LMFDB - Embedded newform 243.2.g.a.226.7

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			226.7
Character	$\chi$	$=$	243.226
Dual form			243.2.g.a.100.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32716 - 1.78269i) q^{2} +(-0.843016 - 2.81587i) q^{4} +(-2.46097 - 1.61861i) q^{5} +(-2.02832 - 2.14989i) q^{7} +(-1.96178 - 0.714030i) q^{8} +(-6.15160 + 2.23900i) q^{10} +(4.74276 + 2.38190i) q^{11} +(-0.291219 + 0.675122i) q^{13} +(-6.52450 + 0.762605i) q^{14} +(1.03509 - 0.680789i) q^{16} +(-1.11298 - 0.933897i) q^{17} +(4.21153 - 3.53390i) q^{19} +(-2.48315 + 8.29430i) q^{20} +(10.5406 - 5.29370i) q^{22} +(-0.309397 + 0.327942i) q^{23} +(1.45610 + 3.37562i) q^{25} +(0.817038 + 1.41515i) q^{26} +(-4.34391 + 7.52387i) q^{28} +(3.53065 + 0.412674i) q^{29} +(-1.08263 - 0.256589i) q^{31} +(0.402873 - 6.91707i) q^{32} +(-3.14195 + 0.744656i) q^{34} +(1.51181 + 8.57387i) q^{35} +(-0.643205 + 3.64780i) q^{37} +(-0.710448 - 12.1979i) q^{38} +(3.67216 + 4.93256i) q^{40} +(6.10675 + 8.20279i) q^{41} +(0.461153 + 7.91770i) q^{43} +(2.70891 - 15.3630i) q^{44} +(0.173998 + 0.986793i) q^{46} +(-5.37376 + 1.27360i) q^{47} +(-0.100945 + 1.73316i) q^{49} +(7.95018 + 1.88423i) q^{50} +(2.14656 + 0.250897i) q^{52} +(1.83020 - 3.17001i) q^{53} +(-7.81644 - 13.5385i) q^{55} +(2.44403 + 5.66589i) q^{56} +(5.42142 - 5.74637i) q^{58} +(-6.40358 + 3.21600i) q^{59} +(-1.24903 + 4.17204i) q^{61} +(-1.89425 + 1.58947i) q^{62} +(-9.89820 - 8.30558i) q^{64} +(1.80944 - 1.19009i) q^{65} +(-11.2400 + 1.31377i) q^{67} +(-1.69148 + 3.92129i) q^{68} +(17.2910 + 8.68386i) q^{70} +(12.6408 - 4.60088i) q^{71} +(3.72979 + 1.35753i) q^{73} +(5.64926 + 5.98787i) q^{74} +(-13.5014 - 8.88000i) q^{76} +(-4.49899 - 15.0277i) q^{77} +(1.69751 - 2.28015i) q^{79} -3.64926 q^{80} +22.7277 q^{82} +(-0.210107 + 0.282223i) q^{83} +(1.22739 + 4.09977i) q^{85} +(14.7268 + 9.68599i) q^{86} +(-7.60351 - 8.05925i) q^{88} +(-5.34347 - 1.94487i) q^{89} +(2.04212 - 0.743272i) q^{91} +(1.18427 + 0.594763i) q^{92} +(-4.86142 + 11.2700i) q^{94} +(-16.0845 + 1.88000i) q^{95} +(5.88981 - 3.87379i) q^{97} +(2.95571 + 2.48014i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{27}\right)$

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 $

$2$	1.32716	−	1.78269i	0.938447	−	1.26055i	−0.0269146	−	0.999638i	$-0.508568\pi$
$2$	1.32716	−	1.78269i	0.938447	−	1.26055i	0.965362	−	0.260915i	$-0.0840244\pi$
$3$		0			0
$3$		0			0
$4$	−0.843016	−	2.81587i	−0.421508	−	1.40794i
$5$	−2.46097	−	1.61861i	−1.10058	−	0.723864i	−0.136811	−	0.990597i	$-0.543685\pi$
$5$	−2.46097	−	1.61861i	−1.10058	−	0.723864i	−0.963770	+	0.266734i	$0.914056\pi$
$6$		0			0
$7$	−2.02832	−	2.14989i	−0.766632	−	0.812582i	0.220008	−	0.975498i	$-0.429392\pi$
$7$	−2.02832	−	2.14989i	−0.766632	−	0.812582i	−0.986640	+	0.162916i	$0.947910\pi$
$8$	−1.96178	−	0.714030i	−0.693594	−	0.252448i
$9$		0			0
$10$	−6.15160	+	2.23900i	−1.94531	+	0.708033i
$11$	4.74276	+	2.38190i	1.43000	+	0.718171i	0.984216	−	0.176971i	$-0.0566299\pi$
$11$	4.74276	+	2.38190i	1.43000	+	0.718171i	0.445781	+	0.895142i	$0.352926\pi$
$12$		0			0
$13$	−0.291219	+	0.675122i	−0.0807696	+	0.187245i	−0.953816	−	0.300393i	$-0.902882\pi$
$13$	−0.291219	+	0.675122i	−0.0807696	+	0.187245i	0.873046	+	0.487638i	$0.162141\pi$
$14$	−6.52450	+	0.762605i	−1.74375	+	0.203815i
$15$		0			0
$16$	1.03509	−	0.680789i	0.258772	−	0.170197i
$17$	−1.11298	−	0.933897i	−0.269936	−	0.226503i	0.497764	−	0.867312i	$-0.334155\pi$
$17$	−1.11298	−	0.933897i	−0.269936	−	0.226503i	−0.767700	+	0.640809i	$0.778599\pi$
$18$		0			0
$19$	4.21153	−	3.53390i	0.966192	−	0.810731i	−0.0157573	−	0.999876i	$-0.505016\pi$
$19$	4.21153	−	3.53390i	0.966192	−	0.810731i	0.981949	+	0.189145i	$0.0605715\pi$
$20$	−2.48315	+	8.29430i	−0.555249	+	1.85466i
$21$		0			0
$22$	10.5406	−	5.29370i	2.24727	−	1.12862i
$23$	−0.309397	+	0.327942i	−0.0645138	+	0.0683806i	−0.758827	−	0.651293i	$-0.774227\pi$
$23$	−0.309397	+	0.327942i	−0.0645138	+	0.0683806i	0.694313	+	0.719673i	$0.255708\pi$
$24$		0			0
$25$	1.45610	+	3.37562i	0.291220	+	0.675125i
$26$	0.817038	+	1.41515i	0.160234	+	0.277534i
$27$		0			0
$28$	−4.34391	+	7.52387i	−0.820921	+	1.42188i
$29$	3.53065	+	0.412674i	0.655625	+	0.0766316i	0.437400	−	0.899267i	$-0.355899\pi$
$29$	3.53065	+	0.412674i	0.655625	+	0.0766316i	0.218225	+	0.975898i	$0.429973\pi$
$30$		0			0
$31$	−1.08263	−	0.256589i	−0.194447	−	0.0460847i	0.132238	−	0.991218i	$-0.457784\pi$
$31$	−1.08263	−	0.256589i	−0.194447	−	0.0460847i	−0.326685	+	0.945133i	$0.605932\pi$
$32$	0.402873	−	6.91707i	0.0712186	−	1.22278i
$33$		0			0
$34$	−3.14195	+	0.744656i	−0.538840	+	0.127707i
$35$	1.51181	+	8.57387i	0.255542	+	1.44925i
$36$		0			0
$37$	−0.643205	+	3.64780i	−0.105742	+	0.599695i	0.885179	+	0.465251i	$0.154036\pi$
$37$	−0.643205	+	3.64780i	−0.105742	+	0.599695i	−0.990921	+	0.134444i	$0.957075\pi$
$38$	−0.710448	−	12.1979i	−0.115250	−	1.97876i
$39$		0			0
$40$	3.67216	+	4.93256i	0.580619	+	0.779907i
$41$	6.10675	+	8.20279i	0.953714	+	1.28106i	0.959685	+	0.281078i	$0.0906921\pi$
$41$	6.10675	+	8.20279i	0.953714	+	1.28106i	−0.00597066	+	0.999982i	$0.501901\pi$
$42$		0			0
$43$	0.461153	+	7.91770i	0.0703252	+	1.20744i	0.830237	+	0.557411i	$0.188205\pi$
$43$	0.461153	+	7.91770i	0.0703252	+	1.20744i	−0.759912	+	0.650026i	$0.774758\pi$
$44$	2.70891	−	15.3630i	0.408383	−	2.31606i
$45$		0			0
$46$	0.173998	+	0.986793i	0.0256546	+	0.145495i
$47$	−5.37376	+	1.27360i	−0.783843	+	0.185774i	−0.603004	−	0.797738i	$-0.706030\pi$
$47$	−5.37376	+	1.27360i	−0.783843	+	0.185774i	−0.180840	+	0.983513i	$0.557881\pi$
$48$		0			0
$49$	−0.100945	+	1.73316i	−0.0144207	+	0.247594i
$50$	7.95018	+	1.88423i	1.12433	+	0.266470i
$51$		0			0
$52$	2.14656	+	0.250897i	0.297674	+	0.0347931i
$53$	1.83020	−	3.17001i	0.251398	−	0.435434i	−0.712513	−	0.701659i	$-0.752443\pi$
$53$	1.83020	−	3.17001i	0.251398	−	0.435434i	0.963911	+	0.266225i	$0.0857764\pi$
$54$		0			0
$55$	−7.81644	−	13.5385i	−1.05397	−	1.82553i
$56$	2.44403	+	5.66589i	0.326597	+	0.757136i
$57$		0			0
$58$	5.42142	−	5.74637i	0.711868	−	0.754536i
$59$	−6.40358	+	3.21600i	−0.833675	+	0.418687i	−0.813821	−	0.581116i	$-0.802616\pi$
$59$	−6.40358	+	3.21600i	−0.833675	+	0.418687i	−0.0198540	+	0.999803i	$0.506320\pi$
$60$		0			0
$61$	−1.24903	+	4.17204i	−0.159922	+	0.534175i	−0.999965	−	0.00834355i	$-0.997344\pi$
$61$	−1.24903	+	4.17204i	−0.159922	+	0.534175i	0.840044	+	0.542519i	$0.182529\pi$
$62$	−1.89425	+	1.58947i	−0.240570	+	0.201862i
$63$		0			0
$64$	−9.89820	−	8.30558i	−1.23728	−	1.03820i
$65$	1.80944	−	1.19009i	0.224433	−	0.147612i
$66$		0			0
$67$	−11.2400	+	1.31377i	−1.37318	+	0.160502i	−0.770481	−	0.637463i	$-0.779984\pi$
$67$	−11.2400	+	1.31377i	−1.37318	+	0.160502i	−0.602704	+	0.797965i	$0.705910\pi$
$68$	−1.69148	+	3.92129i	−0.205122	+	0.475526i
$69$		0			0
$70$	17.2910	+	8.68386i	2.06667	+	1.03792i
$71$	12.6408	−	4.60088i	1.50019	−	0.546024i	0.544079	−	0.839034i	$-0.316879\pi$
$71$	12.6408	−	4.60088i	1.50019	−	0.546024i	0.956109	+	0.293010i	$0.0946568\pi$
$72$		0			0
$73$	3.72979	+	1.35753i	0.436538	+	0.158887i	0.550935	−	0.834548i	$-0.314271\pi$
$73$	3.72979	+	1.35753i	0.436538	+	0.158887i	−0.114397	+	0.993435i	$0.536493\pi$
$74$	5.64926	+	5.98787i	0.656713	+	0.696075i
$75$		0			0
$76$	−13.5014	−	8.88000i	−1.54872	−	1.01861i
$77$	−4.49899	−	15.0277i	−0.512707	−	1.71256i
$78$		0			0
$79$	1.69751	−	2.28015i	0.190985	−	0.256537i	−0.696308	−	0.717743i	$-0.745175\pi$
$79$	1.69751	−	2.28015i	0.190985	−	0.256537i	0.887293	+	0.461205i	$0.152583\pi$
$80$	−3.64926			−0.408000
$81$		0			0
$82$	22.7277			2.50986
$83$	−0.210107	+	0.282223i	−0.0230623	+	0.0309780i	−0.813505	−	0.581558i	$-0.802443\pi$
