LMFDB - Embedded newform 729.2.e.a.163.1

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:	$1$
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			163.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.a.568.1

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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	$-0.711745\pi$
$2$	−0.826352	+	0.300767i	−0.584319	+	0.212675i	0.0329100	+	0.999458i	$0.489523\pi$
$3$		0			0
$3$		0			0
$4$	−0.939693	+	0.788496i	−0.469846	+	0.394248i
$5$	−0.673648	−	3.82045i	−0.301265	−	1.70856i	−0.640586	−	0.767886i	$-0.721309\pi$
$5$	−0.673648	−	3.82045i	−0.301265	−	1.70856i	0.339322	−	0.940670i	$-0.389802\pi$
$6$		0			0
$7$	−1.67365	−	1.40436i	−0.632580	−	0.530797i	0.269150	−	0.963098i	$-0.413257\pi$
$7$	−1.67365	−	1.40436i	−0.632580	−	0.530797i	−0.901729	+	0.432301i	$0.857702\pi$
$8$	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	$-0.952243\pi$
$11$	−0.0282185	+	0.160035i	−0.00850820	+	0.0482524i	0.980258	+	0.197722i	$0.0633544\pi$
$12$		0			0
$13$	−2.26604	−	0.824773i	−0.628488	−	0.228751i	0.00808527	−	0.999967i	$-0.497426\pi$
$13$	−2.26604	−	0.824773i	−0.628488	−	0.228751i	−0.636573	+	0.771217i	$0.719649\pi$
$14$	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	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−1.79813	+	3.11446i	−0.412520	+	0.714506i	−0.995165	−	0.0982214i	$-0.968685\pi$
$19$	−1.79813	+	3.11446i	−0.412520	+	0.714506i	0.582645	+	0.812727i	$0.302018\pi$
$20$	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	$-0.817818\pi$
$23$	−2.17365	+	1.82391i	−0.453237	+	0.380311i	0.387398	+	0.921912i	$0.373374\pi$
$24$		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	$-0.396761\pi$
$29$	6.31180	−	2.29731i	1.17207	−	0.426600i	0.853396	+	0.521264i	$0.174539\pi$
$30$		0			0
$31$	−3.97178	+	3.33272i	−0.713353	+	0.598574i	−0.925538	−	0.378655i	$-0.876387\pi$
$31$	−3.97178	+	3.33272i	−0.713353	+	0.598574i	0.212185	+	0.977230i	$0.431942\pi$
$32$	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	0.998566	+	0.0535438i	$0.0170517\pi$
$37$	3.31908	+	5.74881i	0.545653	+	0.945099i	−0.452912	+	0.891555i	$0.649615\pi$
$38$	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	$-0.538519\pi$
$41$	−5.45084	−	1.98394i	−0.851278	−	0.309840i	−0.730561	+	0.682847i	$0.760741\pi$
$42$		0			0
$43$	−1.08125	+	6.13208i	−0.164889	+	0.935134i	0.784289	+	0.620396i	$0.213028\pi$
$43$	−1.08125	+	6.13208i	−0.164889	+	0.935134i	−0.949178	+	0.314739i	$0.898083\pi$
$44$	−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	$-0.459156\pi$
$47$	−5.66637	−	4.75465i	−0.826526	−	0.693537i	−0.954490	+	0.298241i	$0.903600\pi$
$48$		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	$-0.530736\pi$
$53$	−1.40373			−0.192818			−0.0964088	+	0.995342i	$0.530736\pi$
$54$		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	0.986370	+	0.164542i	$0.0526146\pi$
$59$	0.889185	+	5.04282i	0.115762	+	0.656519i	−0.870608	+	0.491977i	$0.836274\pi$
$60$		0			0
$61$	−2.89646	−	2.43042i	−0.370854	−	0.311183i	0.438246	−	0.898855i	$-0.355600\pi$
$61$	−2.89646	−	2.43042i	−0.370854	−	0.311183i	−0.809099	+	0.587672i	$0.800044\pi$
$62$	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	0.655965	−	0.754791i	$-0.272262\pi$
$67$	5.51114	+	2.00589i	0.673293	+	0.245059i	0.0173282	+	0.999850i	$0.494484\pi$
$68$	−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	−0.815500	−	0.578756i	$-0.803538\pi$
$71$	−7.65910	−	13.2660i	−0.908968	−	1.57438i	−0.0934675	−	0.995622i	$-0.529795\pi$
$72$		0			0
$73$	−4.34002	+	7.51714i	−0.507961	+	0.879815i	0.491996	+	0.870597i	$0.336267\pi$
