LMFDB - Embedded newform 1080.2.m.b.539.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1080,2,Mod(539,1080)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1080, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1080.539");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1080 = 2^{3} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1080.m (of order $2$, degree $1$, 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:	$8.62384341830$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			539.19
Character	$\chi$	$=$	1080.539
Dual form			1080.2.m.b.539.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.205826 + 1.39916i) q^{2} +(-1.91527 - 0.575965i) q^{4} +(-1.94670 + 1.10016i) q^{5} +1.41383 q^{7} +(1.20008 - 2.56121i) q^{8} +(-1.13862 - 2.95018i) q^{10} -1.85786i q^{11} +5.28485 q^{13} +(-0.291002 + 1.97816i) q^{14} +(3.33653 + 2.20626i) q^{16} -3.39687 q^{17} +0.958964 q^{19} +(4.36211 - 0.985877i) q^{20} +(2.59943 + 0.382395i) q^{22} -1.26014i q^{23} +(2.57929 - 4.28337i) q^{25} +(-1.08776 + 7.39432i) q^{26} +(-2.70786 - 0.814315i) q^{28} +6.97811 q^{29} +8.83008i q^{31} +(-3.77364 + 4.21422i) q^{32} +(0.699164 - 4.75275i) q^{34} +(-2.75230 + 1.55544i) q^{35} +7.01845 q^{37} +(-0.197380 + 1.34174i) q^{38} +(0.481558 + 6.30620i) q^{40} +9.81991i q^{41} -7.74226i q^{43} +(-1.07006 + 3.55830i) q^{44} +(1.76313 + 0.259369i) q^{46} +6.43323i q^{47} -5.00109 q^{49} +(5.46222 + 4.49045i) q^{50} +(-10.1219 - 3.04389i) q^{52} -1.38393i q^{53} +(2.04394 + 3.61669i) q^{55} +(1.69670 - 3.62111i) q^{56} +(-1.43628 + 9.76345i) q^{58} -1.37865i q^{59} +6.88857i q^{61} +(-12.3547 - 1.81746i) q^{62} +(-5.11963 - 6.14731i) q^{64} +(-10.2880 + 5.81419i) q^{65} +6.08777i q^{67} +(6.50593 + 1.95648i) q^{68} +(-1.60981 - 4.17104i) q^{70} +3.62010 q^{71} +9.30568i q^{73} +(-1.44458 + 9.81991i) q^{74} +(-1.83668 - 0.552330i) q^{76} -2.62669i q^{77} -7.07671i q^{79} +(-8.92246 - 0.624204i) q^{80} +(-13.7396 - 2.02119i) q^{82} +8.12610 q^{83} +(6.61269 - 3.73711i) q^{85} +(10.8326 + 1.59356i) q^{86} +(-4.75837 - 2.22957i) q^{88} +16.1673i q^{89} +7.47186 q^{91} +(-0.725795 + 2.41351i) q^{92} +(-9.00109 - 1.32413i) q^{94} +(-1.86682 + 1.05502i) q^{95} -16.1841i q^{97} +(1.02935 - 6.99730i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{4} - 2 q^{10} - 28 q^{16} + 24 q^{19} + 40 q^{25} + 56 q^{34} + 18 q^{40} - 32 q^{46} + 104 q^{49} - 100 q^{64} + 10 q^{70} - 120 q^{76} - 56 q^{94}+O(q^{100}) $ 40 * q - 4 * q^4 - 2 * q^10 - 28 * q^16 + 24 * q^19 + 40 * q^25 + 56 * q^34 + 18 * q^40 - 32 * q^46 + 104 * q^49 - 100 * q^64 + 10 * q^70 - 120 * q^76 - 56 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$541$	$1001$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−0.205826	+	1.39916i	−0.145541	+	0.989352i
$2$	−0.205826	+	1.39916i	−0.145541	+	0.989352i
$3$		0			0
$3$		0			0
$4$	−1.91527	−	0.575965i	−0.957636	−	0.287982i
$5$	−1.94670	+	1.10016i	−0.870591	+	0.492007i
$5$	−1.94670	+	1.10016i	−0.870591	+	0.492007i
$6$		0			0
$7$	1.41383			0.534377			0.267188	−	0.963644i	$-0.413905\pi$
$7$	1.41383			0.534377			0.267188	+	0.963644i	$0.413905\pi$
$8$	1.20008	−	2.56121i	0.424291	−	0.905526i
$9$		0			0
$10$	−1.13862	−	2.95018i	−0.360062	−	0.932928i
$11$		−	1.85786i		−	0.560165i	−0.959976	−	0.280082i	$-0.909638\pi$
$11$		−	1.85786i		−	0.560165i	0.959976	−	0.280082i	$-0.0903618\pi$
$12$		0			0
$13$	5.28485			1.46575			0.732876	−	0.680362i	$-0.238177\pi$
$13$	5.28485			1.46575			0.732876	+	0.680362i	$0.238177\pi$
$14$	−0.291002	+	1.97816i	−0.0777737	+	0.528687i
$15$		0			0
$16$	3.33653	+	2.20626i	0.834132	+	0.551565i
$17$	−3.39687			−0.823862			−0.411931	−	0.911215i	$-0.635145\pi$
$17$	−3.39687			−0.823862			−0.411931	+	0.911215i	$0.635145\pi$
$18$		0			0
$19$	0.958964			0.220002			0.110001	−	0.993932i	$-0.464915\pi$
$19$	0.958964			0.220002			0.110001	+	0.993932i	$0.464915\pi$
$20$	4.36211	−	0.985877i	0.975399	−	0.220449i
$21$		0			0
$22$	2.59943	+	0.382395i	0.554200	+	0.0815269i
$23$		−	1.26014i		−	0.262757i	−0.991332	−	0.131378i	$-0.958060\pi$
$23$		−	1.26014i		−	0.262757i	0.991332	−	0.131378i	$-0.0419403\pi$
$24$		0			0
$25$	2.57929	−	4.28337i	0.515858	−	0.856674i
$26$	−1.08776	+	7.39432i	−0.213327	+	1.45015i
$27$		0			0
$28$	−2.70786	−	0.814315i	−0.511738	−	0.153891i
$29$	6.97811			1.29580			0.647901	−	0.761725i	$-0.275647\pi$
$29$	6.97811			1.29580			0.647901	+	0.761725i	$0.275647\pi$
$30$		0			0
$31$			8.83008i			1.58593i	0.609267	+	0.792965i	$0.291464\pi$
$31$			8.83008i			1.58593i	−0.609267	+	0.792965i	$0.708536\pi$
$32$	−3.77364	+	4.21422i	−0.667092	+	0.744975i
$33$		0			0
$34$	0.699164	−	4.75275i	0.119906	−	0.815090i
$35$	−2.75230	+	1.55544i	−0.465224	+	0.262917i
$36$		0			0
$37$	7.01845			1.15383			0.576913	−	0.816805i	$-0.304257\pi$
$37$	7.01845			1.15383			0.576913	+	0.816805i	$0.304257\pi$
$38$	−0.197380	+	1.34174i	−0.0320192	+	0.217659i
$39$		0			0
$40$	0.481558	+	6.30620i	0.0761411	+	0.997097i
$41$			9.81991i			1.53361i	0.641879	+	0.766806i	$0.278155\pi$
$41$			9.81991i			1.53361i	−0.641879	+	0.766806i	$0.721845\pi$
$42$		0			0
$43$		−	7.74226i		−	1.18068i	−0.807153	−	0.590342i	$-0.798993\pi$
$43$		−	7.74226i		−	1.18068i	0.807153	−	0.590342i	$-0.201007\pi$
$44$	−1.07006	+	3.55830i	−0.161318	+	0.536434i
$45$		0			0
$46$	1.76313	+	0.259369i	0.259959	+	0.0382419i
$47$			6.43323i			0.938383i	0.883096	+	0.469192i	$0.155455\pi$
$47$			6.43323i			0.938383i	−0.883096	+	0.469192i	$0.844545\pi$
$48$		0			0
$49$	−5.00109			−0.714442
$50$	5.46222	+	4.49045i	0.772474	+	0.635046i
$51$		0			0
$52$	−10.1219	−	3.04389i	−1.40366	−	0.422111i
$53$		−	1.38393i		−	0.190098i	−0.995473	−	0.0950488i	$-0.969699\pi$
$53$		−	1.38393i		−	0.190098i	0.995473	−	0.0950488i	$-0.0303007\pi$
$54$		0			0
$55$	2.04394	+	3.61669i	0.275605	+	0.487675i
$56$	1.69670	−	3.62111i	0.226731	−	0.483892i
$57$		0			0
$58$	−1.43628	+	9.76345i	−0.188592	+	1.28200i
$59$		−	1.37865i		−	0.179485i	−0.995965	−	0.0897426i	$-0.971396\pi$
$59$		−	1.37865i		−	0.179485i	0.995965	−	0.0897426i	$-0.0286044\pi$
$60$		0			0
$61$			6.88857i			0.881991i	0.897509	+	0.440996i	$0.145375\pi$
$61$			6.88857i			0.881991i	−0.897509	+	0.440996i	$0.854625\pi$
$62$	−12.3547	−	1.81746i	−1.56904	−	0.230818i
$63$		0			0
$64$	−5.11963	−	6.14731i	−0.639954	−	0.768413i
$65$	−10.2880	+	5.81419i	−1.27607	+	0.721161i
$66$		0			0
$67$			6.08777i			0.743740i	0.928285	+	0.371870i	$0.121283\pi$
$67$			6.08777i			0.743740i	−0.928285	+	0.371870i	$0.878717\pi$
$68$	6.50593	+	1.95648i	0.788959	+	0.237258i
$69$		0			0
$70$	−1.60981	−	4.17104i	−0.192409	−	0.498535i
$71$	3.62010			0.429627			0.214813	−	0.976655i	$-0.431086\pi$
$71$	3.62010			0.429627			0.214813	+	0.976655i	$0.431086\pi$
$72$		0			0
$73$			9.30568i			1.08915i	0.838713	+	0.544573i	$0.183308\pi$
