LMFDB - Embedded newform 432.3.bc.a.209.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,3,Mod(65,432)]

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

lf = mfeigenbasis(mf)

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")

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

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			209.4
Character	$\chi$	$=$	432.209
Dual form			432.3.bc.a.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.15873 + 2.08324i) q^{3} +(-0.0496479 + 0.00875427i) q^{5} +(-7.55168 - 6.33661i) q^{7} +(0.320214 + 8.99430i) q^{9} +(-12.0681 - 2.12794i) q^{11} +(-11.4873 - 4.18103i) q^{13} +(-0.125414 - 0.0845305i) q^{15} +(-12.7914 + 7.38513i) q^{17} +(-6.26584 + 10.8527i) q^{19} +(-3.10133 - 29.4110i) q^{21} +(-5.93322 - 7.07093i) q^{23} +(-23.4899 + 8.54963i) q^{25} +(-18.0460 + 20.0833i) q^{27} +(15.1728 + 41.6870i) q^{29} +(24.2140 - 20.3180i) q^{31} +(-21.6188 - 29.7345i) q^{33} +(0.430398 + 0.248490i) q^{35} +(-7.19801 - 12.4673i) q^{37} +(-16.0878 - 32.9565i) q^{39} +(23.5871 - 64.8050i) q^{41} +(-7.01983 + 39.8114i) q^{43} +(-0.0946365 - 0.443745i) q^{45} +(-1.24938 + 1.48895i) q^{47} +(8.36645 + 47.4485i) q^{49} +(-42.9982 - 10.7051i) q^{51} -47.7390i q^{53} +0.617787 q^{55} +(-36.1351 + 10.3749i) q^{57} +(72.6161 - 12.8042i) q^{59} +(-4.54441 - 3.81321i) q^{61} +(54.5752 - 69.9511i) q^{63} +(0.606922 + 0.107017i) q^{65} +(-45.8583 - 16.6910i) q^{67} +(1.92225 - 27.6245i) q^{69} +(8.61519 - 4.97398i) q^{71} +(-44.2472 + 76.6383i) q^{73} +(-68.5193 - 30.4788i) q^{75} +(77.6508 + 92.5406i) q^{77} +(-105.233 + 38.3016i) q^{79} +(-80.7949 + 5.76021i) q^{81} +(6.65732 + 18.2908i) q^{83} +(0.570416 - 0.478636i) q^{85} +(-54.0900 + 121.599i) q^{87} +(-33.9430 - 19.5970i) q^{89} +(60.2547 + 104.364i) q^{91} +(94.5988 + 6.58266i) q^{93} +(0.216078 - 0.593669i) q^{95} +(-0.0670785 + 0.380421i) q^{97} +(15.2749 - 109.226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.15873	+	2.08324i	0.719576	+	0.694414i
$3$	2.15873	+	2.08324i	0.719576	+	0.694414i
$4$		0			0
$5$	−0.0496479	+	0.00875427i	−0.00992959	+	0.00175085i	−0.178611	−	0.983920i	$-0.557160\pi$
$5$	−0.0496479	+	0.00875427i	−0.00992959	+	0.00175085i	0.168681	+	0.985671i	$0.446049\pi$
$6$		0			0
$7$	−7.55168	−	6.33661i	−1.07881	−	0.905230i	−0.0829894	−	0.996550i	$-0.526447\pi$
$7$	−7.55168	−	6.33661i	−1.07881	−	0.905230i	−0.995822	+	0.0913206i	$0.970891\pi$
$8$		0			0
$9$	0.320214	+	8.99430i	0.0355794	+	0.999367i
$10$		0			0
$11$	−12.0681	−	2.12794i	−1.09710	−	0.193449i	−0.404337	−	0.914610i	$-0.632498\pi$
$11$	−12.0681	−	2.12794i	−1.09710	−	0.193449i	−0.692767	+	0.721161i	$0.743609\pi$
$12$		0			0
$13$	−11.4873	−	4.18103i	−0.883637	−	0.321618i	−0.139961	−	0.990157i	$-0.544698\pi$
$13$	−11.4873	−	4.18103i	−0.883637	−	0.321618i	−0.743677	+	0.668539i	$0.766920\pi$
$14$		0			0
$15$	−0.125414	−	0.0845305i	−0.00836091	−	0.00563537i
$16$		0			0
$17$	−12.7914	+	7.38513i	−0.752436	+	0.434419i	−0.826574	−	0.562829i	$-0.809713\pi$
$17$	−12.7914	+	7.38513i	−0.752436	+	0.434419i	0.0741373	+	0.997248i	$0.476380\pi$
$18$		0			0
$19$	−6.26584	+	10.8527i	−0.329781	+	0.571197i	−0.982468	−	0.186430i	$-0.940308\pi$
$19$	−6.26584	+	10.8527i	−0.329781	+	0.571197i	0.652687	+	0.757627i	$0.273642\pi$
$20$		0			0
$21$	−3.10133	−	29.4110i	−0.147683	−	1.40052i
$22$		0			0
$23$	−5.93322	−	7.07093i	−0.257966	−	0.307432i	0.621481	−	0.783430i	$-0.286531\pi$
$23$	−5.93322	−	7.07093i	−0.257966	−	0.307432i	−0.879446	+	0.475998i	$0.842087\pi$
$24$		0			0
$25$	−23.4899	+	8.54963i	−0.939597	+	0.341985i
$26$		0			0
$27$	−18.0460	+	20.0833i	−0.668372	+	0.743827i
$28$		0			0
$29$	15.1728	+	41.6870i	0.523200	+	1.43748i	0.866938	+	0.498416i	$0.166085\pi$
$29$	15.1728	+	41.6870i	0.523200	+	1.43748i	−0.343738	+	0.939066i	$0.611693\pi$
$30$		0			0
$31$	24.2140	−	20.3180i	0.781098	−	0.655419i	−0.162427	−	0.986721i	$-0.551932\pi$
$31$	24.2140	−	20.3180i	0.781098	−	0.655419i	0.943525	+	0.331301i	$0.107488\pi$
$32$		0			0
$33$	−21.6188	−	29.7345i	−0.655116	−	0.901045i
$34$		0			0
$35$	0.430398	+	0.248490i	0.0122971	+	0.00709972i
$36$		0			0
$37$	−7.19801	−	12.4673i	−0.194541	−	0.336954i	0.752209	−	0.658924i	$-0.228988\pi$
$37$	−7.19801	−	12.4673i	−0.194541	−	0.336954i	−0.946750	+	0.321970i	$0.895655\pi$
$38$		0			0
$39$	−16.0878	−	32.9565i	−0.412508	−	0.845038i
$40$		0			0
$41$	23.5871	−	64.8050i	0.575295	−	1.58061i	−0.220724	−	0.975336i	$-0.570842\pi$
$41$	23.5871	−	64.8050i	0.575295	−	1.58061i	0.796018	−	0.605273i	$-0.206936\pi$
$42$		0			0
$43$	−7.01983	+	39.8114i	−0.163252	+	0.925847i	0.787597	+	0.616191i	$0.211325\pi$
$43$	−7.01983	+	39.8114i	−0.163252	+	0.925847i	−0.950849	+	0.309656i	$0.899786\pi$
$44$		0			0
$45$	−0.0946365	−	0.443745i	−0.00210303	−	0.00986101i
$46$		0			0
$47$	−1.24938	+	1.48895i	−0.0265825	+	0.0316797i	−0.779172	−	0.626810i	$-0.784360\pi$
$47$	−1.24938	+	1.48895i	−0.0265825	+	0.0316797i	0.752589	+	0.658490i	$0.228805\pi$
$48$		0			0
$49$	8.36645	+	47.4485i	0.170744	+	0.968336i
$50$		0			0
$51$	−42.9982	−	10.7051i	−0.843102	−	0.209904i
$52$		0			0
$53$		−	47.7390i		−	0.900736i	−0.892843	−	0.450368i	$-0.851293\pi$
$53$		−	47.7390i		−	0.900736i	0.892843	−	0.450368i	$-0.148707\pi$
$54$		0			0
$55$	0.617787			0.0112325
$56$		0			0
$57$	−36.1351	+	10.3749i	−0.633950	+	0.182016i
$58$		0			0
$59$	72.6161	−	12.8042i	1.23078	−	0.217020i	0.479821	−	0.877367i	$-0.340702\pi$
$59$	72.6161	−	12.8042i	1.23078	−	0.217020i	0.750961	+	0.660347i	$0.229591\pi$
$60$		0			0
$61$	−4.54441	−	3.81321i	−0.0744986	−	0.0625117i	0.604778	−	0.796394i	$-0.293262\pi$
$61$	−4.54441	−	3.81321i	−0.0744986	−	0.0625117i	−0.679277	+	0.733882i	$0.737706\pi$
$62$		0			0
$63$	54.5752	−	69.9511i	0.866273	−	1.11034i
$64$		0			0
$65$	0.606922	+	0.107017i	0.00933726	+	0.00164641i
$66$		0			0
$67$	−45.8583	−	16.6910i	−0.684452	−	0.249120i	−0.0236939	−	0.999719i	$-0.507543\pi$
$67$	−45.8583	−	16.6910i	−0.684452	−	0.249120i	−0.660758	+	0.750599i	$0.729765\pi$
$68$		0			0
$69$	1.92225	−	27.6245i	0.0278587	−	0.400356i
$70$		0			0
$71$	8.61519	−	4.97398i	0.121341	−	0.0700561i	−0.438101	−	0.898926i	$-0.644349\pi$
$71$	8.61519	−	4.97398i	0.121341	−	0.0700561i	0.559442	+	0.828870i	$0.311016\pi$
$72$		0			0
$73$	−44.2472	+	76.6383i	−0.606126	+	1.04984i	0.385747	+	0.922605i	$0.373944\pi$
$73$	−44.2472	+	76.6383i	−0.606126	+	1.04984i	−0.991873	+	0.127236i	$0.959390\pi$
$74$		0			0
$75$	−68.5193	−	30.4788i	−0.913591	−	0.406385i
$76$		0			0
$77$	77.6508	+	92.5406i	1.00845	+	1.20183i
$78$		0			0
$79$	−105.233	+	38.3016i	−1.33206	+	0.484831i	−0.907304	−	0.420476i	$-0.861863\pi$
$79$	−105.233	+	38.3016i	−1.33206	+	0.484831i	−0.424758	+	0.905307i	$0.639641\pi$
$80$		0			0
$81$	−80.7949	+	5.76021i	−0.997468	+	0.0711137i
$82$		0			0
$83$	6.65732	+	18.2908i	0.0802087	+	0.220371i	0.973315	−	0.229475i	$-0.0737009\pi$
