LMFDB - Embedded newform 483.2.bc.a.44.51

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(11,483)] 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("483.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([33, 44, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bc (of order $66$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			44.51
Character	$\chi$	$=$	483.44
Dual form			483.2.bc.a.11.51

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.918620 + 1.78187i) q^{2} +(-1.56023 + 0.752120i) q^{3} +(-1.17110 + 1.64458i) q^{4} +(2.94599 - 2.80900i) q^{5} +(-2.77344 - 2.08922i) q^{6} +(-1.97640 - 1.75893i) q^{7} +(-0.0375805 - 0.00540327i) q^{8} +(1.86863 - 2.34696i) q^{9} +(7.71152 + 2.66898i) q^{10} +(0.257306 + 0.132651i) q^{11} +(0.590263 - 3.44673i) q^{12} +(3.86470 + 4.46010i) q^{13} +(1.31863 - 5.13749i) q^{14} +(-2.48372 + 6.59842i) q^{15} +(1.29577 + 3.74387i) q^{16} +(2.07967 - 0.198585i) q^{17} +(5.89855 + 1.17370i) q^{18} +(0.526815 - 5.51706i) q^{19} +(1.16957 + 8.13453i) q^{20} +(4.40657 + 1.25784i) q^{21} +0.580343i q^{22} +(-3.40193 + 3.38036i) q^{23} +(0.0626982 - 0.0198347i) q^{24} +(0.550490 - 11.5562i) q^{25} +(-4.39715 + 10.9835i) q^{26} +(-1.15030 + 5.06723i) q^{27} +(5.20726 - 1.19047i) q^{28} +(0.623226 + 0.284618i) q^{29} +(-14.0391 + 1.63576i) q^{30} +(6.65287 - 2.66341i) q^{31} +(-5.53319 + 5.80304i) q^{32} +(-0.501226 - 0.0134402i) q^{33} +(2.26428 + 3.52329i) q^{34} +(-10.7633 + 0.369915i) q^{35} +(1.67141 + 5.82163i) q^{36} +(-3.31430 - 0.804041i) q^{37} +(10.3146 - 4.12936i) q^{38} +(-9.38435 - 4.05206i) q^{39} +(-0.125890 + 0.0896456i) q^{40} +(-0.0413890 + 0.140958i) q^{41} +(1.80664 + 9.00743i) q^{42} +(-6.90466 + 0.992741i) q^{43} +(-0.519486 + 0.267813i) q^{44} +(-1.08763 - 12.1631i) q^{45} +(-9.14847 - 2.95654i) q^{46} +(1.41487 + 0.816878i) q^{47} +(-4.83753 - 4.86672i) q^{48} +(0.812330 + 6.95271i) q^{49} +(21.0974 - 9.63487i) q^{50} +(-3.09541 + 1.87400i) q^{51} +(-11.8609 + 1.13258i) q^{52} +(-7.27318 - 1.40179i) q^{53} +(-10.0859 + 2.60517i) q^{54} +(1.13064 - 0.331985i) q^{55} +(0.0647703 + 0.0767806i) q^{56} +(3.32754 + 9.00411i) q^{57} +(0.0653548 + 1.37197i) q^{58} +(1.35087 + 0.467539i) q^{59} +(-7.94293 - 11.8121i) q^{60} +(3.70507 - 4.71138i) q^{61} +(10.8573 + 9.40792i) q^{62} +(-7.82130 + 1.35174i) q^{63} +(-7.82062 - 2.29634i) q^{64} +(23.9138 + 2.28349i) q^{65} +(-0.436487 - 0.905468i) q^{66} +(10.4306 + 0.496871i) q^{67} +(-2.10891 + 3.65275i) q^{68} +(2.76535 - 7.83280i) q^{69} +(-10.5465 - 18.8390i) q^{70} +(-5.46332 + 8.50109i) q^{71} +(-0.0829054 + 0.0781033i) q^{72} +(-4.99387 + 7.01291i) q^{73} +(-1.61188 - 6.64428i) q^{74} +(7.83277 + 18.4444i) q^{75} +(8.45629 + 7.32741i) q^{76} +(-0.275217 - 0.714755i) q^{77} +(-1.40038 - 20.4440i) q^{78} +(0.134277 + 0.696695i) q^{79} +(14.3338 + 7.38960i) q^{80} +(-2.01643 - 8.77120i) q^{81} +(-0.289190 + 0.0557369i) q^{82} +(3.82422 - 1.12289i) q^{83} +(-7.22915 + 5.77389i) q^{84} +(5.56887 - 6.42682i) q^{85} +(-8.11170 - 11.3913i) q^{86} +(-1.18644 + 0.0246716i) q^{87} +(-0.00895296 - 0.00637537i) q^{88} +(-3.16380 - 1.26660i) q^{89} +(20.6740 - 13.1113i) q^{90} +(0.206805 - 15.6127i) q^{91} +(-1.57528 - 9.55349i) q^{92} +(-8.37681 + 9.15929i) q^{93} +(-0.155842 + 3.27153i) q^{94} +(-13.9454 - 17.7330i) q^{95} +(4.26846 - 13.2157i) q^{96} +(1.17109 - 3.98837i) q^{97} +(-11.6426 + 7.83437i) q^{98} +(0.792136 - 0.356012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) $ 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.918620	+	1.78187i	0.649562	+	1.25998i	0.951793	+	0.306741i	$0.0992384\pi$
$2$	0.918620	+	1.78187i	0.649562	+	1.25998i	−0.302231	+	0.953235i	$0.597731\pi$
$3$	−1.56023	+	0.752120i	−0.900799	+	0.434237i
$3$	−1.56023	+	0.752120i	−0.900799	+	0.434237i
$4$	−1.17110	+	1.64458i	−0.585550	+	0.822289i
$5$	2.94599	−	2.80900i	1.31749	−	1.25622i	0.372936	−	0.927857i	$-0.378351\pi$
$5$	2.94599	−	2.80900i	1.31749	−	1.25622i	0.944551	−	0.328364i	$-0.106497\pi$
$6$	−2.77344	−	2.08922i	−1.13225	−	0.852921i
$7$	−1.97640	−	1.75893i	−0.747010	−	0.664813i
$7$	−1.97640	−	1.75893i	−0.747010	−	0.664813i
$8$	−0.0375805	−	0.00540327i	−0.0132867	−	0.00191034i
$9$	1.86863	−	2.34696i	0.622877	−	0.782320i
$10$	7.71152	+	2.66898i	2.43860	+	0.844007i
$11$	0.257306	+	0.132651i	0.0775807	+	0.0399957i	0.496580	−	0.867991i	$-0.334589\pi$
$11$	0.257306	+	0.132651i	0.0775807	+	0.0399957i	−0.419000	+	0.907986i	$0.637619\pi$
$12$	0.590263	−	3.44673i	0.170394	−	0.994985i
$13$	3.86470	+	4.46010i	1.07187	+	1.23701i	0.970229	+	0.242188i	$0.0778652\pi$
$13$	3.86470	+	4.46010i	1.07187	+	1.23701i	0.101645	+	0.994821i	$0.467589\pi$
$14$	1.31863	−	5.13749i	0.352419	−	1.37305i
$15$	−2.48372	+	6.59842i	−0.641294	+	1.70370i
$16$	1.29577	+	3.74387i	0.323942	+	0.935968i
$17$	2.07967	−	0.198585i	0.504394	−	0.0481638i	0.160242	−	0.987078i	$-0.448772\pi$
$17$	2.07967	−	0.198585i	0.504394	−	0.0481638i	0.344152	+	0.938914i	$0.388166\pi$
$18$	5.89855	+	1.17370i	1.39030	+	0.276644i
$19$	0.526815	−	5.51706i	0.120860	−	1.26570i	−0.707987	−	0.706225i	$-0.750397\pi$
$19$	0.526815	−	5.51706i	0.120860	−	1.26570i	0.828847	−	0.559475i	$-0.188997\pi$
$20$	1.16957	+	8.13453i	0.261523	+	1.81894i
$21$	4.40657	+	1.25784i	0.961592	+	0.274484i
$22$			0.580343i			0.123730i
$23$	−3.40193	+	3.38036i	−0.709352	+	0.704855i
$23$	−3.40193	+	3.38036i	−0.709352	+	0.704855i
$24$	0.0626982	−	0.0198347i	0.0127982	−	0.00404875i
$25$	0.550490	−	11.5562i	0.110098	−	2.31124i
$26$	−4.39715	+	10.9835i	−0.862352	+	2.15405i
$27$	−1.15030	+	5.06723i	−0.221375	+	0.975189i
$28$	5.20726	−	1.19047i	0.984080	−	0.224977i
$29$	0.623226	+	0.284618i	0.115730	+	0.0528522i	0.472439	−	0.881364i	$-0.343374\pi$
$29$	0.623226	+	0.284618i	0.115730	+	0.0528522i	−0.356709	+	0.934216i	$0.616101\pi$
$30$	−14.0391	+	1.63576i	−2.56319	+	0.298648i
$31$	6.65287	−	2.66341i	1.19489	−	0.478362i	0.312972	−	0.949762i	$-0.398675\pi$
$31$	6.65287	−	2.66341i	1.19489	−	0.478362i	0.881919	+	0.471400i	$0.156251\pi$
$32$	−5.53319	+	5.80304i	−0.978139	+	1.02584i
$33$	−0.501226	−	0.0134402i	−0.0872522	−	0.00233964i
$34$	2.26428	+	3.52329i	0.388321	+	0.604239i
$35$	−10.7633	+	0.369915i	−1.81933	+	0.0625270i
$36$	1.67141	+	5.82163i	0.278568	+	0.970272i
$37$	−3.31430	−	0.804041i	−0.544868	−	0.132183i	−0.0461285	−	0.998936i	$-0.514688\pi$
$37$	−3.31430	−	0.804041i	−0.544868	−	0.132183i	−0.498739	+	0.866752i	$0.666204\pi$
$38$	10.3146	−	4.12936i	1.67326	−	0.669871i
$39$	−9.38435	−	4.05206i	−1.50270	−	0.648849i
$40$	−0.125890	+	0.0896456i	−0.0199049	+	0.0141742i
$41$	−0.0413890	+	0.140958i	−0.00646388	+	0.0220139i	−0.962662	−	0.270707i	$-0.912743\pi$
$41$	−0.0413890	+	0.140958i	−0.00646388	+	0.0220139i	0.956198	+	0.292721i	$0.0945607\pi$
$42$	1.80664	+	9.00743i	0.278771	+	1.38988i
$43$	−6.90466	+	0.992741i	−1.05295	+	0.151392i	−0.646990	−	0.762499i	$-0.723972\pi$
$43$	−6.90466	+	0.992741i	−1.05295	+	0.151392i	−0.405961	+	0.913890i	$0.633063\pi$
$44$	−0.519486	+	0.267813i	−0.0783154	+	0.0403744i
$45$	−1.08763	−	12.1631i	−0.162134	−	1.81317i
$46$	−9.14847	−	2.95654i	−1.34887	−	0.435919i
$47$	1.41487	+	0.816878i	0.206381	+	0.119154i	0.599628	−	0.800279i	$-0.295315\pi$
$47$	1.41487	+	0.816878i	0.206381	+	0.119154i	−0.393248	+	0.919433i	$0.628648\pi$
$48$	−4.83753	−	4.86672i	−0.698237	−	0.702451i
$49$	0.812330	+	6.95271i	0.116047	+	0.993244i
$50$	21.0974	−	9.63487i	2.98363	−	1.36258i
$51$	−3.09541	+	1.87400i	−0.433443	+	0.262412i
$52$	−11.8609	+	1.13258i	−1.64482	+	0.157061i
$53$	−7.27318	−	1.40179i	−0.999048	−	0.192551i	−0.336591	−	0.941651i	$-0.609274\pi$
$53$	−7.27318	−	1.40179i	−0.999048	−	0.192551i	−0.662457	+	0.749100i	$0.730486\pi$
$54$	−10.0859	+	2.60517i	−1.37251	+	0.354519i
$55$	1.13064	−	0.331985i	0.152455	−	0.0447648i
$56$	0.0647703	+	0.0767806i	0.00865529	+	0.0102602i
$57$	3.32754	+	9.00411i	0.440743	+	1.19262i
$58$	0.0653548	+	1.37197i	0.00858151	+	0.180148i
$59$	1.35087	+	0.467539i	0.175868	+	0.0608684i	0.413583	−	0.910467i	$-0.364277\pi$
$59$	1.35087	+	0.467539i	0.175868	+	0.0608684i	−0.237715	+	0.971335i	$0.576398\pi$
$60$	−7.94293	−	11.8121i	−1.02543	−	1.52493i
$61$	3.70507	−	4.71138i	0.474386	−	0.603230i	−0.488691	−	0.872457i	$-0.662526\pi$
$61$	3.70507	−	4.71138i	0.474386	−	0.603230i	0.963077	+	0.269226i	$0.0867680\pi$
$62$	10.8573	+	9.40792i	1.37888	+	1.19481i
$63$	−7.82130	+	1.35174i	−0.985392	+	0.170304i
$64$	−7.82062	−	2.29634i	−0.977578	−	0.287043i
$65$	23.9138	+	2.28349i	2.96614	+	0.283232i
$66$	−0.436487	−	0.905468i	−0.0537279	−	0.111455i
$67$	10.4306	+	0.496871i	1.27430	+	0.0607025i	0.673796	−	0.738918i	$-0.264663\pi$
$67$	10.4306	+	0.496871i	1.27430	+	0.0607025i	0.600506	+	0.799620i	$0.294966\pi$
$68$	−2.10891	+	3.65275i	−0.255743	+	0.442961i
$69$	2.76535	−	7.83280i	0.332910	−	0.942959i
$70$	−10.5465	−	18.8390i	−1.26055	−	2.25169i
$71$	−5.46332	+	8.50109i	−0.648376	+	1.00889i	0.349044	+	0.937106i	$0.386506\pi$
$71$	−5.46332	+	8.50109i	−0.648376	+	1.00889i	−0.997420	+	0.0717867i	$0.977130\pi$
$72$	−0.0829054	+	0.0781033i	−0.00977050	+	0.00920456i
$73$	−4.99387	+	7.01291i	−0.584489	+	0.820799i	−0.995882	−	0.0906584i	$-0.971103\pi$
$73$	−4.99387	+	7.01291i	−0.584489	+	0.820799i	0.411393	+	0.911458i	$0.365042\pi$
$74$	−1.61188	−	6.64428i	−0.187378	−	0.772381i
$75$	7.83277	+	18.4444i	0.904450	+	2.12977i
$76$	8.45629	+	7.32741i	0.970002	+	0.840512i
$77$	−0.275217	−	0.714755i	−0.0313639	−	0.0814538i
$78$	−1.40038	−	20.4440i	−0.158562	−	2.31483i
$79$	0.134277	+	0.696695i	0.0151073	+	0.0783843i	0.988700	−	0.149908i	$-0.0478978\pi$
