LMFDB - Embedded newform 216.2.v.b.59.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(11,216)] 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("216.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.22
Character	$\chi$	$=$	216.59
Dual form			216.2.v.b.11.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.821807 - 1.15093i) q^{2} +(1.73063 + 0.0701536i) q^{3} +(-0.649266 - 1.89168i) q^{4} +(0.426624 - 0.155279i) q^{5} +(1.50299 - 1.93418i) q^{6} +(-1.28150 + 0.225962i) q^{7} +(-2.71076 - 0.807339i) q^{8} +(2.99016 + 0.242820i) q^{9} +(0.171889 - 0.618623i) q^{10} +(0.00602720 - 0.0165596i) q^{11} +(-0.990930 - 3.31935i) q^{12} +(-1.43581 + 1.71113i) q^{13} +(-0.793076 + 1.66060i) q^{14} +(0.749222 - 0.238801i) q^{15} +(-3.15691 + 2.45641i) q^{16} +(1.27216 + 0.734483i) q^{17} +(2.73680 - 3.24190i) q^{18} +(0.677841 + 1.17406i) q^{19} +(-0.570730 - 0.706220i) q^{20} +(-2.23365 + 0.301155i) q^{21} +(-0.0141057 - 0.0205456i) q^{22} +(-0.369486 + 2.09546i) q^{23} +(-4.63468 - 1.58737i) q^{24} +(-3.67233 + 3.08145i) q^{25} +(0.789428 + 3.05873i) q^{26} +(5.15782 + 0.630001i) q^{27} +(1.25948 + 2.27747i) q^{28} +(5.56933 - 4.67322i) q^{29} +(0.340874 - 1.05855i) q^{30} +(-8.87753 - 1.56535i) q^{31} +(0.232774 + 5.65206i) q^{32} +(0.0115926 - 0.0282357i) q^{33} +(1.89081 - 0.860562i) q^{34} +(-0.511630 + 0.295390i) q^{35} +(-1.48207 - 5.81408i) q^{36} +(4.58718 + 2.64841i) q^{37} +(1.90831 + 0.184701i) q^{38} +(-2.60490 + 2.86061i) q^{39} +(-1.28184 + 0.0764919i) q^{40} +(1.56527 - 1.86542i) q^{41} +(-1.48902 + 2.81825i) q^{42} +(-10.1956 - 3.71089i) q^{43} +(-0.0352387 - 0.000649957i) q^{44} +(1.31338 - 0.360715i) q^{45} +(2.10807 + 2.14731i) q^{46} +(0.791397 + 4.48824i) q^{47} +(-5.63576 + 4.02966i) q^{48} +(-4.98668 + 1.81500i) q^{49} +(0.528577 + 6.75893i) q^{50} +(2.15011 + 1.36036i) q^{51} +(4.16913 + 1.60511i) q^{52} +10.4085 q^{53} +(4.96382 - 5.41853i) q^{54} -0.00800062i q^{55} +(3.65625 + 0.422073i) q^{56} +(1.09073 + 2.07941i) q^{57} +(-0.801622 - 10.2504i) q^{58} +(-3.75319 - 10.3118i) q^{59} +(-0.938179 - 1.26224i) q^{60} +(8.87057 - 1.56412i) q^{61} +(-9.09722 + 8.93098i) q^{62} +(-3.88674 + 0.364490i) q^{63} +(6.69641 + 4.37700i) q^{64} +(-0.346849 + 0.952961i) q^{65} +(-0.0229704 - 0.0365465i) q^{66} +(3.70041 + 3.10502i) q^{67} +(0.563436 - 2.88340i) q^{68} +(-0.786447 + 3.60054i) q^{69} +(-0.0804893 + 0.831602i) q^{70} +(-5.03714 + 8.72458i) q^{71} +(-7.90955 - 3.07230i) q^{72} +(-0.339460 - 0.587962i) q^{73} +(6.81790 - 3.10303i) q^{74} +(-6.57161 + 5.07522i) q^{75} +(1.78084 - 2.04453i) q^{76} +(-0.00398198 + 0.0225829i) q^{77} +(1.15163 + 5.34891i) q^{78} +(-5.19665 - 6.19313i) q^{79} +(-0.965387 + 1.53816i) q^{80} +(8.88208 + 1.45214i) q^{81} +(-0.860607 - 3.33452i) q^{82} +(1.29122 + 1.53881i) q^{83} +(2.01992 + 4.02981i) q^{84} +(0.656785 + 0.115809i) q^{85} +(-12.6498 + 8.68475i) q^{86} +(9.96629 - 7.69691i) q^{87} +(-0.0297075 + 0.0400230i) q^{88} +(-0.103744 + 0.0598964i) q^{89} +(0.664188 - 1.80804i) q^{90} +(1.45333 - 2.51724i) q^{91} +(4.20383 - 0.661560i) q^{92} +(-15.2539 - 3.33183i) q^{93} +(5.81601 + 2.77762i) q^{94} +(0.471489 + 0.395626i) q^{95} +(0.00633320 + 9.79796i) q^{96} +(-10.4801 - 3.81446i) q^{97} +(-2.00915 + 7.23088i) q^{98} +(0.0220433 - 0.0480522i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

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

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

$2$	0.821807	−	1.15093i	0.581105	−	0.813828i
$2$	0.821807	−	1.15093i	0.581105	−	0.813828i
$3$	1.73063	+	0.0701536i	0.999179	+	0.0405032i
$3$	1.73063	+	0.0701536i	0.999179	+	0.0405032i
$4$	−0.649266	−	1.89168i	−0.324633	−	0.945840i
$5$	0.426624	−	0.155279i	0.190792	−	0.0694427i	−0.244857	−	0.969559i	$-0.578741\pi$
$5$	0.426624	−	0.155279i	0.190792	−	0.0694427i	0.435649	+	0.900116i	$0.356519\pi$
$6$	1.50299	−	1.93418i	0.613591	−	0.789624i
$7$	−1.28150	+	0.225962i	−0.484360	+	0.0854057i	−0.410495	−	0.911863i	$-0.634644\pi$
$7$	−1.28150	+	0.225962i	−0.484360	+	0.0854057i	−0.0738642	+	0.997268i	$0.523533\pi$
$8$	−2.71076	−	0.807339i	−0.958397	−	0.285437i
$9$	2.99016	+	0.242820i	0.996719	+	0.0809399i
$10$	0.171889	−	0.618623i	0.0543560	−	0.195626i
$11$	0.00602720	−	0.0165596i	0.00181727	−	0.00499290i	−0.938781	−	0.344515i	$-0.888043\pi$
$11$	0.00602720	−	0.0165596i	0.00181727	−	0.00499290i	0.940598	+	0.339522i	$0.110265\pi$
$12$	−0.990930	−	3.31935i	−0.286057	−	0.958213i
$13$	−1.43581	+	1.71113i	−0.398222	+	0.474582i	−0.927477	−	0.373881i	$-0.878027\pi$
$13$	−1.43581	+	1.71113i	−0.398222	+	0.474582i	0.529255	+	0.848463i	$0.322471\pi$
$14$	−0.793076	+	1.66060i	−0.211959	+	0.443815i
$15$	0.749222	−	0.238801i	0.193448	−	0.0616580i
$16$	−3.15691	+	2.45641i	−0.789227	+	0.614102i
$17$	1.27216	+	0.734483i	0.308545	+	0.178138i	0.646275	−	0.763105i	$-0.276326\pi$
$17$	1.27216	+	0.734483i	0.308545	+	0.178138i	−0.337730	+	0.941243i	$0.609659\pi$
$18$	2.73680	−	3.24190i	0.645070	−	0.764123i
$19$	0.677841	+	1.17406i	0.155507	+	0.269347i	0.933244	−	0.359244i	$-0.116965\pi$
$19$	0.677841	+	1.17406i	0.155507	+	0.269347i	−0.777736	+	0.628591i	$0.783632\pi$
$20$	−0.570730	−	0.706220i	−0.127619	−	0.157916i
$21$	−2.23365	+	0.301155i	−0.487421	+	0.0657175i
$22$	−0.0141057	−	0.0205456i	−0.00300734	−	0.00438035i
$23$	−0.369486	+	2.09546i	−0.0770432	+	0.436933i	0.921748	+	0.387788i	$0.126761\pi$
$23$	−0.369486	+	2.09546i	−0.0770432	+	0.436933i	−0.998792	+	0.0491452i	$0.984350\pi$
$24$	−4.63468	−	1.58737i	−0.946050	−	0.324021i
$25$	−3.67233	+	3.08145i	−0.734465	+	0.616289i
$26$	0.789428	+	3.05873i	0.154820	+	0.599866i
$27$	5.15782	+	0.630001i	0.992623	+	0.121244i
$28$	1.25948	+	2.27747i	0.238019	+	0.430401i
$29$	5.56933	−	4.67322i	1.03420	−	0.867796i	0.0428540	−	0.999081i	$-0.486355\pi$
$29$	5.56933	−	4.67322i	1.03420	−	0.867796i	0.991345	+	0.131286i	$0.0419105\pi$
$30$	0.340874	−	1.05855i	0.0622349	−	0.193264i
$31$	−8.87753	−	1.56535i	−1.59445	−	0.281145i	−0.695279	−	0.718740i	$-0.744719\pi$
$31$	−8.87753	−	1.56535i	−1.59445	−	0.281145i	−0.899172	+	0.437595i	$0.855830\pi$
$32$	0.232774	+	5.65206i	0.0411490	+	0.999153i
$33$	0.0115926	−	0.0282357i	0.00201801	−	0.00491520i
$34$	1.89081	−	0.860562i	0.324271	−	0.147585i
$35$	−0.511630	+	0.295390i	−0.0864813	+	0.0499300i
$36$	−1.48207	−	5.81408i	−0.247012	−	0.969013i
$37$	4.58718	+	2.64841i	0.754128	+	0.435396i	0.827183	−	0.561932i	$-0.189942\pi$
$37$	4.58718	+	2.64841i	0.754128	+	0.435396i	−0.0730557	+	0.997328i	$0.523275\pi$
$38$	1.90831	+	0.184701i	0.309568	+	0.0299625i
$39$	−2.60490	+	2.86061i	−0.417117	+	0.458064i
$40$	−1.28184	+	0.0764919i	−0.202676	+	0.0120944i
$41$	1.56527	−	1.86542i	0.244454	−	0.291329i	−0.629841	−	0.776724i	$-0.716880\pi$
$41$	1.56527	−	1.86542i	0.244454	−	0.291329i	0.874295	+	0.485395i	$0.161324\pi$
$42$	−1.48902	+	2.81825i	−0.229761	+	0.434866i
$43$	−10.1956	−	3.71089i	−1.55481	−	0.565906i	−0.585273	−	0.810836i	$-0.699013\pi$
$43$	−10.1956	−	3.71089i	−1.55481	−	0.565906i	−0.969541	+	0.244930i	$0.921235\pi$
$44$	−0.0352387		0.000649957i	−0.00531243		9.79847e-5i
$45$	1.31338	−	0.360715i	0.195787	−	0.0537722i
$46$	2.10807	+	2.14731i	0.310819	+	0.316604i
$47$	0.791397	+	4.48824i	0.115437	+	0.654676i	0.986533	+	0.163563i	$0.0522988\pi$
$47$	0.791397	+	4.48824i	0.115437	+	0.654676i	−0.871096	+	0.491113i	$0.836590\pi$
$48$	−5.63576	+	4.02966i	−0.813452	+	0.581631i
$49$	−4.98668	+	1.81500i	−0.712382	+	0.259286i
$50$	0.528577	+	6.75893i	0.0747520	+	0.955858i
$51$	2.15011	+	1.36036i	0.301076	+	0.190489i
$52$	4.16913	+	1.60511i	0.578155	+	0.222589i
$53$	10.4085			1.42972			0.714860	−	0.699267i	$-0.246490\pi$
$53$	10.4085			1.42972			0.714860	+	0.699267i	$0.246490\pi$
$54$	4.96382	−	5.41853i	0.675490	−	0.737369i
$55$		−	0.00800062i		−	0.00107880i
$56$	3.65625	+	0.422073i	0.488587	+	0.0564018i
$57$	1.09073	+	2.07941i	0.144470	+	0.275424i
$58$	−0.801622	−	10.2504i	−0.105258	−	1.34594i
$59$	−3.75319	−	10.3118i	−0.488624	−	1.34248i	−0.901926	−	0.431890i	$-0.857847\pi$
$59$	−3.75319	−	10.3118i	−0.488624	−	1.34248i	0.413302	−	0.910594i	$-0.364375\pi$
$60$	−0.938179	−	1.26224i	−0.121118	−	0.162955i
$61$	8.87057	−	1.56412i	1.13576	−	0.200265i	0.426010	−	0.904718i	$-0.359919\pi$
$61$	8.87057	−	1.56412i	1.13576	−	0.200265i	0.709750	+	0.704453i	$0.248808\pi$
$62$	−9.09722	+	8.93098i	−1.15535	+	1.13424i
$63$	−3.88674	+	0.364490i	−0.489683	+	0.0459214i
$64$	6.69641	+	4.37700i	0.837051	+	0.547125i
$65$	−0.346849	+	0.952961i	−0.0430214	+	0.118200i
$66$	−0.0229704	−	0.0365465i	−0.00282745	−	0.00449856i
$67$	3.70041	+	3.10502i	0.452078	+	0.379338i	0.840206	−	0.542267i	$-0.182434\pi$
$67$	3.70041	+	3.10502i	0.452078	+	0.379338i	−0.388129	+	0.921605i	$0.626878\pi$
$68$	0.563436	−	2.88340i	0.0683266	−	0.349663i
$69$	−0.786447	+	3.60054i	−0.0946771	+	0.433454i
$70$	−0.0804893	+	0.831602i	−0.00962031	+	0.0993955i
$71$	−5.03714	+	8.72458i	−0.597799	+	1.03542i	0.395347	+	0.918532i	$0.370624\pi$
$71$	−5.03714	+	8.72458i	−0.597799	+	1.03542i	−0.993145	+	0.116886i	$0.962709\pi$
$72$	−7.90955	−	3.07230i	−0.932150	−	0.362074i
$73$	−0.339460	−	0.587962i	−0.0397308	−	0.0688158i	0.845476	−	0.534013i	$-0.179317\pi$
$73$	−0.339460	−	0.587962i	−0.0397308	−	0.0688158i	−0.885207	+	0.465197i	$0.845983\pi$
$74$	6.81790	−	3.10303i	0.792565	−	0.360720i
$75$	−6.57161	+	5.07522i	−0.758824	+	0.586035i
$76$	1.78084	−	2.04453i	0.204276	−	0.234524i
