LMFDB - Embedded newform 864.2.bi.a.95.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 17]))

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

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

chi := DirichletCharacter("864.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			95.2
Character	$\chi$	$=$	864.95
Dual form			864.2.bi.a.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70911 - 0.280941i) q^{3} +(-1.54632 + 1.84283i) q^{5} +(0.573007 - 1.57432i) q^{7} +(2.84214 + 0.960320i) q^{9} +O(q^{10})$	\(q+(-1.70911 - 0.280941i) q^{3} +(-1.54632 + 1.84283i) q^{5} +(0.573007 - 1.57432i) q^{7} +(2.84214 + 0.960320i) q^{9} +(-0.0948219 + 0.0795651i) q^{11} +(-0.326045 + 1.84909i) q^{13} +(3.16056 - 2.71518i) q^{15} +(-0.160050 - 0.0924046i) q^{17} +(1.23319 - 0.711982i) q^{19} +(-1.42163 + 2.52972i) q^{21} +(-1.02980 + 0.374816i) q^{23} +(-0.136680 - 0.775152i) q^{25} +(-4.58776 - 2.43977i) q^{27} +(-9.56592 + 1.68673i) q^{29} +(-2.22181 - 6.10438i) q^{31} +(0.184415 - 0.109346i) q^{33} +(2.01516 + 3.49036i) q^{35} +(0.539935 - 0.935195i) q^{37} +(1.07673 - 3.06871i) q^{39} +(-8.24088 - 1.45309i) q^{41} +(-4.15968 - 4.95731i) q^{43} +(-6.16456 + 3.75262i) q^{45} +(-7.28562 - 2.65175i) q^{47} +(3.21215 + 2.69531i) q^{49} +(0.247583 + 0.202895i) q^{51} +1.82246i q^{53} -0.297773i q^{55} +(-2.30768 + 0.870405i) q^{57} +(1.80264 + 1.51259i) q^{59} +(-3.31861 - 1.20787i) q^{61} +(3.14043 - 3.92419i) q^{63} +(-2.90339 - 3.46013i) q^{65} +(-10.3445 - 1.82401i) q^{67} +(1.86534 - 0.351291i) q^{69} +(-6.76494 + 11.7172i) q^{71} +(-7.30803 - 12.6579i) q^{73} +(0.0158303 + 1.36322i) q^{75} +(0.0709276 + 0.194872i) q^{77} +(-10.7632 + 1.89784i) q^{79} +(7.15557 + 5.45874i) q^{81} +(0.151931 + 0.861641i) q^{83} +(0.417773 - 0.152057i) q^{85} +(16.8231 - 0.195357i) q^{87} +(13.2369 - 7.64235i) q^{89} +(2.72425 + 1.57284i) q^{91} +(2.08236 + 11.0573i) q^{93} +(-0.594840 + 3.37350i) q^{95} +(11.3669 - 9.53799i) q^{97} +(-0.345906 + 0.135076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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			0
$2$		0			0
$3$	−1.70911	−	0.280941i	−0.986758	−	0.162201i
$3$	−1.70911	−	0.280941i	−0.986758	−	0.162201i
$4$		0			0
$5$	−1.54632	+	1.84283i	−0.691534	+	0.824138i	−0.991540	−	0.129799i	$-0.958567\pi$
$5$	−1.54632	+	1.84283i	−0.691534	+	0.824138i	0.300007	+	0.953937i	$0.403011\pi$
$6$		0			0
$7$	0.573007	−	1.57432i	0.216576	−	0.595039i	−0.783062	−	0.621944i	$-0.786343\pi$
$7$	0.573007	−	1.57432i	0.216576	−	0.595039i	0.999638	+	0.0269054i	$0.00856529\pi$
$8$		0			0
$9$	2.84214	+	0.960320i	0.947381	+	0.320107i
$10$		0			0
$11$	−0.0948219	+	0.0795651i	−0.0285899	+	0.0239898i	−0.656971	−	0.753916i	$-0.728162\pi$
$11$	−0.0948219	+	0.0795651i	−0.0285899	+	0.0239898i	0.628381	+	0.777906i	$0.283718\pi$
$12$		0			0
$13$	−0.326045	+	1.84909i	−0.0904286	+	0.512846i	0.905624	+	0.424081i	$0.139403\pi$
$13$	−0.326045	+	1.84909i	−0.0904286	+	0.512846i	−0.996053	+	0.0887645i	$0.971708\pi$
$14$		0			0
$15$	3.16056	−	2.71518i	0.816052	−	0.701057i
$16$		0			0
$17$	−0.160050	−	0.0924046i	−0.0388177	−	0.0224114i	0.480466	−	0.877014i	$-0.340468\pi$
$17$	−0.160050	−	0.0924046i	−0.0388177	−	0.0224114i	−0.519283	+	0.854602i	$0.673801\pi$
$18$		0			0
$19$	1.23319	−	0.711982i	0.282913	−	0.163340i	−0.351829	−	0.936064i	$-0.614440\pi$
$19$	1.23319	−	0.711982i	0.282913	−	0.163340i	0.634741	+	0.772725i	$0.281107\pi$
$20$		0			0
$21$	−1.42163	+	2.52972i	−0.310224	+	0.552030i
$22$		0			0
$23$	−1.02980	+	0.374816i	−0.214728	+	0.0781545i	−0.447144	−	0.894462i	$-0.647559\pi$
$23$	−1.02980	+	0.374816i	−0.214728	+	0.0781545i	0.232417	+	0.972616i	$0.425337\pi$
$24$		0			0
$25$	−0.136680	−	0.775152i	−0.0273360	−	0.155030i
$26$		0			0
$27$	−4.58776	−	2.43977i	−0.882914	−	0.469534i
$28$		0			0
$29$	−9.56592	+	1.68673i	−1.77635	+	0.313218i	−0.963189	−	0.268825i	$-0.913365\pi$
$29$	−9.56592	+	1.68673i	−1.77635	+	0.313218i	−0.813158	+	0.582043i	$0.802253\pi$
$30$		0			0
$31$	−2.22181	−	6.10438i	−0.399050	−	1.09638i	−0.962748	−	0.270399i	$-0.912844\pi$
$31$	−2.22181	−	6.10438i	−0.399050	−	1.09638i	0.563699	−	0.825980i	$-0.309378\pi$
$32$		0			0
$33$	0.184415	−	0.109346i	0.0321025	−	0.0190348i
$34$		0			0
$35$	2.01516	+	3.49036i	0.340624	+	0.589978i
$36$		0			0
$37$	0.539935	−	0.935195i	0.0887648	−	0.153745i	−0.818224	−	0.574899i	$-0.805041\pi$
$37$	0.539935	−	0.935195i	0.0887648	−	0.153745i	0.906989	+	0.421154i	$0.138375\pi$
$38$		0			0
$39$	1.07673	−	3.06871i	0.172415	−	0.491387i
$40$		0			0
$41$	−8.24088	−	1.45309i	−1.28701	−	0.226934i	−0.512055	−	0.858952i	$-0.671116\pi$
$41$	−8.24088	−	1.45309i	−1.28701	−	0.226934i	−0.774954	+	0.632018i	$0.782227\pi$
$42$		0			0
$43$	−4.15968	−	4.95731i	−0.634345	−	0.755983i	0.349120	−	0.937078i	$-0.386480\pi$
$43$	−4.15968	−	4.95731i	−0.634345	−	0.755983i	−0.983466	+	0.181095i	$0.942036\pi$
$44$		0			0
$45$	−6.16456	+	3.75262i	−0.918958	+	0.559408i
$46$		0			0
$47$	−7.28562	−	2.65175i	−1.06272	−	0.386797i	−0.249268	−	0.968434i	$-0.580190\pi$
$47$	−7.28562	−	2.65175i	−1.06272	−	0.386797i	−0.813448	+	0.581637i	$0.802412\pi$
$48$		0			0
$49$	3.21215	+	2.69531i	0.458879	+	0.385045i
$50$		0			0
$51$	0.247583	+	0.202895i	0.0346685	+	0.0284109i
$52$		0			0
$53$			1.82246i			0.250334i	0.992136	+	0.125167i	$0.0399466\pi$
$53$			1.82246i			0.250334i	−0.992136	+	0.125167i	$0.960053\pi$
$54$		0			0
$55$		−	0.297773i		−	0.0401517i
$56$		0			0
$57$	−2.30768	+	0.870405i	−0.305660	+	0.115288i
$58$		0			0
$59$	1.80264	+	1.51259i	0.234683	+	0.196923i	0.752543	−	0.658543i	$-0.228827\pi$
$59$	1.80264	+	1.51259i	0.234683	+	0.196923i	−0.517860	+	0.855465i	$0.673271\pi$
$60$		0			0
$61$	−3.31861	−	1.20787i	−0.424904	−	0.154653i	0.120712	−	0.992688i	$-0.461482\pi$
$61$	−3.31861	−	1.20787i	−0.424904	−	0.154653i	−0.545616	+	0.838035i	$0.683704\pi$
$62$		0			0
$63$	3.14043	−	3.92419i	0.395656	−	0.494401i
$64$		0			0
$65$	−2.90339	−	3.46013i	−0.360121	−	0.429176i
$66$		0			0
$67$	−10.3445	−	1.82401i	−1.26378	−	0.222839i	−0.498702	−	0.866774i	$-0.666190\pi$
$67$	−10.3445	−	1.82401i	−1.26378	−	0.222839i	−0.765080	+	0.643935i	$0.777301\pi$
$68$		0			0
$69$	1.86534	−	0.351291i	0.224561	−	0.0422904i
$70$		0			0
$71$	−6.76494	+	11.7172i	−0.802851	+	1.39058i	0.114882	+	0.993379i	$0.463351\pi$
$71$	−6.76494	+	11.7172i	−0.802851	+	1.39058i	−0.917732	+	0.397199i	$0.869982\pi$
$72$		0			0
$73$	−7.30803	−	12.6579i	−0.855340	−	1.48149i	−0.876329	−	0.481712i	$-0.840015\pi$
$73$	−7.30803	−	12.6579i	−0.855340	−	1.48149i	0.0209896	−	0.999780i	$-0.493318\pi$
$74$		0			0
$75$	0.0158303	+	1.36322i	0.00182792	+	0.157411i
$76$		0			0
$77$	0.0709276	+	0.194872i	0.00808295	+	0.0222077i
$78$		0			0
$79$	−10.7632	+	1.89784i	−1.21095	+	0.213524i	−0.742428	−	0.669926i	$-0.766326\pi$
