LMFDB - Embedded newform 1080.2.m.c.539.9

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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			539.9
Character	$\chi$	$=$	1080.539
Dual form			1080.2.m.c.539.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08245 - 0.910116i) q^{2} +(0.343378 + 1.97030i) q^{4} +(-1.75989 - 1.37942i) q^{5} -1.14666 q^{7} +(1.42152 - 2.44526i) q^{8} +(0.649552 + 3.09485i) q^{10} +0.489523i q^{11} +6.59916 q^{13} +(1.24119 + 1.04359i) q^{14} +(-3.76418 + 1.35312i) q^{16} -4.58091 q^{17} -6.55167 q^{19} +(2.11357 - 3.94117i) q^{20} +(0.445523 - 0.529883i) q^{22} -6.55060i q^{23} +(1.19441 + 4.85524i) q^{25} +(-7.14323 - 6.00600i) q^{26} +(-0.393737 - 2.25926i) q^{28} +0.212237 q^{29} -0.796718i q^{31} +(5.30602 + 1.96117i) q^{32} +(4.95859 + 4.16916i) q^{34} +(2.01799 + 1.58172i) q^{35} -4.78762 q^{37} +(7.09183 + 5.96278i) q^{38} +(-5.87474 + 2.34252i) q^{40} +6.42519i q^{41} +2.15455i q^{43} +(-0.964509 + 0.168092i) q^{44} +(-5.96180 + 7.09067i) q^{46} -1.38063i q^{47} -5.68518 q^{49} +(3.12595 - 6.34259i) q^{50} +(2.26601 + 13.0023i) q^{52} +7.06462i q^{53} +(0.675258 - 0.861506i) q^{55} +(-1.62999 + 2.80387i) q^{56} +(-0.229735 - 0.193160i) q^{58} +8.26229i q^{59} +7.61815i q^{61} +(-0.725106 + 0.862404i) q^{62} +(-3.95859 - 6.95195i) q^{64} +(-11.6138 - 9.10300i) q^{65} +11.2181i q^{67} +(-1.57299 - 9.02578i) q^{68} +(-0.744813 - 3.54873i) q^{70} -11.3201 q^{71} -9.32981i q^{73} +(5.18234 + 4.35729i) q^{74} +(-2.24970 - 12.9088i) q^{76} -0.561315i q^{77} -6.01760i q^{79} +(8.49105 + 2.81105i) q^{80} +(5.84767 - 6.95492i) q^{82} -14.6045 q^{83} +(8.06189 + 6.31900i) q^{85} +(1.96089 - 2.33218i) q^{86} +(1.19701 + 0.695865i) q^{88} +15.7617i q^{89} -7.56697 q^{91} +(12.9067 - 2.24933i) q^{92} +(-1.25653 + 1.49446i) q^{94} +(11.5302 + 9.03749i) q^{95} -6.13586i q^{97} +(6.15390 + 5.17417i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * 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 $

$2$	−1.08245	−	0.910116i	−0.765405	−	0.643549i
$2$	−1.08245	−	0.910116i	−0.765405	−	0.643549i
$3$		0			0
$3$		0			0
$4$	0.343378	+	1.97030i	0.171689	+	0.985151i
$5$	−1.75989	−	1.37942i	−0.787046	−	0.616895i
$5$	−1.75989	−	1.37942i	−0.787046	−	0.616895i
$6$		0			0
$7$	−1.14666			−0.433396			−0.216698	−	0.976239i	$-0.569529\pi$
$7$	−1.14666			−0.433396			−0.216698	+	0.976239i	$0.569529\pi$
$8$	1.42152	−	2.44526i	0.502581	−	0.864530i
$9$		0			0
$10$	0.649552	+	3.09485i	0.205406	+	0.978677i
$11$			0.489523i			0.147597i	0.997273	+	0.0737984i	$0.0235121\pi$
$11$			0.489523i			0.147597i	−0.997273	+	0.0737984i	$0.976488\pi$
$12$		0			0
$13$	6.59916			1.83028			0.915139	−	0.403140i	$-0.132081\pi$
$13$	6.59916			1.83028			0.915139	+	0.403140i	$0.132081\pi$
$14$	1.24119	+	1.04359i	0.331723	+	0.278911i
$15$		0			0
$16$	−3.76418	+	1.35312i	−0.941046	+	0.338279i
$17$	−4.58091			−1.11103			−0.555517	−	0.831505i	$-0.687480\pi$
$17$	−4.58091			−1.11103			−0.555517	+	0.831505i	$0.687480\pi$
$18$		0			0
$19$	−6.55167			−1.50306			−0.751528	−	0.659701i	$-0.770683\pi$
$19$	−6.55167			−1.50306			−0.751528	+	0.659701i	$0.770683\pi$
$20$	2.11357	−	3.94117i	0.472608	−	0.881273i
$21$		0			0
$22$	0.445523	−	0.529883i	0.0949858	−	0.112971i
$23$		−	6.55060i		−	1.36589i	−0.730468	−	0.682947i	$-0.760698\pi$
$23$		−	6.55060i		−	1.36589i	0.730468	−	0.682947i	$-0.239302\pi$
$24$		0			0
$25$	1.19441	+	4.85524i	0.238881	+	0.971049i
$26$	−7.14323	−	6.00600i	−1.40090	−	1.17787i
$27$		0			0
$28$	−0.393737	−	2.25926i	−0.0744093	−	0.426960i
$29$	0.212237			0.0394114			0.0197057	−	0.999806i	$-0.493727\pi$
$29$	0.212237			0.0394114			0.0197057	+	0.999806i	$0.493727\pi$
$30$		0			0
$31$		−	0.796718i		−	0.143095i	−0.997437	−	0.0715474i	$-0.977206\pi$
$31$		−	0.796718i		−	0.143095i	0.997437	−	0.0715474i	$-0.0227937\pi$
$32$	5.30602	+	1.96117i	0.937980	+	0.346688i
$33$		0			0
$34$	4.95859	+	4.16916i	0.850391	+	0.715005i
$35$	2.01799	+	1.58172i	0.341102	+	0.267359i
$36$		0			0
$37$	−4.78762			−0.787081			−0.393540	−	0.919307i	$-0.628750\pi$
$37$	−4.78762			−0.787081			−0.393540	+	0.919307i	$0.628750\pi$
$38$	7.09183	+	5.96278i	1.15045	+	0.967290i
$39$		0			0
$40$	−5.87474	+	2.34252i	−0.928879	+	0.370384i
$41$			6.42519i			1.00345i	0.865028	+	0.501723i	$0.167300\pi$
$41$			6.42519i			1.00345i	−0.865028	+	0.501723i	$0.832700\pi$
$42$		0			0
$43$			2.15455i			0.328565i	0.986413	+	0.164283i	$0.0525309\pi$
$43$			2.15455i			0.328565i	−0.986413	+	0.164283i	$0.947469\pi$
$44$	−0.964509	+	0.168092i	−0.145405	+	0.0253408i
$45$		0			0
$46$	−5.96180	+	7.09067i	−0.879020	+	1.04546i
$47$		−	1.38063i		−	0.201385i	−0.994918	−	0.100693i	$-0.967894\pi$
$47$		−	1.38063i		−	0.201385i	0.994918	−	0.100693i	$-0.0321059\pi$
$48$		0			0
$49$	−5.68518			−0.812168
$50$	3.12595	−	6.34259i	0.442077	−	0.896977i
$51$		0			0
$52$	2.26601	+	13.0023i	0.314239	+	1.80310i
$53$			7.06462i			0.970400i	0.874403	+	0.485200i	$0.161253\pi$
$53$			7.06462i			0.970400i	−0.874403	+	0.485200i	$0.838747\pi$
$54$		0			0
$55$	0.675258	−	0.861506i	0.0910518	−	0.116165i
$56$	−1.62999	+	2.80387i	−0.217817	+	0.374683i
$57$		0			0
$58$	−0.229735	−	0.193160i	−0.0301657	−	0.0253632i
$59$			8.26229i			1.07566i	0.843054	+	0.537829i	$0.180756\pi$
$59$			8.26229i			1.07566i	−0.843054	+	0.537829i	$0.819244\pi$
$60$		0			0
$61$			7.61815i			0.975405i	0.873010	+	0.487702i	$0.162165\pi$
$61$			7.61815i			0.975405i	−0.873010	+	0.487702i	$0.837835\pi$
$62$	−0.725106	+	0.862404i	−0.0920885	+	0.109525i
$63$		0			0
$64$	−3.95859	−	6.95195i	−0.494824	−	0.868993i
$65$	−11.6138	−	9.10300i	−1.44051	−	1.12909i
$66$		0			0
$67$			11.2181i			1.37051i	0.728304	+	0.685254i	$0.240309\pi$
$67$			11.2181i			1.37051i	−0.728304	+	0.685254i	$0.759691\pi$
$68$	−1.57299	−	9.02578i	−0.190753	−	1.09454i
$69$		0			0
$70$	−0.744813	−	3.54873i	−0.0890222	−	0.424154i
$71$	−11.3201			−1.34344			−0.671722	−	0.740804i	$-0.734445\pi$
$71$	−11.3201			−1.34344			−0.671722	+	0.740804i	$0.734445\pi$
$72$		0			0
$73$		−	9.32981i		−	1.09197i	−0.837795	−	0.545986i	$-0.816155\pi$
$73$		−	9.32981i		−	1.09197i	0.837795	−	0.545986i	$-0.183845\pi$
$74$	5.18234	+	4.35729i	0.602435	+	0.506525i
$75$		0			0
$76$	−2.24970	−	12.9088i	−0.258058	−	1.48074i
$77$		−	0.561315i		−	0.0639678i
$78$		0			0
$79$		−	6.01760i		−	0.677033i	−0.940960	−	0.338517i	$-0.890075\pi$
$79$		−	6.01760i		−	0.677033i	0.940960	−	0.338517i	$-0.109925\pi$
$80$	8.49105	+	2.81105i	0.949329	+	0.314285i
$81$		0			0
$82$	5.84767	−	6.95492i	0.645767	−	0.768043i
$83$	−14.6045			−1.60305			−0.801527	−	0.597958i	$-0.795979\pi$
$83$	−14.6045			−1.60305			−0.801527	+	0.597958i	$0.795979\pi$
$84$		0			0
$85$	8.06189	+	6.31900i	0.874435	+	0.685391i