$79$	0.134277	+	0.696695i	0.0151073	+	0.0783843i	−0.973593	+	0.228293i	$0.926686\pi$
$80$	14.3338	+	7.38960i	1.60257	+	0.826183i
$81$	−2.01643	−	8.77120i	−0.224048	−	0.974578i
$82$	−0.289190	+	0.0557369i	−0.0319357	+	0.00615511i
$83$	3.82422	−	1.12289i	0.419762	−	0.123253i	−0.0650287	−	0.997883i	$-0.520714\pi$
$83$	3.82422	−	1.12289i	0.419762	−	0.123253i	0.484791	+	0.874630i	$0.338896\pi$
$84$	−7.22915	+	5.77389i	−0.788765	+	0.629983i
$85$	5.56887	−	6.42682i	0.604029	−	0.697086i
$86$	−8.11170	−	11.3913i	−0.874707	−	1.22835i
$87$	−1.18644	+	0.0246716i	−0.127200	+	0.00264508i
$88$	−0.00895296	−	0.00637537i	−0.000954389	−	0.000679617i
$89$	−3.16380	−	1.26660i	−0.335363	−	0.134259i	0.197868	−	0.980229i	$-0.436598\pi$
$89$	−3.16380	−	1.26660i	−0.335363	−	0.134259i	−0.533231	+	0.845970i	$0.679022\pi$
$90$	20.6740	−	13.1113i	2.17923	−	1.38205i
$91$	0.206805	−	15.6127i	0.0216791	−	1.63665i
$92$	−1.57528	−	9.55349i	−0.164234	−	0.996020i
$93$	−8.37681	+	9.15929i	−0.868634	+	0.949774i
$94$	−0.155842	+	3.27153i	−0.0160739	+	0.337432i
$95$	−13.9454	−	17.7330i	−1.43077	−	1.81937i
$96$	4.26846	−	13.2157i	0.435648	−	1.34882i
$97$	1.17109	−	3.98837i	0.118906	−	0.404957i	−0.878432	−	0.477867i	$-0.841410\pi$
$97$	1.17109	−	3.98837i	0.118906	−	0.404957i	0.997339	+	0.0729094i	$0.0232284\pi$
$98$	−11.6426	+	7.83437i	−1.17608	+	0.791390i
$99$	0.792136	−	0.356012i	0.0796127	−	0.0357806i
$100$	18.3604	+	14.4388i	1.83604	+	1.44388i
$101$	−9.73480	+	10.2096i	−0.968649	+	1.01589i	0.0312166	+	0.999513i	$0.490062\pi$
$101$	−9.73480	+	10.2096i	−0.968649	+	1.01589i	−0.999866	+	0.0163775i	$0.994787\pi$
$102$	−6.18273	−	3.79413i	−0.612182	−	0.375675i
$103$	−11.3560	+	0.540951i	−1.11894	+	0.0533015i	−0.598886	−	0.800834i	$-0.704390\pi$
$103$	−11.3560	+	0.540951i	−1.11894	+	0.0533015i	−0.520050	+	0.854136i	$0.674087\pi$
$104$	−0.121138	−	0.188495i	−0.0118786	−	0.0184835i
$105$	16.5150	−	8.67244i	1.61170	−	0.846343i
$106$	−4.18348	−	14.2476i	−0.406335	−	1.38385i
$107$	−12.7144	−	9.99868i	−1.22914	−	0.966609i	−0.229167	−	0.973387i	$-0.573600\pi$
$107$	−12.7144	−	9.99868i	−1.22914	−	0.966609i	−0.999977	+	0.00677782i	$0.997843\pi$
$108$	−6.98634	−	7.82599i	−0.672261	−	0.753056i
$109$	−0.692259	−	7.24966i	−0.0663064	−	0.694392i	−0.966116	−	0.258109i	$-0.916901\pi$
$109$	−0.692259	−	7.24966i	−0.0663064	−	0.694392i	0.899809	−	0.436283i	$-0.143705\pi$
$110$	1.63018	+	1.70968i	0.155432	+	0.163012i
$111$	5.77581	−	1.23826i	0.548215	−	0.117531i
$112$	4.02425	−	9.67855i	0.380256	−	0.914537i
$113$	2.87874	+	1.85006i	0.270809	+	0.174039i	0.668996	−	0.743266i	$-0.266724\pi$
$113$	2.87874	+	1.85006i	0.270809	+	0.174039i	−0.398187	+	0.917304i	$0.630361\pi$
$114$	−12.9874	+	14.2006i	−1.21639	+	1.33001i
$115$	−0.526627	+	19.5145i	−0.0491082	+	1.81974i
$116$	−1.19794	+	0.691629i	−0.111226	+	0.0642162i
$117$	17.6894	−	0.736006i	1.63538	−	0.0680438i
$118$	0.407836	+	2.83656i	0.0375444	+	0.261127i
$119$	−4.45956	−	3.26551i	−0.408808	−	0.299349i
$120$	0.128993	−	0.234552i	0.0117754	−	0.0214116i
$121$	−6.33202	−	8.89207i	−0.575638	−	0.808370i
$122$	11.7986	+	2.27400i	1.06820	+	0.205878i
$123$	−0.0414410	−	0.251056i	−0.00373661	−	0.0226370i
$124$	−3.41099	+	14.0603i	−0.306316	+	1.26265i
$125$	−17.5114	−	20.2093i	−1.56627	−	1.80757i
$126$	−9.59344	−	12.6948i	−0.854652	−	1.13095i
$127$	−5.03395	+	3.23513i	−0.446691	+	0.287071i	−0.744585	−	0.667528i	$-0.767352\pi$
$127$	−5.03395	+	3.23513i	−0.446691	+	0.287071i	0.297893	+	0.954599i	$0.403716\pi$
$128$	−0.0574798	−	0.298234i	−0.00508055	−	0.0263604i
$129$	10.0262	−	6.74204i	0.882757	−	0.593603i
$130$	17.8988	+	44.7090i	1.56983	+	3.92124i
$131$	−6.82893	+	2.36352i	−0.596646	+	0.206501i	−0.608666	−	0.793426i	$-0.708295\pi$
$131$	−6.82893	+	2.36352i	−0.596646	+	0.206501i	0.0120198	+	0.999928i	$0.496174\pi$
$132$	0.609089	−	0.808566i	0.0530144	−	0.0703766i
$133$	−10.7453	+	9.97729i	−0.931737	+	0.865141i
$134$	8.69641	+	19.0425i	0.751255	+	1.64502i
$135$	10.8451	+	18.1592i	0.933394	+	1.56289i
$136$	−0.0792282	−	0.00377410i	−0.00679376	−	0.000323627i
$137$	10.8239	+	18.7476i	0.924750	+	1.60171i	0.791962	+	0.610570i	$0.209060\pi$
$137$	10.8239	+	18.7476i	0.924750	+	1.60171i	0.132788	+	0.991144i	$0.457607\pi$
$138$	16.4974	−	2.26786i	1.40435	−	0.193053i
$139$	7.69285			0.652499			0.326250	−	0.945284i	$-0.394215\pi$
$139$	7.69285			0.652499			0.326250	+	0.945284i	$0.394215\pi$
$140$	11.9965	−	18.1343i	1.01389	−	1.53263i
$141$	−2.82192	−	0.210362i	−0.237648	−	0.0177157i
$142$	−20.1666	−	1.92567i	−1.69234	−	0.161599i
$143$	0.402776	+	1.66027i	0.0336818	+	0.138838i
$144$	11.2080	+	3.95480i	0.934002	+	0.329567i
$145$	2.63551	−	0.912159i	0.218867	−	0.0757507i
$146$	−17.0836	−	2.45625i	−1.41385	−	0.203281i
$147$	−6.49669	−	10.2368i	−0.535838	−	0.844321i
$148$	5.20368	−	4.50902i	0.427740	−	0.370639i
$149$	0.714896	+	15.0075i	0.0585666	+	1.22946i	0.816583	+	0.577228i	$0.195866\pi$
$149$	0.714896	+	15.0075i	0.0585666	+	1.22946i	−0.758016	+	0.652235i	$0.773831\pi$
$150$	−25.6702	+	30.9004i	−2.09597	+	2.52301i
$151$	3.02788	−	8.74849i	0.246406	−	0.711942i	−0.752189	−	0.658947i	$-0.771002\pi$
$151$	3.02788	−	8.74849i	0.246406	−	0.711942i	0.998595	−	0.0529950i	$-0.0168768\pi$
$152$	−0.0496081	+	0.204488i	−0.00402375	+	0.0165861i
$153$	3.42007	−	5.25199i	0.276496	−	0.424598i
$154$	1.02078	−	1.14699i	0.0822570	−	0.0924272i
$155$	12.1178	−	26.5343i	0.973325	−	2.13128i
$156$	17.6539	−	10.6879i	1.41345	−	0.855719i
$157$	−2.74794	−	1.95680i	−0.219309	−	0.156169i	0.465122	−	0.885246i	$-0.346010\pi$
$157$	−2.74794	−	1.95680i	−0.219309	−	0.156169i	−0.684432	+	0.729077i	$0.739950\pi$
$158$	−1.11807	+	0.879263i	−0.0889491	+	0.0699504i
$159$	12.4021	−	3.28319i	0.983554	−	0.260374i
$160$			32.6384i			2.58029i
$161$	12.6694	−	0.697200i	0.998489	−	0.0549471i
$162$	13.7768	−	11.6504i	1.08241	−	0.915344i
$163$	−0.557424	+	0.287372i	−0.0436608	+	0.0225087i	−0.479919	−	0.877313i	$-0.659334\pi$
$163$	−0.557424	+	0.287372i	−0.0436608	+	0.0225087i	0.436258	+	0.899822i	$0.356304\pi$
$164$	−0.183346	−	0.233143i	−0.0143169	−	0.0182054i
$165$	−1.51436	+	1.36835i	−0.117893	+	0.106526i
$166$	5.51385	+	5.78276i	0.427958	+	0.448829i
$167$	−5.92157	−	2.70429i	−0.458225	−	0.209264i	0.172910	−	0.984938i	$-0.444683\pi$
$167$	−5.92157	−	2.70429i	−0.458225	−	0.209264i	−0.631135	+	0.775673i	$0.717410\pi$
$168$	−0.158805	−	0.0710803i	−0.0122520	−	0.00548396i
$169$	−3.10650	+	21.6062i	−0.238962	+	1.66202i
$170$	16.5675	+	4.01922i	1.27067	+	0.308260i
$171$	−11.9639	−	11.5458i	−0.914901	−	0.882927i
$172$	6.45341	−	12.5179i	0.492068	−	0.954478i
$173$	−5.03329	+	0.239765i	−0.382674	+	0.0182290i	−0.238038	−	0.971256i	$-0.576504\pi$
$173$	−5.03329	+	0.239765i	−0.382674	+	0.0182290i	−0.144636	+	0.989485i	$0.546201\pi$
$174$	−1.13385	−	2.09143i	−0.0859571	−	0.158551i
$175$	−21.4146	+	21.8715i	−1.61879	+	1.65333i
$176$	−0.163218	+	1.13521i	−0.0123030	+	0.0855693i
$177$	−2.45931	+	0.286545i	−0.184853	+	0.0215380i
$178$	−0.649419	−	6.80102i	−0.0486760	−	0.509758i
$179$	−23.3023	+	5.65308i	−1.74170	+	0.422531i	−0.975486	−	0.220061i	$-0.929374\pi$
$179$	−23.3023	+	5.65308i	−1.74170	+	0.422531i	−0.766209	+	0.642591i	$0.777859\pi$
$180$	21.2769	+	12.4555i	1.58589	+	0.928379i
$181$	−0.0652991	+	0.00938859i	−0.00485364	+	0.000697849i	−0.144741	−	0.989470i	$-0.546235\pi$
$181$	−0.0652991	+	0.00938859i	−0.00485364	+	0.000697849i	0.139888	+	0.990167i	$0.455326\pi$
$182$	28.0098	−	13.9736i	2.07623	−	1.03579i
$183$	−2.23724	+	10.1375i	−0.165381	+	0.749385i
$184$	0.146111	−	0.108654i	0.0107715	−	0.00801011i
$185$	−12.0224	+	6.94116i	−0.883908	+	0.510325i
$186$	−24.0158	−	6.51251i	−1.76092	−	0.477520i
$187$	0.561455	+	0.224773i	0.0410576	+	0.0164370i
$188$	−3.00038	+	1.37023i	−0.218825	+	0.0999341i
$189$	11.1864	−	7.99159i	0.813688	−	0.581302i
$190$	18.7875	−	41.1389i	1.36299	−	2.98453i
$191$	−2.82145	−	8.15204i	−0.204153	−	0.589861i	0.795722	−	0.605661i	$-0.207091\pi$
$191$	−2.82145	−	8.15204i	−0.204153	−	0.589861i	−0.999875	+	0.0158009i	$0.994970\pi$
$192$	13.9291	−	2.29922i	1.00525	−	0.165932i
$193$	2.71131	+	2.58523i	0.195164	+	0.186089i	0.781360	−	0.624081i	$-0.214526\pi$
$193$	2.71131	+	2.58523i	0.195164	+	0.186089i	−0.586195	+	0.810170i	$0.699375\pi$
$194$	8.18256	−	1.57706i	0.587473	−	0.113226i
$195$	−39.0284	+	14.4233i	−2.79488	+	1.03287i
$196$	−12.3856	−	6.80637i	−0.884685	−	0.486169i
$197$	6.61539	−	5.73227i	0.471327	−	0.408407i	−0.386545	−	0.922270i	$-0.626332\pi$
$197$	6.61539	−	5.73227i	0.471327	−	0.408407i	0.857872	+	0.513863i	$0.171786\pi$
$198$	1.36204	+	1.08445i	0.0967960	+	0.0770683i
$199$	−0.517688	−	1.29312i	−0.0366979	−	0.0916669i	0.908887	−	0.417043i	$-0.136933\pi$
$199$	−0.517688	−	1.29312i	−0.0366979	−	0.0916669i	−0.945585	+	0.325376i	$0.894509\pi$
$200$	−0.0831290	+	0.431314i	−0.00587811	+	0.0304985i
$201$	−16.6479	+	7.06984i	−1.17425	+	0.498668i
$202$	−27.1348	−	7.96748i	−1.90919	−	0.560590i
$203$	−0.731123	−	1.65873i	−0.0513148	−	0.116420i
$204$	0.543087	−	7.28528i	0.0380237	−	0.510072i
$205$	0.274019	+	0.531523i	0.0191383	+	0.0371232i
$206$	−11.3957	−	19.7380i	−0.793977	−	1.37521i
$207$	1.57662	+	14.3008i	0.109583	+	0.993978i
$208$	−11.6903	+	20.2482i	−0.810576	+	1.40396i
$209$	0.867394	−	1.34969i	0.0599989	−	0.0933601i
$210$	30.6242	+	21.4609i	2.11327	+	1.48095i
$211$	0.959786	+	2.10164i	0.0660744	+	0.144683i	0.939788	−	0.341758i	$-0.111022\pi$
$211$	0.959786	+	2.10164i	0.0660744	+	0.144683i	−0.873714	+	0.486441i	$0.838295\pi$
$212$	10.8230	−	10.3197i	0.743325	−	0.708759i
