LMFDB - Embedded newform 864.2.bf.a.241.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(49,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bf (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			241.20
Character	$\chi$	$=$	864.241
Dual form			864.2.bf.a.337.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.411299 + 1.68251i) q^{3} +(2.15975 + 2.57389i) q^{5} +(1.78453 - 0.649515i) q^{7} +(-2.66167 + 1.38403i) q^{9} +(-3.21944 + 3.83678i) q^{11} +(3.61424 - 0.637289i) q^{13} +(-3.44229 + 4.69244i) q^{15} +(-1.74380 - 3.02034i) q^{17} +(2.73085 + 1.57666i) q^{19} +(1.82679 + 2.73534i) q^{21} +(2.93428 + 1.06799i) q^{23} +(-1.09215 + 6.19390i) q^{25} +(-3.42338 - 3.90903i) q^{27} +(-6.61611 - 1.16660i) q^{29} +(-0.842639 - 0.306695i) q^{31} +(-7.77957 - 3.83868i) q^{33} +(5.52592 + 3.19039i) q^{35} +(6.21485 - 3.58815i) q^{37} +(2.55878 + 5.81888i) q^{39} +(-0.341649 - 1.93759i) q^{41} +(5.36405 - 6.39263i) q^{43} +(-9.31088 - 3.86169i) q^{45} +(-2.63733 + 0.959909i) q^{47} +(-2.59964 + 2.18135i) q^{49} +(4.36453 - 4.17621i) q^{51} -9.52536i q^{53} -16.8287 q^{55} +(-1.52954 + 5.24316i) q^{57} +(6.13695 + 7.31373i) q^{59} +(2.92540 + 8.03747i) q^{61} +(-3.85088 + 4.19863i) q^{63} +(9.44618 + 7.92629i) q^{65} +(-13.7512 + 2.42470i) q^{67} +(-0.590037 + 5.37621i) q^{69} +(-1.50109 - 2.59997i) q^{71} +(0.472663 - 0.818676i) q^{73} +(-10.8705 + 0.709989i) q^{75} +(-3.25314 + 8.93793i) q^{77} +(0.803209 - 4.55523i) q^{79} +(5.16894 - 7.36764i) q^{81} +(-2.12803 - 0.375229i) q^{83} +(4.00787 - 11.0115i) q^{85} +(-0.758385 - 11.6115i) q^{87} +(-7.83712 + 13.5743i) q^{89} +(6.03579 - 3.48477i) q^{91} +(0.169441 - 1.54389i) q^{93} +(1.83982 + 10.4341i) q^{95} +(1.68619 + 1.41488i) q^{97} +(3.25888 - 14.6680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) $ 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$1$

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
$3$	0.411299	+	1.68251i	0.237463	+	0.971396i
$3$	0.411299	+	1.68251i	0.237463	+	0.971396i
$4$		0			0
$5$	2.15975	+	2.57389i	0.965871	+	1.15108i	0.988482	+	0.151335i	$0.0483574\pi$
$5$	2.15975	+	2.57389i	0.965871	+	1.15108i	−0.0226118	+	0.999744i	$0.507198\pi$
$6$		0			0
$7$	1.78453	−	0.649515i	0.674489	−	0.245494i	0.0180093	−	0.999838i	$-0.494267\pi$
$7$	1.78453	−	0.649515i	0.674489	−	0.245494i	0.656479	+	0.754344i	$0.272045\pi$
$8$		0			0
$9$	−2.66167	+	1.38403i	−0.887222	+	0.461342i
$10$		0			0
$11$	−3.21944	+	3.83678i	−0.970699	+	1.15683i	0.0169036	+	0.999857i	$0.494619\pi$
$11$	−3.21944	+	3.83678i	−0.970699	+	1.15683i	−0.987602	+	0.156977i	$0.949825\pi$
$12$		0			0
$13$	3.61424	−	0.637289i	1.00241	−	0.176752i	0.351728	−	0.936102i	$-0.385594\pi$
$13$	3.61424	−	0.637289i	1.00241	−	0.176752i	0.650682	+	0.759350i	$0.274483\pi$
$14$		0			0
$15$	−3.44229	+	4.69244i	−0.888796	+	1.21158i
$16$		0			0
$17$	−1.74380	−	3.02034i	−0.422932	−	0.732541i	0.573292	−	0.819351i	$-0.305666\pi$
$17$	−1.74380	−	3.02034i	−0.422932	−	0.732541i	−0.996225	+	0.0868103i	$0.972333\pi$
$18$		0			0
$19$	2.73085	+	1.57666i	0.626501	+	0.361710i	0.779396	−	0.626532i	$-0.215526\pi$
$19$	2.73085	+	1.57666i	0.626501	+	0.361710i	−0.152895	+	0.988242i	$0.548860\pi$
$20$		0			0
$21$	1.82679	+	2.73534i	0.398638	+	0.596900i
$22$		0			0
$23$	2.93428	+	1.06799i	0.611839	+	0.222691i	0.629308	−	0.777156i	$-0.283338\pi$
$23$	2.93428	+	1.06799i	0.611839	+	0.222691i	−0.0174685	+	0.999847i	$0.505561\pi$
$24$		0			0
$25$	−1.09215	+	6.19390i	−0.218430	+	1.23878i
$26$		0			0
$27$	−3.42338	−	3.90903i	−0.658829	−	0.752293i
$28$		0			0
$29$	−6.61611	−	1.16660i	−1.22858	−	0.216632i	−0.478565	−	0.878052i	$-0.658843\pi$
$29$	−6.61611	−	1.16660i	−1.22858	−	0.216632i	−0.750015	+	0.661420i	$0.769954\pi$
$30$		0			0
$31$	−0.842639	−	0.306695i	−0.151342	−	0.0550841i	0.265238	−	0.964183i	$-0.414549\pi$
$31$	−0.842639	−	0.306695i	−0.151342	−	0.0550841i	−0.416581	+	0.909099i	$0.636772\pi$
$32$		0			0
$33$	−7.77957	−	3.83868i	−1.35425	−	0.668228i
$34$		0			0
$35$	5.52592	+	3.19039i	0.934052	+	0.539275i
$36$		0			0
$37$	6.21485	−	3.58815i	1.02172	−	0.589887i	0.107115	−	0.994247i	$-0.465839\pi$
$37$	6.21485	−	3.58815i	1.02172	−	0.589887i	0.914600	+	0.404359i	$0.132505\pi$
$38$		0			0
$39$	2.55878	+	5.81888i	0.409732	+	0.931766i
$40$		0			0
$41$	−0.341649	−	1.93759i	−0.0533567	−	0.302601i	0.946438	−	0.322887i	$-0.104653\pi$
$41$	−0.341649	−	1.93759i	−0.0533567	−	0.302601i	−0.999794	+	0.0202862i	$0.993542\pi$
$42$		0			0
$43$	5.36405	−	6.39263i	0.818010	−	0.974867i	−0.181954	−	0.983307i	$-0.558242\pi$
$43$	5.36405	−	6.39263i	0.818010	−	0.974867i	0.999964	+	0.00844018i	$0.00268662\pi$
$44$		0			0
$45$	−9.31088	−	3.86169i	−1.38798	−	0.575667i
$46$		0			0
$47$	−2.63733	+	0.959909i	−0.384694	+	0.140017i	−0.527125	−	0.849788i	$-0.676730\pi$
$47$	−2.63733	+	0.959909i	−0.384694	+	0.140017i	0.142432	+	0.989805i	$0.454508\pi$
$48$		0			0
$49$	−2.59964	+	2.18135i	−0.371377	+	0.311622i
$50$		0			0
$51$	4.36453	−	4.17621i	0.611156	−	0.584787i
$52$		0			0
$53$		−	9.52536i		−	1.30841i	−0.756318	−	0.654205i	$-0.773004\pi$
$53$		−	9.52536i		−	1.30841i	0.756318	−	0.654205i	$-0.226996\pi$
$54$		0			0
$55$	−16.8287			−2.26918
$56$		0			0
$57$	−1.52954	+	5.24316i	−0.202593	+	0.694473i
$58$		0			0
$59$	6.13695	+	7.31373i	0.798963	+	0.952167i	0.999622	−	0.0274946i	$-0.00875290\pi$
$59$	6.13695	+	7.31373i	0.798963	+	0.952167i	−0.200659	+	0.979661i	$0.564308\pi$
$60$		0			0
$61$	2.92540	+	8.03747i	0.374559	+	1.02909i	0.973577	+	0.228358i	$0.0733355\pi$
$61$	2.92540	+	8.03747i	0.374559	+	1.02909i	−0.599018	+	0.800735i	$0.704442\pi$
$62$		0			0
$63$	−3.85088	+	4.19863i	−0.485165	+	0.528978i
$64$		0			0
$65$	9.44618	+	7.92629i	1.17165	+	0.983135i
$66$		0			0
$67$	−13.7512	+	2.42470i	−1.67997	+	0.296224i	−0.930631	−	0.365960i	$-0.880741\pi$
$67$	−13.7512	+	2.42470i	−1.67997	+	0.296224i	−0.749341	+	0.662184i	$0.769630\pi$
$68$		0			0
$69$	−0.590037	+	5.37621i	−0.0710321	+	0.647220i
$70$		0			0
$71$	−1.50109	−	2.59997i	−0.178147	−	0.308560i	0.763099	−	0.646282i	$-0.223677\pi$
$71$	−1.50109	−	2.59997i	−0.178147	−	0.308560i	−0.941246	+	0.337722i	$0.890344\pi$
$72$		0			0
$73$	0.472663	−	0.818676i	0.0553210	−	0.0958187i	−0.837039	−	0.547144i	$-0.815715\pi$
$73$	0.472663	−	0.818676i	0.0553210	−	0.0958187i	0.892360	+	0.451325i	$0.149048\pi$
$74$		0			0
$75$	−10.8705	+	0.709989i	−1.25522	+	0.0819825i
$76$		0			0
$77$	−3.25314	+	8.93793i	−0.370730	+	1.01857i
$78$		0			0
$79$	0.803209	−	4.55523i	0.0903681	−	0.512503i	−0.905701	−	0.423918i	$-0.860654\pi$
$79$	0.803209	−	4.55523i	0.0903681	−	0.512503i	0.996069	−	0.0885849i	$-0.0282345\pi$
$80$		0			0
$81$	5.16894	−	7.36764i	0.574327	−	0.818626i
$82$		0			0
$83$	−2.12803	−	0.375229i	−0.233582	−	0.0411868i	0.0556319	−	0.998451i	$-0.482283\pi$
