LMFDB - Embedded newform 864.2.bf.a.529.20

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)

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);

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")

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			529.20
Character	$\chi$	$=$	864.529
Dual form			864.2.bf.a.49.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.368292 + 1.69244i) q^{3} +(0.355965 - 0.978005i) q^{5} +(0.272085 - 1.54307i) q^{7} +(-2.72872 + 1.24663i) q^{9} +(-1.44773 - 3.97760i) q^{11} +(-4.33941 - 5.17151i) q^{13} +(1.78632 + 0.242259i) q^{15} +(-0.494959 - 0.857294i) q^{17} +(-2.70129 - 1.55959i) q^{19} +(2.71177 - 0.107812i) q^{21} +(-1.17888 - 6.68573i) q^{23} +(3.00044 + 2.51767i) q^{25} +(-3.11481 - 4.15908i) q^{27} +(-2.84964 + 3.39607i) q^{29} +(0.409166 + 2.32049i) q^{31} +(6.19868 - 3.91512i) q^{33} +(-1.41228 - 0.815381i) q^{35} +(-3.19157 + 1.84266i) q^{37} +(7.15431 - 9.24883i) q^{39} +(-2.44191 + 2.04900i) q^{41} +(3.71087 + 10.1955i) q^{43} +(0.247877 + 3.11246i) q^{45} +(0.155220 - 0.880296i) q^{47} +(4.27080 + 1.55445i) q^{49} +(1.26863 - 1.15342i) q^{51} -5.00251i q^{53} -4.40546 q^{55} +(1.64465 - 5.14616i) q^{57} +(3.85475 - 10.5908i) q^{59} +(-5.41575 - 0.954943i) q^{61} +(1.18119 + 4.54981i) q^{63} +(-6.60244 + 2.40309i) q^{65} +(0.467287 + 0.556891i) q^{67} +(10.8810 - 4.45748i) q^{69} +(2.52073 + 4.36603i) q^{71} +(7.01816 - 12.1558i) q^{73} +(-3.15597 + 6.00531i) q^{75} +(-6.53164 + 1.15170i) q^{77} +(6.78017 + 5.68924i) q^{79} +(5.89185 - 6.80339i) q^{81} +(4.03223 - 4.80543i) q^{83} +(-1.01463 + 0.178906i) q^{85} +(-6.79716 - 3.57211i) q^{87} +(4.02279 - 6.96768i) q^{89} +(-9.16071 + 5.28894i) q^{91} +(-3.77661 + 1.54711i) q^{93} +(-2.48685 + 2.08672i) q^{95} +(-10.1365 + 3.68937i) q^{97} +(8.90903 + 9.04900i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$	$1$

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
$3$	0.368292	+	1.69244i	0.212633	+	0.977132i
$3$	0.368292	+	1.69244i	0.212633	+	0.977132i
$4$		0			0
$5$	0.355965	−	0.978005i	0.159192	−	0.437377i	−0.834295	−	0.551318i	$-0.814125\pi$
$5$	0.355965	−	0.978005i	0.159192	−	0.437377i	0.993488	+	0.113941i	$0.0363474\pi$
$6$		0			0
$7$	0.272085	−	1.54307i	0.102839	−	0.583227i	−0.889223	−	0.457474i	$-0.848754\pi$
$7$	0.272085	−	1.54307i	0.102839	−	0.583227i	0.992062	−	0.125753i	$-0.0401346\pi$
$8$		0			0
$9$	−2.72872	+	1.24663i	−0.909574	+	0.415542i
$10$		0			0
$11$	−1.44773	−	3.97760i	−0.436507	−	1.19929i	−0.941750	−	0.336315i	$-0.890819\pi$
$11$	−1.44773	−	3.97760i	−0.436507	−	1.19929i	0.505243	−	0.862977i	$-0.331403\pi$
$12$		0			0
$13$	−4.33941	−	5.17151i	−1.20354	−	1.43432i	−0.871039	−	0.491214i	$-0.836553\pi$
$13$	−4.33941	−	5.17151i	−1.20354	−	1.43432i	−0.332497	−	0.943104i	$-0.607891\pi$
$14$		0			0
$15$	1.78632	+	0.242259i	0.461225	+	0.0625509i
$16$		0			0
$17$	−0.494959	−	0.857294i	−0.120045	−	0.207924i	0.799740	−	0.600346i	$-0.204971\pi$
$17$	−0.494959	−	0.857294i	−0.120045	−	0.207924i	−0.919785	+	0.392422i	$0.871637\pi$
$18$		0			0
$19$	−2.70129	−	1.55959i	−0.619719	−	0.357795i	0.157041	−	0.987592i	$-0.449805\pi$
$19$	−2.70129	−	1.55959i	−0.619719	−	0.357795i	−0.776759	+	0.629797i	$0.783138\pi$
$20$		0			0
$21$	2.71177	−	0.107812i	0.591757	−	0.0235266i
$22$		0			0
$23$	−1.17888	−	6.68573i	−0.245812	−	1.39407i	−0.818598	−	0.574367i	$-0.805248\pi$
$23$	−1.17888	−	6.68573i	−0.245812	−	1.39407i	0.572786	−	0.819705i	$-0.305863\pi$
$24$		0			0
$25$	3.00044	+	2.51767i	0.600088	+	0.503533i
$26$		0			0
$27$	−3.11481	−	4.15908i	−0.599445	−	0.800416i
$28$		0			0
$29$	−2.84964	+	3.39607i	−0.529166	+	0.630635i	−0.962722	−	0.270491i	$-0.912814\pi$
$29$	−2.84964	+	3.39607i	−0.529166	+	0.630635i	0.433557	+	0.901126i	$0.357258\pi$
$30$		0			0
$31$	0.409166	+	2.32049i	0.0734883	+	0.416773i	0.999252	+	0.0386704i	$0.0123123\pi$
$31$	0.409166	+	2.32049i	0.0734883	+	0.416773i	−0.925764	+	0.378103i	$0.876577\pi$
$32$		0			0
$33$	6.19868	−	3.91512i	1.07905	−	0.681534i
$34$		0			0
$35$	−1.41228	−	0.815381i	−0.238719	−	0.137825i
$36$		0			0
$37$	−3.19157	+	1.84266i	−0.524691	+	0.302931i	−0.738852	−	0.673868i	$-0.764632\pi$
$37$	−3.19157	+	1.84266i	−0.524691	+	0.302931i	0.214161	+	0.976798i	$0.431298\pi$
$38$		0			0
$39$	7.15431	−	9.24883i	1.14561	−	1.48100i
$40$		0			0
$41$	−2.44191	+	2.04900i	−0.381362	+	0.320000i	−0.813237	−	0.581933i	$-0.802297\pi$
$41$	−2.44191	+	2.04900i	−0.381362	+	0.320000i	0.431875	+	0.901933i	$0.357852\pi$
$42$		0			0
$43$	3.71087	+	10.1955i	0.565903	+	1.55481i	0.810841	+	0.585267i	$0.199010\pi$
$43$	3.71087	+	10.1955i	0.565903	+	1.55481i	−0.244938	+	0.969539i	$0.578767\pi$
$44$		0			0
$45$	0.247877	+	3.11246i	0.0369513	+	0.463978i
$46$		0			0
$47$	0.155220	−	0.880296i	0.0226411	−	0.128404i	−0.971392	−	0.237481i	$-0.923678\pi$
$47$	0.155220	−	0.880296i	0.0226411	−	0.128404i	0.994033	+	0.109077i	$0.0347894\pi$
$48$		0			0
$49$	4.27080	+	1.55445i	0.610115	+	0.222064i
$50$		0			0
$51$	1.26863	−	1.15342i	0.177644	−	0.161512i
$52$		0			0
$53$		−	5.00251i		−	0.687148i	−0.939126	−	0.343574i	$-0.888362\pi$
$53$		−	5.00251i		−	0.687148i	0.939126	−	0.343574i	$-0.111638\pi$
$54$		0			0
$55$	−4.40546			−0.594032
$56$		0			0
$57$	1.64465	−	5.14616i	0.217840	−	0.681626i
$58$		0			0
$59$	3.85475	−	10.5908i	0.501846	−	1.37881i	−0.387625	−	0.921817i	$-0.626704\pi$
$59$	3.85475	−	10.5908i	0.501846	−	1.37881i	0.889470	−	0.456993i	$-0.151073\pi$
$60$		0			0
$61$	−5.41575	−	0.954943i	−0.693416	−	0.122268i	−0.184177	−	0.982893i	$-0.558962\pi$
$61$	−5.41575	−	0.954943i	−0.693416	−	0.122268i	−0.509239	+	0.860625i	$0.670073\pi$
$62$		0			0
$63$	1.18119	+	4.54981i	0.148816	+	0.573222i
$64$		0			0
$65$	−6.60244	+	2.40309i	−0.818932	+	0.298067i
$66$		0			0
$67$	0.467287	+	0.556891i	0.0570882	+	0.0680351i	0.793833	−	0.608136i	$-0.208082\pi$
$67$	0.467287	+	0.556891i	0.0570882	+	0.0680351i	−0.736745	+	0.676171i	$0.763638\pi$
$68$		0			0
$69$	10.8810	−	4.45748i	1.30992	−	0.536617i
$70$		0			0
$71$	2.52073	+	4.36603i	0.299155	+	0.518152i	0.975943	−	0.218026i	$-0.0699618\pi$
$71$	2.52073	+	4.36603i	0.299155	+	0.518152i	−0.676788	+	0.736178i	$0.736628\pi$
$72$		0			0
$73$	7.01816	−	12.1558i	0.821413	−	1.42273i	−0.0832165	−	0.996531i	$-0.526519\pi$
$73$	7.01816	−	12.1558i	0.821413	−	1.42273i	0.904630	−	0.426198i	$-0.140147\pi$
$74$		0			0
$75$	−3.15597	+	6.00531i	−0.364420	+	0.693433i
$76$		0			0
$77$	−6.53164	+	1.15170i	−0.744349	+	0.131249i
$78$		0			0
$79$	6.78017	+	5.68924i	0.762829	+	0.640090i	0.938862	−	0.344295i	$-0.111882\pi$
$79$	6.78017	+	5.68924i	0.762829	+	0.640090i	−0.176032	+	0.984384i	$0.556326\pi$
$80$		0			0
$81$	5.89185	−	6.80339i	0.654650	−	0.755932i
$82$		0			0
$83$	4.03223	−	4.80543i	0.442595	−	0.527464i	−0.497917	−	0.867225i	$-0.665902\pi$