$83$	6.65732	+	18.2908i	0.0802087	+	0.220371i	−0.893106	+	0.449846i	$0.851479\pi$
$84$		0			0
$85$	0.570416	−	0.478636i	0.00671078	−	0.00563101i
$86$		0			0
$87$	−54.0900	+	121.599i	−0.621724	+	1.39769i
$88$		0			0
$89$	−33.9430	−	19.5970i	−0.381382	−	0.220191i	0.297037	−	0.954866i	$-0.404001\pi$
$89$	−33.9430	−	19.5970i	−0.381382	−	0.220191i	−0.678419	+	0.734675i	$0.737335\pi$
$90$		0			0
$91$	60.2547	+	104.364i	0.662140	+	1.14686i
$92$		0			0
$93$	94.5988	+	6.58266i	1.01719	+	0.0707813i
$94$		0			0
$95$	0.216078	−	0.593669i	0.00227451	−	0.00624915i
$96$		0			0
$97$	−0.0670785	+	0.380421i	−0.000691531	+	0.00392187i	−0.985152	−	0.171687i	$-0.945078\pi$
$97$	−0.0670785	+	0.380421i	−0.000691531	+	0.00392187i	0.984460	+	0.175609i	$0.0561894\pi$
$98$		0			0
$99$	15.2749	−	109.226i	0.154292	−	1.10329i
$100$		0			0
$101$	30.6686	−	36.5494i	0.303649	−	0.361875i	−0.592545	−	0.805538i	$-0.701877\pi$
$101$	30.6686	−	36.5494i	0.303649	−	0.361875i	0.896194	+	0.443662i	$0.146321\pi$
$102$		0			0
$103$	3.18310	+	18.0523i	0.0309039	+	0.175265i	0.996353	−	0.0853269i	$-0.0271935\pi$
$103$	3.18310	+	18.0523i	0.0309039	+	0.175265i	−0.965449	+	0.260592i	$0.916082\pi$
$104$		0			0
$105$	0.411447	+	1.43304i	0.00391854	+	0.0136480i
$106$		0			0
$107$		−	68.8842i		−	0.643778i	−0.946777	−	0.321889i	$-0.895682\pi$
$107$		−	68.8842i		−	0.643778i	0.946777	−	0.321889i	$-0.104318\pi$
$108$		0			0
$109$	9.57392			0.0878341			0.0439171	−	0.999035i	$-0.486016\pi$
$109$	9.57392			0.0878341			0.0439171	+	0.999035i	$0.486016\pi$
$110$		0			0
$111$	10.4339	−	41.9087i	0.0939989	−	0.377556i
$112$		0			0
$113$	0.497499	−	0.0877225i	0.00440265	−	0.000776306i	−0.171446	−	0.985193i	$-0.554844\pi$
$113$	0.497499	−	0.0877225i	0.00440265	−	0.000776306i	0.175849	+	0.984417i	$0.443733\pi$
$114$		0			0
$115$	0.356473	+	0.299116i	0.00309976	+	0.00260101i
$116$		0			0
$117$	33.9270	−	104.659i	0.289975	−	0.894521i
$118$		0			0
$119$	143.393	+	25.2841i	1.20499	+	0.212472i
$120$		0			0
$121$	27.4091	+	9.97611i	0.226522	+	0.0824472i
$122$		0			0
$123$	185.922	−	90.7587i	1.51156	−	0.737876i
$124$		0			0
$125$	2.18287	−	1.26028i	0.0174630	−	0.0100823i
$126$		0			0
$127$	−52.2761	+	90.5449i	−0.411623	+	0.712952i	−0.995067	−	0.0992011i	$-0.968371\pi$
$127$	−52.2761	+	90.5449i	−0.411623	+	0.712952i	0.583444	+	0.812153i	$0.301705\pi$
$128$		0			0
$129$	−98.0907	+	71.3181i	−0.760393	+	0.552853i
$130$		0			0
$131$	129.652	+	154.513i	0.989709	+	1.17949i	0.983757	+	0.179507i	$0.0574502\pi$
$131$	129.652	+	154.513i	0.989709	+	1.17949i	0.00595223	+	0.999982i	$0.498105\pi$
$132$		0			0
$133$	116.087	−	42.2523i	0.872836	−	0.317686i
$134$		0			0
$135$	0.720134	−	1.15508i	0.00533432	−	0.00855612i
$136$		0			0
$137$	66.3180	+	182.207i	0.484073	+	1.32998i	0.905972	+	0.423338i	$0.139142\pi$
$137$	66.3180	+	182.207i	0.484073	+	1.32998i	−0.421899	+	0.906643i	$0.638636\pi$
$138$		0			0
$139$	−22.0112	+	18.4696i	−0.158354	+	0.132875i	−0.718522	−	0.695504i	$-0.755181\pi$
$139$	−22.0112	+	18.4696i	−0.158354	+	0.132875i	0.560168	+	0.828379i	$0.310737\pi$
$140$		0			0
$141$	−5.79890	+	0.611483i	−0.0411269	+	0.00433676i
$142$		0			0
$143$	129.733	+	74.9015i	0.907225	+	0.523787i
$144$		0			0
$145$	−1.11824	−	1.93684i	−0.00771199	−	0.0133575i
$146$		0			0
$147$	−80.7857	+	119.858i	−0.549563	+	0.815358i
$148$		0			0
$149$	85.1055	−	233.825i	0.571178	−	1.56930i	−0.231469	−	0.972842i	$-0.574353\pi$
$149$	85.1055	−	233.825i	0.571178	−	1.56930i	0.802646	−	0.596455i	$-0.203425\pi$
$150$		0			0
$151$	25.3887	−	143.986i	0.168137	−	0.953552i	−0.777634	−	0.628717i	$-0.783580\pi$
$151$	25.3887	−	143.986i	0.168137	−	0.953552i	0.945771	−	0.324835i	$-0.105309\pi$
$152$		0			0
$153$	−70.5201	−	112.685i	−0.460915	−	0.736503i
$154$		0			0
$155$	−1.02431	+	1.22072i	−0.00660844	+	0.00787563i
$156$		0			0
$157$	18.0884	+	102.584i	0.115213	+	0.653403i	0.986645	+	0.162887i	$0.0520805\pi$
$157$	18.0884	+	102.584i	0.115213	+	0.653403i	−0.871432	+	0.490516i	$0.836808\pi$
$158$		0			0
$159$	99.4519	−	103.056i	0.625484	−	0.648148i
$160$		0			0
$161$			90.9939i			0.565179i
$162$		0			0
$163$	−126.261			−0.774609			−0.387304	−	0.921952i	$-0.626594\pi$
$163$	−126.261			−0.774609			−0.387304	+	0.921952i	$0.626594\pi$
$164$		0			0
$165$	1.33363	+	1.28700i	0.00808263	+	0.00779999i
$166$		0			0
$167$	−240.870	+	42.4718i	−1.44233	+	0.254322i	−0.839420	−	0.543484i	$-0.817105\pi$
$167$	−240.870	+	42.4718i	−1.44233	+	0.254322i	−0.602914	+	0.797806i	$0.705994\pi$
$168$		0			0
$169$	−14.9848	−	12.5738i	−0.0886676	−	0.0744010i
$170$		0			0
$171$	−99.6193	−	52.8816i	−0.582569	−	0.309249i
$172$		0			0
$173$	90.5467	+	15.9658i	0.523391	+	0.0922880i	0.429101	−	0.903257i	$-0.358831\pi$
$173$	90.5467	+	15.9658i	0.523391	+	0.0922880i	0.0942906	+	0.995545i	$0.469942\pi$
$174$		0			0
$175$	231.564	+	84.2824i	1.32322	+	0.481614i
$176$		0			0
$177$	183.433	+	123.636i	1.03634	+	0.698509i
$178$		0			0
$179$	54.8413	−	31.6626i	0.306376	−	0.176886i	−0.338928	−	0.940812i	$-0.610064\pi$
$179$	54.8413	−	31.6626i	0.306376	−	0.176886i	0.645304	+	0.763926i	$0.276731\pi$
$180$		0			0
$181$	−77.4956	+	134.226i	−0.428153	+	0.741582i	−0.996709	−	0.0810622i	$-0.974169\pi$
$181$	−77.4956	+	134.226i	−0.428153	+	0.741582i	0.568556	+	0.822644i	$0.307502\pi$
$182$		0			0
$183$	−1.86631	−	17.6988i	−0.0101984	−	0.0967147i
$184$		0			0
$185$	0.466509	+	0.555963i	0.00252167	+	0.00300521i
$186$		0			0
$187$	170.084	−	61.9054i	0.909539	−	0.331045i
$188$		0			0
$189$	263.538	−	37.3122i	1.39438	−	0.197419i
$190$		0			0
$191$	−19.6000	−	53.8506i	−0.102618	−	0.281940i	0.877750	−	0.479120i	$-0.159044\pi$
$191$	−19.6000	−	53.8506i	−0.102618	−	0.281940i	−0.980367	+	0.197179i	$0.936822\pi$
$192$		0			0
$193$	−7.03809	+	5.90566i	−0.0364668	+	0.0305993i	−0.660839	−	0.750528i	$-0.729799\pi$
$193$	−7.03809	+	5.90566i	−0.0364668	+	0.0305993i	0.624372	+	0.781127i	$0.285355\pi$
$194$		0			0
$195$	1.08724	+	1.49538i	0.00557558	+	0.00766864i
$196$		0			0
$197$	71.8373	+	41.4753i	0.364657	+	0.210535i	0.671121	−	0.741347i	$-0.265813\pi$
$197$	71.8373	+	41.4753i	0.364657	+	0.210535i	−0.306465	+	0.951882i	$0.599146\pi$
$198$		0			0
$199$	18.3108	+	31.7153i	0.0920141	+	0.159373i	0.908359	−	0.418192i	$-0.137336\pi$
$199$	18.3108	+	31.7153i	0.0920141	+	0.159373i	−0.816344	+	0.577565i	$0.804003\pi$
$200$		0			0
$201$	−64.2241	−	131.565i	−0.319523	−	0.654553i
$202$		0			0
$203$	149.574	−	410.951i	0.736817	−	2.02439i
$204$		0			0
$205$	−0.603730	+	3.42392i	−0.00294502	+	0.0167021i
$206$		0			0
$207$	61.6982	−	55.6294i	0.298059	−	0.268741i
$208$		0			0
$209$	98.7110	−	117.639i	0.472301	−	0.562867i
$210$		0			0
$211$	53.6264	+	304.130i	0.254154	+	1.44138i	0.798236	+	0.602345i	$0.205767\pi$
$211$	53.6264	+	304.130i	0.254154	+	1.44138i	−0.544083	+	0.839032i	$0.683122\pi$
