LMFDB - Embedded newform 486.2.e.e.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [486,2,Mod(55,486)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("486.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(486, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 - 1.80139i$ of defining polynomial
Character	$\chi$	$=$	486.55
Dual form			486.2.e.e.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.362580 - 2.05630i) q^{5} +(-3.07353 - 2.57900i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.04401 - 1.80828i) q^{10} +(-0.0368910 + 0.209219i) q^{11} +(-4.88549 - 1.77817i) q^{13} +(-3.77024 - 1.37225i) q^{14} +(0.173648 - 0.984808i) q^{16} +(1.89276 + 3.27836i) q^{17} +(0.636405 - 1.10229i) q^{19} +(-1.59951 - 1.34215i) q^{20} +(0.0368910 + 0.209219i) q^{22} +(-0.635390 + 0.533155i) q^{23} +(0.601578 - 0.218956i) q^{25} -5.19903 q^{26} -4.01220 q^{28} +(8.65573 - 3.15043i) q^{29} +(2.70866 - 2.27284i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(2.89988 + 2.43329i) q^{34} +(-4.18878 + 7.25517i) q^{35} +(-1.77730 - 3.07838i) q^{37} +(0.221021 - 1.25347i) q^{38} +(-1.96209 - 0.714144i) q^{40} +(2.57419 + 0.936928i) q^{41} +(1.19757 - 6.79176i) q^{43} +(0.106223 + 0.183984i) q^{44} +(-0.414721 + 0.718318i) q^{46} +(0.978448 + 0.821016i) q^{47} +(1.57981 + 8.95957i) q^{49} +(0.490411 - 0.411503i) q^{50} +(-4.88549 + 1.77817i) q^{52} +11.2992 q^{53} +0.443592 q^{55} +(-3.77024 + 1.37225i) q^{56} +(7.05621 - 5.92087i) q^{58} +(1.48640 + 8.42981i) q^{59} +(2.17073 + 1.82146i) q^{61} +(1.76795 - 3.06218i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-1.88506 + 10.6907i) q^{65} +(-9.17192 - 3.33831i) q^{67} +(3.55723 + 1.29473i) q^{68} +(-1.45475 + 8.25028i) q^{70} +(-5.86207 - 10.1534i) q^{71} +(-0.375162 + 0.649800i) q^{73} +(-2.72298 - 2.28485i) q^{74} +(-0.221021 - 1.25347i) q^{76} +(0.652961 - 0.547899i) q^{77} +(2.22499 - 0.809829i) q^{79} -2.08802 q^{80} +2.73940 q^{82} +(-10.7130 + 3.89920i) q^{83} +(6.05500 - 5.08075i) q^{85} +(-1.19757 - 6.79176i) q^{86} +(0.162744 + 0.136558i) q^{88} +(2.69813 - 4.67329i) q^{89} +(10.4298 + 18.0649i) q^{91} +(-0.144031 + 0.816841i) q^{92} +(1.20024 + 0.436853i) q^{94} +(-2.49737 - 0.908969i) q^{95} +(-2.18157 + 12.3723i) q^{97} +(4.54889 + 7.87892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 6 q^{13} - 6 q^{14} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 6 q^{22} + 24 q^{23} + 36 q^{25} - 18 q^{26} + 12 q^{28} + 12 q^{29} + 27 q^{31} + 3 q^{34}+ \cdots + 12 q^{98}+O(q^{100}) $ 12 * q - 6 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 - 6 * q^11 - 6 * q^13 - 6 * q^14 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 6 * q^22 + 24 * q^23 + 36 * q^25 - 18 * q^26 + 12 * q^28 + 12 * q^29 + 27 * q^31 + 3 * q^34 - 3 * q^35 - 15 * q^37 - 12 * q^38 - 3 * q^40 + 3 * q^41 - 27 * q^43 + 3 * q^44 + 3 * q^46 - 36 * q^47 - 3 * q^49 + 9 * q^50 - 6 * q^52 + 12 * q^53 + 18 * q^55 - 6 * q^56 + 15 * q^58 - 12 * q^59 + 9 * q^61 + 12 * q^62 - 6 * q^64 + 42 * q^65 - 45 * q^67 - 12 * q^68 - 33 * q^70 - 12 * q^71 - 21 * q^73 + 30 * q^74 + 12 * q^76 - 48 * q^77 + 3 * q^79 - 6 * q^80 + 6 * q^82 + 18 * q^83 + 27 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 - 30 * q^92 - 27 * q^94 + 33 * q^95 - 15 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.362580	−	2.05630i	−0.162151	−	0.919603i	−0.951954	−	0.306242i	$-0.900928\pi$
$5$	−0.362580	−	2.05630i	−0.162151	−	0.919603i	0.789803	−	0.613361i	$-0.210183\pi$
$6$		0			0
$7$	−3.07353	−	2.57900i	−1.16168	−	0.974769i	−0.161757	−	0.986831i	$-0.551716\pi$
$7$	−3.07353	−	2.57900i	−1.16168	−	0.974769i	−0.999927	+	0.0120620i	$0.996160\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$		0			0
$10$	−1.04401	−	1.80828i	−0.330144	−	0.571827i
$11$	−0.0368910	+	0.209219i	−0.0111231	+	0.0630820i	−0.989864	−	0.142018i	$-0.954641\pi$
$11$	−0.0368910	+	0.209219i	−0.0111231	+	0.0630820i	0.978741	+	0.205100i	$0.0657520\pi$
$12$		0			0
$13$	−4.88549	−	1.77817i	−1.35499	−	0.493176i	−0.440489	−	0.897758i	$-0.645195\pi$
$13$	−4.88549	−	1.77817i	−1.35499	−	0.493176i	−0.914502	+	0.404582i	$0.867417\pi$
$14$	−3.77024	−	1.37225i	−1.00764	−	0.366751i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	1.89276	+	3.27836i	0.459062	+	0.795119i	0.998912	−	0.0466426i	$-0.0148522\pi$
$17$	1.89276	+	3.27836i	0.459062	+	0.795119i	−0.539850	+	0.841762i	$0.681519\pi$
$18$		0			0
$19$	0.636405	−	1.10229i	0.146001	−	0.252882i	−0.783745	−	0.621083i	$-0.786693\pi$
$19$	0.636405	−	1.10229i	0.146001	−	0.252882i	0.929746	+	0.368201i	$0.120026\pi$
$20$	−1.59951	−	1.34215i	−0.357662	−	0.300114i
$21$		0			0
$22$	0.0368910	+	0.209219i	0.00786519	+	0.0446057i
$23$	−0.635390	+	0.533155i	−0.132488	+	0.111171i	−0.706624	−	0.707590i	$-0.749783\pi$
$23$	−0.635390	+	0.533155i	−0.132488	+	0.111171i	0.574136	+	0.818760i	$0.305338\pi$
$24$		0			0
$25$	0.601578	−	0.218956i	0.120316	−	0.0437913i
$26$	−5.19903			−1.01961
$27$		0			0
$28$	−4.01220			−0.758235
$29$	8.65573	−	3.15043i	1.60733	−	0.585020i	0.626419	−	0.779486i	$-0.284520\pi$
$29$	8.65573	−	3.15043i	1.60733	−	0.585020i	0.980909	+	0.194467i	$0.0622977\pi$
$30$		0			0
$31$	2.70866	−	2.27284i	0.486490	−	0.408213i	−0.366277	−	0.930506i	$-0.619368\pi$
$31$	2.70866	−	2.27284i	0.486490	−	0.408213i	0.852766	+	0.522293i	$0.174923\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$		0			0
$34$	2.89988	+	2.43329i	0.497325	+	0.417305i
$35$	−4.18878	+	7.25517i	−0.708032	+	1.22635i
$36$		0			0
$37$	−1.77730	−	3.07838i	−0.292187	−	0.506082i	0.682140	−	0.731222i	$-0.261049\pi$
$37$	−1.77730	−	3.07838i	−0.292187	−	0.506082i	−0.974326	+	0.225140i	$0.927716\pi$
$38$	0.221021	−	1.25347i	0.0358543	−	0.203340i
$39$		0			0
$40$	−1.96209	−	0.714144i	−0.310234	−	0.112916i
$41$	2.57419	+	0.936928i	0.402021	+	0.146324i	0.535114	−	0.844780i	$-0.320269\pi$
$41$	2.57419	+	0.936928i	0.402021	+	0.146324i	−0.133093	+	0.991104i	$0.542491\pi$
$42$		0			0
$43$	1.19757	−	6.79176i	0.182628	−	1.03573i	−0.746338	−	0.665567i	$-0.768190\pi$
$43$	1.19757	−	6.79176i	0.182628	−	1.03573i	0.928966	−	0.370166i	$-0.120699\pi$
$44$	0.106223	+	0.183984i	0.0160138	+	0.0277367i
$45$		0			0
$46$	−0.414721	+	0.718318i	−0.0611473	+	0.105910i
$47$	0.978448	+	0.821016i	0.142721	+	0.119757i	0.711353	−	0.702835i	$-0.248083\pi$
$47$	0.978448	+	0.821016i	0.142721	+	0.119757i	−0.568632	+	0.822592i	$0.692527\pi$
$48$		0			0
$49$	1.57981	+	8.95957i	0.225688	+	1.27994i
$50$	0.490411	−	0.411503i	0.0693545	−	0.0581954i
$51$		0			0
$52$	−4.88549	+	1.77817i	−0.677495	+	0.246588i
$53$	11.2992			1.55207			0.776036	−	0.630689i	$-0.217228\pi$
$53$	11.2992			1.55207			0.776036	+	0.630689i	$0.217228\pi$
$54$		0			0
$55$	0.443592			0.0598140
$56$	−3.77024	+	1.37225i	−0.503819	+	0.183375i
$57$		0			0
$58$	7.05621	−	5.92087i	0.926526	−	0.777448i
$59$	1.48640	+	8.42981i	0.193513	+	1.09747i	0.914520	+	0.404540i	$0.132568\pi$
$59$	1.48640	+	8.42981i	0.193513	+	1.09747i	−0.721007	+	0.692928i	$0.756320\pi$
$60$		0			0
$61$	2.17073	+	1.82146i	0.277933	+	0.233213i	0.771089	−	0.636727i	$-0.219712\pi$
$61$	2.17073	+	1.82146i	0.277933	+	0.233213i	−0.493156	+	0.869941i	$0.664157\pi$
$62$	1.76795	−	3.06218i	0.224530	−	0.388898i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.88506	+	10.6907i	−0.233814	+	1.32602i
$66$		0			0
$67$	−9.17192	−	3.33831i	−1.12053	−	0.407839i	−0.285684	−	0.958324i	$-0.592221\pi$
$67$	−9.17192	−	3.33831i	−1.12053	−	0.407839i	−0.834845	+	0.550485i	$0.814443\pi$
$68$	3.55723	+	1.29473i	0.431377	+	0.157008i
$69$		0			0
$70$	−1.45475	+	8.25028i	−0.173875	+	0.986097i
$71$	−5.86207	−	10.1534i	−0.695700	−	1.20499i	−0.969944	−	0.243327i	$-0.921761\pi$
$71$	−5.86207	−	10.1534i	−0.695700	−	1.20499i	0.274244	−	0.961660i	$-0.411572\pi$
$72$		0			0