$213$	2.13019	−	17.3727i	0.145958	−	1.19036i
$214$	6.13673	−	31.8404i	0.419498	−	2.17656i
$215$	−17.5525	+	22.3198i	−1.19707	+	1.52220i
$216$	0.0706085	−	0.184214i	0.00480430	−	0.0125342i
$217$	−17.8335	−	6.43797i	−1.21062	−	0.437038i
$218$	12.2821	−	7.89320i	0.831846	−	0.534595i
$219$	2.51704	−	14.6977i	0.170086	−	0.993182i
$220$	−0.778113	+	2.24821i	−0.0524603	+	0.151574i
$221$	8.92301	+	8.50807i	0.600227	+	0.572315i
$222$	7.51220	+	9.15427i	0.504186	+	0.614394i
$223$	9.92846	−	11.4581i	0.664859	−	0.767288i	−0.318704	−	0.947854i	$-0.603247\pi$
$223$	9.92846	−	11.4581i	0.664859	−	0.767288i	0.983563	+	0.180566i	$0.0577930\pi$
$224$	21.1430	−	1.73665i	1.41267	−	0.116035i
$225$	−26.0933	−	22.8863i	−1.73955	−	1.52575i
$226$	−0.652096	+	6.82905i	−0.0433768	+	0.454262i
$227$	−4.21866	+	3.31759i	−0.280002	+	0.220196i	−0.748276	−	0.663387i	$-0.769118\pi$
$227$	−4.21866	+	3.31759i	−0.280002	+	0.220196i	0.468274	+	0.883583i	$0.344876\pi$
$228$	−18.7048	−	5.07231i	−1.23876	−	0.335922i
$229$	−19.4902	−	11.2527i	−1.28795	−	0.743597i	−0.309660	−	0.950847i	$-0.600215\pi$
$229$	−19.4902	−	11.2527i	−1.28795	−	0.743597i	−0.978288	+	0.207250i	$0.933549\pi$
$230$	−35.2562	+	16.9881i	−2.32473	+	1.12016i
$231$	0.966983	+	0.908185i	0.0636228	+	0.0597542i
$232$	−0.0218833	−	0.0140636i	−0.00143671	−	0.000923318i
$233$	−1.59118	+	3.97457i	−0.104242	+	0.260383i	−0.971315	−	0.237798i	$-0.923574\pi$
$233$	−1.59118	+	3.97457i	−0.104242	+	0.260383i	0.867073	+	0.498181i	$0.165999\pi$
$234$	17.5613	+	30.8441i	1.14802	+	2.01634i
$235$	6.46281	−	1.56786i	0.421587	−	0.102276i
$236$	−2.35090	+	1.67407i	−0.153031	+	0.108973i
$237$	−0.733501	−	0.986012i	−0.0476460	−	0.0640483i
$238$	1.72209	−	10.9461i	0.111627	−	0.709533i
$239$	7.25472	+	24.7073i	0.469269	+	1.59818i	0.765746	+	0.643143i	$0.222370\pi$
$239$	7.25472	+	24.7073i	0.469269	+	1.59818i	−0.296477	+	0.955040i	$0.595812\pi$
$240$	−27.9219	−	0.748718i	−1.80235	−	0.0483295i
$241$	4.44283	−	8.61790i	0.286188	−	0.555127i	−0.701291	−	0.712875i	$-0.747393\pi$
$241$	4.44283	−	8.61790i	0.286188	−	0.555127i	0.987480	+	0.157747i	$0.0504231\pi$
$242$	10.0278	−	19.4513i	0.644614	−	1.25038i
$243$	9.74309	+	12.1685i	0.625020	+	0.780609i
$244$	3.40923	+	11.6108i	0.218254	+	0.743304i
$245$	21.9232	+	18.2008i	1.40062	+	1.16280i
$246$	0.409282	−	0.304468i	0.0260949	−	0.0194122i
$247$	26.6426	−	18.9721i	1.69523	−	1.20717i
$248$	−0.264410	+	0.0641451i	−0.0167900	+	0.00407322i
$249$	−5.12210	+	4.62824i	−0.324600	+	0.293303i
$250$	19.9240	−	49.7678i	1.26011	−	3.14759i
$251$	22.2799	+	14.3184i	1.40629	+	0.903770i	0.999950	−	0.00995133i	$-0.00316766\pi$
$251$	22.2799	+	14.3184i	1.40629	+	0.903770i	0.406342	+	0.913721i	$0.366804\pi$
$252$	6.93648	−	14.4458i	0.436957	−	0.909998i
$253$	−1.32375	+	0.418521i	−0.0832232	+	0.0263122i
$254$	−10.3889	−	5.99802i	−0.651856	−	0.376349i
$255$	−3.85498	+	14.2158i	−0.241408	+	0.890226i
$256$	−12.3353	+	9.70058i	−0.770955	+	0.606286i
$257$	1.11729	−	11.7008i	0.0696948	−	0.729877i	−0.891319	−	0.453377i	$-0.850219\pi$
$257$	1.11729	−	11.7008i	0.0696948	−	0.729877i	0.961014	−	0.276500i	$-0.0891746\pi$
$258$	21.2237	+	11.6721i	1.32133	+	0.726670i
$259$	5.13614	+	7.41873i	0.319144	+	0.460978i
$260$	−31.7608	+	36.6539i	−1.96972	+	2.27318i
$261$	1.83257	−	0.930841i	0.113433	−	0.0576176i
$262$	−10.4847	−	9.99712i	−0.647746	−	0.617624i
$263$	−9.47706	+	27.3822i	−0.584381	+	1.68846i	0.132433	+	0.991192i	$0.457721\pi$
$263$	−9.47706	+	27.3822i	−0.584381	+	1.68846i	−0.716813	+	0.697265i	$0.754400\pi$
$264$	0.0187637	+	0.00321335i	0.00115483	+	0.000197768i
$265$	−25.3644	+	16.3007i	−1.55812	+	1.00134i
$266$	−27.6492	−	9.98146i	−1.69528	−	0.612003i
$267$	5.88889	−	0.403379i	0.360394	−	0.0246864i
$268$	−13.0324	+	16.5721i	−0.796082	+	1.01230i
$269$	5.01443	−	26.0173i	0.305735	−	1.58630i	−0.426006	−	0.904720i	$-0.640080\pi$
$269$	5.01443	−	26.0173i	0.305735	−	1.58630i	0.731741	−	0.681583i	$-0.238708\pi$
$270$	−22.3949	+	36.0059i	−1.36291	+	2.19125i
$271$	7.26397	−	6.92618i	0.441255	−	0.420736i	−0.436605	−	0.899653i	$-0.643819\pi$
$271$	7.26397	−	6.92618i	0.441255	−	0.420736i	0.877860	+	0.478918i	$0.158971\pi$
$272$	3.43824	+	7.52870i	0.208474	+	0.456495i
$273$	11.4199	+	24.5149i	0.691167	+	1.48371i
$274$	−23.4628	+	36.5088i	−1.41744	+	2.20558i
$275$	1.67458	−	2.90046i	0.100981	−	0.174905i
$276$	9.64316	+	13.7208i	0.580450	+	0.825897i
$277$	7.58327	+	13.1346i	0.455634	+	0.789182i	0.998724	−	0.0504926i	$-0.0160791\pi$
$277$	7.58327	+	13.1346i	0.455634	+	0.789182i	−0.543090	+	0.839674i	$0.682746\pi$
$278$	7.06681	+	13.7077i	0.423839	+	0.822133i
$279$	6.18086	−	20.5910i	0.370038	−	1.23275i
$280$	0.406489	+	0.0442553i	0.0242924	+	0.00264476i
$281$	−26.7064	−	7.84170i	−1.59317	−	0.467796i	−0.639534	−	0.768763i	$-0.720873\pi$
$281$	−26.7064	−	7.84170i	−1.59317	−	0.467796i	−0.953635	+	0.300967i	$0.902691\pi$
$282$	−2.21743	−	5.22155i	−0.132046	−	0.310939i
$283$	−1.94912	+	10.1130i	−0.115863	+	0.601156i	0.876861	+	0.480744i	$0.159633\pi$
$283$	−1.94912	+	10.1130i	−0.115863	+	0.601156i	−0.992724	+	0.120411i	$0.961579\pi$
$284$	−7.58262	−	18.9405i	−0.449946	−	1.12391i
$285$	35.0954	+	17.1790i	2.07887	+	1.01759i
$286$	−2.58839	+	2.24285i	−0.153055	+	0.132623i
$287$	0.329737	−	0.205789i	0.0194637	−	0.0121474i
$288$	3.28001	+	23.8299i	0.193276	+	1.40419i
$289$	−12.4072	+	2.39129i	−0.729835	+	0.140664i
$290$	4.04638	+	3.85822i	0.237612	+	0.226562i
$291$	1.17256	+	7.10357i	0.0687367	+	0.416419i
$292$	−5.68497	−	16.4256i	−0.332688	−	0.961238i
$293$	−4.31378	+	9.44586i	−0.252014	+	0.551833i	−0.992783	−	0.119927i	$-0.961734\pi$
$293$	−4.31378	+	9.44586i	−0.252014	+	0.551833i	0.740769	+	0.671760i	$0.234461\pi$
$294$	12.2728	−	20.9801i	0.715763	−	1.22358i
$295$	5.29295	−	2.41721i	0.308168	−	0.140735i
$296$	0.120209	+	0.0481243i	0.00698699	+	0.00279717i
$297$	−0.968150	+	1.15124i	−0.0561778	+	0.0668018i
$298$	−26.0848	+	15.0601i	−1.51105	+	0.872406i
$299$	−28.2242	−	2.10886i	−1.63225	−	0.121959i
$300$	−39.5062	−	8.71860i	−2.28089	−	0.503369i
$301$	15.3926	+	10.1828i	0.887212	+	0.586925i
$302$	18.3702	−	2.64123i	1.05709	−	0.151986i
$303$	7.50971	−	23.2510i	0.431421	−	1.33574i
$304$	21.3378	−	5.17649i	1.22381	−	0.296892i
$305$	−2.31915	−	24.2872i	−0.132794	−	1.39068i
$306$	12.5001	+	1.26956i	0.714584	+	0.0725757i
$307$	−0.536794	+	3.73348i	−0.0306364	+	0.213081i	−0.999389	−	0.0349475i	$-0.988874\pi$
$307$	−0.536794	+	3.73348i	−0.0306364	+	0.213081i	0.968753	+	0.248029i	$0.0797827\pi$
$308$	1.49778	+	0.384432i	0.0853438	+	0.0219050i
$309$	17.3110	−	9.38505i	0.984791	−	0.533897i
$310$	58.4124	−	2.78253i	3.31760	−	0.158037i
$311$	10.1123	−	19.6150i	0.573413	−	1.11227i	−0.406651	−	0.913584i	$-0.633303\pi$
$311$	10.1123	−	19.6150i	0.573413	−	1.11227i	0.980064	−	0.198683i	$-0.0636663\pi$
$312$	0.330774	+	0.202985i	0.0187264	+	0.0114918i
$313$	−23.3432	−	5.66299i	−1.31943	−	0.320091i	−0.486605	−	0.873622i	$-0.661765\pi$
$313$	−23.3432	−	5.66299i	−1.31943	−	0.320091i	−0.832829	+	0.553531i	$0.813280\pi$
$314$	0.962457	−	6.69403i	0.0543146	−	0.377766i
$315$	−19.2444	+	25.9522i	−1.08430	+	1.46224i
$316$	−1.30302	−	0.595070i	−0.0733007	−	0.0334753i
$317$	11.6440	+	12.2119i	0.653991	+	0.685886i	0.964319	−	0.264743i	$-0.0852872\pi$
$317$	11.6440	+	12.2119i	0.653991	+	0.685886i	−0.310328	+	0.950630i	$0.600439\pi$
$318$	17.2431	+	19.0831i	0.966945	+	1.07013i
$319$	0.122605	+	0.155905i	0.00686458	+	0.00872902i
$320$	−29.4899	+	15.2031i	−1.64854	+	0.849879i
$321$	27.3575	+	6.03752i	1.52695	+	0.336981i
$322$	12.8807	+	21.9348i	0.717813	+	1.22238i
$323$		−	11.5783i		−	0.644233i
$324$	16.7864	+	6.95577i	0.932577	+	0.386432i
$325$	53.6694	−	42.2061i	2.97704	−	2.34117i
$326$	−1.02412	−	0.729274i	−0.0567209	−	0.0403907i
$327$	6.53270	+	10.7905i	0.361259	+	0.596715i
$328$	0.00231706	−	0.00507364i	0.000127938	−	0.000280145i
$329$	−1.35953	−	4.10314i	−0.0749533	−	0.226214i
$330$	−3.82934	−	1.44141i	−0.210798	−	0.0793469i
$331$	3.31183	−	13.6515i	0.182034	−	0.750356i	−0.805453	−	0.592659i	$-0.798078\pi$
$331$	3.31183	−	13.6515i	0.182034	−	0.750356i	0.987488	−	0.157697i	$-0.0504068\pi$
$332$	−2.63185	+	7.60424i	−0.144442	+	0.417337i
$333$	−8.08026	+	6.27607i	−0.442795	+	0.343927i
$334$	−0.620967	−	13.0357i	−0.0339778	−	0.713282i
$335$	32.1242	−	27.8358i	1.75513	−	1.52083i
$336$	1.00068	+	18.1275i	0.0545915	+	0.988935i
$337$	29.2545	+	4.20616i	1.59359	+	0.229124i	0.881230	−	0.472687i	$-0.156716\pi$
$337$	29.2545	+	4.20616i	1.59359	+	0.229124i	0.712363	+	0.701811i	$0.247625\pi$
$338$	−41.3532	+	14.3125i	−2.24932	+	0.778497i
$339$	−5.88296	−	0.721352i	−0.319519	−	0.0391784i
$340$	4.04771	+	16.6849i	0.219518	+	0.904865i
$341$	2.06513	+	0.197196i	0.111833	+	0.0106788i
$342$	9.58283	−	31.9243i	0.518180	−	1.72627i
$343$	10.6238	−	15.1702i	0.573633	−	0.819112i
$344$	0.264845			0.0142795
$345$	−13.8556	−	30.8432i	−0.745961	−	1.66054i
$346$	−5.05091	−	8.74844i	−0.271539	−	0.470319i
$347$	23.4605	+	1.11756i	1.25942	+	0.0599937i	0.666647	−	0.745374i	$-0.267729\pi$
$347$	23.4605	+	1.11756i	1.25942	+	0.0599937i	0.592776	+	0.805367i	$0.298032\pi$
$348$	1.34887	−	1.98009i	0.0723069	−	0.106144i
$349$	1.74608	+	3.82338i	0.0934655	+	0.204661i	0.950590	−	0.310448i	$-0.100479\pi$
$349$	1.74608	+	3.82338i	0.0934655	+	0.204661i	−0.857125	+	0.515108i	$0.827752\pi$
$350$	−58.6440	−	18.0665i	−3.13466	−	0.965695i
$351$	−27.0459	+	14.4529i	−1.44360	+	0.771437i
$352$	−2.19350	+	0.759178i	−0.116914	+	0.0404643i
$353$	−4.00583	−	10.0061i	−0.213209	−	0.532569i	0.782755	−	0.622330i	$-0.213814\pi$