$83$	4.03223	−	4.80543i	0.442595	−	0.527464i	0.940512	+	0.339760i	$0.110346\pi$
$84$		0			0
$85$	−1.01463	+	0.178906i	−0.110052	+	0.0194051i
$86$		0			0
$87$	−6.79716	−	3.57211i	−0.728732	−	0.382971i
$88$		0			0
$89$	4.02279	−	6.96768i	0.426415	−	0.738573i	−0.570136	−	0.821550i	$-0.693110\pi$
$89$	4.02279	−	6.96768i	0.426415	−	0.738573i	0.996551	+	0.0829775i	$0.0264430\pi$
$90$		0			0
$91$	−9.16071	+	5.28894i	−0.960303	+	0.554431i
$92$		0			0
$93$	−3.77661	+	1.54711i	−0.391616	+	0.160428i
$94$		0			0
$95$	−2.48685	+	2.08672i	−0.255146	+	0.214093i
$96$		0			0
$97$	−10.1365	+	3.68937i	−1.02920	+	0.374599i	−0.800777	−	0.598963i	$-0.795580\pi$
$97$	−10.1365	+	3.68937i	−1.02920	+	0.374599i	−0.228425	+	0.973561i	$0.573358\pi$
$98$		0			0
$99$	8.90903	+	9.04900i	0.895391	+	0.909458i
$100$		0			0
$101$	6.50659	+	1.14729i	0.647430	+	0.114159i	0.487714	−	0.873004i	$-0.337831\pi$
$101$	6.50659	+	1.14729i	0.647430	+	0.114159i	0.159716	+	0.987163i	$0.448942\pi$
$102$		0			0
$103$	14.9315	+	5.43464i	1.47125	+	0.535491i	0.948439	−	0.316959i	$-0.102662\pi$
$103$	14.9315	+	5.43464i	1.47125	+	0.535491i	0.522809	+	0.852450i	$0.324884\pi$
$104$		0			0
$105$	0.859854	−	2.69050i	0.0839131	−	0.262566i
$106$		0			0
$107$		−	3.85513i		−	0.372689i	−0.982484	−	0.186345i	$-0.940336\pi$
$107$		−	3.85513i		−	0.372689i	0.982484	−	0.186345i	$-0.0596641\pi$
$108$		0			0
$109$			3.32803i			0.318767i	0.987217	+	0.159384i	$0.0509507\pi$
$109$			3.32803i			0.318767i	−0.987217	+	0.159384i	$0.949049\pi$
$110$		0			0
$111$	−4.29402	−	4.72292i	−0.407570	−	0.448279i
$112$		0			0
$113$	7.85208	+	2.85792i	0.738662	+	0.268851i	0.683827	−	0.729645i	$-0.260314\pi$
$113$	7.85208	+	2.85792i	0.738662	+	0.268851i	0.0548351	+	0.998495i	$0.482537\pi$
$114$		0			0
$115$	−6.95832	−	1.22694i	−0.648867	−	0.114413i
$116$		0			0
$117$	18.2880	+	8.70199i	1.69072	+	0.804499i
$118$		0			0
$119$	−1.45754	+	0.530501i	−0.133612	+	0.0486309i
$120$		0			0
$121$	−5.29891	+	4.44632i	−0.481719	+	0.404211i
$122$		0			0
$123$	−4.36715	−	3.37815i	−0.393773	−	0.304598i
$124$		0			0
$125$	8.03702	−	4.64017i	0.718853	−	0.415030i
$126$		0			0
$127$	−1.83012	+	3.16986i	−0.162397	+	0.281280i	−0.935728	−	0.352723i	$-0.885256\pi$
$127$	−1.83012	+	3.16986i	−0.162397	+	0.281280i	0.773331	+	0.634003i	$0.218589\pi$
$128$		0			0
$129$	−15.8887	+	10.0354i	−1.39892	+	0.883566i
$130$		0			0
$131$	−9.66082	+	1.70346i	−0.844070	+	0.148832i	−0.578930	−	0.815378i	$-0.696529\pi$
$131$	−9.66082	+	1.70346i	−0.844070	+	0.148832i	−0.265140	+	0.964210i	$0.585418\pi$
$132$		0			0
$133$	−3.14155	+	3.74395i	−0.272407	+	0.324641i
$134$		0			0
$135$	−5.17637	+	1.56581i	−0.445511	+	0.134764i
$136$		0			0
$137$	−16.9231	−	14.2001i	−1.44583	−	1.21320i	−0.935550	−	0.353193i	$-0.885096\pi$
$137$	−16.9231	−	14.2001i	−1.44583	−	1.21320i	−0.510284	−	0.860006i	$-0.670460\pi$
$138$		0			0
$139$	4.68849	−	0.826707i	0.397672	−	0.0701203i	0.0287641	−	0.999586i	$-0.490843\pi$
$139$	4.68849	−	0.826707i	0.397672	−	0.0701203i	0.368908	+	0.929466i	$0.379732\pi$
$140$		0			0
$141$	1.54702	−	0.0615050i	0.130282	−	0.00517966i
$142$		0			0
$143$	−14.2879	+	24.7474i	−1.19482	+	2.06948i
$144$		0			0
$145$	2.30701	+	3.99585i	0.191586	+	0.331837i
$146$		0			0
$147$	−1.05791	+	7.80058i	−0.0872547	+	0.643381i
$148$		0			0
$149$	−14.7916	−	17.6280i	−1.21178	−	1.44414i	−0.861700	−	0.507418i	$-0.830600\pi$
$149$	−14.7916	−	17.6280i	−1.21178	−	1.44414i	−0.350076	−	0.936721i	$-0.613844\pi$
$150$		0			0
$151$	−18.6779	+	6.79819i	−1.51998	+	0.553229i	−0.961144	−	0.276047i	$-0.910975\pi$
$151$	−18.6779	+	6.79819i	−1.51998	+	0.553229i	−0.558840	+	0.829276i	$0.688753\pi$
$152$		0			0
$153$	2.41933	+	1.72229i	0.195591	+	0.139239i
$154$		0			0
$155$	2.41510	+	0.425848i	0.193986	+	0.0342049i
$156$		0			0
$157$	−1.67263	+	4.59552i	−0.133491	+	0.366762i	−0.988371	−	0.152063i	$-0.951408\pi$
$157$	−1.67263	+	4.59552i	−0.133491	+	0.366762i	0.854880	+	0.518825i	$0.173631\pi$
$158$		0			0
$159$	8.46647	−	1.84239i	0.671435	−	0.146111i
$160$		0			0
$161$	−10.6373			−0.838339
$162$		0			0
$163$		−	4.18081i		−	0.327466i	−0.986505	−	0.163733i	$-0.947646\pi$
$163$		−	4.18081i		−	0.327466i	0.986505	−	0.163733i	$-0.0523536\pi$
$164$		0			0
$165$	−1.62249	−	7.45598i	−0.126311	−	0.580447i
$166$		0			0
$167$	−5.72775	−	2.08473i	−0.443227	−	0.161321i	0.110759	−	0.993847i	$-0.464672\pi$
$167$	−5.72775	−	2.08473i	−0.443227	−	0.161321i	−0.553986	+	0.832526i	$0.686894\pi$
$168$		0			0
$169$	−5.65659	+	32.0801i	−0.435122	+	2.46770i
$170$		0			0
$171$	9.31530	+	0.888193i	0.712359	+	0.0679218i
$172$		0			0
$173$	−0.453627	−	1.24633i	−0.0344886	−	0.0947567i	0.921253	−	0.388964i	$-0.127167\pi$
$173$	−0.453627	−	1.24633i	−0.0344886	−	0.0947567i	−0.955742	+	0.294207i	$0.904945\pi$
$174$		0			0
$175$	4.70132	−	3.94488i	0.355386	−	0.298205i
$176$		0			0
$177$	19.3441	+	2.62342i	1.45399	+	0.197189i
$178$		0			0
$179$	9.68622	−	5.59234i	0.723982	−	0.417991i	−0.0922343	−	0.995737i	$-0.529401\pi$
$179$	9.68622	−	5.59234i	0.723982	−	0.417991i	0.816217	+	0.577746i	$0.196068\pi$
$180$		0			0
$181$	3.21058	+	1.85363i	0.238641	+	0.137779i	0.614552	−	0.788876i	$-0.289337\pi$
$181$	3.21058	+	1.85363i	0.238641	+	0.137779i	−0.375911	+	0.926656i	$0.622670\pi$
$182$		0			0
$183$	−0.378391	−	9.51754i	−0.0279714	−	0.703557i
$184$		0			0
$185$	0.666039	+	3.77730i	0.0489682	+	0.277712i
$186$		0			0
$187$	−2.69341	+	3.20988i	−0.196961	+	0.234730i
$188$		0			0
$189$	−7.26526	+	3.67475i	−0.528470	+	0.267299i
$190$		0			0
$191$	−13.8306	−	11.6053i	−1.00075	−	0.839729i	−0.0136618	−	0.999907i	$-0.504349\pi$
$191$	−13.8306	−	11.6053i	−1.00075	−	0.839729i	−0.987088	+	0.160178i	$0.948793\pi$
$192$		0			0
$193$	0.770660	+	4.37063i	0.0554733	+	0.314605i	0.999900	−	0.0141163i	$-0.00449352\pi$
$193$	0.770660	+	4.37063i	0.0554733	+	0.314605i	−0.944427	+	0.328721i	$0.893382\pi$
$194$		0			0
$195$	−6.49872	−	10.2892i	−0.465383	−	0.736826i
$196$		0			0
$197$	14.1519	+	8.17063i	1.00828	+	0.582133i	0.910689	−	0.413093i	$-0.135551\pi$
$197$	14.1519	+	8.17063i	1.00828	+	0.582133i	0.0975957	+	0.995226i	$0.468885\pi$
$198$		0			0
$199$	0.458824	+	0.794707i	0.0325252	+	0.0563353i	0.881830	−	0.471568i	$-0.156312\pi$
$199$	0.458824	+	0.794707i	0.0325252	+	0.0563353i	−0.849305	+	0.527903i	$0.822978\pi$
$200$		0			0
$201$	−0.770408	+	0.995955i	−0.0543404	+	0.0702493i
$202$		0			0
$203$	4.46504	+	5.32123i	0.313385	+	0.373477i
$204$		0			0
$205$	1.13470	+	3.11757i	0.0792511	+	0.217741i
$206$		0			0
$207$	11.5514	+	16.7739i	0.802880	+	1.16587i
$208$		0			0
$209$	−2.29270	+	13.0025i	−0.158589	+	0.899403i
$210$		0			0
$211$	2.09734	−	5.76240i	0.144387	−	0.396700i	−0.846327	−	0.532664i	$-0.821191\pi$
