LMFDB - Embedded newform 169.2.h.a.12.10

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			12.10
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.651938 - 0.450000i) q^{2} +(-1.14686 - 0.601918i) q^{3} +(-0.486687 + 1.28329i) q^{4} +(-2.65258 - 2.99414i) q^{5} +(-1.01854 + 0.123674i) q^{6} +(-0.815660 - 3.30926i) q^{7} +(0.639345 + 2.59392i) q^{8} +(-0.751216 - 1.08832i) q^{9} +O(q^{10})$	\(q+(0.651938 - 0.450000i) q^{2} +(-1.14686 - 0.601918i) q^{3} +(-0.486687 + 1.28329i) q^{4} +(-2.65258 - 2.99414i) q^{5} +(-1.01854 + 0.123674i) q^{6} +(-0.815660 - 3.30926i) q^{7} +(0.639345 + 2.59392i) q^{8} +(-0.751216 - 1.08832i) q^{9} +(-3.07668 - 0.758333i) q^{10} +(-0.0864794 - 0.0596924i) q^{11} +(1.33059 - 1.17880i) q^{12} +(3.60323 + 0.129485i) q^{13} +(-2.02093 - 1.79039i) q^{14} +(1.23990 + 5.03049i) q^{15} +(-0.470548 - 0.416869i) q^{16} +(0.528057 - 0.130154i) q^{17} +(-0.979492 - 0.371472i) q^{18} +1.09996i q^{19} +(5.13332 - 1.94681i) q^{20} +(-1.05646 + 4.28621i) q^{21} -0.0832408 q^{22} -0.747912 q^{23} +(0.828090 - 3.35969i) q^{24} +(-1.32603 + 10.9208i) q^{25} +(2.40735 - 1.53704i) q^{26} +(0.674820 + 5.55764i) q^{27} +(4.64371 + 0.563848i) q^{28} +(-5.92507 - 8.58394i) q^{29} +(3.07206 + 2.72161i) q^{30} +(4.48092 - 0.544083i) q^{31} +(-5.79851 - 0.704066i) q^{32} +(0.0632497 + 0.120512i) q^{33} +(0.285691 - 0.322478i) q^{34} +(-7.74479 + 11.2203i) q^{35} +(1.76224 - 0.434353i) q^{36} +(6.81322 - 0.827274i) q^{37} +(0.494981 + 0.717104i) q^{38} +(-4.05445 - 2.31735i) q^{39} +(6.07066 - 8.79487i) q^{40} +(5.07205 - 9.66399i) q^{41} +(1.24005 + 3.26975i) q^{42} +(0.481709 - 3.96723i) q^{43} +(0.118691 - 0.0819264i) q^{44} +(-1.26594 + 5.13611i) q^{45} +(-0.487592 + 0.336561i) q^{46} +(7.74511 - 2.93733i) q^{47} +(0.288731 + 0.761320i) q^{48} +(-4.08772 + 2.14540i) q^{49} +(4.04989 + 7.71642i) q^{50} +(-0.683948 - 0.168578i) q^{51} +(-1.91981 + 4.56096i) q^{52} +(-4.21290 + 1.03839i) q^{53} +(2.94088 + 3.31957i) q^{54} +(0.0506658 + 0.417270i) q^{55} +(8.06248 - 4.23152i) q^{56} +(0.662084 - 1.26150i) q^{57} +(-7.72555 - 2.92992i) q^{58} +(-1.30902 - 1.47758i) q^{59} +(-7.05901 - 0.857119i) q^{60} +(-0.502044 - 0.123743i) q^{61} +(2.67645 - 2.37112i) q^{62} +(-2.98881 + 3.37367i) q^{63} +(-2.98382 + 1.56603i) q^{64} +(-9.17014 - 11.1320i) q^{65} +(0.0954654 + 0.0501041i) q^{66} +(-11.1014 + 4.21020i) q^{67} +(-0.0899728 + 0.740993i) q^{68} +(0.857749 + 0.450181i) q^{69} +10.8001i q^{70} +(0.470463 - 0.896392i) q^{71} +(2.34274 - 2.64441i) q^{72} +(-2.57481 - 1.77726i) q^{73} +(4.06952 - 3.60528i) q^{74} +(8.09421 - 11.7265i) q^{75} +(-1.41156 - 0.535335i) q^{76} +(-0.127000 + 0.334871i) q^{77} +(-3.68606 + 0.313737i) q^{78} +(3.60784 + 9.51309i) q^{79} +2.51466i q^{80} +(1.16452 - 3.07059i) q^{81} +(-1.04213 - 8.58275i) q^{82} +(6.17255 + 11.7608i) q^{83} +(-4.98628 - 3.44178i) q^{84} +(-1.79041 - 1.23583i) q^{85} +(-1.47121 - 2.80316i) q^{86} +(1.62839 + 13.4110i) q^{87} +(0.0995474 - 0.262485i) q^{88} +2.82305i q^{89} +(1.48594 + 3.91809i) q^{90} +(-2.51051 - 12.0296i) q^{91} +(0.363999 - 0.959787i) q^{92} +(-5.46648 - 2.07316i) q^{93} +(3.72753 - 5.40026i) q^{94} +(3.29343 - 2.91772i) q^{95} +(6.22628 + 4.29769i) q^{96} +(5.28070 - 5.96068i) q^{97} +(-1.69951 + 3.23814i) q^{98} +0.138959i 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 $

$2$	0.651938	−	0.450000i	0.460990	−	0.318198i	−0.314835	−	0.949146i	$-0.601949\pi$
$2$	0.651938	−	0.450000i	0.460990	−	0.318198i	0.775825	+	0.630948i	$0.217334\pi$
$3$	−1.14686	−	0.601918i	−0.662139	−	0.347517i	0.0999475	−	0.994993i	$-0.468133\pi$
$3$	−1.14686	−	0.601918i	−0.662139	−	0.347517i	−0.762086	+	0.647475i	$0.775825\pi$
$4$	−0.486687	+	1.28329i	−0.243343	+	0.641644i
$5$	−2.65258	−	2.99414i	−1.18627	−	1.33902i	−0.927835	−	0.372991i	$-0.878332\pi$
$5$	−2.65258	−	2.99414i	−1.18627	−	1.33902i	−0.258433	−	0.966029i	$-0.583206\pi$
$6$	−1.01854	+	0.123674i	−0.415819	+	0.0504895i
$7$	−0.815660	−	3.30926i	−0.308290	−	1.25078i	−0.896852	−	0.442331i	$-0.854152\pi$
$7$	−0.815660	−	3.30926i	−0.308290	−	1.25078i	0.588562	−	0.808452i	$-0.299694\pi$
$8$	0.639345	+	2.59392i	0.226042	+	0.917090i
$9$	−0.751216	−	1.08832i	−0.250405	−	0.362775i
$10$	−3.07668	−	0.758333i	−0.972932	−	0.239806i
$11$	−0.0864794	−	0.0596924i	−0.0260745	−	0.0179979i	0.554956	−	0.831880i	$-0.312735\pi$
$11$	−0.0864794	−	0.0596924i	−0.0260745	−	0.0179979i	−0.581031	+	0.813882i	$0.697350\pi$
