LMFDB - Embedded newform 729.2.g.a.217.8

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			217.8
Character	$\chi$	$=$	729.217
Dual form			729.2.g.a.514.8

$q$-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	$-0.702105\pi$
$2$	0.126512	−	2.17212i	0.0894574	−	1.53592i	0.682579	−	0.730812i	$-0.260858\pi$
$3$		0			0
$3$		0			0
$4$	−2.71564	−	0.317413i	−1.35782	−	0.158707i
$5$	−0.629067	+	0.149092i	−0.281327	+	0.0666758i	−0.368857	−	0.929486i	$-0.620251\pi$
$5$	−0.629067	+	0.149092i	−0.281327	+	0.0666758i	0.0875297	+	0.996162i	$0.472103\pi$
$6$		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	−0.840337	−	0.542065i	$-0.817643\pi$
$11$	−0.830243	+	0.880006i	−0.250328	+	0.265332i	0.590009	+	0.807397i	$0.299124\pi$
$12$		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	0.970864	−	0.239631i	$-0.0770266\pi$
$17$	6.43434	+	2.34191i	1.56056	+	0.567996i	0.589693	+	0.807628i	$0.299249\pi$
$18$		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	−0.564560	−	0.825392i	$-0.690954\pi$
$23$	1.86114	−	2.49994i	0.388074	−	0.521274i	0.952634	+	0.304118i	$0.0983616\pi$
$24$		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	0.00355721	−	0.999994i	$-0.498868\pi$
$29$	−4.91797	−	3.23460i	−0.913244	−	0.600650i	−0.916801	+	0.399344i	$0.869238\pi$
$30$		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	$0.00924084\pi$
$41$	0.0648547	+	1.11351i	0.0101286	+	0.173902i	−0.989450	+	0.144875i	$0.953722\pi$
$42$		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	$0.276447\pi$
$47$	−2.41701	+	5.60327i	−0.352558	+	0.817321i	−0.998543	+	0.0539704i	$0.982812\pi$
$48$		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	$-0.967627\pi$
$53$	−4.26135	−	7.38088i	−0.585342	−	1.01384i	0.409491	−	0.912314i	$-0.365706\pi$
$54$		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	0.813900	−	0.581005i	$-0.197340\pi$
$59$	1.43295	+	1.51884i	0.186554	+	0.197736i	−0.627346	+	0.778741i	$0.715859\pi$
$60$		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	$-0.894874\pi$
$71$	−1.41528	−	8.02646i	−0.167963	−	0.952565i	0.777994	−	0.628272i	$-0.216237\pi$
$72$		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	$-0.861258\pi$
$83$	0.390702	−	6.70809i	0.0428851	−	0.736308i	0.949387	−	0.314107i	$-0.101705\pi$
$84$		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	$-0.635180\pi$
$89$	2.70557	−	15.3441i	0.286790	−	1.62647i	0.698820	−	0.715297i	$-0.253709\pi$
$90$		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	−0.342753	−	0.939426i	$-0.611359\pi$
$101$	−4.61913	+	0.539899i	−0.459621	+	0.0537220i	−0.116868	+	0.993147i	$0.537285\pi$
$102$		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	$0.382761\pi$
$107$	−6.49528	+	11.2502i	−0.627922	+	1.08759i	−0.987968	+	0.154659i	$0.950572\pi$
$108$		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	$-0.680816\pi$
$113$	3.98316	−	13.3047i	0.374704	−	1.25160i	0.912693	−	0.408646i	$-0.133999\pi$
$114$		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	$0.0901799\pi$
$131$	5.77514	+	13.3883i	0.504576	+	1.16974i	−0.455560	+	0.890205i	$0.650561\pi$
$132$		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	−0.434588	−	0.900630i	$-0.643106\pi$
$137$	0.331366	−	0.166418i	0.0283105	−	0.0142181i	0.462898	+	0.886411i	$0.346810\pi$
$138$		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	0.485036	−	0.874494i	$-0.338806\pi$
$149$	0.893861	+	0.448914i	0.0732279	+	0.0367764i	−0.411808	+	0.911270i	$0.635103\pi$
$150$		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	−0.365896	−	0.930656i	$-0.619237\pi$
$167$	−3.55630	+	0.842859i	−0.275195	+	0.0652224i	0.0907011	+	0.995878i	$0.471089\pi$
$168$		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	−0.281338	−	0.959609i	$-0.590778\pi$
$173$	9.11506	−	9.66140i	0.693005	−	0.734543i	0.974344	+	0.225066i	$0.0722598\pi$
$174$		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	0.356656	−	0.934236i	$-0.383917\pi$
$179$	0.392738	+	0.142945i	0.0293546	+	0.0106842i	−0.327301	+	0.944920i	$0.606139\pi$
