LMFDB - Embedded newform 729.2.g.a.514.8

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			514.8
Character	$\chi$	$=$	729.514
Dual form			729.2.g.a.217.8

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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	0.682579	+	0.730812i	$0.260858\pi$
$2$	0.126512	+	2.17212i	0.0894574	+	1.53592i	−0.593122	+	0.805113i	$0.702105\pi$
$3$		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	$-0.472103\pi$
$5$	−0.629067	−	0.149092i	−0.281327	−	0.0666758i	−0.368857	+	0.929486i	$0.620251\pi$
$6$		0			0
$7$	−1.09241	+	1.46736i	−0.412891	+	0.554608i	−0.959110	−	0.283034i	$-0.908659\pi$
$7$	−1.09241	+	1.46736i	−0.412891	+	0.554608i	0.546219	+	0.837642i	$0.316066\pi$
$8$	−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	$-0.299124\pi$
$11$	−0.830243	−	0.880006i	−0.250328	−	0.265332i	−0.840337	+	0.542065i	$0.817643\pi$
$12$		0			0
$13$	−4.76615	+	2.39365i	−1.32189	+	0.663880i	−0.963001	−	0.269499i	$-0.913142\pi$
$13$	−4.76615	+	2.39365i	−1.32189	+	0.663880i	−0.358893	+	0.933379i	$0.616846\pi$
$14$	−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	$-0.299249\pi$
$17$	6.43434	−	2.34191i	1.56056	−	0.567996i	0.970864	+	0.239631i	$0.0770266\pi$
$18$		0			0
$19$	−5.97823	−	2.17590i	−1.37150	−	0.499185i	−0.451909	−	0.892064i	$-0.649257\pi$
$19$	−5.97823	−	2.17590i	−1.37150	−	0.499185i	−0.919590	+	0.392879i	$0.871479\pi$
$20$	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	$-0.0983616\pi$
$23$	1.86114	+	2.49994i	0.388074	+	0.521274i	−0.564560	+	0.825392i	$0.690954\pi$
$24$		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	$-0.869238\pi$
$29$	−4.91797	+	3.23460i	−0.913244	+	0.600650i	0.00355721	+	0.999994i	$0.498868\pi$
$30$		0			0
$31$	−1.09846	+	2.54651i	−0.197288	+	0.457366i	−0.987928	−	0.154916i	$-0.950489\pi$
$31$	−1.09846	+	2.54651i	−0.197288	+	0.457366i	0.790639	+	0.612282i	$0.209748\pi$
$32$	−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	0.548369	−	0.836236i	$-0.315249\pi$
$37$	−1.09453	−	0.918418i	−0.179939	−	0.150987i	−0.728309	+	0.685249i	$0.759693\pi$
$38$	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	−0.989450	−	0.144875i	$-0.953722\pi$
$41$	0.0648547	−	1.11351i	0.0101286	−	0.173902i	0.999579	−	0.0290269i	$-0.00924084\pi$
$42$		0			0
$43$	2.76319	−	9.22968i	0.421382	−	1.40751i	−0.439286	−	0.898347i	$-0.644769\pi$
$43$	2.76319	−	9.22968i	0.421382	−	1.40751i	0.860668	−	0.509167i	$-0.170046\pi$
$44$	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	−0.998543	−	0.0539704i	$-0.982812\pi$
$47$	−2.41701	−	5.60327i	−0.352558	−	0.817321i	0.645985	−	0.763350i	$-0.276447\pi$
$48$		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	0.409491	+	0.912314i	$0.365706\pi$
$53$	−4.26135	+	7.38088i	−0.585342	+	1.01384i	−0.994833	+	0.101528i	$0.967627\pi$
$54$		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	$-0.715859\pi$
$59$	1.43295	−	1.51884i	0.186554	−	0.197736i	0.813900	+	0.581005i	$0.197340\pi$
$60$		0			0
$61$	3.56577	+	0.416778i	0.456550	+	0.0533630i	0.341260	−	0.939969i	$-0.389146\pi$
$61$	3.56577	+	0.416778i	0.456550	+	0.0533630i	0.115290	+	0.993332i	$0.463220\pi$
$62$	−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	0.485730	−	0.874109i	$-0.338554\pi$
$67$	−1.01911	−	0.670277i	−0.124504	−	0.0818873i	−0.610233	+	0.792222i	$0.708924\pi$
$68$	−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	0.777994	+	0.628272i	$0.216237\pi$
$71$	−1.41528	+	8.02646i	−0.167963	+	0.952565i	−0.945957	+	0.324293i	$0.894874\pi$
$72$		0			0
$73$	1.11524	+	6.32482i	0.130529	+	0.740264i	0.977870	+	0.209215i	$0.0670909\pi$
$73$	1.11524	+	6.32482i	0.130529	+	0.740264i	−0.847341	+	0.531049i	$0.821798\pi$