$73$	−0.375162	+	0.649800i	−0.0439094	+	0.0760534i	−0.887145	−	0.461491i	$-0.847315\pi$
$73$	−0.375162	+	0.649800i	−0.0439094	+	0.0760534i	0.843235	+	0.537544i	$0.180648\pi$
$74$	−2.72298	−	2.28485i	−0.316540	−	0.265609i
$75$		0			0
$76$	−0.221021	−	1.25347i	−0.0253529	−	0.143783i
$77$	0.652961	−	0.547899i	0.0744118	−	0.0624389i
$78$		0			0
$79$	2.22499	−	0.809829i	0.250330	−	0.0911128i	−0.213807	−	0.976876i	$-0.568586\pi$
$79$	2.22499	−	0.809829i	0.250330	−	0.0911128i	0.464138	+	0.885763i	$0.346364\pi$
$80$	−2.08802			−0.233447
$81$		0			0
$82$	2.73940			0.302516
$83$	−10.7130	+	3.89920i	−1.17590	+	0.427992i	−0.854752	−	0.519037i	$-0.826291\pi$
$83$	−10.7130	+	3.89920i	−1.17590	+	0.427992i	−0.321148	+	0.947029i	$0.604069\pi$
$84$		0			0
$85$	6.05500	−	5.08075i	0.656757	−	0.551084i
$86$	−1.19757	−	6.79176i	−0.129137	−	0.732374i
$87$		0			0
$88$	0.162744	+	0.136558i	0.0173485	+	0.0145571i
$89$	2.69813	−	4.67329i	0.286001	−	0.495368i	−0.686851	−	0.726799i	$-0.741007\pi$
$89$	2.69813	−	4.67329i	0.286001	−	0.495368i	0.972851	+	0.231431i	$0.0743407\pi$
$90$		0			0
$91$	10.4298	+	18.0649i	1.09334	+	1.89372i
$92$	−0.144031	+	0.816841i	−0.0150163	+	0.0851616i
$93$		0			0
$94$	1.20024	+	0.436853i	0.123796	+	0.0450580i
$95$	−2.49737	−	0.908969i	−0.256225	−	0.0932582i
$96$		0			0
$97$	−2.18157	+	12.3723i	−0.221505	+	1.25622i	0.647750	+	0.761853i	$0.275710\pi$
$97$	−2.18157	+	12.3723i	−0.221505	+	1.25622i	−0.869255	+	0.494364i	$0.835401\pi$
$98$	4.54889	+	7.87892i	0.459508	+	0.795891i
$99$		0			0
$100$	0.320093	−	0.554417i	0.0320093	−	0.0554417i
$101$	2.21733	+	1.86056i	0.220633	+	0.185133i	0.746404	−	0.665493i	$-0.231779\pi$
$101$	2.21733	+	1.86056i	0.220633	+	0.185133i	−0.525771	+	0.850626i	$0.676223\pi$
$102$		0			0
$103$	2.89819	+	16.4365i	0.285567	+	1.61953i	0.703252	+	0.710941i	$0.251731\pi$
$103$	2.89819	+	16.4365i	0.285567	+	1.61953i	−0.417684	+	0.908592i	$0.637158\pi$
$104$	−3.98269	+	3.34187i	−0.390534	+	0.327697i
$105$		0			0
$106$	10.6178	−	3.86457i	1.03129	−	0.375360i
$107$	−0.321371			−0.0310681			−0.0155341	−	0.999879i	$-0.504945\pi$
$107$	−0.321371			−0.0310681			−0.0155341	+	0.999879i	$0.504945\pi$
$108$		0			0
$109$	0.568378			0.0544407			0.0272204	−	0.999629i	$-0.491334\pi$
$109$	0.568378			0.0544407			0.0272204	+	0.999629i	$0.491334\pi$
$110$	0.416841	−	0.151718i	0.0397442	−	0.0144657i
$111$		0			0
$112$	−3.07353	+	2.57900i	−0.290421	+	0.243692i
$113$	0.236129	+	1.33916i	0.0222132	+	0.125977i	0.993898	−	0.110304i	$-0.0351825\pi$
$113$	0.236129	+	1.33916i	0.0222132	+	0.125977i	−0.971685	+	0.236281i	$0.924071\pi$
$114$		0			0
$115$	1.32670	+	1.11324i	0.123716	+	0.103810i
$116$	4.60562	−	7.97716i	0.427621	−	0.740661i
$117$		0			0
$118$	4.27993	+	7.41305i	0.393999	+	0.682427i
$119$	2.63742	−	14.9576i	0.241772	−	1.37116i
$120$		0			0
$121$	10.2942	+	3.74678i	0.935837	+	0.340617i
$122$	2.66279	+	0.969176i	0.241078	+	0.0877451i
$123$		0			0
$124$	0.614003	−	3.48219i	0.0551391	−	0.312710i
$125$	−5.88840	−	10.1990i	−0.526675	−	0.912227i
$126$		0			0
$127$	−0.902007	+	1.56232i	−0.0800402	+	0.138634i	−0.903267	−	0.429079i	$-0.858838\pi$
$127$	−0.902007	+	1.56232i	−0.0800402	+	0.138634i	0.823227	+	0.567713i	$0.192172\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$		0			0
$130$	1.88506	+	10.6907i	0.165331	+	0.937639i
$131$	7.44168	−	6.24431i	0.650183	−	0.545568i	−0.256944	−	0.966426i	$-0.582715\pi$
$131$	7.44168	−	6.24431i	0.650183	−	0.545568i	0.907126	+	0.420858i	$0.138271\pi$
$132$		0			0
$133$	−4.79880	+	1.74662i	−0.416108	+	0.151451i
$134$	−9.76056			−0.843184
$135$		0			0
$136$	3.78552			0.324606
$137$	−8.52106	+	3.10141i	−0.728003	+	0.264972i	−0.679319	−	0.733843i	$-0.737725\pi$
$137$	−8.52106	+	3.10141i	−0.728003	+	0.264972i	−0.0486840	+	0.998814i	$0.515503\pi$
$138$		0			0
$139$	−7.69175	+	6.45415i	−0.652406	+	0.547434i	−0.907800	−	0.419403i	$-0.862239\pi$
$139$	−7.69175	+	6.45415i	−0.652406	+	0.547434i	0.255394	+	0.966837i	$0.417795\pi$
$140$	1.45475	+	8.25028i	0.122949	+	0.697276i
$141$		0			0
$142$	−8.98121	−	7.53613i	−0.753687	−	0.632418i
$143$	0.552258	−	0.956539i	0.0461822	−	0.0799898i
$144$		0			0
$145$	−9.61660	−	16.6564i	−0.798615	−	1.38324i
$146$	−0.130293	+	0.738926i	−0.0107831	+	0.0611539i
$147$		0			0
$148$	−3.34023	−	1.21575i	−0.274566	−	0.0999337i
$149$	14.8870	+	5.41843i	1.21959	+	0.443895i	0.870021	−	0.493015i	$-0.164105\pi$
$149$	14.8870	+	5.41843i	1.21959	+	0.443895i	0.349571	+	0.936910i	$0.386327\pi$
$150$		0			0
$151$	0.921646	−	5.22691i	0.0750025	−	0.425360i	−0.924067	−	0.382231i	$-0.875156\pi$
$151$	0.921646	−	5.22691i	0.0750025	−	0.425360i	0.999069	−	0.0431297i	$-0.0137329\pi$
$152$	−0.636405	−	1.10229i	−0.0516192	−	0.0894071i
$153$		0			0
$154$	0.426190	−	0.738183i	0.0343434	−	0.0594845i
$155$	−5.65573	−	4.74572i	−0.454279	−	0.381185i
$156$		0			0
$157$	−1.99991	−	11.3421i	−0.159610	−	0.905195i	−0.954449	−	0.298374i	$-0.903556\pi$
$157$	−1.99991	−	11.3421i	−0.159610	−	0.905195i	0.794839	−	0.606821i	$-0.207555\pi$
$158$	1.81383	−	1.52198i	0.144300	−	0.121082i
$159$		0			0
$160$	−1.96209	+	0.714144i	−0.155117	+	0.0564580i
$161$	3.32789			0.262275
$162$		0			0
$163$	7.66336			0.600241			0.300120	−	0.953901i	$-0.402973\pi$
$163$	7.66336			0.600241			0.300120	+	0.953901i	$0.402973\pi$
$164$	2.57419	−	0.936928i	0.201010	−	0.0731618i
$165$		0			0
$166$	−8.73328	+	7.32809i	−0.677834	+	0.568770i
$167$	−1.06099	−	6.01717i	−0.0821018	−	0.465622i	−0.997944	−	0.0640851i	$-0.979587\pi$
$167$	−1.06099	−	6.01717i	−0.0821018	−	0.465622i	0.915843	−	0.401537i	$-0.131524\pi$
$168$		0			0
$169$	10.7475	+	9.01824i	0.826732	+	0.693711i
$170$	3.95212	−	6.84527i	0.303114	−	0.525008i
$171$		0			0
$172$	−3.44827	−	5.97257i	−0.262928	−	0.455404i
$173$	1.96283	−	11.1318i	0.149231	−	0.846332i	−0.814641	−	0.579966i	$-0.803066\pi$
$173$	1.96283	−	11.1318i	0.149231	−	0.846332i	0.963872	−	0.266366i	$-0.0858231\pi$
$174$		0			0
$175$	−2.41365	−	0.878498i	−0.182455	−	0.0664082i
$176$	0.199635	+	0.0726611i	0.0150480	+	0.00547703i
$177$		0			0
$178$	0.937049	−	5.31427i	0.0702348	−	0.398321i
$179$	3.46495	+	6.00147i	0.258982	+	0.448571i	0.965970	−	0.258656i	$-0.0832795\pi$
$179$	3.46495	+	6.00147i	0.258982	+	0.448571i	−0.706987	+	0.707226i	$0.749946\pi$
$180$		0			0
$181$	−1.51882	+	2.63067i	−0.112893	+	0.195536i	−0.916935	−	0.399036i	$-0.869345\pi$
$181$	−1.51882	+	2.63067i	−0.112893	+	0.195536i	0.804043	+	0.594572i	$0.202678\pi$
$182$	15.9794	+	13.4083i	1.18447	+	0.993887i
$183$		0			0
$184$	0.144031	+	0.816841i	0.0106181	+	0.0602183i
$185$	−5.68564	+	4.77082i	−0.418016	+	0.350757i
$186$		0			0
$187$	−0.755722	+	0.275060i	−0.0552638	+	0.0201144i
$188$	1.27727			0.0931547
$189$		0			0
$190$	−2.65765			−0.192806
$191$	−4.78978	+	1.74334i	−0.346576	+	0.126144i	−0.509443	−	0.860505i	$-0.670148\pi$
$191$	−4.78978	+	1.74334i	−0.346576	+	0.126144i	0.162866	+	0.986648i	$0.447926\pi$
$192$		0			0
$193$	14.4539	−	12.1283i	1.04042	−	0.873013i	0.0483631	−	0.998830i	$-0.484600\pi$
$193$	14.4539	−	12.1283i	1.04042	−	0.873013i	0.992054	+	0.125817i	$0.0401551\pi$
$194$	2.18157	+	12.3723i	0.156628	+	0.888279i
$195$		0			0
$196$	6.96931	+	5.84795i	0.497808	+	0.417710i
$197$	−10.0220	+	17.3586i	−0.714036	+	1.23675i	0.249294	+	0.968428i	$0.419801\pi$
$197$	−10.0220	+	17.3586i	−0.714036	+	1.23675i	−0.963330	+	0.268319i	$0.913532\pi$
$198$		0			0
$199$	−2.75106	−	4.76498i	−0.195018	−	0.337780i	0.751889	−	0.659290i	$-0.229143\pi$
$199$	−2.75106	−	4.76498i	−0.195018	−	0.337780i	−0.946906	+	0.321510i	$0.895810\pi$
$200$	0.111167	−	0.630460i	0.00786070	−	0.0445802i
$201$		0			0
$202$	2.71996	+	0.989985i	0.191376	+	0.0696551i
$203$	−34.7285	−	12.6402i	−2.43747	−	0.887165i
$204$		0			0
$205$	0.993251	−	5.63301i	0.0693717	−	0.393426i
$206$	8.34501	+	14.4540i	0.581425	+	1.00706i