$180$		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	0.740407	−	0.672159i	$-0.234633\pi$
$191$	5.75588	+	3.78570i	0.416481	+	0.273924i	−0.323927	+	0.946082i	$0.605003\pi$
$192$		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	0.843512	−	0.537111i	$-0.180484\pi$
$197$	6.47094	+	5.42976i	0.461035	+	0.386855i	−0.382476	+	0.923965i	$0.624929\pi$
$198$		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	0.646183	−	0.763182i	$-0.276364\pi$
$227$	13.2754	+	3.14632i	0.881118	+	0.208829i	0.234935	+	0.972011i	$0.424512\pi$
$228$		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	$0.000613031\pi$
$233$	0.930605	+	5.27772i	0.0609660	+	0.345755i	−0.939032	+	0.343829i	$0.888276\pi$
$234$		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	−0.419578	−	0.907719i	$-0.637822\pi$
$239$	−16.0344	−	1.87416i	−1.03718	−	0.121229i	−0.617603	+	0.786490i	$0.711896\pi$
$240$		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	$0.333559\pi$
$251$	−4.21745	+	23.9183i	−0.266203	+	1.50971i	−0.765588	+	0.643331i	$0.777552\pi$
$252$		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	−0.273074	−	0.961993i	$-0.588040\pi$
$257$	8.04903	−	5.29393i	0.502085	−	0.330226i	0.775158	+	0.631767i	$0.217670\pi$
$258$		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	0.0897582	−	0.995964i	$-0.471391\pi$
$263$	6.59689	−	0.771066i	0.406782	−	0.0475460i	0.317024	+	0.948418i	$0.397317\pi$
$264$		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	$-0.480330\pi$
$269$	14.6832	−	25.4321i	0.895251	−	1.55062i	0.833494	−	0.552529i	$-0.186337\pi$
$270$		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	$-0.863740\pi$
$281$	−6.33274	−	21.1528i	−0.377780	−	1.26187i	0.531987	−	0.846753i	$-0.321446\pi$
$282$		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	0.800646	−	0.599138i	$-0.204490\pi$
$293$	−3.15963	−	7.32485i	−0.184588	−	0.427922i	−0.985234	+	0.171215i	$0.945231\pi$
$294$		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	0.786518	−	0.617567i	$-0.211882\pi$
$311$	13.4174	+	6.73846i	0.760830	+	0.382103i	−0.0256887	+	0.999670i	$0.508178\pi$
$312$		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	$0.0801232\pi$
$317$	16.5461	+	22.2253i	0.929323	+	1.24830i	−0.0391636	+	0.999233i	$0.512469\pi$
$318$		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	−0.916254	−	0.400598i	$-0.868802\pi$
$347$	−5.02397	+	6.74836i	−0.269701	+	0.362271i	0.646553	+	0.762869i	$0.276210\pi$
$348$		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	0.948441	−	0.316955i	$-0.102660\pi$
$353$	19.4095	+	12.7659i	1.03307	+	0.679458i	0.0846248	+	0.996413i	$0.473031\pi$
$354$		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	0.554630	−	0.832097i	$-0.312860\pi$
$359$	−3.19290	−	2.67916i	−0.168515	−	0.141401i	−0.723145	+	0.690696i	$0.757304\pi$
$360$		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	0.722046	−	0.691845i	$-0.243202\pi$
$383$	−0.207663	−	0.220110i	−0.0106111	−	0.0112471i	−0.732657	+	0.680598i	$0.761720\pi$
$384$		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	0.0408974	−	0.999163i	$-0.486978\pi$
$389$	−7.31685	−	1.73413i	−0.370979	−	0.0879237i	−0.411876	+	0.911240i	$0.635126\pi$
$390$		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	0.445938	−	0.895064i	$-0.352870\pi$
$401$	13.4856	+	1.57624i	0.673441	+	0.0787139i	0.227502	+	0.973778i	$0.426944\pi$
$402$		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	−0.886162	−	0.463375i	$-0.846638\pi$
$419$	−16.6146	+	10.9276i	−0.811675	+	0.533847i	0.0744874	+	0.997222i	$0.476268\pi$
$420$		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	$0.340839\pi$
$431$	−10.8013	+	18.7084i	−0.520281	+	0.901153i	−0.999722	+	0.0235787i	$0.992494\pi$
$432$		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	0.968211	−	0.250134i	$-0.0804745\pi$
$443$	0.459510	+	1.53487i	0.0218320	+	0.0729238i	−0.946379	+	0.323057i	$0.895289\pi$
$444$		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	−0.812613	−	0.582804i	$-0.801955\pi$