$83$	−0.210107	+	0.282223i	−0.0230623	+	0.0309780i	0.790442	+	0.612536i	$0.209851\pi$
$84$		0			0
$85$	1.22739	+	4.09977i	0.133129	+	0.444682i
$86$	14.7268	+	9.68599i	1.58804	+	1.04447i
$87$		0			0
$88$	−7.60351	−	8.05925i	−0.810537	−	0.859119i
$89$	−5.34347	−	1.94487i	−0.566407	−	0.206155i	0.0429141	−	0.999079i	$-0.486336\pi$
$89$	−5.34347	−	1.94487i	−0.566407	−	0.206155i	−0.609321	+	0.792923i	$0.708558\pi$
$90$		0			0
$91$	2.04212	−	0.743272i	0.214073	−	0.0779160i
$92$	1.18427	+	0.594763i	0.123469	+	0.0620083i
$93$		0			0
$94$	−4.86142	+	11.2700i	−0.501417	+	1.16242i
$95$	−16.0845	+	1.88000i	−1.65023	+	0.192884i
$96$		0			0
$97$	5.88981	−	3.87379i	0.598019	−	0.393323i	−0.214103	−	0.976811i	$-0.568683\pi$
$97$	5.88981	−	3.87379i	0.598019	−	0.393323i	0.812122	+	0.583488i	$0.198312\pi$
$98$	2.95571	+	2.48014i	0.298572	+	0.250532i
$99$		0			0
$100$	8.27780	−	6.94590i	0.827780	−	0.694590i
$101$	3.04350	−	10.1660i	0.302839	−	1.01155i	−0.662174	−	0.749351i	$-0.730366\pi$
$101$	3.04350	−	10.1660i	0.302839	−	1.01155i	0.965013	−	0.262203i	$-0.0844490\pi$
$102$		0			0
$103$	−15.9257	+	7.99820i	−1.56921	+	0.788086i	−0.999432	−	0.0337138i	$-0.989267\pi$
$103$	−15.9257	+	7.99820i	−1.56921	+	0.788086i	−0.569776	+	0.821800i	$0.692970\pi$
$104$	1.05336	−	1.11650i	0.103291	−	0.109482i
$105$		0			0
$106$	−3.22216	−	7.46981i	−0.312964	−	0.725532i
$107$	−0.0249146	−	0.0431534i	−0.00240859	−	0.00417180i	0.864819	−	0.502084i	$-0.167433\pi$
$107$	−0.0249146	−	0.0431534i	−0.00240859	−	0.00417180i	−0.867227	+	0.497913i	$0.834100\pi$
$108$		0			0
$109$	0.202520	−	0.350775i	0.0193979	−	0.0335981i	−0.856164	−	0.516705i	$-0.827158\pi$
$109$	0.202520	−	0.350775i	0.0193979	−	0.0335981i	0.875561	+	0.483107i	$0.160492\pi$
$110$	−34.5086	−	4.03348i	−3.29027	−	0.384577i
$111$		0			0
$112$	−3.56311	−	0.844473i	−0.336682	−	0.0797952i
$113$	−0.661442	+	11.3565i	−0.0622232	+	1.06833i	0.812266	+	0.583287i	$0.198234\pi$
$113$	−0.661442	+	11.3565i	−0.0622232	+	1.06833i	−0.874490	+	0.485044i	$0.838803\pi$
$114$		0			0
$115$	1.29223	−	0.306264i	0.120501	−	0.0285592i
$116$	−1.81436	−	10.2897i	−0.168459	−	0.955379i
$117$		0			0
$118$	−2.76547	+	15.6838i	−0.254582	+	1.44381i
$119$	0.249690	+	4.28701i	0.0228891	+	0.392990i
$120$		0			0
$121$	10.2516	+	13.7703i	0.931962	+	1.25184i
$122$	5.77980	+	7.76362i	0.523278	+	0.702885i
$123$		0			0
$124$	0.190157	+	3.26486i	0.0170766	+	0.293193i
$125$	−0.677067	+	3.83984i	−0.0605587	+	0.343445i
$126$		0			0
$127$	2.26532	+	12.8473i	0.201015	+	1.14001i	0.903589	+	0.428401i	$0.140923\pi$
$127$	2.26532	+	12.8473i	0.201015	+	1.14001i	−0.702574	+	0.711611i	$0.747966\pi$
$128$	−14.4588	+	3.42680i	−1.27799	+	0.302889i
$129$		0			0
$130$	0.279866	−	4.80512i	0.0245459	−	0.421436i
$131$	−7.79184	−	1.84670i	−0.680776	−	0.161347i	−0.124343	−	0.992239i	$-0.539682\pi$
$131$	−7.79184	−	1.84670i	−0.680776	−	0.161347i	−0.556433	+	0.830892i	$0.687830\pi$
$132$		0			0
$133$	−16.1398	−	1.88647i	−1.39950	−	0.163578i
$134$	−12.5753	+	21.7810i	−1.08634	+	1.88160i
$135$		0			0
$136$	1.51658	+	2.62680i	0.130046	+	0.225246i
$137$	4.08774	+	9.47644i	0.349239	+	0.809627i	0.998784	+	0.0493036i	$0.0157002\pi$
$137$	4.08774	+	9.47644i	0.349239	+	0.809627i	−0.649545	+	0.760323i	$0.725041\pi$
$138$		0			0
$139$	11.9776	−	12.6956i	1.01593	−	1.07682i	0.0188987	−	0.999821i	$-0.493984\pi$
$139$	11.9776	−	12.6956i	1.01593	−	1.07682i	0.997031	−	0.0770012i	$-0.0245345\pi$
$140$	22.8684	−	11.4850i	1.93274	−	0.970656i
$141$		0			0
$142$	8.57449	−	28.6408i	0.719555	−	2.40348i
$143$	−2.98926	+	2.50829i	−0.249974	+	0.209753i
$144$		0			0
$145$	−8.02088	−	6.73032i	−0.666098	−	0.558923i
$146$	7.37010	−	4.84739i	0.609954	−	0.401173i
$147$		0			0
$148$	10.8140	−	1.26397i	0.888902	−	0.103898i
$149$	3.29309	−	7.63423i	0.269780	−	0.625421i	−0.728437	−	0.685113i	$-0.759753\pi$
$149$	3.29309	−	7.63423i	0.269780	−	0.625421i	0.998217	+	0.0596926i	$0.0190120\pi$
$150$		0			0
$151$	−15.7285	−	7.89913i	−1.27996	−	0.642822i	−0.326748	−	0.945111i	$-0.605953\pi$
$151$	−15.7285	−	7.89913i	−1.27996	−	0.642822i	−0.953216	+	0.302289i	$0.902249\pi$
$152$	−10.7854	+	3.92557i	−0.874812	+	0.318406i
$153$		0			0
$154$	−32.7606	−	11.9239i	−2.63992	−	0.960854i
$155$	2.24902	+	2.38382i	0.180645	+	0.191473i
$156$		0			0
$157$	1.80033	+	1.18409i	0.143682	+	0.0945009i	0.619315	−	0.785143i	$-0.287411\pi$
$157$	1.80033	+	1.18409i	0.143682	+	0.0945009i	−0.475633	+	0.879644i	$0.657781\pi$
$158$	−1.81193	−	6.05228i	−0.144150	−	0.481493i
$159$		0			0
$160$	−12.1875	+	16.3706i	−0.963505	+	1.29421i
$161$	1.33260			0.105023
$162$		0			0
$163$	9.47594			0.742213			0.371106	−	0.928590i	$-0.378979\pi$
$163$	9.47594			0.742213			0.371106	+	0.928590i	$0.378979\pi$
$164$	17.9499	−	24.1109i	1.40165	−	1.88275i
$165$		0			0
$166$	0.224270	+	0.749113i	0.0174067	+	0.0581424i
$167$	−3.19286	−	2.09998i	−0.247071	−	0.162501i	0.419933	−	0.907555i	$-0.362053\pi$
$167$	−3.19286	−	2.09998i	−0.247071	−	0.162501i	−0.667005	+	0.745054i	$0.732424\pi$
$168$		0			0
$169$	8.55016	+	9.06264i	0.657705	+	0.697126i
$170$	8.93757	+	3.25301i	0.685480	+	0.249494i
$171$		0			0
$172$	21.9064	−	7.97329i	1.67035	−	0.607958i
$173$	−7.47680	−	3.75499i	−0.568451	−	0.285487i	0.141269	−	0.989971i	$-0.454882\pi$
$173$	−7.47680	−	3.75499i	−0.568451	−	0.285487i	−0.709719	+	0.704485i	$0.751178\pi$
$174$		0			0
$175$	4.30378	−	9.97729i	0.325336	−	0.754213i
$176$	6.53076	−	0.763336i	0.492274	−	0.0575386i
$177$		0			0
$178$	−10.5588	+	6.94461i	−0.791413	+	0.520521i
$179$	−4.19854	−	3.52299i	−0.313814	−	0.263321i	0.472252	−	0.881463i	$-0.343441\pi$
$179$	−4.19854	−	3.52299i	−0.313814	−	0.263321i	−0.786066	+	0.618142i	$0.787886\pi$
$180$		0			0
$181$	16.7963	−	14.0938i	1.24846	−	1.04758i	0.251645	−	0.967820i	$-0.419028\pi$
$181$	16.7963	−	14.0938i	1.24846	−	1.04758i	0.996814	−	0.0797621i	$-0.0254161\pi$
$182$	1.38521	−	4.62692i	0.102678	−	0.342970i
$183$		0			0
$184$	0.841130	−	0.422431i	0.0620089	−	0.0311421i
$185$	7.48727	−	7.93604i	0.550475	−	0.583469i
$186$		0			0
$187$	−3.05412	−	7.08025i	−0.223340	−	0.517759i
$188$	8.11647	+	14.0581i	0.591955	+	1.02530i
$189$		0			0
$190$	−17.9953	+	31.1687i	−1.30551	+	2.26122i
$191$	−12.6562	−	1.47930i	−0.915772	−	0.107038i	−0.354865	−	0.934917i	$-0.615473\pi$
$191$	−12.6562	−	1.47930i	−0.915772	−	0.107038i	−0.560907	+	0.827879i	$0.689547\pi$
$192$		0			0
$193$	19.7847	+	4.68906i	1.42413	+	0.337526i	0.869238	−	0.494394i	$-0.164610\pi$
$193$	19.7847	+	4.68906i	1.42413	+	0.337526i	0.554896	+	0.831920i	$0.312758\pi$
$194$	0.910976	−	15.6409i	0.0654043	−	1.12295i
$195$		0			0
$196$	4.96544	−	1.17683i	0.354674	−	0.0840594i
$197$	0.696981	+	3.95277i	0.0496578	+	0.281623i	0.999518	−	0.0310522i	$-0.00988582\pi$
$197$	0.696981	+	3.95277i	0.0496578	+	0.281623i	−0.949860	+	0.312676i	$0.898775\pi$
$198$		0			0
$199$	0.667809	−	3.78734i	0.0473398	−	0.268477i	−0.951946	−	0.306266i	$-0.900920\pi$
$199$	0.667809	−	3.78734i	0.0473398	−	0.268477i	0.999286	+	0.0377889i	$0.0120314\pi$
$200$	−0.446257	−	7.66194i	−0.0315551	−	0.541781i
$201$		0			0
$202$	−14.0836	−	18.9176i	−0.990918	−	1.33103i
$203$	−6.27407	−	8.42754i	−0.440354	−	0.591497i
$204$		0			0
$205$	−1.75145	−	30.0713i	−0.122327	−	2.10027i
$206$	−6.87773	+	39.0056i	−0.479195	+	2.71765i
$207$		0			0
$208$	0.158178	+	0.897070i	0.0109676	+	0.0622006i
$209$	28.3917	−	6.72896i	1.96390	−	0.465452i
$210$		0			0
$211$	−0.414462	+	7.11605i	−0.0285328	+	0.489889i	0.953526	+	0.301312i	$0.0974245\pi$
$211$	−0.414462	+	7.11605i	−0.0285328	+	0.489889i	−0.982058	+	0.188577i	$0.939613\pi$
$212$	−10.4692	−	2.48125i	−0.719029	−	0.170413i
$213$		0			0
