LMFDB - Embedded newform 216.3.u.a.41.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(41,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("216.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.u (of order $18$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.8
Character	$\chi$	$=$	216.41
Dual form			216.3.u.a.137.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.838943 - 2.88031i) q^{3} +(-3.67098 + 4.37491i) q^{5} +(0.364439 + 0.132645i) q^{7} +(-7.59235 + 4.83283i) q^{9} +O(q^{10})$	\(q+(-0.838943 - 2.88031i) q^{3} +(-3.67098 + 4.37491i) q^{5} +(0.364439 + 0.132645i) q^{7} +(-7.59235 + 4.83283i) q^{9} +(12.6654 + 15.0941i) q^{11} +(-0.618143 + 3.50566i) q^{13} +(15.6808 + 6.90327i) q^{15} +(0.882158 + 0.509314i) q^{17} +(-2.37524 - 4.11403i) q^{19} +(0.0763146 - 1.16098i) q^{21} +(9.69292 + 26.6311i) q^{23} +(-1.32250 - 7.50025i) q^{25} +(20.2896 + 17.8138i) q^{27} +(31.0371 - 5.47268i) q^{29} +(-12.1659 + 4.42803i) q^{31} +(32.8500 - 49.1434i) q^{33} +(-1.91816 + 1.10745i) q^{35} +(-26.9637 + 46.7025i) q^{37} +(10.6160 - 1.16061i) q^{39} +(-65.3390 - 11.5210i) q^{41} +(11.1631 - 9.36696i) q^{43} +(6.72821 - 50.9571i) q^{45} +(-23.8137 + 65.4275i) q^{47} +(-37.4210 - 31.3999i) q^{49} +(0.726901 - 2.96817i) q^{51} +42.6520i q^{53} -112.530 q^{55} +(-9.85699 + 10.2928i) q^{57} +(50.1572 - 59.7750i) q^{59} +(-1.51271 - 0.550581i) q^{61} +(-3.40799 + 0.754184i) q^{63} +(-13.0678 - 15.5735i) q^{65} +(6.11046 - 34.6541i) q^{67} +(68.5739 - 50.2605i) q^{69} +(32.4762 + 18.7502i) q^{71} +(-35.8788 - 62.1440i) q^{73} +(-20.4935 + 10.1015i) q^{75} +(2.61362 + 7.18086i) q^{77} +(-20.1994 - 114.557i) q^{79} +(34.2875 - 73.3851i) q^{81} +(127.771 - 22.5294i) q^{83} +(-5.46659 + 1.98968i) q^{85} +(-41.8014 - 84.8051i) q^{87} +(-108.581 + 62.6890i) q^{89} +(-0.690283 + 1.19561i) q^{91} +(22.9606 + 31.3267i) q^{93} +(26.7180 + 4.71110i) q^{95} +(27.3942 - 22.9865i) q^{97} +(-169.107 - 53.3895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q+O(q^{10}) $ 108 * q	$ 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) $ 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.838943	−	2.88031i	−0.279648	−	0.960103i
$3$	−0.838943	−	2.88031i	−0.279648	−	0.960103i
$4$		0			0
$5$	−3.67098	+	4.37491i	−0.734197	+	0.874982i	−0.995927	−	0.0901592i	$-0.971262\pi$
$5$	−3.67098	+	4.37491i	−0.734197	+	0.874982i	0.261730	+	0.965141i	$0.415707\pi$
$6$		0			0
$7$	0.364439	+	0.132645i	0.0520627	+	0.0189493i	0.367920	−	0.929857i	$-0.380070\pi$
$7$	0.364439	+	0.132645i	0.0520627	+	0.0189493i	−0.315858	+	0.948807i	$0.602292\pi$
$8$		0			0
$9$	−7.59235	+	4.83283i	−0.843594	+	0.536981i
$10$		0			0
$11$	12.6654	+	15.0941i	1.15140	+	1.37219i	0.916435	+	0.400183i	$0.131054\pi$
$11$	12.6654	+	15.0941i	1.15140	+	1.37219i	0.234966	+	0.972004i	$0.424502\pi$
$12$		0			0
$13$	−0.618143	+	3.50566i	−0.0475494	+	0.269666i	−0.999309	−	0.0371798i	$-0.988163\pi$
$13$	−0.618143	+	3.50566i	−0.0475494	+	0.269666i	0.951759	+	0.306846i	$0.0992737\pi$
$14$		0			0
$15$	15.6808	+	6.90327i	1.04539	+	0.460218i
$16$		0			0
$17$	0.882158	+	0.509314i	0.0518916	+	0.0299596i	0.525721	−	0.850657i	$-0.323795\pi$
$17$	0.882158	+	0.509314i	0.0518916	+	0.0299596i	−0.473830	+	0.880616i	$0.657129\pi$
$18$		0			0
$19$	−2.37524	−	4.11403i	−0.125012	−	0.216528i	0.796725	−	0.604342i	$-0.206564\pi$
$19$	−2.37524	−	4.11403i	−0.125012	−	0.216528i	−0.921738	+	0.387814i	$0.873230\pi$
$20$		0			0
$21$	0.0763146	−	1.16098i	0.00363403	−	0.0552846i
$22$		0			0
$23$	9.69292	+	26.6311i	0.421431	+	1.15787i	0.950888	+	0.309536i	$0.100174\pi$
$23$	9.69292	+	26.6311i	0.421431	+	1.15787i	−0.529457	+	0.848337i	$0.677604\pi$
$24$		0			0
$25$	−1.32250	−	7.50025i	−0.0528999	−	0.300010i
$26$		0			0
$27$	20.2896	+	17.8138i	0.751466	+	0.659772i
$28$		0			0
$29$	31.0371	−	5.47268i	1.07024	−	0.188713i	0.389347	−	0.921091i	$-0.372701\pi$
$29$	31.0371	−	5.47268i	1.07024	−	0.188713i	0.680898	+	0.732378i	$0.261590\pi$
$30$		0			0
$31$	−12.1659	+	4.42803i	−0.392449	+	0.142840i	−0.530704	−	0.847557i	$-0.678073\pi$
$31$	−12.1659	+	4.42803i	−0.392449	+	0.142840i	0.138256	+	0.990397i	$0.455850\pi$
$32$		0			0
$33$	32.8500	−	49.1434i	0.995453	−	1.48919i
$34$		0			0
$35$	−1.91816	+	1.10745i	−0.0548045	+	0.0316414i
$36$		0			0
$37$	−26.9637	+	46.7025i	−0.728749	+	1.26223i	0.228663	+	0.973506i	$0.426565\pi$
$37$	−26.9637	+	46.7025i	−0.728749	+	1.26223i	−0.957412	+	0.288725i	$0.906769\pi$
$38$		0			0
$39$	10.6160	−	1.16061i	0.272204	−	0.0297592i
$40$		0			0
$41$	−65.3390	−	11.5210i	−1.59363	−	0.281001i	−0.694771	−	0.719231i	$-0.744494\pi$
$41$	−65.3390	−	11.5210i	−1.59363	−	0.281001i	−0.898863	+	0.438231i	$0.855605\pi$
$42$		0			0
$43$	11.1631	−	9.36696i	0.259607	−	0.217836i	−0.503689	−	0.863885i	$-0.668024\pi$
$43$	11.1631	−	9.36696i	0.259607	−	0.217836i	0.763296	+	0.646049i	$0.223580\pi$
$44$		0			0
$45$	6.72821	−	50.9571i	0.149516	−	1.13238i
$46$		0			0
$47$	−23.8137	+	65.4275i	−0.506674	+	1.39207i	0.377975	+	0.925816i	$0.376621\pi$
$47$	−23.8137	+	65.4275i	−0.506674	+	1.39207i	−0.884648	+	0.466259i	$0.845602\pi$
$48$		0			0
$49$	−37.4210	−	31.3999i	−0.763693	−	0.640815i
$50$		0			0
$51$	0.726901	−	2.96817i	0.0142530	−	0.0581994i
$52$		0			0
$53$			42.6520i			0.804754i	0.915474	+	0.402377i	$0.131816\pi$
$53$			42.6520i			0.804754i	−0.915474	+	0.402377i	$0.868184\pi$
$54$		0			0
$55$	−112.530			−2.04599
$56$		0			0
$57$	−9.85699	+	10.2928i	−0.172930	+	0.180576i
$58$		0			0
$59$	50.1572	−	59.7750i	0.850122	−	1.01314i	−0.149580	−	0.988750i	$-0.547792\pi$
$59$	50.1572	−	59.7750i	0.850122	−	1.01314i	0.999703	−	0.0243867i	$-0.00776329\pi$
$60$		0			0
$61$	−1.51271	−	0.550581i	−0.0247985	−	0.00902592i	0.329591	−	0.944124i	$-0.393089\pi$
$61$	−1.51271	−	0.550581i	−0.0247985	−	0.00902592i	−0.354390	+	0.935098i	$0.615311\pi$
$62$		0			0
$63$	−3.40799	+	0.754184i	−0.0540952	+	0.0119712i
$64$		0			0
$65$	−13.0678	−	15.5735i	−0.201042	−	0.239593i
$66$		0			0
$67$	6.11046	−	34.6541i	0.0912008	−	0.517226i	−0.904645	−	0.426167i	$-0.859864\pi$
$67$	6.11046	−	34.6541i	0.0912008	−	0.517226i	0.995846	−	0.0910589i	$-0.0290252\pi$
$68$		0			0
$69$	68.5739	−	50.2605i	0.993824	−	0.728414i
$70$		0			0
$71$	32.4762	+	18.7502i	0.457412	+	0.264087i	0.710955	−	0.703237i	$-0.248263\pi$
$71$	32.4762	+	18.7502i	0.457412	+	0.264087i	−0.253544	+	0.967324i	$0.581596\pi$
$72$		0			0
$73$	−35.8788	−	62.1440i	−0.491491	−	0.851287i	0.508461	−	0.861085i	$-0.330215\pi$
$73$	−35.8788	−	62.1440i	−0.491491	−	0.851287i	−0.999952	+	0.00979776i	$0.996881\pi$
$74$		0			0
$75$	−20.4935	+	10.1015i	−0.273247	+	0.134686i
$76$		0			0
$77$	2.61362	+	7.18086i	0.0339431	+	0.0932579i
$78$		0			0
$79$	−20.1994	−	114.557i	−0.255689	−	1.45008i	−0.794299	−	0.607528i	$-0.792161\pi$
