LMFDB - Embedded newform 459.2.y.a.368.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [459,2,Mod(44,459)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(459, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 9]))

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

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

chi := DirichletCharacter("459.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.y (of order $48$, degree $16$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			368.9
Character	$\chi$	$=$	459.368
Dual form			459.2.y.a.116.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.801255 - 0.105487i) q^{2} +(-1.30097 + 0.348594i) q^{4} +(1.37710 + 2.79247i) q^{5} +(-4.52563 - 2.23179i) q^{7} +(-2.49894 + 1.03509i) q^{8} +(1.39797 + 2.09222i) q^{10} +(-0.780943 + 0.265095i) q^{11} +(1.16796 + 4.35888i) q^{13} +(-3.86161 - 1.31084i) q^{14} +(0.439739 - 0.253884i) q^{16} +(-3.78892 + 1.62606i) q^{17} +(-1.95880 - 0.811360i) q^{19} +(-2.76500 - 3.15288i) q^{20} +(-0.597770 + 0.294788i) q^{22} +(-2.61464 + 2.98142i) q^{23} +(-2.85771 + 3.72424i) q^{25} +(1.39564 + 3.36937i) q^{26} +(6.66570 + 1.32589i) q^{28} +(0.0274451 - 0.418731i) q^{29} +(0.426633 - 1.25682i) q^{31} +(4.61733 - 3.54301i) q^{32} +(-2.86436 + 1.70257i) q^{34} -15.7111i q^{35} +(0.0132231 + 0.0664768i) q^{37} +(-1.65508 - 0.443478i) q^{38} +(-6.33175 - 5.55279i) q^{40} +(3.37615 - 0.221284i) q^{41} +(5.74422 + 4.40769i) q^{43} +(0.923573 - 0.617112i) q^{44} +(-1.78049 + 2.66469i) q^{46} +(-1.39277 + 5.19789i) q^{47} +(11.2391 + 14.6471i) q^{49} +(-1.89689 + 3.28551i) q^{50} +(-3.03896 - 5.26363i) q^{52} +(-2.70319 + 6.52608i) q^{53} +(-1.81570 - 1.81570i) q^{55} +(13.6194 + 0.892662i) q^{56} +(-0.0221803 - 0.338405i) q^{58} +(0.445276 - 3.38221i) q^{59} +(0.762232 - 1.54565i) q^{61} +(0.209263 - 1.05204i) q^{62} +(2.60783 - 2.60783i) q^{64} +(-10.5637 + 9.26409i) q^{65} +(-1.90636 - 1.10063i) q^{67} +(4.36244 - 3.43625i) q^{68} +(-1.65732 - 12.5886i) q^{70} +(2.14171 - 0.426013i) q^{71} +(4.79086 + 3.20115i) q^{73} +(0.0176075 + 0.0518700i) q^{74} +(2.83117 + 0.372731i) q^{76} +(4.12590 + 0.543185i) q^{77} +(-4.25979 - 12.5489i) q^{79} +(1.31453 + 0.878338i) q^{80} +(2.68181 - 0.533446i) q^{82} +(0.479996 + 3.64594i) q^{83} +(-9.75844 - 8.34121i) q^{85} +(5.06754 + 2.92574i) q^{86} +(1.67713 - 1.47080i) q^{88} +(3.26760 - 3.26760i) q^{89} +(4.44238 - 22.3333i) q^{91} +(2.36226 - 4.79019i) q^{92} +(-0.567653 + 4.31175i) q^{94} +(-0.431749 - 6.58721i) q^{95} +(17.3795 + 1.13911i) q^{97} +(10.5505 + 10.5505i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{16}\right)$

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 $

$2$	0.801255	−	0.105487i	0.566573	−	0.0745907i	0.158202	−	0.987407i	$-0.449430\pi$
$2$	0.801255	−	0.105487i	0.566573	−	0.0745907i	0.408371	+	0.912816i	$0.366097\pi$
$3$		0			0
$3$		0			0
$4$	−1.30097	+	0.348594i	−0.650485	+	0.174297i
$5$	1.37710	+	2.79247i	0.615856	+	1.24883i	0.951733	+	0.306926i	$0.0993005\pi$
$5$	1.37710	+	2.79247i	0.615856	+	1.24883i	−0.335878	+	0.941906i	$0.609033\pi$
$6$		0			0
$7$	−4.52563	−	2.23179i	−1.71053	−	0.843539i	−0.988417	−	0.151762i	$-0.951505\pi$
$7$	−4.52563	−	2.23179i	−1.71053	−	0.843539i	−0.722111	−	0.691777i	$-0.756828\pi$
$8$	−2.49894	+	1.03509i	−0.883508	+	0.365961i
$9$		0			0
$10$	1.39797	+	2.09222i	0.442078	+	0.661617i
$11$	−0.780943	+	0.265095i	−0.235463	+	0.0799290i	−0.436677	−	0.899618i	$-0.643845\pi$
$11$	−0.780943	+	0.265095i	−0.235463	+	0.0799290i	0.201214	+	0.979547i	$0.435511\pi$
$12$		0			0
$13$	1.16796	+	4.35888i	0.323934	+	1.20894i	0.915379	+	0.402592i	$0.131891\pi$
$13$	1.16796	+	4.35888i	0.323934	+	1.20894i	−0.591446	+	0.806345i	$0.701443\pi$
$14$	−3.86161	−	1.31084i	−1.03206	−	0.350337i
$15$		0			0
$16$	0.439739	−	0.253884i	0.109935	−	0.0634709i
$17$	−3.78892	+	1.62606i	−0.918948	+	0.394378i
$17$	−3.78892	+	1.62606i	−0.918948	+	0.394378i
$18$		0			0
$19$	−1.95880	−	0.811360i	−0.449379	−	0.186139i	0.146504	−	0.989210i	$-0.453198\pi$
$19$	−1.95880	−	0.811360i	−0.449379	−	0.186139i	−0.595883	+	0.803071i	$0.703198\pi$
$20$	−2.76500	−	3.15288i	−0.618272	−	0.705005i
$21$		0			0
$22$	−0.597770	+	0.294788i	−0.127445	+	0.0628490i
$23$	−2.61464	+	2.98142i	−0.545189	+	0.621669i	−0.957171	−	0.289523i	$-0.906503\pi$
$23$	−2.61464	+	2.98142i	−0.545189	+	0.621669i	0.411982	+	0.911192i	$0.364837\pi$
$24$		0			0
$25$	−2.85771	+	3.72424i	−0.571541	+	0.744847i
$26$	1.39564	+	3.36937i	0.273707	+	0.660788i
$27$		0			0
$28$	6.66570	+	1.32589i	1.25970	+	0.250570i
$29$	0.0274451	−	0.418731i	0.00509643	−	0.0777564i	−0.994553	−	0.104232i	$-0.966762\pi$
$29$	0.0274451	−	0.418731i	0.00509643	−	0.0777564i	0.999649	+	0.0264753i	$0.00842832\pi$
$30$		0			0
$31$	0.426633	−	1.25682i	0.0766256	−	0.225732i	−0.901867	−	0.432014i	$-0.857803\pi$
$31$	0.426633	−	1.25682i	0.0766256	−	0.225732i	0.978493	+	0.206282i	$0.0661365\pi$
$32$	4.61733	−	3.54301i	0.816237	−	0.626321i
$33$		0			0
$34$	−2.86436	+	1.70257i	−0.491234	+	0.291989i
$35$		−	15.7111i		−	2.65566i
$36$		0			0
$37$	0.0132231	+	0.0664768i	0.00217386	+	0.0109287i	0.981857	−	0.189623i	$-0.0607266\pi$
$37$	0.0132231	+	0.0664768i	0.00217386	+	0.0109287i	−0.979683	+	0.200552i	$0.935727\pi$
$38$	−1.65508	−	0.443478i	−0.268490	−	0.0719417i
$39$		0			0
$40$	−6.33175	−	5.55279i	−1.00114	−	0.877974i
$41$	3.37615	−	0.221284i	0.527266	−	0.0345588i	0.200554	−	0.979683i	$-0.435726\pi$
$41$	3.37615	−	0.221284i	0.527266	−	0.0345588i	0.326712	+	0.945124i	$0.394059\pi$
$42$		0			0
$43$	5.74422	+	4.40769i	0.875985	+	0.672167i	0.945573	−	0.325409i	$-0.105502\pi$
$43$	5.74422	+	4.40769i	0.875985	+	0.672167i	−0.0695883	+	0.997576i	$0.522169\pi$
$44$	0.923573	−	0.617112i	0.139234	−	0.0930331i
$45$		0			0
$46$	−1.78049	+	2.66469i	−0.262519	+	0.392887i
$47$	−1.39277	+	5.19789i	−0.203156	+	0.758190i	0.786847	+	0.617148i	$0.211712\pi$
$47$	−1.39277	+	5.19789i	−0.203156	+	0.758190i	−0.990004	+	0.141042i	$0.954955\pi$
$48$		0			0
$49$	11.2391	+	14.6471i	1.60559	+	2.09244i
$50$	−1.89689	+	3.28551i	−0.268261	+	0.464642i
$51$		0			0
$52$	−3.03896	−	5.26363i	−0.421428	−	0.729935i
$53$	−2.70319	+	6.52608i	−0.371312	+	0.896426i	0.622217	+	0.782845i	$0.286232\pi$
$53$	−2.70319	+	6.52608i	−0.371312	+	0.896426i	−0.993529	+	0.113581i	$0.963768\pi$
$54$		0			0
$55$	−1.81570	−	1.81570i	−0.244829	−	0.244829i
$56$	13.6194	+	0.892662i	1.81997	+	0.119287i
$57$		0			0
$58$	−0.0221803	−	0.338405i	−0.00291241	−	0.0444348i
$59$	0.445276	−	3.38221i	0.0579700	−	0.440326i	−0.937706	−	0.347430i	$-0.887054\pi$
$59$	0.445276	−	3.38221i	0.0579700	−	0.440326i	0.995676	−	0.0928957i	$-0.0296123\pi$
$60$		0			0
$61$	0.762232	−	1.54565i	0.0975938	−	0.197901i	−0.842601	−	0.538539i	$-0.818976\pi$
$61$	0.762232	−	1.54565i	0.0975938	−	0.197901i	0.940194	+	0.340638i	$0.110643\pi$
$62$	0.209263	−	1.05204i	0.0265765	−	0.133609i
$63$		0			0
$64$	2.60783	−	2.60783i	0.325978	−	0.325978i
$65$	−10.5637	+	9.26409i	−1.31026	+	1.14907i
$66$		0			0
$67$	−1.90636	−	1.10063i	−0.232898	−	0.134464i	0.379010	−	0.925393i	$-0.376265\pi$
$67$	−1.90636	−	1.10063i	−0.232898	−	0.134464i	−0.611908	+	0.790929i	$0.709598\pi$
$68$	4.36244	−	3.43625i	0.529023	−	0.416707i
$69$		0			0
$70$	−1.65732	−	12.5886i	−0.198088	−	1.50462i
$71$	2.14171	−	0.426013i	0.254174	−	0.0505584i	−0.0663583	−	0.997796i	$-0.521138\pi$
$71$	2.14171	−	0.426013i	0.254174	−	0.0505584i	0.320533	+	0.947237i	$0.396138\pi$
$72$		0			0
$73$	4.79086	+	3.20115i	0.560727	+	0.374666i	0.803398	−	0.595443i	$-0.203023\pi$
$73$	4.79086	+	3.20115i	0.560727	+	0.374666i	−0.242670	+	0.970109i	$0.578023\pi$
$74$	0.0176075	+	0.0518700i	0.00204683	+	0.00602976i
$75$		0			0
