LMFDB - Embedded newform 216.4.l.b.179.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,4,Mod(35,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("216.35");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	216.l (of order $6$, degree $2$, not 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:	$12.7444125612$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.20
Character	$\chi$	$=$	216.179
Dual form			216.4.l.b.35.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.867121 + 2.69223i) q^{2} +(-6.49620 + 4.66898i) q^{4} +(8.51655 - 14.7511i) q^{5} +(-9.57807 + 5.52990i) q^{7} +(-18.2030 - 13.4407i) q^{8} +O(q^{10})$	\(q+(0.867121 + 2.69223i) q^{2} +(-6.49620 + 4.66898i) q^{4} +(8.51655 - 14.7511i) q^{5} +(-9.57807 + 5.52990i) q^{7} +(-18.2030 - 13.4407i) q^{8} +(47.0983 + 10.1375i) q^{10} +(-25.7667 + 14.8764i) q^{11} +(-52.0658 - 30.0602i) q^{13} +(-23.1931 - 20.9913i) q^{14} +(20.4013 - 60.6613i) q^{16} -91.7888i q^{17} -136.507 q^{19} +(13.5474 + 135.590i) q^{20} +(-62.3936 - 56.4703i) q^{22} +(30.0089 - 51.9770i) q^{23} +(-82.5634 - 143.004i) q^{25} +(35.7816 - 166.239i) q^{26} +(36.4021 - 80.6432i) q^{28} +(65.0911 + 112.741i) q^{29} +(148.423 + 85.6920i) q^{31} +(181.004 + 2.32417i) q^{32} +(247.117 - 79.5920i) q^{34} +188.383i q^{35} -259.167i q^{37} +(-118.368 - 367.509i) q^{38} +(-353.292 + 154.045i) q^{40} +(-14.3285 - 8.27259i) q^{41} +(-85.3289 - 147.794i) q^{43} +(97.9281 - 216.945i) q^{44} +(165.955 + 35.7206i) q^{46} +(89.8841 + 155.684i) q^{47} +(-110.340 + 191.115i) q^{49} +(313.407 - 346.282i) q^{50} +(478.581 - 47.8171i) q^{52} +205.014 q^{53} +506.783i q^{55} +(248.675 + 28.0753i) q^{56} +(-247.083 + 273.001i) q^{58} +(-624.620 - 360.624i) q^{59} +(-163.824 + 94.5836i) q^{61} +(-102.002 + 473.894i) q^{62} +(150.696 + 489.321i) q^{64} +(-886.843 + 512.019i) q^{65} +(197.490 - 342.063i) q^{67} +(428.560 + 596.278i) q^{68} +(-507.170 + 163.351i) q^{70} -131.203 q^{71} -410.081 q^{73} +(697.737 - 224.729i) q^{74} +(886.778 - 637.350i) q^{76} +(164.530 - 284.975i) q^{77} +(144.247 - 83.2809i) q^{79} +(-721.072 - 817.566i) q^{80} +(9.84712 - 45.7491i) q^{82} +(430.457 - 248.524i) q^{83} +(-1353.99 - 781.724i) q^{85} +(323.905 - 357.880i) q^{86} +(668.980 + 75.5276i) q^{88} +313.674i q^{89} +664.920 q^{91} +(47.7355 + 477.764i) q^{92} +(-341.196 + 376.985i) q^{94} +(-1162.57 + 2013.63i) q^{95} +(-319.471 - 553.340i) q^{97} +(-610.204 - 131.342i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 3 q^{2} - 17 q^{4}+O(q^{10}) $ 64 * q + 3 * q^2 - 17 * q^4	$ 64 q + 3 q^{2} - 17 q^{4} + 12 q^{10} - 48 q^{11} - 72 q^{14} + 127 q^{16} - 220 q^{19} + 234 q^{20} - 217 q^{22} - 902 q^{25} - 132 q^{28} + 693 q^{32} + 509 q^{34} + 1977 q^{38} - 36 q^{40} - 1620 q^{41} - 292 q^{43} + 48 q^{46} + 1762 q^{49} + 1227 q^{50} + 330 q^{52} - 942 q^{56} - 282 q^{58} - 5592 q^{59} + 1090 q^{64} + 6 q^{65} + 68 q^{67} + 2025 q^{68} + 600 q^{70} - 868 q^{73} + 420 q^{74} - 1471 q^{76} + 362 q^{82} - 3654 q^{83} + 4119 q^{86} + 3155 q^{88} - 1380 q^{91} + 744 q^{92} - 138 q^{94} - 1912 q^{97}+O(q^{100}) $ 64 * q + 3 * q^2 - 17 * q^4 + 12 * q^10 - 48 * q^11 - 72 * q^14 + 127 * q^16 - 220 * q^19 + 234 * q^20 - 217 * q^22 - 902 * q^25 - 132 * q^28 + 693 * q^32 + 509 * q^34 + 1977 * q^38 - 36 * q^40 - 1620 * q^41 - 292 * q^43 + 48 * q^46 + 1762 * q^49 + 1227 * q^50 + 330 * q^52 - 942 * q^56 - 282 * q^58 - 5592 * q^59 + 1090 * q^64 + 6 * q^65 + 68 * q^67 + 2025 * q^68 + 600 * q^70 - 868 * q^73 + 420 * q^74 - 1471 * q^76 + 362 * q^82 - 3654 * q^83 + 4119 * q^86 + 3155 * q^88 - 1380 * q^91 + 744 * q^92 - 138 * q^94 - 1912 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.867121	+	2.69223i	0.306574	+	0.951847i
$2$	0.867121	+	2.69223i	0.306574	+	0.951847i
$3$		0			0
$3$		0			0
$4$	−6.49620	+	4.66898i	−0.812025	+	0.583623i
$5$	8.51655	−	14.7511i	0.761744	−	1.31938i	−0.180207	−	0.983629i	$-0.557677\pi$
$5$	8.51655	−	14.7511i	0.761744	−	1.31938i	0.941951	−	0.335750i	$-0.108990\pi$
$6$		0			0
$7$	−9.57807	+	5.52990i	−0.517167	+	0.298587i	−0.735775	−	0.677226i	$-0.763182\pi$
$7$	−9.57807	+	5.52990i	−0.517167	+	0.298587i	0.218608	+	0.975813i	$0.429849\pi$
$8$	−18.2030	−	13.4407i	−0.804465	−	0.594000i
$9$		0			0
$10$	47.0983	+	10.1375i	1.48938	+	0.320577i
$11$	−25.7667	+	14.8764i	−0.706269	+	0.407765i	−0.809678	−	0.586874i	$-0.800358\pi$
$11$	−25.7667	+	14.8764i	−0.706269	+	0.407765i	0.103409	+	0.994639i	$0.467025\pi$
$12$		0			0
$13$	−52.0658	−	30.0602i	−1.11081	−	0.641324i	−0.171767	−	0.985138i	$-0.554948\pi$
$13$	−52.0658	−	30.0602i	−1.11081	−	0.641324i	−0.939038	+	0.343814i	$0.888281\pi$
$14$	−23.1931	−	20.9913i	−0.442759	−	0.400725i
$15$		0			0
$16$	20.4013	−	60.6613i	0.318770	−	0.947832i
$17$		−	91.7888i		−	1.30953i	−0.755831	−	0.654766i	$-0.772767\pi$
$17$		−	91.7888i		−	1.30953i	0.755831	−	0.654766i	$-0.227233\pi$
$18$		0			0
$19$	−136.507			−1.64826			−0.824129	−	0.566402i	$-0.808335\pi$
$19$	−136.507			−1.64826			−0.824129	+	0.566402i	$0.808335\pi$
$20$	13.5474	+	135.590i	0.151464	+	1.51594i
$21$		0			0
$22$	−62.3936	−	56.4703i	−0.604653	−	0.547250i
$23$	30.0089	−	51.9770i	0.272056	−	0.471215i	−0.697332	−	0.716748i	$-0.745630\pi$
$23$	30.0089	−	51.9770i	0.272056	−	0.471215i	0.969388	+	0.245533i	$0.0789630\pi$
$24$		0			0
$25$	−82.5634	−	143.004i	−0.660507	−	1.14403i
$26$	35.7816	−	166.239i	0.269898	−	1.25393i
$27$		0			0
$28$	36.4021	−	80.6432i	0.245691	−	0.544290i
$29$	65.0911	+	112.741i	0.416797	+	0.721914i	0.995615	−	0.0935428i	$-0.0298192\pi$
$29$	65.0911	+	112.741i	0.416797	+	0.721914i	−0.578818	+	0.815457i	$0.696486\pi$
$30$		0			0
$31$	148.423	+	85.6920i	0.859921	+	0.496475i	0.863986	−	0.503516i	$-0.167961\pi$
$31$	148.423	+	85.6920i	0.859921	+	0.496475i	−0.00406514	+	0.999992i	$0.501294\pi$
$32$	181.004	+	2.32417i	0.999918	+	0.0128393i
$33$		0			0
$34$	247.117	−	79.5920i	1.24647	−	0.401468i
$35$			188.383i			0.909786i
$36$		0			0
$37$		−	259.167i		−	1.15154i	−0.817613	−	0.575768i	$-0.804703\pi$
$37$		−	259.167i		−	1.15154i	0.817613	−	0.575768i	$-0.195297\pi$
$38$	−118.368	−	367.509i	−0.505313	−	1.56889i
$39$		0			0
$40$	−353.292	+	154.045i	−1.39651	+	0.608918i
$41$	−14.3285	−	8.27259i	−0.0545791	−	0.0315113i	0.472462	−	0.881351i	$-0.343365\pi$
$41$	−14.3285	−	8.27259i	−0.0545791	−	0.0315113i	−0.527041	+	0.849840i	$0.676699\pi$
$42$		0			0
$43$	−85.3289	−	147.794i	−0.302617	−	0.524148i	0.674111	−	0.738630i	$-0.264527\pi$
$43$	−85.3289	−	147.794i	−0.302617	−	0.524148i	−0.976728	+	0.214482i	$0.931194\pi$
$44$	97.9281	−	216.945i	0.335528	−	0.743309i
$45$		0			0
$46$	165.955	+	35.7206i	0.531930	+	0.114494i
$47$	89.8841	+	155.684i	0.278956	+	0.483166i	0.971126	−	0.238569i	$-0.0766782\pi$
$47$	89.8841	+	155.684i	0.278956	+	0.483166i	−0.692169	+	0.721735i	$0.743345\pi$
$48$		0			0
$49$	−110.340	+	191.115i	−0.321692	+	0.557187i
$50$	313.407	−	346.282i	0.886449	−	0.979432i
$51$		0			0
$52$	478.581	−	47.8171i	1.27629	−	0.127520i
$53$	205.014			0.531336			0.265668	−	0.964065i	$-0.414407\pi$
$53$	205.014			0.531336			0.265668	+	0.964065i	$0.414407\pi$
$54$		0			0
$55$			506.783i			1.24245i
$56$	248.675	+	28.0753i	0.593403	+	0.0669950i
$57$		0			0
$58$	−247.083	+	273.001i	−0.559372	+	0.618047i
$59$	−624.620	−	360.624i	−1.37828	−	0.795751i	−0.386328	−	0.922362i	$-0.626257\pi$
$59$	−624.620	−	360.624i	−1.37828	−	0.795751i	−0.991952	+	0.126611i	$0.959590\pi$
$60$		0			0
$61$	−163.824	+	94.5836i	−0.343860	+	0.198528i	−0.661978	−	0.749524i	$-0.730283\pi$
$61$	−163.824	+	94.5836i	−0.343860	+	0.198528i	0.318118	+	0.948051i	$0.396949\pi$
$62$	−102.002	+	473.894i	−0.208939	+	0.970719i
$63$		0			0