$207$		0			0
$208$	−2.59951	+	4.50249i	−0.180244	+	0.312191i
$209$	0.207142	+	0.173812i	0.0143283	+	0.0120229i
$210$		0			0
$211$	−4.36641	−	24.7631i	−0.300596	−	1.70476i	−0.643544	−	0.765409i	$-0.722537\pi$
$211$	−4.36641	−	24.7631i	−0.300596	−	1.70476i	0.342948	−	0.939354i	$-0.388575\pi$
$212$	8.65573	−	7.26302i	0.594478	−	0.498826i
$213$		0			0
$214$	−0.301990	+	0.109915i	−0.0206436	+	0.00751366i
$215$	−14.4001			−0.982077
$216$		0			0
$217$	−14.1868			−0.963061
$218$	0.534100	−	0.194397i	0.0361738	−	0.0131662i
$219$		0			0
$220$	0.339811	−	0.285136i	0.0229101	−	0.0192238i
$221$	−3.41758	−	19.3820i	−0.229891	−	1.30378i
$222$		0			0
$223$	−2.87450	−	2.41199i	−0.192491	−	0.161519i	0.541449	−	0.840734i	$-0.317876\pi$
$223$	−2.87450	−	2.41199i	−0.192491	−	0.161519i	−0.733940	+	0.679215i	$0.762320\pi$
$224$	−2.00610	+	3.47467i	−0.134038	+	0.232161i
$225$		0			0
$226$	0.679907	+	1.17763i	0.0452267	+	0.0783350i
$227$	−3.25203	+	18.4432i	−0.215845	+	1.22412i	0.663590	+	0.748096i	$0.269032\pi$
$227$	−3.25203	+	18.4432i	−0.215845	+	1.22412i	−0.879435	+	0.476020i	$0.842079\pi$
$228$		0			0
$229$	3.89345	+	1.41710i	0.257287	+	0.0936447i	0.467443	−	0.884023i	$-0.345175\pi$
$229$	3.89345	+	1.41710i	0.257287	+	0.0936447i	−0.210157	+	0.977668i	$0.567397\pi$
$230$	1.62744	+	0.592341i	0.107310	+	0.0390578i
$231$		0			0
$232$	1.59951	−	9.07129i	0.105013	−	0.595560i
$233$	−0.958556	−	1.66027i	−0.0627971	−	0.108768i	0.832918	−	0.553397i	$-0.186669\pi$
$233$	−0.958556	−	1.66027i	−0.0627971	−	0.108768i	−0.895715	+	0.444629i	$0.853335\pi$
$234$		0			0
$235$	1.33348	−	2.30966i	0.0869869	−	0.150666i
$236$	6.55723	+	5.50217i	0.426839	+	0.358161i
$237$		0			0
$238$	−2.63742	−	14.9576i	−0.170959	−	0.969554i
$239$	−18.5377	+	15.5550i	−1.19911	+	1.00617i	−0.199450	+	0.979908i	$0.563916\pi$
$239$	−18.5377	+	15.5550i	−1.19911	+	1.00617i	−0.999655	+	0.0262606i	$0.991640\pi$
$240$		0			0
$241$	−12.4086	+	4.51635i	−0.799307	+	0.290924i	−0.709199	−	0.705008i	$-0.750943\pi$
$241$	−12.4086	+	4.51635i	−0.799307	+	0.290924i	−0.0901076	+	0.995932i	$0.528721\pi$
$242$	10.9549			0.704205
$243$		0			0
$244$	2.83368			0.181408
$245$	17.8507	−	6.49713i	1.14044	−	0.415086i
$246$		0			0
$247$	−5.06920	+	4.25356i	−0.322545	+	0.270648i
$248$	−0.614003	−	3.48219i	−0.0389892	−	0.221119i
$249$		0			0
$250$	−9.02155	−	7.56998i	−0.570573	−	0.478768i
$251$	−4.32994	+	7.49967i	−0.273303	+	0.473375i	−0.969706	−	0.244276i	$-0.921450\pi$
$251$	−4.32994	+	7.49967i	−0.273303	+	0.473375i	0.696402	+	0.717652i	$0.254783\pi$
$252$		0			0
$253$	−0.0881062	−	0.152604i	−0.00553919	−	0.00959415i
$254$	−0.313264	+	1.77661i	−0.0196559	+	0.111474i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	20.5142	+	7.46656i	1.27964	+	0.465751i	0.890314	−	0.455348i	$-0.150485\pi$
$257$	20.5142	+	7.46656i	1.27964	+	0.465751i	0.389328	+	0.921099i	$0.372707\pi$
$258$		0			0
$259$	−2.47653	+	14.0451i	−0.153884	+	0.872722i
$260$	5.42783	+	9.40127i	0.336620	+	0.583042i
$261$		0			0
$262$	4.85721	−	8.41294i	0.300080	−	0.519753i
$263$	4.35690	+	3.65587i	0.268658	+	0.225431i	0.767157	−	0.641460i	$-0.221671\pi$
$263$	4.35690	+	3.65587i	0.268658	+	0.225431i	−0.498499	+	0.866890i	$0.666115\pi$
$264$		0			0
$265$	−4.09689	−	23.2346i	−0.251670	−	1.42729i
$266$	−3.91201	+	3.28257i	−0.239861	+	0.201267i
$267$		0			0
$268$	−9.17192	+	3.33831i	−0.560264	+	0.203920i
$269$	22.7662			1.38808			0.694041	−	0.719936i	$-0.255829\pi$
$269$	22.7662			1.38808			0.694041	+	0.719936i	$0.255829\pi$
$270$		0			0
$271$	−19.8340			−1.20483			−0.602414	−	0.798184i	$-0.705794\pi$
$271$	−19.8340			−1.20483			−0.602414	+	0.798184i	$0.705794\pi$
$272$	3.55723	−	1.29473i	0.215689	−	0.0785042i
$273$		0			0
$274$	−6.94643	+	5.82875i	−0.419649	+	0.352128i
$275$	0.0236171	+	0.133939i	0.00142416	+	0.00807683i
$276$		0			0
$277$	−18.4899	−	15.5149i	−1.11095	−	0.932198i	−0.112838	−	0.993613i	$-0.535994\pi$
$277$	−18.4899	−	15.5149i	−1.11095	−	0.932198i	−0.998112	+	0.0614159i	$0.980438\pi$
$278$	−5.02044	+	8.69565i	−0.301106	+	0.521530i
$279$		0			0
$280$	4.18878	+	7.25517i	0.250327	+	0.433579i
$281$	4.10770	−	23.2959i	0.245045	−	1.38972i	−0.575344	−	0.817911i	$-0.695132\pi$
$281$	4.10770	−	23.2959i	0.245045	−	1.38972i	0.820389	−	0.571806i	$-0.193757\pi$
$282$		0			0
$283$	10.9231	+	3.97570i	0.649313	+	0.236331i	0.645616	−	0.763663i	$-0.276601\pi$
$283$	10.9231	+	3.97570i	0.649313	+	0.236331i	0.00369734	+	0.999993i	$0.498823\pi$
$284$	−11.0171	−	4.00989i	−0.653744	−	0.237943i
$285$		0			0
$286$	0.191797	−	1.08774i	0.0113412	−	0.0643192i
$287$	−5.49551	−	9.51850i	−0.324390	−	0.561859i
$288$		0			0
$289$	1.33491	−	2.31213i	0.0785239	−	0.136007i
$290$	−14.7335	−	12.3629i	−0.865180	−	0.725973i
$291$		0			0
$292$	0.130293	+	0.738926i	0.00762479	+	0.0432423i
$293$	8.20504	−	6.88485i	0.479344	−	0.402217i	−0.370845	−	0.928695i	$-0.620932\pi$
$293$	8.20504	−	6.88485i	0.479344	−	0.402217i	0.850189	+	0.526478i	$0.176488\pi$
$294$		0			0
$295$	16.7952	−	6.11297i	0.977857	−	0.355911i
$296$	−3.55460			−0.206607
$297$		0			0
$298$	15.8424			0.917728
$299$	4.05223	−	1.47489i	0.234347	−	0.0852952i
$300$		0			0
$301$	−21.1967	+	17.7861i	−1.22176	+	1.02518i
$302$	−0.921646	−	5.22691i	−0.0530348	−	0.300775i
$303$		0			0
$304$	−0.975029	−	0.818146i	−0.0559217	−	0.0469239i
$305$	2.95839	−	5.12408i	0.169397	−	0.293404i
$306$		0			0
$307$	−12.3938	−	21.4667i	−0.707351	−	1.22517i	−0.965836	−	0.259153i	$-0.916557\pi$
$307$	−12.3938	−	21.4667i	−0.707351	−	1.22517i	0.258485	−	0.966015i	$-0.416777\pi$
$308$	0.148014	−	0.839430i	0.00843389	−	0.0478310i
$309$		0			0
$310$	−6.93778	−	2.52514i	−0.394039	−	0.143419i
$311$	−20.4698	−	7.45040i	−1.16074	−	0.422473i	−0.311376	−	0.950287i	$-0.600790\pi$
$311$	−20.4698	−	7.45040i	−1.16074	−	0.422473i	−0.849360	+	0.527813i	$0.823012\pi$
$312$		0			0
$313$	−1.63272	+	9.25962i	−0.0922868	+	0.523385i	0.903258	+	0.429097i	$0.141168\pi$
$313$	−1.63272	+	9.25962i	−0.0922868	+	0.523385i	−0.995545	+	0.0942872i	$0.969943\pi$
$314$	−5.75852	−	9.97404i	−0.324972	−	0.562868i
$315$		0			0
$316$	1.18389	−	2.05056i	0.0665990	−	0.115353i
$317$	11.1121	+	9.32419i	0.624120	+	0.523699i	0.899096	−	0.437752i	$-0.144225\pi$
$317$	11.1121	+	9.32419i	0.624120	+	0.523699i	−0.274976	+	0.961451i	$0.588670\pi$
$318$		0			0
$319$	0.339811	+	1.92717i	0.0190258	+	0.107901i
$320$	−1.59951	+	1.34215i	−0.0894155	+	0.0750285i
$321$		0			0
$322$	3.12720	−	1.13821i	0.174272	−	0.0634298i
$323$	4.81825			0.268095
$324$		0			0
$325$	−3.32834			−0.184623
$326$	7.20120	−	2.62102i	0.398838	−	0.145165i
$327$		0			0
$328$	2.09850	−	1.76085i	0.115870	−	0.0972266i
$329$	−0.889892	−	5.04683i	−0.0490613	−	0.278241i
$330$		0			0
$331$	0.617998	+	0.518562i	0.0339683	+	0.0285028i	0.659614	−	0.751605i	$-0.270720\pi$
$331$	0.617998	+	0.518562i	0.0339683	+	0.0285028i	−0.625645	+	0.780108i	$0.715164\pi$
$332$	−5.70024	+	9.87311i	−0.312842	+	0.541857i
$333$		0			0
$334$	−3.05500	−	5.29141i	−0.167162	−	0.289533i
$335$	−3.53899	+	20.0706i	−0.193355	+	1.09657i
$336$		0			0
$337$	25.0577	+	9.12024i	1.36498	+	0.496811i	0.917590	−	0.397529i	$-0.130132\pi$
$337$	25.0577	+	9.12024i	1.36498	+	0.496811i	0.447388	+	0.894340i	$0.352354\pi$
$338$	13.1838	+	4.79850i	0.717103	+	0.261004i
$339$		0			0
$340$	1.37256	−	7.78415i	0.0744373	−	0.422155i
$341$	0.375596	+	0.650551i	0.0203396	+	0.0352293i
$342$		0			0
$343$	4.20838	−	7.28912i	0.227231	−	0.393576i
$344$	−5.28305	−	4.43301i	−0.284843	−	0.239012i
$345$		0			0
$346$	−1.96283	−	11.1318i	−0.105522	−	0.598447i
$347$	22.2952	−	18.7079i	1.19687	−	1.00429i	0.197154	−	0.980372i	$-0.436830\pi$
$347$	22.2952	−	18.7079i	1.19687	−	1.00429i	0.999714	−	0.0239192i	$-0.00761444\pi$
$348$		0			0
$349$	27.7665	−	10.1062i	1.48631	−	0.540972i	0.533833	−	0.845590i	$-0.320751\pi$
