LMFDB - Embedded newform 225.2.m.b.64.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(19,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("225.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.m (of order $10$, degree $4$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.3
Root			$1.08982i$ of defining polynomial
Character	$\chi$	$=$	225.64
Dual form			225.2.m.b.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.640580 + 0.881682i) q^{2} +(0.251013 - 0.772537i) q^{4} +(-0.741001 - 2.10972i) q^{5} -3.08724i q^{7} +(2.91489 - 0.947104i) q^{8} +O(q^{10})$	\(q+(0.640580 + 0.881682i) q^{2} +(0.251013 - 0.772537i) q^{4} +(-0.741001 - 2.10972i) q^{5} -3.08724i q^{7} +(2.91489 - 0.947104i) q^{8} +(1.38543 - 2.00477i) q^{10} +(-0.929002 + 0.674959i) q^{11} +(-2.39789 + 3.30042i) q^{13} +(2.72197 - 1.97763i) q^{14} +(1.38794 + 1.00840i) q^{16} +(4.40109 - 1.43000i) q^{17} +(1.84452 + 5.67685i) q^{19} +(-1.81584 + 0.0428847i) q^{20} +(-1.19020 - 0.386719i) q^{22} +(1.36700 + 1.88152i) q^{23} +(-3.90184 + 3.12661i) q^{25} -4.44596 q^{26} +(-2.38501 - 0.774937i) q^{28} +(-1.63290 + 5.02554i) q^{29} +(-0.182097 - 0.560438i) q^{31} -4.26010i q^{32} +(4.08005 + 2.96433i) q^{34} +(-6.51322 + 2.28765i) q^{35} +(6.70056 - 9.22252i) q^{37} +(-3.82361 + 5.26275i) q^{38} +(-4.15806 - 5.44779i) q^{40} +(7.67919 + 5.57926i) q^{41} -2.42954i q^{43} +(0.288240 + 0.887112i) q^{44} +(-0.783227 + 2.41052i) q^{46} +(-5.75387 - 1.86955i) q^{47} -2.53108 q^{49} +(-5.25611 - 1.43734i) q^{50} +(1.94779 + 2.68091i) q^{52} +(-3.08503 - 1.00239i) q^{53} +(2.11237 + 1.45979i) q^{55} +(-2.92394 - 8.99897i) q^{56} +(-5.47693 + 1.77956i) q^{58} +(-2.57785 - 1.87292i) q^{59} +(-11.1201 + 8.07922i) q^{61} +(0.377480 - 0.519557i) q^{62} +(6.53194 - 4.74573i) q^{64} +(8.73980 + 2.61327i) q^{65} +(-3.00414 + 0.976103i) q^{67} -3.75895i q^{68} +(-6.18922 - 4.27717i) q^{70} +(-1.99795 + 6.14907i) q^{71} +(4.23792 + 5.83300i) q^{73} +12.4236 q^{74} +4.84857 q^{76} +(2.08376 + 2.86806i) q^{77} +(3.81246 - 11.7336i) q^{79} +(1.09897 - 3.67540i) q^{80} +10.3446i q^{82} +(-11.7875 + 3.82999i) q^{83} +(-6.27811 - 8.22543i) q^{85} +(2.14208 - 1.55631i) q^{86} +(-2.06868 + 2.84729i) q^{88} +(-0.877003 + 0.637180i) q^{89} +(10.1892 + 7.40289i) q^{91} +(1.79668 - 0.583776i) q^{92} +(-2.03747 - 6.27068i) q^{94} +(10.6098 - 8.09797i) q^{95} +(4.30003 + 1.39717i) q^{97} +(-1.62136 - 2.23161i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) $ 16 * q + 2 * q^4 + 30 * q^8	$ 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.640580	+	0.881682i	0.452958	+	0.623444i	0.973030	−	0.230679i	$-0.0740947\pi$
$2$	0.640580	+	0.881682i	0.452958	+	0.623444i	−0.520072	+	0.854123i	$0.674095\pi$
$3$		0			0
$3$		0			0
$4$	0.251013	−	0.772537i	0.125506	−	0.386269i
$5$	−0.741001	−	2.10972i	−0.331386	−	0.943495i
$5$	−0.741001	−	2.10972i	−0.331386	−	0.943495i
$6$		0			0
$7$		−	3.08724i		−	1.16687i	−0.812160	−	0.583434i	$-0.801709\pi$
$7$		−	3.08724i		−	1.16687i	0.812160	−	0.583434i	$-0.198291\pi$
$8$	2.91489	−	0.947104i	1.03057	−	0.334852i
$9$		0			0
$10$	1.38543	−	2.00477i	0.438112	−	0.633964i
$11$	−0.929002	+	0.674959i	−0.280105	+	0.203508i	−0.718963	−	0.695048i	$-0.755383\pi$
$11$	−0.929002	+	0.674959i	−0.280105	+	0.203508i	0.438858	+	0.898556i	$0.355383\pi$
$12$		0			0
$13$	−2.39789	+	3.30042i	−0.665056	+	0.915372i	−0.999636	−	0.0269961i	$-0.991406\pi$
$13$	−2.39789	+	3.30042i	−0.665056	+	0.915372i	0.334579	+	0.942368i	$0.391406\pi$
$14$	2.72197	−	1.97763i	0.727477	−	0.528543i
$15$		0			0
$16$	1.38794	+	1.00840i	0.346986	+	0.252100i
$17$	4.40109	−	1.43000i	1.06742	−	0.346826i	0.277938	−	0.960599i	$-0.410349\pi$
$17$	4.40109	−	1.43000i	1.06742	−	0.346826i	0.789482	+	0.613773i	$0.210349\pi$
$18$		0			0
$19$	1.84452	+	5.67685i	0.423162	+	1.30236i	0.904744	+	0.425957i	$0.140062\pi$
$19$	1.84452	+	5.67685i	0.423162	+	1.30236i	−0.481582	+	0.876401i	$0.659938\pi$
$20$	−1.81584	+	0.0428847i	−0.406034	+	0.00958930i
$21$		0			0
$22$	−1.19020	−	0.386719i	−0.253751	−	0.0824488i
$23$	1.36700	+	1.88152i	0.285040	+	0.392324i	0.927395	−	0.374083i	$-0.122043\pi$
$23$	1.36700	+	1.88152i	0.285040	+	0.392324i	−0.642355	+	0.766407i	$0.722043\pi$
$24$		0			0
$25$	−3.90184	+	3.12661i	−0.780367	+	0.625322i
$26$	−4.44596			−0.871925
$27$		0			0
$28$	−2.38501	−	0.774937i	−0.450725	−	0.146449i
$29$	−1.63290	+	5.02554i	−0.303221	+	0.933220i	0.677113	+	0.735879i	$0.263231\pi$
$29$	−1.63290	+	5.02554i	−0.303221	+	0.933220i	−0.980335	+	0.197341i	$0.936769\pi$
$30$		0			0
$31$	−0.182097	−	0.560438i	−0.0327056	−	0.100658i	0.933371	−	0.358913i	$-0.116852\pi$
$31$	−0.182097	−	0.560438i	−0.0327056	−	0.100658i	−0.966077	+	0.258255i	$0.916852\pi$
$32$		−	4.26010i		−	0.753086i
$33$		0			0
$34$	4.08005	+	2.96433i	0.699723	+	0.508379i
$35$	−6.51322	+	2.28765i	−1.10094	+	0.386684i
$36$		0			0
$37$	6.70056	−	9.22252i	1.10156	−	1.51617i	0.268271	−	0.963344i	$-0.413548\pi$
$37$	6.70056	−	9.22252i	1.10156	−	1.51617i	0.833294	−	0.552830i	$-0.186452\pi$
$38$	−3.82361	+	5.26275i	−0.620272	+	0.853731i
$39$		0			0
$40$	−4.15806	−	5.44779i	−0.657446	−	0.861371i
$41$	7.67919	+	5.57926i	1.19929	+	0.871334i	0.994215	−	0.107413i	$-0.0342567\pi$
$41$	7.67919	+	5.57926i	1.19929	+	0.871334i	0.205073	+	0.978747i	$0.434257\pi$
$42$		0			0
$43$		−	2.42954i		−	0.370501i	−0.982691	−	0.185250i	$-0.940690\pi$
$43$		−	2.42954i		−	0.370501i	0.982691	−	0.185250i	$-0.0593096\pi$
$44$	0.288240	+	0.887112i	0.0434538	+	0.133737i
$45$		0			0
$46$	−0.783227	+	2.41052i	−0.115481	+	0.355412i
$47$	−5.75387	−	1.86955i	−0.839289	−	0.272701i	−0.142336	−	0.989818i	$-0.545461\pi$
$47$	−5.75387	−	1.86955i	−0.839289	−	0.272701i	−0.696953	+	0.717117i	$0.745461\pi$
$48$		0			0
$49$	−2.53108			−0.361583
$50$	−5.25611	−	1.43734i	−0.743327	−	0.203270i
$51$		0			0
$52$	1.94779	+	2.68091i	0.270111	+	0.371775i
$53$	−3.08503	−	1.00239i	−0.423762	−	0.137689i	0.0893696	−	0.995999i	$-0.471515\pi$
$53$	−3.08503	−	1.00239i	−0.423762	−	0.137689i	−0.513132	+	0.858310i	$0.671515\pi$
$54$		0			0
$55$	2.11237	+	1.45979i	0.284831	+	0.196838i
$56$	−2.92394	−	8.99897i	−0.390728	−	1.20254i
$57$		0			0
$58$	−5.47693	+	1.77956i	−0.719157	+	0.233668i
$59$	−2.57785	−	1.87292i	−0.335607	−	0.243833i	0.407199	−	0.913340i	$-0.366506\pi$
$59$	−2.57785	−	1.87292i	−0.335607	−	0.243833i	−0.742806	+	0.669507i	$0.766506\pi$
$60$		0			0
$61$	−11.1201	+	8.07922i	−1.42378	+	1.03444i	−0.432650	+	0.901562i	$0.642421\pi$
$61$	−11.1201	+	8.07922i	−1.42378	+	1.03444i	−0.991133	+	0.132876i	$0.957579\pi$
$62$	0.377480	−	0.519557i	0.0479400	−	0.0659838i
$63$		0			0
$64$	6.53194	−	4.74573i	0.816493	−	0.593217i
$65$	8.73980	+	2.61327i	1.08404	+	0.324137i
$66$		0			0
$67$	−3.00414	+	0.976103i	−0.367014	+	0.119250i	−0.486717	−	0.873560i	$-0.661806\pi$
$67$	−3.00414	+	0.976103i	−0.367014	+	0.119250i	0.119703	+	0.992810i	$0.461806\pi$
$68$		−	3.75895i		−	0.455840i
$69$		0			0
$70$	−6.18922	−	4.27717i	−0.739753	−	0.511220i
$71$	−1.99795	+	6.14907i	−0.237113	+	0.729760i	0.759721	+	0.650250i	$0.225336\pi$
$71$	−1.99795	+	6.14907i	−0.237113	+	0.729760i	−0.996834	+	0.0795103i	$0.974664\pi$
$72$		0			0
$73$	4.23792	+	5.83300i	0.496011	+	0.682701i	0.981482	−	0.191552i	$-0.0613521\pi$
$73$	4.23792	+	5.83300i	0.496011	+	0.682701i	−0.485472	+	0.874252i	$0.661352\pi$
$74$	12.4236			1.44421
$75$		0			0
$76$	4.84857			0.556169
$77$	2.08376	+	2.86806i	0.237467	+	0.326845i
$78$		0			0
$79$	3.81246	−	11.7336i	0.428936	−	1.32013i	−0.470239	−	0.882539i	$-0.655832\pi$
$79$	3.81246	−	11.7336i	0.428936	−	1.32013i	0.899175	−	0.437590i	$-0.144168\pi$
$80$	1.09897	−	3.67540i	0.122869	−	0.410922i
