LMFDB - Embedded newform 864.2.y.d.97.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.2
Character	$\chi$	$=$	864.97
Dual form			864.2.y.d.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65691 + 0.504627i) q^{3} +(1.76220 + 0.641388i) q^{5} +(-0.498467 + 2.82694i) q^{7} +(2.49070 - 1.67224i) q^{9} +O(q^{10})$	\(q+(-1.65691 + 0.504627i) q^{3} +(1.76220 + 0.641388i) q^{5} +(-0.498467 + 2.82694i) q^{7} +(2.49070 - 1.67224i) q^{9} +(-2.96272 + 1.07834i) q^{11} +(-2.02319 + 1.69766i) q^{13} +(-3.24347 - 0.173468i) q^{15} +(1.64182 + 2.84371i) q^{17} +(2.27732 - 3.94443i) q^{19} +(-0.600639 - 4.93553i) q^{21} +(0.724678 + 4.10985i) q^{23} +(-1.13625 - 0.953429i) q^{25} +(-3.28301 + 4.02764i) q^{27} +(-6.88981 - 5.78123i) q^{29} +(0.0483277 + 0.274080i) q^{31} +(4.36480 - 3.28178i) q^{33} +(-2.69157 + 4.66193i) q^{35} +(4.43176 + 7.67603i) q^{37} +(2.49557 - 3.83383i) q^{39} +(-3.27593 + 2.74883i) q^{41} +(-6.11943 + 2.22729i) q^{43} +(5.46167 - 1.34932i) q^{45} +(0.872914 - 4.95054i) q^{47} +(-1.16530 - 0.424133i) q^{49} +(-4.15536 - 3.88327i) q^{51} -7.20464 q^{53} -5.91254 q^{55} +(-1.78284 + 7.68477i) q^{57} +(-6.77067 - 2.46432i) q^{59} +(-1.16026 + 6.58018i) q^{61} +(3.48581 + 7.87463i) q^{63} +(-4.65413 + 1.69397i) q^{65} +(-9.92466 + 8.32778i) q^{67} +(-3.27467 - 6.44396i) q^{69} +(4.24816 + 7.35804i) q^{71} +(-5.32680 + 9.22629i) q^{73} +(2.36379 + 1.00636i) q^{75} +(-1.57159 - 8.91296i) q^{77} +(2.09562 + 1.75844i) q^{79} +(3.40720 - 8.33013i) q^{81} +(-9.51019 - 7.98000i) q^{83} +(1.06929 + 6.06423i) q^{85} +(14.3332 + 6.10220i) q^{87} +(-2.00367 + 3.47046i) q^{89} +(-3.79070 - 6.56569i) q^{91} +(-0.218383 - 0.429738i) q^{93} +(6.54301 - 5.49023i) q^{95} +(10.2199 - 3.71972i) q^{97} +(-5.57600 + 7.64022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 12 q^{9}+O(q^{10}) $ 60 * q + 12 * q^9	$ 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) $ 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	−1.65691	+	0.504627i	−0.956618	+	0.291347i
$3$	−1.65691	+	0.504627i	−0.956618	+	0.291347i
$4$		0			0
$5$	1.76220	+	0.641388i	0.788080	+	0.286838i	0.704538	−	0.709667i	$-0.251154\pi$
$5$	1.76220	+	0.641388i	0.788080	+	0.286838i	0.0835422	+	0.996504i	$0.473377\pi$
$6$		0			0
$7$	−0.498467	+	2.82694i	−0.188403	+	1.06848i	0.733102	+	0.680118i	$0.238072\pi$
$7$	−0.498467	+	2.82694i	−0.188403	+	1.06848i	−0.921505	+	0.388366i	$0.873040\pi$
$8$		0			0
$9$	2.49070	−	1.67224i	0.830234	−	0.557415i
$10$		0			0
$11$	−2.96272	+	1.07834i	−0.893293	+	0.325132i	−0.747562	−	0.664192i	$-0.768776\pi$
$11$	−2.96272	+	1.07834i	−0.893293	+	0.325132i	−0.145731	+	0.989324i	$0.546553\pi$
$12$		0			0
$13$	−2.02319	+	1.69766i	−0.561133	+	0.470847i	−0.878690	−	0.477392i	$-0.841582\pi$
$13$	−2.02319	+	1.69766i	−0.561133	+	0.470847i	0.317557	+	0.948239i	$0.397138\pi$
$14$		0			0
$15$	−3.24347	−	0.173468i	−0.837460	−	0.0447893i
$16$		0			0
$17$	1.64182	+	2.84371i	0.398199	+	0.689701i	0.993504	−	0.113799i	$-0.0363020\pi$
$17$	1.64182	+	2.84371i	0.398199	+	0.689701i	−0.595305	+	0.803500i	$0.702969\pi$
$18$		0			0
$19$	2.27732	−	3.94443i	0.522453	−	0.904915i	−0.477206	−	0.878792i	$-0.658350\pi$
$19$	2.27732	−	3.94443i	0.522453	−	0.904915i	0.999659	−	0.0261235i	$-0.00831632\pi$
$20$		0			0
$21$	−0.600639	−	4.93553i	−0.131070	−	1.07702i
$22$		0			0
$23$	0.724678	+	4.10985i	0.151106	+	0.856963i	0.962260	+	0.272131i	$0.0877285\pi$
$23$	0.724678	+	4.10985i	0.151106	+	0.856963i	−0.811154	+	0.584832i	$0.801160\pi$
$24$		0			0
$25$	−1.13625	−	0.953429i	−0.227250	−	0.190686i
$26$		0			0
$27$	−3.28301	+	4.02764i	−0.631815	+	0.775119i
$28$		0			0
$29$	−6.88981	−	5.78123i	−1.27940	−	1.07355i	−0.993326	−	0.115342i	$-0.963204\pi$
$29$	−6.88981	−	5.78123i	−1.27940	−	1.07355i	−0.286079	−	0.958206i	$-0.592352\pi$
$30$		0			0
$31$	0.0483277	+	0.274080i	0.00867991	+	0.0492262i	0.988840	−	0.148981i	$-0.0475993\pi$
$31$	0.0483277	+	0.274080i	0.00867991	+	0.0492262i	−0.980160	+	0.198207i	$0.936488\pi$
$32$		0			0
$33$	4.36480	−	3.28178i	0.759814	−	0.571285i
$34$		0			0
$35$	−2.69157	+	4.66193i	−0.454958	+	0.788010i
$36$		0			0
$37$	4.43176	+	7.67603i	0.728577	+	1.26193i	0.957485	+	0.288484i	$0.0931511\pi$
$37$	4.43176	+	7.67603i	0.728577	+	1.26193i	−0.228908	+	0.973448i	$0.573516\pi$
$38$		0			0
$39$	2.49557	−	3.83383i	0.399610	−	0.613905i
$40$		0			0
$41$	−3.27593	+	2.74883i	−0.511614	+	0.429295i	−0.861697	−	0.507424i	$-0.830598\pi$
$41$	−3.27593	+	2.74883i	−0.511614	+	0.429295i	0.350083	+	0.936719i	$0.386153\pi$
$42$		0			0
$43$	−6.11943	+	2.22729i	−0.933204	+	0.339658i	−0.763479	−	0.645833i	$-0.776510\pi$
$43$	−6.11943	+	2.22729i	−0.933204	+	0.339658i	−0.169725	+	0.985491i	$0.554288\pi$
$44$		0			0
$45$	5.46167	−	1.34932i	0.814178	−	0.201145i
$46$		0			0
$47$	0.872914	−	4.95054i	0.127328	−	0.722111i	−0.852570	−	0.522612i	$-0.824958\pi$
$47$	0.872914	−	4.95054i	0.127328	−	0.722111i	0.979898	−	0.199499i	$-0.0639313\pi$
$48$		0			0
$49$	−1.16530	−	0.424133i	−0.166471	−	0.0605905i
$50$		0			0
$51$	−4.15536	−	3.88327i	−0.581866	−	0.543766i
$52$		0			0
$53$	−7.20464			−0.989633			−0.494817	−	0.868997i	$-0.664765\pi$
$53$	−7.20464			−0.989633			−0.494817	+	0.868997i	$0.664765\pi$
$54$		0			0
$55$	−5.91254			−0.797247
$56$		0			0
$57$	−1.78284	+	7.68477i	−0.236144	+	1.01787i
$58$		0			0
$59$	−6.77067	−	2.46432i	−0.881467	−	0.320828i	−0.138665	−	0.990339i	$-0.544281\pi$
$59$	−6.77067	−	2.46432i	−0.881467	−	0.320828i	−0.742801	+	0.669512i	$0.766503\pi$
$60$		0			0
$61$	−1.16026	+	6.58018i	−0.148556	+	0.842506i	0.815886	+	0.578213i	$0.196250\pi$
$61$	−1.16026	+	6.58018i	−0.148556	+	0.842506i	−0.964442	+	0.264293i	$0.914861\pi$
$62$		0			0
$63$	3.48581	+	7.87463i	0.439171	+	0.992111i
$64$		0			0
$65$	−4.65413	+	1.69397i	−0.577274	+	0.210111i
$66$		0			0
$67$	−9.92466	+	8.32778i	−1.21249	+	1.01740i	−0.213307	+	0.976985i	$0.568424\pi$
$67$	−9.92466	+	8.32778i	−1.21249	+	1.01740i	−0.999183	+	0.0404148i	$0.987132\pi$
$68$		0			0
$69$	−3.27467	−	6.44396i	−0.394224	−	0.775762i
$70$		0			0
$71$	4.24816	+	7.35804i	0.504164	+	0.873238i	0.999988	+	0.00481530i	$0.00153276\pi$
$71$	4.24816	+	7.35804i	0.504164	+	0.873238i	−0.495824	+	0.868423i	$0.665134\pi$
$72$		0			0
$73$	−5.32680	+	9.22629i	−0.623455	+	1.07985i	0.365383	+	0.930857i	$0.380938\pi$
$73$	−5.32680	+	9.22629i	−0.623455	+	1.07985i	−0.988838	+	0.148998i	$0.952395\pi$
$74$		0			0
$75$	2.36379	+	1.00636i	0.272947	+	0.116205i
$76$		0			0
$77$	−1.57159	−	8.91296i	−0.179100	−	1.01573i
$78$		0			0
$79$	2.09562	+	1.75844i	0.235776	+	0.197840i	0.753019	−	0.657999i	$-0.228597\pi$
$79$	2.09562	+	1.75844i	0.235776	+	0.197840i	−0.517243	+	0.855839i	$0.673041\pi$
$80$		0			0
$81$	3.40720	−	8.33013i	0.378577	−	0.925570i
$82$		0			0
