LMFDB - Embedded newform 169.2.h.a.12.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(12,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([21]))

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.h (of order $26$, degree $12$, 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			12.5
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19961 + 0.828028i) q^{2} +(0.960584 + 0.504153i) q^{3} +(0.0442133 - 0.116581i) q^{4} +(2.00541 + 2.26364i) q^{5} +(-1.56977 + 0.190605i) q^{6} +(0.228271 + 0.926132i) q^{7} +(-0.654173 - 2.65409i) q^{8} +(-1.03564 - 1.50039i) q^{9} +O(q^{10})$	\(q+(-1.19961 + 0.828028i) q^{2} +(0.960584 + 0.504153i) q^{3} +(0.0442133 - 0.116581i) q^{4} +(2.00541 + 2.26364i) q^{5} +(-1.56977 + 0.190605i) q^{6} +(0.228271 + 0.926132i) q^{7} +(-0.654173 - 2.65409i) q^{8} +(-1.03564 - 1.50039i) q^{9} +(-4.28006 - 1.05494i) q^{10} +(0.351207 + 0.242421i) q^{11} +(0.101245 - 0.0896954i) q^{12} +(1.73944 + 3.15822i) q^{13} +(-1.04070 - 0.921978i) q^{14} +(0.785144 + 3.18545i) q^{15} +(3.16906 + 2.80754i) q^{16} +(-4.48180 + 1.10466i) q^{17} +(2.48473 + 0.942332i) q^{18} -0.428231i q^{19} +(0.352563 - 0.133710i) q^{20} +(-0.247639 + 1.00471i) q^{21} -0.622040 q^{22} +0.363115 q^{23} +(0.709678 - 2.87928i) q^{24} +(-0.499715 + 4.11552i) q^{25} +(-4.70173 - 2.34832i) q^{26} +(-0.630688 - 5.19418i) q^{27} +(0.118062 + 0.0143353i) q^{28} +(-2.64175 - 3.82724i) q^{29} +(-3.57951 - 3.17117i) q^{30} +(8.18388 - 0.993703i) q^{31} +(-0.699172 - 0.0848949i) q^{32} +(0.215146 + 0.409927i) q^{33} +(4.46170 - 5.03621i) q^{34} +(-1.63865 + 2.37400i) q^{35} +(-0.220706 + 0.0543991i) q^{36} +(4.25411 - 0.516542i) q^{37} +(0.354587 + 0.513708i) q^{38} +(0.0786471 + 3.91068i) q^{39} +(4.69601 - 6.80335i) q^{40} +(-0.958910 + 1.82705i) q^{41} +(-0.534860 - 1.41031i) q^{42} +(0.489882 - 4.03454i) q^{43} +(0.0437896 - 0.0302258i) q^{44} +(1.31945 - 5.35322i) q^{45} +(-0.435595 + 0.300669i) q^{46} +(10.4726 - 3.97174i) q^{47} +(1.62872 + 4.29457i) q^{48} +(5.39258 - 2.83024i) q^{49} +(-2.80831 - 5.35078i) q^{50} +(-4.86206 - 1.19839i) q^{51} +(0.445094 - 0.0631497i) q^{52} +(-8.46335 + 2.08603i) q^{53} +(5.05750 + 5.70874i) q^{54} +(0.155561 + 1.28116i) q^{55} +(2.30870 - 1.21170i) q^{56} +(0.215894 - 0.411352i) q^{57} +(6.33812 + 2.40373i) q^{58} +(-8.45125 - 9.53949i) q^{59} +(0.406077 + 0.0493066i) q^{60} +(-0.778766 - 0.191949i) q^{61} +(-8.99461 + 7.96853i) q^{62} +(1.15315 - 1.30164i) q^{63} +(-6.58870 + 3.45802i) q^{64} +(-3.66079 + 10.2710i) q^{65} +(-0.597522 - 0.313604i) q^{66} +(1.97707 - 0.749805i) q^{67} +(-0.0693723 + 0.571333i) q^{68} +(0.348803 + 0.183066i) q^{69} -4.20471i q^{70} +(0.0435937 - 0.0830608i) q^{71} +(-3.30467 + 3.73020i) q^{72} +(7.28536 + 5.02872i) q^{73} +(-4.67554 + 4.14217i) q^{74} +(-2.55487 + 3.70137i) q^{75} +(-0.0499235 - 0.0189335i) q^{76} +(-0.144343 + 0.380601i) q^{77} +(-3.33250 - 4.62615i) q^{78} +(-0.959418 - 2.52978i) q^{79} +12.8039i q^{80} +(0.0733877 - 0.193508i) q^{81} +(-0.362535 - 2.98574i) q^{82} +(7.46757 + 14.2283i) q^{83} +(0.106181 + 0.0732916i) q^{84} +(-11.4884 - 7.92988i) q^{85} +(2.75304 + 5.24549i) q^{86} +(-0.608109 - 5.00823i) q^{87} +(0.413655 - 1.09072i) q^{88} -12.6640i q^{89} +(2.84980 + 7.51429i) q^{90} +(-2.52787 + 2.33188i) q^{91} +(0.0160545 - 0.0423323i) q^{92} +(8.36228 + 3.17139i) q^{93} +(-9.27430 + 13.4361i) q^{94} +(0.969361 - 0.858779i) q^{95} +(-0.628814 - 0.434039i) q^{96} +(-11.4690 + 12.9459i) q^{97} +(-4.12545 + 7.86038i) q^{98} -0.778008i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{26}\right)$

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 $

$2$	−1.19961	+	0.828028i	−0.848249	+	0.585504i	−0.910945	−	0.412529i	$-0.864646\pi$
$2$	−1.19961	+	0.828028i	−0.848249	+	0.585504i	0.0626955	+	0.998033i	$0.480030\pi$
$3$	0.960584	+	0.504153i	0.554593	+	0.291073i	0.718643	−	0.695379i	$-0.244763\pi$
$3$	0.960584	+	0.504153i	0.554593	+	0.291073i	−0.164050	+	0.986452i	$0.552456\pi$
$4$	0.0442133	−	0.116581i	0.0221066	−	0.0582904i
$5$	2.00541	+	2.26364i	0.896847	+	1.01233i	0.999844	+	0.0176496i	$0.00561835\pi$
$5$	2.00541	+	2.26364i	0.896847	+	1.01233i	−0.102997	+	0.994682i	$0.532843\pi$
$6$	−1.56977	+	0.190605i	−0.640858	+	0.0778142i
$7$	0.228271	+	0.926132i	0.0862783	+	0.350045i	0.998176	−	0.0603729i	$-0.0192290\pi$
$7$	0.228271	+	0.926132i	0.0862783	+	0.350045i	−0.911898	+	0.410418i	$0.865383\pi$
$8$	−0.654173	−	2.65409i	−0.231285	−	0.938361i
$9$	−1.03564	−	1.50039i	−0.345214	−	0.500129i
$10$	−4.28006	−	1.05494i	−1.35347	−	0.333601i
$11$	0.351207	+	0.242421i	0.105893	+	0.0730925i	0.619834	−	0.784733i	$-0.287200\pi$
$11$	0.351207	+	0.242421i	0.105893	+	0.0730925i	−0.513942	+	0.857825i	$0.671815\pi$
$12$	0.101245	−	0.0896954i	0.0292270	−	0.0258928i
$13$	1.73944	+	3.15822i	0.482433	+	0.875933i
$13$	1.73944	+	3.15822i	0.482433	+	0.875933i
$14$	−1.04070	−	0.921978i	−0.278138	−	0.246409i
$15$	0.785144	+	3.18545i	0.202723	+	0.822480i
$16$	3.16906	+	2.80754i	0.792265	+	0.701886i
$17$	−4.48180	+	1.10466i	−1.08700	+	0.267920i	−0.741807	−	0.670613i	$-0.766031\pi$
$17$	−4.48180	+	1.10466i	−1.08700	+	0.267920i	−0.345188	+	0.938533i	$0.612185\pi$
$18$	2.48473	+	0.942332i	0.585656	+	0.222110i
$19$		−	0.428231i		−	0.0982429i	−0.998793	−	0.0491215i	$-0.984358\pi$
$19$		−	0.428231i		−	0.0982429i	0.998793	−	0.0491215i	$-0.0156421\pi$
$20$	0.352563	−	0.133710i	0.0788355	−	0.0298984i
$21$	−0.247639	+	1.00471i	−0.0540393	+	0.219246i
$22$	−0.622040			−0.132619
$23$	0.363115			0.0757147			0.0378574	−	0.999283i	$-0.487947\pi$
$23$	0.363115			0.0757147			0.0378574	+	0.999283i	$0.487947\pi$
$24$	0.709678	−	2.87928i	0.144862	−	0.587730i
$25$	−0.499715	+	4.11552i	−0.0999430	+	0.823104i
$26$	−4.70173	−	2.34832i	−0.922086	−	0.460543i
$27$	−0.630688	−	5.19418i	−0.121376	−	0.999621i
$28$	0.118062	+	0.0143353i	0.0223116	+	0.00270912i
$29$	−2.64175	−	3.82724i	−0.490561	−	0.710700i	0.497033	−	0.867732i	$-0.334423\pi$
$29$	−2.64175	−	3.82724i	−0.490561	−	0.710700i	−0.987594	+	0.157032i	$0.949807\pi$
$30$	−3.57951	−	3.17117i	−0.653526	−	0.578973i
$31$	8.18388	−	0.993703i	1.46987	−	0.178474i	0.653904	−	0.756578i	$-0.273130\pi$
$31$	8.18388	−	0.993703i	1.46987	−	0.178474i	0.815964	+	0.578103i	$0.196207\pi$
$32$	−0.699172	−	0.0848949i	−0.123597	−	0.0150074i
$33$	0.215146	+	0.409927i	0.0374522	+	0.0713592i
$34$	4.46170	−	5.03621i	0.765175	−	0.863704i
$35$	−1.63865	+	2.37400i	−0.276983	+	0.401279i
$36$	−0.220706	+	0.0543991i	−0.0367843	+	0.00906651i
$37$	4.25411	−	0.516542i	0.699371	−	0.0849191i	0.236875	−	0.971540i	$-0.423877\pi$
$37$	4.25411	−	0.516542i	0.699371	−	0.0849191i	0.462496	+	0.886621i	$0.346954\pi$
$38$	0.354587	+	0.513708i	0.0575216	+	0.0833345i
$39$	0.0786471	+	3.91068i	0.0125936	+	0.626210i
$40$	4.69601	−	6.80335i	0.742505	−	1.07570i
$41$	−0.958910	+	1.82705i	−0.149757	+	0.285337i	−0.948765	−	0.315983i	$-0.897666\pi$
$41$	−0.958910	+	1.82705i	−0.149757	+	0.285337i	0.799008	+	0.601320i	$0.205358\pi$
$42$	−0.534860	−	1.41031i	−0.0825307	−	0.217615i
$43$	0.489882	−	4.03454i	0.0747062	−	0.615261i	−0.906487	−	0.422234i	$-0.861246\pi$
$43$	0.489882	−	4.03454i	0.0747062	−	0.615261i	0.981193	−	0.193028i	$-0.0618307\pi$
$44$	0.0437896	−	0.0302258i	0.00660153	−	0.00455671i
$45$	1.31945	−	5.35322i	0.196692	−	0.798011i
$46$	−0.435595	+	0.300669i	−0.0642250	+	0.0443313i
$47$	10.4726	−	3.97174i	1.52759	−	0.579338i	0.559255	−	0.828996i	$-0.311087\pi$
