LMFDB - Embedded newform 216.3.u.a.41.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("216.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.18
Character	$\chi$	$=$	216.41
Dual form			216.3.u.a.137.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.98761 + 0.272321i) q^{3} +(-5.82981 + 6.94770i) q^{5} +(4.85733 + 1.76792i) q^{7} +(8.85168 + 1.62718i) q^{9} +O(q^{10})$	\(q+(2.98761 + 0.272321i) q^{3} +(-5.82981 + 6.94770i) q^{5} +(4.85733 + 1.76792i) q^{7} +(8.85168 + 1.62718i) q^{9} +(-8.02427 - 9.56295i) q^{11} +(-4.30017 + 24.3875i) q^{13} +(-19.3092 + 19.1695i) q^{15} +(-10.2048 - 5.89175i) q^{17} +(15.1967 + 26.3214i) q^{19} +(14.0304 + 6.60463i) q^{21} +(1.27127 + 3.49279i) q^{23} +(-9.94260 - 56.3873i) q^{25} +(26.0023 + 7.27188i) q^{27} +(15.8810 - 2.80026i) q^{29} +(25.4499 - 9.26301i) q^{31} +(-21.3692 - 30.7556i) q^{33} +(-40.6003 + 23.4406i) q^{35} +(18.4875 - 32.0213i) q^{37} +(-19.4885 + 71.6894i) q^{39} +(43.6776 + 7.70154i) q^{41} +(-11.4119 + 9.57574i) q^{43} +(-62.9088 + 52.0127i) q^{45} +(4.54166 - 12.4781i) q^{47} +(-17.0681 - 14.3218i) q^{49} +(-28.8836 - 20.3813i) q^{51} -32.6975i q^{53} +113.220 q^{55} +(38.2339 + 82.7765i) q^{57} +(-38.0009 + 45.2877i) q^{59} +(-5.41219 - 1.96987i) q^{61} +(40.1188 + 23.5529i) q^{63} +(-144.368 - 172.051i) q^{65} +(22.1465 - 125.599i) q^{67} +(2.84691 + 10.7813i) q^{69} +(-16.0822 - 9.28507i) q^{71} +(-12.4523 - 21.5680i) q^{73} +(-14.3492 - 171.171i) q^{75} +(-22.0700 - 60.6367i) q^{77} +(4.35320 + 24.6882i) q^{79} +(75.7046 + 28.8065i) q^{81} +(86.3752 - 15.2303i) q^{83} +(100.426 - 36.5521i) q^{85} +(48.2090 - 4.04135i) q^{87} +(100.979 - 58.3001i) q^{89} +(-64.0026 + 110.856i) q^{91} +(78.5571 - 20.7438i) q^{93} +(-271.467 - 47.8669i) q^{95} +(-23.1850 + 19.4545i) q^{97} +(-55.4676 - 97.7051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q+O(q^{10}) $ 108 * q	$ 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) $ 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.98761	+	0.272321i	0.995872	+	0.0907736i
$3$	2.98761	+	0.272321i	0.995872	+	0.0907736i
$4$		0			0
$5$	−5.82981	+	6.94770i	−1.16596	+	1.38954i	−0.260306	+	0.965526i	$0.583823\pi$
$5$	−5.82981	+	6.94770i	−1.16596	+	1.38954i	−0.905656	+	0.424013i	$0.860621\pi$
$6$		0			0
$7$	4.85733	+	1.76792i	0.693905	+	0.252561i	0.664806	−	0.747016i	$-0.268514\pi$
$7$	4.85733	+	1.76792i	0.693905	+	0.252561i	0.0290985	+	0.999577i	$0.490736\pi$
$8$		0			0
$9$	8.85168	+	1.62718i	0.983520	+	0.180798i
$10$		0			0
$11$	−8.02427	−	9.56295i	−0.729479	−	0.869359i	0.266036	−	0.963963i	$-0.414286\pi$
$11$	−8.02427	−	9.56295i	−0.729479	−	0.869359i	−0.995515	+	0.0946040i	$0.969842\pi$
$12$		0			0
$13$	−4.30017	+	24.3875i	−0.330783	+	1.87596i	0.134673	+	0.990890i	$0.457002\pi$
$13$	−4.30017	+	24.3875i	−0.330783	+	1.87596i	−0.465455	+	0.885071i	$0.654109\pi$
$14$		0			0
$15$	−19.3092	+	19.1695i	−1.28728	+	1.27796i
$16$		0			0
$17$	−10.2048	−	5.89175i	−0.600283	−	0.346573i	0.168870	−	0.985638i	$-0.445988\pi$
$17$	−10.2048	−	5.89175i	−0.600283	−	0.346573i	−0.769153	+	0.639065i	$0.779322\pi$
$18$		0			0
$19$	15.1967	+	26.3214i	0.799824	+	1.38534i	0.919730	+	0.392551i	$0.128407\pi$
$19$	15.1967	+	26.3214i	0.799824	+	1.38534i	−0.119906	+	0.992785i	$0.538259\pi$
$20$		0			0
$21$	14.0304	+	6.60463i	0.668114	+	0.314506i
$22$		0			0
$23$	1.27127	+	3.49279i	0.0552727	+	0.151860i	0.964256	−	0.264972i	$-0.0853626\pi$
$23$	1.27127	+	3.49279i	0.0552727	+	0.151860i	−0.908984	+	0.416832i	$0.863140\pi$
$24$		0			0
$25$	−9.94260	−	56.3873i	−0.397704	−	2.25549i
$26$		0			0
$27$	26.0023	+	7.27188i	0.963048	+	0.269329i
$28$		0			0
$29$	15.8810	−	2.80026i	0.547622	−	0.0965606i	0.107010	−	0.994258i	$-0.465872\pi$
$29$	15.8810	−	2.80026i	0.547622	−	0.0965606i	0.440612	+	0.897697i	$0.354761\pi$
$30$		0			0
$31$	25.4499	−	9.26301i	0.820965	−	0.298807i	0.102820	−	0.994700i	$-0.467214\pi$
$31$	25.4499	−	9.26301i	0.820965	−	0.298807i	0.718145	+	0.695893i	$0.244991\pi$
$32$		0			0
$33$	−21.3692	−	30.7556i	−0.647552	−	0.931987i
$34$		0			0
$35$	−40.6003	+	23.4406i	−1.16001	+	0.669732i
$36$		0			0
$37$	18.4875	−	32.0213i	0.499662	−	0.865440i	−0.500338	−	0.865830i	$-0.666791\pi$
$37$	18.4875	−	32.0213i	0.499662	−	0.865440i	1.00000		0.000390154i	$0.000124190\pi$
$38$		0			0
$39$	−19.4885	+	71.6894i	−0.499705	+	1.83819i
$40$		0			0
$41$	43.6776	+	7.70154i	1.06531	+	0.187842i	0.678710	−	0.734406i	$-0.262539\pi$
$41$	43.6776	+	7.70154i	1.06531	+	0.187842i	0.386597	+	0.922249i	$0.373650\pi$
$42$		0			0
$43$	−11.4119	+	9.57574i	−0.265394	+	0.222692i	−0.765767	−	0.643118i	$-0.777640\pi$
$43$	−11.4119	+	9.57574i	−0.265394	+	0.222692i	0.500374	+	0.865810i	$0.333196\pi$
$44$		0			0
$45$	−62.9088	+	52.0127i	−1.39797	+	1.15584i
$46$		0			0
$47$	4.54166	−	12.4781i	0.0966311	−	0.265492i	−0.881954	−	0.471336i	$-0.843772\pi$
$47$	4.54166	−	12.4781i	0.0966311	−	0.265492i	0.978585	+	0.205844i	$0.0659941\pi$
$48$		0			0
$49$	−17.0681	−	14.3218i	−0.348328	−	0.292282i
$50$		0			0
$51$	−28.8836	−	20.3813i	−0.566345	−	0.399632i
$52$		0			0
$53$		−	32.6975i		−	0.616935i	−0.951235	−	0.308467i	$-0.900184\pi$
$53$		−	32.6975i		−	0.616935i	0.951235	−	0.308467i	$-0.0998161\pi$
$54$		0			0
$55$	113.220			2.05855
$56$		0			0
$57$	38.2339	+	82.7765i	0.670770	+	1.45222i
$58$		0			0
$59$	−38.0009	+	45.2877i	−0.644083	+	0.767588i	−0.985009	−	0.172502i	$-0.944815\pi$
$59$	−38.0009	+	45.2877i	−0.644083	+	0.767588i	0.340926	+	0.940090i	$0.389259\pi$
$60$		0			0
$61$	−5.41219	−	1.96987i	−0.0887244	−	0.0322930i	0.297277	−	0.954791i	$-0.403922\pi$
$61$	−5.41219	−	1.96987i	−0.0887244	−	0.0322930i	−0.386001	+	0.922498i	$0.626144\pi$
$62$		0			0
$63$	40.1188	+	23.5529i	0.636807	+	0.373855i
$64$		0			0
$65$	−144.368	−	172.051i	−2.22104	−	2.64693i
$66$		0			0
$67$	22.1465	−	125.599i	0.330545	−	1.87461i	−0.136893	−	0.990586i	$-0.543712\pi$
$67$	22.1465	−	125.599i	0.330545	−	1.87461i	0.467438	−	0.884026i	$-0.345177\pi$
$68$		0			0
$69$	2.84691	+	10.7813i	0.0412596	+	0.156251i
$70$		0			0
$71$	−16.0822	−	9.28507i	−0.226510	−	0.130776i	0.382451	−	0.923976i	$-0.375080\pi$
$71$	−16.0822	−	9.28507i	−0.226510	−	0.130776i	−0.608961	+	0.793200i	$0.708413\pi$
$72$		0			0
$73$	−12.4523	−	21.5680i	−0.170579	−	0.295452i	0.768043	−	0.640398i	$-0.221231\pi$
$73$	−12.4523	−	21.5680i	−0.170579	−	0.295452i	−0.938623	+	0.344946i	$0.887897\pi$
$74$		0			0
$75$	−14.3492	−	171.171i	−0.191323	−	2.28228i
$76$		0			0
$77$	−22.0700	−	60.6367i	−0.286623	−	0.787490i
$78$		0			0
$79$	4.35320	+	24.6882i	0.0551038	+	0.312509i	0.999885	−	0.0151939i	$-0.00483656\pi$
$79$	4.35320	+	24.6882i	0.0551038	+	0.312509i	−0.944781	+	0.327703i	$0.893725\pi$
$80$		0			0
$81$	75.7046	+	28.8065i	0.934624	+	0.355636i
$82$		0			0
