LMFDB - Embedded newform 648.2.v.b.35.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,2,Mod(35,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("648.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.v (of order $18$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			35.3
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39125 - 0.253795i) q^{2} +(1.87118 + 0.706186i) q^{4} +(0.715441 + 0.260399i) q^{5} +(3.32699 + 0.586638i) q^{7} +(-2.42406 - 1.45738i) q^{8} +O(q^{10})$	\(q+(-1.39125 - 0.253795i) q^{2} +(1.87118 + 0.706186i) q^{4} +(0.715441 + 0.260399i) q^{5} +(3.32699 + 0.586638i) q^{7} +(-2.42406 - 1.45738i) q^{8} +(-0.929272 - 0.543857i) q^{10} +(-1.95175 - 5.36238i) q^{11} +(-3.36983 - 4.01601i) q^{13} +(-4.47981 - 1.66054i) q^{14} +(3.00260 + 2.64280i) q^{16} +(2.95820 - 1.70792i) q^{17} +(1.27164 - 2.20255i) q^{19} +(1.15483 + 0.992487i) q^{20} +(1.35443 + 7.95577i) q^{22} +(0.947065 + 5.37107i) q^{23} +(-3.38617 - 2.84134i) q^{25} +(3.66905 + 6.44253i) q^{26} +(5.81111 + 3.44718i) q^{28} +(3.27434 + 2.74749i) q^{29} +(-2.33080 + 0.410982i) q^{31} +(-3.50665 - 4.43885i) q^{32} +(-4.54907 + 1.62537i) q^{34} +(2.22751 + 1.28605i) q^{35} +(9.07767 - 5.24099i) q^{37} +(-2.32817 + 2.74157i) q^{38} +(-1.35477 - 1.67389i) q^{40} +(-1.88727 - 2.24916i) q^{41} +(-5.95761 + 2.16839i) q^{43} +(0.134776 - 11.4123i) q^{44} +(0.0455422 - 7.71289i) q^{46} +(0.625921 - 3.54977i) q^{47} +(4.14688 + 1.50934i) q^{49} +(3.98991 + 4.81242i) q^{50} +(-3.46950 - 9.89438i) q^{52} +8.06569 q^{53} -4.34470i q^{55} +(-7.20986 - 6.27073i) q^{56} +(-3.85813 - 4.65347i) q^{58} +(1.63379 - 4.48880i) q^{59} +(2.62747 + 0.463294i) q^{61} +(3.34703 + 0.0197632i) q^{62} +(3.75209 + 7.06554i) q^{64} +(-1.36515 - 3.75071i) q^{65} +(2.16648 - 1.81790i) q^{67} +(6.74143 - 1.10678i) q^{68} +(-2.77263 - 2.35455i) q^{70} +(3.03884 + 5.26343i) q^{71} +(1.40736 - 2.43763i) q^{73} +(-13.9595 + 4.98769i) q^{74} +(3.93488 - 3.22334i) q^{76} +(-3.34767 - 18.9856i) q^{77} +(-7.42577 + 8.84969i) q^{79} +(1.46000 + 2.67264i) q^{80} +(2.05484 + 3.60813i) q^{82} +(-5.47239 + 6.52174i) q^{83} +(2.56116 - 0.451602i) q^{85} +(8.83888 - 1.50478i) q^{86} +(-3.08388 + 15.8431i) q^{88} +(7.79000 + 4.49756i) q^{89} +(-8.85545 - 15.3381i) q^{91} +(-2.02085 + 10.7190i) q^{92} +(-1.77173 + 4.77978i) q^{94} +(1.48333 - 1.24466i) q^{95} +(13.6755 - 4.97747i) q^{97} +(-5.38630 - 3.15233i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	$ 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) $ 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−1.39125	−	0.253795i	−0.983765	−	0.179460i
$2$	−1.39125	−	0.253795i	−0.983765	−	0.179460i
$3$		0			0
$3$		0			0
$4$	1.87118	+	0.706186i	0.935588	+	0.353093i
$5$	0.715441	+	0.260399i	0.319955	+	0.116454i	0.497005	−	0.867748i	$-0.334433\pi$
$5$	0.715441	+	0.260399i	0.319955	+	0.116454i	−0.177050	+	0.984202i	$0.556655\pi$
$6$		0			0
$7$	3.32699	+	0.586638i	1.25748	+	0.221728i	0.762394	−	0.647113i	$-0.224024\pi$
$7$	3.32699	+	0.586638i	1.25748	+	0.221728i	0.495091	+	0.868841i	$0.335135\pi$
$8$	−2.42406	−	1.45738i	−0.857033	−	0.515261i
$9$		0			0
$10$	−0.929272	−	0.543857i	−0.293862	−	0.171983i
$11$	−1.95175	−	5.36238i	−0.588474	−	1.61682i	−0.773296	−	0.634046i	$-0.781393\pi$
$11$	−1.95175	−	5.36238i	−0.588474	−	1.61682i	0.184822	−	0.982772i	$-0.440829\pi$
$12$		0			0
$13$	−3.36983	−	4.01601i	−0.934622	−	1.11384i	−0.993300	−	0.115563i	$-0.963133\pi$
$13$	−3.36983	−	4.01601i	−0.934622	−	1.11384i	0.0586778	−	0.998277i	$-0.481312\pi$
$14$	−4.47981	−	1.66054i	−1.19728	−	0.443797i
$15$		0			0
$16$	3.00260	+	2.64280i	0.750651	+	0.660699i
$17$	2.95820	−	1.70792i	0.717470	−	0.414231i	−0.0963510	−	0.995347i	$-0.530717\pi$
$17$	2.95820	−	1.70792i	0.717470	−	0.414231i	0.813821	+	0.581116i	$0.197384\pi$
$18$		0			0
$19$	1.27164	−	2.20255i	0.291735	−	0.505299i	−0.682485	−	0.730899i	$-0.739101\pi$
$19$	1.27164	−	2.20255i	0.291735	−	0.505299i	0.974220	+	0.225600i	$0.0724342\pi$
$20$	1.15483	+	0.992487i	0.258227	+	0.221927i
$21$		0			0
$22$	1.35443	+	7.95577i	0.288766	+	1.69618i
$23$	0.947065	+	5.37107i	0.197477	+	1.11995i	0.908847	+	0.417129i	$0.136964\pi$
$23$	0.947065	+	5.37107i	0.197477	+	1.11995i	−0.711371	+	0.702817i	$0.751925\pi$
$24$		0			0
$25$	−3.38617	−	2.84134i	−0.677235	−	0.568268i
$26$	3.66905	+	6.44253i	0.719559	+	1.26348i
$27$		0			0
$28$	5.81111	+	3.44718i	1.09820	+	0.651456i
$29$	3.27434	+	2.74749i	0.608029	+	0.510197i	0.894015	−	0.448037i	$-0.147877\pi$
$29$	3.27434	+	2.74749i	0.608029	+	0.510197i	−0.285986	+	0.958234i	$0.592321\pi$
$30$		0			0
$31$	−2.33080	+	0.410982i	−0.418623	+	0.0738146i	−0.378992	−	0.925400i	$-0.623729\pi$
$31$	−2.33080	+	0.410982i	−0.418623	+	0.0738146i	−0.0396309	+	0.999214i	$0.512618\pi$
$32$	−3.50665	−	4.43885i	−0.619895	−	0.784685i
$33$		0			0
$34$	−4.54907	+	1.62537i	−0.780160	+	0.278749i
$35$	2.22751	+	1.28605i	0.376517	+	0.217382i
$36$		0			0
$37$	9.07767	−	5.24099i	1.49236	−	0.861614i	0.492398	−	0.870370i	$-0.336121\pi$
$37$	9.07767	−	5.24099i	1.49236	−	0.861614i	0.999962	+	0.00875627i	$0.00278724\pi$
$38$	−2.32817	+	2.74157i	−0.377679	+	0.444741i
$39$		0			0
$40$	−1.35477	−	1.67389i	−0.214208	−	0.264665i
$41$	−1.88727	−	2.24916i	−0.294742	−	0.351259i	0.598269	−	0.801296i	$-0.295856\pi$
$41$	−1.88727	−	2.24916i	−0.294742	−	0.351259i	−0.893010	+	0.450036i	$0.851411\pi$
$42$		0			0
$43$	−5.95761	+	2.16839i	−0.908528	+	0.330677i	−0.753665	−	0.657259i	$-0.771716\pi$
$43$	−5.95761	+	2.16839i	−0.908528	+	0.330677i	−0.154863	+	0.987936i	$0.549494\pi$
$44$	0.134776	−	11.4123i	0.0203183	−	1.72046i
$45$		0			0
$46$	0.0455422	−	7.71289i	0.00671483	−	1.13720i
$47$	0.625921	−	3.54977i	0.0913000	−	0.517788i	−0.904519	−	0.426434i	$-0.859770\pi$
$47$	0.625921	−	3.54977i	0.0913000	−	0.517788i	0.995819	−	0.0913536i	$-0.0291193\pi$
$48$		0			0
$49$	4.14688	+	1.50934i	0.592412	+	0.215620i
$50$	3.98991	+	4.81242i	0.564259	+	0.680578i
$51$		0			0
$52$	−3.46950	−	9.89438i	−0.481133	−	1.37210i
$53$	8.06569			1.10791			0.553954	−	0.832548i	$-0.313118\pi$
$53$	8.06569			1.10791			0.553954	+	0.832548i	$0.313118\pi$
$54$		0			0
$55$		−	4.34470i		−	0.585839i
$56$	−7.20986	−	6.27073i	−0.963458	−	0.837962i
$57$		0			0
$58$	−3.85813	−	4.65347i	−0.506598	−	0.611031i
$59$	1.63379	−	4.48880i	0.212701	−	0.584392i	−0.786758	−	0.617261i	$-0.788242\pi$
$59$	1.63379	−	4.48880i	0.212701	−	0.584392i	0.999460	+	0.0328691i	$0.0104644\pi$
$60$		0			0
$61$	2.62747	+	0.463294i	0.336413	+	0.0593187i	0.339303	−	0.940677i	$-0.389809\pi$
$61$	2.62747	+	0.463294i	0.336413	+	0.0593187i	−0.00289009	+	0.999996i	$0.500920\pi$
$62$	3.34703	+	0.0197632i	0.425074	+	0.00250993i
$63$		0			0
$64$	3.75209	+	7.06554i	0.469011	+	0.883192i
$65$	−1.36515	−	3.75071i	−0.169326	−	0.465219i
$66$		0			0
$67$	2.16648	−	1.81790i	0.264678	−	0.222091i	−0.500784	−	0.865572i	$-0.666955\pi$
$67$	2.16648	−	1.81790i	0.264678	−	0.222091i	0.765462	+	0.643481i	$0.222510\pi$
$68$	6.74143	−	1.10678i	0.817518	−	0.134216i
$69$		0			0
$70$	−2.77263	−	2.35455i	−0.331393	−	0.281423i
$71$	3.03884	+	5.26343i	0.360644	+	0.624654i	0.988067	−	0.154025i	$-0.0492235\pi$
$71$	3.03884	+	5.26343i	0.360644	+	0.624654i	−0.627423	+	0.778679i	$0.715890\pi$
$72$		0			0
$73$	1.40736	−	2.43763i	0.164720	−	0.285303i	−0.771836	−	0.635822i	$-0.780661\pi$
$73$	1.40736	−	2.43763i	0.164720	−	0.285303i	0.936556	+	0.350519i	$0.113995\pi$
$74$	−13.9595	+	4.98769i	−1.62276	+	0.579807i
$75$		0			0
$76$	3.93488	−	3.22334i	0.451361	−	0.369743i
$77$	−3.34767	−	18.9856i	−0.381502	−	2.16360i
$78$		0			0
$79$	−7.42577	+	8.84969i	−0.835464	+	0.995667i	0.164493	+	0.986378i	$0.447401\pi$
$79$	−7.42577	+	8.84969i	−0.835464	+	0.995667i	−0.999957	+	0.00928911i	$0.997043\pi$
$80$	1.46000	+	2.67264i	0.163233	+	0.298810i
