LMFDB - Embedded newform 432.2.v.a.395.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(35,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			395.12
Character	$\chi$	$=$	432.395
Dual form			432.2.v.a.35.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0112605 + 1.41417i) q^{2} +(-1.99975 + 0.0318485i) q^{4} +(0.759273 + 2.83365i) q^{5} +(1.41719 + 2.45465i) q^{7} +(-0.0675573 - 2.82762i) q^{8} +(-3.99870 + 1.10565i) q^{10} +(-0.212907 + 0.794578i) q^{11} +(-0.864050 - 3.22468i) q^{13} +(-3.45533 + 2.03179i) q^{14} +(3.99797 - 0.127378i) q^{16} +7.28589i q^{17} +(-0.951758 - 0.951758i) q^{19} +(-1.60860 - 5.64239i) q^{20} +(-1.12606 - 0.292138i) q^{22} +(-5.13217 - 2.96306i) q^{23} +(-3.12293 + 1.80302i) q^{25} +(4.55051 - 1.25822i) q^{26} +(-2.91220 - 4.86354i) q^{28} +(0.473770 - 1.76813i) q^{29} +(-2.05610 - 1.18709i) q^{31} +(0.225153 + 5.65237i) q^{32} +(-10.3035 + 0.0820428i) q^{34} +(-5.87957 + 5.87957i) q^{35} +(6.03704 + 6.03704i) q^{37} +(1.33523 - 1.35666i) q^{38} +(7.96118 - 2.33837i) q^{40} +(-4.60866 + 7.98243i) q^{41} +(-1.50209 - 0.402483i) q^{43} +(0.400453 - 1.59574i) q^{44} +(4.13248 - 7.29113i) q^{46} +(-2.85832 - 4.95075i) q^{47} +(-0.516861 + 0.895230i) q^{49} +(-2.58494 - 4.39604i) q^{50} +(1.83058 + 6.42102i) q^{52} +(4.50856 - 4.50856i) q^{53} -2.41321 q^{55} +(6.84507 - 4.17311i) q^{56} +(2.50577 + 0.650080i) q^{58} +(10.6553 - 2.85508i) q^{59} +(8.08106 + 2.16531i) q^{61} +(1.65559 - 2.92104i) q^{62} +(-7.99087 + 0.382053i) q^{64} +(8.48155 - 4.89682i) q^{65} +(11.1746 - 2.99423i) q^{67} +(-0.232045 - 14.5699i) q^{68} +(-8.38090 - 8.24849i) q^{70} -2.98978i q^{71} +12.7280i q^{73} +(-8.46941 + 8.60537i) q^{74} +(1.93359 + 1.87296i) q^{76} +(-2.25214 + 0.603459i) q^{77} +(8.94529 - 5.16457i) q^{79} +(3.39650 + 11.2321i) q^{80} +(-11.3404 - 6.42753i) q^{82} +(3.74713 + 1.00404i) q^{83} +(-20.6456 + 5.53198i) q^{85} +(0.552264 - 2.12873i) q^{86} +(2.26115 + 0.548339i) q^{88} +9.25017 q^{89} +(6.69092 - 6.69092i) q^{91} +(10.3574 + 5.76192i) q^{92} +(6.96901 - 4.09789i) q^{94} +(1.97430 - 3.41959i) q^{95} +(0.148868 + 0.257847i) q^{97} +(-1.27183 - 0.720848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.0112605	+	1.41417i	0.00796238	+	0.999968i
$2$	0.0112605	+	1.41417i	0.00796238	+	0.999968i
$3$		0			0
$3$		0			0
$4$	−1.99975	+	0.0318485i	−0.999873	+	0.0159242i
$5$	0.759273	+	2.83365i	0.339557	+	1.26725i	0.898843	+	0.438270i	$0.144409\pi$
$5$	0.759273	+	2.83365i	0.339557	+	1.26725i	−0.559286	+	0.828975i	$0.688925\pi$
$6$		0			0
$7$	1.41719	+	2.45465i	0.535648	+	0.927769i	0.999132	+	0.0416640i	$0.0132659\pi$
$7$	1.41719	+	2.45465i	0.535648	+	0.927769i	−0.463484	+	0.886105i	$0.653401\pi$
$8$	−0.0675573	−	2.82762i	−0.0238851	−	0.999715i
$9$		0			0
$10$	−3.99870	+	1.10565i	−1.26450	+	0.349637i
$11$	−0.212907	+	0.794578i	−0.0641937	+	0.239574i	−0.990566	−	0.137034i	$-0.956243\pi$
$11$	−0.212907	+	0.794578i	−0.0641937	+	0.239574i	0.926373	+	0.376608i	$0.122910\pi$
$12$		0			0
$13$	−0.864050	−	3.22468i	−0.239644	−	0.894365i	−0.976000	−	0.217770i	$-0.930122\pi$
$13$	−0.864050	−	3.22468i	−0.239644	−	0.894365i	0.736356	−	0.676595i	$-0.236545\pi$
$14$	−3.45533	+	2.03179i	−0.923475	+	0.543018i
$15$		0			0
$16$	3.99797	−	0.127378i	0.999493	−	0.0318445i
$17$			7.28589i			1.76709i	0.468348	+	0.883544i	$0.344849\pi$
$17$			7.28589i			1.76709i	−0.468348	+	0.883544i	$0.655151\pi$
$18$		0			0
$19$	−0.951758	−	0.951758i	−0.218348	−	0.218348i	0.589454	−	0.807802i	$-0.299343\pi$
$19$	−0.951758	−	0.951758i	−0.218348	−	0.218348i	−0.807802	+	0.589454i	$0.799343\pi$
$20$	−1.60860	−	5.64239i	−0.359694	−	1.26168i
$21$		0			0
$22$	−1.12606	−	0.292138i	−0.240078	−	0.0622841i
$23$	−5.13217	−	2.96306i	−1.07013	−	0.617841i	−0.141915	−	0.989879i	$-0.545326\pi$
$23$	−5.13217	−	2.96306i	−1.07013	−	0.617841i	−0.928218	+	0.372038i	$0.878659\pi$
$24$		0			0
$25$	−3.12293	+	1.80302i	−0.624585	+	0.360605i
$26$	4.55051	−	1.25822i	0.892428	−	0.246758i
$27$		0			0
$28$	−2.91220	−	4.86354i	−0.550354	−	0.919122i
$29$	0.473770	−	1.76813i	0.0879768	−	0.328334i	−0.907884	−	0.419221i	$-0.862303\pi$
$29$	0.473770	−	1.76813i	0.0879768	−	0.328334i	0.995861	+	0.0908866i	$0.0289701\pi$
$30$		0			0
$31$	−2.05610	−	1.18709i	−0.369286	−	0.213207i	0.303860	−	0.952717i	$-0.401724\pi$
$31$	−2.05610	−	1.18709i	−0.369286	−	0.213207i	−0.673147	+	0.739509i	$0.735058\pi$
$32$	0.225153	+	5.65237i	0.0398018	+	0.999208i
$33$		0			0
$34$	−10.3035	+	0.0820428i	−1.76703	+	0.0140702i
$35$	−5.87957	+	5.87957i	−0.993828	+	0.993828i
$36$		0			0
$37$	6.03704	+	6.03704i	0.992483	+	0.992483i	0.999972	−	0.00748933i	$-0.00238395\pi$
$37$	6.03704	+	6.03704i	0.992483	+	0.992483i	−0.00748933	+	0.999972i	$0.502384\pi$
$38$	1.33523	−	1.35666i	0.216603	−	0.220080i
$39$		0			0
$40$	7.96118	−	2.33837i	1.25877	−	0.369729i
$41$	−4.60866	+	7.98243i	−0.719751	+	1.24665i	0.241347	+	0.970439i	$0.422411\pi$
$41$	−4.60866	+	7.98243i	−0.719751	+	1.24665i	−0.961098	+	0.276207i	$0.910923\pi$
$42$		0			0
$43$	−1.50209	−	0.402483i	−0.229066	−	0.0613780i	0.142460	−	0.989801i	$-0.454499\pi$
$43$	−1.50209	−	0.402483i	−0.229066	−	0.0613780i	−0.371526	+	0.928423i	$0.621165\pi$
$44$	0.400453	−	1.59574i	0.0603706	−	0.240566i
$45$		0			0
$46$	4.13248	−	7.29113i	0.609301	−	1.07502i
$47$	−2.85832	−	4.95075i	−0.416928	−	0.722141i	0.578701	−	0.815540i	$-0.303560\pi$
$47$	−2.85832	−	4.95075i	−0.416928	−	0.722141i	−0.995629	+	0.0933994i	$0.970227\pi$
$48$		0			0
$49$	−0.516861	+	0.895230i	−0.0738373	+	0.127890i
$50$	−2.58494	−	4.39604i	−0.365566	−	0.621694i
$51$		0			0
$52$	1.83058	+	6.42102i	0.253856	+	0.890435i
$53$	4.50856	−	4.50856i	0.619298	−	0.619298i	−0.326053	−	0.945351i	$-0.605719\pi$
$53$	4.50856	−	4.50856i	0.619298	−	0.619298i	0.945351	+	0.326053i	$0.105719\pi$
$54$		0			0
$55$	−2.41321			−0.325397
$56$	6.84507	−	4.17311i	0.914711	−	0.557655i
$57$		0			0
$58$	2.50577	+	0.650080i	0.329024	+	0.0853597i
$59$	10.6553	−	2.85508i	1.38720	−	0.371700i	0.513471	−	0.858107i	$-0.328360\pi$
$59$	10.6553	−	2.85508i	1.38720	−	0.371700i	0.873732	+	0.486407i	$0.161693\pi$
$60$		0			0
$61$	8.08106	+	2.16531i	1.03467	+	0.277240i	0.735904	−	0.677086i	$-0.236757\pi$
$61$	8.08106	+	2.16531i	1.03467	+	0.277240i	0.298769	+	0.954325i	$0.403424\pi$
$62$	1.65559	−	2.92104i	0.210260	−	0.370972i
$63$		0			0
$64$	−7.99087	+	0.382053i	−0.998859	+	0.0477566i
$65$	8.48155	−	4.89682i	1.05201	−	0.607376i
$66$		0			0
$67$	11.1746	−	2.99423i	1.36520	−	0.365804i	0.499476	−	0.866328i	$-0.333526\pi$
$67$	11.1746	−	2.99423i	1.36520	−	0.365804i	0.865723	+	0.500524i	$0.166859\pi$
$68$	−0.232045	−	14.5699i	−0.0281396	−	1.76686i
$69$		0			0
$70$	−8.38090	−	8.24849i	−1.00171	−	0.985883i
$71$		−	2.98978i		−	0.354821i	−0.984137	−	0.177411i	$-0.943228\pi$
$71$		−	2.98978i		−	0.354821i	0.984137	−	0.177411i	$-0.0567721\pi$
$72$		0			0
$73$			12.7280i			1.48970i	0.667229	+	0.744852i	$0.267480\pi$
$73$			12.7280i			1.48970i	−0.667229	+	0.744852i	$0.732520\pi$
$74$	−8.46941	+	8.60537i	−0.984549	+	1.00035i
$75$		0			0
$76$	1.93359	+	1.87296i	0.221798	+	0.214844i
$77$	−2.25214	+	0.603459i	−0.256655	+	0.0687705i
$78$		0			0
$79$	8.94529	−	5.16457i	1.00642	−	0.581059i	0.0962815	−	0.995354i	$-0.469305\pi$
$79$	8.94529	−	5.16457i	1.00642	−	0.581059i	0.910143	+	0.414295i	$0.135972\pi$
$80$	3.39650	+	11.2321i	0.379740	+	1.25579i
$81$		0			0
$82$	−11.3404	−	6.42753i	−1.25234	−	0.709802i
$83$	3.74713	+	1.00404i	0.411301	+	0.110208i	0.458536	−	0.888676i	$-0.348374\pi$
$83$	3.74713	+	1.00404i	0.411301	+	0.110208i	−0.0472343	+	0.998884i	$0.515041\pi$