$64$	150.696	+	489.321i	0.294327	+	0.955705i
$65$	−886.843	+	512.019i	−1.69230	+	0.977049i
$66$		0			0
$67$	197.490	−	342.063i	0.360108	−	0.623726i	−0.627870	−	0.778318i	$-0.716073\pi$
$67$	197.490	−	342.063i	0.360108	−	0.623726i	0.987978	+	0.154592i	$0.0494064\pi$
$68$	428.560	+	596.278i	0.764273	+	1.06337i
$69$		0			0
$70$	−507.170	+	163.351i	−0.865977	+	0.278917i
$71$	−131.203			−0.219310			−0.109655	−	0.993970i	$-0.534975\pi$
$71$	−131.203			−0.219310			−0.109655	+	0.993970i	$0.534975\pi$
$72$		0			0
$73$	−410.081			−0.657485			−0.328743	−	0.944420i	$-0.606625\pi$
$73$	−410.081			−0.657485			−0.328743	+	0.944420i	$0.606625\pi$
$74$	697.737	−	224.729i	1.09609	−	0.353030i
$75$		0			0
$76$	886.778	−	637.350i	1.33843	−	0.961961i
$77$	164.530	−	284.975i	0.243506	−	0.421765i
$78$		0			0
$79$	144.247	−	83.2809i	0.205431	−	0.118605i	−0.393755	−	0.919215i	$-0.628824\pi$
$79$	144.247	−	83.2809i	0.205431	−	0.118605i	0.599186	+	0.800610i	$0.295491\pi$
$80$	−721.072	−	817.566i	−1.00773	−	1.14258i
$81$		0			0
$82$	9.84712	−	45.7491i	0.0132614	−	0.0616115i
$83$	430.457	−	248.524i	0.569262	−	0.328664i	−0.187592	−	0.982247i	$-0.560068\pi$
$83$	430.457	−	248.524i	0.569262	−	0.328664i	0.756855	+	0.653583i	$0.226735\pi$
$84$		0			0
$85$	−1353.99	−	781.724i	−1.72777	−	0.997528i
$86$	323.905	−	357.880i	0.406134	−	0.448735i
$87$		0			0
$88$	668.980	+	75.5276i	0.810381	+	0.0914917i
$89$			313.674i			0.373588i	0.982399	+	0.186794i	$0.0598097\pi$
$89$			313.674i			0.373588i	−0.982399	+	0.186794i	$0.940190\pi$
$90$		0			0
$91$	664.920			0.765963
$92$	47.7355	+	477.764i	0.0540953	+	0.541417i
$93$		0			0
$94$	−341.196	+	376.985i	−0.374380	+	0.413650i
$95$	−1162.57	+	2013.63i	−1.25555	+	2.17468i
$96$		0			0
$97$	−319.471	−	553.340i	−0.334406	−	0.579208i	0.648965	−	0.760819i	$-0.275202\pi$
$97$	−319.471	−	553.340i	−0.334406	−	0.579208i	−0.983371	+	0.181611i	$0.941869\pi$
$98$	−610.204	−	131.342i	−0.628979	−	0.135383i
$99$		0			0
$100$	1204.03	+	543.496i	1.20403	+	0.543496i
$101$	−592.922	−	1026.97i	−0.584138	−	1.01176i	−0.994982	−	0.100052i	$-0.968099\pi$
$101$	−592.922	−	1026.97i	−0.584138	−	1.01176i	0.410844	−	0.911706i	$-0.365234\pi$
$102$		0			0
$103$	633.840	+	365.947i	0.606350	+	0.350076i	0.771536	−	0.636186i	$-0.219489\pi$
$103$	633.840	+	365.947i	0.606350	+	0.350076i	−0.165185	+	0.986263i	$0.552822\pi$
$104$	543.722	+	1246.99i	0.512657	+	1.17574i
$105$		0			0
$106$	177.772	+	551.944i	0.162894	+	0.505751i
$107$			1377.39i			1.24446i	0.782833	+	0.622232i	$0.213774\pi$
$107$			1377.39i			1.24446i	−0.782833	+	0.622232i	$0.786226\pi$
$108$		0			0
$109$			1978.23i			1.73835i	0.494508	+	0.869173i	$0.335348\pi$
$109$			1978.23i			1.73835i	−0.494508	+	0.869173i	$0.664652\pi$
$110$	−1364.38	+	439.443i	−1.18262	+	0.380902i
$111$		0			0
$112$	140.046	+	693.835i	0.118153	+	0.585368i
$113$	−241.953	−	139.691i	−0.201425	−	0.116293i	0.395895	−	0.918296i	$-0.370434\pi$
$113$	−241.953	−	139.691i	−0.201425	−	0.116293i	−0.597320	+	0.802003i	$0.703768\pi$
$114$		0			0
$115$	−511.145	−	885.330i	−0.414474	−	0.717890i
$116$	−949.231	−	428.480i	−0.759775	−	0.342960i
$117$		0			0
$118$	429.262	−	1994.32i	0.334888	−	1.55587i
$119$	507.583	+	879.160i	0.391009	+	0.677247i
$120$		0			0
$121$	−222.884	+	386.047i	−0.167456	+	0.290043i
$122$	−396.696	−	359.035i	−0.294387	−	0.266439i
$123$		0			0
$124$	−1364.28	+	136.311i	−0.988031	+	0.0987185i
$125$	−683.484			−0.489062
$126$		0			0
$127$			1164.89i			0.813916i	0.913447	+	0.406958i	$0.133410\pi$
$127$			1164.89i			0.813916i	−0.913447	+	0.406958i	$0.866590\pi$
$128$	−1186.69	+	830.008i	−0.819451	+	0.573149i
$129$		0			0
$130$	−2147.47	−	1943.60i	−1.44881	−	1.31127i
$131$	255.579	+	147.558i	0.170458	+	0.0984140i	0.582802	−	0.812614i	$-0.301956\pi$
$131$	255.579	+	147.558i	0.170458	+	0.0984140i	−0.412344	+	0.911028i	$0.635290\pi$
$132$		0			0
$133$	1307.48	−	754.872i	0.852425	−	0.492148i
$134$	1092.16	+	235.079i	0.704092	+	0.151550i
$135$		0			0
$136$	−1233.70	+	1670.83i	−0.777863	+	1.05347i
$137$	2059.29	−	1188.93i	1.28421	−	0.741439i	0.306595	−	0.951840i	$-0.400810\pi$
$137$	2059.29	−	1188.93i	1.28421	−	0.741439i	0.977615	+	0.210401i	$0.0674771\pi$
$138$		0			0
$139$	−948.118	+	1642.19i	−0.578549	+	1.00208i	0.417097	+	0.908862i	$0.363048\pi$
$139$	−948.118	+	1642.19i	−0.578549	+	1.00208i	−0.995646	+	0.0932144i	$0.970286\pi$
$140$	−879.556	−	1223.77i	−0.530972	−	0.738769i
$141$		0			0
$142$	−113.769	−	353.230i	−0.0672345	−	0.208749i
$143$	1788.75			1.04604
$144$		0			0
$145$	2217.41			1.26997
$146$	−355.590	−	1104.03i	−0.201568	−	0.625825i
$147$		0			0
$148$	1210.05	+	1683.60i	0.672062	+	0.935075i
$149$	1512.62	−	2619.94i	0.831669	−	1.44049i	−0.0650446	−	0.997882i	$-0.520719\pi$
$149$	1512.62	−	2619.94i	0.831669	−	1.44049i	0.896714	−	0.442611i	$-0.145948\pi$
$150$		0			0
$151$	1082.68	−	625.086i	0.583492	−	0.336880i	−0.179028	−	0.983844i	$-0.557295\pi$
$151$	1082.68	−	625.086i	0.583492	−	0.336880i	0.762520	+	0.646965i	$0.223962\pi$
$152$	2484.84	+	1834.75i	1.32597	+	0.979066i
$153$		0			0
$154$	909.885	+	195.846i	0.476108	+	0.102478i
$155$	2528.10	−	1459.60i	1.31008	−	0.756374i
$156$		0			0
$157$	−2000.27	−	1154.86i	−1.01681	−	0.587055i	−0.103631	−	0.994616i	$-0.533046\pi$
$157$	−2000.27	−	1154.86i	−1.01681	−	0.587055i	−0.913178	+	0.407561i	$0.866379\pi$
$158$	349.291	+	316.131i	0.175874	+	0.159177i
$159$		0			0
$160$	1575.82	−	2650.22i	0.778621	−	1.30949i
$161$			663.786i			0.324929i
$162$		0			0
$163$	−688.368			−0.330780			−0.165390	−	0.986228i	$-0.552888\pi$
$163$	−688.368			−0.330780			−0.165390	+	0.986228i	$0.552888\pi$
$164$	131.706	−	13.1593i	0.0627103	−	0.00626566i
$165$		0			0
$166$	1042.34	+	943.388i	0.487358	+	0.441091i
$167$	−427.655	+	740.720i	−0.198161	+	0.343225i	−0.947932	−	0.318472i	$-0.896830\pi$
$167$	−427.655	+	740.720i	−0.198161	+	0.343225i	0.749771	+	0.661697i	$0.230164\pi$
$168$		0			0
$169$	708.735	+	1227.56i	0.322592	+	0.558746i
$170$	930.511	−	4323.09i	0.419805	−	1.95039i
$171$		0			0
$172$	1244.36	+	561.700i	0.551637	+	0.249007i
$173$	−2177.53	−	3771.59i	−0.956962	−	1.65751i	−0.729814	−	0.683646i	$-0.760393\pi$
$173$	−2177.53	−	3771.59i	−0.956962	−	1.65751i	−0.227147	−	0.973860i	$-0.572940\pi$
$174$		0			0
$175$	1581.60	+	913.135i	0.683185	+	0.394437i
$176$	376.749	+	1866.54i	0.161355	+	0.799407i
$177$		0			0
$178$	−844.482	+	271.993i	−0.355599	+	0.114532i
$179$			943.783i			0.394087i	0.980395	+	0.197044i	$0.0631341\pi$
$179$			943.783i			0.394087i	−0.980395	+	0.197044i	$0.936866\pi$
$180$		0			0
$181$		−	3910.87i		−	1.60604i	−0.595954	−	0.803019i	$-0.703226\pi$
$181$		−	3910.87i		−	1.60604i	0.595954	−	0.803019i	$-0.296774\pi$
$182$	576.567	+	1790.12i	0.234824	+	0.729079i
$183$		0			0
$184$	−1244.86	+	542.794i	−0.498762	+	0.217475i
$185$	−3823.00	−	2207.21i	−1.51931	−	0.877175i
$186$		0			0
$187$	1365.49	+	2365.10i	0.533981	+	0.924882i
$188$	−1310.79	−	591.686i	−0.508506	−	0.229538i
$189$		0			0
$190$	−6429.25	−	1383.84i	−2.45488	−	0.528393i
$191$	−153.069	−	265.123i	−0.0579878	−	0.100438i	0.835574	−	0.549378i	$-0.185135\pi$
$191$	−153.069	−	265.123i	−0.0579878	−	0.100438i	−0.893562	+	0.448940i	$0.851802\pi$
$192$		0			0
$193$	−568.565	+	984.783i	−0.212053	+	0.367286i	−0.952357	−	0.304986i	$-0.901348\pi$
$193$	−568.565	+	984.783i	−0.212053	+	0.367286i	0.740304	+	0.672272i	$0.234682\pi$
$194$	1212.70	−	1339.90i	0.448797	−	0.495873i
$195$		0			0
$196$	−175.520	−	1756.70i	−0.0639648	−	0.640197i
$197$	5080.25			1.83732			0.918661	−	0.395046i	$-0.129271\pi$
$197$	5080.25			1.83732			0.918661	+	0.395046i	$0.129271\pi$
$198$		0			0