$77$	−0.00398198	+	0.0225829i	−0.000453789	+	0.00257357i
$78$	1.15163	+	5.34891i	0.130396	+	0.605645i
$79$	−5.19665	−	6.19313i	−0.584669	−	0.696782i	0.389903	−	0.920856i	$-0.372509\pi$
$79$	−5.19665	−	6.19313i	−0.584669	−	0.696782i	−0.974572	+	0.224074i	$0.928064\pi$
$80$	−0.965387	+	1.53816i	−0.107934	+	0.171972i
$81$	8.88208	+	1.45214i	0.986897	+	0.161349i
$82$	−0.860607	−	3.33452i	−0.0950382	−	0.368237i
$83$	1.29122	+	1.53881i	0.141729	+	0.168907i	0.832240	−	0.554416i	$-0.187058\pi$
$83$	1.29122	+	1.53881i	0.141729	+	0.168907i	−0.690510	+	0.723323i	$0.742614\pi$
$84$	2.01992	+	4.02981i	0.220391	+	0.439689i
$85$	0.656785	+	0.115809i	0.0712383	+	0.0125612i
$86$	−12.6498	+	8.68475i	−1.36406	+	0.936501i
$87$	9.96629	−	7.69691i	1.06850	−	0.825195i
$88$	−0.0297075	+	0.0400230i	−0.00316683	+	0.00426647i
$89$	−0.103744	+	0.0598964i	−0.0109968	+	0.00634901i	−0.505488	−	0.862833i	$-0.668688\pi$
$89$	−0.103744	+	0.0598964i	−0.0109968	+	0.00634901i	0.494492	+	0.869182i	$0.335354\pi$
$90$	0.664188	−	1.80804i	0.0700116	−	0.190584i
$91$	1.45333	−	2.51724i	0.152351	−	0.263879i
$92$	4.20383	−	0.661560i	0.438280	−	0.0689724i
$93$	−15.2539	−	3.33183i	−1.58176	−	0.345495i
$94$	5.81601	+	2.77762i	0.599875	+	0.286490i
$95$	0.471489	+	0.395626i	0.0483738	+	0.0405904i
$96$	0.00633320	+	9.79796i	0.000646380	+	1.00000i
$97$	−10.4801	−	3.81446i	−1.06410	−	0.387299i	−0.250130	−	0.968212i	$-0.580474\pi$
$97$	−10.4801	−	3.81446i	−1.06410	−	0.387299i	−0.813966	+	0.580913i	$0.802696\pi$
$98$	−2.00915	+	7.23088i	−0.202955	+	0.730429i
$99$	0.0220433	−	0.0480522i	0.00221543	−	0.00482943i
$100$	8.21343	+	4.94619i	0.821343	+	0.494619i
$101$	−2.89743	−	16.4321i	−0.288305	−	1.63506i	−0.693237	−	0.720710i	$-0.743816\pi$
$101$	−2.89743	−	16.4321i	−0.288305	−	1.63506i	0.404932	−	0.914347i	$-0.367295\pi$
$102$	3.33266	−	1.35667i	0.329982	−	0.134330i
$103$	−5.45676	−	14.9923i	−0.537670	−	1.47724i	−0.849753	−	0.527182i	$-0.823249\pi$
$103$	−5.45676	−	14.9923i	−0.537670	−	1.47724i	0.312082	−	0.950055i	$-0.398974\pi$
$104$	5.27359	−	3.47927i	0.517118	−	0.341171i
$105$	−0.906165	+	0.475318i	−0.0884326	+	0.0463862i
$106$	8.55380	−	11.9794i	0.830818	−	1.16355i
$107$		−	6.73607i		−	0.651200i	−0.945508	−	0.325600i	$-0.894434\pi$
$107$		−	6.73607i		−	0.651200i	0.945508	−	0.325600i	$-0.105566\pi$
$108$	−2.15703	−	10.1660i	−0.207561	−	0.978222i
$109$		−	2.91699i		−	0.279397i	−0.990194	−	0.139699i	$-0.955387\pi$
$109$		−	2.91699i		−	0.279397i	0.990194	−	0.139699i	$-0.0446134\pi$
$110$	−0.00920813	−	0.00657497i	−0.000877961	−	0.000626898i
$111$	7.75291	+	4.90522i	0.735874	+	0.465583i
$112$	3.49051	−	3.86121i	0.329822	−	0.364850i
$113$	−6.67148	−	18.3297i	−0.627600	−	1.72432i	−0.687572	−	0.726116i	$-0.741323\pi$
$113$	−6.67148	−	18.3297i	−0.627600	−	1.72432i	0.0599724	−	0.998200i	$-0.480899\pi$
$114$	3.28961	+	0.453524i	0.308101	+	0.0424764i
$115$	0.167748	+	0.951347i	0.0156426	+	0.0887136i
$116$	−12.4562	−	7.50123i	−1.15653	−	0.696471i
$117$	−4.70879	+	4.76791i	−0.435328	+	0.440793i
$118$	−14.9525	−	4.15467i	−1.37649	−	0.382469i
$119$	−1.79623	−	0.653776i	−0.164661	−	0.0599315i
$120$	−2.22375	+	0.0424537i	−0.203000	+	0.00387548i
$121$	8.42625	+	7.07046i	0.766023	+	0.642769i
$122$	5.48971	−	11.4948i	0.497015	−	1.04069i
$123$	2.83977	−	3.11853i	0.256053	−	0.281189i
$124$	2.80274	+	17.8098i	0.251693	+	1.59937i
$125$	−2.22323	+	3.85075i	−0.198852	+	0.344422i
$126$	−2.77465	+	4.77289i	−0.247185	+	0.425203i
$127$	14.9938	−	8.65666i	1.33048	−	0.768154i	0.345108	−	0.938563i	$-0.387842\pi$
$127$	14.9938	−	8.65666i	1.33048	−	0.768154i	0.985373	+	0.170409i	$0.0545088\pi$
$128$	10.5408	−	4.11002i	0.931681	−	0.363278i
$129$	−17.3845	−	7.13744i	−1.53062	−	0.628417i
$130$	0.811745	+	1.18235i	0.0711947	+	0.103699i
$131$	−3.03491	−	0.535137i	−0.265162	−	0.0467552i	0.0394865	−	0.999220i	$-0.487428\pi$
$131$	−3.03491	−	0.535137i	−0.265162	−	0.0467552i	−0.304648	+	0.952465i	$0.598539\pi$
$132$	−0.0609395	−	0.00359696i	−0.00530410	−	0.000313075i
$133$	−1.13394	−	1.35138i	−0.0983252	−	0.117179i
$134$	6.61467	−	1.70718i	0.571421	−	0.147478i
$135$	2.29828	−	0.532125i	0.197804	−	0.0457980i
$136$	−2.85554	−	3.01807i	−0.244861	−	0.258797i
$137$	7.57425	+	9.02665i	0.647112	+	0.771198i	0.985476	−	0.169817i	$-0.0543177\pi$
$137$	7.57425	+	9.02665i	0.647112	+	0.771198i	−0.338363	+	0.941016i	$0.609873\pi$
$138$	3.49765	+	3.86410i	0.297740	+	0.328934i
$139$	−0.930383	+	5.27646i	−0.0789140	+	0.447544i	0.919591	+	0.392878i	$0.128520\pi$
$139$	−0.930383	+	5.27646i	−0.0789140	+	0.447544i	−0.998505	+	0.0546659i	$0.982591\pi$
$140$	0.890967	+	0.776054i	0.0753005	+	0.0655885i
$141$	1.05475	+	7.82299i	0.0888259	+	0.658815i
$142$	5.90180	+	12.9673i	0.495268	+	1.08819i
$143$	0.0196817	+	0.0340897i	0.00164587	+	0.00285073i
$144$	−10.0361	+	6.57848i	−0.836343	+	0.548207i
$145$	1.65036	−	2.85851i	0.137055	−	0.237386i
$146$	−0.955672	−	0.0924978i	−0.0790920	−	0.00765517i
$147$	−8.75742	+	2.79126i	−0.722300	+	0.230219i
$148$	2.03165	−	10.3970i	0.167000	−	0.854628i
$149$	−10.9918	−	9.22325i	−0.900486	−	0.755598i	0.0697991	−	0.997561i	$-0.477764\pi$
$149$	−10.9918	−	9.22325i	−0.900486	−	0.755598i	−0.970285	+	0.241963i	$0.922209\pi$
$150$	0.440607	+	11.7343i	0.0359754	+	0.958101i
$151$	−4.06790	+	11.1765i	−0.331041	+	0.909528i	0.656800	+	0.754065i	$0.271909\pi$
$151$	−4.06790	+	11.1765i	−0.331041	+	0.909528i	−0.987842	+	0.155464i	$0.950313\pi$
$152$	−0.889602	−	3.72983i	−0.0721562	−	0.302529i
$153$	3.62562	+	2.50513i	0.293114	+	0.202527i
$154$	0.0227189	+	0.0231418i	0.00183074	+	0.00186482i
$155$	−4.03044	+	0.710675i	−0.323733	+	0.0570828i
$156$	7.10262	+	3.07034i	0.568665	+	0.245824i
$157$	5.75062	+	15.7997i	0.458950	+	1.26095i	0.926268	+	0.376865i	$0.122998\pi$
$157$	5.75062	+	15.7997i	0.458950	+	1.26095i	−0.467319	+	0.884089i	$0.654780\pi$
$158$	−11.3985	+	0.891409i	−0.906815	+	0.0709167i
$159$	18.0133	+	0.730195i	1.42855	+	0.0579082i
$160$	0.976952	+	2.37516i	0.0772348	+	0.187773i
$161$		−	2.76881i		−	0.218213i
$162$	8.97066	−	9.02924i	0.704802	−	0.709404i
$163$	10.1776			0.797169			0.398585	−	0.917132i	$-0.369502\pi$
$163$	10.1776			0.797169			0.398585	+	0.917132i	$0.369502\pi$
$164$	−4.54505	−	1.74984i	−0.354909	−	0.136640i
$165$	0.000561272	−	0.0138461i	4.36950e−5	−	0.00107792i
$166$	2.83219	−	0.221489i	0.219821	−	0.0171909i
$167$	15.0723	−	5.48587i	1.16633	−	0.424509i	0.314975	−	0.949100i	$-0.398004\pi$
$167$	15.0723	−	5.48587i	1.16633	−	0.424509i	0.851355	+	0.524591i	$0.175782\pi$
$168$	6.29800	+	0.986950i	0.485902	+	0.0761449i
$169$	1.39101	+	7.88879i	0.107000	+	0.606830i
$170$	0.673038	−	0.660739i	0.0516197	−	0.0506764i
$171$	1.74177	+	3.67520i	0.133196	+	0.281050i
$172$	−0.400173	+	21.6962i	−0.0305129	+	1.65432i
$173$	−12.7203	−	4.62982i	−0.967109	−	0.351999i	−0.190293	−	0.981727i	$-0.560944\pi$
$173$	−12.7203	−	4.62982i	−0.967109	−	0.351999i	−0.776815	+	0.629729i	$0.783166\pi$
$174$	−0.668210	−	17.7958i	−0.0506569	−	1.34910i
$175$	4.00978	−	4.77867i	0.303111	−	0.361233i
$176$	0.0216498	+	0.0670823i	0.00163191	+	0.00505652i
$177$	−5.77198	−	18.1092i	−0.433848	−	1.36117i
$178$	−0.0163209	+	0.168625i	−0.00122330	+	0.0126390i
$179$	9.84897	+	5.68630i	0.736146	+	0.425014i	0.820667	−	0.571407i	$-0.193602\pi$
$179$	9.84897	+	5.68630i	0.736146	+	0.425014i	−0.0845201	+	0.996422i	$0.526936\pi$
$180$	−1.53509	−	2.25029i	−0.114419	−	0.167727i
$181$	−12.8369	+	7.41138i	−0.954159	+	0.550884i	−0.894370	−	0.447327i	$-0.852376\pi$
$181$	−12.8369	+	7.41138i	−0.954159	+	0.550884i	−0.0597883	+	0.998211i	$0.519043\pi$
$182$	−1.70281	−	3.74137i	−0.126220	−	0.277329i
$183$	15.4614	−	2.08461i	1.14294	−	0.154099i
$184$	2.69333	−	5.38198i	0.198555	−	0.396765i
$185$	2.36824	+	0.417585i	0.174117	+	0.0307015i
$186$	−16.3705	+	14.8180i	−1.20034	+	1.08651i
$187$	0.0198303	−	0.0166396i	0.00145014	−	0.00121681i
$188$	7.97648	−	4.41113i	0.581745	−	0.321715i
$189$	−6.75208	+	0.358129i	−0.491141	+	0.0260500i
$190$	0.842810	−	0.217521i	0.0611439	−	0.0157806i
$191$	−14.4389	+	12.1157i	−1.04476	+	0.876659i	−0.992533	−	0.121976i	$-0.961077\pi$
$191$	−14.4389	+	12.1157i	−1.04476	+	0.876659i	−0.0522283	+	0.998635i	$0.516632\pi$
$192$	11.2819	+	8.04474i	0.814204	+	0.580579i
$193$	−0.366460	+	2.07830i	−0.0263783	+	0.149599i	−0.995152	−	0.0983471i	$-0.968644\pi$
$193$	−0.366460	+	2.07830i	−0.0263783	+	0.149599i	0.968774	+	0.247946i	$0.0797556\pi$
$194$	−13.0028	+	8.92712i	−0.933547	+	0.640930i
$195$	−0.667121	+	1.62489i	−0.0477735	+	0.116361i
$196$	6.67108	+	8.25478i	0.476506	+	0.589627i
$197$	5.72884	+	9.92264i	0.408163	+	0.706959i	0.994684	−	0.102975i	$-0.0328362\pi$
$197$	5.72884	+	9.92264i	0.408163	+	0.706959i	−0.586521	+	0.809934i	$0.699503\pi$
$198$	−0.0371893	−	0.0648599i	−0.00264293	−	0.00460939i
$199$	4.92181	+	2.84161i	0.348898	+	0.201436i	0.664200	−	0.747555i	$-0.268772\pi$
$199$	4.92181	+	2.84161i	0.348898	+	0.201436i	−0.315302	+	0.948991i	$0.602106\pi$
$200$	12.4426	−	5.38824i	0.879821	−	0.381006i
$201$	6.18622	+	5.63323i	0.436342	+	0.397337i
$202$	−21.2933	−	10.1693i	−1.49819	−	0.715510i
$203$	−6.08110	+	7.24717i	−0.426809	+	0.508652i
$204$	1.17738	−	4.95057i	0.0824331	−	0.346609i
$205$	0.378123	−	1.03889i	0.0264093	−	0.0725589i
$206$	−21.7395	−	6.04047i	−1.51466	−	0.420859i
$207$	−1.61364	+	6.17603i	−0.112156	+	0.429264i
$208$	0.329486	−	8.92881i	0.0228457	−	0.619102i
$209$	0.0235273	−	0.00414851i	0.00162742	−	0.000286958i
