LMFDB - Embedded newform 432.2.y.e.181.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(37,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [72,-4,0,-2,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			181.6
Character	$\chi$	$=$	432.181
Dual form			432.2.y.e.253.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04877 + 0.948722i) q^{2} +(0.199854 - 1.98999i) q^{4} +(-0.00302457 + 0.0112878i) q^{5} +(-1.05753 - 0.610563i) q^{7} +(1.67835 + 2.27665i) q^{8} +(-0.00753693 - 0.0147079i) q^{10} +(-1.83070 + 0.490535i) q^{11} +(5.06759 + 1.35786i) q^{13} +(1.68836 - 0.362956i) q^{14} +(-3.92012 - 0.795413i) q^{16} +1.54238 q^{17} +(4.06823 - 4.06823i) q^{19} +(0.0218582 + 0.00827477i) q^{20} +(1.45461 - 2.25129i) q^{22} +(5.20660 - 3.00603i) q^{23} +(4.33001 + 2.49993i) q^{25} +(-6.60298 + 3.38365i) q^{26} +(-1.42637 + 1.98244i) q^{28} +(-0.798708 - 2.98082i) q^{29} +(2.92831 + 5.07198i) q^{31} +(4.86594 - 2.88489i) q^{32} +(-1.61761 + 1.46329i) q^{34} +(0.0100905 - 0.0100905i) q^{35} +(0.923082 + 0.923082i) q^{37} +(-0.407035 + 8.12628i) q^{38} +(-0.0307748 + 0.0120590i) q^{40} +(3.20829 - 1.85231i) q^{41} +(-4.84015 + 1.29691i) q^{43} +(0.610287 + 3.74111i) q^{44} +(-2.60866 + 8.09227i) q^{46} +(1.31218 - 2.27277i) q^{47} +(-2.75442 - 4.77080i) q^{49} +(-6.91294 + 1.48611i) q^{50} +(3.71490 - 9.81308i) q^{52} +(8.88508 + 8.88508i) q^{53} -0.0221483i q^{55} +(-0.384853 - 3.43236i) q^{56} +(3.66563 + 2.36845i) q^{58} +(-2.35453 + 8.78724i) q^{59} +(3.24737 + 12.1194i) q^{61} +(-7.88303 - 2.54121i) q^{62} +(-2.36631 + 7.64203i) q^{64} +(-0.0306545 + 0.0530952i) q^{65} +(-11.8800 - 3.18324i) q^{67} +(0.308250 - 3.06932i) q^{68} +(-0.00100958 + 0.0201557i) q^{70} -14.2363i q^{71} -4.32091i q^{73} +(-1.84385 - 0.0923563i) q^{74} +(-7.28269 - 8.90879i) q^{76} +(2.23552 + 0.599006i) q^{77} +(-0.261880 + 0.453589i) q^{79} +(0.0208352 - 0.0418439i) q^{80} +(-1.60745 + 4.98643i) q^{82} +(-2.91592 - 10.8824i) q^{83} +(-0.00466503 + 0.0174101i) q^{85} +(3.84581 - 5.95212i) q^{86} +(-4.18933 - 3.34459i) q^{88} +10.7103i q^{89} +(-4.53005 - 4.53005i) q^{91} +(-4.94142 - 10.9619i) q^{92} +(0.780042 + 3.62852i) q^{94} +(0.0336169 + 0.0582262i) q^{95} +(8.78820 - 15.2216i) q^{97} +(7.41493 + 2.39031i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32}+ \cdots - 88 q^{98}+O(q^{100}) $ 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.04877	+	0.948722i	−0.741595	+	0.670848i
$2$	−1.04877	+	0.948722i	−0.741595	+	0.670848i
$3$		0			0
$3$		0			0
$4$	0.199854	−	1.98999i	0.0999268	−	0.994995i
$5$	−0.00302457	+	0.0112878i	−0.00135263	+	0.00504807i	−0.966599	−	0.256294i	$-0.917498\pi$
$5$	−0.00302457	+	0.0112878i	−0.00135263	+	0.00504807i	0.965246	+	0.261342i	$0.0841651\pi$
$6$		0			0
$7$	−1.05753	−	0.610563i	−0.399708	−	0.230771i	0.286650	−	0.958035i	$-0.407458\pi$
$7$	−1.05753	−	0.610563i	−0.399708	−	0.230771i	−0.686358	+	0.727264i	$0.740792\pi$
$8$	1.67835	+	2.27665i	0.593385	+	0.804919i
$9$		0			0
$10$	−0.00753693	−	0.0147079i	−0.00238339	−	0.00465104i
$11$	−1.83070	+	0.490535i	−0.551977	+	0.147902i	−0.524018	−	0.851707i	$-0.675568\pi$
$11$	−1.83070	+	0.490535i	−0.551977	+	0.147902i	−0.0279594	+	0.999609i	$0.508901\pi$
$12$		0			0
$13$	5.06759	+	1.35786i	1.40550	+	0.376602i	0.880315	−	0.474389i	$-0.157331\pi$
$13$	5.06759	+	1.35786i	1.40550	+	0.376602i	0.525181	+	0.850991i	$0.323998\pi$
$14$	1.68836	−	0.362956i	0.451234	−	0.0970040i
$15$		0			0
$16$	−3.92012	−	0.795413i	−0.980029	−	0.198853i
$17$	1.54238			0.374082			0.187041	−	0.982352i	$-0.440110\pi$
$17$	1.54238			0.374082			0.187041	+	0.982352i	$0.440110\pi$
$18$		0			0
$19$	4.06823	−	4.06823i	0.933317	−	0.933317i	−0.0645950	−	0.997912i	$-0.520576\pi$
$19$	4.06823	−	4.06823i	0.933317	−	0.933317i	0.997912	+	0.0645950i	$0.0205756\pi$
$20$	0.0218582	+	0.00827477i	0.00488764	+	0.00185030i
$21$		0			0
$22$	1.45461	−	2.25129i	0.310124	−	0.479976i
$23$	5.20660	−	3.00603i	1.08565	−	0.626801i	0.153236	−	0.988190i	$-0.451030\pi$
$23$	5.20660	−	3.00603i	1.08565	−	0.626801i	0.932415	+	0.361388i	$0.117697\pi$
$24$		0			0
$25$	4.33001	+	2.49993i	0.866002	+	0.499986i
$26$	−6.60298	+	3.38365i	−1.29495	+	0.663588i
$27$		0			0
$28$	−1.42637	+	1.98244i	−0.269558	+	0.374647i
$29$	−0.798708	−	2.98082i	−0.148316	−	0.553524i	−0.999585	−	0.0287946i	$-0.990833\pi$
$29$	−0.798708	−	2.98082i	−0.148316	−	0.553524i	0.851269	−	0.524730i	$-0.175834\pi$
$30$		0			0
$31$	2.92831	+	5.07198i	0.525939	+	0.910954i	0.999543	+	0.0302159i	$0.00961949\pi$
$31$	2.92831	+	5.07198i	0.525939	+	0.910954i	−0.473604	+	0.880738i	$0.657047\pi$
$32$	4.86594	−	2.88489i	0.860185	−	0.509982i
$33$		0			0
$34$	−1.61761	+	1.46329i	−0.277418	+	0.250952i
$35$	0.0100905	−	0.0100905i	0.00170561	−	0.00170561i
$36$		0			0
$37$	0.923082	+	0.923082i	0.151754	+	0.151754i	0.778901	−	0.627147i	$-0.215777\pi$
$37$	0.923082	+	0.923082i	0.151754	+	0.151754i	−0.627147	+	0.778901i	$0.715777\pi$
$38$	−0.407035	+	8.12628i	−0.0660298	+	1.31826i
$39$		0			0
$40$	−0.0307748	+	0.0120590i	−0.00486592	+	0.00190669i
$41$	3.20829	−	1.85231i	0.501051	−	0.289282i	−0.228096	−	0.973639i	$-0.573250\pi$
$41$	3.20829	−	1.85231i	0.501051	−	0.289282i	0.729147	+	0.684357i	$0.239917\pi$
$42$		0			0
$43$	−4.84015	+	1.29691i	−0.738115	+	0.197777i	−0.608240	−	0.793753i	$-0.708124\pi$
$43$	−4.84015	+	1.29691i	−0.738115	+	0.197777i	−0.129875	+	0.991530i	$0.541458\pi$
$44$	0.610287	+	3.74111i	0.0920043	+	0.563994i
$45$		0			0
$46$	−2.60866	+	8.09227i	−0.384626	+	1.19314i
$47$	1.31218	−	2.27277i	0.191402	−	0.331517i	−0.754313	−	0.656515i	$-0.772030\pi$
$47$	1.31218	−	2.27277i	0.191402	−	0.331517i	0.945715	+	0.324997i	$0.105363\pi$
$48$		0			0
$49$	−2.75442	−	4.77080i	−0.393489	−	0.681543i
$50$	−6.91294	+	1.48611i	−0.977637	+	0.210168i
$51$		0			0
$52$	3.71490	−	9.81308i	0.515163	−	1.36083i
$53$	8.88508	+	8.88508i	1.22046	+	1.22046i	0.967469	+	0.252991i	$0.0814144\pi$
$53$	8.88508	+	8.88508i	1.22046	+	1.22046i	0.252991	+	0.967469i	$0.418586\pi$
$54$		0			0
$55$		−	0.0221483i		−	0.00298648i
$56$	−0.384853	−	3.43236i	−0.0514282	−	0.458668i
$57$		0			0
$58$	3.66563	+	2.36845i	0.481321	+	0.310993i
$59$	−2.35453	+	8.78724i	−0.306534	+	1.14400i	0.625082	+	0.780559i	$0.285065\pi$
$59$	−2.35453	+	8.78724i	−0.306534	+	1.14400i	−0.931617	+	0.363443i	$0.881601\pi$
$60$		0			0
$61$	3.24737	+	12.1194i	0.415783	+	1.55172i	0.783262	+	0.621692i	$0.213555\pi$
$61$	3.24737	+	12.1194i	0.415783	+	1.55172i	−0.367478	+	0.930032i	$0.619779\pi$
$62$	−7.88303	−	2.54121i	−1.00115	−	0.322734i
$63$		0			0
$64$	−2.36631	+	7.64203i	−0.295789	+	0.955253i
$65$	−0.0306545	+	0.0530952i	−0.00380223	+	0.00658565i
$66$		0			0
$67$	−11.8800	−	3.18324i	−1.45137	−	0.388895i	−0.554873	−	0.831935i	$-0.687233\pi$
$67$	−11.8800	−	3.18324i	−1.45137	−	0.388895i	−0.896501	+	0.443041i	$0.853900\pi$
$68$	0.308250	−	3.06932i	0.0373808	−	0.372210i
$69$		0			0
$70$	−0.00100958	+	0.0201557i	−0.000120667	+	0.00240907i
$71$		−	14.2363i		−	1.68954i	−0.535129	−	0.844771i	$-0.679737\pi$
$71$		−	14.2363i		−	1.68954i	0.535129	−	0.844771i	$-0.320263\pi$
$72$		0			0
$73$		−	4.32091i		−	0.505724i	−0.967502	−	0.252862i	$-0.918628\pi$
$73$		−	4.32091i		−	0.505724i	0.967502	−	0.252862i	$-0.0813718\pi$
$74$	−1.84385	−	0.0923563i	−0.214344	−	0.0107362i
$75$		0			0
$76$	−7.28269	−	8.90879i	−0.835382	−	1.02191i
$77$	2.23552	+	0.599006i	0.254761	+	0.0682630i
$78$		0			0
$79$	−0.261880	+	0.453589i	−0.0294638	+	0.0510328i	−0.880381	−	0.474267i	$-0.842713\pi$
$79$	−0.261880	+	0.453589i	−0.0294638	+	0.0510328i	0.850918	+	0.525299i	$0.176047\pi$
$80$	0.0208352	−	0.0418439i	0.00232944	−	0.00467829i
$81$		0			0
$82$	−1.60745	+	4.98643i	−0.177513	+	0.550659i
$83$	−2.91592	−	10.8824i	−0.320064	−	1.19450i	−0.919181	−	0.393834i	$-0.871148\pi$