$73$	−4.34002	+	7.51714i	−0.507961	+	0.879815i	−0.999958	+	0.00921733i	$0.997066\pi$
$74$	−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	−0.274089	−	0.961704i	$-0.588376\pi$
$79$	1.19207	−	0.433877i	0.134118	−	0.0488149i	0.408207	+	0.912889i	$0.366154\pi$
$80$	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	$-0.765115\pi$
$83$	−7.96451	+	2.89884i	−0.874218	+	0.318189i	−0.134344	+	0.990935i	$0.542893\pi$
$84$		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	$-0.699120\pi$
$89$	3.86097	−	6.68739i	0.409262	−	0.708862i	0.994807	+	0.101778i	$0.0324530\pi$
$90$		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	0.930804	+	0.365519i	$0.119109\pi$
$97$	−0.678396	+	3.84737i	−0.0688807	+	0.390642i	−0.999684	+	0.0251223i	$0.992002\pi$
$98$	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	$-0.145510\pi$
$101$	6.21554	+	5.21546i	0.618469	+	0.518957i	−0.278853	+	0.960334i	$0.589954\pi$
$102$		0			0
$103$	3.23783	+	18.3626i	0.319032	+	1.80932i	0.548661	+	0.836045i	$0.315138\pi$
$103$	3.23783	+	18.3626i	0.319032	+	1.80932i	−0.229629	+	0.973278i	$0.573751\pi$
$104$	−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	$-0.619676\pi$
$107$	−7.59627			−0.734359			−0.367179	+	0.930150i	$0.619676\pi$
$108$		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	$-0.0208543\pi$
$113$	0.401674	+	2.27801i	0.0377863	+	0.214297i	−0.960068	+	0.279766i	$0.909743\pi$
$114$		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	−0.866953	−	0.498390i	$-0.833925\pi$
$127$	−0.0209445	+	0.0362770i	−0.00185853	+	0.00321906i	0.865095	+	0.501609i	$0.167258\pi$
$128$	−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	−0.229676	+	0.973267i	$0.573767\pi$
$131$	−14.0556	+	11.7940i	−1.22804	+	1.03045i	−0.998364	+	0.0571807i	$0.981789\pi$
$132$		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	$-0.401707\pi$
$137$	13.4500	−	4.89538i	1.14911	−	0.418241i	0.845195	+	0.534459i	$0.179485\pi$
$138$		0			0
$139$	8.03983	−	6.74622i	0.681929	−	0.572207i	−0.234640	−	0.972082i	$-0.575391\pi$
$139$	8.03983	−	6.74622i	0.681929	−	0.572207i	0.916569	+	0.399876i	$0.130947\pi$
$140$	−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	$-0.405472\pi$
$149$	−1.19459	−	0.434796i	−0.0978648	−	0.0356199i	−0.390489	+	0.920608i	$0.627694\pi$
$150$		0			0
$151$	1.36437	−	7.73773i	0.111031	−	0.629688i	−0.877608	−	0.479379i	$-0.840862\pi$
$151$	1.36437	−	7.73773i	0.111031	−	0.629688i	0.988639	−	0.150309i	$-0.0480268\pi$
$152$	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	−0.942454	−	0.334336i	$-0.891488\pi$
$157$	−2.14496	−	12.1647i	−0.171187	−	0.970848i	0.771267	−	0.636512i	$-0.219623\pi$
$158$	−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	$-0.00961999\pi$
$167$	0.645430	+	3.66041i	0.0499448	+	0.283251i	−0.949598	+	0.313469i	$0.898509\pi$
$168$		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	$-0.925564\pi$
$173$	0.270792	−	1.53574i	0.0205879	−	0.116760i	0.993370	+	0.114963i	$0.0366749\pi$
$174$		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	$-0.317262\pi$
$179$	−6.09627	−	10.5590i	−0.455656	−	0.789220i	−0.998726	+	0.0504679i	$0.983929\pi$
$180$		0			0
$181$	8.43629	−	14.6121i	0.627064	−	1.08611i	−0.361073	−	0.932537i	$-0.617590\pi$
$181$	8.43629	−	14.6121i	0.627064	−	1.08611i	0.988138	−	0.153570i	$-0.0490771\pi$
$182$	−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	$-0.828978\pi$
$191$	−16.4217	+	5.97702i	−1.18824	+	0.432482i	−0.329132	+	0.944284i	$0.606756\pi$
$192$		0			0
$193$	−1.52616	+	1.28060i	−0.109855	+	0.0921796i	−0.696061	−	0.717983i	$-0.745066\pi$
