LMFDB - Embedded newform 153.2.s.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	153.11
Dual form			153.2.s.a.14.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06529 + 1.38832i) q^{2} +(-1.29747 - 1.14742i) q^{3} +(-0.274934 + 1.02607i) q^{4} +(2.70285 + 0.177154i) q^{5} +(0.210798 - 3.02363i) q^{6} +(0.103700 + 1.58216i) q^{7} +(1.51606 - 0.627973i) q^{8} +(0.366853 + 2.97749i) q^{9} +O(q^{10})$	\(q+(1.06529 + 1.38832i) q^{2} +(-1.29747 - 1.14742i) q^{3} +(-0.274934 + 1.02607i) q^{4} +(2.70285 + 0.177154i) q^{5} +(0.210798 - 3.02363i) q^{6} +(0.103700 + 1.58216i) q^{7} +(1.51606 - 0.627973i) q^{8} +(0.366853 + 2.97749i) q^{9} +(2.63338 + 3.94113i) q^{10} +(-2.19104 - 1.92149i) q^{11} +(1.53405 - 1.01583i) q^{12} +(0.0576598 + 0.0154499i) q^{13} +(-2.08607 + 1.82943i) q^{14} +(-3.30359 - 3.33116i) q^{15} +(4.32677 + 2.49806i) q^{16} +(-3.87687 + 1.40353i) q^{17} +(-3.74288 + 3.68120i) q^{18} +(-1.06733 - 0.442104i) q^{19} +(-0.924878 + 2.72460i) q^{20} +(1.68085 - 2.17179i) q^{21} +(0.333537 - 5.08880i) q^{22} +(-2.38991 - 7.04045i) q^{23} +(-2.68759 - 0.924784i) q^{24} +(2.31678 + 0.305010i) q^{25} +(0.0399752 + 0.0965087i) q^{26} +(2.94045 - 4.28413i) q^{27} +(-1.65192 - 0.328587i) q^{28} +(-7.40240 + 3.65046i) q^{29} +(1.10540 - 8.13508i) q^{30} +(-1.71429 - 1.95477i) q^{31} +(0.712795 + 5.41421i) q^{32} +(0.638049 + 5.00711i) q^{33} +(-6.07853 - 3.88715i) q^{34} +4.29471i q^{35} +(-3.15597 - 0.442197i) q^{36} +(0.970339 + 4.87822i) q^{37} +(-0.523242 - 1.95277i) q^{38} +(-0.0570843 - 0.0862058i) q^{39} +(4.20893 - 1.42874i) q^{40} +(4.78363 - 9.70024i) q^{41} +(4.80573 + 0.0199644i) q^{42} +(-1.21308 + 9.21423i) q^{43} +(2.57397 - 1.71987i) q^{44} +(0.464075 + 8.11268i) q^{45} +(7.22841 - 10.8181i) q^{46} +(-0.132297 + 0.0354488i) q^{47} +(-2.74752 - 8.20578i) q^{48} +(4.44764 - 0.585543i) q^{49} +(2.04460 + 3.54135i) q^{50} +(6.64055 + 2.62737i) q^{51} +(-0.0317053 + 0.0549153i) q^{52} +(-3.58381 + 8.65209i) q^{53} +(9.08016 - 0.481582i) q^{54} +(-5.58164 - 5.58164i) q^{55} +(1.15077 + 2.33353i) q^{56} +(0.877553 + 1.79830i) q^{57} +(-12.9537 - 6.38806i) q^{58} +(-1.64974 - 1.26589i) q^{59} +(4.32627 - 2.47387i) q^{60} +(6.88267 - 0.451114i) q^{61} +(0.887622 - 4.46238i) q^{62} +(-4.67281 + 0.889186i) q^{63} +(0.308284 - 0.308284i) q^{64} +(0.153109 + 0.0519734i) q^{65} +(-6.27174 + 6.21985i) q^{66} +(-4.28070 + 2.47146i) q^{67} +(-0.374231 - 4.36381i) q^{68} +(-4.97752 + 11.8770i) q^{69} +(-5.96241 + 4.57512i) q^{70} +(-6.84006 + 1.36057i) q^{71} +(2.42595 + 4.28368i) q^{72} +(-2.68314 - 1.79281i) q^{73} +(-5.73882 + 6.54387i) q^{74} +(-2.65598 - 3.05407i) q^{75} +(0.747076 - 0.973608i) q^{76} +(2.81289 - 3.66583i) q^{77} +(0.0588694 - 0.171085i) q^{78} +(-0.790836 + 0.901776i) q^{79} +(11.2521 + 7.51839i) q^{80} +(-8.73084 + 2.18460i) q^{81} +(18.5629 - 3.69240i) q^{82} +(5.91311 - 4.53729i) q^{83} +(1.76628 + 2.32177i) q^{84} +(-10.7272 + 3.10672i) q^{85} +(-14.0845 + 8.13171i) q^{86} +(13.7930 + 3.75731i) q^{87} +(-4.52839 - 1.53718i) q^{88} +(10.1512 - 10.1512i) q^{89} +(-10.7686 + 9.28665i) q^{90} +(-0.0184649 + 0.0928292i) q^{91} +(7.88105 - 0.516552i) q^{92} +(-0.0187079 + 4.50327i) q^{93} +(-0.190149 - 0.145906i) q^{94} +(-2.80652 - 1.38402i) q^{95} +(5.28755 - 7.84265i) q^{96} +(5.55057 + 11.2554i) q^{97} +(5.55095 + 5.55095i) q^{98} +(4.91742 - 7.22869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.06529	+	1.38832i	0.753275	+	0.981687i	0.999921	+	0.0125813i	$0.00400487\pi$
$2$	1.06529	+	1.38832i	0.753275	+	0.981687i	−0.246646	+	0.969106i	$0.579328\pi$
$3$	−1.29747	−	1.14742i	−0.749094	−	0.662463i
$3$	−1.29747	−	1.14742i	−0.749094	−	0.662463i
$4$	−0.274934	+	1.02607i	−0.137467	+	0.513035i
$5$	2.70285	+	0.177154i	1.20875	+	0.0792257i	0.656418	−	0.754398i	$-0.272071\pi$
$5$	2.70285	+	0.177154i	1.20875	+	0.0792257i	0.552333	+	0.833623i	$0.313738\pi$
$6$	0.210798	−	3.02363i	0.0860579	−	1.23439i
$7$	0.103700	+	1.58216i	0.0391950	+	0.598000i	0.971607	+	0.236602i	$0.0760338\pi$
$7$	0.103700	+	1.58216i	0.0391950	+	0.598000i	−0.932412	+	0.361398i	$0.882300\pi$
$8$	1.51606	−	0.627973i	0.536009	−	0.222022i
$9$	0.366853	+	2.97749i	0.122284	+	0.992495i
$10$	2.63338	+	3.94113i	0.832747	+	1.24629i
$11$	−2.19104	−	1.92149i	−0.660623	−	0.579351i	0.261993	−	0.965070i	$-0.415620\pi$
$11$	−2.19104	−	1.92149i	−0.660623	−	0.579351i	−0.922616	+	0.385719i	$0.873953\pi$
$12$	1.53405	−	1.01583i	0.442843	−	0.293244i
$13$	0.0576598	+	0.0154499i	0.0159920	+	0.00428503i	0.266806	−	0.963750i	$-0.414032\pi$
$13$	0.0576598	+	0.0154499i	0.0159920	+	0.00428503i	−0.250814	+	0.968035i	$0.580698\pi$
$14$	−2.08607	+	1.82943i	−0.557524	+	0.488936i
$15$	−3.30359	−	3.33116i	−0.852984	−	0.860101i
$16$	4.32677	+	2.49806i	1.08169	+	0.624515i
$17$	−3.87687	+	1.40353i	−0.940279	+	0.340405i
$17$	−3.87687	+	1.40353i	−0.940279	+	0.340405i
$18$	−3.74288	+	3.68120i	−0.882206	+	0.867667i
$19$	−1.06733	−	0.442104i	−0.244863	−	0.101426i	0.256877	−	0.966444i	$-0.417307\pi$
$19$	−1.06733	−	0.442104i	−0.244863	−	0.101426i	−0.501740	+	0.865019i	$0.667307\pi$
$20$	−0.924878	+	2.72460i	−0.206809	+	0.609240i
$21$	1.68085	−	2.17179i	0.366792	−	0.473924i
$22$	0.333537	−	5.08880i	0.0711104	−	1.08494i
$23$	−2.38991	−	7.04045i	−0.498331	−	1.46803i	−0.847409	−	0.530941i	$-0.821839\pi$
$23$	−2.38991	−	7.04045i	−0.498331	−	1.46803i	0.349078	−	0.937094i	$-0.386495\pi$
$24$	−2.68759	−	0.924784i	−0.548603	−	0.188771i
$25$	2.31678	+	0.305010i	0.463357	+	0.0610021i
$26$	0.0399752	+	0.0965087i	0.00783978	+	0.0189269i
$27$	2.94045	−	4.28413i	0.565889	−	0.824481i
$28$	−1.65192	−	0.328587i	−0.312183	−	0.0620970i
$29$	−7.40240	+	3.65046i	−1.37459	+	0.677874i	−0.971446	−	0.237262i	$-0.923750\pi$
$29$	−7.40240	+	3.65046i	−1.37459	+	0.677874i	−0.403146	+	0.915136i	$0.632083\pi$
$30$	1.10540	−	8.13508i	0.201818	−	1.48526i
$31$	−1.71429	−	1.95477i	−0.307896	−	0.351088i	0.577111	−	0.816665i	$-0.304180\pi$
$31$	−1.71429	−	1.95477i	−0.307896	−	0.351088i	−0.885007	+	0.465578i	$0.845847\pi$
$32$	0.712795	+	5.41421i	0.126006	+	0.957107i
$33$	0.638049	+	5.00711i	0.111070	+	0.871627i
$34$	−6.07853	−	3.88715i	−1.04246	−	0.666641i
$35$			4.29471i			0.725938i
$36$	−3.15597	−	0.442197i	−0.525994	−	0.0736994i
$37$	0.970339	+	4.87822i	0.159523	+	0.801975i	0.974831	+	0.222947i	$0.0715677\pi$
$37$	0.970339	+	4.87822i	0.159523	+	0.801975i	−0.815308	+	0.579028i	$0.803432\pi$
$38$	−0.523242	−	1.95277i	−0.0848810	−	0.316780i
$39$	−0.0570843	−	0.0862058i	−0.00914081	−	0.0138040i
$40$	4.20893	−	1.42874i	0.665491	−	0.225904i
$41$	4.78363	−	9.70024i	0.747077	−	1.51492i	−0.106704	−	0.994291i	$-0.534030\pi$
$41$	4.78363	−	9.70024i	0.747077	−	1.51492i	0.853781	−	0.520632i	$-0.174304\pi$
$42$	4.80573	+	0.0199644i	0.741540	+	0.00308057i
$43$	−1.21308	+	9.21423i	−0.184992	+	1.40516i	0.607036	+	0.794674i	$0.292358\pi$
$43$	−1.21308	+	9.21423i	−0.184992	+	1.40516i	−0.792029	+	0.610484i	$0.790975\pi$
$44$	2.57397	−	1.71987i	0.388041	−	0.259281i
$45$	0.464075	+	8.11268i	0.0691802	+	1.20937i
$46$	7.22841	−	10.8181i	1.06577	−	1.59504i
$47$	−0.132297	+	0.0354488i	−0.0192975	+	0.00517074i	−0.268455	−	0.963292i	$-0.586513\pi$
$47$	−0.132297	+	0.0354488i	−0.0192975	+	0.00517074i	0.249157	+	0.968463i	$0.419846\pi$
$48$	−2.74752	−	8.20578i	−0.396571	−	1.18440i
$49$	4.44764	−	0.585543i	0.635377	−	0.0836490i
$50$	2.04460	+	3.54135i	0.289150	+	0.500823i
$51$	6.64055	+	2.62737i	0.929863	+	0.367905i
$52$	−0.0317053	+	0.0549153i	−0.00439674	+	0.00761538i
$53$	−3.58381	+	8.65209i	−0.492275	+	1.18846i	0.461285	+	0.887252i	$0.347389\pi$
$53$	−3.58381	+	8.65209i	−0.492275	+	1.18846i	−0.953560	+	0.301204i	$0.902611\pi$
$54$	9.08016	−	0.481582i	1.23565	−	0.0655349i
$55$	−5.58164	−	5.58164i	−0.752629	−	0.752629i
$56$	1.15077	+	2.33353i	0.153778	+	0.311831i
$57$	0.877553	+	1.79830i	0.116235	+	0.238190i
$58$	−12.9537	−	6.38806i	−1.70091	−	0.838794i
$59$	−1.64974	−	1.26589i	−0.214777	−	0.164805i	0.495770	−	0.868454i	$-0.334886\pi$
$59$	−1.64974	−	1.26589i	−0.214777	−	0.164805i	−0.710547	+	0.703649i	$0.751553\pi$
$60$	4.32627	−	2.47387i	0.558519	−	0.319375i
$61$	6.88267	−	0.451114i	0.881236	−	0.0577592i	0.381936	−	0.924189i	$-0.375257\pi$
$61$	6.88267	−	0.451114i	0.881236	−	0.0577592i	0.499300	+	0.866429i	$0.333591\pi$
$62$	0.887622	−	4.46238i	0.112728	−	0.566723i
$63$	−4.67281	+	0.889186i	−0.588719	+	0.112027i
$64$	0.308284	−	0.308284i	0.0385355	−	0.0385355i
$65$	0.153109	+	0.0519734i	0.0189908	+	0.00644651i
$66$	−6.27174	+	6.21985i	−0.771998	+	0.765611i
$67$	−4.28070	+	2.47146i	−0.522970	+	0.301937i	−0.738149	−	0.674638i	$-0.764300\pi$
$67$	−4.28070	+	2.47146i	−0.522970	+	0.301937i	0.215179	+	0.976575i	$0.430967\pi$
$68$	−0.374231	−	4.36381i	−0.0453822	−	0.529190i
$69$	−4.97752	+	11.8770i	−0.599223	+	1.42982i
$70$	−5.96241	+	4.57512i	−0.712644	+	0.546831i
$71$	−6.84006	+	1.36057i	−0.811766	+	0.161470i	−0.583484	−	0.812125i	$-0.698311\pi$
$71$	−6.84006	+	1.36057i	−0.811766	+	0.161470i	−0.228282	+	0.973595i	$0.573311\pi$
$72$	2.42595	+	4.28368i	0.285901	+	0.504836i
$73$	−2.68314	−	1.79281i	−0.314037	−	0.209833i	0.388555	−	0.921425i	$-0.372974\pi$
$73$	−2.68314	−	1.79281i	−0.314037	−	0.209833i	−0.702592	+	0.711592i	$0.747974\pi$
$74$	−5.73882	+	6.54387i	−0.667124	+	0.760709i
$75$	−2.65598	−	3.05407i	−0.306686	−	0.352653i
$76$	0.747076	−	0.973608i	0.0856955	−	0.111681i
$77$	2.81289	−	3.66583i	0.320559	−	0.417760i