$79$	−10.7632	+	1.89784i	−1.21095	+	0.213524i	−0.468526	+	0.883450i	$0.655215\pi$
$80$		0			0
$81$	7.15557	+	5.45874i	0.795063	+	0.606526i
$82$		0			0
$83$	0.151931	+	0.861641i	0.0166766	+	0.0945774i	0.992010	−	0.126159i	$-0.0402650\pi$
$83$	0.151931	+	0.861641i	0.0166766	+	0.0945774i	−0.975333	+	0.220737i	$0.929154\pi$
$84$		0			0
$85$	0.417773	−	0.152057i	0.0453139	−	0.0164929i
$86$		0			0
$87$	16.8231	−	0.195357i	1.80363	−	0.0209444i
$88$		0			0
$89$	13.2369	−	7.64235i	1.40311	−	0.810088i	0.408402	−	0.912802i	$-0.366086\pi$
$89$	13.2369	−	7.64235i	1.40311	−	0.810088i	0.994711	+	0.102715i	$0.0327529\pi$
$90$		0			0
$91$	2.72425	+	1.57284i	0.285578	+	0.164879i
$92$		0			0
$93$	2.08236	+	11.0573i	0.215931	+	1.14659i
$94$		0			0
$95$	−0.594840	+	3.37350i	−0.0610293	+	0.346114i
$96$		0			0
$97$	11.3669	−	9.53799i	1.15414	−	0.968437i	0.154330	−	0.988019i	$-0.450678\pi$
$97$	11.3669	−	9.53799i	1.15414	−	0.968437i	0.999808	+	0.0195828i	$0.00623381\pi$
$98$		0			0
$99$	−0.345906	+	0.135076i	−0.0347648	+	0.0135756i
$100$		0			0
$101$	−2.39359	+	6.57634i	−0.238171	+	0.654371i	0.761807	+	0.647804i	$0.224312\pi$
$101$	−2.39359	+	6.57634i	−0.238171	+	0.654371i	−0.999978	+	0.00656652i	$0.997910\pi$
$102$		0			0
$103$	−7.74750	+	9.23311i	−0.763384	+	0.909765i	−0.998057	−	0.0623091i	$-0.980154\pi$
$103$	−7.74750	+	9.23311i	−0.763384	+	0.909765i	0.234673	+	0.972074i	$0.424598\pi$
$104$		0			0
$105$	−2.46355	−	6.53156i	−0.240418	−	0.637415i
$106$		0			0
$107$	13.6874			1.32322			0.661608	−	0.749850i	$-0.269874\pi$
$107$	13.6874			1.32322			0.661608	+	0.749850i	$0.269874\pi$
$108$		0			0
$109$	4.99421			0.478358			0.239179	−	0.970975i	$-0.423122\pi$
$109$	4.99421			0.478358			0.239179	+	0.970975i	$0.423122\pi$
$110$		0			0
$111$	−1.18555	+	1.44667i	−0.112527	+	0.137311i
$112$		0			0
$113$	−5.12752	+	6.11074i	−0.482357	+	0.574850i	−0.951256	−	0.308401i	$-0.900206\pi$
$113$	−5.12752	+	6.11074i	−0.482357	+	0.574850i	0.468900	+	0.883251i	$0.344651\pi$
$114$		0			0
$115$	0.901672	−	2.47732i	0.0840814	−	0.231012i
$116$		0			0
$117$	−2.70239	+	4.94228i	−0.249836	+	0.456914i
$118$		0			0
$119$	−0.237184	+	0.199021i	−0.0217427	+	0.0182443i
$120$		0			0
$121$	−1.90747	+	10.8178i	−0.173406	+	0.983436i
$122$		0			0
$123$	13.6764	+	4.79870i	1.23316	+	0.432684i
$124$		0			0
$125$	−8.77691	−	5.06735i	−0.785031	−	0.453238i
$126$		0			0
$127$	−1.57909	+	0.911686i	−0.140121	+	0.0808991i	−0.568422	−	0.822737i	$-0.692446\pi$
$127$	−1.57909	+	0.911686i	−0.140121	+	0.0808991i	0.428300	+	0.903636i	$0.359112\pi$
$128$		0			0
$129$	5.71666	+	9.64124i	0.503324	+	0.848864i
$130$		0			0
$131$	−2.84390	+	1.03509i	−0.248472	+	0.0904366i	−0.463254	−	0.886226i	$-0.653318\pi$
$131$	−2.84390	+	1.03509i	−0.248472	+	0.0904366i	0.214782	+	0.976662i	$0.431096\pi$
$132$		0			0
$133$	−0.414264	−	2.34941i	−0.0359213	−	0.203720i
$134$		0			0
$135$	11.5902	−	4.68179i	0.997526	−	0.402944i
$136$		0			0
$137$	0.558924	−	0.0985535i	0.0477521	−	0.00841999i	−0.149721	−	0.988728i	$-0.547838\pi$
$137$	0.558924	−	0.0985535i	0.0477521	−	0.00841999i	0.197473	+	0.980308i	$0.436726\pi$
$138$		0			0
$139$	−6.51758	−	17.9069i	−0.552814	−	1.51884i	−0.829851	−	0.557985i	$-0.811575\pi$
$139$	−6.51758	−	17.9069i	−0.552814	−	1.51884i	0.277037	−	0.960859i	$-0.410647\pi$
$140$		0			0
$141$	11.7070	+	6.57897i	0.985905	+	0.554049i
$142$		0			0
$143$	−0.116207	−	0.201276i	−0.00971771	−	0.0168316i
$144$		0			0
$145$	11.6836	−	20.2366i	0.970269	−	1.68056i
$146$		0			0
$147$	−4.73271	−	5.50902i	−0.390347	−	0.454377i
$148$		0			0
$149$	11.8191	+	2.08403i	0.968262	+	0.170731i	0.635347	−	0.772226i	$-0.280857\pi$
$149$	11.8191	+	2.08403i	0.968262	+	0.170731i	0.332914	+	0.942957i	$0.391968\pi$
$150$		0			0
$151$	13.9712	+	16.6502i	1.13696	+	1.35498i	0.926019	+	0.377477i	$0.123208\pi$
$151$	13.9712	+	16.6502i	1.13696	+	1.35498i	0.210941	+	0.977499i	$0.432347\pi$
$152$		0			0
$153$	−0.366146	−	0.416326i	−0.0296011	−	0.0336580i
$154$		0			0
$155$	14.6850	+	5.34489i	1.17952	+	0.429312i
$156$		0			0
$157$	−10.3603	−	8.69329i	−0.826839	−	0.693800i	0.127724	−	0.991810i	$-0.459233\pi$
$157$	−10.3603	−	8.69329i	−0.826839	−	0.693800i	−0.954563	+	0.298010i	$0.903677\pi$
$158$		0			0
$159$	0.512003	−	3.11479i	0.0406044	−	0.247019i
$160$		0			0
$161$			1.83601i			0.144698i
$162$		0			0
$163$		−	16.7954i		−	1.31551i	−0.753230	−	0.657757i	$-0.771505\pi$
$163$		−	16.7954i		−	1.31551i	0.753230	−	0.657757i	$-0.228495\pi$
$164$		0			0
$165$	−0.0836567	+	0.508929i	−0.00651266	+	0.0396200i
$166$		0			0
$167$	−6.85631	−	5.75313i	−0.530557	−	0.445190i	0.337737	−	0.941241i	$-0.390339\pi$
$167$	−6.85631	−	5.75313i	−0.530557	−	0.445190i	−0.868294	+	0.496050i	$0.834783\pi$
$168$		0			0
$169$	8.90317	+	3.24049i	0.684859	+	0.249268i
$170$		0			0
$171$	4.18863	−	0.839299i	0.320313	−	0.0641828i
$172$		0			0
$173$	−13.1053	−	15.6183i	−0.996380	−	1.18744i	−0.982257	−	0.187539i	$-0.939949\pi$
$173$	−13.1053	−	15.6183i	−0.996380	−	1.18744i	−0.0141230	−	0.999900i	$-0.504496\pi$
$174$		0			0
$175$	−1.29866	−	0.228989i	−0.0981694	−	0.0173099i
$176$		0			0
$177$	−2.65596	−	3.09162i	−0.199634	−	0.232381i
$178$		0			0
$179$	−7.77470	+	13.4662i	−0.581109	+	1.00651i	0.414240	+	0.910168i	$0.364048\pi$
$179$	−7.77470	+	13.4662i	−0.581109	+	1.00651i	−0.995348	+	0.0963418i	$0.969286\pi$
$180$		0			0
$181$	1.40905	+	2.44054i	0.104734	+	0.181404i	0.913629	−	0.406548i	$-0.133268\pi$
$181$	1.40905	+	2.44054i	0.104734	+	0.181404i	−0.808896	+	0.587952i	$0.799934\pi$
$182$		0			0
$183$	5.33254	+	2.99673i	0.394193	+	0.221525i
$184$		0			0
$185$	0.888493	+	2.44111i	0.0653233	+	0.179474i
$186$		0			0
$187$	0.0225284	−	0.00397236i	0.00164744	−	0.000290488i
$188$		0			0
$189$	−6.46981	+	5.82461i	−0.470609	+	0.423678i
$190$		0			0
$191$	−2.04718	−	11.6102i	−0.148129	−	0.840082i	−0.964801	−	0.262980i	$-0.915295\pi$
$191$	−2.04718	−	11.6102i	−0.148129	−	0.840082i	0.816672	−	0.577102i	$-0.195816\pi$
$192$		0			0
$193$	12.5148	−	4.55500i	0.900833	−	0.327876i	0.150246	−	0.988649i	$-0.451993\pi$
$193$	12.5148	−	4.55500i	0.900833	−	0.327876i	0.750586	+	0.660772i	$0.229771\pi$
$194$		0			0
$195$	3.99014	+	6.72943i	0.285740	+	0.481905i
$196$		0			0
$197$	6.12149	−	3.53425i	0.436138	−	0.251805i	−0.265820	−	0.964023i	$-0.585643\pi$
$197$	6.12149	−	3.53425i	0.436138	−	0.251805i	0.701958	+	0.712218i	$0.252309\pi$
$198$		0			0
$199$	8.56558	+	4.94534i	0.607198	+	0.350566i	0.771868	−	0.635783i	$-0.219323\pi$
$199$	8.56558	+	4.94534i	0.607198	+	0.350566i	−0.164670	+	0.986349i	$0.552656\pi$
$200$		0			0
$201$	17.1675	+	6.02364i	1.21090	+	0.424875i
$202$		0			0
$203$	−2.82588	+	16.0264i	−0.198338	+	1.12483i
$204$		0			0
$205$	15.4208	−	12.9396i	1.07704	−	0.903740i