$86$	1.96089	−	2.33218i	0.211448	−	0.251485i
$87$		0			0
$88$	1.19701	+	0.695865i	0.127602	+	0.0741795i
$89$			15.7617i			1.67074i	0.549691	+	0.835368i	$0.314746\pi$
$89$			15.7617i			1.67074i	−0.549691	+	0.835368i	$0.685254\pi$
$90$		0			0
$91$	−7.56697			−0.793234
$92$	12.9067	−	2.24933i	1.34561	−	0.234509i
$93$		0			0
$94$	−1.25653	+	1.49446i	−0.129601	+	0.154141i
$95$	11.5302	+	9.03749i	1.18297	+	0.927227i
$96$		0			0
$97$		−	6.13586i		−	0.623002i	−0.950246	−	0.311501i	$-0.899168\pi$
$97$		−	6.13586i		−	0.623002i	0.950246	−	0.311501i	$-0.100832\pi$
$98$	6.15390	+	5.17417i	0.621638	+	0.522670i
$99$		0			0
$100$	−9.15616	+	4.02053i	−0.915616	+	0.402053i
$101$	−9.11507			−0.906983			−0.453491	−	0.891261i	$-0.649822\pi$
$101$	−9.11507			−0.906983			−0.453491	+	0.891261i	$0.649822\pi$
$102$		0			0
$103$	−3.61978			−0.356668			−0.178334	−	0.983970i	$-0.557071\pi$
$103$	−3.61978			−0.356668			−0.178334	+	0.983970i	$0.557071\pi$
$104$	9.38080	−	16.1367i	0.919863	−	1.58233i
$105$		0			0
$106$	6.42962	−	7.64707i	0.624500	−	0.742749i
$107$	−8.02627			−0.775929			−0.387965	−	0.921674i	$-0.626822\pi$
$107$	−8.02627			−0.775929			−0.387965	+	0.921674i	$0.626822\pi$
$108$		0			0
$109$			17.4477i			1.67118i	0.549350	+	0.835592i	$0.314875\pi$
$109$			17.4477i			1.67118i	−0.549350	+	0.835592i	$0.685125\pi$
$110$	−1.51500	+	0.317971i	−0.144450	+	0.0303173i
$111$		0			0
$112$	4.31623	−	1.55156i	0.407845	−	0.146609i
$113$	−4.83818			−0.455138			−0.227569	−	0.973762i	$-0.573078\pi$
$113$	−4.83818			−0.455138			−0.227569	+	0.973762i	$0.573078\pi$
$114$		0			0
$115$	−9.03602	+	11.5283i	−0.842613	+	1.07502i
$116$	0.0728775	+	0.418171i	0.00676651	+	0.0388262i
$117$		0			0
$118$	7.51964	−	8.94349i	0.692239	−	0.823315i
$119$	5.25273			0.481517
$120$		0			0
$121$	10.7604			0.978215
$122$	6.93340	−	8.24624i	0.627721	−	0.746579i
$123$		0			0
$124$	1.56978	−	0.273576i	0.140970	−	0.0245678i
$125$	4.59539	−	10.1923i	0.411024	−	0.911624i
$126$		0			0
$127$	−14.0822			−1.24960			−0.624798	−	0.780786i	$-0.714819\pi$
$127$	−14.0822			−1.24960			−0.624798	+	0.780786i	$0.714819\pi$
$128$	−2.04212	+	11.1279i	−0.180499	+	0.983575i
$129$		0			0
$130$	4.28649	+	20.4234i	0.375950	+	1.79125i
$131$			12.5225i			1.09409i	0.837102	+	0.547046i	$0.184248\pi$
$131$			12.5225i			1.09409i	−0.837102	+	0.547046i	$0.815752\pi$
$132$		0			0
$133$	7.51251			0.651418
$134$	10.2098	−	12.1430i	0.881989	−	1.04899i
$135$		0			0
$136$	−6.51184	+	11.2015i	−0.558385	+	0.960522i
$137$	−2.50573			−0.214079			−0.107040	−	0.994255i	$-0.534137\pi$
$137$	−2.50573			−0.214079			−0.107040	+	0.994255i	$0.534137\pi$
$138$		0			0
$139$	2.86529			0.243031			0.121515	−	0.992590i	$-0.461225\pi$
$139$	2.86529			0.243031			0.121515	+	0.992590i	$0.461225\pi$
$140$	−2.42353	+	4.51917i	−0.204826	+	0.381940i
$141$		0			0
$142$	12.2533	+	10.3026i	1.02828	+	0.864572i
$143$			3.23044i			0.270143i
$144$		0			0
$145$	−0.373513	−	0.292763i	−0.0310186	−	0.0243127i
$146$	−8.49120	+	10.0990i	−0.702737	+	0.835800i
$147$		0			0
$148$	−1.64397	−	9.43307i	−0.135133	−	0.775393i
$149$	20.0127			1.63950			0.819750	−	0.572721i	$-0.194112\pi$
$149$	20.0127			1.63950			0.819750	+	0.572721i	$0.194112\pi$
$150$		0			0
$151$		−	9.18095i		−	0.747135i	−0.927603	−	0.373568i	$-0.878134\pi$
$151$		−	9.18095i		−	0.747135i	0.927603	−	0.373568i	$-0.121866\pi$
$152$	−9.31329	+	16.0205i	−0.755408	+	1.29944i
$153$		0			0
$154$	−0.510862	+	0.607594i	−0.0411664	+	0.0489613i
$155$	−1.09901	+	1.40213i	−0.0882745	+	0.112622i
$156$		0			0
$157$	2.50256			0.199726			0.0998632	−	0.995001i	$-0.468159\pi$
$157$	2.50256			0.199726			0.0998632	+	0.995001i	$0.468159\pi$
$158$	−5.47672	+	6.51373i	−0.435704	+	0.518205i
$159$		0			0
$160$	−6.63273	−	10.7707i	−0.524363	−	0.851495i
$161$			7.51129i			0.591972i
$162$		0			0
$163$		−	16.6545i		−	1.30448i	−0.758012	−	0.652241i	$-0.773829\pi$
$163$		−	16.6545i		−	1.30448i	0.758012	−	0.652241i	$-0.226171\pi$
$164$	−12.6596	+	2.20627i	−0.988546	+	0.172281i
$165$		0			0
$166$	15.8086	+	13.2918i	1.22699	+	1.03164i
$167$			0.665315i			0.0514836i	0.999669	+	0.0257418i	$0.00819478\pi$
$167$			0.665315i			0.0514836i	−0.999669	+	0.0257418i	$0.991805\pi$
$168$		0			0
$169$	30.5489			2.34991
$170$	−2.97554	−	14.1772i	−0.228213	−	1.08734i
$171$		0			0
$172$	−4.24511	+	0.739824i	−0.323686	+	0.0564111i
$173$		−	7.10945i		−	0.540522i	−0.962787	−	0.270261i	$-0.912890\pi$
$173$		−	7.10945i		−	0.540522i	0.962787	−	0.270261i	$-0.0871099\pi$
$174$		0			0
$175$	−1.36957	−	5.56730i	−0.103530	−	0.420848i
$176$	−0.662383	−	1.84266i	−0.0499290	−	0.138895i
$177$		0			0
$178$	14.3450	−	17.0612i	1.07520	−	1.27879i
$179$		−	20.0977i		−	1.50217i	−0.660206	−	0.751085i	$-0.729531\pi$
$179$		−	20.0977i		−	1.50217i	0.660206	−	0.751085i	$-0.270469\pi$
$180$		0			0
$181$			3.67133i			0.272888i	0.990648	+	0.136444i	$0.0435673\pi$
$181$			3.67133i			0.272888i	−0.990648	+	0.136444i	$0.956433\pi$
$182$	8.19083	+	6.88682i	0.607145	+	0.510485i
$183$		0			0
$184$	−16.0179	−	9.31177i	−1.18086	−	0.686473i
$185$	8.42568	+	6.60414i	0.619468	+	0.485546i
$186$		0			0
$187$		−	2.24246i		−	0.163985i
$188$	2.72026	−	0.474078i	0.198395	−	0.0345757i
$189$		0			0
$190$	−4.25565	−	20.2764i	−0.308737	−	1.47101i
$191$	−0.418278			−0.0302656			−0.0151328	−	0.999885i	$-0.504817\pi$
$191$	−0.418278			−0.0302656			−0.0151328	+	0.999885i	$0.504817\pi$
$192$		0			0
$193$		−	13.1064i		−	0.943417i	−0.881754	−	0.471709i	$-0.843637\pi$
$193$		−	13.1064i		−	0.943417i	0.881754	−	0.471709i	$-0.156363\pi$
$194$	−5.58434	+	6.64174i	−0.400932	+	0.476849i
$195$		0			0
$196$	−1.95217	−	11.2015i	−0.139440	−	0.800109i
$197$			4.56693i			0.325380i	0.986677	+	0.162690i	$0.0520170\pi$
$197$			4.56693i			0.325380i	−0.986677	+	0.162690i	$0.947983\pi$
$198$		0			0
$199$		−	13.1531i		−	0.932398i	−0.884680	−	0.466199i	$-0.845623\pi$
$199$		−	13.1531i		−	0.932398i	0.884680	−	0.466199i	$-0.154377\pi$
$200$	13.5702	+	3.98117i	0.959558	+	0.281511i
$201$		0			0
$202$	9.86657	+	8.29577i	0.694209	+	0.583688i
$203$	−0.243363			−0.0170807
$204$		0			0
$205$	8.86303	−	11.3076i	0.619021	−	0.789758i
$206$	3.91822	+	3.29442i	0.272995	+	0.229533i
$207$		0			0
$208$	−24.8404	+	8.92944i	−1.72237	+	0.619145i
$209$		−	3.20720i		−	0.221846i
$210$		0			0
$211$	−0.897033			−0.0617543			−0.0308772	−	0.999523i	$-0.509830\pi$
$211$	−0.897033			−0.0617543			−0.0308772	+	0.999523i	$0.509830\pi$
$212$	−13.9194	+	2.42584i	−0.955990	+	0.166607i
$213$		0			0
$214$	8.68801	+	7.30484i	0.593900	+	0.499349i
$215$	2.97202	−	3.79176i	0.202690	−	0.258596i
$216$		0			0
$217$			0.913562i			0.0620167i
$218$	15.8794	−	18.8862i	1.07549	−	1.27913i
$219$		0			0
$220$	1.92930	+	1.03464i	0.130073	+	0.0697554i