$83$	86.3752	−	15.2303i	1.04066	−	0.183497i	0.372901	−	0.927871i	$-0.378363\pi$
$83$	86.3752	−	15.2303i	1.04066	−	0.183497i	0.667763	+	0.744374i	$0.267252\pi$
$84$		0			0
$85$	100.426	−	36.5521i	1.18148	−	0.430025i
$86$		0			0
$87$	48.2090	−	4.04135i	0.554126	−	0.0464523i
$88$		0			0
$89$	100.979	−	58.3001i	1.13459	−	0.655057i	0.189507	−	0.981879i	$-0.439311\pi$
$89$	100.979	−	58.3001i	1.13459	−	0.655057i	0.945086	+	0.326822i	$0.105978\pi$
$90$		0			0
$91$	−64.0026	+	110.856i	−0.703326	+	1.21820i
$92$		0			0
$93$	78.5571	−	20.7438i	0.844700	−	0.223051i
$94$		0			0
$95$	−271.467	−	47.8669i	−2.85754	−	0.503862i
$96$		0			0
$97$	−23.1850	+	19.4545i	−0.239020	+	0.200562i	−0.754427	−	0.656384i	$-0.772085\pi$
$97$	−23.1850	+	19.4545i	−0.239020	+	0.200562i	0.515407	+	0.856946i	$0.327641\pi$
$98$		0			0
$99$	−55.4676	−	97.7051i	−0.560279	−	0.986920i
$100$		0			0
$101$	−26.5728	+	73.0083i	−0.263097	+	0.722854i	0.735857	+	0.677137i	$0.236780\pi$
$101$	−26.5728	+	73.0083i	−0.263097	+	0.722854i	−0.998954	+	0.0457173i	$0.985443\pi$
$102$		0			0
$103$	18.9732	+	15.9204i	0.184206	+	0.154567i	0.730228	−	0.683204i	$-0.239414\pi$
$103$	18.9732	+	15.9204i	0.184206	+	0.154567i	−0.546022	+	0.837771i	$0.683858\pi$
$104$		0			0
$105$	−127.681	+	58.9752i	−1.21601	+	0.561668i
$106$		0			0
$107$			114.782i			1.07273i	0.843987	+	0.536363i	$0.180202\pi$
$107$			114.782i			1.07273i	−0.843987	+	0.536363i	$0.819798\pi$
$108$		0			0
$109$	3.10056			0.0284455			0.0142228	−	0.999899i	$-0.495473\pi$
$109$	3.10056			0.0284455			0.0142228	+	0.999899i	$0.495473\pi$
$110$		0			0
$111$	63.9536	−	90.6327i	0.576158	−	0.816511i
$112$		0			0
$113$	−62.5956	+	74.5986i	−0.553944	+	0.660164i	−0.968253	−	0.249972i	$-0.919579\pi$
$113$	−62.5956	+	74.5986i	−0.553944	+	0.660164i	0.414309	+	0.910136i	$0.364023\pi$
$114$		0			0
$115$	−31.6781	−	11.5299i	−0.275462	−	0.100260i
$116$		0			0
$117$	−77.7466	+	208.873i	−0.664501	+	1.78524i
$118$		0			0
$119$	−39.1520	−	46.6595i	−0.329008	−	0.392097i
$120$		0			0
$121$	−6.04971	+	34.3096i	−0.0499976	+	0.283551i
$122$		0			0
$123$	128.395	+	34.9036i	1.04386	+	0.283769i
$124$		0			0
$125$	253.363	+	146.279i	2.02690	+	1.17023i
$126$		0			0
$127$	5.20688	+	9.01857i	0.0409990	+	0.0710124i	0.885797	−	0.464073i	$-0.153613\pi$
$127$	5.20688	+	9.01857i	0.0409990	+	0.0710124i	−0.844798	+	0.535086i	$0.820279\pi$
$128$		0			0
$129$	−36.7021	+	25.5009i	−0.284512	+	0.197682i
$130$		0			0
$131$	4.70359	+	12.9230i	0.0359053	+	0.0986489i	0.956350	−	0.292224i	$-0.0943953\pi$
$131$	4.70359	+	12.9230i	0.0359053	+	0.0986489i	−0.920445	+	0.390873i	$0.872173\pi$
$132$		0			0
$133$	27.2810	+	154.718i	0.205120	+	1.16330i
$134$		0			0
$135$	−202.111	+	138.262i	−1.49712	+	1.02417i
$136$		0			0
$137$	100.620	−	17.7421i	0.734454	−	0.129504i	0.206103	−	0.978530i	$-0.433922\pi$
$137$	100.620	−	17.7421i	0.734454	−	0.129504i	0.528351	+	0.849026i	$0.322811\pi$
$138$		0			0
$139$	109.732	−	39.9393i	0.789442	−	0.287333i	0.0843376	−	0.996437i	$-0.473123\pi$
$139$	109.732	−	39.9393i	0.789442	−	0.287333i	0.705104	+	0.709104i	$0.250900\pi$
$140$		0			0
$141$	16.9668	−	36.0430i	0.120332	−	0.255624i
$142$		0			0
$143$	267.722	−	154.569i	1.87218	−	1.08091i
$144$		0			0
$145$	−73.1281	+	126.662i	−0.504332	+	0.873528i
$146$		0			0
$147$	−47.0926	−	47.4360i	−0.320358	−	0.322694i
$148$		0			0
$149$	62.2656	+	10.9791i	0.417890	+	0.0736853i	0.378640	−	0.925544i	$-0.376392\pi$
$149$	62.2656	+	10.9791i	0.417890	+	0.0736853i	0.0392503	+	0.999229i	$0.487503\pi$
$150$		0			0
$151$	−7.57650	+	6.35744i	−0.0501755	+	0.0421022i	−0.667531	−	0.744582i	$-0.732649\pi$
$151$	−7.57650	+	6.35744i	−0.0501755	+	0.0421022i	0.617355	+	0.786685i	$0.288204\pi$
$152$		0			0
$153$	−80.7428	−	68.7569i	−0.527731	−	0.449392i
$154$		0			0
$155$	−84.0116	+	230.820i	−0.542010	+	1.48916i
$156$		0			0
$157$	−198.571	−	166.621i	−1.26478	−	1.06128i	−0.995155	−	0.0983142i	$-0.968655\pi$
$157$	−198.571	−	166.621i	−1.26478	−	1.06128i	−0.269628	−	0.962965i	$-0.586901\pi$
$158$		0			0
$159$	8.90422	−	97.6877i	0.0560014	−	0.614388i
$160$		0			0
$161$			19.2132i			0.119336i
$162$		0			0
$163$	73.8452			0.453038			0.226519	−	0.974007i	$-0.427265\pi$
$163$	73.8452			0.453038			0.226519	+	0.974007i	$0.427265\pi$
$164$		0			0
$165$	338.259	+	30.8323i	2.05005	+	0.186862i
$166$		0			0
$167$	−35.5492	+	42.3659i	−0.212869	+	0.253688i	−0.861905	−	0.507071i	$-0.830728\pi$
$167$	−35.5492	+	42.3659i	−0.212869	+	0.253688i	0.649035	+	0.760758i	$0.275173\pi$
$168$		0			0
$169$	−417.451	−	151.940i	−2.47012	−	0.899051i
$170$		0			0
$171$	91.6864	+	257.716i	0.536178	+	1.50711i
$172$		0			0
$173$	15.8572	+	18.8979i	0.0916600	+	0.109236i	0.809925	−	0.586534i	$-0.199508\pi$
$173$	15.8572	+	18.8979i	0.0916600	+	0.109236i	−0.718265	+	0.695770i	$0.755063\pi$
$174$		0			0
$175$	51.3939	−	291.470i	0.293680	−	1.66554i
$176$		0			0
$177$	−125.865	+	124.954i	−0.711101	+	0.705954i
$178$		0			0
$179$	64.7771	+	37.3991i	0.361883	+	0.208933i	0.669907	−	0.742445i	$-0.266334\pi$
$179$	64.7771	+	37.3991i	0.361883	+	0.208933i	−0.308023	+	0.951379i	$0.599667\pi$
$180$		0			0
$181$	25.6694	+	44.4608i	0.141820	+	0.245640i	0.928182	−	0.372126i	$-0.121371\pi$
$181$	25.6694	+	44.4608i	0.141820	+	0.245640i	−0.786362	+	0.617766i	$0.788038\pi$
$182$		0			0
$183$	−15.6331	−	7.35908i	−0.0854267	−	0.0402135i
$184$		0			0
$185$	114.696	+	315.123i	0.619976	+	1.70337i
$186$		0			0
$187$	25.5436	+	144.865i	0.136597	+	0.774679i
$188$		0			0
$189$	113.446	+	81.2920i	0.600242	+	0.430117i
$190$		0			0
$191$	−71.5883	+	12.6229i	−0.374808	+	0.0660887i	−0.357879	−	0.933768i	$-0.616500\pi$
$191$	−71.5883	+	12.6229i	−0.374808	+	0.0660887i	−0.0169287	+	0.999857i	$0.505389\pi$
$192$		0			0
$193$	211.186	−	76.8653i	1.09423	−	0.398266i	0.269041	−	0.963129i	$-0.413293\pi$
$193$	211.186	−	76.8653i	1.09423	−	0.398266i	0.825185	+	0.564863i	$0.191071\pi$
$194$		0			0
$195$	−384.462	−	553.336i	−1.97160	−	2.83762i
$196$		0			0
$197$	−265.235	+	153.133i	−1.34637	+	0.777327i	−0.987733	−	0.156150i	$-0.950092\pi$
$197$	−265.235	+	153.133i	−1.34637	+	0.777327i	−0.358636	+	0.933477i	$0.616758\pi$
$198$		0			0
$199$	−178.147	+	308.560i	−0.895211	+	1.55055i	−0.0616670	+	0.998097i	$0.519642\pi$
$199$	−178.147	+	308.560i	−0.895211	+	1.55055i	−0.833544	+	0.552454i	$0.813692\pi$
$200$		0			0
$201$	100.368	−	369.210i	0.499345	−	1.83687i
$202$		0			0
$203$	82.0901	+	14.4747i	0.404385	+	0.0713040i
$204$		0			0
$205$	−308.140	+	258.560i	−1.50312	+	1.26127i
$206$		0			0
$207$	5.56950	+	32.9857i	0.0269058	+	0.159351i
$208$		0			0
$209$	129.768	−	356.535i	0.620900	−	1.70591i
$210$		0			0
$211$	150.094	+	125.944i	0.711344	+	0.596889i	0.924976	−	0.380026i	$-0.124085\pi$
$211$	150.094	+	125.944i	0.711344	+	0.596889i	−0.213632	+	0.976914i	$0.568529\pi$
$212$		0			0
