LMFDB - Embedded newform 216.3.u.a.41.17

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			41.17
Character	$\chi$	$=$	216.41
Dual form			216.3.u.a.137.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.95864 - 0.496426i) q^{3} +(4.40241 - 5.24659i) q^{5} +(-1.88768 - 0.687060i) q^{7} +(8.50712 - 2.93749i) q^{9} +O(q^{10})$	\(q+(2.95864 - 0.496426i) q^{3} +(4.40241 - 5.24659i) q^{5} +(-1.88768 - 0.687060i) q^{7} +(8.50712 - 2.93749i) q^{9} +(-4.17798 - 4.97912i) q^{11} +(-0.823444 + 4.66998i) q^{13} +(10.4206 - 17.7083i) q^{15} +(-11.1220 - 6.42127i) q^{17} +(-0.502884 - 0.871020i) q^{19} +(-5.92605 - 1.09567i) q^{21} +(13.1560 + 36.1459i) q^{23} +(-3.80428 - 21.5751i) q^{25} +(23.7113 - 12.9141i) q^{27} +(49.1201 - 8.66120i) q^{29} +(-39.4678 + 14.3651i) q^{31} +(-14.8329 - 12.6574i) q^{33} +(-11.9151 + 6.87918i) q^{35} +(7.52015 - 13.0253i) q^{37} +(-0.117977 + 14.2256i) q^{39} +(45.9021 + 8.09377i) q^{41} +(20.8130 - 17.4642i) q^{43} +(22.0401 - 57.5655i) q^{45} +(-26.0016 + 71.4387i) q^{47} +(-34.4449 - 28.9027i) q^{49} +(-36.0936 - 13.4770i) q^{51} +40.2735i q^{53} -44.5166 q^{55} +(-1.92025 - 2.32739i) q^{57} +(-9.22329 + 10.9919i) q^{59} +(-49.9957 - 18.1969i) q^{61} +(-18.0770 - 0.299856i) q^{63} +(20.8763 + 24.8795i) q^{65} +(-20.5560 + 116.579i) q^{67} +(56.8677 + 100.412i) q^{69} +(-17.5756 - 10.1473i) q^{71} +(-18.0467 - 31.2578i) q^{73} +(-21.9660 - 61.9446i) q^{75} +(4.46574 + 12.2695i) q^{77} +(15.0584 + 85.4004i) q^{79} +(63.7423 - 49.9792i) q^{81} +(-26.2200 + 4.62330i) q^{83} +(-82.6533 + 30.0834i) q^{85} +(141.029 - 50.0098i) q^{87} +(-46.7694 + 27.0023i) q^{89} +(4.76296 - 8.24968i) q^{91} +(-109.640 + 62.0940i) q^{93} +(-6.78379 - 1.19616i) q^{95} +(-55.9727 + 46.9666i) q^{97} +(-50.1687 - 30.0852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.95864	−	0.496426i	0.986214	−	0.165475i
$3$	2.95864	−	0.496426i	0.986214	−	0.165475i
$4$		0			0
$5$	4.40241	−	5.24659i	0.880483	−	1.04932i	−0.117931	−	0.993022i	$-0.537626\pi$
$5$	4.40241	−	5.24659i	0.880483	−	1.04932i	0.998414	−	0.0562967i	$-0.0179293\pi$
$6$		0			0
$7$	−1.88768	−	0.687060i	−0.269669	−	0.0981514i	0.203647	−	0.979044i	$-0.434721\pi$
$7$	−1.88768	−	0.687060i	−0.269669	−	0.0981514i	−0.473315	+	0.880893i	$0.656943\pi$
$8$		0			0
$9$	8.50712	−	2.93749i	0.945236	−	0.326388i
$10$		0			0
$11$	−4.17798	−	4.97912i	−0.379816	−	0.452647i	0.541940	−	0.840417i	$-0.317690\pi$
$11$	−4.17798	−	4.97912i	−0.379816	−	0.452647i	−0.921756	+	0.387770i	$0.873245\pi$
$12$		0			0
$13$	−0.823444	+	4.66998i	−0.0633418	+	0.359229i	0.936619	+	0.350350i	$0.113937\pi$
$13$	−0.823444	+	4.66998i	−0.0633418	+	0.359229i	−0.999961	+	0.00887906i	$0.997174\pi$
$14$		0			0
$15$	10.4206	−	17.7083i	0.694708	−	1.18055i
$16$		0			0
$17$	−11.1220	−	6.42127i	−0.654234	−	0.377722i	0.135843	−	0.990730i	$-0.456626\pi$
$17$	−11.1220	−	6.42127i	−0.654234	−	0.377722i	−0.790076	+	0.613008i	$0.789959\pi$
$18$		0			0
$19$	−0.502884	−	0.871020i	−0.0264676	−	0.0458432i	0.852488	−	0.522746i	$-0.175093\pi$
$19$	−0.502884	−	0.871020i	−0.0264676	−	0.0458432i	−0.878956	+	0.476903i	$0.841759\pi$
$20$		0			0
$21$	−5.92605	−	1.09567i	−0.282193	−	0.0521748i
$22$		0			0
$23$	13.1560	+	36.1459i	0.572001	+	1.57156i	0.801338	+	0.598212i	$0.204122\pi$
$23$	13.1560	+	36.1459i	0.572001	+	1.57156i	−0.229337	+	0.973347i	$0.573656\pi$
$24$		0			0
$25$	−3.80428	−	21.5751i	−0.152171	−	0.863006i
$26$		0			0
$27$	23.7113	−	12.9141i	0.878196	−	0.478301i
$28$		0			0
$29$	49.1201	−	8.66120i	1.69380	−	0.298662i	0.758276	−	0.651934i	$-0.226042\pi$
$29$	49.1201	−	8.66120i	1.69380	−	0.298662i	0.935521	+	0.353272i	$0.114931\pi$
$30$		0			0
$31$	−39.4678	+	14.3651i	−1.27315	+	0.463390i	−0.888162	−	0.459530i	$-0.848018\pi$
$31$	−39.4678	+	14.3651i	−1.27315	+	0.463390i	−0.384992	+	0.922920i	$0.625796\pi$
$32$		0			0
$33$	−14.8329	−	12.6574i	−0.449482	−	0.383557i
$34$		0			0
$35$	−11.9151	+	6.87918i	−0.340431	+	0.196548i
$36$		0			0
$37$	7.52015	−	13.0253i	0.203247	−	0.352035i	−0.746326	−	0.665581i	$-0.768184\pi$
$37$	7.52015	−	13.0253i	0.203247	−	0.352035i	0.949573	+	0.313546i	$0.101517\pi$
$38$		0			0
$39$	−0.117977	+	14.2256i	−0.00302505	+	0.364758i
$40$		0			0
$41$	45.9021	+	8.09377i	1.11956	+	0.197409i	0.702649	−	0.711537i	$-0.252001\pi$
$41$	45.9021	+	8.09377i	1.11956	+	0.197409i	0.416914	+	0.908946i	$0.363112\pi$
$42$		0			0
$43$	20.8130	−	17.4642i	0.484023	−	0.406143i	−0.367856	−	0.929883i	$-0.619908\pi$
$43$	20.8130	−	17.4642i	0.484023	−	0.406143i	0.851878	+	0.523740i	$0.175463\pi$
$44$		0			0
$45$	22.0401	−	57.5655i	0.489779	−	1.27923i
$46$		0			0
$47$	−26.0016	+	71.4387i	−0.553224	+	1.51997i	0.276057	+	0.961141i	$0.410972\pi$
$47$	−26.0016	+	71.4387i	−0.553224	+	1.51997i	−0.829282	+	0.558831i	$0.811250\pi$
$48$		0			0
$49$	−34.4449	−	28.9027i	−0.702957	−	0.589851i
$50$		0			0
$51$	−36.0936	−	13.4770i	−0.707718	−	0.264255i
$52$		0			0
$53$			40.2735i			0.759878i	0.925012	+	0.379939i	$0.124055\pi$
$53$			40.2735i			0.759878i	−0.925012	+	0.379939i	$0.875945\pi$
$54$		0			0
$55$	−44.5166			−0.809392
$56$		0			0
$57$	−1.92025	−	2.32739i	−0.0336886	−	0.0408314i
$58$		0			0
$59$	−9.22329	+	10.9919i	−0.156327	+	0.186303i	−0.838523	−	0.544866i	$-0.816581\pi$
$59$	−9.22329	+	10.9919i	−0.156327	+	0.186303i	0.682196	+	0.731169i	$0.261025\pi$
$60$		0			0
$61$	−49.9957	−	18.1969i	−0.819602	−	0.298311i	−0.102018	−	0.994783i	$-0.532530\pi$
$61$	−49.9957	−	18.1969i	−0.819602	−	0.298311i	−0.717584	+	0.696472i	$0.754752\pi$
$62$		0			0
$63$	−18.0770	−	0.299856i	−0.286936	−	0.00475963i
$64$		0			0
$65$	20.8763	+	24.8795i	0.321175	+	0.382761i
$66$		0			0
$67$	−20.5560	+	116.579i	−0.306806	+	1.73998i	0.308075	+	0.951362i	$0.400315\pi$
$67$	−20.5560	+	116.579i	−0.306806	+	1.73998i	−0.614881	+	0.788620i	$0.710796\pi$
$68$		0			0
$69$	56.8677	+	100.412i	0.824169	+	1.45524i
$70$		0			0
$71$	−17.5756	−	10.1473i	−0.247544	−	0.142920i	0.371095	−	0.928595i	$-0.378982\pi$
$71$	−17.5756	−	10.1473i	−0.247544	−	0.142920i	−0.618639	+	0.785675i	$0.712316\pi$
$72$		0			0
$73$	−18.0467	−	31.2578i	−0.247215	−	0.428188i	0.715537	−	0.698575i	$-0.246182\pi$
$73$	−18.0467	−	31.2578i	−0.247215	−	0.428188i	−0.962752	+	0.270386i	$0.912849\pi$
$74$		0			0
$75$	−21.9660	−	61.9446i	−0.292879	−	0.825928i
$76$		0			0
$77$	4.46574	+	12.2695i	0.0579966	+	0.159344i
$78$		0			0
$79$	15.0584	+	85.4004i	0.190613	+	1.08102i	0.918530	+	0.395352i	$0.129378\pi$
$79$	15.0584	+	85.4004i	0.190613	+	1.08102i	−0.727917	+	0.685665i	$0.759511\pi$
$80$		0			0
$81$	63.7423	−	49.9792i	0.786942	−	0.617027i
$82$		0			0
$83$	−26.2200	+	4.62330i	−0.315904	+	0.0557024i	−0.329352	−	0.944207i	$-0.606830\pi$