$353$	−4.00583	−	10.0061i	−0.213209	−	0.532569i	−0.995963	+	0.0897609i	$0.971390\pi$
$354$	−2.76975	−	4.11895i	−0.147211	−	0.218920i
$355$	7.78464	+	40.3905i	0.413166	+	2.14371i
$356$	5.78815	−	3.71982i	0.306771	−	0.197150i
$357$	9.41400	+	1.74082i	0.498242	+	0.0921342i
$358$	−31.4790	−	36.3287i	−1.66372	−	1.92003i
$359$	−0.255233	+	1.05208i	−0.0134707	+	0.0555268i	−0.978150	−	0.207899i	$-0.933337\pi$
$359$	−0.255233	+	1.05208i	−0.0134707	+	0.0555268i	0.964680	+	0.263426i	$0.0848525\pi$
$360$	−0.0248468	+	0.462973i	−0.00130954	+	0.0244008i
$361$	−11.5038	−	2.21717i	−0.605461	−	0.116693i
$362$	−0.0767143	−	0.107730i	−0.00403202	−	0.00566217i
$363$	16.5673	+	9.11124i	0.869558	+	0.478216i
$364$	25.4341	+	18.6241i	1.33311	+	0.976169i
$365$	4.98735	+	34.6877i	0.261050	+	1.81564i
$366$	−20.1189	+	5.32603i	−1.05163	+	0.278396i
$367$	18.5592	−	10.7152i	0.968783	−	0.559327i	0.0699181	−	0.997553i	$-0.477726\pi$
$367$	18.5592	−	10.7152i	0.968783	−	0.559327i	0.898865	+	0.438226i	$0.144393\pi$
$368$	−17.0638	−	8.35623i	−0.889510	−	0.435598i
$369$	0.253482	+	0.360537i	0.0131957	+	0.0187688i
$370$	−23.4123	−	15.0462i	−1.21715	−	0.782215i
$371$	11.9091	+	15.5635i	0.618289	+	0.808018i
$372$	−5.25310	−	24.5028i	−0.272360	−	1.27041i
$373$	−2.58726	−	2.71344i	−0.133963	−	0.140497i	0.653335	−	0.757069i	$-0.273369\pi$
$373$	−2.58726	−	2.71344i	−0.133963	−	0.140497i	−0.787298	+	0.616572i	$0.788521\pi$
$374$	0.115247	+	1.20692i	0.00595929	+	0.0624085i
$375$	42.5216	+	18.3604i	2.19581	+	0.948127i
$376$	−0.0487579	−	0.0383437i	−0.00251450	−	0.00197742i
$377$	1.13916	+	3.87962i	0.0586696	+	0.199810i
$378$	24.5160	+	12.5914i	1.26097	+	0.647634i
$379$	2.16959	+	3.37595i	0.111444	+	0.173411i	0.892496	−	0.451056i	$-0.148953\pi$
$379$	2.16959	+	3.37595i	0.111444	+	0.173411i	−0.781051	+	0.624467i	$0.785316\pi$
$380$	45.4948	−	2.16718i	2.33383	−	0.111174i
$381$	5.42092	−	8.83367i	0.277722	−	0.452563i
$382$	11.9341	−	12.5161i	0.610600	−	0.640379i
$383$	19.3965	+	15.2536i	0.991117	+	0.779423i	0.975397	−	0.220454i	$-0.0707538\pi$
$383$	19.3965	+	15.2536i	0.991117	+	0.779423i	0.0157192	+	0.999876i	$0.494996\pi$
$384$	0.313989	+	0.422081i	0.0160232	+	0.0215392i
$385$	−2.81853	−	1.33258i	−0.143646	−	0.0679143i
$386$	−2.11589	+	7.20605i	−0.107696	+	0.366778i
$387$	−10.5723	+	18.0600i	−0.537423	+	0.918043i
$388$	5.18772	+	6.59672i	0.263367	+	0.334898i
$389$	0.0643546	−	1.35097i	0.00326291	−	0.0684969i	−0.996649	−	0.0818024i	$-0.973932\pi$
$389$	0.0643546	−	1.35097i	0.00326291	−	0.0684969i	0.999911	+	0.0133055i	$0.00423539\pi$
$390$	−61.5527	−	56.2943i	−3.11684	−	2.85057i
$391$	−6.40361	+	7.70562i	−0.323845	+	0.389690i
$392$	0.00703951	−	0.265676i	0.000355549	−	0.0134186i
$393$	8.87705	−	8.82380i	0.447788	−	0.445102i
$394$	16.2912	+	6.52201i	0.820739	+	0.328574i
$395$	2.35259	+	1.67527i	0.118372	+	0.0842922i
$396$	−0.342180	+	1.71966i	−0.0171952	+	0.0864160i
$397$	9.65704	+	13.5614i	0.484673	+	0.680628i	0.982418	−	0.186696i	$-0.0597778\pi$
$397$	9.65704	+	13.5614i	0.484673	+	0.680628i	−0.497745	+	0.867324i	$0.665838\pi$
$398$	1.82862	−	2.11034i	0.0916605	−	0.105782i
$399$	9.26104	−	23.6486i	0.463632	−	1.18391i
$400$	43.9783	−	12.9132i	2.19891	−	0.645659i
$401$	−4.18395	+	0.806391i	−0.208937	+	0.0402692i	−0.292645	−	0.956221i	$-0.594536\pi$
$401$	−4.18395	+	0.806391i	−0.208937	+	0.0402692i	0.0837088	+	0.996490i	$0.473323\pi$
$402$	−27.8906	−	23.1699i	−1.39106	−	1.15561i
$403$	37.5904	+	19.3792i	1.87251	+	0.965347i
$404$	−5.39002	−	27.9661i	−0.268163	−	1.39136i
$405$	−30.5787	−	20.1757i	−1.51947	−	1.00254i
$406$	2.28403	−	2.82651i	0.113354	−	0.140277i
$407$	−0.746134	−	0.646529i	−0.0369845	−	0.0320472i
$408$	0.126453	−	0.0537006i	0.00626034	−	0.00265858i
$409$	3.49844	+	14.4207i	0.172986	+	0.713060i	0.990542	+	0.137210i	$0.0438136\pi$
$409$	3.49844	+	14.4207i	0.172986	+	0.713060i	−0.817555	+	0.575850i	$0.804671\pi$
$410$	−0.695387	+	0.976535i	−0.0343427	+	0.0482276i
$411$	−30.9882	−	21.1097i	−1.52854	−	1.04126i
$412$	12.4093	−	19.3093i	0.611363	−	0.951300i
$413$	−1.84749	−	3.30012i	−0.0909088	−	0.162389i
$414$	−24.0340	+	15.9464i	−1.18121	+	0.783722i
$415$	8.11191	−	14.0502i	0.398198	−	0.689699i
$416$	−47.2663	−	2.25157i	−2.31742	−	0.110392i
$417$	−12.0026	+	5.78595i	−0.587771	+	0.283339i
$418$	3.20179	+	0.305733i	0.156604	+	0.0149539i
$419$	−15.4802	−	4.54540i	−0.756257	−	0.222057i	−0.119196	−	0.992871i	$-0.538032\pi$
$419$	−15.4802	−	4.54540i	−0.756257	−	0.222057i	−0.637061	+	0.770814i	$0.719850\pi$
$420$	−5.07818	+	37.3165i	−0.247790	+	1.82086i
$421$	−8.78003	−	7.60794i	−0.427913	−	0.370788i	0.414113	−	0.910225i	$-0.364092\pi$
$421$	−8.78003	−	7.60794i	−0.427913	−	0.370788i	−0.842026	+	0.539437i	$0.818637\pi$
$422$	−2.86318	+	3.64083i	−0.139377	+	0.177233i
$423$	4.56106	−	1.79421i	0.221766	−	0.0872374i
$424$	0.265756	+	0.0919790i	0.0129062	+	0.00446690i
$425$	−1.15005	−	24.1425i	−0.0557855	−	1.17108i
$426$	32.9128	−	12.1632i	1.59463	−	0.589308i
$427$	−15.6097	+	2.79462i	−0.755406	+	0.135241i
$428$	31.3334	−	9.20032i	1.51456	−	0.444714i
$429$	−1.87714	−	2.28746i	−0.0906293	−	0.110440i
$430$	−55.8951	−	10.7729i	−2.69550	−	0.519515i
$431$	−13.0620	+	1.24727i	−0.629174	+	0.0600788i	−0.404772	−	0.914418i	$-0.632649\pi$
$431$	−13.0620	+	1.24727i	−0.629174	+	0.0600788i	−0.224402	+	0.974497i	$0.572043\pi$
$432$	−20.4616	+	2.25937i	−0.984458	+	0.108704i
$433$	−24.0704	+	10.9926i	−1.15675	+	0.528270i	−0.899003	−	0.437942i	$-0.855707\pi$
$433$	−24.0704	+	10.9926i	−1.15675	+	0.528270i	−0.257747	+	0.966212i	$0.582980\pi$
$434$	−4.91056	−	37.6911i	−0.235714	−	1.80923i
$435$	−3.42595	+	3.40540i	−0.164262	+	0.163276i
$436$	12.7333	+	7.35160i	0.609817	+	0.352078i
$437$	16.8575	+	20.5495i	0.806403	+	0.983015i
$438$	28.5017	−	9.01660i	1.36187	−	0.430830i
$439$	32.4317	−	16.7197i	1.54788	−	0.797989i	0.548608	−	0.836080i	$-0.315158\pi$
$439$	32.4317	−	16.7197i	1.54788	−	0.797989i	0.999274	+	0.0380912i	$0.0121278\pi$
$440$	−0.0442837	+	0.00636704i	−0.00211114	+	0.000303537i
$441$	17.8357	+	11.0855i	0.849317	+	0.527883i
$442$	−6.96346	+	23.7154i	−0.331218	+	1.12803i
$443$	−6.42672	+	4.57644i	−0.305343	+	0.217433i	−0.722449	−	0.691424i	$-0.756984\pi$
$443$	−6.42672	+	4.57644i	−0.305343	+	0.217433i	0.417106	+	0.908858i	$0.363044\pi$
$444$	−4.72762	+	10.9489i	−0.224363	+	0.519612i
$445$	−12.8784	+	5.15573i	−0.610495	+	0.244405i
$446$	29.5373	+	7.16567i	1.39863	+	0.339304i
$447$	−12.4028	−	22.8775i	−0.586635	−	1.08207i
$448$	11.4176	+	18.2944i	0.539430	+	0.864330i
$449$	−11.0228	−	17.1518i	−0.520197	−	0.809443i	0.477402	−	0.878685i	$-0.341578\pi$
$449$	−11.0228	−	17.1518i	−0.520197	−	0.809443i	−0.997600	+	0.0692417i	$0.977942\pi$
$450$	16.8107	−	67.5188i	0.792462	−	3.18287i
$451$	−0.0293478	+	0.0307791i	−0.00138193	+	0.00144933i
$452$	−6.41386	+	2.56772i	−0.301682	+	0.120775i
$453$	1.85572	+	15.9270i	0.0871895	+	0.748315i
$454$	−9.78687	−	4.46951i	−0.459320	−	0.209765i
$455$	−43.2467	−	46.5757i	−2.02744	−	2.18350i
$456$	−0.0763991	−	0.356359i	−0.00357771	−	0.0166880i
$457$	−3.70443	+	9.25322i	−0.173286	+	0.432847i	−0.989432	−	0.144998i	$-0.953682\pi$
$457$	−3.70443	+	9.25322i	−0.173286	+	0.432847i	0.816146	+	0.577846i	$0.196107\pi$
$458$	2.14676	−	45.0660i	0.100311	−	2.10580i
$459$	−1.38597	+	10.7666i	−0.0646916	+	0.502542i
$460$	−31.4765	−	23.7195i	−1.46760	−	1.10593i
$461$			25.1005i			1.16905i	0.811377	+	0.584524i	$0.198719\pi$
$461$			25.1005i			1.16905i	−0.811377	+	0.584524i	$0.801281\pi$
$462$	−0.729980	+	2.55732i	−0.0339618	+	0.118977i
$463$	2.50543	+	17.4257i	0.116437	+	0.809839i	0.961428	+	0.275058i	$0.0886969\pi$
$463$	2.50543	+	17.4257i	0.116437	+	0.809839i	−0.844991	+	0.534781i	$0.820394\pi$
$464$	−0.258017	+	2.70208i	−0.0119781	+	0.125441i
$465$	1.05041	+	50.5136i	0.0487116	+	2.34251i
$466$	−8.54387	+	0.815841i	−0.395787	+	0.0377931i
$467$	5.89481	+	17.0319i	0.272779	+	0.788144i	0.995304	+	0.0967986i	$0.0308603\pi$
$467$	5.89481	+	17.0319i	0.272779	+	0.788144i	−0.722525	+	0.691345i	$0.757019\pi$
$468$	−19.5056	+	29.9535i	−0.901646	+	1.38460i
$469$	−19.7411	−	19.3287i	−0.911560	−	0.892518i
$470$	8.73060	+	10.0757i	0.402713	+	0.464755i
$471$	5.75916	+	0.986275i	0.265368	+	0.0454451i
$472$	−0.0482400	−	0.0248695i	−0.00222043	−	0.00114471i
$473$	−1.90830	−	0.660469i	−0.0877437	−	0.0303684i
$474$	1.08314	−	2.21278i	0.0497503	−	0.101636i
$475$	−63.4663	−	9.12508i	−2.91203	−	0.418687i
$476$	10.5930	−	3.50986i	0.485529	−	0.160874i
$477$	−16.8808	+	14.4504i	−0.772921	+	0.661640i
$478$	−37.3610	+	35.6236i	−1.70885	+	1.62939i
$479$	7.44068	−	10.4490i	0.339974	−	0.477426i	−0.608826	−	0.793303i	$-0.708359\pi$
$479$	7.44068	−	10.4490i	0.339974	−	0.477426i	0.948800	+	0.315877i	$0.102299\pi$
$480$	−24.5480	−	50.9234i	−1.12046	−	2.32433i
$481$	−9.22267	−	17.8895i	−0.420518	−	0.815691i
$482$	19.4373			0.885344
$483$	−19.2428	+	10.6167i	−0.875578	+	0.483077i
$484$	22.0391			1.00178
$485$	−7.75329	−	15.0393i	−0.352059	−	0.682898i
$486$	−12.7325	+	28.5392i	−0.577559	+	1.29456i
$487$	25.3116	−	35.5451i	1.14698	−	1.61070i	0.451250	−	0.892397i	$-0.350978\pi$
$487$	25.3116	−	35.5451i	1.14698	−	1.61070i	0.695727	−	0.718306i	$-0.255082\pi$
$488$	−0.164695	+	0.157037i	−0.00745541	+	0.00710872i
$489$	0.653571	−	0.867616i	0.0295555	−	0.0392350i
$490$	−12.2924	+	55.7841i	−0.555312	+	2.52007i
$491$	23.3468	+	3.35676i	1.05363	+	0.151489i	0.647297	−	0.762238i	$-0.275899\pi$
$491$	23.3468	+	3.35676i	1.05363	+	0.151489i	0.406330	+	0.913727i	$0.366809\pi$
$492$	0.461414	+	0.225859i	0.0208021	+	0.0101825i
$493$	1.35263	+	0.468149i	0.0609193	+	0.0210844i