$213$	−45.5189	−	32.1197i	−0.213704	−	0.150797i
$214$		0			0
$215$		−	135.111i		−	0.628425i
$216$		0			0
$217$	139.995			0.645138
$218$		0			0
$219$	−31.3293	−	67.8279i	−0.143056	−	0.309717i
$220$		0			0
$221$	187.567	−	223.534i	0.848722	−	1.01147i
$222$		0			0
$223$	70.5441	+	25.6760i	0.316341	+	0.115139i	0.495311	−	0.868716i	$-0.335054\pi$
$223$	70.5441	+	25.6760i	0.316341	+	0.115139i	−0.178970	+	0.983855i	$0.557276\pi$
$224$		0			0
$225$	3.74344	−	515.301i	0.0166375	−	2.29023i
$226$		0			0
$227$	−106.959	−	127.469i	−0.471186	−	0.561537i	0.477144	−	0.878825i	$-0.341672\pi$
$227$	−106.959	−	127.469i	−0.471186	−	0.561537i	−0.948329	+	0.317288i	$0.897228\pi$
$228$		0			0
$229$	−38.2406	+	216.873i	−0.166990	+	0.947045i	0.780000	+	0.625780i	$0.215219\pi$
$229$	−38.2406	+	216.873i	−0.166990	+	0.947045i	−0.946989	+	0.321265i	$0.895892\pi$
$230$		0			0
$231$	−49.4239	−	187.169i	−0.213956	−	0.810257i
$232$		0			0
$233$	71.3485	+	41.1931i	0.306217	+	0.176794i	0.645232	−	0.763986i	$-0.276761\pi$
$233$	71.3485	+	41.1931i	0.306217	+	0.176794i	−0.339015	+	0.940781i	$0.610094\pi$
$234$		0			0
$235$	60.2171	+	104.299i	0.256243	+	0.443826i
$236$		0			0
$237$	6.28257	+	74.9444i	0.0265087	+	0.316221i
$238$		0			0
$239$	93.2652	+	256.244i	0.390231	+	1.07215i	0.966896	+	0.255170i	$0.0821315\pi$
$239$	93.2652	+	256.244i	0.390231	+	1.07215i	−0.576665	+	0.816981i	$0.695646\pi$
$240$		0			0
$241$	−63.9524	−	362.692i	−0.265363	−	1.50495i	−0.768001	−	0.640449i	$-0.778748\pi$
$241$	−63.9524	−	362.692i	−0.265363	−	1.50495i	0.502638	−	0.864497i	$-0.332363\pi$
$242$		0			0
$243$	218.331	+	106.679i	0.898484	+	0.439007i
$244$		0			0
$245$	199.007	−	35.0903i	0.812273	−	0.143226i
$246$		0			0
$247$	−707.261	+	257.422i	−2.86341	+	1.04219i
$248$		0			0
$249$	262.203	−	21.9804i	1.05302	−	0.0882749i
$250$		0			0
$251$	99.9011	−	57.6779i	0.398012	−	0.229793i	−0.287614	−	0.957747i	$-0.592862\pi$
$251$	99.9011	−	57.6779i	0.398012	−	0.229793i	0.685626	+	0.727954i	$0.259529\pi$
$252$		0			0
$253$	23.2004	−	40.1842i	0.0917010	−	0.158831i
$254$		0			0
$255$	309.989	−	81.8556i	1.21564	−	0.321002i
$256$		0			0
$257$	−221.323	−	39.0252i	−0.861178	−	0.151849i	−0.274419	−	0.961610i	$-0.588485\pi$
$257$	−221.323	−	39.0252i	−0.861178	−	0.151849i	−0.586759	+	0.809761i	$0.699597\pi$
$258$		0			0
$259$	146.411	−	122.854i	0.565294	−	0.474338i
$260$		0			0
$261$	145.130	+	1.05431i	0.556055	+	0.00403950i
$262$		0			0
$263$	178.665	−	490.877i	0.679333	−	1.86645i	0.229616	−	0.973281i	$-0.426253\pi$
$263$	178.665	−	490.877i	0.679333	−	1.86645i	0.449717	−	0.893171i	$-0.351525\pi$
$264$		0			0
$265$	227.173	+	190.620i	0.857255	+	0.719322i
$266$		0			0
$267$	317.562	−	146.680i	1.18937	−	0.549362i
$268$		0			0
$269$			441.795i			1.64236i	0.570670	+	0.821179i	$0.306683\pi$
$269$			441.795i			1.64236i	−0.570670	+	0.821179i	$0.693317\pi$
$270$		0			0
$271$	−147.991			−0.546092			−0.273046	−	0.962001i	$-0.588031\pi$
$271$	−147.991			−0.546092			−0.273046	+	0.962001i	$0.588031\pi$
$272$		0			0
$273$	−221.404	+	313.765i	−0.811002	+	1.14932i
$274$		0			0
$275$	−459.447	+	547.547i	−1.67072	+	1.99108i
$276$		0			0
$277$	−236.701	−	86.1520i	−0.854515	−	0.311018i	−0.122635	−	0.992452i	$-0.539135\pi$
$277$	−236.701	−	86.1520i	−0.854515	−	0.311018i	−0.731880	+	0.681434i	$0.761357\pi$
$278$		0			0
$279$	240.347	−	40.5817i	0.861459	−	0.145454i
$280$		0			0
$281$	−191.977	−	228.789i	−0.683191	−	0.814195i	0.307323	−	0.951605i	$-0.400567\pi$
$281$	−191.977	−	228.789i	−0.683191	−	0.814195i	−0.990514	+	0.137410i	$0.956122\pi$
$282$		0			0
$283$	33.3735	−	189.270i	0.117928	−	0.668800i	−0.867331	−	0.497731i	$-0.834167\pi$
$283$	33.3735	−	189.270i	0.117928	−	0.668800i	0.985259	−	0.171069i	$-0.0547222\pi$
$284$		0			0
$285$	−798.003	−	216.934i	−2.80001	−	0.761171i
$286$		0			0
$287$	198.541	+	114.628i	0.691780	+	0.399400i
$288$		0			0
$289$	−75.0746	−	130.033i	−0.259774	−	0.449941i
$290$		0			0
$291$	−74.5656	+	51.8088i	−0.256239	+	0.178037i
$292$		0			0
$293$	−89.1832	−	245.029i	−0.304379	−	0.836276i	−0.993726	−	0.111844i	$-0.964324\pi$
$293$	−89.1832	−	245.029i	−0.304379	−	0.836276i	0.689346	−	0.724432i	$-0.257898\pi$
$294$		0			0
$295$	−93.1073	−	528.037i	−0.315618	−	1.78996i
$296$		0			0
$297$	−139.109	−	307.010i	−0.468380	−	1.03370i
$298$		0			0
$299$	−90.6471	+	15.9835i	−0.303168	+	0.0534566i
$300$		0			0
$301$	−72.3607	+	26.3371i	−0.240401	+	0.0874988i
$302$		0			0
$303$	−99.2711	+	210.884i	−0.327627	+	0.695988i
$304$		0			0
$305$	45.2381	−	26.1182i	0.148322	−	0.0856335i
$306$		0			0
$307$	−18.5076	+	32.0561i	−0.0602854	+	0.104417i	−0.894593	−	0.446882i	$-0.852534\pi$
$307$	−18.5076	+	32.0561i	−0.0602854	+	0.104417i	0.834308	+	0.551299i	$0.185868\pi$
$308$		0			0
$309$	52.3492	+	52.7309i	0.169415	+	0.170650i
$310$		0			0
$311$	371.672	+	65.5358i	1.19509	+	0.210726i	0.735573	−	0.677445i	$-0.236913\pi$
$311$	371.672	+	65.5358i	1.19509	+	0.210726i	0.459513	+	0.888171i	$0.348024\pi$
$312$		0			0
$313$	−83.1751	+	69.7922i	−0.265735	+	0.222978i	−0.765913	−	0.642945i	$-0.777713\pi$
$313$	−83.1751	+	69.7922i	−0.265735	+	0.222978i	0.500178	+	0.865923i	$0.333268\pi$
$314$		0			0
$315$	−397.523	+	141.425i	−1.26198	+	0.448968i
$316$		0			0
$317$	75.1050	−	206.349i	0.236924	−	0.650944i	−0.763065	−	0.646322i	$-0.776306\pi$
$317$	75.1050	−	206.349i	0.236924	−	0.650944i	0.999989	−	0.00462232i	$-0.00147133\pi$
$318$		0			0
$319$	−154.212	−	129.400i	−0.483425	−	0.405641i
$320$		0			0
$321$	−31.2574	+	342.924i	−0.0973752	+	1.06830i
$322$		0			0
$323$		−	358.140i		−	1.10879i
$324$		0			0
$325$	1417.90			4.36277
$326$		0			0
$327$	9.26328	+	0.844347i	0.0283281	+	0.00258210i
$328$		0			0
$329$	44.1207	−	52.5810i	0.134106	−	0.159821i
$330$		0			0
$331$	213.619	+	77.7508i	0.645373	+	0.234897i	0.643909	−	0.765102i	$-0.277312\pi$
$331$	213.619	+	77.7508i	0.645373	+	0.234897i	0.00146448	+	0.999999i	$0.499534\pi$
$332$		0			0
$333$	215.750	−	253.360i	0.647897	−	0.760840i
$334$		0			0
$335$	743.514	+	886.085i	2.21944	+	2.64503i
$336$		0			0
$337$	54.8763	−	311.219i	0.162838	−	0.923498i	−0.788429	−	0.615126i	$-0.789105\pi$
$337$	54.8763	−	311.219i	0.162838	−	0.923498i	0.951266	−	0.308371i	$-0.0997839\pi$
$338$		0			0
$339$	−207.326	+	205.826i	−0.611582	+	0.607156i
$340$		0			0
$341$	−292.799	−	169.047i	−0.858647	−	0.495740i
$342$		0			0
$343$	−184.227	−	319.091i	−0.537106	−	0.930295i
$344$		0			0
$345$	−91.5022	−	43.0735i	−0.265224	−	0.124851i
$346$		0			0
$347$	−66.7953	−	183.519i	−0.192494	−	0.528872i	0.805471	−	0.592635i	$-0.201912\pi$
$347$	−66.7953	−	183.519i	−0.192494	−	0.528872i	−0.997965	+	0.0637625i	$0.979690\pi$
$348$		0			0
$349$	−5.94104	−	33.6933i	−0.0170230	−	0.0965424i	0.975113	−	0.221711i	$-0.0711640\pi$
$349$	−5.94104	−	33.6933i	−0.0170230	−	0.0965424i	−0.992136	+	0.125168i	$0.960053\pi$