$83$	−26.2200	+	4.62330i	−0.315904	+	0.0557024i	0.0134480	+	0.999910i	$0.495719\pi$
$84$		0			0
$85$	−82.6533	+	30.0834i	−0.972392	+	0.353922i
$86$		0			0
$87$	141.029	−	50.0098i	1.62102	−	0.574826i
$88$		0			0
$89$	−46.7694	+	27.0023i	−0.525499	+	0.303397i	−0.739181	−	0.673506i	$-0.764787\pi$
$89$	−46.7694	+	27.0023i	−0.525499	+	0.303397i	0.213683	+	0.976903i	$0.431454\pi$
$90$		0			0
$91$	4.76296	−	8.24968i	0.0523402	−	0.0906559i
$92$		0			0
$93$	−109.640	+	62.0940i	−1.17892	+	0.667677i
$94$		0			0
$95$	−6.78379	−	1.19616i	−0.0714083	−	0.0125912i
$96$		0			0
$97$	−55.9727	+	46.9666i	−0.577038	+	0.484192i	−0.883973	−	0.467538i	$-0.845141\pi$
$97$	−55.9727	+	46.9666i	−0.577038	+	0.484192i	0.306935	+	0.951730i	$0.400697\pi$
$98$		0			0
$99$	−50.1687	−	30.0852i	−0.506754	−	0.303891i
$100$		0			0
$101$	−55.8193	+	153.362i	−0.552666	+	1.51844i	0.277390	+	0.960757i	$0.410530\pi$
$101$	−55.8193	+	153.362i	−0.552666	+	1.51844i	−0.830056	+	0.557680i	$0.811692\pi$
$102$		0			0
$103$	−49.0791	−	41.1823i	−0.476496	−	0.399828i	0.372661	−	0.927967i	$-0.378445\pi$
$103$	−49.0791	−	41.1823i	−0.476496	−	0.399828i	−0.849158	+	0.528139i	$0.822890\pi$
$104$		0			0
$105$	−31.8375	+	26.2680i	−0.303214	+	0.250171i
$106$		0			0
$107$		−	116.796i		−	1.09155i	−0.837930	−	0.545777i	$-0.816234\pi$
$107$		−	116.796i		−	1.09155i	0.837930	−	0.545777i	$-0.183766\pi$
$108$		0			0
$109$	−142.628			−1.30851			−0.654256	−	0.756273i	$-0.727018\pi$
$109$	−142.628			−1.30851			−0.654256	+	0.756273i	$0.727018\pi$
$110$		0			0
$111$	15.7834	−	42.2703i	0.142192	−	0.380814i
$112$		0			0
$113$	119.335	−	142.218i	1.05606	−	1.25856i	0.0911906	−	0.995833i	$-0.470933\pi$
$113$	119.335	−	142.218i	1.05606	−	1.25856i	0.964869	−	0.262730i	$-0.0846228\pi$
$114$		0			0
$115$	247.561	+	90.1048i	2.15270	+	0.783520i
$116$		0			0
$117$	6.71289	+	42.1470i	0.0573751	+	0.360230i
$118$		0			0
$119$	16.5829	+	19.7628i	0.139353	+	0.166074i
$120$		0			0
$121$	13.6753	−	77.5565i	0.113019	−	0.640963i
$122$		0			0
$123$	139.826	+	1.15962i	1.13679	+	0.00942778i
$124$		0			0
$125$	18.3399	+	10.5885i	0.146719	+	0.0847083i
$126$		0			0
$127$	−68.3695	−	118.419i	−0.538343	−	0.932437i	−0.998993	−	0.0448555i	$-0.985717\pi$
$127$	−68.3695	−	118.419i	−0.538343	−	0.932437i	0.460651	−	0.887581i	$-0.347616\pi$
$128$		0			0
$129$	52.9085	−	62.0023i	0.410143	−	0.480638i
$130$		0			0
$131$	−44.6587	−	122.699i	−0.340906	−	0.936633i	−0.985132	−	0.171797i	$-0.945043\pi$
$131$	−44.6587	−	122.699i	−0.340906	−	0.936633i	0.644226	−	0.764835i	$-0.277180\pi$
$132$		0			0
$133$	0.350841	+	1.98972i	0.00263790	+	0.0149603i
$134$		0			0
$135$	36.6317	−	181.257i	0.271346	−	1.34264i
$136$		0			0
$137$	121.424	−	21.4103i	0.886306	−	0.156280i	0.288079	−	0.957606i	$-0.406983\pi$
$137$	121.424	−	21.4103i	0.886306	−	0.156280i	0.598227	+	0.801327i	$0.295872\pi$
$138$		0			0
$139$	172.972	−	62.9568i	1.24441	−	0.452926i	0.365898	−	0.930655i	$-0.380762\pi$
$139$	172.972	−	62.9568i	1.24441	−	0.452926i	0.878507	+	0.477729i	$0.158540\pi$
$140$		0			0
$141$	−41.4653	+	224.269i	−0.294080	+	1.59056i
$142$		0			0
$143$	26.6927	−	15.4110i	0.186662	−	0.107770i
$144$		0			0
$145$	170.805	−	295.843i	1.17797	−	2.04030i
$146$		0			0
$147$	−116.258	−	68.4134i	−0.790872	−	0.465397i
$148$		0			0
$149$	179.662	+	31.6793i	1.20579	+	0.212613i	0.740198	−	0.672389i	$-0.234732\pi$
$149$	179.662	+	31.6793i	1.20579	+	0.212613i	0.465588	+	0.885001i	$0.345843\pi$
$150$		0			0
$151$	102.418	−	85.9388i	0.678264	−	0.569131i	−0.237235	−	0.971452i	$-0.576241\pi$
$151$	102.418	−	85.9388i	0.678264	−	0.569131i	0.915498	+	0.402322i	$0.131797\pi$
$152$		0			0
$153$	−113.478	−	21.9559i	−0.741689	−	0.143502i
$154$		0			0
$155$	−98.3857	+	270.312i	−0.634746	+	1.74395i
$156$		0			0
$157$	203.862	+	171.060i	1.29848	+	1.08956i	0.990405	+	0.138196i	$0.0441304\pi$
$157$	203.862	+	171.060i	1.29848	+	1.08956i	0.308078	+	0.951361i	$0.400314\pi$
$158$		0			0
$159$	19.9928	+	119.155i	0.125741	+	0.749402i
$160$		0			0
$161$		−	77.2709i		−	0.479943i
$162$		0			0
$163$	−76.4307			−0.468900			−0.234450	−	0.972128i	$-0.575329\pi$
$163$	−76.4307			−0.468900			−0.234450	+	0.972128i	$0.575329\pi$
$164$		0			0
$165$	−131.709	+	22.0992i	−0.798234	+	0.133934i
$166$		0			0
$167$	61.1942	−	72.9284i	0.366432	−	0.436697i	−0.551051	−	0.834472i	$-0.685773\pi$
$167$	61.1942	−	72.9284i	0.366432	−	0.436697i	0.917483	+	0.397775i	$0.130217\pi$
$168$		0			0
$169$	137.677	+	50.1105i	0.814659	+	0.296512i
$170$		0			0
$171$	−6.83671	−	5.93266i	−0.0399807	−	0.0346939i
$172$		0			0
$173$	−159.911	−	190.575i	−0.924342	−	1.10159i	−0.994571	−	0.104057i	$-0.966817\pi$
$173$	−159.911	−	190.575i	−0.924342	−	1.10159i	0.0702290	−	0.997531i	$-0.477627\pi$
$174$		0			0
$175$	−7.64215	+	43.3408i	−0.0436694	+	0.247662i
$176$		0			0
$177$	−21.8318	+	37.0997i	−0.123343	+	0.209603i
$178$		0			0
$179$	−219.633	−	126.805i	−1.22700	−	0.708410i	−0.260601	−	0.965447i	$-0.583921\pi$
$179$	−219.633	−	126.805i	−1.22700	−	0.708410i	−0.966402	+	0.257037i	$0.917254\pi$
$180$		0			0
$181$	−3.91416	−	6.77952i	−0.0216252	−	0.0374559i	0.855010	−	0.518611i	$-0.173551\pi$
$181$	−3.91416	−	6.77952i	−0.0216252	−	0.0374559i	−0.876635	+	0.481155i	$0.840217\pi$
$182$		0			0
$183$	−156.953	−	29.0191i	−0.857666	−	0.158574i
$184$		0			0
$185$	−35.2315	−	96.7979i	−0.190441	−	0.523232i
$186$		0			0
$187$	14.4951	+	82.2055i	0.0775137	+	0.439602i
$188$		0			0
$189$	−53.6322	+	8.08671i	−0.283768	+	0.0427868i
$190$		0			0
$191$	38.5694	−	6.80082i	0.201934	−	0.0356064i	−0.0717662	−	0.997421i	$-0.522864\pi$
$191$	38.5694	−	6.80082i	0.201934	−	0.0356064i	0.273700	+	0.961815i	$0.411752\pi$
$192$		0			0
$193$	−358.796	+	130.591i	−1.85905	+	0.676638i	−0.879345	+	0.476186i	$0.842019\pi$
$193$	−358.796	+	130.591i	−1.85905	+	0.676638i	−0.979703	+	0.200452i	$0.935759\pi$
$194$		0			0
$195$	74.1164	+	63.2459i	0.380084	+	0.324338i
$196$		0			0
$197$	15.7967	−	9.12023i	0.0801863	−	0.0462956i	−0.459371	−	0.888245i	$-0.651925\pi$
$197$	15.7967	−	9.12023i	0.0801863	−	0.0462956i	0.539557	+	0.841949i	$0.318592\pi$
$198$		0			0
$199$	39.3608	−	68.1749i	0.197793	−	0.342587i	−0.750020	−	0.661416i	$-0.769956\pi$
$199$	39.3608	−	68.1749i	0.197793	−	0.342587i	0.947813	+	0.318828i	$0.103289\pi$
$200$		0			0
$201$	−2.94511	+	355.119i	−0.0146523	+	1.76676i
$202$		0			0
$203$	−98.6739	−	17.3989i	−0.486078	−	0.0857087i
$204$		0			0
$205$	244.545	−	205.197i	1.19290	−	1.00096i
$206$		0			0
$207$	218.098	+	268.852i	1.05361	+	1.29880i
$208$		0			0
$209$	−2.23587	+	6.14302i	−0.0106980	+	0.0293924i
$210$		0			0
$211$	−143.634	−	120.523i	−0.680729	−	0.571199i	0.235490	−	0.971877i	$-0.424330\pi$
$211$	−143.634	−	120.523i	−0.680729	−	0.571199i	−0.916219	+	0.400677i	$0.868775\pi$
