LMFDB - Embedded newform 169.2.g.a.14.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(14,169)]

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([18]))

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

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

chi := DirichletCharacter("169.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.g (of order $13$, 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:	$156$
Relative dimension:	$13$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			14.11
Character	$\chi$	$=$	169.14
Dual form			169.2.g.a.157.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00858 - 1.46118i) q^{2} +(-2.49701 + 1.31053i) q^{3} +(-0.408612 - 1.07742i) q^{4} +(2.96132 + 2.62350i) q^{5} +(-0.603512 + 4.97037i) q^{6} +(-1.91869 - 0.472914i) q^{7} +(1.46133 + 0.360186i) q^{8} +(2.81336 - 4.07585i) q^{9} +O(q^{10})$	\(q+(1.00858 - 1.46118i) q^{2} +(-2.49701 + 1.31053i) q^{3} +(-0.408612 - 1.07742i) q^{4} +(2.96132 + 2.62350i) q^{5} +(-0.603512 + 4.97037i) q^{6} +(-1.91869 - 0.472914i) q^{7} +(1.46133 + 0.360186i) q^{8} +(2.81336 - 4.07585i) q^{9} +(6.82015 - 1.68102i) q^{10} +(3.06453 + 4.43973i) q^{11} +(2.43230 + 2.15483i) q^{12} +(-1.73651 - 3.15983i) q^{13} +(-2.62617 + 2.32659i) q^{14} +(-10.8326 - 2.67000i) q^{15} +(3.72519 - 3.30023i) q^{16} +(-0.565818 - 0.139462i) q^{17} +(-3.11807 - 8.22167i) q^{18} -3.58257 q^{19} +(1.61658 - 4.26258i) q^{20} +(5.41075 - 1.33363i) q^{21} +9.57810 q^{22} -1.74257 q^{23} +(-4.12099 + 1.01573i) q^{24} +(1.28398 + 10.5745i) q^{25} +(-6.36851 - 0.649594i) q^{26} +(-0.663696 + 5.46603i) q^{27} +(0.274471 + 2.26047i) q^{28} +(4.70408 - 6.81504i) q^{29} +(-14.8269 + 13.1355i) q^{30} +(-0.154435 + 1.27188i) q^{31} +(-0.702252 - 5.78357i) q^{32} +(-13.4705 - 7.06989i) q^{33} +(-0.774453 + 0.686106i) q^{34} +(-4.44116 - 6.43413i) q^{35} +(-5.54097 - 1.36573i) q^{36} +(0.391295 - 3.22260i) q^{37} +(-3.61332 + 5.23479i) q^{38} +(8.47713 + 5.61437i) q^{39} +(3.38252 + 4.90043i) q^{40} +(-4.06177 + 2.13178i) q^{41} +(3.50851 - 9.25118i) q^{42} +(-0.854533 - 7.03771i) q^{43} +(3.53126 - 5.11591i) q^{44} +(19.0242 - 4.68905i) q^{45} +(-1.75753 + 2.54622i) q^{46} +(2.72075 - 7.17403i) q^{47} +(-4.97677 + 13.1227i) q^{48} +(-2.74047 - 1.43831i) q^{49} +(16.7463 + 8.78913i) q^{50} +(1.59562 - 0.393285i) q^{51} +(-2.69491 + 3.16209i) q^{52} +(-2.36101 - 0.581937i) q^{53} +(7.31748 + 6.48272i) q^{54} +(-2.57260 + 21.1872i) q^{55} +(-2.63350 - 1.38217i) q^{56} +(8.94569 - 4.69506i) q^{57} +(-5.21357 - 13.7471i) q^{58} +(2.54652 + 2.25602i) q^{59} +(1.54962 + 12.7623i) q^{60} +(3.10295 - 0.764809i) q^{61} +(1.70270 + 1.50846i) q^{62} +(-7.32548 + 6.48981i) q^{63} +(-0.345656 - 0.181414i) q^{64} +(3.14746 - 13.9130i) q^{65} +(-23.9166 + 12.5524i) q^{66} +(0.844836 - 2.22765i) q^{67} +(0.0809410 + 0.666609i) q^{68} +(4.35121 - 2.28369i) q^{69} -13.8807 q^{70} +(0.968004 - 0.508048i) q^{71} +(5.57931 - 4.94284i) q^{72} +(4.47920 + 6.48924i) q^{73} +(-4.31416 - 3.82201i) q^{74} +(-17.0643 - 24.7219i) q^{75} +(1.46388 + 3.85993i) q^{76} +(-3.78026 - 9.96772i) q^{77} +(16.7535 - 6.72409i) q^{78} +(3.52518 - 9.29515i) q^{79} +19.6896 q^{80} +(-0.237567 - 0.626414i) q^{81} +(-0.981707 + 8.08508i) q^{82} +(-0.798013 - 0.418830i) q^{83} +(-3.64777 - 5.28471i) q^{84} +(-1.30969 - 1.89741i) q^{85} +(-11.1453 - 5.84948i) q^{86} +(-2.81481 + 23.1820i) q^{87} +(2.87916 + 7.59172i) q^{88} -5.24711 q^{89} +(12.3359 - 32.5272i) q^{90} +(1.83749 + 6.88395i) q^{91} +(0.712035 + 1.87748i) q^{92} +(-1.28122 - 3.37830i) q^{93} +(-7.73849 - 11.2111i) q^{94} +(-10.6091 - 9.39886i) q^{95} +(9.33306 + 13.5213i) q^{96} +(-7.86990 + 6.97212i) q^{97} +(-4.86563 + 2.55368i) q^{98} +26.7173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) $ 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{13}\right)$

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 $

$2$	1.00858	−	1.46118i	0.713176	−	1.03321i	−0.284052	−	0.958809i	$-0.591679\pi$
$2$	1.00858	−	1.46118i	0.713176	−	1.03321i	0.997228	−	0.0744049i	$-0.0237057\pi$
$3$	−2.49701	+	1.31053i	−1.44165	+	0.756635i	−0.990719	−	0.135926i	$-0.956599\pi$
$3$	−2.49701	+	1.31053i	−1.44165	+	0.756635i	−0.450928	+	0.892560i	$0.648907\pi$
$4$	−0.408612	−	1.07742i	−0.204306	−	0.538710i
$5$	2.96132	+	2.62350i	1.32434	+	1.17326i	0.971354	+	0.237637i	$0.0763727\pi$
$5$	2.96132	+	2.62350i	1.32434	+	1.17326i	0.352988	+	0.935628i	$0.385166\pi$
$6$	−0.603512	+	4.97037i	−0.246383	+	2.02914i
$7$	−1.91869	−	0.472914i	−0.725196	−	0.178745i	−0.140597	−	0.990067i	$-0.544902\pi$
$7$	−1.91869	−	0.472914i	−0.725196	−	0.178745i	−0.584599	+	0.811322i	$0.698748\pi$
$8$	1.46133	+	0.360186i	0.516659	+	0.127345i
$9$	2.81336	−	4.07585i	0.937786	−	1.35862i
$10$	6.82015	−	1.68102i	2.15672	−	0.531584i
$11$	3.06453	+	4.43973i	0.923989	+	1.33863i	0.940868	+	0.338772i	$0.110012\pi$
$11$	3.06453	+	4.43973i	0.923989	+	1.33863i	−0.0168790	+	0.999858i	$0.505373\pi$
$12$	2.43230	+	2.15483i	0.702144	+	0.622045i
$13$	−1.73651	−	3.15983i	−0.481621	−	0.876380i
$13$	−1.73651	−	3.15983i	−0.481621	−	0.876380i
$14$	−2.62617	+	2.32659i	−0.701874	+	0.621806i
$15$	−10.8326	−	2.67000i	−2.79697	−	0.689390i
$16$	3.72519	−	3.30023i	0.931298	−	0.825058i
$17$	−0.565818	−	0.139462i	−0.137231	−	0.0338244i	0.170102	−	0.985426i	$-0.445590\pi$
$17$	−0.565818	−	0.139462i	−0.137231	−	0.0338244i	−0.307333	+	0.951602i	$0.599436\pi$
$18$	−3.11807	−	8.22167i	−0.734936	−	1.93787i
$19$	−3.58257			−0.821897			−0.410949	−	0.911658i	$-0.634802\pi$
$19$	−3.58257			−0.821897			−0.410949	+	0.911658i	$0.634802\pi$
$20$	1.61658	−	4.26258i	0.361479	−	0.953141i
$21$	5.41075	−	1.33363i	1.18072	−	0.291022i
$22$	9.57810			2.04206
$23$	−1.74257			−0.363351			−0.181676	−	0.983359i	$-0.558152\pi$
$23$	−1.74257			−0.363351			−0.181676	+	0.983359i	$0.558152\pi$
$24$	−4.12099	+	1.01573i	−0.841193	+	0.207336i
$25$	1.28398	+	10.5745i	0.256795	+	2.11490i
$26$	−6.36851	−	0.649594i	−1.24897	−	0.127396i
$27$	−0.663696	+	5.46603i	−0.127728	+	1.05194i
$28$	0.274471	+	2.26047i	0.0518701	+	0.427189i
$29$	4.70408	−	6.81504i	0.873526	−	1.26552i	−0.0894657	−	0.995990i	$-0.528516\pi$
$29$	4.70408	−	6.81504i	0.873526	−	1.26552i	0.962992	−	0.269531i	$-0.0868687\pi$
$30$	−14.8269	+	13.1355i	−2.70702	+	2.39821i
$31$	−0.154435	+	1.27188i	−0.0277373	+	0.228437i	−0.999985	−	0.00551754i	$-0.998244\pi$
$31$	−0.154435	+	1.27188i	−0.0277373	+	0.228437i	0.972247	+	0.233955i	$0.0751668\pi$
$32$	−0.702252	−	5.78357i	−0.124142	−	1.02240i
$33$	−13.4705	−	7.06989i	−2.34492	−	1.23071i
$34$	−0.774453	+	0.686106i	−0.132818	+	0.117666i
$35$	−4.44116	−	6.43413i	−0.750693	−	1.08757i
$36$	−5.54097	−	1.36573i	−0.923496	−	0.227621i
$37$	0.391295	−	3.22260i	0.0643284	−	0.529792i	−0.924549	−	0.381062i	$-0.875558\pi$
$37$	0.391295	−	3.22260i	0.0643284	−	0.529792i	0.988878	−	0.148730i	$-0.0475186\pi$
$38$	−3.61332	+	5.23479i	−0.586157	+	0.849196i
$39$	8.47713	+	5.61437i	1.35743	+	0.899019i
$40$	3.38252	+	4.90043i	0.534824	+	0.774826i
$41$	−4.06177	+	2.13178i	−0.634343	+	0.332929i	−0.751058	−	0.660237i	$-0.770456\pi$
$41$	−4.06177	+	2.13178i	−0.634343	+	0.332929i	0.116715	+	0.993165i	$0.462764\pi$
$42$	3.50851	−	9.25118i	0.541375	−	1.42749i
$43$	−0.854533	−	7.03771i	−0.130315	−	1.07324i	−0.900328	−	0.435212i	$-0.856673\pi$
$43$	−0.854533	−	7.03771i	−0.130315	−	1.07324i	0.770013	−	0.638028i	$-0.220250\pi$
$44$	3.53126	−	5.11591i	0.532357	−	0.771252i
$45$	19.0242	−	4.68905i	2.83597	−	0.699003i
