LMFDB - Embedded newform 192.2.s.a.179.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(11,192)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("192.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			179.16
Character	$\chi$	$=$	192.179
Dual form			192.2.s.a.59.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.246732 + 1.39252i) q^{2} +(-1.19490 - 1.25388i) q^{3} +(-1.87825 + 0.687161i) q^{4} +(0.359364 + 1.80664i) q^{5} +(1.45124 - 1.97330i) q^{6} +(-3.05294 + 1.26457i) q^{7} +(-1.42031 - 2.44596i) q^{8} +(-0.144430 + 2.99652i) q^{9} +O(q^{10})$	\(q+(0.246732 + 1.39252i) q^{2} +(-1.19490 - 1.25388i) q^{3} +(-1.87825 + 0.687161i) q^{4} +(0.359364 + 1.80664i) q^{5} +(1.45124 - 1.97330i) q^{6} +(-3.05294 + 1.26457i) q^{7} +(-1.42031 - 2.44596i) q^{8} +(-0.144430 + 2.99652i) q^{9} +(-2.42713 + 0.946180i) q^{10} +(-2.05692 + 3.07840i) q^{11} +(3.10593 + 1.53401i) q^{12} +(0.534830 + 0.106384i) q^{13} +(-2.51420 - 3.93929i) q^{14} +(1.83591 - 2.60936i) q^{15} +(3.05562 - 2.58132i) q^{16} +(-0.827691 + 0.827691i) q^{17} +(-4.20836 + 0.538216i) q^{18} +(-6.44815 - 1.28262i) q^{19} +(-1.91643 - 3.14638i) q^{20} +(5.23358 + 2.31699i) q^{21} +(-4.79426 - 2.10477i) q^{22} +(7.47552 + 3.09646i) q^{23} +(-1.36981 + 4.70358i) q^{24} +(1.48458 - 0.614932i) q^{25} +(-0.0161829 + 0.771012i) q^{26} +(3.92986 - 3.39944i) q^{27} +(4.86522 - 4.47304i) q^{28} +(-0.420063 + 0.280677i) q^{29} +(4.08657 + 1.91274i) q^{30} +2.79490 q^{31} +(4.34846 + 3.61813i) q^{32} +(6.31776 - 1.09925i) q^{33} +(-1.35680 - 0.948362i) q^{34} +(-3.38175 - 5.06114i) q^{35} +(-1.78782 - 5.72745i) q^{36} +(-0.213702 - 1.07435i) q^{37} +(0.195109 - 9.29567i) q^{38} +(-0.505675 - 0.797731i) q^{39} +(3.90857 - 3.44499i) q^{40} +(-3.82720 + 9.23967i) q^{41} +(-1.93517 + 7.85956i) q^{42} +(3.05140 - 4.56674i) q^{43} +(1.74805 - 7.19543i) q^{44} +(-5.46555 + 0.815908i) q^{45} +(-2.46745 + 11.1738i) q^{46} +(7.47207 + 7.47207i) q^{47} +(-6.88782 - 0.746967i) q^{48} +(2.77158 - 2.77158i) q^{49} +(1.22260 + 1.91559i) q^{50} +(2.02683 + 0.0488175i) q^{51} +(-1.07765 + 0.167698i) q^{52} +(-2.02433 - 1.35261i) q^{53} +(5.70343 + 4.63367i) q^{54} +(-6.30076 - 2.60986i) q^{55} +(7.42922 + 5.67129i) q^{56} +(6.09665 + 9.61781i) q^{57} +(-0.494492 - 0.515695i) q^{58} +(-10.5918 + 2.10685i) q^{59} +(-1.65524 + 6.16258i) q^{60} +(0.153998 - 0.102898i) q^{61} +(0.689591 + 3.89196i) q^{62} +(-3.34838 - 9.33085i) q^{63} +(-3.96543 + 6.94805i) q^{64} +1.00448i q^{65} +(3.08952 + 8.52642i) q^{66} +(1.39419 + 2.08655i) q^{67} +(0.985851 - 2.12337i) q^{68} +(-5.04991 - 13.0734i) q^{69} +(6.21338 - 5.95791i) q^{70} +(-5.26483 - 12.7104i) q^{71} +(7.53450 - 3.90273i) q^{72} +(-3.57907 + 8.64064i) q^{73} +(1.44333 - 0.562662i) q^{74} +(-2.54497 - 1.12670i) q^{75} +(12.9926 - 2.02185i) q^{76} +(2.38681 - 11.9993i) q^{77} +(0.986094 - 0.900991i) q^{78} +(9.99933 + 9.99933i) q^{79} +(5.76160 + 4.59279i) q^{80} +(-8.95828 - 0.865574i) q^{81} +(-13.8108 - 3.04974i) q^{82} +(-1.76923 + 8.89454i) q^{83} +(-11.4221 - 0.755565i) q^{84} +(-1.79279 - 1.19790i) q^{85} +(7.11217 + 3.12238i) q^{86} +(0.853868 + 0.191327i) q^{87} +(10.4511 + 0.658856i) q^{88} +(-4.17398 - 10.0769i) q^{89} +(-2.48470 - 7.40960i) q^{90} +(-1.76734 + 0.351545i) q^{91} +(-16.1686 - 0.679033i) q^{92} +(-3.33962 - 3.50447i) q^{93} +(-8.56143 + 12.2486i) q^{94} -12.1104i q^{95} +(-0.659276 - 9.77575i) q^{96} -15.1389i q^{97} +(4.54333 + 3.17565i) q^{98} +(-8.92742 - 6.60822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$	0.246732	+	1.39252i	0.174466	+	0.984663i
$2$	0.246732	+	1.39252i	0.174466	+	0.984663i
$3$	−1.19490	−	1.25388i	−0.689876	−	0.723928i
$3$	−1.19490	−	1.25388i	−0.689876	−	0.723928i
$4$	−1.87825	+	0.687161i	−0.939123	+	0.343580i
$5$	0.359364	+	1.80664i	0.160712	+	0.807956i	0.974080	+	0.226205i	$0.0726320\pi$
$5$	0.359364	+	1.80664i	0.160712	+	0.807956i	−0.813367	+	0.581751i	$0.802368\pi$
$6$	1.45124	−	1.97330i	0.592465	−	0.805596i
$7$	−3.05294	+	1.26457i	−1.15390	+	0.477963i	−0.875841	−	0.482600i	$-0.839693\pi$
$7$	−3.05294	+	1.26457i	−1.15390	+	0.477963i	−0.278063	+	0.960563i	$0.589693\pi$
$8$	−1.42031	−	2.44596i	−0.502156	−	0.864777i
$9$	−0.144430	+	2.99652i	−0.0481433	+	0.998840i
$10$	−2.42713	+	0.946180i	−0.767525	+	0.299208i
$11$	−2.05692	+	3.07840i	−0.620185	+	0.928173i	0.379810	+	0.925065i	$0.375989\pi$
$11$	−2.05692	+	3.07840i	−0.620185	+	0.928173i	−0.999995	+	0.00310847i	$0.999011\pi$
$12$	3.10593	+	1.53401i	0.896606	+	0.442830i
$13$	0.534830	+	0.106384i	0.148335	+	0.0295057i	0.268699	−	0.963224i	$-0.413406\pi$
$13$	0.534830	+	0.106384i	0.148335	+	0.0295057i	−0.120364	+	0.992730i	$0.538406\pi$
$14$	−2.51420	−	3.93929i	−0.671949	−	1.05282i
$15$	1.83591	−	2.60936i	0.474030	−	0.673733i
$16$	3.05562	−	2.58132i	0.763905	−	0.645329i
$17$	−0.827691	+	0.827691i	−0.200745	+	0.200745i	−0.800319	−	0.599574i	$-0.795337\pi$
$17$	−0.827691	+	0.827691i	−0.200745	+	0.200745i	0.599574	+	0.800319i	$0.295337\pi$
$18$	−4.20836	+	0.538216i	−0.991921	+	0.126859i
$19$	−6.44815	−	1.28262i	−1.47931	−	0.294253i	−0.611536	−	0.791216i	$-0.709448\pi$
$19$	−6.44815	−	1.28262i	−1.47931	−	0.294253i	−0.867771	+	0.496964i	$0.834448\pi$
$20$	−1.91643	−	3.14638i	−0.428527	−	0.703552i
$21$	5.23358	+	2.31699i	1.14206	+	0.505609i
$22$	−4.79426	−	2.10477i	−1.02214	−	0.448739i
$23$	7.47552	+	3.09646i	1.55875	+	0.645657i	0.984872	−	0.173281i	$-0.0554368\pi$
$23$	7.47552	+	3.09646i	1.55875	+	0.645657i	0.573882	+	0.818938i	$0.305437\pi$
$24$	−1.36981	+	4.70358i	−0.279611	+	0.960113i
$25$	1.48458	−	0.614932i	0.296916	−	0.122986i
$26$	−0.0161829	+	0.771012i	−0.00317373	+	0.151208i
$27$	3.92986	−	3.39944i	0.756301	−	0.654223i
$28$	4.86522	−	4.47304i	0.919440	−	0.845325i
$29$	−0.420063	+	0.280677i	−0.0780037	+	0.0521204i	−0.593961	−	0.804494i	$-0.702436\pi$
$29$	−0.420063	+	0.280677i	−0.0780037	+	0.0521204i	0.515957	+	0.856615i	$0.327436\pi$
$30$	4.08657	+	1.91274i	0.746102	+	0.349217i
$31$	2.79490			0.501978			0.250989	−	0.967990i	$-0.419244\pi$
$31$	2.79490			0.501978			0.250989	+	0.967990i	$0.419244\pi$
$32$	4.34846	+	3.61813i	0.768707	+	0.639601i
$33$	6.31776	−	1.09925i	1.09978	−	0.191354i
$34$	−1.35680	−	0.948362i	−0.232689	−	0.162643i
$35$	−3.38175	−	5.06114i	−0.571619	−	0.855489i
$36$	−1.78782	−	5.72745i	−0.297970	−	0.954575i
$37$	−0.213702	−	1.07435i	−0.0351323	−	0.176622i	0.959235	−	0.282609i	$-0.0911999\pi$
$37$	−0.213702	−	1.07435i	−0.0351323	−	0.176622i	−0.994368	+	0.105987i	$0.966200\pi$
$38$	0.195109	−	9.29567i	0.0316508	−	1.50796i
$39$	−0.505675	−	0.797731i	−0.0809728	−	0.127739i
$40$	3.90857	−	3.44499i	0.617999	−	0.544700i
$41$	−3.82720	+	9.23967i	−0.597708	+	1.44299i	0.278204	+	0.960522i	$0.410261\pi$
$41$	−3.82720	+	9.23967i	−0.597708	+	1.44299i	−0.875911	+	0.482472i	$0.839739\pi$
$42$	−1.93517	+	7.85956i	−0.298603	+	1.21276i
$43$	3.05140	−	4.56674i	0.465334	−	0.696421i	−0.522377	−	0.852715i	$-0.674955\pi$
$43$	3.05140	−	4.56674i	0.465334	−	0.696421i	0.987711	+	0.156293i	$0.0499546\pi$
$44$	1.74805	−	7.19543i	0.263528	−	1.08475i
$45$	−5.46555	+	0.815908i	−0.814756	+	0.121628i
$46$	−2.46745	+	11.1738i	−0.363805	+	1.64749i
$47$	7.47207	+	7.47207i	1.08991	+	1.08991i	0.995537	+	0.0943761i	$0.0300856\pi$
$47$	7.47207	+	7.47207i	1.08991	+	1.08991i	0.0943761	+	0.995537i	$0.469914\pi$
$48$	−6.88782	−	0.746967i	−0.994171	−	0.107815i
$49$	2.77158	−	2.77158i	0.395940	−	0.395940i
$50$	1.22260	+	1.91559i	0.172902	+	0.270905i
$51$	2.02683	+	0.0488175i	0.283813	+	0.00683582i
$52$	−1.07765	+	0.167698i	−0.149443	+	0.0232556i
$53$	−2.02433	−	1.35261i	−0.278063	−	0.185796i	0.408717	−	0.912661i	$-0.365976\pi$
$53$	−2.02433	−	1.35261i	−0.278063	−	0.185796i	−0.686780	+	0.726866i	$0.740976\pi$
$54$	5.70343	+	4.63367i	0.776139	+	0.630562i
$55$	−6.30076	−	2.60986i	−0.849594	−	0.351913i
$56$	7.42922	+	5.67129i	0.992771	+	0.757858i
$57$	6.09665	+	9.61781i	0.807520	+	1.27391i
$58$	−0.494492	−	0.515695i	−0.0649300	−	0.0677141i
$59$	−10.5918	+	2.10685i	−1.37894	+	0.274288i	−0.828220	−	0.560403i	$-0.810646\pi$
$59$	−10.5918	+	2.10685i	−1.37894	+	0.274288i	−0.550719	+	0.834691i	$0.685646\pi$
$60$	−1.65524	+	6.16258i	−0.213691	+	0.795586i
$61$	0.153998	−	0.102898i	0.0197175	−	0.0131748i	−0.545672	−	0.837999i	$-0.683726\pi$
$61$	0.153998	−	0.102898i	0.0197175	−	0.0131748i	0.565390	+	0.824824i	$0.308726\pi$
$62$	0.689591	+	3.89196i	0.0875782	+	0.494280i
$63$	−3.34838	−	9.33085i	−0.421856	−	1.17558i
$64$	−3.96543	+	6.94805i	−0.495678	+	0.868506i
$65$			1.00448i			0.124590i
$66$	3.08952	+	8.52642i	0.380294	+	1.04953i
$67$	1.39419	+	2.08655i	0.170327	+	0.254913i	0.906806	−	0.421548i	$-0.138513\pi$
$67$	1.39419	+	2.08655i	0.170327	+	0.254913i	−0.736479	+	0.676460i	$0.763513\pi$
$68$	0.985851	−	2.12337i	0.119552	−	0.257496i
$69$	−5.04991	−	13.0734i	−0.607937	−	1.57385i
$70$	6.21338	−	5.95791i	0.742640	−	0.712106i
$71$	−5.26483	−	12.7104i	−0.624820	−	1.50845i	−0.845981	−	0.533213i	$-0.820985\pi$
$71$	−5.26483	−	12.7104i	−0.624820	−	1.50845i	0.221161	−	0.975237i	$-0.429015\pi$
$72$	7.53450	−	3.90273i	0.887950	−	0.459941i
$73$	−3.57907	+	8.64064i	−0.418899	+	1.01131i	0.563769	+	0.825933i	$0.309351\pi$
$73$	−3.57907	+	8.64064i	−0.418899	+	1.01131i	−0.982667	+	0.185378i	$0.940649\pi$
$74$	1.44333	−	0.562662i	0.167784	−	0.0654081i
$75$	−2.54497	−	1.12670i	−0.293868	−	0.130100i
$76$	12.9926	−	2.02185i	1.49035	−	0.231922i