$12$	1.33059	−	1.17880i	0.384109	−	0.340291i
$13$	3.60323	+	0.129485i	0.999355	+	0.0359127i
$13$	3.60323	+	0.129485i	0.999355	+	0.0359127i
$14$	−2.02093	−	1.79039i	−0.540116	−	0.478501i
$15$	1.23990	+	5.03049i	0.320142	+	1.29887i
$16$	−0.470548	−	0.416869i	−0.117637	−	0.104217i
$17$	0.528057	−	0.130154i	0.128073	−	0.0315670i	−0.174758	−	0.984611i	$-0.555914\pi$
$17$	0.528057	−	0.130154i	0.128073	−	0.0315670i	0.302831	+	0.953044i	$0.402068\pi$
$18$	−0.979492	−	0.371472i	−0.230868	−	0.0875569i
$19$			1.09996i			0.252348i	0.992008	+	0.126174i	$0.0402697\pi$
$19$			1.09996i			0.252348i	−0.992008	+	0.126174i	$0.959730\pi$
$20$	5.13332	−	1.94681i	1.14784	−	0.435320i
$21$	−1.05646	+	4.28621i	−0.230538	+	0.935328i
$22$	−0.0832408			−0.0177470
$23$	−0.747912			−0.155950			−0.0779752	−	0.996955i	$-0.524846\pi$
$23$	−0.747912			−0.155950			−0.0779752	+	0.996955i	$0.524846\pi$
$24$	0.828090	−	3.35969i	0.169033	−	0.685795i
$25$	−1.32603	+	10.9208i	−0.265206	+	2.18417i
$26$	2.40735	−	1.53704i	0.472120	−	0.301438i
$27$	0.674820	+	5.55764i	0.129869	+	1.06957i
$28$	4.64371	+	0.563848i	0.877578	+	0.106557i
$29$	−5.92507	−	8.58394i	−1.10026	−	1.59400i	−0.755299	−	0.655380i	$-0.772509\pi$
$29$	−5.92507	−	8.58394i	−1.10026	−	1.59400i	−0.344958	−	0.938618i	$-0.612107\pi$
$30$	3.07206	+	2.72161i	0.560879	+	0.496895i
$31$	4.48092	−	0.544083i	0.804798	−	0.0977201i	0.292209	−	0.956354i	$-0.405610\pi$
$31$	4.48092	−	0.544083i	0.804798	−	0.0977201i	0.512589	+	0.858634i	$0.328687\pi$
$32$	−5.79851	−	0.704066i	−1.02504	−	0.124463i
$33$	0.0632497	+	0.120512i	0.0110104	+	0.0209785i
$34$	0.285691	−	0.322478i	0.0489955	−	0.0553045i
$35$	−7.74479	+	11.2203i	−1.30911	+	1.89657i
$36$	1.76224	−	0.434353i	0.293707	−	0.0723922i
$37$	6.81322	−	0.827274i	1.12009	−	0.136003i	0.460520	−	0.887649i	$-0.347663\pi$
$37$	6.81322	−	0.827274i	1.12009	−	0.136003i	0.659566	+	0.751646i	$0.270740\pi$
$38$	0.494981	+	0.717104i	0.0802966	+	0.116330i
$39$	−4.05445	−	2.31735i	−0.649231	−	0.371072i
$40$	6.07066	−	8.79487i	0.959855	−	1.39059i
$41$	5.07205	−	9.66399i	0.792122	−	1.50926i	−0.0671506	−	0.997743i	$-0.521391\pi$
$41$	5.07205	−	9.66399i	0.792122	−	1.50926i	0.859272	−	0.511519i	$-0.170917\pi$
$42$	1.24005	+	3.26975i	0.191344	+	0.504533i
$43$	0.481709	−	3.96723i	0.0734599	−	0.604997i	−0.908768	−	0.417303i	$-0.862975\pi$
$43$	0.481709	−	3.96723i	0.0734599	−	0.604997i	0.982227	−	0.187694i	$-0.0601014\pi$
$44$	0.118691	−	0.0819264i	0.0178933	−	0.0123509i
$45$	−1.26594	+	5.13611i	−0.188715	+	0.765646i
$46$	−0.487592	+	0.336561i	−0.0718916	+	0.0496232i
$47$	7.74511	−	2.93733i	1.12974	−	0.428454i	0.282290	−	0.959329i	$-0.408906\pi$
$47$	7.74511	−	2.93733i	1.12974	−	0.428454i	0.847450	+	0.530875i	$0.178137\pi$
$48$	0.288731	+	0.761320i	0.0416747	+	0.109887i
$49$	−4.08772	+	2.14540i	−0.583959	+	0.306486i
$50$	4.04989	+	7.71642i	0.572741	+	1.09127i
$51$	−0.683948	−	0.168578i	−0.0957719	−	0.0236056i
$52$	−1.91981	+	4.56096i	−0.266230	+	0.632491i
$53$	−4.21290	+	1.03839i	−0.578686	+	0.142633i	−0.517785	−	0.855511i	$-0.673243\pi$
$53$	−4.21290	+	1.03839i	−0.578686	+	0.142633i	−0.0609005	+	0.998144i	$0.519397\pi$
$54$	2.94088	+	3.31957i	0.400203	+	0.451736i
$55$	0.0506658	+	0.417270i	0.00683177	+	0.0562647i
$56$	8.06248	−	4.23152i	1.07739	−	0.565460i
$57$	0.662084	−	1.26150i	0.0876952	−	0.167089i
$58$	−7.72555	−	2.92992i	−1.01441	−	0.384717i
$59$	−1.30902	−	1.47758i	−0.170420	−	0.192364i	0.657095	−	0.753807i	$-0.271785\pi$
$59$	−1.30902	−	1.47758i	−0.170420	−	0.192364i	−0.827515	+	0.561443i	$0.810246\pi$
$60$	−7.05901	−	0.857119i	−0.911314	−	0.110654i
$61$	−0.502044	−	0.123743i	−0.0642801	−	0.0158436i	0.207044	−	0.978332i	$-0.433616\pi$
$61$	−0.502044	−	0.123743i	−0.0642801	−	0.0158436i	−0.271325	+	0.962488i	$0.587462\pi$
$62$	2.67645	−	2.37112i	0.339909	−	0.301133i
$63$	−2.98881	+	3.37367i	−0.376555	+	0.425042i
$64$	−2.98382	+	1.56603i	−0.372978	+	0.195754i
$65$	−9.17014	−	11.1320i	−1.13742	−	1.38076i
$66$	0.0954654	+	0.0501041i	0.0117510	+	0.00616739i
$67$	−11.1014	+	4.21020i	−1.35625	+	0.514357i	−0.922263	−	0.386562i	$-0.873662\pi$
$67$	−11.1014	+	4.21020i	−1.35625	+	0.514357i	−0.433986	+	0.900920i	$0.642893\pi$
$68$	−0.0899728	+	0.740993i	−0.0109108	+	0.0898586i
$69$	0.857749	+	0.450181i	0.103261	+	0.0541955i
$70$			10.8001i			1.29086i
$71$	0.470463	−	0.896392i	0.0558337	−	0.106382i	−0.855940	−	0.517075i	$-0.827021\pi$
