LMFDB - Embedded newform 729.2.e.i.568.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			568.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.i.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.826352 + 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(0.673648 - 3.82045i) q^{5} +(-1.67365 + 1.40436i) q^{7} +(-1.41875 - 2.45734i) q^{8} +O(q^{10})$	\(q+(0.826352 + 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(0.673648 - 3.82045i) q^{5} +(-1.67365 + 1.40436i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(1.70574 - 2.95442i) q^{10} +(0.0282185 + 0.160035i) q^{11} +(-2.26604 + 0.824773i) q^{13} +(-1.80541 + 0.657115i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.79813 - 3.11446i) q^{19} +(-3.64543 + 3.05888i) q^{20} +(-0.0248149 + 0.140732i) q^{22} +(2.17365 + 1.82391i) q^{23} +(-9.44356 - 3.43718i) q^{25} -2.12061 q^{26} +2.68004 q^{28} +(-6.31180 - 2.29731i) q^{29} +(-3.97178 - 3.33272i) q^{31} +(-0.979055 + 5.55250i) q^{32} +(-2.02094 + 1.69577i) q^{34} +(4.23783 + 7.34013i) q^{35} +(3.31908 - 5.74881i) q^{37} +(-0.549163 - 3.11446i) q^{38} +(-10.3439 + 3.76487i) q^{40} +(5.45084 - 1.98394i) q^{41} +(-1.08125 - 6.13208i) q^{43} +(0.0996702 - 0.172634i) q^{44} +(1.24763 + 2.16095i) q^{46} +(5.66637 - 4.75465i) q^{47} +(-0.386659 + 2.19285i) q^{49} +(-6.76991 - 5.68063i) q^{50} +(2.77972 + 1.01173i) q^{52} +1.40373 q^{53} +0.630415 q^{55} +(5.82547 + 2.12030i) q^{56} +(-4.52481 - 3.79677i) q^{58} +(-0.889185 + 5.04282i) q^{59} +(-2.89646 + 2.43042i) q^{61} +(-2.27972 - 3.94858i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(1.62449 + 9.21291i) q^{65} +(5.51114 - 2.00589i) q^{67} +(3.45811 - 1.25865i) q^{68} +(1.29426 + 7.34013i) q^{70} +(7.65910 - 13.2660i) q^{71} +(-4.34002 - 7.51714i) q^{73} +(4.47178 - 3.75227i) q^{74} +(-0.766044 + 4.34445i) q^{76} +(-0.271974 - 0.228213i) q^{77} +(1.19207 + 0.433877i) q^{79} -0.162504 q^{80} +5.10101 q^{82} +(7.96451 + 2.89884i) q^{83} +(8.91534 + 7.48086i) q^{85} +(0.950837 - 5.39246i) q^{86} +(0.353226 - 0.296392i) q^{88} +(-3.86097 - 6.68739i) q^{89} +(2.63429 - 4.56272i) q^{91} +(-0.604418 - 3.42782i) q^{92} +(6.11246 - 2.22475i) q^{94} +(-13.1099 + 4.77163i) q^{95} +(-0.678396 - 3.84737i) q^{97} +(-0.979055 + 1.69577i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8	$ 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8} + 15 q^{11} - 9 q^{13} - 15 q^{14} - 18 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 27 q^{22} + 12 q^{23} - 27 q^{25} - 24 q^{26} - 24 q^{28} - 3 q^{29} - 9 q^{31} - 9 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} - 15 q^{38} - 18 q^{40} + 21 q^{41} - 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} - 9 q^{49} - 12 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 21 q^{56} + 3 q^{59} - 27 q^{61} + 12 q^{62} - 12 q^{64} - 3 q^{65} + 27 q^{67} + 27 q^{68} + 18 q^{70} + 9 q^{71} - 6 q^{73} + 12 q^{74} - 24 q^{77} + 18 q^{79} - 6 q^{80} + 36 q^{82} + 15 q^{83} + 9 q^{85} - 6 q^{86} + 27 q^{88} + 6 q^{91} - 51 q^{92} - 27 q^{94} - 30 q^{95} - 36 q^{97} - 9 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8 + 15 * q^11 - 9 * q^13 - 15 * q^14 - 18 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 + 27 * q^22 + 12 * q^23 - 27 * q^25 - 24 * q^26 - 24 * q^28 - 3 * q^29 - 9 * q^31 - 9 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 - 15 * q^38 - 18 * q^40 + 21 * q^41 - 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 - 9 * q^49 - 12 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 21 * q^56 + 3 * q^59 - 27 * q^61 + 12 * q^62 - 12 * q^64 - 3 * q^65 + 27 * q^67 + 27 * q^68 + 18 * q^70 + 9 * q^71 - 6 * q^73 + 12 * q^74 - 24 * q^77 + 18 * q^79 - 6 * q^80 + 36 * q^82 + 15 * q^83 + 9 * q^85 - 6 * q^86 + 27 * q^88 + 6 * q^91 - 51 * q^92 - 27 * q^94 - 30 * q^95 - 36 * q^97 - 9 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.826352	+	0.300767i	0.584319	+	0.212675i	0.617229	−	0.786784i	$-0.288255\pi$
$2$	0.826352	+	0.300767i	0.584319	+	0.212675i	−0.0329100	+	0.999458i	$0.510477\pi$
$3$		0			0
$3$		0			0
$4$	−0.939693	−	0.788496i	−0.469846	−	0.394248i
$5$	0.673648	−	3.82045i	0.301265	−	1.70856i	−0.339322	−	0.940670i	$-0.610198\pi$
$5$	0.673648	−	3.82045i	0.301265	−	1.70856i	0.640586	−	0.767886i	$-0.278691\pi$
$6$		0			0
$7$	−1.67365	+	1.40436i	−0.632580	+	0.530797i	−0.901729	−	0.432301i	$-0.857702\pi$
$7$	−1.67365	+	1.40436i	−0.632580	+	0.530797i	0.269150	+	0.963098i	$0.413257\pi$
$8$	−1.41875	−	2.45734i	−0.501603	−	0.868802i
$9$		0			0
$10$	1.70574	−	2.95442i	0.539401	−	0.934271i
$11$	0.0282185	+	0.160035i	0.00850820	+	0.0482524i	0.988766	−	0.149470i	$-0.0477567\pi$
$11$	0.0282185	+	0.160035i	0.00850820	+	0.0482524i	−0.980258	+	0.197722i	$0.936646\pi$
$12$		0			0
$13$	−2.26604	+	0.824773i	−0.628488	+	0.228751i	−0.636573	−	0.771217i	$-0.719649\pi$
$13$	−2.26604	+	0.824773i	−0.628488	+	0.228751i	0.00808527	+	0.999967i	$0.497426\pi$
$14$	−1.80541	+	0.657115i	−0.482515	+	0.175621i
$15$		0			0
$16$	−0.00727396	−	0.0412527i	−0.00181849	−	0.0103132i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	−1.79813	−	3.11446i	−0.412520	−	0.714506i	0.582645	−	0.812727i	$-0.302018\pi$
$19$	−1.79813	−	3.11446i	−0.412520	−	0.714506i	−0.995165	+	0.0982214i	$0.968685\pi$
$20$	−3.64543	+	3.05888i	−0.815143	+	0.683986i
$21$		0			0
$22$	−0.0248149	+	0.140732i	−0.00529056	+	0.0300043i
$23$	2.17365	+	1.82391i	0.453237	+	0.380311i	0.840635	−	0.541601i	$-0.182182\pi$
$23$	2.17365	+	1.82391i	0.453237	+	0.380311i	−0.387398	+	0.921912i	$0.626626\pi$
$24$		0			0
$25$	−9.44356	−	3.43718i	−1.88871	−	0.687435i
$26$	−2.12061			−0.415887
$27$		0			0
$28$	2.68004			0.506481
$29$	−6.31180	−	2.29731i	−1.17207	−	0.426600i	−0.318677	−	0.947863i	$-0.603239\pi$
$29$	−6.31180	−	2.29731i	−1.17207	−	0.426600i	−0.853396	+	0.521264i	$0.825461\pi$
$30$		0			0
$31$	−3.97178	−	3.33272i	−0.713353	−	0.598574i	0.212185	−	0.977230i	$-0.431942\pi$
$31$	−3.97178	−	3.33272i	−0.713353	−	0.598574i	−0.925538	+	0.378655i	$0.876387\pi$
$32$	−0.979055	+	5.55250i	−0.173074	+	0.981553i
$33$		0			0
$34$	−2.02094	+	1.69577i	−0.346589	+	0.290823i
$35$	4.23783	+	7.34013i	0.716323	+	1.24071i
$36$		0			0
$37$	3.31908	−	5.74881i	0.545653	−	0.945099i	−0.452912	−	0.891555i	$-0.649615\pi$
$37$	3.31908	−	5.74881i	0.545653	−	0.945099i	0.998566	−	0.0535438i	$-0.0170517\pi$
$38$	−0.549163	−	3.11446i	−0.0890860	−	0.505232i
$39$		0			0
$40$	−10.3439	+	3.76487i	−1.63551	+	0.595278i
$41$	5.45084	−	1.98394i	0.851278	−	0.309840i	0.120717	−	0.992687i	$-0.461481\pi$
$41$	5.45084	−	1.98394i	0.851278	−	0.309840i	0.730561	+	0.682847i	$0.239259\pi$
$42$		0			0
$43$	−1.08125	−	6.13208i	−0.164889	−	0.935134i	−0.949178	−	0.314739i	$-0.898083\pi$
$43$	−1.08125	−	6.13208i	−0.164889	−	0.935134i	0.784289	−	0.620396i	$-0.213028\pi$
$44$	0.0996702	−	0.172634i	0.0150259	−	0.0260255i
$45$		0			0
$46$	1.24763	+	2.16095i	0.183952	+	0.318615i
$47$	5.66637	−	4.75465i	0.826526	−	0.693537i	−0.127965	−	0.991779i	$-0.540844\pi$
$47$	5.66637	−	4.75465i	0.826526	−	0.693537i	0.954490	+	0.298241i	$0.0964000\pi$
$48$		0			0
$49$	−0.386659	+	2.19285i	−0.0552370	+	0.313265i
$50$	−6.76991	−	5.68063i	−0.957411	−	0.803363i
$51$		0			0
$52$	2.77972	+	1.01173i	0.385477	+	0.140302i
$53$	1.40373			0.192818			0.0964088	−	0.995342i	$-0.469264\pi$
$53$	1.40373			0.192818			0.0964088	+	0.995342i	$0.469264\pi$
$54$		0			0
$55$	0.630415			0.0850051
$56$	5.82547	+	2.12030i	0.778462	+	0.283337i
$57$		0			0
$58$	−4.52481	−	3.79677i	−0.594137	−	0.498540i
$59$	−0.889185	+	5.04282i	−0.115762	+	0.656519i	0.870608	+	0.491977i	$0.163726\pi$
$59$	−0.889185	+	5.04282i	−0.115762	+	0.656519i	−0.986370	+	0.164542i	$0.947385\pi$
$60$		0			0
$61$	−2.89646	+	2.43042i	−0.370854	+	0.311183i	−0.809099	−	0.587672i	$-0.800044\pi$
$61$	−2.89646	+	2.43042i	−0.370854	+	0.311183i	0.438246	+	0.898855i	$0.355600\pi$
$62$	−2.27972	−	3.94858i	−0.289524	−	0.501470i
$63$		0			0