$74$	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	0.642822	+	0.766015i	$0.277763\pi$
$79$	0.829051	+	14.2343i	0.0932755	+	1.60148i	−0.549547	+	0.835463i	$0.685200\pi$
$80$	1.28832			0.144039
$81$		0			0
$82$	2.42689			0.268006
$83$	0.390702	+	6.70809i	0.0428851	+	0.736308i	0.949387	+	0.314107i	$0.101705\pi$
$83$	0.390702	+	6.70809i	0.0428851	+	0.736308i	−0.906502	+	0.422201i	$0.861258\pi$
$84$		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	0.698820	+	0.715297i	$0.253709\pi$
$89$	2.70557	+	15.3441i	0.286790	+	1.62647i	−0.412030	+	0.911170i	$0.635180\pi$
$90$		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	−0.410668	−	0.911785i	$-0.634704\pi$
$97$	−3.62877	+	0.860034i	−0.368446	+	0.0873232i	0.0422221	+	0.999108i	$0.486556\pi$
$98$	−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	$-0.537285\pi$
$101$	−4.61913	−	0.539899i	−0.459621	−	0.0537220i	−0.342753	+	0.939426i	$0.611359\pi$
$102$		0			0
$103$	−3.54684	+	3.75944i	−0.349481	+	0.370428i	−0.878138	−	0.478407i	$-0.841214\pi$
$103$	−3.54684	+	3.75944i	−0.349481	+	0.370428i	0.528657	+	0.848835i	$0.322696\pi$
$104$	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	−0.987968	−	0.154659i	$-0.950572\pi$
$107$	−6.49528	−	11.2502i	−0.627922	−	1.08759i	0.360046	−	0.932935i	$-0.382761\pi$
$108$		0			0
$109$	−0.888686	+	1.53925i	−0.0851207	+	0.147433i	−0.905443	−	0.424469i	$-0.860461\pi$
$109$	−0.888686	+	1.53925i	−0.0851207	+	0.147433i	0.820322	+	0.571902i	$0.193794\pi$
$110$	−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	0.912693	+	0.408646i	$0.133999\pi$
$113$	3.98316	+	13.3047i	0.374704	+	1.25160i	−0.537989	+	0.842952i	$0.680816\pi$
$114$		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	−0.941887	−	0.335930i	$-0.890949\pi$
$127$	−8.72949	+	7.32491i	−0.774617	+	0.649981i	0.167270	+	0.985911i	$0.446505\pi$
$128$	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	−0.455560	−	0.890205i	$-0.650561\pi$
$131$	5.77514	−	13.3883i	0.504576	−	1.16974i	0.960136	−	0.279534i	$-0.0901799\pi$
$132$		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	$-0.346810\pi$
$137$	0.331366	+	0.166418i	0.0283105	+	0.0142181i	−0.434588	+	0.900630i	$0.643106\pi$
$138$		0			0
$139$	8.94395	+	12.0138i	0.758616	+	1.01900i	0.998834	+	0.0482794i	$0.0153738\pi$
$139$	8.94395	+	12.0138i	0.758616	+	1.01900i	−0.240218	+	0.970719i	$0.577219\pi$
$140$	−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	$-0.635103\pi$
$149$	0.893861	−	0.448914i	0.0732279	−	0.0367764i	0.485036	+	0.874494i	$0.338806\pi$
$150$		0			0
$151$	−0.0134726	−	0.0142801i	−0.00109638	−	0.00116210i	0.726825	−	0.686822i	$-0.240995\pi$
$151$	−0.0134726	−	0.0142801i	−0.00109638	−	0.00116210i	−0.727922	+	0.685660i	$0.759514\pi$
$152$	−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	−0.0838947	−	0.996475i	$-0.526736\pi$
$157$	−7.59419	−	1.79986i	−0.606083	−	0.143644i	−0.522188	+	0.852830i	$0.674884\pi$
$158$	−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	$-0.471089\pi$
$167$	−3.55630	−	0.842859i	−0.275195	−	0.0652224i	−0.365896	+	0.930656i	$0.619237\pi$
$168$		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	$-0.0722598\pi$
$173$	9.11506	+	9.66140i	0.693005	+	0.734543i	−0.281338	+	0.959609i	$0.590778\pi$
$174$		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	$-0.606139\pi$
$179$	0.392738	−	0.142945i	0.0293546	−	0.0106842i	0.356656	+	0.934236i	$0.383917\pi$
$180$		0			0
$181$	−19.5881	−	7.12947i	−1.45597	−	0.529929i	−0.511717	−	0.859154i	$-0.670990\pi$
$181$	−19.5881	−	7.12947i	−1.45597	−	0.529929i	−0.944252	+	0.329225i	$0.893213\pi$
$182$	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	$-0.605003\pi$
$191$	5.75588	−	3.78570i	0.416481	−	0.273924i	0.740407	+	0.672159i	$0.234633\pi$