$83$	−9.51019	−	7.98000i	−1.04388	−	0.875919i	−0.0514425	−	0.998676i	$-0.516382\pi$
$83$	−9.51019	−	7.98000i	−1.04388	−	0.875919i	−0.992437	+	0.122757i	$0.960826\pi$
$84$		0			0
$85$	1.06929	+	6.06423i	0.115980	+	0.657758i
$86$		0			0
$87$	14.3332	+	6.10220i	1.53668	+	0.654224i
$88$		0			0
$89$	−2.00367	+	3.47046i	−0.212389	+	0.367868i	−0.952462	−	0.304658i	$-0.901458\pi$
$89$	−2.00367	+	3.47046i	−0.212389	+	0.367868i	0.740073	+	0.672527i	$0.234791\pi$
$90$		0			0
$91$	−3.79070	−	6.56569i	−0.397373	−	0.688271i
$92$		0			0
$93$	−0.218383	−	0.429738i	−0.0226453	−	0.0445618i
$94$		0			0
$95$	6.54301	−	5.49023i	0.671298	−	0.563286i
$96$		0			0
$97$	10.2199	−	3.71972i	1.03767	−	0.377681i	0.233673	−	0.972315i	$-0.424925\pi$
$97$	10.2199	−	3.71972i	1.03767	−	0.377681i	0.803996	+	0.594634i	$0.202703\pi$
$98$		0			0
$99$	−5.57600	+	7.64022i	−0.560409	+	0.767871i
$100$		0			0
$101$	−1.03953	+	5.89545i	−0.103437	+	0.586619i	0.888396	+	0.459077i	$0.151820\pi$
$101$	−1.03953	+	5.89545i	−0.103437	+	0.586619i	−0.991833	+	0.127542i	$0.959291\pi$
$102$		0			0
$103$	15.3948	+	5.60325i	1.51689	+	0.552104i	0.960370	−	0.278727i	$-0.0899125\pi$
$103$	15.3948	+	5.60325i	1.51689	+	0.552104i	0.556524	+	0.830832i	$0.312135\pi$
$104$		0			0
$105$	2.10715	−	9.08264i	0.205636	−	0.886375i
$106$		0			0
$107$	12.6244			1.22044			0.610222	−	0.792230i	$-0.291080\pi$
$107$	12.6244			1.22044			0.610222	+	0.792230i	$0.291080\pi$
$108$		0			0
$109$	15.1876			1.45471			0.727353	−	0.686263i	$-0.240750\pi$
$109$	15.1876			1.45471			0.727353	+	0.686263i	$0.240750\pi$
$110$		0			0
$111$	−11.2166	−	10.4821i	−1.06463	−	0.994917i
$112$		0			0
$113$	−14.2429	−	5.18398i	−1.33986	−	0.487668i	−0.430089	−	0.902787i	$-0.641518\pi$
$113$	−14.2429	−	5.18398i	−1.33986	−	0.487668i	−0.909767	+	0.415119i	$0.863740\pi$
$114$		0			0
$115$	−1.35898	+	7.70718i	−0.126726	+	0.718698i
$116$		0			0
$117$	−2.20027	+	7.61165i	−0.203415	+	0.703697i
$118$		0			0
$119$	−8.85740	+	3.22383i	−0.811957	+	0.295528i
$120$		0			0
$121$	−0.811607	+	0.681019i	−0.0737825	+	0.0619109i
$122$		0			0
$123$	4.04078	−	6.20769i	0.364345	−	0.559728i
$124$		0			0
$125$	−6.07902	−	10.5292i	−0.543724	−	0.941758i
$126$		0			0
$127$	7.31109	−	12.6632i	0.648754	−	1.12368i	−0.334666	−	0.942337i	$-0.608624\pi$
$127$	7.31109	−	12.6632i	0.648754	−	1.12368i	0.983421	−	0.181339i	$-0.0580431\pi$
$128$		0			0
$129$	9.01539	−	6.77845i	0.793761	−	0.596809i
$130$		0			0
$131$	−1.17232	−	6.64859i	−0.102427	−	0.580890i	−0.992217	−	0.124520i	$-0.960261\pi$
$131$	−1.17232	−	6.64859i	−0.102427	−	0.580890i	0.889791	−	0.456369i	$-0.150850\pi$
$132$		0			0
$133$	10.0155	+	8.40402i	0.868456	+	0.728721i
$134$		0			0
$135$	−8.36860	+	4.99182i	−0.720254	+	0.429627i
$136$		0			0
$137$	−8.04070	−	6.74695i	−0.686963	−	0.576431i	0.231068	−	0.972938i	$-0.425778\pi$
$137$	−8.04070	−	6.74695i	−0.686963	−	0.576431i	−0.918032	+	0.396507i	$0.870222\pi$
$138$		0			0
$139$	−1.50325	−	8.52534i	−0.127504	−	0.723110i	−0.979789	−	0.200033i	$-0.935895\pi$
$139$	−1.50325	−	8.52534i	−0.127504	−	0.723110i	0.852285	−	0.523077i	$-0.175216\pi$
$140$		0			0
$141$	1.05184	+	8.64310i	0.0885808	+	0.727880i
$142$		0			0
$143$	4.16350	−	7.21139i	0.348169	−	0.603047i
$144$		0			0
$145$	−8.43320	−	14.6067i	−0.700339	−	1.21302i
$146$		0			0
$147$	2.14482	+	0.114710i	0.176902	+	0.00946113i
$148$		0			0
$149$	5.21955	−	4.37972i	0.427602	−	0.358801i	−0.403444	−	0.915004i	$-0.632187\pi$
$149$	5.21955	−	4.37972i	0.427602	−	0.358801i	0.831046	+	0.556204i	$0.187743\pi$
$150$		0			0
$151$	1.14684	−	0.417416i	0.0933286	−	0.0339688i	−0.294934	−	0.955518i	$-0.595298\pi$
$151$	1.14684	−	0.417416i	0.0933286	−	0.0339688i	0.388262	+	0.921549i	$0.373075\pi$
$152$		0			0
$153$	8.84466	+	4.33732i	0.715048	+	0.350651i
$154$		0			0
$155$	−0.0906286	+	0.513981i	−0.00727947	+	0.0412839i
$156$		0			0
$157$	16.7226	+	6.08654i	1.33461	+	0.485759i	0.908111	−	0.418729i	$-0.137524\pi$
$157$	16.7226	+	6.08654i	1.33461	+	0.485759i	0.426500	+	0.904488i	$0.359747\pi$
$158$		0			0
$159$	11.9374	−	3.63566i	0.946700	−	0.288326i
$160$		0			0
$161$	−11.9795			−0.944121
$162$		0			0
$163$	20.7748			1.62721			0.813603	−	0.581420i	$-0.197503\pi$
$163$	20.7748			1.62721			0.813603	+	0.581420i	$0.197503\pi$
$164$		0			0
$165$	9.79655	−	2.98363i	0.762660	−	0.232275i
$166$		0			0
$167$	10.8111	+	3.93492i	0.836588	+	0.304493i	0.724560	−	0.689212i	$-0.242043\pi$
$167$	10.8111	+	3.93492i	0.836588	+	0.304493i	0.112028	+	0.993705i	$0.464265\pi$
$168$		0			0
$169$	−1.04617	+	5.93310i	−0.0804743	+	0.456392i
$170$		0			0
$171$	−0.923932	−	13.6326i	−0.0706549	−	1.04251i
$172$		0			0
$173$	11.6809	−	4.25149i	0.888081	−	0.323235i	0.142615	−	0.989778i	$-0.454449\pi$
$173$	11.6809	−	4.25149i	0.888081	−	0.323235i	0.745466	+	0.666543i	$0.232227\pi$
$174$		0			0
$175$	3.26167	−	2.73687i	0.246559	−	0.206888i
$176$		0			0
$177$	12.4620	+	0.666495i	0.936698	+	0.0500968i
$178$		0			0
$179$	11.3566	+	19.6702i	0.848831	+	1.47022i	0.882252	+	0.470778i	$0.156027\pi$
$179$	11.3566	+	19.6702i	0.848831	+	1.47022i	−0.0334206	+	0.999441i	$0.510640\pi$
$180$		0			0
$181$	−7.46651	+	12.9324i	−0.554981	+	0.961256i	0.442924	+	0.896559i	$0.353941\pi$
$181$	−7.46651	+	12.9324i	−0.554981	+	0.961256i	−0.997905	+	0.0646966i	$0.979392\pi$
$182$		0			0
$183$	−1.39809	−	11.4883i	−0.103350	−	0.849237i
$184$		0			0
$185$	2.88633	+	16.3692i	0.212207	+	1.20349i
$186$		0			0
$187$	−7.93073	−	6.65467i	−0.579952	−	0.486638i
$188$		0			0
$189$	−9.74943	−	11.2885i	−0.709167	−	0.821119i
$190$		0			0
$191$	−4.13318	−	3.46815i	−0.299066	−	0.250947i	0.480889	−	0.876781i	$-0.340314\pi$
$191$	−4.13318	−	3.46815i	−0.299066	−	0.250947i	−0.779956	+	0.625835i	$0.784758\pi$
$192$		0			0
$193$	3.10571	+	17.6134i	0.223554	+	1.26784i	0.865430	+	0.501030i	$0.167045\pi$
$193$	3.10571	+	17.6134i	0.223554	+	1.26784i	−0.641876	+	0.766809i	$0.721843\pi$
$194$		0			0
$195$	6.85666	−	5.15535i	0.491016	−	0.369183i
$196$		0			0
$197$	2.98993	−	5.17871i	0.213023	−	0.368968i	−0.739636	−	0.673007i	$-0.765002\pi$
$197$	2.98993	−	5.17871i	0.213023	−	0.368968i	0.952659	+	0.304040i	$0.0983356\pi$
$198$		0			0
$199$	−5.89435	−	10.2093i	−0.417839	−	0.723719i	0.577883	−	0.816120i	$-0.303879\pi$
$199$	−5.89435	−	10.2093i	−0.417839	−	0.723719i	−0.995722	+	0.0924010i	$0.970546\pi$
$200$		0			0
$201$	12.2418	−	18.8066i	0.863473	−	1.32652i
$202$		0			0
$203$	19.7776	−	16.5953i	1.38811	−	1.16476i
$204$		0			0
$205$	−7.53591	+	2.74285i	−0.526331	+	0.191569i
$206$		0			0
$207$	8.67763	+	9.02458i	0.603137	+	0.627252i
$208$		0			0
$209$	−2.49361	+	14.1420i	−0.172487	+	0.978221i
$210$		0			0
$211$	23.7022	+	8.62688i	1.63172	+	0.593899i	0.985564	−	0.169303i	$-0.0541517\pi$
$211$	23.7022	+	8.62688i	1.63172	+	0.593899i	0.646160	+	0.763202i	$0.276374\pi$