$71$	0.470463	−	0.896392i	0.0558337	−	0.106382i	0.911774	+	0.410693i	$0.134713\pi$
$72$	2.34274	−	2.64441i	0.276095	−	0.311647i
$73$	−2.57481	−	1.77726i	−0.301359	−	0.208013i	0.407783	−	0.913079i	$-0.366302\pi$
$73$	−2.57481	−	1.77726i	−0.301359	−	0.208013i	−0.709142	+	0.705066i	$0.750917\pi$
$74$	4.06952	−	3.60528i	0.473072	−	0.419106i
$75$	8.09421	−	11.7265i	0.934638	−	1.35406i
$76$	−1.41156	−	0.535335i	−0.161917	−	0.0614072i
$77$	−0.127000	+	0.334871i	−0.0144730	+	0.0381621i
$78$	−3.68606	+	0.313737i	−0.417364	+	0.0355238i
$79$	3.60784	+	9.51309i	0.405913	+	1.07031i	0.969681	+	0.244373i	$0.0785820\pi$
$79$	3.60784	+	9.51309i	0.405913	+	1.07031i	−0.563768	+	0.825933i	$0.690649\pi$
$80$			2.51466i			0.281148i
$81$	1.16452	−	3.07059i	0.129391	−	0.341176i
$82$	−1.04213	−	8.58275i	−0.115084	−	0.947806i
$83$	6.17255	+	11.7608i	0.677526	+	1.29092i	0.944911	+	0.327327i	$0.106148\pi$
$83$	6.17255	+	11.7608i	0.677526	+	1.29092i	−0.267385	+	0.963590i	$0.586160\pi$
$84$	−4.98628	−	3.44178i	−0.544048	−	0.375529i
$85$	−1.79041	−	1.23583i	−0.194197	−	0.134045i
$86$	−1.47121	−	2.80316i	−0.158645	−	0.302272i
$87$	1.62839	+	13.4110i	0.174581	+	1.43781i
$88$	0.0995474	−	0.262485i	0.0106118	−	0.0279810i
$89$			2.82305i			0.299242i	0.988743	+	0.149621i	$0.0478054\pi$
$89$			2.82305i			0.299242i	−0.988743	+	0.149621i	$0.952195\pi$
$90$	1.48594	+	3.91809i	0.156632	+	0.413003i
$91$	−2.51051	−	12.0296i	−0.263172	−	1.26105i
$92$	0.363999	−	0.959787i	0.0379495	−	0.100065i
$93$	−5.46648	−	2.07316i	−0.566847	−	0.214977i
$94$	3.72753	−	5.40026i	0.384465	−	0.556994i
$95$	3.29343	−	2.91772i	0.337899	−	0.299352i
$96$	6.22628	+	4.29769i	0.635467	+	0.438631i
$97$	5.28070	−	5.96068i	0.536174	−	0.605216i	−0.416527	−	0.909123i	$-0.636753\pi$
$97$	5.28070	−	5.96068i	0.536174	−	0.605216i	0.952702	+	0.303908i	$0.0982914\pi$
$98$	−1.69951	+	3.23814i	−0.171676	+	0.327102i
$99$			0.138959i			0.0139659i
$100$	−13.3692	−	7.01670i	−1.33692	−	0.701670i
$101$	2.15882	−	17.7795i	0.214811	−	1.76913i	−0.343171	−	0.939273i	$-0.611501\pi$
$101$	2.15882	−	17.7795i	0.214811	−	1.76913i	0.557982	−	0.829853i	$-0.311576\pi$
$102$	−0.521752	+	0.197874i	−0.0516611	+	0.0195925i
$103$	1.60963	+	0.844798i	0.158601	+	0.0832404i	0.542156	−	0.840278i	$-0.317608\pi$
$103$	1.60963	+	0.844798i	0.158601	+	0.0832404i	−0.383555	+	0.923518i	$0.625300\pi$
$104$	1.96783	+	9.42928i	0.192961	+	0.924617i
$105$	15.6359	−	8.20633i	1.52590	−	0.800856i
$106$	−2.27927	+	2.57277i	−0.221383	+	0.249889i
$107$	−12.7297	+	11.2775i	−1.23063	+	1.09024i	−0.237723	+	0.971333i	$0.576401\pi$
$107$	−12.7297	+	11.2775i	−1.23063	+	1.09024i	−0.992905	+	0.118908i	$0.962061\pi$
$108$	−7.46048	−	1.83884i	−0.717885	−	0.176943i
$109$	−4.28304	−	0.520055i	−0.410241	−	0.0498123i	−0.0871850	−	0.996192i	$-0.527787\pi$
$109$	−4.28304	−	0.520055i	−0.410241	−	0.0498123i	−0.323056	+	0.946380i	$0.604710\pi$
$110$	0.220803	+	0.249235i	0.0210527	+	0.0237636i
$111$	−8.31175	−	3.15223i	−0.788916	−	0.299196i
$112$	−0.995721	+	1.89719i	−0.0940868	+	0.179267i
$113$	1.06128	−	0.557005i	0.0998372	−	0.0523986i	−0.414065	−	0.910247i	$-0.635892\pi$
$113$	1.06128	−	0.557005i	0.0998372	−	0.0523986i	0.513903	+	0.857848i	$0.328199\pi$
$114$	−0.136036	−	1.12036i	−0.0127409	−	0.104931i
$115$	1.98389	+	2.23935i	0.184999	+	0.208821i
$116$	13.8993	−	3.42588i	1.29052	−	0.318085i
$117$	−2.56588	−	4.01875i	−0.237215	−	0.371533i
$118$	−1.51831	−	0.374230i	−0.139772	−	0.0344507i
$119$	−0.861429	−	1.64132i	−0.0789670	−	0.150459i
$120$	−12.2560	+	6.43243i	−1.11881	+	0.587198i
$121$	−3.89674	−	10.2749i	−0.354249	−	0.934078i
$122$	−0.382985	+	0.145247i	−0.0346739	+	0.0131501i
$123$	−11.6338	+	8.03027i	−1.04899	+	0.724065i
$124$	−1.48259	+	6.01511i	−0.133141	+	0.540173i
$125$	19.7557	−	13.6364i	1.76700	−	1.21967i
$126$	−0.430367	+	3.54439i	−0.0383401	+	0.315759i
$127$	7.08346	+	18.6775i	0.628555	+	1.65736i	0.747338	+	0.664444i	$0.231332\pi$
$127$	7.08346	+	18.6775i	0.628555	+	1.65736i	−0.118783	+	0.992920i	$0.537899\pi$
$128$	4.18843	−	7.98039i	0.370209	−	0.705374i
$129$	−2.94040	+	4.25990i	−0.258888	+	0.375063i
$130$	−10.9878	−	3.13083i	−0.963692	−	0.274592i
$131$	4.21094	+	6.10060i	0.367912	+	0.533012i	0.962594	−	0.270949i	$-0.0873374\pi$
$131$	4.21094	+	6.10060i	0.367912	+	0.533012i	−0.594682	+	0.803961i	$0.702722\pi$
$132$	−0.185435	+	0.0225158i	−0.0161400	+	0.00195975i
$133$	3.64005	−	0.897191i	0.315632	−	0.0777964i