$47$	10.4726	−	3.97174i	1.52759	−	0.579338i	0.968334	+	0.249658i	$0.0803181\pi$
$48$	1.62872	+	4.29457i	0.235085	+	0.619868i
$49$	5.39258	−	2.83024i	0.770368	−	0.404321i
$50$	−2.80831	−	5.35078i	−0.397154	−	0.756715i
$51$	−4.86206	−	1.19839i	−0.680825	−	0.167808i
$52$	0.445094	−	0.0631497i	0.0617235	−	0.00875728i
$53$	−8.46335	+	2.08603i	−1.16253	+	0.286538i	−0.772958	−	0.634457i	$-0.781224\pi$
$53$	−8.46335	+	2.08603i	−1.16253	+	0.286538i	−0.389573	+	0.920996i	$0.627377\pi$
$54$	5.05750	+	5.70874i	0.688239	+	0.776861i
$55$	0.155561	+	1.28116i	0.0209758	+	0.172751i
$56$	2.30870	−	1.21170i	0.308514	−	0.161920i
$57$	0.215894	−	0.411352i	0.0285959	−	0.0544849i
$58$	6.33812	+	2.40373i	0.832235	+	0.315625i
$59$	−8.45125	−	9.53949i	−1.10026	−	1.24194i	−0.968062	−	0.250712i	$-0.919335\pi$
$59$	−8.45125	−	9.53949i	−1.10026	−	1.24194i	−0.132197	−	0.991223i	$-0.542203\pi$
$60$	0.406077	+	0.0493066i	0.0524243	+	0.00636546i
$61$	−0.778766	−	0.191949i	−0.0997108	−	0.0245765i	0.189145	−	0.981949i	$-0.439429\pi$
$61$	−0.778766	−	0.191949i	−0.0997108	−	0.0245765i	−0.288855	+	0.957373i	$0.593275\pi$
$62$	−8.99461	+	7.96853i	−1.14232	+	1.01200i
$63$	1.15315	−	1.30164i	0.145283	−	0.163991i
$64$	−6.58870	+	3.45802i	−0.823587	+	0.432252i
$65$	−3.66079	+	10.2710i	−0.454066	+	1.27396i
$66$	−0.597522	−	0.313604i	−0.0735499	−	0.0386020i
$67$	1.97707	−	0.749805i	0.241538	−	0.0916032i	−0.230866	−	0.972986i	$-0.574156\pi$
$67$	1.97707	−	0.749805i	0.241538	−	0.0916032i	0.472403	+	0.881382i	$0.343387\pi$
$68$	−0.0693723	+	0.571333i	−0.00841263	+	0.0692843i
$69$	0.348803	+	0.183066i	0.0419909	+	0.0220385i
$70$		−	4.20471i		−	0.502559i
$71$	0.0435937	−	0.0830608i	0.00517362	−	0.00985750i	−0.882855	−	0.469645i	$-0.844382\pi$
$71$	0.0435937	−	0.0830608i	0.00517362	−	0.00985750i	0.888029	+	0.459787i	$0.152074\pi$
$72$	−3.30467	+	3.73020i	−0.389459	+	0.439608i
$73$	7.28536	+	5.02872i	0.852687	+	0.588568i	0.912239	−	0.409658i	$-0.134352\pi$
$73$	7.28536	+	5.02872i	0.852687	+	0.588568i	−0.0595520	+	0.998225i	$0.518967\pi$
$74$	−4.67554	+	4.14217i	−0.543521	+	0.481517i
$75$	−2.55487	+	3.70137i	−0.295011	+	0.427398i
$76$	−0.0499235	−	0.0189335i	−0.00572662	−	0.00217182i
$77$	−0.144343	+	0.380601i	−0.0164494	+	0.0433736i
$78$	−3.33250	−	4.62615i	−0.377331	−	0.523808i
$79$	−0.959418	−	2.52978i	−0.107943	−	0.284622i	0.870151	−	0.492785i	$-0.164021\pi$
$79$	−0.959418	−	2.52978i	−0.107943	−	0.284622i	−0.978094	+	0.208162i	$0.933252\pi$
$80$			12.8039i			1.43152i
$81$	0.0733877	−	0.193508i	0.00815419	−	0.0215008i
$82$	−0.362535	−	2.98574i	−0.0400353	−	0.329720i
$83$	7.46757	+	14.2283i	0.819672	+	1.56175i	0.827284	+	0.561783i	$0.189885\pi$
$83$	7.46757	+	14.2283i	0.819672	+	1.56175i	−0.00761251	+	0.999971i	$0.502423\pi$
$84$	0.106181	+	0.0732916i	0.0115853	+	0.00799677i
$85$	−11.4884	−	7.92988i	−1.24609	−	0.860116i
$86$	2.75304	+	5.24549i	0.296868	+	0.565636i
$87$	−0.608109	−	5.00823i	−0.0651961	−	0.536939i
$88$	0.413655	−	1.09072i	0.0440957	−	0.116271i
$89$		−	12.6640i		−	1.34238i	−0.741283	−	0.671192i	$-0.765783\pi$
$89$		−	12.6640i		−	1.34238i	0.741283	−	0.671192i	$-0.234217\pi$
$90$	2.84980	+	7.51429i	0.300395	+	0.792076i
$91$	−2.52787	+	2.33188i	−0.264992	+	0.244447i
$92$	0.0160545	−	0.0423323i	0.00167380	−	0.00441344i
$93$	8.36228	+	3.17139i	0.867128	+	0.328858i
$94$	−9.27430	+	13.4361i	−0.956571	+	1.38583i
$95$	0.969361	−	0.858779i	0.0994544	−	0.0881089i
$96$	−0.628814	−	0.434039i	−0.0641781	−	0.0442989i
$97$	−11.4690	+	12.9459i	−1.16451	+	1.31445i	−0.224034	+	0.974581i	$0.571923\pi$
$97$	−11.4690	+	12.9459i	−1.16451	+	1.31445i	−0.940471	+	0.339873i	$0.889616\pi$
$98$	−4.12545	+	7.86038i	−0.416733	+	0.794018i
$99$		−	0.778008i		−	0.0781927i
$100$	0.457697	+	0.240218i	0.0457697	+	0.0240218i
$101$	−0.438558	+	3.61185i	−0.0436381	+	0.359392i	0.954490	+	0.298241i	$0.0964001\pi$
$101$	−0.438558	+	3.61185i	−0.0436381	+	0.359392i	−0.998129	+	0.0611506i	$0.980523\pi$
$102$	6.82486	−	2.58833i	0.675762	−	0.256283i
$103$	10.3677	+	5.44137i	1.02156	+	0.536154i	0.890386	−	0.455205i	$-0.150434\pi$
$103$	10.3677	+	5.44137i	1.02156	+	0.536154i	0.131170	+	0.991360i	$0.458126\pi$
$104$	7.24430	−	6.68264i	0.710362	−	0.655287i
$105$	−2.77092	+	1.45429i	−0.270415	+	0.141925i
$106$	8.42539	−	9.51030i	0.818347	−	0.923722i
$107$	−4.06757	+	3.60355i	−0.393226	+	0.348368i	−0.836450	−	0.548043i	$-0.815373\pi$
$107$	−4.06757	+	3.60355i	−0.393226	+	0.348368i	0.443224	+	0.896411i	$0.353835\pi$
$108$	−0.633427	−	0.156126i	−0.0609516	−	0.0150232i
$109$	−16.8946	−	2.05138i	−1.61821	−	0.196486i	−0.739266	−	0.673414i	$-0.764827\pi$
$109$	−16.8946	−	2.05138i	−1.61821	−	0.196486i	−0.878943	+	0.476927i	$0.841750\pi$
$110$	−1.24745	−	1.40808i	−0.118939	−	0.134255i
$111$	4.34685	+	1.64854i	0.412584	+	0.156473i
$112$	−1.87675	+	3.57585i	−0.177336	+	0.337886i
$113$	−0.0947873	+	0.0497482i	−0.00891684	+	0.00467992i	−0.469176	−	0.883105i	$-0.655449\pi$
$113$	−0.0947873	+	0.0497482i	−0.00891684	+	0.00467992i	0.460259	+	0.887785i	$0.347757\pi$
$114$	0.0816230	+	0.672226i	0.00764470	+	0.0629598i
$115$	0.728195	+	0.821962i	0.0679045	+	0.0766484i
$116$	−0.562983	+	0.138763i	−0.0522717	+	0.0128838i
$117$	2.93712	−	5.88062i	0.271537	−	0.543663i
$118$	18.0371	+	4.44575i	1.66045	+	0.409265i
$119$	−2.04613	−	3.89857i	−0.187568	−	0.357382i
$120$	7.94085	−	4.16768i	0.724897	−	0.380455i
$121$	−3.83608	−	10.1149i	−0.348734	−	0.919536i
$122$	1.09315	−	0.414577i	0.0989692	−	0.0375341i
$123$	−1.84223	+	1.27160i	−0.166108	+	0.114656i
$124$	0.245989	−	0.998018i	0.0220905	−	0.0896247i
$125$	2.12611	−	1.46755i	0.190165	−	0.131262i
$126$	−0.305533	+	2.51629i	−0.0272191	+	0.224169i
$127$	−3.58597	−	9.45543i	−0.318204	−	0.839034i	−0.994722	−	0.102608i	$-0.967281\pi$
$127$	−3.58597	−	9.45543i	−0.318204	−	0.839034i	0.676518	−	0.736426i	$-0.263488\pi$
$128$	5.69512	−	10.8511i	0.503382	−	0.959115i
$129$	2.50460	−	3.62854i	0.220518	−	0.319475i
$130$	−4.11316	−	15.3524i	−0.360748	−	1.34649i
$131$	−12.2425	−	17.7364i	−1.06964	−	1.54963i	−0.812236	−	0.583329i	$-0.801750\pi$
$131$	−12.2425	−	17.7364i	−1.06964	−	1.54963i	−0.257399	−	0.966305i	$-0.582865\pi$
$132$	0.0573020	−	0.00695773i	0.00498750	−	0.000605592i
$133$	0.396598	−	0.0977527i	0.0343894	−	0.00847624i
$134$	−1.75085	+	2.53654i	−0.151250	+	0.219124i
$135$	10.4930	−	11.8441i	0.903092	−	1.01938i
$136$	5.86375	+	11.1724i	0.502812	+	0.958028i
$137$	−4.20774	−	0.510912i	−0.359491	−	0.0436501i	−0.0612013	−	0.998125i	$-0.519493\pi$
$137$	−4.20774	−	0.510912i	−0.359491	−	0.0436501i	−0.298290	+	0.954475i	$0.596416\pi$
$138$	−0.570009	+	0.0692116i	−0.0485224	+	0.00589168i
$139$	3.52857	+	3.12604i	0.299290	+	0.265147i	0.799380	−	0.600826i	$-0.205161\pi$
$139$	3.52857	+	3.12604i	0.299290	+	0.265147i	−0.500090	+	0.865973i	$0.666700\pi$
$140$	0.204313	+	0.295998i	0.0172676	+	0.0250164i
$141$	12.0622	+	1.46462i	1.01582	+	0.123343i
$142$	0.0164814	+	0.135737i	0.00138309	+	0.0113908i
$143$	−0.154716	+	1.53086i	−0.0129380	+	0.128017i
$144$	0.930388	−	7.66243i	0.0775323	−	0.638536i
$145$	3.36569	−	13.6552i	0.279506	−	1.13400i
$146$	−12.9035			−1.06790
$147$	6.60690			0.544928
$148$	0.127869	−	0.518786i	0.0105108	−	0.0426439i
$149$	−12.0206	+	4.55883i	−0.984769	+	0.373474i	−0.793838	−	0.608130i	$-0.791920\pi$
$149$	−12.0206	+	4.55883i	−0.984769	+	0.373474i	−0.190932	+	0.981603i	$0.561151\pi$
$150$		−	6.55569i		−	0.535270i