$212$		0			0
$213$	−57.0373	−	21.2972i	−0.267781	−	0.0999869i
$214$		0			0
$215$		−	186.082i		−	0.865496i
$216$		0			0
$217$	84.3723			0.388812
$218$		0			0
$219$	−68.9108	−	83.5217i	−0.314661	−	0.381378i
$220$		0			0
$221$	39.1455	−	46.6518i	0.177129	−	0.211094i
$222$		0			0
$223$	144.271	+	52.5103i	0.646955	+	0.235472i	0.644594	−	0.764525i	$-0.277026\pi$
$223$	144.271	+	52.5103i	0.646955	+	0.235472i	0.00236051	+	0.999997i	$0.499249\pi$
$224$		0			0
$225$	−95.7403	−	172.367i	−0.425512	−	0.766077i
$226$		0			0
$227$	174.762	+	208.273i	0.769876	+	0.917503i	0.998429	−	0.0560287i	$-0.0178438\pi$
$227$	174.762	+	208.273i	0.769876	+	0.917503i	−0.228553	+	0.973531i	$0.573399\pi$
$228$		0			0
$229$	−69.8427	+	396.098i	−0.304990	+	1.72968i	0.318562	+	0.947902i	$0.396800\pi$
$229$	−69.8427	+	396.098i	−0.304990	+	1.72968i	−0.623552	+	0.781782i	$0.714311\pi$
$230$		0			0
$231$	19.3034	+	34.0842i	0.0835646	+	0.147551i
$232$		0			0
$233$	−400.492	−	231.224i	−1.71885	−	0.992379i	−0.921036	−	0.389477i	$-0.872656\pi$
$233$	−400.492	−	231.224i	−1.71885	−	0.992379i	−0.797815	−	0.602902i	$-0.794011\pi$
$234$		0			0
$235$	260.340	+	450.922i	1.10783	+	1.91882i
$236$		0			0
$237$	86.9473	+	245.194i	0.366866	+	1.03457i
$238$		0			0
$239$	−57.6310	−	158.340i	−0.241134	−	0.662510i	−0.999937	−	0.0111906i	$-0.996438\pi$
$239$	−57.6310	−	158.340i	−0.241134	−	0.662510i	0.758803	−	0.651320i	$-0.225784\pi$
$240$		0			0
$241$	−2.63522	−	14.9451i	−0.0109345	−	0.0620127i	0.978852	−	0.204568i	$-0.0655791\pi$
$241$	−2.63522	−	14.9451i	−0.0109345	−	0.0620127i	−0.989787	+	0.142556i	$0.954468\pi$
$242$		0			0
$243$	163.780	−	179.514i	0.673990	−	0.738740i
$244$		0			0
$245$	−303.281	+	53.4767i	−1.23788	+	0.218272i
$246$		0			0
$247$	4.48174	−	1.63122i	0.0181447	−	0.00660413i
$248$		0			0
$249$	−75.2806	+	26.6950i	−0.302332	+	0.107209i
$250$		0			0
$251$	−181.596	+	104.845i	−0.723491	+	0.417708i	−0.816036	−	0.578001i	$-0.803833\pi$
$251$	−181.596	+	104.845i	−0.723491	+	0.417708i	0.0925450	+	0.995708i	$0.470500\pi$
$252$		0			0
$253$	125.009	−	216.522i	0.494107	−	0.855818i
$254$		0			0
$255$	−229.607	+	130.037i	−0.900421	+	0.509949i
$256$		0			0
$257$	343.286	+	60.5306i	1.33574	+	0.235528i	0.795486	−	0.605972i	$-0.207216\pi$
$257$	343.286	+	60.5306i	1.33574	+	0.235528i	0.540258	+	0.841500i	$0.318327\pi$
$258$		0			0
$259$	−23.1448	+	19.4208i	−0.0893622	+	0.0749838i
$260$		0			0
$261$	392.428	−	217.972i	1.50356	−	0.835141i
$262$		0			0
$263$	125.491	−	344.783i	0.477151	−	1.31096i	−0.434750	−	0.900551i	$-0.643163\pi$
$263$	125.491	−	344.783i	0.477151	−	1.31096i	0.911901	−	0.410410i	$-0.134614\pi$
$264$		0			0
$265$	211.299	+	177.301i	0.797354	+	0.669059i
$266$		0			0
$267$	−124.969	+	103.108i	−0.468049	+	0.386171i
$268$		0			0
$269$			45.8167i			0.170322i	0.996367	+	0.0851611i	$0.0271405\pi$
$269$			45.8167i			0.170322i	−0.996367	+	0.0851611i	$0.972860\pi$
$270$		0			0
$271$	−321.264			−1.18547			−0.592737	−	0.805396i	$-0.701953\pi$
$271$	−321.264			−1.18547			−0.592737	+	0.805396i	$0.701953\pi$
$272$		0			0
$273$	9.99653	−	26.7723i	0.0366173	−	0.0980671i
$274$		0			0
$275$	−91.5310	+	109.082i	−0.332840	+	0.396663i
$276$		0			0
$277$	−177.630	−	64.6519i	−0.641263	−	0.233400i	0.000863380	−	1.00000i	$-0.499725\pi$
$277$	−177.630	−	64.6519i	−0.641263	−	0.233400i	−0.642126	+	0.766599i	$0.721947\pi$
$278$		0			0
$279$	−293.560	+	238.142i	−1.05219	+	0.853555i
$280$		0			0
$281$	−14.9553	−	17.8230i	−0.0532217	−	0.0634272i	0.738777	−	0.673950i	$-0.235404\pi$
$281$	−14.9553	−	17.8230i	−0.0532217	−	0.0634272i	−0.791999	+	0.610523i	$0.790959\pi$
$282$		0			0
$283$	−0.664550	+	3.76885i	−0.00234823	+	0.0133175i	−0.985959	−	0.166985i	$-0.946597\pi$
$283$	−0.664550	+	3.76885i	−0.00234823	+	0.0133175i	0.983611	+	0.180303i	$0.0577078\pi$
$284$		0			0
$285$	−20.6646	−	0.171378i	−0.0725074	−	0.000601326i
$286$		0			0
$287$	−81.0876	−	46.8159i	−0.282535	−	0.163122i
$288$		0			0
$289$	−62.0345	−	107.447i	−0.214652	−	0.371788i
$290$		0			0
$291$	−142.288	+	166.744i	−0.488961	+	0.573003i
$292$		0			0
$293$	137.837	+	378.704i	0.470433	+	1.29251i	0.917404	+	0.397957i	$0.130281\pi$
$293$	137.837	+	378.704i	0.470433	+	1.29251i	−0.446971	+	0.894549i	$0.647497\pi$
$294$		0			0
$295$	17.0652	+	96.7817i	0.0578482	+	0.328074i
$296$		0			0
$297$	−163.366	−	64.1063i	−0.550054	−	0.215846i
$298$		0			0
$299$	−179.634	+	31.6743i	−0.600782	+	0.105934i
$300$		0			0
$301$	−51.2872	+	18.6670i	−0.170389	+	0.0620167i
$302$		0			0
$303$	−89.0163	+	481.454i	−0.293783	+	1.58896i
$304$		0			0
$305$	−315.574	+	182.197i	−1.03467	+	0.597366i
$306$		0			0
$307$	159.185	−	275.717i	0.518519	−	0.898101i	−0.481250	−	0.876584i	$-0.659817\pi$
$307$	159.185	−	275.717i	0.518519	−	0.898101i	0.999768	−	0.0215173i	$-0.00684969\pi$
$308$		0			0
$309$	−165.652	−	97.4795i	−0.536089	−	0.315468i
$310$		0			0
$311$	−39.6506	−	6.99147i	−0.127494	−	0.0224806i	0.109537	−	0.993983i	$-0.465063\pi$
$311$	−39.6506	−	6.99147i	−0.127494	−	0.0224806i	−0.237031	+	0.971502i	$0.576174\pi$
$312$		0			0
$313$	−36.4896	+	30.6184i	−0.116580	+	0.0978224i	−0.699214	−	0.714912i	$-0.746467\pi$
$313$	−36.4896	+	30.6184i	−0.116580	+	0.0978224i	0.582634	+	0.812735i	$0.302022\pi$
$314$		0			0
$315$	−81.1556	+	93.5224i	−0.257637	+	0.296897i
$316$		0			0
$317$	119.780	−	329.092i	0.377854	−	1.03815i	−0.594390	−	0.804177i	$-0.702606\pi$
$317$	119.780	−	329.092i	0.377854	−	1.03815i	0.972244	−	0.233969i	$-0.0751715\pi$
$318$		0			0
$319$	−248.348	−	208.388i	−0.778519	−	0.653255i
$320$		0			0
$321$	−57.9807	−	345.559i	−0.180625	−	1.07651i
$322$		0			0
$323$			12.9166i			0.0399895i
$324$		0			0
$325$	103.888			0.319656
$326$		0			0
$327$	−421.984	+	70.8041i	−1.29047	+	0.216526i
$328$		0			0
$329$	98.1653	−	116.989i	0.298375	−	0.355589i
$330$		0			0
$331$	170.264	+	61.9711i	0.514393	+	0.187224i	0.586156	−	0.810198i	$-0.300640\pi$
$331$	170.264	+	61.9711i	0.514393	+	0.187224i	−0.0717633	+	0.997422i	$0.522863\pi$
$332$		0			0
$333$	25.7132	−	132.898i	0.0772168	−	0.399093i
$334$		0			0
$335$	521.146	+	621.077i	1.55566	+	1.85396i
$336$		0			0
$337$	24.3640	−	138.175i	0.0722966	−	0.410014i	−0.927085	−	0.374851i	$-0.877694\pi$
$337$	24.3640	−	138.175i	0.0722966	−	0.410014i	0.999382	−	0.0351632i	$-0.0111951\pi$
$338$		0			0
$339$	282.468	−	480.012i	0.833240	−	1.41596i
$340$		0			0
$341$	236.421	+	136.498i	0.693316	+	0.400286i
$342$		0			0
$343$	94.3794	+	163.470i	0.275159	+	0.476589i
$344$		0			0
$345$	777.174	+	143.692i	2.25268	+	0.416499i
$346$		0			0
$347$	48.7417	+	133.917i	0.140466	+	0.385927i	0.989900	−	0.141768i	$-0.0452787\pi$
$347$	48.7417	+	133.917i	0.140466	+	0.385927i	−0.849434	+	0.527695i	$0.823056\pi$
