LMFDB - Embedded newform 729.2.g.d.217.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] 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("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,9,0,9,9,0,9,-18,0,-18,9,0,9,9,0,9,-18,0,-18,45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			217.1
Character	$\chi$	$=$	729.217
Dual form			729.2.g.d.514.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.126512 + 2.17212i) q^{2} +(-2.71564 - 0.317413i) q^{4} +(0.629067 - 0.149092i) q^{5} +(-1.09241 - 1.46736i) q^{7} +(0.277373 - 1.57306i) q^{8} +(0.244261 + 1.38527i) q^{10} +(0.830243 - 0.880006i) q^{11} +(-4.76615 - 2.39365i) q^{13} +(3.32548 - 2.18720i) q^{14} +(-1.93907 - 0.459569i) q^{16} +(-6.43434 - 2.34191i) q^{17} +(-5.97823 + 2.17590i) q^{19} +(-1.75565 + 0.205206i) q^{20} +(1.80645 + 1.91472i) q^{22} +(-1.86114 + 2.49994i) q^{23} +(-4.09467 + 2.05642i) q^{25} +(5.80229 - 10.0499i) q^{26} +(2.50083 + 4.33156i) q^{28} +(4.91797 + 3.23460i) q^{29} +(-1.09846 - 2.54651i) q^{31} +(2.15979 - 7.21421i) q^{32} +(5.90094 - 13.6799i) q^{34} +(-0.905967 - 0.760197i) q^{35} +(-1.09453 + 0.918418i) q^{37} +(-3.97000 - 13.2607i) q^{38} +(-0.0600440 - 1.03092i) q^{40} +(-0.0648547 - 1.11351i) q^{41} +(2.76319 + 9.22968i) q^{43} +(-2.53397 + 2.12625i) q^{44} +(-5.19473 - 4.35890i) q^{46} +(2.41701 - 5.60327i) q^{47} +(1.04784 - 3.50003i) q^{49} +(-3.94877 - 9.15429i) q^{50} +(12.1834 + 8.01315i) q^{52} +(4.26135 + 7.38088i) q^{53} +(0.391077 - 0.677365i) q^{55} +(-2.61124 + 1.31142i) q^{56} +(-7.64814 + 10.2732i) q^{58} +(-1.43295 - 1.51884i) q^{59} +(3.56577 - 0.416778i) q^{61} +(5.67029 - 2.06382i) q^{62} +(11.6517 + 4.24088i) q^{64} +(-3.35511 - 0.795175i) q^{65} +(-1.01911 + 0.670277i) q^{67} +(16.7300 + 8.40213i) q^{68} +(1.76586 - 1.87170i) q^{70} +(1.41528 + 8.02646i) q^{71} +(1.11524 - 6.32482i) q^{73} +(-1.85645 - 2.49364i) q^{74} +(16.9254 - 4.01139i) q^{76} +(-2.19824 - 0.256938i) q^{77} +(0.829051 - 14.2343i) q^{79} -1.28832 q^{80} +2.42689 q^{82} +(-0.390702 + 6.70809i) q^{83} +(-4.39679 - 0.513911i) q^{85} +(-20.3976 + 4.83432i) q^{86} +(-1.15402 - 1.55011i) q^{88} +(-2.70557 + 15.3441i) q^{89} +(1.69423 + 9.60848i) q^{91} +(5.84771 - 6.19821i) q^{92} +(11.8652 + 5.95894i) q^{94} +(-3.43630 + 2.26009i) q^{95} +(-3.62877 - 0.860034i) q^{97} +(7.46994 + 2.71884i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{14}{27}\right)$

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 $

$2$	−0.126512	+	2.17212i	−0.0894574	+	1.53592i	0.593122	+	0.805113i	$0.297895\pi$
$2$	−0.126512	+	2.17212i	−0.0894574	+	1.53592i	−0.682579	+	0.730812i	$0.739142\pi$
$3$		0			0
$3$		0			0
$4$	−2.71564	−	0.317413i	−1.35782	−	0.158707i
$5$	0.629067	−	0.149092i	0.281327	−	0.0666758i	−0.0875297	−	0.996162i	$-0.527897\pi$
$5$	0.629067	−	0.149092i	0.281327	−	0.0666758i	0.368857	+	0.929486i	$0.379749\pi$
$6$		0			0
$7$	−1.09241	−	1.46736i	−0.412891	−	0.554608i	0.546219	−	0.837642i	$-0.316066\pi$
$7$	−1.09241	−	1.46736i	−0.412891	−	0.554608i	−0.959110	+	0.283034i	$0.908659\pi$
$8$	0.277373	−	1.57306i	0.0980662	−	0.556161i
$9$		0			0
$10$	0.244261	+	1.38527i	0.0772422	+	0.438062i
$11$	0.830243	−	0.880006i	0.250328	−	0.265332i	−0.590009	−	0.807397i	$-0.700876\pi$
$11$	0.830243	−	0.880006i	0.250328	−	0.265332i	0.840337	+	0.542065i	$0.182357\pi$
$12$		0			0
$13$	−4.76615	−	2.39365i	−1.32189	−	0.663880i	−0.358893	−	0.933379i	$-0.616846\pi$
$13$	−4.76615	−	2.39365i	−1.32189	−	0.663880i	−0.963001	+	0.269499i	$0.913142\pi$
$14$	3.32548	−	2.18720i	0.888772	−	0.584555i
$15$		0			0
$16$	−1.93907	−	0.459569i	−0.484768	−	0.114892i
$17$	−6.43434	−	2.34191i	−1.56056	−	0.567996i	−0.589693	−	0.807628i	$-0.700751\pi$
$17$	−6.43434	−	2.34191i	−1.56056	−	0.567996i	−0.970864	+	0.239631i	$0.922973\pi$
$18$		0			0
$19$	−5.97823	+	2.17590i	−1.37150	+	0.499185i	−0.919590	−	0.392879i	$-0.871479\pi$
$19$	−5.97823	+	2.17590i	−1.37150	+	0.499185i	−0.451909	+	0.892064i	$0.649257\pi$
$20$	−1.75565	+	0.205206i	−0.392575	+	0.0458854i
$21$		0			0
$22$	1.80645	+	1.91472i	0.385136	+	0.408220i
$23$	−1.86114	+	2.49994i	−0.388074	+	0.521274i	−0.952634	−	0.304118i	$-0.901638\pi$
$23$	−1.86114	+	2.49994i	−0.388074	+	0.521274i	0.564560	+	0.825392i	$0.309046\pi$
$24$		0			0
$25$	−4.09467	+	2.05642i	−0.818933	+	0.411284i
$26$	5.80229	−	10.0499i	1.13792	−	1.97094i
$27$		0			0
$28$	2.50083	+	4.33156i	0.472612	+	0.818588i
$29$	4.91797	+	3.23460i	0.913244	+	0.600650i	0.916801	−	0.399344i	$-0.130762\pi$
$29$	4.91797	+	3.23460i	0.913244	+	0.600650i	−0.00355721	+	0.999994i	$0.501132\pi$
$30$		0			0
$31$	−1.09846	−	2.54651i	−0.197288	−	0.457366i	0.790639	−	0.612282i	$-0.209748\pi$
$31$	−1.09846	−	2.54651i	−0.197288	−	0.457366i	−0.987928	+	0.154916i	$0.950489\pi$
$32$	2.15979	−	7.21421i	0.381801	−	1.27530i
$33$		0			0
$34$	5.90094	−	13.6799i	1.01200	−	2.34609i
$35$	−0.905967	−	0.760197i	−0.153136	−	0.128497i
$36$		0			0
$37$	−1.09453	+	0.918418i	−0.179939	+	0.150987i	−0.728309	−	0.685249i	$-0.759693\pi$
$37$	−1.09453	+	0.918418i	−0.179939	+	0.150987i	0.548369	+	0.836236i	$0.315249\pi$
$38$	−3.97000	−	13.2607i	−0.644019	−	2.15117i
$39$		0			0
$40$	−0.0600440	−	1.03092i	−0.00949379	−	0.163002i
$41$	−0.0648547	−	1.11351i	−0.0101286	−	0.173902i	−0.999579	−	0.0290269i	$-0.990759\pi$
$41$	−0.0648547	−	1.11351i	−0.0101286	−	0.173902i	0.989450	−	0.144875i	$-0.0462779\pi$
$42$		0			0
$43$	2.76319	+	9.22968i	0.421382	+	1.40751i	0.860668	+	0.509167i	$0.170046\pi$
$43$	2.76319	+	9.22968i	0.421382	+	1.40751i	−0.439286	+	0.898347i	$0.644769\pi$
$44$	−2.53397	+	2.12625i	−0.382010	+	0.320545i
$45$		0			0
$46$	−5.19473	−	4.35890i	−0.765922	−	0.642685i
$47$	2.41701	−	5.60327i	0.352558	−	0.817321i	−0.645985	−	0.763350i	$-0.723553\pi$
$47$	2.41701	−	5.60327i	0.352558	−	0.817321i	0.998543	−	0.0539704i	$-0.0171877\pi$
$48$		0			0
$49$	1.04784	−	3.50003i	0.149692	−	0.500005i
$50$	−3.94877	−	9.15429i	−0.558441	−	1.29461i
$51$		0			0
$52$	12.1834	+	8.01315i	1.68953	+	1.11122i
$53$	4.26135	+	7.38088i	0.585342	+	1.01384i	0.994833	+	0.101528i	$0.0323731\pi$
$53$	4.26135	+	7.38088i	0.585342	+	1.01384i	−0.409491	+	0.912314i	$0.634294\pi$
$54$		0			0
$55$	0.391077	−	0.677365i	0.0527328	−	0.0913359i
$56$	−2.61124	+	1.31142i	−0.348942	+	0.175245i
$57$		0			0
$58$	−7.64814	+	10.2732i	−1.00425	+	1.34894i
$59$	−1.43295	−	1.51884i	−0.186554	−	0.197736i	0.627346	−	0.778741i	$-0.284141\pi$
$59$	−1.43295	−	1.51884i	−0.186554	−	0.197736i	−0.813900	+	0.581005i	$0.802660\pi$
$60$		0			0
$61$	3.56577	−	0.416778i	0.456550	−	0.0533630i	0.115290	−	0.993332i	$-0.463220\pi$
$61$	3.56577	−	0.416778i	0.456550	−	0.0533630i	0.341260	+	0.939969i	$0.389146\pi$
$62$	5.67029	−	2.06382i	0.720128	−	0.262105i
$63$		0			0
$64$	11.6517	+	4.24088i	1.45646	+	0.530110i
$65$	−3.35511	−	0.795175i	−0.416150	−	0.0986293i
$66$		0			0
$67$	−1.01911	+	0.670277i	−0.124504	+	0.0818873i	−0.610233	−	0.792222i	$-0.708924\pi$
$67$	−1.01911	+	0.670277i	−0.124504	+	0.0818873i	0.485730	+	0.874109i	$0.338554\pi$
$68$	16.7300	+	8.40213i	2.02881	+	1.01891i
$69$		0			0
$70$	1.76586	−	1.87170i	0.211060	−	0.223711i
$71$	1.41528	+	8.02646i	0.167963	+	0.952565i	0.945957	+	0.324293i	$0.105126\pi$
$71$	1.41528	+	8.02646i	0.167963	+	0.952565i	−0.777994	+	0.628272i	$0.783763\pi$
$72$		0			0
$73$	1.11524	−	6.32482i	0.130529	−	0.740264i	−0.847341	−	0.531049i	$-0.821798\pi$
$73$	1.11524	−	6.32482i	0.130529	−	0.740264i	0.977870	−	0.209215i	$-0.0670909\pi$
$74$	−1.85645	−	2.49364i	−0.215808	−	0.289880i
$75$		0			0
$76$	16.9254	−	4.01139i	1.94148	−	0.460138i
$77$	−2.19824	−	0.256938i	−0.250513	−	0.0292808i
$78$		0			0
$79$	0.829051	−	14.2343i	0.0932755	−	1.60148i	−0.549547	−	0.835463i	$-0.685200\pi$
$79$	0.829051	−	14.2343i	0.0932755	−	1.60148i	0.642822	−	0.766015i	$-0.277763\pi$