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	1.62449	+	9.21291i	0.201493	+	1.14272i
$66$		0			0
$67$	5.51114	−	2.00589i	0.673293	−	0.245059i	0.0173282	−	0.999850i	$-0.494484\pi$
$67$	5.51114	−	2.00589i	0.673293	−	0.245059i	0.655965	+	0.754791i	$0.272262\pi$
$68$	3.45811	−	1.25865i	0.419358	−	0.152634i
$69$		0			0
$70$	1.29426	+	7.34013i	0.154694	+	0.877313i
$71$	7.65910	−	13.2660i	0.908968	−	1.57438i	0.0934675	−	0.995622i	$-0.470205\pi$
$71$	7.65910	−	13.2660i	0.908968	−	1.57438i	0.815500	−	0.578756i	$-0.196462\pi$
$72$		0			0
$73$	−4.34002	−	7.51714i	−0.507961	−	0.879815i	−0.999958	−	0.00921733i	$-0.997066\pi$
$73$	−4.34002	−	7.51714i	−0.507961	−	0.879815i	0.491996	−	0.870597i	$-0.336267\pi$
$74$	4.47178	−	3.75227i	0.519834	−	0.436193i
$75$		0			0
$76$	−0.766044	+	4.34445i	−0.0878713	+	0.498343i
$77$	−0.271974	−	0.228213i	−0.0309943	−	0.0260073i
$78$		0			0
$79$	1.19207	+	0.433877i	0.134118	+	0.0488149i	0.408207	−	0.912889i	$-0.366154\pi$
$79$	1.19207	+	0.433877i	0.134118	+	0.0488149i	−0.274089	+	0.961704i	$0.588376\pi$
$80$	−0.162504			−0.0181685
$81$		0			0
$82$	5.10101			0.563313
$83$	7.96451	+	2.89884i	0.874218	+	0.318189i	0.739874	−	0.672745i	$-0.234885\pi$
$83$	7.96451	+	2.89884i	0.874218	+	0.318189i	0.134344	+	0.990935i	$0.457107\pi$
$84$		0			0
$85$	8.91534	+	7.48086i	0.967005	+	0.811413i
$86$	0.950837	−	5.39246i	0.102531	−	0.581484i
$87$		0			0
$88$	0.353226	−	0.296392i	0.0376540	−	0.0315955i
$89$	−3.86097	−	6.68739i	−0.409262	−	0.708862i	0.585546	−	0.810640i	$-0.300880\pi$
$89$	−3.86097	−	6.68739i	−0.409262	−	0.708862i	−0.994807	+	0.101778i	$0.967547\pi$
$90$		0			0
$91$	2.63429	−	4.56272i	0.276148	−	0.478303i
$92$	−0.604418	−	3.42782i	−0.0630149	−	0.357375i
$93$		0			0
$94$	6.11246	−	2.22475i	0.630452	−	0.229466i
$95$	−13.1099	+	4.77163i	−1.34505	+	0.489559i
$96$		0			0
$97$	−0.678396	−	3.84737i	−0.0688807	−	0.390642i	−0.999684	−	0.0251223i	$-0.992002\pi$
$97$	−0.678396	−	3.84737i	−0.0688807	−	0.390642i	0.930804	−	0.365519i	$-0.119109\pi$
$98$	−0.979055	+	1.69577i	−0.0988995	+	0.171299i
$99$		0			0
$100$	6.16385	+	10.6761i	0.616385	+	1.06761i
$101$	−6.21554	+	5.21546i	−0.618469	+	0.518957i	−0.897322	−	0.441377i	$-0.854490\pi$
$101$	−6.21554	+	5.21546i	−0.618469	+	0.518957i	0.278853	+	0.960334i	$0.410046\pi$
$102$		0			0
$103$	3.23783	−	18.3626i	0.319032	−	1.80932i	−0.229629	−	0.973278i	$-0.573751\pi$
$103$	3.23783	−	18.3626i	0.319032	−	1.80932i	0.548661	−	0.836045i	$-0.315138\pi$
$104$	5.24170	+	4.39831i	0.513991	+	0.431289i
$105$		0			0
$106$	1.15998	+	0.422197i	0.112667	+	0.0410074i
$107$	7.59627			0.734359			0.367179	−	0.930150i	$-0.380324\pi$
$107$	7.59627			0.734359			0.367179	+	0.930150i	$0.380324\pi$
$108$		0			0
$109$	−15.6382			−1.49786			−0.748932	−	0.662647i	$-0.769433\pi$
$109$	−15.6382			−1.49786			−0.748932	+	0.662647i	$0.769433\pi$
$110$	0.520945	+	0.189608i	0.0496701	+	0.0180784i
$111$		0			0
$112$	0.0701076	+	0.0588272i	0.00662454	+	0.00555865i
$113$	−0.401674	+	2.27801i	−0.0377863	+	0.214297i	−0.997855	−	0.0654689i	$-0.979146\pi$
$113$	−0.401674	+	2.27801i	−0.0377863	+	0.214297i	0.960068	+	0.279766i	$0.0902568\pi$
$114$		0			0
$115$	8.43242	−	7.07564i	0.786327	−	0.659807i
$116$	4.11974	+	7.13559i	0.382508	+	0.662523i
$117$		0			0
$118$	−2.25150	+	3.89971i	−0.207267	+	0.358997i
$119$	−1.13816	−	6.45480i	−0.104335	−	0.591711i
$120$		0			0
$121$	10.3118	−	3.75319i	0.937437	−	0.341199i
$122$	−3.12449	+	1.13722i	−0.282878	+	0.102959i
$123$		0			0
$124$	1.10442	+	6.26347i	0.0991797	+	0.562476i
$125$	−9.79473	+	16.9650i	−0.876067	+	1.51739i
$126$		0			0
$127$	−0.0209445	−	0.0362770i	−0.00185853	−	0.00321906i	0.865095	−	0.501609i	$-0.167258\pi$
$127$	−0.0209445	−	0.0362770i	−0.00185853	−	0.00321906i	−0.866953	+	0.498390i	$0.833925\pi$
$128$	5.24170	−	4.39831i	0.463305	−	0.388759i
$129$		0			0
$130$	−1.42855	+	8.10170i	−0.125292	+	0.710566i
$131$	14.0556	+	11.7940i	1.22804	+	1.03045i	0.998364	+	0.0571807i	$0.0182111\pi$
$131$	14.0556	+	11.7940i	1.22804	+	1.03045i	0.229676	+	0.973267i	$0.426233\pi$
$132$		0			0
$133$	7.38326	+	2.68729i	0.640209	+	0.233017i
$134$	5.15745			0.445536
$135$		0			0
$136$	8.51249			0.729940
$137$	−13.4500	−	4.89538i	−1.14911	−	0.418241i	−0.303913	−	0.952700i	$-0.598293\pi$
$137$	−13.4500	−	4.89538i	−1.14911	−	0.418241i	−0.845195	+	0.534459i	$0.820515\pi$
$138$		0			0
$139$	8.03983	+	6.74622i	0.681929	+	0.572207i	0.916569	−	0.399876i	$-0.130947\pi$
$139$	8.03983	+	6.74622i	0.681929	+	0.572207i	−0.234640	+	0.972082i	$0.575391\pi$
$140$	1.80541	−	10.2390i	0.152585	−	0.865351i
$141$		0			0
$142$	10.3191	−	8.65873i	0.865958	−	0.726625i
$143$	−0.195937	−	0.339373i	−0.0163851	−	0.0283798i
$144$		0			0
$145$	−13.0287	+	22.5663i	−1.08197	+	1.87403i
$146$	−1.32547	−	7.51714i	−0.109697	−	0.622123i
$147$		0			0
$148$	−7.65183	+	2.78504i	−0.628976	+	0.228929i
$149$	1.19459	−	0.434796i	0.0978648	−	0.0356199i	−0.292624	−	0.956228i	$-0.594528\pi$
$149$	1.19459	−	0.434796i	0.0978648	−	0.0356199i	0.390489	+	0.920608i	$0.372306\pi$
$150$		0			0
$151$	1.36437	+	7.73773i	0.111031	+	0.629688i	0.988639	+	0.150309i	$0.0480268\pi$
$151$	1.36437	+	7.73773i	0.111031	+	0.629688i	−0.877608	+	0.479379i	$0.840862\pi$
$152$	−5.10220	+	8.83726i	−0.413843	+	0.716797i
$153$		0			0
$154$	−0.156107	−	0.270386i	−0.0125795	−	0.0217883i
$155$	−15.4081	+	12.9289i	−1.23761	+	1.03847i
$156$		0			0
$157$	−2.14496	+	12.1647i	−0.171187	+	0.970848i	0.771267	+	0.636512i	$0.219623\pi$
$157$	−2.14496	+	12.1647i	−0.171187	+	0.970848i	−0.942454	+	0.334336i	$0.891488\pi$
$158$	0.854570	+	0.717070i	0.0679860	+	0.0570470i
$159$		0			0
$160$	20.5535	+	7.48086i	1.62490	+	0.591414i
$161$	−6.19934			−0.488576
$162$		0			0
$163$	−13.7469			−1.07674			−0.538371	−	0.842708i	$-0.680960\pi$
$163$	−13.7469			−1.07674			−0.538371	+	0.842708i	$0.680960\pi$
$164$	−6.68644	−	2.43367i	−0.522123	−	0.190037i
$165$		0			0
$166$	5.70961	+	4.79093i	0.443151	+	0.371848i
$167$	−0.645430	+	3.66041i	−0.0499448	+	0.283251i	−0.999543	−	0.0302175i	$-0.990380\pi$
$167$	−0.645430	+	3.66041i	−0.0499448	+	0.283251i	0.949598	+	0.313469i	$0.101491\pi$
$168$		0			0
$169$	−5.50387	+	4.61830i	−0.423375	+	0.355254i
$170$	5.11721	+	8.86327i	0.392472	+	0.679782i
$171$		0			0
$172$	−3.81908	+	6.61484i	−0.291202	+	0.504377i
$173$	−0.270792	−	1.53574i	−0.0205879	−	0.116760i	0.972782	−	0.231723i	$-0.0744362\pi$
$173$	−0.270792	−	1.53574i	−0.0205879	−	0.116760i	−0.993370	+	0.114963i	$0.963325\pi$
$174$		0			0
$175$	20.6322	−	7.50952i	1.55965	−	0.567666i
$176$	0.00639661	−	0.00232818i	0.000482163	−	0.000175493i
$177$		0			0
$178$	−1.17917	−	6.68739i	−0.0883823	−	0.501241i
$179$	6.09627	−	10.5590i	0.455656	−	0.789220i	−0.543069	−	0.839688i	$-0.682738\pi$
$179$	6.09627	−	10.5590i	0.455656	−	0.789220i	0.998726	+	0.0504679i	$0.0160713\pi$
$180$		0			0
$181$	8.43629	+	14.6121i	0.627064	+	1.08611i	0.988138	+	0.153570i	$0.0490771\pi$
$181$	8.43629	+	14.6121i	0.627064	+	1.08611i	−0.361073	+	0.932537i	$0.617590\pi$
$182$	3.54916	−	2.97810i	0.263081	−	0.220752i
$183$		0			0
$184$	1.39811	−	7.92907i	0.103070	−	0.584538i
$185$	−19.7271	−	16.5530i	−1.45037	−	1.21700i
$186$		0			0
$187$	−0.458111	−	0.166739i	−0.0335004	−	0.0121931i
$188$	−9.07367			−0.661766
$189$		0			0
$190$	−12.2686			−0.890056
$191$	16.4217	+	5.97702i	1.18824	+	0.432482i	0.859104	−	0.511802i	$-0.171022\pi$
$191$	16.4217	+	5.97702i	1.18824	+	0.432482i	0.329132	+	0.944284i	$0.393244\pi$
$192$		0			0
$193$	−1.52616	−	1.28060i	−0.109855	−	0.0921796i	0.586205	−	0.810162i	$-0.300621\pi$
$193$	−1.52616	−	1.28060i	−0.109855	−	0.0921796i	−0.696061	+	0.717983i	$0.745066\pi$
$194$	0.596571	−	3.38332i	0.0428313	−	0.242909i
$195$		0			0
$196$	2.09240	−	1.75573i	0.149457	−	0.125409i
$197$	−10.5963	−	18.3533i	−0.754953	−	1.30762i	−0.945398	−	0.325919i	$-0.894326\pi$
$197$	−10.5963	−	18.3533i	−0.754953	−	1.30762i	0.190445	−	0.981698i	$-0.439007\pi$
$198$		0			0
$199$	1.54189	−	2.67063i	0.109302	−	0.189316i	−0.806186	−	0.591662i	$-0.798472\pi$