$73$			9.30568i			1.08915i	−0.838713	+	0.544573i	$0.816692\pi$
$74$	−1.44458	+	9.81991i	−0.167929	+	1.14154i
$75$		0			0
$76$	−1.83668	−	0.552330i	−0.210681	−	0.0633566i
$77$		−	2.62669i		−	0.299339i
$78$		0			0
$79$		−	7.07671i		−	0.796192i	−0.917344	−	0.398096i	$-0.869671\pi$
$79$		−	7.07671i		−	0.796192i	0.917344	−	0.398096i	$-0.130329\pi$
$80$	−8.92246	−	0.624204i	−0.997562	−	0.0697881i
$81$		0			0
$82$	−13.7396	−	2.02119i	−1.51728	−	0.223203i
$83$	8.12610			0.891956			0.445978	−	0.895044i	$-0.352856\pi$
$83$	8.12610			0.891956			0.445978	+	0.895044i	$0.352856\pi$
$84$		0			0
$85$	6.61269	−	3.73711i	0.717247	−	0.405346i
$86$	10.8326	+	1.59356i	1.16811	+	0.171838i
$87$		0			0
$88$	−4.75837	−	2.22957i	−0.507244	−	0.237673i
$89$			16.1673i			1.71373i	0.515541	+	0.856865i	$0.327591\pi$
$89$			16.1673i			1.71373i	−0.515541	+	0.856865i	$0.672409\pi$
$90$		0			0
$91$	7.47186			0.783264
$92$	−0.725795	+	2.41351i	−0.0756694	+	0.251625i
$93$		0			0
$94$	−9.00109	−	1.32413i	−0.928392	−	0.136573i
$95$	−1.86682	+	1.05502i	−0.191531	+	0.108242i
$96$		0			0
$97$		−	16.1841i		−	1.64325i	−0.570031	−	0.821623i	$-0.693069\pi$
$97$		−	16.1841i		−	1.64325i	0.570031	−	0.821623i	$-0.306931\pi$
$98$	1.02935	−	6.99730i	0.103980	−	0.706834i
$99$		0			0
$100$	−7.40711	+	6.71824i	−0.740711	+	0.671824i
$101$	8.26292			0.822191			0.411096	−	0.911592i	$-0.365146\pi$
$101$	8.26292			0.822191			0.411096	+	0.911592i	$0.365146\pi$
$102$		0			0
$103$	7.01845			0.691549			0.345774	−	0.938318i	$-0.387616\pi$
$103$	7.01845			0.691549			0.345774	+	0.938318i	$0.387616\pi$
$104$	6.34222	−	13.5356i	0.621906	−	1.32728i
$105$		0			0
$106$	1.93633	+	0.284849i	0.188073	+	0.0276670i
$107$	13.6459			1.31920			0.659601	−	0.751616i	$-0.270725\pi$
$107$	13.6459			1.31920			0.659601	+	0.751616i	$0.270725\pi$
$108$		0			0
$109$			3.05122i			0.292254i	0.989266	+	0.146127i	$0.0466808\pi$
$109$			3.05122i			0.292254i	−0.989266	+	0.146127i	$0.953319\pi$
$110$	−5.48101	+	2.11538i	−0.522594	+	0.201694i
$111$		0			0
$112$	4.71728	+	3.11927i	0.445741	+	0.294743i
$113$	−3.34103			−0.314298			−0.157149	−	0.987575i	$-0.550230\pi$
$113$	−3.34103			−0.314298			−0.157149	+	0.987575i	$0.550230\pi$
$114$		0			0
$115$	1.38636	+	2.45311i	0.129278	+	0.228754i
$116$	−13.3650	−	4.01914i	−1.24091	−	0.373168i
$117$		0			0
$118$	1.92895	+	0.283762i	0.177574	+	0.0261224i
$119$	−4.80259			−0.440253
$120$		0			0
$121$	7.54837			0.686215
$122$	−9.63818	−	1.41785i	−0.872600	−	0.128366i
$123$		0			0
$124$	5.08582	−	16.9120i	0.456720	−	1.51874i
$125$	−0.308701	+	11.1761i	−0.0276110	+	0.999619i
$126$		0			0
$127$	10.2948			0.913517			0.456758	−	0.889591i	$-0.349010\pi$
$127$	10.2948			0.913517			0.456758	+	0.889591i	$0.349010\pi$
$128$	9.65479	−	5.89788i	0.853371	−	0.521304i
$129$		0			0
$130$	−6.01741	−	15.5912i	−0.527762	−	1.36744i
$131$		−	11.1492i		−	0.974107i	−0.873372	−	0.487054i	$-0.838072\pi$
$131$		−	11.1492i		−	0.974107i	0.873372	−	0.487054i	$-0.161928\pi$
$132$		0			0
$133$	1.35581			0.117564
$134$	−8.51774	−	1.25302i	−0.735821	−	0.108245i
$135$		0			0
$136$	−4.07650	+	8.70011i	−0.349557	+	0.746028i
$137$	9.44890			0.807274			0.403637	−	0.914919i	$-0.367746\pi$
$137$	9.44890			0.807274			0.403637	+	0.914919i	$0.367746\pi$
$138$		0			0
$139$	−14.7721			−1.25295			−0.626477	−	0.779440i	$-0.715504\pi$
$139$	−14.7721			−1.25295			−0.626477	+	0.779440i	$0.715504\pi$
$140$	6.16728	−	1.39386i	0.521230	−	0.117803i
$141$		0			0
$142$	−0.745110	+	5.06508i	−0.0625282	+	0.425052i
$143$		−	9.81849i		−	0.821063i
$144$		0			0
$145$	−13.5843	+	7.67705i	−1.12811	+	0.637544i
$146$	−13.0201	−	1.91535i	−1.07755	−	0.158515i
$147$		0			0
$148$	−13.4422	−	4.04238i	−1.10495	−	0.332282i
$149$	−15.2225			−1.24708			−0.623540	−	0.781792i	$-0.714306\pi$
$149$	−15.2225			−1.24708			−0.623540	+	0.781792i	$0.714306\pi$
$150$		0			0
$151$			13.8353i			1.12590i	0.826491	+	0.562951i	$0.190334\pi$
$151$			13.8353i			1.12590i	−0.826491	+	0.562951i	$0.809666\pi$
$152$	1.15083	−	2.45611i	0.0933447	−	0.199217i
$153$		0			0
$154$	3.67515	+	0.540641i	0.296152	+	0.0435661i
$155$	−9.71452	−	17.1895i	−0.780289	−	1.38070i
$156$		0			0
$157$	−7.94053			−0.633723			−0.316862	−	0.948472i	$-0.602629\pi$
$157$	−7.94053			−0.633723			−0.316862	+	0.948472i	$0.602629\pi$
$158$	9.90142	+	1.45657i	0.787714	+	0.115879i
$159$		0			0
$160$	2.70983	−	12.3554i	0.214231	−	0.976783i
$161$		−	1.78162i		−	0.140411i
$162$		0			0
$163$		−	9.26632i		−	0.725794i	−0.931829	−	0.362897i	$-0.881788\pi$
$163$		−	9.26632i		−	0.725794i	0.931829	−	0.362897i	$-0.118212\pi$
$164$	5.65592	−	18.8078i	0.441653	−	1.46864i
$165$		0			0
$166$	−1.67256	+	11.3697i	−0.129816	+	0.882458i
$167$		−	24.7574i		−	1.91578i	−0.287129	−	0.957892i	$-0.592701\pi$
$167$		−	24.7574i		−	1.91578i	0.287129	−	0.957892i	$-0.407299\pi$
$168$		0			0
$169$	14.9296			1.14843
$170$	3.86773	+	10.0214i	0.296641	+	0.768604i
$171$		0			0
$172$	−4.45927	+	14.8285i	−0.340016	+	1.13066i
$173$			2.42769i			0.184574i	0.995732	+	0.0922870i	$0.0294177\pi$
$173$			2.42769i			0.184574i	−0.995732	+	0.0922870i	$0.970582\pi$
$174$		0			0
$175$	3.64667	−	6.05595i	0.275662	−	0.457787i
$176$	4.09891	−	6.19879i	0.308967	−	0.467252i
$177$		0			0
$178$	−22.6206	−	3.32765i	−1.69548	−	0.249418i
$179$		−	26.4664i		−	1.97819i	−0.147272	−	0.989096i	$-0.547049\pi$
$179$		−	26.4664i		−	1.97819i	0.147272	−	0.989096i	$-0.452951\pi$
$180$		0			0
$181$			16.4205i			1.22052i	0.792199	+	0.610262i	$0.208936\pi$
$181$			16.4205i			1.22052i	−0.792199	+	0.610262i	$0.791064\pi$
$182$	−1.53790	+	10.4543i	−0.113997	+	0.774924i
$183$		0			0
$184$	−3.22748	−	1.51226i	−0.237933	−	0.111486i
$185$	−13.6628	+	7.72143i	−1.00451	+	0.567691i
$186$		0			0
$187$			6.31090i			0.461498i
$188$	3.70532	−	12.3214i	0.270238	−	0.898629i
$189$		0			0
$190$	−1.09189	−	2.82912i	−0.0792142	−	0.205246i
$191$	0.528127			0.0382140			0.0191070	−	0.999817i	$-0.493918\pi$
$191$	0.528127			0.0382140			0.0191070	+	0.999817i	$0.493918\pi$
$192$		0			0
$193$		−	3.21790i		−	0.231630i	−0.993271	−	0.115815i	$-0.963052\pi$
$193$		−	3.21790i		−	0.231630i	0.993271	−	0.115815i	$-0.0369479\pi$
$194$	22.6441	+	3.33111i	1.62575	+	0.239160i
$195$		0			0
$196$	9.57845	+	2.88045i	0.684175	+	0.205747i
$197$			1.79418i			0.127830i	0.997955	+	0.0639149i	$0.0203586\pi$
$197$			1.79418i			0.127830i	−0.997955	+	0.0639149i	$0.979641\pi$
$198$		0			0
$199$		−	16.5191i		−	1.17101i	−0.810669	−	0.585505i	$-0.800896\pi$
$199$		−	16.5191i		−	1.17101i	0.810669	−	0.585505i	$-0.199104\pi$
$200$	−7.87529	−	11.7465i	−0.556867	−	0.830602i
$201$		0			0
$202$	−1.70072	+	11.5611i	−0.119662	+	0.813437i
$203$	9.86584			0.692446
$204$		0			0
$205$	−10.8035	−	19.1164i	−0.754548	−	1.33515i
$206$	−1.44458	+	9.81991i	−0.100649	+	0.684185i