$134$	−5.34282	+	7.74041i	−0.461549	+	0.668670i
$135$	14.8504	−	16.7626i	1.27811	−	1.44269i
$136$	0.675220	+	1.28652i	0.0578997	+	0.110319i
$137$	9.58394	+	1.16370i	0.818811	+	0.0994217i	0.519214	−	0.854644i	$-0.326225\pi$
$137$	9.58394	+	1.16370i	0.818811	+	0.0994217i	0.299597	+	0.954066i	$0.403148\pi$
$138$	0.761781	−	0.0924970i	0.0648471	−	0.00787386i
$139$	−3.94023	−	3.49074i	−0.334206	−	0.296081i	0.479284	−	0.877660i	$-0.340897\pi$
$139$	−3.94023	−	3.49074i	−0.334206	−	0.296081i	−0.813490	+	0.581579i	$0.802435\pi$
$140$	−10.6295	−	15.3996i	−0.898361	−	1.30150i
$141$	−10.6506	−	1.29321i	−0.896940	−	0.108908i
$142$	−0.0966641	−	0.796101i	−0.00811187	−	0.0668073i
$143$	−0.303875	−	0.226283i	−0.0254113	−	0.0189227i
$144$	−0.100205	+	0.825266i	−0.00835046	+	0.0687722i
$145$	−9.98483	+	40.5100i	−0.829195	+	3.36418i
$146$	−2.47839			−0.205113
$147$	5.97938			0.493171
$148$	−2.25427	+	9.14594i	−0.185300	+	0.751792i
$149$	−12.3558	+	4.68592i	−1.01222	+	0.383886i	−0.804277	−	0.594254i	$-0.797447\pi$
$149$	−12.3558	+	4.68592i	−1.01222	+	0.383886i	−0.207946	+	0.978140i	$0.566678\pi$
$150$		−	11.2873i		−	0.921607i
$151$	20.1641	+	7.64724i	1.64093	+	0.622324i	0.990534	−	0.137269i	$-0.0438323\pi$
$151$	20.1641	+	7.64724i	1.64093	+	0.622324i	0.650399	+	0.759592i	$0.274602\pi$
$152$	−2.85321	+	0.703252i	−0.231426	+	0.0570413i
$153$	−0.538334	−	0.476922i	−0.0435217	−	0.0385569i
$154$	0.0678961	+	0.275465i	0.00547123	+	0.0221976i
$155$	−13.5151	−	11.9733i	−1.08556	−	0.961718i
$156$	4.94707	−	4.07520i	0.396082	−	0.326277i
$157$	10.7312	−	9.50706i	0.856447	−	0.758746i	−0.115659	−	0.993289i	$-0.536898\pi$
$157$	10.7312	−	9.50706i	0.856447	−	0.758746i	0.972106	+	0.234543i	$0.0753595\pi$
$158$	6.63298	+	4.57841i	0.527691	+	0.364239i
$159$	5.45662	+	1.34494i	0.432738	+	0.106660i
$160$	13.2729	+	19.2291i	1.04932	+	1.52020i
$161$	0.610042	+	2.47504i	0.0480780	+	0.195060i
$162$	−0.622570	−	2.52587i	−0.0489137	−	0.198451i
$163$	8.74787	−	1.06218i	0.685186	−	0.0831966i	0.229462	−	0.973318i	$-0.426303\pi$
$163$	8.74787	−	1.06218i	0.685186	−	0.0831966i	0.455724	+	0.890121i	$0.349380\pi$
$164$	9.93318	+	11.2122i	0.775651	+	0.875529i
$165$	0.193056	−	0.509046i	0.0150294	−	0.0396292i
$166$	9.31649	+	4.88967i	0.723100	+	0.379512i
$167$	10.2235	−	7.05679i	0.791120	−	0.546071i	−0.102586	−	0.994724i	$-0.532712\pi$
$167$	10.2235	−	7.05679i	0.791120	−	0.546071i	0.893706	+	0.448653i	$0.148096\pi$
$168$	−11.7935			−0.909892
$169$	12.9665	+	0.933129i	0.997421	+	0.0717791i
$170$	−1.72336			−0.132176
$171$	1.19711	−	0.826306i	0.0915453	−	0.0631892i
$172$	4.85666	+	2.54897i	0.370317	+	0.194357i
$173$	0.324382	−	0.855326i	0.0246623	−	0.0650292i	−0.922120	−	0.386905i	$-0.873544\pi$
$173$	0.324382	−	0.855326i	0.0246623	−	0.0650292i	0.946782	+	0.321876i	$0.104313\pi$
$174$	7.09655	+	8.01034i	0.537988	+	0.607263i
$175$	37.2215	−	4.51950i	2.81368	−	0.341642i
$176$	0.0158088	+	0.0641387i	0.00119163	+	0.00483463i
$177$	0.611880	+	2.48250i	0.0459917	+	0.186596i
$178$	1.27037	+	1.84045i	0.0952184	+	0.137948i
$179$	−0.803126	−	0.197953i	−0.0600284	−	0.0147957i	0.209187	−	0.977876i	$-0.432918\pi$
$179$	−0.803126	−	0.197953i	−0.0600284	−	0.0147957i	−0.269216	+	0.963080i	$0.586764\pi$
$180$	−5.97499	−	4.12424i	−0.445349	−	0.307402i
$181$	−12.0608	+	10.6850i	−0.896474	+	0.794207i	−0.979312	−	0.202356i	$-0.935140\pi$
$181$	−12.0608	+	10.6850i	−0.896474	+	0.794207i	0.0828379	+	0.996563i	$0.473602\pi$
$182$	−7.05003	−	6.71284i	−0.522583	−	0.497589i
$183$	0.501290	+	0.444104i	0.0370564	+	0.0328291i
$184$	−0.478174	−	1.94003i	−0.0352514	−	0.143021i
$185$	−20.5496	−	18.2053i	−1.51083	−	1.33848i
$186$	−4.49673	+	1.10834i	−0.329716	+	0.0812677i
$187$	−0.0534352	−	0.0202653i	−0.00390757	−	0.00148195i
$188$			11.3688i			0.829152i
$189$	17.8413	−	6.76630i	1.29776	−	0.492176i
$190$	0.834135	−	3.38422i	0.0605145	−	0.245517i
$191$	16.3492			1.18299			0.591495	−	0.806309i	$-0.298538\pi$
$191$	16.3492			1.18299			0.591495	+	0.806309i	$0.298538\pi$
$192$	4.36464			0.314991
$193$	−1.76594	+	7.16469i	−0.127115	+	0.515726i	0.872517	+	0.488584i	$0.162487\pi$
$193$	−1.76594	+	7.16469i	−0.127115	+	0.515726i	−0.999632	+	0.0271412i	$0.991360\pi$
$194$	0.760383	−	6.26231i	0.0545923	−	0.449608i
$195$	3.81628	+	18.2865i	0.273289	+	1.30953i
$196$	−0.763727	−	6.28985i	−0.0545519	−	0.449275i
$197$	7.55521	+	0.917369i	0.538287	+	0.0653598i	0.385165	−	0.922848i	$-0.374144\pi$