$84$		0			0
$85$	−20.6456	+	5.53198i	−2.23933	+	0.600028i
$86$	0.552264	−	2.12873i	0.0595522	−	0.229547i
$87$		0			0
$88$	2.26115	+	0.548339i	0.241039	+	0.0584532i
$89$	9.25017			0.980516			0.490258	−	0.871577i	$-0.336903\pi$
$89$	9.25017			0.980516			0.490258	+	0.871577i	$0.336903\pi$
$90$		0			0
$91$	6.69092	−	6.69092i	0.701399	−	0.701399i
$92$	10.3574	+	5.76192i	1.07984	+	0.600722i
$93$		0			0
$94$	6.96901	−	4.09789i	0.718798	−	0.422665i
$95$	1.97430	−	3.41959i	0.202559	−	0.350843i
$96$		0			0
$97$	0.148868	+	0.257847i	0.0151153	+	0.0261804i	0.873484	−	0.486853i	$-0.161855\pi$
$97$	0.148868	+	0.257847i	0.0151153	+	0.0261804i	−0.858369	+	0.513033i	$0.828522\pi$
$98$	−1.27183	−	0.720848i	−0.128474	−	0.0728167i
$99$		0			0
$100$	6.18764	−	3.70505i	0.618764	−	0.370505i
$101$	−7.90610	−	2.11843i	−0.786687	−	0.210792i	−0.156956	−	0.987606i	$-0.550168\pi$
$101$	−7.90610	−	2.11843i	−0.786687	−	0.210792i	−0.629731	+	0.776814i	$0.716835\pi$
$102$		0			0
$103$	−5.72414	+	9.91450i	−0.564016	+	0.976905i	0.433124	+	0.901334i	$0.357411\pi$
$103$	−5.72414	+	9.91450i	−0.564016	+	0.976905i	−0.997140	+	0.0755707i	$0.975922\pi$
$104$	−9.05979	+	2.66106i	−0.888386	+	0.260938i
$105$		0			0
$106$	6.42663	+	6.32509i	0.624209	+	0.614347i
$107$	−0.174948	−	0.174948i	−0.0169128	−	0.0169128i	0.698600	−	0.715513i	$-0.253807\pi$
$107$	−0.174948	−	0.174948i	−0.0169128	−	0.0169128i	−0.715513	+	0.698600i	$0.753807\pi$
$108$		0			0
$109$	1.50900	−	1.50900i	0.144536	−	0.144536i	−0.631136	−	0.775672i	$-0.717411\pi$
$109$	1.50900	−	1.50900i	0.144536	−	0.144536i	0.775672	+	0.631136i	$0.217411\pi$
$110$	−0.0271739	−	3.41268i	−0.00259093	−	0.325386i
$111$		0			0
$112$	5.97856	+	9.63309i	0.564921	+	0.910241i
$113$	0.513633	+	0.296546i	0.0483185	+	0.0278967i	0.523965	−	0.851740i	$-0.324452\pi$
$113$	0.513633	+	0.296546i	0.0483185	+	0.0278967i	−0.475646	+	0.879637i	$0.657786\pi$
$114$		0			0
$115$	4.49955	−	16.7925i	0.419585	−	1.56591i
$116$	−0.891107	+	3.55090i	−0.0827372	+	0.329693i
$117$		0			0
$118$	4.15755	+	15.0363i	0.382734	+	1.38420i
$119$	−17.8843	+	10.3255i	−1.63945	+	0.946537i
$120$		0			0
$121$	8.94025	+	5.16166i	0.812750	+	0.469242i
$122$	−2.97112	+	11.4524i	−0.268993	+	1.03685i
$123$		0			0
$124$	4.14948	+	2.30839i	0.372635	+	0.207300i
$125$	2.89158	+	2.89158i	0.258631	+	0.258631i
$126$		0			0
$127$			14.1816i			1.25841i	0.777240	+	0.629205i	$0.216619\pi$
$127$			14.1816i			1.25841i	−0.777240	+	0.629205i	$0.783381\pi$
$128$	−0.630268	−	11.2961i	−0.0557084	−	0.998447i
$129$		0			0
$130$	7.02044	+	11.9392i	0.615733	+	1.04714i
$131$	−1.03481	−	3.86197i	−0.0904119	−	0.337422i	0.905872	−	0.423551i	$-0.139217\pi$
$131$	−1.03481	−	3.86197i	−0.0904119	−	0.337422i	−0.996284	+	0.0861298i	$0.972550\pi$
$132$		0			0
$133$	0.987407	−	3.68505i	0.0856190	−	0.319535i
$134$	4.36018	+	15.7691i	0.376662	+	1.36224i
$135$		0			0
$136$	20.6017	−	0.492215i	1.76658	−	0.0422071i
$137$	3.98207	+	6.89714i	0.340211	+	0.589262i	0.984472	−	0.175543i	$-0.0561682\pi$
$137$	3.98207	+	6.89714i	0.340211	+	0.589262i	−0.644261	+	0.764806i	$0.722835\pi$
$138$		0			0
$139$	−2.76404	−	10.3155i	−0.234443	−	0.874952i	−0.978399	−	0.206724i	$-0.933720\pi$
$139$	−2.76404	−	10.3155i	−0.234443	−	0.874952i	0.743957	−	0.668228i	$-0.232947\pi$
$140$	11.5704	−	11.9449i	0.977876	−	1.00953i
$141$		0			0
$142$	4.22805	−	0.0336664i	0.354810	−	0.00282522i
$143$	2.74622			0.229651
$144$		0			0
$145$	5.36998			0.445953
$146$	−17.9996	+	0.143324i	−1.48966	+	0.0118616i
$147$		0			0
$148$	−12.2648	−	11.8803i	−1.00816	−	0.976552i
$149$	−1.13642	−	4.24117i	−0.0930990	−	0.347450i	0.903625	−	0.428324i	$-0.140896\pi$
$149$	−1.13642	−	4.24117i	−0.0930990	−	0.347450i	−0.996724	+	0.0808734i	$0.974229\pi$
$150$		0			0
$151$	−6.93783	−	12.0167i	−0.564592	−	0.977903i	−0.997087	−	0.0762664i	$-0.975700\pi$
$151$	−6.93783	−	12.0167i	−0.564592	−	0.977903i	0.432495	−	0.901636i	$-0.357633\pi$
$152$	−2.62691	+	2.75551i	−0.213071	+	0.223501i
$153$		0			0
$154$	−0.878752	−	3.17811i	−0.0708119	−	0.256099i
$155$	1.80265	−	6.72758i	0.144792	−	0.540372i
$156$		0			0
$157$	−1.61187	−	6.01560i	−0.128642	−	0.480097i	0.871302	−	0.490748i	$-0.163276\pi$
$157$	−1.61187	−	6.01560i	−0.128642	−	0.480097i	−0.999943	+	0.0106509i	$0.996610\pi$
$158$	7.40430	+	12.5920i	0.589054	+	1.00177i
$159$		0			0
$160$	−15.8459	+	4.92970i	−1.25273	+	0.389727i
$161$		−	16.7969i		−	1.32378i
$162$		0			0
$163$	3.39010	+	3.39010i	0.265533	+	0.265533i	0.827297	−	0.561764i	$-0.189877\pi$
$163$	3.39010	+	3.39010i	0.265533	+	0.265533i	−0.561764	+	0.827297i	$0.689877\pi$
$164$	8.96191	−	16.1096i	0.699808	−	1.25795i
$165$		0			0
$166$	−1.37769	+	5.31039i	−0.106929	+	0.412166i
$167$	−8.58610	−	4.95718i	−0.664412	−	0.383598i	0.129544	−	0.991574i	$-0.458649\pi$
$167$	−8.58610	−	4.95718i	−0.664412	−	0.383598i	−0.793956	+	0.607975i	$0.791982\pi$
$168$		0			0
$169$	1.60636	−	0.927433i	0.123566	−	0.0713410i
$170$	−8.05564	−	29.1341i	−0.617839	−	2.23449i
$171$		0			0
$172$	3.01661	+	0.757024i	0.230014	+	0.0577225i
$173$	1.94330	−	7.25249i	0.147746	−	0.551396i	−0.851872	−	0.523751i	$-0.824532\pi$
$173$	1.94330	−	7.25249i	0.147746	−	0.551396i	0.999618	−	0.0276457i	$-0.00880101\pi$
$174$		0			0
$175$	−8.85157	−	5.11046i	−0.669116	−	0.386314i
$176$	−0.749983	+	3.20382i	−0.0565321	+	0.241497i
$177$		0			0
$178$	0.104162	+	13.0813i	0.00780724	+	0.980485i
$179$	−0.604756	+	0.604756i	−0.0452016	+	0.0452016i	−0.729346	−	0.684145i	$-0.760176\pi$
$179$	−0.604756	+	0.604756i	−0.0452016	+	0.0452016i	0.684145	+	0.729346i	$0.260176\pi$
$180$		0			0
$181$	−10.1716	−	10.1716i	−0.756048	−	0.756048i	0.219553	−	0.975601i	$-0.429540\pi$
$181$	−10.1716	−	10.1716i	−0.756048	−	0.756048i	−0.975601	+	0.219553i	$0.929540\pi$
$182$	9.53744	+	9.38675i	0.706962	+	0.695792i
$183$		0			0
$184$	−8.03170	+	14.7120i	−0.592105	+	1.08458i
$185$	−12.5231	+	21.6906i	−0.920714	+	1.59472i
$186$		0			0
$187$	−5.78921	−	1.55121i	−0.423349	−	0.113436i
$188$	5.87358	+	9.80921i	0.428375	+	0.715410i
$189$		0			0
$190$	4.85811	+	2.75349i	0.352444	+	0.199759i
$191$	5.80282	+	10.0508i	0.419877	+	0.727249i	0.995927	−	0.0901660i	$-0.0287398\pi$
$191$	5.80282	+	10.0508i	0.419877	+	0.727249i	−0.576049	+	0.817415i	$0.695406\pi$
$192$		0			0
$193$	5.09572	−	8.82605i	0.366798	−	0.635313i	−0.622265	−	0.782807i	$-0.713787\pi$
$193$	5.09572	−	8.82605i	0.366798	−	0.635313i	0.989063	+	0.147494i	$0.0471206\pi$
$194$	−0.362963	+	0.213428i	−0.0260592	+	0.0153232i
$195$		0			0
$196$	1.00508	−	1.80669i	0.0717914	−	0.129050i
$197$	4.32430	−	4.32430i	0.308094	−	0.308094i	−0.536076	−	0.844170i	$-0.680094\pi$
$197$	4.32430	−	4.32430i	0.308094	−	0.308094i	0.844170	+	0.536076i	$0.180094\pi$
$198$		0			0
$199$	−27.7260			−1.96544			−0.982720	−	0.185097i	$-0.940740\pi$
$199$	−27.7260			−1.96544			−0.982720	+	0.185097i	$0.940740\pi$
$200$	5.30924	+	8.70864i	0.375420	+	0.615794i
$201$		0			0
$202$	2.90680	−	11.2044i	0.204521	−	0.788340i
$203$	5.01156	−	1.34284i	0.351743	−	0.0942492i
$204$		0			0
$205$	−26.1186	−	6.99846i	−1.82420	−	0.488793i
$206$	−14.0852	−	7.98326i	−0.981365	−	0.556220i
$207$		0			0
$208$	−3.86520	−	12.7821i	−0.268003	−	0.886280i
$209$	0.958882	−	0.553611i	0.0663272	−	0.0382940i
$210$		0			0
$211$	−19.0391	+	5.10152i	−1.31071	+	0.351203i	−0.845489	−	0.533993i	$-0.820691\pi$
$211$	−19.0391	+	5.10152i	−1.31071	+	0.351203i	−0.465219	+	0.885196i	$0.654024\pi$
$212$	−8.87238	+	9.15956i	−0.609358	+	0.629081i
$213$		0			0
$214$	0.245435	−	0.249375i	0.0167776	−	0.0170470i