$77$	2.38681	−	11.9993i	0.272002	−	1.36745i
$78$	0.986094	−	0.900991i	0.111653	−	0.102017i
$79$	9.99933	+	9.99933i	1.12501	+	1.12501i	0.990976	+	0.134036i	$0.0427939\pi$
$79$	9.99933	+	9.99933i	1.12501	+	1.12501i	0.134036	+	0.990976i	$0.457206\pi$
$80$	5.76160	+	4.59279i	0.644166	+	0.513489i
$81$	−8.95828	−	0.865574i	−0.995364	−	0.0961749i
$82$	−13.8108	−	3.04974i	−1.52514	−	0.336787i
$83$	−1.76923	+	8.89454i	−0.194199	+	0.976302i	0.753576	+	0.657361i	$0.228327\pi$
$83$	−1.76923	+	8.89454i	−0.194199	+	0.976302i	−0.947775	+	0.318941i	$0.896673\pi$
$84$	−11.4221	−	0.755565i	−1.24625	−	0.0824389i
$85$	−1.79279	−	1.19790i	−0.194455	−	0.129931i
$86$	7.11217	+	3.12238i	0.766925	+	0.336695i
$87$	0.853868	+	0.191327i	0.0915442	+	0.0205124i
$88$	10.4511	+	0.658856i	1.11409	+	0.0702343i
$89$	−4.17398	−	10.0769i	−0.442441	−	1.06815i	−0.975090	−	0.221810i	$-0.928803\pi$
$89$	−4.17398	−	10.0769i	−0.442441	−	1.06815i	0.532649	−	0.846336i	$-0.321197\pi$
$90$	−2.48470	−	7.40960i	−0.261910	−	0.781040i
$91$	−1.76734	+	0.351545i	−0.185267	+	0.0368519i
$92$	−16.1686	−	0.679033i	−1.68570	−	0.0707941i
$93$	−3.33962	−	3.50447i	−0.346303	−	0.363396i
$94$	−8.56143	+	12.2486i	−0.883044	+	1.26335i
$95$		−	12.1104i		−	1.24250i
$96$	−0.659276	−	9.77575i	−0.0672871	−	0.997734i
$97$		−	15.1389i		−	1.53712i	−0.639777	−	0.768561i	$-0.720973\pi$
$97$		−	15.1389i		−	1.53712i	0.639777	−	0.768561i	$-0.279027\pi$
$98$	4.54333	+	3.17565i	0.458945	+	0.320789i
$99$	−8.92742	−	6.60822i	−0.897239	−	0.664152i
$100$	−2.36585	+	2.17514i	−0.236585	+	0.217514i
$101$	4.20479	−	0.836385i	0.418392	−	0.0832234i	0.0185952	−	0.999827i	$-0.494081\pi$
$101$	4.20479	−	0.836385i	0.418392	−	0.0832234i	0.399797	+	0.916604i	$0.369081\pi$
$102$	0.432105	+	2.83446i	0.0427848	+	0.280653i
$103$	−3.14426	−	7.59092i	−0.309813	−	0.747956i	−0.999711	−	0.0240486i	$-0.992344\pi$
$103$	−3.14426	−	7.59092i	−0.309813	−	0.747956i	0.689897	−	0.723907i	$-0.257656\pi$
$104$	−0.499414	−	1.45927i	−0.0489716	−	0.143093i
$105$	−2.30522	+	10.2879i	−0.224966	+	1.00399i
$106$	1.38408	−	3.15266i	0.134434	−	0.306213i
$107$	2.57078	+	1.71774i	0.248527	+	0.166060i	0.673594	−	0.739101i	$-0.264750\pi$
$107$	2.57078	+	1.71774i	0.248527	+	0.166060i	−0.425067	+	0.905162i	$0.639750\pi$
$108$	−5.04527	+	9.08544i	−0.485482	+	0.874247i
$109$	−0.569133	+	2.86122i	−0.0545130	+	0.274056i	−0.998422	−	0.0561491i	$-0.982118\pi$
$109$	−0.569133	+	2.86122i	−0.0545130	+	0.274056i	0.943909	+	0.330205i	$0.107118\pi$
$110$	2.07969	−	9.41790i	0.198291	−	0.897961i
$111$	−1.09175	+	1.55170i	−0.103625	+	0.147281i
$112$	−6.06438	+	11.7447i	−0.573030	+	1.10977i
$113$	5.94703	+	5.94703i	0.559449	+	0.559449i	0.929151	−	0.369701i	$-0.120540\pi$
$113$	5.94703	+	5.94703i	0.559449	+	0.559449i	−0.369701	+	0.929151i	$0.620540\pi$
$114$	−11.8888	+	10.8627i	−1.11349	+	1.01739i
$115$	−2.90777	+	14.6184i	−0.271151	+	1.36317i
$116$	0.596111	−	0.815831i	0.0553475	−	0.0757480i
$117$	−0.396028	+	1.58726i	−0.0366128	+	0.146743i
$118$	−5.54718	−	14.2295i	−0.510659	−	1.30994i
$119$	1.48022	−	3.57357i	0.135692	−	0.327589i
$120$	−8.98995	−	0.784461i	−0.820666	−	0.0716111i
$121$	−1.03611	−	2.50139i	−0.0941919	−	0.227399i
$122$	0.181285	+	0.189058i	0.0164128	+	0.0171165i
$123$	16.1586	−	6.24163i	1.45697	−	0.562789i
$124$	−5.24951	+	1.92054i	−0.471420	+	0.172470i
$125$	6.76137	+	10.1191i	0.604756	+	0.905081i
$126$	12.1673	−	6.96492i	1.08395	−	0.620484i
$127$			22.0807i			1.95935i	0.200602	+	0.979673i	$0.435710\pi$
$127$			22.0807i			1.95935i	−0.200602	+	0.979673i	$0.564290\pi$
$128$	−10.6537	−	3.80765i	−0.941665	−	0.336552i
$129$	−9.37226	+	1.63071i	−0.825181	+	0.143576i
$130$	−1.39876	+	0.247837i	−0.122679	+	0.0217367i
$131$	−11.6039	+	7.75347i	−1.01384	+	0.677423i	−0.947296	−	0.320360i	$-0.896196\pi$
$131$	−11.6039	+	7.75347i	−1.01384	+	0.677423i	−0.0665400	+	0.997784i	$0.521196\pi$
$132$	−11.1110	+	6.40598i	−0.967084	+	0.557569i
$133$	21.3078	−	4.23839i	1.84762	−	0.367515i
$134$	−2.56158	+	2.45626i	−0.221287	+	0.212188i
$135$	7.55383	+	5.87822i	0.650131	+	0.505916i
$136$	3.20008	+	0.848919i	0.274404	+	0.0727942i
$137$	8.78236	+	3.63777i	0.750328	+	0.310796i	0.724875	−	0.688880i	$-0.241897\pi$
$137$	8.78236	+	3.63777i	0.750328	+	0.310796i	0.0254526	+	0.999676i	$0.491897\pi$
$138$	16.9590	−	10.2577i	1.44365	−	0.873197i
$139$	9.49037	+	6.34126i	0.804963	+	0.537859i	0.888625	−	0.458635i	$-0.151662\pi$
$139$	9.49037	+	6.34126i	0.804963	+	0.537859i	−0.0836617	+	0.996494i	$0.526662\pi$
$140$	9.82957	+	7.18227i	0.830750	+	0.607012i
$141$	0.440705	−	18.2974i	0.0371140	−	1.54092i
$142$	16.4006	−	10.4675i	1.37631	−	0.878411i
$143$	−1.42760	+	1.42760i	−0.119382	+	0.119382i
$144$	7.29364	+	9.52905i	0.607804	+	0.794087i
$145$	−0.658038	−	0.658038i	−0.0546471	−	0.0546471i
$146$	−12.9154	−	2.85202i	−1.06888	−	0.236035i
$147$	−6.78699	−	0.163469i	−0.559781	−	0.0134827i
$148$	1.13964	+	1.87105i	0.0936775	+	0.153799i
$149$	−4.81608	+	7.20777i	−0.394548	+	0.590484i	−0.974561	−	0.224124i	$-0.928048\pi$
$149$	−4.81608	+	7.20777i	−0.394548	+	0.590484i	0.580012	+	0.814608i	$0.303048\pi$
$150$	0.941030	−	3.82193i	0.0768348	−	0.312059i
$151$	1.60104	−	3.86526i	0.130291	−	0.314551i	−0.845249	−	0.534373i	$-0.820548\pi$
$151$	1.60104	−	3.86526i	0.130291	−	0.314551i	0.975540	+	0.219822i	$0.0705478\pi$
$152$	6.02116	+	17.5936i	0.488380	+	1.42703i
$153$	−2.36065	−	2.59974i	−0.190847	−	0.210176i
$154$	17.2982	+	0.363076i	1.39393	+	0.0292575i
$155$	1.00438	+	5.04938i	0.0806741	+	0.405576i
$156$	1.49795	+	1.15086i	0.119932	+	0.0921422i
$157$	−5.75579	−	8.61415i	−0.459362	−	0.687484i	0.527407	−	0.849613i	$-0.323164\pi$
$157$	−5.75579	−	8.61415i	−0.459362	−	0.687484i	−0.986770	+	0.162128i	$0.948164\pi$
$158$	−11.4572	+	16.3915i	−0.911482	+	1.30404i
$159$	0.722854	+	4.15450i	0.0573261	+	0.329473i
$160$	−4.97399	+	9.15635i	−0.393229	+	0.723873i
$161$	−26.7381			−2.10725
$162$	−1.00496	−	12.6882i	−0.0789574	−	0.996878i
$163$	0.602415	−	0.402521i	0.0471847	−	0.0315278i	−0.531754	−	0.846899i	$-0.678467\pi$
$163$	0.602415	−	0.402521i	0.0471847	−	0.0315278i	0.578939	+	0.815371i	$0.303467\pi$
$164$	0.839278	−	19.9843i	0.0655366	−	1.56051i
$165$	4.25632	+	11.0189i	0.331354	+	0.857822i
$166$	−12.8224	−	0.269132i	−0.995210	−	0.0208887i
$167$	3.14806	−	1.30397i	0.243604	−	0.100904i	−0.257541	−	0.966267i	$-0.582912\pi$
$167$	3.14806	−	1.30397i	0.243604	−	0.100904i	0.501145	+	0.865363i	$0.332912\pi$
$168$	−1.76606	−	16.0920i	−0.136254	−	1.24152i
$169$	−11.7357	−	4.86109i	−0.902747	−	0.373930i
$170$	1.22577	−	2.79206i	0.0940121	−	0.214141i
$171$	4.77469	−	19.1368i	0.365130	−	1.46343i
$172$	−2.59319	+	10.6743i	−0.197729	+	0.813905i
$173$	−0.0807891	−	0.0160700i	−0.00614228	−	0.00122178i	0.192018	−	0.981391i	$-0.438497\pi$
$173$	−0.0807891	−	0.0160700i	−0.00614228	−	0.00122178i	−0.198161	+	0.980170i	$0.563497\pi$
$174$	−0.0557514	+	1.23624i	−0.00422650	+	0.0937189i
$175$	−3.75471	+	3.75471i	−0.283829	+	0.283829i
$176$	1.66115	+	14.7160i	0.125214	+	1.10926i
$177$	15.2979	+	10.7634i	1.14986	+	0.809028i
$178$	13.0024	−	8.29865i	0.974573	−	0.622010i
$179$	15.2598	+	3.03535i	1.14057	+	0.226873i	0.729005	−	0.684508i	$-0.239983\pi$
$179$	15.2598	+	3.03535i	1.14057	+	0.226873i	0.411563	+	0.911381i	$0.364983\pi$
$180$	9.70499	−	5.28819i	0.723367	−	0.394158i
$181$	9.09877	−	13.6173i	0.676306	−	1.01216i	−0.321561	−	0.946889i	$-0.604207\pi$
$181$	9.09877	−	13.6173i	0.676306	−	1.01216i	0.997867	−	0.0652752i	$-0.0207925\pi$
$182$	−0.925594	−	2.37432i	−0.0686096	−	0.175996i
$183$	−0.313035	−	0.0701422i	−0.0231402	−	0.00518506i
$184$	−3.04376	−	22.6828i	−0.224389	−	1.67220i
$185$	1.86417	−	0.772166i	0.137057	−	0.0567708i
$186$	4.05606	−	5.51517i	0.297405	−	0.404392i
$187$	−0.845470	−	4.25046i	−0.0618269	−	0.310825i
$188$	−19.1689	−	8.89987i	−1.39804	−	0.649090i
$189$	−7.69879	+	15.3479i	−0.560005	+	1.11640i
$190$	16.8641	−	2.98804i	1.22345	−	0.216775i
$191$	−1.98808			−0.143852			−0.0719260	−	0.997410i	$-0.522915\pi$
$191$	−1.98808			−0.143852			−0.0719260	+	0.997410i	$0.522915\pi$
$192$	13.4503	−	3.33005i	0.970692	−	0.240326i
$193$	11.9983			0.863656			0.431828	−	0.901956i	$-0.357869\pi$
$193$	11.9983			0.863656			0.431828	+	0.901956i	$0.357869\pi$
$194$	21.0813	−	3.73525i	1.51355	−	0.268175i
$195$	1.25949	−	1.20025i	0.0901943	−	0.0859517i
$196$	−3.30119	+	7.11023i	−0.235799	+	0.507873i
$197$	0.501219	+	2.51980i	0.0357103	+	0.179528i	0.994524	−	0.104508i	$-0.0333266\pi$
$197$	0.501219	+	2.51980i	0.0357103	+	0.179528i	−0.958814	+	0.284036i	$0.908327\pi$
$198$	6.99943	−	14.0621i	0.497428	−	0.999350i
$199$	1.03878	−	0.430275i	0.0736368	−	0.0305014i	−0.345561	−	0.938396i	$-0.612311\pi$
$199$	1.03878	−	0.430275i	0.0736368	−	0.0305014i	0.419198	+	0.907895i	$0.362311\pi$
$200$	−3.61266	−	2.75782i	−0.255454	−	0.195007i
$201$	0.950368	−	4.24136i	0.0670338	−	0.299163i
$202$	2.20214	+	5.64891i	0.154942	+	0.397456i
$203$	0.927492	−	1.38809i	0.0650972	−	0.0974248i
$204$	−3.84044	+	1.30107i	−0.268884	+	0.0910931i
$205$	−18.0682	−	3.59398i	−1.26193	−	0.251014i
$206$	9.79475	−	6.25139i	0.682433	−	0.435555i
$207$	−10.3583	+	21.9533i	−0.719952	+	1.52586i
$208$	1.90885	−	1.05549i	0.132355	−	0.0731854i
$209$	17.2118	−	17.2118i	1.19056	−	1.19056i
$210$	−14.8949	−	0.671723i	−1.02784	−	0.0463533i
$211$	14.1029	+	2.80524i	0.970885	+	0.193121i	0.654960	−	0.755663i	$-0.272685\pi$
