LMFDB - Embedded newform 432.3.bc.a.209.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,3,Mod(65,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.65"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30,0,6,0,-15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			209.5
Character	$\chi$	$=$	432.209
Dual form			432.3.bc.a.401.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.94744 - 0.559079i) q^{3} +(6.15614 - 1.08549i) q^{5} +(6.21846 + 5.21791i) q^{7} +(8.37486 - 3.29571i) q^{9} +(7.99059 + 1.40896i) q^{11} +(-9.12402 - 3.32087i) q^{13} +(17.5380 - 6.64120i) q^{15} +(-13.0143 + 7.51380i) q^{17} +(-8.93226 + 15.4711i) q^{19} +(21.2458 + 11.9029i) q^{21} +(-16.9268 - 20.1726i) q^{23} +(13.2275 - 4.81440i) q^{25} +(22.8419 - 14.3961i) q^{27} +(5.18906 + 14.2568i) q^{29} +(-25.0755 + 21.0408i) q^{31} +(24.3395 - 0.314547i) q^{33} +(43.9457 + 25.3721i) q^{35} +(-15.8096 - 27.3831i) q^{37} +(-28.7492 - 4.68704i) q^{39} +(5.65018 - 15.5238i) q^{41} +(14.5559 - 82.5505i) q^{43} +(47.9794 - 29.3797i) q^{45} +(-8.46562 + 10.0889i) q^{47} +(2.93393 + 16.6391i) q^{49} +(-34.1581 + 29.4225i) q^{51} +25.7140i q^{53} +50.7206 q^{55} +(-17.6778 + 50.5941i) q^{57} +(22.3660 - 3.94373i) q^{59} +(26.1131 + 21.9115i) q^{61} +(69.2755 + 23.2050i) q^{63} +(-59.7736 - 10.5397i) q^{65} +(7.61567 + 2.77188i) q^{67} +(-61.1690 - 49.9942i) q^{69} +(-35.7557 + 20.6436i) q^{71} +(40.4046 - 69.9827i) q^{73} +(36.2956 - 21.5854i) q^{75} +(42.3374 + 50.4557i) q^{77} +(-25.9652 + 9.45057i) q^{79} +(59.2766 - 55.2022i) q^{81} +(6.01607 + 16.5290i) q^{83} +(-71.9616 + 60.3830i) q^{85} +(23.2652 + 39.1201i) q^{87} +(24.4986 + 14.1443i) q^{89} +(-39.4094 - 68.2590i) q^{91} +(-62.1451 + 76.0358i) q^{93} +(-38.1945 + 104.938i) q^{95} +(29.2825 - 166.069i) q^{97} +(71.5636 - 14.5348i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37}+ \cdots - 513 q^{99}+O(q^{100}) $ 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{18}\right)$

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
$3$	2.94744	−	0.559079i	0.982482	−	0.186360i
$3$	2.94744	−	0.559079i	0.982482	−	0.186360i
$4$		0			0
$5$	6.15614	−	1.08549i	1.23123	−	0.217099i	0.480076	−	0.877227i	$-0.340609\pi$
$5$	6.15614	−	1.08549i	1.23123	−	0.217099i	0.751153	+	0.660128i	$0.229498\pi$
$6$		0			0
$7$	6.21846	+	5.21791i	0.888352	+	0.745415i	0.967879	−	0.251417i	$-0.0808966\pi$
$7$	6.21846	+	5.21791i	0.888352	+	0.745415i	−0.0795272	+	0.996833i	$0.525341\pi$
$8$		0			0
$9$	8.37486	−	3.29571i	0.930540	−	0.366190i
$10$		0			0
$11$	7.99059	+	1.40896i	0.726417	+	0.128087i	0.524615	−	0.851339i	$-0.324209\pi$
$11$	7.99059	+	1.40896i	0.726417	+	0.128087i	0.201802	+	0.979426i	$0.435320\pi$
$12$		0			0
$13$	−9.12402	−	3.32087i	−0.701848	−	0.255452i	−0.0336483	−	0.999434i	$-0.510713\pi$
$13$	−9.12402	−	3.32087i	−0.701848	−	0.255452i	−0.668200	+	0.743982i	$0.732935\pi$
$14$		0			0
$15$	17.5380	−	6.64120i	1.16920	−	0.442747i
$16$		0			0
$17$	−13.0143	+	7.51380i	−0.765546	+	0.441988i	−0.831284	−	0.555849i	$-0.812393\pi$
$17$	−13.0143	+	7.51380i	−0.765546	+	0.441988i	0.0657372	+	0.997837i	$0.479060\pi$
$18$		0			0
$19$	−8.93226	+	15.4711i	−0.470119	+	0.814270i	−0.999416	−	0.0341664i	$-0.989122\pi$
$19$	−8.93226	+	15.4711i	−0.470119	+	0.814270i	0.529297	+	0.848437i	$0.322456\pi$
$20$		0			0
$21$	21.2458	+	11.9029i	1.01170	+	0.566804i
$22$		0			0
$23$	−16.9268	−	20.1726i	−0.735949	−	0.877070i	0.260127	−	0.965575i	$-0.416236\pi$
$23$	−16.9268	−	20.1726i	−0.735949	−	0.877070i	−0.996076	+	0.0885045i	$0.971791\pi$
$24$		0			0
$25$	13.2275	−	4.81440i	0.529099	−	0.192576i
$26$		0			0
$27$	22.8419	−	14.3961i	0.845996	−	0.533190i
$28$		0			0
$29$	5.18906	+	14.2568i	0.178933	+	0.491615i	0.996440	−	0.0843038i	$-0.0268666\pi$
$29$	5.18906	+	14.2568i	0.178933	+	0.491615i	−0.817507	+	0.575919i	$0.804644\pi$
$30$		0			0
$31$	−25.0755	+	21.0408i	−0.808886	+	0.678736i	−0.950342	−	0.311209i	$-0.899266\pi$
$31$	−25.0755	+	21.0408i	−0.808886	+	0.678736i	0.141456	+	0.989945i	$0.454822\pi$
$32$		0			0
$33$	24.3395	−	0.314547i	0.737562	−	0.00953171i
$34$		0			0
$35$	43.9457	+	25.3721i	1.25559	+	0.724917i
$36$		0			0
$37$	−15.8096	−	27.3831i	−0.427287	−	0.740083i	0.569344	−	0.822100i	$-0.307197\pi$
$37$	−15.8096	−	27.3831i	−0.427287	−	0.740083i	−0.996631	+	0.0820163i	$0.973864\pi$
$38$		0			0
$39$	−28.7492	−	4.68704i	−0.737159	−	0.120181i
$40$		0			0
$41$	5.65018	−	15.5238i	0.137809	−	0.378628i	−0.851520	−	0.524321i	$-0.824319\pi$
$41$	5.65018	−	15.5238i	0.137809	−	0.378628i	0.989330	+	0.145693i	$0.0465413\pi$
$42$		0			0
$43$	14.5559	−	82.5505i	0.338509	−	1.91978i	−0.0508761	−	0.998705i	$-0.516201\pi$
$43$	14.5559	−	82.5505i	0.338509	−	1.91978i	0.389385	−	0.921075i	$-0.372688\pi$
$44$		0			0
$45$	47.9794	−	29.3797i	1.06621	−	0.652882i
$46$		0			0
$47$	−8.46562	+	10.0889i	−0.180120	+	0.214658i	−0.848548	−	0.529118i	$-0.822523\pi$
$47$	−8.46562	+	10.0889i	−0.180120	+	0.214658i	0.668429	+	0.743776i	$0.266967\pi$
$48$		0			0
$49$	2.93393	+	16.6391i	0.0598761	+	0.339574i
$50$		0			0
$51$	−34.1581	+	29.4225i	−0.669766	+	0.576912i
$52$		0			0
$53$			25.7140i			0.485169i	0.970130	+	0.242585i	$0.0779952\pi$
$53$			25.7140i			0.485169i	−0.970130	+	0.242585i	$0.922005\pi$
$54$		0			0
$55$	50.7206			0.922193
$56$		0			0
$57$	−17.6778	+	50.5941i	−0.310136	+	0.887617i
$58$		0			0
$59$	22.3660	−	3.94373i	0.379085	−	0.0668428i	0.0191407	−	0.999817i	$-0.493907\pi$
$59$	22.3660	−	3.94373i	0.379085	−	0.0668428i	0.359944	+	0.932974i	$0.382796\pi$
$60$		0			0
$61$	26.1131	+	21.9115i	0.428084	+	0.359205i	0.831228	−	0.555931i	$-0.187638\pi$
$61$	26.1131	+	21.9115i	0.428084	+	0.359205i	−0.403144	+	0.915137i	$0.632083\pi$
$62$		0			0
$63$	69.2755	+	23.2050i	1.09961	+	0.368334i
$64$		0			0
$65$	−59.7736	−	10.5397i	−0.919593	−	0.162149i
$66$		0			0
$67$	7.61567	+	2.77188i	0.113667	+	0.0413713i	0.398227	−	0.917287i	$-0.369625\pi$
$67$	7.61567	+	2.77188i	0.113667	+	0.0413713i	−0.284561	+	0.958658i	$0.591848\pi$
$68$		0			0
$69$	−61.1690	−	49.9942i	−0.886507	−	0.724554i
$70$		0			0
$71$	−35.7557	+	20.6436i	−0.503601	+	0.290754i	−0.730199	−	0.683234i	$-0.760573\pi$
$71$	−35.7557	+	20.6436i	−0.503601	+	0.290754i	0.226598	+	0.973988i	$0.427240\pi$
$72$		0			0
$73$	40.4046	−	69.9827i	0.553487	−	0.958668i	−0.444532	−	0.895763i	$-0.646630\pi$
$73$	40.4046	−	69.9827i	0.553487	−	0.958668i	0.998020	−	0.0629050i	$-0.0200365\pi$
$74$		0			0
$75$	36.2956	−	21.5854i	0.483941	−	0.287805i
$76$		0			0
$77$	42.3374	+	50.4557i	0.549836	+	0.655269i
$78$		0			0
$79$	−25.9652	+	9.45057i	−0.328674	+	0.119627i	−0.501086	−	0.865397i	$-0.667066\pi$
$79$	−25.9652	+	9.45057i	−0.328674	+	0.119627i	0.172412	+	0.985025i	$0.444844\pi$
$80$		0			0
$81$	59.2766	−	55.2022i	0.731810	−	0.681508i
$82$		0			0