$199$	1.54189	−	2.67063i	0.109302	−	0.189316i	0.915488	+	0.402346i	$0.131805\pi$
$200$	4.95171	+	28.0826i	0.350139	+	1.98574i
$201$		0			0
$202$	−6.70486	+	2.44037i	−0.471752	+	0.171704i
$203$	13.7900	−	5.01914i	0.967867	−	0.352275i
$204$		0			0
$205$	−3.90760	−	22.1611i	−0.272919	−	1.54780i
$206$	8.19846	−	14.2002i	0.571214	−	0.989372i
$207$		0			0
$208$	0.0505072	+	0.0874810i	0.00350204	+	0.00606572i
$209$	0.447682	−	0.375650i	0.0309668	−	0.0259842i
$210$		0			0
$211$	0.174992	−	0.992431i	0.0120470	−	0.0683218i	−0.978192	−	0.207705i	$-0.933401\pi$
$211$	0.174992	−	0.992431i	0.0120470	−	0.0683218i	0.990239	+	0.139383i	$0.0445118\pi$
$212$	−1.31908	−	1.10684i	−0.0905946	−	0.0760179i
$213$		0			0
$214$	6.27719	+	2.28471i	0.429100	+	0.156180i
$215$	−24.1557			−1.64740
$216$		0			0
$217$	11.3277			0.768974
$218$	−12.9226	−	4.70345i	−0.875230	−	0.318558i
$219$		0			0
$220$	−0.592396	−	0.497079i	−0.0399393	−	0.0335131i
$221$	1.25624	−	7.12452i	0.0845041	−	0.479247i
$222$		0			0
$223$	14.0064	−	11.7528i	0.937938	−	0.787023i	−0.0392875	−	0.999228i	$-0.512509\pi$
$223$	14.0064	−	11.7528i	0.937938	−	0.787023i	0.977225	+	0.212205i	$0.0680644\pi$
$224$	−6.15910	−	10.6679i	−0.411522	−	0.712777i
$225$		0			0
$226$	−1.01707	+	1.76162i	−0.0676548	+	0.117181i
$227$	−0.459293	−	2.60478i	−0.0304843	−	0.172885i	0.965764	−	0.259421i	$-0.0835316\pi$
$227$	−0.459293	−	2.60478i	−0.0304843	−	0.172885i	−0.996249	+	0.0865353i	$0.972420\pi$
$228$		0			0
$229$	3.25402	−	1.18437i	0.215032	−	0.0782652i	−0.232258	−	0.972654i	$-0.574611\pi$
$229$	3.25402	−	1.18437i	0.215032	−	0.0782652i	0.447290	+	0.894389i	$0.352389\pi$
$230$	9.09627	−	3.31077i	0.599790	−	0.218306i
$231$		0			0
$232$	3.30958	+	18.7696i	0.217285	+	1.23228i
$233$	−3.06283	+	5.30498i	−0.200653	+	0.347541i	−0.948739	−	0.316061i	$-0.897640\pi$
$233$	−3.06283	+	5.30498i	−0.200653	+	0.347541i	0.748086	+	0.663602i	$0.230973\pi$
$234$		0			0
$235$	−14.3478	−	24.8511i	−0.935945	−	1.62110i
$236$	4.81180	−	4.03758i	0.313222	−	0.262824i
$237$		0			0
$238$	1.00088	−	5.67626i	0.0648772	−	0.367937i
$239$	−22.1780	−	18.6095i	−1.43457	−	1.20375i	−0.942946	−	0.332946i	$-0.891957\pi$
$239$	−22.1780	−	18.6095i	−1.43457	−	1.20375i	−0.491629	−	0.870805i	$-0.663598\pi$
$240$		0			0
$241$	−20.9795	−	7.63592i	−1.35141	−	0.491873i	−0.438022	−	0.898964i	$-0.644321\pi$
$241$	−20.9795	−	7.63592i	−1.35141	−	0.491873i	−0.913388	+	0.407091i	$0.866543\pi$
$242$	9.65002			0.620326
$243$		0			0
$244$	4.63816			0.296927
$245$	8.11721	+	2.95442i	0.518590	+	0.188751i
$246$		0			0
$247$	6.64337	+	5.57445i	0.422708	+	0.354694i
$248$	−2.55468	+	14.4883i	−0.162222	+	0.920009i
$249$		0			0
$250$	−13.1964	+	11.0731i	−0.834614	+	0.700324i
$251$	11.3610	+	19.6778i	0.717098	+	1.24205i	0.962145	+	0.272539i	$0.0878633\pi$
$251$	11.3610	+	19.6778i	0.717098	+	1.24205i	−0.245047	+	0.969511i	$0.578803\pi$
$252$		0			0
$253$	−0.230552	+	0.399328i	−0.0144947	+	0.0251055i
$254$	−0.00639661	−	0.0362770i	−0.000401359	−	0.00227622i
$255$		0			0
$256$	15.1300	−	5.50687i	0.945625	−	0.344179i
$257$	18.4081	−	6.69999i	1.14826	−	0.417934i	0.303373	−	0.952872i	$-0.401887\pi$
$257$	18.4081	−	6.69999i	1.14826	−	0.417934i	0.844891	+	0.534938i	$0.179665\pi$
$258$		0			0
$259$	2.51842	+	14.2827i	0.156487	+	0.887481i
$260$	5.73783	−	9.93821i	0.355845	−	0.616341i
$261$		0			0
$262$	8.06758	+	13.9735i	0.498417	+	0.863283i
$263$	13.6361	−	11.4420i	0.840838	−	0.705547i	−0.116914	−	0.993142i	$-0.537300\pi$
$263$	13.6361	−	11.4420i	0.840838	−	0.705547i	0.957752	+	0.287595i	$0.0928558\pi$
$264$		0			0
$265$	0.945622	−	5.36289i	0.0580891	−	0.329440i
$266$	5.29292	+	4.44129i	0.324530	+	0.272313i
$267$		0			0
$268$	−6.76042	−	2.46059i	−0.412958	−	0.150305i
$269$	22.7888			1.38946			0.694729	−	0.719272i	$-0.255524\pi$
$269$	22.7888			1.38946			0.694729	+	0.719272i	$0.255524\pi$
$270$		0			0
$271$	−3.44562			−0.209307			−0.104653	−	0.994509i	$-0.533373\pi$
$271$	−3.44562			−0.209307			−0.104653	+	0.994509i	$0.533373\pi$
$272$	0.118089	+	0.0429807i	0.00716017	+	0.00260609i
$273$		0			0
$274$	−9.64203	−	8.09062i	−0.582496	−	0.488772i
$275$	0.283585	−	1.60829i	0.0171008	−	0.0969837i
$276$		0			0
$277$	−2.00206	+	1.67993i	−0.120292	+	0.100937i	−0.700949	−	0.713211i	$-0.747240\pi$
$277$	−2.00206	+	1.67993i	−0.120292	+	0.100937i	0.580657	+	0.814148i	$0.302796\pi$
$278$	4.61468	+	7.99287i	0.276770	+	0.479380i
$279$		0			0
$280$	12.0248	−	20.8276i	0.718620	−	1.24469i
$281$	−2.37639	−	13.4772i	−0.141764	−	0.803982i	−0.969909	−	0.243468i	$-0.921715\pi$
$281$	−2.37639	−	13.4772i	−0.141764	−	0.803982i	0.828145	−	0.560514i	$-0.189396\pi$
$282$		0			0
$283$	−21.5005	+	7.82553i	−1.27807	+	0.465179i	−0.889793	−	0.456363i	$-0.849152\pi$
$283$	−21.5005	+	7.82553i	−1.27807	+	0.465179i	−0.388277	+	0.921543i	$0.626929\pi$
$284$	−17.6573	+	6.42675i	−1.04777	+	0.381357i
$285$		0			0
$286$	−0.0598406	−	0.339373i	−0.00353845	−	0.0200675i
$287$	−6.33662	+	10.9753i	−0.374039	+	0.647854i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−17.5535	+	14.7291i	−1.03078	+	0.864925i
$291$		0			0
$292$	−1.84895	+	10.4859i	−0.108201	+	0.613640i
$293$	18.6006	+	15.6078i	1.08666	+	0.911815i	0.996457	−	0.0841084i	$-0.0268042\pi$
$293$	18.6006	+	15.6078i	1.08666	+	0.911815i	0.0902023	+	0.995923i	$0.471249\pi$
$294$		0			0
$295$	18.6668	+	6.79417i	1.08683	+	0.395572i
$296$	−18.8357			−1.09481
$297$		0			0
$298$	1.11793			0.0647597
$299$	−6.42989	−	2.34029i	−0.371850	−	0.135342i
$300$		0			0
$301$	10.4213	+	8.74449i	0.600672	+	0.504024i
$302$	−1.19981	+	6.80445i	−0.0690412	+	0.391552i
$303$		0			0
$304$	−0.115400	+	0.0968323i	−0.00661865	+	0.00555371i
$305$	7.33409	+	12.7030i	0.419949	+	0.727373i
$306$		0			0
$307$	8.07444	−	13.9853i	0.460833	−	0.798186i	−0.538170	−	0.842836i	$-0.680884\pi$
$307$	8.07444	−	13.9853i	0.460833	−	0.798186i	0.999003	+	0.0446505i	$0.0142174\pi$
$308$	0.0756268	+	0.428901i	0.00430924	+	0.0244389i
$309$		0			0
$310$	−16.6211	+	6.04958i	−0.944014	+	0.343593i
$311$	−17.5817	+	6.39922i	−0.996968	+	0.362867i	−0.788414	−	0.615144i	$-0.789098\pi$
$311$	−17.5817	+	6.39922i	−0.996968	+	0.362867i	−0.208553	+	0.978011i	$0.566875\pi$
$312$		0			0
$313$	0.481582	+	2.73119i	0.0272206	+	0.154376i	0.995388	−	0.0959261i	$-0.0305813\pi$
$313$	0.481582	+	2.73119i	0.0272206	+	0.154376i	−0.968168	+	0.250302i	$0.919470\pi$
$314$	−5.43124	+	9.40718i	−0.306502	+	0.530878i
$315$		0			0
$316$	−0.778066	−	1.34765i	−0.0437696	−	0.0758112i
$317$	13.3923	−	11.2375i	0.752189	−	0.631161i	−0.183892	−	0.982946i	$-0.558870\pi$
$317$	13.3923	−	11.2375i	0.752189	−	0.631161i	0.936081	+	0.351785i	$0.114425\pi$
$318$		0			0
$319$	0.189540	−	1.07494i	0.0106122	−	0.0601849i
$320$	14.9834	+	12.5726i	0.837597	+	0.702827i
$321$		0			0
$322$	−5.12284	−	1.86456i	−0.285485	−	0.103908i
$323$	10.7888			0.600305
$324$		0			0
$325$	24.2344			1.34428
$326$	−11.3598	−	4.13462i	−0.629160	−	0.228996i
$327$		0			0
$328$	−12.6086	−	10.5799i	−0.696193	−	0.584175i
$329$	−2.80628	+	15.9152i	−0.154715	+	0.877435i
$330$		0			0
$331$	−24.8653	+	20.8645i	−1.36672	+	1.14681i	−0.392878	+	0.919590i	$0.628521\pi$
$331$	−24.8653	+	20.8645i	−1.36672	+	1.14681i	−0.973842	+	0.227224i	$0.927035\pi$
$332$	−5.19846	−	9.00400i	−0.285303	−	0.494159i
$333$		0			0
$334$	−1.63429	+	2.83067i	−0.0894241	+	0.154887i
$335$	−3.95084	−	22.4063i	−0.215857	−	1.22419i
$336$		0			0
$337$	−7.78611	+	2.83391i	−0.424137	+	0.154373i	−0.545265	−	0.838264i	$-0.683571\pi$
$337$	−7.78611	+	2.83391i	−0.424137	+	0.154373i	0.121128	+	0.992637i	$0.461349\pi$
$338$	−5.93717	+	2.16095i	−0.322939	+	0.117540i
$339$		0			0
$340$	−2.47906	−	14.0594i	−0.134446	−	0.762479i
$341$	0.421274	−	0.729669i	0.0228133	−	0.0395138i
$342$		0			0
$343$	−10.0792	−	17.4577i	−0.544225	−	0.942626i
$344$	−13.5346	+	11.3569i	−0.729738	+	0.612323i
$345$		0			0
$346$	0.238131	−	1.35051i	0.0128020	−	0.0726037i
$347$	11.4624	+	9.61814i	0.615336	+	0.516329i	0.896334	−	0.443380i	$-0.146221\pi$