$193$	−1.52616	+	1.28060i	−0.109855	+	0.0921796i	0.586205	+	0.810162i	$0.300621\pi$
$194$	−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	−0.190445	−	0.981698i	$-0.560993\pi$
$197$	10.5963	−	18.3533i	0.754953	−	1.30762i	0.945398	−	0.325919i	$-0.105674\pi$
$198$		0			0
$199$	1.54189	+	2.67063i	0.109302	+	0.189316i	0.915488	−	0.402346i	$-0.131805\pi$
$199$	1.54189	+	2.67063i	0.109302	+	0.189316i	−0.806186	+	0.591662i	$0.798472\pi$
$200$	−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	0.990239	−	0.139383i	$-0.0445118\pi$
$211$	0.174992	+	0.992431i	0.0120470	+	0.0683218i	−0.978192	+	0.207705i	$0.933401\pi$
$212$	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	0.977225	−	0.212205i	$-0.0680644\pi$
$223$	14.0064	+	11.7528i	0.937938	+	0.787023i	−0.0392875	+	0.999228i	$0.512509\pi$
$224$	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	$-0.916468\pi$
$227$	0.459293	−	2.60478i	0.0304843	−	0.172885i	0.996249	+	0.0865353i	$0.0275795\pi$
$228$		0			0
$229$	3.25402	+	1.18437i	0.215032	+	0.0782652i	0.447290	−	0.894389i	$-0.352389\pi$
$229$	3.25402	+	1.18437i	0.215032	+	0.0782652i	−0.232258	+	0.972654i	$0.574611\pi$
$230$	−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	$-0.102360\pi$
$233$	3.06283	+	5.30498i	0.200653	+	0.347541i	−0.748086	+	0.663602i	$0.769027\pi$
$234$		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	0.491629	−	0.870805i	$-0.336402\pi$
$239$	22.1780	−	18.6095i	1.43457	−	1.20375i	0.942946	−	0.332946i	$-0.108043\pi$
$240$		0			0
$241$	−20.9795	+	7.63592i	−1.35141	+	0.491873i	−0.913388	−	0.407091i	$-0.866543\pi$
$241$	−20.9795	+	7.63592i	−1.35141	+	0.491873i	−0.438022	+	0.898964i	$0.644321\pi$
$242$	−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	0.245047	+	0.969511i	$0.421197\pi$
$251$	−11.3610	+	19.6778i	−0.717098	+	1.24205i	−0.962145	+	0.272539i	$0.912137\pi$
$252$		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	$-0.598113\pi$
$257$	−18.4081	−	6.69999i	−1.14826	−	0.417934i	−0.844891	+	0.534938i	$0.820335\pi$
$258$		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	$-0.462700\pi$
$263$	−13.6361	−	11.4420i	−0.840838	−	0.705547i	−0.957752	+	0.287595i	$0.907144\pi$
$264$		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	$-0.744476\pi$
$269$	−22.7888			−1.38946			−0.694729	+	0.719272i	$0.744476\pi$
$270$		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	0.580657	−	0.814148i	$-0.302796\pi$
$277$	−2.00206	−	1.67993i	−0.120292	−	0.100937i	−0.700949	+	0.713211i	$0.747240\pi$
$278$	−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	−0.828145	−	0.560514i	$-0.810604\pi$
$281$	2.37639	−	13.4772i	0.141764	−	0.803982i	0.969909	−	0.243468i	$-0.0782851\pi$
$282$		0			0
$283$	−21.5005	−	7.82553i	−1.27807	−	0.465179i	−0.388277	−	0.921543i	$-0.626929\pi$
$283$	−21.5005	−	7.82553i	−1.27807	−	0.465179i	−0.889793	+	0.456363i	$0.849152\pi$
$284$	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	$-0.973196\pi$
$293$	−18.6006	+	15.6078i	−1.08666	+	0.911815i	−0.0902023	+	0.995923i	$0.528751\pi$
$294$		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	0.999003	−	0.0446505i	$-0.0142174\pi$
$307$	8.07444	+	13.9853i	0.460833	+	0.798186i	−0.538170	+	0.842836i	$0.680884\pi$
$308$	−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	$-0.210902\pi$
$311$	17.5817	+	6.39922i	0.996968	+	0.362867i	0.208553	+	0.978011i	$0.433125\pi$
$312$		0			0
$313$	0.481582	−	2.73119i	0.0272206	−	0.154376i	−0.968168	−	0.250302i	$-0.919470\pi$
$313$	0.481582	−	2.73119i	0.0272206	−	0.154376i	0.995388	+	0.0959261i	$0.0305813\pi$
$314$	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	$-0.441130\pi$
