LMFDB - Embedded newform 459.2.y.a.116.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(44,459)] 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("459.44"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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

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

Self dual:	no
Analytic conductor:	$3.66513345278$
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			116.1
Character	$\chi$	$=$	459.116
Dual form			459.2.y.a.368.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.37615 - 0.312826i) q^{2} +(3.61637 + 0.969004i) q^{4} +(0.222937 - 0.452071i) q^{5} +(-0.665919 + 0.328395i) q^{7} +(-3.86148 - 1.59948i) q^{8} +(-0.671150 + 1.00445i) q^{10} +(-0.966772 - 0.328175i) q^{11} +(1.39452 - 5.20440i) q^{13} +(1.68505 - 0.571999i) q^{14} +(2.19038 + 1.26462i) q^{16} +(3.71857 + 1.78107i) q^{17} +(-3.37354 + 1.39737i) q^{19} +(1.24428 - 1.41883i) q^{20} +(2.19453 + 1.08222i) q^{22} +(-0.352872 - 0.402373i) q^{23} +(2.88914 + 3.76520i) q^{25} +(-4.94165 + 11.9302i) q^{26} +(-2.72643 + 0.542320i) q^{28} +(-0.414188 - 6.31929i) q^{29} +(-0.330507 - 0.973643i) q^{31} +(1.82278 + 1.39867i) q^{32} +(-8.27872 - 5.39536i) q^{34} +0.374254i q^{35} +(2.20919 - 11.1064i) q^{37} +(8.45317 - 2.26502i) q^{38} +(-1.58394 + 1.38908i) q^{40} +(6.68958 + 0.438458i) q^{41} +(2.33510 - 1.79179i) q^{43} +(-3.17821 - 2.12361i) q^{44} +(0.712603 + 1.06649i) q^{46} +(-3.06452 - 11.4370i) q^{47} +(-3.92573 + 5.11610i) q^{49} +(-5.68718 - 9.85048i) q^{50} +(10.0862 - 17.4698i) q^{52} +(-3.30651 - 7.98262i) q^{53} +(-0.363887 + 0.363887i) q^{55} +(3.09669 - 0.202968i) q^{56} +(-0.992666 + 15.1452i) q^{58} +(-1.14780 - 8.71842i) q^{59} +(-2.81827 - 5.71489i) q^{61} +(0.480754 + 2.41691i) q^{62} +(-7.47053 - 7.47053i) q^{64} +(-2.04187 - 1.79067i) q^{65} +(8.82398 - 5.09452i) q^{67} +(11.7219 + 10.0443i) q^{68} +(0.117076 - 0.889283i) q^{70} +(4.19907 + 0.835247i) q^{71} +(2.65455 - 1.77371i) q^{73} +(-8.72372 + 25.6993i) q^{74} +(-13.5540 + 1.78442i) q^{76} +(0.751563 - 0.0989451i) q^{77} +(-3.32914 + 9.80734i) q^{79} +(1.06001 - 0.708279i) q^{80} +(-15.7583 - 3.13452i) q^{82} +(0.169437 - 1.28700i) q^{83} +(1.63418 - 1.28399i) q^{85} +(-6.10907 + 3.52707i) q^{86} +(3.20826 + 2.81357i) q^{88} +(2.39586 + 2.39586i) q^{89} +(0.780465 + 3.92366i) q^{91} +(-0.886215 - 1.79707i) q^{92} +(3.70399 + 28.1346i) q^{94} +(-0.120377 + 1.83661i) q^{95} +(15.9021 - 1.04228i) q^{97} +(10.9286 - 10.9286i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{16}\right)$

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 $

$2$	−2.37615	−	0.312826i	−1.68019	−	0.221201i	−0.770781	−	0.637101i	$-0.780134\pi$
$2$	−2.37615	−	0.312826i	−1.68019	−	0.221201i	−0.909411	+	0.415899i	$0.863467\pi$
$3$		0			0
$3$		0			0
$4$	3.61637	+	0.969004i	1.80819	+	0.484502i
$5$	0.222937	−	0.452071i	0.0997003	−	0.202172i	−0.841308	−	0.540557i	$-0.818214\pi$
$5$	0.222937	−	0.452071i	0.0997003	−	0.202172i	0.941008	+	0.338384i	$0.109880\pi$
$6$		0			0
$7$	−0.665919	+	0.328395i	−0.251694	+	0.124122i	−0.563760	−	0.825939i	$-0.690646\pi$
$7$	−0.665919	+	0.328395i	−0.251694	+	0.124122i	0.312066	+	0.950060i	$0.398979\pi$
$8$	−3.86148	−	1.59948i	−1.36524	−	0.565500i
$9$		0			0
$10$	−0.671150	+	1.00445i	−0.212236	+	0.317634i
$11$	−0.966772	−	0.328175i	−0.291493	−	0.0989485i	0.171863	−	0.985121i	$-0.445021\pi$
$11$	−0.966772	−	0.328175i	−0.291493	−	0.0989485i	−0.463356	+	0.886172i	$0.653355\pi$
$12$		0			0
$13$	1.39452	−	5.20440i	0.386769	−	1.44344i	−0.448591	−	0.893737i	$-0.648074\pi$
$13$	1.39452	−	5.20440i	0.386769	−	1.44344i	0.835360	−	0.549704i	$-0.185259\pi$
$14$	1.68505	−	0.571999i	0.450349	−	0.152873i
$15$		0			0
$16$	2.19038	+	1.26462i	0.547596	+	0.316155i
$17$	3.71857	+	1.78107i	0.901886	+	0.431973i
$17$	3.71857	+	1.78107i	0.901886	+	0.431973i
$18$		0			0
$19$	−3.37354	+	1.39737i	−0.773944	+	0.320578i	−0.734469	−	0.678643i	$-0.762569\pi$
$19$	−3.37354	+	1.39737i	−0.773944	+	0.320578i	−0.0394751	+	0.999221i	$0.512569\pi$
$20$	1.24428	−	1.41883i	0.278230	−	0.317260i
$21$		0			0
$22$	2.19453	+	1.08222i	0.467876	+	0.230731i
$23$	−0.352872	−	0.402373i	−0.0735788	−	0.0839006i	0.713879	−	0.700269i	$-0.246937\pi$
$23$	−0.352872	−	0.402373i	−0.0735788	−	0.0839006i	−0.787458	+	0.616368i	$0.788603\pi$
$24$		0			0
$25$	2.88914	+	3.76520i	0.577828	+	0.753040i
$26$	−4.94165	+	11.9302i	−0.969137	+	2.33970i
$27$		0			0
$28$	−2.72643	+	0.542320i	−0.515246	+	0.102489i
$29$	−0.414188	−	6.31929i	−0.0769129	−	1.17346i	−0.845592	−	0.533829i	$-0.820753\pi$
$29$	−0.414188	−	6.31929i	−0.0769129	−	1.17346i	0.768679	−	0.639634i	$-0.220914\pi$
$30$		0			0
$31$	−0.330507	−	0.973643i	−0.0593609	−	0.174871i	0.913204	−	0.407502i	$-0.133600\pi$
$31$	−0.330507	−	0.973643i	−0.0593609	−	0.174871i	−0.972565	+	0.232631i	$0.925267\pi$
$32$	1.82278	+	1.39867i	0.322225	+	0.247252i
$33$		0			0
$34$	−8.27872	−	5.39536i	−1.41979	−	0.925296i
$35$			0.374254i			0.0632604i
$36$		0			0
$37$	2.20919	−	11.1064i	0.363189	−	1.82587i	−0.176856	−	0.984237i	$-0.556593\pi$
$37$	2.20919	−	11.1064i	0.363189	−	1.82587i	0.540045	−	0.841636i	$-0.318407\pi$
$38$	8.45317	−	2.26502i	1.37129	−	0.367435i
$39$		0			0
$40$	−1.58394	+	1.38908i	−0.250443	+	0.219633i
$41$	6.68958	+	0.438458i	1.04474	+	0.0684757i	0.578094	−	0.815970i	$-0.303797\pi$
$41$	6.68958	+	0.438458i	1.04474	+	0.0684757i	0.466643	+	0.884446i	$0.345463\pi$
$42$		0			0
$43$	2.33510	−	1.79179i	0.356100	−	0.273245i	−0.415183	−	0.909738i	$-0.636282\pi$
$43$	2.33510	−	1.79179i	0.356100	−	0.273245i	0.771282	+	0.636493i	$0.219616\pi$
$44$	−3.17821	−	2.12361i	−0.479133	−	0.320146i
$45$		0			0
$46$	0.712603	+	1.06649i	0.105068	+	0.157245i
$47$	−3.06452	−	11.4370i	−0.447007	−	1.66825i	−0.710583	−	0.703614i	$-0.751569\pi$
$47$	−3.06452	−	11.4370i	−0.447007	−	1.66825i	0.263576	−	0.964639i	$-0.415098\pi$
$48$		0			0
$49$	−3.92573	+	5.11610i	−0.560818	+	0.730872i
$50$	−5.68718	−	9.85048i	−0.804288	−	1.39307i
$51$		0			0
$52$	10.0862	−	17.4698i	1.39870	−	2.42262i
$53$	−3.30651	−	7.98262i	−0.454184	−	1.09650i	−0.970716	−	0.240230i	$-0.922777\pi$
$53$	−3.30651	−	7.98262i	−0.454184	−	1.09650i	0.516532	−	0.856268i	$-0.327223\pi$
$54$		0			0
$55$	−0.363887	+	0.363887i	−0.0490666	+	0.0490666i
$56$	3.09669	−	0.202968i	0.413813	−	0.0271227i
$57$		0			0
$58$	−0.992666	+	15.1452i	−0.130343	+	1.98866i
$59$	−1.14780	−	8.71842i	−0.149431	−	1.13504i	−0.887663	−	0.460494i	$-0.847672\pi$
$59$	−1.14780	−	8.71842i	−0.149431	−	1.13504i	0.738232	−	0.674547i	$-0.235661\pi$
$60$		0			0
$61$	−2.81827	−	5.71489i	−0.360843	−	0.731716i	0.638437	−	0.769674i	$-0.279581\pi$
$61$	−2.81827	−	5.71489i	−0.360843	−	0.731716i	−0.999279	+	0.0379579i	$0.987915\pi$
$62$	0.480754	+	2.41691i	0.0610558	+	0.306948i
$63$		0			0
$64$	−7.47053	−	7.47053i	−0.933817	−	0.933817i
$65$	−2.04187	−	1.79067i	−0.253263	−	0.222105i
$66$		0			0
$67$	8.82398	−	5.09452i	1.07802	−	0.622395i	0.147659	−	0.989038i	$-0.452826\pi$
$67$	8.82398	−	5.09452i	1.07802	−	0.622395i	0.930362	+	0.366643i	$0.119493\pi$
$68$	11.7219	+	10.0443i	1.42149	+	1.21805i
$69$		0			0
$70$	0.117076	−	0.889283i	0.0139933	−	0.106290i
$71$	4.19907	+	0.835247i	0.498338	+	0.0991255i	0.437858	−	0.899044i	$-0.355737\pi$
$71$	4.19907	+	0.835247i	0.498338	+	0.0991255i	0.0604793	+	0.998169i	$0.480737\pi$
$72$		0			0
$73$	2.65455	−	1.77371i	0.310691	−	0.207597i	−0.390442	−	0.920627i	$-0.627678\pi$
$73$	2.65455	−	1.77371i	0.310691	−	0.207597i	0.701133	+	0.713030i	$0.252678\pi$
$74$	−8.72372	+	25.6993i	−1.01411	+	2.98748i
$75$		0			0
$76$	−13.5540	+	1.78442i	−1.55476	+	0.204687i
$77$	0.751563	−	0.0989451i	0.0856485	−	0.0112758i