$81$		0			0
$82$			10.3446i			1.14237i
$83$	−11.7875	+	3.82999i	−1.29384	+	0.420396i	−0.873436	−	0.486939i	$-0.838113\pi$
$83$	−11.7875	+	3.82999i	−1.29384	+	0.420396i	−0.420409	+	0.907335i	$0.638113\pi$
$84$		0			0
$85$	−6.27811	−	8.22543i	−0.680957	−	0.892173i
$86$	2.14208	−	1.55631i	0.230986	−	0.167821i
$87$		0			0
$88$	−2.06868	+	2.84729i	−0.220522	+	0.303522i
$89$	−0.877003	+	0.637180i	−0.0929621	+	0.0675409i	−0.633295	−	0.773910i	$-0.718298\pi$
$89$	−0.877003	+	0.637180i	−0.0929621	+	0.0675409i	0.540333	+	0.841451i	$0.318298\pi$
$90$		0			0
$91$	10.1892	+	7.40289i	1.06812	+	0.776034i
$92$	1.79668	−	0.583776i	0.187317	−	0.0608628i
$93$		0			0
$94$	−2.03747	−	6.27068i	−0.210149	−	0.646772i
$95$	10.6098	−	8.09797i	1.08854	−	0.830834i
$96$		0			0
$97$	4.30003	+	1.39717i	0.436602	+	0.141861i	0.519067	−	0.854733i	$-0.326279\pi$
$97$	4.30003	+	1.39717i	0.436602	+	0.141861i	−0.0824653	+	0.996594i	$0.526279\pi$
$98$	−1.62136	−	2.23161i	−0.163782	−	0.225426i
$99$		0			0
$100$	1.43601	+	3.79913i	0.143601	+	0.379913i
$101$	6.61332			0.658050			0.329025	−	0.944321i	$-0.393280\pi$
$101$	6.61332			0.658050			0.329025	+	0.944321i	$0.393280\pi$
$102$		0			0
$103$	−4.00047	−	1.29983i	−0.394178	−	0.128076i	0.105220	−	0.994449i	$-0.466445\pi$
$103$	−4.00047	−	1.29983i	−0.394178	−	0.128076i	−0.499398	+	0.866373i	$0.666445\pi$
$104$	−3.86375	+	11.8914i	−0.378872	+	1.16605i
$105$		0			0
$106$	−1.09242	−	3.36213i	−0.106105	−	0.326559i
$107$			4.01195i			0.387849i	0.981016	+	0.193925i	$0.0621218\pi$
$107$			4.01195i			0.387849i	−0.981016	+	0.193925i	$0.937878\pi$
$108$		0			0
$109$	7.35691	+	5.34511i	0.704664	+	0.511969i	0.881448	−	0.472281i	$-0.156569\pi$
$109$	7.35691	+	5.34511i	0.704664	+	0.511969i	−0.176784	+	0.984250i	$0.556569\pi$
$110$	0.0660697	+	2.79755i	0.00629950	+	0.266736i
$111$		0			0
$112$	3.11318	−	4.28492i	0.294168	−	0.404887i
$113$	2.20693	−	3.03758i	0.207610	−	0.285751i	−0.692496	−	0.721422i	$-0.743489\pi$
$113$	2.20693	−	3.03758i	0.207610	−	0.285751i	0.900106	+	0.435671i	$0.143489\pi$
$114$		0			0
$115$	2.95653	−	4.27820i	0.275697	−	0.398944i
$116$	3.47254	+	2.52295i	0.322417	+	0.234250i
$117$		0			0
$118$		−	3.47260i		−	0.319678i
$119$	−4.41476	−	13.5872i	−0.404700	−	1.24554i
$120$		0			0
$121$	−2.99171	+	9.20755i	−0.271974	+	0.837050i
$122$	−14.2466	−	4.62901i	−1.28983	−	0.419091i
$123$		0			0
$124$	−0.478668			−0.0429856
$125$	9.48753	+	5.91496i	0.848591	+	0.529050i
$126$		0			0
$127$	−6.67623	−	9.18904i	−0.592419	−	0.815395i	0.402569	−	0.915390i	$-0.368117\pi$
$127$	−6.67623	−	9.18904i	−0.592419	−	0.815395i	−0.994988	+	0.0999946i	$0.968117\pi$
$128$	0.265268	+	0.0861909i	0.0234466	+	0.00761827i
$129$		0			0
$130$	3.29446	+	9.37974i	0.288944	+	0.822658i
$131$	0.642289	+	1.97676i	0.0561170	+	0.172711i	0.975186	−	0.221385i	$-0.0710578\pi$
$131$	0.642289	+	1.97676i	0.0561170	+	0.172711i	−0.919069	+	0.394096i	$0.871058\pi$
$132$		0			0
$133$	17.5258	−	5.69448i	1.51968	−	0.493774i
$134$	−2.78500	−	2.02342i	−0.240587	−	0.174797i
$135$		0			0
$136$	11.4743	−	8.33657i	0.983914	−	0.714855i
$137$	11.4049	−	15.6975i	0.974387	−	1.34113i	0.0345870	−	0.999402i	$-0.488988\pi$
$137$	11.4049	−	15.6975i	0.974387	−	1.34113i	0.939800	−	0.341726i	$-0.111012\pi$
$138$		0			0
$139$	−13.8830	+	10.0866i	−1.17754	+	0.855531i	−0.991892	−	0.127086i	$-0.959438\pi$
$139$	−13.8830	+	10.0866i	−1.17754	+	0.855531i	−0.185646	+	0.982617i	$0.559438\pi$
$140$	0.132395	+	5.60593i	0.0111895	+	0.473788i
$141$		0			0
$142$	−6.70137	+	2.17741i	−0.562367	+	0.182724i
$143$		−	4.68458i		−	0.391744i
$144$		0			0
$145$	11.8125	−	0.278975i	0.980972	−	0.0231676i
$146$	−2.42812	+	7.47300i	−0.200953	+	0.618470i
$147$		0			0
$148$	−5.44282	−	7.49140i	−0.447397	−	0.615789i
$149$	0.210127			0.0172143			0.00860714	−	0.999963i	$-0.497260\pi$
$149$	0.210127			0.0172143			0.00860714	+	0.999963i	$0.497260\pi$
$150$		0			0
$151$	−4.05924			−0.330336			−0.165168	−	0.986265i	$-0.552817\pi$
$151$	−4.05924			−0.330336			−0.165168	+	0.986265i	$0.552817\pi$
$152$	10.7531	+	14.8004i	0.872194	+	1.20047i
$153$		0			0
$154$	−1.19390	+	3.67444i	−0.0962070	+	0.296095i
$155$	−1.04743	+	0.799459i	−0.0841318	+	0.0642141i
$156$		0			0
$157$			0.440336i			0.0351426i	0.999846	+	0.0175713i	$0.00559341\pi$
$157$			0.440336i			0.0351426i	−0.999846	+	0.0175713i	$0.994407\pi$
$158$	12.7875	−	4.15490i	1.01732	−	0.330546i
$159$		0			0
$160$	−8.98762	+	3.15674i	−0.710533	+	0.249562i
$161$	5.80871	−	4.22027i	0.457790	−	0.332604i
$162$		0			0
$163$	−1.90506	+	2.62210i	−0.149216	+	0.205378i	−0.877081	−	0.480342i	$-0.840513\pi$
$163$	−1.90506	+	2.62210i	−0.149216	+	0.205378i	0.727865	+	0.685720i	$0.240513\pi$
$164$	6.23776	−	4.53200i	0.487087	−	0.353889i
$165$		0			0
$166$	−10.9277	−	7.93941i	−0.848151	−	0.616218i
$167$	−15.1793	+	4.93207i	−1.17461	+	0.381655i	−0.830363	−	0.557223i	$-0.811867\pi$
$167$	−15.1793	+	4.93207i	−1.17461	+	0.381655i	−0.344250	+	0.938878i	$0.611867\pi$
$168$		0			0
$169$	−1.12565	−	3.46438i	−0.0865882	−	0.266491i
$170$	3.23059	−	10.8043i	0.247775	−	0.828655i
$171$		0			0
$172$	−1.87691	−	0.609844i	−0.143113	−	0.0465002i
$173$	−0.330212	−	0.454497i	−0.0251055	−	0.0345548i	0.796280	−	0.604929i	$-0.206798\pi$
$173$	−0.330212	−	0.454497i	−0.0251055	−	0.0345548i	−0.821385	+	0.570374i	$0.806798\pi$
$174$		0			0
$175$	9.65261	+	12.0459i	0.729668	+	0.910586i
$176$	−1.97003			−0.148497
$177$		0			0
$178$	−1.12358	−	0.365073i	−0.0842159	−	0.0273634i
$179$	4.92532	−	15.1586i	0.368136	−	1.13301i	−0.579858	−	0.814718i	$-0.696892\pi$
$179$	4.92532	−	15.1586i	0.368136	−	1.13301i	0.947994	−	0.318288i	$-0.103108\pi$
$180$		0			0
$181$	−6.64001	−	20.4358i	−0.493548	−	1.51898i	−0.819208	−	0.573497i	$-0.805586\pi$
$181$	−6.64001	−	20.4358i	−0.493548	−	1.51898i	0.325660	−	0.945487i	$-0.394414\pi$
$182$			13.7258i			1.01742i
$183$		0			0
$184$	5.76665	+	4.18972i	0.425123	+	0.308870i
$185$	−24.4221	−	7.30240i	−1.79555	−	0.536883i
$186$		0			0
$187$	−3.12343	+	4.29903i	−0.228408	+	0.314376i
$188$	−2.88859	+	3.97580i	−0.210672	+	0.289965i
$189$		0			0
$190$	13.9362	+	4.16705i	1.01104	+	0.302310i
$191$	−14.8810	−	10.8117i	−1.07675	−	0.782304i	−0.0996355	−	0.995024i	$-0.531768\pi$
$191$	−14.8810	−	10.8117i	−1.07675	−	0.782304i	−0.977113	+	0.212720i	$0.931768\pi$
$192$		0			0
$193$			2.02523i			0.145780i	0.997340	+	0.0728898i	$0.0232221\pi$
$193$			2.02523i			0.145780i	−0.997340	+	0.0728898i	$0.976778\pi$
$194$	1.52266	+	4.68626i	0.109320	+	0.336454i
$195$		0			0
$196$	−0.635333	+	1.95535i	−0.0453809	+	0.139668i
$197$	−10.9804	−	3.56774i	−0.782319	−	0.254191i	−0.109489	−	0.993988i	$-0.534921\pi$
$197$	−10.9804	−	3.56774i	−0.782319	−	0.254191i	−0.672830	+	0.739797i	$0.734921\pi$
$198$		0			0
$199$	−22.9779			−1.62886			−0.814431	−	0.580260i	$-0.802951\pi$
$199$	−22.9779			−1.62886			−0.814431	+	0.580260i	$0.802951\pi$
$200$	−8.41218	+	12.8092i	−0.594831	+	0.905744i
$201$		0			0
$202$	4.23636	+	5.83085i	0.298069	+	0.410257i
$203$	15.5151	+	5.04115i	1.08894	+	0.353820i
$204$		0			0
$205$	6.08038	−	20.3352i	0.424672	−	1.42027i
$206$	−1.41658	−	4.35979i	−0.0986978	−	0.303761i
$207$		0			0
$208$	−6.65628	+	2.16276i	−0.461530	+	0.149960i
$209$	−5.54520	−	4.02882i	−0.383570	−	0.278680i
$210$		0			0
$211$	5.56717	−	4.04479i	0.383260	−	0.278455i	−0.379428	−	0.925221i	$-0.623879\pi$
$211$	5.56717	−	4.04479i	0.383260	−	0.278455i	0.762688	+	0.646767i	$0.223879\pi$
$212$	−1.54876	+	2.13169i	−0.106370	+	0.146405i
$213$		0			0
$214$	−3.53726	+	2.56997i	−0.241802	+	0.175680i
$215$	−5.12564	+	1.80029i	−0.349566	+	0.122779i
$216$		0			0
$217$	−1.73021	+	0.562179i	−0.117454	+	0.0381632i