$78$	0.0588694	−	0.171085i	0.00666565	−	0.0193716i
$79$	−0.790836	+	0.901776i	−0.0889760	+	0.101458i	−0.794614	−	0.607114i	$-0.792327\pi$
$79$	−0.790836	+	0.901776i	−0.0889760	+	0.101458i	0.705638	+	0.708572i	$0.250660\pi$
$80$	11.2521	+	7.51839i	1.25802	+	0.840581i
$81$	−8.73084	+	2.18460i	−0.970093	+	0.242733i
$82$	18.5629	−	3.69240i	2.04993	−	0.407757i
$83$	5.91311	−	4.53729i	0.649048	−	0.498032i	−0.230977	−	0.972959i	$-0.574192\pi$
$83$	5.91311	−	4.53729i	0.649048	−	0.498032i	0.880025	+	0.474927i	$0.157526\pi$
$84$	1.76628	+	2.32177i	0.192717	+	0.253326i
$85$	−10.7272	+	3.10672i	−1.16353	+	0.336971i
$86$	−14.0845	+	8.13171i	−1.51878	+	0.876865i
$87$	13.7930	+	3.75731i	1.47877	+	0.402826i
$88$	−4.52839	−	1.53718i	−0.482728	−	0.163864i
$89$	10.1512	−	10.1512i	1.07602	−	1.07602i	0.0791578	−	0.996862i	$-0.474777\pi$
$89$	10.1512	−	10.1512i	1.07602	−	1.07602i	0.996862	−	0.0791578i	$-0.0252231\pi$
$90$	−10.7686	+	9.28665i	−1.13511	+	0.978899i
$91$	−0.0184649	+	0.0928292i	−0.00193565	+	0.00973115i
$92$	7.88105	−	0.516552i	0.821657	−	0.0538542i
$93$	−0.0187079	+	4.50327i	−0.00193992	+	0.466967i
$94$	−0.190149	−	0.145906i	−0.0196124	−	0.0150491i
$95$	−2.80652	−	1.38402i	−0.287943	−	0.141998i
$96$	5.28755	−	7.84265i	0.539658	−	0.800437i
$97$	5.55057	+	11.2554i	0.563575	+	1.14282i	0.973071	+	0.230505i	$0.0740380\pi$
$97$	5.55057	+	11.2554i	0.563575	+	1.14282i	−0.409496	+	0.912312i	$0.634295\pi$
$98$	5.55095	+	5.55095i	0.560731	+	0.560731i
$99$	4.91742	−	7.22869i	0.494219	−	0.726510i
$100$	−0.949925	+	2.29332i	−0.0949925	+	0.229332i
$101$	6.17752	−	10.6998i	0.614686	−	1.06467i	−0.375753	−	0.926720i	$-0.622616\pi$
$101$	6.17752	−	10.6998i	0.614686	−	1.06467i	0.990439	−	0.137948i	$-0.0440507\pi$
$102$	3.42652	+	12.0181i	0.339276	+	1.18997i
$103$	3.53868	+	6.12918i	0.348677	+	0.603926i	0.986015	−	0.166659i	$-0.0532978\pi$
$103$	3.53868	+	6.12918i	0.348677	+	0.603926i	−0.637338	+	0.770584i	$0.719964\pi$
$104$	0.0971180	−	0.0127858i	0.00952320	−	0.00125375i
$105$	4.92784	−	5.57225i	0.480908	−	0.543796i
$106$	−15.8296	+	4.24154i	−1.53751	+	0.411975i
$107$	7.68188	−	11.4967i	0.742635	−	1.11143i	−0.247166	−	0.968973i	$-0.579499\pi$
$107$	7.68188	−	11.4967i	0.742635	−	1.11143i	0.989801	−	0.142459i	$-0.0455008\pi$
$108$	3.58738	+	4.19496i	0.345196	+	0.403660i
$109$	7.20324	−	4.81305i	0.689946	−	0.461007i	−0.160523	−	0.987032i	$-0.551318\pi$
$109$	7.20324	−	4.81305i	0.689946	−	0.461007i	0.850469	+	0.526025i	$0.176318\pi$
$110$	1.80300	−	13.6952i	0.171910	−	1.30578i
$111$	4.33839	−	7.44273i	0.411782	−	0.706433i
$112$	−3.50365	+	7.10469i	−0.331063	+	0.671330i
$113$	13.0107	−	4.41653i	1.22394	−	0.415473i	0.366678	−	0.930348i	$-0.380495\pi$
$113$	13.0107	−	4.41653i	1.22394	−	0.415473i	0.857265	+	0.514875i	$0.172162\pi$
$114$	−1.56175	+	3.13403i	−0.146271	+	0.293529i
$115$	−5.21232	−	19.4526i	−0.486051	−	1.81397i
$116$	−1.71045	−	8.59901i	−0.158811	−	0.798398i
$117$	−0.0248492	+	0.177349i	−0.00229731	+	0.0163959i
$118$		−	3.63889i		−	0.334987i
$119$	−2.62264	−	5.98828i	−0.240417	−	0.548945i
$120$	−7.10033	−	2.97567i	−0.648168	−	0.271640i
$121$	−0.327260	−	2.48578i	−0.0297509	−	0.225980i
$122$	7.95834	+	9.07475i	0.720514	+	0.821589i
$123$	−17.3369	+	7.09693i	−1.56321	+	0.639909i
$124$	2.47705	−	1.22155i	0.222446	−	0.109698i
$125$	−7.07513	−	1.40733i	−0.632819	−	0.125876i
$126$	−6.21238	−	5.54010i	−0.553443	−	0.493551i
$127$	8.29944	+	20.0366i	0.736456	+	1.77796i	0.619754	+	0.784796i	$0.287232\pi$
$127$	8.29944	+	20.0366i	0.736456	+	1.77796i	0.116703	+	0.993167i	$0.462768\pi$
$128$	11.5848	+	1.52517i	1.02396	+	0.134807i
$129$	12.1465	−	10.5633i	1.06944	−	0.930045i
$130$	0.0909500	+	0.267930i	0.00797684	+	0.0234990i
$131$	−1.28513	+	19.6073i	−0.112282	+	1.71309i	0.455767	+	0.890099i	$0.349365\pi$
$131$	−1.28513	+	19.6073i	−0.112282	+	1.71309i	−0.568049	+	0.822995i	$0.692302\pi$
$132$	−5.31307	−	0.721945i	−0.462443	−	0.0628373i
$133$	0.588796	−	1.73454i	0.0510551	−	0.150404i
$134$	−7.99136	−	3.31013i	−0.690348	−	0.285952i
$135$	8.70653	−	11.0584i	0.749339	−	0.951759i
$136$	−4.99619	+	4.56240i	−0.428420	+	0.391223i
$137$	−0.365975	−	0.211296i	−0.0312673	−	0.0180522i	0.484285	−	0.874910i	$-0.339080\pi$
$137$	−0.365975	−	0.211296i	−0.0312673	−	0.0180522i	−0.515552	+	0.856858i	$0.672413\pi$
$138$	−21.7915	+	5.74210i	−1.85502	+	0.488800i
$139$	−0.637582	+	0.559145i	−0.0540790	+	0.0474260i	−0.685959	−	0.727640i	$-0.740617\pi$
$139$	−0.637582	+	0.559145i	−0.0540790	+	0.0474260i	0.631880	+	0.775066i	$0.282284\pi$
$140$	−4.40667	−	1.18076i	−0.372431	−	0.0997927i
$141$	0.212326	+	0.105806i	0.0178811	+	0.00891050i
$142$	−9.17557	−	8.04676i	−0.769996	−	0.675269i
$143$	−0.0966481	−	0.144644i	−0.00808212	−	0.0120957i
$144$	−5.85065	+	13.7993i	−0.487554	+	1.14994i
$145$	−20.6543	+	8.55528i	−1.71524	+	0.710477i
$146$	−0.369331	−	5.63491i	−0.0305661	−	0.466348i
$147$	−6.44254	−	4.34359i	−0.531372	−	0.358253i
$148$	−5.27217	−	0.345557i	−0.433370	−	0.0284046i
$149$	−2.91728	+	10.8874i	−0.238993	+	0.891933i	0.737315	+	0.675549i	$0.236093\pi$
$149$	−2.91728	+	10.8874i	−0.238993	+	0.891933i	−0.976308	+	0.216384i	$0.930574\pi$
$150$	1.41061	−	6.94081i	0.115176	−	0.566715i
$151$	−0.706524	−	0.920760i	−0.0574961	−	0.0749304i	0.763720	−	0.645547i	$-0.223371\pi$
$151$	−0.706524	−	0.920760i	−0.0574961	−	0.0749304i	−0.821216	+	0.570617i	$0.806704\pi$
$152$	−1.89577			−0.153767
$153$	−5.60122	−	11.0284i	−0.452832	−	0.891596i
$154$	8.08588			0.651579
$155$	−4.28717	−	5.58715i	−0.344354	−	0.448771i
$156$	0.104148	−	0.0348715i	0.00833848	−	0.00279196i
$157$	3.13630	−	11.7048i	0.250304	−	0.934146i	−0.720339	−	0.693622i	$-0.756014\pi$
$157$	3.13630	−	11.7048i	0.250304	−	0.934146i	0.970643	−	0.240524i	$-0.0773194\pi$
$158$	−2.09442	−	0.137276i	−0.166623	−	0.0109211i
$159$	14.5775	−	7.11368i	1.15607	−	0.564152i
$160$	0.967427	+	14.7601i	0.0764818	+	1.16689i
$161$	10.8913	−	4.51131i	0.858353	−	0.355541i
$162$	−12.3338	−	9.79392i	−0.969035	−	0.769483i
$163$	−2.09236	−	3.13144i	−0.163886	−	0.245273i	0.740433	−	0.672130i	$-0.234621\pi$
$163$	−2.09236	−	3.13144i	−0.163886	−	0.245273i	−0.904319	+	0.426857i	$0.859621\pi$
$164$	8.63793	+	7.57526i	0.674509	+	0.591529i
$165$	0.837520	+	13.6465i	0.0652008	+	1.06238i
$166$	12.5984	+	3.37572i	0.977823	+	0.262007i
$167$	0.400144	−	0.350917i	0.0309641	−	0.0271548i	−0.643724	−	0.765258i	$-0.722611\pi$
$167$	0.400144	−	0.350917i	0.0309641	−	0.0271548i	0.674688	+	0.738103i	$0.264278\pi$
$168$	1.18445	−	4.34810i	0.0913824	−	0.335463i
$169$	−11.2552	−	6.49822i	−0.865788	−	0.499863i
$170$	−15.7407	−	11.5832i	−1.20726	−	0.888392i
$171$	0.924804	−	3.34016i	0.0707215	−	0.255428i
$172$	−9.12092	−	3.77801i	−0.695464	−	0.288071i
$173$	−3.15543	+	9.29559i	−0.239903	+	0.706731i	0.758576	+	0.651585i	$0.225896\pi$
$173$	−3.15543	+	9.29559i	−0.239903	+	0.706731i	−0.998478	+	0.0551457i	$0.982438\pi$
$174$	9.47725	+	23.1517i	0.718468	+	1.75512i
$175$	−0.242324	+	3.69715i	−0.0183180	+	0.279478i
$176$	−4.68012	−	13.7872i	−0.352777	−	1.03925i
$177$	0.687978	+	3.53539i	0.0517116	+	0.265736i
$178$	24.9069	+	3.27906i	1.86685	+	0.245776i
$179$	−4.85593	−	11.7232i	−0.362949	−	0.876236i	−0.994866	−	0.101200i	$-0.967732\pi$
$179$	−4.85593	−	11.7232i	−0.362949	−	0.876236i	0.631917	−	0.775036i	$-0.282268\pi$
$180$	−8.45176	−	1.75428i	−0.629957	−	0.130757i
$181$	−24.9297	−	4.95882i	−1.85301	−	0.368586i	−0.862503	−	0.506052i	$-0.831104\pi$
$181$	−24.9297	−	4.95882i	−1.85301	−	0.368586i	−0.990507	+	0.137466i	$0.956104\pi$
$182$	−0.148547	+	0.0732551i	−0.0110110	+	0.00543003i
$183$	−9.44767	−	7.31201i	−0.698392	−	0.540519i
$184$	−8.04446	−	9.17295i	−0.593046	−	0.676239i
$185$	1.75848	+	13.3570i	0.129286	+	0.982026i
$186$	−6.27189	+	4.77132i	−0.459877	+	0.349850i
$187$	11.1912	+	4.37418i	0.818384	+	0.319872i
$188$		−	0.145492i		−	0.0106111i
$189$	7.08310	+	4.20799i	0.515220	+	0.306086i
$190$	−1.06830	−	5.37072i	−0.0775029	−	0.389633i
$191$	2.40399	+	8.97182i	0.173947	+	0.649178i	0.996729	+	0.0808210i	$0.0257542\pi$
$191$	2.40399	+	8.97182i	0.173947	+	0.649178i	−0.822782	+	0.568357i	$0.807579\pi$
$192$	−0.753721	+	0.0462577i	−0.0543951	+	0.00333836i
$193$	−11.0798	+	3.76110i	−0.797544	+	0.270730i	−0.690319	−	0.723505i	$-0.742530\pi$
$193$	−11.0798	+	3.76110i	−0.797544	+	0.270730i	−0.107225	+	0.994235i	$0.534197\pi$
$194$	−9.71313	+	19.6963i	−0.697362	+	1.41411i
$195$	−0.139019	−	0.243114i	−0.00995533	−	0.0174098i
$196$	−0.622002	+	4.72457i	−0.0444287	+	0.337469i
$197$	−18.8701	+	12.6086i	−1.34444	+	0.898328i	−0.999192	−	0.0401830i	$-0.987206\pi$
$197$	−18.8701	+	12.6086i	−1.34444	+	0.898328i	−0.345250	+	0.938511i	$0.612206\pi$
$198$	15.2742	−	0.873738i	1.08549	−	0.0620938i
$199$	13.3536	−	19.9851i	0.946611	−	1.41670i	0.0378986	−	0.999282i	$-0.487934\pi$
$199$	13.3536	−	19.9851i	0.946611	−	1.41670i	0.908713	−	0.417422i	$-0.137066\pi$
$200$	3.70392	−	0.992464i	0.261907	−	0.0701778i
$201$	8.38988	+	1.70511i	0.591776	+	0.120269i
$202$	21.4355	−	2.82204i	1.50820	−	0.198558i
$203$	−6.54324	−	11.3332i	−0.459246	−	0.795437i
$204$	−4.52158	+	6.09131i	−0.316574	+	0.426477i
$205$	14.6479	−	25.3708i	1.02305	−	1.77198i
$206$	−4.73950	+	11.4422i	−0.330217	+	0.797213i
$207$	20.0861	−	9.69873i	1.39608	−	0.674108i
$208$	0.210886	+	0.210886i	0.0146223	+	0.0146223i
$209$	1.48907	+	3.01954i	0.103001	+	0.208866i
$210$	12.9856	+	0.905315i	0.896093	+	0.0624727i
$211$	21.5579	+	10.6312i	1.48410	+	0.731879i	0.990462	−	0.137785i	$-0.0439984\pi$