$151$	−4.67435	−	1.77275i	−0.380393	−	0.144264i	0.156994	−	0.987599i	$-0.449820\pi$
$151$	−4.67435	−	1.77275i	−0.380393	−	0.144264i	−0.537388	+	0.843335i	$0.680589\pi$
$152$	−1.13656	+	0.280137i	−0.0921873	+	0.0227221i
$153$	6.29897	+	5.58040i	0.509241	+	0.451148i
$154$	−0.141994	−	0.576092i	−0.0114422	−	0.0464228i
$155$	18.6614	+	16.5326i	1.49892	+	1.32793i
$156$	0.459388	+	0.163735i	0.0367805	+	0.0131093i
$157$	−11.7153	+	10.3789i	−0.934983	+	0.828322i	−0.985374	−	0.170407i	$-0.945492\pi$
$157$	−11.7153	+	10.3789i	−0.934983	+	0.828322i	0.0503910	+	0.998730i	$0.483953\pi$
$158$	3.24565	+	2.24031i	0.258210	+	0.178229i
$159$	−9.18144	−	2.26302i	−0.728136	−	0.179469i
$160$	−1.20996	−	1.75293i	−0.0956555	−	0.138581i
$161$	0.0828887	+	0.336293i	0.00653254	+	0.0265036i
$162$	0.0721933	+	0.292900i	0.00567204	+	0.0230124i
$163$	9.76586	−	1.18579i	0.764921	−	0.0928782i	0.271229	−	0.962515i	$-0.412570\pi$
$163$	9.76586	−	1.18579i	0.764921	−	0.0928782i	0.493692	+	0.869637i	$0.335647\pi$
$164$	0.170602	+	0.192570i	0.0133218	+	0.0150372i
$165$	−0.496471	+	1.30909i	−0.0386503	+	0.101912i
$166$	−20.7395	−	10.8849i	−1.60970	−	0.844835i
$167$	−4.74797	+	3.27729i	−0.367409	+	0.253604i	−0.737436	−	0.675417i	$-0.763964\pi$
$167$	−4.74797	+	3.27729i	−0.367409	+	0.253604i	0.370027	+	0.929021i	$0.379348\pi$
$168$	2.82859			0.218230
$169$	−6.94872	+	10.9871i	−0.534517	+	0.845158i
$170$	20.3477			1.56060
$171$	−0.642513	+	0.443494i	−0.0491342	+	0.0339149i
$172$	−0.448691	−	0.235491i	−0.0342123	−	0.0179560i
$173$	3.04707	−	8.03446i	0.231664	−	0.610849i	−0.767894	−	0.640577i	$-0.778695\pi$
$173$	3.04707	−	8.03446i	0.231664	−	0.610849i	0.999558	+	0.0297286i	$0.00946431\pi$
$174$	4.87644	+	5.50437i	0.369682	+	0.417285i
$175$	−3.92559	+	0.476653i	−0.296746	+	0.0360315i
$176$	0.432389	+	1.75427i	0.0325926	+	0.132233i
$177$	−3.30877	−	13.4242i	−0.248702	−	1.00903i
$178$	10.4862	+	15.1918i	0.785971	+	1.13868i
$179$	4.52776	+	1.11599i	0.338421	+	0.0834132i	0.404864	−	0.914377i	$-0.367319\pi$
$179$	4.52776	+	1.11599i	0.338421	+	0.0834132i	−0.0664432	+	0.997790i	$0.521165\pi$
$180$	−0.565746	−	0.390506i	−0.0421682	−	0.0291066i
$181$	−2.34694	+	2.07921i	−0.174446	+	0.154546i	−0.745828	−	0.666138i	$-0.767946\pi$
$181$	−2.34694	+	2.07921i	−0.174446	+	0.154546i	0.571382	+	0.820684i	$0.306408\pi$
$182$	1.10158	−	4.89048i	0.0816547	−	0.362506i
$183$	−0.651299	−	0.577000i	−0.0481454	−	0.0426531i
$184$	−0.237540	−	0.963739i	−0.0175117	−	0.0710477i
$185$	9.70051	+	8.59390i	0.713195	+	0.631836i
$186$	−12.6574	+	3.11978i	−0.928089	+	0.228753i
$187$	−1.84183	−	0.698514i	−0.134688	−	0.0510804i
$188$		−	1.39651i		−	0.101851i
$189$	4.66653	−	1.76978i	0.339440	−	0.128733i
$190$	−0.451758	+	1.83285i	−0.0327740	+	0.132969i
$191$	11.5891			0.838558			0.419279	−	0.907857i	$-0.362283\pi$
$191$	11.5891			0.838558			0.419279	+	0.907857i	$0.362283\pi$
$192$	−8.07237			−0.582573
$193$	−6.04650	+	24.5316i	−0.435236	+	1.76582i	0.186356	+	0.982482i	$0.440332\pi$
$193$	−6.04650	+	24.5316i	−0.435236	+	1.76582i	−0.621593	+	0.783341i	$0.713514\pi$
$194$	3.03878	−	25.0266i	0.218172	−	1.79681i
$195$	−8.69466	+	8.02055i	−0.622637	+	0.574364i
$196$	−0.0915286	−	0.753806i	−0.00653776	−	0.0538433i
$197$	−20.8181	−	2.52777i	−1.48323	−	0.180096i	−0.661485	−	0.749958i	$-0.730073\pi$
$197$	−20.8181	−	2.52777i	−1.48323	−	0.180096i	−0.821740	+	0.569862i	$0.806997\pi$
$198$	0.644212	+	0.933302i	0.0457821	+	0.0663269i
$199$	−6.66585	−	5.90543i	−0.472530	−	0.418625i	0.392957	−	0.919557i	$-0.371452\pi$
$199$	−6.66585	−	5.90543i	−0.472530	−	0.418625i	−0.865487	+	0.500932i	$0.832991\pi$
$200$	11.2498	−	1.36598i	0.795484	−	0.0965893i
$201$	2.27716	+	0.276497i	0.160619	+	0.0195026i
$202$	−2.46461	−	4.69593i	−0.173410	−	0.330404i
$203$	2.94149	−	3.32026i	0.206452	−	0.233036i
$204$	−0.354677	+	0.513839i	−0.0248324	+	0.0359759i
$205$	−6.05879	+	1.49336i	−0.423165	+	0.104301i
$206$	−16.9427	+	2.05722i	−1.18046	+	0.143333i
$207$	−0.376058	−	0.544814i	−0.0261378	−	0.0378672i
$208$	−3.35446	+	14.8921i	−0.232590	+	1.03258i
$209$	0.103812	−	0.150398i	0.00718082	−	0.0104032i
$210$	2.11982	−	4.03898i	0.146282	−	0.278716i
$211$	−8.28860	−	21.8552i	−0.570611	−	1.50458i	−0.840569	−	0.541705i	$-0.817779\pi$
$211$	−8.28860	−	21.8552i	−0.570611	−	1.50458i	0.269958	−	0.962872i	$-0.412990\pi$
$212$	−0.131002	+	1.07890i	−0.00899723	+	0.0740988i
$213$	0.0837508	−	0.0578090i	0.00573851	−	0.00396101i
$214$	1.89564	−	7.69089i	0.129583	−	0.525739i
$215$	10.1152	−	6.98199i	0.689848	−	0.476168i
$216$	−13.3732	+	5.07180i	−0.909933	+	0.345092i
$217$	2.78844	+	7.35252i	0.189292	+	0.499121i
$218$	21.9654	−	11.5284i	1.48769	−	0.780799i
$219$	4.46296	+	8.50345i	0.301579	+	0.574610i
$220$	0.156237	+	0.0385088i	0.0105335	+	0.00259627i
$221$	−11.2846	−	12.2330i	−0.759083	−	0.822882i
$222$	−6.57954	+	1.62171i	−0.441590	+	0.108842i
$223$	−16.0544	−	18.1217i	−1.07508	−	1.21352i	−0.975847	−	0.218453i	$-0.929899\pi$
$223$	−16.0544	−	18.1217i	−1.07508	−	1.21352i	−0.0992347	−	0.995064i	$-0.531639\pi$
$224$	−0.0809769	−	0.666905i	−0.00541050	−	0.0445595i
$225$	6.69241	−	3.51245i	0.446160	−	0.234163i
$226$	0.0725145	−	0.138165i	0.00482359	−	0.00919058i
$227$	16.1709	+	6.13283i	1.07330	+	0.407050i	0.827034	−	0.562152i	$-0.190026\pi$
$227$	16.1709	+	6.13283i	1.07330	+	0.407050i	0.246268	+	0.969202i	$0.420796\pi$
$228$	−0.0384104	−	0.0433563i	−0.00254379	−	0.00287134i
$229$	−6.95331	−	0.844284i	−0.459487	−	0.0557919i	−0.112479	−	0.993654i	$-0.535879\pi$
$229$	−6.95331	−	0.844284i	−0.459487	−	0.0557919i	−0.347008	+	0.937862i	$0.612802\pi$
$230$	−1.55415	−	0.383065i	−0.102478	−	0.0252585i
$231$	−0.330535	+	0.292829i	−0.0217476	+	0.0192667i
$232$	−8.42965	+	9.51511i	−0.553434	+	0.624697i
$233$	1.91201	−	1.00350i	0.125260	−	0.0657416i	−0.400929	−	0.916109i	$-0.631313\pi$
$233$	1.91201	−	1.00350i	0.125260	−	0.0657416i	0.526189	+	0.850367i	$0.323620\pi$
$234$	1.34593	+	9.48644i	0.0879862	+	0.620148i
$235$	29.9925	+	15.7413i	1.95650	+	1.02685i
$236$	−1.48578	+	0.563482i	−0.0967160	+	0.0366795i
$237$	0.353794	−	2.91376i	0.0229814	−	0.189269i
$238$	5.68268	+	2.98250i	0.368353	+	0.193327i
$239$			1.90323i			0.123110i	0.998104	+	0.0615549i	$0.0196059\pi$
$239$			1.90323i			0.123110i	−0.998104	+	0.0615549i	$0.980394\pi$
$240$	−6.45513	+	12.2992i	−0.416677	+	0.793911i
$241$	−2.65088	+	2.99223i	−0.170758	+	0.192746i	−0.827660	−	0.561230i	$-0.810328\pi$
$241$	−2.65088	+	2.99223i	−0.170758	+	0.192746i	0.656901	+	0.753977i	$0.271867\pi$
$242$	12.9772	+	8.95751i	0.834206	+	0.575811i
$243$	−11.5813	+	10.2602i	−0.742942	+	0.658189i
$244$	−0.0568093	+	0.0823026i	−0.00363685	+	0.00526888i
$245$	17.2210	+	6.53106i	1.10021	+	0.417254i
$246$	1.15703	−	3.05083i	0.0737694	−	0.194514i
$247$	1.35245	−	0.744881i	0.0860542	−	0.0473956i
$248$	−7.99105	−	21.0707i	−0.507432	−	1.33799i
$249$			17.4322i			1.10472i
$250$	−1.33533	+	3.52096i	−0.0844534	+	0.222685i
$251$	2.02574	+	16.6834i	0.127863	+	1.05305i	0.905503	+	0.424339i	$0.139494\pi$
$251$	2.02574	+	16.6834i	0.127863	+	1.05305i	−0.777640	+	0.628710i	$0.783583\pi$
$252$	−0.100761	−	0.191985i	−0.00634738	−	0.0120939i
$253$	0.127528	+	0.0880265i	0.00801765	+	0.00553418i
$254$	12.1311	+	8.37350i	0.761174	+	0.525400i
$255$	−7.03771	−	13.4092i	−0.440719	−	0.839719i
$256$	0.359321	+	2.95927i	0.0224576	+	0.184955i
$257$	6.26821	−	16.5279i	0.391000	−	1.03098i	−0.584580	−	0.811336i	$-0.698741\pi$
$257$	6.26821	−	16.5279i	0.391000	−	1.03098i	0.975580	−	0.219646i	$-0.0704902\pi$