$218$			9.91043i			0.671219i
$219$		0			0
$220$	1.65797	−	1.26546i	0.111780	−	0.0853170i
$221$	−5.83375	+	17.9544i	−0.392420	+	1.20775i
$222$		0			0
$223$	4.77652	+	6.57432i	0.319860	+	0.440249i	0.938424	−	0.345485i	$-0.112286\pi$
$223$	4.77652	+	6.57432i	0.319860	+	0.440249i	−0.618565	+	0.785734i	$0.712286\pi$
$224$	−13.1520			−0.878753
$225$		0			0
$226$	4.09189			0.272188
$227$	15.0649	+	20.7351i	0.999895	+	1.37624i	0.925390	+	0.379017i	$0.123738\pi$
$227$	15.0649	+	20.7351i	0.999895	+	1.37624i	0.0745050	+	0.997221i	$0.476262\pi$
$228$		0			0
$229$	−0.381062	+	1.17279i	−0.0251813	+	0.0775001i	−0.962857	−	0.270010i	$-0.912973\pi$
$229$	−0.381062	+	1.17279i	−0.0251813	+	0.0775001i	0.937676	+	0.347510i	$0.112973\pi$
$230$	5.66590	−	0.133812i	0.373599	−	0.00882329i
$231$		0			0
$232$			16.1954i			1.06328i
$233$	2.85305	−	0.927012i	0.186909	−	0.0607306i	−0.214067	−	0.976819i	$-0.568671\pi$
$233$	2.85305	−	0.927012i	0.186909	−	0.0607306i	0.400976	+	0.916088i	$0.368671\pi$
$234$		0			0
$235$	0.319406	+	13.5244i	0.0208357	+	0.882234i
$236$	−2.09397	+	1.52136i	−0.136306	+	0.0990320i
$237$		0			0
$238$	9.15162	−	12.5961i	0.593211	−	0.816485i
$239$	−17.9069	+	13.0101i	−1.15830	+	0.841554i	−0.989562	−	0.144107i	$-0.953969\pi$
$239$	−17.9069	+	13.0101i	−1.15830	+	0.841554i	−0.168738	+	0.985661i	$0.553969\pi$
$240$		0			0
$241$	10.8734	+	7.89999i	0.700418	+	0.508883i	0.880068	−	0.474847i	$-0.157497\pi$
$241$	10.8734	+	7.89999i	0.700418	+	0.508883i	−0.179651	+	0.983730i	$0.557497\pi$
$242$	−10.0346	+	3.26043i	−0.645046	+	0.209588i
$243$		0			0
$244$	3.45022	+	10.6187i	0.220877	+	0.679791i
$245$	1.87553	+	5.33987i	0.119823	+	0.341152i
$246$		0			0
$247$	−23.1589	−	7.52479i	−1.47357	−	0.478791i
$248$	−1.06159	−	1.46115i	−0.0674107	−	0.0927829i
$249$		0			0
$250$	0.862406	+	12.1540i	0.0545434	+	0.768686i
$251$	−18.8799			−1.19169			−0.595843	−	0.803101i	$-0.703182\pi$
$251$	−18.8799			−1.19169			−0.595843	+	0.803101i	$0.703182\pi$
$252$		0			0
$253$	−2.53990	−	0.825262i	−0.159682	−	0.0518838i
$254$	3.82516	−	11.7726i	0.240012	−	0.738680i
$255$		0			0
$256$	−4.89603	−	15.0684i	−0.306002	−	0.941776i
$257$		−	7.06320i		−	0.440590i	−0.975433	−	0.220295i	$-0.929298\pi$
$257$		−	7.06320i		−	0.440590i	0.975433	−	0.220295i	$-0.0707020\pi$
$258$		0			0
$259$	−28.4722	−	20.6863i	−1.76918	−	1.28538i
$260$	4.21265	−	6.09586i	0.261257	−	0.378049i
$261$		0			0
$262$	−1.33144	+	1.83257i	−0.0822566	+	0.113216i
$263$	12.0118	−	16.5328i	0.740677	−	1.01945i	−0.257903	−	0.966171i	$-0.583031\pi$
$263$	12.0118	−	16.5328i	0.740677	−	1.01945i	0.998579	−	0.0532829i	$-0.0169685\pi$
$264$		0			0
$265$	0.171255	+	7.25133i	0.0105201	+	0.445446i
$266$	16.2474	+	11.8044i	0.996192	+	0.723776i
$267$		0			0
$268$			2.56582i			0.156732i
$269$	6.54880	+	20.1551i	0.399287	+	1.22888i	0.925572	+	0.378571i	$0.123584\pi$
$269$	6.54880	+	20.1551i	0.399287	+	1.22888i	−0.526285	+	0.850308i	$0.676416\pi$
$270$		0			0
$271$	3.07570	−	9.46603i	0.186835	−	0.575020i	−0.813140	−	0.582069i	$-0.802244\pi$
$271$	3.07570	−	9.46603i	0.186835	−	0.575020i	0.999975	+	0.00704817i	$0.00224352\pi$
$272$	7.55047	+	2.45330i	0.457814	+	0.148753i
$273$		0			0
$274$	21.1460			1.27747
$275$	1.51448	−	5.53820i	0.0913265	−	0.333966i
$276$		0			0
$277$	11.0121	+	15.1569i	0.661654	+	0.910689i	0.999535	−	0.0304998i	$-0.00970991\pi$
$277$	11.0121	+	15.1569i	0.661654	+	0.910689i	−0.337880	+	0.941189i	$0.609710\pi$
$278$	−17.7863	−	5.77912i	−1.06675	−	0.346608i
$279$		0			0
$280$	−16.8187	+	12.8369i	−1.00511	+	0.767154i
$281$	−8.98981	−	27.6678i	−0.536287	−	1.65052i	−0.740852	−	0.671668i	$-0.765578\pi$
$281$	−8.98981	−	27.6678i	−0.536287	−	1.65052i	0.204565	−	0.978853i	$-0.434422\pi$
$282$		0			0
$283$	6.82865	−	2.21876i	0.405921	−	0.131892i	−0.0989379	−	0.995094i	$-0.531545\pi$
$283$	6.82865	−	2.21876i	0.405921	−	0.131892i	0.504859	+	0.863202i	$0.331545\pi$
$284$	4.24887	+	3.08699i	0.252124	+	0.183179i
$285$		0			0
$286$	4.13031	−	3.00084i	0.244230	−	0.177444i
$287$	17.2245	−	23.7075i	1.01673	−	1.39941i
$288$		0			0
$289$	3.57138	−	2.59476i	0.210081	−	0.152633i
$290$	7.81279	+	10.2361i	0.458783	+	0.601087i
$291$		0			0
$292$	5.56998	−	1.80980i	0.325958	−	0.105910i
$293$		−	1.79825i		−	0.105055i	−0.998619	−	0.0525276i	$-0.983272\pi$
$293$		−	1.79825i		−	0.105055i	0.998619	−	0.0525276i	$-0.0167277\pi$
$294$		0			0
$295$	−2.04114	+	6.82637i	−0.118840	+	0.397447i
$296$	10.7967	−	33.2287i	0.627544	−	1.93138i
$297$		0			0
$298$	0.134603	+	0.185265i	0.00779735	+	0.0107321i
$299$	−9.48773			−0.548689
$300$		0			0
$301$	−7.50057			−0.432326
$302$	−2.60027	−	3.57896i	−0.149629	−	0.205946i
$303$		0			0
$304$	−3.16444	+	9.73915i	−0.181493	+	0.558579i
$305$	25.2849	+	17.4736i	1.44781	+	1.00053i
$306$		0			0
$307$		−	5.98864i		−	0.341790i	−0.985289	−	0.170895i	$-0.945334\pi$
$307$		−	5.98864i		−	0.341790i	0.985289	−	0.170895i	$-0.0546659\pi$
$308$	2.73873	−	0.889867i	0.156054	−	0.0507049i
$309$		0			0
$310$	−1.37583	−	0.411385i	−0.0781421	−	0.0233651i
$311$	19.3099	−	14.0295i	1.09497	−	0.795539i	0.114735	−	0.993396i	$-0.463398\pi$
$311$	19.3099	−	14.0295i	1.09497	−	0.795539i	0.980231	+	0.197857i	$0.0633982\pi$
$312$		0			0
$313$	3.38513	−	4.65924i	0.191339	−	0.263356i	−0.702559	−	0.711625i	$-0.747959\pi$
$313$	3.38513	−	4.65924i	0.191339	−	0.263356i	0.893898	+	0.448269i	$0.147959\pi$
$314$	−0.388236	+	0.282070i	−0.0219094	+	0.0159181i
$315$		0			0
$316$	−8.10763	−	5.89054i	−0.456090	−	0.331369i
$317$	11.6486	−	3.78487i	0.654253	−	0.212580i	0.0369645	−	0.999317i	$-0.488231\pi$
$317$	11.6486	−	3.78487i	0.654253	−	0.212580i	0.617288	+	0.786737i	$0.288231\pi$
$318$		0			0
$319$	−1.87507	−	5.77088i	−0.104984	−	0.323107i
$320$	−14.8523	−	10.2640i	−0.830271	−	0.573773i
$321$		0			0
$322$	7.44188	+	2.41801i	0.414720	+	0.134751i
$323$	16.2358	+	22.3466i	0.903383	+	1.24340i
$324$		0			0
$325$	−0.962929	−	20.3750i	−0.0534137	−	1.13020i
$326$	−3.53220			−0.195631
$327$		0			0
$328$	27.6681	+	8.98991i	1.52772	+	0.496385i
$329$	−5.77175	+	17.7636i	−0.318207	+	0.979340i
$330$		0			0
$331$	−1.86306	−	5.73391i	−0.102403	−	0.315164i	0.886709	−	0.462328i	$-0.152986\pi$
$331$	−1.86306	−	5.73391i	−0.102403	−	0.315164i	−0.989112	+	0.147163i	$0.952986\pi$
$332$			10.0676i			0.552534i
$333$		0			0
$334$	−14.0721	−	10.2240i	−0.769991	−	0.559431i
$335$	4.28537	+	5.61459i	0.234135	+	0.306758i
$336$		0			0
$337$	−3.25094	+	4.47454i	−0.177090	+	0.243744i	−0.888330	−	0.459206i	$-0.848134\pi$
$337$	−3.25094	+	4.47454i	−0.177090	+	0.243744i	0.711240	+	0.702949i	$0.248134\pi$
$338$	2.33342	−	3.21168i	0.126921	−	0.174692i
$339$		0			0
$340$	−7.93033	+	2.78539i	−0.430083	+	0.151059i
$341$	0.547441	+	0.397739i	0.0296456	+	0.0215388i
$342$		0			0
$343$		−	13.7967i		−	0.744949i
$344$	−2.30102	−	7.08182i	−0.124063	−	0.381826i
$345$		0			0
$346$	0.189195	−	0.582283i	0.0101712	−	0.0313038i
$347$	−24.6747	−	8.01729i	−1.32461	−	0.430391i	−0.440532	−	0.897737i	$-0.645210\pi$
$347$	−24.6747	−	8.01729i	−1.32461	−	0.430391i	−0.884075	+	0.467346i	$0.845210\pi$
$348$		0			0
$349$	19.0025			1.01718			0.508591	−	0.861008i	$-0.330167\pi$
$349$	19.0025			1.01718			0.508591	+	0.861008i	$0.330167\pi$
$350$	−4.43741	+	16.2269i	−0.237190	+	0.867365i
$351$		0			0
$352$	2.87539	+	3.95764i	0.153259	+	0.210943i
$353$	−7.79043	−	2.53126i	−0.414642	−	0.134726i	0.0942642	−	0.995547i	$-0.469950\pi$
$353$	−7.79043	−	2.53126i	−0.414642	−	0.134726i	−0.508907	+	0.860822i	$0.669950\pi$
$354$		0			0
$355$	14.4533	−	0.341344i	0.767101	−	0.0181166i
$356$	0.272106	+	0.837457i	0.0144216	+	0.0443852i
$357$		0			0
$358$	16.5201	−	5.36771i	0.873116	−	0.283692i