$79$	−20.1994	−	114.557i	−0.255689	−	1.45008i	0.538610	−	0.842555i	$-0.318950\pi$
$80$		0			0
$81$	34.2875	−	73.3851i	0.423303	−	0.905988i
$82$		0			0
$83$	127.771	−	22.5294i	1.53940	−	0.271439i	0.661379	−	0.750052i	$-0.269972\pi$
$83$	127.771	−	22.5294i	1.53940	−	0.271439i	0.878026	+	0.478613i	$0.158860\pi$
$84$		0			0
$85$	−5.46659	+	1.98968i	−0.0643128	+	0.0234080i
$86$		0			0
$87$	−41.8014	−	84.8051i	−0.480475	−	0.974772i
$88$		0			0
$89$	−108.581	+	62.6890i	−1.22001	+	0.704371i	−0.964919	−	0.262547i	$-0.915437\pi$
$89$	−108.581	+	62.6890i	−1.22001	+	0.704371i	−0.255087	+	0.966918i	$0.582104\pi$
$90$		0			0
$91$	−0.690283	+	1.19561i	−0.00758553	+	0.0131385i
$92$		0			0
$93$	22.9606	+	31.3267i	0.246888	+	0.336846i
$94$		0			0
$95$	26.7180	+	4.71110i	0.281242	+	0.0495905i
$96$		0			0
$97$	27.3942	−	22.9865i	0.282414	−	0.236974i	−0.490566	−	0.871404i	$-0.663210\pi$
$97$	27.3942	−	22.9865i	0.282414	−	0.236974i	0.772980	+	0.634430i	$0.218765\pi$
$98$		0			0
$99$	−169.107	−	53.3895i	−1.70815	−	0.539288i
$100$		0			0
$101$	−20.0792	+	55.1672i	−0.198804	+	0.546210i	−0.998533	−	0.0541517i	$-0.982755\pi$
$101$	−20.0792	+	55.1672i	−0.198804	+	0.546210i	0.799729	+	0.600362i	$0.204977\pi$
$102$		0			0
$103$	134.193	+	112.601i	1.30285	+	1.09322i	0.989646	+	0.143531i	$0.0458458\pi$
$103$	134.193	+	112.601i	1.30285	+	1.09322i	0.313201	+	0.949687i	$0.398599\pi$
$104$		0			0
$105$	4.79902	+	4.59580i	0.0457049	+	0.0437695i
$106$		0			0
$107$			133.931i			1.25170i	0.779945	+	0.625848i	$0.215247\pi$
$107$			133.931i			1.25170i	−0.779945	+	0.625848i	$0.784753\pi$
$108$		0			0
$109$	113.089			1.03752			0.518759	−	0.854921i	$-0.326394\pi$
$109$	113.089			1.03752			0.518759	+	0.854921i	$0.326394\pi$
$110$		0			0
$111$	157.139	+	38.4831i	1.41566	+	0.346694i
$112$		0			0
$113$	−38.5592	+	45.9530i	−0.341232	+	0.406664i	−0.909182	−	0.416399i	$-0.863292\pi$
$113$	−38.5592	+	45.9530i	−0.341232	+	0.406664i	0.567950	+	0.823063i	$0.307736\pi$
$114$		0			0
$115$	−152.091	−	55.3566i	−1.32253	−	0.481362i
$116$		0			0
$117$	−12.2491	−	29.6036i	−0.104693	−	0.253022i
$118$		0			0
$119$	0.253934	+	0.302627i	0.00213390	+	0.00254309i
$120$		0			0
$121$	−46.4063	+	263.183i	−0.383523	+	2.17507i
$122$		0			0
$123$	21.6316	+	197.862i	0.175867	+	1.60863i
$124$		0			0
$125$	−85.9798	−	49.6405i	−0.687839	−	0.397124i
$126$		0			0
$127$	−85.8693	−	148.730i	−0.676136	−	1.17110i	−0.976135	−	0.217163i	$-0.930320\pi$
$127$	−85.8693	−	148.730i	−0.676136	−	1.17110i	0.299999	−	0.953939i	$-0.403014\pi$
$128$		0			0
$129$	−36.3449	−	24.2948i	−0.281744	−	0.188332i
$130$		0			0
$131$	−79.9314	−	219.610i	−0.610164	−	1.67641i	−0.729857	−	0.683600i	$-0.760413\pi$
$131$	−79.9314	−	219.610i	−0.610164	−	1.67641i	0.119693	−	0.992811i	$-0.461809\pi$
$132$		0			0
$133$	−0.319923	−	1.81437i	−0.00240544	−	0.0136419i
$134$		0			0
$135$	−152.417	+	23.3708i	−1.12901	+	0.173117i
$136$		0			0
$137$	201.078	−	35.4554i	1.46772	−	0.258799i	0.618061	−	0.786130i	$-0.287918\pi$
$137$	201.078	−	35.4554i	1.46772	−	0.258799i	0.849660	+	0.527331i	$0.176807\pi$
$138$		0			0
$139$	96.8958	−	35.2672i	0.697092	−	0.253721i	0.0309232	−	0.999522i	$-0.490155\pi$
$139$	96.8958	−	35.2672i	0.697092	−	0.253721i	0.666169	+	0.745801i	$0.267933\pi$
$140$		0			0
$141$	208.430	+	13.7007i	1.47822	+	0.0971683i
$142$		0			0
$143$	−60.7437	+	35.0704i	−0.424781	+	0.245247i
$144$		0			0
$145$	−89.9942	+	155.875i	−0.620650	+	1.07500i
$146$		0			0
$147$	−59.0474	+	134.127i	−0.401683	+	0.912426i
$148$		0			0
$149$	79.7283	+	14.0582i	0.535089	+	0.0943506i	0.434662	−	0.900594i	$-0.356868\pi$
$149$	79.7283	+	14.0582i	0.535089	+	0.0943506i	0.100427	+	0.994944i	$0.467979\pi$
$150$		0			0
$151$	37.4920	−	31.4595i	0.248291	−	0.208341i	−0.510145	−	0.860089i	$-0.670408\pi$
$151$	37.4920	−	31.4595i	0.248291	−	0.208341i	0.758436	+	0.651747i	$0.225964\pi$
$152$		0			0
$153$	−9.15908	+	0.396428i	−0.0598632	+	0.00259103i
$154$		0			0
$155$	25.2886	−	69.4800i	0.163152	−	0.448258i
$156$		0			0
$157$	176.599	+	148.184i	1.12484	+	0.943850i	0.998839	−	0.0481803i	$-0.0153422\pi$
$157$	176.599	+	148.184i	1.12484	+	0.943850i	0.125998	+	0.992030i	$0.459787\pi$
$158$		0			0
$159$	122.851	−	35.7826i	0.772647	−	0.225048i
$160$		0			0
$161$			10.9911i			0.0682677i
$162$		0			0
$163$	−66.9175			−0.410537			−0.205269	−	0.978706i	$-0.565807\pi$
$163$	−66.9175			−0.410537			−0.205269	+	0.978706i	$0.565807\pi$
$164$		0			0
$165$	94.4060	+	324.120i	0.572157	+	1.96436i
$166$		0			0
$167$	54.4104	−	64.8437i	0.325811	−	0.388286i	−0.578130	−	0.815945i	$-0.696217\pi$
$167$	54.4104	−	64.8437i	0.325811	−	0.388286i	0.903940	+	0.427659i	$0.140662\pi$
$168$		0			0
$169$	146.900	+	53.4674i	0.869234	+	0.316375i
$170$		0			0
$171$	37.9160	+	19.7560i	0.221731	+	0.115532i
$172$		0			0
$173$	−32.1975	−	38.3715i	−0.186113	−	0.221801i	0.664918	−	0.746916i	$-0.268466\pi$
$173$	−32.1975	−	38.3715i	−0.186113	−	0.221801i	−0.851031	+	0.525116i	$0.824022\pi$
$174$		0			0
$175$	0.512900	−	2.90880i	0.00293086	−	0.0166217i
$176$		0			0
$177$	−214.250	−	94.3204i	−1.21045	−	0.532883i
$178$		0			0
$179$	98.4557	+	56.8434i	0.550032	+	0.317561i	0.749135	−	0.662418i	$-0.230470\pi$
$179$	98.4557	+	56.8434i	0.550032	+	0.317561i	−0.199103	+	0.979979i	$0.563803\pi$
$180$		0			0
$181$	91.9582	+	159.276i	0.508056	+	0.879980i	0.999956	+	0.00932792i	$0.00296921\pi$
$181$	91.9582	+	159.276i	0.508056	+	0.879980i	−0.491900	+	0.870652i	$0.663697\pi$
$182$		0			0
$183$	−0.316766	+	4.81897i	−0.00173096	+	0.0263332i
$184$		0			0
$185$	−105.336	−	289.408i	−0.569384	−	1.56437i
$186$		0			0
$187$	3.48528	+	19.7660i	0.0186379	+	0.105701i
$188$		0			0
$189$	5.03140	+	9.18336i	0.0266211	+	0.0485892i
$190$		0			0
$191$	−130.507	+	23.0119i	−0.683283	+	0.120481i	−0.504506	−	0.863408i	$-0.668325\pi$
$191$	−130.507	+	23.0119i	−0.683283	+	0.120481i	−0.178777	+	0.983890i	$0.557214\pi$
$192$		0			0
$193$	129.764	−	47.2303i	0.672353	−	0.244716i	0.0167921	−	0.999859i	$-0.494655\pi$
$193$	129.764	−	47.2303i	0.672353	−	0.244716i	0.655560	+	0.755143i	$0.272432\pi$
$194$		0			0
$195$	−33.8935	+	50.7045i	−0.173813	+	0.260023i
$196$		0			0
$197$	−127.214	+	73.4471i	−0.645757	+	0.372828i	−0.786829	−	0.617171i	$-0.788279\pi$
$197$	−127.214	+	73.4471i	−0.645757	+	0.372828i	0.141072	+	0.989999i	$0.454945\pi$
$198$		0			0
$199$	−37.0765	+	64.2184i	−0.186314	+	0.322705i	−0.944019	−	0.329892i	$-0.892988\pi$
$199$	−37.0765	+	64.2184i	−0.186314	+	0.322705i	0.757704	+	0.652598i	$0.226321\pi$
$200$		0			0
$201$	−104.941	+	11.4728i	−0.522094	+	0.0570788i
$202$		0			0
$203$	12.0370	+	2.12245i	0.0592958	+	0.0104554i
$204$		0			0
$205$	290.262	−	243.559i	1.41591	−	1.18809i
$206$		0			0
$207$	−202.295	−	155.348i	−0.977273	−	0.750474i