$211$	2.09734	−	5.76240i	0.144387	−	0.396700i	0.990714	+	0.135964i	$0.0434131\pi$
$212$		0			0
$213$	−6.46089	+	5.87416i	−0.442693	+	0.402491i
$214$		0			0
$215$	11.2922			0.770124
$216$		0			0
$217$	3.69202			0.250631
$218$		0			0
$219$	23.1577	+	7.40094i	1.56485	+	0.500109i
$220$		0			0
$221$	−2.28567	+	6.27983i	−0.153751	+	0.422427i
$222$		0			0
$223$	3.72326	−	21.1156i	0.249328	−	1.41401i	−0.560896	−	0.827887i	$-0.689543\pi$
$223$	3.72326	−	21.1156i	0.249328	−	1.41401i	0.810223	−	0.586121i	$-0.199346\pi$
$224$		0			0
$225$	−11.3260	−	3.12959i	−0.755063	−	0.208639i
$226$		0			0
$227$	6.36438	+	17.4860i	0.422419	+	1.16059i	0.950319	+	0.311279i	$0.100757\pi$
$227$	6.36438	+	17.4860i	0.422419	+	1.16059i	−0.527900	+	0.849307i	$0.677020\pi$
$228$		0			0
$229$	5.70813	+	6.80268i	0.377204	+	0.449534i	0.920930	−	0.389729i	$-0.127431\pi$
$229$	5.70813	+	6.80268i	0.377204	+	0.449534i	−0.543726	+	0.839263i	$0.682987\pi$
$230$		0			0
$231$	−4.35474	−	10.6303i	−0.286521	−	0.699420i
$232$		0			0
$233$	9.39731	+	16.2766i	0.615638	+	1.06632i	0.990272	+	0.139144i	$0.0444350\pi$
$233$	9.39731	+	16.2766i	0.615638	+	1.06632i	−0.374634	+	0.927173i	$0.622232\pi$
$234$		0			0
$235$	−0.805681	−	0.465160i	−0.0525568	−	0.0303437i
$236$		0			0
$237$	−7.13163	+	13.5704i	−0.463249	+	0.881489i
$238$		0			0
$239$	−3.56653	−	20.2268i	−0.230700	−	1.30836i	−0.851483	−	0.524382i	$-0.824297\pi$
$239$	−3.56653	−	20.2268i	−0.230700	−	1.30836i	0.620784	−	0.783982i	$-0.286815\pi$
$240$		0			0
$241$	−10.5529	−	8.85497i	−0.679775	−	0.570399i	0.236166	−	0.971713i	$-0.424109\pi$
$241$	−10.5529	−	8.85497i	−0.679775	−	0.570399i	−0.915941	+	0.401314i	$0.868554\pi$
$242$		0			0
$243$	13.6843	+	7.46598i	0.877846	+	0.478943i
$244$		0			0
$245$	3.04051	−	3.62354i	0.194251	−	0.231499i
$246$		0			0
$247$	3.65657	+	20.7374i	0.232662	+	1.31949i
$248$		0			0
$249$	9.61795	+	5.05452i	0.609513	+	0.320317i
$250$		0			0
$251$	0.419101	+	0.241968i	0.0264534	+	0.0152729i	0.513168	−	0.858288i	$-0.328472\pi$
$251$	0.419101	+	0.241968i	0.0264534	+	0.0152729i	−0.486715	+	0.873561i	$0.661805\pi$
$252$		0			0
$253$	−24.8865	+	14.3682i	−1.56460	+	0.903323i
$254$		0			0
$255$	−0.676466	−	1.65131i	−0.0423620	−	0.103409i
$256$		0			0
$257$	13.5896	−	11.4030i	0.847695	−	0.711300i	−0.111586	−	0.993755i	$-0.535593\pi$
$257$	13.5896	−	11.4030i	0.847695	−	0.711300i	0.959281	+	0.282454i	$0.0911486\pi$
$258$		0			0
$259$	1.97497	+	5.42619i	0.122719	+	0.337167i
$260$		0			0
$261$	3.54226	−	12.8194i	0.219260	−	0.793500i
$262$		0			0
$263$	−1.39832	+	7.93029i	−0.0862243	+	0.489002i	0.910861	+	0.412712i	$0.135419\pi$
$263$	−1.39832	+	7.93029i	−0.0862243	+	0.489002i	−0.997086	+	0.0762899i	$0.975693\pi$
$264$		0			0
$265$	−4.89249	−	1.78072i	−0.300543	−	0.109389i
$266$		0			0
$267$	13.2740	+	4.24220i	0.812353	+	0.259619i
$268$		0			0
$269$		−	6.56538i		−	0.400298i	−0.979765	−	0.200149i	$-0.935857\pi$
$269$		−	6.56538i		−	0.400298i	0.979765	−	0.200149i	$-0.0641426\pi$
$270$		0			0
$271$	−10.8623			−0.659839			−0.329919	−	0.944009i	$-0.607022\pi$
$271$	−10.8623			−0.659839			−0.329919	+	0.944009i	$0.607022\pi$
$272$		0			0
$273$	−12.3250	−	13.5561i	−0.745945	−	0.820452i
$274$		0			0
$275$	5.67046	−	15.5795i	0.341941	−	0.939476i
$276$		0			0
$277$	31.2235	+	5.50555i	1.87604	+	0.330796i	0.990907	−	0.134546i	$-0.0429575\pi$
$277$	31.2235	+	5.50555i	1.87604	+	0.330796i	0.885131	+	0.465342i	$0.154069\pi$
$278$		0			0
$279$	−4.00929	−	5.82191i	−0.240030	−	0.348549i
$280$		0			0
$281$	−18.4488	+	6.71481i	−1.10056	+	0.400572i	−0.827523	−	0.561431i	$-0.810251\pi$
$281$	−18.4488	+	6.71481i	−1.10056	+	0.400572i	−0.273039	+	0.962003i	$0.588029\pi$
$282$		0			0
$283$	−12.6768	−	15.1076i	−0.753556	−	0.898053i	0.243866	−	0.969809i	$-0.421584\pi$
$283$	−12.6768	−	15.1076i	−0.753556	−	0.898053i	−0.997422	+	0.0717558i	$0.977140\pi$
$284$		0			0
$285$	−4.44754	−	3.44033i	−0.263449	−	0.203788i
$286$		0			0
$287$	2.49735	+	4.32554i	0.147414	+	0.255329i
$288$		0			0
$289$	8.01003	−	13.8738i	0.471178	−	0.816105i
$290$		0			0
$291$	−9.97723	−	15.7966i	−0.584875	−	0.926014i
$292$		0			0
$293$	26.1866	−	4.61741i	1.52984	−	0.269752i	0.655549	−	0.755153i	$-0.272437\pi$
$293$	26.1866	−	4.61741i	1.52984	−	0.269752i	0.874292	+	0.485401i	$0.161326\pi$
$294$		0			0
$295$	−8.98574	−	7.53993i	−0.523170	−	0.438992i
$296$		0			0
$297$	−12.0338	+	18.4107i	−0.698271	+	1.06830i
$298$		0			0
$299$	−29.4597	+	35.1087i	−1.70370	+	2.03039i
$300$		0			0
$301$	16.7421	−	2.95209i	0.965001	−	0.170156i
$302$		0			0
$303$	0.454606	+	11.4346i	0.0261164	+	0.656898i
$304$		0			0
$305$	−2.86175	+	4.95671i	−0.163864	+	0.283820i
$306$		0			0
$307$	−20.0407	+	11.5705i	−1.14379	+	0.660365i	−0.947365	−	0.320155i	$-0.896265\pi$
$307$	−20.0407	+	11.5705i	−1.14379	+	0.660365i	−0.196420	+	0.980520i	$0.562932\pi$
$308$		0			0
$309$	−3.69864	+	27.2723i	−0.210409	+	1.55147i
$310$		0			0
$311$	18.6806	−	15.6749i	1.05928	−	0.888842i	0.0652424	−	0.997869i	$-0.479218\pi$
$311$	18.6806	−	15.6749i	1.05928	−	0.888842i	0.994039	+	0.109027i	$0.0347735\pi$
$312$		0			0
$313$	24.2156	−	8.81377i	1.36875	−	0.498184i	0.450000	−	0.893028i	$-0.351424\pi$
$313$	24.2156	−	8.81377i	1.36875	−	0.498184i	0.918748	+	0.394845i	$0.129202\pi$
$314$		0			0
$315$	4.87020	+	0.464362i	0.274405	+	0.0261639i
$316$		0			0
$317$	−18.1371	−	3.19806i	−1.01868	−	0.179621i	−0.360721	−	0.932674i	$-0.617469\pi$
$317$	−18.1371	−	3.19806i	−1.01868	−	0.179621i	−0.657960	+	0.753053i	$0.728580\pi$
$318$		0			0
$319$	17.6337	+	6.41816i	0.987300	+	0.359348i
$320$		0			0
$321$	6.52458	−	1.41981i	0.364167	−	0.0792462i
$322$		0			0
$323$			3.08773i			0.171806i
$324$		0			0
$325$		−	26.4420i		−	1.46674i
$326$		0			0
$327$	−5.63249	+	1.22568i	−0.311478	+	0.0677805i
$328$		0			0
$329$	−1.31613	−	0.479031i	−0.0725605	−	0.0264099i
$330$		0			0
$331$	15.2370	+	2.68670i	0.837502	+	0.147674i	0.575919	−	0.817507i	$-0.304644\pi$
$331$	15.2370	+	2.68670i	0.837502	+	0.147674i	0.261583	+	0.965181i	$0.415755\pi$
$332$		0			0
$333$	6.41181	−	9.00679i	0.351365	−	0.493569i
$334$		0			0
$335$	0.710980	−	0.258776i	0.0388450	−	0.0141384i
$336$		0			0
$337$	9.32566	−	7.82516i	0.508001	−	0.426264i	−0.352424	−	0.935840i	$-0.614643\pi$
$337$	9.32566	−	7.82516i	0.508001	−	0.426264i	0.860425	+	0.509577i	$0.170198\pi$
$338$		0			0
$339$	−1.94501	+	14.3417i	−0.105639	+	0.778937i
$340$		0			0
$341$	8.63764	−	4.98695i	0.467755	−	0.270058i
$342$		0			0
$343$	9.04472	−	15.6659i	0.488369	−	0.845880i
$344$		0			0
$345$	−0.486168	−	12.2284i	−0.0261744	−	0.658356i
$346$		0			0
$347$	−23.2143	+	4.09332i	−1.24621	+	0.219741i	−0.757576	−	0.652747i	$-0.773616\pi$
$347$	−23.2143	+	4.09332i	−1.24621	+	0.219741i	−0.488636	+	0.872488i	$0.662505\pi$
$348$		0			0
$349$	−14.7087	+	17.5291i	−0.787338	+	0.938312i	−0.999240	−	0.0389784i	$-0.987590\pi$