$211$	14.1029	+	2.80524i	0.970885	+	0.193121i	0.315924	+	0.948784i	$0.397685\pi$
$212$	4.73165	+	1.14950i	0.324971	+	0.0789480i
$213$	−9.64640	+	21.7891i	−0.660961	+	1.49297i
$214$	−1.75770	+	4.00370i	−0.120154	+	0.273687i
$215$	9.34703	+	3.87167i	0.637462	+	0.264046i
$216$	−13.8965	−	4.78400i	−0.945539	−	0.325510i
$217$	−8.53266	+	3.53434i	−0.579235	+	0.239927i
$218$	−4.12475	−	0.0865751i	−0.279363	−	0.00586361i
$219$	15.1110	−	5.83698i	1.02110	−	0.394426i
$220$	13.6278	+	0.572324i	0.918784	+	0.0385861i
$221$	−0.530727	+	0.354621i	−0.0357006	+	0.0238544i
$222$	−2.43015	−	1.13744i	−0.163101	−	0.0763401i
$223$	17.0025			1.13857			0.569286	−	0.822140i	$-0.307220\pi$
$223$	17.0025			1.13857			0.569286	+	0.822140i	$0.307220\pi$
$224$	−17.8510	−	5.54701i	−1.19272	−	0.370625i
$225$	1.62824	+	4.53738i	0.108549	+	0.302492i
$226$	−6.81406	+	9.74870i	−0.453264	+	0.648474i
$227$	−9.29893	−	13.9168i	−0.617192	−	0.923693i	0.382808	−	0.923828i	$-0.374957\pi$
$227$	−9.29893	−	13.9168i	−0.617192	−	0.923693i	−1.00000		0.000135074i	$0.999957\pi$
$228$	−18.0600	−	13.8752i	−1.19605	−	0.918910i
$229$	−1.72964	−	8.69549i	−0.114298	−	0.574614i	−0.994909	−	0.100775i	$-0.967868\pi$
$229$	−1.72964	−	8.69549i	−0.114298	−	0.574614i	0.880611	−	0.473839i	$-0.157132\pi$
$230$	−21.0739	−	0.442324i	−1.38957	−	0.0291660i
$231$	−17.8977	+	11.3452i	−1.17758	+	0.746459i
$232$	1.28314	+	0.628807i	0.0842425	+	0.0412832i
$233$	4.61203	−	11.1344i	0.302144	−	0.729441i	−0.697770	−	0.716322i	$-0.745824\pi$
$233$	4.61203	−	11.1344i	0.302144	−	0.729441i	0.999914	−	0.0131185i	$-0.00417587\pi$
$234$	−2.30802	−	0.159850i	−0.150880	−	0.0104497i
$235$	−10.8142	+	16.1846i	−0.705439	+	1.05576i
$236$	18.4463	−	11.2355i	1.20075	−	0.731367i
$237$	0.589764	−	24.4862i	0.0383093	−	1.59055i
$238$	5.34150	+	1.17953i	0.346238	+	0.0764575i
$239$	12.7729	+	12.7729i	0.826209	+	0.826209i	0.986990	−	0.160781i	$-0.0514014\pi$
$239$	12.7729	+	12.7729i	0.826209	+	0.826209i	−0.160781	+	0.986990i	$0.551401\pi$
$240$	−1.12573	−	12.7123i	−0.0726655	−	0.820573i
$241$	−1.12018	+	1.12018i	−0.0721574	+	0.0721574i	−0.742264	−	0.670107i	$-0.766248\pi$
$241$	−1.12018	+	1.12018i	−0.0721574	+	0.0721574i	0.670107	+	0.742264i	$0.266248\pi$
$242$	3.22761	−	2.05998i	0.207478	−	0.132421i
$243$	9.61892	+	12.2669i	0.617054	+	0.786921i
$244$	−0.218539	+	0.299090i	−0.0139905	+	0.0191473i
$245$	6.00326	+	4.01125i	0.383534	+	0.256269i
$246$	12.6785	+	20.9612i	0.808349	+	1.33643i
$247$	−3.31221	−	1.37196i	−0.210751	−	0.0872960i
$248$	−3.96963	−	6.83620i	−0.252072	−	0.434099i
$249$	13.2667	−	8.40967i	0.840745	−	0.532941i
$250$	−12.4229	+	11.9121i	−0.785691	+	0.753387i
$251$	4.95413	−	0.985437i	0.312702	−	0.0622002i	−0.0362446	−	0.999343i	$-0.511540\pi$
$251$	4.95413	−	0.985437i	0.312702	−	0.0622002i	0.348946	+	0.937143i	$0.386540\pi$
$252$	12.7009	+	15.2248i	0.800080	+	0.959070i
$253$	−24.9087	+	16.6435i	−1.56600	+	1.04637i
$254$	−30.7479	+	5.44802i	−1.92930	+	0.341839i
$255$	0.640175	+	3.67931i	0.0400893	+	0.230407i
$256$	2.67362	−	15.7750i	0.167101	−	0.985940i
$257$		−	21.3362i		−	1.33092i	−0.746435	−	0.665458i	$-0.768236\pi$
$257$		−	21.3362i		−	1.33092i	0.746435	−	0.665458i	$-0.231764\pi$
$258$	−4.58324	−	12.6487i	−0.285340	−	0.787477i
$259$	2.01101	+	3.00969i	0.124958	+	0.187013i
$260$	−0.690238	−	1.88666i	−0.0428068	−	0.117006i
$261$	−0.780385	−	1.29926i	−0.0483046	−	0.0804225i
$262$	−13.6599	−	14.2457i	−0.843914	−	0.880099i
$263$	1.14122	+	2.75514i	0.0703705	+	0.169889i	0.955151	−	0.296118i	$-0.0956921\pi$
$263$	1.14122	+	2.75514i	0.0703705	+	0.169889i	−0.884781	+	0.466007i	$0.845692\pi$
$264$	−11.6619	−	13.8917i	−0.717741	−	0.854976i
$265$	1.71622	−	4.14332i	0.105426	−	0.254522i
$266$	11.1594	+	28.6259i	0.684225	+	1.75517i
$267$	−7.64770	+	17.2745i	−0.468032	+	1.05718i
$268$	−4.05242	−	2.96102i	−0.247541	−	0.180873i
$269$	−2.86161	+	14.3863i	−0.174476	+	0.877148i	0.790026	+	0.613073i	$0.210067\pi$
$269$	−2.86161	+	14.3863i	−0.174476	+	0.877148i	−0.964502	+	0.264075i	$0.914933\pi$
$270$	−6.32178	+	11.9692i	−0.384731	+	0.728425i
$271$	−14.9476	−	14.9476i	−0.907999	−	0.907999i	0.0881113	−	0.996111i	$-0.471917\pi$
$271$	−14.9476	−	14.9476i	−0.907999	−	0.907999i	−0.996111	+	0.0881113i	$0.971917\pi$
$272$	−0.392577	+	4.66564i	−0.0238035	+	0.282896i
$273$	2.55258	+	1.79597i	0.154489	+	0.108697i
$274$	−2.89880	+	13.1272i	−0.175123	+	0.793044i
$275$	−1.16065	+	5.83499i	−0.0699900	+	0.351863i
$276$	18.4685	+	21.0849i	1.11167	+	1.26916i
$277$	0.819369	+	0.547485i	0.0492311	+	0.0328952i	0.579942	−	0.814658i	$-0.303075\pi$
$277$	0.819369	+	0.547485i	0.0492311	+	0.0328952i	−0.530711	+	0.847553i	$0.678075\pi$
$278$	−6.48878	+	14.7802i	−0.389171	+	0.886456i
$279$	−0.403667	+	8.37497i	−0.0241669	+	0.501396i
$280$	−7.57621	+	15.4600i	−0.452765	+	0.923912i
$281$	−5.35268	−	12.9225i	−0.319314	−	0.770893i	−0.999291	−	0.0376590i	$-0.988010\pi$
$281$	−5.35268	−	12.9225i	−0.319314	−	0.770893i	0.679976	−	0.733234i	$-0.261990\pi$
$282$	25.5884	−	3.90088i	1.52376	−	0.232294i
$283$	−2.79329	+	0.555619i	−0.166044	+	0.0330281i	−0.277412	−	0.960751i	$-0.589477\pi$
$283$	−2.79329	+	0.555619i	−0.166044	+	0.0330281i	0.111368	+	0.993779i	$0.464477\pi$
$284$	18.6228	+	20.2555i	1.10506	+	1.20194i
$285$	−15.1850	+	14.4708i	−0.899484	+	0.857174i
$286$	−2.34020	−	1.63573i	−0.138379	−	0.0967227i
$287$		−	33.0480i		−	1.95076i
$288$	−11.4699	+	12.5077i	−0.675868	+	0.737023i
$289$			15.6299i			0.919403i
$290$	0.753975	−	1.07869i	0.0442749	−	0.0633431i
$291$	−18.9823	+	18.0895i	−1.11276	+	1.06042i
$292$	0.784866	−	18.6887i	0.0459308	−	1.09367i
$293$	28.5066	−	5.67031i	1.66537	−	0.331263i	0.729602	−	0.683872i	$-0.239706\pi$
$293$	28.5066	−	5.67031i	1.66537	−	0.331263i	0.935771	+	0.352609i	$0.114706\pi$
$294$	−1.44693	−	9.49137i	−0.0843869	−	0.553548i
$295$	−7.61264	−	18.3785i	−0.443225	−	1.07004i
$296$	−2.32429	+	2.04862i	−0.135097	+	0.119074i
$297$	2.38145	+	19.0901i	0.138185	+	1.10772i
$298$	−11.2253	−	4.92812i	−0.650263	−	0.285478i
$299$	3.66872	+	2.45136i	0.212168	+	0.141766i
$300$	5.55431	+	0.367414i	0.320678	+	0.0212127i
$301$	−3.54078	+	17.8007i	−0.204087	+	1.02602i
$302$	5.77750	+	1.27581i	0.332458	+	0.0734145i
$303$	−6.07303	−	4.27291i	−0.348886	−	0.245472i
$304$	−23.0139	+	12.7255i	−1.31994	+	0.729859i
$305$	0.241242	+	0.241242i	0.0138135	+	0.0138135i
$306$	3.03775	−	3.92870i	0.173657	−	0.224589i
$307$	2.86761	−	14.4164i	0.163663	−	0.822790i	−0.808502	−	0.588493i	$-0.799721\pi$
$307$	2.86761	−	14.4164i	0.163663	−	0.822790i	0.972165	−	0.234296i	$-0.0752786\pi$
$308$	3.76244	+	24.1778i	0.214385	+	1.37766i
$309$	−5.76103	+	13.0129i	−0.327733	+	0.740279i
$310$	−6.78357	+	2.64448i	−0.385281	+	0.150196i
$311$	1.95981	−	4.73141i	0.111131	−	0.268294i	−0.858523	−	0.512775i	$-0.828618\pi$
$311$	1.95981	−	4.73141i	0.111131	−	0.268294i	0.969654	+	0.244481i	$0.0786176\pi$
$312$	−1.23300	+	2.36989i	−0.0698049	+	0.134168i
$313$	−0.752332	−	1.81629i	−0.0425243	−	0.102663i	0.901190	−	0.433424i	$-0.142695\pi$
$313$	−0.752332	−	1.81629i	−0.0425243	−	0.102663i	−0.943715	+	0.330761i	$0.892695\pi$
$314$	10.5753	−	10.1405i	0.596797	−	0.572260i
$315$	15.6542	−	9.40250i	0.882017	−	0.529771i
$316$	−25.6524	−	11.9101i	−1.44306	−	0.669993i
$317$	6.37904	+	9.54690i	0.358282	+	0.536208i	0.966200	−	0.257792i	$-0.0829950\pi$
$317$	6.37904	+	9.54690i	0.358282	+	0.536208i	−0.607918	+	0.794000i	$0.707995\pi$
$318$	−5.60689	+	2.03164i	−0.314419	+	0.113929i
$319$		−	1.87045i		−	0.104725i
$320$	−13.9777	−	4.66724i	−0.781376	−	0.260907i
$321$	−0.917985	−	5.27598i	−0.0512369	−	0.294477i
$322$	−6.59714	−	37.2334i	−0.367644	−	2.07494i
$323$	6.39869	−	4.27547i	0.356033	−	0.237893i
$324$	17.4206	−	4.53002i	0.967814	−	0.251668i
$325$	0.859416	−	0.170948i	0.0476718	−	0.00948251i
$326$	0.709155	+	0.739562i	0.0392764	+	0.0409605i
$327$	4.26769	−	2.70525i	0.236004	−	0.149601i
$328$	28.0357	−	3.76205i	1.54801	−	0.207724i
$329$	−32.2607	−	13.3628i	−1.77859	−	0.736717i
$330$	−14.2939	+	8.64576i	−0.786855	+	0.475933i
$331$	−28.1107	−	18.7830i	−1.54510	−	1.03240i	−0.977962	−	0.208784i	$-0.933050\pi$
$331$	−28.1107	−	18.7830i	−1.54510	−	1.03240i	−0.567141	−	0.823621i	$-0.691950\pi$
$332$	−2.78892	−	17.9219i	−0.153062	−	0.983591i
$333$	3.25018	−	0.485193i	0.178109	−	0.0265884i
$334$	2.59254	+	4.06202i	0.141857	+	0.222264i
$335$	−3.26863	+	3.26863i	−0.178584	+	0.178584i
$336$	21.9727	−	6.42968i	1.19871	−	0.350768i
$337$	−2.58232	−	2.58232i	−0.140668	−	0.140668i	0.633266	−	0.773934i	$-0.281714\pi$
$337$	−2.58232	−	2.58232i	−0.140668	−	0.140668i	−0.773934	+	0.633266i	$0.781714\pi$
$338$	3.87361	−	17.5416i	0.210696	−	0.954140i
$339$	0.350758	−	14.5630i	0.0190505	−	0.790951i
$340$	4.19044	+	1.01802i	0.227259	+	0.0552099i
$341$	−5.74889	+	8.60382i	−0.311320	+	0.465923i
$342$	27.8265	+	1.92722i	1.50468	+	0.104212i
$343$	3.89538	−	9.40427i	0.210331	−	0.507783i
$344$	−15.5040	−	0.977398i	−0.835919	−	0.0526978i
$345$	21.8042	−	13.8215i	1.17390	−	0.744124i
$346$	0.00244452	−	0.116466i	0.000131418	−	0.00626124i
$347$	−5.96824	−	30.0043i	−0.320392	−	1.61072i	−0.719961	−	0.694015i	$-0.755840\pi$
$347$	−5.96824	−	30.0043i	−0.320392	−	1.61072i	0.399569	−	0.916703i	$-0.369160\pi$
$348$	−1.73525	+	0.227385i	−0.0930190	+	0.0121891i
$349$	6.31423	+	9.44991i	0.337993	+	0.505842i	0.961065	−	0.276322i	$-0.0891157\pi$
$349$	6.31423	+	9.44991i	0.337993	+	0.505842i	−0.623072	+	0.782164i	$0.714116\pi$