$208$		0			0
$209$	32.0140	−	87.9578i	0.153177	−	0.420851i
$210$		0			0
$211$	71.3639	+	59.8814i	0.338218	+	0.283798i	0.796038	−	0.605246i	$-0.206925\pi$
$211$	71.3639	+	59.8814i	0.338218	+	0.283798i	−0.457821	+	0.889045i	$0.651370\pi$
$212$		0			0
$213$	26.7605	−	109.272i	0.125636	−	0.513013i
$214$		0			0
$215$			83.2235i			0.387086i
$216$		0			0
$217$	−5.02108			−0.0231386
$218$		0			0
$219$	−148.893	+	155.477i	−0.679879	+	0.709942i
$220$		0			0
$221$	−2.33078	+	2.77772i	−0.0105465	+	0.0125689i
$222$		0			0
$223$	322.886	+	117.521i	1.44792	+	0.527000i	0.942009	−	0.335587i	$-0.108935\pi$
$223$	322.886	+	117.521i	1.44792	+	0.527000i	0.505910	+	0.862586i	$0.331157\pi$
$224$		0			0
$225$	46.2883	+	50.5531i	0.205726	+	0.224681i
$226$		0			0
$227$	83.8235	+	99.8970i	0.369267	+	0.440075i	0.918396	−	0.395663i	$-0.129485\pi$
$227$	83.8235	+	99.8970i	0.369267	+	0.440075i	−0.549129	+	0.835737i	$0.685041\pi$
$228$		0			0
$229$	14.9427	−	84.7444i	0.0652521	−	0.370063i	−0.934643	−	0.355587i	$-0.884281\pi$
$229$	14.9427	−	84.7444i	0.0652521	−	0.370063i	0.999895	−	0.0144757i	$-0.00460793\pi$
$230$		0			0
$231$	18.4904	−	13.5524i	0.0800450	−	0.0586682i
$232$		0			0
$233$	−239.136	−	138.065i	−1.02633	−	0.592554i	−0.110401	−	0.993887i	$-0.535213\pi$
$233$	−239.136	−	138.065i	−1.02633	−	0.592554i	−0.915932	+	0.401334i	$0.868547\pi$
$234$		0			0
$235$	−198.820	−	344.366i	−0.846042	−	1.46539i
$236$		0			0
$237$	−313.012	+	154.287i	−1.32073	+	0.651000i
$238$		0			0
$239$	−118.854	−	326.547i	−0.497295	−	1.36631i	−0.893879	−	0.448309i	$-0.852027\pi$
$239$	−118.854	−	326.547i	−0.497295	−	1.36631i	0.396584	−	0.917999i	$-0.370196\pi$
$240$		0			0
$241$	−75.0789	−	425.793i	−0.311531	−	1.76678i	−0.591047	−	0.806637i	$-0.701285\pi$
$241$	−75.0789	−	425.793i	−0.311531	−	1.76678i	0.279517	−	0.960141i	$-0.409826\pi$
$242$		0			0
$243$	−240.137	−	37.1927i	−0.988217	−	0.153057i
$244$		0			0
$245$	274.743	−	48.4447i	1.12140	−	0.197733i
$246$		0			0
$247$	15.8906	−	5.78372i	0.0643345	−	0.0234159i
$248$		0			0
$249$	−172.084	−	349.118i	−0.691100	−	1.40208i
$250$		0			0
$251$	88.8502	−	51.2977i	0.353985	−	0.204373i	−0.312454	−	0.949933i	$-0.601151\pi$
$251$	88.8502	−	51.2977i	0.353985	−	0.204373i	0.666439	+	0.745560i	$0.267818\pi$
$252$		0			0
$253$	−279.206	+	483.599i	−1.10358	+	1.91146i
$254$		0			0
$255$	10.3170	+	14.0762i	0.0404590	+	0.0552009i
$256$		0			0
$257$	−350.993	−	61.8895i	−1.36573	−	0.240815i	−0.557742	−	0.830014i	$-0.688332\pi$
$257$	−350.993	−	61.8895i	−1.36573	−	0.240815i	−0.807988	+	0.589199i	$0.799443\pi$
$258$		0			0
$259$	−16.0215	+	13.4436i	−0.0618590	+	0.0519058i
$260$		0			0
$261$	−209.196	+	191.547i	−0.801517	+	0.733898i
$262$		0			0
$263$	51.7018	−	142.050i	0.196585	−	0.540112i	−0.801759	−	0.597648i	$-0.796102\pi$
$263$	51.7018	−	142.050i	0.196585	−	0.540112i	0.998343	+	0.0575357i	$0.0183243\pi$
$264$		0			0
$265$	−186.599	−	156.575i	−0.704145	−	0.590848i
$266$		0			0
$267$	271.657	+	260.153i	1.01744	+	0.974355i
$268$		0			0
$269$		−	308.813i		−	1.14800i	−0.818854	−	0.574001i	$-0.805390\pi$
$269$		−	308.813i		−	1.14800i	0.818854	−	0.574001i	$-0.194610\pi$
$270$		0			0
$271$	409.340			1.51048			0.755240	−	0.655448i	$-0.227520\pi$
$271$	409.340			1.51048			0.755240	+	0.655448i	$0.227520\pi$
$272$		0			0
$273$	4.02282	+	0.985183i	0.0147356	+	0.00360873i
$274$		0			0
$275$	96.4592	−	114.956i	0.350761	−	0.418020i
$276$		0			0
$277$	−146.867	−	53.4552i	−0.530206	−	0.192979i	0.0630243	−	0.998012i	$-0.479925\pi$
$277$	−146.867	−	53.4552i	−0.530206	−	0.192979i	−0.593230	+	0.805033i	$0.702148\pi$
$278$		0			0
$279$	70.9679	−	92.4149i	0.254365	−	0.331236i
$280$		0			0
$281$	141.592	+	168.743i	0.503886	+	0.600508i	0.956692	−	0.291101i	$-0.0940215\pi$
$281$	141.592	+	168.743i	0.503886	+	0.600508i	−0.452806	+	0.891609i	$0.649577\pi$
$282$		0			0
$283$	31.7969	−	180.329i	0.112357	−	0.637206i	−0.875669	−	0.482913i	$-0.839579\pi$
$283$	31.7969	−	180.329i	0.112357	−	0.637206i	0.988025	−	0.154293i	$-0.0493100\pi$
$284$		0			0
$285$	−8.84544	−	80.9083i	−0.0310366	−	0.283889i
$286$		0			0
$287$	−22.2838	−	12.8656i	−0.0776440	−	0.0448278i
$288$		0			0
$289$	−143.981	−	249.383i	−0.498205	−	0.862916i
$290$		0			0
$291$	−89.1903	−	59.6194i	−0.306496	−	0.204878i
$292$		0			0
$293$	120.994	+	332.427i	0.412947	+	1.13456i	0.955616	+	0.294616i	$0.0951919\pi$
$293$	120.994	+	332.427i	0.412947	+	1.13456i	−0.542668	+	0.839947i	$0.682586\pi$
$294$		0			0
$295$	77.3840	+	438.866i	0.262319	+	1.48768i
$296$		0			0
$297$	−11.9069	+	531.872i	−0.0400907	+	1.79081i
$298$		0			0
$299$	−99.3511	+	17.5183i	−0.332278	+	0.0585896i
$300$		0			0
$301$	5.31075	−	1.93295i	0.0176437	−	0.00642177i
$302$		0			0
$303$	175.744	+	11.5522i	0.580013	+	0.0381261i
$304$		0			0
$305$	7.96187	−	4.59679i	0.0261045	−	0.0150714i
$306$		0			0
$307$	−129.511	+	224.320i	−0.421861	+	0.730685i	−0.996122	−	0.0879877i	$-0.971956\pi$
$307$	−129.511	+	224.320i	−0.421861	+	0.730685i	0.574260	+	0.818673i	$0.305290\pi$
$308$		0			0
$309$	211.746	−	480.984i	0.685264	−	1.55658i
$310$		0			0
$311$	−455.961	−	80.3983i	−1.46611	−	0.258515i	−0.617099	−	0.786885i	$-0.711692\pi$
$311$	−455.961	−	80.3983i	−1.46611	−	0.258515i	−0.849014	+	0.528370i	$0.822803\pi$
$312$		0			0
$313$	159.879	−	134.154i	0.510795	−	0.428608i	−0.350614	−	0.936520i	$-0.614027\pi$
$313$	159.879	−	134.154i	0.510795	−	0.428608i	0.861409	+	0.507912i	$0.169583\pi$
$314$		0			0
$315$	9.21121	−	17.6783i	0.0292419	−	0.0561215i
$316$		0			0
$317$	20.7134	−	56.9097i	0.0653421	−	0.179526i	−0.902725	−	0.430219i	$-0.858436\pi$
$317$	20.7134	−	56.9097i	0.0653421	−	0.179526i	0.968067	+	0.250693i	$0.0806585\pi$
$318$		0			0
$319$	475.703	+	399.162i	1.49123	+	1.25129i
$320$		0			0
$321$	385.764	−	112.361i	1.20176	−	0.350034i
$322$		0			0
$323$		−	4.83896i		−	0.0149813i
$324$		0			0
$325$	27.1108			0.0834179
$326$		0			0
$327$	−94.8756	−	325.732i	−0.290139	−	0.996124i
$328$		0			0
$329$	−17.3572	+	20.6856i	−0.0527576	+	0.0628740i
$330$		0			0
$331$	−109.046	−	39.6895i	−0.329444	−	0.119908i	0.172002	−	0.985097i	$-0.444976\pi$
$331$	−109.046	−	39.6895i	−0.329444	−	0.119908i	−0.501446	+	0.865189i	$0.667199\pi$
$332$		0			0
$333$	−20.9874	−	484.893i	−0.0630253	−	1.45614i
$334$		0			0
$335$	129.177	+	153.947i	0.385604	+	0.459544i
$336$		0			0
$337$	−85.7660	+	486.403i	−0.254499	+	1.44333i	0.542858	+	0.839825i	$0.317342\pi$
$337$	−85.7660	+	486.403i	−0.254499	+	1.44333i	−0.797356	+	0.603509i	$0.793769\pi$
$338$		0			0
$339$	164.708	+	72.5103i	0.485864	+	0.213895i
$340$		0			0
$341$	−220.923	−	127.550i	−0.647869	−	0.374047i
$342$		0			0
$343$	−18.9744	−	32.8646i	−0.0553189	−	0.0958151i
$344$		0			0
$345$	−31.8484	+	484.510i	−0.0923141	+	1.40438i
$346$		0			0