$349$	27.7665	−	10.1062i	1.48631	−	0.540972i	0.952474	+	0.304618i	$0.0985289\pi$
$350$	−2.56856			−0.137295
$351$		0			0
$352$	0.212447			0.0113235
$353$	5.87548	−	2.13850i	0.312720	−	0.113821i	−0.180892	−	0.983503i	$-0.557898\pi$
$353$	5.87548	−	2.13850i	0.312720	−	0.113821i	0.493612	+	0.869682i	$0.335676\pi$
$354$		0			0
$355$	−18.7529	+	15.7356i	−0.995302	+	0.835158i
$356$	−0.937049	−	5.31427i	−0.0496635	−	0.281656i
$357$		0			0
$358$	5.30861	+	4.45445i	0.280569	+	0.235425i
$359$	−1.29314	+	2.23979i	−0.0682495	+	0.118212i	−0.898131	−	0.439728i	$-0.855075\pi$
$359$	−1.29314	+	2.23979i	−0.0682495	+	0.118212i	0.829881	+	0.557940i	$0.188408\pi$
$360$		0			0
$361$	8.68998	+	15.0515i	0.457367	+	0.792183i
$362$	−0.527479	+	2.99148i	−0.0277237	+	0.157229i
$363$		0			0
$364$	19.6016	+	7.13439i	1.02740	+	0.373944i
$365$	1.47221	+	0.535840i	0.0770589	+	0.0280471i
$366$		0			0
$367$	3.24396	−	18.3974i	0.169333	−	0.960336i	−0.775150	−	0.631777i	$-0.782326\pi$
$367$	3.24396	−	18.3974i	0.169333	−	0.960336i	0.944483	−	0.328559i	$-0.106563\pi$
$368$	0.414721	+	0.718318i	0.0216188	+	0.0374449i
$369$		0			0
$370$	−3.71104	+	6.42770i	−0.192928	+	0.334160i
$371$	−34.7285	−	29.1407i	−1.80302	−	1.51291i
$372$		0			0
$373$	2.34879	+	13.3206i	0.121616	+	0.689717i	0.983261	+	0.182205i	$0.0583235\pi$
$373$	2.34879	+	13.3206i	0.121616	+	0.689717i	−0.861645	+	0.507512i	$0.830565\pi$
$374$	−0.616070	+	0.516944i	−0.0318562	+	0.0267305i
$375$		0			0
$376$	1.20024	−	0.436853i	0.0618979	−	0.0225290i
$377$	−47.8894			−2.46643
$378$		0			0
$379$	30.2178			1.55218			0.776092	−	0.630620i	$-0.217199\pi$
$379$	30.2178			1.55218			0.776092	+	0.630620i	$0.217199\pi$
$380$	−2.49737	+	0.908969i	−0.128112	+	0.0466291i
$381$		0			0
$382$	−3.90467	+	3.27640i	−0.199780	+	0.167635i
$383$	6.70092	+	38.0028i	0.342401	+	1.94185i	0.335968	+	0.941873i	$0.390936\pi$
$383$	6.70092	+	38.0028i	0.342401	+	1.94185i	0.00643265	+	0.999979i	$0.497952\pi$
$384$		0			0
$385$	−1.36339	−	1.14402i	−0.0694850	−	0.0583048i
$386$	9.43413	−	16.3404i	0.480185	−	0.831704i
$387$		0			0
$388$	6.28158	+	10.8800i	0.318899	+	0.552349i
$389$	0.976976	−	5.54071i	0.0495347	−	0.280925i	−0.949972	−	0.312335i	$-0.898889\pi$
$389$	0.976976	−	5.54071i	0.0495347	−	0.280925i	0.999507	+	0.0314103i	$0.00999986\pi$
$390$		0			0
$391$	−2.95052	−	1.07390i	−0.149214	−	0.0543095i
$392$	8.54912	+	3.11163i	0.431796	+	0.157161i
$393$		0			0
$394$	−3.48060	+	19.7394i	−0.175350	+	0.994459i
$395$	−2.47198	−	4.28160i	−0.124379	−	0.215431i
$396$		0			0
$397$	−3.85809	+	6.68240i	−0.193632	+	0.335380i	−0.946451	−	0.322847i	$-0.895360\pi$
$397$	−3.85809	+	6.68240i	−0.193632	+	0.335380i	0.752819	+	0.658227i	$0.228693\pi$
$398$	−4.21487	−	3.53670i	−0.211272	−	0.177279i
$399$		0			0
$400$	−0.111167	−	0.630460i	−0.00555835	−	0.0315230i
$401$	−27.8682	+	23.3842i	−1.39167	+	1.16775i	−0.427014	+	0.904245i	$0.640434\pi$
$401$	−27.8682	+	23.3842i	−1.39167	+	1.16775i	−0.964658	+	0.263506i	$0.915121\pi$
$402$		0			0
$403$	−17.2746	+	6.28745i	−0.860510	+	0.313200i
$404$	2.89452			0.144008
$405$		0			0
$406$	−36.9574			−1.83416
$407$	0.709622	−	0.258281i	0.0351747	−	0.0128025i
$408$		0			0
$409$	4.49490	−	3.77167i	0.222259	−	0.186497i	−0.524859	−	0.851189i	$-0.675882\pi$
$409$	4.49490	−	3.77167i	0.222259	−	0.186497i	0.747117	+	0.664692i	$0.231437\pi$
$410$	−0.993251	−	5.63301i	−0.0490532	−	0.278194i
$411$		0			0
$412$	12.7853	+	10.7281i	0.629886	+	0.528538i
$413$	17.1719	−	29.7427i	0.844976	−	1.46354i
$414$		0			0
$415$	11.9022	+	20.6152i	0.584256	+	1.01196i
$416$	−0.902802	+	5.12004i	−0.0442635	+	0.251031i
$417$		0			0
$418$	0.254097	+	0.0924837i	0.0124283	+	0.00452353i
$419$	19.8610	+	7.22880i	0.970271	+	0.353150i	0.778050	−	0.628202i	$-0.216209\pi$
$419$	19.8610	+	7.22880i	0.970271	+	0.353150i	0.192221	+	0.981352i	$0.438431\pi$
$420$		0			0
$421$	1.29245	−	7.32984i	0.0629901	−	0.357234i	−0.936979	−	0.349385i	$-0.886390\pi$
$421$	1.29245	−	7.32984i	0.0629901	−	0.357234i	0.999969	−	0.00784908i	$-0.00249847\pi$
$422$	−12.5726	−	21.7763i	−0.612023	−	1.06005i
$423$		0			0
$424$	5.64962	−	9.78544i	0.274370	−	0.475223i
$425$	1.85646	+	1.55776i	0.0900516	+	0.0755623i
$426$		0			0
$427$	−1.97426	−	11.1966i	−0.0955411	−	0.541841i
$428$	−0.246185	+	0.206573i	−0.0118998	+	0.00998510i
$429$		0			0
$430$	−13.5316	+	4.92512i	−0.652554	+	0.237510i
$431$	13.0502			0.628607			0.314303	−	0.949323i	$-0.398229\pi$
$431$	13.0502			0.628607			0.314303	+	0.949323i	$0.398229\pi$
$432$		0			0
$433$	0.143533			0.00689775			0.00344887	−	0.999994i	$-0.498902\pi$
$433$	0.143533			0.00689775			0.00344887	+	0.999994i	$0.498902\pi$
$434$	−13.3312	+	4.85216i	−0.639918	+	0.232911i
$435$		0			0
$436$	0.435403	−	0.365346i	0.0208520	−	0.0174969i
$437$	0.183324	+	1.03968i	0.00876959	+	0.0497348i
$438$		0			0
$439$	10.3849	+	8.71396i	0.495644	+	0.415895i	0.856044	−	0.516903i	$-0.172915\pi$
$439$	10.3849	+	8.71396i	0.495644	+	0.415895i	−0.360400	+	0.932798i	$0.617360\pi$
$440$	0.221796	−	0.384162i	0.0105737	−	0.0183142i
$441$		0			0
$442$	−9.84052	−	17.0443i	−0.468066	−	0.810714i
$443$	−2.13262	+	12.0947i	−0.101324	+	0.574636i	0.891301	+	0.453412i	$0.149793\pi$
$443$	−2.13262	+	12.0947i	−0.101324	+	0.574636i	−0.992625	+	0.121225i	$0.961318\pi$
$444$		0			0
$445$	−10.5879	−	3.85370i	−0.501917	−	0.182683i
$446$	−3.52610	−	1.28339i	−0.166965	−	0.0607705i
$447$		0			0
$448$	−0.696712	+	3.95125i	−0.0329166	+	0.186679i
$449$	20.3323	+	35.2165i	0.959540	+	1.66197i	0.723620	+	0.690199i	$0.242477\pi$
$449$	20.3323	+	35.2165i	0.959540	+	1.66197i	0.235920	+	0.971772i	$0.424190\pi$
$450$		0			0
$451$	−0.290988	+	0.504006i	−0.0137021	+	0.0237327i
$452$	1.04168	+	0.874072i	0.0489964	+	0.0411129i
$453$		0			0
$454$	3.25203	+	18.4432i	0.152625	+	0.865581i
$455$	33.3652	−	27.9967i	1.56418	−	1.31251i
$456$		0			0
$457$	−30.6255	+	11.1468i	−1.43260	+	0.521424i	−0.937676	−	0.347512i	$-0.887027\pi$
$457$	−30.6255	+	11.1468i	−1.43260	+	0.521424i	−0.494925	+	0.868936i	$0.664804\pi$
$458$	4.14333			0.193605
$459$		0			0
$460$	1.73189			0.0807498
$461$	−25.6728	+	9.34414i	−1.19570	+	0.435200i	−0.861722	−	0.507380i	$-0.830614\pi$
$461$	−25.6728	+	9.34414i	−1.19570	+	0.435200i	−0.333980	+	0.942580i	$0.608392\pi$
$462$		0			0
$463$	−2.60393	+	2.18495i	−0.121015	+	0.101543i	−0.701287	−	0.712879i	$-0.747391\pi$
$463$	−2.60393	+	2.18495i	−0.121015	+	0.101543i	0.580272	+	0.814423i	$0.302946\pi$
$464$	−1.59951	−	9.07129i	−0.0742556	−	0.421124i
$465$		0			0
$466$	−1.46859	−	1.23230i	−0.0680312	−	0.0570850i
$467$	16.4988	−	28.5767i	0.763473	−	1.32237i	−0.177577	−	0.984107i	$-0.556826\pi$
$467$	16.4988	−	28.5767i	0.763473	−	1.32237i	0.941050	−	0.338267i	$-0.109841\pi$
$468$		0			0
$469$	19.5807	+	33.9147i	0.904152	+	1.56604i
$470$	0.463114	−	2.62645i	0.0213619	−	0.121149i
$471$		0			0
$472$	8.04363	+	2.92764i	0.370238	+	0.134756i
$473$	1.37679	+	0.501110i	0.0633047	+	0.0230410i
$474$		0			0
$475$	0.141495	−	0.802455i	0.00649221	−	0.0368192i
$476$	−7.59415	−	13.1534i	−0.348077	−	0.602887i
$477$		0			0
$478$	−12.0996	+	20.9572i	−0.553424	+	0.958559i
$479$	17.6522	+	14.8119i	0.806548	+	0.676774i	0.949781	−	0.312915i	$-0.101305\pi$
$479$	17.6522	+	14.8119i	0.806548	+	0.676774i	−0.143233	+	0.989689i	$0.545750\pi$
$480$		0			0
$481$	3.20910	+	18.1997i	0.146322	+	0.829836i
$482$	−10.1156	+	8.48797i	−0.460751	+	0.386616i
$483$		0			0
$484$	10.2942	−	3.74678i	0.467919	−	0.170308i
$485$	26.2321			1.19114
$486$		0			0
$487$	26.9315			1.22038			0.610192	−	0.792254i	$-0.291092\pi$
$487$	26.9315			1.22038			0.610192	+	0.792254i	$0.291092\pi$
$488$	2.66279	−	0.969176i	0.120539	−	0.0438725i
$489$		0			0
$490$	14.5520	−	12.2106i	0.657394	−	0.551619i
$491$	0.0430636	+	0.244226i	0.00194343	+	0.0110217i	0.985764	−	0.168135i	$-0.0537743\pi$