$212$		0			0
$213$	−10.7519	−	10.0479i	−0.736708	−	0.688468i
$214$		0			0
$215$	−12.2122			−0.832866
$216$		0			0
$217$	−0.798898			−0.0542328
$218$		0			0
$219$	4.17019	−	17.9752i	0.281795	−	1.21465i
$220$		0			0
$221$	−8.14937	−	2.96613i	−0.548186	−	0.199523i
$222$		0			0
$223$	0.835391	−	4.73774i	0.0559419	−	0.317262i	−0.943977	−	0.330012i	$-0.892947\pi$
$223$	0.835391	−	4.73774i	0.0559419	−	0.317262i	0.999919	+	0.0127494i	$0.00405836\pi$
$224$		0			0
$225$	−4.42443	−	0.474616i	−0.294962	−	0.0316410i
$226$		0			0
$227$	4.22216	−	1.53674i	0.280235	−	0.101997i	−0.198079	−	0.980186i	$-0.563470\pi$
$227$	4.22216	−	1.53674i	0.280235	−	0.101997i	0.478314	+	0.878189i	$0.341248\pi$
$228$		0			0
$229$	−2.72144	+	2.28356i	−0.179838	+	0.150902i	−0.728263	−	0.685298i	$-0.759672\pi$
$229$	−2.72144	+	2.28356i	−0.179838	+	0.150902i	0.548425	+	0.836200i	$0.315228\pi$
$230$		0			0
$231$	7.10171	+	13.9749i	0.467259	+	0.919481i
$232$		0			0
$233$	−1.49539	−	2.59009i	−0.0979661	−	0.169682i	0.812877	−	0.582436i	$-0.197900\pi$
$233$	−1.49539	−	2.59009i	−0.0979661	−	0.169682i	−0.910843	+	0.412754i	$0.864567\pi$
$234$		0			0
$235$	4.71347	−	8.16397i	0.307473	−	0.532559i
$236$		0			0
$237$	−4.35961	−	1.85606i	−0.283187	−	0.120564i
$238$		0			0
$239$	−0.947732	−	5.37486i	−0.0613037	−	0.347671i	−0.999996	−	0.00291385i	$-0.999072\pi$
$239$	−0.947732	−	5.37486i	−0.0613037	−	0.347671i	0.938692	−	0.344757i	$-0.112039\pi$
$240$		0			0
$241$	−6.73892	−	5.65462i	−0.434092	−	0.364246i	0.399401	−	0.916776i	$-0.369218\pi$
$241$	−6.73892	−	5.65462i	−0.434092	−	0.364246i	−0.833493	+	0.552530i	$0.813663\pi$
$242$		0			0
$243$	−1.44181	+	15.5216i	−0.0924919	+	0.995713i
$244$		0			0
$245$	−1.78145	−	1.49482i	−0.113813	−	0.0955003i
$246$		0			0
$247$	2.08885	+	11.8465i	0.132911	+	0.753773i
$248$		0			0
$249$	19.7845	+	8.42304i	1.25379	+	0.533788i
$250$		0			0
$251$	−15.6072	+	27.0324i	−0.985117	+	1.70627i	−0.343700	+	0.939080i	$0.611680\pi$
$251$	−15.6072	+	27.0324i	−0.985117	+	1.70627i	−0.641417	+	0.767192i	$0.721653\pi$
$252$		0			0
$253$	−6.57884	−	11.3949i	−0.413608	−	0.716390i
$254$		0			0
$255$	−4.83189	−	9.50829i	−0.302585	−	0.595432i
$256$		0			0
$257$	−7.85231	+	6.58887i	−0.489814	+	0.411003i	−0.853960	−	0.520339i	$-0.825805\pi$
$257$	−7.85231	+	6.58887i	−0.489814	+	0.411003i	0.364146	+	0.931342i	$0.381361\pi$
$258$		0			0
$259$	−23.9088	+	8.70209i	−1.48562	+	0.540722i
$260$		0			0
$261$	−26.8281	−	2.87789i	−1.66062	−	0.178137i
$262$		0			0
$263$	−2.80160	+	15.8887i	−0.172754	+	0.979737i	0.767950	+	0.640509i	$0.221277\pi$
$263$	−2.80160	+	15.8887i	−0.172754	+	0.979737i	−0.940704	+	0.339227i	$0.889834\pi$
$264$		0			0
$265$	−12.6960	−	4.62097i	−0.779910	−	0.283864i
$266$		0			0
$267$	1.56862	−	6.76136i	0.0959977	−	0.413788i
$268$		0			0
$269$	12.8018			0.780540			0.390270	−	0.920700i	$-0.372382\pi$
$269$	12.8018			0.780540			0.390270	+	0.920700i	$0.372382\pi$
$270$		0			0
$271$	−16.4628			−1.00005			−0.500023	−	0.866012i	$-0.666675\pi$
$271$	−16.4628			−1.00005			−0.500023	+	0.866012i	$0.666675\pi$
$272$		0			0
$273$	9.59408	+	8.96586i	0.580660	+	0.542639i
$274$		0			0
$275$	4.39452	+	1.59947i	0.264999	+	0.0964519i
$276$		0			0
$277$	−1.18947	+	6.74581i	−0.0714682	+	0.405317i	0.927996	+	0.372590i	$0.121530\pi$
$277$	−1.18947	+	6.74581i	−0.0714682	+	0.405317i	−0.999464	+	0.0327266i	$0.989581\pi$
$278$		0			0
$279$	0.578699	+	0.601836i	0.0346458	+	0.0360310i
$280$		0			0
$281$	4.53096	−	1.64913i	0.270294	−	0.0983791i	−0.203317	−	0.979113i	$-0.565172\pi$
$281$	4.53096	−	1.64913i	0.270294	−	0.0983791i	0.473612	+	0.880734i	$0.342950\pi$
$282$		0			0
$283$	17.2075	−	14.4388i	1.02288	−	0.858300i	0.0328947	−	0.999459i	$-0.489527\pi$
$283$	17.2075	−	14.4388i	1.02288	−	0.858300i	0.989987	+	0.141159i	$0.0450829\pi$
$284$		0			0
$285$	−8.07065	+	12.3986i	−0.478064	+	0.734430i
$286$		0			0
$287$	−6.13785	−	10.6311i	−0.362306	−	0.627532i
$288$		0			0
$289$	3.10888	−	5.38473i	0.182875	−	0.316749i
$290$		0			0
$291$	−15.0563	+	11.3205i	−0.882617	+	0.663618i
$292$		0			0
$293$	−0.884736	−	5.01759i	−0.0516868	−	0.293131i	0.947997	−	0.318280i	$-0.103105\pi$
$293$	−0.884736	−	5.01759i	−0.0516868	−	0.293131i	−0.999684	+	0.0251490i	$0.991994\pi$
$294$		0			0
$295$	−10.3507	−	8.68526i	−0.602641	−	0.505675i
$296$		0			0
$297$	5.38347	−	15.4730i	0.312380	−	0.897832i
$298$		0			0
$299$	−8.44330	−	7.08477i	−0.488289	−	0.409723i
$300$		0			0
$301$	−3.24609	−	18.4095i	−0.187102	−	1.06111i
$302$		0			0
$303$	−1.25260	−	10.2928i	−0.0719601	−	0.591306i
$304$		0			0
$305$	−6.26507	+	10.8514i	−0.358737	+	0.621350i
$306$		0			0
$307$	−7.98049	−	13.8226i	−0.455471	−	0.788898i	0.543245	−	0.839574i	$-0.317196\pi$
$307$	−7.98049	−	13.8226i	−0.455471	−	0.788898i	−0.998715	+	0.0506764i	$0.983862\pi$
$308$		0			0
$309$	−28.3353	−	1.51544i	−1.61194	−	0.0862104i
$310$		0			0
$311$	22.2810	−	18.6960i	1.26344	−	1.06015i	0.268131	−	0.963382i	$-0.413594\pi$
$311$	22.2810	−	18.6960i	1.26344	−	1.06015i	0.995307	−	0.0967680i	$-0.0308505\pi$
$312$		0			0
$313$	−29.9509	+	10.9012i	−1.69293	+	0.616174i	−0.994989	−	0.0999852i	$-0.968120\pi$
$313$	−29.9509	+	10.9012i	−1.69293	+	0.616174i	−0.697936	+	0.716160i	$0.745898\pi$
$314$		0			0
$315$	1.09200	+	16.1124i	0.0615270	+	0.907833i
$316$		0			0
$317$	−1.12082	+	6.35648i	−0.0629514	+	0.357015i	0.937019	+	0.349279i	$0.113574\pi$
$317$	−1.12082	+	6.35648i	−0.0629514	+	0.357015i	−0.999970	+	0.00773594i	$0.997538\pi$
$318$		0			0
$319$	26.6467	+	9.69861i	1.49193	+	0.543018i
$320$		0			0
$321$	−20.9174	+	6.37060i	−1.16750	+	0.355572i
$322$		0			0
$323$	14.9558			0.832161
$324$		0			0
$325$	3.91746			0.217301
$326$		0			0
$327$	−25.1645	+	7.66407i	−1.39160	+	0.423824i
$328$		0			0
$329$	13.5598	+	4.93536i	0.747575	+	0.272095i
$330$		0			0
$331$	−3.95150	+	22.4101i	−0.217194	+	1.23177i	0.659864	+	0.751385i	$0.270614\pi$
$331$	−3.95150	+	22.4101i	−0.217194	+	1.23177i	−0.877058	+	0.480384i	$0.840497\pi$
$332$		0			0
$333$	23.8744	+	11.7077i	1.30831	+	0.641579i
$334$		0			0
$335$	−22.8306	+	8.30965i	−1.24737	+	0.454005i
$336$		0			0
$337$	18.4178	−	15.4544i	1.00328	−	0.841854i	0.0158470	−	0.999874i	$-0.494956\pi$
$337$	18.4178	−	15.4544i	1.00328	−	0.841854i	0.987436	+	0.158020i	$0.0505111\pi$
$338$		0			0
$339$	26.2151	+	1.40205i	1.42381	+	0.0761487i
$340$		0			0
$341$	−0.438733	−	0.759908i	−0.0237587	−	0.0411513i
$342$		0			0
$343$	−8.26708	+	14.3190i	−0.446380	+	0.773153i
$344$		0			0
$345$	−1.63754	−	13.4559i	−0.0881622	−	0.724441i
$346$		0			0
$347$	−5.24592	−	29.7511i	−0.281616	−	1.59712i	−0.717129	−	0.696941i	$-0.754544\pi$
$347$	−5.24592	−	29.7511i	−0.281616	−	1.59712i	0.435513	−	0.900182i	$-0.356567\pi$
$348$		0			0
$349$	7.69736	+	6.45885i	0.412030	+	0.345734i	0.825122	−	0.564955i	$-0.191107\pi$