$83$	−2.12803	−	0.375229i	−0.233582	−	0.0411868i	−0.289214	+	0.957265i	$0.593394\pi$
$84$		0			0
$85$	4.00787	−	11.0115i	0.434715	−	1.19437i
$86$		0			0
$87$	−0.758385	−	11.6115i	−0.0813074	−	1.24488i
$88$		0			0
$89$	−7.83712	+	13.5743i	−0.830733	+	1.43887i	0.0667245	+	0.997771i	$0.478745\pi$
$89$	−7.83712	+	13.5743i	−0.830733	+	1.43887i	−0.897458	+	0.441101i	$0.854588\pi$
$90$		0			0
$91$	6.03579	−	3.48477i	0.632723	−	0.365303i
$92$		0			0
$93$	0.169441	−	1.54389i	0.0175703	−	0.160094i
$94$		0			0
$95$	1.83982	+	10.4341i	0.188761	+	1.07052i
$96$		0			0
$97$	1.68619	+	1.41488i	0.171207	+	0.143659i	0.724365	−	0.689417i	$-0.242133\pi$
$97$	1.68619	+	1.41488i	0.171207	+	0.143659i	−0.553158	+	0.833076i	$0.686578\pi$
$98$		0			0
$99$	3.25888	−	14.6680i	0.327529	−	1.47419i
$100$		0			0
$101$	6.12830	+	16.8374i	0.609789	+	1.67538i	0.730684	+	0.682716i	$0.239201\pi$
$101$	6.12830	+	16.8374i	0.609789	+	1.67538i	−0.120895	+	0.992665i	$0.538576\pi$
$102$		0			0
$103$	10.6973	−	8.97613i	1.05404	−	0.884444i	0.0605268	−	0.998167i	$-0.480722\pi$
$103$	10.6973	−	8.97613i	1.05404	−	0.884444i	0.993513	+	0.113723i	$0.0362775\pi$
$104$		0			0
$105$	−3.09506	+	10.6096i	−0.302047	+	1.03539i
$106$		0			0
$107$			12.3518i			1.19409i	0.802207	+	0.597046i	$0.203659\pi$
$107$			12.3518i			1.19409i	−0.802207	+	0.597046i	$0.796341\pi$
$108$		0			0
$109$			2.18468i			0.209255i	0.994511	+	0.104627i	$0.0333650\pi$
$109$			2.18468i			0.209255i	−0.994511	+	0.104627i	$0.966635\pi$
$110$		0			0
$111$	8.59324	+	8.98074i	0.815634	+	0.852414i
$112$		0			0
$113$	12.1210	−	10.1708i	1.14025	−	0.956785i	0.140805	−	0.990037i	$-0.455031\pi$
$113$	12.1210	−	10.1708i	1.14025	−	0.956785i	0.999447	+	0.0332523i	$0.0105865\pi$
$114$		0			0
$115$	3.58842	+	9.85911i	0.334622	+	0.919367i
$116$		0			0
$117$	−8.73789	+	6.69846i	−0.807818	+	0.619273i
$118$		0			0
$119$	−5.07361	−	4.25727i	−0.465097	−	0.390263i
$120$		0			0
$121$	−2.44596	−	13.8717i	−0.222360	−	1.26107i
$122$		0			0
$123$	3.11949	−	1.37176i	0.281275	−	0.123687i
$124$		0			0
$125$	−3.75209	+	2.16627i	−0.335597	+	0.193757i
$126$		0			0
$127$	5.17381	−	8.96131i	0.459102	−	0.795187i	−0.539812	−	0.841786i	$-0.681505\pi$
$127$	5.17381	−	8.96131i	0.459102	−	0.795187i	0.998914	+	0.0465982i	$0.0148381\pi$
$128$		0			0
$129$	12.9619	+	6.39578i	1.14123	+	0.563117i
$130$		0			0
$131$	3.07414	−	8.44614i	0.268589	−	0.737942i	−0.729929	−	0.683523i	$-0.760447\pi$
$131$	3.07414	−	8.44614i	0.268589	−	0.737942i	0.998518	−	0.0544195i	$-0.0173308\pi$
$132$		0			0
$133$	5.89735	+	1.03986i	0.511365	+	0.0901675i
$134$		0			0
$135$	2.66777	−	17.2539i	0.229605	−	1.48498i
$136$		0			0
$137$	2.92683	−	16.5989i	0.250056	−	1.41814i	−0.558395	−	0.829575i	$-0.688583\pi$
$137$	2.92683	−	16.5989i	0.250056	−	1.41814i	0.808451	−	0.588563i	$-0.200306\pi$
$138$		0			0
$139$	3.76833	−	10.3534i	0.319626	−	0.878164i	−0.670988	−	0.741469i	$-0.734130\pi$
$139$	3.76833	−	10.3534i	0.319626	−	0.878164i	0.990613	−	0.136695i	$-0.0436482\pi$
$140$		0			0
$141$	−2.69978	−	4.04252i	−0.227363	−	0.340441i
$142$		0			0
$143$	−9.19071	+	15.9188i	−0.768566	+	1.33120i
$144$		0			0
$145$	−11.2865	−	19.5487i	−0.937289	−	1.62343i
$146$		0			0
$147$	−4.73937	−	3.47672i	−0.390897	−	0.286755i
$148$		0			0
$149$	10.6491	−	1.87772i	0.872406	−	0.153829i	0.280518	−	0.959849i	$-0.409494\pi$
$149$	10.6491	−	1.87772i	0.872406	−	0.153829i	0.591888	+	0.806020i	$0.298383\pi$
$150$		0			0
$151$	0.489785	+	0.410979i	0.0398582	+	0.0334450i	0.662499	−	0.749063i	$-0.269496\pi$
$151$	0.489785	+	0.410979i	0.0398582	+	0.0334450i	−0.622641	+	0.782508i	$0.713940\pi$
$152$		0			0
$153$	8.82164	+	5.62569i	0.713187	+	0.454810i
$154$		0			0
$155$	−1.03049	−	2.83125i	−0.0827709	−	0.227411i
$156$		0			0
$157$	−5.93021	−	7.06735i	−0.473282	−	0.564036i	0.475602	−	0.879661i	$-0.342230\pi$
$157$	−5.93021	−	7.06735i	−0.473282	−	0.564036i	−0.948884	+	0.315625i	$0.897786\pi$
$158$		0			0
$159$	16.0265	−	3.91777i	1.27098	−	0.310699i
$160$		0			0
$161$	5.92998			0.467348
$162$		0			0
$163$		−	8.36032i		−	0.654831i	−0.944881	−	0.327415i	$-0.893822\pi$
$163$		−	8.36032i		−	0.654831i	0.944881	−	0.327415i	$-0.106178\pi$
$164$		0			0
$165$	−6.92161	−	28.3144i	−0.538847	−	2.20427i
$166$		0			0
$167$	4.77570	−	4.00729i	0.369555	−	0.310094i	−0.439030	−	0.898472i	$-0.644678\pi$
$167$	4.77570	−	4.00729i	0.369555	−	0.310094i	0.808586	+	0.588379i	$0.200234\pi$
$168$		0			0
$169$	0.440614	−	0.160370i	0.0338934	−	0.0123362i
$170$		0			0
$171$	−9.45076	−	0.416967i	−0.722717	−	0.0318863i
$172$		0			0
$173$	−5.72780	+	6.82613i	−0.435477	+	0.518981i	−0.938494	−	0.345295i	$-0.887779\pi$
$173$	−5.72780	+	6.82613i	−0.435477	+	0.518981i	0.503017	+	0.864276i	$0.332223\pi$
$174$		0			0
$175$	2.07406	+	11.7626i	0.156784	+	0.889167i
$176$		0			0
$177$	−9.78129	+	13.3336i	−0.735207	+	1.00221i
$178$		0			0
$179$	−12.5035	+	7.21893i	−0.934559	+	0.539568i	−0.888251	−	0.459359i	$-0.848079\pi$
$179$	−12.5035	+	7.21893i	−0.934559	+	0.539568i	−0.0463085	+	0.998927i	$0.514746\pi$
$180$		0			0
$181$	4.19806	+	2.42375i	0.312039	+	0.180156i	0.647839	−	0.761778i	$-0.275673\pi$
$181$	4.19806	+	2.42375i	0.312039	+	0.180156i	−0.335799	+	0.941934i	$0.609006\pi$
$182$		0			0
$183$	−12.3199	+	8.22781i	−0.910713	+	0.608217i
$184$		0			0
$185$	22.6580	+	8.24685i	1.66585	+	0.606321i
$186$		0			0
$187$	17.2024	+	3.03326i	1.25797	+	0.221814i
$188$		0			0
$189$	−8.64809	−	4.75224i	−0.629056	−	0.345674i
$190$		0			0
$191$	4.56335	−	25.8800i	0.330192	−	1.87261i	−0.140153	−	0.990130i	$-0.544759\pi$
$191$	4.56335	−	25.8800i	0.330192	−	1.87261i	0.470345	−	0.882483i	$-0.344129\pi$
$192$		0			0
$193$	3.82953	+	1.39383i	0.275655	+	0.100330i	0.476149	−	0.879365i	$-0.342032\pi$
$193$	3.82953	+	1.39383i	0.275655	+	0.100330i	−0.200494	+	0.979695i	$0.564255\pi$
$194$		0			0
$195$	−9.45084	+	19.1534i	−0.676789	+	1.37160i
$196$		0			0
$197$	8.91014	+	5.14427i	0.634821	+	0.366514i	0.782617	−	0.622504i	$-0.213884\pi$
$197$	8.91014	+	5.14427i	0.634821	+	0.366514i	−0.147796	+	0.989018i	$0.547218\pi$
$198$		0			0
$199$	−0.690545	−	1.19606i	−0.0489514	−	0.0847864i	0.840511	−	0.541794i	$-0.182255\pi$
$199$	−0.690545	−	1.19606i	−0.0489514	−	0.0847864i	−0.889463	+	0.457007i	$0.848921\pi$
$200$		0			0
$201$	−9.73541	−	22.1392i	−0.686683	−	1.56158i
$202$		0			0
$203$	−12.5644	+	2.21544i	−0.881845	+	0.155493i
$204$		0			0
$205$	4.24927	−	5.06408i	0.296782	−	0.353691i
$206$		0			0
$207$	−9.28820	+	1.21849i	−0.645574	+	0.0846906i
$208$		0			0
$209$	−14.8411	+	5.40173i	−1.02658	+	0.373645i
$210$		0			0
$211$	7.42731	+	8.85152i	0.511317	+	0.609364i	0.958505	−	0.285076i	$-0.0920189\pi$
$211$	7.42731	+	8.85152i	0.511317	+	0.609364i	−0.447188	+	0.894440i	$0.647574\pi$
$212$		0			0
$213$	3.75707	−	3.59497i	0.257430	−	0.246323i