$350$		0			0
$351$	−289.157	+	602.861i	−0.823810	+	1.71755i
$352$		0			0
$353$	−578.312	+	101.972i	−1.63828	+	0.288872i	−0.915533	−	0.402243i	$-0.868231\pi$
$353$	−578.312	+	101.972i	−1.63828	+	0.288872i	−0.722744	+	0.691116i	$0.757119\pi$
$354$		0			0
$355$	158.266	−	57.6041i	0.445820	−	0.162265i
$356$		0			0
$357$	−104.265	−	150.063i	−0.292058	−	0.420343i
$358$		0			0
$359$	90.7994	−	52.4230i	0.252923	−	0.146025i	−0.368179	−	0.929755i	$-0.620019\pi$
$359$	90.7994	−	52.4230i	0.252923	−	0.146025i	0.621102	+	0.783730i	$0.286685\pi$
$360$		0			0
$361$	−281.377	+	487.359i	−0.779438	+	1.35003i
$362$		0			0
$363$	−27.4174	+	100.856i	−0.0755301	+	0.277841i
$364$		0			0
$365$	222.443	+	39.2226i	0.609432	+	0.107459i
$366$		0			0
$367$	−511.458	+	429.164i	−1.39362	+	1.16938i	−0.429769	+	0.902939i	$0.641405\pi$
$367$	−511.458	+	429.164i	−1.39362	+	1.16938i	−0.963850	+	0.266446i	$0.914151\pi$
$368$		0			0
$369$	374.089	+	139.243i	1.01379	+	0.377352i
$370$		0			0
$371$	57.8068	−	158.823i	0.155813	−	0.428094i
$372$		0			0
$373$	−160.782	−	134.912i	−0.431052	−	0.361696i	0.401296	−	0.915948i	$-0.368560\pi$
$373$	−160.782	−	134.912i	−0.431052	−	0.361696i	−0.832349	+	0.554253i	$0.813004\pi$
$374$		0			0
$375$	717.116	+	506.022i	1.91231	+	1.34939i
$376$		0			0
$377$			399.341i			1.05926i
$378$		0			0
$379$	252.724			0.666819			0.333409	−	0.942782i	$-0.391801\pi$
$379$	252.724			0.666819			0.333409	+	0.942782i	$0.391801\pi$
$380$		0			0
$381$	13.1002	+	28.3620i	0.0343837	+	0.0744409i
$382$		0			0
$383$	35.4631	−	42.2632i	0.0925929	−	0.110348i	−0.717758	−	0.696292i	$-0.754832\pi$
$383$	35.4631	−	42.2632i	0.0925929	−	0.110348i	0.810351	+	0.585944i	$0.199276\pi$
$384$		0			0
$385$	549.949	+	200.165i	1.42844	+	0.519909i
$386$		0			0
$387$	−116.596	+	66.1922i	−0.301282	+	0.171039i
$388$		0			0
$389$	−151.871	−	180.992i	−0.390413	−	0.465276i	0.534659	−	0.845068i	$-0.320440\pi$
$389$	−151.871	−	180.992i	−0.390413	−	0.465276i	−0.925072	+	0.379792i	$0.875996\pi$
$390$		0			0
$391$	7.60556	−	43.1333i	0.0194516	−	0.110315i
$392$		0			0
$393$	10.5333	+	39.8899i	0.0268023	+	0.101501i
$394$		0			0
$395$	−196.905	−	113.683i	−0.498493	−	0.287805i
$396$		0			0
$397$	−299.747	−	519.177i	−0.755030	−	1.30775i	−0.945360	−	0.326029i	$-0.894289\pi$
$397$	−299.747	−	519.177i	−0.755030	−	1.30775i	0.190330	−	0.981720i	$-0.439044\pi$
$398$		0			0
$399$	39.3722	+	469.668i	0.0986771	+	1.17711i
$400$		0			0
$401$	51.5224	+	141.557i	0.128485	+	0.353009i	0.987210	−	0.159428i	$-0.0509650\pi$
$401$	51.5224	+	141.557i	0.128485	+	0.353009i	−0.858725	+	0.512437i	$0.828743\pi$
$402$		0			0
$403$	116.463	+	660.492i	0.288989	+	1.63894i
$404$		0			0
$405$	−641.482	+	358.036i	−1.58391	+	0.884039i
$406$		0			0
$407$	−454.567	+	80.1524i	−1.11687	+	0.196935i
$408$		0			0
$409$	458.833	−	167.001i	1.12184	−	0.408317i	0.286517	−	0.958075i	$-0.407503\pi$
$409$	458.833	−	167.001i	1.12184	−	0.408317i	0.835324	+	0.549759i	$0.185280\pi$
$410$		0			0
$411$	305.446	−	25.6055i	0.743178	−	0.0623004i
$412$		0			0
$413$	−264.648	+	152.795i	−0.640795	+	0.369963i
$414$		0			0
$415$	−397.735	+	688.898i	−0.958398	+	1.65999i
$416$		0			0
$417$	338.714	−	89.4409i	0.812265	−	0.214487i
$418$		0			0
$419$	−694.811	−	122.514i	−1.65826	−	0.292396i	−0.735429	−	0.677602i	$-0.763019\pi$
$419$	−694.811	−	122.514i	−1.65826	−	0.292396i	−0.922831	+	0.385206i	$0.874130\pi$
$420$		0			0
$421$	185.913	−	155.999i	0.441598	−	0.370545i	−0.394709	−	0.918806i	$-0.629155\pi$
$421$	185.913	−	155.999i	0.441598	−	0.370545i	0.836307	+	0.548261i	$0.184710\pi$
$422$		0			0
$423$	60.5055	−	103.062i	0.143039	−	0.243646i
$424$		0			0
$425$	−230.757	+	634.001i	−0.542958	+	1.49177i
$426$		0			0
$427$	−22.8062	−	19.1367i	−0.0534103	−	0.0448166i
$428$		0			0
$429$	841.943	−	388.888i	1.96257	−	0.906498i
$430$		0			0
$431$		−	536.154i		−	1.24398i	−0.783026	−	0.621989i	$-0.786325\pi$
$431$		−	536.154i		−	1.24398i	0.783026	−	0.621989i	$-0.213675\pi$
$432$		0			0
$433$	−471.669			−1.08931			−0.544653	−	0.838662i	$-0.683339\pi$
$433$	−471.669			−1.08931			−0.544653	+	0.838662i	$0.683339\pi$
$434$		0			0
$435$	−252.971	+	358.502i	−0.581543	+	0.824142i
$436$		0			0
$437$	−72.6160	+	86.5404i	−0.166169	+	0.198033i
$438$		0			0
$439$	317.485	+	115.555i	0.723201	+	0.263224i	0.677284	−	0.735722i	$-0.263157\pi$
$439$	317.485	+	115.555i	0.723201	+	0.263224i	0.0459168	+	0.998945i	$0.485379\pi$
$440$		0			0
$441$	−127.777	−	154.545i	−0.289744	−	0.350442i
$442$		0			0
$443$	292.258	+	348.299i	0.659724	+	0.786229i	0.987346	−	0.158580i	$-0.0506916\pi$
$443$	292.258	+	348.299i	0.659724	+	0.786229i	−0.327622	+	0.944809i	$0.606247\pi$
$444$		0			0
$445$	−183.635	+	1041.45i	−0.412664	+	2.34033i
$446$		0			0
$447$	183.036	+	49.7576i	0.409476	+	0.111314i
$448$		0			0
$449$	64.6866	+	37.3468i	0.144068	+	0.0831778i	0.570301	−	0.821435i	$-0.306826\pi$
$449$	64.6866	+	37.3468i	0.144068	+	0.0831778i	−0.426233	+	0.904613i	$0.640160\pi$
$450$		0			0
$451$	−276.831	−	479.486i	−0.613817	−	1.06316i
$452$		0			0
$453$	−24.3669	+	16.9303i	−0.0537901	+	0.0373738i
$454$		0			0
$455$	−397.069	−	1090.94i	−0.872680	−	2.39767i
$456$		0			0
$457$	137.019	+	777.072i	0.299822	+	1.70038i	0.646928	+	0.762551i	$0.276053\pi$
$457$	137.019	+	777.072i	0.299822	+	1.70038i	−0.347106	+	0.937826i	$0.612836\pi$
$458$		0			0
$459$	−222.504	−	227.407i	−0.484759	−	0.495440i
$460$		0			0
$461$	−564.667	+	99.5661i	−1.22487	+	0.215978i	−0.748423	−	0.663222i	$-0.769189\pi$
$461$	−564.667	+	99.5661i	−1.22487	+	0.215978i	−0.476452	+	0.879200i	$0.658077\pi$
$462$		0			0
$463$	847.662	−	308.524i	1.83080	−	0.666358i	0.838139	−	0.545456i	$-0.183643\pi$
$463$	847.662	−	308.524i	1.83080	−	0.666358i	0.992664	−	0.120902i	$-0.0385787\pi$
$464$		0			0
$465$	−313.851	+	666.723i	−0.674949	+	1.43381i
$466$		0			0
$467$	−110.344	+	63.7074i	−0.236284	+	0.136418i	−0.613467	−	0.789720i	$-0.710226\pi$
$467$	−110.344	+	63.7074i	−0.236284	+	0.136418i	0.377184	+	0.926138i	$0.376892\pi$
$468$		0			0
$469$	329.622	−	570.923i	0.702820	−	1.21732i
$470$		0			0
$471$	−547.879	−	551.874i	−1.16323	−	1.17171i
$472$		0			0
$473$	183.145	+	32.2933i	0.387198	+	0.0682735i
$474$		0			0
$475$	1333.10	−	1118.60i	2.80652	−	2.35495i
$476$		0			0
$477$	53.2047	−	289.428i	0.111540	−	0.606768i
$478$		0			0
$479$	281.307	−	772.884i	0.587279	−	1.61354i	−0.188177	−	0.982135i	$-0.560258\pi$
$479$	281.307	−	772.884i	0.587279	−	1.61354i	0.775457	−	0.631401i	$-0.217520\pi$
$480$		0			0
$481$	701.420	+	588.561i	1.45825	+	1.22362i
$482$		0			0
$483$	−5.23214	+	57.4015i	−0.0108326	+	0.118844i
$484$		0			0
$485$		−	274.498i		−	0.565976i
$486$		0			0
$487$	−345.025			−0.708469			−0.354235	−	0.935157i	$-0.615259\pi$
$487$	−345.025			−0.708469			−0.354235	+	0.935157i	$0.615259\pi$