$192$		0			0
$193$	−3.46427	+	8.03108i	−0.249363	+	0.578089i	−0.996217	−	0.0868989i	$-0.972304\pi$
$193$	−3.46427	+	8.03108i	−0.249363	+	0.578089i	0.746854	+	0.664988i	$0.231564\pi$
$194$	−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	$-0.624929\pi$
$197$	6.47094	−	5.42976i	0.461035	−	0.386855i	0.843512	+	0.537111i	$0.180484\pi$
$198$		0			0
$199$	9.66790	+	8.11233i	0.685339	+	0.575068i	0.917561	−	0.397595i	$-0.130155\pi$
$199$	9.66790	+	8.11233i	0.685339	+	0.575068i	−0.232222	+	0.972663i	$0.574599\pi$
$200$	−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	0.995562	−	0.0941110i	$-0.0300009\pi$
$211$	1.62787	+	5.43746i	0.112067	+	0.374330i	−0.883495	+	0.468441i	$0.844816\pi$
$212$	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	−0.138174	−	0.990408i	$-0.544123\pi$
$223$	−7.48192	−	0.874511i	−0.501027	−	0.0585616i	−0.362853	+	0.931846i	$0.618197\pi$
$224$	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	$-0.424512\pi$
$227$	13.2754	−	3.14632i	0.881118	−	0.208829i	0.646183	+	0.763182i	$0.276364\pi$
$228$		0			0
$229$	−13.3632	−	8.78913i	−0.883067	−	0.580802i	0.0249721	−	0.999688i	$-0.492050\pi$
$229$	−13.3632	−	8.78913i	−0.883067	−	0.580802i	−0.908039	+	0.418886i	$0.862421\pi$
$230$	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	−0.939032	−	0.343829i	$-0.888276\pi$
$233$	0.930605	−	5.27772i	0.0609660	−	0.345755i	0.999998	−	0.00192589i	$-0.000613031\pi$
$234$		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	$-0.711896\pi$
$239$	−16.0344	+	1.87416i	−1.03718	+	0.121229i	−0.419578	+	0.907719i	$0.637822\pi$
$240$		0			0
$241$	1.35989	+	23.3484i	0.0875982	+	1.50400i	0.700391	+	0.713759i	$0.253009\pi$
$241$	1.35989	+	23.3484i	0.0875982	+	1.50400i	−0.612793	+	0.790244i	$0.709954\pi$
$242$	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	−0.765588	−	0.643331i	$-0.777552\pi$
$251$	−4.21745	−	23.9183i	−0.266203	−	1.50971i	0.499385	−	0.866380i	$-0.333559\pi$
$252$		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	$-0.217670\pi$
$257$	8.04903	+	5.29393i	0.502085	+	0.330226i	−0.273074	+	0.961993i	$0.588040\pi$
$258$		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	$-0.397317\pi$
$263$	6.59689	+	0.771066i	0.406782	+	0.0475460i	0.0897582	+	0.995964i	$0.471391\pi$
$264$		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	0.833494	+	0.552529i	$0.186337\pi$
$269$	14.6832	+	25.4321i	0.895251	+	1.55062i	0.0617568	+	0.998091i	$0.480330\pi$
$270$		0			0
$271$	9.43957	−	16.3498i	0.573413	−	0.993180i	−0.422799	−	0.906223i	$-0.638952\pi$
$271$	9.43957	−	16.3498i	0.573413	−	0.993180i	0.996212	−	0.0869568i	$-0.0277142\pi$
$272$	−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	0.999604	+	0.0281297i	$0.00895515\pi$
$277$	5.56045	+	12.8906i	0.334095	+	0.774519i	−0.665509	+	0.746390i	$0.731786\pi$
$278$	−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	0.531987	+	0.846753i	$0.321446\pi$
$281$	−6.33274	+	21.1528i	−0.377780	+	1.26187i	−0.909767	+	0.415120i	$0.863740\pi$
$282$		0			0
$283$	−0.230048	+	3.94978i	−0.0136750	+	0.234790i	0.984544	+	0.175136i	$0.0560367\pi$
$283$	−0.230048	+	3.94978i	−0.0136750	+	0.234790i	−0.998219	+	0.0596536i	$0.981000\pi$
$284$	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	$-0.945231\pi$
$293$	−3.15963	+	7.32485i	−0.184588	+	0.427922i	0.800646	+	0.599138i	$0.204490\pi$
$294$		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	−0.285534	−	0.958369i	$-0.592171\pi$
$307$	1.95823	−	0.712736i	0.111762	−	0.0406780i	0.397296	+	0.917691i	$0.369949\pi$
$308$	−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	$-0.508178\pi$
$311$	13.4174	−	6.73846i	0.760830	−	0.382103i	0.786518	+	0.617567i	$0.211882\pi$