$215$		−	4.56197i		−	0.311124i
$216$		0			0
$217$		−	6.72933i		−	0.456817i
$218$	2.15098	+	2.11699i	0.145683	+	0.143381i
$219$		0			0
$220$	4.82580	−	0.0768570i	0.325356	−	0.00518170i
$221$	23.4947	−	6.29538i	1.58042	−	0.423473i
$222$		0			0
$223$	10.9074	−	6.29741i	0.730416	−	0.421706i	−0.0881582	−	0.996106i	$-0.528098\pi$
$223$	10.9074	−	6.29741i	0.730416	−	0.421706i	0.818574	+	0.574401i	$0.194765\pi$
$224$	−13.5555	+	8.56316i	−0.905714	+	0.572150i
$225$		0			0
$226$	−0.413582	+	0.729702i	−0.0275111	+	0.0485391i
$227$	11.6445	+	3.12014i	0.772874	+	0.207091i	0.623641	−	0.781711i	$-0.285653\pi$
$227$	11.6445	+	3.12014i	0.772874	+	0.207091i	0.149233	+	0.988802i	$0.452320\pi$
$228$		0			0
$229$	−5.47149	+	1.46608i	−0.361566	+	0.0968814i	−0.435029	−	0.900417i	$-0.643262\pi$
$229$	−5.47149	+	1.46608i	−0.361566	+	0.0968814i	0.0734624	+	0.997298i	$0.476595\pi$
$230$	23.7982	+	6.17403i	1.56920	+	0.407103i
$231$		0			0
$232$	−5.03161	−	1.22019i	−0.330342	−	0.0801094i
$233$	−10.1291			−0.663580			−0.331790	−	0.943353i	$-0.607653\pi$
$233$	−10.1291			−0.663580			−0.331790	+	0.943353i	$0.607653\pi$
$234$		0			0
$235$	11.8584	−	11.8584i	0.773558	−	0.773558i
$236$	−21.2170	+	6.04879i	−1.38111	+	0.393743i
$237$		0			0
$238$	−14.8034	−	25.1751i	−0.959561	−	1.63186i
$239$	−0.263562	+	0.456503i	−0.0170484	+	0.0295287i	−0.874424	−	0.485163i	$-0.838760\pi$
$239$	−0.263562	+	0.456503i	−0.0170484	+	0.0295287i	0.857375	+	0.514692i	$0.172094\pi$
$240$		0			0
$241$	9.74338	+	16.8760i	0.627626	+	1.08708i	0.988027	+	0.154283i	$0.0493068\pi$
$241$	9.74338	+	16.8760i	0.627626	+	1.08708i	−0.360400	+	0.932798i	$0.617360\pi$
$242$	−7.19878	+	12.7012i	−0.462755	+	0.816461i
$243$		0			0
$244$	−16.2290	−	4.07271i	−1.03896	−	0.260728i
$245$	−2.92920	−	0.784878i	−0.187140	−	0.0501440i
$246$		0			0
$247$	−2.24675	+	3.89148i	−0.142957	+	0.247609i
$248$	−3.21773	+	5.89406i	−0.204326	+	0.374273i
$249$		0			0
$250$	−4.05662	+	4.12174i	−0.256563	+	0.260682i
$251$	−17.9199	−	17.9199i	−1.13110	−	1.13110i	−0.989995	−	0.141101i	$-0.954936\pi$
$251$	−17.9199	−	17.9199i	−1.13110	−	1.13110i	−0.141101	−	0.989995i	$-0.545064\pi$
$252$		0			0
$253$	3.44706	−	3.44706i	0.216715	−	0.216715i
$254$	−20.0551	+	0.159691i	−1.25837	+	0.0100199i
$255$		0			0
$256$	15.9675	−	1.01851i	0.997972	−	0.0636566i
$257$	−14.6152	−	8.43809i	−0.911671	−	0.526353i	−0.0307025	−	0.999529i	$-0.509774\pi$
$257$	−14.6152	−	8.43809i	−0.911671	−	0.526353i	−0.880968	+	0.473175i	$0.843108\pi$
$258$		0			0
$259$	−6.26316	+	23.3744i	−0.389174	+	1.45242i
$260$	−16.8050	+	10.0625i	−1.04220	+	0.624052i
$261$		0			0
$262$	5.44982	−	1.50688i	0.336691	−	0.0930957i
$263$	18.8065	−	10.8579i	1.15966	−	0.669528i	0.208435	−	0.978036i	$-0.433163\pi$
$263$	18.8065	−	10.8579i	1.15966	−	0.669528i	0.951222	+	0.308508i	$0.0998297\pi$
$264$		0			0
$265$	16.1989	+	9.35243i	0.995090	+	0.574515i
$266$	5.22241	+	1.35486i	0.320206	+	0.0830721i
$267$		0			0
$268$	−22.2511	+	6.34360i	−1.35920	+	0.387497i
$269$	3.50729	+	3.50729i	0.213843	+	0.213843i	0.805898	−	0.592055i	$-0.201683\pi$
$269$	3.50729	+	3.50729i	0.213843	+	0.213843i	−0.592055	+	0.805898i	$0.701683\pi$
$270$		0			0
$271$		−	2.25749i		−	0.137133i	−0.997647	−	0.0685665i	$-0.978157\pi$
$271$		−	2.25749i		−	0.137133i	0.997647	−	0.0685665i	$-0.0218425\pi$
$272$	0.928061	+	29.1288i	0.0562720	+	1.76619i
$273$		0			0
$274$	−9.70888	+	5.70898i	−0.586535	+	0.344892i
$275$	−0.767751	−	2.86529i	−0.0462971	−	0.172783i
$276$		0			0
$277$	4.75826	−	17.7581i	0.285896	−	1.06698i	−0.662286	−	0.749251i	$-0.730414\pi$
$277$	4.75826	−	17.7581i	0.285896	−	1.06698i	0.948182	−	0.317727i	$-0.102920\pi$
$278$	14.5568	−	4.02498i	0.873058	−	0.241402i
$279$		0			0
$280$	17.0224	+	16.2280i	1.01728	+	0.969807i
$281$	−4.38270	−	7.59106i	−0.261450	−	0.452845i	0.705177	−	0.709031i	$-0.250867\pi$
$281$	−4.38270	−	7.59106i	−0.261450	−	0.452845i	−0.966627	+	0.256186i	$0.917534\pi$
$282$		0			0
$283$	4.18474	+	15.6177i	0.248757	+	0.928375i	0.971458	+	0.237213i	$0.0762340\pi$
$283$	4.18474	+	15.6177i	0.248757	+	0.928375i	−0.722700	+	0.691161i	$0.757099\pi$
$284$	0.0952199	+	5.97879i	0.00565026	+	0.354776i
$285$		0			0
$286$	0.0309238	+	3.88362i	0.00182856	+	0.229643i
$287$	−26.1254			−1.54213
$288$		0			0
$289$	−36.0842			−2.12260
$290$	0.0604687	+	7.59406i	0.00355084	+	0.445939i
$291$		0			0
$292$	−0.405369	−	25.4529i	−0.0237224	−	1.48952i
$293$	−3.24540	−	12.1120i	−0.189598	−	0.707589i	−0.993599	−	0.112962i	$-0.963966\pi$
$293$	−3.24540	−	12.1120i	−0.189598	−	0.707589i	0.804001	−	0.594628i	$-0.202700\pi$
$294$		0			0
$295$	16.1806	+	28.0256i	0.942070	+	1.63171i
$296$	16.6626	−	17.4783i	0.968494	−	1.01591i
$297$		0			0
$298$	5.98494	−	1.65485i	0.346698	−	0.0958626i
$299$	−5.12047	+	19.1098i	−0.296124	+	1.10515i
$300$		0			0
$301$	−1.14079	−	4.25749i	−0.0657540	−	0.245397i
$302$	16.9155	−	9.94657i	0.973376	−	0.572361i
$303$		0			0
$304$	−3.92633	−	3.68387i	−0.225191	−	0.211284i
$305$			24.5429i			1.40532i
$306$		0			0
$307$	18.9168	+	18.9168i	1.07964	+	1.07964i	0.996542	+	0.0830950i	$0.0264805\pi$
$307$	18.9168	+	18.9168i	1.07964	+	1.07964i	0.0830950	+	0.996542i	$0.473519\pi$
$308$	4.48449	−	1.27849i	0.255527	−	0.0728488i
$309$		0			0
$310$	9.53423	+	2.47349i	0.541508	+	0.140485i
$311$	5.08666	+	2.93678i	0.288438	+	0.166530i	0.637237	−	0.770668i	$-0.280077\pi$
$311$	5.08666	+	2.93678i	0.288438	+	0.166530i	−0.348799	+	0.937197i	$0.613411\pi$
$312$		0			0
$313$	14.3490	−	8.28438i	0.811051	−	0.468261i	−0.0362694	−	0.999342i	$-0.511547\pi$
$313$	14.3490	−	8.28438i	0.811051	−	0.468261i	0.847321	+	0.531081i	$0.178214\pi$
$314$	8.48892	−	2.34720i	0.479057	−	0.132460i
$315$		0			0
$316$	−17.7238	+	10.6127i	−0.997044	+	0.597012i
$317$	1.80531	−	6.73750i	0.101396	−	0.378416i	−0.896515	−	0.443013i	$-0.853910\pi$
$317$	1.80531	−	6.73750i	0.101396	−	0.378416i	0.997911	+	0.0645973i	$0.0205763\pi$
$318$		0			0
$319$	1.30405	+	0.752894i	0.0730128	+	0.0421540i
$320$	−7.14986	−	22.3532i	−0.399689	−	1.24958i
$321$		0			0
$322$	23.7537	−	0.189142i	1.32374	−	0.0105404i
$323$	6.93441	−	6.93441i	0.385841	−	0.385841i
$324$		0			0
$325$	8.51253	+	8.51253i	0.472190	+	0.472190i
$326$	−4.75600	+	4.83235i	−0.263410	+	0.267639i
$327$		0			0
$328$	22.8826	+	12.4923i	1.26348	+	0.689769i
$329$	8.10156	−	14.0323i	0.446653	−	0.773626i
$330$		0			0
$331$	−21.7853	−	5.83736i	−1.19743	−	0.320850i	−0.395612	−	0.918418i	$-0.629467\pi$
$331$	−21.7853	−	5.83736i	−1.19743	−	0.320850i	−0.801819	+	0.597567i	$0.796134\pi$
$332$	−7.52530	−	1.88849i	−0.413004	−	0.103644i
$333$		0			0
$334$	6.91361	−	12.1980i	0.378296	−	0.667445i
$335$	16.9692	+	29.3915i	0.927126	+	1.60583i
$336$		0			0
$337$	5.04210	−	8.73317i	0.274661	−	0.475726i	−0.695389	−	0.718634i	$-0.744768\pi$
$337$	5.04210	−	8.73317i	0.274661	−	0.475726i	0.970049	+	0.242908i	$0.0781012\pi$
$338$	1.32963	+	2.26122i	0.0723226	+	0.122994i
$339$		0			0
$340$	41.1099	−	11.7201i	2.22950	−	0.635611i
$341$	1.38099	−	1.38099i	0.0747849	−	0.0747849i
$342$		0			0
$343$	16.9107			0.913093
$344$	−1.03659	+	4.27452i	−0.0558893	+	0.230467i
$345$		0			0
$346$	10.2781	+	2.66648i	0.552555	+	0.143351i
$347$	28.7569	−	7.70540i	1.54375	−	0.413647i	0.616277	−	0.787530i	$-0.288640\pi$
$347$	28.7569	−	7.70540i	1.54375	−	0.413647i	0.927476	+	0.373882i	$0.121974\pi$
$348$		0			0
$349$	8.65259	+	2.31845i	0.463163	+	0.124104i	0.482852	−	0.875702i	$-0.339601\pi$
$349$	8.65259	+	2.31845i	0.463163	+	0.124104i	−0.0196892	+	0.999806i	$0.506268\pi$
$350$	7.12737	−	12.5752i	0.380974	−	0.672171i
$351$		0			0