$199$		−	4952.26i		−	1.76410i	−0.471154	−	0.882051i	$-0.656162\pi$
$199$		−	4952.26i		−	1.76410i	0.471154	−	0.882051i	$-0.343838\pi$
$200$	−419.174	+	3712.81i	−0.148201	+	1.31268i
$201$		0			0
$202$	2250.71	−	2486.79i	0.783957	−	0.866188i
$203$	−1246.89	−	719.895i	−0.431108	−	0.248900i
$204$		0			0
$205$	−244.060	+	140.908i	−0.0831506	+	0.0480070i
$206$	−435.599	+	2023.76i	−0.147328	+	0.684477i
$207$		0			0
$208$	−2885.70	+	2545.11i	−0.961958	+	0.848423i
$209$	3517.34	−	2030.74i	1.16411	−	0.672101i
$210$		0			0
$211$	2281.12	−	3951.02i	0.744261	−	1.28910i	−0.206279	−	0.978493i	$-0.566135\pi$
$211$	2281.12	−	3951.02i	0.744261	−	1.28910i	0.950539	−	0.310604i	$-0.100531\pi$
$212$	−1331.81	+	957.205i	−0.431458	+	0.310100i
$213$		0			0
$214$	−3708.26	+	1194.37i	−1.18454	+	0.381520i
$215$	−2906.83			−0.922067
$216$		0			0
$217$	−1895.47			−0.592964
$218$	−5325.84	+	1715.36i	−1.65464	+	0.532931i
$219$		0			0
$220$	−2366.16	−	3292.17i	−0.725121	−	1.00890i
$221$	−2759.19	+	4779.06i	−0.839834	+	1.45464i
$222$		0			0
$223$	−2534.14	+	1463.08i	−0.760979	+	0.439352i	−0.829647	−	0.558288i	$-0.811458\pi$
$223$	−2534.14	+	1463.08i	−0.760979	+	0.439352i	0.0686679	+	0.997640i	$0.478125\pi$
$224$	−1746.53	+	978.676i	−0.520958	+	0.291922i
$225$		0			0
$226$	166.279	−	772.521i	0.0489412	−	0.227378i
$227$	−153.706	+	88.7420i	−0.0449418	+	0.0259472i	−0.522303	−	0.852760i	$-0.674927\pi$
$227$	−153.706	+	88.7420i	−0.0449418	+	0.0259472i	0.477361	+	0.878707i	$0.341594\pi$
$228$		0			0
$229$	−964.186	−	556.673i	−0.278232	−	0.160638i	0.354391	−	0.935098i	$-0.384688\pi$
$229$	−964.186	−	556.673i	−0.278232	−	0.160638i	−0.632623	+	0.774460i	$0.718022\pi$
$230$	1940.29	−	2143.81i	0.556255	−	0.614602i
$231$		0			0
$232$	330.468	−	2927.09i	0.0935184	−	0.828332i
$233$			3511.90i			0.987434i	0.869623	+	0.493717i	$0.164362\pi$
$233$			3511.90i			0.987434i	−0.869623	+	0.493717i	$0.835638\pi$
$234$		0			0
$235$	3062.01			0.849973
$236$	5741.40	−	573.649i	1.58362	−	0.158226i
$237$		0			0
$238$	−1926.76	+	2128.87i	−0.524763	+	0.579807i
$239$	1232.78	−	2135.23i	0.333647	−	0.577894i	−0.649577	−	0.760296i	$-0.725054\pi$
$239$	1232.78	−	2135.23i	0.333647	−	0.577894i	0.983224	+	0.182402i	$0.0583873\pi$
$240$		0			0
$241$	1304.59	+	2259.62i	0.348698	+	0.603963i	0.986018	−	0.166636i	$-0.0532905\pi$
$241$	1304.59	+	2259.62i	0.348698	+	0.603963i	−0.637320	+	0.770599i	$0.719957\pi$
$242$	−1232.59	−	265.306i	−0.327414	−	0.0704732i
$243$		0			0
$244$	622.622	−	1379.32i	0.163358	−	0.361894i
$245$	1879.44	+	3255.28i	0.490094	+	0.848867i
$246$		0			0
$247$	7107.36	+	4103.44i	1.83089	+	1.05707i
$248$	−1549.98	−	3554.75i	−0.396869	−	0.910190i
$249$		0			0
$250$	−592.664	−	1840.10i	−0.149933	−	0.465512i
$251$		−	7597.18i		−	1.91048i	−0.295835	−	0.955239i	$-0.595598\pi$
$251$		−	7597.18i		−	1.91048i	0.295835	−	0.955239i	$-0.404402\pi$
$252$		0			0
$253$			1785.70i			0.443739i
$254$	−3136.15	+	1010.10i	−0.774723	+	0.249525i
$255$		0			0
$256$	−3263.58	−	2475.13i	−0.796772	−	0.604280i
$257$	2611.66	+	1507.84i	0.633894	+	0.365979i	0.782259	−	0.622954i	$-0.214068\pi$
$257$	2611.66	+	1507.84i	0.633894	+	0.365979i	−0.148364	+	0.988933i	$0.547401\pi$
$258$		0			0
$259$	1433.17	+	2482.32i	0.343833	+	0.595536i
$260$	3370.50	−	7466.83i	0.803961	−	1.78105i
$261$		0			0
$262$	−175.643	+	816.028i	−0.0414171	+	0.192421i
$263$	−1054.16	−	1825.85i	−0.247156	−	0.428088i	0.715579	−	0.698532i	$-0.246163\pi$
$263$	−1054.16	−	1825.85i	−0.247156	−	0.428088i	−0.962736	+	0.270444i	$0.912830\pi$
$264$		0			0
$265$	1746.01	−	3024.18i	0.404742	−	0.701034i
$266$	3166.03	+	2865.46i	0.729781	+	0.660499i
$267$		0			0
$268$	314.150	+	3144.19i	0.0716035	+	0.716649i
$269$	−3771.97			−0.854949			−0.427475	−	0.904027i	$-0.640597\pi$
$269$	−3771.97			−0.854949			−0.427475	+	0.904027i	$0.640597\pi$
$270$		0			0
$271$		−	912.714i		−	0.204588i	−0.994754	−	0.102294i	$-0.967382\pi$
$271$		−	912.714i		−	0.204588i	0.994754	−	0.102294i	$-0.0326183\pi$
$272$	−5568.02	−	1872.61i	−1.24122	−	0.417439i
$273$		0			0
$274$	4986.52	+	4513.13i	1.09944	+	0.995065i
$275$	4254.78	+	2456.50i	0.932991	+	0.538663i
$276$		0			0
$277$	3177.08	−	1834.29i	0.689141	−	0.397876i	−0.114149	−	0.993464i	$-0.536414\pi$
$277$	3177.08	−	1834.29i	0.689141	−	0.397876i	0.803290	+	0.595588i	$0.203081\pi$
$278$	−5243.28	−	1128.57i	−1.13119	−	0.243480i
$279$		0			0
$280$	2532.00	−	3429.13i	0.540413	−	0.731891i
$281$	178.841	−	103.254i	0.0379671	−	0.0219203i	−0.480896	−	0.876777i	$-0.659689\pi$
$281$	178.841	−	103.254i	0.0379671	−	0.0219203i	0.518863	+	0.854857i	$0.326355\pi$
$282$		0			0
$283$	−166.076	+	287.652i	−0.0348841	+	0.0604210i	−0.882940	−	0.469485i	$-0.844440\pi$
$283$	−166.076	+	287.652i	−0.0348841	+	0.0604210i	0.848056	+	0.529906i	$0.177773\pi$
$284$	852.324	−	612.586i	0.178085	−	0.127994i
$285$		0			0
$286$	1551.07	+	4815.74i	0.320687	+	0.995666i
$287$	182.986			0.0376354
$288$		0			0
$289$	−3512.18			−0.714876
$290$	1922.76	+	5969.77i	0.389340	+	1.20882i
$291$		0			0
$292$	2663.97	−	1914.66i	0.533894	−	0.383723i
$293$	1010.55	−	1750.33i	0.201492	−	0.348994i	−0.747518	−	0.664242i	$-0.768754\pi$
$293$	1010.55	−	1750.33i	0.201492	−	0.348994i	0.949009	+	0.315248i	$0.102088\pi$
$294$		0			0
$295$	−10639.2	+	6142.55i	−2.09979	+	1.21232i
$296$	−3483.38	+	4717.61i	−0.684012	+	0.926370i
$297$		0			0
$298$	8365.09	+	1800.52i	1.62610	+	0.350004i
$299$	−3124.88	+	1804.15i	−0.604403	+	0.348952i
$300$		0			0
$301$	1634.57	+	943.721i	0.313007	+	0.180715i
$302$	2621.69	+	2372.80i	0.499541	+	0.452117i
$303$		0			0
$304$	−2784.92	+	8280.70i	−0.525415	+	1.56227i
$305$			3222.11i			0.604909i
$306$		0			0
$307$	−6085.37			−1.13130			−0.565652	−	0.824644i	$-0.691376\pi$
$307$	−6085.37			−1.13130			−0.565652	+	0.824644i	$0.691376\pi$
$308$	261.720	+	2619.44i	0.0484184	+	0.484599i
$309$		0			0
$310$	6121.75	+	5540.58i	1.12159	+	1.01511i
$311$	1912.33	−	3312.26i	0.348676	−	0.603925i	−0.637338	−	0.770584i	$-0.719965\pi$
$311$	1912.33	−	3312.26i	0.348676	−	0.603925i	0.986015	+	0.166659i	$0.0532979\pi$
$312$		0			0
$313$	−2367.38	−	4100.42i	−0.427515	−	0.740478i	0.569136	−	0.822243i	$-0.307278\pi$
$313$	−2367.38	−	4100.42i	−0.427515	−	0.740478i	−0.996652	+	0.0817649i	$0.973944\pi$
$314$	1374.66	−	6386.59i	0.247060	−	1.14782i
$315$		0			0
$316$	−548.219	+	1214.49i	−0.0975940	+	0.216205i
$317$	2191.42	+	3795.64i	0.388272	+	0.672507i	0.992217	−	0.124519i	$-0.0397388\pi$
$317$	2191.42	+	3795.64i	0.388272	+	0.672507i	−0.603945	+	0.797026i	$0.706405\pi$
$318$		0			0
$319$	−3354.37	−	1936.65i	−0.588742	−	0.339910i
$320$	8501.43	+	1944.40i	1.48514	+	0.339673i
$321$		0			0
$322$	−1787.06	+	575.583i	−0.309283	+	0.0996148i
$323$			12529.8i			2.15845i
$324$		0			0
$325$			9927.50i			1.69440i
$326$	−596.898	−	1853.24i	−0.101408	−	0.314852i
$327$		0			0
$328$	149.633	+	343.171i	0.0251893	+	0.0577697i
$329$	−1721.83	−	994.100i	−0.288534	−	0.166585i
$330$		0			0
$331$	−650.703	−	1127.05i	−0.108054	−	0.187155i	0.806928	−	0.590650i	$-0.201129\pi$
$331$	−650.703	−	1127.05i	−0.108054	−	0.187155i	−0.914982	+	0.403495i	$0.867795\pi$
$332$	−1635.98	+	3624.26i	−0.270440	+	0.599118i
$333$		0			0
$334$	−2365.02	−	509.051i	−0.387449	−	0.0833953i
$335$	−3363.87	−	5826.40i	−0.548621	−	0.950239i
$336$		0			0
$337$	−3214.30	+	5567.33i	−0.519567	+	0.899916i	0.480174	+	0.877173i	$0.340573\pi$
$337$	−3214.30	+	5567.33i	−0.519567	+	0.899916i	−0.999741	+	0.0227432i	$0.992760\pi$
$338$	−2690.33	+	2972.53i	−0.432942	+	0.478355i
$339$		0			0
$340$	12445.6	−	1243.50i	1.98517	−	0.198347i
$341$	−5099.16			−0.809780
$342$		0			0
$343$		−	6234.20i		−	0.981385i
$344$	−433.215	+	3837.17i	−0.0678993	+	0.601413i