$80$	−1.28832			−0.144039
$81$		0			0
$82$	2.42689			0.268006
$83$	−0.390702	+	6.70809i	−0.0428851	+	0.736308i	0.906502	+	0.422201i	$0.138742\pi$
$83$	−0.390702	+	6.70809i	−0.0428851	+	0.736308i	−0.949387	+	0.314107i	$0.898295\pi$
$84$		0			0
$85$	−4.39679	−	0.513911i	−0.476899	−	0.0557415i
$86$	−20.3976	+	4.83432i	−2.19953	+	0.521298i
$87$		0			0
$88$	−1.15402	−	1.55011i	−0.123018	−	0.165243i
$89$	−2.70557	+	15.3441i	−0.286790	+	1.62647i	0.412030	+	0.911170i	$0.364820\pi$
$89$	−2.70557	+	15.3441i	−0.286790	+	1.62647i	−0.698820	+	0.715297i	$0.746291\pi$
$90$		0			0
$91$	1.69423	+	9.60848i	0.177604	+	1.00724i
$92$	5.84771	−	6.19821i	0.609666	−	0.646208i
$93$		0			0
$94$	11.8652	+	5.95894i	1.22380	+	0.614617i
$95$	−3.43630	+	2.26009i	−0.352557	+	0.231880i
$96$		0			0
$97$	−3.62877	−	0.860034i	−0.368446	−	0.0873232i	0.0422221	−	0.999108i	$-0.486556\pi$
$97$	−3.62877	−	0.860034i	−0.368446	−	0.0873232i	−0.410668	+	0.911785i	$0.634704\pi$
$98$	7.46994	+	2.71884i	0.754578	+	0.274644i
$99$		0			0
$100$	11.7724	−	4.28480i	1.17724	−	0.428480i
$101$	4.61913	−	0.539899i	0.459621	−	0.0537220i	0.116868	−	0.993147i	$-0.462715\pi$
$101$	4.61913	−	0.539899i	0.459621	−	0.0537220i	0.342753	+	0.939426i	$0.388641\pi$
$102$		0			0
$103$	−3.54684	−	3.75944i	−0.349481	−	0.370428i	0.528657	−	0.848835i	$-0.322696\pi$
$103$	−3.54684	−	3.75944i	−0.349481	−	0.370428i	−0.878138	+	0.478407i	$0.841214\pi$
$104$	−5.08736	+	6.83351i	−0.498857	+	0.670081i
$105$		0			0
$106$	−16.5713	+	8.32243i	−1.60955	+	0.808345i
$107$	6.49528	−	11.2502i	0.627922	−	1.08759i	−0.360046	−	0.932935i	$-0.617239\pi$
$107$	6.49528	−	11.2502i	0.627922	−	1.08759i	0.987968	−	0.154659i	$-0.0494278\pi$
$108$		0			0
$109$	−0.888686	−	1.53925i	−0.0851207	−	0.147433i	0.820322	−	0.571902i	$-0.193794\pi$
$109$	−0.888686	−	1.53925i	−0.0851207	−	0.147433i	−0.905443	+	0.424469i	$0.860461\pi$
$110$	1.42185	+	0.935163i	0.135568	+	0.0891643i
$111$		0			0
$112$	1.44390	+	3.34734i	0.136436	+	0.316294i
$113$	−3.98316	+	13.3047i	−0.374704	+	1.25160i	0.537989	+	0.842952i	$0.319184\pi$
$113$	−3.98316	+	13.3047i	−0.374704	+	1.25160i	−0.912693	+	0.408646i	$0.866001\pi$
$114$		0			0
$115$	−0.798061	+	1.85011i	−0.0744196	+	0.172524i
$116$	−12.3288	−	10.3451i	−1.14470	−	0.960514i
$117$		0			0
$118$	3.48039	−	2.92040i	0.320396	−	0.268844i
$119$	3.59250	+	11.9998i	0.329324	+	1.10002i
$120$		0			0
$121$	0.554486	+	9.52015i	0.0504078	+	0.865468i
$122$	0.454183	+	7.79802i	0.0411198	+	0.705999i
$123$		0			0
$124$	2.17472	+	7.26407i	0.195296	+	0.652332i
$125$	−4.74544	+	3.98190i	−0.424445	+	0.356152i
$126$		0			0
$127$	−8.72949	−	7.32491i	−0.774617	−	0.649981i	0.167270	−	0.985911i	$-0.446505\pi$
$127$	−8.72949	−	7.32491i	−0.774617	−	0.649981i	−0.941887	+	0.335930i	$0.890949\pi$
$128$	−4.72038	+	10.9431i	−0.417226	+	0.967239i
$129$		0			0
$130$	2.15168	−	7.18711i	0.188715	−	0.630351i
$131$	−5.77514	−	13.3883i	−0.504576	−	1.16974i	−0.960136	−	0.279534i	$-0.909820\pi$
$131$	−5.77514	−	13.3883i	−0.504576	−	1.16974i	0.455560	−	0.890205i	$-0.349439\pi$
$132$		0			0
$133$	9.72346	+	6.39522i	0.843131	+	0.554536i
$134$	−1.32700	−	2.29842i	−0.114635	−	0.198554i
$135$		0			0
$136$	−5.46868	+	9.47202i	−0.468935	+	0.812219i
$137$	−0.331366	+	0.166418i	−0.0283105	+	0.0142181i	−0.462898	−	0.886411i	$-0.653190\pi$
$137$	−0.331366	+	0.166418i	−0.0283105	+	0.0142181i	0.434588	+	0.900630i	$0.356894\pi$
$138$		0			0
$139$	8.94395	−	12.0138i	0.758616	−	1.01900i	−0.240218	−	0.970719i	$-0.577219\pi$
$139$	8.94395	−	12.0138i	0.758616	−	1.01900i	0.998834	−	0.0482794i	$-0.0153738\pi$
$140$	2.21899	+	2.35199i	0.187539	+	0.198779i
$141$		0			0
$142$	−17.6135	+	2.05872i	−1.47809	+	0.172764i
$143$	−6.06349	+	2.20693i	−0.507055	+	0.184553i
$144$		0			0
$145$	3.57599	+	1.30155i	0.296970	+	0.108088i
$146$	13.5972	+	3.22260i	1.12531	+	0.266704i
$147$		0			0
$148$	3.26387	−	2.14668i	0.268288	−	0.176456i
$149$	−0.893861	−	0.448914i	−0.0732279	−	0.0367764i	0.411808	−	0.911270i	$-0.364897\pi$
$149$	−0.893861	−	0.448914i	−0.0732279	−	0.0367764i	−0.485036	+	0.874494i	$0.661194\pi$
$150$		0			0
$151$	−0.0134726	+	0.0142801i	−0.00109638	+	0.00116210i	−0.727922	−	0.685660i	$-0.759514\pi$
$151$	−0.0134726	+	0.0142801i	−0.00109638	+	0.00116210i	0.726825	+	0.686822i	$0.240995\pi$
$152$	1.76462	+	10.0076i	0.143129	+	0.811727i
$153$		0			0
$154$	0.836205	−	4.74235i	0.0673833	−	0.382150i
$155$	−1.07067	−	1.43815i	−0.0859979	−	0.115515i
$156$		0			0
$157$	−7.59419	+	1.79986i	−0.606083	+	0.143644i	−0.522188	−	0.852830i	$-0.674884\pi$
$157$	−7.59419	+	1.79986i	−0.606083	+	0.143644i	−0.0838947	+	0.996475i	$0.526736\pi$
$158$	30.8137	+	3.60160i	2.45141	+	0.286528i
$159$		0			0
$160$	0.283076	−	4.86023i	0.0223791	−	0.384235i
$161$	5.70142			0.449335
$162$		0			0
$163$	−15.3947			−1.20581			−0.602905	−	0.797813i	$-0.705990\pi$
$163$	−15.3947			−1.20581			−0.602905	+	0.797813i	$0.705990\pi$
$164$	−0.177321	+	3.04449i	−0.0138465	+	0.237735i
$165$		0			0
$166$	−14.5214	−	1.69731i	−1.12708	−	0.131736i
$167$	3.55630	−	0.842859i	0.275195	−	0.0652224i	−0.0907011	−	0.995878i	$-0.528911\pi$
$167$	3.55630	−	0.842859i	0.275195	−	0.0652224i	0.365896	+	0.930656i	$0.380763\pi$
$168$		0			0
$169$	9.22359	+	12.3894i	0.709507	+	0.953033i
$170$	1.67253	−	9.48537i	0.128277	−	0.727494i
$171$		0			0
$172$	−4.57421	−	25.9416i	−0.348780	−	1.97803i
$173$	−9.11506	+	9.66140i	−0.693005	+	0.734543i	−0.974344	−	0.225066i	$-0.927740\pi$
$173$	−9.11506	+	9.66140i	−0.693005	+	0.734543i	0.281338	+	0.959609i	$0.409222\pi$
$174$		0			0
$175$	7.49053	+	3.76189i	0.566231	+	0.284372i
$176$	−2.01432	+	1.32484i	−0.151835	+	0.0998637i
$177$		0			0
$178$	−32.9869	−	7.81805i	−2.47248	−	0.585987i
$179$	−0.392738	−	0.142945i	−0.0293546	−	0.0106842i	0.327301	−	0.944920i	$-0.393861\pi$
$179$	−0.392738	−	0.142945i	−0.0293546	−	0.0106842i	−0.356656	+	0.934236i	$0.616083\pi$
$180$		0			0
$181$	−19.5881	+	7.12947i	−1.45597	+	0.529929i	−0.944252	−	0.329225i	$-0.893213\pi$
$181$	−19.5881	+	7.12947i	−1.45597	+	0.529929i	−0.511717	+	0.859154i	$0.670990\pi$
$182$	−21.0852	+	2.46450i	−1.56294	+	0.182681i
$183$		0			0
$184$	3.41633	+	3.62110i	0.251855	+	0.266951i
$185$	−0.551604	+	0.740932i	−0.0405547	+	0.0544744i
$186$		0			0
$187$	−7.40296	+	3.71791i	−0.541358	+	0.271880i
$188$	−8.34230	+	14.4493i	−0.608425	+	1.05382i
$189$		0			0
$190$	−4.47446	−	7.75000i	−0.324612	−	0.562244i
$191$	−5.75588	−	3.78570i	−0.416481	−	0.273924i	0.323927	−	0.946082i	$-0.394997\pi$
$191$	−5.75588	−	3.78570i	−0.416481	−	0.273924i	−0.740407	+	0.672159i	$0.765367\pi$
$192$		0			0
$193$	−3.46427	−	8.03108i	−0.249363	−	0.578089i	0.746854	−	0.664988i	$-0.231564\pi$
$193$	−3.46427	−	8.03108i	−0.249363	−	0.578089i	−0.996217	+	0.0868989i	$0.972304\pi$
$194$	2.32718	−	7.77334i	0.167082	−	0.558093i
$195$		0			0
$196$	−3.95652	+	9.17224i	−0.282609	+	0.655160i
$197$	−6.47094	−	5.42976i	−0.461035	−	0.386855i	0.382476	−	0.923965i	$-0.375071\pi$
$197$	−6.47094	−	5.42976i	−0.461035	−	0.386855i	−0.843512	+	0.537111i	$0.819516\pi$
$198$		0			0
$199$	9.66790	−	8.11233i	0.685339	−	0.575068i	−0.232222	−	0.972663i	$-0.574599\pi$
$199$	9.66790	−	8.11233i	0.685339	−	0.575068i	0.917561	+	0.397595i	$0.130155\pi$
$200$	2.09912	+	7.01155i	0.148430	+	0.495792i
$201$		0			0
$202$	0.588353	+	10.1016i	0.0413964	+	0.710749i
$203$	−0.626111	−	10.7499i	−0.0439444	−	0.754495i
$204$		0			0
$205$	−0.206814	−	0.690805i	−0.0144445	−	0.0482479i
$206$	8.61468	−	7.22858i	0.600213	−	0.503639i
$207$		0			0
$208$	8.14187	+	6.83184i	0.564537	+	0.473703i
$209$	−3.04858	+	7.06740i	−0.210875	+	0.488862i
$210$		0			0
$211$	1.62787	−	5.43746i	0.112067	−	0.374330i	−0.883495	−	0.468441i	$-0.844816\pi$
$211$	1.62787	−	5.43746i	0.112067	−	0.374330i	0.995562	+	0.0941110i	$0.0300009\pi$