$221$	−30.2302			−2.03350
$222$		0			0
$223$	9.57525			0.641206			0.320603	−	0.947214i	$-0.396114\pi$
$223$	9.57525			0.641206			0.320603	+	0.947214i	$0.396114\pi$
$224$	−6.08418	−	2.24878i	−0.406516	−	0.150253i
$225$		0			0
$226$	5.23707	+	4.40331i	0.348365	+	0.292903i
$227$	−15.7980			−1.04855			−0.524276	−	0.851549i	$-0.675664\pi$
$227$	−15.7980			−1.04855			−0.524276	+	0.851549i	$0.675664\pi$
$228$		0			0
$229$		−	15.6346i		−	1.03317i	−0.856237	−	0.516583i	$-0.827204\pi$
$229$		−	15.6346i		−	1.03317i	0.856237	−	0.516583i	$-0.172796\pi$
$230$	20.2731	−	4.25495i	1.33677	−	0.280563i
$231$		0			0
$232$	0.301698	−	0.518974i	0.0198074	−	0.0340723i
$233$	5.68606			0.372506			0.186253	−	0.982502i	$-0.440366\pi$
$233$	5.68606			0.372506			0.186253	+	0.982502i	$0.440366\pi$
$234$		0			0
$235$	−1.90447	+	2.42975i	−0.124234	+	0.158500i
$236$	−16.2792	+	2.83709i	−1.05969	+	0.184679i
$237$		0			0
$238$	−5.68580	−	4.78060i	−0.368556	−	0.309880i
$239$	−29.6817			−1.91995			−0.959974	−	0.280090i	$-0.909636\pi$
$239$	−29.6817			−1.91995			−0.959974	+	0.280090i	$0.909636\pi$
$240$		0			0
$241$	−3.70042			−0.238365			−0.119183	−	0.992872i	$-0.538027\pi$
$241$	−3.70042			−0.238365			−0.119183	+	0.992872i	$0.538027\pi$
$242$	−11.6475	−	9.79318i	−0.748731	−	0.629529i
$243$		0			0
$244$	−15.0101	+	2.61591i	−0.960921	+	0.167466i
$245$	10.0053	+	7.84224i	0.639213	+	0.501022i
$246$		0			0
$247$	−43.2355			−2.75101
$248$	−1.94818	−	1.13255i	−0.123710	−	0.0719168i
$249$		0			0
$250$	−14.2504	+	6.85024i	−0.901275	+	0.433247i
$251$			29.2951i			1.84909i	0.381074	+	0.924545i	$0.375554\pi$
$251$			29.2951i			1.84909i	−0.381074	+	0.924545i	$0.624446\pi$
$252$		0			0
$253$	3.20667			0.201602
$254$	15.2433	+	12.8165i	0.956447	+	0.804176i
$255$		0			0
$256$	12.3381	−	10.1868i	0.771134	−	0.636673i
$257$	15.4159			0.961615			0.480807	−	0.876826i	$-0.340344\pi$
$257$	15.4159			0.961615			0.480807	+	0.876826i	$0.340344\pi$
$258$		0			0
$259$	5.48976			0.341117
$260$	13.9478	−	26.0084i	0.865003	−	1.61297i
$261$		0			0
$262$	11.3969	−	13.5549i	0.704102	−	0.837424i
$263$			13.1012i			0.807854i	0.914791	+	0.403927i	$0.132355\pi$
$263$			13.1012i			0.807854i	−0.914791	+	0.403927i	$0.867645\pi$
$264$		0			0
$265$	9.74507	−	12.4329i	0.598635	−	0.763749i
$266$	−8.13189	−	6.83726i	−0.498598	−	0.419219i
$267$		0			0
$268$	−22.1030	+	3.85205i	−1.35016	+	0.235301i
$269$	−0.677971			−0.0413366			−0.0206683	−	0.999786i	$-0.506579\pi$
$269$	−0.677971			−0.0413366			−0.0206683	+	0.999786i	$0.506579\pi$
$270$		0			0
$271$		−	26.6785i		−	1.62060i	−0.586015	−	0.810300i	$-0.699304\pi$
$271$		−	26.6785i		−	1.62060i	0.586015	−	0.810300i	$-0.300696\pi$
$272$	17.2434	−	6.19851i	1.04553	−	0.375840i
$273$		0			0
$274$	2.71232	+	2.28051i	0.163857	+	0.137770i
$275$	−2.37676	+	0.584690i	−0.143324	+	0.0352581i
$276$		0			0
$277$	−15.0012			−0.901333			−0.450667	−	0.892692i	$-0.648814\pi$
$277$	−15.0012			−0.901333			−0.450667	+	0.892692i	$0.648814\pi$
$278$	−3.10152	−	2.60775i	−0.186017	−	0.156402i
$279$		0			0
$280$	6.73631	−	2.68606i	0.402572	−	0.160523i
$281$		−	21.2166i		−	1.26567i	−0.774285	−	0.632837i	$-0.781890\pi$
$281$		−	21.2166i		−	1.26567i	0.774285	−	0.632837i	$-0.218110\pi$
$282$		0			0
$283$			26.1597i			1.55504i	0.628861	+	0.777518i	$0.283521\pi$
$283$			26.1597i			1.55504i	−0.628861	+	0.777518i	$0.716479\pi$
$284$	−3.88706	−	22.3039i	−0.230655	−	1.32350i
$285$		0			0
$286$	2.94008	−	3.49678i	0.173850	−	0.206769i
$287$		−	7.36749i		−	0.434889i
$288$		0			0
$289$	3.98476			0.234397
$290$	0.137859	+	0.656841i	0.00809535	+	0.0385710i
$291$		0			0
$292$	18.3825	−	3.20365i	1.07576	−	0.187480i
$293$		−	15.2115i		−	0.888663i	−0.895862	−	0.444332i	$-0.853441\pi$
$293$		−	15.2115i		−	0.888663i	0.895862	−	0.444332i	$-0.146559\pi$
$294$		0			0
$295$	11.3972	−	14.5407i	0.663569	−	0.846593i
$296$	−6.80568	+	11.7070i	−0.395572	+	0.680455i
$297$		0			0
$298$	−21.6626	−	18.2138i	−1.25488	−	1.05510i
$299$		−	43.2284i		−	2.49996i
$300$		0			0
$301$		−	2.47052i		−	0.142399i
$302$	−8.35573	+	9.93788i	−0.480818	+	0.571861i
$303$		0			0
$304$	24.6617	−	8.86518i	1.41444	−	0.508453i
$305$	10.5086	−	13.4071i	0.601722	−	0.767688i
$306$		0			0
$307$		−	14.0725i		−	0.803159i	−0.915824	−	0.401580i	$-0.868461\pi$
$307$		−	14.0725i		−	0.803159i	0.915824	−	0.401580i	$-0.131539\pi$
$308$	1.10596	−	0.192743i	0.0630180	−	0.0109826i
$309$		0			0
$310$	2.46572	−	0.517510i	0.140044	−	0.0293926i
$311$	1.78682			0.101321			0.0506605	−	0.998716i	$-0.483867\pi$
$311$	1.78682			0.101321			0.0506605	+	0.998716i	$0.483867\pi$
$312$		0			0
$313$			0.380682i			0.0215174i	0.999942	+	0.0107587i	$0.00342467\pi$
$313$			0.380682i			0.0215174i	−0.999942	+	0.0107587i	$0.996575\pi$
$314$	−2.70889	−	2.27762i	−0.152872	−	0.128534i
$315$		0			0
$316$	11.8565	−	2.06631i	0.666980	−	0.116239i
$317$		−	16.1536i		−	0.907278i	−0.891185	−	0.453639i	$-0.850126\pi$
$317$		−	16.1536i		−	0.907278i	0.891185	−	0.453639i	$-0.149874\pi$
$318$		0			0
$319$			0.103895i			0.00581700i
$320$	−2.62298	+	17.6952i	−0.146629	+	0.989192i
$321$		0			0
$322$	6.83614	−	8.13056i	0.380963	−	0.453098i
$323$	30.0126			1.66995
$324$		0			0
$325$	7.88208	+	32.0405i	0.437219	+	1.77729i
$326$	−15.1575	+	18.0276i	−0.839498	+	0.998456i
$327$		0			0
$328$	15.7113	+	9.13351i	0.867509	+	0.504314i
$329$			1.58311i			0.0872795i
$330$		0			0
$331$	−9.53637			−0.524166			−0.262083	−	0.965045i	$-0.584409\pi$
$331$	−9.53637			−0.524166			−0.262083	+	0.965045i	$0.584409\pi$
$332$	−5.01487	−	28.7753i	−0.275227	−	1.57925i
$333$		0			0
$334$	0.605514	−	0.720168i	0.0331323	−	0.0394058i
$335$	15.4744	−	19.7426i	0.845459	−	1.07865i
$336$		0			0
$337$		−	24.7926i		−	1.35054i	−0.737572	−	0.675269i	$-0.764028\pi$
$337$		−	24.7926i		−	1.35054i	0.737572	−	0.675269i	$-0.235972\pi$
$338$	−33.0675	−	27.8030i	−1.79864	−	1.51228i
$339$		0			0
$340$	−9.68206	+	18.0542i	−0.525083	+	0.979125i
$341$	0.390012			0.0211204
$342$		0			0
$343$	14.5455			0.785386
$344$	5.26842	+	3.06272i	0.284054	+	0.165131i
$345$		0			0
$346$	−6.47043	+	7.69560i	−0.347852	+	0.413718i
$347$	30.6459			1.64516			0.822579	−	0.568650i	$-0.192534\pi$
$347$	30.6459			1.64516			0.822579	+	0.568650i	$0.192534\pi$
$348$		0			0
$349$			24.1005i			1.29007i	0.764153	+	0.645035i	$0.223157\pi$
$349$			24.1005i			1.29007i	−0.764153	+	0.645035i	$0.776843\pi$
$350$	−3.58440	+	7.27277i	−0.191594	+	0.388746i
$351$		0			0
$352$	−0.960037	+	2.59742i	−0.0511701	+	0.138443i
$353$	−14.3991			−0.766385			−0.383192	−	0.923669i	$-0.625175\pi$
$353$	−14.3991			−0.766385			−0.383192	+	0.923669i	$0.625175\pi$
$354$		0			0
$355$	19.9220	+	15.6151i	1.05735	+	0.828763i