$76$	2.83117	+	0.372731i	0.324758	+	0.0427552i
$77$	4.12590	+	0.543185i	0.470190	+	0.0619017i
$78$		0			0
$79$	−4.25979	−	12.5489i	−0.479263	−	1.41186i	−0.870771	−	0.491689i	$-0.836380\pi$
$79$	−4.25979	−	12.5489i	−0.479263	−	1.41186i	0.391507	−	0.920175i	$-0.371954\pi$
$80$	1.31453	+	0.878338i	0.146968	+	0.0982012i
$81$		0			0
$82$	2.68181	−	0.533446i	0.296157	−	0.0589092i
$83$	0.479996	+	3.64594i	0.0526865	+	0.400193i	0.997386	+	0.0722565i	$0.0230200\pi$
$83$	0.479996	+	3.64594i	0.0526865	+	0.400193i	−0.944700	+	0.327937i	$0.893647\pi$
$84$		0			0
$85$	−9.75844	−	8.34121i	−1.05845	−	0.904732i
$86$	5.06754	+	2.92574i	0.546447	+	0.315491i
$87$		0			0
$88$	1.67713	−	1.47080i	0.178783	−	0.156788i
$89$	3.26760	−	3.26760i	0.346365	−	0.346365i	−0.512389	−	0.858754i	$-0.671239\pi$
$89$	3.26760	−	3.26760i	0.346365	−	0.346365i	0.858754	+	0.512389i	$0.171239\pi$
$90$		0			0
$91$	4.44238	−	22.3333i	0.465688	−	2.34117i
$92$	2.36226	−	4.79019i	0.246282	−	0.499411i
$93$		0			0
$94$	−0.567653	+	4.31175i	−0.0585489	+	0.444723i
$95$	−0.431749	−	6.58721i	−0.0442965	−	0.675833i
$96$		0			0
$97$	17.3795	+	1.13911i	1.76462	+	0.115659i	0.912859	−	0.408276i	$-0.133870\pi$
$97$	17.3795	+	1.13911i	1.76462	+	0.115659i	0.851758	+	0.523935i	$0.175537\pi$
$98$	10.5505	+	10.5505i	1.06576	+	1.06576i
$99$		0			0
$100$	2.41954	−	5.84130i	0.241954	−	0.584130i
$101$	−7.22857	−	12.5203i	−0.719270	−	1.24581i	−0.961289	−	0.275541i	$-0.911143\pi$
$101$	−7.22857	−	12.5203i	−0.719270	−	1.24581i	0.242020	−	0.970271i	$-0.422190\pi$
$102$		0			0
$103$	−0.972232	+	1.68395i	−0.0957968	+	0.165925i	−0.909941	−	0.414738i	$-0.863873\pi$
$103$	−0.972232	+	1.68395i	−0.0957968	+	0.165925i	0.814144	+	0.580663i	$0.197207\pi$
$104$	−7.43051	−	9.68363i	−0.728621	−	0.949558i
$105$		0			0
$106$	−1.47753	+	5.51420i	−0.143510	+	0.535587i
$107$	−2.20029	+	3.29297i	−0.212710	+	0.318344i	−0.922447	−	0.386123i	$-0.873814\pi$
$107$	−2.20029	+	3.29297i	−0.212710	+	0.318344i	0.709737	+	0.704467i	$0.248814\pi$
$108$		0			0
$109$	−12.7255	+	8.50289i	−1.21888	+	0.814430i	−0.987374	−	0.158404i	$-0.949365\pi$
$109$	−12.7255	+	8.50289i	−1.21888	+	0.814430i	−0.231506	+	0.972834i	$0.574365\pi$
$110$	−1.64637	−	1.26331i	−0.156976	−	0.120452i
$111$		0			0
$112$	−2.55671	+	0.167576i	−0.241587	+	0.0158344i
$113$	0.316254	+	0.277347i	0.0297506	+	0.0260906i	0.674092	−	0.738647i	$-0.264535\pi$
$113$	0.316254	+	0.277347i	0.0297506	+	0.0260906i	−0.644341	+	0.764738i	$0.722868\pi$
$114$		0			0
$115$	−11.9261	−	3.19560i	−1.11212	−	0.297991i
$116$	0.110262	+	0.554324i	0.0102376	+	0.0514677i
$117$		0			0
$118$		−	2.75698i		−	0.253801i
$119$	20.7763	+	1.09713i	1.90456	+	0.100574i
$120$		0			0
$121$	−8.18729	+	6.28233i	−0.744299	+	0.571121i
$122$	0.447695	−	1.31887i	0.0405324	−	0.119405i
$123$		0			0
$124$	−0.116917	+	1.78381i	−0.0104995	+	0.160191i
$125$	0.933539	+	0.185692i	0.0834983	+	0.0166088i
$126$		0			0
$127$	6.87458	+	16.5967i	0.610020	+	1.47272i	0.862978	+	0.505241i	$0.168596\pi$
$127$	6.87458	+	16.5967i	0.610020	+	1.47272i	−0.252958	+	0.967477i	$0.581404\pi$
$128$	−5.27157	+	6.87004i	−0.465945	+	0.607232i
$129$		0			0
$130$	−7.48695	+	8.53723i	−0.656649	+	0.748765i
$131$	−8.97762	+	4.42727i	−0.784378	+	0.386812i	−0.789949	−	0.613172i	$-0.789893\pi$
$131$	−8.97762	+	4.42727i	−0.784378	+	0.386812i	0.00557139	+	0.999984i	$0.498227\pi$
$132$		0			0
$133$	7.05401	+	8.04355i	0.611660	+	0.697464i
$134$	−1.64358	−	0.680793i	−0.141984	−	0.0588115i
$135$		0			0
$136$	7.78515	−	7.98532i	0.667571	−	0.684735i
$137$	0.180228	−	0.104055i	0.0153979	−	0.00889001i	−0.492281	−	0.870436i	$-0.663837\pi$
$137$	0.180228	−	0.104055i	0.0153979	−	0.00889001i	0.507679	+	0.861546i	$0.330504\pi$
$138$		0			0
$139$	−4.01066	−	1.36144i	−0.340180	−	0.115475i	0.146122	−	0.989267i	$-0.453321\pi$
$139$	−4.01066	−	1.36144i	−0.340180	−	0.115475i	−0.486301	+	0.873791i	$0.661654\pi$
$140$	5.47679	+	20.4397i	0.462873	+	1.72747i
$141$		0			0
$142$	1.67112	−	0.567268i	0.140237	−	0.0476041i
$143$	−2.06763	−	3.09442i	−0.172904	−	0.258769i
$144$		0			0
$145$	1.20709	−	0.499993i	0.100243	−	0.0415222i
$146$	4.17638	+	2.05956i	0.345639	+	0.170450i
$147$		0			0
$148$	−0.0403762	−	0.0818748i	−0.00331890	−	0.00673007i
$149$	−22.7638	+	6.09953i	−1.86488	+	0.499693i	−0.999997	−	0.00227989i	$-0.999274\pi$
$149$	−22.7638	+	6.09953i	−1.86488	+	0.499693i	−0.864883	+	0.501973i	$0.832608\pi$
$150$		0			0
$151$	−12.4407	+	1.63785i	−1.01241	+	0.133287i	−0.618437	−	0.785834i	$-0.712234\pi$
$151$	−12.4407	+	1.63785i	−1.01241	+	0.133287i	−0.393976	+	0.919121i	$0.628901\pi$
$152$	5.73475			0.465149
$153$		0			0
$154$	3.36319			0.271014
$155$	4.09715	−	0.539400i	0.329091	−	0.0433257i
$156$		0			0
$157$	9.34317	−	2.50349i	0.745666	−	0.199801i	0.134071	−	0.990972i	$-0.457195\pi$
$157$	9.34317	−	2.50349i	0.745666	−	0.199801i	0.611595	+	0.791171i	$0.290528\pi$
$158$	−4.73692	−	9.60553i	−0.376849	−	0.764175i
$159$		0			0
$160$	16.2523	+	8.01473i	1.28485	+	0.633620i
$161$	18.4868	−	7.65748i	1.45696	−	0.603494i
$162$		0			0
$163$	−0.147654	−	0.220979i	−0.0115651	−	0.0173084i	0.825642	−	0.564194i	$-0.190813\pi$
$163$	−0.147654	−	0.220979i	−0.0115651	−	0.0173084i	−0.837207	+	0.546886i	$0.815813\pi$
$164$	−4.31513	+	1.46479i	−0.336955	+	0.114381i
$165$		0			0
$166$	0.769199	+	2.87069i	0.0597014	+	0.222809i
$167$	1.69588	+	0.575674i	0.131231	+	0.0445470i	0.386282	−	0.922381i	$-0.373759\pi$
$167$	1.69588	+	0.575674i	0.131231	+	0.0445470i	−0.255051	+	0.966928i	$0.582092\pi$
$168$		0			0
$169$	−6.37741	+	3.68200i	−0.490570	+	0.283231i
$170$	−8.69889	−	5.65405i	−0.667174	−	0.433646i
$171$		0			0
$172$	−9.00955	−	3.73188i	−0.686972	−	0.284553i
$173$	−11.6422	−	13.2754i	−0.885143	−	1.00931i	−0.999873	−	0.0159158i	$-0.994934\pi$
$173$	−11.6422	−	13.2754i	−0.885143	−	1.00931i	0.114730	−	0.993397i	$-0.463400\pi$
$174$		0			0
$175$	21.2447	−	10.4767i	1.60595	−	0.791964i
$176$	−0.276108	+	0.314841i	−0.0208124	+	0.0237320i
$177$		0			0
$178$	2.27349	−	2.96287i	0.170405	−	0.222076i
$179$	8.88505	+	21.4504i	0.664100	+	1.60328i	0.791319	+	0.611403i	$0.209395\pi$
$179$	8.88505	+	21.4504i	0.664100	+	1.60328i	−0.127220	+	0.991875i	$0.540605\pi$
$180$		0			0
$181$	−9.79946	−	1.94923i	−0.728388	−	0.144885i	−0.183052	−	0.983103i	$-0.558598\pi$
$181$	−9.79946	−	1.94923i	−0.728388	−	0.144885i	−0.545336	+	0.838218i	$0.683598\pi$
$182$	1.20360	−	18.3633i	0.0892164	−	1.36118i
$183$		0			0
$184$	3.44776	−	10.1568i	0.254172	−	0.748768i
$185$	−0.167425	+	0.128470i	−0.0123093	+	0.00944529i
$186$		0			0
$187$	2.52787	−	2.27429i	0.184856	−	0.166312i
$188$		−	7.24781i		−	0.528601i
$189$		0			0
$190$	−1.04081	−	5.23249i	−0.0755081	−	0.379605i
$191$	7.40789	+	1.98494i	0.536016	+	0.143625i	0.516665	−	0.856188i	$-0.327173\pi$
$191$	7.40789	+	1.98494i	0.536016	+	0.143625i	0.0193512	+	0.999813i	$0.493840\pi$
$192$		0			0
$193$	8.68803	+	7.61919i	0.625378	+	0.548442i	0.912305	−	0.409511i	$-0.134301\pi$
$193$	8.68803	+	7.61919i	0.625378	+	0.548442i	−0.286928	+	0.957952i	$0.592634\pi$
$194$	14.0455	−	0.920593i	1.00841	−	0.0660947i
$195$		0			0
$196$	−19.7276	−	15.1375i	−1.40912	−	1.08125i
$197$	1.59072	−	1.06288i	0.113334	−	0.0757274i	−0.497611	−	0.867400i	$-0.665789\pi$
$197$	1.59072	−	1.06288i	0.113334	−	0.0757274i	0.610946	+	0.791673i	$0.290789\pi$
$198$		0			0
$199$	−7.63607	+	11.4282i	−0.541306	+	0.810122i	−0.996785	−	0.0801245i	$-0.974468\pi$
$199$	−7.63607	+	11.4282i	−0.541306	+	0.810122i	0.455478	+	0.890247i	$0.349468\pi$
$200$	3.28630	−	12.2646i	0.232376	−	0.867240i
$201$		0			0
$202$	−7.11265	−	9.26939i	−0.500445	−	0.652192i
$203$	−1.05873	+	1.83377i	−0.0743082	+	0.128705i
$204$		0			0
$205$	5.26721	+	9.12307i	0.367878	+	0.637183i