$206$		0			0
$207$	−3.28678	+	0.0763449i	−0.228447	+	0.00530634i
$208$		0			0
$209$	−0.0602845	+	0.165630i	−0.00416996	+	0.0114569i
$210$		0			0
$211$	−3.29291	+	3.92434i	−0.226694	+	0.270163i	−0.867387	−	0.497634i	$-0.834202\pi$
$211$	−3.29291	+	3.92434i	−0.226694	+	0.270163i	0.640694	+	0.767797i	$0.278647\pi$
$212$		0			0
$213$	14.8539	−	18.1255i	1.01777	−	1.24194i
$214$		0			0
$215$	15.5677			1.06171
$216$		0			0
$217$	−10.8834			−0.738813
$218$		0			0
$219$	8.93414	+	23.6869i	0.603713	+	1.60061i
$220$		0			0
$221$	0.223048	−	0.265818i	0.0150038	−	0.0178809i
$222$		0			0
$223$	−5.58894	+	15.3555i	−0.374263	+	1.02828i	0.599433	+	0.800425i	$0.295393\pi$
$223$	−5.58894	+	15.3555i	−0.374263	+	1.02828i	−0.973695	+	0.227853i	$0.926829\pi$
$224$		0			0
$225$	0.355929	−	2.33435i	0.0237286	−	0.155623i
$226$		0			0
$227$	3.69536	−	3.10078i	0.245270	−	0.205806i	−0.511863	−	0.859067i	$-0.671044\pi$
$227$	3.69536	−	3.10078i	0.245270	−	0.205806i	0.757132	+	0.653262i	$0.226600\pi$
$228$		0			0
$229$	−0.206048	+	1.16856i	−0.0136160	+	0.0772204i	−0.990859	−	0.134904i	$-0.956927\pi$
$229$	−0.206048	+	1.16856i	−0.0136160	+	0.0772204i	0.977243	+	0.212125i	$0.0680384\pi$
$230$		0			0
$231$	−0.0664759	−	0.352985i	−0.00437379	−	0.0232247i
$232$		0			0
$233$	−5.49416	−	3.17205i	−0.359934	−	0.207808i	0.309118	−	0.951024i	$-0.399966\pi$
$233$	−5.49416	−	3.17205i	−0.359934	−	0.207808i	−0.669052	+	0.743216i	$0.733300\pi$
$234$		0			0
$235$	16.1526	−	9.32570i	1.05368	−	0.608342i
$236$		0			0
$237$	18.9287	−	0.219808i	1.22955	−	0.0142780i
$238$		0			0
$239$	−22.3289	+	8.12707i	−1.44434	+	0.525697i	−0.941004	−	0.338395i	$-0.890116\pi$
$239$	−22.3289	+	8.12707i	−1.44434	+	0.525697i	−0.503335	+	0.864091i	$0.667894\pi$
$240$		0			0
$241$	2.51876	+	14.2846i	0.162247	+	0.920150i	0.951857	+	0.306541i	$0.0991717\pi$
$241$	2.51876	+	14.2846i	0.162247	+	0.920150i	−0.789610	+	0.613609i	$0.789717\pi$
$242$		0			0
$243$	−10.6961	−	11.3399i	−0.686156	−	0.727455i
$244$		0			0
$245$	−9.93400	+	1.75163i	−0.634660	+	0.111908i
$246$		0			0
$247$	0.914445	+	2.51242i	0.0581847	+	0.159861i
$248$		0			0
$249$	−0.0175966	−	1.51533i	−0.00111514	−	0.0960300i
$250$		0			0
$251$	13.1013	+	22.6921i	0.826945	+	1.43231i	0.900424	+	0.435013i	$0.143256\pi$
$251$	13.1013	+	22.6921i	0.826945	+	1.43231i	−0.0734793	+	0.997297i	$0.523410\pi$
$252$		0			0
$253$	0.0678252	−	0.117477i	0.00426413	−	0.00738569i
$254$		0			0
$255$	−0.756741	+	0.142513i	−0.0473890	+	0.00892453i
$256$		0			0
$257$	−15.4023	−	2.71584i	−0.960768	−	0.169409i	−0.328796	−	0.944401i	$-0.606643\pi$
$257$	−15.4023	−	2.71584i	−0.960768	−	0.169409i	−0.631971	+	0.774992i	$0.717754\pi$
$258$		0			0
$259$	−1.16291	−	1.38591i	−0.0722599	−	0.0861160i
$260$		0			0
$261$	−28.8075	−	4.39242i	−1.78314	−	0.271884i
$262$		0			0
$263$	6.99179	+	2.54480i	0.431132	+	0.156919i	0.548465	−	0.836173i	$-0.315212\pi$
$263$	6.99179	+	2.54480i	0.431132	+	0.156919i	−0.117333	+	0.993093i	$0.537435\pi$
$264$		0			0
$265$	−3.35847	−	2.81810i	−0.206309	−	0.173114i
$266$		0			0
$267$	−24.7705	+	9.34285i	−1.51593	+	0.571773i
$268$		0			0
$269$		−	1.49269i		−	0.0910108i	−0.998964	−	0.0455054i	$-0.985510\pi$
$269$		−	1.49269i		−	0.0910108i	0.998964	−	0.0455054i	$-0.0144898\pi$
$270$		0			0
$271$			2.96711i			0.180239i	0.995931	+	0.0901196i	$0.0287249\pi$
$271$			2.96711i			0.180239i	−0.995931	+	0.0901196i	$0.971275\pi$
$272$		0			0
$273$	−4.21417	−	3.45352i	−0.255053	−	0.209017i
$274$		0			0
$275$	0.0746353	+	0.0626264i	0.00450068	+	0.00377652i
$276$		0			0
$277$	26.7601	+	9.73988i	1.60786	+	0.585213i	0.981015	−	0.193932i	$-0.0621242\pi$
$277$	26.7601	+	9.73988i	1.60786	+	0.585213i	0.626844	+	0.779145i	$0.284346\pi$
$278$		0			0
$279$	−0.452554	−	19.4832i	−0.0270937	−	1.16643i
$280$		0			0
$281$	2.30793	+	2.75049i	0.137680	+	0.164080i	0.830479	−	0.557051i	$-0.188067\pi$
$281$	2.30793	+	2.75049i	0.137680	+	0.164080i	−0.692799	+	0.721131i	$0.743623\pi$
$282$		0			0
$283$	8.85623	+	1.56159i	0.526448	+	0.0928270i	0.430554	−	0.902565i	$-0.358318\pi$
$283$	8.85623	+	1.56159i	0.526448	+	0.0928270i	0.0958936	+	0.995392i	$0.469429\pi$
$284$		0			0
$285$	1.96440	−	5.59859i	0.116361	−	0.331632i
$286$		0			0
$287$	−7.00972	+	12.1412i	−0.413771	+	0.716672i
$288$		0			0
$289$	−8.48292	−	14.6929i	−0.498995	−	0.864285i
$290$		0			0
$291$	−22.1070	+	13.1081i	−1.29594	+	0.768410i
$292$		0			0
$293$	7.25436	+	19.9312i	0.423804	+	1.16439i	0.949513	+	0.313728i	$0.101578\pi$
$293$	7.25436	+	19.9312i	0.423804	+	1.16439i	−0.525709	+	0.850665i	$0.676200\pi$
$294$		0			0
$295$	−5.57489	+	0.983003i	−0.324583	+	0.0572327i
$296$		0			0
$297$	0.629141	−	0.133681i	0.0365064	−	0.00775697i
$298$		0			0
$299$	−0.357309	−	2.02640i	−0.0206637	−	0.117190i
$300$		0			0
$301$	−10.1880	+	3.70811i	−0.587224	+	0.213732i
$302$		0			0
$303$	5.93849	−	10.5673i	0.341157	−	0.607073i
$304$		0			0
$305$	7.35753	−	4.24787i	0.421291	−	0.243232i
$306$		0			0
$307$	−16.9173	−	9.76719i	−0.965519	−	0.557443i	−0.0676519	−	0.997709i	$-0.521551\pi$
$307$	−16.9173	−	9.76719i	−0.965519	−	0.557443i	−0.897867	+	0.440266i	$0.854884\pi$
$308$		0			0
$309$	15.8353	−	13.6038i	0.900840	−	0.773896i
$310$		0			0
$311$	0.274935	−	1.55924i	0.0155901	−	0.0884161i	−0.976020	−	0.217681i	$-0.930151\pi$
$311$	0.274935	−	1.55924i	0.0155901	−	0.0884161i	0.991610	+	0.129265i	$0.0412618\pi$
$312$		0			0
$313$	−16.7124	+	14.0233i	−0.944639	+	0.792647i	−0.978387	−	0.206784i	$-0.933700\pi$
$313$	−16.7124	+	14.0233i	−0.944639	+	0.792647i	0.0337472	+	0.999430i	$0.489256\pi$
$314$		0			0
$315$	2.37551	+	11.8553i	0.133845	+	0.667970i
$316$		0			0
$317$	7.01193	−	19.2651i	0.393829	−	1.08204i	−0.571409	−	0.820665i	$-0.693603\pi$
$317$	7.01193	−	19.2651i	0.393829	−	1.08204i	0.965238	−	0.261371i	$-0.0841748\pi$
$318$		0			0
$319$	0.772854	−	0.921052i	0.0432715	−	0.0515690i
$320$		0			0
$321$	−23.3934	−	3.84536i	−1.30569	−	0.214627i
$322$		0			0
$323$	−0.263162			−0.0146427
$324$		0			0
$325$	1.47789			0.0819786
$326$		0			0
$327$	−8.53567	−	1.40308i	−0.472024	−	0.0775904i
$328$		0			0
$329$	−8.34942	+	9.95046i	−0.460319	+	0.548586i
$330$		0			0
$331$	−7.78386	+	21.3860i	−0.427840	+	1.17548i	0.519281	+	0.854603i	$0.326200\pi$
$331$	−7.78386	+	21.3860i	−0.427840	+	1.17548i	−0.947121	+	0.320876i	$0.896023\pi$
$332$		0			0
$333$	2.43266	−	2.13945i	0.133309	−	0.117241i
$334$		0			0
$335$	19.3572	−	16.2426i	1.05760	−	0.887430i
$336$		0			0
$337$	−4.59541	+	26.0619i	−0.250328	+	1.41968i	0.557458	+	0.830205i	$0.311777\pi$
$337$	−4.59541	+	26.0619i	−0.250328	+	1.41968i	−0.807786	+	0.589475i	$0.799335\pi$
$338$		0			0
$339$	10.4803	−	9.00343i	0.569211	−	0.488999i
$340$		0			0
$341$	0.696372	+	0.402051i	0.0377107	+	0.0217723i
$342$		0			0
$343$	16.2402	−	9.37630i	0.876890	−	0.506272i