$356$	−31.0553	+	5.41222i	−1.64593	+	0.286847i
$357$		0			0
$358$	−18.2912	+	21.7546i	−0.966720	+	1.14977i
$359$	8.68429			0.458340			0.229170	−	0.973386i	$-0.426399\pi$
$359$	8.68429			0.458340			0.229170	+	0.973386i	$0.426399\pi$
$360$		0			0
$361$	23.9244			1.25918
$362$	3.34134	−	3.97402i	0.175617	−	0.208870i
$363$		0			0
$364$	−2.59833	−	14.9092i	−0.136190	−	0.781455i
$365$	−12.8697	+	16.4194i	−0.673631	+	0.859431i
$366$		0			0
$367$	−24.8041			−1.29477			−0.647383	−	0.762165i	$-0.724136\pi$
$367$	−24.8041			−1.29477			−0.647383	+	0.762165i	$0.724136\pi$
$368$	8.86373	+	24.6576i	0.462054	+	1.28537i
$369$		0			0
$370$	−3.10981	−	14.8170i	−0.161671	−	0.770298i
$371$		−	8.10069i		−	0.420567i
$372$		0			0
$373$	25.4828			1.31945			0.659726	−	0.751506i	$-0.270672\pi$
$373$	25.4828			1.31945			0.659726	+	0.751506i	$0.270672\pi$
$374$	−2.04090	+	2.42735i	−0.105533	+	0.125515i
$375$		0			0
$376$	−3.37600	−	1.96258i	−0.174104	−	0.101213i
$377$	1.40058			0.0721338
$378$		0			0
$379$	−24.6997			−1.26874			−0.634368	−	0.773031i	$-0.718740\pi$
$379$	−24.6997			−1.26874			−0.634368	+	0.773031i	$0.718740\pi$
$380$	−13.8474	+	25.8213i	−0.710356	+	1.32460i
$381$		0			0
$382$	0.452764	+	0.380682i	0.0231654	+	0.0194774i
$383$		−	1.39738i		−	0.0714026i	−0.999363	−	0.0357013i	$-0.988634\pi$
$383$		−	1.39738i		−	0.0714026i	0.999363	−	0.0357013i	$-0.0113665\pi$
$384$		0			0
$385$	−0.774289	+	0.987852i	−0.0394614	+	0.0503456i
$386$	−11.9283	+	14.1869i	−0.607135	+	0.722096i
$387$		0			0
$388$	12.0895	−	2.10692i	0.613751	−	0.106963i
$389$	24.5591			1.24520			0.622599	−	0.782541i	$-0.286077\pi$
$389$	24.5591			1.24520			0.622599	+	0.782541i	$0.286077\pi$
$390$		0			0
$391$			30.0077i			1.51755i
$392$	−8.08157	+	13.9017i	−0.408181	+	0.702144i
$393$		0			0
$394$	4.15643	−	4.94345i	0.209398	−	0.249047i
$395$	−8.30080	+	10.5903i	−0.417658	+	0.532856i
$396$		0			0
$397$	−29.3723			−1.47415			−0.737077	−	0.675809i	$-0.763794\pi$
$397$	−29.3723			−1.47415			−0.737077	+	0.675809i	$0.763794\pi$
$398$	−11.9708	+	14.2375i	−0.600044	+	0.713662i
$399$		0			0
$400$	−11.0657	−	16.6599i	−0.553284	−	0.832993i
$401$			14.9880i			0.748465i	0.927335	+	0.374233i	$0.122094\pi$
$401$			14.9880i			0.748465i	−0.927335	+	0.374233i	$0.877906\pi$
$402$		0			0
$403$		−	5.25767i		−	0.261903i
$404$	−3.12992	−	17.9594i	−0.155719	−	0.893515i
$405$		0			0
$406$	0.263427	+	0.221488i	0.0130737	+	0.0109923i
$407$		−	2.34365i		−	0.116171i
$408$		0			0
$409$	−20.3845			−1.00795			−0.503973	−	0.863719i	$-0.668129\pi$
$409$	−20.3845			−1.00795			−0.503973	+	0.863719i	$0.668129\pi$
$410$	−19.8850	+	4.17349i	−0.982050	+	0.206114i
$411$		0			0
$412$	−1.24295	−	7.13206i	−0.0612359	−	0.351371i
$413$		−	9.47401i		−	0.466186i
$414$		0			0
$415$	25.7023	+	20.1458i	1.26168	+	0.988916i
$416$	35.0153	+	12.9420i	1.71676	+	0.634536i
$417$		0			0
$418$	−2.91892	+	3.47162i	−0.142769	+	0.169802i
$419$		−	8.04348i		−	0.392950i	−0.980509	−	0.196475i	$-0.937051\pi$
$419$		−	8.04348i		−	0.392950i	0.980509	−	0.196475i	$-0.0629494\pi$
$420$		0			0
$421$			25.5919i			1.24728i	0.781714	+	0.623638i	$0.214346\pi$
$421$			25.5919i			1.24728i	−0.781714	+	0.623638i	$0.785654\pi$
$422$	0.970990	+	0.816404i	0.0472671	+	0.0397419i
$423$		0			0
$424$	17.2748	+	10.0425i	0.838940	+	0.487705i
$425$	−5.47147	−	22.2414i	−0.265405	−	1.07887i
$426$		0			0
$427$		−	8.73541i		−	0.422736i
$428$	−2.75605	−	15.8142i	−0.133219	−	0.764408i
$429$		0			0
$430$	−6.66799	+	1.39949i	−0.321559	+	0.0674894i
$431$	3.17732			0.153046			0.0765231	−	0.997068i	$-0.475618\pi$
$431$	3.17732			0.153046			0.0765231	+	0.997068i	$0.475618\pi$
$432$		0			0
$433$			21.8507i			1.05008i	0.851079	+	0.525038i	$0.175949\pi$
$433$			21.8507i			1.05008i	−0.851079	+	0.525038i	$0.824051\pi$
$434$	0.831448	−	0.988882i	0.0399108	−	0.0474679i
$435$		0			0
$436$	−34.3772	+	5.99115i	−1.64637	+	0.286924i
$437$			42.9173i			2.05301i
$438$		0			0
$439$			1.44034i			0.0687435i	0.999409	+	0.0343717i	$0.0109430\pi$
$439$			1.44034i			0.0687435i	−0.999409	+	0.0343717i	$0.989057\pi$
$440$	−1.14672	−	2.87583i	−0.0546676	−	0.137100i
$441$		0			0
$442$	32.7225	+	27.5130i	1.55645	+	1.30866i
$443$	30.9735			1.47160			0.735798	−	0.677201i	$-0.236807\pi$
$443$	30.9735			1.47160			0.735798	+	0.677201i	$0.236807\pi$
$444$		0			0
$445$	21.7420	−	27.7388i	1.03067	−	1.31495i
$446$	−10.3647	−	8.71459i	−0.490782	−	0.412648i
$447$		0			0
$448$	4.53914	+	7.97150i	0.214454	+	0.376618i
$449$			9.93183i			0.468712i	0.972151	+	0.234356i	$0.0752982\pi$
$449$			9.93183i			0.468712i	−0.972151	+	0.234356i	$0.924702\pi$
$450$		0			0
$451$	−3.14528			−0.148106
$452$	−1.66133	−	9.53268i	−0.0781422	−	0.448380i
$453$		0			0
$454$	17.1005	+	14.3780i	0.802567	+	0.674794i
$455$	13.3170	+	10.4380i	0.624311	+	0.489342i
$456$		0			0
$457$			21.6719i			1.01377i	0.862014	+	0.506885i	$0.169203\pi$
$457$			21.6719i			1.01377i	−0.862014	+	0.506885i	$0.830797\pi$
$458$	−14.2293	+	16.9236i	−0.664893	+	0.790790i
$459$		0			0
$460$	−25.8170	−	13.8451i	−1.20373	−	0.645532i
$461$	−3.57008			−0.166275			−0.0831376	−	0.996538i	$-0.526494\pi$
$461$	−3.57008			−0.166275			−0.0831376	+	0.996538i	$0.526494\pi$
$462$		0			0
$463$	−25.5094			−1.18552			−0.592762	−	0.805378i	$-0.701962\pi$
$463$	−25.5094			−1.18552			−0.592762	+	0.805378i	$0.701962\pi$
$464$	−0.798898	+	0.287181i	−0.0370879	+	0.0133321i
$465$		0			0
$466$	−6.15485	−	5.17497i	−0.285118	−	0.239726i
$467$	20.4328			0.945516			0.472758	−	0.881192i	$-0.343258\pi$
$467$	20.4328			0.945516			0.472758	+	0.881192i	$0.343258\pi$
$468$		0			0
$469$		−	12.8633i		−	0.593972i
$470$	4.27284	−	0.896790i	0.197091	−	0.0413658i
$471$		0			0
$472$	20.2035	+	11.7450i	0.929939	+	0.540606i
$473$	−1.05470			−0.0484952
$474$		0			0
$475$	−7.82536	−	31.8099i	−0.359052	−	1.45954i
$476$	1.80367	+	10.3495i	0.0826713	+	0.474367i
$477$		0			0
$478$	32.1288	+	27.0138i	1.46954	+	1.23558i
$479$	−18.6566			−0.852442			−0.426221	−	0.904619i	$-0.640155\pi$
$479$	−18.6566			−0.852442			−0.426221	+	0.904619i	$0.640155\pi$
$480$		0			0
$481$	−31.5943			−1.44058
$482$	4.00551	+	3.36781i	0.182446	+	0.153400i
$483$		0			0
$484$	3.69488	+	21.2012i	0.167949	+	0.963690i
$485$	−8.46392	+	10.7984i	−0.384327	+	0.490331i
$486$		0			0
$487$	12.2903			0.556929			0.278464	−	0.960447i	$-0.410175\pi$
$487$	12.2903			0.556929			0.278464	+	0.960447i	$0.410175\pi$
$488$	18.6284	+	10.8293i	0.843266	+	0.490220i
$489$		0			0
$490$	−3.69282	−	17.5948i	−0.166824	−	0.794850i
$491$		−	12.6888i		−	0.572637i	−0.958135	−	0.286318i	$-0.907569\pi$
$491$		−	12.6888i		−	0.572637i	0.958135	−	0.286318i	$-0.0924315\pi$
$492$		0			0
$493$	−0.972238			−0.0437874
$494$	46.8001	+	39.3493i	2.10564	+	1.77041i
$495$		0			0