$46$	−1.75753	+	2.54622i	−0.259133	+	0.375420i
$47$	2.72075	−	7.17403i	0.396863	−	1.04644i	−0.576485	−	0.817107i	$-0.695576\pi$
$47$	2.72075	−	7.17403i	0.396863	−	1.04644i	0.973348	−	0.229333i	$-0.0736545\pi$
$48$	−4.97677	+	13.1227i	−0.718335	+	1.89409i
$49$	−2.74047	−	1.43831i	−0.391496	−	0.205473i
$50$	16.7463	+	8.78913i	2.36828	+	1.24297i
$51$	1.59562	−	0.393285i	0.223431	−	0.0550709i
$52$	−2.69491	+	3.16209i	−0.373717	+	0.438503i
$53$	−2.36101	−	0.581937i	−0.324310	−	0.0799352i	0.0737997	−	0.997273i	$-0.476487\pi$
$53$	−2.36101	−	0.581937i	−0.324310	−	0.0799352i	−0.398110	+	0.917338i	$0.630334\pi$
$54$	7.31748	+	6.48272i	0.995783	+	0.882187i
$55$	−2.57260	+	21.1872i	−0.346889	+	2.85689i
$56$	−2.63350	−	1.38217i	−0.351917	−	0.184700i
$57$	8.94569	−	4.69506i	1.18489	−	0.621876i
$58$	−5.21357	−	13.7471i	−0.684576	−	1.80508i
$59$	2.54652	+	2.25602i	0.331529	+	0.293709i	0.812422	−	0.583070i	$-0.198149\pi$
$59$	2.54652	+	2.25602i	0.331529	+	0.293709i	−0.480892	+	0.876780i	$0.659687\pi$
$60$	1.54962	+	12.7623i	0.200055	+	1.64760i
$61$	3.10295	−	0.764809i	0.397292	−	0.0979237i	−0.0356075	−	0.999366i	$-0.511337\pi$
$61$	3.10295	−	0.764809i	0.397292	−	0.0979237i	0.432900	+	0.901442i	$0.357490\pi$
$62$	1.70270	+	1.50846i	0.216243	+	0.191575i
$63$	−7.32548	+	6.48981i	−0.922924	+	0.817639i
$64$	−0.345656	−	0.181414i	−0.0432070	−	0.0226768i
$65$	3.14746	−	13.9130i	0.390395	−	1.72569i
$66$	−23.9166	+	12.5524i	−2.94393	+	1.54509i
$67$	0.844836	−	2.22765i	0.103213	−	0.272151i	−0.873455	−	0.486905i	$-0.838126\pi$
$67$	0.844836	−	2.22765i	0.103213	−	0.272151i	0.976668	+	0.214754i	$0.0688951\pi$
$68$	0.0809410	+	0.666609i	0.00981554	+	0.0808382i
$69$	4.35121	−	2.28369i	0.523824	−	0.274924i
$70$	−13.8807			−1.65906
$71$	0.968004	−	0.508048i	0.114881	−	0.0602942i	−0.406304	−	0.913738i	$-0.633183\pi$
$71$	0.968004	−	0.508048i	0.114881	−	0.0602942i	0.521185	+	0.853444i	$0.325490\pi$
$72$	5.57931	−	4.94284i	0.657528	−	0.582519i
$73$	4.47920	+	6.48924i	0.524251	+	0.759508i	0.992255	−	0.124218i	$-0.0396423\pi$
$73$	4.47920	+	6.48924i	0.524251	+	0.759508i	−0.468004	+	0.883726i	$0.655027\pi$
$74$	−4.31416	−	3.82201i	−0.501511	−	0.444300i
$75$	−17.0643	−	24.7219i	−1.97041	−	2.85464i
$76$	1.46388	+	3.85993i	0.167918	+	0.442764i
$77$	−3.78026	−	9.96772i	−0.430800	−	1.13593i
$78$	16.7535	−	6.72409i	1.89696	−	0.761353i
$79$	3.52518	−	9.29515i	0.396614	−	1.04579i	−0.576831	−	0.816864i	$-0.695711\pi$
$79$	3.52518	−	9.29515i	0.396614	−	1.04579i	0.973445	−	0.228922i	$-0.0735201\pi$
$80$	19.6896			2.20137
$81$	−0.237567	−	0.626414i	−0.0263964	−	0.0696016i
$82$	−0.981707	+	8.08508i	−0.108411	+	0.892848i
$83$	−0.798013	−	0.418830i	−0.0875933	−	0.0459725i	0.420358	−	0.907358i	$-0.361905\pi$
$83$	−0.798013	−	0.418830i	−0.0875933	−	0.0459725i	−0.507951	+	0.861386i	$0.669597\pi$
$84$	−3.64777	−	5.28471i	−0.398005	−	0.576609i
$85$	−1.30969	−	1.89741i	−0.142056	−	0.205803i
$86$	−11.1453	−	5.84948i	−1.20182	−	0.630766i
$87$	−2.81481	+	23.1820i	−0.301779	+	2.48537i
$88$	2.87916	+	7.59172i	0.306919	+	0.809280i
$89$	−5.24711			−0.556192			−0.278096	−	0.960553i	$-0.589703\pi$
$89$	−5.24711			−0.556192			−0.278096	+	0.960553i	$0.589703\pi$
$90$	12.3359	−	32.5272i	1.30032	−	3.42867i
$91$	1.83749	+	6.88395i	0.192621	+	0.721634i
$92$	0.712035	+	1.87748i	0.0742348	+	0.195741i
$93$	−1.28122	−	3.37830i	−0.132856	−	0.350313i
$94$	−7.73849	−	11.2111i	−0.798164	−	1.15634i
$95$	−10.6091	−	9.39886i	−1.08847	−	0.964303i
$96$	9.33306	+	13.5213i	0.952552	+	1.38001i
$97$	−7.86990	+	6.97212i	−0.799067	+	0.707911i	−0.960289	−	0.279007i	$-0.909995\pi$
$97$	−7.86990	+	6.97212i	−0.799067	+	0.707911i	0.161222	+	0.986918i	$0.448456\pi$
$98$	−4.86563	+	2.55368i	−0.491503	+	0.257961i
$99$	26.7173			2.68519
$100$	10.8685	−	5.70424i	1.08685	−	0.570424i
$101$	0.403482	+	3.32298i	0.0401480	+	0.330648i	0.998920	+	0.0464709i	$0.0147975\pi$
$101$	0.403482	+	3.32298i	0.0401480	+	0.330648i	−0.958772	+	0.284178i	$0.908279\pi$
$102$	1.03465	−	2.72815i	0.102446	−	0.270128i
$103$	−1.45068	+	0.761376i	−0.142940	+	0.0750206i	−0.534677	−	0.845057i	$-0.679567\pi$
$103$	−1.45068	+	0.761376i	−0.142940	+	0.0750206i	0.391737	+	0.920077i	$0.371874\pi$
$104$	−1.39949	−	5.24303i	−0.137231	−	0.514121i
$105$	19.5217	+	10.2458i	1.90512	+	0.999886i
$106$	−3.23159	+	2.86294i	−0.313880	+	0.278074i
$107$	−4.03996	−	3.57909i	−0.390558	−	0.346004i	0.444879	−	0.895591i	$-0.353247\pi$
$107$	−4.03996	−	3.57909i	−0.390558	−	0.346004i	−0.835437	+	0.549587i	$0.814785\pi$
$108$	6.16040	−	1.51840i	0.592785	−	0.146108i
$109$	1.32444	+	10.9077i	0.126858	+	1.04477i	0.907576	+	0.419888i	$0.137931\pi$
$109$	1.32444	+	10.9077i	0.126858	+	1.04477i	−0.780718	+	0.624884i	$0.785146\pi$
$110$	28.3638	+	25.1281i	2.70438	+	2.39587i
$111$	3.24625	+	8.55966i	0.308120	+	0.812447i
$112$	−8.70821	+	4.57042i	−0.822849	+	0.431864i
$113$	7.28454	+	3.82322i	0.685272	+	0.359658i	0.771156	−	0.636647i	$-0.219679\pi$
$113$	7.28454	+	3.82322i	0.685272	+	0.359658i	−0.0858836	+	0.996305i	$0.527371\pi$
$114$	2.16212	−	17.8067i	0.202501	−	1.66775i
$115$	−5.16031	−	4.57164i	−0.481201	−	0.426307i
$116$	−9.26480	−	2.28357i	−0.860215	−	0.212024i
$117$	−17.7644	−	1.81199i	−1.64232	−	0.167518i
$118$	5.86485	−	1.44556i	0.539903	−	0.133074i
$119$	1.01967	+	0.535167i	0.0934734	+	0.0490586i
$120$	−14.8683	−	7.80350i	−1.35729	−	0.712359i
$121$	−6.41925	+	16.9262i	−0.583568	+	1.53874i
$122$	2.01206	−	5.30536i	0.182163	−	0.480324i
$123$	7.34851	−	10.6462i	0.662593	−	0.959931i
$124$	1.43346	−	0.353316i	0.128728	−	0.0317287i
$125$	−12.7028	+	18.4032i	−1.13617	+	1.64603i
$126$	2.09446	+	17.2494i	0.186589	+	1.53670i
$127$	−3.44373	+	9.08037i	−0.305582	+	0.805753i	0.690978	+	0.722876i	$0.257180\pi$
$127$	−3.44373	+	9.08037i	−0.305582	+	0.805753i	−0.996560	+	0.0828771i	$0.973589\pi$
$128$	9.70371	−	5.09290i	0.857695	−	0.450153i
$129$	11.3569	+	16.4533i	0.999919	+	1.44863i
$130$	−17.1550	−	18.6314i	−1.50459	−	1.63409i
$131$	−6.18642	+	8.96257i	−0.540510	+	0.783063i	−0.994137	−	0.108128i	$-0.965514\pi$
$131$	−6.18642	+	8.96257i	−0.540510	+	0.783063i	0.453627	+	0.891191i	$0.350130\pi$
$132$	−2.11302	+	17.4023i	−0.183915	+	1.51467i
$133$	6.87383	+	1.69425i	0.596037	+	0.146910i
$134$	−2.40292	−	3.48123i	−0.207581	−	0.300732i
$135$	−16.3055	+	14.4454i	−1.40336	+	1.24327i
$136$	−0.776615	−	0.407599i	−0.0665942	−	0.0349513i
$137$	1.04052	+	8.56949i	0.0888980	+	0.732141i	0.967197	+	0.254028i	$0.0817557\pi$
$137$	1.04052	+	8.56949i	0.0888980	+	0.732141i	−0.878299	+	0.478112i	$0.841321\pi$
$138$	1.05166	−	8.66122i	0.0895235	−	0.737292i
$139$	15.6469	−	13.8619i	1.32715	−	1.17575i	0.356764	−	0.934194i	$-0.383880\pi$
$139$	15.6469	−	13.8619i	1.32715	−	1.17575i	0.970386	−	0.241559i	$-0.0776586\pi$
$140$	−5.11755	+	7.41405i	−0.432512	+	0.626602i
$141$	2.60805	+	21.4792i	0.219638	+	1.80888i
$142$	0.233961	−	1.92684i	0.0196336	−	0.161697i
$143$	8.70723	−	17.3930i	0.728136	−	1.45448i
$144$	−2.97096	−	24.4681i	−0.247580	−	2.03900i
$145$	31.8095	−	7.84035i	2.64164	−	0.651105i
$146$	13.9996			1.15862
$147$	8.72793			0.719867
$148$	−3.63198	+	0.895203i	−0.298547	+	0.0735853i
$149$	−5.38798	+	14.2069i	−0.441401	+	1.16388i	0.511148	+	0.859492i	$0.329220\pi$
$149$	−5.38798	+	14.2069i	−0.441401	+	1.16388i	−0.952549	+	0.304385i	$0.901549\pi$
$150$	−53.3340			−4.35470
$151$	−8.06001	−	21.2525i	−0.655915	−	1.72950i	−0.683568	−	0.729887i	$-0.739573\pi$
$151$	−8.06001	−	21.2525i	−0.655915	−	1.72950i	0.0276533	−	0.999618i	$-0.491197\pi$