$349$	7.69736	+	6.45885i	0.412030	+	0.345734i	−0.413091	+	0.910690i	$0.635551\pi$
$350$		0			0
$351$	−0.195397	−	13.7221i	−0.0104295	−	0.732433i
$352$		0			0
$353$	12.6507	+	10.6152i	0.673331	+	0.564992i	0.914049	−	0.405603i	$-0.132939\pi$
$353$	12.6507	+	10.6152i	0.673331	+	0.564992i	−0.240718	+	0.970595i	$0.577383\pi$
$354$		0			0
$355$	2.76676	+	15.6911i	0.146844	+	0.832795i
$356$		0			0
$357$	13.0491	−	9.81128i	0.690631	−	0.519268i
$358$		0			0
$359$	−2.23696	+	3.87454i	−0.118062	+	0.204490i	−0.919000	−	0.394258i	$-0.871002\pi$
$359$	−2.23696	+	3.87454i	−0.118062	+	0.204490i	0.800937	+	0.598748i	$0.204335\pi$
$360$		0			0
$361$	−0.872371	−	1.51099i	−0.0459143	−	0.0795258i
$362$		0			0
$363$	1.00110	−	1.53795i	0.0525441	−	0.0807213i
$364$		0			0
$365$	−15.3045	+	12.8420i	−0.801075	+	0.672182i
$366$		0			0
$367$	−28.8800	+	10.5115i	−1.50753	+	0.548695i	−0.957996	−	0.286780i	$-0.907415\pi$
$367$	−28.8800	+	10.5115i	−1.50753	+	0.548695i	−0.549529	+	0.835474i	$0.685193\pi$
$368$		0			0
$369$	−3.56264	+	12.3247i	−0.185464	+	0.641597i
$370$		0			0
$371$	3.59127	−	20.3671i	0.186449	−	1.05741i
$372$		0			0
$373$	6.38058	+	2.32234i	0.330374	+	0.120246i	0.501881	−	0.864937i	$-0.332641\pi$
$373$	6.38058	+	2.32234i	0.330374	+	0.120246i	−0.171507	+	0.985183i	$0.554864\pi$
$374$		0			0
$375$	15.3857	+	14.3783i	0.794514	+	0.742490i
$376$		0			0
$377$	23.7540			1.22339
$378$		0			0
$379$	19.4404			0.998588			0.499294	−	0.866433i	$-0.333593\pi$
$379$	19.4404			0.998588			0.499294	+	0.866433i	$0.333593\pi$
$380$		0			0
$381$	−5.72363	+	24.6711i	−0.293231	+	1.26394i
$382$		0			0
$383$	28.2718	+	10.2901i	1.44462	+	0.525800i	0.941084	−	0.338173i	$-0.109809\pi$
$383$	28.2718	+	10.2901i	1.44462	+	0.525800i	0.503539	+	0.863972i	$0.332031\pi$
$384$		0			0
$385$	2.94720	−	16.7144i	0.150203	−	0.851846i
$386$		0			0
$387$	−11.5171	+	15.7807i	−0.585447	+	0.802178i
$388$		0			0
$389$	26.3870	−	9.60407i	1.33787	−	0.486946i	0.428730	−	0.903433i	$-0.358961\pi$
$389$	26.3870	−	9.60407i	1.33787	−	0.486946i	0.909142	+	0.416487i	$0.136739\pi$
$390$		0			0
$391$	−10.4974	+	8.80840i	−0.530878	+	0.445460i
$392$		0			0
$393$	5.29750	+	10.4245i	0.267223	+	0.525847i
$394$		0			0
$395$	2.56507	+	4.44282i	0.129062	+	0.223543i
$396$		0			0
$397$	−11.9594	+	20.7143i	−0.600225	+	1.03962i	0.392561	+	0.919726i	$0.371589\pi$
$397$	−11.9594	+	20.7143i	−0.600225	+	1.03962i	−0.992787	+	0.119895i	$0.961744\pi$
$398$		0			0
$399$	−20.8357	−	8.87060i	−1.04309	−	0.444086i
$400$		0			0
$401$	−1.96017	−	11.1167i	−0.0978862	−	0.555140i	−0.993825	−	0.110962i	$-0.964607\pi$
$401$	−1.96017	−	11.1167i	−0.0978862	−	0.555140i	0.895939	−	0.444178i	$-0.146504\pi$
$402$		0			0
$403$	−0.563071	−	0.472473i	−0.0280486	−	0.0235356i
$404$		0			0
$405$	11.3470	−	12.4940i	0.563837	−	0.620833i
$406$		0			0
$407$	−21.4074	−	17.9630i	−1.06113	−	0.890391i
$408$		0			0
$409$	−4.83306	−	27.4097i	−0.238980	−	1.35532i	−0.834069	−	0.551661i	$-0.813994\pi$
$409$	−4.83306	−	27.4097i	−0.238980	−	1.35532i	0.595089	−	0.803660i	$-0.297117\pi$
$410$		0			0
$411$	16.7274	+	7.12153i	0.825103	+	0.351279i
$412$		0			0
$413$	10.3415	−	17.9119i	0.508870	−	0.881389i
$414$		0			0
$415$	−11.6406	−	20.1621i	−0.571414	−	0.989718i
$416$		0			0
$417$	6.79287	+	13.3671i	0.332648	+	0.654592i
$418$		0			0
$419$	−26.1586	+	21.9496i	−1.27793	+	1.07231i	−0.284403	+	0.958705i	$0.591795\pi$
$419$	−26.1586	+	21.9496i	−1.27793	+	1.07231i	−0.993526	+	0.113605i	$0.963760\pi$
$420$		0			0
$421$	22.8149	−	8.30395i	1.11193	−	0.404710i	0.280230	−	0.959933i	$-0.409589\pi$
$421$	22.8149	−	8.30395i	1.11193	−	0.404710i	0.831702	+	0.555223i	$0.187367\pi$
$422$		0			0
$423$	−6.10435	−	13.7901i	−0.296804	−	0.670495i
$424$		0			0
$425$	0.845757	−	4.79653i	0.0410252	−	0.232666i
$426$		0			0
$427$	−18.0234	−	6.56000i	−0.872216	−	0.317461i
$428$		0			0
$429$	−3.25948	+	14.0496i	−0.157369	+	0.678323i
$430$		0			0
$431$	−20.5003			−0.987463			−0.493732	−	0.869614i	$-0.664367\pi$
$431$	−20.5003			−0.987463			−0.493732	+	0.869614i	$0.664367\pi$
$432$		0			0
$433$	28.3215			1.36104			0.680522	−	0.732728i	$-0.261753\pi$
$433$	28.3215			1.36104			0.680522	+	0.732728i	$0.261753\pi$
$434$		0			0
$435$	21.3440	+	19.9464i	1.02337	+	0.956358i
$436$		0			0
$437$	17.8614	+	6.50100i	0.854425	+	0.310985i
$438$		0			0
$439$	1.00142	−	5.67935i	0.0477953	−	0.271061i	−0.951540	−	0.307526i	$-0.900499\pi$
$439$	1.00142	−	5.67935i	0.0477953	−	0.271061i	0.999335	+	0.0364656i	$0.0116100\pi$
$440$		0			0
$441$	−3.61166	+	0.892271i	−0.171984	+	0.0424891i
$442$		0			0
$443$	−11.0242	+	4.01246i	−0.523773	+	0.190638i	−0.590356	−	0.807143i	$-0.701013\pi$
$443$	−11.0242	+	4.01246i	−0.523773	+	0.190638i	0.0665827	+	0.997781i	$0.478790\pi$
$444$		0			0
$445$	−5.75679	+	4.83052i	−0.272898	+	0.228989i
$446$		0			0
$447$	−6.43819	+	9.89073i	−0.304516	+	0.467815i
$448$		0			0
$449$	−0.112620	−	0.195064i	−0.00531487	−	0.00920563i	0.863356	−	0.504596i	$-0.168358\pi$
$449$	−0.112620	−	0.195064i	−0.00531487	−	0.00920563i	−0.868671	+	0.495390i	$0.835025\pi$
$450$		0			0
$451$	6.74147	−	11.6766i	0.317444	−	0.549829i
$452$		0			0
$453$	−1.68957	+	1.27035i	−0.0793830	+	0.0596862i
$454$		0			0
$455$	−2.46882	−	14.0014i	−0.115740	−	0.656394i
$456$		0			0
$457$	−1.25408	−	1.05230i	−0.0586633	−	0.0492244i	0.612985	−	0.790095i	$-0.289969\pi$
$457$	−1.25408	−	1.05230i	−0.0586633	−	0.0492244i	−0.671648	+	0.740870i	$0.734413\pi$
$458$		0			0
$459$	−16.8435	−	2.72329i	−0.786189	−	0.127112i
$460$		0			0
$461$	−26.8434	−	22.5242i	−1.25022	−	1.04906i	−0.996654	−	0.0817406i	$-0.973952\pi$
$461$	−26.8434	−	22.5242i	−1.25022	−	1.04906i	−0.253566	−	0.967318i	$-0.581603\pi$
$462$		0			0
$463$	4.81663	+	27.3165i	0.223848	+	1.26950i	0.864876	+	0.501986i	$0.167397\pi$
$463$	4.81663	+	27.3165i	0.223848	+	1.26950i	−0.641028	+	0.767517i	$0.721492\pi$
$464$		0			0
$465$	−0.109205	−	0.897353i	−0.00506427	−	0.0416138i
$466$		0			0
$467$	−10.6201	+	18.3945i	−0.491438	+	0.851195i	−0.999951	−	0.00985871i	$-0.996862\pi$
$467$	−10.6201	+	18.3945i	−0.491438	+	0.851195i	0.508514	+	0.861054i	$0.330195\pi$
$468$		0			0
$469$	−18.5951	−	32.2076i	−0.858640	−	1.48721i
$470$		0			0
$471$	−30.7793	−	1.64615i	−1.41824	−	0.0758506i
$472$		0			0
$473$	15.7284	−	13.1977i	0.723191	−	0.606829i
$474$		0			0
$475$	−6.34834	+	2.31061i	−0.291282	+	0.106018i
$476$		0			0
$477$	−17.9446	+	12.0479i	−0.821627	+	0.551636i
$478$		0			0
$479$	−5.01584	+	28.4462i	−0.229179	+	1.29974i	0.625353	+	0.780342i	$0.284955\pi$
$479$	−5.01584	+	28.4462i	−0.229179	+	1.29974i	−0.854532	+	0.519399i	$0.826156\pi$
$480$		0			0
$481$	−21.9976	−	8.00648i	−1.00300	−	0.365064i
$482$		0			0
$483$	19.8490	−	6.04521i	0.903162	−	0.275067i
$484$		0			0