$494$	58.2804	+	30.0456i	2.62216	+	1.35182i
$495$	1.33359	−	3.27392i	0.0599403	−	0.147152i
$496$	18.5920	+	21.4563i	0.834807	+	0.963418i
$497$	25.7505	−	7.19197i	1.15507	−	0.322604i
$498$	−12.9522	−	4.87536i	−0.580402	−	0.218470i
$499$	2.60248	+	7.51939i	0.116503	+	0.336614i	0.988144	−	0.153532i	$-0.0490648\pi$
$499$	2.60248	+	7.51939i	0.116503	+	0.336614i	−0.871640	+	0.490146i	$0.836944\pi$
$500$	53.7434	−	5.13187i	2.40348	−	0.229504i
$501$	11.2730	−	0.234417i	0.503639	−	0.0104730i
$502$	−5.04686	+	52.8531i	−0.225252	+	2.35895i
$503$	−0.918442	−	6.38790i	−0.0409513	−	0.284823i	−0.999999	−	0.00157712i	$-0.999498\pi$
$503$	−0.918442	−	6.38790i	−0.0409513	−	0.284823i	0.959047	−	0.283245i	$-0.0914111\pi$
$504$	0.301233	−	0.00853863i	0.0134180	−	0.000380341i
$505$			57.4223i			2.55526i
$506$	−1.96177	−	1.97429i	−0.0872113	−	0.0877677i
$507$	−11.4036	−	36.0471i	−0.506452	−	1.60091i
$508$	0.574841	−	12.0674i	0.0255044	−	0.535404i
$509$	5.14487	−	12.8513i	0.228042	−	0.569622i	−0.769579	−	0.638551i	$-0.779534\pi$
$509$	5.14487	−	12.8513i	0.228042	−	0.569622i	0.997622	+	0.0689293i	$0.0219583\pi$
$510$	−28.8720	+	6.18981i	−1.27847	+	0.274089i
$511$	22.2051	−	5.07646i	0.982297	−	0.224570i
$512$	−29.1692	−	13.3211i	−1.28911	−	0.588716i
$513$	27.3502	+	9.01576i	1.20754	+	0.398056i
$514$	21.8757	−	8.75773i	0.964898	−	0.386287i
$515$	−31.9350	+	33.4925i	−1.40723	+	1.47586i
$516$	−0.653862	+	24.3845i	−0.0287847	+	1.07347i
$517$	0.255697	+	0.397872i	0.0112455	+	0.0174984i
$518$	−8.50109	+	15.9670i	−0.373516	+	0.701548i
$519$	7.67276	−	4.15973i	0.336797	−	0.182592i
$520$	−0.886354	−	0.215027i	−0.0388692	−	0.00942957i
$521$	3.19151	−	1.27769i	0.139822	−	0.0559765i	−0.300696	−	0.953720i	$-0.597219\pi$
$521$	3.19151	−	1.27769i	0.139822	−	0.0559765i	0.440518	+	0.897744i	$0.354795\pi$
$522$	3.34207	+	2.41032i	0.146279	+	0.105497i
$523$	4.79445	−	3.41412i	0.209647	−	0.149289i	−0.470411	−	0.882448i	$-0.655894\pi$
$523$	4.79445	−	3.41412i	0.209647	−	0.149289i	0.680057	+	0.733159i	$0.261955\pi$
$524$	4.11037	−	13.9986i	0.179562	−	0.611533i
$525$	16.9617	−	50.2308i	0.740268	−	2.19225i
$526$	−57.4974	+	8.26688i	−2.50701	+	0.360453i
$527$	13.3069	−	6.86017i	0.579657	−	0.298834i
$528$	−0.599153	−	1.89394i	−0.0260748	−	0.0824232i
$529$	0.146274	−	22.9995i	0.00635973	−	0.999980i
$530$	−52.3460	−	30.2220i	−2.27376	−	1.31276i
$531$	3.62157	−	2.29677i	0.157163	−	0.0996713i
$532$	−3.82461	−	29.3559i	−0.165818	−	1.27274i
$533$	−0.788643	+	0.360161i	−0.0341599	+	0.0156003i
$534$	6.12843	+	10.1227i	0.265203	+	0.438053i
$535$	−65.5427	+	6.25857i	−2.83366	+	0.270581i
$536$	−0.389303	−	0.0750321i	−0.0168153	−	0.00324089i
$537$	32.1051	−	26.3462i	1.38544	−	1.13692i
$538$	50.9659	−	14.9649i	2.19730	−	0.645185i
$539$	−0.713263	+	1.89673i	−0.0307224	+	0.0816980i
$540$	−42.5649	−	3.43067i	−1.83170	−	0.147633i
$541$	−1.14240	−	23.9820i	−0.0491157	−	1.03107i	−0.880106	−	0.474778i	$-0.842528\pi$
$541$	−1.14240	−	23.9820i	−0.0491157	−	1.03107i	0.830990	−	0.556287i	$-0.187775\pi$
$542$	19.0144	+	6.58095i	0.816739	+	0.282676i
$543$	0.0948202	−	0.0637611i	0.00406912	−	0.00273625i
$544$	−10.3548	+	13.1672i	−0.443959	+	0.564540i
$545$	−22.4037	−	19.4129i	−0.959668	−	0.831557i
$546$	−33.1919	+	42.8688i	−1.42048	+	1.83462i
$547$	36.9785	+	10.8579i	1.58109	+	0.464249i	0.950204	−	0.311629i	$-0.100875\pi$
$547$	36.9785	+	10.8579i	1.58109	+	0.464249i	0.630883	+	0.775878i	$0.282693\pi$
$548$	−43.5078	−	4.15449i	−1.85856	−	0.177471i
$549$	−4.13400	−	17.4995i	−0.176435	−	0.746860i
$550$	6.70657	+	0.319473i	0.285969	+	0.0136224i
$551$	1.89858	−	3.28844i	0.0808822	−	0.140092i
$552$	−0.146246	+	0.279419i	−0.00622465	+	0.0118929i
$553$	0.960053	−	1.61313i	0.0408256	−	0.0685974i
$554$	−16.4381	+	25.5781i	−0.698387	+	1.08671i
$555$	13.5372	−	19.8721i	0.574622	−	0.843525i
$556$	−9.00910	+	12.6515i	−0.382071	+	0.536543i
$557$	8.30420	+	34.2304i	0.351860	+	1.45039i	0.822855	+	0.568252i	$0.192380\pi$
$557$	8.30420	+	34.2304i	0.351860	+	1.45039i	−0.470994	+	0.882136i	$0.656105\pi$
$558$	42.3683	−	7.90175i	1.79360	−	0.334508i
$559$	−31.1122	−	26.9588i	−1.31590	−	1.14024i
$560$	−15.3316	−	39.8170i	−0.647879	−	1.68258i
$561$	−1.04505	+	0.0715845i	−0.0441222	+	0.00302230i
$562$	−10.5601	−	54.7909i	−0.445450	−	2.31122i
$563$	−4.98263	−	2.56873i	−0.209993	−	0.108259i	0.350022	−	0.936742i	$-0.386174\pi$
$563$	−4.98263	−	2.56873i	−0.209993	−	0.108259i	−0.560015	+	0.828483i	$0.689205\pi$
$564$	3.65070	−	4.39451i	0.153722	−	0.185042i
$565$	13.6775	−	2.63613i	0.575419	−	0.110903i
$566$	−19.8106	+	5.81692i	−0.832702	+	0.244503i
$567$	−11.4427	+	20.8822i	−0.480546	+	0.876969i
$568$	0.251248	−	0.289956i	0.0105421	−	0.0121663i
$569$	−18.4561	−	25.9179i	−0.773719	−	1.08654i	−0.993814	−	0.111057i	$-0.964576\pi$
$569$	−18.4561	−	25.9179i	−0.773719	−	1.08654i	0.220095	−	0.975478i	$-0.429363\pi$
$570$	1.62856	+	78.3165i	0.0682130	+	3.28032i
$571$	13.7740	+	9.80841i	0.576424	+	0.410469i	0.830747	−	0.556650i	$-0.187913\pi$
$571$	13.7740	+	9.80841i	0.576424	+	0.410469i	−0.254324	+	0.967119i	$0.581853\pi$
$572$	−3.20213	−	1.28194i	−0.133888	−	0.0536006i
$573$	10.5334	+	10.5970i	0.440040	+	0.442695i
$574$	0.669594	+	0.398507i	0.0279483	+	0.0166334i
$575$	37.1915	+	41.1743i	1.55099	+	1.71709i
$576$	−20.0033	+	14.0637i	−0.833470	+	0.585986i
$577$	1.59060	−	33.3908i	0.0662176	−	1.39008i	−0.684287	−	0.729213i	$-0.739886\pi$
$577$	1.59060	−	33.3908i	0.0662176	−	1.39008i	0.750504	−	0.660866i	$-0.229811\pi$
$578$	−15.6585	−	19.9114i	−0.651306	−	0.828204i
$579$	−6.17466	−	1.99432i	−0.256610	−	0.0828811i
$580$	−1.58633	+	5.40253i	−0.0658686	+	0.224328i
$581$	−9.53327	−	4.50724i	−0.395507	−	0.186992i
$582$	−11.5805	+	8.61484i	−0.480028	+	0.357096i
$583$	−1.68549	−	1.32548i	−0.0698057	−	0.0548958i
$584$	0.225565	−	0.236566i	0.00933395	−	0.00978917i
$585$	50.0453	−	51.8576i	2.06912	−	2.14405i
$586$	−20.7940	+	0.990543i	−0.858994	+	0.0409189i
$587$	−12.2572	−	19.0725i	−0.505908	−	0.787208i	0.490540	−	0.871419i	$-0.336799\pi$
$587$	−12.2572	−	19.0725i	−0.505908	−	0.787208i	−0.996448	+	0.0842106i	$0.973163\pi$
$588$	24.4436	+	1.30405i	1.00804	+	0.0537779i
$589$	−11.1893	−	38.1074i	−0.461049	−	1.57019i
$590$	9.16938	+	7.21088i	0.377497	+	0.296867i
$591$	−6.01017	+	13.9192i	−0.247225	+	0.572560i
$592$	−1.28433	−	13.4502i	−0.0527858	−	0.552798i
$593$	11.9504	+	12.5332i	0.490744	+	0.514677i	0.921809	−	0.387643i	$-0.126711\pi$
$593$	11.9504	+	12.5332i	0.490744	+	0.514677i	−0.431066	+	0.902321i	$0.641862\pi$
$594$	−2.94073	−	0.667568i	−0.120660	−	0.0273906i
$595$	−22.3107	+	2.90672i	−0.914647	+	0.119164i
$596$	−25.5183	−	16.3996i	−1.04527	−	0.671753i
$597$	1.78029	+	1.62820i	0.0728626	+	0.0666379i
$598$	−22.1696	−	52.2292i	−0.906582	−	2.13581i
$599$	11.3734	−	6.56643i	0.464704	−	0.268297i	−0.249316	−	0.968422i	$-0.580206\pi$
$599$	11.3734	−	6.56643i	0.464704	−	0.268297i	0.714020	+	0.700125i	$0.246873\pi$
$600$	−0.194700	−	0.735472i	−0.00794858	−	0.0300255i
$601$	−1.21481	−	8.44918i	−0.0495531	−	0.344649i	−0.999482	−	0.0321832i	$-0.989754\pi$
$601$	−1.21481	−	8.44918i	−0.0495531	−	0.344649i	0.949929	−	0.312466i	$-0.101155\pi$
$602$	−4.00450	+	36.7817i	−0.163211	+	1.49911i
$603$	20.6571	−	23.5517i	0.841222	−	0.959101i
$604$	10.8416	+	15.2249i	0.441140	+	0.619494i
$605$	−43.6319	−	8.40935i	−1.77389	−	0.341889i
$606$	48.3289	−	7.97749i	1.96323	−	0.324063i
$607$	−1.47082	+	6.06281i	−0.0596988	+	0.246082i	−0.993840	−	0.110821i	$-0.964652\pi$
$607$	−1.47082	+	6.06281i	−0.0596988	+	0.246082i	0.934142	+	0.356903i	$0.116167\pi$
$608$	29.1008	+	33.5841i	1.18019	+	1.36201i
$609$	2.38828	+	2.03811i	0.0967782	+	0.0825884i
$610$	41.1463	−	26.4431i	1.66597	−	1.07065i
$611$	1.82470	+	9.46747i	0.0738197	+	0.383013i
$612$	4.63206	+	11.7752i	0.187240	+	0.475983i
$613$	3.27562	+	8.18210i	0.132301	+	0.330472i	0.979695	−	0.200492i	$-0.0642541\pi$
$613$	3.27562	+	8.18210i	0.132301	+	0.330472i	−0.847394	+	0.530964i	$0.821830\pi$
$614$	−7.14571	+	2.47315i	−0.288377	+	0.0998083i
$615$	−0.827301	−	0.623202i	−0.0333600	−	0.0251299i
$616$	0.00648081	+	0.0283479i	0.000261119	+	0.00114217i
$617$	−13.1685	−	28.8349i	−0.530142	−	1.16085i	−0.965455	−	0.260570i	$-0.916089\pi$
$617$	−13.1685	−	28.8349i	−0.530142	−	1.16085i	0.435313	−	0.900279i	$-0.356638\pi$
$618$	32.6252	+	22.2248i	1.31238	+	0.894013i
$619$	−14.8675	−	0.708227i	−0.597576	−	0.0284661i	−0.253385	−	0.967366i	$-0.581544\pi$
$619$	−14.8675	−	0.708227i	−0.597576	−	0.0284661i	−0.344191	+	0.938900i	$0.611847\pi$
$620$	29.4466	+	51.0029i	1.18260	+	2.04833i
$621$	−13.2158	−	21.1268i	−0.530333	−	0.847789i
$622$	44.2408			1.77390
$623$	4.02510	+	8.06821i	0.161262	+	0.323246i
$624$	3.01048	−	40.3843i	0.120516	−	1.61667i
$625$	−50.7716	−	4.84810i	−2.03086	−	0.193924i
$626$	−11.3528	−	46.7967i	−0.453748	−	1.87037i
$627$	−0.338204	+	2.75821i	−0.0135066	+	0.110152i
$628$	6.43622	−	2.22760i	0.256833	−	0.0888908i
$629$	−7.05233	−	1.01397i	−0.281195	−	0.0404297i
$630$	−63.9220	−	10.4509i	−2.54671	−	0.416376i
$631$	−9.08534	+	7.87249i	−0.361682	+	0.313399i	−0.816677	−	0.577095i	$-0.804186\pi$
$631$	−9.08534	+	7.87249i	−0.361682	+	0.313399i	0.454995	+	0.890494i	$0.349641\pi$
$632$	−0.00128177	−	0.0269077i	−5.09862e−5	−	0.00107033i
$633$	−3.07817	−	2.55716i	−0.122346	−	0.101638i
$634$	−11.0636	+	31.9662i	−0.439392	+	1.26954i
$635$	−5.74252	+	23.6710i	−0.227885	+	0.939355i
$636$	−9.12468	+	24.2413i	−0.361817	+	0.961228i
$637$	−27.8704	+	30.4932i	−1.10426	+	1.20818i
$638$	−0.165176	+	0.361685i	−0.00653938	+	0.0143192i