$345$		0			0
$346$	8265.80	−	9132.83i	1.28431	−	1.41903i
$347$	−4391.49	−	2535.43i	−0.679388	−	0.392245i	0.120236	−	0.992745i	$-0.461635\pi$
$347$	−4391.49	−	2535.43i	−0.679388	−	0.392245i	−0.799624	+	0.600500i	$0.794968\pi$
$348$		0			0
$349$	1404.61	−	810.954i	0.215436	−	0.124382i	−0.388399	−	0.921491i	$-0.626972\pi$
$349$	1404.61	−	810.954i	0.215436	−	0.124382i	0.603835	+	0.797109i	$0.293638\pi$
$350$	−1086.93	+	5049.82i	−0.165997	+	0.771212i
$351$		0			0
$352$	−4698.46	+	2632.81i	−0.711446	+	0.398663i
$353$	−567.462	+	327.624i	−0.0855607	+	0.0493985i	−0.542170	−	0.840269i	$-0.682397\pi$
$353$	−567.462	+	327.624i	−0.0855607	+	0.0493985i	0.456609	+	0.889667i	$0.349064\pi$
$354$		0			0
$355$	−1117.40	+	1935.40i	−0.167058	+	0.289352i
$356$	−1464.54	−	2037.69i	−0.218034	−	0.303363i
$357$		0			0
$358$	−2540.88	+	818.374i	−0.375111	+	0.120817i
$359$	4876.78			0.716954			0.358477	−	0.933538i	$-0.383296\pi$
$359$	4876.78			0.716954			0.358477	+	0.933538i	$0.383296\pi$
$360$		0			0
$361$	11775.2			1.71676
$362$	10529.0	−	3391.20i	1.52870	−	0.492369i
$363$		0			0
$364$	−4319.46	+	3104.50i	−0.621981	+	0.447033i
$365$	−3492.48	+	6049.16i	−0.500835	+	0.867472i
$366$		0			0
$367$	4731.01	−	2731.45i	0.672907	−	0.388503i	−0.124270	−	0.992248i	$-0.539659\pi$
$367$	4731.01	−	2731.45i	0.672907	−	0.388503i	0.797177	+	0.603745i	$0.206326\pi$
$368$	−2540.77	−	2880.77i	−0.359910	−	0.408073i
$369$		0			0
$370$	2627.31	−	12206.3i	0.369155	−	1.71507i
$371$	−1963.64	+	1133.71i	−0.274790	+	0.158650i
$372$		0			0
$373$	−691.653	−	399.326i	−0.0960119	−	0.0554325i	0.451225	−	0.892410i	$-0.350987\pi$
$373$	−691.653	−	399.326i	−0.0960119	−	0.0554325i	−0.547237	+	0.836978i	$0.684320\pi$
$374$	−5183.34	+	5727.04i	−0.716642	+	0.791813i
$375$		0			0
$376$	456.341	−	4042.01i	0.0625905	−	0.554390i
$377$		−	7826.62i		−	1.06921i
$378$		0			0
$379$	−8792.42			−1.19165			−0.595827	−	0.803113i	$-0.703175\pi$
$379$	−8792.42			−1.19165			−0.595827	+	0.803113i	$0.703175\pi$
$380$	−1849.31	−	18509.0i	−0.249652	−	2.49866i
$381$		0			0
$382$	581.043	−	641.990i	0.0778239	−	0.0859871i
$383$	−2819.36	+	4883.27i	−0.376142	+	0.651497i	−0.990497	−	0.137532i	$-0.956083\pi$
$383$	−2819.36	+	4883.27i	−0.376142	+	0.651497i	0.614355	+	0.789030i	$0.289416\pi$
$384$		0			0
$385$	−2802.46	−	4854.01i	−0.370978	−	0.642554i
$386$	−3144.28	−	676.781i	−0.414610	−	0.0892415i
$387$		0			0
$388$	4658.88	+	2103.00i	0.609585	+	0.275165i
$389$	2191.36	+	3795.54i	0.285620	+	0.494708i	0.972759	−	0.231817i	$-0.0744672\pi$
$389$	2191.36	+	3795.54i	0.285620	+	0.494708i	−0.687139	+	0.726526i	$0.741134\pi$
$390$		0			0
$391$	−4770.90	−	2754.48i	−0.617072	−	0.356266i
$392$	4577.24	−	1995.81i	0.589759	−	0.257152i
$393$		0			0
$394$	4405.19	+	13677.2i	0.563275	+	1.74885i
$395$		−	2837.06i		−	0.361388i
$396$		0			0
$397$			12772.4i			1.61469i	0.590082	+	0.807344i	$0.299096\pi$
$397$			12772.4i			1.61469i	−0.590082	+	0.807344i	$0.700904\pi$
$398$	13332.6	−	4294.21i	1.67916	−	0.540827i
$399$		0			0
$400$	−10359.2	+	2090.94i	−1.29490	+	0.261367i
$401$	−1752.46	−	1011.79i	−0.218239	−	0.126000i	0.386896	−	0.922124i	$-0.373547\pi$
$401$	−1752.46	−	1011.79i	−0.218239	−	0.126000i	−0.605135	+	0.796123i	$0.706881\pi$
$402$		0			0
$403$	−5151.84	−	8923.25i	−0.636803	−	1.10297i
$404$	8646.65	+	3903.07i	1.06482	+	0.480656i
$405$		0			0
$406$	856.914	−	3981.16i	0.104749	−	0.486655i
$407$	3855.48	+	6677.88i	0.469555	+	0.813293i
$408$		0			0
$409$	6852.57	−	11869.0i	0.828454	−	1.43492i	−0.0707969	−	0.997491i	$-0.522554\pi$
$409$	6852.57	−	11869.0i	0.828454	−	1.43492i	0.899251	−	0.437434i	$-0.144112\pi$
$410$	−590.986	−	534.880i	−0.0711871	−	0.0644289i
$411$		0			0
$412$	−5826.15	+	582.116i	−0.696684	+	0.0696088i
$413$	7976.87			0.950402
$414$		0			0
$415$		−	8466.28i		−	1.00143i
$416$	−9354.28	−	5562.04i	−1.10248	−	0.655533i
$417$		0			0
$418$	8517.18	+	7708.60i	0.996624	+	0.902009i
$419$	−10367.2	−	5985.52i	−1.20876	−	0.697881i	−0.246275	−	0.969200i	$-0.579207\pi$
$419$	−10367.2	−	5985.52i	−1.20876	−	0.697881i	−0.962489	+	0.271319i	$0.912540\pi$
$420$		0			0
$421$	7018.33	−	4052.04i	0.812477	−	0.469084i	−0.0353385	−	0.999375i	$-0.511251\pi$
$421$	7018.33	−	4052.04i	0.812477	−	0.469084i	0.847815	+	0.530292i	$0.177918\pi$
$422$	12615.1	+	2715.29i	1.45519	+	0.313219i
$423$		0			0
$424$	−3731.86	−	2755.53i	−0.427441	−	0.315614i
$425$	−13126.2	+	7578.40i	−1.49815	+	0.864956i
$426$		0			0
$427$	1046.08	−	1811.86i	0.118555	−	0.205344i
$428$	−6431.02	−	8947.82i	−0.726297	−	1.01054i
$429$		0			0
$430$	−2520.58	−	7825.86i	−0.282681	−	0.877666i
$431$	2632.17			0.294170			0.147085	−	0.989124i	$-0.453011\pi$
$431$	2632.17			0.294170			0.147085	+	0.989124i	$0.453011\pi$
$432$		0			0
$433$	−2392.15			−0.265495			−0.132747	−	0.991150i	$-0.542380\pi$
$433$	−2392.15			−0.265495			−0.132747	+	0.991150i	$0.542380\pi$
$434$	−1643.61	−	5103.05i	−0.181787	−	0.564411i
$435$		0			0
$436$	−9236.30	−	12851.0i	−1.01454	−	1.41158i
$437$	−4096.43	+	7095.23i	−0.448419	+	0.776684i
$438$		0			0
$439$	−13175.7	+	7606.99i	−1.43244	+	0.827020i	−0.997307	−	0.0733455i	$-0.976632\pi$
$439$	−13175.7	+	7606.99i	−1.43244	+	0.827020i	−0.435134	+	0.900366i	$0.643299\pi$
$440$	6811.52	−	9224.96i	0.738015	−	0.999506i
$441$		0			0
$442$	−15258.9	−	3284.35i	−1.64206	−	0.353441i
$443$	−1983.58	+	1145.22i	−0.212738	+	0.122824i	−0.602583	−	0.798056i	$-0.705862\pi$
$443$	−1983.58	+	1145.22i	−0.212738	+	0.122824i	0.389845	+	0.920880i	$0.372528\pi$
$444$		0			0
$445$	4627.03	+	2671.42i	0.492904	+	0.284579i
$446$	−6136.37	−	5553.81i	−0.651492	−	0.589642i
$447$		0			0
$448$	−4149.27	−	3853.42i	−0.437577	−	0.406377i
$449$			458.702i			0.0482126i	0.999709	+	0.0241063i	$0.00767402\pi$
$449$			458.702i			0.0482126i	−0.999709	+	0.0241063i	$0.992326\pi$
$450$		0			0
$451$	492.266			0.0513967
$452$	2223.99	−	222.208i	0.231433	−	0.0231235i
$453$		0			0
$454$	−372.195	−	336.861i	−0.0384757	−	0.0348230i
$455$	5662.83	−	9808.31i	0.583467	−	1.01060i
$456$		0			0
$457$	−2863.81	−	4960.26i	−0.293136	−	0.507727i	0.681413	−	0.731899i	$-0.261366\pi$
$457$	−2863.81	−	4960.26i	−0.293136	−	0.507727i	−0.974550	+	0.224172i	$0.928032\pi$
$458$	662.625	−	3078.51i	0.0676036	−	0.314082i
$459$		0			0
$460$	7454.09	+	3364.75i	0.755541	+	0.341049i
$461$	−416.155	−	720.802i	−0.0420440	−	0.0728223i	0.844238	−	0.535969i	$-0.180054\pi$
$461$	−416.155	−	720.802i	−0.0420440	−	0.0728223i	−0.886282	+	0.463147i	$0.846720\pi$
$462$		0			0
$463$	−8632.04	−	4983.71i	−0.866447	−	0.500244i	−0.000281312	−	1.00000i	$-0.500090\pi$
$463$	−8632.04	−	4983.71i	−0.866447	−	0.500244i	−0.866166	+	0.499756i	$0.833423\pi$
$464$	8166.96	−	1648.45i	0.817116	−	0.164930i
$465$		0			0
$466$	−9454.83	+	3045.24i	−0.939886	+	0.302721i
$467$		−	436.159i		−	0.0432185i	−0.999766	−	0.0216092i	$-0.993121\pi$
$467$		−	436.159i		−	0.0432185i	0.999766	−	0.0216092i	$-0.00687897\pi$
$468$		0			0
$469$			4368.41i			0.430094i
$470$	2655.14	+	8243.64i	0.260579	+	0.809044i
$471$		0			0
$472$	6522.89	+	14959.7i	0.636102	+	1.45885i
$473$	4397.29	+	2538.78i	0.427458	+	0.246793i
$474$		0			0
$475$	11270.5	+	19521.1i	1.08869	+	1.88566i
$476$	−7402.14	−	3341.30i	−0.712766	−	0.321740i
$477$		0			0
$478$	6817.50	+	1467.41i	0.652354	+	0.140414i
$479$	801.979	+	1389.07i	0.0764997	+	0.132501i	0.901737	−	0.432284i	$-0.142292\pi$
$479$	801.979	+	1389.07i	0.0764997	+	0.132501i	−0.825238	+	0.564785i	$0.808959\pi$
$480$		0			0
$481$	−7790.62	+	13493.8i	−0.738507	+	1.27913i
$482$	−4952.18	+	5471.63i	−0.467978	+	0.517066i
$483$		0			0
$484$	−354.544	−	3548.48i	−0.0332968	−	0.333253i
$485$	−10883.2			−1.01893
$486$		0			0