$485$	20.3952			0.926099
$486$		0			0
$487$	−30.1531			−1.36637			−0.683184	−	0.730247i	$-0.739405\pi$
$487$	−30.1531			−1.36637			−0.683184	+	0.730247i	$0.739405\pi$
$488$		0			0
$489$	−34.4219	+	10.4835i	−1.55661	+	0.474081i
$490$		0			0
$491$	−1.71008	−	0.622418i	−0.0771748	−	0.0280893i	0.303144	−	0.952945i	$-0.401964\pi$
$491$	−1.71008	−	0.622418i	−0.0771748	−	0.0280893i	−0.380319	+	0.924855i	$0.624186\pi$
$492$		0			0
$493$	5.12835	−	29.0843i	0.230969	−	1.30989i
$494$		0			0
$495$	−14.7264	+	9.88721i	−0.661901	+	0.444397i
$496$		0			0
$497$	−22.9183	+	8.34159i	−1.02803	+	0.374171i
$498$		0			0
$499$	6.59371	−	5.53278i	0.295175	−	0.247681i	−0.483158	−	0.875533i	$-0.660510\pi$
$499$	6.59371	−	5.53278i	0.295175	−	0.247681i	0.778333	+	0.627852i	$0.216066\pi$
$500$		0			0
$501$	−19.8987	−	1.06423i	−0.889008	−	0.0475463i
$502$		0			0
$503$	21.8797	+	37.8968i	0.975570	+	1.68974i	0.678042	+	0.735023i	$0.262829\pi$
$503$	21.8797	+	37.8968i	0.975570	+	1.68974i	0.297528	+	0.954713i	$0.403838\pi$
$504$		0			0
$505$	−5.61312	+	9.72222i	−0.249781	+	0.432633i
$506$		0			0
$507$	−1.26060	−	10.3585i	−0.0559853	−	0.460039i
$508$		0			0
$509$	1.08181	+	6.13527i	0.0479505	+	0.271941i	0.999351	−	0.0360146i	$-0.0114663\pi$
$509$	1.08181	+	6.13527i	0.0479505	+	0.271941i	−0.951401	+	0.307956i	$0.900355\pi$
$510$		0			0
$511$	−23.4270	−	19.6576i	−1.03635	−	0.869599i
$512$		0			0
$513$	8.41028	+	22.1218i	0.371323	+	0.976703i
$514$		0			0
$515$	23.5349	+	19.7481i	1.03707	+	0.870205i
$516$		0			0
$517$	2.75218	+	15.6084i	0.121041	+	0.686455i
$518$		0			0
$519$	−17.2087	+	12.9388i	−0.755380	+	0.567952i
$520$		0			0
$521$	−2.72018	+	4.71149i	−0.119173	+	0.206414i	−0.919440	−	0.393230i	$-0.871358\pi$
$521$	−2.72018	+	4.71149i	−0.119173	+	0.206414i	0.800267	+	0.599644i	$0.204691\pi$
$522$		0			0
$523$	13.1732	+	22.8166i	0.576022	+	0.997699i	0.995930	+	0.0901327i	$0.0287291\pi$
$523$	13.1732	+	22.8166i	0.576022	+	0.997699i	−0.419908	+	0.907567i	$0.637938\pi$
$524$		0			0
$525$	−4.02320	+	6.18067i	−0.175587	+	0.269747i
$526$		0			0
$527$	−0.700059	+	0.587419i	−0.0304950	+	0.0255884i
$528$		0			0
$529$	5.24721	−	1.90983i	0.228139	−	0.0830359i
$530$		0			0
$531$	−20.9847	+	5.18433i	−0.910658	+	0.224981i
$532$		0			0
$533$	1.96126	−	11.1228i	0.0849514	−	0.481783i
$534$		0			0
$535$	22.2467	+	8.09713i	0.961807	+	0.350069i
$536$		0			0
$537$	−28.7430	−	26.8609i	−1.24035	−	1.15913i
$538$		0			0
$539$	3.90981			0.168407
$540$		0			0
$541$	38.3462			1.64863			0.824315	−	0.566131i	$-0.191560\pi$
$541$	38.3462			1.64863			0.824315	+	0.566131i	$0.191560\pi$
$542$		0			0
$543$	5.84531	−	25.1956i	0.250846	−	1.08125i
$544$		0			0
$545$	26.7636	+	9.74114i	1.14642	+	0.417265i
$546$		0			0
$547$	−2.32477	+	13.1844i	−0.0994000	+	0.563726i	0.893910	+	0.448247i	$0.147951\pi$
$547$	−2.32477	+	13.1844i	−0.0994000	+	0.563726i	−0.993310	+	0.115479i	$0.963160\pi$
$548$		0			0
$549$	8.11380	+	18.3295i	0.346289	+	0.782285i
$550$		0			0
$551$	−38.4940	+	14.0107i	−1.63990	+	0.596874i
$552$		0			0
$553$	−6.01560	+	5.04769i	−0.255809	+	0.214649i
$554$		0			0
$555$	−13.0427	−	25.6657i	−0.553633	−	1.08945i
$556$		0			0
$557$	16.8144	+	29.1234i	0.712448	+	1.23400i	0.963936	+	0.266136i	$0.0857470\pi$
$557$	16.8144	+	29.1234i	0.712448	+	1.23400i	−0.251487	+	0.967861i	$0.580920\pi$
$558$		0			0
$559$	8.59961	−	14.8950i	0.363725	−	0.629990i
$560$		0			0
$561$	16.4986	+	7.02413i	0.696573	+	0.296559i
$562$		0			0
$563$	0.647266	+	3.67083i	0.0272790	+	0.154707i	0.995405	−	0.0957582i	$-0.0305276\pi$
$563$	0.647266	+	3.67083i	0.0272790	+	0.154707i	−0.968126	+	0.250465i	$0.919416\pi$
$564$		0			0
$565$	−21.7738	−	18.2704i	−0.916032	−	0.768642i
$566$		0			0
$567$	21.8504	+	13.7842i	0.917632	+	0.578884i
$568$		0			0
$569$	26.5303	+	22.2615i	1.11221	+	0.933252i	0.998185	−	0.0602260i	$-0.0191821\pi$
$569$	26.5303	+	22.2615i	1.11221	+	0.933252i	0.114022	+	0.993478i	$0.463627\pi$
$570$		0			0
$571$	−1.78292	−	10.1114i	−0.0746128	−	0.423150i	−0.999118	−	0.0419817i	$-0.986633\pi$
$571$	−1.78292	−	10.1114i	−0.0746128	−	0.423150i	0.924506	−	0.381169i	$-0.124478\pi$
$572$		0			0
$573$	8.59843	+	3.66070i	0.359205	+	0.152928i
$574$		0			0
$575$	3.09503	−	5.36076i	0.129072	−	0.223559i
$576$		0			0
$577$	−22.9218	−	39.7017i	−0.954246	−	1.65280i	−0.736084	−	0.676890i	$-0.763327\pi$
$577$	−22.9218	−	39.7017i	−0.954246	−	1.65280i	−0.218162	−	0.975913i	$-0.570006\pi$
$578$		0			0
$579$	−14.0341	−	27.6166i	−0.583237	−	1.14770i
$580$		0			0
$581$	27.2995	−	22.9070i	1.13258	−	0.950343i
$582$		0			0
$583$	21.3453	−	7.76906i	0.884033	−	0.321762i
$584$		0			0
$585$	−8.75934	+	12.0020i	−0.362154	+	0.496222i
$586$		0			0
$587$	2.65820	−	15.0754i	0.109715	−	0.622227i	−0.879516	−	0.475869i	$-0.842134\pi$
$587$	2.65820	−	15.0754i	0.109715	−	0.622227i	0.989232	−	0.146358i	$-0.0467552\pi$
$588$		0			0
$589$	1.19115	+	0.433542i	0.0490804	+	0.0178638i
$590$		0			0
$591$	−2.34072	+	10.0894i	−0.0962845	+	0.415024i
$592$		0			0
$593$	−30.5293			−1.25369			−0.626844	−	0.779145i	$-0.715654\pi$
$593$	−30.5293			−1.25369			−0.626844	+	0.779145i	$0.715654\pi$
$594$		0			0
$595$	−17.6762			−0.724655
$596$		0			0
$597$	14.9183	+	13.9415i	0.610566	+	0.570586i
$598$		0			0
$599$	−0.734445	−	0.267316i	−0.0300086	−	0.0109222i	0.326972	−	0.945034i	$-0.393972\pi$
$599$	−0.734445	−	0.267316i	−0.0300086	−	0.0109222i	−0.356981	+	0.934112i	$0.616194\pi$
$600$		0			0
$601$	5.05108	−	28.6461i	0.206038	−	1.16850i	−0.689760	−	0.724038i	$-0.742284\pi$
$601$	5.05108	−	28.6461i	0.206038	−	1.16850i	0.895798	−	0.444461i	$-0.146605\pi$
$602$		0			0
$603$	−10.7933	+	37.3385i	−0.439537	+	1.52054i
$604$		0			0
$605$	−1.86701	+	0.679537i	−0.0759049	+	0.0276271i
$606$		0			0
$607$	13.9906	−	11.7395i	0.567860	−	0.476491i	−0.313075	−	0.949728i	$-0.601359\pi$
$607$	13.9906	−	11.7395i	0.567860	−	0.476491i	0.880935	+	0.473237i	$0.156915\pi$
$608$		0			0
$609$	−24.3952	+	37.4773i	−0.988542	+	1.51866i
$610$		0			0
$611$	6.63827	+	11.4978i	0.268556	+	0.465152i
$612$		0			0
$613$	−8.12291	+	14.0693i	−0.328081	+	0.568254i	−0.982131	−	0.188198i	$-0.939735\pi$
$613$	−8.12291	+	14.0693i	−0.328081	+	0.568254i	0.654050	+	0.756452i	$0.273069\pi$
$614$		0			0
$615$	11.1022	−	8.34747i	0.447684	−	0.336603i
$616$		0			0
$617$	0.182805	+	1.03674i	0.00735947	+	0.0417376i	0.988266	−	0.152740i	$-0.0488098\pi$
$617$	0.182805	+	1.03674i	0.00735947	+	0.0417376i	−0.980907	+	0.194478i	$0.937699\pi$
$618$		0			0
$619$	17.0456	+	14.3029i	0.685119	+	0.574883i	0.917497	−	0.397742i	$-0.130206\pi$
$619$	17.0456	+	14.3029i	0.685119	+	0.574883i	−0.232378	+	0.972626i	$0.574651\pi$
$620$		0			0
$621$	−18.9321	−	10.5739i	−0.759719	−	0.424318i
$622$		0			0
$623$	−8.81204	−	7.39418i	−0.353047	−	0.296242i
$624$		0			0