$496$	1.07805	+	2.99899i	0.0484060	+	0.134659i
$497$	12.9802			0.582242
$498$		0			0
$499$	−16.7725			−0.750838			−0.375419	−	0.926855i	$-0.622501\pi$
$499$	−16.7725			−0.750838			−0.375419	+	0.926855i	$0.622501\pi$
$500$	21.6598	+	5.55451i	0.968656	+	0.248405i
$501$		0			0
$502$	26.6619	−	31.7103i	1.18998	−	1.41530i
$503$			21.8493i			0.974213i	0.873343	+	0.487106i	$0.161948\pi$
$503$			21.8493i			0.974213i	−0.873343	+	0.487106i	$0.838052\pi$
$504$		0			0
$505$	16.0415	+	12.5735i	0.713837	+	0.559513i
$506$	−3.47105	−	2.91844i	−0.154307	−	0.129741i
$507$		0			0
$508$	−4.83553	−	27.7463i	−0.214542	−	1.23104i
$509$	15.6889			0.695397			0.347699	−	0.937606i	$-0.386963\pi$
$509$	15.6889			0.695397			0.347699	+	0.937606i	$0.386963\pi$
$510$		0			0
$511$			10.6981i			0.473255i
$512$	−22.6265	−	0.202518i	−0.999960	−	0.00895011i
$513$		0			0
$514$	−16.6868	−	14.0302i	−0.736025	−	0.618846i
$515$	6.37041	+	4.99319i	0.280714	+	0.220026i
$516$		0			0
$517$	0.675850			0.0297239
$518$	−5.94237	−	4.99632i	−0.261093	−	0.219526i
$519$		0			0
$520$	−38.7684	+	15.4586i	−1.70011	+	0.677906i
$521$		−	36.4911i		−	1.59870i	−0.600862	−	0.799352i	$-0.705176\pi$
$521$		−	36.4911i		−	1.59870i	0.600862	−	0.799352i	$-0.294824\pi$
$522$		0			0
$523$			37.2814i			1.63020i	0.579318	+	0.815102i	$0.303319\pi$
$523$			37.2814i			1.63020i	−0.579318	+	0.815102i	$0.696681\pi$
$524$	−24.6730	+	4.29994i	−1.07785	+	0.187844i
$525$		0			0
$526$	11.9236	−	14.1813i	0.519894	−	0.618335i
$527$			3.64970i			0.158983i
$528$		0			0
$529$	−19.9103			−0.865666
$530$	−21.8639	+	4.58883i	−0.949708	+	0.199326i
$531$		0			0
$532$	2.57963	+	14.8019i	0.111841	+	0.641745i
$533$			42.4009i			1.83658i
$534$		0			0
$535$	14.1253	+	11.0716i	0.610692	+	0.478667i
$536$	27.4311	+	15.9467i	1.18484	+	0.688792i
$537$		0			0
$538$	0.733867	+	0.617032i	0.0316392	+	0.0266021i
$539$		−	2.78303i		−	0.119874i
$540$		0			0
$541$		−	32.7256i		−	1.40699i	−0.710703	−	0.703493i	$-0.751623\pi$
$541$		−	32.7256i		−	1.40699i	0.710703	−	0.703493i	$-0.248377\pi$
$542$	−24.2805	+	28.8780i	−1.04294	+	1.24042i
$543$		0			0
$544$	−24.3064	−	8.98393i	−1.04213	−	0.385183i
$545$	24.0677	−	30.7060i	1.03095	−	1.31530i
$546$		0			0
$547$			9.73699i			0.416324i	0.978094	+	0.208162i	$0.0667481\pi$
$547$			9.73699i			0.416324i	−0.978094	+	0.208162i	$0.933252\pi$
$548$	−0.860414	−	4.93705i	−0.0367551	−	0.210900i
$549$		0			0
$550$	3.10485	+	1.53023i	0.132391	+	0.0652491i
$551$	−1.39051			−0.0592375
$552$		0			0
$553$			6.90013i			0.293423i
$554$	16.2380	+	13.6528i	0.689885	+	0.580052i
$555$		0			0
$556$	0.983879	+	5.64549i	0.0417258	+	0.239422i
$557$		−	6.15870i		−	0.260953i	−0.991451	−	0.130476i	$-0.958349\pi$
$557$		−	6.15870i		−	0.260953i	0.991451	−	0.130476i	$-0.0416506\pi$
$558$		0			0
$559$			14.2182i			0.601365i
$560$	−9.73632	−	3.22331i	−0.411435	−	0.136210i
$561$		0			0
$562$	−19.3095	+	22.9658i	−0.814524	+	0.968754i
$563$	−5.69834			−0.240156			−0.120078	−	0.992764i	$-0.538315\pi$
$563$	−5.69834			−0.240156			−0.120078	+	0.992764i	$0.538315\pi$
$564$		0			0
$565$	8.51465	+	6.67388i	0.358214	+	0.280772i
$566$	23.8084	−	28.3165i	1.00074	−	1.19023i
$567$		0			0
$568$	−16.0916	+	27.6805i	−0.675190	+	1.16145i
$569$			11.5832i			0.485595i	0.970077	+	0.242797i	$0.0780650\pi$
$569$			11.5832i			0.485595i	−0.970077	+	0.242797i	$0.921935\pi$
$570$		0			0
$571$	22.2369			0.930585			0.465293	−	0.885157i	$-0.345949\pi$
$571$	22.2369			0.930585			0.465293	+	0.885157i	$0.345949\pi$
$572$	−6.36495	+	1.10926i	−0.266132	+	0.0463806i
$573$		0			0
$574$	−6.70527	+	7.97491i	−0.279873	+	0.332866i
$575$	31.8047	−	7.82408i	1.32635	−	0.326287i
$576$		0			0
$577$			0.506621i			0.0210909i	0.999944	+	0.0105454i	$0.00335678\pi$
$577$			0.506621i			0.0210909i	−0.999944	+	0.0105454i	$0.996643\pi$
$578$	−4.31328	−	3.62659i	−0.179409	−	0.150846i
$579$		0			0
$580$	0.448576	−	0.836462i	0.0186261	−	0.0347322i
$581$	16.7464			0.694757
$582$		0			0
$583$	−3.45830			−0.143228
$584$	−22.8138	−	13.2625i	−0.944042	−	0.548804i
$585$		0			0
$586$	−13.8442	+	16.4656i	−0.571898	+	0.680187i
$587$	−20.7492			−0.856412			−0.428206	−	0.903681i	$-0.640854\pi$
$587$	−20.7492			−0.856412			−0.428206	+	0.903681i	$0.640854\pi$
$588$		0			0
$589$			5.21983i			0.215079i
$590$	−25.5705	+	5.36679i	−1.05272	+	0.220947i
$591$		0			0
$592$	18.0215	−	6.47822i	0.740679	−	0.266253i
$593$	35.1903			1.44509			0.722546	−	0.691323i	$-0.242972\pi$
$593$	35.1903			1.44509			0.722546	+	0.691323i	$0.242972\pi$
$594$		0			0
$595$	−9.24422	−	7.24572i	−0.378976	−	0.297046i
$596$	6.87191	+	39.4310i	0.281484	+	1.61516i
$597$		0			0
$598$	−39.3429	+	46.7924i	−1.60885	+	1.91348i
$599$	1.94245			0.0793664			0.0396832	−	0.999212i	$-0.487365\pi$
$599$	1.94245			0.0793664			0.0396832	+	0.999212i	$0.487365\pi$
$600$		0			0
$601$	−10.1652			−0.414646			−0.207323	−	0.978272i	$-0.566475\pi$
$601$	−10.1652			−0.414646			−0.207323	+	0.978272i	$0.566475\pi$
$602$	−2.24846	+	2.67421i	−0.0916405	+	0.108993i
$603$		0			0
$604$	18.0893	−	3.15254i	0.736041	−	0.128275i
$605$	−18.9370	−	14.8431i	−0.769900	−	0.603456i
$606$		0			0
$607$	9.55777			0.387938			0.193969	−	0.981008i	$-0.437864\pi$
$607$	9.55777			0.387938			0.193969	+	0.981008i	$0.437864\pi$
$608$	−34.7633	−	12.8489i	−1.40984	−	0.521092i
$609$		0			0
$610$	−23.5770	+	4.94839i	−0.954606	+	0.200354i
$611$		−	9.11099i		−	0.368591i
$612$		0			0
$613$	−17.3616			−0.701229			−0.350615	−	0.936520i	$-0.614027\pi$
$613$	−17.3616			−0.701229			−0.350615	+	0.936520i	$0.614027\pi$
$614$	−12.8076	+	15.2327i	−0.516872	+	0.614742i
$615$		0			0
$616$	−1.37256	−	0.797918i	−0.0553021	−	0.0321490i
$617$	−18.8571			−0.759160			−0.379580	−	0.925159i	$-0.623931\pi$
$617$	−18.8571			−0.759160			−0.379580	+	0.925159i	$0.623931\pi$
$618$		0			0
$619$	21.7161			0.872843			0.436422	−	0.899742i	$-0.356246\pi$
$619$	21.7161			0.872843			0.436422	+	0.899742i	$0.356246\pi$
$620$	−3.14000	−	1.68392i	−0.126106	−	0.0676277i
$621$		0			0
$622$	−1.93413	−	1.62621i	−0.0775516	−	0.0652050i
$623$		−	18.0733i		−	0.724090i
$624$		0			0
$625$	−22.1468	+	11.5983i	−0.885871	+	0.463931i
$626$	0.346464	−	0.412067i	0.0138475	−	0.0164695i
$627$		0			0
$628$	0.859326	+	4.93081i	0.0342908	+	0.196761i
$629$	21.9317			0.874474
$630$		0			0
$631$		−	36.4253i		−	1.45007i	−0.688713	−	0.725034i	$-0.741824\pi$
$631$		−	36.4253i		−	1.45007i	0.688713	−	0.725034i	$-0.258176\pi$
$632$	−14.7146	−	8.55412i	−0.585316	−	0.340264i
$633$		0			0
$634$	−14.7017	+	17.4854i	−0.583878	+	0.694435i
$635$	24.7831	+	19.4253i	0.983489	+	0.770869i
$636$		0			0
$637$	−37.5174			−1.48649
$638$	0.0945564	−	0.112461i	0.00374352	−	0.00445236i
$639$		0			0
$640$	18.9439	−	16.7669i	0.748824	−	0.662769i