$212$	−9.22953	−	21.3965i	−0.633887	−	1.46952i
$213$		0			0
$214$	23.6150	+	15.5318i	1.61429	+	1.06173i
$215$	3.11430	+	5.39413i	0.212393	+	0.367876i
$216$		0			0
$217$	−2.53667	+	4.39364i	−0.172200	+	0.298260i
$218$	3.45587	−	1.73560i	0.234061	−	0.117550i
$219$		0			0
$220$	−1.27703	+	1.71535i	−0.0860974	+	0.115649i
$221$	25.0613	+	26.5635i	1.68581	+	1.78685i
$222$		0			0
$223$	−7.48192	+	0.874511i	−0.501027	+	0.0585616i	−0.362853	−	0.931846i	$-0.618197\pi$
$223$	−7.48192	+	0.874511i	−0.501027	+	0.0585616i	−0.138174	+	0.990408i	$0.544123\pi$
$224$	−12.9452	+	4.71166i	−0.864936	+	0.314811i
$225$		0			0
$226$	−28.3955	−	10.3351i	−1.88884	−	0.687481i
$227$	−13.2754	−	3.14632i	−0.881118	−	0.208829i	−0.234935	−	0.972011i	$-0.575488\pi$
$227$	−13.2754	−	3.14632i	−0.881118	−	0.208829i	−0.646183	+	0.763182i	$0.723636\pi$
$228$		0			0
$229$	−13.3632	+	8.78913i	−0.883067	+	0.580802i	−0.908039	−	0.418886i	$-0.862421\pi$
$229$	−13.3632	+	8.78913i	−0.883067	+	0.580802i	0.0249721	+	0.999688i	$0.492050\pi$
$230$	−3.91771	−	1.96755i	−0.258326	−	0.129736i
$231$		0			0
$232$	6.45233	−	6.83907i	0.423616	−	0.449007i
$233$	−0.930605	−	5.27772i	−0.0609660	−	0.345755i	−0.999998	−	0.00192589i	$-0.999387\pi$
$233$	−0.930605	−	5.27772i	−0.0609660	−	0.345755i	0.939032	−	0.343829i	$-0.111724\pi$
$234$		0			0
$235$	0.685064	−	3.88519i	0.0446886	−	0.253442i
$236$	3.40928	+	4.57946i	0.221925	+	0.298098i
$237$		0			0
$238$	−26.5195	+	6.28524i	−1.71900	+	0.407412i
$239$	16.0344	+	1.87416i	1.03718	+	0.121229i	0.617603	−	0.786490i	$-0.288104\pi$
$239$	16.0344	+	1.87416i	1.03718	+	0.121229i	0.419578	+	0.907719i	$0.362178\pi$
$240$		0			0
$241$	1.35989	−	23.3484i	0.0875982	−	1.50400i	−0.612793	−	0.790244i	$-0.709954\pi$
$241$	1.35989	−	23.3484i	0.0875982	−	1.50400i	0.700391	−	0.713759i	$-0.253009\pi$
$242$	−20.7491			−1.33380
$243$		0			0
$244$	−9.81564			−0.628382
$245$	0.137337	−	2.35798i	0.00877412	−	0.150646i
$246$		0			0
$247$	33.7015	+	3.93914i	2.14437	+	0.250641i
$248$	−4.31049	+	1.02160i	−0.273716	+	0.0648720i
$249$		0			0
$250$	−8.04882	−	10.8114i	−0.509052	−	0.683776i
$251$	4.21745	−	23.9183i	0.266203	−	1.50971i	−0.499385	−	0.866380i	$-0.666441\pi$
$251$	4.21745	−	23.9183i	0.266203	−	1.50971i	0.765588	−	0.643331i	$-0.222448\pi$
$252$		0			0
$253$	0.654768	+	3.71337i	0.0411649	+	0.233458i
$254$	17.0150	−	18.0349i	1.06762	−	1.13161i
$255$		0			0
$256$	−1.01133	−	0.507909i	−0.0632081	−	0.0317443i
$257$	−8.04903	+	5.29393i	−0.502085	+	0.330226i	−0.775158	−	0.631767i	$-0.782330\pi$
$257$	−8.04903	+	5.29393i	−0.502085	+	0.330226i	0.273074	+	0.961993i	$0.411960\pi$
$258$		0			0
$259$	2.54332	+	0.602777i	0.158034	+	0.0374547i
$260$	8.85887	+	3.22437i	0.549404	+	0.199967i
$261$		0			0
$262$	29.8116	−	10.8505i	1.84177	−	0.670349i
$263$	−6.59689	+	0.771066i	−0.406782	+	0.0475460i	−0.317024	−	0.948418i	$-0.602683\pi$
$263$	−6.59689	+	0.771066i	−0.406782	+	0.0475460i	−0.0897582	+	0.995964i	$0.528609\pi$
$264$		0			0
$265$	3.78111	+	4.00774i	0.232272	+	0.246194i
$266$	−15.1214	+	20.3115i	−0.927150	+	1.24538i
$267$		0			0
$268$	2.98028	−	1.49676i	0.182050	−	0.0914289i
$269$	−14.6832	+	25.4321i	−0.895251	+	1.55062i	−0.0617568	+	0.998091i	$0.519670\pi$
$269$	−14.6832	+	25.4321i	−0.895251	+	1.55062i	−0.833494	+	0.552529i	$0.813663\pi$
$270$		0			0
$271$	9.43957	+	16.3498i	0.573413	+	0.993180i	0.996212	+	0.0869568i	$0.0277142\pi$
$271$	9.43957	+	16.3498i	0.573413	+	0.993180i	−0.422799	+	0.906223i	$0.638952\pi$
$272$	11.4004	+	7.49815i	0.691250	+	0.454642i
$273$		0			0
$274$	−0.319560	−	0.740823i	−0.0193053	−	0.0447547i
$275$	−1.58991	+	5.31066i	−0.0958750	+	0.320245i
$276$		0			0
$277$	5.56045	−	12.8906i	0.334095	−	0.774519i	−0.665509	−	0.746390i	$-0.731786\pi$
$277$	5.56045	−	12.8906i	0.334095	−	0.774519i	0.999604	−	0.0281297i	$-0.00895515\pi$
$278$	24.9640	+	20.9473i	1.49724	+	1.25633i
$279$		0			0
$280$	−1.44713	+	1.21428i	−0.0864824	+	0.0725673i
$281$	6.33274	+	21.1528i	0.377780	+	1.26187i	0.909767	+	0.415120i	$0.136260\pi$
$281$	6.33274	+	21.1528i	0.377780	+	1.26187i	−0.531987	+	0.846753i	$0.678554\pi$
$282$		0			0
$283$	−0.230048	−	3.94978i	−0.0136750	−	0.234790i	−0.998219	−	0.0596536i	$-0.981000\pi$
$283$	−0.230048	−	3.94978i	−0.0136750	−	0.234790i	0.984544	−	0.175136i	$-0.0560367\pi$
$284$	−1.29570	−	22.2462i	−0.0768854	−	1.32007i
$285$		0			0
$286$	−4.02663	−	13.4499i	−0.238099	−	0.795307i
$287$	−1.56307	+	1.31157i	−0.0922652	+	0.0774197i
$288$		0			0
$289$	22.8934	+	19.2099i	1.34667	+	1.12999i
$290$	−3.27954	+	7.60283i	−0.192581	+	0.446453i
$291$		0			0
$292$	−5.03617	+	16.8220i	−0.294719	+	0.984431i
$293$	3.15963	+	7.32485i	0.184588	+	0.427922i	0.985234	−	0.171215i	$-0.0547694\pi$
$293$	3.15963	+	7.32485i	0.184588	+	0.427922i	−0.800646	+	0.599138i	$0.795510\pi$
$294$		0			0
$295$	−1.12787	−	0.741811i	−0.0656671	−	0.0431899i
$296$	1.14114	+	1.97650i	0.0663271	+	0.114882i
$297$		0			0
$298$	1.08818	−	1.88478i	0.0630366	−	0.109183i
$299$	14.8545	−	7.46020i	0.859056	−	0.431434i
$300$		0			0
$301$	10.5247	−	14.1371i	0.606634	−	0.814851i
$302$	−0.0293137	−	0.0310707i	−0.00168681	−	0.00178792i
$303$		0			0
$304$	12.5922	−	1.47182i	0.722211	−	0.0844144i
$305$	2.18097	−	0.793808i	0.124882	−	0.0454533i
$306$		0			0
$307$	1.95823	+	0.712736i	0.111762	+	0.0406780i	0.397296	−	0.917691i	$-0.369949\pi$
$307$	1.95823	+	0.712736i	0.111762	+	0.0406780i	−0.285534	+	0.958369i	$0.592171\pi$
$308$	5.88809	+	1.39550i	0.335505	+	0.0795162i
$309$		0			0
$310$	3.25930	−	2.14367i	0.185116	−	0.121753i
$311$	−13.4174	−	6.73846i	−0.760830	−	0.382103i	0.0256887	−	0.999670i	$-0.491822\pi$
$311$	−13.4174	−	6.73846i	−0.760830	−	0.382103i	−0.786518	+	0.617567i	$0.788118\pi$
$312$		0			0
$313$	−3.49359	+	3.70299i	−0.197469	+	0.209305i	−0.818540	−	0.574449i	$-0.805216\pi$
$313$	−3.49359	+	3.70299i	−0.197469	+	0.209305i	0.621071	+	0.783754i	$0.286698\pi$
$314$	−2.94876	−	16.7232i	−0.166408	−	0.943747i
$315$		0			0
$316$	−6.76955	+	38.3920i	−0.380817	+	2.15972i
$317$	−16.5461	−	22.2253i	−0.929323	−	1.24830i	−0.968487	−	0.249065i	$-0.919877\pi$
$317$	−16.5461	−	22.2253i	−0.929323	−	1.24830i	0.0391636	−	0.999233i	$-0.487531\pi$
$318$		0			0
$319$	6.92958	−	1.64234i	0.387982	−	0.0919534i
$320$	7.96199	+	0.930623i	0.445089	+	0.0520234i
$321$		0			0
$322$	−0.721298	+	12.3842i	−0.0401964	+	0.690145i
$323$	43.5617			2.42384
$324$		0			0
$325$	24.4382			1.35559
$326$	1.94762	−	33.4393i	0.107869	−	1.85203i
$327$		0			0
$328$	−1.76961	−	0.206838i	−0.0977105	−	0.0114207i
$329$	−10.8623	+	2.57442i	−0.598860	+	0.141933i
$330$		0			0
$331$	16.2840	+	21.8732i	0.895049	+	1.20226i	0.978603	+	0.205756i	$0.0659653\pi$
$331$	16.2840	+	21.8732i	0.895049	+	1.20226i	−0.0835546	+	0.996503i	$0.526627\pi$
$332$	3.19024	−	18.0928i	0.175087	−	0.992969i
$333$		0			0
$334$	1.38088	+	7.83136i	0.0755584	+	0.428513i
$335$	−0.541154	+	0.573589i	−0.0295664	+	0.0313385i
$336$		0			0
$337$	−11.3657	−	5.70808i	−0.619130	−	0.310939i	0.111445	−	0.993771i	$-0.464452\pi$
$337$	−11.3657	−	5.70808i	−0.619130	−	0.310939i	−0.730576	+	0.682832i	$0.760748\pi$
$338$	−28.0783	+	18.4674i	−1.52726	+	1.00449i
$339$		0			0
$340$	11.7770	+	2.79120i	0.638698	+	0.151374i
$341$	−3.15292	−	1.14757i	−0.170740	−	0.0621444i
$342$		0			0
$343$	−18.3136	+	6.66560i	−0.988840	+	0.359908i
$344$	15.2853	−	1.78659i	0.824127	−	0.0963267i
$345$		0			0
$346$	−19.8326	−	21.0213i	−1.06621	−	1.13011i
$347$	5.02397	−	6.74836i	0.269701	−	0.362271i	−0.646553	−	0.762869i	$-0.723790\pi$
$347$	5.02397	−	6.74836i	0.269701	−	0.362271i	0.916254	+	0.400598i	$0.131198\pi$
$348$		0			0
$349$	26.9370	−	13.5282i	1.44190	−	0.724150i	0.455768	−	0.890099i	$-0.349365\pi$
$349$	26.9370	−	13.5282i	1.44190	−	0.724150i	0.986134	+	0.165948i	$0.0530685\pi$
$350$	−9.11893	+	15.7944i	−0.487427	+	0.844249i