$207$		0			0
$208$	17.6330	+	11.6597i	1.22263	+	0.808457i
$209$		−	1.78162i		−	0.123237i
$210$		0			0
$211$	12.8886			0.887286			0.443643	−	0.896204i	$-0.353686\pi$
$211$	12.8886			0.887286			0.443643	+	0.896204i	$0.353686\pi$
$212$	−0.797096	+	2.65060i	−0.0547448	+	0.182044i
$213$		0			0
$214$	−2.80869	+	19.0928i	−0.191998	+	1.30516i
$215$	8.51774	+	15.0719i	0.580905	+	1.02789i
$216$		0			0
$217$			12.4842i			0.847484i
$218$	−4.26913	−	0.628021i	−0.289142	−	0.0425349i
$219$		0			0
$220$	−1.83162	−	8.10418i	−0.123488	−	0.546384i
$221$	−17.9519			−1.20758
$222$		0			0
$223$	7.01845			0.469990			0.234995	−	0.971997i	$-0.424493\pi$
$223$	7.01845			0.469990			0.234995	+	0.971997i	$0.424493\pi$
$224$	−5.33528	+	5.95818i	−0.356478	+	0.398097i
$225$		0			0
$226$	0.687671	−	4.67462i	0.0457432	−	0.310951i
$227$	26.0959			1.73204			0.866022	−	0.500006i	$-0.166669\pi$
$227$	26.0959			1.73204			0.866022	+	0.500006i	$0.166669\pi$
$228$		0			0
$229$			27.3805i			1.80935i	0.426098	+	0.904677i	$0.359888\pi$
$229$			27.3805i			1.80935i	−0.426098	+	0.904677i	$0.640112\pi$
$230$	−3.71763	+	1.43481i	−0.245133	+	0.0946088i
$231$		0			0
$232$	8.37426	−	17.8724i	0.549797	−	1.17338i
$233$	−9.60062			−0.628957			−0.314479	−	0.949265i	$-0.601830\pi$
$233$	−9.60062			−0.628957			−0.314479	+	0.949265i	$0.601830\pi$
$234$		0			0
$235$	−7.07760	−	12.5236i	−0.461691	−	0.816948i
$236$	−0.794055	+	2.64049i	−0.0516886	+	0.171881i
$237$		0			0
$238$	0.988497	−	6.71957i	0.0640748	−	0.435565i
$239$	−17.6898			−1.14426			−0.572130	−	0.820163i	$-0.693883\pi$
$239$	−17.6898			−1.14426			−0.572130	+	0.820163i	$0.693883\pi$
$240$		0			0
$241$	3.99330			0.257231			0.128615	−	0.991695i	$-0.458947\pi$
$241$	3.99330			0.257231			0.128615	+	0.991695i	$0.458947\pi$
$242$	−1.55365	+	10.5613i	−0.0998724	+	0.678909i
$243$		0			0
$244$	3.96758	−	13.1935i	0.253998	−	0.844626i
$245$	9.73563	−	5.50201i	0.621986	−	0.351510i
$246$		0			0
$247$	5.06798			0.322468
$248$	22.6157	+	10.5968i	1.43610	+	0.672896i
$249$		0			0
$250$	−15.5735	−	2.73225i	−0.984956	−	0.172802i
$251$		−	19.6398i		−	1.23965i	−0.784738	−	0.619827i	$-0.787203\pi$
$251$		−	19.6398i		−	1.23965i	0.784738	−	0.619827i	$-0.212797\pi$
$252$		0			0
$253$	−2.34116			−0.147187
$254$	−2.11894	+	14.4040i	−0.132954	+	0.903790i
$255$		0			0
$256$	6.26485	+	14.7225i	0.391553	+	0.920156i
$257$	0.736991			0.0459723			0.0229861	−	0.999736i	$-0.492683\pi$
$257$	0.736991			0.0459723			0.0229861	+	0.999736i	$0.492683\pi$
$258$		0			0
$259$	9.92289			0.616578
$260$	23.0531	−	5.21021i	1.42969	−	0.323123i
$261$		0			0
$262$	15.5994	+	2.29479i	0.963735	+	0.141772i
$263$			10.6712i			0.658016i	0.944327	+	0.329008i	$0.106714\pi$
$263$			10.6712i			0.658016i	−0.944327	+	0.329008i	$0.893286\pi$
$264$		0			0
$265$	1.52255	+	2.69410i	0.0935294	+	0.165497i
$266$	−0.279061	+	1.89699i	−0.0171103	+	0.116312i
$267$		0			0
$268$	3.50634	−	11.6597i	0.214184	−	0.712232i
$269$	22.0409			1.34386			0.671928	−	0.740616i	$-0.265466\pi$
$269$	22.0409			1.34386			0.671928	+	0.740616i	$0.265466\pi$
$270$		0			0
$271$			14.4928i			0.880373i	0.897906	+	0.440186i	$0.145088\pi$
$271$			14.4928i			0.880373i	−0.897906	+	0.440186i	$0.854912\pi$
$272$	−11.3338	−	7.49437i	−0.687210	−	0.454413i
$273$		0			0
$274$	−1.94483	+	13.2205i	−0.117491	+	0.798679i
$275$	−7.95789	−	4.79195i	−0.479879	−	0.288965i
$276$		0			0
$277$	8.92588			0.536304			0.268152	−	0.963377i	$-0.413587\pi$
$277$	8.92588			0.536304			0.268152	+	0.963377i	$0.413587\pi$
$278$	3.04049	−	20.6685i	0.182356	−	1.23961i
$279$		0			0
$280$	0.680840	+	8.91587i	0.0406880	+	0.532825i
$281$			11.9703i			0.714091i	0.934087	+	0.357046i	$0.116216\pi$
$281$			11.9703i			0.714091i	−0.934087	+	0.357046i	$0.883784\pi$
$282$		0			0
$283$			17.0086i			1.01106i	0.862810	+	0.505528i	$0.168702\pi$
$283$			17.0086i			1.01106i	−0.862810	+	0.505528i	$0.831298\pi$
$284$	−6.93347	−	2.08505i	−0.411426	−	0.123725i
$285$		0			0
$286$	13.7376	+	2.02090i	0.812321	+	0.119498i
$287$			13.8837i			0.819526i
$288$		0			0
$289$	−5.46128			−0.321252
$290$	−7.94538	−	20.5867i	−0.466569	−	1.20889i
$291$		0			0
$292$	5.35974	−	17.8229i	0.313655	−	1.04301i
$293$		−	9.28221i		−	0.542272i	−0.962541	−	0.271136i	$-0.912601\pi$
$293$		−	9.28221i		−	0.542272i	0.962541	−	0.271136i	$-0.0873994\pi$
$294$		0			0
$295$	1.51674	+	2.68382i	0.0883080	+	0.156258i
$296$	8.42269	−	17.9758i	0.489559	−	1.04482i
$297$		0			0
$298$	3.13319	−	21.2987i	0.181501	−	1.23380i
$299$		−	6.65964i		−	0.385137i
$300$		0			0
$301$		−	10.9462i		−	0.630930i
$302$	−19.3577	−	2.84767i	−1.11391	−	0.163865i
$303$		0			0
$304$	3.19961	+	2.11572i	0.183510	+	0.121345i
$305$	−7.57854	−	13.4100i	−0.433946	−	0.767854i
$306$		0			0
$307$		−	28.2257i		−	1.61093i	−0.592646	−	0.805463i	$-0.701917\pi$
$307$		−	28.2257i		−	1.61093i	0.592646	−	0.805463i	$-0.298083\pi$
$308$	−1.51288	+	5.03082i	−0.0862044	+	0.286658i
$309$		0			0
$310$	26.0503	−	10.0541i	1.47956	−	0.571033i
$311$	−27.3716			−1.55210			−0.776050	−	0.630671i	$-0.782780\pi$
$311$	−27.3716			−1.55210			−0.776050	+	0.630671i	$0.782780\pi$
$312$		0			0
$313$		−	27.1781i		−	1.53620i	−0.640332	−	0.768098i	$-0.721203\pi$
$313$		−	27.1781i		−	1.53620i	0.640332	−	0.768098i	$-0.278797\pi$
$314$	1.63437	−	11.1100i	0.0922327	−	0.626976i
$315$		0			0
$316$	−4.07594	+	13.5538i	−0.229289	+	0.762462i
$317$		−	2.01745i		−	0.113311i	−0.998394	−	0.0566555i	$-0.981956\pi$
$317$		−	2.01745i		−	0.113311i	0.998394	−	0.0566555i	$-0.0180437\pi$
$318$		0			0
$319$		−	12.9643i		−	0.725863i
$320$	16.7294	+	6.33455i	0.935203	+	0.354112i
$321$		0			0
$322$	2.49276	+	0.366703i	0.138916	+	0.0204356i
$323$	−3.25748			−0.181251
$324$		0			0
$325$	13.6311	−	22.6370i	0.756120	−	1.25567i
$326$	12.9650	+	1.90725i	0.718066	+	0.105633i
$327$		0			0
$328$	25.1509	+	11.7846i	1.38873	+	0.650698i
$329$			9.09548i			0.501450i
$330$		0			0
$331$	−25.5573			−1.40475			−0.702377	−	0.711805i	$-0.747878\pi$
$331$	−25.5573			−1.40475			−0.702377	+	0.711805i	$0.747878\pi$
$332$	−15.5637	−	4.68035i	−0.854168	−	0.256868i
$333$		0			0
$334$	34.6394	+	5.09571i	1.89539	+	0.278825i
$335$	−6.69754	−	11.8511i	−0.365925	−	0.647493i
$336$		0			0
$337$		−	2.38790i		−	0.130077i	−0.997883	−	0.0650385i	$-0.979283\pi$
$337$		−	2.38790i		−	0.130077i	0.997883	−	0.0650385i	$-0.0207170\pi$
$338$	−3.07290	+	20.8888i	−0.167144	+	1.13620i
$339$		0			0
$340$	−14.8175	+	3.34889i	−0.803594	+	0.181619i
$341$	16.4050			0.888382
$342$		0			0
$343$	−16.9675			−0.916158
$344$	−19.8296	−	9.29131i	−1.06914	−	0.500954i
$345$		0			0
$346$	−3.39672	−	0.499682i	−0.182609	−	0.0268631i
$347$	17.6403			0.946980			0.473490	−	0.880799i	$-0.342994\pi$
$347$	17.6403			0.946980			0.473490	+	0.880799i	$0.342994\pi$
$348$		0			0