$81$		0			0
$82$	2.05484	+	3.60813i	0.226919	+	0.398451i
$83$	−5.47239	+	6.52174i	−0.600673	+	0.715854i	−0.977620	−	0.210381i	$-0.932530\pi$
$83$	−5.47239	+	6.52174i	−0.600673	+	0.715854i	0.376947	+	0.926235i	$0.376974\pi$
$84$		0			0
$85$	2.56116	−	0.451602i	0.277797	−	0.0489831i
$86$	8.83888	−	1.50478i	0.953121	−	0.162264i
$87$		0			0
$88$	−3.08388	+	15.8431i	−0.328743	+	1.68888i
$89$	7.79000	+	4.49756i	0.825739	+	0.476740i	0.852391	−	0.522904i	$-0.175152\pi$
$89$	7.79000	+	4.49756i	0.825739	+	0.476740i	−0.0266528	+	0.999645i	$0.508485\pi$
$90$		0			0
$91$	−8.85545	−	15.3381i	−0.928303	−	1.60787i
$92$	−2.02085	+	10.7190i	−0.210688	+	1.11754i
$93$		0			0
$94$	−1.77173	+	4.77978i	−0.182740	+	0.492997i
$95$	1.48333	−	1.24466i	0.152186	−	0.127699i
$96$		0			0
$97$	13.6755	−	4.97747i	1.38854	−	0.505386i	0.463781	−	0.885950i	$-0.346492\pi$
$97$	13.6755	−	4.97747i	1.38854	−	0.505386i	0.924755	+	0.380564i	$0.124270\pi$
$98$	−5.38630	−	3.15233i	−0.544099	−	0.318434i
$99$		0			0
$100$	−4.32962	−	7.70791i	−0.432962	−	0.770791i
$101$	0.867234	−	4.91833i	0.0862930	−	0.489392i	−0.910777	−	0.412898i	$-0.864516\pi$
$101$	0.867234	−	4.91833i	0.0862930	−	0.489392i	0.997070	−	0.0764934i	$-0.0243724\pi$
$102$		0			0
$103$	1.64778	−	4.52724i	0.162360	−	0.446082i	−0.831659	−	0.555287i	$-0.812608\pi$
$103$	1.64778	−	4.52724i	0.162360	−	0.446082i	0.994019	+	0.109205i	$0.0348306\pi$
$104$	2.31581	+	14.6461i	0.227084	+	1.43617i
$105$		0			0
$106$	−11.2214	−	2.04703i	−1.08992	−	0.198825i
$107$			2.56818i			0.248275i	0.992265	+	0.124138i	$0.0396164\pi$
$107$			2.56818i			0.248275i	−0.992265	+	0.124138i	$0.960384\pi$
$108$		0			0
$109$		−	7.69169i		−	0.736730i	−0.929681	−	0.368365i	$-0.879918\pi$
$109$		−	7.69169i		−	0.736730i	0.929681	−	0.368365i	$-0.120082\pi$
$110$	−1.10266	+	6.04458i	−0.105135	+	0.576328i
$111$		0			0
$112$	8.43927	+	10.5540i	0.797436	+	0.997260i
$113$	2.07354	−	5.69700i	0.195062	−	0.535928i	−0.803145	−	0.595783i	$-0.796842\pi$
$113$	2.07354	−	5.69700i	0.195062	−	0.535928i	0.998207	+	0.0598551i	$0.0190639\pi$
$114$		0			0
$115$	−0.721054	+	4.08930i	−0.0672386	+	0.381329i
$116$	4.18662	+	7.45334i	0.388718	+	0.692025i
$117$		0			0
$118$	−3.41225	+	5.83042i	−0.314123	+	0.536733i
$119$	10.8438	−	3.94684i	0.994054	−	0.361806i
$120$		0			0
$121$	−16.5193	+	13.8613i	−1.50175	+	1.26012i
$122$	−3.53789	−	1.31140i	−0.320306	−	0.118728i
$123$		0			0
$124$	−4.65156	−	0.876956i	−0.417722	−	0.0787529i
$125$	−3.58612	−	6.21133i	−0.320752	−	0.555559i
$126$		0			0
$127$	2.68591	+	1.55071i	0.238336	+	0.137603i	0.614412	−	0.788986i	$-0.289393\pi$
$127$	2.68591	+	1.55071i	0.238336	+	0.137603i	−0.376076	+	0.926589i	$0.622727\pi$
$128$	−3.42692	−	10.7822i	−0.302899	−	0.953023i
$129$		0			0
$130$	0.947357	+	5.56466i	0.0830887	+	0.488053i
$131$	−15.9872	+	2.81898i	−1.39681	+	0.246295i	−0.820832	−	0.571170i	$-0.806490\pi$
$131$	−15.9872	+	2.81898i	−1.39681	+	0.246295i	−0.575978	+	0.817465i	$0.695379\pi$
$132$		0			0
$133$	5.52284	−	6.58187i	0.478891	−	0.570720i
$134$	−3.47550	+	1.97931i	−0.300238	+	0.170987i
$135$		0			0
$136$	−9.65994	−	0.171133i	−0.828333	−	0.0146745i
$137$	−0.0788460	+	0.0939650i	−0.00673627	+	0.00802797i	−0.769402	−	0.638765i	$-0.779446\pi$
$137$	−0.0788460	+	0.0939650i	−0.00673627	+	0.00802797i	0.762666	+	0.646793i	$0.223890\pi$
$138$		0			0
$139$	2.78791	+	15.8110i	0.236467	+	1.34107i	0.839502	+	0.543357i	$0.182847\pi$
$139$	2.78791	+	15.8110i	0.236467	+	1.34107i	−0.603035	+	0.797715i	$0.706042\pi$
$140$	3.25986	+	3.97946i	0.275509	+	0.336326i
$141$		0			0
$142$	−2.89197	−	8.09401i	−0.242689	−	0.679234i
$143$	−14.9583	+	25.9085i	−1.25088	+	2.16658i
$144$		0			0
$145$	1.62715	+	2.81830i	0.135127	+	0.234047i
$146$	−2.57666	+	3.03418i	−0.213246	+	0.251110i
$147$		0			0
$148$	20.6870	−	3.39630i	1.70046	−	0.279174i
$149$	−14.4253	+	12.1043i	−1.18177	+	0.991623i	−0.181805	+	0.983335i	$0.558194\pi$
$149$	−14.4253	+	12.1043i	−1.18177	+	0.991623i	−0.999966	+	0.00828872i	$0.997362\pi$
$150$		0			0
$151$	5.65105	+	15.5261i	0.459876	+	1.26350i	0.925578	+	0.378557i	$0.123580\pi$
$151$	5.65105	+	15.5261i	0.459876	+	1.26350i	−0.465702	+	0.884942i	$0.654198\pi$
$152$	−6.29248	+	3.48584i	−0.510387	+	0.282739i
$153$		0			0
$154$	−0.160982	+	27.2634i	−0.0129723	+	2.19694i
$155$	−1.77457	−	0.312904i	−0.142537	−	0.0251330i
$156$		0			0
$157$	−3.99126	+	10.9659i	−0.318537	+	0.875174i	0.672320	+	0.740260i	$0.265298\pi$
$157$	−3.99126	+	10.9659i	−0.318537	+	0.875174i	−0.990857	+	0.134913i	$0.956924\pi$
$158$	12.5771	−	10.4275i	1.00058	−	0.829571i
$159$		0			0
$160$	−1.35293	−	4.08886i	−0.106959	−	0.323253i
$161$			18.4251i			1.45210i
$162$		0			0
$163$	2.29194			0.179518			0.0897591	−	0.995964i	$-0.471390\pi$
$163$	2.29194			0.179518			0.0897591	+	0.995964i	$0.471390\pi$
$164$	−1.94309	−	5.54133i	−0.151729	−	0.432705i
$165$		0			0
$166$	9.26867	−	7.68454i	0.719388	−	0.596436i
$167$	7.85034	+	2.85729i	0.607478	+	0.221104i	0.627399	−	0.778698i	$-0.284119\pi$
$167$	7.85034	+	2.85729i	0.607478	+	0.221104i	−0.0199215	+	0.999802i	$0.506342\pi$
$168$		0			0
$169$	−2.51513	+	14.2640i	−0.193471	+	1.09723i
$170$	−3.67784	−	0.0217165i	−0.282077	−	0.00166558i
$171$		0			0
$172$	−12.6790	−	0.149737i	−0.966767	−	0.0114173i
$173$	4.31220	−	1.56951i	0.327850	−	0.119328i	−0.172851	−	0.984948i	$-0.555298\pi$
$173$	4.31220	−	1.56951i	0.327850	−	0.119328i	0.500701	+	0.865620i	$0.333076\pi$
$174$		0			0
$175$	−9.59894	−	11.4396i	−0.725611	−	0.864750i
$176$	8.31136	−	21.2592i	0.626493	−	1.60247i
$177$		0			0
$178$	−9.69641	−	8.23431i	−0.726777	−	0.617188i
$179$	8.01534	−	4.62766i	0.599094	−	0.345887i	−0.169591	−	0.985515i	$-0.554245\pi$
$179$	8.01534	−	4.62766i	0.599094	−	0.345887i	0.768685	+	0.639627i	$0.220911\pi$
$180$		0			0
$181$	10.1708	+	5.87212i	0.755990	+	0.436471i	0.827854	−	0.560943i	$-0.189561\pi$
$181$	10.1708	+	5.87212i	0.755990	+	0.436471i	−0.0718639	+	0.997414i	$0.522895\pi$
$182$	8.42745	+	23.5866i	0.624684	+	1.74836i
$183$		0			0
$184$	5.53195	−	14.4000i	0.407821	−	1.06158i
$185$	7.85928	−	1.38580i	0.577826	−	0.101886i
$186$		0			0
$187$	−14.9322	−	12.5296i	−1.09195	−	0.916254i
$188$	3.67801	−	6.20024i	0.268246	−	0.452199i
$189$		0			0
$190$	−2.37957	+	1.35518i	−0.172632	+	0.0983148i
$191$	9.19786	+	7.71792i	0.665534	+	0.558449i	0.911740	−	0.410768i	$-0.134740\pi$
$191$	9.19786	+	7.71792i	0.665534	+	0.558449i	−0.246206	+	0.969218i	$0.579184\pi$
$192$		0			0
$193$	0.0875504	+	0.496523i	0.00630202	+	0.0357405i	0.987797	−	0.155749i	$-0.0497792\pi$
$193$	0.0875504	+	0.496523i	0.00630202	+	0.0357405i	−0.981495	+	0.191490i	$0.938668\pi$
$194$	−20.2893	+	3.45416i	−1.45669	+	0.247994i
$195$		0			0
$196$	6.69367	+	5.75271i	0.478119	+	0.410908i
$197$	−1.86464	+	3.22964i	−0.132850	+	0.230103i	−0.924774	−	0.380517i	$-0.875746\pi$
$197$	−1.86464	+	3.22964i	−0.132850	+	0.230103i	0.791924	+	0.610619i	$0.209079\pi$
$198$		0			0
$199$	−22.4920	+	12.9857i	−1.59441	+	0.920534i	−0.601876	+	0.798590i	$0.705580\pi$
$199$	−22.4920	+	12.9857i	−1.59441	+	0.920534i	−0.992537	+	0.121945i	$0.961087\pi$
$200$	4.06737	+	11.8225i	0.287606	+	0.835977i
$201$		0			0
$202$	−2.45479	+	6.62254i	−0.172718	+	0.465960i
$203$	9.28190	+	11.0617i	0.651462	+	0.776382i
$204$		0			0
$205$	−0.764549	−	2.10058i	−0.0533984	−	0.146711i
$206$	−3.44147	+	5.88034i	−0.239778	+	0.409703i
$207$		0			0
$208$	0.495236	−	20.9642i	0.0343384	−	1.45361i
$209$	−14.2928	−	2.52021i	−0.988655	−	0.174327i
$210$		0			0
$211$	−5.28560	−	1.92380i	−0.363875	−	0.132440i	0.153611	−	0.988131i	$-0.450910\pi$
$211$	−5.28560	−	1.92380i	−0.363875	−	0.132440i	−0.517486	+	0.855692i	$0.673132\pi$
$212$	15.0923	+	5.69588i	1.03655	+	0.391194i
$213$		0			0
$214$	0.651790	−	3.57299i	0.0445555	−	0.244244i
$215$	−4.82697			−0.329196