$78$		0			0
$79$	−3.32914	+	9.80734i	−0.374558	+	1.10341i	0.582330	+	0.812953i	$0.302141\pi$
$79$	−3.32914	+	9.80734i	−0.374558	+	1.10341i	−0.956887	+	0.290459i	$0.906192\pi$
$80$	1.06001	−	0.708279i	0.118513	−	0.0791880i
$81$		0			0
$82$	−15.7583	−	3.13452i	−1.74021	−	0.346149i
$83$	0.169437	−	1.28700i	0.0185982	−	0.141267i	−0.979627	−	0.200828i	$-0.935637\pi$
$83$	0.169437	−	1.28700i	0.0185982	−	0.141267i	0.998225	+	0.0595610i	$0.0189701\pi$
$84$		0			0
$85$	1.63418	−	1.28399i	0.177251	−	0.139269i
$86$	−6.10907	+	3.52707i	−0.658758	+	0.380334i
$87$		0			0
$88$	3.20826	+	2.81357i	0.342002	+	0.299927i
$89$	2.39586	+	2.39586i	0.253961	+	0.253961i	0.822592	−	0.568632i	$-0.192527\pi$
$89$	2.39586	+	2.39586i	0.253961	+	0.253961i	−0.568632	+	0.822592i	$0.692527\pi$
$90$		0			0
$91$	0.780465	+	3.92366i	0.0818149	+	0.411311i
$92$	−0.886215	−	1.79707i	−0.0923943	−	0.187357i
$93$		0			0
$94$	3.70399	+	28.1346i	0.382037	+	2.90186i
$95$	−0.120377	+	1.83661i	−0.0123505	+	0.188432i
$96$		0			0
$97$	15.9021	−	1.04228i	1.61461	−	0.105827i	0.768863	−	0.639413i	$-0.220823\pi$
$97$	15.9021	−	1.04228i	1.61461	−	0.105827i	0.845746	+	0.533586i	$0.179156\pi$
$98$	10.9286	−	10.9286i	1.10395	−	1.10395i
$99$		0			0
$100$	6.79971	+	16.4160i	0.679971	+	1.64160i
$101$	−6.54019	+	11.3279i	−0.650773	+	1.12717i	0.332163	+	0.943222i	$0.392222\pi$
$101$	−6.54019	+	11.3279i	−0.650773	+	1.12717i	−0.982936	+	0.183949i	$0.941112\pi$
$102$		0			0
$103$	−3.23969	−	5.61131i	−0.319216	−	0.552899i	0.661108	−	0.750290i	$-0.270086\pi$
$103$	−3.23969	−	5.61131i	−0.319216	−	0.552899i	−0.980325	+	0.197391i	$0.936753\pi$
$104$	−13.7092	+	17.8662i	−1.34430	+	1.75192i
$105$		0			0
$106$	5.35959	+	20.0023i	0.520570	+	1.94279i
$107$	8.20002	+	12.2722i	0.792726	+	1.18640i	0.978992	+	0.203899i	$0.0653614\pi$
$107$	8.20002	+	12.2722i	0.792726	+	1.18640i	−0.186266	+	0.982499i	$0.559639\pi$
$108$		0			0
$109$	0.866335	+	0.578867i	0.0829798	+	0.0554454i	0.596368	−	0.802711i	$-0.296610\pi$
$109$	0.866335	+	0.578867i	0.0829798	+	0.0554454i	−0.513388	+	0.858156i	$0.671610\pi$
$110$	0.978484	−	0.750817i	0.0932948	−	0.0715876i
$111$		0			0
$112$	−1.87391	−	0.122823i	−0.177068	−	0.0116057i
$113$	−3.58041	+	3.13993i	−0.336817	+	0.295380i	−0.811000	−	0.585046i	$-0.801077\pi$
$113$	−3.58041	+	3.13993i	−0.336817	+	0.295380i	0.474184	+	0.880426i	$0.342743\pi$
$114$		0			0
$115$	−0.260569	+	0.0698193i	−0.0242982	+	0.00651068i
$116$	4.62556	−	23.2543i	0.429473	−	2.15911i
$117$		0			0
$118$			21.0753i			1.94014i
$119$	−3.06116	+	0.0351111i	−0.280616	+	0.00321863i
$120$		0			0
$121$	−7.89994	−	6.06183i	−0.718176	−	0.551076i
$122$	4.90887	+	14.4611i	0.444428	+	1.30924i
$123$		0			0
$124$	−0.251773	−	3.84132i	−0.0226099	−	0.344961i
$125$	4.81807	−	0.958374i	0.430941	−	0.0857195i
$126$		0			0
$127$	−2.87472	+	6.94019i	−0.255090	+	0.615843i	−0.998601	−	0.0528818i	$-0.983159\pi$
$127$	−2.87472	+	6.94019i	−0.255090	+	0.615843i	0.743510	+	0.668724i	$0.233159\pi$
$128$	12.6168	+	16.4425i	1.11518	+	1.45333i
$129$		0			0
$130$	4.29162	+	4.89365i	0.376400	+	0.429202i
$131$	−3.94700	−	1.94645i	−0.344851	−	0.170062i	0.261612	−	0.965173i	$-0.415746\pi$
$131$	−3.94700	−	1.94645i	−0.344851	−	0.170062i	−0.606464	+	0.795111i	$0.707412\pi$
$132$		0			0
$133$	1.78762	−	2.03839i	0.155006	−	0.176751i
$134$	−22.5608	+	9.34498i	−1.94895	+	0.807284i
$135$		0			0
$136$	−11.5104	−	12.8253i	−0.987009	−	1.09976i
$137$	−5.46680	−	3.15626i	−0.467060	−	0.269657i	0.247948	−	0.968773i	$-0.420244\pi$
$137$	−5.46680	−	3.15626i	−0.467060	−	0.269657i	−0.715008	+	0.699116i	$0.753577\pi$
$138$		0			0
$139$	−14.3494	+	4.87096i	−1.21710	+	0.413149i	−0.854822	−	0.518922i	$-0.826334\pi$
$139$	−14.3494	+	4.87096i	−1.21710	+	0.413149i	−0.362276	+	0.932071i	$0.618000\pi$
$140$	−0.362654	+	1.35344i	−0.0306498	+	0.114387i
$141$		0			0
$142$	−9.71633	−	3.29825i	−0.815376	−	0.276783i
$143$	−3.05613	+	4.57383i	−0.255567	+	0.382483i
$144$		0			0
$145$	−2.94911	−	1.22156i	−0.244910	−	0.101445i
$146$	−6.86246	+	3.38419i	−0.567941	+	0.280078i
$147$		0			0
$148$	18.7514	−	38.0240i	1.54135	−	3.12555i
$149$	7.14890	+	1.91554i	0.585661	+	0.156927i	0.539469	−	0.842005i	$-0.318625\pi$
$149$	7.14890	+	1.91554i	0.585661	+	0.156927i	0.0461915	+	0.998933i	$0.485292\pi$
$150$		0			0
$151$	2.43620	+	0.320732i	0.198255	+	0.0261008i	0.229000	−	0.973427i	$-0.426455\pi$
$151$	2.43620	+	0.320732i	0.198255	+	0.0261008i	−0.0307447	+	0.999527i	$0.509788\pi$
$152$	15.2619			1.23790
$153$		0			0
$154$	−1.81678			−0.146400
$155$	−0.513838	−	0.0676480i	−0.0412724	−	0.00543362i
$156$		0			0
$157$	9.25817	+	2.48072i	0.738883	+	0.197983i	0.608581	−	0.793491i	$-0.291739\pi$
$157$	9.25817	+	2.48072i	0.738883	+	0.197983i	0.130301	+	0.991474i	$0.458406\pi$
$158$	10.9785	−	22.2623i	0.873405	−	1.77109i
$159$		0			0
$160$	1.03866	−	0.512211i	0.0821133	−	0.0404938i
$161$	0.367121	+	0.152067i	0.0289332	+	0.0119845i
$162$		0			0
$163$	3.62885	−	5.43096i	0.284234	−	0.425386i	−0.661689	−	0.749779i	$-0.730160\pi$
$163$	3.62885	−	5.43096i	0.284234	−	0.425386i	0.945922	+	0.324393i	$0.105160\pi$
$164$	23.7671	+	8.06786i	1.85590	+	0.629994i
$165$		0			0
$166$	−0.805217	+	3.00511i	−0.0624970	+	0.233242i
$167$	−3.86302	+	1.31132i	−0.298929	+	0.101473i	−0.466875	−	0.884323i	$-0.654620\pi$
$167$	−3.86302	+	1.31132i	−0.298929	+	0.101473i	0.167945	+	0.985796i	$0.446287\pi$
$168$		0			0
$169$	−13.8828	−	8.01523i	−1.06791	−	0.616556i
$170$	−4.28471	+	2.53974i	−0.328623	+	0.194790i
$171$		0			0
$172$	10.1809	−	4.21705i	0.776283	−	0.321547i
$173$	−5.42802	+	6.18947i	−0.412685	+	0.470577i	−0.920417	−	0.390938i	$-0.872151\pi$
$173$	−5.42802	+	6.18947i	−0.412685	+	0.470577i	0.507732	+	0.861515i	$0.330484\pi$
$174$		0			0
$175$	−3.16041	−	1.55854i	−0.238904	−	0.117815i
$176$	−1.70259	−	1.94143i	−0.128337	−	0.146341i
$177$		0			0
$178$	−4.94343	−	6.44241i	−0.370526	−	0.482879i
$179$	−4.54443	+	10.9712i	−0.339667	+	0.820028i	0.658081	+	0.752947i	$0.271369\pi$
$179$	−4.54443	+	10.9712i	−0.339667	+	0.820028i	−0.997748	+	0.0670807i	$0.978631\pi$
$180$		0			0
$181$	17.5732	−	3.49554i	1.30621	−	0.259821i	0.507559	−	0.861617i	$-0.330548\pi$
$181$	17.5732	−	3.49554i	1.30621	−	0.259821i	0.798650	+	0.601796i	$0.205548\pi$
$182$	−0.627077	−	9.56735i	−0.0464821	−	0.709179i
$183$		0			0
$184$	0.719020	+	2.11816i	0.0530068	+	0.156153i
$185$	−4.52835	−	3.47472i	−0.332931	−	0.255467i
$186$		0			0
$187$	−3.01051	−	2.94223i	−0.220150	−	0.215157i
$188$		−	44.3299i		−	3.23309i
$189$		0			0
$190$	0.860573	−	4.32639i	0.0624325	−	0.313869i
$191$	20.7356	−	5.55608i	1.50037	−	0.402024i	0.587148	−	0.809479i	$-0.300251\pi$
$191$	20.7356	−	5.55608i	1.50037	−	0.402024i	0.913225	+	0.407456i	$0.133584\pi$
$192$		0			0
$193$	−6.77019	+	5.93730i	−0.487329	+	0.427376i	−0.867423	−	0.497572i	$-0.834225\pi$
$193$	−6.77019	+	5.93730i	−0.487329	+	0.427376i	0.380094	+	0.924948i	$0.375892\pi$
$194$	−38.1117	−	2.49797i	−2.73626	−	0.179344i
$195$		0			0
$196$	−19.1544	+	14.6977i	−1.36817	+	1.04984i
$197$	−15.1511	−	10.1237i	−1.07947	−	0.721281i	−0.117130	−	0.993117i	$-0.537369\pi$
$197$	−15.1511	−	10.1237i	−1.07947	−	0.721281i	−0.962344	+	0.271836i	$0.912369\pi$
$198$		0			0
$199$	13.9975	+	20.9487i	0.992255	+	1.48501i	0.870326	+	0.492476i	$0.163908\pi$
$199$	13.9975	+	20.9487i	0.992255	+	1.48501i	0.121929	+	0.992539i	$0.461092\pi$
$200$	−5.13400	−	19.1603i	−0.363029	−	1.35484i
$201$		0			0
$202$	19.0841	−	24.8709i	1.34275	−	1.74991i
$203$	2.35104	+	4.07212i	0.165011	+	0.285807i
$204$		0			0
$205$	1.68957	−	2.92642i	0.118004	−	0.204390i
$206$	5.94263	+	14.3468i	0.414043	+	0.999587i
$207$		0			0