$212$		0			0
$213$	28.9599	+	7.21004i	0.135962	+	0.0338500i
$214$		0			0
$215$		−	2.03801i		−	0.00947911i
$216$		0			0
$217$	−311.604			−1.43596
$218$		0			0
$219$	−255.174	+	73.2638i	−1.16518	+	0.334538i
$220$		0			0
$221$	177.816	−	31.3538i	0.804598	−	0.141872i
$222$		0			0
$223$	−237.313	−	199.130i	−1.06419	−	0.892958i	−0.0696724	−	0.997570i	$-0.522195\pi$
$223$	−237.313	−	199.130i	−1.06419	−	0.892958i	−0.994513	+	0.104612i	$0.966640\pi$
$224$		0			0
$225$	−84.4198	−	208.538i	−0.375199	−	0.926835i
$226$		0			0
$227$	164.338	+	28.9773i	0.723957	+	0.127653i	0.523471	−	0.852044i	$-0.324637\pi$
$227$	164.338	+	28.9773i	0.723957	+	0.127653i	0.200486	+	0.979697i	$0.435748\pi$
$228$		0			0
$229$	218.452	+	79.5101i	0.953939	+	0.347206i	0.771656	−	0.636040i	$-0.219429\pi$
$229$	218.452	+	79.5101i	0.953939	+	0.347206i	0.182284	+	0.983246i	$0.441651\pi$
$230$		0			0
$231$	−25.1574	+	361.535i	−0.108907	+	1.56509i
$232$		0			0
$233$	−98.2315	+	56.7140i	−0.421594	+	0.243408i	−0.695759	−	0.718275i	$-0.744932\pi$
$233$	−98.2315	+	56.7140i	−0.421594	+	0.243408i	0.274165	+	0.961683i	$0.411599\pi$
$234$		0			0
$235$	0.0489943	−	0.0848606i	0.000208486	−	0.000361109i
$236$		0			0
$237$	−306.961	−	136.543i	−1.29519	−	0.576129i
$238$		0			0
$239$	22.6159	+	26.9525i	0.0946270	+	0.112772i	0.811280	−	0.584658i	$-0.198771\pi$
$239$	22.6159	+	26.9525i	0.0946270	+	0.112772i	−0.716653	+	0.697430i	$0.754327\pi$
$240$		0			0
$241$	−240.771	+	87.6335i	−0.999050	+	0.363624i	−0.789218	−	0.614113i	$-0.789514\pi$
$241$	−240.771	+	87.6335i	−0.999050	+	0.363624i	−0.209832	+	0.977737i	$0.567292\pi$
$242$		0			0
$243$	−186.414	−	155.881i	−0.767137	−	0.641484i
$244$		0			0
$245$	−0.830753	−	2.28248i	−0.00339083	−	0.00931623i
$246$		0			0
$247$	117.353	−	98.4709i	0.475114	−	0.398668i
$248$		0			0
$249$	−23.7329	+	53.3537i	−0.0953127	+	0.214272i
$250$		0			0
$251$	−339.228	−	195.854i	−1.35151	−	0.780293i	−0.363046	−	0.931771i	$-0.618263\pi$
$251$	−339.228	−	195.854i	−1.35151	−	0.780293i	−0.988461	+	0.151478i	$0.951597\pi$
$252$		0			0
$253$	56.5564	+	97.9585i	0.223543	+	0.387188i
$254$		0			0
$255$	2.22849	+	0.155069i	0.00873916	+	0.000608115i
$256$		0			0
$257$	−97.6997	+	268.428i	−0.380155	+	1.04447i	0.591136	+	0.806572i	$0.298680\pi$
$257$	−97.6997	+	268.428i	−0.380155	+	1.04447i	−0.971291	+	0.237895i	$0.923543\pi$
$258$		0			0
$259$	−24.6435	+	139.760i	−0.0951486	+	0.539614i
$260$		0			0
$261$	−370.087	+	149.818i	−1.41796	+	0.574014i
$262$		0			0
$263$	−290.740	+	346.490i	−1.10547	+	1.31745i	−0.161709	+	0.986838i	$0.551701\pi$
$263$	−290.740	+	346.490i	−1.10547	+	1.31745i	−0.943766	+	0.330615i	$0.892744\pi$
$264$		0			0
$265$	0.417920	+	2.37014i	0.00157706	+	0.00894394i
$266$		0			0
$267$	−32.4484	−	113.016i	−0.121530	−	0.423281i
$268$		0			0
$269$		−	277.616i		−	1.03203i	−0.856580	−	0.516014i	$-0.827415\pi$
$269$		−	277.616i		−	1.03203i	0.856580	−	0.516014i	$-0.172585\pi$
$270$		0			0
$271$	−310.311			−1.14506			−0.572530	−	0.819884i	$-0.694038\pi$
$271$	−310.311			−1.14506			−0.572530	+	0.819884i	$0.694038\pi$
$272$		0			0
$273$	−87.3423	+	350.819i	−0.319935	+	1.28505i
$274$		0			0
$275$	301.673	−	53.1931i	1.09699	−	0.193429i
$276$		0			0
$277$	−263.622	−	221.206i	−0.951706	−	0.798576i	0.0278782	−	0.999611i	$-0.491125\pi$
$277$	−263.622	−	221.206i	−0.951706	−	0.798576i	−0.979584	+	0.201035i	$0.935569\pi$
$278$		0			0
$279$	190.500	+	211.282i	0.682795	+	0.757284i
$280$		0			0
$281$	−433.676	−	76.4687i	−1.54333	−	0.272131i	−0.663776	−	0.747931i	$-0.731047\pi$
$281$	−433.676	−	76.4687i	−1.54333	−	0.272131i	−0.879553	+	0.475801i	$0.842158\pi$
$282$		0			0
$283$	14.0232	+	5.10404i	0.0495521	+	0.0180355i	0.366677	−	0.930348i	$-0.380495\pi$
$283$	14.0232	+	5.10404i	0.0495521	+	0.0180355i	−0.317125	+	0.948384i	$0.602718\pi$
$284$		0			0
$285$	1.70321	−	0.831428i	0.00597618	−	0.00291729i
$286$		0			0
$287$	−588.766	+	339.924i	−2.05145	+	1.18440i
$288$		0			0
$289$	−35.4198	+	61.3489i	−0.122560	+	0.212280i
$290$		0			0
$291$	−0.937313	+	0.681485i	−0.00322101	+	0.00234187i
$292$		0			0
$293$	−104.147	−	124.118i	−0.355451	−	0.423610i	0.558456	−	0.829534i	$-0.311394\pi$
$293$	−104.147	−	124.118i	−0.355451	−	0.423610i	−0.913907	+	0.405924i	$0.866950\pi$
$294$		0			0
$295$	−3.49315	+	1.27140i	−0.0118412	+	0.00430984i
$296$		0			0
$297$	260.518	−	203.968i	0.877166	−	0.686760i
$298$		0			0
$299$	38.5928	+	106.033i	0.129073	+	0.354625i
$300$		0			0
$301$	305.281	−	256.161i	1.01422	−	0.851034i
$302$		0			0
$303$	142.346	−	15.0102i	0.469790	−	0.0495385i
$304$		0			0
$305$	0.259003	+	0.149535i	0.000849189	+	0.000490279i
$306$		0			0
$307$	−69.5247	−	120.420i	−0.226465	−	0.392248i	0.730293	−	0.683134i	$-0.239383\pi$
$307$	−69.5247	−	120.420i	−0.226465	−	0.392248i	−0.956758	+	0.290886i	$0.906050\pi$
$308$		0			0
$309$	−30.7358	+	45.6011i	−0.0994686	+	0.147576i
$310$		0			0
$311$	61.7283	−	169.597i	0.198483	−	0.545328i	−0.800023	−	0.599970i	$-0.795179\pi$
$311$	61.7283	−	169.597i	0.198483	−	0.545328i	0.998506	+	0.0546413i	$0.0174015\pi$
$312$		0			0
$313$	100.622	−	570.654i	0.321475	−	1.82317i	−0.211895	−	0.977292i	$-0.567963\pi$
$313$	100.622	−	570.654i	0.321475	−	1.82317i	0.533370	−	0.845882i	$-0.320925\pi$
$314$		0			0
$315$	−2.09718	+	3.95070i	−0.00665770	+	0.0125419i
$316$		0			0
$317$	−324.996	+	387.315i	−1.02522	+	1.22181i	−0.0504239	+	0.998728i	$0.516057\pi$
$317$	−324.996	+	387.315i	−1.02522	+	1.22181i	−0.974799	+	0.223085i	$0.928387\pi$
$318$		0			0
$319$	−94.4004	−	535.371i	−0.295926	−	1.67828i
$320$		0			0
$321$	143.502	−	148.702i	0.447048	−	0.463247i
$322$		0			0
$323$		−	185.096i		−	0.573053i
$324$		0			0
$325$	305.582			0.940251
$326$		0			0
$327$	20.6675	+	19.9448i	0.0632033	+	0.0609932i
$328$		0			0
$329$	18.8698	−	3.32725i	0.0573549	−	0.0101132i
$330$		0			0
$331$	173.811	+	145.845i	0.525108	+	0.440618i	0.866408	−	0.499336i	$-0.166423\pi$
$331$	173.811	+	145.845i	0.525108	+	0.440618i	−0.341300	+	0.939954i	$0.610867\pi$
$332$		0			0
$333$	109.830	−	68.7333i	0.329820	−	0.206406i
$334$		0			0
$335$	2.42289	+	0.427220i	0.00723250	+	0.00127528i
$336$		0			0
$337$	90.1787	+	32.8224i	0.267593	+	0.0973957i	0.472332	−	0.881421i	$-0.343412\pi$
$337$	90.1787	+	32.8224i	0.267593	+	0.0973957i	−0.204739	+	0.978817i	$0.565635\pi$
$338$		0			0
$339$	1.25671	+	0.847042i	0.00370712	+	0.00249865i
$340$		0			0
$341$	−335.454	+	193.674i	−0.983736	+	0.567960i
$342$		0			0
$343$	−4.03963	+	6.99685i	−0.0117774	+	0.0203990i
$344$		0			0
$345$	0.146397	+	1.38833i	0.000424339	+	0.00402414i
$346$		0			0
$347$	−166.349	−	198.247i	−0.479393	−	0.571318i	0.471094	−	0.882083i	$-0.343859\pi$
$347$	−166.349	−	198.247i	−0.479393	−	0.571318i	−0.950487	+	0.310765i	$0.899415\pi$
$348$		0			0
$349$	−258.307	+	94.0161i	−0.740135	+	0.269387i	−0.684448	−	0.729061i	$-0.739957\pi$