$344$		0			0
$345$	−2.23704	+	3.98071i	−0.120438	+	0.214314i
$346$		0			0
$347$	−17.1452	+	6.24034i	−0.920402	+	0.334999i	−0.758398	−	0.651791i	$-0.774018\pi$
$347$	−17.1452	+	6.24034i	−0.920402	+	0.334999i	−0.162003	+	0.986790i	$0.551796\pi$
$348$		0			0
$349$	0.462847	+	2.62494i	0.0247756	+	0.140510i	0.994686	−	0.102951i	$-0.0328285\pi$
$349$	0.462847	+	2.62494i	0.0247756	+	0.140510i	−0.969911	+	0.243461i	$0.921717\pi$
$350$		0			0
$351$	6.00718	−	7.68771i	0.320639	−	0.410340i
$352$		0			0
$353$	−14.0682	+	2.48061i	−0.748777	+	0.132030i	−0.534999	−	0.844853i	$-0.679688\pi$
$353$	−14.0682	+	2.48061i	−0.748777	+	0.132030i	−0.213778	+	0.976882i	$0.568577\pi$
$354$		0			0
$355$	−11.1321	−	30.5852i	−0.590830	−	1.62329i
$356$		0			0
$357$	0.461289	−	0.273516i	0.0244140	−	0.0144760i
$358$		0			0
$359$	−13.8932	−	24.0637i	−0.733256	−	1.27004i	−0.955484	−	0.295041i	$-0.904667\pi$
$359$	−13.8932	−	24.0637i	−0.733256	−	1.27004i	0.222229	−	0.974995i	$-0.428667\pi$
$360$		0			0
$361$	−8.48616	+	14.6985i	−0.446640	+	0.773604i
$362$		0			0
$363$	6.29924	−	17.9530i	0.330625	−	0.942286i
$364$		0			0
$365$	34.6268	+	6.10564i	1.81245	+	0.319584i
$366$		0			0
$367$	15.5436	+	18.5241i	0.811367	+	0.966950i	0.999886	−	0.0151198i	$-0.00481297\pi$
$367$	15.5436	+	18.5241i	0.811367	+	0.966950i	−0.188518	+	0.982070i	$0.560369\pi$
$368$		0			0
$369$	−22.0263	−	12.0438i	−1.14665	−	0.626974i
$370$		0			0
$371$	2.86914	+	1.04428i	0.148958	+	0.0542164i
$372$		0			0
$373$	−24.6884	−	20.7160i	−1.27831	−	1.07263i	−0.993474	−	0.114059i	$-0.963615\pi$
$373$	−24.6884	−	20.7160i	−1.27831	−	1.07263i	−0.284841	−	0.958575i	$-0.591941\pi$
$374$		0			0
$375$	13.5771	+	11.1265i	0.701119	+	0.574569i
$376$		0			0
$377$		−	18.2382i		−	0.939316i
$378$		0			0
$379$		−	2.64588i		−	0.135910i	−0.997688	−	0.0679549i	$-0.978353\pi$
$379$		−	2.64588i		−	0.135910i	0.997688	−	0.0679549i	$-0.0216474\pi$
$380$		0			0
$381$	2.95497	−	1.11455i	0.151388	−	0.0570999i
$382$		0			0
$383$	−18.6760	−	15.6710i	−0.954297	−	0.800750i	0.0257190	−	0.999669i	$-0.491812\pi$
$383$	−18.6760	−	15.6710i	−0.954297	−	0.800750i	−0.980016	+	0.198919i	$0.936257\pi$
$384$		0			0
$385$	−0.468792	−	0.170626i	−0.0238918	−	0.00869592i
$386$		0			0
$387$	−7.06181	−	18.0840i	−0.358972	−	0.919263i
$388$		0			0
$389$	−9.92606	−	11.8294i	−0.503271	−	0.599775i	0.453270	−	0.891373i	$-0.350257\pi$
$389$	−9.92606	−	11.8294i	−0.503271	−	0.599775i	−0.956541	+	0.291598i	$0.905813\pi$
$390$		0			0
$391$	0.199453	+	0.0351690i	0.0100868	+	0.00177857i
$392$		0			0
$393$	5.15135	−	0.970127i	0.259851	−	0.0489364i
$394$		0			0
$395$	13.1459	−	22.7694i	0.661443	−	1.14565i
$396$		0			0
$397$	3.80408	+	6.58886i	0.190921	+	0.330685i	0.945556	−	0.325460i	$-0.105519\pi$
$397$	3.80408	+	6.58886i	0.190921	+	0.330685i	−0.754634	+	0.656145i	$0.772186\pi$
$398$		0			0
$399$	0.0479800	+	4.13179i	0.00240200	+	0.206848i
$400$		0			0
$401$	12.8302	+	35.2508i	0.640712	+	1.76034i	0.649478	+	0.760380i	$0.274987\pi$
$401$	12.8302	+	35.2508i	0.640712	+	1.76034i	−0.00876589	+	0.999962i	$0.502790\pi$
$402$		0			0
$403$	12.0120	−	2.11804i	0.598359	−	0.105507i
$404$		0			0
$405$	−21.1243	+	4.74555i	−1.04967	+	0.235808i
$406$		0			0
$407$	0.0232111	+	0.131637i	0.00115053	+	0.00652500i
$408$		0			0
$409$	−5.95146	+	2.16615i	−0.294281	+	0.107109i	−0.484942	−	0.874547i	$-0.661159\pi$
$409$	−5.95146	+	2.16615i	−0.294281	+	0.107109i	0.190661	+	0.981656i	$0.438937\pi$
$410$		0			0
$411$	−0.982954	+	0.0114144i	−0.0484855	+	0.000563032i
$412$		0			0
$413$	3.41423	−	1.97121i	0.168003	−	0.0969968i
$414$		0			0
$415$	−1.82279	−	1.05239i	−0.0894772	−	0.0516597i
$416$		0			0
$417$	6.10851	+	32.4360i	0.299135	+	1.58840i
$418$		0			0
$419$	2.74169	−	15.5489i	0.133940	−	0.759613i	−0.841652	−	0.540021i	$-0.818416\pi$
$419$	2.74169	−	15.5489i	0.133940	−	0.759613i	0.975592	−	0.219592i	$-0.0704725\pi$
$420$		0			0
$421$	23.5685	−	19.7763i	1.14866	−	0.963840i	0.148972	−	0.988841i	$-0.452403\pi$
$421$	23.5685	−	19.7763i	1.14866	−	0.963840i	0.999687	+	0.0250014i	$0.00795901\pi$
$422$		0			0
$423$	−18.1602	−	14.5332i	−0.882982	−	0.706627i
$424$		0			0
$425$	−0.0497520	+	0.136693i	−0.00241333	+	0.00663056i
$426$		0			0
$427$	−3.80317	+	4.53245i	−0.184049	+	0.219340i
$428$		0			0
$429$	0.142064	+	0.376651i	0.00685892	+	0.0181849i
$430$		0			0
$431$	9.74244			0.469277			0.234638	−	0.972083i	$-0.424609\pi$
$431$	9.74244			0.469277			0.234638	+	0.972083i	$0.424609\pi$
$432$		0			0
$433$	−21.5067			−1.03354			−0.516772	−	0.856123i	$-0.672867\pi$
$433$	−21.5067			−1.03354			−0.516772	+	0.856123i	$0.672867\pi$
$434$		0			0
$435$	−25.6539	+	31.3042i	−1.23001	+	1.50092i
$436$		0			0
$437$	−1.00307	+	1.19542i	−0.0479835	+	0.0571845i
$438$		0			0
$439$	3.27258	−	8.99133i	0.156192	−	0.429133i	−0.836772	−	0.547551i	$-0.815560\pi$
$439$	3.27258	−	8.99133i	0.156192	−	0.429133i	0.992964	+	0.118418i	$0.0377824\pi$
$440$		0			0
$441$	6.54103	+	10.7452i	0.311478	+	0.511675i
$442$		0			0
$443$	29.4014	−	24.6707i	1.39690	−	1.17214i	0.434450	−	0.900696i	$-0.356943\pi$
$443$	29.4014	−	24.6707i	1.39690	−	1.17214i	0.962454	−	0.271446i	$-0.0875018\pi$
$444$		0			0
$445$	−6.38496	+	36.2109i	−0.302676	+	1.71656i
$446$		0			0
$447$	−19.6148	−	6.88233i	−0.927747	−	0.325523i
$448$		0			0
$449$	2.86268	+	1.65277i	0.135098	+	0.0779989i	0.566026	−	0.824388i	$-0.308480\pi$
$449$	2.86268	+	1.65277i	0.135098	+	0.0779989i	−0.430928	+	0.902386i	$0.641814\pi$
$450$		0			0
$451$	0.897031	−	0.517901i	0.0422396	−	0.0243870i
$452$		0			0
$453$	−19.2006	−	32.3822i	−0.902125	−	1.52145i
$454$		0			0
$455$	−7.11103	+	2.58820i	−0.333370	+	0.121337i
$456$		0			0
$457$	3.24492	+	18.4028i	0.151791	+	0.860849i	0.961661	+	0.274240i	$0.0884262\pi$
$457$	3.24492	+	18.4028i	0.151791	+	0.860849i	−0.809870	+	0.586609i	$0.800463\pi$
$458$		0			0
$459$	0.508822	+	0.814414i	0.0237498	+	0.0380136i
$460$		0			0
$461$	7.51932	−	1.32586i	0.350210	−	0.0617514i	0.00422362	−	0.999991i	$-0.498656\pi$
$461$	7.51932	−	1.32586i	0.350210	−	0.0617514i	0.345986	+	0.938240i	$0.387544\pi$
$462$		0			0
$463$	−6.41347	−	17.6209i	−0.298059	−	0.818911i	−0.994824	−	0.101612i	$-0.967600\pi$
$463$	−6.41347	−	17.6209i	−0.298059	−	0.818911i	0.696765	−	0.717300i	$-0.254622\pi$
$464$		0			0
$465$	−23.5967	−	13.2606i	−1.09427	−	0.614947i
$466$		0			0
$467$	−4.47325	−	7.74790i	−0.206998	−	0.358530i	0.743770	−	0.668436i	$-0.233036\pi$
$467$	−4.47325	−	7.74790i	−0.206998	−	0.358530i	−0.950767	+	0.309906i	$0.899703\pi$
$468$		0			0
$469$	−8.79907	+	15.2404i	−0.406303	+	0.703738i
$470$		0			0
$471$	15.2646	+	17.7684i	0.703354	+	0.818727i
$472$		0			0
$473$	0.788858	+	0.139097i	0.0362717	+	0.00639569i
$474$		0			0
$475$	−0.720446	−	0.858594i	−0.0330563	−	0.0393950i