$214$	−0.109995	−	0.0128566i	−0.00751911	−	0.000878858i
$215$	11.6808	−	20.2317i	0.796621	−	1.37979i
$216$		0			0
$217$	1.64429	+	2.84799i	0.111621	+	0.193334i
$218$	−0.356546	−	0.826566i	−0.0241483	−	0.0559821i
$219$		0			0
$220$	−31.5332	+	33.4233i	−2.12597	+	2.25340i
$221$	0.954614	−	0.479425i	0.0642143	−	0.0322496i
$222$		0			0
$223$	−4.25881	+	14.2254i	−0.285191	+	0.952604i	0.688596	+	0.725145i	$0.258227\pi$
$223$	−4.25881	+	14.2254i	−0.285191	+	0.952604i	−0.973788	+	0.227460i	$0.926958\pi$
$224$	−15.6881	+	13.1639i	−1.04820	+	0.879548i
$225$		0			0
$226$	19.3673	+	16.2511i	1.28829	+	1.08101i
$227$	−11.2427	+	7.39441i	−0.746201	+	0.490784i	−0.864774	−	0.502161i	$-0.832538\pi$
$227$	−11.2427	+	7.39441i	−0.746201	+	0.490784i	0.118573	+	0.992945i	$0.462168\pi$
$228$		0			0
$229$	3.23737	−	0.378394i	0.213931	−	0.0250050i	−0.00845203	−	0.999964i	$-0.502690\pi$
$229$	3.23737	−	0.378394i	0.213931	−	0.0250050i	0.222383	+	0.974959i	$0.428616\pi$
$230$	1.16903	−	2.71011i	0.0770833	−	0.178699i
$231$		0			0
$232$	−6.63170	−	3.33056i	−0.435392	−	0.218662i
$233$	−7.77413	+	2.82955i	−0.509300	+	0.185370i	−0.583872	−	0.811846i	$-0.698463\pi$
$233$	−7.77413	+	2.82955i	−0.509300	+	0.185370i	0.0745722	+	0.997216i	$0.476241\pi$
$234$		0			0
$235$	15.2861	+	5.56370i	0.997158	+	0.362936i
$236$	14.4542	+	15.3205i	0.940886	+	0.997280i
$237$		0			0
$238$	7.97380	+	5.24445i	0.516865	+	0.339947i
$239$	3.74646	+	12.5141i	0.242339	+	0.809467i	0.989463	+	0.144783i	$0.0462485\pi$
$239$	3.74646	+	12.5141i	0.242339	+	0.809467i	−0.747125	+	0.664684i	$0.768566\pi$
$240$		0			0
$241$	−0.377857	+	0.507550i	−0.0243399	+	0.0326941i	−0.814127	−	0.580687i	$-0.802784\pi$
$241$	−0.377857	+	0.507550i	−0.0243399	+	0.0326941i	0.789787	+	0.613382i	$0.210191\pi$
$242$	38.1537			2.45261
$243$		0			0
$244$	12.8009			0.819493
$245$	3.05372	−	4.10186i	0.195095	−	0.262058i
$246$		0			0
$247$	1.15933	+	3.87244i	0.0737665	+	0.246397i
$248$	1.94068	+	1.27640i	0.123233	+	0.0810517i
$249$		0			0
$250$	5.94666	+	6.30310i	0.376100	+	0.398643i
$251$	−12.9984	−	4.73104i	−0.820454	−	0.298621i	−0.102519	−	0.994731i	$-0.532690\pi$
$251$	−12.9984	−	4.73104i	−0.820454	−	0.298621i	−0.717935	+	0.696110i	$0.754912\pi$
$252$		0			0
$253$	−2.24852	+	0.818396i	−0.141364	+	0.0514521i
$254$	25.9092	+	13.0121i	1.62569	+	0.816451i
$255$		0			0
$256$	−2.84463	+	6.59459i	−0.177789	+	0.412162i
$257$	26.0284	−	3.04229i	1.62361	−	0.189773i	0.744916	−	0.667158i	$-0.232490\pi$
$257$	26.0284	−	3.04229i	1.62361	−	0.189773i	0.878694	+	0.477386i	$0.158415\pi$
$258$		0			0
$259$	9.14699	−	6.01607i	0.568366	−	0.373820i
$260$	−4.87652	−	4.09189i	−0.302429	−	0.253768i
$261$		0			0
$262$	−13.6332	+	11.4396i	−0.842259	+	0.706739i
$263$	0.407994	−	1.36280i	0.0251580	−	0.0840336i	−0.944489	−	0.328544i	$-0.893442\pi$
$263$	0.407994	−	1.36280i	0.0251580	−	0.0840336i	0.969647	+	0.244510i	$0.0786272\pi$
$264$		0			0
$265$	−9.63508	+	4.83892i	−0.591878	+	0.297252i
$266$	−24.7832	+	26.2686i	−1.51955	+	1.61063i
$267$		0			0
$268$	13.1749	+	30.5429i	0.804785	+	1.86570i
$269$	2.73320	+	4.73405i	0.166646	+	0.288640i	0.937239	−	0.348688i	$-0.113373\pi$
$269$	2.73320	+	4.73405i	0.166646	+	0.288640i	−0.770592	+	0.637328i	$0.780039\pi$
$270$		0			0
$271$	−15.3667	+	26.6158i	−0.933458	+	1.61680i	−0.156099	+	0.987741i	$0.549892\pi$
$271$	−15.3667	+	26.6158i	−0.933458	+	1.61680i	−0.777360	+	0.629056i	$0.783442\pi$
$272$	−1.78782	−	0.208966i	−0.108402	−	0.0126704i
$273$		0			0
$274$	22.3187	+	5.28962i	1.34832	+	0.319558i
$275$	−1.13447	+	19.4781i	−0.0684111	+	1.17457i
$276$		0			0
$277$	4.43276	−	1.05058i	0.266339	−	0.0631234i	−0.0952766	−	0.995451i	$-0.530374\pi$
$277$	4.43276	−	1.05058i	0.266339	−	0.0631234i	0.361615	+	0.932327i	$0.382225\pi$
$278$	−6.73596	−	38.2015i	−0.403996	−	2.29117i
$279$		0			0
$280$	3.15617	−	17.8995i	0.188617	−	1.06970i
$281$	1.06252	+	18.2428i	0.0633848	+	1.08827i	0.868671	+	0.495389i	$0.164974\pi$
$281$	1.06252	+	18.2428i	0.0633848	+	1.08827i	−0.805287	+	0.592886i	$0.797989\pi$
$282$		0			0
$283$	−14.1444	−	18.9992i	−0.840794	−	1.12938i	−0.990068	−	0.140587i	$-0.955101\pi$
$283$	−14.1444	−	18.9992i	−0.840794	−	1.12938i	0.149274	−	0.988796i	$-0.452306\pi$
$284$	−23.6119	−	31.7163i	−1.40111	−	1.88202i
$285$		0			0
$286$	0.504261	+	8.65783i	0.0298176	+	0.511948i
$287$	5.24867	−	29.7667i	0.309819	−	1.75707i
$288$		0			0
$289$	−2.58547	−	14.6629i	−0.152086	−	0.862525i
$290$	−22.6431	+	5.36652i	−1.32965	+	0.315133i
$291$		0			0
$292$	0.678361	−	11.6470i	0.0396981	−	0.681590i
$293$	4.63951	+	1.09958i	0.271043	+	0.0642384i	0.363890	−	0.931442i	$-0.381448\pi$
$293$	4.63951	+	1.09958i	0.271043	+	0.0642384i	−0.0928467	+	0.995680i	$0.529597\pi$
$294$		0			0
$295$	20.9645	+	2.45040i	1.22060	+	0.142668i
$296$	3.86647	−	6.69691i	0.224734	−	0.389250i
$297$		0			0
$298$	−9.23901	−	16.0024i	−0.535202	−	0.926996i
$299$	−0.131298	−	0.304384i	−0.00759318	−	0.0176030i
$300$		0			0
$301$	16.0868	−	17.0510i	0.927228	−	0.982804i
$302$	−34.9560	+	17.5556i	−2.01149	+	1.01021i
$303$		0			0
$304$	1.95348	−	6.52506i	0.112040	−	0.374238i
$305$	9.82673	−	8.24560i	0.562677	−	0.472142i
$306$		0			0
$307$	−8.26674	−	6.93662i	−0.471808	−	0.395894i	0.375646	−	0.926763i	$-0.377421\pi$
$307$	−8.26674	−	6.93662i	−0.471808	−	0.395894i	−0.847453	+	0.530870i	$0.821865\pi$
$308$	−38.5233	+	25.3371i	−2.19507	+	1.44372i
$309$		0			0
$310$	7.23443	−	0.845583i	0.410888	−	0.0480259i
$311$	−3.83460	+	8.88961i	−0.217440	+	0.504083i	−0.991667	−	0.128825i	$-0.958880\pi$
$311$	−3.83460	+	8.88961i	−0.217440	+	0.504083i	0.774227	+	0.632908i	$0.218139\pi$
$312$		0			0
$313$	−5.70772	−	2.86653i	−0.322620	−	0.162026i	0.280117	−	0.959966i	$-0.409627\pi$
$313$	−5.70772	−	2.86653i	−0.322620	−	0.162026i	−0.602737	+	0.797940i	$0.705923\pi$
$314$	4.50020	−	1.63794i	0.253961	−	0.0924343i
$315$		0			0
$316$	−7.85165	−	2.85777i	−0.441690	−	0.160762i
$317$	−14.1442	−	14.9919i	−0.794416	−	0.842032i	0.195935	−	0.980617i	$-0.437226\pi$
$317$	−14.1442	−	14.9919i	−0.794416	−	0.842032i	−0.990351	+	0.138585i	$0.955745\pi$
$318$		0			0
$319$	15.7621	+	10.3669i	0.882507	+	0.580434i
$320$	10.9157	+	36.4611i	0.610209	+	2.03824i
$321$		0			0
$322$	1.76857	−	2.37561i	0.0985587	−	0.132387i
$323$	−7.98763			−0.444444
$324$		0			0
$325$	−2.70300			−0.149936
$326$	12.5761	−	16.8927i	0.696527	−	0.935599i
$327$		0			0
$328$	−6.12307	−	20.4525i	−0.338090	−	1.12930i
$329$	13.6378	+	8.96972i	0.751876	+	0.494517i
$330$		0			0
$331$	−13.9290	−	14.7639i	−0.765610	−	0.811499i	0.220884	−	0.975300i	$-0.429106\pi$
$331$	−13.9290	−	14.7639i	−0.765610	−	0.811499i	−0.986493	+	0.163801i	$0.947624\pi$
$332$	0.971828	+	0.353716i	0.0533360	+	0.0194127i
$333$		0			0
$334$	−7.98107	+	2.90487i	−0.436705	+	0.158948i
$335$	29.7878	+	14.9600i	1.62748	+	0.817353i
$336$		0			0
$337$	−1.44819	+	3.35728i	−0.0788880	+	0.182883i	−0.953096	−	0.302669i	$-0.902122\pi$
$337$	−1.44819	+	3.35728i	−0.0788880	+	0.182883i	0.874208	+	0.485552i	$0.161381\pi$
$338$	27.5034	−	3.21468i	1.49599	−	0.174856i
$339$		0			0
$340$	10.5097	−	6.91234i	0.569969	−	0.374874i
$341$	−4.52350	−	3.79567i	−0.244961	−	0.205547i
$342$		0			0
$343$	−11.9185	+	10.0008i	−0.643537	+	0.539992i
$344$	4.74879	−	15.8621i	0.256038	−	0.855225i
$345$		0			0
$346$	−16.6169	+	8.34534i	−0.893332	+	0.448648i
$347$	20.0082	−	21.2074i	1.07410	−	1.13848i	0.0842334	−	0.996446i	$-0.473156\pi$
$347$	20.0082	−	21.2074i	1.07410	−	1.13848i	0.989862	−	0.142029i	$-0.0453627\pi$
$348$		0			0
$349$	6.70643	+	15.5473i	0.358987	+	0.832225i	0.998011	+	0.0630387i	$0.0200792\pi$
$349$	6.70643	+	15.5473i	0.358987	+	0.832225i	−0.639024	+	0.769187i	$0.720662\pi$