$152$	−5.23532	−	1.29039i	−0.424640	−	0.104664i
$153$	−2.16027	+	1.91383i	−0.174648	+	0.154724i
$154$	−18.3774	−	4.52962i	−1.48089	−	0.365007i
$155$	−3.79412	+	3.36130i	−0.304751	+	0.269986i
$156$	2.58519	−	11.4275i	0.206981	−	0.914934i
$157$	−9.07444	−	8.03925i	−0.724219	−	0.641602i	0.218251	−	0.975893i	$-0.429965\pi$
$157$	−9.07444	−	8.03925i	−0.724219	−	0.641602i	−0.942470	+	0.334291i	$0.891503\pi$
$158$	−10.0265	−	14.5259i	−0.797665	−	1.15562i
$159$	6.65811	−	1.64108i	0.528022	−	0.130146i
$160$	13.0936	−	18.9693i	1.03514	−	1.49966i
$161$	3.34345	+	0.824087i	0.263501	+	0.0649472i
$162$	−1.15491	−	0.284661i	−0.0907385	−	0.0223650i
$163$	−2.30709	+	19.0006i	−0.180706	+	1.48824i	0.566727	+	0.823906i	$0.308210\pi$
$163$	−2.30709	+	19.0006i	−0.180706	+	1.48824i	−0.747432	+	0.664338i	$0.768714\pi$
$164$	3.95651	+	3.50517i	0.308952	+	0.273707i
$165$	−21.3427	−	56.2761i	−1.66153	−	4.38109i
$166$	−1.41685	+	0.743620i	−0.109969	+	0.0577161i
$167$	−2.59340	+	3.75719i	−0.200683	+	0.290740i	−0.910385	−	0.413762i	$-0.864214\pi$
$167$	−2.59340	+	3.75719i	−0.200683	+	0.290740i	0.709702	+	0.704502i	$0.248830\pi$
$168$	8.38725			0.647090
$169$	−6.96908	+	10.9741i	−0.536083	+	0.844165i
$170$	−4.09340			−0.313950
$171$	−10.0790	+	14.6020i	−0.770763	+	1.11664i
$172$	−7.23340	+	3.79638i	−0.551541	+	0.289471i
$173$	0.400939	+	1.05719i	0.0304829	+	0.0803767i	0.949394	−	0.314089i	$-0.101699\pi$
$173$	0.400939	+	1.05719i	0.0304829	+	0.0803767i	−0.918911	+	0.394466i	$0.870930\pi$
$174$	31.0343	+	27.4940i	2.35270	+	2.08431i
$175$	2.53728	−	20.8964i	0.191800	−	1.57962i
$176$	26.0681	+	6.42521i	1.96496	+	0.484318i
$177$	−9.31527	−	2.29601i	−0.700179	−	0.172579i
$178$	−5.29214	+	7.66699i	−0.396663	+	0.574665i
$179$	−1.41563	+	0.348921i	−0.105809	+	0.0260796i	−0.291865	−	0.956460i	$-0.594276\pi$
$179$	−1.41563	+	0.348921i	−0.105809	+	0.0260796i	0.186056	+	0.982539i	$0.440430\pi$
$180$	−12.8256	−	18.5811i	−0.955964	−	1.38495i
$181$	−10.0322	−	8.88776i	−0.745688	−	0.660622i	0.202157	−	0.979353i	$-0.435205\pi$
$181$	−10.0322	−	8.88776i	−0.745688	−	0.660622i	−0.947845	+	0.318731i	$0.896743\pi$
$182$	11.9120	+	4.25813i	0.882975	+	0.315633i
$183$	−6.74578	+	5.97624i	−0.498662	+	0.441776i
$184$	−2.54648	−	0.627650i	−0.187729	−	0.0462710i
$185$	9.61324	−	8.51659i	0.706779	−	0.626152i
$186$	−6.22853	−	1.53519i	−0.456698	−	0.112566i
$187$	−1.11479	−	2.93946i	−0.0815216	−	0.214955i
$188$	−8.84118			−0.644809
$189$	3.85839	−	10.1737i	0.280656	−	0.740030i
$190$	−24.4337	+	6.02236i	−1.77260	+	0.436908i
$191$	−7.06999			−0.511567			−0.255783	−	0.966734i	$-0.582333\pi$
$191$	−7.06999			−0.511567			−0.255783	+	0.966734i	$0.582333\pi$
$192$	1.10085			0.0794473
$193$	−10.5945	+	2.61132i	−0.762611	+	0.187967i	−0.601394	−	0.798952i	$-0.705388\pi$
$193$	−10.5945	+	2.61132i	−0.762611	+	0.187967i	−0.161217	+	0.986919i	$0.551542\pi$
$194$	2.25011	+	18.5313i	0.161549	+	1.33047i
$195$	10.3742	+	38.8657i	0.742909	+	2.78323i
$196$	−0.429877	+	3.54035i	−0.0307055	+	0.252882i
$197$	−2.97383	−	24.4917i	−0.211876	−	1.74496i	−0.579489	−	0.814980i	$-0.696748\pi$
$197$	−2.97383	−	24.4917i	−0.211876	−	1.74496i	0.367612	−	0.929979i	$-0.380175\pi$
$198$	26.9466	−	39.0389i	1.91501	−	2.77437i
$199$	−7.65587	+	6.78251i	−0.542711	+	0.480800i	−0.889368	−	0.457192i	$-0.848855\pi$
$199$	−7.65587	+	6.78251i	−0.542711	+	0.480800i	0.346657	+	0.937992i	$0.387317\pi$
$200$	−1.93247	+	15.9153i	−0.136646	+	1.12538i
$201$	0.809840	+	6.66963i	0.0571217	+	0.470440i
$202$	5.26243	+	2.76194i	0.370263	+	0.194329i
$203$	−12.2486	+	10.8513i	−0.859683	+	0.761613i
$204$	−1.07572	−	1.55845i	−0.0753155	−	0.109113i
$205$	−17.6209	−	4.34317i	−1.23070	−	0.303340i
$206$	−0.350621	+	2.88762i	−0.0244289	+	0.201190i
$207$	−4.90248	+	7.10246i	−0.340746	+	0.493655i
$208$	−16.8970	−	6.04010i	−1.17160	−	0.418806i
$209$	−10.9789	−	15.9056i	−0.759424	−	1.10022i
$210$	34.6603	−	18.1911i	2.39179	−	1.25531i
$211$	2.05340	−	5.41436i	0.141362	−	0.372740i	−0.845573	−	0.533859i	$-0.820741\pi$
$211$	2.05340	−	5.41436i	0.141362	−	0.372740i	0.986935	+	0.161119i	$0.0515104\pi$
$212$	0.337746	+	2.78159i	0.0231965	+	0.191040i
$213$	−1.75130	+	2.53720i	−0.119997	+	0.173846i
$214$	−9.30435	+	2.29332i	−0.636032	+	0.156768i
$215$	15.9329	−	23.0828i	1.08661	−	1.57423i
$216$	−2.93867	+	7.74862i	−0.199951	+	0.527227i
$217$	0.897805	−	2.36732i	0.0609470	−	0.160704i
$218$	17.2740	+	9.06611i	1.16994	+	0.614034i
$219$	−19.6889	−	10.3335i	−1.33045	−	0.698276i
$220$	23.8788	−	5.88558i	1.60991	−	0.396806i
$221$	0.541872	+	2.03007i	0.0364503	+	0.136557i
$222$	15.7814	+	3.88975i	1.05918	+	0.261063i
$223$	16.0027	+	14.1772i	1.07162	+	0.949373i	0.998849	−	0.0479752i	$-0.0152769\pi$
$223$	16.0027	+	14.1772i	1.07162	+	0.949373i	0.0727725	+	0.997349i	$0.476815\pi$
$224$	−1.38773	+	11.4290i	−0.0927215	+	0.763630i
$225$	46.7123	+	24.5165i	3.11415	+	1.63443i
$226$	12.9335	−	6.78802i	0.860324	−	0.451533i
$227$	−6.61622	−	17.4455i	−0.439134	−	1.15790i	−0.953782	−	0.300499i	$-0.902847\pi$
$227$	−6.61622	−	17.4455i	−0.439134	−	1.15790i	0.514648	−	0.857401i	$-0.327923\pi$
$228$	−8.71387	−	7.71981i	−0.577090	−	0.511257i
$229$	1.41336	+	11.6401i	0.0933977	+	0.769199i	0.961879	+	0.273477i	$0.0881736\pi$
$229$	1.41336	+	11.6401i	0.0933977	+	0.769199i	−0.868481	+	0.495723i	$0.834903\pi$
$230$	−11.8846	+	2.92929i	−0.783648	+	0.193152i
$231$	22.5023	+	19.9353i	1.48054	+	1.31165i
$232$	9.32890	−	8.26469i	0.612473	−	0.542603i
$233$	12.1388	+	6.37093i	0.795239	+	0.417374i	0.812851	−	0.582471i	$-0.197914\pi$
$233$	12.1388	+	6.37093i	0.795239	+	0.417374i	−0.0176123	+	0.999845i	$0.505606\pi$
$234$	−20.5645	+	24.1296i	−1.34435	+	1.57740i
$235$	26.8781	−	14.1067i	1.75333	−	0.920220i
$236$	1.39015	−	3.66551i	0.0904908	−	0.238605i
$237$	3.37916	+	27.8299i	0.219500	+	1.80775i
$238$	1.81040	−	0.950173i	0.117351	−	0.0615906i
$239$	6.56845			0.424878			0.212439	−	0.977174i	$-0.431859\pi$
$239$	6.56845			0.424878			0.212439	+	0.977174i	$0.431859\pi$
$240$	−49.1651	+	25.8039i	−3.17360	+	1.66563i
$241$	12.4176	−	11.0011i	0.799891	−	0.708641i	−0.160580	−	0.987023i	$-0.551336\pi$
$241$	12.4176	−	11.0011i	0.799891	−	0.708641i	0.960471	+	0.278381i	$0.0897979\pi$
$242$	18.2579	+	26.4512i	1.17366	+	1.70035i
$243$	−10.9501	−	9.70098i	−0.702452	−	0.622318i
$244$	−2.09192	−	3.03067i	−0.133922	−	0.194019i
$245$	−4.34201	−	11.4489i	−0.277401	−	0.731445i
$246$	−8.14442	−	21.4751i	−0.519269	−	1.36920i
$247$	6.22116	+	11.3203i	0.395843	+	0.720294i
$248$	−0.683795	+	1.80302i	−0.0434211	+	0.114492i
$249$	2.54153			0.161063
$250$	14.0786	+	37.1222i	0.890409	+	2.34782i
$251$	−2.24721	+	18.5074i	−0.141843	+	1.16818i	0.731768	+	0.681554i	$0.238695\pi$
$251$	−2.24721	+	18.5074i	−0.141843	+	1.16818i	−0.873611	+	0.486625i	$0.838228\pi$
$252$	9.98553	+	5.24081i	0.629029	+	0.330140i
$253$	−5.34016	−	7.73655i	−0.335733	−	0.486393i
$254$	9.79481	+	14.1902i	0.614581	+	0.890375i
$255$	5.75692	+	3.02146i	0.360512	+	0.189211i
$256$	2.43944	−	20.0906i	0.152465	−	1.25566i
$257$	−10.2048	−	26.9080i	−0.636561	−	1.67847i	−0.730515	−	0.682897i	$-0.760720\pi$
$257$	−10.2048	−	26.9080i	−0.636561	−	1.67847i	0.0939539	−	0.995577i	$-0.470049\pi$
$258$	35.4957			2.20987
$259$	−2.27479	+	5.99812i	−0.141348	+	0.372705i
$260$	−16.2762	+	2.29387i	−1.00941	+	0.142260i
$261$	−14.5428	−	38.3463i	−0.900178	−	2.37357i
$262$	6.85646	+	18.0790i	0.423593	+	1.11692i
$263$	−2.24625	−	3.25426i	−0.138510	−	0.200666i	0.747590	−	0.664161i	$-0.231211\pi$