$349$	−258.307	+	94.0161i	−0.740135	+	0.269387i	−0.0556864	+	0.998448i	$0.517735\pi$
$350$		0			0
$351$	291.269	−	155.252i	0.829826	−	0.442313i
$352$		0			0
$353$	90.5211	+	248.705i	0.256434	+	0.704545i	0.999380	+	0.0351951i	$0.0112053\pi$
$353$	90.5211	+	248.705i	0.256434	+	0.704545i	−0.742947	+	0.669350i	$0.766573\pi$
$354$		0			0
$355$	−0.384183	+	0.322368i	−0.00108221	+	0.000908078i
$356$		0			0
$357$	256.874	+	353.304i	0.719536	+	0.989648i
$358$		0			0
$359$	−183.469	−	105.926i	−0.511055	−	0.295058i	0.222212	−	0.974998i	$-0.428672\pi$
$359$	−183.469	−	105.926i	−0.511055	−	0.295058i	−0.733267	+	0.679941i	$0.762006\pi$
$360$		0			0
$361$	101.979	+	176.632i	0.282489	+	0.489286i
$362$		0			0
$363$	38.3862	+	78.6355i	0.105747	+	0.216627i
$364$		0			0
$365$	1.52587	−	4.19229i	0.00418046	−	0.0114857i
$366$		0			0
$367$	112.035	−	635.384i	0.305273	−	1.73129i	−0.316943	−	0.948445i	$-0.602656\pi$
$367$	112.035	−	635.384i	0.305273	−	1.73129i	0.622216	−	0.782846i	$-0.286233\pi$
$368$		0			0
$369$	590.428	+	191.398i	1.60008	+	0.518693i
$370$		0			0
$371$	−302.504	+	360.510i	−0.815373	+	0.971724i
$372$		0			0
$373$	−122.107	−	692.506i	−0.327366	−	1.85658i	−0.492499	−	0.870313i	$-0.663917\pi$
$373$	−122.107	−	692.506i	−0.327366	−	1.85658i	0.165133	−	0.986271i	$-0.447195\pi$
$374$		0			0
$375$	7.33770	+	1.82684i	0.0195672	+	0.00487158i
$376$		0			0
$377$		−	542.308i		−	1.43848i
$378$		0			0
$379$	352.196			0.929278			0.464639	−	0.885500i	$-0.346184\pi$
$379$	352.196			0.929278			0.464639	+	0.885500i	$0.346184\pi$
$380$		0			0
$381$	−301.477	+	86.5581i	−0.791278	+	0.227187i
$382$		0			0
$383$	266.149	−	46.9293i	0.694906	−	0.122531i	0.184972	−	0.982744i	$-0.440781\pi$
$383$	266.149	−	46.9293i	0.694906	−	0.122531i	0.509935	+	0.860213i	$0.329670\pi$
$384$		0			0
$385$	−4.66533	−	3.91467i	−0.0121177	−	0.0101680i
$386$		0			0
$387$	−360.324	−	50.3903i	−0.931070	−	0.130207i
$388$		0			0
$389$	216.727	+	38.2149i	0.557140	+	0.0982388i	0.445126	−	0.895468i	$-0.353159\pi$
$389$	216.727	+	38.2149i	0.557140	+	0.0982388i	0.112014	+	0.993707i	$0.464270\pi$
$390$		0			0
$391$	128.114	+	46.6297i	0.327657	+	0.119257i
$392$		0			0
$393$	−42.0048	+	603.648i	−0.106883	+	1.53600i
$394$		0			0
$395$	4.88929	−	2.82283i	0.0123780	−	0.00714642i
$396$		0			0
$397$	58.0173	−	100.489i	0.146139	−	0.253121i	−0.783658	−	0.621192i	$-0.786649\pi$
$397$	58.0173	−	100.489i	0.146139	−	0.253121i	0.929797	+	0.368072i	$0.119982\pi$
$398$		0			0
$399$	338.622	+	150.626i	0.848678	+	0.377510i
$400$		0			0
$401$	−122.249	−	145.690i	−0.304860	−	0.363317i	0.591764	−	0.806111i	$-0.298432\pi$
$401$	−122.249	−	145.690i	−0.304860	−	0.363317i	−0.896623	+	0.442794i	$0.853987\pi$
$402$		0			0
$403$	−363.104	+	132.159i	−0.901002	+	0.327938i
$404$		0			0
$405$	3.96088	−	0.993283i	0.00977994	−	0.00245255i
$406$		0			0
$407$	60.3369	+	165.774i	0.148248	+	0.407308i
$408$		0			0
$409$	−18.2230	+	15.2909i	−0.0445550	+	0.0373861i	−0.664793	−	0.747027i	$-0.731480\pi$
$409$	−18.2230	+	15.2909i	−0.0445550	+	0.0373861i	0.620238	+	0.784413i	$0.287036\pi$
$410$		0			0
$411$	−236.419	+	531.493i	−0.575229	+	1.29317i
$412$		0			0
$413$	−629.508	−	363.447i	−1.52423	−	0.880017i
$414$		0			0
$415$	−0.490645	−	0.849822i	−0.00118228	−	0.00204776i
$416$		0			0
$417$	−85.9929	−	5.98381i	−0.206218	−	0.0143497i
$418$		0			0
$419$	−117.310	+	322.307i	−0.279977	+	0.769230i	0.717387	+	0.696674i	$0.245338\pi$
$419$	−117.310	+	322.307i	−0.279977	+	0.769230i	−0.997364	+	0.0725558i	$0.976884\pi$
$420$		0			0
$421$	−85.7847	+	486.509i	−0.203764	+	1.15560i	0.695608	+	0.718421i	$0.255135\pi$
$421$	−85.7847	+	486.509i	−0.203764	+	1.15560i	−0.899372	+	0.437183i	$0.855976\pi$
$422$		0			0
$423$	−13.7921	−	10.7605i	−0.0326055	−	0.0254385i
$424$		0			0
$425$	237.329	−	282.838i	0.558422	−	0.665501i
$426$		0			0
$427$	10.1551	+	57.5923i	0.0237824	+	0.134877i
$428$		0			0
$429$	124.021	+	431.957i	0.289093	+	1.00689i
$430$		0			0
$431$		−	519.074i		−	1.20435i	−0.798365	−	0.602174i	$-0.794301\pi$
$431$		−	519.074i		−	1.20435i	0.798365	−	0.602174i	$-0.205699\pi$
$432$		0			0
$433$	290.297			0.670433			0.335216	−	0.942141i	$-0.391191\pi$
$433$	290.297			0.670433			0.335216	+	0.942141i	$0.391191\pi$
$434$		0			0
$435$	1.62094	−	6.51068i	0.00372631	−	0.0149671i
$436$		0			0
$437$	113.916	−	20.0864i	0.260676	−	0.0459643i
$438$		0			0
$439$	−255.941	−	214.760i	−0.583009	−	0.489203i	0.302925	−	0.953015i	$-0.402037\pi$
$439$	−255.941	−	214.760i	−0.583009	−	0.489203i	−0.885934	+	0.463812i	$0.846481\pi$
$440$		0			0
$441$	−424.087	+	90.4440i	−0.961648	+	0.205088i
$442$		0			0
$443$	327.502	+	57.7474i	0.739282	+	0.130355i	0.530593	−	0.847627i	$-0.321969\pi$
$443$	327.502	+	57.7474i	0.739282	+	0.130355i	0.208689	+	0.977982i	$0.433080\pi$
$444$		0			0
$445$	1.85676	+	0.675805i	0.00417249	+	0.00151866i
$446$		0			0
$447$	670.834	−	327.470i	1.50075	−	0.732596i
$448$		0			0
$449$	−291.154	+	168.098i	−0.648449	+	0.374382i	−0.787862	−	0.615852i	$-0.788812\pi$
$449$	−291.154	+	168.098i	−0.648449	+	0.374382i	0.139413	+	0.990234i	$0.455479\pi$
$450$		0			0
$451$	−422.553	+	731.884i	−0.936925	+	1.62280i
$452$		0			0
$453$	354.765	−	257.937i	0.783147	−	0.569396i
$454$		0			0
$455$	−3.90515	−	4.65398i	−0.00858276	−	0.0102285i
$456$		0			0
$457$	746.228	−	271.605i	1.63288	−	0.594321i	0.647110	−	0.762397i	$-0.275977\pi$
$457$	746.228	−	271.605i	1.63288	−	0.594321i	0.985774	+	0.168076i	$0.0537553\pi$
$458$		0			0
$459$	82.5164	−	390.167i	0.179774	−	0.850036i
$460$		0			0
$461$	97.6760	+	268.363i	0.211878	+	0.582131i	0.999417	−	0.0341338i	$-0.0108672\pi$
$461$	97.6760	+	268.363i	0.211878	+	0.582131i	−0.787539	+	0.616265i	$0.788645\pi$
$462$		0			0
$463$	102.894	−	86.3380i	0.222232	−	0.186475i	−0.524873	−	0.851180i	$-0.675887\pi$
$463$	102.894	−	86.3380i	0.222232	−	0.186475i	0.747106	+	0.664705i	$0.231443\pi$
$464$		0			0
$465$	−4.75426	+	0.501328i	−0.0102242	+	0.00107813i
$466$		0			0
$467$	232.832	+	134.426i	0.498570	+	0.287849i	0.728123	−	0.685447i	$-0.240393\pi$
$467$	232.832	+	134.426i	0.498570	+	0.287849i	−0.229553	+	0.973296i	$0.573726\pi$
$468$		0			0
$469$	240.542	+	416.631i	0.512883	+	0.888339i
$470$		0			0
$471$	−174.660	+	259.134i	−0.370828	+	0.550178i
$472$		0			0
$473$	169.433	−	465.512i	0.358209	−	0.984170i
$474$		0			0
$475$	54.3970	−	308.501i	0.114520	−	0.649476i
$476$		0			0
$477$	429.379	−	15.2867i	0.900166	−	0.0320477i
$478$		0			0
$479$	−61.2759	+	73.0257i	−0.127925	+	0.152455i	−0.826205	−	0.563370i	$-0.809505\pi$
$479$	−61.2759	+	73.0257i	−0.127925	+	0.152455i	0.698280	+	0.715825i	$0.253949\pi$
$480$		0			0
$481$	30.5593	+	173.311i	0.0635330	+	0.360313i
$482$		0			0
$483$	−189.562	+	196.431i	−0.392468	+	0.406689i
$484$		0			0
$485$		−	0.0194743i		−	4.01533e-5i
$486$		0			0
$487$	210.939			0.433139			0.216569	−	0.976267i	$-0.430513\pi$