$476$		0			0
$477$	−1.75014	+	5.17969i	−0.0801335	+	0.237162i
$478$		0			0
$479$	−27.4967	−	10.0080i	−1.25636	−	0.457277i	−0.373813	−	0.927504i	$-0.621950\pi$
$479$	−27.4967	−	10.0080i	−1.25636	−	0.457277i	−0.882545	+	0.470227i	$0.844172\pi$
$480$		0			0
$481$	1.55322	+	1.30330i	0.0708207	+	0.0594256i
$482$		0			0
$483$	0.515810	−	3.13795i	0.0234702	−	0.142782i
$484$		0			0
$485$			35.6961i			1.62088i
$486$		0			0
$487$			5.04696i			0.228699i	0.993441	+	0.114350i	$0.0364784\pi$
$487$			5.04696i			0.228699i	−0.993441	+	0.114350i	$0.963522\pi$
$488$		0			0
$489$	−4.71850	+	28.7052i	−0.213378	+	1.29809i
$490$		0			0
$491$	−11.7303	−	9.84289i	−0.529381	−	0.444203i	0.338507	−	0.940964i	$-0.390078\pi$
$491$	−11.7303	−	9.84289i	−0.529381	−	0.444203i	−0.867888	+	0.496761i	$0.834523\pi$
$492$		0			0
$493$	1.68688	+	0.613975i	0.0759734	+	0.0276521i
$494$		0			0
$495$	0.285958	−	0.846315i	0.0128528	−	0.0380390i
$496$		0			0
$497$	14.5703	+	17.3643i	0.653569	+	0.778894i
$498$		0			0
$499$	27.4638	+	4.84260i	1.22945	+	0.216785i	0.750388	−	0.660998i	$-0.229867\pi$
$499$	27.4638	+	4.84260i	1.22945	+	0.216785i	0.479059	+	0.877783i	$0.340978\pi$
$500$		0			0
$501$	10.1019	+	11.7590i	0.451321	+	0.525352i
$502$		0			0
$503$	3.01406	−	5.22051i	0.134390	−	0.232771i	−0.790974	−	0.611850i	$-0.790426\pi$
$503$	3.01406	−	5.22051i	0.134390	−	0.232771i	0.925364	+	0.379079i	$0.123759\pi$
$504$		0			0
$505$	−8.41782	−	14.5801i	−0.374588	−	0.648805i
$506$		0			0
$507$	−14.3061	−	8.03963i	−0.635358	−	0.357052i
$508$		0			0
$509$	−2.70442	−	7.43033i	−0.119871	−	0.329344i	0.865216	−	0.501399i	$-0.167181\pi$
$509$	−2.70442	−	7.43033i	−0.119871	−	0.329344i	−0.985087	+	0.172056i	$0.944959\pi$
$510$		0			0
$511$	−24.1152	+	4.25215i	−1.06679	+	0.188104i
$512$		0			0
$513$	−7.39464	+	0.257701i	−0.326481	+	0.0113778i
$514$		0			0
$515$	−5.03495	−	28.5546i	−0.221866	−	1.25827i
$516$		0			0
$517$	0.901823	−	0.328237i	0.0396621	−	0.0144358i
$518$		0			0
$519$	18.0107	+	30.3753i	0.790582	+	1.33333i
$520$		0			0
$521$	33.5824	−	19.3888i	1.47127	−	0.849440i	0.471795	−	0.881709i	$-0.343606\pi$
$521$	33.5824	−	19.3888i	1.47127	−	0.849440i	0.999479	+	0.0322682i	$0.0102731\pi$
$522$		0			0
$523$	28.7525	+	16.6002i	1.25726	+	0.725878i	0.972540	−	0.232734i	$-0.0747671\pi$
$523$	28.7525	+	16.6002i	1.25726	+	0.725878i	0.284717	+	0.958612i	$0.408100\pi$
$524$		0			0
$525$	2.15523	+	0.756214i	0.0940617	+	0.0330039i
$526$		0			0
$527$	−0.208473	+	1.18231i	−0.00908123	+	0.0515022i
$528$		0			0
$529$	−16.6990	+	14.0121i	−0.726045	+	0.609224i
$530$		0			0
$531$	3.67078	+	6.03011i	0.159298	+	0.261684i
$532$		0			0
$533$	5.37379	−	14.7644i	0.232765	−	0.639516i
$534$		0			0
$535$	−21.1651	+	25.2236i	−0.915048	+	1.09051i
$536$		0			0
$537$	17.0711	−	20.8310i	0.736671	−	0.898925i
$538$		0			0
$539$	−0.519035			−0.0223564
$540$		0			0
$541$	−32.6053			−1.40181			−0.700905	−	0.713255i	$-0.747220\pi$
$541$	−32.6053			−1.40181			−0.700905	+	0.713255i	$0.747220\pi$
$542$		0			0
$543$	−1.72257	−	4.56702i	−0.0739227	−	0.195990i
$544$		0			0
$545$	−7.72263	+	9.20347i	−0.330801	+	0.394233i
$546$		0			0
$547$	−14.4354	+	39.6609i	−0.617213	+	1.69578i	0.0964946	+	0.995334i	$0.469237\pi$
$547$	−14.4354	+	39.6609i	−0.617213	+	1.69578i	−0.713707	+	0.700444i	$0.752985\pi$
$548$		0			0
$549$	−8.27202	−	6.61988i	−0.353041	−	0.282530i
$550$		0			0
$551$	−10.5957	+	8.89082i	−0.451390	+	0.378762i
$552$		0			0
$553$	−3.17957	+	18.0322i	−0.135209	+	0.766809i
$554$		0			0
$555$	−0.832727	−	4.42176i	−0.0353473	−	0.187693i
$556$		0			0
$557$	25.1746	+	14.5346i	1.06668	+	0.615849i	0.927273	−	0.374386i	$-0.122146\pi$
$557$	25.1746	+	14.5346i	1.06668	+	0.615849i	0.139409	+	0.990235i	$0.455480\pi$
$558$		0			0
$559$	10.5228	−	6.07533i	0.445066	−	0.256959i
$560$		0			0
$561$	−0.0396196		0.000460078i	−0.00167274		1.94245e-5i
$562$		0			0
$563$	28.1038	−	10.2289i	1.18443	−	0.431098i	0.326667	−	0.945139i	$-0.394074\pi$
$563$	28.1038	−	10.2289i	1.18443	−	0.431098i	0.857766	+	0.514041i	$0.171852\pi$
$564$		0			0
$565$	−3.33228	−	18.8983i	−0.140190	−	0.795057i
$566$		0			0
$567$	12.6940	−	8.13729i	0.533099	−	0.341734i
$568$		0			0
$569$	5.50738	−	0.971100i	0.230882	−	0.0407106i	−0.0570102	−	0.998374i	$-0.518157\pi$
$569$	5.50738	−	0.971100i	0.230882	−	0.0407106i	0.287892	+	0.957663i	$0.407046\pi$
$570$		0			0
$571$	−1.38745	−	3.81200i	−0.0580631	−	0.159527i	0.907270	−	0.420549i	$-0.138163\pi$
$571$	−1.38745	−	3.81200i	−0.0580631	−	0.159527i	−0.965333	+	0.261022i	$0.915940\pi$
$572$		0			0
$573$	0.237104	+	20.4182i	0.00990517	+	0.852984i
$574$		0			0
$575$	0.431292	+	0.747020i	0.0179861	+	0.0311529i
$576$		0			0
$577$	11.5165	−	19.9472i	0.479440	−	0.830415i	−0.520282	−	0.853995i	$-0.674173\pi$
$577$	11.5165	−	19.9472i	0.479440	−	0.830415i	0.999722	+	0.0235799i	$0.00750640\pi$
$578$		0			0
$579$	−22.6689	+	4.26911i	−0.942086	+	0.177418i
$580$		0			0
$581$	1.44356	+	0.254539i	0.0598890	+	0.0105600i
$582$		0			0
$583$	−0.145004	−	0.172809i	−0.00600545	−	0.00715701i
$584$		0			0
$585$	−4.92903	−	12.6224i	−0.203790	−	0.521870i
$586$		0			0
$587$	−21.8549	−	7.95454i	−0.902049	−	0.328319i	−0.150975	−	0.988538i	$-0.548241\pi$
$587$	−21.8549	−	7.95454i	−0.902049	−	0.328319i	−0.751073	+	0.660219i	$0.770464\pi$
$588$		0			0
$589$	−7.08612	−	5.94596i	−0.291979	−	0.244999i
$590$		0			0
$591$	−11.4552	+	4.32065i	−0.471206	+	0.177728i
$592$		0			0
$593$		−	26.7627i		−	1.09901i	−0.835490	−	0.549506i	$-0.814816\pi$
$593$		−	26.7627i		−	1.09901i	0.835490	−	0.549506i	$-0.185184\pi$
$594$		0			0
$595$		−	0.744840i		−	0.0305355i
$596$		0			0
$597$	−13.2502	−	10.8586i	−0.542295	−	0.444412i
$598$		0			0
$599$	−2.31431	−	1.94194i	−0.0945602	−	0.0793454i	0.594282	−	0.804257i	$-0.297436\pi$
$599$	−2.31431	−	1.94194i	−0.0945602	−	0.0793454i	−0.688842	+	0.724911i	$0.741881\pi$
$600$		0			0
$601$	−5.47961	−	1.99442i	−0.223518	−	0.0813539i	0.227834	−	0.973700i	$-0.426836\pi$
$601$	−5.47961	−	1.99442i	−0.223518	−	0.0813539i	−0.451352	+	0.892346i	$0.649058\pi$
$602$		0			0
$603$	−27.6489	−	15.1181i	−1.12595	−	0.615658i
$604$		0			0
$605$	−16.9858	−	20.2429i	−0.690570	−	0.822990i
$606$		0			0
$607$	15.8689	+	2.79811i	0.644098	+	0.113572i	0.486150	−	0.873875i	$-0.338401\pi$
$607$	15.8689	+	2.79811i	0.644098	+	0.113572i	0.157948	+	0.987447i	$0.449512\pi$
$608$		0			0
$609$	9.33222	−	26.5970i	0.378161	−	1.07776i
$610$		0			0
$611$	7.27876	−	12.6072i	0.294467	−	0.510032i
$612$		0			0
$613$	−6.47615	−	11.2170i	−0.261569	−	0.453052i	0.705090	−	0.709118i	$-0.250907\pi$
$613$	−6.47615	−	11.2170i	−0.261569	−	0.453052i	−0.966659	+	0.256067i	$0.917573\pi$
$614$		0			0
$615$	−29.9912	+	17.7829i	−1.20936	+	0.717076i
$616$		0			0
$617$	−4.72692	−	12.9871i	−0.190299	−	0.522841i	0.807448	−	0.589939i	$-0.200848\pi$
