LMFDB - Embedded newform 243.2.g.a.10.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(10,243)] 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("243.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			10.7
Character	$\chi$	$=$	243.10
Dual form			243.2.g.a.73.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.89071 + 0.949549i) q^{2} +(1.47882 + 1.98639i) q^{4} +(1.11651 + 3.72940i) q^{5} +(-1.32100 - 3.06243i) q^{7} +(0.175036 + 0.992677i) q^{8} +(-1.43025 + 8.11138i) q^{10} +(-0.736337 + 0.174515i) q^{11} +(-2.07722 - 1.36621i) q^{13} +(0.410296 - 7.04452i) q^{14} +(0.808837 - 2.70170i) q^{16} +(0.700932 - 0.255119i) q^{17} +(4.21736 + 1.53499i) q^{19} +(-5.75694 + 7.73291i) q^{20} +(-1.55791 - 0.369231i) q^{22} +(0.905723 - 2.09970i) q^{23} +(-8.48436 + 5.58025i) q^{25} +(-2.63013 - 4.55552i) q^{26} +(4.12967 - 7.15280i) q^{28} +(0.0269788 + 0.463208i) q^{29} +(3.91546 - 0.457651i) q^{31} +(5.47813 - 5.80647i) q^{32} +(1.56751 + 0.183215i) q^{34} +(9.94610 - 8.34577i) q^{35} +(-3.64375 - 3.05747i) q^{37} +(6.51625 + 6.90682i) q^{38} +(-3.50665 + 1.76111i) q^{40} +(-4.37210 + 2.19575i) q^{41} +(-4.07702 - 4.32138i) q^{43} +(-1.43556 - 1.20458i) q^{44} +(3.70623 - 3.10990i) q^{46} +(-10.6936 - 1.24990i) q^{47} +(-2.82973 + 2.99934i) q^{49} +(-21.3402 + 2.49431i) q^{50} +(-0.357995 - 6.14654i) q^{52} +(-5.75294 + 9.96438i) q^{53} +(-1.47296 - 2.55124i) q^{55} +(2.80878 - 1.84736i) q^{56} +(-0.388830 + 0.901409i) q^{58} +(4.03735 + 0.956869i) q^{59} +(0.159571 - 0.214341i) q^{61} +(7.83755 + 2.85264i) q^{62} +(10.5709 - 3.84748i) q^{64} +(2.77590 - 9.27214i) q^{65} +(0.111496 - 1.91430i) q^{67} +(1.54332 + 1.01506i) q^{68} +(26.7299 - 6.33510i) q^{70} +(-1.17278 + 6.65118i) q^{71} +(1.37723 + 7.81064i) q^{73} +(-3.98605 - 9.24071i) q^{74} +(3.18760 + 10.6473i) q^{76} +(1.50714 + 2.02444i) q^{77} +(3.85762 + 1.93737i) q^{79} +10.9788 q^{80} -10.3513 q^{82} +(2.27599 + 1.14304i) q^{83} +(1.73403 + 2.32921i) q^{85} +(-3.60508 - 12.0418i) q^{86} +(-0.302122 - 0.700398i) q^{88} +(0.935549 + 5.30576i) q^{89} +(-1.43990 + 8.16609i) q^{91} +(5.51024 - 1.30595i) q^{92} +(-19.0315 - 12.5172i) q^{94} +(-1.01588 + 17.4421i) q^{95} +(-2.72130 + 9.08977i) q^{97} +(-8.19821 + 2.98391i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

Coefficient data

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

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

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

$2$	1.89071	+	0.949549i	1.33693	+	0.671433i	0.966317	−	0.257354i	$-0.0828506\pi$
$2$	1.89071	+	0.949549i	1.33693	+	0.671433i	0.370615	+	0.928786i	$0.379147\pi$
$3$		0			0
$3$		0			0
$4$	1.47882	+	1.98639i	0.739408	+	0.993197i
$5$	1.11651	+	3.72940i	0.499317	+	1.66784i	0.721172	+	0.692756i	$0.243604\pi$
$5$	1.11651	+	3.72940i	0.499317	+	1.66784i	−0.221854	+	0.975080i	$0.571211\pi$
$6$		0			0
$7$	−1.32100	−	3.06243i	−0.499292	−	1.15749i	−0.962510	−	0.271245i	$-0.912565\pi$
$7$	−1.32100	−	3.06243i	−0.499292	−	1.15749i	0.463218	−	0.886244i	$-0.346695\pi$
$8$	0.175036	+	0.992677i	0.0618845	+	0.350964i
$9$		0			0
$10$	−1.43025	+	8.11138i	−0.452286	+	2.56504i
$11$	−0.736337	+	0.174515i	−0.222014	+	0.0526183i	−0.340117	−	0.940383i	$-0.610467\pi$
$11$	−0.736337	+	0.174515i	−0.222014	+	0.0526183i	0.118103	+	0.993001i	$0.462319\pi$
$12$		0			0
$13$	−2.07722	−	1.36621i	−0.576116	−	0.378918i	0.227757	−	0.973718i	$-0.426861\pi$
$13$	−2.07722	−	1.36621i	−0.576116	−	0.378918i	−0.803873	+	0.594800i	$0.797231\pi$
$14$	0.410296	−	7.04452i	0.109656	−	1.88273i
$15$		0			0
$16$	0.808837	−	2.70170i	0.202209	−	0.675426i
$17$	0.700932	−	0.255119i	0.170001	−	0.0618753i	−0.255617	−	0.966778i	$-0.582279\pi$
$17$	0.700932	−	0.255119i	0.170001	−	0.0618753i	0.425619	+	0.904903i	$0.360057\pi$
$18$		0			0
$19$	4.21736	+	1.53499i	0.967530	+	0.352152i	0.776980	−	0.629526i	$-0.216751\pi$
$19$	4.21736	+	1.53499i	0.967530	+	0.352152i	0.190550	+	0.981678i	$0.438973\pi$
$20$	−5.75694	+	7.73291i	−1.28729	+	1.72913i
$21$		0			0
$22$	−1.55791	−	0.369231i	−0.332147	−	0.0787203i
$23$	0.905723	−	2.09970i	0.188856	−	0.437818i	−0.797312	−	0.603568i	$-0.793745\pi$
$23$	0.905723	−	2.09970i	0.188856	−	0.437818i	0.986168	+	0.165750i	$0.0530044\pi$
$24$		0			0
$25$	−8.48436	+	5.58025i	−1.69687	+	1.11605i
$26$	−2.63013	−	4.55552i	−0.515811	−	0.893410i
$27$		0			0
$28$	4.12967	−	7.15280i	0.780435	−	1.35175i
$29$	0.0269788	+	0.463208i	0.00500984	+	0.0860156i	0.999886	−	0.0150831i	$-0.00480127\pi$
$29$	0.0269788	+	0.463208i	0.00500984	+	0.0860156i	−0.994876	+	0.101099i	$0.967764\pi$
$30$		0			0
$31$	3.91546	−	0.457651i	0.703237	−	0.0821966i	0.243044	−	0.970015i	$-0.421854\pi$
$31$	3.91546	−	0.457651i	0.703237	−	0.0821966i	0.460193	+	0.887819i	$0.347780\pi$
$32$	5.47813	−	5.80647i	0.968405	−	1.02645i
$33$		0			0
$34$	1.56751	+	0.183215i	0.268825	+	0.0314212i
$35$	9.94610	−	8.34577i	1.68120	−	1.41069i
$36$		0			0
$37$	−3.64375	−	3.05747i	−0.599029	−	0.502645i	0.292104	−	0.956387i	$-0.405645\pi$
$37$	−3.64375	−	3.05747i	−0.599029	−	0.502645i	−0.891134	+	0.453741i	$0.850089\pi$
$38$	6.51625	+	6.90682i	1.05708	+	1.12043i
$39$		0			0
$40$	−3.50665	+	1.76111i	−0.554451	+	0.278456i
$41$	−4.37210	+	2.19575i	−0.682807	+	0.342919i	−0.756160	−	0.654387i	$-0.772927\pi$
$41$	−4.37210	+	2.19575i	−0.682807	+	0.342919i	0.0733521	+	0.997306i	$0.476630\pi$
$42$		0			0
$43$	−4.07702	−	4.32138i	−0.621739	−	0.659005i	0.337591	−	0.941293i	$-0.390388\pi$
$43$	−4.07702	−	4.32138i	−0.621739	−	0.659005i	−0.959330	+	0.282288i	$0.908907\pi$
$44$	−1.43556	−	1.20458i	−0.216419	−	0.181597i
$45$		0			0
$46$	3.70623	−	3.10990i	0.546454	−	0.458529i
$47$	−10.6936	−	1.24990i	−1.55981	−	0.182316i	−0.708020	−	0.706192i	$-0.750411\pi$
$47$	−10.6936	−	1.24990i	−1.55981	−	0.182316i	−0.851795	+	0.523876i	$0.824485\pi$
$48$		0			0
$49$	−2.82973	+	2.99934i	−0.404247	+	0.428477i
$50$	−21.3402	+	2.49431i	−3.01796	+	0.352748i
$51$		0			0
$52$	−0.357995	−	6.14654i	−0.0496450	−	0.852372i
$53$	−5.75294	+	9.96438i	−0.790227	+	1.36871i	0.135600	+	0.990764i	$0.456704\pi$
$53$	−5.75294	+	9.96438i	−0.790227	+	1.36871i	−0.925826	+	0.377949i	$0.876629\pi$
$54$		0			0
$55$	−1.47296	−	2.55124i	−0.198614	−	0.344010i
$56$	2.80878	−	1.84736i	0.375339	−	0.246864i
$57$		0			0
$58$	−0.388830	+	0.901409i	−0.0510559	+	0.118361i
$59$	4.03735	+	0.956869i	0.525618	+	0.124574i	0.484854	−	0.874595i	$-0.338873\pi$
$59$	4.03735	+	0.956869i	0.525618	+	0.124574i	0.0407637	+	0.999169i	$0.487021\pi$
$60$		0			0
$61$	0.159571	−	0.214341i	0.0204310	−	0.0274436i	−0.791790	−	0.610793i	$-0.790851\pi$
$61$	0.159571	−	0.214341i	0.0204310	−	0.0274436i	0.812221	+	0.583349i	$0.198258\pi$
$62$	7.83755	+	2.85264i	0.995370	+	0.362285i
$63$		0			0
$64$	10.5709	−	3.84748i	1.32136	−	0.480935i
$65$	2.77590	−	9.27214i	0.344308	−	1.15007i
$66$		0			0
$67$	0.111496	−	1.91430i	0.0136213	−	0.233870i	−0.984625	−	0.174679i	$-0.944111\pi$
$67$	0.111496	−	1.91430i	0.0136213	−	0.233870i	0.998247	−	0.0591902i	$-0.0188518\pi$
$68$	1.54332	+	1.01506i	0.187155	+	0.123094i
$69$		0			0
$70$	26.7299	−	6.33510i	3.19483	−	0.757189i
$71$	−1.17278	+	6.65118i	−0.139184	+	0.789350i	0.832671	+	0.553768i	$0.186811\pi$
$71$	−1.17278	+	6.65118i	−0.139184	+	0.789350i	−0.971855	+	0.235582i	$0.924300\pi$
$72$		0			0
$73$	1.37723	+	7.81064i	0.161192	+	0.914167i	0.952904	+	0.303272i	$0.0980791\pi$
$73$	1.37723	+	7.81064i	0.161192	+	0.914167i	−0.791712	+	0.610895i	$0.790810\pi$
$74$	−3.98605	−	9.24071i	−0.463369	−	1.07421i
$75$		0			0
$76$	3.18760	+	10.6473i	0.365643	+	1.22133i
$77$	1.50714	+	2.02444i	0.171755	+	0.230707i
$78$		0			0
$79$	3.85762	+	1.93737i	0.434016	+	0.217971i	0.652373	−	0.757898i	$-0.273773\pi$
