LMFDB - Embedded newform 648.2.v.b.35.1

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			35.1
Character	$\chi$	$=$	648.35
Dual form			648.2.v.b.611.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41380 - 0.0343398i) q^{2} +(1.99764 + 0.0970990i) q^{4} +(2.25586 + 0.821067i) q^{5} +(-1.95474 - 0.344674i) q^{7} +(-2.82092 - 0.205877i) q^{8} +O(q^{10})$	\(q+(-1.41380 - 0.0343398i) q^{2} +(1.99764 + 0.0970990i) q^{4} +(2.25586 + 0.821067i) q^{5} +(-1.95474 - 0.344674i) q^{7} +(-2.82092 - 0.205877i) q^{8} +(-3.16114 - 1.23829i) q^{10} +(-0.553700 - 1.52128i) q^{11} +(3.57715 + 4.26309i) q^{13} +(2.75177 + 0.554424i) q^{14} +(3.98114 + 0.387938i) q^{16} +(6.40600 - 3.69851i) q^{17} +(-1.39557 + 2.41719i) q^{19} +(4.42668 + 1.85924i) q^{20} +(0.730579 + 2.16979i) q^{22} +(0.465506 + 2.64002i) q^{23} +(0.584547 + 0.490493i) q^{25} +(-4.91098 - 6.14998i) q^{26} +(-3.87141 - 0.878338i) q^{28} +(0.138481 + 0.116199i) q^{29} +(1.76926 - 0.311969i) q^{31} +(-5.61521 - 0.685177i) q^{32} +(-9.18379 + 5.00895i) q^{34} +(-4.12663 - 2.38251i) q^{35} +(-3.55469 + 2.05230i) q^{37} +(2.05606 - 3.36950i) q^{38} +(-6.19458 - 2.78060i) q^{40} +(2.85334 + 3.40048i) q^{41} +(11.1139 - 4.04511i) q^{43} +(-0.958380 - 3.09273i) q^{44} +(-0.567474 - 3.74843i) q^{46} +(-2.08588 + 11.8296i) q^{47} +(-2.87563 - 1.04664i) q^{49} +(-0.809587 - 0.713530i) q^{50} +(6.73193 + 8.86346i) q^{52} +10.1087 q^{53} -3.88642i q^{55} +(5.44322 + 1.37474i) q^{56} +(-0.191794 - 0.169038i) q^{58} +(1.96718 - 5.40478i) q^{59} +(7.60780 + 1.34146i) q^{61} +(-2.51209 + 0.380305i) q^{62} +(7.91523 + 1.16153i) q^{64} +(4.56929 + 12.5540i) q^{65} +(1.38817 - 1.16481i) q^{67} +(13.1560 - 6.76627i) q^{68} +(5.75240 + 3.51010i) q^{70} +(1.25119 + 2.16713i) q^{71} +(-3.79038 + 6.56514i) q^{73} +(5.09608 - 2.77947i) q^{74} +(-3.02255 + 4.69318i) q^{76} +(0.557996 + 3.16455i) q^{77} +(6.77140 - 8.06984i) q^{79} +(8.66239 + 4.14392i) q^{80} +(-3.91727 - 4.90557i) q^{82} +(-0.718131 + 0.855836i) q^{83} +(17.4878 - 3.08357i) q^{85} +(-15.8516 + 5.33732i) q^{86} +(1.24875 + 4.40541i) q^{88} +(-9.87804 - 5.70309i) q^{89} +(-5.52304 - 9.56619i) q^{91} +(0.673572 + 5.31901i) q^{92} +(3.35523 - 16.6530i) q^{94} +(-5.13289 + 4.30701i) q^{95} +(-5.25587 + 1.91298i) q^{97} +(4.02961 + 1.57849i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.41380	−	0.0343398i	−0.999705	−	0.0242819i
$2$	−1.41380	−	0.0343398i	−0.999705	−	0.0242819i
$3$		0			0
$3$		0			0
$4$	1.99764	+	0.0970990i	0.998821	+	0.0485495i
$5$	2.25586	+	0.821067i	1.00885	+	0.367192i	0.792992	−	0.609232i	$-0.208522\pi$
$5$	2.25586	+	0.821067i	1.00885	+	0.367192i	0.215861	+	0.976424i	$0.430744\pi$
$6$		0			0
$7$	−1.95474	−	0.344674i	−0.738823	−	0.130274i	−0.208443	−	0.978034i	$-0.566840\pi$
$7$	−1.95474	−	0.344674i	−0.738823	−	0.130274i	−0.530380	+	0.847760i	$0.677951\pi$
$8$	−2.82092	−	0.205877i	−0.997347	−	0.0727884i
$9$		0			0
$10$	−3.16114	−	1.23829i	−0.999639	−	0.391581i
$11$	−0.553700	−	1.52128i	−0.166947	−	0.458683i	0.827803	−	0.561019i	$-0.189590\pi$
$11$	−0.553700	−	1.52128i	−0.166947	−	0.458683i	−0.994750	+	0.102336i	$0.967368\pi$
$12$		0			0
$13$	3.57715	+	4.26309i	0.992124	+	1.18237i	0.983223	+	0.182407i	$0.0583889\pi$
$13$	3.57715	+	4.26309i	0.992124	+	1.18237i	0.00890108	+	0.999960i	$0.497167\pi$
$14$	2.75177	+	0.554424i	0.735442	+	0.148176i
$15$		0			0
$16$	3.98114	+	0.387938i	0.995286	+	0.0969845i
$17$	6.40600	−	3.69851i	1.55368	−	0.897020i	0.555846	−	0.831285i	$-0.312394\pi$
$17$	6.40600	−	3.69851i	1.55368	−	0.897020i	0.997837	−	0.0657345i	$-0.0209390\pi$
$18$		0			0
$19$	−1.39557	+	2.41719i	−0.320165	+	0.554543i	−0.980522	−	0.196410i	$-0.937072\pi$
$19$	−1.39557	+	2.41719i	−0.320165	+	0.554543i	0.660357	+	0.750952i	$0.270405\pi$
$20$	4.42668	+	1.85924i	0.989836	+	0.415739i
$21$		0			0
$22$	0.730579	+	2.16979i	0.155760	+	0.462601i
$23$	0.465506	+	2.64002i	0.0970648	+	0.550482i	0.994095	+	0.108513i	$0.0346088\pi$
$23$	0.465506	+	2.64002i	0.0970648	+	0.550482i	−0.897030	+	0.441969i	$0.854280\pi$
$24$		0			0
$25$	0.584547	+	0.490493i	0.116909	+	0.0980986i
$26$	−4.91098	−	6.14998i	−0.963122	−	1.20611i
$27$		0			0
$28$	−3.87141	−	0.878338i	−0.731627	−	0.165990i
$29$	0.138481	+	0.116199i	0.0257153	+	0.0215777i	0.655555	−	0.755148i	$-0.272435\pi$
$29$	0.138481	+	0.116199i	0.0257153	+	0.0215777i	−0.629839	+	0.776725i	$0.716879\pi$
$30$		0			0
$31$	1.76926	−	0.311969i	0.317769	−	0.0560313i	−0.0124887	−	0.999922i	$-0.503975\pi$
$31$	1.76926	−	0.311969i	0.317769	−	0.0560313i	0.330258	+	0.943891i	$0.392864\pi$
$32$	−5.61521	−	0.685177i	−0.992637	−	0.121123i
$33$		0			0
$34$	−9.18379	+	5.00895i	−1.57501	+	0.859029i
$35$	−4.12663	−	2.38251i	−0.697528	−	0.402718i
$36$		0			0
$37$	−3.55469	+	2.05230i	−0.584387	+	0.337396i	−0.762875	−	0.646546i	$-0.776213\pi$
$37$	−3.55469	+	2.05230i	−0.584387	+	0.337396i	0.178488	+	0.983942i	$0.442880\pi$
$38$	2.05606	−	3.36950i	0.333536	−	0.546605i
$39$		0			0
$40$	−6.19458	−	2.78060i	−0.979449	−	0.439651i
$41$	2.85334	+	3.40048i	0.445617	+	0.531066i	0.941360	−	0.337404i	$-0.109549\pi$
$41$	2.85334	+	3.40048i	0.445617	+	0.531066i	−0.495743	+	0.868469i	$0.665104\pi$
$42$		0			0
$43$	11.1139	−	4.04511i	1.69485	−	0.616874i	0.699625	−	0.714510i	$-0.253350\pi$
$43$	11.1139	−	4.04511i	1.69485	−	0.616874i	0.995222	+	0.0976364i	$0.0311282\pi$
$44$	−0.958380	−	3.09273i	−0.144481	−	0.466247i
$45$		0			0
$46$	−0.567474	−	3.74843i	−0.0836694	−	0.552676i
$47$	−2.08588	+	11.8296i	−0.304257	+	1.72552i	0.322727	+	0.946492i	$0.395401\pi$
$47$	−2.08588	+	11.8296i	−0.304257	+	1.72552i	−0.626983	+	0.779033i	$0.715711\pi$
$48$		0			0
$49$	−2.87563	−	1.04664i	−0.410804	−	0.149520i
$50$	−0.809587	−	0.713530i	−0.114493	−	0.100908i
$51$		0			0
$52$	6.73193	+	8.86346i	0.933551	+	1.22914i
$53$	10.1087			1.38854			0.694271	−	0.719714i	$-0.255727\pi$
$53$	10.1087			1.38854			0.694271	+	0.719714i	$0.255727\pi$
$54$		0			0
$55$		−	3.88642i		−	0.524045i
$56$	5.44322	+	1.37474i	0.727381	+	0.183707i
$57$		0			0
$58$	−0.191794	−	0.169038i	−0.0251838	−	0.0221957i
$59$	1.96718	−	5.40478i	0.256105	−	0.703642i	−0.743294	−	0.668965i	$-0.766738\pi$
$59$	1.96718	−	5.40478i	0.256105	−	0.703642i	0.999399	−	0.0346769i	$-0.0110402\pi$
$60$		0			0
$61$	7.60780	+	1.34146i	0.974079	+	0.171756i	0.637965	−	0.770065i	$-0.279776\pi$
$61$	7.60780	+	1.34146i	0.974079	+	0.171756i	0.336113	+	0.941822i	$0.390887\pi$
$62$	−2.51209	+	0.380305i	−0.319036	+	0.0482987i
$63$		0			0
$64$	7.91523	+	1.16153i	0.989404	+	0.145191i
$65$	4.56929	+	12.5540i	0.566751	+	1.55714i
$66$		0			0
$67$	1.38817	−	1.16481i	0.169592	−	0.142305i	−0.554041	−	0.832489i	$-0.686915\pi$
$67$	1.38817	−	1.16481i	0.169592	−	0.142305i	0.723633	+	0.690184i	$0.242471\pi$
$68$	13.1560	−	6.76627i	1.59540	−	0.820531i
$69$		0			0
$70$	5.75240	+	3.51010i	0.687544	+	0.419537i
$71$	1.25119	+	2.16713i	0.148489	+	0.257191i	0.930669	−	0.365862i	$-0.119226\pi$
$71$	1.25119	+	2.16713i	0.148489	+	0.257191i	−0.782180	+	0.623052i	$0.785892\pi$
$72$		0			0
$73$	−3.79038	+	6.56514i	−0.443631	+	0.768391i	−0.997956	−	0.0639093i	$-0.979643\pi$
$73$	−3.79038	+	6.56514i	−0.443631	+	0.768391i	0.554325	+	0.832300i	$0.312976\pi$
$74$	5.09608	−	2.77947i	0.592408	−	0.323107i
$75$		0			0
$76$	−3.02255	+	4.69318i	−0.346710	+	0.538345i
$77$	0.557996	+	3.16455i	0.0635896	+	0.360634i
$78$		0			0
$79$	6.77140	−	8.06984i	0.761842	−	0.907928i	−0.236121	−	0.971724i	$-0.575876\pi$
$79$	6.77140	−	8.06984i	0.761842	−	0.907928i	0.997963	+	0.0637957i	$0.0203206\pi$
$80$	8.66239	+	4.14392i	0.968485	+	0.463304i
$81$		0			0
$82$	−3.91727	−	4.90557i	−0.432590	−	0.541729i