$350$	−6.15493	−	4.30211i	−0.328995	−	0.229958i
$351$	2.46345	−	1.40005i	0.131489	−	0.0747291i
$352$	−20.0825	+	5.94411i	−1.07040	+	0.316822i
$353$	−18.7391			−0.997379			−0.498690	−	0.866781i	$-0.666185\pi$
$353$	−18.7391			−0.997379			−0.498690	+	0.866781i	$0.666185\pi$
$354$	−11.2138	+	23.9584i	−0.596008	+	1.27337i
$355$	21.0712	−	14.0793i	1.11834	−	0.747254i
$356$	14.7642	+	16.0587i	0.782500	+	0.851107i
$357$	−6.24954	+	2.41404i	−0.330761	+	0.127764i
$358$	−0.461731	+	21.9985i	−0.0244032	+	1.16266i
$359$	−18.0775	+	7.48794i	−0.954094	+	0.395199i	−0.804768	−	0.593590i	$-0.797710\pi$
$359$	−18.0775	+	7.48794i	−0.954094	+	0.395199i	−0.149326	+	0.988788i	$0.547710\pi$
$360$	9.75846	+	12.2097i	0.514316	+	0.643506i
$361$	22.3798	+	9.27003i	1.17789	+	0.487896i
$362$	21.2073	+	9.31044i	1.11463	+	0.489346i
$363$	−1.89840	+	4.28807i	−0.0996400	+	0.225065i
$364$	3.07793	−	1.87473i	0.161327	−	0.0982627i
$365$	−16.8968	−	3.36097i	−0.884417	−	0.175921i
$366$	0.0204389	−	0.453215i	0.00106836	−	0.0236899i
$367$	−1.66204	+	1.66204i	−0.0867576	+	0.0867576i	−0.749154	−	0.662396i	$-0.769540\pi$
$367$	−1.66204	+	1.66204i	−0.0867576	+	0.0867576i	0.662396	+	0.749154i	$0.269540\pi$
$368$	30.8353	−	9.83507i	1.60740	−	0.512689i
$369$	−27.1341	−	12.8028i	−1.41255	−	0.666485i
$370$	1.53521	+	2.40539i	0.0798118	+	0.125050i
$371$	7.89063	+	1.56954i	0.409661	+	0.0814867i
$372$	8.68076	+	4.28739i	0.450077	+	0.222291i
$373$	3.60356	−	5.39311i	0.186585	−	0.279245i	−0.726370	−	0.687304i	$-0.758794\pi$
$373$	3.60356	−	5.39311i	0.186585	−	0.279245i	0.912956	+	0.408059i	$0.133794\pi$
$374$	5.71027	−	2.22606i	0.295271	−	0.115107i
$375$	4.60899	−	20.5693i	0.238007	−	1.06219i
$376$	7.66370	−	28.8890i	0.395225	−	1.48984i
$377$	−0.254522	+	0.105426i	−0.0131085	+	0.00542973i
$378$	−23.2719	−	6.93394i	−1.19697	−	0.356643i
$379$	0.395416	+	1.98789i	0.0203112	+	0.102111i	0.989611	−	0.143770i	$-0.0459226\pi$
$379$	0.395416	+	1.98789i	0.0203112	+	0.102111i	−0.969300	+	0.245881i	$0.920923\pi$
$380$	8.32182	+	22.7464i	0.426900	+	1.16687i
$381$	27.6866	−	26.3842i	1.41842	−	1.35170i
$382$	−0.490522	−	2.76844i	−0.0250973	−	0.141646i
$383$	−24.1070			−1.23181			−0.615905	−	0.787821i	$-0.711209\pi$
$383$	−24.1070			−1.23181			−0.615905	+	0.787821i	$0.711209\pi$
$384$	7.95580	+	17.9082i	0.405993	+	0.913876i
$385$	22.5362			1.14855
$386$	2.96037	+	16.7079i	0.150679	+	0.850410i
$387$	13.2436	+	9.80315i	0.673211	+	0.498322i
$388$	10.4029	+	28.4346i	0.528125	+	1.44355i
$389$	7.20317	+	36.2128i	0.365215	+	1.83606i	0.527802	+	0.849367i	$0.323016\pi$
$389$	7.20317	+	36.2128i	0.365215	+	1.83606i	−0.162587	+	0.986694i	$0.551984\pi$
$390$	1.98214	+	1.45774i	0.100369	+	0.0738154i
$391$	−8.75034	+	3.62451i	−0.442524	+	0.183299i
$392$	−10.7157	−	2.84266i	−0.541223	−	0.143576i
$393$	23.5874	+	5.28526i	1.18983	+	0.266606i
$394$	−3.38521	+	1.31967i	−0.170544	+	0.0664842i
$395$	−14.4718	+	21.6586i	−0.728157	+	1.08976i
$396$	21.3088	+	6.27730i	1.07081	+	0.315446i
$397$	30.1732	+	6.00182i	1.51435	+	0.301223i	0.881176	−	0.472788i	$-0.156752\pi$
$397$	30.1732	+	6.00182i	1.51435	+	0.301223i	0.633173	+	0.774011i	$0.281752\pi$
$398$	0.855467	+	1.34036i	0.0428807	+	0.0671860i
$399$	−30.7751	−	21.6530i	−1.54068	−	1.08400i
$400$	2.94897	−	5.71116i	0.147449	−	0.285558i
$401$	9.14394	−	9.14394i	0.456626	−	0.456626i	−0.440920	−	0.897546i	$-0.645348\pi$
$401$	9.14394	−	9.14394i	0.456626	−	0.456626i	0.897546	+	0.440920i	$0.145348\pi$
$402$	6.14068	+	0.276930i	0.306270	+	0.0138120i
$403$	1.49479	+	0.297333i	0.0744610	+	0.0148112i
$404$	−7.32290	+	4.46030i	−0.364328	+	0.221908i
$405$	−1.65550	−	16.4955i	−0.0822623	−	0.819667i
$406$	2.16179	+	0.949068i	0.107288	+	0.0471015i
$407$	3.74685	+	1.55200i	0.185725	+	0.0769296i
$408$	−2.75933	−	5.02689i	−0.136607	−	0.248868i
$409$	−25.5396	+	10.5789i	−1.26285	+	0.523091i	−0.910784	−	0.412883i	$-0.864522\pi$
$409$	−25.5396	+	10.5789i	−1.26285	+	0.523091i	−0.352069	+	0.935974i	$0.614522\pi$
$410$	0.546708	−	26.0471i	0.0270000	−	1.28637i
$411$	−5.93271	−	15.3588i	−0.292639	−	0.757594i
$412$	11.1219	+	12.0970i	0.547936	+	0.595977i
$413$	29.6720	−	19.8262i	1.46006	−	0.975583i
$414$	−33.1263	−	9.00760i	−1.62807	−	0.442699i
$415$	−16.7051			−0.820019
$416$	1.94078	+	2.39769i	0.0951544	+	0.117557i
$417$	−3.38886	−	19.4770i	−0.165953	−	0.953791i
$418$	28.2145	+	19.7211i	1.38002	+	0.964590i
$419$	−10.6745	−	15.9755i	−0.521484	−	0.780455i	0.473468	−	0.880811i	$-0.343002\pi$
$419$	−10.6745	−	15.9755i	−0.521484	−	0.780455i	−0.994952	+	0.100356i	$0.968002\pi$
$420$	−2.73965	−	20.9072i	−0.133681	−	1.02017i
$421$	4.39818	+	22.1111i	0.214354	+	1.07763i	0.926700	+	0.375802i	$0.122633\pi$
$421$	4.39818	+	22.1111i	0.214354	+	1.07763i	−0.712346	+	0.701829i	$0.752367\pi$
$422$	−0.426727	+	20.3308i	−0.0207727	+	0.989687i
$423$	−23.4694	+	21.3110i	−1.14112	+	1.03618i
$424$	−0.433257	+	6.87255i	−0.0210408	+	0.333761i
$425$	−0.719798	+	1.73775i	−0.0349153	+	0.0842931i
$426$	−32.7220	−	8.05676i	−1.58539	−	0.390351i
$427$	−0.340026	+	0.508885i	−0.0164550	+	0.0246267i
$428$	−6.00893	−	1.45980i	−0.290453	−	0.0705622i
$429$	3.49587	+	0.0842002i	0.168782	+	0.00406522i
$430$	−3.08518	+	13.9712i	−0.148780	+	0.673753i
$431$	−10.8612	−	10.8612i	−0.523167	−	0.523167i	0.395359	−	0.918527i	$-0.370620\pi$
$431$	−10.8612	−	10.8612i	−0.523167	−	0.523167i	−0.918527	+	0.395359i	$0.870620\pi$
$432$	3.23311	−	20.5316i	0.155553	−	0.987828i
$433$	6.03352	−	6.03352i	0.289952	−	0.289952i	−0.547109	−	0.837061i	$-0.684272\pi$
$433$	6.03352	−	6.03352i	0.289952	−	0.289952i	0.837061	+	0.547109i	$0.184272\pi$
$434$	−7.02694	−	11.0099i	−0.337304	−	0.528492i
$435$	−0.0388113	+	1.61139i	−0.00186086	+	0.0772603i
$436$	−0.897150	−	5.76517i	−0.0429657	−	0.276102i
$437$	−44.2317	−	29.5547i	−2.11589	−	1.41379i
$438$	11.8565	+	19.6022i	0.566525	+	0.936630i
$439$	12.3126	+	5.10006i	0.587650	+	0.243412i	0.656639	−	0.754205i	$-0.271977\pi$
$439$	12.3126	+	5.10006i	0.587650	+	0.243412i	−0.0689894	+	0.997617i	$0.521977\pi$
$440$	2.56543	+	19.1182i	0.122302	+	0.911425i
$441$	7.90480	+	8.70539i	0.376419	+	0.414543i
$442$	−0.624766	−	0.651554i	−0.0297171	−	0.0309913i
$443$	39.4508	−	7.84725i	1.87436	−	0.372834i	0.879658	−	0.475607i	$-0.157772\pi$
$443$	39.4508	−	7.84725i	1.87436	−	0.372834i	0.994705	+	0.102774i	$0.0327717\pi$
$444$	0.984319	−	3.66468i	0.0467137	−	0.173918i
$445$	16.7053	−	11.1622i	0.791909	−	0.529137i
$446$	4.19506	+	23.6764i	0.198642	+	1.12111i
$447$	14.7924	−	2.57378i	0.699657	−	0.121736i
$448$	3.31993	−	26.2266i	0.156852	−	1.23909i
$449$			6.27965i			0.296355i	0.988961	+	0.148178i	$0.0473407\pi$
$449$			6.27965i			0.296355i	−0.988961	+	0.148178i	$0.952659\pi$
$450$	−5.91668	+	3.38688i	−0.278915	+	0.159659i
$451$	−20.5712	−	30.7869i	−0.968659	−	1.44970i
$452$	−15.2565	−	7.08342i	−0.717608	−	0.333176i
$453$	−6.75966	+	2.61108i	−0.317597	+	0.122679i
$454$	17.0852	−	16.3827i	0.801847	−	0.768879i
$455$	−1.27023	−	3.06662i	−0.0595495	−	0.143765i
$456$	14.8656	−	28.5724i	0.696146	−	1.33803i
$457$	−3.03960	+	7.33824i	−0.142186	+	0.343268i	−0.978890	−	0.204388i	$-0.934480\pi$
$457$	−3.03960	+	7.33824i	−0.142186	+	0.343268i	0.836704	+	0.547656i	$0.184480\pi$
$458$	11.6819	−	4.55402i	0.545860	−	0.212795i
$459$	−0.439018	+	6.06640i	−0.0204916	+	0.283155i
$460$	−4.58366	−	29.4550i	−0.213714	−	1.37335i
$461$	−4.23707	+	21.3012i	−0.197340	+	0.992096i	0.747425	+	0.664347i	$0.231290\pi$
$461$	−4.23707	+	21.3012i	−0.197340	+	0.992096i	−0.944765	+	0.327749i	$0.893710\pi$
$462$	−20.2144	−	22.1237i	−0.940459	−	1.02929i
$463$	24.9132	+	24.9132i	1.15781	+	1.15781i	0.984945	+	0.172869i	$0.0553036\pi$
$463$	24.9132	+	24.9132i	1.15781	+	1.15781i	0.172869	+	0.984945i	$0.444696\pi$
$464$	−0.559036	+	1.94196i	−0.0259526	+	0.0901530i
$465$	5.13118	−	7.29289i	0.237953	−	0.338199i
$466$	16.6429	+	3.67514i	0.770967	+	0.170248i
$467$	−4.59236	+	23.0874i	−0.212509	+	1.06836i	0.716299	+	0.697794i	$0.245835\pi$
$467$	−4.59236	+	23.0874i	−0.212509	+	1.06836i	−0.928808	+	0.370562i	$0.879165\pi$
$468$	−0.346868	−	3.25341i	−0.0160340	−	0.150389i
$469$	−6.89497	−	4.60707i	−0.318380	−	0.212735i
$470$	−25.2056	−	11.0657i	−1.16265	−	0.510425i
$471$	−3.92352	+	17.5101i	−0.180786	+	0.806824i
$472$	20.1970	+	22.9148i	0.929640	+	1.05474i
$473$	7.78177	+	18.7869i	0.357806	+	0.863821i
$474$	34.2431	−	5.22026i	1.57284	−	0.239775i
$475$	−10.3615	+	2.06103i	−0.475418	+	0.0945666i
$476$	−0.324602	+	7.72919i	−0.0148781	+	0.354267i
$477$	4.34550	−	5.87058i	0.198967	−	0.268795i
$478$	−14.6351	+	20.9380i	−0.669392	+	0.957683i
$479$			16.8605i			0.770374i	0.922838	+	0.385187i	$0.125863\pi$
$479$			16.8605i			0.770374i	−0.922838	+	0.385187i	$0.874137\pi$
$480$	17.4244	−	4.70413i	0.795311	−	0.214713i
$481$		−	0.597330i		−	0.0272359i
$482$	−1.83627	−	1.28350i	−0.0836397	−	0.0584617i
$483$	31.9493	+	33.5263i	1.45374	+	1.52550i
$484$	3.66493	+	3.98626i	0.166588	+	0.181194i
$485$	27.3506	−	5.44037i	1.24193	−	0.247034i
$486$	−14.7086	+	16.4212i	−0.667197	+	0.744881i
$487$	−5.51670	−	13.3185i	−0.249986	−	0.603519i	0.748216	−	0.663455i	$-0.230910\pi$
$487$	−5.51670	−	13.3185i	−0.249986	−	0.603519i	−0.998202	+	0.0599357i	$0.980910\pi$
$488$	−0.470411	−	0.230526i	−0.0212945	−	0.0104354i
$489$	−1.22454	−	0.274384i	−0.0553755	−	0.0124081i
$490$	−4.10457	+	9.34939i	−0.185425	+	0.422362i
$491$	8.17112	+	5.45977i	0.368758	+	0.246396i	0.726117	−	0.687571i	$-0.241323\pi$