$83$	−2.91592	−	10.8824i	−0.320064	−	1.19450i	0.599117	−	0.800661i	$-0.295518\pi$
$84$		0			0
$85$	−0.00466503	+	0.0174101i	−0.000505994	+	0.00188839i
$86$	3.84581	−	5.95212i	0.414704	−	0.641834i
$87$		0			0
$88$	−4.18933	−	3.34459i	−0.446584	−	0.356534i
$89$			10.7103i			1.13529i	0.823274	+	0.567644i	$0.192145\pi$
$89$			10.7103i			1.13529i	−0.823274	+	0.567644i	$0.807855\pi$
$90$		0			0
$91$	−4.53005	−	4.53005i	−0.474879	−	0.474879i
$92$	−4.94142	−	10.9619i	−0.515178	−	1.14285i
$93$		0			0
$94$	0.780042	+	3.62852i	0.0804551	+	0.374253i
$95$	0.0336169	+	0.0582262i	0.00344902	+	0.00597388i
$96$		0			0
$97$	8.78820	−	15.2216i	0.892306	−	1.54552i	0.0552025	−	0.998475i	$-0.482420\pi$
$97$	8.78820	−	15.2216i	0.892306	−	1.54552i	0.837104	−	0.547044i	$-0.184247\pi$
$98$	7.41493	+	2.39031i	0.749022	+	0.241458i
$99$		0			0
$100$	5.84021	−	8.11705i	0.584021	−	0.811705i
$101$	−6.73117	+	1.80361i	−0.669776	+	0.179466i	−0.577654	−	0.816282i	$-0.696032\pi$
$101$	−6.73117	+	1.80361i	−0.669776	+	0.179466i	−0.0921222	+	0.995748i	$0.529365\pi$
$102$		0			0
$103$	−2.20609	+	1.27369i	−0.217373	+	0.125500i	−0.604733	−	0.796428i	$-0.706720\pi$
$103$	−2.20609	+	1.27369i	−0.217373	+	0.125500i	0.387360	+	0.921928i	$0.373387\pi$
$104$	5.41379	+	13.8161i	0.530866	+	1.35478i
$105$		0			0
$106$	−17.7479	−	0.888971i	−1.72383	−	0.0863445i
$107$	−3.52175	−	3.52175i	−0.340460	−	0.340460i	0.516080	−	0.856540i	$-0.327391\pi$
$107$	−3.52175	−	3.52175i	−0.340460	−	0.340460i	−0.856540	+	0.516080i	$0.827391\pi$
$108$		0			0
$109$	3.14334	−	3.14334i	0.301077	−	0.301077i	−0.540358	−	0.841435i	$-0.681711\pi$
$109$	3.14334	−	3.14334i	0.301077	−	0.301077i	0.841435	+	0.540358i	$0.181711\pi$
$110$	0.0210126	+	0.0232286i	0.00200347	+	0.00221476i
$111$		0			0
$112$	3.65998	+	3.23465i	0.345835	+	0.305646i
$113$	−7.90904	−	13.6989i	−0.744020	−	1.28868i	−0.950651	−	0.310262i	$-0.899583\pi$
$113$	−7.90904	−	13.6989i	−0.744020	−	1.28868i	0.206631	−	0.978419i	$-0.433750\pi$
$114$		0			0
$115$	0.0181839	+	0.0678632i	0.00169566	+	0.00632828i
$116$	−6.09142	+	0.993693i	−0.565574	+	0.0922621i
$117$		0			0
$118$	−5.86727	−	11.4496i	−0.540126	−	1.05402i
$119$	−1.63111	−	0.941721i	−0.149523	−	0.0863274i
$120$		0			0
$121$	−6.41543	+	3.70395i	−0.583221	+	0.336723i
$122$	−14.9037	−	9.62961i	−1.34931	−	0.871824i
$123$		0			0
$124$	10.6784	−	4.81365i	0.958950	−	0.432278i
$125$	−0.0826316	+	0.0826316i	−0.00739079	+	0.00739079i
$126$		0			0
$127$	−5.72603			−0.508103			−0.254052	−	0.967191i	$-0.581763\pi$
$127$	−5.72603			−0.508103			−0.254052	+	0.967191i	$0.581763\pi$
$128$	−4.76843	−	10.2597i	−0.421474	−	0.906841i
$129$		0			0
$130$	−0.0182229	−	0.0847675i	−0.00159825	−	0.00743460i
$131$	−6.56224	−	1.75835i	−0.573346	−	0.153628i	−0.0395151	−	0.999219i	$-0.512581\pi$
$131$	−6.56224	−	1.75835i	−0.573346	−	0.153628i	−0.533831	+	0.845591i	$0.679248\pi$
$132$		0			0
$133$	−6.78618	+	1.81835i	−0.588436	+	0.157671i
$134$	15.4795	−	7.93233i	1.33722	−	0.685249i
$135$		0			0
$136$	2.58865	+	3.51147i	0.221975	+	0.301106i
$137$	3.64923	+	2.10688i	0.311775	+	0.180003i	0.647720	−	0.761878i	$-0.275722\pi$
$137$	3.64923	+	2.10688i	0.311775	+	0.180003i	−0.335946	+	0.941881i	$0.609056\pi$
$138$		0			0
$139$	−4.19392	+	15.6519i	−0.355724	+	1.32758i	0.523847	+	0.851812i	$0.324496\pi$
$139$	−4.19392	+	15.6519i	−0.355724	+	1.32758i	−0.879571	+	0.475767i	$0.842170\pi$
$140$	−0.0180634	−	0.0220966i	−0.00152663	−	0.00186750i
$141$		0			0
$142$	13.5063	+	14.9307i	1.13342	+	1.25296i
$143$	−9.94332			−0.831502
$144$		0			0
$145$	0.0360627			0.00299485
$146$	4.09934	+	4.53165i	0.339264	+	0.375042i
$147$		0			0
$148$	2.02141	−	1.65244i	0.166159	−	0.135830i
$149$	−1.00877	+	3.76477i	−0.0826415	+	0.308422i	−0.994857	−	0.101288i	$-0.967704\pi$
$149$	−1.00877	+	3.76477i	−0.0826415	+	0.308422i	0.912216	+	0.409710i	$0.134370\pi$
$150$		0			0
$151$	13.0073	+	7.50979i	1.05852	+	0.611138i	0.925023	−	0.379911i	$-0.124045\pi$
$151$	13.0073	+	7.50979i	1.05852	+	0.611138i	0.133499	+	0.991049i	$0.457379\pi$
$152$	16.0899	+	2.43406i	1.30506	+	0.197428i
$153$		0			0
$154$	−2.91284	+	1.49266i	−0.234724	+	0.120282i
$155$	−0.0661085	+	0.0177137i	−0.00530996	+	0.00142280i
$156$		0			0
$157$	−9.47288	−	2.53825i	−0.756018	−	0.202574i	−0.139832	−	0.990175i	$-0.544656\pi$
$157$	−9.47288	−	2.53825i	−0.756018	−	0.202574i	−0.616186	+	0.787601i	$0.711323\pi$
$158$	−0.155677	−	0.724164i	−0.0123850	−	0.0576114i
$159$		0			0
$160$	0.0178468	+	0.0636515i	0.00141092	+	0.00503209i
$161$	−7.34150			−0.578591
$162$		0			0
$163$	5.22606	−	5.22606i	0.409336	−	0.409336i	−0.472171	−	0.881507i	$-0.656529\pi$
$163$	5.22606	−	5.22606i	0.409336	−	0.409336i	0.881507	+	0.472171i	$0.156529\pi$
$164$	−3.04488	−	6.75466i	−0.237766	−	0.527450i
$165$		0			0
$166$	13.3825	+	8.64675i	1.03868	+	0.671118i
$167$	6.31476	−	3.64583i	0.488651	−	0.282123i	−0.235364	−	0.971907i	$-0.575628\pi$
$167$	6.31476	−	3.64583i	0.488651	−	0.282123i	0.724015	+	0.689785i	$0.242295\pi$
$168$		0			0
$169$	12.5783	+	7.26211i	0.967565	+	0.558624i
$170$	−0.0116248	−	0.0226851i	−0.000891583	−	0.00173987i
$171$		0			0
$172$	1.61352	+	9.89103i	0.123030	+	0.754184i
$173$	6.14659	+	22.9394i	0.467317	+	1.74405i	0.649092	+	0.760710i	$0.275149\pi$
$173$	6.14659	+	22.9394i	0.467317	+	1.74405i	−0.181775	+	0.983340i	$0.558184\pi$
$174$		0			0
$175$	−3.05273	−	5.28749i	−0.230765	−	0.399697i
$176$	7.56674	−	0.466790i	0.570365	−	0.0351856i
$177$		0			0
$178$	−10.1611	−	11.2327i	−0.761606	−	0.841925i
$179$	−11.4489	+	11.4489i	−0.855732	+	0.855732i	−0.990832	−	0.135100i	$-0.956864\pi$
$179$	−11.4489	+	11.4489i	−0.855732	+	0.855732i	0.135100	+	0.990832i	$0.456864\pi$
$180$		0			0
$181$	−3.01327	−	3.01327i	−0.223974	−	0.223974i	0.586195	−	0.810170i	$-0.300625\pi$
$181$	−3.01327	−	3.01327i	−0.223974	−	0.223974i	−0.810170	+	0.586195i	$0.800625\pi$
$182$	9.04876	+	0.453241i	0.670739	+	0.0335965i
$183$		0			0
$184$	15.5822	+	6.80848i	1.14873	+	0.501927i
$185$	−0.0132115	+	0.00762768i	−0.000971331	+	0.000560798i
$186$		0			0
$187$	−2.82364	+	0.756592i	−0.206485	+	0.0553275i
$188$	−4.26054	−	3.06545i	−0.310732	−	0.223571i
$189$		0			0
$190$	−0.0904970	−	0.0291730i	−0.00656534	−	0.00211643i
$191$	2.25702	−	3.90928i	0.163313	−	0.282866i	−0.772742	−	0.634720i	$-0.781115\pi$
$191$	2.25702	−	3.90928i	0.163313	−	0.282866i	0.936055	+	0.351854i	$0.114449\pi$
$192$		0			0
$193$	−1.75793	−	3.04482i	−0.126539	−	0.219171i	0.795795	−	0.605566i	$-0.207053\pi$
$193$	−1.75793	−	3.04482i	−0.126539	−	0.219171i	−0.922333	+	0.386395i	$0.873720\pi$
$194$	5.22424	+	24.3016i	0.375078	+	1.74475i
$195$		0			0
$196$	−10.0443	+	4.52781i	−0.717452	+	0.323415i
$197$	4.81922	+	4.81922i	0.343355	+	0.343355i	0.857627	−	0.514272i	$-0.171938\pi$
$197$	4.81922	+	4.81922i	0.343355	+	0.343355i	−0.514272	+	0.857627i	$0.671938\pi$
$198$		0			0
$199$			4.66322i			0.330567i	0.986246	+	0.165284i	$0.0528539\pi$
$199$			4.66322i			0.330567i	−0.986246	+	0.165284i	$0.947146\pi$
$200$	1.57577	+	14.0537i	0.111424	+	0.993746i
$201$		0			0
$202$	5.34835	−	8.27759i	0.376308	−	0.582409i
$203$	−0.975324	+	3.63996i	−0.0684543	+	0.255475i
$204$		0			0
$205$	0.0112049	+	0.0418171i	0.000782581	+	0.00292063i
$206$	1.10532	−	3.42878i	0.0770110	−	0.238894i
$207$		0			0
$208$	−18.7855	−	9.35378i	−1.30254	−	0.648568i
$209$	−5.45211	+	9.44333i	−0.377130	+	0.653209i
$210$		0			0
$211$	−17.4452	−	4.67442i	−1.20097	−	0.321800i	−0.397760	−	0.917490i	$-0.630212\pi$
$211$	−17.4452	−	4.67442i	−1.20097	−	0.321800i	−0.803215	+	0.595689i	$0.796879\pi$
$212$	19.4569	−	15.9055i	1.33631	−	1.09239i
$213$		0			0
$214$	7.03468	+	0.352358i	0.480881	+	0.0240867i
$215$		−	0.0585574i		−	0.00399358i
$216$		0			0
$217$		−	7.15167i		−	0.485487i
$218$	−0.314498	+	6.27881i	−0.0213005	+	0.425254i
$219$		0			0