$349$	−14.7087	+	17.5291i	−0.787338	+	0.938312i	0.211902	+	0.977291i	$0.432034\pi$
$350$		0			0
$351$	−7.99230	+	34.1562i	−0.426598	+	1.82312i
$352$		0			0
$353$	0.541929	+	0.454733i	0.0288440	+	0.0242030i	0.657096	−	0.753807i	$-0.271785\pi$
$353$	0.541929	+	0.454733i	0.0288440	+	0.0242030i	−0.628252	+	0.778010i	$0.716229\pi$
$354$		0			0
$355$	5.16729	−	0.911132i	0.274251	−	0.0483579i
$356$		0			0
$357$	−1.43464	−	2.27142i	−0.0759293	−	0.120216i
$358$		0			0
$359$	5.07907	−	8.79721i	0.268063	−	0.464299i	−0.700298	−	0.713850i	$-0.746950\pi$
$359$	5.07907	−	8.79721i	0.268063	−	0.464299i	0.968362	+	0.249551i	$0.0802831\pi$
$360$		0			0
$361$	−4.63535	−	8.02867i	−0.243966	−	0.422561i
$362$		0			0
$363$	−9.47668	−	7.33056i	−0.497397	−	0.384755i
$364$		0			0
$365$	−9.39023	−	11.1908i	−0.491507	−	0.585755i
$366$		0			0
$367$	1.79478	−	0.653245i	0.0936866	−	0.0340991i	−0.294752	−	0.955574i	$-0.595237\pi$
$367$	1.79478	−	0.653245i	0.0936866	−	0.0340991i	0.388438	+	0.921475i	$0.373015\pi$
$368$		0			0
$369$	4.10894	−	8.63530i	0.213903	−	0.449536i
$370$		0			0
$371$	−7.71925	−	1.36111i	−0.400763	−	0.0706654i
$372$		0			0
$373$	11.8307	−	32.5046i	0.612571	−	1.68303i	−0.111899	−	0.993720i	$-0.535693\pi$
$373$	11.8307	−	32.5046i	0.612571	−	1.68303i	0.724470	−	0.689306i	$-0.242084\pi$
$374$		0			0
$375$	10.8132	+	11.8932i	0.558391	+	0.614165i
$376$		0			0
$377$	29.9286			1.54140
$378$		0			0
$379$		−	27.1937i		−	1.39685i	−0.715685	−	0.698423i	$-0.753886\pi$
$379$		−	27.1937i		−	1.39685i	0.715685	−	0.698423i	$-0.246114\pi$
$380$		0			0
$381$	−6.03883	−	1.92994i	−0.309378	−	0.0988738i
$382$		0			0
$383$	5.67775	+	2.06653i	0.290120	+	0.105595i	0.482980	−	0.875631i	$-0.339554\pi$
$383$	5.67775	+	2.06653i	0.290120	+	0.105595i	−0.192861	+	0.981226i	$0.561777\pi$
$384$		0			0
$385$	−1.19866	+	6.79794i	−0.0610894	+	0.346455i
$386$		0			0
$387$	−22.8360	−	23.1947i	−1.16082	−	1.17905i
$388$		0			0
$389$	3.99747	+	10.9830i	0.202680	+	0.556858i	0.998836	−	0.0482330i	$-0.0153590\pi$
$389$	3.99747	+	10.9830i	0.202680	+	0.556858i	−0.796156	+	0.605091i	$0.793137\pi$
$390$		0			0
$391$	−5.14814	+	4.31980i	−0.260353	+	0.218462i
$392$		0			0
$393$	−6.44102	−	15.7230i	−0.324906	−	0.793121i
$394$		0			0
$395$	7.97761	−	4.60588i	0.401397	−	0.231747i
$396$		0			0
$397$	−2.31327	−	1.33556i	−0.116099	−	0.0670301i	0.440826	−	0.897593i	$-0.354686\pi$
$397$	−2.31327	−	1.33556i	−0.116099	−	0.0670301i	−0.556925	+	0.830563i	$0.688019\pi$
$398$		0			0
$399$	−7.49342	−	3.93802i	−0.375140	−	0.197148i
$400$		0			0
$401$	−2.15776	−	12.2372i	−0.107753	−	0.611099i	−0.990085	−	0.140470i	$-0.955138\pi$
$401$	−2.15776	−	12.2372i	−0.107753	−	0.611099i	0.882332	−	0.470628i	$-0.155973\pi$
$402$		0			0
$403$	10.2249	−	12.1856i	0.509339	−	0.607007i
$404$		0			0
$405$	−4.55646	−	8.18403i	−0.226412	−	0.406668i
$406$		0			0
$407$	11.9499	+	10.0271i	0.592334	+	0.497027i
$408$		0			0
$409$	−0.895032	−	5.07598i	−0.0442565	−	0.250991i	0.954651	−	0.297728i	$-0.0962288\pi$
$409$	−0.895032	−	5.07598i	−0.0442565	−	0.250991i	−0.998907	+	0.0467370i	$0.985118\pi$
$410$		0			0
$411$	17.8003	−	33.8711i	0.878023	−	1.67074i
$412$		0			0
$413$	−15.2936	−	8.82978i	−0.752550	−	0.434485i
$414$		0			0
$415$	−3.26440	−	5.65411i	−0.160243	−	0.277549i
$416$		0			0
$417$	3.12588	+	7.63052i	0.153075	+	0.373668i
$418$		0			0
$419$	−1.84481	−	2.19856i	−0.0901248	−	0.107407i	0.719097	−	0.694909i	$-0.244556\pi$
$419$	−1.84481	−	2.19856i	−0.0901248	−	0.107407i	−0.809222	+	0.587503i	$0.800111\pi$
$420$		0			0
$421$	4.61049	+	12.6672i	0.224701	+	0.617362i	0.999897	−	0.0143594i	$-0.00457089\pi$
$421$	4.61049	+	12.6672i	0.224701	+	0.617362i	−0.775195	+	0.631721i	$0.782349\pi$
$422$		0			0
$423$	0.673847	+	2.59558i	0.0327636	+	0.126202i
$424$		0			0
$425$	0.673287	−	3.81840i	0.0326592	−	0.185220i
$426$		0			0
$427$	−2.94709	+	8.09707i	−0.142620	+	0.391845i
$428$		0			0
$429$	−47.1457	−	15.0672i	−2.27621	−	0.727452i
$430$		0			0
$431$	−25.2153			−1.21458			−0.607290	−	0.794480i	$-0.707743\pi$
$431$	−25.2153			−1.21458			−0.607290	+	0.794480i	$0.707743\pi$
$432$		0			0
$433$	−15.5658			−0.748046			−0.374023	−	0.927419i	$-0.622022\pi$
$433$	−15.5658			−0.748046			−0.374023	+	0.927419i	$0.622022\pi$
$434$		0			0
$435$	−5.91309	+	5.37611i	−0.283511	+	0.257765i
$436$		0			0
$437$	−7.24252	+	19.8987i	−0.346457	+	0.951882i
$438$		0			0
$439$	−5.53290	+	31.3787i	−0.264071	+	1.49762i	0.507596	+	0.861595i	$0.330534\pi$
$439$	−5.53290	+	31.3787i	−0.264071	+	1.49762i	−0.771667	+	0.636026i	$0.780577\pi$
$440$		0			0
$441$	−13.5916	+	1.08244i	−0.647221	+	0.0515449i
$442$		0			0
$443$	−2.16330	−	5.94362i	−0.102782	−	0.282390i	0.877634	−	0.479332i	$-0.159121\pi$
$443$	−2.16330	−	5.94362i	−0.102782	−	0.282390i	−0.980415	+	0.196942i	$0.936899\pi$
$444$		0			0
$445$	−5.38246	−	6.41456i	−0.255153	−	0.304079i
$446$		0			0
$447$	24.3867	−	31.5262i	1.15345	−	1.49114i
$448$		0			0
$449$	−4.18149	−	7.24256i	−0.197337	−	0.341797i	0.750327	−	0.661067i	$-0.229896\pi$
$449$	−4.18149	−	7.24256i	−0.197337	−	0.341797i	−0.947664	+	0.319269i	$0.896563\pi$
$450$		0			0
$451$	11.6853	+	6.74653i	0.550241	+	0.317682i
$452$		0			0
$453$	−18.3845	−	29.1075i	−0.863777	−	1.36759i
$454$		0			0
$455$	1.91172	+	10.8419i	0.0896228	+	0.508276i
$456$		0			0
$457$	−21.5741	−	18.1028i	−1.00919	−	0.846812i	−0.0209605	−	0.999780i	$-0.506672\pi$
$457$	−21.5741	−	18.1028i	−1.00919	−	0.846812i	−0.988231	+	0.152968i	$0.951117\pi$
$458$		0			0
$459$	−2.02385	+	4.72888i	−0.0944655	+	0.220725i
$460$		0			0
$461$	−16.8013	+	20.0230i	−0.782513	+	0.932563i	−0.999044	−	0.0437126i	$-0.986081\pi$
$461$	−16.8013	+	20.0230i	−0.782513	+	0.932563i	0.216531	+	0.976276i	$0.430526\pi$
$462$		0			0
$463$	−3.84612	−	21.8124i	−0.178744	−	1.01371i	−0.933733	−	0.357971i	$-0.883469\pi$
$463$	−3.84612	−	21.8124i	−0.178744	−	1.01371i	0.754988	−	0.655738i	$-0.227642\pi$
$464$		0			0
$465$	0.168740	+	4.24426i	0.00782513	+	0.196823i
$466$		0			0
$467$	19.1663	+	11.0657i	0.886910	+	0.512058i	0.872930	−	0.487845i	$-0.162217\pi$
$467$	19.1663	+	11.0657i	0.886910	+	0.512058i	0.0139792	+	0.999902i	$0.495550\pi$
$468$		0			0
$469$	0.986466	−	0.569536i	0.0455508	−	0.0262987i
$470$		0			0
$471$	−8.39367	−	1.13834i	−0.386760	−	0.0524520i
$472$		0			0
$473$	35.1815	−	29.5208i	1.61765	−	1.35737i
$474$		0			0
$475$	−4.17853	−	11.4804i	−0.191724	−	0.526757i
$476$		0			0
$477$	6.23626	+	13.6505i	0.285539	+	0.625012i
$478$		0			0
$479$	2.06488	−	11.7105i	0.0943470	−	0.535068i	−0.900599	−	0.434652i	$-0.856871\pi$
$479$	2.06488	−	11.7105i	0.0943470	−	0.535068i	0.994946	−	0.100416i	$-0.0320175\pi$
$480$		0			0
$481$	23.3788	+	8.50920i	1.06598	+	0.387986i
$482$		0			0