$263$	−2.24625	−	3.25426i	−0.138510	−	0.200666i	−0.886100	+	0.463494i	$0.846595\pi$
$264$	−17.1385	−	15.1833i	−1.05480	−	0.934470i
$265$	−5.46500	−	7.91741i	−0.335712	−	0.486363i
$266$	9.40844	−	8.33515i	0.576868	−	0.511061i
$267$	13.1021	−	6.87649i	0.801833	−	0.420834i
$268$	−2.74532			−0.167697
$269$	21.5357	−	11.3028i	1.31305	−	0.689144i	0.344698	−	0.938714i	$-0.387981\pi$
$269$	21.5357	−	11.3028i	1.31305	−	0.689144i	0.968357	+	0.249569i	$0.0802890\pi$
$270$	4.66198	+	38.3948i	0.283719	+	2.33663i
$271$	0.855256	−	2.25512i	0.0519531	−	0.136989i	−0.906528	−	0.422147i	$-0.861277\pi$
$271$	0.855256	−	2.25512i	0.0519531	−	0.136989i	0.958481	+	0.285158i	$0.0920460\pi$
$272$	−2.56804	+	1.34781i	−0.155710	+	0.0817229i
$273$	−13.6098	−	14.7812i	−0.823706	−	0.894598i
$274$	13.5711	+	7.12264i	0.819858	+	0.430294i
$275$	−43.0131	+	38.1063i	−2.59379	+	2.29790i
$276$	−4.23845	−	3.75494i	−0.255125	−	0.226021i
$277$	−9.29118	+	2.29007i	−0.558253	+	0.137597i	−0.508340	−	0.861157i	$-0.669741\pi$
$277$	−9.29118	+	2.29007i	−0.558253	+	0.137597i	−0.0499132	+	0.998754i	$0.515894\pi$
$278$	−4.47366	−	36.8439i	−0.268312	−	2.20975i
$279$	4.74953	+	4.20772i	0.284347	+	0.251910i
$280$	−4.17252	−	11.0020i	−0.249356	−	0.657498i
$281$	−1.31539	+	0.690370i	−0.0784696	+	0.0411840i	−0.503502	−	0.863994i	$-0.667955\pi$
$281$	−1.31539	+	0.690370i	−0.0784696	+	0.0411840i	0.425032	+	0.905178i	$0.360263\pi$
$282$	34.0156	+	17.8527i	2.02560	+	1.06312i
$283$	−1.84300	+	15.1785i	−0.109555	+	0.902266i	0.829502	+	0.558504i	$0.188624\pi$
$283$	−1.84300	+	15.1785i	−0.109555	+	0.902266i	−0.939057	+	0.343762i	$0.888299\pi$
$284$	−0.942919	−	0.835353i	−0.0559519	−	0.0495691i
$285$	38.8085	+	9.56545i	2.29882	+	0.566608i
$286$	−16.6324	−	30.2652i	−0.983497	−	1.78962i
$287$	8.80143	−	2.16936i	0.519532	−	0.128053i
$288$	−25.5486	−	13.4090i	−1.50547	−	0.790131i
$289$	−14.7521	−	7.74247i	−0.867768	−	0.455440i
$290$	20.6264	−	54.3872i	1.21122	−	3.19373i
$291$	10.5140	−	27.7232i	0.616342	−	1.62516i
$292$	5.16138	−	7.47756i	0.302047	−	0.437591i
$293$	−24.5143	+	6.04222i	−1.43214	+	0.352990i	−0.877690	−	0.479228i	$-0.840917\pi$
$293$	−24.5143	+	6.04222i	−1.43214	+	0.352990i	−0.554448	+	0.832219i	$0.687070\pi$
$294$	8.80284	−	12.7531i	0.513392	−	0.743777i
$295$	1.62239	+	13.3616i	0.0944594	+	0.777943i
$296$	1.73255	−	4.56835i	0.100702	−	0.265530i
$297$	−26.3016	+	13.8042i	−1.52617	+	0.800998i
$298$	15.3247	+	22.2017i	0.887738	+	1.28611i
$299$	3.02599	+	5.50624i	0.174998	+	0.318434i
$300$	−19.6632	+	28.4870i	−1.13525	+	1.64470i
$301$	−1.68865	+	13.9073i	−0.0973322	+	0.801603i
$302$	−39.1830	−	9.65775i	−2.25473	−	0.555741i
$303$	−5.36236	−	7.76872i	−0.308059	−	0.446301i
$304$	−13.3458	+	11.8233i	−0.765431	+	0.678113i
$305$	11.1953	+	5.87575i	0.641041	+	0.336444i
$306$	0.617651	+	5.08682i	0.0353088	+	0.290794i
$307$	2.02243	−	16.6562i	0.115426	−	0.950622i	−0.813809	−	0.581133i	$-0.802610\pi$
$307$	2.02243	−	16.6562i	0.115426	−	0.950622i	0.929235	−	0.369489i	$-0.120467\pi$
$308$	−9.19477	+	8.14585i	−0.523921	+	0.464153i
$309$	2.62455	−	3.80232i	0.149306	−	0.216307i
$310$	1.08479	+	8.93406i	0.0616120	+	0.507420i
$311$	−0.936419	+	7.71210i	−0.0530994	+	0.437313i	0.941779	+	0.336233i	$0.109153\pi$
$311$	−0.936419	+	7.71210i	−0.0530994	+	0.437313i	−0.994878	+	0.101080i	$0.967770\pi$
$312$	10.3657	+	11.2578i	0.586841	+	0.637348i
$313$	−1.27206	−	10.4763i	−0.0719009	−	0.592157i	−0.983478	−	0.181028i	$-0.942058\pi$
$313$	−1.27206	−	10.4763i	−0.0719009	−	0.592157i	0.911577	−	0.411129i	$-0.134865\pi$
$314$	−20.8992	+	5.15118i	−1.17941	+	0.290698i
$315$	−38.7191			−2.18157
$316$	−11.4552			−0.644406
$317$	10.9731	−	2.70462i	0.616309	−	0.151907i	0.0812116	−	0.996697i	$-0.474121\pi$
$317$	10.9731	−	2.70462i	0.616309	−	0.151907i	0.535097	+	0.844790i	$0.320275\pi$
$318$	4.31734	−	11.3839i	0.242104	−	0.638377i
$319$	44.6727			2.50119
$320$	−0.547658	−	1.44405i	−0.0306150	−	0.0807251i
$321$	14.7783	+	3.64253i	0.824845	+	0.203306i
$322$	4.57629	−	4.05424i	0.255027	−	0.225934i
$323$	2.02708	+	0.499630i	0.112790	+	0.0278002i
$324$	−0.577838	+	0.511920i	−0.0321021	+	0.0284400i
$325$	31.1840	−	22.4198i	1.72978	−	1.24363i
$326$	25.4365	+	22.5348i	1.40880	+	1.24809i
$327$	−17.6020	−	25.5010i	−0.973395	−	1.41021i
$328$	−6.70344	+	1.65225i	−0.370135	+	0.0912302i
$329$	−8.61298	+	12.4781i	−0.474849	+	0.687938i
$330$	−103.756	−	25.5735i	−5.71157	−	1.40777i
$331$	30.5818	+	7.53774i	1.68093	+	0.414311i	0.960291	−	0.279001i	$-0.0900033\pi$
$331$	30.5818	+	7.53774i	1.68093	+	0.414311i	0.720637	+	0.693313i	$0.243849\pi$
$332$	−0.125178	+	1.03093i	−0.00687004	+	0.0565798i
$333$	−12.0340	−	10.6612i	−0.659459	−	0.584229i
$334$	2.87429	+	7.57888i	0.157274	+	0.414698i
$335$	8.34606	−	4.38035i	0.455994	−	0.239324i
$336$	15.7548	−	22.8247i	0.859494	−	1.24519i
$337$	−27.6500			−1.50619			−0.753097	−	0.657910i	$-0.771441\pi$
$337$	−27.6500			−1.50619			−0.753097	+	0.657910i	$0.771441\pi$
$338$	9.00637	+	21.2515i	0.489882	+	1.15593i
$339$	−23.2000			−1.26005
$340$	−1.50916	+	2.18639i	−0.0818455	+	0.118574i
$341$	−6.12010	+	3.21208i	−0.331422	+	0.173944i
$342$	11.1707	+	29.4547i	0.604042	+	1.59273i
$343$	14.9319	+	13.2285i	0.806247	+	0.714272i
$344$	1.28613	−	10.5922i	0.0693434	−	0.571094i
$345$	18.8766	+	4.65266i	1.01628	+	0.250491i
$346$	1.94913	+	0.480418i	0.104786	+	0.0258274i
$347$	−10.3670	+	15.0192i	−0.556529	+	0.806271i	−0.995749	−	0.0921086i	$-0.970639\pi$
$347$	−10.3670	+	15.0192i	−0.556529	+	0.806271i	0.439220	+	0.898379i	$0.355255\pi$
$348$	26.1269	−	6.43971i	1.40055	−	0.345205i
$349$	14.2003	+	20.5726i	0.760123	+	1.10123i	0.991720	+	0.128416i	$0.0409893\pi$
$349$	14.2003	+	20.5726i	0.760123	+	1.10123i	−0.231598	+	0.972812i	$0.574395\pi$
$350$	−27.9744	−	24.7832i	−1.49529	−	1.32472i
$351$	18.4242	−	7.39463i	0.983413	−	0.394696i
$352$	23.5254	−	20.8417i	1.25391	−	1.11087i
$353$	10.1890	+	2.51135i	0.542303	+	0.133666i	0.500946	−	0.865479i	$-0.332986\pi$
$353$	10.1890	+	2.51135i	0.542303	+	0.133666i	0.0413575	+	0.999144i	$0.486832\pi$
$354$	−12.7501	+	11.2956i	−0.677661	+	0.600355i
$355$	4.19943	+	1.03507i	0.222883	+	0.0549357i
$356$	2.14403	+	5.65334i	0.113633	+	0.299626i
$357$	−3.24749			−0.171875
$358$	−0.917940	+	2.42041i	−0.0485147	+	0.127923i
$359$	4.46156	−	1.09968i	0.235472	−	0.0580386i	−0.119814	−	0.992796i	$-0.538230\pi$
$359$	4.46156	−	1.09968i	0.235472	−	0.0580386i	0.355286	+	0.934758i	$0.384384\pi$
$360$	29.4896			1.55424
$361$	−6.16521			−0.324485
$362$	−23.1050	+	5.69486i	−1.21437	+	0.299315i
$363$	−6.15335	−	50.6774i	−0.322967	−	2.65987i
$364$	6.66609	−	4.79261i	0.349398	−	0.251201i
$365$	−3.76018	+	30.9679i	−0.196817	+	1.62093i
$366$	1.92871	+	15.8844i	0.100815	+	0.830289i
$367$	−17.2695	+	25.0191i	−0.901459	+	1.30599i	0.0501709	+	0.998741i	$0.484023\pi$
$367$	−17.2695	+	25.0191i	−0.901459	+	1.30599i	−0.951630	+	0.307248i	$0.900592\pi$
$368$	−6.49141	+	5.75089i	−0.338388	+	0.299786i
$369$	−2.73839	+	22.5527i	−0.142555	+	1.17404i
$370$	−2.74856	−	22.6364i	−0.142891	−	1.17681i
$371$	4.25484	+	2.23311i	0.220900	+	0.115937i
$372$	−3.11632	+	2.76082i	−0.161574	+	0.143142i
$373$	2.29340	+	3.32256i	0.118748	+	0.172036i	0.877850	−	0.478936i	$-0.158977\pi$
$373$	2.29340	+	3.32256i	0.118748	+	0.172036i	−0.759102	+	0.650971i	$0.774362\pi$
$374$	−5.41946	−	1.33578i	−0.280234	−	0.0690714i
$375$	7.60104	−	62.6002i	0.392516	−	3.23266i
$376$	6.55991	−	9.50367i	0.338301	−	0.490114i