$312$		0			0
$313$	−3.49359	−	3.70299i	−0.197469	−	0.209305i	0.621071	−	0.783754i	$-0.286698\pi$
$313$	−3.49359	−	3.70299i	−0.197469	−	0.209305i	−0.818540	+	0.574449i	$0.805216\pi$
$314$	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	−0.0391636	−	0.999233i	$-0.512469\pi$
$317$	16.5461	−	22.2253i	0.929323	−	1.24830i	0.968487	−	0.249065i	$-0.0801232\pi$
$318$		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	−0.0835546	−	0.996503i	$-0.526627\pi$
$331$	16.2840	−	21.8732i	0.895049	−	1.20226i	0.978603	−	0.205756i	$-0.0659653\pi$
$332$	−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	−0.730576	−	0.682832i	$-0.760748\pi$
$337$	−11.3657	+	5.70808i	−0.619130	+	0.310939i	0.111445	+	0.993771i	$0.464452\pi$
$338$	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	$-0.276210\pi$
$347$	−5.02397	−	6.74836i	−0.269701	−	0.362271i	−0.916254	+	0.400598i	$0.868802\pi$
$348$		0			0
$349$	26.9370	+	13.5282i	1.44190	+	0.724150i	0.986134	−	0.165948i	$-0.0530685\pi$
$349$	26.9370	+	13.5282i	1.44190	+	0.724150i	0.455768	+	0.890099i	$0.349365\pi$
$350$	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	$-0.473031\pi$
$353$	19.4095	−	12.7659i	1.03307	−	0.679458i	0.948441	+	0.316955i	$0.102660\pi$
$354$		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	$-0.757304\pi$
$359$	−3.19290	+	2.67916i	−0.168515	+	0.141401i	0.554630	+	0.832097i	$0.312860\pi$
$360$		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	−0.824324	−	0.566118i	$-0.808445\pi$
$367$	3.36163	−	11.2286i	0.175476	−	0.586130i	0.999800	−	0.0200114i	$-0.00637025\pi$
$368$	−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	−0.592572	−	0.805518i	$-0.701887\pi$
$373$	−10.4315	−	34.8438i	−0.540124	−	1.80414i	0.0524474	−	0.998624i	$-0.483298\pi$
$374$	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	0.965740	−	0.259513i	$-0.0835620\pi$
$379$	5.02516	+	8.70383i	0.258125	+	0.447086i	−0.707615	+	0.706599i	$0.750229\pi$
$380$	−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	$-0.761720\pi$
$383$	−0.207663	+	0.220110i	−0.0106111	+	0.0112471i	0.722046	+	0.691845i	$0.243202\pi$
$384$		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	$-0.635126\pi$
$389$	−7.31685	+	1.73413i	−0.370979	+	0.0879237i	0.0408974	+	0.999163i	$0.486978\pi$
$390$		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	0.964448	+	0.264271i	$0.0851314\pi$
$397$	2.95983	+	16.7860i	0.148549	+	0.842466i	−0.815899	+	0.578195i	$0.803757\pi$
$398$	−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	$-0.426944\pi$
$401$	13.4856	−	1.57624i	0.673441	−	0.0787139i	0.445938	+	0.895064i	$0.352870\pi$
$402$		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	−0.0995665	−	0.995031i	$-0.531746\pi$
$409$	0.667804	−	0.0780551i	0.0330208	−	0.00385958i	0.132587	+	0.991171i	$0.457672\pi$
$410$	−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	$-0.476268\pi$
$419$	−16.6146	−	10.9276i	−0.811675	−	0.533847i	−0.886162	+	0.463375i	$0.846638\pi$
$420$		0			0
$421$	12.2171	−	2.89551i	0.595426	−	0.141119i	0.0781566	−	0.996941i	$-0.475097\pi$
$421$	12.2171	−	2.89551i	0.595426	−	0.141119i	0.517270	+	0.855822i	$0.326948\pi$
$422$	−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	−0.999722	−	0.0235787i	$-0.992494\pi$
$431$	−10.8013	−	18.7084i	−0.520281	−	0.901153i	0.479441	−	0.877574i	$-0.340839\pi$
$432$		0			0
$433$	−1.99970	+	3.46358i	−0.0960993	+	0.166449i	−0.910067	−	0.414461i	$-0.863970\pi$
$433$	−1.99970	+	3.46358i	−0.0960993	+	0.166449i	0.813968	+	0.580910i	$0.197303\pi$
$434$	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	−0.907706	−	0.419607i	$-0.862168\pi$
$439$	−12.3621	−	28.6586i	−0.590011	−	1.36780i	0.317695	−	0.948193i	$-0.397091\pi$