$625$	−2.67133	−	15.1498i	−0.106853	−	0.605993i
$626$		0			0
$627$	−3.00474	−	24.6903i	−0.119998	−	0.986037i
$628$		0			0
$629$	−14.5523	+	25.2053i	−0.580237	+	1.00500i
$630$		0			0
$631$	1.80760	+	3.13085i	0.0719594	+	0.124637i	0.899760	−	0.436385i	$-0.143741\pi$
$631$	1.80760	+	3.13085i	0.0719594	+	0.124637i	−0.827801	+	0.561022i	$0.810408\pi$
$632$		0			0
$633$	−43.6257	−	2.33321i	−1.73397	−	0.0927366i
$634$		0			0
$635$	21.0056	−	17.6258i	0.833583	−	0.699459i
$636$		0			0
$637$	3.07766	−	1.12018i	0.121941	−	0.0443830i
$638$		0			0
$639$	22.8854	+	11.2227i	0.905330	+	0.443963i
$640$		0			0
$641$	5.39753	−	30.6109i	0.213190	−	1.20906i	−0.670831	−	0.741611i	$-0.734062\pi$
$641$	5.39753	−	30.6109i	0.213190	−	1.20906i	0.884020	−	0.467448i	$-0.154827\pi$
$642$		0			0
$643$	−21.5267	−	7.83509i	−0.848931	−	0.308986i	−0.119327	−	0.992855i	$-0.538074\pi$
$643$	−21.5267	−	7.83509i	−0.848931	−	0.308986i	−0.729605	+	0.683869i	$0.760296\pi$
$644$		0			0
$645$	20.2345	−	6.16262i	0.796734	−	0.242653i
$646$		0			0
$647$	22.2277			0.873861			0.436931	−	0.899495i	$-0.356066\pi$
$647$	22.2277			0.873861			0.436931	+	0.899495i	$0.356066\pi$
$648$		0			0
$649$	22.7170			0.891719
$650$		0			0
$651$	1.32370	−	0.403146i	0.0518800	−	0.0158005i
$652$		0			0
$653$	−7.89423	−	2.87327i	−0.308925	−	0.112440i	0.182905	−	0.983131i	$-0.441450\pi$
$653$	−7.89423	−	2.87327i	−0.308925	−	0.112440i	−0.491831	+	0.870691i	$0.663672\pi$
$654$		0			0
$655$	2.19845	−	12.4681i	0.0859007	−	0.487167i
$656$		0			0
$657$	2.16114	+	31.8876i	0.0843140	+	1.24406i
$658$		0			0
$659$	13.6616	−	4.97240i	0.532179	−	0.193697i	−0.0619320	−	0.998080i	$-0.519726\pi$
$659$	13.6616	−	4.97240i	0.532179	−	0.193697i	0.594111	+	0.804383i	$0.297504\pi$
$660$		0			0
$661$	−23.5466	+	19.7580i	−0.915859	+	0.768497i	−0.973224	−	0.229857i	$-0.926174\pi$
$661$	−23.5466	+	19.7580i	−0.915859	+	0.768497i	0.0573660	+	0.998353i	$0.481730\pi$
$662$		0			0
$663$	14.9996	+	0.802212i	0.582535	+	0.0311553i
$664$		0			0
$665$	12.2591	+	21.2334i	0.475388	+	0.823397i
$666$		0			0
$667$	18.7671	−	32.5056i	0.726666	−	1.25862i
$668$		0			0
$669$	1.00663	+	8.27157i	0.0389184	+	0.319797i
$670$		0			0
$671$	−3.65815	−	20.7464i	−0.141221	−	0.800905i
$672$		0			0
$673$	−3.56170	−	2.98862i	−0.137294	−	0.115203i	0.571555	−	0.820564i	$-0.306340\pi$
$673$	−3.56170	−	2.98862i	−0.137294	−	0.115203i	−0.708848	+	0.705361i	$0.750785\pi$
$674$		0			0
$675$	7.57039	−	1.44629i	0.291384	−	0.0556679i
$676$		0			0
$677$	17.4011	+	14.6013i	0.668779	+	0.561172i	0.912704	−	0.408622i	$-0.133991\pi$
$677$	17.4011	+	14.6013i	0.668779	+	0.561172i	−0.243925	+	0.969794i	$0.578435\pi$
$678$		0			0
$679$	5.42120	+	30.7451i	0.208046	+	1.17989i
$680$		0			0
$681$	−6.22026	+	4.67686i	−0.238361	+	0.179218i
$682$		0			0
$683$	−1.55639	+	2.69575i	−0.0595536	+	0.103150i	−0.894265	−	0.447538i	$-0.852301\pi$
$683$	−1.55639	+	2.69575i	−0.0595536	+	0.103150i	0.834711	+	0.550688i	$0.185634\pi$
$684$		0			0
$685$	−9.84191	−	17.0467i	−0.376040	−	0.651320i
$686$		0			0
$687$	3.35683	−	5.15696i	0.128071	−	0.196750i
$688$		0			0
$689$	14.5764	−	12.2310i	0.555316	−	0.465966i
$690$		0			0
$691$	−22.1896	+	8.07635i	−0.844132	+	0.307239i	−0.727646	−	0.685953i	$-0.759385\pi$
$691$	−22.1896	+	8.07635i	−0.844132	+	0.307239i	−0.116486	+	0.993192i	$0.537163\pi$
$692$		0			0
$693$	−18.8190	−	19.5714i	−0.714875	−	0.743457i
$694$		0			0
$695$	2.81903	−	15.9875i	0.106932	−	0.606441i
$696$		0			0
$697$	−13.1953	−	4.80271i	−0.499809	−	0.181916i
$698$		0			0
$699$	3.78475	+	3.53693i	0.143152	+	0.133779i
$700$		0			0
$701$	−28.7981			−1.08769			−0.543845	−	0.839186i	$-0.683032\pi$
$701$	−28.7981			−1.08769			−0.543845	+	0.839186i	$0.683032\pi$
$702$		0			0
$703$	40.3701			1.52259
$704$		0			0
$705$	−3.69003	+	15.9055i	−0.138975	+	0.599036i
$706$		0			0
$707$	−16.1479	−	5.87737i	−0.607305	−	0.221041i
$708$		0			0
$709$	−1.45519	+	8.25280i	−0.0546509	+	0.309941i	−0.999864	−	0.0165145i	$-0.994743\pi$
$709$	−1.45519	+	8.25280i	−0.0546509	+	0.309941i	0.945213	+	0.326455i	$0.105854\pi$
$710$		0			0
$711$	8.16011	+	0.875347i	0.306028	+	0.0328281i
$712$		0			0
$713$	−1.09141	+	0.397239i	−0.0408735	+	0.0148767i
$714$		0			0
$715$	11.9622	−	10.0375i	0.447362	−	0.375381i
$716$		0			0
$717$	4.28261	+	8.42740i	0.159937	+	0.314727i
$718$		0			0
$719$	−16.6094	−	28.7684i	−0.619427	−	1.07288i	−0.989590	−	0.143913i	$-0.954032\pi$
$719$	−16.6094	−	28.7684i	−0.619427	−	1.07288i	0.370163	−	0.928967i	$-0.379302\pi$
$720$		0			0
$721$	−23.5139	+	40.7272i	−0.875702	+	1.51676i
$722$		0			0
$723$	14.0193	+	5.96856i	0.521382	+	0.221973i
$724$		0			0
$725$	2.31656	+	13.1379i	0.0860350	+	0.487928i
$726$		0			0
$727$	15.5839	+	13.0764i	0.577974	+	0.484978i	0.884281	−	0.466955i	$-0.154649\pi$
$727$	15.5839	+	13.0764i	0.577974	+	0.484978i	−0.306307	+	0.951933i	$0.599093\pi$
$728$		0			0
$729$	−5.44370	−	26.4455i	−0.201619	−	0.979464i
$730$		0			0
$731$	−16.3807	−	13.7451i	−0.605864	−	0.508380i
$732$		0			0
$733$	−4.08812	−	23.1849i	−0.150998	−	0.856354i	−0.962354	−	0.271801i	$-0.912381\pi$
$733$	−4.08812	−	23.1849i	−0.150998	−	0.856354i	0.811355	−	0.584553i	$-0.198730\pi$
$734$		0			0
$735$	3.70603	+	1.57781i	0.136699	+	0.0581982i
$736$		0			0
$737$	20.4238	−	35.3750i	0.752320	−	1.30306i
$738$		0			0
$739$	−5.80464	−	10.0539i	−0.213527	−	0.369840i	0.739289	−	0.673388i	$-0.235162\pi$
$739$	−5.80464	−	10.0539i	−0.213527	−	0.369840i	−0.952816	+	0.303549i	$0.901829\pi$
$740$		0			0
$741$	−9.43910	−	18.5745i	−0.346754	−	0.682350i
$742$		0			0
$743$	7.71959	−	6.47750i	0.283204	−	0.237637i	−0.490108	−	0.871661i	$-0.663043\pi$
$743$	7.71959	−	6.47750i	0.283204	−	0.237637i	0.773313	+	0.634025i	$0.218598\pi$
$744$		0			0
$745$	12.0070	−	4.37019i	0.439902	−	0.160111i
$746$		0			0
$747$	−37.0316	−	3.97243i	−1.35491	−	0.145344i
$748$		0			0
$749$	−6.29283	+	35.6884i	−0.229935	+	1.30403i
$750$		0			0
$751$	−38.5171	−	14.0191i	−1.40551	−	0.511563i	−0.475700	−	0.879608i	$-0.657805\pi$
$751$	−38.5171	−	14.0191i	−1.40551	−	0.511563i	−0.929808	+	0.368045i	$0.880027\pi$
$752$		0			0
$753$	12.2184	−	52.6661i	0.445263	−	1.91926i
$754$		0			0
$755$	2.28869			0.0832939
$756$		0			0
$757$	−18.2157			−0.662062			−0.331031	−	0.943620i	$-0.607396\pi$
$757$	−18.2157			−0.662062			−0.331031	+	0.943620i	$0.607396\pi$
$758$		0			0
$759$	16.6507	+	15.5604i	0.604383	+	0.564808i
$760$		0			0
$761$	1.57995	+	0.575056i	0.0572733	+	0.0208458i	0.370498	−	0.928833i	$-0.379187\pi$
$761$	1.57995	+	0.575056i	0.0572733	+	0.0208458i	−0.313225	+	0.949679i	$0.601409\pi$
$762$		0			0
$763$	−7.57050	+	42.9344i	−0.274071	+	1.55433i
$764$		0			0
$765$	12.8041	+	13.3161i	0.462935	+	0.481444i
$766$		0			0
$767$	17.8820	−	6.50851i	0.645681	−	0.235009i
$768$		0			0