$220$	−0.0440749	−	0.00442642i	−0.00297153	−	0.000298429i
$221$	7.81615	+	2.09433i	0.525771	+	0.140880i
$222$		0			0
$223$	2.85769	−	4.94966i	0.191365	−	0.331454i	−0.754338	−	0.656486i	$-0.772042\pi$
$223$	2.85769	−	4.94966i	0.191365	−	0.331454i	0.945703	+	0.325032i	$0.105375\pi$
$224$	−6.90727	+	0.0798841i	−0.461512	+	0.00533748i
$225$		0			0
$226$	21.2912	+	6.86353i	1.41627	+	0.456555i
$227$	5.27233	+	19.6766i	0.349937	+	1.30598i	0.886738	+	0.462272i	$0.152966\pi$
$227$	5.27233	+	19.6766i	0.349937	+	1.30598i	−0.536802	+	0.843709i	$0.680368\pi$
$228$		0			0
$229$	−0.992819	+	3.70525i	−0.0656073	+	0.244850i	−0.990940	−	0.134307i	$-0.957119\pi$
$229$	−0.992819	+	3.70525i	−0.0656073	+	0.244850i	0.925332	+	0.379157i	$0.123786\pi$
$230$	−0.0834542	−	0.0539217i	−0.00550280	−	0.00355549i
$231$		0			0
$232$	5.44579	−	6.82122i	0.357533	−	0.447835i
$233$		−	5.33043i		−	0.349208i	−0.984639	−	0.174604i	$-0.944136\pi$
$233$		−	5.33043i		−	0.349208i	0.984639	−	0.174604i	$-0.0558645\pi$
$234$		0			0
$235$	0.0216859	+	0.0216859i	0.00141463	+	0.00141463i
$236$	17.0160	+	6.44166i	1.10764	+	0.419316i
$237$		0			0
$238$	2.60410	−	0.559816i	0.168798	−	0.0362875i
$239$	13.8380	+	23.9681i	0.895104	+	1.55037i	0.833676	+	0.552254i	$0.186232\pi$
$239$	13.8380	+	23.9681i	0.895104	+	1.55037i	0.0614282	+	0.998112i	$0.480434\pi$
$240$		0			0
$241$	0.847203	−	1.46740i	0.0545731	−	0.0945234i	−0.837448	−	0.546517i	$-0.815954\pi$
$241$	0.847203	−	1.46740i	0.0545731	−	0.0945234i	0.892021	+	0.451993i	$0.149287\pi$
$242$	3.21432	−	9.97107i	0.206624	−	0.640965i
$243$		0			0
$244$	24.7664	−	4.04014i	1.58551	−	0.258643i
$245$	0.0621830	−	0.0166619i	0.00397273	−	0.00106449i
$246$		0			0
$247$	26.1402	−	15.0921i	1.66326	−	0.960284i
$248$	−6.63243	+	15.1793i	−0.421160	+	0.963885i
$249$		0			0
$250$	0.00826746	−	0.165056i	0.000522880	−	0.0104391i
$251$	−0.987980	−	0.987980i	−0.0623607	−	0.0623607i	0.675239	−	0.737599i	$-0.264041\pi$
$251$	−0.987980	−	0.987980i	−0.0623607	−	0.0623607i	−0.737599	+	0.675239i	$0.764041\pi$
$252$		0			0
$253$	−8.05717	+	8.05717i	−0.506550	+	0.506550i
$254$	6.00531	−	5.43241i	0.376807	−	0.340860i
$255$		0			0
$256$	14.7346	+	6.23623i	0.920915	+	0.389764i
$257$	−11.8214	−	20.4753i	−0.737401	−	1.27722i	−0.953662	−	0.300881i	$-0.902719\pi$
$257$	−11.8214	−	20.4753i	−0.737401	−	1.27722i	0.216260	−	0.976336i	$-0.430614\pi$
$258$		0			0
$259$	−0.412584	−	1.53978i	−0.0256367	−	0.0956776i
$260$	0.0995325	+	0.0716134i	0.00617274	+	0.00444128i
$261$		0			0
$262$	8.55049	−	4.38163i	0.528251	−	0.270698i
$263$	22.2619	+	12.8529i	1.37273	+	0.792545i	0.991271	−	0.131841i	$-0.0420888\pi$
$263$	22.2619	+	12.8529i	1.37273	+	0.792545i	0.381458	+	0.924386i	$0.375422\pi$
$264$		0			0
$265$	−0.127167	+	0.0734198i	−0.00781180	+	0.00451015i
$266$	5.39206	−	8.34523i	0.330608	−	0.511679i
$267$		0			0
$268$	−8.70888	+	23.0049i	−0.531979	+	1.40525i
$269$	13.6891	−	13.6891i	0.834637	−	0.834637i	−0.153510	−	0.988147i	$-0.549058\pi$
$269$	13.6891	−	13.6891i	0.834637	−	0.834637i	0.988147	+	0.153510i	$0.0490577\pi$
$270$		0			0
$271$	−7.11000			−0.431902			−0.215951	−	0.976404i	$-0.569285\pi$
$271$	−7.11000			−0.431902			−0.215951	+	0.976404i	$0.569285\pi$
$272$	−6.04631	−	1.22683i	−0.366612	−	0.0743875i
$273$		0			0
$274$	−5.82607	+	1.25246i	−0.351966	+	0.0756639i
$275$	−9.15326	−	2.45261i	−0.551962	−	0.147898i
$276$		0			0
$277$	−21.7174	+	5.81917i	−1.30487	+	0.349640i	−0.843291	−	0.537457i	$-0.819385\pi$
$277$	−21.7174	+	5.81917i	−1.30487	+	0.349640i	−0.461583	+	0.887097i	$0.652718\pi$
$278$	−10.4509	−	20.3942i	−0.626801	−	1.22316i
$279$		0			0
$280$	0.0399079	+	0.00603724i	0.00238496	+	0.000360794i
$281$	−19.7952	−	11.4288i	−1.18088	−	0.681783i	−0.224664	−	0.974436i	$-0.572128\pi$
$281$	−19.7952	−	11.4288i	−1.18088	−	0.681783i	−0.956218	+	0.292654i	$0.905462\pi$
$282$		0			0
$283$	1.59958	−	5.96971i	0.0950851	−	0.354862i	−0.901947	−	0.431846i	$-0.857862\pi$
$283$	1.59958	−	5.96971i	0.0950851	−	0.354862i	0.997032	+	0.0769838i	$0.0245290\pi$
$284$	−28.3301	−	2.84518i	−1.68108	−	0.168830i
$285$		0			0
$286$	10.4283	−	9.43344i	0.616638	−	0.557811i
$287$	−4.52381			−0.267032
$288$		0			0
$289$	−14.6211			−0.860063
$290$	−0.0378217	+	0.0342135i	−0.00222096	+	0.00200909i
$291$		0			0
$292$	−8.59856	−	0.863549i	−0.503192	−	0.0505354i
$293$	−1.00950	+	3.76752i	−0.0589758	+	0.220101i	−0.989124	−	0.147083i	$-0.953011\pi$
$293$	−1.00950	+	3.76752i	−0.0589758	+	0.220101i	0.930148	+	0.367184i	$0.119678\pi$
$294$		0			0
$295$	−0.0920675	−	0.0531552i	−0.00536038	−	0.00309482i
$296$	−0.552289	+	3.65079i	−0.0321011	+	0.212198i
$297$		0			0
$298$	−2.51375	−	4.90543i	−0.145618	−	0.284164i
$299$	30.4667	−	8.16352i	1.76193	−	0.472109i
$300$		0			0
$301$	5.91043	+	1.58370i	0.340672	+	0.0912827i
$302$	−20.7665	+	4.46427i	−1.19498	+	0.256890i
$303$		0			0
$304$	−19.1839	+	12.7120i	−1.10027	+	0.729084i
$305$	−0.146623			−0.00839562
$306$		0			0
$307$	10.8111	−	10.8111i	0.617023	−	0.617023i	−0.327743	−	0.944767i	$-0.606288\pi$
$307$	10.8111	−	10.8111i	0.617023	−	0.617023i	0.944767	+	0.327743i	$0.106288\pi$
$308$	1.63879	−	4.32895i	0.0933788	−	0.246665i
$309$		0			0
$310$	0.0525275	−	0.0812963i	0.00298336	−	0.00461732i
$311$	−19.5372	+	11.2798i	−1.10785	+	0.639619i	−0.938273	−	0.345897i	$-0.887575\pi$
$311$	−19.5372	+	11.2798i	−1.10785	+	0.639619i	−0.169581	+	0.985516i	$0.554241\pi$
$312$		0			0
$313$	−5.17232	−	2.98624i	−0.292357	−	0.168792i	0.346647	−	0.937996i	$-0.387320\pi$
$313$	−5.17232	−	2.98624i	−0.292357	−	0.168792i	−0.639004	+	0.769203i	$0.720653\pi$
$314$	12.3430	−	6.32508i	0.696556	−	0.356945i
$315$		0			0
$316$	0.850300	+	0.611789i	0.0478331	+	0.0344158i
$317$	−4.81751	−	17.9792i	−0.270579	−	1.00981i	−0.958747	−	0.284262i	$-0.908252\pi$
$317$	−4.81751	−	17.9792i	−0.270579	−	1.00981i	0.688168	−	0.725551i	$-0.258415\pi$
$318$		0			0
$319$	2.92439	+	5.06520i	0.163735	+	0.283597i
$320$	−0.0791049	−	0.0498244i	−0.00442210	−	0.00278527i
$321$		0			0
$322$	7.69957	−	6.96504i	0.429080	−	0.388146i
$323$	6.27476	−	6.27476i	0.349137	−	0.349137i
$324$		0			0
$325$	18.5482	+	18.5482i	1.02887	+	1.02887i
$326$	−0.522878	+	10.4390i	−0.0289595	+	0.578164i
$327$		0			0
$328$	9.60169	+	4.19536i	0.530164	+	0.231650i
$329$	−2.77534	+	1.60234i	−0.153009	+	0.0883400i
$330$		0			0
$331$	−10.1869	+	2.72957i	−0.559923	+	0.150031i	−0.527671	−	0.849449i	$-0.676935\pi$
$331$	−10.1869	+	2.72957i	−0.559923	+	0.150031i	−0.0322521	+	0.999480i	$0.510268\pi$
$332$	−22.2386	+	3.62777i	−1.22050	+	0.199100i
$333$		0			0
$334$	−3.16388	+	9.81461i	−0.173120	+	0.537031i
$335$	0.0718638	−	0.124472i	0.00392634	−	0.00680062i
$336$		0			0
$337$	12.1222	+	20.9962i	0.660336	+	1.14374i	0.980527	+	0.196382i	$0.0629194\pi$
$337$	12.1222	+	20.9962i	0.660336	+	1.14374i	−0.320192	+	0.947353i	$0.603747\pi$
$338$	−20.0816	+	4.31704i	−1.09229	+	0.234816i
$339$		0			0
$340$	0.0337137	+	0.0127628i	0.00182838	+	0.000692163i
$341$	−7.84884	−	7.84884i	−0.425038	−	0.425038i
$342$		0			0
$343$			15.2749i			0.824767i
$344$	−11.0761	−	8.84267i	−0.597181	−	0.476765i
$345$		0			0
$346$	−28.2095	−	18.2268i	−1.51655	−	0.979881i
$347$	−4.97570	+	18.5696i	−0.267110	+	0.996867i	0.693837	+	0.720132i	$0.255919\pi$
$347$	−4.97570	+	18.5696i	−0.267110	+	0.996867i	−0.960946	+	0.276735i	$0.910748\pi$
$348$		0			0
$349$	−4.19134	−	15.6423i	−0.224357	−	0.837313i	−0.982661	−	0.185411i	$-0.940638\pi$
$349$	−4.19134	−	15.6423i	−0.224357	−	0.837313i	0.758304	−	0.651901i	$-0.226028\pi$
$350$	8.21798	+	2.64919i	0.439270	+	0.141605i
$351$		0			0
$352$	−7.49295	+	7.66829i	−0.399376	+	0.408721i
$353$	7.69391	−	13.3262i	0.409505	−	0.709284i	−0.585329	−	0.810796i	$-0.699035\pi$
$353$	7.69391	−	13.3262i	0.409505	−	0.709284i	0.994834	+	0.101512i	$0.0323680\pi$
$354$		0			0
$355$	0.160697	+	0.0430587i	0.00852893	+	0.00228532i