$83$	6.01607	+	16.5290i	0.0724827	+	0.199145i	0.970644	−	0.240522i	$-0.0773187\pi$
$83$	6.01607	+	16.5290i	0.0724827	+	0.199145i	−0.898161	+	0.439667i	$0.855096\pi$
$84$		0			0
$85$	−71.9616	+	60.3830i	−0.846607	+	0.710388i
$86$		0			0
$87$	23.2652	+	39.1201i	0.267416	+	0.449657i
$88$		0			0
$89$	24.4986	+	14.1443i	0.275265	+	0.158924i	0.631278	−	0.775557i	$-0.282531\pi$
$89$	24.4986	+	14.1443i	0.275265	+	0.158924i	−0.356013	+	0.934481i	$0.615864\pi$
$90$		0			0
$91$	−39.4094	−	68.2590i	−0.433070	−	0.750099i
$92$		0			0
$93$	−62.1451	+	76.0358i	−0.668227	+	0.817589i
$94$		0			0
$95$	−38.1945	+	104.938i	−0.402047	+	1.10461i
$96$		0			0
$97$	29.2825	−	166.069i	0.301881	−	1.71205i	−0.335953	−	0.941879i	$-0.609058\pi$
$97$	29.2825	−	166.069i	0.301881	−	1.71205i	0.637834	−	0.770174i	$-0.279831\pi$
$98$		0			0
$99$	71.5636	−	14.5348i	0.722865	−	0.146816i
$100$		0			0
$101$	−44.8847	+	53.4915i	−0.444403	+	0.529619i	−0.941020	−	0.338351i	$-0.890131\pi$
$101$	−44.8847	+	53.4915i	−0.444403	+	0.529619i	0.496617	+	0.867970i	$0.334575\pi$
$102$		0			0
$103$	−12.1315	−	68.8014i	−0.117782	−	0.667974i	−0.985335	−	0.170630i	$-0.945420\pi$
$103$	−12.1315	−	68.8014i	−0.117782	−	0.667974i	0.867553	−	0.497344i	$-0.165691\pi$
$104$		0			0
$105$	143.713	+	50.2137i	1.36869	+	0.478226i
$106$		0			0
$107$			121.432i			1.13488i	0.823416	+	0.567438i	$0.192065\pi$
$107$			121.432i			1.13488i	−0.823416	+	0.567438i	$0.807935\pi$
$108$		0			0
$109$	−119.633			−1.09755			−0.548777	−	0.835969i	$-0.684907\pi$
$109$	−119.633			−1.09755			−0.548777	+	0.835969i	$0.684907\pi$
$110$		0			0
$111$	−61.9073	−	71.8713i	−0.557723	−	0.647489i
$112$		0			0
$113$	122.474	−	21.5955i	1.08384	−	0.191111i	0.396929	−	0.917849i	$-0.370076\pi$
$113$	122.474	−	21.5955i	1.08384	−	0.191111i	0.686914	+	0.726738i	$0.258965\pi$
$114$		0			0
$115$	−126.101	−	105.811i	−1.09653	−	0.920100i
$116$		0			0
$117$	−87.3571	+	2.25826i	−0.746642	+	0.0193013i
$118$		0			0
$119$	−120.135	−	21.1831i	−1.00954	−	0.178009i
$120$		0			0
$121$	−51.8384	−	18.8676i	−0.428417	−	0.155931i
$122$		0			0
$123$	7.97461	−	48.9143i	0.0648342	−	0.397677i
$124$		0			0
$125$	−59.1363	+	34.1424i	−0.473091	+	0.273139i
$126$		0			0
$127$	−58.7300	+	101.723i	−0.462441	+	0.800971i	−0.999082	−	0.0428396i	$-0.986360\pi$
$127$	−58.7300	+	101.723i	−0.462441	+	0.800971i	0.536641	+	0.843811i	$0.319693\pi$
$128$		0			0
$129$	−3.24957	−	251.451i	−0.0251905	−	1.94923i
$130$		0			0
$131$	−3.02933	−	3.61022i	−0.0231247	−	0.0275589i	0.754358	−	0.656463i	$-0.227948\pi$
$131$	−3.02933	−	3.61022i	−0.0231247	−	0.0275589i	−0.777483	+	0.628904i	$0.783504\pi$
$132$		0			0
$133$	−136.272	+	49.5989i	−1.02460	+	0.372924i
$134$		0			0
$135$	124.991	−	113.419i	0.925859	−	0.840143i
$136$		0			0
$137$	75.5147	+	207.475i	0.551202	+	1.51442i	0.832071	+	0.554669i	$0.187155\pi$
$137$	75.5147	+	207.475i	0.551202	+	1.51442i	−0.280869	+	0.959746i	$0.590623\pi$
$138$		0			0
$139$	27.3980	−	22.9896i	0.197108	−	0.165393i	−0.538892	−	0.842375i	$-0.681157\pi$
$139$	27.3980	−	22.9896i	0.197108	−	0.165393i	0.736000	+	0.676982i	$0.236712\pi$
$140$		0			0
$141$	−19.3114	+	34.4695i	−0.136961	+	0.244465i
$142$		0			0
$143$	−68.2274	−	39.3911i	−0.477114	−	0.275462i
$144$		0			0
$145$	47.4203	+	82.1344i	0.327037	+	0.566444i
$146$		0			0
$147$	17.9502	+	47.4026i	0.122110	+	0.322467i
$148$		0			0
$149$	−57.3691	+	157.620i	−0.385028	+	1.05786i	0.584183	+	0.811622i	$0.301415\pi$
$149$	−57.3691	+	157.620i	−0.385028	+	1.05786i	−0.969211	+	0.246233i	$0.920807\pi$
$150$		0			0
$151$	14.5375	−	82.4463i	0.0962748	−	0.546002i	−0.898074	−	0.439844i	$-0.855034\pi$
$151$	14.5375	−	82.4463i	0.0962748	−	0.546002i	0.994349	−	0.106158i	$-0.0338550\pi$
$152$		0			0
$153$	−84.2296	+	105.818i	−0.550520	+	0.691623i
$154$		0			0
$155$	−131.528	+	156.750i	−0.848571	+	1.01129i
$156$		0			0
$157$	−12.9271	−	73.3133i	−0.0823383	−	0.466963i	−0.997899	−	0.0647844i	$-0.979364\pi$
$157$	−12.9271	−	73.3133i	−0.0823383	−	0.466963i	0.915561	−	0.402179i	$-0.131747\pi$
$158$		0			0
$159$	14.3761	+	75.7905i	0.0904159	+	0.476670i
$160$		0			0
$161$		−	213.765i		−	1.32773i
$162$		0			0
$163$	−254.830			−1.56337			−0.781687	−	0.623670i	$-0.785641\pi$
$163$	−254.830			−1.56337			−0.781687	+	0.623670i	$0.785641\pi$
$164$		0			0
$165$	149.496	−	28.3568i	0.906038	−	0.171859i
$166$		0			0
$167$	156.190	−	27.5405i	0.935269	−	0.164913i	0.314813	−	0.949154i	$-0.398058\pi$
$167$	156.190	−	27.5405i	0.935269	−	0.164913i	0.620457	+	0.784241i	$0.286947\pi$
$168$		0			0
$169$	−57.2419	−	48.0317i	−0.338710	−	0.284211i
$170$		0			0
$171$	−23.8181	+	159.007i	−0.139287	+	0.929864i
$172$		0			0
$173$	−293.553	−	51.7613i	−1.69684	−	0.299198i	−0.760249	−	0.649632i	$-0.774923\pi$
$173$	−293.553	−	51.7613i	−1.69684	−	0.299198i	−0.936587	+	0.350434i	$0.886034\pi$
$174$		0			0
$175$	107.376	+	39.0815i	0.613575	+	0.223323i
$176$		0			0
$177$	63.7177	−	24.1283i	0.359987	−	0.136318i
$178$		0			0
$179$	−25.3997	+	14.6645i	−0.141898	+	0.0819248i	−0.569268	−	0.822152i	$-0.692773\pi$
$179$	−25.3997	+	14.6645i	−0.141898	+	0.0819248i	0.427370	+	0.904077i	$0.359440\pi$
$180$		0			0
$181$	−41.7019	+	72.2299i	−0.230397	+	0.399060i	−0.957925	−	0.287018i	$-0.907336\pi$
$181$	−41.7019	+	72.2299i	−0.230397	+	0.399060i	0.727528	+	0.686078i	$0.240669\pi$
$182$		0			0
$183$	89.2173	+	49.9837i	0.487526	+	0.273135i
$184$		0			0
$185$	−127.050	−	151.413i	−0.686759	−	0.818448i
$186$		0			0
$187$	−114.578	+	41.7031i	−0.612719	+	0.223011i
$188$		0			0
$189$	217.159	+	29.6651i	1.14899	+	0.156958i
$190$		0			0
$191$	−53.6797	−	147.484i	−0.281046	−	0.772166i	−0.997239	−	0.0742641i	$-0.976339\pi$
$191$	−53.6797	−	147.484i	−0.281046	−	0.772166i	0.716193	−	0.697902i	$-0.245883\pi$
$192$		0			0
$193$	−31.7673	+	26.6559i	−0.164598	+	0.138114i	−0.721366	−	0.692554i	$-0.756485\pi$
$193$	−31.7673	+	26.6559i	−0.164598	+	0.138114i	0.556769	+	0.830668i	$0.312041\pi$
$194$		0			0
$195$	−182.072	+	2.35296i	−0.933702	+	0.0120665i
$196$		0			0
$197$	−182.437	−	105.330i	−0.926074	−	0.534669i	−0.0405063	−	0.999179i	$-0.512897\pi$
$197$	−182.437	−	105.330i	−0.926074	−	0.534669i	−0.885568	+	0.464510i	$0.846230\pi$
$198$		0			0
$199$	−87.7654	−	152.014i	−0.441032	−	0.763890i	0.556734	−	0.830691i	$-0.312054\pi$
$199$	−87.7654	−	152.014i	−0.441032	−	0.763890i	−0.997766	+	0.0668004i	$0.978721\pi$
$200$		0			0
$201$	23.9965	+	3.91220i	0.119385	+	0.0194637i
$202$		0			0
$203$	−42.1229	+	115.732i	−0.207502	+	0.570107i
$204$		0			0
$205$	17.9324	−	101.700i	0.0874751	−	0.496096i
$206$		0			0
$207$	−208.243	−	113.157i	−1.00600	−	0.546652i
$208$		0			0
$209$	−93.1722	+	111.038i	−0.445800	+	0.531284i
$210$		0			0
$211$	45.2968	+	256.891i	0.214677	+	1.21749i	0.881466	+	0.472247i	$0.156557\pi$