$208$	9.63611	−	9.63611i	0.668144	−	0.668144i
$209$	3.72003	−	0.243824i	0.257320	−	0.0168656i
$210$		0			0
$211$	0.988397	−	15.0800i	0.0680441	−	1.03815i	−0.818200	−	0.574934i	$-0.805028\pi$
$211$	0.988397	−	15.0800i	0.0680441	−	1.03815i	0.886244	−	0.463218i	$-0.153305\pi$
$212$	−4.22238	−	32.0722i	−0.289994	−	2.20273i
$213$		0			0
$214$	−15.6454	−	31.7258i	−1.06950	−	2.16873i
$215$	−0.289435	−	1.45509i	−0.0197393	−	0.0992361i
$216$		0			0
$217$	0.539830	+	0.539830i	0.0366461	+	0.0366461i
$218$	−1.87746	−	1.64649i	−0.127157	−	0.111514i
$219$		0			0
$220$	−1.66856	+	0.963344i	−0.112494	+	0.0649487i
$221$	14.4550	−	16.8692i	0.972350	−	1.13475i
$222$		0			0
$223$	−2.01017	+	15.2687i	−0.134611	+	1.02247i	0.782166	+	0.623070i	$0.214115\pi$
$223$	−2.01017	+	15.2687i	−0.134611	+	1.02247i	−0.916777	+	0.399400i	$0.869218\pi$
$224$	−1.67314	−	0.332808i	−0.111791	−	0.0222366i
$225$		0			0
$226$	9.48984	−	6.34091i	0.631255	−	0.421791i
$227$	−5.72342	+	16.8607i	−0.379877	+	1.11908i	0.573993	+	0.818860i	$0.305394\pi$
$227$	−5.72342	+	16.8607i	−0.379877	+	1.11908i	−0.953870	+	0.300221i	$0.902940\pi$
$228$		0			0
$229$	−7.87450	+	1.03670i	−0.520362	+	0.0685069i	−0.386132	−	0.922443i	$-0.626189\pi$
$229$	−7.87450	+	1.03670i	−0.520362	+	0.0685069i	−0.134229	+	0.990950i	$0.542856\pi$
$230$	0.640993	−	0.0843883i	0.0422658	−	0.00556440i
$231$		0			0
$232$	−8.50818	+	25.0643i	−0.558589	+	1.64555i
$233$	15.3673	−	10.2681i	1.00675	−	0.672687i	0.0611841	−	0.998126i	$-0.480512\pi$
$233$	15.3673	−	10.2681i	1.00675	−	0.672687i	0.945563	+	0.325440i	$0.105512\pi$
$234$		0			0
$235$	−5.85351	−	1.16434i	−0.381841	−	0.0759529i
$236$	4.29731	−	32.6413i	0.279731	−	2.12477i
$237$		0			0
$238$	7.28476	+	0.874182i	0.472201	+	0.0566648i
$239$	−14.9969	+	8.65844i	−0.970067	+	0.560068i	−0.899257	−	0.437422i	$-0.855892\pi$
$239$	−14.9969	+	8.65844i	−0.970067	+	0.560068i	−0.0708101	+	0.997490i	$0.522558\pi$
$240$		0			0
$241$	9.34914	+	8.19898i	0.602231	+	0.528143i	0.905271	−	0.424835i	$-0.139668\pi$
$241$	9.34914	+	8.19898i	0.602231	+	0.528143i	−0.303039	+	0.952978i	$0.598001\pi$
$242$	16.8751	+	16.8751i	1.08477	+	1.08477i
$243$		0			0
$244$	−4.65417	−	23.3981i	−0.297953	−	1.49791i
$245$	1.43765	+	2.91527i	0.0918483	+	0.186250i
$246$		0			0
$247$	2.56800	+	19.5059i	0.163398	+	1.24113i
$248$	−0.281073	+	4.28834i	−0.0178481	+	0.272310i
$249$		0			0
$250$	−11.7483	+	0.770021i	−0.743025	+	0.0487004i
$251$	−12.5986	+	12.5986i	−0.795218	+	0.795218i	−0.982337	−	0.187119i	$-0.940085\pi$
$251$	−12.5986	+	12.5986i	−0.795218	+	0.795218i	0.187119	+	0.982337i	$0.440085\pi$
$252$		0			0
$253$	0.209098	+	0.504807i	0.0131459	+	0.0317369i
$254$	9.00184	−	15.5916i	0.564826	−	0.978307i
$255$		0			0
$256$	−14.2708	−	24.7178i	−0.891925	−	1.54486i
$257$	6.82292	−	8.89180i	0.425602	−	0.554655i	−0.530502	−	0.847684i	$-0.677996\pi$
$257$	6.82292	−	8.89180i	0.425602	−	0.554655i	0.956104	+	0.293029i	$0.0946631\pi$
$258$		0			0
$259$	2.17613	+	8.12142i	0.135218	+	0.504640i
$260$	−5.64900	−	8.45432i	−0.350336	−	0.524315i
$261$		0			0
$262$	8.76977	+	5.85977i	0.541798	+	0.362018i
$263$	−13.2633	+	10.1773i	−0.817853	+	0.627560i	−0.930590	−	0.366064i	$-0.880705\pi$
$263$	−13.2633	+	10.1773i	−0.817853	+	0.627560i	0.112737	+	0.993625i	$0.464038\pi$
$264$		0			0
$265$	−4.34585	−	0.284842i	−0.266964	−	0.0174977i
$266$	−4.88531	+	4.28430i	−0.299537	+	0.262687i
$267$		0			0
$268$	36.8474	−	9.87323i	2.25081	−	0.603104i
$269$	−1.87839	+	9.44333i	−0.114528	+	0.575770i	0.880319	+	0.474382i	$0.157328\pi$
$269$	−1.87839	+	9.44333i	−0.114528	+	0.575770i	−0.994847	+	0.101388i	$0.967672\pi$
$270$		0			0
$271$		−	21.5828i		−	1.31106i	−0.755168	−	0.655531i	$-0.772445\pi$
$271$		−	21.5828i		−	1.31106i	0.755168	−	0.655531i	$-0.227555\pi$
$272$	5.89273	+	8.60381i	0.357299	+	0.521682i
$273$		0			0
$274$	12.0026	+	9.20990i	0.725102	+	0.556390i
$275$	−1.55750	−	4.58823i	−0.0939205	−	0.276681i
$276$		0			0
$277$	1.67954	+	25.6248i	0.100914	+	1.53964i	0.685356	+	0.728208i	$0.259647\pi$
$277$	1.67954	+	25.6248i	0.100914	+	1.53964i	−0.584443	+	0.811435i	$0.698687\pi$
$278$	35.6200	−	7.08526i	2.13635	−	0.424946i
$279$		0			0
$280$	0.598610	−	1.44517i	0.0357738	−	0.0863656i
$281$	−7.10351	−	9.25748i	−0.423760	−	0.552255i	0.531869	−	0.846826i	$-0.321490\pi$
$281$	−7.10351	−	9.25748i	−0.423760	−	0.552255i	−0.955629	+	0.294572i	$0.904823\pi$
$282$		0			0
$283$	0.720976	+	0.822116i	0.0428576	+	0.0488697i	0.772871	−	0.634563i	$-0.218820\pi$
$283$	0.720976	+	0.822116i	0.0428576	+	0.0488697i	−0.730014	+	0.683432i	$0.760486\pi$
$284$	14.3760	+	7.08948i	0.853061	+	0.420683i
$285$		0			0
$286$	8.69264	−	9.91206i	0.514007	−	0.586112i
$287$	−4.59870	+	1.90485i	−0.271453	+	0.112439i
$288$		0			0
$289$	10.6556	+	13.2461i	0.626798	+	0.779182i
$290$	6.62538	+	3.82517i	0.389056	+	0.224622i
$291$		0			0
$292$	11.3186	−	3.84213i	0.662369	−	0.224844i
$293$	−0.611280	+	2.28133i	−0.0357113	+	0.133276i	−0.981480	−	0.191564i	$-0.938644\pi$
$293$	−0.611280	+	2.28133i	−0.0357113	+	0.133276i	0.945769	+	0.324841i	$0.105311\pi$
$294$		0			0
$295$	−4.19723	−	1.42477i	−0.244372	−	0.0829532i
$296$	−26.2951	+	39.3534i	−1.52837	+	2.28737i
$297$		0			0
$298$	−16.3876	−	6.78798i	−0.949310	−	0.393217i
$299$	−2.58620	+	1.27537i	−0.149564	+	0.0737566i
$300$		0			0
$301$	−0.966575	+	1.96002i	−0.0557125	+	0.112974i
$302$	−5.68844	−	1.52421i	−0.327333	−	0.0877086i
$303$		0			0
$304$	−9.15649	−	1.20547i	−0.525161	−	0.0691387i
$305$	−3.21183			−0.183909
$306$		0			0
$307$	−31.4910			−1.79729			−0.898644	−	0.438678i	$-0.855447\pi$
$307$	−31.4910			−1.79729			−0.898644	+	0.438678i	$0.855447\pi$
$308$	2.81381	+	0.370445i	0.160332	+	0.0211081i
$309$		0			0
$310$	1.19979	+	0.321484i	0.0681437	+	0.0182590i
$311$	4.98640	−	10.1114i	0.282753	−	0.573366i	−0.708443	−	0.705768i	$-0.750602\pi$
$311$	4.98640	−	10.1114i	0.282753	−	0.573366i	0.991196	+	0.132402i	$0.0422689\pi$
$312$		0			0
$313$	7.54591	−	3.72123i	0.426520	−	0.210336i	−0.216343	−	0.976317i	$-0.569413\pi$
$313$	7.54591	−	3.72123i	0.426520	−	0.210336i	0.642863	+	0.765981i	$0.277746\pi$
$314$	−21.2228	−	8.79076i	−1.19767	−	0.496091i
$315$		0			0
$316$	−21.5428	+	32.2411i	−1.21188	+	1.81370i
$317$	−1.22576	−	0.416090i	−0.0688456	−	0.0233699i	0.286804	−	0.957989i	$-0.407407\pi$
$317$	−1.22576	−	0.416090i	−0.0688456	−	0.0233699i	−0.355650	+	0.934619i	$0.615740\pi$
$318$		0			0
$319$	−1.67341	+	6.24524i	−0.0936929	+	0.349667i
$320$	−5.04267	+	1.71175i	−0.281894	+	0.0956900i
$321$		0			0
$322$	−0.824764	−	0.476178i	−0.0459623	−	0.0265364i
$323$	−15.0336	−	0.812309i	−0.836491	−	0.0451981i
$324$		0			0
$325$	23.6246	−	9.78561i	1.31045	−	0.542808i
$326$	−10.3216	+	11.7696i	−0.571663	+	0.651856i
$327$		0			0
$328$	−25.1303	−	12.3929i	−1.38759	−	0.684284i
$329$	5.79656	+	6.60972i	0.319575	+	0.364405i
$330$		0			0
$331$	4.04081	+	5.26609i	0.222103	+	0.289450i	0.891093	−	0.453821i	$-0.149940\pi$
$331$	4.04081	+	5.26609i	0.222103	+	0.289450i	−0.668990	+	0.743272i	$0.733273\pi$
$332$	1.85986	−	4.49010i	0.102073	−	0.246426i
$333$		0			0
$334$	9.58932	−	1.90744i	0.524705	−	0.104370i
$335$	−0.335898	−	5.12482i	−0.0183521	−	0.279999i
$336$		0			0
$337$	−2.42739	−	7.15085i	−0.132228	−	0.389532i	0.860570	−	0.509333i	$-0.170108\pi$
$337$	−2.42739	−	7.15085i	−0.132228	−	0.389532i	−0.992798	+	0.119801i	$0.961774\pi$
$338$	30.4802	+	23.3883i	1.65790	+	1.27215i
$339$		0			0
$340$	7.15399	−	3.05987i	0.387980	−	0.165945i
$341$			1.04976i			0.0568474i
$342$		0			0
$343$	1.94808	−	9.79366i	0.105186	−	0.528808i
$344$	−11.8829	+	3.18400i	−0.640681	+	0.171670i
$345$		0			0
$346$	14.8340	−	13.0091i	0.797482	−	0.699373i