$211$	21.5579	+	10.6312i	1.48410	+	0.731879i	0.493643	+	0.869665i	$0.335665\pi$
$212$	−7.89233	−	6.05600i	−0.542047	−	0.415928i
$213$	10.4359	+	6.08313i	0.715058	+	0.416809i
$214$	24.1445	−	1.58252i	1.65049	−	0.108179i
$215$	−4.91110	+	24.6898i	−0.334934	+	1.68383i
$216$	1.76758	−	8.34153i	0.120269	−	0.567569i
$217$	2.91499	−	2.91499i	0.197883	−	0.197883i
$218$	14.3556	+	4.87307i	0.972283	+	0.330046i
$219$	1.42417	+	5.40481i	0.0962368	+	0.365223i
$220$	7.26174	−	4.19257i	0.489586	−	0.282663i
$221$	−0.245224	+	0.0210299i	−0.0164955	+	0.00141462i
$222$	14.9545	−	1.90563i	1.00368	−	0.127898i
$223$	−5.36540	+	4.11702i	−0.359294	+	0.275696i	−0.772596	−	0.634898i	$-0.781042\pi$
$223$	−5.36540	+	4.11702i	−0.359294	+	0.275696i	0.413302	+	0.910594i	$0.364375\pi$
$224$	−8.49223	+	1.68921i	−0.567411	+	0.112865i
$225$	−0.0582448	+	7.01008i	−0.00388299	+	0.467339i
$226$	19.9917	+	13.3580i	1.32983	+	0.888564i
$227$	−17.6063	+	20.0761i	−1.16857	+	1.33250i	−0.235897	+	0.971778i	$0.575803\pi$
$227$	−17.6063	+	20.0761i	−1.16857	+	1.33250i	−0.932674	+	0.360721i	$0.882531\pi$
$228$	−2.08645	+	0.406017i	−0.138178	+	0.0268891i
$229$	4.15682	−	5.41728i	0.274691	−	0.357984i	−0.635553	−	0.772057i	$-0.719228\pi$
$229$	4.15682	−	5.41728i	0.274691	−	0.357984i	0.910243	+	0.414074i	$0.135894\pi$
$230$	21.4538	−	27.9591i	1.41462	−	1.84357i
$231$	−7.85589	+	1.52873i	−0.516880	+	0.100583i
$232$	−8.93011	+	10.1828i	−0.586290	+	0.668536i
$233$	−0.901442	−	0.602324i	−0.0590554	−	0.0394596i	0.525692	−	0.850675i	$-0.323806\pi$
$233$	−0.901442	−	0.602324i	−0.0590554	−	0.0394596i	−0.584747	+	0.811215i	$0.698806\pi$
$234$	−0.272688	+	0.154430i	−0.0178262	+	0.0100954i
$235$	−0.363858	+	0.0723759i	−0.0237355	+	0.00472128i
$236$	1.75246	−	1.34471i	0.114075	−	0.0875330i
$237$	2.06080	−	0.262605i	0.133863	−	0.0170580i
$238$	5.51975	−	10.0203i	0.357792	−	0.649520i
$239$	−2.06984	+	1.19502i	−0.133887	+	0.0772995i	−0.565447	−	0.824784i	$-0.691296\pi$
$239$	−2.06984	+	1.19502i	−0.133887	+	0.0772995i	0.431561	+	0.902084i	$0.357963\pi$
$240$	−5.97245	−	22.6657i	−0.385520	−	1.46307i
$241$	2.74639	+	0.932275i	0.176911	+	0.0600531i	0.408489	−	0.912763i	$-0.366056\pi$
$241$	2.74639	+	0.932275i	0.176911	+	0.0600531i	−0.231579	+	0.972816i	$0.574389\pi$
$242$	3.10242	−	3.10242i	0.199431	−	0.199431i
$243$	13.8346	+	7.18349i	0.887493	+	0.460821i
$244$	−1.42941	+	7.18612i	−0.0915085	+	0.460044i
$245$	12.1250	−	0.794716i	0.774639	−	0.0507726i
$246$	−28.3216	−	16.5087i	−1.80572	−	1.05256i
$247$	−0.0547118	−	0.0419818i	−0.00348123	−	0.00267124i
$248$	−3.82652	−	1.88703i	−0.242984	−	0.119826i
$249$	−12.8782	−	0.897829i	−0.816126	−	0.0568976i
$250$	−5.58326	−	11.3217i	−0.353116	−	0.716049i
$251$	−5.69148	−	5.69148i	−0.359243	−	0.359243i	0.504291	−	0.863534i	$-0.331754\pi$
$251$	−5.69148	−	5.69148i	−0.359243	−	0.359243i	−0.863534	+	0.504291i	$0.831754\pi$
$252$	0.372351	−	5.03910i	0.0234559	−	0.317433i
$253$	−8.29176	+	20.0181i	−0.521298	+	1.25853i
$254$	−18.9758	+	32.8671i	−1.19065	+	2.06226i
$255$	17.4830	+	8.27777i	1.09483	+	0.518374i
$256$	9.78783	+	16.9530i	0.611739	+	1.05956i
$257$	7.03848	−	0.926633i	0.439048	−	0.0578018i	0.0922377	−	0.995737i	$-0.470598\pi$
$257$	7.03848	−	0.926633i	0.439048	−	0.0578018i	0.346810	+	0.937935i	$0.387265\pi$
$258$	27.6048	+	5.61024i	1.71860	+	0.349278i
$259$	−7.61750	+	2.04110i	−0.473329	+	0.126828i
$260$	−0.0954232	+	0.142811i	−0.00591790	+	0.00885676i
$261$	−13.5848	−	20.7014i	−0.840877	−	1.28138i
$262$	−28.5901	+	19.1033i	−1.76630	+	1.18020i
$263$	0.736763	−	5.59627i	0.0454308	−	0.345081i	−0.953601	−	0.301075i	$-0.902655\pi$
$263$	0.736763	−	5.59627i	0.0454308	−	0.345081i	0.999031	−	0.0440060i	$-0.0140121\pi$
$264$	4.11166	+	7.19042i	0.253055	+	0.442540i
$265$	−11.2193	+	22.7504i	−0.689193	+	1.39755i
$266$	3.03533	−	1.03035i	0.186108	−	0.0631751i
$267$	−24.8184	+	1.52317i	−1.51886	+	0.0932164i
$268$	−1.35898	−	5.07178i	−0.0830129	−	0.309808i
$269$	1.22383	+	6.15259i	0.0746180	+	0.375130i	0.999992	−	0.00392470i	$-0.00124927\pi$
$269$	1.22383	+	6.15259i	0.0746180	+	0.375130i	−0.925374	+	0.379055i	$0.876249\pi$
$270$	24.6276	+	0.306944i	1.49879	+	0.0186800i
$271$		−	16.0106i		−	0.972576i	−0.873799	−	0.486288i	$-0.838351\pi$
$271$		−	16.0106i		−	0.972576i	0.873799	−	0.486288i	$-0.161649\pi$
$272$	−20.2804	−	3.61192i	−1.22968	−	0.219005i
$273$	0.130472	−	0.0992561i	0.00789651	−	0.00600725i
$274$	−0.0965250	−	0.733180i	−0.00583129	−	0.0442930i
$275$	−4.49009	−	5.11996i	−0.270762	−	0.308745i
$276$	−10.8181	−	8.37267i	−0.651175	−	0.503976i
$277$	2.60612	−	1.28519i	0.156586	−	0.0772199i	−0.362307	−	0.932059i	$-0.618011\pi$
$277$	2.60612	−	1.28519i	0.156586	−	0.0772199i	0.518893	+	0.854839i	$0.326344\pi$
$278$	−1.45548	−	0.289513i	−0.0872939	−	0.0173638i
$279$	5.19142	−	5.82139i	0.310802	−	0.348517i
$280$	2.69696	+	6.51104i	0.161174	+	0.389109i
$281$	−4.43302	−	0.583619i	−0.264452	−	0.0348158i	−0.00286588	−	0.999996i	$-0.500912\pi$
$281$	−4.43302	−	0.583619i	−0.264452	−	0.0348158i	−0.261586	+	0.965180i	$0.584246\pi$
$282$	0.0792964	+	0.407490i	0.00472203	+	0.0242656i
$283$	−0.378618	−	1.11537i	−0.0225065	−	0.0663021i	0.935096	−	0.354393i	$-0.115313\pi$
$283$	−0.378618	−	1.11537i	−0.0225065	−	0.0663021i	−0.957603	+	0.288091i	$0.906979\pi$
$284$	0.484527	−	7.39245i	0.0287514	−	0.438661i
$285$	2.05332	+	5.01599i	0.121628	+	0.297121i
$286$	0.0978531	−	0.288266i	0.00578618	−	0.0170455i
$287$	15.8434	+	6.56255i	0.935206	+	0.387375i
$288$	−15.8593	+	4.10856i	−0.934515	+	0.242099i
$289$	13.0602	−	10.8826i	0.768249	−	0.640152i
$290$	−33.8802	−	19.5608i	−1.98952	−	1.14865i
$291$	5.71303	−	20.9724i	0.334904	−	1.22943i
$292$	2.57724	−	2.26018i	0.150821	−	0.132267i
$293$	24.0838	+	6.45324i	1.40699	+	0.377002i	0.880850	−	0.473395i	$-0.156972\pi$
$293$	24.0838	+	6.45324i	1.40699	+	0.377002i	0.526141	+	0.850397i	$0.323638\pi$
$294$	−0.832914	−	13.5715i	−0.0485765	−	0.791504i
$295$	−4.23473	−	3.71376i	−0.246556	−	0.216223i
$296$	4.53449	+	6.78634i	0.263562	+	0.394448i
$297$	−14.6745	+	3.73666i	−0.851503	+	0.216823i
$298$	−18.2229	+	7.54819i	−1.05563	+	0.437255i
$299$	−0.0290276	−	0.442875i	−0.00167871	−	0.0256121i
$300$	3.86390	−	1.88555i	0.223083	−	0.108862i
$301$	−14.7042	−	0.963763i	−0.847535	−	0.0555504i
$302$	0.525651	−	1.96176i	0.0302478	−	0.112886i
$303$	−20.2923	+	6.79442i	−1.16576	+	0.390329i
$304$	−3.51370	−	4.57915i	−0.201525	−	0.262632i
$305$	18.6827			1.06977
$306$	9.34400	−	19.5248i	0.534161	−	1.11616i
$307$	−5.12708			−0.292618			−0.146309	−	0.989239i	$-0.546739\pi$
$307$	−5.12708			−0.292618			−0.146309	+	0.989239i	$0.546739\pi$
$308$	2.98804	+	3.89408i	0.170259	+	0.221886i
$309$	2.44141	−	12.0128i	0.138887	−	0.683383i
$310$	3.18964	−	11.9039i	0.181159	−	0.676095i
$311$	−12.7879	−	0.838161i	−0.725133	−	0.0475277i	−0.301633	−	0.953424i	$-0.597532\pi$
$311$	−12.7879	−	0.838161i	−0.725133	−	0.0475277i	−0.423500	+	0.905896i	$0.639199\pi$
$312$	−0.140678	−	0.0948459i	−0.00796434	−	0.00536959i
$313$	1.10629	+	16.8787i	0.0625312	+	0.954042i	0.907721	+	0.419575i	$0.137821\pi$
$313$	1.10629	+	16.8787i	0.0625312	+	0.954042i	−0.845189	+	0.534467i	$0.820512\pi$
$314$	19.5910	−	8.11488i	1.10559	−	0.457949i
$315$	−12.7874	+	1.57553i	−0.720490	+	0.0887709i
$316$	−0.707856	−	1.05938i	−0.0398200	−	0.0595949i
$317$	−1.37155	−	1.20282i	−0.0770340	−	0.0675570i	0.619963	−	0.784631i	$-0.287148\pi$
$317$	−1.37155	−	1.20282i	−0.0770340	−	0.0675570i	−0.696997	+	0.717074i	$0.745481\pi$
$318$	25.4053	+	12.6600i	1.42466	+	0.709936i
$319$	23.2333	+	6.22534i	1.30081	+	0.348552i
$320$	0.887859	−	0.778632i	0.0496328	−	0.0435268i
$321$	−23.1586	+	6.10233i	−1.29259	+	0.340599i
$322$	17.8655	+	10.3147i	0.995606	+	0.574813i
$323$	4.75842	+	0.215948i	0.264765	+	0.0120157i
$324$	0.158858	−	9.55906i	0.00882545	−	0.531059i
$325$	0.128873	+	0.0533809i	0.00714859	+	0.00296104i
$326$	2.11845	−	6.24075i	0.117330	−	0.345643i
$327$	−14.8686	−	2.02036i	−0.822235	−	0.111726i
$328$	1.16078	−	17.7102i	0.0640936	−	0.977880i
$329$	−0.0698049	−	0.205639i	−0.00384847	−	0.0113372i
$330$	−18.0534	+	15.7002i	−0.993810	+	0.864270i
$331$	0.157998	+	0.0208008i	0.00868434	+	0.00114332i	0.134867	−	0.990864i	$-0.456939\pi$
$331$	0.157998	+	0.0208008i	0.00868434	+	0.00114332i	−0.126183	+	0.992007i	$0.540273\pi$
$332$	3.02985	+	7.31471i	0.166285	+	0.401447i
$333$	−14.1689	+	4.67876i	−0.776449	+	0.256394i
$334$	0.913454	+	0.181697i	0.0499820	+	0.00994203i
$335$	−12.0079	+	5.92164i	−0.656062	+	0.323534i
$336$	12.6979	−	5.19796i	0.692729	−	0.283572i
$337$	2.70927	+	3.08933i	0.147583	+	0.168287i	0.820908	−	0.571060i	$-0.193468\pi$
$337$	2.70927	+	3.08933i	0.147583	+	0.168287i	−0.673325	+	0.739347i	$0.735134\pi$
$338$	−2.96854	−	22.5483i	−0.161467	−	1.22647i
$339$	−21.9486	−	9.19841i	−1.19208	−	0.499589i
$340$	−0.238423	−	11.8610i	−0.0129303	−	0.643254i
$341$			7.57697i			0.410316i
$342$	5.62238	−	2.27432i	0.304023	−	0.122981i
$343$	3.55293	+	17.8618i	0.191840	+	0.964445i
$344$	3.94719	+	14.7311i	0.212818	+	0.794249i
$345$	−15.5575	+	31.2199i	−0.837590	+	1.68082i
$346$	−16.2667	+	5.52179i	−0.874501	+	0.296853i
$347$	−5.48711	+	11.1268i	−0.294563	+	0.597316i	−0.992967	−	0.118388i	$-0.962227\pi$
$347$	−5.48711	+	11.1268i	−0.294563	+	0.597316i	0.698404	+	0.715704i	$0.253894\pi$
$348$	−7.64743	+	13.1196i	−0.409945	+	0.703282i
$349$	2.55597	−	19.4145i	0.136818	−	1.03923i	−0.775961	−	0.630781i	$-0.782735\pi$