$206$	−0.601370	+	1.45183i	−0.0418994	+	0.101154i
$207$		0			0
$208$	1.62025	+	1.62025i	0.112344	+	0.112344i
$209$	1.74480	+	0.114360i	0.120690	+	0.00791045i
$210$		0			0
$211$	−0.528242	−	8.05942i	−0.0363657	−	0.554833i	−0.976704	−	0.214592i	$-0.931158\pi$
$211$	−0.528242	−	8.05942i	−0.0363657	−	0.554833i	0.940338	−	0.340241i	$-0.110509\pi$
$212$	1.24182	−	9.43255i	0.0852884	−	0.647830i
$213$		0			0
$214$	−1.41563	+	2.87061i	−0.0967704	+	0.196231i
$215$	−4.39803	+	22.1104i	−0.299943	+	1.50792i
$216$		0			0
$217$	−4.73575	+	4.73575i	−0.321484	+	0.321484i
$218$	−9.29941	+	8.15536i	−0.629835	+	0.552351i
$219$		0			0
$220$	2.99512	+	1.72923i	0.201931	+	0.116585i
$221$	−11.5131	−	14.6163i	−0.774457	−	0.983198i
$222$		0			0
$223$	2.37603	+	18.0478i	0.159111	+	1.20857i	0.865561	+	0.500804i	$0.166962\pi$
$223$	2.37603	+	18.0478i	0.159111	+	1.20857i	−0.706450	+	0.707763i	$0.749704\pi$
$224$	−28.8036	+	5.72939i	−1.92452	+	0.382811i
$225$		0			0
$226$	0.282656	+	0.188865i	0.0188020	+	0.0125631i
$227$	−7.49766	−	22.0874i	−0.497637	−	1.46599i	−0.848313	−	0.529495i	$-0.822382\pi$
$227$	−7.49766	−	22.0874i	−0.497637	−	1.46599i	0.350676	−	0.936497i	$-0.385952\pi$
$228$		0			0
$229$	14.6011	+	1.92227i	0.964866	+	0.127027i	0.596464	−	0.802640i	$-0.296572\pi$
$229$	14.6011	+	1.92227i	0.964866	+	0.127027i	0.368402	+	0.929667i	$0.379905\pi$
$230$	−9.89297	−	1.30243i	−0.652323	−	0.0858800i
$231$		0			0
$232$	0.364842	+	1.07479i	0.0239531	+	0.0705635i
$233$	−20.3987	−	13.6300i	−1.33636	−	0.892930i	−0.337535	−	0.941313i	$-0.609593\pi$
$233$	−20.3987	−	13.6300i	−1.33636	−	0.892930i	−0.998829	+	0.0483830i	$0.984593\pi$
$234$		0			0
$235$	−16.4329	+	3.26871i	−1.07197	+	0.213227i
$236$	0.599726	+	4.55537i	0.0390388	+	0.296529i
$237$		0			0
$238$	16.7628	−	1.31255i	1.08657	−	0.0850803i
$239$	23.2883	+	13.4455i	1.50639	+	0.869717i	0.999972	+	0.00743049i	$0.00236522\pi$
$239$	23.2883	+	13.4455i	1.50639	+	0.869717i	0.506421	+	0.862286i	$0.330968\pi$
$240$		0			0
$241$	−6.95983	+	6.10361i	−0.448322	+	0.393168i	−0.853519	−	0.521061i	$-0.825536\pi$
$241$	−6.95983	+	6.10361i	−0.448322	+	0.393168i	0.405197	+	0.914229i	$0.367203\pi$
$242$	−5.89740	+	5.89740i	−0.379099	+	0.379099i
$243$		0			0
$244$	−0.452835	+	2.27656i	−0.0289898	+	0.145742i
$245$	−25.4243	+	51.5553i	−1.62430	+	3.29375i
$246$		0			0
$247$	1.24883	−	9.48581i	0.0794612	−	0.603567i
$248$	0.234798	+	3.58232i	0.0149097	+	0.227478i
$249$		0			0
$250$	0.767591	+	0.0503106i	0.0485467	+	0.00318192i
$251$	−12.0194	−	12.0194i	−0.758657	−	0.758657i	0.217421	−	0.976078i	$-0.430236\pi$
$251$	−12.0194	−	12.0194i	−0.758657	−	0.758657i	−0.976078	+	0.217421i	$0.930236\pi$
$252$		0			0
$253$	1.25152	−	3.02145i	0.0786827	−	0.189957i
$254$	7.25902	+	12.5730i	0.455472	+	0.788900i
$255$		0			0
$256$	−7.18719	+	12.4486i	−0.449200	+	0.778036i
$257$	10.2997	+	13.4228i	0.642477	+	0.837292i	0.995141	−	0.0984576i	$-0.0313909\pi$
$257$	10.2997	+	13.4228i	0.642477	+	0.837292i	−0.352664	+	0.935750i	$0.614724\pi$
$258$		0			0
$259$	0.0885198	−	0.330360i	0.00550035	−	0.0205276i
$260$	10.5136	−	15.7347i	0.652027	−	0.975827i
$261$		0			0
$262$	−6.72634	+	4.49440i	−0.415555	+	0.277665i
$263$	17.2622	+	13.2458i	1.06444	+	0.816770i	0.983673	−	0.179963i	$-0.0575978\pi$
$263$	17.2622	+	13.2458i	1.06444	+	0.816770i	0.0807624	+	0.996733i	$0.474264\pi$
$264$		0			0
$265$	−21.9464	+	1.43845i	−1.34816	+	0.0883630i
$266$	6.50055	+	5.70083i	0.398574	+	0.349540i
$267$		0			0
$268$	2.86379	+	0.767349i	0.174934	+	0.0468733i
$269$	−0.232394	−	1.16832i	−0.0141693	−	0.0712339i	0.973054	−	0.230579i	$-0.0740619\pi$
$269$	−0.232394	−	1.16832i	−0.0141693	−	0.0712339i	−0.987223	+	0.159345i	$0.949062\pi$
$270$		0			0
$271$			18.6384i			1.13220i	0.824336	+	0.566101i	$0.191549\pi$
$271$			18.6384i			1.13220i	−0.824336	+	0.566101i	$0.808451\pi$
$272$	−1.25331	+	1.67699i	−0.0759929	+	0.101682i
$273$		0			0
$274$	0.133432	−	0.102386i	0.00806094	−	0.00618538i
$275$	1.24443	−	3.66598i	0.0750421	−	0.221067i
$276$		0			0
$277$	−0.716507	+	10.9318i	−0.0430507	+	0.656827i	0.920742	+	0.390173i	$0.127585\pi$
$277$	−0.716507	+	10.9318i	−0.0430507	+	0.656827i	−0.963792	+	0.266654i	$0.914082\pi$
$278$	−3.35717	−	0.667784i	−0.201350	−	0.0400510i
$279$		0			0
$280$	16.2625	+	39.2610i	0.971868	+	2.34630i
$281$	16.4155	−	21.3931i	0.979266	−	1.27620i	0.0182154	−	0.999834i	$-0.494202\pi$
$281$	16.4155	−	21.3931i	0.979266	−	1.27620i	0.961051	−	0.276371i	$-0.0891318\pi$
$282$		0			0
$283$	−6.05533	+	6.90478i	−0.359952	+	0.410447i	−0.903265	−	0.429084i	$-0.858836\pi$
$283$	−6.05533	+	6.90478i	−0.359952	+	0.410447i	0.543313	+	0.839530i	$0.317170\pi$
$284$	−2.63780	+	1.30082i	−0.156525	+	0.0771893i
$285$		0			0
$286$	−1.98312	−	2.26131i	−0.117264	−	0.133714i
$287$	−15.7731	−	6.53342i	−0.931054	−	0.385655i
$288$		0			0
$289$	11.7118	−	12.3220i	0.688931	−	0.724826i
$290$	0.914444	−	0.527954i	0.0536980	−	0.0310025i
$291$		0			0
$292$	−7.34866	−	2.49453i	−0.430048	−	0.145982i
$293$	1.14029	+	4.25560i	0.0666162	+	0.248615i	0.991202	−	0.132359i	$-0.0422553\pi$
$293$	1.14029	+	4.25560i	0.0666162	+	0.248615i	−0.924586	+	0.380974i	$0.875589\pi$
$294$		0			0
$295$	10.0579	−	3.41420i	0.585594	−	0.198782i
$296$	−0.101853	−	0.152434i	−0.00592010	−	0.00886006i
$297$		0			0
$298$	−17.5962	+	7.28857i	−1.01932	+	0.422215i
$299$	−16.0495	−	7.91472i	−0.928164	−	0.457720i
$300$		0			0
$301$	−16.1592	−	32.7675i	−0.931398	−	1.88869i
$302$	−9.79543	+	2.62468i	−0.563664	+	0.151033i
$303$		0			0
$304$	−1.06735	+	0.140519i	−0.0612168	+	0.00805934i
$305$	5.36586			0.307248
$306$		0			0
$307$	16.0286			0.914801			0.457400	−	0.889261i	$-0.348781\pi$
$307$	16.0286			0.914801			0.457400	+	0.889261i	$0.348781\pi$
$308$	−5.55702	+	0.731596i	−0.316641	+	0.0416865i
$309$		0			0
$310$	3.22596	−	0.864394i	0.183222	−	0.0490943i
$311$	−6.02290	−	12.2132i	−0.341528	−	0.692549i	0.656566	−	0.754269i	$-0.272008\pi$
$311$	−6.02290	−	12.2132i	−0.341528	−	0.692549i	−0.998094	+	0.0617192i	$0.980342\pi$
$312$		0			0
$313$	−1.94022	−	0.956812i	−0.109668	−	0.0540822i	0.386627	−	0.922236i	$-0.373640\pi$
$313$	−1.94022	−	0.956812i	−0.109668	−	0.0540822i	−0.496295	+	0.868154i	$0.665307\pi$
$314$	7.22217	−	2.99152i	0.407571	−	0.168821i
$315$		0			0
$316$	9.91633	+	14.8408i	0.557837	+	0.834862i
$317$	8.63970	−	2.93278i	0.485254	−	0.164722i	−0.0680819	−	0.997680i	$-0.521688\pi$
$317$	8.63970	−	2.93278i	0.485254	−	0.164722i	0.553336	+	0.832958i	$0.313355\pi$
$318$		0			0
$319$	0.0895703	+	0.334281i	0.00501497	+	0.0187161i
$320$	10.8735	+	3.69106i	0.607848	+	0.206337i
$321$		0			0
$322$	14.0049	−	8.08572i	0.780461	−	0.450599i
$323$	8.74105	−	0.110949i	0.486365	−	0.00617335i
$324$		0			0
$325$	−19.5712	−	8.10665i	−1.08561	−	0.449676i
$326$	−0.141619	−	0.161485i	−0.00784353	−	0.00894383i
$327$		0			0
$328$	−8.20773	+	4.04761i	−0.453196	+	0.223492i
$329$	17.9038	−	20.4153i	0.987067	−	1.12553i
$330$		0			0
$331$	0.826504	−	1.07712i	0.0454288	−	0.0592039i	−0.770087	−	0.637939i	$-0.779787\pi$
$331$	0.826504	−	1.07712i	0.0454288	−	0.0592039i	0.815515	+	0.578736i	$0.196454\pi$
$332$	−1.89541	−	4.57593i	−0.104024	−	0.251137i
$333$		0			0
$334$	1.41956	+	0.282368i	0.0776747	+	0.0154505i
$335$	0.448260	−	6.83912i	0.0244911	−	0.373661i
$336$		0			0
$337$	7.70958	−	22.7117i	0.419968	−	1.23718i	−0.506968	−	0.861965i	$-0.669234\pi$
$337$	7.70958	−	22.7117i	0.419968	−	1.23718i	0.926936	−	0.375220i	$-0.122433\pi$
$338$	−4.72152	+	3.62295i	−0.256817	+	0.197063i
$339$		0			0
$340$	15.6031	+	7.44994i	0.846199	+	0.404029i
$341$			1.09460i			0.0592761i
$342$		0			0
$343$	−11.2838	−	56.7273i	−0.609266	−	3.06299i
$344$	−18.9168	−	5.06875i	−1.01993	−	0.273289i
$345$		0			0