$347$	27.3689	+	1.79386i	1.46924	+	0.0962992i	0.778884	−	0.627168i	$-0.215786\pi$
$347$	27.3689	+	1.79386i	1.46924	+	0.0962992i	0.690358	+	0.723468i	$0.257453\pi$
$348$		0			0
$349$	−8.60687	+	6.60428i	−0.460715	+	0.353519i	−0.812892	−	0.582414i	$-0.802108\pi$
$349$	−8.60687	+	6.60428i	−0.460715	+	0.353519i	0.352177	+	0.935933i	$0.385442\pi$
$350$	7.02204	+	4.69198i	0.375344	+	0.250797i
$351$		0			0
$352$	−1.30320	−	1.95038i	−0.0694610	−	0.103956i
$353$	1.82756	+	6.82053i	0.0972710	+	0.363020i	0.997354	−	0.0726982i	$-0.0231610\pi$
$353$	1.82756	+	6.82053i	0.0972710	+	0.363020i	−0.900083	+	0.435719i	$0.856494\pi$
$354$		0			0
$355$	1.31372	−	1.71207i	0.0697249	−	0.0908672i
$356$	6.34272	+	10.9859i	0.336164	+	0.582253i
$357$		0			0
$358$	14.2303	−	24.6477i	0.752096	−	1.30267i
$359$	−1.46983	−	3.54849i	−0.0775748	−	0.187282i	0.880334	−	0.474354i	$-0.157318\pi$
$359$	−1.46983	−	3.54849i	−0.0775748	−	0.187282i	−0.957909	+	0.287072i	$0.907318\pi$
$360$		0			0
$361$	−4.00687	+	4.00687i	−0.210888	+	0.210888i
$362$	−42.8501	+	2.80855i	−2.25215	+	0.147614i
$363$		0			0
$364$	−0.979593	+	14.9457i	−0.0513446	+	0.783367i
$365$	−0.210047	−	1.59547i	−0.0109944	−	0.0835106i
$366$		0			0
$367$	−6.58764	−	13.3584i	−0.343872	−	0.697303i	0.654395	−	0.756153i	$-0.272923\pi$
$367$	−6.58764	−	13.3584i	−0.343872	−	0.697303i	−0.998267	+	0.0588497i	$0.981257\pi$
$368$	−0.264076	−	1.32760i	−0.0137659	−	0.0692059i
$369$		0			0
$370$	9.67305	+	9.67305i	0.502878	+	0.502878i
$371$	4.82332	+	4.22994i	0.250414	+	0.219607i
$372$		0			0
$373$	3.87184	−	2.23541i	0.200476	−	0.115745i	−0.396401	−	0.918077i	$-0.629741\pi$
$373$	3.87184	−	2.23541i	0.200476	−	0.115745i	0.596878	+	0.802332i	$0.296408\pi$
$374$	6.23301	+	7.93295i	0.322302	+	0.410203i
$375$		0			0
$376$	−6.45956	+	49.0652i	−0.333126	+	2.53034i
$377$	−33.4657	−	6.65675i	−1.72357	−	0.342840i
$378$		0			0
$379$	−12.0411	+	8.04562i	−0.618511	+	0.413276i	−0.824968	−	0.565180i	$-0.808807\pi$
$379$	−12.0411	+	8.04562i	−0.618511	+	0.413276i	0.206457	+	0.978456i	$0.433807\pi$
$380$	−2.21501	+	6.52520i	−0.113628	+	0.334736i
$381$		0			0
$382$	−51.0089	+	6.71545i	−2.60984	+	0.343592i
$383$	−1.46284	+	0.192586i	−0.0747475	+	0.00984070i	−0.167807	−	0.985820i	$-0.553669\pi$
$383$	−1.46284	+	0.192586i	−0.0747475	+	0.00984070i	0.0930597	+	0.995661i	$0.470335\pi$
$384$		0			0
$385$	0.122821	−	0.361818i	0.00625952	−	0.0184400i
$386$	17.9443	−	11.9900i	0.913342	−	0.610276i
$387$		0			0
$388$	58.5178	+	11.6399i	2.97079	+	0.590927i
$389$	4.98165	−	37.8394i	0.252580	−	1.91854i	−0.124247	−	0.992251i	$-0.539652\pi$
$389$	4.98165	−	37.8394i	0.252580	−	1.91854i	0.376827	−	0.926284i	$-0.377015\pi$
$390$		0			0
$391$	−0.595524	−	2.12474i	−0.0301169	−	0.107453i
$392$	23.3422	−	13.4766i	1.17896	−	0.680672i
$393$		0			0
$394$	32.8344	+	28.7950i	1.65417	+	1.45067i
$395$	3.69142	+	3.69142i	0.185736	+	0.185736i
$396$		0			0
$397$	−1.08068	−	5.43296i	−0.0542379	−	0.272673i	0.944144	−	0.329533i	$-0.106891\pi$
$397$	−1.08068	−	5.43296i	−0.0542379	−	0.272673i	−0.998382	+	0.0568600i	$0.981891\pi$
$398$	−26.7068	−	54.1560i	−1.33869	−	2.71460i
$399$		0			0
$400$	1.56678	+	11.9009i	0.0783391	+	0.595045i
$401$	−1.34048	+	20.4518i	−0.0669404	+	1.02131i	0.823823	+	0.566847i	$0.191837\pi$
$401$	−1.34048	+	20.4518i	−0.0669404	+	1.02131i	−0.890764	+	0.454467i	$0.849830\pi$
$402$		0			0
$403$	−5.52813	+	0.362332i	−0.275376	+	0.0180491i
$404$	−34.6286	+	34.6286i	−1.72284	+	1.72284i
$405$		0			0
$406$	−4.31256	−	10.4114i	−0.214029	−	0.516711i
$407$	−5.78061	+	10.0123i	−0.286534	+	0.496292i
$408$		0			0
$409$	11.6707	+	20.2142i	0.577078	+	0.999528i	0.995812	+	0.0914193i	$0.0291404\pi$
$409$	11.6707	+	20.2142i	0.577078	+	0.999528i	−0.418735	+	0.908109i	$0.637526\pi$
$410$	−4.93012	+	6.42506i	−0.243481	+	0.317311i
$411$		0			0
$412$	−6.27855	−	23.4319i	−0.309322	−	1.15441i
$413$	3.62743	+	5.42883i	0.178494	+	0.267135i
$414$		0			0
$415$	−0.544044	−	0.363518i	−0.0267060	−	0.0178444i
$416$	9.82111	−	7.53600i	0.481520	−	0.369483i
$417$		0			0
$418$	−8.91562	−	0.584360i	−0.436077	−	0.0285820i
$419$	−26.0377	+	22.8345i	−1.27203	+	1.11554i	−0.284402	+	0.958705i	$0.591795\pi$
$419$	−26.0377	+	22.8345i	−1.27203	+	1.11554i	−0.987625	+	0.156833i	$0.949872\pi$
$420$		0			0
$421$	2.92019	−	0.782462i	0.142321	−	0.0381349i	−0.186955	−	0.982368i	$-0.559862\pi$
$421$	2.92019	−	0.782462i	0.142321	−	0.0381349i	0.329276	+	0.944234i	$0.393195\pi$
$422$	−7.06601	+	35.5232i	−0.343968	+	1.72924i
$423$		0			0
$424$			36.1134i			1.75382i
$425$	4.03739	+	19.1469i	0.195842	+	0.928763i
$426$		0			0
$427$	3.75348	+	2.88015i	0.181644	+	0.139380i
$428$	17.7625	+	52.3267i	0.858584	+	2.52931i
$429$		0			0
$430$	0.232551	+	3.54805i	0.0112146	+	0.171102i
$431$	38.4058	−	7.63939i	1.84994	−	0.367977i	0.860098	−	0.510128i	$-0.170402\pi$
$431$	38.4058	−	7.63939i	1.84994	−	0.367977i	0.989845	+	0.142151i	$0.0454020\pi$
$432$		0			0
$433$	9.24045	−	22.3084i	0.444068	−	1.07207i	−0.530441	−	0.847722i	$-0.677973\pi$
$433$	9.24045	−	22.3084i	0.444068	−	1.07207i	0.974508	−	0.224352i	$-0.0720265\pi$
$434$	−1.11384	−	1.45159i	−0.0534663	−	0.0696786i
$435$		0			0
$436$	2.57207	+	2.93288i	0.123180	+	0.140459i
$437$	1.75269	+	0.864331i	0.0838426	+	0.0413466i
$438$		0			0
$439$	−25.0661	+	28.5824i	−1.19634	+	1.36417i	−0.281901	+	0.959443i	$0.590965\pi$
$439$	−25.0661	+	28.5824i	−1.19634	+	1.36417i	−0.914440	+	0.404722i	$0.867368\pi$
$440$	1.98717	−	0.823114i	0.0947347	−	0.0392404i
$441$		0			0
$442$	−39.6244	+	35.5619i	−1.88474	+	1.69151i
$443$	33.1913	+	19.1630i	1.57697	+	0.910462i	0.995280	+	0.0970494i	$0.0309405\pi$
$443$	33.1913	+	19.1630i	1.57697	+	0.910462i	0.581687	+	0.813413i	$0.302393\pi$
$444$		0			0
$445$	1.61722	−	0.548973i	0.0766637	−	0.0260238i
$446$	9.55292	−	35.6520i	0.452344	−	1.68817i
$447$		0			0
$448$	7.42805	+	2.52148i	0.350943	+	0.119129i
$449$	8.96395	−	13.4155i	0.423035	−	0.633116i	−0.557334	−	0.830288i	$-0.688176\pi$
$449$	8.96395	−	13.4155i	0.423035	−	0.633116i	0.980369	+	0.197172i	$0.0631758\pi$
$450$		0			0
$451$	−6.32341	−	2.61924i	−0.297758	−	0.123335i
$452$	−15.9907	+	7.88574i	−0.752140	+	0.370914i
$453$		0			0
$454$	18.8741	−	38.2730i	0.885808	−	1.79624i
$455$	1.94777	+	0.521903i	0.0913127	+	0.0244672i
$456$		0			0
$457$	−19.4616	−	2.56216i	−0.910374	−	0.119853i	−0.339230	−	0.940703i	$-0.610167\pi$
$457$	−19.4616	−	2.56216i	−0.910374	−	0.119853i	−0.571143	+	0.820850i	$0.693500\pi$
$458$	19.0353			0.889461
$459$		0			0
$460$	−1.00997			−0.0470901
$461$	13.2905	+	1.74972i	0.618999	+	0.0814927i	0.433503	−	0.901152i	$-0.357277\pi$
$461$	13.2905	+	1.74972i	0.618999	+	0.0814927i	0.185496	+	0.982645i	$0.440611\pi$
$462$		0			0
$463$	−0.913894	−	0.244877i	−0.0424722	−	0.0113804i	0.237520	−	0.971383i	$-0.423665\pi$
$463$	−0.913894	−	0.244877i	−0.0424722	−	0.0113804i	−0.279993	+	0.960002i	$0.590332\pi$
$464$	7.08427	−	14.3655i	0.328879	−	0.666900i
$465$		0			0
$466$	−39.7272	+	19.5913i	−1.84033	+	0.907549i
$467$	27.8933	+	11.5538i	1.29075	+	0.534644i	0.919208	−	0.393773i	$-0.128831\pi$
$467$	27.8933	+	11.5538i	1.29075	+	0.534644i	0.371538	+	0.928418i	$0.378831\pi$
$468$		0			0
$469$	−4.20304	+	6.29029i	−0.194078	+	0.290459i
$470$	13.5446	+	4.59777i	0.624765	+	0.212079i
$471$		0			0
$472$	−9.51269	+	35.5018i	−0.437857	+	1.63410i
$473$	−2.84553	+	0.965928i	−0.130838	+	0.0444134i
$474$		0			0
$475$	−15.0080	−	8.66488i	−0.688614	−	0.397572i
$476$	−11.1043	−	2.83931i	−0.508966	−	0.130139i
$477$		0			0
$478$	38.3434	−	15.8823i	1.75379	−	0.726442i
$479$	14.1926	−	16.1835i	0.648476	−	0.739445i	−0.330413	−	0.943836i	$-0.607188\pi$
$479$	14.1926	−	16.1835i	0.648476	−	0.739445i	0.978889	+	0.204391i	$0.0655215\pi$