$214$		0			0
$215$	28.0390			1.91224
$216$		0			0
$217$	−1.70292			−0.115602
$218$		0			0
$219$	1.57183	+	0.458539i	0.106215	+	0.0309852i
$220$		0			0
$221$	−8.22733	−	9.80495i	−0.553430	−	0.659552i
$222$		0			0
$223$	−2.85912	+	1.04063i	−0.191461	+	0.0696860i	−0.435971	−	0.899961i	$-0.643595\pi$
$223$	−2.85912	+	1.04063i	−0.191461	+	0.0696860i	0.244510	+	0.969647i	$0.421373\pi$
$224$		0			0
$225$	−5.66558	−	17.9977i	−0.377705	−	1.19984i
$226$		0			0
$227$	−0.641654	+	0.764693i	−0.0425881	+	0.0507545i	−0.786918	−	0.617058i	$-0.788325\pi$
$227$	−0.641654	+	0.764693i	−0.0425881	+	0.0507545i	0.744330	+	0.667812i	$0.232769\pi$
$228$		0			0
$229$	0.846018	−	0.149176i	0.0559064	−	0.00985781i	−0.145625	−	0.989340i	$-0.546519\pi$
$229$	0.846018	−	0.149176i	0.0559064	−	0.00985781i	0.201531	+	0.979482i	$0.435408\pi$
$230$		0			0
$231$	−16.3762	−	1.79728i	−1.07747	−	0.118252i
$232$		0			0
$233$	−5.17379	−	8.96127i	−0.338946	−	0.587072i	0.645288	−	0.763939i	$-0.276737\pi$
$233$	−5.17379	−	8.96127i	−0.338946	−	0.587072i	−0.984235	+	0.176867i	$0.943404\pi$
$234$		0			0
$235$	−8.16668	−	4.71503i	−0.532735	−	0.307575i
$236$		0			0
$237$	7.99456	−	0.522152i	0.519303	−	0.0339174i
$238$		0			0
$239$	11.5092	+	4.18901i	0.744469	+	0.270965i	0.686277	−	0.727341i	$-0.259244\pi$
$239$	11.5092	+	4.18901i	0.744469	+	0.270965i	0.0581928	+	0.998305i	$0.481466\pi$
$240$		0			0
$241$	−2.60278	+	14.7611i	−0.167660	+	0.950846i	0.778620	+	0.627496i	$0.215920\pi$
$241$	−2.60278	+	14.7611i	−0.167660	+	0.950846i	−0.946279	+	0.323350i	$0.895191\pi$
$242$		0			0
$243$	14.5221	+	5.66649i	0.931592	+	0.363505i
$244$		0			0
$245$	−11.2291	−	1.98000i	−0.717404	−	0.126498i
$246$		0			0
$247$	10.8748	+	3.95809i	0.691944	+	0.251847i
$248$		0			0
$249$	−0.243930	−	3.73476i	−0.0154584	−	0.236681i
$250$		0			0
$251$	13.8356	+	7.98801i	0.873298	+	0.504199i	0.868443	−	0.495789i	$-0.165121\pi$
$251$	13.8356	+	7.98801i	0.873298	+	0.504199i	0.00485525	+	0.999988i	$0.498455\pi$
$252$		0			0
$253$	−13.5444	+	7.81986i	−0.851528	+	0.491630i
$254$		0			0
$255$	20.1754	+	2.21425i	1.26343	+	0.138661i
$256$		0			0
$257$	−1.36142	−	7.72098i	−0.0849229	−	0.481622i	−0.997373	−	0.0724341i	$-0.976923\pi$
$257$	−1.36142	−	7.72098i	−0.0849229	−	0.481622i	0.912450	−	0.409187i	$-0.134188\pi$
$258$		0			0
$259$	8.76002	−	10.4398i	0.544321	−	0.648697i
$260$		0			0
$261$	19.2245	−	6.05177i	1.18997	−	0.374595i
$262$		0			0
$263$	19.3707	−	7.05037i	1.19445	−	0.434744i	0.333166	−	0.942868i	$-0.391883\pi$
$263$	19.3707	−	7.05037i	1.19445	−	0.434744i	0.861284	+	0.508124i	$0.169661\pi$
$264$		0			0
$265$	24.5173	−	20.5724i	1.50608	−	1.26375i
$266$		0			0
$267$	−26.0623	−	7.60293i	−1.59498	−	0.465292i
$268$		0			0
$269$			15.9724i			0.973852i	0.873443	+	0.486926i	$0.161882\pi$
$269$			15.9724i			0.973852i	−0.873443	+	0.486926i	$0.838118\pi$
$270$		0			0
$271$	−7.19443			−0.437031			−0.218515	−	0.975834i	$-0.570121\pi$
$271$	−7.19443			−0.437031			−0.218515	+	0.975834i	$0.570121\pi$
$272$		0			0
$273$	8.34566	+	8.72199i	0.505102	+	0.527879i
$274$		0			0
$275$	−20.2485	−	24.1313i	−1.22103	−	1.45517i
$276$		0			0
$277$	−6.45750	−	17.7418i	−0.387993	−	1.06600i	−0.967903	−	0.251322i	$-0.919135\pi$
$277$	−6.45750	−	17.7418i	−0.387993	−	1.06600i	0.579910	−	0.814680i	$-0.303088\pi$
$278$		0			0
$279$	2.66730	−	0.349913i	0.159687	−	0.0209488i
$280$		0			0
$281$	−14.1133	−	11.8425i	−0.841932	−	0.706465i	0.116066	−	0.993242i	$-0.462972\pi$
$281$	−14.1133	−	11.8425i	−0.841932	−	0.706465i	−0.957997	+	0.286777i	$0.907416\pi$
$282$		0			0
$283$	8.62324	−	1.52051i	0.512599	−	0.0903850i	0.0886349	−	0.996064i	$-0.471750\pi$
$283$	8.62324	−	1.52051i	0.512599	−	0.0903850i	0.423964	+	0.905679i	$0.360638\pi$
$284$		0			0
$285$	−16.7988	+	7.38704i	−0.995073	+	0.437571i
$286$		0			0
$287$	−1.86818	−	3.23578i	−0.110275	−	0.191002i
$288$		0			0
$289$	2.41836	−	4.18872i	0.142256	−	0.246395i
$290$		0			0
$291$	−1.68702	+	3.41897i	−0.0988950	+	0.200423i
$292$		0			0
$293$	4.67724	−	12.8506i	0.273247	−	0.750741i	−0.724840	−	0.688918i	$-0.758086\pi$
$293$	4.67724	−	12.8506i	0.273247	−	0.750741i	0.998087	−	0.0618236i	$-0.0196916\pi$
$294$		0			0
$295$	−5.57047	+	31.5917i	−0.324325	+	1.83934i
$296$		0			0
$297$	26.0195	−	0.549857i	1.50980	−	0.0319060i
$298$		0			0
$299$	11.2858	+	1.98999i	0.652675	+	0.115084i
$300$		0			0
$301$	5.42020	−	14.8919i	0.312415	−	0.858353i
$302$		0			0
$303$	−25.8085	+	17.2361i	−1.48266	+	0.990188i
$304$		0			0
$305$	−14.3695	+	24.8886i	−0.822792	+	1.42512i
$306$		0			0
$307$	−21.3532	+	12.3283i	−1.21869	+	0.703612i	−0.964638	−	0.263578i	$-0.915097\pi$
$307$	−21.3532	+	12.3283i	−1.21869	+	0.703612i	−0.254053	+	0.967190i	$0.581764\pi$
$308$		0			0
$309$	19.5022	+	14.3065i	1.10944	+	0.813867i
$310$		0			0
$311$	−0.221479	−	1.25607i	−0.0125589	−	0.0712250i	0.977884	−	0.209147i	$-0.0670688\pi$
$311$	−0.221479	−	1.25607i	−0.0125589	−	0.0712250i	−0.990443	+	0.137922i	$0.955958\pi$
$312$		0			0
$313$	15.3438	+	12.8749i	0.867280	+	0.727735i	0.963524	−	0.267623i	$-0.0862382\pi$
$313$	15.3438	+	12.8749i	0.867280	+	0.727735i	−0.0962433	+	0.995358i	$0.530683\pi$
$314$		0			0
$315$	−19.1238	−	0.843740i	−1.07750	−	0.0475393i
$316$		0			0
$317$	−2.05364	−	5.64232i	−0.115344	−	0.316904i	0.868565	−	0.495575i	$-0.165043\pi$
$317$	−2.05364	−	5.64232i	−0.115344	−	0.316904i	−0.983909	+	0.178671i	$0.942820\pi$
$318$		0			0
$319$	25.7762	−	21.6288i	1.44319	−	1.21098i
$320$		0			0
$321$	−20.7820	+	5.08027i	−1.15994	+	0.283553i
$322$		0			0
$323$		−	10.9975i		−	0.611916i
$324$		0			0
$325$			23.0823i			1.28038i
$326$		0			0
$327$	−3.67575	+	0.898558i	−0.203269	+	0.0496904i
$328$		0			0
$329$	−4.08291	+	3.42597i	−0.225098	+	0.188880i
$330$		0			0
$331$	−6.69009	−	18.3809i	−0.367721	−	1.01030i	−0.976226	−	0.216755i	$-0.930453\pi$
$331$	−6.69009	−	18.3809i	−0.367721	−	1.01030i	0.608505	−	0.793550i	$-0.291769\pi$
$332$		0			0
$333$	−11.5758	+	18.1520i	−0.634348	+	0.994722i
$334$		0			0
$335$	−35.9400	−	30.1573i	−1.96361	−	1.64767i
$336$		0			0
$337$	3.82769	+	21.7079i	0.208508	+	1.18251i	0.891824	+	0.452383i	$0.149426\pi$
$337$	3.82769	+	21.7079i	0.208508	+	1.18251i	−0.683316	+	0.730123i	$0.739463\pi$
$338$		0			0
$339$	22.0978	+	16.2105i	1.20019	+	0.880435i
$340$		0			0
$341$	3.88955	−	2.24563i	0.210631	−	0.121608i
$342$		0			0
$343$	−9.86900	+	17.0936i	−0.532876	+	0.922968i
$344$		0			0
$345$	−15.1121	+	10.0926i	−0.813609	+	0.543367i
$346$		0			0
$347$	−0.0110975	+	0.0304900i	−0.000595743	+	0.00163679i	−0.939990	−	0.341202i	$-0.889166\pi$
$347$	−0.0110975	+	0.0304900i	−0.000595743	+	0.00163679i	0.939394	+	0.342838i	$0.111388\pi$
$348$		0			0
$349$	−32.0493	−	5.65116i	−1.71556	−	0.302500i	−0.772474	−	0.635046i	$-0.780981\pi$
$349$	−32.0493	−	5.65116i	−1.71556	−	0.302500i	−0.943087	+	0.332546i	$0.892092\pi$