$440$	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	$-0.895289\pi$
$443$	0.459510	−	1.53487i	0.0218320	−	0.0729238i	0.968211	+	0.250134i	$0.0804745\pi$
$444$		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	$-0.357511\pi$
$449$	−8.04720	−	6.75241i	−0.379771	−	0.318666i	−0.812613	+	0.582804i	$0.801955\pi$
$450$		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	−0.654375	+	0.756171i	$0.727068\pi$
$457$	−34.3727	+	22.6073i	−1.60789	+	1.05752i	−0.953513	+	0.301353i	$0.902562\pi$
$458$	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	$-0.0573572\pi$
$461$	30.6506	+	15.3933i	1.42754	+	0.716939i	0.443734	+	0.896159i	$0.353654\pi$
$462$		0			0
$463$	−19.9050	−	26.7371i	−0.925066	−	1.24258i	−0.969880	−	0.243584i	$-0.921677\pi$
$463$	−19.9050	−	26.7371i	−0.925066	−	1.24258i	0.0448139	−	0.998995i	$-0.485731\pi$
$464$	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	$-0.311608\pi$
$467$	9.76380	+	3.55373i	0.451815	+	0.164447i	−0.106082	+	0.994357i	$0.533831\pi$
$468$		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	$-0.949769\pi$
$479$	−12.1202	+	16.2803i	−0.553787	+	0.743865i	0.433788	+	0.901015i	$0.357177\pi$
$480$		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	$-0.499978\pi$
$491$	−9.94187	−	2.35627i	−0.448670	−	0.106337i	−0.448738	+	0.893663i	$0.648126\pi$
$492$		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	−0.615013	−	0.788517i	$-0.710849\pi$
$499$	−7.81359	+	3.92413i	−0.349785	+	0.175668i	0.265228	+	0.964186i	$0.414553\pi$
$500$	−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	$-0.516895\pi$
$503$	12.2947	−	4.47489i	0.548192	−	0.199526i	0.601243	+	0.799066i	$0.294672\pi$
$504$		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	0.995012	+	0.0997537i	$0.0318055\pi$
$509$	18.1662	+	24.4014i	0.805202	+	1.08157i	−0.189810	+	0.981821i	$0.560787\pi$
$510$		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	$-0.798117\pi$
$521$	−8.25925	+	6.93034i	−0.361845	+	0.303624i	0.443681	+	0.896185i	$0.353672\pi$
$522$		0			0
$523$	9.44644	+	7.92650i	0.413064	+	0.346602i	0.825517	−	0.564377i	$-0.190884\pi$
$523$	9.44644	+	7.92650i	0.413064	+	0.346602i	−0.412453	+	0.910979i	$0.635328\pi$
$524$	−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	0.985105	−	0.171953i	$-0.0550078\pi$
$541$	7.99279	+	13.8439i	0.343637	+	0.595196i	−0.641468	+	0.767149i	$0.721674\pi$
$542$	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	0.0897943	−	0.995960i	$-0.471379\pi$
$547$	−1.22825	−	0.143562i	−0.0525161	−	0.00613825i	−0.142310	+	0.989822i	$0.545453\pi$
$548$	−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	0.897499	+	0.441017i	$0.145382\pi$
$557$	−2.28246	+	12.9445i	−0.0967109	+	0.548475i	−0.994210	+	0.107458i	$0.965729\pi$
$558$		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	$-0.496082\pi$
$563$	6.04774	−	0.706879i	0.254882	−	0.0297914i	0.242574	+	0.970133i	$0.422008\pi$
$564$		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	0.956303	+	0.292377i	$0.0944463\pi$
$569$	0.963908	+	16.5497i	0.0404091	+	0.693798i	−0.915894	+	0.401420i	$0.868517\pi$
$570$		0			0
$571$	−34.6117	+	4.04552i	−1.44845	+	0.169300i	−0.803674	−	0.595069i	$-0.797125\pi$
$571$	−34.6117	+	4.04552i	−1.44845	+	0.169300i	−0.644779	+	0.764369i	$0.723050\pi$
$572$	−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	−0.639854	−	0.768497i	$-0.721005\pi$
$577$	5.38675	−	30.5498i	0.224254	−	1.27180i	0.864107	−	0.503308i	$-0.167884\pi$
$578$	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	$-0.834184\pi$
$587$	−44.2431	−	5.17128i	−1.82611	−	0.213442i	−0.958752	+	0.284243i	$0.908258\pi$
$588$		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	$-0.300011\pi$