$491$	0.0430636	+	0.244226i	0.00194343	+	0.0110217i	−0.983821	+	0.179156i	$0.942663\pi$
$492$		0			0
$493$	26.7115	+	22.4136i	1.20302	+	1.00946i
$494$	−3.30869	+	5.73081i	−0.148865	+	0.257841i
$495$		0			0
$496$	−1.76795	−	3.06218i	−0.0793834	−	0.137496i
$497$	−8.16835	+	46.3250i	−0.366401	+	2.07796i
$498$		0			0
$499$	25.1070	+	9.13819i	1.12394	+	0.409082i	0.836090	−	0.548593i	$-0.184836\pi$
$499$	25.1070	+	9.13819i	1.12394	+	0.409082i	0.287853	+	0.957675i	$0.407058\pi$
$500$	−11.0666	−	4.02790i	−0.494912	−	0.180133i
$501$		0			0
$502$	−1.50377	+	8.52832i	−0.0671166	+	0.380637i
$503$	13.0871	+	22.6676i	0.583527	+	1.01070i	0.995057	+	0.0993022i	$0.0316611\pi$
$503$	13.0871	+	22.6676i	0.583527	+	1.01070i	−0.411530	+	0.911396i	$0.635006\pi$
$504$		0			0
$505$	3.02190	−	5.23409i	0.134473	−	0.232914i
$506$	−0.134986	−	0.113267i	−0.00600088	−	0.00503534i
$507$		0			0
$508$	0.313264	+	1.77661i	0.0138988	+	0.0788242i
$509$	−4.18093	+	3.50821i	−0.185316	+	0.155499i	−0.730726	−	0.682671i	$-0.760818\pi$
$509$	−4.18093	+	3.50821i	−0.185316	+	0.155499i	0.545410	+	0.838169i	$0.316374\pi$
$510$		0			0
$511$	2.82890	−	1.02964i	0.125143	−	0.0455484i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	21.8308			0.962914
$515$	32.7474	−	11.9191i	1.44302	−	0.525217i
$516$		0			0
$517$	−0.207868	+	0.174422i	−0.00914203	+	0.00767107i
$518$	2.47653	+	14.0451i	0.108813	+	0.617107i
$519$		0			0
$520$	8.31592	+	6.97788i	0.364677	+	0.306000i
$521$	−13.0596	+	22.6199i	−0.572151	+	0.990995i	0.424194	+	0.905572i	$0.360558\pi$
$521$	−13.0596	+	22.6199i	−0.572151	+	0.990995i	−0.996345	+	0.0854234i	$0.972776\pi$
$522$		0			0
$523$	−3.70382	−	6.41521i	−0.161957	−	0.280518i	0.773614	−	0.633658i	$-0.218447\pi$
$523$	−3.70382	−	6.41521i	−0.161957	−	0.280518i	−0.935570	+	0.353140i	$0.885114\pi$
$524$	1.68689	−	9.56684i	0.0736922	−	0.417930i
$525$		0			0
$526$	5.34453	+	1.94525i	0.233033	+	0.0848169i
$527$	12.5780	+	4.57802i	0.547907	+	0.199422i
$528$		0			0
$529$	−3.87444	+	21.9731i	−0.168454	+	0.955350i
$530$	−11.7965	−	20.4322i	−0.512408	−	0.887516i
$531$		0			0
$532$	−2.55339	+	4.42259i	−0.110703	+	0.191744i
$533$	−10.9102	−	9.15470i	−0.472571	−	0.396534i
$534$		0			0
$535$	0.116523	+	0.660834i	0.00503772	+	0.0285703i
$536$	−7.47702	+	6.27396i	−0.322958	+	0.270994i
$537$		0			0
$538$	21.3933	−	7.78651i	0.922329	−	0.335700i
$539$	−1.93280			−0.0832514
$540$		0			0
$541$	11.3209			0.486725			0.243362	−	0.969935i	$-0.421750\pi$
$541$	11.3209			0.486725			0.243362	+	0.969935i	$0.421750\pi$
$542$	−18.6378	+	6.78361i	−0.800563	+	0.291381i
$543$		0			0
$544$	2.89988	−	2.43329i	0.124331	−	0.104326i
$545$	−0.206083	−	1.16875i	−0.00882761	−	0.0500638i
$546$		0			0
$547$	−8.14893	−	6.83776i	−0.348423	−	0.292362i	0.451733	−	0.892153i	$-0.350806\pi$
$547$	−8.14893	−	6.83776i	−0.348423	−	0.292362i	−0.800156	+	0.599791i	$0.795250\pi$
$548$	−4.53396	+	7.85305i	−0.193681	+	0.335466i
$549$		0			0
$550$	0.0680027	+	0.117784i	0.00289964	+	0.00502233i
$551$	2.03588	−	11.5460i	0.0867312	−	0.491877i
$552$		0			0
$553$	−8.92710	−	3.24920i	−0.379619	−	0.138170i
$554$	−22.6812	−	8.25528i	−0.963632	−	0.350733i
$555$		0			0
$556$	−1.74358	+	9.88833i	−0.0739442	+	0.419358i
$557$	−5.92385	−	10.2604i	−0.251001	−	0.434747i	0.712800	−	0.701367i	$-0.247427\pi$
$557$	−5.92385	−	10.2604i	−0.251001	−	0.434747i	−0.963802	+	0.266620i	$0.914093\pi$
$558$		0			0
$559$	−17.9276	+	31.0516i	−0.758258	+	1.31334i
$560$	6.41758	+	5.38499i	0.271192	+	0.227557i
$561$		0			0
$562$	−4.10770	−	23.2959i	−0.173273	−	0.982678i
$563$	−4.60236	+	3.86183i	−0.193966	+	0.162757i	−0.734599	−	0.678502i	$-0.762629\pi$
$563$	−4.60236	+	3.86183i	−0.193966	+	0.162757i	0.540632	+	0.841259i	$0.318185\pi$
$564$		0			0
$565$	2.66808	−	0.971103i	0.112247	−	0.0408546i
$566$	11.6242			0.488600
$567$		0			0
$568$	−11.7241			−0.491934
$569$	−27.4281	+	9.98301i	−1.14985	+	0.418510i	−0.845460	−	0.534039i	$-0.820673\pi$
$569$	−27.4281	+	9.98301i	−1.14985	+	0.418510i	−0.304386	+	0.952549i	$0.598451\pi$
$570$		0			0
$571$	16.7105	−	14.0218i	0.699314	−	0.586794i	−0.222264	−	0.974986i	$-0.571345\pi$
$571$	16.7105	−	14.0218i	0.699314	−	0.586794i	0.921578	+	0.388192i	$0.126900\pi$
$572$	−0.191797	−	1.08774i	−0.00801945	−	0.0454805i
$573$		0			0
$574$	−8.41961	−	7.06489i	−0.351428	−	0.294883i
$575$	−0.265499	+	0.459857i	−0.0110721	+	0.0191774i
$576$		0			0
$577$	−20.0399	−	34.7102i	−0.834273	−	1.44500i	−0.894621	−	0.446826i	$-0.852554\pi$
$577$	−20.0399	−	34.7102i	−0.834273	−	1.44500i	0.0603476	−	0.998177i	$-0.480779\pi$
$578$	0.463608	−	2.62925i	0.0192836	−	0.109363i
$579$		0			0
$580$	−18.0733	−	6.57814i	−0.750453	−	0.273143i
$581$	42.9826	+	15.6444i	1.78322	+	0.649038i
$582$		0			0
$583$	−0.416841	+	2.36402i	−0.0172638	+	0.0979077i
$584$	0.375162	+	0.649800i	0.0155243	+	0.0268889i
$585$		0			0
$586$	5.35546	−	9.27593i	0.221232	−	0.383185i
$587$	20.5803	+	17.2689i	0.849441	+	0.712766i	0.959666	−	0.281141i	$-0.0907129\pi$
$587$	20.5803	+	17.2689i	0.849441	+	0.712766i	−0.110226	+	0.993907i	$0.535157\pi$
$588$		0			0
$589$	−0.781509	−	4.43216i	−0.0322015	−	0.182624i
$590$	13.6916	−	11.4886i	0.563674	−	0.472979i
$591$		0			0
$592$	−3.34023	+	1.21575i	−0.137283	+	0.0499668i
$593$	−30.4609			−1.25088			−0.625440	−	0.780272i	$-0.715081\pi$
$593$	−30.4609			−1.25088			−0.625440	+	0.780272i	$0.715081\pi$
$594$		0			0
$595$	−31.7134			−1.30012
$596$	14.8870	−	5.41843i	0.609796	−	0.221948i
$597$		0			0
$598$	3.30341	−	2.77189i	0.135086	−	0.113351i
$599$	5.06859	+	28.7454i	0.207097	+	1.17451i	0.894106	+	0.447856i	$0.147812\pi$
$599$	5.06859	+	28.7454i	0.207097	+	1.17451i	−0.687009	+	0.726649i	$0.741077\pi$
$600$		0			0
$601$	−17.7890	−	14.9267i	−0.725627	−	0.608873i	0.203309	−	0.979115i	$-0.434830\pi$
$601$	−17.7890	−	14.9267i	−0.725627	−	0.608873i	−0.928935	+	0.370242i	$0.879275\pi$
$602$	−13.8352	+	23.9632i	−0.563879	+	0.976667i
$603$		0			0
$604$	−2.65377	−	4.59647i	−0.107981	−	0.187028i
$605$	3.97202	−	22.5264i	0.161486	−	0.915830i
$606$		0			0
$607$	−40.0979	−	14.5945i	−1.62752	−	0.592371i	−0.642730	−	0.766093i	$-0.722198\pi$
$607$	−40.0979	−	14.5945i	−1.62752	−	0.592371i	−0.984795	+	0.173722i	$0.944421\pi$
$608$	−1.19605	−	0.435326i	−0.0485062	−	0.0176548i
$609$		0			0
$610$	1.02744	−	5.82688i	0.0415997	−	0.235924i
$611$	−3.32029	−	5.75091i	−0.134325	−	0.232657i
$612$		0			0
$613$	6.80411	−	11.7851i	0.274815	−	0.475994i	−0.695273	−	0.718746i	$-0.744717\pi$
$613$	6.80411	−	11.7851i	0.274815	−	0.475994i	0.970089	+	0.242752i	$0.0780500\pi$
$614$	−18.9884	−	15.9332i	−0.766309	−	0.643010i
$615$		0			0
$616$	−0.148014	−	0.839430i	−0.00596366	−	0.0338216i
$617$	−21.5477	+	18.0807i	−0.867478	+	0.727900i	−0.963565	−	0.267473i	$-0.913811\pi$
$617$	−21.5477	+	18.0807i	−0.867478	+	0.727900i	0.0960878	+	0.995373i	$0.469367\pi$
$618$		0			0
$619$	18.3211	−	6.66832i	0.736385	−	0.268022i	0.0535202	−	0.998567i	$-0.482956\pi$
$619$	18.3211	−	6.66832i	0.736385	−	0.268022i	0.682865	+	0.730544i	$0.260734\pi$
$620$	−7.38303			−0.296510
$621$		0			0
$622$	−21.7835			−0.873439
$623$	−20.3452	+	7.40503i	−0.815111	+	0.296676i
$624$		0			0
$625$	−16.3851	+	13.7487i	−0.655404	+	0.549949i
$626$	1.63272	+	9.25962i	0.0652566	+	0.370089i
$627$		0			0
$628$	−8.82256	−	7.40301i	−0.352058	−	0.295412i
$629$	6.72802	−	11.6533i	0.268264	−	0.464646i
$630$		0			0
$631$	−6.27471	−	10.8681i	−0.249792	−	0.432653i	0.713676	−	0.700476i	$-0.247029\pi$
$631$	−6.27471	−	10.8681i	−0.249792	−	0.432653i	−0.963468	+	0.267823i	$0.913696\pi$
$632$	0.411161	−	2.33181i	0.0163551	−	0.0927544i
$633$		0			0
$634$	13.6311	+	4.96130i	0.541358	+	0.197038i
$635$	3.53965	+	1.28833i	0.140467	+	0.0511257i
$636$		0			0
$637$	8.21350	−	46.5811i	0.325431	−	1.84561i
$638$	0.978448	+	1.69472i	0.0387371	+	0.0670947i