$83$	−0.718131	+	0.855836i	−0.0788251	+	0.0939402i	−0.804016	−	0.594608i	$-0.797307\pi$
$83$	−0.718131	+	0.855836i	−0.0788251	+	0.0939402i	0.725191	+	0.688548i	$0.241752\pi$
$84$		0			0
$85$	17.4878	−	3.08357i	1.89682	−	0.334460i
$86$	−15.8516	+	5.33732i	−1.70933	+	0.575538i
$87$		0			0
$88$	1.24875	+	4.40541i	0.133117	+	0.469618i
$89$	−9.87804	−	5.70309i	−1.04707	−	0.604526i	−0.125243	−	0.992126i	$-0.539971\pi$
$89$	−9.87804	−	5.70309i	−1.04707	−	0.604526i	−0.921828	+	0.387600i	$0.873304\pi$
$90$		0			0
$91$	−5.52304	−	9.56619i	−0.578972	−	1.00281i
$92$	0.673572	+	5.31901i	0.0702247	+	0.554545i
$93$		0			0
$94$	3.35523	−	16.6530i	0.346066	−	1.71763i
$95$	−5.13289	+	4.30701i	−0.526623	+	0.441890i
$96$		0			0
$97$	−5.25587	+	1.91298i	−0.533652	+	0.194234i	−0.594768	−	0.803897i	$-0.702756\pi$
$97$	−5.25587	+	1.91298i	−0.533652	+	0.194234i	0.0611161	+	0.998131i	$0.480534\pi$
$98$	4.02961	+	1.57849i	0.407052	+	0.159451i
$99$		0			0
$100$	1.12009	+	1.03659i	0.112009	+	0.103659i
$101$	1.90061	−	10.7789i	0.189117	−	1.07254i	−0.731433	−	0.681913i	$-0.761148\pi$
$101$	1.90061	−	10.7789i	0.189117	−	1.07254i	0.920550	−	0.390624i	$-0.127741\pi$
$102$		0			0
$103$	−5.15163	+	14.1540i	−0.507605	+	1.39463i	0.376095	+	0.926581i	$0.377266\pi$
$103$	−5.15163	+	14.1540i	−0.507605	+	1.39463i	−0.883701	+	0.468053i	$0.844956\pi$
$104$	−9.21321	−	12.7623i	−0.903430	−	1.25145i
$105$		0			0
$106$	−14.2917	−	0.347132i	−1.38813	−	0.0337164i
$107$			1.83241i			0.177146i	0.996070	+	0.0885728i	$0.0282306\pi$
$107$			1.83241i			0.177146i	−0.996070	+	0.0885728i	$0.971769\pi$
$108$		0			0
$109$			2.84696i			0.272689i	0.990661	+	0.136345i	$0.0435355\pi$
$109$			2.84696i			0.272689i	−0.990661	+	0.136345i	$0.956465\pi$
$110$	−0.133459	+	5.49461i	−0.0127248	+	0.523890i
$111$		0			0
$112$	−7.64840	−	2.13052i	−0.722706	−	0.201315i
$113$	−4.14703	+	11.3939i	−0.390120	+	1.07185i	0.576826	+	0.816867i	$0.304291\pi$
$113$	−4.14703	+	11.3939i	−0.390120	+	1.07185i	−0.966946	+	0.254980i	$0.917931\pi$
$114$		0			0
$115$	−1.11751	+	6.33773i	−0.104209	+	0.590997i
$116$	0.265353	+	0.245571i	0.0246374	+	0.0228007i
$117$		0			0
$118$	−2.96679	+	7.57370i	−0.273115	+	0.697216i
$119$	−13.7969	+	5.02165i	−1.26476	+	0.460334i
$120$		0			0
$121$	6.41878	−	5.38600i	0.583526	−	0.489636i
$122$	−10.7098	−	2.15780i	−0.969621	−	0.195358i
$123$		0			0
$124$	3.56465	−	0.451408i	0.320115	−	0.0405377i
$125$	−5.08567	−	8.80864i	−0.454876	−	0.787869i
$126$		0			0
$127$	0.655158	+	0.378256i	0.0581359	+	0.0335648i	0.528786	−	0.848755i	$-0.322647\pi$
$127$	0.655158	+	0.378256i	0.0581359	+	0.0335648i	−0.470650	+	0.882320i	$0.655981\pi$
$128$	−11.1506	−	1.91397i	−0.985586	−	0.169173i
$129$		0			0
$130$	−6.02895	−	17.9057i	−0.528774	−	1.57044i
$131$	−3.17397	+	0.559656i	−0.277311	+	0.0488974i	−0.310574	−	0.950549i	$-0.600521\pi$
$131$	−3.17397	+	0.559656i	−0.277311	+	0.0488974i	0.0332631	+	0.999447i	$0.489410\pi$
$132$		0			0
$133$	3.56112	−	4.24398i	0.308788	−	0.368000i
$134$	−2.00259	+	1.59914i	−0.172998	+	0.138145i
$135$		0			0
$136$	−18.8323	+	9.11436i	−1.61485	+	0.781550i
$137$	6.88493	−	8.20513i	0.588219	−	0.701012i	−0.387044	−	0.922061i	$-0.626504\pi$
$137$	6.88493	−	8.20513i	0.588219	−	0.701012i	0.975263	+	0.221049i	$0.0709482\pi$
$138$		0			0
$139$	−3.48804	−	19.7816i	−0.295851	−	1.67786i	−0.663722	−	0.747980i	$-0.731024\pi$
$139$	−3.48804	−	19.7816i	−0.295851	−	1.67786i	0.367870	−	0.929877i	$-0.380087\pi$
$140$	−8.01219	−	5.16010i	−0.677154	−	0.436108i
$141$		0			0
$142$	−1.69451	−	3.10684i	−0.142200	−	0.260720i
$143$	4.50467	−	7.80232i	0.376700	−	0.652463i
$144$		0			0
$145$	0.216987	+	0.375832i	0.0180198	+	0.0312112i
$146$	5.58428	−	9.15161i	0.462158	−	0.757392i
$147$		0			0
$148$	−7.30027	+	3.75460i	−0.600079	+	0.308627i
$149$	−10.3687	+	8.70041i	−0.849441	+	0.712765i	−0.959666	−	0.281141i	$-0.909287\pi$
$149$	−10.3687	+	8.70041i	−0.849441	+	0.712765i	0.110226	+	0.993907i	$0.464843\pi$
$150$		0			0
$151$	−3.05584	−	8.39584i	−0.248680	−	0.683244i	−0.999735	−	0.0230040i	$-0.992677\pi$
$151$	−3.05584	−	8.39584i	−0.248680	−	0.683244i	0.751055	−	0.660240i	$-0.229545\pi$
$152$	4.43444	−	6.53141i	0.359680	−	0.529767i
$153$		0			0
$154$	−0.680223	−	4.49320i	−0.0548139	−	0.362072i
$155$	4.24737	+	0.748925i	0.341157	+	0.0601551i
$156$		0			0
$157$	2.25685	−	6.20065i	0.180116	−	0.494866i	−0.816473	−	0.577383i	$-0.804074\pi$
$157$	2.25685	−	6.20065i	0.180116	−	0.494866i	0.996590	+	0.0825175i	$0.0262960\pi$
$158$	−9.85050	+	11.1766i	−0.783664	+	0.889161i
$159$		0			0
$160$	−12.1046	−	6.15613i	−0.956950	−	0.486685i
$161$		−	5.32100i		−	0.419354i
$162$		0			0
$163$	2.05597			0.161036			0.0805178	−	0.996753i	$-0.474343\pi$
$163$	2.05597			0.161036			0.0805178	+	0.996753i	$0.474343\pi$
$164$	5.36977	+	7.07000i	0.419309	+	0.552074i
$165$		0			0
$166$	1.04468	−	1.18532i	0.0810830	−	0.0919984i
$167$	4.05523	+	1.47598i	0.313803	+	0.114215i	0.494120	−	0.869394i	$-0.335490\pi$
$167$	4.05523	+	1.47598i	0.313803	+	0.114215i	−0.180317	+	0.983608i	$0.557712\pi$
$168$		0			0
$169$	−3.12045	+	17.6969i	−0.240034	+	1.36130i
$170$	−24.8301	+	3.75901i	−1.90438	+	0.288303i
$171$		0			0
$172$	22.5943	−	7.00154i	1.72280	−	0.533863i
$173$	−3.48473	+	1.26834i	−0.264939	+	0.0964298i	−0.471074	−	0.882094i	$-0.656134\pi$
$173$	−3.48473	+	1.26834i	−0.264939	+	0.0964298i	0.206135	+	0.978524i	$0.433911\pi$
$174$		0			0
$175$	−0.973578	−	1.16027i	−0.0735956	−	0.0877078i
$176$	−1.61420	−	6.27123i	−0.121675	−	0.472712i
$177$		0			0
$178$	13.7697	+	8.40222i	1.03208	+	0.629773i
$179$	−4.83050	+	2.78889i	−0.361048	+	0.208451i	−0.669541	−	0.742776i	$-0.733509\pi$
$179$	−4.83050	+	2.78889i	−0.361048	+	0.208451i	0.308492	+	0.951227i	$0.400176\pi$
$180$		0			0
$181$	−21.9838	−	12.6923i	−1.63404	−	0.943415i	−0.982829	−	0.184520i	$-0.940927\pi$
$181$	−21.9838	−	12.6923i	−1.63404	−	0.943415i	−0.651213	−	0.758895i	$-0.725740\pi$
$182$	7.47996	+	13.7143i	0.554451	+	1.01657i
$183$		0			0
$184$	−0.769640	−	7.54313i	−0.0567386	−	0.556087i
$185$	−9.70397	+	1.71107i	−0.713450	+	0.125800i
$186$		0			0
$187$	−9.17346	−	7.69745i	−0.670830	−	0.562893i
$188$	−5.31548	+	23.4288i	−0.387671	+	1.70872i
$189$		0			0
$190$	7.40476	−	5.91297i	0.537198	−	0.428972i
$191$	−16.1419	−	13.5447i	−1.16799	−	0.980060i	−0.168006	−	0.985786i	$-0.553733\pi$
$191$	−16.1419	−	13.5447i	−1.16799	−	0.980060i	−0.999984	+	0.00572593i	$0.998177\pi$
$192$		0			0
$193$	2.14750	+	12.1791i	0.154580	+	0.876668i	0.959169	+	0.282835i	$0.0912748\pi$
$193$	2.14750	+	12.1791i	0.154580	+	0.876668i	−0.804589	+	0.593833i	$0.797614\pi$
$194$	7.49642	−	2.52408i	0.538211	−	0.181218i
$195$		0			0
$196$	−5.64285	−	2.37004i	−0.403061	−	0.169288i
$197$	5.95187	−	10.3089i	0.424054	−	0.734482i	−0.572278	−	0.820060i	$-0.693940\pi$
$197$	5.95187	−	10.3089i	0.424054	−	0.734482i	0.996332	+	0.0855775i	$0.0272735\pi$
$198$		0			0
$199$	−18.0680	+	10.4316i	−1.28081	+	0.739475i	−0.976996	−	0.213256i	$-0.931593\pi$
$199$	−18.0680	+	10.4316i	−1.28081	+	0.739475i	−0.303813	+	0.952732i	$0.598260\pi$
$200$	−1.54798	−	1.50399i	−0.109459	−	0.106348i
$201$		0			0
$202$	−3.05721	+	15.1739i	−0.215105	+	1.06763i
$203$	−0.230644	−	0.274871i	−0.0161880	−	0.0192921i
$204$		0			0
$205$	3.64473	+	10.0138i	0.254559	+	0.699394i
$206$	7.76940	−	19.8340i	0.541320	−	1.38190i
$207$		0			0
$208$	12.5874	+	18.3597i	0.872776	+	1.27301i
$209$	4.44995	+	0.784647i	0.307810	+	0.0542751i
$210$		0			0
$211$	−2.06728	−	0.752429i	−0.142317	−	0.0517993i	0.269879	−	0.962894i	$-0.413016\pi$
$211$	−2.06728	−	0.752429i	−0.142317	−	0.0517993i	−0.412197	+	0.911095i	$0.635238\pi$
$212$	20.1936	+	0.981548i	1.38690	+	0.0674130i
