-2.06352 - 13.0286i) q^{69} +(-0.617012 + 0.314384i) q^{71} -1.63367 q^{73} +(-12.4040 + 8.27475i) q^{75} +(0.100484 + 0.309256i) q^{77} +(9.28790 + 9.28790i) q^{79} -8.05027 q^{81} -8.68291i q^{83} +(-15.5057 + 6.06218i) q^{85} +(-0.575791 - 1.77210i) q^{87} +(-2.87604 - 0.455520i) q^{89} -0.159163i q^{91} +(-6.03439 - 11.8432i) q^{93} +(2.28336 - 8.73701i) q^{95} +(-5.23384 + 10.2720i) q^{97} +(16.8972 + 33.1626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 4 q^{11} - 10 q^{15} - 4 q^{19} + 12 q^{25} + 8 q^{29} - 8 q^{31} - 6 q^{35} + 40 q^{39} + 28 q^{41} - 4 q^{45} + 20 q^{49} - 32 q^{51} - 50 q^{55} + 12 q^{59} + 40 q^{61} - 10 q^{65} - 28 q^{69}+ \cdots + 4 q^{99}+O(q^{100}) \) 176 * q + 4 * q^11 - 10 * q^15 - 4 * q^19 + 12 * q^25 + 8 * q^29 - 8 * q^31 - 6 * q^35 + 40 * q^39 + 28 * q^41 - 4 * q^45 + 20 * q^49 - 32 * q^51 - 50 * q^55 + 12 * q^59 + 40 * q^61 - 10 * q^65 - 28 * q^69 - 108 * q^71 + 52 * q^75 + 48 * q^79 - 328 * q^81 + 98 * q^85 - 16 * q^89 + 26 * q^95 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more