$347$	70.9571	+	194.953i	0.204487	+	0.561824i	0.998966	−	0.0454679i	$-0.0144779\pi$
$347$	70.9571	+	194.953i	0.204487	+	0.561824i	−0.794478	+	0.607292i	$0.792256\pi$
$348$		0			0
$349$	−60.3405	−	342.208i	−0.172896	−	0.980539i	−0.940545	−	0.339669i	$-0.889685\pi$
$349$	−60.3405	−	342.208i	−0.172896	−	0.980539i	0.767649	−	0.640870i	$-0.221426\pi$
$350$		0			0
$351$	−74.9911	+	60.1169i	−0.213650	+	0.171273i
$352$		0			0
$353$	278.603	−	49.1253i	0.789244	−	0.139165i	0.235525	−	0.971868i	$-0.424319\pi$
$353$	278.603	−	49.1253i	0.789244	−	0.139165i	0.553719	+	0.832703i	$0.313208\pi$
$354$		0			0
$355$	−201.250	+	73.2490i	−0.566901	+	0.206335i
$356$		0			0
$357$	0.658623	−	0.985297i	0.00184488	−	0.00275993i
$358$		0			0
$359$	−111.360	+	64.2936i	−0.310194	+	0.179091i	−0.647013	−	0.762479i	$-0.723982\pi$
$359$	−111.360	+	64.2936i	−0.310194	+	0.179091i	0.336819	+	0.941569i	$0.390649\pi$
$360$		0			0
$361$	169.217	−	293.092i	0.468744	−	0.811888i
$362$		0			0
$363$	796.981	−	87.1313i	2.19554	−	0.240031i
$364$		0			0
$365$	403.585	+	71.1629i	1.10571	+	0.194967i
$366$		0			0
$367$	−401.466	+	336.870i	−1.09391	+	0.917902i	−0.997001	−	0.0773912i	$-0.975341\pi$
$367$	−401.466	+	336.870i	−1.09391	+	0.917902i	−0.0969119	+	0.995293i	$0.530897\pi$
$368$		0			0
$369$	551.755	−	228.300i	1.49527	−	0.618700i
$370$		0			0
$371$	−5.65756	+	15.5440i	−0.0152495	+	0.0418976i
$372$		0			0
$373$	−515.141	−	432.255i	−1.38107	−	1.15886i	−0.968813	−	0.247794i	$-0.920294\pi$
$373$	−515.141	−	432.255i	−1.38107	−	1.15886i	−0.412262	−	0.911065i	$-0.635261\pi$
$374$		0			0
$375$	−70.8477	+	289.294i	−0.188927	+	0.771450i
$376$		0			0
$377$			112.188i			0.297582i
$378$		0			0
$379$	97.2648			0.256635			0.128318	−	0.991733i	$-0.459042\pi$
$379$	97.2648			0.256635			0.128318	+	0.991733i	$0.459042\pi$
$380$		0			0
$381$	−356.349	+	372.106i	−0.935299	+	0.976656i
$382$		0			0
$383$	0.894862	−	1.06645i	0.00233645	−	0.00278448i	−0.764875	−	0.644179i	$-0.777199\pi$
$383$	0.894862	−	1.06645i	0.00233645	−	0.00278448i	0.767211	+	0.641394i	$0.221644\pi$
$384$		0			0
$385$	−41.0102	−	14.9265i	−0.106520	−	0.0387701i
$386$		0			0
$387$	−39.4853	+	125.067i	−0.102029	+	0.323170i
$388$		0			0
$389$	109.718	+	130.757i	0.282052	+	0.336137i	0.888406	−	0.459058i	$-0.151813\pi$
$389$	109.718	+	130.757i	0.282052	+	0.336137i	−0.606354	+	0.795195i	$0.707369\pi$
$390$		0			0
$391$	−5.01290	+	28.4295i	−0.0128207	+	0.0727098i
$392$		0			0
$393$	−565.486	+	414.467i	−1.43890	+	1.05462i
$394$		0			0
$395$	575.326	+	332.165i	1.45652	+	0.840923i
$396$		0			0
$397$	70.8171	+	122.659i	0.178381	+	0.308964i	0.941326	−	0.337499i	$-0.109581\pi$
$397$	70.8171	+	122.659i	0.178381	+	0.308964i	−0.762945	+	0.646463i	$0.776248\pi$
$398$		0			0
$399$	−4.95756	+	2.44363i	−0.0124250	+	0.00612440i
$400$		0			0
$401$	226.393	+	622.011i	0.564572	+	1.55115i	0.812858	+	0.582462i	$0.197911\pi$
$401$	226.393	+	622.011i	0.564572	+	1.55115i	−0.248285	+	0.968687i	$0.579867\pi$
$402$		0			0
$403$	−8.00290	−	45.3867i	−0.0198583	−	0.112622i
$404$		0			0
$405$	195.184	+	419.400i	0.481936	+	1.03556i
$406$		0			0
$407$	−1046.44	+	184.515i	−2.57110	+	0.453354i
$408$		0			0
$409$	−193.022	+	70.2543i	−0.471937	+	0.171771i	−0.567029	−	0.823698i	$-0.691907\pi$
$409$	−193.022	+	70.2543i	−0.471937	+	0.171771i	0.0950928	+	0.995468i	$0.469685\pi$
$410$		0			0
$411$	−270.815	−	549.421i	−0.658918	−	1.33679i
$412$		0			0
$413$	26.2081	−	15.1312i	0.0634578	−	0.0366374i
$414$		0			0
$415$	−370.480	+	641.690i	−0.892722	+	1.54624i
$416$		0			0
$417$	−182.870	−	249.503i	−0.438538	−	0.598327i
$418$		0			0
$419$	240.772	+	42.4547i	0.574636	+	0.101324i	0.453411	−	0.891301i	$-0.350207\pi$
$419$	240.772	+	42.4547i	0.574636	+	0.101324i	0.121224	+	0.992625i	$0.461318\pi$
$420$		0			0
$421$	−163.599	+	137.276i	−0.388595	+	0.326070i	−0.816066	−	0.577959i	$-0.803849\pi$
$421$	−163.599	+	137.276i	−0.388595	+	0.326070i	0.427470	+	0.904029i	$0.359405\pi$
$422$		0			0
$423$	−135.398	−	611.836i	−0.320091	−	1.44642i
$424$		0			0
$425$	2.65333	−	7.28997i	0.00624313	−	0.0171529i
$426$		0			0
$427$	−0.478258	−	0.401306i	−0.00112004	−	0.000939826i
$428$		0			0
$429$	151.974	+	145.538i	0.354252	+	0.339251i
$430$		0			0
$431$			779.947i			1.80962i	0.425813	+	0.904811i	$0.359988\pi$
$431$			779.947i			1.80962i	−0.425813	+	0.904811i	$0.640012\pi$
$432$		0			0
$433$	342.855			0.791814			0.395907	−	0.918291i	$-0.370430\pi$
$433$	342.855			0.791814			0.395907	+	0.918291i	$0.370430\pi$
$434$		0			0
$435$	524.467	+	128.441i	1.20567	+	0.295267i
$436$		0			0
$437$	86.5381	−	103.132i	0.198028	−	0.236000i
$438$		0			0
$439$	−200.441	−	72.9546i	−0.456586	−	0.166184i	0.103481	−	0.994631i	$-0.467002\pi$
$439$	−200.441	−	72.9546i	−0.456586	−	0.166184i	−0.560066	+	0.828448i	$0.689224\pi$
$440$		0			0
$441$	435.863	+	57.5500i	0.988352	+	0.130499i
$442$		0			0
$443$	71.4539	+	85.1554i	0.161295	+	0.192224i	0.840639	−	0.541596i	$-0.182180\pi$
$443$	71.4539	+	85.1554i	0.161295	+	0.192224i	−0.679343	+	0.733820i	$0.737735\pi$
$444$		0			0
$445$	124.339	−	705.160i	0.279413	−	1.58463i
$446$		0			0
$447$	−26.3954	−	241.436i	−0.0590501	−	0.540125i
$448$		0			0
$449$	596.202	+	344.218i	1.32784	+	0.766631i	0.984966	−	0.172748i	$-0.0552647\pi$
$449$	596.202	+	344.218i	1.32784	+	0.766631i	0.342879	+	0.939380i	$0.388598\pi$
$450$		0			0
$451$	−653.646	−	1132.15i	−1.44933	−	2.51031i
$452$		0			0
$453$	−122.067	−	81.5957i	−0.269463	−	0.180123i
$454$		0			0
$455$	−2.69665	−	7.40897i	−0.00592669	−	0.0162835i
$456$		0			0
$457$	107.760	+	611.138i	0.235799	+	1.33728i	0.840925	+	0.541152i	$0.182012\pi$
$457$	107.760	+	611.138i	0.235799	+	1.33728i	−0.605126	+	0.796130i	$0.706877\pi$
$458$		0			0
$459$	8.82578	+	26.0484i	0.0192283	+	0.0567503i
$460$		0			0
$461$	−362.631	+	63.9417i	−0.786619	+	0.138702i	−0.552508	−	0.833508i	$-0.686329\pi$
$461$	−362.631	+	63.9417i	−0.786619	+	0.138702i	−0.234111	+	0.972210i	$0.575218\pi$
$462$		0			0
$463$	715.065	−	260.262i	1.54442	−	0.562121i	0.577317	−	0.816520i	$-0.304100\pi$
$463$	715.065	−	260.262i	1.54442	−	0.562121i	0.967099	+	0.254399i	$0.0818776\pi$
$464$		0			0
$465$	−221.339	−	14.5493i	−0.475999	−	0.0312889i
$466$		0			0
$467$	−34.1349	+	19.7078i	−0.0730940	+	0.0422009i	−0.536102	−	0.844153i	$-0.680104\pi$
$467$	−34.1349	+	19.7078i	−0.0730940	+	0.0422009i	0.463008	+	0.886354i	$0.346770\pi$
$468$		0			0
$469$	6.82357	−	11.8188i	0.0145492	−	0.0251999i
$470$		0			0
$471$	278.660	−	632.979i	0.591635	−	1.34390i
$472$		0			0
$473$	282.771	+	49.8601i	0.597824	+	0.105413i
$474$		0			0
$475$	−27.7150	+	23.2557i	−0.0583474	+	0.0489593i
$476$		0			0
$477$	−206.130	−	323.829i	−0.432138	−	0.678886i
$478$		0			0
$479$	45.5463	−	125.138i	0.0950863	−	0.261247i	−0.883026	−	0.469323i	$-0.844498\pi$