$213$		0			0
$214$	0.0629246	−	2.59065i	0.00430143	−	0.177093i
$215$	28.3927			1.93636
$216$		0			0
$217$	−3.56598			−0.242075
$218$	0.0977640	−	4.02502i	0.00662141	−	0.272609i
$219$		0			0
$220$	0.377368	−	7.76368i	0.0254421	−	0.523427i
$221$	38.6823	+	14.0792i	2.60205	+	0.947070i
$222$		0			0
$223$	−18.9371	−	3.33912i	−1.26812	−	0.223604i	−0.501193	−	0.865336i	$-0.667105\pi$
$223$	−18.9371	−	3.33912i	−1.26812	−	0.223604i	−0.766929	+	0.641732i	$0.778216\pi$
$224$	10.7401	+	3.27476i	0.717604	+	0.218804i
$225$		0			0
$226$	6.25433	−	15.9662i	0.416032	−	1.06206i
$227$	−5.41355	−	14.8736i	−0.359310	−	0.987195i	−0.979269	−	0.202562i	$-0.935073\pi$
$227$	−5.41355	−	14.8736i	−0.359310	−	0.987195i	0.619960	−	0.784634i	$-0.287149\pi$
$228$		0			0
$229$	11.5655	+	13.7832i	0.764268	+	0.910819i	0.998110	−	0.0614553i	$-0.0195742\pi$
$229$	11.5655	+	13.7832i	0.764268	+	0.910819i	−0.233842	+	0.972275i	$0.575130\pi$
$230$	1.79757	−	8.92189i	0.118528	−	0.588292i
$231$		0			0
$232$	−0.366722	−	0.356300i	−0.0240765	−	0.0233922i
$233$	−4.58811	+	2.64895i	−0.300577	+	0.173538i	−0.642702	−	0.766116i	$-0.722187\pi$
$233$	−4.58811	+	2.64895i	−0.300577	+	0.173538i	0.342125	+	0.939654i	$0.388853\pi$
$234$		0			0
$235$	−14.4184	+	24.9733i	−0.940550	+	1.62908i
$236$	4.45451	−	10.6058i	0.289964	−	0.690379i
$237$		0			0
$238$	19.6784	−	6.62581i	1.27556	−	0.429487i
$239$	−4.48956	−	25.4615i	−0.290405	−	1.64697i	−0.685312	−	0.728249i	$-0.740334\pi$
$239$	−4.48956	−	25.4615i	−0.290405	−	1.64697i	0.394907	−	0.918721i	$-0.370777\pi$
$240$		0			0
$241$	−18.4759	−	15.5031i	−1.19014	−	0.998644i	−0.999857	−	0.0169143i	$-0.994616\pi$
$241$	−18.4759	−	15.5031i	−1.19014	−	0.998644i	−0.190281	−	0.981730i	$-0.560940\pi$
$242$	−9.25981	+	7.39429i	−0.595243	+	0.475323i
$243$		0			0
$244$	15.0674	+	3.41847i	0.964591	+	0.218845i
$245$	−5.62766	−	4.72217i	−0.359538	−	0.301688i
$246$		0			0
$247$	−15.2969	+	2.69725i	−0.973317	+	0.171622i
$248$	−5.05519	+	0.515791i	−0.321005	+	0.0327527i
$249$		0			0
$250$	6.88762	+	12.6283i	0.435611	+	0.798682i
$251$	−2.91308	−	1.68187i	−0.183872	−	0.106159i	0.405239	−	0.914211i	$-0.367188\pi$
$251$	−2.91308	−	1.68187i	−0.183872	−	0.106159i	−0.589111	+	0.808052i	$0.700522\pi$
$252$		0			0
$253$	3.75845	−	2.16994i	0.236292	−	0.136423i
$254$	−0.913271	−	0.557275i	−0.0573037	−	0.0349665i
$255$		0			0
$256$	15.6990	+	3.08887i	0.981188	+	0.193055i
$257$	−1.68413	−	2.00707i	−0.105053	−	0.125198i	0.710956	−	0.703237i	$-0.248263\pi$
$257$	−1.68413	−	2.00707i	−0.105053	−	0.125198i	−0.816009	+	0.578039i	$0.803818\pi$
$258$		0			0
$259$	7.65588	−	2.78651i	0.475713	−	0.173145i
$260$	7.90882	+	25.5221i	0.490484	+	1.58281i
$261$		0			0
$262$	4.50656	−	0.682246i	0.278416	−	0.0421493i
$263$	−0.304745	+	1.72830i	−0.0187914	+	0.106571i	−0.992761	−	0.120108i	$-0.961676\pi$
$263$	−0.304745	+	1.72830i	−0.0187914	+	0.106571i	0.973969	+	0.226679i	$0.0727870\pi$
$264$		0			0
$265$	22.8039	+	8.29996i	1.40083	+	0.509862i
$266$	−5.18044	+	5.87783i	−0.317633	+	0.360393i
$267$		0			0
$268$	2.88617	−	2.19209i	0.176301	−	0.133903i
$269$	−28.6840			−1.74889			−0.874447	−	0.485121i	$-0.838776\pi$
$269$	−28.6840			−1.74889			−0.874447	+	0.485121i	$0.838776\pi$
$270$		0			0
$271$			0.381213i			0.0231571i	0.999933	+	0.0115785i	$0.00368564\pi$
$271$			0.381213i			0.0231571i	−0.999933	+	0.0115785i	$0.996314\pi$
$272$	26.9380	−	12.2392i	1.63336	−	0.742108i
$273$		0			0
$274$	−10.0156	+	11.3640i	−0.605067	+	0.686522i
$275$	0.422513	−	1.16084i	0.0254785	−	0.0700015i
$276$		0			0
$277$	−15.5188	−	2.73638i	−0.932435	−	0.164413i	−0.313261	−	0.949667i	$-0.601421\pi$
$277$	−15.5188	−	2.73638i	−0.932435	−	0.164413i	−0.619174	+	0.785254i	$0.712532\pi$
$278$	4.25208	+	28.0870i	0.255023	+	1.68455i
$279$		0			0
$280$	11.1504	+	7.57047i	0.666365	+	0.452422i
$281$	2.04517	+	5.61906i	0.122005	+	0.335205i	0.985627	−	0.168933i	$-0.0540323\pi$
$281$	2.04517	+	5.61906i	0.122005	+	0.335205i	−0.863623	+	0.504139i	$0.831810\pi$
$282$		0			0
$283$	2.23671	−	1.87682i	0.132959	−	0.111566i	−0.573883	−	0.818937i	$-0.694564\pi$
$283$	2.23671	−	1.87682i	0.132959	−	0.111566i	0.706842	+	0.707372i	$0.250119\pi$
$284$	2.28901	+	4.45063i	0.135828	+	0.264096i
$285$		0			0
$286$	−6.63662	+	10.8762i	−0.392432	+	0.643123i
$287$	−4.40549	−	7.63053i	−0.260048	−	0.450416i
$288$		0			0
$289$	18.8579	−	32.6628i	1.10929	−	1.92134i
$290$	−0.293869	−	0.538802i	−0.0172566	−	0.0316395i
$291$		0			0
$292$	−8.20929	+	12.7467i	−0.480413	+	0.745947i
$293$	−0.0144950	−	0.0822052i	−0.000846807	−	0.00480248i	0.984381	−	0.176049i	$-0.0563317\pi$
$293$	−0.0144950	−	0.0822052i	−0.000846807	−	0.00480248i	−0.985228	+	0.171246i	$0.945221\pi$
$294$		0			0
$295$	8.87537	−	10.5773i	0.516744	−	0.615832i
$296$	10.4500	−	5.05756i	0.607396	−	0.293965i
$297$		0			0
$298$	14.9581	−	11.9445i	0.866497	−	0.691929i
$299$	−9.58944	+	11.4282i	−0.554571	+	0.660913i
$300$		0			0
$301$	−23.1190	+	4.07650i	−1.33256	+	0.234965i
$302$	4.03202	+	11.9749i	0.232017	+	0.689081i
$303$		0			0
$304$	−6.49368	+	9.08181i	−0.372438	+	0.520877i
$305$	16.0607	+	9.27266i	0.919634	+	0.530951i
$306$		0			0
$307$	15.0297	+	26.0322i	0.857789	+	1.48573i	0.874033	+	0.485866i	$0.161496\pi$
$307$	15.0297	+	26.0322i	0.857789	+	1.48573i	−0.0162438	+	0.999868i	$0.505171\pi$
$308$	0.807402	+	6.37583i	0.0460060	+	0.363296i
$309$		0			0
$310$	−5.97919	−	1.20468i	−0.339595	−	0.0684213i
$311$	−21.1476	+	17.7450i	−1.19917	+	1.00622i	−0.199518	+	0.979894i	$0.563938\pi$
$311$	−21.1476	+	17.7450i	−1.19917	+	1.00622i	−0.999653	+	0.0263305i	$0.991618\pi$
$312$		0			0
$313$	7.89699	−	2.87427i	0.446365	−	0.162463i	−0.109051	−	0.994036i	$-0.534781\pi$
$313$	7.89699	−	2.87427i	0.446365	−	0.162463i	0.555416	+	0.831573i	$0.312559\pi$
$314$	−3.40366	+	8.68896i	−0.192080	+	0.490346i
$315$		0			0
$316$	14.3104	−	15.4632i	0.805023	−	0.869870i
$317$	4.49026	−	25.4655i	0.252198	−	1.43029i	−0.550965	−	0.834528i	$-0.685740\pi$
$317$	4.49026	−	25.4655i	0.252198	−	1.43029i	0.803163	−	0.595759i	$-0.203149\pi$
$318$		0			0
$319$	0.100095	−	0.275008i	0.00560423	−	0.0153975i
$320$	16.9020	+	9.11918i	0.944850	+	0.509778i
$321$		0			0
$322$	−0.182722	+	7.52282i	−0.0101827	+	0.419230i
$323$			20.6461i			1.14878i
$324$		0			0
$325$			4.24654i			0.235556i
$326$	−2.90672	−	0.0706014i	−0.160988	−	0.00391025i
$327$		0			0
$328$	−7.34898	−	10.1799i	−0.405780	−	0.562093i
$329$	8.15471	−	22.4049i	0.449584	−	1.23522i
$330$		0			0
$331$	1.02889	−	5.83510i	0.0565527	−	0.320726i	−0.943387	−	0.331694i	$-0.892380\pi$
$331$	1.02889	−	5.83510i	0.0565527	−	0.320726i	0.999940	+	0.0109673i	$0.00349108\pi$
$332$	−1.51767	+	1.63992i	−0.0832929	+	0.0900025i
$333$		0			0
$334$	−5.68258	−	2.22599i	−0.310937	−	0.121801i
$335$	4.08791	−	1.48788i	0.223347	−	0.0812915i
$336$		0			0
$337$	−7.82014	+	6.56188i	−0.425990	+	0.357448i	−0.830436	−	0.557114i	$-0.811909\pi$
$337$	−7.82014	+	6.56188i	−0.425990	+	0.357448i	0.404446	+	0.914562i	$0.367464\pi$
$338$	5.01939	−	24.9127i	0.273019	−	1.35507i
$339$		0			0
$340$	35.2337	−	4.46182i	1.91082	−	0.241976i
$341$	−1.45423	−	2.51881i	−0.0787511	−	0.136401i
$342$		0			0
$343$	17.2932	+	9.98422i	0.933743	+	0.539097i
$344$	−32.1841	+	9.12287i	−1.73525	+	0.491872i
$345$		0			0
$346$	4.97025	−	1.67350i	0.267202	−	0.0899682i
$347$	25.6701	−	4.52634i	1.37805	−	0.242987i	0.564954	−	0.825123i	$-0.308894\pi$
$347$	25.6701	−	4.52634i	1.37805	−	0.242987i	0.813091	+	0.582136i	$0.197783\pi$
$348$		0			0
$349$	3.94641	−	4.70314i	0.211246	−	0.251753i	−0.650008	−	0.759927i	$-0.725235\pi$
$349$	3.94641	−	4.70314i	0.211246	−	0.251753i	0.861255	+	0.508173i	$0.169679\pi$