$346$	−10.7288	−	9.40890i	−0.576783	−	0.505825i
$347$	4.13052	−	0.270728i	0.221738	−	0.0145335i	0.0458707	−	0.998947i	$-0.485394\pi$
$347$	4.13052	−	0.270728i	0.221738	−	0.0145335i	0.175867	+	0.984414i	$0.443727\pi$
$348$		0			0
$349$	1.34809	+	1.03443i	0.0721618	+	0.0553717i	0.644212	−	0.764847i	$-0.277185\pi$
$349$	1.34809	+	1.03443i	0.0721618	+	0.0553717i	−0.572051	+	0.820218i	$0.693852\pi$
$350$	15.9172	−	10.6355i	0.850811	−	0.568494i
$351$		0			0
$352$	−2.66664	+	3.99092i	−0.142133	+	0.212717i
$353$	−4.91469	+	18.3419i	−0.261582	+	0.976238i	0.702727	+	0.711460i	$0.251966\pi$
$353$	−4.91469	+	18.3419i	−0.261582	+	0.976238i	−0.964309	+	0.264779i	$0.914701\pi$
$354$		0			0
$355$	4.13897	+	5.39401i	0.219674	+	0.286284i
$356$	−3.11198	+	5.39011i	−0.164935	+	0.285675i
$357$		0			0
$358$	9.38193	+	16.2500i	0.495850	+	0.858838i
$359$	−9.63555	+	23.2623i	−0.508545	+	1.22774i	0.436176	+	0.899861i	$0.356333\pi$
$359$	−9.63555	+	23.2623i	−0.508545	+	1.22774i	−0.944721	+	0.327875i	$0.893667\pi$
$360$		0			0
$361$	−10.2564	−	10.2564i	−0.539813	−	0.539813i
$362$	−8.05748	−	0.528115i	−0.423492	−	0.0277571i
$363$		0			0
$364$	2.00587	+	30.6036i	0.105136	+	1.60406i
$365$	−2.34165	+	17.7866i	−0.122568	+	0.930994i
$366$		0			0
$367$	4.54401	−	9.21434i	0.237195	−	0.480985i	−0.745430	−	0.666584i	$-0.767756\pi$
$367$	4.54401	−	9.21434i	0.237195	−	0.480985i	0.982626	+	0.185599i	$0.0594225\pi$
$368$	−0.392824	+	1.97486i	−0.0204774	+	0.102947i
$369$		0			0
$370$	−0.120598	+	0.120598i	−0.00626961	+	0.00626961i
$371$	26.7985	−	23.5017i	1.39131	−	1.22015i
$372$		0			0
$373$	5.50433	+	3.17793i	0.285004	+	0.164547i	0.635686	−	0.771947i	$-0.280717\pi$
$373$	5.50433	+	3.17793i	0.285004	+	0.164547i	−0.350683	+	0.936494i	$0.614050\pi$
$374$	1.78556	−	2.08894i	0.0923292	−	0.108017i
$375$		0			0
$376$	−1.89986	−	14.4308i	−0.0979776	−	0.744214i
$377$	1.85726	−	0.369431i	0.0956535	−	0.0190267i
$378$		0			0
$379$	6.75771	+	4.51536i	0.347120	+	0.231938i	0.716892	−	0.697184i	$-0.245564\pi$
$379$	6.75771	+	4.51536i	0.347120	+	0.231938i	−0.369772	+	0.929123i	$0.620564\pi$
$380$	2.85795	+	8.41926i	0.146610	+	0.431899i
$381$		0			0
$382$	6.14499	+	0.809004i	0.314405	+	0.0413922i
$383$	−16.4005	−	2.15916i	−0.838026	−	0.110328i	−0.300716	−	0.953714i	$-0.597226\pi$
$383$	−16.4005	−	2.15916i	−0.838026	−	0.110328i	−0.537309	+	0.843385i	$0.680559\pi$
$384$		0			0
$385$	4.16493	+	12.2695i	0.212264	+	0.625310i
$386$	7.76505	+	5.18844i	0.395231	+	0.264085i
$387$		0			0
$388$	−23.0072	+	4.57643i	−1.16802	+	0.232333i
$389$	0.312441	+	2.37323i	0.0158414	+	0.120327i	0.997538	−	0.0701220i	$-0.0223389\pi$
$389$	0.312441	+	2.37323i	0.0158414	+	0.120327i	−0.981697	+	0.190449i	$0.939006\pi$
$390$		0			0
$391$	5.05867	−	15.5479i	0.255828	−	0.786293i
$392$	−43.2469	−	24.9686i	−2.18430	−	1.26111i
$393$		0			0
$394$	1.16245	−	1.01944i	0.0585634	−	0.0513587i
$395$	29.1764	−	29.1764i	1.46802	−	1.46802i
$396$		0			0
$397$	−1.66437	+	8.36734i	−0.0835322	+	0.419945i	0.916280	+	0.400539i	$0.131177\pi$
$397$	−1.66437	+	8.36734i	−0.0835322	+	0.419945i	−0.999812	+	0.0194052i	$0.993823\pi$
$398$	−4.91291	+	9.96239i	−0.246262	+	0.499370i
$399$		0			0
$400$	−0.311124	+	2.36322i	−0.0155562	+	0.118161i
$401$	0.562463	+	8.58153i	0.0280881	+	0.428541i	0.988626	+	0.150393i	$0.0480539\pi$
$401$	0.562463	+	8.58153i	0.0280881	+	0.428541i	−0.960538	+	0.278148i	$0.910279\pi$
$402$		0			0
$403$	5.97663	+	0.391729i	0.297717	+	0.0195134i
$404$	13.7686	+	13.7686i	0.685015	+	0.685015i
$405$		0			0
$406$	−0.654872	+	1.58100i	−0.0325007	+	0.0784637i
$407$	−0.0279491	−	0.0484092i	−0.00138538	−	0.00239956i
$408$		0			0
$409$	8.77562	−	15.1998i	0.433926	−	0.751582i	−0.563281	−	0.826265i	$-0.690461\pi$
$409$	8.77562	−	15.1998i	0.433926	−	0.751582i	0.997207	+	0.0746830i	$0.0237945\pi$
$410$	5.18274	+	6.75428i	0.255957	+	0.333570i
$411$		0			0
$412$	0.677828	−	2.52969i	0.0333942	−	0.124629i
$413$	−9.56355	+	14.3129i	−0.470591	+	0.704290i
$414$		0			0
$415$	−9.52017	+	6.36118i	−0.467327	+	0.312258i
$416$	20.8364	+	15.9883i	1.02159	+	0.783893i
$417$		0			0
$418$	1.41009	−	0.0924222i	0.0689698	−	0.00452052i
$419$	−2.19918	−	1.92863i	−0.107437	−	0.0942197i	0.603942	−	0.797028i	$-0.293596\pi$
$419$	−2.19918	−	1.92863i	−0.107437	−	0.0942197i	−0.711379	+	0.702808i	$0.751929\pi$
$420$		0			0
$421$	13.5300	+	3.62534i	0.659410	+	0.176688i	0.572980	−	0.819569i	$-0.305787\pi$
$421$	13.5300	+	3.62534i	0.659410	+	0.176688i	0.0864304	+	0.996258i	$0.472454\pi$
$422$	−1.27342	−	6.40192i	−0.0619892	−	0.311641i
$423$		0			0
$424$		−	19.1063i		−	0.927885i
$425$	4.77178	−	18.7576i	0.231465	−	0.909879i
$426$		0			0
$427$	−6.89916	+	5.29391i	−0.333874	+	0.256190i
$428$	1.71461	−	5.05107i	0.0828786	−	0.244152i
$429$		0			0
$430$	−1.19158	+	18.1800i	−0.0574631	+	0.876717i
$431$	−21.7828	−	4.33286i	−1.04924	−	0.208707i	−0.359785	−	0.933035i	$-0.617150\pi$
$431$	−21.7828	−	4.33286i	−1.04924	−	0.208707i	−0.689455	+	0.724329i	$0.742150\pi$
$432$		0			0
$433$	−13.5406	−	32.6900i	−0.650721	−	1.57098i	−0.811734	−	0.584027i	$-0.801476\pi$
$433$	−13.5406	−	32.6900i	−0.650721	−	1.57098i	0.161014	−	0.986952i	$-0.448524\pi$
$434$	−3.29498	+	4.29410i	−0.158164	+	0.206124i
$435$		0			0
$436$	13.5914	−	15.4980i	0.650911	−	0.742221i
$437$	7.54055	−	3.71859i	0.360713	−	0.177884i
$438$		0			0
$439$	9.74245	+	11.1091i	0.464982	+	0.530210i	0.936041	−	0.351892i	$-0.114461\pi$
$439$	9.74245	+	11.1091i	0.464982	+	0.530210i	−0.471059	+	0.882102i	$0.656128\pi$
$440$	6.41675	+	2.65790i	0.305907	+	0.126711i
$441$		0			0
$442$	−10.7668	−	10.4969i	−0.512123	−	0.499286i
$443$	16.9977	−	9.81360i	0.807583	−	0.466258i	−0.0385327	−	0.999257i	$-0.512268\pi$
$443$	16.9977	−	9.81360i	0.807583	−	0.466258i	0.846116	+	0.532999i	$0.178935\pi$
$444$		0			0
$445$	13.6245	+	4.62488i	0.645862	+	0.219241i
$446$	3.80762	+	14.2102i	0.180296	+	0.672873i
$447$		0			0
$448$	−17.6222	+	5.98193i	−0.832571	+	0.282620i
$449$	10.8428	+	16.2274i	0.511703	+	0.765818i	0.993905	−	0.110242i	$-0.0351627\pi$
$449$	10.8428	+	16.2274i	0.511703	+	0.765818i	−0.482202	+	0.876060i	$0.660163\pi$
$450$		0			0
$451$	−2.57792	+	1.06781i	−0.121389	+	0.0502812i
$452$	−0.508118	−	0.250576i	−0.0238999	−	0.0117861i
$453$		0			0
$454$	−8.33747	−	16.9067i	−0.391297	−	0.793472i
$455$	68.4828	−	18.3499i	3.21053	−	0.860258i
$456$		0			0
$457$	−16.2263	+	2.13623i	−0.759034	+	0.0999287i	−0.500101	−	0.865967i	$-0.666704\pi$
$457$	−16.2263	+	2.13623i	−0.759034	+	0.0999287i	−0.258932	+	0.965896i	$0.583371\pi$
$458$	11.9019			0.556142
$459$		0			0
$460$	16.6295			0.775355
$461$	−26.1730	+	3.44575i	−1.21900	+	0.160484i	−0.712448	−	0.701725i	$-0.752414\pi$
$461$	−26.1730	+	3.44575i	−1.21900	+	0.160484i	−0.506552	+	0.862209i	$0.669080\pi$
$462$		0			0
$463$	29.5309	−	7.91277i	1.37242	−	0.367738i	0.504055	−	0.863671i	$-0.331841\pi$
$463$	29.5309	−	7.91277i	1.37242	−	0.367738i	0.868360	+	0.495934i	$0.165174\pi$
$464$	−0.0942403	−	0.191100i	−0.00437500	−	0.00887161i
$465$		0			0
$466$	−17.7824	−	8.76929i	−0.823752	−	0.406229i
$467$	32.3041	−	13.3808i	1.49486	−	0.619190i	0.522489	−	0.852646i	$-0.325004\pi$
$467$	32.3041	−	13.3808i	1.49486	−	0.619190i	0.972367	+	0.233456i	$0.0750035\pi$
$468$		0			0
$469$	6.17107	+	9.23566i	0.284954	+	0.426463i
$470$	−12.8222	+	4.35254i	−0.591442	+	0.200768i
$471$		0			0
$472$	2.38819	+	8.91283i	0.109925	+	0.410246i
$473$	−5.65437	−	1.91940i	−0.259988	−	0.0882540i
$474$		0			0
$475$	8.61937	−	4.97639i	0.395484	−	0.228333i
$476$	−27.4118	+	5.81516i	−1.25642	+	0.266537i
$477$		0			0
$478$	20.0782	+	8.31665i	0.918354	+	0.380395i
$479$	6.12119	+	6.97988i	0.279684	+	0.318919i	0.874577	−	0.484886i	$-0.161139\pi$