$317$	−13.3923	−	11.2375i	−0.752189	−	0.631161i	−0.936081	+	0.351785i	$0.885575\pi$
$318$		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	−0.973842	−	0.227224i	$-0.927035\pi$
$331$	−24.8653	−	20.8645i	−1.36672	−	1.14681i	−0.392878	−	0.919590i	$-0.628521\pi$
$332$	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	0.121128	−	0.992637i	$-0.461349\pi$
$337$	−7.78611	−	2.83391i	−0.424137	−	0.154373i	−0.545265	+	0.838264i	$0.683571\pi$
$338$	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	$-0.853779\pi$
$347$	−11.4624	+	9.61814i	−0.615336	+	0.516329i	0.280997	+	0.959709i	$0.409335\pi$
$348$		0			0
$349$	−31.6168	+	11.5076i	−1.69241	+	0.615986i	−0.994925	−	0.100615i	$-0.967919\pi$
$349$	−31.6168	+	11.5076i	−1.69241	+	0.615986i	−0.697483	+	0.716601i	$0.745697\pi$
$350$	−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	$-0.748816\pi$
$353$	−14.8037	+	5.38809i	−0.787919	+	0.286779i	−0.0834482	+	0.996512i	$0.526593\pi$
$354$		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	$-0.674580\pi$
$359$	9.06283	−	15.6973i	0.478318	−	0.828471i	0.999691	+	0.0248577i	$0.00791328\pi$
$360$		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	0.766322	+	0.642457i	$0.222085\pi$
$367$	−3.32413	+	18.8521i	−0.173518	+	0.984071i	−0.939840	+	0.341614i	$0.889026\pi$
$368$	−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	−0.973364	−	0.229265i	$-0.926368\pi$
$373$	−2.64812	−	15.0182i	−0.137114	−	0.777614i	0.836250	−	0.548349i	$-0.184743\pi$
$374$	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	−0.803892	−	0.594775i	$-0.797241\pi$
$383$	−4.92989	−	27.9588i	−0.251906	−	1.42863i	0.551986	−	0.833853i	$-0.313870\pi$
$384$		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	0.898660	+	0.438646i	$0.144542\pi$
$389$	−1.89006	+	10.7191i	−0.0958300	+	0.543479i	−0.994490	+	0.104833i	$0.966569\pi$
$390$		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	−0.544270	−	0.838910i	$-0.683193\pi$
$397$	9.05350	−	15.6811i	0.454382	−	0.787013i	0.998652	+	0.0518969i	$0.0165267\pi$
$398$	−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	$-0.733620\pi$
$401$	−1.09833	+	0.921605i	−0.0548478	+	0.0460228i	0.614952	+	0.788565i	$0.289176\pi$
$402$		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	−0.465123	−	0.885246i	$-0.653990\pi$
$409$	6.59105	−	5.53055i	0.325907	−	0.273468i	0.791029	+	0.611778i	$0.209545\pi$
$410$	−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	$-0.486118\pi$
$419$	−11.5689	−	4.21074i	−0.565179	−	0.205708i	−0.608778	+	0.793341i	$0.708340\pi$
$420$		0			0
$421$	1.93036	−	10.9476i	0.0940800	−	0.533554i	−0.900945	−	0.433932i	$-0.857126\pi$
$421$	1.93036	−	10.9476i	0.0940800	−	0.533554i	0.995025	−	0.0996216i	$-0.0317632\pi$
$422$	−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	$-0.151676\pi$
$431$	36.8958			1.77721			0.888604	+	0.458675i	$0.151676\pi$
$432$		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	0.646473	−	0.762937i	$-0.276243\pi$
$439$	0.154763	+	0.129862i	0.00738644	+	0.00619796i	−0.639087	+	0.769135i	$0.720688\pi$
$440$	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	0.762825	+	0.646605i	$0.223812\pi$
$443$	−3.68644	+	20.9068i	−0.175148	+	0.993314i	−0.937973	+	0.346709i	$0.887299\pi$
$444$		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	−0.929116	−	0.369788i	$-0.879430\pi$
$449$	−16.6297	−	28.8035i	−0.784804	−	1.35932i	0.144312	−	0.989532i	$-0.453903\pi$
$450$		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	−0.341270	−	0.939965i	$-0.610857\pi$
$457$	0.0320889	−	0.0116794i	0.00150105	−	0.000546339i	0.342771	+	0.939419i	$0.388635\pi$