$258$			6.42669i			0.400108i
$259$	1.44948	+	3.82196i	0.0900661	+	0.237485i
$260$	1.03555	+	0.880893i	0.0642218	+	0.0546307i
$261$	−3.00643	+	7.92730i	−0.186093	+	0.490688i
$262$	29.3724	+	11.1395i	1.81463	+	0.688200i
$263$	−12.0445	+	17.4494i	−0.742694	+	1.07598i	0.251446	+	0.967871i	$0.419094\pi$
$263$	−12.0445	+	17.4494i	−0.742694	+	1.07598i	−0.994139	+	0.108106i	$0.965521\pi$
$264$	0.947239	−	0.839181i	0.0582985	−	0.0516480i
$265$	−21.6945	−	14.9747i	−1.33268	−	0.919886i
$266$	−0.394820	+	0.445659i	−0.0242079	+	0.0273251i
$267$	6.38461	−	12.1649i	0.390732	−	0.744477i
$268$		−	0.263640i		−	0.0161044i
$269$	22.0959	+	11.5968i	1.34721	+	0.707070i	0.975234	−	0.221173i	$-0.0709887\pi$
$269$	22.0959	+	11.5968i	1.34721	+	0.707070i	0.371974	+	0.928243i	$0.378681\pi$
$270$	−2.78017	+	22.8968i	−0.169196	+	1.39345i
$271$	6.81355	−	2.58404i	0.413894	−	0.156969i	−0.138863	−	0.990312i	$-0.544345\pi$
$271$	6.81355	−	2.58404i	0.413894	−	0.156969i	0.552757	+	0.833342i	$0.313576\pi$
$272$	−17.3045	−	9.08209i	−1.04924	−	0.550683i
$273$	−3.60385	+	0.965533i	−0.218115	+	0.0584367i
$274$	5.47067	−	2.87123i	0.330495	−	0.173457i
$275$	−1.17319	+	1.32426i	−0.0707460	+	0.0798558i
$276$	0.0367637	−	0.0325698i	0.00221291	−	0.00196047i
$277$	6.00822	+	1.48089i	0.360999	+	0.0889783i	0.415643	−	0.909528i	$-0.363556\pi$
$277$	6.00822	+	1.48089i	0.360999	+	0.0889783i	−0.0546445	+	0.998506i	$0.517403\pi$
$278$	−6.82135	−	0.828261i	−0.409117	−	0.0496758i
$279$	−9.96651	−	11.2499i	−0.596680	−	0.673512i
$280$	7.37276	+	2.79612i	0.440607	+	0.167100i
$281$	−7.77918	+	14.8220i	−0.464067	+	0.884206i	0.535155	+	0.844754i	$0.320253\pi$
$281$	−7.77918	+	14.8220i	−0.464067	+	0.884206i	−0.999221	+	0.0394515i	$0.987439\pi$
$282$	−15.6826	+	8.23088i	−0.933887	+	0.490142i
$283$	−3.40082	−	28.0083i	−0.202158	−	1.66492i	−0.641893	−	0.766794i	$-0.721851\pi$
$283$	−3.40082	−	28.0083i	−0.202158	−	1.66492i	0.439735	−	0.898127i	$-0.355072\pi$
$284$	−0.00775588	−	0.00875458i	−0.000460227	−	0.000519489i
$285$	1.36411	−	0.336223i	0.0808029	−	0.0199161i
$286$	−1.08200	−	1.96454i	−0.0639800	−	0.116166i
$287$	−1.91098	−	0.471014i	−0.112802	−	0.0278031i
$288$	0.596718	+	1.13695i	0.0351619	+	0.0669955i
$289$	3.81348	−	2.00147i	0.224322	−	0.117733i
$290$	7.26935	+	19.1677i	0.426871	+	1.12557i
$291$	−17.5437	+	6.65344i	−1.02843	+	0.390032i
$292$	0.908363	−	0.626998i	0.0531579	−	0.0366923i
$293$	−4.31413	+	17.5031i	−0.252034	+	1.02254i	0.699410	+	0.714721i	$0.253446\pi$
$293$	−4.31413	+	17.5031i	−0.252034	+	1.02254i	−0.951444	+	0.307822i	$0.900400\pi$
$294$	−7.92568	+	5.47070i	−0.462235	+	0.319058i
$295$	4.64575	−	38.2612i	0.270486	−	2.22765i
$296$	−4.15387	−	10.9529i	−0.241439	−	0.636622i
$297$	1.03767	−	1.97712i	0.0602120	−	0.114724i
$298$	10.6452	−	15.4222i	0.616659	−	0.893385i
$299$	0.631616	+	1.14680i	0.0365273	+	0.0663210i
$300$	0.318550	+	0.461499i	0.0183915	+	0.0266447i
$301$	3.84834	−	0.467273i	0.221815	−	0.0269332i
$302$	7.07526	−	1.74389i	0.407135	−	0.100350i
$303$	−2.24220	+	3.24838i	−0.128811	+	0.186615i
$304$	1.20228	−	1.35709i	0.0689553	−	0.0778344i
$305$	−1.12724	−	2.14778i	−0.0645458	−	0.122982i
$306$	−12.1770	−	1.47856i	−0.696113	−	0.0845234i
$307$	4.66153	−	0.566012i	0.266047	−	0.0323040i	0.0135741	−	0.999908i	$-0.495679\pi$
$307$	4.66153	−	0.566012i	0.266047	−	0.0323040i	0.252473	+	0.967604i	$0.418756\pi$
$308$	0.0379890	+	0.0336553i	0.00216462	+	0.00191769i
$309$	7.21573	+	10.4538i	0.410489	+	0.594696i
$310$	−36.0758	−	4.38039i	−2.04897	−	0.248790i
$311$	1.30320	+	10.7328i	0.0738979	+	0.608604i	0.981868	+	0.189568i	$0.0607087\pi$
$311$	1.30320	+	10.7328i	0.0738979	+	0.608604i	−0.907970	+	0.419036i	$0.862368\pi$
$312$	10.3278	−	2.76700i	0.584698	−	0.156650i
$313$	−2.06040	+	16.9689i	−0.116461	+	0.959140i	0.810955	+	0.585108i	$0.198948\pi$
$313$	−2.06040	+	16.9689i	−0.116461	+	0.959140i	−0.927416	+	0.374032i	$0.877975\pi$
$314$	5.45976	−	22.1511i	0.308112	−	1.25006i
$315$	5.25898			0.296310
$316$	−0.337343			−0.0189770
$317$	4.34382	−	17.6236i	0.243974	−	0.989839i	−0.713347	−	0.700811i	$-0.752822\pi$
$317$	4.34382	−	17.6236i	0.243974	−	0.989839i	0.957321	−	0.289028i	$-0.0933322\pi$
$318$	12.8880	−	4.88776i	0.722720	−	0.274092i
$319$		−	1.98457i		−	0.111114i
$320$	−21.0408	−	7.97971i	−1.17621	−	0.446079i
$321$	−5.72398	+	1.41083i	−0.319481	+	0.0787451i
$322$	−0.377893	−	0.334784i	−0.0210592	−	0.0186568i
$323$	0.473051	+	1.91924i	0.0263213	+	0.106790i
$324$	−0.0193146	−	0.0171112i	−0.00107303	−	0.000950623i
$325$	−13.8669	+	5.58048i	−0.769200	+	0.309549i
$326$	−10.7333	+	9.50888i	−0.594463	+	0.526648i
$327$	−15.1945	−	10.4880i	−0.840256	−	0.579987i
$328$	5.47644	+	1.34982i	0.302386	+	0.0745314i
$329$	6.06895	+	8.79240i	0.334592	+	0.484741i
$330$	−0.488391	−	1.98148i	−0.0268850	−	0.109077i
$331$	4.42072	+	17.9356i	0.242985	+	0.985828i	0.958011	+	0.286731i	$0.0925685\pi$
$331$	4.42072	+	17.9356i	0.242985	+	0.985828i	−0.715026	+	0.699097i	$0.753585\pi$
$332$	1.98891	−	0.241497i	0.109156	−	0.0132539i
$333$	−5.18075	−	5.84786i	−0.283904	−	0.320461i
$334$	2.98201	−	7.86291i	0.163168	−	0.430239i
$335$	5.66213	+	2.97172i	0.309355	+	0.162362i
$336$	−3.60555	+	2.48873i	−0.196699	+	0.135772i
$337$	10.8091			0.588812			0.294406	−	0.955680i	$-0.404878\pi$
$337$	10.8091			0.588812			0.294406	+	0.955680i	$0.404878\pi$
$338$	−0.761860	−	18.9339i	−0.0414397	−	1.02987i
$339$	−0.116132			−0.00630742
$340$	−1.43241	+	0.988723i	−0.0776835	+	0.0536210i
$341$	3.11513	+	1.63494i	0.168694	+	0.0885372i
$342$	0.403536	−	1.06404i	0.0218207	−	0.0575365i
$343$	8.27978	+	9.34594i	0.447066	+	0.504633i
$344$	−11.0285	+	1.33910i	−0.594616	+	0.0721994i
$345$	0.285098	+	1.15669i	0.0153491	+	0.0622739i
$346$	2.99748	+	12.1612i	0.161145	+	0.653792i
$347$	8.18284	+	11.8549i	0.439278	+	0.636404i	0.978618	−	0.205684i	$-0.0659419\pi$
$347$	8.18284	+	11.8549i	0.439278	+	0.636404i	−0.539341	+	0.842088i	$0.681327\pi$
$348$	−0.610750	−	0.150536i	−0.0327397	−	0.00806960i
$349$	−14.1086	−	9.73843i	−0.755214	−	0.521286i	0.127133	−	0.991886i	$-0.459422\pi$
$349$	−14.1086	−	9.73843i	−0.755214	−	0.521286i	−0.882347	+	0.470599i	$0.844038\pi$
$350$	4.31447	−	3.82229i	0.230618	−	0.204310i
$351$	15.3073	−	11.0268i	0.817045	−	0.588567i
$352$	−0.224974	−	0.199309i	−0.0119911	−	0.0106232i
$353$	6.03846	+	24.4990i	0.321395	+	1.30395i	0.880181	+	0.474639i	$0.157421\pi$
$353$	6.03846	+	24.4990i	0.321395	+	1.30395i	−0.558786	+	0.829312i	$0.688733\pi$
$354$	15.0848	+	13.3640i	0.801750	+	0.710288i
$355$	0.275443	−	0.0678906i	0.0146190	−	0.00360326i
$356$	−1.47638	−	0.559918i	−0.0782482	−	0.0296756i
$357$		−	4.77647i		−	0.252798i
$358$	−6.35560	+	2.41036i	−0.335904	+	0.127391i
$359$	3.41544	−	13.8570i	0.180260	−	0.731343i	−0.809321	−	0.587366i	$-0.800165\pi$
$359$	3.41544	−	13.8570i	0.180260	−	0.731343i	0.989581	−	0.143977i	$-0.0459891\pi$
$360$	−15.0711			−0.794314
$361$	18.8166			0.990348
$362$	1.09376	−	4.43756i	0.0574867	−	0.233233i
$363$	1.41459	−	11.6502i	0.0742466	−	0.611476i
$364$	0.160087	+	0.397801i	0.00839084	+	0.0208504i
$365$	3.22692	+	26.5761i	0.168905	+	1.39106i
$366$	1.25907	+	0.152879i	0.0658128	+	0.00799113i
$367$	2.50254	+	3.62555i	0.130631	+	0.189252i	0.882841	−	0.469671i	$-0.155628\pi$
$367$	2.50254	+	3.62555i	0.130631	+	0.189252i	−0.752210	+	0.658923i	$0.771012\pi$
$368$	1.15073	+	1.01946i	0.0599861	+	0.0531431i
$369$	3.73437	−	0.453435i	0.194404	−	0.0236049i