$483$	−3.91764	−	18.0031i	−0.178259	−	0.819168i
$484$		0			0
$485$			11.2268i			0.509783i
$486$		0			0
$487$	−22.1183			−1.00228			−0.501138	−	0.865367i	$-0.667085\pi$
$487$	−22.1183			−1.00228			−0.501138	+	0.865367i	$0.667085\pi$
$488$		0			0
$489$	7.07578	−	1.53976i	0.319978	−	0.0696303i
$490$		0			0
$491$	−2.55319	+	7.01484i	−0.115224	+	0.316575i	−0.983877	−	0.178845i	$-0.942764\pi$
$491$	−2.55319	+	7.01484i	−0.115224	+	0.316575i	0.868653	+	0.495421i	$0.164986\pi$
$492$		0			0
$493$	4.32189	+	0.762066i	0.194648	+	0.0343217i
$494$		0			0
$495$	12.0213	−	5.49195i	0.540316	−	0.246845i
$496$		0			0
$497$	7.42295	−	2.70173i	0.332965	−	0.121189i
$498$		0			0
$499$	6.65452	+	7.93054i	0.297897	+	0.355020i	0.894143	−	0.447782i	$-0.147786\pi$
$499$	6.65452	+	7.93054i	0.297897	+	0.355020i	−0.596246	+	0.802802i	$0.703342\pi$
$500$		0			0
$501$	1.41880	−	10.4617i	0.0633874	−	0.467393i
$502$		0			0
$503$	16.9435	+	29.3471i	0.755475	+	1.30852i	0.945138	+	0.326672i	$0.105927\pi$
$503$	16.9435	+	29.3471i	0.755475	+	1.30852i	−0.189663	+	0.981849i	$0.560739\pi$
$504$		0			0
$505$	3.43817	−	5.95508i	0.152997	−	0.264998i
$506$		0			0
$507$	−56.3770	+	2.24139i	−2.50379	+	0.0995436i
$508$		0			0
$509$	16.7517	−	2.95378i	0.742508	−	0.130924i	0.210417	−	0.977612i	$-0.432518\pi$
$509$	16.7517	−	2.95378i	0.742508	−	0.130924i	0.532090	+	0.846688i	$0.321407\pi$
$510$		0			0
$511$	−16.8478	−	14.1370i	−0.745301	−	0.625382i
$512$		0			0
$513$	1.92753	+	16.0927i	0.0851026	+	0.710511i
$514$		0			0
$515$	10.6302	−	12.6686i	0.468423	−	0.558245i
$516$		0			0
$517$	−3.72618	+	0.657026i	−0.163877	+	0.0288960i
$518$		0			0
$519$	1.94227	−	1.22675i	0.0852564	−	0.0538484i
$520$		0			0
$521$	−14.6553	+	25.3837i	−0.642060	+	1.11208i	0.342912	+	0.939368i	$0.388587\pi$
$521$	−14.6553	+	25.3837i	−0.642060	+	1.11208i	−0.984972	+	0.172714i	$0.944746\pi$
$522$		0			0
$523$	3.33680	−	1.92651i	0.145908	−	0.0842402i	−0.425269	−	0.905067i	$-0.639820\pi$
$523$	3.33680	−	1.92651i	0.145908	−	0.0842402i	0.571177	+	0.820827i	$0.306487\pi$
$524$		0			0
$525$	8.40793	+	6.50385i	0.366952	+	0.283851i
$526$		0			0
$527$	1.78683	−	1.49932i	0.0778353	−	0.0653116i
$528$		0			0
$529$	−21.6963	+	7.89682i	−0.943319	+	0.343340i
$530$		0			0
$531$	2.68427	+	33.7049i	0.116487	+	1.46267i
$532$		0			0
$533$	21.1929	+	3.73687i	0.917965	+	0.161862i
$534$		0			0
$535$	−3.77033	−	1.37229i	−0.163006	−	0.0593292i
$536$		0			0
$537$	13.0321	+	14.3338i	0.562376	+	0.618547i
$538$		0			0
$539$		−	19.2380i		−	0.828638i
$540$		0			0
$541$		−	4.51542i		−	0.194133i	−0.995278	−	0.0970665i	$-0.969054\pi$
$541$		−	4.51542i		−	0.194133i	0.995278	−	0.0970665i	$-0.0309460\pi$
$542$		0			0
$543$	−1.95473	+	6.11640i	−0.0838856	+	0.262480i
$544$		0			0
$545$	3.25483	+	1.18466i	0.139421	+	0.0507453i
$546$		0			0
$547$	12.3037	+	2.16948i	0.526069	+	0.0927602i	0.430374	−	0.902651i	$-0.358382\pi$
$547$	12.3037	+	2.16948i	0.526069	+	0.0927602i	0.0956949	+	0.995411i	$0.469493\pi$
$548$		0			0
$549$	15.9685	−	4.14564i	0.681520	−	0.176931i
$550$		0			0
$551$	12.9942	−	4.72950i	0.553572	−	0.201484i
$552$		0			0
$553$	10.6237	−	8.91435i	0.451766	−	0.379077i
$554$		0			0
$555$	−6.14756	+	2.51838i	−0.260949	+	0.106899i
$556$		0			0
$557$	−3.03004	+	1.74940i	−0.128387	+	0.0741243i	−0.562818	−	0.826581i	$-0.690283\pi$
$557$	−3.03004	+	1.74940i	−0.128387	+	0.0741243i	0.434431	+	0.900705i	$0.356949\pi$
$558$		0			0
$559$	36.6233	−	63.4335i	1.54900	−	2.68295i
$560$		0			0
$561$	−6.42449	−	3.37627i	−0.271242	−	0.142546i
$562$		0			0
$563$	−26.9436	+	4.75088i	−1.13554	+	0.200226i	−0.709653	−	0.704552i	$-0.751148\pi$
$563$	−26.9436	+	4.75088i	−1.13554	+	0.200226i	−0.425885	+	0.904777i	$0.640037\pi$
$564$		0			0
$565$	5.59013	−	6.66206i	0.235179	−	0.280275i
$566$		0			0
$567$	−8.89504	−	10.9427i	−0.373557	−	0.459549i
$568$		0			0
$569$	3.15771	+	2.64963i	0.132378	+	0.111078i	0.706573	−	0.707640i	$-0.250240\pi$
$569$	3.15771	+	2.64963i	0.132378	+	0.111078i	−0.574195	+	0.818719i	$0.694685\pi$
$570$		0			0
$571$	−2.91629	+	0.514220i	−0.122043	+	0.0215194i	−0.234336	−	0.972156i	$-0.575292\pi$
$571$	−2.91629	+	0.514220i	−0.122043	+	0.0215194i	0.112293	+	0.993675i	$0.464180\pi$
$572$		0			0
$573$	14.5476	−	27.6817i	0.607733	−	1.15642i
$574$		0			0
$575$	13.2953	−	23.0281i	0.554453	−	0.960340i
$576$		0			0
$577$	−4.23106	−	7.32841i	−0.176141	−	0.305086i	0.764414	−	0.644725i	$-0.223028\pi$
$577$	−4.23106	−	7.32841i	−0.176141	−	0.305086i	−0.940556	+	0.339640i	$0.889695\pi$
$578$		0			0
$579$	−7.11321	+	2.91396i	−0.295615	+	0.121100i
$580$		0			0
$581$	−6.31802	−	7.52952i	−0.262115	−	0.312377i
$582$		0			0
$583$	−19.8980	+	7.24228i	−0.824092	+	0.299945i
$584$		0			0
$585$	15.0205	−	14.7881i	0.621020	−	0.611414i
$586$		0			0
$587$	45.4714	+	8.01784i	1.87681	+	0.330932i	0.991079	−	0.133275i	$-0.0425493\pi$
$587$	45.4714	+	8.01784i	1.87681	+	0.330932i	0.885727	+	0.464206i	$0.153660\pi$
$588$		0			0
$589$	2.51375	−	6.90646i	0.103577	−	0.284576i
$590$		0			0
$591$	−8.61628	+	26.9605i	−0.354426	+	1.10901i
$592$		0			0
$593$	22.0816			0.906784			0.453392	−	0.891311i	$-0.350214\pi$
$593$	22.0816			0.906784			0.453392	+	0.891311i	$0.350214\pi$
$594$		0			0
$595$			1.61432i			0.0661807i
$596$		0			0
$597$	−1.17601	+	1.06922i	−0.0481311	+	0.0437602i
$598$		0			0
$599$	23.2555	+	8.46431i	0.950194	+	0.345842i	0.770184	−	0.637822i	$-0.220165\pi$
$599$	23.2555	+	8.46431i	0.950194	+	0.345842i	0.180010	+	0.983665i	$0.442387\pi$
$600$		0			0
$601$	2.55983	−	14.5175i	0.104418	−	0.592182i	−0.887034	−	0.461705i	$-0.847238\pi$
$601$	2.55983	−	14.5175i	0.104418	−	0.592182i	0.991451	−	0.130477i	$-0.0416509\pi$
$602$		0			0
$603$	−1.96933	−	0.937069i	−0.0801974	−	0.0381604i
$604$		0			0
$605$	2.46229	+	6.76510i	0.100107	+	0.275040i
$606$		0			0
$607$	23.2768	−	19.5315i	0.944775	−	0.792761i	−0.0336346	−	0.999434i	$-0.510708\pi$
$607$	23.2768	−	19.5315i	0.944775	−	0.792761i	0.978410	+	0.206674i	$0.0662638\pi$
$608$		0			0
$609$	−7.36144	+	9.51660i	−0.298301	+	0.385632i
$610$		0			0
$611$	−5.22602	+	3.01724i	−0.211422	+	0.122065i
$612$		0			0
$613$	8.97166	+	5.17979i	0.362362	+	0.209210i	0.670116	−	0.742256i	$-0.266244\pi$
$613$	8.97166	+	5.17979i	0.362362	+	0.209210i	−0.307754	+	0.951466i	$0.599578\pi$
$614$		0			0
$615$	−4.85841	+	3.06859i	−0.195910	+	0.123738i
$616$		0			0
$617$	2.09885	+	11.9032i	0.0844965	+	0.479204i	0.997464	+	0.0711715i	$0.0226738\pi$
$617$	2.09885	+	11.9032i	0.0844965	+	0.479204i	−0.912968	+	0.408032i	$0.866215\pi$
$618$		0			0
$619$	1.25371	−	1.49411i	0.0503908	−	0.0600535i	−0.740260	−	0.672320i	$-0.765298\pi$
$619$	1.25371	−	1.49411i	0.0503908	−	0.0600535i	0.790651	+	0.612267i	$0.209742\pi$
$620$		0			0
$621$	−24.1345	+	25.7278i	−0.968486	+	1.03242i
$622$		0			0