$458$	−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	$-0.724587\pi$
$461$	−14.0826	+	5.12565i	−0.655892	+	0.238725i	−0.00743018	+	0.999972i	$0.502365\pi$
$462$		0			0
$463$	−23.3203	+	19.5680i	−1.08378	+	0.909403i	−0.996230	−	0.0867566i	$-0.972350\pi$
$463$	−23.3203	+	19.5680i	−1.08378	+	0.909403i	−0.0875549	+	0.996160i	$0.527905\pi$
$464$	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	$-0.837095\pi$
$467$	−0.255367	+	0.442308i	−0.0118170	+	0.0204676i	0.860056	+	0.510199i	$0.170428\pi$
$468$		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	$-0.162946\pi$
$479$	11.8359	+	9.93150i	0.540796	+	0.453782i	−0.331014	+	0.943626i	$0.607391\pi$
$480$		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	$-0.0710577\pi$
$491$	−0.374638	−	2.12467i	−0.0169072	−	0.0958852i	−0.992094	+	0.125500i	$0.959947\pi$
$492$		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	0.179523	−	0.983754i	$-0.442544\pi$
$499$	−7.04323	−	2.56353i	−0.315298	−	0.114759i	−0.494822	+	0.868994i	$0.664767\pi$
$500$	−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	0.985975	+	0.166894i	$0.0533739\pi$
$503$	14.2981	+	24.7651i	0.637522	+	1.10422i	−0.348453	+	0.937326i	$0.613293\pi$
$504$		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	$-0.710284\pi$
$509$	1.29607	−	1.08754i	0.0574475	−	0.0482041i	0.671059	+	0.741404i	$0.265840\pi$
$510$		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	$-0.996615\pi$
$521$	−11.2019	+	19.4022i	−0.490763	+	0.850026i	0.509181	+	0.860660i	$0.329948\pi$
$522$		0			0
$523$	−1.21436	−	2.10332i	−0.0531000	−	0.0919720i	0.838254	−	0.545281i	$-0.183577\pi$
$523$	−1.21436	−	2.10332i	−0.0531000	−	0.0919720i	−0.891354	+	0.453309i	$0.850244\pi$
$524$	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	0.370061	−	0.929007i	$-0.379337\pi$
$547$	−11.2396	−	9.43118i	−0.480572	−	0.403248i	−0.850633	+	0.525759i	$0.823781\pi$
$548$	−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	$-0.242277\pi$
$557$	−5.55350	−	9.61894i	−0.235309	−	0.407568i	−0.959363	+	0.282176i	$0.908944\pi$
$558$		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	$-0.833886\pi$
$563$	−12.4927	+	10.4826i	−0.526506	+	0.441791i	0.340387	+	0.940285i	$0.389442\pi$
$564$		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	$-0.338775\pi$
$569$	33.8444	−	12.3183i	1.41883	−	0.516412i	0.933708	+	0.358035i	$0.116553\pi$
$570$		0			0
$571$	29.9971	−	25.1705i	1.25534	−	1.05335i	0.259176	−	0.965830i	$-0.416549\pi$
$571$	29.9971	−	25.1705i	1.25534	−	1.05335i	0.996162	−	0.0875234i	$-0.0278953\pi$
$572$	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	0.716600	−	0.697484i	$-0.245697\pi$
$577$	−5.90286	−	10.2240i	−0.245739	−	0.425633i	−0.962339	+	0.271852i	$0.912364\pi$
$578$	−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	0.995300	+	0.0968406i	$0.0308737\pi$
$587$	30.6122	+	25.6867i	1.26350	+	1.06020i	0.268201	+	0.963363i	$0.413571\pi$
$588$		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	$-0.294533\pi$
$593$	29.2995			1.20319			0.601594	+	0.798802i	$0.294533\pi$
$594$		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	−0.999465	−	0.0327053i	$-0.989588\pi$
$599$	−1.74897	−	9.91890i	−0.0714610	−	0.405275i	0.928004	−	0.372570i	$-0.121523\pi$
$600$		0			0
$601$	−23.3025	−	19.5531i	−0.950528	−	0.797587i	0.0288587	−	0.999584i	$-0.490813\pi$
$601$	−23.3025	−	19.5531i	−0.950528	−	0.797587i	−0.979386	+	0.201996i	$0.935257\pi$
$602$	−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	0.742240	−	0.670134i	$-0.233763\pi$