$377$	−29.7031	−	3.02974i	−1.52979	−	0.156039i
$378$	−10.9742	−	15.8989i	−0.564452	−	0.817750i
$379$	13.8529	−	7.27055i	0.711574	−	0.373463i	−0.0697702	−	0.997563i	$-0.522227\pi$
$379$	13.8529	−	7.27055i	0.711574	−	0.373463i	0.781344	+	0.624100i	$0.214534\pi$
$380$	−5.79151	+	15.2710i	−0.297098	+	0.783384i
$381$	−3.30108	−	27.1869i	−0.169120	−	1.39282i
$382$	−7.13067	+	10.3306i	−0.364837	+	0.528558i
$383$	−1.47263	+	0.362970i	−0.0752477	+	0.0185469i	−0.276760	−	0.960939i	$-0.589261\pi$
$383$	−1.47263	+	0.362970i	−0.0752477	+	0.0185469i	0.201512	+	0.979486i	$0.435414\pi$
$384$	−17.5558	+	25.4340i	−0.895892	+	1.29792i
$385$	14.9558	−	39.4351i	0.762216	−	2.00980i
$386$	−6.86985	+	18.1143i	−0.349666	+	0.921993i
$387$	−31.0888	−	16.3166i	−1.58033	−	0.829421i
$388$	10.7276	+	5.63030i	0.544613	+	0.285835i
$389$	−29.2377	+	7.20645i	−1.48241	+	0.365382i	−0.895789	−	0.444479i	$-0.853389\pi$
$389$	−29.2377	+	7.20645i	−1.48241	+	0.365382i	−0.586623	+	0.809860i	$0.699543\pi$
$390$	67.2532	+	24.0407i	3.40550	+	1.21735i
$391$	0.985978	+	0.243022i	0.0498631	+	0.0122901i
$392$	−3.48668	−	3.08893i	−0.176104	−	0.156015i
$393$	3.70180	−	30.4871i	0.186731	−	1.53787i
$394$	−38.7862	−	20.3566i	−1.95402	−	1.02555i
$395$	34.8250	−	18.2776i	1.75224	−	0.919645i
$396$	−10.9170	−	28.7857i	−0.548600	−	1.44654i
$397$	3.32524	+	2.94591i	0.166889	+	0.147851i	0.742434	−	0.669920i	$-0.233671\pi$
$397$	3.32524	+	2.94591i	0.166889	+	0.147851i	−0.575545	+	0.817770i	$0.695210\pi$
$398$	2.18892	+	18.0274i	0.109721	+	0.903631i
$399$	−19.3844	+	4.77782i	−0.970432	+	0.239190i
$400$	39.6813	+	35.1546i	1.98407	+	1.75773i
$401$	−10.7148	+	9.49248i	−0.535071	+	0.474032i	−0.886854	−	0.462050i	$-0.847114\pi$
$401$	−10.7148	+	9.49248i	−0.535071	+	0.474032i	0.351783	+	0.936082i	$0.385576\pi$
$402$	10.5624	+	5.54355i	0.526803	+	0.276487i
$403$	4.28712	−	1.72065i	0.213557	−	0.0857117i
$404$	3.41537	−	1.79253i	0.169921	−	0.0891815i
$405$	0.939884	−	2.47827i	0.0467032	−	0.123146i
$406$	3.50204	+	28.8419i	0.173803	+	1.43140i
$407$	15.5066	−	8.13850i	0.768635	−	0.403411i
$408$	2.47338			0.122451
$409$	8.50933	−	4.46604i	0.420759	−	0.220831i	−0.241036	−	0.970516i	$-0.577487\pi$
$409$	8.50933	−	4.46604i	0.420759	−	0.220831i	0.661795	+	0.749685i	$0.269795\pi$
$410$	−24.1184	+	21.3670i	−1.19112	+	1.05524i
$411$	−13.8288	−	20.0344i	−0.682123	−	0.988225i
$412$	1.41309	+	1.25189i	0.0696178	+	0.0616760i
$413$	−3.81908	−	5.53290i	−0.187925	−	0.272256i
$414$	5.43346	+	14.3268i	0.267040	+	0.704126i
$415$	−1.26437	−	3.33387i	−0.0620656	−	0.163653i
$416$	−17.0556	+	12.2622i	−0.836221	+	0.601204i
$417$	−20.9039	+	55.1190i	−1.02367	+	2.69919i
$418$	−34.3142			−1.67836
$419$	−4.48047	−	11.8140i	−0.218885	−	0.577153i	0.779927	−	0.625870i	$-0.215256\pi$
$419$	−4.48047	−	11.8140i	−0.218885	−	0.577153i	−0.998813	+	0.0487173i	$0.984487\pi$
$420$	3.06222	−	25.2196i	0.149421	−	1.23059i
$421$	−9.79439	−	5.14049i	−0.477349	−	0.250532i	0.208847	−	0.977948i	$-0.433029\pi$
$421$	−9.79439	−	5.14049i	−0.477349	−	0.250532i	−0.686197	+	0.727416i	$0.740721\pi$
$422$	−5.84036	−	8.46122i	−0.284304	−	0.411886i
$423$	−21.5858	−	31.2725i	−1.04954	−	1.52052i
$424$	−3.24062	−	1.70081i	−0.157378	−	0.0825985i
$425$	0.748239	−	6.16230i	0.0362949	−	0.298915i
$426$	1.94098	+	5.11795i	0.0940409	+	0.247965i
$427$	−6.31528			−0.305618
$428$	−2.20541	+	5.81519i	−0.106603	+	0.281088i
$429$	1.05206	+	54.8416i	0.0507937	+	2.64778i
$430$	−17.6586	−	46.5618i	−0.851571	−	2.24541i
$431$	8.84728	+	23.3284i	0.426158	+	1.12369i	0.960466	+	0.278397i	$0.0898031\pi$
$431$	8.84728	+	23.3284i	0.426158	+	1.12369i	−0.534308	+	0.845290i	$0.679428\pi$
$432$	15.5668	+	22.5523i	0.748956	+	1.08505i
$433$	17.9109	+	15.8677i	0.860745	+	0.762553i	0.972922	−	0.231135i	$-0.0742439\pi$
$433$	17.9109	+	15.8677i	0.860745	+	0.762553i	−0.112177	+	0.993688i	$0.535782\pi$
$434$	−2.55358	−	3.69949i	−0.122576	−	0.177581i
$435$	−69.1536	+	61.2647i	−3.31566	+	2.93742i
$436$	11.2110	−	5.88400i	0.536911	−	0.281793i
$437$	6.24288			0.298638
$438$	−34.9571	+	18.3469i	−1.67032	+	0.876650i
$439$	3.97911	+	32.7710i	0.189913	+	1.56407i	0.706422	+	0.707791i	$0.250308\pi$
$439$	3.97911	+	32.7710i	0.189913	+	1.56407i	−0.516509	+	0.856281i	$0.672769\pi$
$440$	−11.3908	+	30.0350i	−0.543033	+	1.43186i
$441$	−13.5723	+	7.12328i	−0.646299	+	0.339204i
$442$	3.51282	+	1.25571i	0.167088	+	0.0597282i
$443$	−19.9739	−	10.4831i	−0.948987	−	0.498067i	−0.0821288	−	0.996622i	$-0.526172\pi$
$443$	−19.9739	−	10.4831i	−0.948987	−	0.498067i	−0.866858	+	0.498555i	$0.833864\pi$
$444$	7.89589	−	6.99515i	0.374722	−	0.331975i
$445$	−15.5384	−	13.7658i	−0.736589	−	0.652561i
$446$	36.8555	−	9.08407i	1.74516	−	0.430143i
$447$	−5.16480	−	42.5359i	−0.244286	−	2.01188i
$448$	0.577413	+	0.511543i	0.0272802	+	0.0241682i
$449$	8.35639	+	22.0340i	0.394362	+	1.03985i	0.974313	+	0.225196i	$0.0723024\pi$
$449$	8.35639	+	22.0340i	0.394362	+	1.03985i	−0.579951	+	0.814651i	$0.696928\pi$
$450$	82.9364	−	43.5284i	3.90966	−	2.05195i
$451$	−21.9120	−	11.5003i	−1.03179	−	0.541527i
$452$	1.14267	−	9.41072i	0.0537466	−	0.442643i
$453$	47.9779	+	42.5048i	2.25420	+	1.99705i
$454$	−32.1642	−	7.92775i	−1.50954	−	0.372068i
$455$	−12.6187	+	25.2062i	−0.591572	+	1.18169i
$456$	14.7637	−	3.63893i	0.691374	−	0.170409i
$457$	36.3950	+	19.1016i	1.70249	+	0.893534i	0.979177	+	0.203009i	$0.0650722\pi$
$457$	36.3950	+	19.1016i	1.70249	+	0.893534i	0.723309	+	0.690524i	$0.242620\pi$
$458$	18.4338	+	9.67482i	0.861356	+	0.452075i
$459$	1.13783	−	3.00022i	0.0531094	−	0.140038i
$460$	−2.81701	+	7.42785i	−0.131344	+	0.346325i
$461$	16.6601	−	24.1364i	0.775940	−	1.12414i	−0.213178	−	0.977013i	$-0.568381\pi$
$461$	16.6601	−	24.1364i	0.775940	−	1.12414i	0.989117	−	0.147129i	$-0.0470033\pi$
$462$	51.8247	−	12.7736i	2.41110	−	0.594283i
$463$	3.54342	−	5.13352i	0.164677	−	0.238575i	−0.731955	−	0.681353i	$-0.761392\pi$
$463$	3.54342	−	5.13352i	0.164677	−	0.238575i	0.896631	+	0.442778i	$0.146007\pi$
$464$	−4.96760	−	40.9119i	−0.230615	−	1.89929i
$465$	5.06886	−	13.3655i	0.235063	−	0.619810i
$466$	21.5521	−	11.3114i	0.998381	−	0.523991i
$467$	12.1274	+	17.5696i	0.561191	+	0.813025i	0.996172	−	0.0874142i	$-0.0278603\pi$
$467$	12.1274	+	17.5696i	0.561191	+	0.813025i	−0.434981	+	0.900440i	$0.643245\pi$
$468$	5.30648	+	19.8801i	0.245292	+	0.918960i
$469$	−2.67446	+	3.87463i	−0.123495	+	0.178914i
$470$	6.49628	−	53.5016i	0.299651	−	2.46785i
$471$	33.1946	+	8.18174i	1.52953	+	0.376995i
$472$	2.90873	+	4.21402i	0.133885	+	0.193966i
$473$	28.6268	−	25.3611i	1.31626	−	1.16611i
$474$	44.0728	+	23.1312i	2.02433	+	1.06245i
$475$	−4.59993	−	37.8838i	−0.211059	−	1.73823i
$476$	0.159948	−	1.31729i	0.00733122	−	0.0603780i
$477$	−9.01426	+	7.98593i	−0.412734	+	0.365651i
$478$	6.62482	−	9.59772i	0.303012	−	0.438989i
$479$	−4.32582	−	35.6264i	−0.197652	−	1.62781i	−0.667183	−	0.744894i	$-0.732500\pi$
$479$	−4.32582	−	35.6264i	−0.197652	−	1.62781i	0.469531	−	0.882916i	$-0.344423\pi$
$480$	−7.83489	+	64.5261i	−0.357612	+	2.94520i
$481$	−10.8624	+	4.35965i	−0.495281	+	0.198783i
$482$	−3.55038	−	29.2400i	−0.161715	−	1.33184i
$483$	−9.42861	+	2.32394i	−0.429017	+	0.105743i
$484$	20.8596			0.948163
$485$	−41.5966			−1.88881
$486$	−25.2191	+	6.21594i	−1.14396	+	0.281961i
$487$	−10.8172	+	28.5227i	−0.490175	+	1.29249i	0.430653	+	0.902518i	$0.358283\pi$
$487$	−10.8172	+	28.5227i	−0.490175	+	1.29249i	−0.920828	+	0.389968i	$0.872486\pi$
$488$	4.80991			0.217735
$489$	−19.1401	−	50.4682i	−0.865544	−	2.28225i