$79$	3.85762	+	1.93737i	0.434016	+	0.217971i	−0.218357	+	0.975869i	$0.570070\pi$
$80$	10.9788			1.22747
$81$		0			0
$82$	−10.3513			−1.14311
$83$	2.27599	+	1.14304i	0.249822	+	0.125465i	0.569304	−	0.822127i	$-0.307213\pi$
$83$	2.27599	+	1.14304i	0.249822	+	0.125465i	−0.319482	+	0.947592i	$0.603509\pi$
$84$		0			0
$85$	1.73403	+	2.32921i	0.188082	+	0.252639i
$86$	−3.60508	−	12.0418i	−0.388746	−	1.29850i
$87$		0			0
$88$	−0.302122	−	0.700398i	−0.0322063	−	0.0746627i
$89$	0.935549	+	5.30576i	0.0991680	+	0.562410i	0.993390	+	0.114786i	$0.0366184\pi$
$89$	0.935549	+	5.30576i	0.0991680	+	0.562410i	−0.894222	+	0.447623i	$0.852271\pi$
$90$		0			0
$91$	−1.43990	+	8.16609i	−0.150943	+	0.856039i
$92$	5.51024	−	1.30595i	0.574482	−	0.136155i
$93$		0			0
$94$	−19.0315	−	12.5172i	−1.96295	−	1.29106i
$95$	−1.01588	+	17.4421i	−0.104227	+	1.78952i
$96$		0			0
$97$	−2.72130	+	9.08977i	−0.276306	+	0.922926i	0.701368	+	0.712799i	$0.252573\pi$
$97$	−2.72130	+	9.08977i	−0.276306	+	0.922926i	−0.977674	+	0.210127i	$0.932612\pi$
$98$	−8.19821	+	2.98391i	−0.828145	+	0.301420i
$99$		0			0
$100$	−23.6314	−	8.60112i	−2.36314	−	0.860112i
$101$	7.34963	−	9.87227i	0.731315	−	0.982327i	−0.268503	−	0.963279i	$-0.586529\pi$
$101$	7.34963	−	9.87227i	0.731315	−	0.982327i	0.999819	−	0.0190483i	$-0.00606363\pi$
$102$		0			0
$103$	16.2209	+	3.84443i	1.59830	+	0.378803i	0.930719	−	0.365736i	$-0.119183\pi$
$103$	16.2209	+	3.84443i	1.59830	+	0.378803i	0.667578	+	0.744539i	$0.267331\pi$
$104$	0.992615	−	2.30114i	0.0973339	−	0.225645i
$105$		0			0
$106$	−20.3388	+	13.3770i	−1.97548	+	1.29929i
$107$	−1.84694	−	3.19899i	−0.178550	−	0.309258i	0.762834	−	0.646595i	$-0.223807\pi$
$107$	−1.84694	−	3.19899i	−0.178550	−	0.309258i	−0.941384	+	0.337336i	$0.890474\pi$
$108$		0			0
$109$	8.66961	−	15.0162i	0.830398	−	1.43829i	−0.0673245	−	0.997731i	$-0.521446\pi$
$109$	8.66961	−	15.0162i	0.830398	−	1.43829i	0.897723	−	0.440561i	$-0.145220\pi$
$110$	−0.362408	−	6.22231i	−0.0345543	−	0.593274i
$111$		0			0
$112$	−9.34225	+	1.09195i	−0.882760	+	0.103180i
$113$	−7.07449	+	7.49852i	−0.665512	+	0.705401i	−0.968896	−	0.247467i	$-0.920402\pi$
$113$	−7.07449	+	7.49852i	−0.665512	+	0.705401i	0.303385	+	0.952868i	$0.401883\pi$
$114$		0			0
$115$	8.84187	+	1.03347i	0.824508	+	0.0963712i
$116$	−0.880217	+	0.738590i	−0.0817261	+	0.0685764i
$117$		0			0
$118$	6.72485	+	5.64282i	0.619072	+	0.519464i
$119$	−1.70722	−	1.80954i	−0.156500	−	0.165881i
$120$		0			0
$121$	−9.31822	+	4.67979i	−0.847111	+	0.425435i
$122$	0.505229	−	0.253736i	0.0457413	−	0.0229722i
$123$		0			0
$124$	6.69932	+	7.10086i	0.601617	+	0.637676i
$125$	−15.3730	−	12.8995i	−1.37500	−	1.15376i
$126$		0			0
$127$	−10.1217	+	8.49315i	−0.898159	+	0.753645i	−0.969830	−	0.243783i	$-0.921611\pi$
$127$	−10.1217	+	8.49315i	−0.898159	+	0.753645i	0.0716705	+	0.997428i	$0.477167\pi$
$128$	7.78215	+	0.909603i	0.687852	+	0.0803983i
$129$		0			0
$130$	14.0528	−	14.8951i	1.23251	−	1.30638i
$131$	9.99331	−	1.16805i	0.873120	−	0.102053i	0.332282	−	0.943180i	$-0.392181\pi$
$131$	9.99331	−	1.16805i	0.873120	−	0.102053i	0.540838	+	0.841127i	$0.318107\pi$
$132$		0			0
$133$	−0.870337	−	14.9431i	−0.0754678	−	1.29573i
$134$	2.02853	−	3.51352i	0.175238	−	0.303522i
$135$		0			0
$136$	0.375938	+	0.651145i	0.0322365	+	0.0558352i
$137$	−7.91093	+	5.20310i	−0.675876	+	0.444531i	−0.840490	−	0.541827i	$-0.817733\pi$
$137$	−7.91093	+	5.20310i	−0.675876	+	0.444531i	0.164614	+	0.986358i	$0.447362\pi$
$138$		0			0
$139$	−4.15897	+	9.64158i	−0.352760	+	0.817788i	0.645768	+	0.763534i	$0.276537\pi$
$139$	−4.15897	+	9.64158i	−0.352760	+	0.817788i	−0.998527	+	0.0542545i	$0.982722\pi$
$140$	31.2864	+	7.41502i	2.64419	+	0.626684i
$141$		0			0
$142$	−8.53302	+	11.4618i	−0.716075	+	0.961855i
$143$	1.76795	+	0.643483i	0.147844	+	0.0538107i
$144$		0			0
$145$	−1.69736	+	0.617790i	−0.140958	+	0.0513047i
$146$	−4.81266	+	16.0754i	−0.398298	+	1.33041i
$147$		0			0
$148$	0.684905	−	11.7594i	0.0562989	−	0.966614i
$149$	10.3846	+	6.83006i	0.850740	+	0.559541i	0.898328	−	0.439326i	$-0.144783\pi$
$149$	10.3846	+	6.83006i	0.850740	+	0.559541i	−0.0475872	+	0.998867i	$0.515153\pi$
$150$		0			0
$151$	−17.7357	+	4.20344i	−1.44331	+	0.342071i	−0.876350	−	0.481674i	$-0.840029\pi$
$151$	−17.7357	+	4.20344i	−1.44331	+	0.342071i	−0.566960	+	0.823745i	$0.691881\pi$
$152$	−0.785565	+	4.45516i	−0.0637177	+	0.361361i
$153$		0			0
$154$	0.927258	+	5.25874i	0.0747206	+	0.423761i
$155$	6.07840	+	14.0913i	0.488229	+	1.13184i
$156$		0			0
$157$	−6.70313	−	22.3900i	−0.534968	−	1.78692i	−0.613136	−	0.789978i	$-0.710092\pi$
$157$	−6.70313	−	22.3900i	−0.534968	−	1.78692i	0.0781675	−	0.996940i	$-0.475093\pi$
$158$	5.45401	+	7.32601i	0.433898	+	0.582826i
$159$		0			0
$160$	27.7710	+	13.9471i	2.19549	+	1.10262i
$161$	−7.62665			−0.601064
$162$		0			0
$163$	11.7238			0.918278			0.459139	−	0.888364i	$-0.348158\pi$
$163$	11.7238			0.918278			0.459139	+	0.888364i	$0.348158\pi$
$164$	−10.8272	−	5.43761i	−0.845459	−	0.424606i
$165$		0			0
$166$	3.21785	+	4.32232i	0.249754	+	0.335477i
$167$	−6.94439	−	23.1959i	−0.537373	−	1.79495i	−0.603772	−	0.797157i	$-0.706336\pi$
$167$	−6.94439	−	23.1959i	−0.537373	−	1.79495i	0.0663994	−	0.997793i	$-0.478849\pi$
$168$		0			0
$169$	−2.70073	−	6.26100i	−0.207748	−	0.481615i
$170$	1.06685	+	6.05041i	0.0818237	+	0.464045i
$171$		0			0
$172$	2.55482	−	14.4891i	0.194803	−	1.10478i
$173$	15.0943	−	3.57742i	1.14760	−	0.271986i	0.387548	−	0.921849i	$-0.373322\pi$
$173$	15.0943	−	3.57742i	1.14760	−	0.271986i	0.760051	+	0.649863i	$0.225174\pi$
$174$		0			0
$175$	28.2970	+	18.6112i	2.13905	+	1.40688i
$176$	−0.124089	+	2.13052i	−0.00935353	+	0.160594i
$177$		0			0
$178$	−3.26923	+	10.9200i	−0.245039	+	0.818489i
$179$	−6.75474	+	2.45852i	−0.504873	+	0.183759i	−0.581884	−	0.813271i	$-0.697684\pi$
$179$	−6.75474	+	2.45852i	−0.504873	+	0.183759i	0.0770114	+	0.997030i	$0.475462\pi$
$180$		0			0
$181$	7.27112	+	2.64647i	0.540458	+	0.196711i	0.597802	−	0.801644i	$-0.296041\pi$
$181$	7.27112	+	2.64647i	0.540458	+	0.196711i	−0.0573439	+	0.998354i	$0.518263\pi$
$182$	−10.4765	+	14.0724i	−0.776573	+	1.04312i
$183$		0			0
$184$	2.24286	+	0.531567i	0.165346	+	0.0391877i
$185$	7.33424	−	17.0027i	0.539224	−	1.25006i
$186$		0			0
$187$	−0.471600	+	0.310176i	−0.0344868	+	0.0226824i
$188$	−13.3310	−	23.0900i	−0.972264	−	1.68401i
$189$		0			0
$190$	−18.4828	+	32.0132i	−1.34089	+	2.32248i
$191$	−0.585993	−	10.0611i	−0.0424010	−	0.727996i	−0.950783	−	0.309856i	$-0.899719\pi$
$191$	−0.585993	−	10.0611i	−0.0424010	−	0.727996i	0.908382	−	0.418140i	$-0.137318\pi$
$192$		0			0
$193$	15.8841	−	1.85659i	1.14337	−	0.133640i	0.476748	−	0.879040i	$-0.341815\pi$
$193$	15.8841	−	1.85659i	1.14337	−	0.133640i	0.666618	+	0.745400i	$0.267741\pi$
$194$	−13.7764	+	14.6021i	−0.989086	+	1.04837i
$195$		0			0
$196$	−10.1425	−	1.18549i	−0.724466	−	0.0846779i
$197$	−8.40349	+	7.05136i	−0.598724	+	0.502389i	−0.891035	−	0.453934i	$-0.850020\pi$
$197$	−8.40349	+	7.05136i	−0.598724	+	0.502389i	0.292311	+	0.956323i	$0.405576\pi$
$198$		0			0
$199$	2.68937	+	2.25665i	0.190644	+	0.159970i	0.733114	−	0.680106i	$-0.238066\pi$
$199$	2.68937	+	2.25665i	0.190644	+	0.159970i	−0.542470	+	0.840075i	$0.682511\pi$
$200$	−7.02445	−	7.44548i	−0.496704	−	0.526475i
$201$		0			0
$202$	23.2702	−	11.6867i	1.63729	−	0.822276i
$203$	1.38290	−	0.694520i	0.0970607	−	0.0487457i
$204$		0			0
$205$	−13.0703	−	13.8537i	−0.912870	−	0.967586i
$206$	27.0186	+	22.6713i	1.88247	+	1.57958i
$207$		0			0
$208$	−5.37122	+	4.50698i	−0.372427	+	0.312503i
$209$	−3.37328	−	0.394280i	−0.233335	−	0.0272729i
$210$		0			0