$593$	−9.90549	−	17.1568i	−0.406770	−	0.704546i	−0.994526	+	0.104493i	$0.966678\pi$
$594$		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	−0.950393	−	0.311051i	$-0.899319\pi$
$599$	−8.00993	−	26.7550i	−0.327277	−	1.09318i	0.623116	−	0.782129i	$-0.285866\pi$
$600$		0			0
$601$	−4.01814	−	9.31508i	−0.163903	−	0.379970i	0.816395	−	0.577494i	$-0.195969\pi$
$601$	−4.01814	−	9.31508i	−0.163903	−	0.379970i	−0.980298	+	0.197524i	$0.936710\pi$
$602$	−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	0.961196	+	0.275868i	$0.0889651\pi$
$607$	−0.628918	+	10.7981i	−0.0255270	+	0.438282i	−0.986723	+	0.162414i	$0.948072\pi$
$608$	−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	−0.555372	−	0.831602i	$-0.687424\pi$
$613$	4.13859	−	3.47269i	0.167156	−	0.140261i	0.722528	+	0.691341i	$0.242980\pi$
$614$	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	−0.593403	−	0.804905i	$-0.702216\pi$
$617$	9.91795	−	22.9924i	0.399282	−	0.925639i	0.992685	−	0.120734i	$-0.0385247\pi$
$618$		0			0
$619$	−21.2925	+	14.0043i	−0.855817	+	0.562880i	−0.899874	−	0.436149i	$-0.856342\pi$
$619$	−21.2925	+	14.0043i	−0.855817	+	0.562880i	0.0440575	+	0.999029i	$0.485972\pi$
$620$	−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	−0.687451	−	0.726231i	$-0.741270\pi$
$631$	−18.7709	+	6.83203i	−0.747256	+	0.271979i	−0.0598054	+	0.998210i	$0.519048\pi$
$632$	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	$-0.739868\pi$
$641$	5.33236	−	7.16261i	0.210616	−	0.282906i	0.894860	+	0.446347i	$0.147275\pi$
$642$		0			0
$643$	13.0387	+	3.09023i	0.514197	+	0.121867i	0.479519	−	0.877532i	$-0.340811\pi$
$643$	13.0387	+	3.09023i	0.514197	+	0.121867i	0.0346781	+	0.999399i	$0.488959\pi$
$644$	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	0.138113	−	0.990416i	$-0.455896\pi$
$653$	−4.67541	−	1.10809i	−0.182963	−	0.0433630i	−0.321076	+	0.947053i	$0.604044\pi$
$654$		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	$-0.404707\pi$
$659$	−17.3570	−	18.3974i	−0.676133	−	0.716659i	−0.971053	+	0.238863i	$0.923225\pi$
$660$		0			0
$661$	−12.6327	+	6.34438i	−0.491355	+	0.246768i	−0.677183	−	0.735814i	$-0.736800\pi$
$661$	−12.6327	+	6.34438i	−0.491355	+	0.246768i	0.185828	+	0.982582i	$0.440503\pi$
$662$	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	0.494147	−	0.869378i	$-0.335481\pi$
$673$	2.38363	+	1.19711i	0.0918823	+	0.0461450i	−0.402265	+	0.915523i	$0.631777\pi$
$674$	−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	$-0.776742\pi$
$677$	−12.3339	+	8.11215i	−0.474031	+	0.311775i	0.289918	+	0.957051i	$0.406372\pi$
$678$		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	$-0.590753\pi$
$683$	16.0712	−	13.4854i	0.614948	−	0.516003i	0.896211	+	0.443628i	$0.146309\pi$
$684$		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	0.527507	+	0.849551i	$0.323127\pi$
$691$	−9.99045	+	33.3704i	−0.380055	+	1.26947i	−0.907561	+	0.419920i	$0.862058\pi$
$692$	−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	0.0794276	+	0.996841i	$0.474691\pi$
$701$	−21.8053	+	37.7679i	−0.823576	+	1.42647i	−0.903003	+	0.429634i	$0.858643\pi$
$702$		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	−0.231654	−	0.972798i	$-0.574414\pi$
$709$	−18.1438	−	2.12071i	−0.681406	−	0.0796449i	−0.449752	+	0.893153i	$0.648488\pi$
$710$	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	−0.868018	−	0.496532i	$-0.834607\pi$
$719$	3.15002	−	17.8647i	0.117476	−	0.666240i	0.985494	−	0.169708i	$-0.0542824\pi$
$720$		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	−0.947057	−	0.321065i	$-0.895959\pi$
$727$	−1.17766	−	20.2197i	−0.0436770	−	0.749906i	0.903380	−	0.428841i	$-0.141078\pi$
$728$	−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	−0.0836007	−	0.996499i	$-0.526642\pi$