$211$	45.2968	+	256.891i	0.214677	+	1.21749i	−0.666789	+	0.745246i	$0.732332\pi$
$212$		0			0
$213$	−93.8465	+	80.8360i	−0.440594	+	0.379512i
$214$		0			0
$215$		−	523.993i		−	2.43718i
$216$		0			0
$217$	−265.720			−1.22452
$218$		0			0
$219$	79.9643	−	228.860i	0.365134	−	1.04502i
$220$		0			0
$221$	143.695	−	25.3373i	0.650204	−	0.114648i
$222$		0			0
$223$	298.157	+	250.184i	1.33703	+	1.12190i	0.982379	+	0.186901i	$0.0598445\pi$
$223$	298.157	+	250.184i	1.33703	+	1.12190i	0.354650	+	0.934999i	$0.384600\pi$
$224$		0			0
$225$	94.9113	−	83.9138i	0.421828	−	0.372950i
$226$		0			0
$227$	343.139	+	60.5046i	1.51162	+	0.266540i	0.867135	−	0.498074i	$-0.165959\pi$
$227$	343.139	+	60.5046i	1.51162	+	0.266540i	0.644489	+	0.764614i	$0.277070\pi$
$228$		0			0
$229$	342.540	+	124.675i	1.49581	+	0.544430i	0.954972	−	0.296696i	$-0.0958849\pi$
$229$	342.540	+	124.675i	1.49581	+	0.544430i	0.540838	+	0.841127i	$0.318107\pi$
$230$		0			0
$231$	152.996	+	125.045i	0.662319	+	0.541323i
$232$		0			0
$233$	164.260	−	94.8353i	0.704976	−	0.407018i	−0.104222	−	0.994554i	$-0.533235\pi$
$233$	164.260	−	94.8353i	0.704976	−	0.407018i	0.809198	+	0.587536i	$0.199902\pi$
$234$		0			0
$235$	−41.1641	+	71.2983i	−0.175166	+	0.303397i
$236$		0			0
$237$	−71.2475	+	42.3716i	−0.300622	+	0.178783i
$238$		0			0
$239$	196.756	+	234.485i	0.823249	+	0.981110i	0.999995	−	0.00314661i	$-0.00100160\pi$
$239$	196.756	+	234.485i	0.823249	+	0.981110i	−0.176746	+	0.984256i	$0.556557\pi$
$240$		0			0
$241$	277.120	−	100.864i	1.14988	−	0.418521i	0.304406	−	0.952542i	$-0.401542\pi$
$241$	277.120	−	100.864i	1.14988	−	0.418521i	0.845471	+	0.534021i	$0.179320\pi$
$242$		0			0
$243$	143.852	−	195.846i	0.591984	−	0.805949i
$244$		0			0
$245$	36.1234	+	99.2481i	0.147442	+	0.405094i
$246$		0			0
$247$	132.876	−	111.496i	0.537959	−	0.451401i
$248$		0			0
$249$	26.9730	+	45.3549i	0.108325	+	0.182148i
$250$		0			0
$251$	−158.404	−	91.4547i	−0.631092	−	0.364361i	0.150083	−	0.988673i	$-0.452046\pi$
$251$	−158.404	−	91.4547i	−0.631092	−	0.364361i	−0.781175	+	0.624312i	$0.785379\pi$
$252$		0			0
$253$	−106.833	−	185.040i	−0.422265	−	0.731384i
$254$		0			0
$255$	−178.344	+	218.208i	−0.699388	+	0.855716i
$256$		0			0
$257$	−91.7859	+	252.180i	−0.357144	+	0.981244i	0.622872	+	0.782324i	$0.285966\pi$
$257$	−91.7859	+	252.180i	−0.357144	+	0.981244i	−0.980016	+	0.198920i	$0.936256\pi$
$258$		0			0
$259$	44.5708	−	252.774i	0.172088	−	0.975961i
$260$		0			0
$261$	90.4440	+	102.297i	0.346529	+	0.391944i
$262$		0			0
$263$	−226.246	+	269.629i	−0.860250	+	1.02521i	0.139139	+	0.990273i	$0.455566\pi$
$263$	−226.246	+	269.629i	−0.860250	+	1.02521i	−0.999390	+	0.0349337i	$0.988878\pi$
$264$		0			0
$265$	27.9123	+	158.299i	0.105330	+	0.597354i
$266$		0			0
$267$	80.1160	+	27.9928i	0.300060	+	0.104842i
$268$		0			0
$269$		−	164.243i		−	0.610570i	−0.952261	−	0.305285i	$-0.901248\pi$
$269$		−	164.243i		−	0.610570i	0.952261	−	0.305285i	$-0.0987518\pi$
$270$		0			0
$271$	128.850			0.475462			0.237731	−	0.971331i	$-0.423596\pi$
$271$	128.850			0.475462			0.237731	+	0.971331i	$0.423596\pi$
$272$		0			0
$273$	−154.319	−	179.157i	−0.565272	−	0.656252i
$274$		0			0
$275$	112.479	−	19.8330i	0.409013	−	0.0721200i
$276$		0			0
$277$	115.074	+	96.5583i	0.415428	+	0.348586i	0.826421	−	0.563053i	$-0.190373\pi$
$277$	115.074	+	96.5583i	0.415428	+	0.348586i	−0.410992	+	0.911639i	$0.634818\pi$
$278$		0			0
$279$	−140.659	+	258.855i	−0.504155	+	0.927797i
$280$		0			0
$281$	453.995	+	80.0516i	1.61564	+	0.284881i	0.907140	−	0.420828i	$-0.138261\pi$
$281$	453.995	+	80.0516i	1.61564	+	0.284881i	0.708501	+	0.705710i	$0.249372\pi$
$282$		0			0
$283$	−64.7049	−	23.5506i	−0.228639	−	0.0832178i	0.225160	−	0.974322i	$-0.427709\pi$
$283$	−64.7049	−	23.5506i	−0.228639	−	0.0832178i	−0.453799	+	0.891104i	$0.649932\pi$
$284$		0			0
$285$	−53.9072	+	330.654i	−0.189148	+	1.16019i
$286$		0			0
$287$	116.137	−	67.0517i	0.404658	−	0.233630i
$288$		0			0
$289$	−31.5856	+	54.7078i	−0.109293	+	0.189300i
$290$		0			0
$291$	−6.53725	−	505.851i	−0.0224648	−	1.73832i
$292$		0			0
$293$	328.314	+	391.270i	1.12053	+	1.33539i	0.935772	+	0.352607i	$0.114705\pi$
$293$	328.314	+	391.270i	1.12053	+	1.33539i	0.184755	+	0.982785i	$0.440851\pi$
$294$		0			0
$295$	133.407	−	48.5563i	0.452228	−	0.164598i
$296$		0			0
$297$	202.804	−	82.8503i	0.682841	−	0.278957i
$298$		0			0
$299$	87.4501	+	240.267i	0.292475	+	0.803569i
$300$		0			0
$301$	521.256	−	437.386i	1.73175	−	1.45311i
$302$		0			0
$303$	−102.389	+	182.757i	−0.337919	+	0.603160i
$304$		0			0
$305$	184.541	+	106.545i	0.605053	+	0.349327i
$306$		0			0
$307$	26.3017	+	45.5559i	0.0856734	+	0.148391i	0.905678	−	0.423966i	$-0.139363\pi$
$307$	26.3017	+	45.5559i	0.0856734	+	0.148391i	−0.820005	+	0.572357i	$0.806029\pi$
$308$		0			0
$309$	−74.2224	−	196.006i	−0.240202	−	0.634323i
$310$		0			0
$311$	121.357	−	333.427i	0.390217	−	1.07211i	−0.576686	−	0.816966i	$-0.695654\pi$
$311$	121.357	−	333.427i	0.390217	−	1.07211i	0.966903	−	0.255146i	$-0.0821234\pi$
$312$		0			0
$313$	29.2161	−	165.693i	0.0933421	−	0.529369i	−0.901901	−	0.431943i	$-0.857828\pi$
$313$	29.2161	−	165.693i	0.0933421	−	0.529369i	0.995243	−	0.0974258i	$-0.0310609\pi$
$314$		0			0
$315$	451.658	+	67.6554i	1.43384	+	0.214779i
$316$		0			0
$317$	327.814	−	390.674i	1.03411	−	1.23241i	0.0619572	−	0.998079i	$-0.480266\pi$
$317$	327.814	−	390.674i	1.03411	−	1.23241i	0.972157	−	0.234330i	$-0.0752898\pi$
$318$		0			0
$319$	21.3764	+	121.232i	0.0670107	+	0.380037i
$320$		0			0
$321$	67.8898	+	357.913i	0.211495	+	1.11499i
$322$		0			0
$323$		−	268.461i		−	0.831149i
$324$		0			0
$325$	−136.676			−0.420541
$326$		0			0
$327$	−352.613	+	66.8845i	−1.07833	+	0.204540i
$328$		0			0
$329$	−105.286	+	18.5648i	−0.320019	+	0.0564280i
$330$		0			0
$331$	259.951	+	218.125i	0.785350	+	0.658987i	0.944590	−	0.328253i	$-0.106460\pi$
$331$	259.951	+	218.125i	0.785350	+	0.658987i	−0.159240	+	0.987240i	$0.550904\pi$
$332$		0			0
$333$	−222.650	−	177.226i	−0.668619	−	0.532209i
$334$		0			0
$335$	49.8920	+	8.79731i	0.148931	+	0.0262606i
$336$		0			0
$337$	64.1227	+	23.3388i	0.190275	+	0.0692545i	0.435400	−	0.900237i	$-0.356607\pi$
$337$	64.1227	+	23.3388i	0.190275	+	0.0692545i	−0.245125	+	0.969491i	$0.578829\pi$
$338$		0			0
$339$	348.913	−	132.124i	1.02924	−	0.389748i
$340$		0			0
$341$	−230.013	+	132.798i	−0.674526	+	0.389438i
$342$		0			0
$343$	130.305	−	225.695i	0.379897	−	0.658002i
$344$		0			0
$345$	−430.833	−	241.373i	−1.24879	−	0.699632i
$346$		0			0
$347$	111.265	+	132.600i	0.320648	+	0.382134i	0.902158	−	0.431406i	$-0.141982\pi$
$347$	111.265	+	132.600i	0.320648	+	0.382134i	−0.581510	+	0.813539i	$0.697538\pi$
$348$		0			0
$349$	−431.866	+	157.186i	−1.23744	+	0.450390i	−0.876138	−	0.482060i	$-0.839889\pi$