$350$	−12.0746	−	20.9138i	−0.645415	−	1.11789i
$351$		0			0
$352$	18.3865	−	31.8464i	0.980005	−	1.69742i
$353$	−22.5947	−	2.64094i	−1.20259	−	0.140563i	−0.508894	−	0.860829i	$-0.669946\pi$
$353$	−22.5947	−	2.64094i	−1.20259	−	0.140563i	−0.693698	+	0.720266i	$0.744020\pi$
$354$		0			0
$355$	−38.5557	−	9.13788i	−2.04633	−	0.484988i
$356$	−0.971854	+	16.6861i	−0.0515082	+	0.884361i
$357$		0			0
$358$	−11.8526	+	2.80911i	−0.626428	+	0.148466i
$359$	2.65948	+	15.0826i	0.140362	+	0.796032i	0.970975	+	0.239182i	$0.0768791\pi$
$359$	2.65948	+	15.0826i	0.140362	+	0.796032i	−0.830613	+	0.556850i	$0.812010\pi$
$360$		0			0
$361$	1.94928	−	11.0549i	0.102593	−	0.581836i
$362$	−2.83339	−	48.6474i	−0.148920	−	2.55685i
$363$		0			0
$364$	−3.81450	−	5.12376i	−0.199934	−	0.268558i
$365$	−6.98160	−	9.37791i	−0.365433	−	0.490862i
$366$		0			0
$367$	−0.816173	−	14.0131i	−0.0426039	−	0.731480i	−0.950201	−	0.311638i	$-0.899122\pi$
$367$	−0.816173	−	14.0131i	−0.0426039	−	0.731480i	0.907597	−	0.419842i	$-0.137915\pi$
$368$	−0.0969946	+	0.550084i	−0.00505619	+	0.0286751i
$369$		0			0
$370$	−4.21068	−	23.8799i	−0.218903	−	1.24146i
$371$	−10.5274	+	2.49504i	−0.546555	+	0.129536i
$372$		0			0
$373$	1.58424	−	27.2004i	0.0820290	−	1.40838i	−0.666610	−	0.745406i	$-0.732255\pi$
$373$	1.58424	−	27.2004i	0.0820290	−	1.40838i	0.748639	−	0.662978i	$-0.230708\pi$
$374$	−16.6752	−	3.95210i	−0.862256	−	0.204358i
$375$		0			0
$376$	11.4515	+	1.33849i	0.590567	+	0.0690274i
$377$	−1.30680	+	2.26344i	−0.0673035	+	0.116573i
$378$		0			0
$379$	−4.29852	−	7.44526i	−0.220800	−	0.382437i	0.734251	−	0.678878i	$-0.237534\pi$
$379$	−4.29852	−	7.44526i	−0.220800	−	0.382437i	−0.955051	+	0.296441i	$0.904200\pi$
$380$	18.8533	+	43.7069i	0.967155	+	2.24212i
$381$		0			0
$382$	−19.4340	+	20.5989i	−0.994331	+	1.05393i
$383$	17.2369	−	8.65669i	0.880764	−	0.442336i	0.0498624	−	0.998756i	$-0.484122\pi$
$383$	17.2369	−	8.65669i	0.880764	−	0.442336i	0.830901	+	0.556420i	$0.187825\pi$
$384$		0			0
$385$	−13.2520	+	44.2648i	−0.675385	+	2.25594i
$386$	34.6167	−	29.0469i	1.76194	−	1.47845i
$387$		0			0
$388$	−15.8733	−	13.3193i	−0.805844	−	0.676183i
$389$	−26.0189	+	17.1129i	−1.31921	+	0.867659i	−0.996877	−	0.0789664i	$-0.974838\pi$
$389$	−26.0189	+	17.1129i	−1.31921	+	0.867659i	−0.322335	+	0.946626i	$0.604468\pi$
$390$		0			0
$391$	0.650616	−	0.0760461i	0.0329031	−	0.00384582i
$392$	1.43556	−	3.32799i	0.0725066	−	0.168089i
$393$		0			0
$394$	7.97158	+	4.00348i	0.401603	+	0.201692i
$395$	−7.86821	+	2.86379i	−0.395893	+	0.144093i
$396$		0			0
$397$	−10.0204	−	3.64712i	−0.502908	−	0.183044i	0.0780935	−	0.996946i	$-0.475117\pi$
$397$	−10.0204	−	3.64712i	−0.502908	−	0.183044i	−0.581002	+	0.813902i	$0.697339\pi$
$398$	−5.86536	−	6.21692i	−0.294004	−	0.311626i
$399$		0			0
$400$	3.80528	+	2.50277i	0.190264	+	0.125139i
$401$	−2.32332	−	7.76042i	−0.116021	−	0.387537i	0.880178	−	0.474644i	$-0.157423\pi$
$401$	−2.32332	−	7.76042i	−0.116021	−	0.387537i	−0.996199	+	0.0871067i	$0.972238\pi$
$402$		0			0
$403$	0.488512	−	0.656186i	0.0243345	−	0.0326869i
$404$	−31.1918			−1.55185
$405$		0			0
$406$	−23.3504			−1.15886
$407$	−11.7393	+	15.7686i	−0.581895	+	0.781620i
$408$		0			0
$409$	10.7499	+	35.9072i	0.531549	+	1.77550i	0.625839	+	0.779952i	$0.284757\pi$
$409$	10.7499	+	35.9072i	0.531549	+	1.77550i	−0.0942897	+	0.995545i	$0.530058\pi$
$410$	−55.9323	−	36.7872i	−2.76230	−	1.81679i
$411$		0			0
$412$	35.9475	+	38.1022i	1.77101	+	1.87716i
$413$	19.9025	+	7.24393i	0.979339	+	0.356450i
$414$		0			0
$415$	0.973877	−	0.354462i	0.0478058	−	0.0173999i
$416$	4.55254	+	2.28637i	0.223207	+	0.112099i
$417$		0			0
$418$	25.6848	−	59.5441i	1.25629	−	2.91240i
$419$	−12.8086	+	1.49711i	−0.625739	+	0.0731384i	−0.423052	−	0.906105i	$-0.639041\pi$
$419$	−12.8086	+	1.49711i	−0.625739	+	0.0731384i	−0.202687	+	0.979244i	$0.564967\pi$
$420$		0			0
$421$	−19.3273	+	12.7118i	−0.941955	+	0.619533i	−0.924855	−	0.380320i	$-0.875814\pi$
$421$	−19.3273	+	12.7118i	−0.941955	+	0.619533i	−0.0171000	+	0.999854i	$0.505443\pi$
$422$	12.1357	+	10.1830i	0.590754	+	0.495702i
$423$		0			0
$424$	−5.85394	+	4.91204i	−0.284292	+	0.238550i
$425$	1.53188	−	5.11684i	0.0743071	−	0.248203i
$426$		0			0
$427$	11.5029	−	5.77695i	0.556662	−	0.279566i
$428$	−0.100511	+	0.106535i	−0.00485838	+	0.00514959i
$429$		0			0
$430$	−20.5645	−	47.6739i	−0.991710	−	2.29904i
$431$	−11.3499	−	19.6586i	−0.546706	−	0.946923i	−0.998497	−	0.0547992i	$-0.982548\pi$
$431$	−11.3499	−	19.6586i	−0.546706	−	0.946923i	0.451791	−	0.892124i	$-0.350785\pi$
$432$		0			0
$433$	9.10550	−	15.7712i	0.437583	−	0.757915i	−0.559920	−	0.828547i	$-0.689168\pi$
$433$	9.10550	−	15.7712i	0.437583	−	0.757915i	0.997502	+	0.0706315i	$0.0225015\pi$
$434$	7.25932	+	0.848493i	0.348458	+	0.0407289i
$435$		0			0
$436$	−1.15846	−	0.274561i	−0.0554803	−	0.0131491i
$437$	−0.144124	+	2.47452i	−0.00689440	+	0.118372i
$438$		0			0
$439$	26.7551	−	6.34107i	1.27695	−	0.302643i	0.464448	−	0.885600i	$-0.346253\pi$
$439$	26.7551	−	6.34107i	1.27695	−	0.302643i	0.812503	+	0.582958i	$0.198105\pi$
$440$	5.66727	+	32.1407i	0.270177	+	1.53225i
$441$		0			0
$442$	0.412263	−	2.33806i	0.0196093	−	0.111210i
$443$	0.712965	+	12.2411i	0.0338740	+	0.581594i	0.971953	+	0.235173i	$0.0755658\pi$
$443$	0.712965	+	12.2411i	0.0338740	+	0.581594i	−0.938079	+	0.346420i	$0.887397\pi$
$444$		0			0
$445$	10.0022	+	13.4353i	0.474149	+	0.636892i
$446$	19.7074	+	26.4716i	0.933172	+	1.25347i
$447$		0			0
$448$	2.22061	+	38.1264i	0.104914	+	1.80130i
$449$	1.20505	−	6.83416i	0.0568697	−	0.322524i	−0.943080	−	0.332566i	$-0.892085\pi$
$449$	1.20505	−	6.83416i	0.0568697	−	0.322524i	0.999950	+	0.0100422i	$0.00319658\pi$
$450$		0			0
$451$	9.42460	+	53.4496i	0.443787	+	2.51684i
$452$	32.5361	−	7.71119i	1.53037	−	0.362704i
$453$		0			0
$454$	−1.73890	+	29.8558i	−0.0816107	+	1.40120i
$455$	−6.22867	−	1.47622i	−0.292005	−	0.0692064i
$456$		0			0
$457$	−29.6629	−	3.46709i	−1.38757	−	0.162184i	−0.610709	−	0.791855i	$-0.709116\pi$
$457$	−29.6629	−	3.46709i	−1.38757	−	0.162184i	−0.776862	+	0.629671i	$0.783190\pi$
$458$	3.62196	−	6.27342i	0.169243	−	0.293138i
$459$		0			0
$460$	−1.95177	−	3.38056i	−0.0910017	−	0.157620i
$461$	−0.324961	−	0.753345i	−0.0151350	−	0.0350868i	0.910481	−	0.413551i	$-0.135712\pi$
$461$	−0.324961	−	0.753345i	−0.0151350	−	0.0350868i	−0.925616	+	0.378464i	$0.876452\pi$
$462$		0			0
$463$	19.6398	−	20.8169i	0.912738	−	0.967445i	−0.0868483	−	0.996222i	$-0.527680\pi$
$463$	19.6398	−	20.8169i	0.912738	−	0.967445i	0.999586	+	0.0287763i	$0.00916103\pi$
$464$	3.93548	−	1.97647i	0.182700	−	0.0917555i
$465$		0			0
$466$	−5.27333	+	17.6141i	−0.244282	+	0.815960i
$467$	−9.57011	+	8.03027i	−0.442852	+	0.371597i	−0.836775	−	0.547546i	$-0.815562\pi$
$467$	−9.57011	+	8.03027i	−0.442852	+	0.371597i	0.393924	+	0.919143i	$0.371117\pi$
$468$		0			0
$469$	25.6227	+	21.5000i	1.18315	+	0.992779i
$470$	30.2056	−	19.8665i	1.39328	−	0.916375i
$471$		0			0
$472$	14.8587	−	1.73674i	0.683929	−	0.0799398i
$473$	−16.6721	+	38.6502i	−0.766582	+	1.77714i
$474$		0			0
$475$	18.0615	+	9.07084i	0.828720	+	0.416199i
$476$	11.8612	−	4.31712i	0.543656	−	0.197875i
$477$		0			0
$478$	27.2809	+	9.92943i	1.24780	+	0.454161i
$479$	3.11272	+	3.29929i	0.142224	+	0.150749i	0.794570	−	0.607173i	$-0.207696\pi$
$479$	3.11272	+	3.29929i	0.142224	+	0.150749i	−0.652346	+	0.757922i	$0.726215\pi$
$480$		0			0
$481$	−2.27539	−	1.49655i	−0.103749	−	0.0682368i
$482$	0.403326	+	1.34720i	0.0183710	+	0.0613634i
$483$		0			0
$484$	30.1330	−	40.4757i	1.36968	−	1.83980i
$485$	−20.7648			−0.942881
$486$		0			0
$487$	−28.2887			−1.28188			−0.640941	−	0.767590i	$-0.721456\pi$