$350$	1.33660	+	1.67381i	0.0714442	+	0.0894690i
$351$		0			0
$352$	2.06679	+	8.92167i	0.110161	+	0.475527i
$353$	−4.80018	+	5.72064i	−0.255488	+	0.304479i	−0.878508	−	0.477727i	$-0.841461\pi$
$353$	−4.80018	+	5.72064i	−0.255488	+	0.304479i	0.623020	+	0.782206i	$0.285905\pi$
$354$		0			0
$355$	1.04316	+	5.91605i	0.0553652	+	0.313992i
$356$	−19.1790	−	12.3519i	−1.01649	−	0.654648i
$357$		0			0
$358$	6.92511	−	3.77704i	0.366004	−	0.199623i
$359$	1.79899	−	3.11595i	0.0949473	−	0.164454i	−0.814639	−	0.579968i	$-0.803065\pi$
$359$	1.79899	−	3.11595i	0.0949473	−	0.164454i	0.909587	+	0.415514i	$0.136398\pi$
$360$		0			0
$361$	5.60478	+	9.70776i	0.294988	+	0.510935i
$362$	30.6448	+	18.6993i	1.61065	+	0.982814i
$363$		0			0
$364$	−10.1042	−	19.6461i	−0.529604	−	1.02974i
$365$	−13.9410	+	11.6979i	−0.729705	+	0.612296i
$366$		0			0
$367$	−6.74224	−	18.5242i	−0.351942	−	0.966954i	−0.981746	−	0.190199i	$-0.939087\pi$
$367$	−6.74224	−	18.5242i	−0.351942	−	0.966954i	0.629803	−	0.776755i	$-0.283135\pi$
$368$	0.829085	+	10.6909i	0.0432190	+	0.557301i
$369$		0			0
$370$	13.7782	−	2.08588i	0.716294	−	0.108439i
$371$	−19.7600	−	3.48422i	−1.02589	−	0.180892i
$372$		0			0
$373$	3.75330	−	10.3121i	0.194339	−	0.533941i	−0.803802	−	0.594897i	$-0.797193\pi$
$373$	3.75330	−	10.3121i	0.194339	−	0.533941i	0.998140	+	0.0609560i	$0.0194149\pi$
$374$	12.7051	+	11.1976i	0.656964	+	0.579016i
$375$		0			0
$376$	8.31955	−	32.9410i	0.429048	−	1.69880i
$377$			1.00602i			0.0518127i
$378$		0			0
$379$	28.6955			1.47399			0.736993	−	0.675900i	$-0.236245\pi$
$379$	28.6955			1.47399			0.736993	+	0.675900i	$0.236245\pi$
$380$	−10.6719	+	8.10546i	−0.547456	+	0.415801i
$381$		0			0
$382$	22.3563	+	19.7038i	1.14385	+	1.00813i
$383$	13.4068	+	4.87966i	0.685054	+	0.249339i	0.661016	−	0.750372i	$-0.270126\pi$
$383$	13.4068	+	4.87966i	0.685054	+	0.249339i	0.0240379	+	0.999711i	$0.492348\pi$
$384$		0			0
$385$	−1.33955	+	7.59695i	−0.0682697	+	0.387177i
$386$	−2.61790	−	17.2925i	−0.133247	−	0.880163i
$387$		0			0
$388$	−10.6851	+	3.31111i	−0.542453	+	0.168096i
$389$	1.60139	−	0.582859i	0.0811938	−	0.0295521i	−0.301104	−	0.953591i	$-0.597355\pi$
$389$	1.60139	−	0.582859i	0.0811938	−	0.0295521i	0.382298	+	0.924039i	$0.375133\pi$
$390$		0			0
$391$	12.7462	+	15.1903i	0.644601	+	0.768205i
$392$	7.89645	+	3.54453i	0.398831	+	0.179026i
$393$		0			0
$394$	−8.76875	+	14.3704i	−0.441763	+	0.723969i
$395$	21.9012	−	12.6447i	1.10197	−	0.636223i
$396$		0			0
$397$	−18.7381	−	10.8185i	−0.940440	−	0.542963i	−0.0503416	−	0.998732i	$-0.516031\pi$
$397$	−18.7381	−	10.8185i	−0.940440	−	0.542963i	−0.890098	+	0.455769i	$0.849364\pi$
$398$	25.9027	−	14.1277i	1.29839	−	0.708157i
$399$		0			0
$400$	2.13688	+	2.17949i	0.106844	+	0.108975i
$401$	−2.47080	+	0.435668i	−0.123386	+	0.0217562i	−0.235000	−	0.971995i	$-0.575509\pi$
$401$	−2.47080	+	0.435668i	−0.123386	+	0.0217562i	0.111614	+	0.993752i	$0.464398\pi$
$402$		0			0
$403$	7.65888	+	6.42656i	0.381516	+	0.320130i
$404$	4.84334	−	21.3478i	0.240965	−	1.06209i
$405$		0			0
$406$	0.316645	+	0.396532i	0.0157148	+	0.0196795i
$407$	5.09035	+	4.27131i	0.252319	+	0.211721i
$408$		0			0
$409$	3.62286	+	20.5463i	0.179139	+	1.01595i	0.933257	+	0.359209i	$0.116953\pi$
$409$	3.62286	+	20.5463i	0.179139	+	1.01595i	−0.754118	+	0.656739i	$0.771935\pi$
$410$	−4.80903	−	14.2826i	−0.237501	−	0.705369i
$411$		0			0
$412$	−11.6654	+	27.7744i	−0.574715	+	1.36835i
$413$	−5.70821	+	9.88691i	−0.280883	+	0.486503i
$414$		0			0
$415$	−2.32270	+	1.34101i	−0.114017	+	0.0658278i
$416$	−17.1655	−	26.3891i	−0.841607	−	1.29383i
$417$		0			0
$418$	−6.26438	−	1.26214i	−0.306401	−	0.0617334i
$419$	12.9085	+	15.3838i	0.630621	+	0.751545i	0.982858	−	0.184366i	$-0.0590231\pi$
$419$	12.9085	+	15.3838i	0.630621	+	0.751545i	−0.352236	+	0.935911i	$0.614579\pi$
$420$		0			0
$421$	8.54145	+	23.4674i	0.416285	+	1.14373i	0.953790	+	0.300473i	$0.0971444\pi$
$421$	8.54145	+	23.4674i	0.416285	+	1.14373i	−0.537506	+	0.843260i	$0.680633\pi$
$422$	2.89688	+	1.13477i	0.141018	+	0.0552398i
$423$		0			0
$424$	−28.5160	−	2.08116i	−1.38486	−	0.101070i
$425$	5.55870	+	0.980148i	0.269636	+	0.0475442i
$426$		0			0
$427$	−14.4089	−	5.24442i	−0.697297	−	0.253795i
$428$	−0.177925	+	3.66050i	−0.00860033	+	0.176937i
$429$		0			0
$430$	−40.1414	−	0.974998i	−1.93579	−	0.0470186i
$431$	3.07869			0.148295			0.0741477	−	0.997247i	$-0.476376\pi$
$431$	3.07869			0.148295			0.0741477	+	0.997247i	$0.476376\pi$
$432$		0			0
$433$	−13.9338			−0.669615			−0.334808	−	0.942287i	$-0.608671\pi$
$433$	−13.9338			−0.669615			−0.334808	+	0.942287i	$0.608671\pi$
$434$	5.04158	+	0.122455i	0.242003	+	0.00587804i
$435$		0			0
$436$	−0.276437	+	5.68720i	−0.0132389	+	0.272368i
$437$	−7.03108	−	2.55911i	−0.336342	−	0.122419i
$438$		0			0
$439$	27.1825	+	4.79300i	1.29735	+	0.228757i	0.779331	−	0.626613i	$-0.215559\pi$
$439$	27.1825	+	4.79300i	1.29735	+	0.228757i	0.518017	+	0.855370i	$0.326670\pi$
$440$	−0.800124	+	10.9633i	−0.0381444	+	0.522655i
$441$		0			0
$442$	−54.2054	−	21.2335i	−2.57829	−	1.00997i
$443$	−7.98934	−	21.9505i	−0.379585	−	1.04290i	−0.971529	−	0.236922i	$-0.923861\pi$
$443$	−7.98934	−	21.9505i	−0.379585	−	1.04290i	0.591944	−	0.805979i	$-0.298361\pi$
$444$		0			0
$445$	−17.6009	−	20.9759i	−0.834363	−	0.994355i
$446$	26.6585	+	5.37114i	1.26232	+	0.254331i
$447$		0			0
$448$	−15.0719	−	4.99866i	−0.712080	−	0.236164i
$449$	−2.35310	+	1.35856i	−0.111050	+	0.0641146i	−0.554496	−	0.832186i	$-0.687089\pi$
$449$	−2.35310	+	1.35856i	−0.111050	+	0.0641146i	0.443446	+	0.896301i	$0.353756\pi$
$450$		0			0
$451$	3.59318	−	6.22357i	0.169196	−	0.293057i
$452$	−9.39062	+	22.3582i	−0.441698	+	1.05164i
$453$		0			0
$454$	7.14290	+	21.2141i	0.335233	+	0.995629i
$455$	−4.60475	−	26.1148i	−0.215874	−	1.22428i
$456$		0			0
$457$	−20.8383	−	17.4854i	−0.974775	−	0.817933i	0.00851782	−	0.999964i	$-0.497289\pi$
$457$	−20.8383	−	17.4854i	−0.974775	−	0.817933i	−0.983293	+	0.182030i	$0.941733\pi$
$458$	−15.8779	−	19.8838i	−0.741926	−	0.929109i
$459$		0			0
$460$	−2.84778	+	12.5520i	−0.132778	+	0.585240i
$461$	2.70287	+	2.26798i	0.125885	+	0.105630i	0.703557	−	0.710639i	$-0.251594\pi$
$461$	2.70287	+	2.26798i	0.125885	+	0.105630i	−0.577672	+	0.816269i	$0.696039\pi$
$462$		0			0
$463$	−4.87079	+	0.858852i	−0.226365	+	0.0399142i	−0.285680	−	0.958325i	$-0.592219\pi$
$463$	−4.87079	+	0.858852i	−0.226365	+	0.0399142i	0.0593151	+	0.998239i	$0.481108\pi$
$464$	0.506235	+	0.516329i	0.0235014	+	0.0239700i
$465$		0			0
$466$	6.57762	−	3.58751i	0.304702	−	0.166188i
$467$	20.1954	+	11.6598i	0.934532	+	0.539552i	0.888242	−	0.459376i	$-0.151927\pi$
$467$	20.1954	+	11.6598i	0.934532	+	0.539552i	0.0462901	+	0.998928i	$0.485260\pi$
$468$		0			0
$469$	−3.11500	+	1.79845i	−0.143837	+	0.0830445i
$470$	21.2422	−	34.8121i	0.979830	−	1.60576i
$471$		0			0
$472$	−6.66198	+	14.8415i	−0.306642	+	0.683134i
$473$	−12.3075	−	14.6675i	−0.565899	−	0.674412i
$474$		0			0
$475$	−2.00139	+	0.728447i	−0.0918301	+	0.0334234i
$476$	−28.0488	+	8.69179i	−1.28561	+	0.398388i
$477$		0			0
$478$	5.47298	+	36.1516i	0.250328	+	1.65354i
$479$	−3.57935	+	20.2995i	−0.163545	+	0.927509i	0.787007	+	0.616944i	$0.211629\pi$
$479$	−3.57935	+	20.2995i	−0.163545	+	0.927509i	−0.950552	+	0.310565i	$0.899482\pi$
$480$		0			0
$481$	−21.4648	−	7.81255i	−0.978711	−	0.356222i
$482$	25.5888	+	22.5527i	1.16554	+	1.02725i
$483$		0			0
$484$	13.3454	−	10.1360i	0.606609	−	0.460729i
$485$	−13.4272			−0.609698
$486$		0			0
$487$		−	8.50350i		−	0.385330i	−0.981265	−	0.192665i	$-0.938287\pi$
$487$		−	8.50350i		−	0.385330i	0.981265	−	0.192665i	$-0.0617131\pi$