$356$	21.3134	+	2.14049i	1.12961	+	0.113446i
$357$		0			0
$358$	1.14549	−	22.8692i	0.0605409	−	1.20867i
$359$			2.97883i			0.157217i	0.996906	+	0.0786083i	$0.0250476\pi$
$359$			2.97883i			0.157217i	−0.996906	+	0.0786083i	$0.974952\pi$
$360$		0			0
$361$		−	14.1010i		−	0.742159i
$362$	6.01899	+	0.301484i	0.316351	+	0.0158456i
$363$		0			0
$364$	−9.92011	+	8.10941i	−0.519955	+	0.425049i
$365$	0.0487737	+	0.0130689i	0.00255293	+	0.000684056i
$366$		0			0
$367$	12.5585	−	21.7519i	0.655547	−	1.13544i	−0.326210	−	0.945297i	$-0.605772\pi$
$367$	12.5585	−	21.7519i	0.655547	−	1.13544i	0.981756	−	0.190143i	$-0.0608952\pi$
$368$	−22.8015	+	7.64260i	−1.18861	+	0.398398i
$369$		0			0
$370$	0.00661936	−	0.0205338i	0.000344124	−	0.00106750i
$371$	−3.97131	−	14.8211i	−0.206180	−	0.769474i
$372$		0			0
$373$	7.71816	−	28.8046i	0.399631	−	1.49144i	−0.414116	−	0.910224i	$-0.635909\pi$
$373$	7.71816	−	28.8046i	0.399631	−	1.49144i	0.813747	−	0.581220i	$-0.197424\pi$
$374$	2.24356	−	3.47234i	0.116012	−	0.179551i
$375$		0			0
$376$	7.37661	−	0.827102i	0.380420	−	0.0426545i
$377$		−	16.1901i		−	0.833832i
$378$		0			0
$379$	10.1985	+	10.1985i	0.523864	+	0.523864i	0.918736	−	0.394872i	$-0.129211\pi$
$379$	10.1985	+	10.1985i	0.523864	+	0.523864i	−0.394872	+	0.918736i	$0.629211\pi$
$380$	0.122588	−	0.0552606i	0.00628863	−	0.00283481i
$381$		0			0
$382$	1.34171	+	6.24124i	0.0686479	+	0.319330i
$383$	−10.5750	−	18.3164i	−0.540356	−	0.935924i	−0.998883	−	0.0472436i	$-0.984956\pi$
$383$	−10.5750	−	18.3164i	−0.540356	−	0.935924i	0.458528	−	0.888680i	$-0.348377\pi$
$384$		0			0
$385$	−0.0135230	+	0.0234224i	−0.000689194	+	0.00119372i
$386$	4.73236	+	1.52555i	0.240871	+	0.0776482i
$387$		0			0
$388$	−28.5345	−	20.5305i	−1.44862	−	1.04228i
$389$	−30.3488	+	8.13193i	−1.53874	+	0.412305i	−0.925860	−	0.377867i	$-0.876658\pi$
$389$	−30.3488	+	8.13193i	−1.53874	+	0.412305i	−0.612884	+	0.790173i	$0.709991\pi$
$390$		0			0
$391$	8.03056	−	4.63645i	0.406123	−	0.234475i
$392$	6.23860	−	14.2779i	0.315097	−	0.721144i
$393$		0			0
$394$	−9.62638	−	0.482173i	−0.484970	−	0.0242915i
$395$	−0.00432797	−	0.00432797i	−0.000217764	−	0.000217764i
$396$		0			0
$397$	−3.24113	+	3.24113i	−0.162668	+	0.162668i	−0.783747	−	0.621080i	$-0.786694\pi$
$397$	−3.24113	+	3.24113i	−0.162668	+	0.162668i	0.621080	+	0.783747i	$0.286694\pi$
$398$	−4.42410	−	4.89067i	−0.221760	−	0.245147i
$399$		0			0
$400$	−14.9857	−	13.2442i	−0.749283	−	0.662209i
$401$	10.7429	+	18.6073i	0.536476	+	0.929203i	0.999090	+	0.0426439i	$0.0135781\pi$
$401$	10.7429	+	18.6073i	0.536476	+	0.929203i	−0.462614	+	0.886560i	$0.653089\pi$
$402$		0			0
$403$	7.95244	+	29.6789i	0.396139	+	1.47841i
$404$	2.24392	+	13.7554i	0.111639	+	0.684357i
$405$		0			0
$406$	−2.43041	−	4.74280i	−0.120619	−	0.235381i
$407$	−2.14269	−	1.23708i	−0.106209	−	0.0613200i
$408$		0			0
$409$	−23.1426	+	13.3614i	−1.14433	+	0.660678i	−0.947499	−	0.319760i	$-0.896398\pi$
$409$	−23.1426	+	13.3614i	−1.14433	+	0.660678i	−0.196829	+	0.980438i	$0.563064\pi$
$410$	−0.0514242	−	0.0332264i	−0.00253966	−	0.00164093i
$411$		0			0
$412$	2.09373	+	4.64465i	0.103151	+	0.228825i
$413$	7.85515	−	7.85515i	0.386527	−	0.386527i
$414$		0			0
$415$	0.131658			0.00646283
$416$	28.5759	−	8.01219i	1.40105	−	0.392830i
$417$		0			0
$418$	−3.24106	−	15.0765i	−0.158526	−	0.737414i
$419$	8.83989	+	2.36864i	0.431857	+	0.115716i	0.468198	−	0.883624i	$-0.344903\pi$
$419$	8.83989	+	2.36864i	0.431857	+	0.115716i	−0.0363407	+	0.999339i	$0.511570\pi$
$420$		0			0
$421$	−28.9344	+	7.75295i	−1.41018	+	0.377856i	−0.881988	−	0.471272i	$-0.843795\pi$
$421$	−28.9344	+	7.75295i	−1.41018	+	0.377856i	−0.528188	+	0.849127i	$0.677128\pi$
$422$	22.7308	−	11.6482i	1.10652	−	0.567026i
$423$		0			0
$424$	−5.31603	+	35.1405i	−0.258169	+	1.70657i
$425$	6.67852	+	3.85585i	0.323956	+	0.187036i
$426$		0			0
$427$	3.96545	−	14.7993i	0.191902	−	0.716187i
$428$	−7.71208	+	6.30441i	−0.372777	+	0.304735i
$429$		0			0
$430$	0.0555547	+	0.0614135i	0.00267908	+	0.00296162i
$431$	7.05544			0.339849			0.169924	−	0.985457i	$-0.445648\pi$
$431$	7.05544			0.339849			0.169924	+	0.985457i	$0.445648\pi$
$432$		0			0
$433$	13.1552			0.632201			0.316100	−	0.948726i	$-0.397626\pi$
$433$	13.1552			0.632201			0.316100	+	0.948726i	$0.397626\pi$
$434$	6.78494	+	7.50048i	0.325688	+	0.360035i
$435$		0			0
$436$	−5.62700	−	6.88342i	−0.269485	−	0.329656i
$437$	8.95243	−	33.4109i	0.428253	−	1.59826i
$438$		0			0
$439$	−12.8757	−	7.43381i	−0.614525	−	0.354796i	0.160209	−	0.987083i	$-0.448783\pi$
$439$	−12.8757	−	7.43381i	−0.614525	−	0.354796i	−0.774734	+	0.632287i	$0.782116\pi$
$440$	0.0504241	−	0.0371725i	0.00240387	−	0.00177213i
$441$		0			0
$442$	−10.1843	+	5.21887i	−0.484418	+	0.248236i
$443$	2.97678	−	0.797625i	0.141431	−	0.0378963i	−0.187409	−	0.982282i	$-0.560009\pi$
$443$	2.97678	−	0.797625i	0.141431	−	0.0378963i	0.328840	+	0.944386i	$0.393342\pi$
$444$		0			0
$445$	−0.120896	−	0.0323940i	−0.00573102	−	0.00153562i
$446$	1.69878	+	7.90223i	0.0804398	+	0.374182i
$447$		0			0
$448$	7.16838	−	6.63686i	0.338674	−	0.313562i
$449$	21.8550			1.03140			0.515701	−	0.856769i	$-0.327532\pi$
$449$	21.8550			1.03140			0.515701	+	0.856769i	$0.327532\pi$
$450$		0			0
$451$	−4.96480	+	4.96480i	−0.233783	+	0.233783i
$452$	−28.8412	+	13.0011i	−1.35658	+	0.611522i
$453$		0			0
$454$	−24.1971	−	15.6343i	−1.13563	−	0.733755i
$455$	0.0648360	−	0.0374331i	0.00303956	−	0.00175489i
$456$		0			0
$457$	−2.32261	−	1.34096i	−0.108647	−	0.0627275i	0.444692	−	0.895684i	$-0.353313\pi$
$457$	−2.32261	−	1.34096i	−0.108647	−	0.0627275i	−0.553339	+	0.832956i	$0.686647\pi$
$458$	−2.47401	−	4.82788i	−0.115603	−	0.225592i
$459$		0			0
$460$	0.138681	−	0.0226231i	0.00646605	−	0.00105481i
$461$	−2.74844	−	10.2573i	−0.128008	−	0.477732i	0.871921	−	0.489646i	$-0.162874\pi$
$461$	−2.74844	−	10.2573i	−0.128008	−	0.477732i	−0.999929	+	0.0119146i	$0.996207\pi$
$462$		0			0
$463$	11.8249	+	20.4814i	0.549550	+	0.951849i	0.998305	+	0.0581943i	$0.0185343\pi$
$463$	11.8249	+	20.4814i	0.549550	+	0.951849i	−0.448755	+	0.893655i	$0.648132\pi$
$464$	0.760046	+	12.3205i	0.0352842	+	0.571963i
$465$		0			0
$466$	5.05709	+	5.59041i	0.234265	+	0.258971i
$467$	−2.22540	+	2.22540i	−0.102979	+	0.102979i	−0.756719	−	0.653740i	$-0.773199\pi$
$467$	−2.22540	+	2.22540i	−0.102979	+	0.102979i	0.653740	+	0.756719i	$0.273199\pi$
$468$		0			0
$469$	10.6199	+	10.6199i	0.490380	+	0.490380i
$470$	−0.0433174	−	0.00216972i	−0.00199808	−	0.000100082i
$471$		0			0
$472$	−23.9572	+	9.38756i	−1.10272	+	0.432098i
$473$	8.22468	−	4.74852i	0.378171	−	0.218337i
$474$		0			0
$475$	27.7858	−	7.44518i	1.27490	−	0.341608i
$476$	−2.20000	+	3.05768i	−0.100837	+	0.140149i
$477$		0			0
$478$	−37.2519	−	12.0087i	−1.70386	−	0.549265i
$479$	6.23896	−	10.8062i	0.285066	−	0.493748i	−0.687559	−	0.726128i	$-0.741318\pi$
$479$	6.23896	−	10.8062i	0.285066	−	0.493748i	0.972625	+	0.232380i	$0.0746513\pi$
$480$		0			0
$481$	3.42439	+	5.93121i	0.156139	+	0.270440i
$482$	0.503629	+	2.34273i	0.0229397	+	0.106708i
$483$		0			0
$484$	6.08868	+	13.5069i	0.276758	+	0.613950i
$485$	0.145238	+	0.145238i	0.00659494	+	0.00659494i
$486$		0			0
$487$			12.5314i			0.567853i	0.958846	+	0.283927i	$0.0916372\pi$
$487$			12.5314i			0.567853i	−0.958846	+	0.283927i	$0.908363\pi$
$488$	−22.1414	+	27.7336i	−1.00229	+	1.25544i
$489$		0			0
$490$	−0.0494084	+	0.0764689i	−0.00223204	+	0.00345451i
$491$	3.93613	−	14.6898i	0.177635	−	0.662942i	−0.818453	−	0.574574i	$-0.805168\pi$
$491$	3.93613	−	14.6898i	0.177635	−	0.662942i	0.996088	−	0.0883688i	$-0.0281654\pi$
$492$		0			0
$493$	−1.23191	−	4.59756i	−0.0554825	−	0.207064i
$494$	−13.0970	+	40.6279i	−0.589262	+	1.82794i
$495$		0			0
$496$	−7.44499	−	22.2120i	−0.334290	−	0.997346i
$497$	−8.69218	+	15.0553i	−0.389898	+	0.675322i