$491$	8.17112	+	5.45977i	0.368758	+	0.246396i	−0.357360	+	0.933967i	$0.616323\pi$
$492$	−26.0607	+	22.8269i	−1.17491	+	1.02911i
$493$	0.115368	−	0.579996i	0.00519593	−	0.0261217i
$494$	1.09326	−	4.95085i	0.0491882	−	0.222749i
$495$	8.73052	−	18.5034i	0.392408	−	0.831667i
$496$	8.54014	−	7.21451i	0.383464	−	0.323941i
$497$	32.1465	+	32.1465i	1.44197	+	1.44197i
$498$	14.9840	+	16.3993i	0.671449	+	0.734871i
$499$	3.78425	−	19.0247i	0.169407	−	0.851664i	−0.798816	−	0.601575i	$-0.794540\pi$
$499$	3.78425	−	19.0247i	0.169407	−	0.851664i	0.968223	−	0.250089i	$-0.0804599\pi$
$500$	−19.6530	−	14.3600i	−0.878908	−	0.642200i
$501$	−5.39664	−	2.38918i	−0.241104	−	0.106741i
$502$	2.59459	+	6.65560i	0.115802	+	0.297054i
$503$	−4.59413	+	11.0912i	−0.204842	+	0.494532i	−0.992597	−	0.121457i	$-0.961243\pi$
$503$	−4.59413	+	11.0912i	−0.204842	+	0.494532i	0.787755	+	0.615989i	$0.211243\pi$
$504$	−18.0671	+	21.4427i	−0.804774	+	0.955134i
$505$	3.02210	+	7.29599i	0.134482	+	0.324667i
$506$	−29.3222	−	30.5795i	−1.30353	−	1.35943i
$507$	7.92777	+	20.5237i	0.352085	+	0.911489i
$508$	−15.1730	−	41.4730i	−0.673193	−	1.84007i
$509$	13.6072	+	20.3646i	0.603129	+	0.902647i	0.999883	−	0.0152784i	$-0.00486345\pi$
$509$	13.6072	+	20.3646i	0.603129	+	0.902647i	−0.396754	+	0.917925i	$0.629863\pi$
$510$	−4.96558	+	1.79926i	−0.219879	+	0.0796727i
$511$		−	30.9054i		−	1.36717i
$512$	22.6268	−	0.169126i	0.999972	−	0.00747439i
$513$	−29.7005	+	16.8796i	−1.31131	+	0.745254i
$514$	29.7112	−	5.26433i	1.31050	−	0.232200i
$515$	12.5842	−	8.40847i	0.554524	−	0.370521i
$516$	16.4829	−	9.50312i	0.725617	−	0.418352i
$517$	−38.3715	+	7.63256i	−1.68758	+	0.335680i
$518$	−3.69489	+	3.54297i	−0.162344	+	0.155669i
$519$	0.0763851	+	0.120502i	0.00335293	+	0.00528944i
$520$	2.45691	−	1.42667i	0.107743	−	0.0625637i
$521$	−9.74629	−	4.03705i	−0.426993	−	0.176866i	0.158829	−	0.987306i	$-0.449228\pi$
$521$	−9.74629	−	4.03705i	−0.426993	−	0.176866i	−0.585822	+	0.810440i	$0.699228\pi$
$522$	1.61671	−	1.40727i	0.0707615	−	0.0615947i
$523$	8.73360	+	5.83560i	0.381894	+	0.255173i	0.731669	−	0.681661i	$-0.238742\pi$
$523$	8.73360	+	5.83560i	0.381894	+	0.255173i	−0.349775	+	0.936834i	$0.613742\pi$
$524$	16.4671	−	22.5367i	0.719367	−	0.984518i
$525$	9.19445	+	0.221454i	0.401279	+	0.00966504i
$526$	−3.55503	+	2.26896i	−0.155007	+	0.0989312i
$527$	−2.31331	+	2.31331i	−0.100769	+	0.100769i
$528$	16.4672	−	19.6670i	0.716642	−	0.855897i
$529$	30.0319	+	30.0319i	1.30574	+	1.30574i
$530$	6.19312	+	1.36759i	0.269012	+	0.0594041i
$531$	−4.78343	−	32.0429i	−0.207583	−	1.39054i
$532$	−37.1089	+	22.6026i	−1.60887	+	0.979948i
$533$	−3.02986	+	4.53450i	−0.131238	+	0.196411i
$534$	−25.9421	−	6.38743i	−1.12262	−	0.276411i
$535$	−2.17950	+	5.26178i	−0.0942281	+	0.227487i
$536$	3.12343	−	6.37368i	0.134912	−	0.275301i
$537$	−14.4279	−	22.7608i	−0.622610	−	0.982203i
$538$	−20.7393	−	0.435302i	−0.894136	−	0.0187672i
$539$	2.83111	+	14.2330i	0.121945	+	0.613057i
$540$	−18.2272	−	5.85004i	−0.784376	−	0.251746i
$541$	22.1758	+	33.1885i	0.953413	+	1.42688i	0.903722	+	0.428119i	$0.140824\pi$
$541$	22.1758	+	33.1885i	0.953413	+	1.42688i	0.0496911	+	0.998765i	$0.484176\pi$
$542$	17.1268	−	24.5029i	0.735658	−	1.05249i
$543$	−27.9465	+	4.86251i	−1.19930	+	0.208670i
$544$	−6.59388	+	0.604490i	−0.282710	+	0.0259173i
$545$	−5.37374			−0.230186
$546$	−1.87112	+	3.99766i	−0.0800766	+	0.171084i
$547$	−0.839814	+	0.561146i	−0.0359079	+	0.0239929i	−0.573395	−	0.819279i	$-0.694374\pi$
$547$	−0.839814	+	0.561146i	−0.0359079	+	0.0239929i	0.537487	+	0.843272i	$0.319374\pi$
$548$	−18.9952	−	0.797739i	−0.811434	−	0.0340777i
$549$	0.286095	+	0.476321i	0.0122103	+	0.0203289i
$550$	−8.41174	−	0.176556i	−0.358678	−	0.00752836i
$551$	3.06863	−	1.27107i	0.130728	−	0.0541493i
$552$	−24.8045	+	30.9201i	−1.05575	+	1.31605i
$553$	−43.1723	−	17.8825i	−1.83587	−	0.760443i
$554$	−0.560221	+	1.27607i	−0.0238015	+	0.0542152i
$555$	−3.19570	−	1.41479i	−0.135650	−	0.0600544i
$556$	−22.1827	−	5.38904i	−0.940757	−	0.228546i
$557$	−31.2872	−	6.22341i	−1.32568	−	0.263694i	−0.519047	−	0.854746i	$-0.673713\pi$
$557$	−31.2872	−	6.22341i	−1.32568	−	0.263694i	−0.806634	+	0.591052i	$0.798713\pi$
$558$	−11.7619	+	1.50426i	−0.497923	+	0.0636804i
$559$	2.11781	−	2.11781i	0.0895738	−	0.0895738i
$560$	−23.3977	−	6.73557i	−0.988735	−	0.284630i
$561$	−4.31932	+	6.13899i	−0.182362	+	0.259189i
$562$	16.6742	−	10.6421i	0.703361	−	0.448912i
$563$	0.331921	+	0.0660232i	0.0139888	+	0.00278255i	0.202080	−	0.979369i	$-0.435230\pi$
$563$	0.331921	+	0.0660232i	0.0139888	+	0.00278255i	−0.188091	+	0.982152i	$0.560230\pi$
$564$	11.7455	+	34.6699i	0.494576	+	1.45987i
$565$	−8.60702	+	12.8813i	−0.362100	+	0.541921i
$566$	−1.46291	−	3.75263i	−0.0614905	−	0.157735i
$567$	28.4437	−	8.68583i	1.19452	−	0.364771i
$568$	−23.6115	+	30.9303i	−0.990715	+	1.29781i
$569$	4.20099	−	1.74011i	0.176115	−	0.0729491i	−0.292884	−	0.956148i	$-0.594615\pi$
$569$	4.20099	−	1.74011i	0.176115	−	0.0729491i	0.468999	+	0.883199i	$0.344615\pi$
$570$	−23.8975	−	17.5751i	−1.00096	−	0.736141i
$571$	6.40640	+	32.2071i	0.268099	+	1.34783i	0.846637	+	0.532171i	$0.178624\pi$
$571$	6.40640	+	32.2071i	0.268099	+	1.34783i	−0.578537	+	0.815656i	$0.696376\pi$
$572$	1.70039	−	3.66237i	0.0710969	−	0.153131i
$573$	2.37555	+	2.49281i	0.0992400	+	0.104139i
$574$	46.0201	−	8.15399i	1.92084	−	0.340341i
$575$	13.0021			0.542226
$576$	−20.2473	−	12.8860i	−0.843635	−	0.536916i
$577$	−29.0303			−1.20855			−0.604274	−	0.796777i	$-0.706537\pi$
$577$	−29.0303			−1.20855			−0.604274	+	0.796777i	$0.706537\pi$
$578$	−21.7649	+	3.85639i	−0.905302	+	0.160405i
$579$	−14.3368	−	15.0444i	−0.595815	−	0.625225i
$580$	1.68814	+	0.783780i	0.0700961	+	0.0325447i
$581$	−5.84640	−	29.3918i	−0.242550	−	1.21938i
$582$	−29.8736	−	21.9701i	−1.23830	−	0.910691i
$583$	8.32777	−	3.44947i	0.344901	−	0.142863i
$584$	26.2181	−	3.51815i	1.08491	−	0.145582i
$585$	−3.00994	−	0.145077i	−0.124446	−	0.00599818i
$586$	14.9295	+	38.2971i	0.616733	+	1.58204i
$587$	−6.76560	+	10.1254i	−0.279246	+	0.417922i	−0.944407	−	0.328779i	$-0.893363\pi$
$587$	−6.76560	+	10.1254i	−0.279246	+	0.417922i	0.665161	+	0.746700i	$0.268363\pi$
$588$	12.8600	−	4.35672i	0.530336	−	0.179668i
$589$	−18.0219	−	3.58478i	−0.742580	−	0.147708i
$590$	23.7143	−	15.1354i	0.976301	−	0.623113i
$591$	2.56062	−	3.63937i	0.105330	−	0.149704i
$592$	−3.42623	−	2.73118i	−0.140817	−	0.112251i
$593$	−13.3642	+	13.3642i	−0.548802	+	0.548802i	−0.926094	−	0.377292i	$-0.876855\pi$
$593$	−13.3642	+	13.3642i	−0.548802	+	0.548802i	0.377292	+	0.926094i	$0.376855\pi$
$594$	−25.9958	+	8.02636i	−1.06662	+	0.329325i
$595$	6.98810	+	1.39002i	0.286484	+	0.0569853i
$596$	4.09288	−	16.8474i	0.167651	−	0.690096i
$597$	−1.78075	−	0.788364i	−0.0728811	−	0.0322656i
$598$	−2.50839	+	5.71361i	−0.102576	+	0.233647i
$599$	−6.94122	−	2.87515i	−0.283610	−	0.117475i	0.236344	−	0.971670i	$-0.424051\pi$
$599$	−6.94122	−	2.87515i	−0.283610	−	0.117475i	−0.519954	+	0.854194i	$0.674051\pi$
$600$	0.858794	+	7.82516i	0.0350601	+	0.319461i
$601$	32.8120	−	13.5912i	1.33843	−	0.554395i	0.405381	−	0.914148i	$-0.367139\pi$
$601$	32.8120	−	13.5912i	1.33843	−	0.554395i	0.933048	+	0.359753i	$0.117139\pi$
$602$	−25.6615	−	0.538615i	−1.04589	−	0.0219523i
$603$	−6.45375	+	3.87635i	−0.262817	+	0.157857i
$604$	−0.351098	+	8.36009i	−0.0142860	+	0.340167i
$605$	4.14679	−	2.77079i	0.168591	−	0.112649i
$606$	4.45171	−	9.51110i	0.180838	−	0.386362i
$607$	17.6571			0.716678			0.358339	−	0.933592i	$-0.383343\pi$
$607$	17.6571			0.716678			0.358339	+	0.933592i	$0.383343\pi$
$608$	−23.3989	−	28.9077i	−0.948950	−	1.17236i
$609$	−2.84876	+	0.495664i	−0.115437	+	0.0200853i
$610$	−0.276414	+	0.395458i	−0.0111917	+	0.0160116i
$611$	3.20137	+	4.79120i	0.129514	+	0.193831i
$612$	6.22032	+	3.26080i	0.251442	+	0.131810i
$613$	−4.92328	−	24.7510i	−0.198849	−	0.999683i	−0.943284	−	0.331987i	$-0.892281\pi$
$613$	−4.92328	−	24.7510i	−0.198849	−	0.999683i	0.744434	−	0.667696i	$-0.232719\pi$
$614$	20.7828	+	0.436214i	0.838724	+	0.0176042i
$615$	17.0832	+	26.9497i	0.688861	+	1.08672i
$616$	−32.7398	+	11.2047i	−1.31913	+	0.451451i
$617$	4.75928	−	11.4899i	0.191602	−	0.462567i	−0.798661	−	0.601782i	$-0.794458\pi$
$617$	4.75928	−	11.4899i	0.191602	−	0.462567i	0.990262	+	0.139215i	$0.0444578\pi$
$618$	−19.5422	−	4.81166i	−0.786104	−	0.193553i
$619$	−1.24045	+	1.85647i	−0.0498579	+	0.0746176i	−0.855561	−	0.517702i	$-0.826788\pi$
$619$	−1.24045	+	1.85647i	−0.0498579	+	0.0746176i	0.805703	+	0.592319i	$0.201788\pi$
$620$	−5.35622	−	8.79381i	−0.215111	−	0.353168i
$621$	39.9040	−	13.2440i	1.60129	−	0.531462i
$622$	7.07215	+	1.56170i	0.283567	+	0.0626183i
$623$	25.4858	+	25.4858i	1.02107	+	1.02107i
$624$	−3.60435	−	1.13226i	−0.144289	−	0.0453265i
$625$	−10.1706	+	10.1706i	−0.406824	+	0.406824i
$626$	2.34360	−	1.49578i	0.0936693	−	0.0597833i
$627$	−42.1478	−	1.01516i	−1.68322	−	0.0405414i
$628$	16.7301	+	12.2243i	0.667604	+	0.487805i
$629$	1.06611	+	0.712352i	0.0425086	+	0.0284033i
$630$	16.9556	+	19.4790i	0.675528	+	0.776062i
$631$	−3.29336	−	1.36415i	−0.131106	−	0.0543061i	0.316166	−	0.948704i	$-0.397604\pi$
$631$	−3.29336	−	1.36415i	−0.131106	−	0.0543061i	−0.447272	+	0.894398i	$0.647604\pi$
$632$	10.2558	−	38.6601i	0.407953	−	1.53782i
$633$	−13.3341	−	21.0353i	−0.529984	−	0.836080i
$634$	−11.7204	+	11.2385i	−0.465476	+	0.446338i
$635$	−39.8920	+	7.93501i	−1.58306	+	0.314891i