$370$	−18.7528	−	2.27700i	−0.974910	−	0.118376i
$371$	−3.86388	−	7.36200i	−0.200603	−	0.382216i
$372$	0.739448	−	0.834664i	0.0383386	−	0.0432753i
$373$	18.5350	−	26.8525i	0.959704	−	1.39037i	0.0393753	−	0.999224i	$-0.487463\pi$
$373$	18.5350	−	26.8525i	0.959704	−	1.39037i	0.920328	−	0.391146i	$-0.127921\pi$
$374$	2.78786	−	0.687146i	0.144157	−	0.0355315i
$375$	2.78218	−	0.337818i	0.143671	−	0.0174448i
$376$	−17.3923	−	25.1970i	−0.896937	−	1.29944i
$377$	7.49210	−	15.0005i	0.385863	−	0.772563i
$378$	−4.13257	+	5.98706i	−0.212556	+	0.307941i
$379$	−3.32596	+	6.33708i	−0.170843	+	0.325514i	−0.955791	−	0.294048i	$-0.904997\pi$
$379$	−3.32596	+	6.33708i	−0.170843	+	0.325514i	0.784948	+	0.619562i	$0.212690\pi$
$380$	−0.0572586	−	0.150978i	−0.00293730	−	0.00774503i
$381$	1.32236	−	10.8906i	0.0677466	−	0.557943i
$382$	−13.9024	+	9.59610i	−0.711306	+	0.490979i
$383$	8.16872	−	33.1418i	0.417402	−	1.69347i	−0.266453	−	0.963848i	$-0.585852\pi$
$383$	8.16872	−	33.1418i	0.417402	−	1.69347i	0.683855	−	0.729618i	$-0.260302\pi$
$384$	10.9413	−	7.55222i	0.558345	−	0.385398i
$385$	−1.15101	+	0.436521i	−0.0586610	+	0.0222472i
$386$	−13.0594	−	34.4349i	−0.664708	−	1.75269i
$387$	−6.56071	+	3.44333i	−0.333500	+	0.175034i
$388$	1.00216	+	1.90945i	0.0508768	+	0.0969377i
$389$	−18.3951	−	4.53399i	−0.932669	−	0.229882i	−0.256429	−	0.966563i	$-0.582546\pi$
$389$	−18.3951	−	4.53399i	−0.932669	−	0.229882i	−0.676241	+	0.736681i	$0.736392\pi$
$390$	3.78892	−	16.8209i	0.191859	−	0.851760i
$391$	−1.62741	+	0.401120i	−0.0823016	+	0.0202855i
$392$	−11.0394	−	12.4609i	−0.557573	−	0.629370i
$393$	−2.81813	−	23.2094i	−0.142156	−	1.17076i
$394$	27.0665	−	14.2056i	1.36359	−	0.715668i
$395$	3.80248	−	7.24502i	0.191324	−	0.364537i
$396$	−0.0907008	−	0.0343983i	−0.00455789	−	0.00172858i
$397$	11.7270	+	13.2370i	0.588561	+	0.664348i	0.965048	−	0.262074i	$-0.0844064\pi$
$397$	11.7270	+	13.2370i	0.588561	+	0.664348i	−0.376487	+	0.926422i	$0.622868\pi$
$398$	12.8862	+	1.56467i	0.645929	+	0.0784300i
$399$	0.430248	+	0.106047i	0.0215394	+	0.00530898i
$400$	−13.1381	+	11.6394i	−0.656906	+	0.581968i
$401$	10.4201	−	11.7619i	0.520356	−	0.587360i	−0.428314	−	0.903630i	$-0.640892\pi$
$401$	10.4201	−	11.7619i	0.520356	−	0.587360i	0.948669	+	0.316270i	$0.102431\pi$
$402$	−2.96064	+	1.55386i	−0.147663	+	0.0774997i
$403$	17.3737	+	24.1180i	0.865444	+	1.20140i
$404$	0.401682	+	0.210819i	0.0199844	+	0.0104886i
$405$	0.585204	−	0.221939i	0.0290790	−	0.0110282i
$406$	−0.779363	+	6.41863i	−0.0386792	+	0.318551i
$407$	1.61929	+	0.849870i	0.0802654	+	0.0421265i
$408$			13.6883i			0.677671i
$409$	5.54879	−	10.5723i	0.274370	−	0.522769i	−0.708812	−	0.705398i	$-0.750768\pi$
$409$	5.54879	−	10.5723i	0.274370	−	0.522769i	0.983182	+	0.182629i	$0.0584608\pi$
$410$	6.03162	−	6.80829i	0.297880	−	0.336238i
$411$	−3.78431	−	2.61212i	−0.186666	−	0.128846i
$412$	1.09275	−	0.968091i	0.0538359	−	0.0476944i
$413$	6.90565	−	10.0046i	0.339805	−	0.492292i
$414$	0.902242	+	0.342175i	0.0443428	+	0.0168170i
$415$	−17.2321	+	45.4374i	−0.845892	+	2.23043i
$416$	−0.948049	−	2.35581i	−0.0464819	−	0.115503i
$417$	1.81349	+	4.78177i	0.0888068	+	0.234164i
$418$			0.266377i			0.0130289i
$419$	−9.40349	+	24.7950i	−0.459391	+	1.21131i	0.482649	+	0.875814i	$0.339675\pi$
$419$	−9.40349	+	24.7950i	−0.459391	+	1.21131i	−0.942040	+	0.335500i	$0.891095\pi$
$420$	0.0470311	+	0.387336i	0.00229488	+	0.0189001i
$421$	−1.04329	−	1.98783i	−0.0508469	−	0.0968807i	0.858707	−	0.512468i	$-0.171269\pi$
$421$	−1.04329	−	1.98783i	−0.0508469	−	0.0968807i	−0.909553	+	0.415587i	$0.863576\pi$
$422$	28.0398	+	19.3545i	1.36496	+	0.942161i
$423$	−16.8051	−	11.5997i	−0.817090	−	0.563996i
$424$	11.0730	+	21.0978i	0.537752	+	1.02460i
$425$	−2.30665	−	18.9970i	−0.111889	−	0.921488i
$426$	−0.0526004	+	0.138696i	−0.00254850	+	0.00671984i
$427$		−	0.765057i		−	0.0370237i
$428$	0.240264	+	0.633525i	0.0116136	+	0.0306226i
$429$	−0.920408	+	1.39252i	−0.0444377	+	0.0672316i
$430$	−6.35292	+	16.7513i	−0.306365	+	0.807818i
$431$	3.86166	+	1.46453i	0.186010	+	0.0705441i	0.445851	−	0.895107i	$-0.352901\pi$
$431$	3.86166	+	1.46453i	0.186010	+	0.0705441i	−0.259842	+	0.965651i	$0.583670\pi$
$432$	12.5842	−	18.2314i	0.605458	−	0.877157i
$433$	7.73125	−	6.84929i	0.371540	−	0.329156i	−0.456605	−	0.889670i	$-0.650935\pi$
$433$	7.73125	−	6.84929i	0.371540	−	0.329156i	0.828145	+	0.560514i	$0.189396\pi$
$434$	−9.43312	−	6.51121i	−0.452804	−	0.312548i
$435$	10.1173	−	11.4201i	0.485089	−	0.547552i
$436$	−0.986117	+	1.87889i	−0.0472264	+	0.0899824i
$437$		−	0.155497i		−	0.00743844i
$438$	−12.3949	−	6.50534i	−0.592250	−	0.310837i
$439$	−3.91352	+	32.2308i	−0.186782	+	1.53829i	0.534212	+	0.845350i	$0.320608\pi$
$439$	−3.91352	+	32.2308i	−0.186782	+	1.53829i	−0.720995	+	0.692941i	$0.756315\pi$
$440$	3.29854	−	1.25097i	0.157252	−	0.0596378i
$441$	−9.83125	−	5.15984i	−0.468155	−	0.245707i
$442$	23.6663	+	5.33085i	1.12569	+	0.253563i
$443$	−28.4156	+	14.9136i	−1.35007	+	0.708569i	−0.975782	−	0.218746i	$-0.929803\pi$
$443$	−28.4156	+	14.9136i	−1.35007	+	0.708569i	−0.374283	+	0.927314i	$0.622111\pi$
$444$	0.384377	−	0.433872i	0.0182417	−	0.0205906i
$445$	28.6668	−	25.3966i	1.35894	−	1.20391i
$446$	34.2642	+	8.44537i	1.62246	+	0.399900i
$447$	−13.8452	−	1.68111i	−0.654855	−	0.0795138i
$448$	−4.70659	−	5.31264i	−0.222365	−	0.250999i
$449$	31.9429	+	12.1143i	1.50748	+	0.571710i	0.963575	−	0.267439i	$-0.0861773\pi$
$449$	31.9429	+	12.1143i	1.50748	+	0.571710i	0.543902	+	0.839149i	$0.316947\pi$
$450$	−5.11984	+	9.75505i	−0.241352	+	0.459857i
$451$	−0.779690	+	0.409213i	−0.0367142	+	0.0192691i
$452$	0.00160883	+	0.0132499i	7.56731e−5	+	0.000623224i
$453$	−3.59637	−	4.05946i	−0.168972	−	0.190730i
$454$	−24.4769	+	6.03301i	−1.14876	+	0.283143i
$455$	−10.3480	−	1.04581i	−0.485119	−	0.0490283i
$456$	−1.23300	−	0.303906i	−0.0577403	−	0.0142317i
$457$	−17.1842	−	32.7417i	−0.803841	−	1.53159i	−0.846431	−	0.532498i	$-0.821253\pi$
$457$	−17.1842	−	32.7417i	−0.803841	−	1.53159i	0.0425900	−	0.999093i	$-0.486439\pi$
$458$	9.04032	−	4.74472i	0.422426	−	0.221706i
$459$	8.56444	+	22.5826i	0.399754	+	1.05406i
$460$	0.128021	−	0.0485520i	0.00596901	−	0.00226375i
$461$	31.8403	−	21.9778i	1.48295	−	1.02361i	0.494989	−	0.868899i	$-0.335172\pi$
$461$	31.8403	−	21.9778i	1.48295	−	1.02361i	0.987960	−	0.154707i	$-0.0494432\pi$
$462$	0.154042	−	0.624971i	0.00716666	−	0.0290763i
$463$	−12.7202	+	8.78014i	−0.591159	+	0.408048i	−0.825742	−	0.564049i	$-0.809243\pi$
$463$	−12.7202	+	8.78014i	−0.591159	+	0.408048i	0.234583	+	0.972096i	$0.424628\pi$
$464$	2.37326	−	19.5456i	0.110176	−	0.907380i
$465$	9.59091	+	25.2892i	0.444768	+	1.17276i
$466$	−1.46273	+	2.78701i	−0.0677599	+	0.129106i
$467$	−12.1026	+	17.5337i	−0.560042	+	0.811361i	−0.996070	−	0.0885721i	$-0.971770\pi$
$467$	−12.1026	+	17.5337i	−0.560042	+	0.811361i	0.436028	+	0.899933i	$0.356385\pi$
$468$	−0.555708	−	0.602414i	−0.0256876	−	0.0278466i
$469$	1.14573	+	1.65987i	0.0529047	+	0.0766457i
$470$	−49.0134	+	5.95131i	−2.26082	+	0.274513i
$471$	−16.4861	+	4.06345i	−0.759638	+	0.187234i
$472$	−19.7900	+	28.6708i	−0.910910	+	1.31968i
$473$	1.15010	−	1.29820i	0.0528819	−	0.0596913i
$474$	1.98826	+	3.78831i	0.0913237	+	0.174003i
$475$	1.76239	+	0.213993i	0.0808642	+	0.00981869i
$476$	−0.544965	+	0.0661708i	−0.0249784	+	0.00303293i
$477$	11.8949	+	10.5379i	0.544629	+	0.482499i
$478$	−1.57593	−	2.28313i	−0.0720812	−	0.104428i