$210$	−0.197637	+	1.43355i	−0.0136382	+	0.0989243i
$211$	15.6412	−	5.69295i	1.07679	−	0.391919i	0.258077	−	0.966124i	$-0.416911\pi$
$211$	15.6412	−	5.69295i	1.07679	−	0.391919i	0.818711	+	0.574206i	$0.194689\pi$
$212$	−6.75790	−	19.6896i	−0.464134	−	1.35229i
$213$	−9.32948	+	14.7456i	−0.639246	+	1.01036i
$214$	−7.75272	−	5.53575i	−0.529965	−	0.378416i
$215$	−4.92591			−0.335945
$216$	−13.4730	−	5.87189i	−0.916719	−	0.399531i
$217$	11.7302			0.796300
$218$	−3.35725	−	2.39721i	−0.227382	−	0.162359i
$219$	−0.546232	−	1.04136i	−0.0369109	−	0.0703685i
$220$	−0.0151346	+	0.00519453i	−0.00102038	+	0.000350215i
$221$	−3.08338	+	1.12226i	−0.207410	+	0.0754912i
$222$	12.0170	−	4.89189i	0.806525	−	0.328322i
$223$	−2.73564	+	0.482367i	−0.183192	+	0.0323017i	−0.264491	−	0.964388i	$-0.585204\pi$
$223$	−2.73564	+	0.482367i	−0.183192	+	0.0323017i	0.0812995	+	0.996690i	$0.474093\pi$
$224$	−1.57545	−	7.19049i	−0.105264	−	0.480435i
$225$	−11.7291	+	8.32230i	−0.781938	+	0.554820i
$226$	−26.5789	−	7.38512i	−1.76800	−	0.491251i
$227$	−8.45693	+	23.2352i	−0.561306	+	1.54218i	0.256418	+	0.966566i	$0.417458\pi$
$227$	−8.45693	+	23.2352i	−0.561306	+	1.54218i	−0.817724	+	0.575611i	$0.804764\pi$
$228$	3.22540	−	3.41340i	0.213607	−	0.226058i
$229$	−10.0744	+	12.0062i	−0.665736	+	0.793393i	−0.988197	−	0.153190i	$-0.951045\pi$
$229$	−10.0744	+	12.0062i	−0.665736	+	0.793393i	0.322461	+	0.946583i	$0.395490\pi$
$230$	1.23279	+	0.588758i	0.0812876	+	0.0388216i
$231$	−0.00847561	+	0.0388034i	−0.000557654	+	0.00255307i
$232$	−18.8700	+	8.17163i	−1.23887	+	0.536494i
$233$	17.5198	+	10.1151i	1.14776	+	0.662659i	0.948340	−	0.317255i	$-0.102761\pi$
$233$	17.5198	+	10.1151i	1.14776	+	0.662659i	0.199419	+	0.979914i	$0.436094\pi$
$234$	1.61779	+	9.33777i	0.105758	+	0.610429i
$235$	1.03456	+	1.79190i	0.0674870	+	0.116891i
$236$	−17.0698	+	13.7949i	−1.11115	+	0.897975i
$237$	−8.55901	−	11.0826i	−0.555968	−	0.719891i
$238$	−2.22861	+	1.53006i	−0.144459	+	0.0991789i
$239$	1.48780	−	8.43773i	0.0962378	−	0.545791i	−0.898123	−	0.439744i	$-0.855069\pi$
$239$	1.48780	−	8.43773i	0.0962378	−	0.545791i	0.994361	−	0.106048i	$-0.0338196\pi$
$240$	−1.77863	+	2.59427i	−0.114810	+	0.167459i
$241$	11.0727	−	9.29110i	0.713255	−	0.598492i	−0.212255	−	0.977214i	$-0.568081\pi$
$241$	11.0727	−	9.29110i	0.713255	−	0.598492i	0.925510	+	0.378722i	$0.123636\pi$
$242$	15.0623	−	3.88744i	0.968244	−	0.249894i
$243$	15.2697	+	3.13622i	0.979552	+	0.201189i
$244$	−8.71818	−	15.7648i	−0.558124	−	1.00924i
$245$	−1.84561	+	1.54865i	−0.117912	+	0.0989395i
$246$	−1.25546	−	5.83120i	−0.0800455	−	0.371784i
$247$	−2.98221	−	0.525844i	−0.189754	−	0.0334587i
$248$	22.8011	+	11.4105i	1.44787	+	0.724565i
$249$	2.12666	+	2.75370i	0.134772	+	0.174508i
$250$	2.60486	+	5.72335i	0.164746	+	0.361977i
$251$	12.7128	−	7.33976i	0.802427	−	0.463281i	−0.0418921	−	0.999122i	$-0.513339\pi$
$251$	12.7128	−	7.33976i	0.802427	−	0.463281i	0.844319	+	0.535841i	$0.180005\pi$
$252$	3.21303	+	7.11582i	0.202402	+	0.448254i
$253$	0.0324730	+	0.0187483i	0.00204156	+	0.00117869i
$254$	2.35881	−	24.3708i	0.148005	−	1.52916i
$255$	1.12853	+	0.246498i	0.0706711	+	0.0154363i
$256$	3.93214	−	15.5093i	0.245759	−	0.969331i
$257$	−14.4703	+	17.2450i	−0.902633	+	1.07572i	0.0941497	+	0.995558i	$0.469987\pi$
$257$	−14.4703	+	17.2450i	−0.902633	+	1.07572i	−0.996782	+	0.0801575i	$0.974458\pi$
$258$	−22.5014	+	14.1427i	−1.40087	+	0.880483i
$259$	−6.47689	−	2.35739i	−0.402454	−	0.146481i
$260$	2.02789	+	0.0374033i	0.125765	+	0.00231966i
$261$	17.7879	−	12.6213i	1.10104	−	0.781240i
$262$	−3.11002	+	3.05318i	−0.192138	+	0.188626i
$263$	3.07511	+	17.4398i	0.189620	+	1.07539i	0.919875	+	0.392212i	$0.128290\pi$
$263$	3.07511	+	17.4398i	0.189620	+	1.07539i	−0.730255	+	0.683175i	$0.760599\pi$
$264$	−0.0542204	+	0.0671809i	−0.00333703	+	0.00413470i
$265$	4.44053	−	1.61622i	0.272780	−	0.0992836i
$266$	−2.48722	+	0.194511i	−0.152501	+	0.0119262i
$267$	−0.183744	+	0.0963806i	−0.0112449	+	0.00589839i
$268$	3.47115	−	9.01598i	0.212034	−	0.550739i
$269$	10.2475			0.624803			0.312402	−	0.949950i	$-0.398867\pi$
$269$	10.2475			0.624803			0.312402	+	0.949950i	$0.398867\pi$
$270$	1.27630	−	3.08245i	0.0776734	−	0.187592i
$271$			18.7315i			1.13786i	0.822386	+	0.568929i	$0.192642\pi$
$271$			18.7315i			1.13786i	−0.822386	+	0.568929i	$0.807358\pi$
$272$	−5.82029	+	0.806251i	−0.352907	+	0.0488861i
$273$	2.69177	−	4.25446i	0.162913	−	0.257492i
$274$	16.6136	−	1.29925i	1.00366	−	0.0784906i
$275$	0.0288937	+	0.0793847i	0.00174235	+	0.00478708i
$276$	7.32169	−	0.850002i	0.440714	−	0.0511641i
$277$	21.4560	−	3.78327i	1.28917	−	0.227315i	0.513299	−	0.858210i	$-0.328423\pi$
$277$	21.4560	−	3.78327i	1.28917	−	0.227315i	0.775868	+	0.630895i	$0.217312\pi$
$278$	5.30823	+	5.40704i	0.318366	+	0.324293i
$279$	−26.1651	−	6.83628i	−1.56646	−	0.409277i
$280$	1.62538	−	0.387671i	0.0971353	−	0.0231678i
$281$	−3.95262	+	10.8597i	−0.235793	+	0.647837i	0.764203	+	0.644976i	$0.223133\pi$
$281$	−3.95262	+	10.8597i	−0.235793	+	0.647837i	−0.999996	+	0.00286067i	$0.999089\pi$
$282$	9.87049	+	5.21505i	0.587779	+	0.310552i
$283$	−3.28791	−	2.75888i	−0.195446	−	0.163998i	0.539813	−	0.841785i	$-0.318495\pi$
$283$	−3.28791	−	2.75888i	−0.195446	−	0.163998i	−0.735259	+	0.677786i	$0.762939\pi$
$284$	19.7746	+	3.86409i	1.17340	+	0.229291i
$285$	0.788218	+	0.717759i	0.0466900	+	0.0425164i
$286$	0.0554093	+	0.00536297i	0.00327642	+	0.000317119i
$287$	−1.58437	+	2.74421i	−0.0935226	+	0.161986i
$288$	−0.676401	+	16.9571i	−0.0398573	+	0.999205i
$289$	−7.42107	−	12.8537i	−0.436533	−	0.756098i
$290$	−1.93366	−	4.24859i	−0.113548	−	0.249486i
$291$	−17.8696	−	7.33663i	−1.04754	−	0.430081i
$292$	−0.891837	+	1.02389i	−0.0521908	+	0.0599189i
$293$	−2.18285	+	12.3796i	−0.127523	+	0.723221i	0.852254	+	0.523129i	$0.175235\pi$
$293$	−2.18285	+	12.3796i	−0.127523	+	0.723221i	−0.979777	+	0.200092i	$0.935876\pi$
$294$	−3.98437	+	12.3730i	−0.232373	+	0.721610i
$295$	−3.20241	−	3.81648i	−0.186451	−	0.222204i
$296$	−10.2966	−	10.8826i	−0.598476	−	0.632538i
$297$	0.0415197	−	0.0816142i	0.00240922	−	0.00473574i
$298$	−19.6485	+	5.07107i	−1.13820	+	0.293759i
$299$	−3.05509	−	3.64092i	−0.176681	−	0.210560i
$300$	13.8674	+	9.13622i	0.800635	+	0.527480i
$301$	13.9041	+	2.45167i	0.801421	+	0.141312i
$302$	9.52027	+	13.8668i	0.547830	+	0.797943i
$303$	−3.86160	−	28.6412i	−0.221843	−	1.64539i
$304$	−5.02384	−	2.04133i	−0.288137	−	0.117078i
$305$	3.54153	−	2.04470i	0.202787	−	0.117079i
$306$	5.86277	−	2.11409i	0.335153	−	0.120854i
$307$	7.46768	−	12.9344i	0.426203	−	0.738205i	−0.570329	−	0.821416i	$-0.693184\pi$
$307$	7.46768	−	12.9344i	0.426203	−	0.738205i	0.996532	+	0.0832113i	$0.0265176\pi$
$308$	0.0453051	−	0.00712969i	0.00258150	−	0.000406252i
$309$	−8.39186	−	26.3290i	−0.477396	−	1.49780i
$310$	−2.49431	+	5.22278i	−0.141667	+	0.296634i
$311$	0.935160	+	0.784692i	0.0530280	+	0.0444958i	0.668916	−	0.743338i	$-0.266758\pi$
$311$	0.935160	+	0.784692i	0.0530280	+	0.0444958i	−0.615888	+	0.787833i	$0.711203\pi$
$312$	9.37072	−	5.65137i	0.530512	−	0.319946i
$313$	−3.74180	−	1.36190i	−0.211499	−	0.0769794i	0.234098	−	0.972213i	$-0.424786\pi$
$313$	−3.74180	−	1.36190i	−0.211499	−	0.0769794i	−0.445597	+	0.895234i	$0.647009\pi$
$314$	22.9102	+	6.36576i	1.29290	+	0.359241i
$315$	−1.60158	+	0.759028i	−0.0902389	+	0.0427664i
$316$	−8.34141	+	13.8514i	−0.469241	+	0.779202i
$317$	−1.28552	−	7.29053i	−0.0722018	−	0.409477i	−0.999391	−	0.0348844i	$-0.988894\pi$
$317$	−1.28552	−	7.29053i	−0.0722018	−	0.409477i	0.927190	−	0.374593i	$-0.122217\pi$
$318$	15.6439	−	20.1319i	0.877264	−	1.12894i
$319$	−0.0438192	−	0.120392i	−0.00245340	−	0.00674067i
$320$	3.53651	+	0.827527i	0.197697	+	0.0462601i
$321$	0.472559	−	11.6576i	0.0263757	−	0.650666i
$322$	−3.18670	−	2.27543i	−0.177588	−	0.126805i
$323$			1.99145i			0.110807i
$324$	−3.01985	−	17.7449i	−0.167769	−	0.985826i
$325$		−	10.7082i		−	0.593984i
$326$	8.36400	−	11.7136i	0.463239	−	0.648759i
$327$	0.204638	−	5.04824i	0.0113165	−	0.279168i
$328$	−5.74909	+	3.79299i	−0.317440	+	0.209433i
$329$	−2.02834	−	5.57283i	−0.111826	−	0.307240i
$330$	−0.0154746	−	0.0120248i	−0.000851849	−	0.000661944i
$331$	0.520452	+	2.95163i	0.0286066	+	0.162236i	0.995765	−	0.0919400i	$-0.0293068\pi$
$331$	0.520452	+	2.95163i	0.0286066	+	0.162236i	−0.967158	+	0.254176i	$0.918196\pi$
$332$	2.07260	−	3.44167i	0.113749	−	0.188886i
$333$	13.0733	+	9.03302i	0.716412	+	0.495006i
$334$	6.07269	−	21.8554i	0.332283	−	1.19588i
$335$	2.06083	+	0.750081i	0.112595	+	0.0409813i
$336$	6.31165	−	6.43746i	0.344329	−	0.351192i
$337$	−10.0788	−	8.45709i	−0.549025	−	0.460687i	0.325586	−	0.945513i	$-0.394439\pi$
$337$	−10.0788	−	8.45709i	−0.549025	−	0.460687i	−0.874611	+	0.484826i	$0.838883\pi$
$338$	10.2226	+	4.88212i	0.556034	+	0.265552i
$339$	−10.2600	−	32.1900i	−0.557244	−	1.74832i
$340$	−0.207355	−	1.31762i	−0.0112454	−	0.0714579i
$341$	−0.0794281	+	0.137574i	−0.00430127	+	0.00745003i
$342$	5.66129	+	1.01566i	0.306127	+	0.0549206i
$343$	13.8688	−	8.00714i	0.748844	−	0.432345i
$344$	24.6418	+	18.2906i	1.32860	+	0.986165i
$345$	0.223570	+	1.65820i	0.0120366	+	0.0892744i
$346$	−15.7822	+	10.8353i	−0.848459	+	0.582512i
$347$	28.8369	+	5.08472i	1.54804	+	0.272962i	0.881385	−	0.472400i	$-0.156612\pi$
$347$	28.8369	+	5.08472i	1.54804	+	0.272962i	0.666660	+	0.745362i	$0.267723\pi$
$348$	−21.0309	−	13.8557i	−1.12737	−	0.742743i