$487$	210.939			0.433139			0.216569	+	0.976267i	$0.430513\pi$
$488$		0			0
$489$	−272.564	−	263.033i	−0.557390	−	0.537899i
$490$		0			0
$491$	588.397	−	103.750i	1.19837	−	0.211304i	0.461373	−	0.887206i	$-0.347357\pi$
$491$	588.397	−	103.750i	1.19837	−	0.211304i	0.736992	+	0.675902i	$0.236246\pi$
$492$		0			0
$493$	−501.945	−	421.182i	−1.01814	−	0.854325i
$494$		0			0
$495$	0.197824	+	5.55656i	0.000399645	+	0.0112254i
$496$		0			0
$497$	−96.5773	−	17.0292i	−0.194321	−	0.0342640i
$498$		0			0
$499$	865.738	+	315.103i	1.73495	+	0.631469i	0.998963	−	0.0455319i	$-0.0144983\pi$
$499$	865.738	+	315.103i	1.73495	+	0.631469i	0.735983	+	0.677000i	$0.236720\pi$
$500$		0			0
$501$	−608.451	−	410.105i	−1.21447	−	0.818572i
$502$		0			0
$503$	−797.759	+	460.587i	−1.58600	+	0.915679i	−0.592046	+	0.805904i	$0.701680\pi$
$503$	−797.759	+	460.587i	−1.58600	+	0.915679i	−0.993956	+	0.109775i	$0.964987\pi$
$504$		0			0
$505$	−1.20267	+	2.08308i	−0.00238152	+	0.00412492i
$506$		0			0
$507$	−6.15399	−	58.3604i	−0.0121381	−	0.115109i
$508$		0			0
$509$	266.365	+	317.442i	0.523311	+	0.623658i	0.961360	−	0.275293i	$-0.0887750\pi$
$509$	266.365	+	317.442i	0.523311	+	0.623658i	−0.438049	+	0.898951i	$0.644331\pi$
$510$		0			0
$511$	819.767	−	298.371i	1.60424	−	0.583896i
$512$		0			0
$513$	−104.886	−	321.688i	−0.204456	−	0.627072i
$514$		0			0
$515$	−0.316069	−	0.868393i	−0.000613726	−	0.00168620i
$516$		0			0
$517$	18.2460	−	15.3102i	0.0352921	−	0.0296136i
$518$		0			0
$519$	162.205	+	223.096i	0.312534	+	0.429858i
$520$		0			0
$521$	700.211	+	404.267i	1.34397	+	0.775944i	0.987388	−	0.158318i	$-0.0506073\pi$
$521$	700.211	+	404.267i	1.34397	+	0.775944i	0.356586	+	0.934262i	$0.383941\pi$
$522$		0			0
$523$	75.3714	+	130.547i	0.144114	+	0.249612i	0.929042	−	0.369975i	$-0.120634\pi$
$523$	75.3714	+	130.547i	0.144114	+	0.249612i	−0.784928	+	0.619587i	$0.787300\pi$
$524$		0			0
$525$	324.303	+	664.346i	0.617720	+	1.26542i
$526$		0			0
$527$	−159.681	+	438.720i	−0.303000	+	0.832485i
$528$		0			0
$529$	77.0649	−	437.057i	0.145680	−	0.826194i
$530$		0			0
$531$	138.417	+	649.031i	0.260673	+	1.22228i
$532$		0			0
$533$	−541.903	+	645.815i	−1.01670	+	1.21166i
$534$		0			0
$535$	0.603031	+	3.41996i	0.00112716	+	0.00639245i
$536$		0			0
$537$	184.348	+	45.8966i	0.343293	+	0.0854686i
$538$		0			0
$539$		−	590.418i		−	1.09540i
$540$		0			0
$541$	−764.505			−1.41313			−0.706567	−	0.707646i	$-0.749757\pi$
$541$	−764.505			−1.41313			−0.706567	+	0.707646i	$0.749757\pi$
$542$		0			0
$543$	−446.918	+	128.316i	−0.823053	+	0.236310i
$544$		0			0
$545$	−0.475325	+	0.0838127i	−0.000872157	+	0.000153785i
$546$		0			0
$547$	−222.538	−	186.732i	−0.406834	−	0.341374i	0.416294	−	0.909230i	$-0.363329\pi$
$547$	−222.538	−	186.732i	−0.406834	−	0.341374i	−0.823128	+	0.567856i	$0.807773\pi$
$548$		0			0
$549$	32.8420	−	42.0949i	0.0598215	−	0.0766755i
$550$		0			0
$551$	−547.488	−	96.5370i	−0.993627	−	0.175203i
$552$		0			0
$553$	1037.39	+	377.578i	1.87593	+	0.682781i
$554$		0			0
$555$	−0.151140	+	2.17202i	−0.000272325	+	0.00391356i
$556$		0			0
$557$	−490.922	+	283.434i	−0.881368	+	0.508858i	−0.871109	−	0.491089i	$-0.836599\pi$
$557$	−490.922	+	283.434i	−0.881368	+	0.508858i	−0.0102587	+	0.999947i	$0.503266\pi$
$558$		0			0
$559$	247.092	−	427.975i	0.442024	−	0.765609i
$560$		0			0
$561$	496.128	+	220.688i	0.884364	+	0.393384i
$562$		0			0
$563$	−647.051	−	771.125i	−1.14929	−	1.36967i	−0.917901	−	0.396810i	$-0.870117\pi$
$563$	−647.051	−	771.125i	−1.14929	−	1.36967i	−0.231390	−	0.972861i	$-0.574327\pi$
$564$		0			0
$565$	−0.0239319	+	0.00871049i	−4.23573e−5	+	1.54168e-5i
$566$		0			0
$567$	646.637	+	468.467i	1.14045	+	0.826220i
$568$		0			0
$569$	47.4246	+	130.298i	0.0833472	+	0.228995i	0.974365	−	0.224974i	$-0.0722299\pi$
$569$	47.4246	+	130.298i	0.0833472	+	0.228995i	−0.891017	+	0.453969i	$0.850008\pi$
$570$		0			0
$571$	401.032	−	336.506i	0.702333	−	0.589327i	−0.220103	−	0.975477i	$-0.570639\pi$
$571$	401.032	−	336.506i	0.702333	−	0.589327i	0.922436	+	0.386149i	$0.126195\pi$
$572$		0			0
$573$	69.8727	−	157.080i	0.121942	−	0.274137i
$574$		0			0
$575$	199.825	+	115.369i	0.347521	+	0.200641i
$576$		0			0
$577$	−477.478	−	827.016i	−0.827518	−	1.43330i	−0.899979	−	0.435933i	$-0.856419\pi$
$577$	−477.478	−	827.016i	−0.827518	−	1.43330i	0.0724610	−	0.997371i	$-0.476915\pi$
$578$		0			0
$579$	−27.4962	−	1.91333i	−0.0474892	−	0.00330454i
$580$		0			0
$581$	65.6279	−	180.311i	0.112957	−	0.310346i
$582$		0			0
$583$	−101.586	+	576.121i	−0.174247	+	0.988201i
$584$		0			0
$585$	−0.768195	+	5.49311i	−0.00131315	+	0.00938993i
$586$		0			0
$587$	480.945	−	573.168i	0.819327	−	0.976435i	−0.180648	−	0.983548i	$-0.557820\pi$
$587$	480.945	−	573.168i	0.819327	−	0.976435i	0.999975	+	0.00711237i	$0.00226396\pi$
$588$		0			0
$589$	68.7848	+	390.098i	0.116782	+	0.662306i
$590$		0			0
$591$	68.6742	+	239.188i	0.116200	+	0.404718i
$592$		0			0
$593$			164.211i			0.276916i	0.990368	+	0.138458i	$0.0442145\pi$
$593$			164.211i			0.276916i	−0.990368	+	0.138458i	$0.955785\pi$
$594$		0			0
$595$	−7.34053			−0.0123370
$596$		0			0
$597$	−26.5425	+	106.610i	−0.0444597	+	0.178577i
$598$		0			0
$599$	−152.697	+	26.9245i	−0.254919	+	0.0449491i	−0.299647	−	0.954050i	$-0.596869\pi$
$599$	−152.697	+	26.9245i	−0.254919	+	0.0449491i	0.0447281	+	0.998999i	$0.485758\pi$
$600$		0			0
$601$	568.060	+	476.659i	0.945191	+	0.793110i	0.978481	−	0.206336i	$-0.0661540\pi$
$601$	568.060	+	476.659i	0.945191	+	0.793110i	−0.0332899	+	0.999446i	$0.510598\pi$
$602$		0			0
$603$	135.440	−	417.808i	0.224610	−	0.692882i
$604$		0			0
$605$	−1.44814	−	0.255346i	−0.00239362	−	0.000422060i
$606$		0			0
$607$	−781.335	−	284.383i	−1.28721	−	0.468505i	−0.394398	−	0.918940i	$-0.629047\pi$
$607$	−781.335	−	284.383i	−1.28721	−	0.468505i	−0.892810	+	0.450434i	$0.851269\pi$
$608$		0			0
$609$	1179.00	−	575.532i	1.93596	−	0.945045i
$610$		0			0
$611$	20.5773	−	11.8803i	0.0336780	−	0.0194440i
$612$		0			0
$613$	−197.308	+	341.747i	−0.321873	+	0.557500i	−0.980874	−	0.194642i	$-0.937646\pi$
$613$	−197.308	+	341.747i	−0.321873	+	0.557500i	0.659002	+	0.752141i	$0.270979\pi$
$614$		0			0
$615$	−8.43614	+	6.13360i	−0.0137173	+	0.00997333i
$616$		0			0
$617$	4.31265	+	5.13962i	0.00698971	+	0.00833001i	0.769528	−	0.638613i	$-0.220492\pi$
$617$	4.31265	+	5.13962i	0.00698971	+	0.00833001i	−0.762538	+	0.646943i	$0.776047\pi$
$618$		0			0
$619$	−338.641	+	123.255i	−0.547078	+	0.199120i	−0.600748	−	0.799439i	$-0.705130\pi$
$619$	−338.641	+	123.255i	−0.547078	+	0.199120i	0.0536699	+	0.998559i	$0.482908\pi$
$620$		0			0
$621$	249.079	+	8.44355i	0.401093	+	0.0135967i
$622$		0			0
$623$	132.148	+	363.074i	0.212116	+	0.582783i
$624$		0			0
$625$	478.632	−	401.620i	0.765811	−	0.642592i
$626$		0			0
$627$	458.161	−	48.3122i	0.730719	−	0.0770530i
$628$		0			0