$733$	1.75603	−	0.205251i	0.0648606	−	0.00758111i	0.148461	+	0.988918i	$0.452568\pi$
$734$	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	−0.999982	−	0.00602346i	$-0.998083\pi$
$739$	−1.58340	+	8.97988i	−0.0582461	+	0.330330i	0.941736	+	0.336354i	$0.109194\pi$
$740$	−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	$-0.433891\pi$
$743$	−16.6442	−	10.9471i	−0.610616	−	0.401608i	−0.816813	+	0.576902i	$0.804261\pi$
$744$		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	−0.0342262	−	0.999414i	$-0.510897\pi$
$751$	26.4586	−	28.0445i	0.965487	−	1.02336i	0.999713	−	0.0239424i	$-0.00762184\pi$
$752$	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	0.135606	−	0.990763i	$-0.456702\pi$
$757$	25.4729	−	44.1204i	0.925829	−	1.60358i	0.790223	−	0.612820i	$-0.209965\pi$
$758$	−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	0.881080	+	0.472967i	$0.156817\pi$
$761$	11.1682	+	37.3045i	0.404848	+	1.35229i	−0.476233	+	0.879319i	$0.657998\pi$
$762$		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	0.750792	+	0.660539i	$0.229672\pi$
$769$	−1.98573	+	34.0937i	−0.0716073	+	1.22945i	−0.822399	+	0.568911i	$0.807365\pi$
$770$	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	$-0.260437\pi$
$773$	2.31945	+	1.94625i	0.0834247	+	0.0700016i	−0.600122	+	0.799909i	$0.704881\pi$
$774$		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	0.825639	−	0.564199i	$-0.190815\pi$
$787$	1.35626	+	1.82178i	0.0483456	+	0.0649394i	−0.777293	+	0.629139i	$0.783408\pi$
$788$	−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	$-0.719687\pi$
$797$	−11.2447	+	5.64728i	−0.398306	+	0.200037i	0.238359	+	0.971177i	$0.423390\pi$
$798$		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	−0.932820	−	0.360344i	$-0.882659\pi$
$821$	−35.4816	−	37.6083i	−1.23832	−	1.31254i	−0.305496	−	0.952193i	$-0.598822\pi$
$822$		0			0
$823$	18.2164	−	9.14864i	0.634985	−	0.318902i	−0.102026	−	0.994782i	$-0.532533\pi$
$823$	18.2164	−	9.14864i	0.634985	−	0.318902i	0.737012	+	0.675880i	$0.236236\pi$
$824$	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	$-0.879083\pi$
$827$	−40.3124	+	14.6725i	−1.40180	+	0.510213i	−0.473087	+	0.881016i	$0.656860\pi$
$828$		0			0
$829$	−13.4165	−	4.88321i	−0.465975	−	0.169601i	0.0983534	−	0.995152i	$-0.468642\pi$
$829$	−13.4165	−	4.88321i	−0.465975	−	0.169601i	−0.564328	+	0.825551i	$0.690865\pi$
$830$	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	$-0.511538\pi$
$839$	25.1136	−	16.5175i	0.867018	−	0.570247i	0.903259	+	0.429096i	$0.141168\pi$
$840$		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	0.568010	+	0.823022i	$0.307713\pi$
$853$	−10.4796	+	35.0042i	−0.358813	+	1.19852i	−0.926823	+	0.375498i	$0.877472\pi$
$854$	−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	0.877128	+	0.480256i	$0.159456\pi$
$857$	18.2829	+	42.3845i	0.624532	+	1.44783i	−0.252596	+	0.967572i	$0.581284\pi$
$858$		0			0
$859$	0.0885216	+	0.295683i	0.00302032	+	0.0100886i	0.959486	−	0.281755i	$-0.0909165\pi$
$859$	0.0885216	+	0.295683i	0.00302032	+	0.0100886i	−0.956466	+	0.291844i	$0.905731\pi$
$860$	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	0.442409	+	0.896813i	$0.354124\pi$
$863$	−16.3176	+	28.2630i	−0.555459	+	0.962083i	−0.997868	+	0.0652694i	$0.979209\pi$
$864$		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	0.447631	−	0.894218i	$-0.352268\pi$
$877$	−5.80901	−	3.82065i	−0.196156	−	0.129014i	−0.643788	+	0.765204i	$0.722638\pi$
$878$	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	0.657142	+	0.753767i	$0.271765\pi$
$881$	−6.47573	+	36.7257i	−0.218173	+	1.23732i	−0.875315	+	0.483553i	$0.839346\pi$
$882$		0			0