$636$	−4.21251	−	7.30645i	−0.167037	−	0.289720i
$637$	1.77718	−	1.18747i	0.0704143	−	0.0470493i
$638$	2.60465	−	0.461501i	0.103119	−	0.0182710i
$639$	38.8475	−	13.9404i	1.53678	−	0.551474i
$640$	3.05050	−	20.6158i	0.120581	−	0.814912i
$641$			5.80247i			0.229184i	0.993413	+	0.114592i	$0.0365560\pi$
$641$			5.80247i			0.229184i	−0.993413	+	0.114592i	$0.963444\pi$
$642$	7.12043	−	2.58007i	0.281021	−	0.101827i
$643$	20.9923	+	31.4171i	0.827854	+	1.23897i	0.968525	+	0.248915i	$0.0800738\pi$
$643$	20.9923	+	31.4171i	0.827854	+	1.23897i	−0.140672	+	0.990056i	$0.544926\pi$
$644$	50.2207	−	18.3733i	1.97897	−	0.724011i
$645$	−6.31416	−	16.3463i	−0.248620	−	0.643636i
$646$	7.53245	+	7.85543i	0.296360	+	0.309068i
$647$	−6.78354	−	16.3769i	−0.266688	−	0.643843i	0.732635	−	0.680622i	$-0.238290\pi$
$647$	−6.78354	−	16.3769i	−0.266688	−	0.643843i	−0.999323	+	0.0367789i	$0.988290\pi$
$648$	10.6064	+	23.1410i	0.416659	+	0.909063i
$649$	15.3009	−	36.9395i	0.600611	−	1.45000i
$650$	0.450095	+	1.15458i	0.0176542	+	0.0452863i
$651$	14.6273	+	6.47575i	0.573290	+	0.253805i
$652$	−0.854887	+	1.16999i	−0.0334799	+	0.0458203i
$653$	−1.38945	+	6.98522i	−0.0543733	+	0.273353i	−0.998402	−	0.0565103i	$-0.982003\pi$
$653$	−1.38945	+	6.98522i	−0.0543733	+	0.273353i	0.944029	+	0.329863i	$0.107003\pi$
$654$	4.82010	+	5.27539i	0.188481	+	0.206284i
$655$	−18.1778	−	18.1778i	−0.710264	−	0.710264i
$656$	12.1560	+	38.1121i	0.474614	+	1.48803i
$657$	−25.3749	−	11.9727i	−0.989971	−	0.467101i
$658$	10.6483	−	48.2209i	0.415114	−	1.87985i
$659$	−4.43616	+	22.3021i	−0.172808	+	0.868765i	0.792943	+	0.609296i	$0.208548\pi$
$659$	−4.43616	+	22.3021i	−0.172808	+	0.868765i	−0.965751	+	0.259469i	$0.916452\pi$
$660$	−15.5662	−	17.7715i	−0.605913	−	0.691753i
$661$	−19.0702	−	12.7423i	−0.741745	−	0.495618i	0.126369	−	0.991983i	$-0.459668\pi$
$661$	−19.0702	−	12.7423i	−0.741745	−	0.495618i	−0.868114	+	0.496365i	$0.834668\pi$
$662$	19.2199	−	43.7792i	0.747003	−	1.70153i
$663$	1.07882	+	0.241732i	0.0418978	+	0.00938811i
$664$	24.2685	−	8.30554i	0.941802	−	0.322318i
$665$	15.3145	+	36.9725i	0.593871	+	1.43373i
$666$	1.47757	+	4.40624i	0.0572546	+	0.170738i
$667$	−4.00929	+	0.797498i	−0.155240	+	0.0308792i
$668$	−5.01680	+	4.61240i	−0.194106	+	0.178459i
$669$	−20.3163	−	21.3191i	−0.785473	−	0.824244i
$670$	−5.35812	−	3.74517i	−0.207002	−	0.144689i
$671$			0.685723i			0.0264720i
$672$	14.3749	+	29.0111i	0.554522	+	1.11913i
$673$			23.4212i			0.902821i	0.892316	+	0.451410i	$0.149079\pi$
$673$			23.4212i			0.902821i	−0.892316	+	0.451410i	$0.850921\pi$
$674$	2.95880	−	4.23309i	0.113969	−	0.163052i
$675$	3.74375	−	7.46333i	0.144097	−	0.287264i
$676$	25.3829	+	1.06600i	0.976266	+	0.0410001i
$677$	−8.49094	+	1.68895i	−0.326333	+	0.0649117i	−0.355538	−	0.934662i	$-0.615702\pi$
$677$	−8.49094	+	1.68895i	−0.326333	+	0.0649117i	0.0292050	+	0.999573i	$0.490702\pi$
$678$	20.3658	−	3.10471i	0.782144	−	0.119236i
$679$	19.1442	+	46.2182i	0.734687	+	1.77369i
$680$	−0.383701	+	6.08647i	−0.0147143	+	0.233406i
$681$	−6.33875	+	28.2890i	−0.242901	+	1.08404i
$682$	−13.3995	−	5.88262i	−0.513092	−	0.225257i
$683$	−1.10592	−	0.738953i	−0.0423169	−	0.0282753i	0.534232	−	0.845338i	$-0.320601\pi$
$683$	−1.10592	−	0.738953i	−0.0423169	−	0.0282753i	−0.576549	+	0.817063i	$0.695601\pi$
$684$	4.18199	+	39.2246i	0.159902	+	1.49979i
$685$	−3.41610	+	17.1739i	−0.130522	+	0.656181i
$686$	14.0568	+	3.10407i	0.536691	+	0.118514i
$687$	−8.83635	+	12.5590i	−0.337128	+	0.479156i
$688$	−2.46428	−	21.8308i	−0.0939500	−	0.832293i
$689$	−0.938774	−	0.938774i	−0.0357644	−	0.0357644i
$690$	24.6265	+	26.9526i	0.937516	+	1.02607i
$691$	5.02517	−	25.2633i	0.191167	−	0.961059i	−0.759420	−	0.650600i	$-0.774517\pi$
$691$	5.02517	−	25.2633i	0.191167	−	0.961059i	0.950587	−	0.310459i	$-0.100483\pi$
$692$	0.162785	−	0.0253318i	0.00618814	−	0.000962971i
$693$	35.6115	+	8.88519i	1.35277	+	0.337520i
$694$	40.3092	−	15.7139i	1.53012	−	0.596493i
$695$	−8.04591	+	19.4245i	−0.305199	+	0.736815i
$696$	−0.744780	−	2.36027i	−0.0282308	−	0.0894658i
$697$	−4.47986	−	10.8153i	−0.169687	−	0.409660i
$698$	−11.6013	+	11.1243i	−0.439116	+	0.421061i
$699$	−19.4722	+	7.52159i	−0.736504	+	0.284493i
$700$	4.47218	−	9.63235i	0.169032	−	0.364069i
$701$	−8.51430	−	12.7425i	−0.321581	−	0.481279i	0.635096	−	0.772434i	$-0.280961\pi$
$701$	−8.51430	−	12.7425i	−0.321581	−	0.481279i	−0.956676	+	0.291154i	$0.905961\pi$
$702$	2.55742	+	3.08498i	0.0965235	+	0.116435i
$703$			7.20167i			0.271616i
$704$	−13.2323	−	26.4988i	−0.498711	−	0.998710i
$705$	33.2153	−	5.77924i	1.25096	−	0.217659i
$706$	−4.62353	−	26.0946i	−0.174009	−	0.982082i
$707$	−11.7793	+	7.87069i	−0.443007	+	0.296008i
$708$	−36.1294	−	9.70422i	−1.35783	−	0.364707i
$709$	−15.1060	+	3.00477i	−0.567317	+	0.112846i	−0.470411	−	0.882447i	$-0.655894\pi$
$709$	−15.1060	+	3.00477i	−0.567317	+	0.112846i	−0.0969055	+	0.995294i	$0.530894\pi$
$710$	24.8048	+	25.8684i	0.930906	+	0.970822i
$711$	−31.4074	+	28.5190i	−1.17787	+	1.06955i
$712$	−18.7193	+	24.5217i	−0.701534	+	0.918989i
$713$	20.8933	+	8.65430i	0.782461	+	0.324106i
$714$	−4.90357	−	8.10702i	−0.183511	−	0.303397i
$715$	−3.09219	−	2.06613i	−0.115641	−	0.0772690i
$716$	−30.7474	+	4.78477i	−1.14908	+	0.178815i
$717$	0.753349	−	31.2780i	0.0281343	−	1.16810i
$718$	−14.8874	−	23.3258i	−0.555594	−	0.870512i
$719$	10.7173	−	10.7173i	0.399686	−	0.399686i	−0.478436	−	0.878122i	$-0.658796\pi$
$719$	10.7173	−	10.7173i	0.399686	−	0.399686i	0.878122	+	0.478436i	$0.158796\pi$
$720$	−14.5945	+	16.6014i	−0.543906	+	0.618698i
$721$	19.1985	+	19.1985i	0.714990	+	0.714990i
$722$	−7.38692	+	33.4517i	−0.274913	+	1.24494i
$723$	2.74308	+	0.0660688i	0.102016	+	0.00245713i
$724$	−7.73248	+	31.8289i	−0.287375	+	1.18291i
$725$	−0.451018	+	0.674997i	−0.0167504	+	0.0250687i
$726$	−6.43964	−	1.58556i	−0.238997	−	0.0588456i
$727$	−1.37029	+	3.30817i	−0.0508212	+	0.122693i	−0.947251	−	0.320492i	$-0.896152\pi$
$727$	−1.37029	+	3.30817i	−0.0508212	+	0.122693i	0.896430	+	0.443185i	$0.146152\pi$
$728$	3.37003	+	3.82353i	0.124902	+	0.141709i
$729$	3.88755	−	26.7187i	0.143983	−	0.989580i
$730$	0.511263	−	24.3584i	0.0189227	−	0.901545i
$731$	1.25424	+	6.30547i	0.0463896	+	0.233216i
$732$	0.636156	−	0.0833611i	0.0235130	−	0.00308111i
$733$	−4.88457	−	7.31028i	−0.180416	−	0.270011i	0.730228	−	0.683204i	$-0.239414\pi$
$733$	−4.88457	−	7.31028i	−0.180416	−	0.270011i	−0.910644	+	0.413192i	$0.864414\pi$
$734$	−2.72450	−	1.90435i	−0.100563	−	0.0702908i
$735$	−2.14367	−	12.3204i	−0.0790704	−	0.454445i
$736$	21.3036	+	40.5123i	0.785262	+	1.49330i
$737$	−9.29098			−0.342237
$738$	11.1333	−	40.9438i	0.409822	−	1.50716i
$739$	26.6757	−	17.8242i	0.981283	−	0.655673i	0.0421088	−	0.999113i	$-0.486592\pi$
$739$	26.6757	−	17.8242i	0.981283	−	0.655673i	0.939174	+	0.343441i	$0.111592\pi$
$740$	−2.97077	+	2.73130i	−0.109208	+	0.100405i
$741$	2.23749	+	5.79248i	0.0821961	+	0.212792i
$742$	−0.238755	+	11.3751i	−0.00876498	+	0.417595i
$743$	40.3779	−	16.7251i	1.48132	−	0.613583i	0.511912	−	0.859038i	$-0.328937\pi$
$743$	40.3779	−	16.7251i	1.48132	−	0.613583i	0.969408	+	0.245455i	$0.0789374\pi$
$744$	−3.82847	+	13.1460i	−0.140359	+	0.481956i
$745$	−14.7526	−	6.11073i	−0.540493	−	0.223880i
$746$	8.39916	+	3.68739i	0.307515	+	0.135005i
$747$	−26.3971	−	6.58618i	−0.965821	−	0.240976i
$748$	4.50875	+	7.40244i	0.164856	+	0.270660i
$749$	−10.0207	−	1.99323i	−0.366147	−	0.0728312i
$750$	29.7804	+	1.34302i	1.08743	+	0.0490403i
$751$	25.3960	−	25.3960i	0.926712	−	0.926712i	−0.0707803	−	0.997492i	$-0.522549\pi$
$751$	25.3960	−	25.3960i	0.926712	−	0.926712i	0.997492	+	0.0707803i	$0.0225489\pi$
$752$	42.1195	+	3.54403i	1.53594	+	0.129238i
$753$	−7.15531	−	5.03438i	−0.260754	−	0.183463i
$754$	−0.209607	−	0.328415i	−0.00763345	−	0.0119602i
$755$	7.55851	+	1.50348i	0.275082	+	0.0547173i
$756$	3.91376	−	34.1174i	0.142342	−	1.24084i
$757$	3.36700	−	5.03906i	0.122376	−	0.183148i	−0.765224	−	0.643764i	$-0.777372\pi$
$757$	3.36700	−	5.03906i	0.122376	−	0.183148i	0.887599	+	0.460617i	$0.152372\pi$
$758$	−2.67063	+	1.04110i	−0.0970015	+	0.0378146i
$759$	50.6324	+	11.3453i	1.83784	+	0.411807i
$760$	−29.6216	+	17.2006i	−1.07449	+	0.623931i
$761$	2.07072	−	0.857719i	0.0750635	−	0.0310923i	−0.344836	−	0.938663i	$-0.612065\pi$
$761$	2.07072	−	0.857719i	0.0750635	−	0.0310923i	0.419899	+	0.907571i	$0.362065\pi$
$762$	43.5718	+	32.0444i	1.57844	+	1.16084i
$763$	−1.88069	−	9.45486i	−0.0680855	−	0.342289i
$764$	3.73410	−	1.36613i	0.135095	−	0.0494248i
$765$	3.84847	−	5.19911i	0.139142	−	0.187974i
$766$	−5.94797	−	33.5696i	−0.214909	−	1.21292i
$767$	−5.88896			−0.212638
$768$	−22.9747	+	15.4972i	−0.829028	+	0.559206i
$769$	7.95821			0.286981			0.143490	−	0.989652i	$-0.454167\pi$
$769$	7.95821			0.286981			0.143490	+	0.989652i	$0.454167\pi$
$770$	5.56041	+	31.3822i	0.200383	+	1.13094i
$771$	−26.7530	+	25.4946i	−0.963487	+	0.918166i
$772$	−22.5358	+	8.24476i	−0.811080	+	0.296735i
$773$	−3.37161	−	16.9502i	−0.121268	−	0.609658i	−0.992846	−	0.119400i	$-0.961903\pi$
$773$	−3.37161	−	16.9502i	−0.121268	−	0.609658i	0.871578	−	0.490257i	$-0.163097\pi$
$774$	−10.3835	+	20.8608i	−0.373227	+	0.749826i
$775$	4.14924	−	1.71867i	0.149045	−	0.0617365i
$776$	−37.0291	+	21.5019i	−1.32927	+	0.771875i
$777$	1.37084	−	6.11785i	0.0491784	−	0.219477i
$778$	−48.6499	+	18.9655i	−1.74418	+	0.679944i