$349$	−431.866	+	157.186i	−1.23744	+	0.450390i	−0.361299	+	0.932450i	$0.617667\pi$
$350$		0			0
$351$	−256.218	+	55.4956i	−0.729965	+	0.158107i
$352$		0			0
$353$	−137.578	−	377.991i	−0.389738	−	1.07080i	−0.967119	−	0.254322i	$-0.918148\pi$
$353$	−137.578	−	377.991i	−0.389738	−	1.07080i	0.577381	−	0.816475i	$-0.304075\pi$
$354$		0			0
$355$	−197.709	+	165.897i	−0.556926	+	0.467316i
$356$		0			0
$357$	−365.935	+	4.72908i	−1.02503	+	0.0132467i
$358$		0			0
$359$	197.249	+	113.882i	0.549439	+	0.317219i	0.748896	−	0.662688i	$-0.230584\pi$
$359$	197.249	+	113.882i	0.549439	+	0.317219i	−0.199457	+	0.979907i	$0.563918\pi$
$360$		0			0
$361$	20.9294	+	36.2507i	0.0579761	+	0.100418i
$362$		0			0
$363$	−163.339	−	26.6296i	−0.449971	−	0.0733597i
$364$		0			0
$365$	172.770	−	474.683i	0.473343	−	1.30050i
$366$		0			0
$367$	40.8884	−	231.890i	0.111413	−	0.631852i	−0.877052	−	0.480396i	$-0.840493\pi$
$367$	40.8884	−	231.890i	0.111413	−	0.631852i	0.988464	−	0.151456i	$-0.0483960\pi$
$368$		0			0
$369$	−3.84223	−	148.631i	−0.0104126	−	0.402793i
$370$		0			0
$371$	−134.173	+	159.901i	−0.361653	+	0.431001i
$372$		0			0
$373$	113.349	+	642.835i	0.303885	+	1.72342i	0.628707	+	0.777642i	$0.283585\pi$
$373$	113.349	+	642.835i	0.303885	+	1.72342i	−0.324822	+	0.945775i	$0.605304\pi$
$374$		0			0
$375$	−155.213	+	133.695i	−0.413901	+	0.356519i
$376$		0			0
$377$		−	147.312i		−	0.390748i
$378$		0			0
$379$	−625.053			−1.64922			−0.824608	−	0.565705i	$-0.808604\pi$
$379$	−625.053			−1.64922			−0.824608	+	0.565705i	$0.808604\pi$
$380$		0			0
$381$	−116.232	+	332.659i	−0.305071	+	0.873119i
$382$		0			0
$383$	−104.921	+	18.5004i	−0.273945	+	0.0483039i	−0.308933	−	0.951084i	$-0.599972\pi$
$383$	−104.921	+	18.5004i	−0.273945	+	0.0483039i	0.0349879	+	0.999388i	$0.488861\pi$
$384$		0			0
$385$	315.404	+	264.656i	0.819232	+	0.687417i
$386$		0			0
$387$	−150.159	−	739.321i	−0.388007	−	1.91039i
$388$		0			0
$389$	−584.613	−	103.083i	−1.50286	−	0.264995i	−0.639190	−	0.769049i	$-0.720730\pi$
$389$	−584.613	−	103.083i	−1.50286	−	0.264995i	−0.863672	+	0.504054i	$0.831841\pi$
$390$		0			0
$391$	371.864	+	135.347i	0.951058	+	0.346157i
$392$		0			0
$393$	−10.9472	−	8.94729i	−0.0278555	−	0.0227666i
$394$		0			0
$395$	−149.587	+	86.3642i	−0.378702	+	0.218643i
$396$		0			0
$397$	−187.410	+	324.603i	−0.472064	+	0.817640i	−0.999489	−	0.0319623i	$-0.989824\pi$
$397$	−187.410	+	324.603i	−0.472064	+	0.817640i	0.527425	+	0.849602i	$0.323158\pi$
$398$		0			0
$399$	−373.924	+	222.377i	−0.937153	+	0.557335i
$400$		0			0
$401$	−176.385	−	210.207i	−0.439862	−	0.524207i	0.499879	−	0.866095i	$-0.333378\pi$
$401$	−176.385	−	210.207i	−0.439862	−	0.524207i	−0.939741	+	0.341889i	$0.888933\pi$
$402$		0			0
$403$	298.663	−	108.704i	0.741099	−	0.269738i
$404$		0			0
$405$	304.994	−	404.177i	0.753071	−	0.997968i
$406$		0			0
$407$	−87.7467	−	241.082i	−0.215594	−	0.592339i
$408$		0			0
$409$	−422.454	+	354.481i	−1.03289	+	0.866701i	−0.991193	−	0.132429i	$-0.957722\pi$
$409$	−422.454	+	354.481i	−1.03289	+	0.866701i	−0.0417017	+	0.999130i	$0.513278\pi$
$410$		0			0
$411$	338.570	+	569.302i	0.823772	+	1.38516i
$412$		0			0
$413$	159.660	+	92.1798i	0.386586	+	0.223196i
$414$		0			0
$415$	54.9779	+	95.2245i	0.132477	+	0.229457i
$416$		0			0
$417$	67.9010	−	83.0783i	0.162832	−	0.199228i
$418$		0			0
$419$	29.9567	−	82.3055i	0.0714958	−	0.196433i	−0.898798	−	0.438363i	$-0.855558\pi$
$419$	29.9567	−	82.3055i	0.0714958	−	0.196433i	0.970294	+	0.241930i	$0.0777805\pi$
$420$		0			0
$421$	51.4449	−	291.759i	0.122197	−	0.693013i	−0.860736	−	0.509051i	$-0.829996\pi$
$421$	51.4449	−	291.759i	0.122197	−	0.693013i	0.982933	−	0.183962i	$-0.0588924\pi$
$422$		0			0
$423$	−37.6482	+	112.394i	−0.0890029	+	0.265706i
$424$		0			0
$425$	−135.972	+	162.045i	−0.319933	+	0.381281i
$426$		0			0
$427$	48.0512	+	272.512i	0.112532	+	0.638201i
$428$		0			0
$429$	−223.119	−	77.9586i	−0.520091	−	0.181722i
$430$		0			0
$431$		−	586.175i		−	1.36003i	−0.733196	−	0.680017i	$-0.761972\pi$
$431$		−	586.175i		−	1.36003i	0.733196	−	0.680017i	$-0.238028\pi$
$432$		0			0
$433$	415.367			0.959277			0.479639	−	0.877466i	$-0.340768\pi$
$433$	415.367			0.959277			0.479639	+	0.877466i	$0.340768\pi$
$434$		0			0
$435$	185.688	+	215.575i	0.426870	+	0.495575i
$436$		0			0
$437$	463.288	−	81.6902i	1.06016	−	0.186934i
$438$		0			0
$439$	−256.133	−	214.921i	−0.583447	−	0.489570i	0.302630	−	0.953108i	$-0.402135\pi$
$439$	−256.133	−	214.921i	−0.583447	−	0.489570i	−0.886077	+	0.463538i	$0.846580\pi$
$440$		0			0
$441$	79.4090	+	129.681i	0.180066	+	0.294062i
$442$		0			0
$443$	−444.780	−	78.4268i	−1.00402	−	0.177036i	−0.352616	−	0.935768i	$-0.614708\pi$
$443$	−444.780	−	78.4268i	−1.00402	−	0.177036i	−0.651402	+	0.758732i	$0.725819\pi$
$444$		0			0
$445$	166.170	+	60.4810i	0.373416	+	0.135912i
$446$		0			0
$447$	−80.9702	+	496.651i	−0.181141	+	1.11108i
$448$		0			0
$449$	−165.422	+	95.5067i	−0.368424	+	0.212710i	−0.672770	−	0.739852i	$-0.734896\pi$
$449$	−165.422	+	95.5067i	−0.368424	+	0.212710i	0.304346	+	0.952562i	$0.401562\pi$
$450$		0			0
$451$	67.0206	−	116.083i	0.148604	−	0.257390i
$452$		0			0
$453$	−3.24547	−	251.133i	−0.00716438	−	0.554378i
$454$		0			0
$455$	−316.704	−	377.434i	−0.696054	−	0.829525i
$456$		0			0
$457$	362.489	−	131.935i	0.793192	−	0.288698i	0.0865297	−	0.996249i	$-0.472422\pi$
$457$	362.489	−	131.935i	0.793192	−	0.288698i	0.706662	+	0.707551i	$0.250200\pi$
$458$		0			0
$459$	−189.101	+	358.985i	−0.411985	+	0.782102i
$460$		0			0
$461$	148.113	+	406.937i	0.321286	+	0.882727i	0.990234	+	0.139417i	$0.0445229\pi$
$461$	148.113	+	406.937i	0.321286	+	0.882727i	−0.668947	+	0.743310i	$0.733255\pi$
$462$		0			0
$463$	−423.513	+	355.369i	−0.914714	+	0.767536i	−0.973010	−	0.230763i	$-0.925878\pi$
$463$	−423.513	+	355.369i	−0.914714	+	0.767536i	0.0582960	+	0.998299i	$0.481433\pi$
$464$		0			0
$465$	−300.038	+	535.545i	−0.645242	+	1.15171i
$466$		0			0
$467$	186.467	+	107.657i	0.399286	+	0.230528i	0.686176	−	0.727436i	$-0.259288\pi$
$467$	186.467	+	107.657i	0.399286	+	0.230528i	−0.286890	+	0.957964i	$0.592621\pi$
$468$		0			0
$469$	32.8943	+	56.9747i	0.0701372	+	0.121481i
$470$		0			0
$471$	−79.0898	−	208.860i	−0.167919	−	0.443439i
$472$		0			0
$473$	232.620	−	639.119i	0.491798	−	1.35120i
$474$		0			0
$475$	−43.6669	+	247.647i	−0.0919304	+	0.521363i
$476$		0			0
$477$	84.7457	+	215.351i	0.177664	+	0.451469i
$478$		0			0
$479$	145.585	−	173.501i	0.303935	−	0.362216i	−0.592360	−	0.805673i	$-0.701804\pi$
$479$	145.585	−	173.501i	0.303935	−	0.362216i	0.896295	+	0.443457i	$0.146248\pi$
$480$		0			0
$481$	53.3117	+	302.346i	0.110835	+	0.628577i
$482$		0			0
$483$	−119.512	−	630.061i	−0.247436	−	1.30447i
$484$		0			0
$485$		−	1054.13i		−	2.17347i
$486$		0			0