$216$		0			0
$217$	−7.99564			−0.542779
$218$	−1.95211	+	10.7011i	−0.132214	+	0.724770i
$219$		0			0
$220$	3.06816	−	8.12969i	0.206856	−	0.548104i
$221$	−16.8277	−	6.12476i	−1.13195	−	0.411996i
$222$		0			0
$223$	−1.15220	−	0.203163i	−0.0771568	−	0.0136048i	0.134937	−	0.990854i	$-0.456917\pi$
$223$	−1.15220	−	0.203163i	−0.0771568	−	0.0136048i	−0.212093	+	0.977249i	$0.568028\pi$
$224$	−9.06261	−	16.8252i	−0.605521	−	1.12418i
$225$		0			0
$226$	−4.33069	+	7.39972i	−0.288073	+	0.492222i
$227$	3.74301	+	10.2838i	0.248432	+	0.682563i	0.999744	+	0.0226152i	$0.00719925\pi$
$227$	3.74301	+	10.2838i	0.248432	+	0.682563i	−0.751312	+	0.659947i	$0.770579\pi$
$228$		0			0
$229$	3.60038	+	4.29076i	0.237920	+	0.283542i	0.871771	−	0.489913i	$-0.162971\pi$
$229$	3.60038	+	4.29076i	0.237920	+	0.283542i	−0.633852	+	0.773455i	$0.718527\pi$
$230$	2.04101	−	5.50625i	0.134580	−	0.363072i
$231$		0			0
$232$	−3.93303	−	11.4320i	−0.258216	−	0.750549i
$233$	12.0089	−	6.93335i	0.786730	−	0.454219i	−0.0520803	−	0.998643i	$-0.516585\pi$
$233$	12.0089	−	6.93335i	0.786730	−	0.454219i	0.838810	+	0.544424i	$0.183252\pi$
$234$		0			0
$235$	1.37217	−	2.37666i	0.0895103	−	0.155036i
$236$	6.22704	−	7.24558i	0.405346	−	0.471647i
$237$		0			0
$238$	−16.0882	+	2.73894i	−1.04285	+	0.177539i
$239$	−3.00765	−	17.0573i	−0.194549	−	1.10334i	−0.913060	−	0.407826i	$-0.866287\pi$
$239$	−3.00765	−	17.0573i	−0.194549	−	1.10334i	0.718511	−	0.695516i	$-0.244824\pi$
$240$		0			0
$241$	−1.47032	−	1.23374i	−0.0947115	−	0.0794724i	0.594202	−	0.804316i	$-0.297468\pi$
$241$	−1.47032	−	1.23374i	−0.0947115	−	0.0794724i	−0.688914	+	0.724843i	$0.741912\pi$
$242$	26.5005	−	15.0921i	1.70351	−	0.970159i
$243$		0			0
$244$	4.58929	+	2.72239i	0.293799	+	0.174283i
$245$	2.57382	+	2.15969i	0.164435	+	0.137977i
$246$		0			0
$247$	−13.1307	+	2.31529i	−0.835484	+	0.147318i
$248$	6.24893	+	2.40061i	0.396808	+	0.152439i
$249$		0			0
$250$	3.41279	+	9.55168i	0.215844	+	0.604101i
$251$	−18.6528	−	10.7692i	−1.17735	−	0.679746i	−0.221953	−	0.975057i	$-0.571243\pi$
$251$	−18.6528	−	10.7692i	−1.17735	−	0.679746i	−0.955401	+	0.295311i	$0.904577\pi$
$252$		0			0
$253$	26.9533	−	15.5615i	1.69454	−	0.978342i
$254$	−3.34322	−	2.83910i	−0.209772	−	0.178141i
$255$		0			0
$256$	2.03124	+	15.8705i	0.126952	+	0.991909i
$257$	5.79174	+	6.90232i	0.361279	+	0.430555i	0.915813	−	0.401606i	$-0.131548\pi$
$257$	5.79174	+	6.90232i	0.361279	+	0.430555i	−0.554534	+	0.832161i	$0.687103\pi$
$258$		0			0
$259$	33.2759	−	12.1114i	2.06766	−	0.752568i
$260$	0.0942693	−	7.98230i	0.00584634	−	0.495041i
$261$		0			0
$262$	22.9577	+	0.135558i	1.41833	+	0.00837482i
$263$	1.07833	−	6.11552i	0.0664927	−	0.377099i	−0.933343	−	0.358985i	$-0.883123\pi$
$263$	1.07833	−	6.11552i	0.0664927	−	0.377099i	0.999836	−	0.0181137i	$-0.00576609\pi$
$264$		0			0
$265$	5.77052	+	2.10030i	0.354480	+	0.129020i
$266$	−9.35412	+	7.75538i	−0.573538	+	0.475513i
$267$		0			0
$268$	5.33764	−	1.87166i	0.326049	−	0.114330i
$269$	−1.29437			−0.0789188			−0.0394594	−	0.999221i	$-0.512564\pi$
$269$	−1.29437			−0.0789188			−0.0394594	+	0.999221i	$0.512564\pi$
$270$		0			0
$271$		−	3.86099i		−	0.234539i	−0.993100	−	0.117269i	$-0.962586\pi$
$271$		−	3.86099i		−	0.234539i	0.993100	−	0.117269i	$-0.0374141\pi$
$272$	13.3960	+	2.68973i	0.812251	+	0.163089i
$273$		0			0
$274$	0.133543	−	0.110719i	0.00806761	−	0.00668875i
$275$	−8.62737	+	23.7035i	−0.520250	+	1.42938i
$276$		0			0
$277$	−24.2259	−	4.27169i	−1.45560	−	0.256661i	−0.610815	−	0.791774i	$-0.709158\pi$
$277$	−24.2259	−	4.27169i	−1.45560	−	0.256661i	−0.844780	+	0.535113i	$0.820269\pi$
$278$	0.134064	−	22.7047i	0.00804063	−	1.36174i
$279$		0			0
$280$	−3.52533	−	6.36378i	−0.210679	−	0.380309i
$281$	−1.24545	−	3.42184i	−0.0742972	−	0.204130i	0.896985	−	0.442062i	$-0.145753\pi$
$281$	−1.24545	−	3.42184i	−0.0742972	−	0.204130i	−0.971282	+	0.237932i	$0.923531\pi$
$282$		0			0
$283$	2.81306	−	2.36044i	0.167219	−	0.140314i	−0.555338	−	0.831625i	$-0.687411\pi$
$283$	2.81306	−	2.36044i	0.167219	−	0.140314i	0.722557	+	0.691311i	$0.242967\pi$
$284$	1.96925	+	11.9948i	0.116853	+	0.711760i
$285$		0			0
$286$	27.3862	−	32.2490i	1.61938	−	1.90692i
$287$	−4.95948	−	8.59007i	−0.292749	−	0.507056i
$288$		0			0
$289$	−2.66602	+	4.61769i	−0.156825	+	0.271629i
$290$	−1.54851	−	4.33394i	−0.0909314	−	0.254498i
$291$		0			0
$292$	4.35485	−	3.56737i	0.254848	−	0.208765i
$293$	−5.15756	−	29.2500i	−0.301308	−	1.70880i	−0.640394	−	0.768046i	$-0.721229\pi$
$293$	−5.15756	−	29.2500i	−0.301308	−	1.70880i	0.339086	−	0.940755i	$-0.389882\pi$
$294$		0			0
$295$	2.33776	−	2.78603i	0.136110	−	0.162209i
$296$	−29.6429	−	0.525145i	−1.72296	−	0.0305235i
$297$		0			0
$298$	23.1413	−	13.1791i	1.34054	−	0.763444i
$299$	18.3788	−	21.9030i	1.06287	−	1.26668i
$300$		0			0
$301$	−21.0930	+	3.71926i	−1.21578	+	0.214375i
$302$	−3.92160	−	23.0350i	−0.225663	−	1.32552i
$303$		0			0
$304$	9.63913	−	3.25268i	0.552842	−	0.186554i
$305$	1.75916	+	1.01565i	0.100729	+	0.0581559i
$306$		0			0
$307$	4.62536	+	8.01136i	0.263983	+	0.457232i	0.967297	−	0.253648i	$-0.0816303\pi$
$307$	4.62536	+	8.01136i	0.263983	+	0.457232i	−0.703314	+	0.710880i	$0.748297\pi$
$308$	7.14326	−	37.8894i	0.407025	−	2.15895i
$309$		0			0
$310$	2.38946	+	0.885704i	0.135712	+	0.0503046i
$311$	−20.0930	+	16.8601i	−1.13937	+	0.956046i	−0.999418	−	0.0341122i	$-0.989140\pi$
$311$	−20.0930	+	16.8601i	−1.13937	+	0.956046i	−0.139953	+	0.990158i	$0.544695\pi$
$312$		0			0
$313$	18.7936	−	6.84033i	1.06228	−	0.386638i	0.248995	−	0.968505i	$-0.419900\pi$
$313$	18.7936	−	6.84033i	1.06228	−	0.386638i	0.813284	+	0.581866i	$0.197677\pi$
$314$	8.33594	−	14.2434i	0.470424	−	0.803801i
$315$		0			0
$316$	−20.1444	+	11.3153i	−1.13321	+	0.636538i
$317$	−4.07115	+	23.0886i	−0.228659	+	1.29679i	0.626907	+	0.779094i	$0.284320\pi$
$317$	−4.07115	+	23.0886i	−0.228659	+	1.29679i	−0.855566	+	0.517694i	$0.826791\pi$
$318$		0			0
$319$	8.34243	−	22.9206i	0.467086	−	1.28331i
$320$	0.844539	+	6.03201i	0.0472112	+	0.337200i
$321$		0			0
$322$	4.67619	−	25.6340i	0.260594	−	1.42853i
$323$		−	8.68745i		−	0.483383i
$324$		0			0
$325$			23.1737i			1.28545i
$326$	−3.18867	−	0.581681i	−0.176604	−	0.0322164i
$327$		0			0
$328$	1.29696	+	8.20254i	0.0716129	+	0.452910i
$329$	4.16487	−	11.4429i	0.229617	−	0.630866i
$330$		0			0
$331$	−3.95158	+	22.4105i	−0.217198	+	1.23179i	0.659853	+	0.751395i	$0.270619\pi$
$331$	−3.95158	+	22.4105i	−0.217198	+	1.23179i	−0.877051	+	0.480397i	$0.840492\pi$
$332$	−14.8454	+	8.33880i	−0.814746	+	0.457651i
$333$		0			0
$334$	−10.1967	−	5.96759i	−0.557936	−	0.326532i
$335$	2.02337	−	0.736446i	0.110548	−	0.0402363i
$336$		0			0
$337$	24.5647	−	20.6122i	1.33812	−	1.12282i	0.356018	−	0.934479i	$-0.384134\pi$
$337$	24.5647	−	20.6122i	1.33812	−	1.12282i	0.982104	−	0.188338i	$-0.0603101\pi$
$338$	7.11931	−	19.2065i	0.387240	−	1.04470i
$339$		0			0
$340$	5.11130	+	0.963630i	0.277199	+	0.0522601i
$341$	6.75296	+	11.6965i	0.365693	+	0.633400i
$342$		0			0
$343$	−7.56875	−	4.36982i	−0.408674	−	0.235948i
$344$	17.6018	+	3.42620i	0.949023	+	0.184728i
$345$		0			0
$346$	−6.39770	+	1.08918i	−0.343942	+	0.0585545i
$347$	−14.5793	+	2.57072i	−0.782658	+	0.138004i	−0.550679	−	0.834717i	$-0.685631\pi$
$347$	−14.5793	+	2.57072i	−0.782658	+	0.138004i	−0.231979	+	0.972721i	$0.574520\pi$
$348$		0			0
$349$	−16.2504	+	19.3665i	−0.869864	+	1.03666i	0.129121	+	0.991629i	$0.458784\pi$
$349$	−16.2504	+	19.3665i	−0.869864	+	1.03666i	−0.998985	+	0.0450350i	$0.985660\pi$
$350$	10.4513	+	18.3515i	0.558643	+	0.980929i
$351$		0			0
$352$	−16.9587	+	27.4675i	−0.903901	+	1.46402i
$353$	−0.289344	+	0.344827i	−0.0154002	+	0.0183533i	−0.773690	−	0.633565i	$-0.781591\pi$
$353$	−0.289344	+	0.344827i	−0.0154002	+	0.0183533i	0.758289	+	0.651918i	$0.226035\pi$