$449$	−8.04720	+	6.75241i	−0.379771	+	0.318666i	0.432841	+	0.901470i	$0.357511\pi$
$450$		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	0.443734	−	0.896159i	$-0.353654\pi$
$461$	30.6506	−	15.3933i	1.42754	−	0.716939i	0.983809	+	0.179219i	$0.0573572\pi$
$462$		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	−0.106082	−	0.994357i	$-0.533831\pi$
$467$	9.76380	−	3.55373i	0.451815	−	0.164447i	0.557897	+	0.829910i	$0.311608\pi$
$468$		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	0.433788	−	0.901015i	$-0.357177\pi$
$479$	−12.1202	−	16.2803i	−0.553787	−	0.743865i	−0.987575	+	0.157150i	$0.949769\pi$
$480$		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	−0.448738	−	0.893663i	$-0.648126\pi$
$491$	−9.94187	+	2.35627i	−0.448670	+	0.106337i	6.80725e−5		1.00000i	$0.499978\pi$
$492$		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	0.601243	−	0.799066i	$-0.294672\pi$
$503$	12.2947	+	4.47489i	0.548192	+	0.199526i	−0.0530509	+	0.998592i	$0.516895\pi$
$504$		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	$-0.560787\pi$
$509$	18.1662	−	24.4014i	0.805202	−	1.08157i	0.995012	−	0.0997537i	$-0.0318055\pi$
$510$		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	0.443681	−	0.896185i	$-0.353672\pi$
$521$	−8.25925	−	6.93034i	−0.361845	−	0.303624i	−0.805525	+	0.592561i	$0.798117\pi$
$522$		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	$-0.965729\pi$
$557$	−2.28246	−	12.9445i	−0.0967109	−	0.548475i	0.897499	−	0.441017i	$-0.145382\pi$
$558$		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	0.242574	−	0.970133i	$-0.422008\pi$
$563$	6.04774	+	0.706879i	0.254882	+	0.0297914i	0.0123076	+	0.999924i	$0.496082\pi$
$564$		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	$-0.868517\pi$
$569$	0.963908	−	16.5497i	0.0404091	−	0.693798i	0.956303	−	0.292377i	$-0.0944463\pi$
$570$		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	−0.958752	−	0.284243i	$-0.908258\pi$
$587$	−44.2431	+	5.17128i	−1.82611	+	0.213442i	−0.867358	+	0.497685i	$0.834184\pi$
$588$		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	−0.994526	−	0.104493i	$-0.966678\pi$
$593$	−9.90549	+	17.1568i	−0.406770	+	0.704546i	0.587756	+	0.809038i	$0.300011\pi$
$594$		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	$0.285866\pi$
$599$	−8.00993	+	26.7550i	−0.327277	+	1.09318i	−0.950393	+	0.311051i	$0.899319\pi$
$600$		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	$0.0385247\pi$
$617$	9.91795	+	22.9924i	0.399282	+	0.925639i	−0.593403	+	0.804905i	$0.702216\pi$
$618$		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	0.894860	−	0.446347i	$-0.147275\pi$
$641$	5.33236	+	7.16261i	0.210616	+	0.282906i	−0.684244	+	0.729253i	$0.739868\pi$
$642$		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	$-0.0928736\pi$
$647$	48.7223			1.91547			0.957736	+	0.287649i	$0.0928736\pi$
$648$		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	−0.321076	−	0.947053i	$-0.604044\pi$
$653$	−4.67541	+	1.10809i	−0.182963	+	0.0433630i	0.138113	+	0.990416i	$0.455896\pi$
$654$		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	−0.971053	−	0.238863i	$-0.923225\pi$
$659$	−17.3570	+	18.3974i	−0.676133	+	0.716659i	0.294920	+	0.955522i	$0.404707\pi$
$660$		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	0.289918	−	0.957051i	$-0.406372\pi$
$677$	−12.3339	−	8.11215i	−0.474031	−	0.311775i	−0.763949	+	0.645276i	$0.776742\pi$
$678$		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	0.896211	−	0.443628i	$-0.146309\pi$
$683$	16.0712	+	13.4854i	0.614948	+	0.516003i	−0.281263	+	0.959631i	$0.590753\pi$
$684$		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	$-0.858643\pi$
$701$	−21.8053	−	37.7679i	−0.823576	−	1.42647i	0.0794276	−	0.996841i	$-0.474691\pi$
$702$		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	$0.0542824\pi$
$719$	3.15002	+	17.8647i	0.117476	+	0.666240i	−0.868018	+	0.496532i	$0.834607\pi$
$720$		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	−0.816813	−	0.576902i	$-0.804261\pi$