$349$	−13.4766	−	16.0608i	−0.721385	−	0.859713i	0.273380	−	0.961906i	$-0.411859\pi$
$349$	−13.4766	−	16.0608i	−0.721385	−	0.859713i	−0.994765	+	0.102193i	$0.967414\pi$
$350$	−2.20463	−	8.54210i	−0.117843	−	0.456595i
$351$	−8.48366	+	7.92114i	−0.452824	+	0.422799i
$352$	0.0949988	+	0.0302114i	0.00506345	+	0.00161028i
$353$	2.02760	+	2.41640i	0.107918	+	0.128612i	0.817300	−	0.576213i	$-0.195470\pi$
$353$	2.02760	+	2.41640i	0.107918	+	0.128612i	−0.709381	+	0.704825i	$0.751026\pi$
$354$	−25.5858	−	8.23917i	−1.35987	−	0.437907i
$355$	−0.794226	+	4.50428i	−0.0421532	+	0.239062i
$356$	0.180662	+	0.157361i	0.00957507	+	0.00834013i
$357$	−3.06275	−	1.25746i	−0.162098	−	0.0665516i
$358$	14.6385	−	6.66240i	0.773667	−	0.352119i
$359$	−15.2950	−	26.4917i	−0.807240	−	1.39818i	−0.914768	−	0.403979i	$-0.867627\pi$
$359$	−15.2950	−	26.4917i	−0.807240	−	1.39818i	0.107529	−	0.994202i	$-0.465706\pi$
$360$	−3.85147	−	0.0825326i	−0.202990	−	0.00434985i
$361$	8.58106	−	14.8628i	0.451635	−	0.782255i
$362$	−2.01949	+	20.8651i	−0.106142	+	1.09664i
$363$	14.0867	+	12.8275i	0.739360	+	0.673268i
$364$	−5.70542	−	1.11488i	−0.299045	−	0.0584355i
$365$	−0.236120	−	0.198128i	−0.0123591	−	0.0103705i
$366$	10.3071	−	19.5081i	0.538758	−	1.01970i
$367$	−7.65245	+	21.0249i	−0.399455	+	1.09749i	0.563096	+	0.826391i	$0.309610\pi$
$367$	−7.65245	+	21.0249i	−0.399455	+	1.09749i	−0.962551	+	0.271101i	$0.912612\pi$
$368$	−3.98087	−	7.52278i	−0.207517	−	0.392152i
$369$	5.13336	−	5.19781i	0.267232	−	0.270587i
$370$	2.42685	−	2.38250i	0.126166	−	0.123860i
$371$	−13.3385	+	2.35193i	−0.692499	+	0.122106i
$372$	3.60108	+	31.0188i	0.186707	+	1.60825i
$373$	3.91132	+	10.7463i	0.202521	+	0.556421i	0.998824	−	0.0484764i	$-0.0154366\pi$
$373$	3.91132	+	10.7463i	0.202521	+	0.556421i	−0.796304	+	0.604897i	$0.793214\pi$
$374$	−0.00285428	−	0.0364978i	−0.000147591	−	0.00188725i
$375$	−4.11773	+	6.50825i	−0.212639	+	0.336085i
$376$	1.47824	−	12.8054i	0.0762346	−	0.660390i
$377$			16.2397i			0.836387i
$378$	−5.13673	+	8.06546i	−0.264205	+	0.414843i
$379$	−21.7004			−1.11468			−0.557338	−	0.830286i	$-0.688177\pi$
$379$	−21.7004			−1.11468			−0.557338	+	0.830286i	$0.688177\pi$
$380$	0.442277	−	1.14877i	0.0226883	−	0.0589308i
$381$	26.5560	−	13.9296i	1.36050	−	0.713635i
$382$	2.07826	+	26.5748i	0.106333	+	1.35969i
$383$	31.1726	−	11.3459i	1.59285	−	0.579749i	0.614900	−	0.788605i	$-0.289196\pi$
$383$	31.1726	−	11.3459i	1.59285	−	0.579749i	0.977946	+	0.208856i	$0.0669740\pi$
$384$	18.5305	−	6.37346i	0.945630	−	0.325244i
$385$	0.00180784	+	0.0102528i	9.21359e−5	+	0.000522529i
$386$	2.09081	+	2.12973i	0.106419	+	0.108400i
$387$	−29.5854	−	13.5718i	−1.50391	−	0.689896i
$388$	−0.411341	+	22.3017i	−0.0208827	+	1.13220i
$389$	6.54404	+	2.38183i	0.331796	+	0.120764i	0.502546	−	0.864551i	$-0.332397\pi$
$389$	6.54404	+	2.38183i	0.331796	+	0.120764i	−0.170750	+	0.985314i	$0.554619\pi$
$390$	1.32188	+	2.10315i	0.0669362	+	0.106497i
$391$	−2.00913	+	2.39438i	−0.101606	+	0.121089i
$392$	14.9830	−	0.894090i	0.756755	−	0.0451584i
$393$	−5.21477	−	1.13903i	−0.263050	−	0.0574567i
$394$	16.1282	+	1.56102i	0.812529	+	0.0786432i
$395$	−3.17868	−	1.83521i	−0.159937	−	0.0923395i
$396$	−0.105211	−	0.0105001i	−0.00528707	−	0.000527651i
$397$	−31.8597	+	18.3942i	−1.59899	+	0.923178i	−0.607308	+	0.794466i	$0.707751\pi$
$397$	−31.8597	+	18.3942i	−1.59899	+	0.923178i	−0.991682	+	0.128712i	$0.958916\pi$
$398$	7.31526	−	3.32939i	0.366681	−	0.166887i
$399$	−1.86763	−	2.41829i	−0.0934984	−	0.121066i
$400$	4.02391	−	18.7486i	0.201195	−	0.937428i
$401$	3.00611	+	0.530059i	0.150118	+	0.0264699i	0.248202	−	0.968708i	$-0.420160\pi$
$401$	3.00611	+	0.530059i	0.150118	+	0.0264699i	−0.0980840	+	0.995178i	$0.531271\pi$
$402$	11.5673	−	2.49046i	0.576925	−	0.124213i
$403$	15.4250	−	12.9431i	0.768372	−	0.644740i
$404$	−29.2031	+	16.1498i	−1.45291	+	0.803483i
$405$	4.01480	−	0.759679i	0.199497	−	0.0377487i
$406$	3.34347	+	12.9547i	0.165934	+	0.642930i
$407$	0.0715044	−	0.0599993i	0.00354434	−	0.00297406i
$408$	−4.73016	−	5.42349i	−0.234178	−	0.268503i
$409$	−4.18256	+	23.7205i	−0.206814	+	1.17290i	0.687745	+	0.725952i	$0.258601\pi$
$409$	−4.18256	+	23.7205i	−0.206814	+	1.17290i	−0.894559	+	0.446949i	$0.852511\pi$
$410$	−0.884936	−	1.28896i	−0.0437039	−	0.0636570i
$411$	12.4750	+	16.1531i	0.615345	+	0.796776i
$412$	−24.8178	+	20.0564i	−1.22268	+	0.988110i
$413$	7.13978	+	12.3665i	0.351326	+	0.608514i
$414$	5.78206	+	6.93269i	0.284173	+	0.340723i
$415$	0.789809	+	0.455997i	0.0387702	+	0.0223840i
$416$	−10.0056	−	7.71698i	−0.490567	−	0.378356i
$417$	−1.98031	+	9.06633i	−0.0969762	+	0.443980i
$418$	0.0145603	−	0.0304875i	0.000712168	−	0.00149119i
$419$	−19.0854	+	22.7451i	−0.932383	+	1.11117i	0.0612068	+	0.998125i	$0.480505\pi$
$419$	−19.0854	+	22.7451i	−0.932383	+	1.11117i	−0.993590	+	0.113046i	$0.963939\pi$
$420$	1.48749	+	1.40557i	0.0725821	+	0.0685846i
$421$	9.82045	−	26.9815i	0.478619	−	1.31500i	−0.432046	−	0.901851i	$-0.642208\pi$
$421$	9.82045	−	26.9815i	0.478619	−	1.31500i	0.910666	−	0.413144i	$-0.135570\pi$
$422$	6.30192	−	22.6804i	0.306773	−	1.10407i
$423$	1.27657	+	13.6127i	0.0620689	+	0.661872i
$424$	−28.2150	−	8.40321i	−1.37024	−	0.408096i
$425$	−6.93506	+	1.22284i	−0.336400	+	0.0593164i
$426$	9.30413	+	22.8556i	0.450786	+	1.10736i
$427$	−11.0142	+	4.00883i	−0.533013	+	0.194001i
$428$	−12.7425	+	4.37350i	−0.615931	+	0.211401i
$429$	0.0316702	+	0.0603774i	0.00152905	+	0.00291505i
$430$	−4.04815	+	5.66937i	−0.195219	+	0.273401i
$431$	−26.5585			−1.27928			−0.639639	−	0.768675i	$-0.720916\pi$
$431$	−26.5585			−1.27928			−0.639639	+	0.768675i	$0.720916\pi$
$432$	−17.8303	+	10.6808i	−0.857861	+	0.513882i
$433$	−1.55270			−0.0746180			−0.0373090	−	0.999304i	$-0.511879\pi$
$433$	−1.55270			−0.0746180			−0.0373090	+	0.999304i	$0.511879\pi$
$434$	9.63998	−	13.5006i	0.462734	−	0.648051i
$435$	3.05670	−	4.83124i	0.146557	−	0.231640i
$436$	−5.51802	+	1.89390i	−0.264265	+	0.0907016i
$437$	−2.71064	+	0.986591i	−0.129667	+	0.0471951i
$438$	−1.64743	−	0.227123i	−0.0787170	−	0.0108524i
$439$	1.13120	−	0.199460i	0.0539891	−	0.00951973i	−0.146588	−	0.989198i	$-0.546829\pi$
$439$	1.13120	−	0.199460i	0.0539891	−	0.00951973i	0.200577	+	0.979678i	$0.435718\pi$
$440$	−0.00645921	+	0.0216877i	−0.000307931	+	0.00103392i
$441$	−15.3517	+	4.21628i	−0.731032	+	0.200775i
$442$	−1.24231	+	4.47102i	−0.0590904	+	0.212665i
$443$	5.79518	−	15.9221i	0.275337	−	0.756483i	−0.722538	−	0.691331i	$-0.757025\pi$
$443$	5.79518	−	15.9221i	0.275337	−	0.756483i	0.997875	−	0.0651518i	$-0.0207532\pi$
$444$	4.24541	−	17.8508i	0.201478	−	0.847163i
$445$	−0.0349590	+	0.0416625i	−0.00165721	+	0.00197499i
$446$	−1.69300	+	3.54493i	−0.0801658	+	0.167857i
$447$	−18.3758	−	16.7331i	−0.869143	−	0.791450i
$448$	−9.57045	−	4.09597i	−0.452161	−	0.193516i
$449$	−26.5725	−	15.3416i	−1.25403	−	0.724017i	−0.282126	−	0.959377i	$-0.591039\pi$
$449$	−26.5725	−	15.3416i	−1.25403	−	0.724017i	−0.971908	+	0.235361i	$0.924373\pi$
$450$	−0.0606753	+	20.3386i	−0.00286026	+	0.958772i
$451$	−0.0214563	−	0.0371634i	−0.00101034	−	0.00174996i
$452$	−30.3424	+	24.5212i	−1.42719	+	1.15338i
$453$	−7.82410	+	19.0570i	−0.367608	+	0.895374i
$454$	19.7921	+	28.8282i	0.928889	+	1.35297i
$455$	0.229153	−	1.29959i	0.0107428	−	0.0609257i
$456$	−1.27791	−	6.51735i	−0.0598436	−	0.305203i
$457$	5.48725	−	4.60435i	0.256683	−	0.215382i	−0.505361	−	0.862908i	$-0.668641\pi$
$457$	5.48725	−	4.60435i	0.256683	−	0.215382i	0.762044	+	0.647526i	$0.224196\pi$
$458$	5.53905	+	21.4617i	0.258823	+	1.00284i
$459$	6.09886	+	4.58979i	0.284670	+	0.214233i
$460$	1.69073	−	0.935003i	0.0788308	−	0.0435948i
$461$	6.34887	−	5.32733i	0.295696	−	0.248119i	−0.482854	−	0.875701i	$-0.660400\pi$
$461$	6.34887	−	5.32733i	0.295696	−	0.248119i	0.778550	+	0.627582i	$0.215955\pi$
$462$	0.0376945	+	0.0416437i	0.00175371	+	0.00193744i
$463$	0.381159	+	0.0672086i	0.0177140	+	0.00312345i	0.182498	−	0.983206i	$-0.441582\pi$
$463$	0.381159	+	0.0672086i	0.0177140	+	0.00312345i	−0.164784	+	0.986330i	$0.552693\pi$
$464$	−6.10253	+	28.4335i	−0.283303	+	1.31999i
$465$	−7.02505	+	0.947165i	−0.325779	+	0.0439237i
$466$	26.0396	−	11.8514i	1.20626	−	0.549004i
$467$	−5.76908	+	3.33078i	−0.266961	+	0.154130i	−0.627506	−	0.778612i	$-0.715924\pi$
$467$	−5.76908	+	3.33078i	−0.266961	+	0.154130i	0.360545	+	0.932742i	$0.382591\pi$
$468$	12.0766	+	5.81189i	0.558241	+	0.268655i
$469$	−5.44368	−	3.14291i	−0.251366	−	0.145126i
$470$	2.91256	+	0.281901i	0.134346	+	0.0130031i
$471$	8.84379	+	27.7469i	0.407500	+	1.27851i
$472$	1.84886	+	30.9829i	0.0851009	+	1.42610i
$473$	−0.122902	+	0.146469i	−0.00565103	+	0.00673463i
$474$	−19.7891	+	0.743054i	−0.908943	+	0.0341296i
$475$	−6.10704	−	2.22278i	−0.280210	−	0.101988i
$476$	−0.0705015	+	3.82238i	−0.00323143	+	0.175198i
$477$	31.1231	+	2.52739i	1.42503	+	0.115721i
$478$	−8.48853	−	8.64654i	−0.388256	−	0.395483i
$479$	−0.196814	−	1.11619i	−0.00899268	−	0.0510000i	0.979981	−	0.199090i	$-0.0637986\pi$
$479$	−0.196814	−	1.11619i	−0.00899268	−	0.0510000i	−0.988974	+	0.148090i	$0.952687\pi$
$480$	1.52412	+	4.17906i	0.0695660	+	0.190747i
$481$	−11.1181	+	4.04665i	−0.506941	+	0.184511i
$482$	−1.59375	−	20.3794i	−0.0725934	−	0.928255i
$483$	0.194242	−	4.79179i	0.00883832	−	0.218034i
$484$	7.90418	−	20.5304i	0.359281	−	0.933199i
$485$	−5.06338			−0.229916
$486$	16.1583	−	14.9970i	0.732956	−	0.680276i
$487$			41.9634i			1.90154i	0.309896	+	0.950771i	$0.399706\pi$