$629$	184.145	+	106.316i	0.292759	+	0.169025i
$630$		0			0
$631$	−394.087	−	682.578i	−0.624543	−	1.08174i	−0.988629	−	0.150375i	$-0.951952\pi$
$631$	−394.087	−	682.578i	−0.624543	−	1.08174i	0.364086	−	0.931365i	$-0.381381\pi$
$632$		0			0
$633$	−517.812	+	768.252i	−0.818029	+	1.21367i
$634$		0			0
$635$	1.80275	−	4.95301i	0.00283897	−	0.00780001i
$636$		0			0
$637$	102.276	−	580.034i	0.160558	−	0.910572i
$638$		0			0
$639$	47.4962	+	75.8949i	0.0743290	+	0.118771i
$640$		0			0
$641$	750.028	−	893.849i	1.17009	−	1.39446i	0.267722	−	0.963496i	$-0.413729\pi$
$641$	750.028	−	893.849i	1.17009	−	1.39446i	0.902369	−	0.430964i	$-0.141826\pi$
$642$		0			0
$643$	50.6737	+	287.385i	0.0788083	+	0.446944i	0.998522	+	0.0543538i	$0.0173099\pi$
$643$	50.6737	+	287.385i	0.0788083	+	0.446944i	−0.919713	+	0.392590i	$0.871579\pi$
$644$		0			0
$645$	4.24566	−	4.39951i	0.00658243	−	0.00682094i
$646$		0			0
$647$			547.391i			0.846045i	0.906119	+	0.423023i	$0.139031\pi$
$647$			547.391i			0.846045i	−0.906119	+	0.423023i	$0.860969\pi$
$648$		0			0
$649$	−903.588			−1.39228
$650$		0			0
$651$	−672.668	−	649.146i	−1.03328	−	0.997152i
$652$		0			0
$653$	430.668	−	75.9385i	0.659523	−	0.116292i	0.166138	−	0.986103i	$-0.446870\pi$
$653$	430.668	−	75.9385i	0.659523	−	0.116292i	0.493385	+	0.869811i	$0.335759\pi$
$654$		0			0
$655$	−7.78960	−	6.53625i	−0.0118925	−	0.00997901i
$656$		0			0
$657$	−703.477	−	373.432i	−1.07074	−	0.568389i
$658$		0			0
$659$	7.11079	+	1.25382i	0.0107903	+	0.00190262i	0.179041	−	0.983842i	$-0.442701\pi$
$659$	7.11079	+	1.25382i	0.0107903	+	0.00190262i	−0.168250	+	0.985744i	$0.553812\pi$
$660$		0			0
$661$	−830.669	−	302.339i	−1.25669	−	0.457396i	−0.374030	−	0.927416i	$-0.622024\pi$
$661$	−830.669	−	302.339i	−1.25669	−	0.457396i	−0.882656	+	0.470020i	$0.844247\pi$
$662$		0			0
$663$	449.174	+	302.749i	0.677487	+	0.456636i
$664$		0			0
$665$	−5.39360	+	3.11400i	−0.00811068	+	0.00468270i
$666$		0			0
$667$	204.742	−	354.624i	0.306960	−	0.531670i
$668$		0			0
$669$	−97.4602	−	924.248i	−0.145680	−	1.38154i
$670$		0			0
$671$	46.7283	+	55.6886i	0.0696398	+	0.0829935i
$672$		0			0
$673$	−445.775	+	162.249i	−0.662370	+	0.241083i	−0.651259	−	0.758855i	$-0.725759\pi$
$673$	−445.775	+	162.249i	−0.662370	+	0.241083i	−0.0111109	+	0.999938i	$0.503537\pi$
$674$		0			0
$675$	252.195	−	626.043i	0.373622	−	0.927471i
$676$		0			0
$677$	−109.514	−	300.887i	−0.161763	−	0.444441i	0.832157	−	0.554540i	$-0.187106\pi$
$677$	−109.514	−	300.887i	−0.161763	−	0.444441i	−0.993921	+	0.110098i	$0.964883\pi$
$678$		0			0
$679$	2.91714	−	2.44777i	0.00429622	−	0.00360496i
$680$		0			0
$681$	294.395	+	404.910i	0.432298	+	0.594581i
$682$		0			0
$683$	812.276	+	468.967i	1.18928	+	0.686629i	0.958142	−	0.286293i	$-0.0924231\pi$
$683$	812.276	+	468.967i	1.18928	+	0.686629i	0.231134	+	0.972922i	$0.425756\pi$
$684$		0			0
$685$	−4.88765	−	8.46565i	−0.00713525	−	0.0123586i
$686$		0			0
$687$	305.940	+	626.729i	0.445328	+	0.912269i
$688$		0			0
$689$	−199.598	+	548.392i	−0.289693	+	0.795924i
$690$		0			0
$691$	10.2172	−	57.9445i	0.0147861	−	0.0838560i	−0.976522	−	0.215419i	$-0.930888\pi$
$691$	10.2172	−	57.9445i	0.0147861	−	0.0838560i	0.991308	+	0.131563i	$0.0419995\pi$
$692$		0			0
$693$	−807.473	+	728.048i	−1.16519	+	1.05057i
$694$		0			0
$695$	0.931124	−	1.10967i	0.00133975	−	0.00159665i
$696$		0			0
$697$	176.881	+	1003.14i	0.253774	+	1.43923i
$698$		0			0
$699$	−330.204	−	82.2098i	−0.472395	−	0.117611i
$700$		0			0
$701$		−	591.380i		−	0.843623i	−0.906683	−	0.421812i	$-0.861394\pi$
$701$		−	591.380i		−	0.843623i	0.906683	−	0.421812i	$-0.138606\pi$
$702$		0			0
$703$	180.406			0.256623
$704$		0			0
$705$	0.282550	−	0.0811240i	0.000400781	−	0.000115070i
$706$		0			0
$707$	−463.199	+	81.6744i	−0.655161	+	0.115523i
$708$		0			0
$709$	337.105	+	282.865i	0.475465	+	0.398963i	0.848783	−	0.528741i	$-0.177336\pi$
$709$	337.105	+	282.865i	0.475465	+	0.398963i	−0.373318	+	0.927703i	$0.621780\pi$
$710$		0			0
$711$	−378.194	−	934.232i	−0.531918	−	1.31397i
$712$		0			0
$713$	−287.334	−	50.6648i	−0.402993	−	0.0710586i
$714$		0			0
$715$	−7.09669	−	2.58299i	−0.00992545	−	0.00361257i
$716$		0			0
$717$	−7.32712	+	105.297i	−0.0102191	+	0.146858i
$718$		0			0
$719$	499.498	−	288.385i	0.694712	−	0.401092i	−0.110663	−	0.993858i	$-0.535297\pi$
$719$	499.498	−	288.385i	0.694712	−	0.401092i	0.805375	+	0.592766i	$0.201964\pi$
$720$		0			0
$721$	90.3525	−	156.495i	0.125315	−	0.217053i
$722$		0			0
$723$	−702.321	−	312.407i	−0.971398	−	0.432098i
$724$		0			0
$725$	−712.817	−	849.502i	−0.983195	−	1.17173i
$726$		0			0
$727$	−562.999	+	204.915i	−0.774414	+	0.281863i	−0.698841	−	0.715277i	$-0.746301\pi$
$727$	−562.999	+	204.915i	−0.774414	+	0.281863i	−0.0755723	+	0.997140i	$0.524078\pi$
$728$		0			0
$729$	−77.6808	−	724.849i	−0.106558	−	0.994306i
$730$		0			0
$731$	−204.219	−	561.087i	−0.279369	−	0.767561i
$732$		0			0
$733$	−424.519	+	356.213i	−0.579152	+	0.485966i	−0.884669	−	0.466220i	$-0.845615\pi$
$733$	−424.519	+	356.213i	−0.579152	+	0.485966i	0.305516	+	0.952187i	$0.401171\pi$
$734$		0			0
$735$	2.96158	−	6.65791i	0.00402936	−	0.00905838i
$736$		0			0
$737$	517.906	+	299.013i	0.702723	+	0.405717i
$738$		0			0
$739$	708.201	+	1226.64i	0.958324	+	1.65987i	0.726572	+	0.687090i	$0.241112\pi$
$739$	708.201	+	1226.64i	0.958324	+	1.65987i	0.231752	+	0.972775i	$0.425554\pi$
$740$		0			0
$741$	458.472	+	31.9028i	0.618721	+	0.0430537i
$742$		0			0
$743$	−103.170	+	283.457i	−0.138856	+	0.381504i	−0.989556	−	0.144147i	$-0.953956\pi$
$743$	−103.170	+	283.457i	−0.138856	+	0.381504i	0.850700	+	0.525651i	$0.176178\pi$
$744$		0			0
$745$	−2.17834	+	12.3540i	−0.00292395	+	0.0165825i
$746$		0			0
$747$	−162.381	+	65.7349i	−0.217378	+	0.0879986i
$748$		0			0
$749$	−436.492	+	520.191i	−0.582767	+	0.694514i
$750$		0			0
$751$	86.3699	+	489.828i	0.115007	+	0.652235i	0.986747	+	0.162267i	$0.0518805\pi$
$751$	86.3699	+	489.828i	0.115007	+	0.652235i	−0.871740	+	0.489968i	$0.837008\pi$
$752$		0			0
$753$	−324.292	−	1129.49i	−0.430666	−	1.49998i
$754$		0			0
$755$			7.37088i			0.00976276i
$756$		0			0
$757$	1028.94			1.35924			0.679620	−	0.733565i	$-0.262145\pi$
$757$	1028.94			1.35924			0.679620	+	0.733565i	$0.262145\pi$
$758$		0			0
$759$	−81.9814	+	329.286i	−0.108012	+	0.433842i
$760$		0			0
$761$	−37.0662	+	6.53577i	−0.0487073	+	0.00858840i	−0.197949	−	0.980212i	$-0.563428\pi$
$761$	−37.0662	+	6.53577i	−0.0487073	+	0.00858840i	0.149241	+	0.988801i	$0.452317\pi$
$762$		0			0
$763$	−72.2991	−	60.6662i	−0.0947564	−	0.0795101i
$764$		0			0
$765$	4.48765	+	4.97723i	0.00586621	+	0.00650618i
$766$		0			0
$767$	−887.696	−	156.525i	−1.15736	−	0.204074i
$768$		0			0
$769$	−1065.80	−	387.921i	−1.38596	−	0.504449i	−0.461981	−	0.886890i	$-0.652861\pi$
$769$	−1065.80	−	387.921i	−1.38596	−	0.504449i	−0.923980	+	0.382441i	$0.875084\pi$