$607$	21.6827	+	7.89187i	0.880075	+	0.320321i	0.137835	+	0.990455i	$0.455986\pi$
$608$	−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	−0.873652	−	0.486551i	$-0.838255\pi$
$613$	−0.382789	+	0.663010i	−0.0154607	+	0.0267787i	0.858192	+	0.513330i	$0.171588\pi$
$614$	−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	$-0.662357\pi$
$617$	7.11515	−	5.97032i	0.286445	−	0.240356i	0.774676	+	0.632359i	$0.217913\pi$
$618$		0			0
$619$	32.9666	−	11.9989i	1.32504	−	0.482275i	0.419970	−	0.907538i	$-0.362040\pi$
$619$	32.9666	−	11.9989i	1.32504	−	0.482275i	0.905070	+	0.425263i	$0.139818\pi$
$620$	−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	−0.964168	−	0.265291i	$-0.914532\pi$
$631$	−17.8810	−	30.9709i	−0.711833	−	1.23293i	0.252336	−	0.967640i	$-0.418801\pi$
$632$	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	$-0.296184\pi$
$641$	−2.24170	−	1.88101i	−0.0885417	−	0.0742953i	−0.685984	+	0.727616i	$0.740628\pi$
$642$		0			0
$643$	−3.51666	−	19.9440i	−0.138684	−	0.786514i	−0.972223	−	0.234055i	$-0.924801\pi$
$643$	−3.51666	−	19.9440i	−0.138684	−	0.786514i	0.833540	−	0.552459i	$-0.186311\pi$
$644$	−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	$-0.567594\pi$
$647$	−10.7219			−0.421523			−0.210761	+	0.977538i	$0.567594\pi$
$648$		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	−0.825596	−	0.564262i	$-0.809161\pi$
$653$	−6.20393	−	35.1842i	−0.242778	−	1.37686i	0.582818	−	0.812603i	$-0.301950\pi$
$654$		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	0.682580	+	0.730811i	$0.260858\pi$
$659$	−5.35978	+	30.3969i	−0.208788	+	1.18409i	−0.891367	+	0.453282i	$0.850253\pi$
$660$		0			0
$661$	9.25402	+	3.36819i	0.359940	+	0.131007i	0.515659	−	0.856794i	$-0.327547\pi$
$661$	9.25402	+	3.36819i	0.359940	+	0.131007i	−0.155719	+	0.987801i	$0.549769\pi$
$662$	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	0.0403273	−	0.999187i	$-0.487160\pi$
$673$	18.5094	−	6.73687i	0.713485	−	0.259687i	0.673157	+	0.739499i	$0.264938\pi$
$674$	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	$-0.795283\pi$
$677$	−26.7408	+	9.73286i	−1.02773	+	0.374064i	−0.227516	+	0.973774i	$0.573060\pi$
$678$		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	$-0.756397\pi$
$683$	6.25537	−	10.8346i	0.239355	−	0.414575i	0.960529	+	0.278179i	$0.0897307\pi$
$684$		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	−0.435676	−	0.900104i	$-0.643491\pi$
$691$	7.40184	−	41.9779i	0.281579	−	1.59691i	0.717255	−	0.696811i	$-0.245398\pi$
$692$	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	$-0.932599\pi$
$701$	−51.7701			−1.95533			−0.977665	+	0.210167i	$0.932599\pi$
$702$		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	0.834247	−	0.551391i	$-0.185903\pi$
$709$	11.6120	+	9.74362i	0.436098	+	0.365929i	−0.398149	+	0.917321i	$0.630347\pi$
$710$	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	$-0.182194\pi$
$719$	−1.30747	−	2.26460i	−0.0487603	−	0.0844553i	−0.889375	+	0.457178i	$0.848860\pi$
$720$		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	−0.269598	−	0.962973i	$-0.586891\pi$
$727$	3.85204	−	1.40203i	0.142864	−	0.0519984i	0.412463	+	0.910974i	$0.364669\pi$
$728$	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	−0.996010	−	0.0892443i	$-0.971555\pi$
$733$	−29.2690	+	24.5596i	−1.08108	+	0.907131i	−0.0850668	+	0.996375i	$0.527110\pi$
$734$	−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	0.998072	−	0.0620725i	$-0.0197710\pi$
$739$	12.1047	+	20.9660i	0.445279	+	0.771247i	−0.552792	+	0.833319i	$0.686438\pi$
$740$	−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	$-0.408235\pi$