$487$	−28.2887			−1.28188			−0.640941	+	0.767590i	$0.721456\pi$
$488$	5.42928	−	7.29279i	0.245772	−	0.330129i
$489$		0			0
$490$	−3.25956	−	10.8877i	−0.147252	−	0.491856i
$491$	−16.3623	−	10.7617i	−0.738421	−	0.485667i	0.123732	−	0.992316i	$-0.460514\pi$
$491$	−16.3623	−	10.7617i	−0.738421	−	0.485667i	−0.862153	+	0.506649i	$0.830884\pi$
$492$		0			0
$493$	−3.54413	−	3.75656i	−0.159620	−	0.169187i
$494$	8.44198	+	3.07263i	0.379823	+	0.138244i
$495$		0			0
$496$	−1.29531	+	0.471453i	−0.0581609	+	0.0211688i
$497$	−35.5310	−	17.8443i	−1.59378	−	0.800427i
$498$		0			0
$499$	−11.7236	+	27.1785i	−0.524823	+	1.21668i	0.425372	+	0.905019i	$0.360143\pi$
$499$	−11.7236	+	27.1785i	−0.524823	+	1.21668i	−0.950195	+	0.311657i	$0.899116\pi$
$500$	11.3833	−	1.33051i	0.509075	−	0.0595023i
$501$		0			0
$502$	−25.6851	+	16.8933i	−1.14638	+	0.753986i
$503$	18.2284	+	15.2955i	0.812765	+	0.681991i	0.951266	−	0.308371i	$-0.0997839\pi$
$503$	18.2284	+	15.2955i	0.812765	+	0.681991i	−0.138501	+	0.990362i	$0.544228\pi$
$504$		0			0
$505$	−23.9447	+	20.0920i	−1.06553	+	0.894082i
$506$	−1.52521	+	5.09457i	−0.0678041	+	0.226481i
$507$		0			0
$508$	34.2666	−	17.2093i	1.52033	−	0.763541i
$509$	−8.53666	+	9.04834i	−0.378381	+	0.401060i	−0.888376	−	0.459117i	$-0.848166\pi$
$509$	−8.53666	+	9.04834i	−0.378381	+	0.401060i	0.509995	+	0.860178i	$0.329647\pi$
$510$		0			0
$511$	−4.64664	−	10.7721i	−0.205555	−	0.476531i
$512$	−6.87849	−	11.9139i	−0.303989	−	0.526525i
$513$		0			0
$514$	29.1206	−	50.4383i	1.28445	−	2.22474i
$515$	52.1387	+	6.09414i	2.29751	+	0.268540i
$516$		0			0
$517$	−28.5201	−	6.75938i	−1.25431	−	0.297277i
$518$	1.41477	−	24.2906i	0.0621612	−	1.06727i
$519$		0			0
$520$	−4.39948	+	1.04270i	−0.192930	+	0.0457253i
$521$	6.26330	+	35.5209i	0.274400	+	1.55620i	0.740861	+	0.671659i	$0.234418\pi$
$521$	6.26330	+	35.5209i	0.274400	+	1.55620i	−0.466461	+	0.884542i	$0.654471\pi$
$522$		0			0
$523$	−3.40284	+	19.2985i	−0.148796	+	0.843864i	0.815445	+	0.578835i	$0.196493\pi$
$523$	−3.40284	+	19.2985i	−0.148796	+	0.843864i	−0.964241	+	0.265029i	$0.914619\pi$
$524$	1.36858	+	23.4976i	0.0597867	+	1.02650i
$525$		0			0
$526$	−1.88797	−	2.53598i	−0.0823194	−	0.110574i
$527$	0.965317	+	1.29665i	0.0420499	+	0.0564828i
$528$		0			0
$529$	1.32551	+	22.7582i	0.0576309	+	0.989485i
$530$	−4.16104	+	23.5984i	−0.180744	+	1.02505i
$531$		0			0
$532$	8.29406	+	47.0379i	0.359593	+	2.03935i
$533$	−7.31628	+	1.73399i	−0.316903	+	0.0751075i
$534$		0			0
$535$	−0.00853420	+	0.146527i	−0.000368966	+	0.00633489i
$536$	22.9885	+	5.44837i	0.992951	+	0.235334i
$537$		0			0
$538$	12.0668	+	1.41040i	0.520235	+	0.0608068i
$539$	−4.60697	+	7.97951i	−0.198436	+	0.343702i
$540$		0			0
$541$	9.81665	+	17.0029i	0.422051	+	0.731013i	0.996140	−	0.0877794i	$-0.0279771\pi$
$541$	9.81665	+	17.0029i	0.422051	+	0.731013i	−0.574089	+	0.818793i	$0.694644\pi$
$542$	27.0537	+	62.7176i	1.16206	+	2.69395i
$543$		0			0
$544$	−6.90822	+	7.32228i	−0.296187	+	0.313940i
$545$	−1.06616	+	0.535447i	−0.0456694	+	0.0229360i
$546$		0			0
$547$	8.77306	−	29.3041i	0.375109	−	1.25295i	−0.537202	−	0.843453i	$-0.680519\pi$
$547$	8.77306	−	29.3041i	0.375109	−	1.25295i	0.912311	−	0.409497i	$-0.134296\pi$
$548$	23.2384	−	19.4993i	0.992695	−	0.832970i
$549$		0			0
$550$	33.2178	+	27.8730i	1.41641	+	1.18851i
$551$	16.3278	−	10.7390i	0.695588	−	0.457495i
$552$		0			0
$553$	−8.34517	+	0.975411i	−0.354873	+	0.0414787i
$554$	4.01014	−	9.29654i	0.170374	−	0.394972i
$555$		0			0
$556$	−45.8464	−	23.0249i	−1.94432	−	0.976474i
$557$	−31.4323	+	11.4404i	−1.33183	+	0.484746i	−0.907230	−	0.420636i	$-0.861807\pi$
$557$	−31.4323	+	11.4404i	−1.33183	+	0.484746i	−0.424599	+	0.905382i	$0.639585\pi$
$558$		0			0
$559$	−5.47970	−	1.99445i	−0.231767	−	0.0843562i
$560$	7.40185	+	7.84550i	0.312785	+	0.331533i
$561$		0			0
$562$	33.9314	+	22.3171i	1.43131	+	0.941388i
$563$	0.0602063	+	0.201103i	0.00253739	+	0.00847548i	0.959249	−	0.282563i	$-0.0911845\pi$
$563$	0.0602063	+	0.201103i	0.00253739	+	0.00847548i	−0.956711	+	0.291038i	$0.905999\pi$
$564$		0			0
$565$	20.0095	−	26.8775i	0.841808	−	1.13074i
$566$	−52.6415			−2.21269
$567$		0			0
$568$	−28.0837			−1.17836
$569$	24.4396	−	32.8281i	1.02456	−	1.37623i	0.100089	−	0.994978i	$-0.468087\pi$
$569$	24.4396	−	32.8281i	1.02456	−	1.37623i	0.924473	−	0.381248i	$-0.124505\pi$
$570$		0			0
$571$	−8.06199	−	26.9289i	−0.337384	−	1.12694i	−0.943447	−	0.331523i	$-0.892437\pi$
$571$	−8.06199	−	26.9289i	−0.337384	−	1.12694i	0.606063	−	0.795416i	$-0.292748\pi$
$572$	9.58300	+	6.30284i	0.400685	+	0.263535i
$573$		0			0
$574$	−46.0990	−	48.8621i	−1.92413	−	2.03946i
$575$	−1.55752	−	0.566892i	−0.0649532	−	0.0236410i
$576$		0			0
$577$	−12.8095	+	4.66227i	−0.533266	+	0.194093i	−0.594596	−	0.804025i	$-0.702688\pi$
$577$	−12.8095	+	4.66227i	−0.533266	+	0.194093i	0.0613301	+	0.998118i	$0.480466\pi$
$578$	−29.5708	−	14.8510i	−1.22998	−	0.617721i
$579$		0			0
$580$	−12.1900	+	28.2595i	−0.506161	+	1.17341i
$581$	1.03291	−	0.120730i	0.0428524	−	0.00500873i
$582$		0			0
$583$	16.2309	−	10.6752i	0.672214	−	0.442122i
$584$	−6.34770	−	5.32636i	−0.262670	−	0.220406i
$585$		0			0
$586$	8.11761	−	6.81149i	0.335336	−	0.281380i
$587$	8.05995	−	26.9221i	0.332670	−	1.11119i	−0.614086	−	0.789239i	$-0.710475\pi$
$587$	8.05995	−	26.9221i	0.332670	−	1.11119i	0.946755	−	0.321954i	$-0.104340\pi$
$588$		0			0
$589$	−5.46631	+	2.74528i	−0.225235	+	0.113117i
$590$	32.1916	−	34.1211i	1.32531	−	1.40474i
$591$		0			0
$592$	1.81761	+	4.21369i	0.0747032	+	0.173181i
$593$	2.12487	+	3.68039i	0.0872581	+	0.151135i	0.906351	−	0.422525i	$-0.138856\pi$
$593$	2.12487	+	3.68039i	0.0872581	+	0.151135i	−0.819093	+	0.573661i	$0.805523\pi$
$594$		0			0
$595$	6.32451	−	10.9544i	0.259280	−	0.449086i
$596$	−24.2731	−	2.83712i	−0.994266	−	0.116213i
$597$		0			0
$598$	−0.716877	−	0.169903i	−0.0293153	−	0.00694785i
$599$	1.23410	−	21.1887i	0.0504239	−	0.865746i	−0.874366	−	0.485267i	$-0.838722\pi$
$599$	1.23410	−	21.1887i	0.0504239	−	0.865746i	0.924790	−	0.380478i	$-0.124241\pi$
$600$		0			0
$601$	−37.9901	+	9.00383i	−1.54965	+	0.367274i	−0.914328	−	0.404974i	$-0.867281\pi$
$601$	−37.9901	+	9.00383i	−1.54965	+	0.367274i	−0.635322	+	0.772247i	$0.719133\pi$
$602$	−9.04687	−	51.3073i	−0.368723	−	2.09113i
$603$		0			0
$604$	−8.98358	+	50.9484i	−0.365537	+	2.07306i
$605$	−2.94021	−	50.4815i	−0.119537	−	2.05237i
$606$		0			0
$607$	26.6915	+	35.8529i	1.08337	+	1.45522i	0.879299	+	0.476270i	$0.158011\pi$
$607$	26.6915	+	35.8529i	1.08337	+	1.45522i	0.204076	+	0.978955i	$0.434581\pi$
$608$	−22.7475	−	30.5552i	−0.922532	−	1.23918i
$609$		0			0
$610$	−1.65768	−	28.4613i	−0.0671176	−	1.15236i
$611$	0.705103	−	3.99884i	0.0285254	−	0.161776i
$612$		0			0
$613$	−7.96425	−	45.1675i	−0.321673	−	1.82430i	−0.532091	−	0.846687i	$-0.678594\pi$
$613$	−7.96425	−	45.1675i	−0.321673	−	1.82430i	0.210418	−	0.977611i	$-0.432517\pi$
$614$	−23.3372	+	5.53101i	−0.941812	+	0.223213i
$615$		0			0
$616$	−1.90417	+	32.6934i	−0.0767214	+	1.31725i
$617$	21.1271	+	5.00721i	0.850544	+	0.201583i	0.632696	−	0.774400i	$-0.281948\pi$
$617$	21.1271	+	5.00721i	0.850544	+	0.201583i	0.217848	+	0.975983i	$0.430096\pi$
$618$		0			0
$619$	29.2625	+	3.42030i	1.17616	+	0.137473i	0.681636	−	0.731691i	$-0.261269\pi$
$619$	29.2625	+	3.42030i	1.17616	+	0.137473i	0.494523	+	0.869164i	$0.335343\pi$
$620$	4.81657	−	8.34254i	0.193438	−	0.335044i
$621$		0			0
$622$	10.7583	+	18.6339i	0.431368	+	0.747151i
$623$	6.65701	+	15.4327i	0.266708	+	0.618297i
$624$		0			0
$625$	20.4955	−	21.7240i	0.819821	−	0.868960i
$626$	−12.6852	+	6.37076i	−0.507003	+	0.254627i
$627$		0			0
$628$	1.81655	−	6.06770i	0.0724882	−	0.242127i