$641$			16.9125i			0.668003i	0.942573	+	0.334002i	$0.108399\pi$
$641$			16.9125i			0.668003i	−0.942573	+	0.334002i	$0.891601\pi$
$642$		0			0
$643$			12.8665i			0.507406i	0.967282	+	0.253703i	$0.0816486\pi$
$643$			12.8665i			0.507406i	−0.967282	+	0.253703i	$0.918351\pi$
$644$	−14.7995	+	2.57921i	−0.583182	+	0.101635i
$645$		0			0
$646$	−32.4870	−	27.3150i	−1.27819	−	1.07469i
$647$			2.93265i			0.115294i	0.998337	+	0.0576472i	$0.0183599\pi$
$647$			2.93265i			0.115294i	−0.998337	+	0.0576472i	$0.981640\pi$
$648$		0			0
$649$	−4.04459			−0.158764
$650$	20.6287	−	41.8557i	0.809123	−	1.64172i
$651$		0			0
$652$	32.8144	−	5.71879i	1.28511	−	0.223965i
$653$		−	40.6276i		−	1.58988i	−0.606687	−	0.794941i	$-0.707502\pi$
$653$		−	40.6276i		−	1.58988i	0.606687	−	0.794941i	$-0.292498\pi$
$654$		0			0
$655$	17.2737	−	22.0381i	0.674940	−	0.861101i
$656$	−8.69404	−	24.1856i	−0.339445	−	0.944289i
$657$		0			0
$658$	1.44081	−	1.71363i	0.0561687	−	0.0668042i
$659$		−	18.3239i		−	0.713796i	−0.934143	−	0.356898i	$-0.883834\pi$
$659$		−	18.3239i		−	0.713796i	0.934143	−	0.356898i	$-0.116166\pi$
$660$		0			0
$661$			5.77979i			0.224808i	0.993663	+	0.112404i	$0.0358550\pi$
$661$			5.77979i			0.224808i	−0.993663	+	0.112404i	$0.964145\pi$
$662$	10.3226	+	8.67920i	0.401199	+	0.337327i
$663$		0			0
$664$	−20.7605	+	35.7118i	−0.805666	+	1.38589i
$665$	−13.2212	−	10.3629i	−0.512695	−	0.401856i
$666$		0			0
$667$		−	1.39028i		−	0.0538318i
$668$	−1.31087	+	0.228455i	−0.0507192	+	0.00883918i
$669$		0			0
$670$	−34.7183	+	7.28673i	−1.34128	+	0.281511i
$671$	−3.72927			−0.143967
$672$		0			0
$673$			18.2760i			0.704489i	0.935908	+	0.352244i	$0.114581\pi$
$673$			18.2760i			0.704489i	−0.935908	+	0.352244i	$0.885419\pi$
$674$	−22.5641	+	26.8366i	−0.869137	+	1.03371i
$675$		0			0
$676$	10.4898	+	60.1905i	0.403455	+	2.31502i
$677$		−	19.8228i		−	0.761853i	−0.924605	−	0.380926i	$-0.875605\pi$
$677$		−	19.8228i		−	0.761853i	0.924605	−	0.380926i	$-0.124395\pi$
$678$		0			0
$679$			7.03572i			0.270006i
$680$	26.9117	−	10.7309i	1.03202	−	0.411510i
$681$		0			0
$682$	−0.422167	−	0.354956i	−0.0161656	−	0.0135920i
$683$	−34.8118			−1.33204			−0.666018	−	0.745935i	$-0.732003\pi$
$683$	−34.8118			−1.33204			−0.666018	+	0.745935i	$0.732003\pi$
$684$		0			0
$685$	4.40981	+	3.45645i	0.168490	+	0.132064i
$686$	−15.7448	−	13.2381i	−0.601138	−	0.505434i
$687$		0			0
$688$	−2.91535	−	8.11010i	−0.111147	−	0.309195i
$689$			46.6205i			1.77610i
$690$		0			0
$691$	−25.7607			−0.979982			−0.489991	−	0.871727i	$-0.663000\pi$
$691$	−25.7607			−0.979982			−0.489991	+	0.871727i	$0.663000\pi$
$692$	14.0078	−	2.44123i	0.532496	−	0.0928017i
$693$		0			0
$694$	−33.1725	−	27.8913i	−1.25921	−	1.05874i
$695$	−5.04259	−	3.95244i	−0.191276	−	0.149925i
$696$		0			0
$697$		−	29.4332i		−	1.11486i
$698$	21.9342	−	26.0875i	0.830223	−	0.987426i
$699$		0			0
$700$	10.4990	−	4.61017i	0.396824	−	0.174248i
$701$	−31.8004			−1.20109			−0.600543	−	0.799592i	$-0.705049\pi$
$701$	−31.8004			−1.20109			−0.600543	+	0.799592i	$0.705049\pi$
$702$		0			0
$703$	31.3669			1.18303
$704$	3.40314	−	1.93782i	0.128261	−	0.0730344i
$705$		0			0
$706$	15.5862	+	13.1048i	0.586595	+	0.493206i
$707$	10.4519			0.393082
$708$		0			0
$709$		−	41.6760i		−	1.56517i	−0.622541	−	0.782587i	$-0.713900\pi$
$709$		−	41.6760i		−	1.56517i	0.622541	−	0.782587i	$-0.286100\pi$
$710$	−7.35296	−	35.0339i	−0.275952	−	1.31480i
$711$		0			0
$712$	38.5414	+	22.4055i	1.44440	+	0.839681i
$713$	−5.21898			−0.195452
$714$		0			0
$715$	4.45613	−	5.68522i	0.166650	−	0.212615i
$716$	39.5985	−	6.90110i	1.47986	−	0.257906i
$717$		0			0
$718$	−9.40028	−	7.90371i	−0.350815	−	0.294964i
$719$	−21.2412			−0.792164			−0.396082	−	0.918215i	$-0.629630\pi$
$719$	−21.2412			−0.792164			−0.396082	+	0.918215i	$0.629630\pi$
$720$		0			0
$721$	4.15065			0.154578
$722$	−25.8968	−	21.7739i	−0.963780	−	0.810342i
$723$		0			0
$724$	−7.23363	+	1.26065i	−0.268836	+	0.0468519i
$725$	0.253497	+	1.03046i	0.00941465	+	0.0382704i
$726$		0			0
$727$	15.7303			0.583405			0.291703	−	0.956509i	$-0.405778\pi$
$727$	15.7303			0.583405			0.291703	+	0.956509i	$0.405778\pi$
$728$	−10.7566	+	18.5032i	−0.398665	+	0.685774i
$729$		0			0
$730$	28.8743	−	6.06019i	1.06869	−	0.224298i
$731$		−	9.86979i		−	0.365047i
$732$		0			0
$733$	11.7966			0.435718			0.217859	−	0.975980i	$-0.430093\pi$
$733$	11.7966			0.435718			0.217859	+	0.975980i	$0.430093\pi$
$734$	26.8491	+	22.5746i	0.991020	+	0.833245i
$735$		0			0
$736$	12.8468	−	34.7576i	0.473539	−	1.28118i
$737$	−5.49152			−0.202283
$738$		0			0
$739$	36.7306			1.35116			0.675579	−	0.737288i	$-0.263894\pi$
$739$	36.7306			1.35116			0.675579	+	0.737288i	$0.263894\pi$
$740$	−10.1190	+	18.8689i	−0.371980	+	0.693633i
$741$		0			0
$742$	−7.37257	+	8.76856i	−0.270655	+	0.321904i
$743$		−	37.2346i		−	1.36600i	−0.730416	−	0.683002i	$-0.760674\pi$
$743$		−	37.2346i		−	1.36600i	0.730416	−	0.683002i	$-0.239326\pi$
$744$		0			0
$745$	−35.2200	−	27.6058i	−1.29036	−	1.01140i
$746$	−27.5838	−	23.1923i	−1.00991	−	0.849132i
$747$		0			0
$748$	4.41833	−	0.770013i	0.161550	−	0.0281545i
$749$	9.20338			0.336284
$750$		0			0
$751$			35.3474i			1.28984i	0.764248	+	0.644922i	$0.223110\pi$
$751$			35.3474i			1.28984i	−0.764248	+	0.644922i	$0.776890\pi$
$752$	1.86815	+	5.19694i	0.0681246	+	0.189513i
$753$		0			0
$754$	−1.51606	−	1.27469i	−0.0552115	−	0.0464216i
$755$	−12.6644	+	16.1574i	−0.460904	+	0.588030i
$756$		0			0
$757$	−23.6211			−0.858524			−0.429262	−	0.903180i	$-0.641226\pi$
$757$	−23.6211			−0.858524			−0.429262	+	0.903180i	$0.641226\pi$
$758$	26.7360	+	22.4795i	0.971097	+	0.816494i
$759$		0			0
$760$	38.4894	−	15.3474i	1.39616	−	0.556708i
$761$		−	29.4215i		−	1.06653i	−0.845949	−	0.533264i	$-0.820965\pi$
$761$		−	29.4215i		−	1.06653i	0.845949	−	0.533264i	$-0.179035\pi$
$762$		0			0
$763$		−	20.0065i		−	0.724284i
$764$	−0.143628	−	0.824135i	−0.00519627	−	0.0298161i
$765$		0			0
$766$	−1.27178	+	1.51259i	−0.0459511	+	0.0546519i
$767$			54.5242i			1.96875i
$768$		0			0
$769$	10.4615			0.377253			0.188627	−	0.982049i	$-0.439596\pi$
$769$	10.4615			0.377253			0.188627	+	0.982049i	$0.439596\pi$
$770$	1.73719	−	0.364603i	0.0626038	−	0.0131394i
$771$		0			0
$772$	25.8235	−	4.50044i	0.929409	−	0.161975i
$773$			47.2231i			1.69850i	0.527993	+	0.849249i	$0.322945\pi$
$773$			47.2231i			1.69850i	−0.527993	+	0.849249i	$0.677055\pi$
$774$		0			0
$775$	3.86826	−	0.951606i	0.138952	−	0.0341827i
$776$	−15.0038	−	8.72222i	−0.538604	−	0.313109i
$777$		0			0
$778$	−26.5840	−	22.3517i	−0.953081	−	0.801346i
$779$		−	42.0957i		−	1.50824i
$780$		0			0
$781$		−	5.54143i		−	0.198288i
$782$	27.3105	−	32.4817i	0.976621	−	1.16154i