$770$		0			0
$771$	−770.107	+	375.931i	−0.998842	+	0.487588i
$772$		0			0
$773$	−441.262	+	254.763i	−0.570843	+	0.329577i	−0.757486	−	0.652851i	$-0.773573\pi$
$773$	−441.262	+	254.763i	−0.570843	+	0.329577i	0.186643	+	0.982428i	$0.440239\pi$
$774$		0			0
$775$	−395.075	+	684.289i	−0.509774	+	0.882954i
$776$		0			0
$777$	−344.353	+	250.366i	−0.443182	+	0.322221i
$778$		0			0
$779$	555.519	+	662.042i	0.713118	+	0.849861i
$780$		0			0
$781$	−114.554	+	41.6941i	−0.146676	+	0.0533856i
$782$		0			0
$783$	−1111.02	−	447.564i	−1.41893	−	0.571601i
$784$		0			0
$785$	−1.79610	−	4.93474i	−0.00228803	−	0.00628630i
$786$		0			0
$787$	−203.516	+	170.770i	−0.258597	+	0.216988i	−0.762864	−	0.646560i	$-0.776207\pi$
$787$	−203.516	+	170.770i	−0.258597	+	0.216988i	0.504267	+	0.863548i	$0.331763\pi$
$788$		0			0
$789$	−1349.45	+	142.297i	−1.71033	+	0.180351i
$790$		0			0
$791$	−4.31282	−	2.49001i	−0.00545236	−	0.00314792i
$792$		0			0
$793$	36.2598	+	62.8038i	0.0457248	+	0.0791977i
$794$		0			0
$795$	−4.03541	+	5.98713i	−0.00507598	+	0.00753098i
$796$		0			0
$797$	−153.358	+	421.349i	−0.192420	+	0.528668i	−0.997958	−	0.0638752i	$-0.979654\pi$
$797$	−153.358	+	421.349i	−0.192420	+	0.528668i	0.805538	+	0.592544i	$0.201876\pi$
$798$		0			0
$799$	4.98521	−	28.2725i	0.00623932	−	0.0353849i
$800$		0			0
$801$	165.392	−	311.569i	0.206482	−	0.388975i
$802$		0			0
$803$	697.063	−	830.727i	0.868073	−	1.03453i
$804$		0			0
$805$	−0.796585	−	4.51766i	−0.000989547	−	0.00561200i
$806$		0			0
$807$	578.340	−	599.296i	0.716654	−	0.742623i
$808$		0			0
$809$		−	357.505i		−	0.441910i	−0.975284	−	0.220955i	$-0.929083\pi$
$809$		−	357.505i		−	0.441910i	0.975284	−	0.220955i	$-0.0709174\pi$
$810$		0			0
$811$	−1269.44			−1.56528			−0.782638	−	0.622477i	$-0.786126\pi$
$811$	−1269.44			−1.56528			−0.782638	+	0.622477i	$0.786126\pi$
$812$		0			0
$813$	−669.878	−	646.453i	−0.823958	−	0.795145i
$814$		0			0
$815$	6.26861	−	1.10533i	0.00769155	−	0.00135623i
$816$		0			0
$817$	−388.078	−	325.636i	−0.475004	−	0.398576i
$818$		0			0
$819$	−919.389	+	575.368i	−1.12257	+	0.702525i
$820$		0			0
$821$	1142.82	+	201.510i	1.39199	+	0.245445i	0.818846	−	0.574013i	$-0.194614\pi$
$821$	1142.82	+	201.510i	1.39199	+	0.245445i	0.573140	+	0.819458i	$0.305725\pi$
$822$		0			0
$823$	−776.798	−	282.731i	−0.943862	−	0.343538i	−0.176172	−	0.984359i	$-0.556371\pi$
$823$	−776.798	−	282.731i	−0.943862	−	0.343538i	−0.767690	+	0.640822i	$0.778594\pi$
$824$		0			0
$825$	762.044	+	513.628i	0.923689	+	0.622579i
$826$		0			0
$827$	−74.5639	+	43.0495i	−0.0901619	+	0.0520550i	−0.544403	−	0.838824i	$-0.683244\pi$
$827$	−74.5639	+	43.0495i	−0.0901619	+	0.0520550i	0.454241	+	0.890879i	$0.349910\pi$
$828$		0			0
$829$	316.737	−	548.604i	0.382071	−	0.661766i	−0.609287	−	0.792949i	$-0.708544\pi$
$829$	316.737	−	548.604i	0.382071	−	0.661766i	0.991358	+	0.131184i	$0.0418778\pi$
$830$		0			0
$831$	−108.265	−	1026.71i	−0.130283	−	1.23551i
$832$		0			0
$833$	−457.432	−	545.146i	−0.549138	−	0.654437i
$834$		0			0
$835$	11.5869	−	4.21728i	0.0138765	−	0.00505063i
$836$		0			0
$837$	−28.9145	+	852.958i	−0.0345454	+	1.01907i
$838$		0			0
$839$	251.928	+	692.167i	0.300272	+	0.824990i	0.994452	+	0.105189i	$0.0335447\pi$
$839$	251.928	+	692.167i	0.300272	+	0.824990i	−0.694180	+	0.719801i	$0.744233\pi$
$840$		0			0
$841$	−863.345	+	724.433i	−1.02657	+	0.861394i
$842$		0			0
$843$	−776.885	−	1068.53i	−0.921572	−	1.26753i
$844$		0			0
$845$	0.854040	+	0.493080i	0.00101070	+	0.000583527i
$846$		0			0
$847$	−143.770	−	249.017i	−0.169741	−	0.293999i
$848$		0			0
$849$	19.6394	+	40.2320i	0.0231324	+	0.0473876i
$850$		0			0
$851$	−45.4482	+	124.868i	−0.0534056	+	0.146731i
$852$		0			0
$853$	−284.876	+	1615.61i	−0.333970	+	1.89404i	0.103204	+	0.994660i	$0.467091\pi$
$853$	−284.876	+	1615.61i	−0.333970	+	1.89404i	−0.437174	+	0.899377i	$0.644020\pi$
$854$		0			0
$855$	5.40883	+	1.75337i	0.00632612	+	0.00205072i
$856$		0			0
$857$	−219.660	+	261.780i	−0.256312	+	0.305461i	−0.878821	−	0.477152i	$-0.841669\pi$
$857$	−219.660	+	261.780i	−0.256312	+	0.305461i	0.622509	+	0.782613i	$0.286114\pi$
$858$		0			0
$859$	−53.2766	−	302.146i	−0.0620216	−	0.351742i	−0.999987	−	0.00501434i	$-0.998404\pi$
$859$	−53.2766	−	302.146i	−0.0620216	−	0.351742i	0.937966	−	0.346728i	$-0.112707\pi$
$860$		0			0
$861$	−1979.13	−	492.737i	−2.29864	−	0.572285i
$862$		0			0
$863$		−	1546.03i		−	1.79146i	−0.444596	−	0.895731i	$-0.646653\pi$
$863$		−	1546.03i		−	1.79146i	0.444596	−	0.895731i	$-0.353347\pi$
$864$		0			0
$865$	−4.63522			−0.00535864
$866$		0			0
$867$	−204.266	+	58.6476i	−0.235601	+	0.0676443i
$868$		0			0
$869$	1351.47	−	238.300i	1.55520	−	0.274224i
$870$		0			0
$871$	457.001	+	383.469i	0.524686	+	0.440263i
$872$		0			0
$873$	−3.44310	−	0.481508i	−0.00394399	−	0.000551556i
$874$		0			0
$875$	−24.4703	−	4.31477i	−0.0279660	−	0.00493116i
$876$		0			0
$877$	254.149	+	92.5028i	0.289794	+	0.105476i	0.482827	−	0.875716i	$-0.339610\pi$
$877$	254.149	+	92.5028i	0.289794	+	0.105476i	−0.193033	+	0.981192i	$0.561832\pi$
$878$		0			0
$879$	33.7418	−	484.900i	0.0383865	−	0.551650i
$880$		0			0
$881$	−240.352	+	138.767i	−0.272817	+	0.157511i	−0.630167	−	0.776460i	$-0.717014\pi$
$881$	−240.352	+	138.767i	−0.272817	+	0.157511i	0.357350	+	0.933970i	$0.383680\pi$
$882$		0			0
$883$	−334.464	+	579.308i	−0.378781	+	0.656068i	−0.990885	−	0.134709i	$-0.956990\pi$
$883$	−334.464	+	579.308i	−0.378781	+	0.656068i	0.612104	+	0.790777i	$0.290323\pi$
$884$		0			0
$885$	−10.1894	−	4.53246i	−0.0115134	−	0.00512142i
$886$		0			0
$887$	707.659	+	843.355i	0.797811	+	0.950795i	0.999590	−	0.0286367i	$-0.00911658\pi$
$887$	707.659	+	843.355i	0.797811	+	0.950795i	−0.201779	+	0.979431i	$0.564672\pi$
$888$		0			0
$889$	968.520	−	352.512i	1.08945	−	0.396527i
$890$		0			0
$891$	987.302	+	102.412i	1.10808	+	0.114940i
$892$		0			0
$893$	−8.33079	−	22.8887i	−0.00932899	−	0.0256312i
$894$		0			0
$895$	−2.44557	+	2.05208i	−0.00273249	+	0.00229283i
$896$		0			0
$897$	−137.580	+	309.294i	−0.153378	+	0.344809i
$898$		0			0
$899$	1214.39	+	701.129i	1.35082	+	0.779899i
$900$		0			0
$901$	352.559	+	610.650i	0.391297	+	0.677747i
$902$		0			0
$903$	1192.66	+	82.9915i	1.32078	+	0.0919065i
$904$		0			0
$905$	2.67244	−	7.34248i	0.00295298	−	0.00811324i
$906$		0			0
$907$	−159.627	+	905.289i	−0.175994	+	0.998114i	0.760995	+	0.648757i	$0.224711\pi$
$907$	−159.627	+	905.289i	−0.175994	+	0.998114i	−0.936990	+	0.349357i	$0.886400\pi$
$908$		0			0
$909$	338.557	+	264.139i	0.372450	+	0.290582i
$910$		0			0
$911$	−109.112	+	130.035i	−0.119772	+	0.142739i	−0.822599	−	0.568623i	$-0.807476\pi$
$911$	−109.112	+	130.035i	−0.119772	+	0.142739i	0.702827	+	0.711361i	$0.251921\pi$
$912$		0			0
$913$	−41.4197	−	234.903i	−0.0453666	−	0.257287i
$914$		0			0