$351$		0			0
$352$	−4.55540	−	7.89018i	−0.242803	−	0.420548i
$353$	−19.4095	−	12.7659i	−1.03307	−	0.679458i	−0.0846248	−	0.996413i	$-0.526969\pi$
$353$	−19.4095	−	12.7659i	−1.03307	−	0.679458i	−0.948441	+	0.316955i	$0.897340\pi$
$354$		0			0
$355$	2.08698	+	4.83817i	0.110766	+	0.256784i
$356$	12.2178	−	40.8102i	0.647541	−	2.16294i
$357$		0			0
$358$	0.360180	−	0.834992i	0.0190361	−	0.0441307i
$359$	3.19290	+	2.67916i	0.168515	+	0.141401i	0.723145	−	0.690696i	$-0.242696\pi$
$359$	3.19290	+	2.67916i	0.168515	+	0.141401i	−0.554630	+	0.832097i	$0.687140\pi$
$360$		0			0
$361$	16.4498	−	13.8030i	0.865780	−	0.726476i
$362$	−13.0080	−	43.4497i	−0.683684	−	2.28366i
$363$		0			0
$364$	−1.55108	−	26.6310i	−0.0812986	−	1.39584i
$365$	−0.241419	−	4.14501i	−0.0126365	−	0.216960i
$366$		0			0
$367$	3.36163	+	11.2286i	0.175476	+	0.586130i	0.999800	+	0.0200114i	$0.00637025\pi$
$367$	3.36163	+	11.2286i	0.175476	+	0.586130i	−0.824324	+	0.566118i	$0.808445\pi$
$368$	4.75778	−	3.99225i	0.248016	−	0.208110i
$369$		0			0
$370$	−1.53961	−	1.29189i	−0.0800407	−	0.0671621i
$371$	6.17525	−	14.3158i	0.320603	−	0.743241i
$372$		0			0
$373$	−10.4315	+	34.8438i	−0.540124	+	1.80414i	0.0524474	+	0.998624i	$0.483298\pi$
$373$	−10.4315	+	34.8438i	−0.540124	+	1.80414i	−0.592572	+	0.805518i	$0.701887\pi$
$374$	−7.13919	−	16.5505i	−0.369159	−	0.855806i
$375$		0			0
$376$	−8.14387	−	5.35630i	−0.419988	−	0.276230i
$377$	−15.6973	−	27.1885i	−0.808452	−	1.40028i
$378$		0			0
$379$	5.02516	−	8.70383i	0.258125	−	0.447086i	−0.707615	−	0.706599i	$-0.750229\pi$
$379$	5.02516	−	8.70383i	0.258125	−	0.447086i	0.965740	+	0.259513i	$0.0835620\pi$
$380$	10.0491	−	5.04687i	0.515510	−	0.258899i
$381$		0			0
$382$	8.95120	−	12.0235i	0.457983	−	0.615178i
$383$	0.207663	+	0.220110i	0.0106111	+	0.0112471i	0.732657	−	0.680598i	$-0.238280\pi$
$383$	0.207663	+	0.220110i	0.0106111	+	0.0112471i	−0.722046	+	0.691845i	$0.756798\pi$
$384$		0			0
$385$	−1.42115	+	0.166109i	−0.0724285	+	0.00846568i
$386$	17.8828	−	6.50880i	0.910209	−	0.331289i
$387$		0			0
$388$	9.58146	+	3.48737i	0.486425	+	0.177044i
$389$	7.31685	+	1.73413i	0.370979	+	0.0879237i	0.411876	−	0.911240i	$-0.364874\pi$
$389$	7.31685	+	1.73413i	0.370979	+	0.0879237i	−0.0408974	+	0.999163i	$0.513022\pi$
$390$		0			0
$391$	17.8298	−	11.7269i	0.901694	−	0.593053i
$392$	−5.21512	−	2.61913i	−0.263403	−	0.132286i
$393$		0			0
$394$	12.6128	−	13.3688i	0.635422	−	0.673508i
$395$	−1.60068	−	9.07791i	−0.0805390	−	0.456759i
$396$		0			0
$397$	2.95983	−	16.7860i	0.148549	−	0.842466i	−0.815899	−	0.578195i	$-0.803757\pi$
$397$	2.95983	−	16.7860i	0.148549	−	0.842466i	0.964448	−	0.264271i	$-0.0851314\pi$
$398$	16.3979	+	22.0262i	0.821952	+	1.10407i
$399$		0			0
$400$	8.88492	−	2.10576i	0.444246	−	0.105288i
$401$	−13.4856	−	1.57624i	−0.673441	−	0.0787139i	−0.227502	−	0.973778i	$-0.573056\pi$
$401$	−13.4856	−	1.57624i	−0.673441	−	0.0787139i	−0.445938	+	0.895064i	$0.647130\pi$
$402$		0			0
$403$	−0.860042	+	14.7664i	−0.0428418	+	0.735565i
$404$	−12.7153			−0.632609
$405$		0			0
$406$	23.4293			1.16278
$407$	−0.100511	+	1.72570i	−0.00498213	+	0.0855399i
$408$		0			0
$409$	0.667804	+	0.0780551i	0.0330208	+	0.00385958i	0.132587	−	0.991171i	$-0.457672\pi$
$409$	0.667804	+	0.0780551i	0.0330208	+	0.00385958i	−0.0995665	+	0.995031i	$0.531746\pi$
$410$	1.52668	−	0.361830i	0.0753973	−	0.0178695i
$411$		0			0
$412$	8.43867	+	11.3351i	0.415744	+	0.558441i
$413$	−0.663313	+	3.76184i	−0.0326395	+	0.185108i
$414$		0			0
$415$	0.754343	+	4.27809i	0.0370292	+	0.210003i
$416$	−27.5622	+	29.2143i	−1.35135	+	1.43235i
$417$		0			0
$418$	−14.9656	−	7.51600i	−0.731991	−	0.367620i
$419$	16.6146	−	10.9276i	0.811675	−	0.533847i	−0.0744874	−	0.997222i	$-0.523732\pi$
$419$	16.6146	−	10.9276i	0.811675	−	0.533847i	0.886162	+	0.463375i	$0.153362\pi$
$420$		0			0
$421$	12.2171	+	2.89551i	0.595426	+	0.141119i	0.517270	−	0.855822i	$-0.326948\pi$
$421$	12.2171	+	2.89551i	0.595426	+	0.141119i	0.0781566	+	0.996941i	$0.475097\pi$
$422$	11.6049	+	4.22384i	0.564918	+	0.205613i
$423$		0			0
$424$	12.7926	−	4.65611i	0.621262	−	0.226121i
$425$	31.1624	−	3.64236i	1.51160	−	0.176681i
$426$		0			0
$427$	−4.50682	−	4.77696i	−0.218101	−	0.231173i
$428$	−21.2098	+	28.4897i	−1.02522	+	1.37710i
$429$		0			0
$430$	−12.1107	+	6.08223i	−0.584030	+	0.293311i
$431$	10.8013	−	18.7084i	0.520281	−	0.901153i	−0.479441	−	0.877574i	$-0.659161\pi$
$431$	10.8013	−	18.7084i	0.520281	−	0.901153i	0.999722	−	0.0235787i	$-0.00750603\pi$
$432$		0			0
$433$	−1.99970	−	3.46358i	−0.0960993	−	0.166449i	0.813968	−	0.580910i	$-0.197303\pi$
$433$	−1.99970	−	3.46358i	−0.0960993	−	0.166449i	−0.910067	+	0.414461i	$0.863970\pi$
$434$	−9.22262	−	6.06581i	−0.442700	−	0.291168i
$435$		0			0
$436$	1.92478	+	4.46213i	0.0921801	+	0.213697i
$437$	5.68669	−	18.9949i	0.272031	−	0.908648i
$438$		0			0
$439$	−12.3621	+	28.6586i	−0.590011	+	1.36780i	0.317695	+	0.948193i	$0.397091\pi$
$439$	−12.3621	+	28.6586i	−0.590011	+	1.36780i	−0.907706	+	0.419607i	$0.862168\pi$
$440$	−0.957063	−	0.803071i	−0.0456262	−	0.0382849i
$441$		0			0
$442$	−60.8697	+	51.0758i	−2.89528	+	2.42943i
$443$	−0.459510	−	1.53487i	−0.0218320	−	0.0729238i	0.946379	−	0.323057i	$-0.104711\pi$
$443$	−0.459510	−	1.53487i	−0.0218320	−	0.0729238i	−0.968211	+	0.250134i	$0.919525\pi$
$444$		0			0
$445$	0.585685	+	10.0558i	0.0277641	+	0.476692i
$446$	−0.952996	−	16.3623i	−0.0451257	−	0.774778i
$447$		0			0
$448$	−6.50552	−	21.7300i	−0.307357	−	1.02664i
$449$	8.04720	−	6.75241i	0.379771	−	0.318666i	−0.432841	−	0.901470i	$-0.642489\pi$
$449$	8.04720	−	6.75241i	0.379771	−	0.318666i	0.812613	+	0.582804i	$0.198045\pi$
$450$		0			0
$451$	−1.03374	−	0.867414i	−0.0486771	−	0.0408449i
$452$	15.0399	−	34.8664i	0.707418	−	1.63998i
$453$		0			0
$454$	8.51370	−	28.4378i	0.399568	−	1.33465i
$455$	2.49833	+	5.79179i	0.117124	+	0.271523i
$456$		0			0
$457$	−34.3727	−	22.6073i	−1.60789	−	1.05752i	−0.953513	−	0.301353i	$-0.902562\pi$
$457$	−34.3727	−	22.6073i	−1.60789	−	1.05752i	−0.654375	−	0.756171i	$-0.727068\pi$
$458$	−17.4005	−	30.1385i	−0.813071	−	1.40828i
$459$		0			0
$460$	2.75450	−	4.77093i	0.128429	−	0.222446i
$461$	−30.6506	+	15.3933i	−1.42754	+	0.716939i	−0.983809	−	0.179219i	$-0.942643\pi$
$461$	−30.6506	+	15.3933i	−1.42754	+	0.716939i	−0.443734	+	0.896159i	$0.646346\pi$
$462$		0			0
$463$	−19.9050	+	26.7371i	−0.925066	+	1.24258i	0.0448139	+	0.998995i	$0.485731\pi$
$463$	−19.9050	+	26.7371i	−0.925066	+	1.24258i	−0.969880	+	0.243584i	$0.921677\pi$
$464$	−8.04978	−	8.53227i	−0.373702	−	0.396101i
$465$		0			0
$466$	11.5816	−	1.35370i	0.536508	−	0.0627087i
$467$	−9.76380	+	3.55373i	−0.451815	+	0.164447i	−0.557897	−	0.829910i	$-0.688392\pi$
$467$	−9.76380	+	3.55373i	−0.451815	+	0.164447i	0.106082	+	0.994357i	$0.466169\pi$
$468$		0			0
$469$	2.09681	+	0.763177i	0.0968218	+	0.0352402i
$470$	8.35245	+	1.97957i	0.385270	+	0.0913106i
$471$		0			0
$472$	−2.78669	+	1.83283i	−0.128268	+	0.0843630i
$473$	10.4163	+	5.23126i	0.478942	+	0.240534i
$474$		0			0
$475$	20.0043	−	21.2033i	0.917860	−	0.972874i
$476$	−5.94706	−	33.7274i	−0.272583	−	1.54589i
$477$		0			0
$478$	−6.09945	+	34.5917i	−0.278982	+	1.58219i
$479$	12.1202	+	16.2803i	0.553787	+	0.743865i	0.987575	−	0.157150i	$-0.0502306\pi$
$479$	12.1202	+	16.2803i	0.553787	+	0.743865i	−0.433788	+	0.901015i	$0.642823\pi$
$480$		0			0
$481$	7.41507	−	1.75740i	0.338098	−	0.0801307i
$482$	50.5436	+	5.90770i	2.30220	+	0.269088i
$483$		0			0
$484$	1.51604	−	26.0293i	0.0689108	−	1.18315i
$485$	−2.41096			−0.109476
$486$		0			0
$487$	−27.5716			−1.24939			−0.624694	−	0.780870i	$-0.714776\pi$
$487$	−27.5716			−1.24939			−0.624694	+	0.780870i	$0.714776\pi$
$488$	0.333430	−	5.72477i	0.0150937	−	0.259148i
$489$		0			0
$490$	5.10445	+	0.596625i	0.230596	+	0.0269528i