$639$		0			0
$640$	−1.04401	+	1.80828i	−0.0412681	+	0.0714784i
$641$	10.6885	+	8.96870i	0.422170	+	0.354242i	0.828988	−	0.559267i	$-0.188917\pi$
$641$	10.6885	+	8.96870i	0.422170	+	0.354242i	−0.406818	+	0.913509i	$0.633362\pi$
$642$		0			0
$643$	7.12845	+	40.4274i	0.281119	+	1.59430i	0.718829	+	0.695187i	$0.244678\pi$
$643$	7.12845	+	40.4274i	0.281119	+	1.59430i	−0.437711	+	0.899116i	$0.644211\pi$
$644$	2.54931	−	2.13913i	0.100457	−	0.0842935i
$645$		0			0
$646$	4.52767	−	1.64794i	0.178139	−	0.0648373i
$647$	−0.303995			−0.0119513			−0.00597563	−	0.999982i	$-0.501902\pi$
$647$	−0.303995			−0.0119513			−0.00597563	+	0.999982i	$0.501902\pi$
$648$		0			0
$649$	−1.81851			−0.0713829
$650$	−3.12762	+	1.13836i	−0.122675	+	0.0446502i
$651$		0			0
$652$	5.87047	−	4.92591i	0.229905	−	0.192914i
$653$	−8.18178	−	46.4012i	−0.320178	−	1.81582i	−0.541596	−	0.840639i	$-0.682180\pi$
$653$	−8.18178	−	46.4012i	−0.320178	−	1.81582i	0.221419	−	0.975179i	$-0.428931\pi$
$654$		0			0
$655$	−15.5384	−	13.0382i	−0.607134	−	0.509446i
$656$	1.36970	−	2.37239i	0.0534777	−	0.0926261i
$657$		0			0
$658$	−2.56234	−	4.43811i	−0.0998905	−	0.173015i
$659$	7.46093	−	42.3130i	0.290637	−	1.64828i	−0.393790	−	0.919200i	$-0.628836\pi$
$659$	7.46093	−	42.3130i	0.290637	−	1.64828i	0.684427	−	0.729081i	$-0.260052\pi$
$660$		0			0
$661$	−25.8661	−	9.41451i	−1.00608	−	0.366182i	−0.214152	−	0.976800i	$-0.568699\pi$
$661$	−25.8661	−	9.41451i	−1.00608	−	0.366182i	−0.791925	+	0.610619i	$0.790921\pi$
$662$	0.758087	+	0.275921i	0.0294639	+	0.0107240i
$663$		0			0
$664$	−1.97967	+	11.2273i	−0.0768263	+	0.435703i
$665$	5.33151	+	9.23445i	0.206747	+	0.358097i
$666$		0			0
$667$	−3.82009	+	6.61659i	−0.147915	+	0.256196i
$668$	−4.68053	−	3.92743i	−0.181095	−	0.151957i
$669$		0			0
$670$	3.53899	+	20.0706i	0.136723	+	0.775394i
$671$	−0.461164	+	0.386962i	−0.0178030	+	0.0149385i
$672$		0			0
$673$	31.6139	−	11.5065i	1.21863	−	0.443543i	0.348938	−	0.937146i	$-0.386542\pi$
$673$	31.6139	−	11.5065i	1.21863	−	0.443543i	0.869688	+	0.493602i	$0.164320\pi$
$674$	26.6658			1.02713
$675$		0			0
$676$	14.0299			0.539611
$677$	32.0333	−	11.6592i	1.23114	−	0.448098i	0.357151	−	0.934047i	$-0.383748\pi$
$677$	32.0333	−	11.6592i	1.23114	−	0.448098i	0.873987	+	0.485949i	$0.161526\pi$
$678$		0			0
$679$	38.6132	−	32.4003i	1.48184	−	1.24341i
$680$	−1.37256	−	7.78415i	−0.0526351	−	0.298509i
$681$		0			0
$682$	0.575446	+	0.482856i	0.0220350	+	0.0184895i
$683$	−8.22650	+	14.2487i	−0.314778	+	0.545212i	−0.979390	−	0.201976i	$-0.935264\pi$
$683$	−8.22650	+	14.2487i	−0.314778	+	0.545212i	0.664612	+	0.747189i	$0.268597\pi$
$684$		0			0
$685$	9.46699	+	16.3973i	0.361715	+	0.626509i
$686$	1.46155	−	8.28888i	0.0558024	−	0.316471i
$687$		0			0
$688$	−6.48062	−	2.35875i	−0.247071	−	0.0899266i
$689$	−55.2023	−	20.0920i	−2.10304	−	0.765445i
$690$		0			0
$691$	−2.47781	+	14.0524i	−0.0942603	+	0.534577i	0.900711	+	0.434418i	$0.143046\pi$
$691$	−2.47781	+	14.0524i	−0.0942603	+	0.534577i	−0.994972	+	0.100158i	$0.968065\pi$
$692$	−5.65174	−	9.78911i	−0.214847	−	0.372126i
$693$		0			0
$694$	14.5521	−	25.2051i	0.552392	−	0.956771i
$695$	16.0605	+	13.4764i	0.609210	+	0.511188i
$696$		0			0
$697$	1.80074	+	10.2125i	0.0682079	+	0.386826i
$698$	22.6355	−	18.9934i	0.856765	−	0.718911i
$699$		0			0
$700$	−2.41365	+	0.878498i	−0.0912275	+	0.0332041i
$701$	−15.8891			−0.600123			−0.300062	−	0.953920i	$-0.597007\pi$
$701$	−15.8891			−0.600123			−0.300062	+	0.953920i	$0.597007\pi$
$702$		0			0
$703$	−4.52433			−0.170638
$704$	0.199635	−	0.0726611i	0.00752401	−	0.00273852i
$705$		0			0
$706$	4.78974	−	4.01907i	0.180264	−	0.151260i
$707$	−2.01665	−	11.4370i	−0.0758439	−	0.430132i
$708$		0			0
$709$	−6.31358	−	5.29773i	−0.237112	−	0.198960i	0.516487	−	0.856295i	$-0.327239\pi$
$709$	−6.31358	−	5.29773i	−0.237112	−	0.198960i	−0.753599	+	0.657335i	$0.771684\pi$
$710$	−12.2401	+	21.2005i	−0.459363	+	0.795640i
$711$		0			0
$712$	−2.69813	−	4.67329i	−0.101117	−	0.175139i
$713$	−0.509280	+	2.88827i	−0.0190727	+	0.108167i
$714$		0			0
$715$	−2.16717	−	0.788784i	−0.0810474	−	0.0294988i
$716$	6.51197	+	2.37016i	0.243364	+	0.0885772i
$717$		0			0
$718$	−0.449104	+	2.54700i	−0.0167604	+	0.0950531i
$719$	10.9348	+	18.9397i	0.407801	+	0.706331i	0.994643	−	0.103370i	$-0.0329625\pi$
$719$	10.9348	+	18.9397i	0.407801	+	0.706331i	−0.586842	+	0.809701i	$0.699629\pi$
$720$		0			0
$721$	33.4819	−	57.9923i	1.24693	−	2.15975i
$722$	13.3138	+	11.1716i	0.495489	+	0.415765i
$723$		0			0
$724$	0.527479	+	2.99148i	0.0196036	+	0.111178i
$725$	4.51729	−	3.79045i	0.167768	−	0.140774i
$726$		0			0
$727$	−45.7236	+	16.6420i	−1.69579	+	0.617219i	−0.995336	−	0.0964735i	$-0.969244\pi$
$727$	−45.7236	+	16.6420i	−1.69579	+	0.617219i	−0.700459	+	0.713692i	$0.747021\pi$
$728$	20.8596			0.773107
$729$		0			0
$730$	1.56669			0.0579858
$731$	24.5325	−	8.92912i	0.907369	−	0.330255i
$732$		0			0
$733$	−20.0537	+	16.8270i	−0.740700	+	0.621521i	−0.933026	−	0.359810i	$-0.882842\pi$
$733$	−20.0537	+	16.8270i	−0.740700	+	0.621521i	0.192325	+	0.981331i	$0.438397\pi$
$734$	−3.24396	−	18.3974i	−0.119737	−	0.679060i
$735$		0			0
$736$	0.635390	+	0.533155i	0.0234208	+	0.0196524i
$737$	1.03680	−	1.79579i	0.0381910	−	0.0661487i
$738$		0			0
$739$	−1.28655	−	2.22838i	−0.0473267	−	0.0819722i	0.841392	−	0.540426i	$-0.181737\pi$
$739$	−1.28655	−	2.22838i	−0.0473267	−	0.0819722i	−0.888718	+	0.458454i	$0.848404\pi$
$740$	−1.28883	+	7.30931i	−0.0473783	+	0.268696i
$741$		0			0
$742$	−42.6009	−	15.5054i	−1.56393	−	0.569223i
$743$	−46.0421	−	16.7580i	−1.68912	−	0.614790i	−0.694608	−	0.719388i	$-0.744422\pi$
$743$	−46.0421	−	16.7580i	−1.68912	−	0.614790i	−0.994515	+	0.104598i	$0.966644\pi$
$744$		0			0
$745$	5.74415	−	32.5767i	0.210450	−	1.19352i
$746$	6.76307	+	11.7140i	0.247614	+	0.428879i
$747$		0			0
$748$	−0.402111	+	0.696477i	−0.0147026	+	0.0254657i
$749$	0.987743	+	0.828815i	0.0360913	+	0.0302842i
$750$		0			0
$751$	1.47790	+	8.38157i	0.0539293	+	0.305848i	0.999827	−	0.0186178i	$-0.00592658\pi$
$751$	1.47790	+	8.38157i	0.0539293	+	0.305848i	−0.945897	+	0.324466i	$0.894815\pi$
$752$	0.978448	−	0.821016i	0.0356803	−	0.0299394i
$753$		0			0
$754$	−45.0014	+	16.3792i	−1.63885	+	0.596494i
$755$	−11.0822			−0.403324
$756$		0			0
$757$	17.3242			0.629658			0.314829	−	0.949148i	$-0.398053\pi$
$757$	17.3242			0.629658			0.314829	+	0.949148i	$0.398053\pi$
$758$	28.3954	−	10.3351i	1.03137	−	0.375387i
$759$		0			0
$760$	−2.03588	+	1.70830i	−0.0738490	+	0.0619667i
$761$	−1.81406	−	10.2880i	−0.0657596	−	0.372941i	−0.999873	−	0.0159637i	$-0.994918\pi$
$761$	−1.81406	−	10.2880i	−0.0657596	−	0.372941i	0.934113	−	0.356978i	$-0.116193\pi$
$762$		0			0
$763$	−1.74692	−	1.46584i	−0.0632429	−	0.0530671i
$764$	−2.54859	+	4.41429i	−0.0922047	+	0.159703i
$765$		0			0
$766$	19.2945	+	33.4191i	0.697140	+	1.20748i
$767$	7.72785	−	43.8268i	0.279036	−	1.58249i
$768$		0			0
$769$	−37.0705	−	13.4926i	−1.33680	−	0.486554i	−0.427995	−	0.903781i	$-0.640780\pi$
$769$	−37.0705	−	13.4926i	−1.33680	−	0.486554i	−0.908802	+	0.417227i	$0.863002\pi$
$770$	−1.67245	−	0.608722i	−0.0602709	−	0.0219368i
$771$		0			0
$772$	3.27644	−	18.5816i	0.117922	−	0.668767i
$773$	−11.6713	−	20.2152i	−0.419786	−	0.727091i	0.576131	−	0.817357i	$-0.304562\pi$
$773$	−11.6713	−	20.2152i	−0.419786	−	0.727091i	−0.995918	+	0.0902659i	$0.971228\pi$
$774$		0			0
$775$	1.13182	−	1.96037i	0.0406561	−	0.0704184i
$776$	9.62394	+	8.07544i	0.345479	+	0.289892i
$777$		0			0
$778$	−0.976976	−	5.54071i	−0.0350263	−	0.198644i
$779$	2.67099	−	2.24123i	0.0956981	−	0.0803002i
$780$		0			0
$781$	2.34055	−	0.851889i	0.0837513	−	0.0304830i
$782$	−3.13987			−0.112282
$783$		0			0
$784$	9.09779			0.324921
$785$	−22.5975	+	8.22482i	−0.806539	+	0.293556i