$352$	−4.53919	−	1.02453i	−0.241939	−	0.0546074i
$353$	−28.1794	+	16.2694i	−1.49984	+	0.865933i	−1.00000		0.000184008i	$-0.999941\pi$
$353$	−28.1794	+	16.2694i	−1.49984	+	0.865933i	−0.499841	+	0.866117i	$0.666608\pi$
$354$		0			0
$355$	8.47197	−	2.27006i	0.449645	−	0.120482i
$356$	−18.4980	+	0.294604i	−0.980392	+	0.0156140i
$357$		0			0
$358$	−0.862037	−	0.848417i	−0.0455601	−	0.0448402i
$359$		−	0.581843i		−	0.0307085i	−0.999882	−	0.0153542i	$-0.995112\pi$
$359$		−	0.581843i		−	0.0307085i	0.999882	−	0.0153542i	$-0.00488760\pi$
$360$		0			0
$361$		−	17.1883i		−	0.904648i
$362$	14.2698	−	14.4989i	0.750004	−	0.762044i
$363$		0			0
$364$	−13.1671	+	13.5932i	−0.690141	+	0.712480i
$365$	−36.0668	+	9.66406i	−1.88782	+	0.505840i
$366$		0			0
$367$	−3.68240	+	2.12603i	−0.192220	+	0.110978i	−0.593021	−	0.805187i	$-0.702065\pi$
$367$	−3.68240	+	2.12603i	−0.192220	+	0.110978i	0.400802	+	0.916165i	$0.368732\pi$
$368$	−20.8957	−	11.1925i	−1.08926	−	0.583450i
$369$		0			0
$370$	−30.8152	−	17.4655i	−1.60200	−	0.907987i
$371$	17.4564	+	4.67743i	0.906291	+	0.242840i
$372$		0			0
$373$	6.02298	−	1.61385i	0.311858	−	0.0835621i	−0.0994955	−	0.995038i	$-0.531723\pi$
$373$	6.02298	−	1.61385i	0.311858	−	0.0835621i	0.411353	+	0.911476i	$0.365056\pi$
$374$	2.12849	−	8.20439i	0.110062	−	0.424239i
$375$		0			0
$376$	−13.8057	+	8.41669i	−0.711976	+	0.434058i
$377$	−6.11102			−0.314733
$378$		0			0
$379$	−8.99791	+	8.99791i	−0.462192	+	0.462192i	−0.899373	−	0.437182i	$-0.855977\pi$
$379$	−8.99791	+	8.99791i	−0.462192	+	0.462192i	0.437182	+	0.899373i	$0.355977\pi$
$380$	−3.83919	+	6.90119i	−0.196946	+	0.354024i
$381$		0			0
$382$	−14.1482	+	8.31934i	−0.723883	+	0.425655i
$383$	4.35960	−	7.55105i	0.222765	−	0.385840i	−0.732882	−	0.680356i	$-0.761825\pi$
$383$	4.35960	−	7.55105i	0.222765	−	0.385840i	0.955647	+	0.294516i	$0.0951584\pi$
$384$		0			0
$385$	−3.41998	−	5.92357i	−0.174298	−	0.301893i
$386$	12.5389	+	7.10683i	0.638213	+	0.361728i
$387$		0			0
$388$	−0.305910	−	0.510887i	−0.0155302	−	0.0259364i
$389$	−26.9041	−	7.20893i	−1.36409	−	0.365507i	−0.498774	−	0.866732i	$-0.666216\pi$
$389$	−26.9041	−	7.20893i	−1.36409	−	0.365507i	−0.865317	+	0.501225i	$0.832883\pi$
$390$		0			0
$391$	21.5886	−	37.3925i	1.09178	−	1.89102i
$392$	2.56629	+	1.40101i	0.129617	+	0.0707616i
$393$		0			0
$394$	6.16398	+	6.06659i	0.310537	+	0.305631i
$395$	21.4265	+	21.4265i	1.07808	+	1.07808i
$396$		0			0
$397$	3.82319	−	3.82319i	0.191880	−	0.191880i	−0.604628	−	0.796508i	$-0.706678\pi$
$397$	3.82319	−	3.82319i	0.191880	−	0.191880i	0.796508	+	0.604628i	$0.206678\pi$
$398$	−0.312208	−	39.2092i	−0.0156496	−	1.96538i
$399$		0			0
$400$	−12.2557	+	7.60623i	−0.612785	+	0.380311i
$401$	24.9442	+	14.4015i	1.24565	+	0.719178i	0.970239	−	0.242148i	$-0.0778518\pi$
$401$	24.9442	+	14.4015i	1.24565	+	0.719178i	0.275414	+	0.961326i	$0.411185\pi$
$402$		0			0
$403$	−2.05141	+	7.65596i	−0.102188	+	0.381371i
$404$	15.8777	+	3.98453i	0.789944	+	0.198238i
$405$		0			0
$406$	1.95544	+	7.07207i	0.0970469	+	0.350981i
$407$	−6.08222	+	3.51157i	−0.301485	+	0.174062i
$408$		0			0
$409$	−9.11179	−	5.26069i	−0.450549	−	0.260125i	0.257513	−	0.966275i	$-0.417097\pi$
$409$	−9.11179	−	5.26069i	−0.450549	−	0.260125i	−0.708062	+	0.706150i	$0.750430\pi$
$410$	9.60289	−	37.0149i	0.474253	−	1.82804i
$411$		0			0
$412$	11.1311	−	20.0088i	0.548388	−	0.985763i
$413$	22.1088	+	22.1088i	1.08790	+	1.08790i
$414$		0			0
$415$			11.3804i			0.558642i
$416$	18.0325	−	5.60998i	0.884118	−	0.275052i
$417$		0			0
$418$	0.793696	+	1.34979i	0.0388210	+	0.0660202i
$419$	3.32320	+	12.4024i	0.162349	+	0.605895i	0.998363	+	0.0571875i	$0.0182133\pi$
$419$	3.32320	+	12.4024i	0.162349	+	0.605895i	−0.836014	+	0.548708i	$0.815120\pi$
$420$		0			0
$421$	2.46909	−	9.21476i	0.120336	−	0.449100i	−0.879295	−	0.476278i	$-0.841985\pi$
$421$	2.46909	−	9.21476i	0.120336	−	0.449100i	0.999631	+	0.0271782i	$0.00865216\pi$
$422$	−7.42880	−	26.8671i	−0.361628	−	1.30787i
$423$		0			0
$424$	−13.0531	−	12.4439i	−0.633913	−	0.604329i
$425$	−13.1366	−	22.7533i	−0.637220	−	1.10370i
$426$		0			0
$427$	6.13732	+	22.9048i	0.297006	+	1.10844i
$428$	0.355423	+	0.344279i	0.0171800	+	0.0166414i
$429$		0			0
$430$	6.45140	−	0.0513701i	0.311114	−	0.00247729i
$431$	−16.4451			−0.792131			−0.396065	−	0.918222i	$-0.629625\pi$
$431$	−16.4451			−0.792131			−0.396065	+	0.918222i	$0.629625\pi$
$432$		0			0
$433$	−3.51715			−0.169023			−0.0845116	−	0.996422i	$-0.526933\pi$
$433$	−3.51715			−0.169023			−0.0845116	+	0.996422i	$0.526933\pi$
$434$	9.51641	−	0.0757756i	0.456802	−	0.00363735i
$435$		0			0
$436$	−2.96957	+	3.06568i	−0.142216	+	0.146820i
$437$	2.06447	+	7.70471i	0.0987570	+	0.368566i
$438$		0			0
$439$	10.4483	+	18.0969i	0.498668	+	0.863719i	0.999999	−	0.00153725i	$-0.000489321\pi$
$439$	10.4483	+	18.0969i	0.498668	+	0.863719i	−0.501331	+	0.865256i	$0.667156\pi$
$440$	0.163030	+	6.82363i	0.00777214	+	0.325304i
$441$		0			0
$442$	9.16728	+	33.1545i	0.436043	+	1.57700i
$443$	−2.86151	+	10.6793i	−0.135954	+	0.507389i	0.864038	+	0.503427i	$0.167928\pi$
$443$	−2.86151	+	10.6793i	−0.135954	+	0.507389i	−0.999992	+	0.00396162i	$0.998739\pi$
$444$		0			0
$445$	7.02341	+	26.2117i	0.332941	+	1.24255i
$446$	9.02843	+	15.3540i	0.427508	+	0.727035i
$447$		0			0
$448$	−12.2624	−	19.0733i	−0.579344	−	0.901130i
$449$		−	17.5860i		−	0.829933i	−0.909837	−	0.414966i	$-0.863793\pi$
$449$		−	17.5860i		−	0.829933i	0.909837	−	0.414966i	$-0.136207\pi$
$450$		0			0
$451$	−5.36145	−	5.36145i	−0.252461	−	0.252461i
$452$	−1.03658	−	0.576658i	−0.0487566	−	0.0271237i
$453$		0			0
$454$	−4.28128	+	16.5024i	−0.200930	+	0.774498i
$455$	24.0399	+	13.8795i	1.12701	+	0.650680i
$456$		0			0
$457$	−18.6606	+	10.7737i	−0.872905	+	0.503972i	−0.868313	−	0.496017i	$-0.834795\pi$
$457$	−18.6606	+	10.7737i	−0.872905	+	0.503972i	−0.00459262	+	0.999989i	$0.501462\pi$
$458$	−2.13490	−	7.72110i	−0.0997572	−	0.360783i
$459$		0			0
$460$	−8.46314	+	33.7241i	−0.394596	+	1.57240i
$461$	4.55312	−	16.9925i	0.212060	−	0.791419i	−0.775121	−	0.631813i	$-0.782311\pi$
$461$	4.55312	−	16.9925i	0.212060	−	0.791419i	0.987181	−	0.159606i	$-0.0510223\pi$
$462$		0			0
$463$	−18.4389	−	10.6457i	−0.856930	−	0.494749i	0.00605328	−	0.999982i	$-0.498073\pi$
$463$	−18.4389	−	10.6457i	−0.856930	−	0.494749i	−0.862983	+	0.505233i	$0.831407\pi$
$464$	1.66890	−	7.12929i	0.0774766	−	0.330969i
$465$		0			0
$466$	−0.114059	−	14.3243i	−0.00528367	−	0.663559i
$467$	−2.62864	+	2.62864i	−0.121639	+	0.121639i	−0.765306	−	0.643667i	$-0.777412\pi$
$467$	−2.62864	+	2.62864i	−0.121639	+	0.121639i	0.643667	+	0.765306i	$0.277412\pi$
$468$		0			0
$469$	23.1864	+	23.1864i	1.07065	+	1.07065i
$470$	16.9033	+	16.6363i	0.779693	+	0.767374i
$471$		0			0
$472$	−8.79293	−	29.9363i	−0.404727	−	1.37793i
$473$	0.639608	−	1.10783i	0.0294092	−	0.0509382i
$474$		0			0
$475$	4.68831	+	1.25623i	0.215115	+	0.0576398i
$476$	35.4352	−	21.2180i	1.62417	−	0.972524i
$477$		0			0
$478$	−0.648540	−	0.367581i	−0.0296635	−	0.0168127i
$479$	−10.7530	−	18.6247i	−0.491317	−	0.850986i	0.508633	−	0.860983i	$-0.330151\pi$
$479$	−10.7530	−	18.6247i	−0.491317	−	0.850986i	−0.999950	+	0.00999740i	$0.996818\pi$
$480$		0			0
$481$	14.2512	−	24.6838i	0.649799	−	1.12548i
$482$	−23.7558	+	13.9688i	−1.08205	+	0.636262i
$483$		0			0
$484$	−18.0426	−	10.0373i	−0.820120	−	0.456240i
$485$	−0.617616	+	0.617616i	−0.0280445	+	0.0280445i
$486$		0			0
$487$	−14.6445			−0.663607			−0.331804	−	0.943348i	$-0.607657\pi$
$487$	−14.6445			−0.663607			−0.331804	+	0.943348i	$0.607657\pi$