$350$		0			0
$351$	−14.8641	−	11.9465i	−0.793387	−	0.637657i
$352$		0			0
$353$	−0.185474	+	1.05188i	−0.00987180	+	0.0559857i	−0.989346	−	0.145585i	$-0.953494\pi$
$353$	−0.185474	+	1.05188i	−0.00987180	+	0.0559857i	0.979474	+	0.201571i	$0.0646046\pi$
$354$		0			0
$355$	3.45005	−	9.47895i	0.183110	−	0.503090i
$356$		0			0
$357$	5.07612	−	10.2874i	0.268656	−	0.544467i
$358$		0			0
$359$	−5.68242	+	9.84224i	−0.299907	+	0.519453i	−0.976114	−	0.217258i	$-0.930289\pi$
$359$	−5.68242	+	9.84224i	−0.299907	+	0.519453i	0.676208	+	0.736711i	$0.263622\pi$
$360$		0			0
$361$	−4.52830	−	7.84324i	−0.238331	−	0.412802i
$362$		0			0
$363$	22.3333	−	9.82077i	1.17219	−	0.515457i
$364$		0			0
$365$	3.12802	−	0.551554i	0.163728	−	0.0288697i
$366$		0			0
$367$	−6.59453	−	5.53346i	−0.344231	−	0.288844i	0.454237	−	0.890881i	$-0.349912\pi$
$367$	−6.59453	−	5.53346i	−0.344231	−	0.288844i	−0.798469	+	0.602036i	$0.794356\pi$
$368$		0			0
$369$	3.59103	+	4.68437i	0.186942	+	0.243858i
$370$		0			0
$371$	−6.18687	−	16.9983i	−0.321206	−	0.882507i
$372$		0			0
$373$	24.5912	+	29.3067i	1.27328	+	1.51744i	0.742318	+	0.670048i	$0.233726\pi$
$373$	24.5912	+	29.3067i	1.27328	+	1.51744i	0.530966	+	0.847393i	$0.321829\pi$
$374$		0			0
$375$	−5.18799	−	5.42193i	−0.267907	−	0.279988i
$376$		0			0
$377$	−24.6557			−1.26983
$378$		0			0
$379$			22.1132i			1.13588i	0.823071	+	0.567939i	$0.192259\pi$
$379$			22.1132i			1.13588i	−0.823071	+	0.567939i	$0.807741\pi$
$380$		0			0
$381$	17.2055	+	5.01921i	0.881462	+	0.257142i
$382$		0			0
$383$	1.25391	−	1.05215i	0.0640717	−	0.0537626i	−0.610189	−	0.792256i	$-0.708907\pi$
$383$	1.25391	−	1.05215i	0.0640717	−	0.0537626i	0.674261	+	0.738493i	$0.264462\pi$
$384$		0			0
$385$	−30.0312	+	10.9305i	−1.53053	+	0.557069i
$386$		0			0
$387$	−5.42975	+	24.4390i	−0.276010	+	1.24231i
$388$		0			0
$389$	7.37158	−	8.78511i	0.373754	−	0.445423i	−0.546079	−	0.837734i	$-0.683880\pi$
$389$	7.37158	−	8.78511i	0.373754	−	0.445423i	0.919832	+	0.392311i	$0.128324\pi$
$390$		0			0
$391$	−1.89109	−	10.7249i	−0.0956363	−	0.542380i
$392$		0			0
$393$	15.4751	+	1.69838i	0.780615	+	0.0856722i
$394$		0			0
$395$	13.4594	−	7.77079i	0.677216	−	0.390991i
$396$		0			0
$397$	−2.58188	−	1.49065i	−0.129581	−	0.0748137i	0.433808	−	0.901005i	$-0.357170\pi$
$397$	−2.58188	−	1.49065i	−0.129581	−	0.0748137i	−0.563389	+	0.826192i	$0.690503\pi$
$398$		0			0
$399$	0.675996	+	10.3500i	0.0338421	+	0.518150i
$400$		0			0
$401$	−8.85877	−	3.22433i	−0.442386	−	0.161015i	0.111217	−	0.993796i	$-0.464525\pi$
$401$	−8.85877	−	3.22433i	−0.442386	−	0.161015i	−0.553603	+	0.832781i	$0.686747\pi$
$402$		0			0
$403$	−3.24096	−	0.571468i	−0.161443	−	0.0284668i
$404$		0			0
$405$	30.1271	−	2.60797i	1.49703	−	0.129591i
$406$		0			0
$407$	−6.24142	+	35.3969i	−0.309376	+	1.75456i
$408$		0			0
$409$	−24.0695	−	8.76058i	−1.19016	−	0.433183i	−0.330380	−	0.943848i	$-0.607177\pi$
$409$	−24.0695	−	8.76058i	−1.19016	−	0.433183i	−0.859779	+	0.510665i	$0.829399\pi$
$410$		0			0
$411$	29.1316	−	1.90268i	1.43695	−	0.0938523i
$412$		0			0
$413$	15.7019	+	9.06552i	0.772642	+	0.446085i
$414$		0			0
$415$	−3.63022	−	6.28773i	−0.178201	−	0.308652i
$416$		0			0
$417$	18.9696	+	2.08191i	0.928945	+	0.101951i
$418$		0			0
$419$	2.41298	−	0.425474i	0.117882	−	0.0207858i	−0.114396	−	0.993435i	$-0.536493\pi$
$419$	2.41298	−	0.425474i	0.117882	−	0.0207858i	0.232278	+	0.972649i	$0.425382\pi$
$420$		0			0
$421$	8.35420	−	9.95615i	0.407159	−	0.485233i	−0.523030	−	0.852314i	$-0.675198\pi$
$421$	8.35420	−	9.95615i	0.407159	−	0.485233i	0.930189	+	0.367081i	$0.119643\pi$
$422$		0			0
$423$	5.69115	−	6.20509i	0.276713	−	0.301702i
$424$		0			0
$425$	20.6122	−	7.50223i	0.999838	−	0.363911i
$426$		0			0
$427$	10.4409	+	12.4430i	0.505272	+	0.602160i
$428$		0			0
$429$	−30.5636	−	8.91608i	−1.47562	−	0.430472i
$430$		0			0
$431$	−26.6357			−1.28300			−0.641499	−	0.767124i	$-0.721687\pi$
$431$	−26.6357			−1.28300			−0.641499	+	0.767124i	$0.721687\pi$
$432$		0			0
$433$	27.8356			1.33769			0.668846	−	0.743401i	$-0.266788\pi$
$433$	27.8356			1.33769			0.668846	+	0.743401i	$0.266788\pi$
$434$		0			0
$435$	28.2488	−	27.0299i	1.35442	−	1.29599i
$436$		0			0
$437$	6.32923	+	7.54288i	0.302768	+	0.360825i
$438$		0			0
$439$	−15.2198	+	5.53956i	−0.726402	+	0.264389i	−0.678641	−	0.734470i	$-0.737431\pi$
$439$	−15.2198	+	5.53956i	−0.726402	+	0.264389i	−0.0477612	+	0.998859i	$0.515209\pi$
$440$		0			0
$441$	3.90032	−	9.40401i	0.185729	−	0.447810i
$442$		0			0
$443$	−11.8910	+	14.1711i	−0.564957	+	0.673290i	−0.970588	−	0.240747i	$-0.922607\pi$
$443$	−11.8910	+	14.1711i	−0.564957	+	0.673290i	0.405631	+	0.914037i	$0.367052\pi$
$444$		0			0
$445$	−51.8650	+	9.14520i	−2.45864	+	0.433524i
$446$		0			0
$447$	7.53923	+	17.1449i	0.356593	+	0.810924i
$448$		0			0
$449$	3.76662	+	6.52398i	0.177758	+	0.307886i	0.941112	−	0.338094i	$-0.109782\pi$
$449$	3.76662	+	6.52398i	0.177758	+	0.307886i	−0.763354	+	0.645980i	$0.776449\pi$
$450$		0			0
$451$	8.53403	+	4.92713i	0.401852	+	0.232009i
$452$		0			0
$453$	−0.490027	+	0.993103i	−0.0230235	+	0.0466600i
$454$		0			0
$455$	22.0052	+	8.00925i	1.03162	+	0.375479i
$456$		0			0
$457$	−2.46966	+	14.0062i	−0.115526	+	0.655180i	0.870962	+	0.491350i	$0.163496\pi$
$457$	−2.46966	+	14.0062i	−0.115526	+	0.655180i	−0.986488	+	0.163831i	$0.947615\pi$
$458$		0			0
$459$	−5.83693	+	17.1563i	−0.272445	+	0.800788i
$460$		0			0
$461$	−12.3225	−	2.17278i	−0.573914	−	0.101197i	−0.120844	−	0.992672i	$-0.538560\pi$
$461$	−12.3225	−	2.17278i	−0.573914	−	0.101197i	−0.453070	+	0.891475i	$0.649671\pi$
$462$		0			0
$463$	5.11858	+	1.86301i	0.237881	+	0.0865815i	0.458210	−	0.888844i	$-0.348491\pi$
$463$	5.11858	+	1.86301i	0.237881	+	0.0865815i	−0.220329	+	0.975426i	$0.570713\pi$
$464$		0			0
$465$	4.33976	−	2.89830i	0.201251	−	0.134405i
$466$		0			0
$467$	6.32947	+	3.65432i	0.292893	+	0.169102i	0.639246	−	0.769003i	$-0.279247\pi$
$467$	6.32947	+	3.65432i	0.292893	+	0.169102i	−0.346353	+	0.938104i	$0.612580\pi$
$468$		0			0
$469$	−22.9645	+	13.2585i	−1.06040	+	0.612222i
$470$		0			0
$471$	9.45179	−	12.8844i	0.435515	−	0.593683i
$472$		0			0
$473$	7.25787	+	41.1614i	0.333717	+	1.89260i
$474$		0			0
$475$	−12.7482	+	15.1927i	−0.584926	+	0.697088i
$476$		0			0
$477$	13.1834	+	25.3533i	0.603624	+	1.16085i
$478$		0			0
$479$	−6.51285	+	2.37048i	−0.297580	+	0.108310i	−0.486495	−	0.873683i	$-0.661725\pi$
$479$	−6.51285	+	2.37048i	−0.297580	+	0.108310i	0.188916	+	0.981993i	$0.439503\pi$
$480$		0			0
$481$	20.1753	−	16.9291i	0.919914	−	0.771900i
$482$		0			0
$483$	2.43899	+	9.97724i	0.110978	+	0.453980i
$484$		0			0
$485$			7.39586i			0.335829i
$486$		0			0
$487$	−29.6823			−1.34503			−0.672517	−	0.740081i	$-0.734787\pi$