$487$	443.130			0.909919			0.454959	−	0.890512i	$-0.349654\pi$
$487$	443.130			0.909919			0.454959	+	0.890512i	$0.349654\pi$
$488$		0			0
$489$	−751.098	+	142.470i	−1.53599	+	0.291350i
$490$		0			0
$491$	657.316	−	115.902i	1.33873	−	0.236054i	0.541993	−	0.840383i	$-0.317670\pi$
$491$	657.316	−	115.902i	1.33873	−	0.236054i	0.796735	+	0.604329i	$0.206559\pi$
$492$		0			0
$493$	−174.655	−	146.553i	−0.354270	−	0.297268i
$494$		0			0
$495$	424.778	−	167.160i	0.858138	−	0.337698i
$496$		0			0
$497$	−330.061	−	58.1987i	−0.664108	−	0.117100i
$498$		0			0
$499$	−54.0177	−	19.6608i	−0.108252	−	0.0394005i	0.287326	−	0.957833i	$-0.407234\pi$
$499$	−54.0177	−	19.6608i	−0.108252	−	0.0394005i	−0.395578	+	0.918432i	$0.629456\pi$
$500$		0			0
$501$	444.964	−	168.497i	0.888152	−	0.336321i
$502$		0			0
$503$	−423.202	+	244.336i	−0.841356	+	0.485757i	−0.857725	−	0.514109i	$-0.828123\pi$
$503$	−423.202	+	244.336i	−0.841356	+	0.485757i	0.0163686	+	0.999866i	$0.494789\pi$
$504$		0			0
$505$	−218.252	+	378.024i	−0.432182	+	0.748562i
$506$		0			0
$507$	−195.571	−	109.568i	−0.385741	−	0.216110i
$508$		0			0
$509$	182.714	+	217.750i	0.358966	+	0.427799i	0.915058	−	0.403322i	$-0.132144\pi$
$509$	182.714	+	217.750i	0.358966	+	0.427799i	−0.556093	+	0.831120i	$0.687700\pi$
$510$		0			0
$511$	616.418	−	224.358i	1.20630	−	0.439056i
$512$		0			0
$513$	18.6946	+	481.980i	0.0364417	+	0.939532i
$514$		0			0
$515$	−149.367	−	410.382i	−0.290033	−	0.796859i
$516$		0			0
$517$	−81.8602	+	68.6889i	−0.158337	+	0.132860i
$518$		0			0
$519$	−894.169	+	11.5556i	−1.72287	+	0.0222651i
$520$		0			0
$521$	35.1966	+	20.3207i	0.0675558	+	0.0390033i	0.533397	−	0.845865i	$-0.320915\pi$
$521$	35.1966	+	20.3207i	0.0675558	+	0.0390033i	−0.465842	+	0.884868i	$0.654248\pi$
$522$		0			0
$523$	174.951	+	303.024i	0.334514	+	0.579395i	0.983391	−	0.181498i	$-0.0580946\pi$
$523$	174.951	+	303.024i	0.334514	+	0.579395i	−0.648877	+	0.760893i	$0.724761\pi$
$524$		0			0
$525$	338.333	+	55.1592i	0.644444	+	0.105065i
$526$		0			0
$527$	168.243	−	462.243i	0.319246	−	0.877122i
$528$		0			0
$529$	−28.5567	+	161.953i	−0.0539825	+	0.306150i
$530$		0			0
$531$	174.315	−	106.740i	0.328276	−	0.201017i
$532$		0			0
$533$	−103.105	+	122.876i	−0.193442	+	0.230536i
$534$		0			0
$535$	131.813	+	747.550i	0.246380	+	1.39729i
$536$		0			0
$537$	−66.6656	+	57.4233i	−0.124145	+	0.106934i
$538$		0			0
$539$			137.090i			0.254342i
$540$		0			0
$541$	145.531			0.269003			0.134501	−	0.990913i	$-0.457057\pi$
$541$	145.531			0.269003			0.134501	+	0.990913i	$0.457057\pi$
$542$		0			0
$543$	−82.5320	+	236.208i	−0.151993	+	0.435006i
$544$		0			0
$545$	−736.481	+	129.861i	−1.35134	+	0.238278i
$546$		0			0
$547$	−372.320	−	312.413i	−0.680657	−	0.571139i	0.235541	−	0.971864i	$-0.424314\pi$
$547$	−372.320	−	312.413i	−0.680657	−	0.571139i	−0.916198	+	0.400725i	$0.868758\pi$
$548$		0			0
$549$	290.908	+	97.4448i	0.529887	+	0.177495i
$550$		0			0
$551$	−266.919	−	47.0651i	−0.484427	−	0.0854176i
$552$		0			0
$553$	−210.776	−	76.7162i	−0.381150	−	0.138727i
$554$		0			0
$555$	−459.126	−	375.250i	−0.827254	−	0.676126i
$556$		0			0
$557$	2.82805	−	1.63278i	0.00507730	−	0.00293138i	−0.497459	−	0.867487i	$-0.665734\pi$
$557$	2.82805	−	1.63278i	0.00507730	−	0.00293138i	0.502537	+	0.864556i	$0.332400\pi$
$558$		0			0
$559$	−406.948	+	704.855i	−0.727993	+	1.26092i
$560$		0			0
$561$	−314.398	+	186.976i	−0.560425	+	0.333291i
$562$		0			0
$563$	427.292	+	509.227i	0.758956	+	0.904489i	0.997781	−	0.0665739i	$-0.0212068\pi$
$563$	427.292	+	509.227i	0.758956	+	0.904489i	−0.238825	+	0.971063i	$0.576762\pi$
$564$		0			0
$565$	730.527	−	265.890i	1.29297	−	0.470602i
$566$		0			0
$567$	656.649	−	33.9726i	1.15811	−	0.0599164i
$568$		0			0
$569$	25.9713	+	71.3556i	0.0456438	+	0.125405i	0.960420	−	0.278555i	$-0.0898555\pi$
$569$	25.9713	+	71.3556i	0.0456438	+	0.125405i	−0.914776	+	0.403960i	$0.867633\pi$
$570$		0			0
$571$	225.287	−	189.038i	0.394548	−	0.331065i	−0.423834	−	0.905740i	$-0.639316\pi$
$571$	225.287	−	189.038i	0.394548	−	0.331065i	0.818382	+	0.574675i	$0.194871\pi$
$572$		0			0
$573$	−240.673	−	404.689i	−0.420023	−	0.706264i
$574$		0			0
$575$	−321.018	−	185.340i	−0.558292	−	0.322330i
$576$		0			0
$577$	−529.296	−	916.768i	−0.917325	−	1.58885i	−0.803461	−	0.595357i	$-0.797011\pi$
$577$	−529.296	−	916.768i	−0.917325	−	1.58885i	−0.113864	−	0.993496i	$-0.536323\pi$
$578$		0			0
$579$	−78.7297	+	96.3274i	−0.135975	+	0.166369i
$580$		0			0
$581$	−48.8362	+	134.176i	−0.0840554	+	0.230940i
$582$		0			0
$583$	−36.2299	+	205.470i	−0.0621438	+	0.352435i
$584$		0			0
$585$	−535.331	+	108.728i	−0.915096	+	0.185859i
$586$		0			0
$587$	−89.2844	+	106.405i	−0.152103	+	0.181269i	−0.836715	−	0.547638i	$-0.815527\pi$
$587$	−89.2844	+	106.405i	−0.152103	+	0.181269i	0.684612	+	0.728907i	$0.259971\pi$
$588$		0			0
$589$	−101.545	−	575.888i	−0.172402	−	0.977738i
$590$		0			0
$591$	−596.609	−	208.457i	−1.00949	−	0.352720i
$592$		0			0
$593$			145.309i			0.245040i	0.992466	+	0.122520i	$0.0390975\pi$
$593$			145.309i			0.245040i	−0.992466	+	0.122520i	$0.960902\pi$
$594$		0			0
$595$	−762.563			−1.28162
$596$		0			0
$597$	−343.672	−	398.986i	−0.575664	−	0.668318i
$598$		0			0
$599$	22.6235	−	3.98914i	0.0377688	−	0.00665966i	−0.154732	−	0.987957i	$-0.549451\pi$
$599$	22.6235	−	3.98914i	0.0377688	−	0.00665966i	0.192501	+	0.981297i	$0.438340\pi$
$600$		0			0
$601$	−710.406	−	596.102i	−1.18204	−	0.991849i	−0.999963	−	0.00856516i	$-0.997274\pi$
$601$	−710.406	−	596.102i	−1.18204	−	0.991849i	−0.182077	−	0.983284i	$-0.558282\pi$
$602$		0			0
$603$	72.9155	−	1.88493i	0.120921	−	0.00312592i
$604$		0			0
$605$	−339.605	−	59.8816i	−0.561331	−	0.0989779i
$606$		0			0
$607$	492.373	+	179.209i	0.811158	+	0.295237i	0.714102	−	0.700042i	$-0.246835\pi$
$607$	492.373	+	179.209i	0.811158	+	0.295237i	0.0970557	+	0.995279i	$0.469057\pi$
$608$		0			0
$609$	−59.4517	+	364.663i	−0.0976219	+	0.598789i
$610$		0			0
$611$	110.745	−	63.9384i	0.181251	−	0.104646i
$612$		0			0
$613$	−35.0848	+	60.7687i	−0.0572346	+	0.0991333i	−0.893223	−	0.449614i	$-0.851562\pi$
$613$	−35.0848	+	60.7687i	−0.0572346	+	0.0991333i	0.835988	+	0.548747i	$0.184895\pi$
$614$		0			0
$615$	−4.00337	−	309.780i	−0.00650954	−	0.503707i
$616$		0			0
$617$	427.172	+	509.083i	0.692337	+	0.825095i	0.991636	−	0.129064i	$-0.0411974\pi$
$617$	427.172	+	509.083i	0.692337	+	0.825095i	−0.299299	+	0.954159i	$0.596753\pi$
$618$		0			0
$619$	−912.210	+	332.017i	−1.47368	+	0.536377i	−0.949098	−	0.314981i	$-0.898002\pi$
$619$	−912.210	+	332.017i	−1.47368	+	0.536377i	−0.524585	+	0.851358i	$0.675780\pi$
$620$		0			0
$621$	−677.048	−	217.100i	−1.09025	−	0.349597i
$622$		0			0
$623$	78.5400	+	215.787i	0.126067	+	0.346367i
$624$		0			0
$625$	−596.569	+	500.581i	−0.954510	+	0.800929i