$349$			3.06501i			0.164066i	0.996630	+	0.0820332i	$0.0261414\pi$
$349$			3.06501i			0.164066i	−0.996630	+	0.0820332i	$0.973859\pi$
$350$	7.72264	+	6.34873i	0.412792	+	0.339354i
$351$		0			0
$352$	7.82941	+	7.01089i	0.417309	+	0.373682i
$353$	−10.9754			−0.584162			−0.292081	−	0.956394i	$-0.594348\pi$
$353$	−10.9754			−0.584162			−0.292081	+	0.956394i	$0.594348\pi$
$354$		0			0
$355$	−7.04725	+	3.98269i	−0.374029	+	0.211379i
$356$	9.31180	−	30.9648i	0.493524	−	1.64113i
$357$		0			0
$358$	37.0306	+	5.44747i	1.95713	+	0.287908i
$359$	21.1071			1.11399			0.556996	−	0.830515i	$-0.311954\pi$
$359$	21.1071			1.11399			0.556996	+	0.830515i	$0.311954\pi$
$360$		0			0
$361$	−18.0804			−0.951599
$362$	−22.9748	−	3.37976i	−1.20753	−	0.177636i
$363$		0			0
$364$	−14.3106	−	4.30353i	−0.750082	−	0.225566i
$365$	−10.2377	−	18.1154i	−0.535868	−	0.948202i
$366$		0			0
$367$	−26.1942			−1.36733			−0.683664	−	0.729797i	$-0.739615\pi$
$367$	−26.1942			−1.36733			−0.683664	+	0.729797i	$0.739615\pi$
$368$	2.78019	−	4.20449i	0.144927	−	0.219174i
$369$		0			0
$370$	−7.99132	−	20.7057i	−0.415449	−	1.07644i
$371$		−	1.95664i		−	0.101584i
$372$		0			0
$373$	−6.92866			−0.358753			−0.179376	−	0.983781i	$-0.557408\pi$
$373$	−6.92866			−0.358753			−0.179376	+	0.983781i	$0.557408\pi$
$374$	−8.82993	−	1.29895i	−0.456585	−	0.0671669i
$375$		0			0
$376$	16.4769	+	7.72037i	0.849730	+	0.398148i
$377$	36.8782			1.89932
$378$		0			0
$379$	23.3481			1.19931			0.599656	−	0.800258i	$-0.295304\pi$
$379$	23.3481			1.19931			0.599656	+	0.800258i	$0.295304\pi$
$380$	4.18311	−	0.945421i	0.214589	−	0.0484991i
$381$		0			0
$382$	−0.108702	+	0.738932i	−0.00556170	+	0.0378071i
$383$			10.6684i			0.545129i	0.962138	+	0.272564i	$0.0878718\pi$
$383$			10.6684i			0.545129i	−0.962138	+	0.272564i	$0.912128\pi$
$384$		0			0
$385$	2.88978	+	5.11338i	0.147277	+	0.260602i
$386$	4.50235	+	0.662328i	0.229163	+	0.0337116i
$387$		0			0
$388$	−9.32147	+	30.9969i	−0.473226	+	1.57363i
$389$	−15.8584			−0.804054			−0.402027	−	0.915628i	$-0.631694\pi$
$389$	−15.8584			−0.804054			−0.402027	+	0.915628i	$0.631694\pi$
$390$		0			0
$391$			4.28052i			0.216475i
$392$	−6.00169	+	12.8089i	−0.303131	+	0.646945i
$393$		0			0
$394$	−2.51033	−	0.369288i	−0.126469	−	0.0186045i
$395$	7.78553	+	13.7762i	0.391732	+	0.693158i
$396$		0			0
$397$	−22.5850			−1.13351			−0.566754	−	0.823887i	$-0.691801\pi$
$397$	−22.5850			−1.13351			−0.566754	+	0.823887i	$0.691801\pi$
$398$	23.1128	+	3.40007i	1.15854	+	0.170430i
$399$		0			0
$400$	18.0561	−	8.60102i	0.902805	−	0.430051i
$401$			15.2185i			0.759973i	0.924992	+	0.379987i	$0.124071\pi$
$401$			15.2185i			0.759973i	−0.924992	+	0.379987i	$0.875929\pi$
$402$		0			0
$403$			46.6656i			2.32458i
$404$	−15.8257	−	4.75915i	−0.787359	−	0.236777i
$405$		0			0
$406$	−2.03065	+	13.8038i	−0.100779	+	0.685073i
$407$		−	13.0393i		−	0.646333i
$408$		0			0
$409$	−16.1485			−0.798494			−0.399247	−	0.916843i	$-0.630728\pi$
$409$	−16.1485			−0.798494			−0.399247	+	0.916843i	$0.630728\pi$
$410$	28.9705	−	11.1811i	1.43075	−	0.552195i
$411$		0			0
$412$	−13.4422	−	4.04238i	−0.662252	−	0.199154i
$413$		−	1.94918i		−	0.0959127i
$414$		0			0
$415$	−15.8191	+	8.94003i	−0.776529	+	0.438849i
$416$	−19.9431	+	22.2715i	−0.977792	+	1.09195i
$417$		0			0
$418$	2.49276	+	0.366703i	0.121925	+	0.0179360i
$419$			12.9802i			0.634123i	0.948405	+	0.317062i	$0.102696\pi$
$419$			12.9802i			0.634123i	−0.948405	+	0.317062i	$0.897304\pi$
$420$		0			0
$421$		−	3.77558i		−	0.184010i	−0.995759	−	0.0920052i	$-0.970672\pi$
$421$		−	3.77558i		−	0.184010i	0.995759	−	0.0920052i	$-0.0293276\pi$
$422$	−2.65280	+	18.0331i	−0.129136	+	0.877838i
$423$		0			0
$424$	−3.54454	−	1.66082i	−0.172138	−	0.0806567i
$425$	−8.76150	+	14.5501i	−0.424995	+	0.705781i
$426$		0			0
$427$			9.73926i			0.471316i
$428$	−26.1357	−	7.85958i	−1.26332	−	0.379907i
$429$		0			0
$430$	−22.8411	+	8.81546i	−1.10149	+	0.425119i
$431$	9.99810			0.481591			0.240796	−	0.970576i	$-0.422592\pi$
$431$	9.99810			0.481591			0.240796	+	0.970576i	$0.422592\pi$
$432$		0			0
$433$			18.9200i			0.909238i	0.890686	+	0.454619i	$0.150225\pi$
$433$			18.9200i			0.909238i	−0.890686	+	0.454619i	$0.849775\pi$
$434$	−17.4674	−	2.56958i	−0.838460	−	0.123344i
$435$		0			0
$436$	1.75740	−	5.84392i	0.0841641	−	0.279873i
$437$		−	1.20843i		−	0.0578069i
$438$		0			0
$439$		−	35.3788i		−	1.68854i	−0.535920	−	0.844269i	$-0.680035\pi$
$439$		−	35.3788i		−	1.68854i	0.535920	−	0.844269i	$-0.319965\pi$
$440$	11.7160	−	0.894666i	0.558539	−	0.0426515i
$441$		0			0
$442$	3.69497	−	25.1175i	0.175752	−	1.19472i
$443$	−24.6061			−1.16907			−0.584536	−	0.811368i	$-0.698723\pi$
$443$	−24.6061			−1.16907			−0.584536	+	0.811368i	$0.698723\pi$
$444$		0			0
$445$	−17.7866	−	31.4729i	−0.843168	−	1.49196i
$446$	−1.44458	+	9.81991i	−0.0684028	+	0.464986i
$447$		0			0
$448$	−7.23828	−	8.69123i	−0.341976	−	0.410622i
$449$		−	4.53892i		−	0.214205i	−0.994248	−	0.107102i	$-0.965843\pi$
$449$		−	4.53892i		−	0.214205i	0.994248	−	0.107102i	$-0.0341573\pi$
$450$		0			0
$451$	18.2440			0.859076
$452$	6.39898	+	1.92432i	0.300983	+	0.0905122i
$453$		0			0
$454$	−5.37121	+	36.5122i	−0.252083	+	1.71360i
$455$	−14.5455	+	8.22026i	−0.681903	+	0.385372i
$456$		0			0
$457$			8.34915i			0.390557i	0.980748	+	0.195278i	$0.0625610\pi$
$457$			8.34915i			0.390557i	−0.980748	+	0.195278i	$0.937439\pi$
$458$	−38.3096	−	5.63562i	−1.79009	−	0.263335i
$459$		0			0
$460$	−1.24234	−	5.49687i	−0.0579244	−	0.256293i
$461$	−10.5909			−0.493269			−0.246635	−	0.969109i	$-0.579325\pi$
$461$	−10.5909			−0.493269			−0.246635	+	0.969109i	$0.579325\pi$
$462$		0			0
$463$	−20.7805			−0.965751			−0.482875	−	0.875689i	$-0.660408\pi$
$463$	−20.7805			−0.965751			−0.482875	+	0.875689i	$0.660408\pi$
$464$	23.2826	+	15.3955i	1.08087	+	0.714718i
$465$		0			0
$466$	1.97606	−	13.4328i	0.0915390	−	0.622260i
$467$	15.4779			0.716233			0.358116	−	0.933677i	$-0.383419\pi$
$467$	15.4779			0.716233			0.358116	+	0.933677i	$0.383419\pi$
$468$		0			0
$469$			8.60706i			0.397437i
$470$	18.9792	−	7.32498i	0.875444	−	0.337876i
$471$		0			0
$472$	−3.53102	−	1.65449i	−0.162528	−	0.0761540i
$473$	−14.3840			−0.661378
$474$		0			0
$475$	2.47345	−	4.10760i	0.113489	−	0.188470i
$476$	9.19826	+	2.76612i	0.421602	+	0.126785i
$477$		0			0
$478$	3.64103	−	24.7508i	0.166537	−	1.13208i
$479$	38.1553			1.74336			0.871680	−	0.490075i	$-0.163031\pi$
$479$	38.1553			1.74336			0.871680	+	0.490075i	$0.163031\pi$
$480$		0			0
$481$	37.0915			1.69122
$482$	−0.821924	+	5.58724i	−0.0374376	+	0.254492i
$483$		0			0
$484$	−14.4572	−	4.34760i	−0.657144	−	0.197618i
$485$	17.8051	+	31.5056i	0.808489	+	1.43060i
$486$		0			0
$487$	−32.2405			−1.46096			−0.730478	−	0.682937i	$-0.760703\pi$
$487$	−32.2405			−1.46096			−0.730478	+	0.682937i	$0.760703\pi$