$348$		0			0
$349$	−48.9050	−	277.354i	−0.140129	−	0.794710i	−0.971150	−	0.238470i	$-0.923354\pi$
$349$	−48.9050	−	277.354i	−0.140129	−	0.794710i	0.831021	−	0.556241i	$-0.187757\pi$
$350$		0			0
$351$	40.7839	+	121.365i	0.116193	+	0.345770i
$352$		0			0
$353$	37.8936	−	6.68167i	0.107347	−	0.0189282i	−0.119716	−	0.992808i	$-0.538199\pi$
$353$	37.8936	−	6.68167i	0.107347	−	0.0189282i	0.227064	+	0.973880i	$0.427087\pi$
$354$		0			0
$355$	−130.614	+	47.5395i	−0.367926	+	0.133914i
$356$		0			0
$357$	58.8738	+	50.2388i	0.164912	+	0.140725i
$358$		0			0
$359$	424.355	−	245.001i	1.18205	−	0.682455i	0.225560	−	0.974229i	$-0.427579\pi$
$359$	424.355	−	245.001i	1.18205	−	0.682455i	0.956487	+	0.291774i	$0.0942456\pi$
$360$		0			0
$361$	179.994	−	311.759i	0.498599	−	0.863599i
$362$		0			0
$363$	1.95930	−	236.251i	0.00539752	−	0.650828i
$364$		0			0
$365$	−243.446	−	42.9260i	−0.666974	−	0.117606i
$366$		0			0
$367$	79.1061	−	66.3779i	0.215548	−	0.180866i	−0.528620	−	0.848858i	$-0.677290\pi$
$367$	79.1061	−	66.3779i	0.215548	−	0.180866i	0.744168	+	0.667992i	$0.232846\pi$
$368$		0			0
$369$	414.270	−	65.9822i	1.12268	−	0.178813i
$370$		0			0
$371$	27.6703	−	76.0236i	0.0745831	−	0.204915i
$372$		0			0
$373$	33.1321	+	27.8012i	0.0888261	+	0.0745339i	0.686119	−	0.727489i	$-0.259313\pi$
$373$	33.1321	+	27.8012i	0.0888261	+	0.0745339i	−0.597293	+	0.802023i	$0.703757\pi$
$374$		0			0
$375$	59.5176	+	22.2233i	0.158714	+	0.0592621i
$376$		0			0
$377$			236.522i			0.627379i
$378$		0			0
$379$	−633.947			−1.67268			−0.836341	−	0.548209i	$-0.815310\pi$
$379$	−633.947			−1.67268			−0.836341	+	0.548209i	$0.815310\pi$
$380$		0			0
$381$	−261.067	−	316.420i	−0.685216	−	0.830500i
$382$		0			0
$383$	188.474	−	224.615i	0.492100	−	0.586461i	−0.461651	−	0.887062i	$-0.652743\pi$
$383$	188.474	−	224.615i	0.492100	−	0.586461i	0.953750	+	0.300600i	$0.0971870\pi$
$384$		0			0
$385$	84.0331	+	30.5856i	0.218268	+	0.0794430i
$386$		0			0
$387$	125.758	−	209.708i	0.324956	−	0.541881i
$388$		0			0
$389$	−262.221	−	312.503i	−0.674090	−	0.803349i	0.315245	−	0.949010i	$-0.397913\pi$
$389$	−262.221	−	312.503i	−0.674090	−	0.803349i	−0.989334	+	0.145662i	$0.953469\pi$
$390$		0			0
$391$	85.7816	−	486.492i	0.219390	−	1.24422i
$392$		0			0
$393$	−193.040	−	340.852i	−0.491196	−	0.867309i
$394$		0			0
$395$	514.354	+	296.963i	1.30216	+	0.751804i
$396$		0			0
$397$	281.196	+	487.046i	0.708302	+	1.22682i	0.965487	+	0.260453i	$0.0838718\pi$
$397$	281.196	+	487.046i	0.708302	+	1.22682i	−0.257185	+	0.966362i	$0.582795\pi$
$398$		0			0
$399$	2.02576	+	5.71270i	0.00507710	+	0.0143175i
$400$		0			0
$401$	17.7490	+	48.7650i	0.0442619	+	0.121608i	0.959854	−	0.280499i	$-0.0905000\pi$
$401$	17.7490	+	48.7650i	0.0442619	+	0.121608i	−0.915592	+	0.402108i	$0.868278\pi$
$402$		0			0
$403$	−34.5852	−	196.143i	−0.0858194	−	0.486706i
$404$		0			0
$405$	18.3995	−	554.459i	0.0454309	−	1.36903i
$406$		0			0
$407$	−96.2734	+	16.9756i	−0.236544	+	0.0417091i
$408$		0			0
$409$	120.765	−	43.9549i	0.295269	−	0.107469i	−0.190138	−	0.981757i	$-0.560894\pi$
$409$	120.765	−	43.9549i	0.295269	−	0.107469i	0.485407	+	0.874288i	$0.338671\pi$
$410$		0			0
$411$	348.621	−	123.623i	0.848227	−	0.300787i
$412$		0			0
$413$	24.9627	−	14.4122i	0.0604425	−	0.0348965i
$414$		0			0
$415$	−91.1749	+	157.920i	−0.219699	+	0.380529i
$416$		0			0
$417$	480.510	−	272.134i	1.15230	−	0.652601i
$418$		0			0
$419$	−298.308	−	52.5997i	−0.711952	−	0.125536i	−0.194069	−	0.980988i	$-0.562169\pi$
$419$	−298.308	−	52.5997i	−0.711952	−	0.125536i	−0.517883	+	0.855451i	$0.673280\pi$
$420$		0			0
$421$	−364.312	+	305.694i	−0.865349	+	0.726114i	−0.963113	−	0.269096i	$-0.913275\pi$
$421$	−364.312	+	305.694i	−0.865349	+	0.726114i	0.0977648	+	0.995210i	$0.468831\pi$
$422$		0			0
$423$	−11.3480	+	684.117i	−0.0268273	+	1.61730i
$424$		0			0
$425$	−96.2288	+	264.387i	−0.226421	+	0.622086i
$426$		0			0
$427$	81.8736	+	68.7001i	0.191741	+	0.160890i
$428$		0			0
$429$	71.3237	−	58.8467i	0.166256	−	0.137172i
$430$		0			0
$431$		−	255.291i		−	0.592322i	−0.955138	−	0.296161i	$-0.904294\pi$
$431$		−	255.291i		−	0.592322i	0.955138	−	0.296161i	$-0.0957065\pi$
$432$		0			0
$433$	−578.499			−1.33602			−0.668012	−	0.744150i	$-0.732855\pi$
$433$	−578.499			−1.33602			−0.668012	+	0.744150i	$0.732855\pi$
$434$		0			0
$435$	358.487	−	960.086i	0.824109	−	2.20709i
$436$		0			0
$437$	24.8678	−	29.6363i	0.0569058	−	0.0678176i
$438$		0			0
$439$	−778.468	−	283.339i	−1.77328	−	0.645420i	−0.999935	−	0.0114308i	$-0.996361\pi$
$439$	−778.468	−	283.339i	−1.77328	−	0.645420i	−0.773342	−	0.633989i	$-0.781416\pi$
$440$		0			0
$441$	−377.928	−	144.697i	−0.856980	−	0.328112i
$442$		0			0
$443$	264.372	+	315.066i	0.596777	+	0.711211i	0.976893	−	0.213728i	$-0.0685606\pi$
$443$	264.372	+	315.066i	0.596777	+	0.711211i	−0.380117	+	0.924939i	$0.624116\pi$
$444$		0			0
$445$	−64.2280	+	364.255i	−0.144333	+	0.818551i
$446$		0			0
$447$	547.282	+	4.53878i	1.22435	+	0.0101539i
$448$		0			0
$449$	167.922	+	96.9497i	0.373991	+	0.215924i	0.675200	−	0.737634i	$-0.264057\pi$
$449$	167.922	+	96.9497i	0.373991	+	0.215924i	−0.301210	+	0.953558i	$0.597390\pi$
$450$		0			0
$451$	−151.478	−	262.367i	−0.335871	−	0.581746i
$452$		0			0
$453$	260.355	−	305.105i	0.574736	−	0.673521i
$454$		0			0
$455$	−22.3142	−	61.3078i	−0.0490422	−	0.134742i
$456$		0			0
$457$	143.398	+	813.248i	0.313780	+	1.77954i	0.578979	+	0.815343i	$0.303451\pi$
$457$	143.398	+	813.248i	0.313780	+	1.77954i	−0.265198	+	0.964194i	$0.585437\pi$
$458$		0			0
$459$	−346.642	−	8.62600i	−0.755210	−	0.0187930i
$460$		0			0
$461$	−173.062	+	30.5155i	−0.375406	+	0.0661942i	−0.358168	−	0.933657i	$-0.616598\pi$
$461$	−173.062	+	30.5155i	−0.375406	+	0.0661942i	−0.0172382	+	0.999851i	$0.505487\pi$
$462$		0			0
$463$	154.684	−	56.3005i	0.334092	−	0.121599i	−0.169527	−	0.985526i	$-0.554224\pi$
$463$	154.684	−	56.3005i	0.334092	−	0.121599i	0.503619	+	0.863926i	$0.332002\pi$
$464$		0			0
$465$	−156.898	+	848.599i	−0.337415	+	1.82494i
$466$		0			0
$467$	423.560	−	244.543i	0.906982	−	0.523646i	0.0275229	−	0.999621i	$-0.491238\pi$
$467$	423.560	−	244.543i	0.906982	−	0.523646i	0.879459	+	0.475975i	$0.157905\pi$
$468$		0			0
$469$	118.900	−	205.941i	0.253518	−	0.439106i
$470$		0			0
$471$	688.073	+	404.904i	1.46088	+	0.859669i
$472$		0			0
$473$	−173.912	−	30.6654i	−0.367679	−	0.0648318i
$474$		0			0
$475$	−16.8793	+	14.1634i	−0.0355353	+	0.0298177i
$476$		0			0
$477$	118.303	+	342.612i	0.248015	+	0.718264i
$478$		0			0
$479$	35.2072	−	96.7309i	0.0735014	−	0.201944i	−0.897501	−	0.441012i	$-0.854620\pi$
$479$	35.2072	−	96.7309i	0.0735014	−	0.201944i	0.971003	+	0.239068i	$0.0768419\pi$