$743$	−3.11169	−	1.13256i	−0.114157	−	0.0415497i	−0.398467	+	0.917183i	$0.630458\pi$
$744$		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	0.996935	+	0.0782335i	$0.0249280\pi$
$751$	2.38089	+	13.5027i	0.0868800	+	0.492721i	−0.910055	+	0.414487i	$0.863961\pi$
$752$	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	$-0.0994415\pi$
$761$	−1.31671	−	7.46745i	−0.0477308	−	0.270695i	−0.999328	+	0.0366529i	$0.988330\pi$
$762$		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	0.286935	−	0.957950i	$-0.407364\pi$
$769$	−3.02317	−	1.10034i	−0.109018	−	0.0396794i	−0.395953	+	0.918271i	$0.629586\pi$
$770$	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	$-0.167723\pi$
$773$	−0.0922341	−	0.159754i	−0.00331743	−	0.00574596i	−0.867679	+	0.497124i	$0.834389\pi$
$774$		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	−0.649291	−	0.760540i	$-0.724934\pi$
$787$	−0.366181	+	0.307263i	−0.0130530	+	0.0109527i	0.636238	+	0.771493i	$0.280490\pi$
$788$	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	$-0.306225\pi$
$797$	13.6245	+	4.95891i	0.482604	+	0.175653i	−0.0892494	+	0.996009i	$0.528447\pi$
$798$		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	$-0.415790\pi$
$809$	14.8743			0.522954			0.261477	+	0.965210i	$0.415790\pi$
$810$		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	$-0.926208\pi$
$821$	0.569803	−	3.23151i	0.0198863	−	0.112781i	0.993135	+	0.116973i	$0.0373191\pi$
$822$		0			0
$823$	−12.9033	−	4.69643i	−0.449782	−	0.163707i	0.107190	−	0.994239i	$-0.465815\pi$
$823$	−12.9033	−	4.69643i	−0.449782	−	0.163707i	−0.556972	+	0.830531i	$0.688037\pi$
$824$	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	$-0.0522434\pi$
$827$	10.1163	+	17.5220i	0.351779	+	0.609300i	−0.634782	+	0.772691i	$0.718910\pi$
$828$		0			0
$829$	−12.7638	+	22.1076i	−0.443306	+	0.767828i	−0.997932	−	0.0642710i	$-0.979528\pi$
$829$	−12.7638	+	22.1076i	−0.443306	+	0.767828i	0.554627	+	0.832099i	$0.312861\pi$
$830$	−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	$-0.514120\pi$
$839$	16.3319	−	5.94431i	0.563839	−	0.205221i	0.608184	+	0.793796i	$0.291898\pi$
$840$		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	−0.919383	−	0.393363i	$-0.871311\pi$
$853$	2.30999	−	13.1006i	0.0790927	−	0.448557i	0.998476	−	0.0551932i	$-0.0175775\pi$
$854$	−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	$-0.167266\pi$
$857$	15.2606	+	12.8051i	0.521292	+	0.437416i	−0.343790	+	0.939046i	$0.611711\pi$
$858$		0			0
$859$	4.57469	+	25.9444i	0.156087	+	0.885211i	0.957786	+	0.287483i	$0.0928185\pi$
$859$	4.57469	+	25.9444i	0.156087	+	0.885211i	−0.801699	+	0.597728i	$0.796070\pi$
$860$	−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	$-0.726013\pi$
$863$	−38.2995			−1.30373			−0.651866	+	0.758334i	$0.726013\pi$
$864$		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	0.733526	−	0.679661i	$-0.237873\pi$
$877$	25.4256	+	9.25417i	0.858562	+	0.312491i	0.125036	+	0.992152i	$0.460095\pi$
$878$	−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	0.999847	+	0.0175162i	$0.00557586\pi$
$881$	15.2888	+	26.4810i	0.515093	+	0.892167i	−0.484754	+	0.874651i	$0.661091\pi$
$882$		0			0
$883$	−22.0526	+	38.1963i	−0.742130	+	1.28541i	0.209394	+	0.977831i	$0.432851\pi$
$883$	−22.0526	+	38.1963i	−0.742130	+	1.28541i	−0.951524	+	0.307575i	$0.900482\pi$
$884$	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	$-0.679965\pi$
$887$	6.03983	−	5.06802i	0.202798	−	0.170167i	0.738530	+	0.674220i	$0.235520\pi$
$888$		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	0.924723	+	0.380640i	$0.124296\pi$