$490$	−21.1083	−	5.20272i	−0.953575	−	0.235035i
$491$	4.42609	−	3.92118i	0.199747	−	0.176960i	−0.557320	−	0.830298i	$-0.688170\pi$
$491$	4.42609	−	3.92118i	0.199747	−	0.176960i	0.757067	+	0.653338i	$0.226632\pi$
$492$	−14.4731	−	3.56729i	−0.652496	−	0.160826i
$493$	−3.61209	+	3.20003i	−0.162680	+	0.144122i
$494$	22.8156	+	2.32721i	1.02652	+	0.104706i
$495$	79.1184	+	70.0928i	3.55611	+	3.15044i
$496$	3.62222	+	5.24769i	0.162642	+	0.235628i
$497$	−2.09756	+	0.517003i	−0.0940885	+	0.0231907i
$498$	2.56335	−	3.71365i	0.114866	−	0.166413i
$499$	−31.1426	−	7.67597i	−1.39414	−	0.343624i	−0.530477	−	0.847700i	$-0.677987\pi$
$499$	−31.1426	−	7.67597i	−1.39414	−	0.343624i	−0.863659	+	0.504076i	$0.831833\pi$
$500$	25.0184	+	6.16649i	1.11886	+	0.275774i
$501$	1.55183	−	12.7805i	0.0693306	−	0.570989i
$502$	24.7763	+	21.9499i	1.10582	+	0.979671i
$503$	12.3090	+	32.4561i	0.548830	+	1.44715i	0.866612	+	0.498983i	$0.166293\pi$
$503$	12.3090	+	32.4561i	0.548830	+	1.44715i	−0.317781	+	0.948164i	$0.602938\pi$
$504$	−13.0425	+	6.84523i	−0.580959	+	0.304911i
$505$	−7.52299	+	10.8989i	−0.334768	+	0.484996i
$506$	−16.6905			−0.741984
$507$	3.01988	−	36.5357i	0.134118	−	1.62261i
$508$	11.1905			0.496499
$509$	14.8199	−	21.4703i	0.656879	−	0.951653i	−0.343045	−	0.939319i	$-0.611458\pi$
$509$	14.8199	−	21.4703i	0.656879	−	0.951653i	0.999924	−	0.0123345i	$-0.00392628\pi$
$510$	10.2212	−	5.36452i	0.452604	−	0.237545i
$511$	−5.52533	−	14.5691i	−0.244426	−	0.644499i
$512$	−10.4898	−	9.29316i	−0.463589	−	0.410704i
$513$	2.37774	−	19.5824i	0.104980	−	0.864585i
$514$	−49.6100	−	12.2278i	−2.18820	−	0.539343i
$515$	−6.29340	−	1.55118i	−0.277320	−	0.0683533i
$516$	13.0866	−	18.9592i	0.576104	−	0.834631i
$517$	40.1886	−	9.90560i	1.76749	−	0.435648i
$518$	6.47005	+	9.37349i	0.284278	+	0.411847i
$519$	−2.38663	−	2.11437i	−0.104761	−	0.0928105i
$520$	9.61075	−	19.1978i	0.421459	−	0.841881i
$521$	−5.98847	+	5.30532i	−0.262359	+	0.232430i	−0.784039	−	0.620711i	$-0.786844\pi$
$521$	−5.98847	+	5.30532i	−0.262359	+	0.232430i	0.521680	+	0.853141i	$0.325306\pi$
$522$	−70.6986	−	17.4256i	−3.09439	−	0.762700i
$523$	15.7133	−	13.9208i	0.687097	−	0.608715i	−0.245602	−	0.969371i	$-0.578986\pi$
$523$	15.7133	−	13.9208i	0.687097	−	0.608715i	0.932699	+	0.360656i	$0.117447\pi$
$524$	12.1843	+	3.00316i	0.532273	+	0.131194i
$525$	21.0497	+	55.5035i	0.918685	+	2.42237i
$526$	−7.02061			−0.306113
$527$	0.264761	−	0.698117i	0.0115332	−	0.0304105i
$528$	−73.5126	+	18.1192i	−3.19923	+	0.788538i
$529$	−19.9634			−0.867976
$530$	−17.0807			−0.741939
$531$	16.3595	−	4.03225i	0.709942	−	0.174985i
$532$	−0.983311	−	8.09829i	−0.0426319	−	0.351106i
$533$	13.7894	+	9.13266i	0.597284	+	0.395580i
$534$	3.16669	−	26.0800i	0.137036	−	1.12859i
$535$	−2.57386	−	21.1977i	−0.111278	−	0.916455i
$536$	2.03695	−	2.95103i	0.0879829	−	0.127465i
$537$	3.07756	−	2.72648i	0.132807	−	0.117656i
$538$	5.20505	−	42.8675i	0.224406	−	1.84815i
$539$	−2.01253	−	16.5747i	−0.0866860	−	0.713923i
$540$	22.2264	+	11.6653i	0.956474	+	0.501996i
$541$	24.1928	−	21.4329i	1.04013	−	0.921473i	0.0431434	−	0.999069i	$-0.486263\pi$
$541$	24.1928	−	21.4329i	1.04013	−	0.921473i	0.996985	+	0.0775956i	$0.0247243\pi$
$542$	−2.43256	−	3.52417i	−0.104487	−	0.151376i
$543$	36.6982	+	9.04528i	1.57487	+	0.388170i
$544$	−0.409238	+	3.37038i	−0.0175460	+	0.144504i
$545$	−24.6943	+	35.7759i	−1.05779	+	1.53247i
$546$	−35.3247	+	4.97845i	−1.51176	+	0.213058i
$547$	−0.876111	−	1.26927i	−0.0374598	−	0.0542699i	0.803807	−	0.594891i	$-0.202805\pi$
$547$	−0.876111	−	1.26927i	−0.0374598	−	0.0542699i	−0.841266	+	0.540621i	$0.818189\pi$
$548$	8.80777	−	4.62267i	0.376249	−	0.197471i
$549$	5.61246	−	14.7988i	0.239534	−	0.631599i
$550$	12.2980	+	101.284i	0.524390	+	4.31874i
$551$	−16.8527	+	24.4153i	−0.717949	+	1.04013i
$552$	7.18112	−	1.76999i	0.305649	−	0.0753356i
$553$	−11.1595	+	16.1674i	−0.474552	+	0.687507i
$554$	−6.02471	+	15.8859i	−0.255965	+	0.674926i
$555$	−12.8431	+	33.8644i	−0.545158	+	1.43746i
$556$	−21.3286	−	11.1941i	−0.904534	−	0.474736i
$557$	29.5274	+	15.4972i	1.25112	+	0.656637i	0.954458	−	0.298347i	$-0.0964352\pi$
$557$	29.5274	+	15.4972i	1.25112	+	0.656637i	0.296659	+	0.954983i	$0.404127\pi$
$558$	10.9386	−	2.69611i	0.463066	−	0.114135i
$559$	−20.7541	+	14.9212i	−0.877804	+	0.631100i
$560$	−37.7783	−	9.31151i	−1.59642	−	0.393483i
$561$	6.63590	+	5.87889i	0.280168	+	0.248207i
$562$	−0.317922	+	2.61833i	−0.0134107	+	0.110447i
$563$	23.0332	+	12.0887i	0.970732	+	0.509479i	0.874050	−	0.485836i	$-0.161485\pi$
$563$	23.0332	+	12.0887i	0.970732	+	0.509479i	0.0966817	+	0.995315i	$0.469177\pi$
$564$	22.0765	−	11.5866i	0.929587	−	0.487885i
$565$	11.5416	+	30.4328i	0.485560	+	1.28032i
$566$	20.3197	+	18.0017i	0.854102	+	0.756668i
$567$	0.159578	+	1.31424i	0.00670164	+	0.0551930i
$568$	1.59757	−	0.393765i	0.0670324	−	0.0165220i
$569$	−20.7092	−	18.3468i	−0.868175	−	0.769136i	0.106134	−	0.994352i	$-0.466153\pi$
$569$	−20.7092	−	18.3468i	−0.868175	−	0.769136i	−0.974309	+	0.225216i	$0.927691\pi$
$570$	53.1185	−	47.0589i	2.22489	−	1.97108i
$571$	−12.5880	−	6.60668i	−0.526791	−	0.276481i	0.180291	−	0.983613i	$-0.442296\pi$
$571$	−12.5880	−	6.60668i	−0.526791	−	0.276481i	−0.707081	+	0.707132i	$0.749989\pi$
$572$	−22.2975	−	2.27436i	−0.932304	−	0.0950958i
$573$	17.6538	−	9.26543i	0.737499	−	0.387069i
$574$	5.70714	−	15.0485i	0.238211	−	0.628112i
$575$	−2.23742	−	18.4268i	−0.0933069	−	0.768451i
$576$	−1.71187	+	0.898460i	−0.0713280	+	0.0374358i
$577$	−17.4359			−0.725868			−0.362934	−	0.931815i	$-0.618225\pi$
$577$	−17.4359			−0.725868			−0.362934	+	0.931815i	$0.618225\pi$
$578$	−26.1919	+	13.7465i	−1.08944	+	0.571781i
$579$	23.0324	−	20.4049i	0.957194	−	0.848000i
$580$	−21.4451	−	31.0686i	−0.890459	−	1.29005i
$581$	1.33307	+	1.18100i	0.0553050	+	0.0489959i
$582$	−29.9044	−	43.3240i	−1.23958	−	1.79584i
$583$	−4.65174	−	12.2656i	−0.192655	−	0.507990i
$584$	4.20826	+	11.0963i	0.174139	+	0.459167i
$585$	−47.8524	−	51.9708i	−1.97845	−	2.14873i
$586$	−15.8959	+	41.9139i	−0.656652	+	1.73145i
$587$	−30.5982			−1.26292			−0.631462	−	0.775407i	$-0.717545\pi$
$587$	−30.5982			−1.26292			−0.631462	+	0.775407i	$0.717545\pi$
$588$	−3.56633	−	9.40365i	−0.147073	−	0.387800i
$589$	0.553273	−	4.55661i	0.0227972	−	0.187752i
$590$	21.1601	+	11.1057i	0.871148	+	0.457213i
$591$	39.5227	+	57.2586i	1.62575	+	2.35530i
$592$	−9.17768	−	13.2962i	−0.377200	−	0.546469i
$593$	−21.3311	−	11.1954i	−0.875963	−	0.459741i	−0.0340912	−	0.999419i	$-0.510854\pi$
$593$	−21.3311	−	11.1954i	−0.875963	−	0.459741i	−0.841872	+	0.539678i	$0.818546\pi$
$594$	−6.35694	+	52.3541i	−0.260829	+	2.14812i
$595$	1.61557	+	4.25992i	0.0662320	+	0.174639i
$596$	17.5084			0.717173
$597$	10.2281	−	26.9692i	0.418607	−	1.10378i
$598$	11.0976	+	1.13196i	0.453814	+	0.0462894i
$599$	0.124746	+	0.328928i	0.00509699	+	0.0134396i	0.937541	−	0.347876i	$-0.113097\pi$
$599$	0.124746	+	0.328928i	0.00509699	+	0.0134396i	−0.932444	+	0.361316i	$0.882328\pi$
$600$	−16.0321	−	42.2732i	−0.654508	−	1.72580i
$601$	10.9535	+	15.8689i	0.446804	+	0.647307i	0.980073	−	0.198639i	$-0.0636520\pi$
$601$	10.9535	+	15.8689i	0.446804	+	0.647307i	−0.533269	+	0.845946i	$0.679037\pi$
$602$	18.6180	+	16.4941i	0.758812	+	0.672249i
$603$	−6.70274	−	9.71059i	−0.272957	−	0.395446i
$604$	−19.6045	+	17.3680i	−0.797694	+	0.706695i
$605$	−63.4153	+	33.2829i	−2.57820	+	1.35314i
$606$	−16.7599			−0.680825