$498$		0			0
$499$	29.4298	+	7.88570i	1.31746	+	0.353012i	0.848026	−	0.529955i	$-0.177791\pi$
$499$	29.4298	+	7.88570i	1.31746	+	0.353012i	0.469434	+	0.882967i	$0.344458\pi$
$500$	0.147922	+	0.180950i	0.00661526	+	0.00809234i
$501$		0			0
$502$	1.97349	+	0.0988495i	0.0880810	+	0.00441187i
$503$			1.90106i			0.0847639i	0.999101	+	0.0423820i	$0.0134946\pi$
$503$			1.90106i			0.0847639i	−0.999101	+	0.0423820i	$0.986505\pi$
$504$		0			0
$505$		−	0.0814355i		−	0.00362383i
$506$	0.806137	−	16.0942i	0.0358372	−	0.715473i
$507$		0			0
$508$	−1.14437	+	11.3947i	−0.0507731	+	0.505560i
$509$	−12.4896	−	3.34659i	−0.553593	−	0.148335i	−0.0288320	−	0.999584i	$-0.509179\pi$
$509$	−12.4896	−	3.34659i	−0.553593	−	0.148335i	−0.524761	+	0.851249i	$0.675845\pi$
$510$		0			0
$511$	−2.63819	+	4.56947i	−0.116706	+	0.202142i
$512$	−21.3697	+	7.43868i	−0.944418	+	0.328746i
$513$		0			0
$514$	31.8234	+	10.2587i	1.40367	+	0.452494i
$515$	−0.00770471	−	0.0287544i	−0.000339510	−	0.00126707i
$516$		0			0
$517$	−1.28734	+	4.80444i	−0.0566174	+	0.211299i
$518$	1.89353	+	1.22346i	0.0831971	+	0.0537557i
$519$		0			0
$520$	−0.172328	+	0.0193223i	−0.00755710	+	0.000847339i
$521$			1.24885i			0.0547130i	0.999626	+	0.0273565i	$0.00870893\pi$
$521$			1.24885i			0.0547130i	−0.999626	+	0.0273565i	$0.991291\pi$
$522$		0			0
$523$	9.58031	+	9.58031i	0.418918	+	0.418918i	0.884831	−	0.465913i	$-0.154274\pi$
$523$	9.58031	+	9.58031i	0.418918	+	0.418918i	−0.465913	+	0.884831i	$0.654274\pi$
$524$	−4.81058	+	12.7074i	−0.210151	+	0.555125i
$525$		0			0
$526$	−35.5416	+	7.64056i	−1.54969	+	0.333144i
$527$	4.51656	+	7.82292i	0.196745	+	0.340772i
$528$		0			0
$529$	6.57248	−	11.3839i	0.285760	−	0.494951i
$530$	0.0637143	−	0.197647i	0.00276757	−	0.00858523i
$531$		0			0
$532$	2.26226	+	13.8678i	0.0980813	+	0.601247i
$533$	18.7735	−	5.03034i	0.813169	−	0.217888i
$534$		0			0
$535$	0.0504047	−	0.0291012i	0.00217918	−	0.00125815i
$536$	−12.6916	−	32.3893i	−0.548195	−	1.39900i
$537$		0			0
$538$	−1.36962	+	27.3439i	−0.0590485	+	1.17888i
$539$	7.38278	+	7.38278i	0.317999	+	0.317999i
$540$		0			0
$541$	13.0165	−	13.0165i	0.559622	−	0.559622i	−0.369578	−	0.929200i	$-0.620498\pi$
$541$	13.0165	−	13.0165i	0.559622	−	0.559622i	0.929200	+	0.369578i	$0.120498\pi$
$542$	7.45678	−	6.74541i	0.320296	−	0.289740i
$543$		0			0
$544$	7.50513	−	4.44960i	0.321780	−	0.190775i
$545$	0.0259743	+	0.0449887i	0.00111262	+	0.00192711i
$546$		0			0
$547$	2.61540	+	9.76080i	0.111826	+	0.417341i	0.999030	−	0.0440366i	$-0.0140218\pi$
$547$	2.61540	+	9.76080i	0.111826	+	0.417341i	−0.887204	+	0.461378i	$0.847355\pi$
$548$	4.92199	−	6.84086i	0.210257	−	0.292227i
$549$		0			0
$550$	11.9265	−	6.11167i	0.508550	−	0.260602i
$551$	−15.3760	−	8.87733i	−0.655039	−	0.378187i
$552$		0			0
$553$	0.553890	−	0.319788i	0.0235538	−	0.0135988i
$554$	17.2559	−	26.7068i	0.733133	−	1.13466i
$555$		0			0
$556$	30.3090	+	11.4740i	1.28539	+	0.486604i
$557$	−26.6259	+	26.6259i	−1.12818	+	1.12818i	−0.137702	+	0.990474i	$0.543971\pi$
$557$	−26.6259	+	26.6259i	−1.12818	+	1.12818i	−0.990474	+	0.137702i	$0.956029\pi$
$558$		0			0
$559$	−26.2889			−1.11190
$560$	−0.0475821	+	0.0315298i	−0.00201071	+	0.00133238i
$561$		0			0
$562$	31.6034	−	6.79395i	1.33311	−	0.286585i
$563$	21.1660	+	5.67141i	0.892039	+	0.239021i	0.675594	−	0.737274i	$-0.263887\pi$
$563$	21.1660	+	5.67141i	0.892039	+	0.239021i	0.216445	+	0.976295i	$0.430554\pi$
$564$		0			0
$565$	0.178552	−	0.0478429i	0.00751174	−	0.00201276i
$566$	3.98600	+	7.77843i	0.167544	+	0.326952i
$567$		0			0
$568$	32.4112	−	23.8935i	1.35994	−	1.00255i
$569$	−8.15901	−	4.71061i	−0.342044	−	0.197479i	0.319132	−	0.947710i	$-0.396609\pi$
$569$	−8.15901	−	4.71061i	−0.342044	−	0.197479i	−0.661175	+	0.750231i	$0.729942\pi$
$570$		0			0
$571$	7.61666	−	28.4258i	0.318747	−	1.18958i	−0.601702	−	0.798720i	$-0.705511\pi$
$571$	7.61666	−	28.4258i	0.318747	−	1.18958i	0.920450	−	0.390861i	$-0.127823\pi$
$572$	−1.98721	+	19.7871i	−0.0830894	+	0.827340i
$573$		0			0
$574$	4.74445	−	4.29183i	0.198029	−	0.179138i
$575$	30.0595			1.25357
$576$		0			0
$577$	−42.9309			−1.78724			−0.893618	−	0.448828i	$-0.851842\pi$
$577$	−42.9309			−1.78724			−0.893618	+	0.448828i	$0.851842\pi$
$578$	15.3342	−	13.8713i	0.637818	−	0.576971i
$579$		0			0
$580$	0.00720727	−	0.0717645i	0.000299266	−	0.00297986i
$581$	−3.56071	+	13.2888i	−0.147723	+	0.551310i
$582$		0			0
$583$	−20.6244	−	11.9075i	−0.854175	−	0.493158i
$584$	9.83721	−	7.25197i	0.407067	−	0.300089i
$585$		0			0
$586$	−2.51559	−	4.90901i	−0.103918	−	0.202789i
$587$	−30.3611	+	8.13523i	−1.25314	+	0.335777i	−0.823548	−	0.567247i	$-0.808008\pi$
$587$	−30.3611	+	8.13523i	−1.25314	+	0.335777i	−0.429589	+	0.903024i	$0.641342\pi$
$588$		0			0
$589$	32.5470	+	8.72095i	1.34108	+	0.359340i
$590$	0.146988	−	0.0315987i	0.00605138	−	0.00130090i
$591$		0			0
$592$	−2.88436	−	4.35282i	−0.118546	−	0.178900i
$593$	−0.434128			−0.0178275			−0.00891374	−	0.999960i	$-0.502837\pi$
$593$	−0.434128			−0.0178275			−0.00891374	+	0.999960i	$0.502837\pi$
$594$		0			0
$595$	0.0155634	−	0.0155634i	0.000638037	−	0.000638037i
$596$	7.29025	+	2.75984i	0.298620	+	0.113047i
$597$		0			0
$598$	−24.2078	+	37.4661i	−0.989929	+	1.53210i
$599$	−3.46143	+	1.99846i	−0.141430	+	0.0816547i	−0.569045	−	0.822306i	$-0.692687\pi$
$599$	−3.46143	+	1.99846i	−0.141430	+	0.0816547i	0.427615	+	0.903961i	$0.359354\pi$
$600$		0			0
$601$	−3.54563	−	2.04707i	−0.144629	−	0.0835019i	0.425939	−	0.904752i	$-0.359944\pi$
$601$	−3.54563	−	2.04707i	−0.144629	−	0.0835019i	−0.570569	+	0.821250i	$0.693277\pi$
$602$	−7.70119	+	3.94642i	−0.313877	+	0.160844i
$603$		0			0
$604$	17.5440	−	24.3836i	0.713854	−	0.992155i
$605$	−0.0224057	−	0.0836192i	−0.000910922	−	0.00339961i
$606$		0			0
$607$	16.8996	+	29.2709i	0.685932	+	1.18807i	0.973143	+	0.230202i	$0.0739386\pi$
$607$	16.8996	+	29.2709i	0.685932	+	1.18807i	−0.287211	+	0.957867i	$0.592728\pi$
$608$	8.05937	−	31.5322i	0.326851	−	1.27880i
$609$		0			0
$610$	0.153775	−	0.139105i	0.00622615	−	0.00563218i
$611$	9.73570	−	9.73570i	0.393864	−	0.393864i
$612$		0			0
$613$	1.73094	+	1.73094i	0.0699119	+	0.0699119i	0.741198	−	0.671286i	$-0.234258\pi$
$613$	1.73094	+	1.73094i	0.0699119	+	0.0699119i	−0.671286	+	0.741198i	$0.734258\pi$
$614$	−1.08168	+	21.5952i	−0.0436529	+	0.871510i
$615$		0			0
$616$	2.38824	+	6.09484i	0.0962251	+	0.245568i
$617$	14.9093	−	8.60788i	0.600225	−	0.346540i	−0.168905	−	0.985632i	$-0.554023\pi$
$617$	14.9093	−	8.60788i	0.600225	−	0.346540i	0.769130	+	0.639092i	$0.220690\pi$
$618$		0			0
$619$	6.34645	−	1.70053i	0.255085	−	0.0683499i	−0.129010	−	0.991643i	$-0.541180\pi$
$619$	6.34645	−	1.70053i	0.255085	−	0.0683499i	0.384095	+	0.923293i	$0.374513\pi$
$620$	0.0220381	+	0.135095i	0.000885071	+	0.00542556i
$621$		0			0
$622$	9.78871	−	30.3653i	0.392491	−	1.21754i
$623$	6.53931	−	11.3264i	0.261992	−	0.453783i
$624$		0			0
$625$	12.4990	+	21.6489i	0.499959	+	0.865954i
$626$	8.25771	−	1.77520i	0.330045	−	0.0709514i
$627$		0			0
$628$	−6.94428	+	18.3437i	−0.277107	+	0.731992i
$629$	1.42374	+	1.42374i	0.0567684	+	0.0567684i
$630$		0			0
$631$		−	13.3295i		−	0.530639i	−0.964161	−	0.265319i	$-0.914523\pi$
$631$		−	13.3295i		−	0.530639i	0.964161	−	0.265319i	$-0.0854774\pi$
$632$	−1.47219	+	0.165069i	−0.0585606	+	0.00656610i
$633$		0			0
$634$	22.1098	+	14.2856i	0.878091	+	0.567355i
$635$	0.0173188	−	0.0646345i	0.000687274	−	0.00256494i
$636$		0			0
$637$	−7.48023	−	27.9166i	−0.296377	−	1.10610i
$638$	−7.87249	−	2.53781i	−0.311675	−	0.100473i
$639$		0			0
$640$	0.130233	−	0.0227940i	0.00514790	−	0.000901012i
$641$	−8.26044	+	14.3075i	−0.326268	+	0.565113i	−0.981768	−	0.190082i	$-0.939124\pi$
$641$	−8.26044	+	14.3075i	−0.326268	+	0.565113i	0.655500	+	0.755195i	$0.272458\pi$