$197$	7.55521	+	0.917369i	0.538287	+	0.0653598i	0.153121	+	0.988207i	$0.451067\pi$
$198$	0.0625318	+	0.0905929i	0.00444394	+	0.00643816i
$199$	−12.1150	−	10.7330i	−0.858811	−	0.760841i	0.113744	−	0.993510i	$-0.463715\pi$
$199$	−12.1150	−	10.7330i	−0.858811	−	0.760841i	−0.972556	+	0.232670i	$0.925254\pi$
$200$	−29.1756	+	3.54256i	−2.06303	+	0.250497i
$201$	15.2659	+	1.85362i	1.07677	+	0.130744i
$202$	−6.59336	−	12.5626i	−0.463907	−	0.883901i
$203$	−23.5737	+	26.6092i	−1.65455	+	1.86760i
$204$	0.549203	−	0.795657i	0.0384519	−	0.0557072i
$205$	−42.3893	+	10.4480i	−2.96060	+	0.729722i
$206$	1.42954	−	0.173577i	0.0996006	−	0.0120937i
$207$	0.561843	+	0.813970i	0.0390508	+	0.0565749i
$208$	−1.64151	−	1.56300i	−0.113818	−	0.108375i
$209$	0.0656591	−	0.0951237i	0.00454174	−	0.00657984i
$210$	6.50076	−	12.3862i	0.448595	−	0.854726i
$211$	2.98458	+	7.86968i	0.205467	+	0.541771i	0.997650	−	0.0685116i	$-0.0218250\pi$
$211$	2.98458	+	7.86968i	0.205467	+	0.541771i	−0.792184	+	0.610283i	$0.791056\pi$
$212$	0.717814	−	5.91173i	0.0492996	−	0.406019i
$213$	−1.07911	+	0.744855i	−0.0739393	+	0.0510366i
$214$	−3.22409	+	13.0806i	−0.220394	+	0.894174i
$215$	−13.1562	+	9.08108i	−0.897246	+	0.619325i
$216$	−13.9847	+	5.30368i	−0.951536	+	0.360870i
$217$	−5.45542	−	14.3848i	−0.370338	−	0.976501i
$218$	−3.02630	+	1.58833i	−0.204967	+	0.107575i
$219$	1.88318	+	3.58810i	0.127253	+	0.242461i
$220$	−0.560136	−	0.138061i	−0.0377644	−	0.00930808i
$221$	1.91956	−	0.400600i	0.129124	−	0.0269472i
$222$	−6.83725	+	1.68523i	−0.458886	+	0.113105i
$223$	−11.7070	−	13.2144i	−0.783956	−	0.884904i	0.211764	−	0.977321i	$-0.432079\pi$
$223$	−11.7070	−	13.2144i	−0.783956	−	0.884904i	−0.995720	+	0.0924171i	$0.970541\pi$
$224$	2.39967	+	19.7631i	0.160335	+	1.32047i
$225$	12.8815	−	6.76075i	0.858769	−	0.450717i
$226$	0.441239	−	0.840711i	0.0293508	−	0.0559232i
$227$	−18.1847	−	6.89656i	−1.20696	−	0.457741i	−0.332626	−	0.943059i	$-0.607935\pi$
$227$	−18.1847	−	6.89656i	−1.20696	−	0.457741i	−0.874338	+	0.485318i	$0.838704\pi$
$228$	1.29663	+	1.46360i	0.0858717	+	0.0969291i
$229$	11.8697	+	1.44124i	0.784371	+	0.0952398i	0.502917	−	0.864335i	$-0.332260\pi$
$229$	11.8697	+	1.44124i	0.784371	+	0.0952398i	0.281454	+	0.959575i	$0.409183\pi$
$230$	2.30109	+	0.567167i	0.151729	+	0.0373979i
$231$	0.347216	−	0.307607i	0.0228451	−	0.0202390i
$232$	18.4779	−	20.8573i	1.21314	−	1.36935i
$233$	3.49644	−	1.83508i	0.229060	−	0.120220i	−0.346289	−	0.938128i	$-0.612559\pi$
$233$	3.49644	−	1.83508i	0.229060	−	0.120220i	0.575349	+	0.817908i	$0.304866\pi$
$234$	−3.48123	−	1.46533i	−0.227575	−	0.0957915i
$235$	−29.3393	−	15.3984i	−1.91388	−	1.00448i
$236$	2.53324	−	0.960732i	0.164900	−	0.0625383i
$237$	1.58842	−	13.0818i	0.103179	−	0.849753i
$238$	−1.30019	−	0.682393i	−0.0842788	−	0.0442329i
$239$		−	17.4108i		−	1.12621i	−0.826385	−	0.563106i	$-0.809606\pi$
$239$		−	17.4108i		−	1.12621i	0.826385	−	0.563106i	$-0.190394\pi$
$240$	1.51362	−	2.88396i	0.0977037	−	0.186159i
$241$	6.25374	−	7.05902i	0.402839	−	0.454711i	−0.511727	−	0.859148i	$-0.670994\pi$
$241$	6.25374	−	7.05902i	0.402839	−	0.454711i	0.914566	+	0.404437i	$0.132532\pi$
$242$	−7.16412	−	4.94503i	−0.460527	−	0.317879i
$243$	9.38775	−	8.31682i	0.602225	−	0.533524i
$244$	0.403135	−	0.584042i	0.0258081	−	0.0373895i
$245$	17.2666	+	6.54836i	1.10312	+	0.418359i
$246$	−3.97093	+	10.4705i	−0.253177	+	0.667573i
$247$	−0.142428	+	3.96340i	−0.00906249	+	0.252185i
$248$	4.27616	+	11.2753i	0.271537	+	0.715983i
$249$		−	17.2034i		−	1.09022i
$250$	6.74311	−	17.7801i	0.426472	−	1.12451i
$251$	−0.224179	−	1.84628i	−0.0141501	−	0.116536i	0.983922	−	0.178597i	$-0.0571558\pi$
$251$	−0.224179	−	1.84628i	−0.0141501	−	0.116536i	−0.998072	+	0.0620607i	$0.980233\pi$
$252$	−2.87477	−	5.47743i	−0.181094	−	0.345045i
$253$	0.0646790	+	0.0446447i	0.00406633	+	0.00280679i
$254$	13.0229	+	8.98904i	0.817128	+	0.564023i
$255$	1.30948	+	2.49500i	0.0820027	+	0.156243i
$256$	−1.67295	−	13.7780i	−0.104560	−	0.861126i
$257$	−6.41098	+	16.9044i	−0.399906	+	1.05446i	0.572240	+	0.820086i	$0.306075\pi$
$257$	−6.41098	+	16.9044i	−0.399906	+	1.05446i	−0.972145	+	0.234378i	$0.924695\pi$
$258$			4.10037i			0.255278i
$259$	−8.29493	−	21.8719i	−0.515422	−	1.35906i
$260$	18.7486	−	6.35011i	1.16274	−	0.393817i
$261$	−4.89110	+	12.8968i	−0.302752	+	0.798291i
$262$	5.49055	+	2.08229i	0.339207	+	0.128644i