$354$		0			0
$355$	0.803519	+	4.55698i	0.0426464	+	0.241860i
$356$	11.4004	+	13.9169i	0.604217	+	0.737595i
$357$		0			0
$358$	−12.3258	+	4.40400i	−0.651441	+	0.232758i
$359$	1.58856	−	2.75146i	0.0838408	−	0.145216i	−0.821056	−	0.570848i	$-0.806615\pi$
$359$	1.58856	−	2.75146i	0.0838408	−	0.145216i	0.904897	+	0.425631i	$0.139948\pi$
$360$		0			0
$361$	6.26585	+	10.8528i	0.329782	+	0.571199i
$362$	−12.6599	−	10.7509i	−0.665388	−	0.565055i
$363$		0			0
$364$	−5.73856	−	34.9539i	−0.300782	−	1.83208i
$365$	1.64164	−	1.37750i	0.0859275	−	0.0721017i
$366$		0			0
$367$	11.2504	+	30.9103i	0.587268	+	1.61351i	0.775476	+	0.631377i	$0.217510\pi$
$367$	11.2504	+	30.9103i	0.587268	+	1.61351i	−0.188208	+	0.982129i	$0.560268\pi$
$368$	−11.3510	+	18.6301i	−0.591712	+	0.971161i
$369$		0			0
$370$	−11.2860	−	0.0666402i	−0.586730	−	0.00346446i
$371$	26.8345	+	4.73164i	1.39318	+	0.245655i
$372$		0			0
$373$	−4.07881	+	11.2064i	−0.211193	+	0.580247i	−0.999381	−	0.0351875i	$-0.988797\pi$
$373$	−4.07881	+	11.2064i	−0.211193	+	0.580247i	0.788188	+	0.615434i	$0.211019\pi$
$374$	17.5945	+	21.2215i	0.909790	+	1.09734i
$375$		0			0
$376$	−6.69064	+	7.69265i	−0.345043	+	0.396718i
$377$		−	22.4083i		−	1.15409i
$378$		0			0
$379$	1.35817			0.0697646			0.0348823	−	0.999391i	$-0.488894\pi$
$379$	1.35817			0.0697646			0.0348823	+	0.999391i	$0.488894\pi$
$380$	3.65453	−	1.28147i	0.187473	−	0.0657381i
$381$		0			0
$382$	−10.8378	−	13.0720i	−0.554510	−	0.668819i
$383$	27.9805	+	10.1841i	1.42973	+	0.520381i	0.936855	−	0.349717i	$-0.113722\pi$
$383$	27.9805	+	10.1841i	1.42973	+	0.520381i	0.492879	+	0.870098i	$0.335944\pi$
$384$		0			0
$385$	2.54877	−	14.4548i	0.129897	−	0.736683i
$386$	0.00421010	−	0.713010i	0.000214289	−	0.0362912i
$387$		0			0
$388$	29.1043	+	0.343716i	1.47755	+	0.0174495i
$389$	−5.43932	+	1.97975i	−0.275784	+	0.100377i	−0.476210	−	0.879332i	$-0.657990\pi$
$389$	−5.43932	+	1.97975i	−0.275784	+	0.100377i	0.200426	+	0.979709i	$0.435768\pi$
$390$		0			0
$391$	11.9750	+	14.2712i	0.605600	+	0.721726i
$392$	−7.85259	−	9.70231i	−0.396616	−	0.490041i
$393$		0			0
$394$	3.41385	−	4.02002i	0.171987	−	0.202526i
$395$	−7.61715	+	4.39776i	−0.383260	+	0.221275i
$396$		0			0
$397$	−13.5494	−	7.82276i	−0.680026	−	0.392613i	0.119839	−	0.992793i	$-0.461762\pi$
$397$	−13.5494	−	7.82276i	−0.680026	−	0.392613i	−0.799865	+	0.600180i	$0.795096\pi$
$398$	34.5877	−	12.3581i	1.73373	−	0.619456i
$399$		0			0
$400$	−2.65825	−	17.4804i	−0.132913	−	0.874019i
$401$	−32.9174	+	5.80423i	−1.64382	+	0.289850i	−0.917568	−	0.397580i	$-0.869850\pi$
$401$	−32.9174	+	5.80423i	−1.64382	+	0.289850i	−0.726251	+	0.687429i	$0.758739\pi$
$402$		0			0
$403$	9.50489	+	7.97555i	0.473472	+	0.397290i
$404$	5.09600	−	8.59063i	0.253536	−	0.427400i
$405$		0			0
$406$	−10.1061	−	17.7454i	−0.501556	−	0.880689i
$407$	−45.8215	−	38.4488i	−2.27129	−	1.90584i
$408$		0			0
$409$	−4.03315	−	22.8731i	−0.199426	−	1.13100i	−0.905973	−	0.423336i	$-0.860859\pi$
$409$	−4.03315	−	22.8731i	−0.199426	−	1.13100i	0.706547	−	0.707666i	$-0.250252\pi$
$410$	0.530565	+	3.11648i	0.0262028	+	0.153912i
$411$		0			0
$412$	6.28036	−	7.30762i	0.309411	−	0.360020i
$413$	8.06891	−	13.9758i	0.397045	−	0.687702i
$414$		0			0
$415$	−5.61343	+	3.24091i	−0.275552	+	0.159090i
$416$	−6.00962	+	29.0409i	−0.294646	+	1.42385i
$417$		0			0
$418$	19.2453	+	7.13370i	0.941320	+	0.348920i
$419$	−1.20391	−	1.43476i	−0.0588147	−	0.0700926i	0.735835	−	0.677161i	$-0.236790\pi$
$419$	−1.20391	−	1.43476i	−0.0588147	−	0.0700926i	−0.794650	+	0.607068i	$0.792345\pi$
$420$		0			0
$421$	−6.15422	−	16.9086i	−0.299938	−	0.824073i	−0.994509	−	0.104649i	$-0.966628\pi$
$421$	−6.15422	−	16.9086i	−0.299938	−	0.824073i	0.694571	−	0.719424i	$-0.255594\pi$
$422$	6.86536	+	4.01795i	0.334200	+	0.195591i
$423$		0			0
$424$	−19.5517	−	11.7548i	−0.949513	−	0.570862i
$425$	−14.8698	−	2.62194i	−0.721290	−	0.127183i
$426$		0			0
$427$	8.46978	+	3.08275i	0.409881	+	0.149185i
$428$	−1.81361	+	4.80551i	−0.0876642	+	0.232283i
$429$		0			0
$430$	6.71554	+	1.22506i	0.323852	+	0.0590776i
$431$	−28.7176			−1.38328			−0.691640	−	0.722242i	$-0.743111\pi$
$431$	−28.7176			−1.38328			−0.691640	+	0.722242i	$0.743111\pi$
$432$		0			0
$433$	−6.95359			−0.334168			−0.167084	−	0.985943i	$-0.553435\pi$
$433$	−6.95359			−0.334168			−0.167084	+	0.985943i	$0.553435\pi$
$434$	11.1240	+	2.02925i	0.533967	+	0.0974072i
$435$		0			0
$436$	5.43177	−	14.3925i	0.260134	−	0.689276i
$437$	13.0344	+	4.74412i	0.623519	+	0.226942i
$438$		0			0
$439$	32.5793	+	5.74462i	1.55493	+	0.274176i	0.884050	−	0.467393i	$-0.154807\pi$
$439$	32.5793	+	5.74462i	1.55493	+	0.274176i	0.670877	+	0.741568i	$0.265918\pi$
$440$	−6.33187	+	10.5318i	−0.301860	+	0.502083i
$441$		0			0
$442$	21.8571	+	12.7919i	1.03964	+	0.608447i
$443$	−6.00559	−	16.5002i	−0.285334	−	0.783949i	−0.996703	−	0.0811307i	$-0.974147\pi$
$443$	−6.00559	−	16.5002i	−0.285334	−	0.783949i	0.711369	−	0.702818i	$-0.248075\pi$
$444$		0			0
$445$	4.40212	+	5.24625i	0.208681	+	0.248696i
$446$	1.55144	+	0.575073i	0.0734626	+	0.0272305i
$447$		0			0
$448$	8.33826	+	25.7081i	0.393946	+	1.21459i
$449$	−35.9869	+	20.7770i	−1.69833	+	0.980529i	−0.750974	+	0.660332i	$0.770416\pi$
$449$	−35.9869	+	20.7770i	−1.69833	+	0.980529i	−0.947351	+	0.320197i	$0.896251\pi$
$450$		0			0
$451$	−8.37736	+	14.5100i	−0.394475	+	0.683250i
$452$	7.90309	−	9.19578i	0.371730	−	0.432533i
$453$		0			0
$454$	−2.59750	−	15.2574i	−0.121907	−	0.716065i
$455$	−2.34152	−	13.2794i	−0.109772	−	0.622550i
$456$		0			0
$457$	13.2175	+	11.0908i	0.618287	+	0.518804i	0.897265	−	0.441493i	$-0.145551\pi$
$457$	13.2175	+	11.0908i	0.618287	+	0.518804i	−0.278978	+	0.960298i	$0.589996\pi$
$458$	−3.92007	−	6.88330i	−0.183173	−	0.321635i
$459$		0			0
$460$	−4.23702	+	7.14260i	−0.197552	+	0.333025i
$461$	12.7382	+	10.6886i	0.593276	+	0.497817i	0.889276	−	0.457370i	$-0.151209\pi$
$461$	12.7382	+	10.6886i	0.593276	+	0.497817i	−0.296001	+	0.955188i	$0.595653\pi$
$462$		0			0
$463$	22.8699	−	4.03258i	1.06285	−	0.187410i	0.385232	−	0.922820i	$-0.374122\pi$
$463$	22.8699	−	4.03258i	1.06285	−	0.187410i	0.677622	+	0.735410i	$0.263010\pi$
$464$	2.57046	+	16.9030i	0.119330	+	0.784704i
$465$		0			0
$466$	−18.4671	+	6.59825i	−0.855471	+	0.305658i
$467$	19.4081	+	11.2053i	0.898099	+	0.518518i	0.876583	−	0.481251i	$-0.159817\pi$
$467$	19.4081	+	11.2053i	0.898099	+	0.518518i	0.0215159	+	0.999769i	$0.493151\pi$
$468$		0			0
$469$	8.27432	−	4.77718i	0.382073	−	0.220590i
$470$	−2.51222	+	2.95829i	−0.115880	+	0.136456i
$471$		0			0
$472$	−10.5023	+	8.50005i	−0.483407	+	0.391247i
$473$	23.2555	+	27.7148i	1.06929	+	1.27433i
$474$		0			0
$475$	−10.5642	+	3.84505i	−0.484718	+	0.176423i
$476$	23.0780	+	0.272546i	1.05778	+	0.0124921i
$477$		0			0
$478$	−0.144631	+	24.4943i	−0.00661528	+	1.12034i
$479$	5.11572	−	29.0127i	0.233743	−	1.32562i	−0.611502	−	0.791243i	$-0.709434\pi$
$479$	5.11572	−	29.0127i	0.233743	−	1.32562i	0.845245	−	0.534379i	$-0.179455\pi$
$480$		0			0
$481$	−51.6380	−	18.7947i	−2.35449	−	0.856965i
$482$	1.73247	+	2.08961i	0.0789118	+	0.0951791i
$483$		0			0
$484$	−40.6992	+	14.2713i	−1.84996	+	0.648696i
$485$	11.0801			0.503123
$486$		0			0
$487$		−	27.2531i		−	1.23496i	−0.786587	−	0.617479i	$-0.788154\pi$
$487$		−	27.2531i		−	1.23496i	0.786587	−	0.617479i	$-0.211846\pi$
$488$	−5.69393	−	4.95227i	−0.257752	−	0.224179i
$489$		0			0
$490$	−3.03272	−	3.65790i	−0.137004	−	0.165247i
$491$	5.33019	−	14.6446i	0.240548	−	0.660900i	−0.759399	−	0.650625i	$-0.774507\pi$
$491$	5.33019	−	14.6446i	0.240548	−	0.660900i	0.999947	−	0.0102751i	$-0.00327073\pi$
$492$		0			0
$493$	14.3787	+	2.53534i	0.647582	+	0.114186i
$494$	18.8557	+	0.111337i	0.848358	+	0.00500929i
$495$		0			0
$496$	−8.08459	−	4.92581i	−0.363009	−	0.221175i