$639$	9.74277	+	28.7076i	0.385418	+	1.13565i
$640$	−1.00707	−	0.717133i	−0.0398080	−	0.0283472i
$641$	21.9841	−	17.2885i	0.868319	−	0.682853i	−0.0811546	−	0.996702i	$-0.525861\pi$
$641$	21.9841	−	17.2885i	0.868319	−	0.682853i	0.949473	+	0.313848i	$0.101618\pi$
$642$	14.3731	+	54.2939i	0.567260	+	2.14281i
$643$		−	28.0339i		−	1.10555i	−0.833330	−	0.552775i	$-0.813569\pi$
$643$		−	28.0339i		−	1.10555i	0.833330	−	0.552775i	$-0.186431\pi$
$644$	−13.6905	+	21.6523i	−0.539483	+	0.853221i
$645$	10.5987	−	48.0255i	0.417324	−	1.89100i
$646$	20.6311	−	10.6360i	0.811718	−	0.418470i
$647$	−2.88113	−	3.66365i	−0.113269	−	0.144033i	0.726113	−	0.687576i	$-0.241325\pi$
$647$	−2.88113	−	3.66365i	−0.113269	−	0.144033i	−0.839382	+	0.543543i	$0.817083\pi$
$648$	0.0283855	+	0.340522i	0.00111509	+	0.0133770i
$649$	0.285567	+	0.299494i	0.0112095	+	0.0117562i
$650$	124.508	+	56.8607i	4.88359	+	2.23026i
$651$	32.6665	−	3.36822i	1.28030	−	0.132011i
$652$	0.180193	−	1.25327i	0.00705690	−	0.0490818i
$653$	33.1808	+	8.04959i	1.29847	+	0.315005i	0.824662	−	0.565625i	$-0.191365\pi$
$653$	33.1808	+	8.04959i	1.29847	+	0.315005i	0.473805	+	0.880630i	$0.342880\pi$
$654$	−13.2262	+	21.5528i	−0.517186	+	0.842781i
$655$	−13.4789	+	26.1453i	−0.526663	+	1.02158i
$656$	−0.581359	+	0.0276935i	−0.0226983	+	0.00108125i
$657$	7.12731	+	24.8250i	0.278063	+	0.968514i
$658$	6.06240	−	6.19174i	0.236337	−	0.241379i
$659$	0.214021	−	1.48855i	0.00833707	−	0.0579856i	−0.985228	−	0.171247i	$-0.945221\pi$
$659$	0.214021	−	1.48855i	0.00833707	−	0.0579856i	0.993565	+	0.113261i	$0.0361296\pi$
$660$	−0.476888	−	4.09296i	−0.0185628	−	0.159318i
$661$	2.72589	+	28.5468i	0.106025	+	1.11034i	0.879299	+	0.476270i	$0.158012\pi$
$661$	2.72589	+	28.5468i	0.106025	+	1.11034i	−0.773274	+	0.634072i	$0.781382\pi$
$662$	27.3676	−	6.63931i	1.06367	−	0.258044i
$663$	−20.3210	−	6.56337i	−0.789204	−	0.254900i
$664$	−0.149783	+	0.0215356i	−0.00581272	+	0.000835743i
$665$	−3.62942	+	59.5766i	−0.140743	+	2.31028i
$666$	−18.6059	−	8.63268i	−0.720962	−	0.334510i
$667$	−3.08229	+	1.13848i	−0.119347	+	0.0440822i
$668$	11.3822	−	6.57150i	0.440389	−	0.254259i
$669$	−6.87285	+	25.3446i	−0.265720	+	0.979879i
$670$	79.1098	+	31.6708i	3.05628	+	1.22355i
$671$	1.57830	−	0.720788i	0.0609298	−	0.0278257i
$672$	−31.6817	+	18.6116i	−1.22215	+	0.717958i
$673$	11.1555	−	24.4272i	0.430014	−	0.941600i	−0.563310	−	0.826246i	$-0.690472\pi$
$673$	11.1555	−	24.4272i	0.430014	−	0.941600i	0.993324	−	0.115354i	$-0.0368004\pi$
$674$	19.3789	+	55.9917i	0.746448	+	2.15672i
$675$	57.9248	+	16.0826i	2.22953	+	0.619018i
$676$	−31.8951	−	30.4119i	−1.22673	−	1.16969i
$677$	−8.83250	+	1.70233i	−0.339461	+	0.0654257i	−0.356133	−	0.934435i	$-0.615905\pi$
$677$	−8.83250	+	1.70233i	−0.339461	+	0.0654257i	0.0166722	+	0.999861i	$0.494693\pi$
$678$	−4.11885	−	11.1453i	−0.158183	−	0.428034i
$679$	−9.32980	+	5.82275i	−0.358045	+	0.223457i
$680$	−0.244007	+	0.211433i	−0.00935724	+	0.00810809i
$681$	4.08685	−	8.34913i	0.156608	−	0.319939i
$682$	1.54569	+	3.86095i	0.0591875	+	0.147843i
$683$	−4.15640	+	21.5654i	−0.159040	+	0.825179i	0.811521	+	0.584323i	$0.198640\pi$
$683$	−4.15640	+	21.5654i	−0.159040	+	0.825179i	−0.970561	+	0.240855i	$0.922572\pi$
$684$	32.9988	−	6.15432i	1.26174	−	0.235316i
$685$	84.5491	+	24.8259i	3.23045	+	0.948547i
$686$	36.7906	+	4.99471i	1.40467	+	0.190699i
$687$	38.8725	+	2.89778i	1.48308	+	0.110557i
$688$	−12.6635	−	24.5638i	−0.482792	−	0.936486i
$689$	−21.8565	−	37.8566i	−0.832668	−	1.44222i
$690$	42.2307	−	53.0222i	1.60770	−	2.01852i
$691$	−21.6951	+	37.5769i	−0.825319	+	1.42949i	0.0763569	+	0.997081i	$0.475671\pi$
$691$	−21.6951	+	37.5769i	−0.825319	+	1.42949i	−0.901676	+	0.432413i	$0.857662\pi$
$692$	5.50017	−	8.55843i	0.209085	−	0.325343i
$693$	−2.19178	−	0.689689i	−0.0832588	−	0.0261991i
$694$	19.5599	+	42.8302i	0.742483	+	1.62581i
$695$	22.6631	−	21.6092i	0.859660	−	0.819684i
$696$	0.0447205	+	0.00548349i	0.00169513	+	0.000207851i
$697$	−0.0580835	+	0.301366i	−0.00220007	+	0.0114150i
$698$	−5.20880	+	6.62353i	−0.197156	+	0.250704i
$699$	−0.506751	−	7.39800i	−0.0191671	−	0.279818i
$700$	−10.8908	−	60.8316i	−0.411632	−	2.29922i
$701$	−37.0576	+	23.8155i	−1.39965	+	0.899499i	−0.999854	−	0.0171064i	$-0.994555\pi$
$701$	−37.0576	+	23.8155i	−1.39965	+	0.899499i	−0.399794	+	0.916605i	$0.630918\pi$
$702$	−50.5981	−	34.9157i	−1.90970	−	1.31781i
$703$	−6.18196	+	17.8616i	−0.233157	+	0.673664i
$704$	−1.70768	−	1.62827i	−0.0643607	−	0.0613678i
$705$	−8.90425	+	7.30703i	−0.335353	+	0.275199i
$706$	14.1497	−	16.3297i	0.532532	−	0.614575i
$707$	37.1978	−	3.05537i	1.39897	−	0.114909i
$708$	2.40885	−	4.38010i	0.0905300	−	0.164614i
$709$	−3.38671	+	35.4672i	−0.127191	+	1.33200i	0.676276	+	0.736649i	$0.263593\pi$
$709$	−3.38671	+	35.4672i	−0.127191	+	1.33200i	−0.803466	+	0.595351i	$0.797013\pi$
$710$	−64.8198	+	50.9748i	−2.43264	+	1.91305i
$711$	1.88603	+	0.986724i	0.0707316	+	0.0370050i
$712$	0.112054	+	0.0646943i	0.00419939	+	0.00242452i
$713$	−13.6293	+	31.5499i	−0.510422	+	1.18155i
$714$	5.54596	+	18.3737i	0.207552	+	0.687619i
$715$	5.85026	+	3.75973i	0.218787	+	0.140606i
$716$	17.9924	−	44.9428i	0.672407	−	1.67959i
$717$	−29.9019	−	33.0927i	−1.11671	−	1.23587i
$718$	−2.10914	+	0.511672i	−0.0787125	+	0.0190954i
$719$	−9.84502	+	7.01061i	−0.367157	+	0.261451i	−0.748713	−	0.662894i	$-0.769328\pi$
$719$	−9.84502	+	7.01061i	−0.367157	+	0.261451i	0.381556	+	0.924346i	$0.375388\pi$
$720$	44.1277	−	19.8325i	1.64454	−	0.739112i
$721$	23.3954	+	18.9052i	0.871292	+	0.704066i
$722$	−6.61687	−	22.5350i	−0.246254	−	0.838665i
$723$	−0.450150	+	16.7874i	−0.0167413	+	0.624332i
$724$	0.0610314	−	0.118384i	0.00226822	−	0.00439972i
$725$	3.63219	−	7.04546i	0.134896	−	0.261662i
$726$	−1.01602	+	37.8906i	−0.0377082	+	1.40625i
$727$	3.99047	+	13.5903i	0.147998	+	0.504036i	0.999804	−	0.0198228i	$-0.00631020\pi$
$727$	3.99047	+	13.5903i	0.147998	+	0.504036i	−0.851805	+	0.523859i	$0.824492\pi$
$728$	−0.0921314	+	0.585616i	−0.00341462	+	0.0217044i
$729$	−24.3536	−	11.6577i	−0.901986	−	0.431765i
$730$	−57.2277	+	40.7517i	−2.11809	+	1.50829i
$731$	−14.1623	+	3.43573i	−0.523811	+	0.127075i
$732$	−14.0519	−	15.5513i	−0.519372	−	0.574793i
$733$	0.756301	−	1.88915i	0.0279346	−	0.0697773i	−0.913745	−	0.406289i	$-0.866823\pi$
$733$	0.756301	−	1.88915i	0.0279346	−	0.0697773i	0.941679	+	0.336511i	$0.109247\pi$
$734$	36.1419	+	23.2270i	1.33402	+	0.857325i
$735$	−47.8944	−	11.9085i	−1.76661	−	0.439251i
$736$	−0.792866	−	38.4457i	−0.0292254	−	1.41713i
$737$	2.61795	+	1.51147i	0.0964335	+	0.0556759i
$738$	−0.409578	+	0.782869i	−0.0150768	+	0.0288178i
$739$	−0.658467	+	0.517824i	−0.0242221	+	0.0190485i	−0.630197	−	0.776436i	$-0.717026\pi$
$739$	−0.658467	+	0.517824i	−0.0242221	+	0.0190485i	0.605975	+	0.795484i	$0.292783\pi$
$740$	2.66419	−	27.9007i	0.0979376	−	1.02565i
$741$	−27.2993	+	49.6393i	−1.00286	+	1.82355i
$742$	−16.7923	+	35.5174i	−0.616465	+	1.30389i
$743$	8.59792	−	9.92253i	0.315427	−	0.364022i	−0.575791	−	0.817597i	$-0.695306\pi$
$743$	8.59792	−	9.92253i	0.315427	−	0.364022i	0.891218	+	0.453575i	$0.149851\pi$
$744$	0.364295	−	0.298949i	0.0133557	−	0.0109600i
$745$	44.2621	+	42.2039i	1.62164	+	1.54623i
$746$	2.45830	−	7.10280i	0.0900048	−	0.260052i
$747$	4.51067	−	11.0735i	0.165037	−	0.405160i
$748$	−1.02718	+	0.660126i	−0.0375573	+	0.0241366i
$749$	7.54170	+	42.1251i	0.275568	+	1.53922i
$750$	6.34531	+	92.6345i	0.231698	+	3.38253i
$751$	−9.90710	+	12.5979i	−0.361515	+	0.459704i	−0.932454	−	0.361289i	$-0.882337\pi$
$751$	−9.90710	+	12.5979i	−0.361515	+	0.459704i	0.570939	+	0.820993i	$0.306579\pi$
$752$	−1.22494	+	6.35559i	−0.0446689	+	0.231764i
$753$	−45.5309	−	5.58286i	−1.65924	−	0.203451i
$754$	−5.86653	+	5.59373i	−0.213647	+	0.203712i
$755$	−15.6544	−	34.2783i	−0.569721	−	1.24751i
$756$	0.0424601	+	27.7558i	0.00154426	+	1.00947i
$757$	−5.76106	+	8.96438i	−0.209389	+	0.325816i	−0.930024	−	0.367499i	$-0.880214\pi$
$757$	−5.76106	+	8.96438i	−0.209389	+	0.325816i	0.720635	+	0.693315i	$0.243851\pi$
$758$	−4.02249	+	6.96716i	−0.146103	+	0.253058i
$759$	1.75057	−	1.64860i	0.0635416	−	0.0598405i
$760$	0.428260	+	0.741767i	0.0155346	+	0.0269067i
$761$	−11.1873	−	21.7003i	−0.405539	−	0.786636i	0.594306	−	0.804239i	$-0.297427\pi$
$761$	−11.1873	−	21.7003i	−0.405539	−	0.786636i	−0.999845	+	0.0176027i	$0.994397\pi$
$762$	20.7203	+	1.54461i	0.750616	+	0.0559553i
$763$	−11.3835	+	15.5459i	−0.412109	+	0.562799i
$764$	16.7109	+	4.90675i	0.604578	+	0.177520i
$765$	−4.67731	−	25.0793i	−0.169109	−	0.906743i
$766$	−9.36196	+	48.5745i	−0.338261	+	1.75507i
$767$	3.13542	+	7.83190i	0.113213	+	0.282793i
$768$	11.9499	−	24.4127i	0.431204	−	0.880919i
$769$	18.8359	−	16.3214i	0.679241	−	0.588566i	−0.245392	−	0.969424i	$-0.578917\pi$
$769$	18.8359	−	16.3214i	0.679241	−	0.588566i	0.924634	+	0.380858i	$0.124371\pi$
$770$	−0.214677	−	6.24640i	−0.00773644	−	0.225105i
$771$	7.05718	+	19.0963i	0.254158	+	0.687736i
$772$	−7.42682	+	1.43140i	−0.267297	+	0.0515173i
$773$	26.1137	+	24.8994i	0.939246	+	0.895569i	0.994693	−	0.102892i	$-0.0328097\pi$
$773$	26.1137	+	24.8994i	0.939246	+	0.895569i	−0.0554463	+	0.998462i	$0.517658\pi$
$774$	−41.8927	−	2.24829i	−1.50580	−	0.0808133i
$775$	−27.1166	−	78.3482i	−0.974056	−	2.81435i
$776$	−0.0655604	+	0.143557i	−0.00235348	+	0.00515341i
$777$	−13.5933	−	7.71193i	−0.487658	−	0.276664i
$778$	2.46638	−	1.12636i	0.0884239	−	0.0403818i
$779$	0.755869	+	0.302604i	0.0270818	+	0.0108419i
$780$	21.9860	−	81.0764i	0.787224	−	2.90300i
$781$	−2.53342	+	1.46267i	−0.0906529	+	0.0523385i