$479$	6.12119	+	6.97988i	0.279684	+	0.318919i	−0.594893	+	0.803805i	$0.702806\pi$
$480$		0			0
$481$	−0.274320	+	0.135280i	−0.0125079	+	0.00616823i
$482$	−4.93275	+	5.62472i	−0.224680	+	0.256199i
$483$		0			0
$484$	8.46144	−	11.0272i	0.384611	−	0.501235i
$485$	20.7522	+	50.1003i	0.942311	+	2.27494i
$486$		0			0
$487$	−4.25328	−	0.846029i	−0.192734	−	0.0383373i	0.0977791	−	0.995208i	$-0.468826\pi$
$487$	−4.25328	−	0.846029i	−0.192734	−	0.0383373i	−0.290514	+	0.956871i	$0.593826\pi$
$488$	−0.304874	+	4.65147i	−0.0138010	+	0.210562i
$489$		0			0
$490$	−14.9329	+	43.9909i	−0.674599	+	1.98731i
$491$	14.5255	−	11.1458i	0.655527	−	0.503004i	−0.226616	−	0.973984i	$-0.572766\pi$
$491$	14.5255	−	11.1458i	0.655527	−	0.503004i	0.882144	+	0.470980i	$0.156100\pi$
$492$		0			0
$493$	0.576896	+	1.63117i	0.0259821	+	0.0734640i
$494$		−	7.73228i		−	0.347892i
$495$		0			0
$496$	−0.131479	−	0.660989i	−0.00590357	−	0.0296793i
$497$	−10.6434	−	2.85188i	−0.477421	−	0.127924i
$498$		0			0
$499$	−19.5224	−	17.1207i	−0.873942	−	0.766426i	0.0995780	−	0.995030i	$-0.468251\pi$
$499$	−19.5224	−	17.1207i	−0.873942	−	0.766426i	−0.973520	+	0.228604i	$0.926584\pi$
$500$	−1.27924	+	0.0838457i	−0.0572092	+	0.00374969i
$501$		0			0
$502$	−10.8985	−	8.36270i	−0.486423	−	0.373246i
$503$	15.4167	−	10.3011i	0.687399	−	0.459305i	−0.162184	−	0.986761i	$-0.551854\pi$
$503$	15.4167	−	10.3011i	0.687399	−	0.459305i	0.849583	+	0.527455i	$0.176854\pi$
$504$		0			0
$505$	25.0080	−	37.4272i	1.11284	−	1.66549i
$506$	0.684066	−	2.55297i	0.0304104	−	0.113493i
$507$		0			0
$508$	−14.7291	−	19.1954i	−0.653499	−	0.851657i
$509$	−2.96228	+	5.13082i	−0.131301	+	0.227420i	−0.924178	−	0.381961i	$-0.875249\pi$
$509$	−2.96228	+	5.13082i	−0.131301	+	0.227420i	0.792877	+	0.609381i	$0.208582\pi$
$510$		0			0
$511$	−14.5373	−	25.1794i	−0.643094	−	1.11387i
$512$	2.18209	−	5.26802i	0.0964355	−	0.232816i
$513$		0			0
$514$	9.66861	+	9.66861i	0.426464	+	0.426464i
$515$	−6.04125	−	0.395965i	−0.266209	−	0.0174483i
$516$		0			0
$517$	−0.290257	−	4.42847i	−0.0127655	−	0.194764i
$518$	0.0360781	−	0.274041i	0.00158518	−	0.0120407i
$519$		0			0
$520$	16.8088	−	34.0848i	0.737113	−	1.49472i
$521$	5.18504	−	26.0670i	0.227161	−	1.14202i	−0.683847	−	0.729626i	$-0.739694\pi$
$521$	5.18504	−	26.0670i	0.227161	−	1.14202i	0.911008	−	0.412389i	$-0.135306\pi$
$522$		0			0
$523$	−1.49694	+	1.49694i	−0.0654567	+	0.0654567i	−0.739077	−	0.673621i	$-0.764738\pi$
$523$	−1.49694	+	1.49694i	−0.0654567	+	0.0654567i	0.673621	+	0.739077i	$0.264738\pi$
$524$	10.1363	−	8.88929i	0.442806	−	0.388330i
$525$		0			0
$526$	15.2287	+	8.79231i	0.664004	+	0.383363i
$527$	0.427191	+	5.45573i	0.0186087	+	0.237655i
$528$		0			0
$529$	0.949552	+	7.21256i	0.0412849	+	0.313590i
$530$	−17.4330	+	3.46763i	−0.757239	+	0.150624i
$531$		0			0
$532$	−11.9810	−	8.00544i	−0.519441	−	0.347080i
$533$	4.90776	+	14.4578i	0.212579	+	0.626236i
$534$		0			0
$535$	−12.2255	−	1.60952i	−0.528556	−	0.0695858i
$536$	5.90312	+	0.777161i	0.254976	+	0.0335682i
$537$		0			0
$538$	−0.309450	−	0.911610i	−0.0133413	−	0.0393023i
$539$	−12.6600	−	8.45912i	−0.545303	−	0.364360i
$540$		0			0
$541$	16.6949	−	3.32083i	0.717772	−	0.142774i	0.177325	−	0.984152i	$-0.443255\pi$
$541$	16.6949	−	3.32083i	0.717772	−	0.142774i	0.540446	+	0.841379i	$0.318255\pi$
$542$	1.96611	+	14.9341i	0.0844518	+	0.641475i
$543$		0			0
$544$	−11.7336	+	20.9322i	−0.503072	+	0.897462i
$545$	−41.2683	−	23.8263i	−1.76774	−	1.02061i
$546$		0			0
$547$	22.8366	−	20.0272i	0.976424	−	0.856301i	−0.0132100	−	0.999913i	$-0.504205\pi$
$547$	22.8366	−	20.0272i	0.976424	−	0.856301i	0.989634	+	0.143612i	$0.0458717\pi$
$548$	−0.198199	+	0.198199i	−0.00846663	+	0.00846663i
$549$		0			0
$550$	0.610393	−	3.06866i	0.0260273	−	0.130848i
$551$	−0.393501	+	0.797942i	−0.0167637	+	0.0339935i
$552$		0			0
$553$	−8.72840	+	66.2988i	−0.371169	+	2.81931i
$554$	0.579058	+	8.83472i	0.0246018	+	0.375351i
$555$		0			0
$556$	5.69234	+	0.373095i	0.241409	+	0.0158228i
$557$	−17.8937	−	17.8937i	−0.758182	−	0.758182i	0.217809	−	0.975991i	$-0.430109\pi$
$557$	−17.8937	−	17.8937i	−0.758182	−	0.758182i	−0.975991	+	0.217809i	$0.930109\pi$
$558$		0			0
$559$	−12.5036	+	30.1864i	−0.528846	+	1.27675i
$560$	−3.98879	−	6.90879i	−0.168557	−	0.291950i
$561$		0			0
$562$	10.8963	−	18.8729i	0.459633	−	0.796107i
$563$	−16.0519	−	20.9192i	−0.676506	−	0.881640i	0.321358	−	0.946958i	$-0.395861\pi$
$563$	−16.0519	−	20.9192i	−0.676506	−	0.881640i	−0.997865	+	0.0653178i	$0.979194\pi$
$564$		0			0
$565$	−0.338973	+	1.26506i	−0.0142607	+	0.0532216i
$566$	−4.12350	+	6.17125i	−0.173323	+	0.259397i
$567$		0			0
$568$	−4.91104	+	3.28145i	−0.206063	+	0.137687i
$569$	10.1086	+	7.75657i	0.423773	+	0.325172i	0.798535	−	0.601949i	$-0.205609\pi$
$569$	10.1086	+	7.75657i	0.423773	+	0.325172i	−0.374762	+	0.927121i	$0.622276\pi$
$570$		0			0
$571$	26.0799	−	1.70937i	1.09141	−	0.0715349i	0.490949	−	0.871188i	$-0.336650\pi$
$571$	26.0799	−	1.70937i	1.09141	−	0.0715349i	0.600462	+	0.799653i	$0.294983\pi$
$572$	3.76862	+	3.30499i	0.157574	+	0.138188i
$573$		0			0
$574$	−13.3274	−	3.57107i	−0.556276	−	0.149054i
$575$	−3.63165	−	18.2576i	−0.151450	−	0.761393i
$576$		0			0
$577$		−	0.792090i		−	0.0329751i	−0.999864	−	0.0164876i	$-0.994752\pi$
$577$		−	0.792090i		−	0.0329751i	0.999864	−	0.0164876i	$-0.00524839\pi$
$578$	8.08435	−	11.1085i	0.336264	−	0.462055i
$579$		0			0
$580$	−1.39609	+	1.07126i	−0.0579696	+	0.0444817i
$581$	5.96469	−	17.5714i	0.247457	−	0.728985i
$582$		0			0
$583$	0.381011	−	5.81310i	0.0157798	−	0.240754i
$584$	−15.2855	−	3.04048i	−0.632520	−	0.125816i
$585$		0			0
$586$	1.36257	+	3.28954i	0.0562873	+	0.135890i
$587$	−4.71260	+	6.14158i	−0.194510	+	0.253490i	−0.880419	−	0.474197i	$-0.842738\pi$
$587$	−4.71260	+	6.14158i	−0.194510	+	0.253490i	0.685909	+	0.727688i	$0.259405\pi$
$588$		0			0
$589$	−1.85542	+	2.11570i	−0.0764514	+	0.0871761i
$590$	7.69879	−	3.79663i	0.316954	−	0.156305i
$591$		0			0
$592$	0.0226921	+	0.0258753i	0.000932638	+	0.00106347i
$593$	27.9427	+	11.5742i	1.14747	+	0.475297i	0.873684	−	0.486495i	$-0.161725\pi$
$593$	27.9427	+	11.5742i	1.14747	+	0.475297i	0.273784	+	0.961791i	$0.411725\pi$
$594$		0			0
$595$	25.5472	+	59.5281i	1.04733	+	2.44041i
$596$	27.4887	−	15.8706i	1.12598	−	0.650086i
$597$		0			0
$598$	−13.6946	−	4.64869i	−0.560014	−	0.190099i
$599$	−7.63845	−	28.5071i	−0.312098	−	1.16477i	−0.926661	−	0.375899i	$-0.877334\pi$
$599$	−7.63845	−	28.5071i	−0.312098	−	1.16477i	0.614562	−	0.788868i	$-0.289333\pi$
$600$		0			0
$601$	−2.10832	+	0.715679i	−0.0860002	+	0.0291931i	−0.364108	−	0.931357i	$-0.618626\pi$
$601$	−2.10832	+	0.715679i	−0.0860002	+	0.0291931i	0.278108	+	0.960550i	$0.410293\pi$
$602$	−16.4042	−	24.5505i	−0.668583	−	1.00061i
$603$		0			0
$604$	15.6141	−	6.46757i	0.635328	−	0.263162i
$605$	−28.8179	−	14.2114i	−1.17161	−	0.577776i
$606$		0			0
$607$	3.93237	+	7.97406i	0.159610	+	0.323657i	0.961957	−	0.273201i	$-0.0880823\pi$
$607$	3.93237	+	7.97406i	0.159610	+	0.323657i	−0.802347	+	0.596858i	$0.796416\pi$
$608$	−11.9191	+	3.19371i	−0.483382	+	0.129522i
$609$		0			0
$610$	4.29942	−	0.566029i	0.174078	−	0.0229179i
$611$	−24.2837			−0.982413
$612$		0			0
$613$	45.0558			1.81979			0.909893	−	0.414842i	$-0.136163\pi$
$613$	45.0558			1.81979			0.909893	+	0.414842i	$0.136163\pi$
$614$	12.8430	−	1.69081i	0.518301	−	0.0682356i
$615$		0			0
$616$	−10.8726	+	2.91331i	−0.438070	+	0.117380i
$617$	17.9929	+	36.4860i	0.724367	+	1.46887i	0.876951	+	0.480580i	$0.159574\pi$
$617$	17.9929	+	36.4860i	0.724367	+	1.46887i	−0.152584	+	0.988291i	$0.548759\pi$
$618$		0			0
$619$	−10.2190	−	5.03947i	−0.410737	−	0.202553i	0.225169	−	0.974320i	$-0.427707\pi$