$479$	−0.829008	−	0.100660i	−0.0378784	−	0.00459926i	0.101576	−	0.994828i	$-0.467612\pi$
$479$	−0.829008	−	0.100660i	−0.0378784	−	0.00459926i	−0.139454	+	0.990229i	$0.544535\pi$
$480$	−0.278522	−	2.29384i	−0.0127127	−	0.104699i
$481$	9.03111	+	12.5369i	0.411783	+	0.571635i
$482$	0.702366	−	5.78450i	0.0319919	−	0.263477i
$483$	−0.0899215	+	0.364826i	−0.00409157	+	0.0166002i
$484$	−1.34881			−0.0613095
$485$	−52.3050			−2.37505
$486$	5.39732	−	21.8978i	0.244827	−	0.993304i
$487$	−2.89173	+	1.09669i	−0.131037	+	0.0496957i	−0.419252	−	0.907870i	$-0.637707\pi$
$487$	−2.89173	+	1.09669i	−0.131037	+	0.0496957i	0.288215	+	0.957566i	$0.406938\pi$
$488$			2.19248i			0.0992489i
$489$	9.97875	+	3.78444i	0.451255	+	0.171138i
$490$	−26.0663	+	6.42477i	−1.17756	+	0.290241i
$491$	19.6215	+	17.3832i	0.885507	+	0.784491i	0.977427	−	0.211275i	$-0.0677617\pi$
$491$	19.6215	+	17.3832i	0.885507	+	0.784491i	−0.0919193	+	0.995766i	$0.529300\pi$
$492$	0.0667930	+	0.270990i	0.00301126	+	0.0122172i
$493$	16.0676	+	14.2347i	0.723648	+	0.641096i
$494$	−1.00562	+	2.01343i	−0.0452451	+	0.0905884i
$495$	1.76113	−	1.56023i	0.0791569	−	0.0701269i
$496$	28.7251	+	19.8275i	1.28979	+	0.890280i
$497$	0.0868764	+	0.0214131i	0.00389694	+	0.000960510i
$498$	−14.4344	−	20.9118i	−0.646820	−	0.937081i
$499$	6.08259	+	24.6780i	0.272294	+	1.10474i	0.934655	+	0.355556i	$0.115708\pi$
$499$	6.08259	+	24.6780i	0.272294	+	1.10474i	−0.662361	+	0.749185i	$0.730445\pi$
$500$	−0.0770858	−	0.312749i	−0.00344738	−	0.0139866i
$501$	−6.21309	+	0.754405i	−0.277580	+	0.0337043i
$502$	−16.2444	−	18.3362i	−0.725025	−	0.818384i
$503$	7.16655	−	18.8966i	0.319541	−	0.842559i	−0.674962	−	0.737852i	$-0.735840\pi$
$503$	7.16655	−	18.8966i	0.319541	−	0.842559i	0.994503	−	0.104707i	$-0.0333906\pi$
$504$	−4.20902	−	2.20906i	−0.187485	−	0.0983995i
$505$	−9.05541	+	6.25050i	−0.402961	+	0.278144i
$506$	−0.225872			−0.0100412
$507$	−12.2140	+	7.05076i	−0.542442	+	0.313135i
$508$	−1.26087			−0.0559421
$509$	2.77375	−	1.91458i	0.122944	−	0.0848622i	−0.505006	−	0.863116i	$-0.668510\pi$
$509$	2.77375	−	1.91458i	0.122944	−	0.0848622i	0.627950	+	0.778254i	$0.283894\pi$
$510$	19.5457	+	10.2584i	0.865498	+	0.454248i
$511$	−2.99422	+	7.89512i	−0.132457	+	0.349260i
$512$	13.3716	+	15.0934i	0.590945	+	0.667039i
$513$	−2.22431	+	0.270080i	−0.0982057	+	0.0119243i
$514$	6.16619	+	25.0172i	0.271979	+	1.10346i
$515$	8.47413	+	34.3809i	0.373415	+	1.51500i
$516$	−0.312281	−	0.452418i	−0.0137474	−	0.0199166i
$517$	4.64089	+	1.14388i	0.204106	+	0.0503076i
$518$	−4.90349	−	3.38463i	−0.215447	−	0.148712i
$519$	6.97757	−	6.18159i	0.306281	−	0.271341i
$520$	29.6549	+	2.99705i	1.30045	+	0.131429i
$521$	−23.3136	−	20.6541i	−1.02139	−	0.904872i	−0.0258923	−	0.999665i	$-0.508243\pi$
$521$	−23.3136	−	20.6541i	−1.02139	−	0.904872i	−0.995497	+	0.0947927i	$0.969781\pi$
$522$	−2.95750	−	11.9990i	−0.129446	−	0.525184i
$523$	−26.0304	−	23.0609i	−1.13823	−	1.00838i	−0.999838	−	0.0180040i	$-0.994269\pi$
$523$	−26.0304	−	23.0609i	−1.13823	−	1.00838i	−0.138390	−	0.990378i	$-0.544193\pi$
$524$	−2.60900	+	0.643062i	−0.113975	+	0.0280923i
$525$	−4.01116	−	1.52123i	−0.175061	−	0.0663921i
$526$		−	30.9056i		−	1.34755i
$527$	−35.5808	+	13.4940i	−1.54992	+	0.587808i
$528$	−0.469076	+	1.90312i	−0.0204139	+	0.0828226i
$529$	−22.8681			−0.994267
$530$	38.4243			1.66905
$531$	−5.56046	+	22.5597i	−0.241303	+	0.979006i
$532$	0.00613882	−	0.0505578i	0.000266152	−	0.00219196i
$533$	−7.43819	+	0.149588i	−0.322184	+	0.00647939i
$534$	2.41383	+	19.8797i	0.104457	+	0.860278i
$535$	−16.3143	−	1.98091i	−0.705328	−	0.0856423i
$536$	−3.28339	−	4.75682i	−0.141821	−	0.205463i
$537$	3.78666	+	3.35469i	0.163406	+	0.144766i
$538$	−36.1088	+	4.38440i	−1.55676	+	0.189025i
$539$	2.58002	+	0.313271i	0.111129	+	0.0134935i
$540$	−0.916869	−	1.74695i	−0.0394558	−	0.0751767i
$541$	14.7258	−	16.6220i	0.633113	−	0.714637i	−0.341161	−	0.940005i	$-0.610820\pi$
$541$	14.7258	−	16.6220i	0.633113	−	0.714637i	0.974274	+	0.225368i	$0.0723584\pi$
$542$	−6.03392	+	8.74164i	−0.259179	+	0.375485i
$543$	−3.30267	+	0.814035i	−0.141731	+	0.0349336i
$544$	3.22733	−	0.391869i	0.138371	−	0.0168012i
$545$	−29.2370	−	42.3572i	−1.25238	−	1.81438i
$546$	3.52371	−	4.14235i	0.150801	−	0.177276i
$547$	13.6811	−	19.8204i	0.584960	−	0.847461i	−0.413038	−	0.910714i	$-0.635532\pi$
$547$	13.6811	−	19.8204i	0.584960	−	0.847461i	0.997998	+	0.0632532i	$0.0201476\pi$
$548$	−0.245600	+	0.467953i	−0.0104915	+	0.0199899i
$549$	0.518526	+	1.36724i	0.0221302	+	0.0583525i
$550$	0.310843	−	2.56002i	0.0132544	−	0.109160i
$551$	−1.63894	+	1.13128i	−0.0698212	+	0.0481941i
$552$	0.257695	−	1.04551i	0.0109682	−	0.0444998i
$553$	2.12390	−	1.46602i	0.0903174	−	0.0623416i
$554$	−8.43371	+	3.19849i	−0.358314	+	0.135891i
$555$	4.98551	+	13.1457i	0.211623	+	0.558004i
$556$	0.520447	−	0.273151i	0.0220719	−	0.0115842i
$557$	18.4252	+	35.1063i	0.780701	+	1.48750i	0.870837	+	0.491572i	$0.163578\pi$
$557$	18.4252	+	35.1063i	0.780701	+	1.48750i	−0.0901356	+	0.995930i	$0.528730\pi$
$558$	21.2711	+	5.24285i	0.900477	+	0.221948i
$559$	13.5941	−	5.47067i	0.574968	−	0.231385i
$560$	−11.8581	+	2.92276i	−0.501096	+	0.123509i
$561$	−1.41708	−	1.59955i	−0.0598290	−	0.0675329i
$562$	−2.94107	−	24.2219i	−0.124062	−	1.02174i
$563$	−24.8600	+	13.0475i	−1.04772	+	0.549887i	−0.898526	−	0.438920i	$-0.855361\pi$
$563$	−24.8600	+	13.0475i	−1.04772	+	0.549887i	−0.149197	+	0.988808i	$0.547669\pi$
$564$	0.704056	−	1.34147i	0.0296461	−	0.0564859i
$565$	−0.302700	−	0.114799i	−0.0127347	−	0.00482962i
$566$	27.2713	+	30.7829i	1.14630	+	1.29390i
$567$	0.195966	+	0.0237946i	0.00822979	+	0.000999277i
$568$	−0.248968	−	0.0613652i	−0.0104465	−	0.00257483i
$569$	−13.7440	+	12.1761i	−0.576177	+	0.510448i	−0.900128	−	0.435626i	$-0.856527\pi$
$569$	−13.7440	+	12.1761i	−0.576177	+	0.510448i	0.323951	+	0.946074i	$0.394989\pi$
$570$	−1.35799	+	1.53286i	−0.0568800	+	0.0642043i
$571$	−9.15371	+	4.80424i	−0.383071	+	0.201051i	−0.645256	−	0.763967i	$-0.723249\pi$
$571$	−9.15371	+	4.80424i	−0.383071	+	0.201051i	0.262185	+	0.965018i	$0.415557\pi$
$572$	0.171629	+	0.0857214i	0.00717617	+	0.00358419i
$573$	11.1323	+	5.84269i	0.465059	+	0.244082i
$574$	2.68244	−	1.01731i	0.111963	−	0.0424619i
$575$	−0.181454	+	1.49441i	−0.00756715	+	0.0623211i
$576$	12.0119	+	6.30433i	0.500496	+	0.262681i
$577$			8.84858i			0.368371i	0.982891	+	0.184186i	$0.0589648\pi$
$577$			8.84858i			0.368371i	−0.982891	+	0.184186i	$0.941035\pi$
$578$	−2.91740	+	5.55864i	−0.121348	+	0.231209i
$579$	−18.1759	+	20.5163i	−0.755363	+	0.852628i
$580$	−1.44312	−	0.996115i	−0.0599224	−	0.0413614i
$581$	−11.4726	+	10.1639i	−0.475964	+	0.421668i
$582$	15.5363	−	22.5082i	0.643999	−	0.932994i
$583$	−3.47808	−	1.31906i	−0.144047	−	0.0546300i
$584$	8.58077	−	22.6256i	0.355075	−	0.936256i
$585$	19.2018	−	5.14447i	0.793895	−	0.212698i
$586$	−9.31782	−	24.5691i	−0.384915	−	1.01494i
$587$			26.0426i			1.07489i	0.843298	+	0.537446i	$0.180611\pi$
$587$			26.0426i			1.07489i	−0.843298	+	0.537446i	$0.819389\pi$
$588$	0.292113	−	0.770238i	0.0120465	−	0.0317641i
$589$	−0.425534	−	3.50459i	−0.0175338	−	0.144404i
$590$	26.1083	+	49.7451i	1.07486	+	2.04798i
$591$	−18.7231	−	12.9236i	−0.770166	−	0.531607i
$592$	14.9317	+	10.3066i	0.613691	+	0.423600i
$593$	−8.73396	−	16.6412i	−0.358661	−	0.683371i	0.637544	−	0.770414i	$-0.279951\pi$
$593$	−8.73396	−	16.6412i	−0.358661	−	0.683371i	−0.996205	+	0.0870431i	$0.972258\pi$