$349$	2.55597	−	19.4145i	0.136818	−	1.03923i	0.912779	−	0.408454i	$-0.133932\pi$
$350$	−5.39096	+	3.60212i	−0.288159	+	0.192541i
$351$	0.235735	−	0.201593i	0.0125826	−	0.0107602i
$352$	8.84159	−	13.2324i	0.471258	−	0.705288i
$353$	33.9996	−	9.11017i	1.80962	−	0.484885i	0.814206	−	0.580576i	$-0.197173\pi$
$353$	33.9996	−	9.11017i	1.80962	−	0.484885i	0.995411	+	0.0956908i	$0.0305060\pi$
$354$	−4.17534	+	4.72135i	−0.221917	+	0.250937i
$355$	−18.7287	+	2.46568i	−0.994016	+	0.130865i
$356$	7.62488	+	13.2067i	0.404118	+	0.699953i
$357$	−3.46828	+	10.7789i	−0.183561	+	0.570479i
$358$	11.1026	−	19.2302i	0.586790	−	1.01635i
$359$	4.36840	−	10.5462i	0.230555	−	0.556609i	−0.765688	−	0.643212i	$-0.777601\pi$
$359$	4.36840	−	10.5462i	0.230555	−	0.556609i	0.996243	+	0.0866031i	$0.0276012\pi$
$360$	5.79811	+	12.0079i	0.305587	+	0.632872i
$361$	−12.4913	−	12.4913i	−0.657436	−	0.657436i
$362$	−19.6730	−	39.8929i	−1.03399	−	2.09672i
$363$	−2.42763	+	3.60073i	−0.127417	+	0.188989i
$364$	−0.0901726	−	0.0444682i	−0.00472633	−	0.00233077i
$365$	−6.93451	−	5.32103i	−0.362969	−	0.278516i
$366$	0.0868486	−	20.9058i	0.00453965	−	1.09276i
$367$	9.55254	−	0.626106i	0.498638	−	0.0326825i	0.185990	−	0.982552i	$-0.440451\pi$
$367$	9.55254	−	0.626106i	0.498638	−	0.0326825i	0.312648	+	0.949869i	$0.398784\pi$
$368$	7.24688	−	36.4325i	0.377770	−	1.89918i
$369$	30.6372	+	10.6846i	1.59491	+	0.556219i
$370$	−16.6704	+	16.6704i	−0.866654	+	0.866654i
$371$	−14.0606	−	4.77294i	−0.729991	−	0.247799i
$372$	−4.61552	−	1.25730i	−0.239304	−	0.0651879i
$373$	−14.4471	+	8.34104i	−0.748043	+	0.431883i	−0.824986	−	0.565153i	$-0.808817\pi$
$373$	−14.4471	+	8.34104i	−0.748043	+	0.431883i	0.0769434	+	0.997035i	$0.475484\pi$
$374$	5.84918	+	20.1967i	0.302454	+	1.04435i
$375$	7.56496	+	9.94412i	0.390653	+	0.513512i
$376$	−0.178309	+	0.136821i	−0.00919559	+	0.00705603i
$377$	−0.483221	+	0.0961186i	−0.0248871	+	0.00495036i
$378$	1.70355	+	14.3163i	0.0876213	+	0.736352i
$379$	16.8002	+	11.2256i	0.862970	+	0.576618i	0.906391	−	0.422439i	$-0.138826\pi$
$379$	16.8002	+	11.2256i	0.862970	+	0.576618i	−0.0434215	+	0.999057i	$0.513826\pi$
$380$	2.19171	−	2.49917i	0.112432	−	0.128205i
$381$	12.2222	−	35.5199i	0.626160	−	1.81974i
$382$	−9.89476	+	12.8951i	−0.506260	+	0.659771i
$383$	−1.06928	+	1.39352i	−0.0546378	+	0.0712053i	−0.819873	−	0.572545i	$-0.805956\pi$
$383$	−1.06928	+	1.39352i	−0.0546378	+	0.0712053i	0.765235	+	0.643751i	$0.222623\pi$
$384$	−13.2810	−	15.2715i	−0.677741	−	0.779323i
$385$	8.25224	−	9.40987i	0.420573	−	0.479571i
$386$	−17.0249	−	11.3756i	−0.866542	−	0.579005i
$387$	−27.8803	−	0.231649i	−1.41723	−	0.0117754i
$388$	−13.0749	+	2.60076i	−0.663778	+	0.132034i
$389$	9.15450	−	7.02449i	0.464151	−	0.356156i	−0.350057	−	0.936728i	$-0.613838\pi$
$389$	9.15450	−	7.02449i	0.464151	−	0.356156i	0.814209	+	0.580572i	$0.197171\pi$
$390$	0.189424	−	0.451989i	0.00959184	−	0.0228874i
$391$	19.1468	+	23.9406i	0.968296	+	1.21073i
$392$	6.37519	−	3.68072i	0.321996	−	0.185904i
$393$	24.1652	−	23.9652i	1.21897	−	1.20889i
$394$	−37.6070	−	12.7658i	−1.89461	−	0.643134i
$395$	−2.29726	+	2.29726i	−0.115588	+	0.115588i
$396$	6.06517	+	7.03302i	0.304786	+	0.353423i
$397$	2.52247	−	12.6813i	0.126599	−	0.636457i	−0.864424	−	0.502764i	$-0.832316\pi$
$397$	2.52247	−	12.6813i	0.126599	−	0.636457i	0.991023	−	0.133693i	$-0.0426836\pi$
$398$	41.9710	−	2.75093i	2.10382	−	0.137892i
$399$	−2.75419	+	1.57491i	−0.137882	+	0.0788443i
$400$	9.26225	+	7.10718i	0.463113	+	0.355359i
$401$	−31.5194	−	15.5437i	−1.57401	−	0.776214i	−0.574889	−	0.818231i	$-0.694955\pi$
$401$	−31.5194	−	15.5437i	−1.57401	−	0.776214i	−0.999117	+	0.0420177i	$0.986621\pi$
$402$	6.57043	+	13.4642i	0.327703	+	0.671535i
$403$	−0.0686446	−	0.139198i	−0.00341943	−	0.00693392i
$404$	9.28030	+	9.28030i	0.461712	+	0.461712i
$405$	−23.9851	+	4.35794i	−1.19183	+	0.216548i
$406$	8.76363	−	21.1573i	0.434932	−	1.05002i
$407$	7.24740	−	12.5529i	0.359240	−	0.622223i
$408$	11.7174	−	0.186843i	0.580098	−	0.00925008i
$409$	−2.34951	−	4.06948i	−0.116176	−	0.201223i	0.802073	−	0.597226i	$-0.203730\pi$
$409$	−2.34951	−	4.06948i	−0.116176	−	0.201223i	−0.918249	+	0.396003i	$0.870397\pi$
$410$	50.8270	−	6.69150i	2.51017	−	0.330469i
$411$	0.232396	+	0.694077i	0.0114633	+	0.0342363i
$412$	−7.26186	+	1.94581i	−0.357766	+	0.0958632i
$413$	1.83176	−	2.74142i	0.0901349	−	0.134896i
$414$	34.8624	+	17.5538i	1.71339	+	0.862724i
$415$	16.7860	−	11.2161i	0.823994	−	0.550575i
$416$	−0.0425495	+	0.323195i	−0.00208616	+	0.0158460i
$417$	1.46882	+	0.00610189i	0.0719283	+	0.000298811i
$418$	−2.60577	+	5.28399i	−0.127453	+	0.258448i
$419$	−1.89610	+	0.643641i	−0.0926308	+	0.0314439i	−0.367370	−	0.930075i	$-0.619742\pi$
$419$	−1.89610	+	0.643641i	−0.0926308	+	0.0314439i	0.274739	+	0.961519i	$0.411408\pi$
$420$	4.36269	+	6.58831i	0.212877	+	0.321476i
$421$	3.57239	+	13.3323i	0.174108	+	0.649778i	0.996702	+	0.0811497i	$0.0258592\pi$
$421$	3.57239	+	13.3323i	0.174108	+	0.649778i	−0.822594	+	0.568629i	$0.807474\pi$
$422$	8.20601	+	41.2544i	0.399462	+	2.00823i
$423$	−0.154082	−	0.380907i	−0.00749171	−	0.0185203i
$424$			15.3676i			0.746319i
$425$	−9.40995	+	2.06918i	−0.456450	+	0.100370i
$426$	2.67200	+	20.9687i	0.129459	+	1.01593i
$427$	1.42747	+	10.8427i	0.0690801	+	0.524715i
$428$	9.68444	+	11.0430i	0.468115	+	0.533783i
$429$	−0.0405696	+	0.298567i	−0.00195872	+	0.0144150i
$430$	−39.5089	+	19.4837i	−1.90529	+	0.939585i
$431$	19.9058	+	3.95950i	0.958827	+	0.190722i	0.649609	−	0.760269i	$-0.274933\pi$
$431$	19.9058	+	3.95950i	0.958827	+	0.190722i	0.309218	+	0.950991i	$0.399933\pi$
$432$	23.4247	−	11.1910i	1.12702	−	0.538429i
$433$	−9.44212	−	22.7953i	−0.453759	−	1.09547i	−0.970882	−	0.239560i	$-0.922997\pi$
$433$	−9.44212	−	22.7953i	−0.453759	−	1.09547i	0.517122	−	0.855912i	$-0.327003\pi$
$434$	7.15224	+	0.941611i	0.343319	+	0.0451988i
$435$	36.6148	+	12.5989i	1.75554	+	0.604072i
$436$	2.95811	+	8.71430i	0.141668	+	0.417339i
$437$	−0.561779	+	8.57109i	−0.0268735	+	0.410011i
$438$	−5.98641	+	7.73490i	−0.286042	+	0.369588i
$439$	−4.12407	+	12.1491i	−0.196831	+	0.579845i	−0.999871	−	0.0160803i	$-0.994881\pi$
$439$	−4.12407	+	12.1491i	−0.196831	+	0.579845i	0.803040	+	0.595925i	$0.203215\pi$
$440$	−11.9672	−	4.95699i	−0.570516	−	0.236315i
$441$	3.37507	+	13.0280i	0.160718	+	0.620380i
$442$	−0.290431	−	0.318045i	−0.0138144	−	0.0151279i
$443$	−18.7164	−	10.8059i	−0.889241	−	0.513404i	−0.0155470	−	0.999879i	$-0.504949\pi$
$443$	−18.7164	−	10.8059i	−0.889241	−	0.513404i	−0.873694	+	0.486475i	$0.838282\pi$
$444$	6.44398	+	6.49775i	0.305818	+	0.308369i
$445$	29.2353	−	25.6387i	1.38589	−	1.21539i
$446$	−11.4314	−	3.06304i	−0.541294	−	0.145039i
$447$	16.2775	−	10.7788i	0.769901	−	0.509818i
$448$	0.519724	+	0.455786i	0.0245546	+	0.0215338i
$449$	−11.8403	−	17.7202i	−0.558778	−	0.836270i	0.439294	−	0.898343i	$-0.355229\pi$
$449$	−11.8403	−	17.7202i	−0.558778	−	0.836270i	−0.998072	+	0.0620736i	$0.980229\pi$
$450$	−9.79425	+	7.38692i	−0.461705	+	0.348223i
$451$	−29.1200	+	12.0619i	−1.37121	+	0.567973i
$452$	0.954583	+	14.5641i	0.0448998	+	0.685039i
$453$	−0.139806	+	2.00534i	−0.00656864	+	0.0942190i
$454$	−46.6278	−	3.05615i	−2.18835	−	0.143432i
$455$	−0.0663528	+	0.247632i	−0.00311067	+	0.0116092i
$456$	2.45971	+	2.17525i	0.115186	+	0.101865i
$457$	−8.63390	−	11.2519i	−0.403877	−	0.526343i	0.546493	−	0.837463i	$-0.315962\pi$
$457$	−8.63390	−	11.2519i	−0.403877	−	0.526343i	−0.950370	+	0.311121i	$0.899296\pi$
$458$	11.9491			0.558346
$459$	−5.38683	+	20.7360i	−0.251436	+	0.967874i
$460$	21.3928			0.997445
$461$	16.6878	+	21.7479i	0.777227	+	1.01290i	0.999283	+	0.0378679i	$0.0120566\pi$
$461$	16.6878	+	21.7479i	0.777227	+	1.01290i	−0.222056	+	0.975034i	$0.571277\pi$
$462$	−10.4912	−	9.27790i	−0.488094	−	0.431647i
$463$	−1.10002	+	4.10532i	−0.0511221	+	0.190790i	−0.986765	−	0.162159i	$-0.948154\pi$
$463$	−1.10002	+	4.10532i	−0.0511221	+	0.190790i	0.935643	+	0.352949i	$0.114821\pi$
$464$	−41.1476	−	2.69695i	−1.91023	−	0.125203i
$465$	−0.848337	+	12.1683i	−0.0393407	+	0.564293i
$466$	−0.124083	−	1.89314i	−0.00574802	−	0.0876978i
$467$	−17.7184	+	7.33920i	−0.819910	+	0.339618i	−0.752900	−	0.658135i	$-0.771346\pi$
$467$	−17.7184	+	7.33920i	−0.819910	+	0.339618i	−0.0670094	+	0.997752i	$0.521346\pi$
$468$	−0.175141	−	0.0742564i	−0.00809588	−	0.00343250i
$469$	−4.35416	−	6.51645i	−0.201056	−	0.300902i
$470$	−0.488096	−	0.428048i	−0.0225142	−	0.0197444i
$471$	−17.4996	+	11.5880i	−0.806339	+	0.533946i
$472$	−3.29605	−	0.883173i	−0.151713	−	0.0406513i
$473$	20.3629	−	17.8578i	0.936289	−	0.821104i
$474$	2.55993	+	2.58129i	0.117582	+	0.118563i
$475$	−2.33793	−	1.34981i	−0.107272	−	0.0619334i
$476$	6.86544	−	1.04462i	0.314677	−	0.0478802i
$477$	−27.0762	−	7.49671i	−1.23973	−	0.343251i
$478$	−3.86405	−	1.60054i	−0.176737	−	0.0732071i
$479$	−2.68794	+	7.91842i	−0.122815	+	0.361802i	−0.990898	−	0.134618i	$-0.957019\pi$
$479$	−2.68794	+	7.91842i	−0.122815	+	0.361802i	0.868082	+	0.496420i	$0.165352\pi$
$480$	15.6808	−	20.2608i	0.715728	−	0.924774i
$481$	−0.0194185	+	0.296269i	−0.000885408	+	0.0135087i
$482$	1.63142	+	4.80600i	0.0743091	+	0.218907i
$483$	−19.3075	−	6.64358i	−0.878520	−	0.302293i
$484$	2.64056	+	0.347636i	0.120025	+	0.0158017i
$485$	13.0084	+	31.4051i	0.590681	+	1.42603i
$486$	4.76498	+	26.8594i	0.216144	+	1.21837i
$487$	−0.136538	−	0.0271590i	−0.00618712	−	0.00123069i	0.191996	−	0.981396i	$-0.438504\pi$