$488$	5.57675	−	22.9964i	0.252447	−	1.04100i
$489$		0			0
$490$	1.07697	−	4.15123i	0.0486523	−	0.187533i
$491$	−42.2317	+	11.3160i	−1.90589	+	0.510682i	−0.910658	+	0.413161i	$0.864425\pi$
$491$	−42.2317	+	11.3160i	−1.90589	+	0.510682i	−0.995233	+	0.0975209i	$0.968909\pi$
$492$		0			0
$493$	12.8824	+	3.45183i	0.580195	+	0.155463i
$494$	−5.52851	−	3.13346i	−0.248739	−	0.140981i
$495$		0			0
$496$	−8.37143	−	4.48405i	−0.375888	−	0.201340i
$497$	7.33885	−	4.23708i	0.329192	−	0.190059i
$498$		0			0
$499$	7.91419	−	2.12060i	0.354288	−	0.0949311i	−0.0772856	−	0.997009i	$-0.524625\pi$
$499$	7.91419	−	2.12060i	0.354288	−	0.0949311i	0.431573	+	0.902078i	$0.357959\pi$
$500$	−5.87452	−	5.69034i	−0.262717	−	0.254480i
$501$		0			0
$502$	25.1400	−	25.5436i	1.12205	−	1.14007i
$503$			1.90408i			0.0848988i	0.999099	+	0.0424494i	$0.0135161\pi$
$503$			1.90408i			0.0848988i	−0.999099	+	0.0424494i	$0.986484\pi$
$504$		0			0
$505$		−	24.0116i		−	1.06850i
$506$	4.91354	+	4.83591i	0.218433	+	0.214982i
$507$		0			0
$508$	−0.451661	−	28.3595i	−0.0200392	−	1.25825i
$509$	7.27785	−	1.95009i	0.322585	−	0.0864364i	−0.0938926	−	0.995582i	$-0.529931\pi$
$509$	7.27785	−	1.95009i	0.322585	−	0.0864364i	0.416478	+	0.909146i	$0.363264\pi$
$510$		0			0
$511$	−31.2428	+	18.0381i	−1.38210	+	0.797957i
$512$	1.62014	+	22.5693i	0.0716008	+	0.997433i
$513$		0			0
$514$	11.7683	−	20.7634i	0.519078	−	0.915833i
$515$	−32.4404	−	8.69237i	−1.42949	−	0.383032i
$516$		0			0
$517$	4.54231	−	1.21711i	0.199771	−	0.0535284i
$518$	−33.1259	−	8.59396i	−1.45547	−	0.377597i
$519$		0			0
$520$	−14.4193	−	23.6518i	−0.632330	−	1.03720i
$521$	29.5974			1.29669			0.648343	−	0.761349i	$-0.275462\pi$
$521$	29.5974			1.29669			0.648343	+	0.761349i	$0.275462\pi$
$522$		0			0
$523$	29.1710	−	29.1710i	1.27556	−	1.27556i	0.332431	−	0.943128i	$-0.392131\pi$
$523$	29.1710	−	29.1710i	1.27556	−	1.27556i	0.943128	−	0.332431i	$-0.107869\pi$
$524$	2.19236	+	7.69000i	0.0957736	+	0.335939i
$525$		0			0
$526$	15.5667	+	26.4733i	0.678741	+	1.15429i
$527$	8.64900	−	14.9805i	0.376756	−	0.652561i
$528$		0			0
$529$	6.05948	+	10.4953i	0.263456	+	0.456318i
$530$	−13.0435	+	23.0133i	−0.566574	+	0.999632i
$531$		0			0
$532$	−1.85720	+	7.40062i	−0.0805198	+	0.320858i
$533$	29.7229	+	7.96422i	1.28744	+	0.344969i
$534$		0			0
$535$	0.362907	−	0.628573i	0.0156898	−	0.0271756i
$536$	−9.22148	−	31.3953i	−0.398307	−	1.35607i
$537$		0			0
$538$	−4.92040	+	4.99939i	−0.212134	+	0.215539i
$539$	−0.601287	−	0.601287i	−0.0258993	−	0.0258993i
$540$		0			0
$541$	7.87135	−	7.87135i	0.338416	−	0.338416i	−0.517355	−	0.855771i	$-0.673083\pi$
$541$	7.87135	−	7.87135i	0.338416	−	0.338416i	0.855771	+	0.517355i	$0.173083\pi$
$542$	3.19248	−	0.0254205i	0.137129	−	0.00109190i
$543$		0			0
$544$	−41.1826	+	1.64044i	−1.76569	+	0.0703333i
$545$	5.42173	+	3.13024i	0.232241	+	0.134085i
$546$		0			0
$547$	−0.817385	+	3.05052i	−0.0349488	+	0.130431i	−0.981196	−	0.193013i	$-0.938174\pi$
$547$	−0.817385	+	3.05052i	−0.0349488	+	0.130431i	0.946247	+	0.323444i	$0.104841\pi$
$548$	−8.18279	−	13.6657i	−0.349551	−	0.583770i
$549$		0			0
$550$	4.04335	−	1.11799i	0.172409	−	0.0476714i
$551$	−2.13375	+	1.23192i	−0.0909007	+	0.0524816i
$552$		0			0
$553$	25.3544	+	14.6384i	1.07818	+	0.622486i
$554$	25.1665	+	6.52902i	1.06922	+	0.277391i
$555$		0			0
$556$	5.85591	+	20.5404i	0.248346	+	0.871108i
$557$	−22.4110	−	22.4110i	−0.949583	−	0.949583i	0.0492055	−	0.998789i	$-0.484331\pi$
$557$	−22.4110	−	22.4110i	−0.949583	−	0.949583i	−0.998789	+	0.0492055i	$0.984331\pi$
$558$		0			0
$559$			5.19151i			0.219577i
$560$	−22.7574	+	24.2553i	−0.961676	+	1.02497i
$561$		0			0
$562$	10.6857	−	6.28336i	0.450749	−	0.265048i
$563$	8.11646	+	30.2910i	0.342068	+	1.27661i	0.896000	+	0.444053i	$0.146460\pi$
$563$	8.11646	+	30.2910i	0.342068	+	1.27661i	−0.553933	+	0.832561i	$0.686873\pi$
$564$		0			0
$565$	−0.450319	+	1.68061i	−0.0189450	+	0.0707039i
$566$	−22.0389	+	6.09380i	−0.926365	+	0.256141i
$567$		0			0
$568$	−8.45395	+	0.201981i	−0.354720	+	0.00847494i
$569$	−2.78787	−	4.82873i	−0.116874	−	0.202431i	0.801654	−	0.597789i	$-0.203954\pi$
$569$	−2.78787	−	4.82873i	−0.116874	−	0.202431i	−0.918527	+	0.395358i	$0.870621\pi$
$570$		0			0
$571$	5.39076	+	20.1186i	0.225596	+	0.841937i	0.982165	+	0.188023i	$0.0602078\pi$
$571$	5.39076	+	20.1186i	0.225596	+	0.841937i	−0.756568	+	0.653915i	$0.773126\pi$
$572$	−5.49175	+	0.0874630i	−0.229621	+	0.00365701i
$573$		0			0
$574$	−0.294185	−	36.9457i	−0.0122790	−	1.54208i
$575$	21.3699			0.891185
$576$		0			0
$577$	20.3551			0.847394			0.423697	−	0.905804i	$-0.360732\pi$
$577$	20.3551			0.847394			0.423697	+	0.905804i	$0.360732\pi$
$578$	−0.406326	−	51.0292i	−0.0169010	−	2.12253i
$579$		0			0
$580$	−10.7386	+	0.171026i	−0.445896	+	0.00710146i
$581$	2.84584	+	10.6208i	0.118065	+	0.440626i
$582$		0			0
$583$	2.62250	+	4.54230i	0.108613	+	0.188123i
$584$	35.9901	−	0.859872i	1.48928	−	0.0355818i
$585$		0			0
$586$	17.0918	−	4.72592i	0.706057	−	0.195226i
$587$	8.19230	−	30.5741i	0.338132	−	1.26193i	−0.562301	−	0.826933i	$-0.690084\pi$
$587$	8.19230	−	30.5741i	0.338132	−	1.26193i	0.900433	−	0.434994i	$-0.143250\pi$
$588$		0			0
$589$	0.827087	+	3.08673i	0.0340795	+	0.127186i
$590$	−39.4507	+	23.1977i	−1.62416	+	0.955032i
$591$		0			0
$592$	24.9049	+	23.3669i	1.02358	+	0.960374i
$593$		−	18.8148i		−	0.772633i	−0.922366	−	0.386317i	$-0.873747\pi$
$593$		−	18.8148i		−	0.772633i	0.922366	−	0.386317i	$-0.126253\pi$
$594$		0			0
$595$	−42.8379	−	42.8379i	−1.75618	−	1.75618i
$596$	2.40762	+	8.44507i	0.0986201	+	0.345924i
$597$		0			0
$598$	−27.0822	−	7.02602i	−1.10747	−	0.287315i
$599$	−0.618276	−	0.356962i	−0.0252621	−	0.0145851i	0.487316	−	0.873226i	$-0.337976\pi$
$599$	−0.618276	−	0.356962i	−0.0252621	−	0.0145851i	−0.512578	+	0.858641i	$0.671309\pi$
$600$		0			0
$601$	−39.9427	+	23.0610i	−1.62930	+	0.940676i	−0.644996	+	0.764186i	$0.723141\pi$
$601$	−39.9427	+	23.0610i	−1.62930	+	0.940676i	−0.984302	+	0.176490i	$0.943526\pi$
$602$	6.00796	−	1.66121i	0.244866	−	0.0677059i
$603$		0			0
$604$	14.2566	+	23.8093i	0.580093	+	0.968788i
$605$	−7.83822	+	29.2526i	−0.318669	+	1.18929i
$606$		0			0
$607$	25.9512	+	14.9830i	1.05333	+	0.608139i	0.923579	−	0.383408i	$-0.125250\pi$
$607$	25.9512	+	14.9830i	1.05333	+	0.608139i	0.129749	+	0.991547i	$0.458583\pi$
$608$	5.16540	−	5.59398i	0.209485	−	0.226866i
$609$		0			0
$610$	−34.7078	+	0.276366i	−1.40528	+	0.0111897i
$611$	−13.4948	+	13.4948i	−0.545943	+	0.545943i
$612$		0			0
$613$	−4.31839	−	4.31839i	−0.174418	−	0.174418i	0.614499	−	0.788917i	$-0.289358\pi$
$613$	−4.31839	−	4.31839i	−0.174418	−	0.174418i	−0.788917	+	0.614499i	$0.789358\pi$
$614$	−26.5385	+	26.9645i	−1.07101	+	1.08820i
$615$		0			0
$616$	1.85850	+	6.32742i	0.0748811	+	0.254939i
$617$	14.3245	−	24.8108i	0.576683	−	0.998844i	−0.419174	−	0.907906i	$-0.637680\pi$
$617$	14.3245	−	24.8108i	0.576683	−	0.998844i	0.995857	−	0.0909377i	$-0.0289864\pi$
$618$		0			0
$619$	−31.5053	−	8.44181i	−1.26630	−	0.339305i	−0.437690	−	0.899126i	$-0.644203\pi$
$619$	−31.5053	−	8.44181i	−1.26630	−	0.339305i	−0.828614	+	0.559821i	$0.810870\pi$
$620$	−3.39058	+	13.5109i	−0.136169	+	0.542609i
$621$		0			0
$622$	−4.09583	+	7.22646i	−0.164228	+	0.289755i
$623$	13.1093	+	22.7059i	0.525211	+	0.909693i
$624$		0			0
$625$	−15.0133	+	26.0039i	−0.600533	+	1.04015i
$626$	11.8771	+	20.1986i	0.474704	+	0.807297i
$627$		0			0
$628$	3.41493	+	11.9783i	0.136270	+	0.477987i
$629$	−43.9852	+	43.9852i	−1.75380	+	1.75380i
$630$		0			0