$786$		0			0
$787$	29.0251	−	24.3549i	1.03463	−	0.868160i	0.0432374	−	0.999065i	$-0.486233\pi$
$787$	29.0251	−	24.3549i	1.03463	−	0.868160i	0.991395	+	0.130905i	$0.0417884\pi$
$788$	3.48060	+	19.7394i	0.123991	+	0.703188i
$789$		0			0
$790$	−3.78730	−	3.17792i	−0.134746	−	0.113065i
$791$	2.72793	−	4.72491i	0.0969939	−	0.167998i
$792$		0			0
$793$	−7.36619	−	12.7586i	−0.261581	−	0.453072i
$794$	−1.33990	+	7.59895i	−0.0475513	+	0.269677i
$795$		0			0
$796$	−5.17030	−	1.88184i	−0.183257	−	0.0666999i
$797$	−2.54138	−	0.924988i	−0.0900204	−	0.0327647i	0.296617	−	0.954996i	$-0.404141\pi$
$797$	−2.54138	−	0.924988i	−0.0900204	−	0.0327647i	−0.386638	+	0.922232i	$0.626364\pi$
$798$		0			0
$799$	−0.839615	+	4.76169i	−0.0297034	+	0.168457i
$800$	−0.320093	−	0.554417i	−0.0113170	−	0.0196016i
$801$		0			0
$802$	−18.1897	+	31.5054i	−0.642300	+	1.11250i
$803$	−0.122111	−	0.102463i	−0.00430919	−	0.00361584i
$804$		0			0
$805$	−1.20663	−	6.84313i	−0.0425281	−	0.241189i
$806$	−14.0824	+	11.8165i	−0.496031	+	0.416220i
$807$		0			0
$808$	2.71996	−	0.989985i	0.0956879	−	0.0348275i
$809$	22.3977			0.787460			0.393730	−	0.919226i	$-0.371185\pi$
$809$	22.3977			0.787460			0.393730	+	0.919226i	$0.371185\pi$
$810$		0			0
$811$	−35.0916			−1.23223			−0.616117	−	0.787655i	$-0.711295\pi$
$811$	−35.0916			−1.23223			−0.616117	+	0.787655i	$0.711295\pi$
$812$	−34.7285	+	12.6402i	−1.21873	+	0.443583i
$813$		0			0
$814$	0.578489	−	0.485410i	0.0202760	−	0.0170136i
$815$	−2.77858	−	15.7581i	−0.0973295	−	0.551983i
$816$		0			0
$817$	−6.72432	−	5.64237i	−0.235254	−	0.197402i
$818$	2.93384	−	5.08156i	0.102579	−	0.177672i
$819$		0			0
$820$	−2.85995	−	4.95358i	−0.0998739	−	0.172987i
$821$	−2.46023	+	13.9527i	−0.0858627	+	0.486952i	0.911304	+	0.411733i	$0.135076\pi$
$821$	−2.46023	+	13.9527i	−0.0858627	+	0.486952i	−0.997167	+	0.0752183i	$0.976035\pi$
$822$		0			0
$823$	32.5132	+	11.8338i	1.13334	+	0.412502i	0.839504	−	0.543354i	$-0.182846\pi$
$823$	32.5132	+	11.8338i	1.13334	+	0.412502i	0.293836	+	0.955856i	$0.405068\pi$
$824$	15.6835	+	5.70832i	0.546360	+	0.198859i
$825$		0			0
$826$	5.96375	−	33.8221i	0.207506	−	1.17682i
$827$	25.3847	+	43.9676i	0.882713	+	1.52890i	0.848312	+	0.529496i	$0.177619\pi$
$827$	25.3847	+	43.9676i	0.882713	+	1.52890i	0.0344011	+	0.999408i	$0.489048\pi$
$828$		0			0
$829$	−27.2911	+	47.2695i	−0.947859	+	1.64174i	−0.197935	+	0.980215i	$0.563423\pi$
$829$	−27.2911	+	47.2695i	−0.947859	+	1.64174i	−0.749924	+	0.661524i	$0.769910\pi$
$830$	18.2352	+	15.3012i	0.632954	+	0.531112i
$831$		0			0
$832$	0.902802	+	5.12004i	0.0312990	+	0.177506i
$833$	−26.3825	+	22.1375i	−0.914099	+	0.767020i
$834$		0			0
$835$	−11.9884	+	4.36341i	−0.414875	+	0.151002i
$836$	0.270404			0.00935213
$837$		0			0
$838$	21.1356			0.730117
$839$	−10.4104	+	3.78906i	−0.359406	+	0.130813i	−0.515411	−	0.856943i	$-0.672361\pi$
$839$	−10.4104	+	3.78906i	−0.359406	+	0.130813i	0.156005	+	0.987756i	$0.450138\pi$
$840$		0			0
$841$	42.7811	−	35.8976i	1.47521	−	1.23785i
$842$	−1.29245	−	7.32984i	−0.0445407	−	0.252603i
$843$		0			0
$844$	−19.2623	−	16.1630i	−0.663035	−	0.556353i
$845$	14.6473	−	25.3699i	0.503883	−	0.872751i
$846$		0			0
$847$	−21.9766	−	38.0646i	−0.755124	−	1.30791i
$848$	1.96209	−	11.1276i	0.0673786	−	0.382123i
$849$		0			0
$850$	2.27729	+	0.828865i	0.0781103	+	0.0284298i
$851$	2.77053	+	1.00839i	0.0949726	+	0.0345672i
$852$		0			0
$853$	−4.41726	+	25.0515i	−0.151244	+	0.857748i	0.810895	+	0.585191i	$0.198981\pi$
$853$	−4.41726	+	25.0515i	−0.151244	+	0.857748i	−0.962140	+	0.272557i	$0.912131\pi$
$854$	−5.68465	−	9.84611i	−0.194525	−	0.336927i
$855$		0			0
$856$	−0.160686	+	0.278316i	−0.00549212	+	0.00951263i
$857$	−36.1557	−	30.3382i	−1.23506	−	1.03633i	−0.997894	−	0.0648639i	$-0.979339\pi$
$857$	−36.1557	−	30.3382i	−1.23506	−	1.03633i	−0.237161	−	0.971470i	$-0.576217\pi$
$858$		0			0
$859$	−4.26079	−	24.1641i	−0.145376	−	0.824469i	−0.967064	−	0.254532i	$-0.918079\pi$
$859$	−4.26079	−	24.1641i	−0.145376	−	0.824469i	0.821688	−	0.569937i	$-0.193033\pi$
$860$	−11.0311	+	9.25619i	−0.376157	+	0.315634i
$861$		0			0
$862$	12.2632	−	4.46343i	0.417686	−	0.152025i
$863$	−28.4215			−0.967479			−0.483740	−	0.875212i	$-0.660722\pi$
$863$	−28.4215			−0.967479			−0.483740	+	0.875212i	$0.660722\pi$
$864$		0			0
$865$	−23.6019			−0.802488
$866$	0.134877	−	0.0490911i	0.00458330	−	0.00166818i
$867$		0			0
$868$	−10.8677	+	9.11908i	−0.368874	+	0.309522i
$869$	0.0873498	+	0.495385i	0.00296314	+	0.0168048i
$870$		0			0
$871$	38.8732	+	32.6185i	1.31717	+	1.10524i
$872$	0.284189	−	0.492229i	0.00962385	−	0.0166690i
$873$		0			0
$874$	0.527861	+	0.914282i	0.0178552	+	0.0309261i
$875$	−8.20504	+	46.5331i	−0.277381	+	1.57311i
$876$		0			0
$877$	−40.6428	−	14.7928i	−1.37241	−	0.499517i	−0.452542	−	0.891743i	$-0.649483\pi$
$877$	−40.6428	−	14.7928i	−1.37241	−	0.499517i	−0.919869	+	0.392226i	$0.871705\pi$
$878$	12.7390	+	4.63660i	0.429919	+	0.156478i
$879$		0			0
$880$	0.0770290	−	0.436853i	0.00259665	−	0.0147263i
$881$	−10.2218	−	17.7047i	−0.344381	−	0.596485i	0.640860	−	0.767658i	$-0.278578\pi$
$881$	−10.2218	−	17.7047i	−0.344381	−	0.596485i	−0.985241	+	0.171173i	$0.945244\pi$
$882$		0			0
$883$	14.1469	−	24.5031i	0.476080	−	0.824595i	−0.523544	−	0.851999i	$-0.675391\pi$
$883$	14.1469	−	24.5031i	0.476080	−	0.824595i	0.999624	+	0.0274033i	$0.00872385\pi$
$884$	−15.0766	−	12.6507i	−0.507079	−	0.425490i
$885$		0			0
$886$	2.13262	+	12.0947i	0.0716468	+	0.406329i
$887$	44.0025	−	36.9225i	1.47746	−	1.23974i	0.568615	−	0.822604i	$-0.307479\pi$
$887$	44.0025	−	36.9225i	1.47746	−	1.23974i	0.908846	−	0.417133i	$-0.136965\pi$
$888$		0			0
$889$	6.80157	−	2.47557i	0.228117	−	0.0830279i
$890$	−11.2675			−0.377686
$891$		0			0
$892$	−3.75239			−0.125639
$893$	1.52768	−	0.556031i	0.0511219	−	0.0186069i
$894$		0			0
$895$	11.0845	−	9.30097i	0.370513	−	0.310897i
$896$	0.696712	+	3.95125i	0.0232755	+	0.132002i
$897$		0			0
$898$	31.1509	+	26.1387i	1.03952	+	0.872259i
$899$	16.2850	−	28.2065i	0.543136	−	0.940739i
$900$		0			0
$901$	21.3868	+	37.0430i	0.712497	+	1.23408i
$902$	−0.101059	+	0.573134i	−0.00336490	+	0.0190833i
$903$		0			0
$904$	1.27781	+	0.465084i	0.0424992	+	0.0154685i
$905$	5.96012	+	2.16931i	0.198121	+	0.0721102i
$906$		0			0
$907$	−4.94703	+	28.0560i	−0.164263	+	0.931585i	0.785557	+	0.618789i	$0.212377\pi$
$907$	−4.94703	+	28.0560i	−0.164263	+	0.931585i	−0.949821	+	0.312795i	$0.898735\pi$
$908$	9.36384	+	16.2186i	0.310750	+	0.538235i
$909$		0			0
$910$	21.7776	−	37.7198i	0.721919	−	1.25040i
$911$	14.5384	+	12.1992i	0.481680	+	0.404178i	0.851034	−	0.525111i	$-0.175976\pi$
$911$	14.5384	+	12.1992i	0.481680	+	0.404178i	−0.369353	+	0.929289i	$0.620421\pi$
$912$		0			0
$913$	−0.420575	−	2.38520i	−0.0139190	−	0.0789386i
$914$	−24.9661	+	20.9491i	−0.825806	+	0.692934i
$915$		0			0
$916$	3.89345	−	1.41710i	0.128643	−	0.0468223i
$917$	−38.9763			−1.28711
$918$		0			0
$919$	−13.1481			−0.433715			−0.216857	−	0.976203i	$-0.569581\pi$
$919$	−13.1481			−0.433715			−0.216857	+	0.976203i	$0.569581\pi$
$920$	1.62744	−	0.592341i	0.0536552	−	0.0195289i
$921$		0			0
$922$	−20.9287	+	17.5612i	−0.689249	+	0.578349i
$923$	10.5846	+	60.0281i	0.348396	+	1.97585i
$924$		0			0
$925$	−1.74322	−	1.46273i	−0.0573166	−	0.0480943i
$926$	−1.69959	+	2.94378i	−0.0558521	+	0.0967386i
$927$		0			0
$928$	−4.60562	−	7.97716i	−0.151187	−	0.261863i
$929$	−4.75483	+	26.9660i	−0.156001	+	0.884725i	0.801864	+	0.597506i	$0.203842\pi$
$929$	−4.75483	+	26.9660i	−0.156001	+	0.884725i	−0.957865	+	0.287219i	$0.907269\pi$
$930$		0			0
$931$	10.8814	+	3.96051i	0.356624	+	0.129800i
$932$	−1.80150	−	0.655691i	−0.0590099	−	0.0214779i
$933$		0			0
$934$	5.72997	−	32.4963i	0.187490	−	1.06331i
$935$	0.839615	+	1.45426i	0.0274583	+	0.0475592i
$936$		0			0