$487$		−	17352.2i		−	1.61458i	−0.590152	−	0.807292i	$-0.700932\pi$
$487$		−	17352.2i		−	1.61458i	0.590152	−	0.807292i	$-0.299068\pi$
$488$	4253.35	+	480.201i	0.394549	+	0.0445444i
$489$		0			0
$490$	−7134.27	+	7882.61i	−0.657742	+	0.726735i
$491$	−534.280	−	308.467i	−0.0491073	−	0.0283521i	0.475245	−	0.879853i	$-0.342359\pi$
$491$	−534.280	−	308.467i	−0.0491073	−	0.0283521i	−0.524353	+	0.851501i	$0.675693\pi$
$492$		0			0
$493$	10348.4	−	5974.64i	0.945370	−	0.545810i
$494$	−4884.45	+	22692.8i	−0.444862	+	2.06680i
$495$		0			0
$496$	8226.20	−	7255.30i	0.744692	−	0.656799i
$497$	1256.68	−	725.542i	0.113420	−	0.0654829i
$498$		0			0
$499$	3190.76	−	5526.56i	0.286249	−	0.495797i	−0.686663	−	0.726976i	$-0.740925\pi$
$499$	3190.76	−	5526.56i	0.286249	−	0.495797i	0.972911	+	0.231179i	$0.0742584\pi$
$500$	4440.05	−	3191.18i	0.397130	−	0.285427i
$501$		0			0
$502$	20453.4	−	6587.68i	1.81848	−	0.585702i
$503$	−518.133			−0.0459292			−0.0229646	−	0.999736i	$-0.507311\pi$
$503$	−518.133			−0.0459292			−0.0229646	+	0.999736i	$0.507311\pi$
$504$		0			0
$505$	−20198.6			−1.77986
$506$	−4807.52	+	1548.42i	−0.422372	+	0.136039i
$507$		0			0
$508$	−5438.85	−	7567.36i	−0.475019	−	0.660920i
$509$	7194.61	−	12461.4i	0.626513	−	1.08515i	−0.361733	−	0.932282i	$-0.617815\pi$
$509$	7194.61	−	12461.4i	0.626513	−	1.08515i	0.988246	−	0.152871i	$-0.0488520\pi$
$510$		0			0
$511$	3927.79	−	2267.71i	0.340030	−	0.196316i
$512$	3833.70	−	10932.5i	0.330913	−	0.943661i
$513$		0			0
$514$	−1794.83	+	8338.67i	−0.154021	+	0.715570i
$515$	10796.3	−	6233.22i	0.923767	−	0.533337i
$516$		0			0
$517$	−4632.04	−	2674.31i	−0.394036	−	0.227497i
$518$	−5440.25	+	6010.89i	−0.461449	+	0.509852i
$519$		0			0
$520$	23025.1	+	2599.52i	1.94176	+	0.219224i
$521$		−	15224.9i		−	1.28026i	−0.768267	−	0.640130i	$-0.778881\pi$
$521$		−	15224.9i		−	1.28026i	0.768267	−	0.640130i	$-0.221119\pi$
$522$		0			0
$523$	6328.57			0.529118			0.264559	−	0.964369i	$-0.414774\pi$
$523$	6328.57			0.529118			0.264559	+	0.964369i	$0.414774\pi$
$524$	−2349.24	+	234.723i	−0.195853	+	0.0195685i
$525$		0			0
$526$	4001.54	−	4421.27i	0.331702	−	0.366496i
$527$	7865.57	−	13623.6i	0.650151	−	1.12609i
$528$		0			0
$529$	4282.43	+	7417.39i	0.351971	+	0.609631i
$530$	9655.79	+	2078.33i	0.791360	+	0.170334i
$531$		0			0
$532$	−4969.15	+	11008.4i	−0.404962	+	0.897131i
$533$	497.352	+	861.439i	0.0404178	+	0.0700057i
$534$		0			0
$535$	20318.1	+	11730.6i	1.64192	+	0.947963i
$536$	−8192.47	+	3572.16i	−0.660188	+	0.287861i
$537$		0			0
$538$	−3270.76	−	10155.0i	−0.262105	−	0.813781i
$539$		−	6565.88i		−	0.524698i
$540$		0			0
$541$		−	5488.92i		−	0.436206i	−0.975926	−	0.218103i	$-0.930013\pi$
$541$		−	5488.92i		−	0.436206i	0.975926	−	0.218103i	$-0.0699868\pi$
$542$	2457.24	−	791.434i	0.194737	−	0.0627214i
$543$		0			0
$544$	213.333	−	16614.2i	0.0168135	−	1.30942i
$545$	29181.0	+	16847.7i	2.29354	+	1.32417i
$546$		0			0
$547$	−10861.9	−	18813.4i	−0.849037	−	1.47058i	−0.882069	−	0.471121i	$-0.843849\pi$
$547$	−10861.9	−	18813.4i	−0.849037	−	1.47058i	0.0330315	−	0.999454i	$-0.489484\pi$
$548$	−7826.45	+	17338.3i	−0.610090	+	1.35156i
$549$		0			0
$550$	−2924.04	+	13584.9i	−0.226694	+	1.05320i
$551$	−8885.41	−	15390.0i	−0.686989	−	1.18990i
$552$		0			0
$553$	−921.070	+	1595.34i	−0.0708280	+	0.122678i
$554$	7693.23	+	6962.87i	0.589989	+	0.533978i
$555$		0			0
$556$	−1508.18	−	15094.7i	−0.115038	−	1.15137i
$557$	17630.6			1.34117			0.670586	−	0.741832i	$-0.266043\pi$
$557$	17630.6			1.34117			0.670586	+	0.741832i	$0.266043\pi$
$558$		0			0
$559$			10260.0i			0.776302i
$560$	11427.5	+	3843.25i	0.862325	+	0.290012i
$561$		0			0
$562$	433.060	+	391.947i	0.0325045	+	0.0294187i
$563$	16401.0	+	9469.15i	1.22775	+	0.708840i	0.966558	−	0.256447i	$-0.0825521\pi$
$563$	16401.0	+	9469.15i	1.22775	+	0.708840i	0.261189	+	0.965288i	$0.415885\pi$
$564$		0			0
$565$	−4121.21	+	2379.38i	−0.306868	+	0.177170i
$566$	−918.434	−	197.685i	−0.0682061	−	0.0146808i
$567$		0			0
$568$	2388.29	+	1763.46i	0.176427	+	0.130270i
$569$	−6640.91	+	3834.13i	−0.489282	+	0.282487i	−0.724277	−	0.689510i	$-0.757826\pi$
$569$	−6640.91	+	3834.13i	−0.489282	+	0.282487i	0.234995	+	0.971997i	$0.424493\pi$
$570$		0			0
$571$	−9216.49	+	15963.4i	−0.675478	+	1.16996i	0.300850	+	0.953671i	$0.402730\pi$
$571$	−9216.49	+	15963.4i	−0.675478	+	1.16996i	−0.976329	+	0.216292i	$0.930604\pi$
$572$	−11620.1	+	8351.66i	−0.849408	+	0.610490i
$573$		0			0
$574$	158.671	+	492.642i	0.0115380	+	0.0358231i
$575$	−9910.56			−0.718780
$576$		0			0
$577$	21712.7			1.56657			0.783286	−	0.621662i	$-0.213542\pi$
$577$	21712.7			1.56657			0.783286	+	0.621662i	$0.213542\pi$
$578$	−3045.49	−	9455.61i	−0.219162	−	0.680452i
$579$		0			0
$580$	−14404.7	+	10353.0i	−1.03125	+	0.741184i
$581$	−2748.63	+	4760.77i	−0.196269	+	0.339948i
$582$		0			0
$583$	−5282.53	+	3049.87i	−0.375266	+	0.216660i
$584$	7464.70	+	5511.78i	0.528924	+	0.390546i
$585$		0			0
$586$	5588.55	+	1202.89i	0.393961	+	0.0847969i
$587$	−398.575	+	230.117i	−0.0280255	+	0.0161805i	−0.513947	−	0.857822i	$-0.671817\pi$
$587$	−398.575	+	230.117i	−0.0280255	+	0.0161805i	0.485922	+	0.874002i	$0.338484\pi$
$588$		0			0
$589$	−20260.8	−	11697.6i	−1.41737	−	0.818320i
$590$	−25762.7	−	23316.9i	−1.79768	−	1.62702i
$591$		0			0
$592$	−15721.4	−	5287.33i	−1.09146	−	0.367074i
$593$			11291.5i			0.781930i	0.920406	+	0.390965i	$0.127859\pi$
$593$			11291.5i			0.781930i	−0.920406	+	0.390965i	$0.872141\pi$
$594$		0			0
$595$	17291.4			1.19139
$596$	2406.14	+	24082.0i	0.165368	+	1.65510i
$597$		0			0
$598$	−7566.84	−	6848.48i	−0.517443	−	0.468319i
$599$	−13786.9	+	23879.6i	−0.940431	+	1.62887i	−0.175781	+	0.984429i	$0.556245\pi$
$599$	−13786.9	+	23879.6i	−0.940431	+	1.62887i	−0.764650	+	0.644445i	$0.777088\pi$
$600$		0			0
$601$	2266.68	+	3926.00i	0.153843	+	0.266464i	0.932637	−	0.360816i	$-0.117502\pi$
$601$	2266.68	+	3926.00i	0.153843	+	0.266464i	−0.778794	+	0.627280i	$0.784168\pi$
$602$	−1123.34	+	5218.97i	−0.0760531	+	0.353337i
$603$		0			0
$604$	−4114.80	+	9115.70i	−0.277200	+	0.614094i
$605$	3796.41	+	6575.58i	0.255117	+	0.441876i
$606$		0			0
$607$	9493.59	+	5481.13i	0.634815	+	0.366511i	0.782615	−	0.622507i	$-0.213886\pi$
$607$	9493.59	+	5481.13i	0.634815	+	0.366511i	−0.147799	+	0.989017i	$0.547219\pi$
$608$	−24708.4	−	317.266i	−1.64812	−	0.0211625i
$609$		0			0
$610$	−8674.65	+	2793.96i	−0.575781	+	0.185449i
$611$		−	10807.7i		−	0.715605i
$612$		0			0
$613$			17689.3i			1.16552i	0.812644	+	0.582760i	$0.198027\pi$
$613$			17689.3i			1.16552i	−0.812644	+	0.582760i	$0.801973\pi$
$614$	−5276.76	−	16383.2i	−0.346828	−	1.07683i
$615$		0			0
$616$	−6825.20	+	2975.98i	−0.446421	+	0.194652i
$617$	−11483.7	−	6630.14i	−0.749300	−	0.432609i	0.0761408	−	0.997097i	$-0.475740\pi$
$617$	−11483.7	−	6630.14i	−0.749300	−	0.432609i	−0.825441	+	0.564488i	$0.809073\pi$
$618$		0			0
$619$	400.480	+	693.652i	0.0260043	+	0.0450408i	0.878735	−	0.477311i	$-0.158388\pi$
$619$	400.480	+	693.652i	0.0260043	+	0.0450408i	−0.852730	+	0.522351i	$0.825055\pi$
$620$	−9608.22	+	21285.5i	−0.622380	+	1.37879i
$621$		0			0
$622$	10575.6	+	2276.31i	0.681739	+	0.146739i
$623$	−1734.59	−	3004.39i	−0.111548	−	0.193208i
$624$		0			0
$625$	4499.49	−	7793.35i	0.287968	−	0.498774i
$626$	8986.48	−	9929.10i	0.573757	−	0.633940i
$627$		0			0
$628$	18386.2	−	1837.04i	1.16829	−	0.116729i
$629$	−23788.6			−1.50797
$630$		0			0
$631$			12560.3i			0.792422i	0.918160	+	0.396211i	$0.129675\pi$
$631$			12560.3i			0.792422i	−0.918160	+	0.396211i	$0.870325\pi$
$632$	−3745.07	−	422.817i	−0.235713	−	0.0266120i
$633$		0			0
$634$	−8318.52	+	9191.08i	−0.521089	+	0.575748i