$631$	19.5062			0.776529			0.388265	−	0.921548i	$-0.373075\pi$
$631$	19.5062			0.776529			0.388265	+	0.921548i	$0.373075\pi$
$632$	−15.2078	−	24.9450i	−0.604932	−	0.992258i
$633$		0			0
$634$	9.54829	+	2.47714i	0.379211	+	0.0983798i
$635$	−40.1855	+	10.7677i	−1.59471	+	0.427302i
$636$		0			0
$637$	3.33342	+	0.893188i	0.132075	+	0.0353894i
$638$	−1.05003	+	1.85263i	−0.0415713	+	0.0733461i
$639$		0			0
$640$	31.5307	−	10.3628i	1.24636	−	0.409626i
$641$	−0.569361	+	0.328721i	−0.0224884	+	0.0129837i	−0.511202	−	0.859461i	$-0.670800\pi$
$641$	−0.569361	+	0.328721i	−0.0224884	+	0.0129837i	0.488714	+	0.872444i	$0.337466\pi$
$642$		0			0
$643$	23.4845	−	6.29265i	0.926138	−	0.248158i	0.235931	−	0.971770i	$-0.424186\pi$
$643$	23.4845	−	6.29265i	0.926138	−	0.248158i	0.690207	+	0.723612i	$0.257519\pi$
$644$	0.534956	+	33.5895i	0.0210802	+	1.32361i
$645$		0			0
$646$	9.88451	+	9.72834i	0.388901	+	0.382756i
$647$			21.5984i			0.849122i	0.905399	+	0.424561i	$0.139572\pi$
$647$			21.5984i			0.849122i	−0.905399	+	0.424561i	$0.860428\pi$
$648$		0			0
$649$			9.07434i			0.356199i
$650$	−11.9423	+	12.1340i	−0.468416	+	0.475935i
$651$		0			0
$652$	−6.88731	−	6.67137i	−0.269728	−	0.261271i
$653$	−38.1014	+	10.2092i	−1.49102	+	0.399519i	−0.910082	−	0.414427i	$-0.863982\pi$
$653$	−38.1014	+	10.2092i	−1.49102	+	0.399519i	−0.580941	+	0.813946i	$0.697315\pi$
$654$		0			0
$655$	10.1577	−	5.86458i	0.396896	−	0.229148i
$656$	−17.4085	+	32.5005i	−0.679687	+	1.26893i
$657$		0			0
$658$	19.9353	+	11.2990i	0.777158	+	0.440479i
$659$	−13.5220	−	3.62321i	−0.526742	−	0.141140i	−0.0143586	−	0.999897i	$-0.504571\pi$
$659$	−13.5220	−	3.62321i	−0.526742	−	0.141140i	−0.512383	+	0.858757i	$0.671237\pi$
$660$		0			0
$661$	−40.1488	+	10.7578i	−1.56161	+	0.418432i	−0.933172	−	0.359430i	$-0.882971\pi$
$661$	−40.1488	+	10.7578i	−1.56161	+	0.418432i	−0.628436	+	0.777861i	$0.716305\pi$
$662$	8.00970	−	30.8739i	0.311306	−	1.19995i
$663$		0			0
$664$	2.58590	−	10.6633i	0.100352	−	0.413816i
$665$	11.1918			0.434001
$666$		0			0
$667$	−7.67055	+	7.67055i	−0.297005	+	0.297005i
$668$	17.3279	+	9.63966i	0.670436	+	0.372970i
$669$		0			0
$670$	−41.3735	+	24.3283i	−1.59840	+	0.939883i
$671$	−3.44102	+	5.96002i	−0.132839	+	0.230084i
$672$		0			0
$673$	2.88063	+	4.98940i	0.111040	+	0.192327i	0.916190	−	0.400744i	$-0.131248\pi$
$673$	2.88063	+	4.98940i	0.111040	+	0.192327i	−0.805150	+	0.593072i	$0.797915\pi$
$674$	12.4070	+	7.03204i	0.477898	+	0.270864i
$675$		0			0
$676$	−3.18278	+	1.90579i	−0.122414	+	0.0732996i
$677$	27.1438	+	7.27316i	1.04322	+	0.279530i	0.739447	−	0.673214i	$-0.235087\pi$
$677$	27.1438	+	7.27316i	1.04322	+	0.279530i	0.303773	+	0.952744i	$0.401754\pi$
$678$		0			0
$679$	−0.421949	+	0.730837i	−0.0161929	+	0.0280469i
$680$	17.0371	+	58.0043i	0.653343	+	2.22436i
$681$		0			0
$682$	1.96851	+	1.93740i	0.0753780	+	0.0741871i
$683$	−4.50875	−	4.50875i	−0.172522	−	0.172522i	0.615564	−	0.788087i	$-0.288928\pi$
$683$	−4.50875	−	4.50875i	−0.172522	−	0.172522i	−0.788087	+	0.615564i	$0.788928\pi$
$684$		0			0
$685$	−16.5206	+	16.5206i	−0.631219	+	0.631219i
$686$	0.190423	+	23.9146i	0.00727039	+	0.913064i
$687$		0			0
$688$	−6.05656	−	1.41778i	−0.230904	−	0.0540524i
$689$	−18.4343	−	10.6430i	−0.702290	−	0.405467i
$690$		0			0
$691$	−2.65522	+	9.90941i	−0.101009	+	0.376972i	−0.997862	−	0.0653578i	$-0.979181\pi$
$691$	−2.65522	+	9.90941i	−0.101009	+	0.376972i	0.896853	+	0.442329i	$0.145848\pi$
$692$	−3.65512	+	14.5650i	−0.138947	+	0.553679i
$693$		0			0
$694$	11.2205	+	40.5804i	0.425926	+	1.54041i
$695$	27.1319	−	15.6646i	1.02917	−	0.594193i
$696$		0			0
$697$	−58.1591	−	33.5782i	−2.20293	−	1.27186i
$698$	−3.18125	+	12.2623i	−0.120412	+	0.464136i
$699$		0			0
$700$	17.8637	+	9.93771i	0.675183	+	0.375610i
$701$	−16.5518	−	16.5518i	−0.625154	−	0.625154i	0.321691	−	0.946845i	$-0.395749\pi$
$701$	−16.5518	−	16.5518i	−0.625154	−	0.625154i	−0.946845	+	0.321691i	$0.895749\pi$
$702$		0			0
$703$		−	11.4916i		−	0.433414i
$704$	1.39774	−	6.43071i	0.0526792	−	0.242367i
$705$		0			0
$706$	−23.3250	−	39.6673i	−0.877848	−	1.49290i
$707$	−6.00445	−	22.4089i	−0.225821	−	0.842774i
$708$		0			0
$709$	10.7915	−	40.2743i	0.405282	−	1.51253i	−0.398253	−	0.917276i	$-0.630383\pi$
$709$	10.7915	−	40.2743i	0.405282	−	1.51253i	0.803535	−	0.595257i	$-0.202950\pi$
$710$	3.30564	+	11.9552i	0.124059	+	0.448672i
$711$		0			0
$712$	−0.624916	−	26.1560i	−0.0234197	−	0.980236i
$713$	7.03484	+	12.1847i	0.263457	+	0.456320i
$714$		0			0
$715$	2.08513	+	7.78182i	0.0779795	+	0.291023i
$716$	1.19010	−	1.22862i	0.0444761	−	0.0459157i
$717$		0			0
$718$	0.822824	−	0.00655184i	0.0307075	−	0.000244513i
$719$	26.8494			1.00131			0.500656	−	0.865646i	$-0.333092\pi$
$719$	26.8494			1.00131			0.500656	+	0.865646i	$0.333092\pi$
$720$		0			0
$721$	−32.4488			−1.20846
$722$	24.3072	−	0.193549i	0.904619	−	0.00720315i
$723$		0			0
$724$	20.6645	+	20.0166i	0.767991	+	0.743912i
$725$	1.70843	+	6.37597i	0.0634497	+	0.236797i
$726$		0			0
$727$	−12.1681	−	21.0758i	−0.451290	−	0.781657i	0.547176	−	0.837017i	$-0.315703\pi$
$727$	−12.1681	−	21.0758i	−0.451290	−	0.781657i	−0.998466	+	0.0553600i	$0.982369\pi$
$728$	−19.3714	−	18.4674i	−0.717952	−	0.684446i
$729$		0			0
$730$	−14.0727	−	50.8957i	−0.520856	−	1.88373i
$731$	2.93245	−	10.9440i	0.108460	−	0.404780i
$732$		0			0
$733$	5.85501	+	21.8512i	0.216260	+	0.807093i	0.985719	+	0.168397i	$0.0538591\pi$
$733$	5.85501	+	21.8512i	0.216260	+	0.807093i	−0.769459	+	0.638696i	$0.779474\pi$
$734$	−3.04804	−	5.18359i	−0.112505	−	0.191330i
$735$		0			0
$736$	15.5928	−	29.6761i	0.574758	−	1.09388i
$737$			9.51661i			0.350549i
$738$		0			0
$739$	−12.6742	−	12.6742i	−0.466230	−	0.466230i	0.434461	−	0.900691i	$-0.356939\pi$
$739$	−12.6742	−	12.6742i	−0.466230	−	0.466230i	−0.900691	+	0.434461i	$0.856939\pi$
$740$	24.3521	−	43.7745i	0.895202	−	1.60918i
$741$		0			0
$742$	−6.41811	+	24.7390i	−0.235616	+	0.908196i
$743$	−25.2864	−	14.5991i	−0.927667	−	0.535589i	−0.0415943	−	0.999135i	$-0.513244\pi$
$743$	−25.2864	−	14.5991i	−0.927667	−	0.535589i	−0.886073	+	0.463546i	$0.846577\pi$
$744$		0			0
$745$	11.1551	−	6.44042i	0.408692	−	0.235959i
$746$	2.35008	+	8.49933i	0.0860426	+	0.311183i
$747$		0			0
$748$	11.6264	+	2.91766i	0.425102	+	0.106680i
$749$	0.181500	−	0.677369i	0.00663188	−	0.0247505i
$750$		0			0
$751$	−23.9864	−	13.8486i	−0.875277	−	0.505341i	−0.00617885	−	0.999981i	$-0.501967\pi$
$751$	−23.9864	−	13.8486i	−0.875277	−	0.505341i	−0.869098	+	0.494639i	$0.835300\pi$
$752$	−12.0581	−	19.4289i	−0.439713	−	0.708498i
$753$		0			0
$754$	−0.0688131	−	8.64201i	−0.00250603	−	0.314724i
$755$	28.7833	−	28.7833i	1.04753	−	1.04753i
$756$		0			0
$757$	−6.84906	−	6.84906i	−0.248933	−	0.248933i	0.571599	−	0.820533i	$-0.306323\pi$
$757$	−6.84906	−	6.84906i	−0.248933	−	0.248933i	−0.820533	+	0.571599i	$0.806323\pi$
$758$	−12.8259	−	12.6232i	−0.465857	−	0.458497i
$759$		0			0
$760$	−9.80268	−	5.35156i	−0.355581	−	0.194121i
$761$	6.92685	−	11.9977i	0.251098	−	0.434915i	−0.712730	−	0.701438i	$-0.752542\pi$
$761$	6.92685	−	11.9977i	0.251098	−	0.434915i	0.963828	+	0.266523i	$0.0858750\pi$
$762$		0			0
$763$	5.84262	+	1.56553i	0.211517	+	0.0566758i
$764$	−11.9243	−	19.9142i	−0.431405	−	0.720470i
$765$		0			0
$766$	10.7275	+	6.08018i	0.387602	+	0.219686i
$767$	−18.4134	−	31.8930i	−0.664871	−	1.15159i
$768$		0			0
$769$	5.15368	−	8.92644i	0.185846	−	0.321896i	−0.758015	−	0.652237i	$-0.773831\pi$
$769$	5.15368	−	8.92644i	0.185846	−	0.321896i	0.943861	+	0.330342i	$0.107164\pi$
$770$	8.33842	−	4.90313i	0.300496	−	0.176696i