$487$			41.9634i			1.90154i	−0.309896	+	0.950771i	$0.600294\pi$
$488$	−25.3087	−	2.92161i	−1.14567	−	0.132255i
$489$	17.6136	+	0.713993i	0.796515	+	0.0322879i
$490$	0.265648	+	3.39685i	0.0120007	+	0.153454i
$491$	−7.04382	−	19.3527i	−0.317883	−	0.873377i	−0.991003	−	0.133843i	$-0.957268\pi$
$491$	−7.04382	−	19.3527i	−0.317883	−	0.873377i	0.673119	−	0.739534i	$-0.264954\pi$
$492$	−7.74303	−	3.34718i	−0.349083	−	0.150902i
$493$	10.5175	−	1.85452i	0.473684	−	0.0835233i
$494$	−3.05601	+	3.00016i	−0.137496	+	0.134984i
$495$	0.00194271	−	0.0239231i	8.73182e−5	−	0.00107526i
$496$	31.8707	−	16.8652i	1.43104	−	0.757268i
$497$	4.48365	−	12.3187i	0.201119	−	0.552570i
$498$	4.91701	−	0.184627i	0.220337	−	0.00827334i
$499$	7.68110	+	6.44521i	0.343853	+	0.288527i	0.798316	−	0.602239i	$-0.205724\pi$
$499$	7.68110	+	6.44521i	0.343853	+	0.288527i	−0.454463	+	0.890766i	$0.650169\pi$
$500$	8.72786	+	1.70548i	0.390322	+	0.0762715i
$501$	26.4694	−	8.43663i	1.18257	−	0.376921i
$502$	1.99997	−	20.6634i	0.0892632	−	0.922253i
$503$	12.3849	−	21.4513i	0.552216	−	0.956466i	−0.445898	−	0.895084i	$-0.647116\pi$
$503$	12.3849	−	21.4513i	0.552216	−	0.956466i	0.998114	−	0.0613824i	$-0.0195509\pi$
$504$	10.8303	+	2.14987i	0.482419	+	0.0957630i
$505$	−3.78767	−	6.56044i	−0.168549	−	0.291936i
$506$	0.0482644	−	0.0219665i	0.00214562	−	0.000976532i
$507$	1.85389	+	13.7502i	0.0823341	+	0.610666i
$508$	−26.1106	−	22.7429i	−1.15847	−	1.00906i
$509$	−5.29018	+	30.0021i	−0.234483	+	1.32982i	0.609217	+	0.793004i	$0.291484\pi$
$509$	−5.29018	+	30.0021i	−0.234483	+	1.32982i	−0.843700	+	0.536816i	$0.819627\pi$
$510$	1.21113	−	1.09628i	0.0536299	−	0.0485440i
$511$	0.567874	+	0.676766i	0.0251213	+	0.0299383i
$512$	−14.6186	−	17.2713i	−0.646057	−	0.763289i
$513$	2.75653	+	6.48260i	0.121704	+	0.286214i
$514$	7.95597	+	30.8264i	0.350923	+	1.35969i
$515$	−4.65597	−	5.54877i	−0.205167	−	0.244508i
$516$	−2.21462	+	37.5200i	−0.0974930	+	1.65172i
$517$	0.0790932	+	0.0139463i	0.00347852	+	0.000613356i
$518$	−8.03594	+	5.51710i	−0.353079	+	0.242408i
$519$	−21.6894	−	8.90488i	−0.952058	−	0.390881i
$520$	1.70959	−	2.30322i	0.0749703	−	0.101003i
$521$	−2.67309	+	1.54331i	−0.117110	+	0.0676136i	−0.557411	−	0.830237i	$-0.688205\pi$
$521$	−2.67309	+	1.54331i	−0.117110	+	0.0676136i	0.440301	+	0.897850i	$0.354872\pi$
$522$	0.0920181	−	30.8449i	0.00402752	−	1.35004i
$523$	−6.24198	+	10.8114i	−0.272943	+	0.472750i	−0.969614	−	0.244640i	$-0.921330\pi$
$523$	−6.24198	+	10.8114i	−0.272943	+	0.472750i	0.696671	+	0.717390i	$0.254664\pi$
$524$	0.958157	+	6.08853i	0.0418573	+	0.265979i
$525$	7.27468	−	7.98880i	0.317493	−	0.348660i
$526$	22.5991	+	10.7930i	0.985369	+	0.470595i
$527$	−10.1439	−	8.51177i	−0.441877	−	0.370779i
$528$	0.0327617	+	0.117613i	0.00142577	+	0.00511847i
$529$	17.3585	+	6.31798i	0.754717	+	0.274695i
$530$	1.78911	−	6.43895i	0.0777139	−	0.279690i
$531$	−8.71872	−	31.7453i	−0.378360	−	1.37763i
$532$	−1.82015	+	3.02246i	−0.0789134	+	0.131040i
$533$	0.944542	+	5.35676i	0.0409126	+	0.232027i
$534$	−0.0400750	+	0.290682i	−0.00173422	+	0.0125790i
$535$	−1.04597	−	2.87377i	−0.0452211	−	0.124244i
$536$	−7.52412	−	11.4044i	−0.324993	−	0.492596i
$537$	16.6460	+	10.5318i	0.718328	+	0.454482i
$538$	8.42150	−	11.7942i	0.363076	−	0.508482i
$539$			0.0935167i			0.00402805i
$540$	−2.49880	−	4.00212i	−0.107531	−	0.172224i
$541$		−	35.0866i		−	1.50849i	−0.656592	−	0.754246i	$-0.728003\pi$
$541$		−	35.0866i		−	1.50849i	0.656592	−	0.754246i	$-0.271997\pi$
$542$	21.5586	+	15.3937i	0.926021	+	0.661216i
$543$	−22.7358	+	11.9258i	−0.975688	+	0.511785i
$544$	−3.85522	+	7.36131i	−0.165291	+	0.315613i
$545$	−0.452947	−	1.24446i	−0.0194021	−	0.0533069i
$546$	−2.68446	−	6.59438i	−0.114884	−	0.282213i
$547$	−0.423952	−	2.40435i	−0.0181269	−	0.102803i	0.974402	−	0.224813i	$-0.0721771\pi$
$547$	−0.423952	−	2.40435i	−0.0181269	−	0.102803i	−0.992529	+	0.122010i	$0.961066\pi$
$548$	12.1578	−	20.1888i	0.519356	−	0.862421i
$549$	26.9042	−	2.52302i	1.14824	−	0.107680i
$550$	0.115111	+	0.0319844i	0.00490835	+	0.00136382i
$551$	9.26174	+	3.37100i	0.394563	+	0.143609i
$552$	5.03873	−	9.12527i	0.214462	−	0.388397i
$553$	8.05890	+	6.76222i	0.342699	+	0.287559i
$554$	13.2784	−	27.8034i	0.564147	−	1.18125i
$555$	4.06926	+	0.888826i	0.172730	+	0.0377286i
$556$	10.5854	−	1.66584i	0.448923	−	0.0706473i
$557$	3.41195	−	5.90968i	0.144569	−	0.250401i	−0.784643	−	0.619948i	$-0.787154\pi$
$557$	3.41195	−	5.90968i	0.144569	−	0.250401i	0.929212	+	0.369547i	$0.120487\pi$
$558$	−29.3707	+	24.4960i	−1.24336	+	1.03700i
$559$	20.9888	−	12.1179i	0.887730	−	0.512531i
$560$	0.889572	−	2.18929i	0.0375913	−	0.0925144i
$561$	0.0354862	−	0.0274058i	0.00149823	−	0.00115707i
$562$	9.25046	+	13.4738i	0.390207	+	0.568357i
$563$	20.6520	+	3.64150i	0.870377	+	0.153471i	0.590962	−	0.806699i	$-0.298748\pi$
$563$	20.6520	+	3.64150i	0.870377	+	0.153471i	0.279415	+	0.960170i	$0.409859\pi$
$564$	14.1138	−	7.07445i	0.594298	−	0.297888i
$565$	−5.69243	−	6.78397i	−0.239482	−	0.285404i
$566$	−5.87730	+	1.51687i	−0.247041	+	0.0637589i
$567$	−11.7105	+	0.146105i	−0.491793	+	0.00613585i
$568$	20.6982	−	19.5835i	0.868476	−	0.821707i
$569$	−20.8313	−	24.8258i	−0.873295	−	1.04075i	−0.998815	−	0.0486610i	$-0.984505\pi$
$569$	−20.8313	−	24.8258i	−0.873295	−	1.04075i	0.125521	−	0.992091i	$-0.459940\pi$
$570$	1.47385	−	0.317322i	0.0617329	−	0.0132912i
$571$	−0.396543	+	2.24891i	−0.0165948	+	0.0941139i	−0.991980	−	0.126393i	$-0.959660\pi$
$571$	−0.396543	+	2.24891i	−0.0165948	+	0.0941139i	0.975385	+	0.220507i	$0.0707711\pi$
$572$	0.0517082	−	0.0593648i	0.00216203	−	0.00248217i
$573$	−25.8383	+	19.9548i	−1.07941	+	0.833623i
$574$	1.85634	+	4.07871i	0.0774822	+	0.170242i
$575$	−5.10017	−	8.83376i	−0.212692	−	0.368393i
$576$	18.9605	+	14.7139i	0.790020	+	0.613081i
$577$	−10.7395	+	18.6014i	−0.447092	+	0.774387i	−0.998195	−	0.0600507i	$-0.980874\pi$
$577$	−10.7395	+	18.6014i	−0.447092	+	0.774387i	0.551103	+	0.834437i	$0.314207\pi$
$578$	−20.8923	−	2.02213i	−0.869006	−	0.0841095i
$579$	−0.780006	+	3.57105i	−0.0324159	+	0.148408i
$580$	−6.47891	−	1.26602i	−0.269022	−	0.0525688i
$581$	−2.00240	−	1.68021i	−0.0830736	−	0.0697070i
$582$	−23.1293	+	14.5373i	−0.958741	+	0.602592i
$583$	0.0627342	−	0.172361i	0.00259818	−	0.00713845i
$584$	0.445509	+	1.86788i	0.0184353	+	0.0772935i
$585$	−1.26853	+	2.76528i	−0.0524473	+	0.114330i
$586$	12.4541	+	12.6859i	0.514473	+	0.524050i
$587$	18.6609	−	3.29041i	0.770216	−	0.135810i	0.225287	−	0.974292i	$-0.427668\pi$
$587$	18.6609	−	3.29041i	0.770216	−	0.135810i	0.544928	+	0.838483i	$0.316557\pi$
$588$	10.9661	+	14.7540i	0.452233	+	0.608443i
$589$	−4.17975	−	11.4838i	−0.172224	−	0.473180i
$590$	−7.02425	+	0.549326i	−0.289184	+	0.0226154i
$591$	9.21839	+	17.5743i	0.379194	+	0.722911i
$592$	−20.9869	+	2.90719i	−0.862555	+	0.119485i
$593$		−	23.6650i		−	0.971804i	−0.874013	−	0.485902i	$-0.838491\pi$
$593$		−	23.6650i		−	0.971804i	0.874013	−	0.485902i	$-0.161509\pi$
$594$	−0.0598108	−	0.114857i	−0.00245407	−	0.00471265i
$595$	−0.867835			−0.0355778
$596$	−10.3108	+	26.7814i	−0.422347	+	1.09701i
$597$	8.31848	+	5.26305i	0.340453	+	0.215402i
$598$	−6.70113	+	0.524056i	−0.274029	+	0.0214302i
$599$	8.37844	−	3.04950i	0.342334	−	0.124599i	−0.165131	−	0.986272i	$-0.552805\pi$
$599$	8.37844	−	3.04950i	0.342334	−	0.124599i	0.507465	+	0.861672i	$0.330583\pi$
$600$	21.9115	−	8.45216i	0.894531	−	0.345058i
$601$	4.44934	+	25.2334i	0.181492	+	1.02929i	0.930380	+	0.366597i	$0.119477\pi$
$601$	4.44934	+	25.2334i	0.181492	+	1.02929i	−0.748888	+	0.662697i	$0.769412\pi$
$602$	14.2482	−	13.9878i	0.580714	−	0.570102i
$603$	10.3109	+	10.1830i	0.419891	+	0.414685i
$604$	23.7835	+	0.438672i	0.967735	+	0.0178493i
$605$	4.69274	+	1.70802i	0.190787	+	0.0694407i
$606$	−36.1374	−	19.0931i	−1.46798	−	0.775604i
$607$	8.91382	−	10.6231i	0.361801	−	0.431177i	−0.554182	−	0.832396i	$-0.686969\pi$
$607$	8.91382	−	10.6231i	0.361801	−	0.431177i	0.915982	+	0.401218i	$0.131413\pi$
$608$	−6.47805	+	4.10449i	−0.262720	+	0.166459i
$609$	−11.0325	+	12.1156i	−0.447061	+	0.490947i
$610$	0.557151	−	5.75639i	0.0225584	−	0.233070i
$611$	−8.81625	−	5.09007i	−0.356667	−	0.205922i
$612$	2.38491	−	8.48500i	0.0964042	−	0.342986i
$613$	−17.7329	+	10.2381i	−0.716224	+	0.413512i	−0.813361	−	0.581759i	$-0.802365\pi$
$613$	−17.7329	+	10.2381i	−0.716224	+	0.413512i	0.0971374	+	0.995271i	$0.469031\pi$
$614$	−8.74955	−	19.2243i	−0.353103	−	0.775831i
$615$	0.727273	−	1.77140i	0.0293265	−	0.0714297i
$616$	0.0290263	−	0.0580021i	0.00116950	−	0.00233697i
$617$	45.9610	+	8.10416i	1.85032	+	0.326261i	0.984675	−	0.174399i	$-0.0557983\pi$
$617$	45.9610	+	8.10416i	1.85032	+	0.326261i	0.865644	+	0.500660i	$0.166909\pi$
$618$	−37.1992	−	11.9789i	−1.49637	−	0.481862i
$619$	−20.3900	+	17.1092i	−0.819542	+	0.687678i	−0.952865	−	0.303395i	$-0.901880\pi$
$619$	−20.3900	+	17.1092i	−0.819542	+	0.687678i	0.133323	+	0.991073i	$0.457435\pi$
$620$	3.96119	+	7.16288i	0.159085	+	0.287668i
$621$	−3.22588	+	10.5752i	−0.129450	+	0.424369i
$622$	1.67164	−	0.431435i	0.0670268	−	0.0172990i
$623$	0.119413	−	0.100199i	0.00478417	−	0.00401439i
$624$	1.19661	−	15.4294i	0.0479026	−	0.617668i
$625$	3.81170	−	21.6172i	0.152468	−	0.864688i
$626$	−4.64249	+	3.18732i	−0.185551	+	0.127391i
$627$	0.0410081	−	0.00552900i	0.00163771	−	0.000220807i
$628$	26.1543	−	21.1365i	1.04367	−	0.843440i
$629$	3.89042	+	6.73841i	0.155121	+	0.268678i