$347$	11.4624	+	9.61814i	0.615336	+	0.516329i	−0.280997	+	0.959709i	$0.590665\pi$
$348$		0			0
$349$	−31.6168	−	11.5076i	−1.69241	−	0.615986i	−0.697483	−	0.716601i	$-0.745697\pi$
$349$	−31.6168	−	11.5076i	−1.69241	−	0.615986i	−0.994925	+	0.100615i	$0.967919\pi$
$350$	19.3081			1.03206
$351$		0			0
$352$	−0.916222			−0.0488348
$353$	14.8037	+	5.38809i	0.787919	+	0.286779i	0.704471	−	0.709733i	$-0.251184\pi$
$353$	14.8037	+	5.38809i	0.787919	+	0.286779i	0.0834482	+	0.996512i	$0.473407\pi$
$354$		0			0
$355$	−45.5223	−	38.1978i	−2.41608	−	2.02733i
$356$	−1.64486	+	9.32845i	−0.0871772	+	0.494407i
$357$		0			0
$358$	8.21348	−	6.89193i	0.434096	−	0.364250i
$359$	−9.06283	−	15.6973i	−0.478318	−	0.828471i	0.521373	−	0.853329i	$-0.325420\pi$
$359$	−9.06283	−	15.6973i	−0.478318	−	0.828471i	−0.999691	+	0.0248577i	$0.992087\pi$
$360$		0			0
$361$	3.03343	−	5.25406i	0.159654	−	0.276529i
$362$	2.57650	+	14.6121i	0.135418	+	0.767994i
$363$		0			0
$364$	−6.07310	+	2.21043i	−0.318317	+	0.115858i
$365$	−31.6425	+	11.5169i	−1.65624	+	0.602823i
$366$		0			0
$367$	−3.32413	−	18.8521i	−0.173518	−	0.984071i	−0.939840	−	0.341614i	$-0.889026\pi$
$367$	−3.32413	−	18.8521i	−0.173518	−	0.984071i	0.766322	−	0.642457i	$-0.222085\pi$
$368$	0.0594300	−	0.102936i	0.00309800	−	0.00536590i
$369$		0			0
$370$	−11.3229	−	19.6119i	−0.588652	−	1.01958i
$371$	−2.34936	+	1.97134i	−0.121972	+	0.102347i
$372$		0			0
$373$	−2.64812	+	15.0182i	−0.137114	+	0.777614i	0.836250	+	0.548349i	$0.184743\pi$
$373$	−2.64812	+	15.0182i	−0.137114	+	0.777614i	−0.973364	+	0.229265i	$0.926368\pi$
$374$	−0.328411	−	0.275570i	−0.0169817	−	0.0142494i
$375$		0			0
$376$	−19.7230	−	7.17858i	−1.01713	−	0.370207i
$377$	16.1976			0.834218
$378$		0			0
$379$	9.84760			0.505837			0.252919	−	0.967488i	$-0.418610\pi$
$379$	9.84760			0.505837			0.252919	+	0.967488i	$0.418610\pi$
$380$	16.0817	+	5.85327i	0.824975	+	0.300266i
$381$		0			0
$382$	11.7724	+	9.87825i	0.602330	+	0.505415i
$383$	4.92989	−	27.9588i	0.251906	−	1.42863i	−0.551986	−	0.833853i	$-0.686130\pi$
$383$	4.92989	−	27.9588i	0.251906	−	1.42863i	0.803892	−	0.594775i	$-0.202759\pi$
$384$		0			0
$385$	−1.05509	+	0.885328i	−0.0537725	+	0.0451205i
$386$	−0.875982	−	1.51724i	−0.0445863	−	0.0772257i
$387$		0			0
$388$	−2.39615	+	4.15026i	−0.121646	+	0.210698i
$389$	1.89006	+	10.7191i	0.0958300	+	0.543479i	0.994490	+	0.104833i	$0.0334307\pi$
$389$	1.89006	+	10.7191i	0.0958300	+	0.543479i	−0.898660	+	0.438646i	$0.855458\pi$
$390$		0			0
$391$	−7.99912	+	2.91144i	−0.404533	+	0.147238i
$392$	5.93717	−	2.16095i	0.299872	−	0.109145i
$393$		0			0
$394$	−3.23618	−	18.3533i	−0.163036	−	0.924624i
$395$	2.46064	−	4.26195i	0.123808	−	0.214442i
$396$		0			0
$397$	9.05350	+	15.6811i	0.454382	+	0.787013i	0.998652	−	0.0518969i	$-0.0165267\pi$
$397$	9.05350	+	15.6811i	0.454382	+	0.787013i	−0.544270	+	0.838910i	$0.683193\pi$
$398$	2.07738	−	1.74313i	0.104130	−	0.0873752i
$399$		0			0
$400$	−0.0731006	+	0.414574i	−0.00365503	+	0.0207287i
$401$	1.09833	+	0.921605i	0.0548478	+	0.0460228i	0.669799	−	0.742542i	$-0.266380\pi$
$401$	1.09833	+	0.921605i	0.0548478	+	0.0460228i	−0.614952	+	0.788565i	$0.710824\pi$
$402$		0			0
$403$	11.7490	+	4.27628i	0.585258	+	0.213016i
$404$	9.95306			0.495183
$405$		0			0
$406$	12.9050			0.640463
$407$	1.01367	+	0.368946i	0.0502458	+	0.0182880i
$408$		0			0
$409$	6.59105	+	5.53055i	0.325907	+	0.273468i	0.791029	−	0.611778i	$-0.209545\pi$
$409$	6.59105	+	5.53055i	0.325907	+	0.273468i	−0.465123	+	0.885246i	$0.653990\pi$
$410$	3.43629	−	19.4882i	0.169706	−	0.962452i
$411$		0			0
$412$	−17.5214	+	14.7022i	−0.863218	+	0.724326i
$413$	−5.59374	−	9.68864i	−0.275250	−	0.476747i
$414$		0			0
$415$	16.4402	−	28.4752i	0.807016	−	1.39779i
$416$	−2.36097	−	13.3897i	−0.115756	−	0.656484i
$417$		0			0
$418$	0.482926	−	0.175771i	0.0236207	−	0.00859722i
$419$	11.5689	−	4.21074i	0.565179	−	0.205708i	−0.0435988	−	0.999049i	$-0.513882\pi$
$419$	11.5689	−	4.21074i	0.565179	−	0.205708i	0.608778	+	0.793341i	$0.291660\pi$
$420$		0			0
$421$	1.93036	+	10.9476i	0.0940800	+	0.533554i	0.995025	+	0.0996216i	$0.0317632\pi$
$421$	1.93036	+	10.9476i	0.0940800	+	0.533554i	−0.900945	+	0.433932i	$0.857126\pi$
$422$	0.443096	−	0.767465i	0.0215696	−	0.0373596i
$423$		0			0
$424$	−1.99154	−	3.44946i	−0.0967179	−	0.167520i
$425$	23.0954	−	19.3793i	1.12029	−	0.940036i
$426$		0			0
$427$	1.43448	−	8.13533i	0.0694193	−	0.393696i
$428$	−7.13816	−	5.98962i	−0.345036	−	0.289519i
$429$		0			0
$430$	−19.9611	−	7.26525i	−0.962610	−	0.350361i
$431$	−36.8958			−1.77721			−0.888604	−	0.458675i	$-0.848324\pi$
$431$	−36.8958			−1.77721			−0.888604	+	0.458675i	$0.848324\pi$
$432$		0			0
$433$	−37.9982			−1.82608			−0.913040	−	0.407871i	$-0.866271\pi$
$433$	−37.9982			−1.82608			−0.913040	+	0.407871i	$0.866271\pi$
$434$	9.36066	+	3.40700i	0.449326	+	0.163541i
$435$		0			0
$436$	14.6951	+	12.3306i	0.703766	+	0.590530i
$437$	1.77197	−	10.0494i	0.0847650	−	0.480726i
$438$		0			0
$439$	0.154763	−	0.129862i	0.00738644	−	0.00619796i	−0.639087	−	0.769135i	$-0.720688\pi$
$439$	0.154763	−	0.129862i	0.00738644	−	0.00619796i	0.646473	+	0.762937i	$0.276243\pi$
$440$	−0.894400	−	1.54915i	−0.0426388	−	0.0738526i
$441$		0			0
$442$	3.18092	−	5.50952i	0.151301	−	0.262061i
$443$	3.68644	+	20.9068i	0.175148	+	0.993314i	0.937973	+	0.346709i	$0.112701\pi$
$443$	3.68644	+	20.9068i	0.175148	+	0.993314i	−0.762825	+	0.646605i	$0.776188\pi$
$444$		0			0
$445$	−28.1498	+	10.2457i	−1.33443	+	0.485692i
$446$	15.1091	−	5.49925i	0.715435	−	0.260397i
$447$		0			0
$448$	−1.91282	−	10.8481i	−0.0903722	−	0.512526i
$449$	16.6297	−	28.8035i	0.784804	−	1.35932i	−0.144312	−	0.989532i	$-0.546097\pi$
$449$	16.6297	−	28.8035i	0.784804	−	1.35932i	0.929116	−	0.369788i	$-0.120570\pi$
$450$		0			0
$451$	0.471315	+	0.816341i	0.0221933	+	0.0384400i
$452$	2.17365	−	1.82391i	0.102240	−	0.0857894i
$453$		0			0
$454$	0.403895	−	2.29061i	0.0189558	−	0.107503i
$455$	−15.6570	−	13.1378i	−0.734013	−	0.615910i
$456$		0			0
$457$	0.0320889	+	0.0116794i	0.00150105	+	0.000546339i	0.342771	−	0.939419i	$-0.388635\pi$
$457$	0.0320889	+	0.0116794i	0.00150105	+	0.000546339i	−0.341270	+	0.939965i	$0.610857\pi$
$458$	3.04519			0.142292
$459$		0			0
$460$	−13.5030			−0.629580
$461$	14.0826	+	5.12565i	0.655892	+	0.238725i	0.648462	−	0.761247i	$-0.275413\pi$
$461$	14.0826	+	5.12565i	0.655892	+	0.238725i	0.00743018	+	0.999972i	$0.497635\pi$
$462$		0			0
$463$	−23.3203	−	19.5680i	−1.08378	−	0.909403i	−0.0875549	−	0.996160i	$-0.527905\pi$
$463$	−23.3203	−	19.5680i	−1.08378	−	0.909403i	−0.996230	+	0.0867566i	$0.972350\pi$
$464$	−0.0488583	+	0.277089i	−0.00226819	+	0.0128635i
$465$		0			0
$466$	−4.12654	+	3.46258i	−0.191158	+	0.160401i
$467$	0.255367	+	0.442308i	0.0118170	+	0.0204676i	0.871873	−	0.489731i	$-0.162905\pi$
$467$	0.255367	+	0.442308i	0.0118170	+	0.0204676i	−0.860056	+	0.510199i	$0.829572\pi$
$468$		0			0
$469$	−6.40673	+	11.0968i	−0.295835	+	0.512401i
$470$	−4.38191	−	24.8511i	−0.202123	−	1.14629i
$471$		0			0
$472$	13.6535	−	4.96946i	0.628452	−	0.228738i
$473$	0.950837	−	0.346076i	0.0437195	−	0.0159126i
$474$		0			0
$475$	6.27584	+	35.5921i	0.287955	+	1.63308i
$476$	−4.02007	+	6.96296i	−0.184259	+	0.319147i
$477$		0			0
$478$	−12.7297	−	22.0484i	−0.582242	−	1.00847i
$479$	−11.8359	+	9.93150i	−0.540796	+	0.453782i	−0.871810	−	0.489844i	$-0.837054\pi$
$479$	−11.8359	+	9.93150i	−0.540796	+	0.453782i	0.331014	+	0.943626i	$0.392609\pi$
$480$		0			0
$481$	−2.77972	+	15.7645i	−0.126744	+	0.718801i
$482$	−15.0398	−	12.6199i	−0.685045	−	0.574821i
$483$		0			0
$484$	−12.6493	−	4.60397i	−0.574968	−	0.209271i
$485$	−15.1557			−0.688185
$486$		0			0
$487$	29.5107			1.33726			0.668629	−	0.743596i	$-0.266881\pi$
$487$	29.5107			1.33726			0.668629	+	0.743596i	$0.266881\pi$
$488$	10.0817	+	3.66945i	0.456378	+	0.166108i
$489$		0			0
$490$	5.81908	+	4.88279i	0.262879	+	0.220582i