$782$	−19.6129	−	4.33190i	−0.701357	−	0.154908i
$783$	−2.15912	+	2.83064i	−0.0771607	+	0.101159i
$784$	−24.9774	+	12.0503i	−0.892051	+	0.430369i
$785$	−13.5920	+	1.95424i	−0.485121	+	0.0697498i
$786$	23.8775	+	7.71207i	0.851684	+	0.275080i
$787$	−13.1145	+	3.18153i	−0.467480	+	0.113409i	−0.462578	−	0.886579i	$-0.653076\pi$
$787$	−13.1145	+	3.18153i	−0.467480	+	0.113409i	−0.00490196	+	0.999988i	$0.501560\pi$
$788$	1.67989	+	17.5926i	0.0598435	+	0.626710i
$789$	−5.80828	−	49.8504i	−0.206780	−	1.77472i
$790$	−0.823988	+	5.73096i	−0.0293162	+	0.203899i
$791$	−2.43543	−	8.71996i	−0.0865941	−	0.310046i
$792$	−0.0316925	+	0.00909901i	−0.00112614	+	0.000323319i
$793$	35.3322	−	1.68308i	1.25468	−	0.0597679i
$794$	−15.2936	+	29.6654i	−0.542749	+	1.05279i
$795$	27.3141	−	44.5098i	0.968733	−	1.57860i
$796$	2.73290	+	0.662995i	0.0968652	+	0.0234992i
$797$	4.97328	−	34.5899i	0.176163	−	1.22524i	−0.689379	−	0.724401i	$-0.742116\pi$
$797$	4.97328	−	34.5899i	0.176163	−	1.22524i	0.865542	−	0.500837i	$-0.166974\pi$
$798$	50.6463	−	5.22210i	1.79286	−	0.184860i
$799$	3.10469	+	1.41787i	0.109836	+	0.0501605i
$800$	64.0152	+	67.1373i	2.26328	+	2.37366i
$801$	−8.88463	+	5.05852i	−0.313923	+	0.178734i
$802$	−5.28035	−	6.71451i	−0.186456	−	0.237098i
$803$	−2.21522	+	1.14203i	−0.0781735	+	0.0403012i
$804$	7.86939	−	35.6582i	0.277532	−	1.25757i
$805$	35.3655	−	37.6423i	1.24647	−	1.32672i
$806$			84.7835i			2.98637i
$807$	11.7445	+	44.3644i	0.413425	+	1.56170i
$808$	0.421004	−	0.331081i	0.0148109	−	0.0116474i
$809$	4.61348	+	3.28524i	0.162201	+	0.115503i	0.658275	−	0.752777i	$-0.271286\pi$
$809$	4.61348	+	3.28524i	0.162201	+	0.115503i	−0.496074	+	0.868280i	$0.665226\pi$
$810$	7.86044	−	73.0212i	0.276188	−	2.56570i
$811$	16.7217	−	36.6154i	0.587178	−	1.28574i	−0.349954	−	0.936767i	$-0.613803\pi$
$811$	16.7217	−	36.6154i	0.587178	−	1.28574i	0.937132	−	0.348974i	$-0.113470\pi$
$812$	3.58413	+	0.740150i	0.125778	+	0.0259742i
$813$	−6.12414	+	16.2698i	−0.214783	+	0.570607i
$814$	0.466619	−	1.92343i	0.0163550	−	0.0674162i
$815$	−0.834939	+	2.41240i	−0.0292466	+	0.0845026i
$816$	−11.0269	−	9.16053i	−0.386020	−	0.320683i
$817$	1.83953	+	38.6164i	0.0643569	+	1.35102i
$818$	−22.4822	+	19.4810i	−0.786072	+	0.681136i
$819$	−36.2559	−	29.6597i	−1.26688	−	1.03639i
$820$	−1.19503	−	0.171820i	−0.0417324	−	0.00600021i
$821$	46.8045	−	16.1992i	1.63349	−	0.565356i	0.652225	−	0.758026i	$-0.273836\pi$
$821$	46.8045	−	16.1992i	1.63349	−	0.565356i	0.981264	+	0.192670i	$0.0617147\pi$
$822$	9.14833	−	74.6089i	0.319084	−	2.60228i
$823$	−11.8440	−	48.8216i	−0.412856	−	1.70182i	−0.675868	−	0.737023i	$-0.736231\pi$
$823$	−11.8440	−	48.8216i	−0.412856	−	1.70182i	0.263012	−	0.964792i	$-0.415284\pi$
$824$	0.429686	+	0.0410300i	0.0149688	+	0.00142935i
$825$	−0.431238	+	5.78488i	−0.0150138	+	0.201404i
$826$	4.18327	−	6.32355i	0.145555	−	0.220024i
$827$	−8.42773			−0.293061			−0.146531	−	0.989206i	$-0.546811\pi$
$827$	−8.42773			−0.293061			−0.146531	+	0.989206i	$0.546811\pi$
$828$	−25.3653	−	14.1548i	−0.881503	−	0.491915i
$829$	16.5714	+	28.7025i	0.575549	+	0.996881i	0.995982	+	0.0895568i	$0.0285451\pi$
$829$	16.5714	+	28.7025i	0.575549	+	0.996881i	−0.420432	+	0.907324i	$0.638122\pi$
$830$	32.4875	+	1.54757i	1.12766	+	0.0537170i
$831$	−21.7104	−	14.7895i	−0.753127	−	0.513041i
$832$	−19.9824	−	43.7554i	−0.692766	−	1.51695i
$833$	3.07008	+	14.2980i	0.106372	+	0.495397i
$834$	−21.3357	−	16.0721i	−0.738794	−	0.556530i
$835$	−25.0412	+	8.66686i	−0.866588	+	0.299929i
$836$	1.20387	+	3.00712i	0.0416367	+	0.104003i
$837$	5.84331	+	36.7754i	0.201974	+	1.27114i
$838$	−6.12109	−	31.7593i	−0.211450	−	1.09711i
$839$	46.6716	−	29.9940i	1.61128	−	1.03551i	0.650006	−	0.759929i	$-0.274766\pi$
$839$	46.6716	−	29.9940i	1.61128	−	1.03551i	0.961278	−	0.275580i	$-0.0888700\pi$
$840$	−0.667501	+	0.236680i	−0.0230310	+	0.00816624i
$841$	−18.6836	−	21.5620i	−0.644261	−	0.743516i
$842$	5.49088	−	22.6337i	0.189228	−	0.780010i
$843$	47.5660	−	7.85154i	1.63826	−	0.270422i
$844$	−4.58031	−	0.882783i	−0.157661	−	0.0303867i
$845$	51.5400	+	72.3778i	1.77303	+	2.48987i
$846$	7.38693	+	6.47904i	0.253968	+	0.222754i
$847$	−3.12592	+	28.7119i	−0.107408	+	0.986552i
$848$	−4.17622	−	29.0462i	−0.143412	−	0.997452i
$849$	−4.56511	−	17.2446i	−0.156674	−	0.591832i
$850$	41.9624	−	24.2270i	1.43930	−	0.830979i
$851$	13.9930	−	8.46825i	0.479673	−	0.290288i
$852$	26.0761	+	23.8484i	0.893353	+	0.817034i
$853$	−20.3476	−	13.0766i	−0.696687	−	0.447734i	0.143770	−	0.989611i	$-0.454077\pi$
$853$	−20.3476	−	13.0766i	−0.696687	−	0.447734i	−0.840458	+	0.541877i	$0.817714\pi$
$854$	−19.3190	−	25.2473i	−0.661084	−	0.863945i
$855$	−67.6775	−	0.407196i	−2.31452	−	0.0139258i
$856$	0.423787	+	0.444455i	0.0144847	+	0.0151912i
$857$	−2.42673	−	25.4139i	−0.0828955	−	0.868121i	−0.937303	−	0.348517i	$-0.886685\pi$
$857$	−2.42673	−	25.4139i	−0.0828955	−	0.868121i	0.854407	−	0.519604i	$-0.173921\pi$
$858$	2.35159	−	5.44614i	0.0802818	−	0.185928i
$859$	16.3071	+	12.8241i	0.556392	+	0.437552i	0.856346	−	0.516402i	$-0.172729\pi$
$859$	16.3071	+	12.8241i	0.556392	+	0.437552i	−0.299954	+	0.953954i	$0.596971\pi$
$860$	−16.1510	−	55.0051i	−0.550743	−	1.87566i
$861$	−0.359687	+	0.569080i	−0.0122581	+	0.0193942i
$862$	−14.2215	−	22.1291i	−0.484386	−	0.753719i
$863$	−31.9190	+	1.52049i	−1.08654	+	0.0517581i	−0.583196	−	0.812331i	$-0.698198\pi$
$863$	−31.9190	+	1.52049i	−1.08654	+	0.0517581i	−0.503339	+	0.864089i	$0.667895\pi$
$864$	−23.0405	−	34.7132i	−0.783854	−	1.18097i
$865$	−14.1545	+	14.8448i	−0.481268	+	0.504740i
$866$	−41.6990	−	32.7924i	−1.41699	−	1.11433i
$867$	17.5595	−	13.0627i	0.596353	−	0.443631i
$868$	31.4726	−	21.7891i	1.06825	−	0.739570i
$869$	−0.0578667	+	0.197076i	−0.00196299	+	0.00668534i
$870$	−9.21513	−	2.97634i	−0.312422	−	0.100907i
$871$	38.0951	+	48.4418i	1.29080	+	1.64139i
$872$	−0.0131564	+	0.276187i	−0.000445532	+	0.00935286i
$873$	−7.17220	−	10.2013i	−0.242742	−	0.345261i
$874$	−21.1310	+	48.9151i	−0.714766	+	1.65458i
$875$	−0.937061	+	70.7430i	−0.0316784	+	2.39155i
$876$	21.2239	+	21.3520i	0.717089	+	0.721417i
$877$	−9.53498	−	3.81723i	−0.321973	−	0.128899i	0.205045	−	0.978753i	$-0.434266\pi$
$877$	−9.53498	−	3.81723i	−0.321973	−	0.128899i	−0.527018	+	0.849854i	$0.676690\pi$
$878$	59.5849	+	42.4302i	2.01089	+	1.43195i
$879$	−0.373933	−	17.9822i	−0.0126124	−	0.606524i
$880$	2.70795	+	3.80278i	0.0912849	+	0.128192i
$881$	3.45507	−	3.98736i	0.116404	−	0.134338i	−0.694557	−	0.719438i	$-0.744399\pi$
$881$	3.45507	−	3.98736i	0.116404	−	0.134338i	0.810961	+	0.585100i	$0.198945\pi$
$882$	−3.36884	+	41.9643i	−0.113435	+	1.41301i
$883$	−21.5931	+	6.34032i	−0.726667	+	0.213369i	−0.624086	−	0.781356i	$-0.714528\pi$
$883$	−21.5931	+	6.34032i	−0.726667	+	0.213369i	−0.102581	+	0.994725i	$0.532710\pi$
$884$	−24.4419	+	4.71080i	−0.822071	+	0.158441i
$885$	−6.44019	+	7.75234i	−0.216485	+	0.260592i
$886$	−14.0584	−	7.24759i	−0.472300	−	0.243487i
$887$	−7.27163	−	37.7288i	−0.244157	−	1.26681i	−0.872401	−	0.488792i	$-0.837438\pi$
$887$	−7.27163	−	37.7288i	−0.244157	−	1.26681i	0.628243	−	0.778017i	$-0.283774\pi$
$888$	−0.223749	+	0.0153264i	−0.00750851	+	0.000514321i
$889$	15.6395	+	2.46046i	0.524531	+	0.0825213i
$890$	−21.0172	−	18.2115i	−0.704499	−	0.610452i
$891$	0.644665	−	2.52437i	0.0215971	−	0.0845694i
$892$	7.21646	+	29.7467i	0.241625	+	0.995992i
$893$	5.25214	−	7.37560i	0.175756	−	0.246815i
$894$	29.3713	−	43.1160i	0.982323	−	1.44202i
$895$	−52.7689	+	82.1100i	−1.76387	+	2.74463i
$896$	−0.410969	+	0.690533i	−0.0137295	+	0.0230691i
$897$	45.6223	−	17.9377i	1.52329	−	0.598921i
$898$	20.4366	−	35.3972i	0.681978	−	1.18122i
$899$	4.90430	+	0.233621i	0.163568	+	0.00779168i
$900$	68.1962	−	16.1104i	2.27321	−	0.537013i
$901$	−15.4042	−	1.47092i	−0.513189	−	0.0490036i
$902$	−0.0818040	−	0.0240198i	−0.00272377	−	0.000799772i
$903$	−31.6746	−	4.31040i	−1.05406	−	0.143441i
$904$	−0.0981884	−	0.0850807i	−0.00326570	−	0.00282974i
$905$	−0.165998	+	0.211084i	−0.00551796	+	0.00701666i
$906$	−26.6752	+	17.9375i	−0.886224	+	0.595934i
$907$	−38.1054	−	13.1884i	−1.26527	−	0.437914i	−0.389671	−	0.920954i	$-0.627411\pi$
$907$	−38.1054	−	13.1884i	−1.26527	−	0.437914i	−0.875598	+	0.483041i	$0.839532\pi$
$908$	−0.515570	−	10.8231i	−0.0171098	−	0.359178i
$909$	5.77068	+	41.9251i	0.191401	+	1.39057i
$910$	43.2648	−	119.846i	1.43421	−	3.97284i
$911$	−13.5049	+	3.96539i	−0.447437	+	0.131379i	−0.497686	−	0.867357i	$-0.665817\pi$
$911$	−13.5049	+	3.96539i	−0.447437	+	0.131379i	0.0502490	+	0.998737i	$0.483998\pi$
$912$	−29.3985	+	24.1251i	−0.973481	+	0.798861i
$913$	1.13295	+	0.218358i	0.0374951	+	0.00722658i
$914$	−19.8910	+	1.89936i	−0.657937	+	0.0628254i
$915$	21.8853	+	36.1493i	0.723505	+	1.19506i
$916$	41.3308	−	18.8752i	1.36561	−	0.623653i
$917$	17.6540	+	7.34035i	0.582985	+	0.242400i
$918$	−20.4579	+	7.42079i	−0.675212	+	0.244923i
$919$	−3.75342	−	2.16704i	−0.123814	−	0.0714841i	0.436814	−	0.899552i	$-0.356107\pi$
$919$	−3.75342	−	2.16704i	−0.123814	−	0.0714841i	−0.560628	+	0.828068i	$0.689440\pi$
$920$	0.125233	−	0.730521i	0.00412881	−	0.0240846i
$921$	−1.97050	−	6.22882i	−0.0649303	−	0.205247i
$922$	−44.7259	+	23.0578i	−1.47297	+	0.759369i
$923$	−59.0298	+	8.48720i	−1.94299	+	0.279360i
$924$	−2.62601	+	0.526706i	−0.0863895	+	0.0173274i
$925$	−11.1162	+	37.8582i	−0.365497	+	1.24477i
$926$	−28.7488	+	20.4719i	−0.944744	+	0.672749i
$927$	−19.9505	+	27.6628i	−0.655261	+	0.908566i
$928$	−5.10008	+	2.04176i	−0.167418	+	0.0670242i
$929$	−38.6661	−	9.38028i	−1.26859	−	0.307757i	−0.455680	−	0.890144i	$-0.650604\pi$