$623$	−9.65710	−	8.10327i	−0.386904	−	0.324651i
$624$		0			0
$625$	1.72350	+	9.77447i	0.0689401	+	0.390979i
$626$		0			0
$627$	−22.8504	+	0.908468i	−0.912557	+	0.0362807i
$628$		0			0
$629$	3.15939	+	1.82408i	0.125973	+	0.0727307i
$630$		0			0
$631$	6.64702	+	11.5130i	0.264614	+	0.458325i	0.967462	−	0.253015i	$-0.0814222\pi$
$631$	6.64702	+	11.5130i	0.264614	+	0.458325i	−0.702849	+	0.711340i	$0.748089\pi$
$632$		0			0
$633$	10.5250	+	1.42739i	0.418330	+	0.0567335i
$634$		0			0
$635$	2.44868	+	2.91823i	0.0971730	+	0.115806i
$636$		0			0
$637$	−10.4939	−	28.8319i	−0.415785	−	1.14236i
$638$		0			0
$639$	−12.3212	−	8.77127i	−0.487418	−	0.346986i
$640$		0			0
$641$	4.99251	−	28.3139i	0.197192	−	1.11833i	−0.712069	−	0.702109i	$-0.752242\pi$
$641$	4.99251	−	28.3139i	0.197192	−	1.11833i	0.909262	−	0.416225i	$-0.136647\pi$
$642$		0			0
$643$	12.8078	−	35.1891i	0.505090	−	1.38772i	−0.381157	−	0.924510i	$-0.624474\pi$
$643$	12.8078	−	35.1891i	0.505090	−	1.38772i	0.886247	−	0.463213i	$-0.153303\pi$
$644$		0			0
$645$	4.15884	+	19.1115i	0.163754	+	0.752513i
$646$		0			0
$647$	23.8383			0.937182			0.468591	−	0.883415i	$-0.344762\pi$
$647$	23.8383			0.937182			0.468591	+	0.883415i	$0.344762\pi$
$648$		0			0
$649$	−47.7068			−1.87266
$650$		0			0
$651$	1.35974	+	6.24853i	0.0532925	+	0.244899i
$652$		0			0
$653$	−16.8138	+	46.1955i	−0.657974	+	1.80777i	−0.0720526	+	0.997401i	$0.522955\pi$
$653$	−16.8138	+	46.1955i	−0.657974	+	1.80777i	−0.585921	+	0.810368i	$0.699267\pi$
$654$		0			0
$655$	−1.77292	+	10.0547i	−0.0692736	+	0.392870i
$656$		0			0
$657$	−3.99687	+	41.9188i	−0.155933	+	1.63541i
$658$		0			0
$659$	9.01137	+	24.7585i	0.351033	+	0.964456i	0.982039	+	0.188678i	$0.0604202\pi$
$659$	9.01137	+	24.7585i	0.351033	+	0.964456i	−0.631006	+	0.775778i	$0.717358\pi$
$660$		0			0
$661$	0.937603	+	1.11739i	0.0364685	+	0.0434615i	0.783970	−	0.620798i	$-0.213191\pi$
$661$	0.937603	+	1.11739i	0.0364685	+	0.0434615i	−0.747502	+	0.664260i	$0.768747\pi$
$662$		0			0
$663$	−11.4701	−	1.55556i	−0.445460	−	0.0604128i
$664$		0			0
$665$	2.54332	+	4.40516i	0.0986258	+	0.170825i
$666$		0			0
$667$	26.0646	+	15.0484i	1.00923	+	0.582677i
$668$		0			0
$669$	37.1082	−	1.47532i	1.43469	−	0.0570392i
$670$		0			0
$671$	4.04215	+	22.9242i	0.156046	+	0.884979i
$672$		0			0
$673$	14.2562	+	11.9623i	0.549534	+	0.461114i	0.874783	−	0.484514i	$-0.161004\pi$
$673$	14.2562	+	11.9623i	0.549534	+	0.461114i	−0.325249	+	0.945628i	$0.605448\pi$
$674$		0			0
$675$	1.12540	−	20.3211i	0.0433165	−	0.782160i
$676$		0			0
$677$	−2.04257	+	2.43424i	−0.0785022	+	0.0935553i	−0.803866	−	0.594810i	$-0.797227\pi$
$677$	−2.04257	+	2.43424i	−0.0785022	+	0.0935553i	0.725364	+	0.688366i	$0.241672\pi$
$678$		0			0
$679$	2.93499	+	16.6451i	0.112634	+	0.638782i
$680$		0			0
$681$	−27.2501	+	17.2113i	−1.04423	+	0.659538i
$682$		0			0
$683$	7.95770	+	4.59438i	0.304493	+	0.175799i	0.644459	−	0.764639i	$-0.277082\pi$
$683$	7.95770	+	4.59438i	0.304493	+	0.175799i	−0.339967	+	0.940437i	$0.610416\pi$
$684$		0			0
$685$	−19.9118	+	11.4961i	−0.760792	+	0.439243i
$686$		0			0
$687$	−9.41089	+	12.1660i	−0.359048	+	0.464164i
$688$		0			0
$689$	−25.8705	+	21.7080i	−0.985589	+	0.827008i
$690$		0			0
$691$	6.14708	+	16.8890i	0.233846	+	0.642487i	1.00000		0.000170287i	$-5.42042e-5\pi$
$691$	6.14708	+	16.8890i	0.233846	+	0.642487i	−0.766154	+	0.642657i	$0.777832\pi$
$692$		0			0
$693$	16.3873	−	11.2852i	0.622501	−	0.428689i
$694$		0			0
$695$	0.860413	−	4.87964i	0.0326373	−	0.185095i
$696$		0			0
$697$	2.96524	+	1.07926i	0.112316	+	0.0408799i
$698$		0			0
$699$	−24.0863	+	21.8989i	−0.911027	+	0.828294i
$700$		0			0
$701$			19.1567i			0.723538i	0.932268	+	0.361769i	$0.117827\pi$
$701$			19.1567i			0.723538i	−0.932268	+	0.361769i	$0.882173\pi$
$702$		0			0
$703$	11.4952			0.433548
$704$		0			0
$705$	0.490531	−	1.53488i	0.0184745	−	0.0578070i
$706$		0			0
$707$	3.54070	−	9.72798i	0.133162	−	0.365858i
$708$		0			0
$709$	−9.23990	−	1.62924i	−0.347012	−	0.0611875i	−0.00257396	−	0.999997i	$-0.500819\pi$
$709$	−9.23990	−	1.62924i	−0.347012	−	0.0611875i	−0.344438	+	0.938809i	$0.611930\pi$
$710$		0			0
$711$	−25.5936	−	7.07202i	−0.959834	−	0.265222i
$712$		0			0
$713$	15.0318	−	5.47115i	0.562947	−	0.204896i
$714$		0			0
$715$	19.1171	+	22.7829i	0.714938	+	0.852031i
$716$		0			0
$717$	32.9192	−	13.4855i	1.22939	−	0.503626i
$718$		0			0
$719$	−10.7417	−	18.6051i	−0.400596	−	0.693853i	0.593202	−	0.805054i	$-0.297864\pi$
$719$	−10.7417	−	18.6051i	−0.400596	−	0.693853i	−0.993798	+	0.111201i	$0.964530\pi$
$720$		0			0
$721$	12.4487	−	21.5618i	0.463614	−	0.803003i
$722$		0			0
$723$	11.1000	−	21.1215i	0.412812	−	0.785516i
$724$		0			0
$725$	−17.1004	+	3.01526i	−0.635092	+	0.111984i
$726$		0			0
$727$	22.5451	+	18.9176i	0.836151	+	0.701614i	0.956694	−	0.291094i	$-0.0940193\pi$
$727$	22.5451	+	18.9176i	0.836151	+	0.701614i	−0.120543	+	0.992708i	$0.538464\pi$
$728$		0			0
$729$	−7.59595	+	25.9095i	−0.281331	+	0.959611i
$730$		0			0
$731$	6.90385	−	8.22768i	0.255348	−	0.304312i
$732$		0			0
$733$	43.1488	−	7.60829i	1.59374	−	0.281019i	0.694835	−	0.719170i	$-0.255478\pi$
$733$	43.1488	−	7.60829i	1.59374	−	0.281019i	0.898901	+	0.438151i	$0.144366\pi$
$734$		0			0
$735$	7.25243	+	3.81137i	0.267510	+	0.140584i
$736$		0			0
$737$	1.53859	−	2.66491i	0.0566746	−	0.0981632i
$738$		0			0
$739$	−21.9574	+	12.6771i	−0.807716	+	0.466335i	−0.846162	−	0.532926i	$-0.821093\pi$
$739$	−21.9574	+	12.6771i	−0.807716	+	0.466335i	0.0384462	+	0.999261i	$0.487759\pi$
$740$		0			0
$741$	−33.7503	+	13.8260i	−1.23985	+	0.507910i
$742$		0			0
$743$	3.44991	−	2.89482i	0.126565	−	0.106201i	−0.577308	−	0.816526i	$-0.695897\pi$
$743$	3.44991	−	2.89482i	0.126565	−	0.106201i	0.703873	+	0.710326i	$0.251452\pi$
$744$		0			0
$745$	−22.5055	+	8.19135i	−0.824539	+	0.300108i
$746$		0			0
$747$	−5.01228	+	18.1394i	−0.183390	+	0.663685i
$748$		0			0
$749$	−5.94874	−	1.04892i	−0.217362	−	0.0383268i
$750$		0			0
$751$	−36.9941	−	13.4647i	−1.34993	−	0.491335i	−0.437006	−	0.899459i	$-0.643961\pi$
$751$	−36.9941	−	13.4647i	−1.34993	−	0.491335i	−0.912927	+	0.408124i	$0.866183\pi$
$752$		0			0
$753$	−0.255166	+	0.798419i	−0.00929875	+	0.0290960i
$754$		0			0
$755$			20.6870i			0.752876i
$756$		0			0
$757$		−	33.7213i		−	1.22562i	−0.790229	−	0.612811i	$-0.790039\pi$
$757$		−	33.7213i		−	1.22562i	0.790229	−	0.612811i	$-0.209961\pi$
$758$		0			0
$759$	−33.4829	−	36.8273i	−1.21535	−	1.33674i
$760$		0			0
$761$	−34.7776	−	12.6580i	−1.26069	−	0.458852i	−0.376687	−	0.926341i	$-0.622937\pi$
$761$	−34.7776	−	12.6580i	−1.26069	−	0.458852i	−0.883999	+	0.467489i	$0.845159\pi$
$762$		0			0
$763$	5.13539	+	0.905508i	0.185914	+	0.0327816i
$764$		0			0
$765$	2.54560	−	1.75304i	0.0920365	−	0.0633814i
$766$		0			0