$491$	0.374638	−	2.12467i	0.0169072	−	0.0958852i	−0.975187	−	0.221385i	$-0.928942\pi$
$491$	0.374638	−	2.12467i	0.0169072	−	0.0958852i	0.992094	+	0.125500i	$0.0400534\pi$
$492$		0			0
$493$	15.4363	−	12.9526i	0.695215	−	0.583355i
$494$	3.81315	+	6.60457i	0.171562	+	0.297153i
$495$		0			0
$496$	−0.108593	+	0.188089i	−0.00487597	+	0.00844543i
$497$	5.81150	+	32.9586i	0.260681	+	1.47840i
$498$		0			0
$499$	−7.04323	+	2.56353i	−0.315298	+	0.114759i	−0.494822	−	0.868994i	$-0.664767\pi$
$499$	−7.04323	+	2.56353i	−0.315298	+	0.114759i	0.179523	+	0.983754i	$0.442544\pi$
$500$	22.5808	−	8.21875i	1.00985	−	0.367554i
$501$		0			0
$502$	3.46972	+	19.6778i	0.154861	+	0.878262i
$503$	−14.2981	+	24.7651i	−0.637522	+	1.10422i	0.348453	+	0.937326i	$0.386707\pi$
$503$	−14.2981	+	24.7651i	−0.637522	+	1.10422i	−0.985975	+	0.166894i	$0.946626\pi$
$504$		0			0
$505$	15.7383	+	27.2595i	0.700345	+	1.21303i
$506$	−0.310622	+	0.260643i	−0.0138088	+	0.0115870i
$507$		0			0
$508$	−0.00892283	+	0.0506039i	−0.000395887	+	0.00224518i
$509$	−1.29607	−	1.08754i	−0.0574475	−	0.0482041i	0.613612	−	0.789608i	$-0.289716\pi$
$509$	−1.29607	−	1.08754i	−0.0574475	−	0.0482041i	−0.671059	+	0.741404i	$0.734160\pi$
$510$		0			0
$511$	17.8204	+	6.48610i	0.788329	+	0.286928i
$512$	0.473897			0.0209435
$513$		0			0
$514$	17.2267			0.759836
$515$	−67.9723	−	24.7399i	−2.99522	−	1.09017i
$516$		0			0
$517$	0.920807	+	0.772649i	0.0404971	+	0.0339811i
$518$	−2.21466	+	12.5600i	−0.0973066	+	0.551853i
$519$		0			0
$520$	20.3346	−	17.0627i	0.891729	−	0.748250i
$521$	11.2019	+	19.4022i	0.490763	+	0.850026i	0.999943	−	0.0106337i	$-0.00338487\pi$
$521$	11.2019	+	19.4022i	0.490763	+	0.850026i	−0.509181	+	0.860660i	$0.670052\pi$
$522$		0			0
$523$	−1.21436	+	2.10332i	−0.0531000	+	0.0919720i	−0.891354	−	0.453309i	$-0.850244\pi$
$523$	−1.21436	+	2.10332i	−0.0531000	+	0.0919720i	0.838254	+	0.545281i	$0.183577\pi$
$524$	−3.90838	−	22.1655i	−0.170738	−	0.968304i
$525$		0			0
$526$	14.7096	−	5.35386i	0.641369	−	0.233439i
$527$	14.6163	−	5.31991i	0.636698	−	0.231739i
$528$		0			0
$529$	−2.59580	−	14.7215i	−0.112861	−	0.640066i
$530$	2.39440	−	4.14722i	0.104006	−	0.180144i
$531$		0			0
$532$	−4.81908	−	8.34689i	−0.208934	−	0.361883i
$533$	−10.7155	+	8.99140i	−0.464141	+	0.389461i
$534$		0			0
$535$	5.11721	−	29.0211i	0.221236	−	1.25469i
$536$	−12.7481	−	10.6969i	−0.550634	−	0.462037i
$537$		0			0
$538$	18.8316	+	6.85413i	0.811886	+	0.295503i
$539$	−0.361844			−0.0155857
$540$		0			0
$541$	38.9394			1.67414			0.837069	−	0.547098i	$-0.184267\pi$
$541$	38.9394			1.67414			0.837069	+	0.547098i	$0.184267\pi$
$542$	−2.84730	−	1.03633i	−0.122302	−	0.0445142i
$543$		0			0
$544$	−12.9572	−	10.8724i	−0.555537	−	0.466151i
$545$	−10.5346	+	59.7448i	−0.451253	+	2.55918i
$546$		0			0
$547$	−11.2396	+	9.43118i	−0.480572	+	0.403248i	−0.850633	−	0.525759i	$-0.823781\pi$
$547$	−11.2396	+	9.43118i	−0.480572	+	0.403248i	0.370061	+	0.929007i	$0.379337\pi$
$548$	8.77884	+	15.2054i	0.375013	+	0.649542i
$549$		0			0
$550$	0.718063	−	1.24372i	0.0306183	−	0.0530325i
$551$	4.19459	+	23.7887i	0.178696	+	1.01343i
$552$		0			0
$553$	−2.60442	+	0.947931i	−0.110751	+	0.0403101i
$554$	−2.15967	+	0.786057i	−0.0917557	+	0.0333963i
$555$		0			0
$556$	−2.23560	−	12.6787i	−0.0948107	−	0.537698i
$557$	5.55350	−	9.61894i	0.235309	−	0.407568i	−0.724053	−	0.689744i	$-0.757723\pi$
$557$	5.55350	−	9.61894i	0.235309	−	0.407568i	0.959363	+	0.282176i	$0.0910563\pi$
$558$		0			0
$559$	7.50774	+	13.0038i	0.317544	+	0.550002i
$560$	0.271974	−	0.228213i	0.0114930	−	0.00964378i
$561$		0			0
$562$	2.08976	−	11.8516i	0.0881514	−	0.499931i
$563$	12.4927	+	10.4826i	0.526506	+	0.441791i	0.866893	−	0.498495i	$-0.166114\pi$
$563$	12.4927	+	10.4826i	0.526506	+	0.441791i	−0.340387	+	0.940285i	$0.610558\pi$
$564$		0			0
$565$	8.43242	+	3.06915i	0.354755	+	0.129120i
$566$	−20.1206			−0.845733
$567$		0			0
$568$	−43.4653			−1.82376
$569$	−33.8444	−	12.3183i	−1.41883	−	0.516412i	−0.485121	−	0.874447i	$-0.661225\pi$
$569$	−33.8444	−	12.3183i	−1.41883	−	0.516412i	−0.933708	+	0.358035i	$0.883447\pi$
$570$		0			0
$571$	29.9971	+	25.1705i	1.25534	+	1.05335i	0.996162	+	0.0875234i	$0.0278953\pi$
$571$	29.9971	+	25.1705i	1.25534	+	1.05335i	0.259176	+	0.965830i	$0.416549\pi$
$572$	−0.0834734	+	0.473401i	−0.00349020	+	0.0197939i
$573$		0			0
$574$	−8.53730	+	7.16365i	−0.356340	+	0.299005i
$575$	−14.2579	−	24.6954i	−0.594595	−	1.02987i
$576$		0			0
$577$	−5.90286	+	10.2240i	−0.245739	+	0.425633i	−0.962339	−	0.271852i	$-0.912364\pi$
$577$	−5.90286	+	10.2240i	−0.245739	+	0.425633i	0.716600	+	0.697484i	$0.245697\pi$
$578$	1.22163	+	6.92820i	0.0508131	+	0.288175i
$579$		0			0
$580$	30.0364	−	10.9324i	1.24719	−	0.453942i
$581$	−17.4008	+	6.33337i	−0.721907	+	0.262753i
$582$		0			0
$583$	0.0396112	+	0.224647i	0.00164053	+	0.00930391i
$584$	−12.3148	+	21.3299i	−0.509590	+	0.882636i
$585$		0			0
$586$	10.6763	+	18.4920i	0.441035	+	0.763896i
$587$	−30.6122	+	25.6867i	−1.26350	+	1.06020i	−0.268201	+	0.963363i	$0.586429\pi$
$587$	−30.6122	+	25.6867i	−1.26350	+	1.06020i	−0.995300	+	0.0968406i	$0.969126\pi$
$588$		0			0
$589$	−3.23783	+	18.3626i	−0.133412	+	0.756619i
$590$	13.3819	+	11.2288i	0.550925	+	0.462281i
$591$		0			0
$592$	−0.261297	−	0.0951042i	−0.0107392	−	0.00390876i
$593$	−29.2995			−1.20319			−0.601594	−	0.798802i	$-0.705467\pi$
$593$	−29.2995			−1.20319			−0.601594	+	0.798802i	$0.705467\pi$
$594$		0			0
$595$	−25.4270			−1.04240
$596$	−1.46538	−	0.533356i	−0.0600245	−	0.0218471i
$597$		0			0
$598$	−4.60947	−	3.86780i	−0.188495	−	0.158166i
$599$	1.74897	−	9.91890i	0.0714610	−	0.405275i	−0.928004	−	0.372570i	$-0.878477\pi$
$599$	1.74897	−	9.91890i	0.0714610	−	0.405275i	0.999465	−	0.0327053i	$-0.0104123\pi$
$600$		0			0
$601$	−23.3025	+	19.5531i	−0.950528	+	0.797587i	−0.979386	−	0.201996i	$-0.935257\pi$
$601$	−23.3025	+	19.5531i	−0.950528	+	0.797587i	0.0288587	+	0.999584i	$0.490813\pi$
$602$	5.98158	+	10.3604i	0.243791	+	0.422259i
$603$		0			0
$604$	4.81908	−	8.34689i	0.196085	−	0.339630i
$605$	−7.39234	−	41.9240i	−0.300541	−	1.70445i
$606$		0			0
$607$	21.6827	−	7.89187i	0.880075	−	0.320321i	0.137835	−	0.990455i	$-0.455986\pi$
$607$	21.6827	−	7.89187i	0.880075	−	0.320321i	0.742240	+	0.670134i	$0.233763\pi$
$608$	19.0535	−	6.93491i	0.772721	−	0.281248i
$609$		0			0
$610$	2.23989	+	12.7030i	0.0906903	+	0.514330i
$611$	−8.91875	+	15.4477i	−0.360814	+	0.624948i
$612$		0			0
$613$	−0.382789	−	0.663010i	−0.0154607	−	0.0267787i	0.858192	−	0.513330i	$-0.171588\pi$
$613$	−0.382789	−	0.663010i	−0.0154607	−	0.0267787i	−0.873652	+	0.486551i	$0.838255\pi$
$614$	10.8787	−	9.12829i	0.439027	−	0.368388i
$615$		0			0
$616$	−0.174936	+	0.992112i	−0.00704837	+	0.0399733i
$617$	−7.11515	−	5.97032i	−0.286445	−	0.240356i	0.488231	−	0.872715i	$-0.337643\pi$
$617$	−7.11515	−	5.97032i	−0.286445	−	0.240356i	−0.774676	+	0.632359i	$0.782087\pi$
$618$		0			0
$619$	32.9666	+	11.9989i	1.32504	+	0.482275i	0.905070	−	0.425263i	$-0.139818\pi$
$619$	32.9666	+	11.9989i	1.32504	+	0.482275i	0.419970	+	0.907538i	$0.362040\pi$
$620$	24.6732			0.990901
$621$		0			0
$622$	−16.4534			−0.659720
$623$	15.8534	+	5.77016i	0.635153	+	0.231177i
$624$		0			0
$625$	19.7233	+	16.5498i	0.788931	+	0.661992i
$626$	−0.423496	+	2.40176i	−0.0169263	+	0.0959938i
$627$		0			0
$628$	11.6074	−	9.73977i	0.463186	−	0.388659i
$629$	9.95723	+	17.2464i	0.397021	+	0.687660i
$630$		0			0
$631$	−17.8810	+	30.9709i	−0.711833	+	1.23293i	0.252336	+	0.967640i	$0.418801\pi$
$631$	−17.8810	+	30.9709i	−0.711833	+	1.23293i	−0.964168	+	0.265291i	$0.914532\pi$
$632$	−0.625058	−	3.54488i	−0.0248635	−	0.141008i
$633$		0			0
$634$	14.4467	−	5.25815i	0.573750	−	0.208828i
$635$	−0.152704	+	0.0555796i	−0.00605986	+	0.00220561i
$636$		0			0
$637$	−0.932419	−	5.28801i	−0.0369438	−	0.209519i
$638$	0.479933	−	0.831268i	0.0190007	−	0.0329102i
$639$		0			0
$640$	−13.2724	−	22.9885i	−0.524639	−	0.908702i
$641$	2.24170	−	1.88101i	0.0885417	−	0.0742953i	−0.597442	−	0.801912i	$-0.703816\pi$