$488$		0			0
$489$	220.621	+	20.1096i	0.451168	+	0.0411239i
$490$		0			0
$491$	569.914	−	679.197i	1.16072	−	1.38329i	0.251044	−	0.967976i	$-0.419226\pi$
$491$	569.914	−	679.197i	1.16072	−	1.38329i	0.909676	−	0.415318i	$-0.136330\pi$
$492$		0			0
$493$	−178.561	−	64.9910i	−0.362193	−	0.131828i
$494$		0			0
$495$	1002.19	+	184.230i	2.02463	+	0.372181i
$496$		0			0
$497$	−61.7013	−	73.5328i	−0.124148	−	0.147953i
$498$		0			0
$499$	128.020	−	726.037i	0.256553	−	1.45498i	−0.535501	−	0.844534i	$-0.679877\pi$
$499$	128.020	−	726.037i	0.256553	−	1.45498i	0.792054	−	0.610450i	$-0.209012\pi$
$500$		0			0
$501$	−117.744	+	116.892i	−0.235019	+	0.233318i
$502$		0			0
$503$	−543.101	−	313.559i	−1.07972	−	0.623378i	−0.148901	−	0.988852i	$-0.547574\pi$
$503$	−543.101	−	313.559i	−1.07972	−	0.623378i	−0.930822	+	0.365474i	$0.880907\pi$
$504$		0			0
$505$	−352.325	−	610.244i	−0.697673	−	1.20840i
$506$		0			0
$507$	−1205.81	−	567.617i	−2.37831	−	1.11956i
$508$		0			0
$509$	−154.185	−	423.621i	−0.302918	−	0.832261i	−0.993990	−	0.109475i	$-0.965083\pi$
$509$	−154.185	−	423.621i	−0.302918	−	0.832261i	0.691071	−	0.722787i	$-0.257139\pi$
$510$		0			0
$511$	−22.3543	−	126.778i	−0.0437463	−	0.248097i
$512$		0			0
$513$	203.742	+	794.925i	0.397158	+	1.54956i
$514$		0			0
$515$	−221.221	+	39.0072i	−0.429554	+	0.0757420i
$516$		0			0
$517$	−155.771	+	56.6961i	−0.301298	+	0.109664i
$518$		0			0
$519$	42.2289	+	60.7777i	0.0813658	+	0.117105i
$520$		0			0
$521$	170.332	−	98.3414i	0.326934	−	0.188755i	−0.327545	−	0.944835i	$-0.606221\pi$
$521$	170.332	−	98.3414i	0.326934	−	0.188755i	0.654479	+	0.756080i	$0.272888\pi$
$522$		0			0
$523$	−42.9560	+	74.4020i	−0.0821338	+	0.142260i	−0.904166	−	0.427181i	$-0.859507\pi$
$523$	−42.9560	+	74.4020i	−0.0821338	+	0.142260i	0.822032	+	0.569441i	$0.192840\pi$
$524$		0			0
$525$	232.918	−	856.803i	0.443654	−	1.63201i
$526$		0			0
$527$	−314.287	−	55.4172i	−0.596370	−	0.105156i
$528$		0			0
$529$	394.654	−	331.154i	0.746038	−	0.626000i
$530$		0			0
$531$	−410.063	+	339.038i	−0.772247	+	0.638490i
$532$		0			0
$533$	−375.643	+	1032.07i	−0.704771	+	1.93634i
$534$		0			0
$535$	−797.469	−	669.156i	−1.49060	−	1.25076i
$536$		0			0
$537$	183.345	+	129.374i	0.341424	+	0.240920i
$538$		0			0
$539$			278.143i			0.516035i
$540$		0			0
$541$	41.8885			0.0774280			0.0387140	−	0.999250i	$-0.487674\pi$
$541$	41.8885			0.0774280			0.0387140	+	0.999250i	$0.487674\pi$
$542$		0			0
$543$	64.5828	+	139.822i	0.118937	+	0.257499i
$544$		0			0
$545$	−18.0757	+	21.5418i	−0.0331664	+	0.0395262i
$546$		0			0
$547$	−309.456	−	112.633i	−0.565734	−	0.205910i	0.0432895	−	0.999063i	$-0.486216\pi$
$547$	−309.456	−	112.633i	−0.565734	−	0.205910i	−0.609023	+	0.793152i	$0.708438\pi$
$548$		0			0
$549$	−44.7016	−	26.2433i	−0.0814237	−	0.0478020i
$550$		0			0
$551$	315.045	+	375.457i	0.571770	+	0.681409i
$552$		0			0
$553$	−22.5020	+	127.615i	−0.0406907	+	0.230769i
$554$		0			0
$555$	256.851	+	972.701i	0.462795	+	1.75262i
$556$		0			0
$557$	−155.332	−	89.6808i	−0.278872	−	0.161007i	0.354041	−	0.935230i	$-0.384807\pi$
$557$	−155.332	−	89.6808i	−0.278872	−	0.161007i	−0.632913	+	0.774223i	$0.718141\pi$
$558$		0			0
$559$	−184.455	−	319.486i	−0.329973	−	0.571531i
$560$		0			0
$561$	36.8647	+	439.757i	0.0657125	+	0.783880i
$562$		0			0
$563$	262.510	+	721.242i	0.466271	+	1.28107i	0.920695	+	0.390283i	$0.127623\pi$
$563$	262.510	+	721.242i	0.466271	+	1.28107i	−0.454424	+	0.890785i	$0.650155\pi$
$564$		0			0
$565$	−153.368	−	869.791i	−0.271447	−	1.53945i
$566$		0			0
$567$	316.795	+	273.763i	0.558721	+	0.482827i
$568$		0			0
$569$	708.762	−	124.974i	1.24563	−	0.219638i	0.488302	−	0.872675i	$-0.337617\pi$
$569$	708.762	−	124.974i	1.24563	−	0.219638i	0.757326	+	0.653037i	$0.226506\pi$
$570$		0			0
$571$	−695.872	+	253.277i	−1.21869	+	0.443567i	−0.869710	−	0.493564i	$-0.835694\pi$
$571$	−695.872	+	253.277i	−1.21869	+	0.443567i	−0.348980	+	0.937130i	$0.613472\pi$
$572$		0			0
$573$	−217.316	+	18.2175i	−0.379259	+	0.0317932i
$574$		0			0
$575$	184.309	−	106.411i	0.320538	−	0.185063i
$576$		0			0
$577$	0.950090	−	1.64560i	0.00164660	−	0.00285200i	−0.865201	−	0.501425i	$-0.832809\pi$
$577$	0.950090	−	1.64560i	0.00164660	−	0.00285200i	0.866848	+	0.498573i	$0.166143\pi$
$578$		0			0
$579$	651.873	−	172.134i	1.12586	−	0.297295i
$580$		0			0
$581$	446.479	+	78.7263i	0.768466	+	0.135501i
$582$		0			0
$583$	−312.685	+	262.374i	−0.536338	+	0.450041i
$584$		0			0
$585$	−997.940	−	1757.85i	−1.70588	−	3.00487i
$586$		0			0
$587$	−152.561	+	419.159i	−0.259900	+	0.714069i	0.739273	+	0.673406i	$0.235169\pi$
$587$	−152.561	+	419.159i	−0.259900	+	0.714069i	−0.999173	+	0.0406634i	$0.987053\pi$
$588$		0			0
$589$	630.569	+	529.110i	1.07058	+	0.898320i
$590$		0			0
$591$	−834.121	+	385.275i	−1.41137	+	0.651903i
$592$		0			0
$593$		−	787.081i		−	1.32729i	−0.748049	−	0.663643i	$-0.769009\pi$
$593$		−	787.081i		−	1.32729i	0.748049	−	0.663643i	$-0.230991\pi$
$594$		0			0
$595$	552.425			0.928445
$596$		0			0
$597$	−616.262	+	873.344i	−1.03226	+	1.46289i
$598$		0			0
$599$	576.208	−	686.698i	0.961950	−	1.14641i	−0.0272196	−	0.999629i	$-0.508665\pi$
$599$	576.208	−	686.698i	0.961950	−	1.14641i	0.989169	−	0.146778i	$-0.0468902\pi$
$600$		0			0
$601$	511.873	+	186.306i	0.851702	+	0.309994i	0.730734	−	0.682662i	$-0.239178\pi$
$601$	511.873	+	186.306i	0.851702	+	0.309994i	0.120968	+	0.992656i	$0.461400\pi$
$602$		0			0
$603$	400.406	−	1075.73i	0.664023	−	1.78396i
$604$		0			0
$605$	−203.104	−	242.050i	−0.335709	−	0.400083i
$606$		0			0
$607$	−115.488	+	654.967i	−0.190261	+	1.07902i	0.728747	+	0.684783i	$0.240103\pi$
$607$	−115.488	+	654.967i	−0.190261	+	1.07902i	−0.919008	+	0.394240i	$0.871008\pi$
$608$		0			0
$609$	241.312	+	65.5997i	0.396243	+	0.107717i
$610$		0			0
$611$	284.780	+	164.418i	0.466089	+	0.269096i
$612$		0			0
$613$	−306.294	−	530.517i	−0.499664	−	0.865443i	0.500336	−	0.865831i	$-0.333210\pi$
$613$	−306.294	−	530.517i	−0.499664	−	0.865443i	−1.00000		0.000387906i	$0.999877\pi$
$614$		0			0
$615$	−991.015	+	688.566i	−1.61141	+	1.11962i
$616$		0			0
$617$	332.810	+	914.388i	0.539401	+	1.48199i	0.847583	+	0.530664i	$0.178057\pi$
$617$	332.810	+	914.388i	0.539401	+	1.48199i	−0.308182	+	0.951327i	$0.599721\pi$
$618$		0			0
$619$	96.0746	+	544.866i	0.155209	+	0.880236i	0.958594	+	0.284776i	$0.0919192\pi$
$619$	96.0746	+	544.866i	0.155209	+	0.880236i	−0.803385	+	0.595460i	$0.796970\pi$
$620$		0			0
$621$	7.65685	+	100.065i	0.0123299	+	0.161135i
$622$		0			0
$623$	593.557	−	104.660i	0.952741	−	0.167994i
$624$		0			0
$625$	−1148.26	+	417.932i	−1.83721	+	0.668691i
$626$		0			0
$627$	484.789	−	1029.85i	0.773188	−	1.64250i
$628$		0			0
$629$	−377.323	+	217.847i	−0.599877	+	0.346339i
$630$		0			0