$619$	−10.2190	−	5.03947i	−0.410737	−	0.202553i	−0.635906	+	0.771767i	$0.719373\pi$
$620$	−5.14224	+	2.12999i	−0.206517	+	0.0855423i
$621$		0			0
$622$	−6.11422	−	9.15058i	−0.245158	−	0.366905i
$623$	−22.0805	+	7.49534i	−0.884638	+	0.300294i
$624$		0			0
$625$	6.84190	+	25.5343i	0.273676	+	1.02137i
$626$	−1.65554	−	0.561982i	−0.0661689	−	0.0224613i
$627$		0			0
$628$	−11.2825	+	6.51394i	−0.450220	+	0.259935i
$629$	−0.158197	−	0.230374i	−0.00630771	−	0.00918560i
$630$		0			0
$631$	4.28340	+	1.77424i	0.170520	+	0.0706315i	0.466310	−	0.884621i	$-0.345583\pi$
$631$	4.28340	+	1.77424i	0.170520	+	0.0706315i	−0.295791	+	0.955253i	$0.595583\pi$
$632$	23.6342	+	26.9497i	0.940120	+	1.07200i
$633$		0			0
$634$	6.61323	−	3.26128i	0.262645	−	0.129522i
$635$	−36.8789	+	42.0523i	−1.46349	+	1.66879i
$636$		0			0
$637$	−50.7181	+	66.0971i	−2.00953	+	2.61886i
$638$	0.107031	+	0.258396i	0.00423740	+	0.0102300i
$639$		0			0
$640$	−26.4439	−	5.26001i	−1.04529	−	0.207920i
$641$	−0.425807	+	6.49656i	−0.0168184	+	0.256599i	0.981167	+	0.193160i	$0.0618735\pi$
$641$	−0.425807	+	6.49656i	−0.0168184	+	0.256599i	−0.997986	+	0.0634391i	$0.979793\pi$
$642$		0			0
$643$	−8.29150	+	24.4260i	−0.326985	+	0.963266i	0.651803	+	0.758388i	$0.274013\pi$
$643$	−8.29150	+	24.4260i	−0.326985	+	0.963266i	−0.978788	+	0.204877i	$0.934320\pi$
$644$	−21.3814	+	16.4065i	−0.842546	+	0.646508i
$645$		0			0
$646$	6.99211	−	1.01097i	0.275101	−	0.0397760i
$647$			32.6053i			1.28185i	0.767604	+	0.640924i	$0.221449\pi$
$647$			32.6053i			1.28185i	−0.767604	+	0.640924i	$0.778551\pi$
$648$		0			0
$649$	0.548869	+	2.75935i	0.0215450	+	0.108314i
$650$	−16.5367	−	4.43099i	−0.648621	−	0.173798i
$651$		0			0
$652$	0.269125	+	0.236016i	0.0105397	+	0.00924311i
$653$	39.1805	−	2.56802i	1.53325	−	0.100495i	0.724759	−	0.689002i	$-0.241951\pi$
$653$	39.1805	−	2.56802i	1.53325	−	0.100495i	0.808492	+	0.588508i	$0.200284\pi$
$654$		0			0
$655$	−24.7261	−	18.9730i	−0.966127	−	0.741336i
$656$	1.42844	−	0.954456i	0.0557714	−	0.0372652i
$657$		0			0
$658$	12.1919	−	18.2465i	0.475291	−	0.711323i
$659$	2.37308	−	8.85644i	0.0924420	−	0.344998i	−0.904177	−	0.427157i	$-0.859515\pi$
$659$	2.37308	−	8.85644i	0.0924420	−	0.344998i	0.996619	+	0.0821594i	$0.0261817\pi$
$660$		0			0
$661$	9.51560	+	12.4010i	0.370114	+	0.482342i	0.940865	−	0.338781i	$-0.110015\pi$
$661$	9.51560	+	12.4010i	0.370114	+	0.482342i	−0.570751	+	0.821123i	$0.693348\pi$
$662$	0.548618	−	0.950234i	0.0213226	−	0.0369319i
$663$		0			0
$664$	−4.97337	−	8.61412i	−0.193004	−	0.334293i
$665$	−12.7474	+	30.7749i	−0.494322	+	1.19340i
$666$		0			0
$667$	1.17666	+	1.17666i	0.0455603	+	0.0455603i
$668$	−2.40696	−	0.157761i	−0.0931283	−	0.00610395i
$669$		0			0
$670$	−0.362270	−	5.52717i	−0.0139957	−	0.213533i
$671$	−0.185516	+	1.40913i	−0.00716175	+	0.0543989i
$672$		0			0
$673$	−14.2403	+	28.8764i	−0.548923	+	1.11311i	0.428838	+	0.903381i	$0.358923\pi$
$673$	−14.2403	+	28.8764i	−0.548923	+	1.11311i	−0.977761	+	0.209724i	$0.932744\pi$
$674$	3.78154	−	19.0111i	0.145660	−	0.732281i
$675$		0			0
$676$	7.01329	−	7.01329i	0.269742	−	0.269742i
$677$	13.0734	−	11.4650i	0.502450	−	0.440637i	−0.370222	−	0.928943i	$-0.620718\pi$
$677$	13.0734	−	11.4650i	0.502450	−	0.440637i	0.872672	+	0.488306i	$0.162385\pi$
$678$		0			0
$679$	−76.1108	−	43.9426i	−2.92086	−	1.68636i
$680$	33.0197	+	10.7433i	1.26625	+	0.411985i
$681$		0			0
$682$	0.115467	+	0.877057i	0.00442145	+	0.0335842i
$683$	−39.2414	+	7.80559i	−1.50153	+	0.298673i	−0.876299	−	0.481768i	$-0.839995\pi$
$683$	−39.2414	+	7.80559i	−1.50153	+	0.298673i	−0.625230	+	0.780441i	$0.714995\pi$
$684$		0			0
$685$	0.538762	+	0.359989i	0.0205850	+	0.0137545i
$686$	−15.0252	−	44.2627i	−0.573664	−	1.68996i
$687$		0			0
$688$	3.64500	+	0.479873i	0.138964	+	0.0182950i
$689$	−31.6036	−	4.16070i	−1.20400	−	0.158510i
$690$		0			0
$691$	−6.50427	−	19.1610i	−0.247434	−	0.728917i	−0.997700	−	0.0677814i	$-0.978408\pi$
$691$	−6.50427	−	19.1610i	−0.247434	−	0.728917i	0.750266	−	0.661136i	$-0.229925\pi$
$692$	19.7739	+	13.2125i	0.751692	+	0.502265i
$693$		0			0
$694$	3.28104	−	0.652639i	0.124547	−	0.0247738i
$695$	−1.72129	−	13.0745i	−0.0652922	−	0.495944i
$696$		0			0
$697$	−12.4321	+	6.32826i	−0.470901	+	0.239700i
$698$	1.18928	+	0.686634i	0.0450151	+	0.0259895i
$699$		0			0
$700$	−23.9865	+	21.0356i	−0.906606	+	0.795072i
$701$	−14.1508	+	14.1508i	−0.534469	+	0.534469i	−0.921899	−	0.387430i	$-0.873363\pi$
$701$	−14.1508	+	14.1508i	−0.534469	+	0.534469i	0.387430	+	0.921899i	$0.373363\pi$
$702$		0			0
$703$	0.0280353	−	0.140943i	0.00105737	−	0.00531577i
$704$	−1.34524	+	2.72789i	−0.0507008	+	0.102811i
$705$		0			0
$706$	−2.00308	+	15.2149i	−0.0753871	+	0.572622i
$707$	4.77122	+	72.7948i	0.179440	+	2.73773i
$708$		0			0
$709$	17.7197	+	1.16141i	0.665476	+	0.0436176i	0.394398	−	0.918940i	$-0.370953\pi$
$709$	17.7197	+	1.16141i	0.665476	+	0.0436176i	0.271078	+	0.962557i	$0.412620\pi$
$710$	3.88537	+	3.88537i	0.145815	+	0.145815i
$711$		0			0
$712$	−4.78325	+	11.5478i	−0.179260	+	0.432772i
$713$	2.63162	+	4.55810i	0.0985550	+	0.170702i
$714$		0			0
$715$	5.79377	−	10.0351i	0.216675	−	0.375292i
$716$	−19.0367	−	24.8091i	−0.711433	−	0.927158i
$717$		0			0
$718$	−5.26666	+	19.6554i	−0.196550	+	0.733535i
$719$	27.9359	−	41.8091i	1.04183	−	1.55922i	0.231862	−	0.972749i	$-0.425518\pi$
$719$	27.9359	−	41.8091i	1.04183	−	1.55922i	0.809973	−	0.586467i	$-0.199482\pi$
$720$		0			0
$721$	8.15820	−	5.45114i	0.303827	−	0.203011i
$722$	−9.29995	−	7.13610i	−0.346108	−	0.265578i
$723$		0			0
$724$	13.4283	−	0.880137i	0.499059	−	0.0327100i
$725$	1.48102	+	1.29882i	0.0550038	+	0.0482371i
$726$		0			0
$727$	−5.23752	−	1.40339i	−0.194249	−	0.0520488i	0.160383	−	0.987055i	$-0.448727\pi$
$727$	−5.23752	−	1.40339i	−0.194249	−	0.0520488i	−0.354632	+	0.935006i	$0.615394\pi$
$728$	12.0159	+	60.4079i	0.445338	+	2.23887i
$729$		0			0
$730$			14.4986i			0.536618i
$731$	−28.9316	−	7.35994i	−1.07007	−	0.272217i
$732$		0			0
$733$	28.5784	−	21.9290i	1.05557	−	0.809966i	0.0732741	−	0.997312i	$-0.476655\pi$
$733$	28.5784	−	21.9290i	1.05557	−	0.809966i	0.982294	+	0.187346i	$0.0599885\pi$
$734$	2.66891	−	7.86237i	0.0985115	−	0.290205i
$735$		0			0
$736$	−1.50946	+	23.0299i	−0.0556394	+	0.848893i
$737$	1.78053	+	0.354169i	0.0655866	+	0.0130460i
$738$		0			0
$739$	−0.924601	−	2.23219i	−0.0340120	−	0.0821123i	0.905961	−	0.423362i	$-0.139150\pi$
$739$	−0.924601	−	2.23219i	−0.0340120	−	0.0821123i	−0.939973	+	0.341249i	$0.889150\pi$
$740$	0.173031	−	0.225499i	0.00636076	−	0.00828950i
$741$		0			0
$742$	18.9933	−	21.6577i	0.697266	−	0.795080i
$743$	−32.1039	+	15.8319i	−1.17778	+	0.580815i	−0.922479	−	0.386047i	$-0.873840\pi$
$743$	−32.1039	+	15.8319i	−1.17778	+	0.580815i	−0.255298	+	0.966863i	$0.582173\pi$
$744$		0			0
$745$	−48.3807	−	55.1676i	−1.77253	−	2.02118i
$746$	4.74561	+	1.96569i	0.173749	+	0.0719692i
$747$		0			0
$748$	−2.49588	+	3.83998i	−0.0912585	+	0.140403i
$749$	17.3070	−	9.99217i	0.632382	−	0.365106i
$750$		0			0
$751$	−1.32298	−	0.449091i	−0.0482762	−	0.0163875i	0.297197	−	0.954816i	$-0.403948\pi$
$751$	−1.32298	−	0.449091i	−0.0482762	−	0.0163875i	−0.345473	+	0.938429i	$0.612282\pi$
$752$	0.707203	+	2.63932i	0.0257890	+	0.0962460i
$753$		0			0
$754$	1.44916	−	0.491925i	0.0527754	−	0.0179149i
$755$	−21.7057	−	32.4850i	−0.789953	−	1.18225i
$756$		0			0
$757$	−34.0649	+	14.1101i	−1.23811	+	0.512842i	−0.903123	−	0.429382i	$-0.858732\pi$
$757$	−34.0649	+	14.1101i	−1.23811	+	0.512842i	−0.334986	+	0.942223i	$0.608732\pi$
$758$	5.89096	+	2.90510i	0.213969	+	0.105518i
$759$		0			0
$760$	7.89729	+	16.0141i	0.286465	+	0.580893i
$761$	24.0278	−	6.43824i	0.871008	−	0.233386i	0.204484	−	0.978870i	$-0.434448\pi$