$641$	2.24170	−	1.88101i	0.0885417	−	0.0742953i	0.685984	+	0.727616i	$0.259372\pi$
$642$		0			0
$643$	−3.51666	+	19.9440i	−0.138684	+	0.786514i	0.833540	+	0.552459i	$0.186311\pi$
$643$	−3.51666	+	19.9440i	−0.138684	+	0.786514i	−0.972223	+	0.234055i	$0.924801\pi$
$644$	5.82547	+	4.88815i	0.229556	+	0.192620i
$645$		0			0
$646$	8.91534	+	3.24492i	0.350770	+	0.127670i
$647$	10.7219			0.421523			0.210761	−	0.977538i	$-0.432406\pi$
$647$	10.7219			0.421523			0.210761	+	0.977538i	$0.432406\pi$
$648$		0			0
$649$	−0.832119			−0.0326635
$650$	20.0262	+	7.28893i	0.785491	+	0.285895i
$651$		0			0
$652$	12.9179	+	10.8394i	0.505903	+	0.424503i
$653$	6.20393	−	35.1842i	0.242778	−	1.37686i	−0.582818	−	0.812603i	$-0.698050\pi$
$653$	6.20393	−	35.1842i	0.242778	−	1.37686i	0.825596	−	0.564262i	$-0.190839\pi$
$654$		0			0
$655$	54.5269	−	45.7535i	2.13054	−	1.78774i
$656$	−0.121492	−	0.210430i	−0.00474347	−	0.00821593i
$657$		0			0
$658$	−7.10576	+	12.3075i	−0.277011	+	0.479798i
$659$	5.35978	+	30.3969i	0.208788	+	1.18409i	0.891367	+	0.453282i	$0.149747\pi$
$659$	5.35978	+	30.3969i	0.208788	+	1.18409i	−0.682580	+	0.730811i	$0.739142\pi$
$660$		0			0
$661$	9.25402	−	3.36819i	0.359940	−	0.131007i	−0.155719	−	0.987801i	$-0.549769\pi$
$661$	9.25402	−	3.36819i	0.359940	−	0.131007i	0.515659	+	0.856794i	$0.327547\pi$
$662$	−26.8228	+	9.76272i	−1.04250	+	0.379439i
$663$		0			0
$664$	−4.17617	−	23.6843i	−0.162067	−	0.919128i
$665$	15.2404	−	26.3971i	0.590996	−	1.02363i
$666$		0			0
$667$	−9.52956	−	16.5057i	−0.368986	−	0.639103i
$668$	3.49273	−	2.93075i	0.135138	−	0.113394i
$669$		0			0
$670$	3.47431	−	19.7038i	0.134224	−	0.761223i
$671$	−0.470686	−	0.394952i	−0.0181706	−	0.0152470i
$672$		0			0
$673$	18.5094	+	6.73687i	0.713485	+	0.259687i	0.673157	−	0.739499i	$-0.264938\pi$
$673$	18.5094	+	6.73687i	0.713485	+	0.259687i	0.0403273	+	0.999187i	$0.487160\pi$
$674$	−7.28642			−0.280662
$675$		0			0
$676$	8.81345			0.338979
$677$	26.7408	+	9.73286i	1.02773	+	0.374064i	0.800217	−	0.599710i	$-0.204717\pi$
$677$	26.7408	+	9.73286i	1.02773	+	0.374064i	0.227516	+	0.973774i	$0.426940\pi$
$678$		0			0
$679$	6.53849	+	5.48644i	0.250924	+	0.210550i
$680$	5.73442	−	32.5215i	0.219905	−	1.24714i
$681$		0			0
$682$	0.567581	−	0.476257i	0.0217338	−	0.0182368i
$683$	−6.25537	−	10.8346i	−0.239355	−	0.414575i	0.721174	−	0.692754i	$-0.243603\pi$
$683$	−6.25537	−	10.8346i	−0.239355	−	0.414575i	−0.960529	+	0.278179i	$0.910269\pi$
$684$		0			0
$685$	−27.7631	+	48.0871i	−1.06077	+	1.83731i
$686$	−3.07826	−	17.4577i	−0.117528	−	0.666537i
$687$		0			0
$688$	−0.245100	+	0.0892091i	−0.00934435	+	0.00340106i
$689$	−3.18092	+	1.15776i	−0.121183	+	0.0441072i
$690$		0			0
$691$	7.40184	+	41.9779i	0.281579	+	1.59691i	0.717255	+	0.696811i	$0.245398\pi$
$691$	7.40184	+	41.9779i	0.281579	+	1.59691i	−0.435676	+	0.900104i	$0.643491\pi$
$692$	−0.956462	+	1.65664i	−0.0363592	+	0.0629760i
$693$		0			0
$694$	6.57919	+	11.3955i	0.249743	+	0.432567i
$695$	31.1896	−	26.1712i	1.18309	−	0.992729i
$696$		0			0
$697$	−3.02182	+	17.1376i	−0.114460	+	0.649133i
$698$	−22.6655	−	19.0186i	−0.857902	−	0.719865i
$699$		0			0
$700$	−25.3092	−	9.21179i	−0.956597	−	0.348173i
$701$	51.7701			1.95533			0.977665	−	0.210167i	$-0.0674008\pi$
$701$	51.7701			1.95533			0.977665	+	0.210167i	$0.0674008\pi$
$702$		0			0
$703$	−23.8726			−0.900371
$704$	−0.769915	−	0.280226i	−0.0290173	−	0.0105614i
$705$		0			0
$706$	10.6125	+	8.90491i	0.399405	+	0.335141i
$707$	3.07826	−	17.4577i	0.115770	−	0.656563i
$708$		0			0
$709$	11.6120	−	9.74362i	0.436098	−	0.365929i	−0.398149	−	0.917321i	$-0.630347\pi$
$709$	11.6120	−	9.74362i	0.436098	−	0.365929i	0.834247	+	0.551391i	$0.185903\pi$
$710$	−26.1288	−	45.2564i	−0.980597	−	1.69844i
$711$		0			0
$712$	−10.9555	+	18.9754i	−0.410574	+	0.711135i
$713$	−2.55468	−	14.4883i	−0.0956736	−	0.542592i
$714$		0			0
$715$	−1.42855	+	0.519949i	−0.0534247	+	0.0194450i
$716$	−14.0544	+	5.11538i	−0.525237	+	0.191171i
$717$		0			0
$718$	−2.76786	−	15.6973i	−0.103295	−	0.585818i
$719$	1.30747	−	2.26460i	0.0487603	−	0.0844553i	−0.840615	−	0.541633i	$-0.817806\pi$
$719$	1.30747	−	2.26460i	0.0487603	−	0.0844553i	0.889375	+	0.457178i	$0.151140\pi$
$720$		0			0
$721$	20.3687	+	35.2796i	0.758570	+	1.31388i
$722$	4.08693	−	3.42934i	0.152100	−	0.127627i
$723$		0			0
$724$	3.59405	−	20.3828i	0.133572	−	0.757522i
$725$	51.7097	+	43.3896i	1.92045	+	1.61145i
$726$		0			0
$727$	3.85204	+	1.40203i	0.142864	+	0.0519984i	0.412463	−	0.910974i	$-0.364669\pi$
$727$	3.85204	+	1.40203i	0.142864	+	0.0519984i	−0.269598	+	0.962973i	$0.586891\pi$
$728$	−14.9495			−0.554067
$729$		0			0
$730$	−29.6117			−1.09598
$731$	17.5535	+	6.38895i	0.649240	+	0.236304i
$732$		0			0
$733$	−29.2690	−	24.5596i	−1.08108	−	0.907131i	−0.0850668	−	0.996375i	$-0.527110\pi$
$733$	−29.2690	−	24.5596i	−1.08108	−	0.907131i	−0.996010	+	0.0892443i	$0.971555\pi$
$734$	2.92319	−	16.5782i	0.107897	−	0.611914i
$735$		0			0
$736$	−12.2554	+	10.2835i	−0.451739	+	0.379054i
$737$	0.476529	+	0.825373i	0.0175532	+	0.0304030i
$738$		0			0
$739$	12.1047	−	20.9660i	0.445279	−	0.771247i	−0.552792	−	0.833319i	$-0.686438\pi$
$739$	12.1047	−	20.9660i	0.445279	−	0.771247i	0.998072	+	0.0620725i	$0.0197710\pi$
$740$	5.48545	+	31.1095i	0.201649	+	1.14361i
$741$		0			0
$742$	−2.53431	+	0.922414i	−0.0930375	+	0.0338629i
$743$	3.11169	−	1.13256i	0.114157	−	0.0415497i	−0.284310	−	0.958732i	$-0.591765\pi$
$743$	3.11169	−	1.13256i	0.114157	−	0.0415497i	0.398467	+	0.917183i	$0.369542\pi$
$744$		0			0
$745$	−0.856381	−	4.85678i	−0.0313754	−	0.177939i
$746$	−6.70527	+	11.6139i	−0.245497	+	0.425214i
$747$		0			0
$748$	0.299011	+	0.517902i	0.0109329	+	0.0189364i
$749$	−12.7135	+	10.6679i	−0.464540	+	0.389796i
$750$		0			0
$751$	2.38089	−	13.5027i	0.0868800	−	0.492721i	−0.910055	−	0.414487i	$-0.863961\pi$
$751$	2.38089	−	13.5027i	0.0868800	−	0.492721i	0.996935	−	0.0782335i	$-0.0249280\pi$
$752$	−0.237359	−	0.199168i	−0.00865560	−	0.00726291i
$753$		0			0
$754$	13.3849	+	4.87171i	0.487449	+	0.177417i
$755$	30.4807			1.10931
$756$		0			0
$757$	12.3833			0.450079			0.225040	−	0.974350i	$-0.427749\pi$
$757$	12.3833			0.450079			0.225040	+	0.974350i	$0.427749\pi$
$758$	8.13758	+	2.96184i	0.295570	+	0.107579i
$759$		0			0
$760$	30.3252	+	25.4459i	1.10001	+	0.923019i
$761$	1.31671	−	7.46745i	0.0477308	−	0.270695i	−0.951597	−	0.307348i	$-0.900558\pi$
$761$	1.31671	−	7.46745i	0.0477308	−	0.270695i	0.999328	+	0.0366529i	$0.0116696\pi$
$762$		0			0
$763$	26.1728	−	21.9616i	0.947518	−	0.795062i
$764$	−10.7185	−	18.5650i	−0.387783	−	0.671660i
$765$		0			0
$766$	12.4829	−	21.6211i	0.451026	−	0.781201i
$767$	−2.14425	−	12.1606i	−0.0774243	−	0.439095i
$768$		0			0
$769$	−3.02317	+	1.10034i	−0.109018	+	0.0396794i	−0.395953	−	0.918271i	$-0.629586\pi$
$769$	−3.02317	+	1.10034i	−0.109018	+	0.0396794i	0.286935	+	0.957950i	$0.407364\pi$
$770$	−1.13816	+	0.414255i	−0.0410163	+	0.0149287i
$771$		0			0
$772$	0.424373	+	2.40674i	0.0152735	+	0.0866205i
$773$	0.0922341	−	0.159754i	0.00331743	−	0.00574596i	−0.864362	−	0.502870i	$-0.832277\pi$
$773$	0.0922341	−	0.159754i	0.00331743	−	0.00574596i	0.867679	+	0.497124i	$0.165611\pi$
$774$		0			0
$775$	26.0526	+	45.1245i	0.935838	+	1.62092i
$776$	−8.49185	+	7.12551i	−0.304840	+	0.255791i
$777$		0			0
$778$	−1.66209	+	9.42620i	−0.0595889	+	0.337946i
$779$	−15.9802	−	13.4090i	−0.572551	−	0.480428i
$780$		0			0
$781$	2.33915	+	0.851379i	0.0837012	+	0.0304647i
$782$	−7.48576			−0.267690
$783$		0			0
$784$	0.0932736			0.00333120
$785$	45.0296	+	16.3894i	1.60718	+	0.584964i
$786$		0			0
$787$	−0.366181	−	0.307263i	−0.0130530	−	0.0109527i	0.636238	−	0.771493i	$-0.280490\pi$
$787$	−0.366181	−	0.307263i	−0.0130530	−	0.0109527i	−0.649291	+	0.760540i	$0.724934\pi$
$788$	−4.51424	+	25.6015i	−0.160813	+	0.912017i
$789$		0			0
$790$	3.31521	−	2.78179i	0.117950	−	0.0989716i
$791$	−2.52687	−	4.37667i	−0.0898453	−	0.155617i