$480$		0			0
$481$	−54.7212	−	26.9855i	−2.49507	−	1.23043i
$482$	−19.6501	−	22.4067i	−0.895038	−	1.02060i
$483$		0			0
$484$	−22.6952	−	29.5769i	−1.03160	−	1.34441i
$485$	3.07397	−	7.42122i	0.139582	−	0.336980i
$486$		0			0
$487$	−9.83269	+	1.95584i	−0.445562	+	0.0886277i	−0.412772	−	0.910835i	$-0.635439\pi$
$487$	−9.83269	+	1.95584i	−0.445562	+	0.0886277i	−0.0327900	+	0.999462i	$0.510439\pi$
$488$	1.74186	+	26.5757i	0.0788503	+	1.20302i
$489$		0			0
$490$	−2.50411	−	7.37686i	−0.113124	−	0.333253i
$491$	3.43095	+	2.63266i	0.154837	+	0.118810i	0.683274	−	0.730162i	$-0.260555\pi$
$491$	3.43095	+	2.63266i	0.154837	+	0.118810i	−0.528438	+	0.848972i	$0.677222\pi$
$492$		0			0
$493$	9.71492	−	24.2365i	0.437538	−	1.09156i
$494$		−	47.1523i		−	2.12148i
$495$		0			0
$496$	0.507349	−	2.55062i	0.0227807	−	0.114526i
$497$	−3.07053	+	0.822746i	−0.137732	+	0.0369052i
$498$		0			0
$499$	17.5954	−	15.4308i	0.787679	−	0.690776i	−0.167805	−	0.985820i	$-0.553668\pi$
$499$	17.5954	−	15.4308i	0.787679	−	0.690776i	0.955483	+	0.295045i	$0.0953345\pi$
$500$	18.3526	+	1.20289i	0.820754	+	0.0537950i
$501$		0			0
$502$	33.8774	−	25.9950i	1.51202	−	1.16022i
$503$	−9.17711	−	6.13195i	−0.409187	−	0.273410i	0.333895	−	0.942610i	$-0.391637\pi$
$503$	−9.17711	−	6.13195i	−0.409187	−	0.273410i	−0.743082	+	0.669200i	$0.766637\pi$
$504$		0			0
$505$	3.66298	+	5.48204i	0.163001	+	0.243948i
$506$	−0.338931	−	1.26491i	−0.0150673	−	0.0562320i
$507$		0			0
$508$	−17.1211	+	22.3127i	−0.759628	+	0.989967i
$509$	−13.6706	−	23.6782i	−0.605939	−	1.04952i	−0.991902	−	0.127003i	$-0.959464\pi$
$509$	−13.6706	−	23.6782i	−0.605939	−	1.04952i	0.385963	−	0.922514i	$-0.373869\pi$
$510$		0			0
$511$	−1.18523	+	2.05289i	−0.0524317	+	0.0908144i
$512$	10.3147	+	24.9019i	0.455850	+	1.10052i
$513$		0			0
$514$	−18.9939	+	18.9939i	−0.837783	+	0.837783i
$515$	−3.25896	+	0.213603i	−0.143607	+	0.00941249i
$516$		0			0
$517$	−0.790627	+	12.0626i	−0.0347717	+	0.530514i
$518$	−2.63021	−	19.9784i	−0.115565	−	0.877803i
$519$		0			0
$520$	5.02050	+	10.1806i	0.220163	+	0.446447i
$521$	−0.254038	−	1.27713i	−0.0111296	−	0.0559523i	0.974821	−	0.222987i	$-0.0715808\pi$
$521$	−0.254038	−	1.27713i	−0.0111296	−	0.0559523i	−0.985951	+	0.167035i	$0.946581\pi$
$522$		0			0
$523$	−4.98904	−	4.98904i	−0.218155	−	0.218155i	0.589565	−	0.807721i	$-0.299299\pi$
$523$	−4.98904	−	4.98904i	−0.218155	−	0.218155i	−0.807721	+	0.589565i	$0.799299\pi$
$524$	−12.3877	−	10.8637i	−0.541160	−	0.474585i
$525$		0			0
$526$	34.6994	−	20.0337i	1.51297	−	0.873511i
$527$	0.505112	−	4.20922i	0.0220030	−	0.183356i
$528$		0			0
$529$	2.96472	−	22.5193i	0.128901	−	0.979098i
$530$	10.2373	+	2.03632i	0.444680	+	0.0884523i
$531$		0			0
$532$	8.43990	−	5.63936i	0.365916	−	0.244497i
$533$	11.6106	−	34.2038i	0.502912	−	1.48153i
$534$		0			0
$535$	7.37599	−	0.971068i	0.318892	−	0.0419829i
$536$	−42.2221	+	5.55865i	−1.82372	+	0.240097i
$537$		0			0
$538$	7.41746	−	21.8511i	0.319790	−	0.942070i
$539$	5.47426	−	3.65778i	0.235793	−	0.157552i
$540$		0			0
$541$	40.2772	+	8.01163i	1.73165	+	0.344447i	0.957474	−	0.288521i	$-0.0931634\pi$
$541$	40.2772	+	8.01163i	1.73165	+	0.344447i	0.774178	+	0.632968i	$0.218163\pi$
$542$	−6.75166	+	51.2840i	−0.290009	+	2.20284i
$543$		0			0
$544$	4.28701	+	8.44754i	0.183804	+	0.362185i
$545$	0.454827	−	0.262594i	0.0194826	−	0.0112483i
$546$		0			0
$547$	−27.5805	−	24.1874i	−1.17926	−	1.03418i	−0.998718	−	0.0506126i	$-0.983883\pi$
$547$	−27.5805	−	24.1874i	−1.17926	−	1.03418i	−0.180538	−	0.983568i	$-0.557784\pi$
$548$	−16.7116	−	16.7116i	−0.713883	−	0.713883i
$549$		0			0
$550$	2.26552	+	11.3896i	0.0966022	+	0.485652i
$551$	10.2277	+	20.7396i	0.435713	+	0.883538i
$552$		0			0
$553$	−1.00374	−	7.62417i	−0.0426834	−	0.324213i
$554$	4.02526	−	61.4137i	0.171017	−	2.60922i
$555$		0			0
$556$	−56.6127	+	3.71059i	−2.40091	+	0.157364i
$557$	4.48661	−	4.48661i	0.190104	−	0.190104i	−0.605637	−	0.795741i	$-0.707082\pi$
$557$	4.48661	−	4.48661i	0.190104	−	0.190104i	0.795741	+	0.605637i	$0.207082\pi$
$558$		0			0
$559$	−6.06884	−	14.6515i	−0.256685	−	0.619692i
$560$	−0.473288	+	0.819760i	−0.0200001	+	0.0346412i
$561$		0			0
$562$	13.9830	+	24.2193i	0.589838	+	1.02163i
$563$	−11.5661	+	15.0732i	−0.487452	+	0.635260i	−0.970720	−	0.240212i	$-0.922783\pi$
$563$	−11.5661	+	15.0732i	−0.487452	+	0.635260i	0.483268	+	0.875472i	$0.339450\pi$
$564$		0			0
$565$	0.621268	+	2.31861i	0.0261370	+	0.0975445i
$566$	−1.45597	−	2.17901i	−0.0611989	−	0.0915906i
$567$		0			0
$568$	−14.8786	−	9.94159i	−0.624294	−	0.417140i
$569$	−15.2156	+	11.6753i	−0.637869	+	0.489454i	−0.876339	−	0.481696i	$-0.840021\pi$
$569$	−15.2156	+	11.6753i	−0.637869	+	0.489454i	0.238469	+	0.971150i	$0.423354\pi$
$570$		0			0
$571$	28.0613	+	1.83924i	1.17433	+	0.0769696i	0.640046	−	0.768336i	$-0.278915\pi$
$571$	28.0613	+	1.83924i	1.17433	+	0.0769696i	0.534283	+	0.845306i	$0.320582\pi$
$572$	−15.4842	+	13.5793i	−0.647426	+	0.567777i
$573$		0			0
$574$	11.5231	−	3.08760i	0.480965	−	0.128874i
$575$	0.495519	−	2.49114i	0.0206646	−	0.103888i
$576$		0			0
$577$		−	44.0005i		−	1.83176i	−0.401449	−	0.915881i	$-0.631493\pi$
$577$		−	44.0005i		−	1.83176i	0.401449	−	0.915881i	$-0.368507\pi$
$578$	−21.1755	−	34.8080i	−0.880785	−	1.44782i
$579$		0			0
$580$	−9.48138	−	7.27532i	−0.393693	−	0.302091i
$581$	0.309814	+	0.912683i	0.0128533	+	0.0378645i
$582$		0			0
$583$	0.576946	+	8.80249i	0.0238947	+	0.364562i
$584$	−13.0875	+	2.60326i	−0.541564	+	0.107724i
$585$		0			0
$586$	2.16615	−	5.22955i	0.0894828	−	0.216031i
$587$	−6.52486	−	8.50336i	−0.269310	−	0.350971i	0.639047	−	0.769168i	$-0.279329\pi$
$587$	−6.52486	−	8.50336i	−0.269310	−	0.350971i	−0.908357	+	0.418196i	$0.862662\pi$
$588$		0			0
$589$	2.47552	+	2.82279i	0.102002	+	0.116311i
$590$	9.52754	+	4.69846i	0.392243	+	0.193433i
$591$		0			0
$592$	18.8843	−	21.5334i	0.776139	−	0.885017i
$593$	17.9488	−	7.43464i	0.737069	−	0.305304i	0.0176157	−	0.999845i	$-0.494392\pi$
$593$	17.9488	−	7.43464i	0.737069	−	0.305304i	0.719453	+	0.694541i	$0.244392\pi$
$594$		0			0
$595$	−0.666573	+	1.39169i	−0.0273268	+	0.0570537i
$596$	23.9969	+	13.8546i	0.982953	+	0.567508i
$597$		0			0
$598$	6.54416	−	2.22144i	0.267610	−	0.0908415i
$599$	−4.18348	+	15.6130i	−0.170932	+	0.637929i	0.826276	+	0.563265i	$0.190455\pi$
$599$	−4.18348	+	15.6130i	−0.170932	+	0.637929i	−0.997209	+	0.0746637i	$0.976212\pi$
$600$		0			0
$601$	16.3911	+	5.56403i	0.668607	+	0.226962i	0.635045	−	0.772475i	$-0.280981\pi$
$601$	16.3911	+	5.56403i	0.668607	+	0.226962i	0.0335622	+	0.999437i	$0.489315\pi$
$602$	2.90987	−	4.35493i	0.118598	−	0.177494i
$603$		0			0
$604$	8.49941	+	3.52057i	0.345836	+	0.143250i
$605$	−4.50157	+	2.21993i	−0.183015	+	0.0902528i
$606$		0			0
$607$	2.48444	−	5.03794i	0.100840	−	0.204484i	−0.840606	−	0.541647i	$-0.817801\pi$
$607$	2.48444	−	5.03794i	0.100840	−	0.204484i	0.941446	+	0.337164i	$0.109468\pi$
$608$	−8.10367	−	2.17137i	−0.328647	−	0.0880607i
$609$		0			0
$610$	7.63179	+	1.00474i	0.309002	+	0.0406809i
$611$	−63.7961			−2.58091
$612$		0			0
$613$	−24.3856			−0.984927			−0.492463	−	0.870333i	$-0.663903\pi$
$613$	−24.3856			−0.984927			−0.492463	+	0.870333i	$0.663903\pi$
$614$	74.8274	+	9.85121i	3.01979	+	0.397563i
$615$		0			0
$616$	−3.06040	−	0.820033i	−0.123307	−	0.0330401i
$617$	−8.14777	+	16.5220i	−0.328017	+	0.665152i	−0.996939	−	0.0781799i	$-0.975089\pi$
$617$	−8.14777	+	16.5220i	−0.328017	+	0.665152i	0.668922	+	0.743332i	$0.266756\pi$
$618$		0			0
$619$	8.35682	−	4.12113i	0.335889	−	0.165642i	−0.266521	−	0.963829i	$-0.585874\pi$
$619$	8.35682	−	4.12113i	0.335889	−	0.165642i	0.602410	+	0.798187i	$0.294207\pi$