$883$	1.07456	+	6.09412i	0.0361618	+	0.205084i	0.997536	−	0.0701625i	$-0.0223518\pi$
$883$	1.07456	+	6.09412i	0.0361618	+	0.205084i	−0.961374	+	0.275246i	$0.911241\pi$
$884$	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	$-0.638256\pi$
$887$	−18.4976	+	2.16206i	−0.621088	+	0.0725948i	−0.200271	+	0.979740i	$0.564182\pi$
$888$		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	0.215285	−	0.976551i	$-0.430932\pi$
$907$	25.4769	−	6.03814i	0.845947	−	0.200493i	0.630661	+	0.776058i	$0.282784\pi$
$908$	−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	$-0.420860\pi$
$911$	7.90750	+	0.924254i	0.261987	+	0.0306219i	0.0159147	+	0.999873i	$0.494934\pi$
$912$		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	−0.0916606	+	0.995790i	$0.529217\pi$
$919$	−27.5324	+	47.6875i	−0.908210	+	1.57307i	−0.816549	+	0.577276i	$0.804116\pi$
$920$	−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	0.458989	+	0.888442i	$0.348212\pi$
$929$	−12.5788	+	42.0162i	−0.412697	+	1.37851i	−0.871687	+	0.490063i	$0.836974\pi$
$930$		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	−0.123741	−	0.992315i	$-0.539489\pi$
$937$	25.4682	−	21.3704i	0.832010	−	0.698140i	0.955752	+	0.294175i	$0.0950449\pi$
$938$	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	$-0.928849\pi$
$941$	−4.43921	+	10.2912i	−0.144714	+	0.335485i	0.830407	+	0.557157i	$0.188108\pi$
$942$		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	$-0.376345\pi$
$947$	−4.22787	−	2.12331i	−0.137387	−	0.0689984i	−0.516165	+	0.856489i	$0.672641\pi$
$948$		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	$-0.398632\pi$
$953$	−1.77553	−	0.646238i	−0.0575149	−	0.0209337i	−0.370617	+	0.928786i	$0.620854\pi$
$954$		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	−0.772236	−	0.635336i	$-0.780862\pi$
$967$	−54.3404	−	12.8789i	−1.74747	−	0.414158i	−0.975234	+	0.221178i	$0.929010\pi$
$968$	−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	−0.239177	−	0.970976i	$-0.576878\pi$
$977$	−27.7777	−	6.58343i	−0.888687	−	0.210623i	−0.649510	+	0.760353i	$0.725026\pi$
$978$		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	$-0.355266\pi$
$983$	−15.1504	−	16.0585i	−0.483224	−	0.512187i	−0.922412	+	0.386208i	$0.873785\pi$
$984$		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	0.813221	−	0.581955i	$-0.197712\pi$
$991$	33.4354	+	12.1695i	1.06211	+	0.386577i	0.248890	+	0.968532i	$0.419934\pi$
$992$	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	0.885727	−	0.464206i	$-0.153660\pi$
$997$	32.9108	+	16.5284i	1.04230	+	0.523461i	0.156570	+	0.987667i	$0.449956\pi$
$998$	−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.514.8		144
3.2	odd	2		729.2.g.d.514.1		144
9.2	odd	6		729.2.g.c.28.1		144
9.4	even	3		243.2.g.a.10.1		144
9.5	odd	6		81.2.g.a.13.8	✓	144
9.7	even	3		729.2.g.b.28.8		144
81.2	odd	54		729.2.g.d.217.1		144
81.22	even	27		6561.2.a.d.1.8		72
81.25	even	27		729.2.g.b.703.8		144
81.29	odd	54		81.2.g.a.25.8	yes	144
81.52	even	27		243.2.g.a.73.1		144
81.56	odd	54		729.2.g.c.703.1		144
81.59	odd	54		6561.2.a.c.1.65		72
81.79	even	27	inner	729.2.g.a.217.8		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.8	✓	144	9.5	odd	6
81.2.g.a.25.8	yes	144	81.29	odd	54
243.2.g.a.10.1		144	9.4	even	3
243.2.g.a.73.1		144	81.52	even	27
729.2.g.a.217.8		144	81.79	even	27	inner
729.2.g.a.514.8		144	1.1	even	1	trivial
729.2.g.b.28.8		144	9.7	even	3
729.2.g.b.703.8		144	81.25	even	27
729.2.g.c.28.1		144	9.2	odd	6
729.2.g.c.703.1		144	81.56	odd	54
729.2.g.d.217.1		144	81.2	odd	54
729.2.g.d.514.1		144	3.2	odd	2
6561.2.a.c.1.65		72	81.59	odd	54
6561.2.a.d.1.8		72	81.22	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

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