$211$	5.27290	−	5.58895i	0.363002	−	0.384759i	−0.519971	−	0.854184i	$-0.674057\pi$
$211$	5.27290	−	5.58895i	0.363002	−	0.384759i	0.882972	+	0.469425i	$0.155539\pi$
$212$	−28.3007	+	3.30788i	−1.94370	+	0.227186i
$213$		0			0
$214$	−0.454422	−	7.80212i	−0.0310636	−	0.533342i
$215$	11.5641	−	20.0297i	0.788667	−	1.36601i
$216$		0			0
$217$	−6.57386	−	11.3863i	−0.446262	−	0.772949i
$218$	30.6503	−	20.1590i	2.07590	−	1.36534i
$219$		0			0
$220$	2.88954	−	6.69870i	0.194813	−	0.451626i
$221$	−1.80453	−	0.427682i	−0.121386	−	0.0287690i
$222$		0			0
$223$	6.47575	−	8.69845i	0.433649	−	0.582491i	−0.530556	−	0.847650i	$-0.678017\pi$
$223$	6.47575	−	8.69845i	0.433649	−	0.582491i	0.964205	+	0.265159i	$0.0854243\pi$
$224$	−25.0185	−	9.10600i	−1.67162	−	0.608420i
$225$		0			0
$226$	−20.4960	+	7.45993i	−1.36337	+	0.496227i
$227$	−3.11507	+	10.4051i	−0.206754	+	0.690608i	0.790216	+	0.612828i	$0.209968\pi$
$227$	−3.11507	+	10.4051i	−0.206754	+	0.690608i	−0.996971	+	0.0777796i	$0.975217\pi$
$228$		0			0
$229$	−0.133120	+	2.28559i	−0.00879685	+	0.151036i	0.991049	+	0.133496i	$0.0426204\pi$
$229$	−0.133120	+	2.28559i	−0.00879685	+	0.151036i	−0.999846	+	0.0175398i	$0.994417\pi$
$230$	15.7361	+	10.3498i	1.03761	+	0.682444i
$231$		0			0
$232$	−0.455094	+	0.107859i	−0.0298784	+	0.00708130i
$233$	−3.09286	+	17.5405i	−0.202620	+	1.14912i	0.698521	+	0.715590i	$0.253842\pi$
$233$	−3.09286	+	17.5405i	−0.202620	+	1.14912i	−0.901141	+	0.433526i	$0.857269\pi$
$234$		0			0
$235$	−7.27807	−	41.2760i	−0.474769	−	2.69255i
$236$	4.06977	+	9.43480i	0.264920	+	0.614153i
$237$		0			0
$238$	−1.50960	−	5.04240i	−0.0978526	−	0.326851i
$239$	7.32490	+	9.83905i	0.473808	+	0.636435i	0.973205	−	0.229938i	$-0.0738524\pi$
$239$	7.32490	+	9.83905i	0.473808	+	0.636435i	−0.499397	+	0.866373i	$0.666445\pi$
$240$		0			0
$241$	15.6381	+	7.85375i	1.00734	+	0.505904i	0.874393	−	0.485219i	$-0.161260\pi$
$241$	15.6381	+	7.85375i	1.00734	+	0.505904i	0.132946	+	0.991123i	$0.457556\pi$
$242$	−22.0617			−1.41818
$243$		0			0
$244$	0.661742			0.0423637
$245$	−14.3451	−	7.20440i	−0.916477	−	0.460272i
$246$		0			0
$247$	−6.66326	−	8.95031i	−0.423973	−	0.569494i
$248$	1.13964	+	3.80668i	0.0723675	+	0.241724i
$249$		0			0
$250$	−16.8172	−	38.9865i	−1.06361	−	2.46573i
$251$	−3.26810	−	18.5343i	−0.206281	−	1.16988i	−0.895412	−	0.445239i	$-0.853119\pi$
$251$	−3.26810	−	18.5343i	−0.206281	−	1.16988i	0.689131	−	0.724637i	$-0.257992\pi$
$252$		0			0
$253$	−0.300488	+	1.70415i	−0.0188915	+	0.107139i
$254$	−27.2019	+	6.44697i	−1.70680	+	0.404519i
$255$		0			0
$256$	−4.94720	−	3.25382i	−0.309200	−	0.203364i
$257$	1.00260	−	17.2139i	0.0625403	−	1.07378i	−0.810378	−	0.585908i	$-0.800738\pi$
$257$	1.00260	−	17.2139i	0.0625403	−	1.07378i	0.872918	−	0.487867i	$-0.162225\pi$
$258$		0			0
$259$	−4.54988	+	15.1977i	−0.282716	+	0.944337i
$260$	22.5232	−	8.19776i	1.39683	−	0.508404i
$261$		0			0
$262$	20.0036	+	7.28070i	1.23582	+	0.449803i
$263$	14.6970	−	19.7415i	0.906255	−	1.21731i	−0.0693091	−	0.997595i	$-0.522079\pi$
$263$	14.6970	−	19.7415i	0.906255	−	1.21731i	0.975564	−	0.219716i	$-0.0705131\pi$
$264$		0			0
$265$	−43.5843	−	10.3297i	−2.67736	−	0.634547i
$266$	12.5437	−	29.0795i	0.769101	−	1.78298i
$267$		0			0
$268$	3.96745	−	2.60943i	0.242350	−	0.159396i
$269$	5.32448	+	9.22227i	0.324639	+	0.562292i	0.981439	−	0.191773i	$-0.0614238\pi$
$269$	5.32448	+	9.22227i	0.324639	+	0.562292i	−0.656800	+	0.754065i	$0.728090\pi$
$270$		0			0
$271$	2.35817	−	4.08447i	0.143249	−	0.248114i	−0.785469	−	0.618900i	$-0.787578\pi$
$271$	2.35817	−	4.08447i	0.143249	−	0.248114i	0.928718	+	0.370786i	$0.120912\pi$
$272$	−0.122315	−	2.10006i	−0.00741641	−	0.127335i
$273$		0			0
$274$	−19.8979	+	2.32573i	−1.20207	+	0.140502i
$275$	5.27351	−	5.58959i	0.318005	−	0.337065i
$276$		0			0
$277$	6.56691	+	0.767562i	0.394567	+	0.0461183i	0.311063	−	0.950389i	$-0.399315\pi$
$277$	6.56691	+	0.767562i	0.394567	+	0.0461183i	0.0835039	+	0.996507i	$0.473389\pi$
$278$	−17.0186	+	14.2803i	−1.02071	+	0.856474i
$279$		0			0
$280$	10.0256	+	8.41245i	0.599142	+	0.502740i
$281$	−1.69927	−	1.80112i	−0.101370	−	0.107446i	0.674702	−	0.738090i	$-0.264272\pi$
$281$	−1.69927	−	1.80112i	−0.101370	−	0.107446i	−0.776072	+	0.630644i	$0.782791\pi$
$282$		0			0
$283$	0.828536	−	0.416107i	0.0492514	−	0.0247350i	−0.424003	−	0.905661i	$-0.639375\pi$
$283$	0.828536	−	0.416107i	0.0492514	−	0.0247350i	0.473254	+	0.880926i	$0.343079\pi$
$284$	−14.9462	+	7.50627i	−0.886894	+	0.445415i
$285$		0			0
$286$	2.73167	+	2.89540i	0.161527	+	0.171208i
$287$	12.4999	+	10.4887i	0.737845	+	0.619126i
$288$		0			0
$289$	−12.5965	+	10.5697i	−0.740973	+	0.621750i
$290$	−3.79584	−	0.443670i	−0.222900	−	0.0260532i
$291$		0			0
$292$	−13.4784	+	14.2862i	−0.788761	+	0.836038i
$293$	2.32920	−	0.272245i	0.136073	−	0.0159047i	−0.0477835	−	0.998858i	$-0.515216\pi$
$293$	2.32920	−	0.272245i	0.136073	−	0.0159047i	0.183857	+	0.982953i	$0.441142\pi$
$294$		0			0
$295$	0.939186	+	16.1252i	0.0546815	+	0.938846i
$296$	2.39729	−	4.15224i	0.139340	−	0.241344i
$297$		0			0
$298$	13.1488	+	22.7744i	0.761688	+	1.31928i
$299$	−4.75001	+	3.12413i	−0.274700	+	0.180673i
$300$		0			0
$301$	−7.84818	+	18.1941i	−0.452362	+	1.04869i
$302$	−37.5244	−	8.89345i	−2.15929	−	0.511760i
$303$		0			0
$304$	7.55826	−	10.1525i	0.433496	−	0.582286i
$305$	0.977524	+	0.355790i	0.0559729	+	0.0203725i
$306$		0			0
$307$	14.3376	−	5.21846i	0.818289	−	0.297833i	0.101246	−	0.994861i	$-0.467717\pi$
$307$	14.3376	−	5.21846i	0.818289	−	0.297833i	0.717043	+	0.697028i	$0.245495\pi$
$308$	−1.79256	+	5.98756i	−0.102140	+	0.341173i
$309$		0			0
$310$	−1.88792	+	32.4143i	−0.107227	+	1.84101i
$311$	−13.9891	−	9.20078i	−0.793249	−	0.521728i	0.0870178	−	0.996207i	$-0.472266\pi$
$311$	−13.9891	−	9.20078i	−0.793249	−	0.521728i	−0.880267	+	0.474478i	$0.842637\pi$
$312$		0			0
$313$	31.6953	−	7.51193i	1.79153	−	0.424599i	0.805693	−	0.592334i	$-0.201793\pi$
$313$	31.6953	−	7.51193i	1.79153	−	0.424599i	0.985832	+	0.167734i	$0.0536451\pi$
$314$	8.58676	−	48.6979i	0.484579	−	2.74818i
$315$		0			0
$316$	1.85633	+	10.5278i	0.104427	+	0.592234i
$317$	−8.58338	−	19.8985i	−0.482091	−	1.11761i	−0.969645	−	0.244519i	$-0.921370\pi$
$317$	−8.58338	−	19.8985i	−0.482091	−	1.11761i	0.487554	−	0.873093i	$-0.337889\pi$
$318$		0			0
$319$	−0.100702	−	0.336369i	−0.00563824	−	0.0188330i
$320$	26.1512	+	35.1272i	1.46190	+	1.96367i
$321$		0			0
$322$	−14.4198	−	7.24188i	−0.803582	−	0.403574i
$323$	3.34769			0.186271
$324$		0			0
$325$	25.2476			1.40049
$326$	22.1663	+	11.1323i	1.22768	+	0.616562i
$327$		0			0
$328$	−2.94495	−	3.95575i	−0.162607	−	0.218420i
$329$	10.2985	+	34.3994i	0.567774	+	1.89650i
$330$		0			0
$331$	9.43153	+	21.8648i	0.518404	+	1.20180i	0.953495	+	0.301409i	$0.0974569\pi$
$331$	9.43153	+	21.8648i	0.518404	+	1.20180i	−0.435091	+	0.900386i	$0.643284\pi$
$332$	1.09523	+	6.21136i	0.0601086	+	0.340893i
$333$		0			0
$334$	8.89581	−	50.4507i	0.486757	−	2.76054i
$335$	7.26368	−	1.72152i	0.396857	−	0.0940569i
$336$		0			0
$337$	15.3690	+	10.1084i	0.837204	+	0.550638i	0.894164	−	0.447739i	$-0.147770\pi$
$337$	15.3690	+	10.1084i	0.837204	+	0.550638i	−0.0569604	+	0.998376i	$0.518141\pi$
$338$	0.838832	−	14.4022i	0.0456265	−	0.783376i
$339$		0			0
$340$	−2.06242	+	6.88895i	−0.111850	+	0.373606i
$341$	−2.80323	+	1.02029i	−0.151803	+	0.0552519i
$342$		0			0
$343$	−9.01506	−	3.28121i	−0.486767	−	0.177169i
$344$	3.57611	−	4.80356i	0.192811	−	0.258990i
$345$		0			0
$346$	31.9359	+	7.56894i	1.71688	+	0.406909i
$347$	6.69815	−	15.5281i	0.359576	−	0.833590i	−0.638383	−	0.769719i	$-0.720396\pi$
$347$	6.69815	−	15.5281i	0.359576	−	0.833590i	0.997958	−	0.0638707i	$-0.0203445\pi$