$479$	45.5463	−	125.138i	0.0950863	−	0.261247i	0.978113	+	0.208076i	$0.0667201\pi$
$480$		0			0
$481$	−147.056	−	123.395i	−0.305730	−	0.256538i
$482$		0			0
$483$	31.6578	−	9.22091i	0.0655440	−	0.0190909i
$484$		0			0
$485$			204.230i			0.421093i
$486$		0			0
$487$	659.894			1.35502			0.677509	−	0.735514i	$-0.263059\pi$
$487$	659.894			1.35502			0.677509	+	0.735514i	$0.263059\pi$
$488$		0			0
$489$	56.1400	+	192.743i	0.114806	+	0.394158i
$490$		0			0
$491$	227.538	−	271.169i	0.463418	−	0.552280i	−0.482834	−	0.875712i	$-0.660392\pi$
$491$	227.538	−	271.169i	0.463418	−	0.552280i	0.946251	+	0.323432i	$0.104837\pi$
$492$		0			0
$493$	30.1669	+	10.9799i	0.0611905	+	0.0222715i
$494$		0			0
$495$	854.364	−	543.837i	1.72599	−	1.09866i
$496$		0			0
$497$	9.34848	+	11.1411i	0.0188098	+	0.0224167i
$498$		0			0
$499$	−23.3266	+	132.292i	−0.0467467	+	0.265114i	−0.999219	−	0.0395112i	$-0.987420\pi$
$499$	−23.3266	+	132.292i	−0.0467467	+	0.265114i	0.952472	+	0.304625i	$0.0985310\pi$
$500$		0			0
$501$	−232.417	−	102.318i	−0.463906	−	0.204228i
$502$		0			0
$503$	−480.345	−	277.327i	−0.954960	−	0.551346i	−0.0603418	−	0.998178i	$-0.519219\pi$
$503$	−480.345	−	277.327i	−0.954960	−	0.551346i	−0.894618	+	0.446831i	$0.852552\pi$
$504$		0			0
$505$	−167.641	−	290.363i	−0.331962	−	0.574976i
$506$		0			0
$507$	30.7614	−	467.975i	0.0606735	−	0.923027i
$508$		0			0
$509$	149.125	+	409.717i	0.292976	+	0.804944i	0.995628	+	0.0934106i	$0.0297769\pi$
$509$	149.125	+	409.717i	0.292976	+	0.804944i	−0.702652	+	0.711534i	$0.748001\pi$
$510$		0			0
$511$	−4.83256	−	27.4068i	−0.00945706	−	0.0536337i
$512$		0			0
$513$	25.0941	−	125.784i	0.0489163	−	0.245193i
$514$		0			0
$515$	−985.242	+	173.725i	−1.91309	+	0.337330i
$516$		0			0
$517$	−1289.18	+	469.222i	−2.49357	+	0.907586i
$518$		0			0
$519$	−83.5099	+	124.930i	−0.160905	+	0.240713i
$520$		0			0
$521$	444.417	−	256.584i	0.853007	−	0.492484i	−0.00865731	−	0.999963i	$-0.502756\pi$
$521$	444.417	−	256.584i	0.853007	−	0.492484i	0.861664	+	0.507479i	$0.169422\pi$
$522$		0			0
$523$	14.6233	−	25.3282i	0.0279603	−	0.0484287i	−0.851707	−	0.524019i	$-0.824432\pi$
$523$	14.6233	−	25.3282i	0.0279603	−	0.0484287i	0.879667	+	0.475590i	$0.157765\pi$
$524$		0			0
$525$	−8.80854	+	0.963009i	−0.0167782	+	0.00183430i
$526$		0			0
$527$	−12.9875	−	2.29005i	−0.0246442	−	0.00434544i
$528$		0			0
$529$	−210.024	+	176.231i	−0.397021	+	0.333140i
$530$		0			0
$531$	−91.9285	+	696.234i	−0.173123	+	1.31118i
$532$		0			0
$533$	80.7776	−	221.935i	0.151553	−	0.416388i
$534$		0			0
$535$	−585.938	−	491.660i	−1.09521	−	0.918991i
$536$		0			0
$537$	81.1278	−	331.271i	0.151076	−	0.616892i
$538$		0			0
$539$		−	962.527i		−	1.78576i
$540$		0			0
$541$	836.162			1.54559			0.772793	−	0.634658i	$-0.218859\pi$
$541$	836.162			1.54559			0.772793	+	0.634658i	$0.218859\pi$
$542$		0			0
$543$	381.617	−	398.492i	0.702794	−	0.733871i
$544$		0			0
$545$	−415.150	+	494.756i	−0.761742	+	0.907809i
$546$		0			0
$547$	−614.722	−	223.741i	−1.12381	−	0.409032i	−0.287766	−	0.957701i	$-0.592913\pi$
$547$	−614.722	−	223.741i	−1.12381	−	0.409032i	−0.836040	+	0.548669i	$0.815135\pi$
$548$		0			0
$549$	14.1459	−	3.13046i	0.0257666	−	0.00570211i
$550$		0			0
$551$	−96.2352	−	114.689i	−0.174656	−	0.208146i
$552$		0			0
$553$	7.83389	−	44.4282i	0.0141662	−	0.0803403i
$554$		0			0
$555$	−745.214	+	546.197i	−1.34273	+	0.984139i
$556$		0			0
$557$	−151.804	−	87.6442i	−0.272539	−	0.157350i	0.357502	−	0.933912i	$-0.383629\pi$
$557$	−151.804	−	87.6442i	−0.272539	−	0.157350i	−0.630041	+	0.776562i	$0.716962\pi$
$558$		0			0
$559$	25.9370	+	44.9242i	0.0463989	+	0.0803653i
$560$		0			0
$561$	54.0082	−	26.6212i	0.0962714	−	0.0474532i
$562$		0			0
$563$	25.9270	+	71.2338i	0.0460515	+	0.126525i	0.960586	−	0.277982i	$-0.0896654\pi$
$563$	25.9270	+	71.2338i	0.0460515	+	0.126525i	−0.914535	+	0.404507i	$0.867443\pi$
$564$		0			0
$565$	−59.4902	−	337.386i	−0.105292	−	0.597143i
$566$		0			0
$567$	22.2298	−	22.1963i	0.0392061	−	0.0391469i
$568$		0			0
$569$	972.430	−	171.466i	1.70902	−	0.301346i	0.768187	−	0.640226i	$-0.221159\pi$
$569$	972.430	−	171.466i	1.70902	−	0.301346i	0.940830	+	0.338880i	$0.110048\pi$
$570$		0			0
$571$	−115.251	+	41.9479i	−0.201840	+	0.0734639i	−0.440962	−	0.897526i	$-0.645363\pi$
$571$	−115.251	+	41.9479i	−0.201840	+	0.0734639i	0.239122	+	0.970990i	$0.423140\pi$
$572$		0			0
$573$	175.769	+	356.595i	0.306753	+	0.622329i
$574$		0			0
$575$	186.921	−	107.919i	0.325080	−	0.187685i
$576$		0			0
$577$	−201.581	+	349.149i	−0.349361	+	0.605111i	−0.986136	−	0.165939i	$-0.946935\pi$
$577$	−201.581	+	349.149i	−0.349361	+	0.605111i	0.636775	+	0.771050i	$0.280268\pi$
$578$		0			0
$579$	−244.902	−	334.137i	−0.422975	−	0.577093i
$580$		0			0
$581$	49.5529	+	8.73752i	0.0852891	+	0.0150388i
$582$		0			0
$583$	−643.791	+	540.205i	−1.10427	+	0.926595i
$584$		0			0
$585$	174.479	+	55.0856i	0.298255	+	0.0941634i
$586$		0			0
$587$	34.7802	−	95.5577i	0.0592507	−	0.162790i	−0.906535	−	0.422130i	$-0.861283\pi$
$587$	34.7802	−	95.5577i	0.0592507	−	0.162790i	0.965786	+	0.259340i	$0.0835049\pi$
$588$		0			0
$589$	47.1139	+	39.5333i	0.0799897	+	0.0671193i
$590$		0			0
$591$	318.276	+	304.798i	0.538538	+	0.515733i
$592$		0			0
$593$		−	652.564i		−	1.10044i	−0.835018	−	0.550222i	$-0.814543\pi$
$593$		−	652.564i		−	1.10044i	0.835018	−	0.550222i	$-0.185457\pi$
$594$		0			0
$595$	−2.25616			−0.00379186
$596$		0			0
$597$	216.074	+	52.9162i	0.361933	+	0.0886368i
$598$		0			0
$599$	−450.723	+	537.151i	−0.752459	+	0.896746i	−0.997346	−	0.0728056i	$-0.976805\pi$
$599$	−450.723	+	537.151i	−0.752459	+	0.896746i	0.244887	+	0.969552i	$0.421249\pi$
$600$		0			0
$601$	−576.656	−	209.886i	−0.959494	−	0.349227i	−0.185659	−	0.982614i	$-0.559442\pi$
$601$	−576.656	−	209.886i	−0.959494	−	0.349227i	−0.773835	+	0.633387i	$0.781664\pi$
$602$		0			0
$603$	121.085	+	292.637i	0.200804	+	0.485302i
$604$		0			0
$605$	−981.046	−	1169.16i	−1.62156	−	1.93250i
$606$		0			0
$607$	−62.0988	+	352.180i	−0.102305	+	0.580198i	0.889958	+	0.456042i	$0.150733\pi$
$607$	−62.0988	+	352.180i	−0.102305	+	0.580198i	−0.992263	+	0.124156i	$0.960378\pi$
$608$		0			0
$609$	−3.98507	−	36.4510i	−0.00654362	−	0.0598539i
$610$		0			0
$611$	−214.646	−	123.926i	−0.351304	−	0.202825i
$612$		0			0
$613$	−298.489	−	516.998i	−0.486931	−	0.843390i	0.512956	−	0.858415i	$-0.328550\pi$
$613$	−298.489	−	516.998i	−0.486931	−	0.843390i	−0.999887	+	0.0150252i	$0.995217\pi$
$614$		0			0
$615$	−945.037	−	631.712i	−1.53665	−	1.02717i
$616$		0			0
$617$	−153.522	−	421.799i	−0.248821	−	0.683629i	−0.999730	−	0.0232244i	$-0.992607\pi$
$617$	−153.522	−	421.799i	−0.248821	−	0.683629i	0.750909	−	0.660405i	$-0.229615\pi$
$618$		0			0