$767$	−71.4980	+	26.0231i	−2.58164	+	0.939641i
$768$		0			0
$769$	−4.44297	+	3.72810i	−0.160218	+	0.134439i	−0.719372	−	0.694625i	$-0.755570\pi$
$769$	−4.44297	+	3.72810i	−0.160218	+	0.134439i	0.559154	+	0.829064i	$0.311126\pi$
$770$		0			0
$771$	24.3039	+	18.7999i	0.875283	+	0.677064i
$772$		0			0
$773$	−36.8149	+	21.2551i	−1.32414	+	0.764492i	−0.984386	−	0.176022i	$-0.943677\pi$
$773$	−36.8149	+	21.2551i	−1.32414	+	0.764492i	−0.339753	+	0.940515i	$0.610344\pi$
$774$		0			0
$775$	−4.61456	+	7.99264i	−0.165760	+	0.287104i
$776$		0			0
$777$	−8.45615	+	5.34095i	−0.303363	+	0.191605i
$778$		0			0
$779$	9.79190	−	1.72658i	0.350831	−	0.0618610i
$780$		0			0
$781$	13.7170	−	16.3473i	0.490833	−	0.584951i
$782$		0			0
$783$	23.0006	+	1.27379i	0.821976	+	0.0455216i
$784$		0			0
$785$	3.89904	+	3.27169i	0.139163	+	0.116771i
$786$		0			0
$787$	16.8983	−	2.97963i	0.602359	−	0.106212i	0.135851	−	0.990729i	$-0.456623\pi$
$787$	16.8983	−	2.97963i	0.602359	−	0.106212i	0.466508	+	0.884517i	$0.345512\pi$
$788$		0			0
$789$	−13.9365	+	0.554078i	−0.496154	+	0.0197257i
$790$		0			0
$791$	6.54642	−	11.3387i	0.232764	−	0.403159i
$792$		0			0
$793$	18.5627	+	32.1515i	0.659179	+	1.14173i
$794$		0			0
$795$	1.21190	−	8.93607i	0.0429817	−	0.316930i
$796$		0			0
$797$	−4.53298	−	5.40220i	−0.160567	−	0.191356i	0.679763	−	0.733432i	$-0.262083\pi$
$797$	−4.53298	−	5.40220i	−0.160567	−	0.191356i	−0.840329	+	0.542076i	$0.817638\pi$
$798$		0			0
$799$	−0.831499	+	0.302641i	−0.0294163	+	0.0107067i
$800$		0			0
$801$	−2.29100	+	24.0278i	−0.0809483	+	0.848980i
$802$		0			0
$803$	−58.5114	−	10.3171i	−2.06482	−	0.364084i
$804$		0			0
$805$	−3.78652	+	10.4034i	−0.133457	+	0.366670i
$806$		0			0
$807$	11.1115	−	2.41797i	0.391144	−	0.0851167i
$808$		0			0
$809$	−34.2649			−1.20469			−0.602345	−	0.798236i	$-0.705767\pi$
$809$	−34.2649			−1.20469			−0.602345	+	0.798236i	$0.705767\pi$
$810$		0			0
$811$			5.06146i			0.177732i	0.996044	+	0.0888659i	$0.0283243\pi$
$811$			5.06146i			0.177732i	−0.996044	+	0.0888659i	$0.971676\pi$
$812$		0			0
$813$	−4.00050	−	18.3839i	−0.140304	−	0.644750i
$814$		0			0
$815$	−4.08885	−	1.48822i	−0.143226	−	0.0521301i
$816$		0			0
$817$	5.87673	−	33.3286i	0.205601	−	1.16602i
$818$		0			0
$819$	18.4037	−	25.8520i	0.643077	−	0.903342i
$820$		0			0
$821$	5.19050	+	14.2608i	0.181150	+	0.497705i	0.996718	−	0.0809566i	$-0.0257975\pi$
$821$	5.19050	+	14.2608i	0.181150	+	0.497705i	−0.815568	+	0.578661i	$0.803575\pi$
$822$		0			0
$823$	−22.8496	+	19.1731i	−0.796487	+	0.668332i	−0.947342	−	0.320224i	$-0.896242\pi$
$823$	−22.8496	+	19.1731i	−0.796487	+	0.668332i	0.150855	+	0.988556i	$0.451797\pi$
$824$		0			0
$825$	28.4557	+	3.85914i	0.990701	+	0.134358i
$826$		0			0
$827$	7.24554	−	4.18322i	0.251952	−	0.145465i	−0.368706	−	0.929546i	$-0.620199\pi$
$827$	7.24554	−	4.18322i	0.251952	−	0.145465i	0.620658	+	0.784082i	$0.286866\pi$
$828$		0			0
$829$	26.4946	+	15.2967i	0.920196	+	0.531276i	0.883698	−	0.468058i	$-0.155046\pi$
$829$	26.4946	+	15.2967i	0.920196	+	0.531276i	0.0364987	+	0.999334i	$0.488380\pi$
$830$		0			0
$831$	2.18154	+	54.8716i	0.0756768	+	1.90348i
$832$		0			0
$833$	−0.781255	−	4.43072i	−0.0270689	−	0.153515i
$834$		0			0
$835$	−4.07776	+	4.85968i	−0.141117	+	0.168176i
$836$		0			0
$837$	8.37666	−	8.92965i	0.289540	−	0.308654i
$838$		0			0
$839$	−5.60536	−	4.70346i	−0.193519	−	0.162381i	0.540880	−	0.841100i	$-0.318091\pi$
$839$	−5.60536	−	4.70346i	−0.193519	−	0.162381i	−0.734399	+	0.678718i	$0.762536\pi$
$840$		0			0
$841$	1.62295	+	9.20422i	0.0559639	+	0.317387i
$842$		0			0
$843$	−18.1590	−	28.7505i	−0.625428	−	0.990219i
$844$		0			0
$845$	29.3610	+	16.9516i	1.01005	+	0.583151i
$846$		0			0
$847$	5.41924	+	9.38639i	0.186207	+	0.322520i
$848$		0			0
$849$	20.9000	−	27.0187i	0.717285	−	0.927280i
$850$		0			0
$851$	16.0820	+	19.1657i	0.551283	+	0.656993i
$852$		0			0
$853$	15.5473	+	42.7160i	0.532331	+	1.46257i	0.856290	+	0.516496i	$0.172764\pi$
$853$	15.5473	+	42.7160i	0.532331	+	1.46257i	−0.323959	+	0.946071i	$0.605014\pi$
$854$		0			0
$855$	4.18458	−	8.79424i	0.143109	−	0.300757i
$856$		0			0
$857$	−3.84017	+	21.7787i	−0.131178	+	0.743946i	0.846268	+	0.532758i	$0.178844\pi$
$857$	−3.84017	+	21.7787i	−0.131178	+	0.743946i	−0.977445	+	0.211188i	$0.932267\pi$
$858$		0			0
$859$	10.5655	−	29.0285i	0.360491	−	0.990441i	−0.618365	−	0.785891i	$-0.712205\pi$
$859$	10.5655	−	29.0285i	0.360491	−	0.990441i	0.978856	−	0.204550i	$-0.0655730\pi$
$860$		0			0
$861$	−6.40098	+	5.81969i	−0.218145	+	0.198335i
$862$		0			0
$863$	27.4661			0.934956			0.467478	−	0.884005i	$-0.345163\pi$
$863$	27.4661			0.934956			0.467478	+	0.884005i	$0.345163\pi$
$864$		0			0
$865$	−1.38039			−0.0469348
$866$		0			0
$867$	26.4306	+	8.44692i	0.897630	+	0.286872i
$868$		0			0
$869$	12.8137	−	35.2053i	0.434675	−	1.19426i
$870$		0			0
$871$	0.852216	−	4.83316i	0.0288762	−	0.163765i
$872$		0			0
$873$	23.0603	−	22.7036i	0.780474	−	0.768402i
$874$		0			0
$875$	−4.97337	−	13.6642i	−0.168131	−	0.461935i
$876$		0			0
$877$	−7.68788	−	9.16206i	−0.259601	−	0.309381i	0.620463	−	0.784236i	$-0.286945\pi$
$877$	−7.68788	−	9.16206i	−0.259601	−	0.309381i	−0.880064	+	0.474855i	$0.842500\pi$
$878$		0			0
$879$	17.4590	+	42.6188i	0.588879	+	1.43750i
$880$		0			0
$881$	18.8243	+	32.6046i	0.634205	+	1.09848i	0.986683	+	0.162655i	$0.0520059\pi$
$881$	18.8243	+	32.6046i	0.634205	+	1.09848i	−0.352478	+	0.935820i	$0.614661\pi$
$882$		0			0
$883$	19.8345	+	11.4515i	0.667485	+	0.385373i	0.795123	−	0.606448i	$-0.207406\pi$
$883$	19.8345	+	11.4515i	0.667485	+	0.385373i	−0.127638	+	0.991821i	$0.540739\pi$
$884$		0			0
$885$	9.45153	−	17.9847i	0.317710	−	0.604551i
$886$		0			0
$887$	−0.995710	−	5.64695i	−0.0334327	−	0.189606i	0.963518	−	0.267645i	$-0.0862454\pi$
$887$	−0.995710	−	5.64695i	−0.0334327	−	0.189606i	−0.996950	+	0.0780387i	$0.975134\pi$
$888$		0			0
$889$	4.39338	+	3.68648i	0.147349	+	0.123641i
$890$		0			0
$891$	−35.5910	−	13.5860i	−1.19234	−	0.455147i
$892$		0			0
$893$	−1.79219	+	2.13585i	−0.0599735	+	0.0714737i
$894$		0			0
$895$	−2.02139	−	11.4639i	−0.0675675	−	0.383194i
$896$		0			0
$897$	−70.2692	−	36.9286i	−2.34622	−	1.23301i
$898$		0			0
$899$	−9.04655	−	5.22303i	−0.301719	−	0.174198i
$900$		0			0
$901$	−4.28862	+	2.47604i	−0.142875	+	0.0824888i
$902$		0			0
$903$	11.1622	+	27.2479i	0.371456	+	0.906753i
$904$		0			0
$905$	2.95572	−	2.48014i	0.0982513	−	0.0824426i
$906$		0			0
$907$	8.42248	+	23.1406i	0.279664	+	0.768370i	0.997401	+	0.0720557i	$0.0229559\pi$
$907$	8.42248	+	23.1406i	0.279664	+	0.768370i	−0.717737	+	0.696315i	$0.754822\pi$
$908$		0			0
$909$	−19.1849	+	4.98065i	−0.636323	+	0.165198i
$910$		0			0
$911$	−6.32793	+	35.8875i	−0.209654	+	1.18901i	0.680293	+	0.732940i	$0.261853\pi$