$617$	−4.72692	−	12.9871i	−0.190299	−	0.522841i	−0.997746	+	0.0670978i	$0.978626\pi$
$618$		0			0
$619$	23.0999	−	4.07314i	0.928465	−	0.163713i	0.311088	−	0.950381i	$-0.399306\pi$
$619$	23.0999	−	4.07314i	0.928465	−	0.163713i	0.617377	+	0.786667i	$0.288195\pi$
$620$		0			0
$621$	5.63893	+	0.792908i	0.226282	+	0.0318183i
$622$		0			0
$623$	−4.44668	−	25.2184i	−0.178152	−	1.01035i
$624$		0			0
$625$	26.6083	−	9.68464i	1.06433	−	0.387386i
$626$		0			0
$627$	0.149565	−	0.266145i	0.00597306	−	0.0106288i
$628$		0			0
$629$	−0.172833	+	0.0997850i	−0.00689129	+	0.00397869i
$630$		0			0
$631$	20.7869	+	12.0013i	0.827515	+	0.477766i	0.853001	−	0.521909i	$-0.174780\pi$
$631$	20.7869	+	12.0013i	0.827515	+	0.477766i	−0.0254860	+	0.999675i	$0.508113\pi$
$632$		0			0
$633$	6.73047	−	5.78204i	0.267512	−	0.229815i
$634$		0			0
$635$	0.761687	−	4.31974i	0.0302266	−	0.171424i
$636$		0			0
$637$	−6.03119	+	5.06077i	−0.238964	+	0.200515i
$638$		0			0
$639$	−30.4792	+	26.8055i	−1.20574	+	1.06041i
$640$		0			0
$641$	−13.8584	+	38.0757i	−0.547375	+	1.50390i	0.289865	+	0.957067i	$0.406389\pi$
$641$	−13.8584	+	38.0757i	−0.547375	+	1.50390i	−0.837241	+	0.546834i	$0.815833\pi$
$642$		0			0
$643$	−12.5262	+	14.9281i	−0.493985	+	0.588709i	−0.954226	−	0.299085i	$-0.903319\pi$
$643$	−12.5262	+	14.9281i	−0.493985	+	0.588709i	0.460241	+	0.887794i	$0.347763\pi$
$644$		0			0
$645$	−26.6069	−	4.37359i	−1.04765	−	0.172210i
$646$		0			0
$647$	12.2131			0.480148			0.240074	−	0.970755i	$-0.422828\pi$
$647$	12.2131			0.480148			0.240074	+	0.970755i	$0.422828\pi$
$648$		0			0
$649$	−0.291279			−0.0114337
$650$		0			0
$651$	18.6010	+	3.05759i	0.729030	+	0.119836i
$652$		0			0
$653$	6.40628	−	7.63471i	0.250697	−	0.298769i	−0.625989	−	0.779832i	$-0.715305\pi$
$653$	6.40628	−	7.63471i	0.250697	−	0.298769i	0.876686	+	0.481063i	$0.159749\pi$
$654$		0			0
$655$	2.49006	−	6.84140i	0.0972949	−	0.267315i
$656$		0			0
$657$	−8.61486	−	42.9935i	−0.336098	−	1.67734i
$658$		0			0
$659$	−14.1513	+	11.8743i	−0.551255	+	0.462558i	−0.875366	−	0.483461i	$-0.839379\pi$
$659$	−14.1513	+	11.8743i	−0.551255	+	0.462558i	0.324110	+	0.946019i	$0.394935\pi$
$660$		0			0
$661$	−7.35930	+	41.7367i	−0.286244	+	1.62337i	0.414565	+	0.910020i	$0.363934\pi$
$661$	−7.35930	+	41.7367i	−0.286244	+	1.62337i	−0.700809	+	0.713349i	$0.747177\pi$
$662$		0			0
$663$	−0.455894	+	0.391651i	−0.0177054	+	0.0152104i
$664$		0			0
$665$	4.97014	+	2.86951i	0.192734	+	0.111275i
$666$		0			0
$667$	9.21875	−	5.32245i	0.356951	−	0.206086i
$668$		0			0
$669$	13.8661	−	24.6741i	0.536095	−	0.953956i
$670$		0			0
$671$	0.410782	−	0.149512i	0.0158580	−	0.00577186i
$672$		0			0
$673$	−1.59995	−	9.07378i	−0.0616736	−	0.349768i	−0.999992	−	0.00399595i	$-0.998728\pi$
$673$	−1.59995	−	9.07378i	−0.0616736	−	0.349768i	0.938318	−	0.345772i	$-0.112383\pi$
$674$		0			0
$675$	−1.26414	+	3.88968i	−0.0486567	+	0.149714i
$676$		0			0
$677$	−12.9015	+	2.27488i	−0.495845	+	0.0874309i	−0.415978	−	0.909375i	$-0.636561\pi$
$677$	−12.9015	+	2.27488i	−0.495845	+	0.0874309i	−0.0798672	+	0.996806i	$0.525450\pi$
$678$		0			0
$679$	−8.50256	−	23.3606i	−0.326298	−	0.896497i
$680$		0			0
$681$	−7.18693	+	4.26140i	−0.275404	+	0.163297i
$682$		0			0
$683$	14.5782	+	25.2502i	0.557820	+	0.966172i	0.997678	+	0.0681049i	$0.0216953\pi$
$683$	14.5782	+	25.2502i	0.557820	+	0.966172i	−0.439859	+	0.898067i	$0.644971\pi$
$684$		0			0
$685$	−0.682657	+	1.18240i	−0.0260830	+	0.0451771i
$686$		0			0
$687$	0.680455	−	1.93931i	0.0259610	−	0.0739893i
$688$		0			0
$689$	−3.36989	−	0.594203i	−0.128383	−	0.0226373i
$690$		0			0
$691$	3.56996	+	4.25451i	0.135808	+	0.161849i	0.829662	−	0.558266i	$-0.188533\pi$
$691$	3.56996	+	4.25451i	0.135808	+	0.161849i	−0.693854	+	0.720115i	$0.744089\pi$
$692$		0			0
$693$	0.0144470	+	0.621967i	0.000548796	+	0.0236266i
$694$		0			0
$695$	43.0776	+	15.6790i	1.63403	+	0.594737i
$696$		0			0
$697$	1.18468	+	0.994062i	0.0448728	+	0.0376528i
$698$		0			0
$699$	8.49899	+	6.96494i	0.321461	+	0.263438i
$700$		0			0
$701$			0.748051i			0.0282535i	0.999900	+	0.0141268i	$0.00449683\pi$
$701$			0.748051i			0.0282535i	−0.999900	+	0.0141268i	$0.995503\pi$
$702$		0			0
$703$		−	1.53770i		−	0.0579953i
$704$		0			0
$705$	−30.2266	+	11.4008i	−1.13840	+	0.429378i
$706$		0			0
$707$	8.98175	+	7.53658i	0.337794	+	0.283442i
$708$		0			0
$709$	26.5946	+	9.67963i	0.998780	+	0.363526i	0.789114	−	0.614247i	$-0.210540\pi$
$709$	26.5946	+	9.67963i	0.998780	+	0.363526i	0.209666	+	0.977773i	$0.432762\pi$
$710$		0			0
$711$	−32.4131	−	4.94218i	−1.21559	−	0.185346i
$712$		0			0
$713$	4.57604	+	5.45351i	0.171374	+	0.204236i
$714$		0			0
$715$	0.550610	+	0.0970874i	0.0205917	+	0.00363086i
$716$		0			0
$717$	40.4460	−	7.61698i	1.51048	−	0.284461i
$718$		0			0
$719$	−8.80190	+	15.2453i	−0.328255	+	0.568555i	−0.982166	−	0.188017i	$-0.939794\pi$
$719$	−8.80190	+	15.2453i	−0.328255	+	0.568555i	0.653910	+	0.756572i	$0.273127\pi$
$720$		0			0
$721$	10.0965	+	17.4877i	0.376015	+	0.651277i
$722$		0			0
$723$	−0.291721	−	25.1216i	−0.0108492	−	0.934282i
$724$		0			0
$725$	2.61494	+	7.18450i	0.0971166	+	0.266826i
$726$		0			0
$727$	27.1246	−	4.78280i	1.00600	−	0.177384i	0.353708	−	0.935356i	$-0.384921\pi$
$727$	27.1246	−	4.78280i	1.00600	−	0.177384i	0.652287	+	0.757972i	$0.273810\pi$
$728$		0			0
$729$	15.0950	+	22.3862i	0.559075	+	0.829117i
$730$		0			0
$731$	0.207676	+	1.17779i	0.00768118	+	0.0435621i
$732$		0			0
$733$	−32.2254	+	11.7291i	−1.19027	+	0.433224i	−0.859819	−	0.510599i	$-0.829424\pi$
$733$	−32.2254	+	11.7291i	−1.19027	+	0.433224i	−0.330453	+	0.943822i	$0.607202\pi$
$734$		0			0
$735$	17.4705	−	0.202874i	0.644407	−	0.00748310i
$736$		0			0
$737$	1.12601	−	0.650104i	0.0414772	−	0.0239469i
$738$		0			0
$739$	2.52982	+	1.46059i	0.0930610	+	0.0537288i	0.545808	−	0.837910i	$-0.316223\pi$
$739$	2.52982	+	1.46059i	0.0930610	+	0.0537288i	−0.452747	+	0.891639i	$0.649556\pi$
$740$		0			0
$741$	−0.857051	−	4.55091i	−0.0314845	−	0.167182i
$742$		0			0
$743$	1.76170	−	9.99111i	0.0646306	−	0.366538i	−0.935289	−	0.353884i	$-0.884861\pi$
$743$	1.76170	−	9.99111i	0.0646306	−	0.366538i	0.999920	−	0.0126544i	$-0.00402812\pi$
$744$		0			0
$745$	−22.1166	+	18.5581i	−0.810291	+	0.679915i
$746$		0			0
$747$	−0.395643	+	2.59481i	−0.0144758	+	0.0949392i
$748$		0			0
$749$	7.84301	−	21.5485i	0.286577	−	0.787365i
$750$		0			0
$751$	2.48974	−	2.96715i	0.0908518	−	0.108273i	−0.718703	−	0.695317i	$-0.755264\pi$
$751$	2.48974	−	2.96715i	0.0908518	−	0.108273i	0.809555	+	0.587044i	$0.199708\pi$
$752$		0			0
$753$	−16.0164	−	42.4640i	−0.583671	−	1.54747i
$754$		0			0
$755$	−52.2874			−1.90293
$756$		0			0
$757$	30.1039			1.09414			0.547072	−	0.837086i	$-0.315742\pi$