$619$	158.292	+	897.717i	0.255722	+	1.45027i	0.794214	+	0.607639i	$0.207883\pi$
$619$	158.292	+	897.717i	0.255722	+	1.45027i	−0.538492	+	0.842631i	$0.681006\pi$
$620$		0			0
$621$	−277.736	+	713.002i	−0.447240	+	1.14815i
$622$		0			0
$623$	−47.8863	+	8.44365i	−0.0768641	+	0.0135532i
$624$		0			0
$625$	711.720	−	259.045i	1.13875	−	0.414472i
$626$		0			0
$627$	−280.204	−	18.4187i	−0.446896	−	0.0293759i
$628$		0			0
$629$	−47.5725	+	27.4660i	−0.0756320	+	0.0436661i
$630$		0			0
$631$	338.418	−	586.157i	0.536320	−	0.928934i	−0.462778	−	0.886474i	$-0.653147\pi$
$631$	338.418	−	586.157i	0.536320	−	0.928934i	0.999098	−	0.0424597i	$-0.0135194\pi$
$632$		0			0
$633$	112.607	−	255.787i	0.177894	−	0.404087i
$634$		0			0
$635$	965.905	+	170.315i	1.52111	+	0.268213i
$636$		0			0
$637$	133.209	−	111.776i	0.209119	−	0.175472i
$638$		0			0
$639$	−337.187	+	14.5943i	−0.527679	+	0.0228393i
$640$		0			0
$641$	−427.296	+	1173.99i	−0.666609	+	1.83149i	−0.122520	+	0.992466i	$0.539098\pi$
$641$	−427.296	+	1173.99i	−0.666609	+	1.83149i	−0.544089	+	0.839027i	$0.683125\pi$
$642$		0			0
$643$	−210.451	−	176.590i	−0.327296	−	0.274634i	0.464301	−	0.885677i	$-0.346306\pi$
$643$	−210.451	−	176.590i	−0.327296	−	0.274634i	−0.791597	+	0.611044i	$0.790750\pi$
$644$		0			0
$645$	239.709	−	69.8198i	0.371643	−	0.108248i
$646$		0			0
$647$		−	757.869i		−	1.17136i	−0.810543	−	0.585680i	$-0.800828\pi$
$647$		−	757.869i		−	1.17136i	0.810543	−	0.585680i	$-0.199172\pi$
$648$		0			0
$649$	1537.51			2.36904
$650$		0			0
$651$	4.21240	+	14.4623i	0.00647066	+	0.0222155i
$652$		0			0
$653$	−828.032	+	986.810i	−1.26804	+	1.51119i	−0.507937	+	0.861394i	$0.669592\pi$
$653$	−828.032	+	986.810i	−1.26804	+	1.51119i	−0.760105	+	0.649800i	$0.774853\pi$
$654$		0			0
$655$	1254.20	+	456.491i	1.91481	+	0.696934i
$656$		0			0
$657$	572.736	+	298.422i	0.871744	+	0.454220i
$658$		0			0
$659$	88.1142	+	105.010i	0.133709	+	0.159348i	0.828744	−	0.559627i	$-0.189056\pi$
$659$	88.1142	+	105.010i	0.133709	+	0.159348i	−0.695035	+	0.718976i	$0.744611\pi$
$660$		0			0
$661$	193.775	−	1098.96i	0.293155	−	1.66256i	−0.381453	−	0.924388i	$-0.624576\pi$
$661$	193.775	−	1098.96i	0.293155	−	1.66256i	0.674608	−	0.738176i	$-0.264313\pi$
$662$		0			0
$663$	9.95608	+	4.38302i	0.0150167	+	0.00661089i
$664$		0			0
$665$	9.11215	+	5.26090i	0.0137025	+	0.00791113i
$666$		0			0
$667$	446.583	+	773.505i	0.669540	+	1.15968i
$668$		0			0
$669$	67.6134	−	1028.60i	0.101066	−	1.53753i
$670$		0			0
$671$	−10.8486	−	29.8062i	−0.0161678	−	0.0444206i
$672$		0			0
$673$	85.6892	+	485.968i	0.127324	+	0.722092i	0.979900	+	0.199488i	$0.0639280\pi$
$673$	85.6892	+	485.968i	0.127324	+	0.722092i	−0.852576	+	0.522603i	$0.824961\pi$
$674$		0			0
$675$	106.775	−	175.736i	0.158186	−	0.260349i
$676$		0			0
$677$	776.245	−	136.873i	1.14660	−	0.202176i	0.432106	−	0.901823i	$-0.357770\pi$
$677$	776.245	−	136.873i	1.14660	−	0.202176i	0.714489	+	0.699647i	$0.246659\pi$
$678$		0			0
$679$	13.0325	−	4.74346i	0.0191937	−	0.00698594i
$680$		0			0
$681$	217.411	−	325.246i	0.319253	−	0.477600i
$682$		0			0
$683$	964.040	−	556.589i	1.41148	−	0.814918i	0.415951	−	0.909387i	$-0.363449\pi$
$683$	964.040	−	556.589i	1.41148	−	0.814918i	0.995528	+	0.0944693i	$0.0301154\pi$
$684$		0			0
$685$	−583.039	+	1009.85i	−0.851152	+	1.47424i
$686$		0			0
$687$	−256.626	+	28.0561i	−0.373546	+	0.0408385i
$688$		0			0
$689$	−149.523	−	26.3650i	−0.217015	−	0.0382656i
$690$		0			0
$691$	678.617	−	569.427i	0.982080	−	0.824063i	−0.00232204	−	0.999997i	$-0.500739\pi$
$691$	678.617	−	569.427i	0.982080	−	0.824063i	0.984402	+	0.175934i	$0.0562947\pi$
$692$		0			0
$693$	−54.5474	−	41.8884i	−0.0787119	−	0.0604450i
$694$		0			0
$695$	−201.412	+	553.376i	−0.289802	+	0.796224i
$696$		0			0
$697$	−51.7715	−	43.4414i	−0.0742776	−	0.0623263i
$698$		0			0
$699$	−197.049	+	804.613i	−0.281901	+	1.15109i
$700$		0			0
$701$			90.4404i			0.129016i	0.997917	+	0.0645081i	$0.0205478\pi$
$701$			90.4404i			0.129016i	−0.997917	+	0.0645081i	$0.979452\pi$
$702$		0			0
$703$	256.181			0.364411
$704$		0			0
$705$	−825.082	+	861.566i	−1.17033	+	1.22208i
$706$		0			0
$707$	−14.6353	+	17.4417i	−0.0207006	+	0.0246700i
$708$		0			0
$709$	1178.47	+	428.927i	1.66215	+	0.604974i	0.990699	−	0.136071i	$-0.0434476\pi$
$709$	1178.47	+	428.927i	1.66215	+	0.604974i	0.671455	+	0.741046i	$0.265670\pi$
$710$		0			0
$711$	706.993	+	772.133i	0.994365	+	1.08598i
$712$		0			0
$713$	−235.846	−	281.071i	−0.330780	−	0.394209i
$714$		0			0
$715$	69.5594	−	394.491i	0.0972859	−	0.551736i
$716$		0			0
$717$	−840.846	+	616.290i	−1.17273	+	0.859539i
$718$		0			0
$719$	368.436	+	212.717i	0.512429	+	0.295851i	0.733831	−	0.679332i	$-0.237730\pi$
$719$	368.436	+	212.717i	0.512429	+	0.295851i	−0.221403	+	0.975182i	$0.571064\pi$
$720$		0			0
$721$	33.9692	+	58.8364i	0.0471140	+	0.0816038i
$722$		0			0
$723$	−1163.43	+	573.467i	−1.60917	+	0.793177i
$724$		0			0
$725$	−82.0929	−	225.548i	−0.113232	−	0.311101i
$726$		0			0
$727$	−21.5447	−	122.186i	−0.0296350	−	0.168069i	0.966398	−	0.257049i	$-0.0827502\pi$
$727$	−21.5447	−	122.186i	−0.0296350	−	0.168069i	−0.996033	+	0.0889805i	$0.971639\pi$
$728$		0			0
$729$	94.3346	+	722.871i	0.129403	+	0.991592i
$730$		0			0
$731$	14.6183	−	2.57761i	0.0199977	−	0.00352614i
$732$		0			0
$733$	−353.077	+	128.510i	−0.481688	+	0.175320i	−0.571440	−	0.820644i	$-0.693615\pi$
$733$	−353.077	+	128.510i	−0.481688	+	0.175320i	0.0897515	+	0.995964i	$0.471393\pi$
$734$		0			0
$735$	−370.030	−	750.704i	−0.503442	−	1.02137i
$736$		0			0
$737$	600.463	−	346.677i	0.814739	−	0.470390i
$738$		0			0
$739$	−118.043	+	204.456i	−0.159733	+	0.276666i	−0.934772	−	0.355247i	$-0.884397\pi$
$739$	−118.043	+	204.456i	−0.159733	+	0.276666i	0.775039	+	0.631913i	$0.217730\pi$
$740$		0			0
$741$	−29.9902	−	40.9177i	−0.0404726	−	0.0552196i
$742$		0			0
$743$	285.084	+	50.2680i	0.383693	+	0.0676555i	0.362168	−	0.932113i	$-0.382037\pi$
$743$	285.084	+	50.2680i	0.383693	+	0.0676555i	0.0215253	+	0.999768i	$0.493148\pi$
$744$		0			0
$745$	−354.185	+	297.196i	−0.475416	+	0.398921i
$746$		0			0
$747$	−861.198	+	788.544i	−1.15288	+	1.05562i
$748$		0			0
$749$	−17.7653	+	48.8098i	−0.0237187	+	0.0651666i
$750$		0			0
$751$	−119.567	−	100.328i	−0.159210	−	0.133593i	0.559702	−	0.828694i	$-0.310915\pi$
$751$	−119.567	−	100.328i	−0.159210	−	0.133593i	−0.718913	+	0.695100i	$0.755360\pi$
$752$		0			0
$753$	−222.293	−	212.880i	−0.295210	−	0.282709i
$754$		0			0
$755$			279.511i			0.370214i
$756$		0			0
$757$	103.142			0.136251			0.0681257	−	0.997677i	$-0.478298\pi$
$757$	103.142			0.136251			0.0681257	+	0.997677i	$0.478298\pi$
$758$		0			0
$759$	1627.15	+	398.487i	2.14381	+	0.525016i
$760$		0			0
$761$	217.656	−	259.393i	0.286013	−	0.340858i	−0.603839	−	0.797107i	$-0.706363\pi$