$779$	36.5293	−	54.6700i	1.30880	−	1.95875i
$780$	−1.54088	+	3.11984i	−0.0551722	+	0.111708i
$781$	49.9571	+	9.93709i	1.78761	+	0.355577i
$782$	−7.20621	−	11.2908i	−0.257694	−	0.403757i
$783$	−0.696641	+	2.53100i	−0.0248959	+	0.0904505i
$784$	1.31457	−	15.6232i	0.0469490	−	0.557972i
$785$	13.4943	−	13.4943i	0.481632	−	0.481632i
$786$	−1.54009	+	34.1500i	−0.0549330	+	1.21809i
$787$	6.03809	+	1.20105i	0.215235	+	0.0428128i	0.301530	−	0.953457i	$-0.402503\pi$
$787$	6.03809	+	1.20105i	0.215235	+	0.0428128i	−0.0862951	+	0.996270i	$0.527503\pi$
$788$	−2.67292	−	4.38838i	−0.0952187	−	0.156330i
$789$	2.09098	−	4.72307i	0.0744408	−	0.168146i
$790$	−33.7308	−	14.8085i	−1.20009	−	0.526863i
$791$	−25.6764	−	10.6355i	−0.912947	−	0.378155i
$792$	−3.48373	+	31.2218i	−0.123789	+	1.10942i
$793$	0.0933098	−	0.0386502i	0.00331353	−	0.00137251i
$794$	−0.912983	+	43.4977i	−0.0324005	+	1.54368i
$795$	−7.24593	+	2.79892i	−0.256987	+	0.0992674i
$796$	−1.65541	+	1.52197i	−0.0586744	+	0.0539447i
$797$	−7.45915	+	4.98405i	−0.264217	+	0.176544i	−0.680621	−	0.732635i	$-0.738290\pi$
$797$	−7.45915	+	4.98405i	−0.264217	+	0.176544i	0.416404	+	0.909179i	$0.363290\pi$
$798$	22.5591	−	48.1976i	0.798583	−	1.70618i
$799$	−12.3691			−0.437588
$800$	8.68054	+	2.69738i	0.306903	+	0.0953670i
$801$	30.7984	−	11.0520i	1.08821	−	0.390504i
$802$	14.9893	+	10.4770i	0.529289	+	0.369957i
$803$	−19.2375	−	28.7910i	−0.678877	−	1.01601i
$804$	1.12947	+	8.61938i	0.0398334	+	0.303982i
$805$	−9.60869	−	48.3061i	−0.338662	−	1.70257i
$806$	−0.0452296	+	2.15490i	−0.00159315	+	0.0759031i
$807$	21.4580	−	13.6021i	0.755359	−	0.478815i
$808$	−8.01787	−	9.09681i	−0.282068	−	0.320025i
$809$	9.87605	−	23.8429i	0.347224	−	0.838272i	−0.649722	−	0.760172i	$-0.725115\pi$
$809$	9.87605	−	23.8429i	0.347224	−	0.838272i	0.996946	−	0.0781000i	$-0.0248853\pi$
$810$	22.5619	−	6.37529i	0.792744	−	0.224005i
$811$	−9.69074	+	14.5032i	−0.340288	+	0.509277i	−0.961662	−	0.274237i	$-0.911575\pi$
$811$	−9.69074	+	14.5032i	−0.340288	+	0.509277i	0.621374	+	0.783514i	$0.286575\pi$
$812$	−0.788217	+	3.24451i	−0.0276610	+	0.113860i
$813$	−0.881612	+	36.6033i	−0.0309195	+	1.28373i
$814$	−1.23672	+	5.60051i	−0.0433472	+	0.196298i
$815$	0.943697	+	0.943697i	0.0330563	+	0.0330563i
$816$	6.31925	−	5.08273i	0.221218	−	0.177931i
$817$	−25.5333	+	25.5333i	−0.893295	+	0.893295i
$818$	−21.0328	−	32.9544i	−0.735393	−	1.15222i
$819$	−0.798156	−	5.34663i	−0.0278898	−	0.186827i
$820$	36.4061	−	5.66535i	1.27136	−	0.197843i
$821$	−9.95404	−	6.65108i	−0.347398	−	0.232124i	0.369613	−	0.929186i	$-0.379490\pi$
$821$	−9.95404	−	6.65108i	−0.347398	−	0.232124i	−0.717011	+	0.697062i	$0.754490\pi$
$822$	19.9237	−	12.0510i	0.694919	−	0.420325i
$823$	−25.2779	−	10.4704i	−0.881131	−	0.364976i	−0.104195	−	0.994557i	$-0.533227\pi$
$823$	−25.2779	−	10.4704i	−0.881131	−	0.364976i	−0.776935	+	0.629581i	$0.783227\pi$
$824$	−14.1012	+	18.4722i	−0.491240	+	0.643510i
$825$	8.70325	−	5.51691i	0.303008	−	0.192074i
$826$	34.9295	+	36.4272i	1.21535	+	1.26746i
$827$	−41.4125	+	8.23747i	−1.44006	+	0.286445i	−0.852495	−	0.522735i	$-0.824912\pi$
$827$	−41.4125	+	8.23747i	−1.44006	+	0.286445i	−0.587560	+	0.809180i	$0.699912\pi$
$828$	4.36997	−	48.3516i	0.151867	−	1.68034i
$829$	13.6752	−	9.13744i	0.474958	−	0.317357i	−0.294949	−	0.955513i	$-0.595303\pi$
$829$	13.6752	−	9.13744i	0.474958	−	0.317357i	0.769907	+	0.638156i	$0.220303\pi$
$830$	−4.12167	−	23.2622i	−0.143065	−	0.807442i
$831$	−0.292584	−	1.68158i	−0.0101496	−	0.0583334i
$832$	−2.85999	+	3.29417i	−0.0991524	+	0.114205i
$833$			4.58802i			0.158966i
$834$	26.2860	−	9.52466i	0.910210	−	0.329812i
$835$	3.48711	+	5.21883i	0.120676	+	0.180605i
$836$	−20.5007	+	44.1552i	−0.709031	+	1.52714i
$837$	10.9835	−	9.50110i	0.379647	−	0.328406i
$838$	19.6126	−	18.8062i	0.677504	−	0.649649i
$839$	17.8164	+	43.0125i	0.615090	+	1.48496i	0.857343	+	0.514745i	$0.172113\pi$
$839$	17.8164	+	43.0125i	0.615090	+	1.48496i	−0.242254	+	0.970213i	$0.577887\pi$
$840$	28.4378	−	8.97351i	0.981198	−	0.309615i
$841$	−11.0001	+	26.5567i	−0.379315	+	0.915748i
$842$	−29.7051	+	11.5801i	−1.02371	+	0.399076i
$843$	−9.80737	+	22.1527i	−0.337784	+	0.762981i
$844$	−28.4164	+	4.42203i	−0.978133	+	0.152213i
$845$	4.56487	−	22.9491i	0.157036	−	0.789475i
$846$	−35.4668	−	27.4236i	−1.21937	−	0.942842i
$847$	6.32638	+	6.32638i	0.217377	+	0.217377i
$848$	−9.67709	+	1.09236i	−0.332313	+	0.0375117i
$849$	4.03438	+	2.83854i	0.138459	+	0.0974183i
$850$	−2.59745	−	0.573578i	−0.0890918	−	0.0196736i
$851$	1.72916	−	8.69306i	0.0592747	−	0.297994i
$852$	3.14567	−	47.5540i	0.107769	−	1.62917i
$853$	7.94078	+	5.30586i	0.271887	+	0.181669i	0.684038	−	0.729447i	$-0.260222\pi$
$853$	7.94078	+	5.30586i	0.271887	+	0.181669i	−0.412151	+	0.911116i	$0.635222\pi$
$854$	−0.792530	−	0.347936i	−0.0271198	−	0.0119061i
$855$	36.2892	+	1.74911i	1.24106	+	0.0598183i
$856$	0.550212	−	8.72776i	0.0188059	−	0.298309i
$857$	18.5434	+	44.7677i	0.633430	+	1.52923i	0.835284	+	0.549819i	$0.185303\pi$
$857$	18.5434	+	44.7677i	0.633430	+	1.52923i	−0.201854	+	0.979416i	$0.564697\pi$
$858$	0.745293	+	4.88886i	0.0254439	+	0.166903i
$859$	−18.8663	+	3.75274i	−0.643709	+	0.128042i	−0.506141	−	0.862451i	$-0.668929\pi$
$859$	−18.8663	+	3.75274i	−0.643709	+	0.128042i	−0.137568	+	0.990492i	$0.543929\pi$
$860$	−20.2165	−	0.849030i	−0.689377	−	0.0289517i
$861$	−41.4382	+	39.4890i	−1.41221	+	1.34578i
$862$	12.4447	−	17.8043i	0.423869	−	0.606418i
$863$			3.38582i			0.115255i	0.998338	+	0.0576274i	$0.0183535\pi$
$863$			3.38582i			0.115255i	−0.998338	+	0.0576274i	$0.981646\pi$
$864$	29.3885	−	0.563625i	0.999816	−	0.0191749i
$865$		−	0.151732i		−	0.00515905i
$866$	9.89048	+	6.91316i	0.336092	+	0.234919i
$867$	19.5980	−	18.6761i	0.665582	−	0.634274i
$868$	13.5978	−	12.5017i	0.461539	−	0.424335i
$869$	−51.3498	+	10.2141i	−1.74192	+	0.346490i
$870$	−2.25348	+	0.343536i	−0.0764000	+	0.0116470i
$871$	0.523677	+	1.26427i	0.0177441	+	0.0428381i
$872$	7.80678	−	2.67176i	0.264371	−	0.0904771i
$873$	45.3640	+	2.18651i	1.53534	+	0.0740021i
$874$	30.2422	−	68.8859i	1.02296	−	2.33010i
$875$	−33.4384	−	22.3428i	−1.13043	−	0.755326i
$876$	−24.3712	+	21.3469i	−0.823425	+	0.721246i
$877$	7.86570	−	39.5435i	0.265606	−	1.33529i	−0.585660	−	0.810557i	$-0.699165\pi$
$877$	7.86570	−	39.5435i	0.265606	−	1.33529i	0.851266	−	0.524734i	$-0.175835\pi$
$878$	−4.06403	+	18.4040i	−0.137154	+	0.621104i
$879$	−41.1724	−	28.9684i	−1.38871	−	0.977079i
$880$	−25.9896	+	8.28951i	−0.876109	+	0.279439i
$881$	−5.13574	−	5.13574i	−0.173028	−	0.173028i	0.615281	−	0.788308i	$-0.289043\pi$
$881$	−5.13574	−	5.13574i	−0.173028	−	0.173028i	−0.788308	+	0.615281i	$0.789043\pi$
$882$	−10.1721	+	13.1555i	−0.342513	+	0.442969i
$883$	−1.53900	+	7.73710i	−0.0517916	+	0.260374i	−0.998002	−	0.0631770i	$-0.979877\pi$
$883$	−1.53900	+	7.73710i	−0.0517916	+	0.260374i	0.946211	+	0.323551i	$0.104877\pi$
$884$	0.753155	−	1.03076i	0.0253314	−	0.0346682i
$885$	−13.9481	+	31.5058i	−0.468862	+	1.05906i
$886$	20.6613	+	53.0000i	0.694128	+	1.78057i
$887$	−15.1105	+	36.4799i	−0.507360	+	1.22488i	0.438037	+	0.898957i	$0.355674\pi$
$887$	−15.1105	+	36.4799i	−0.507360	+	1.22488i	−0.945397	+	0.325920i	$0.894326\pi$
$888$	5.34602	+	0.466493i	0.179401	+	0.0156545i
$889$	−27.9226	−	67.4111i	−0.936494	−	2.26090i
$890$	19.6653	+	20.5085i	0.659183	+	0.687447i
$891$	21.0911	−	25.7968i	0.706577	−	0.864224i
$892$	−31.9349	+	11.6835i	−1.06926	+	0.391191i
$893$	−38.5972	−	57.7648i	−1.29161	−	1.93303i
$894$	7.23381	+	19.9637i	0.241935	+	0.667688i
$895$			28.6597i			0.957990i
$896$	37.3403	−	1.84786i	1.24745	−	0.0617326i
$897$	−1.31004	−	7.52926i	−0.0437410	−	0.251395i
$898$	−8.74457	+	1.54939i	−0.291810	+	0.0517039i
$899$	−1.17403	+	0.784463i	−0.0391561	+	0.0261633i
$900$	−6.17615	−	7.40346i	−0.205872	−	0.246782i
$901$	2.79506	−	0.555973i	0.0931170	−	0.0185221i
$902$	37.7960	−	36.2420i	1.25847	−	1.20673i
$903$	26.5508	−	16.8303i	0.883556	−	0.560079i
$904$	6.09955	−	22.9928i	0.202868	−	0.764730i
$905$	27.8713	+	11.5447i	0.926475	+	0.383758i
$906$	−5.30382	−	8.76875i	−0.176208	−	0.291322i
$907$	−30.0747	−	20.0953i	−0.998614	−	0.667252i	−0.0550638	−	0.998483i	$-0.517536\pi$
$907$	−30.0747	−	20.0953i	−0.998614	−	0.667252i	−0.943550	+	0.331230i	$0.892536\pi$
$908$	27.0288	+	19.7494i	0.896982	+	0.655406i
$909$	1.89895	+	12.7205i	0.0629841	+	0.421914i
$910$	3.95693	−	2.52546i	0.131171	−	0.0837183i
$911$	30.1032	−	30.1032i	0.997363	−	0.997363i	−0.00263353	−	0.999997i	$-0.500838\pi$
$911$	30.1032	−	30.1032i	0.997363	−	0.997363i	0.999997	+	0.00263353i	$0.000838280\pi$
$912$	43.4556	+	13.6510i	1.43896	+	0.452030i
$913$	−23.7418	−	23.7418i	−0.785738	−	0.785738i
$914$	−10.9686	−	2.42213i	−0.362810	−	0.0801171i
$915$	0.0142286	−	0.590749i	0.000470381	−	0.0195296i
$916$	9.22389	+	15.1437i	0.304766	+	0.500363i
$917$	25.6212	−	38.3448i	0.846086	−	1.26626i
$918$	−8.55593	+	0.885433i	−0.282388	+	0.0292236i
$919$	2.76576	−	6.67714i	0.0912341	−	0.220259i	−0.871675	−	0.490084i	$-0.836966\pi$
$919$	2.76576	−	6.67714i	0.0912341	−	0.220259i	0.962909	+	0.269826i	$0.0869660\pi$
$920$	39.8859	−	13.6503i	1.31500	−	0.450039i
$921$	−21.5030	+	13.6306i	−0.708548	+	0.449142i
$922$	−30.7079	−	0.644533i	−1.01131	−	0.0212266i
$923$	−1.46360	−	7.35801i	−0.0481750	−	0.242192i
$924$	25.8203	−	33.6077i	0.849426	−	1.10561i
$925$	−0.977910	−	1.46355i	−0.0321535	−	0.0481211i
$926$	−28.5453	+	40.8391i	−0.938057	+	1.34206i