$263$	2.19648	−	3.18215i	0.135441	−	0.196220i	−0.749395	−	0.662124i	$-0.769655\pi$
$263$	2.19648	−	3.18215i	0.135441	−	0.196220i	0.884835	+	0.465904i	$0.154271\pi$
$264$	−0.272161	+	0.241114i	−0.0167503	+	0.0148395i
$265$	14.2841	+	9.85960i	0.877465	+	0.605671i
$266$	1.96935	−	2.22294i	0.120749	−	0.136297i
$267$	1.69924	−	3.23763i	0.103992	−	0.198140i
$268$		−	16.2953i		−	0.995395i
$269$	−5.04514	−	2.64789i	−0.307607	−	0.161445i	0.303855	−	0.952718i	$-0.401726\pi$
$269$	−5.04514	−	2.64789i	−0.307607	−	0.161445i	−0.611462	+	0.791273i	$0.709418\pi$
$270$	2.13834	−	17.6108i	0.130135	−	1.07176i
$271$	8.12293	−	3.08062i	0.493433	−	0.187134i	−0.0953213	−	0.995447i	$-0.530388\pi$
$271$	8.12293	−	3.08062i	0.493433	−	0.187134i	0.588754	+	0.808312i	$0.299619\pi$
$272$	−0.302733	−	0.158887i	−0.0183559	−	0.00963391i
$273$	−4.36165	+	15.3074i	−0.263979	+	0.926446i
$274$	6.77180	−	3.55412i	0.409099	−	0.214712i
$275$	0.766565	−	0.865273i	0.0462256	−	0.0521779i
$276$	−0.995168	+	0.881642i	−0.0599021	+	0.0530686i
$277$	13.5751	+	3.34595i	0.815647	+	0.201039i	0.625005	−	0.780621i	$-0.285097\pi$
$277$	13.5751	+	3.34595i	0.815647	+	0.201039i	0.190642	+	0.981660i	$0.438943\pi$
$278$	−4.13962	−	0.502641i	−0.248278	−	0.0301464i
$279$	−3.95828	−	4.46797i	−0.236976	−	0.267490i
$280$	−34.0561	−	12.9158i	−2.03524	−	0.771865i
$281$	2.32349	−	4.42705i	0.138608	−	0.264096i	−0.806251	−	0.591574i	$-0.798507\pi$
$281$	2.32349	−	4.42705i	0.138608	−	0.264096i	0.944859	+	0.327479i	$0.106199\pi$
$282$	−7.52546	+	3.94966i	−0.448134	+	0.235199i
$283$	−1.49456	−	12.3088i	−0.0888424	−	0.731683i	−0.967260	−	0.253789i	$-0.918323\pi$
$283$	−1.49456	−	12.3088i	−0.0888424	−	0.731683i	0.878417	−	0.477894i	$-0.158600\pi$
$284$	0.921361	+	1.04000i	0.0546727	+	0.0617128i
$285$	−5.53332	+	1.36384i	−0.327766	+	0.0807870i
$286$	−0.299935	−	0.0107784i	−0.0177355	−	0.000637343i
$287$	−36.1177	−	8.90222i	−2.13196	−	0.525481i
$288$	3.58968	+	6.83956i	0.211524	+	0.403025i
$289$	−14.7908	+	7.76284i	−0.870050	+	0.456637i
$290$	11.7200	+	30.9032i	0.688225	+	1.81470i
$291$	−9.64406	+	3.65751i	−0.565345	+	0.214407i
$292$	3.53387	−	2.43925i	0.206804	−	0.142747i
$293$	−2.87216	+	11.6528i	−0.167793	+	0.680764i	0.825426	+	0.564510i	$0.190935\pi$
$293$	−2.87216	+	11.6528i	−0.167793	+	0.680764i	−0.993220	+	0.116254i	$0.962911\pi$
$294$	3.89819	−	2.69072i	0.227347	−	0.156926i
$295$	−0.951800	+	7.83878i	−0.0554160	+	0.456392i
$296$	6.50188	+	17.1441i	0.377914	+	0.996478i
$297$	0.273391	−	0.520903i	0.0158638	−	0.0302259i
$298$	−5.94652	+	8.61503i	−0.344473	+	0.499055i
$299$	−2.69490	−	0.0968435i	−0.155850	−	0.00560061i
$300$	11.1091	+	16.0943i	0.641385	+	0.929206i
$301$	−13.5215	+	1.64181i	−0.779367	+	0.0946323i
$302$	16.5870	−	4.08833i	0.954476	−	0.235257i
$303$	−13.1777	+	19.0911i	−0.757036	+	1.09676i
$304$	0.458538	−	0.517583i	0.0262990	−	0.0296854i
$305$	0.961206	+	1.83143i	0.0550385	+	0.104867i
$306$	−0.565576	−	0.0686733i	−0.0323318	−	0.00392579i
$307$	−26.2884	+	3.19199i	−1.50036	+	0.182176i	−0.829122	−	0.559068i	$-0.811159\pi$
$307$	−26.2884	+	3.19199i	−1.50036	+	0.182176i	−0.671235	+	0.741244i	$0.734236\pi$
$308$	−0.367927	−	0.325955i	−0.0209646	−	0.0185730i
$309$	−1.33752	−	1.93773i	−0.0760887	−	0.110233i
$310$	−14.1990	−	1.72407i	−0.806447	−	0.0979204i
$311$	1.79015	+	14.7432i	0.101510	+	0.836009i	0.951168	+	0.308675i	$0.0998855\pi$
$311$	1.79015	+	14.7432i	0.101510	+	0.836009i	−0.849658	+	0.527335i	$0.823191\pi$
$312$	3.41883	−	11.9985i	0.193553	−	0.679282i
$313$	2.51459	−	20.7095i	0.142133	−	1.17057i	−0.730751	−	0.682644i	$-0.760830\pi$
$313$	2.51459	−	20.7095i	0.142133	−	1.17057i	0.872884	−	0.487927i	$-0.162247\pi$
$314$	2.71793	−	11.0271i	0.153382	−	0.622294i
$315$	18.0293			1.01584
$316$	−13.9639			−0.785532
$317$	−4.63619	+	18.8097i	−0.260394	+	1.05646i	0.684481	+	0.729030i	$0.260029\pi$
$317$	−4.63619	+	18.8097i	−0.260394	+	1.05646i	−0.944875	+	0.327430i	$0.893817\pi$
$318$	4.16260	−	1.57866i	0.233427	−	0.0885271i
$319$			1.09602i			0.0613651i
$320$	12.6037	+	4.77997i	0.704570	+	0.267208i
$321$	21.3873	−	5.27150i	1.19372	−	0.294227i
$322$	1.51148	+	1.33905i	0.0842313	+	0.0746224i
$323$	0.143164	+	0.580840i	0.00796587	+	0.0323188i
$324$	3.37369	+	2.98883i	0.187427	+	0.166046i
$325$	−6.19207	+	39.1785i	−0.343474	+	2.17323i
$326$	5.22508	−	4.62902i	0.289391	−	0.256378i
$327$	4.59901	+	3.17447i	0.254326	+	0.175548i
$328$	28.3104	+	6.97790i	1.56318	+	0.385290i