$348$		0			0
$349$	−6.82361	+	4.48796i	−0.365259	+	0.240235i	−0.718850	−	0.695166i	$-0.755331\pi$
$349$	−6.82361	+	4.48796i	−0.365259	+	0.240235i	0.353590	+	0.935400i	$0.384961\pi$
$350$	35.8291	+	62.0578i	1.91514	+	3.31713i
$351$		0			0
$352$	−3.02043	+	5.23154i	−0.160989	+	0.278842i
$353$	1.43120	+	24.5728i	0.0761752	+	1.30788i	0.792397	+	0.610005i	$0.208833\pi$
$353$	1.43120	+	24.5728i	0.0761752	+	1.30788i	−0.716222	+	0.697872i	$0.754130\pi$
$354$		0			0
$355$	−26.1143	+	3.05233i	−1.38600	+	0.162001i
$356$	−9.15584	+	9.70462i	−0.485258	+	0.514344i
$357$		0			0
$358$	−15.1057	−	1.76561i	−0.798363	−	0.0933152i
$359$	9.68682	−	8.12821i	0.511251	−	0.428990i	−0.350318	−	0.936631i	$-0.613927\pi$
$359$	9.68682	−	8.12821i	0.511251	−	0.428990i	0.861569	+	0.507640i	$0.169482\pi$
$360$		0			0
$361$	0.875105	+	0.734300i	0.0460582	+	0.0386474i
$362$	11.2346	+	11.9080i	0.590478	+	0.625870i
$363$		0			0
$364$	−18.3504	+	9.21593i	−0.961824	+	0.483046i
$365$	−27.5913	+	13.8569i	−1.44419	+	0.725302i
$366$		0			0
$367$	7.20152	+	7.63317i	0.375917	+	0.398448i	0.887517	−	0.460775i	$-0.152429\pi$
$367$	7.20152	+	7.63317i	0.375917	+	0.398448i	−0.511600	+	0.859224i	$0.670947\pi$
$368$	−4.94019	−	4.14531i	−0.257525	−	0.216089i
$369$		0			0
$370$	30.0118	−	25.1829i	1.56024	−	1.30920i
$371$	38.1148	+	4.45499i	1.97882	+	0.231291i
$372$		0			0
$373$	−8.09518	+	8.58039i	−0.419152	+	0.444276i	−0.902200	−	0.431319i	$-0.858048\pi$
$373$	−8.09518	+	8.58039i	−0.419152	+	0.444276i	0.483047	+	0.875594i	$0.339530\pi$
$374$	−1.18619	+	0.138645i	−0.0613362	+	0.00716918i
$375$		0			0
$376$	−0.631010	−	10.8340i	−0.0325418	−	0.558722i
$377$	0.576797	−	0.999042i	0.0297066	−	0.0514533i
$378$		0			0
$379$	−9.06853	−	15.7072i	−0.465819	−	0.806823i	0.533419	−	0.845851i	$-0.320907\pi$
$379$	−9.06853	−	15.7072i	−0.465819	−	0.806823i	−0.999238	+	0.0390286i	$0.987574\pi$
$380$	−36.1491	+	23.7756i	−1.85441	+	1.21966i
$381$		0			0
$382$	8.44558	−	19.5791i	0.432113	−	1.00175i
$383$	−15.0994	−	3.57861i	−0.771541	−	0.182859i	−0.174053	−	0.984736i	$-0.555686\pi$
$383$	−15.0994	−	3.57861i	−0.771541	−	0.182859i	−0.597488	+	0.801878i	$0.703834\pi$
$384$		0			0
$385$	−5.86722	+	7.88104i	−0.299021	+	0.401655i
$386$	31.7952	+	11.5725i	1.61833	+	0.589025i
$387$		0			0
$388$	−22.0802	+	8.03653i	−1.12095	+	0.407993i
$389$	−4.42661	+	14.7859i	−0.224438	+	0.749675i	0.769393	+	0.638775i	$0.220559\pi$
$389$	−4.42661	+	14.7859i	−0.224438	+	0.749675i	−0.993832	+	0.110900i	$0.964627\pi$
$390$		0			0
$391$	0.0991778	−	1.70282i	0.00501563	−	0.0861151i
$392$	−3.47268	−	2.28402i	−0.175397	−	0.115360i
$393$		0			0
$394$	−22.5842	+	5.35254i	−1.13777	+	0.269657i
$395$	−2.91816	+	16.5497i	−0.146828	+	0.832705i
$396$		0			0
$397$	0.354695	+	2.01157i	0.0178016	+	0.100958i	0.992414	−	0.122941i	$-0.0392326\pi$
$397$	0.354695	+	2.01157i	0.0178016	+	0.100958i	−0.974612	+	0.223899i	$0.928121\pi$
$398$	2.94201	+	6.82036i	0.147470	+	0.341874i
$399$		0			0
$400$	8.21372	+	27.4357i	0.410686	+	1.37179i
$401$	−8.93000	−	11.9951i	−0.445943	−	0.599005i	0.521139	−	0.853472i	$-0.325507\pi$
$401$	−8.93000	−	11.9951i	−0.445943	−	0.599005i	−0.967081	+	0.254467i	$0.918100\pi$
$402$		0			0
$403$	−8.75850	−	4.39868i	−0.436292	−	0.219114i
$404$	30.4790			1.51639
$405$		0			0
$406$	3.27415			0.162493
$407$	3.21660	+	1.61544i	0.159441	+	0.0800744i
$408$		0			0
$409$	6.20362	+	8.33291i	0.306749	+	0.412036i	0.928590	−	0.371108i	$-0.121022\pi$
$409$	6.20362	+	8.33291i	0.306749	+	0.412036i	−0.621840	+	0.783144i	$0.713615\pi$
$410$	−11.5574	−	38.6042i	−0.570777	−	1.90653i
$411$		0			0
$412$	16.3512	+	37.9064i	0.805567	+	1.86751i
$413$	−2.40300	−	13.6281i	−0.118244	−	0.670595i
$414$		0			0
$415$	−1.72170	+	9.76427i	−0.0845151	+	0.479309i
$416$	−19.3121	+	4.57705i	−0.946853	+	0.224408i
$417$		0			0
$418$	−6.00350	−	3.94856i	−0.293641	−	0.193131i
$419$	0.0308229	−	0.529208i	0.00150580	−	0.0258535i	−0.997472	−	0.0710667i	$-0.977360\pi$
$419$	0.0308229	−	0.529208i	0.00150580	−	0.0258535i	0.998977	+	0.0452132i	$0.0143967\pi$
$420$		0			0
$421$	9.19654	−	30.7186i	0.448212	−	1.49713i	−0.373717	−	0.927543i	$-0.621917\pi$
$421$	9.19654	−	30.7186i	0.448212	−	1.49713i	0.821929	−	0.569590i	$-0.192898\pi$
$422$	15.2765	−	5.56019i	0.743649	−	0.270666i
$423$		0			0
$424$	−10.8984	−	3.96668i	−0.529272	−	0.192639i
$425$	−4.52334	+	6.07590i	−0.219414	+	0.294724i
$426$		0			0
$427$	−0.867198	−	0.205530i	−0.0419666	−	0.00994628i
$428$	3.62318	−	8.39947i	0.175133	−	0.406004i
$429$		0			0
$430$	40.8835	−	26.8895i	1.97158	−	1.29673i
$431$	2.69146	+	4.66175i	0.129643	+	0.224549i	0.923538	−	0.383506i	$-0.125283\pi$
$431$	2.69146	+	4.66175i	0.129643	+	0.224549i	−0.793895	+	0.608055i	$0.791950\pi$
$432$		0			0
$433$	−16.6465	+	28.8325i	−0.799978	+	1.38560i	0.119652	+	0.992816i	$0.461822\pi$
$433$	−16.6465	+	28.8325i	−0.799978	+	1.38560i	−0.919630	+	0.392787i	$0.871511\pi$
$434$	−1.61743	−	27.7703i	−0.0776394	−	1.33302i
$435$		0			0
$436$	42.6489	−	4.98494i	2.04251	−	0.238735i
$437$	7.04280	−	7.46493i	0.336903	−	0.357096i
$438$		0			0
$439$	18.5556	+	2.16884i	0.885612	+	0.103513i	0.546723	−	0.837313i	$-0.315875\pi$
$439$	18.5556	+	2.16884i	0.885612	+	0.103513i	0.338889	+	0.940827i	$0.389949\pi$
$440$	2.27474	−	1.90873i	0.108444	−	0.0909953i
$441$		0			0
$442$	−3.00574	−	2.52212i	−0.142968	−	0.119965i
$443$	−12.9497	−	13.7259i	−0.615260	−	0.652138i	0.342563	−	0.939495i	$-0.388705\pi$
$443$	−12.9497	−	13.7259i	−0.615260	−	0.652138i	−0.957824	+	0.287357i	$0.907223\pi$
$444$		0			0
$445$	−18.7427	+	9.41296i	−0.888491	+	0.446217i
$446$	20.5034	−	10.2972i	0.970862	−	0.487585i
$447$		0			0
$448$	−25.7468	−	27.2900i	−1.21642	−	1.28933i
$449$	5.33643	+	4.47780i	0.251842	+	0.211320i	0.759965	−	0.649964i	$-0.225216\pi$
$449$	5.33643	+	4.47780i	0.251842	+	0.211320i	−0.508123	+	0.861284i	$0.669661\pi$
$450$		0			0
$451$	2.83615	−	2.37981i	0.133549	−	0.112061i
$452$	−25.3569	−	2.96379i	−1.19269	−	0.139405i
$453$		0			0
$454$	−15.7698	+	16.7150i	−0.740113	+	0.784474i
$455$	−32.0622	+	3.74754i	−1.50310	+	0.175687i
$456$		0			0
$457$	−2.18611	−	37.5341i	−0.102262	−	1.75577i	−0.526459	−	0.850201i	$-0.676481\pi$
$457$	−2.18611	−	37.5341i	−0.102262	−	1.75577i	0.424197	−	0.905570i	$-0.360556\pi$
$458$	−2.42197	+	4.19498i	−0.113171	+	0.196018i
$459$		0			0
$460$	11.0226	+	19.0917i	0.513932	+	0.890157i
$461$	−23.0904	+	15.1868i	−1.07543	+	0.707320i	−0.958291	−	0.285796i	$-0.907742\pi$
$461$	−23.0904	+	15.1868i	−1.07543	+	0.707320i	−0.117137	+	0.993116i	$0.537372\pi$
$462$		0			0
$463$	9.73063	−	22.5581i	0.452220	−	1.04836i	−0.527782	−	0.849380i	$-0.676976\pi$
$463$	9.73063	−	22.5581i	0.452220	−	1.04836i	0.980003	−	0.198985i	$-0.0637645\pi$
$464$	1.27327	+	0.301771i	0.0591102	+	0.0140094i
$465$		0			0
$466$	−22.5033	+	30.2271i	−1.04244	+	1.40025i
$467$	7.38677	+	2.68856i	0.341819	+	0.124412i	0.507225	−	0.861814i	$-0.330671\pi$
$467$	7.38677	+	2.68856i	0.341819	+	0.124412i	−0.165406	+	0.986226i	$0.552893\pi$
$468$		0			0
$469$	−6.00971	+	2.18735i	−0.277503	+	0.101003i
$470$	25.4329	−	84.9517i	1.17313	−	3.91853i
$471$		0			0
$472$	−0.243182	+	4.17527i	−0.0111933	+	0.192182i
$473$	3.75620	+	2.47049i	0.172710	+	0.113593i
$474$		0			0
$475$	−44.3473	+	10.5105i	−2.03479	+	0.482255i
$476$	1.06981	−	6.06719i	0.0490346	−	0.278089i
$477$		0			0
$478$	4.50659	+	25.5581i	0.206127	+	1.16900i
$479$	7.01520	+	16.2631i	0.320533	+	0.743079i	0.999956	+	0.00933231i	$0.00297061\pi$
$479$	7.01520	+	16.2631i	0.320533	+	0.743079i	−0.679424	+	0.733746i	$0.737770\pi$
$480$		0			0
$481$	3.39173	+	11.3292i	0.154649	+	0.516565i
$482$	22.1096	+	29.6983i	1.00706	+	1.35272i
$483$		0			0