$911$	−6.32793	+	35.8875i	−0.209654	+	1.18901i	−0.889947	+	0.456065i	$0.849259\pi$
$912$		0			0
$913$	−24.9517	−	9.08166i	−0.825780	−	0.300559i
$914$		0			0
$915$	−9.44290	−	3.01784i	−0.312173	−	0.0997668i
$916$		0			0
$917$			15.3708i			0.507590i
$918$		0			0
$919$	−27.8245			−0.917845			−0.458923	−	0.888476i	$-0.651764\pi$
$919$	−27.8245			−0.917845			−0.458923	+	0.888476i	$0.651764\pi$
$920$		0			0
$921$	−26.9633	−	29.6565i	−0.888470	−	0.977213i
$922$		0			0
$923$	11.6405	−	31.9819i	0.383151	−	1.05270i
$924$		0			0
$925$	−14.2153	−	2.50654i	−0.467397	−	0.0824146i
$926$		0			0
$927$	−47.5190	+	3.78443i	−1.56073	+	0.124297i
$928$		0			0
$929$	14.0864	−	5.12703i	0.462160	−	0.168212i	−0.100438	−	0.994943i	$-0.532024\pi$
$929$	14.0864	−	5.12703i	0.462160	−	0.168212i	0.562598	+	0.826731i	$0.309802\pi$
$930$		0			0
$931$	−9.11238	−	10.8597i	−0.298646	−	0.355913i
$932$		0			0
$933$	33.4088	+	25.8429i	1.09375	+	0.846060i
$934$		0			0
$935$	2.18052	+	3.77677i	0.0713106	+	0.123514i
$936$		0			0
$937$	−9.57278	+	16.5805i	−0.312729	+	0.541663i	−0.978952	−	0.204090i	$-0.934577\pi$
$937$	−9.57278	+	16.5805i	−0.312729	+	0.541663i	0.666223	+	0.745753i	$0.267910\pi$
$938$		0			0
$939$	23.8352	+	37.7375i	0.777833	+	1.23152i
$940$		0			0
$941$	36.4053	−	6.41923i	1.18678	−	0.209261i	0.454803	−	0.890592i	$-0.349710\pi$
$941$	36.4053	−	6.41923i	1.18678	−	0.209261i	0.731975	+	0.681331i	$0.238599\pi$
$942$		0			0
$943$	16.5778	+	13.9104i	0.539847	+	0.452985i
$944$		0			0
$945$	1.00775	+	8.41355i	0.0327820	+	0.273693i
$946$		0			0
$947$	16.0406	−	19.1164i	0.521248	−	0.621199i	−0.439627	−	0.898180i	$-0.644890\pi$
$947$	16.0406	−	19.1164i	0.521248	−	0.621199i	0.960875	+	0.276981i	$0.0893340\pi$
$948$		0			0
$949$	−93.3185	+	16.4546i	−3.02925	+	0.534138i
$950$		0			0
$951$	−1.26721	−	31.8738i	−0.0410922	−	1.03358i
$952$		0			0
$953$	−7.31014	+	12.6615i	−0.236799	+	0.410147i	−0.959794	−	0.280706i	$-0.909432\pi$
$953$	−7.31014	+	12.6615i	−0.236799	+	0.410147i	0.722995	+	0.690853i	$0.242765\pi$
$954$		0			0
$955$	−16.2733	+	9.39537i	−0.526590	+	0.304027i
$956$		0			0
$957$	−4.36800	+	32.2079i	−0.141197	+	1.04113i
$958$		0			0
$959$	−26.5164	+	22.2499i	−0.856258	+	0.718486i
$960$		0			0
$961$	23.9132	−	8.70369i	0.771393	−	0.280764i
$962$		0			0
$963$	4.80590	+	10.5196i	0.154868	+	0.338988i
$964$		0			0
$965$	4.54883	+	0.802081i	0.146432	+	0.0258199i
$966$		0			0
$967$	−48.8192	−	17.7687i	−1.56992	−	0.571404i	−0.596937	−	0.802288i	$-0.703616\pi$
$967$	−48.8192	−	17.7687i	−1.56992	−	0.571404i	−0.972981	+	0.230884i	$0.925838\pi$
$968$		0			0
$969$	−5.22581	+	1.13719i	−0.167877	+	0.0365317i
$970$		0			0
$971$			20.4952i			0.657724i	0.944378	+	0.328862i	$0.106665\pi$
$971$			20.4952i			0.657724i	−0.944378	+	0.328862i	$0.893335\pi$
$972$		0			0
$973$		−	7.45961i		−	0.239144i
$974$		0			0
$975$	44.7515	−	9.73837i	1.43320	−	0.311877i
$976$		0			0
$977$	−7.72505	−	2.81169i	−0.247146	−	0.0899539i	0.215477	−	0.976509i	$-0.430869\pi$
$977$	−7.72505	−	2.81169i	−0.247146	−	0.0899539i	−0.462623	+	0.886555i	$0.653092\pi$
$978$		0			0
$979$	−33.5386	−	5.91376i	−1.07190	−	0.189004i
$980$		0			0
$981$	−4.14880	−	9.08126i	−0.132461	−	0.289942i
$982$		0			0
$983$	22.5289	−	8.19984i	0.718559	−	0.261534i	0.0432453	−	0.999064i	$-0.486230\pi$
$983$	22.5289	−	8.19984i	0.718559	−	0.261534i	0.675314	+	0.737530i	$0.264008\pi$
$984$		0			0
$985$	13.0285	−	10.9322i	0.415123	−	0.348330i
$986$		0			0
$987$	0.326014	−	2.40389i	0.0103771	−	0.0765168i
$988$		0			0
$989$	63.7900	−	36.8292i	2.02840	−	1.17110i
$990$		0			0
$991$	−8.43544	+	14.6106i	−0.267960	+	0.464121i	−0.968335	−	0.249654i	$-0.919683\pi$
$991$	−8.43544	+	14.6106i	−0.267960	+	0.464121i	0.700375	+	0.713776i	$0.253016\pi$
$992$		0			0
$993$	1.06459	+	26.7773i	0.0337837	+	0.849751i
$994$		0			0
$995$	0.940553	−	0.165845i	0.0298175	−	0.00525763i
$996$		0			0
$997$	21.3234	−	25.4122i	0.675317	−	0.804812i	−0.314180	−	0.949363i	$-0.601730\pi$
$997$	21.3234	−	25.4122i	0.675317	−	0.804812i	0.989497	+	0.144552i	$0.0461740\pi$
$998$		0			0
$999$	17.6049	+	7.53450i	0.556994	+	0.238381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bf.a.529.20		204
4.3	odd	2		216.2.t.a.205.32	yes	204
8.3	odd	2		216.2.t.a.205.18	yes	204
8.5	even	2	inner	864.2.bf.a.529.15		204
12.11	even	2		648.2.t.a.613.3		204
24.11	even	2		648.2.t.a.613.17		204
27.22	even	9	inner	864.2.bf.a.49.15		204
108.59	even	18		648.2.t.a.37.17		204
108.103	odd	18		216.2.t.a.157.18	✓	204
216.59	even	18		648.2.t.a.37.3		204
216.157	even	18	inner	864.2.bf.a.49.20		204
216.211	odd	18		216.2.t.a.157.32	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.18	✓	204	108.103	odd	18
216.2.t.a.157.32	yes	204	216.211	odd	18
216.2.t.a.205.18	yes	204	8.3	odd	2
216.2.t.a.205.32	yes	204	4.3	odd	2
648.2.t.a.37.3		204	216.59	even	18
648.2.t.a.37.17		204	108.59	even	18
648.2.t.a.613.3		204	12.11	even	2
648.2.t.a.613.17		204	24.11	even	2
864.2.bf.a.49.15		204	27.22	even	9	inner
864.2.bf.a.49.20		204	216.157	even	18	inner
864.2.bf.a.529.15		204	8.5	even	2	inner
864.2.bf.a.529.20		204	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.368292 + 1.69244i) q^{3} +(0.355965 - 0.978005i) q^{5} +(0.272085 - 1.54307i) q^{7} +(-2.72872 + 1.24663i) q^{9} +(-1.44773 - 3.97760i) q^{11} +(-4.33941 - 5.17151i) q^{13} +(1.78632 + 0.242259i) q^{15} +(-0.494959 - 0.857294i) q^{17} +(-2.70129 - 1.55959i) q^{19} +(2.71177 - 0.107812i) q^{21} +(-1.17888 - 6.68573i) q^{23} +(3.00044 + 2.51767i) q^{25} +(-3.11481 - 4.15908i) q^{27} +(-2.84964 + 3.39607i) q^{29} +(0.409166 + 2.32049i) q^{31} +(6.19868 - 3.91512i) q^{33} +(-1.41228 - 0.815381i) q^{35} +(-3.19157 + 1.84266i) q^{37} +(7.15431 - 9.24883i) q^{39} +(-2.44191 + 2.04900i) q^{41} +(3.71087 + 10.1955i) q^{43} +(0.247877 + 3.11246i) q^{45} +(0.155220 - 0.880296i) q^{47} +(4.27080 + 1.55445i) q^{49} +(1.26863 - 1.15342i) q^{51} -5.00251i q^{53} -4.40546 q^{55} +(1.64465 - 5.14616i) q^{57} +(3.85475 - 10.5908i) q^{59} +(-5.41575 - 0.954943i) q^{61} +(1.18119 + 4.54981i) q^{63} +(-6.60244 + 2.40309i) q^{65} +(0.467287 + 0.556891i) q^{67} +(10.8810 - 4.45748i) q^{69} +(2.52073 + 4.36603i) q^{71} +(7.01816 - 12.1558i) q^{73} +(-3.15597 + 6.00531i) q^{75} +(-6.53164 + 1.15170i) q^{77} +(6.78017 + 5.68924i) q^{79} +(5.89185 - 6.80339i) q^{81} +(4.03223 - 4.80543i) q^{83} +(-1.01463 + 0.178906i) q^{85} +(-6.79716 - 3.57211i) q^{87} +(4.02279 - 6.96768i) q^{89} +(-9.16071 + 5.28894i) q^{91} +(-3.77661 + 1.54711i) q^{93} +(-2.48685 + 2.08672i) q^{95} +(-10.1365 + 3.68937i) q^{97} +(8.90903 + 9.04900i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73}+ \cdots - 12 q^{97}+O(q^{100}) \) 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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