$488$	−21.1848	−	5.35043i	−0.958993	−	0.242202i
$489$		0			0
$490$	7.79421	+	6.86944i	0.352107	+	0.310330i
$491$	10.7502	−	29.5360i	0.485151	−	1.33294i	−0.419874	−	0.907583i	$-0.637926\pi$
$491$	10.7502	−	29.5360i	0.485151	−	1.33294i	0.905025	−	0.425359i	$-0.139852\pi$
$492$		0			0
$493$	1.31687	+	0.232200i	0.0593090	+	0.0104578i
$494$	21.7193	−	3.28807i	0.977197	−	0.147937i
$495$		0			0
$496$	7.16472	−	0.555629i	0.321705	−	0.0249485i
$497$	−1.69881	−	4.66743i	−0.0762018	−	0.209363i
$498$		0			0
$499$	−17.3039	+	14.5197i	−0.774628	+	0.649990i	−0.941890	−	0.335923i	$-0.890952\pi$
$499$	−17.3039	+	14.5197i	−0.774628	+	0.649990i	0.167262	+	0.985913i	$0.446507\pi$
$500$	−9.30404	−	18.0903i	−0.416089	−	0.809023i
$501$		0			0
$502$	4.06075	+	2.47785i	0.181240	+	0.110592i
$503$	9.33255	+	16.1645i	0.416118	+	0.720738i	0.995545	−	0.0942866i	$-0.0300570\pi$
$503$	9.33255	+	16.1645i	0.416118	+	0.720738i	−0.579427	+	0.815024i	$0.696724\pi$
$504$		0			0
$505$	13.1377	−	22.7551i	0.584619	−	1.01259i
$506$	−5.38820	+	2.93879i	−0.239535	+	0.130645i
$507$		0			0
$508$	1.27204	+	0.819235i	0.0564378	+	0.0363477i
$509$	−1.23732	−	7.01719i	−0.0548432	−	0.311031i	0.945029	−	0.326985i	$-0.106033\pi$
$509$	−1.23732	−	7.01719i	−0.0548432	−	0.311031i	−0.999873	+	0.0159536i	$0.994922\pi$
$510$		0			0
$511$	9.67205	−	11.5267i	0.427867	−	0.509911i
$512$	−22.0891	−	4.90614i	−0.976211	−	0.216823i
$513$		0			0
$514$	2.31210	+	2.89543i	0.101982	+	0.127712i
$515$	−23.2427	+	27.6996i	−1.02420	+	1.22059i
$516$		0			0
$517$	19.1511	−	3.37685i	0.842263	−	0.148514i
$518$	−10.9195	+	3.67666i	−0.479777	+	0.161543i
$519$		0			0
$520$	−10.3050	−	36.3547i	−0.451906	−	1.59426i
$521$	−20.6589	−	11.9274i	−0.905083	−	0.522550i	−0.0262370	−	0.999656i	$-0.508352\pi$
$521$	−20.6589	−	11.9274i	−0.905083	−	0.522550i	−0.878846	+	0.477106i	$0.841686\pi$
$522$		0			0
$523$	−17.6879	−	30.6364i	−0.773440	−	1.33964i	−0.935667	−	0.352884i	$-0.885201\pi$
$523$	−17.6879	−	30.6364i	−0.773440	−	1.33964i	0.162227	−	0.986753i	$-0.448132\pi$
$524$	−6.39479	+	0.809803i	−0.279358	+	0.0353764i
$525$		0			0
$526$	0.490198	−	2.43300i	0.0213736	−	0.106084i
$527$	10.1801	−	8.54211i	0.443452	−	0.372100i
$528$		0			0
$529$	14.8599	−	5.40857i	0.646084	−	0.235155i
$530$	−31.9551	−	12.5175i	−1.38804	−	0.543727i
$531$		0			0
$532$	7.52593	−	8.13217i	0.326290	−	0.352574i
$533$	−4.28970	+	24.3281i	−0.185807	+	1.05377i
$534$		0			0
$535$	−1.50453	+	4.13366i	−0.0650465	+	0.178714i
$536$	−4.15573	+	3.00006i	−0.179500	+	0.129583i
$537$		0			0
$538$	40.5533	+	0.985003i	1.74838	+	0.0424665i
$539$			4.95416i			0.213391i
$540$		0			0
$541$			25.7473i			1.10696i	0.832862	+	0.553480i	$0.186701\pi$
$541$			25.7473i			1.10696i	−0.832862	+	0.553480i	$0.813299\pi$
$542$	0.0130908	−	0.538958i	0.000562298	−	0.0231502i
$543$		0			0
$544$	−38.5051	+	16.3786i	−1.65089	+	0.702228i
$545$	−2.33755	+	6.42235i	−0.100129	+	0.275103i
$546$		0			0
$547$	−1.96276	+	11.1313i	−0.0839214	+	0.475942i	0.913663	+	0.406473i	$0.133242\pi$
$547$	−1.96276	+	11.1313i	−0.0839214	+	0.475942i	−0.997584	+	0.0694689i	$0.977870\pi$
$548$	14.5503	−	15.7224i	0.621559	−	0.671628i
$549$		0			0
$550$	−0.637210	+	1.62669i	−0.0271707	+	0.0693622i
$551$	−0.474136	+	0.172572i	−0.0201989	+	0.00735179i
$552$		0			0
$553$	−16.0178	+	13.4405i	−0.681147	+	0.571550i
$554$	21.8465	+	4.40160i	0.928167	+	0.187006i
$555$		0			0
$556$	−5.04707	−	39.8553i	−0.214043	−	1.69024i
$557$	−3.17566	−	5.50041i	−0.134557	−	0.233060i	0.790871	−	0.611983i	$-0.209628\pi$
$557$	−3.17566	−	5.50041i	−0.134557	−	0.233060i	−0.925428	+	0.378923i	$0.876295\pi$
$558$		0			0
$559$	57.0006	+	32.9093i	2.41087	+	1.39192i
$560$	−15.5045	−	11.0860i	−0.655183	−	0.468469i
$561$		0			0
$562$	−2.69850	−	8.01444i	−0.113829	−	0.338069i
$563$	2.69663	−	0.475489i	0.113649	−	0.0200395i	−0.116534	−	0.993187i	$-0.537178\pi$
$563$	2.69663	−	0.475489i	0.113649	−	0.0200395i	0.230184	+	0.973147i	$0.426067\pi$
$564$		0			0
$565$	−18.7103	+	22.2981i	−0.787148	+	0.938086i
$566$	−3.22670	+	2.57664i	−0.135628	+	0.108304i
$567$		0			0
$568$	−3.08336	−	6.37089i	−0.129375	−	0.267317i
$569$	−2.40329	+	2.86413i	−0.100751	+	0.120071i	−0.814064	−	0.580775i	$-0.802749\pi$
$569$	−2.40329	+	2.86413i	−0.100751	+	0.120071i	0.713313	+	0.700846i	$0.247194\pi$
$570$		0			0
$571$	2.53820	+	14.3948i	0.106220	+	0.602405i	0.990726	+	0.135876i	$0.0433847\pi$
$571$	2.53820	+	14.3948i	0.106220	+	0.602405i	−0.884506	+	0.466529i	$0.845504\pi$
$572$	9.75632	−	15.1488i	0.407932	−	0.633405i
$573$		0			0
$574$	5.96644	+	10.9393i	0.249034	+	0.456598i
$575$	−1.02280	+	1.77154i	−0.0426537	+	0.0738784i
$576$		0			0
$577$	−4.35731	−	7.54709i	−0.181397	−	0.314189i	0.760959	−	0.648800i	$-0.224729\pi$
$577$	−4.35731	−	7.54709i	−0.181397	−	0.314189i	−0.942357	+	0.334610i	$0.891395\pi$
$578$	−27.7829	+	45.5310i	−1.15561	+	1.89384i
$579$		0			0
$580$	0.396969	+	0.771847i	0.0164832	+	0.0320492i
$581$	1.69875	−	1.42542i	0.0704759	−	0.0591363i
$582$		0			0
$583$	−5.59721	−	15.3782i	−0.231813	−	0.636900i
$584$	12.0440	−	17.7394i	0.498384	−	0.734062i
$585$		0			0
$586$	0.0176701	+	0.116719i	0.000729944	+	0.00482163i
$587$	−2.90950	−	0.513023i	−0.120088	−	0.0211747i	0.113281	−	0.993563i	$-0.463864\pi$
$587$	−2.90950	−	0.513023i	−0.120088	−	0.0211747i	−0.233369	+	0.972388i	$0.574975\pi$
$588$		0			0
$589$	−1.71504	+	4.71203i	−0.0706669	+	0.194156i
$590$	−12.9112	+	14.6493i	−0.531545	+	0.603102i
$591$		0			0
$592$	−14.9479	+	6.79151i	−0.614355	+	0.279129i
$593$		−	28.7111i		−	1.17902i	−0.807760	−	0.589511i	$-0.799320\pi$
$593$		−	28.7111i		−	1.17902i	0.807760	−	0.589511i	$-0.200680\pi$
$594$		0			0
$595$	−35.2470			−1.44498
$596$	−21.5578	+	16.3735i	−0.883043	+	0.670685i
$597$		0			0
$598$	13.9500	−	15.8279i	0.570456	−	0.647252i
$599$	10.3057	+	3.75098i	0.421080	+	0.153261i	0.543865	−	0.839173i	$-0.316960\pi$
$599$	10.3057	+	3.75098i	0.421080	+	0.153261i	−0.122785	+	0.992433i	$0.539182\pi$
$600$		0			0
$601$	5.74041	−	32.5555i	0.234156	−	1.32797i	−0.610227	−	0.792226i	$-0.708922\pi$
$601$	5.74041	−	32.5555i	0.234156	−	1.32797i	0.844384	−	0.535739i	$-0.179967\pi$
$602$	32.8255	−	4.96944i	1.33787	−	0.202539i
$603$		0			0
$604$	−5.28924	−	17.0686i	−0.215216	−	0.694511i
$605$	18.9022	−	6.87983i	0.768482	−	0.279705i
$606$		0			0
$607$	−4.64372	−	5.53417i	−0.188483	−	0.224625i	0.663525	−	0.748154i	$-0.269060\pi$
$607$	−4.64372	−	5.53417i	−0.188483	−	0.224625i	−0.852008	+	0.523529i	$0.824615\pi$
$608$	9.49261	−	12.6168i	0.384976	−	0.511680i
$609$		0			0
$610$	−22.3882	−	13.6612i	−0.906471	−	0.553125i
$611$	−57.8921	+	33.4240i	−2.34206	+	1.35219i
$612$		0			0
$613$	−24.6364	−	14.2239i	−0.995057	−	0.574496i	−0.0882748	−	0.996096i	$-0.528135\pi$
$613$	−24.6364	−	14.2239i	−0.995057	−	0.574496i	−0.906782	+	0.421600i	$0.861469\pi$
$614$	−20.3550	−	37.3203i	−0.821460	−	1.50613i
$615$		0			0
$616$	−0.922557	−	9.04185i	−0.0371709	−	0.364306i
$617$	−21.5217	+	3.79486i	−0.866432	+	0.152775i	−0.589160	−	0.808016i	$-0.700541\pi$
$617$	−21.5217	+	3.79486i	−0.866432	+	0.152775i	−0.277272	+	0.960792i	$0.589430\pi$
$618$		0			0
$619$	4.96839	+	4.16897i	0.199696	+	0.167565i	0.737152	−	0.675727i	$-0.236170\pi$
$619$	4.96839	+	4.16897i	0.199696	+	0.167565i	−0.537456	+	0.843292i	$0.680615\pi$
$620$	8.41199	+	1.90850i	0.337834	+	0.0766472i
$621$		0			0
$622$	30.5078	−	24.3616i	1.22325	−	0.976810i
$623$	17.3433	+	14.5528i	0.694846	+	0.583045i
$624$		0			0
$625$	−4.90262	−	27.8042i	−0.196105	−	1.11217i
$626$	−11.2634	+	3.79245i	−0.450178	+	0.151577i
$627$		0			0
$628$	5.11046	−	12.1675i	0.203930	−	0.485538i
$629$	−15.1809	+	26.2941i	−0.605302	+	1.04841i