$761$	24.0278	−	6.43824i	0.871008	−	0.233386i	0.666524	+	0.745484i	$0.267782\pi$
$762$		0			0
$763$	76.5676	−	10.0803i	2.77193	−	0.364932i
$764$	−10.3294			−0.373704
$765$		0			0
$766$	−13.3687			−0.483032
$767$	15.2627	−	2.00937i	0.551105	−	0.0725543i
$768$		0			0
$769$	−39.1986	+	10.5032i	−1.41354	+	0.378757i	−0.883187	−	0.469021i	$-0.844607\pi$
$769$	−39.1986	+	10.5032i	−1.41354	+	0.378757i	−0.530352	+	0.847778i	$0.677940\pi$
$770$	4.63144	+	9.39163i	0.166905	+	0.338451i
$771$		0			0
$772$	−13.9589	−	6.88375i	−0.502391	−	0.247752i
$773$	−40.1788	+	16.6426i	−1.44513	+	0.598593i	−0.961036	−	0.276422i	$-0.910851\pi$
$773$	−40.1788	+	16.6426i	−1.44513	+	0.598593i	−0.484096	+	0.875015i	$0.660851\pi$
$774$		0			0
$775$	3.46150	+	5.18051i	0.124341	+	0.186089i
$776$	−44.6093	+	15.1428i	−1.60138	+	0.543595i
$777$		0			0
$778$	0.500690	+	1.86860i	0.0179506	+	0.0669925i
$779$	−6.79273	−	2.30582i	−0.243375	−	0.0826146i
$780$		0			0
$781$	−1.55962	+	0.900448i	−0.0558077	+	0.0322206i
$782$	2.41317	−	12.9915i	0.0862950	−	0.464574i
$783$		0			0
$784$	8.66093	+	3.58748i	0.309319	+	0.128124i
$785$	19.8574	+	22.6430i	0.708740	+	0.808163i
$786$		0			0
$787$	−13.4590	+	6.63725i	−0.479762	+	0.236592i	−0.666056	−	0.745902i	$-0.732019\pi$
$787$	−13.4590	+	6.63725i	−0.479762	+	0.236592i	0.186294	+	0.982494i	$0.440352\pi$
$788$	−1.69896	+	1.93730i	−0.0605231	+	0.0690133i
$789$		0			0
$790$	20.3000	−	26.4555i	0.722241	−	0.941243i
$791$	−0.812266	−	1.96098i	−0.0288809	−	0.0697246i
$792$		0			0
$793$	7.62758	+	1.51722i	0.270863	+	0.0538780i
$794$	−0.450935	+	6.87994i	−0.0160031	+	0.244160i
$795$		0			0
$796$	5.95050	−	17.5296i	0.210910	−	0.621320i
$797$	7.94728	−	6.09816i	0.281507	−	0.216008i	−0.458350	−	0.888772i	$-0.651560\pi$
$797$	7.94728	−	6.09816i	0.281507	−	0.216008i	0.739858	+	0.672764i	$0.234893\pi$
$798$		0			0
$799$	−3.17500	−	21.9591i	−0.112323	−	0.776858i
$800$			27.3209i			0.965940i
$801$		0			0
$802$	1.35592	+	6.81666i	0.0478791	+	0.240705i
$803$	−4.58999	−	1.22988i	−0.161977	−	0.0434017i
$804$		0			0
$805$	46.8414	+	41.0788i	1.65094	+	1.44784i
$806$	4.83012	−	0.316583i	0.170134	−	0.0111512i
$807$		0			0
$808$	31.0234	+	23.8051i	1.09140	+	0.837460i
$809$	43.7755	−	29.2499i	1.53907	−	1.02837i	0.559125	−	0.829084i	$-0.311137\pi$
$809$	43.7755	−	29.2499i	1.53907	−	1.02837i	0.979941	−	0.199287i	$-0.0638627\pi$
$810$		0			0
$811$	−25.6922	+	38.4511i	−0.902175	+	1.35020i	0.0342802	+	0.999412i	$0.489086\pi$
$811$	−25.6922	+	38.4511i	−0.902175	+	1.35020i	−0.936455	+	0.350788i	$0.885914\pi$
$812$	0.738132	−	2.75475i	0.0259034	−	0.0966727i
$813$		0			0
$814$	−0.0275009	−	0.0358399i	−0.000963906	−	0.00125619i
$815$	0.413745	−	0.716628i	0.0144929	−	0.0251024i
$816$		0			0
$817$	−7.67553	−	13.2944i	−0.268533	−	0.465113i
$818$	5.42812	−	13.1046i	0.189790	−	0.458193i
$819$		0			0
$820$	−10.0327	−	10.0327i	−0.350358	−	0.350358i
$821$	40.5886	+	2.66032i	1.41655	+	0.0928457i	0.754346	−	0.656477i	$-0.227954\pi$
$821$	40.5886	+	2.66032i	1.41655	+	0.0928457i	0.662205	+	0.749323i	$0.269621\pi$
$822$		0			0
$823$	0.457694	+	6.98305i	0.0159542	+	0.243414i	0.998386	+	0.0567922i	$0.0180872\pi$
$823$	0.457694	+	6.98305i	0.0159542	+	0.243414i	−0.982432	+	0.186622i	$0.940246\pi$
$824$	0.686495	−	5.21445i	0.0239152	−	0.181654i
$825$		0			0
$826$	−6.15302	+	12.4771i	−0.214091	+	0.434133i
$827$	−8.31435	+	41.7991i	−0.289118	+	1.45350i	0.514058	+	0.857755i	$0.328141\pi$
$827$	−8.31435	+	41.7991i	−0.289118	+	1.45350i	−0.803177	+	0.595741i	$0.796859\pi$
$828$		0			0
$829$	−13.5908	+	13.5908i	−0.472029	+	0.472029i	−0.902571	−	0.430542i	$-0.858322\pi$
$829$	−13.5908	+	13.5908i	−0.472029	+	0.472029i	0.430542	+	0.902571i	$0.358322\pi$
$830$	−6.95706	+	6.10118i	−0.241483	+	0.211775i
$831$		0			0
$832$	14.4131	+	8.32138i	0.499683	+	0.288492i
$833$	−66.4012	−	37.2211i	−2.30066	−	1.28964i
$834$		0			0
$835$	0.727835	+	5.52846i	0.0251878	+	0.191320i
$836$	−2.30979	+	0.459447i	−0.0798859	+	0.0158903i
$837$		0			0
$838$	−1.96555	−	1.31334i	−0.0678988	−	0.0453685i
$839$	−10.0456	−	29.5934i	−0.346813	−	1.02168i	−0.970727	−	0.240185i	$-0.922792\pi$
$839$	−10.0456	−	29.5934i	−0.346813	−	1.02168i	0.623914	−	0.781493i	$-0.285542\pi$
$840$		0			0
$841$	28.5773	+	3.76228i	0.985425	+	0.129734i
$842$	11.2234	+	1.47759i	0.386783	+	0.0509210i
$843$		0			0
$844$	3.49669	+	10.3009i	0.120361	+	0.354572i
$845$	−19.0642	−	12.7383i	−0.655828	−	0.438210i
$846$		0			0
$847$	51.0735	−	10.1592i	1.75491	−	0.349073i
$848$	0.468165	+	3.55607i	0.0160769	+	0.122116i
$849$		0			0
$850$	1.84472	−	15.5330i	0.0632734	−	0.532778i
$851$	−0.232769	−	0.134389i	−0.00797921	−	0.00460680i
$852$		0			0
$853$	−13.9130	+	12.2014i	−0.476373	+	0.417768i	−0.863570	−	0.504229i	$-0.831777\pi$
$853$	−13.9130	+	12.2014i	−0.476373	+	0.417768i	0.387197	+	0.921997i	$0.373443\pi$
$854$	−4.96954	+	4.96954i	−0.170054	+	0.170054i
$855$		0			0
$856$	2.08986	−	10.5064i	0.0714300	−	0.359103i
$857$	1.95578	−	3.96593i	0.0668082	−	0.135474i	−0.860907	−	0.508762i	$-0.830103\pi$
$857$	1.95578	−	3.96593i	0.0668082	−	0.135474i	0.927715	+	0.373289i	$0.121770\pi$
$858$		0			0
$859$	3.86989	−	29.3947i	0.132039	−	1.00294i	−0.789254	−	0.614067i	$-0.789533\pi$
$859$	3.86989	−	29.3947i	0.132039	−	1.00294i	0.921293	−	0.388869i	$-0.127134\pi$
$860$	−1.98584	−	30.2981i	−0.0677166	−	1.03316i
$861$		0			0
$862$	−17.9106	−	1.17392i	−0.610038	−	0.0399840i
$863$	5.63591	+	5.63591i	0.191849	+	0.191849i	0.796494	−	0.604646i	$-0.206685\pi$
$863$	5.63591	+	5.63591i	0.191849	+	0.191849i	−0.604646	+	0.796494i	$0.706685\pi$
$864$		0			0
$865$	21.0388	−	50.7922i	0.715341	−	1.72699i
$866$	−14.2979	−	24.7646i	−0.485861	−	0.841536i
$867$		0			0
$868$	4.51022	−	7.81192i	0.153087	−	0.265154i
$869$	6.65330	+	8.67075i	0.225698	+	0.294135i
$870$		0			0
$871$	2.57099	−	9.59508i	0.0871148	−	0.325117i
$872$	22.9989	−	34.4203i	0.778841	−	1.16562i
$873$		0			0
$874$	5.64964	−	3.77497i	0.191102	−	0.127690i
$875$	−3.81043	−	2.92384i	−0.128816	−	0.0988439i
$876$		0			0
$877$	−31.7829	+	2.08316i	−1.07323	+	0.0703433i	−0.591756	−	0.806117i	$-0.701565\pi$
$877$	−31.7829	+	2.08316i	−1.07323	+	0.0703433i	−0.481474	+	0.876460i	$0.659899\pi$
$878$	8.97806	+	7.87354i	0.302995	+	0.265719i
$879$		0			0
$880$	−1.25941	−	0.337459i	−0.0424548	−	0.0113757i
$881$	−2.24207	−	11.2716i	−0.0755371	−	0.379751i	0.924462	−	0.381275i	$-0.124515\pi$
$881$	−2.24207	−	11.2716i	−0.0755371	−	0.379751i	−0.999999	+	0.00152420i	$0.999515\pi$
$882$		0			0
$883$			20.4281i			0.687460i	0.939068	+	0.343730i	$0.111691\pi$
$883$			20.4281i			0.687460i	−0.939068	+	0.343730i	$0.888309\pi$
$884$	20.0734	+	15.0019i	0.675141	+	0.504570i
$885$		0			0
$886$	12.5842	−	9.65623i	0.422776	−	0.324407i
$887$	6.81537	−	20.0774i	0.228838	−	0.674134i	−0.770489	−	0.637453i	$-0.779988\pi$
$887$	6.81537	−	20.0774i	0.228838	−	0.674134i	0.999327	−	0.0366814i	$-0.0116787\pi$
$888$		0			0
$889$	5.92861	−	90.4532i	0.198839	−	3.03370i
$890$	11.4045	+	2.26850i	0.382281	+	0.0760404i
$891$		0			0
$892$	−9.38249	−	22.6513i	−0.314149	−	0.758422i
$893$	6.94551	−	9.05157i	0.232423	−	0.302899i
$894$		0			0
$895$	−47.6641	+	54.3505i	−1.59324	+	1.81674i
$896$	39.1897	−	19.3262i	1.30924	−	0.645644i
$897$		0			0
$898$	10.3996	+	11.8585i	0.347040	+	0.395723i
$899$	−0.514561	−	0.213138i	−0.0171616	−	0.00710856i
$900$		0			0
$901$	−0.369645	−	29.1223i	−0.0123147	−	0.970206i
$902$	−1.95293	+	1.12752i	−0.0650254	+	0.0375425i
$903$		0			0
$904$	−1.07738	−	0.365721i	−0.0358331	−	0.0121637i
$905$	−8.05161	−	30.0490i	−0.267644	−	0.998863i
$906$		0			0
$907$	36.8376	−	12.5047i	1.22317	−	0.415212i	0.366183	−	0.930543i	$-0.380664\pi$