$487$	−0.136538	−	0.0271590i	−0.00618712	−	0.00123069i	−0.198183	+	0.980165i	$0.563504\pi$
$488$	10.1513	−	5.00605i	0.459526	−	0.226613i
$489$	−0.878302	+	6.46376i	−0.0397182	+	0.292301i
$490$	14.0200	+	15.9868i	0.633359	+	0.722208i
$491$	3.22313	+	24.4821i	0.145458	+	1.10486i	0.896005	+	0.444045i	$0.146457\pi$
$491$	3.22313	+	24.4821i	0.145458	+	1.10486i	−0.750547	+	0.660817i	$0.770210\pi$
$492$	−2.51544	−	19.7400i	−0.113405	−	0.889949i
$493$	23.5746	−	24.5418i	1.06175	−	1.10531i
$494$		−	0.120680i		−	0.00542966i
$495$	14.5716	−	18.6669i	0.654946	−	0.839015i
$496$	−2.53419	−	12.7403i	−0.113789	−	0.572054i
$497$	−2.86196	−	10.6810i	−0.128376	−	0.479107i
$498$	−12.4726	−	18.8355i	−0.558912	−	0.844040i
$499$	28.2179	−	9.57869i	1.26321	−	0.428801i	0.392113	−	0.919917i	$-0.371744\pi$
$499$	28.2179	−	9.57869i	1.26321	−	0.428801i	0.871094	+	0.491116i	$0.163411\pi$
$500$	3.38922	−	6.87265i	0.151570	−	0.307354i
$501$	−0.921824	−	0.00382952i	−0.0411841	−	0.000171090i
$502$	1.83848	−	13.9647i	0.0820555	−	0.623273i
$503$	36.3824	−	24.3099i	1.62221	−	1.08393i	0.688897	−	0.724859i	$-0.258095\pi$
$503$	36.3824	−	24.3099i	1.62221	−	1.08393i	0.933312	−	0.359067i	$-0.116905\pi$
$504$	−6.52589	+	4.28246i	−0.290686	+	0.190756i
$505$	18.5924	−	27.8255i	0.827351	−	1.23822i
$506$	−36.6245	+	9.81351i	−1.62816	+	0.436264i
$507$	7.14715	+	21.3457i	0.317416	+	0.947997i
$508$	−22.8408	+	3.00704i	−1.01340	+	0.133416i
$509$	−16.9628	−	29.3804i	−0.751861	−	1.30226i	−0.946920	−	0.321470i	$-0.895823\pi$
$509$	−16.9628	−	29.3804i	−0.751861	−	1.30226i	0.195059	−	0.980792i	$-0.437510\pi$
$510$	7.13230	+	33.0901i	0.315823	+	1.46525i
$511$	2.55828	−	4.43106i	0.113171	−	0.196019i
$512$	−4.16608	+	10.0578i	−0.184116	+	0.444496i
$513$	−5.03247	+	3.27261i	−0.222189	+	0.144489i
$514$	8.78449	+	8.78449i	0.387467	+	0.387467i
$515$	8.47871	+	17.1931i	0.373617	+	0.757620i
$516$	7.49915	+	15.3674i	0.330132	+	0.676512i
$517$	0.357982	+	0.176537i	0.0157440	+	0.00776409i
$518$	−10.9486	−	8.40112i	−0.481052	−	0.369124i
$519$	14.7600	−	8.44014i	0.647893	−	0.370481i
$520$	0.264760	−	0.0173533i	0.0116105	−	0.000760993i
$521$	−2.83039	+	14.2293i	−0.124002	+	0.623399i	0.867936	+	0.496675i	$0.165446\pi$
$521$	−2.83039	+	14.2293i	−0.124002	+	0.623399i	−0.991938	+	0.126723i	$0.959554\pi$
$522$	14.2683	−	40.9130i	0.624505	−	1.79071i
$523$	−20.3511	+	20.3511i	−0.889890	+	0.889890i	−0.994512	−	0.104622i	$-0.966637\pi$
$523$	−20.3511	+	20.3511i	−0.889890	+	0.889890i	0.104622	+	0.994512i	$0.466637\pi$
$524$	−19.7651	−	6.70934i	−0.863441	−	0.293099i
$525$	4.55659	−	4.51889i	0.198866	−	0.197221i
$526$	8.55426	−	4.93880i	0.372983	−	0.215342i
$527$	9.38966	+	5.17235i	0.409020	+	0.225311i
$528$	−9.74739	+	23.2585i	−0.424201	+	1.01220i
$529$	−25.6091	+	19.6506i	−1.11344	+	0.854372i
$530$	−43.5365	+	8.65995i	−1.89111	+	0.376164i
$531$	3.16395	−	5.37646i	0.137304	−	0.233319i
$532$	1.61788	+	1.08103i	0.0701438	+	0.0468686i
$533$	0.425691	−	0.485408i	0.0184387	−	0.0210253i
$534$	−28.5535	−	32.8332i	−1.23563	−	1.42083i
$535$	22.7996	−	29.7131i	0.985715	−	1.28461i
$536$	−4.93779	+	6.43505i	−0.213280	+	0.277952i
$537$	−7.15107	+	20.7823i	−0.308592	+	0.896824i
$538$	−7.23800	+	8.25335i	−0.312052	+	0.355827i
$539$	−10.8701	−	7.26314i	−0.468207	−	0.312846i
$540$	8.95300	+	11.9739i	0.385276	+	0.515273i
$541$	−4.10266	+	0.816069i	−0.176387	+	0.0350856i	−0.282493	−	0.959269i	$-0.591162\pi$
$541$	−4.10266	+	0.816069i	−0.176387	+	0.0350856i	0.106106	+	0.994355i	$0.466162\pi$
$542$	22.2278	−	17.0560i	0.954765	−	0.732617i
$543$	26.6557	+	35.0388i	1.14390	+	1.50366i
$544$	−10.3624	−	19.9898i	−0.444285	−	0.857054i
$545$	20.3219	−	11.7329i	0.870496	−	0.502581i
$546$	0.276789	+	0.0753992i	0.0118455	+	0.00322679i
$547$	−38.7357	−	13.1490i	−1.65622	−	0.562211i	−0.672216	−	0.740355i	$-0.734657\pi$
$547$	−38.7357	−	13.1490i	−1.65622	−	0.562211i	−0.984004	+	0.178144i	$0.942991\pi$
$548$	0.317423	−	0.317423i	0.0135596	−	0.0135596i
$549$	3.86811	+	20.3276i	0.165087	+	0.867559i
$550$	2.32487	−	11.6879i	0.0991328	−	0.498374i
$551$	9.51472	−	0.623627i	0.405341	−	0.0265674i
$552$	−0.0877884	+	21.1320i	−0.00373652	+	0.899438i
$553$	−1.50876	−	1.15771i	−0.0641591	−	0.0492310i
$554$	4.56053	+	2.24900i	0.193758	+	0.0955511i
$555$	13.0445	−	19.3480i	0.553709	−	0.821277i
$556$	−0.398428	−	0.807932i	−0.0168971	−	0.0342639i
$557$	−4.82152	−	4.82152i	−0.204294	−	0.204294i	0.597543	−	0.801837i	$-0.296144\pi$
$557$	−4.82152	−	4.82152i	−0.204294	−	0.204294i	−0.801837	+	0.597543i	$0.796144\pi$
$558$	13.6123	+	1.00585i	0.576254	+	0.0425808i
$559$	−0.212305	+	0.512549i	−0.00897954	+	0.0216785i
$560$	−10.7284	+	18.5822i	−0.453360	+	0.785242i
$561$	−9.50125	−	18.5164i	−0.401143	−	0.781763i
$562$	−3.91222	−	6.77616i	−0.165027	−	0.285835i
$563$	−33.4728	+	4.40677i	−1.41071	+	0.185723i	−0.797081	−	0.603872i	$-0.793624\pi$
$563$	−33.4728	+	4.40677i	−1.41071	+	0.185723i	−0.613628	+	0.789595i	$0.710290\pi$
$564$	−0.166940	+	0.188771i	−0.00702945	+	0.00794870i
$565$	35.9483	−	9.63233i	1.51236	−	0.405235i
$566$	1.14515	−	1.71384i	0.0481343	−	0.0720380i
$567$	−4.36177	−	13.5870i	−0.183177	−	0.570602i
$568$	−9.51555	+	6.35809i	−0.399264	+	0.266780i
$569$	1.08832	−	8.26658i	0.0456246	−	0.346553i	−0.953373	−	0.301794i	$-0.902415\pi$
$569$	1.08832	−	8.26658i	0.0456246	−	0.346553i	0.998998	−	0.0447593i	$-0.0142521\pi$
$570$	−4.77639	+	8.19414i	−0.200061	+	0.343215i
$571$	4.54306	−	9.21241i	0.190121	−	0.385527i	−0.780852	−	0.624716i	$-0.785215\pi$
$571$	4.54306	−	9.21241i	0.190121	−	0.385527i	0.970973	+	0.239189i	$0.0768814\pi$
$572$	0.174987	−	0.0594000i	0.00731656	−	0.00248364i
$573$	7.17535	−	14.3991i	0.299754	−	0.601529i
$574$	7.76695	+	28.9866i	0.324186	+	1.20988i
$575$	−3.38949	−	17.0401i	−0.141352	−	0.710623i
$576$	1.03101	+	0.804817i	0.0429586	+	0.0335340i
$577$		−	4.76545i		−	0.198388i	−0.995068	−	0.0991942i	$-0.968373\pi$
$577$		−	4.76545i		−	0.198388i	0.995068	−	0.0991942i	$-0.0316265\pi$
$578$	29.0214	+	6.53859i	1.20713	+	0.271969i
$579$	18.6913	+	7.83333i	0.776785	+	0.325542i
$580$	−3.09974	−	23.5448i	−0.128710	−	0.977647i
$581$	7.79190	+	8.88496i	0.323263	+	0.368610i
$582$	35.2024	−	14.4103i	1.45919	−	0.597325i
$583$	24.4772	−	12.0708i	1.01374	−	0.499922i
$584$	−5.19364	−	1.03308i	−0.214914	−	0.0427491i
$585$	−0.0985817	+	0.474946i	−0.00407585	+	0.0196366i
$586$	16.6972	+	40.3105i	0.689753	+	1.66521i
$587$	−4.55931	−	0.600244i	−0.188183	−	0.0247747i	0.0358457	−	0.999357i	$-0.488588\pi$
$587$	−4.55931	−	0.600244i	−0.188183	−	0.0247747i	−0.224028	+	0.974583i	$0.571921\pi$
$588$	6.22810	−	5.41629i	0.256842	−	0.223364i
$589$	0.965506	+	2.84429i	0.0397830	+	0.117197i
$590$	0.644645	−	9.83538i	0.0265396	−	0.404916i
$591$	38.9508	+	5.29268i	1.60222	+	0.217712i
$592$	−7.98767	+	23.5309i	−0.328291	+	0.967115i
$593$	−22.8624	−	9.46991i	−0.938846	−	0.388883i	−0.139818	−	0.990177i	$-0.544652\pi$
$593$	−22.8624	−	9.46991i	−0.938846	−	0.388883i	−0.799027	+	0.601295i	$0.794652\pi$
$594$	−20.8203	−	16.3923i	−0.854268	−	0.672582i
$595$	−6.02774	−	16.6500i	−0.247113	−	0.682584i
$596$	−10.3692	−	5.98666i	−0.424739	−	0.245223i
$597$	−40.2572	+	10.6078i	−1.64762	+	0.434149i
$598$	0.583927	−	0.512090i	0.0238786	−	0.0209409i
$599$	−15.1406	−	4.05692i	−0.618629	−	0.165761i	−0.0641245	−	0.997942i	$-0.520425\pi$
$599$	−15.1406	−	4.05692i	−0.618629	−	0.165761i	−0.554504	+	0.832181i	$0.687092\pi$
$600$	−5.94450	−	2.96227i	−0.242683	−	0.120934i
$601$	2.38349	+	2.09027i	0.0972247	+	0.0852637i	0.706578	−	0.707635i	$-0.250238\pi$
$601$	2.38349	+	2.09027i	0.0972247	+	0.0852637i	−0.609354	+	0.792898i	$0.708571\pi$
$602$	−14.3262	−	21.4407i	−0.583894	−	0.873859i
$603$	−8.92913	−	11.8390i	−0.363622	−	0.482123i
$604$	1.13901	−	0.471794i	0.0463457	−	0.0191970i
$605$	−0.444167	−	6.77667i	−0.0180579	−	0.275511i
$606$	−31.0500	−	20.9340i	−1.26132	−	0.850387i
$607$	23.2008	+	1.52066i	0.941691	+	0.0617217i	0.528510	−	0.848927i	$-0.322751\pi$
$607$	23.2008	+	1.52066i	0.941691	+	0.0617217i	0.413181	+	0.910649i	$0.364418\pi$
$608$	1.63286	−	6.09390i	0.0662211	−	0.247140i
$609$	−4.51432	+	22.2124i	−0.182930	+	0.900091i
$610$	19.9026	+	25.9375i	0.805831	+	1.05018i
$611$	−0.00817589			−0.000330761
$612$	12.8559	−	2.71515i	0.519669	−	0.109753i
$613$	−7.68237			−0.310288			−0.155144	−	0.987892i	$-0.549584\pi$
$613$	−7.68237			−0.310288			−0.155144	+	0.987892i	$0.549584\pi$
$614$	−5.46183	−	7.11800i	−0.220422	−	0.287259i
$615$	−48.1162	+	16.1106i	−1.94023	+	0.649643i
$616$	1.96247	−	7.32405i	0.0790703	−	0.295094i
$617$	21.9816	+	1.44075i	0.884946	+	0.0580024i	0.501095	−	0.865392i	$-0.332931\pi$
$617$	21.9816	+	1.44075i	0.884946	+	0.0580024i	0.383851	+	0.923395i	$0.374597\pi$
$618$	19.2783	−	9.40766i	0.775488	−	0.378432i
$619$	−1.15016	−	17.5480i	−0.0462287	−	0.705313i	−0.956579	−	0.291474i	$-0.905854\pi$
$619$	−1.15016	−	17.5480i	−0.0462287	−	0.705313i	0.910350	−	0.413839i	$-0.135812\pi$
$620$	6.91149	−	2.86283i	0.277572	−	0.114974i
$621$	−37.1896	−	10.4634i	−1.49237	−	0.419881i
$622$	−12.4592	−	18.6465i	−0.499567	−	0.747655i
$623$	17.1134	+	15.0081i	0.685635	+	0.601285i
$624$	−0.0316432	−	0.515593i	−0.00126674	−	0.0206402i
$625$	−30.1594	−	8.08120i	−1.20638	−	0.323248i
$626$	−22.2545	+	19.5166i	−0.889467	+	0.780042i
$627$	1.53265	−	5.62635i	0.0612083	−	0.224695i
$628$	11.1477	+	6.43611i	0.444841	+	0.256829i
$629$	−10.6086	−	17.5503i	−0.422992	−	0.699778i
$630$	−15.8097	−	16.0746i	−0.629872	−	0.640427i