$929$	−38.6661	−	9.38028i	−1.26859	−	0.307757i	−0.812912	+	0.582386i	$0.802119\pi$
$930$	−89.0439	+	48.2745i	−2.91987	+	1.58298i
$931$	38.7864	−	0.818883i	1.27117	−	0.0268378i
$932$	−4.67307	−	7.27143i	−0.153071	−	0.238184i
$933$	−1.02458	+	38.2096i	−0.0335432	+	1.25093i
$934$	−24.9337	+	26.1497i	−0.815854	+	0.855643i
$935$	2.28543	−	0.914947i	0.0747414	−	0.0299220i
$936$	−0.668753	−	0.0679209i	−0.0218589	−	0.00222006i
$937$	4.68394	+	2.13908i	0.153018	+	0.0698809i	0.490452	−	0.871468i	$-0.336832\pi$
$937$	4.68394	+	2.13908i	0.153018	+	0.0698809i	−0.337434	+	0.941349i	$0.609559\pi$
$938$	16.3068	−	52.9320i	0.532435	−	1.72829i
$939$	40.6800	−	8.72130i	1.32754	−	0.284609i
$940$	−4.99012	+	12.4647i	−0.162760	+	0.406555i
$941$	−0.759713	+	15.9483i	−0.0247659	+	0.519901i	0.952066	+	0.305893i	$0.0989550\pi$
$941$	−0.759713	+	15.9483i	−0.0247659	+	0.519901i	−0.976832	+	0.214008i	$0.931348\pi$
$942$	3.53306	+	11.1681i	0.115113	+	0.363877i
$943$	−0.335687	−	0.619440i	−0.0109315	−	0.0201717i
$944$			5.66329i			0.184324i
$945$	10.5066	−	54.9656i	0.341778	−	1.78803i
$946$	−0.576130	−	4.00707i	−0.0187316	−	0.130281i
$947$	4.15792	−	43.5437i	0.135114	−	1.41498i	−0.632744	−	0.774361i	$-0.718071\pi$
$947$	4.15792	−	43.5437i	0.135114	−	1.41498i	0.767858	−	0.640620i	$-0.221323\pi$
$948$	2.48058	−	0.0515826i	0.0805654	−	0.00167533i
$949$	−50.5781	+	4.82962i	−1.64184	+	0.156776i
$950$	−42.0417	−	121.471i	−1.36401	−	3.94105i
$951$	−27.3521	−	10.2956i	−0.886952	−	0.333859i
$952$	0.149948	+	0.146816i	0.00485986	+	0.00475833i
$953$	16.2807	+	18.7890i	0.527385	+	0.608634i	0.955464	−	0.295107i	$-0.0953552\pi$
$953$	16.2807	+	18.7890i	0.527385	+	0.608634i	−0.428080	+	0.903741i	$0.640810\pi$
$954$	−41.2559	−	16.8051i	−1.33571	−	0.544085i
$955$	−31.2110	−	16.0904i	−1.00996	−	0.520673i
$956$	−49.1291	−	17.0038i	−1.58895	−	0.549941i
$957$	−0.308552	−	0.151034i	−0.00997407	−	0.00488224i
$958$	25.4539	+	3.65972i	0.822379	+	0.118240i
$959$	11.5833	−	56.0913i	0.374043	−	1.81128i
$960$	34.5764	−	45.9002i	1.11595	−	1.48142i
$961$	14.7312	−	14.0462i	0.475201	−	0.453103i
$962$	23.4047	−	32.8673i	0.754598	−	1.05968i
$963$	−47.2250	+	11.1562i	−1.52180	+	0.359504i
$964$	8.96981	+	17.3990i	0.288898	+	0.560384i
$965$	15.2494			0.490895
$966$	−36.5945	−	24.5355i	−1.17741	−	0.789418i
$967$	−23.7280			−0.763040			−0.381520	−	0.924361i	$-0.624599\pi$
$967$	−23.7280			−0.763040			−0.381520	+	0.924361i	$0.624599\pi$
$968$	0.189914	+	0.368382i	0.00610408	+	0.0118403i
$969$	8.70826	+	18.0648i	0.279750	+	0.580325i
$970$	19.6758	−	27.6308i	0.631751	−	0.887170i
$971$	22.7076	−	21.6516i	0.728721	−	0.694834i	−0.231887	−	0.972743i	$-0.574490\pi$
$971$	22.7076	−	21.6516i	0.728721	−	0.694834i	0.960607	+	0.277909i	$0.0896413\pi$
$972$	−31.4222	+	1.77278i	−1.00787	+	0.0568618i
$973$	−15.2042	−	13.5312i	−0.487423	−	0.433790i
$974$	86.5887	+	12.4496i	2.77448	+	0.398910i
$975$	−51.9925	+	106.217i	−1.66509	+	3.40166i
$976$	22.4397	+	7.76645i	0.718277	+	0.248598i
$977$	41.9323	+	21.6176i	1.34153	+	0.691608i	0.971417	−	0.237378i	$-0.0762879\pi$
$977$	41.9323	+	21.6176i	1.34153	+	0.691608i	0.370115	+	0.928986i	$0.379318\pi$
$978$	2.14637	+	0.367572i	0.0686332	+	0.0117537i
$979$	−0.646052	−	0.745584i	−0.0206479	−	0.0238290i
$980$	−55.6069	+	14.7396i	−1.77630	+	0.470839i
$981$	−18.3082	−	11.9222i	−0.584537	−	0.380648i
$982$	15.4655	+	44.6847i	0.493524	+	1.42594i
$983$	−15.0936	+	1.44127i	−0.481412	+	0.0459692i	−0.332941	−	0.942948i	$-0.608041\pi$
$983$	−15.0936	+	1.44127i	−0.481412	+	0.0459692i	−0.148470	+	0.988917i	$0.547435\pi$
$984$	0.000200850		0.00965875i	6.40287e−6		0.000307910i
$985$	3.38696	−	35.4698i	0.107917	−	1.13016i
$986$	0.408368	+	2.84026i	0.0130051	+	0.0904524i
$987$	5.20723	+	5.37932i	0.165748	+	0.171226i
$988$			66.0341i			2.10083i
$989$	20.1334	−	26.7175i	0.640204	−	0.849567i
$990$	7.05877	−	0.631197i	0.224342	−	0.0200608i
$991$	−0.0851279	+	1.78705i	−0.00270418	+	0.0567676i	−0.999816	−	0.0191789i	$-0.993895\pi$
$991$	−0.0851279	+	1.78705i	−0.00270418	+	0.0567676i	0.997112	+	0.0759465i	$0.0241978\pi$
$992$	−21.3557	+	53.3441i	−0.678045	+	1.69368i
$993$	5.10038	+	23.7904i	0.161856	+	0.754966i
$994$	36.4701	+	39.2775i	1.15676	+	1.24581i
$995$	−5.15748	−	2.35534i	−0.163503	−	0.0746693i
$996$	−1.61301	−	13.8438i	−0.0511100	−	0.438659i
$997$	−15.9352	+	6.37950i	−0.504674	+	0.202041i	−0.610007	−	0.792396i	$-0.708833\pi$
$997$	−15.9352	+	6.37950i	−0.504674	+	0.202041i	0.105333	+	0.994437i	$0.466409\pi$
$998$	−11.0079	+	11.5448i	−0.348449	+	0.365443i
$999$	7.88670	−	15.8694i	0.249524	−	0.502087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bc.a.44.51	yes	1200
3.2	odd	2	inner	483.2.bc.a.44.10	yes	1200
7.4	even	3	inner	483.2.bc.a.389.10	yes	1200
21.11	odd	6	inner	483.2.bc.a.389.51	yes	1200
23.11	odd	22	inner	483.2.bc.a.149.51	yes	1200
69.11	even	22	inner	483.2.bc.a.149.10	yes	1200
161.11	odd	66	inner	483.2.bc.a.11.10	✓	1200
483.11	even	66	inner	483.2.bc.a.11.51	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bc.a.11.10	✓	1200	161.11	odd	66	inner
483.2.bc.a.11.51	yes	1200	483.11	even	66	inner
483.2.bc.a.44.10	yes	1200	3.2	odd	2	inner
483.2.bc.a.44.51	yes	1200	1.1	even	1	trivial
483.2.bc.a.149.10	yes	1200	69.11	even	22	inner
483.2.bc.a.149.51	yes	1200	23.11	odd	22	inner
483.2.bc.a.389.10	yes	1200	7.4	even	3	inner
483.2.bc.a.389.51	yes	1200	21.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.918620 + 1.78187i) q^{2} +(-1.56023 + 0.752120i) q^{3} +(-1.17110 + 1.64458i) q^{4} +(2.94599 - 2.80900i) q^{5} +(-2.77344 - 2.08922i) q^{6} +(-1.97640 - 1.75893i) q^{7} +(-0.0375805 - 0.00540327i) q^{8} +(1.86863 - 2.34696i) q^{9} +(7.71152 + 2.66898i) q^{10} +(0.257306 + 0.132651i) q^{11} +(0.590263 - 3.44673i) q^{12} +(3.86470 + 4.46010i) q^{13} +(1.31863 - 5.13749i) q^{14} +(-2.48372 + 6.59842i) q^{15} +(1.29577 + 3.74387i) q^{16} +(2.07967 - 0.198585i) q^{17} +(5.89855 + 1.17370i) q^{18} +(0.526815 - 5.51706i) q^{19} +(1.16957 + 8.13453i) q^{20} +(4.40657 + 1.25784i) q^{21} +0.580343i q^{22} +(-3.40193 + 3.38036i) q^{23} +(0.0626982 - 0.0198347i) q^{24} +(0.550490 - 11.5562i) q^{25} +(-4.39715 + 10.9835i) q^{26} +(-1.15030 + 5.06723i) q^{27} +(5.20726 - 1.19047i) q^{28} +(0.623226 + 0.284618i) q^{29} +(-14.0391 + 1.63576i) q^{30} +(6.65287 - 2.66341i) q^{31} +(-5.53319 + 5.80304i) q^{32} +(-0.501226 - 0.0134402i) q^{33} +(2.26428 + 3.52329i) q^{34} +(-10.7633 + 0.369915i) q^{35} +(1.67141 + 5.82163i) q^{36} +(-3.31430 - 0.804041i) q^{37} +(10.3146 - 4.12936i) q^{38} +(-9.38435 - 4.05206i) q^{39} +(-0.125890 + 0.0896456i) q^{40} +(-0.0413890 + 0.140958i) q^{41} +(1.80664 + 9.00743i) q^{42} +(-6.90466 + 0.992741i) q^{43} +(-0.519486 + 0.267813i) q^{44} +(-1.08763 - 12.1631i) q^{45} +(-9.14847 - 2.95654i) q^{46} +(1.41487 + 0.816878i) q^{47} +(-4.83753 - 4.86672i) q^{48} +(0.812330 + 6.95271i) q^{49} +(21.0974 - 9.63487i) q^{50} +(-3.09541 + 1.87400i) q^{51} +(-11.8609 + 1.13258i) q^{52} +(-7.27318 - 1.40179i) q^{53} +(-10.0859 + 2.60517i) q^{54} +(1.13064 - 0.331985i) q^{55} +(0.0647703 + 0.0767806i) q^{56} +(3.32754 + 9.00411i) q^{57} +(0.0653548 + 1.37197i) q^{58} +(1.35087 + 0.467539i) q^{59} +(-7.94293 - 11.8121i) q^{60} +(3.70507 - 4.71138i) q^{61} +(10.8573 + 9.40792i) q^{62} +(-7.82130 + 1.35174i) q^{63} +(-7.82062 - 2.29634i) q^{64} +(23.9138 + 2.28349i) q^{65} +(-0.436487 - 0.905468i) q^{66} +(10.4306 + 0.496871i) q^{67} +(-2.10891 + 3.65275i) q^{68} +(2.76535 - 7.83280i) q^{69} +(-10.5465 - 18.8390i) q^{70} +(-5.46332 + 8.50109i) q^{71} +(-0.0829054 + 0.0781033i) q^{72} +(-4.99387 + 7.01291i) q^{73} +(-1.61188 - 6.64428i) q^{74} +(7.83277 + 18.4444i) q^{75} +(8.45629 + 7.32741i) q^{76} +(-0.275217 - 0.714755i) q^{77} +(-1.40038 - 20.4440i) q^{78} +(0.134277 + 0.696695i) q^{79} +(14.3338 + 7.38960i) q^{80} +(-2.01643 - 8.77120i) q^{81} +(-0.289190 + 0.0557369i) q^{82} +(3.82422 - 1.12289i) q^{83} +(-7.22915 + 5.77389i) q^{84} +(5.56887 - 6.42682i) q^{85} +(-8.11170 - 11.3913i) q^{86} +(-1.18644 + 0.0246716i) q^{87} +(-0.00895296 - 0.00637537i) q^{88} +(-3.16380 - 1.26660i) q^{89} +(20.6740 - 13.1113i) q^{90} +(0.206805 - 15.6127i) q^{91} +(-1.57528 - 9.55349i) q^{92} +(-8.37681 + 9.15929i) q^{93} +(-0.155842 + 3.27153i) q^{94} +(-13.9454 - 17.7330i) q^{95} +(4.26846 - 13.2157i) q^{96} +(1.17109 - 3.98837i) q^{97} +(-11.6426 + 7.83437i) q^{98} +(0.792136 - 0.356012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 9 q^{3} - 74 q^{4} - 20 q^{6} - 44 q^{7} - 13 q^{9} - 22 q^{10} - 25 q^{12} - 72 q^{13} - 44 q^{15} + 38 q^{16} - 45 q^{18} - 22 q^{19} + 44 q^{21} + 2 q^{24} + 18 q^{25} - 90 q^{27} - 44 q^{28}+ \cdots - 308 q^{99}+O(q^{100}) \) 1200 * q - 9 * q^3 - 74 * q^4 - 20 * q^6 - 44 * q^7 - 13 * q^9 - 22 * q^10 - 25 * q^12 - 72 * q^13 - 44 * q^15 + 38 * q^16 - 45 * q^18 - 22 * q^19 + 44 * q^21 + 2 * q^24 + 18 * q^25 - 90 * q^27 - 44 * q^28 - 55 * q^30 - 18 * q^31 - 11 * q^33 - 88 * q^34 - 108 * q^36 - 66 * q^37 + q^39 - 22 * q^40 - 22 * q^42 - 2 * q^46 - 228 * q^48 - 128 * q^49 - 11 * q^51 - 166 * q^52 + 35 * q^54 - 160 * q^55 - 44 * q^57 - 126 * q^58 - 11 * q^60 + 66 * q^61 + 33 * q^63 + 40 * q^64 + 22 * q^66 - 22 * q^67 - 24 * q^69 + 68 * q^70 - 149 * q^72 - 42 * q^73 + 123 * q^75 - 88 * q^76 - 108 * q^78 - 66 * q^79 - 81 * q^81 - 14 * q^82 + 44 * q^84 - 200 * q^85 + 75 * q^87 + 66 * q^88 + 16 * q^93 - 146 * q^94 + 5 * q^96 - 88 * q^97 - 308 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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