$359$	21.6701	+	15.7442i	1.14370	+	0.830948i	0.987631	−	0.156797i	$-0.0501170\pi$
$359$	21.6701	+	15.7442i	1.14370	+	0.830948i	0.156071	+	0.987746i	$0.450117\pi$
$360$		0			0
$361$	−13.4530	+	9.77419i	−0.708053	+	0.514431i
$362$	13.7645	−	18.9452i	0.723444	−	0.995736i
$363$		0			0
$364$	8.27662	−	6.01332i	0.433813	−	0.315184i
$365$	9.16568	−	13.2631i	0.479754	−	0.694221i
$366$		0			0
$367$	17.9306	−	5.82600i	0.935968	−	0.304114i	0.198967	−	0.980006i	$-0.436241\pi$
$367$	17.9306	−	5.82600i	0.935968	−	0.304114i	0.737001	+	0.675892i	$0.236241\pi$
$368$			3.98992i			0.207989i
$369$		0			0
$370$	−9.20588	−	26.2103i	−0.478591	−	1.36261i
$371$	−3.09462	+	9.52426i	−0.160665	+	0.494475i
$372$		0			0
$373$	10.4906	+	14.4391i	0.543183	+	0.747627i	0.989067	−	0.147464i	$-0.0471109\pi$
$373$	10.4906	+	14.4391i	0.543183	+	0.747627i	−0.445885	+	0.895090i	$0.647111\pi$
$374$	−5.79118			−0.299455
$375$		0			0
$376$	−18.5425			−0.956259
$377$	−12.6709	−	17.4400i	−0.652583	−	0.898204i
$378$		0			0
$379$	−3.88290	+	11.9503i	−0.199451	+	0.613848i	0.800445	+	0.599407i	$0.204597\pi$
$379$	−3.88290	+	11.9503i	−0.199451	+	0.613848i	−0.999896	+	0.0144408i	$0.995403\pi$
$380$	−3.59280	−	10.2291i	−0.184307	−	0.524743i
$381$		0			0
$382$		−	20.0460i		−	1.02564i
$383$	7.16849	−	2.32918i	0.366292	−	0.119016i	−0.120087	−	0.992763i	$-0.538317\pi$
$383$	7.16849	−	2.32918i	0.366292	−	0.119016i	0.486379	+	0.873748i	$0.338317\pi$
$384$		0			0
$385$	4.50672	−	6.52139i	0.229684	−	0.332361i
$386$	−1.78561	+	1.29732i	−0.0908854	+	0.0660321i
$387$		0			0
$388$	2.15872	−	2.97123i	0.109593	−	0.150841i
$389$	11.1103	−	8.07211i	0.563315	−	0.409272i	−0.269356	−	0.963041i	$-0.586811\pi$
$389$	11.1103	−	8.07211i	0.563315	−	0.409272i	0.832671	+	0.553768i	$0.186811\pi$
$390$		0			0
$391$	8.70687	+	6.32591i	0.440325	+	0.319915i
$392$	−7.37781	+	2.39719i	−0.372636	+	0.121077i
$393$		0			0
$394$	−3.88819	−	11.9666i	−0.195884	−	0.602869i
$395$	−27.5796	+	0.651347i	−1.38768	+	0.0327728i
$396$		0			0
$397$	−12.3658	−	4.01790i	−0.620623	−	0.201653i	−0.0182061	−	0.999834i	$-0.505796\pi$
$397$	−12.3658	−	4.01790i	−0.620623	−	0.201653i	−0.602417	+	0.798182i	$0.705796\pi$
$398$	−14.7192	−	20.2592i	−0.737807	−	1.01550i
$399$		0			0
$400$	−8.56840	+	0.404946i	−0.428420	+	0.0202473i
$401$	6.47047			0.323120			0.161560	−	0.986863i	$-0.448347\pi$
$401$	6.47047			0.323120			0.161560	+	0.986863i	$0.448347\pi$
$402$		0			0
$403$	2.28633	+	0.742874i	0.113890	+	0.0370052i
$404$	1.66003	−	5.10904i	0.0825894	−	0.254184i
$405$		0			0
$406$	5.49395	+	16.9086i	0.272660	+	0.839161i
$407$			13.0903i			0.648864i
$408$		0			0
$409$	−0.899629	−	0.653619i	−0.0444838	−	0.0323194i	0.565321	−	0.824871i	$-0.308752\pi$
$409$	−0.899629	−	0.653619i	−0.0444838	−	0.0323194i	−0.609805	+	0.792552i	$0.708752\pi$
$410$	21.8241	−	7.66533i	1.07782	−	0.378564i
$411$		0			0
$412$	−2.00833	+	2.76424i	−0.0989435	+	0.136184i
$413$	−5.78215	+	7.95845i	−0.284521	+	0.391610i
$414$		0			0
$415$	16.8147	+	22.0303i	0.825403	+	1.08142i
$416$	14.0601	+	10.2153i	0.689354	+	0.500845i
$417$		0			0
$418$		−	7.46989i		−	0.365364i
$419$	3.64430	+	11.2160i	0.178036	+	0.547938i	0.999759	−	0.0219489i	$-0.00698712\pi$
$419$	3.64430	+	11.2160i	0.178036	+	0.547938i	−0.821723	+	0.569887i	$0.806987\pi$
$420$		0			0
$421$	−3.12900	+	9.63007i	−0.152498	+	0.469341i	−0.997899	−	0.0647918i	$-0.979362\pi$
$421$	−3.12900	+	9.63007i	−0.152498	+	0.469341i	0.845401	+	0.534133i	$0.179362\pi$
$422$	7.13244	+	2.31747i	0.347202	+	0.112813i
$423$		0			0
$424$	−9.94189			−0.482821
$425$	−12.7013	+	19.3401i	−0.616102	+	0.938133i
$426$		0			0
$427$	24.9425	+	34.3305i	1.20705	+	1.66137i
$428$	3.09938	+	1.00705i	0.149814	+	0.0486775i
$429$		0			0
$430$	−4.87066	−	3.36596i	−0.234884	−	0.162321i
$431$	1.75911	+	5.41397i	0.0847332	+	0.260782i	0.984442	−	0.175708i	$-0.0562214\pi$
$431$	1.75911	+	5.41397i	0.0847332	+	0.260782i	−0.899709	+	0.436490i	$0.856221\pi$
$432$		0			0
$433$	−31.4313	+	10.2126i	−1.51049	+	0.490788i	−0.943057	−	0.332631i	$-0.892064\pi$
$433$	−31.4313	+	10.2126i	−1.51049	+	0.490788i	−0.567434	+	0.823419i	$0.692064\pi$
$434$	−1.60400	−	1.16537i	−0.0769945	−	0.0559397i
$435$		0			0
$436$	5.97597	−	4.34180i	0.286197	−	0.207934i
$437$	−8.15963	+	11.2308i	−0.390328	+	0.537240i
$438$		0			0
$439$	9.27430	−	6.73818i	0.442638	−	0.321596i	−0.344044	−	0.938954i	$-0.611797\pi$
$439$	9.27430	−	6.73818i	0.442638	−	0.321596i	0.786682	+	0.617358i	$0.211797\pi$
$440$	7.53988	+	2.25448i	0.359449	+	0.107478i
$441$		0			0
$442$	−19.5671	+	6.35773i	−0.930711	+	0.302406i
$443$			17.8993i			0.850422i	0.905094	+	0.425211i	$0.139800\pi$
$443$			17.8993i			0.850422i	−0.905094	+	0.425211i	$0.860200\pi$
$444$		0			0
$445$	1.99413	+	1.37808i	0.0945309	+	0.0653272i
$446$	−2.73672	+	8.42275i	−0.129587	+	0.398829i
$447$		0			0
$448$	−14.6512	−	20.1657i	−0.692206	−	0.952740i
$449$	−6.82040			−0.321874			−0.160937	−	0.986965i	$-0.551452\pi$
$449$	−6.82040			−0.321874			−0.160937	+	0.986965i	$0.551452\pi$
$450$		0			0
$451$	−10.8998			−0.513249
$452$	−1.79267	−	2.46740i	−0.0843203	−	0.116057i
$453$		0			0
$454$	−8.63148	+	26.5650i	−0.405096	+	1.24676i
$455$	8.06781	−	26.9819i	0.378225	−	1.26493i
$456$		0			0
$457$			2.76381i			0.129286i	0.997908	+	0.0646429i	$0.0205908\pi$
$457$			2.76381i			0.129286i	−0.997908	+	0.0646429i	$0.979409\pi$
$458$	−1.27813	+	0.415289i	−0.0597230	+	0.0194052i
$459$		0			0
$460$	−2.56294	−	3.35791i	−0.119498	−	0.156563i
$461$	−7.25254	+	5.26928i	−0.337784	+	0.245415i	−0.743726	−	0.668484i	$-0.766943\pi$
$461$	−7.25254	+	5.26928i	−0.337784	+	0.245415i	0.405942	+	0.913899i	$0.366943\pi$
$462$		0			0
$463$	−7.73623	+	10.6480i	−0.359533	+	0.494855i	−0.950019	−	0.312193i	$-0.898936\pi$
$463$	−7.73623	+	10.6480i	−0.359533	+	0.494855i	0.590485	+	0.807048i	$0.298936\pi$
$464$	−7.33412	+	5.32855i	−0.340478	+	0.247372i
$465$		0			0
$466$	2.64494	+	1.92166i	0.122524	+	0.0890191i
$467$	−20.7335	+	6.73671i	−0.959430	+	0.311738i	−0.746542	−	0.665339i	$-0.768287\pi$
$467$	−20.7335	+	6.73671i	−0.959430	+	0.311738i	−0.212889	+	0.977076i	$0.568287\pi$
$468$		0			0
$469$	3.01347	+	9.27450i	0.139149	+	0.428257i
$470$	−11.7196	+	8.94507i	−0.540586	+	0.412605i
$471$		0			0
$472$	−9.28798	−	3.01785i	−0.427514	−	0.138908i
$473$	1.63984	+	2.25704i	0.0753998	+	0.103779i
$474$		0			0
$475$	−24.9463	−	16.3830i	−1.14461	−	0.751705i
$476$	−11.6048			−0.531905
$477$		0			0
$478$	−22.9416	−	7.45417i	−1.04932	−	0.340946i
$479$	13.2102	−	40.6567i	0.603588	−	1.85765i	0.0973673	−	0.995249i	$-0.468958\pi$
$479$	13.2102	−	40.6567i	0.603588	−	1.85765i	0.506221	−	0.862404i	$-0.331042\pi$
$480$		0			0
$481$	14.3710	+	44.2293i	0.655260	+	2.01668i
$482$			14.6475i			0.667174i
$483$		0			0
$484$	6.36221	+	4.62242i	0.289192	+	0.210110i
$485$	−0.238701	−	10.1072i	−0.0108389	−	0.458943i
$486$		0			0
$487$	6.67121	−	9.18213i	0.302301	−	0.416082i	−0.630660	−	0.776059i	$-0.717216\pi$
$487$	6.67121	−	9.18213i	0.302301	−	0.416082i	0.932961	+	0.359978i	$0.117216\pi$
$488$	−24.7619	+	34.0819i	−1.12092	+	1.54281i
$489$		0			0
$490$	−3.50664	+	5.07424i	−0.158414	+	0.229231i
$491$	13.4739	+	9.78936i	0.608068	+	0.441788i	0.848734	−	0.528821i	$-0.177366\pi$
$491$	13.4739	+	9.78936i	0.608068	+	0.441788i	−0.240665	+	0.970608i	$0.577366\pi$
$492$		0			0
$493$			24.4529i			1.10130i
$494$	−8.20067	−	25.2391i	−0.368965	−	1.13556i
$495$		0			0
$496$	0.312405	−	0.961483i	0.0140274	−	0.0431718i
$497$	18.9837	+	6.16817i	0.851534	+	0.276680i
$498$		0			0
$499$	12.2321			0.547584			0.273792	−	0.961789i	$-0.411722\pi$
$499$	12.2321			0.547584			0.273792	+	0.961789i	$0.411722\pi$