$757$	30.1039			1.09414			0.547072	+	0.837086i	$0.315742\pi$
$758$		0			0
$759$	−0.148925	+	0.181726i	−0.00540563	+	0.00659624i
$760$		0			0
$761$	4.84261	−	5.77120i	0.175545	−	0.209206i	−0.671097	−	0.741370i	$-0.734177\pi$
$761$	4.84261	−	5.77120i	0.175545	−	0.209206i	0.846641	+	0.532164i	$0.178621\pi$
$762$		0			0
$763$	2.86172	−	7.86251i	0.103601	−	0.284642i
$764$		0			0
$765$	1.33339	−	0.0309720i	0.0482090	−	0.00111979i
$766$		0			0
$767$	−3.38466	+	2.84007i	−0.122213	+	0.102549i
$768$		0			0
$769$	−0.0439313	+	0.249147i	−0.00158420	+	0.00898445i	−0.985590	−	0.169154i	$-0.945896\pi$
$769$	−0.0439313	+	0.249147i	−0.00158420	+	0.00898445i	0.984005	+	0.178139i	$0.0570075\pi$
$770$		0			0
$771$	25.5613	+	8.96881i	0.920566	+	0.323004i
$772$		0			0
$773$	23.6376	+	13.6472i	0.850186	+	0.490855i	0.860714	−	0.509090i	$-0.170018\pi$
$773$	23.6376	+	13.6472i	0.850186	+	0.490855i	−0.0105277	+	0.999945i	$0.503351\pi$
$774$		0			0
$775$	−4.42815	+	2.55659i	−0.159064	+	0.0918355i
$776$		0			0
$777$	1.59819	+	2.69538i	0.0573349	+	0.0966963i
$778$		0			0
$779$	−11.1971	+	4.07542i	−0.401179	+	0.146017i
$780$		0			0
$781$	−0.290817	−	1.64930i	−0.0104062	−	0.0590167i
$782$		0			0
$783$	48.0014	+	15.6004i	1.71543	+	0.557511i
$784$		0			0
$785$	32.0405	−	5.64960i	1.14357	−	0.201643i
$786$		0			0
$787$	4.61963	+	12.6923i	0.164672	+	0.452433i	0.994393	−	0.105745i	$-0.0337228\pi$
$787$	4.61963	+	12.6923i	0.164672	+	0.452433i	−0.829721	+	0.558178i	$0.811501\pi$
$788$		0			0
$789$	−11.2348	−	6.31364i	−0.399971	−	0.224772i
$790$		0			0
$791$	6.68219	+	11.5739i	0.237591	+	0.411520i
$792$		0			0
$793$	3.31549	−	5.74259i	0.117736	−	0.203925i
$794$		0			0
$795$	4.94830	+	5.75998i	0.175498	+	0.204285i
$796$		0			0
$797$	14.9580	+	2.63751i	0.529841	+	0.0934253i	0.432168	−	0.901793i	$-0.357749\pi$
$797$	14.9580	+	2.63751i	0.529841	+	0.0934253i	0.0976733	+	0.995219i	$0.468860\pi$
$798$		0			0
$799$	0.921026	+	1.09764i	0.0325836	+	0.0388316i
$800$		0			0
$801$	44.9604	−	9.00896i	1.58860	−	0.318316i
$802$		0			0
$803$	1.70009	+	0.618781i	0.0599947	+	0.0218363i
$804$		0			0
$805$	−3.38345	−	2.83905i	−0.119251	−	0.100063i
$806$		0			0
$807$	−0.419357	+	2.55117i	−0.0147621	+	0.0898056i
$808$		0			0
$809$		−	55.8195i		−	1.96251i	−0.192715	−	0.981255i	$-0.561729\pi$
$809$		−	55.8195i		−	1.96251i	0.192715	−	0.981255i	$-0.438271\pi$
$810$		0			0
$811$			42.6537i			1.49777i	0.662698	+	0.748887i	$0.269411\pi$
$811$			42.6537i			1.49777i	−0.662698	+	0.748887i	$0.730589\pi$
$812$		0			0
$813$	0.833583	−	5.07114i	0.0292350	−	0.177852i
$814$		0			0
$815$	30.9509	+	25.9709i	1.08416	+	0.909722i
$816$		0			0
$817$	−8.65919	−	3.15169i	−0.302947	−	0.110264i
$818$		0			0
$819$	6.23226	+	7.08640i	0.217773	+	0.247619i
$820$		0			0
$821$	0.0236294	+	0.0281604i	0.000824672	+	0.000982806i	0.766457	−	0.642296i	$-0.222018\pi$
$821$	0.0236294	+	0.0281604i	0.000824672	+	0.000982806i	−0.765632	+	0.643279i	$0.777574\pi$
$822$		0			0
$823$	30.0169	+	5.29279i	1.04632	+	0.184495i	0.670281	−	0.742107i	$-0.266173\pi$
$823$	30.0169	+	5.29279i	1.04632	+	0.184495i	0.376043	+	0.926602i	$0.377285\pi$
$824$		0			0
$825$	−0.109966	−	0.128004i	−0.00382852	−	0.00445652i
$826$		0			0
$827$	8.65820	−	14.9964i	0.301075	−	0.521477i	−0.675305	−	0.737539i	$-0.735988\pi$
$827$	8.65820	−	14.9964i	0.301075	−	0.521477i	0.976380	+	0.216062i	$0.0693212\pi$
$828$		0			0
$829$	17.2114	+	29.8110i	0.597776	+	1.03538i	0.993149	+	0.116857i	$0.0372820\pi$
$829$	17.2114	+	29.8110i	0.597776	+	1.03538i	−0.395373	+	0.918521i	$0.629385\pi$
$830$		0			0
$831$	−42.9997	−	24.1646i	−1.49164	−	0.838260i
$832$		0			0
$833$	−0.265044	−	0.728201i	−0.00918322	−	0.0252307i
$834$		0			0
$835$	21.2040	−	3.73884i	0.733796	−	0.129388i
$836$		0			0
$837$	−4.70016	+	33.4261i	−0.162461	+	1.15538i
$838$		0			0
$839$	2.54563	+	14.4370i	0.0878848	+	0.498419i	0.996697	+	0.0812133i	$0.0258795\pi$
$839$	2.54563	+	14.4370i	0.0878848	+	0.498419i	−0.908812	+	0.417206i	$0.863009\pi$
$840$		0			0
$841$	61.4107	−	22.3517i	2.11761	−	0.770747i
$842$		0			0
$843$	−3.17180	−	5.34929i	−0.109243	−	0.184239i
$844$		0			0
$845$	−19.7388	+	11.3962i	−0.679035	+	0.392041i
$846$		0			0
$847$	15.9377	+	9.20165i	0.547627	+	0.316173i
$848$		0			0
$849$	−14.6976	−	5.15702i	−0.504420	−	0.176988i
$850$		0			0
$851$	−0.205498	+	1.16544i	−0.00704438	+	0.0399507i
$852$		0			0
$853$	13.5707	−	11.3872i	0.464652	−	0.389889i	−0.380187	−	0.924910i	$-0.624140\pi$
$853$	13.5707	−	11.3872i	0.464652	−	0.389889i	0.844839	+	0.535020i	$0.179696\pi$
$854$		0			0
$855$	−4.93026	+	9.01675i	−0.168611	+	0.308366i
$856$		0			0
$857$	−1.68379	+	4.62617i	−0.0575171	+	0.158027i	−0.965123	−	0.261795i	$-0.915685\pi$
$857$	−1.68379	+	4.62617i	−0.0575171	+	0.158027i	0.907606	+	0.419822i	$0.137908\pi$
$858$		0			0
$859$	−17.3702	+	20.7010i	−0.592665	+	0.706310i	−0.976116	−	0.217251i	$-0.930291\pi$
$859$	−17.3702	+	20.7010i	−0.592665	+	0.706310i	0.383451	+	0.923561i	$0.374735\pi$
$860$		0			0
$861$	15.3914	−	18.7814i	0.524536	−	0.640067i
$862$		0			0
$863$	36.4862			1.24201			0.621003	−	0.783808i	$-0.286725\pi$
$863$	36.4862			1.24201			0.621003	+	0.783808i	$0.286725\pi$
$864$		0			0
$865$	49.0469			1.66764
$866$		0			0
$867$	10.3705	+	27.4950i	0.352199	+	0.933778i
$868$		0			0
$869$	0.869586	−	1.03633i	0.0294987	−	0.0351551i
$870$		0			0
$871$	6.74554	−	18.5332i	0.228564	−	0.627974i
$872$		0			0
$873$	41.4660	−	16.1925i	1.40341	−	0.548032i
$874$		0			0
$875$	−13.0069	+	10.9141i	−0.439713	+	0.368963i
$876$		0			0
$877$	−5.13319	+	29.1118i	−0.173336	+	0.983035i	0.766712	+	0.641991i	$0.221892\pi$
$877$	−5.13319	+	29.1118i	−0.173336	+	0.983035i	−0.940047	+	0.341044i	$0.889220\pi$
$878$		0			0
$879$	−6.79904	−	36.1027i	−0.229326	−	1.21771i
$880$		0			0
$881$	29.0860	+	16.7928i	0.979932	+	0.565764i	0.902250	−	0.431214i	$-0.141915\pi$
$881$	29.0860	+	16.7928i	0.979932	+	0.565764i	0.0776823	+	0.996978i	$0.475248\pi$
$882$		0			0
$883$	−13.3780	+	7.72381i	−0.450207	+	0.259927i	−0.707918	−	0.706295i	$-0.750365\pi$
$883$	−13.3780	+	7.72381i	−0.450207	+	0.259927i	0.257711	+	0.966222i	$0.417032\pi$
$884$		0			0
$885$	9.80429	−	0.113851i	0.329568	−	0.00382706i
$886$		0			0
$887$	27.4408	−	9.98765i	0.921374	−	0.335353i	0.162589	−	0.986694i	$-0.448016\pi$
$887$	27.4408	−	9.98765i	0.921374	−	0.335353i	0.758785	+	0.651341i	$0.225793\pi$
$888$		0			0
$889$	0.530462	+	3.00840i	0.0177911	+	0.100898i
$890$		0			0
$891$	−1.11283	+	0.0517253i	−0.0372812	+	0.00173286i
$892$		0			0
$893$	−10.8725	+	1.91712i	−0.363835	+	0.0641540i
$894$		0			0
$895$	−12.7937	−	35.1504i	−0.427646	−	1.17495i
$896$		0			0
$897$	0.0413834	+	3.56373i	0.00138175	+	0.118989i
$898$		0			0
$899$	31.5501	+	54.6465i	1.05226	+	1.82256i
$900$		0			0
$901$	0.168403	−	0.291683i	0.00561033	−	0.00971738i