$487$	−29.6823			−1.34503			−0.672517	+	0.740081i	$0.734787\pi$
$488$		0			0
$489$	14.0663	−	3.43859i	0.636100	−	0.155498i
$490$		0			0
$491$	−5.65695	−	6.74169i	−0.255295	−	0.304248i	0.623140	−	0.782110i	$-0.285856\pi$
$491$	−5.65695	−	6.74169i	−0.255295	−	0.304248i	−0.878435	+	0.477862i	$0.841412\pi$
$492$		0			0
$493$	8.01361	+	22.0172i	0.360915	+	0.991606i
$494$		0			0
$495$	44.7923	−	23.2913i	2.01326	−	1.04687i
$496$		0			0
$497$	−4.36747	−	3.66474i	−0.195908	−	0.164386i
$498$		0			0
$499$	−14.6580	+	2.58460i	−0.656181	+	0.115702i	−0.491819	−	0.870698i	$-0.663668\pi$
$499$	−14.6580	+	2.58460i	−0.656181	+	0.115702i	−0.164362	+	0.986400i	$0.552557\pi$
$500$		0			0
$501$	8.70654	+	6.38697i	0.388980	+	0.285349i
$502$		0			0
$503$	5.25851	+	9.10801i	0.234465	+	0.406106i	0.959117	−	0.283009i	$-0.0913327\pi$
$503$	5.25851	+	9.10801i	0.234465	+	0.406106i	−0.724652	+	0.689115i	$0.757999\pi$
$504$		0			0
$505$	−30.1020	+	52.1381i	−1.33952	+	2.32012i
$506$		0			0
$507$	0.451049	+	0.675377i	0.0200318	+	0.0299945i
$508$		0			0
$509$	8.68462	−	23.8608i	0.384939	−	1.05761i	−0.584310	−	0.811531i	$-0.698635\pi$
$509$	8.68462	−	23.8608i	0.384939	−	1.05761i	0.969249	−	0.246081i	$-0.0791430\pi$
$510$		0			0
$511$	0.311738	−	1.76795i	0.0137905	−	0.0782096i
$512$		0			0
$513$	−3.18553	−	16.0725i	−0.140645	−	0.709617i
$514$		0			0
$515$	46.2072	+	8.14757i	2.03613	+	0.359025i
$516$		0			0
$517$	4.80776	−	13.2092i	0.211445	−	0.580941i
$518$		0			0
$519$	−13.8409	−	6.82949i	−0.607546	−	0.299782i
$520$		0			0
$521$	−5.54892	+	9.61101i	−0.243103	+	0.421066i	−0.961596	−	0.274467i	$-0.911498\pi$
$521$	−5.54892	+	9.61101i	−0.243103	+	0.421066i	0.718494	+	0.695533i	$0.244832\pi$
$522$		0			0
$523$	−21.2339	+	12.2594i	−0.928493	+	0.536066i	−0.886335	−	0.463045i	$-0.846757\pi$
$523$	−21.2339	+	12.2594i	−0.928493	+	0.536066i	−0.0421586	+	0.999111i	$0.513423\pi$
$524$		0			0
$525$	−18.9376	+	8.32755i	−0.826503	+	0.363444i
$526$		0			0
$527$	0.543064	+	3.07987i	0.0236563	+	0.134161i
$528$		0			0
$529$	−10.1496	−	8.51656i	−0.441289	−	0.370285i
$530$		0			0
$531$	−26.4569	−	10.9730i	−1.14813	−	0.476188i
$532$		0			0
$533$	−2.46961	−	6.78519i	−0.106971	−	0.293899i
$534$		0			0
$535$	−31.7922	+	26.6768i	−1.37450	+	1.15334i
$536$		0			0
$537$	−17.2886	−	18.0682i	−0.746058	−	0.779700i
$538$		0			0
$539$		−	16.9970i		−	0.732112i
$540$		0			0
$541$			10.1117i			0.434737i	0.976090	+	0.217369i	$0.0697474\pi$
$541$			10.1117i			0.434737i	−0.976090	+	0.217369i	$0.930253\pi$
$542$		0			0
$543$	−2.35132	+	8.06015i	−0.100905	+	0.345894i
$544$		0			0
$545$	−5.62314	+	4.71838i	−0.240869	+	0.202113i
$546$		0			0
$547$	9.82775	+	27.0015i	0.420204	+	1.15450i	0.951590	+	0.307371i	$0.0994493\pi$
$547$	9.82775	+	27.0015i	0.420204	+	1.15450i	−0.531386	+	0.847130i	$0.678328\pi$
$548$		0			0
$549$	−18.9105	−	17.3442i	−0.807081	−	0.740234i
$550$		0			0
$551$	−16.2283	−	13.6172i	−0.691348	−	0.580110i
$552$		0			0
$553$	−1.52534	−	8.65063i	−0.0648640	−	0.367862i
$554$		0			0
$555$	−4.55617	+	41.5143i	−0.193399	+	1.76218i
$556$		0			0
$557$	−10.4290	+	6.02119i	−0.441891	+	0.255126i	−0.704400	−	0.709804i	$-0.748784\pi$
$557$	−10.4290	+	6.02119i	−0.441891	+	0.255126i	0.262508	+	0.964930i	$0.415450\pi$
$558$		0			0
$559$	15.3130	−	26.5230i	0.647673	−	1.12180i
$560$		0			0
$561$	1.97187	+	30.1908i	0.0832523	+	1.27466i
$562$		0			0
$563$	−1.52700	+	4.19539i	−0.0643553	+	0.176815i	−0.967702	−	0.252096i	$-0.918880\pi$
$563$	−1.52700	+	4.19539i	−0.0643553	+	0.176815i	0.903347	+	0.428910i	$0.141102\pi$
$564$		0			0
$565$	52.3569	+	9.23194i	2.20267	+	0.388390i
$566$		0			0
$567$	4.43873	−	16.5051i	0.186409	−	0.693148i
$568$		0			0
$569$	5.31792	−	30.1594i	0.222939	−	1.26435i	−0.643648	−	0.765322i	$-0.722580\pi$
$569$	5.31792	−	30.1594i	0.222939	−	1.26435i	0.866586	−	0.499027i	$-0.166309\pi$
$570$		0			0
$571$	4.43557	−	12.1866i	0.185623	−	0.509994i	−0.811621	−	0.584184i	$-0.801415\pi$
$571$	4.43557	−	12.1866i	0.185623	−	0.509994i	0.997244	+	0.0741895i	$0.0236370\pi$
$572$		0			0
$573$	45.4202	−	2.96655i	1.89746	−	0.123929i
$574$		0			0
$575$	−9.81971	+	17.0082i	−0.409510	+	0.709292i
$576$		0			0
$577$	−9.34815	−	16.1915i	−0.389169	−	0.674060i	0.603169	−	0.797613i	$-0.293904\pi$
$577$	−9.34815	−	16.1915i	−0.389169	−	0.674060i	−0.992338	+	0.123553i	$0.960571\pi$
$578$		0			0
$579$	−0.770057	+	7.01649i	−0.0320025	+	0.291595i
$580$		0			0
$581$	−4.04125	+	0.712582i	−0.167659	+	0.0295629i
$582$		0			0
$583$	36.5468	+	30.6664i	1.51361	+	1.27007i
$584$		0			0
$585$	−36.1128	−	8.02337i	−1.49308	−	0.331726i
$586$		0			0
$587$	−9.91990	−	27.2547i	−0.409438	−	1.12492i	−0.957487	−	0.288475i	$-0.906852\pi$
$587$	−9.91990	−	27.2547i	−0.409438	−	1.12492i	0.548049	−	0.836446i	$-0.315371\pi$
$588$		0			0
$589$	−1.81757	−	2.16609i	−0.0748916	−	0.0892523i
$590$		0			0
$591$	−4.99055	+	17.1072i	−0.205284	+	0.703697i
$592$		0			0
$593$	12.4895			0.512883			0.256441	−	0.966560i	$-0.417450\pi$
$593$	12.4895			0.512883			0.256441	+	0.966560i	$0.417450\pi$
$594$		0			0
$595$		−	22.2536i		−	0.912308i
$596$		0			0
$597$	1.72836	−	1.65379i	0.0707370	−	0.0676849i
$598$		0			0
$599$	−7.49705	+	6.29078i	−0.306321	+	0.257034i	−0.782970	−	0.622060i	$-0.786296\pi$
$599$	−7.49705	+	6.29078i	−0.306321	+	0.257034i	0.476648	+	0.879094i	$0.341852\pi$
$600$		0			0
$601$	27.8247	−	10.1274i	1.13499	−	0.413103i	0.294890	−	0.955531i	$-0.404717\pi$
$601$	27.8247	−	10.1274i	1.13499	−	0.413103i	0.840102	+	0.542428i	$0.182495\pi$
$602$		0			0
$603$	33.2452	−	25.4857i	1.35385	−	1.03786i
$604$		0			0
$605$	30.4217	−	36.2551i	1.23682	−	1.47398i
$606$		0			0
$607$	−1.41051	−	7.99939i	−0.0572507	−	0.324685i	0.942709	−	0.333615i	$-0.108269\pi$
$607$	−1.41051	−	7.99939i	−0.0572507	−	0.324685i	−0.999960	+	0.00892998i	$0.997157\pi$
$608$		0			0
$609$	−8.89519	−	20.2284i	−0.360451	−	0.819698i
$610$		0			0
$611$	−8.92020	+	5.15008i	−0.360873	+	0.208350i
$612$		0			0
$613$	−10.1533	−	5.86202i	−0.410088	−	0.236765i	0.280739	−	0.959784i	$-0.409420\pi$
$613$	−10.1533	−	5.86202i	−0.410088	−	0.236765i	−0.690828	+	0.723019i	$0.742754\pi$
$614$		0			0
$615$	10.2681	+	5.06658i	0.414049	+	0.204304i
$616$		0			0
$617$	−1.24227	−	0.452149i	−0.0500118	−	0.0182028i	0.316893	−	0.948461i	$-0.397360\pi$
$617$	−1.24227	−	0.452149i	−0.0500118	−	0.0182028i	−0.366905	+	0.930258i	$0.619583\pi$
$618$		0			0
$619$	−25.4782	−	4.49249i	−1.02405	−	0.180568i	−0.363695	−	0.931518i	$-0.618485\pi$
$619$	−25.4782	−	4.49249i	−1.02405	−	0.180568i	−0.660359	+	0.750950i	$0.729596\pi$
$620$		0			0
$621$	−5.87033	−	15.1263i	−0.235568	−	0.606998i
$622$		0			0
$623$	−5.16886	+	29.3141i	−0.207086	+	1.17444i
$624$		0			0
$625$	15.8714	+	5.77673i	0.634858	+	0.231069i
$626$		0			0
$627$	−15.1926	−	22.7486i	−0.606733	−	0.908491i
$628$		0			0