$607$	26.4862	−	13.9010i	1.07504	−	0.564225i	0.168223	−	0.985749i	$-0.446197\pi$
$607$	26.4862	−	13.9010i	1.07504	−	0.564225i	0.906817	+	0.421524i	$0.138505\pi$
$608$	2.51587	+	20.7200i	0.102032	+	0.840308i
$609$	16.3639	−	43.1479i	0.663097	−	1.74844i
$610$	19.8769	−	10.4322i	0.804794	−	0.422388i
$611$	−27.3934	+	3.86065i	−1.10822	+	0.156185i
$612$	2.94471	+	1.54551i	0.119033	+	0.0624734i
$613$	−7.71748	+	6.83709i	−0.311706	+	0.276148i	−0.804442	−	0.594031i	$-0.797535\pi$
$613$	−7.71748	+	6.83709i	−0.311706	+	0.276148i	0.492736	+	0.870179i	$0.335997\pi$
$614$	−22.2980	−	19.7543i	−0.899876	−	0.797221i
$615$	49.6915	−	12.2478i	2.00375	−	0.493881i
$616$	−1.93398	−	15.9277i	−0.0779222	−	0.641747i
$617$	11.9624	+	10.5977i	0.481586	+	0.426648i	0.868666	−	0.495398i	$-0.164978\pi$
$617$	11.9624	+	10.5977i	0.481586	+	0.426648i	−0.387080	+	0.922046i	$0.626516\pi$
$618$	−2.90882	−	7.66992i	−0.117010	−	0.308529i
$619$	21.8501	−	11.4678i	0.878229	−	0.460930i	0.0355634	−	0.999367i	$-0.488677\pi$
$619$	21.8501	−	11.4678i	0.878229	−	0.460930i	0.842666	+	0.538437i	$0.180985\pi$
$620$	5.17185	+	2.71440i	0.207706	+	0.109013i
$621$	1.15654	−	9.52495i	0.0464103	−	0.382223i
$622$	10.3243	+	9.14658i	0.413969	+	0.366744i
$623$	10.0676	+	2.48143i	0.403349	+	0.0994165i
$624$	50.1077	−	7.06186i	2.00591	−	0.282701i
$625$	−34.1846	+	8.42574i	−1.36738	+	0.337030i
$626$	−16.5908	−	8.70754i	−0.663103	−	0.348023i
$627$	48.2591	+	25.3283i	1.92728	+	1.01152i
$628$	−4.95373	+	13.0619i	−0.197675	+	0.521227i
$629$	−0.670830	+	1.76883i	−0.0267478	+	0.0705280i
$630$	−39.0514	+	56.5758i	−1.55585	+	2.25403i
$631$	−26.8293	+	6.61282i	−1.06806	+	0.263252i	−0.733895	−	0.679263i	$-0.762299\pi$
$631$	−26.8293	+	6.61282i	−1.06806	+	0.263252i	−0.334162	+	0.942516i	$0.608453\pi$
$632$	8.49944	−	12.3136i	0.338090	−	0.489808i
$633$	1.96834	+	16.2107i	0.0782344	+	0.644318i
$634$	7.11531	−	18.7615i	0.282585	−	0.745115i
$635$	−34.0203	+	17.8553i	−1.35006	+	0.708564i
$636$	−4.48871	−	6.50302i	−0.177989	−	0.257861i
$637$	0.214032	+	11.1571i	0.00848026	+	0.442059i
$638$	45.0562	−	65.2751i	1.78379	−	2.58427i
$639$	0.652614	−	5.37476i	0.0258170	−	0.212622i
$640$	42.0970	+	10.3760i	1.66403	+	0.410147i
$641$	−8.83724	−	12.8029i	−0.349050	−	0.505686i	0.608656	−	0.793434i	$-0.291709\pi$
$641$	−8.83724	−	12.8029i	−0.349050	−	0.505686i	−0.957706	+	0.287748i	$0.907093\pi$
$642$	20.2276	−	17.9201i	0.798318	−	0.707248i
$643$	−35.1844	−	18.4662i	−1.38754	−	0.728237i	−0.405004	−	0.914315i	$-0.632730\pi$
$643$	−35.1844	−	18.4662i	−1.38754	−	0.728237i	−0.982535	+	0.186078i	$0.940422\pi$
$644$	−0.478285	−	3.93904i	−0.0188471	−	0.155220i
$645$	−9.53385	+	78.5183i	−0.375395	+	3.09166i
$646$	2.77453	−	2.45802i	0.109162	−	0.0967095i
$647$	2.62337	−	3.80061i	0.103135	−	0.149417i	−0.768018	−	0.640428i	$-0.778757\pi$
$647$	2.62337	−	3.80061i	0.103135	−	0.149417i	0.871154	+	0.491011i	$0.163372\pi$
$648$	−0.121539	−	1.00097i	−0.00477452	−	0.0393217i
$649$	−2.21225	+	18.2195i	−0.0868385	+	0.715179i
$650$	−1.30789	−	68.1778i	−0.0512997	−	2.67415i
$651$	0.860615	+	7.08780i	0.0337302	+	0.277793i
$652$	21.4144	−	5.27817i	0.838651	−	0.206709i
$653$	40.3536			1.57916			0.789579	−	0.613649i	$-0.210299\pi$
$653$	40.3536			1.57916			0.789579	+	0.613649i	$0.210299\pi$
$654$	−55.0147			−2.15125
$655$	−41.8332	+	10.3110i	−1.63456	+	0.402883i
$656$	−8.09551	+	21.3461i	−0.316076	+	0.833425i
$657$	39.0508			1.52351
$658$	9.54584	+	25.1703i	0.372136	+	0.981241i
$659$	0.396866	+	0.0978186i	0.0154597	+	0.00381047i	0.247038	−	0.969006i	$-0.420543\pi$
$659$	0.396866	+	0.0978186i	0.0154597	+	0.00381047i	−0.231578	+	0.972816i	$0.574389\pi$
$660$	−51.9122	+	45.9902i	−2.02068	+	1.79016i
$661$	−15.5088	−	3.82258i	−0.603223	−	0.148681i	−0.0741353	−	0.997248i	$-0.523620\pi$
$661$	−15.5088	−	3.82258i	−0.603223	−	0.148681i	−0.529088	+	0.848567i	$0.677466\pi$
$662$	41.8583	−	37.0832i	1.62687	−	1.44128i
$663$	−4.01352	−	4.35895i	−0.155872	−	0.169287i
$664$	−1.01531	−	0.899482i	−0.0394015	−	0.0349067i
$665$	15.9107	+	23.0507i	0.616992	+	0.893868i
$666$	−27.7152	+	6.83119i	−1.07394	+	0.264703i
$667$	−8.19720	+	11.8757i	−0.317397	+	0.459829i
$668$	5.10776	+	1.25895i	0.197625	+	0.0487103i
$669$	−58.5385	−	14.4284i	−2.26323	−	0.557836i
$670$	2.01719	−	16.6131i	0.0779310	−	0.641819i
$671$	12.9046	+	11.4325i	0.498177	+	0.441347i
$672$	−11.5128	−	30.3569i	−0.444117	−	1.17104i
$673$	−12.4922	+	6.55639i	−0.481537	+	0.252730i	−0.687982	−	0.725728i	$-0.741503\pi$
$673$	−12.4922	+	6.55639i	−0.481537	+	0.252730i	0.206445	+	0.978458i	$0.433811\pi$
$674$	−27.8874	+	40.4018i	−1.07418	+	1.55622i
$675$	−58.6526			−2.25754
$676$	14.6714	+	3.02446i	0.564285	+	0.116325i
$677$	−10.5272			−0.404595			−0.202297	−	0.979324i	$-0.564841\pi$
$677$	−10.5272			−0.404595			−0.202297	+	0.979324i	$0.564841\pi$
$678$	−23.3991	+	33.8995i	−0.898638	+	1.30190i
$679$	18.3971	−	9.65554i	0.706016	−	0.370546i
$680$	−1.23047	−	3.24448i	−0.0471863	−	0.124420i
$681$	39.3836	+	34.8909i	1.50918	+	1.33702i
$682$	−1.47919	+	12.1822i	−0.0566412	+	0.466482i
$683$	41.5990	+	10.2532i	1.59174	+	0.392329i	0.932953	−	0.359999i	$-0.117223\pi$
$683$	41.5990	+	10.2532i	1.59174	+	0.392329i	0.658788	+	0.752328i	$0.271069\pi$
$684$	19.8509	+	4.89281i	0.759019	+	0.187081i
$685$	−19.4007	+	28.1068i	−0.741263	+	1.07391i
$686$	34.3894	−	8.47622i	1.31299	−	0.323623i
$687$	−18.7839	−	27.2131i	−0.716649	−	1.03825i
$688$	−26.4094	−	23.3967i	−1.00685	−	0.891989i
$689$	2.26109	+	8.47094i	0.0861408	+	0.322717i
$690$	25.8370	−	22.8896i	0.983598	−	0.871392i
$691$	−26.9354	−	6.63898i	−1.02467	−	0.252559i	−0.309049	−	0.951046i	$-0.600011\pi$
$691$	−26.9354	−	6.63898i	−1.02467	−	0.252559i	−0.715623	+	0.698487i	$0.753857\pi$
$692$	0.975210	−	0.863960i	0.0370719	−	0.0328429i
$693$	−51.2622	−	12.6350i	−1.94729	−	0.479964i
$694$	11.4898	+	30.2961i	0.436147	+	1.15003i
$695$	82.7021			3.13707
$696$	−12.4632	+	32.8628i	−0.472417	+	1.24566i
$697$	2.59553	−	0.639740i	0.0983126	−	0.0242319i
$698$	44.3826			1.67991
$699$	−38.6599			−1.46225
$700$	−23.5509	+	5.80478i	−0.890141	+	0.219400i
$701$	−5.23550	−	43.1182i	−0.197742	−	1.62855i	−0.666696	−	0.745330i	$-0.732292\pi$
$701$	−5.23550	−	43.1182i	−0.197742	−	1.62855i	0.468954	−	0.883223i	$-0.344631\pi$
$702$	7.77745	−	34.3793i	0.293541	−	1.29756i
$703$	−1.40184	+	11.5452i	−0.0528714	+	0.435435i
$704$	−0.253841	−	2.09057i	−0.00956700	−	0.0787913i
$705$	−48.6275	+	70.4491i	−1.83142	+	2.65327i
$706$	13.9460	−	12.3550i	0.524863	−	0.464988i
$707$	0.797326	−	6.56657i	0.0299865	−	0.246961i
$708$	1.33256	+	10.9746i	0.0500808	+	0.412452i
$709$	−35.8028	−	18.7907i	−1.34460	−	0.705701i	−0.369871	−	0.929083i	$-0.620598\pi$
$709$	−35.8028	−	18.7907i	−1.34460	−	0.705701i	−0.974731	+	0.223382i	$0.928290\pi$
$710$	5.74790	−	5.09220i	0.215715	−	0.191107i
$711$	−27.9680	−	40.5187i	−1.04888	−	1.51957i
$712$	−7.66776	−	1.88993i	−0.287362	−	0.0708283i
$713$	0.269114	−	2.21635i	0.0100784	−	0.0830030i
$714$	−3.27536	+	4.74518i	−0.122577	+	0.177584i
$715$	71.4155	−	28.6628i	2.67079	−	1.07193i
$716$	0.954376	+	1.38265i	0.0356667	+	0.0516722i
$717$	−16.4015	+	8.60815i	−0.612523	+	0.321477i
$718$	2.89302	−	7.62827i	0.107967	−	0.284685i
$719$	−2.19567	−	18.0830i	−0.0818847	−	0.674381i	−0.974630	−	0.223820i	$-0.928147\pi$
$719$	−2.19567	−	18.0830i	−0.0818847	−	0.674381i	0.892746	−	0.450561i	$-0.148776\pi$
$720$	55.3940	−	80.2520i	2.06441	−	2.99082i
$721$	3.14347	−	0.774796i	0.117069	−	0.0288549i
$722$	−6.21813	+	9.00851i	−0.231415	+	0.335262i