$484$	−23.0758	−	11.5891i	−1.04890	−	0.526778i
$485$	−36.9377			−1.67725
$486$		0			0
$487$	−42.1146			−1.90840			−0.954198	−	0.299175i	$-0.903289\pi$
$487$	−42.1146			−1.90840			−0.954198	+	0.299175i	$0.903289\pi$
$488$	0.240702	+	0.120885i	0.0108961	+	0.00547221i
$489$		0			0
$490$	−20.2815	−	27.2428i	−0.916226	−	1.23071i
$491$	−2.08723	−	6.97182i	−0.0941952	−	0.314634i	0.897887	−	0.440227i	$-0.145102\pi$
$491$	−2.08723	−	6.97182i	−0.0941952	−	0.314634i	−0.992082	+	0.125593i	$0.959917\pi$
$492$		0			0
$493$	0.137083	+	0.317795i	0.00617392	+	0.0143128i
$494$	−4.09952	−	23.2495i	−0.184446	−	1.04604i
$495$		0			0
$496$	1.93053	−	10.9486i	0.0866833	−	0.491606i
$497$	21.9180	−	5.19467i	0.983158	−	0.233013i
$498$		0			0
$499$	−13.4764	−	8.86359i	−0.603288	−	0.396789i	0.210801	−	0.977529i	$-0.432393\pi$
$499$	−13.4764	−	8.86359i	−0.603288	−	0.396789i	−0.814089	+	0.580740i	$0.802763\pi$
$500$	2.88961	−	49.6128i	0.129228	−	2.21875i
$501$		0			0
$502$	11.4202	−	38.1462i	0.509710	−	1.70255i
$503$	−34.7114	+	12.6339i	−1.54771	+	0.563319i	−0.967878	−	0.251421i	$-0.919102\pi$
$503$	−34.7114	+	12.6339i	−1.54771	+	0.563319i	−0.579827	+	0.814739i	$0.696880\pi$
$504$		0			0
$505$	45.0235	+	16.3872i	2.00352	+	0.729221i
$506$	−2.18631	+	2.93672i	−0.0971933	+	0.130553i
$507$		0			0
$508$	−31.8389	−	7.54597i	−1.41262	−	0.334798i
$509$	−4.62698	+	10.7265i	−0.205087	+	0.475445i	−0.989453	−	0.144853i	$-0.953729\pi$
$509$	−4.62698	+	10.7265i	−0.205087	+	0.475445i	0.784366	+	0.620298i	$0.212988\pi$
$510$		0			0
$511$	22.1002	−	14.5355i	0.977656	−	0.643015i
$512$	−14.0992	−	24.4205i	−0.623101	−	1.07924i
$513$		0			0
$514$	18.2411	−	31.5945i	0.804580	−	1.39357i
$515$	3.77339	+	64.7866i	0.166276	+	2.85484i
$516$		0			0
$517$	8.09218	−	0.945840i	0.355894	−	0.0415980i
$518$	−23.0334	+	24.4140i	−1.01203	+	1.07269i
$519$		0			0
$520$	9.69012	+	1.13261i	0.424940	+	0.0496683i
$521$	0.659940	−	0.553755i	0.0289125	−	0.0242605i	−0.628217	−	0.778038i	$-0.716215\pi$
$521$	0.659940	−	0.553755i	0.0289125	−	0.0242605i	0.657129	+	0.753778i	$0.271771\pi$
$522$		0			0
$523$	−6.06895	−	5.09246i	−0.265377	−	0.222678i	0.500383	−	0.865804i	$-0.333192\pi$
$523$	−6.06895	−	5.09246i	−0.265377	−	0.222678i	−0.765760	+	0.643126i	$0.777637\pi$
$524$	17.0985	+	18.1233i	0.746951	+	0.791721i
$525$		0			0
$526$	46.5332	−	23.3699i	2.02894	−	1.01897i
$527$	2.62772	−	1.31969i	0.114465	−	0.0574866i
$528$		0			0
$529$	12.1951	+	12.9261i	0.530224	+	0.562004i
$530$	−72.5967	−	60.9158i	−3.15340	−	2.64601i
$531$		0			0
$532$	28.3958	−	23.8269i	1.23112	−	1.03303i
$533$	12.0817	+	1.41214i	0.523314	+	0.0611667i
$534$		0			0
$535$	9.86818	−	10.4597i	0.426639	−	0.452211i
$536$	1.91980	−	0.224393i	0.0829228	−	0.00969228i
$537$		0			0
$538$	1.31004	+	22.4925i	0.0564797	+	0.969720i
$539$	1.56020	−	2.70235i	0.0672028	−	0.116399i
$540$		0			0
$541$	6.01461	+	10.4176i	0.258588	+	0.447888i	0.965864	−	0.259050i	$-0.0834094\pi$
$541$	6.01461	+	10.4176i	0.258588	+	0.447888i	−0.707276	+	0.706938i	$0.750076\pi$
$542$	8.33703	−	5.48335i	0.358106	−	0.235530i
$543$		0			0
$544$	2.35846	−	5.46752i	0.101118	−	0.234418i
$545$	65.6811	+	15.5667i	2.81347	+	0.666804i
$546$		0			0
$547$	−3.81051	+	5.11840i	−0.162926	+	0.218847i	−0.876087	−	0.482152i	$-0.839855\pi$
$547$	−3.81051	+	5.11840i	−0.162926	+	0.218847i	0.713162	+	0.701000i	$0.247263\pi$
$548$	−22.0342	−	8.01980i	−0.941255	−	0.342589i
$549$		0			0
$550$	15.2783	−	5.56083i	0.651467	−	0.237115i
$551$	−0.597243	+	1.99493i	−0.0254434	+	0.0849868i
$552$		0			0
$553$	0.837130	−	14.3730i	0.0355984	−	0.611201i
$554$	11.6873	+	7.68684i	0.496545	+	0.326583i
$555$		0			0
$556$	−25.3023	+	5.99677i	−1.07306	+	0.254320i
$557$	6.99671	−	39.6803i	0.296460	−	1.68131i	−0.364747	−	0.931107i	$-0.618844\pi$
$557$	6.99671	−	39.6803i	0.296460	−	1.68131i	0.661207	−	0.750203i	$-0.270044\pi$
$558$		0			0
$559$	2.56494	+	14.5465i	0.108485	+	0.615251i
$560$	−14.5030	−	33.6218i	−0.612864	−	1.42078i
$561$		0			0
$562$	−1.50257	−	5.01892i	−0.0633820	−	0.211711i
$563$	0.946894	+	1.27190i	0.0399068	+	0.0536042i	0.821629	−	0.570023i	$-0.193066\pi$
$563$	0.946894	+	1.27190i	0.0399068	+	0.0536042i	−0.781722	+	0.623627i	$0.785658\pi$
$564$		0			0
$565$	−35.8637	−	18.0114i	−1.50880	−	0.757745i
$566$	1.96163			0.0824536
$567$		0			0
$568$	−6.80775			−0.285647
$569$	−9.86944	−	4.95662i	−0.413748	−	0.207792i	0.229733	−	0.973254i	$-0.426215\pi$
$569$	−9.86944	−	4.95662i	−0.413748	−	0.207792i	−0.643482	+	0.765461i	$0.722511\pi$
$570$		0			0
$571$	4.72230	+	6.34315i	0.197622	+	0.265452i	0.889877	−	0.456201i	$-0.150790\pi$
$571$	4.72230	+	6.34315i	0.197622	+	0.265452i	−0.692255	+	0.721653i	$0.743383\pi$
$572$	1.33627	+	4.46345i	0.0558722	+	0.186626i
$573$		0			0
$574$	13.6742	+	31.7002i	0.570748	+	1.32314i
$575$	4.03238	+	22.8688i	0.168162	+	0.953695i
$576$		0			0
$577$	−8.01656	+	45.4642i	−0.333734	+	1.89270i	0.105658	+	0.994402i	$0.466305\pi$
$577$	−8.01656	+	45.4642i	−0.333734	+	1.89270i	−0.439392	+	0.898295i	$0.644806\pi$
$578$	−33.8529	+	8.02328i	−1.40809	+	0.333724i
$579$		0			0
$580$	−3.73726	−	2.45804i	−0.155181	−	0.102064i
$581$	0.493904	−	8.48001i	0.0204906	−	0.351810i
$582$		0			0
$583$	2.49717	−	8.34111i	0.103422	−	0.345454i
$584$	−7.51238	+	2.73428i	−0.310865	+	0.113145i
$585$		0			0
$586$	4.66235	+	1.69696i	0.192600	+	0.0701007i
$587$	−21.9518	+	29.4864i	−0.906049	+	1.21703i	0.0695732	+	0.997577i	$0.477836\pi$
$587$	−21.9518	+	29.4864i	−0.906049	+	1.21703i	−0.975622	+	0.219458i	$0.929571\pi$
$588$		0			0
$589$	17.2154	+	4.08013i	0.709348	+	0.168119i
$590$	−13.5360	+	31.3799i	−0.557266	+	1.29189i
$591$		0			0
$592$	−11.2076	+	7.37135i	−0.460629	+	0.302960i
$593$	7.17407	+	12.4258i	0.294604	+	0.510268i	0.974893	−	0.222676i	$-0.0714791\pi$
$593$	7.17407	+	12.4258i	0.294604	+	0.510268i	−0.680289	+	0.732944i	$0.738146\pi$
$594$		0			0
$595$	4.84238	−	8.38725i	0.198518	−	0.343844i
$596$	1.78972	+	30.7283i	0.0733099	+	1.25868i
$597$		0			0
$598$	−11.9474	+	1.39645i	−0.488565	+	0.0571051i
$599$	−8.93203	+	9.46739i	−0.364953	+	0.386827i	−0.883664	−	0.468122i	$-0.844931\pi$
$599$	−8.93203	+	9.46739i	−0.364953	+	0.386827i	0.518711	+	0.854950i	$0.326412\pi$
$600$		0			0
$601$	6.25526	+	0.731135i	0.255157	+	0.0298236i	0.242710	−	0.970099i	$-0.421964\pi$
$601$	6.25526	+	0.731135i	0.255157	+	0.0298236i	0.0124474	+	0.999923i	$0.496038\pi$
$602$	−32.1148	+	26.9476i	−1.30890	+	1.09830i
$603$		0			0
$604$	−34.5775	−	29.0140i	−1.40694	−	1.18056i
$605$	−27.8566	−	29.5263i	−1.13253	−	1.20042i
$606$		0			0
$607$	11.7509	−	5.90153i	0.476955	−	0.239536i	−0.194046	−	0.980992i	$-0.562161\pi$
$607$	11.7509	−	5.90153i	0.476955	−	0.239536i	0.671001	+	0.741457i	$0.265865\pi$
$608$	32.0162	−	16.0791i	1.29843	−	0.652094i
$609$		0			0
$610$	1.51037	+	1.60090i	0.0611532	+	0.0648186i
$611$	20.5052	+	17.2059i	0.829552	+	0.696076i
$612$		0			0
$613$	−28.3321	+	23.7734i	−1.14432	+	0.960200i	−0.999572	−	0.0292684i	$-0.990682\pi$
$613$	−28.3321	+	23.7734i	−1.14432	+	0.960200i	−0.144750	+	0.989468i	$0.546238\pi$
$614$	32.0634	+	3.74767i	1.29397	+	0.151244i
$615$		0			0
$616$	−1.74581	+	1.85046i	−0.0703409	+	0.0745570i
$617$	32.2582	−	3.77044i	1.29867	−	0.151792i	0.561484	−	0.827487i	$-0.310231\pi$
$617$	32.2582	−	3.77044i	1.29867	−	0.151792i	0.737181	+	0.675695i	$0.236156\pi$
$618$		0			0
$619$	2.49564	+	42.8485i	0.100308	+	1.72223i	0.555232	+	0.831696i	$0.312629\pi$
$619$	2.49564	+	42.8485i	0.100308	+	1.72223i	−0.454924	+	0.890530i	$0.650333\pi$
$620$	−19.0021	+	32.9126i	−0.763142	+	1.32180i
$621$		0			0
$622$	−17.7127	−	30.6793i	−0.710215	−	1.23013i
$623$	15.0127	−	9.87398i	0.601470	−	0.395593i
$624$		0			0
$625$	10.8323	−	25.1120i	0.433290	−	1.00448i