$626$		0			0
$627$	−212.541	+	379.370i	−0.338981	+	0.605056i
$628$		0			0
$629$	411.502	+	237.581i	0.654216	+	0.377712i
$630$		0			0
$631$	−94.6588	−	163.954i	−0.150014	−	0.259832i	0.781218	−	0.624258i	$-0.214599\pi$
$631$	−94.6588	−	163.954i	−0.150014	−	0.259832i	−0.931232	+	0.364426i	$0.881265\pi$
$632$		0			0
$633$	277.132	+	731.848i	0.437808	+	1.15616i
$634$		0			0
$635$	−251.130	+	689.974i	−0.395480	+	1.08657i
$636$		0			0
$637$	28.4872	−	161.559i	0.0447209	−	0.253625i
$638$		0			0
$639$	−231.414	+	290.727i	−0.362150	+	0.454972i
$640$		0			0
$641$	−445.262	+	530.643i	−0.694637	+	0.827836i	−0.991908	−	0.126957i	$-0.959479\pi$
$641$	−445.262	+	530.643i	−0.694637	+	0.827836i	0.297271	+	0.954793i	$0.403923\pi$
$642$		0			0
$643$	−184.867	−	1048.43i	−0.287506	−	1.63053i	−0.696193	−	0.717854i	$-0.745124\pi$
$643$	−184.867	−	1048.43i	−0.287506	−	1.63053i	0.408687	−	0.912675i	$-0.365987\pi$
$644$		0			0
$645$	−292.953	−	1544.44i	−0.454191	−	2.39448i
$646$		0			0
$647$		−	352.755i		−	0.545217i	−0.962125	−	0.272608i	$-0.912114\pi$
$647$		−	352.755i		−	0.545217i	0.962125	−	0.272608i	$-0.0878863\pi$
$648$		0			0
$649$	184.274			0.283935
$650$		0			0
$651$	−783.195	+	148.558i	−1.20306	+	0.228200i
$652$		0			0
$653$	461.316	−	81.3425i	0.706457	−	0.124567i	0.191135	−	0.981564i	$-0.438783\pi$
$653$	461.316	−	81.3425i	0.706457	−	0.124567i	0.515322	+	0.856996i	$0.327672\pi$
$654$		0			0
$655$	−22.5679	−	18.9367i	−0.0344548	−	0.0289110i
$656$		0			0
$657$	107.740	−	719.257i	0.163988	−	1.09476i
$658$		0			0
$659$	84.6349	+	14.9234i	0.128429	+	0.0226455i	0.237493	−	0.971389i	$-0.423674\pi$
$659$	84.6349	+	14.9234i	0.128429	+	0.0226455i	−0.109064	+	0.994035i	$0.534785\pi$
$660$		0			0
$661$	−115.687	−	42.1068i	−0.175019	−	0.0637016i	0.253024	−	0.967460i	$-0.418575\pi$
$661$	−115.687	−	42.1068i	−0.175019	−	0.0637016i	−0.428043	+	0.903758i	$0.640797\pi$
$662$		0			0
$663$	409.368	−	155.017i	0.617447	−	0.233812i
$664$		0			0
$665$	−785.070	+	453.260i	−1.18056	+	0.681594i
$666$		0			0
$667$	199.763	−	346.000i	0.299495	−	0.518741i
$668$		0			0
$669$	1018.67	+	570.709i	1.52268	+	0.853078i
$670$		0			0
$671$	177.787	+	211.878i	0.264958	+	0.315765i
$672$		0			0
$673$	598.221	−	217.735i	0.888887	−	0.323528i	0.143096	−	0.989709i	$-0.454294\pi$
$673$	598.221	−	217.735i	0.888887	−	0.323528i	0.745791	+	0.666180i	$0.232072\pi$
$674$		0			0
$675$	232.832	−	300.394i	0.344936	−	0.445029i
$676$		0			0
$677$	56.5391	+	155.340i	0.0835141	+	0.229453i	0.974420	−	0.224735i	$-0.0721516\pi$
$677$	56.5391	+	155.340i	0.0835141	+	0.229453i	−0.890906	+	0.454188i	$0.849929\pi$
$678$		0			0
$679$	1048.63	−	879.901i	1.54437	−	1.29588i
$680$		0			0
$681$	1045.21	−	13.5075i	1.53481	−	0.0198348i
$682$		0			0
$683$	1129.58	+	652.163i	1.65385	+	0.954851i	0.975468	+	0.220142i	$0.0706522\pi$
$683$	1129.58	+	652.163i	1.65385	+	0.954851i	0.678383	+	0.734709i	$0.262681\pi$
$684$		0			0
$685$	690.092	+	1195.27i	1.00743	+	1.74493i
$686$		0			0
$687$	1079.32	+	175.964i	1.57107	+	0.256134i
$688$		0			0
$689$	85.3928	−	234.615i	0.123937	−	0.340515i
$690$		0			0
$691$	62.8288	−	356.320i	0.0909245	−	0.515658i	−0.904996	−	0.425421i	$-0.860126\pi$
$691$	62.8288	−	356.320i	0.0909245	−	0.515658i	0.995920	−	0.0902378i	$-0.0287627\pi$
$692$		0			0
$693$	520.857	+	283.028i	0.751597	+	0.408410i
$694$		0			0
$695$	143.711	−	171.268i	0.206778	−	0.246428i
$696$		0			0
$697$	43.1093	+	244.485i	0.0618498	+	0.350767i
$698$		0			0
$699$	431.125	−	371.356i	0.616775	−	0.531267i
$700$		0			0
$701$		−	893.344i		−	1.27438i	−0.770705	−	0.637192i	$-0.780096\pi$
$701$		−	893.344i		−	1.27438i	0.770705	−	0.637192i	$-0.219904\pi$
$702$		0			0
$703$	564.863			0.803504
$704$		0			0
$705$	−81.4675	+	233.162i	−0.115557	+	0.330726i
$706$		0			0
$707$	−558.228	+	98.4307i	−0.789573	+	0.139223i
$708$		0			0
$709$	−529.040	−	443.917i	−0.746178	−	0.626118i	0.188311	−	0.982109i	$-0.439699\pi$
$709$	−529.040	−	443.917i	−0.746178	−	0.626118i	−0.934489	+	0.355992i	$0.884143\pi$
$710$		0			0
$711$	−186.309	+	164.721i	−0.262038	+	0.231675i
$712$		0			0
$713$	848.896	+	149.683i	1.19060	+	0.209935i
$714$		0			0
$715$	−462.776	−	168.437i	−0.647239	−	0.235576i
$716$		0			0
$717$	711.025	+	581.130i	0.991666	+	0.810502i
$718$		0			0
$719$	−417.508	+	241.049i	−0.580679	+	0.335255i	−0.761403	−	0.648279i	$-0.775489\pi$
$719$	−417.508	+	241.049i	−0.580679	+	0.335255i	0.180724	+	0.983534i	$0.442156\pi$
$720$		0			0
$721$	283.560	−	491.140i	0.393287	−	0.681192i
$722$		0			0
$723$	760.406	−	452.222i	1.05174	−	0.625480i
$724$		0			0
$725$	137.276	+	163.600i	0.189347	+	0.225655i
$726$		0			0
$727$	324.225	−	118.008i	0.445977	−	0.162322i	−0.109263	−	0.994013i	$-0.534849\pi$
$727$	324.225	−	118.008i	0.445977	−	0.162322i	0.555239	+	0.831691i	$0.312627\pi$
$728$		0			0
$729$	314.503	−	657.669i	0.431418	−	0.902152i
$730$		0			0
$731$	430.834	+	1183.71i	0.589376	+	1.61930i
$732$		0			0
$733$	413.108	−	346.639i	0.563585	−	0.472904i	−0.315925	−	0.948784i	$-0.602315\pi$
$733$	413.108	−	346.639i	0.563585	−	0.472904i	0.879510	+	0.475880i	$0.157870\pi$
$734$		0			0
$735$	161.959	+	272.333i	0.220353	+	0.370521i
$736$		0			0
$737$	56.9482	+	32.8791i	0.0772704	+	0.0446121i
$738$		0			0
$739$	368.737	+	638.671i	0.498968	+	0.864237i	0.999999	−	0.00119161i	$-0.000379300\pi$
$739$	368.737	+	638.671i	0.498968	+	0.864237i	−0.501032	+	0.865429i	$0.667046\pi$
$740$		0			0
$741$	329.309	−	402.917i	0.444412	−	0.543747i
$742$		0			0
$743$	356.128	−	978.454i	0.479311	−	1.31690i	−0.430768	−	0.902463i	$-0.641757\pi$
$743$	356.128	−	978.454i	0.479311	−	1.31690i	0.910079	−	0.414434i	$-0.136020\pi$
$744$		0			0
$745$	−182.077	+	1032.61i	−0.244398	+	1.38605i
$746$		0			0
$747$	104.858	+	118.601i	0.140373	+	0.158770i
$748$		0			0
$749$	−633.619	+	755.118i	−0.845953	+	1.00817i
$750$		0			0
$751$	−41.8554	−	237.374i	−0.0557329	−	0.316077i	0.944178	−	0.329436i	$-0.106859\pi$
$751$	−41.8554	−	237.374i	−0.0557329	−	0.316077i	−0.999911	+	0.0133592i	$0.995748\pi$
$752$		0			0
$753$	−518.018	−	180.997i	−0.687939	−	0.240368i
$754$		0			0
$755$		−	523.331i		−	0.693154i
$756$		0			0
$757$	32.7615			0.0432781			0.0216391	−	0.999766i	$-0.493112\pi$
$757$	32.7615			0.0432781			0.0216391	+	0.999766i	$0.493112\pi$
$758$		0			0
$759$	−418.336	−	485.668i	−0.551168	−	0.639879i
$760$		0			0
$761$	314.502	−	55.4551i	0.413274	−	0.0728714i	0.0368545	−	0.999321i	$-0.488266\pi$
$761$	314.502	−	55.4551i	0.413274	−	0.0728714i	0.376420	+	0.926449i	$0.377155\pi$
$762$		0			0
$763$	−743.936	−	624.236i	−0.975014	−	0.818134i
$764$		0			0
$765$	−403.664	+	742.863i	−0.527665	+	0.971063i
$766$		0			0
$767$	−217.164	−	38.2920i	−0.283135	−	0.0499243i
$768$		0			0
$769$	447.488	+	162.872i	0.581910	+	0.211798i	0.616167	−	0.787615i	$-0.288685\pi$