$723$	−16.5897	+	43.7434i	−0.616978	+	1.62684i
$724$	−5.47657	+	14.4405i	−0.203535	+	0.536678i
$725$	78.1055	+	40.9929i	2.90076	+	1.52244i
$726$	−80.2552	−	42.1212i	−2.97855	−	1.56326i
$727$	−2.84010	+	0.700023i	−0.105334	+	0.0259624i	−0.291630	−	0.956531i	$-0.594198\pi$
$727$	−2.84010	+	0.700023i	−0.105334	+	0.0259624i	0.186297	+	0.982494i	$0.440351\pi$
$728$	0.205678	+	10.7216i	0.00762293	+	0.397368i
$729$	42.0075	+	10.3539i	1.55583	+	0.383478i
$730$	41.4573	+	36.7280i	1.53440	+	1.35936i
$731$	−0.497980	+	4.10124i	−0.0184185	+	0.151690i
$732$	9.19533	+	4.82608i	0.339869	+	0.178377i
$733$	−14.9995	+	7.87233i	−0.554018	+	0.290771i	−0.718405	−	0.695625i	$-0.755128\pi$
$733$	−14.9995	+	7.87233i	−0.554018	+	0.290771i	0.164387	+	0.986396i	$0.447435\pi$
$734$	19.1399	+	50.4678i	0.706466	+	1.86280i
$735$	25.8462	+	22.8977i	0.953351	+	0.844595i
$736$	1.22372	+	10.0783i	0.0451071	+	0.371490i
$737$	12.4792	−	3.07584i	0.459677	−	0.113300i
$738$	30.1917	+	26.7475i	1.11137	+	0.984590i
$739$	33.1754	−	29.3908i	1.22038	−	1.08116i	0.226123	−	0.974099i	$-0.427395\pi$
$739$	33.1754	−	29.3908i	1.22038	−	1.08116i	0.994253	−	0.107060i	$-0.0341435\pi$
$740$	−13.1040	−	6.87752i	−0.481713	−	0.252823i
$741$	−30.3699	−	20.1139i	−1.11567	−	0.738902i
$742$	7.55435	−	3.96483i	0.277329	−	0.145553i
$743$	14.1278	−	37.2520i	0.518300	−	1.36664i	−0.379071	−	0.925368i	$-0.623756\pi$
$743$	14.1278	−	37.2520i	0.518300	−	1.36664i	0.897371	−	0.441277i	$-0.145474\pi$
$744$	−0.655471	−	5.39829i	−0.0240307	−	0.197911i
$745$	−53.2274	+	27.9359i	−1.95010	+	1.02349i
$746$	7.16795			0.262437
$747$	−3.95218	+	2.07427i	−0.144603	+	0.0758934i
$748$	−2.71152	+	2.40220i	−0.0991430	+	0.0878330i
$749$	6.05882	+	8.77772i	0.221385	+	0.320731i
$750$	−83.8042	−	74.2440i	−3.06010	−	2.71101i
$751$	9.40893	+	13.6312i	0.343337	+	0.497409i	0.956174	−	0.292800i	$-0.0945871\pi$
$751$	9.40893	+	13.6312i	0.343337	+	0.497409i	−0.612837	+	0.790210i	$0.709972\pi$
$752$	−13.5407	−	35.7038i	−0.493777	−	1.30198i
$753$	−18.6433	−	49.1582i	−0.679398	−	1.79143i
$754$	−34.3850	+	40.3459i	−1.25223	+	1.46931i
$755$	31.8877	−	84.0809i	1.16051	−	3.06002i
$756$	−12.5380			−0.456001
$757$	−0.335966	−	0.885870i	−0.0122109	−	0.0321975i	0.928772	−	0.370651i	$-0.120865\pi$
$757$	−0.335966	−	0.885870i	−0.0122109	−	0.0321975i	−0.940983	+	0.338454i	$0.890096\pi$
$758$	3.34816	−	27.5746i	0.121611	−	1.00155i
$759$	23.4734	+	12.3198i	0.852030	+	0.447180i
$760$	−12.1181	−	17.5561i	−0.439570	−	0.636827i
$761$	−20.6723	−	29.9490i	−0.749370	−	1.08565i	−0.993267	−	0.115849i	$-0.963041\pi$
$761$	−20.6723	−	29.9490i	−0.749370	−	1.08565i	0.243897	−	0.969801i	$-0.421574\pi$
$762$	−43.0544	−	22.5967i	−1.55970	−	0.818593i
$763$	2.61724	−	21.5549i	0.0947504	−	0.780339i
$764$	2.88888	+	7.61735i	0.104516	+	0.275586i
$765$	−11.4182			−0.412826
$766$	−0.954900	+	2.51786i	−0.0345019	+	0.0909741i
$767$	2.70660	−	11.9642i	0.0977295	−	0.432002i
$768$	20.2380

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.g (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00858 - 1.46118i) q^{2} +(-2.49701 + 1.31053i) q^{3} +(-0.408612 - 1.07742i) q^{4} +(2.96132 + 2.62350i) q^{5} +(-0.603512 + 4.97037i) q^{6} +(-1.91869 - 0.472914i) q^{7} +(1.46133 + 0.360186i) q^{8} +(2.81336 - 4.07585i) q^{9} +O(q^{10})\)	\(q+(1.00858 - 1.46118i) q^{2} +(-2.49701 + 1.31053i) q^{3} +(-0.408612 - 1.07742i) q^{4} +(2.96132 + 2.62350i) q^{5} +(-0.603512 + 4.97037i) q^{6} +(-1.91869 - 0.472914i) q^{7} +(1.46133 + 0.360186i) q^{8} +(2.81336 - 4.07585i) q^{9} +(6.82015 - 1.68102i) q^{10} +(3.06453 + 4.43973i) q^{11} +(2.43230 + 2.15483i) q^{12} +(-1.73651 - 3.15983i) q^{13} +(-2.62617 + 2.32659i) q^{14} +(-10.8326 - 2.67000i) q^{15} +(3.72519 - 3.30023i) q^{16} +(-0.565818 - 0.139462i) q^{17} +(-3.11807 - 8.22167i) q^{18} -3.58257 q^{19} +(1.61658 - 4.26258i) q^{20} +(5.41075 - 1.33363i) q^{21} +9.57810 q^{22} -1.74257 q^{23} +(-4.12099 + 1.01573i) q^{24} +(1.28398 + 10.5745i) q^{25} +(-6.36851 - 0.649594i) q^{26} +(-0.663696 + 5.46603i) q^{27} +(0.274471 + 2.26047i) q^{28} +(4.70408 - 6.81504i) q^{29} +(-14.8269 + 13.1355i) q^{30} +(-0.154435 + 1.27188i) q^{31} +(-0.702252 - 5.78357i) q^{32} +(-13.4705 - 7.06989i) q^{33} +(-0.774453 + 0.686106i) q^{34} +(-4.44116 - 6.43413i) q^{35} +(-5.54097 - 1.36573i) q^{36} +(0.391295 - 3.22260i) q^{37} +(-3.61332 + 5.23479i) q^{38} +(8.47713 + 5.61437i) q^{39} +(3.38252 + 4.90043i) q^{40} +(-4.06177 + 2.13178i) q^{41} +(3.50851 - 9.25118i) q^{42} +(-0.854533 - 7.03771i) q^{43} +(3.53126 - 5.11591i) q^{44} +(19.0242 - 4.68905i) q^{45} +(-1.75753 + 2.54622i) q^{46} +(2.72075 - 7.17403i) q^{47} +(-4.97677 + 13.1227i) q^{48} +(-2.74047 - 1.43831i) q^{49} +(16.7463 + 8.78913i) q^{50} +(1.59562 - 0.393285i) q^{51} +(-2.69491 + 3.16209i) q^{52} +(-2.36101 - 0.581937i) q^{53} +(7.31748 + 6.48272i) q^{54} +(-2.57260 + 21.1872i) q^{55} +(-2.63350 - 1.38217i) q^{56} +(8.94569 - 4.69506i) q^{57} +(-5.21357 - 13.7471i) q^{58} +(2.54652 + 2.25602i) q^{59} +(1.54962 + 12.7623i) q^{60} +(3.10295 - 0.764809i) q^{61} +(1.70270 + 1.50846i) q^{62} +(-7.32548 + 6.48981i) q^{63} +(-0.345656 - 0.181414i) q^{64} +(3.14746 - 13.9130i) q^{65} +(-23.9166 + 12.5524i) q^{66} +(0.844836 - 2.22765i) q^{67} +(0.0809410 + 0.666609i) q^{68} +(4.35121 - 2.28369i) q^{69} -13.8807 q^{70} +(0.968004 - 0.508048i) q^{71} +(5.57931 - 4.94284i) q^{72} +(4.47920 + 6.48924i) q^{73} +(-4.31416 - 3.82201i) q^{74} +(-17.0643 - 24.7219i) q^{75} +(1.46388 + 3.85993i) q^{76} +(-3.78026 - 9.96772i) q^{77} +(16.7535 - 6.72409i) q^{78} +(3.52518 - 9.29515i) q^{79} +19.6896 q^{80} +(-0.237567 - 0.626414i) q^{81} +(-0.981707 + 8.08508i) q^{82} +(-0.798013 - 0.418830i) q^{83} +(-3.64777 - 5.28471i) q^{84} +(-1.30969 - 1.89741i) q^{85} +(-11.1453 - 5.84948i) q^{86} +(-2.81481 + 23.1820i) q^{87} +(2.87916 + 7.59172i) q^{88} -5.24711 q^{89} +(12.3359 - 32.5272i) q^{90} +(1.83749 + 6.88395i) q^{91} +(0.712035 + 1.87748i) q^{92} +(-1.28122 - 3.37830i) q^{93} +(-7.73849 - 11.2111i) q^{94} +(-10.6091 - 9.39886i) q^{95} +(9.33306 + 13.5213i) q^{96} +(-7.86990 + 6.97212i) q^{97} +(-4.86563 + 2.55368i) q^{98} +26.7173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9	\( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) 156 * q - 10 * q^2 - 9 * q^3 - 20 * q^4 - 7 * q^5 - q^6 - 5 * q^7 + 2 * q^8 - 14 * q^9 + q^10 - q^11 + 11 * q^12 - 65 * q^13 + 9 * q^14 - 41 * q^15 + 3 * q^17 - 13 * q^18 - 6 * q^19 + 29 * q^20 + 19 * q^21 - 22 * q^22 - 82 * q^23 - 31 * q^24 + 2 * q^25 + 26 * q^26 + 21 * q^27 + 43 * q^28 + 13 * q^29 - 81 * q^30 - 33 * q^31 - 93 * q^32 + 35 * q^33 - 24 * q^34 + 27 * q^35 + 54 * q^36 + 25 * q^37 - 56 * q^38 - 13 * q^39 - 52 * q^40 + 29 * q^41 - 63 * q^42 + 21 * q^43 + 45 * q^44 + 33 * q^46 - 69 * q^47 + 54 * q^48 - 54 * q^49 + 80 * q^50 - 16 * q^51 + 13 * q^52 - 45 * q^53 + 29 * q^54 - 83 * q^55 + 91 * q^56 - 11 * q^57 + 25 * q^58 - 57 * q^59 + 51 * q^60 + 39 * q^61 + 4 * q^62 + 26 * q^63 + 86 * q^64 + 65 * q^65 - 138 * q^66 - 101 * q^67 + 36 * q^68 + 32 * q^69 - 90 * q^70 + 20 * q^71 + 13 * q^72 + 61 * q^73 - 4 * q^74 - 67 * q^75 - 107 * q^76 + 67 * q^77 + 13 * q^78 + 57 * q^79 + 160 * q^80 + 78 * q^81 - 31 * q^82 - 59 * q^83 - 36 * q^84 - 61 * q^85 + 41 * q^86 - 9 * q^87 - 45 * q^88 - 66 * q^89 + 191 * q^90 + 39 * q^91 + 79 * q^92 - 80 * q^93 - 21 * q^94 - 28 * q^95 + 70 * q^96 + 7 * q^97 + 158 * q^98 + 130 * q^99

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