$642$		0			0
$643$	−24.0050	−	6.43213i	−0.946667	−	0.253659i	−0.247719	−	0.968832i	$-0.579681\pi$
$643$	−24.0050	−	6.43213i	−0.946667	−	0.253659i	−0.698947	+	0.715173i	$0.746348\pi$
$644$	−1.46722	+	14.6095i	−0.0578168	+	0.575695i
$645$		0			0
$646$	−0.627803	+	12.5338i	−0.0247006	+	0.493136i
$647$			26.9660i			1.06014i	0.847954	+	0.530071i	$0.177835\pi$
$647$			26.9660i			1.06014i	−0.847954	+	0.530071i	$0.822165\pi$
$648$		0			0
$649$		−	17.2418i		−	0.676800i
$650$	−37.0499	−	1.85578i	−1.45322	−	0.0727897i
$651$		0			0
$652$	−9.35535	−	11.4442i	−0.366384	−	0.448191i
$653$	−5.27782	−	1.41419i	−0.206537	−	0.0553414i	0.154067	−	0.988060i	$-0.450763\pi$
$653$	−5.27782	−	1.41419i	−0.206537	−	0.0553414i	−0.360604	+	0.932719i	$0.617429\pi$
$654$		0			0
$655$	0.0396959	−	0.0687553i	0.00155105	−	0.00268649i
$656$	−14.0502	+	4.70935i	−0.548569	+	0.183869i
$657$		0			0
$658$	1.39053	−	4.31352i	0.0542083	−	0.168159i
$659$	0.184661	+	0.689165i	0.00719337	+	0.0268460i	0.969429	−	0.245371i	$-0.0789098\pi$
$659$	0.184661	+	0.689165i	0.00719337	+	0.0268460i	−0.962236	+	0.272217i	$0.912243\pi$
$660$		0			0
$661$	9.89344	−	36.9228i	0.384810	−	1.43613i	−0.453656	−	0.891177i	$-0.649880\pi$
$661$	9.89344	−	36.9228i	0.384810	−	1.43613i	0.838466	−	0.544954i	$-0.183453\pi$
$662$	8.09416	−	12.5272i	0.314588	−	0.486885i
$663$		0			0
$664$	19.8815	−	24.9029i	0.771551	−	0.966421i
$665$		−	0.0821010i		−	0.00318374i
$666$		0			0
$667$	−13.1190	−	13.1190i	−0.507970	−	0.507970i
$668$	−5.99314	−	13.2949i	−0.231881	−	0.514397i
$669$		0			0
$670$	0.0427202	+	0.198721i	0.00165042	+	0.00767728i
$671$	−11.8899	−	20.5940i	−0.459006	−	0.795022i
$672$		0			0
$673$	−6.39173	+	11.0708i	−0.246383	+	0.426748i	−0.962520	−	0.271212i	$-0.912575\pi$
$673$	−6.39173	+	11.0708i	−0.246383	+	0.426748i	0.716137	+	0.697960i	$0.245909\pi$
$674$	−32.6329	−	10.5197i	−1.25697	−	0.405204i
$675$		0			0
$676$	16.9654	−	23.5794i	0.652514	−	0.906901i
$677$	25.4595	−	6.82184i	0.978487	−	0.262185i	0.266079	−	0.963951i	$-0.414272\pi$
$677$	25.4595	−	6.82184i	0.978487	−	0.262185i	0.712407	+	0.701766i	$0.247605\pi$
$678$		0			0
$679$	−18.5875	+	10.7315i	−0.713323	+	0.411837i
$680$	−0.0474664	+	0.0185996i	−0.00182025	+	0.000713261i
$681$		0			0
$682$	15.6780	+	0.785293i	0.600343	+	0.0300704i
$683$	−9.42670	−	9.42670i	−0.360703	−	0.360703i	0.503369	−	0.864072i	$-0.332094\pi$
$683$	−9.42670	−	9.42670i	−0.360703	−	0.360703i	−0.864072	+	0.503369i	$0.832094\pi$
$684$		0			0
$685$	−0.0348195	+	0.0348195i	−0.00133039	+	0.00133039i
$686$	−14.4916	−	16.0199i	−0.553293	−	0.611643i
$687$		0			0
$688$	20.0055	−	1.23413i	0.762703	−	0.0470509i
$689$	32.9613	+	57.0906i	1.25572	+	2.17498i
$690$		0			0
$691$	4.07041	+	15.1910i	0.154846	+	0.577891i	0.999119	+	0.0419780i	$0.0133660\pi$
$691$	4.07041	+	15.1910i	0.154846	+	0.577891i	−0.844273	+	0.535913i	$0.819967\pi$
$692$	46.8776	−	7.64714i	1.78202	−	0.290700i
$693$		0			0
$694$	−12.3990	−	24.1958i	−0.470659	−	0.918462i
$695$	−0.163992	−	0.0946807i	−0.00622056	−	0.00359144i
$696$		0			0
$697$	4.94841	−	2.85696i	0.187434	−	0.108215i
$698$	19.2360	+	12.4288i	0.728091	+	0.470437i
$699$		0			0
$700$	−11.1321	+	5.01818i	−0.420756	+	0.189670i
$701$	−9.62303	+	9.62303i	−0.363457	+	0.363457i	−0.865084	−	0.501627i	$-0.832735\pi$
$701$	−9.62303	+	9.62303i	−0.363457	+	0.363457i	0.501627	+	0.865084i	$0.332735\pi$
$702$		0			0
$703$	7.51063			0.283269
$704$	0.583333	−	15.1510i	0.0219852	−	0.571026i
$705$		0			0
$706$	4.57372	+	21.2756i	0.172134	+	0.800717i
$707$	8.21961	+	2.20244i	0.309130	+	0.0828312i
$708$		0			0
$709$	40.3893	−	10.8223i	1.51685	−	0.406439i	0.598148	−	0.801386i	$-0.295904\pi$
$709$	40.3893	−	10.8223i	1.51685	−	0.406439i	0.918704	+	0.394947i	$0.129237\pi$
$710$	−0.209386	+	0.107298i	−0.00785812	+	0.00402683i
$711$		0			0
$712$	−24.3836	+	17.9756i	−0.913816	+	0.673663i
$713$	30.4931	+	17.6052i	1.14197	+	0.659319i
$714$		0			0
$715$	0.0300742	−	0.112239i	0.00112471	−	0.00419749i
$716$	20.4951	+	25.0713i	0.765938	+	0.936959i
$717$		0			0
$718$	−2.82608	−	3.12412i	−0.105468	−	0.116591i
$719$	−48.7757			−1.81903			−0.909514	−	0.415674i	$-0.863546\pi$
$719$	−48.7757			−1.81903			−0.909514	+	0.415674i	$0.863546\pi$
$720$		0			0
$721$	3.11067			0.115847
$722$	13.3780	+	14.7888i	0.497876	+	0.550382i
$723$		0			0
$724$	−6.59858	+	5.39416i	−0.245234	+	0.200472i
$725$	3.99343	−	14.9037i	0.148312	−	0.553509i
$726$		0			0
$727$	−34.9918	−	20.2025i	−1.29777	−	0.749270i	−0.317755	−	0.948173i	$-0.602929\pi$
$727$	−34.9918	−	20.2025i	−1.29777	−	0.749270i	−0.980019	+	0.198902i	$0.936262\pi$
$728$	2.71037	−	17.9164i	0.100453	−	0.664024i
$729$		0			0
$730$	−0.0635513	+	0.0325664i	−0.00235214	+	0.00120534i
$731$	−7.46535	+	2.00033i	−0.276116	+	0.0739850i
$732$		0			0
$733$	−28.4006	−	7.60991i	−1.04900	−	0.281078i	−0.307161	−	0.951658i	$-0.599379\pi$
$733$	−28.4006	−	7.60991i	−1.04900	−	0.281078i	−0.741838	+	0.670579i	$0.766046\pi$
$734$	7.46552	+	34.7273i	0.275557	+	1.28181i
$735$		0			0
$736$	16.6630	−	29.6477i	0.614205	−	1.09283i
$737$	23.3102			0.858644
$738$		0			0
$739$	15.4222	−	15.4222i	0.567316	−	0.567316i	−0.364060	−	0.931376i	$-0.618610\pi$
$739$	15.4222	−	15.4222i	0.567316	−	0.567316i	0.931376	+	0.364060i	$0.118610\pi$
$740$	0.0125386	+	0.0278152i	0.000460929	+	0.00102251i
$741$		0			0
$742$	18.2261	+	11.7763i	0.669102	+	0.432323i
$743$	21.5896	−	12.4647i	0.792045	−	0.457287i	−0.0486373	−	0.998817i	$-0.515488\pi$
$743$	21.5896	−	12.4647i	0.792045	−	0.457287i	0.840682	+	0.541529i	$0.182155\pi$
$744$		0			0
$745$	−0.0394451	−	0.0227736i	−0.00144515	−	0.000834361i
$746$	19.2329	+	37.5319i	0.704167	+	1.37414i
$747$		0			0
$748$	0.941295	+	5.77022i	0.0344172	+	0.210980i
$749$	1.57409	+	5.87459i	0.0575161	+	0.214653i
$750$		0			0
$751$	−21.2809	−	36.8596i	−0.776551	−	1.34503i	−0.933919	−	0.357486i	$-0.883634\pi$
$751$	−21.2809	−	36.8596i	−0.776551	−	1.34503i	0.157368	−	0.987540i	$-0.449699\pi$
$752$	−6.95171	+	7.86579i	−0.253503	+	0.286836i
$753$		0			0
$754$	15.3599	+	16.9797i	0.559374	+	0.618366i
$755$	−0.124111	+	0.124111i	−0.00451686	+	0.00451686i
$756$		0			0
$757$	1.80855	+	1.80855i	0.0657328	+	0.0657328i	0.739209	−	0.673476i	$-0.235200\pi$
$757$	1.80855	+	1.80855i	0.0657328	+	0.0657328i	−0.673476	+	0.739209i	$0.735200\pi$
$758$	−20.3715	−	1.02038i	−0.739927	−	0.0370621i
$759$		0			0
$760$	−0.0761402	+	0.174258i	−0.00276189	+	0.00632099i
$761$	−18.5805	+	10.7275i	−0.673543	+	0.388870i	−0.797418	−	0.603428i	$-0.793801\pi$
$761$	−18.5805	+	10.7275i	−0.673543	+	0.388870i	0.123875	+	0.992298i	$0.460468\pi$
$762$		0			0
$763$	−5.24337	+	1.40496i	−0.189823	+	0.0508629i
$764$	−7.32835	−	5.27274i	−0.265130	−	0.190761i
$765$		0			0
$766$	28.4679	+	9.17705i	1.02859	+	0.331580i
$767$	−23.8636	+	41.3330i	−0.861665	+	1.49245i
$768$		0			0
$769$	−9.98382	−	17.2925i	−0.360026	−	0.623583i	0.627939	−	0.778263i	$-0.283899\pi$
$769$	−9.98382	−	17.2925i	−0.360026	−	0.623583i	−0.987965	+	0.154680i	$0.950565\pi$
$770$	−0.00803886	−	0.0373944i	−0.000289701	−	0.00134760i
$771$		0			0
$772$	−6.41050	+	2.88974i	−0.230719	+	0.104004i
$773$	−24.8049	−	24.8049i	−0.892171	−	0.892171i	0.102557	−	0.994727i	$-0.467298\pi$
$773$	−24.8049	−	24.8049i	−0.892171	−	0.892171i	−0.994727	+	0.102557i	$0.967298\pi$
$774$		0			0
$775$			29.2823i			1.05185i
$776$	49.4040	−	5.53942i	1.77350	−	0.198853i
$777$		0			0
$778$	24.1141	−	37.3211i	0.864531	−	1.33803i
$779$	5.51646	−	20.5877i	0.197648	−	0.737631i
$780$		0			0
$781$	6.98342	+	26.0625i	0.249886	+	0.932589i
$782$	−4.02355	+	12.4814i	−0.143882	+	0.446332i
$783$		0			0
$784$	7.00291	+	20.8930i	0.250104	+	0.746179i
$785$	0.0573027	−	0.0992512i	0.00204522	−	0.00354243i
$786$		0			0
$787$	10.3344	+	2.76911i	0.368383	+	0.0987080i	0.438261	−	0.898848i	$-0.355594\pi$