$500$	6.95101	−	5.84474i	0.310859	−	0.261385i
$501$		0			0
$502$	−12.0941	−	16.6460i	−0.539784	−	0.742949i
$503$	1.24557	+	0.404709i	0.0555371	+	0.0180451i	0.336654	−	0.941629i	$-0.390705\pi$
$503$	1.24557	+	0.404709i	0.0555371	+	0.0180451i	−0.281117	+	0.959674i	$0.590705\pi$
$504$		0			0
$505$	−4.90048	−	13.9523i	−0.218069	−	0.620868i
$506$	−0.899387	−	2.76803i	−0.0399826	−	0.123054i
$507$		0			0
$508$	−8.77469	+	2.85107i	−0.389314	+	0.126496i
$509$	−14.3453	−	10.4225i	−0.635844	−	0.461968i	0.222576	−	0.974915i	$-0.428553\pi$
$509$	−14.3453	−	10.4225i	−0.635844	−	0.461968i	−0.858420	+	0.512948i	$0.828553\pi$
$510$		0			0
$511$	18.0079	−	13.0835i	0.796622	−	0.578780i
$512$	10.4772	−	14.4206i	0.463029	−	0.637305i
$513$		0			0
$514$	6.22750	−	4.52454i	0.274683	−	0.199569i
$515$	0.222072	+	9.40304i	0.00978565	+	0.414347i
$516$		0			0
$517$	6.60723	−	2.14682i	0.290586	−	0.0944170i
$518$		−	38.3546i		−	1.68521i
$519$		0			0
$520$	27.9506	−	0.660109i	1.22571	−	0.0289477i
$521$	−8.11527	+	24.9762i	−0.355536	+	1.09423i	0.600162	+	0.799879i	$0.295103\pi$
$521$	−8.11527	+	24.9762i	−0.355536	+	1.09423i	−0.955698	+	0.294349i	$0.904897\pi$
$522$		0			0
$523$	1.50281	+	2.06844i	0.0657134	+	0.0904467i	0.840609	−	0.541643i	$-0.182197\pi$
$523$	1.50281	+	2.06844i	0.0657134	+	0.0904467i	−0.774895	+	0.632090i	$0.782197\pi$
$524$	1.68834			0.0737557
$525$		0			0
$526$	22.2711			0.971068
$527$	−1.60285	−	2.20614i	−0.0698213	−	0.0961008i
$528$		0			0
$529$	5.43598	−	16.7302i	0.236347	−	0.727401i
$530$	−6.28367	+	4.79605i	−0.272945	+	0.208327i
$531$		0			0
$532$		−	14.9687i		−	0.648977i
$533$	−36.8278	+	11.9661i	−1.59519	+	0.518308i
$534$		0			0
$535$	8.46408	−	2.97286i	0.365934	−	0.128528i
$536$	−7.83224	+	5.69046i	−0.338301	+	0.245790i
$537$		0			0
$538$	−13.5754	+	18.6849i	−0.585277	+	0.805564i
$539$	2.35138	−	1.70838i	0.101281	−	0.0735849i
$540$		0			0
$541$	−7.59599	−	5.51881i	−0.326577	−	0.237272i	0.412400	−	0.911003i	$-0.364691\pi$
$541$	−7.59599	−	5.51881i	−0.326577	−	0.237272i	−0.738977	+	0.673731i	$0.764691\pi$
$542$	10.3163	−	3.35196i	0.443121	−	0.143979i
$543$		0			0
$544$	−6.09194	−	18.7491i	−0.261190	−	0.803860i
$545$	5.82520	−	19.4818i	0.249524	−	0.834507i
$546$		0			0
$547$	−33.1490	−	10.7708i	−1.41735	−	0.460524i	−0.502590	−	0.864525i	$-0.667619\pi$
$547$	−33.1490	−	10.7708i	−1.41735	−	0.460524i	−0.914759	+	0.404000i	$0.867619\pi$
$548$	−9.26413	−	12.7510i	−0.395744	−	0.544695i
$549$		0			0
$550$	5.85308	−	2.21237i	0.249576	−	0.0943359i
$551$	−31.5411			−1.34370
$552$		0			0
$553$	−36.2244	−	11.7700i	−1.54042	−	0.500512i
$554$	−6.30942	+	19.4184i	−0.268062	+	0.825009i
$555$		0			0
$556$	4.30745	+	13.2570i	0.182676	+	0.562220i
$557$			14.1466i			0.599411i	0.954032	+	0.299705i	$0.0968884\pi$
$557$			14.1466i			0.599411i	−0.954032	+	0.299705i	$0.903112\pi$
$558$		0			0
$559$	8.01849	+	5.82577i	0.339146	+	0.246404i
$560$	−11.3468	−	3.39280i	−0.479492	−	0.143372i
$561$		0			0
$562$	18.6355	−	25.6496i	0.786091	−	1.08196i
$563$	22.4448	−	30.8926i	0.945936	−	1.30197i	−0.00737325	−	0.999973i	$-0.502347\pi$
$563$	22.4448	−	30.8926i	0.945936	−	1.30197i	0.953309	−	0.301996i	$-0.0976530\pi$
$564$		0			0
$565$	−8.04377	−	2.40515i	−0.338404	−	0.101186i
$566$	6.33054	+	4.59941i	0.266092	+	0.193327i
$567$		0			0
$568$			19.8161i			0.831465i
$569$	9.15622	+	28.1799i	0.383849	+	1.18136i	0.937312	+	0.348491i	$0.113306\pi$
$569$	9.15622	+	28.1799i	0.383849	+	1.18136i	−0.553463	+	0.832873i	$0.686694\pi$
$570$		0			0
$571$	10.0895	−	31.0524i	0.422234	−	1.29950i	−0.483385	−	0.875408i	$-0.660593\pi$
$571$	10.0895	−	31.0524i	0.422234	−	1.29950i	0.905618	−	0.424093i	$-0.139407\pi$
$572$	−3.61901	−	1.17589i	−0.151318	−	0.0491663i
$573$		0			0
$574$	31.9362			1.33299
$575$	−11.2166	−	3.06729i	−0.467764	−	0.127915i
$576$		0			0
$577$	−13.3094	−	18.3188i	−0.554077	−	0.762622i	0.436481	−	0.899713i	$-0.356225\pi$
$577$	−13.3094	−	18.3188i	−0.554077	−	0.762622i	−0.990558	+	0.137091i	$0.956225\pi$
$578$	4.57551	+	1.48667i	0.190316	+	0.0618374i
$579$		0			0
$580$	2.74956	−	9.19559i	0.114169	−	0.381826i
$581$	11.8241	+	36.3909i	0.490547	+	1.50975i
$582$		0			0
$583$	3.54257	−	1.15105i	0.146718	−	0.0476717i
$584$	17.8775	+	12.9888i	0.739776	+	0.537479i
$585$		0			0
$586$	1.58549	−	1.15193i	0.0654960	−	0.0475856i
$587$	−24.4323	+	33.6281i	−1.00843	+	1.38798i	−0.0884196	+	0.996083i	$0.528182\pi$
$587$	−24.4323	+	33.6281i	−1.00843	+	1.38798i	−0.920008	+	0.391899i	$0.871818\pi$
$588$		0			0
$589$	2.84564	−	2.06748i	0.117252	−	0.0851889i
$590$	−7.32620	+	2.57320i	−0.301615	+	0.105937i
$591$		0			0
$592$	18.6000	−	6.04350i	0.764454	−	0.248386i
$593$			2.09050i			0.0858465i	0.999078	+	0.0429233i	$0.0136671\pi$
$593$			2.09050i			0.0858465i	−0.999078	+	0.0429233i	$0.986333\pi$
$594$		0			0
$595$	−25.3939	+	19.3821i	−1.04105	+	0.794587i
$596$	0.0527445	−	0.162331i	0.00216050	−	0.00664933i
$597$		0			0
$598$	−6.07765	−	8.36516i	−0.248533	−	0.342077i
$599$	17.9768			0.734511			0.367255	−	0.930120i	$-0.380298\pi$
$599$	17.9768			0.734511			0.367255	+	0.930120i	$0.380298\pi$
$600$		0			0
$601$	−1.11000			−0.0452778			−0.0226389	−	0.999744i	$-0.507207\pi$
$601$	−1.11000			−0.0452778			−0.0226389	+	0.999744i	$0.507207\pi$
$602$	−4.80471	−	6.61312i	−0.195826	−	0.269531i
$603$		0			0
$604$	−1.01892	+	3.13591i	−0.0414593	+	0.127599i
$605$	21.6422	−	0.511124i	0.879881	−	0.0207802i
$606$		0			0
$607$		−	12.2310i		−	0.496441i	−0.968704	−	0.248220i	$-0.920154\pi$
$607$		−	12.2310i		−	0.496441i	0.968704	−	0.248220i	$-0.0798457\pi$
$608$	24.1839	−	7.85783i	0.980788	−	0.318677i
$609$		0			0
$610$	0.790851	+	33.4865i	0.0320206	+	1.35583i
$611$	19.9675	−	14.5072i	0.807798	−	0.586899i
$612$		0			0
$613$	7.62804	−	10.4991i	0.308094	−	0.424055i	−0.626692	−	0.779267i	$-0.715591\pi$
$613$	7.62804	−	10.4991i	0.308094	−	0.424055i	0.934786	+	0.355213i	$0.115591\pi$
$614$	5.28008	−	3.83620i	0.213087	−	0.154817i
$615$		0			0
$616$	8.79028	+	6.38651i	0.354171	+	0.257320i
$617$	19.4891	−	6.33241i	0.784603	−	0.254933i	0.110799	−	0.993843i	$-0.464659\pi$
$617$	19.4891	−	6.33241i	0.784603	−	0.254933i	0.673804	+	0.738910i	$0.264659\pi$
$618$		0			0
$619$	12.6838	+	39.0367i	0.509804	+	1.56902i	0.792541	+	0.609819i	$0.208758\pi$
$619$	12.6838	+	39.0367i	0.509804	+	1.56902i	−0.282737	+	0.959198i	$0.591242\pi$
$620$	0.354693	+	1.00985i	0.0142448	+	0.0405567i
$621$		0			0
$622$	24.7391	+	8.03822i	0.991948	+	0.322303i
$623$	1.96713	+	2.70752i	0.0788114	+	0.108475i
$624$		0			0
$625$	5.44863	−	24.3990i	0.217945	−	0.975961i
$626$	6.27641			0.250856
$627$		0			0
$628$	0.340176	+	0.110530i	0.0135745	+	0.00441062i
$629$	16.3015	−	50.1709i	0.649984	−	2.00045i
$630$		0			0
$631$	4.35319	+	13.3977i	0.173298	+	0.533356i	0.999552	−	0.0299421i	$-0.00953228\pi$
$631$	4.35319	+	13.3977i	0.173298	+	0.533356i	−0.826254	+	0.563298i	$0.809532\pi$
$632$		−	37.8128i		−	1.50411i
$633$		0			0
$634$	10.7989	+	7.84589i	0.428881	+	0.311600i
$635$	−14.4392	+	20.8941i	−0.573002	+	0.829155i
$636$		0			0
$637$	6.06926	−	8.35362i	0.240473	−	0.330983i
$638$	3.88695	−	5.34992i	0.153886	−	0.211806i
$639$		0			0
$640$	−0.0147254	−	0.623510i	−0.000582074	−	0.0246464i
$641$	−23.0050	−	16.7141i	−0.908644	−	0.660168i	0.0320278	−	0.999487i	$-0.489803\pi$
$641$	−23.0050	−	16.7141i	−0.908644	−	0.660168i	−0.940671	+	0.339319i	$0.889803\pi$
$642$		0			0
$643$			10.8408i			0.427521i	0.976886	+	0.213761i	$0.0685713\pi$
$643$			10.8408i			0.427521i	−0.976886	+	0.213761i	$0.931429\pi$
$644$	−1.80226	−	5.54678i	−0.0710189	−	0.218574i
$645$		0			0
$646$	−9.30232	+	28.6296i	−0.365995	+	1.12642i