$488$	17.6431	+	8.26682i	0.798666	+	0.374221i
$489$		0			0
$490$	5.69432	+	14.7541i	0.257243	+	0.666523i
$491$			12.2064i			0.550865i	0.961320	+	0.275433i	$0.0888211\pi$
$491$			12.2064i			0.550865i	−0.961320	+	0.275433i	$0.911179\pi$
$492$		0			0
$493$	−23.7037			−1.06756
$494$	−1.04312	+	7.09089i	−0.0469323	+	0.319034i
$495$		0			0
$496$	−19.4814	+	29.4618i	−0.874743	+	1.32288i
$497$	5.11819			0.229582
$498$		0			0
$499$	−38.3721			−1.71777			−0.858886	−	0.512167i	$-0.828843\pi$
$499$	−38.3721			−1.71777			−0.858886	+	0.512167i	$0.828843\pi$
$500$	7.02827	−	21.2274i	0.314314	−	0.949319i
$501$		0			0
$502$	27.4792	+	4.04238i	1.22645	+	0.180420i
$503$		−	10.4283i		−	0.464974i	−0.972600	−	0.232487i	$-0.925314\pi$
$503$		−	10.4283i		−	0.464974i	0.972600	−	0.232487i	$-0.0746863\pi$
$504$		0			0
$505$	−16.0854	+	9.09055i	−0.715792	+	0.404524i
$506$	0.481871	−	3.27564i	0.0214218	−	0.145620i
$507$		0			0
$508$	−19.7174	−	5.92945i	−0.874816	−	0.263077i
$509$	9.51620			0.421798			0.210899	−	0.977508i	$-0.432361\pi$
$509$	9.51620			0.421798			0.210899	+	0.977508i	$0.432361\pi$
$510$		0			0
$511$			13.1566i			0.582015i
$512$	−21.8885	+	5.73522i	−0.967345	+	0.253463i
$513$		0			0
$514$	−0.151692	+	1.03117i	−0.00669085	+	0.0454828i
$515$	−13.6628	+	7.72143i	−0.602056	+	0.340247i
$516$		0			0
$517$	11.9520			0.525649
$518$	−2.04239	+	13.8837i	−0.0897374	+	0.610013i
$519$		0			0
$520$	2.54496	+	33.3273i	0.111604	+	1.46150i
$521$			12.3260i			0.540010i	0.962859	+	0.270005i	$0.0870253\pi$
$521$			12.3260i			0.540010i	−0.962859	+	0.270005i	$0.912975\pi$
$522$		0			0
$523$		−	26.5712i		−	1.16188i	−0.813947	−	0.580939i	$-0.802685\pi$
$523$		−	26.5712i		−	1.16188i	0.813947	−	0.580939i	$-0.197315\pi$
$524$	−6.42153	+	21.3537i	−0.280526	+	0.932840i
$525$		0			0
$526$	−14.9307	−	2.19641i	−0.651009	−	0.0957682i
$527$		−	29.9946i		−	1.30659i
$528$		0			0
$529$	21.4121			0.930959
$530$	−4.08284	+	1.57577i	−0.177347	+	0.0684469i
$531$		0			0
$532$	−2.59674	−	0.780899i	−0.112583	−	0.0338563i
$533$			51.8967i			2.24790i
$534$		0			0
$535$	−26.5646	+	15.0127i	−1.14849	+	0.649057i
$536$	15.5921	+	7.30580i	0.673476	+	0.315562i
$537$		0			0
$538$	−4.53659	+	30.8386i	−0.195586	+	1.32955i
$539$			9.29131i			0.400205i
$540$		0			0
$541$		−	36.6675i		−	1.57646i	−0.615382	−	0.788229i	$-0.710998\pi$
$541$		−	36.6675i		−	1.57646i	0.615382	−	0.788229i	$-0.289002\pi$
$542$	−20.2776	−	2.98299i	−0.870999	−	0.128130i
$543$		0			0
$544$	12.8186	−	14.3151i	0.549592	−	0.613757i
$545$	−3.35684	−	5.93982i	−0.143791	−	0.254434i
$546$		0			0
$547$			27.7063i			1.18463i	0.805705	+	0.592317i	$0.201787\pi$
$547$			27.7063i			1.18463i	−0.805705	+	0.592317i	$0.798213\pi$
$548$	−18.0972	−	5.44224i	−0.773075	−	0.232481i
$549$		0			0
$550$	8.34262	−	10.1480i	0.355731	−	0.432713i
$551$	6.69175			0.285078
$552$		0			0
$553$		−	10.0052i		−	0.425466i
$554$	−1.83718	+	12.4887i	−0.0780542	+	0.530593i
$555$		0			0
$556$	28.2926	+	8.50822i	1.19987	+	0.360829i
$557$		−	17.7763i		−	0.753206i	−0.926375	−	0.376603i	$-0.877092\pi$
$557$		−	17.7763i		−	0.753206i	0.926375	−	0.376603i	$-0.122908\pi$
$558$		0			0
$559$		−	40.9167i		−	1.73059i
$560$	−12.6148	−	0.882517i	−0.533074	−	0.0372931i
$561$		0			0
$562$	−16.7484	−	2.46381i	−0.706488	−	0.103929i
$563$	−36.7044			−1.54690			−0.773452	−	0.633854i	$-0.781472\pi$
$563$	−36.7044			−1.54690			−0.773452	+	0.633854i	$0.781472\pi$
$564$		0			0
$565$	6.50399	−	3.67567i	0.273625	−	0.154637i
$566$	−23.7976	−	3.50081i	−1.00029	−	0.147150i
$567$		0			0
$568$	4.34440	−	9.27184i	0.182287	−	0.389038i
$569$			5.97856i			0.250634i	0.992117	+	0.125317i	$0.0399949\pi$
$569$			5.97856i			0.250634i	−0.992117	+	0.125317i	$0.960005\pi$
$570$		0			0
$571$	26.6100			1.11359			0.556796	−	0.830649i	$-0.312030\pi$
$571$	26.6100			1.11359			0.556796	+	0.830649i	$0.312030\pi$
$572$	−5.65511	+	18.8051i	−0.236452	+	0.786279i
$573$		0			0
$574$	−19.4254	−	2.85762i	−0.810800	−	0.119275i
$575$	−5.39764	−	3.25026i	−0.225097	−	0.135545i
$576$		0			0
$577$			47.2797i			1.96828i	0.177398	+	0.984139i	$0.443232\pi$
$577$			47.2797i			1.96828i	−0.177398	+	0.984139i	$0.556768\pi$
$578$	1.12407	−	7.64118i	0.0467553	−	0.317831i
$579$		0			0
$580$	30.4393	−	6.87955i	1.26392	−	0.285658i
$581$	11.4889			0.476640
$582$		0			0
$583$	−2.57115			−0.106486
$584$	23.8338	+	11.1675i	0.986251	+	0.462116i
$585$		0			0
$586$	12.9873	+	1.91052i	0.536498	+	0.0789228i
$587$	9.59894			0.396191			0.198095	−	0.980183i	$-0.436524\pi$
$587$	9.59894			0.396191			0.198095	+	0.980183i	$0.436524\pi$
$588$		0			0
$589$			8.46774i			0.348907i
$590$	−4.06727	+	1.56975i	−0.167447	+	0.0646258i
$591$		0			0
$592$	23.4173	+	15.4845i	0.962444	+	0.636410i
$593$	−34.4142			−1.41322			−0.706610	−	0.707603i	$-0.749777\pi$
$593$	−34.4142			−1.41322			−0.706610	+	0.707603i	$0.749777\pi$
$594$		0			0
$595$	9.34920	−	5.28362i	0.383280	−	0.216607i
$596$	29.1553	+	8.76765i	1.19425	+	0.359137i
$597$		0			0
$598$	9.31787	+	1.37073i	0.381036	+	0.0560532i
$599$	3.71332			0.151722			0.0758611	−	0.997118i	$-0.475829\pi$
$599$	3.71332			0.151722			0.0758611	+	0.997118i	$0.475829\pi$
$600$		0			0
$601$	−45.0267			−1.83668			−0.918338	−	0.395797i	$-0.870468\pi$
$601$	−45.0267			−1.83668			−0.918338	+	0.395797i	$0.870468\pi$
$602$	15.3155	+	2.25302i	0.624212	+	0.0918261i
$603$		0			0
$604$	7.96865	−	26.4984i	0.324240	−	1.07820i
$605$	−14.6944	+	8.30443i	−0.597413	+	0.337623i
$606$		0			0
$607$	4.98395			0.202292			0.101146	−	0.994872i	$-0.467749\pi$
$607$	4.98395			0.202292			0.101146	+	0.994872i	$0.467749\pi$
$608$	−3.61879	+	4.04128i	−0.146761	+	0.163896i
$609$		0			0
$610$	20.3225	−	7.84344i	0.822835	−	0.317571i
$611$			33.9986i			1.37544i
$612$		0			0
$613$	14.1267			0.570572			0.285286	−	0.958442i	$-0.407911\pi$
$613$	14.1267			0.570572			0.285286	+	0.958442i	$0.407911\pi$
$614$	39.4921	+	5.80958i	1.59377	+	0.234456i
$615$		0			0
$616$	−6.72751	−	3.15223i	−0.271059	−	0.127007i
$617$	34.3479			1.38279			0.691396	−	0.722476i	$-0.256996\pi$
$617$	34.3479			1.38279			0.691396	+	0.722476i	$0.256996\pi$
$618$		0			0
$619$	−35.3327			−1.42014			−0.710071	−	0.704130i	$-0.751337\pi$
$619$	−35.3327			−1.42014			−0.710071	+	0.704130i	$0.751337\pi$
$620$	8.70538	+	38.5178i	0.349616	+	1.54691i
$621$		0			0
$622$	5.63378	−	38.2971i	0.225894	−	1.53557i
$623$			22.8578i			0.915777i
$624$		0			0
$625$	−11.6945	−	22.0961i	−0.467782	−	0.883844i
$626$	38.0264	+	5.59396i	1.51984	+	0.223580i
$627$		0			0
$628$	15.2083	+	4.57347i	0.606876	+	0.182501i
$629$	−23.8408			−0.950594
$630$		0			0
$631$			7.89084i			0.314129i	0.987588	+	0.157065i	$0.0502031\pi$
$631$			7.89084i			0.314129i	−0.987588	+	0.157065i	$0.949797\pi$
$632$	−18.1250	−	8.49260i	−0.720972	−	0.337817i
$633$		0			0