$769$	447.488	+	162.872i	0.581910	+	0.211798i	−0.0342578	+	0.999413i	$0.510907\pi$
$770$		0			0
$771$	−129.546	+	794.601i	−0.168023	+	1.03061i
$772$		0			0
$773$	1122.62	−	648.147i	1.45229	−	0.838482i	0.453682	−	0.891164i	$-0.350110\pi$
$773$	1122.62	−	648.147i	1.45229	−	0.838482i	0.998611	+	0.0526817i	$0.0167769\pi$
$774$		0			0
$775$	−230.386	+	399.040i	−0.297272	+	0.514890i
$776$		0			0
$777$	−9.95035	−	769.955i	−0.0128061	−	0.990934i
$778$		0			0
$779$	189.701	+	226.077i	0.243519	+	0.290214i
$780$		0			0
$781$	−314.795	+	114.576i	−0.403066	+	0.146704i
$782$		0			0
$783$	323.771	+	250.951i	0.413501	+	0.320499i
$784$		0			0
$785$	−159.162	−	437.295i	−0.202754	−	0.557063i
$786$		0			0
$787$	−659.528	+	553.410i	−0.838028	+	0.703189i	−0.957119	−	0.289694i	$-0.906446\pi$
$787$	−659.528	+	553.410i	−0.838028	+	0.703189i	0.119091	+	0.992883i	$0.462002\pi$
$788$		0			0
$789$	−516.103	+	921.207i	−0.654123	+	1.16756i
$790$		0			0
$791$	874.285	+	504.769i	1.10529	+	0.638140i
$792$		0			0
$793$	−165.492	−	286.640i	−0.208690	−	0.361462i
$794$		0			0
$795$	170.772	+	450.972i	0.214807	+	0.567260i
$796$		0			0
$797$	−198.415	+	545.140i	−0.248952	+	0.683990i	0.750774	+	0.660560i	$0.229681\pi$
$797$	−198.415	+	545.140i	−0.248952	+	0.683990i	−0.999725	+	0.0234300i	$0.992541\pi$
$798$		0			0
$799$	34.3678	−	194.909i	0.0430135	−	0.243942i
$800$		0			0
$801$	251.788	+	37.7161i	0.314342	+	0.0470863i
$802$		0			0
$803$	421.459	−	502.275i	0.524855	−	0.625498i
$804$		0			0
$805$	−232.041	−	1315.97i	−0.288249	−	1.63474i
$806$		0			0
$807$	−91.8250	−	484.098i	−0.113786	−	0.599874i
$808$		0			0
$809$			661.323i			0.817457i	0.912656	+	0.408729i	$0.134028\pi$
$809$			661.323i			0.817457i	−0.912656	+	0.408729i	$0.865972\pi$
$810$		0			0
$811$	168.725			0.208045			0.104023	−	0.994575i	$-0.466829\pi$
$811$	168.725			0.208045			0.104023	+	0.994575i	$0.466829\pi$
$812$		0			0
$813$	379.779	−	72.0374i	0.467133	−	0.0886069i
$814$		0			0
$815$	−1568.77	+	276.617i	−1.92487	+	0.339407i
$816$		0			0
$817$	1147.13	+	962.559i	1.40408	+	1.17816i
$818$		0			0
$819$	−555.010	−	441.778i	−0.677668	−	0.539412i
$820$		0			0
$821$	149.275	+	26.3213i	0.181822	+	0.0320600i	0.263817	−	0.964573i	$-0.415018\pi$
$821$	149.275	+	26.3213i	0.181822	+	0.0320600i	−0.0819959	+	0.996633i	$0.526129\pi$
$822$		0			0
$823$	211.263	+	76.8935i	0.256699	+	0.0934307i	0.467164	−	0.884171i	$-0.345276\pi$
$823$	211.263	+	76.8935i	0.256699	+	0.0934307i	−0.210465	+	0.977601i	$0.567498\pi$
$824$		0			0
$825$	320.436	−	121.341i	0.388407	−	0.147080i
$826$		0			0
$827$	−292.855	+	169.080i	−0.354117	+	0.204449i	−0.666497	−	0.745508i	$-0.732207\pi$
$827$	−292.855	+	169.080i	−0.354117	+	0.204449i	0.312380	+	0.949957i	$0.398874\pi$
$828$		0			0
$829$	401.806	−	695.949i	0.484688	−	0.839504i	−0.515157	−	0.857096i	$-0.672267\pi$
$829$	401.806	−	695.949i	0.484688	−	0.839504i	0.999845	+	0.0175917i	$0.00559990\pi$
$830$		0			0
$831$	393.157	+	220.265i	0.473113	+	0.265060i
$832$		0			0
$833$	−163.206	−	194.502i	−0.195926	−	0.233495i
$834$		0			0
$835$	931.633	−	339.087i	1.11573	−	0.406092i
$836$		0			0
$837$	−269.865	+	841.601i	−0.322419	+	1.00550i
$838$		0			0
$839$	−292.066	−	802.443i	−0.348111	−	0.956428i	−0.982965	−	0.183795i	$-0.941162\pi$
$839$	−292.066	−	802.443i	−0.348111	−	0.956428i	0.634853	−	0.772633i	$-0.281061\pi$
$840$		0			0
$841$	467.912	−	392.625i	0.556376	−	0.466855i
$842$		0			0
$843$	1382.88	−	17.8714i	1.64043	−	0.0211997i
$844$		0			0
$845$	−404.527	−	233.554i	−0.478731	−	0.276395i
$846$		0			0
$847$	−223.906	−	387.816i	−0.264351	−	0.457870i
$848$		0			0
$849$	−203.881	−	33.2391i	−0.240142	−	0.0391509i
$850$		0			0
$851$	−284.781	+	782.430i	−0.334643	+	0.919424i
$852$		0			0
$853$	−138.765	+	786.975i	−0.162679	+	0.922596i	0.788747	+	0.614718i	$0.210730\pi$
$853$	−138.765	+	786.975i	−0.162679	+	0.922596i	−0.951426	+	0.307878i	$0.900381\pi$
$854$		0			0
$855$	25.9729	+	1004.72i	0.0303777	+	1.17511i
$856$		0			0
$857$	998.416	−	1189.87i	1.16501	−	1.38841i	0.258616	−	0.965980i	$-0.416734\pi$
$857$	998.416	−	1189.87i	1.16501	−	1.38841i	0.906397	−	0.422427i	$-0.138822\pi$
$858$		0			0
$859$	4.90592	+	27.8228i	0.00571119	+	0.0323898i	0.987530	−	0.157430i	$-0.0503208\pi$
$859$	4.90592	+	27.8228i	0.00571119	+	0.0323898i	−0.981819	+	0.189820i	$0.939210\pi$
$860$		0			0
$861$	304.820	−	262.561i	0.354030	−	0.304949i
$862$		0			0
$863$			951.550i			1.10261i	0.834305	+	0.551304i	$0.185869\pi$
$863$			951.550i			1.10261i	−0.834305	+	0.551304i	$0.814131\pi$
$864$		0			0
$865$	−1863.34			−2.15415
$866$		0			0
$867$	−62.5107	+	178.907i	−0.0721000	+	0.206352i
$868$		0			0
$869$	−220.793	+	38.9318i	−0.254077	+	0.0448006i
$870$		0			0
$871$	−60.2805	−	50.5813i	−0.0692084	−	0.0580727i
$872$		0			0
$873$	−302.079	−	1487.31i	−0.346024	−	1.70368i
$874$		0			0
$875$	−545.889	−	96.2549i	−0.623873	−	0.110006i
$876$		0			0
$877$	214.431	+	78.0465i	0.244505	+	0.0889926i	0.461366	−	0.887210i	$-0.347360\pi$
$877$	214.431	+	78.0465i	0.244505	+	0.0889926i	−0.216861	+	0.976203i	$0.569582\pi$
$878$		0			0
$879$	1186.44	+	969.692i	1.34976	+	1.10318i
$880$		0			0
$881$	−1343.36	+	775.592i	−1.52482	+	0.880354i	−0.525250	+	0.850948i	$0.676028\pi$
$881$	−1343.36	+	775.592i	−1.52482	+	0.880354i	−0.999568	+	0.0294054i	$0.990639\pi$
$882$		0			0
$883$	781.794	−	1354.11i	0.885384	−	1.53353i	0.0401121	−	0.999195i	$-0.487228\pi$
$883$	781.794	−	1354.11i	0.885384	−	1.53353i	0.845272	−	0.534336i	$-0.179438\pi$
$884$		0			0
$885$	366.064	−	217.702i	0.413632	−	0.245991i
$886$		0			0
$887$	−451.340	−	537.886i	−0.508839	−	0.606411i	0.449065	−	0.893499i	$-0.351757\pi$
$887$	−451.340	−	537.886i	−0.508839	−	0.606411i	−0.957904	+	0.287088i	$0.907313\pi$
$888$		0			0
$889$	−895.993	+	326.115i	−1.00787	+	0.366833i
$890$		0			0
$891$	551.433	−	357.580i	0.618892	−	0.401324i
$892$		0			0
$893$	−80.4701	−	221.090i	−0.0901121	−	0.247581i
$894$		0			0
$895$	−140.446	+	117.848i	−0.156923	+	0.131674i
$896$		0			0
$897$	392.083	+	659.283i	0.437104	+	0.734986i
$898$		0			0
$899$	−430.094	−	248.315i	−0.478413	−	0.276212i
$900$		0			0
$901$	−193.210	−	334.649i	−0.214439	−	0.371419i
$902$		0			0
$903$	1291.84	−	1580.59i	1.43061	−	1.75038i
$904$		0			0
$905$	−178.318	+	489.924i	−0.197036	+	0.541353i
$906$		0			0
$907$	−280.357	+	1589.99i	−0.309104	+	1.75302i	0.294424	+	0.955675i	$0.404872\pi$
$907$	−280.357	+	1589.99i	−0.309104	+	1.75302i	−0.603528	+	0.797341i	$0.706239\pi$
$908$		0			0
$909$	−199.611	+	595.911i	−0.219594	+	0.655568i
$910$		0			0
$911$	394.005	−	469.556i	0.432497	−	0.515430i	−0.505144	−	0.863035i	$-0.668561\pi$
$911$	394.005	−	469.556i	0.432497	−	0.515430i	0.937641	+	0.347605i	$0.113005\pi$
$912$		0			0
$913$	24.7833	+	140.553i	0.0271449	+	0.153946i
$914$		0			0