$915$	0.247598	+	0.862371i	0.000270599	+	0.000942482i
$916$		0			0
$917$		−	1988.39i		−	2.16836i
$918$		0			0
$919$	−120.333			−0.130939			−0.0654697	−	0.997855i	$-0.520855\pi$
$919$	−120.333			−0.130939			−0.0654697	+	0.997855i	$0.520855\pi$
$920$		0			0
$921$	100.780	−	404.791i	0.109424	−	0.439513i
$922$		0			0
$923$	−119.762	+	21.1172i	−0.129752	+	0.0228789i
$924$		0			0
$925$	275.672	+	231.316i	0.298023	+	0.250071i
$926$		0			0
$927$	−161.348	+	34.4104i	−0.174054	+	0.0371202i
$928$		0			0
$929$	989.307	+	174.442i	1.06492	+	0.187773i	0.678537	−	0.734566i	$-0.262614\pi$
$929$	989.307	+	174.442i	1.06492	+	0.187773i	0.386379	+	0.922340i	$0.373726\pi$
$930$		0			0
$931$	−567.369	−	206.505i	−0.609419	−	0.221810i
$932$		0			0
$933$	486.566	−	237.519i	0.521507	−	0.254576i
$934$		0			0
$935$	−7.90237	+	4.56244i	−0.00845173	+	0.00487961i
$936$		0			0
$937$	−374.211	+	648.153i	−0.399372	+	0.691732i	−0.993649	−	0.112528i	$-0.964105\pi$
$937$	−374.211	+	648.153i	−0.399372	+	0.691732i	0.594277	+	0.804261i	$0.297438\pi$
$938$		0			0
$939$	1406.02	−	1022.27i	1.49736	−	1.08868i
$940$		0			0
$941$	952.151	+	1134.73i	1.01185	+	1.20588i	0.978461	+	0.206434i	$0.0661858\pi$
$941$	952.151	+	1134.73i	1.01185	+	1.20588i	0.0333896	+	0.999442i	$0.489370\pi$
$942$		0			0
$943$	−598.179	+	217.719i	−0.634336	+	0.230879i
$944$		0			0
$945$	−12.7575	+	4.15956i	−0.0135000	+	0.00440165i
$946$		0			0
$947$	−160.976	−	442.278i	−0.169985	−	0.467030i	0.825223	−	0.564807i	$-0.191049\pi$
$947$	−160.976	−	442.278i	−0.169985	−	0.467030i	−0.995208	+	0.0977764i	$0.968827\pi$
$948$		0			0
$949$	828.707	−	695.368i	0.873242	−	0.732737i
$950$		0			0
$951$	−1508.45	+	159.063i	−1.58617	+	0.167259i
$952$		0			0
$953$	733.980	+	423.764i	0.770179	+	0.444663i	0.832938	−	0.553366i	$-0.186657\pi$
$953$	733.980	+	423.764i	0.770179	+	0.444663i	−0.0627596	+	0.998029i	$0.519990\pi$
$954$		0			0
$955$	1.44452	+	2.50199i	0.00151259	+	0.00261988i
$956$		0			0
$957$	911.522	−	1352.38i	0.952479	−	1.41314i
$958$		0			0
$959$	653.764	−	1796.20i	0.681715	−	1.87300i
$960$		0			0
$961$	6.62309	−	37.5614i	0.00689187	−	0.0390857i
$962$		0			0
$963$	619.565	−	22.0577i	0.643370	−	0.0229052i
$964$		0			0
$965$	0.297727	−	0.354817i	0.000308525	−	0.000367686i
$966$		0			0
$967$	17.9690	+	101.907i	0.0185822	+	0.105385i	0.992688	−	0.120707i	$-0.0385162\pi$
$967$	17.9690	+	101.907i	0.0185822	+	0.105385i	−0.974106	+	0.226092i	$0.927405\pi$
$968$		0			0
$969$	385.600	−	399.572i	0.397936	−	0.412355i
$970$		0			0
$971$			171.424i			0.176543i	0.996096	+	0.0882717i	$0.0281344\pi$
$971$			171.424i			0.176543i	−0.996096	+	0.0882717i	$0.971866\pi$
$972$		0			0
$973$	283.256			0.291116
$974$		0			0
$975$	659.668	+	636.600i	0.676582	+	0.652923i
$976$		0			0
$977$	−1695.45	+	298.954i	−1.73536	+	0.305991i	−0.949816	−	0.312809i	$-0.898730\pi$
$977$	−1695.45	+	298.954i	−1.73536	+	0.305991i	−0.785548	+	0.618801i	$0.787619\pi$
$978$		0			0
$979$	367.928	+	308.728i	0.375820	+	0.315350i
$980$		0			0
$981$	3.06571	+	86.1107i	0.00312508	+	0.0877785i
$982$		0			0
$983$	1292.07	+	227.827i	1.31442	+	0.231767i	0.786532	−	0.617550i	$-0.211874\pi$
$983$	1292.07	+	227.827i	1.31442	+	0.231767i	0.527884	+	0.849317i	$0.322986\pi$
$984$		0			0
$985$	−3.92966	−	1.43028i	−0.00398950	−	0.00145206i
$986$		0			0
$987$	47.6661	+	32.1276i	0.0482940	+	0.0325508i
$988$		0			0
$989$	323.154	−	186.573i	0.326748	−	0.188648i
$990$		0			0
$991$	964.265	−	1670.16i	0.973022	−	1.68532i	0.286707	−	0.958018i	$-0.407439\pi$
$991$	964.265	−	1670.16i	0.973022	−	1.68532i	0.686314	−	0.727305i	$-0.259227\pi$
$992$		0			0
$993$	71.3809	+	676.929i	0.0718841	+	0.681700i
$994$		0			0
$995$	−1.18674	−	1.41430i	−0.00119270	−	0.00142141i
$996$		0			0
$997$	−1167.31	+	424.866i	−1.17082	+	0.426144i	−0.852952	−	0.521990i	$-0.825190\pi$
$997$	−1167.31	+	424.866i	−1.17082	+	0.426144i	−0.317870	+	0.948134i	$0.602968\pi$
$998$		0			0
$999$	380.281	+	80.4257i	0.380662	+	0.0805062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.a.209.4		30
4.3	odd	2		27.3.f.a.20.2	✓	30
12.11	even	2		81.3.f.a.62.4		30
27.23	odd	18	inner	432.3.bc.a.401.4		30
36.7	odd	6		243.3.f.c.107.2		30
36.11	even	6		243.3.f.b.107.4		30
36.23	even	6		243.3.f.a.26.2		30
36.31	odd	6		243.3.f.d.26.4		30
108.23	even	18		27.3.f.a.23.2	yes	30
108.31	odd	18		81.3.f.a.17.4		30
108.59	even	18		243.3.f.d.215.4		30
108.67	odd	18		243.3.f.b.134.4		30
108.79	odd	18		729.3.b.a.728.21		30
108.83	even	18		729.3.b.a.728.10		30
108.95	even	18		243.3.f.c.134.2		30
108.103	odd	18		243.3.f.a.215.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.20.2	✓	30	4.3	odd	2
27.3.f.a.23.2	yes	30	108.23	even	18
81.3.f.a.17.4		30	108.31	odd	18
81.3.f.a.62.4		30	12.11	even	2
243.3.f.a.26.2		30	36.23	even	6
243.3.f.a.215.2		30	108.103	odd	18
243.3.f.b.107.4		30	36.11	even	6
243.3.f.b.134.4		30	108.67	odd	18
243.3.f.c.107.2		30	36.7	odd	6
243.3.f.c.134.2		30	108.95	even	18
243.3.f.d.26.4		30	36.31	odd	6
243.3.f.d.215.4		30	108.59	even	18
432.3.bc.a.209.4		30	1.1	even	1	trivial
432.3.bc.a.401.4		30	27.23	odd	18	inner
729.3.b.a.728.10		30	108.83	even	18
729.3.b.a.728.21		30	108.79	odd	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.15873 + 2.08324i) q^{3} +(-0.0496479 + 0.00875427i) q^{5} +(-7.55168 - 6.33661i) q^{7} +(0.320214 + 8.99430i) q^{9} +(-12.0681 - 2.12794i) q^{11} +(-11.4873 - 4.18103i) q^{13} +(-0.125414 - 0.0845305i) q^{15} +(-12.7914 + 7.38513i) q^{17} +(-6.26584 + 10.8527i) q^{19} +(-3.10133 - 29.4110i) q^{21} +(-5.93322 - 7.07093i) q^{23} +(-23.4899 + 8.54963i) q^{25} +(-18.0460 + 20.0833i) q^{27} +(15.1728 + 41.6870i) q^{29} +(24.2140 - 20.3180i) q^{31} +(-21.6188 - 29.7345i) q^{33} +(0.430398 + 0.248490i) q^{35} +(-7.19801 - 12.4673i) q^{37} +(-16.0878 - 32.9565i) q^{39} +(23.5871 - 64.8050i) q^{41} +(-7.01983 + 39.8114i) q^{43} +(-0.0946365 - 0.443745i) q^{45} +(-1.24938 + 1.48895i) q^{47} +(8.36645 + 47.4485i) q^{49} +(-42.9982 - 10.7051i) q^{51} -47.7390i q^{53} +0.617787 q^{55} +(-36.1351 + 10.3749i) q^{57} +(72.6161 - 12.8042i) q^{59} +(-4.54441 - 3.81321i) q^{61} +(54.5752 - 69.9511i) q^{63} +(0.606922 + 0.107017i) q^{65} +(-45.8583 - 16.6910i) q^{67} +(1.92225 - 27.6245i) q^{69} +(8.61519 - 4.97398i) q^{71} +(-44.2472 + 76.6383i) q^{73} +(-68.5193 - 30.4788i) q^{75} +(77.6508 + 92.5406i) q^{77} +(-105.233 + 38.3016i) q^{79} +(-80.7949 + 5.76021i) q^{81} +(6.65732 + 18.2908i) q^{83} +(0.570416 - 0.478636i) q^{85} +(-54.0900 + 121.599i) q^{87} +(-33.9430 - 19.5970i) q^{89} +(60.2547 + 104.364i) q^{91} +(94.5988 + 6.58266i) q^{93} +(0.216078 - 0.593669i) q^{95} +(-0.0670785 + 0.380421i) q^{97} +(15.2749 - 109.226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37}+ \cdots - 513 q^{99}+O(q^{100}) \) 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

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