$634$	2.82272	+	0.415243i	0.112105	+	0.0164914i
$635$	−20.0409	+	11.3260i	−0.795299	+	0.449457i
$636$		0			0
$637$	−26.4300			−1.04719
$638$	18.1391	+	2.66839i	0.718134	+	0.105643i
$639$		0			0
$640$	−12.3064	+	22.1032i	−0.486452	+	0.873707i
$641$		−	48.6371i		−	1.92105i	−0.278195	−	0.960525i	$-0.589736\pi$
$641$		−	48.6371i		−	1.92105i	0.278195	−	0.960525i	$-0.410264\pi$
$642$		0			0
$643$		−	18.4399i		−	0.727200i	−0.931555	−	0.363600i	$-0.881547\pi$
$643$		−	18.4399i		−	0.727200i	0.931555	−	0.363600i	$-0.118453\pi$
$644$	−1.02615	+	3.41228i	−0.0404360	+	0.134463i
$645$		0			0
$646$	0.670473	−	4.55772i	0.0263794	−	0.179321i
$647$			36.7711i			1.44562i	0.691046	+	0.722811i	$0.257150\pi$
$647$			36.7711i			1.44562i	−0.691046	+	0.722811i	$0.742850\pi$
$648$		0			0
$649$	−2.56134			−0.100541
$650$	28.8670	+	23.7314i	1.13226	+	0.930821i
$651$		0			0
$652$	−5.33707	+	17.7475i	−0.209016	+	0.695046i
$653$			8.74915i			0.342381i	0.985238	+	0.171190i	$0.0547613\pi$
$653$			8.74915i			0.342381i	−0.985238	+	0.171190i	$0.945239\pi$
$654$		0			0
$655$	12.2659	+	21.7041i	0.479268	+	0.848049i
$656$	−21.6653	+	32.7644i	−0.845886	+	1.27924i
$657$		0			0
$658$	−12.7260	−	1.87209i	−0.496111	−	0.0729815i
$659$			13.4862i			0.525349i	0.964885	+	0.262674i	$0.0846045\pi$
$659$			13.4862i			0.525349i	−0.964885	+	0.262674i	$0.915395\pi$
$660$		0			0
$661$		−	11.8459i		−	0.460751i	−0.973102	−	0.230375i	$-0.926005\pi$
$661$		−	11.8459i		−	0.460751i	0.973102	−	0.230375i	$-0.0739954\pi$
$662$	5.26035	−	35.7586i	0.204449	−	1.38980i
$663$		0			0
$664$	9.75195	−	20.8127i	0.378449	−	0.807689i
$665$	−2.63936	+	1.49161i	−0.102350	+	0.0578422i
$666$		0			0
$667$		−	8.79338i		−	0.340481i
$668$	−14.2594	+	47.4171i	−0.551712	+	1.83462i
$669$		0			0
$670$	17.9600	−	6.93163i	0.693856	−	0.267792i
$671$	12.7980			0.494061
$672$		0			0
$673$		−	3.43550i		−	0.132429i	−0.997805	−	0.0662144i	$-0.978908\pi$
$673$		−	3.43550i		−	0.132429i	0.997805	−	0.0662144i	$-0.0210921\pi$
$674$	3.34104	+	0.491491i	0.128692	+	0.0189315i
$675$		0			0
$676$	−28.5942	−	8.59893i	−1.09978	−	0.330728i
$677$		−	40.8927i		−	1.57163i	−0.618459	−	0.785817i	$-0.712243\pi$
$677$		−	40.8927i		−	1.57163i	0.618459	−	0.785817i	$-0.287757\pi$
$678$		0			0
$679$		−	22.8815i		−	0.878112i
$680$	−1.63579	−	21.4213i	−0.0627297	−	0.821470i
$681$		0			0
$682$	−3.37658	+	22.9532i	−0.129296	+	0.878923i
$683$	−44.9939			−1.72164			−0.860822	−	0.508906i	$-0.830050\pi$
$683$	−44.9939			−1.72164			−0.860822	+	0.508906i	$0.830050\pi$
$684$		0			0
$685$	−18.3942	+	10.3953i	−0.702806	+	0.397185i
$686$	3.49235	−	23.7401i	0.133338	−	0.906403i
$687$		0			0
$688$	17.0814	−	25.8323i	0.651223	−	0.984846i
$689$		−	7.31386i		−	0.278636i
$690$		0			0
$691$	−42.6781			−1.62355			−0.811776	−	0.583969i	$-0.801499\pi$
$691$	−42.6781			−1.62355			−0.811776	+	0.583969i	$0.801499\pi$
$692$	1.39827	−	4.64969i	0.0531541	−	0.176755i
$693$		0			0
$694$	−3.63083	+	24.6815i	−0.137824	+	0.936897i
$695$	28.7569	−	16.2517i	1.09081	−	0.616463i
$696$		0			0
$697$		−	33.3569i		−	1.26348i
$698$	−4.28843	−	0.630859i	−0.162319	−	0.0238784i
$699$		0			0
$700$	−10.4724	+	9.49843i	−0.395819	+	0.359007i
$701$	3.25752			0.123035			0.0615174	−	0.998106i	$-0.480406\pi$
$701$	3.25752			0.123035			0.0615174	+	0.998106i	$0.480406\pi$
$702$		0			0
$703$	6.73045			0.253844
$704$	−11.4208	+	9.51154i	−0.430438	+	0.358480i
$705$		0			0
$706$	2.25903	−	15.3563i	0.0850195	−	0.577942i
$707$	11.6823			0.439360
$708$		0			0
$709$			42.0351i			1.57866i	0.613968	+	0.789331i	$0.289572\pi$
$709$			42.0351i			1.57866i	−0.613968	+	0.789331i	$0.710428\pi$
$710$	−4.12190	−	10.6799i	−0.154692	−	0.400811i
$711$		0			0
$712$	41.4079	+	19.4020i	1.55183	+	0.727121i
$713$	11.1271			0.416714
$714$		0			0
$715$	10.8019	+	19.1137i	0.403969	+	0.714810i
$716$	−15.2437	+	50.6904i	−0.569685	+	1.89439i
$717$		0			0
$718$	−4.34440	+	29.5322i	−0.162131	+	1.10213i
$719$	−42.2143			−1.57433			−0.787163	−	0.616745i	$-0.788451\pi$
$719$	−42.2143			−1.57433			−0.787163	+	0.616745i	$0.788451\pi$
$720$		0			0
$721$	9.92289			0.369548
$722$	3.72141	−	25.2973i	0.138497	−	0.941467i
$723$		0			0
$724$	9.45762	−	31.4497i	0.351490	−	1.16882i
$725$	17.9985	−	29.8898i	0.668449	−	1.11008i
$726$		0			0
$727$	36.5526			1.35566			0.677830	−	0.735219i	$-0.262921\pi$
$727$	36.5526			1.35566			0.677830	+	0.735219i	$0.262921\pi$
$728$	8.96681	−	19.1370i	0.332332	−	0.709266i
$729$		0			0
$730$	27.4534	−	10.5956i	1.01610	−	0.392160i
$731$			26.2995i			0.972720i
$732$		0			0
$733$	−27.9037			−1.03065			−0.515323	−	0.856996i	$-0.672328\pi$
$733$	−27.9037			−1.03065			−0.515323	+	0.856996i	$0.672328\pi$
$734$	5.39146	−	36.6498i	0.199002	−	1.35277i
$735$		0			0
$736$	5.31050	+	4.75531i	0.195747	+	0.175283i
$737$	11.3102			0.416617
$738$		0			0
$739$	4.57103			0.168148			0.0840740	−	0.996460i	$-0.473207\pi$
$739$	4.57103			0.168148			0.0840740	+	0.996460i	$0.473207\pi$
$740$	30.6153	−	6.91933i	1.12544	−	0.254360i
$741$		0			0
$742$	2.73764	+	0.402727i	0.100502	+	0.0147846i
$743$			31.6650i			1.16168i	0.814019	+	0.580839i	$0.197275\pi$
$743$			31.6650i			1.16168i	−0.814019	+	0.580839i	$0.802725\pi$
$744$		0			0
$745$	29.6337	−	16.7473i	1.08570	−	0.613572i
$746$	1.42610	−	9.69428i	0.0522132	−	0.354933i
$747$		0			0
$748$	3.63486	−	12.0871i	0.132903	−	0.441947i
$749$	19.2930			0.704951
$750$		0			0
$751$		−	24.8129i		−	0.905434i	−0.891654	−	0.452717i	$-0.850455\pi$
$751$		−	24.8129i		−	0.905434i	0.891654	−	0.452717i	$-0.149545\pi$
$752$	−14.1934	+	21.4647i	−0.517579	+	0.782736i
$753$		0			0
$754$	−7.59049	+	51.5984i	−0.276430	+	1.87910i
$755$	−15.2211	−	26.9332i	−0.553952	−	0.980200i
$756$		0			0
$757$	25.9889			0.944584			0.472292	−	0.881442i	$-0.343427\pi$
$757$	25.9889			0.944584			0.472292	+	0.881442i	$0.343427\pi$
$758$	−4.80565	+	32.6676i	−0.174549	+	1.18654i
$759$		0			0
$760$	0.461797	+	6.04742i	0.0167511	+	0.219363i
$761$		−	33.5362i		−	1.21569i	−0.794057	−	0.607843i	$-0.792035\pi$
$761$		−	33.5362i		−	1.21569i	0.794057	−	0.607843i	$-0.207965\pi$
$762$		0			0
$763$			4.31390i			0.156174i
$764$	−1.01151	−	0.304183i	−0.0365951	−	0.0110050i
$765$		0			0
$766$	−14.9267	−	2.19583i	−0.539324	−	0.0793386i
$767$		−	7.28596i		−	0.263081i
$768$		0			0
$769$	6.84258			0.246750			0.123375	−	0.992360i	$-0.460628\pi$
$769$	6.84258			0.246750			0.123375	+	0.992360i	$0.460628\pi$
$770$	−7.74920	+	2.99079i	−0.279262	+	0.107781i
$771$		0			0
$772$	−1.85340	+	6.16316i	−0.0667053	+	0.221817i
$773$		−	38.3944i		−	1.38095i	−0.723355	−	0.690476i	$-0.757401\pi$
$773$		−	38.3944i		−	1.38095i	0.723355	−	0.690476i	$-0.242599\pi$
$774$		0			0
$775$	37.8225	+	22.7753i	1.35863	+	0.818114i
$776$	−41.4509	−	19.4222i	−1.48800	−	0.697215i
$777$		0			0
$778$	3.26408	−	22.1884i	0.117023	−	0.795493i