$630$		0			0
$631$	31.9060	−	18.4209i	1.27016	−	0.733325i	0.295139	−	0.955454i	$-0.404634\pi$
$631$	31.9060	−	18.4209i	1.27016	−	0.733325i	0.975017	+	0.222129i	$0.0713006\pi$
$632$	−20.7630	+	21.3703i	−0.825908	+	0.850066i
$633$		0			0
$634$	−7.22280	+	35.8489i	−0.286854	+	1.42374i
$635$	1.16737	+	1.39122i	0.0463258	+	0.0552090i
$636$		0			0
$637$	−5.82464	−	16.0031i	−0.230781	−	0.634064i
$638$	−0.150957	+	0.385368i	−0.00597645	+	0.0152569i
$639$		0			0
$640$	−23.5828	−	13.4731i	−0.932193	−	0.532570i
$641$	−21.8735	−	3.85688i	−0.863950	−	0.152338i	−0.275923	−	0.961180i	$-0.588984\pi$
$641$	−21.8735	−	3.85688i	−0.863950	−	0.152338i	−0.588026	+	0.808842i	$0.700095\pi$
$642$		0			0
$643$	14.8220	+	5.39476i	0.584522	+	0.212749i	0.617318	−	0.786714i	$-0.288219\pi$
$643$	14.8220	+	5.39476i	0.584522	+	0.212749i	−0.0327965	+	0.999462i	$0.510441\pi$
$644$	0.516664	−	10.6295i	0.0203594	−	0.418859i
$645$		0			0
$646$	0.708982	−	29.1893i	0.0278945	−	1.14844i
$647$	−23.4148			−0.920530			−0.460265	−	0.887782i	$-0.652246\pi$
$647$	−23.4148			−0.920530			−0.460265	+	0.887782i	$0.652246\pi$
$648$		0			0
$649$	−9.31140			−0.365504
$650$	0.145825	−	6.00375i	0.00571974	−	0.235486i
$651$		0			0
$652$	4.10708	+	0.199632i	0.160846	+	0.00781820i
$653$	20.9780	+	7.63537i	0.820933	+	0.298795i	0.718132	−	0.695907i	$-0.244997\pi$
$653$	20.9780	+	7.63537i	0.820933	+	0.298795i	0.102801	+	0.994702i	$0.467220\pi$
$654$		0			0
$655$	−7.61955	−	1.34353i	−0.297720	−	0.0524962i
$656$	10.0404	+	14.6447i	0.392011	+	0.571780i
$657$		0			0
$658$	−12.2985	+	31.3959i	−0.479445	+	1.22394i
$659$	12.5163	+	34.3882i	0.487565	+	1.33957i	0.902878	+	0.429896i	$0.141450\pi$
$659$	12.5163	+	34.3882i	0.487565	+	1.33957i	−0.415313	+	0.909679i	$0.636328\pi$
$660$		0			0
$661$	−12.4241	−	14.8064i	−0.483240	−	0.575902i	0.468245	−	0.883599i	$-0.344886\pi$
$661$	−12.4241	−	14.8064i	−0.483240	−	0.575902i	−0.951485	+	0.307696i	$0.900442\pi$
$662$	−1.65501	+	8.21432i	−0.0643239	+	0.319259i
$663$		0			0
$664$	2.20199	−	2.26640i	0.0854538	−	0.0879534i
$665$	11.5180	−	6.64992i	0.446649	−	0.257873i
$666$		0			0
$667$	−0.242305	+	0.419684i	−0.00938207	+	0.0162502i
$668$	7.95757	+	3.34224i	0.307888	+	0.129315i
$669$		0			0
$670$	−5.83057	+	1.96318i	−0.225255	+	0.0758443i
$671$	−2.17170	−	12.3163i	−0.0838377	−	0.475467i
$672$		0			0
$673$	22.1943	+	18.6232i	0.855526	+	0.717872i	0.960999	−	0.276550i	$-0.0891912\pi$
$673$	22.1943	+	18.6232i	0.855526	+	0.717872i	−0.105473	+	0.994422i	$0.533636\pi$
$674$	11.2814	−	9.00862i	0.434544	−	0.346999i
$675$		0			0
$676$	−7.95189	+	35.0491i	−0.305842	+	1.34804i
$677$	21.1510	+	17.7478i	0.812897	+	0.682102i	0.951297	−	0.308275i	$-0.0997516\pi$
$677$	21.1510	+	17.7478i	0.812897	+	0.682102i	−0.138400	+	0.990376i	$0.544196\pi$
$678$		0			0
$679$	10.9332	−	1.92782i	0.419578	−	0.0739830i
$680$	−49.9666	+	5.09818i	−1.91613	+	0.195506i
$681$		0			0
$682$	1.96949	+	3.61102i	0.0754159	+	0.138273i
$683$	26.7048	+	15.4180i	1.02183	+	0.589954i	0.914633	−	0.404284i	$-0.132479\pi$
$683$	26.7048	+	15.4180i	1.02183	+	0.589954i	0.107196	+	0.994238i	$0.465813\pi$
$684$		0			0
$685$	22.2684	−	12.8567i	0.850833	−	0.491228i
$686$	−24.1062	−	14.7095i	−0.920378	−	0.561611i
$687$		0			0
$688$	45.8151	−	11.7927i	1.74668	−	0.449592i
$689$	36.1605	+	43.0944i	1.37761	+	1.64177i
$690$		0			0
$691$	−5.99355	+	2.18147i	−0.228006	+	0.0829872i	−0.453497	−	0.891258i	$-0.649824\pi$
$691$	−5.99355	+	2.18147i	−0.228006	+	0.0829872i	0.225491	+	0.974245i	$0.427601\pi$
$692$	−7.08439	+	2.19532i	−0.269308	+	0.0834535i
$693$		0			0
$694$	−36.4478	+	5.51781i	−1.38354	+	0.209453i
$695$	8.37352	−	47.4886i	0.317626	−	1.80135i
$696$		0			0
$697$	30.8552	+	11.2304i	1.16872	+	0.425381i
$698$	−5.74092	+	6.51377i	−0.217297	+	0.246550i
$699$		0			0
$700$	−1.83220	−	2.41233i	−0.0692506	−	0.0911774i
$701$	−4.03941			−0.152566			−0.0762832	−	0.997086i	$-0.524305\pi$
$701$	−4.03941			−0.152566			−0.0762832	+	0.997086i	$0.524305\pi$
$702$		0			0
$703$		−	11.4565i		−	0.432090i
$704$	−2.61566	−	12.6844i	−0.0985814	−	0.478062i
$705$		0			0
$706$	6.98293	−	7.92298i	0.262806	−	0.298185i
$707$	−7.43039	+	20.4148i	−0.279449	+	0.767779i
$708$		0			0
$709$	9.31231	+	1.64201i	0.349731	+	0.0616670i	0.345754	−	0.938325i	$-0.387623\pi$
$709$	9.31231	+	1.64201i	0.349731	+	0.0616670i	0.00397676	+	0.999992i	$0.498734\pi$
$710$	−1.27166	−	8.39992i	−0.0477246	−	0.315243i
$711$		0			0
$712$	26.6911	+	18.1217i	1.00029	+	0.679138i
$713$	1.64721	+	4.52566i	0.0616884	+	0.169487i
$714$		0			0
$715$	16.5682	−	13.9023i	0.619614	−	0.519918i
$716$	−9.92040	+	5.10216i	−0.370743	+	0.190677i
$717$		0			0
$718$	−2.65041	+	4.34354i	−0.0989125	+	0.162100i
$719$	16.9409	+	29.3425i	0.631789	+	1.09429i	0.987186	+	0.159575i	$0.0510125\pi$
$719$	16.9409	+	29.3425i	0.631789	+	1.09429i	−0.355397	+	0.934716i	$0.615654\pi$
$720$		0			0
$721$	14.9486	−	25.8918i	0.556716	−	0.964260i
$722$	−7.59066	−	13.9173i	−0.282495	−	0.517947i
$723$		0			0
$724$	−42.6833	−	27.4894i	−1.58631	−	1.02163i
$725$	0.0239537	+	0.135848i	0.000889617	+	0.00504527i
$726$		0			0
$727$	−23.2473	+	27.7051i	−0.862196	+	1.02753i	0.137120	+	0.990554i	$0.456215\pi$
$727$	−23.2473	+	27.7051i	−0.862196	+	1.02753i	−0.999316	+	0.0369707i	$0.988229\pi$
$728$	13.6106	+	28.1226i	0.504443	+	1.04229i
$729$		0			0
$730$	20.1114	−	16.0597i	0.744358	−	0.594396i
$731$	56.2345	−	67.0177i	2.07991	−	2.47874i
$732$		0			0
$733$	36.2493	−	6.39173i	1.33890	−	0.236084i	0.542092	−	0.840319i	$-0.317632\pi$
$733$	36.2493	−	6.39173i	1.33890	−	0.236084i	0.796806	+	0.604235i	$0.206521\pi$
$734$	8.89605	+	26.4209i	0.328359	+	0.975214i
$735$		0			0
$736$	−0.805035	−	15.1432i	−0.0296740	−	0.558186i
$737$	−2.54064	−	1.46684i	−0.0935855	−	0.0540316i
$738$		0			0
$739$	5.13319	+	8.89094i	0.188827	+	0.327058i	0.944860	−	0.327476i	$-0.106198\pi$
$739$	5.13319	+	8.89094i	0.188827	+	0.327058i	−0.756032	+	0.654534i	$0.772865\pi$
$740$	−19.5512	+	2.47586i	−0.718716	+	0.0910145i
$741$		0			0
$742$	27.8170	+	5.60453i	1.02119	+	0.205749i
$743$	6.80751	−	5.71218i	0.249743	−	0.209559i	−0.509319	−	0.860578i	$-0.670102\pi$
$743$	6.80751	−	5.71218i	0.249743	−	0.209559i	0.759062	+	0.651019i	$0.225658\pi$
$744$		0			0
$745$	−30.5341	+	11.1135i	−1.11868	+	0.407167i
$746$	−5.66053	+	14.4504i	−0.207247	+	0.529065i
$747$		0			0
$748$	−17.5779	−	16.2675i	−0.642711	−	0.594798i
$749$	0.631584	−	3.58189i	0.0230776	−	0.130879i
$750$		0			0
$751$	−2.65250	+	7.28768i	−0.0967911	+	0.265931i	−0.978633	−	0.205613i	$-0.934081\pi$
$751$	−2.65250	+	7.28768i	−0.0967911	+	0.265931i	0.881842	+	0.471545i	$0.156303\pi$
$752$	−12.8933	+	46.2862i	−0.470171	+	1.68788i
$753$		0			0
$754$	0.0345465	−	1.42231i	0.00125811	−	0.0517974i
$755$		−	21.4489i		−	0.780606i
$756$		0			0
$757$		−	5.79367i		−	0.210575i	−0.994442	−	0.105287i	$-0.966424\pi$
$757$		−	5.79367i		−	0.210575i	0.994442	−	0.105287i	$-0.0335762\pi$
$758$	−40.5695	−	0.985396i	−1.47355	−	0.0357912i
$759$		0			0
$760$	15.3662	−	11.0930i	0.557391	−	0.402385i
$761$	−4.04229	+	11.1061i	−0.146533	+	0.402596i	−0.991145	−	0.132782i	$-0.957609\pi$
$761$	−4.04229	+	11.1061i	−0.146533	+	0.402596i	0.844612	+	0.535379i	$0.179831\pi$
$762$		0			0
$763$	0.981273	−	5.56507i	0.0355245	−	0.201469i
$764$	−30.9306	−	28.6248i	−1.11903	−	1.03561i
$765$		0			0
$766$	−18.7869	−	7.35924i	−0.678797	−	0.265900i
$767$	30.0779	−	10.9475i	1.08605	−	0.395290i
$768$		0			0
$769$	24.2973	−	20.3879i	0.876183	−	0.735205i	−0.0892076	−	0.996013i	$-0.528433\pi$
$769$	24.2973	−	20.3879i	0.876183	−	0.735205i	0.965391	+	0.260808i	$0.0839890\pi$
$770$	2.15473	−	10.6945i	0.0776509	−	0.385405i