$783$		0			0
$784$	21.4000	−	7.69272i	0.764287	−	0.274740i
$785$	−4.40423	−	3.45208i	−0.157194	−	0.123210i
$786$		0			0
$787$			15.4485i			0.550681i	0.961347	+	0.275340i	$0.0887905\pi$
$787$			15.4485i			0.550681i	−0.961347	+	0.275340i	$0.911209\pi$
$788$	−8.99822	+	1.56818i	−0.320548	+	0.0558642i
$789$		0			0
$790$	18.6236	−	3.90875i	0.662597	−	0.139067i
$791$	5.54773			0.197255
$792$		0			0
$793$			50.2734i			1.78526i
$794$	31.7939	+	26.7322i	1.12832	+	0.948690i
$795$		0			0
$796$	25.9156	−	4.51648i	0.918553	−	0.160083i
$797$		−	41.5439i		−	1.47156i	−0.677220	−	0.735781i	$-0.736815\pi$
$797$		−	41.5439i		−	1.47156i	0.677220	−	0.735781i	$-0.263185\pi$
$798$		0			0
$799$			6.32454i			0.223746i
$800$	−3.18439	+	28.1044i	−0.112585	+	0.993642i
$801$		0			0
$802$	13.6408	−	16.2237i	0.481674	−	0.572879i
$803$	4.56716			0.161172
$804$		0			0
$805$	10.3612	−	13.2190i	0.365185	−	0.465909i
$806$	−4.78509	+	5.69114i	−0.168548	+	0.200462i
$807$		0			0
$808$	−12.9572	+	22.2887i	−0.455833	+	0.784114i
$809$			19.3029i			0.678654i	0.940669	+	0.339327i	$0.110199\pi$
$809$			19.3029i			0.678654i	−0.940669	+	0.339327i	$0.889801\pi$
$810$		0			0
$811$	38.3252			1.34578			0.672890	−	0.739743i	$-0.265053\pi$
$811$	38.3252			1.34578			0.672890	+	0.739743i	$0.265053\pi$
$812$	−0.0835655	−	0.479498i	−0.00293257	−	0.0168271i
$813$		0			0
$814$	−2.13300	+	2.53688i	−0.0747615	+	0.0889176i
$815$	−22.9735	+	29.3100i	−0.804728	+	1.02669i
$816$		0			0
$817$		−	14.1159i		−	0.493852i
$818$	22.0651	+	18.5522i	0.771487	+	0.648663i
$819$		0			0
$820$	25.3228	+	13.5801i	0.884310	+	0.474236i
$821$	13.2266			0.461612			0.230806	−	0.973000i	$-0.425864\pi$
$821$	13.2266			0.461612			0.230806	+	0.973000i	$0.425864\pi$
$822$		0			0
$823$	28.2201			0.983689			0.491845	−	0.870683i	$-0.336323\pi$
$823$	28.2201			0.983689			0.491845	+	0.870683i	$0.336323\pi$
$824$	−5.14557	+	8.85130i	−0.179255	+	0.308350i
$825$		0			0
$826$	−8.62245	+	10.2551i	−0.300013	+	0.356821i
$827$	21.0109			0.730619			0.365309	−	0.930886i	$-0.380963\pi$
$827$	21.0109			0.730619			0.365309	+	0.930886i	$0.380963\pi$
$828$		0			0
$829$			37.3553i			1.29740i	0.761044	+	0.648701i	$0.224687\pi$
$829$			37.3553i			1.29740i	−0.761044	+	0.648701i	$0.775313\pi$
$830$	−9.48639	−	45.1988i	−0.329278	−	1.56887i
$831$		0			0
$832$	−26.1234	−	45.8770i	−0.905664	−	1.59050i
$833$	26.0433			0.902347
$834$		0			0
$835$	0.917749	−	1.17088i	0.0317600	−	0.0405200i
$836$	6.31914	−	1.10128i	0.218552	−	0.0380886i
$837$		0			0
$838$	−7.32050	+	8.70664i	−0.252883	+	0.300766i
$839$	−43.2068			−1.49166			−0.745832	−	0.666134i	$-0.767948\pi$
$839$	−43.2068			−1.49166			−0.745832	+	0.666134i	$0.767948\pi$
$840$		0			0
$841$	−28.9550			−0.998447
$842$	23.2916	−	27.7019i	0.802683	−	0.954670i
$843$		0			0
$844$	−0.308022	−	1.76743i	−0.0106025	−	0.0608373i
$845$	−53.7626	−	42.1397i	−1.84949	−	1.44965i
$846$		0			0
$847$	−12.3384			−0.423954
$848$	−9.55926	−	26.5925i	−0.328266	−	0.913190i
$849$		0			0
$850$	−14.3197	+	29.0548i	−0.491162	+	0.996573i
$851$			31.3618i			1.07507i
$852$		0			0
$853$	−29.4729			−1.00913			−0.504566	−	0.863373i	$-0.668348\pi$
$853$	−29.4729			−1.00913			−0.504566	+	0.863373i	$0.668348\pi$
$854$	−7.95023	+	9.45561i	−0.272051	+	0.323564i
$855$		0			0
$856$	−11.4095	+	19.6263i	−0.389968	+	0.670814i
$857$	38.3026			1.30839			0.654196	−	0.756325i	$-0.273007\pi$
$857$	38.3026			1.30839			0.654196	+	0.756325i	$0.273007\pi$
$858$		0			0
$859$	21.9526			0.749014			0.374507	−	0.927224i	$-0.377812\pi$
$859$	21.9526			0.749014			0.374507	+	0.927224i	$0.377812\pi$
$860$	8.49144	+	4.55377i	0.289556	+	0.155282i
$861$		0			0
$862$	−3.43928	−	2.89173i	−0.117142	−	0.0984927i
$863$			19.3390i			0.658306i	0.944277	+	0.329153i	$0.106763\pi$
$863$			19.3390i			0.658306i	−0.944277	+	0.329153i	$0.893237\pi$
$864$		0			0
$865$	−9.80691	+	12.5118i	−0.333445	+	0.425415i
$866$	19.8866	−	23.6522i	0.675775	−	0.803733i
$867$		0			0
$868$	−1.79999	+	0.313697i	−0.0610958	+	0.0106476i
$869$	2.94576			0.0999280
$870$		0			0
$871$			74.0299i			2.50841i
$872$	42.6641	+	24.8021i	1.44479	+	0.839907i
$873$		0			0
$874$	39.0597	−	46.4557i	1.32122	−	1.57139i
$875$	−5.26934	+	11.6870i	−0.178136	+	0.395094i
$876$		0			0
$877$	−12.2495			−0.413637			−0.206818	−	0.978379i	$-0.566311\pi$
$877$	−12.2495			−0.413637			−0.206818	+	0.978379i	$0.566311\pi$
$878$	1.31087	−	1.55909i	0.0442398	−	0.0526166i
$879$		0			0
$880$	−1.37608	+	4.15657i	−0.0463875	+	0.140118i
$881$		−	10.6156i		−	0.357649i	−0.983881	−	0.178825i	$-0.942771\pi$
$881$		−	10.6156i		−	0.357649i	0.983881	−	0.178825i	$-0.0572294\pi$
$882$		0			0
$883$		−	46.6874i		−	1.57115i	−0.618764	−	0.785577i	$-0.712366\pi$
$883$		−	46.6874i		−	1.57115i	0.618764	−	0.785577i	$-0.287634\pi$
$884$	−10.3804	−	59.5626i	−0.349130	−	2.00331i
$885$		0			0
$886$	−33.5272	−	28.1895i	−1.12637	−	0.947044i
$887$		−	16.3552i		−	0.549153i	−0.961565	−	0.274576i	$-0.911462\pi$
$887$		−	16.3552i		−	0.549153i	0.961565	−	0.274576i	$-0.0885376\pi$
$888$		0			0
$889$	16.1475			0.541569
$890$	−48.7801	+	10.2380i	−1.63511	+	0.343180i
$891$		0			0
$892$	3.28793	+	18.8661i	0.110088	+	0.631685i
$893$			9.04542i			0.302694i
$894$		0			0
$895$	−27.7231	+	35.3696i	−0.926681	+	1.18228i
$896$	2.34161	−	12.7599i	0.0782277	−	0.426277i
$897$		0			0
$898$	9.03912	−	10.7507i	0.301639	−	0.358755i
$899$		−	0.169093i		−	0.00563957i
$900$		0			0
$901$		−	32.3624i		−	1.07815i
$902$	3.40460	+	2.86257i	0.113361	+	0.0953132i
$903$		0			0
$904$	−6.87755	+	11.8306i	−0.228744	+	0.393480i
$905$	5.06430	−	6.46113i	0.168343	−	0.214775i
$906$		0			0
$907$		−	52.1267i		−	1.73084i	−0.501049	−	0.865419i	$-0.667052\pi$
$907$		−	52.1267i		−	1.73084i	0.501049	−	0.865419i	$-0.332948\pi$
$908$	−5.42470	−	31.1269i	−0.180025	−	1.03298i
$909$		0			0
$910$	−4.91514	−	23.4186i	−0.162935	−	0.776320i
$911$	44.8923			1.48735			0.743674	−	0.668542i	$-0.233081\pi$
$911$	44.8923			1.48735			0.743674	+	0.668542i	$0.233081\pi$
$912$		0			0
$913$		−	7.14926i		−	0.236606i
$914$	19.7240	−	23.4587i	0.652410	−	0.775944i
$915$		0			0
$916$	30.8049	−	5.36859i	1.01782	−	0.177383i
$917$		−	14.3590i		−	0.474175i
$918$		0			0
$919$			32.5801i			1.07472i	0.843354	+	0.537359i	$0.180578\pi$
$919$			32.5801i			1.07472i	−0.843354	+	0.537359i	$0.819422\pi$
$920$	15.3449	+	38.4831i	0.505906	+	1.26875i
$921$		0			0
$922$	3.86442	+	3.24919i	0.127268	+	0.107006i
$923$	−74.7028			−2.45887
$924$		0			0
$925$	−5.71837	−	23.2451i	−0.188019	−	0.764294i
$926$	27.6126	+	23.2165i	0.907406	+	0.762943i
$927$		0			0
$928$	1.12613	+	0.416232i	0.0369671	+	0.0136635i
$929$			40.9245i			1.34269i	0.741146	+	0.671344i	$0.234283\pi$
$929$			40.9245i			1.34269i	−0.741146	+	0.671344i	$0.765717\pi$