$620$	−1.79268	−	0.742552i	−0.0719957	−	0.0298216i
$621$		0			0
$622$	−15.0115	+	22.4664i	−0.601908	+	0.900819i
$623$	−2.38224	−	0.808660i	−0.0954423	−	0.0323983i
$624$		0			0
$625$	−5.50082	+	20.5293i	−0.220033	+	0.821173i
$626$	−19.0943	+	6.48164i	−0.763162	+	0.259059i
$627$		0			0
$628$	31.0772	+	17.9424i	1.24011	+	0.715981i
$629$	27.9962	−	37.3651i	1.11628	−	1.48984i
$630$		0			0
$631$	−5.45994	+	2.26158i	−0.217357	+	0.0900321i	−0.488705	−	0.872449i	$-0.662531\pi$
$631$	−5.45994	+	2.26158i	−0.217357	+	0.0900321i	0.271348	+	0.962481i	$0.412531\pi$
$632$	28.5420	−	32.5459i	1.13534	−	1.29461i
$633$		0			0
$634$	2.78243	+	1.37214i	0.110504	+	0.0544947i
$635$	2.49658	+	2.84680i	0.0990737	+	0.112972i
$636$		0			0
$637$	21.1518	+	27.5655i	0.838064	+	1.09219i
$638$	5.92994	−	14.3161i	0.234769	−	0.566782i
$639$		0			0
$640$	10.2459	−	2.03804i	0.405006	−	0.0805607i
$641$	1.02804	+	15.6849i	0.0406052	+	0.619516i	0.968866	+	0.247586i	$0.0796372\pi$
$641$	1.02804	+	15.6849i	0.0406052	+	0.619516i	−0.928261	+	0.371930i	$0.878696\pi$
$642$		0			0
$643$	−10.3410	−	30.4637i	−0.407810	−	1.20137i	−0.935926	−	0.352197i	$-0.885435\pi$
$643$	−10.3410	−	30.4637i	−0.407810	−	1.20137i	0.528116	−	0.849172i	$-0.322899\pi$
$644$	1.18029	+	0.905672i	0.0465101	+	0.0356885i
$645$		0			0
$646$	35.4679	+	6.63306i	1.39547	+	0.260974i
$647$			22.2315i			0.874010i	0.899459	+	0.437005i	$0.143961\pi$
$647$			22.2315i			0.874010i	−0.899459	+	0.437005i	$0.856039\pi$
$648$		0			0
$649$	−1.75150	+	8.80540i	−0.0687525	+	0.345642i
$650$	−59.1967	+	15.8617i	−2.32188	+	0.622147i
$651$		0			0
$652$	18.3859	−	16.1240i	0.720048	−	0.631465i
$653$	3.61153	+	0.236712i	0.141330	+	0.00926325i	0.135904	−	0.990722i	$-0.456606\pi$
$653$	3.61153	+	0.236712i	0.141330	+	0.00926325i	0.00542604	+	0.999985i	$0.498273\pi$
$654$		0			0
$655$	−1.75986	+	1.35039i	−0.0687636	+	0.0527641i
$656$	14.0983	+	9.42016i	0.550445	+	0.367795i
$657$		0			0
$658$	−11.7058	−	17.5190i	−0.456340	−	0.682961i
$659$	1.86369	+	6.95540i	0.0725992	+	0.270944i	0.992678	−	0.120789i	$-0.0385424\pi$
$659$	1.86369	+	6.95540i	0.0725992	+	0.270944i	−0.920079	+	0.391733i	$0.871876\pi$
$660$		0			0
$661$	−15.2860	+	19.9211i	−0.594556	+	0.774841i	−0.989604	−	0.143820i	$-0.954061\pi$
$661$	−15.2860	+	19.9211i	−0.594556	+	0.774841i	0.395048	+	0.918661i	$0.370728\pi$
$662$	−7.95420	−	13.7771i	−0.309149	−	0.535461i
$663$		0			0
$664$	−2.71281	+	4.69873i	−0.105277	+	0.182346i
$665$	−0.522970	−	1.26256i	−0.0202799	−	0.0489600i
$666$		0			0
$667$	−2.39656	+	2.39656i	−0.0927951	+	0.0927951i
$668$	−15.2408	+	0.998934i	−0.589684	+	0.0386499i
$669$		0			0
$670$	−0.805032	+	12.2824i	−0.0311011	+	0.474511i
$671$	0.849143	+	6.44988i	0.0327808	+	0.248995i
$672$		0			0
$673$	13.9828	+	28.3543i	0.538997	+	1.09298i	0.980646	+	0.195790i	$0.0627271\pi$
$673$	13.9828	+	28.3543i	0.538997	+	1.09298i	−0.441649	+	0.897188i	$0.645606\pi$
$674$	3.53086	+	17.7508i	0.136004	+	0.683737i
$675$		0			0
$676$	−42.4386	−	42.4386i	−1.63225	−	1.63225i
$677$	30.8797	+	27.0808i	1.18680	+	1.04080i	0.998274	+	0.0587308i	$0.0187053\pi$
$677$	30.8797	+	27.0808i	1.18680	+	1.04080i	0.188529	+	0.982068i	$0.439628\pi$
$678$		0			0
$679$	−10.2472	+	5.91623i	−0.393252	+	0.227044i
$680$	−8.36405	+	2.34428i	−0.320747	+	0.0898990i
$681$		0			0
$682$	0.328391	−	2.49438i	0.0125747	−	0.0955146i
$683$	37.3073	+	7.42089i	1.42753	+	0.283953i	0.847565	−	0.530692i	$-0.178068\pi$
$683$	37.3073	+	7.42089i	1.42753	+	0.283953i	0.579961	+	0.814644i	$0.303068\pi$
$684$		0			0
$685$	−2.64560	+	1.76774i	−0.101083	+	0.0675417i
$686$	−7.69264	+	22.6618i	−0.293706	+	0.865231i
$687$		0			0
$688$	7.38070	−	0.971687i	0.281387	−	0.0370452i
$689$	−46.1558	+	6.07652i	−1.75839	+	0.231497i
$690$		0			0
$691$	−0.339026	+	0.998739i	−0.0128972	+	0.0379938i	−0.953188	−	0.302378i	$-0.902220\pi$
$691$	−0.339026	+	0.998739i	−0.0128972	+	0.0379938i	0.940291	+	0.340372i	$0.110553\pi$
$692$	−25.6274	+	17.1237i	−0.974207	+	0.650944i
$693$		0			0
$694$	−64.4715	−	12.8242i	−2.44731	−	0.486799i
$695$	−0.996985	+	7.57285i	−0.0378178	+	0.287255i
$696$		0			0
$697$	24.0948	+	13.5451i	0.912654	+	0.513056i
$698$	22.5172	−	13.0003i	0.852289	−	0.492069i
$699$		0			0
$700$	−9.91898	−	8.69871i	−0.374902	−	0.328780i
$701$	−13.4241	−	13.4241i	−0.507022	−	0.507022i	0.406589	−	0.913611i	$-0.366718\pi$
$701$	−13.4241	−	13.4241i	−0.507022	−	0.507022i	−0.913611	+	0.406589i	$0.866718\pi$
$702$		0			0
$703$	8.06685	+	40.5548i	0.304247	+	1.52955i
$704$	4.77066	+	9.67395i	0.179801	+	0.364601i
$705$		0			0
$706$	−2.20891	−	16.7783i	−0.0831333	−	0.631460i
$707$	0.635198	−	9.69125i	0.0238891	−	0.364477i
$708$		0			0
$709$	18.1644	−	1.19056i	0.682177	−	0.0447123i	0.279625	−	0.960109i	$-0.409790\pi$
$709$	18.1644	−	1.19056i	0.682177	−	0.0447123i	0.402552	+	0.915397i	$0.368123\pi$
$710$	−3.65717	+	3.65717i	−0.137251	+	0.137251i
$711$		0			0
$712$	−5.41943	−	13.0837i	−0.203102	−	0.490331i
$713$	−0.275141	+	0.476558i	−0.0103041	+	0.0178472i
$714$		0			0
$715$	1.38637	+	2.40126i	0.0518473	+	0.0898021i
$716$	−27.0655	+	35.2725i	−1.01149	+	1.31819i
$717$		0			0
$718$	2.38248	+	8.89154i	0.0889134	+	0.331829i
$719$	−13.0787	−	19.5737i	−0.487754	−	0.729976i	0.503201	−	0.864170i	$-0.332156\pi$
$719$	−13.0787	−	19.5737i	−0.487754	−	0.729976i	−0.990955	+	0.134193i	$0.957156\pi$
$720$		0			0
$721$	4.00010	+	2.67278i	0.148971	+	0.0995395i
$722$	10.7744	−	8.26747i	0.400981	−	0.307683i
$723$		0			0
$724$	66.9386	+	4.38739i	2.48775	+	0.163056i
$725$	22.5968	−	19.8168i	0.839223	−	0.735978i
$726$		0			0
$727$	−4.15025	+	1.11206i	−0.153924	+	0.0412439i	−0.334958	−	0.942233i	$-0.608722\pi$
$727$	−4.15025	+	1.11206i	−0.153924	+	0.0412439i	0.181034	+	0.983477i	$0.442056\pi$
$728$	3.26206	−	16.3995i	0.120900	−	0.607804i
$729$		0			0
$730$			3.85678i			0.142746i
$731$	11.8746	−	2.50391i	0.439196	−	0.0926104i
$732$		0			0
$733$	8.51833	+	6.53634i	0.314632	+	0.241425i	0.753989	−	0.656887i	$-0.228127\pi$
$733$	8.51833	+	6.53634i	0.314632	+	0.241425i	−0.439357	+	0.898312i	$0.644794\pi$
$734$	11.4744	+	33.8024i	0.423526	+	1.24767i
$735$		0			0
$736$	−0.0804209	−	1.22699i	−0.00296435	−	0.0452273i
$737$	−10.2027	+	2.02944i	−0.375820	+	0.0747553i
$738$		0			0
$739$	6.20725	−	14.9856i	0.228337	−	0.551255i	−0.767638	−	0.640884i	$-0.778568\pi$
$739$	6.20725	−	14.9856i	0.228337	−	0.551255i	0.995975	+	0.0896286i	$0.0285680\pi$
$740$	−13.0092	−	16.9539i	−0.478227	−	0.623237i
$741$		0			0
$742$	−10.1377	−	11.5598i	−0.372167	−	0.424375i
$743$	15.3702	+	7.57977i	0.563880	+	0.278075i	0.701806	−	0.712368i	$-0.252377\pi$
$743$	15.3702	+	7.57977i	0.563880	+	0.278075i	−0.137927	+	0.990442i	$0.544044\pi$
$744$		0			0
$745$	2.45971	−	2.80477i	0.0901169	−	0.102759i
$746$	−9.89937	+	4.10045i	−0.362442	+	0.150128i
$747$		0			0
$748$	−8.03609	−	13.5574i	−0.293829	−	0.495708i
$749$	−9.49068	−	5.47945i	−0.346782	−	0.200215i
$750$		0			0
$751$	6.32030	−	2.14545i	0.230631	−	0.0782886i	−0.203732	−	0.979027i	$-0.565307\pi$
$751$	6.32030	−	2.14545i	0.230631	−	0.0782886i	0.434363	+	0.900738i	$0.356974\pi$
$752$	7.75091	−	28.9268i	0.282647	−	1.05485i
$753$		0			0
$754$	77.4372	+	26.2864i	2.82010	+	0.957293i
$755$	0.688111	−	1.02983i	0.0250429	−	0.0374794i
$756$		0			0
$757$	9.34496	+	3.87081i	0.339648	+	0.140687i	0.545987	−	0.837794i	$-0.316155\pi$
$757$	9.34496	+	3.87081i	0.339648	+	0.140687i	−0.206339	+	0.978481i	$0.566155\pi$
$758$	31.1284	−	15.3508i	1.13063	−	0.557567i
$759$		0			0
$760$	3.40244	−	6.89947i	0.123419	−	0.250270i
$761$	11.8235	+	3.16811i	0.428603	+	0.114844i	0.466670	−	0.884431i	$-0.345454\pi$
$761$	11.8235	+	3.16811i	0.428603	+	0.114844i	−0.0380675	+	0.999275i	$0.512120\pi$