$635$	17183.4	+	9920.85i	1.07386	+	0.619995i
$636$		0			0
$637$	11489.9	−	6633.71i	0.714674	−	0.412617i
$638$	2305.25	−	10710.0i	0.143050	−	0.664600i
$639$		0			0
$640$	2137.00	+	24573.8i	0.131988	+	1.51776i
$641$	18575.0	−	10724.3i	1.14457	−	0.660816i	0.197010	−	0.980401i	$-0.436877\pi$
$641$	18575.0	−	10724.3i	1.14457	−	0.660816i	0.947558	+	0.319585i	$0.103544\pi$
$642$		0			0
$643$	−1549.71	+	2684.17i	−0.0950458	+	0.164624i	−0.909628	−	0.415424i	$-0.863633\pi$
$643$	−1549.71	+	2684.17i	−0.0950458	+	0.164624i	0.814582	+	0.580049i	$0.196966\pi$
$644$	−3099.20	−	4312.08i	−0.189636	−	0.263851i
$645$		0			0
$646$	−33733.2	+	10864.9i	−2.05451	+	0.661723i
$647$	−7913.28			−0.480840			−0.240420	−	0.970669i	$-0.577285\pi$
$647$	−7913.28			−0.480840			−0.240420	+	0.970669i	$0.577285\pi$
$648$		0			0
$649$	21459.2			1.29792
$650$	−26727.1	+	8608.35i	−1.61281	+	0.519457i
$651$		0			0
$652$	4471.78	−	3213.98i	0.268602	−	0.193051i
$653$	3180.84	−	5509.37i	0.190621	−	0.330166i	−0.754835	−	0.655915i	$-0.772283\pi$
$653$	3180.84	−	5509.37i	0.190621	−	0.330166i	0.945456	+	0.325749i	$0.105616\pi$
$654$		0			0
$655$	4353.30	−	2513.38i	0.259691	−	0.149933i
$656$	−794.146	+	700.417i	−0.0472655	+	0.0416870i
$657$		0			0
$658$	1183.31	−	5497.57i	0.0701066	−	0.325711i
$659$	−20242.2	+	11686.8i	−1.19654	+	0.690825i	−0.959783	−	0.280742i	$-0.909419\pi$
$659$	−20242.2	+	11686.8i	−1.19654	+	0.690825i	−0.236762	+	0.971568i	$0.576086\pi$
$660$		0			0
$661$	−3037.57	−	1753.74i	−0.178741	−	0.103196i	0.407960	−	0.913000i	$-0.366240\pi$
$661$	−3037.57	−	1753.74i	−0.178741	−	0.103196i	−0.586701	+	0.809804i	$0.699574\pi$
$662$	2470.04	−	2729.13i	0.145016	−	0.160228i
$663$		0			0
$664$	−11175.9	−	1261.76i	−0.653178	−	0.0737435i
$665$		−	25715.6i		−	1.49956i
$666$		0			0
$667$	7813.26			0.453569
$668$	−680.275	−	6808.58i	−0.0394021	−	0.394359i
$669$		0			0
$670$	12769.1	−	14108.5i	0.736289	−	0.813521i
$671$	2814.13	−	4874.22i	0.161905	−	0.280428i
$672$		0			0
$673$	12801.6	+	22173.1i	0.733234	+	1.27000i	0.955494	+	0.295010i	$0.0953231\pi$
$673$	12801.6	+	22173.1i	0.733234	+	1.27000i	−0.222261	+	0.974987i	$0.571344\pi$
$674$	−17775.7	−	3826.08i	−1.01587	−	0.218657i
$675$		0			0
$676$	−10335.6	−	4665.44i	−0.588050	−	0.265444i
$677$	−3433.18	−	5946.45i	−0.194901	−	0.337578i	0.751967	−	0.659201i	$-0.229105\pi$
$677$	−3433.18	−	5946.45i	−0.194901	−	0.337578i	−0.946868	+	0.321622i	$0.895772\pi$
$678$		0			0
$679$	6119.83	+	3533.29i	0.345887	+	0.199698i
$680$	14139.6	+	32428.2i	0.797398	+	1.82877i
$681$		0			0
$682$	−4421.59	−	13728.1i	−0.248257	−	0.770787i
$683$			5563.45i			0.311683i	0.987782	+	0.155841i	$0.0498089\pi$
$683$			5563.45i			0.311683i	−0.987782	+	0.155841i	$0.950191\pi$
$684$		0			0
$685$		−	40502.3i		−	2.25915i
$686$	16783.9	−	5405.81i	0.934128	−	0.300867i
$687$		0			0
$688$	−10706.2	+	2160.98i	−0.593270	+	0.119748i
$689$	−10674.2	−	6162.76i	−0.590211	−	0.340758i
$690$		0			0
$691$	16086.6	+	27862.8i	0.885620	+	1.53394i	0.845001	+	0.534765i	$0.179600\pi$
$691$	16086.6	+	27862.8i	0.885620	+	1.53394i	0.0406192	+	0.999175i	$0.487067\pi$
$692$	31755.1	+	14334.2i	1.74443	+	0.787432i
$693$		0			0
$694$	3018.00	−	14021.4i	0.165075	−	0.766925i
$695$	16149.4	+	27971.6i	0.881412	+	1.52665i
$696$		0			0
$697$	−759.331	+	1315.20i	−0.0412650	+	0.0714731i
$698$	3401.25	+	3078.35i	0.184440	+	0.166930i
$699$		0			0
$700$	−14537.8	+	1452.53i	−0.784966	+	0.0784294i
$701$	−18575.6			−1.00084			−0.500422	−	0.865782i	$-0.666822\pi$
$701$	−18575.6			−1.00084			−0.500422	+	0.865782i	$0.666822\pi$
$702$		0			0
$703$			35378.2i			1.89803i
$704$	−11162.3	−	10366.4i	−0.597577	−	0.554968i
$705$		0			0
$706$	−1374.10	−	1243.65i	−0.0732505	−	0.0662964i
$707$	11358.1	+	6557.60i	0.604194	+	0.348832i
$708$		0			0
$709$	−11602.4	+	6698.64i	−0.614579	+	0.354827i	−0.774756	−	0.632261i	$-0.782127\pi$
$709$	−11602.4	+	6698.64i	−0.614579	+	0.354827i	0.160176	+	0.987088i	$0.448794\pi$
$710$	−6179.45	−	1330.08i	−0.326635	−	0.0703055i
$711$		0			0
$712$	4215.99	−	5709.79i	0.221911	−	0.300539i
$713$	8908.02	−	5143.05i	0.467893	−	0.270138i
$714$		0			0
$715$	15234.0	−	26386.1i	0.796812	−	1.38012i
$716$	−4406.50	−	6131.00i	−0.229998	−	0.320009i
$717$		0			0
$718$	4228.76	+	13129.4i	0.219799	+	0.682431i
$719$	−10940.1			−0.567449			−0.283724	−	0.958906i	$-0.591570\pi$
$719$	−10940.1			−0.567449			−0.283724	+	0.958906i	$0.591570\pi$
$720$		0			0
$721$	−8094.61			−0.418113
$722$	10210.5	+	31701.6i	0.526312	+	1.63409i
$723$		0			0
$724$	18259.8	+	25405.8i	0.937320	+	1.30414i
$725$	10748.3	−	18616.6i	0.550595	−	0.953659i
$726$		0			0
$727$	21844.7	−	12612.0i	1.11441	−	0.643403i	0.174439	−	0.984668i	$-0.444189\pi$
$727$	21844.7	−	12612.0i	1.11441	−	0.643403i	0.939967	+	0.341265i	$0.110855\pi$
$728$	−12103.5	−	8936.99i	−0.616190	−	0.454982i
$729$		0			0
$730$	−19314.1	−	4157.21i	−0.979243	−	0.210774i
$731$	−13565.8	+	7832.24i	−0.686389	+	0.396287i
$732$		0			0
$733$	−18183.8	−	10498.4i	−0.916281	−	0.529015i	−0.0338341	−	0.999427i	$-0.510772\pi$
$733$	−18183.8	−	10498.4i	−0.916281	−	0.529015i	−0.882447	+	0.470413i	$0.844105\pi$
$734$	11456.1	+	10368.5i	0.576091	+	0.521400i
$735$		0			0
$736$	5552.55	−	9338.32i	0.278084	−	0.467683i
$737$			11751.8i			0.587358i
$738$		0			0
$739$	−13554.1			−0.674691			−0.337346	−	0.941381i	$-0.609529\pi$
$739$	−13554.1			−0.674691			−0.337346	+	0.941381i	$0.609529\pi$
$740$	35140.4	−	3511.03i	1.74566	−	0.174416i
$741$		0			0
$742$	−4754.91	−	4303.50i	−0.235254	−	0.212920i
$743$	3833.05	−	6639.04i	0.189261	−	0.327810i	−0.755743	−	0.654868i	$-0.772724\pi$
$743$	3833.05	−	6639.04i	0.189261	−	0.327810i	0.945004	+	0.327058i	$0.106057\pi$
$744$		0			0
$745$	−25764.6	−	44625.7i	−1.26704	−	2.19457i
$746$	475.330	−	2208.35i	0.0233285	−	0.108383i
$747$		0			0
$748$	−19913.1	−	8988.70i	−0.973388	−	0.439384i
$749$	−7616.85	−	13192.8i	−0.371580	−	0.643596i
$750$		0			0
$751$	−19535.6	−	11278.9i	−0.949220	−	0.548032i	−0.0563812	−	0.998409i	$-0.517956\pi$
$751$	−19535.6	−	11278.9i	−0.949220	−	0.548032i	−0.892838	+	0.450377i	$0.851290\pi$
$752$	11277.7	−	2276.34i	0.546883	−	0.110385i
$753$		0			0
$754$	21071.1	−	6786.63i	1.01772	−	0.327791i
$755$		−	21294.3i		−	1.02646i
$756$		0			0
$757$			1488.41i			0.0714625i	0.999361	+	0.0357312i	$0.0113760\pi$
$757$			1488.41i			0.0714625i	−0.999361	+	0.0357312i	$0.988624\pi$
$758$	−7624.10	−	23671.2i	−0.365330	−	1.13427i
$759$		0			0
$760$	48226.9	−	21028.3i	2.30181	−	1.00365i
$761$	−6200.52	−	3579.87i	−0.295360	−	0.170526i	0.344997	−	0.938604i	$-0.387880\pi$
$761$	−6200.52	−	3579.87i	−0.295360	−	0.170526i	−0.640356	+	0.768078i	$0.721213\pi$
$762$		0			0
$763$	−10939.4	−	18947.6i	−0.519047	−	0.899016i
$764$	2232.22	+	1007.62i	0.105705	+	0.0477150i
$765$		0			0
$766$	−15591.6	−	3355.97i	−0.735441	−	0.158298i
$767$	21680.9	+	37552.4i	1.02067	+	1.76785i
$768$		0			0
$769$	−13431.2	+	23263.6i	−0.629835	+	1.09091i	0.357750	+	0.933818i	$0.383544\pi$
$769$	−13431.2	+	23263.6i	−0.629835	+	1.09091i	−0.987585	+	0.157089i	$0.949789\pi$
$770$	10638.0	−	11753.9i	0.497880	−	0.550105i
$771$		0			0
$772$	−904.422	−	9051.97i	−0.0421643	−	0.422004i
$773$	30329.6			1.41123			0.705613	−	0.708597i	$-0.250672\pi$
$773$	30329.6			1.41123			0.705613	+	0.708597i	$0.250672\pi$
$774$		0			0
$775$		−	28300.1i		−	1.31170i
$776$	−1621.95	+	14366.3i	−0.0750319	+	0.664589i
$777$		0			0
$778$	−8318.29	+	9190.83i	−0.383323	+	0.423531i
$779$	1955.95	+	1129.27i	0.0899605	+	0.0519387i
$780$		0			0
$781$	3380.68	−	1951.84i	0.154892	−	0.0894267i
$782$	3278.75	−	15232.8i	0.149933	−	0.696580i
$783$		0			0
$784$	9342.20	+	10592.4i	0.425574	+	0.482524i