$771$		0			0
$772$	3.10735	+	24.5379i	0.111836	+	0.883139i
$773$	13.7342	+	23.7883i	0.493984	+	0.855605i	0.999976	−	0.00693313i	$-0.00220690\pi$
$773$	13.7342	+	23.7883i	0.493984	+	0.855605i	−0.505992	+	0.862538i	$0.668874\pi$
$774$		0			0
$775$	1.18724	+	0.685451i	0.0426468	+	0.0246221i
$776$	15.2202	−	4.31431i	0.546375	−	0.154875i
$777$		0			0
$778$	−2.28406	+	0.769052i	−0.0818874	+	0.0275719i
$779$	−12.2017	+	2.15148i	−0.437170	+	0.0770848i
$780$		0			0
$781$	2.60402	−	3.10335i	0.0931791	−	0.111047i
$782$	−17.4988	−	21.9137i	−0.625757	−	0.783631i
$783$		0			0
$784$	−11.0423	−	5.28240i	−0.394366	−	0.188657i
$785$	10.1823	−	12.1348i	0.363422	−	0.433109i
$786$		0			0
$787$	3.52810	+	20.0088i	0.125763	+	0.713238i	0.980852	+	0.194756i	$0.0623915\pi$
$787$	3.52810	+	20.0088i	0.125763	+	0.713238i	−0.855089	+	0.518482i	$0.826497\pi$
$788$	12.8907	−	20.0157i	0.459212	−	0.713029i
$789$		0			0
$790$	−31.3981	+	17.1249i	−1.11709	+	0.609278i
$791$	12.0336	−	20.8427i	0.427864	−	0.741083i
$792$		0			0
$793$	21.4955	+	37.2313i	0.763328	+	1.32212i
$794$	26.1204	+	15.9386i	0.926978	+	0.565639i
$795$		0			0
$796$	−37.1063	+	19.0842i	−1.31520	+	0.676421i
$797$	−32.7465	+	27.4776i	−1.15994	+	0.973305i	−0.999905	−	0.0138066i	$-0.995605\pi$
$797$	−32.7465	+	27.4776i	−1.15994	+	0.973305i	−0.160035	+	0.987111i	$0.551161\pi$
$798$		0			0
$799$	30.3897	+	83.4951i	1.07511	+	2.95384i
$800$	−2.94628	−	3.15474i	−0.104167	−	0.111537i
$801$		0			0
$802$	3.50816	−	0.531099i	0.123878	−	0.0187538i
$803$	12.0861	+	2.13111i	0.426510	+	0.0752053i
$804$		0			0
$805$	4.36890	−	12.0035i	0.153984	−	0.423066i
$806$	−10.6074	−	9.34886i	−0.373630	−	0.329300i
$807$		0			0
$808$	−7.58058	+	30.0151i	−0.266684	+	1.05593i
$809$		−	8.70983i		−	0.306221i	−0.988209	−	0.153111i	$-0.951071\pi$
$809$		−	8.70983i		−	0.306221i	0.988209	−	0.153111i	$-0.0489291\pi$
$810$		0			0
$811$	8.59239			0.301719			0.150860	−	0.988555i	$-0.451796\pi$
$811$	8.59239			0.301719			0.150860	+	0.988555i	$0.451796\pi$
$812$	−0.434054	−	0.571489i	−0.0152323	−	0.0200553i
$813$		0			0
$814$	−7.05005	−	6.21357i	−0.247104	−	0.217785i
$815$	4.63798	+	1.68809i	0.162461	+	0.0591311i
$816$		0			0
$817$	−5.73232	+	32.5096i	−0.200548	+	1.13737i
$818$	−4.41643	−	29.1727i	−0.154417	−	1.02000i
$819$		0			0
$820$	6.30853	+	20.3579i	0.220303	+	0.710928i
$821$	−9.68233	+	3.52408i	−0.337916	+	0.122991i	−0.505404	−	0.862883i	$-0.668657\pi$
$821$	−9.68233	+	3.52408i	−0.337916	+	0.122991i	0.167488	+	0.985874i	$0.446434\pi$
$822$		0			0
$823$	−25.2011	−	30.0335i	−0.878455	−	1.04690i	−0.998533	−	0.0541373i	$-0.982759\pi$
$823$	−25.2011	−	30.0335i	−0.878455	−	1.04690i	0.120079	−	0.992764i	$-0.461685\pi$
$824$	17.4463	−	38.8667i	0.607772	−	1.35399i
$825$		0			0
$826$	8.40977	−	13.7821i	0.292613	−	0.479539i
$827$	6.85389	−	3.95709i	0.238333	−	0.137602i	−0.376077	−	0.926588i	$-0.622727\pi$
$827$	6.85389	−	3.95709i	0.238333	−	0.137602i	0.614410	+	0.788987i	$0.289394\pi$
$828$		0			0
$829$	12.0986	+	6.98514i	0.420202	+	0.242604i	0.695164	−	0.718851i	$-0.255332\pi$
$829$	12.0986	+	6.98514i	0.420202	+	0.242604i	−0.274962	+	0.961455i	$0.588665\pi$
$830$	3.32988	−	1.81616i	0.115582	−	0.0630398i
$831$		0			0
$832$	23.3623	+	37.8983i	0.809943	+	1.31389i
$833$	−22.2923	+	3.93073i	−0.772382	+	0.136192i
$834$		0			0
$835$	7.93615	+	6.65922i	0.274642	+	0.230452i
$836$	8.81322	+	1.99953i	0.304812	+	0.0691551i
$837$		0			0
$838$	−17.7217	−	22.1928i	−0.612187	−	0.766636i
$839$	28.1095	+	23.5867i	0.970449	+	0.814303i	0.982621	−	0.185623i	$-0.0594302\pi$
$839$	28.1095	+	23.5867i	0.970449	+	0.814303i	−0.0121723	+	0.999926i	$0.503875\pi$
$840$		0			0
$841$	−5.03012	−	28.5272i	−0.173452	−	0.983698i
$842$	−11.2700	−	33.4715i	−0.388390	−	1.15350i
$843$		0			0
$844$	−4.05663	−	1.70381i	−0.139635	−	0.0586477i
$845$	−21.5697	+	37.3598i	−0.742020	+	1.28522i
$846$		0			0
$847$	−14.4035	+	8.31586i	−0.494910	+	0.285736i
$848$	40.2443	+	3.92156i	1.38200	+	0.134667i
$849$		0			0
$850$	−7.82521	−	1.57661i	−0.268402	−	0.0540774i
$851$	−7.07284	−	8.42908i	−0.242454	−	0.288945i
$852$		0			0
$853$	6.77335	+	18.6096i	0.231915	+	0.637181i	0.999995	−	0.00317269i	$-0.00100990\pi$
$853$	6.77335	+	18.6096i	0.231915	+	0.637181i	−0.768080	+	0.640354i	$0.778788\pi$
$854$	20.1912	+	7.90934i	0.690928	+	0.270652i
$855$		0			0
$856$	0.377251	−	5.16909i	0.0128942	−	0.176676i
$857$	36.8632	+	6.49998i	1.25922	+	0.222035i	0.763136	−	0.646238i	$-0.223658\pi$
$857$	36.8632	+	6.49998i	1.25922	+	0.222035i	0.496087	+	0.868273i	$0.334770\pi$
$858$		0			0
$859$	−42.5547	−	15.4886i	−1.45195	−	0.528466i	−0.508813	−	0.860877i	$-0.669916\pi$
$859$	−42.5547	−	15.4886i	−1.45195	−	0.528466i	−0.943135	+	0.332411i	$0.892138\pi$
$860$	56.7183	+	2.75690i	1.93408	+	0.0940094i
$861$		0			0
$862$	−4.35264	−	0.105722i	−0.148252	−	0.00360089i
$863$	−13.2305			−0.450371			−0.225186	−	0.974316i	$-0.572299\pi$
$863$	−13.2305			−0.450371			−0.225186	+	0.974316i	$0.572299\pi$
$864$		0			0
$865$	−8.90245			−0.302693
$866$	19.6995	+	0.478483i	0.669418	+	0.0162595i
$867$		0			0
$868$	−7.12356	−	0.346253i	−0.241789	−	0.0117526i
$869$	−16.0258	−	5.83291i	−0.543638	−	0.197868i
$870$		0			0
$871$	9.93140	+	1.75117i	0.336513	+	0.0593363i
$872$	0.586123	−	8.03106i	0.0198486	−	0.271966i
$873$		0			0
$874$	9.85264	+	3.85950i	0.333271	+	0.130550i
$875$	6.90507	+	18.9715i	0.233434	+	0.641354i
$876$		0			0
$877$	−10.6749	−	12.7219i	−0.360467	−	0.429588i	0.555081	−	0.831796i	$-0.312687\pi$
$877$	−10.6749	−	12.7219i	−0.360467	−	0.429588i	−0.915548	+	0.402208i	$0.868243\pi$
$878$	−38.2659	−	7.70977i	−1.29141	−	0.260192i
$879$		0			0
$880$	1.50769	−	15.4724i	0.0508242	−	0.521575i
$881$	2.10484	−	1.21523i	0.0709140	−	0.0409422i	−0.464124	−	0.885770i	$-0.653631\pi$
$881$	2.10484	−	1.21523i	0.0709140	−	0.0409422i	0.535038	+	0.844828i	$0.320297\pi$
$882$		0			0
$883$	−26.9993	+	46.7641i	−0.908598	+	1.57374i	−0.0925850	+	0.995705i	$0.529513\pi$
$883$	−26.9993	+	46.7641i	−0.908598	+	1.57374i	−0.816013	+	0.578033i	$0.803820\pi$
$884$	75.9063	+	31.8812i	2.55301	+	1.07228i
$885$		0			0
$886$	10.5415	+	31.3079i	0.354149	+	1.05181i
$887$	−6.75263	−	38.2961i	−0.226731	−	1.28586i	−0.859348	−	0.511391i	$-0.829130\pi$
$887$	−6.75263	−	38.2961i	−0.226731	−	1.28586i	0.632617	−	0.774465i	$-0.281981\pi$
$888$		0			0
$889$	−1.15029	−	0.965209i	−0.0385795	−	0.0323721i
$890$	24.1638	+	30.2601i	0.809972	+	1.01432i
$891$		0			0
$892$	−37.5053	−	8.50914i	−1.25577	−	0.284907i
$893$	−25.6835	−	21.5510i	−0.859465	−	0.721176i
$894$		0			0
$895$	−13.1868	+	2.32519i	−0.440786	+	0.0777225i
$896$	21.1369	+	7.58465i	0.706135	+	0.253385i
$897$		0			0
$898$	3.37346	−	1.83993i	0.112574	−	0.0613992i
$899$	0.281260	+	0.162386i	0.00938055	+	0.00541586i
$900$		0			0
$901$	64.7566	−	37.3872i	2.15736	−	1.24555i
$902$	−5.29374	+	8.67548i	−0.176262	+	0.288862i
$903$		0			0
$904$	14.0442	−	31.2875i	0.467103	−	1.04061i
$905$	−39.1712	−	46.6824i	−1.30209	−	1.55177i
$906$		0			0
$907$	20.5550	−	7.48139i	0.682516	−	0.248416i	0.0225887	−	0.999745i	$-0.492809\pi$
$907$	20.5550	−	7.48139i	0.682516	−	0.248416i	0.659928	+	0.751329i	$0.270587\pi$
$908$	−9.37011	−	30.2378i	−0.310958	−	1.00348i
$909$		0			0
$910$	5.61340	+	37.0792i	0.186082	+	1.22916i
$911$	−8.10127	+	45.9446i	−0.268407	+	1.52221i	0.490748	+	0.871302i	$0.336724\pi$
$911$	−8.10127	+	45.9446i	−0.268407	+	1.52221i	−0.759155	+	0.650910i	$0.774388\pi$
$912$		0			0
$913$	1.69959	+	0.618601i	0.0562483	+	0.0204727i
$914$	28.8607	+	25.4364i	0.954627	+	0.841362i
$915$		0			0
$916$	21.7653	+	28.6569i	0.719147	+	0.946850i
$917$	6.39719			0.211254
$918$		0			0