$930$		0			0
$931$	37.2474			1.22073
$932$	1.95247	+	11.2033i	0.0639553	+	0.366975i
$933$		0			0
$934$	−22.1174	−	18.5962i	−0.723703	−	0.608486i
$935$	−3.09330	+	3.94648i	−0.101162	+	0.129064i
$936$		0			0
$937$			48.3115i			1.57827i	0.614220	+	0.789135i	$0.289471\pi$
$937$			48.3115i			1.57827i	−0.614220	+	0.789135i	$0.710529\pi$
$938$	−11.7071	+	13.9238i	−0.382250	+	0.454629i
$939$		0			0
$940$	−5.44130	−	2.91805i	−0.177476	−	0.0951763i
$941$	24.8258			0.809298			0.404649	−	0.914472i	$-0.367394\pi$
$941$	24.8258			0.809298			0.404649	+	0.914472i	$0.367394\pi$
$942$		0			0
$943$	42.0888			1.37060
$944$	−11.1799	−	31.1008i	−0.363873	−	1.01224i
$945$		0			0
$946$	1.14166	+	0.959900i	0.0371185	+	0.0312090i
$947$	−26.7823			−0.870307			−0.435153	−	0.900356i	$-0.643306\pi$
$947$	−26.7823			−0.870307			−0.435153	+	0.900356i	$0.643306\pi$
$948$		0			0
$949$		−	61.5689i		−	1.99861i
$950$	−20.4802	+	41.5545i	−0.664466	+	1.34821i
$951$		0			0
$952$	7.46684	−	12.8443i	0.242002	−	0.416286i
$953$	−3.99329			−0.129355			−0.0646777	−	0.997906i	$-0.520602\pi$
$953$	−3.99329			−0.129355			−0.0646777	+	0.997906i	$0.520602\pi$
$954$		0			0
$955$	0.736123	+	0.576981i	0.0238204	+	0.0186707i
$956$	−10.1920	−	58.4819i	−0.329634	−	1.89144i
$957$		0			0
$958$	20.1948	+	16.9797i	0.652463	+	0.548588i
$959$	2.87321			0.0927810
$960$		0			0
$961$	30.3652			0.979524
$962$	34.1991	+	28.7545i	1.10262	+	0.927081i
$963$		0			0
$964$	−1.27064	−	7.29095i	−0.0409247	−	0.234826i
$965$	−18.0792	+	23.0657i	−0.581989	+	0.742513i
$966$		0			0
$967$	−56.6352			−1.82127			−0.910633	−	0.413216i	$-0.864405\pi$
$967$	−56.6352			−1.82127			−0.910633	+	0.413216i	$0.864405\pi$
$968$	15.2960	−	26.3119i	0.491633	−	0.845696i
$969$		0			0
$970$	18.9895	−	3.98556i	0.609718	−	0.127969i
$971$			0.738503i			0.0236997i	0.999930	+	0.0118499i	$0.00377201\pi$
$971$			0.738503i			0.0236997i	−0.999930	+	0.0118499i	$0.996228\pi$
$972$		0			0
$973$	−3.28551			−0.105329
$974$	−13.3036	−	11.1856i	−0.426276	−	0.358411i
$975$		0			0
$976$	−10.3083	−	28.6761i	−0.329959	−	0.917900i
$977$	−61.6990			−1.97393			−0.986964	−	0.160943i	$-0.948547\pi$
$977$	−61.6990			−1.97393			−0.986964	+	0.160943i	$0.948547\pi$
$978$		0			0
$979$	−7.71572			−0.246596
$980$	−12.0160	+	22.4063i	−0.383837	+	0.715742i
$981$		0			0
$982$	−11.5483	+	13.7349i	−0.368520	+	0.438299i
$983$		−	39.8608i		−	1.27136i	−0.771952	−	0.635681i	$-0.780719\pi$
$983$		−	39.8608i		−	1.27136i	0.771952	−	0.635681i	$-0.219281\pi$
$984$		0			0
$985$	6.29970	−	8.03727i	0.200725	−	0.256089i
$986$	1.05240	+	0.884849i	0.0335151	+	0.0281793i
$987$		0			0
$988$	−14.8461	−	85.1870i	−0.472318	−	2.71016i
$989$	14.1136			0.448785
$990$		0			0
$991$		−	56.9673i		−	1.80963i	−0.425808	−	0.904814i	$-0.640010\pi$
$991$		−	56.9673i		−	1.80963i	0.425808	−	0.904814i	$-0.359990\pi$
$992$	1.56250	−	4.22740i	0.0496093	−	0.134220i
$993$		0			0
$994$	−14.0504	−	11.8135i	−0.445651	−	0.374702i
$995$	−18.1436	+	23.1480i	−0.575191	+	0.733839i
$996$		0			0
$997$	−20.2875			−0.642512			−0.321256	−	0.946992i	$-0.604105\pi$
$997$	−20.2875			−0.642512			−0.321256	+	0.946992i	$0.604105\pi$
$998$	18.1553	+	15.2649i	0.574695	+	0.483201i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1080.2.m.c.539.9	✓	48
3.2	odd	2	inner	1080.2.m.c.539.40	yes	48
4.3	odd	2		4320.2.m.c.2159.10		48
5.4	even	2	inner	1080.2.m.c.539.39	yes	48
8.3	odd	2	inner	1080.2.m.c.539.12	yes	48
8.5	even	2		4320.2.m.c.2159.39		48
12.11	even	2		4320.2.m.c.2159.40		48
15.14	odd	2	inner	1080.2.m.c.539.10	yes	48
20.19	odd	2		4320.2.m.c.2159.11		48
24.5	odd	2		4320.2.m.c.2159.9		48
24.11	even	2	inner	1080.2.m.c.539.37	yes	48
40.19	odd	2	inner	1080.2.m.c.539.38	yes	48
40.29	even	2		4320.2.m.c.2159.38		48
60.59	even	2		4320.2.m.c.2159.37		48
120.29	odd	2		4320.2.m.c.2159.12		48
120.59	even	2	inner	1080.2.m.c.539.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1080.2.m.c.539.9	✓	48	1.1	even	1	trivial
1080.2.m.c.539.10	yes	48	15.14	odd	2	inner
1080.2.m.c.539.11	yes	48	120.59	even	2	inner
1080.2.m.c.539.12	yes	48	8.3	odd	2	inner
1080.2.m.c.539.37	yes	48	24.11	even	2	inner
1080.2.m.c.539.38	yes	48	40.19	odd	2	inner
1080.2.m.c.539.39	yes	48	5.4	even	2	inner
1080.2.m.c.539.40	yes	48	3.2	odd	2	inner
4320.2.m.c.2159.9		48	24.5	odd	2
4320.2.m.c.2159.10		48	4.3	odd	2
4320.2.m.c.2159.11		48	20.19	odd	2
4320.2.m.c.2159.12		48	120.29	odd	2
4320.2.m.c.2159.37		48	60.59	even	2
4320.2.m.c.2159.38		48	40.29	even	2
4320.2.m.c.2159.39		48	8.5	even	2
4320.2.m.c.2159.40		48	12.11	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)

\(f(q)\)	\(=\)	\(q+(-1.08245 - 0.910116i) q^{2} +(0.343378 + 1.97030i) q^{4} +(-1.75989 - 1.37942i) q^{5} -1.14666 q^{7} +(1.42152 - 2.44526i) q^{8} +(0.649552 + 3.09485i) q^{10} +0.489523i q^{11} +6.59916 q^{13} +(1.24119 + 1.04359i) q^{14} +(-3.76418 + 1.35312i) q^{16} -4.58091 q^{17} -6.55167 q^{19} +(2.11357 - 3.94117i) q^{20} +(0.445523 - 0.529883i) q^{22} -6.55060i q^{23} +(1.19441 + 4.85524i) q^{25} +(-7.14323 - 6.00600i) q^{26} +(-0.393737 - 2.25926i) q^{28} +0.212237 q^{29} -0.796718i q^{31} +(5.30602 + 1.96117i) q^{32} +(4.95859 + 4.16916i) q^{34} +(2.01799 + 1.58172i) q^{35} -4.78762 q^{37} +(7.09183 + 5.96278i) q^{38} +(-5.87474 + 2.34252i) q^{40} +6.42519i q^{41} +2.15455i q^{43} +(-0.964509 + 0.168092i) q^{44} +(-5.96180 + 7.09067i) q^{46} -1.38063i q^{47} -5.68518 q^{49} +(3.12595 - 6.34259i) q^{50} +(2.26601 + 13.0023i) q^{52} +7.06462i q^{53} +(0.675258 - 0.861506i) q^{55} +(-1.62999 + 2.80387i) q^{56} +(-0.229735 - 0.193160i) q^{58} +8.26229i q^{59} +7.61815i q^{61} +(-0.725106 + 0.862404i) q^{62} +(-3.95859 - 6.95195i) q^{64} +(-11.6138 - 9.10300i) q^{65} +11.2181i q^{67} +(-1.57299 - 9.02578i) q^{68} +(-0.744813 - 3.54873i) q^{70} -11.3201 q^{71} -9.32981i q^{73} +(5.18234 + 4.35729i) q^{74} +(-2.24970 - 12.9088i) q^{76} -0.561315i q^{77} -6.01760i q^{79} +(8.49105 + 2.81105i) q^{80} +(5.84767 - 6.95492i) q^{82} -14.6045 q^{83} +(8.06189 + 6.31900i) q^{85} +(1.96089 - 2.33218i) q^{86} +(1.19701 + 0.695865i) q^{88} +15.7617i q^{89} -7.56697 q^{91} +(12.9067 - 2.24933i) q^{92} +(-1.25653 + 1.49446i) q^{94} +(11.5302 + 9.03749i) q^{95} -6.13586i q^{97} +(6.15390 + 5.17417i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{10} + 4 q^{16} - 16 q^{19} - 4 q^{34} + 16 q^{40} + 36 q^{46} + 48 q^{49} + 52 q^{64} + 28 q^{70} - 64 q^{76} + 92 q^{94}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^10 + 4 * q^16 - 16 * q^19 - 4 * q^34 + 16 * q^40 + 36 * q^46 + 48 * q^49 + 52 * q^64 + 28 * q^70 - 64 * q^76 + 92 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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