$480$		0			0
$481$	54.6354	+	45.8446i	0.113587	+	0.0953109i
$482$		0			0
$483$	−38.3592	−	228.617i	−0.0794187	−	0.473327i
$484$		0			0
$485$			500.432i			1.03182i
$486$		0			0
$487$	−882.964			−1.81307			−0.906534	−	0.422133i	$-0.861282\pi$
$487$	−882.964			−1.81307			−0.906534	+	0.422133i	$0.861282\pi$
$488$		0			0
$489$	−226.131	+	37.9422i	−0.462436	+	0.0775913i
$490$		0			0
$491$	−473.723	+	564.561i	−0.964812	+	1.14982i	0.0238586	+	0.999715i	$0.492405\pi$
$491$	−473.723	+	564.561i	−0.964812	+	1.14982i	−0.988670	+	0.150103i	$0.952040\pi$
$492$		0			0
$493$	−601.928	−	219.084i	−1.22095	−	0.444389i
$494$		0			0
$495$	−378.708	+	130.767i	−0.765067	+	0.264176i
$496$		0			0
$497$	26.2054	+	31.2304i	0.0527271	+	0.0628377i
$498$		0			0
$499$	101.786	−	577.260i	0.203981	−	1.15683i	−0.695054	−	0.718957i	$-0.744620\pi$
$499$	101.786	−	577.260i	0.203981	−	1.15683i	0.899035	−	0.437876i	$-0.144269\pi$
$500$		0			0
$501$	144.848	−	246.147i	0.289118	−	0.491312i
$502$		0			0
$503$	483.520	+	279.161i	0.961273	+	0.554991i	0.896565	−	0.442913i	$-0.146055\pi$
$503$	483.520	+	279.161i	0.961273	+	0.554991i	0.0647083	+	0.997904i	$0.479388\pi$
$504$		0			0
$505$	558.889	+	968.024i	1.10671	+	1.91688i
$506$		0			0
$507$	432.214	+	79.9124i	0.852494	+	0.157618i
$508$		0			0
$509$	−154.057	−	423.267i	−0.302665	−	0.831567i	−0.994035	−	0.109065i	$-0.965214\pi$
$509$	−154.057	−	423.267i	−0.302665	−	0.831567i	0.691369	−	0.722502i	$-0.257008\pi$
$510$		0			0
$511$	12.5904	+	71.4039i	0.0246388	+	0.139734i
$512$		0			0
$513$	−23.1725	−	14.1587i	−0.0451705	−	0.0275998i
$514$		0			0
$515$	−432.133	+	76.1968i	−0.839094	+	0.147955i
$516$		0			0
$517$	464.335	−	169.004i	0.898134	−	0.326894i
$518$		0			0
$519$	−567.726	−	484.458i	−1.09388	−	0.933446i
$520$		0			0
$521$	−529.757	+	305.855i	−1.01681	+	0.587054i	−0.913178	−	0.407562i	$-0.866379\pi$
$521$	−529.757	+	305.855i	−1.01681	+	0.587054i	−0.103630	+	0.994616i	$0.533046\pi$
$522$		0			0
$523$	−4.84278	+	8.38794i	−0.00925961	+	0.0160381i	−0.870618	−	0.491960i	$-0.836281\pi$
$523$	−4.84278	+	8.38794i	−0.00925961	+	0.0160381i	0.861358	+	0.507998i	$0.169614\pi$
$524$		0			0
$525$	−1.09491	+	132.024i	−0.00208555	+	0.251474i
$526$		0			0
$527$	531.202	+	93.6652i	1.00797	+	0.177733i
$528$		0			0
$529$	−728.205	+	611.036i	−1.37657	+	1.15508i
$530$		0			0
$531$	−46.1751	+	120.603i	−0.0869588	+	0.227124i
$532$		0			0
$533$	−75.5955	+	207.697i	−0.141830	+	0.389675i
$534$		0			0
$535$	−612.783	−	514.186i	−1.14539	−	0.961095i
$536$		0			0
$537$	−712.766	−	266.140i	−1.32731	−	0.495605i
$538$		0			0
$539$			292.260i			0.542226i
$540$		0			0
$541$	−49.4040			−0.0913197			−0.0456599	−	0.998957i	$-0.514539\pi$
$541$	−49.4040			−0.0913197			−0.0456599	+	0.998957i	$0.514539\pi$
$542$		0			0
$543$	−14.9461	−	18.1151i	−0.0275251	−	0.0333611i
$544$		0			0
$545$	−627.906	+	748.310i	−1.15212	+	1.37305i
$546$		0			0
$547$	927.279	+	337.502i	1.69521	+	0.617006i	0.995266	−	0.0971928i	$-0.0309864\pi$
$547$	927.279	+	337.502i	1.69521	+	0.617006i	0.699943	+	0.714198i	$0.253209\pi$
$548$		0			0
$549$	−478.773	−	7.94177i	−0.872082	−	0.0144659i
$550$		0			0
$551$	−32.2458	−	38.4290i	−0.0585223	−	0.0697441i
$552$		0			0
$553$	30.2497	−	171.555i	0.0547012	−	0.310226i
$554$		0			0
$555$	−152.290	−	268.900i	−0.274397	−	0.484505i
$556$		0			0
$557$	279.201	+	161.197i	0.501258	+	0.289402i	0.729233	−	0.684265i	$-0.239877\pi$
$557$	279.201	+	161.197i	0.501258	+	0.289402i	−0.227975	+	0.973667i	$0.573210\pi$
$558$		0			0
$559$	64.4190	+	111.577i	0.115240	+	0.199601i
$560$		0			0
$561$	83.6946	+	236.021i	0.149188	+	0.420715i
$562$		0			0
$563$	68.2431	+	187.496i	0.121213	+	0.333031i	0.985428	−	0.170092i	$-0.0544065\pi$
$563$	68.2431	+	187.496i	0.121213	+	0.333031i	−0.864215	+	0.503123i	$0.832184\pi$
$564$		0			0
$565$	−220.797	−	1252.20i	−0.390791	−	2.21629i
$566$		0			0
$567$	−154.664	+	50.5500i	−0.272776	+	0.0891535i
$568$		0			0
$569$	620.765	−	109.458i	1.09098	−	0.192368i	0.400912	−	0.916117i	$-0.368693\pi$
$569$	620.765	−	109.458i	1.09098	−	0.192368i	0.690064	+	0.723748i	$0.257582\pi$
$570$		0			0
$571$	36.9288	−	13.4410i	0.0646740	−	0.0235394i	−0.309481	−	0.950906i	$-0.600155\pi$
$571$	36.9288	−	13.4410i	0.0646740	−	0.0235394i	0.374155	+	0.927366i	$0.377933\pi$
$572$		0			0
$573$	110.737	−	39.2680i	0.193258	−	0.0685306i
$574$		0			0
$575$	729.803	−	421.352i	1.26922	−	0.732786i
$576$		0			0
$577$	−184.181	+	319.011i	−0.319204	+	0.552878i	−0.980322	−	0.197404i	$-0.936749\pi$
$577$	−184.181	+	319.011i	−0.319204	+	0.552878i	0.661118	+	0.750282i	$0.270082\pi$
$578$		0			0
$579$	−996.721	+	564.488i	−1.72145	+	0.974936i
$580$		0			0
$581$	52.6716	+	9.28742i	0.0906568	+	0.0159852i
$582$		0			0
$583$	200.527	−	168.262i	0.343956	−	0.288614i
$584$		0			0
$585$	250.681	+	150.329i	0.428514	+	0.256972i
$586$		0			0
$587$	238.415	−	655.040i	0.406159	−	1.11591i	−0.553034	−	0.833159i	$-0.686530\pi$
$587$	238.415	−	655.040i	0.406159	−	1.11591i	0.959193	−	0.282753i	$-0.0912477\pi$
$588$		0			0
$589$	32.3600	+	27.1532i	0.0549405	+	0.0461006i
$590$		0			0
$591$	42.2093	−	34.8254i	0.0714201	−	0.0589262i
$592$		0			0
$593$			294.385i			0.496434i	0.968704	+	0.248217i	$0.0798446\pi$
$593$			294.385i			0.496434i	−0.968704	+	0.248217i	$0.920155\pi$
$594$		0			0
$595$	176.692			0.296962
$596$		0			0
$597$	82.6107	−	221.245i	0.138376	−	0.370594i
$598$		0			0
$599$	−276.872	+	329.963i	−0.462224	+	0.550857i	−0.945929	−	0.324374i	$-0.894846\pi$
$599$	−276.872	+	329.963i	−0.462224	+	0.550857i	0.483705	+	0.875231i	$0.339291\pi$
$600$		0			0
$601$	−720.781	−	262.343i	−1.19930	−	0.436511i	−0.336322	−	0.941747i	$-0.609183\pi$
$601$	−720.781	−	262.343i	−1.19930	−	0.436511i	−0.862981	+	0.505236i	$0.831405\pi$
$602$		0			0
$603$	167.577	+	1052.13i	0.277905	+	1.74483i
$604$		0			0
$605$	−346.703	−	413.184i	−0.573063	−	0.682949i
$606$		0			0
$607$	−56.8076	+	322.172i	−0.0935874	+	0.530761i	0.901584	+	0.432605i	$0.142405\pi$
$607$	−56.8076	+	322.172i	−0.0935874	+	0.530761i	−0.995171	+	0.0981558i	$0.968706\pi$
$608$		0			0
$609$	−300.578	−	2.49278i	−0.493560	−	0.00409324i
$610$		0			0
$611$	−312.206	−	180.252i	−0.510976	−	0.295012i
$612$		0			0
$613$	261.784	+	453.424i	0.427054	+	0.739680i	0.996610	−	0.0822730i	$-0.0262179\pi$
$613$	261.784	+	453.424i	0.427054	+	0.739680i	−0.569555	+	0.821953i	$0.692885\pi$
$614$		0			0
$615$	621.655	−	728.503i	1.01082	−	1.18456i
$616$		0			0
$617$	190.171	+	522.491i	0.308219	+	0.846825i	0.993004	+	0.118080i	$0.0376738\pi$
$617$	190.171	+	522.491i	0.308219	+	0.846825i	−0.684785	+	0.728745i	$0.740104\pi$
$618$		0			0
$619$	−2.07367	−	11.7604i	−0.00335003	−	0.0189990i	0.983087	−	0.183140i	$-0.0586260\pi$