$792$		0			0
$793$	4.55896	−	7.89636i	0.161894	−	0.280408i
$794$	2.76500	+	15.6811i	0.0981264	+	0.556502i
$795$		0			0
$796$	−3.55468	+	1.29380i	−0.125992	+	0.0458575i
$797$	−13.6245	+	4.95891i	−0.482604	+	0.175653i	−0.571853	−	0.820356i	$-0.693775\pi$
$797$	−13.6245	+	4.95891i	−0.482604	+	0.175653i	0.0892494	+	0.996009i	$0.471553\pi$
$798$		0			0
$799$	3.85339	+	21.8537i	0.136323	+	0.773127i
$800$	28.3307	−	49.0702i	1.00164	−	1.73489i
$801$		0			0
$802$	0.630415	+	1.09191i	0.0222607	+	0.0385567i
$803$	1.08054	−	0.906678i	0.0381313	−	0.0319960i
$804$		0			0
$805$	−4.17617	+	23.6843i	−0.147191	+	0.834761i
$806$	8.42262	+	7.06742i	0.296674	+	0.248939i
$807$		0			0
$808$	21.6344	+	7.87429i	0.761097	+	0.277017i
$809$	−14.8743			−0.522954			−0.261477	−	0.965210i	$-0.584210\pi$
$809$	−14.8743			−0.522954			−0.261477	+	0.965210i	$0.584210\pi$
$810$		0			0
$811$	21.5963			0.758347			0.379174	−	0.925325i	$-0.376208\pi$
$811$	21.5963			0.758347			0.379174	+	0.925325i	$0.376208\pi$
$812$	−16.9159	−	6.15689i	−0.593632	−	0.216064i
$813$		0			0
$814$	0.726682	+	0.609758i	0.0254702	+	0.0213720i
$815$	−9.26058	+	52.5194i	−0.324384	+	1.83967i
$816$		0			0
$817$	−17.1539	+	14.3938i	−0.600138	+	0.503576i
$818$	3.78312	+	6.55255i	0.132274	+	0.229105i
$819$		0			0
$820$	−13.8020	+	23.9058i	−0.481987	+	0.834826i
$821$	−0.569803	−	3.23151i	−0.0198863	−	0.112781i	0.973249	−	0.229754i	$-0.0737920\pi$
$821$	−0.569803	−	3.23151i	−0.0198863	−	0.112781i	−0.993135	+	0.116973i	$0.962681\pi$
$822$		0			0
$823$	−12.9033	+	4.69643i	−0.449782	+	0.163707i	−0.556972	−	0.830531i	$-0.688037\pi$
$823$	−12.9033	+	4.69643i	−0.449782	+	0.163707i	0.107190	+	0.994239i	$0.465815\pi$
$824$	−49.7169	+	18.0955i	−1.73197	+	0.630386i
$825$		0			0
$826$	−1.70837	−	9.68864i	−0.0594418	−	0.337111i
$827$	−10.1163	+	17.5220i	−0.351779	+	0.609300i	−0.986561	−	0.163392i	$-0.947757\pi$
$827$	−10.1163	+	17.5220i	−0.351779	+	0.609300i	0.634782	+	0.772691i	$0.281090\pi$
$828$		0			0
$829$	−12.7638	−	22.1076i	−0.443306	−	0.767828i	0.554627	−	0.832099i	$-0.312861\pi$
$829$	−12.7638	−	22.1076i	−0.443306	−	0.767828i	−0.997932	+	0.0642710i	$0.979528\pi$
$830$	22.1498	−	18.5859i	0.768830	−	0.645125i
$831$		0			0
$832$	2.11128	−	11.9737i	0.0731955	−	0.415112i
$833$	−5.11721	−	4.29385i	−0.177301	−	0.148773i
$834$		0			0
$835$	13.5496	+	4.93166i	0.468904	+	0.170667i
$836$	−0.716881			−0.0247939
$837$		0			0
$838$	10.8265			0.373994
$839$	−16.3319	−	5.94431i	−0.563839	−	0.205221i	0.0443457	−	0.999016i	$-0.485880\pi$
$839$	−16.3319	−	5.94431i	−0.563839	−	0.205221i	−0.608184	+	0.793796i	$0.708102\pi$
$840$		0			0
$841$	12.3460	+	10.3595i	0.425722	+	0.357224i
$842$	−1.69753	+	9.62717i	−0.0585007	+	0.331774i
$843$		0			0
$844$	−0.946967	+	0.794599i	−0.0325959	+	0.0273512i
$845$	13.9363	+	24.1384i	0.479423	+	0.830385i
$846$		0			0
$847$	−11.9875	+	20.7630i	−0.411896	+	0.713424i
$848$	−0.0102107	−	0.0579078i	−0.000350637	−	0.00198856i
$849$		0			0
$850$	24.9136	−	9.06781i	0.854529	−	0.311023i
$851$	17.6998	−	6.44220i	0.606742	−	0.220836i
$852$		0			0
$853$	2.30999	+	13.1006i	0.0790927	+	0.448557i	0.998476	+	0.0551932i	$0.0175775\pi$
$853$	2.30999	+	13.1006i	0.0790927	+	0.448557i	−0.919383	+	0.393363i	$0.871311\pi$
$854$	3.63223	−	6.29120i	0.124292	−	0.215280i
$855$		0			0
$856$	−10.7772	−	18.6666i	−0.368357	−	0.638013i
$857$	−15.2606	+	12.8051i	−0.521292	+	0.437416i	−0.865082	−	0.501631i	$-0.832734\pi$
$857$	−15.2606	+	12.8051i	−0.521292	+	0.437416i	0.343790	+	0.939046i	$0.388289\pi$
$858$		0			0
$859$	4.57469	−	25.9444i	0.156087	−	0.885211i	−0.801699	−	0.597728i	$-0.796070\pi$
$859$	4.57469	−	25.9444i	0.156087	−	0.885211i	0.957786	−	0.287483i	$-0.0928185\pi$
$860$	22.6989	+	19.0467i	0.774027	+	0.649486i
$861$		0			0
$862$	−30.4889	−	11.0971i	−1.03846	−	0.377967i
$863$	38.2995			1.30373			0.651866	−	0.758334i	$-0.273987\pi$
$863$	38.2995			1.30373			0.651866	+	0.758334i	$0.273987\pi$
$864$		0			0
$865$	−6.04963			−0.205694
$866$	−31.3999	−	11.4286i	−1.06701	−	0.388361i
$867$		0			0
$868$	−10.6446	−	8.93184i	−0.361300	−	0.303166i
$869$	−0.0357972	+	0.203016i	−0.00121434	+	0.00688684i
$870$		0			0
$871$	−10.8341	+	9.09088i	−0.367099	+	0.308033i
$872$	22.1866	+	38.4283i	0.751333	+	1.30135i
$873$		0			0
$874$	4.48680	−	7.77136i	0.151768	−	0.262870i
$875$	−7.43195	−	42.1487i	−0.251246	−	1.42489i
$876$		0			0
$877$	25.4256	−	9.25417i	0.858562	−	0.312491i	0.125036	−	0.992152i	$-0.460095\pi$
$877$	25.4256	−	9.25417i	0.858562	−	0.312491i	0.733526	+	0.679661i	$0.237873\pi$
$878$	0.166947	−	0.0607637i	0.00563418	−	0.00205068i
$879$		0			0
$880$	−0.00458561	−	0.0260063i	−0.000154581	−	0.000876672i
$881$	−15.2888	+	26.4810i	−0.515093	+	0.892167i	0.484754	+	0.874651i	$0.338909\pi$
$881$	−15.2888	+	26.4810i	−0.515093	+	0.892167i	−0.999847	+	0.0175162i	$0.994424\pi$
$882$		0			0
$883$	−22.0526	−	38.1963i	−0.742130	−	1.28541i	−0.951524	−	0.307575i	$-0.900482\pi$
$883$	−22.0526	−	38.1963i	−0.742130	−	1.28541i	0.209394	−	0.977831i	$-0.432851\pi$
$884$	−6.79813	+	5.70431i	−0.228646	+	0.191857i
$885$		0			0
$886$	−3.24180	+	18.3852i	−0.108910	+	0.617662i
$887$	−6.03983	−	5.06802i	−0.202798	−	0.170167i	0.535733	−	0.844388i	$-0.320035\pi$
$887$	−6.03983	−	5.06802i	−0.202798	−	0.170167i	−0.738530	+	0.674220i	$0.764480\pi$
$888$		0			0
$889$	0.0859997	+	0.0313013i	0.00288434	+	0.00104981i
$890$	−26.3432			−0.883025
$891$		0			0
$892$	−22.4287			−0.750969
$893$	−24.9971	−	9.09819i	−0.836495	−	0.304459i
$894$		0			0
$895$	−36.2335	−	30.4036i	−1.21115	−	1.01628i
$896$	−2.59596	+	14.7224i	−0.0867250	+	0.491842i
$897$		0			0
$898$	22.4051	−	18.8001i	0.747669	−	0.627369i
$899$	17.4128	+	30.1599i	0.580750	+	1.00589i
$900$		0			0
$901$	−2.10560	+	3.64701i	−0.0701477	+	0.121499i
$902$	0.143943	+	0.816341i	0.00479278	+	0.0271812i
$903$		0			0
$904$	6.16772	−	2.24487i	0.205135	−	0.0746631i
$905$	61.5078	−	22.3870i	2.04459	−	0.744169i
$906$		0			0
$907$	−2.24123	−	12.7106i	−0.0744188	−	0.422050i	−0.999142	−	0.0414103i	$-0.986815\pi$
$907$	−2.24123	−	12.7106i	−0.0744188	−	0.422050i	0.924723	−	0.380640i	$-0.124296\pi$
$908$	−1.62226	+	2.80984i	−0.0538367	+	0.0932479i
$909$		0			0
$910$	−8.98680	−	15.5656i	−0.297909	−	0.515994i
$911$	16.2292	−	13.6179i	0.537698	−	0.451182i	−0.333052	−	0.942908i	$-0.608078\pi$
$911$	16.2292	−	13.6179i	0.537698	−	0.451182i	0.870750	+	0.491727i	$0.163634\pi$
$912$		0			0
$913$	−0.239170	+	1.35640i	−0.00791538	+	0.0448903i
$914$	0.0230039	+	0.0193026i	0.000760902	+	0.000638473i
$915$		0			0
$916$	−3.99165	−	1.45284i	−0.131888	−	0.0480032i
$917$	−40.0871			−1.32379
$918$		0			0
$919$	31.4688			1.03806			0.519031	−	0.854756i	$-0.326293\pi$
$919$	31.4688			1.03806			0.519031	+	0.854756i	$0.326293\pi$
$920$	−29.3508	−	10.6828i	−0.967666	−	0.352202i
$921$		0			0
$922$	10.0956	+	8.47117i	0.332479	+	0.278983i
$923$	−6.41447	+	36.3783i	−0.211135	+	1.19740i
$924$		0			0
$925$	−51.1036	+	42.8810i	−1.68028	+	1.40992i
$926$	−13.3853	−	23.1840i	−0.439869	−	0.761875i
$927$		0			0
$928$	18.9354	−	32.7971i	0.621585	−	1.07662i
$929$	−0.404038	−	2.29141i	−0.0132561	−	0.0751788i	0.977462	−	0.211111i	$-0.0677082\pi$
$929$	−0.404038	−	2.29141i	−0.0132561	−	0.0751788i	−0.990718	+	0.135932i	$0.956597\pi$
$930$		0			0
$931$	7.52481	−	2.73881i	0.246616	−	0.0897608i
$932$	7.06108	−	2.57002i	0.231293	−	0.0841839i
$933$		0			0
$934$	0.0779909	+	0.442308i	0.00255194	+	0.0144728i
$935$	−0.945622	+	1.63787i	−0.0309252	+	0.0535639i
$936$		0			0
$937$	5.49912	+	9.52476i	0.179649	+	0.311160i	0.941760	−	0.336285i	$-0.109171\pi$
$937$	5.49912	+	9.52476i	0.179649	+	0.311160i	−0.762112	+	0.647446i	$0.775837\pi$
$938$	−8.63176	+	7.24291i	−0.281837	+	0.236489i
$939$		0			0
$940$	−6.11246	+	34.6655i	−0.199367	+	1.13066i
$941$	−18.4645	−	15.4936i	−0.601926	−	0.505076i	0.290138	−	0.956985i	$-0.406299\pi$
$941$	−18.4645	−	15.4936i	−0.601926	−	0.505076i	−0.892064	+	0.451909i	$0.850743\pi$
$942$		0			0