$761$	217.656	−	259.393i	0.286013	−	0.340858i	0.889852	+	0.456249i	$0.150807\pi$
$762$		0			0
$763$	41.2142	+	15.0007i	0.0540159	+	0.0196602i
$764$		0			0
$765$	31.8885	−	41.5254i	0.0416843	−	0.0542816i
$766$		0			0
$767$	178.547	+	212.784i	0.232786	+	0.277423i
$768$		0			0
$769$	−10.0662	+	57.0881i	−0.0130899	+	0.0742368i	−0.990653	−	0.136406i	$-0.956445\pi$
$769$	−10.0662	+	57.0881i	−0.0130899	+	0.0742368i	0.977563	+	0.210643i	$0.0675558\pi$
$770$		0			0
$771$	116.202	+	1062.89i	0.150716	+	1.37858i
$772$		0			0
$773$	−261.859	−	151.184i	−0.338757	−	0.195581i	0.320965	−	0.947091i	$-0.395993\pi$
$773$	−261.859	−	151.184i	−0.338757	−	0.195581i	−0.659722	+	0.751510i	$0.729326\pi$
$774$		0			0
$775$	49.3007	+	85.3913i	0.0636138	+	0.110182i
$776$		0			0
$777$	52.1628	+	34.8684i	0.0671337	+	0.0448756i
$778$		0			0
$779$	107.798	+	296.172i	0.138380	+	0.380195i
$780$		0			0
$781$	128.309	+	727.676i	0.164288	+	0.931724i
$782$		0			0
$783$	727.219	+	441.851i	0.928760	+	0.564306i
$784$		0			0
$785$	−1296.59	+	228.623i	−1.65170	+	0.291240i
$786$		0			0
$787$	606.441	−	220.727i	0.770574	−	0.280466i	0.0733373	−	0.997307i	$-0.476635\pi$
$787$	606.441	−	220.727i	0.770574	−	0.280466i	0.697236	+	0.716841i	$0.254413\pi$
$788$		0			0
$789$	−452.521	−	29.7456i	−0.573538	−	0.0377004i
$790$		0			0
$791$	−20.1479	+	11.6324i	−0.0254714	+	0.0147059i
$792$		0			0
$793$	2.86522	−	4.96271i	0.00361314	−	0.00625814i
$794$		0			0
$795$	−294.438	+	668.819i	−0.370362	+	0.841281i
$796$		0			0
$797$	244.483	+	43.1090i	0.306754	+	0.0540891i	0.324906	−	0.945746i	$-0.394667\pi$
$797$	244.483	+	43.1090i	0.306754	+	0.0540891i	−0.0181521	+	0.999835i	$0.505778\pi$
$798$		0			0
$799$	−54.3306	+	45.5888i	−0.0679982	+	0.0570573i
$800$		0			0
$801$	521.416	−	1000.71i	0.650956	−	1.24932i
$802$		0			0
$803$	483.584	−	1328.64i	0.602222	−	1.65459i
$804$		0			0
$805$	−48.0851	−	40.3482i	−0.0597330	−	0.0501220i
$806$		0			0
$807$	−889.476	+	259.076i	−1.10220	+	0.321036i
$808$		0			0
$809$		−	1029.54i		−	1.27260i	−0.771441	−	0.636301i	$-0.780463\pi$
$809$		−	1029.54i		−	1.27260i	0.771441	−	0.636301i	$-0.219537\pi$
$810$		0			0
$811$	902.912			1.11333			0.556666	−	0.830737i	$-0.312080\pi$
$811$	902.912			1.11333			0.556666	+	0.830737i	$0.312080\pi$
$812$		0			0
$813$	−343.413	−	1179.03i	−0.422402	−	1.45022i
$814$		0			0
$815$	245.653	−	292.758i	0.301415	−	0.359212i
$816$		0			0
$817$	−65.0510	−	23.6766i	−0.0796217	−	0.0289799i
$818$		0			0
$819$	−0.537287	−	12.4135i	−0.000656028	−	0.0151569i
$820$		0			0
$821$	−925.664	−	1103.16i	−1.12748	−	1.34368i	−0.931782	−	0.363019i	$-0.881746\pi$
$821$	−925.664	−	1103.16i	−1.12748	−	1.34368i	−0.195702	−	0.980664i	$-0.562698\pi$
$822$		0			0
$823$	59.6550	−	338.320i	0.0724848	−	0.411082i	−0.926877	−	0.375365i	$-0.877517\pi$
$823$	59.6550	−	338.320i	0.0724848	−	0.411082i	0.999362	−	0.0357168i	$-0.0113714\pi$
$824$		0			0
$825$	−412.031	−	181.391i	−0.499432	−	0.219868i
$826$		0			0
$827$	488.768	+	282.190i	0.591013	+	0.341222i	0.765498	−	0.643438i	$-0.222493\pi$
$827$	488.768	+	282.190i	0.591013	+	0.341222i	−0.174485	+	0.984660i	$0.555826\pi$
$828$		0			0
$829$	25.8761	+	44.8187i	0.0312136	+	0.0540636i	0.881210	−	0.472725i	$-0.156729\pi$
$829$	25.8761	+	44.8187i	0.0312136	+	0.0540636i	−0.849997	+	0.526788i	$0.823396\pi$
$830$		0			0
$831$	−30.7544	+	467.868i	−0.0370090	+	0.563018i
$832$		0			0
$833$	−17.0188	−	46.7587i	−0.0204307	−	0.0561329i
$834$		0			0
$835$	83.9459	+	476.081i	0.100534	+	0.570157i
$836$		0			0
$837$	−325.721	−	126.879i	−0.389153	−	0.151587i
$838$		0			0
$839$	−228.804	+	40.3443i	−0.272710	+	0.0480861i	−0.308331	−	0.951279i	$-0.599770\pi$
$839$	−228.804	+	40.3443i	−0.272710	+	0.0480861i	0.0356207	+	0.999365i	$0.488659\pi$
$840$		0			0
$841$	143.070	−	52.0731i	0.170118	−	0.0619181i
$842$		0			0
$843$	367.244	−	549.394i	0.435639	−	0.651713i
$844$		0			0
$845$	−773.184	+	446.398i	−0.915011	+	0.528282i
$846$		0			0
$847$	−51.8221	+	89.7586i	−0.0611832	+	0.105972i
$848$		0			0
$849$	−546.080	+	59.7011i	−0.643203	+	0.0703193i
$850$		0			0
$851$	−1505.10	−	265.389i	−1.76862	−	0.311856i
$852$		0			0
$853$	38.0360	−	31.9160i	0.0445909	−	0.0374162i	−0.620220	−	0.784428i	$-0.712957\pi$
$853$	38.0360	−	31.9160i	0.0445909	−	0.0374162i	0.664811	+	0.747012i	$0.268512\pi$
$854$		0			0
$855$	−225.620	+	93.3551i	−0.263883	+	0.109187i
$856$		0			0
$857$	−406.056	+	1115.63i	−0.473811	+	1.30179i	0.440856	+	0.897578i	$0.354675\pi$
$857$	−406.056	+	1115.63i	−0.473811	+	1.30179i	−0.914667	+	0.404208i	$0.867547\pi$
$858$		0			0
$859$	−999.373	−	838.573i	−1.16341	−	0.976220i	−0.163467	−	0.986549i	$-0.552268\pi$
$859$	−999.373	−	838.573i	−1.16341	−	0.976220i	−0.999947	+	0.0103284i	$0.996712\pi$
$860$		0			0
$861$	−18.3620	+	74.9778i	−0.0213263	+	0.0870822i
$862$		0			0
$863$			45.2209i			0.0523997i	0.999657	+	0.0261998i	$0.00834062\pi$
$863$			45.2209i			0.0523997i	−0.999657	+	0.0261998i	$0.991659\pi$
$864$		0			0
$865$	286.068			0.330715
$866$		0			0
$867$	−597.507	+	623.928i	−0.689166	+	0.719640i
$868$		0			0
$869$	1473.29	−	1755.80i	1.69538	−	2.02048i
$870$		0			0
$871$	117.708	+	42.8424i	0.135142	+	0.0491876i
$872$		0			0
$873$	−96.8967	+	306.913i	−0.110993	+	0.351561i
$874$		0			0
$875$	−24.7498	−	29.4957i	−0.0282855	−	0.0337093i
$876$		0			0
$877$	−191.837	+	1087.96i	−0.218742	+	1.24055i	0.655551	+	0.755151i	$0.272436\pi$
$877$	−191.837	+	1087.96i	−0.218742	+	1.24055i	−0.874293	+	0.485398i	$0.838675\pi$
$878$		0			0
$879$	855.986	−	627.386i	0.973818	−	0.713750i
$880$		0			0
$881$	−996.015	−	575.049i	−1.13055	−	0.652724i	−0.186477	−	0.982459i	$-0.559707\pi$
$881$	−996.015	−	575.049i	−1.13055	−	0.652724i	−0.944073	+	0.329736i	$0.893040\pi$
$882$		0			0
$883$	−47.1393	−	81.6476i	−0.0533853	−	0.0924661i	0.838098	−	0.545520i	$-0.183668\pi$
$883$	−47.1393	−	81.6476i	−0.0533853	−	0.0924661i	−0.891483	+	0.453054i	$0.850334\pi$
$884$		0			0
$885$	1199.15	−	591.074i	1.35497	−	0.667880i
$886$		0			0
$887$	398.652	+	1095.29i	0.449439	+	1.23482i	0.933116	+	0.359577i	$0.117079\pi$
$887$	398.652	+	1095.29i	0.449439	+	1.23482i	−0.483677	+	0.875247i	$0.660699\pi$
$888$		0			0
$889$	−11.5658	−	65.5931i	−0.0130099	−	0.0737830i
$890$		0			0
$891$	1541.94	−	411.914i	1.73058	−	0.462306i
$892$		0			0
$893$	325.734	−	57.4357i	0.364764	−	0.0643177i
$894$		0			0
$895$	−610.114	+	222.063i	−0.681692	+	0.248115i
$896$		0			0
$897$	133.808	+	271.465i	0.149173	+	0.302637i
$898$		0			0
$899$	−353.361	+	204.013i	−0.393060	+	0.226934i
$900$		0			0
$901$	−21.7233	+	37.6258i	−0.0241102	+	0.0417600i
$902$		0			0
$903$	−10.0229	−	13.6749i	−0.0110996	−	0.0151439i
$904$		0			0
$905$	−1034.40	−	182.392i	−1.14298	−	0.201538i
$906$		0			0