$491$	9.94187	−	2.35627i	0.448670	−	0.106337i	−6.80725e−5	−	1.00000i	$-0.500022\pi$
$491$	9.94187	−	2.35627i	0.448670	−	0.106337i	0.448738	+	0.893663i	$0.351874\pi$
$492$		0			0
$493$	−24.0688	−	32.3300i	−1.08400	−	1.45607i
$494$	−12.8199	+	72.7055i	−0.576796	+	3.27117i
$495$		0			0
$496$	0.959690	+	5.44267i	0.0430914	+	0.244383i
$497$	10.2316	−	10.8449i	0.458950	−	0.486459i
$498$		0			0
$499$	−7.81359	−	3.92413i	−0.349785	−	0.175668i	0.265228	−	0.964186i	$-0.414553\pi$
$499$	−7.81359	−	3.92413i	−0.349785	−	0.175668i	−0.615013	+	0.788517i	$0.710849\pi$
$500$	14.1508	−	9.30715i	0.632845	−	0.416228i
$501$		0			0
$502$	51.4200	+	12.1868i	2.29499	+	0.543922i
$503$	−12.2947	−	4.47489i	−0.548192	−	0.199526i	0.0530509	−	0.998592i	$-0.483105\pi$
$503$	−12.2947	−	4.47489i	−0.548192	−	0.199526i	−0.601243	+	0.799066i	$0.705328\pi$
$504$		0			0
$505$	2.82525	−	1.02831i	0.125722	−	0.0457591i
$506$	−8.14875	+	0.952452i	−0.362256	+	0.0423417i
$507$		0			0
$508$	21.3812	+	22.6627i	0.948636	+	1.00550i
$509$	−18.1662	+	24.4014i	−0.805202	+	1.08157i	0.189810	+	0.981821i	$0.439213\pi$
$509$	−18.1662	+	24.4014i	−0.805202	+	1.08157i	−0.995012	+	0.0997537i	$0.968195\pi$
$510$		0			0
$511$	−10.4990	+	5.27282i	−0.464451	+	0.233256i
$512$	−10.6866	+	18.5097i	−0.472284	+	0.818019i
$513$		0			0
$514$	−10.4808	−	18.1532i	−0.462287	−	0.800705i
$515$	−2.79170	−	1.83613i	−0.123017	−	0.0809097i
$516$		0			0
$517$	−2.92420	−	6.77906i	−0.128606	−	0.298143i
$518$	−1.63107	+	5.44814i	−0.0716649	+	0.239378i
$519$		0			0
$520$	−2.18147	+	5.05722i	−0.0956640	+	0.221774i
$521$	8.25925	+	6.93034i	0.361845	+	0.303624i	0.805525	−	0.592561i	$-0.201883\pi$
$521$	8.25925	+	6.93034i	0.361845	+	0.303624i	−0.443681	+	0.896185i	$0.646328\pi$
$522$		0			0
$523$	9.44644	−	7.92650i	0.413064	−	0.346602i	−0.412453	−	0.910979i	$-0.635328\pi$
$523$	9.44644	−	7.92650i	0.413064	−	0.346602i	0.825517	+	0.564377i	$0.190884\pi$
$524$	11.4336	+	38.1909i	0.499479	+	1.66838i
$525$		0			0
$526$	−0.840267	−	14.4268i	−0.0366374	−	0.629040i
$527$	1.10415	+	18.9576i	0.0480976	+	0.825804i
$528$		0			0
$529$	3.81060	+	12.7283i	0.165678	+	0.553403i
$530$	−9.18367	+	7.70601i	−0.398913	+	0.334728i
$531$		0			0
$532$	−24.3755	−	20.4535i	−1.05681	−	0.886772i
$533$	−2.35626	+	5.46241i	−0.102061	+	0.236603i
$534$		0			0
$535$	2.40866	−	8.04550i	0.104136	−	0.347837i
$536$	0.771713	+	1.78903i	0.0333329	+	0.0772744i
$537$		0			0
$538$	−53.3840	−	35.1112i	−2.30155	−	1.51375i
$539$	−2.21009	−	3.82798i	−0.0951952	−	0.164883i
$540$		0			0
$541$	7.99279	−	13.8439i	0.343637	−	0.595196i	−0.641468	−	0.767149i	$-0.721674\pi$
$541$	7.99279	−	13.8439i	0.343637	−	0.595196i	0.985105	+	0.171953i	$0.0550078\pi$
$542$	−36.7080	+	18.4355i	−1.57675	+	0.791871i
$543$		0			0
$544$	−30.7919	+	41.3607i	−1.32019	+	1.77332i
$545$	−0.788533	−	0.835796i	−0.0337770	−	0.0358016i
$546$		0			0
$547$	−1.22825	+	0.143562i	−0.0525161	+	0.00613825i	−0.142310	−	0.989822i	$-0.545453\pi$
$547$	−1.22825	+	0.143562i	−0.0525161	+	0.00613825i	0.0897943	+	0.995960i	$0.471379\pi$
$548$	0.952696	−	0.346753i	0.0406972	−	0.0148126i
$549$		0			0
$550$	−11.3343	−	4.12534i	−0.483295	−	0.175905i
$551$	−36.4389	−	8.63618i	−1.55235	−	0.367914i
$552$		0			0
$553$	−21.7924	+	14.3331i	−0.926706	+	0.609504i
$554$	27.2965	+	13.7088i	1.15972	+	0.582431i
$555$		0			0
$556$	−28.1019	+	29.7863i	−1.19179	+	1.26322i
$557$	2.28246	+	12.9445i	0.0967109	+	0.548475i	0.994210	+	0.107458i	$0.0342710\pi$
$557$	2.28246	+	12.9445i	0.0967109	+	0.548475i	−0.897499	+	0.441017i	$0.854618\pi$
$558$		0			0
$559$	8.92289	−	50.6042i	0.377398	−	2.14033i
$560$	1.40737	+	1.89043i	0.0594724	+	0.0798853i
$561$		0			0
$562$	−46.7478	+	11.0794i	−1.97194	+	0.467357i
$563$	−6.04774	−	0.706879i	−0.254882	−	0.0297914i	−0.0123076	−	0.999924i	$-0.503918\pi$
$563$	−6.04774	−	0.706879i	−0.254882	−	0.0297914i	−0.242574	+	0.970133i	$0.577992\pi$
$564$		0			0
$565$	−0.522058	+	8.96339i	−0.0219631	+	0.377092i
$566$	8.60852			0.361843
$567$		0			0
$568$	13.0187			0.546251
$569$	−0.963908	+	16.5497i	−0.0404091	+	0.693798i	0.915894	+	0.401420i	$0.131483\pi$
$569$	−0.963908	+	16.5497i	−0.0404091	+	0.693798i	−0.956303	+	0.292377i	$0.905554\pi$
$570$		0			0
$571$	−34.6117	−	4.04552i	−1.44845	−	0.169300i	−0.644779	−	0.764369i	$-0.723050\pi$
$571$	−34.6117	−	4.04552i	−1.44845	−	0.169300i	−0.803674	+	0.595069i	$0.797125\pi$
$572$	17.1668	−	4.06861i	0.717780	−	0.170117i
$573$		0			0
$574$	−2.65115	−	3.56112i	−0.110657	−	0.148638i
$575$	2.47981	−	14.0637i	0.103415	−	0.586497i
$576$		0			0
$577$	5.38675	+	30.5498i	0.224254	+	1.27180i	0.864107	+	0.503308i	$0.167884\pi$
$577$	5.38675	+	30.5498i	0.224254	+	1.27180i	−0.639854	+	0.768497i	$0.721005\pi$
$578$	−44.6225	+	47.2971i	−1.85605	+	1.96730i
$579$		0			0
$580$	−9.29798	−	4.66962i	−0.386078	−	0.193895i
$581$	10.2700	−	6.75465i	0.426069	−	0.280230i
$582$		0			0
$583$	10.0332	+	2.37791i	0.415532	+	0.0984829i
$584$	−9.63999	−	3.50867i	−0.398906	−	0.145190i
$585$		0			0
$586$	−16.3102	+	5.93644i	−0.673769	+	0.245232i
$587$	44.2431	−	5.17128i	1.82611	−	0.213442i	0.867358	−	0.497685i	$-0.165816\pi$
$587$	44.2431	−	5.17128i	1.82611	−	0.213442i	0.958752	+	0.284243i	$0.0917424\pi$
$588$		0			0
$589$	12.1077	+	12.8335i	0.498891	+	0.528794i
$590$	1.75399	−	2.35602i	0.0722108	−	0.0969960i
$591$		0			0
$592$	2.54445	−	1.27787i	0.104576	−	0.0525201i
$593$	9.90549	−	17.1568i	0.406770	−	0.704546i	−0.587756	−	0.809038i	$-0.699989\pi$
$593$	9.90549	−	17.1568i	0.406770	−	0.704546i	0.994526	+	0.104493i	$0.0333219\pi$
$594$		0			0
$595$	4.04899	+	7.01306i	0.165992	+	0.287507i
$596$	2.28492	+	1.50281i	0.0935938	+	0.0615576i
$597$		0			0
$598$	14.3252	+	33.2096i	0.585801	+	1.35804i
$599$	8.00993	−	26.7550i	0.327277	−	1.09318i	−0.623116	−	0.782129i	$-0.714134\pi$
$599$	8.00993	−	26.7550i	0.327277	−	1.09318i	0.950393	−	0.311051i	$-0.100681\pi$
$600$		0			0
$601$	−4.01814	+	9.31508i	−0.163903	+	0.379970i	−0.980298	−	0.197524i	$-0.936710\pi$
$601$	−4.01814	+	9.31508i	−0.163903	+	0.379970i	0.816395	+	0.577494i	$0.195969\pi$
$602$	29.3761	+	24.6495i	1.19728	+	1.00464i
$603$		0			0
$604$	0.0411194	−	0.0345033i	0.00167313	−	0.00140392i
$605$	1.76818	+	5.90615i	0.0718869	+	0.240119i
$606$		0			0
$607$	−0.628918	−	10.7981i	−0.0255270	−	0.438282i	−0.986723	−	0.162414i	$-0.948072\pi$
$607$	−0.628918	−	10.7981i	−0.0255270	−	0.438282i	0.961196	−	0.275868i	$-0.0889651\pi$
$608$	2.78565	+	47.8277i	0.112973	+	1.93967i
$609$		0			0
$610$	1.44833	+	4.83776i	0.0586412	+	0.195875i
$611$	−24.9321	+	20.9205i	−1.00865	+	0.846355i
$612$		0			0
$613$	4.13859	+	3.47269i	0.167156	+	0.140261i	0.722528	−	0.691341i	$-0.242980\pi$
$613$	4.13859	+	3.47269i	0.167156	+	0.140261i	−0.555372	+	0.831602i	$0.687424\pi$
$614$	−1.79589	+	4.16334i	−0.0724763	+	0.168019i
$615$		0			0
$616$	−1.01391	+	3.38670i	−0.0408517	+	0.136454i
$617$	−9.91795	−	22.9924i	−0.399282	−	0.925639i	−0.992685	−	0.120734i	$-0.961475\pi$
$617$	−9.91795	−	22.9924i	−0.399282	−	0.925639i	0.593403	−	0.804905i	$-0.297784\pi$
$618$		0			0
$619$	−21.2925	−	14.0043i	−0.855817	−	0.562880i	0.0440575	−	0.999029i	$-0.485972\pi$
$619$	−21.2925	−	14.0043i	−0.855817	−	0.562880i	−0.899874	+	0.436149i	$0.856342\pi$
$620$	2.45106	+	4.24535i	0.0984368	+	0.170498i
$621$		0			0
$622$	16.3342	−	28.2917i	0.654943	−	1.13439i
$623$	25.4708	−	12.7919i	1.02047	−	0.512497i
$624$		0			0
$625$	11.2895	−	15.1644i	0.451580	−	0.606578i
$626$	−7.60137	−	8.05698i	−0.303812	−	0.322022i
$627$		0			0
$628$	21.1944	−	2.47727i	0.845750	−	0.0988540i
$629$	9.19342	−	3.34613i	0.366566	−	0.133419i
$630$		0			0
$631$	−18.7709	−	6.83203i	−0.747256	−	0.271979i	−0.0598054	−	0.998210i	$-0.519048\pi$
$631$	−18.7709	−	6.83203i	−0.747256	−	0.271979i	−0.687451	+	0.726231i	$0.741270\pi$