$771$		0			0
$772$	−9.90906	+	17.8122i	−0.356635	+	0.641073i
$773$	29.0684	−	29.0684i	1.04552	−	1.04552i	0.0466043	−	0.998913i	$-0.485160\pi$
$773$	29.0684	−	29.0684i	1.04552	−	1.04552i	0.998913	−	0.0466043i	$-0.0148400\pi$
$774$		0			0
$775$	8.56139			0.307534
$776$	0.719036	−	0.438362i	0.0258119	−	0.0157363i
$777$		0			0
$778$	9.89168	−	38.1281i	0.354634	−	1.36696i
$779$	11.9837	−	3.21101i	0.429359	−	0.115046i
$780$		0			0
$781$	2.37561	+	0.636543i	0.0850060	+	0.0227773i
$782$	53.1224	+	30.1088i	1.89965	+	1.07669i
$783$		0			0
$784$	−1.95236	+	3.64494i	−0.0697273	+	0.130176i
$785$	15.8222	−	9.13496i	0.564719	−	0.326041i
$786$		0			0
$787$	−35.9593	+	9.63526i	−1.28181	+	0.343460i	−0.834544	−	0.550941i	$-0.814269\pi$
$787$	−35.9593	+	9.63526i	−1.28181	+	0.343460i	−0.447266	+	0.894401i	$0.647602\pi$
$788$	−8.50978	+	8.78522i	−0.303148	+	0.312961i
$789$		0			0
$790$	−30.0594	+	30.5419i	−1.06946	+	1.08663i
$791$			1.68105i			0.0597712i
$792$		0			0
$793$		−	27.9297i		−	0.991814i
$794$	5.44969	+	5.36359i	0.193402	+	0.190347i
$795$		0			0
$796$	55.4449	−	0.883030i	1.96519	−	0.0312982i
$797$	−9.38318	+	2.51421i	−0.332369	+	0.0890580i	−0.421144	−	0.906994i	$-0.638371\pi$
$797$	−9.38318	+	2.51421i	−0.332369	+	0.0890580i	0.0887752	+	0.996052i	$0.471705\pi$
$798$		0			0
$799$	36.0706	−	20.8254i	1.27609	−	0.736749i
$800$	−10.8945	−	17.2460i	−0.385178	−	0.609738i
$801$		0			0
$802$	−20.0853	+	35.4375i	−0.709237	+	1.25134i
$803$	−10.1134	−	2.70988i	−0.356895	−	0.0956297i
$804$		0			0
$805$	47.5965	−	12.7534i	1.67756	−	0.449500i
$806$	−10.8499	−	2.81483i	−0.382172	−	0.0991481i
$807$		0			0
$808$	−5.45601	+	22.4986i	−0.191942	+	0.791497i
$809$	−13.1867			−0.463620			−0.231810	−	0.972761i	$-0.574465\pi$
$809$	−13.1867			−0.463620			−0.231810	+	0.972761i	$0.574465\pi$
$810$		0			0
$811$	−11.0093	+	11.0093i	−0.386587	+	0.386587i	−0.873468	−	0.486881i	$-0.838135\pi$
$811$	−11.0093	+	11.0093i	−0.386587	+	0.386587i	0.486881	+	0.873468i	$0.338135\pi$
$812$	−9.97909	+	2.84496i	−0.350197	+	0.0998385i
$813$		0			0
$814$	−5.03444	−	8.56175i	−0.176457	−	0.300089i
$815$	−7.03233	+	12.1804i	−0.246332	+	0.426659i
$816$		0			0
$817$	1.04656	+	1.81269i	0.0366144	+	0.0634179i
$818$	7.33690	−	12.9448i	0.256529	−	0.452606i
$819$		0			0
$820$	52.4535	+	13.1633i	1.83175	+	0.459682i
$821$	4.17943	+	1.11987i	0.145863	+	0.0390839i	0.331012	−	0.943627i	$-0.392610\pi$
$821$	4.17943	+	1.11987i	0.145863	+	0.0390839i	−0.185149	+	0.982711i	$0.559277\pi$
$822$		0			0
$823$	23.8576	−	41.3225i	0.831622	−	1.44041i	−0.0651287	−	0.997877i	$-0.520746\pi$
$823$	23.8576	−	41.3225i	0.831622	−	1.44041i	0.896751	−	0.442535i	$-0.145921\pi$
$824$	28.4212	+	15.5159i	0.990098	+	0.540522i
$825$		0			0
$826$	−31.0167	+	31.5146i	−1.07921	+	1.09653i
$827$	1.38625	+	1.38625i	0.0482045	+	0.0482045i	0.730798	−	0.682594i	$-0.239148\pi$
$827$	1.38625	+	1.38625i	0.0482045	+	0.0482045i	−0.682594	+	0.730798i	$0.739148\pi$
$828$		0			0
$829$	−21.8345	+	21.8345i	−0.758345	+	0.758345i	−0.976021	−	0.217676i	$-0.930152\pi$
$829$	−21.8345	+	21.8345i	−0.758345	+	0.758345i	0.217676	+	0.976021i	$0.430152\pi$
$830$	−16.0938	+	0.128149i	−0.558624	+	0.00444812i
$831$		0			0
$832$	8.13651	+	25.4379i	0.282083	+	0.881900i
$833$	−6.52255	−	3.76580i	−0.225993	−	0.130477i
$834$		0			0
$835$	7.52771	−	28.0938i	0.260507	−	0.972227i
$836$	−1.89989	+	1.13762i	−0.0657090	+	0.0393454i
$837$		0			0
$838$	−17.5016	+	4.83923i	−0.604583	+	0.167168i
$839$	27.8914	−	16.1031i	0.962916	−	0.555940i	0.0658470	−	0.997830i	$-0.479025\pi$
$839$	27.8914	−	16.1031i	0.962916	−	0.555940i	0.897069	+	0.441890i	$0.145692\pi$
$840$		0			0
$841$	22.2129	+	12.8246i	0.765962	+	0.442228i
$842$	13.0590	+	3.38794i	0.450044	+	0.116756i
$843$		0			0
$844$	37.9109	−	10.8081i	1.30495	−	0.372031i
$845$	3.84768	+	3.84768i	0.132364	+	0.132364i
$846$		0			0
$847$			29.2602i			1.00539i
$848$	17.4508	−	18.5994i	0.599263	−	0.638705i
$849$		0			0
$850$	32.0291	−	18.8336i	1.09859	−	0.645988i
$851$	−13.0950	−	48.8712i	−0.448891	−	1.67528i
$852$		0			0
$853$	−12.0354	+	44.9166i	−0.412083	+	1.53791i	0.378525	+	0.925591i	$0.376431\pi$
$853$	−12.0354	+	44.9166i	−0.412083	+	1.53791i	−0.790608	+	0.612323i	$0.790235\pi$
$854$	−32.3221	+	8.93713i	−1.10604	+	0.305822i
$855$		0			0
$856$	−0.482866	+	0.506504i	−0.0165040	+	0.0173120i
$857$	10.0139	+	17.3446i	0.342068	+	0.592480i	0.984817	−	0.173598i	$-0.0555392\pi$
$857$	10.0139	+	17.3446i	0.342068	+	0.592480i	−0.642748	+	0.766077i	$0.722206\pi$
$858$		0			0
$859$	−4.47358	−	16.6956i	−0.152637	−	0.569648i	−0.999296	−	0.0375129i	$-0.988056\pi$
$859$	−4.47358	−	16.6956i	−0.152637	−	0.569648i	0.846659	−	0.532135i	$-0.178610\pi$
$860$	0.145292	+	9.12279i	0.00495442	+	0.311085i
$861$		0			0
$862$	−0.185180	−	23.2561i	−0.00630725	−	0.792106i
$863$	24.4242			0.831410			0.415705	−	0.909499i	$-0.363535\pi$
$863$	24.4242			0.831410			0.415705	+	0.909499i	$0.363535\pi$
$864$		0			0
$865$	22.0265			0.748923
$866$	−0.0396048	−	4.97384i	−0.00134583	−	0.169018i
$867$		0			0
$868$	0.214319	+	13.4569i	0.00727446	+	0.456759i
$869$	2.19914	+	8.20731i	0.0746007	+	0.278414i
$870$		0			0
$871$	−19.3109	−	33.4474i	−0.654324	−	1.13332i
$872$	−4.36883	−	4.16495i	−0.147947	−	0.141043i
$873$		0			0
$874$	−10.8725	+	3.00627i	−0.367768	+	0.101689i
$875$	−2.99989	+	11.1957i	−0.101415	+	0.378485i
$876$		0			0
$877$	−9.26415	−	34.5743i	−0.312828	−	1.16749i	−0.925995	−	0.377537i	$-0.876771\pi$
$877$	−9.26415	−	34.5743i	−0.312828	−	1.16749i	0.613167	−	0.789954i	$-0.289895\pi$
$878$	−25.4744	+	14.9794i	−0.859721	+	0.505530i
$879$		0			0
$880$	−9.64793	+	0.307389i	−0.325232	+	0.0103621i
$881$			45.8264i			1.54393i	0.635664	+	0.771966i	$0.280726\pi$
$881$			45.8264i			1.54393i	−0.635664	+	0.771966i	$0.719274\pi$
$882$		0			0
$883$	7.22790	+	7.22790i	0.243238	+	0.243238i	0.818188	−	0.574950i	$-0.194979\pi$
$883$	7.22790	+	7.22790i	0.243238	+	0.243238i	−0.574950	+	0.818188i	$0.694979\pi$
$884$	−46.7829	+	13.3374i	−1.57348	+	0.448586i
$885$		0			0
$886$	−15.1345	−	3.92640i	−0.508455	−	0.131910i
$887$	36.9502	+	21.3332i	1.24067	+	0.716300i	0.969230	−	0.246156i	$-0.0791676\pi$
$887$	36.9502	+	21.3332i	1.24067	+	0.716300i	0.271438	+	0.962456i	$0.412501\pi$
$888$		0			0
$889$	−34.8107	+	20.0980i	−1.16751	+	0.674065i
$890$	−36.9887	+	10.2274i	−1.23986	+	0.342824i
$891$		0			0
$892$	−21.6115	+	12.9406i	−0.723608	+	0.433284i
$893$	−1.99149	+	7.43234i	−0.0666426	+	0.248714i
$894$		0			0
$895$	−2.17284	−	1.25449i	−0.0726300	−	0.0419330i
$896$	26.8348	−	17.5559i	0.896489	−	0.586501i
$897$		0			0
$898$	24.8695	−	0.198027i	0.829906	−	0.00660824i
$899$	−3.07305	+	3.07305i	−0.102492	+	0.102492i
$900$		0			0
$901$	32.8489	+	32.8489i	1.09435	+	1.09435i
$902$	7.52162	−	7.64236i	0.250443	−	0.254463i
$903$		0			0
$904$	0.803819	−	1.47239i	0.0267346	−	0.0489710i
$905$	21.0997	−	36.5457i	0.701376	−	1.21482i
$906$		0			0
$907$	38.9844	+	10.4458i	1.29445	+	0.346848i	0.839351	−	0.543590i	$-0.182935\pi$
$907$	38.9844	+	10.4458i	1.29445	+	0.346848i	0.455104	+	0.890438i	$0.349602\pi$
$908$	−23.3855	−	5.86863i	−0.776074	−	0.194757i
$909$		0			0
$910$	−19.3572	+	34.1528i	−0.641685	+	1.13216i
$911$	−22.6553	−	39.2402i	−0.750605	−	1.30009i	−0.947530	−	0.319667i	$-0.896429\pi$
$911$	−22.6553	−	39.2402i	−0.750605	−	1.30009i	0.196925	−	0.980419i	$-0.436905\pi$
$912$		0			0
$913$	−1.59558	+	2.76362i	−0.0528060	+	0.0914626i
$914$	−15.4459	−	26.2679i	−0.510906	−	0.868865i
$915$		0			0
$916$	10.8949	−	3.10605i	0.359978	−	0.102627i