$779$			9.41694i			0.337397i
$780$		0			0
$781$		−	6.72562i		−	0.240662i
$782$	−5.98912	−	0.881043i	−0.214170	−	0.0315060i
$783$		0			0
$784$	−16.6863	−	11.0337i	−0.595939	−	0.394061i
$785$	15.4578	−	8.73587i	0.551714	−	0.311796i
$786$		0			0
$787$		−	37.3993i		−	1.33314i	−0.745442	−	0.666571i	$-0.767761\pi$
$787$		−	37.3993i		−	1.33314i	0.745442	−	0.666571i	$-0.232239\pi$
$788$	1.03338	−	3.43633i	0.0368127	−	0.122414i
$789$		0			0
$790$	−20.8776	+	8.05765i	−0.742790	+	0.286678i
$791$	−4.72364			−0.167953
$792$		0			0
$793$			36.4051i			1.29278i
$794$	4.64858	−	31.5999i	0.164972	−	1.12144i
$795$		0			0
$796$	−9.51444	+	31.6386i	−0.337230	+	1.12140i
$797$			29.6980i			1.05196i	0.850497	+	0.525979i	$0.176301\pi$
$797$			29.6980i			1.05196i	−0.850497	+	0.525979i	$0.823699\pi$
$798$		0			0
$799$		−	21.8528i		−	0.773098i
$800$	8.31774	+	27.0336i	0.294077	+	0.955782i
$801$		0			0
$802$	−21.2930	−	3.13235i	−0.751881	−	0.110607i
$803$	17.2886			0.610102
$804$		0			0
$805$	1.96007	+	3.46828i	0.0690833	+	0.122241i
$806$	−65.2925	−	9.60500i	−2.29983	−	0.338322i
$807$		0			0
$808$	9.91614	−	21.1631i	0.348849	−	0.744515i
$809$		−	41.0881i		−	1.44458i	−0.691590	−	0.722290i	$-0.743089\pi$
$809$		−	41.0881i		−	1.44458i	0.691590	−	0.722290i	$-0.256911\pi$
$810$		0			0
$811$	30.7023			1.07810			0.539052	−	0.842272i	$-0.318783\pi$
$811$	30.7023			1.07810			0.539052	+	0.842272i	$0.318783\pi$
$812$	−18.8958	−	5.68238i	−0.663111	−	0.199412i
$813$		0			0
$814$	18.2440	+	2.68382i	0.639451	+	0.0940679i
$815$	10.1944	+	18.0387i	0.357096	+	0.631870i
$816$		0			0
$817$		−	7.42455i		−	0.259752i
$818$	3.32379	−	22.5943i	0.116214	−	0.789991i
$819$		0			0
$820$	9.68122	+	42.8356i	0.338083	+	1.49588i
$821$	−13.3388			−0.465528			−0.232764	−	0.972533i	$-0.574777\pi$
$821$	−13.3388			−0.465528			−0.232764	+	0.972533i	$0.574777\pi$
$822$		0			0
$823$	8.08650			0.281877			0.140939	−	0.990018i	$-0.454988\pi$
$823$	8.08650			0.281877			0.140939	+	0.990018i	$0.454988\pi$
$824$	8.42269	−	17.9758i	0.293418	−	0.626215i
$825$		0			0
$826$	2.72720	+	0.401191i	0.0948914	+	0.0139592i
$827$	22.7070			0.789601			0.394800	−	0.918767i	$-0.370814\pi$
$827$	22.7070			0.789601			0.394800	+	0.918767i	$0.370814\pi$
$828$		0			0
$829$			46.8393i			1.62680i	0.581708	+	0.813398i	$0.302385\pi$
$829$			46.8393i			1.62680i	−0.581708	+	0.813398i	$0.697615\pi$
$830$	−9.25251	−	23.9735i	−0.321159	−	0.832131i
$831$		0			0
$832$	−27.0565	−	32.4876i	−0.938014	−	1.12630i
$833$	16.9881			0.588601
$834$		0			0
$835$	27.2371	+	48.1952i	0.942580	+	1.66786i
$836$	−1.02615	+	3.41228i	−0.0354901	+	0.118016i
$837$		0			0
$838$	−18.1613	−	2.67166i	−0.627371	−	0.0922909i
$839$	−51.3436			−1.77258			−0.886289	−	0.463132i	$-0.846726\pi$
$839$	−51.3436			−1.77258			−0.886289	+	0.463132i	$0.846726\pi$
$840$		0			0
$841$	19.6940			0.679102
$842$	5.28262	+	0.777112i	0.182051	+	0.0267810i
$843$		0			0
$844$	−24.6851	−	7.42336i	−0.849696	−	0.255523i
$845$	−29.0635	+	16.4250i	−0.999814	+	0.565036i
$846$		0			0
$847$	10.6721			0.366697
$848$	3.05331	−	4.61753i	0.104851	−	0.158566i
$849$		0			0
$850$	−18.5544	−	15.2535i	−0.636412	−	0.523190i
$851$		−	8.84422i		−	0.303176i
$852$		0			0
$853$	48.8546			1.67275			0.836375	−	0.548158i	$-0.184671\pi$
$853$	48.8546			1.67275			0.836375	+	0.548158i	$0.184671\pi$
$854$	−13.6267	−	2.00459i	−0.466297	−	0.0685957i
$855$		0			0
$856$	16.3762	−	34.9502i	0.559726	−	1.19457i
$857$	23.8972			0.816312			0.408156	−	0.912912i	$-0.366172\pi$
$857$	23.8972			0.816312			0.408156	+	0.912912i	$0.366172\pi$
$858$		0			0
$859$	18.7193			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$859$	18.7193			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$860$	−7.63292	−	33.7726i	−0.260280	−	1.15164i
$861$		0			0
$862$	−2.05787	+	13.9889i	−0.0700913	+	0.476463i
$863$		−	43.0074i		−	1.46399i	−0.681311	−	0.731994i	$-0.738590\pi$
$863$		−	43.0074i		−	1.46399i	0.681311	−	0.731994i	$-0.261410\pi$
$864$		0			0
$865$	−2.67085	−	4.72599i	−0.0908117	−	0.160688i
$866$	−26.4721	−	3.89423i	−0.899557	−	0.132331i
$867$		0			0
$868$	7.19047	−	23.9107i	0.244061	−	0.811581i
$869$	−13.1475			−0.445999
$870$		0			0
$871$			32.1729i			1.09014i
$872$	7.81483	+	3.66170i	0.264644	+	0.124001i
$873$		0			0
$874$	1.69078	+	0.248726i	0.0571914	+	0.00841327i
$875$	−0.436450	+	15.8010i	−0.0147547	+	0.534173i
$876$		0			0
$877$	−21.5156			−0.726531			−0.363265	−	0.931686i	$-0.618338\pi$
$877$	−21.5156			−0.726531			−0.363265	+	0.931686i	$0.618338\pi$
$878$	49.5004	+	7.28187i	1.67056	+	0.245751i
$879$		0			0
$880$	−1.15968	+	16.5767i	−0.0390929	+	0.558799i
$881$		−	8.76271i		−	0.295223i	−0.989045	−	0.147612i	$-0.952841\pi$
$881$		−	8.76271i		−	0.295223i	0.989045	−	0.147612i	$-0.0471586\pi$
$882$		0			0
$883$		−	34.2208i		−	1.15162i	−0.817583	−	0.575811i	$-0.804687\pi$
$883$		−	34.2208i		−	1.15162i	0.817583	−	0.575811i	$-0.195313\pi$
$884$	34.3828	+	10.3397i	1.15642	+	0.347761i
$885$		0			0
$886$	5.06458	−	34.4278i	0.170148	−	1.15662i
$887$		−	3.61165i		−	0.121267i	−0.998160	−	0.0606337i	$-0.980688\pi$
$887$		−	3.61165i		−	0.121267i	0.998160	−	0.0606337i	$-0.0193121\pi$
$888$		0			0
$889$	14.5551			0.488162
$890$	47.6964	−	18.4083i	1.59879	−	0.617049i
$891$		0			0
$892$	−13.4422	−	4.04238i	−0.450080	−	0.135349i
$893$			6.16924i			0.206446i
$894$		0			0
$895$	29.1173	+	51.5222i	0.973285	+	1.72220i
$896$	13.6502	−	8.33859i	0.456022	−	0.278573i
$897$		0			0
$898$	6.35066	+	0.934228i	0.211924	+	0.0311756i
$899$			61.6173i			2.05505i
$900$		0			0
$901$			4.70103i			0.156614i
$902$	−3.75509	+	25.5262i	−0.125031	+	0.849928i
$903$		0			0
$904$	−4.00949	+	8.55709i	−0.133354	+	0.284605i
$905$	−18.0652	−	31.9658i	−0.600507	−	1.06258i
$906$		0			0
$907$			0.296316i			0.00983900i	0.999988	+	0.00491950i	$0.00156593\pi$
$907$			0.296316i			0.00983900i	−0.999988	+	0.00491950i	$0.998434\pi$
$908$	−49.9807	−	15.0303i	−1.65867	−	0.498798i
$909$		0			0
$910$	−8.50758	−	22.0433i	−0.282024	−	0.730729i
$911$	38.2561			1.26748			0.633741	−	0.773545i	$-0.281518\pi$
$911$	38.2561			1.26748			0.633741	+	0.773545i	$0.281518\pi$
$912$		0			0
$913$		−	15.0971i		−	0.499642i
$914$	−11.6818	−	1.71847i	−0.386398	−	0.0568420i
$915$		0			0
$916$	15.7702	−	52.4411i	0.521062	−	1.73270i
$917$		−	15.7630i		−	0.520540i
$918$		0			0
$919$		−	27.0814i		−	0.893332i	−0.894701	−	0.446666i	$-0.852611\pi$
$919$		−	27.0814i		−	0.893332i	0.894701	−	0.446666i	$-0.147389\pi$
$920$	7.94668	−	0.606830i	0.261994	−	0.0200066i
$921$		0			0
$922$	2.17989	−	14.8184i	0.0717908	−	0.488017i
$923$	19.1317			0.629726
$924$		0			0
$925$	18.1026	−	30.0626i	0.595210	−	0.988454i
$926$	4.27716	−	29.0751i	0.140556	−	0.955468i
$927$		0			0
$928$	−26.3329	+	29.4072i	−0.864419	+	0.965340i