$632$	−22.1614	−	5.25234i	−0.881533	−	0.208927i
$633$		0			0
$634$	50.3694	−	33.1285i	2.00043	−	1.31570i
$635$	−6.58352	−	3.30637i	−0.261259	−	0.131209i
$636$		0			0
$637$	−13.3720	+	14.1735i	−0.529819	+	0.561575i
$638$	2.69069	+	15.2597i	0.106526	+	0.604137i
$639$		0			0
$640$	−1.33792	+	7.58769i	−0.0528857	+	0.299930i
$641$	−5.33236	−	7.16261i	−0.210616	−	0.282906i	0.684244	−	0.729253i	$-0.260132\pi$
$641$	−5.33236	−	7.16261i	−0.210616	−	0.282906i	−0.894860	+	0.446347i	$0.852725\pi$
$642$		0			0
$643$	13.0387	−	3.09023i	0.514197	−	0.121867i	0.0346781	−	0.999399i	$-0.488959\pi$
$643$	13.0387	−	3.09023i	0.514197	−	0.121867i	0.479519	+	0.877532i	$0.340811\pi$
$644$	−15.4830	−	1.80971i	−0.610117	−	0.0713125i
$645$		0			0
$646$	−5.51107	+	94.6214i	−0.216830	+	3.72283i
$647$	−48.7223			−1.91547			−0.957736	−	0.287649i	$-0.907126\pi$
$647$	−48.7223			−1.91547			−0.957736	+	0.287649i	$0.907126\pi$
$648$		0			0
$649$	−2.52628			−0.0991653
$650$	−3.09172	+	53.0827i	−0.121267	+	2.08208i
$651$		0			0
$652$	41.8066	+	4.88650i	1.63727	+	0.191370i
$653$	4.67541	−	1.10809i	0.182963	−	0.0433630i	−0.138113	−	0.990416i	$-0.544104\pi$
$653$	4.67541	−	1.10809i	0.182963	−	0.0433630i	0.321076	+	0.947053i	$0.395956\pi$
$654$		0			0
$655$	−5.62903	−	7.56110i	−0.219944	−	0.295437i
$656$	−0.385978	+	2.18899i	−0.0150699	+	0.0854656i
$657$		0			0
$658$	−4.21775	−	23.9201i	−0.164425	−	0.932501i
$659$	17.3570	−	18.3974i	0.676133	−	0.716659i	−0.294920	−	0.955522i	$-0.595293\pi$
$659$	17.3570	−	18.3974i	0.676133	−	0.716659i	0.971053	+	0.238863i	$0.0767746\pi$
$660$		0			0
$661$	−12.6327	−	6.34438i	−0.491355	−	0.246768i	0.185828	−	0.982582i	$-0.440503\pi$
$661$	−12.6327	−	6.34438i	−0.491355	−	0.246768i	−0.677183	+	0.735814i	$0.736800\pi$
$662$	−49.5714	+	32.6036i	−1.92665	+	1.26718i
$663$		0			0
$664$	10.4439	+	2.47524i	0.405300	+	0.0960579i
$665$	7.07019	+	2.57334i	0.274170	+	0.0997898i
$666$		0			0
$667$	−17.2393	+	6.27461i	−0.667510	+	0.242954i
$668$	−9.92518	+	1.16009i	−0.384017	+	0.0448851i
$669$		0			0
$670$	−1.17745	−	1.24802i	−0.0454887	−	0.0482152i
$671$	2.59368	−	3.48392i	0.100128	−	0.134495i
$672$		0			0
$673$	2.38363	−	1.19711i	0.0918823	−	0.0461450i	−0.402265	−	0.915523i	$-0.631777\pi$
$673$	2.38363	−	1.19711i	0.0918823	−	0.0461450i	0.494147	+	0.869378i	$0.335481\pi$
$674$	13.8366	−	23.9656i	0.532965	−	0.923122i
$675$		0			0
$676$	−21.1154	−	36.5730i	−0.812131	−	1.40665i
$677$	12.3339	+	8.11215i	0.474031	+	0.311775i	0.763949	−	0.645276i	$-0.223258\pi$
$677$	12.3339	+	8.11215i	0.474031	+	0.311775i	−0.289918	+	0.957051i	$0.593628\pi$
$678$		0			0
$679$	2.70211	+	6.26420i	0.103698	+	0.240398i
$680$	−2.02797	+	6.77388i	−0.0777689	+	0.259766i
$681$		0			0
$682$	2.89155	−	6.70336i	0.110723	−	0.256685i
$683$	−16.0712	−	13.4854i	−0.614948	−	0.516003i	0.281263	−	0.959631i	$-0.409247\pi$
$683$	−16.0712	−	13.4854i	−0.614948	−	0.516003i	−0.896211	+	0.443628i	$0.853691\pi$
$684$		0			0
$685$	−0.183640	+	0.154092i	−0.00701653	+	0.00588756i
$686$	−12.1616	−	40.6226i	−0.464333	−	1.55098i
$687$		0			0
$688$	−1.11634	−	19.1669i	−0.0425602	−	0.730731i
$689$	−2.64300	−	45.3786i	−0.100690	−	1.72879i
$690$		0			0
$691$	−9.99045	−	33.3704i	−0.380055	−	1.26947i	−0.907561	−	0.419920i	$-0.862058\pi$
$691$	−9.99045	−	33.3704i	−0.380055	−	1.26947i	0.527507	−	0.849551i	$-0.323127\pi$
$692$	27.8199	−	23.3437i	1.05755	−	0.887394i
$693$		0			0
$694$	14.0227	+	11.7664i	0.532294	+	0.446648i
$695$	3.83519	−	8.89097i	0.145477	−	0.337254i
$696$		0			0
$697$	−2.19045	+	7.31660i	−0.0829691	+	0.277136i
$698$	25.9772	+	60.2219i	0.983251	+	2.27943i
$699$		0			0
$700$	−19.1475	−	12.5935i	−0.723709	−	0.475991i
$701$	21.8053	+	37.7679i	0.823576	+	1.42647i	0.903003	+	0.429634i	$0.141357\pi$
$701$	21.8053	+	37.7679i	0.823576	+	1.42647i	−0.0794276	+	0.996841i	$0.525309\pi$
$702$		0			0
$703$	4.54496	−	7.87209i	0.171416	−	0.296902i
$704$	13.4057	−	6.73262i	0.505248	−	0.253745i
$705$		0			0
$706$	30.1846	−	40.5449i	1.13601	−	1.52593i
$707$	−5.83819	−	6.18812i	−0.219568	−	0.232728i
$708$		0			0
$709$	−18.1438	+	2.12071i	−0.681406	+	0.0796449i	−0.449752	−	0.893153i	$-0.648488\pi$
$709$	−18.1438	+	2.12071i	−0.681406	+	0.0796449i	−0.231654	+	0.972798i	$0.574414\pi$
$710$	−10.7731	+	3.92111i	−0.404309	+	0.147156i
$711$		0			0
$712$	23.3867	+	8.51206i	0.876453	+	0.319003i
$713$	8.41050	+	1.99332i	0.314976	+	0.0746506i
$714$		0			0
$715$	−3.48531	+	2.29233i	−0.130343	+	0.0857281i
$716$	1.02116	+	0.512848i	0.0381627	+	0.0191660i
$717$		0			0
$718$	−6.22342	+	6.59644i	−0.232256	+	0.246177i
$719$	−3.15002	−	17.8647i	−0.117476	−	0.666240i	−0.985494	−	0.169708i	$-0.945718\pi$
$719$	−3.15002	−	17.8647i	−0.117476	−	0.666240i	0.868018	−	0.496532i	$-0.165393\pi$
$720$		0			0
$721$	−1.64184	+	9.31131i	−0.0611451	+	0.346771i
$722$	27.9008	+	37.4773i	1.03836	+	1.39476i
$723$		0			0
$724$	55.4572	−	13.1436i	2.06105	−	0.488478i
$725$	−26.7891	−	3.13120i	−0.994924	−	0.116290i
$726$		0			0
$727$	−1.17766	+	20.2197i	−0.0436770	+	0.749906i	0.903380	+	0.428841i	$0.141078\pi$
$727$	−1.17766	+	20.2197i	−0.0436770	+	0.749906i	−0.947057	+	0.321065i	$0.895959\pi$
$728$	15.5847			0.577606
$729$		0			0
$730$	9.03402			0.334364
$731$	3.83580	−	65.8581i	0.141872	−	2.43585i
$732$		0			0
$733$	1.75603	+	0.205251i	0.0648606	+	0.00758111i	0.148461	−	0.988918i	$-0.452568\pi$
$733$	1.75603	+	0.205251i	0.0648606	+	0.00758111i	−0.0836007	+	0.996499i	$0.526642\pi$
$734$	−24.8153	+	5.88133i	−0.915948	+	0.217084i
$735$		0			0
$736$	14.0154	+	18.8260i	0.516616	+	0.693936i
$737$	−0.256258	+	1.45331i	−0.00943939	+	0.0535334i
$738$		0			0
$739$	−1.58340	−	8.97988i	−0.0582461	−	0.330330i	0.941736	−	0.336354i	$-0.109194\pi$
$739$	−1.58340	−	8.97988i	−0.0582461	−	0.330330i	−0.999982	+	0.00602346i	$0.998083\pi$
$740$	1.73314	−	1.83702i	0.0637115	−	0.0675303i
$741$		0			0
$742$	30.3145	+	15.2245i	1.11288	+	0.558910i
$743$	16.6442	−	10.9471i	0.610616	−	0.401608i	−0.206197	−	0.978510i	$-0.566109\pi$
$743$	16.6442	−	10.9471i	0.610616	−	0.401608i	0.816813	+	0.576902i	$0.195739\pi$
$744$		0			0
$745$	−0.629228	−	0.149130i	−0.0230531	−	0.00546369i
$746$	−74.3653	−	27.0667i	−2.72271	−	0.990984i
$747$		0			0
$748$	21.2839	−	7.74671i	0.778217	−	0.283248i
$749$	−23.6035	+	2.75885i	−0.862451	+	0.100806i
$750$		0			0
$751$	26.4586	+	28.0445i	0.965487	+	1.02336i	0.999713	+	0.0239424i	$0.00762184\pi$
$751$	26.4586	+	28.0445i	0.965487	+	1.02336i	−0.0342262	+	0.999414i	$0.510897\pi$
$752$	−7.26185	+	9.75436i	−0.264812	+	0.355705i
$753$		0			0
$754$	61.0427	−	30.6568i	2.22305	−	1.11646i
$755$	−0.00634611	+	0.0109918i	−0.000230959	+	0.000400032i
$756$		0			0
$757$	25.4729	+	44.1204i	0.925829	+	1.60358i	0.790223	+	0.612820i	$0.209965\pi$
$757$	25.4729	+	44.1204i	0.925829	+	1.60358i	0.135606	+	0.990763i	$0.456702\pi$
$758$	18.2701	+	12.0164i	0.663599	+	0.436456i
$759$		0			0
$760$	2.60212	+	6.03239i	0.0943889	+	0.218818i
$761$	−11.1682	+	37.3045i	−0.404848	+	1.35229i	0.476233	+	0.879319i	$0.342002\pi$
$761$	−11.1682	+	37.3045i	−0.404848	+	1.35229i	−0.881080	+	0.472967i	$0.843183\pi$
$762$		0			0
$763$	−1.28782	+	2.98550i	−0.0466222	+	0.108082i
$764$	14.4293	+	12.1076i	0.522033	+	0.438038i
$765$		0			0
$766$	−0.504379	+	0.423224i	−0.0182239	+	0.0152917i
$767$	3.19409	+	10.6690i	0.115332	+	0.385235i
$768$		0			0
$769$	−1.98573	−	34.0937i	−0.0716073	−	1.22945i	−0.822399	−	0.568911i	$-0.807365\pi$
$769$	−1.98573	−	34.0937i	−0.0716073	−	1.22945i	0.750792	−	0.660539i	$-0.229672\pi$
$770$	−0.181016	−	3.10793i	−0.00652338	−	0.112002i
$771$		0			0
$772$	6.85855	+	22.9091i	0.246845	+	0.824518i
$773$	−2.31945	+	1.94625i	−0.0834247	+	0.0700016i	−0.683546	−	0.729907i	$-0.739563\pi$
$773$	−2.31945	+	1.94625i	−0.0834247	+	0.0700016i	0.600122	+	0.799909i	$0.295119\pi$
$774$		0			0