$629$	−21.6749	−	12.5140i	−0.864233	−	0.498965i
$630$		0			0
$631$	6.70635	+	11.6157i	0.266976	+	0.462415i	0.968079	−	0.250644i	$-0.0806424\pi$
$631$	6.70635	+	11.6157i	0.266976	+	0.462415i	−0.701104	+	0.713059i	$0.747309\pi$
$632$		0			0
$633$	−11.8379	+	16.1371i	−0.470515	+	0.641393i
$634$		0			0
$635$	34.2396	−	6.03736i	1.35876	−	0.239585i
$636$		0			0
$637$	−8.00557	+	9.54067i	−0.317192	+	0.378015i
$638$		0			0
$639$	7.59384	+	4.84270i	0.300408	+	0.191574i
$640$		0			0
$641$	−30.4904	+	11.0976i	−1.20430	+	0.438328i	−0.864722	−	0.502251i	$-0.832505\pi$
$641$	−30.4904	+	11.0976i	−1.20430	+	0.438328i	−0.339575	+	0.940579i	$0.610283\pi$
$642$		0			0
$643$	−17.3052	−	20.6235i	−0.682449	−	0.813312i	0.307971	−	0.951396i	$-0.400350\pi$
$643$	−17.3052	−	20.6235i	−0.682449	−	0.813312i	−0.990420	+	0.138084i	$0.955906\pi$
$644$		0			0
$645$	11.5324	+	47.1758i	0.454087	+	1.85755i
$646$		0			0
$647$	−25.1491			−0.988713			−0.494356	−	0.869259i	$-0.664596\pi$
$647$	−25.1491			−0.988713			−0.494356	+	0.869259i	$0.664596\pi$
$648$		0			0
$649$	−47.8188			−1.87705
$650$		0			0
$651$	−0.700407	−	2.86517i	−0.0274511	−	0.112295i
$652$		0			0
$653$	−13.3995	−	15.9689i	−0.524363	−	0.624912i	0.437243	−	0.899343i	$-0.355955\pi$
$653$	−13.3995	−	15.9689i	−0.524363	−	0.624912i	−0.961607	+	0.274431i	$0.911510\pi$
$654$		0			0
$655$	28.3788	−	10.3291i	1.10885	−	0.403589i
$656$		0			0
$657$	−0.125002	+	2.83322i	−0.00487678	+	0.110534i
$658$		0			0
$659$	−18.1622	+	21.6448i	−0.707497	+	0.843162i	−0.993353	−	0.115110i	$-0.963278\pi$
$659$	−18.1622	+	21.6448i	−0.707497	+	0.843162i	0.285856	+	0.958273i	$0.407722\pi$
$660$		0			0
$661$	−37.0880	+	6.53962i	−1.44256	+	0.254362i	−0.839510	−	0.543344i	$-0.817158\pi$
$661$	−37.0880	+	6.53962i	−1.44256	+	0.254362i	−0.603046	+	0.797706i	$0.706047\pi$
$662$		0			0
$663$	13.1130	−	17.8753i	0.509267	−	0.694220i
$664$		0			0
$665$	10.0603	+	17.4250i	0.390123	+	0.675712i
$666$		0			0
$667$	−18.1676	−	10.4891i	−0.703452	−	0.406138i
$668$		0			0
$669$	−2.92682	−	4.38248i	−0.113158	−	0.169436i
$670$		0			0
$671$	−40.2562	−	14.6521i	−1.55407	−	0.565636i
$672$		0			0
$673$	0.887037	−	5.03064i	0.0341928	−	0.193917i	−0.962927	−	0.269763i	$-0.913055\pi$
$673$	0.887037	−	5.03064i	0.0341928	−	0.193917i	0.997120	+	0.0758462i	$0.0241658\pi$
$674$		0			0
$675$	27.9510	−	16.9348i	1.07583	−	0.651821i
$676$		0			0
$677$	−29.3482	−	5.17487i	−1.12794	−	0.198887i	−0.421617	−	0.906774i	$-0.638537\pi$
$677$	−29.3482	−	5.17487i	−1.12794	−	0.198887i	−0.706325	+	0.707888i	$0.749648\pi$
$678$		0			0
$679$	3.92804	+	1.42969i	0.150744	+	0.0548665i
$680$		0			0
$681$	−1.55051	−	0.765070i	−0.0594158	−	0.0293176i
$682$		0			0
$683$	−41.0964	−	23.7270i	−1.57251	−	0.907889i	−0.995860	−	0.0908981i	$-0.971026\pi$
$683$	−41.0964	−	23.7270i	−1.57251	−	0.907889i	−0.576650	−	0.816991i	$-0.695640\pi$
$684$		0			0
$685$	49.0450	−	28.3161i	1.87391	−	1.08190i
$686$		0			0
$687$	0.598956	+	1.36208i	0.0228516	+	0.0519664i
$688$		0			0
$689$	−6.07041	−	34.4270i	−0.231264	−	1.31156i
$690$		0			0
$691$	−19.5742	+	23.3276i	−0.744637	+	0.887424i	−0.996773	−	0.0802677i	$-0.974422\pi$
$691$	−19.5742	+	23.3276i	−0.744637	+	0.887424i	0.252136	+	0.967692i	$0.418867\pi$
$692$		0			0
$693$	−3.71156	−	28.2922i	−0.140990	−	1.07473i
$694$		0			0
$695$	34.7872	−	12.6615i	1.31955	−	0.480278i
$696$		0			0
$697$	−5.25642	+	4.41066i	−0.199101	+	0.167066i
$698$		0			0
$699$	12.9494	−	12.3907i	0.489793	−	0.468659i
$700$		0			0
$701$		−	22.9653i		−	0.867386i	−0.901061	−	0.433693i	$-0.857210\pi$
$701$		−	22.9653i		−	0.867386i	0.901061	−	0.433693i	$-0.142790\pi$
$702$		0			0
$703$	22.6291			0.853473
$704$		0			0
$705$	4.57414	−	15.6798i	0.172272	−	0.590535i
$706$		0			0
$707$	21.8723	+	26.0664i	0.822591	+	0.980326i
$708$		0			0
$709$	−12.4178	−	34.1176i	−0.466361	−	1.28132i	−0.920625	−	0.390448i	$-0.872320\pi$
$709$	−12.4178	−	34.1176i	−0.466361	−	1.28132i	0.454264	−	0.890867i	$-0.349902\pi$
$710$		0			0
$711$	4.16668	+	13.2362i	0.156263	+	0.496395i
$712$		0			0
$713$	−2.14499	−	1.79986i	−0.0803305	−	0.0674053i
$714$		0			0
$715$	−60.8229	+	10.7247i	−2.27465	+	0.401082i
$716$		0			0
$717$	−2.31432	+	21.0873i	−0.0864299	+	0.787519i
$718$		0			0
$719$	−13.7419	−	23.8016i	−0.512485	−	0.887651i	−0.999895	−	0.0144775i	$-0.995392\pi$
$719$	−13.7419	−	23.8016i	−0.512485	−	0.887651i	0.487410	−	0.873173i	$-0.337942\pi$
$720$		0			0
$721$	13.2596	−	22.9662i	0.493812	−	0.855308i
$722$		0			0
$723$	−25.9062	+	1.69202i	−0.963462	+	0.0629270i
$724$		0			0
$725$	14.4516	−	39.7054i	0.536719	−	1.47462i
$726$		0			0
$727$	0.612001	−	3.47083i	0.0226979	−	0.128726i	−0.971353	−	0.237640i	$-0.923626\pi$
$727$	0.612001	−	3.47083i	0.0226979	−	0.128726i	0.994051	+	0.108914i	$0.0347373\pi$
$728$		0			0
$729$	−3.56100	+	26.7641i	−0.131889	+	0.991265i
$730$		0			0
$731$	−28.6617	−	5.05384i	−1.06009	−	0.186923i
$732$		0			0
$733$	4.83027	−	13.2711i	0.178410	−	0.490178i	−0.817963	−	0.575271i	$-0.804897\pi$
$733$	4.83027	−	13.2711i	0.178410	−	0.490178i	0.996373	+	0.0850933i	$0.0271188\pi$
$734$		0			0
$735$	−1.28716	−	19.7075i	−0.0474778	−	0.726922i
$736$		0			0
$737$	34.9680	−	60.5664i	1.28806	−	2.23099i
$738$		0			0
$739$	2.52352	−	1.45695i	0.0928291	−	0.0535949i	−0.452867	−	0.891578i	$-0.649599\pi$
$739$	2.52352	−	1.45695i	0.0928291	−	0.0535949i	0.545696	+	0.837983i	$0.316265\pi$
$740$		0			0
$741$	−2.18674	+	19.9248i	−0.0803319	+	0.731956i
$742$		0			0
$743$	−0.918280	−	5.20783i	−0.0336884	−	0.191057i	0.963319	−	0.268358i	$-0.0864809\pi$
$743$	−0.918280	−	5.20783i	−0.0336884	−	0.191057i	−0.997008	+	0.0773010i	$0.975370\pi$
$744$		0			0
$745$	27.8324	+	23.3542i	1.01970	+	0.855631i
$746$		0			0
$747$	6.18344	−	1.94652i	0.226240	−	0.0712193i
$748$		0			0
$749$	8.02267	+	22.0421i	0.293142	+	0.805401i
$750$		0			0
$751$	27.0071	−	22.6616i	0.985502	−	0.826935i	0.000591865	−	1.00000i	$-0.499812\pi$
$751$	27.0071	−	22.6616i	0.985502	−	0.826935i	0.984910	+	0.173065i	$0.0553672\pi$
$752$		0			0
$753$	−7.74931	+	26.5640i	−0.282401	+	0.968047i
$754$		0			0
$755$			2.14827i			0.0781834i
$756$		0			0
$757$		−	38.9874i		−	1.41702i	−0.705700	−	0.708511i	$-0.749367\pi$
$757$		−	38.9874i		−	1.41702i	0.705700	−	0.708511i	$-0.250633\pi$
$758$		0			0
$759$	−18.7278	−	19.5722i	−0.679775	−	0.710428i
$760$		0			0
$761$	31.7399	−	26.6329i	1.15057	−	0.965443i	0.150837	−	0.988559i	$-0.451803\pi$
$761$	31.7399	−	26.6329i	1.15057	−	0.965443i	0.999733	+	0.0231155i	$0.00735856\pi$
$762$		0			0
$763$	1.41899	+	3.89863i	0.0513708	+	0.141140i
$764$		0			0
$765$	4.57264	+	34.8560i	0.165324	+	1.26022i
$766$		0			0
$767$	26.8414	+	22.5226i	0.969186	+	0.813244i
$768$		0			0
$769$	8.75977	+	49.6791i	0.315886	+	1.79148i	0.567210	+	0.823573i	$0.308023\pi$
$769$	8.75977	+	49.6791i	0.315886	+	1.79148i	−0.251325	+	0.967903i	$0.580866\pi$