$626$	67.0595	+	15.8934i	2.68024	+	0.635228i
$627$		0			0
$628$	34.5627	−	46.4258i	1.37920	−	1.85259i
$629$	−3.33404	−	1.21349i	−0.132937	−	0.0483851i
$630$		0			0
$631$	13.0635	−	4.75472i	0.520049	−	0.189282i	−0.0686408	−	0.997641i	$-0.521866\pi$
$631$	13.0635	−	4.75472i	0.520049	−	0.189282i	0.588690	+	0.808359i	$0.299644\pi$
$632$	−1.24796	+	4.16848i	−0.0496412	+	0.165813i
$633$		0			0
$634$	2.66595	−	45.7726i	0.105878	−	1.81786i
$635$	−42.9753	−	28.2653i	−1.70542	−	1.12167i
$636$		0			0
$637$	9.97568	−	2.36428i	0.395251	−	0.0936761i
$638$	0.129000	−	0.731597i	0.00510717	−	0.0289642i
$639$		0			0
$640$	5.29656	+	30.0383i	0.209365	+	1.18737i
$641$	1.03758	+	2.40538i	0.0409819	+	0.0950068i	0.937477	−	0.348046i	$-0.113155\pi$
$641$	1.03758	+	2.40538i	0.0409819	+	0.0950068i	−0.896496	+	0.443053i	$0.853895\pi$
$642$		0			0
$643$	0.0293991	+	0.0981997i	0.00115939	+	0.00387262i	0.958567	−	0.284866i	$-0.0919492\pi$
$643$	0.0293991	+	0.0981997i	0.00115939	+	0.00387262i	−0.957408	+	0.288739i	$0.906764\pi$
$644$	−11.2784	−	15.1495i	−0.444432	−	0.596975i
$645$		0			0
$646$	6.32951	+	3.17880i	0.249031	+	0.125068i
$647$	25.1564			0.988998			0.494499	−	0.869178i	$-0.335351\pi$
$647$	25.1564			0.988998			0.494499	+	0.869178i	$0.335351\pi$
$648$		0			0
$649$	−3.13983			−0.123249
$650$	47.7359	+	23.9739i	1.87236	+	0.940332i
$651$		0			0
$652$	17.3373	+	23.2881i	0.678982	+	0.912031i
$653$	−2.13941	−	7.14613i	−0.0837217	−	0.279650i	0.905870	−	0.423557i	$-0.139219\pi$
$653$	−2.13941	−	7.14613i	−0.0837217	−	0.279650i	−0.989591	+	0.143907i	$0.954033\pi$
$654$		0			0
$655$	15.5137	+	35.9649i	0.606172	+	1.40526i
$656$	2.39595	+	13.5881i	0.0935463	+	0.530527i
$657$		0			0
$658$	−13.1924	+	74.8181i	−0.514295	+	2.91671i
$659$	−15.8217	+	3.74981i	−0.616325	+	0.146072i	−0.526908	−	0.849922i	$-0.676649\pi$
$659$	−15.8217	+	3.74981i	−0.616325	+	0.146072i	−0.0894175	+	0.995994i	$0.528501\pi$
$660$		0			0
$661$	−15.7657	−	10.3693i	−0.613214	−	0.403318i	0.204562	−	0.978854i	$-0.434423\pi$
$661$	−15.7657	−	10.3693i	−0.613214	−	0.403318i	−0.817776	+	0.575536i	$0.804793\pi$
$662$	−2.92938	+	50.2956i	−0.113854	+	1.95479i
$663$		0			0
$664$	−0.736294	+	2.45939i	−0.0285737	+	0.0954429i
$665$	54.7570	−	19.9299i	2.12339	−	0.772849i
$666$		0			0
$667$	0.997034	+	0.362891i	0.0386053	+	0.0140512i
$668$	35.8067	−	48.0967i	1.38540	−	1.86092i
$669$		0			0
$670$	15.3682	+	3.64233i	0.593725	+	0.140715i
$671$	−0.0800923	+	0.185675i	−0.00309193	+	0.00716789i
$672$		0			0
$673$	6.83522	−	4.49560i	0.263478	−	0.173293i	−0.410896	−	0.911682i	$-0.634784\pi$
$673$	6.83522	−	4.49560i	0.263478	−	0.173293i	0.674374	+	0.738390i	$0.264414\pi$
$674$	19.4599	+	33.7056i	0.749569	+	1.29829i
$675$		0			0
$676$	8.44293	−	14.6236i	0.324728	−	0.562445i
$677$	−1.34268	−	23.0529i	−0.0516033	−	0.885995i	−0.920437	−	0.390891i	$-0.872167\pi$
$677$	−1.34268	−	23.0529i	−0.0516033	−	0.885995i	0.868834	−	0.495104i	$-0.164870\pi$
$678$		0			0
$679$	31.4316	−	3.67383i	1.20623	−	0.140989i
$680$	−2.00864	+	2.12903i	−0.0770277	+	0.0816446i
$681$		0			0
$682$	−6.26891	−	0.732730i	−0.240049	−	0.0280577i
$683$	14.3566	−	12.0466i	0.549340	−	0.460951i	−0.325378	−	0.945584i	$-0.605491\pi$
$683$	14.3566	−	12.0466i	0.549340	−	0.460951i	0.874717	+	0.484633i	$0.161047\pi$
$684$		0			0
$685$	−28.2370	−	23.6937i	−1.07888	−	0.905289i
$686$	−13.9292	−	14.7641i	−0.531818	−	0.563694i
$687$		0			0
$688$	−14.9727	+	7.51959i	−0.570830	+	0.286682i
$689$	25.5635	−	12.8385i	0.973892	−	0.489107i
$690$		0			0
$691$	4.56302	+	4.83652i	0.173586	+	0.183990i	0.808325	−	0.588736i	$-0.200374\pi$
$691$	4.56302	+	4.83652i	0.173586	+	0.183990i	−0.634740	+	0.772726i	$0.718893\pi$
$692$	29.4279	+	24.6929i	1.11868	+	0.938684i
$693$		0			0
$694$	27.4089	−	22.9988i	1.04043	−	0.873023i
$695$	−40.6008	−	4.74555i	−1.54008	−	0.180009i
$696$		0			0
$697$	−2.50437	+	2.65448i	−0.0948598	+	0.100546i
$698$	−17.1630	+	2.00607i	−0.649629	+	0.0759307i
$699$		0			0
$700$	4.87681	+	83.7316i	0.184326	+	3.16476i
$701$	−12.1477	+	21.0405i	−0.458813	+	0.794687i	−0.998899	−	0.0469230i	$-0.985058\pi$
$701$	−12.1477	+	21.0405i	−0.458813	+	0.794687i	0.540086	+	0.841610i	$0.318392\pi$
$702$		0			0
$703$	−10.6738	−	18.4876i	−0.402571	−	0.697274i
$704$	−7.11227	+	4.67782i	−0.268054	+	0.176302i
$705$		0			0
$706$	−20.6271	+	47.8190i	−0.776311	+	1.79969i
$707$	−39.9420	−	9.46643i	−1.50217	−	0.356022i
$708$		0			0
$709$	17.8682	−	24.0012i	0.671054	−	0.901382i	−0.328008	−	0.944675i	$-0.606377\pi$
$709$	17.8682	−	24.0012i	0.671054	−	0.901382i	0.999062	+	0.0432925i	$0.0137847\pi$
$710$	−52.2729	−	19.0258i	−1.96177	−	0.714024i
$711$		0			0
$712$	−5.10315	+	1.85740i	−0.191249	+	0.0696089i
$713$	2.58539	−	8.63580i	0.0968236	−	0.323413i
$714$		0			0
$715$	−0.425867	+	7.31185i	−0.0159265	+	0.273448i
$716$	−14.8726	−	9.78188i	−0.555816	−	0.365566i
$717$		0			0
$718$	26.0331	−	6.16995i	0.971546	−	0.230261i
$719$	2.12889	−	12.0735i	0.0793943	−	0.450267i	−0.919032	−	0.394183i	$-0.871027\pi$
$719$	2.12889	−	12.0735i	0.0793943	−	0.450267i	0.998426	−	0.0560838i	$-0.0178614\pi$
$720$		0			0
$721$	−9.65461	−	54.7540i	−0.359556	−	2.03915i
$722$	0.957314	+	2.21930i	0.0356275	+	0.0825939i
$723$		0			0
$724$	5.49571	+	18.3570i	0.204247	+	0.682231i
$725$	−2.81372	−	3.77948i	−0.104499	−	0.140366i
$726$		0			0
$727$	−43.8058	−	22.0001i	−1.62467	−	0.815938i	−0.999368	−	0.0355521i	$-0.988681\pi$
$727$	−43.8058	−	22.0001i	−1.62467	−	0.815938i	−0.625298	−	0.780386i	$-0.715023\pi$
$728$	−8.35832			−0.309780
$729$		0			0
$730$	−65.3249			−2.41778
$731$	−3.96018	−	1.98888i	−0.146472	−	0.0735612i
$732$		0			0
$733$	−12.0622	−	16.2024i	−0.445528	−	0.598448i	0.521458	−	0.853277i	$-0.325388\pi$
$733$	−12.0622	−	16.2024i	−0.445528	−	0.598448i	−0.966986	+	0.254829i	$0.917981\pi$
$734$	6.36791	+	21.2703i	0.235044	+	0.785101i
$735$		0			0
$736$	−7.23020	−	16.7615i	−0.266509	−	0.617837i
$737$	0.251977	+	1.42903i	0.00928168	+	0.0526390i
$738$		0			0
$739$	0.349401	−	1.98155i	0.0128529	−	0.0728925i	−0.977707	−	0.209975i	$-0.932662\pi$
$739$	0.349401	−	1.98155i	0.0128529	−	0.0728925i	0.990560	+	0.137083i	$0.0437727\pi$
$740$	44.6200	−	10.5751i	1.64027	−	0.388750i
$741$		0			0
$742$	67.8338	+	44.6150i	2.49026	+	1.63787i
$743$	1.25430	−	21.5356i	0.0460160	−	0.790064i	−0.893818	−	0.448431i	$-0.851983\pi$
$743$	1.25430	−	21.5356i	0.0460160	−	0.790064i	0.939834	−	0.341633i	$-0.110980\pi$
$744$		0			0
$745$	−13.8775	+	46.3541i	−0.508433	+	1.69828i
$746$	−23.4531	+	8.53624i	−0.858680	+	0.312534i
$747$		0			0
$748$	−1.31354	−	0.478091i	−0.0480279	−	0.0174807i
$749$	−7.35687	+	9.88200i	−0.268814	+	0.361080i
$750$		0			0
$751$	−14.0873	−	3.33875i	−0.514053	−	0.121833i	−0.0346015	−	0.999401i	$-0.511016\pi$
$751$	−14.0873	−	3.33875i	−0.514053	−	0.121833i	−0.479451	+	0.877568i	$0.659164\pi$
$752$	−12.0262	+	27.8798i	−0.438550	+	1.01667i
$753$		0			0
$754$	2.03919	−	1.34120i	0.0742631	−	0.0488436i
$755$	−35.4783	−	61.4503i	−1.29119	−	2.23640i
$756$		0			0
$757$	−5.26451	+	9.11840i	−0.191342	+	0.331414i	−0.945695	−	0.325055i	$-0.894617\pi$
$757$	−5.26451	+	9.11840i	−0.191342	+	0.331414i	0.754353	+	0.656469i	$0.227951\pi$
$758$	−2.23123	−	38.3087i	−0.0810418	−	1.39143i
$759$		0			0
$760$	−17.4921	+	2.04454i	−0.634506	+	0.0741632i
$761$	−29.0111	+	30.7500i	−1.05165	+	1.11469i	−0.0584483	+	0.998290i	$0.518615\pi$
$761$	−29.0111	+	30.7500i	−1.05165	+	1.11469i	−0.993203	+	0.116395i	$0.962866\pi$
$762$		0			0
$763$	−57.4387	−	6.71362i	−2.07942	−	0.243049i
$764$	19.1188	−	16.0425i	0.691693	−	0.580399i
$765$		0			0
$766$	−25.1504	−	21.1037i	−0.908721	−	0.762507i
$767$	−7.07916	−	7.50347i	−0.255614	−	0.270935i