$630$	−0.442605	+	2.46708i	−0.0176338	+	0.0982907i
$631$	−24.6191	−	14.2138i	−0.980071	−	0.565844i	−0.0777793	−	0.996971i	$-0.524783\pi$
$631$	−24.6191	−	14.2138i	−0.980071	−	0.565844i	−0.902292	+	0.431126i	$0.858116\pi$
$632$	9.08691	+	20.9835i	0.361458	+	0.834680i
$633$	27.4686	−	8.75510i	1.09178	−	0.347984i
$634$	−9.44732	−	4.51187i	−0.375201	−	0.179189i
$635$	5.05252	−	6.02135i	0.200503	−	0.238950i
$636$	−10.3141	−	34.5495i	−0.408981	−	1.36998i
$637$	4.05421	−	11.1389i	0.160634	−	0.441337i
$638$	−0.174574	−	0.0485065i	−0.00691143	−	0.00192039i
$639$	−17.1803	+	24.8648i	−0.679644	+	0.983635i
$640$	3.85875	−	3.39019i	0.152530	−	0.134009i
$641$	19.2764	−	3.39896i	0.761373	−	0.134251i	0.220537	−	0.975379i	$-0.429219\pi$
$641$	19.2764	−	3.39896i	0.761373	−	0.134251i	0.540836	+	0.841128i	$0.318108\pi$
$642$	−13.0287	−	10.1242i	−0.514203	−	0.399571i
$643$	−10.2317	+	3.72402i	−0.403497	+	0.146861i	−0.535793	−	0.844349i	$-0.679987\pi$
$643$	−10.2317	+	3.72402i	−0.403497	+	0.146861i	0.132296	+	0.991210i	$0.457765\pi$
$644$	−5.23770	+	1.79769i	−0.206394	+	0.0708391i
$645$	−8.52493	−	0.345571i	−0.335669	−	0.0136068i
$646$	2.29201	+	1.63659i	0.0901781	+	0.0643907i
$647$	−19.0202			−0.747763			−0.373881	−	0.927477i	$-0.621973\pi$
$647$	−19.0202			−0.747763			−0.373881	+	0.927477i	$0.621973\pi$
$648$	−22.9048	−	11.1072i	−0.899785	−	0.436334i
$649$	−0.193381			−0.00759085
$650$	−12.3244	−	8.80007i	−0.483401	−	0.345167i
$651$	20.3007	+	0.822917i	0.795646	+	0.0322527i
$652$	−6.60795	−	19.2527i	−0.258787	−	0.753995i
$653$	−11.7763	+	4.28623i	−0.460843	+	0.167733i	−0.562000	−	0.827137i	$-0.689968\pi$
$653$	−11.7763	+	4.28623i	−0.460843	+	0.167733i	0.101157	+	0.994871i	$0.467746\pi$
$654$	−5.64198	−	4.38420i	−0.220619	−	0.171436i
$655$	−1.37786	+	0.242955i	−0.0538376	+	0.00949302i
$656$	−0.359194	+	9.73389i	−0.0140242	+	0.380044i
$657$	−0.872270	−	1.84053i	−0.0340305	−	0.0718058i
$658$	−8.08082	−	2.24531i	−0.315023	−	0.0875315i
$659$	9.65592	−	26.5294i	0.376141	−	1.03344i	−0.596801	−	0.802389i	$-0.703562\pi$
$659$	9.65592	−	26.5294i	0.376141	−	1.03344i	0.972942	−	0.231050i	$-0.0742160\pi$
$660$	−0.0265568	+	0.00792805i	−0.00103372	+	0.000308599i
$661$	10.6735	−	12.7202i	0.415150	−	0.494757i	−0.517427	−	0.855727i	$-0.673110\pi$
$661$	10.6735	−	12.7202i	0.415150	−	0.494757i	0.932577	+	0.360971i	$0.117555\pi$
$662$	3.82482	+	1.82667i	0.148656	+	0.0709955i
$663$	−5.41491	+	1.72590i	−0.210298	+	0.0670285i
$664$	−2.25783	−	5.21379i	−0.0876208	−	0.202334i
$665$	−0.693608	−	0.400455i	−0.0268970	−	0.0155290i
$666$	21.1401	−	7.62302i	0.819161	−	0.295386i
$667$	7.73476	+	13.3970i	0.299491	+	0.518734i
$668$	−20.1634	−	24.9502i	−0.780147	−	0.965352i
$669$	−4.76822	+	0.642884i	−0.184350	+	0.0248553i
$670$	2.55689	−	1.75544i	0.0987814	−	0.0678187i
$671$	0.0275635	−	0.156320i	0.00106408	−	0.00603468i
$672$	−2.22208	−	12.5546i	−0.0857187	−	0.484304i
$673$	4.64214	−	3.89522i	0.178941	−	0.150150i	−0.548918	−	0.835876i	$-0.684960\pi$
$673$	4.64214	−	3.89522i	0.178941	−	0.150150i	0.727859	+	0.685727i	$0.240516\pi$
$674$	−18.0163	+	4.64982i	−0.693962	+	0.179105i
$675$	−20.8825	+	13.5800i	−0.803768	+	0.522694i
$676$	14.0199	−	7.75326i	0.539228	−	0.298202i
$677$	−5.34485	+	4.48486i	−0.205419	+	0.172367i	−0.739693	−	0.672944i	$-0.765029\pi$
$677$	−5.34485	+	4.48486i	−0.205419	+	0.172367i	0.534274	+	0.845311i	$0.320585\pi$
$678$	−45.4800	−	14.6455i	−1.74665	−	0.562458i
$679$	14.2922	+	2.52009i	0.548483	+	0.0967123i
$680$	−1.68689	−	0.844178i	−0.0646892	−	0.0323727i
$681$	−16.2659	+	39.6183i	−0.623309	+	1.51818i
$682$	0.0930625	+	0.204475i	0.00356355	+	0.00782975i
$683$	25.8624	−	14.9317i	0.989597	−	0.571344i	0.0844432	−	0.996428i	$-0.473089\pi$
$683$	25.8624	−	14.9317i	0.989597	−	0.571344i	0.905154	+	0.425084i	$0.139756\pi$
$684$	5.82144	−	5.68105i	0.222588	−	0.217220i
$685$	4.63301	+	2.67487i	0.177018	+	0.102201i
$686$	2.18183	−	22.5423i	0.0833025	−	0.860668i
$687$	−18.2773	+	20.0715i	−0.697324	+	0.765777i
$688$	41.3020	−	13.3296i	1.57463	−	0.508185i
$689$	−14.9446	+	17.8103i	−0.569346	+	0.678520i
$690$	2.09220	+	1.10541i	0.0796485	+	0.0420821i
$691$	31.1175	+	11.3259i	1.18377	+	0.430856i	0.857531	−	0.514432i	$-0.171997\pi$
$691$	31.1175	+	11.3259i	1.18377	+	0.430856i	0.326236	+	0.945288i	$0.394220\pi$
$692$	−0.499268	+	27.0688i	−0.0189793	+	1.02900i
$693$	−0.0173903	+	0.0665597i	−0.000660604	+	0.00252839i
$694$	29.5505	−	29.0105i	1.12172	−	1.10122i
$695$	0.422398	+	2.39554i	0.0160225	+	0.0908679i
$696$	−33.2302	+	12.8183i	−1.25959	+	0.485875i
$697$	3.36139	−	1.22345i	0.127322	−	0.0463414i
$698$	−29.5599	+	2.31171i	−1.11886	+	0.0874995i
$699$	29.6107	+	18.7345i	1.11998	+	0.708603i
$700$	−11.6431	−	4.48259i	−0.440069	−	0.169426i
$701$	−9.68894			−0.365946			−0.182973	−	0.983118i	$-0.558572\pi$
$701$	−9.68894			−0.365946			−0.182973	+	0.983118i	$0.558572\pi$
$702$	2.14472	+	16.2737i	0.0809473	+	0.614212i
$703$			7.18080i			0.270829i
$704$	0.112842	−	0.0845087i	0.00425289	−	0.00318504i
$705$	1.66473	+	3.17370i	0.0626972	+	0.119528i
$706$	4.44740	−	0.347805i	0.167380	−	0.0130898i
$707$	7.42607	+	20.4030i	0.279286	+	0.767333i
$708$	−30.5093	+	22.6764i	−1.14661	+	0.852233i
$709$	−24.6853	+	4.35269i	−0.927077	+	0.163469i	−0.616748	−	0.787161i	$-0.711550\pi$
$709$	−24.6853	+	4.35269i	−0.927077	+	0.163469i	−0.310329	+	0.950629i	$0.600439\pi$
$710$	4.53140	+	4.61575i	0.170060	+	0.173226i
$711$	−14.0350	−	19.7803i	−0.526354	−	0.741819i
$712$	0.329581	−	0.0786084i	0.0123516	−	0.00294597i
$713$	6.56025	−	18.0241i	0.245683	−	0.675009i
$714$	−3.96423	+	2.49162i	−0.148358	+	0.0932464i
$715$	0.0136901	+	0.0114874i	0.000511981	+	0.000429603i
$716$	4.36207	−	22.3230i	0.163018	−	0.834250i
$717$	3.16677	−	14.4982i	0.118265	−	0.541446i
$718$	−43.0596	−	4.16766i	−1.60697	−	0.155536i
$719$	16.4482	−	28.4892i	0.613415	−	1.06247i	−0.377245	−	0.926113i	$-0.623129\pi$
$719$	16.4482	−	28.4892i	0.613415	−	1.06247i	0.990660	−	0.136353i	$-0.0435381\pi$
$720$	−3.26015	+	4.36493i	−0.121499	+	0.162672i
$721$	10.3805	+	17.9796i	0.386590	+	0.669594i
$722$	−10.0541	−	22.0906i	−0.374173	−	0.822126i
$723$	19.8145	−	15.3027i	0.736911	−	0.569112i
$724$	22.3545	+	19.4713i	0.830799	+	0.723647i
$725$	−6.05210	+	34.3232i	−0.224769	+	1.27473i
$726$	26.3401	−	5.67104i	0.977571	−	0.210472i
$727$	20.0843	+	23.9355i	0.744884	+	0.887719i	0.996792	−	0.0800327i	$-0.0255025\pi$
$727$	20.0843	+	23.9355i	0.744884	+	0.887719i	−0.251908	+	0.967751i	$0.581058\pi$
$728$	−5.97190	+	5.65031i	−0.221333	+	0.209414i
$729$	26.2062	+	6.49886i	0.970600	+	0.240699i
$730$	−0.422076	+	0.108934i	−0.0156217	+	0.00403182i
$731$	−10.2449	−	12.2094i	−0.378920	−	0.451579i
$732$	−13.9820	−	27.8946i	−0.516789	−	1.03101i
$733$	−16.2456	−	2.86454i	−0.600046	−	0.105804i	−0.134630	−	0.990896i	$-0.542984\pi$
$733$	−16.2456	−	2.86454i	−0.600046	−	0.105804i	−0.465417	+	0.885092i	$0.654096\pi$
$734$	17.9093	+	26.0858i	0.661045	+	0.962846i
$735$	−3.30271	+	2.55066i	−0.121822	+	0.0940825i
$736$	−11.9297	−	1.60059i	−0.439734	−	0.0589985i
$737$	0.0737209	−	0.0425628i	0.00271554	−	0.00156782i
$738$	−1.76366	−	10.1797i	−0.0649213	−	0.374721i
$739$	−11.5876	+	20.0704i	−0.426258	+	0.738301i	−0.996537	−	0.0831501i	$-0.973502\pi$
$739$	−11.5876	+	20.0704i	−0.426258	+	0.738301i	0.570279	+	0.821451i	$0.306835\pi$
$740$	−0.747682	−	4.75108i	−0.0274853	−	0.174653i
$741$	−5.12421	−	1.11925i	−0.188243	−	0.0411168i
$742$	−8.25475	+	17.2844i	−0.303041	+	0.634532i
$743$	2.55778	+	2.14623i	0.0938358	+	0.0787376i	0.688499	−	0.725238i	$-0.258270\pi$
$743$	2.55778	+	2.14623i	0.0938358	+	0.0787376i	−0.594663	+	0.803975i	$0.702714\pi$
$744$	38.6597	+	21.3469i	1.41733	+	0.782614i
$745$	−6.12156	−	2.22807i	−0.224277	−	0.0816300i
$746$	15.5825	+	4.32971i	0.570517	+	0.158522i
$747$	3.48729	+	4.91482i	0.127593	+	0.179824i
$748$	−0.0443519	−	0.0267091i	−0.00162167	−	0.000976580i
$749$	1.52210	+	8.63224i	0.0556162	+	0.315415i
$750$	4.10654	+	10.0877i	0.149950	+	0.368352i
$751$	0.701648	+	1.92776i	0.0256035	+	0.0703450i	0.951836	−	0.306608i	$-0.0991940\pi$
$751$	0.701648	+	1.92776i	0.0256035	+	0.0703450i	−0.926232	+	0.376953i	$0.876972\pi$
$752$	−13.5233	−	12.2250i	−0.493144	−	0.445798i
$753$	22.5161	−	11.8106i	0.820533	−	0.430400i
$754$	18.6907	+	13.3459i	0.680676	+	0.486029i
$755$			5.39982i			0.196519i
$756$	5.06136	+	12.5403i	0.184080	+	0.456084i
$757$		−	41.6394i		−	1.51341i	−0.653756	−	0.756705i	$-0.726808\pi$
$757$		−	41.6394i		−	1.51341i	0.653756	−	0.756705i	$-0.273192\pi$
$758$	−17.8336	+	24.9756i	−0.647744	+	0.907154i
$759$	0.0548834	+	0.0347244i	0.00199214	+	0.00126042i
$760$	−0.958688	−	1.45310i	−0.0347753	−	0.0527094i
$761$	−14.1101	−	38.7671i	−0.511490	−	1.40531i	−0.879684	−	0.475558i	$-0.842246\pi$
$761$	−14.1101	−	38.7671i	−0.511490	−	1.40531i	0.368195	−	0.929749i	$-0.379976\pi$
$762$	5.79193	−	42.0114i	0.209819	−	1.52191i
$763$	0.659130	+	3.73811i	0.0238621	+	0.135329i
$764$	32.2936	+	19.4475i	1.16834	+	0.703585i
$765$	1.93577	+	0.505767i	0.0699879	+	0.0182860i
$766$	12.5596	−	45.2016i	0.453796	−	1.63320i
$767$	23.0337	+	8.38359i	0.831700	+	0.302714i
$768$	7.89311	−	26.5650i	0.284818	−	0.958582i
$769$	−33.4132	−	28.0370i	−1.20491	−	1.01104i	−0.999476	−	0.0323712i	$-0.989694\pi$
$769$	−33.4132	−	28.0370i	−1.20491	−	1.01104i	−0.205437	−	0.978670i	$-0.565861\pi$
$770$	0.0132859	+	0.00634510i	0.000478789	+	0.000228662i
$771$	−26.2525	+	28.8296i	−0.945462	+	1.03827i