$927$	23.2005	−	8.32549i	0.762004	−	0.273445i
$928$	−2.84215	−	0.299328i	−0.0932982	−	0.00982593i
$929$	−4.22030			−0.138463			−0.0692317	−	0.997601i	$-0.522055\pi$
$929$	−4.22030			−0.138463			−0.0692317	+	0.997601i	$0.522055\pi$
$930$	11.4215	+	5.34591i	0.374527	+	0.175299i
$931$	−21.4264	+	14.3167i	−0.702223	+	0.469210i
$932$	−1.01139	+	24.0824i	−0.0331291	+	0.788846i
$933$	−8.27440	+	3.19619i	−0.270892	+	0.104638i
$934$	−33.2828	−	0.698579i	−1.08905	−	0.0228582i
$935$	7.37524	−	3.05493i	0.241196	−	0.0999067i
$936$	4.44487	−	1.28574i	0.145285	−	0.0420258i
$937$	−15.9759	−	6.61744i	−0.521911	−	0.216182i	0.106145	−	0.994351i	$-0.466149\pi$
$937$	−15.9759	−	6.61744i	−0.521911	−	0.216182i	−0.628056	+	0.778168i	$0.716149\pi$
$938$	4.71425	−	10.7381i	0.153926	−	0.350612i
$939$	−1.37845	+	3.11362i	−0.0449840	+	0.101609i
$940$	9.19029	−	37.8297i	0.299754	−	1.23387i
$941$	15.5482	+	3.09272i	0.506855	+	0.100820i	0.441893	−	0.897068i	$-0.354307\pi$
$941$	15.5482	+	3.09272i	0.506855	+	0.100820i	0.0649626	+	0.997888i	$0.479307\pi$
$942$	−25.3513	−	1.14328i	−0.825991	−	0.0372502i
$943$	−57.2206	+	57.2206i	−1.86336	+	1.86336i
$944$	−26.9262	+	33.7786i	−0.876372	+	1.09940i
$945$	−30.4948	−	8.39350i	−0.991998	−	0.273041i
$946$	−24.2411	+	15.4716i	−0.788147	+	0.503026i
$947$	18.2131	+	3.62281i	0.591845	+	0.117725i	0.481921	−	0.876215i	$-0.339939\pi$
$947$	18.2131	+	3.62281i	0.591845	+	0.117725i	0.109924	+	0.993940i	$0.464939\pi$
$948$	15.7182	+	46.3963i	0.510504	+	1.50688i
$949$	−2.83342	+	4.24052i	−0.0919768	+	0.137653i
$950$	−5.42655	−	13.9201i	−0.176061	−	0.451628i
$951$	4.34836	−	19.4061i	0.141005	−	0.629287i
$952$	−10.8432	+	1.45502i	−0.351429	+	0.0471576i
$953$	−48.0723	+	19.9122i	−1.55721	+	0.645019i	−0.984602	−	0.174808i	$-0.944069\pi$
$953$	−48.0723	+	19.9122i	−1.55721	+	0.645019i	−0.572611	+	0.819827i	$0.694069\pi$
$954$	9.24710	+	4.60276i	0.299386	+	0.149020i
$955$	−0.714442	−	3.59174i	−0.0231188	−	0.116226i
$956$	−32.7676	−	15.2136i	−1.05978	−	0.492043i
$957$	−2.34532	+	2.23500i	−0.0758135	+	0.0722474i
$958$	−23.4786	+	4.16002i	−0.758559	+	0.134404i
$959$	−31.4123			−1.01436
$960$	10.8498	+	23.1032i	0.350175	+	0.745653i
$961$	−23.1886			−0.748018
$962$	0.831796	−	0.147380i	0.0268182	−	0.00475174i
$963$	−5.51855	+	7.45531i	−0.177833	+	0.240244i
$964$	1.33423	−	2.87373i	0.0429728	−	0.0925565i
$965$	4.31175	+	21.6766i	0.138800	+	0.697796i
$966$	−38.8033	+	52.7622i	−1.24847	+	1.69760i
$967$	34.7862	−	14.4089i	1.11865	−	0.463360i	0.254741	−	0.967009i	$-0.418010\pi$
$967$	34.7862	−	14.4089i	1.11865	−	0.463360i	0.863908	+	0.503650i	$0.168010\pi$
$968$	−4.64670	+	6.08704i	−0.149351	+	0.195645i
$969$	−13.0067	−	2.91443i	−0.417836	−	0.0936251i
$970$	14.3241	+	36.7440i	0.459920	+	1.17978i
$971$	19.1965	−	28.7296i	0.616045	−	0.921976i	−0.383954	−	0.923352i	$-0.625438\pi$
$971$	19.1965	−	28.7296i	0.616045	−	0.921976i	0.999999	+	0.00137607i	$0.000438016\pi$
$972$	−26.4960	−	16.4305i	−0.849860	−	0.527008i
$973$	−36.9926	−	7.35828i	−1.18593	−	0.235896i
$974$	17.1852	−	10.9682i	0.550649	−	0.351445i
$975$	−1.24126	−	0.873338i	−0.0397523	−	0.0279692i
$976$	0.204947	−	0.711937i	0.00656020	−	0.0227885i
$977$	−22.5815	+	22.5815i	−0.722445	+	0.722445i	−0.969103	−	0.246658i	$-0.920668\pi$
$977$	−22.5815	+	22.5815i	−0.722445	+	0.722445i	0.246658	+	0.969103i	$0.420668\pi$
$978$	0.0799534	−	1.77290i	0.00255663	−	0.0566910i
$979$	39.6062	+	7.87816i	1.26582	+	0.251787i
$980$	−14.0320	−	3.40891i	−0.448235	−	0.108894i
$981$	−8.49152	−	2.11866i	−0.271113	−	0.0676438i
$982$	−5.58678	+	12.7256i	−0.178281	+	0.406090i
$983$	−12.0098	−	4.97461i	−0.383053	−	0.158666i	0.182844	−	0.983142i	$-0.441470\pi$
$983$	−12.0098	−	4.97461i	−0.383053	−	0.158666i	−0.565896	+	0.824476i	$0.691470\pi$
$984$	−38.2170	−	30.6581i	−1.21831	−	0.977344i
$985$	−4.37225	+	1.81105i	−0.139312	+	0.0577048i
$986$	0.836123	+	0.0175496i	0.0266276	+	0.000558892i
$987$	21.7930	+	56.4184i	0.693678	+	1.79582i
$988$	7.16392	+	0.300862i	0.227915	+	0.00957170i
$989$	36.9515	−	24.6902i	1.17499	−	0.785104i
$990$	27.9206	+	7.59207i	0.887374	+	0.241292i
$991$	−39.8014			−1.26433			−0.632167	−	0.774832i	$-0.717834\pi$
$991$	−39.8014			−1.26433			−0.632167	+	0.774832i	$0.717834\pi$
$992$	12.1535	+	10.1123i	0.385874	+	0.321066i
$993$	10.0379	+	57.6912i	0.318542	+	1.83077i
$994$	−36.8332	+	52.6963i	−1.16828	+	1.67142i
$995$	1.15065	+	1.72207i	0.0364781	+	0.0545934i
$996$	−19.1394	+	24.9118i	−0.606455	+	0.789361i
$997$	7.72518	+	38.8371i	0.244659	+	1.22998i	0.886348	+	0.463019i	$0.153234\pi$
$997$	7.72518	+	38.8371i	0.244659	+	1.22998i	−0.641689	+	0.766965i	$0.721766\pi$
$998$	27.4261	+	0.575652i	0.868158	+	0.0182219i
$999$	−4.49201	−	3.49558i	−0.142121	−	0.110595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.179.16	yes	240
3.2	odd	2	inner	192.2.s.a.179.15	yes	240
4.3	odd	2		768.2.s.a.623.23		240
12.11	even	2		768.2.s.a.623.19		240
64.5	even	16		768.2.s.a.143.19		240
64.59	odd	16	inner	192.2.s.a.59.15	✓	240
192.5	odd	16		768.2.s.a.143.23		240
192.59	even	16	inner	192.2.s.a.59.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.59.15	✓	240	64.59	odd	16	inner
192.2.s.a.59.16	yes	240	192.59	even	16	inner
192.2.s.a.179.15	yes	240	3.2	odd	2	inner
192.2.s.a.179.16	yes	240	1.1	even	1	trivial
768.2.s.a.143.19		240	64.5	even	16
768.2.s.a.143.23		240	192.5	odd	16
768.2.s.a.623.19		240	12.11	even	2
768.2.s.a.623.23		240	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.246732 + 1.39252i) q^{2} +(-1.19490 - 1.25388i) q^{3} +(-1.87825 + 0.687161i) q^{4} +(0.359364 + 1.80664i) q^{5} +(1.45124 - 1.97330i) q^{6} +(-3.05294 + 1.26457i) q^{7} +(-1.42031 - 2.44596i) q^{8} +(-0.144430 + 2.99652i) q^{9} +O(q^{10})\)	\(q+(0.246732 + 1.39252i) q^{2} +(-1.19490 - 1.25388i) q^{3} +(-1.87825 + 0.687161i) q^{4} +(0.359364 + 1.80664i) q^{5} +(1.45124 - 1.97330i) q^{6} +(-3.05294 + 1.26457i) q^{7} +(-1.42031 - 2.44596i) q^{8} +(-0.144430 + 2.99652i) q^{9} +(-2.42713 + 0.946180i) q^{10} +(-2.05692 + 3.07840i) q^{11} +(3.10593 + 1.53401i) q^{12} +(0.534830 + 0.106384i) q^{13} +(-2.51420 - 3.93929i) q^{14} +(1.83591 - 2.60936i) q^{15} +(3.05562 - 2.58132i) q^{16} +(-0.827691 + 0.827691i) q^{17} +(-4.20836 + 0.538216i) q^{18} +(-6.44815 - 1.28262i) q^{19} +(-1.91643 - 3.14638i) q^{20} +(5.23358 + 2.31699i) q^{21} +(-4.79426 - 2.10477i) q^{22} +(7.47552 + 3.09646i) q^{23} +(-1.36981 + 4.70358i) q^{24} +(1.48458 - 0.614932i) q^{25} +(-0.0161829 + 0.771012i) q^{26} +(3.92986 - 3.39944i) q^{27} +(4.86522 - 4.47304i) q^{28} +(-0.420063 + 0.280677i) q^{29} +(4.08657 + 1.91274i) q^{30} +2.79490 q^{31} +(4.34846 + 3.61813i) q^{32} +(6.31776 - 1.09925i) q^{33} +(-1.35680 - 0.948362i) q^{34} +(-3.38175 - 5.06114i) q^{35} +(-1.78782 - 5.72745i) q^{36} +(-0.213702 - 1.07435i) q^{37} +(0.195109 - 9.29567i) q^{38} +(-0.505675 - 0.797731i) q^{39} +(3.90857 - 3.44499i) q^{40} +(-3.82720 + 9.23967i) q^{41} +(-1.93517 + 7.85956i) q^{42} +(3.05140 - 4.56674i) q^{43} +(1.74805 - 7.19543i) q^{44} +(-5.46555 + 0.815908i) q^{45} +(-2.46745 + 11.1738i) q^{46} +(7.47207 + 7.47207i) q^{47} +(-6.88782 - 0.746967i) q^{48} +(2.77158 - 2.77158i) q^{49} +(1.22260 + 1.91559i) q^{50} +(2.02683 + 0.0488175i) q^{51} +(-1.07765 + 0.167698i) q^{52} +(-2.02433 - 1.35261i) q^{53} +(5.70343 + 4.63367i) q^{54} +(-6.30076 - 2.60986i) q^{55} +(7.42922 + 5.67129i) q^{56} +(6.09665 + 9.61781i) q^{57} +(-0.494492 - 0.515695i) q^{58} +(-10.5918 + 2.10685i) q^{59} +(-1.65524 + 6.16258i) q^{60} +(0.153998 - 0.102898i) q^{61} +(0.689591 + 3.89196i) q^{62} +(-3.34838 - 9.33085i) q^{63} +(-3.96543 + 6.94805i) q^{64} +1.00448i q^{65} +(3.08952 + 8.52642i) q^{66} +(1.39419 + 2.08655i) q^{67} +(0.985851 - 2.12337i) q^{68} +(-5.04991 - 13.0734i) q^{69} +(6.21338 - 5.95791i) q^{70} +(-5.26483 - 12.7104i) q^{71} +(7.53450 - 3.90273i) q^{72} +(-3.57907 + 8.64064i) q^{73} +(1.44333 - 0.562662i) q^{74} +(-2.54497 - 1.12670i) q^{75} +(12.9926 - 2.02185i) q^{76} +(2.38681 - 11.9993i) q^{77} +(0.986094 - 0.900991i) q^{78} +(9.99933 + 9.99933i) q^{79} +(5.76160 + 4.59279i) q^{80} +(-8.95828 - 0.865574i) q^{81} +(-13.8108 - 3.04974i) q^{82} +(-1.76923 + 8.89454i) q^{83} +(-11.4221 - 0.755565i) q^{84} +(-1.79279 - 1.19790i) q^{85} +(7.11217 + 3.12238i) q^{86} +(0.853868 + 0.191327i) q^{87} +(10.4511 + 0.658856i) q^{88} +(-4.17398 - 10.0769i) q^{89} +(-2.48470 - 7.40960i) q^{90} +(-1.76734 + 0.351545i) q^{91} +(-16.1686 - 0.679033i) q^{92} +(-3.33962 - 3.50447i) q^{93} +(-8.56143 + 12.2486i) q^{94} -12.1104i q^{95} +(-0.659276 - 9.77575i) q^{96} -15.1389i q^{97} +(4.54333 + 3.17565i) q^{98} +(-8.92742 - 6.60822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9}+O(q^{10}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28} - 88 q^{30} - 32 q^{31} - 16 q^{34} - 88 q^{36} - 16 q^{37} - 8 q^{39} - 16 q^{40} - 48 q^{42} - 16 q^{43} - 8 q^{45} - 16 q^{46} - 8 q^{48} - 16 q^{49} - 8 q^{51} + 32 q^{52} - 8 q^{54} - 80 q^{55} - 8 q^{57} + 128 q^{58} - 8 q^{60} - 16 q^{61} + 80 q^{64} - 24 q^{66} - 144 q^{67} - 8 q^{69} + 80 q^{70} - 8 q^{72} - 16 q^{73} - 8 q^{75} + 96 q^{76} + 16 q^{78} - 48 q^{79} - 8 q^{81} + 64 q^{82} + 104 q^{84} - 16 q^{85} - 8 q^{87} + 64 q^{88} + 136 q^{90} - 16 q^{91} - 32 q^{93} + 80 q^{94} + 128 q^{96} - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

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