$907$	−2.24123	+	12.7106i	−0.0744188	+	0.422050i	−0.999142	+	0.0414103i	$0.986815\pi$
$908$	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	$-0.391922\pi$
$911$	−16.2292	−	13.6179i	−0.537698	−	0.451182i	−0.870750	+	0.491727i	$0.836366\pi$
$912$		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	$-0.932292\pi$
$929$	0.404038	−	2.29141i	0.0132561	−	0.0751788i	0.990718	+	0.135932i	$0.0434029\pi$
$930$		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	−0.762112	−	0.647446i	$-0.775837\pi$
$937$	5.49912	−	9.52476i	0.179649	−	0.311160i	0.941760	+	0.336285i	$0.109171\pi$
$938$	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	$-0.593701\pi$
$941$	18.4645	−	15.4936i	0.601926	−	0.505076i	0.892064	+	0.451909i	$0.149257\pi$
$942$		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	$-0.673149\pi$
$947$	−11.2007	+	4.07672i	−0.363973	+	0.132475i	0.153558	+	0.988140i	$0.450927\pi$
$948$		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	0.396830	+	0.917892i	$0.370110\pi$
$953$	−18.4145	+	31.8948i	−0.596503	+	1.03317i	−0.993333	+	0.115281i	$0.963223\pi$
$954$		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	0.650101	+	0.759847i	$0.274726\pi$
$967$	9.30066	+	52.7467i	0.299089	+	1.69622i	−0.351012	+	0.936371i	$0.614162\pi$
$968$	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	$-0.825927\pi$
$971$	−53.2327			−1.70832			−0.854159	+	0.520012i	$0.825927\pi$
$972$		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	−0.999100	−	0.0424160i	$-0.986495\pi$
$977$	−2.33678	−	13.2525i	−0.0747602	−	0.423986i	0.924340	−	0.381570i	$-0.124617\pi$
$978$		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	$-0.892223\pi$
$983$	1.77837	−	10.0856i	0.0567212	−	0.321682i	0.999945	+	0.0104756i	$0.00333453\pi$
$984$		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	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$	−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	−0.844012	−	0.536324i	$-0.819813\pi$
$997$	−36.1796	+	13.1683i	−1.14582	+	0.417045i	−0.301808	+	0.953369i	$0.597590\pi$
$998$	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.a.163.1		6
3.2	odd	2		729.2.e.i.163.1		6
9.2	odd	6		729.2.e.b.406.1		6
9.4	even	3		729.2.e.h.649.1		6
9.5	odd	6		729.2.e.c.649.1		6
9.7	even	3		729.2.e.g.406.1		6
27.2	odd	18		243.2.a.f.1.1	yes	3
27.4	even	9	inner	729.2.e.a.568.1		6
27.5	odd	18		729.2.e.c.82.1		6
27.7	even	9		243.2.c.f.163.1		6
27.11	odd	18		243.2.c.e.82.3		6
27.13	even	9		729.2.e.g.325.1		6
27.14	odd	18		729.2.e.b.325.1		6
27.16	even	9		243.2.c.f.82.1		6
27.20	odd	18		243.2.c.e.163.3		6
27.22	even	9		729.2.e.h.82.1		6
27.23	odd	18		729.2.e.i.568.1		6
27.25	even	9		243.2.a.e.1.3	✓	3
108.79	odd	18		3888.2.a.bd.1.1		3
108.83	even	18		3888.2.a.bk.1.3		3
135.29	odd	18		6075.2.a.bq.1.3		3
135.79	even	18		6075.2.a.bv.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.3	✓	3	27.25	even	9
243.2.a.f.1.1	yes	3	27.2	odd	18
243.2.c.e.82.3		6	27.11	odd	18
243.2.c.e.163.3		6	27.20	odd	18
243.2.c.f.82.1		6	27.16	even	9
243.2.c.f.163.1		6	27.7	even	9
729.2.e.a.163.1		6	1.1	even	1	trivial
729.2.e.a.568.1		6	27.4	even	9	inner
729.2.e.b.325.1		6	27.14	odd	18
729.2.e.b.406.1		6	9.2	odd	6
729.2.e.c.82.1		6	27.5	odd	18
729.2.e.c.649.1		6	9.5	odd	6
729.2.e.g.325.1		6	27.13	even	9
729.2.e.g.406.1		6	9.7	even	3
729.2.e.h.82.1		6	27.22	even	9
729.2.e.h.649.1		6	9.4	even	3
729.2.e.i.163.1		6	3.2	odd	2
729.2.e.i.568.1		6	27.23	odd	18
3888.2.a.bd.1.1		3	108.79	odd	18
3888.2.a.bk.1.3		3	108.83	even	18
6075.2.a.bq.1.3		3	135.29	odd	18
6075.2.a.bv.1.1		3	135.79	even	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