$619$	−2.07367	−	11.7604i	−0.00335003	−	0.0189990i	−0.986437	+	0.164141i	$0.947515\pi$
$620$		0			0
$621$	778.739	+	687.166i	1.25401	+	1.10655i
$622$		0			0
$623$	106.838	−	18.8384i	0.171489	−	0.0302382i
$624$		0			0
$625$	650.963	−	236.931i	1.04154	−	0.379090i
$626$		0			0
$627$	−3.56560	+	19.2849i	−0.00568677	+	0.0307575i
$628$		0			0
$629$	−167.278	+	96.5779i	−0.265943	+	0.153542i
$630$		0			0
$631$	351.404	−	608.650i	0.556900	−	0.964580i	−0.440852	−	0.897580i	$-0.645324\pi$
$631$	351.404	−	608.650i	0.556900	−	0.964580i	0.997753	−	0.0670004i	$-0.0213429\pi$
$632$		0			0
$633$	−484.792	−	285.281i	−0.765864	−	0.450681i
$634$		0			0
$635$	−922.290	−	162.625i	−1.45242	−	0.256102i
$636$		0			0
$637$	163.338	−	137.057i	0.256418	−	0.215160i
$638$		0			0
$639$	−179.325	−	34.6960i	−0.280635	−	0.0542974i
$640$		0			0
$641$	169.072	−	464.523i	0.263764	−	0.724684i	−0.735142	−	0.677913i	$-0.762885\pi$
$641$	169.072	−	464.523i	0.263764	−	0.724684i	0.998906	−	0.0467714i	$-0.0148932\pi$
$642$		0			0
$643$	700.134	+	587.482i	1.08886	+	0.913658i	0.996626	−	0.0820793i	$-0.0261561\pi$
$643$	700.134	+	587.482i	1.08886	+	0.913658i	0.0922299	+	0.995738i	$0.470601\pi$
$644$		0			0
$645$	−92.3757	−	550.549i	−0.143218	−	0.853565i
$646$		0			0
$647$			323.326i			0.499731i	0.968281	+	0.249866i	$0.0803864\pi$
$647$			323.326i			0.499731i	−0.968281	+	0.249866i	$0.919614\pi$
$648$		0			0
$649$	93.2646			0.143705
$650$		0			0
$651$	249.627	−	41.8846i	0.383452	−	0.0643388i
$652$		0			0
$653$	482.804	−	575.383i	0.739363	−	0.881138i	−0.256995	−	0.966413i	$-0.582732\pi$
$653$	482.804	−	575.383i	0.739363	−	0.881138i	0.996357	+	0.0852745i	$0.0271767\pi$
$654$		0			0
$655$	−840.357	−	305.865i	−1.28299	−	0.466970i
$656$		0			0
$657$	−245.345	−	212.902i	−0.373432	−	0.324051i
$658$		0			0
$659$	−406.462	−	484.402i	−0.616786	−	0.735057i	0.363728	−	0.931505i	$-0.381504\pi$
$659$	−406.462	−	484.402i	−0.616786	−	0.735057i	−0.980514	+	0.196448i	$0.937059\pi$
$660$		0			0
$661$	32.7094	−	185.504i	0.0494847	−	0.280641i	−0.950017	−	0.312197i	$-0.898935\pi$
$661$	32.7094	−	185.504i	0.0494847	−	0.280641i	0.999502	+	0.0315557i	$0.0100462\pi$
$662$		0			0
$663$	92.6585	−	157.459i	0.139756	−	0.237495i
$664$		0			0
$665$	11.9838	+	6.91885i	0.0180207	+	0.0104043i
$666$		0			0
$667$	959.291	+	1661.54i	1.43822	+	2.49107i
$668$		0			0
$669$	452.913	+	83.7394i	0.677000	+	0.125171i
$670$		0			0
$671$	118.276	+	324.961i	0.176268	+	0.484293i
$672$		0			0
$673$	−2.93198	−	16.6281i	−0.00435658	−	0.0247074i	0.982552	−	0.185988i	$-0.0595486\pi$
$673$	−2.93198	−	16.6281i	−0.00435658	−	0.0247074i	−0.986909	+	0.161281i	$0.948438\pi$
$674$		0			0
$675$	−368.829	−	462.445i	−0.546413	−	0.685104i
$676$		0			0
$677$	606.281	−	106.904i	0.895540	−	0.157908i	0.293109	−	0.956079i	$-0.405310\pi$
$677$	606.281	−	106.904i	0.895540	−	0.157908i	0.602431	+	0.798171i	$0.294199\pi$
$678$		0			0
$679$	137.928	−	50.2015i	0.203133	−	0.0739345i
$680$		0			0
$681$	620.450	+	529.449i	0.911087	+	0.777459i
$682$		0			0
$683$	−399.443	+	230.619i	−0.584837	+	0.337656i	−0.763053	−	0.646336i	$-0.776301\pi$
$683$	−399.443	+	230.619i	−0.584837	+	0.337656i	0.178217	+	0.983991i	$0.442967\pi$
$684$		0			0
$685$	422.227	−	731.319i	0.616390	−	1.06762i
$686$		0			0
$687$	−10.0066	+	1206.58i	−0.0145656	+	1.75631i
$688$		0			0
$689$	−188.077	−	33.1630i	−0.272970	−	0.0481320i
$690$		0			0
$691$	−661.205	+	554.817i	−0.956881	+	0.802919i	−0.980443	−	0.196804i	$-0.936944\pi$
$691$	−661.205	+	554.817i	−0.956881	+	0.802919i	0.0235616	+	0.999722i	$0.492499\pi$
$692$		0			0
$693$	74.0322	+	91.2602i	0.106828	+	0.131689i
$694$		0			0
$695$	431.187	−	1184.68i	0.620413	−	1.70457i
$696$		0			0
$697$	−458.549	−	384.768i	−0.657890	−	0.552035i
$698$		0			0
$699$	−1299.70	−	485.295i	−1.85937	−	0.694271i
$700$		0			0
$701$		−	15.5413i		−	0.0221702i	−0.999939	−	0.0110851i	$-0.996471\pi$
$701$		−	15.5413i		−	0.0221702i	0.999939	−	0.0110851i	$-0.00352857\pi$
$702$		0			0
$703$	−15.1270			−0.0215178
$704$		0			0
$705$	994.102	+	1204.88i	1.41007	+	1.70905i
$706$		0			0
$707$	210.738	−	251.148i	0.298074	−	0.355230i
$708$		0			0
$709$	386.459	+	140.660i	0.545076	+	0.198391i	0.599857	−	0.800107i	$-0.295224\pi$
$709$	386.459	+	140.660i	0.545076	+	0.198391i	−0.0547814	+	0.998498i	$0.517446\pi$
$710$		0			0
$711$	378.967	+	682.278i	0.533005	+	0.959603i
$712$		0			0
$713$	−1038.48	−	1237.61i	−1.45649	−	1.73578i
$714$		0			0
$715$	36.6569	−	207.892i	0.0512684	−	0.290757i
$716$		0			0
$717$	−249.114	−	439.862i	−0.347439	−	0.613475i
$718$		0			0
$719$	−412.387	−	238.092i	−0.573557	−	0.331143i	0.185012	−	0.982736i	$-0.440768\pi$
$719$	−412.387	−	238.092i	−0.573557	−	0.331143i	−0.758569	+	0.651593i	$0.774101\pi$
$720$		0			0
$721$	64.3511	+	111.459i	0.0892526	+	0.154590i
$722$		0			0
$723$	−15.2158	−	42.9089i	−0.0210453	−	0.0593484i
$724$		0			0
$725$	−373.733	−	1026.82i	−0.515494	−	1.41631i
$726$		0			0
$727$	−20.6563	−	117.148i	−0.0284130	−	0.161138i	0.967300	−	0.253635i	$-0.0816263\pi$
$727$	−20.6563	−	117.148i	−0.0284130	−	0.161138i	−0.995713	+	0.0924969i	$0.970515\pi$
$728$		0			0
$729$	395.450	−	612.422i	0.542456	−	0.840084i
$730$		0			0
$731$	−343.624	+	60.5901i	−0.470073	+	0.0828866i
$732$		0			0
$733$	−486.414	+	177.040i	−0.663593	+	0.241528i	−0.651787	−	0.758402i	$-0.725980\pi$
$733$	−486.414	+	177.040i	−0.663593	+	0.241528i	−0.0118063	+	0.999930i	$0.503758\pi$
$734$		0			0
$735$	−870.753	+	308.775i	−1.18470	+	0.420102i
$736$		0			0
$737$	666.342	−	384.713i	0.904128	−	0.521998i
$738$		0			0
$739$	−147.189	+	254.940i	−0.199174	+	0.344979i	−0.948261	−	0.317493i	$-0.897159\pi$
$739$	−147.189	+	254.940i	−0.199174	+	0.344979i	0.749087	+	0.662472i	$0.230492\pi$
$740$		0			0
$741$	12.4501	−	7.05105i	0.0168017	−	0.00951559i
$742$		0			0
$743$	−786.200	−	138.628i	−1.05814	−	0.186579i	−0.382611	−	0.923910i	$-0.624975\pi$
$743$	−786.200	−	138.628i	−1.05814	−	0.186579i	−0.675532	+	0.737331i	$0.736086\pi$
$744$		0			0
$745$	957.155	−	803.149i	1.28477	−	1.07805i
$746$		0			0
$747$	−209.476	+	116.352i	−0.280423	+	0.155759i
$748$		0			0
$749$	−80.2461	+	220.474i	−0.107138	+	0.294358i
$750$		0			0
$751$	469.598	+	394.039i	0.625296	+	0.524686i	0.899463	−	0.436996i	$-0.143958\pi$
$751$	469.598	+	394.039i	0.625296	+	0.524686i	−0.274167	+	0.961682i	$0.588402\pi$
$752$		0			0
$753$	−485.231	+	400.347i	−0.644397	+	0.531669i
$754$		0			0
$755$		−	915.683i		−	1.21282i
$756$		0			0
$757$	609.525			0.805185			0.402593	−	0.915379i	$-0.368109\pi$
$757$	609.525			0.805185			0.402593	+	0.915379i	$0.368109\pi$
$758$		0			0
$759$	262.370	−	702.668i	0.345678	−	0.925782i
$760$		0			0