$631$	145.793	−	252.521i	0.231051	−	0.400192i	−0.727067	−	0.686567i	$-0.759117\pi$
$631$	145.793	−	252.521i	0.231051	−	0.400192i	0.958118	+	0.286375i	$0.0924503\pi$
$632$		0			0
$633$	414.125	+	417.144i	0.654226	+	0.658996i
$634$		0			0
$635$	−93.0134	−	16.4008i	−0.146478	−	0.0258280i
$636$		0			0
$637$	422.668	−	354.661i	0.663530	−	0.556768i
$638$		0			0
$639$	−127.246	−	108.357i	−0.199133	−	0.169573i
$640$		0			0
$641$	212.431	−	583.650i	0.331406	−	0.910531i	−0.656341	−	0.754465i	$-0.727897\pi$
$641$	212.431	−	583.650i	0.331406	−	0.910531i	0.987747	−	0.156066i	$-0.0498812\pi$
$642$		0			0
$643$	−425.321	−	356.887i	−0.661463	−	0.555034i	0.249062	−	0.968488i	$-0.419878\pi$
$643$	−425.321	−	356.887i	−0.661463	−	0.555034i	−0.910525	+	0.413454i	$0.864322\pi$
$644$		0			0
$645$	36.7936	−	403.661i	0.0570443	−	0.625830i
$646$		0			0
$647$			46.3565i			0.0716484i	0.999358	+	0.0358242i	$0.0114056\pi$
$647$			46.3565i			0.0716484i	−0.999358	+	0.0358242i	$0.988594\pi$
$648$		0			0
$649$	738.014			1.13716
$650$		0			0
$651$	418.251	+	38.1235i	0.642475	+	0.0585615i
$652$		0			0
$653$	358.818	−	427.622i	0.549491	−	0.654858i	−0.417797	−	0.908541i	$-0.637198\pi$
$653$	358.818	−	427.622i	0.549491	−	0.654858i	0.967287	+	0.253683i	$0.0816420\pi$
$654$		0			0
$655$	−117.206	−	42.6596i	−0.178941	−	0.0651291i
$656$		0			0
$657$	−75.1288	−	211.175i	−0.114351	−	0.321424i
$658$		0			0
$659$	454.676	+	541.862i	0.689948	+	0.822248i	0.991349	−	0.131249i	$-0.0418988\pi$
$659$	454.676	+	541.862i	0.689948	+	0.822248i	−0.301401	+	0.953497i	$0.597454\pi$
$660$		0			0
$661$	19.9324	−	113.042i	0.0301549	−	0.171017i	−0.966011	−	0.258501i	$-0.916772\pi$
$661$	19.9324	−	113.042i	0.0301549	−	0.171017i	0.996166	+	0.0874839i	$0.0278826\pi$
$662$		0			0
$663$	621.252	−	616.756i	0.937032	−	0.930250i
$664$		0			0
$665$	−1233.98	−	712.438i	−1.85561	−	1.07134i
$666$		0			0
$667$	29.9698	+	51.9093i	0.0449323	+	0.0778250i
$668$		0			0
$669$	203.767	+	95.9205i	0.304584	+	0.143379i
$670$		0			0
$671$	24.5910	+	67.5633i	0.0366483	+	0.100690i
$672$		0			0
$673$	32.9696	+	186.980i	0.0489889	+	0.277830i	0.999455	−	0.0329969i	$-0.0105051\pi$
$673$	32.9696	+	186.980i	0.0489889	+	0.277830i	−0.950467	+	0.310827i	$0.899394\pi$
$674$		0			0
$675$	151.511	−	1538.50i	0.224461	−	2.27926i
$676$		0			0
$677$	411.494	−	72.5575i	0.607820	−	0.107175i	0.138737	−	0.990329i	$-0.455696\pi$
$677$	411.494	−	72.5575i	0.607820	−	0.107175i	0.469083	+	0.883154i	$0.344585\pi$
$678$		0			0
$679$	−147.011	+	53.5077i	−0.216511	+	0.0788037i
$680$		0			0
$681$	−284.840	−	409.955i	−0.418268	−	0.601990i
$682$		0			0
$683$	−980.831	+	566.283i	−1.43606	+	0.829111i	−0.997573	−	0.0696254i	$-0.977820\pi$
$683$	−980.831	+	566.283i	−1.43606	+	0.829111i	−0.438489	+	0.898736i	$0.644486\pi$
$684$		0			0
$685$	−463.330	+	802.512i	−0.676395	+	1.17155i
$686$		0			0
$687$	−173.307	+	637.520i	−0.252267	+	0.927977i
$688$		0			0
$689$	797.411	+	140.605i	1.15735	+	0.204071i
$690$		0			0
$691$	−644.252	+	540.592i	−0.932348	+	0.782333i	−0.976237	−	0.216704i	$-0.930470\pi$
$691$	−644.252	+	540.592i	−0.932348	+	0.782333i	0.0438894	+	0.999036i	$0.486025\pi$
$692$		0			0
$693$	−96.6895	−	572.649i	−0.139523	−	0.826333i
$694$		0			0
$695$	−362.233	+	995.226i	−0.521198	+	1.43198i
$696$		0			0
$697$	−400.346	−	335.930i	−0.574385	−	0.481966i
$698$		0			0
$699$	201.944	+	142.499i	0.288904	+	0.203861i
$700$		0			0
$701$			717.568i			1.02363i	0.859094	+	0.511817i	$0.171028\pi$
$701$			717.568i			1.02363i	−0.859094	+	0.511817i	$0.828972\pi$
$702$		0			0
$703$	1123.79			1.59857
$704$		0			0
$705$	151.503	+	328.004i	0.214898	+	0.465254i
$706$		0			0
$707$	−258.146	+	307.647i	−0.365129	+	0.435144i
$708$		0			0
$709$	414.922	+	151.019i	0.585221	+	0.213003i	0.617626	−	0.786472i	$-0.288094\pi$
$709$	414.922	+	151.019i	0.585221	+	0.213003i	−0.0324052	+	0.999475i	$0.510317\pi$
$710$		0			0
$711$	−1.63900	+	225.616i	−0.00230521	+	0.317322i
$712$		0			0
$713$	64.7075	+	77.1154i	0.0907539	+	0.108156i
$714$		0			0
$715$	−486.868	+	2761.16i	−0.680934	+	3.86177i
$716$		0			0
$717$	208.860	+	790.956i	0.291297	+	1.10315i
$718$		0			0
$719$	−34.3680	−	19.8423i	−0.0477997	−	0.0275971i	0.475910	−	0.879494i	$-0.342119\pi$
$719$	−34.3680	−	19.8423i	−0.0477997	−	0.0275971i	−0.523709	+	0.851897i	$0.675452\pi$
$720$		0			0
$721$	64.0132	+	110.874i	0.0887839	+	0.153778i
$722$		0			0
$723$	−92.2965	−	1101.00i	−0.127658	−	1.52282i
$724$		0			0
$725$	−315.798	−	867.647i	−0.435583	−	1.19675i
$726$		0			0
$727$	−133.609	−	757.733i	−0.183781	−	1.04227i	−0.927512	−	0.373794i	$-0.878057\pi$
$727$	−133.609	−	757.733i	−0.183781	−	1.04227i	0.743731	−	0.668479i	$-0.233054\pi$
$728$		0			0
$729$	623.240	+	378.171i	0.854924	+	0.518753i
$730$		0			0
$731$	172.874	−	30.4824i	0.236490	−	0.0416996i
$732$		0			0
$733$	−861.165	+	313.438i	−1.17485	+	0.427610i	−0.854380	−	0.519649i	$-0.826063\pi$
$733$	−861.165	+	313.438i	−1.17485	+	0.427610i	−0.320469	+	0.947259i	$0.603841\pi$
$734$		0			0
$735$	604.112	−	50.6426i	0.821921	−	0.0689015i
$736$		0			0
$737$	−1378.81	+	796.054i	−1.87084	+	1.08013i
$738$		0			0
$739$	−611.069	+	1058.40i	−0.826887	+	1.43221i	0.0735823	+	0.997289i	$0.476557\pi$
$739$	−611.069	+	1058.40i	−0.826887	+	1.43221i	−0.900469	+	0.434920i	$0.856776\pi$
$740$		0			0
$741$	−2183.13	+	576.476i	−2.94619	+	0.777970i
$742$		0			0
$743$	995.223	+	175.485i	1.33947	+	0.236184i	0.797043	−	0.603922i	$-0.206396\pi$
$743$	995.223	+	175.485i	1.33947	+	0.236184i	0.542422	+	0.840106i	$0.317507\pi$
$744$		0			0
$745$	−439.276	+	368.596i	−0.589632	+	0.494760i
$746$		0			0
$747$	789.348	+	5.73427i	1.05669	+	0.00767640i
$748$		0			0
$749$	−202.925	+	557.533i	−0.270929	+	0.744370i
$750$		0			0
$751$	457.171	+	383.612i	0.608749	+	0.510801i	0.894244	−	0.447579i	$-0.147714\pi$
$751$	457.171	+	383.612i	0.608749	+	0.510801i	−0.285495	+	0.958380i	$0.592158\pi$
$752$		0			0
$753$	314.173	−	145.114i	0.417228	−	0.192715i
$754$		0			0
$755$		−	89.7018i		−	0.118810i
$756$		0			0
$757$	−1157.69			−1.52932			−0.764659	−	0.644435i	$-0.777093\pi$
$757$	−1157.69			−1.52932			−0.764659	+	0.644435i	$0.777093\pi$
$758$		0			0
$759$	80.2567	−	113.737i	0.105740	−	0.149851i
$760$		0			0
$761$	231.925	−	276.397i	0.304763	−	0.363202i	−0.591826	−	0.806066i	$-0.701593\pi$
$761$	231.925	−	276.397i	0.304763	−	0.363202i	0.896589	+	0.442863i	$0.146037\pi$
$762$		0			0
$763$	15.0605	+	5.48156i	0.0197385	+	0.00718422i
$764$		0			0
$765$	948.417	−	160.137i	1.23976	−	0.209329i
$766$		0			0
$767$	−941.044	−	1121.49i	−1.22692	−	1.46218i
$768$		0			0
$769$	26.2139	−	148.667i	0.0340883	−	0.193325i	−0.963008	−	0.269472i	$-0.913151\pi$
$769$	26.2139	−	148.667i	0.0340883	−	0.193325i	0.997097	+	0.0761474i	$0.0242619\pi$
$770$		0			0