$329$	−16.0378	−	23.2347i	−0.884191	−	1.28097i
$330$	−0.103211	−	0.418742i	−0.00568155	−	0.0230510i
$331$	−7.63614	−	30.9811i	−0.419720	−	1.70287i	−0.676534	−	0.736412i	$-0.736519\pi$
$331$	−7.63614	−	30.9811i	−0.419720	−	1.70287i	0.256813	−	0.966461i	$-0.417327\pi$
$332$	−18.0966	+	2.19733i	−0.993181	+	0.120594i
$333$	−6.01854	−	6.79352i	−0.329814	−	0.372283i
$334$	3.48955	−	9.20118i	0.190939	−	0.503466i
$335$	42.0532	+	22.0712i	2.29761	+	1.20588i
$336$	2.28390	−	1.57646i	0.124597	−	0.0860031i
$337$	30.0074			1.63461			0.817304	−	0.576207i	$-0.195468\pi$
$337$	30.0074			1.63461			0.817304	+	0.576207i	$0.195468\pi$
$338$	8.87324	−	5.22657i	0.482641	−	0.284288i
$339$	−1.55241			−0.0843155
$340$	2.45730	−	1.69615i	0.133266	−	0.0919866i
$341$	−0.419985	−	0.220425i	−0.0227435	−	0.0119367i
$342$	0.408604	−	1.07740i	0.0220948	−	0.0582591i
$343$	−5.38698	−	6.08064i	−0.290869	−	0.328324i
$344$	10.5987	−	1.28691i	0.571442	−	0.0693856i
$345$	−0.927339	−	3.76236i	−0.0499262	−	0.202559i
$346$	−0.173420	−	0.703592i	−0.00932310	−	0.0378253i
$347$	7.24145	+	10.4910i	0.388741	+	0.563189i	0.967680	−	0.252182i	$-0.0811482\pi$
$347$	7.24145	+	10.4910i	0.388741	+	0.563189i	−0.578938	+	0.815371i	$0.696533\pi$
$348$	−18.0026	−	4.43725i	−0.965043	−	0.237862i
$349$	−1.37758	−	0.950872i	−0.0737399	−	0.0508990i	0.530624	−	0.847607i	$-0.321957\pi$
$349$	−1.37758	−	0.950872i	−0.0737399	−	0.0508990i	−0.604364	+	0.796708i	$0.706573\pi$
$350$	22.2323	−	19.6961i	1.18837	−	1.05280i
$351$	1.71190	+	20.1128i	0.0913743	+	1.07354i
$352$	0.459424	+	0.407014i	0.0244874	+	0.0216939i
$353$	1.96459	+	7.97066i	0.104565	+	0.424236i	0.999771	−	0.0214171i	$-0.00681779\pi$
$353$	1.96459	+	7.97066i	0.104565	+	0.424236i	−0.895206	+	0.445653i	$0.852972\pi$
$354$	1.51603	+	1.34309i	0.0805762	+	0.0713843i
$355$	−3.93186	+	0.969117i	−0.208682	+	0.0514354i
$356$	−3.62278	−	1.37394i	−0.192007	−	0.0728186i
$357$			2.40086i			0.127067i
$358$	−0.612667	+	0.232354i	−0.0323805	+	0.0122803i
$359$	−1.06881	+	4.33635i	−0.0564098	+	0.228864i	−0.992380	−	0.123216i	$-0.960679\pi$
$359$	−1.06881	+	4.33635i	−0.0564098	+	0.228864i	0.935970	+	0.352080i	$0.114525\pi$
$360$	−14.1320			−0.744824
$361$	17.7901			0.936321
$362$	−3.05468	+	12.3933i	−0.160550	+	0.651378i
$363$	−1.71561	+	14.1293i	−0.0900461	+	0.741597i
$364$	16.6593	+	2.63296i	0.873185	+	0.138005i
$365$	1.50851	+	12.4237i	0.0789589	+	0.650285i
$366$	0.526657	+	0.0639477i	0.0275288	+	0.00334260i
$367$	6.99280	+	10.1308i	0.365021	+	0.528825i	0.961862	−	0.273535i	$-0.0881929\pi$
$367$	6.99280	+	10.1308i	0.365021	+	0.528825i	−0.596841	+	0.802360i	$0.703578\pi$
$368$	0.351928	+	0.311781i	0.0183455	+	0.0162527i
$369$	−14.3278	+	1.73970i	−0.745873	+	0.0905654i
$370$	−21.5894	−	2.62143i	−1.12238	−	0.136282i
$371$	6.87258	+	13.0946i	0.356806	+	0.679838i
$372$	5.32092	−	6.00608i	0.275877	−	0.311401i
$373$	−11.3466	+	16.4383i	−0.587502	+	0.851144i	−0.998159	−	0.0606457i	$-0.980684\pi$
$373$	−11.3466	+	16.4383i	−0.587502	+	0.851144i	0.410657	+	0.911790i	$0.365299\pi$
$374$	−0.0439558	+	0.0108341i	−0.00227290	+	0.000560220i
$375$	−30.8649	+	3.74768i	−1.59386	+	0.193529i
$376$	12.5710	+	18.2122i	0.648300	+	0.939225i
$377$	−20.2379	−	31.6971i	−1.04230	−	1.63248i
$378$	8.58656	−	12.4398i	0.441645	−	0.639834i
$379$	11.9204	−	22.7124i	0.612310	−	1.16666i	−0.359998	−	0.932953i	$-0.617222\pi$
$379$	11.9204	−	22.7124i	0.612310	−	1.16666i	0.972307	−	0.233706i	$-0.0750852\pi$
$380$	2.14141	+	5.64643i	0.109852	+	0.289656i
$381$	3.11862	−	25.6842i	0.159772	−	1.31584i
$382$	10.6587	−	7.35716i	0.545346	−	0.376425i
$383$	−5.56780	+	22.5895i	−0.284501	+	1.15427i	0.638547	+	0.769583i	$0.279536\pi$
$383$	−5.56780	+	22.5895i	−0.284501	+	1.15427i	−0.923048	+	0.384685i	$0.874310\pi$
$384$	−9.60708	+	6.63129i	−0.490259	+	0.338401i
$385$	1.33953	−	0.508016i	0.0682687	−	0.0258909i
$386$	2.07283	+	5.46560i	0.105504	+	0.278192i
$387$	−4.67950	+	2.45599i	−0.237872	+	0.124845i
$388$	5.07922	+	9.67765i	0.257858	+	0.491308i
$389$	5.72407	+	1.41086i	0.290222	+	0.0715333i	0.381739	−	0.924270i	$-0.375325\pi$
$389$	5.72407	+	1.41086i	0.290222	+	0.0715333i	−0.0915168	+	0.995804i	$0.529172\pi$
$390$	10.7169	+	10.2044i	0.542672	+	0.516718i
$391$	−0.394940	+	0.0973439i	−0.0199730	+	0.00492289i
$392$	−8.17846	−	9.23157i	−0.413075	−	0.466265i
$393$	−1.15729	−	9.53117i	−0.0583777	−	0.480784i
$394$	5.33835	−	2.80178i	0.268942	−	0.141152i