$594$	0.392313	+	3.23099i	0.0160968	+	0.132569i
$595$	4.72164	−	12.4499i	0.193568	−	0.510398i
$596$			1.60294i			0.0656589i
$597$	−3.42587	−	9.03327i	−0.140211	−	0.369707i
$598$	−1.70727	−	0.852709i	−0.0698155	−	0.0348699i
$599$	12.4384	−	32.7974i	0.508220	−	1.34007i	−0.398049	−	0.917364i	$-0.630313\pi$
$599$	12.4384	−	32.7974i	0.508220	−	1.34007i	0.906269	−	0.422702i	$-0.138918\pi$
$600$	11.4951	+	4.35951i	0.469285	+	0.177976i
$601$	24.6046	−	35.6459i	1.00364	−	1.45403i	0.116136	−	0.993233i	$-0.462949\pi$
$601$	24.6046	−	35.6459i	1.00364	−	1.45403i	0.887507	−	0.460794i	$-0.152435\pi$
$602$	−4.22957	+	3.74708i	−0.172385	+	0.152719i
$603$	−3.17254	−	2.18985i	−0.129196	−	0.0891774i
$604$	−0.413337	+	0.466561i	−0.0168184	+	0.0189841i
$605$	15.2036	−	28.9680i	0.618114	−	1.17772i
$606$		−	5.75338i		−	0.233715i
$607$	7.82681	+	4.10783i	0.317680	+	0.166732i	0.616025	−	0.787727i	$-0.288742\pi$
$607$	7.82681	+	4.10783i	0.317680	+	0.166732i	−0.298344	+	0.954458i	$0.596434\pi$
$608$	−0.0363546	+	0.299407i	−0.00147437	+	0.0121426i
$609$	4.49947	−	1.70642i	0.182328	−	0.0691478i
$610$	3.13067	+	1.64310i	0.126757	+	0.0665273i
$611$	30.7601	+	26.1663i	1.24442	+	1.05857i
$612$	0.929066	−	0.487611i	0.0375553	−	0.0197105i
$613$	−17.2365	+	19.4560i	−0.696177	+	0.785822i	−0.985183	−	0.171506i	$-0.945137\pi$
$613$	−17.2365	+	19.4560i	−0.696177	+	0.785822i	0.289006	+	0.957327i	$0.406675\pi$
$614$	−5.12332	+	4.53886i	−0.206760	+	0.183174i
$615$	−6.57286	−	1.62007i	−0.265043	−	0.0653273i
$616$	1.10457	+	0.134120i	0.0445046	+	0.00540383i
$617$	7.11435	+	8.03044i	0.286413	+	0.323293i	0.874054	−	0.485828i	$-0.161482\pi$
$617$	7.11435	+	8.03044i	0.286413	+	0.323293i	−0.587642	+	0.809121i	$0.699943\pi$
$618$	−17.3121	−	6.56560i	−0.696393	−	0.264107i
$619$	9.98809	−	19.0307i	0.401455	−	0.764909i	−0.597872	−	0.801592i	$-0.703987\pi$
$619$	9.98809	−	19.0307i	0.401455	−	0.764909i	0.999327	+	0.0366829i	$0.0116792\pi$
$620$	2.75247	−	1.44461i	0.110542	−	0.0580168i
$621$	−0.229012	−	1.88609i	−0.00918995	−	0.0756860i
$622$	−10.4504	−	11.7961i	−0.419024	−	0.472980i
$623$	11.7286	−	2.89083i	0.469895	−	0.115819i
$624$	−10.7302	+	12.6140i	−0.429550	+	0.504964i
$625$	27.7121	+	6.83043i	1.10849	+	0.273217i
$626$	−11.5791	−	22.0621i	−0.462793	−	0.881778i
$627$	0.175544	−	0.0921324i	0.00701054	−	0.00367941i
$628$	0.692003	+	1.82466i	0.0276139	+	0.0728120i
$629$	−18.4955	+	7.01440i	−0.737462	+	0.279682i
$630$	−6.30870	+	4.35458i	−0.251345	+	0.173491i
$631$	0.566141	−	2.29692i	0.0225377	−	0.0914391i	−0.958596	−	0.284770i	$-0.908083\pi$
$631$	0.566141	−	2.29692i	0.0225377	−	0.0914391i	0.981134	+	0.193331i	$0.0619290\pi$
$632$	−6.08662	+	4.20129i	−0.242113	+	0.167118i
$633$	3.05650	−	25.1725i	0.121485	−	1.00052i
$634$	9.38195	+	24.7382i	0.372605	+	0.982478i
$635$	14.2124	−	27.0794i	0.564000	−	1.07461i
$636$	−0.669767	+	0.970325i	−0.0265580	+	0.0384759i
$637$	18.3186	+	12.1079i	0.725809	+	0.479734i
$638$	1.64328	+	2.38070i	0.0650579	+	0.0942526i
$639$	−0.169771	+	0.0206139i	−0.00671603	+	0.000815474i
$640$	35.9842	−	8.86930i	1.42240	−	0.350590i
$641$	−9.41535	+	13.6405i	−0.371884	+	0.538767i	−0.963589	−	0.267388i	$-0.913840\pi$
$641$	−9.41535	+	13.6405i	−0.371884	+	0.538767i	0.591705	+	0.806154i	$0.298455\pi$
$642$	5.69831	−	6.43206i	0.224894	−	0.253853i
$643$	−14.4642	−	27.5592i	−0.570412	−	1.08683i	−0.984300	−	0.176502i	$-0.943522\pi$
$643$	−14.4642	−	27.5592i	−0.570412	−	1.08683i	0.413888	−	0.910328i	$-0.364171\pi$
$644$	0.0428701	+	0.00520537i	0.00168932	+	0.000205120i
$645$	13.2365	−	1.60720i	0.521185	−	0.0632833i
$646$	−2.15666	−	1.91064i	−0.0848528	−	0.0751730i
$647$	−17.4796	−	25.3236i	−0.687194	−	0.995573i	−0.998968	−	0.0454165i	$-0.985539\pi$
$647$	−17.4796	−	25.3236i	−0.687194	−	0.995573i	0.311774	−	0.950156i	$-0.399077\pi$
$648$	−0.561594	−	0.0681898i	−0.0220615	−	0.00267875i
$649$	−0.655568	−	5.39909i	−0.0257333	−	0.211933i
$650$	12.0141	−	18.1766i	0.471231	−	0.712945i
$651$	−1.02826	+	8.46851i	−0.0403008	+	0.331907i
$652$	0.293540	−	1.19094i	0.0114959	−	0.0466408i
$653$	17.1206			0.669981			0.334990	−	0.942222i	$-0.391267\pi$
$653$	17.1206			0.669981			0.334990	+	0.942222i	$0.391267\pi$
$654$	26.9117			1.05233
$655$	15.5975	−	63.2814i	0.609444	−	2.47261i
$656$	−8.16836	+	3.09785i	−0.318921	+	0.120951i
$657$		−	16.1388i		−	0.629636i
$658$	−14.5607	−	5.52215i	−0.567635	−	0.215276i
$659$	−16.0050	+	3.94488i	−0.623466	+	0.153671i	−0.538379	−	0.842703i	$-0.680963\pi$
$659$	−16.0050	+	3.94488i	−0.623466	+	0.153671i	−0.0850871	+	0.996374i	$0.527117\pi$
$660$	0.130664	+	0.115758i	0.00508609	+	0.00450588i
$661$	−4.66122	−	18.9113i	−0.181301	−	0.735565i	−0.989240	−	0.146300i	$-0.953263\pi$
$661$	−4.66122	−	18.9113i	−0.181301	−	0.735565i	0.807940	−	0.589265i	$-0.200583\pi$
$662$	−20.1543	−	17.8551i	−0.783318	−	0.693959i
$663$	−4.67247	−	17.4400i	−0.181464	−	0.677313i
$664$	32.8779	−	29.1273i	1.27591	−	1.13036i
$665$	1.01662	+	0.701722i	0.0394228	+	0.0272116i
$666$	11.0571	+	2.72532i	0.428452	+	0.105604i
$667$	−0.959259	−	1.38973i	−0.0371427	−	0.0538105i
$668$	0.172146	+	0.698423i	0.00666052	+	0.0270228i
$669$	−6.28550	−	25.5013i	−0.243011	−	0.985936i
$670$	−9.25299	+	1.12352i	−0.357474	+	0.0434052i
$671$	−0.226976	−	0.256203i	−0.00876230	−	0.00989059i
$672$	0.258437	−	0.681443i	0.00996944	−	0.0262872i
$673$	15.2380	+	7.99751i	0.587381	+	0.308281i	0.732106	−	0.681191i	$-0.238537\pi$
$673$	15.2380	+	7.99751i	0.587381	+	0.308281i	−0.144725	+	0.989472i	$0.546230\pi$
$674$	−12.9667	+	8.95027i	−0.499459	+	0.344752i
$675$	21.6919			0.834923
$676$	0.973654	+	1.29586i	0.0374482	+	0.0498408i
$677$	−12.2080			−0.469192			−0.234596	−	0.972093i	$-0.575377\pi$
$677$	−12.2080			−0.469192			−0.234596	+	0.972093i	$0.575377\pi$
$678$	0.139312	−	0.0961605i	0.00535026	−	0.00369302i
$679$	−14.6076	−	7.66668i	−0.560590	−	0.294220i
$680$	−13.5312	+	35.6787i	−0.518896	+	1.36822i
$681$	12.4417	+	14.0437i	0.476765	+	0.538157i
$682$	−5.09070	+	0.618123i	−0.194933	+	0.0236692i
$683$	0.929362	+	3.77057i	0.0355610	+	0.144277i	0.986039	−	0.166516i	$-0.0532517\pi$
$683$	0.929362	+	3.77057i	0.0355610	+	0.144277i	−0.950478	+	0.310793i	$0.899406\pi$
$684$	0.0232954	+	0.0945130i	0.000890721	+	0.00361380i
$685$	−7.28172	−	10.5494i	−0.278220	−	0.403072i
$686$	−17.6712	−	4.35555i	−0.674688	−	0.166296i
$687$	−6.25359	−	4.31654i	−0.238589	−	0.164686i
$688$	12.8796	−	11.4103i	0.491030	−	0.435015i
$689$	−21.3096	−	23.1006i	−0.811831	−	0.880064i
$690$	−1.29977	−	1.15150i	−0.0494815	−	0.0438368i
$691$	8.47892	+	34.4003i	0.322553	+	1.30865i	0.878624	+	0.477515i	$0.158462\pi$
$691$	8.47892	+	34.4003i	0.322553	+	1.30865i	−0.556071	+	0.831135i	$0.687692\pi$
$692$	−0.801943	−	0.710460i	−0.0304853	−	0.0270076i
$693$	0.720538	−	0.177597i	0.0273710	−	0.00674634i
$694$	−19.6323	−	7.44557i	−0.745234	−	0.282630i
$695$			14.2564i			0.540777i
$696$	−12.8945	+	4.89022i	−0.488763	+	0.185363i
$697$	2.27936	−	9.24774i	0.0863370	−	0.350283i
$698$	24.9884			0.945825
$699$	2.34257			0.0886041
$700$	−0.117995	+	0.478723i	−0.00445977	+	0.0180940i
$701$	3.59515	−	29.6087i	0.135787	−	1.11831i	−0.752362	−	0.658750i	$-0.771085\pi$
$701$	3.59515	−	29.6087i	0.135787	−	1.11831i	0.888149	−	0.459556i	$-0.151992\pi$
$702$	−9.23226	+	25.9027i	−0.348449	+	0.977635i
$703$	−0.221199	−	1.82174i	−0.00834270	−	0.0687083i
$704$	−3.15229	−	0.382757i	−0.118806	−	0.0144257i
$705$	20.8743	+	30.2417i	0.786172	+	1.13897i