$907$	36.8376	−	12.5047i	1.22317	−	0.415212i	0.856991	+	0.515331i	$0.172331\pi$
$908$	17.4538	+	26.1214i	0.579223	+	0.866869i
$909$		0			0
$910$	52.9365	−	21.9270i	1.75483	−	0.726874i
$911$	16.8905	+	8.32947i	0.559607	+	0.275968i	0.700017	−	0.714126i	$-0.253176\pi$
$911$	16.8905	+	8.32947i	0.559607	+	0.275968i	−0.140410	+	0.990093i	$0.544842\pi$
$912$		0			0
$913$	−1.34137	−	2.72002i	−0.0443928	−	0.0900197i
$914$	−12.7760	+	3.42333i	−0.422594	+	0.113234i
$915$		0			0
$916$	−19.6656	+	2.58903i	−0.649771	+	0.0855440i
$917$	50.5101			1.66799
$918$		0			0
$919$	−1.78397			−0.0588476			−0.0294238	−	0.999567i	$-0.509367\pi$
$919$	−1.78397			−0.0588476			−0.0294238	+	0.999567i	$0.509367\pi$
$920$	33.1104	−	4.35907i	1.09162	−	0.143714i
$921$		0			0
$922$	−20.6078	+	5.52184i	−0.678681	+	0.181852i
$923$	4.35837	+	8.83791i	0.143458	+	0.290903i
$924$		0			0
$925$	−0.285363	−	0.140725i	−0.00938267	−	0.00462702i
$926$	22.8271	−	9.45527i	0.750143	−	0.310720i
$927$		0			0
$928$	−1.35684	−	2.03066i	−0.0445406	−	0.0666597i
$929$	21.4783	−	7.29092i	0.704682	−	0.239207i	0.0539815	−	0.998542i	$-0.482809\pi$
$929$	21.4783	−	7.29092i	0.704682	−	0.239207i	0.650700	+	0.759335i	$0.274475\pi$
$930$		0			0
$931$	−10.1311	−	37.8096i	−0.332032	−	1.23916i
$932$	31.2894	+	10.6213i	1.02492	+	0.347913i
$933$		0			0
$934$	24.4723	−	14.1291i	0.800759	−	0.462318i
$935$	9.83200	+	3.92711i	0.321541	+	0.128430i
$936$		0			0
$937$	−40.8313	−	16.9129i	−1.33390	−	0.552520i	−0.402136	−	0.915580i	$-0.631732\pi$
$937$	−40.8313	−	16.9129i	−1.33390	−	0.552520i	−0.931766	+	0.363060i	$0.881732\pi$
$938$	5.91884	+	6.74915i	0.193257	+	0.220367i
$939$		0			0
$940$	20.2393	−	9.98092i	0.660133	−	0.325542i
$941$	−11.3524	+	12.9449i	−0.370078	+	0.421993i	−0.906665	−	0.421852i	$-0.861380\pi$
$941$	−11.3524	+	12.9449i	−0.370078	+	0.421993i	0.536587	+	0.843845i	$0.319713\pi$
$942$		0			0
$943$	−8.16766	+	10.6443i	−0.265976	+	0.346626i
$944$	−0.662882	−	1.60034i	−0.0215750	−	0.0520866i
$945$		0			0
$946$	−4.73306	−	0.941464i	−0.153885	−	0.0306096i
$947$	−3.72847	+	56.8854i	−0.121159	+	1.84853i	0.315531	+	0.948915i	$0.397817\pi$
$947$	−3.72847	+	56.8854i	−0.121159	+	1.84853i	−0.436690	+	0.899612i	$0.643849\pi$
$948$		0			0
$949$	−8.35790	+	24.6216i	−0.271309	+	0.799251i
$950$	6.38136	−	4.89659i	0.207039	−	0.158866i
$951$		0			0
$952$	−53.0543	+	18.7638i	−1.71950	+	0.608137i
$953$			26.5831i			0.861112i	0.902564	+	0.430556i	$0.141682\pi$
$953$			26.5831i			0.861112i	−0.902564	+	0.430556i	$0.858318\pi$
$954$		0			0
$955$	4.65849	+	23.4198i	0.150745	+	0.757846i
$956$	−34.9844	−	9.37403i	−1.13148	−	0.303178i
$957$		0			0
$958$	5.64092	+	4.94695i	0.182250	+	0.159829i
$959$	−1.04788	+	0.0686814i	−0.0338377	+	0.00221784i
$960$		0			0
$961$	23.1964	+	17.7992i	0.748270	+	0.574168i
$962$	−0.205530	+	0.137331i	−0.00662656	+	0.00442773i
$963$		0			0
$964$	6.92685	−	10.3668i	0.223099	−	0.333891i
$965$	−9.31215	+	34.7534i	−0.299769	+	1.11875i
$966$		0			0
$967$	3.37951	+	4.40426i	0.108678	+	0.141631i	0.844525	−	0.535516i	$-0.179883\pi$
$967$	3.37951	+	4.40426i	0.108678	+	0.141631i	−0.735848	+	0.677147i	$0.763216\pi$
$968$	13.9567	−	24.1738i	0.448586	−	0.776974i
$969$		0			0
$970$	21.9128	+	37.9540i	0.703577	+	1.21863i
$971$	3.10599	−	7.49852i	0.0996759	−	0.240639i	−0.866173	−	0.499744i	$-0.833428\pi$
$971$	3.10599	−	7.49852i	0.0996759	−	0.240639i	0.965849	+	0.259105i	$0.0834275\pi$
$972$		0			0
$973$	15.1123	+	15.1123i	0.484479	+	0.484479i
$974$	−3.49720	−	0.229219i	−0.112058	−	0.00734465i
$975$		0			0
$976$	−0.0572327	−	0.873202i	−0.00183197	−	0.0279505i
$977$	1.75362	−	13.3200i	0.0561031	−	0.426146i	−0.940227	−	0.340549i	$-0.889387\pi$
$977$	1.75362	−	13.3200i	0.0561031	−	0.426146i	0.996330	−	0.0855966i	$-0.0272796\pi$
$978$		0			0
$979$	−1.68559	+	3.41803i	−0.0538716	+	0.109241i
$980$	15.1043	−	75.9347i	0.482491	−	2.42564i
$981$		0			0
$982$	10.4629	−	10.4629i	0.333884	−	0.333884i
$983$	−46.0381	+	40.3743i	−1.46839	+	1.28774i	−0.592181	+	0.805805i	$0.701733\pi$
$983$	−46.0381	+	40.3743i	−1.46839	+	1.28774i	−0.876206	+	0.481936i	$0.839934\pi$
$984$		0			0
$985$	5.15865	+	2.97835i	0.164368	+	0.0948980i
$986$	0.634308	+	1.24612i	0.0202005	+	0.0396847i
$987$		0			0
$988$	1.68200	+	12.7761i	0.0535117	+	0.406461i
$989$	−28.1602	+	5.60142i	−0.895444	+	0.178115i
$990$		0			0
$991$	7.14926	+	4.77698i	0.227104	+	0.151746i	0.663917	−	0.747806i	$-0.268893\pi$
$991$	7.14926	+	4.77698i	0.227104	+	0.151746i	−0.436813	+	0.899552i	$0.643893\pi$
$992$	−2.48301	−	7.31473i	−0.0788358	−	0.232243i
$993$		0			0
$994$	−8.82889	−	1.16235i	−0.280035	−	0.0368674i
$995$	−42.4285	−	5.58582i	−1.34507	−	0.177082i
$996$		0			0
$997$	15.1502	+	44.6310i	0.479811	+	1.41348i	0.870141	+	0.492802i	$0.164027\pi$
$997$	15.1502	+	44.6310i	0.479811	+	1.41348i	−0.390331	+	0.920675i	$0.627639\pi$
$998$	−17.4484	−	11.6587i	−0.552320	−	0.369048i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.368.9		256
3.2	odd	2		153.2.s.a.113.8	yes	256
9.2	odd	6	inner	459.2.y.a.62.9		256
9.7	even	3		153.2.s.a.11.8	✓	256
17.14	odd	16	inner	459.2.y.a.422.9		256
51.14	even	16		153.2.s.a.14.8	yes	256
153.65	even	48	inner	459.2.y.a.116.9		256
153.133	odd	48		153.2.s.a.65.8	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.8	✓	256	9.7	even	3
153.2.s.a.14.8	yes	256	51.14	even	16
153.2.s.a.65.8	yes	256	153.133	odd	48
153.2.s.a.113.8	yes	256	3.2	odd	2
459.2.y.a.62.9		256	9.2	odd	6	inner
459.2.y.a.116.9		256	153.65	even	48	inner
459.2.y.a.368.9		256	1.1	even	1	trivial
459.2.y.a.422.9		256	17.14	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.y (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.801255 - 0.105487i) q^{2} +(-1.30097 + 0.348594i) q^{4} +(1.37710 + 2.79247i) q^{5} +(-4.52563 - 2.23179i) q^{7} +(-2.49894 + 1.03509i) q^{8} +(1.39797 + 2.09222i) q^{10} +(-0.780943 + 0.265095i) q^{11} +(1.16796 + 4.35888i) q^{13} +(-3.86161 - 1.31084i) q^{14} +(0.439739 - 0.253884i) q^{16} +(-3.78892 + 1.62606i) q^{17} +(-1.95880 - 0.811360i) q^{19} +(-2.76500 - 3.15288i) q^{20} +(-0.597770 + 0.294788i) q^{22} +(-2.61464 + 2.98142i) q^{23} +(-2.85771 + 3.72424i) q^{25} +(1.39564 + 3.36937i) q^{26} +(6.66570 + 1.32589i) q^{28} +(0.0274451 - 0.418731i) q^{29} +(0.426633 - 1.25682i) q^{31} +(4.61733 - 3.54301i) q^{32} +(-2.86436 + 1.70257i) q^{34} -15.7111i q^{35} +(0.0132231 + 0.0664768i) q^{37} +(-1.65508 - 0.443478i) q^{38} +(-6.33175 - 5.55279i) q^{40} +(3.37615 - 0.221284i) q^{41} +(5.74422 + 4.40769i) q^{43} +(0.923573 - 0.617112i) q^{44} +(-1.78049 + 2.66469i) q^{46} +(-1.39277 + 5.19789i) q^{47} +(11.2391 + 14.6471i) q^{49} +(-1.89689 + 3.28551i) q^{50} +(-3.03896 - 5.26363i) q^{52} +(-2.70319 + 6.52608i) q^{53} +(-1.81570 - 1.81570i) q^{55} +(13.6194 + 0.892662i) q^{56} +(-0.0221803 - 0.338405i) q^{58} +(0.445276 - 3.38221i) q^{59} +(0.762232 - 1.54565i) q^{61} +(0.209263 - 1.05204i) q^{62} +(2.60783 - 2.60783i) q^{64} +(-10.5637 + 9.26409i) q^{65} +(-1.90636 - 1.10063i) q^{67} +(4.36244 - 3.43625i) q^{68} +(-1.65732 - 12.5886i) q^{70} +(2.14171 - 0.426013i) q^{71} +(4.79086 + 3.20115i) q^{73} +(0.0176075 + 0.0518700i) q^{74} +(2.83117 + 0.372731i) q^{76} +(4.12590 + 0.543185i) q^{77} +(-4.25979 - 12.5489i) q^{79} +(1.31453 + 0.878338i) q^{80} +(2.68181 - 0.533446i) q^{82} +(0.479996 + 3.64594i) q^{83} +(-9.75844 - 8.34121i) q^{85} +(5.06754 + 2.92574i) q^{86} +(1.67713 - 1.47080i) q^{88} +(3.26760 - 3.26760i) q^{89} +(4.44238 - 22.3333i) q^{91} +(2.36226 - 4.79019i) q^{92} +(-0.567653 + 4.31175i) q^{94} +(-0.431749 - 6.58721i) q^{95} +(17.3795 + 1.13911i) q^{97} +(10.5505 + 10.5505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Introduction

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