$631$	33.4430	+	13.8525i	1.33134	+	0.551460i	0.931038	−	0.364922i	$-0.118904\pi$
$631$	33.4430	+	13.8525i	1.33134	+	0.551460i	0.400305	+	0.916382i	$0.368904\pi$
$632$	−0.632665	+	1.86377i	−0.0251661	+	0.0741369i
$633$	−15.7723	−	38.5295i	−0.626891	−	1.53141i
$634$	0.208789	−	3.18550i	0.00829206	−	0.126512i
$635$	18.8826	+	55.6263i	0.749332	+	2.20746i
$636$	3.29128	+	16.9133i	0.130508	+	0.670656i
$637$	0.265497	+	0.0349533i	0.0105194	+	0.00138490i
$638$	16.1075	+	38.8869i	0.637701	+	1.53955i
$639$	−6.56038	−	19.8671i	−0.259525	−	0.785929i
$640$	31.0419	+	6.17461i	1.22704	+	0.244073i
$641$	−19.5346	+	9.63339i	−0.771570	+	0.380496i	−0.785065	−	0.619413i	$-0.787371\pi$
$641$	−19.5346	+	9.63339i	−0.771570	+	0.380496i	0.0134958	+	0.999909i	$0.495704\pi$
$642$	−33.1426	−	25.6507i	−1.30803	−	1.01235i
$643$	−17.4032	−	19.8446i	−0.686316	−	0.782593i	0.298831	−	0.954306i	$-0.403403\pi$
$643$	−17.4032	−	19.8446i	−0.686316	−	0.782593i	−0.985147	+	0.171713i	$0.945070\pi$
$644$	1.63453	+	12.4155i	0.0644097	+	0.489240i
$645$	34.7016	−	26.3991i	1.36637	−	1.03946i
$646$	4.76930	+	6.83623i	0.187646	+	0.268968i
$647$		−	8.74993i		−	0.343995i	−0.985097	−	0.171998i	$-0.944978\pi$
$647$		−	8.74993i		−	0.343995i	0.985097	−	0.171998i	$-0.0550221\pi$
$648$	−11.8646	+	8.79472i	−0.466086	+	0.345489i
$649$	1.18225	+	5.94356i	0.0464073	+	0.233305i
$650$	0.0631777	+	0.235783i	0.00247803	+	0.00924815i
$651$	−7.12683	+	0.437391i	−0.279323	+	0.0171427i
$652$	3.78833	−	1.28597i	0.148363	−	0.0503623i
$653$	−5.49856	+	11.1500i	−0.215175	+	0.436332i	−0.977521	−	0.210838i	$-0.932381\pi$
$653$	−5.49856	+	11.1500i	−0.215175	+	0.436332i	0.762346	+	0.647170i	$0.224048\pi$
$654$	−13.0345	−	22.7946i	−0.509689	−	0.891338i
$655$	−6.94701	+	52.7678i	−0.271442	+	2.06181i
$656$	44.9295	−	30.0209i	1.75420	−	1.17212i
$657$	4.35376	−	8.64670i	0.169856	−	0.337340i
$658$	0.211129	−	0.315976i	0.00823065	−	0.0123180i
$659$	25.1204	−	6.73100i	0.978553	−	0.262202i	0.266118	−	0.963941i	$-0.414259\pi$
$659$	25.1204	−	6.73100i	0.978553	−	0.262202i	0.712435	+	0.701738i	$0.247592\pi$
$660$	−14.2325	−	2.89254i	−0.554000	−	0.112592i
$661$	−33.0261	+	4.34797i	−1.28457	+	0.169116i	−0.741717	−	0.670713i	$-0.765988\pi$
$661$	−33.0261	+	4.34797i	−1.28457	+	0.169116i	−0.542850	+	0.839830i	$0.682655\pi$
$662$	0.139436	+	0.241510i	0.00541932	+	0.00938654i
$663$	0.342301	+	0.254089i	0.0132939	+	0.00986801i
$664$	6.11534	−	10.5921i	0.237321	−	0.411052i
$665$	1.89871	−	4.58389i	0.0736287	−	0.177756i
$666$	−21.5896	−	14.6866i	−0.836579	−	0.569094i
$667$	43.3920	+	43.3920i	1.68014	+	1.68014i
$668$	0.250052	+	0.507055i	0.00967480	+	0.0196185i
$669$	11.6854	+	0.814668i	0.451784	+	0.0314969i
$670$	−21.0130	−	10.3625i	−0.811804	−	0.400337i
$671$	−15.9470	−	12.2366i	−0.615627	−	0.472387i
$672$	12.9566	+	7.55246i	0.499814	+	0.291343i
$673$	−3.89047	+	0.254995i	−0.149967	+	0.00982934i	−0.140202	−	0.990123i	$-0.544775\pi$
$673$	−3.89047	+	0.254995i	−0.149967	+	0.00982934i	−0.00976516	+	0.999952i	$0.503108\pi$
$674$	−1.40280	+	7.05236i	−0.0540339	+	0.271647i
$675$	8.11908	−	9.02853i	0.312504	−	0.347508i
$676$	9.76208	−	9.76208i	0.375464	−	0.375464i
$677$	7.27125	+	2.46826i	0.279457	+	0.0948628i	0.457649	−	0.889133i	$-0.348692\pi$
$677$	7.27125	+	2.46826i	0.279457	+	0.0948628i	−0.178192	+	0.983996i	$0.557025\pi$
$678$	−10.6114	−	40.2706i	−0.407527	−	1.54658i
$679$	−17.2323	+	9.94908i	−0.661316	+	0.381811i
$680$	−14.3122	+	11.4464i	−0.548848	+	0.438949i
$681$	45.8794	−	5.84634i	1.75810	−	0.224032i
$682$	−10.5192	+	8.07169i	−0.402802	+	0.309081i
$683$	−24.0653	+	4.78690i	−0.920835	+	0.183165i	−0.632676	−	0.774417i	$-0.718043\pi$
$683$	−24.0653	+	4.78690i	−0.920835	+	0.183165i	−0.288159	+	0.957582i	$0.593043\pi$
$684$	3.17297	+	1.86724i	0.121322	+	0.0713956i
$685$	−0.951743	−	0.635934i	−0.0363642	−	0.0242978i
$686$	−21.0129	+	23.9606i	−0.802275	+	0.914819i
$687$	−11.6092	+	2.25913i	−0.442920	+	0.0861911i
$688$	−28.2664	+	36.8375i	−1.07765	+	1.40442i
$689$	−0.340316	+	0.443508i	−0.0129650	+	0.0168963i
$690$	−59.9164	+	11.6596i	−2.28098	+	0.443872i
$691$	−14.6214	+	16.6725i	−0.556224	+	0.634251i	−0.959797	−	0.280696i	$-0.909435\pi$
$691$	−14.6214	+	16.6725i	−0.556224	+	0.634251i	0.403573	+	0.914947i	$0.367768\pi$
$692$	−8.67038	−	5.79337i	−0.329599	−	0.220231i
$693$	11.9469	+	7.03052i	0.453824	+	0.267067i
$694$	−21.2928	+	4.23540i	−0.808264	+	0.160774i
$695$	−1.82234	+	1.39833i	−0.0691254	+	0.0530418i
$696$	23.2705	−	2.96533i	0.882067	−	0.112401i
$697$	−4.93095	+	44.3205i	−0.186773	+	1.67876i
$698$	29.6763	−	17.1336i	1.12326	−	0.648517i
$699$	0.478474	+	1.81583i	0.0180975	+	0.0686810i
$700$	−3.72691	−	1.26512i	−0.140864	−	0.0478169i
$701$	15.9461	−	15.9461i	0.602276	−	0.602276i	−0.338640	−	0.940916i	$-0.609967\pi$
$701$	15.9461	−	15.9461i	0.602276	−	0.602276i	0.940916	+	0.338640i	$0.109967\pi$
$702$	0.531001	+	0.112520i	0.0200413	+	0.00424678i
$703$	1.12101	−	5.63568i	0.0422796	−	0.212554i
$704$	−1.26783	+	0.0830978i	−0.0477830	+	0.00313186i
$705$	0.555140	+	0.323593i	0.0209078	+	0.0121872i
$706$	48.8673	+	37.4972i	1.83914	+	1.41123i
$707$	17.5694	+	8.66425i	0.660764	+	0.325853i
$708$	−3.81671	−	0.266088i	−0.143441	−	0.0100002i
$709$	16.2245	+	32.9001i	0.609325	+	1.23559i	0.954824	+	0.297171i	$0.0960430\pi$
$709$	16.2245	+	32.9001i	0.609325	+	1.23559i	−0.345499	+	0.938419i	$0.612290\pi$
$710$	−23.3747	−	23.3747i	−0.877235	−	0.877235i
$711$	−2.97514	−	2.02388i	−0.111577	−	0.0759016i
$712$	9.01512	−	21.7644i	0.337856	−	0.815656i
$713$	−9.66548	+	16.7411i	−0.361975	+	0.626959i
$714$	−18.6592	+	6.66757i	−0.698303	+	0.249528i
$715$	−0.235601	−	0.408073i	−0.00881097	−	0.0152610i
$716$	13.3639	−	1.75939i	0.499433	−	0.0657516i
$717$	4.05674	+	0.824471i	0.151502	+	0.0307904i
$718$	19.2951	−	5.17011i	0.720088	−	0.192947i
$719$	−9.54937	+	14.2916i	−0.356131	+	0.532988i	−0.965671	−	0.259767i	$-0.916354\pi$
$719$	−9.54937	+	14.2916i	−0.356131	+	0.532988i	0.609540	+	0.792755i	$0.291354\pi$
$720$	−18.2580	+	36.2610i	−0.680437	+	1.35137i
$721$	−9.33037	+	6.23436i	−0.347481	+	0.232180i
$722$	4.03498	−	30.6487i	0.150166	−	1.14063i
$723$	−2.49365	−	4.36087i	−0.0927398	−	0.162182i
$724$	11.9421	−	24.2162i	0.443826	−	0.899989i
$725$	−18.2632	+	6.19952i	−0.678278	+	0.230244i
$726$	−7.58508	+	0.465515i	−0.281509	+	0.0172769i
$727$	−1.83742	−	6.85734i	−0.0681461	−	0.254325i	0.923446	−	0.383729i	$-0.125360\pi$
$727$	−1.83742	−	6.85734i	−0.0681461	−	0.254325i	−0.991592	+	0.129404i	$0.958694\pi$
$728$	0.0303004	+	0.152330i	0.00112301	+	0.00564574i
$729$	−9.70755	−	25.1945i	−0.359539	−	0.933130i
$730$		−	15.2957i		−	0.566120i
$731$	−8.22948	−	37.4250i	−0.304378	−	1.38421i
$732$	10.1001	−	7.68364i	0.373311	−	0.283996i
$733$	−2.19611	−	16.6811i	−0.0811151	−	0.616131i	−0.982926	−	0.184000i	$-0.941095\pi$
$733$	−2.19611	−	16.6811i	−0.0811151	−	0.616131i	0.901811	−	0.432131i	$-0.142238\pi$
$734$	11.0455	+	12.5949i	0.407696	+	0.464888i
$735$	−16.6437	−	12.8814i	−0.613913	−	0.475137i
$736$	36.4150	−	17.9579i	1.34227	−	0.661936i
$737$	14.1281	+	2.81024i	0.520414	+	0.103517i
$738$	17.8039	+	53.9163i	0.655372	+	1.98469i
$739$	9.59552	+	23.1656i	0.352977	+	0.852162i	0.996250	+	0.0865247i	$0.0275761\pi$
$739$	9.59552	+	23.1656i	0.352977	+	0.852162i	−0.643273	+	0.765637i	$0.722424\pi$
$740$	−14.1887	−	1.86797i	−0.521586	−	0.0686681i
$741$	0.0228161	+	0.117248i	0.000838169	+	0.00430720i
$742$	−8.35233	−	24.6052i	−0.306624	−	0.903284i
$743$	1.44541	−	22.0526i	0.0530268	−	0.809033i	−0.885676	−	0.464305i	$-0.846304\pi$
$743$	1.44541	−	22.0526i	0.0530268	−	0.809033i	0.938702	−	0.344729i	$-0.112029\pi$
$744$	2.79957	+	6.83898i	0.102637	+	0.250729i
$745$	−9.81371	+	28.9103i	−0.359547	+	1.05919i
$746$	−26.9704	−	11.1715i	−0.987456	−	0.409018i
$747$	15.6789	+	15.9417i	0.573663	+	0.583275i
$748$	−7.56506	+	10.2804i	−0.276606	+	0.375887i
$749$	18.9863	+	10.9617i	0.693744	+	0.400533i
$750$	−5.74668	+	21.0959i	−0.209839	+	0.770315i
$751$	−29.7655	+	26.1037i	−1.08616	+	0.952536i	−0.999046	−	0.0436622i	$-0.986097\pi$
$751$	−29.7655	+	26.1037i	−1.08616	+	0.952536i	−0.0871131	+	0.996198i	$0.527764\pi$
$752$	−0.660971	−	0.177107i	−0.0241031	−	0.00645842i
$753$	0.854001	+	13.9151i	0.0311215	+	0.507093i
$754$	−0.648214	−	0.568468i	−0.0236066	−	0.0207024i
$755$	−1.74651	−	2.61384i	−0.0635621	−	0.0951274i
$756$	−6.26508	+	6.11083i	−0.227859	+	0.222249i
$757$	48.2630	−	19.9912i	1.75415	−	0.726592i	0.756815	−	0.653630i	$-0.226755\pi$
$757$	48.2630	−	19.9912i	1.75415	−	0.726592i	0.997335	−	0.0729628i	$-0.0232454\pi$
$758$	2.31254	+	35.2825i	0.0839952	+	1.28152i
$759$	33.7274	−	16.4587i	1.22423	−	0.597413i
$760$	−5.12399	−	0.335844i	−0.185867	−	0.0121823i
$761$	−5.75270	+	21.4694i	−0.208535	+	0.778264i	0.779807	+	0.626019i	$0.215317\pi$
$761$	−5.75270	+	21.4694i	−0.208535	+	0.778264i	−0.988343	+	0.152245i	$0.951350\pi$
$762$	62.3329	−	20.8708i	2.25808	−	0.756069i
$763$	8.36200	+	10.8976i	0.302725	+	0.394518i
$764$	−9.86665			−0.356963
$765$	−13.1855	−	30.8005i	−0.476724	−	1.11359i
$766$	−3.07374			−0.111059
$767$	−0.0755657	−	0.0984791i	−0.00272852	−	0.00355588i
$768$	6.75283	−	33.2268i	0.243672	−	1.19897i
$769$	−3.45443	+	12.8921i	−0.124570	+	0.464901i	−0.999824	−	0.0187621i	$-0.994027\pi$
$769$	−3.45443	+	12.8921i	−0.124570	+	0.464901i	0.875254	+	0.483664i	$0.160694\pi$
$770$	21.8549	+	1.43245i	0.787596	+	0.0516218i
$771$	−10.1954	−	6.87381i	−0.367180	−	0.247554i