$769$	7.41588	−	6.22267i	0.267424	−	0.224395i	−0.499208	−	0.866482i	$-0.666376\pi$
$769$	7.41588	−	6.22267i	0.267424	−	0.224395i	0.766632	+	0.642087i	$0.221931\pi$
$770$		0			0
$771$	9.68565	−	14.8797i	0.348820	−	0.535878i
$772$		0			0
$773$	3.26001	+	5.64651i	0.117254	+	0.203091i	0.918679	−	0.395006i	$-0.129257\pi$
$773$	3.26001	+	5.64651i	0.117254	+	0.203091i	−0.801424	+	0.598096i	$0.795924\pi$
$774$		0			0
$775$	0.206403	−	0.357501i	0.00741422	−	0.0128418i
$776$		0			0
$777$	35.2234	−	26.4836i	1.26363	−	0.950094i
$778$		0			0
$779$	3.38224	+	19.1816i	0.121181	+	0.687254i
$780$		0			0
$781$	−20.5206	−	17.2188i	−0.734285	−	0.616138i
$782$		0			0
$783$	45.9040	−	8.76979i	1.64048	−	0.313407i
$784$		0			0
$785$	25.5648	+	21.4514i	0.912446	+	0.765633i
$786$		0			0
$787$	−1.94641	−	11.0387i	−0.0693821	−	0.393486i	−0.999646	−	0.0265952i	$-0.991533\pi$
$787$	−1.94641	−	11.0387i	−0.0693821	−	0.393486i	0.930264	−	0.366890i	$-0.119578\pi$
$788$		0			0
$789$	−3.37586	−	27.7398i	−0.120184	−	0.987565i
$790$		0			0
$791$	21.7544	−	37.6797i	0.773498	−	1.33974i
$792$		0			0
$793$	−8.82348	−	15.2827i	−0.313331	−	0.542705i
$794$		0			0
$795$	23.3680	+	1.24978i	0.828778	+	0.0443250i
$796$		0			0
$797$	11.4196	−	9.58220i	0.404504	−	0.339419i	−0.417728	−	0.908572i	$-0.637173\pi$
$797$	11.4196	−	9.58220i	0.404504	−	0.339419i	0.822231	+	0.569153i	$0.192729\pi$
$798$		0			0
$799$	15.5111	−	5.64557i	0.548742	−	0.199726i
$800$		0			0
$801$	0.812911	+	11.9945i	0.0287228	+	0.423806i
$802$		0			0
$803$	5.83272	−	33.0790i	0.205832	−	1.16733i
$804$		0			0
$805$	−21.1104	−	7.68354i	−0.744043	−	0.270809i
$806$		0			0
$807$	−21.2114	+	6.46014i	−0.746678	+	0.227408i
$808$		0			0
$809$	38.1950			1.34287			0.671433	−	0.741065i	$-0.265679\pi$
$809$	38.1950			1.34287			0.671433	+	0.741065i	$0.265679\pi$
$810$		0			0
$811$	5.73883			0.201518			0.100759	−	0.994911i	$-0.467873\pi$
$811$	5.73883			0.201518			0.100759	+	0.994911i	$0.467873\pi$
$812$		0			0
$813$	27.2774	−	8.30759i	0.956661	−	0.291360i
$814$		0			0
$815$	36.6093	+	13.3247i	1.28237	+	0.466744i
$816$		0			0
$817$	−5.15050	+	29.2099i	−0.180193	+	1.02193i
$818$		0			0
$819$	−20.4209	−	10.0142i	−0.713565	−	0.349924i
$820$		0			0
$821$	32.2467	−	11.7368i	1.12542	−	0.409618i	0.288791	−	0.957392i	$-0.406747\pi$
$821$	32.2467	−	11.7368i	1.12542	−	0.409618i	0.836626	+	0.547774i	$0.184525\pi$
$822$		0			0
$823$	10.9678	−	9.20307i	0.382313	−	0.320799i	−0.431297	−	0.902210i	$-0.641944\pi$
$823$	10.9678	−	9.20307i	0.382313	−	0.320799i	0.813610	+	0.581411i	$0.197499\pi$
$824$		0			0
$825$	−8.08846	−	0.432590i	−0.281604	−	0.0150608i
$826$		0			0
$827$	9.51028	+	16.4723i	0.330705	+	0.572798i	0.982650	−	0.185468i	$-0.0593802\pi$
$827$	9.51028	+	16.4723i	0.330705	+	0.572798i	−0.651945	+	0.758266i	$0.726047\pi$
$828$		0			0
$829$	9.41160	−	16.3014i	0.326878	−	0.566170i	−0.655012	−	0.755618i	$-0.727337\pi$
$829$	9.41160	−	16.3014i	0.326878	−	0.566170i	0.981891	+	0.189448i	$0.0606699\pi$
$830$		0			0
$831$	−1.43328	−	11.7774i	−0.0497199	−	0.408555i
$832$		0			0
$833$	−0.707091	−	4.01011i	−0.0244993	−	0.138942i
$834$		0			0
$835$	16.5275	+	13.8682i	0.571958	+	0.479930i
$836$		0			0
$837$	−1.26255	−	0.705161i	−0.0436403	−	0.0243739i
$838$		0			0
$839$	−0.415959	−	0.349031i	−0.0143605	−	0.0120499i	0.635579	−	0.772036i	$-0.280761\pi$
$839$	−0.415959	−	0.349031i	−0.0143605	−	0.0120499i	−0.649940	+	0.759986i	$0.725206\pi$
$840$		0			0
$841$	9.01097	+	51.1037i	0.310723	+	1.76220i
$842$		0			0
$843$	−6.67519	+	5.01891i	−0.229906	+	0.172861i
$844$		0			0
$845$	−5.64897	+	9.78431i	−0.194331	+	0.336590i
$846$		0			0
$847$	−1.52065	−	2.63383i	−0.0522500	−	0.0904996i
$848$		0			0
$849$	−21.2251	+	32.6072i	−0.728444	+	1.11908i
$850$		0			0
$851$	−28.3358	+	23.7765i	−0.971337	+	0.815049i
$852$		0			0
$853$	−22.4360	+	8.16602i	−0.768192	+	0.279599i	−0.696240	−	0.717809i	$-0.745145\pi$
$853$	−22.4360	+	8.16602i	−0.768192	+	0.279599i	−0.0719523	+	0.997408i	$0.522923\pi$
$854$		0			0
$855$	7.11567	−	24.6160i	0.243351	−	0.841851i
$856$		0			0
$857$	5.01145	−	28.4213i	0.171188	−	0.970854i	−0.771265	−	0.636514i	$-0.780376\pi$
$857$	5.01145	−	28.4213i	0.171188	−	0.970854i	0.942453	−	0.334340i	$-0.108513\pi$
$858$		0			0
$859$	−35.0335	−	12.7511i	−1.19533	−	0.435063i	−0.333735	−	0.942667i	$-0.608309\pi$
$859$	−35.0335	−	12.7511i	−1.19533	−	0.435063i	−0.861591	+	0.507604i	$0.830531\pi$
$860$		0			0
$861$	15.5346	+	14.5174i	0.529417	+	0.494751i
$862$		0			0
$863$	19.2361			0.654804			0.327402	−	0.944885i	$-0.393827\pi$
$863$	19.2361			0.654804			0.327402	+	0.944885i	$0.393827\pi$
$864$		0			0
$865$	23.3109			0.792595
$866$		0			0
$867$	−2.43385	+	10.4908i	−0.0826577	+	0.356288i
$868$		0			0
$869$	−8.10493	−	2.94995i	−0.274941	−	0.100070i
$870$		0			0
$871$	5.94177	−	33.6974i	0.201329	−	1.14179i
$872$		0			0
$873$	19.2343	−	26.3548i	0.650984	−	0.891976i
$874$		0			0
$875$	32.7956	−	11.9366i	1.10869	−	0.403531i
$876$		0			0
$877$	39.2440	−	32.9297i	1.32518	−	1.11196i	0.339998	−	0.940426i	$-0.389574\pi$
$877$	39.2440	−	32.9297i	1.32518	−	1.11196i	0.985179	−	0.171530i	$-0.0548709\pi$
$878$		0			0
$879$	3.99794	+	7.86723i	0.134847	+	0.265355i
$880$		0			0
$881$	−8.98717	−	15.5662i	−0.302785	−	0.524440i	0.673980	−	0.738749i	$-0.264583\pi$
$881$	−8.98717	−	15.5662i	−0.302785	−	0.524440i	−0.976766	+	0.214309i	$0.931250\pi$
$882$		0			0
$883$	11.4959	−	19.9114i	0.386867	−	0.670073i	−0.605159	−	0.796104i	$-0.706891\pi$
$883$	11.4959	−	19.9114i	0.386867	−	0.670073i	0.992026	+	0.126031i	$0.0402239\pi$
$884$		0			0
$885$	21.5330	+	9.16746i	0.723823	+	0.308161i
$886$		0			0
$887$	9.61603	+	54.5352i	0.322875	+	1.83111i	0.524208	+	0.851590i	$0.324362\pi$
$887$	9.61603	+	54.5352i	0.322875	+	1.83111i	−0.201333	+	0.979523i	$0.564527\pi$
$888$		0			0
$889$	32.1538	+	26.9802i	1.07840	+	0.904887i
$890$		0			0
$891$	−1.11184	+	28.3539i	−0.0372481	+	0.949893i
$892$		0			0
$893$	−17.5392	−	14.7171i	−0.586926	−	0.492490i
$894$		0			0
$895$	7.39635	+	41.9468i	0.247233	+	1.40213i
$896$		0			0
$897$	17.5650	+	7.47811i	0.586477	+	0.249687i
$898$		0			0
$899$	1.25155	−	2.16775i	0.0417416	−	0.0722986i
$900$		0			0
$901$	−11.8287	−	20.4879i	−0.394071	−	0.682551i
$902$		0			0
$903$	14.6684	+	28.8648i	0.488135	+	0.960562i
$904$		0			0
$905$	−21.4522	+	18.0005i	−0.713094	+	0.598357i
$906$		0			0
$907$	−16.1960	+	5.89486i	−0.537779	+	0.195736i	−0.596609	−	0.802532i	$-0.703485\pi$
$907$	−16.1960	+	5.89486i	−0.537779	+	0.195736i	0.0588293	+	0.998268i	$0.481263\pi$
$908$		0			0
$909$	7.26948	+	16.4221i	0.241113	+	0.544688i
$910$		0			0
$911$	−5.64553	+	32.0174i	−0.187045	+	1.06078i	0.736255	+	0.676704i	$0.236592\pi$
$911$	−5.64553	+	32.0174i	−0.187045	+	1.06078i	−0.923300	+	0.384079i	$0.874519\pi$
$912$		0			0