$762$		0			0
$763$	−0.767006	−	0.100978i	−0.0277675	−	0.00365566i
$764$	80.3714			2.90774
$765$		0			0
$766$	3.53617			0.127767
$767$	−46.9748	−	6.18434i	−1.69616	−	0.223304i
$768$		0			0
$769$	−21.6739	−	5.80750i	−0.781581	−	0.209424i	−0.154099	−	0.988055i	$-0.549248\pi$
$769$	−21.6739	−	5.80750i	−0.781581	−	0.209424i	−0.627482	+	0.778631i	$0.715914\pi$
$770$	−0.405027	+	0.821313i	−0.0145961	+	0.0295981i
$771$		0			0
$772$	−30.2368	+	14.9111i	−1.08825	+	0.536664i
$773$	−29.2000	−	12.0950i	−1.05025	−	0.435029i	−0.210270	−	0.977643i	$-0.567434\pi$
$773$	−29.2000	−	12.0950i	−1.05025	−	0.435029i	−0.839982	+	0.542615i	$0.817434\pi$
$774$		0			0
$775$	2.71108	−	4.05742i	0.0973848	−	0.145747i
$776$	−63.0725	−	21.4102i	−2.26417	−	0.768583i
$777$		0			0
$778$	−23.6743	+	88.3537i	−0.848765	+	3.16763i
$779$	−23.1803	+	7.86864i	−0.830519	+	0.281923i
$780$		0			0
$781$	−3.78544	−	2.18552i	−0.135454	−	0.0782041i
$782$	0.750379	+	5.23500i	0.0268335	+	0.187203i
$783$		0			0
$784$	−15.0688	+	6.24169i	−0.538170	+	0.222917i
$785$	3.18545	−	3.63231i	0.113694	−	0.129643i
$786$		0			0
$787$	25.7992	+	12.7228i	0.919642	+	0.453517i	0.839557	−	0.543271i	$-0.182814\pi$
$787$	25.7992	+	12.7228i	0.919642	+	0.453517i	0.0800845	+	0.996788i	$0.474481\pi$
$788$	−44.9823	−	51.2925i	−1.60243	−	1.82722i
$789$		0			0
$790$	−7.61660	−	9.92615i	−0.270987	−	0.353157i
$791$	1.35312	−	3.26673i	0.0481115	−	0.116152i
$792$		0			0
$793$	−33.6727	+	6.69791i	−1.19575	+	0.237850i
$794$	0.868293	+	13.2476i	0.0308146	+	0.470140i
$795$		0			0
$796$	30.3207	+	89.3220i	1.07469	+	3.16593i
$797$	−20.2134	−	15.5103i	−0.715994	−	0.549401i	0.185262	−	0.982689i	$-0.440687\pi$
$797$	−20.2134	−	15.5103i	−0.715994	−	0.549401i	−0.901256	+	0.433288i	$0.857353\pi$
$798$		0			0
$799$	8.97439	−	47.9873i	0.317491	−	1.69767i
$800$			10.9041i			0.385517i
$801$		0			0
$802$	9.58303	−	48.1771i	0.338389	−	1.70119i
$803$	−3.14843	+	0.843619i	−0.111106	+	0.0297707i
$804$		0			0
$805$	0.150590	−	0.132064i	0.00530759	−	0.00465463i
$806$	13.2490	+	0.868385i	0.466676	+	0.0305876i
$807$		0			0
$808$	43.3735	−	33.2817i	1.52588	−	1.17085i
$809$	1.47986	+	0.988813i	0.0520292	+	0.0347648i	0.581313	−	0.813680i	$-0.302539\pi$
$809$	1.47986	+	0.988813i	0.0520292	+	0.0347648i	−0.529284	+	0.848445i	$0.677539\pi$
$810$		0			0
$811$	27.6326	+	41.3552i	0.970314	+	1.45218i	0.890295	+	0.455383i	$0.150498\pi$
$811$	27.6326	+	41.3552i	0.970314	+	1.45218i	0.0800181	+	0.996793i	$0.474502\pi$
$812$	4.55634	+	17.0045i	0.159896	+	0.596740i
$813$		0			0
$814$	16.8677	−	21.9824i	0.591213	−	0.770484i
$815$	−1.64618	−	2.85126i	−0.0576630	−	0.0998752i
$816$		0			0
$817$	−5.37378	+	9.30767i	−0.188005	+	0.325634i
$818$	−21.4077	−	51.6828i	−0.748504	−	1.80705i
$819$		0			0
$820$	8.94581	−	8.94581i	0.312401	−	0.312401i
$821$	36.8211	−	2.41338i	1.28506	−	0.0842275i	0.592492	−	0.805576i	$-0.298144\pi$
$821$	36.8211	−	2.41338i	1.28506	−	0.0842275i	0.692572	+	0.721349i	$0.256477\pi$
$822$		0			0
$823$	−0.722027	+	11.0160i	−0.0251683	+	0.383994i	0.966630	+	0.256178i	$0.0824633\pi$
$823$	−0.722027	+	11.0160i	−0.0251683	+	0.383994i	−0.991798	+	0.127816i	$0.959203\pi$
$824$	3.53484	+	26.8498i	0.123142	+	0.935356i
$825$		0			0
$826$	−6.92103	−	14.0345i	−0.240813	−	0.488321i
$827$	−4.01743	−	20.1970i	−0.139700	−	0.702318i	−0.985616	−	0.169002i	$-0.945946\pi$
$827$	−4.01743	−	20.1970i	−0.139700	−	0.702318i	0.845916	−	0.533316i	$-0.179054\pi$
$828$		0			0
$829$	−10.5506	−	10.5506i	−0.366437	−	0.366437i	0.499739	−	0.866176i	$-0.333429\pi$
$829$	−10.5506	−	10.5506i	−0.366437	−	0.366437i	−0.866176	+	0.499739i	$0.833429\pi$
$830$	1.17901	+	1.03396i	0.0409241	+	0.0358894i
$831$		0			0
$832$	−49.2974	+	28.4619i	−1.70908	+	0.986738i
$833$	−23.7102	+	12.0326i	−0.821511	+	0.416905i
$834$		0			0
$835$	−0.268400	+	2.03870i	−0.00928836	+	0.0705521i
$836$	13.6893	+	2.72297i	0.473454	+	0.0941758i
$837$		0			0
$838$	69.0128	−	46.1129i	2.38401	−	1.59294i
$839$	7.12023	−	20.9755i	0.245818	−	0.724155i	−0.752063	−	0.659091i	$-0.770941\pi$
$839$	7.12023	−	20.9755i	0.245818	−	0.724155i	0.997881	−	0.0650645i	$-0.0207253\pi$
$840$		0			0
$841$	−11.0100	+	1.44950i	−0.379656	+	0.0499827i
$842$	−7.18358	+	0.945736i	−0.247562	+	0.0325922i
$843$		0			0
$844$	18.1870	−	53.5773i	0.626023	−	1.84421i
$845$	−6.71844	+	4.48912i	−0.231121	+	0.154430i
$846$		0			0
$847$	7.25139	+	1.44239i	0.249161	+	0.0495612i
$848$	2.85245	−	21.6665i	0.0979534	−	0.744030i
$849$		0			0
$850$	−3.60377	−	46.7590i	−0.123608	−	1.60382i
$851$	−5.24846	+	3.03020i	−0.179915	+	0.103874i
$852$		0			0
$853$	20.4168	+	17.9051i	0.699058	+	0.613057i	0.933290	−	0.359123i	$-0.116924\pi$
$853$	20.4168	+	17.9051i	0.699058	+	0.613057i	−0.234232	+	0.972181i	$0.575258\pi$
$854$	−8.01784	−	8.01784i	−0.274365	−	0.274365i
$855$		0			0
$856$	−12.0351	−	60.5046i	−0.411351	−	2.06800i
$857$	−14.7603	−	29.9309i	−0.504202	−	1.02242i	−0.989017	−	0.147804i	$-0.952780\pi$
$857$	−14.7603	−	29.9309i	−0.504202	−	1.02242i	0.484815	−	0.874617i	$-0.338887\pi$
$858$		0			0
$859$	−1.82866	−	13.8901i	−0.0623931	−	0.473923i	−0.993907	−	0.110218i	$-0.964845\pi$
$859$	−1.82866	−	13.8901i	−0.0623931	−	0.473923i	0.931514	−	0.363705i	$-0.118488\pi$
$860$	0.363281	−	5.54260i	0.0123878	−	0.189001i
$861$		0			0
$862$	−93.6478	+	6.13800i	−3.18966	+	0.209061i
$863$	−4.06464	+	4.06464i	−0.138362	+	0.138362i	−0.772895	−	0.634533i	$-0.781192\pi$
$863$	−4.06464	+	4.06464i	−0.138362	+	0.138362i	0.634533	+	0.772895i	$0.281192\pi$
$864$		0			0
$865$	1.58798	+	3.83371i	0.0539928	+	0.130350i
$866$	−28.9353	+	50.1175i	−0.983263	+	1.70306i
$867$		0			0
$868$	1.42913	+	2.47533i	0.0485078	+	0.0840181i
$869$	6.43705	−	8.38892i	0.218362	−	0.284575i
$870$		0			0
$871$	−14.2088	−	53.0279i	−0.481446	−	1.79678i
$872$	−2.41945	−	3.62096i	−0.0819329	−	0.122621i
$873$		0			0
$874$	−3.89427	−	2.60207i	−0.131726	−	0.0880163i
$875$	−2.89372	+	2.22043i	−0.0978255	+	0.0750642i
$876$		0			0
$877$	6.51572	+	0.427063i	0.220020	+	0.0144209i	0.175015	−	0.984566i	$-0.444003\pi$
$877$	6.51572	+	0.427063i	0.220020	+	0.0144209i	0.0450057	+	0.998987i	$0.485669\pi$
$878$	68.5022	−	60.0748i	2.31184	−	2.02743i
$879$		0			0
$880$	−1.25723	+	0.336874i	−0.0423813	+	0.0113560i
$881$	−5.82712	+	29.2949i	−0.196321	+	0.986971i	0.749431	+	0.662082i	$0.230327\pi$
$881$	−5.82712	+	29.2949i	−0.196321	+	0.986971i	−0.945752	+	0.324889i	$0.894673\pi$
$882$		0			0
$883$			49.5960i			1.66904i	0.550978	+	0.834520i	$0.314255\pi$
$883$			49.5960i			1.66904i	−0.550978	+	0.834520i	$0.685745\pi$
$884$	68.6211	−	46.9984i	2.30798	−	1.58073i
$885$		0			0
$886$	−72.8728	−	55.9173i	−2.44821	−	1.87858i
$887$	−4.91600	−	14.4821i	−0.165063	−	0.486261i	0.832654	−	0.553794i	$-0.186820\pi$
$887$	−4.91600	−	14.4821i	−0.165063	−	0.486261i	−0.997717	+	0.0675332i	$0.978487\pi$
$888$		0			0
$889$	−0.364792	−	5.56565i	−0.0122347	−	0.186666i
$890$	−4.01450	+	0.798533i	−0.134566	+	0.0267669i
$891$		0			0
$892$	−22.0650	+	53.2696i	−0.738791	+	1.78360i
$893$	26.3199	+	34.3008i	0.880763	+	1.14783i
$894$		0			0
$895$	3.94665	+	4.50029i	0.131922	+	0.150428i
$896$	−13.8014	−	6.80610i	−0.461073	−	0.227376i
$897$		0			0
$898$	−25.4964	+	29.0731i	−0.850825	+	0.970181i
$899$	−6.01584	+	2.49184i	−0.200640	+	0.0831077i
$900$		0			0
$901$	1.92212	−	35.5731i	0.0640351	−	1.18511i
$902$	14.2060	+	8.20183i	0.473008	+	0.273091i
$903$		0			0
$904$	18.8479	−	6.39801i	0.626872	−	0.212794i
$905$	2.33749	−	8.72364i	0.0777008	−	0.289983i
$906$		0			0
$907$	0.302207	+	0.102585i	0.0100346	+	0.00340629i	0.326452	−	0.945214i	$-0.394147\pi$
$907$	0.302207	+	0.102585i	0.0100346	+	0.00340629i	−0.316418	+	0.948620i	$0.602480\pi$