$629$	4.12254	−	3.45922i	0.164376	−	0.137928i
$630$		0			0
$631$	−23.1628	−	19.4359i	−0.922098	−	0.773732i	0.0522840	−	0.998632i	$-0.483350\pi$
$631$	−23.1628	−	19.4359i	−0.922098	−	0.773732i	−0.974382	+	0.224900i	$0.927794\pi$
$632$	−4.95824	+	3.26109i	−0.197228	+	0.129719i
$633$		0			0
$634$	−45.4977	+	5.31791i	−1.80694	+	0.211201i
$635$	15.2198	−	35.2835i	0.603980	−	1.40018i
$636$		0			0
$637$	−1.14069	−	0.572878i	−0.0451960	−	0.0226983i
$638$	39.3998	−	14.3404i	1.55985	−	0.567741i
$639$		0			0
$640$	41.1293	+	14.9699i	1.62578	+	0.591735i
$641$	−0.420317	−	0.445510i	−0.0166015	−	0.0175966i	0.719020	−	0.694990i	$-0.244591\pi$
$641$	−0.420317	−	0.445510i	−0.0166015	−	0.0175966i	−0.735621	+	0.677393i	$0.763110\pi$
$642$		0			0
$643$	−15.5963	−	10.2578i	−0.615056	−	0.404529i	0.203402	−	0.979095i	$-0.434800\pi$
$643$	−15.5963	−	10.2578i	−0.615056	−	0.404529i	−0.818458	+	0.574566i	$0.805171\pi$
$644$	−1.12340	−	3.75242i	−0.0442681	−	0.147866i
$645$		0			0
$646$	−10.6009	+	14.2395i	−0.417087	+	0.560245i
$647$	44.8197			1.76204			0.881022	−	0.473075i	$-0.156856\pi$
$647$	44.8197			1.76204			0.881022	+	0.473075i	$0.156856\pi$
$648$		0			0
$649$	−38.0309			−1.49284
$650$	−3.58733	+	4.81862i	−0.140707	+	0.189002i
$651$		0			0
$652$	−7.98837	−	26.6830i	−0.312849	−	1.04499i
$653$	41.3488	+	27.1956i	1.61810	+	1.06424i	0.946188	+	0.323618i	$0.104899\pi$
$653$	41.3488	+	27.1956i	1.61810	+	1.06424i	0.671917	+	0.740626i	$0.265471\pi$
$654$		0			0
$655$	16.1864	+	17.1566i	0.632456	+	0.670365i
$656$	11.9054	+	4.33321i	0.464828	+	0.169183i
$657$		0			0
$658$	34.0898	−	12.4077i	1.32896	−	0.483702i
$659$	−10.1695	−	5.10730i	−0.396146	−	0.198952i	0.239563	−	0.970881i	$-0.422996\pi$
$659$	−10.1695	−	5.10730i	−0.396146	−	0.198952i	−0.635709	+	0.771929i	$0.719292\pi$
$660$		0			0
$661$	1.04678	−	2.42670i	0.0407149	−	0.0943878i	−0.896645	−	0.442750i	$-0.854003\pi$
$661$	1.04678	−	2.42670i	0.0407149	−	0.0943878i	0.937360	+	0.348362i	$0.113262\pi$
$662$	−44.8057	+	5.23703i	−1.74142	+	0.203543i
$663$		0			0
$664$	0.613700	−	0.403637i	0.0238162	−	0.0156642i
$665$	36.6662	+	30.7666i	1.42185	+	1.19308i
$666$		0			0
$667$	−1.22771	+	1.03017i	−0.0475370	+	0.0398883i
$668$	−3.22163	+	10.7610i	−0.124649	+	0.416356i
$669$		0			0
$670$	66.2024	−	33.2481i	2.55762	−	1.28449i
$671$	−15.8612	+	16.8119i	−0.612317	+	0.649018i
$672$		0			0
$673$	−0.928417	−	2.15231i	−0.0357878	−	0.0829655i	0.899385	−	0.437158i	$-0.144015\pi$
$673$	−0.928417	−	2.15231i	−0.0357878	−	0.0829655i	−0.935172	+	0.354193i	$0.884756\pi$
$674$	4.06301	+	7.03734i	0.156501	+	0.271068i
$675$		0			0
$676$	18.3113	−	31.7161i	0.704281	−	1.21985i
$677$	9.27787	+	1.08443i	0.356578	+	0.0416779i	0.292496	−	0.956267i	$-0.405514\pi$
$677$	9.27787	+	1.08443i	0.356578	+	0.0416779i	0.0640815	+	0.997945i	$0.479588\pi$
$678$		0			0
$679$	−20.2746	−	4.80517i	−0.778068	−	0.184405i
$680$	0.519486	−	8.91924i	0.0199214	−	0.342037i
$681$		0			0
$682$	−12.7699	+	3.02653i	−0.488986	+	0.115892i
$683$	5.08900	+	28.8612i	0.194725	+	1.10434i	0.912809	+	0.408386i	$0.133908\pi$
$683$	5.08900	+	28.8612i	0.194725	+	1.10434i	−0.718084	+	0.695956i	$0.754981\pi$
$684$		0			0
$685$	5.27883	−	29.9377i	0.201694	−	1.14386i
$686$	2.01054	+	34.5197i	0.0767628	+	1.31797i
$687$		0			0
$688$	5.86761	+	7.88157i	0.223701	+	0.300482i
$689$	1.60715	+	2.15878i	0.0612275	+	0.0822428i
$690$		0			0
$691$	0.791645	+	13.5920i	0.0301156	+	0.517065i	0.979309	+	0.202371i	$0.0648648\pi$
$691$	0.791645	+	13.5920i	0.0301156	+	0.517065i	−0.949193	+	0.314694i	$0.898098\pi$
$692$	−4.27050	+	24.2192i	−0.162340	+	0.920677i
$693$		0			0
$694$	−11.2522	−	63.8142i	−0.427126	−	2.42235i
$695$	−50.0258	+	11.8563i	−1.89759	+	0.449736i
$696$		0			0
$697$	0.863899	−	14.8326i	0.0327225	−	0.561824i
$698$	36.6165	+	8.67827i	1.38595	+	0.328477i
$699$		0			0
$700$	−31.7229	−	3.70788i	−1.19901	−	0.140145i
$701$	−20.8102	+	36.0443i	−0.785989	+	1.36137i	0.142418	+	0.989807i	$0.454512\pi$
$701$	−20.8102	+	36.0443i	−0.785989	+	1.36137i	−0.928407	+	0.371566i	$0.878821\pi$
$702$		0			0
$703$	10.1821	+	17.6358i	0.384024	+	0.665149i
$704$	−27.1617	−	62.9680i	−1.02370	−	2.37319i
$705$		0			0
$706$	−34.6948	+	36.7743i	−1.30576	+	1.38402i
$707$	−28.0289	+	14.0767i	−1.05414	+	0.529407i
$708$		0			0
$709$	3.31071	−	11.0585i	0.124336	−	0.415312i	−0.873045	−	0.487640i	$-0.837858\pi$
$709$	3.31071	−	11.0585i	0.124336	−	0.415312i	0.997381	+	0.0723284i	$0.0230430\pi$
$710$	−67.4598	+	56.6055i	−2.53172	+	2.12437i
$711$		0			0
$712$	9.09403	+	7.63080i	0.340813	+	0.285976i
$713$	0.419110	−	0.275653i	0.0156958	−	0.0103233i
$714$		0			0
$715$	11.4164	−	1.33439i	0.426950	−	0.0499033i
$716$	−6.38086	+	14.7925i	−0.238464	+	0.552821i
$717$		0			0
$718$	30.4173	+	15.2761i	1.13516	+	0.570100i
$719$	−29.9388	+	10.8968i	−1.11653	+	0.406383i	−0.833384	−	0.552695i	$-0.813599\pi$
$719$	−29.9388	+	10.8968i	−1.11653	+	0.406383i	−0.283143	+	0.959078i	$0.591377\pi$
$720$		0			0
$721$	49.4976	+	18.0157i	1.84339	+	0.670939i
$722$	−17.1205	−	18.1466i	−0.637157	−	0.675347i
$723$		0			0
$724$	−53.8458	−	35.4149i	−2.00116	−	1.31619i
$725$	3.74796	+	12.5190i	0.139196	+	0.464946i
$726$		0			0
$727$	−18.0298	+	24.2183i	−0.668690	+	0.898206i	−0.998956	−	0.0456817i	$-0.985454\pi$
$727$	−18.0298	+	24.2183i	−0.668690	+	0.898206i	0.330266	+	0.943888i	$0.392861\pi$
$728$	−4.53691			−0.168149
$729$		0			0
$730$	−25.9836			−0.961698
$731$	6.88106	−	9.24287i	0.254505	−	0.341860i
$732$		0			0
$733$	4.58780	+	15.3243i	0.169454	+	0.566017i	0.999959	+	0.00900594i	$0.00286672\pi$
$733$	4.58780	+	15.3243i	0.169454	+	0.566017i	−0.830505	+	0.557011i	$0.811948\pi$
$734$	−26.0643	−	17.1428i	−0.962051	−	0.632751i
$735$		0			0
$736$	2.14375	+	2.27224i	0.0790196	+	0.0837559i
$737$	−56.4379	−	20.5417i	−2.07892	−	0.756664i
$738$		0			0
$739$	13.9238	−	5.06784i	0.512194	−	0.186423i	−0.0729763	−	0.997334i	$-0.523250\pi$
$739$	13.9238	−	5.06784i	0.512194	−	0.186423i	0.585171	+	0.810910i	$0.301028\pi$
$740$	−28.6588	−	14.3930i	−1.05352	−	0.529096i
$741$		0			0
$742$	−9.52370	+	22.0784i	−0.349626	+	0.810524i
$743$	−1.03225	+	0.120653i	−0.0378695	+	0.00442631i	−0.135007	−	0.990845i	$-0.543106\pi$
$743$	−1.03225	+	0.120653i	−0.0378695	+	0.00442631i	0.0971371	+	0.995271i	$0.469031\pi$
$744$		0			0
$745$	−20.4610	+	13.4574i	−0.749634	+	0.493042i
$746$	−46.3874	−	38.9236i	−1.69836	−	1.42510i
$747$		0			0
$748$	−17.3624	+	14.5688i	−0.634832	+	0.532688i
$749$	−0.0422403	+	0.141093i	−0.00154343	+	0.00515541i
$750$		0			0
$751$	−29.5011	+	14.8160i	−1.07651	+	0.540643i	−0.896510	−	0.443024i	$-0.853906\pi$
$751$	−29.5011	+	14.8160i	−1.07651	+	0.540643i	−0.179999	+	0.983667i	$0.557609\pi$
$752$	−4.69527	+	4.97669i	−0.171219	+	0.181481i
$753$		0			0
$754$	2.30068	+	5.33357i	0.0837858	+	0.194237i
$755$	25.9217	+	44.8978i	0.943389	+	1.63400i
$756$		0			0
$757$	16.5939	−	28.7414i	0.603114	−	1.04462i	−0.389232	−	0.921140i	$-0.627260\pi$
$757$	16.5939	−	28.7414i	0.603114	−	1.04462i	0.992346	−	0.123485i	$-0.0394070\pi$
$758$	−18.9774	−	2.21814i	−0.689292	−	0.0805667i
$759$		0			0
$760$	32.8966	+	7.79663i	1.19328	+	0.282814i
$761$	2.17243	−	37.2992i	0.0787505	−	1.35209i	−0.695185	−	0.718831i	$-0.744678\pi$
$761$	2.17243	−	37.2992i	0.0787505	−	1.35209i	0.773936	−	0.633264i	$-0.218285\pi$
$762$		0			0
$763$	−1.16490	+	0.276087i	−0.0421722	+	0.00999501i
$764$	6.50388	+	36.8853i	0.235302	+	1.33446i
$765$		0			0
$766$	7.44398	−	42.2169i	0.268962	−	1.52536i
$767$	−0.306346	−	5.25976i	−0.0110615	−	0.189919i
$768$		0			0
$769$	−25.5369	−	34.3020i	−0.920884	−	1.23696i	−0.971209	−	0.238229i	$-0.923433\pi$
$769$	−25.5369	−	34.3020i	−0.920884	−	1.23696i	0.0503249	−	0.998733i	$-0.483974\pi$