$771$	−650.600	−	176.863i	−0.843839	−	0.229394i
$772$		0			0
$773$	817.654	+	472.073i	1.05777	+	0.610702i	0.924814	−	0.380420i	$-0.124221\pi$
$773$	817.654	+	472.073i	1.05777	+	0.610702i	0.132954	+	0.991122i	$0.457554\pi$
$774$		0			0
$775$	−775.354	−	1342.95i	−1.00046	−	1.73284i
$776$		0			0
$777$	470.876	−	327.168i	0.606018	−	0.421066i
$778$		0			0
$779$	461.039	+	1266.69i	0.591834	+	1.62605i
$780$		0			0
$781$	40.2553	+	228.299i	0.0515433	+	0.292317i
$782$		0			0
$783$	433.307	+	42.6719i	0.553393	+	0.0544980i
$784$		0			0
$785$	2315.26	−	408.243i	2.94938	−	0.520055i
$786$		0			0
$787$	1056.71	−	384.613i	1.34271	−	0.488707i	0.432046	−	0.901851i	$-0.357792\pi$
$787$	1056.71	−	384.613i	1.34271	−	0.488707i	0.910666	+	0.413144i	$0.135569\pi$
$788$		0			0
$789$	667.457	−	1417.90i	0.845953	−	1.79708i
$790$		0			0
$791$	−435.933	+	251.686i	−0.551116	+	0.318187i
$792$		0			0
$793$	71.3137	−	123.519i	0.0899289	−	0.155762i
$794$		0			0
$795$	626.794	+	631.364i	0.788420	+	0.794169i
$796$		0			0
$797$	35.8631	+	6.32363i	0.0449976	+	0.00793429i	0.196102	−	0.980584i	$-0.437172\pi$
$797$	35.8631	+	6.32363i	0.0449976	+	0.00793429i	−0.151104	+	0.988518i	$0.548283\pi$
$798$		0			0
$799$	−119.865	+	100.578i	−0.150018	+	0.125880i
$800$		0			0
$801$	988.696	−	351.744i	1.23433	−	0.439130i
$802$		0			0
$803$	−106.333	+	292.148i	−0.132420	+	0.363821i
$804$		0			0
$805$	−133.487	−	112.009i	−0.165823	−	0.139142i
$806$		0			0
$807$	−120.310	+	1319.91i	−0.149083	+	1.63558i
$808$		0			0
$809$			621.122i			0.767765i	0.923382	+	0.383882i	$0.125413\pi$
$809$			621.122i			0.767765i	−0.923382	+	0.383882i	$0.874587\pi$
$810$		0			0
$811$	801.482			0.988264			0.494132	−	0.869387i	$-0.335486\pi$
$811$	801.482			0.988264			0.494132	+	0.869387i	$0.335486\pi$
$812$		0			0
$813$	−442.140	−	40.3010i	−0.543837	−	0.0495707i
$814$		0			0
$815$	−430.503	+	513.054i	−0.528225	+	0.629514i
$816$		0			0
$817$	−425.470	−	154.858i	−0.520771	−	0.189545i
$818$		0			0
$819$	−746.913	+	877.117i	−0.911982	+	1.07096i
$820$		0			0
$821$	−915.994	−	1091.64i	−1.11571	−	1.32965i	−0.938424	−	0.345485i	$-0.887714\pi$
$821$	−915.994	−	1091.64i	−1.11571	−	1.32965i	−0.177281	−	0.984160i	$-0.556730\pi$
$822$		0			0
$823$	−97.7553	+	554.398i	−0.118779	+	0.673630i	0.866030	+	0.499992i	$0.166664\pi$
$823$	−97.7553	+	554.398i	−0.118779	+	0.673630i	−0.984809	+	0.173639i	$0.944448\pi$
$824$		0			0
$825$	−1521.76	+	1510.74i	−1.84456	+	1.83120i
$826$		0			0
$827$	376.018	+	217.094i	0.454677	+	0.262508i	0.709803	−	0.704400i	$-0.248784\pi$
$827$	376.018	+	217.094i	0.454677	+	0.262508i	−0.255126	+	0.966908i	$0.582117\pi$
$828$		0			0
$829$	−281.047	−	486.788i	−0.339020	−	0.587199i	0.645229	−	0.763989i	$-0.276762\pi$
$829$	−281.047	−	486.788i	−0.339020	−	0.587199i	−0.984249	+	0.176790i	$0.943429\pi$
$830$		0			0
$831$	−683.710	−	321.848i	−0.822755	−	0.387302i
$832$		0			0
$833$	89.7958	+	246.712i	0.107798	+	0.296173i
$834$		0			0
$835$	−87.1002	−	493.970i	−0.104312	−	0.591581i
$836$		0			0
$837$	729.116	−	55.7909i	0.871106	−	0.0666559i
$838$		0			0
$839$	−265.532	+	46.8204i	−0.316486	+	0.0558050i	−0.329635	−	0.944109i	$-0.606926\pi$
$839$	−265.532	+	46.8204i	−0.316486	+	0.0558050i	0.0131489	+	0.999914i	$0.495814\pi$
$840$		0			0
$841$	−545.915	+	198.697i	−0.649127	+	0.236263i
$842$		0			0
$843$	−511.248	−	735.812i	−0.606463	−	0.872850i
$844$		0			0
$845$	3489.29	−	2014.54i	4.12933	−	2.38407i
$846$		0			0
$847$	−90.0423	+	155.958i	−0.106307	+	0.184130i
$848$		0			0
$849$	151.249	−	556.379i	0.178150	−	0.655334i
$850$		0			0
$851$	135.346	+	23.8652i	0.159044	+	0.0280437i
$852$		0			0
$853$	−506.158	+	424.717i	−0.593386	+	0.497910i	−0.889312	−	0.457301i	$-0.848816\pi$
$853$	−506.158	+	424.717i	−0.593386	+	0.497910i	0.295926	+	0.955211i	$0.404372\pi$
$854$		0			0
$855$	−2325.05	−	865.427i	−2.71936	−	1.01220i
$856$		0			0
$857$	−437.846	+	1202.97i	−0.510906	+	1.40370i	0.369389	+	0.929275i	$0.379567\pi$
$857$	−437.846	+	1202.97i	−0.510906	+	1.40370i	−0.880295	+	0.474427i	$0.842655\pi$
$858$		0			0
$859$	26.7671	+	22.4603i	0.0311608	+	0.0261470i	0.658235	−	0.752812i	$-0.271303\pi$
$859$	26.7671	+	22.4603i	0.0311608	+	0.0261470i	−0.627074	+	0.778959i	$0.715748\pi$
$860$		0			0
$861$	561.948	+	396.530i	0.652669	+	0.460546i
$862$		0			0
$863$			385.685i			0.446912i	0.974714	+	0.223456i	$0.0717339\pi$
$863$			385.685i			0.446912i	−0.974714	+	0.223456i	$0.928266\pi$
$864$		0			0
$865$	−223.741			−0.258660
$866$		0			0
$867$	−188.883	−	408.933i	−0.217859	−	0.471664i
$868$		0			0
$869$	201.161	−	239.734i	0.231486	−	0.275874i
$870$		0			0
$871$	2967.81	+	1080.20i	3.40736	+	1.24018i
$872$		0			0
$873$	−236.882	+	134.479i	−0.271342	+	0.154042i
$874$		0			0
$875$	972.058	+	1158.45i	1.11092	+	1.32395i
$876$		0			0
$877$	195.623	−	1109.43i	0.223059	−	1.26503i	−0.643302	−	0.765613i	$-0.722436\pi$
$877$	195.623	−	1109.43i	0.223059	−	1.26503i	0.866361	−	0.499418i	$-0.166453\pi$
$878$		0			0
$879$	−199.719	−	756.338i	−0.227211	−	0.860453i
$880$		0			0
$881$	182.389	+	105.303i	0.207025	+	0.119526i	0.599928	−	0.800054i	$-0.295196\pi$
$881$	182.389	+	105.303i	0.207025	+	0.119526i	−0.392903	+	0.919580i	$0.628529\pi$
$882$		0			0
$883$	−286.233	−	495.770i	−0.324160	−	0.561461i	0.657182	−	0.753732i	$-0.271748\pi$
$883$	−286.233	−	495.770i	−0.324160	−	0.561461i	−0.981342	+	0.192270i	$0.938415\pi$
$884$		0			0
$885$	−134.373	−	1602.93i	−0.151834	−	1.81122i
$886$		0			0
$887$	37.8904	+	104.103i	0.0427175	+	0.117365i	0.959217	−	0.282670i	$-0.0912201\pi$
$887$	37.8904	+	104.103i	0.0427175	+	0.117365i	−0.916500	+	0.400035i	$0.868998\pi$
$888$		0			0
$889$	9.34737	+	53.0116i	0.0105145	+	0.0596306i
$890$		0			0
$891$	−331.998	−	955.111i	−0.372613	−	1.07195i
$892$		0			0
$893$	397.460	−	70.0828i	0.445083	−	0.0784802i
$894$		0			0
$895$	−637.476	+	232.022i	−0.712263	+	0.259243i
$896$		0			0
$897$	−275.171	+	23.0676i	−0.306769	+	0.0257163i
$898$		0			0
$899$	378.232	−	218.373i	0.420726	−	0.242906i
$900$		0			0
$901$	−192.646	+	333.672i	−0.213813	+	0.370335i
$902$		0			0
$903$	−223.358	+	58.9799i	−0.247351	+	0.0653155i
$904$		0			0
$905$	−458.548	−	80.8544i	−0.506683	−	0.0893418i
$906$		0			0
$907$	1173.50	−	984.682i	1.29382	−	1.08565i	0.302647	−	0.953103i	$-0.402130\pi$
$907$	1173.50	−	984.682i	1.29382	−	1.08565i	0.991177	−	0.132545i	$-0.0423148\pi$
$908$		0			0
$909$	−354.012	+	603.007i	−0.389452	+	0.663375i
$910$		0			0
$911$	377.644	−	1037.57i	0.414538	−	1.13893i	−0.540213	−	0.841529i	$-0.681656\pi$
$911$	377.644	−	1037.57i	0.414538	−	1.13893i	0.954751	−	0.297406i	$-0.0961216\pi$
$912$		0			0
$913$	−838.744	−	703.790i	−0.918668	−	0.770854i
$914$		0			0
$915$	142.267	−	65.7119i	0.155483	−	0.0718163i
$916$		0			0
$917$			71.0869i			0.0775212i
$918$		0			0