$787$	10.3344	+	2.76911i	0.368383	+	0.0987080i	−0.0698783	+	0.997556i	$0.522261\pi$
$788$	10.5533	−	8.62706i	0.375947	−	0.307326i
$789$		0			0
$790$	0.00864510		0.000433022i	0.000307579		1.54062e-5i
$791$			19.3159i			0.686794i
$792$		0			0
$793$			65.8254i			2.33753i
$794$	0.324282	−	6.47414i	0.0115083	−	0.229759i
$795$		0			0
$796$	9.27977	+	0.931962i	0.328913	+	0.0330325i
$797$	−46.8027	−	12.5408i	−1.65784	−	0.444216i	−0.696046	−	0.717997i	$-0.745059\pi$
$797$	−46.8027	−	12.5408i	−1.65784	−	0.444216i	−0.961792	+	0.273781i	$0.911726\pi$
$798$		0			0
$799$	2.02389	−	3.50547i	0.0716000	−	0.124015i
$800$	28.2816	−	0.327083i	0.999906	−	0.0115641i
$801$		0			0
$802$	−28.9200	−	9.32279i	−1.02120	−	0.329199i
$803$	2.11956	+	7.91029i	0.0747975	+	0.279148i
$804$		0			0
$805$	0.0222048	−	0.0828696i	0.000782618	−	0.00292077i
$806$	−36.4973	−	23.5818i	−1.28556	−	0.830634i
$807$		0			0
$808$	−15.4034	−	12.2975i	−0.541890	−	0.432623i
$809$			51.3577i			1.80564i	0.430019	+	0.902820i	$0.358507\pi$
$809$			51.3577i			1.80564i	−0.430019	+	0.902820i	$0.641493\pi$
$810$		0			0
$811$	−2.55652	−	2.55652i	−0.0897715	−	0.0897715i	0.660795	−	0.750566i	$-0.270219\pi$
$811$	−2.55652	−	2.55652i	−0.0897715	−	0.0897715i	−0.750566	+	0.660795i	$0.770219\pi$
$812$	7.04855	+	2.66834i	0.247356	+	0.0936405i
$813$		0			0
$814$	3.42085	−	0.735398i	0.119901	−	0.0257757i
$815$	0.0431843	+	0.0747975i	0.00151268	+	0.00262004i
$816$		0			0
$817$	−14.4147	+	24.9670i	−0.504306	+	0.873484i
$818$	11.5951	−	35.9690i	0.405414	−	1.25763i
$819$		0			0
$820$	0.0854549	−	0.0139403i	0.00298422	−	0.000486815i
$821$	−0.179113	+	0.0479933i	−0.00625110	+	0.00167498i	−0.261943	−	0.965083i	$-0.584363\pi$
$821$	−0.179113	+	0.0479933i	−0.00625110	+	0.00167498i	0.255692	+	0.966758i	$0.417697\pi$
$822$		0			0
$823$	−16.8590	+	9.73353i	−0.587667	+	0.339290i	−0.764174	−	0.645010i	$-0.776853\pi$
$823$	−16.8590	+	9.73353i	−0.587667	+	0.339290i	0.176508	+	0.984299i	$0.443520\pi$
$824$	−6.60233	−	2.88482i	−0.230003	−	0.100497i
$825$		0			0
$826$	−0.785924	+	15.6906i	−0.0273458	+	0.545947i
$827$	−7.70731	−	7.70731i	−0.268009	−	0.268009i	0.560288	−	0.828298i	$-0.310690\pi$
$827$	−7.70731	−	7.70731i	−0.268009	−	0.268009i	−0.828298	+	0.560288i	$0.810690\pi$
$828$		0			0
$829$	−23.8166	+	23.8166i	−0.827184	+	0.827184i	−0.987126	−	0.159942i	$-0.948869\pi$
$829$	−23.8166	+	23.8166i	−0.827184	+	0.827184i	0.159942	+	0.987126i	$0.448869\pi$
$830$	−0.138079	+	0.124907i	−0.00479280	+	0.00433557i
$831$		0			0
$832$	−22.3683	+	35.5135i	−0.775480	+	1.23121i
$833$	−4.24837	−	7.35839i	−0.147197	−	0.254953i
$834$		0			0
$835$	0.0220541	+	0.0823071i	0.000763214	+	0.00284835i
$836$	17.7025	+	12.7369i	0.612254	+	0.440516i
$837$		0			0
$838$	−11.5182	+	5.90243i	−0.397891	+	0.203896i
$839$	−18.6769	−	10.7831i	−0.644799	−	0.372275i	0.141662	−	0.989915i	$-0.454755\pi$
$839$	−18.6769	−	10.7831i	−0.644799	−	0.372275i	−0.786461	+	0.617640i	$0.788089\pi$
$840$		0			0
$841$	16.8674	−	9.73839i	0.581634	−	0.335807i
$842$	22.9903	−	35.5818i	0.792296	−	1.22623i
$843$		0			0
$844$	−12.7885	+	33.7815i	−0.440199	+	1.16281i
$845$	−0.120018	+	0.120018i	−0.00412873	+	0.00412873i
$846$		0			0
$847$	9.04599			0.310824
$848$	−27.7633	−	41.8979i	−0.953394	−	1.43878i
$849$		0			0
$850$	−10.6624	+	2.29215i	−0.365717	+	0.0786200i
$851$	7.58094	+	2.03131i	0.259871	+	0.0696323i
$852$		0			0
$853$	38.5967	−	10.3419i	1.32153	−	0.354102i	0.471976	−	0.881611i	$-0.343541\pi$
$853$	38.5967	−	10.3419i	1.32153	−	0.354102i	0.849549	+	0.527510i	$0.176874\pi$
$854$	9.88153	+	19.2832i	0.338139	+	0.659857i
$855$		0			0
$856$	2.10709	−	13.9285i	0.0720190	−	0.476067i
$857$	−14.5777	−	8.41643i	−0.497964	−	0.287500i	0.229908	−	0.973212i	$-0.426157\pi$
$857$	−14.5777	−	8.41643i	−0.497964	−	0.287500i	−0.727872	+	0.685713i	$0.759491\pi$
$858$		0			0
$859$	−5.55582	+	20.7346i	−0.189562	+	0.707455i	0.804046	+	0.594568i	$0.202677\pi$
$859$	−5.55582	+	20.7346i	−0.189562	+	0.707455i	−0.993608	+	0.112888i	$0.963990\pi$
$860$	−0.116529	−	0.0117029i	−0.00397359	−	0.000399066i
$861$		0			0
$862$	−7.39956	+	6.69365i	−0.252030	+	0.227987i
$863$	−20.3421			−0.692455			−0.346227	−	0.938151i	$-0.612537\pi$
$863$	−20.3421			−0.692455			−0.346227	+	0.938151i	$0.612537\pi$
$864$		0			0
$865$	−0.277527			−0.00943620
$866$	−13.7969	+	12.4807i	−0.468837	+	0.424110i
$867$		0			0
$868$	−14.2317	−	1.42929i	−0.483057	−	0.0485132i
$869$	0.256922	−	0.958848i	0.00871550	−	0.0325267i
$870$		0			0
$871$	−55.8806	−	32.2627i	−1.89344	−	1.09318i
$872$	12.4319	+	1.88069i	0.420997	+	0.0636882i
$873$		0			0
$874$	22.3086	+	43.5339i	0.754599	+	1.47255i
$875$	0.137837	−	0.0369333i	0.00465974	−	0.00124857i
$876$		0			0
$877$	−18.6156	−	4.98805i	−0.628606	−	0.168434i	−0.0695688	−	0.997577i	$-0.522162\pi$
$877$	−18.6156	−	4.98805i	−0.628606	−	0.168434i	−0.559037	+	0.829143i	$0.688829\pi$
$878$	20.5563	−	4.41911i	0.693743	−	0.149138i
$879$		0			0
$880$	−0.0176171	+	0.0868240i	−0.000593871	+	0.00292684i
$881$	−37.3378			−1.25794			−0.628972	−	0.777428i	$-0.716524\pi$
$881$	−37.3378			−1.25794			−0.628972	+	0.777428i	$0.716524\pi$
$882$		0			0
$883$	−16.7468	+	16.7468i	−0.563576	+	0.563576i	−0.930321	−	0.366745i	$-0.880472\pi$
$883$	−16.7468	+	16.7468i	−0.563576	+	0.563576i	0.366745	+	0.930321i	$0.380472\pi$
$884$	5.72978	−	15.1355i	0.192713	−	0.509062i
$885$		0			0
$886$	−2.36524	+	3.66066i	−0.0794619	+	0.122982i
$887$	−36.4841	+	21.0641i	−1.22502	+	0.707263i	−0.965983	−	0.258606i	$-0.916737\pi$
$887$	−36.4841	+	21.0641i	−1.22502	+	0.707263i	−0.259033	+	0.965869i	$0.583404\pi$
$888$		0			0
$889$	6.05543	+	3.49611i	0.203093	+	0.117256i
$890$	0.157526	−	0.0807228i	0.00528027	−	0.00270583i
$891$		0			0
$892$	−9.27866	−	6.67598i	−0.310673	−	0.223528i
$893$	−3.90788	−	14.5844i	−0.130772	−	0.488049i
$894$		0			0
$895$	−0.0946055	−	0.163862i	−0.00316231	−	0.00547729i
$896$	−1.22148	+	13.7614i	−0.0408066	+	0.459735i
$897$		0			0
$898$	−22.9210	+	20.7343i	−0.764882	+	0.691913i
$899$	12.7798	−	12.7798i	0.426229	−	0.426229i
$900$		0			0
$901$	13.7042	+	13.7042i	0.456552	+	0.456552i
$902$	0.496739	−	9.91717i	0.0165396	−	0.330206i
$903$		0			0
$904$	17.9135	−	40.9976i	0.595793	−	1.36356i
$905$	0.0431271	−	0.0248994i	0.00143359	−	0.000827685i
$906$		0			0
$907$	1.02635	−	0.275009i	0.0340794	−	0.00913154i	−0.241739	−	0.970341i	$-0.577718\pi$
$907$	1.02635	−	0.275009i	0.0340794	−	0.00913154i	0.275818	+	0.961210i	$0.411051\pi$
$908$	40.2099	−	6.55943i	1.33441	−	0.217682i
$909$		0			0
$910$	−0.0324847	+	0.100770i	−0.00107686	+	0.00334050i
$911$	−1.91307	+	3.31354i	−0.0633829	+	0.109782i	−0.895976	−	0.444103i	$-0.853522\pi$
$911$	−1.91307	+	3.31354i	−0.0633829	+	0.109782i	0.832593	+	0.553886i	$0.186856\pi$
$912$		0			0
$913$	10.6764	+	18.4920i	0.353336	+	0.611996i
$914$	3.70809	−	0.797148i	0.122653	−	0.0263673i
$915$		0			0
$916$	7.17499	+	2.71621i	0.237068	+	0.0897460i
$917$	5.86616	+	5.86616i	0.193718	+	0.193718i
$918$		0			0
$919$			5.73779i			0.189272i	0.995512	+	0.0946361i	$0.0301688\pi$
$919$			5.73779i			0.189272i	−0.995512	+	0.0946361i	$0.969831\pi$
$920$	−0.123982	+	0.155296i	−0.00408758	+	0.00511997i
$921$		0			0
$922$	12.6139	+	8.15011i	0.415415	+	0.268410i
$923$	19.3309	−	72.1438i	0.636284	−	2.37464i
$924$		0			0
$925$	1.68931	+	6.30460i	0.0555442	+	0.207294i
$926$	−31.8328	−	10.2618i	−1.04609	−	0.337222i
$927$		0			0
$928$	−12.4858	−	12.2003i	−0.409867	−	0.400495i
$929$	20.2911	−	35.1451i	0.665728	−	1.15307i	−0.313359	−	0.949635i	$-0.601454\pi$
$929$	20.2911	−	35.1451i	0.665728	−	1.15307i	0.979087	−	0.203440i	$-0.0652122\pi$
$930$		0			0
$931$	−30.6144	−	8.20310i	−1.00335	−	0.268846i
$932$	−10.6075	−	1.06531i	−0.347460	−	0.0348952i
$933$		0			0
$934$	0.222656	−	4.44522i	0.00728552	−	0.145452i
$935$		−	0.0341611i		−	0.00111719i