$943$	15.4667	+	5.62943i	0.503666	+	0.183319i
$944$	0.214498			0.00698131
$945$		0			0
$946$	0.889814			0.0289304
$947$	11.2007	+	4.07672i	0.363973	+	0.132475i	0.517532	−	0.855664i	$-0.326851\pi$
$947$	11.2007	+	4.07672i	0.363973	+	0.132475i	−0.153558	+	0.988140i	$0.549073\pi$
$948$		0			0
$949$	16.0346	+	13.4546i	0.520506	+	0.436756i
$950$	−5.51889	+	31.2992i	−0.179056	+	1.01548i
$951$		0			0
$952$	−14.2469	+	11.9546i	−0.461745	+	0.387450i
$953$	18.4145	+	31.8948i	0.596503	+	1.03317i	0.993333	+	0.115281i	$0.0367770\pi$
$953$	18.4145	+	31.8948i	0.596503	+	1.03317i	−0.396830	+	0.917892i	$0.629890\pi$
$954$		0			0
$955$	33.8974	−	58.7120i	1.09689	−	1.89988i
$956$	6.16695	+	34.9745i	0.199453	+	1.13116i
$957$		0			0
$958$	−12.7677	+	4.64706i	−0.412505	+	0.150140i
$959$	29.3854	−	10.6954i	0.948903	−	0.345372i
$960$		0			0
$961$	−0.715070	−	4.05537i	−0.0230668	−	0.130818i
$962$	−7.03849	+	12.1910i	−0.226930	+	0.393054i
$963$		0			0
$964$	13.6934	+	23.7177i	0.441035	+	0.763895i
$965$	−5.92056	+	4.96794i	−0.190590	+	0.159924i
$966$		0			0
$967$	9.30066	−	52.7467i	0.299089	−	1.69622i	−0.351012	−	0.936371i	$-0.614162\pi$
$967$	9.30066	−	52.7467i	0.299089	−	1.69622i	0.650101	−	0.759847i	$-0.274726\pi$
$968$	−23.8527	−	20.0148i	−0.766656	−	0.643301i
$969$		0			0
$970$	−12.5239	−	4.55834i	−0.402119	−	0.146359i
$971$	53.2327			1.70832			0.854159	−	0.520012i	$-0.174073\pi$
$971$	53.2327			1.70832			0.854159	+	0.520012i	$0.174073\pi$
$972$		0			0
$973$	−22.9299			−0.735100
$974$	24.3862	+	8.87587i	0.781386	+	0.284401i
$975$		0			0
$976$	0.121330	+	0.101808i	0.00388368	+	0.00325879i
$977$	2.33678	−	13.2525i	0.0747602	−	0.423986i	−0.924340	−	0.381570i	$-0.875383\pi$
$977$	2.33678	−	13.2525i	0.0747602	−	0.423986i	0.999100	−	0.0424160i	$-0.0135055\pi$
$978$		0			0
$979$	0.961266	−	0.806598i	0.0307222	−	0.0257790i
$980$	−5.29813	−	9.17664i	−0.169243	−	0.293137i
$981$		0			0
$982$	0.948615	−	1.64305i	0.0302715	−	0.0524318i
$983$	−1.77837	−	10.0856i	−0.0567212	−	0.321682i	0.943224	−	0.332158i	$-0.107777\pi$
$983$	−1.77837	−	10.0856i	−0.0567212	−	0.321682i	−0.999945	+	0.0104756i	$0.996665\pi$
$984$		0			0
$985$	−77.2559	+	28.1188i	−2.46158	+	0.895941i
$986$	16.6515	−	6.06066i	0.530292	−	0.193011i
$987$		0			0
$988$	−1.84730	−	10.4765i	−0.0587703	−	0.333303i
$989$	8.83409	−	15.3011i	0.280908	−	0.486547i
$990$		0			0
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	22.3935	−	18.7904i	0.710995	−	0.596596i
$993$		0			0
$994$	−5.11055	+	28.9834i	−0.162097	+	0.919296i
$995$	−9.16431	−	7.68977i	−0.290528	−	0.243782i
$996$		0			0
$997$	−36.1796	−	13.1683i	−1.14582	−	0.417045i	−0.301808	−	0.953369i	$-0.597590\pi$
$997$	−36.1796	−	13.1683i	−1.14582	−	0.417045i	−0.844012	+	0.536324i	$0.819813\pi$
$998$	−6.59121			−0.208641
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.i.568.1		6
3.2	odd	2		729.2.e.a.568.1		6
9.2	odd	6		729.2.e.h.82.1		6
9.4	even	3		729.2.e.b.325.1		6
9.5	odd	6		729.2.e.g.325.1		6
9.7	even	3		729.2.e.c.82.1		6
27.2	odd	18		729.2.e.g.406.1		6
27.4	even	9		243.2.c.e.82.3		6
27.5	odd	18		243.2.c.f.163.1		6
27.7	even	9	inner	729.2.e.i.163.1		6
27.11	odd	18		729.2.e.h.649.1		6
27.13	even	9		243.2.a.f.1.1	yes	3
27.14	odd	18		243.2.a.e.1.3	✓	3
27.16	even	9		729.2.e.c.649.1		6
27.20	odd	18		729.2.e.a.163.1		6
27.22	even	9		243.2.c.e.163.3		6
27.23	odd	18		243.2.c.f.82.1		6
27.25	even	9		729.2.e.b.406.1		6
108.67	odd	18		3888.2.a.bk.1.3		3
108.95	even	18		3888.2.a.bd.1.1		3
135.14	odd	18		6075.2.a.bv.1.1		3
135.94	even	18		6075.2.a.bq.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.3	✓	3	27.14	odd	18
243.2.a.f.1.1	yes	3	27.13	even	9
243.2.c.e.82.3		6	27.4	even	9
243.2.c.e.163.3		6	27.22	even	9
243.2.c.f.82.1		6	27.23	odd	18
243.2.c.f.163.1		6	27.5	odd	18
729.2.e.a.163.1		6	27.20	odd	18
729.2.e.a.568.1		6	3.2	odd	2
729.2.e.b.325.1		6	9.4	even	3
729.2.e.b.406.1		6	27.25	even	9
729.2.e.c.82.1		6	9.7	even	3
729.2.e.c.649.1		6	27.16	even	9
729.2.e.g.325.1		6	9.5	odd	6
729.2.e.g.406.1		6	27.2	odd	18
729.2.e.h.82.1		6	9.2	odd	6
729.2.e.h.649.1		6	27.11	odd	18
729.2.e.i.163.1		6	27.7	even	9	inner
729.2.e.i.568.1		6	1.1	even	1	trivial
3888.2.a.bd.1.1		3	108.95	even	18
3888.2.a.bk.1.3		3	108.67	odd	18
6075.2.a.bq.1.3		3	135.94	even	18
6075.2.a.bv.1.1		3	135.14	odd	18

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.826352 + 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(0.673648 - 3.82045i) q^{5} +(-1.67365 + 1.40436i) q^{7} +(-1.41875 - 2.45734i) q^{8} +O(q^{10})\)	\(q+(0.826352 + 0.300767i) q^{2} +(-0.939693 - 0.788496i) q^{4} +(0.673648 - 3.82045i) q^{5} +(-1.67365 + 1.40436i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(1.70574 - 2.95442i) q^{10} +(0.0282185 + 0.160035i) q^{11} +(-2.26604 + 0.824773i) q^{13} +(-1.80541 + 0.657115i) q^{14} +(-0.00727396 - 0.0412527i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.79813 - 3.11446i) q^{19} +(-3.64543 + 3.05888i) q^{20} +(-0.0248149 + 0.140732i) q^{22} +(2.17365 + 1.82391i) q^{23} +(-9.44356 - 3.43718i) q^{25} -2.12061 q^{26} +2.68004 q^{28} +(-6.31180 - 2.29731i) q^{29} +(-3.97178 - 3.33272i) q^{31} +(-0.979055 + 5.55250i) q^{32} +(-2.02094 + 1.69577i) q^{34} +(4.23783 + 7.34013i) q^{35} +(3.31908 - 5.74881i) q^{37} +(-0.549163 - 3.11446i) q^{38} +(-10.3439 + 3.76487i) q^{40} +(5.45084 - 1.98394i) q^{41} +(-1.08125 - 6.13208i) q^{43} +(0.0996702 - 0.172634i) q^{44} +(1.24763 + 2.16095i) q^{46} +(5.66637 - 4.75465i) q^{47} +(-0.386659 + 2.19285i) q^{49} +(-6.76991 - 5.68063i) q^{50} +(2.77972 + 1.01173i) q^{52} +1.40373 q^{53} +0.630415 q^{55} +(5.82547 + 2.12030i) q^{56} +(-4.52481 - 3.79677i) q^{58} +(-0.889185 + 5.04282i) q^{59} +(-2.89646 + 2.43042i) q^{61} +(-2.27972 - 3.94858i) q^{62} +(-2.52094 + 4.36640i) q^{64} +(1.62449 + 9.21291i) q^{65} +(5.51114 - 2.00589i) q^{67} +(3.45811 - 1.25865i) q^{68} +(1.29426 + 7.34013i) q^{70} +(7.65910 - 13.2660i) q^{71} +(-4.34002 - 7.51714i) q^{73} +(4.47178 - 3.75227i) q^{74} +(-0.766044 + 4.34445i) q^{76} +(-0.271974 - 0.228213i) q^{77} +(1.19207 + 0.433877i) q^{79} -0.162504 q^{80} +5.10101 q^{82} +(7.96451 + 2.89884i) q^{83} +(8.91534 + 7.48086i) q^{85} +(0.950837 - 5.39246i) q^{86} +(0.353226 - 0.296392i) q^{88} +(-3.86097 - 6.68739i) q^{89} +(2.63429 - 4.56272i) q^{91} +(-0.604418 - 3.42782i) q^{92} +(6.11246 - 2.22475i) q^{94} +(-13.1099 + 4.77163i) q^{95} +(-0.678396 - 3.84737i) q^{97} +(-0.979055 + 1.69577i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8	\( 6 q + 6 q^{2} + 3 q^{5} - 9 q^{7} - 6 q^{8} + 15 q^{11} - 9 q^{13} - 15 q^{14} - 18 q^{16} - 9 q^{17} + 3 q^{19} - 6 q^{20} + 27 q^{22} + 12 q^{23} - 27 q^{25} - 24 q^{26} - 24 q^{28} - 3 q^{29} - 9 q^{31} - 9 q^{32} - 9 q^{34} + 6 q^{35} + 3 q^{37} - 15 q^{38} - 18 q^{40} + 21 q^{41} - 9 q^{43} + 15 q^{44} - 9 q^{46} + 15 q^{47} - 9 q^{49} - 12 q^{50} - 9 q^{52} + 36 q^{53} + 18 q^{55} - 21 q^{56} + 3 q^{59} - 27 q^{61} + 12 q^{62} - 12 q^{64} - 3 q^{65} + 27 q^{67} + 27 q^{68} + 18 q^{70} + 9 q^{71} - 6 q^{73} + 12 q^{74} - 24 q^{77} + 18 q^{79} - 6 q^{80} + 36 q^{82} + 15 q^{83} + 9 q^{85} - 6 q^{86} + 27 q^{88} + 6 q^{91} - 51 q^{92} - 27 q^{94} - 30 q^{95} - 36 q^{97} - 9 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 3 * q^5 - 9 * q^7 - 6 * q^8 + 15 * q^11 - 9 * q^13 - 15 * q^14 - 18 * q^16 - 9 * q^17 + 3 * q^19 - 6 * q^20 + 27 * q^22 + 12 * q^23 - 27 * q^25 - 24 * q^26 - 24 * q^28 - 3 * q^29 - 9 * q^31 - 9 * q^32 - 9 * q^34 + 6 * q^35 + 3 * q^37 - 15 * q^38 - 18 * q^40 + 21 * q^41 - 9 * q^43 + 15 * q^44 - 9 * q^46 + 15 * q^47 - 9 * q^49 - 12 * q^50 - 9 * q^52 + 36 * q^53 + 18 * q^55 - 21 * q^56 + 3 * q^59 - 27 * q^61 + 12 * q^62 - 12 * q^64 - 3 * q^65 + 27 * q^67 + 27 * q^68 + 18 * q^70 + 9 * q^71 - 6 * q^73 + 12 * q^74 - 24 * q^77 + 18 * q^79 - 6 * q^80 + 36 * q^82 + 15 * q^83 + 9 * q^85 - 6 * q^86 + 27 * q^88 + 6 * q^91 - 51 * q^92 - 27 * q^94 - 30 * q^95 - 36 * q^97 - 9 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more