$768$		0			0
$769$	−8.05989	+	4.04783i	−0.290647	+	0.145968i	−0.588149	−	0.808753i	$-0.700143\pi$
$769$	−8.05989	+	4.04783i	−0.290647	+	0.145968i	0.297501	+	0.954721i	$0.403847\pi$
$770$	−18.5766	+	9.32953i	−0.669455	+	0.336213i
$771$		0			0
$772$	27.1777	+	28.8066i	0.978145	+	1.03677i
$773$	−0.551231	−	0.462537i	−0.0198264	−	0.0166363i	0.632821	−	0.774298i	$-0.281897\pi$
$773$	−0.551231	−	0.462537i	−0.0198264	−	0.0166363i	−0.652647	+	0.757662i	$0.726342\pi$
$774$		0			0
$775$	−30.6663	+	25.7321i	−1.10157	+	0.924325i
$776$	−9.49953	−	1.11034i	−0.341013	−	0.0398587i
$777$		0			0
$778$	−22.4094	+	23.7526i	−0.803415	+	0.851570i
$779$	−21.8092	+	2.54913i	−0.781396	+	0.0913321i
$780$		0			0
$781$	−0.297168	−	5.10218i	−0.0106335	−	0.182570i
$782$	1.80442	−	3.12535i	0.0645261	−	0.111762i
$783$		0			0
$784$	5.81453	+	10.0711i	0.207662	+	0.359681i
$785$	76.0171	−	49.9972i	2.71317	−	1.78448i
$786$		0			0
$787$	6.11050	−	14.1657i	0.217816	−	0.504953i	−0.773915	−	0.633289i	$-0.781704\pi$
$787$	6.11050	−	14.1657i	0.217816	−	0.504953i	0.991731	+	0.128336i	$0.0409636\pi$
$788$	−26.4340	−	6.26497i	−0.941672	−	0.223180i
$789$		0			0
$790$	−21.2321	+	28.5197i	−0.755405	+	1.01469i
$791$	32.3091	+	11.7595i	1.14878	+	0.418121i
$792$		0			0
$793$	−0.624297	+	0.227226i	−0.0221695	+	0.00806902i
$794$	−1.23946	+	4.14010i	−0.0439869	+	0.146927i
$795$		0			0
$796$	−0.505513	+	8.67932i	−0.0179174	+	0.307630i
$797$	11.6388	+	7.65494i	0.412266	+	0.271152i	0.738655	−	0.674084i	$-0.235461\pi$
$797$	11.6388	+	7.65494i	0.412266	+	0.271152i	−0.326389	+	0.945236i	$0.605832\pi$
$798$		0			0
$799$	−7.81433	+	1.85203i	−0.276451	+	0.0655201i
$800$	−14.0768	+	79.8335i	−0.497690	+	2.82254i
$801$		0			0
$802$	−5.49411	−	31.1586i	−0.194004	−	1.10025i
$803$	−2.37718	−	5.51092i	−0.0838888	−	0.194476i
$804$		0			0
$805$	−8.51521	−	28.4428i	−0.300122	−	1.00248i
$806$	−12.3830	−	16.6333i	−0.436173	−	0.585881i
$807$		0			0
$808$	11.0864	+	5.56781i	0.390019	+	0.195875i
$809$	40.8781			1.43720			0.718599	−	0.695424i	$-0.244784\pi$
$809$	40.8781			1.43720			0.718599	+	0.695424i	$0.244784\pi$
$810$		0			0
$811$	51.1039			1.79450			0.897250	−	0.441524i	$-0.145562\pi$
$811$	51.1039			1.79450			0.897250	+	0.441524i	$0.145562\pi$
$812$	3.42465	+	1.71992i	0.120182	+	0.0603575i
$813$		0			0
$814$	4.54772	+	6.10865i	0.159398	+	0.214108i
$815$	13.0897	+	43.7226i	0.458512	+	1.53154i
$816$		0			0
$817$	−10.5610	−	24.4830i	−0.369481	−	0.856553i
$818$	3.81673	+	21.6457i	0.133449	+	0.756825i
$819$		0			0
$820$	8.19037	−	46.4499i	0.286020	−	1.62210i
$821$	47.2620	−	11.2013i	1.64946	−	0.390928i	0.702345	−	0.711836i	$-0.252136\pi$
$821$	47.2620	−	11.2013i	1.64946	−	0.390928i	0.947110	+	0.320908i	$0.103988\pi$
$822$		0			0
$823$	−22.5809	−	14.8517i	−0.787119	−	0.517696i	0.0911649	−	0.995836i	$-0.470941\pi$
$823$	−22.5809	−	14.8517i	−0.787119	−	0.517696i	−0.878284	+	0.478139i	$0.841311\pi$
$824$	−0.977036	+	16.7751i	−0.0340367	+	0.584387i
$825$		0			0
$826$	8.39718	−	28.0485i	0.292175	−	0.975934i
$827$	14.9793	−	5.45201i	0.520880	−	0.189585i	−0.0681816	−	0.997673i	$-0.521720\pi$
$827$	14.9793	−	5.45201i	0.520880	−	0.189585i	0.589062	+	0.808088i	$0.299497\pi$
$828$		0			0
$829$	1.59698	+	0.581253i	0.0554654	+	0.0201877i	0.369604	−	0.929189i	$-0.379493\pi$
$829$	1.59698	+	0.581253i	0.0554654	+	0.0201877i	−0.314138	+	0.949377i	$0.601716\pi$
$830$	−12.5269	+	16.8265i	−0.434815	+	0.584058i
$831$		0			0
$832$	−27.2144	−	6.44994i	−0.943490	−	0.223611i
$833$	−1.21826	+	2.82425i	−0.0422103	+	0.0978545i
$834$		0			0
$835$	78.7531	−	51.7967i	2.72536	−	1.79250i
$836$	−4.20527	−	7.28373i	−0.145442	−	0.251913i
$837$		0			0
$838$	0.560786	−	0.971310i	0.0193720	−	0.0335534i
$839$	−2.69510	−	46.2731i	−0.0930453	−	1.59753i	−0.645353	−	0.763885i	$-0.723290\pi$
$839$	−2.69510	−	46.2731i	−0.0930453	−	1.59753i	0.552307	−	0.833641i	$-0.313747\pi$
$840$		0			0
$841$	28.5901	−	3.34170i	0.985865	−	0.115231i
$842$	46.5568	−	49.3473i	1.60445	−	1.70062i
$843$		0			0
$844$	18.8995	+	2.20904i	0.650548	+	0.0760382i
$845$	20.3343	−	17.0625i	0.699523	−	0.586969i
$846$		0			0
$847$	26.6409	+	22.3544i	0.915393	+	0.768106i
$848$	22.2676	+	23.6023i	0.764673	+	0.810506i
$849$		0			0
$850$	−14.3217	+	7.19262i	−0.491229	+	0.246705i
$851$	−9.72001	+	4.88157i	−0.333198	+	0.167338i
$852$		0			0
$853$	16.6035	+	17.5986i	0.568492	+	0.602566i	0.946289	−	0.323322i	$-0.104800\pi$
$853$	16.6035	+	17.5986i	0.568492	+	0.602566i	−0.377797	+	0.925888i	$0.623318\pi$
$854$	−1.44446	−	1.21204i	−0.0494283	−	0.0414753i
$855$		0			0
$856$	2.85228	−	2.39335i	0.0974891	−	0.0818031i
$857$	−12.7419	−	1.48931i	−0.435254	−	0.0508739i	−0.104355	−	0.994540i	$-0.533278\pi$
$857$	−12.7419	−	1.48931i	−0.435254	−	0.0508739i	−0.330899	+	0.943666i	$0.607352\pi$
$858$		0			0
$859$	−14.0817	+	14.9257i	−0.480461	+	0.509259i	−0.921579	−	0.388190i	$-0.873100\pi$
$859$	−14.0817	+	14.9257i	−0.480461	+	0.509259i	0.441118	+	0.897449i	$0.354582\pi$
$860$	56.8880	−	6.64926i	1.93987	−	0.226738i
$861$		0			0
$862$	0.662209	+	11.3697i	0.0225549	+	0.387253i
$863$	−18.5110	+	32.0620i	−0.630121	+	1.09140i	0.357405	+	0.933949i	$0.383662\pi$
$863$	−18.5110	+	32.0620i	−0.630121	+	1.09140i	−0.987527	+	0.157453i	$0.949672\pi$
$864$		0			0
$865$	30.1945	+	52.2984i	1.02664	+	1.77820i
$866$	−58.8515	+	38.7072i	−1.99986	+	1.31533i
$867$		0			0
$868$	12.8961	−	29.8965i	0.437721	−	1.01475i
$869$	−3.17861	−	0.753344i	−0.107827	−	0.0255555i
$870$		0			0
$871$	−2.84694	+	3.82410i	−0.0964648	+	0.129575i
$872$	16.4237	+	5.97775i	0.556178	+	0.202432i
$873$		0			0
$874$	20.4042	−	7.42652i	0.690182	−	0.251206i
$875$	−19.1959	+	64.1189i	−0.648941	+	2.16762i
$876$		0			0
$877$	−2.52161	+	43.2944i	−0.0851488	+	1.46195i	0.637349	+	0.770575i	$0.280031\pi$
$877$	−2.52161	+	43.2944i	−0.0851488	+	1.46195i	−0.722498	+	0.691373i	$0.757006\pi$
$878$	33.0239	+	21.7201i	1.11450	+	0.733019i
$879$		0			0
$880$	−8.08409	+	1.91596i	−0.272515	+	0.0645872i
$881$	−1.78531	+	10.1250i	−0.0601486	+	0.341120i	−1.00000		0.000464198i	$-0.999852\pi$
$881$	−1.78531	+	10.1250i	−0.0601486	+	0.341120i	0.939851	+	0.341584i	$0.110963\pi$
$882$		0			0
$883$	1.36337	+	7.73205i	0.0458810	+	0.260204i	0.999117	−	0.0420240i	$-0.0133806\pi$
$883$	1.36337	+	7.73205i	0.0458810	+	0.260204i	−0.953236	+	0.302228i	$0.902269\pi$
$884$	−1.81903	−	4.21698i	−0.0611805	−	0.141832i
$885$		0			0
$886$	−11.4507	−	38.2481i	−0.384695	−	1.28497i
$887$	20.8967	+	28.0692i	0.701643	+	0.942471i	0.999928	−	0.0120063i	$-0.00382182\pi$
$887$	20.8967	+	28.0692i	0.701643	+	0.942471i	−0.298284	+	0.954477i	$0.596414\pi$
$888$		0			0
$889$	39.3805	+	19.7776i	1.32078	+	0.663321i
$890$	−44.3751			−1.48746
$891$		0			0
$892$	26.8550			0.899172
$893$	−43.1800	−	21.6858i	−1.44496	−	0.725688i
$894$		0			0
$895$	−16.7105	−	22.4461i	−0.558571	−	0.750292i
$896$	−7.49465	−	25.0339i	−0.250379	−	0.836323i
$897$		0			0
$898$	5.83774	+	13.5334i	0.194808	+	0.451616i
$899$	0.317622	+	1.80133i	0.0105933	+	0.0600776i
$900$		0			0
$901$	−1.49032	+	8.45204i	−0.0496498	+	0.281578i
$902$	7.62207	−	1.80646i	0.253787	−	0.0601487i
$903$		0			0
$904$	−8.68189	−	5.71017i	−0.288755	−	0.189917i
$905$	−1.75148	+	30.0717i	−0.0582210	+	0.999616i
$906$		0			0
$907$	14.4087	−	48.1283i	0.478432	−	1.59807i	−0.289257	−	0.957251i	$-0.593408\pi$
$907$	14.4087	−	48.1283i	0.478432	−	1.59807i	0.767689	−	0.640822i	$-0.221407\pi$
$908$	−25.2752	+	9.19941i	−0.838786	+	0.305293i
$909$		0			0
$910$	−64.1788	−	23.3592i	−2.12751	−	0.774349i
$911$	14.7268	−	19.7816i	0.487922	−	0.655393i	−0.488170	−	0.872748i	$-0.662336\pi$
$911$	14.7268	−	19.7816i	0.487922	−	0.655393i	0.976093	+	0.217355i	$0.0697429\pi$