$785$	−34070.8	+	19670.8i	−1.54910	+	0.894371i
$786$		0			0
$787$	−13373.7	+	23164.0i	−0.605746	+	1.04918i	0.386187	+	0.922421i	$0.373792\pi$
$787$	−13373.7	+	23164.0i	−0.605746	+	1.04918i	−0.991933	+	0.126763i	$0.959541\pi$
$788$	−33002.3	+	23719.6i	−1.49195	+	1.07230i
$789$		0			0
$790$	7638.03	−	2460.08i	0.343986	−	0.110792i
$791$	3089.92			0.138894
$792$		0			0
$793$	11372.8			0.509282
$794$	−34386.4	+	11075.3i	−1.53693	+	0.495021i
$795$		0			0
$796$	23122.0	+	32170.9i	1.02957	+	1.43250i
$797$	17637.8	−	30549.6i	0.783894	−	1.35775i	−0.145763	−	0.989320i	$-0.546564\pi$
$797$	17637.8	−	30549.6i	0.783894	−	1.35775i	0.929657	−	0.368426i	$-0.120103\pi$
$798$		0			0
$799$	14290.0	−	8250.35i	0.632722	−	0.365302i
$800$	−14612.0	−	26076.2i	−0.645764	−	1.15242i
$801$		0			0
$802$	1204.36	−	5595.38i	0.0530267	−	0.246359i
$803$	10566.5	−	6100.55i	0.464361	−	0.268099i
$804$		0			0
$805$	9791.57	+	5653.17i	0.428705	+	0.247513i
$806$	19556.2	−	21607.5i	0.854636	−	0.944282i
$807$		0			0
$808$	−3010.27	+	26663.2i	−0.131065	+	1.16090i
$809$			15744.5i			0.684238i	0.939657	+	0.342119i	$0.111145\pi$
$809$			15744.5i			0.684238i	−0.939657	+	0.342119i	$0.888855\pi$
$810$		0			0
$811$	−24665.7			−1.06798			−0.533989	−	0.845491i	$-0.679308\pi$
$811$	−24665.7			−1.06798			−0.533989	+	0.845491i	$0.679308\pi$
$812$	11461.3	−	1145.14i	0.495334	−	0.0494910i
$813$		0			0
$814$	−14635.2	+	16170.4i	−0.630178	+	0.696279i
$815$	−5862.52	+	10154.2i	−0.251970	+	0.436424i
$816$		0			0
$817$	11648.0	+	20174.9i	0.498791	+	0.863932i
$818$	37896.1	+	8156.83i	1.61981	+	0.348651i
$819$		0			0
$820$	927.565	−	2054.88i	0.0395024	−	0.0875114i
$821$	−8244.80	−	14280.4i	−0.350482	−	0.607052i	0.635852	−	0.771811i	$-0.280649\pi$
$821$	−8244.80	−	14280.4i	−0.350482	−	0.607052i	−0.986334	+	0.164759i	$0.947315\pi$
$822$		0			0
$823$	19313.2	+	11150.5i	0.818004	+	0.472275i	0.849728	−	0.527222i	$-0.176766\pi$
$823$	19313.2	+	11150.5i	0.818004	+	0.472275i	−0.0317237	+	0.999497i	$0.510100\pi$
$824$	−6619.17	−	15180.6i	−0.279842	−	0.641796i
$825$		0			0
$826$	6916.91	+	21475.6i	0.291368	+	0.904637i
$827$		−	25362.4i		−	1.06643i	−0.845980	−	0.533214i	$-0.820984\pi$
$827$		−	25362.4i		−	1.06643i	0.845980	−	0.533214i	$-0.179016\pi$
$828$		0			0
$829$			14068.1i			0.589390i	0.955591	+	0.294695i	$0.0952180\pi$
$829$			14068.1i			0.589390i	−0.955591	+	0.294695i	$0.904782\pi$
$830$	22793.2	−	7341.30i	0.953208	−	0.307012i
$831$		0			0
$832$	6863.00	−	30006.8i	0.285976	−	1.25036i
$833$	17542.2	+	10128.0i	0.729655	+	0.421266i
$834$		0			0
$835$	7284.29	+	12616.8i	0.301896	+	0.522899i
$836$	−13367.9	+	29614.5i	−0.553036	+	1.22517i
$837$		0			0
$838$	7124.76	−	33101.1i	0.293700	−	1.36451i
$839$	−17579.0	−	30447.8i	−0.723355	−	1.25289i	−0.959647	−	0.281206i	$-0.909266\pi$
$839$	−17579.0	−	30447.8i	−0.723355	−	1.25289i	0.236292	−	0.971682i	$-0.424068\pi$
$840$		0			0
$841$	3720.79	−	6444.60i	0.152560	−	0.264242i
$842$	16994.8	+	15381.4i	0.695580	+	0.629545i
$843$		0			0
$844$	3628.60	+	36317.1i	0.147988	+	1.48115i
$845$	24143.9			0.982930
$846$		0			0
$847$		−	4930.11i		−	0.200001i
$848$	4182.54	−	12436.4i	0.169374	−	0.503617i
$849$		0			0
$850$	−31784.8	−	28767.3i	−1.28260	−	1.16083i
$851$	−13470.7	−	7777.32i	−0.542621	−	0.313282i
$852$		0			0
$853$	−24779.3	+	14306.3i	−0.994637	+	0.574254i	−0.906657	−	0.421868i	$-0.861374\pi$
$853$	−24779.3	+	14306.3i	−0.994637	+	0.574254i	−0.0879799	+	0.996122i	$0.528041\pi$
$854$	5785.01	+	1245.18i	0.231802	+	0.0498936i
$855$		0			0
$856$	18513.1	−	25072.6i	0.739212	−	1.00113i
$857$	3490.42	−	2015.20i	0.139126	−	0.0803242i	−0.428822	−	0.903389i	$-0.641071\pi$
$857$	3490.42	−	2015.20i	0.139126	−	0.0803242i	0.567947	+	0.823065i	$0.307738\pi$
$858$		0			0
$859$	16530.6	−	28631.9i	0.656599	−	1.13726i	−0.324892	−	0.945751i	$-0.605328\pi$
$859$	16530.6	−	28631.9i	0.656599	−	1.13726i	0.981490	−	0.191511i	$-0.0613387\pi$
$860$	18883.4	−	13571.9i	0.748741	−	0.538139i
$861$		0			0
$862$	2282.41	+	7086.41i	0.0901847	+	0.280005i
$863$	7712.99			0.304233			0.152117	−	0.988363i	$-0.451391\pi$
$863$	7712.99			0.304233			0.152117	+	0.988363i	$0.451391\pi$
$864$		0			0
$865$	−74180.1			−2.91584
$866$	−2074.28	−	6440.21i	−0.0813938	−	0.252711i
$867$		0			0
$868$	12313.4	−	8849.93i	0.481501	−	0.346067i
$869$	−2477.84	+	4291.75i	−0.0967262	+	0.167535i
$870$		0			0
$871$	−20565.0	+	11873.2i	−0.800021	+	0.461892i
$872$	26588.7	−	36009.6i	1.03258	−	1.39844i
$873$		0			0
$874$	−22654.1	−	4876.11i	−0.876758	−	0.188715i
$875$	6546.46	−	3779.60i	0.252927	−	0.146027i
$876$		0			0
$877$	6756.94	+	3901.12i	0.260166	+	0.150207i	0.624410	−	0.781096i	$-0.285339\pi$
$877$	6756.94	+	3901.12i	0.260166	+	0.150207i	−0.364244	+	0.931303i	$0.618673\pi$
$878$	−31904.7	−	28875.8i	−1.22635	−	1.10992i
$879$		0			0
$880$	30742.1	+	10339.0i	1.17763	+	0.396055i
$881$			13478.5i			0.515439i	0.966220	+	0.257720i	$0.0829711\pi$
$881$			13478.5i			0.515439i	−0.966220	+	0.257720i	$0.917029\pi$
$882$		0			0
$883$	7582.25			0.288973			0.144486	−	0.989507i	$-0.453847\pi$
$883$	7582.25			0.288973			0.144486	+	0.989507i	$0.453847\pi$
$884$	−4389.07	−	43928.4i	−0.166992	−	1.67135i
$885$		0			0
$886$	−4803.20	−	4347.21i	−0.182130	−	0.164839i
$887$	−23011.6	+	39857.2i	−0.871086	+	1.50877i	−0.0102115	+	0.999948i	$0.503250\pi$
$887$	−23011.6	+	39857.2i	−0.871086	+	1.50877i	−0.860874	+	0.508817i	$0.830083\pi$
$888$		0			0
$889$	−6441.73	−	11157.4i	−0.243024	−	0.420930i
$890$	−3179.87	+	14773.5i	−0.119764	+	0.556414i
$891$		0			0
$892$	9631.15	−	21336.3i	0.361519	−	0.800889i
$893$	−12269.8	−	21252.0i	−0.459792	−	0.796383i
$894$		0			0
$895$	13921.8	+	8037.78i	0.519951	+	0.300194i
$896$	6776.36	−	14512.2i	0.252659	−	0.541091i
$897$		0			0
$898$	−1234.93	+	397.750i	−0.0458911	+	0.0147807i
$899$			22311.2i			0.827718i
$900$		0			0
$901$		−	18818.0i		−	0.695802i
$902$	426.855	+	1325.29i	0.0157569	+	0.0489218i
$903$		0			0
$904$	2526.70	+	5794.81i	0.0929612	+	0.213200i
$905$	−57689.7	−	33307.1i	−2.11897	−	1.22339i
$906$		0			0
$907$	−23434.9	−	40590.5i	−0.857931	−	1.48598i	−0.873899	−	0.486108i	$-0.838416\pi$
$907$	−23434.9	−	40590.5i	−0.857931	−	1.48598i	0.0159676	−	0.999873i	$-0.494917\pi$
$908$	584.168	−	1294.13i	0.0213505	−	0.0472988i
$909$		0			0
$910$	31316.6	+	6740.65i	1.14081	+	0.245550i
$911$	19401.4	+	33604.1i	0.705593	+	1.22212i	0.966477	+	0.256753i	$0.0826527\pi$
$911$	19401.4	+	33604.1i	0.705593	+	1.22212i	−0.260884	+	0.965370i	$0.584014\pi$
$912$		0			0
$913$	−7394.31	+	12807.3i	−0.268035	+	0.464250i
$914$	10870.9	−	12011.2i	0.393411	−	0.434677i
$915$		0			0
$916$	8862.64	−	885.506i	0.319683	−	0.0319410i
$917$	−3263.93			−0.117540
$918$		0			0
$919$			7904.72i			0.283735i	0.989886	+	0.141868i	$0.0453107\pi$
$919$			7904.72i			0.283735i	−0.989886	+	0.141868i	$0.954689\pi$
$920$	−2595.08	+	22985.8i	−0.0929972	+	0.823715i
$921$		0			0
$922$	1579.71	−	1745.41i	0.0564261	−	0.0623448i
$923$	6831.22	+	3944.00i	0.243610	+	0.140648i
$924$		0			0
$925$	−37061.9	+	21397.7i	−1.31739	+	0.760597i
$926$	5932.27	−	27560.9i	0.210525	−	0.978087i
$927$		0			0
$928$	11519.8	+	20557.9i	0.407494	+	0.727206i
$929$	10521.4	−	6074.56i	0.371579	−	0.214532i	−0.302569	−	0.953128i	$-0.597844\pi$
$929$	10521.4	−	6074.56i	0.371579	−	0.214532i	0.674148	+	0.738596i	$0.264511\pi$
$930$		0			0
$931$	15062.3	−	26088.6i	0.530232	−	0.918388i
$932$	−16397.0	−	22814.0i	−0.576289	−	0.801821i
$933$		0			0
$934$	1174.24	−	378.203i	0.0411374	−	0.0132497i
$935$	46517.0			1.62703
$936$		0			0
$937$	−16651.7			−0.580561			−0.290281	−	0.956942i	$-0.593749\pi$
$937$	−16651.7			−0.580561			−0.290281	+	0.956942i	$0.593749\pi$