$743$	−16.6442	+	10.9471i	−0.610616	+	0.401608i	0.206197	+	0.978510i	$0.433891\pi$
$744$		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	$-0.657998\pi$
$761$	11.1682	−	37.3045i	0.404848	−	1.35229i	0.881080	−	0.472967i	$-0.156817\pi$
$762$		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	−0.600122	−	0.799909i	$-0.704881\pi$
$773$	2.31945	−	1.94625i	0.0834247	−	0.0700016i	0.683546	+	0.729907i	$0.260437\pi$
$774$		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	0.238359	−	0.971177i	$-0.423390\pi$
$797$	−11.2447	−	5.64728i	−0.398306	−	0.200037i	−0.636665	+	0.771140i	$0.719687\pi$
$798$		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	$-0.422503\pi$
$809$	13.7132			0.482129			0.241065	+	0.970509i	$0.422503\pi$
$810$		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	$0.598822\pi$
$821$	−35.4816	+	37.6083i	−1.23832	+	1.31254i	−0.932820	+	0.360344i	$0.882659\pi$
$822$		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	−0.473087	−	0.881016i	$-0.656860\pi$
$827$	−40.3124	−	14.6725i	−1.40180	−	0.510213i	−0.928712	+	0.370803i	$0.879083\pi$
$828$		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	0.903259	−	0.429096i	$-0.141168\pi$
$839$	25.1136	+	16.5175i	0.867018	+	0.570247i	−0.0362407	+	0.999343i	$0.511538\pi$
$840$		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	$-0.581284\pi$
$857$	18.2829	−	42.3845i	0.624532	−	1.44783i	0.877128	−	0.480256i	$-0.159456\pi$
$858$		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	$-0.979209\pi$
$863$	−16.3176	−	28.2630i	−0.555459	−	0.962083i	0.442409	−	0.896813i	$-0.354124\pi$
$864$		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	$-0.839346\pi$
$881$	−6.47573	−	36.7257i	−0.218173	−	1.23732i	0.657142	−	0.753767i	$-0.271765\pi$
$882$		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	−0.200271	−	0.979740i	$-0.564182\pi$
$887$	−18.4976	−	2.16206i	−0.621088	−	0.0725948i	−0.420817	+	0.907146i	$0.638256\pi$
$888$		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	0.0159147	−	0.999873i	$-0.494934\pi$
$911$	7.90750	−	0.924254i	0.261987	−	0.0306219i	0.246072	+	0.969251i	$0.420860\pi$
$912$		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	$-0.836974\pi$
$929$	−12.5788	−	42.0162i	−0.412697	−	1.37851i	0.458989	−	0.888442i	$-0.348212\pi$
$930$		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	0.830407	−	0.557157i	$-0.188108\pi$
$941$	−4.43921	−	10.2912i	−0.144714	−	0.335485i	−0.975121	+	0.221672i	$0.928849\pi$
$942$		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	−0.516165	−	0.856489i	$-0.672641\pi$
$947$	−4.22787	+	2.12331i	−0.137387	+	0.0689984i	0.378778	+	0.925488i	$0.376345\pi$
$948$		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	−0.370617	−	0.928786i	$-0.620854\pi$
$953$	−1.77553	+	0.646238i	−0.0575149	+	0.0209337i	0.313102	+	0.949719i	$0.398632\pi$
$954$		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	$-0.468663\pi$
$971$	6.12547			0.196576			0.0982879	+	0.995158i	$0.468663\pi$
$972$		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	−0.649510	−	0.760353i	$-0.725026\pi$
$977$	−27.7777	+	6.58343i	−0.888687	+	0.210623i	−0.239177	+	0.970976i	$0.576878\pi$
$978$		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	−0.922412	−	0.386208i	$-0.873785\pi$
$983$	−15.1504	+	16.0585i	−0.483224	+	0.512187i	0.439188	+	0.898395i	$0.355266\pi$
$984$		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.a.217.8		144
3.2	odd	2		729.2.g.d.217.1		144
9.2	odd	6		81.2.g.a.25.8	yes	144
9.4	even	3		729.2.g.b.703.8		144
9.5	odd	6		729.2.g.c.703.1		144
9.7	even	3		243.2.g.a.73.1		144
81.11	odd	54		6561.2.a.c.1.65		72
81.13	even	27		729.2.g.b.28.8		144
81.14	odd	54		81.2.g.a.13.8	✓	144
81.40	even	27	inner	729.2.g.a.514.8		144
81.41	odd	54		729.2.g.d.514.1		144
81.67	even	27		243.2.g.a.10.1		144
81.68	odd	54		729.2.g.c.28.1		144
81.70	even	27		6561.2.a.d.1.8		72

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

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more