$772$	−0.812919	−	12.4027i	−0.0292576	−	0.446384i
$773$	−14.7654	+	6.11601i	−0.531073	+	0.219978i	−0.632073	−	0.774909i	$-0.717796\pi$
$773$	−14.7654	+	6.11601i	−0.531073	+	0.219978i	0.101000	+	0.994886i	$0.467796\pi$
$774$	−29.3790	−	38.9534i	−1.05601	−	1.40015i
$775$	−3.37541	−	5.05166i	−0.121248	−	0.181461i
$776$	15.4831	+	13.5783i	0.555812	+	0.487434i
$777$	12.2255	+	6.09221i	0.438587	+	0.218557i
$778$	19.5044	+	5.22619i	0.699267	+	0.187368i
$779$	−9.39424	+	8.23853i	−0.336584	+	0.295176i
$780$	0.287673	−	0.0758023i	0.0103003	−	0.00271416i
$781$	17.6012	+	10.1620i	0.629819	+	0.363626i
$782$	−12.8401	+	52.0855i	−0.459162	+	1.86257i
$783$	−6.12732	+	42.4468i	−0.218973	+	1.51693i
$784$	20.7066	+	8.57697i	0.739522	+	0.306320i
$785$	10.5505	−	31.0807i	0.376563	−	1.10932i
$786$	59.0142	+	8.01892i	2.10497	+	0.286025i
$787$	2.77431	−	42.3277i	0.0988933	−	1.50882i	−0.603690	−	0.797219i	$-0.706303\pi$
$787$	2.77431	−	42.3277i	0.0988933	−	1.50882i	0.702583	−	0.711602i	$-0.252030\pi$
$788$	−7.74927	−	22.8286i	−0.276056	−	0.813236i
$789$	−7.37720	+	6.41561i	−0.262635	+	0.228402i
$790$	−5.63658	−	0.742070i	−0.200541	−	0.0264017i
$791$	8.33687	+	20.1270i	0.296425	+	0.715634i
$792$	2.91568	−	14.0471i	0.103604	−	0.499143i
$793$	0.403823	+	0.0803255i	0.0143402	+	0.00285244i
$794$	20.2928	−	10.0073i	0.720166	−	0.355147i
$795$	40.6609	−	16.6447i	1.44209	−	0.590328i
$796$	16.8347	+	19.1963i	0.596690	+	0.680395i
$797$	−3.76096	−	28.5673i	−0.133220	−	1.01191i	−0.919238	−	0.393703i	$-0.871194\pi$
$797$	−3.76096	−	28.5673i	−0.133220	−	1.01191i	0.786018	−	0.618204i	$-0.212139\pi$
$798$	−5.12049	−	2.14594i	−0.181263	−	0.0759655i
$799$	0.463144	−	0.323113i	0.0163849	−	0.0114309i
$800$			12.7610i			0.451168i
$801$	33.9489	+	26.5009i	1.19952	+	0.936364i
$802$	−11.9979	−	60.3175i	−0.423660	−	2.12988i
$803$	2.43398	+	9.08374i	0.0858933	+	0.320558i
$804$	−4.05623	+	8.13980i	−0.143052	+	0.287069i
$805$	30.2367	−	10.2640i	1.06570	−	0.361757i
$806$	0.120123	−	0.243586i	0.00423117	−	0.00857996i
$807$	5.47173	−	9.38703i	0.192614	−	0.330439i
$808$	2.64633	−	20.1008i	0.0930974	−	0.707145i
$809$	20.5769	−	13.7490i	0.723444	−	0.483390i	−0.138520	−	0.990360i	$-0.544234\pi$
$809$	20.5769	−	13.7490i	0.723444	−	0.483390i	0.861964	+	0.506970i	$0.169234\pi$
$810$	−31.6014	−	28.6565i	−1.11036	−	1.00689i
$811$	−24.5341	+	36.7178i	−0.861507	+	1.28934i	0.0943601	+	0.995538i	$0.469920\pi$
$811$	−24.5341	+	36.7178i	−0.861507	+	1.28934i	−0.955867	+	0.293799i	$0.905080\pi$
$812$	13.4276	−	3.59793i	0.471218	−	0.126262i
$813$	−18.3709	+	20.7733i	−0.644296	+	0.728551i
$814$	25.1479	−	3.31079i	0.881434	−	0.116043i
$815$	−5.10058	−	8.83447i	−0.178666	−	0.309458i
$816$	22.1688	+	27.9565i	0.776064	+	0.978674i
$817$	5.36841	−	9.29836i	0.187817	−	0.325308i
$818$	3.14680	−	7.59704i	0.110025	−	0.265624i
$819$	−0.283172	−	0.0209242i	−0.00989481	−	0.000731152i
$820$	22.0050	+	22.0050i	0.768449	+	0.768449i
$821$	22.4506	+	45.5254i	0.783533	+	1.58885i	0.808025	+	0.589148i	$0.200536\pi$
$821$	22.4506	+	45.5254i	0.783533	+	1.58885i	−0.0244924	+	0.999700i	$0.507797\pi$
$822$	−0.716027	+	1.06203i	−0.0249743	+	0.0370427i
$823$	−25.8226	−	12.7343i	−0.900120	−	0.443890i	−0.0674899	−	0.997720i	$-0.521499\pi$
$823$	−25.8226	−	12.7343i	−0.900120	−	0.443890i	−0.832630	+	0.553830i	$0.813166\pi$
$824$	9.21382	+	7.07001i	0.320979	+	0.246296i
$825$	−0.0489998	+	11.7950i	−0.00170596	+	0.410650i
$826$	5.75731	−	0.377354i	0.200322	−	0.0131298i
$827$	−2.52147	+	12.6763i	−0.0876800	+	0.440797i	0.911861	+	0.410499i	$0.134646\pi$
$827$	−2.52147	+	12.6763i	−0.0876800	+	0.440797i	−0.999541	+	0.0302977i	$0.990354\pi$
$828$	4.42921	+	23.2762i	0.153926	+	0.808905i
$829$	6.58216	−	6.58216i	0.228608	−	0.228608i	−0.583503	−	0.812111i	$-0.698318\pi$
$829$	6.58216	−	6.58216i	0.228608	−	0.228608i	0.812111	+	0.583503i	$0.198318\pi$
$830$	33.4535	+	11.3559i	1.16119	+	0.394170i
$831$	−4.85602	−	1.32281i	−0.168453	−	0.0458878i
$832$	0.0225386	−	0.0130127i	0.000781384	−	0.000451132i
$833$	−16.4211	+	8.51245i	−0.568957	+	0.294939i
$834$	1.55625	+	2.04568i	0.0538884	+	0.0708362i
$835$	1.14370	−	0.877589i	0.0395792	−	0.0303702i
$836$	−3.50765	+	0.697715i	−0.121315	+	0.0241310i
$837$	−13.4153	+	1.59634i	−0.463700	+	0.0551774i
$838$	−2.91348	−	1.94673i	−0.100645	−	0.0672485i
$839$	−3.39828	+	3.87500i	−0.117322	+	0.133780i	−0.807519	−	0.589841i	$-0.799190\pi$
$839$	−3.39828	+	3.87500i	−0.117322	+	0.133780i	0.690198	+	0.723621i	$0.257524\pi$
$840$	3.97168	−	11.5424i	0.137036	−	0.398252i
$841$	23.8156	−	31.0371i	0.821228	−	1.07025i
$842$	−14.7038	+	19.1624i	−0.506728	+	0.660381i
$843$	5.08206	+	5.84377i	0.175035	+	0.201270i
$844$	−16.8353	+	19.1970i	−0.579495	+	0.660788i
$845$	−29.2700	−	19.5576i	−1.00692	−	0.672802i
$846$	0.364677	−	0.619691i	0.0125379	−	0.0213054i
$847$	3.89897	−	0.775553i	0.133970	−	0.0266483i
$848$	−37.1198	+	28.4830i	−1.27470	+	0.978111i
$849$	−0.788557	+	1.88160i	−0.0270632	+	0.0645762i
$850$	−12.8970	−	10.8597i	−0.442364	−	0.372485i
$851$	32.0258	−	18.4901i	1.09783	−	0.633834i
$852$	−9.11090	+	9.03552i	−0.312134	+	0.309552i
$853$	−31.1724	−	10.5816i	−1.06732	−	0.362307i	−0.268130	−	0.963383i	$-0.586406\pi$
$853$	−31.1724	−	10.5816i	−1.06732	−	0.362307i	−0.799192	+	0.601076i	$0.794739\pi$
$854$	−13.5324	+	13.5324i	−0.463070	+	0.463070i
$855$	3.09133	−	8.86411i	0.105721	−	0.303146i
$856$	4.42655	−	22.2538i	0.151296	−	0.760619i
$857$	−13.9802	+	0.916312i	−0.477555	+	0.0313006i	−0.302281	−	0.953219i	$-0.597748\pi$
$857$	−13.9802	+	0.916312i	−0.477555	+	0.0313006i	−0.175275	+	0.984520i	$0.556081\pi$
$858$	−0.457724	+	0.261738i	−0.0156264	+	0.00893558i
$859$	−13.0775	−	10.0347i	−0.446197	−	0.342379i	0.361097	−	0.932528i	$-0.382402\pi$
$859$	−13.0775	−	10.0347i	−0.446197	−	0.342379i	−0.807294	+	0.590149i	$0.799069\pi$
$860$	−23.9832	−	11.8272i	−0.817820	−	0.403304i
$861$	−13.0263	−	26.6937i	−0.443936	−	0.909720i
$862$	15.7084	+	31.8535i	0.535030	+	1.08493i
$863$	−15.8984	−	15.8984i	−0.541189	−	0.541189i	0.382688	−	0.923878i	$-0.374998\pi$
$863$	−15.8984	−	15.8984i	−0.541189	−	0.541189i	−0.923878	+	0.382688i	$0.874998\pi$
$864$	25.2911	+	12.8665i	0.860422	+	0.437727i
$865$	−10.1754	+	24.5656i	−0.345974	+	0.835255i
$866$	21.5884	−	37.3923i	0.733605	−	1.27064i
$867$	−29.4321	−	0.865755i	−0.999568	−	0.0294026i
$868$	2.18955	+	3.79241i	0.0743182	+	0.128723i
$869$	3.46550	−	0.456242i	0.117559	−	0.0154770i
$870$	21.5142	+	64.2544i	0.729398	+	2.17843i
$871$	−0.285008	+	0.0763677i	−0.00965713	+	0.00258762i
$872$	7.89809	−	11.8203i	0.267463	−	0.400287i
$873$	−31.4767	+	20.6558i	−1.06532	+	0.699094i
$874$	−12.4978	+	8.35079i	−0.422746	+	0.282470i
$875$	1.49293	−	11.3399i	0.0504702	−	0.383359i
$876$	−5.93726	−	0.0246651i	−0.200601	−	0.000833356i
$877$	−4.00248	+	8.11623i	−0.135154	+	0.274066i	−0.953919	−	0.300063i	$-0.902992\pi$
$877$	−4.00248	+	8.11623i	−0.135154	+	0.274066i	0.818765	+	0.574129i	$0.194659\pi$
$878$	−21.2601	+	7.21684i	−0.717494	+	0.243556i
$879$	−23.8434	−	36.0071i	−0.804219	−	1.21449i
$880$	−10.2072	−	38.0938i	−0.344085	−	1.28414i
$881$	−7.06742	−	35.5303i	−0.238107	−	1.19705i	−0.896041	−	0.443971i	$-0.853569\pi$
$881$	−7.06742	−	35.5303i	−0.238107	−	1.19705i	0.657934	−	0.753076i	$-0.271431\pi$
$882$	−14.4915	+	18.5643i	−0.487954	+	0.625091i
$883$		−	27.9322i		−	0.939993i	−0.882668	−	0.469997i	$-0.844255\pi$
$883$		−	27.9322i		−	0.939993i	0.882668	−	0.469997i	$-0.155745\pi$
$884$	0.0458424	−	0.257399i	0.00154185	−	0.00865725i
$885$	1.23319	+	9.67751i	0.0414532	+	0.325306i
$886$	−4.93639	−	37.4956i	−0.165841	−	1.25969i
$887$	22.0945	+	25.1940i	0.741862	+	0.845931i	0.992512	−	0.122147i	$-0.0389778\pi$
$887$	22.0945	+	25.1940i	0.741862	+	0.845931i	−0.250650	+	0.968078i	$0.580644\pi$
$888$	1.90343	−	14.0080i	0.0638748	−	0.470079i
$889$	−30.8405	+	15.2088i	−1.03436	+	0.510088i
$890$	66.7388	+	13.2752i	2.23709	+	0.444985i
$891$	23.3273	+	11.9897i	0.781493	+	0.401669i
$892$	−2.74921	−	6.63718i	−0.0920504	−	0.222229i
$893$	0.156877	+	0.0206532i	0.00524968	+	0.000691134i
$894$	32.3046	+	11.1158i	1.08043	+	0.371769i
$895$	−11.0480	−	32.5464i	−0.369294	−	1.08791i
$896$	−1.21172	+	18.4872i	−0.0404806	+	0.617615i
$897$	−0.470501	+	0.607923i	−0.0157096	+	0.0202980i
$898$	11.9879	−	35.3153i	0.400042	−	1.17849i
$899$	19.8257	+	8.21207i	0.661224	+	0.273888i
$900$	−7.17682	−	1.98708i	−0.239227	−	0.0662359i
$901$	1.75053	−	38.5730i	0.0583187	−	1.28505i
$902$	−47.7670	−	27.5783i	−1.59047	−	0.918257i
$903$	17.9724	+	18.1223i	0.598084	+	0.603074i
$904$	16.9515	−	14.8661i	0.563800	−	0.494439i
$905$	−66.5027	−	17.8193i	−2.21062	−	0.592335i
$906$	−2.93298	+	1.94218i	−0.0974416	+	0.0645245i
$907$	10.5740	+	9.27318i	0.351105	+	0.307911i	0.816672	−	0.577102i	$-0.195816\pi$
$907$	10.5740	+	9.27318i	0.351105	+	0.307911i	−0.465567	+	0.885013i	$0.654150\pi$
$908$	−15.7589	−	23.5849i	−0.522978	−	0.782692i
$909$	34.1247	+	14.4682i	1.13184	+	0.479881i
$910$	−0.414477	+	0.171682i	−0.0137398	+	0.00569120i
$911$	1.67256	+	25.5184i	0.0554145	+	0.845462i	0.931599	+	0.363487i	$0.118414\pi$
$911$	1.67256	+	25.5184i	0.0554145	+	0.845462i	−0.876185	+	0.481975i	$0.839920\pi$
$912$	−0.695285	+	9.97300i	−0.0230232	+	0.330239i
$913$	−21.6742	−	1.42060i	−0.717311	−	0.0470150i
$914$	6.42359	−	23.9732i	0.212473	−	0.792962i
$915$	−24.2403	−	21.4370i	−0.801359	−	0.708684i
$916$	4.41565	+	5.75458i	0.145897	+	0.190137i
$917$	−31.1551			−1.02883