$936$		0			0
$937$		−	27.9974i		−	0.914635i	−0.889304	−	0.457317i	$-0.848810\pi$
$937$		−	27.9974i		−	0.914635i	0.889304	−	0.457317i	$-0.151190\pi$
$938$	−21.2131	−	1.06254i	−0.692633	−	0.0346931i
$939$		0			0
$940$	0.0474886	−	0.0388206i	0.00154891	−	0.00126619i
$941$	36.1343	+	9.68215i	1.17794	+	0.315629i	0.794111	−	0.607773i	$-0.207937\pi$
$941$	36.1343	+	9.68215i	1.17794	+	0.315629i	0.383833	+	0.923402i	$0.374604\pi$
$942$		0			0
$943$	11.1362	−	19.2885i	0.362645	−	0.628119i
$944$	16.2195	−	32.5742i	0.527901	−	1.06020i
$945$		0			0
$946$	−4.12081	+	12.7831i	−0.133979	+	0.415613i
$947$	4.92887	+	18.3948i	0.160167	+	0.597751i	0.998607	+	0.0527575i	$0.0168010\pi$
$947$	4.92887	+	18.3948i	0.160167	+	0.597751i	−0.838441	+	0.544993i	$0.816532\pi$
$948$		0			0
$949$	5.86717	−	21.8966i	0.190456	−	0.710793i
$950$	−22.0776	+	34.1693i	−0.716292	+	1.10860i
$951$		0			0
$952$	−0.593590	−	5.29400i	−0.0192384	−	0.171580i
$953$		−	2.49861i		−	0.0809380i	−0.999181	−	0.0404690i	$-0.987115\pi$
$953$		−	2.49861i		−	0.0809380i	0.999181	−	0.0404690i	$-0.0128852\pi$
$954$		0			0
$955$	0.0373008	+	0.0373008i	0.00120703	+	0.00120703i
$956$	50.4618	−	22.7473i	1.63205	−	0.735701i
$957$		0			0
$958$	3.70882	+	17.2523i	0.119826	+	0.557397i
$959$	−2.57277	−	4.45617i	−0.0830792	−	0.143897i
$960$		0			0
$961$	−1.64996	+	2.85782i	−0.0532246	+	0.0921877i
$962$	−9.21848	−	2.97171i	−0.297216	−	0.0958118i
$963$		0			0
$964$	−2.75079	−	1.97919i	−0.0885970	−	0.0637454i
$965$	0.0396865	−	0.0106340i	0.00127755	−	0.000342319i
$966$		0			0
$967$	−3.08638	+	1.78192i	−0.0992513	+	0.0573028i	−0.548804	−	0.835951i	$-0.684917\pi$
$967$	−3.08638	+	1.78192i	−0.0992513	+	0.0573028i	0.449553	+	0.893254i	$0.351583\pi$
$968$	−19.1999	−	8.38922i	−0.617109	−	0.269640i
$969$		0			0
$970$	−0.290113	−	0.0145314i	−0.00931498	−	0.000466576i
$971$	0.578866	+	0.578866i	0.0185767	+	0.0185767i	0.716334	−	0.697757i	$-0.245819\pi$
$971$	0.578866	+	0.578866i	0.0185767	+	0.0185767i	−0.697757	+	0.716334i	$0.745819\pi$
$972$		0			0
$973$	13.9917	−	13.9917i	0.448553	−	0.448553i
$974$	−11.8888	−	13.1426i	−0.380943	−	0.421117i
$975$		0			0
$976$	−3.09018	−	50.0923i	−0.0989142	−	1.60342i
$977$	−10.3841	−	17.9859i	−0.332218	−	0.575418i	0.650728	−	0.759310i	$-0.274464\pi$
$977$	−10.3841	−	17.9859i	−0.332218	−	0.575418i	−0.982946	+	0.183892i	$0.941130\pi$
$978$		0			0
$979$	−5.25377	−	19.6074i	−0.167911	−	0.626654i
$980$	−0.0207295	−	0.127073i	−0.000662179	−	0.00405921i
$981$		0			0
$982$	9.80845	+	19.1406i	0.313000	+	0.610801i
$983$	−9.13353	−	5.27325i	−0.291314	−	0.168190i	0.347220	−	0.937784i	$-0.387126\pi$
$983$	−9.13353	−	5.27325i	−0.291314	−	0.168190i	−0.638534	+	0.769593i	$0.720459\pi$
$984$		0			0
$985$	−0.0689747	+	0.0398225i	−0.00219772	+	0.00126885i
$986$	5.65380	+	3.65306i	0.180054	+	0.116337i
$987$		0			0
$988$	−24.8088	−	55.0349i	−0.789273	−	1.75089i
$989$	−21.3022	+	21.3022i	−0.677369	+	0.677369i
$990$		0			0
$991$	−24.1374			−0.766749			−0.383374	−	0.923593i	$-0.625238\pi$
$991$	−24.1374			−0.766749			−0.383374	+	0.923593i	$0.625238\pi$
$992$	28.8811	+	16.2321i	0.916975	+	0.515370i
$993$		0			0
$994$	−5.16716	−	24.0361i	−0.163892	−	0.762378i
$995$	−0.0526377	−	0.0141042i	−0.00166873	−	0.000447134i
$996$		0			0
$997$	−22.4986	+	6.02848i	−0.712538	+	0.190924i	−0.596840	−	0.802361i	$-0.703577\pi$
$997$	−22.4986	+	6.02848i	−0.712538	+	0.190924i	−0.115698	+	0.993284i	$0.536910\pi$
$998$	−38.3466	+	19.6504i	−1.21384	+	0.622023i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.y.e.181.6		72
3.2	odd	2		144.2.x.e.133.13	yes	72
4.3	odd	2		1728.2.bc.e.1585.10		72
9.4	even	3	inner	432.2.y.e.37.7		72
9.5	odd	6		144.2.x.e.85.12	yes	72
12.11	even	2		576.2.bb.e.241.14		72
16.3	odd	4		1728.2.bc.e.721.9		72
16.13	even	4	inner	432.2.y.e.397.7		72
36.23	even	6		576.2.bb.e.49.4		72
36.31	odd	6		1728.2.bc.e.1009.9		72
48.29	odd	4		144.2.x.e.61.12	yes	72
48.35	even	4		576.2.bb.e.529.4		72
144.13	even	12	inner	432.2.y.e.253.6		72
144.67	odd	12		1728.2.bc.e.145.10		72
144.77	odd	12		144.2.x.e.13.13	✓	72
144.131	even	12		576.2.bb.e.337.14		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.13	✓	72	144.77	odd	12
144.2.x.e.61.12	yes	72	48.29	odd	4
144.2.x.e.85.12	yes	72	9.5	odd	6
144.2.x.e.133.13	yes	72	3.2	odd	2
432.2.y.e.37.7		72	9.4	even	3	inner
432.2.y.e.181.6		72	1.1	even	1	trivial
432.2.y.e.253.6		72	144.13	even	12	inner
432.2.y.e.397.7		72	16.13	even	4	inner
576.2.bb.e.49.4		72	36.23	even	6
576.2.bb.e.241.14		72	12.11	even	2
576.2.bb.e.337.14		72	144.131	even	12
576.2.bb.e.529.4		72	48.35	even	4
1728.2.bc.e.145.10		72	144.67	odd	12
1728.2.bc.e.721.9		72	16.3	odd	4
1728.2.bc.e.1009.9		72	36.31	odd	6
1728.2.bc.e.1585.10		72	4.3	odd	2

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.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.04877 + 0.948722i) q^{2} +(0.199854 - 1.98999i) q^{4} +(-0.00302457 + 0.0112878i) q^{5} +(-1.05753 - 0.610563i) q^{7} +(1.67835 + 2.27665i) q^{8} +(-0.00753693 - 0.0147079i) q^{10} +(-1.83070 + 0.490535i) q^{11} +(5.06759 + 1.35786i) q^{13} +(1.68836 - 0.362956i) q^{14} +(-3.92012 - 0.795413i) q^{16} +1.54238 q^{17} +(4.06823 - 4.06823i) q^{19} +(0.0218582 + 0.00827477i) q^{20} +(1.45461 - 2.25129i) q^{22} +(5.20660 - 3.00603i) q^{23} +(4.33001 + 2.49993i) q^{25} +(-6.60298 + 3.38365i) q^{26} +(-1.42637 + 1.98244i) q^{28} +(-0.798708 - 2.98082i) q^{29} +(2.92831 + 5.07198i) q^{31} +(4.86594 - 2.88489i) q^{32} +(-1.61761 + 1.46329i) q^{34} +(0.0100905 - 0.0100905i) q^{35} +(0.923082 + 0.923082i) q^{37} +(-0.407035 + 8.12628i) q^{38} +(-0.0307748 + 0.0120590i) q^{40} +(3.20829 - 1.85231i) q^{41} +(-4.84015 + 1.29691i) q^{43} +(0.610287 + 3.74111i) q^{44} +(-2.60866 + 8.09227i) q^{46} +(1.31218 - 2.27277i) q^{47} +(-2.75442 - 4.77080i) q^{49} +(-6.91294 + 1.48611i) q^{50} +(3.71490 - 9.81308i) q^{52} +(8.88508 + 8.88508i) q^{53} -0.0221483i q^{55} +(-0.384853 - 3.43236i) q^{56} +(3.66563 + 2.36845i) q^{58} +(-2.35453 + 8.78724i) q^{59} +(3.24737 + 12.1194i) q^{61} +(-7.88303 - 2.54121i) q^{62} +(-2.36631 + 7.64203i) q^{64} +(-0.0306545 + 0.0530952i) q^{65} +(-11.8800 - 3.18324i) q^{67} +(0.308250 - 3.06932i) q^{68} +(-0.00100958 + 0.0201557i) q^{70} -14.2363i q^{71} -4.32091i q^{73} +(-1.84385 - 0.0923563i) q^{74} +(-7.28269 - 8.90879i) q^{76} +(2.23552 + 0.599006i) q^{77} +(-0.261880 + 0.453589i) q^{79} +(0.0208352 - 0.0418439i) q^{80} +(-1.60745 + 4.98643i) q^{82} +(-2.91592 - 10.8824i) q^{83} +(-0.00466503 + 0.0174101i) q^{85} +(3.84581 - 5.95212i) q^{86} +(-4.18933 - 3.34459i) q^{88} +10.7103i q^{89} +(-4.53005 - 4.53005i) q^{91} +(-4.94142 - 10.9619i) q^{92} +(0.780042 + 3.62852i) q^{94} +(0.0336169 + 0.0582262i) q^{95} +(8.78820 - 15.2216i) q^{97} +(7.41493 + 2.39031i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{2} - 2 q^{4} - 4 q^{5} + 8 q^{8} - 20 q^{10} + 2 q^{11} - 16 q^{13} + 4 q^{14} - 10 q^{16} + 16 q^{17} + 28 q^{19} - 12 q^{20} - 8 q^{22} + 4 q^{26} - 16 q^{28} - 4 q^{29} + 28 q^{31} + 46 q^{32}+ \cdots - 88 q^{98}+O(q^{100}) \) 72 * q - 4 * q^2 - 2 * q^4 - 4 * q^5 + 8 * q^8 - 20 * q^10 + 2 * q^11 - 16 * q^13 + 4 * q^14 - 10 * q^16 + 16 * q^17 + 28 * q^19 - 12 * q^20 - 8 * q^22 + 4 * q^26 - 16 * q^28 - 4 * q^29 + 28 * q^31 + 46 * q^32 - 14 * q^34 + 16 * q^35 + 16 * q^37 - 2 * q^38 - 10 * q^40 - 10 * q^43 - 60 * q^44 + 20 * q^46 + 56 * q^47 + 4 * q^49 + 36 * q^50 + 6 * q^52 + 8 * q^53 - 52 * q^56 - 14 * q^58 + 14 * q^59 - 32 * q^61 - 16 * q^62 - 44 * q^64 + 64 * q^65 - 18 * q^67 - 16 * q^68 + 14 * q^70 - 38 * q^74 + 10 * q^76 + 36 * q^77 + 44 * q^79 - 144 * q^80 - 88 * q^82 - 20 * q^83 - 8 * q^85 - 76 * q^86 - 42 * q^88 - 80 * q^91 + 68 * q^92 + 20 * q^94 - 48 * q^95 + 40 * q^97 - 88 * q^98

Introduction

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