$915$	603.491	+	210.862i	0.659554	+	0.230450i
$916$		0			0
$917$		−	38.2568i		−	0.0417195i
$918$		0			0
$919$	−628.091			−0.683451			−0.341725	−	0.939800i	$-0.611011\pi$
$919$	−628.091			−0.683451			−0.341725	+	0.939800i	$0.611011\pi$
$920$		0			0
$921$	102.992	+	119.569i	0.111827	+	0.129825i
$922$		0			0
$923$	394.790	−	69.6122i	0.427725	−	0.0754195i
$924$		0			0
$925$	−340.955	−	286.095i	−0.368600	−	0.309292i
$926$		0			0
$927$	−328.349	−	536.220i	−0.354206	−	0.578446i
$928$		0			0
$929$	1234.51	+	217.678i	1.32886	+	0.234314i	0.792603	−	0.609738i	$-0.208726\pi$
$929$	1234.51	+	217.678i	1.32886	+	0.234314i	0.536260	+	0.844053i	$0.319837\pi$
$930$		0			0
$931$	−283.633	−	103.234i	−0.304654	−	0.110885i
$932$		0			0
$933$	171.282	−	1050.61i	0.183583	−	1.12605i
$934$		0			0
$935$	−660.093	+	381.105i	−0.705981	+	0.407599i
$936$		0			0
$937$	460.132	−	796.972i	0.491070	−	0.850557i	−0.508878	−	0.860839i	$-0.669939\pi$
$937$	460.132	−	796.972i	0.491070	−	0.850557i	0.999947	+	0.0102815i	$0.00327275\pi$
$938$		0			0
$939$	−6.52243	−	504.704i	−0.00694614	−	0.537491i
$940$		0			0
$941$	−439.314	−	523.554i	−0.466859	−	0.556381i	0.480317	−	0.877095i	$-0.340522\pi$
$941$	−439.314	−	523.554i	−0.466859	−	0.556381i	−0.947176	+	0.320714i	$0.896077\pi$
$942$		0			0
$943$	−408.794	+	148.789i	−0.433504	+	0.157783i
$944$		0			0
$945$	1369.06	−	53.1020i	1.44874	−	0.0561926i
$946$		0			0
$947$	287.907	+	791.018i	0.304020	+	0.835288i	0.993791	+	0.111261i	$0.0354889\pi$
$947$	287.907	+	791.018i	0.304020	+	0.835288i	−0.689771	+	0.724027i	$0.742289\pi$
$948$		0			0
$949$	−601.056	+	504.346i	−0.633357	+	0.531450i
$950$		0			0
$951$	747.797	−	1334.76i	0.786327	−	1.40354i
$952$		0			0
$953$	1277.52	+	737.576i	1.34052	+	0.773952i	0.986884	−	0.161430i	$-0.0516105\pi$
$953$	1277.52	+	737.576i	1.34052	+	0.773952i	0.353640	+	0.935382i	$0.384944\pi$
$954$		0			0
$955$	−490.553	−	849.662i	−0.513668	−	0.889698i
$956$		0			0
$957$	130.784	+	345.373i	0.136660	+	0.360891i
$958$		0			0
$959$	−613.000	+	1684.20i	−0.639207	+	1.75621i
$960$		0			0
$961$	19.1872	−	108.816i	0.0199659	−	0.113232i
$962$		0			0
$963$	400.203	+	1016.97i	0.415580	+	1.05605i
$964$		0			0
$965$	−166.629	+	198.581i	−0.172673	+	0.205783i
$966$		0			0
$967$	−56.3919	−	319.814i	−0.0583163	−	0.330728i	0.941667	−	0.336547i	$-0.109259\pi$
$967$	−56.3919	−	319.814i	−0.0583163	−	0.330728i	−0.999983	+	0.00581841i	$0.998148\pi$
$968$		0			0
$969$	−150.091	−	791.274i	−0.154892	−	0.816588i
$970$		0			0
$971$		−	1203.37i		−	1.23931i	−0.784873	−	0.619657i	$-0.787272\pi$
$971$		−	1203.37i		−	1.23931i	0.784873	−	0.619657i	$-0.212728\pi$
$972$		0			0
$973$	290.331			0.298387
$974$		0			0
$975$	−402.844	+	76.4125i	−0.413174	+	0.0783718i
$976$		0			0
$977$	186.452	−	32.8765i	0.190841	−	0.0336505i	−0.0774104	−	0.996999i	$-0.524665\pi$
$977$	186.452	−	32.8765i	0.190841	−	0.0336505i	0.268252	+	0.963349i	$0.413554\pi$
$978$		0			0
$979$	175.829	+	147.538i	0.179601	+	0.150703i
$980$		0			0
$981$	−1001.91	+	394.277i	−1.02132	+	0.401913i
$982$		0			0
$983$	1245.48	+	219.613i	1.26702	+	0.223411i	0.766462	−	0.642290i	$-0.222016\pi$
$983$	1245.48	+	219.613i	1.26702	+	0.223411i	0.500562	+	0.865701i	$0.333127\pi$
$984$		0			0
$985$	−1237.44	−	450.391i	−1.25628	−	0.457250i
$986$		0			0
$987$	−299.946	+	113.582i	−0.303897	+	0.115078i
$988$		0			0
$989$	−1911.64	+	1103.69i	−1.93291	+	1.11596i
$990$		0			0
$991$	−697.271	+	1207.71i	−0.703604	+	1.21868i	0.263589	+	0.964635i	$0.415094\pi$
$991$	−697.271	+	1207.71i	−0.703604	+	1.21868i	−0.967193	+	0.254043i	$0.918240\pi$
$992$		0			0
$993$	888.140	+	497.578i	0.894401	+	0.501085i
$994$		0			0
$995$	−705.307	−	840.552i	−0.708851	−	0.844776i
$996$		0			0
$997$	−947.882	+	345.001i	−0.950734	+	0.346039i	−0.770396	−	0.637566i	$-0.779941\pi$
$997$	−947.882	+	345.001i	−0.950734	+	0.346039i	−0.180338	+	0.983605i	$0.557719\pi$
$998$		0			0
$999$	−755.332	−	397.884i	−0.756088	−	0.398282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.a.209.5		30
4.3	odd	2		27.3.f.a.20.5	✓	30
12.11	even	2		81.3.f.a.62.1		30
27.23	odd	18	inner	432.3.bc.a.401.5		30
36.7	odd	6		243.3.f.c.107.5		30
36.11	even	6		243.3.f.b.107.1		30
36.23	even	6		243.3.f.a.26.5		30
36.31	odd	6		243.3.f.d.26.1		30
108.23	even	18		27.3.f.a.23.5	yes	30
108.31	odd	18		81.3.f.a.17.1		30
108.59	even	18		243.3.f.d.215.1		30
108.67	odd	18		243.3.f.b.134.1		30
108.79	odd	18		729.3.b.a.728.5		30
108.83	even	18		729.3.b.a.728.26		30
108.95	even	18		243.3.f.c.134.5		30
108.103	odd	18		243.3.f.a.215.5		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.5	✓	30	4.3	odd	2
27.3.f.a.23.5	yes	30	108.23	even	18
81.3.f.a.17.1		30	108.31	odd	18
81.3.f.a.62.1		30	12.11	even	2
243.3.f.a.26.5		30	36.23	even	6
243.3.f.a.215.5		30	108.103	odd	18
243.3.f.b.107.1		30	36.11	even	6
243.3.f.b.134.1		30	108.67	odd	18
243.3.f.c.107.5		30	36.7	odd	6
243.3.f.c.134.5		30	108.95	even	18
243.3.f.d.26.1		30	36.31	odd	6
243.3.f.d.215.1		30	108.59	even	18
432.3.bc.a.209.5		30	1.1	even	1	trivial
432.3.bc.a.401.5		30	27.23	odd	18	inner
729.3.b.a.728.5		30	108.79	odd	18
729.3.b.a.728.26		30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.94744 - 0.559079i) q^{3} +(6.15614 - 1.08549i) q^{5} +(6.21846 + 5.21791i) q^{7} +(8.37486 - 3.29571i) q^{9} +(7.99059 + 1.40896i) q^{11} +(-9.12402 - 3.32087i) q^{13} +(17.5380 - 6.64120i) q^{15} +(-13.0143 + 7.51380i) q^{17} +(-8.93226 + 15.4711i) q^{19} +(21.2458 + 11.9029i) q^{21} +(-16.9268 - 20.1726i) q^{23} +(13.2275 - 4.81440i) q^{25} +(22.8419 - 14.3961i) q^{27} +(5.18906 + 14.2568i) q^{29} +(-25.0755 + 21.0408i) q^{31} +(24.3395 - 0.314547i) q^{33} +(43.9457 + 25.3721i) q^{35} +(-15.8096 - 27.3831i) q^{37} +(-28.7492 - 4.68704i) q^{39} +(5.65018 - 15.5238i) q^{41} +(14.5559 - 82.5505i) q^{43} +(47.9794 - 29.3797i) q^{45} +(-8.46562 + 10.0889i) q^{47} +(2.93393 + 16.6391i) q^{49} +(-34.1581 + 29.4225i) q^{51} +25.7140i q^{53} +50.7206 q^{55} +(-17.6778 + 50.5941i) q^{57} +(22.3660 - 3.94373i) q^{59} +(26.1131 + 21.9115i) q^{61} +(69.2755 + 23.2050i) q^{63} +(-59.7736 - 10.5397i) q^{65} +(7.61567 + 2.77188i) q^{67} +(-61.1690 - 49.9942i) q^{69} +(-35.7557 + 20.6436i) q^{71} +(40.4046 - 69.9827i) q^{73} +(36.2956 - 21.5854i) q^{75} +(42.3374 + 50.4557i) q^{77} +(-25.9652 + 9.45057i) q^{79} +(59.2766 - 55.2022i) q^{81} +(6.01607 + 16.5290i) q^{83} +(-71.9616 + 60.3830i) q^{85} +(23.2652 + 39.1201i) q^{87} +(24.4986 + 14.1443i) q^{89} +(-39.4094 - 68.2590i) q^{91} +(-62.1451 + 76.0358i) q^{93} +(-38.1945 + 104.938i) q^{95} +(29.2825 - 166.069i) q^{97} +(71.5636 - 14.5348i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37}+ \cdots - 513 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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