$908$	−37.0361	+	55.4284i	−1.22909	+	1.83946i
$909$		0			0
$910$	−4.46492	−	1.84943i	−0.148011	−	0.0613080i
$911$	14.5927	−	7.19632i	0.483477	−	0.238425i	−0.184181	−	0.982892i	$-0.558963\pi$
$911$	14.5927	−	7.19632i	0.483477	−	0.238425i	0.667659	+	0.744468i	$0.267297\pi$
$912$		0			0
$913$	−0.586170	+	1.18864i	−0.0193994	+	0.0393381i
$914$	45.4421	+	12.1762i	1.50309	+	0.402752i
$915$		0			0
$916$	−29.4817	−	3.88134i	−0.974103	−	0.128243i
$917$	3.26759			0.107905
$918$		0			0
$919$	−32.6543			−1.07716			−0.538582	−	0.842573i	$-0.681040\pi$
$919$	−32.6543			−1.07716			−0.538582	+	0.842573i	$0.681040\pi$
$920$	1.11786	+	0.147169i	0.0368546	+	0.00485200i
$921$		0			0
$922$	−31.0328	−	8.31521i	−1.02201	−	0.273847i
$923$	10.2026	−	20.6889i	0.335823	−	0.680983i
$924$		0			0
$925$	48.2003	−	23.7698i	1.58482	−	0.781545i
$926$	2.09494	+	0.867754i	0.0688441	+	0.0285162i
$927$		0			0
$928$	8.08361	−	12.0980i	0.265357	−	0.397136i
$929$	−13.4095	−	4.55192i	−0.439952	−	0.149344i	0.0926698	−	0.995697i	$-0.470460\pi$
$929$	−13.4095	−	4.55192i	−0.439952	−	0.149344i	−0.532622	+	0.846353i	$0.678793\pi$
$930$		0			0
$931$	6.09453	−	22.7451i	0.199740	−	0.745440i
$932$	65.5238	−	22.2423i	2.14630	−	0.728572i
$933$		0			0
$934$	−62.6642	−	36.1792i	−2.05044	−	1.18382i
$935$	−2.00125	+	0.705032i	−0.0654479	+	0.0230570i
$936$		0			0
$937$	−25.9564	+	10.7515i	−0.847959	+	0.351236i	−0.763987	−	0.645232i	$-0.776761\pi$
$937$	−25.9564	+	10.7515i	−0.847959	+	0.351236i	−0.0839723	+	0.996468i	$0.526761\pi$
$938$	11.9548	−	13.6318i	0.390338	−	0.445096i
$939$		0			0
$940$	−20.0402	−	9.88275i	−0.653641	−	0.322340i
$941$	3.68514	+	4.20210i	0.120132	+	0.136984i	0.808780	−	0.588112i	$-0.200129\pi$
$941$	3.68514	+	4.20210i	0.120132	+	0.136984i	−0.688647	+	0.725096i	$0.741795\pi$
$942$		0			0
$943$	−2.18414	−	2.84643i	−0.0711254	−	0.0926924i
$944$	8.51135	−	20.5482i	0.277021	−	0.668787i
$945$		0			0
$946$	7.06358	−	1.40503i	0.229657	−	0.0456816i
$947$	1.86646	+	28.4767i	0.0606518	+	0.925367i	0.914434	+	0.404736i	$0.132637\pi$
$947$	1.86646	+	28.4767i	0.0606518	+	0.925367i	−0.853782	+	0.520631i	$0.825697\pi$
$948$		0			0
$949$	−5.52930	−	16.2888i	−0.179489	−	0.528756i
$950$	32.9507	+	25.2839i	1.06906	+	0.820319i
$951$		0			0
$952$	11.8768	+	4.76068i	0.384928	+	0.154294i
$953$			37.4674i			1.21369i	0.794821	+	0.606844i	$0.207565\pi$
$953$			37.4674i			1.21369i	−0.794821	+	0.606844i	$0.792435\pi$
$954$		0			0
$955$	2.11098	−	10.6126i	0.0683096	−	0.343416i
$956$	−62.6243	+	16.7801i	−2.02542	+	0.542709i
$957$		0			0
$958$	−38.7863	+	34.0147i	−1.25313	+	1.09897i
$959$	4.67695	+	0.306543i	0.151026	+	0.00989880i
$960$		0			0
$961$	23.7552	−	18.2280i	0.766297	−	0.588000i
$962$	121.584	+	81.2398i	3.92002	+	2.61927i
$963$		0			0
$964$	25.8651	+	38.7099i	0.833060	+	1.24676i
$965$	1.17476	+	4.38425i	0.0378167	+	0.141134i
$966$		0			0
$967$	−2.82928	+	3.68719i	−0.0909836	+	0.118572i	−0.836627	−	0.547773i	$-0.815476\pi$
$967$	−2.82928	+	3.68719i	−0.0909836	+	0.118572i	0.745643	+	0.666345i	$0.232142\pi$
$968$	20.8097	+	36.0434i	0.668848	+	1.15848i
$969$		0			0
$970$	−9.62576	+	16.6723i	−0.309065	+	0.535316i
$971$	−17.1196	−	41.3304i	−0.549394	−	1.32636i	−0.917930	−	0.396742i	$-0.870141\pi$
$971$	−17.1196	−	41.3304i	−0.549394	−	1.32636i	0.368536	−	0.929614i	$-0.379859\pi$
$972$		0			0
$973$	7.95592	−	7.95592i	0.255055	−	0.255055i
$974$	23.9758	−	1.57146i	0.768233	−	0.0503527i
$975$		0			0
$976$	1.05406	−	16.0818i	0.0337396	−	0.514767i
$977$	3.87397	+	29.4257i	0.123939	+	0.941411i	0.934551	+	0.355828i	$0.115801\pi$
$977$	3.87397	+	29.4257i	0.123939	+	0.941411i	−0.810612	+	0.585583i	$0.800866\pi$
$978$		0			0
$979$	−1.52999	−	3.10251i	−0.0488987	−	0.0991567i
$980$	2.37418	+	11.9358i	0.0758404	+	0.381276i
$981$		0			0
$982$	−7.32889	−	7.32889i	−0.233874	−	0.233874i
$983$	−21.7491	−	19.0734i	−0.693688	−	0.608348i	0.238148	−	0.971229i	$-0.423460\pi$
$983$	−21.7491	−	19.0734i	−0.693688	−	0.608348i	−0.931835	+	0.362881i	$0.881793\pi$
$984$		0			0
$985$	−7.95436	+	4.59245i	−0.253447	+	0.146328i
$986$	−30.6659	+	54.5504i	−0.976601	+	1.73724i
$987$		0			0
$988$	−9.61446	+	73.0291i	−0.305877	+	2.32337i
$989$	−1.54496	−	0.307311i	−0.0491268	−	0.00977193i
$990$		0			0
$991$	−15.8269	+	10.5752i	−0.502759	+	0.335933i	−0.780951	−	0.624593i	$-0.785265\pi$
$991$	−15.8269	+	10.5752i	−0.502759	+	0.335933i	0.278191	+	0.960526i	$0.410265\pi$
$992$	0.759360	−	2.23700i	0.0241097	−	0.0710249i
$993$		0			0
$994$	7.55341	−	0.994426i	0.239580	−	0.0315413i
$995$	12.5909	−	1.65762i	0.399157	−	0.0525500i
$996$		0			0
$997$	−10.2998	+	30.3423i	−0.326199	+	0.960951i	0.652879	+	0.757463i	$0.273561\pi$
$997$	−10.2998	+	30.3423i	−0.326199	+	0.960951i	−0.979077	+	0.203488i	$0.934772\pi$
$998$	−46.6365	+	31.1615i	−1.47625	+	0.986400i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.116.1		256
3.2	odd	2		153.2.s.a.65.16	yes	256
9.4	even	3		153.2.s.a.14.16	yes	256
9.5	odd	6	inner	459.2.y.a.422.1		256
17.11	odd	16	inner	459.2.y.a.62.1		256
51.11	even	16		153.2.s.a.11.16	✓	256
153.113	even	48	inner	459.2.y.a.368.1		256
153.130	odd	48		153.2.s.a.113.16	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.16	✓	256	51.11	even	16
153.2.s.a.14.16	yes	256	9.4	even	3
153.2.s.a.65.16	yes	256	3.2	odd	2
153.2.s.a.113.16	yes	256	153.130	odd	48
459.2.y.a.62.1		256	17.11	odd	16	inner
459.2.y.a.116.1		256	1.1	even	1	trivial
459.2.y.a.368.1		256	153.113	even	48	inner
459.2.y.a.422.1		256	9.5	odd	6	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-2.37615 - 0.312826i) q^{2} +(3.61637 + 0.969004i) q^{4} +(0.222937 - 0.452071i) q^{5} +(-0.665919 + 0.328395i) q^{7} +(-3.86148 - 1.59948i) q^{8} +(-0.671150 + 1.00445i) q^{10} +(-0.966772 - 0.328175i) q^{11} +(1.39452 - 5.20440i) q^{13} +(1.68505 - 0.571999i) q^{14} +(2.19038 + 1.26462i) q^{16} +(3.71857 + 1.78107i) q^{17} +(-3.37354 + 1.39737i) q^{19} +(1.24428 - 1.41883i) q^{20} +(2.19453 + 1.08222i) q^{22} +(-0.352872 - 0.402373i) q^{23} +(2.88914 + 3.76520i) q^{25} +(-4.94165 + 11.9302i) q^{26} +(-2.72643 + 0.542320i) q^{28} +(-0.414188 - 6.31929i) q^{29} +(-0.330507 - 0.973643i) q^{31} +(1.82278 + 1.39867i) q^{32} +(-8.27872 - 5.39536i) q^{34} +0.374254i q^{35} +(2.20919 - 11.1064i) q^{37} +(8.45317 - 2.26502i) q^{38} +(-1.58394 + 1.38908i) q^{40} +(6.68958 + 0.438458i) q^{41} +(2.33510 - 1.79179i) q^{43} +(-3.17821 - 2.12361i) q^{44} +(0.712603 + 1.06649i) q^{46} +(-3.06452 - 11.4370i) q^{47} +(-3.92573 + 5.11610i) q^{49} +(-5.68718 - 9.85048i) q^{50} +(10.0862 - 17.4698i) q^{52} +(-3.30651 - 7.98262i) q^{53} +(-0.363887 + 0.363887i) q^{55} +(3.09669 - 0.202968i) q^{56} +(-0.992666 + 15.1452i) q^{58} +(-1.14780 - 8.71842i) q^{59} +(-2.81827 - 5.71489i) q^{61} +(0.480754 + 2.41691i) q^{62} +(-7.47053 - 7.47053i) q^{64} +(-2.04187 - 1.79067i) q^{65} +(8.82398 - 5.09452i) q^{67} +(11.7219 + 10.0443i) q^{68} +(0.117076 - 0.889283i) q^{70} +(4.19907 + 0.835247i) q^{71} +(2.65455 - 1.77371i) q^{73} +(-8.72372 + 25.6993i) q^{74} +(-13.5540 + 1.78442i) q^{76} +(0.751563 - 0.0989451i) q^{77} +(-3.32914 + 9.80734i) q^{79} +(1.06001 - 0.708279i) q^{80} +(-15.7583 - 3.13452i) q^{82} +(0.169437 - 1.28700i) q^{83} +(1.63418 - 1.28399i) q^{85} +(-6.10907 + 3.52707i) q^{86} +(3.20826 + 2.81357i) q^{88} +(2.39586 + 2.39586i) q^{89} +(0.780465 + 3.92366i) q^{91} +(-0.886215 - 1.79707i) q^{92} +(3.70399 + 28.1346i) q^{94} +(-0.120377 + 1.83661i) q^{95} +(15.9021 - 1.04228i) q^{97} +(10.9286 - 10.9286i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 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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