$772$	4.16940	−	0.656142i	0.150060	−	0.0236151i
$773$	−3.52468	+	6.10492i	−0.126774	+	0.219579i	−0.922425	−	0.386176i	$-0.873796\pi$
$773$	−3.52468	+	6.10492i	−0.126774	+	0.219579i	0.795651	+	0.605755i	$0.207129\pi$
$774$	−39.9337	+	22.8971i	−1.43539	+	0.823021i
$775$	37.4247	−	21.6072i	1.34434	−	0.776153i
$776$	25.3295	+	18.8011i	0.909277	+	0.674920i
$777$	−11.0437	−	4.53415i	−0.396191	−	0.162662i
$778$	8.11926	−	5.57430i	0.291089	−	0.199848i
$779$	3.25111	+	0.573258i	0.116483	+	0.0205391i
$780$	3.50691	+	0.206995i	0.125567	+	0.00741162i
$781$	0.114116	+	0.135998i	0.00408338	+	0.00486638i
$782$	1.10465	+	4.28008i	0.0395020	+	0.153055i
$783$	31.6697	−	20.5950i	1.13178	−	0.736004i
$784$	11.2841	−	17.9791i	0.403004	−	0.642111i
$785$	4.90671	+	5.84759i	0.175128	+	0.208709i
$786$	−5.59648	+	5.06575i	−0.199620	+	0.180689i
$787$	8.03739	−	45.5823i	0.286502	−	1.62483i	−0.413369	−	0.910564i	$-0.635648\pi$
$787$	8.03739	−	45.5823i	0.286502	−	1.62483i	0.699871	−	0.714270i	$-0.253241\pi$
$788$	15.0509	−	17.2796i	0.536167	−	0.615559i
$789$	4.09842	+	30.3976i	0.145907	+	1.08218i
$790$	−4.72446	+	2.15024i	−0.168089	+	0.0765021i
$791$	12.6913	+	21.9820i	0.451250	+	0.781589i
$792$	−0.0985484	+	0.112462i	−0.00350176	+	0.00399615i
$793$	−10.0600	+	17.4245i	−0.357242	+	0.618762i
$794$	−5.01214	+	51.7846i	−0.177874	+	1.83777i
$795$	7.79830	−	2.48556i	0.276577	−	0.0881537i
$796$	2.17985	−	11.1554i	0.0772628	−	0.395394i
$797$	−10.7323	−	9.00550i	−0.380159	−	0.318991i	0.432606	−	0.901583i	$-0.357594\pi$
$797$	−10.7323	−	9.00550i	−0.380159	−	0.318991i	−0.812765	+	0.582592i	$0.802039\pi$
$798$	−4.31810	+	0.162139i	−0.152859	+	0.00573966i
$799$	−2.28975	+	6.29103i	−0.0810054	+	0.222561i
$800$	−18.2714	−	20.0389i	−0.645990	−	0.708483i
$801$	−0.324754	+	0.153909i	−0.0114746	+	0.00543810i
$802$	3.08050	−	3.02421i	0.108776	−	0.106789i
$803$	−0.0117824	+	0.00207756i	−0.000415792	+	7.33153e-5i
$804$	6.63977	−	15.3598i	0.234167	−	0.541699i
$805$	−0.429937	−	1.18124i	−0.0151533	−	0.0416333i
$806$	−2.22019	−	28.3897i	−0.0782030	−	0.999985i
$807$	17.7347	+	0.718901i	0.624290	+	0.0253065i
$808$	−5.41207	+	46.8827i	−0.190396	+	1.64933i
$809$			25.2574i			0.888002i	0.896026	+	0.444001i	$0.146441\pi$
$809$			25.2574i			0.888002i	−0.896026	+	0.444001i	$0.853559\pi$
$810$	2.42505	−	5.24505i	0.0852077	−	0.184292i
$811$	−36.9593			−1.29782			−0.648908	−	0.760867i	$-0.724774\pi$
$811$	−36.9593			−1.29782			−0.648908	+	0.760867i	$0.724774\pi$
$812$	17.6576	+	6.79815i	0.619659	+	0.238568i
$813$	−1.31408	+	32.4173i	−0.0460869	+	1.13692i
$814$	−0.0102920	−	0.131604i	−0.000360734	−	0.00461272i
$815$	4.34200	−	1.58036i	0.152094	−	0.0553576i
$816$	−10.1293	+	0.987008i	−0.354597	+	0.0345522i
$817$	−2.55420	−	14.4856i	−0.0893602	−	0.506787i
$818$	23.8633	+	24.3075i	0.834359	+	0.849890i
$819$	4.95693	−	7.17406i	0.173209	−	0.250682i
$820$	−2.21074	−	0.0407758i	−0.0772024	−	0.00142395i
$821$	−5.42437	−	1.97431i	−0.189312	−	0.0689038i	0.245625	−	0.969365i	$-0.421007\pi$
$821$	−5.42437	−	1.97431i	−0.189312	−	0.0689038i	−0.434936	+	0.900461i	$0.643229\pi$
$822$	28.8431	−	1.08302i	1.00602	−	0.0377747i
$823$	12.2571	−	14.6074i	0.427254	−	0.509182i	−0.508874	−	0.860841i	$-0.669938\pi$
$823$	12.2571	−	14.6074i	0.427254	−	0.509182i	0.936128	+	0.351659i	$0.114382\pi$
$824$	2.68806	+	45.0460i	0.0936430	+	1.56925i
$825$	0.0444351	+	0.139412i	0.00154703	+	0.00485372i
$826$	20.1004	+	1.94548i	0.699383	+	0.0676920i
$827$	−23.7503	−	13.7122i	−0.825878	−	0.476821i	0.0265613	−	0.999647i	$-0.491544\pi$
$827$	−23.7503	−	13.7122i	−0.825878	−	0.476821i	−0.852439	+	0.522826i	$0.824878\pi$
$828$	12.7308	−	0.957396i	0.442425	−	0.0332718i
$829$	−23.8710	+	13.7819i	−0.829073	+	0.478666i	−0.853535	−	0.521035i	$-0.825546\pi$
$829$	−23.8710	+	13.7819i	−0.829073	+	0.478666i	0.0244622	+	0.999701i	$0.492213\pi$
$830$	1.17389	−	0.534271i	0.0407463	−	0.0185448i
$831$	37.3978	−	5.04223i	1.29732	−	0.174913i
$832$	−17.1044	+	5.17389i	−0.592988	+	0.179372i
$833$	−7.67695	−	1.35365i	−0.265991	−	0.0469013i
$834$	8.80725	+	9.72997i	0.304970	+	0.336921i
$835$	5.57837	−	4.68081i	0.193048	−	0.161986i
$836$	−0.0231231	−	0.0418127i	−0.000799731	−	0.00144612i
$837$	−44.8025	−	13.6666i	−1.54860	−	0.472388i
$838$	10.4934	+	40.6580i	0.362489	+	1.40451i
$839$	22.7744	−	19.1100i	0.786259	−	0.659750i	−0.158558	−	0.987350i	$-0.550684\pi$
$839$	22.7744	−	19.1100i	0.786259	−	0.659750i	0.944816	+	0.327600i	$0.106240\pi$
$840$	2.84014	−	0.556888i	0.0979940	−	0.0192145i
$841$	4.14263	−	23.4940i	0.142849	−	0.810138i
$842$	−22.9832	−	33.4762i	−0.792052	−	1.15367i
$843$	−7.60237	+	18.5169i	−0.261839	+	0.637755i
$844$	−20.9246	−	25.8920i	−0.720253	−	0.891240i
$845$	1.81840	+	3.14956i	0.0625548	+	0.108348i
$846$	16.7163	+	9.71777i	0.574719	+	0.334104i
$847$	−12.3959	−	7.15675i	−0.425927	−	0.245909i
$848$	−32.8587	+	25.5676i	−1.12837	+	0.877993i
$849$	−5.49660	−	5.00526i	−0.188643	−	0.171780i
$850$	−4.29189	+	8.98669i	−0.147210	+	0.308241i
$851$	−7.24453	+	8.63370i	−0.248339	+	0.295959i
$852$	33.9514	+	8.07456i	1.16315	+	0.276630i
$853$	−14.9845	+	41.1697i	−0.513061	+	1.40962i	0.364970	+	0.931019i	$0.381079\pi$
$853$	−14.9845	+	41.1697i	−0.513061	+	1.40962i	−0.878031	+	0.478604i	$0.841143\pi$
$854$	−4.43765	+	15.9710i	−0.151853	+	0.546516i
$855$	1.31376	+	1.29747i	0.0449297	+	0.0443726i
$856$	−5.43829	+	18.2598i	−0.185877	+	0.624109i
$857$	−12.6966	+	2.23875i	−0.433708	+	0.0764744i	−0.386240	−	0.922398i	$-0.626226\pi$
$857$	−12.6966	+	2.23875i	−0.433708	+	0.0764744i	−0.0474680	+	0.998873i	$0.515115\pi$
$858$	0.0955168	+	0.0131685i	0.00326089	+	0.000449564i
$859$	−26.7551	+	9.73806i	−0.912872	+	0.332258i	−0.755399	−	0.655265i	$-0.772557\pi$
$859$	−26.7551	+	9.73806i	−0.912872	+	0.332258i	−0.157473	+	0.987523i	$0.550335\pi$
$860$	3.19823	+	9.31826i	0.109059	+	0.317750i
$861$	−2.93448	+	4.63807i	−0.100007	+	0.158065i
$862$	−21.8260	+	30.5669i	−0.743396	+	1.04111i
$863$	46.6170			1.58686			0.793431	−	0.608660i	$-0.208293\pi$
$863$	46.6170			1.58686			0.793431	+	0.608660i	$0.208293\pi$
$864$	−2.36020	+	29.2990i	−0.0802956	+	0.996771i
$865$	−6.14571			−0.208961
$866$	−1.27602	+	1.78704i	−0.0433609	+	0.0607262i
$867$	−11.9414	−	22.7656i	−0.405551	−	0.773159i
$868$	−7.61603	−	22.1898i	−0.258505	−	0.753172i
$869$	−0.133877	+	0.0487272i	−0.00454146	+	0.00165296i
$870$	−3.04839	−	7.48838i	−0.103350	−	0.253880i
$871$	−10.6262	+	1.87368i	−0.360054	+	0.0634873i
$872$	−2.35500	+	7.90726i	−0.0797505	+	0.267774i
$873$	−30.4110	−	13.9506i	−1.02926	−	0.472157i
$874$	−1.09213	+	3.93053i	−0.0369417	+	0.132952i
$875$	1.97894	−	5.43708i	0.0669003	−	0.183807i
$876$	−1.61527	+	1.70942i	−0.0545749	+	0.0577558i
$877$	−3.98303	+	4.74679i	−0.134497	+	0.160288i	−0.829089	−	0.559116i	$-0.811141\pi$
$877$	−3.98303	+	4.74679i	−0.134497	+	0.160288i	0.694592	+	0.719404i	$0.255585\pi$
$878$	0.700061	−	1.46584i	0.0236259	−	0.0494698i
$879$	−4.64617	+	21.2713i	−0.156712	+	0.717463i
$880$	0.0196528	+	0.0252572i	0.000662495	+	0.000851421i
$881$	−21.9173	−	12.6539i	−0.738412	−	0.426322i	0.0830799	−	0.996543i	$-0.473524\pi$
$881$	−21.9173	−	12.6539i	−0.738412	−	0.426322i	−0.821492	+	0.570221i	$0.806858\pi$
$882$	−7.76348	+	21.1336i	−0.261410	+	0.711606i
$883$	15.7424	+	27.2667i	0.529775	+	0.917597i	0.999397	+	0.0347290i	$0.0110568\pi$
$883$	15.7424	+	27.2667i	0.529775	+	0.917597i	−0.469622	+	0.882868i	$0.655610\pi$
$884$	4.12488	+	5.10412i	0.138735	+	0.171670i
$885$	−5.27444	−	6.82958i	−0.177298	−	0.229574i
$886$	−13.5627	−	19.7547i	−0.455647	−	0.663674i
$887$	0.0310073	−	0.175851i	0.00104112	−	0.00590451i	−0.984283	−	0.176600i	$-0.943490\pi$
$887$	0.0310073	−	0.175851i	0.00104112	−	0.00590451i	0.985324	+	0.170695i	$0.0546013\pi$
$888$	−17.0561	−	19.5561i	−0.572365	−	0.656260i
$889$	−17.2584	+	14.4815i	−0.578827	+	0.485694i
$890$	0.0192209	+	0.0744737i	0.000644287	+	0.00249636i
$891$	0.0775808	−	0.138331i	0.00259906	−	0.00463427i
$892$	2.68864	+	4.86177i	0.0900223	+	0.162784i
$893$	−4.73299	+	3.97145i	−0.158384	+	0.132900i
$894$	−34.3599	+	7.39773i	−1.14917	+	0.247417i
$895$	5.08477	+	0.896582i	0.169965	+	0.0299694i
$896$	−12.5792	+	7.64879i	−0.420243	+	0.255528i
$897$	−5.03181	−	6.51541i	−0.168007	−	0.217543i
$898$	−39.4946	+	17.9751i	−1.31795	+	0.599838i
$899$	−56.7571	+	32.7687i	−1.89296	+	1.09290i
$900$	23.3584	+	16.7843i	0.778613	+	0.559475i
$901$	13.2413	+	7.64488i	0.441132	+	0.254688i
$902$	−0.0604054	−	0.00584653i	−0.00201128	−	0.000194668i
$903$	23.8909	+	5.21836i	0.795040	+	0.173656i
$904$	3.28644	+	55.0736i	0.109305	+	1.83172i
$905$	−4.32570	+	5.15517i	−0.143791	+	0.171364i
$906$	15.5033	+	24.6661i	0.515061	+	0.819477i
$907$	−18.2575	−	6.64519i	−0.606231	−	0.220650i	0.0206225	−	0.999787i	$-0.493435\pi$
$907$	−18.2575	−	6.64519i	−0.606231	−	0.220650i	−0.626853	+	0.779137i	$0.715657\pi$
$908$	49.4444	+	0.911974i	1.64087	+	0.0302649i
$909$	−4.67372	−	49.8382i	−0.155017	−	1.65303i
$910$	−1.30741	−	1.33175i	−0.0433403	−	0.0441471i
$911$	−0.423720	−	2.40304i	−0.0140385	−	0.0796161i	0.976984	−	0.213314i	$-0.0684258\pi$
$911$	−0.423720	−	2.40304i	−0.0140385	−	0.0796161i	−0.991022	+	0.133698i	$0.957315\pi$
$912$	−8.55120	−	3.88523i	−0.283158	−	0.128653i
$913$	0.0332645	−	0.0121073i	0.00110089	−	0.000400693i
$914$	−0.789808	−	10.0993i	−0.0261245	−	0.334055i
$915$	6.27252	−	3.29017i	0.207363	−	0.108770i
$916$	29.2529	+	11.2623i	0.966542	+	0.372118i
$917$	4.01015			0.132427