$497$	7.02247	+	19.2941i	0.315001	+	0.865458i
$498$		0			0
$499$	4.83664	−	4.05842i	0.216518	−	0.181680i	−0.528077	−	0.849196i	$-0.677087\pi$
$499$	4.83664	−	4.05842i	0.216518	−	0.181680i	0.744595	+	0.667516i	$0.232642\pi$
$500$	−2.32390	−	14.1550i	−0.103928	−	0.633029i
$501$		0			0
$502$	23.2176	+	19.7167i	1.03625	+	0.879998i
$503$	3.45933	+	5.99174i	0.154244	+	0.267159i	0.932784	−	0.360437i	$-0.117372\pi$
$503$	3.45933	+	5.99174i	0.154244	+	0.267159i	−0.778539	+	0.627596i	$0.784039\pi$
$504$		0			0
$505$	1.90118	−	3.29294i	0.0846015	−	0.146534i
$506$	−41.4483	+	14.8094i	−1.84260	+	0.658357i
$507$		0			0
$508$	3.93072	+	4.79840i	0.174397	+	0.212895i
$509$	6.85834	+	38.8956i	0.303991	+	1.72402i	0.628218	+	0.778037i	$0.283785\pi$
$509$	6.85834	+	38.8956i	0.303991	+	1.72402i	−0.324227	+	0.945979i	$0.605104\pi$
$510$		0			0
$511$	6.11230	−	7.28435i	0.270392	−	0.322241i
$512$	1.20189	−	22.5955i	0.0531166	−	0.998588i
$513$		0			0
$514$	−6.30600	−	11.0728i	−0.278146	−	0.488400i
$515$	2.35778	−	2.80989i	0.103896	−	0.123818i
$516$		0			0
$517$	−20.2569	+	3.57183i	−0.890896	+	0.157089i
$518$	−49.3690	+	8.40483i	−2.16915	+	0.369287i
$519$		0			0
$520$	−2.15702	+	11.0815i	−0.0945915	+	0.485955i
$521$	−0.808019	−	0.466510i	−0.0353999	−	0.0204382i	0.482196	−	0.876064i	$-0.339839\pi$
$521$	−0.808019	−	0.466510i	−0.0353999	−	0.0204382i	−0.517596	+	0.855625i	$0.673173\pi$
$522$		0			0
$523$	−18.5482	−	32.1264i	−0.811057	−	1.40479i	−0.912125	−	0.409912i	$-0.865560\pi$
$523$	−18.5482	−	32.1264i	−0.811057	−	1.40479i	0.101069	−	0.994879i	$-0.467774\pi$
$524$	−31.9056	−	6.01515i	−1.39380	−	0.262773i
$525$		0			0
$526$	−3.05232	+	8.23457i	−0.133087	+	0.359044i
$527$	−6.19304	+	5.19658i	−0.269773	+	0.226367i
$528$		0			0
$529$	−6.33854	+	2.30704i	−0.275589	+	0.100306i
$530$	−7.49522	−	4.38658i	−0.325571	−	0.190541i
$531$		0			0
$532$	14.9822	−	8.41568i	0.649562	−	0.364866i
$533$	−2.67286	+	15.1585i	−0.115774	+	0.656590i
$534$		0			0
$535$	−0.668751	+	1.83738i	−0.0289126	+	0.0794368i
$536$	−7.90104	+	1.24929i	−0.341273	+	0.0539612i
$537$		0			0
$538$	1.80079	+	0.328503i	0.0776376	+	0.0141628i
$539$		−	25.1830i		−	1.08471i
$540$		0			0
$541$			25.5189i			1.09714i	0.836104	+	0.548571i	$0.184828\pi$
$541$			25.5189i			1.09714i	−0.836104	+	0.548571i	$0.815172\pi$
$542$	−0.979901	+	5.37163i	−0.0420903	+	0.230731i
$543$		0			0
$544$	−17.9546	−	7.14193i	−0.769797	−	0.306208i
$545$	2.00291	−	5.50295i	0.0857952	−	0.235720i
$546$		0			0
$547$	−3.90042	+	22.1204i	−0.166770	+	0.945800i	0.780451	+	0.625218i	$0.214990\pi$
$547$	−3.90042	+	22.1204i	−0.166770	+	0.945800i	−0.947221	+	0.320582i	$0.896121\pi$
$548$	−0.213892	+	0.120145i	−0.00913700	+	0.00513235i
$549$		0			0
$550$	18.0187	−	30.7880i	0.768320	−	1.31281i
$551$	10.2153	−	3.71805i	0.435185	−	0.158394i
$552$		0			0
$553$	−29.8970	+	25.0866i	−1.27135	+	1.06679i
$554$	32.6203	+	12.0914i	1.38590	+	0.513715i
$555$		0			0
$556$	−5.94885	+	31.5539i	−0.252287	+	1.33819i
$557$	12.6918	+	21.9828i	0.537768	+	0.931441i	0.999024	+	0.0441741i	$0.0140656\pi$
$557$	12.6918	+	21.9828i	0.537768	+	0.931441i	−0.461256	+	0.887267i	$0.652601\pi$
$558$		0			0
$559$	28.7844	+	16.6187i	1.21745	+	0.702896i
$560$	3.28954	+	9.74835i	0.139008	+	0.411943i
$561$		0			0
$562$	0.864290	+	5.07674i	0.0364579	+	0.214149i
$563$	24.4865	−	4.31763i	1.03198	−	0.181966i	0.368087	−	0.929791i	$-0.380013\pi$
$563$	24.4865	−	4.31763i	1.03198	−	0.181966i	0.663896	+	0.747825i	$0.268902\pi$
$564$		0			0
$565$	2.96699	−	3.53592i	0.124822	−	0.148757i
$566$	−4.51275	+	2.57003i	−0.189685	+	0.108026i
$567$		0			0
$568$	0.304491	−	17.1876i	0.0127761	−	0.721175i
$569$	7.57957	−	9.03298i	0.317752	−	0.378682i	−0.583400	−	0.812185i	$-0.698278\pi$
$569$	7.57957	−	9.03298i	0.317752	−	0.378682i	0.901152	+	0.433503i	$0.142723\pi$
$570$		0			0
$571$	−5.98228	−	33.9272i	−0.250351	−	1.41981i	−0.807731	−	0.589551i	$-0.799305\pi$
$571$	−5.98228	−	33.9272i	−0.250351	−	1.41981i	0.557380	−	0.830257i	$-0.311807\pi$
$572$	−46.2858	+	37.9161i	−1.93531	+	1.58535i
$573$		0			0
$574$	4.71978	+	13.2097i	0.197000	+	0.551361i
$575$	12.0541	−	20.8783i	0.502691	−	0.870686i
$576$		0			0
$577$	21.3516	+	36.9821i	0.888880	+	1.53958i	0.841201	+	0.540722i	$0.181849\pi$
$577$	21.3516	+	36.9821i	0.888880	+	1.53958i	0.0476781	+	0.998863i	$0.484818\pi$
$578$	4.88106	−	5.74775i	0.203025	−	0.239075i
$579$		0			0
$580$	1.05443	+	6.42261i	0.0437830	+	0.266684i
$581$	−22.0325	+	18.4875i	−0.914062	+	0.766989i
$582$		0			0
$583$	−15.7422	−	43.2513i	−0.651974	−	1.79128i
$584$	−6.96408	+	3.85788i	−0.288176	+	0.159640i
$585$		0			0
$586$	−0.248015	+	42.0031i	−0.0102454	+	1.73513i
$587$	0.937739	+	0.165349i	0.0387046	+	0.00682467i	0.192967	−	0.981205i	$-0.438189\pi$
$587$	0.937739	+	0.165349i	0.0387046	+	0.00682467i	−0.154262	+	0.988030i	$0.549300\pi$
$588$		0			0
$589$	−2.05873	+	5.65631i	−0.0848285	+	0.233064i
$590$	−3.95950	+	3.28277i	−0.163010	+	0.135149i
$591$		0			0
$592$	41.1075	+	8.25382i	1.68951	+	0.339230i
$593$			11.5209i			0.473108i	0.971618	+	0.236554i	$0.0760180\pi$
$593$			11.5209i			0.473108i	−0.971618	+	0.236554i	$0.923982\pi$
$594$		0			0
$595$	8.78588			0.360186
$596$	−35.5403	+	12.4623i	−1.45579	+	0.510476i
$597$		0			0
$598$	−31.1285	+	25.8082i	−1.27294	+	1.05538i
$599$	45.3618	+	16.5103i	1.85343	+	0.674594i	0.983360	+	0.181668i	$0.0581495\pi$
$599$	45.3618	+	16.5103i	1.85343	+	0.674594i	0.870071	+	0.492926i	$0.164073\pi$
$600$		0			0
$601$	4.24537	−	24.0767i	0.173172	−	0.982109i	−0.767060	−	0.641575i	$-0.778281\pi$
$601$	4.24537	−	24.0767i	0.173172	−	0.982109i	0.940232	−	0.340534i	$-0.110608\pi$
$602$	30.2896	+	0.178851i	1.23451	+	0.00728943i
$603$		0			0
$604$	−0.390229	+	33.0428i	−0.0158782	+	1.34449i
$605$	−15.4281	+	5.61535i	−0.627240	+	0.228297i
$606$		0			0
$607$	−18.4241	−	21.9570i	−0.747812	−	0.891207i	0.249201	−	0.968452i	$-0.419832\pi$
$607$	−18.4241	−	21.9570i	−0.747812	−	0.891207i	−0.997012	+	0.0772447i	$0.975388\pi$
$608$	−14.2360	+	2.07895i	−0.577346	+	0.0843126i
$609$		0			0
$610$	−2.18967	−	1.85949i	−0.0886570	−	0.0752886i
$611$	−16.3652	+	9.44843i	−0.662064	+	0.382243i
$612$		0			0
$613$	−32.4005	−	18.7064i	−1.30864	−	0.755546i	−0.326774	−	0.945102i	$-0.605962\pi$
$613$	−32.4005	−	18.7064i	−1.30864	−	0.755546i	−0.981870	+	0.189556i	$0.939295\pi$
$614$	−4.40181	−	12.3197i	−0.177643	−	0.497184i
$615$		0			0
$616$	−19.5542	+	50.9009i	−0.787862	+	2.05085i
$617$	−6.61066	+	1.16564i	−0.266135	+	0.0469268i	−0.305123	−	0.952313i	$-0.598698\pi$
$617$	−6.61066	+	1.16564i	−0.266135	+	0.0469268i	0.0389880	+	0.999240i	$0.487587\pi$
$618$		0			0
$619$	−5.88154	−	4.93520i	−0.236399	−	0.198362i	0.516890	−	0.856052i	$-0.327090\pi$
$619$	−5.88154	−	4.93520i	−0.236399	−	0.198362i	−0.753289	+	0.657689i	$0.771534\pi$
$620$	−3.09956	−	1.83867i	−0.124481	−	0.0738428i
$621$		0			0
$622$	32.2335	−	18.3571i	1.29245	−	0.736053i
$623$	23.2788	+	19.5333i	0.932647	+	0.782583i
$624$		0			0
$625$	2.88969	+	16.3882i	0.115588	+	0.655530i
$626$	−27.8828	+	4.74691i	−1.11442	+	0.189724i
$627$		0			0
$628$	−15.2123	+	17.7005i	−0.607037	+	0.706329i
$629$	17.9024	−	31.0079i	0.713815	−	1.23636i
$630$		0			0
$631$	−2.13355	+	1.23181i	−0.0849353	+	0.0490374i	−0.541866	−	0.840465i	$-0.682282\pi$
$631$	−2.13355	+	1.23181i	−0.0849353	+	0.0490374i	0.456931	+	0.889502i	$0.348949\pi$
$632$	30.8978	−	10.6300i	1.22905	−	0.422837i
$633$		0			0
$634$	11.5238	−	31.0889i	0.457668	−	1.23470i
$635$	1.51780	+	1.80885i	0.0602322	+	0.0717820i
$636$		0			0
$637$	−7.91276	−	21.7401i	−0.313515	−	0.861375i
$638$	−17.4236	+	29.7712i	−0.689806	+	1.17865i
$639$		0			0
$640$	0.355926	−	8.60640i	0.0140692	−	0.340198i
$641$	34.3110	+	6.04995i	1.35520	+	0.238959i	0.803610	−	0.595156i	$-0.202910\pi$