$929$		−	2.41533i		−	0.0792443i	−0.999215	−	0.0396222i	$-0.987385\pi$
$929$		−	2.41533i		−	0.0792443i	0.999215	−	0.0396222i	$-0.0126154\pi$
$930$		0			0
$931$	−4.79587			−0.157178
$932$	18.3878	+	5.52962i	0.602312	+	0.181129i
$933$		0			0
$934$	−3.18576	+	21.6560i	−0.104241	+	0.708606i
$935$	−6.94301	−	12.2854i	−0.227061	−	0.401776i
$936$		0			0
$937$		−	14.7062i		−	0.480432i	−0.970720	−	0.240216i	$-0.922782\pi$
$937$		−	14.7062i		−	0.480432i	0.970720	−	0.240216i	$-0.0772182\pi$
$938$	−12.0426	−	1.77156i	−0.393205	−	0.0578434i
$939$		0			0
$940$	6.34237	+	28.0625i	0.206865	+	0.915298i
$941$	22.6540			0.738500			0.369250	−	0.929330i	$-0.379615\pi$
$941$	22.6540			0.738500			0.369250	+	0.929330i	$0.379615\pi$
$942$		0			0
$943$	12.3744			0.402967
$944$	3.04166	−	4.59991i	0.0989977	−	0.149714i
$945$		0			0
$946$	2.96060	−	20.1255i	0.0962575	−	0.654335i
$947$	−39.0269			−1.26820			−0.634101	−	0.773250i	$-0.718630\pi$
$947$	−39.0269			−1.26820			−0.634101	+	0.773250i	$0.718630\pi$
$948$		0			0
$949$			49.1791i			1.59642i
$950$	5.23807	+	4.30619i	0.169945	+	0.139711i
$951$		0			0
$952$	−5.76348	+	12.3005i	−0.186795	+	0.398660i
$953$	9.05724			0.293393			0.146696	−	0.989182i	$-0.453136\pi$
$953$	9.05724			0.293393			0.146696	+	0.989182i	$0.453136\pi$
$954$		0			0
$955$	−1.02811	+	0.581026i	−0.0332687	+	0.0188015i
$956$	33.8809	+	10.1887i	1.09579	+	0.329527i
$957$		0			0
$958$	−7.85335	+	53.3852i	−0.253730	+	1.72480i
$959$	13.3591			0.431389
$960$		0			0
$961$	−46.9704			−1.51517
$962$	−7.63438	+	51.8967i	−0.246142	+	1.67322i
$963$		0			0
$964$	−7.64825	−	2.30000i	−0.246334	−	0.0740780i
$965$	3.54021	+	6.26429i	0.113963	+	0.201655i
$966$		0			0
$967$	0.330822			0.0106385			0.00531926	−	0.999986i	$-0.498307\pi$
$967$	0.330822			0.0106385			0.00531926	+	0.999986i	$0.498307\pi$
$968$	9.05862	−	19.3330i	0.291155	−	0.621386i
$969$		0			0
$970$	−47.7460	+	18.4275i	−1.53303	+	0.591670i
$971$			3.23651i			0.103865i	0.998651	+	0.0519323i	$0.0165380\pi$
$971$			3.23651i			0.103865i	−0.998651	+	0.0519323i	$0.983462\pi$
$972$		0			0
$973$	−20.8852			−0.669550
$974$	6.63593	−	45.1094i	0.212629	−	1.44540i
$975$		0			0
$976$	−15.1980	+	22.9839i	−0.486475	+	0.735697i
$977$	34.3972			1.10046			0.550231	−	0.835012i	$-0.314540\pi$
$977$	34.3972			1.10046			0.550231	+	0.835012i	$0.314540\pi$
$978$		0			0
$979$	30.0365			0.959971
$980$	−21.8153	+	4.93046i	−0.696865	+	0.157498i
$981$		0			0
$982$	−17.0786	−	2.51239i	−0.545000	−	0.0801735i
$983$		−	4.15590i		−	0.132553i	−0.997801	−	0.0662763i	$-0.978888\pi$
$983$		−	4.15590i		−	0.132553i	0.997801	−	0.0662763i	$-0.0211119\pi$
$984$		0			0
$985$	−1.97388	−	3.49272i	−0.0628932	−	0.111287i
$986$	4.87884	−	33.1652i	0.155374	−	1.05619i
$987$		0			0
$988$	−9.70656	−	2.91898i	−0.308807	−	0.0928651i
$989$	−9.75632			−0.310233
$990$		0			0
$991$		−	21.0947i		−	0.670095i	−0.942201	−	0.335047i	$-0.891248\pi$
$991$		−	21.0947i		−	0.670095i	0.942201	−	0.335047i	$-0.108752\pi$
$992$	−37.2119	−	33.3216i	−1.18148	−	1.05796i
$993$		0			0
$994$	−1.05346	+	7.16115i	−0.0334136	+	0.227138i
$995$	18.1737	+	32.1578i	0.576145	+	1.01947i
$996$		0			0
$997$	27.0375			0.856288			0.428144	−	0.903711i	$-0.359168\pi$
$997$	27.0375			0.856288			0.428144	+	0.903711i	$0.359168\pi$
$998$	7.89798	−	53.6885i	0.250006	−	1.69948i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.m.b.539.19	yes	40
3.2	odd	2	inner	1080.2.m.b.539.22	yes	40
4.3	odd	2		4320.2.m.b.2159.7		40
5.4	even	2	inner	1080.2.m.b.539.21	yes	40
8.3	odd	2	inner	1080.2.m.b.539.18	yes	40
8.5	even	2		4320.2.m.b.2159.34		40
12.11	even	2		4320.2.m.b.2159.33		40
15.14	odd	2	inner	1080.2.m.b.539.20	yes	40
20.19	odd	2		4320.2.m.b.2159.6		40
24.5	odd	2		4320.2.m.b.2159.8		40
24.11	even	2	inner	1080.2.m.b.539.23	yes	40
40.19	odd	2	inner	1080.2.m.b.539.24	yes	40
40.29	even	2		4320.2.m.b.2159.35		40
60.59	even	2		4320.2.m.b.2159.36		40
120.29	odd	2		4320.2.m.b.2159.5		40
120.59	even	2	inner	1080.2.m.b.539.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.m.b.539.17	✓	40	120.59	even	2	inner
1080.2.m.b.539.18	yes	40	8.3	odd	2	inner
1080.2.m.b.539.19	yes	40	1.1	even	1	trivial
1080.2.m.b.539.20	yes	40	15.14	odd	2	inner
1080.2.m.b.539.21	yes	40	5.4	even	2	inner
1080.2.m.b.539.22	yes	40	3.2	odd	2	inner
1080.2.m.b.539.23	yes	40	24.11	even	2	inner
1080.2.m.b.539.24	yes	40	40.19	odd	2	inner
4320.2.m.b.2159.5		40	120.29	odd	2
4320.2.m.b.2159.6		40	20.19	odd	2
4320.2.m.b.2159.7		40	4.3	odd	2
4320.2.m.b.2159.8		40	24.5	odd	2
4320.2.m.b.2159.33		40	12.11	even	2
4320.2.m.b.2159.34		40	8.5	even	2
4320.2.m.b.2159.35		40	40.29	even	2
4320.2.m.b.2159.36		40	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.205826 + 1.39916i) q^{2} +(-1.91527 - 0.575965i) q^{4} +(-1.94670 + 1.10016i) q^{5} +1.41383 q^{7} +(1.20008 - 2.56121i) q^{8} +(-1.13862 - 2.95018i) q^{10} -1.85786i q^{11} +5.28485 q^{13} +(-0.291002 + 1.97816i) q^{14} +(3.33653 + 2.20626i) q^{16} -3.39687 q^{17} +0.958964 q^{19} +(4.36211 - 0.985877i) q^{20} +(2.59943 + 0.382395i) q^{22} -1.26014i q^{23} +(2.57929 - 4.28337i) q^{25} +(-1.08776 + 7.39432i) q^{26} +(-2.70786 - 0.814315i) q^{28} +6.97811 q^{29} +8.83008i q^{31} +(-3.77364 + 4.21422i) q^{32} +(0.699164 - 4.75275i) q^{34} +(-2.75230 + 1.55544i) q^{35} +7.01845 q^{37} +(-0.197380 + 1.34174i) q^{38} +(0.481558 + 6.30620i) q^{40} +9.81991i q^{41} -7.74226i q^{43} +(-1.07006 + 3.55830i) q^{44} +(1.76313 + 0.259369i) q^{46} +6.43323i q^{47} -5.00109 q^{49} +(5.46222 + 4.49045i) q^{50} +(-10.1219 - 3.04389i) q^{52} -1.38393i q^{53} +(2.04394 + 3.61669i) q^{55} +(1.69670 - 3.62111i) q^{56} +(-1.43628 + 9.76345i) q^{58} -1.37865i q^{59} +6.88857i q^{61} +(-12.3547 - 1.81746i) q^{62} +(-5.11963 - 6.14731i) q^{64} +(-10.2880 + 5.81419i) q^{65} +6.08777i q^{67} +(6.50593 + 1.95648i) q^{68} +(-1.60981 - 4.17104i) q^{70} +3.62010 q^{71} +9.30568i q^{73} +(-1.44458 + 9.81991i) q^{74} +(-1.83668 - 0.552330i) q^{76} -2.62669i q^{77} -7.07671i q^{79} +(-8.92246 - 0.624204i) q^{80} +(-13.7396 - 2.02119i) q^{82} +8.12610 q^{83} +(6.61269 - 3.73711i) q^{85} +(10.8326 + 1.59356i) q^{86} +(-4.75837 - 2.22957i) q^{88} +16.1673i q^{89} +7.47186 q^{91} +(-0.725795 + 2.41351i) q^{92} +(-9.00109 - 1.32413i) q^{94} +(-1.86682 + 1.05502i) q^{95} -16.1841i q^{97} +(1.02935 - 6.99730i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{4} - 2 q^{10} - 28 q^{16} + 24 q^{19} + 40 q^{25} + 56 q^{34} + 18 q^{40} - 32 q^{46} + 104 q^{49} - 100 q^{64} + 10 q^{70} - 120 q^{76} - 56 q^{94}+O(q^{100}) \) 40 * q - 4 * q^4 - 2 * q^10 - 28 * q^16 + 24 * q^19 + 40 * q^25 + 56 * q^34 + 18 * q^40 - 32 * q^46 + 104 * q^49 - 100 * q^64 + 10 * q^70 - 120 * q^76 - 56 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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