$918$	10.2946	−	3.24741i	0.339772	−	0.107181i
$919$			2.20402i			0.0727038i	0.999339	+	0.0363519i	$0.0115737\pi$
$919$			2.20402i			0.0727038i	−0.999339	+	0.0363519i	$0.988426\pi$
$920$	0.313335	−	2.71430i	0.0103304	−	0.0894879i
$921$	13.8312	−	21.8608i	0.455753	−	0.720337i
$922$	−0.913825	−	11.6851i	−0.0300952	−	0.384829i
$923$	−7.69653	−	21.1460i	−0.253334	−	0.696030i
$924$	0.0789065	−	0.00916055i	0.00259583	−	0.000301360i
$925$	−25.0065	+	4.40933i	−0.822210	+	0.144978i
$926$	0.390591	−	0.383454i	0.0128356	−	0.0126011i
$927$	−12.6761	−	46.1544i	−0.416339	−	1.51591i
$928$	27.7097	+	30.3904i	0.909617	+	0.997614i
$929$	3.30889	−	9.09111i	0.108561	−	0.298270i	−0.873502	−	0.486820i	$-0.838157\pi$
$929$	3.30889	−	9.09111i	0.108561	−	0.298270i	0.982063	+	0.188551i	$0.0603789\pi$
$930$	−4.68312	+	8.86371i	−0.153566	+	0.290652i
$931$	−5.51109	−	4.62435i	−0.180619	−	0.151557i
$932$	7.75945	−	39.7092i	0.254169	−	1.30072i
$933$	1.56337	+	1.42362i	0.0511823	+	0.0466071i
$934$	−0.907587	+	9.37704i	−0.0296972	+	0.306826i
$935$	0.00587632	−	0.0101781i	0.000192176	−	0.000332859i
$936$	16.6137	−	9.12304i	0.543036	−	0.298196i
$937$	−22.2202	−	38.4864i	−0.725901	−	1.25730i	−0.958602	−	0.284749i	$-0.908090\pi$
$937$	−22.2202	−	38.4864i	−0.725901	−	1.25730i	0.232701	−	0.972548i	$-0.425243\pi$
$938$	−8.09091	+	3.68241i	−0.264178	+	0.120235i
$939$	−6.38013	−	2.61945i	−0.208208	−	0.0854826i
$940$	2.71801	−	3.12047i	0.0886516	−	0.101779i
$941$	7.38960	−	41.9085i	0.240894	−	1.36618i	−0.588944	−	0.808174i	$-0.700456\pi$
$941$	7.38960	−	41.9085i	0.240894	−	1.36618i	0.829838	−	0.558004i	$-0.188433\pi$
$942$	39.2025	+	12.6240i	1.27729	+	0.411313i
$943$	3.33056	+	3.96920i	0.108458	+	0.129255i
$944$	37.1785	+	23.3341i	1.21006	+	0.759460i
$945$	−2.82499	+	1.20124i	−0.0918970	+	0.0390763i
$946$	0.0675731	+	0.261820i	0.00219699	+	0.00851250i
$947$	30.3650	+	36.1877i	0.986731	+	1.17594i	0.984400	+	0.175943i	$0.0562976\pi$
$947$	30.3650	+	36.1877i	0.986731	+	1.17594i	0.00233119	+	0.999997i	$0.499258\pi$
$948$	−15.4076	+	23.3865i	−0.500416	+	0.759557i
$949$	1.49348	+	0.263341i	0.0484804	+	0.00854841i
$950$	−7.57707	+	5.20206i	−0.245833	+	0.168777i
$951$	−1.71330	−	12.7074i	−0.0555575	−	0.412065i
$952$	4.34134	+	3.22240i	0.140704	+	0.104439i
$953$	−23.8540	+	13.7721i	−0.772707	+	0.446123i	−0.833840	−	0.552007i	$-0.813862\pi$
$953$	−23.8540	+	13.7721i	−0.772707	+	0.446123i	0.0611321	+	0.998130i	$0.480529\pi$
$954$	28.4860	−	33.7434i	0.922270	−	1.09248i
$955$	−4.27868	+	7.41089i	−0.138455	+	0.239811i
$956$	−16.9275	+	2.66389i	−0.547473	+	0.0861563i
$957$	−0.0673888	−	0.211428i	−0.00217837	−	0.00683451i
$958$	−1.44640	−	0.690774i	−0.0467309	−	0.0223179i
$959$	−11.7461	−	9.85611i	−0.379300	−	0.318270i
$960$	6.06233	+	1.68024i	0.195661	+	0.0542295i
$961$	47.2298	+	17.1902i	1.52354	+	0.554524i
$962$	−4.47952	+	16.1217i	−0.144426	+	0.519784i
$963$	1.63565	−	20.1419i	0.0527081	−	0.649064i
$964$	−24.7649	−	14.9136i	−0.797624	−	0.480335i
$965$	0.166374	+	0.943555i	0.00535578	+	0.0303741i
$966$	−5.35537	−	4.16148i	−0.172306	−	0.133894i
$967$	−0.543982	−	1.49458i	−0.0174933	−	0.0480624i	0.930639	−	0.365939i	$-0.119252\pi$
$967$	−0.543982	−	1.49458i	−0.0174933	−	0.0480624i	−0.948132	+	0.317877i	$0.897030\pi$
$968$	−17.1333	−	25.9692i	−0.550684	−	0.834680i
$969$	−0.139707	+	3.44646i	−0.00448805	+	0.110716i
$970$	−4.16113	+	5.82759i	−0.133606	+	0.187113i
$971$		−	9.93969i		−	0.318980i	−0.987200	−	0.159490i	$-0.949015\pi$
$971$		−	9.93969i		−	0.318980i	0.987200	−	0.159490i	$-0.0509849\pi$
$972$	−3.98137	−	30.9217i	−0.127702	−	0.991813i
$973$		−	6.97199i		−	0.223512i
$974$	48.2968	+	34.4858i	1.54753	+	1.10500i
$975$	0.751218	−	18.5319i	0.0240582	−	0.593496i
$976$	−24.1615	+	26.7275i	−0.773390	+	0.855527i
$977$	13.5121	+	37.1242i	0.432290	+	1.18771i	0.944403	+	0.328789i	$0.106641\pi$
$977$	13.5121	+	37.1242i	0.432290	+	1.18771i	−0.512113	+	0.858918i	$0.671137\pi$
$978$	15.2967	−	19.6852i	0.489136	−	0.629464i
$979$	0.000366577		0.00207896i	1.17158e−5		6.64438e-5i
$980$	4.12784	+	2.48581i	0.131859	+	0.0794064i
$981$	0.708304	−	8.72227i	0.0226144	−	0.278481i
$982$	−28.0622	−	7.79730i	−0.895502	−	0.248822i
$983$	−30.2880	−	11.0239i	−0.966036	−	0.351608i	−0.189640	−	0.981854i	$-0.560732\pi$
$983$	−30.2880	−	11.0239i	−0.966036	−	0.351608i	−0.776396	+	0.630245i	$0.782954\pi$
$984$	−10.2156	+	6.16093i	−0.325663	+	0.196403i
$985$	3.98484	+	3.34368i	0.126967	+	0.106538i
$986$	6.50894	−	13.6289i	0.207287	−	0.434033i
$987$	−3.11936	−	9.78679i	−0.0992902	−	0.311517i
$988$	0.941518	+	5.98280i	0.0299537	+	0.190338i
$989$	11.5432	−	19.9933i	0.367051	−	0.635751i
$990$	−0.0259372	−	0.0218961i	−0.000824339	−	0.000695904i
$991$	2.66599	−	1.53921i	0.0846881	−	0.0488947i	−0.457058	−	0.889437i	$-0.651097\pi$
$991$	2.66599	−	1.53921i	0.0846881	−	0.0488947i	0.541746	+	0.840542i	$0.317763\pi$
$992$	6.78099	−	50.5407i	0.215297	−	1.60467i
$993$	0.693642	+	5.14469i	0.0220121	+	0.163262i
$994$	−10.4932	−	15.2840i	−0.332826	−	0.484778i
$995$	2.54100	+	0.448048i	0.0805553	+	0.0142041i
$996$	3.82834	−	5.81085i	0.121306	−	0.184124i
$997$	27.9424	+	33.3004i	0.884944	+	1.05464i	0.998134	+	0.0610619i	$0.0194487\pi$
$997$	27.9424	+	33.3004i	0.884944	+	1.05464i	−0.113190	+	0.993573i	$0.536107\pi$
$998$	13.7303	−	3.54367i	0.434626	−	0.112173i
$999$	21.9913	+	16.5499i	0.695775	+	0.523617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.59.22	yes	192
3.2	odd	2		648.2.v.b.611.11		192
4.3	odd	2		864.2.bh.b.815.2		192
8.3	odd	2	inner	216.2.v.b.59.5	yes	192
8.5	even	2		864.2.bh.b.815.1		192
24.11	even	2		648.2.v.b.611.28		192
27.11	odd	18	inner	216.2.v.b.11.5	✓	192
27.16	even	9		648.2.v.b.35.28		192
108.11	even	18		864.2.bh.b.335.1		192
216.11	even	18	inner	216.2.v.b.11.22	yes	192
216.43	odd	18		648.2.v.b.35.11		192
216.173	odd	18		864.2.bh.b.335.2		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.5	✓	192	27.11	odd	18	inner
216.2.v.b.11.22	yes	192	216.11	even	18	inner
216.2.v.b.59.5	yes	192	8.3	odd	2	inner
216.2.v.b.59.22	yes	192	1.1	even	1	trivial
648.2.v.b.35.11		192	216.43	odd	18
648.2.v.b.35.28		192	27.16	even	9
648.2.v.b.611.11		192	3.2	odd	2
648.2.v.b.611.28		192	24.11	even	2
864.2.bh.b.335.1		192	108.11	even	18
864.2.bh.b.335.2		192	216.173	odd	18
864.2.bh.b.815.1		192	8.5	even	2
864.2.bh.b.815.2		192	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.821807 - 1.15093i) q^{2} +(1.73063 + 0.0701536i) q^{3} +(-0.649266 - 1.89168i) q^{4} +(0.426624 - 0.155279i) q^{5} +(1.50299 - 1.93418i) q^{6} +(-1.28150 + 0.225962i) q^{7} +(-2.71076 - 0.807339i) q^{8} +(2.99016 + 0.242820i) q^{9} +(0.171889 - 0.618623i) q^{10} +(0.00602720 - 0.0165596i) q^{11} +(-0.990930 - 3.31935i) q^{12} +(-1.43581 + 1.71113i) q^{13} +(-0.793076 + 1.66060i) q^{14} +(0.749222 - 0.238801i) q^{15} +(-3.15691 + 2.45641i) q^{16} +(1.27216 + 0.734483i) q^{17} +(2.73680 - 3.24190i) q^{18} +(0.677841 + 1.17406i) q^{19} +(-0.570730 - 0.706220i) q^{20} +(-2.23365 + 0.301155i) q^{21} +(-0.0141057 - 0.0205456i) q^{22} +(-0.369486 + 2.09546i) q^{23} +(-4.63468 - 1.58737i) q^{24} +(-3.67233 + 3.08145i) q^{25} +(0.789428 + 3.05873i) q^{26} +(5.15782 + 0.630001i) q^{27} +(1.25948 + 2.27747i) q^{28} +(5.56933 - 4.67322i) q^{29} +(0.340874 - 1.05855i) q^{30} +(-8.87753 - 1.56535i) q^{31} +(0.232774 + 5.65206i) q^{32} +(0.0115926 - 0.0282357i) q^{33} +(1.89081 - 0.860562i) q^{34} +(-0.511630 + 0.295390i) q^{35} +(-1.48207 - 5.81408i) q^{36} +(4.58718 + 2.64841i) q^{37} +(1.90831 + 0.184701i) q^{38} +(-2.60490 + 2.86061i) q^{39} +(-1.28184 + 0.0764919i) q^{40} +(1.56527 - 1.86542i) q^{41} +(-1.48902 + 2.81825i) q^{42} +(-10.1956 - 3.71089i) q^{43} +(-0.0352387 - 0.000649957i) q^{44} +(1.31338 - 0.360715i) q^{45} +(2.10807 + 2.14731i) q^{46} +(0.791397 + 4.48824i) q^{47} +(-5.63576 + 4.02966i) q^{48} +(-4.98668 + 1.81500i) q^{49} +(0.528577 + 6.75893i) q^{50} +(2.15011 + 1.36036i) q^{51} +(4.16913 + 1.60511i) q^{52} +10.4085 q^{53} +(4.96382 - 5.41853i) q^{54} -0.00800062i q^{55} +(3.65625 + 0.422073i) q^{56} +(1.09073 + 2.07941i) q^{57} +(-0.801622 - 10.2504i) q^{58} +(-3.75319 - 10.3118i) q^{59} +(-0.938179 - 1.26224i) q^{60} +(8.87057 - 1.56412i) q^{61} +(-9.09722 + 8.93098i) q^{62} +(-3.88674 + 0.364490i) q^{63} +(6.69641 + 4.37700i) q^{64} +(-0.346849 + 0.952961i) q^{65} +(-0.0229704 - 0.0365465i) q^{66} +(3.70041 + 3.10502i) q^{67} +(0.563436 - 2.88340i) q^{68} +(-0.786447 + 3.60054i) q^{69} +(-0.0804893 + 0.831602i) q^{70} +(-5.03714 + 8.72458i) q^{71} +(-7.90955 - 3.07230i) q^{72} +(-0.339460 - 0.587962i) q^{73} +(6.81790 - 3.10303i) q^{74} +(-6.57161 + 5.07522i) q^{75} +(1.78084 - 2.04453i) q^{76} +(-0.00398198 + 0.0225829i) q^{77} +(1.15163 + 5.34891i) q^{78} +(-5.19665 - 6.19313i) q^{79} +(-0.965387 + 1.53816i) q^{80} +(8.88208 + 1.45214i) q^{81} +(-0.860607 - 3.33452i) q^{82} +(1.29122 + 1.53881i) q^{83} +(2.01992 + 4.02981i) q^{84} +(0.656785 + 0.115809i) q^{85} +(-12.6498 + 8.68475i) q^{86} +(9.96629 - 7.69691i) q^{87} +(-0.0297075 + 0.0400230i) q^{88} +(-0.103744 + 0.0598964i) q^{89} +(0.664188 - 1.80804i) q^{90} +(1.45333 - 2.51724i) q^{91} +(4.20383 - 0.661560i) q^{92} +(-15.2539 - 3.33183i) q^{93} +(5.81601 + 2.77762i) q^{94} +(0.471489 + 0.395626i) q^{95} +(0.00633320 + 9.79796i) q^{96} +(-10.4801 - 3.81446i) q^{97} +(-2.00915 + 7.23088i) q^{98} +(0.0220433 - 0.0480522i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more