$641$	34.3110	+	6.04995i	1.35520	+	0.238959i	0.551592	+	0.834114i	$0.314021\pi$
$642$		0			0
$643$	45.2740	+	16.4784i	1.78543	+	0.649844i	0.999503	+	0.0315285i	$0.0100375\pi$
$643$	45.2740	+	16.4784i	1.78543	+	0.649844i	0.785930	+	0.618316i	$0.212185\pi$
$644$	−13.0115	+	34.4766i	−0.512727	+	1.35857i
$645$		0			0
$646$	−2.20483	+	12.0864i	−0.0867478	+	0.475535i
$647$	−0.709735			−0.0279025			−0.0139513	−	0.999903i	$-0.504441\pi$
$647$	−0.709735			−0.0279025			−0.0139513	+	0.999903i	$0.504441\pi$
$648$		0			0
$649$	−27.2594			−1.07002
$650$	5.88137	−	32.2405i	0.230686	−	1.26458i
$651$		0			0
$652$	4.28862	+	1.61853i	0.167955	+	0.0633867i
$653$	0.660215	+	0.240299i	0.0258362	+	0.00940361i	0.354906	−	0.934902i	$-0.384513\pi$
$653$	0.660215	+	0.240299i	0.0258362	+	0.00940361i	−0.329070	+	0.944306i	$0.606735\pi$
$654$		0			0
$655$	−12.1720	−	2.14625i	−0.475598	−	0.0838608i
$656$	0.277356	−	11.7410i	0.0108289	−	0.458409i
$657$		0			0
$658$	−8.69853	+	14.8629i	−0.339104	+	0.579418i
$659$	12.8249	+	35.2362i	0.499589	+	1.37261i	0.891673	+	0.452680i	$0.149532\pi$
$659$	12.8249	+	35.2362i	0.499589	+	1.37261i	−0.392084	+	0.919929i	$0.628246\pi$
$660$		0			0
$661$	−2.70452	−	3.22312i	−0.105194	−	0.125365i	0.710879	−	0.703314i	$-0.248297\pi$
$661$	−2.70452	−	3.22312i	−0.105194	−	0.125365i	−0.816072	+	0.577950i	$0.803853\pi$
$662$	11.1853	−	30.1758i	0.434730	−	1.17282i
$663$		0			0
$664$	22.7700	−	7.83371i	0.883649	−	0.304007i
$665$	5.66518	−	3.27079i	0.219686	−	0.126836i
$666$		0			0
$667$	−11.6560	+	20.1887i	−0.451321	+	0.781711i
$668$	12.6716	+	10.8903i	0.490279	+	0.421358i
$669$		0			0
$670$	−3.00193	+	0.511063i	−0.115975	+	0.0197441i
$671$	−2.64380	−	14.9937i	−0.102063	−	0.578826i
$672$		0			0
$673$	−30.4222	−	25.5272i	−1.17269	−	0.984002i	−0.172689	−	0.984976i	$-0.555245\pi$
$673$	−30.4222	−	25.5272i	−1.17269	−	0.984002i	−1.00000		0.000974390i	$0.999690\pi$
$674$	−39.4069	+	22.4424i	−1.51790	+	0.864449i
$675$		0			0
$676$	−14.7793	+	24.9143i	−0.568434	+	0.958243i
$677$	2.47156	+	2.07389i	0.0949899	+	0.0797060i	0.689046	−	0.724718i	$-0.258030\pi$
$677$	2.47156	+	2.07389i	0.0949899	+	0.0797060i	−0.594056	+	0.804424i	$0.702474\pi$
$678$		0			0
$679$	48.4182	−	8.53744i	1.85812	−	0.327637i
$680$	−6.86655	−	2.63787i	−0.263320	−	0.101158i
$681$		0			0
$682$	−6.42658	−	17.9866i	−0.246087	−	0.688744i
$683$	−10.7853	−	6.22690i	−0.412689	−	0.238266i	0.279256	−	0.960217i	$-0.409912\pi$
$683$	−10.7853	−	6.22690i	−0.412689	−	0.238266i	−0.691944	+	0.721951i	$0.743246\pi$
$684$		0			0
$685$	−0.0808781	+	0.0466950i	−0.00309019	+	0.00178412i
$686$	9.42102	+	8.00044i	0.359696	+	0.305458i
$687$		0			0
$688$	−23.6190	−	9.23394i	−0.900465	−	0.352041i
$689$	−27.1800	−	32.3918i	−1.03547	−	1.23403i
$690$		0			0
$691$	−33.7240	+	12.2745i	−1.28292	+	0.466945i	−0.891397	−	0.453222i	$-0.850274\pi$
$691$	−33.7240	+	12.2745i	−1.28292	+	0.466945i	−0.391524	+	0.920168i	$0.628052\pi$
$692$	9.17725	+	0.108382i	0.348867	+	0.00412005i
$693$		0			0
$694$	20.9359	+	0.123620i	0.794718	+	0.00469256i
$695$	−2.12259	+	12.0378i	−0.0805144	+	0.456620i
$696$		0			0
$697$	−9.42430	−	3.43016i	−0.356971	−	0.129927i
$698$	27.5236	−	22.8194i	1.04178	−	0.863728i
$699$		0			0
$700$	−9.88284	−	28.1841i	−0.373536	−	1.06526i
$701$	35.4138			1.33756			0.668781	−	0.743459i	$-0.266816\pi$
$701$	35.4138			1.33756			0.668781	+	0.743459i	$0.266816\pi$
$702$		0			0
$703$		−	26.6587i		−	1.00545i
$704$	30.5650	−	33.9103i	1.15196	−	1.27804i
$705$		0			0
$706$	0.490066	−	0.406308i	0.0184439	−	0.0152916i
$707$	5.77056	−	15.8545i	0.217024	−	0.596269i
$708$		0			0
$709$	2.07523	+	0.365919i	0.0779368	+	0.0137424i	0.212481	−	0.977165i	$-0.431846\pi$
$709$	2.07523	+	0.365919i	0.0779368	+	0.0137424i	−0.134544	+	0.990908i	$0.542957\pi$
$710$	0.0386394	−	6.54385i	0.00145011	−	0.245586i
$711$		0			0
$712$	−12.3287	−	22.2553i	−0.462039	−	0.834053i
$713$	−4.41483	−	12.1296i	−0.165337	−	0.454259i
$714$		0			0
$715$	−17.4483	+	14.6409i	−0.652530	+	0.547538i
$716$	18.2661	−	2.99884i	0.682636	−	0.112072i
$717$		0			0
$718$	−2.90839	+	3.42481i	−0.108540	+	0.127813i
$719$	−2.79238	−	4.83654i	−0.104138	−	0.180373i	0.809248	−	0.587468i	$-0.199875\pi$
$719$	−2.79238	−	4.83654i	−0.104138	−	0.180373i	−0.913386	+	0.407095i	$0.866542\pi$
$720$		0			0
$721$	8.13800	−	14.0954i	0.303075	−	0.524941i
$722$	−5.96302	−	16.6892i	−0.221920	−	0.621108i
$723$		0			0
$724$	14.8846	+	18.1703i	0.553181	+	0.675292i
$725$	−3.28091	−	18.6070i	−0.121850	−	0.691046i
$726$		0			0
$727$	3.41147	−	4.06563i	0.126524	−	0.150786i	−0.699063	−	0.715060i	$-0.746399\pi$
$727$	3.41147	−	4.06563i	0.126524	−	0.150786i	0.825588	+	0.564274i	$0.190844\pi$
$728$	−0.887312	+	50.0861i	−0.0328860	+	1.85632i
$729$		0			0
$730$	−2.63354	+	1.49981i	−0.0974719	+	0.0555106i
$731$	−13.9204	+	16.5897i	−0.514864	+	0.613591i
$732$		0			0
$733$	44.4108	−	7.83081i	1.64035	−	0.289238i	0.724054	−	0.689743i	$-0.242277\pi$
$733$	44.4108	−	7.83081i	1.64035	−	0.289238i	0.916294	+	0.400505i	$0.131165\pi$
$734$	−7.80734	−	45.8594i	−0.288174	−	1.69270i
$735$		0			0
$736$	20.5203	−	23.0384i	0.756390	−	0.849205i
$737$	−13.9767	−	8.06943i	−0.514837	−	0.297241i
$738$		0			0
$739$	9.87524	+	17.1044i	0.363267	+	0.629196i	0.988496	−	0.151244i	$-0.0483280\pi$
$739$	9.87524	+	17.1044i	0.363267	+	0.629196i	−0.625230	+	0.780441i	$0.714995\pi$
$740$	15.6847	+	2.95703i	0.576583	+	0.108703i
$741$		0			0
$742$	−36.1327	−	13.3934i	−1.32647	−	0.491686i
$743$	8.50460	−	7.13621i	0.312004	−	0.261802i	−0.473316	−	0.880893i	$-0.656943\pi$
$743$	8.50460	−	7.13621i	0.312004	−	0.261802i	0.785320	+	0.619091i	$0.212499\pi$
$744$		0			0
$745$	−13.4724	+	4.90356i	−0.493592	+	0.179653i
$746$	8.51879	−	14.5558i	0.311895	−	0.532926i
$747$		0			0
$748$	−19.0925	−	33.9899i	−0.698091	−	1.24280i
$749$	−1.50659	+	8.54431i	−0.0550497	+	0.312202i
$750$		0			0
$751$	1.58243	−	4.34770i	0.0577439	−	0.158650i	−0.907467	−	0.420124i	$-0.861986\pi$
$751$	1.58243	−	4.34770i	0.0577439	−	0.158650i	0.965210	+	0.261474i	$0.0842087\pi$
$752$	11.2607	−	9.00438i	0.410637	−	0.328356i
$753$		0			0
$754$	−5.68712	+	31.1757i	−0.207113	+	1.13535i
$755$			12.5796i			0.457817i
$756$		0			0
$757$			11.0029i			0.399907i	0.979805	+	0.199954i	$0.0640792\pi$
$757$			11.0029i			0.399907i	−0.979805	+	0.199954i	$0.935921\pi$
$758$	−1.88956	−	0.344697i	−0.0686320	−	0.0125200i
$759$		0			0
$760$	−5.40960	+	0.855352i	−0.196227	+	0.0310269i
$761$	3.02165	−	8.30192i	0.109535	−	0.300944i	−0.872799	−	0.488079i	$-0.837698\pi$
$761$	3.02165	−	8.30192i	0.109535	−	0.300944i	0.982334	+	0.187135i	$0.0599200\pi$
$762$		0			0
$763$	4.51224	−	25.5902i	0.163354	−	0.926427i
$764$	11.7605	+	20.9370i	0.425481	+	0.757474i
$765$		0			0
$766$	−36.3433	−	21.2699i	−1.31314	−	0.768513i
$767$	−23.5326	+	8.56518i	−0.849714	+	0.309271i
$768$		0			0
$769$	38.6343	−	32.4180i	1.39319	−	1.16902i	0.429158	−	0.903229i	$-0.358810\pi$
$769$	38.6343	−	32.4180i	1.39319	−	1.16902i	0.964030	−	0.265794i	$-0.0856342\pi$
$770$	−7.21453	+	19.4634i	−0.259993	+	0.701412i
$771$		0			0
$772$	−0.186815	+	0.990909i	−0.00672364	+	0.0356636i
$773$	−10.6364	−	18.4228i	−0.382565	−	0.662622i	0.608863	−	0.793275i	$-0.291626\pi$
$773$	−10.6364	−	18.4228i	−0.382565	−	0.662622i	−0.991428	+	0.130653i	$0.958293\pi$
$774$		0			0
$775$	9.06022	+	5.23092i	0.325453	+	0.187900i
$776$	−40.4042	−	7.86471i	−1.45043	−	0.282327i
$777$		0			0
$778$	8.06992	−	1.37386i	0.289321	−	0.0492554i
$779$	−7.35380	+	1.29667i	−0.263477	+	0.0464582i
$780$		0			0
$781$	22.2934	−	26.5683i	0.797722	−	0.950688i
$782$	−13.0383	−	22.8941i	−0.466247	−	0.818690i
$783$		0			0
$784$	8.46255	+	15.4913i	0.302234	+	0.553261i
$785$	−5.71102	+	6.80613i	−0.203835	+	0.242921i
$786$		0			0
$787$	−0.282984	−	1.60488i	−0.0100873	−	0.0572079i	0.979349	−	0.202179i	$-0.0648022\pi$