$761$	−662.649	+	789.715i	−0.870761	+	1.03773i	0.128181	+	0.991751i	$0.459086\pi$
$761$	−662.649	+	789.715i	−0.870761	+	1.03773i	−0.998942	+	0.0459822i	$0.985358\pi$
$762$		0			0
$763$	269.236	+	97.9938i	0.352865	+	0.128432i
$764$		0			0
$765$	−614.773	+	498.716i	−0.803624	+	0.651917i
$766$		0			0
$767$	−43.7371	−	52.1238i	−0.0570235	−	0.0679580i
$768$		0			0
$769$	−3.44736	+	19.5509i	−0.00448291	+	0.0254238i	−0.986967	−	0.160922i	$-0.948553\pi$
$769$	−3.44736	+	19.5509i	−0.00448291	+	0.0254238i	0.982484	+	0.186346i	$0.0596644\pi$
$770$		0			0
$771$	1045.71	+	8.67239i	1.35630	+	0.0112482i
$772$		0			0
$773$	246.666	+	142.413i	0.319102	+	0.184234i	0.650992	−	0.759084i	$-0.274353\pi$
$773$	246.666	+	142.413i	0.319102	+	0.184234i	−0.331890	+	0.943318i	$0.607686\pi$
$774$		0			0
$775$	460.076	+	796.874i	0.593646	+	1.02822i
$776$		0			0
$777$	−58.8362	+	68.9489i	−0.0757223	+	0.0887373i
$778$		0			0
$779$	−16.0336	−	44.0518i	−0.0205822	−	0.0565492i
$780$		0			0
$781$	22.9060	+	129.906i	0.0293290	+	0.166333i
$782$		0			0
$783$	1052.85	−	839.712i	1.34463	−	1.07243i
$784$		0			0
$785$	1794.97	−	316.501i	2.28658	−	0.403187i
$786$		0			0
$787$	552.537	−	201.107i	0.702079	−	0.255536i	0.0337810	−	0.999429i	$-0.489245\pi$
$787$	552.537	−	201.107i	0.702079	−	0.255536i	0.668298	+	0.743893i	$0.267023\pi$
$788$		0			0
$789$	200.123	−	1082.39i	0.253641	−	1.37184i
$790$		0			0
$791$	−322.978	+	186.472i	−0.408316	+	0.235742i
$792$		0			0
$793$	126.148	−	218.495i	0.159077	−	0.275529i
$794$		0			0
$795$	713.174	+	419.675i	0.897074	+	0.527893i
$796$		0			0
$797$	256.074	+	45.1528i	0.321298	+	0.0566534i	0.331971	−	0.943290i	$-0.392286\pi$
$797$	256.074	+	45.1528i	0.321298	+	0.0566534i	−0.0106734	+	0.999943i	$0.503398\pi$
$798$		0			0
$799$	747.916	−	627.576i	0.936065	−	0.785452i
$800$		0			0
$801$	−318.554	+	367.097i	−0.397695	+	0.458298i
$802$		0			0
$803$	−80.2375	+	220.451i	−0.0999221	+	0.274534i
$804$		0			0
$805$	−405.409	−	340.178i	−0.503613	−	0.422582i
$806$		0			0
$807$	22.7446	+	135.555i	0.0281841	+	0.167974i
$808$		0			0
$809$		−	1145.96i		−	1.41652i	−0.705952	−	0.708260i	$-0.749480\pi$
$809$		−	1145.96i		−	1.41652i	0.705952	−	0.708260i	$-0.250520\pi$
$810$		0			0
$811$	1191.97			1.46976			0.734878	−	0.678199i	$-0.237239\pi$
$811$	1191.97			1.46976			0.734878	+	0.678199i	$0.237239\pi$
$812$		0			0
$813$	−950.504	+	159.483i	−1.16913	+	0.196167i
$814$		0			0
$815$	−336.480	+	401.001i	−0.412858	+	0.492025i
$816$		0			0
$817$	−25.6781	−	9.34608i	−0.0314298	−	0.0114395i
$818$		0			0
$819$	16.2857	−	84.1722i	0.0198849	−	0.102774i
$820$		0			0
$821$	−534.684	−	637.211i	−0.651259	−	0.776141i	0.334844	−	0.942274i	$-0.391316\pi$
$821$	−534.684	−	637.211i	−0.651259	−	0.776141i	−0.986103	+	0.166133i	$0.946872\pi$
$822$		0			0
$823$	219.252	−	1243.44i	0.266406	−	1.51086i	−0.498597	−	0.866834i	$-0.666151\pi$
$823$	219.252	−	1243.44i	0.266406	−	1.51086i	0.765002	−	0.644028i	$-0.222738\pi$
$824$		0			0
$825$	−216.656	+	368.174i	−0.262614	+	0.446272i
$826$		0			0
$827$	273.567	+	157.944i	0.330794	+	0.190984i	0.656194	−	0.754593i	$-0.272165\pi$
$827$	273.567	+	157.944i	0.330794	+	0.190984i	−0.325400	+	0.945577i	$0.605499\pi$
$828$		0			0
$829$	273.514	+	473.740i	0.329933	+	0.571460i	0.982498	−	0.186272i	$-0.0596406\pi$
$829$	273.514	+	473.740i	0.329933	+	0.571460i	−0.652566	+	0.757732i	$0.726307\pi$
$830$		0			0
$831$	−557.638	−	103.102i	−0.671044	−	0.124070i
$832$		0			0
$833$	197.503	+	542.635i	0.237098	+	0.651423i
$834$		0			0
$835$	−113.223	−	642.122i	−0.135597	−	0.769008i
$836$		0			0
$837$	−750.319	+	850.307i	−0.896438	+	1.01590i
$838$		0			0
$839$	181.853	−	32.0657i	0.216750	−	0.0382189i	−0.0642184	−	0.997936i	$-0.520455\pi$
$839$	181.853	−	32.0657i	0.216750	−	0.0382189i	0.280969	+	0.959717i	$0.409344\pi$
$840$		0			0
$841$	1547.49	−	563.239i	1.84005	−	0.669725i
$842$		0			0
$843$	−53.0952	−	45.3078i	−0.0629836	−	0.0537459i
$844$		0			0
$845$	869.022	−	501.730i	1.02843	−	0.593763i
$846$		0			0
$847$	−79.1006	+	137.006i	−0.0933891	+	0.161755i
$848$		0			0
$849$	−0.0952119	+	11.4806i	−0.000112146	+	0.0135225i
$850$		0			0
$851$	569.745	+	100.461i	0.669501	+	0.118051i
$852$		0			0
$853$	−250.666	+	210.333i	−0.293864	+	0.246581i	−0.777785	−	0.628531i	$-0.783657\pi$
$853$	−250.666	+	210.333i	−0.293864	+	0.246581i	0.483921	+	0.875112i	$0.339212\pi$
$854$		0			0
$855$	−61.2242	+	9.75139i	−0.0716073	+	0.0114051i
$856$		0			0
$857$	−240.317	+	660.265i	−0.280416	+	0.770437i	0.716897	+	0.697179i	$0.245562\pi$
$857$	−240.317	+	660.265i	−0.280416	+	0.770437i	−0.997313	+	0.0732581i	$0.976660\pi$
$858$		0			0
$859$	618.984	+	519.389i	0.720587	+	0.604644i	0.927548	−	0.373705i	$-0.121913\pi$
$859$	618.984	+	519.389i	0.720587	+	0.604644i	−0.206961	+	0.978349i	$0.566357\pi$
$860$		0			0
$861$	−263.150	−	98.2576i	−0.305633	−	0.114120i
$862$		0			0
$863$			1139.05i			1.31987i	0.751322	+	0.659936i	$0.229416\pi$
$863$			1139.05i			1.31987i	−0.751322	+	0.659936i	$0.770584\pi$
$864$		0			0
$865$	−1703.86			−1.96978
$866$		0			0
$867$	−236.877	−	287.101i	−0.273215	−	0.331143i
$868$		0			0
$869$	362.305	−	431.778i	0.416922	−	0.496868i
$870$		0			0
$871$	−527.494	−	191.992i	−0.605619	−	0.220427i
$872$		0			0
$873$	−338.202	+	563.970i	−0.387402	+	0.646014i
$874$		0			0
$875$	−27.3449	−	32.5884i	−0.0312513	−	0.0372439i
$876$		0			0
$877$	−44.0838	+	250.012i	−0.0502666	+	0.285076i	−0.999571	−	0.0292817i	$-0.990678\pi$
$877$	−44.0838	+	250.012i	−0.0502666	+	0.285076i	0.949305	+	0.314358i	$0.101789\pi$
$878$		0			0
$879$	595.809	+	1052.02i	0.677826	+	1.19684i
$880$		0			0
$881$	−166.117	−	95.9076i	−0.188555	−	0.108862i	0.402751	−	0.915310i	$-0.368054\pi$
$881$	−166.117	−	95.9076i	−0.188555	−	0.108862i	−0.591306	+	0.806447i	$0.701387\pi$
$882$		0			0
$883$	−321.941	−	557.619i	−0.364600	−	0.631505i	0.624112	−	0.781335i	$-0.285461\pi$
$883$	−321.941	−	557.619i	−0.364600	−	0.631505i	−0.988712	+	0.149830i	$0.952127\pi$
$884$		0			0
$885$	98.5348	+	277.871i	0.111339	+	0.313978i
$886$		0			0
$887$	−361.256	−	992.542i	−0.407278	−	1.11899i	−0.958615	−	0.284705i	$-0.908104\pi$
$887$	−361.256	−	992.542i	−0.407278	−	1.11899i	0.551337	−	0.834283i	$-0.314118\pi$
$888$		0			0
$889$	47.6986	+	270.512i	0.0536542	+	0.304288i
$890$		0			0
$891$	−515.166	−	108.569i	−0.578189	−	0.121850i
$892$		0			0
$893$	75.3003	−	13.2775i	0.0843228	−	0.0148684i
$894$		0			0
$895$	−1632.21	+	594.077i	−1.82370	+	0.663773i
$896$		0			0
$897$	−515.748	+	182.888i	−0.574970	+	0.203888i
$898$		0			0
$899$	−1814.24	+	1047.45i	−2.01807	+	1.16513i
$900$		0			0
$901$	258.607	−	447.921i	0.287023	−	0.497138i
$902$		0			0
$903$	−142.474	+	80.6893i	−0.157778	+	0.0893570i
$904$		0			0