$902$		0			0
$903$	18.4541	−	3.47537i	0.614115	−	0.115653i
$904$		0			0
$905$	−6.67633	−	1.17722i	−0.221929	−	0.0391320i
$906$		0			0
$907$	−18.4534	−	21.9919i	−0.612735	−	0.730229i	0.367068	−	0.930194i	$-0.380362\pi$
$907$	−18.4534	−	21.9919i	−0.612735	−	0.730229i	−0.979803	+	0.199965i	$0.935917\pi$
$908$		0			0
$909$	−13.1183	+	16.3923i	−0.435108	+	0.543698i
$910$		0			0
$911$	2.78935	+	1.01524i	0.0924152	+	0.0336364i	0.387814	−	0.921738i	$-0.373230\pi$
$911$	2.78935	+	1.01524i	0.0924152	+	0.0336364i	−0.295399	+	0.955374i	$0.595453\pi$
$912$		0			0
$913$	−0.0829629	−	0.0696141i	−0.00274567	−	0.00230389i
$914$		0			0
$915$	−13.7683	+	5.19307i	−0.455164	+	0.171677i
$916$		0			0
$917$			5.07033i			0.167437i
$918$		0			0
$919$		−	26.7936i		−	0.883839i	−0.897055	−	0.441919i	$-0.854298\pi$
$919$		−	26.7936i		−	0.883839i	0.897055	−	0.441919i	$-0.145702\pi$
$920$		0			0
$921$	26.1695	+	21.4460i	0.862316	+	0.706669i
$922$		0			0
$923$	−19.4605	−	16.3293i	−0.640552	−	0.537487i
$924$		0			0
$925$	−0.798716	−	0.290709i	−0.0262616	−	0.00955845i
$926$		0			0
$927$	−30.8862	+	18.8017i	−1.01444	+	0.617530i
$928$		0			0
$929$	12.9049	+	15.3795i	0.423396	+	0.504584i	0.935005	−	0.354635i	$-0.115395\pi$
$929$	12.9049	+	15.3795i	0.423396	+	0.504584i	−0.511609	+	0.859218i	$0.670950\pi$
$930$		0			0
$931$	5.88020	+	1.03684i	0.192716	+	0.0339810i
$932$		0			0
$933$	−0.907949	+	2.58767i	−0.0297249	+	0.0847166i
$934$		0			0
$935$	−0.0275156	+	0.0476585i	−0.000899858	+	0.00155860i
$936$		0			0
$937$	−22.7272	−	39.3647i	−0.742466	−	1.28599i	−0.951369	−	0.308053i	$-0.900323\pi$
$937$	−22.7272	−	39.3647i	−0.742466	−	1.28599i	0.208903	−	0.977936i	$-0.433011\pi$
$938$		0			0
$939$	32.5031	−	19.2723i	1.06070	−	0.628928i
$940$		0			0
$941$	−4.42783	−	12.1654i	−0.144343	−	0.396580i	0.846362	−	0.532609i	$-0.178788\pi$
$941$	−4.42783	−	12.1654i	−0.144343	−	0.396580i	−0.990705	+	0.136029i	$0.956566\pi$
$942$		0			0
$943$	9.03108	−	1.59242i	0.294092	−	0.0518564i
$944$		0			0
$945$	−0.729384	−	20.9294i	−0.0237269	−	0.680835i
$946$		0			0
$947$	0.502783	+	2.85142i	0.0163383	+	0.0926588i	0.991887	−	0.127127i	$-0.0405754\pi$
$947$	0.502783	+	2.85142i	0.0163383	+	0.0926588i	−0.975548	+	0.219785i	$0.929464\pi$
$948$		0			0
$949$	25.7883	−	9.38618i	0.837124	−	0.304688i
$950$		0			0
$951$	−17.3965	+	30.9564i	−0.564122	+	1.00383i
$952$		0			0
$953$	2.78951	−	1.61052i	0.0903610	−	0.0521699i	−0.454139	−	0.890931i	$-0.650053\pi$
$953$	2.78951	−	1.61052i	0.0903610	−	0.0521699i	0.544500	+	0.838761i	$0.316720\pi$
$954$		0			0
$955$	24.5611	+	14.1804i	0.794779	+	0.458866i
$956$		0			0
$957$	−1.57966	+	1.35706i	−0.0510631	+	0.0438674i
$958$		0			0
$959$	0.165113	−	0.936400i	0.00533177	−	0.0302379i
$960$		0			0
$961$	−8.57966	+	7.19919i	−0.276763	+	0.232232i
$962$		0			0
$963$	38.9017	+	13.1443i	1.25359	+	0.423570i
$964$		0			0
$965$	−10.9577	+	30.1060i	−0.352741	+	0.969148i
$966$		0			0
$967$	−33.9424	+	40.4509i	−1.09151	+	1.30081i	−0.141041	+	0.990004i	$0.545045\pi$
$967$	−33.9424	+	40.4509i	−1.09151	+	1.30081i	−0.950472	+	0.310810i	$0.899400\pi$
$968$		0			0
$969$	0.449773	+	0.0739329i	0.0144488	+	0.00237507i
$970$		0			0
$971$	−36.7234			−1.17851			−0.589255	−	0.807947i	$-0.700579\pi$
$971$	−36.7234			−1.17851			−0.589255	+	0.807947i	$0.700579\pi$
$972$		0			0
$973$	−31.9259			−1.02350
$974$		0			0
$975$	−2.52588	−	0.415200i	−0.0808931	−	0.0132970i
$976$		0			0
$977$	11.4029	−	13.5895i	0.364811	−	0.434765i	−0.552148	−	0.833746i	$-0.686192\pi$
$977$	11.4029	−	13.5895i	0.364811	−	0.434765i	0.916959	+	0.398981i	$0.130636\pi$
$978$		0			0
$979$	−0.647088	+	1.77786i	−0.0206810	+	0.0568207i
$980$		0			0
$981$	14.1943	+	4.79604i	0.453188	+	0.153126i
$982$		0			0
$983$	8.26710	−	6.93692i	0.263680	−	0.221253i	−0.501357	−	0.865241i	$-0.667166\pi$
$983$	8.26710	−	6.93692i	0.263680	−	0.221253i	0.765036	+	0.643987i	$0.222721\pi$
$984$		0			0
$985$	−2.95276	+	16.7459i	−0.0940827	+	0.533570i
$986$		0			0
$987$	17.0656	−	14.6608i	0.543204	−	0.466658i
$988$		0			0
$989$	6.14171	+	3.54592i	0.195295	+	0.112754i
$990$		0			0
$991$	−9.99579	+	5.77107i	−0.317527	+	0.183324i	−0.650290	−	0.759686i	$-0.725352\pi$
$991$	−9.99579	+	5.77107i	−0.317527	+	0.183324i	0.332763	+	0.943011i	$0.392019\pi$
$992$		0			0
$993$	19.3117	−	34.3643i	0.612838	−	1.09052i
$994$		0			0
$995$	−22.3585	+	8.13783i	−0.708812	+	0.257987i
$996$		0			0
$997$	−2.87637	−	16.3127i	−0.0910957	−	0.516629i	−0.995874	−	0.0907466i	$-0.971075\pi$
$997$	−2.87637	−	16.3127i	−0.0910957	−	0.516629i	0.904778	−	0.425883i	$-0.140036\pi$
$998$		0			0
$999$	−4.75875	+	2.97313i	−0.150560	+	0.0940656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.95.2	✓	216
4.3	odd	2	inner	864.2.bi.a.95.35	yes	216
27.2	odd	18	inner	864.2.bi.a.191.35	yes	216
108.83	even	18	inner	864.2.bi.a.191.2	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.95.2	✓	216	1.1	even	1	trivial
864.2.bi.a.95.35	yes	216	4.3	odd	2	inner
864.2.bi.a.191.2	yes	216	108.83	even	18	inner
864.2.bi.a.191.35	yes	216	27.2	odd	18	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70911 - 0.280941i) q^{3} +(-1.54632 + 1.84283i) q^{5} +(0.573007 - 1.57432i) q^{7} +(2.84214 + 0.960320i) q^{9} +O(q^{10})\)	\(q+(-1.70911 - 0.280941i) q^{3} +(-1.54632 + 1.84283i) q^{5} +(0.573007 - 1.57432i) q^{7} +(2.84214 + 0.960320i) q^{9} +(-0.0948219 + 0.0795651i) q^{11} +(-0.326045 + 1.84909i) q^{13} +(3.16056 - 2.71518i) q^{15} +(-0.160050 - 0.0924046i) q^{17} +(1.23319 - 0.711982i) q^{19} +(-1.42163 + 2.52972i) q^{21} +(-1.02980 + 0.374816i) q^{23} +(-0.136680 - 0.775152i) q^{25} +(-4.58776 - 2.43977i) q^{27} +(-9.56592 + 1.68673i) q^{29} +(-2.22181 - 6.10438i) q^{31} +(0.184415 - 0.109346i) q^{33} +(2.01516 + 3.49036i) q^{35} +(0.539935 - 0.935195i) q^{37} +(1.07673 - 3.06871i) q^{39} +(-8.24088 - 1.45309i) q^{41} +(-4.15968 - 4.95731i) q^{43} +(-6.16456 + 3.75262i) q^{45} +(-7.28562 - 2.65175i) q^{47} +(3.21215 + 2.69531i) q^{49} +(0.247583 + 0.202895i) q^{51} +1.82246i q^{53} -0.297773i q^{55} +(-2.30768 + 0.870405i) q^{57} +(1.80264 + 1.51259i) q^{59} +(-3.31861 - 1.20787i) q^{61} +(3.14043 - 3.92419i) q^{63} +(-2.90339 - 3.46013i) q^{65} +(-10.3445 - 1.82401i) q^{67} +(1.86534 - 0.351291i) q^{69} +(-6.76494 + 11.7172i) q^{71} +(-7.30803 - 12.6579i) q^{73} +(0.0158303 + 1.36322i) q^{75} +(0.0709276 + 0.194872i) q^{77} +(-10.7632 + 1.89784i) q^{79} +(7.15557 + 5.45874i) q^{81} +(0.151931 + 0.861641i) q^{83} +(0.417773 - 0.152057i) q^{85} +(16.8231 - 0.195357i) q^{87} +(13.2369 - 7.64235i) q^{89} +(2.72425 + 1.57284i) q^{91} +(2.08236 + 11.0573i) q^{93} +(-0.594840 + 3.37350i) q^{95} +(11.3669 - 9.53799i) q^{97} +(-0.345906 + 0.135076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more