$937$	−20.0466	+	34.7218i	−0.654895	+	1.13431i	0.327025	+	0.945016i	$0.393954\pi$
$937$	−20.0466	+	34.7218i	−0.654895	+	1.13431i	−0.981920	+	0.189296i	$0.939380\pi$
$938$	29.9993	+	25.1724i	0.979513	+	0.821909i
$939$		0			0
$940$	−0.463114	−	2.62645i	−0.0151051	−	0.0856654i
$941$	2.61149	−	2.19130i	0.0851323	−	0.0714344i	−0.599228	−	0.800578i	$-0.704526\pi$
$941$	2.61149	−	2.19130i	0.0851323	−	0.0714344i	0.684361	+	0.729144i	$0.260081\pi$
$942$		0			0
$943$	−2.13514	+	0.777128i	−0.0695298	+	0.0253068i
$944$	8.55985			0.278600
$945$		0			0
$946$	1.46515			0.0476360
$947$	3.60378	−	1.31167i	0.117107	−	0.0426235i	−0.282802	−	0.959178i	$-0.591264\pi$
$947$	3.60378	−	1.31167i	0.117107	−	0.0426235i	0.399909	+	0.916555i	$0.369042\pi$
$948$		0			0
$949$	2.98831	−	2.50749i	0.0970046	−	0.0813965i
$950$	−0.141495	−	0.802455i	−0.00459069	−	0.0260351i
$951$		0			0
$952$	−11.6349	−	9.76285i	−0.377090	−	0.316416i
$953$	−26.3964	+	45.7200i	−0.855065	+	1.48102i	0.0215205	+	0.999768i	$0.493149\pi$
$953$	−26.3964	+	45.7200i	−0.855065	+	1.48102i	−0.876585	+	0.481247i	$0.840184\pi$
$954$		0			0
$955$	5.32150	+	9.21711i	0.172200	+	0.298259i
$956$	−4.20216	+	23.8316i	−0.135908	+	0.770770i
$957$		0			0
$958$	21.6536	+	7.88126i	0.699596	+	0.254632i
$959$	34.1882	+	12.4435i	1.10400	+	0.401822i
$960$		0			0
$961$	−3.21204	+	18.2164i	−0.103614	+	0.587625i
$962$	9.24024	+	16.0046i	0.297917	+	0.516008i
$963$		0			0
$964$	−6.60247	+	11.4358i	−0.212651	+	0.368323i
$965$	−30.1800	−	25.3241i	−0.971530	−	0.815211i
$966$		0			0
$967$	1.74407	+	9.89114i	0.0560857	+	0.318078i	0.999924	−	0.0123301i	$-0.00392488\pi$
$967$	1.74407	+	9.89114i	0.0560857	+	0.318078i	−0.943838	+	0.330408i	$0.892814\pi$
$968$	8.39191	−	7.04165i	0.269726	−	0.226327i
$969$		0			0
$970$	24.6501	−	8.97190i	0.791467	−	0.288070i
$971$	−4.06174			−0.130348			−0.0651738	−	0.997874i	$-0.520760\pi$
$971$	−4.06174			−0.130348			−0.0651738	+	0.997874i	$0.520760\pi$
$972$		0			0
$973$	40.2860			1.29151
$974$	25.3074	−	9.21113i	0.810900	−	0.295143i
$975$		0			0
$976$	2.17073	−	1.82146i	0.0694832	−	0.0583034i
$977$	−3.16544	−	17.9521i	−0.101271	−	0.574338i	−0.992644	−	0.121068i	$-0.961368\pi$
$977$	−3.16544	−	17.9521i	−0.101271	−	0.574338i	0.891373	−	0.453271i	$-0.149743\pi$
$978$		0			0
$979$	0.878205	+	0.736902i	0.0280676	+	0.0235515i
$980$	9.49817	−	16.4513i	0.303408	−	0.525518i
$981$		0			0
$982$	0.123997	+	0.214768i	0.00395689	+	0.00685354i
$983$	7.30071	−	41.4044i	0.232857	−	1.32060i	−0.614224	−	0.789131i	$-0.710531\pi$
$983$	7.30071	−	41.4044i	0.232857	−	1.32060i	0.847081	−	0.531464i	$-0.178358\pi$
$984$		0			0
$985$	39.3281	+	14.3143i	1.25310	+	0.456090i
$986$	32.7665	+	11.9260i	1.04350	+	0.379802i
$987$		0			0
$988$	−1.14909	+	6.51684i	−0.0365576	+	0.207328i
$989$	2.86014	+	4.95391i	0.0909471	+	0.157525i
$990$		0			0
$991$	15.9365	−	27.6029i	0.506241	−	0.876834i	−0.493733	−	0.869613i	$-0.664368\pi$
$991$	15.9365	−	27.6029i	0.506241	−	0.876834i	0.999974	−	0.00722097i	$-0.00229853\pi$
$992$	−2.70866	−	2.27284i	−0.0860000	−	0.0721626i
$993$		0			0
$994$	8.16835	+	46.3250i	0.259084	+	1.46934i
$995$	−8.80072	+	7.38468i	−0.279002	+	0.234110i
$996$		0			0
$997$	30.0699	−	10.9446i	0.952324	−	0.346618i	0.181303	−	0.983427i	$-0.441969\pi$
$997$	30.0699	−	10.9446i	0.952324	−	0.346618i	0.771021	+	0.636810i	$0.219746\pi$
$998$	26.7183			0.845753
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.e.e.55.1		12
3.2	odd	2		486.2.e.h.55.2		12
9.2	odd	6		54.2.e.b.43.2	✓	12
9.4	even	3		486.2.e.g.217.1		12
9.5	odd	6		486.2.e.f.217.2		12
9.7	even	3		162.2.e.b.127.2		12
27.2	odd	18		1458.2.a.g.1.4		6
27.4	even	9	inner	486.2.e.e.433.1		12
27.5	odd	18		486.2.e.f.271.2		12
27.7	even	9		1458.2.c.g.487.4		12
27.11	odd	18		1458.2.c.f.973.3		12
27.13	even	9		162.2.e.b.37.2		12
27.14	odd	18		54.2.e.b.49.2	yes	12
27.16	even	9		1458.2.c.g.973.4		12
27.20	odd	18		1458.2.c.f.487.3		12
27.22	even	9		486.2.e.g.271.1		12
27.23	odd	18		486.2.e.h.433.2		12
27.25	even	9		1458.2.a.f.1.3		6
36.11	even	6		432.2.u.b.97.1		12
108.95	even	18		432.2.u.b.49.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.2	✓	12	9.2	odd	6
54.2.e.b.49.2	yes	12	27.14	odd	18
162.2.e.b.37.2		12	27.13	even	9
162.2.e.b.127.2		12	9.7	even	3
432.2.u.b.49.1		12	108.95	even	18
432.2.u.b.97.1		12	36.11	even	6
486.2.e.e.55.1		12	1.1	even	1	trivial
486.2.e.e.433.1		12	27.4	even	9	inner
486.2.e.f.217.2		12	9.5	odd	6
486.2.e.f.271.2		12	27.5	odd	18
486.2.e.g.217.1		12	9.4	even	3
486.2.e.g.271.1		12	27.22	even	9
486.2.e.h.55.2		12	3.2	odd	2
486.2.e.h.433.2		12	27.23	odd	18
1458.2.a.f.1.3		6	27.25	even	9
1458.2.a.g.1.4		6	27.2	odd	18
1458.2.c.f.487.3		12	27.20	odd	18
1458.2.c.f.973.3		12	27.11	odd	18
1458.2.c.g.487.4		12	27.7	even	9
1458.2.c.g.973.4		12	27.16	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.766044 - 0.642788i) q^{4} +(-0.362580 - 2.05630i) q^{5} +(-3.07353 - 2.57900i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.04401 - 1.80828i) q^{10} +(-0.0368910 + 0.209219i) q^{11} +(-4.88549 - 1.77817i) q^{13} +(-3.77024 - 1.37225i) q^{14} +(0.173648 - 0.984808i) q^{16} +(1.89276 + 3.27836i) q^{17} +(0.636405 - 1.10229i) q^{19} +(-1.59951 - 1.34215i) q^{20} +(0.0368910 + 0.209219i) q^{22} +(-0.635390 + 0.533155i) q^{23} +(0.601578 - 0.218956i) q^{25} -5.19903 q^{26} -4.01220 q^{28} +(8.65573 - 3.15043i) q^{29} +(2.70866 - 2.27284i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(2.89988 + 2.43329i) q^{34} +(-4.18878 + 7.25517i) q^{35} +(-1.77730 - 3.07838i) q^{37} +(0.221021 - 1.25347i) q^{38} +(-1.96209 - 0.714144i) q^{40} +(2.57419 + 0.936928i) q^{41} +(1.19757 - 6.79176i) q^{43} +(0.106223 + 0.183984i) q^{44} +(-0.414721 + 0.718318i) q^{46} +(0.978448 + 0.821016i) q^{47} +(1.57981 + 8.95957i) q^{49} +(0.490411 - 0.411503i) q^{50} +(-4.88549 + 1.77817i) q^{52} +11.2992 q^{53} +0.443592 q^{55} +(-3.77024 + 1.37225i) q^{56} +(7.05621 - 5.92087i) q^{58} +(1.48640 + 8.42981i) q^{59} +(2.17073 + 1.82146i) q^{61} +(1.76795 - 3.06218i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(-1.88506 + 10.6907i) q^{65} +(-9.17192 - 3.33831i) q^{67} +(3.55723 + 1.29473i) q^{68} +(-1.45475 + 8.25028i) q^{70} +(-5.86207 - 10.1534i) q^{71} +(-0.375162 + 0.649800i) q^{73} +(-2.72298 - 2.28485i) q^{74} +(-0.221021 - 1.25347i) q^{76} +(0.652961 - 0.547899i) q^{77} +(2.22499 - 0.809829i) q^{79} -2.08802 q^{80} +2.73940 q^{82} +(-10.7130 + 3.89920i) q^{83} +(6.05500 - 5.08075i) q^{85} +(-1.19757 - 6.79176i) q^{86} +(0.162744 + 0.136558i) q^{88} +(2.69813 - 4.67329i) q^{89} +(10.4298 + 18.0649i) q^{91} +(-0.144031 + 0.816841i) q^{92} +(1.20024 + 0.436853i) q^{94} +(-2.49737 - 0.908969i) q^{95} +(-2.18157 + 12.3723i) q^{97} +(4.54889 + 7.87892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 6 q^{13} - 6 q^{14} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 6 q^{22} + 24 q^{23} + 36 q^{25} - 18 q^{26} + 12 q^{28} + 12 q^{29} + 27 q^{31} + 3 q^{34}+ \cdots + 12 q^{98}+O(q^{100}) \) 12 * q - 6 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 - 6 * q^11 - 6 * q^13 - 6 * q^14 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 6 * q^22 + 24 * q^23 + 36 * q^25 - 18 * q^26 + 12 * q^28 + 12 * q^29 + 27 * q^31 + 3 * q^34 - 3 * q^35 - 15 * q^37 - 12 * q^38 - 3 * q^40 + 3 * q^41 - 27 * q^43 + 3 * q^44 + 3 * q^46 - 36 * q^47 - 3 * q^49 + 9 * q^50 - 6 * q^52 + 12 * q^53 + 18 * q^55 - 6 * q^56 + 15 * q^58 - 12 * q^59 + 9 * q^61 + 12 * q^62 - 6 * q^64 + 42 * q^65 - 45 * q^67 - 12 * q^68 - 33 * q^70 - 12 * q^71 - 21 * q^73 + 30 * q^74 + 12 * q^76 - 48 * q^77 + 3 * q^79 - 6 * q^80 + 6 * q^82 + 18 * q^83 + 27 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 - 30 * q^92 - 27 * q^94 + 33 * q^95 - 15 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more