$913$	36.7812	+	13.3873i	1.21728	+	0.443054i
$914$		0			0
$915$	4.90473	−	21.1413i	0.162145	−	0.698911i
$916$		0			0
$917$	19.3795			0.639969
$918$		0			0
$919$	−7.66165			−0.252735			−0.126367	−	0.991984i	$-0.540332\pi$
$919$	−7.66165			−0.252735			−0.126367	+	0.991984i	$0.540332\pi$
$920$		0			0
$921$	20.1982	+	18.8757i	0.665554	+	0.621974i
$922$		0			0
$923$	−21.0863	−	7.67479i	−0.694065	−	0.252619i
$924$		0			0
$925$	2.28295	−	12.9473i	0.0750630	−	0.425704i
$926$		0			0
$927$	47.7139	−	11.7878i	1.56713	−	0.387164i
$928$		0			0
$929$	−47.4436	+	17.2681i	−1.55657	+	0.566547i	−0.969948	−	0.243311i	$-0.921767\pi$
$929$	−47.4436	+	17.2681i	−1.55657	+	0.566547i	−0.586626	+	0.809858i	$0.699544\pi$
$930$		0			0
$931$	−4.32672	+	3.63055i	−0.141802	+	0.118986i
$932$		0			0
$933$	−27.4831	+	42.2211i	−0.899756	+	1.38226i
$934$		0			0
$935$	−9.70730	−	16.8135i	−0.317463	−	0.549862i
$936$		0			0
$937$	−18.0800	+	31.3155i	−0.590649	+	1.02303i	0.403497	+	0.914981i	$0.367795\pi$
$937$	−18.0800	+	31.3155i	−0.590649	+	1.02303i	−0.994145	+	0.108052i	$0.965539\pi$
$938$		0			0
$939$	44.1249	−	33.1764i	1.43996	−	1.08267i
$940$		0			0
$941$	6.84897	+	38.8424i	0.223270	+	1.26623i	0.865965	+	0.500105i	$0.166705\pi$
$941$	6.84897	+	38.8424i	0.223270	+	1.26623i	−0.642695	+	0.766122i	$0.722184\pi$
$942$		0			0
$943$	−13.6713	−	11.4716i	−0.445198	−	0.373565i
$944$		0			0
$945$	−9.94012	−	26.1458i	−0.323352	−	0.850523i
$946$		0			0
$947$	−34.1975	−	28.6951i	−1.11127	−	0.932467i	−0.113140	−	0.993579i	$-0.536091\pi$
$947$	−34.1975	−	28.6951i	−1.11127	−	0.932467i	−0.998131	+	0.0611124i	$0.980535\pi$
$948$		0			0
$949$	−4.88596	−	27.7097i	−0.158605	−	0.899494i
$950$		0			0
$951$	−1.35056	−	11.0977i	−0.0437948	−	0.359868i
$952$		0			0
$953$	12.7138	−	22.0210i	0.411842	−	0.713331i	−0.583249	−	0.812293i	$-0.698219\pi$
$953$	12.7138	−	22.0210i	0.411842	−	0.713331i	0.995091	+	0.0989620i	$0.0315522\pi$
$954$		0			0
$955$	−5.05906	−	8.76255i	−0.163707	−	0.283549i
$956$		0			0
$957$	−49.0454	−	2.62306i	−1.58541	−	0.0847915i
$958$		0			0
$959$	23.0813	−	19.3675i	0.745333	−	0.625409i
$960$		0			0
$961$	29.0577	−	10.5761i	0.937345	−	0.341166i
$962$		0			0
$963$	31.4435	−	21.1110i	1.01325	−	0.680294i
$964$		0			0
$965$	−5.82413	+	33.0303i	−0.187485	+	1.06328i
$966$		0			0
$967$	29.2870	+	10.6596i	0.941807	+	0.342790i	0.766879	−	0.641792i	$-0.221809\pi$
$967$	29.2870	+	10.6596i	0.941807	+	0.342790i	0.174928	+	0.984581i	$0.444031\pi$
$968$		0			0
$969$	−24.7804	+	7.54709i	−0.796060	+	0.242447i
$970$		0			0
$971$	−14.0853			−0.452020			−0.226010	−	0.974125i	$-0.572568\pi$
$971$	−14.0853			−0.452020			−0.226010	+	0.974125i	$0.572568\pi$
$972$		0			0
$973$	24.8500			0.796654
$974$		0			0
$975$	−6.49088	+	1.97686i	−0.207874	+	0.0633101i
$976$		0			0
$977$	−37.7646	−	13.7452i	−1.20820	−	0.439748i	−0.342119	−	0.939657i	$-0.611145\pi$
$977$	−37.7646	−	13.7452i	−1.20820	−	0.439748i	−0.866078	+	0.499909i	$0.833367\pi$
$978$		0			0
$979$	2.19398	−	12.4427i	0.0701198	−	0.397669i
$980$		0			0
$981$	37.8277	−	25.3974i	1.20775	−	0.810875i
$982$		0			0
$983$	11.3852	−	4.14388i	0.363132	−	0.132169i	−0.154009	−	0.988069i	$-0.549218\pi$
$983$	11.3852	−	4.14388i	0.363132	−	0.132169i	0.517141	+	0.855900i	$0.326996\pi$
$984$		0			0
$985$	8.59041	−	7.20821i	0.273713	−	0.229673i
$986$		0			0
$987$	−24.9579	−	1.33481i	−0.794418	−	0.0424873i
$988$		0			0
$989$	−13.5884	−	23.5359i	−0.432087	−	0.748397i
$990$		0			0
$991$	−15.3101	+	26.5178i	−0.486340	+	0.842365i	−0.999877	−	0.0157021i	$-0.995002\pi$
$991$	−15.3101	+	26.5178i	−0.486340	+	0.842365i	0.513537	+	0.858068i	$0.328335\pi$
$992$		0			0
$993$	−4.76145	−	39.1255i	−0.151100	−	1.24161i
$994$		0			0
$995$	−3.83889	−	21.7714i	−0.121701	−	0.690200i
$996$		0			0
$997$	−13.5989	−	11.4108i	−0.430682	−	0.361385i	0.401527	−	0.915847i	$-0.368480\pi$
$997$	−13.5989	−	11.4108i	−0.430682	−	0.361385i	−0.832209	+	0.554462i	$0.812924\pi$
$998$		0			0
$999$	−45.4658	−	7.35097i	−1.43847	−	0.232574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.d.97.2	✓	60
4.3	odd	2	inner	864.2.y.d.97.9	yes	60
27.22	even	9	inner	864.2.y.d.481.2	yes	60
108.103	odd	18	inner	864.2.y.d.481.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.d.97.2	✓	60	1.1	even	1	trivial
864.2.y.d.97.9	yes	60	4.3	odd	2	inner
864.2.y.d.481.2	yes	60	27.22	even	9	inner
864.2.y.d.481.9	yes	60	108.103	odd	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65691 + 0.504627i) q^{3} +(1.76220 + 0.641388i) q^{5} +(-0.498467 + 2.82694i) q^{7} +(2.49070 - 1.67224i) q^{9} +O(q^{10})\)	\(q+(-1.65691 + 0.504627i) q^{3} +(1.76220 + 0.641388i) q^{5} +(-0.498467 + 2.82694i) q^{7} +(2.49070 - 1.67224i) q^{9} +(-2.96272 + 1.07834i) q^{11} +(-2.02319 + 1.69766i) q^{13} +(-3.24347 - 0.173468i) q^{15} +(1.64182 + 2.84371i) q^{17} +(2.27732 - 3.94443i) q^{19} +(-0.600639 - 4.93553i) q^{21} +(0.724678 + 4.10985i) q^{23} +(-1.13625 - 0.953429i) q^{25} +(-3.28301 + 4.02764i) q^{27} +(-6.88981 - 5.78123i) q^{29} +(0.0483277 + 0.274080i) q^{31} +(4.36480 - 3.28178i) q^{33} +(-2.69157 + 4.66193i) q^{35} +(4.43176 + 7.67603i) q^{37} +(2.49557 - 3.83383i) q^{39} +(-3.27593 + 2.74883i) q^{41} +(-6.11943 + 2.22729i) q^{43} +(5.46167 - 1.34932i) q^{45} +(0.872914 - 4.95054i) q^{47} +(-1.16530 - 0.424133i) q^{49} +(-4.15536 - 3.88327i) q^{51} -7.20464 q^{53} -5.91254 q^{55} +(-1.78284 + 7.68477i) q^{57} +(-6.77067 - 2.46432i) q^{59} +(-1.16026 + 6.58018i) q^{61} +(3.48581 + 7.87463i) q^{63} +(-4.65413 + 1.69397i) q^{65} +(-9.92466 + 8.32778i) q^{67} +(-3.27467 - 6.44396i) q^{69} +(4.24816 + 7.35804i) q^{71} +(-5.32680 + 9.22629i) q^{73} +(2.36379 + 1.00636i) q^{75} +(-1.57159 - 8.91296i) q^{77} +(2.09562 + 1.75844i) q^{79} +(3.40720 - 8.33013i) q^{81} +(-9.51019 - 7.98000i) q^{83} +(1.06929 + 6.06423i) q^{85} +(14.3332 + 6.10220i) q^{87} +(-2.00367 + 3.47046i) q^{89} +(-3.79070 - 6.56569i) q^{91} +(-0.218383 - 0.429738i) q^{93} +(6.54301 - 5.49023i) q^{95} +(10.2199 - 3.71972i) q^{97} +(-5.57600 + 7.64022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 12 q^{9}+O(q^{10}) \) 60 * q + 12 * q^9	\( 60 q + 12 q^{9} - 12 q^{17} + 24 q^{21} - 24 q^{25} + 6 q^{29} - 12 q^{33} - 30 q^{37} - 30 q^{41} - 90 q^{45} + 42 q^{49} - 36 q^{53} - 60 q^{57} + 48 q^{61} + 12 q^{65} + 78 q^{69} - 48 q^{73} - 12 q^{77} + 12 q^{81} - 102 q^{85} - 12 q^{89} - 36 q^{93} + 12 q^{97}+O(q^{100}) \) 60 * q + 12 * q^9 - 12 * q^17 + 24 * q^21 - 24 * q^25 + 6 * q^29 - 12 * q^33 - 30 * q^37 - 30 * q^41 - 90 * q^45 + 42 * q^49 - 36 * q^53 - 60 * q^57 + 48 * q^61 + 12 * q^65 + 78 * q^69 - 48 * q^73 - 12 * q^77 + 12 * q^81 - 102 * q^85 - 12 * q^89 - 36 * q^93 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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