$770$		0			0
$771$	12.4307	−	5.46622i	0.447679	−	0.196861i
$772$		0			0
$773$	26.2565	−	15.1592i	0.944379	−	0.545238i	0.0530488	−	0.998592i	$-0.483106\pi$
$773$	26.2565	−	15.1592i	0.944379	−	0.545238i	0.891330	+	0.453354i	$0.149773\pi$
$774$		0			0
$775$	2.81993	−	4.88427i	0.101295	−	0.175448i
$776$		0			0
$777$	21.1680	+	10.4449i	0.759398	+	0.374710i
$778$		0			0
$779$	2.12192	−	5.82994i	0.0760258	−	0.208879i
$780$		0			0
$781$	14.8082	+	2.61109i	0.529879	+	0.0934320i
$782$		0			0
$783$	18.0892	+	29.8563i	0.646454	+	1.06698i
$784$		0			0
$785$	5.38281	−	30.5275i	0.192121	−	1.08957i
$786$		0			0
$787$	9.23473	−	25.3722i	0.329182	−	0.904421i	−0.659137	−	0.752023i	$-0.729078\pi$
$787$	9.23473	−	25.3722i	0.329182	−	0.904421i	0.988319	−	0.152398i	$-0.0486996\pi$
$788$		0			0
$789$	19.8295	+	29.6916i	0.705947	+	1.05705i
$790$		0			0
$791$	15.0243	−	26.0228i	0.534202	−	0.925265i
$792$		0			0
$793$	15.6953	+	27.1851i	0.557356	+	0.965370i
$794$		0			0
$795$	44.6972	+	32.7891i	1.58525	+	1.16291i
$796$		0			0
$797$	−52.0759	+	9.18239i	−1.84462	+	0.325257i	−0.983186	−	0.182608i	$-0.941546\pi$
$797$	−52.0759	+	9.18239i	−1.84462	+	0.325257i	−0.861437	+	0.507864i	$0.830435\pi$
$798$		0			0
$799$	7.49821	+	6.29175i	0.265268	+	0.222586i
$800$		0			0
$801$	2.07262	−	46.9770i	0.0732326	−	1.65985i
$802$		0			0
$803$	1.61937	+	4.44918i	0.0571463	+	0.157008i
$804$		0			0
$805$	12.8073	+	15.2631i	0.451398	+	0.537955i
$806$		0			0
$807$	−26.8736	+	6.56941i	−0.945996	+	0.231254i
$808$		0			0
$809$	−18.3017			−0.643453			−0.321727	−	0.946833i	$-0.604263\pi$
$809$	−18.3017			−0.643453			−0.321727	+	0.946833i	$0.604263\pi$
$810$		0			0
$811$			34.2759i			1.20359i	0.798650	+	0.601795i	$0.205548\pi$
$811$			34.2759i			1.20359i	−0.798650	+	0.601795i	$0.794452\pi$
$812$		0			0
$813$	−2.95906	−	12.1047i	−0.103779	−	0.424530i
$814$		0			0
$815$	21.5186	−	18.0562i	0.753762	−	0.632482i
$816$		0			0
$817$	24.7274	−	9.00005i	0.865103	−	0.314872i
$818$		0			0
$819$	−11.2423	+	17.6290i	−0.392836	+	0.616007i
$820$		0			0
$821$	−16.1380	+	19.2325i	−0.563221	+	0.671220i	−0.970225	−	0.242206i	$-0.922129\pi$
$821$	−16.1380	+	19.2325i	−0.563221	+	0.671220i	0.407004	+	0.913426i	$0.366573\pi$
$822$		0			0
$823$	5.65012	+	32.0434i	0.196951	+	1.11696i	0.909613	+	0.415456i	$0.136378\pi$
$823$	5.65012	+	32.0434i	0.196951	+	1.11696i	−0.712662	+	0.701507i	$0.752511\pi$
$824$		0			0
$825$	32.2729	−	43.9935i	1.12360	−	1.53166i
$826$		0			0
$827$	39.6695	−	22.9032i	1.37944	−	0.796423i	0.387352	−	0.921932i	$-0.373390\pi$
$827$	39.6695	−	22.9032i	1.37944	−	0.796423i	0.992092	+	0.125509i	$0.0400565\pi$
$828$		0			0
$829$	17.0001	+	9.81500i	0.590437	+	0.340889i	0.765270	−	0.643709i	$-0.222605\pi$
$829$	17.0001	+	9.81500i	0.590437	+	0.340889i	−0.174833	+	0.984598i	$0.555939\pi$
$830$		0			0
$831$	27.1948	−	18.1620i	0.943377	−	0.630032i
$832$		0			0
$833$	11.1217	+	4.04796i	0.385343	+	0.140253i
$834$		0			0
$835$	20.6287	+	3.63739i	0.713885	+	0.125877i
$836$		0			0
$837$	1.68579	+	4.34383i	0.0582694	+	0.150145i
$838$		0			0
$839$	8.40287	−	47.6550i	0.290099	−	1.64523i	−0.396381	−	0.918086i	$-0.629734\pi$
$839$	8.40287	−	47.6550i	0.290099	−	1.64523i	0.686480	−	0.727149i	$-0.259155\pi$
$840$		0			0
$841$	15.1609	+	5.51810i	0.522788	+	0.190279i
$842$		0			0
$843$	14.1203	−	28.6166i	0.486329	−	0.985609i
$844$		0			0
$845$	1.36439	+	0.787733i	0.0469366	+	0.0270989i
$846$		0			0
$847$	−13.3748	−	23.1658i	−0.459563	−	0.795987i
$848$		0			0
$849$	6.10500	+	13.8833i	0.209523	+	0.476473i
$850$		0			0
$851$	22.0682	−	3.89122i	0.756488	−	0.133389i
$852$		0			0
$853$	−30.1220	+	35.8980i	−1.03136	+	1.22912i	−0.0583624	+	0.998295i	$0.518588\pi$
$853$	−30.1220	+	35.8980i	−1.03136	+	1.22912i	−0.972995	+	0.230828i	$0.925857\pi$
$854$		0			0
$855$	−19.3381	−	25.2258i	−0.661348	−	0.862703i
$856$		0			0
$857$	−5.93538	+	2.16030i	−0.202749	+	0.0737946i	−0.441399	−	0.897311i	$-0.645517\pi$
$857$	−5.93538	+	2.16030i	−0.202749	+	0.0737946i	0.238650	+	0.971106i	$0.423295\pi$
$858$		0			0
$859$	19.3877	+	23.1054i	0.661501	+	0.788346i	0.987600	−	0.156990i	$-0.0501789\pi$
$859$	19.3877	+	23.1054i	0.661501	+	0.788346i	−0.326100	+	0.945335i	$0.605734\pi$
$860$		0			0
$861$	4.67584	−	4.47410i	0.159352	−	0.152477i
$862$		0			0
$863$	−48.6885			−1.65737			−0.828687	−	0.559712i	$-0.810912\pi$
$863$	−48.6885			−1.65737			−0.828687	+	0.559712i	$0.810912\pi$
$864$		0			0
$865$	−29.9404			−1.01800
$866$		0			0
$867$	8.04221	+	2.34609i	0.273128	+	0.0796774i
$868$		0			0
$869$	14.8915	+	17.7470i	0.505161	+	0.602027i
$870$		0			0
$871$	−48.1548	+	17.5269i	−1.63166	+	0.593877i
$872$		0			0
$873$	−6.44631	−	1.43221i	−0.218174	−	0.0484730i
$874$		0			0
$875$	−5.28869	+	6.30281i	−0.178790	+	0.213074i
$876$		0			0
$877$	−34.7601	+	6.12915i	−1.17377	+	0.206967i	−0.726328	−	0.687348i	$-0.758775\pi$
$877$	−34.7601	+	6.12915i	−1.17377	+	0.206967i	−0.447438	+	0.894315i	$0.647664\pi$
$878$		0			0
$879$	23.5450	+	2.58406i	0.794154	+	0.0871581i
$880$		0			0
$881$	7.22906	+	12.5211i	0.243553	+	0.421847i	0.961724	−	0.274020i	$-0.0883536\pi$
$881$	7.22906	+	12.5211i	0.243553	+	0.421847i	−0.718171	+	0.695867i	$0.755020\pi$
$882$		0			0
$883$	30.6193	+	17.6781i	1.03042	+	0.594915i	0.917106	−	0.398644i	$-0.130519\pi$
$883$	30.6193	+	17.6781i	1.03042	+	0.594915i	0.113317	+	0.993559i	$0.463852\pi$
$884$		0			0
$885$	−55.4444	+	3.62126i	−1.86374	+	0.121727i
$886$		0			0
$887$	33.6657	+	12.2533i	1.13038	+	0.411426i	0.838432	−	0.545007i	$-0.183473\pi$
$887$	33.6657	+	12.2533i	1.13038	+	0.411426i	0.291952	+	0.956433i	$0.405695\pi$
$888$		0			0
$889$	3.41231	−	19.3522i	0.114445	−	0.649051i
$890$		0			0
$891$	11.6269	+	43.5518i	0.389516	+	1.45904i
$892$		0			0
$893$	−8.71560	−	1.53680i	−0.291656	−	0.0514269i
$894$		0			0
$895$	−45.5853	−	16.5917i	−1.52375	−	0.554599i
$896$		0			0
$897$	1.29366	+	19.8070i	0.0431940	+	0.661335i
$898$		0			0
$899$	5.21720	+	3.01215i	0.174003	+	0.100461i
$900$		0			0
$901$	−28.7699	+	16.6103i	−0.958463	+	0.553369i
$902$		0			0
$903$	27.2850	+	2.99452i	0.907988	+	0.0996514i
$904$		0			0
$905$	2.82829	+	16.0401i	0.0940157	+	0.533189i
$906$		0			0
$907$	−5.65021	+	6.73365i	−0.187612	+	0.223587i	−0.851649	−	0.524112i	$-0.824397\pi$
$907$	−5.65021	+	6.73365i	−0.187612	+	0.223587i	0.664037	+	0.747700i	$0.268842\pi$
$908$		0			0
$909$	−39.6149	−	36.3337i	−1.31394	−	1.20511i
$910$		0			0
$911$	−13.4129	+	4.88190i	−0.444389	+	0.161744i	−0.554516	−	0.832173i	$-0.687097\pi$
$911$	−13.4129	+	4.88190i	−0.444389	+	0.161744i	0.110127	+	0.993918i	$0.464874\pi$
$912$		0			0
$913$	8.29075	−	6.95676i	0.274384	−	0.230235i
$914$		0			0
$915$	−47.7854	−	13.9401i	−1.57974	−	0.460844i
$916$		0			0
$917$		−	17.0691i		−	0.563671i
$918$		0			0