$647$	32.9435	+	10.7040i	1.29514	+	0.420817i	0.873889	−	0.486126i	$-0.161590\pi$
$647$	32.9435	+	10.7040i	1.29514	+	0.420817i	0.421253	+	0.906943i	$0.361590\pi$
$648$		0			0
$649$	3.65897			0.143627
$650$	17.3474	−	13.9008i	0.680422	−	0.545234i
$651$		0			0
$652$	1.54747	+	2.12991i	0.0606037	+	0.0834138i
$653$	−3.95170	−	1.28398i	−0.154642	−	0.0502462i	0.230673	−	0.973031i	$-0.425907\pi$
$653$	−3.95170	−	1.28398i	−0.154642	−	0.0502462i	−0.385315	+	0.922785i	$0.625907\pi$
$654$		0			0
$655$	3.69448	−	2.81983i	0.144355	−	0.110180i
$656$	5.03216	+	15.4874i	0.196473	+	0.604681i
$657$		0			0
$658$	−19.3591	+	6.29016i	−0.754698	+	0.245216i
$659$	3.24759	+	2.35951i	0.126508	+	0.0919135i	0.649240	−	0.760584i	$-0.275087\pi$
$659$	3.24759	+	2.35951i	0.126508	+	0.0919135i	−0.522732	+	0.852497i	$0.675087\pi$
$660$		0			0
$661$	−15.9107	+	11.5598i	−0.618853	+	0.449623i	−0.852521	−	0.522694i	$-0.824927\pi$
$661$	−15.9107	+	11.5598i	−0.618853	+	0.449623i	0.233668	+	0.972316i	$0.424927\pi$
$662$	3.86205	−	5.31566i	0.150103	−	0.206599i
$663$		0			0
$664$	−30.7318	+	22.3279i	−1.19262	+	0.866492i
$665$	−25.0004	−	32.7549i	−0.969474	−	1.27018i
$666$		0			0
$667$	−11.6878	+	3.79760i	−0.452554	+	0.147044i
$668$			12.9646i			0.501616i
$669$		0			0
$670$	−2.20516	+	7.37493i	−0.0851929	+	0.284918i
$671$	4.87744	−	15.0112i	0.188292	−	0.579502i
$672$		0			0
$673$	−24.3615	−	33.5308i	−0.939068	−	1.29252i	−0.956215	−	0.292663i	$-0.905458\pi$
$673$	−24.3615	−	33.5308i	−0.939068	−	1.29252i	0.0171473	−	0.999853i	$-0.494542\pi$
$674$	−6.02761			−0.232175
$675$		0			0
$676$	−2.95892			−0.113804
$677$	10.6881	+	14.7109i	0.410777	+	0.565386i	0.963408	−	0.268040i	$-0.0863760\pi$
$677$	10.6881	+	14.7109i	0.410777	+	0.565386i	−0.552631	+	0.833426i	$0.686376\pi$
$678$		0			0
$679$	4.31339	−	13.2753i	0.165533	−	0.509457i
$680$	−26.0903	−	18.0302i	−1.00052	−	0.691425i
$681$		0			0
$682$			0.737453i			0.0282385i
$683$	−27.0597	+	8.79224i	−1.03541	+	0.336426i	−0.776928	−	0.629590i	$-0.783223\pi$
$683$	−27.0597	+	8.79224i	−1.03541	+	0.336426i	−0.258484	+	0.966015i	$0.583223\pi$
$684$		0			0
$685$	−41.5684	−	12.4293i	−1.58825	−	0.474899i
$686$	12.1643	−	8.83786i	0.464434	−	0.337431i
$687$		0			0
$688$	2.44994	−	3.37206i	0.0934032	−	0.128558i
$689$	10.7059	−	7.77828i	0.407862	−	0.296329i
$690$		0			0
$691$	−19.7541	−	14.3522i	−0.751483	−	0.545984i	0.144803	−	0.989460i	$-0.453745\pi$
$691$	−19.7541	−	14.3522i	−0.751483	−	0.545984i	−0.896286	+	0.443476i	$0.853745\pi$
$692$	−0.434003	+	0.141016i	−0.0164983	+	0.00536063i
$693$		0			0
$694$	−8.73740	−	26.8910i	−0.331667	−	1.02077i
$695$	31.5671	+	21.8150i	1.19741	+	0.827490i
$696$		0			0
$697$	41.7751	+	13.5736i	1.58235	+	0.514135i
$698$	12.1726	+	16.7542i	0.460741	+	0.634155i
$699$		0			0
$700$	11.7288	−	4.43332i	0.443309	−	0.167564i
$701$	25.0371			0.945638			0.472819	−	0.881159i	$-0.343236\pi$
$701$	25.0371			0.945638			0.472819	+	0.881159i	$0.343236\pi$
$702$		0			0
$703$	64.7142	+	21.0269i	2.44074	+	0.793045i
$704$	−2.86501	+	8.81759i	−0.107979	+	0.332325i
$705$		0			0
$706$	−2.75862	−	8.49016i	−0.103822	−	0.319531i
$707$		−	20.4170i		−	0.767858i
$708$		0			0
$709$	29.5804	+	21.4914i	1.11091	+	0.807126i	0.982807	−	0.184634i	$-0.0591101\pi$
$709$	29.5804	+	21.4914i	1.11091	+	0.807126i	0.128107	+	0.991760i	$0.459110\pi$
$710$	9.55944	+	12.5246i	0.358760	+	0.470038i
$711$		0			0
$712$	−1.95289	+	2.68792i	−0.0731876	+	0.100734i
$713$	0.805546	−	1.10874i	0.0301679	−	0.0415226i
$714$		0			0
$715$	−9.88314	+	3.47128i	−0.369609	+	0.129818i
$716$	−10.4743	−	7.60999i	−0.391441	−	0.284399i
$717$		0			0
$718$			29.1915i			1.08942i
$719$	−2.23596	−	6.88157i	−0.0833872	−	0.256639i	0.900667	−	0.434511i	$-0.143079\pi$
$719$	−2.23596	−	6.88157i	−0.0833872	−	0.256639i	−0.984054	+	0.177872i	$0.943079\pi$
$720$		0			0
$721$	−4.01289	+	12.3504i	−0.149448	+	0.459954i
$722$	−17.2355	−	5.60014i	−0.641437	−	0.208416i
$723$		0			0
$724$	−17.4542			−0.648679
$725$	−9.34161	−	24.7143i	−0.346939	−	0.917865i
$726$		0			0
$727$	−7.82337	−	10.7680i	−0.290153	−	0.399361i	0.638911	−	0.769281i	$-0.279385\pi$
$727$	−7.82337	−	10.7680i	−0.290153	−	0.399361i	−0.929064	+	0.369920i	$0.879385\pi$
$728$	36.7117	+	11.9283i	1.36062	+	0.442094i
$729$		0			0
$730$	17.5652	−	0.414837i	0.650116	−	0.0153538i
$731$	−3.47424	−	10.6926i	−0.128499	−	0.395480i
$732$		0			0
$733$	−27.3709	+	8.89333i	−1.01097	+	0.328483i	−0.767239	−	0.641361i	$-0.778370\pi$
$733$	−27.3709	+	8.89333i	−1.01097	+	0.328483i	−0.243727	+	0.969844i	$0.578370\pi$
$734$	16.6226	+	12.0771i	0.613553	+	0.445772i
$735$		0			0
$736$	8.01545	−	5.82357i	0.295454	−	0.214660i
$737$	2.13202	−	2.93447i	0.0785339	−	0.108093i
$738$		0			0
$739$	32.6202	−	23.7000i	1.19995	−	0.871818i	0.205674	−	0.978621i	$-0.434061\pi$
$739$	32.6202	−	23.7000i	1.19995	−	0.871818i	0.994280	+	0.106803i	$0.0340614\pi$
$740$	−11.7716	+	17.0340i	−0.432733	+	0.626181i
$741$		0			0
$742$	−10.3797	+	3.37258i	−0.381051	+	0.123811i
$743$			27.8114i			1.02030i	0.860085	+	0.510151i	$0.170411\pi$
$743$			27.8114i			1.02030i	−0.860085	+	0.510151i	$0.829589\pi$
$744$		0			0
$745$	−0.155704	−	0.443309i	−0.00570457	−	0.0162416i
$746$	−6.01061	+	18.4988i	−0.220064	+	0.677288i
$747$		0			0
$748$	2.53714	+	3.49207i	0.0927670	+	0.127683i
$749$	12.3859			0.452569
$750$		0			0
$751$	−11.4124			−0.416443			−0.208221	−	0.978082i	$-0.566767\pi$
$751$	−11.4124			−0.416443			−0.208221	+	0.978082i	$0.566767\pi$
$752$	−6.10080	−	8.39703i	−0.222473	−	0.306208i
$753$		0			0
$754$	7.25980	−	22.3434i	0.264386	−	0.813698i
$755$	3.00790	+	8.56386i	0.109469	+	0.311671i
$756$		0			0
$757$			13.7637i			0.500251i	0.968213	+	0.250126i	$0.0804719\pi$
$757$			13.7637i			0.500251i	−0.968213	+	0.250126i	$0.919528\pi$
$758$	−13.0237	+	4.23166i	−0.473042	+	0.153701i
$759$		0			0
$760$	23.2566	−	33.6532i	0.843607	−	1.22073i
$761$	−11.9257	+	8.66451i	−0.432305	+	0.314088i	−0.782570	−	0.622562i	$-0.786092\pi$
$761$	−11.9257	+	8.66451i	−0.432305	+	0.314088i	0.350265	+	0.936651i	$0.386092\pi$
$762$		0			0
$763$	16.5017	−	22.7126i	0.597400	−	0.822251i
$764$	−12.0877	+	8.78224i	−0.437318	+	0.317730i
$765$		0			0
$766$	6.64559	+	4.82830i	0.240115	+	0.174454i
$767$	12.3628	−	4.01692i	0.446395	−	0.145043i
$768$		0			0
$769$	0.753239	+	2.31823i	0.0271625	+	0.0835976i	0.963719	−	0.266920i	$-0.0860058\pi$
$769$	0.753239	+	2.31823i	0.0271625	+	0.0835976i	−0.936556	+	0.350517i	$0.886006\pi$
$770$	8.63671	−	0.203973i	0.311245	−	0.00735069i
$771$		0			0
$772$	1.56457	+	0.508359i	0.0563101	+	0.0182963i
$773$	−14.8910	−	20.4957i	−0.535592	−	0.737180i	0.452377	−	0.891827i	$-0.350576\pi$
$773$	−14.8910	−	20.4957i	−0.535592	−	0.737180i	−0.987970	+	0.154647i	$0.950576\pi$
$774$		0			0
$775$	2.46278	+	1.61739i	0.0884658	+	0.0580983i
$776$	13.8574			0.497450
$777$		0			0
$778$	14.2341	+	4.62493i	0.510317	+	0.165812i
$779$	−17.5082	+	53.8846i	−0.627296	+	1.93062i
$780$		0			0
$781$	−2.29427	−	7.06103i	−0.0820953	−	0.252664i
$782$			11.7289i			0.419426i
$783$		0			0
$784$	−3.51299	−	2.55234i	−0.125464	−	0.0911550i
$785$	0.928985	−	0.326289i	0.0331569	−	0.0116458i
$786$		0			0
$787$	−22.7167	+	31.2669i	−0.809763	+	1.11454i	0.181597	+	0.983373i	$0.441873\pi$
$787$	−22.7167	+	31.2669i	−0.809763	+	1.11454i	−0.991360	+	0.131170i	$0.958127\pi$
$788$	−5.51242	+	7.58719i	−0.196372	+	0.270283i
$789$		0			0
$790$	−18.2412	−	23.8992i	−0.648992	−	0.850295i
$791$	−9.37774	−	6.81333i	−0.333434	−	0.242254i
$792$		0			0
$793$		−	56.0741i		−	1.99125i
$794$	−4.37879	−	13.4765i	−0.155397	−	0.478264i
$795$		0			0
$796$	−5.76775	+	17.7513i	−0.204432	+	0.629178i
$797$	−49.5519	−	16.1004i	−1.75522	−	0.570306i	−0.758533	−	0.651635i	$-0.774083\pi$