$918$	−34.5267	+	14.6113i	−1.13955	+	0.482244i
$919$	−59.7459			−1.97083			−0.985417	−	0.170156i	$-0.945573\pi$
$919$	−59.7459			−1.97083			−0.985417	+	0.170156i	$0.945573\pi$
$920$	−20.1179	−	26.2182i	−0.663269	−	0.864389i
$921$	6.65223	+	5.88291i	0.219198	+	0.193849i
$922$	−12.4156	+	46.3358i	−0.408887	+	1.52599i
$923$	−0.415418	−	0.0272279i	−0.0136736	−	0.000896218i
$924$	0.591267	−	8.48099i	0.0194512	−	0.279004i
$925$	0.760157	+	11.5977i	0.0249938	+	0.381332i
$926$	−6.87131	+	2.84619i	−0.225805	+	0.0935317i
$927$	−16.9514	+	12.7849i	−0.556756	+	0.419911i
$928$	−25.0408	−	37.4762i	−0.822004	−	1.23022i
$929$	−18.7878	−	16.4764i	−0.616407	−	0.540574i	0.293197	−	0.956052i	$-0.405281\pi$
$929$	−18.7878	−	16.4764i	−0.616407	−	0.540574i	−0.909603	+	0.415478i	$0.863614\pi$
$930$	−17.7972	+	11.7851i	−0.583594	+	0.386448i
$931$	−5.00598	−	1.34135i	−0.164065	−	0.0439610i
$932$	0.865863	−	0.759342i	0.0283623	−	0.0248731i
$933$	15.6301	+	15.7605i	0.511708	+	0.515977i
$934$	−29.0644	−	16.7803i	−0.951016	−	0.549069i
$935$	29.4733	+	13.8053i	0.963880	+	0.451482i
$936$	0.0736976	+	0.284477i	0.00240888	+	0.00929842i
$937$	−26.8876	−	11.1372i	−0.878381	−	0.363837i	−0.102512	−	0.994732i	$-0.532688\pi$
$937$	−26.8876	−	11.1372i	−0.878381	−	0.363837i	−0.775869	+	0.630894i	$0.782688\pi$
$938$	4.40845	−	12.9869i	0.143941	−	0.424036i
$939$	17.9316	−	23.1690i	0.585176	−	0.756092i
$940$	0.0257745	−	0.393242i	0.000840670	−	0.0128261i
$941$	8.93648	+	26.3260i	0.291321	+	0.858204i	0.989786	+	0.142560i	$0.0455334\pi$
$941$	8.93648	+	26.3260i	0.291321	+	0.858204i	−0.698465	+	0.715644i	$0.746133\pi$
$942$	−34.7300	−	11.9504i	−1.13156	−	0.389364i
$943$	−79.7265	−	10.4962i	−2.59625	−	0.341803i
$944$	−3.97577	−	9.59835i	−0.129400	−	0.312400i
$945$	18.3991	+	12.6284i	0.598523	+	0.410801i
$946$	46.4848	+	9.24639i	1.51135	+	0.300626i
$947$	−25.8407	+	12.7432i	−0.839710	+	0.414099i	−0.810687	−	0.585480i	$-0.800906\pi$
$947$	−25.8407	+	12.7432i	−0.839710	+	0.414099i	−0.0290226	+	0.999579i	$0.509239\pi$
$948$	−0.297134	+	2.18672i	−0.00965048	+	0.0710215i
$949$	−0.127010	−	0.144828i	−0.00412293	−	0.00470130i
$950$	−0.616624	−	4.68373i	−0.0200059	−	0.151960i
$951$	0.399408	+	3.13437i	0.0129517	+	0.101639i
$952$	−7.73656	−	7.43166i	−0.250743	−	0.240861i
$953$			8.00428i			0.259284i	0.991561	+	0.129642i	$0.0413828\pi$
$953$			8.00428i			0.259284i	−0.991561	+	0.129642i	$0.958617\pi$
$954$	−18.4363	−	45.5765i	−0.596896	−	1.47559i
$955$	4.90823	+	24.6754i	0.158827	+	0.798476i
$956$	−0.657105	−	2.45235i	−0.0212523	−	0.0793147i
$957$	−23.0014	−	34.7355i	−0.743529	−	1.12284i
$958$	−13.8567	+	4.70371i	−0.447690	+	0.151970i
$959$	0.296352	−	0.600942i	0.00956970	−	0.0194054i
$960$	−2.04539	−	0.00849713i	−0.0660146	−	0.000274244i
$961$	3.16396	−	24.0327i	0.102063	−	0.775248i
$962$	−0.432001	+	0.288654i	−0.0139283	+	0.00930658i
$963$	37.0495	+	18.6551i	1.19390	+	0.601151i
$964$	−1.71166	+	2.56168i	−0.0551287	+	0.0825060i
$965$	−30.6134	+	8.20284i	−0.985481	+	0.264059i
$966$	−11.3447	−	33.8822i	−0.365010	−	1.09014i
$967$	27.9918	−	3.68519i	0.900155	−	0.118508i	0.333776	−	0.942653i	$-0.391677\pi$
$967$	27.9918	−	3.68519i	0.900155	−	0.118508i	0.566379	+	0.824145i	$0.308344\pi$
$968$	−2.05715	−	3.56309i	−0.0661193	−	0.114522i
$969$	−5.92612	−	5.74009i	−0.190374	−	0.184398i
$970$	−29.7424	+	51.5153i	−0.954971	+	1.65406i
$971$	−22.6404	+	54.6588i	−0.726565	+	1.75408i	−0.0728496	+	0.997343i	$0.523209\pi$
$971$	−22.6404	+	54.6588i	−0.726565	+	1.75408i	−0.653716	+	0.756740i	$0.726791\pi$
$972$	−11.1744	+	12.2203i	−0.358418	+	0.391967i
$973$	−0.950774	−	0.950774i	−0.0304804	−	0.0304804i
$974$	−0.107747	−	0.218490i	−0.00345244	−	0.00700086i
$975$	−0.105958	−	0.217132i	−0.00339338	−	0.00695378i
$976$	30.9066	+	15.2415i	0.989298	+	0.487868i
$977$	−6.13834	−	4.71012i	−0.196383	−	0.150690i	0.505889	−	0.862598i	$-0.331164\pi$
$977$	−6.13834	−	4.71012i	−0.196383	−	0.150690i	−0.702272	+	0.711908i	$0.747831\pi$
$978$	−9.90938	+	5.66643i	−0.316867	+	0.181192i
$979$	−41.7469	+	2.73624i	−1.33424	+	0.0874505i
$980$	−2.51815	+	12.6596i	−0.0804394	+	0.404396i
$981$	16.9733	+	19.6819i	0.541917	+	0.628394i
$982$	−30.5553	+	30.5553i	−0.975059	+	0.975059i
$983$	−20.2640	−	6.87869i	−0.646320	−	0.219396i	−0.0210182	−	0.999779i	$-0.506691\pi$
$983$	−20.2640	−	6.87869i	−0.646320	−	0.219396i	−0.625302	+	0.780383i	$0.715024\pi$
$984$	−21.8271	+	21.6465i	−0.695822	+	0.690064i
$985$	−53.2368	+	30.7363i	−1.69627	+	0.979340i
$986$	59.1856	+	6.58480i	1.88485	+	0.209703i
$987$	−0.145384	+	0.346905i	−0.00462763	+	0.0110421i
$988$	0.0581184	−	0.0445958i	0.00184899	−	0.00141878i
$989$	67.7715	−	13.4806i	2.15501	−	0.428658i
$990$	41.4386	+	0.344301i	1.31700	+	0.0109426i
$991$	20.4059	+	13.6348i	0.648216	+	0.433124i	0.835732	−	0.549138i	$-0.185044\pi$
$991$	20.4059	+	13.6348i	0.648216	+	0.433124i	−0.187516	+	0.982261i	$0.560044\pi$
$992$	9.36163	−	10.6749i	0.297232	−	0.338928i
$993$	−0.181130	−	0.208278i	−0.00574799	−	0.00660951i
$994$	11.7797	−	15.3517i	0.373631	−	0.486925i
$995$	39.6332	−	51.6510i	1.25646	−	1.63745i
$996$	4.46191	−	12.9671i	0.141381	−	0.410879i
$997$	19.5781	−	22.3245i	0.620043	−	0.707024i	−0.353524	−	0.935426i	$-0.615017\pi$
$997$	19.5781	−	22.3245i	0.620043	−	0.707024i	0.973567	+	0.228402i	$0.0733500\pi$
$998$	43.3585	+	28.9713i	1.37249	+	0.917069i
$999$	23.7522	+	10.1871i	0.751485	+	0.322305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.11.13	✓	256
3.2	odd	2		459.2.y.a.62.4		256
9.4	even	3		459.2.y.a.368.4		256
9.5	odd	6	inner	153.2.s.a.113.13	yes	256
17.14	odd	16	inner	153.2.s.a.65.13	yes	256
51.14	even	16		459.2.y.a.116.4		256
153.14	even	48	inner	153.2.s.a.14.13	yes	256
153.31	odd	48		459.2.y.a.422.4		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.13	✓	256	1.1	even	1	trivial
153.2.s.a.14.13	yes	256	153.14	even	48	inner
153.2.s.a.65.13	yes	256	17.14	odd	16	inner
153.2.s.a.113.13	yes	256	9.5	odd	6	inner
459.2.y.a.62.4		256	3.2	odd	2
459.2.y.a.116.4		256	51.14	even	16
459.2.y.a.368.4		256	9.4	even	3
459.2.y.a.422.4		256	153.31	odd	48

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06529 + 1.38832i) q^{2} +(-1.29747 - 1.14742i) q^{3} +(-0.274934 + 1.02607i) q^{4} +(2.70285 + 0.177154i) q^{5} +(0.210798 - 3.02363i) q^{6} +(0.103700 + 1.58216i) q^{7} +(1.51606 - 0.627973i) q^{8} +(0.366853 + 2.97749i) q^{9} +O(q^{10})\)	\(q+(1.06529 + 1.38832i) q^{2} +(-1.29747 - 1.14742i) q^{3} +(-0.274934 + 1.02607i) q^{4} +(2.70285 + 0.177154i) q^{5} +(0.210798 - 3.02363i) q^{6} +(0.103700 + 1.58216i) q^{7} +(1.51606 - 0.627973i) q^{8} +(0.366853 + 2.97749i) q^{9} +(2.63338 + 3.94113i) q^{10} +(-2.19104 - 1.92149i) q^{11} +(1.53405 - 1.01583i) q^{12} +(0.0576598 + 0.0154499i) q^{13} +(-2.08607 + 1.82943i) q^{14} +(-3.30359 - 3.33116i) q^{15} +(4.32677 + 2.49806i) q^{16} +(-3.87687 + 1.40353i) q^{17} +(-3.74288 + 3.68120i) q^{18} +(-1.06733 - 0.442104i) q^{19} +(-0.924878 + 2.72460i) q^{20} +(1.68085 - 2.17179i) q^{21} +(0.333537 - 5.08880i) q^{22} +(-2.38991 - 7.04045i) q^{23} +(-2.68759 - 0.924784i) q^{24} +(2.31678 + 0.305010i) q^{25} +(0.0399752 + 0.0965087i) q^{26} +(2.94045 - 4.28413i) q^{27} +(-1.65192 - 0.328587i) q^{28} +(-7.40240 + 3.65046i) q^{29} +(1.10540 - 8.13508i) q^{30} +(-1.71429 - 1.95477i) q^{31} +(0.712795 + 5.41421i) q^{32} +(0.638049 + 5.00711i) q^{33} +(-6.07853 - 3.88715i) q^{34} +4.29471i q^{35} +(-3.15597 - 0.442197i) q^{36} +(0.970339 + 4.87822i) q^{37} +(-0.523242 - 1.95277i) q^{38} +(-0.0570843 - 0.0862058i) q^{39} +(4.20893 - 1.42874i) q^{40} +(4.78363 - 9.70024i) q^{41} +(4.80573 + 0.0199644i) q^{42} +(-1.21308 + 9.21423i) q^{43} +(2.57397 - 1.71987i) q^{44} +(0.464075 + 8.11268i) q^{45} +(7.22841 - 10.8181i) q^{46} +(-0.132297 + 0.0354488i) q^{47} +(-2.74752 - 8.20578i) q^{48} +(4.44764 - 0.585543i) q^{49} +(2.04460 + 3.54135i) q^{50} +(6.64055 + 2.62737i) q^{51} +(-0.0317053 + 0.0549153i) q^{52} +(-3.58381 + 8.65209i) q^{53} +(9.08016 - 0.481582i) q^{54} +(-5.58164 - 5.58164i) q^{55} +(1.15077 + 2.33353i) q^{56} +(0.877553 + 1.79830i) q^{57} +(-12.9537 - 6.38806i) q^{58} +(-1.64974 - 1.26589i) q^{59} +(4.32627 - 2.47387i) q^{60} +(6.88267 - 0.451114i) q^{61} +(0.887622 - 4.46238i) q^{62} +(-4.67281 + 0.889186i) q^{63} +(0.308284 - 0.308284i) q^{64} +(0.153109 + 0.0519734i) q^{65} +(-6.27174 + 6.21985i) q^{66} +(-4.28070 + 2.47146i) q^{67} +(-0.374231 - 4.36381i) q^{68} +(-4.97752 + 11.8770i) q^{69} +(-5.96241 + 4.57512i) q^{70} +(-6.84006 + 1.36057i) q^{71} +(2.42595 + 4.28368i) q^{72} +(-2.68314 - 1.79281i) q^{73} +(-5.73882 + 6.54387i) q^{74} +(-2.65598 - 3.05407i) q^{75} +(0.747076 - 0.973608i) q^{76} +(2.81289 - 3.66583i) q^{77} +(0.0588694 - 0.171085i) q^{78} +(-0.790836 + 0.901776i) q^{79} +(11.2521 + 7.51839i) q^{80} +(-8.73084 + 2.18460i) q^{81} +(18.5629 - 3.69240i) q^{82} +(5.91311 - 4.53729i) q^{83} +(1.76628 + 2.32177i) q^{84} +(-10.7272 + 3.10672i) q^{85} +(-14.0845 + 8.13171i) q^{86} +(13.7930 + 3.75731i) q^{87} +(-4.52839 - 1.53718i) q^{88} +(10.1512 - 10.1512i) q^{89} +(-10.7686 + 9.28665i) q^{90} +(-0.0184649 + 0.0928292i) q^{91} +(7.88105 - 0.516552i) q^{92} +(-0.0187079 + 4.50327i) q^{93} +(-0.190149 - 0.145906i) q^{94} +(-2.80652 - 1.38402i) q^{95} +(5.28755 - 7.84265i) q^{96} +(5.55057 + 11.2554i) q^{97} +(5.55095 + 5.55095i) q^{98} +(4.91742 - 7.22869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

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