$770$	61.3229	+	82.3709i	2.20992	+	2.96844i
$771$		0			0
$772$	−3.47504	−	59.6641i	−0.125069	−	2.14736i
$773$	4.28338	−	24.2923i	0.154062	−	0.873732i	−0.805575	−	0.592493i	$-0.798144\pi$
$773$	4.28338	−	24.2923i	0.154062	−	0.873732i	0.959638	−	0.281239i	$-0.0907452\pi$
$774$		0			0
$775$	−0.710278	−	4.02818i	−0.0255139	−	0.144697i
$776$	−14.3205	+	3.39402i	−0.514076	+	0.121838i
$777$		0			0
$778$	−4.02435	+	69.0954i	−0.144280	+	2.47719i
$779$	54.7066	+	12.9657i	1.96007	+	0.464544i
$780$		0			0
$781$	70.9112	+	8.28834i	2.53740	+	0.296580i
$782$	0.727908	−	1.26077i	0.0260299	−	0.0450851i
$783$		0			0
$784$	1.07543	+	1.86269i	0.0384081	+	0.0665248i
$785$	−2.51397	−	5.82805i	−0.0897276	−	0.208012i
$786$		0			0
$787$	−23.4304	+	24.8348i	−0.835205	+	0.885265i	−0.994793	−	0.101918i	$-0.967502\pi$
$787$	−23.4304	+	24.8348i	−0.835205	+	0.885265i	0.159588	+	0.987184i	$0.448983\pi$
$788$	10.5429	−	5.29486i	0.375576	−	0.188622i
$789$		0			0
$790$	−5.33715	+	17.8273i	−0.189887	+	0.634267i
$791$	25.7569	−	21.6126i	0.915809	−	0.768455i
$792$		0			0
$793$	−2.45290	−	2.05822i	−0.0871049	−	0.0730897i
$794$	−19.8004	+	13.0229i	−0.702689	+	0.462166i
$795$		0			0
$796$	−11.2276	+	1.31232i	−0.397952	+	0.0465140i
$797$	6.70953	−	15.5544i	0.237664	−	0.550967i	−0.757085	−	0.653317i	$-0.773377\pi$
$797$	6.70953	−	15.5544i	0.237664	−	0.550967i	0.994748	+	0.102350i	$0.0326362\pi$
$798$		0			0
$799$	7.17028	+	3.60105i	0.253666	+	0.127396i
$800$	23.9360	−	8.71201i	0.846267	−	0.308016i
$801$		0			0
$802$	−16.9179	−	6.15760i	−0.597390	−	0.217432i
$803$	14.4560	+	15.3224i	0.510140	+	0.540717i
$804$		0			0
$805$	−3.27948	−	2.15695i	−0.115587	−	0.0760225i
$806$	−0.521441	−	1.74173i	−0.0183670	−	0.0613499i
$807$		0			0
$808$	−13.2295	+	17.7703i	−0.465412	+	0.625157i
$809$	18.5465			0.652062			0.326031	−	0.945359i	$-0.394289\pi$
$809$	18.5465			0.652062			0.326031	+	0.945359i	$0.394289\pi$
$810$		0			0
$811$	24.9560			0.876325			0.438163	−	0.898896i	$-0.355629\pi$
$811$	24.9560			0.876325			0.438163	+	0.898896i	$0.355629\pi$
$812$	−18.4417	+	24.7715i	−0.647178	+	0.869310i
$813$		0			0
$814$	12.5306	+	41.8550i	0.439196	+	1.46702i
$815$	−23.3200	−	15.3378i	−0.816865	−	0.537261i
$816$		0			0
$817$	29.9225	+	31.7160i	1.04685	+	1.10960i
$818$	78.2784	+	28.4910i	2.73694	+	0.996164i
$819$		0			0
$820$	−83.2004	+	30.2825i	−2.90548	+	1.05751i
$821$	−1.20736	−	0.606359i	−0.0421372	−	0.0211621i	0.427606	−	0.903965i	$-0.359357\pi$
$821$	−1.20736	−	0.606359i	−0.0421372	−	0.0211621i	−0.469743	+	0.882803i	$0.655653\pi$
$822$		0			0
$823$	17.3834	−	40.2993i	0.605948	−	1.40475i	−0.288459	−	0.957492i	$-0.593143\pi$
$823$	17.3834	−	40.2993i	0.605948	−	1.40475i	0.894407	−	0.447254i	$-0.147598\pi$
$824$	36.9537	−	4.31927i	1.28734	−	0.150469i
$825$		0			0
$826$	39.3276	−	25.8662i	1.36838	−	0.900000i
$827$	−43.1798	−	36.2322i	−1.50151	−	1.25992i	−0.878539	−	0.477670i	$-0.841481\pi$
$827$	−43.1798	−	36.2322i	−1.50151	−	1.25992i	−0.622970	−	0.782246i	$-0.714074\pi$
$828$		0			0
$829$	11.2414	−	9.43268i	0.390431	−	0.327610i	−0.426350	−	0.904558i	$-0.640201\pi$
$829$	11.2414	−	9.43268i	0.390431	−	0.327610i	0.816781	+	0.576948i	$0.195756\pi$
$830$	0.660598	−	2.20655i	0.0229297	−	0.0765906i
$831$		0			0
$832$	8.48982	−	4.26375i	0.294332	−	0.147819i
$833$	1.73094	−	1.83469i	0.0599735	−	0.0635682i
$834$		0			0
$835$	4.45851	+	10.3360i	0.154293	+	0.357692i
$836$	−42.8825	−	74.2747i	−1.48312	−	2.56885i
$837$		0			0
$838$	−14.3302	+	24.8206i	−0.495028	+	0.857414i
$839$	0.941795	+	0.110080i	0.0325144	+	0.00380039i	0.132335	−	0.991205i	$-0.457753\pi$
$839$	0.941795	+	0.110080i	0.0325144	+	0.00380039i	−0.0998202	+	0.995005i	$0.531827\pi$
$840$		0			0
$841$	−15.9231	−	3.77385i	−0.549073	−	0.130133i
$842$	−2.98935	+	51.3252i	−0.103020	+	1.76878i
$843$		0			0
$844$	20.3873	−	4.83187i	0.701759	−	0.166320i
$845$	−6.37286	−	36.1423i	−0.219233	−	1.24333i
$846$		0			0
$847$	8.81110	−	49.9702i	0.302753	−	1.71700i
$848$	−0.263681	−	4.52722i	−0.00905483	−	0.155465i
$849$		0			0
$850$	−7.08868	−	9.52175i	−0.243140	−	0.326593i
$851$	−0.997261	−	1.33955i	−0.0341857	−	0.0459193i
$852$		0			0
$853$	−0.185823	−	3.19045i	−0.00636244	−	0.109239i	0.993632	−	0.112677i	$-0.0359426\pi$
$853$	−0.185823	−	3.19045i	−0.00636244	−	0.109239i	−0.999994	+	0.00343826i	$0.998906\pi$
$854$	4.96766	−	28.1730i	0.169990	−	0.964060i
$855$		0			0
$856$	0.0180642	+	0.102447i	0.000617423	+	0.00350158i
$857$	28.8859	−	6.84607i	0.986722	−	0.233857i	0.294586	−	0.955625i	$-0.404818\pi$
$857$	28.8859	−	6.84607i	0.986722	−	0.233857i	0.692136	+	0.721767i	$0.256670\pi$
$858$		0			0
$859$	0.804437	−	13.8116i	0.0274470	−	0.471247i	−0.956380	−	0.292126i	$-0.905637\pi$
$859$	0.804437	−	13.8116i	0.0274470	−	0.471247i	0.983827	−	0.179122i	$-0.0573255\pi$
$860$	−66.8168	−	15.8359i	−2.27844	−	0.539999i
$861$		0			0
$862$	−50.1085	−	5.85684i	−1.70670	−	0.199485i
$863$	28.9772	−	50.1899i	0.986394	−	1.70849i	0.350826	−	0.936440i	$-0.385901\pi$
$863$	28.9772	−	50.1899i	0.986394	−	1.70849i	0.635568	−	0.772045i	$-0.280766\pi$
$864$		0			0
$865$	12.3224	+	21.3429i	0.418973	+	0.725682i
$866$	−16.0307	−	37.1633i	−0.544744	−	1.26286i
$867$		0			0
$868$	6.63340	−	7.03099i	0.225152	−	0.238648i
$869$	13.4820	−	6.77092i	0.457346	−	0.229688i
$870$		0			0
$871$	2.38635	−	7.97096i	0.0808584	−	0.270086i
$872$	−0.647763	+	0.543538i	−0.0219360	+	0.0184065i
$873$		0			0
$874$	4.22002	+	3.54102i	0.142744	+	0.119777i
$875$	9.62853	−	6.33278i	0.325504	−	0.214087i
$876$		0			0
$877$	−13.4759	+	1.57511i	−0.455050	+	0.0531877i	−0.340531	−	0.940233i	$-0.610607\pi$
$877$	−13.4759	+	1.57511i	−0.455050	+	0.0531877i	−0.114519	+	0.993421i	$0.536533\pi$
$878$	24.2042	−	56.1117i	0.816853	−	1.89368i
$879$		0			0
$880$	−17.3076	−	8.69219i	−0.583438	−	0.293014i
$881$	2.92937	−	1.06621i	0.0986931	−	0.0359214i	−0.292202	−	0.956357i	$-0.594388\pi$
$881$	2.92937	−	1.06621i	0.0986931	−	0.0359214i	0.390895	+	0.920435i	$0.372166\pi$
$882$		0			0
$883$	5.52287	+	2.01016i	0.185859	+	0.0676472i	0.433273	−	0.901263i	$-0.357359\pi$
$883$	5.52287	+	2.01016i	0.185859	+	0.0676472i	−0.247414	+	0.968910i	$0.579581\pi$
$884$	−2.15475	−	2.28391i	−0.0724722	−	0.0768161i
$885$		0			0
$886$	22.7684	+	14.9750i	0.764919	+	0.503095i
$887$	−1.34266	−	4.48479i	−0.0450821	−	0.150585i	0.932485	−	0.361208i	$-0.117636\pi$
$887$	−1.34266	−	4.48479i	−0.0450821	−	0.150585i	−0.977567	+	0.210624i	$0.932451\pi$
$888$		0			0
$889$	23.0255	−	30.9286i	0.772249	−	1.03731i
$890$	37.2255			1.24780
$891$		0			0
$892$	43.6472			1.46142
$893$	−18.1310	+	24.3541i	−0.606730	+	0.814980i
$894$		0			0
$895$	4.63015	+	15.4658i	0.154769	+	0.516964i
$896$	36.6942	+	24.1342i	1.22587	+	0.806266i
$897$		0			0
$898$	−10.5839	−	11.2183i	−0.353190	−	0.374359i
$899$	−3.71651	−	1.35270i	−0.123953	−	0.0451151i
$900$		0			0
$901$	−4.99743	+	1.81892i	−0.166489	+	0.0605969i
$902$	107.792	+	54.1352i	3.58908	+	1.80251i
$903$		0			0
$904$	9.40649	−	21.8067i	0.312855	−	0.725280i
$905$	−64.1475	+	7.49777i	−2.13234	+	0.249234i
$906$		0			0
$907$	−0.779754	+	0.512852i	−0.0258913	+	0.0170290i	−0.562389	−	0.826873i	$-0.690118\pi$
$907$	−0.779754	+	0.512852i	−0.0258913	+	0.0170290i	0.536497	+	0.843902i	$0.319747\pi$
$908$	30.2994	+	25.4243i	1.00552	+	0.843734i
$909$		0			0
$910$	−10.8981	+	9.14461i	−0.361269	+	0.303141i
$911$	−13.0328	+	43.5327i	−0.431797	+	1.44230i	0.414724	+	0.909947i	$0.363878\pi$
$911$	−13.0328	+	43.5327i	−0.431797	+	1.44230i	−0.846521	+	0.532356i	$0.821307\pi$
$912$		0			0
$913$	−1.66872	+	0.838061i	−0.0552265	+	0.0277358i
$914$	−45.5483	+	48.2784i	−1.50660	+	1.59691i
$915$		0			0
$916$	−3.79466	−	8.79702i	−0.125379	−	0.290662i