$797$	−49.5519	−	16.1004i	−1.75522	−	0.570306i	−0.996687	+	0.0813294i	$0.974083\pi$
$798$		0			0
$799$	−27.9968			−0.990454
$800$	13.3197	+	16.6222i	0.470921	+	0.587684i
$801$		0			0
$802$	4.14485	+	5.70490i	0.146360	+	0.201447i
$803$	−7.87407	−	2.55844i	−0.277870	−	0.0902854i
$804$		0			0
$805$	−13.2078	−	9.12752i	−0.465515	−	0.321703i
$806$	0.809598	+	2.49169i	0.0285169	+	0.0877659i
$807$		0			0
$808$	19.2771	−	6.26350i	0.678166	−	0.220349i
$809$	−25.7217	−	18.6879i	−0.904328	−	0.657033i	0.0352461	−	0.999379i	$-0.488778\pi$
$809$	−25.7217	−	18.6879i	−0.904328	−	0.657033i	−0.939574	+	0.342346i	$0.888778\pi$
$810$		0			0
$811$	25.1777	−	18.2927i	0.884108	−	0.642342i	−0.0502268	−	0.998738i	$-0.515994\pi$
$811$	25.1777	−	18.2927i	0.884108	−	0.642342i	0.934335	+	0.356395i	$0.115994\pi$
$812$	7.78896	−	10.7206i	0.273339	−	0.376219i
$813$		0			0
$814$	−11.5415	+	8.38541i	−0.404530	+	0.293908i
$815$	6.94354	+	2.07618i	0.243222	+	0.0727253i
$816$		0			0
$817$	13.7921	−	4.48133i	0.482525	−	0.156782i
$818$		−	1.21188i		−	0.0423725i
$819$		0			0
$820$	−14.1834	−	9.80171i	−0.495307	−	0.342290i
$821$	14.5319	−	44.7247i	0.507168	−	1.56090i	−0.289927	−	0.957049i	$-0.593631\pi$
$821$	14.5319	−	44.7247i	0.507168	−	1.56090i	0.797095	−	0.603854i	$-0.206369\pi$
$822$		0			0
$823$	16.6593	+	22.9296i	0.580708	+	0.799276i	0.993773	−	0.111426i	$-0.0355418\pi$
$823$	16.6593	+	22.9296i	0.580708	+	0.799276i	−0.413065	+	0.910702i	$0.635542\pi$
$824$	−12.8920			−0.449113
$825$		0			0
$826$	−10.7208			−0.373023
$827$	−8.32775	−	11.4622i	−0.289584	−	0.398579i	0.639295	−	0.768962i	$-0.279226\pi$
$827$	−8.32775	−	11.4622i	−0.289584	−	0.398579i	−0.928879	+	0.370383i	$0.879226\pi$
$828$		0			0
$829$	−0.468647	+	1.44235i	−0.0162768	+	0.0500948i	−0.958865	−	0.283862i	$-0.908384\pi$
$829$	−0.468647	+	1.44235i	−0.0162768	+	0.0500948i	0.942588	+	0.333957i	$0.108384\pi$
$830$	−8.65252	+	28.9374i	−0.300333	+	1.00443i
$831$		0			0
$832$			32.9379i			1.14192i
$833$	−11.1395	+	3.61944i	−0.385961	+	0.125406i
$834$		0			0
$835$	21.6532	+	28.3695i	0.749339	+	0.981766i
$836$	−4.50433	+	3.27259i	−0.155786	+	0.113185i
$837$		0			0
$838$	−7.55449	+	10.3979i	−0.260965	+	0.359188i
$839$	−8.48811	+	6.16697i	−0.293042	+	0.212908i	−0.724586	−	0.689184i	$-0.757969\pi$
$839$	−8.48811	+	6.16697i	−0.293042	+	0.212908i	0.431544	+	0.902092i	$0.357969\pi$
$840$		0			0
$841$	0.871777	+	0.633383i	0.0300613	+	0.0218408i
$842$	−10.4950	+	3.41004i	−0.361683	+	0.117518i
$843$		0			0
$844$	−1.72732	−	5.31614i	−0.0594568	−	0.182989i
$845$	−6.47477	+	4.94191i	−0.222739	+	0.170007i
$846$		0			0
$847$	28.4259	+	9.23615i	0.976727	+	0.317358i
$848$	−3.27104	−	4.50221i	−0.112328	−	0.154606i
$849$		0			0
$850$	−25.1880	+	1.19040i	−0.863941	+	0.0408302i
$851$	26.5120			0.908820
$852$		0			0
$853$	−14.1300	−	4.59110i	−0.483801	−	0.157196i	0.0569538	−	0.998377i	$-0.481861\pi$
$853$	−14.1300	−	4.59110i	−0.483801	−	0.157196i	−0.540755	+	0.841180i	$0.681861\pi$
$854$	−14.2909	+	43.9828i	−0.489024	+	1.50506i
$855$		0			0
$856$	3.79973	+	11.6944i	0.129872	+	0.399705i
$857$		−	26.4088i		−	0.902109i	−0.892496	−	0.451054i	$-0.851048\pi$
$857$		−	26.4088i		−	0.902109i	0.892496	−	0.451054i	$-0.148952\pi$
$858$		0			0
$859$	−7.38643	−	5.36656i	−0.252022	−	0.183105i	0.454601	−	0.890695i	$-0.349782\pi$
$859$	−7.38643	−	5.36656i	−0.252022	−	0.183105i	−0.706622	+	0.707591i	$0.749782\pi$
$860$	0.104190	+	4.41164i	0.00355284	+	0.150436i
$861$		0			0
$862$	−3.64656	+	5.01906i	−0.124202	+	0.170950i
$863$	−7.33532	+	10.0962i	−0.249697	+	0.343679i	−0.915405	−	0.402534i	$-0.868130\pi$
$863$	−7.33532	+	10.0962i	−0.249697	+	0.343679i	0.665708	+	0.746212i	$0.268130\pi$
$864$		0			0
$865$	−0.714175	+	1.03344i	−0.0242827	+	0.0351379i
$866$	−29.1386	−	21.1704i	−0.990168	−	0.719399i
$867$		0			0
$868$			1.47776i			0.0501586i
$869$	4.37789	+	13.4738i	0.148510	+	0.457066i
$870$		0			0
$871$	3.98205	−	12.2555i	0.134927	−	0.415262i
$872$	26.5069	+	8.61262i	0.897638	+	0.291660i
$873$		0			0
$874$	−15.1289			−0.511741
$875$	18.2609	−	29.2903i	0.617332	−	0.990194i
$876$		0			0
$877$	−23.9888	−	33.0177i	−0.810043	−	1.11493i	−0.991317	−	0.131496i	$-0.958022\pi$
$877$	−23.9888	−	33.0177i	−0.810043	−	1.11493i	0.181273	−	0.983433i	$-0.441978\pi$
$878$	11.8819	+	3.86065i	0.400993	+	0.130291i
$879$		0			0
$880$	1.45979	+	4.15621i	0.0492097	+	0.140106i
$881$	1.12544	+	3.46374i	0.0379170	+	0.116696i	0.968223	−	0.250087i	$-0.0804591\pi$
$881$	1.12544	+	3.46374i	0.0379170	+	0.116696i	−0.930306	+	0.366783i	$0.880459\pi$
$882$		0			0
$883$	0.316564	−	0.102858i	0.0106532	−	0.00346144i	−0.303686	−	0.952772i	$-0.598217\pi$
$883$	0.316564	−	0.102858i	0.0106532	−	0.00346144i	0.314339	+	0.949311i	$0.398217\pi$
$884$	12.4061	+	9.01357i	0.417263	+	0.303159i
$885$		0			0
$886$	−15.7815	+	11.4659i	−0.530190	+	0.385206i
$887$	0.671685	−	0.924496i	0.0225530	−	0.0310415i	−0.797592	−	0.603198i	$-0.793893\pi$
$887$	0.671685	−	0.924496i	0.0225530	−	0.0310415i	0.820145	+	0.572156i	$0.193893\pi$
$888$		0			0
$889$	−28.3688	+	20.6111i	−0.951459	+	0.691276i
$890$	0.0623716	+	2.64096i	0.00209070	+	0.0885252i
$891$		0			0
$892$	6.27787	−	2.03980i	0.210199	−	0.0682977i
$893$		−	36.1123i		−	1.20845i
$894$		0			0
$895$	−35.6300	+	0.841475i	−1.19098	+	0.0281274i
$896$	0.266092	−	0.818948i	0.00888953	−	0.0273591i
$897$		0			0
$898$	−4.36901	−	6.01342i	−0.145796	−	0.200671i
$899$	3.11385			0.103853
$900$		0			0
$901$	−15.0109			−0.500086
$902$	−6.98216	−	9.61012i	−0.232481	−	0.319982i
$903$		0			0
$904$	3.55604	−	10.9444i	0.118272	−	0.364004i
$905$	−38.1936	+	29.1515i	−1.26960	+	0.969030i
$906$		0			0
$907$		−	18.4202i		−	0.611632i	−0.952091	−	0.305816i	$-0.901071\pi$
$907$		−	18.4202i		−	0.611632i	0.952091	−	0.305816i	$-0.0989293\pi$
$908$	19.8001	−	6.43345i	0.657090	−	0.213502i
$909$		0			0
$910$	28.9576	−	10.1708i	0.959933	−	0.337159i
$911$	14.7651	−	10.7274i	0.489188	−	0.355416i	−0.315684	−	0.948864i	$-0.602234\pi$
$911$	14.7651	−	10.7274i	0.489188	−	0.355416i	0.804872	+	0.593449i	$0.202234\pi$
$912$		0			0
$913$	8.36551	−	11.5141i	0.276858	−	0.381062i
$914$	−2.43681	+	1.77044i	−0.0806024	+	0.0585611i
$915$		0			0
$916$	0.810372	+	0.588770i	0.0267754	+	0.0194535i
$917$	6.10275	−	1.98290i	0.201531	−	0.0654812i
$918$		0			0
$919$	−3.34919	−	10.3078i	−0.110480	−	0.340022i	0.880498	−	0.474050i	$-0.157209\pi$
$919$	−3.34919	−	10.3078i	−0.110480	−	0.340022i	−0.990977	+	0.134029i	$0.957209\pi$
$920$	4.56603	−	15.2706i	0.150538	−	0.503457i
$921$		0			0
$922$	−9.29166	−	3.01904i	−0.306005	−	0.0994269i
$923$	−15.5036	−	21.3389i	−0.510308	−	0.702378i
$924$		0			0
$925$	2.69076	+	56.9348i	0.0884717	+	1.87200i
$926$	−14.3438			−0.471368
$927$		0			0
$928$	21.4093	+	6.95631i	0.702795	+	0.228352i
$929$	−16.1768	+	49.7870i	−0.530743	+	1.63346i	0.221930	+	0.975063i	$0.428764\pi$
$929$	−16.1768	+	49.7870i	−0.530743	+	1.63346i	−0.752673	+	0.658395i	$0.771236\pi$
$930$		0			0
$931$	−4.66862	−	14.3685i	−0.153008	−	0.470910i
$932$		−	2.43678i		−	0.0798193i
$933$		0			0
$934$	−19.2211	−	13.9649i	−0.628933	−	0.456947i
$935$	11.3842	+	3.40397i	0.372303	+	0.111322i
$936$		0			0
$937$	−0.000771322		0.00106163i	−2.51980e−5		3.46821e-5i	−0.809030	−	0.587768i	$-0.800007\pi$
$937$	−0.000771322		0.00106163i	−2.51980e−5		3.46821e-5i	0.809004	+	0.587803i	$0.200007\pi$
$938$	−6.24680	+	8.59798i	−0.203965	+	0.280734i
$939$		0			0
$940$	10.5283	+	3.14804i	0.343394	+	0.102678i
$941$	−17.5737	−	12.7680i	−0.572885	−	0.416225i	0.263267	−	0.964723i	$-0.415200\pi$
$941$	−17.5737	−	12.7680i	−0.572885	−	0.416225i	−0.836152	+	0.548498i	$0.815200\pi$