$938$	−11760.8	+	3787.94i	−0.409384	+	0.131856i
$939$		0			0
$940$	−19891.4	+	14296.5i	−0.690199	+	0.496063i
$941$	−19863.7	+	34404.9i	−0.688138	+	1.19189i	0.284301	+	0.958735i	$0.408238\pi$
$941$	−19863.7	+	34404.9i	−0.688138	+	1.19189i	−0.972439	+	0.233155i	$0.925095\pi$
$942$		0			0
$943$	−859.968	+	496.503i	−0.0296972	+	0.0171457i
$944$	−34618.9	+	30533.0i	−1.19359	+	1.05272i
$945$		0			0
$946$	−3021.99	+	14039.9i	−0.103862	+	0.482535i
$947$	7635.77	−	4408.51i	0.262016	−	0.151275i	−0.363238	−	0.931696i	$-0.618329\pi$
$947$	7635.77	−	4408.51i	0.262016	−	0.151275i	0.625254	+	0.780421i	$0.284995\pi$
$948$		0			0
$949$	21351.2	+	12327.1i	0.730338	+	0.421661i
$950$	−42782.3	+	47269.9i	−1.46110	+	1.61436i
$951$		0			0
$952$	2577.00	−	22825.6i	0.0877322	−	0.777081i
$953$			13435.9i			0.456697i	0.973579	+	0.228348i	$0.0733326\pi$
$953$			13435.9i			0.456697i	−0.973579	+	0.228348i	$0.926667\pi$
$954$		0			0
$955$	−5214.47			−0.176687
$956$	1960.99	+	19626.7i	0.0663419	+	0.663988i
$957$		0			0
$958$	−3044.28	+	3363.60i	−0.102668	+	0.113437i
$959$	−13149.3	+	22775.3i	−0.442767	+	0.766896i
$960$		0			0
$961$	−209.265	−	362.458i	−0.00702444	−	0.0121667i
$962$	−43083.7	−	9273.42i	−1.44394	−	0.310797i
$963$		0			0
$964$	−19025.0	−	8587.84i	−0.635638	−	0.286925i
$965$	9684.43	+	16773.9i	0.323060	+	0.559556i
$966$		0			0
$967$	−20368.5	−	11759.8i	−0.677361	−	0.391075i	0.121499	−	0.992592i	$-0.461230\pi$
$967$	−20368.5	−	11759.8i	−0.677361	−	0.391075i	−0.798860	+	0.601517i	$0.794563\pi$
$968$	9245.89	−	4031.48i	0.306998	−	0.133860i
$969$		0			0
$970$	−9437.03	−	29300.0i	−0.312376	−	0.969862i
$971$			47072.5i			1.55575i	0.628422	+	0.777873i	$0.283701\pi$
$971$			47072.5i			1.55575i	−0.628422	+	0.777873i	$0.716299\pi$
$972$		0			0
$973$		−	20972.0i		−	0.690988i
$974$	46716.1	−	15046.4i	1.53684	−	0.494989i
$975$		0			0
$976$	2395.36	+	11867.4i	0.0785589	+	0.389206i
$977$	22592.2	+	13043.6i	0.739805	+	0.427126i	0.821998	−	0.569490i	$-0.192859\pi$
$977$	22592.2	+	13043.6i	0.739805	+	0.427126i	−0.0821936	+	0.996616i	$0.526193\pi$
$978$		0			0
$979$	−4666.34	−	8082.34i	−0.152336	−	0.263854i
$980$	−27408.1	−	12371.9i	−0.893387	−	0.403272i
$981$		0			0
$982$	367.177	−	1705.88i	0.0119319	−	0.0554347i
$983$	−7003.52	−	12130.5i	−0.227241	−	0.393593i	0.729749	−	0.683716i	$-0.239637\pi$
$983$	−7003.52	−	12130.5i	−0.227241	−	0.393593i	−0.956989	+	0.290123i	$0.906304\pi$
$984$		0			0
$985$	43266.2	−	74939.3i	1.39957	−	2.42413i
$986$	25058.4	+	22679.5i	0.809353	+	0.732517i
$987$		0			0
$988$	−65329.7	+	6527.38i	−2.10366	+	0.210186i
$989$	−10242.5			−0.329315
$990$		0			0
$991$			27361.4i			0.877056i	0.898718	+	0.438528i	$0.144500\pi$
$991$			27361.4i			0.877056i	−0.898718	+	0.438528i	$0.855500\pi$
$992$	26666.0	+	15855.6i	0.853475	+	0.507475i
$993$		0			0
$994$	3043.02	+	2754.13i	0.0971012	+	0.0878829i
$995$	−73051.3	−	42176.2i	−2.32752	−	1.34379i
$996$		0			0
$997$	12223.6	−	7057.31i	0.388291	−	0.224180i	−0.293128	−	0.956073i	$-0.594696\pi$
$997$	12223.6	−	7057.31i	0.388291	−	0.224180i	0.681419	+	0.731893i	$0.261363\pi$
$998$	17645.5	+	3798.06i	0.559679	+	0.120466i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.4.l.b.179.20		64
3.2	odd	2		72.4.l.b.59.13	yes	64
4.3	odd	2		864.4.p.b.719.30		64
8.3	odd	2	inner	216.4.l.b.179.8		64
8.5	even	2		864.4.p.b.719.3		64
9.2	odd	6	inner	216.4.l.b.35.8		64
9.7	even	3		72.4.l.b.11.25	yes	64
12.11	even	2		288.4.p.b.239.17		64
24.5	odd	2		288.4.p.b.239.18		64
24.11	even	2		72.4.l.b.59.25	yes	64
36.7	odd	6		288.4.p.b.47.18		64
36.11	even	6		864.4.p.b.143.3		64
72.11	even	6	inner	216.4.l.b.35.20		64
72.29	odd	6		864.4.p.b.143.30		64
72.43	odd	6		72.4.l.b.11.13	✓	64
72.61	even	6		288.4.p.b.47.17		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.13	✓	64	72.43	odd	6
72.4.l.b.11.25	yes	64	9.7	even	3
72.4.l.b.59.13	yes	64	3.2	odd	2
72.4.l.b.59.25	yes	64	24.11	even	2
216.4.l.b.35.8		64	9.2	odd	6	inner
216.4.l.b.35.20		64	72.11	even	6	inner
216.4.l.b.179.8		64	8.3	odd	2	inner
216.4.l.b.179.20		64	1.1	even	1	trivial
288.4.p.b.47.17		64	72.61	even	6
288.4.p.b.47.18		64	36.7	odd	6
288.4.p.b.239.17		64	12.11	even	2
288.4.p.b.239.18		64	24.5	odd	2
864.4.p.b.143.3		64	36.11	even	6
864.4.p.b.143.30		64	72.29	odd	6
864.4.p.b.719.3		64	8.5	even	2
864.4.p.b.719.30		64	4.3	odd	2

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	216.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.867121 + 2.69223i) q^{2} +(-6.49620 + 4.66898i) q^{4} +(8.51655 - 14.7511i) q^{5} +(-9.57807 + 5.52990i) q^{7} +(-18.2030 - 13.4407i) q^{8} +O(q^{10})\)	\(q+(0.867121 + 2.69223i) q^{2} +(-6.49620 + 4.66898i) q^{4} +(8.51655 - 14.7511i) q^{5} +(-9.57807 + 5.52990i) q^{7} +(-18.2030 - 13.4407i) q^{8} +(47.0983 + 10.1375i) q^{10} +(-25.7667 + 14.8764i) q^{11} +(-52.0658 - 30.0602i) q^{13} +(-23.1931 - 20.9913i) q^{14} +(20.4013 - 60.6613i) q^{16} -91.7888i q^{17} -136.507 q^{19} +(13.5474 + 135.590i) q^{20} +(-62.3936 - 56.4703i) q^{22} +(30.0089 - 51.9770i) q^{23} +(-82.5634 - 143.004i) q^{25} +(35.7816 - 166.239i) q^{26} +(36.4021 - 80.6432i) q^{28} +(65.0911 + 112.741i) q^{29} +(148.423 + 85.6920i) q^{31} +(181.004 + 2.32417i) q^{32} +(247.117 - 79.5920i) q^{34} +188.383i q^{35} -259.167i q^{37} +(-118.368 - 367.509i) q^{38} +(-353.292 + 154.045i) q^{40} +(-14.3285 - 8.27259i) q^{41} +(-85.3289 - 147.794i) q^{43} +(97.9281 - 216.945i) q^{44} +(165.955 + 35.7206i) q^{46} +(89.8841 + 155.684i) q^{47} +(-110.340 + 191.115i) q^{49} +(313.407 - 346.282i) q^{50} +(478.581 - 47.8171i) q^{52} +205.014 q^{53} +506.783i q^{55} +(248.675 + 28.0753i) q^{56} +(-247.083 + 273.001i) q^{58} +(-624.620 - 360.624i) q^{59} +(-163.824 + 94.5836i) q^{61} +(-102.002 + 473.894i) q^{62} +(150.696 + 489.321i) q^{64} +(-886.843 + 512.019i) q^{65} +(197.490 - 342.063i) q^{67} +(428.560 + 596.278i) q^{68} +(-507.170 + 163.351i) q^{70} -131.203 q^{71} -410.081 q^{73} +(697.737 - 224.729i) q^{74} +(886.778 - 637.350i) q^{76} +(164.530 - 284.975i) q^{77} +(144.247 - 83.2809i) q^{79} +(-721.072 - 817.566i) q^{80} +(9.84712 - 45.7491i) q^{82} +(430.457 - 248.524i) q^{83} +(-1353.99 - 781.724i) q^{85} +(323.905 - 357.880i) q^{86} +(668.980 + 75.5276i) q^{88} +313.674i q^{89} +664.920 q^{91} +(47.7355 + 477.764i) q^{92} +(-341.196 + 376.985i) q^{94} +(-1162.57 + 2013.63i) q^{95} +(-319.471 - 553.340i) q^{97} +(-610.204 - 131.342i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 3 q^{2} - 17 q^{4}+O(q^{10}) \) 64 * q + 3 * q^2 - 17 * q^4	\( 64 q + 3 q^{2} - 17 q^{4} + 12 q^{10} - 48 q^{11} - 72 q^{14} + 127 q^{16} - 220 q^{19} + 234 q^{20} - 217 q^{22} - 902 q^{25} - 132 q^{28} + 693 q^{32} + 509 q^{34} + 1977 q^{38} - 36 q^{40} - 1620 q^{41} - 292 q^{43} + 48 q^{46} + 1762 q^{49} + 1227 q^{50} + 330 q^{52} - 942 q^{56} - 282 q^{58} - 5592 q^{59} + 1090 q^{64} + 6 q^{65} + 68 q^{67} + 2025 q^{68} + 600 q^{70} - 868 q^{73} + 420 q^{74} - 1471 q^{76} + 362 q^{82} - 3654 q^{83} + 4119 q^{86} + 3155 q^{88} - 1380 q^{91} + 744 q^{92} - 138 q^{94} - 1912 q^{97}+O(q^{100}) \) 64 * q + 3 * q^2 - 17 * q^4 + 12 * q^10 - 48 * q^11 - 72 * q^14 + 127 * q^16 - 220 * q^19 + 234 * q^20 - 217 * q^22 - 902 * q^25 - 132 * q^28 + 693 * q^32 + 509 * q^34 + 1977 * q^38 - 36 * q^40 - 1620 * q^41 - 292 * q^43 + 48 * q^46 + 1762 * q^49 + 1227 * q^50 + 330 * q^52 - 942 * q^56 - 282 * q^58 - 5592 * q^59 + 1090 * q^64 + 6 * q^65 + 68 * q^67 + 2025 * q^68 + 600 * q^70 - 868 * q^73 + 420 * q^74 - 1471 * q^76 + 362 * q^82 - 3654 * q^83 + 4119 * q^86 + 3155 * q^88 - 1380 * q^91 + 744 * q^92 - 138 * q^94 - 1912 * q^97

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