$775$	9.73449	+	8.16820i	0.349673	+	0.293411i
$776$	−2.35941	+	5.46972i	−0.0846978	+	0.196352i
$777$		0			0
$778$	−4.69241	+	15.6737i	−0.168231	+	0.561930i
$779$	2.81061	+	6.51572i	0.100700	+	0.233450i
$780$		0			0
$781$	8.23836	+	5.41845i	0.294792	+	0.193887i
$782$	23.2165	+	40.2122i	0.830222	+	1.43799i
$783$		0			0
$784$	−3.64034	+	6.30526i	−0.130012	+	0.225188i
$785$	−4.50892	+	2.26446i	−0.160930	+	0.0808221i
$786$		0			0
$787$	1.35626	−	1.82178i	0.0483456	−	0.0649394i	−0.777293	−	0.629139i	$-0.783408\pi$
$787$	1.35626	−	1.82178i	0.0483456	−	0.0649394i	0.825639	+	0.564199i	$0.190815\pi$
$788$	15.8493	+	16.7993i	0.564608	+	0.598449i
$789$		0			0
$790$	19.9209	−	2.32841i	0.708752	−	0.0828413i
$791$	23.8739	−	8.68939i	0.848858	−	0.308959i
$792$		0			0
$793$	−17.9926	−	6.54878i	−0.638936	−	0.232554i
$794$	36.0869	+	8.55274i	1.28067	+	0.303525i
$795$		0			0
$796$	−28.8295	+	18.9615i	−1.02184	+	0.672072i
$797$	11.2447	+	5.64728i	0.398306	+	0.200037i	0.636665	−	0.771140i	$-0.280313\pi$
$797$	11.2447	+	5.64728i	0.398306	+	0.200037i	−0.238359	+	0.971177i	$0.576610\pi$
$798$		0			0
$799$	−28.6742	+	30.3929i	−1.01442	+	1.07522i
$800$	5.99181	+	33.9812i	0.211842	+	1.20142i
$801$		0			0
$802$	5.12989	−	29.0931i	0.181143	−	1.02731i
$803$	−4.63996	−	6.23255i	−0.163741	−	0.219942i
$804$		0			0
$805$	3.58658	−	0.850035i	0.126410	−	0.0299598i
$806$	−31.9656	−	3.73624i	−1.12594	−	0.131603i
$807$		0			0
$808$	0.431929	−	7.41593i	0.0151952	−	0.260891i
$809$	−13.7132			−0.482129			−0.241065	−	0.970509i	$-0.577497\pi$
$809$	−13.7132			−0.482129			−0.241065	+	0.970509i	$0.577497\pi$
$810$		0			0
$811$	1.72288			0.0604985			0.0302493	−	0.999542i	$-0.490370\pi$
$811$	1.72288			0.0604985			0.0302493	+	0.999542i	$0.490370\pi$
$812$	−1.71187	+	29.3917i	−0.0600748	+	1.03144i
$813$		0			0
$814$	−3.73572	−	0.436644i	−0.130937	−	0.0153043i
$815$	−9.68433	+	2.29523i	−0.339227	+	0.0803983i
$816$		0			0
$817$	−36.6018	−	49.1647i	−1.28053	−	1.72006i
$818$	−0.254031	+	1.44068i	−0.00888198	+	0.0503722i
$819$		0			0
$820$	0.342361	+	1.94163i	0.0119558	+	0.0678046i
$821$	35.4816	−	37.6083i	1.23832	−	1.31254i	0.305496	−	0.952193i	$-0.401178\pi$
$821$	35.4816	−	37.6083i	1.23832	−	1.31254i	0.932820	−	0.360344i	$-0.117341\pi$
$822$		0			0
$823$	18.2164	+	9.14864i	0.634985	+	0.318902i	0.737012	−	0.675880i	$-0.236236\pi$
$823$	18.2164	+	9.14864i	0.634985	+	0.318902i	−0.102026	+	0.994782i	$0.532533\pi$
$824$	−6.89762	+	4.53664i	−0.240290	+	0.158041i
$825$		0			0
$826$	−8.08726	−	1.91672i	−0.281392	−	0.0666911i
$827$	40.3124	+	14.6725i	1.40180	+	0.510213i	0.928712	−	0.370803i	$-0.120917\pi$
$827$	40.3124	+	14.6725i	1.40180	+	0.510213i	0.473087	+	0.881016i	$0.343140\pi$
$828$		0			0
$829$	−13.4165	+	4.88321i	−0.465975	+	0.169601i	−0.564328	−	0.825551i	$-0.690865\pi$
$829$	−13.4165	+	4.88321i	−0.465975	+	0.169601i	0.0983534	+	0.995152i	$0.468642\pi$
$830$	−9.38798	+	1.09730i	−0.325861	+	0.0380877i
$831$		0			0
$832$	−45.3827	−	48.1028i	−1.57336	−	1.66767i
$833$	−14.9389	+	20.0664i	−0.517603	+	0.695261i
$834$		0			0
$835$	2.11149	−	1.06043i	0.0730711	−	0.0366977i
$836$	10.5221	−	18.2249i	0.363916	−	0.630321i
$837$		0			0
$838$	21.6341	+	37.4714i	0.747338	+	1.29443i
$839$	−25.1136	−	16.5175i	−0.867018	−	0.570247i	0.0362407	−	0.999343i	$-0.488462\pi$
$839$	−25.1136	−	16.5175i	−0.867018	−	0.570247i	−0.903259	+	0.429096i	$0.858832\pi$
$840$		0			0
$841$	2.23748	+	5.18707i	0.0771545	+	0.178864i
$842$	−7.83502	+	26.1708i	−0.270013	+	0.901905i
$843$		0			0
$844$	−6.14664	+	14.2495i	−0.211576	+	0.490488i
$845$	7.64942	+	6.41863i	0.263148	+	0.220807i
$846$		0			0
$847$	13.3637	−	11.2135i	0.459183	−	0.385300i
$848$	−4.87105	−	16.2704i	−0.167273	−	0.558730i
$849$		0			0
$850$	3.96925	+	68.1495i	0.136144	+	2.33751i
$851$	−0.258925	−	4.44556i	−0.00887582	−	0.152392i
$852$		0			0
$853$	−10.4796	−	35.0042i	−0.358813	−	1.19852i	−0.926823	−	0.375498i	$-0.877472\pi$
$853$	−10.4796	−	35.0042i	−0.358813	−	1.19852i	0.568010	−	0.823022i	$-0.307713\pi$
$854$	10.9463	−	9.18504i	0.374575	−	0.314306i
$855$		0			0
$856$	−15.8956	−	13.3380i	−0.543299	−	0.455882i
$857$	−18.2829	+	42.3845i	−0.624532	+	1.44783i	0.252596	+	0.967572i	$0.418716\pi$
$857$	−18.2829	+	42.3845i	−0.624532	+	1.44783i	−0.877128	+	0.480256i	$0.840544\pi$
$858$		0			0
$859$	0.0885216	−	0.295683i	0.00302032	−	0.0100886i	−0.956466	−	0.291844i	$-0.905731\pi$
$859$	0.0885216	−	0.295683i	0.00302032	−	0.0100886i	0.959486	+	0.281755i	$0.0909165\pi$
$860$	−6.74516	−	15.6370i	−0.230008	−	0.533219i
$861$		0			0
$862$	39.2705	+	25.8286i	1.33756	+	0.879727i
$863$	16.3176	+	28.2630i	0.555459	+	0.962083i	0.997868	+	0.0652694i	$0.0207907\pi$
$863$	16.3176	+	28.2630i	0.555459	+	0.962083i	−0.442409	+	0.896813i	$0.645876\pi$
$864$		0			0
$865$	−4.29355	+	7.43665i	−0.145985	+	0.252854i
$866$	7.77630	−	3.90541i	0.264250	−	0.132711i
$867$		0			0
$868$	8.28329	−	11.1264i	0.281153	−	0.377654i
$869$	−11.8379	−	12.5475i	−0.401574	−	0.425643i
$870$		0			0
$871$	6.46163	−	0.755256i	0.218944	−	0.0255909i
$872$	−2.66783	+	0.971011i	−0.0903441	+	0.0328826i
$873$		0			0
$874$	40.5398	+	14.7553i	1.37128	+	0.499105i
$875$	11.0268	+	2.61340i	0.372774	+	0.0883491i
$876$		0			0
$877$	−5.80901	+	3.82065i	−0.196156	+	0.129014i	−0.643788	−	0.765204i	$-0.722638\pi$
$877$	−5.80901	+	3.82065i	−0.196156	+	0.129014i	0.447631	+	0.894218i	$0.352268\pi$
$878$	−60.6861	−	30.4777i	−2.04806	−	1.02857i
$879$		0			0
$880$	−1.06962	+	1.13373i	−0.0360570	+	0.0382182i
$881$	6.47573	+	36.7257i	0.218173	+	1.23732i	0.875315	+	0.483553i	$0.160654\pi$
$881$	6.47573	+	36.7257i	0.218173	+	1.23732i	−0.657142	+	0.753767i	$0.728235\pi$
$882$		0			0
$883$	1.07456	−	6.09412i	0.0361618	−	0.205084i	−0.961374	−	0.275246i	$-0.911241\pi$
$883$	1.07456	−	6.09412i	0.0361618	−	0.205084i	0.997536	+	0.0701625i	$0.0223518\pi$
$884$	−59.6261	−	80.0917i	−2.00544	−	2.69378i
$885$		0			0
$886$	3.39206	−	0.803933i	0.113958	−	0.0270087i
$887$	18.4976	+	2.16206i	0.621088	+	0.0725948i	0.420817	−	0.907146i	$-0.361744\pi$
$887$	18.4976	+	2.16206i	0.621088	+	0.0725948i	0.200271	+	0.979740i	$0.435818\pi$
$888$		0			0
$889$	−1.21211	+	20.8110i	−0.0406527	+	0.697980i
$890$	−21.9166			−0.734646
$891$		0			0
$892$	20.5958			0.689599
$893$	−2.25733	+	38.7568i	−0.0755385	+	1.29695i
$894$		0			0
$895$	−0.268371	−	0.0313680i	−0.00897064	−	0.00104852i
$896$	21.2139	−	5.02779i	0.708708	−	0.167967i
$897$		0			0
$898$	13.6490	+	18.3338i	0.455473	+	0.611807i
$899$	2.83476	−	16.0767i	0.0945444	−	0.536188i
$900$		0			0
$901$	−10.1337	−	57.4708i	−0.337601	−	1.91463i
$902$	2.01491	−	2.13568i	0.0670892	−	0.0711104i
$903$		0			0
$904$	19.8242	+	9.95610i	0.659344	+	0.331135i
$905$	−11.2593	+	7.40533i	−0.374271	+	0.246162i
$906$		0			0
$907$	25.4769	+	6.03814i	0.845947	+	0.200493i	0.630661	−	0.776058i	$-0.282784\pi$
$907$	25.4769	+	6.03814i	0.845947	+	0.200493i	0.215285	+	0.976551i	$0.430932\pi$
$908$	35.0525	+	12.7581i	1.16326	+	0.423392i
$909$		0			0
$910$	−12.8966	+	4.69396i	−0.427516	+	0.155603i
$911$	−7.90750	+	0.924254i	−0.261987	+	0.0306219i	−0.246072	−	0.969251i	$-0.579140\pi$
$911$	−7.90750	+	0.924254i	−0.261987	+	0.0306219i	−0.0159147	+	0.999873i	$0.505066\pi$
$912$		0			0
$913$	5.57878	+	5.91316i	0.184631	+	0.195697i
$914$	53.4544	−	71.8017i	1.76811	−	2.37499i
$915$		0			0
$916$	39.0795	−	19.6265i	1.29122	−	0.648477i
$917$	−13.3366	+	23.0996i	−0.440412	+	0.762816i
$918$		0			0
$919$	−27.5324	−	47.6875i	−0.908210	−	1.57307i	−0.816549	−	0.577276i	$-0.804116\pi$
$919$	−27.5324	−	47.6875i	−0.908210	−	1.57307i	−0.0916606	−	0.995790i	$-0.529217\pi$
$920$	2.68898	+	1.76857i	0.0886530	+	0.0583080i
$921$		0			0
$922$	−29.5586	−	68.5245i	−0.973460	−	2.25673i
$923$	12.4671	−	41.6430i	0.410360	−	1.37070i
$924$		0			0
$925$	2.59308	−	6.01143i	0.0852598	−	0.197654i