$942$		0			0
$943$			22.0754i			0.718874i
$944$	−1.68926	−	5.19900i	−0.0549807	−	0.169213i
$945$		0			0
$946$	−0.939548	+	2.89163i	−0.0305473	+	0.0940151i
$947$	32.2661	+	10.4839i	1.04851	+	0.340681i	0.782083	−	0.623174i	$-0.214157\pi$
$947$	32.2661	+	10.4839i	1.04851	+	0.340681i	0.266426	+	0.963855i	$0.414157\pi$
$948$		0			0
$949$	−29.4134			−0.954800
$950$	−1.53546	−	32.4893i	−0.0498169	−	1.05409i
$951$		0			0
$952$	−25.7370	−	35.4240i	−0.834142	−	1.14810i
$953$	−7.89670	−	2.56579i	−0.255799	−	0.0831142i	0.178310	−	0.983974i	$-0.442937\pi$
$953$	−7.89670	−	2.56579i	−0.255799	−	0.0831142i	−0.434109	+	0.900860i	$0.642937\pi$
$954$		0			0
$955$	−11.7827	+	39.4061i	−0.381281	+	1.27515i
$956$	5.55594	+	17.0994i	0.179692	+	0.553035i
$957$		0			0
$958$	44.3085	−	14.3967i	1.43154	−	0.465136i
$959$	−48.4620	−	35.2097i	−1.56492	−	1.13698i
$960$		0			0
$961$	24.7986	−	18.0172i	0.799955	−	0.581201i
$962$	−29.7904	+	41.0030i	−0.960482	+	1.32199i
$963$		0			0
$964$	8.83240	−	6.41711i	0.284472	−	0.206681i
$965$	4.27268	−	1.50070i	0.137542	−	0.0483093i
$966$		0			0
$967$	−26.4313	+	8.58804i	−0.849972	+	0.276173i	−0.701434	−	0.712734i	$-0.747457\pi$
$967$	−26.4313	+	8.58804i	−0.849972	+	0.276173i	−0.148538	+	0.988907i	$0.547457\pi$
$968$			29.6724i			0.953707i
$969$		0			0
$970$	8.75840	−	6.68490i	0.281215	−	0.214639i
$971$	9.59377	−	29.5266i	0.307879	−	0.947554i	−0.670708	−	0.741721i	$-0.734010\pi$
$971$	9.59377	−	29.5266i	0.307879	−	0.947554i	0.978587	−	0.205833i	$-0.0659902\pi$
$972$		0			0
$973$	31.1397	+	42.8601i	0.998292	+	1.37403i
$974$	12.3692			0.396333
$975$		0			0
$976$	−23.5811			−0.754814
$977$	26.0928	+	35.9137i	0.834783	+	1.14898i	0.987014	+	0.160635i	$0.0513543\pi$
$977$	26.0928	+	35.9137i	0.834783	+	1.14898i	−0.152231	+	0.988345i	$0.548646\pi$
$978$		0			0
$979$	0.384667	−	1.18388i	0.0122940	−	0.0378370i
$980$	4.59603	−	0.108544i	0.146815	−	0.00346733i
$981$		0			0
$982$			18.1506i			0.579208i
$983$	41.6427	−	13.5305i	1.32820	−	0.431557i	0.442894	−	0.896574i	$-0.353952\pi$
$983$	41.6427	−	13.5305i	1.32820	−	0.431557i	0.885302	+	0.465017i	$0.153952\pi$
$984$		0			0
$985$	0.609536	+	25.8092i	0.0194214	+	0.822349i
$986$	−21.5597	+	15.6640i	−0.686600	+	0.498844i
$987$		0			0
$988$	−11.6264	+	16.0023i	−0.369884	+	0.509102i
$989$	4.57121	−	3.32118i	0.145356	−	0.105607i
$990$		0			0
$991$	−27.8586	−	20.2404i	−0.884957	−	0.642959i	0.0496015	−	0.998769i	$-0.484205\pi$
$991$	−27.8586	−	20.2404i	−0.884957	−	0.642959i	−0.934558	+	0.355810i	$0.884205\pi$
$992$	−2.38752	+	0.775752i	−0.0758039	+	0.0246302i
$993$		0			0
$994$	6.72219	+	20.6888i	0.213215	+	0.656208i
$995$	17.0267	+	48.4770i	0.539782	+	1.53682i
$996$		0			0
$997$	18.4401	+	5.99154i	0.584002	+	0.189754i	0.586093	−	0.810244i	$-0.300665\pi$
$997$	18.4401	+	5.99154i	0.584002	+	0.189754i	−0.00209042	+	0.999998i	$0.500665\pi$
$998$	7.83564	+	10.7848i	0.248033	+	0.341388i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.m.b.64.3		16
3.2	odd	2		75.2.i.a.64.2	yes	16
15.2	even	4		375.2.g.e.301.3		16
15.8	even	4		375.2.g.d.301.2		16
15.14	odd	2		375.2.i.c.199.3		16
25.3	odd	20		5625.2.a.t.1.4		8
25.9	even	10	inner	225.2.m.b.109.3		16
25.22	odd	20		5625.2.a.bd.1.5		8
75.29	odd	10		1875.2.b.h.1249.6		16
75.38	even	20		375.2.g.d.76.2		16
75.41	odd	10		375.2.i.c.49.3		16
75.47	even	20		1875.2.a.m.1.4		8
75.53	even	20		1875.2.a.p.1.5		8
75.59	odd	10		75.2.i.a.34.2	✓	16
75.62	even	20		375.2.g.e.76.3		16
75.71	odd	10		1875.2.b.h.1249.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.34.2	✓	16	75.59	odd	10
75.2.i.a.64.2	yes	16	3.2	odd	2
225.2.m.b.64.3		16	1.1	even	1	trivial
225.2.m.b.109.3		16	25.9	even	10	inner
375.2.g.d.76.2		16	75.38	even	20
375.2.g.d.301.2		16	15.8	even	4
375.2.g.e.76.3		16	75.62	even	20
375.2.g.e.301.3		16	15.2	even	4
375.2.i.c.49.3		16	75.41	odd	10
375.2.i.c.199.3		16	15.14	odd	2
1875.2.a.m.1.4		8	75.47	even	20
1875.2.a.p.1.5		8	75.53	even	20
1875.2.b.h.1249.6		16	75.29	odd	10
1875.2.b.h.1249.11		16	75.71	odd	10
5625.2.a.t.1.4		8	25.3	odd	20
5625.2.a.bd.1.5		8	25.22	odd	20

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.640580 + 0.881682i) q^{2} +(0.251013 - 0.772537i) q^{4} +(-0.741001 - 2.10972i) q^{5} -3.08724i q^{7} +(2.91489 - 0.947104i) q^{8} +O(q^{10})\)	\(q+(0.640580 + 0.881682i) q^{2} +(0.251013 - 0.772537i) q^{4} +(-0.741001 - 2.10972i) q^{5} -3.08724i q^{7} +(2.91489 - 0.947104i) q^{8} +(1.38543 - 2.00477i) q^{10} +(-0.929002 + 0.674959i) q^{11} +(-2.39789 + 3.30042i) q^{13} +(2.72197 - 1.97763i) q^{14} +(1.38794 + 1.00840i) q^{16} +(4.40109 - 1.43000i) q^{17} +(1.84452 + 5.67685i) q^{19} +(-1.81584 + 0.0428847i) q^{20} +(-1.19020 - 0.386719i) q^{22} +(1.36700 + 1.88152i) q^{23} +(-3.90184 + 3.12661i) q^{25} -4.44596 q^{26} +(-2.38501 - 0.774937i) q^{28} +(-1.63290 + 5.02554i) q^{29} +(-0.182097 - 0.560438i) q^{31} -4.26010i q^{32} +(4.08005 + 2.96433i) q^{34} +(-6.51322 + 2.28765i) q^{35} +(6.70056 - 9.22252i) q^{37} +(-3.82361 + 5.26275i) q^{38} +(-4.15806 - 5.44779i) q^{40} +(7.67919 + 5.57926i) q^{41} -2.42954i q^{43} +(0.288240 + 0.887112i) q^{44} +(-0.783227 + 2.41052i) q^{46} +(-5.75387 - 1.86955i) q^{47} -2.53108 q^{49} +(-5.25611 - 1.43734i) q^{50} +(1.94779 + 2.68091i) q^{52} +(-3.08503 - 1.00239i) q^{53} +(2.11237 + 1.45979i) q^{55} +(-2.92394 - 8.99897i) q^{56} +(-5.47693 + 1.77956i) q^{58} +(-2.57785 - 1.87292i) q^{59} +(-11.1201 + 8.07922i) q^{61} +(0.377480 - 0.519557i) q^{62} +(6.53194 - 4.74573i) q^{64} +(8.73980 + 2.61327i) q^{65} +(-3.00414 + 0.976103i) q^{67} -3.75895i q^{68} +(-6.18922 - 4.27717i) q^{70} +(-1.99795 + 6.14907i) q^{71} +(4.23792 + 5.83300i) q^{73} +12.4236 q^{74} +4.84857 q^{76} +(2.08376 + 2.86806i) q^{77} +(3.81246 - 11.7336i) q^{79} +(1.09897 - 3.67540i) q^{80} +10.3446i q^{82} +(-11.7875 + 3.82999i) q^{83} +(-6.27811 - 8.22543i) q^{85} +(2.14208 - 1.55631i) q^{86} +(-2.06868 + 2.84729i) q^{88} +(-0.877003 + 0.637180i) q^{89} +(10.1892 + 7.40289i) q^{91} +(1.79668 - 0.583776i) q^{92} +(-2.03747 - 6.27068i) q^{94} +(10.6098 - 8.09797i) q^{95} +(4.30003 + 1.39717i) q^{97} +(-1.62136 - 2.23161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 30 q^{8}+O(q^{10}) \) 16 * q + 2 * q^4 + 30 * q^8	\( 16 q + 2 q^{4} + 30 q^{8} + 6 q^{11} + 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} - 20 q^{20} - 30 q^{22} + 20 q^{23} - 10 q^{25} - 12 q^{26} + 30 q^{28} - 16 q^{29} + 6 q^{31} - 36 q^{34} - 10 q^{35} - 10 q^{37} - 30 q^{38} + 10 q^{40} + 14 q^{41} - 26 q^{44} + 16 q^{46} - 40 q^{47} - 20 q^{50} + 40 q^{52} - 10 q^{53} + 10 q^{55} + 10 q^{58} - 12 q^{59} + 10 q^{62} + 8 q^{64} + 70 q^{65} - 40 q^{67} + 30 q^{70} + 8 q^{71} - 20 q^{73} + 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 10 q^{83} - 20 q^{85} + 36 q^{86} - 40 q^{88} - 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} + 40 q^{95} + 40 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 2 * q^4 + 30 * q^8 + 6 * q^11 + 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 - 20 * q^20 - 30 * q^22 + 20 * q^23 - 10 * q^25 - 12 * q^26 + 30 * q^28 - 16 * q^29 + 6 * q^31 - 36 * q^34 - 10 * q^35 - 10 * q^37 - 30 * q^38 + 10 * q^40 + 14 * q^41 - 26 * q^44 + 16 * q^46 - 40 * q^47 - 20 * q^50 + 40 * q^52 - 10 * q^53 + 10 * q^55 + 10 * q^58 - 12 * q^59 + 10 * q^62 + 8 * q^64 + 70 * q^65 - 40 * q^67 + 30 * q^70 + 8 * q^71 - 20 * q^73 + 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 10 * q^83 - 20 * q^85 + 36 * q^86 - 40 * q^88 - 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 + 40 * q^95 + 40 * q^97 - 60 * q^98

Introduction

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