$919$	−1746.70			−1.90065			−0.950324	−	0.311262i	$-0.899248\pi$
$919$	−1746.70			−1.90065			−0.950324	+	0.311262i	$0.899248\pi$
$920$		0			0
$921$	−64.0232	+	90.7314i	−0.0695149	+	0.0985140i
$922$		0			0
$923$	295.596	−	352.277i	0.320256	−	0.381666i
$924$		0			0
$925$	−1989.41	−	724.085i	−2.15071	−	0.782794i
$926$		0			0
$927$	142.040	+	171.795i	0.153225	+	0.185324i
$928$		0			0
$929$	584.182	+	696.201i	0.628829	+	0.749409i	0.982562	−	0.185937i	$-0.0595321\pi$
$929$	584.182	+	696.201i	0.628829	+	0.749409i	−0.353733	+	0.935347i	$0.615088\pi$
$930$		0			0
$931$	117.592	−	666.898i	0.126307	−	0.716325i
$932$		0			0
$933$	1092.57	+	297.010i	1.17102	+	0.318338i
$934$		0			0
$935$	−1155.39	−	667.066i	−1.23571	−	0.713440i
$936$		0			0
$937$	−573.133	−	992.695i	−0.611668	−	1.05944i	−0.990959	−	0.134163i	$-0.957165\pi$
$937$	−573.133	−	992.695i	−0.611668	−	1.05944i	0.379291	−	0.925277i	$-0.376168\pi$
$938$		0			0
$939$	−267.501	+	185.862i	−0.284878	+	0.197936i
$940$		0			0
$941$	−376.884	−	1035.48i	−0.400515	−	1.10041i	−0.962031	−	0.272939i	$-0.912004\pi$
$941$	−376.884	−	1035.48i	−0.400515	−	1.10041i	0.561517	−	0.827466i	$-0.310218\pi$
$942$		0			0
$943$	28.6263	+	162.348i	0.0303566	+	0.172161i
$944$		0			0
$945$	−1226.16	+	314.269i	−1.29752	+	0.332560i
$946$		0			0
$947$	−1705.86	+	300.790i	−1.80133	+	0.317624i	−0.970899	−	0.239490i	$-0.923020\pi$
$947$	−1705.86	+	300.790i	−1.80133	+	0.317624i	−0.830436	+	0.557114i	$0.811909\pi$
$948$		0			0
$949$	579.537	−	210.934i	0.610682	−	0.222270i
$950$		0			0
$951$	280.578	−	596.039i	0.295035	−	0.626750i
$952$		0			0
$953$	−1433.68	+	827.738i	−1.50439	+	0.868560i	−0.504403	+	0.863468i	$0.668288\pi$
$953$	−1433.68	+	827.738i	−1.50439	+	0.868560i	−0.999987	+	0.00509205i	$0.998379\pi$
$954$		0			0
$955$	329.645	−	570.963i	0.345178	−	0.597867i
$956$		0			0
$957$	−425.489	−	428.591i	−0.444607	−	0.447849i
$958$		0			0
$959$	520.113	+	91.7099i	0.542349	+	0.0956308i
$960$		0			0
$961$	−174.274	+	146.233i	−0.181346	+	0.152168i
$962$		0			0
$963$	−186.770	+	1016.01i	−0.193946	+	1.05505i
$964$		0			0
$965$	−697.135	+	1915.36i	−0.722420	+	1.98483i
$966$		0			0
$967$	1108.09	+	929.801i	1.14591	+	0.961532i	0.999616	−	0.0277096i	$-0.00882138\pi$
$967$	1108.09	+	929.801i	1.14591	+	0.961532i	0.146293	+	0.989241i	$0.453266\pi$
$968$		0			0
$969$	97.5288	−	1069.98i	0.100649	−	1.10421i
$970$		0			0
$971$		−	1171.45i		−	1.20644i	−0.797577	−	0.603218i	$-0.793885\pi$
$971$		−	1171.45i		−	1.20644i	0.797577	−	0.603218i	$-0.206115\pi$
$972$		0			0
$973$	603.616			0.620366
$974$		0			0
$975$	4236.14	+	386.123i	4.34476	+	0.396024i
$976$		0			0
$977$	−112.626	+	134.222i	−0.115277	+	0.137382i	−0.820597	−	0.571507i	$-0.806359\pi$
$977$	−112.626	+	134.222i	−0.115277	+	0.137382i	0.705320	+	0.708889i	$0.250803\pi$
$978$		0			0
$979$	−1367.80	−	497.839i	−1.39714	−	0.508518i
$980$		0			0
$981$	27.4452	+	5.04517i	0.0279767	+	0.00514288i
$982$		0			0
$983$	−330.289	−	393.623i	−0.336001	−	0.400430i	0.571417	−	0.820660i	$-0.306394\pi$
$983$	−330.289	−	393.623i	−0.336001	−	0.400430i	−0.907418	+	0.420230i	$0.861950\pi$
$984$		0			0
$985$	482.344	−	2735.51i	0.489689	−	2.77717i
$986$		0			0
$987$	146.135	−	145.077i	0.148059	−	0.146988i
$988$		0			0
$989$	−47.9537	−	27.6861i	−0.0484871	−	0.0279940i
$990$		0			0
$991$	818.042	+	1416.89i	0.825471	+	1.42976i	0.901559	+	0.432657i	$0.142424\pi$
$991$	818.042	+	1416.89i	0.825471	+	1.42976i	−0.0760875	+	0.997101i	$0.524243\pi$
$992$		0			0
$993$	617.037	+	290.462i	0.621386	+	0.292510i
$994$		0			0
$995$	−1105.22	−	3036.55i	−1.11077	−	3.05181i
$996$		0			0
$997$	−185.698	−	1053.15i	−0.186257	−	1.05631i	−0.924330	−	0.381594i	$-0.875375\pi$
$997$	−185.698	−	1053.15i	−0.186257	−	1.05631i	0.738073	−	0.674720i	$-0.235736\pi$
$998$		0			0
$999$	713.572	−	698.188i	0.714287	−	0.698887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.u.a.41.18	✓	108
4.3	odd	2		432.3.bc.d.257.1		108
27.2	odd	18	inner	216.3.u.a.137.18	yes	108
108.83	even	18		432.3.bc.d.353.1		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.u.a.41.18	✓	108	1.1	even	1	trivial
216.3.u.a.137.18	yes	108	27.2	odd	18	inner
432.3.bc.d.257.1		108	4.3	odd	2
432.3.bc.d.353.1		108	108.83	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(2.98761 + 0.272321i) q^{3} +(-5.82981 + 6.94770i) q^{5} +(4.85733 + 1.76792i) q^{7} +(8.85168 + 1.62718i) q^{9} +O(q^{10})\)	\(q+(2.98761 + 0.272321i) q^{3} +(-5.82981 + 6.94770i) q^{5} +(4.85733 + 1.76792i) q^{7} +(8.85168 + 1.62718i) q^{9} +(-8.02427 - 9.56295i) q^{11} +(-4.30017 + 24.3875i) q^{13} +(-19.3092 + 19.1695i) q^{15} +(-10.2048 - 5.89175i) q^{17} +(15.1967 + 26.3214i) q^{19} +(14.0304 + 6.60463i) q^{21} +(1.27127 + 3.49279i) q^{23} +(-9.94260 - 56.3873i) q^{25} +(26.0023 + 7.27188i) q^{27} +(15.8810 - 2.80026i) q^{29} +(25.4499 - 9.26301i) q^{31} +(-21.3692 - 30.7556i) q^{33} +(-40.6003 + 23.4406i) q^{35} +(18.4875 - 32.0213i) q^{37} +(-19.4885 + 71.6894i) q^{39} +(43.6776 + 7.70154i) q^{41} +(-11.4119 + 9.57574i) q^{43} +(-62.9088 + 52.0127i) q^{45} +(4.54166 - 12.4781i) q^{47} +(-17.0681 - 14.3218i) q^{49} +(-28.8836 - 20.3813i) q^{51} -32.6975i q^{53} +113.220 q^{55} +(38.2339 + 82.7765i) q^{57} +(-38.0009 + 45.2877i) q^{59} +(-5.41219 - 1.96987i) q^{61} +(40.1188 + 23.5529i) q^{63} +(-144.368 - 172.051i) q^{65} +(22.1465 - 125.599i) q^{67} +(2.84691 + 10.7813i) q^{69} +(-16.0822 - 9.28507i) q^{71} +(-12.4523 - 21.5680i) q^{73} +(-14.3492 - 171.171i) q^{75} +(-22.0700 - 60.6367i) q^{77} +(4.35320 + 24.6882i) q^{79} +(75.7046 + 28.8065i) q^{81} +(86.3752 - 15.2303i) q^{83} +(100.426 - 36.5521i) q^{85} +(48.2090 - 4.04135i) q^{87} +(100.979 - 58.3001i) q^{89} +(-64.0026 + 110.856i) q^{91} +(78.5571 - 20.7438i) q^{93} +(-271.467 - 47.8669i) q^{95} +(-23.1850 + 19.4545i) q^{97} +(-55.4676 - 97.7051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q+O(q^{10}) \) 108 * q	\( 108 q - 18 q^{11} - 24 q^{15} + 48 q^{21} + 72 q^{23} + 174 q^{27} + 108 q^{29} + 18 q^{33} - 144 q^{39} + 90 q^{41} - 90 q^{43} + 108 q^{45} - 72 q^{49} + 84 q^{51} - 18 q^{57} - 252 q^{59} + 144 q^{61} - 360 q^{63} - 216 q^{65} + 126 q^{67} - 120 q^{69} - 252 q^{75} - 504 q^{77} - 552 q^{81} - 180 q^{83} - 60 q^{87} - 486 q^{89} - 360 q^{93} - 1116 q^{95} + 270 q^{97} - 564 q^{99}+O(q^{100}) \) 108 * q - 18 * q^11 - 24 * q^15 + 48 * q^21 + 72 * q^23 + 174 * q^27 + 108 * q^29 + 18 * q^33 - 144 * q^39 + 90 * q^41 - 90 * q^43 + 108 * q^45 - 72 * q^49 + 84 * q^51 - 18 * q^57 - 252 * q^59 + 144 * q^61 - 360 * q^63 - 216 * q^65 + 126 * q^67 - 120 * q^69 - 252 * q^75 - 504 * q^77 - 552 * q^81 - 180 * q^83 - 60 * q^87 - 486 * q^89 - 360 * q^93 - 1116 * q^95 + 270 * q^97 - 564 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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