$917$	11.8341	+	20.4973i	0.390797	+	0.676880i
$918$		0			0
$919$	−20.1320	+	34.8697i	−0.664095	+	1.15025i	0.315435	+	0.948947i	$0.397849\pi$
$919$	−20.1320	+	34.8697i	−0.664095	+	1.15025i	−0.979530	+	0.201299i	$0.935484\pi$
$920$	−2.75375	−	0.321867i	−0.0907885	−	0.0106116i
$921$		0			0
$922$	−1.77426	−	0.420507i	−0.0584321	−	0.0138487i
$923$	−0.575092	+	9.87395i	−0.0189294	+	0.325005i
$924$		0			0
$925$	−13.2502	+	3.14035i	−0.435663	+	0.103254i
$926$	−11.0450	−	62.6392i	−0.362960	−	2.05845i
$927$		0			0
$928$	4.27690	−	24.2555i	0.140396	−	0.796225i
$929$	0.761518	+	13.0748i	0.0249846	+	0.428969i	0.987487	+	0.157697i	$0.0504071\pi$
$929$	0.761518	+	13.0748i	0.0249846	+	0.428969i	−0.962503	+	0.271271i	$0.912556\pi$
$930$		0			0
$931$	5.69966	+	7.65597i	0.186799	+	0.250914i
$932$	14.5214	+	19.5056i	0.475663	+	0.638927i
$933$		0			0
$934$	1.61439	+	27.7180i	0.0528245	+	0.906962i
$935$	−3.94404	+	22.3677i	−0.128984	+	0.731504i
$936$		0			0
$937$	−5.42867	−	30.7875i	−0.177347	−	1.00578i	−0.935400	−	0.353591i	$-0.884960\pi$
$937$	−5.42867	−	30.7875i	−0.177347	−	1.00578i	0.758053	−	0.652193i	$-0.226151\pi$
$938$	72.3335	−	17.1434i	2.36177	−	0.559750i
$939$		0			0
$940$	2.78020	−	47.7341i	0.0906800	−	1.55691i
$941$	−45.7331	−	10.8389i	−1.49086	−	0.353339i	−0.597200	−	0.802093i	$-0.703720\pi$
$941$	−45.7331	−	10.8389i	−1.49086	−	0.353339i	−0.893656	+	0.448753i	$0.851868\pi$
$942$		0			0
$943$	−4.57945	−	0.535261i	−0.149127	−	0.0174305i
$944$	−4.43886	+	7.68833i	−0.144473	+	0.250234i
$945$		0			0
$946$	46.7748	+	81.0163i	1.52078	+	2.63407i
$947$	−12.1510	−	28.1691i	−0.394853	−	0.915373i	−0.993444	−	0.114318i	$-0.963532\pi$
$947$	−12.1510	−	28.1691i	−0.394853	−	0.915373i	0.598591	−	0.801055i	$-0.295727\pi$
$948$		0			0
$949$	−2.00268	+	2.12272i	−0.0650099	+	0.0689064i
$950$	40.1411	−	20.1596i	1.30235	−	0.654065i
$951$		0			0
$952$	2.57122	−	8.58847i	0.0833336	−	0.278354i
$953$	−5.18464	+	4.35043i	−0.167947	+	0.140924i	−0.722887	−	0.690966i	$-0.757185\pi$
$953$	−5.18464	+	4.35043i	−0.167947	+	0.140924i	0.554940	+	0.831890i	$0.312741\pi$
$954$		0			0
$955$	28.7522	+	24.1260i	0.930400	+	0.780698i
$956$	32.0796	−	21.0991i	1.03753	−	0.682394i
$957$		0			0
$958$	10.0127	−	1.17032i	0.323496	−	0.0378113i
$959$	12.0821	−	28.0094i	0.390151	−	0.904471i
$960$		0			0
$961$	−26.5964	−	13.3572i	−0.857947	−	0.430877i
$962$	−5.68771	+	2.07016i	−0.183379	+	0.0667446i
$963$		0			0
$964$	1.74773	+	0.636123i	0.0562907	+	0.0204881i
$965$	−41.0999	−	43.5633i	−1.32305	−	1.40235i
$966$		0			0
$967$	−16.1418	−	10.6166i	−0.519085	−	0.341407i	0.262780	−	0.964856i	$-0.415361\pi$
$967$	−16.1418	−	10.6166i	−0.519085	−	0.341407i	−0.781864	+	0.623448i	$0.785731\pi$
$968$	−10.2790	−	34.3342i	−0.330379	−	1.10354i
$969$		0			0
$970$	−27.5583	+	37.0172i	−0.884844	+	1.18855i
$971$	42.4827			1.36333			0.681667	−	0.731662i	$-0.261255\pi$
$971$	42.4827			1.36333			0.681667	+	0.731662i	$0.261255\pi$
$972$		0			0
$973$	−51.5885			−1.65385
$974$	−37.5437	+	50.4299i	−1.20298	+	1.61588i
$975$		0			0
$976$	1.54743	+	5.16876i	0.0495319	+	0.165448i
$977$	31.7530	+	20.8843i	1.01587	+	0.668147i	0.944231	−	0.329284i	$-0.106807\pi$
$977$	31.7530	+	20.8843i	1.01587	+	0.668147i	0.0716371	+	0.997431i	$0.477178\pi$
$978$		0			0
$979$	−20.7103	−	21.9517i	−0.661906	−	0.701579i
$980$	−14.1247	−	5.14095i	−0.451196	−	0.164222i
$981$		0			0
$982$	−40.9002	+	14.8865i	−1.30518	+	0.475046i
$983$	4.94761	+	2.48479i	0.157804	+	0.0792524i	0.525949	−	0.850516i	$-0.323710\pi$
$983$	4.94761	+	2.48479i	0.157804	+	0.0792524i	−0.368144	+	0.929769i	$0.620007\pi$
$984$		0			0
$985$	4.68274	−	10.8558i	0.149204	−	0.345895i
$986$	−11.4004	+	1.33252i	−0.363064	+	0.0424361i
$987$		0			0
$988$	9.92694	−	6.52905i	0.315818	−	0.207717i
$989$	−2.73922	−	2.29848i	−0.0871023	−	0.0730875i
$990$		0			0
$991$	16.9547	−	14.2267i	0.538583	−	0.451925i	−0.332470	−	0.943114i	$-0.607882\pi$
$991$	16.9547	−	14.2267i	0.538583	−	0.451925i	0.871053	+	0.491189i	$0.163438\pi$
$992$	−2.21101	+	7.38528i	−0.0701995	+	0.234483i
$993$		0			0
$994$	−78.9663	+	39.6584i	−2.50466	+	1.25789i
$995$	−7.77367	+	8.23961i	−0.246442	+	0.261213i
$996$		0			0
$997$	8.11635	+	18.8158i	0.257048	+	0.595903i	0.997055	−	0.0766960i	$-0.0244371\pi$
$997$	8.11635	+	18.8158i	0.257048	+	0.595903i	−0.740007	+	0.672599i	$0.765178\pi$
$998$	32.8916	+	56.9700i	1.04117	+	1.80335i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.226.7		144
3.2	odd	2		81.2.g.a.58.2	yes	144
9.2	odd	6		729.2.g.d.433.7		144
9.4	even	3		729.2.g.b.676.7		144
9.5	odd	6		729.2.g.c.676.2		144
9.7	even	3		729.2.g.a.433.2		144
81.7	even	27	inner	243.2.g.a.100.7		144
81.13	even	27		6561.2.a.d.1.62		72
81.20	odd	54		729.2.g.c.55.2		144
81.34	even	27		729.2.g.a.298.2		144
81.47	odd	54		729.2.g.d.298.7		144
81.61	even	27		729.2.g.b.55.7		144
81.68	odd	54		6561.2.a.c.1.11		72
81.74	odd	54		81.2.g.a.7.2	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.2	✓	144	81.74	odd	54
81.2.g.a.58.2	yes	144	3.2	odd	2
243.2.g.a.100.7		144	81.7	even	27	inner
243.2.g.a.226.7		144	1.1	even	1	trivial
729.2.g.a.298.2		144	81.34	even	27
729.2.g.a.433.2		144	9.7	even	3
729.2.g.b.55.7		144	81.61	even	27
729.2.g.b.676.7		144	9.4	even	3
729.2.g.c.55.2		144	81.20	odd	54
729.2.g.c.676.2		144	9.5	odd	6
729.2.g.d.298.7		144	81.47	odd	54
729.2.g.d.433.7		144	9.2	odd	6
6561.2.a.c.1.11		72	81.68	odd	54
6561.2.a.d.1.62		72	81.13	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)

\(f(q)\)	\(=\)	\(q+(1.32716 - 1.78269i) q^{2} +(-0.843016 - 2.81587i) q^{4} +(-2.46097 - 1.61861i) q^{5} +(-2.02832 - 2.14989i) q^{7} +(-1.96178 - 0.714030i) q^{8} +(-6.15160 + 2.23900i) q^{10} +(4.74276 + 2.38190i) q^{11} +(-0.291219 + 0.675122i) q^{13} +(-6.52450 + 0.762605i) q^{14} +(1.03509 - 0.680789i) q^{16} +(-1.11298 - 0.933897i) q^{17} +(4.21153 - 3.53390i) q^{19} +(-2.48315 + 8.29430i) q^{20} +(10.5406 - 5.29370i) q^{22} +(-0.309397 + 0.327942i) q^{23} +(1.45610 + 3.37562i) q^{25} +(0.817038 + 1.41515i) q^{26} +(-4.34391 + 7.52387i) q^{28} +(3.53065 + 0.412674i) q^{29} +(-1.08263 - 0.256589i) q^{31} +(0.402873 - 6.91707i) q^{32} +(-3.14195 + 0.744656i) q^{34} +(1.51181 + 8.57387i) q^{35} +(-0.643205 + 3.64780i) q^{37} +(-0.710448 - 12.1979i) q^{38} +(3.67216 + 4.93256i) q^{40} +(6.10675 + 8.20279i) q^{41} +(0.461153 + 7.91770i) q^{43} +(2.70891 - 15.3630i) q^{44} +(0.173998 + 0.986793i) q^{46} +(-5.37376 + 1.27360i) q^{47} +(-0.100945 + 1.73316i) q^{49} +(7.95018 + 1.88423i) q^{50} +(2.14656 + 0.250897i) q^{52} +(1.83020 - 3.17001i) q^{53} +(-7.81644 - 13.5385i) q^{55} +(2.44403 + 5.66589i) q^{56} +(5.42142 - 5.74637i) q^{58} +(-6.40358 + 3.21600i) q^{59} +(-1.24903 + 4.17204i) q^{61} +(-1.89425 + 1.58947i) q^{62} +(-9.89820 - 8.30558i) q^{64} +(1.80944 - 1.19009i) q^{65} +(-11.2400 + 1.31377i) q^{67} +(-1.69148 + 3.92129i) q^{68} +(17.2910 + 8.68386i) q^{70} +(12.6408 - 4.60088i) q^{71} +(3.72979 + 1.35753i) q^{73} +(5.64926 + 5.98787i) q^{74} +(-13.5014 - 8.88000i) q^{76} +(-4.49899 - 15.0277i) q^{77} +(1.69751 - 2.28015i) q^{79} -3.64926 q^{80} +22.7277 q^{82} +(-0.210107 + 0.282223i) q^{83} +(1.22739 + 4.09977i) q^{85} +(14.7268 + 9.68599i) q^{86} +(-7.60351 - 8.05925i) q^{88} +(-5.34347 - 1.94487i) q^{89} +(2.04212 - 0.743272i) q^{91} +(1.18427 + 0.594763i) q^{92} +(-4.86142 + 11.2700i) q^{94} +(-16.0845 + 1.88000i) q^{95} +(5.88981 - 3.87379i) q^{97} +(2.95571 + 2.48014i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 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

Modular forms

Varieties

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Database

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