$706$	−27.5296	−	24.3891i	−1.03609	−	0.917897i
$707$	−3.44516	+	0.418318i	−0.129568	+	0.0157325i
$708$	−1.71130	−	0.207789i	−0.0643145	−	0.00780919i
$709$	12.7121	+	24.2208i	0.477412	+	0.909633i	0.998426	+	0.0560848i	$0.0178617\pi$
$709$	12.7121	+	24.2208i	0.477412	+	0.909633i	−0.521014	+	0.853548i	$0.674446\pi$
$710$	−0.274208	+	0.309517i	−0.0102908	+	0.0116159i
$711$	−2.80203	+	4.05944i	−0.105084	+	0.152241i
$712$	−33.6114	+	8.28447i	−1.25964	+	0.310474i
$713$	2.97169	−	0.360828i	0.111291	−	0.0135131i
$714$	3.95505	+	5.72988i	0.148014	+	0.214435i
$715$	−3.77560	+	2.71979i	−0.141199	+	0.101714i
$716$	0.330290	−	0.478508i	0.0123435	−	0.0178827i
$717$	−0.959520	+	1.82821i	−0.0358339	+	0.0682758i
$718$	7.37678	+	19.4510i	0.275299	+	0.725904i
$719$	4.49471	−	37.0172i	0.167624	−	1.38051i	−0.629644	−	0.776884i	$-0.716799\pi$
$719$	4.49471	−	37.0172i	0.167624	−	1.38051i	0.797268	−	0.603626i	$-0.206278\pi$
$720$	19.2108	−	13.2603i	0.715945	−	0.494181i
$721$	−2.67279	+	10.8439i	−0.0995399	+	0.403849i
$722$	−22.5725	+	15.5807i	−0.840062	+	0.579853i
$723$	−4.05494	+	1.53784i	−0.150805	+	0.0571927i
$724$	0.138630	+	0.365536i	0.00515213	+	0.0135851i
$725$	17.0712	−	8.95965i	0.634008	−	0.332753i
$726$	7.94973	+	15.1469i	0.295042	+	0.562156i
$727$	−40.5981	−	10.0065i	−1.50570	−	0.371122i	−0.601723	−	0.798704i	$-0.705519\pi$
$727$	−40.5981	−	10.0065i	−1.50570	−	0.371122i	−0.903976	+	0.427583i	$0.859365\pi$
$728$	7.84267	+	5.18372i	0.290669	+	0.192122i
$729$	−16.9003	+	4.16556i	−0.625939	+	0.154280i
$730$	−25.8768	−	29.2089i	−0.957743	−	1.08107i
$731$	2.26126	+	18.6231i	0.0836357	+	0.688802i
$732$	−0.0960633	+	0.0504179i	−0.00355060	+	0.00186350i
$733$	−9.71652	+	18.5133i	−0.358888	+	0.683803i	−0.996228	−	0.0867794i	$-0.972342\pi$
$733$	−9.71652	+	18.5133i	−0.358888	+	0.683803i	0.637340	+	0.770583i	$0.280035\pi$
$734$	−6.00411	−	2.27706i	−0.221616	−	0.0840478i
$735$	13.2496	+	14.9557i	0.488717	+	0.551648i
$736$	−0.253880	−	0.0308266i	−0.00935814	−	0.00113628i
$737$	0.876129	+	0.215946i	0.0322726	+	0.00795449i
$738$	−4.10432	+	3.63611i	−0.151082	+	0.133847i
$739$	−15.3454	+	17.3214i	−0.564489	+	0.637176i	−0.959570	−	0.281470i	$-0.909178\pi$
$739$	−15.3454	+	17.3214i	−0.564489	+	0.637176i	0.395081	+	0.918646i	$0.370716\pi$
$740$	1.43078	−	0.750929i	0.0525964	−	0.0276047i
$741$	1.67467	−	0.0336791i	0.0615207	−	0.00123723i
$742$	10.7311	+	5.63210i	0.393950	+	0.206761i
$743$	−18.4348	+	6.99138i	−0.676306	+	0.256489i	−0.668755	−	0.743483i	$-0.733173\pi$
$743$	−18.4348	+	6.99138i	−0.676306	+	0.256489i	−0.00755038	+	0.999971i	$0.502403\pi$
$744$	2.94677	−	24.2688i	0.108034	−	0.889739i
$745$	−34.4259	−	18.0681i	−1.26127	−	0.661964i
$746$			47.5599i			1.74129i
$747$	13.6142	−	25.9396i	0.498117	−	0.949082i
$748$	−0.162867	+	0.183839i	−0.00595500	+	0.00672181i
$749$	−4.26587	−	2.94452i	−0.155871	−	0.107590i
$750$	−3.05780	+	2.70897i	−0.111655	+	0.0989177i
$751$	7.18630	−	10.4111i	0.262232	−	0.379908i	−0.669646	−	0.742680i	$-0.733554\pi$
$751$	7.18630	−	10.4111i	0.262232	−	0.379908i	0.931878	+	0.362772i	$0.118170\pi$
$752$	44.3392	+	16.8156i	1.61688	+	0.613203i
$753$	−6.46512	+	17.0471i	−0.235602	+	0.621232i
$754$	3.43324	+	24.1983i	0.125031	+	0.881250i
$755$	−5.36113	−	14.1361i	−0.195112	−	0.514467i
$756$		−	0.622276i		−	0.0226320i
$757$	4.51157	−	11.8960i	0.163976	−	0.432369i	−0.827693	−	0.561181i	$-0.810347\pi$
$757$	4.51157	−	11.8960i	0.163976	−	0.432369i	0.991669	+	0.128812i	$0.0411164\pi$
$758$	−1.25744	−	10.3560i	−0.0456724	−	0.376146i
$759$	0.0781229	+	0.148851i	0.00283568	+	0.00540294i
$760$	−2.91340	−	2.01098i	−0.105680	−	0.0729458i
$761$	11.1489	+	7.69555i	0.404149	+	0.278964i	0.752749	−	0.658308i	$-0.228728\pi$
$761$	11.1489	+	7.69555i	0.404149	+	0.278964i	−0.348600	+	0.937272i	$0.613343\pi$
$762$	7.43142	+	14.1594i	0.269212	+	0.512941i
$763$	−1.95670	−	16.1149i	−0.0708374	−	0.583398i
$764$	0.512392	−	1.35107i	0.0185377	−	0.0488799i
$765$			25.4496i			0.920132i
$766$	17.6431	+	46.5210i	0.637471	+	1.68087i

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.h (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19961 + 0.828028i) q^{2} +(0.960584 + 0.504153i) q^{3} +(0.0442133 - 0.116581i) q^{4} +(2.00541 + 2.26364i) q^{5} +(-1.56977 + 0.190605i) q^{6} +(0.228271 + 0.926132i) q^{7} +(-0.654173 - 2.65409i) q^{8} +(-1.03564 - 1.50039i) q^{9} +O(q^{10})\)	\(q+(-1.19961 + 0.828028i) q^{2} +(0.960584 + 0.504153i) q^{3} +(0.0442133 - 0.116581i) q^{4} +(2.00541 + 2.26364i) q^{5} +(-1.56977 + 0.190605i) q^{6} +(0.228271 + 0.926132i) q^{7} +(-0.654173 - 2.65409i) q^{8} +(-1.03564 - 1.50039i) q^{9} +(-4.28006 - 1.05494i) q^{10} +(0.351207 + 0.242421i) q^{11} +(0.101245 - 0.0896954i) q^{12} +(1.73944 + 3.15822i) q^{13} +(-1.04070 - 0.921978i) q^{14} +(0.785144 + 3.18545i) q^{15} +(3.16906 + 2.80754i) q^{16} +(-4.48180 + 1.10466i) q^{17} +(2.48473 + 0.942332i) q^{18} -0.428231i q^{19} +(0.352563 - 0.133710i) q^{20} +(-0.247639 + 1.00471i) q^{21} -0.622040 q^{22} +0.363115 q^{23} +(0.709678 - 2.87928i) q^{24} +(-0.499715 + 4.11552i) q^{25} +(-4.70173 - 2.34832i) q^{26} +(-0.630688 - 5.19418i) q^{27} +(0.118062 + 0.0143353i) q^{28} +(-2.64175 - 3.82724i) q^{29} +(-3.57951 - 3.17117i) q^{30} +(8.18388 - 0.993703i) q^{31} +(-0.699172 - 0.0848949i) q^{32} +(0.215146 + 0.409927i) q^{33} +(4.46170 - 5.03621i) q^{34} +(-1.63865 + 2.37400i) q^{35} +(-0.220706 + 0.0543991i) q^{36} +(4.25411 - 0.516542i) q^{37} +(0.354587 + 0.513708i) q^{38} +(0.0786471 + 3.91068i) q^{39} +(4.69601 - 6.80335i) q^{40} +(-0.958910 + 1.82705i) q^{41} +(-0.534860 - 1.41031i) q^{42} +(0.489882 - 4.03454i) q^{43} +(0.0437896 - 0.0302258i) q^{44} +(1.31945 - 5.35322i) q^{45} +(-0.435595 + 0.300669i) q^{46} +(10.4726 - 3.97174i) q^{47} +(1.62872 + 4.29457i) q^{48} +(5.39258 - 2.83024i) q^{49} +(-2.80831 - 5.35078i) q^{50} +(-4.86206 - 1.19839i) q^{51} +(0.445094 - 0.0631497i) q^{52} +(-8.46335 + 2.08603i) q^{53} +(5.05750 + 5.70874i) q^{54} +(0.155561 + 1.28116i) q^{55} +(2.30870 - 1.21170i) q^{56} +(0.215894 - 0.411352i) q^{57} +(6.33812 + 2.40373i) q^{58} +(-8.45125 - 9.53949i) q^{59} +(0.406077 + 0.0493066i) q^{60} +(-0.778766 - 0.191949i) q^{61} +(-8.99461 + 7.96853i) q^{62} +(1.15315 - 1.30164i) q^{63} +(-6.58870 + 3.45802i) q^{64} +(-3.66079 + 10.2710i) q^{65} +(-0.597522 - 0.313604i) q^{66} +(1.97707 - 0.749805i) q^{67} +(-0.0693723 + 0.571333i) q^{68} +(0.348803 + 0.183066i) q^{69} -4.20471i q^{70} +(0.0435937 - 0.0830608i) q^{71} +(-3.30467 + 3.73020i) q^{72} +(7.28536 + 5.02872i) q^{73} +(-4.67554 + 4.14217i) q^{74} +(-2.55487 + 3.70137i) q^{75} +(-0.0499235 - 0.0189335i) q^{76} +(-0.144343 + 0.380601i) q^{77} +(-3.33250 - 4.62615i) q^{78} +(-0.959418 - 2.52978i) q^{79} +12.8039i q^{80} +(0.0733877 - 0.193508i) q^{81} +(-0.362535 - 2.98574i) q^{82} +(7.46757 + 14.2283i) q^{83} +(0.106181 + 0.0732916i) q^{84} +(-11.4884 - 7.92988i) q^{85} +(2.75304 + 5.24549i) q^{86} +(-0.608109 - 5.00823i) q^{87} +(0.413655 - 1.09072i) q^{88} -12.6640i q^{89} +(2.84980 + 7.51429i) q^{90} +(-2.52787 + 2.33188i) q^{91} +(0.0160545 - 0.0423323i) q^{92} +(8.36228 + 3.17139i) q^{93} +(-9.27430 + 13.4361i) q^{94} +(0.969361 - 0.858779i) q^{95} +(-0.628814 - 0.434039i) q^{96} +(-11.4690 + 12.9459i) q^{97} +(-4.12545 + 7.86038i) q^{98} -0.778008i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

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