$907$	−318.925	+	267.610i	−0.351626	+	0.295050i	−0.801443	−	0.598071i	$-0.795934\pi$
$907$	−318.925	+	267.610i	−0.351626	+	0.295050i	0.449816	+	0.893121i	$0.351489\pi$
$908$		0			0
$909$	−114.165	−	515.888i	−0.125594	−	0.567534i
$910$		0			0
$911$	318.199	−	874.246i	0.349286	−	0.959655i	−0.633310	−	0.773898i	$-0.718304\pi$
$911$	318.199	−	874.246i	0.349286	−	0.959655i	0.982596	−	0.185757i	$-0.0594736\pi$
$912$		0			0
$913$	1958.33	+	1643.23i	2.14494	+	1.79982i
$914$		0			0
$915$	−19.9197	−	19.0762i	−0.0217702	−	0.0208483i
$916$		0			0
$917$		−	90.6368i		−	0.0988406i
$918$		0			0
$919$	−56.9376			−0.0619561			−0.0309780	−	0.999520i	$-0.509862\pi$
$919$	−56.9376			−0.0619561			−0.0309780	+	0.999520i	$0.509862\pi$
$920$		0			0
$921$	754.764	+	184.841i	0.819505	+	0.200696i
$922$		0			0
$923$	−85.8066	+	102.260i	−0.0929649	+	0.110791i
$924$		0			0
$925$	385.940	+	140.471i	0.417233	+	0.151860i
$926$		0			0
$927$	−1563.03	−	206.377i	−1.68611	−	0.222629i
$928$		0			0
$929$	−493.681	−	588.346i	−0.531411	−	0.633311i	0.431828	−	0.901956i	$-0.357869\pi$
$929$	−493.681	−	588.346i	−0.531411	−	0.633311i	−0.963239	+	0.268645i	$0.913424\pi$
$930$		0			0
$931$	−40.2966	+	228.533i	−0.0432831	+	0.245471i
$932$		0			0
$933$	150.954	+	1380.76i	0.161794	+	1.47991i
$934$		0			0
$935$	−99.2689	−	57.3129i	−0.106170	−	0.0612973i
$936$		0			0
$937$	−662.157	−	1146.89i	−0.706677	−	1.22400i	−0.966083	−	0.258233i	$-0.916860\pi$
$937$	−662.157	−	1146.89i	−0.706677	−	1.22400i	0.259405	−	0.965769i	$-0.416473\pi$
$938$		0			0
$939$	−520.535	−	347.952i	−0.554350	−	0.370556i
$940$		0			0
$941$	65.3646	+	179.588i	0.0694629	+	0.190848i	0.969566	−	0.244828i	$-0.0787316\pi$
$941$	65.3646	+	179.588i	0.0694629	+	0.190848i	−0.900104	+	0.435676i	$0.856509\pi$
$942$		0			0
$943$	−326.508	−	1851.72i	−0.346244	−	1.96365i
$944$		0			0
$945$	−58.6465	−	11.7001i	−0.0620598	−	0.0123810i
$946$		0			0
$947$	1798.57	−	317.136i	1.89923	−	0.334885i	0.903606	−	0.428364i	$-0.140910\pi$
$947$	1798.57	−	317.136i	1.89923	−	0.334885i	0.995621	+	0.0934792i	$0.0297989\pi$
$948$		0			0
$949$	240.034	−	87.3652i	0.252934	−	0.0920603i
$950$		0			0
$951$	−181.295	−	11.9171i	−0.190636	−	0.0125311i
$952$		0			0
$953$	859.093	−	495.998i	0.901462	−	0.520459i	0.0237876	−	0.999717i	$-0.492427\pi$
$953$	859.093	−	495.998i	0.901462	−	0.520459i	0.877674	+	0.479258i	$0.159094\pi$
$954$		0			0
$955$	378.414	−	655.433i	0.396245	−	0.686317i
$956$		0			0
$957$	750.622	−	1705.04i	0.784349	−	1.78166i
$958$		0			0
$959$	77.9835	+	13.7506i	0.0813175	+	0.0143385i
$960$		0			0
$961$	−607.767	+	509.977i	−0.632432	+	0.530673i
$962$		0			0
$963$	−647.268	−	1016.85i	−0.672137	−	1.05592i
$964$		0			0
$965$	−269.734	+	741.087i	−0.279517	+	0.767966i
$966$		0			0
$967$	20.2704	+	17.0089i	0.0209621	+	0.0175893i	0.653209	−	0.757178i	$-0.273423\pi$
$967$	20.2704	+	17.0089i	0.0209621	+	0.0175893i	−0.632246	+	0.774767i	$0.717867\pi$
$968$		0			0
$969$	−13.9377	+	4.05962i	−0.0143836	+	0.00418949i
$970$		0			0
$971$			382.443i			0.393865i	0.980417	+	0.196932i	$0.0630980\pi$
$971$			382.443i			0.393865i	−0.980417	+	0.196932i	$0.936902\pi$
$972$		0			0
$973$	39.9906			0.0411003
$974$		0			0
$975$	−22.7444	−	78.0875i	−0.0233276	−	0.0800898i
$976$		0			0
$977$	−71.7934	+	85.5601i	−0.0734835	+	0.0875743i	−0.801534	−	0.597950i	$-0.795982\pi$
$977$	−71.7934	+	85.5601i	−0.0734835	+	0.0875743i	0.728050	+	0.685524i	$0.240427\pi$
$978$		0			0
$979$	−2321.45	−	844.938i	−2.37125	−	0.863063i
$980$		0			0
$981$	−858.614	+	546.542i	−0.875244	+	0.557127i
$982$		0			0
$983$	−130.905	−	156.006i	−0.133169	−	0.158704i	0.695339	−	0.718682i	$-0.255254\pi$
$983$	−130.905	−	156.006i	−0.133169	−	0.158704i	−0.828508	+	0.559978i	$0.810810\pi$
$984$		0			0
$985$	145.677	−	826.174i	0.147895	−	0.838755i
$986$		0			0
$987$	74.1425	+	32.6402i	0.0751191	+	0.0330701i
$988$		0			0
$989$	357.655	+	206.492i	0.361633	+	0.208789i
$990$		0			0
$991$	−542.542	−	939.711i	−0.547470	−	0.948245i	−0.998447	−	0.0557098i	$-0.982258\pi$
$991$	−542.542	−	939.711i	−0.547470	−	0.948245i	0.450977	−	0.892535i	$-0.351076\pi$
$992$		0			0
$993$	−22.8346	+	347.383i	−0.0229956	+	0.349832i
$994$		0			0
$995$	−144.842	−	397.951i	−0.145570	−	0.399951i
$996$		0			0
$997$	10.0693	+	57.1056i	0.0100996	+	0.0572775i	0.989441	−	0.144936i	$-0.0462976\pi$
$997$	10.0693	+	57.1056i	0.0100996	+	0.0572775i	−0.979341	+	0.202213i	$0.935187\pi$
$998$		0			0
$999$	−1379.03	+	467.248i	−1.38041	+	0.467716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.u.a.41.8	✓	108
4.3	odd	2		432.3.bc.d.257.11		108
27.2	odd	18	inner	216.3.u.a.137.8	yes	108
108.83	even	18		432.3.bc.d.353.11		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.u.a.41.8	✓	108	1.1	even	1	trivial
216.3.u.a.137.8	yes	108	27.2	odd	18	inner
432.3.bc.d.257.11		108	4.3	odd	2
432.3.bc.d.353.11		108	108.83	even	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.u (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.838943 - 2.88031i) q^{3} +(-3.67098 + 4.37491i) q^{5} +(0.364439 + 0.132645i) q^{7} +(-7.59235 + 4.83283i) q^{9} +O(q^{10})\)	\(q+(-0.838943 - 2.88031i) q^{3} +(-3.67098 + 4.37491i) q^{5} +(0.364439 + 0.132645i) q^{7} +(-7.59235 + 4.83283i) q^{9} +(12.6654 + 15.0941i) q^{11} +(-0.618143 + 3.50566i) q^{13} +(15.6808 + 6.90327i) q^{15} +(0.882158 + 0.509314i) q^{17} +(-2.37524 - 4.11403i) q^{19} +(0.0763146 - 1.16098i) q^{21} +(9.69292 + 26.6311i) q^{23} +(-1.32250 - 7.50025i) q^{25} +(20.2896 + 17.8138i) q^{27} +(31.0371 - 5.47268i) q^{29} +(-12.1659 + 4.42803i) q^{31} +(32.8500 - 49.1434i) q^{33} +(-1.91816 + 1.10745i) q^{35} +(-26.9637 + 46.7025i) q^{37} +(10.6160 - 1.16061i) q^{39} +(-65.3390 - 11.5210i) q^{41} +(11.1631 - 9.36696i) q^{43} +(6.72821 - 50.9571i) q^{45} +(-23.8137 + 65.4275i) q^{47} +(-37.4210 - 31.3999i) q^{49} +(0.726901 - 2.96817i) q^{51} +42.6520i q^{53} -112.530 q^{55} +(-9.85699 + 10.2928i) q^{57} +(50.1572 - 59.7750i) q^{59} +(-1.51271 - 0.550581i) q^{61} +(-3.40799 + 0.754184i) q^{63} +(-13.0678 - 15.5735i) q^{65} +(6.11046 - 34.6541i) q^{67} +(68.5739 - 50.2605i) q^{69} +(32.4762 + 18.7502i) q^{71} +(-35.8788 - 62.1440i) q^{73} +(-20.4935 + 10.1015i) q^{75} +(2.61362 + 7.18086i) q^{77} +(-20.1994 - 114.557i) q^{79} +(34.2875 - 73.3851i) q^{81} +(127.771 - 22.5294i) q^{83} +(-5.46659 + 1.98968i) q^{85} +(-41.8014 - 84.8051i) q^{87} +(-108.581 + 62.6890i) q^{89} +(-0.690283 + 1.19561i) q^{91} +(22.9606 + 31.3267i) q^{93} +(26.7180 + 4.71110i) q^{95} +(27.3942 - 22.9865i) q^{97} +(-169.107 - 53.3895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q+O(q^{10}) \) 108 * q	\( 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) \) 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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