$917$	8.01324	−	8.01324i	0.264621	−	0.264621i
$918$		0			0
$919$	−3.91688			−0.129206			−0.0646030	−	0.997911i	$-0.520578\pi$
$919$	−3.91688			−0.129206			−0.0646030	+	0.997911i	$0.520578\pi$
$920$	−47.7869	−	11.5886i	−1.57549	−	0.382063i
$921$		0			0
$922$	24.0815	+	6.24754i	0.793082	+	0.205752i
$923$	−9.64107	+	2.58332i	−0.317340	+	0.0850309i
$924$		0			0
$925$	−29.7381	−	7.96831i	−0.977784	−	0.261996i
$926$	14.8472	−	26.1956i	0.487910	−	0.860842i
$927$		0			0
$928$	10.1008	+	2.27982i	0.331575	+	0.0748388i
$929$	13.7214	−	7.92207i	0.450185	−	0.259915i	−0.257723	−	0.966219i	$-0.582972\pi$
$929$	13.7214	−	7.92207i	0.450185	−	0.259915i	0.707908	+	0.706304i	$0.249639\pi$
$930$		0			0
$931$	1.34397	−	0.360116i	0.0440468	−	0.0118023i
$932$	20.2556	−	0.322597i	0.663496	−	0.0105670i
$933$		0			0
$934$	−3.74694	−	3.68774i	−0.122604	−	0.120667i
$935$		−	17.5824i		−	0.575005i
$936$		0			0
$937$		−	38.0380i		−	1.24265i	−0.783554	−	0.621324i	$-0.786595\pi$
$937$		−	38.0380i		−	1.24265i	0.783554	−	0.621324i	$-0.213405\pi$
$938$	−32.5284	+	33.0505i	−1.06209	+	1.07914i
$939$		0			0
$940$	−23.3362	+	24.0915i	−0.761142	+	0.785779i
$941$	49.4756	−	13.2570i	1.61286	−	0.432164i	0.663966	−	0.747762i	$-0.268872\pi$
$941$	49.4756	−	13.2570i	1.61286	−	0.432164i	0.948893	+	0.315598i	$0.102205\pi$
$942$		0			0
$943$	47.3048	−	27.3115i	1.54046	−	0.889384i
$944$	42.2359	−	12.7718i	1.37466	−	0.415686i
$945$		0			0
$946$	1.57387	+	0.892039i	0.0511708	+	0.0290027i
$947$	−15.8269	−	4.24080i	−0.514305	−	0.137808i	−0.00767376	−	0.999971i	$-0.502443\pi$
$947$	−15.8269	−	4.24080i	−0.514305	−	0.137808i	−0.506631	+	0.862163i	$0.669109\pi$
$948$		0			0
$949$	41.0438	−	10.9977i	1.33234	−	0.356999i
$950$	−1.72373	+	6.64421i	−0.0559251	+	0.215567i
$951$		0			0
$952$	30.4048	+	49.8724i	0.985426	+	1.61637i
$953$	−19.2107			−0.622295			−0.311147	−	0.950362i	$-0.600713\pi$
$953$	−19.2107			−0.622295			−0.311147	+	0.950362i	$0.600713\pi$
$954$		0			0
$955$	−24.0744	+	24.0744i	−0.779030	+	0.779030i
$956$	0.512518	−	0.921284i	0.0165760	−	0.0297964i
$957$		0			0
$958$	26.2174	−	15.4163i	0.847047	−	0.498077i
$959$	−11.2867	+	19.5491i	−0.364466	+	0.631274i
$960$		0			0
$961$	−12.6816	−	21.9652i	−0.409085	−	0.708556i
$962$	35.0675	+	19.8756i	1.13062	+	0.640817i
$963$		0			0
$964$	−20.0218	−	33.4375i	−0.644858	−	1.07695i
$965$	28.8789	+	7.73809i	0.929646	+	0.249098i
$966$		0			0
$967$	−17.0779	+	29.5798i	−0.549188	+	0.951222i	0.449142	+	0.893460i	$0.351730\pi$
$967$	−17.0779	+	29.5798i	−0.549188	+	0.951222i	−0.998330	+	0.0577615i	$0.981604\pi$
$968$	13.9912	−	25.6284i	0.449695	−	0.823726i
$969$		0			0
$970$	−0.880367	−	0.866458i	−0.0282669	−	0.0278203i
$971$	−20.2022	−	20.2022i	−0.648318	−	0.648318i	0.304268	−	0.952586i	$-0.401588\pi$
$971$	−20.2022	−	20.2022i	−0.648318	−	0.648318i	−0.952586	+	0.304268i	$0.901588\pi$
$972$		0			0
$973$	21.4038	−	21.4038i	0.686175	−	0.686175i
$974$	−0.164905	−	20.7099i	−0.00528389	−	0.663586i
$975$		0			0
$976$	32.5836	+	7.62751i	1.04298	+	0.244151i
$977$	7.37615	+	4.25862i	0.235984	+	0.136245i	0.613329	−	0.789827i	$-0.289830\pi$
$977$	7.37615	+	4.25862i	0.235984	+	0.136245i	−0.377346	+	0.926072i	$0.623163\pi$
$978$		0			0
$979$	−1.96942	+	7.34998i	−0.0629430	+	0.234906i
$980$	5.88266	+	1.47627i	0.187915	+	0.0471576i
$981$		0			0
$982$	−16.4782	−	59.5954i	−0.525841	−	1.90176i
$983$	−47.6844	+	27.5306i	−1.52090	+	0.878090i	−0.521200	+	0.853435i	$0.674515\pi$
$983$	−47.6844	+	27.5306i	−1.52090	+	0.878090i	−0.999696	+	0.0246553i	$0.992151\pi$
$984$		0			0
$985$	15.5369	+	8.97021i	0.495045	+	0.285815i
$986$	−4.73641	+	18.2568i	−0.150838	+	0.581415i
$987$		0			0
$988$	4.36899	−	7.85353i	0.138996	−	0.249854i
$989$	6.51638	+	6.51638i	0.207209	+	0.207209i
$990$		0			0
$991$		−	61.9180i		−	1.96689i	−0.181210	−	0.983444i	$-0.558001\pi$
$991$		−	61.9180i		−	1.96689i	0.181210	−	0.983444i	$-0.441999\pi$
$992$	6.24693	−	11.8891i	0.198340	−	0.377480i
$993$		0			0
$994$	6.07459	+	10.3307i	0.192674	+	0.327668i
$995$	−21.0516	−	78.5655i	−0.667380	−	2.49069i
$996$		0			0
$997$	−4.65375	+	17.3680i	−0.147386	+	0.550051i	0.852252	+	0.523132i	$0.175236\pi$
$997$	−4.65375	+	17.3680i	−0.147386	+	0.550051i	−0.999638	+	0.0269194i	$0.991430\pi$
$998$	3.08800	+	11.1681i	0.0977490	+	0.353520i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.395.12		88
3.2	odd	2		144.2.u.a.59.11	yes	88
4.3	odd	2		1728.2.z.a.719.20		88
9.2	odd	6	inner	432.2.v.a.251.5		88
9.7	even	3		144.2.u.a.11.18	✓	88
12.11	even	2		576.2.y.a.527.15		88
16.3	odd	4	inner	432.2.v.a.179.5		88
16.13	even	4		1728.2.z.a.1583.20		88
36.7	odd	6		576.2.y.a.335.19		88
36.11	even	6		1728.2.z.a.143.20		88
48.29	odd	4		576.2.y.a.239.19		88
48.35	even	4		144.2.u.a.131.18	yes	88
144.29	odd	12		1728.2.z.a.1007.20		88
144.61	even	12		576.2.y.a.47.15		88
144.83	even	12	inner	432.2.v.a.35.12		88
144.115	odd	12		144.2.u.a.83.11	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.18	✓	88	9.7	even	3
144.2.u.a.59.11	yes	88	3.2	odd	2
144.2.u.a.83.11	yes	88	144.115	odd	12
144.2.u.a.131.18	yes	88	48.35	even	4
432.2.v.a.35.12		88	144.83	even	12	inner
432.2.v.a.179.5		88	16.3	odd	4	inner
432.2.v.a.251.5		88	9.2	odd	6	inner
432.2.v.a.395.12		88	1.1	even	1	trivial
576.2.y.a.47.15		88	144.61	even	12
576.2.y.a.239.19		88	48.29	odd	4
576.2.y.a.335.19		88	36.7	odd	6
576.2.y.a.527.15		88	12.11	even	2
1728.2.z.a.143.20		88	36.11	even	6
1728.2.z.a.719.20		88	4.3	odd	2
1728.2.z.a.1007.20		88	144.29	odd	12
1728.2.z.a.1583.20		88	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0112605 + 1.41417i) q^{2} +(-1.99975 + 0.0318485i) q^{4} +(0.759273 + 2.83365i) q^{5} +(1.41719 + 2.45465i) q^{7} +(-0.0675573 - 2.82762i) q^{8} +(-3.99870 + 1.10565i) q^{10} +(-0.212907 + 0.794578i) q^{11} +(-0.864050 - 3.22468i) q^{13} +(-3.45533 + 2.03179i) q^{14} +(3.99797 - 0.127378i) q^{16} +7.28589i q^{17} +(-0.951758 - 0.951758i) q^{19} +(-1.60860 - 5.64239i) q^{20} +(-1.12606 - 0.292138i) q^{22} +(-5.13217 - 2.96306i) q^{23} +(-3.12293 + 1.80302i) q^{25} +(4.55051 - 1.25822i) q^{26} +(-2.91220 - 4.86354i) q^{28} +(0.473770 - 1.76813i) q^{29} +(-2.05610 - 1.18709i) q^{31} +(0.225153 + 5.65237i) q^{32} +(-10.3035 + 0.0820428i) q^{34} +(-5.87957 + 5.87957i) q^{35} +(6.03704 + 6.03704i) q^{37} +(1.33523 - 1.35666i) q^{38} +(7.96118 - 2.33837i) q^{40} +(-4.60866 + 7.98243i) q^{41} +(-1.50209 - 0.402483i) q^{43} +(0.400453 - 1.59574i) q^{44} +(4.13248 - 7.29113i) q^{46} +(-2.85832 - 4.95075i) q^{47} +(-0.516861 + 0.895230i) q^{49} +(-2.58494 - 4.39604i) q^{50} +(1.83058 + 6.42102i) q^{52} +(4.50856 - 4.50856i) q^{53} -2.41321 q^{55} +(6.84507 - 4.17311i) q^{56} +(2.50577 + 0.650080i) q^{58} +(10.6553 - 2.85508i) q^{59} +(8.08106 + 2.16531i) q^{61} +(1.65559 - 2.92104i) q^{62} +(-7.99087 + 0.382053i) q^{64} +(8.48155 - 4.89682i) q^{65} +(11.1746 - 2.99423i) q^{67} +(-0.232045 - 14.5699i) q^{68} +(-8.38090 - 8.24849i) q^{70} -2.98978i q^{71} +12.7280i q^{73} +(-8.46941 + 8.60537i) q^{74} +(1.93359 + 1.87296i) q^{76} +(-2.25214 + 0.603459i) q^{77} +(8.94529 - 5.16457i) q^{79} +(3.39650 + 11.2321i) q^{80} +(-11.3404 - 6.42753i) q^{82} +(3.74713 + 1.00404i) q^{83} +(-20.6456 + 5.53198i) q^{85} +(0.552264 - 2.12873i) q^{86} +(2.26115 + 0.548339i) q^{88} +9.25017 q^{89} +(6.69092 - 6.69092i) q^{91} +(10.3574 + 5.76192i) q^{92} +(6.96901 - 4.09789i) q^{94} +(1.97430 - 3.41959i) q^{95} +(0.148868 + 0.257847i) q^{97} +(-1.27183 - 0.720848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Introduction

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