$787$	−0.282984	−	1.60488i	−0.0100873	−	0.0572079i	−0.989436	+	0.144971i	$0.953691\pi$
$788$	−5.76979	+	4.72645i	−0.205540	+	0.168373i
$789$		0			0
$790$	11.7135	−	4.18521i	0.416748	−	0.148903i
$791$	10.2407	−	17.7374i	0.364118	−	0.630671i
$792$		0			0
$793$	−6.99353	−	12.1131i	−0.248347	−	0.430150i
$794$	16.8653	+	14.3222i	0.598527	+	0.508277i
$795$		0			0
$796$	−51.2568	+	8.41509i	−1.81675	+	0.298265i
$797$	6.03133	−	5.06088i	0.213641	−	0.179266i	−0.529687	−	0.848193i	$-0.677691\pi$
$797$	6.03133	−	5.06088i	0.213641	−	0.179266i	0.743328	+	0.668927i	$0.233246\pi$
$798$		0			0
$799$	−4.21113	−	11.5700i	−0.148979	−	0.409316i
$800$	−0.738124	+	24.9943i	−0.0260966	+	0.883682i
$801$		0			0
$802$	47.2696	+	0.279113i	1.66915	+	0.00985581i
$803$	−15.8183	−	2.78919i	−0.558216	−	0.0984285i
$804$		0			0
$805$	−4.79788	+	13.1821i	−0.169103	+	0.464607i
$806$	−11.1996	−	13.5083i	−0.394488	−	0.475810i
$807$		0			0
$808$	−9.27009	+	10.6584i	−0.326121	+	0.374961i
$809$		−	3.21158i		−	0.112913i	−0.998405	−	0.0564566i	$-0.982020\pi$
$809$		−	3.21158i		−	0.112913i	0.998405	−	0.0564566i	$-0.0179802\pi$
$810$		0			0
$811$	20.5556			0.721806			0.360903	−	0.932603i	$-0.382469\pi$
$811$	20.5556			0.721806			0.360903	+	0.932603i	$0.382469\pi$
$812$	9.55643	+	27.2532i	0.335365	+	0.956401i
$813$		0			0
$814$	53.9912	+	65.1213i	1.89239	+	2.28250i
$815$	1.63974	+	0.596818i	0.0574377	+	0.0209056i
$816$		0			0
$817$	−2.79996	+	15.8794i	−0.0979581	+	0.555548i
$818$	−0.193945	+	32.8459i	−0.00678113	+	1.14843i
$819$		0			0
$820$	0.0527954	−	4.47047i	0.00184369	−	0.156116i
$821$	−13.9182	+	5.06579i	−0.485747	+	0.176797i	−0.573272	−	0.819365i	$-0.694326\pi$
$821$	−13.9182	+	5.06579i	−0.485747	+	0.176797i	0.0875255	+	0.996162i	$0.472104\pi$
$822$		0			0
$823$	−6.69751	−	7.98178i	−0.233460	−	0.278227i	0.636577	−	0.771213i	$-0.280350\pi$
$823$	−6.69751	−	7.98178i	−0.233460	−	0.278227i	−0.870037	+	0.492986i	$0.835905\pi$
$824$	−10.5922	+	8.57283i	−0.368997	+	0.298649i
$825$		0			0
$826$	−14.7729	+	17.3960i	−0.514014	+	0.605284i
$827$	39.8873	−	23.0289i	1.38702	−	0.800794i	0.394038	−	0.919094i	$-0.371078\pi$
$827$	39.8873	−	23.0289i	1.38702	−	0.800794i	0.992978	+	0.118300i	$0.0377444\pi$
$828$		0			0
$829$	−0.902728	−	0.521190i	−0.0313531	−	0.0181017i	0.484242	−	0.874934i	$-0.339096\pi$
$829$	−0.902728	−	0.521190i	−0.0313531	−	0.0181017i	−0.515595	+	0.856833i	$0.672429\pi$
$830$	8.63223	−	3.08428i	0.299629	−	0.107057i
$831$		0			0
$832$	15.7313	−	38.8781i	0.545386	−	1.34785i
$833$	14.8452	−	2.61760i	0.514354	−	0.0906945i
$834$		0			0
$835$	4.87242	+	4.08844i	0.168617	+	0.141486i
$836$	−24.9646	−	14.8091i	−0.863420	−	0.512185i
$837$		0			0
$838$	1.31081	+	2.30166i	0.0452810	+	0.0795095i
$839$	8.47456	+	7.11100i	0.292574	+	0.245499i	0.777246	−	0.629197i	$-0.216616\pi$
$839$	8.47456	+	7.11100i	0.292574	+	0.245499i	−0.484671	+	0.874696i	$0.661061\pi$
$840$		0			0
$841$	−1.86324	−	10.5670i	−0.0642498	−	0.364379i
$842$	4.27077	+	25.0860i	0.147180	+	0.864521i
$843$		0			0
$844$	−8.53172	−	7.33238i	−0.293674	−	0.252391i
$845$	−5.51376	+	9.55011i	−0.189679	+	0.328534i
$846$		0			0
$847$	−63.0911	+	36.4257i	−2.16784	+	1.25160i
$848$	24.2180	+	21.3160i	0.831651	+	0.731994i
$849$		0			0
$850$	20.0222	+	7.42166i	0.686756	+	0.254561i
$851$	36.7469	+	43.7932i	1.25967	+	1.50121i
$852$		0			0
$853$	6.84425	+	18.8044i	0.234343	+	0.643851i	1.00000		0.000602347i	$0.000191733\pi$
$853$	6.84425	+	18.8044i	0.234343	+	0.643851i	−0.765657	+	0.643249i	$0.777586\pi$
$854$	−11.0012	−	6.43847i	−0.376454	−	0.220320i
$855$		0			0
$856$	3.74281	−	6.22540i	0.127927	−	0.212780i
$857$	−29.9891	−	5.28788i	−1.02441	−	0.180631i	−0.363890	−	0.931442i	$-0.618552\pi$
$857$	−29.9891	−	5.28788i	−1.02441	−	0.180631i	−0.660517	+	0.750811i	$0.729663\pi$
$858$		0			0
$859$	−27.6630	−	10.0685i	−0.943851	−	0.343533i	−0.176165	−	0.984361i	$-0.556369\pi$
$859$	−27.6630	−	10.0685i	−0.943851	−	0.343533i	−0.767685	+	0.640827i	$0.778592\pi$
$860$	−9.03211	−	3.40874i	−0.307992	−	0.116237i
$861$		0			0
$862$	39.9535	+	7.28839i	1.36082	+	0.248243i
$863$	−4.08631			−0.139100			−0.0695498	−	0.997578i	$-0.522156\pi$
$863$	−4.08631			−0.139100			−0.0695498	+	0.997578i	$0.522156\pi$
$864$		0			0
$865$	3.49382			0.118794
$866$	9.67421	+	1.76478i	0.328743	+	0.0599698i
$867$		0			0
$868$	−14.9612	−	5.64641i	−0.507818	−	0.191652i
$869$	61.9486	+	22.5474i	2.10146	+	0.764869i
$870$		0			0
$871$	−14.6014	−	2.57461i	−0.494748	−	0.0872374i
$872$	−11.2097	+	18.6451i	−0.379609	+	0.631402i
$873$		0			0
$874$	−16.9301	−	9.90834i	−0.572669	−	0.335154i
$875$	−8.28717	−	22.7688i	−0.280157	−	0.769726i
$876$		0			0
$877$	34.0441	+	40.5721i	1.14959	+	1.37002i	0.917697	+	0.397282i	$0.130046\pi$
$877$	34.0441	+	40.5721i	1.14959	+	1.37002i	0.231890	+	0.972742i	$0.425509\pi$
$878$	−43.8682	−	16.2607i	−1.48048	−	0.548772i
$879$		0			0
$880$	11.4822	−	13.0454i	0.387063	−	0.439760i
$881$	36.3618	−	20.9935i	1.22506	−	0.707288i	0.259067	−	0.965859i	$-0.416585\pi$
$881$	36.3618	−	20.9935i	1.22506	−	0.707288i	0.965992	+	0.258571i	$0.0832516\pi$
$882$		0			0
$883$	15.5284	−	26.8959i	0.522571	−	0.905120i	−0.477084	−	0.878858i	$-0.658306\pi$
$883$	15.5284	−	26.8959i	0.522571	−	0.905120i	0.999655	−	0.0262620i	$-0.00836041\pi$
$884$	−27.1623	−	23.3440i	−0.913566	−	0.785143i
$885$		0			0
$886$	4.16763	+	24.4802i	0.140014	+	0.822428i
$887$	3.83931	+	21.7738i	0.128911	+	0.731092i	0.978908	+	0.204304i	$0.0654929\pi$
$887$	3.83931	+	21.7738i	0.128911	+	0.731092i	−0.849996	+	0.526789i	$0.823396\pi$
$888$		0			0
$889$	8.02628	+	6.73485i	0.269193	+	0.225880i
$890$	−4.79300	−	8.41610i	−0.160662	−	0.282108i
$891$		0			0
$892$	−2.01249	−	1.19382i	−0.0673832	−	0.0399720i
$893$	−7.02260	−	5.89266i	−0.235002	−	0.197190i
$894$		0			0
$895$	6.93953	−	1.22363i	0.231963	−	0.0409013i
$896$	−5.07605	−	37.8827i	−0.169579	−	1.26557i
$897$		0			0
$898$	55.3400	−	19.7728i	1.84672	−	0.659828i
$899$	−8.76098	−	5.05815i	−0.292195	−	0.168699i
$900$		0			0
$901$	23.8599	−	13.7755i	0.794890	−	0.458930i
$902$	15.3376	−	18.0610i	0.510687	−	0.601365i
$903$		0			0
$904$	−13.3291	+	10.7879i	−0.443318	+	0.358800i
$905$	5.74752	+	6.84962i	0.191054	+	0.227689i
$906$		0			0
$907$	−17.8490	+	6.49651i	−0.592666	+	0.215713i	−0.620902	−	0.783888i	$-0.713233\pi$
$907$	−17.8490	+	6.49651i	−0.592666	+	0.215713i	0.0282353	+	0.999601i	$0.491011\pi$
$908$	−0.258471	+	21.8861i	−0.00857766	+	0.726317i
$909$		0			0
$910$	−0.112599	+	19.0694i	−0.00373261	+	0.632143i
$911$	1.05476	−	5.98186i	0.0349458	−	0.198188i	−0.962337	−	0.271861i	$-0.912361\pi$
$911$	1.05476	−	5.98186i	0.0349458	−	0.198188i	0.997282	+	0.0736730i	$0.0234721\pi$
$912$		0			0
$913$	45.6528	+	16.6162i	1.51089	+	0.549917i
$914$	−15.5741	−	18.7846i	−0.515145	−	0.621340i
$915$		0			0
$916$	3.70686	+	10.5713i	0.122478	+	0.349286i
$917$	−54.8431			−1.81108
$918$		0			0
$919$		−	0.413428i		−	0.0136377i	−0.999977	−	0.00681886i	$-0.997829\pi$
$919$		−	0.413428i		−	0.0136377i	0.999977	−	0.00681886i	$-0.00217053\pi$
$920$	7.70753	−	8.86184i	0.254110	−	0.292166i
$921$		0			0
$922$	−15.0093	−	18.1034i	−0.494306	−	0.596205i
$923$	10.8976	−	29.9409i	0.358698	−	0.985515i
$924$		0			0
$925$	−45.6300	−	8.04580i	−1.50031	−	0.264544i
$926$	−32.8413	−	0.193918i	−1.07923	−	0.00637253i
$927$		0			0
$928$	0.713746	−	24.1688i	0.0234299	−	0.793380i
$929$	−9.19985	−	25.2764i	−0.301837	−	0.829291i	−0.994181	−	0.107723i	$-0.965644\pi$
$929$	−9.19985	−	25.2764i	−0.301837	−	0.829291i	0.692344	−	0.721568i	$-0.256578\pi$
$930$		0			0
$931$	8.59775	−	7.21437i	0.281780	−	0.236441i
$932$	27.3670	−	4.49299i	0.896436	−	0.147173i
$933$		0			0
$934$	−24.1577	−	20.5150i	−0.790465	−	0.671272i
$935$	−7.42039	−	12.8525i	−0.242673	−	0.420322i
$936$		0			0