$905$	−52.8011	−	9.31026i	−0.0583438	−	0.0102876i
$906$		0			0
$907$	−1110.27	+	931.626i	−1.22411	+	1.02715i	−0.225512	+	0.974240i	$0.572405\pi$
$907$	−1110.27	+	931.626i	−1.22411	+	1.02715i	−0.998599	+	0.0529109i	$0.983150\pi$
$908$		0			0
$909$	−24.3614	+	1468.64i	−0.0268002	+	1.61566i
$910$		0			0
$911$	−466.336	+	1281.25i	−0.511894	+	1.40642i	0.367366	+	0.930076i	$0.380260\pi$
$911$	−466.336	+	1281.25i	−0.511894	+	1.40642i	−0.879260	+	0.476341i	$0.841963\pi$
$912$		0			0
$913$	132.567	+	111.237i	0.145199	+	0.121836i
$914$		0			0
$915$	−843.223	+	695.713i	−0.921555	+	0.760342i
$916$		0			0
$917$			262.300i			0.286041i
$918$		0			0
$919$	−464.905			−0.505881			−0.252941	−	0.967482i	$-0.581398\pi$
$919$	−464.905			−0.505881			−0.252941	+	0.967482i	$0.581398\pi$
$920$		0			0
$921$	334.099	−	894.771i	0.362757	−	0.971522i
$922$		0			0
$923$	61.8602	−	73.7221i	0.0670208	−	0.0798722i
$924$		0			0
$925$	−309.631	−	112.697i	−0.334736	−	0.121834i
$926$		0			0
$927$	−538.495	−	206.173i	−0.580901	−	0.222409i
$928$		0			0
$929$	−329.990	−	393.267i	−0.355210	−	0.423323i	0.558617	−	0.829426i	$-0.311332\pi$
$929$	−329.990	−	393.267i	−0.355210	−	0.423323i	−0.913828	+	0.406102i	$0.866888\pi$
$930$		0			0
$931$	−7.85305	+	44.5369i	−0.00843507	+	0.0478377i
$932$		0			0
$933$	−120.783	−	1.00169i	−0.129456	−	0.00107362i
$934$		0			0
$935$	495.112	+	285.853i	0.529532	+	0.305725i
$936$		0			0
$937$	−559.312	−	968.756i	−0.596917	−	1.03389i	−0.993273	−	0.115794i	$-0.963059\pi$
$937$	−559.312	−	968.756i	−0.596917	−	1.03389i	0.396356	−	0.918097i	$-0.370275\pi$
$938$		0			0
$939$	−92.7599	+	108.703i	−0.0987859	+	0.115765i
$940$		0			0
$941$	60.7589	+	166.934i	0.0645685	+	0.177400i	0.967781	−	0.251793i	$-0.0810202\pi$
$941$	60.7589	+	166.934i	0.0645685	+	0.177400i	−0.903213	+	0.429193i	$0.858798\pi$
$942$		0			0
$943$	311.332	+	1765.65i	0.330150	+	1.87238i
$944$		0			0
$945$	−193.683	+	316.987i	−0.204956	+	0.335436i
$946$		0			0
$947$	−717.433	+	126.503i	−0.757585	+	0.133583i	−0.539082	−	0.842254i	$-0.681229\pi$
$947$	−717.433	+	126.503i	−0.757585	+	0.133583i	−0.218503	+	0.975836i	$0.570117\pi$
$948$		0			0
$949$	160.834	−	58.5386i	0.169477	−	0.0616845i
$950$		0			0
$951$	191.016	−	1033.13i	0.200858	−	1.08636i
$952$		0			0
$953$	1188.23	−	686.025i	1.24683	−	0.719858i	0.276355	−	0.961056i	$-0.410874\pi$
$953$	1188.23	−	686.025i	1.24683	−	0.719858i	0.970476	+	0.241198i	$0.0775402\pi$
$954$		0			0
$955$	134.117	−	232.298i	0.140437	−	0.243244i
$956$		0			0
$957$	−838.221	−	493.261i	−0.875884	−	0.515424i
$958$		0			0
$959$	−243.920	−	43.0097i	−0.254348	−	0.0448485i
$960$		0			0
$961$	615.181	−	516.198i	0.640146	−	0.537146i
$962$		0			0
$963$	−343.088	−	993.601i	−0.356270	−	1.03178i
$964$		0			0
$965$	−894.411	+	2457.37i	−0.926851	+	2.54650i
$966$		0			0
$967$	1103.59	+	926.025i	1.14125	+	0.957627i	0.999479	−	0.0322722i	$-0.0102743\pi$
$967$	1103.59	+	926.025i	1.14125	+	0.957627i	0.141776	+	0.989899i	$0.454719\pi$
$968$		0			0
$969$	6.41214	+	38.2156i	0.00661727	+	0.0394382i
$970$		0			0
$971$			588.039i			0.605602i	0.953054	+	0.302801i	$0.0979217\pi$
$971$			588.039i			0.605602i	−0.953054	+	0.302801i	$0.902078\pi$
$972$		0			0
$973$	−369.772			−0.380033
$974$		0			0
$975$	307.368	−	51.5727i	0.315249	−	0.0528951i
$976$		0			0
$977$	278.265	−	331.623i	0.284816	−	0.339430i	−0.604600	−	0.796529i	$-0.706667\pi$
$977$	278.265	−	331.623i	0.284816	−	0.339430i	0.889416	+	0.457099i	$0.151112\pi$
$978$		0			0
$979$	329.849	+	120.055i	0.336924	+	0.122630i
$980$		0			0
$981$	−1213.35	+	418.968i	−1.23685	+	0.427082i
$982$		0			0
$983$	−142.062	−	169.303i	−0.144519	−	0.172231i	0.688929	−	0.724829i	$-0.258081\pi$
$983$	−142.062	−	169.303i	−0.144519	−	0.172231i	−0.833448	+	0.552598i	$0.813637\pi$
$984$		0			0
$985$	21.6935	−	123.030i	0.0220238	−	0.124903i
$986$		0			0
$987$	232.360	−	394.860i	0.235420	−	0.400061i
$988$		0			0
$989$	905.073	+	522.544i	0.915140	+	0.528356i
$990$		0			0
$991$	−106.703	−	184.815i	−0.107672	−	0.186494i	0.807155	−	0.590340i	$-0.201006\pi$
$991$	−106.703	−	184.815i	−0.107672	−	0.186494i	−0.914827	+	0.403846i	$0.867673\pi$
$992$		0			0
$993$	534.515	+	98.8267i	0.538282	+	0.0995234i
$994$		0			0
$995$	−184.403	−	506.644i	−0.185330	−	0.509190i
$996$		0			0
$997$	136.357	+	773.320i	0.136767	+	0.775646i	0.973613	+	0.228207i	$0.0732863\pi$
$997$	136.357	+	773.320i	0.136767	+	0.775646i	−0.836845	+	0.547440i	$0.815603\pi$
$998$		0			0
$999$	10.1022	−	405.963i	0.0101123	−	0.406369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.u.a.41.17	✓	108
4.3	odd	2		432.3.bc.d.257.2		108
27.2	odd	18	inner	216.3.u.a.137.17	yes	108
108.83	even	18		432.3.bc.d.353.2		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.u.a.41.17	✓	108	1.1	even	1	trivial
216.3.u.a.137.17	yes	108	27.2	odd	18	inner
432.3.bc.d.257.2		108	4.3	odd	2
432.3.bc.d.353.2		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)

\(f(q)\)	\(=\)	\(q+(2.95864 - 0.496426i) q^{3} +(4.40241 - 5.24659i) q^{5} +(-1.88768 - 0.687060i) q^{7} +(8.50712 - 2.93749i) q^{9} +O(q^{10})\)	\(q+(2.95864 - 0.496426i) q^{3} +(4.40241 - 5.24659i) q^{5} +(-1.88768 - 0.687060i) q^{7} +(8.50712 - 2.93749i) q^{9} +(-4.17798 - 4.97912i) q^{11} +(-0.823444 + 4.66998i) q^{13} +(10.4206 - 17.7083i) q^{15} +(-11.1220 - 6.42127i) q^{17} +(-0.502884 - 0.871020i) q^{19} +(-5.92605 - 1.09567i) q^{21} +(13.1560 + 36.1459i) q^{23} +(-3.80428 - 21.5751i) q^{25} +(23.7113 - 12.9141i) q^{27} +(49.1201 - 8.66120i) q^{29} +(-39.4678 + 14.3651i) q^{31} +(-14.8329 - 12.6574i) q^{33} +(-11.9151 + 6.87918i) q^{35} +(7.52015 - 13.0253i) q^{37} +(-0.117977 + 14.2256i) q^{39} +(45.9021 + 8.09377i) q^{41} +(20.8130 - 17.4642i) q^{43} +(22.0401 - 57.5655i) q^{45} +(-26.0016 + 71.4387i) q^{47} +(-34.4449 - 28.9027i) q^{49} +(-36.0936 - 13.4770i) q^{51} +40.2735i q^{53} -44.5166 q^{55} +(-1.92025 - 2.32739i) q^{57} +(-9.22329 + 10.9919i) q^{59} +(-49.9957 - 18.1969i) q^{61} +(-18.0770 - 0.299856i) q^{63} +(20.8763 + 24.8795i) q^{65} +(-20.5560 + 116.579i) q^{67} +(56.8677 + 100.412i) q^{69} +(-17.5756 - 10.1473i) q^{71} +(-18.0467 - 31.2578i) q^{73} +(-21.9660 - 61.9446i) q^{75} +(4.46574 + 12.2695i) q^{77} +(15.0584 + 85.4004i) q^{79} +(63.7423 - 49.9792i) q^{81} +(-26.2200 + 4.62330i) q^{83} +(-82.6533 + 30.0834i) q^{85} +(141.029 - 50.0098i) q^{87} +(-46.7694 + 27.0023i) q^{89} +(4.76296 - 8.24968i) q^{91} +(-109.640 + 62.0940i) q^{93} +(-6.78379 - 1.19616i) q^{95} +(-55.9727 + 46.9666i) q^{97} +(-50.1687 - 30.0852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q+O(q^{10}) \) 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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