$919$	54.9336			1.81209			0.906046	−	0.423179i	$-0.139086\pi$
$919$	54.9336			1.81209			0.906046	+	0.423179i	$0.139086\pi$
$920$		0			0
$921$	−29.5250	−	30.8563i	−0.972881	−	1.01675i
$922$		0			0
$923$	−7.08225	−	8.44030i	−0.233115	−	0.277816i
$924$		0			0
$925$	15.4371	+	42.4130i	0.507567	+	1.39453i
$926$		0			0
$927$	−16.0495	+	38.6968i	−0.527136	+	1.27097i
$928$		0			0
$929$	20.0336	+	16.8102i	0.657282	+	0.551525i	0.909271	−	0.416205i	$-0.136640\pi$
$929$	20.0336	+	16.8102i	0.657282	+	0.551525i	−0.251989	+	0.967730i	$0.581085\pi$
$930$		0			0
$931$	−10.5385	+	1.85822i	−0.345385	+	0.0609006i
$932$		0			0
$933$	2.02225	−	0.889258i	0.0662055	−	0.0291130i
$934$		0			0
$935$	29.3458	+	50.8283i	0.959709	+	1.66226i
$936$		0			0
$937$	30.0604	−	52.0662i	0.982031	−	1.70093i	0.327580	−	0.944823i	$-0.393767\pi$
$937$	30.0604	−	52.0662i	0.982031	−	1.70093i	0.654451	−	0.756105i	$-0.272900\pi$
$938$		0			0
$939$	−15.3513	+	31.1114i	−0.500972	+	1.01528i
$940$		0			0
$941$	−19.3533	+	53.1728i	−0.630900	+	1.73338i	0.0476846	+	0.998862i	$0.484816\pi$
$941$	−19.3533	+	53.1728i	−0.630900	+	1.73338i	−0.678585	+	0.734522i	$0.737406\pi$
$942$		0			0
$943$	1.06683	−	6.05031i	0.0347408	−	0.197025i
$944$		0			0
$945$	−6.44598	−	32.5229i	−0.209688	−	1.05797i
$946$		0			0
$947$	−45.6408	−	8.04770i	−1.48313	−	0.261515i	−0.627299	−	0.778778i	$-0.715840\pi$
$947$	−45.6408	−	8.04770i	−1.48313	−	0.261515i	−0.855826	+	0.517263i	$0.826951\pi$
$948$		0			0
$949$	1.18659	−	3.26012i	0.0385182	−	0.105828i
$950$		0			0
$951$	8.64859	−	5.77594i	0.280450	−	0.187298i
$952$		0			0
$953$	−2.93376	+	5.08142i	−0.0950338	+	0.164603i	−0.909623	−	0.415435i	$-0.863629\pi$
$953$	−2.93376	+	5.08142i	−0.0950338	+	0.164603i	0.814589	+	0.580039i	$0.196963\pi$
$954$		0			0
$955$	76.4681	−	44.1489i	2.47445	−	1.42862i
$956$		0			0
$957$	46.9923	+	34.4727i	1.51905	+	1.11435i
$958$		0			0
$959$	−5.55822	−	31.5222i	−0.179484	−	1.01791i
$960$		0			0
$961$	−23.1314	−	19.4095i	−0.746174	−	0.626114i
$962$		0			0
$963$	−17.0952	−	32.8763i	−0.550885	−	1.05943i
$964$		0			0
$965$	4.68325	+	12.8671i	0.150759	+	0.414207i
$966$		0			0
$967$	17.2553	−	14.4789i	0.554893	−	0.465610i	−0.321701	−	0.946841i	$-0.604255\pi$
$967$	17.2553	−	14.4789i	0.554893	−	0.465610i	0.876594	+	0.481231i	$0.159810\pi$
$968$		0			0
$969$	18.5033	−	4.52325i	0.594413	−	0.145308i
$970$		0			0
$971$			21.9521i			0.704475i	0.935911	+	0.352238i	$0.114579\pi$
$971$			21.9521i			0.704475i	−0.935911	+	0.352238i	$0.885421\pi$
$972$		0			0
$973$		−	20.9235i		−	0.670778i
$974$		0			0
$975$	−38.8361	+	9.49371i	−1.24375	+	0.304042i
$976$		0			0
$977$	−36.9729	+	31.0239i	−1.18287	+	0.992543i	−0.182911	+	0.983129i	$0.558552\pi$
$977$	−36.9729	+	31.0239i	−1.18287	+	0.992543i	−0.999956	+	0.00941403i	$0.997003\pi$
$978$		0			0
$979$	−26.8504	−	73.7710i	−0.858144	−	2.35773i
$980$		0			0
$981$	−3.02366	−	5.81490i	−0.0965381	−	0.185656i
$982$		0			0
$983$	35.0417	+	29.4034i	1.11766	+	0.937824i	0.998484	−	0.0550493i	$-0.0175316\pi$
$983$	35.0417	+	29.4034i	1.11766	+	0.937824i	0.119172	+	0.992874i	$0.461976\pi$
$984$		0			0
$985$	6.00289	+	34.0441i	0.191268	+	1.08474i
$986$		0			0
$987$	−7.44352	−	5.46044i	−0.236930	−	0.173808i
$988$		0			0
$989$	22.5669	−	13.0290i	0.717585	−	0.414298i
$990$		0			0
$991$	−6.44420	+	11.1617i	−0.204707	+	0.354562i	−0.950039	−	0.312130i	$-0.898957\pi$
$991$	−6.44420	+	11.1617i	−0.204707	+	0.354562i	0.745333	+	0.666693i	$0.232291\pi$
$992$		0			0
$993$	28.1744	−	18.8162i	0.894086	−	0.597113i
$994$		0			0
$995$	1.58712	−	4.36058i	0.0503151	−	0.138240i
$996$		0			0
$997$	−4.83400	−	0.852365i	−0.153094	−	0.0269947i	0.0965756	−	0.995326i	$-0.469211\pi$
$997$	−4.83400	−	0.852365i	−0.153094	−	0.0269947i	−0.249670	+	0.968331i	$0.580322\pi$
$998$		0			0
$999$	−35.3019	−	12.0105i	−1.11690	−	0.379994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.241.20		204
4.3	odd	2		216.2.t.a.133.29	yes	204
8.3	odd	2		216.2.t.a.133.3	yes	204
8.5	even	2	inner	864.2.bf.a.241.15		204
12.11	even	2		648.2.t.a.397.6		204
24.11	even	2		648.2.t.a.397.32		204
27.13	even	9	inner	864.2.bf.a.337.15		204
108.67	odd	18		216.2.t.a.13.3	✓	204
108.95	even	18		648.2.t.a.253.32		204
216.13	even	18	inner	864.2.bf.a.337.20		204
216.67	odd	18		216.2.t.a.13.29	yes	204
216.203	even	18		648.2.t.a.253.6		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.3	✓	204	108.67	odd	18
216.2.t.a.13.29	yes	204	216.67	odd	18
216.2.t.a.133.3	yes	204	8.3	odd	2
216.2.t.a.133.29	yes	204	4.3	odd	2
648.2.t.a.253.6		204	216.203	even	18
648.2.t.a.253.32		204	108.95	even	18
648.2.t.a.397.6		204	12.11	even	2
648.2.t.a.397.32		204	24.11	even	2
864.2.bf.a.241.15		204	8.5	even	2	inner
864.2.bf.a.241.20		204	1.1	even	1	trivial
864.2.bf.a.337.15		204	27.13	even	9	inner
864.2.bf.a.337.20		204	216.13	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bf (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.411299 + 1.68251i) q^{3} +(2.15975 + 2.57389i) q^{5} +(1.78453 - 0.649515i) q^{7} +(-2.66167 + 1.38403i) q^{9} +(-3.21944 + 3.83678i) q^{11} +(3.61424 - 0.637289i) q^{13} +(-3.44229 + 4.69244i) q^{15} +(-1.74380 - 3.02034i) q^{17} +(2.73085 + 1.57666i) q^{19} +(1.82679 + 2.73534i) q^{21} +(2.93428 + 1.06799i) q^{23} +(-1.09215 + 6.19390i) q^{25} +(-3.42338 - 3.90903i) q^{27} +(-6.61611 - 1.16660i) q^{29} +(-0.842639 - 0.306695i) q^{31} +(-7.77957 - 3.83868i) q^{33} +(5.52592 + 3.19039i) q^{35} +(6.21485 - 3.58815i) q^{37} +(2.55878 + 5.81888i) q^{39} +(-0.341649 - 1.93759i) q^{41} +(5.36405 - 6.39263i) q^{43} +(-9.31088 - 3.86169i) q^{45} +(-2.63733 + 0.959909i) q^{47} +(-2.59964 + 2.18135i) q^{49} +(4.36453 - 4.17621i) q^{51} -9.52536i q^{53} -16.8287 q^{55} +(-1.52954 + 5.24316i) q^{57} +(6.13695 + 7.31373i) q^{59} +(2.92540 + 8.03747i) q^{61} +(-3.85088 + 4.19863i) q^{63} +(9.44618 + 7.92629i) q^{65} +(-13.7512 + 2.42470i) q^{67} +(-0.590037 + 5.37621i) q^{69} +(-1.50109 - 2.59997i) q^{71} +(0.472663 - 0.818676i) q^{73} +(-10.8705 + 0.709989i) q^{75} +(-3.25314 + 8.93793i) q^{77} +(0.803209 - 4.55523i) q^{79} +(5.16894 - 7.36764i) q^{81} +(-2.12803 - 0.375229i) q^{83} +(4.00787 - 11.0115i) q^{85} +(-0.758385 - 11.6115i) q^{87} +(-7.83712 + 13.5743i) q^{89} +(6.03579 - 3.48477i) q^{91} +(0.169441 - 1.54389i) q^{93} +(1.83982 + 10.4341i) q^{95} +(1.68619 + 1.41488i) q^{97} +(3.25888 - 14.6680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 204 * q + 12 * q^7 - 12 * q^9 + 12 * q^15 - 6 * q^17 + 12 * q^23 - 12 * q^25 + 12 * q^31 + 12 * q^39 - 24 * q^41 + 12 * q^47 - 12 * q^49 + 24 * q^55 - 30 * q^57 + 72 * q^63 - 12 * q^65 + 90 * q^71 - 6 * q^73 + 12 * q^79 - 12 * q^81 + 48 * q^87 - 6 * q^89 + 42 * q^95 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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