$937$	16.3866	−	28.3824i	0.535326	−	0.927211i	−0.463822	−	0.885928i	$-0.653522\pi$
$937$	16.3866	−	28.3824i	0.535326	−	0.927211i	0.999148	−	0.0412827i	$-0.0131444\pi$
$938$	−12.7241	+	4.54629i	−0.415457	+	0.148442i
$939$		0			0
$940$	4.24593	−	3.47815i	0.138487	−	0.113445i
$941$	−2.14333	−	12.1554i	−0.0698705	−	0.396255i	−0.999607	−	0.0280300i	$-0.991077\pi$
$941$	−2.14333	−	12.1554i	−0.0698705	−	0.396255i	0.929737	−	0.368225i	$-0.120034\pi$
$942$		0			0
$943$	10.2930	−	12.2667i	0.335187	−	0.399460i
$944$	16.7686	−	9.16031i	0.545772	−	0.298143i
$945$		0			0
$946$	−25.3204	−	44.4605i	−0.823238	−	1.44553i
$947$	−6.78558	+	8.08674i	−0.220502	+	0.262784i	−0.864943	−	0.501870i	$-0.832646\pi$
$947$	−6.78558	+	8.08674i	−0.220502	+	0.262784i	0.644441	+	0.764654i	$0.277090\pi$
$948$		0			0
$949$	−14.5321	+	2.56240i	−0.471732	+	0.0831791i
$950$	15.6733	−	2.66831i	0.508510	−	0.0865712i
$951$		0			0
$952$	−32.0381	−	6.23625i	−1.03836	−	0.202118i
$953$	3.50537	+	2.02383i	0.113550	+	0.0655581i	0.555699	−	0.831383i	$-0.312451\pi$
$953$	3.50537	+	2.02383i	0.113550	+	0.0655581i	−0.442149	+	0.896941i	$0.645784\pi$
$954$		0			0
$955$	4.57078	+	7.91683i	0.147907	+	0.256183i
$956$	6.41775	−	34.0411i	0.207565	−	1.10097i
$957$		0			0
$958$	−14.4805	+	39.0656i	−0.467844	+	1.26215i
$959$	−0.317444	+	0.266367i	−0.0102508	+	0.00860143i
$960$		0			0
$961$	−23.8668	+	8.68679i	−0.769896	+	0.280219i
$962$	67.0716	+	39.2537i	2.16248	+	1.26559i
$963$		0			0
$964$	−1.87997	−	3.34687i	−0.0605498	−	0.107795i
$965$	−0.0666570	+	0.378031i	−0.00214577	+	0.0121692i
$966$		0			0
$967$	−5.69598	+	15.6496i	−0.183170	+	0.503256i	−0.996961	−	0.0779019i	$-0.975178\pi$
$967$	−5.69598	+	15.6496i	−0.183170	+	0.503256i	0.813791	+	0.581158i	$0.197400\pi$
$968$	60.2449	−	9.52576i	1.93634	−	0.306170i
$969$		0			0
$970$	−15.4153	−	2.81208i	−0.494955	−	0.0902905i
$971$			0.618203i			0.0198391i	0.999951	+	0.00991953i	$0.00315754\pi$
$971$			0.618203i			0.0198391i	−0.999951	+	0.00991953i	$0.996842\pi$
$972$		0			0
$973$			54.2386i			1.73881i
$974$	−6.91671	+	37.9160i	−0.221626	+	1.21491i
$975$		0			0
$976$	6.66485	+	8.33495i	0.213337	+	0.266795i
$977$	18.4051	−	50.5677i	0.588833	−	1.61780i	−0.183809	−	0.982962i	$-0.558843\pi$
$977$	18.4051	−	50.5677i	0.588833	−	1.61780i	0.772642	−	0.634842i	$-0.218935\pi$
$978$		0			0
$979$	8.91351	−	50.5510i	0.284877	−	1.61562i
$980$	3.29092	+	5.85875i	0.105125	+	0.187151i
$981$		0			0
$982$	−11.1324	+	19.0215i	−0.355248	+	0.607002i
$983$	−14.7088	+	5.35358i	−0.469139	+	0.170753i	−0.565762	−	0.824568i	$-0.691418\pi$
$983$	−14.7088	+	5.35358i	−0.469139	+	0.170753i	0.0966232	+	0.995321i	$0.469196\pi$
$984$		0			0
$985$	−2.17503	+	1.82507i	−0.0693023	+	0.0581515i
$986$	−19.3609	−	7.17653i	−0.616577	−	0.228547i
$987$		0			0
$988$	−26.2048	−	4.94038i	−0.833686	−	0.157174i
$989$	−17.2888	−	29.9452i	−0.549753	−	0.952201i
$990$		0			0
$991$	13.5526	+	7.82457i	0.430511	+	0.248556i	0.699564	−	0.714570i	$-0.253377\pi$
$991$	13.5526	+	7.82457i	0.430511	+	0.248556i	−0.269053	+	0.963125i	$0.586711\pi$
$992$	9.99758	+	8.90488i	0.317424	+	0.282730i
$993$		0			0
$994$	−4.87331	−	28.6252i	−0.154572	−	0.907938i
$995$	−19.4731	+	3.43364i	−0.617340	+	0.108854i
$996$		0			0
$997$	5.45472	−	6.50068i	0.172753	−	0.205879i	−0.672720	−	0.739897i	$-0.734874\pi$
$997$	5.45472	−	6.50068i	0.172753	−	0.205879i	0.845473	+	0.534018i	$0.179319\pi$
$998$	−7.75901	+	4.41879i	−0.245607	+	0.139874i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.35.3		192
3.2	odd	2		216.2.v.b.11.30	yes	192
8.3	odd	2	inner	648.2.v.b.35.20		192
12.11	even	2		864.2.bh.b.335.31		192
24.5	odd	2		864.2.bh.b.335.32		192
24.11	even	2		216.2.v.b.11.13	✓	192
27.5	odd	18	inner	648.2.v.b.611.20		192
27.22	even	9		216.2.v.b.59.13	yes	192
108.103	odd	18		864.2.bh.b.815.32		192
216.59	even	18	inner	648.2.v.b.611.3		192
216.157	even	18		864.2.bh.b.815.31		192
216.211	odd	18		216.2.v.b.59.30	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.13	✓	192	24.11	even	2
216.2.v.b.11.30	yes	192	3.2	odd	2
216.2.v.b.59.13	yes	192	27.22	even	9
216.2.v.b.59.30	yes	192	216.211	odd	18
648.2.v.b.35.3		192	1.1	even	1	trivial
648.2.v.b.35.20		192	8.3	odd	2	inner
648.2.v.b.611.3		192	216.59	even	18	inner
648.2.v.b.611.20		192	27.5	odd	18	inner
864.2.bh.b.335.31		192	12.11	even	2
864.2.bh.b.335.32		192	24.5	odd	2
864.2.bh.b.815.31		192	216.157	even	18
864.2.bh.b.815.32		192	108.103	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.v (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39125 - 0.253795i) q^{2} +(1.87118 + 0.706186i) q^{4} +(0.715441 + 0.260399i) q^{5} +(3.32699 + 0.586638i) q^{7} +(-2.42406 - 1.45738i) q^{8} +O(q^{10})\)	\(q+(-1.39125 - 0.253795i) q^{2} +(1.87118 + 0.706186i) q^{4} +(0.715441 + 0.260399i) q^{5} +(3.32699 + 0.586638i) q^{7} +(-2.42406 - 1.45738i) q^{8} +(-0.929272 - 0.543857i) q^{10} +(-1.95175 - 5.36238i) q^{11} +(-3.36983 - 4.01601i) q^{13} +(-4.47981 - 1.66054i) q^{14} +(3.00260 + 2.64280i) q^{16} +(2.95820 - 1.70792i) q^{17} +(1.27164 - 2.20255i) q^{19} +(1.15483 + 0.992487i) q^{20} +(1.35443 + 7.95577i) q^{22} +(0.947065 + 5.37107i) q^{23} +(-3.38617 - 2.84134i) q^{25} +(3.66905 + 6.44253i) q^{26} +(5.81111 + 3.44718i) q^{28} +(3.27434 + 2.74749i) q^{29} +(-2.33080 + 0.410982i) q^{31} +(-3.50665 - 4.43885i) q^{32} +(-4.54907 + 1.62537i) q^{34} +(2.22751 + 1.28605i) q^{35} +(9.07767 - 5.24099i) q^{37} +(-2.32817 + 2.74157i) q^{38} +(-1.35477 - 1.67389i) q^{40} +(-1.88727 - 2.24916i) q^{41} +(-5.95761 + 2.16839i) q^{43} +(0.134776 - 11.4123i) q^{44} +(0.0455422 - 7.71289i) q^{46} +(0.625921 - 3.54977i) q^{47} +(4.14688 + 1.50934i) q^{49} +(3.98991 + 4.81242i) q^{50} +(-3.46950 - 9.89438i) q^{52} +8.06569 q^{53} -4.34470i q^{55} +(-7.20986 - 6.27073i) q^{56} +(-3.85813 - 4.65347i) q^{58} +(1.63379 - 4.48880i) q^{59} +(2.62747 + 0.463294i) q^{61} +(3.34703 + 0.0197632i) q^{62} +(3.75209 + 7.06554i) q^{64} +(-1.36515 - 3.75071i) q^{65} +(2.16648 - 1.81790i) q^{67} +(6.74143 - 1.10678i) q^{68} +(-2.77263 - 2.35455i) q^{70} +(3.03884 + 5.26343i) q^{71} +(1.40736 - 2.43763i) q^{73} +(-13.9595 + 4.98769i) q^{74} +(3.93488 - 3.22334i) q^{76} +(-3.34767 - 18.9856i) q^{77} +(-7.42577 + 8.84969i) q^{79} +(1.46000 + 2.67264i) q^{80} +(2.05484 + 3.60813i) q^{82} +(-5.47239 + 6.52174i) q^{83} +(2.56116 - 0.451602i) q^{85} +(8.83888 - 1.50478i) q^{86} +(-3.08388 + 15.8431i) q^{88} +(7.79000 + 4.49756i) q^{89} +(-8.85545 - 15.3381i) q^{91} +(-2.02085 + 10.7190i) q^{92} +(-1.77173 + 4.77978i) q^{94} +(1.48333 - 1.24466i) q^{95} +(13.6755 - 4.97747i) q^{97} +(-5.38630 - 3.15233i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8} - 3 q^{10} + 30 q^{11} - 9 q^{14} - 6 q^{16} + 18 q^{17} - 6 q^{19} + 27 q^{20} - 18 q^{22} - 12 q^{25} - 12 q^{28} + 36 q^{32} + 12 q^{34} + 18 q^{35} + 102 q^{38} + 9 q^{40} - 18 q^{41} - 42 q^{43} + 81 q^{44} - 3 q^{46} - 12 q^{49} - 57 q^{50} + 21 q^{52} + 69 q^{56} - 33 q^{58} + 84 q^{59} - 90 q^{62} - 51 q^{64} + 12 q^{65} + 30 q^{67} - 63 q^{68} - 33 q^{70} - 6 q^{73} - 51 q^{74} + 30 q^{76} - 12 q^{82} + 72 q^{83} - 42 q^{86} - 78 q^{88} - 144 q^{89} - 6 q^{91} + 3 q^{92} - 33 q^{94} - 42 q^{97} - 162 q^{98}+O(q^{100}) \) 192 * q + 6 * q^2 - 6 * q^4 + 9 * q^8 - 3 * q^10 + 30 * q^11 - 9 * q^14 - 6 * q^16 + 18 * q^17 - 6 * q^19 + 27 * q^20 - 18 * q^22 - 12 * q^25 - 12 * q^28 + 36 * q^32 + 12 * q^34 + 18 * q^35 + 102 * q^38 + 9 * q^40 - 18 * q^41 - 42 * q^43 + 81 * q^44 - 3 * q^46 - 12 * q^49 - 57 * q^50 + 21 * q^52 + 69 * q^56 - 33 * q^58 + 84 * q^59 - 90 * q^62 - 51 * q^64 + 12 * q^65 + 30 * q^67 - 63 * q^68 - 33 * q^70 - 6 * q^73 - 51 * q^74 + 30 * q^76 - 12 * q^82 + 72 * q^83 - 42 * q^86 - 78 * q^88 - 144 * q^89 - 6 * q^91 + 3 * q^92 - 33 * q^94 - 42 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more