$926$	−55.5581	−	46.6188i	−1.82575	−	1.53199i
$927$		0			0
$928$	33.9569	−	28.4932i	1.11469	−	0.935336i
$929$	12.5788	+	42.0162i	0.412697	+	1.37851i	0.871687	+	0.490063i	$0.163026\pi$
$929$	12.5788	+	42.0162i	0.412697	+	1.37851i	−0.458989	+	0.888442i	$0.651788\pi$
$930$		0			0
$931$	1.35148	+	23.2040i	0.0442929	+	0.760480i
$932$	0.851973	+	14.6278i	0.0279073	+	0.479150i
$933$		0			0
$934$	−6.48392	−	21.6578i	−0.212160	−	0.708664i
$935$	−4.10265	+	3.44253i	−0.134171	+	0.112583i
$936$		0			0
$937$	25.4682	+	21.3704i	0.832010	+	0.698140i	0.955752	−	0.294175i	$-0.0950449\pi$
$937$	25.4682	+	21.3704i	0.832010	+	0.698140i	−0.123741	+	0.992315i	$0.539489\pi$
$938$	−1.92299	+	4.45799i	−0.0627878	+	0.145558i
$939$		0			0
$940$	−3.09360	+	10.3333i	−0.100902	+	0.337037i
$941$	4.43921	+	10.2912i	0.144714	+	0.335485i	0.975121	−	0.221672i	$-0.0711514\pi$
$941$	4.43921	+	10.2912i	0.144714	+	0.335485i	−0.830407	+	0.557157i	$0.811892\pi$
$942$		0			0
$943$	2.90442	+	1.91027i	0.0945810	+	0.0622069i
$944$	2.08058	+	3.60368i	0.0677172	+	0.117290i
$945$		0			0
$946$	−12.6807	+	21.9637i	−0.412286	+	0.714101i
$947$	4.22787	−	2.12331i	0.137387	−	0.0689984i	−0.378778	−	0.925488i	$-0.623655\pi$
$947$	4.22787	−	2.12331i	0.137387	−	0.0689984i	0.516165	+	0.856489i	$0.327359\pi$
$948$		0			0
$949$	−20.4548	+	27.4756i	−0.663991	+	0.891895i
$950$	43.5254	+	46.1343i	1.41215	+	1.49679i
$951$		0			0
$952$	19.8728	−	2.32280i	0.644082	−	0.0752824i
$953$	1.77553	−	0.646238i	0.0575149	−	0.0209337i	−0.313102	−	0.949719i	$-0.601368\pi$
$953$	1.77553	−	0.646238i	0.0575149	−	0.0209337i	0.370617	+	0.928786i	$0.379146\pi$
$954$		0			0
$955$	−4.18525	−	1.52331i	−0.135432	−	0.0492930i
$956$	−42.9489	−	10.1791i	−1.38907	−	0.329215i
$957$		0			0
$958$	−36.8962	+	24.2670i	−1.19206	+	0.784031i
$959$	0.606181	+	0.304436i	0.0195746	+	0.00983074i
$960$		0			0
$961$	15.9954	−	16.9541i	0.515981	−	0.546908i
$962$	2.87920	+	16.3288i	0.0928293	+	0.526461i
$963$		0			0
$964$	−11.1041	+	62.9743i	−0.357638	+	2.02827i
$965$	−3.37662	−	4.53559i	−0.108697	−	0.146006i
$966$		0			0
$967$	−54.3404	+	12.8789i	−1.74747	+	0.414158i	−0.975234	−	0.221178i	$-0.929010\pi$
$967$	−54.3404	+	12.8789i	−1.74747	+	0.414158i	−0.772236	+	0.635336i	$0.780862\pi$
$968$	15.1296	+	1.76839i	0.486283	+	0.0568383i
$969$		0			0
$970$	0.305016	−	5.23692i	0.00979346	−	0.168147i
$971$	−6.12547			−0.196576			−0.0982879	−	0.995158i	$-0.531337\pi$
$971$	−6.12547			−0.196576			−0.0982879	+	0.995158i	$0.531337\pi$
$972$		0			0
$973$	−27.3990			−0.878370
$974$	3.48813	−	59.8889i	0.111767	−	1.91896i
$975$		0			0
$976$	−7.10582	−	0.830551i	−0.227452	−	0.0265853i
$977$	27.7777	−	6.58343i	0.888687	−	0.210623i	0.239177	−	0.970976i	$-0.423122\pi$
$977$	27.7777	−	6.58343i	0.888687	−	0.210623i	0.649510	+	0.760353i	$0.274974\pi$
$978$		0			0
$979$	11.2566	+	15.1202i	0.359762	+	0.483244i
$980$	−1.12141	+	6.35984i	−0.0358222	+	0.203158i
$981$		0			0
$982$	3.86034	+	21.8931i	0.123188	+	0.698636i
$983$	15.1504	−	16.0585i	0.483224	−	0.512187i	−0.439188	−	0.898395i	$-0.644734\pi$
$983$	15.1504	−	16.0585i	0.483224	−	0.512187i	0.922412	+	0.386208i	$0.126215\pi$
$984$		0			0
$985$	−4.88019	−	2.45092i	−0.155496	−	0.0780929i
$986$	73.2697	−	48.1902i	2.33338	−	1.53469i
$987$		0			0
$988$	−90.2709	−	21.3946i	−2.87190	−	0.680653i
$989$	−28.2164	−	10.2699i	−0.897228	−	0.326564i
$990$		0			0
$991$	33.4354	−	12.1695i	1.06211	−	0.386577i	0.248890	−	0.968532i	$-0.419934\pi$
$991$	33.4354	−	12.1695i	1.06211	−	0.386577i	0.813221	+	0.581955i	$0.197712\pi$
$992$	−20.7435	+	2.42456i	−0.658606	+	0.0769800i
$993$		0			0
$994$	22.2620	+	23.5963i	0.706107	+	0.748430i
$995$	4.87228	−	6.54461i	0.154462	−	0.207478i
$996$		0			0
$997$	32.9108	−	16.5284i	1.04230	−	0.523461i	0.156570	−	0.987667i	$-0.449956\pi$
$997$	32.9108	−	16.5284i	1.04230	−	0.523461i	0.885727	+	0.464206i	$0.153660\pi$
$998$	9.51222	−	16.4757i	0.301104	−	0.521528i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.d.217.1		144
3.2	odd	2		729.2.g.a.217.8		144
9.2	odd	6		243.2.g.a.73.1		144
9.4	even	3		729.2.g.c.703.1		144
9.5	odd	6		729.2.g.b.703.8		144
9.7	even	3		81.2.g.a.25.8	yes	144
81.11	odd	54		6561.2.a.d.1.8		72
81.13	even	27		729.2.g.c.28.1		144
81.14	odd	54		243.2.g.a.10.1		144
81.40	even	27	inner	729.2.g.d.514.1		144
81.41	odd	54		729.2.g.a.514.8		144
81.67	even	27		81.2.g.a.13.8	✓	144
81.68	odd	54		729.2.g.b.28.8		144
81.70	even	27		6561.2.a.c.1.65		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.8	✓	144	81.67	even	27
81.2.g.a.25.8	yes	144	9.7	even	3
243.2.g.a.10.1		144	81.14	odd	54
243.2.g.a.73.1		144	9.2	odd	6
729.2.g.a.217.8		144	3.2	odd	2
729.2.g.a.514.8		144	81.41	odd	54
729.2.g.b.28.8		144	81.68	odd	54
729.2.g.b.703.8		144	9.5	odd	6
729.2.g.c.28.1		144	81.13	even	27
729.2.g.c.703.1		144	9.4	even	3
729.2.g.d.217.1		144	1.1	even	1	trivial
729.2.g.d.514.1		144	81.40	even	27	inner
6561.2.a.c.1.65		72	81.70	even	27
6561.2.a.d.1.8		72	81.11	odd	54

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.126512 + 2.17212i) q^{2} +(-2.71564 - 0.317413i) q^{4} +(0.629067 - 0.149092i) q^{5} +(-1.09241 - 1.46736i) q^{7} +(0.277373 - 1.57306i) q^{8} +(0.244261 + 1.38527i) q^{10} +(0.830243 - 0.880006i) q^{11} +(-4.76615 - 2.39365i) q^{13} +(3.32548 - 2.18720i) q^{14} +(-1.93907 - 0.459569i) q^{16} +(-6.43434 - 2.34191i) q^{17} +(-5.97823 + 2.17590i) q^{19} +(-1.75565 + 0.205206i) q^{20} +(1.80645 + 1.91472i) q^{22} +(-1.86114 + 2.49994i) q^{23} +(-4.09467 + 2.05642i) q^{25} +(5.80229 - 10.0499i) q^{26} +(2.50083 + 4.33156i) q^{28} +(4.91797 + 3.23460i) q^{29} +(-1.09846 - 2.54651i) q^{31} +(2.15979 - 7.21421i) q^{32} +(5.90094 - 13.6799i) q^{34} +(-0.905967 - 0.760197i) q^{35} +(-1.09453 + 0.918418i) q^{37} +(-3.97000 - 13.2607i) q^{38} +(-0.0600440 - 1.03092i) q^{40} +(-0.0648547 - 1.11351i) q^{41} +(2.76319 + 9.22968i) q^{43} +(-2.53397 + 2.12625i) q^{44} +(-5.19473 - 4.35890i) q^{46} +(2.41701 - 5.60327i) q^{47} +(1.04784 - 3.50003i) q^{49} +(-3.94877 - 9.15429i) q^{50} +(12.1834 + 8.01315i) q^{52} +(4.26135 + 7.38088i) q^{53} +(0.391077 - 0.677365i) q^{55} +(-2.61124 + 1.31142i) q^{56} +(-7.64814 + 10.2732i) q^{58} +(-1.43295 - 1.51884i) q^{59} +(3.56577 - 0.416778i) q^{61} +(5.67029 - 2.06382i) q^{62} +(11.6517 + 4.24088i) q^{64} +(-3.35511 - 0.795175i) q^{65} +(-1.01911 + 0.670277i) q^{67} +(16.7300 + 8.40213i) q^{68} +(1.76586 - 1.87170i) q^{70} +(1.41528 + 8.02646i) q^{71} +(1.11524 - 6.32482i) q^{73} +(-1.85645 - 2.49364i) q^{74} +(16.9254 - 4.01139i) q^{76} +(-2.19824 - 0.256938i) q^{77} +(0.829051 - 14.2343i) q^{79} -1.28832 q^{80} +2.42689 q^{82} +(-0.390702 + 6.70809i) q^{83} +(-4.39679 - 0.513911i) q^{85} +(-20.3976 + 4.83432i) q^{86} +(-1.15402 - 1.55011i) q^{88} +(-2.70557 + 15.3441i) q^{89} +(1.69423 + 9.60848i) q^{91} +(5.84771 - 6.19821i) q^{92} +(11.8652 + 5.95894i) q^{94} +(-3.43630 + 2.26009i) q^{95} +(-3.62877 - 0.860034i) q^{97} +(7.46994 + 2.71884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 + 45 * q^20 + 9 * q^22 - 45 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 + 36 * q^29 + 9 * q^31 - 99 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 + 18 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 - 99 * q^47 + 9 * q^49 + 126 * q^50 - 27 * q^52 + 45 * q^53 - 9 * q^55 - 225 * q^56 + 9 * q^58 + 72 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 - 81 * q^65 - 45 * q^67 + 117 * q^68 - 99 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 - 153 * q^76 + 81 * q^77 - 99 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 - 99 * q^85 + 81 * q^86 - 153 * q^88 - 81 * q^89 - 18 * q^91 + 207 * q^92 - 99 * q^94 - 171 * q^95 - 45 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

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