$912$		0			0
$913$	−1.87537	−	0.444471i	−0.0620657	−	0.0147098i
$914$	31.5072	−	73.0418i	1.04216	−	2.41601i
$915$		0			0
$916$	−4.73694	+	3.11554i	−0.156513	+	0.102940i
$917$	−16.7783	−	29.0608i	−0.554067	−	0.959672i
$918$		0			0
$919$	−4.12738	+	7.14883i	−0.136150	+	0.235818i	−0.926036	−	0.377435i	$-0.876806\pi$
$919$	−4.12738	+	7.14883i	−0.136150	+	0.235818i	0.789886	+	0.613253i	$0.210139\pi$
$920$	0.521745	+	8.95801i	0.0172014	+	0.295337i
$921$		0			0
$922$	−58.0779	+	6.78833i	−1.91269	+	0.223562i
$923$	11.5230	−	12.2137i	0.379285	−	0.402018i
$924$		0			0
$925$	47.9764	+	5.60763i	1.57745	+	0.184378i
$926$	39.8178	−	33.4111i	1.30849	−	1.09796i
$927$		0			0
$928$	2.83740	+	2.38086i	0.0931422	+	0.0781556i
$929$	−6.73053	−	7.13394i	−0.220821	−	0.234057i	0.607487	−	0.794330i	$-0.292178\pi$
$929$	−6.73053	−	7.13394i	−0.220821	−	0.234057i	−0.828308	+	0.560273i	$0.810696\pi$
$930$		0			0
$931$	−16.5380	+	8.30568i	−0.542010	+	0.272208i
$932$	−39.4161	+	19.7955i	−1.29112	+	0.648424i
$933$		0			0
$934$	11.4133	+	12.0974i	0.373455	+	0.395839i
$935$	−1.68332	−	1.41247i	−0.0550503	−	0.0461927i
$936$		0			0
$937$	33.8490	−	28.4027i	1.10580	−	0.927875i	0.107997	−	0.994151i	$-0.465556\pi$
$937$	33.8490	−	28.4027i	1.10580	−	0.927875i	0.997801	+	0.0662763i	$0.0211119\pi$
$938$	−13.4396	−	1.57086i	−0.438819	−	0.0512905i
$939$		0			0
$940$	71.2275	−	75.4967i	2.32318	−	2.46243i
$941$	−10.5684	+	1.23526i	−0.344519	+	0.0402684i	−0.286593	−	0.958052i	$-0.592523\pi$
$941$	−10.5684	+	1.23526i	−0.344519	+	0.0402684i	−0.0579256	+	0.998321i	$0.518449\pi$
$942$		0			0
$943$	0.650512	+	11.1689i	0.0211836	+	0.363708i
$944$	5.85073	−	10.1338i	0.190425	−	0.329826i
$945$		0			0
$946$	4.75603	+	8.23768i	0.154632	+	0.267830i
$947$	−9.18551	+	6.04140i	−0.298489	+	0.196319i	−0.689915	−	0.723890i	$-0.742352\pi$
$947$	−9.18551	+	6.04140i	−0.298489	+	0.196319i	0.391426	+	0.920209i	$0.371982\pi$
$948$		0			0
$949$	7.81015	−	18.1060i	0.253528	−	0.587745i
$950$	−93.8280	−	22.2376i	−3.04418	−	0.721485i
$951$		0			0
$952$	1.49747	−	2.01145i	0.0485332	−	0.0651914i
$953$	−39.7723	−	14.4759i	−1.28835	−	0.468921i	−0.395165	−	0.918610i	$-0.629313\pi$
$953$	−39.7723	−	14.4759i	−1.28835	−	0.468921i	−0.893185	+	0.449689i	$0.851535\pi$
$954$		0			0
$955$	36.8676	−	13.4187i	1.19301	−	0.434219i
$956$	−8.71206	+	29.1003i	−0.281768	+	0.941171i
$957$		0			0
$958$	−2.17888	+	37.4100i	−0.0703965	+	1.20866i
$959$	26.3845	+	17.3533i	0.851999	+	0.560369i
$960$		0			0
$961$	−15.0430	+	3.56526i	−0.485259	+	0.115008i
$962$	−4.34483	+	24.6407i	−0.140083	+	0.794449i
$963$		0			0
$964$	7.52523	+	42.6777i	0.242371	+	1.37456i
$965$	24.6587	+	57.1654i	0.793793	+	1.84022i
$966$		0			0
$967$	2.38375	+	7.96226i	0.0766561	+	0.256049i	0.987724	−	0.156206i	$-0.0499264\pi$
$967$	2.38375	+	7.96226i	0.0766561	+	0.256049i	−0.911068	+	0.412255i	$0.864741\pi$
$968$	−6.27654	−	8.43085i	−0.201736	−	0.270978i
$969$		0			0
$970$	−69.8384	−	35.0742i	−2.24238	−	1.12616i
$971$	17.9539			0.576169			0.288084	−	0.957605i	$-0.406982\pi$
$971$	17.9539			0.576169			0.288084	+	0.957605i	$0.406982\pi$
$972$		0			0
$973$	35.0207			1.12271
$974$	−79.6265	−	39.9899i	−2.55140	−	1.28136i
$975$		0			0
$976$	−0.450019	−	0.604480i	−0.0144048	−	0.0193489i
$977$	−7.00093	−	23.3847i	−0.223979	−	0.748144i	−0.993927	−	0.110037i	$-0.964903\pi$
$977$	−7.00093	−	23.3847i	−0.223979	−	0.748144i	0.769948	−	0.638107i	$-0.220282\pi$
$978$		0			0
$979$	−1.61482	−	3.74356i	−0.0516097	−	0.119645i
$980$	−6.90304	−	39.1491i	−0.220509	−	1.25057i
$981$		0			0
$982$	2.67375	−	15.1636i	0.0853228	−	0.483890i
$983$	−45.3567	+	10.7497i	−1.44665	+	0.342863i	−0.877583	−	0.479425i	$-0.840845\pi$
$983$	−45.3567	+	10.7497i	−1.44665	+	0.342863i	−0.569071	+	0.822288i	$0.692697\pi$
$984$		0			0
$985$	−35.6799	−	23.4670i	−1.13686	−	0.747722i
$986$	−0.0425773	+	0.731025i	−0.00135594	+	0.0232806i
$987$		0			0
$988$	7.92511	−	26.4717i	0.252131	−	0.842177i
$989$	−12.7663	+	4.64654i	−0.405944	+	0.147751i
$990$		0			0
$991$	−55.3339	−	20.1399i	−1.75774	−	0.639765i	−0.757820	−	0.652464i	$-0.773735\pi$
$991$	−55.3339	−	20.1399i	−1.75774	−	0.639765i	−0.999919	+	0.0126995i	$0.995958\pi$
$992$	18.7920	−	25.2421i	0.596648	−	0.801437i
$993$		0			0
$994$	46.3732	+	10.9906i	1.47087	+	0.348602i
$995$	−5.41324	+	12.5493i	−0.171611	+	0.397839i
$996$		0			0
$997$	−50.3721	+	33.1302i	−1.59530	+	1.04925i	−0.634154	+	0.773207i	$0.718651\pi$
$997$	−50.3721	+	33.1302i	−1.59530	+	1.04925i	−0.961147	+	0.276038i	$0.910978\pi$
$998$	−17.0636	−	29.5550i	−0.540138	−	0.935547i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.10.7		144
3.2	odd	2		81.2.g.a.13.2	✓	144
9.2	odd	6		729.2.g.d.514.7		144
9.4	even	3		729.2.g.b.28.2		144
9.5	odd	6		729.2.g.c.28.7		144
9.7	even	3		729.2.g.a.514.2		144
81.2	odd	54		729.2.g.c.703.7		144
81.5	odd	54		6561.2.a.c.1.12		72
81.25	even	27	inner	243.2.g.a.73.7		144
81.29	odd	54		729.2.g.d.217.7		144
81.52	even	27		729.2.g.a.217.2		144
81.56	odd	54		81.2.g.a.25.2	yes	144
81.76	even	27		6561.2.a.d.1.61		72
81.79	even	27		729.2.g.b.703.2		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.2	✓	144	3.2	odd	2
81.2.g.a.25.2	yes	144	81.56	odd	54
243.2.g.a.10.7		144	1.1	even	1	trivial
243.2.g.a.73.7		144	81.25	even	27	inner
729.2.g.a.217.2		144	81.52	even	27
729.2.g.a.514.2		144	9.7	even	3
729.2.g.b.28.2		144	9.4	even	3
729.2.g.b.703.2		144	81.79	even	27
729.2.g.c.28.7		144	9.5	odd	6
729.2.g.c.703.7		144	81.2	odd	54
729.2.g.d.217.7		144	81.29	odd	54
729.2.g.d.514.7		144	9.2	odd	6
6561.2.a.c.1.12		72	81.5	odd	54
6561.2.a.d.1.61		72	81.76	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.89071 + 0.949549i) q^{2} +(1.47882 + 1.98639i) q^{4} +(1.11651 + 3.72940i) q^{5} +(-1.32100 - 3.06243i) q^{7} +(0.175036 + 0.992677i) q^{8} +(-1.43025 + 8.11138i) q^{10} +(-0.736337 + 0.174515i) q^{11} +(-2.07722 - 1.36621i) q^{13} +(0.410296 - 7.04452i) q^{14} +(0.808837 - 2.70170i) q^{16} +(0.700932 - 0.255119i) q^{17} +(4.21736 + 1.53499i) q^{19} +(-5.75694 + 7.73291i) q^{20} +(-1.55791 - 0.369231i) q^{22} +(0.905723 - 2.09970i) q^{23} +(-8.48436 + 5.58025i) q^{25} +(-2.63013 - 4.55552i) q^{26} +(4.12967 - 7.15280i) q^{28} +(0.0269788 + 0.463208i) q^{29} +(3.91546 - 0.457651i) q^{31} +(5.47813 - 5.80647i) q^{32} +(1.56751 + 0.183215i) q^{34} +(9.94610 - 8.34577i) q^{35} +(-3.64375 - 3.05747i) q^{37} +(6.51625 + 6.90682i) q^{38} +(-3.50665 + 1.76111i) q^{40} +(-4.37210 + 2.19575i) q^{41} +(-4.07702 - 4.32138i) q^{43} +(-1.43556 - 1.20458i) q^{44} +(3.70623 - 3.10990i) q^{46} +(-10.6936 - 1.24990i) q^{47} +(-2.82973 + 2.99934i) q^{49} +(-21.3402 + 2.49431i) q^{50} +(-0.357995 - 6.14654i) q^{52} +(-5.75294 + 9.96438i) q^{53} +(-1.47296 - 2.55124i) q^{55} +(2.80878 - 1.84736i) q^{56} +(-0.388830 + 0.901409i) q^{58} +(4.03735 + 0.956869i) q^{59} +(0.159571 - 0.214341i) q^{61} +(7.83755 + 2.85264i) q^{62} +(10.5709 - 3.84748i) q^{64} +(2.77590 - 9.27214i) q^{65} +(0.111496 - 1.91430i) q^{67} +(1.54332 + 1.01506i) q^{68} +(26.7299 - 6.33510i) q^{70} +(-1.17278 + 6.65118i) q^{71} +(1.37723 + 7.81064i) q^{73} +(-3.98605 - 9.24071i) q^{74} +(3.18760 + 10.6473i) q^{76} +(1.50714 + 2.02444i) q^{77} +(3.85762 + 1.93737i) q^{79} +10.9788 q^{80} -10.3513 q^{82} +(2.27599 + 1.14304i) q^{83} +(1.73403 + 2.32921i) q^{85} +(-3.60508 - 12.0418i) q^{86} +(-0.302122 - 0.700398i) q^{88} +(0.935549 + 5.30576i) q^{89} +(-1.43990 + 8.16609i) q^{91} +(5.51024 - 1.30595i) q^{92} +(-19.0315 - 12.5172i) q^{94} +(-1.01588 + 17.4421i) q^{95} +(-2.72130 + 9.08977i) q^{97} +(-8.19821 + 2.98391i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

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