$919$		−	35.1223i		−	1.15858i	−0.815122	−	0.579289i	$-0.803330\pi$
$919$		−	35.1223i		−	1.15858i	0.815122	−	0.579289i	$-0.196670\pi$
$920$	4.45721	−	17.6482i	0.146950	−	0.581844i
$921$		0			0
$922$	−3.74343	−	3.29927i	−0.123283	−	0.108656i
$923$	−4.76295	+	13.0861i	−0.156774	+	0.430734i
$924$		0			0
$925$	−3.08452	−	0.543884i	−0.101418	−	0.0178828i
$926$	6.91580	−	1.04698i	0.227267	−	0.0344059i
$927$		0			0
$928$	−0.697982	−	0.747368i	−0.0229124	−	0.0245335i
$929$	−20.6174	−	56.6459i	−0.676436	−	1.85849i	−0.477948	−	0.878388i	$-0.658619\pi$
$929$	−20.6174	−	56.6459i	−0.676436	−	1.85849i	−0.198488	−	0.980103i	$-0.563603\pi$
$930$		0			0
$931$	6.54308	−	5.49029i	0.214441	−	0.179937i
$932$	−9.42260	+	4.84614i	−0.308648	+	0.158741i
$933$		0			0
$934$	−28.1518	−	17.1781i	−0.921155	−	0.562086i
$935$	−14.3740	−	24.8964i	−0.470079	−	0.814200i
$936$		0			0
$937$	−7.33770	+	12.7093i	−0.239712	+	0.415194i	−0.960632	−	0.277825i	$-0.910386\pi$
$937$	−7.33770	+	12.7093i	−0.239712	+	0.415194i	0.720919	+	0.693019i	$0.243720\pi$
$938$	4.46573	−	2.43567i	0.145811	−	0.0795274i
$939$		0			0
$940$	−31.2276	+	48.4877i	−1.01853	+	1.58150i
$941$	−7.44311	−	42.2120i	−0.242638	−	1.37607i	−0.825914	−	0.563796i	$-0.809340\pi$
$941$	−7.44311	−	42.2120i	−0.242638	−	1.37607i	0.583276	−	0.812274i	$-0.301771\pi$
$942$		0			0
$943$	−7.64908	+	9.11582i	−0.249088	+	0.296852i
$944$	9.92834	−	20.7540i	0.323140	−	0.675487i
$945$		0			0
$946$	16.8966	+	21.1595i	0.549356	+	0.687954i
$947$	14.9721	−	17.8430i	0.486527	−	0.579820i	−0.465804	−	0.884888i	$-0.654235\pi$
$947$	14.9721	−	17.8430i	0.486527	−	0.579820i	0.952331	+	0.305068i	$0.0986791\pi$
$948$		0			0
$949$	−41.5465	+	7.32577i	−1.34866	+	0.237805i
$950$	2.85458	−	0.961148i	0.0926147	−	0.0311838i
$951$		0			0
$952$	39.9538	−	11.3252i	1.29491	−	0.367053i
$953$	40.0401	+	23.1172i	1.29703	+	0.748838i	0.979889	−	0.199542i	$-0.0639453\pi$
$953$	40.0401	+	23.1172i	1.29703	+	0.748838i	0.317136	+	0.948380i	$0.397279\pi$
$954$		0			0
$955$	−25.2929	−	43.8086i	−0.818459	−	1.41761i
$956$	−6.49624	−	51.2990i	−0.210103	−	1.65913i
$957$		0			0
$958$	5.75756	−	28.5765i	0.186018	−	0.923264i
$959$	−16.2864	+	13.6659i	−0.525914	+	0.441294i
$960$		0			0
$961$	−26.0975	+	9.49871i	−0.841855	+	0.306410i
$962$	30.0786	+	11.7825i	0.969773	+	0.379882i
$963$		0			0
$964$	−35.4029	−	32.7637i	−1.14025	−	1.05525i
$965$	−5.15536	+	29.2375i	−0.165957	+	0.941189i
$966$		0			0
$967$	12.2837	−	33.7493i	0.395018	−	1.08530i	−0.569662	−	0.821879i	$-0.692926\pi$
$967$	12.2837	−	33.7493i	0.395018	−	1.08530i	0.964680	−	0.263425i	$-0.0848520\pi$
$968$	−19.2158	+	13.8720i	−0.617618	+	0.445864i
$969$		0			0
$970$	18.9833	+	0.461087i	0.609518	+	0.0148046i
$971$		−	8.00721i		−	0.256963i	−0.991712	−	0.128482i	$-0.958990\pi$
$971$		−	8.00721i		−	0.256963i	0.991712	−	0.128482i	$-0.0410104\pi$
$972$		0			0
$973$			39.8703i			1.27818i
$974$	−0.292008	+	12.0222i	−0.00935656	+	0.385217i
$975$		0			0
$976$	29.7673	+	8.29190i	0.952829	+	0.265417i
$977$	−1.76473	+	4.84855i	−0.0564587	+	0.155119i	−0.964716	−	0.263294i	$-0.915191\pi$
$977$	−1.76473	+	4.84855i	−0.0564587	+	0.155119i	0.908257	+	0.418413i	$0.137413\pi$
$978$		0			0
$979$	−3.20652	+	18.1851i	−0.102481	+	0.581197i
$980$	−10.7835	−	9.97964i	−0.344467	−	0.318788i
$981$		0			0
$982$	−16.2129	+	41.3888i	−0.517374	+	1.32077i
$983$	−38.8483	+	14.1396i	−1.23907	+	0.450984i	−0.876693	−	0.481049i	$-0.840256\pi$
$983$	−38.8483	+	14.1396i	−1.23907	+	0.450984i	−0.362374	+	0.932033i	$0.618034\pi$
$984$		0			0
$985$	21.8910	−	18.3687i	0.697504	−	0.585275i
$986$	−1.85382	−	0.373505i	−0.0590376	−	0.0118948i
$987$		0			0
$988$	−30.8196	+	3.90283i	−0.980501	+	0.124166i
$989$	15.8527	+	27.4578i	0.504088	+	0.873106i
$990$		0			0
$991$	7.71200	+	4.45253i	0.244980	+	0.141439i	0.617463	−	0.786600i	$-0.288160\pi$
$991$	7.71200	+	4.45253i	0.244980	+	0.141439i	−0.372484	+	0.928039i	$0.621494\pi$
$992$	−10.1485	+	0.539511i	−0.322216	+	0.0171295i
$993$		0			0
$994$	2.24149	+	6.65713i	0.0710956	+	0.211151i
$995$	−49.3240	+	8.69716i	−1.56368	+	0.275719i
$996$		0			0
$997$	−25.0177	+	29.8149i	−0.792317	+	0.944247i	−0.999419	−	0.0340726i	$-0.989152\pi$
$997$	−25.0177	+	29.8149i	−0.792317	+	0.944247i	0.207102	+	0.978319i	$0.433597\pi$
$998$	24.9628	−	19.9337i	0.790182	−	0.630989i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.v.b.35.1		192
3.2	odd	2		216.2.v.b.11.32	yes	192
8.3	odd	2	inner	648.2.v.b.35.17		192
12.11	even	2		864.2.bh.b.335.5		192
24.5	odd	2		864.2.bh.b.335.6		192
24.11	even	2		216.2.v.b.11.16	✓	192
27.5	odd	18	inner	648.2.v.b.611.17		192
27.22	even	9		216.2.v.b.59.16	yes	192
108.103	odd	18		864.2.bh.b.815.6		192
216.59	even	18	inner	648.2.v.b.611.1		192
216.157	even	18		864.2.bh.b.815.5		192
216.211	odd	18		216.2.v.b.59.32	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.16	✓	192	24.11	even	2
216.2.v.b.11.32	yes	192	3.2	odd	2
216.2.v.b.59.16	yes	192	27.22	even	9
216.2.v.b.59.32	yes	192	216.211	odd	18
648.2.v.b.35.1		192	1.1	even	1	trivial
648.2.v.b.35.17		192	8.3	odd	2	inner
648.2.v.b.611.1		192	216.59	even	18	inner
648.2.v.b.611.17		192	27.5	odd	18	inner
864.2.bh.b.335.5		192	12.11	even	2
864.2.bh.b.335.6		192	24.5	odd	2
864.2.bh.b.815.5		192	216.157	even	18
864.2.bh.b.815.6		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)

\(f(q)\)	\(=\)	\(q+(-1.41380 - 0.0343398i) q^{2} +(1.99764 + 0.0970990i) q^{4} +(2.25586 + 0.821067i) q^{5} +(-1.95474 - 0.344674i) q^{7} +(-2.82092 - 0.205877i) q^{8} +O(q^{10})\)	\(q+(-1.41380 - 0.0343398i) q^{2} +(1.99764 + 0.0970990i) q^{4} +(2.25586 + 0.821067i) q^{5} +(-1.95474 - 0.344674i) q^{7} +(-2.82092 - 0.205877i) q^{8} +(-3.16114 - 1.23829i) q^{10} +(-0.553700 - 1.52128i) q^{11} +(3.57715 + 4.26309i) q^{13} +(2.75177 + 0.554424i) q^{14} +(3.98114 + 0.387938i) q^{16} +(6.40600 - 3.69851i) q^{17} +(-1.39557 + 2.41719i) q^{19} +(4.42668 + 1.85924i) q^{20} +(0.730579 + 2.16979i) q^{22} +(0.465506 + 2.64002i) q^{23} +(0.584547 + 0.490493i) q^{25} +(-4.91098 - 6.14998i) q^{26} +(-3.87141 - 0.878338i) q^{28} +(0.138481 + 0.116199i) q^{29} +(1.76926 - 0.311969i) q^{31} +(-5.61521 - 0.685177i) q^{32} +(-9.18379 + 5.00895i) q^{34} +(-4.12663 - 2.38251i) q^{35} +(-3.55469 + 2.05230i) q^{37} +(2.05606 - 3.36950i) q^{38} +(-6.19458 - 2.78060i) q^{40} +(2.85334 + 3.40048i) q^{41} +(11.1139 - 4.04511i) q^{43} +(-0.958380 - 3.09273i) q^{44} +(-0.567474 - 3.74843i) q^{46} +(-2.08588 + 11.8296i) q^{47} +(-2.87563 - 1.04664i) q^{49} +(-0.809587 - 0.713530i) q^{50} +(6.73193 + 8.86346i) q^{52} +10.1087 q^{53} -3.88642i q^{55} +(5.44322 + 1.37474i) q^{56} +(-0.191794 - 0.169038i) q^{58} +(1.96718 - 5.40478i) q^{59} +(7.60780 + 1.34146i) q^{61} +(-2.51209 + 0.380305i) q^{62} +(7.91523 + 1.16153i) q^{64} +(4.56929 + 12.5540i) q^{65} +(1.38817 - 1.16481i) q^{67} +(13.1560 - 6.76627i) q^{68} +(5.75240 + 3.51010i) q^{70} +(1.25119 + 2.16713i) q^{71} +(-3.79038 + 6.56514i) q^{73} +(5.09608 - 2.77947i) q^{74} +(-3.02255 + 4.69318i) q^{76} +(0.557996 + 3.16455i) q^{77} +(6.77140 - 8.06984i) q^{79} +(8.66239 + 4.14392i) q^{80} +(-3.91727 - 4.90557i) q^{82} +(-0.718131 + 0.855836i) q^{83} +(17.4878 - 3.08357i) q^{85} +(-15.8516 + 5.33732i) q^{86} +(1.24875 + 4.40541i) q^{88} +(-9.87804 - 5.70309i) q^{89} +(-5.52304 - 9.56619i) q^{91} +(0.673572 + 5.31901i) q^{92} +(3.35523 - 16.6530i) q^{94} +(-5.13289 + 4.30701i) q^{95} +(-5.25587 + 1.91298i) q^{97} +(4.02961 + 1.57849i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{2} - 6 q^{4} + 9 q^{8}+O(q^{10}) \) 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

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