$395$	18.9134	−	36.0366i	0.951639	−	1.81320i
$396$	−0.178325	−	0.0676297i	−0.00896116	−	0.00339852i
$397$	21.1509	+	23.8744i	1.06153	+	1.19822i	0.979469	+	0.201596i	$0.0646129\pi$
$397$	21.1509	+	23.8744i	1.06153	+	1.19822i	0.0820647	+	0.996627i	$0.473849\pi$
$398$	−12.7281	−	1.54547i	−0.638001	−	0.0774674i
$399$	−4.71465	−	1.16206i	−0.236028	−	0.0581757i
$400$	5.17651	−	4.58599i	0.258826	−	0.229300i
$401$	−14.2448	+	16.0791i	−0.711352	+	0.802950i	−0.987409	−	0.158191i	$-0.949434\pi$
$401$	−14.2448	+	16.0791i	−0.711352	+	0.802950i	0.276057	+	0.961141i	$0.410972\pi$
$402$	10.7865	−	5.66122i	0.537984	−	0.282356i
$403$	16.2162	−	1.38024i	0.807788	−	0.0687546i
$404$	21.7655	+	11.4234i	1.08288	+	0.568337i
$405$	−12.2827	+	4.65823i	−0.610334	+	0.231469i
$406$	−3.39443	+	27.9557i	−0.168463	+	1.38742i
$407$	−0.638585	−	0.335155i	−0.0316535	−	0.0166130i
$408$		−	1.88189i		−	0.0931673i
$409$	2.00948	−	3.82874i	0.0993623	−	0.189319i	−0.830701	−	0.556719i	$-0.812060\pi$
$409$	2.00948	−	3.82874i	0.0993623	−	0.189319i	0.930063	+	0.367400i	$0.119752\pi$
$410$	−22.9336	+	25.8867i	−1.13261	+	1.27845i
$411$	−10.2910	−	7.10334i	−0.507616	−	0.350382i
$412$	−1.86750	+	1.65446i	−0.0920053	+	0.0815096i
$413$	−3.82198	+	5.53709i	−0.188067	+	0.272462i
$414$	0.732574	+	0.277829i	0.0360040	+	0.0136545i
$415$	18.8404	−	49.6779i	0.924837	−	2.43859i
$416$	−20.8022	−	3.28773i	−1.01991	−	0.161194i
$417$	2.41775	+	6.37508i	0.118398	+	0.312189i
$418$		−	0.0915614i		−	0.00447841i
$419$	1.58307	−	4.17422i	0.0773381	−	0.203924i	−0.890771	−	0.454452i	$-0.849835\pi$
$419$	1.58307	−	4.17422i	0.0773381	−	0.203924i	0.968109	+	0.250528i	$0.0806043\pi$
$420$	2.92132	+	24.0592i	0.142546	+	1.17397i
$421$	−8.52673	−	16.2463i	−0.415568	−	0.791798i	0.584237	−	0.811583i	$-0.301394\pi$
$421$	−8.52673	−	16.2463i	−0.415568	−	0.791798i	−0.999804	+	0.0197854i	$0.993702\pi$
$422$	5.48712	+	3.78748i	0.267109	+	0.184372i
$423$	−9.01501	−	6.22261i	−0.438325	−	0.302554i
$424$	−5.38699	−	10.2640i	−0.261615	−	0.498466i
$425$	0.721174	+	5.93940i	0.0349821	+	0.288103i
$426$	−0.368327	+	0.971198i	−0.0178455	+	0.0470547i
$427$			1.76232i			0.0852849i
$428$	−8.27695	−	21.8245i	−0.400081	−	1.05493i
$429$	0.212298	+	0.442422i	0.0102499	+	0.0213604i
$430$	−4.49055	+	11.8406i	−0.216553	+	0.571005i
$431$	−23.7406	−	9.00360i	−1.14354	−	0.433688i	−0.291194	−	0.956664i	$-0.594053\pi$
$431$	−23.7406	−	9.00360i	−1.14354	−	0.433688i	−0.852348	+	0.522976i	$0.824822\pi$
$432$	1.99927	−	2.89645i	0.0961901	−	0.139355i
$433$	−1.90795	+	1.69030i	−0.0916903	+	0.0812305i	−0.707723	−	0.706490i	$-0.750277\pi$
$433$	−1.90795	+	1.69030i	−0.0916903	+	0.0812305i	0.616033	+	0.787721i	$0.288739\pi$
$434$	−10.0297	−	6.92303i	−0.481443	−	0.332316i
$435$	35.8349	−	40.4492i	1.71815	−	1.93939i
$436$	2.75188	−	5.24327i	0.131791	−	0.251107i
$437$		−	0.822672i		−	0.0393537i
$438$	2.84236	+	1.49179i	0.135813	+	0.0712803i
$439$	−2.16092	+	17.7967i	−0.103135	+	0.849392i	0.845709	+	0.533645i	$0.179178\pi$
$439$	−2.16092	+	17.7967i	−0.103135	+	0.849392i	−0.948843	+	0.315747i	$0.897745\pi$
$440$	−1.04997	+	0.398202i	−0.0500555	+	0.0189836i
$441$	5.40564	+	2.83710i	0.257412	+	0.135100i
$442$	1.07116	−	1.12497i	0.0509501	−	0.0535093i
$443$	8.74848	−	4.59156i	0.415653	−	0.218152i	−0.243915	−	0.969797i	$-0.578432\pi$
$443$	8.74848	−	4.59156i	0.415653	−	0.218152i	0.659568	+	0.751645i	$0.270739\pi$
$444$	8.09043	−	9.13221i	0.383955	−	0.433396i
$445$	8.45260	−	7.48835i	0.400691	−	0.354982i
$446$	−13.5787	−	3.34685i	−0.642971	−	0.158478i
$447$	16.9908	+	2.06306i	0.803639	+	0.0975795i
$448$	7.61619	+	8.59690i	0.359831	+	0.406165i
$449$	33.8413	+	12.8343i	1.59707	+	0.605689i	0.983007	−	0.183567i	$-0.0587644\pi$
$449$	33.8413	+	12.8343i	1.59707	+	0.605689i	0.614064	+	0.789256i	$0.289534\pi$
$450$	5.35562	−	10.2043i	0.252466	−	0.481034i
$451$	−1.01549	+	0.532973i	−0.0478178	+	0.0250967i
$452$	0.198285	+	1.63302i	0.00932652	+	0.0768108i
$453$	−18.5224	−	20.9074i	−0.870257	−	0.982317i
$454$	−14.9588	+	3.68701i	−0.702050	+	0.173040i
$455$	−29.3591	+	39.4263i	−1.37638	+	1.84833i
$456$	3.69552	+	0.910865i	0.173059	+	0.0426551i
$457$	−9.43405	−	17.9751i	−0.441306	−	0.840839i	−0.999935	−	0.0114207i	$-0.996365\pi$
$457$	−9.43405	−	17.9751i	−0.441306	−	0.840839i	0.558629	−	0.829418i	$-0.311328\pi$
$458$	8.38685	−	4.40176i	0.391892	−	0.205681i
$459$	1.07969	+	2.84692i	0.0503958	+	0.132883i
$460$	−3.83927	+	1.45604i	−0.179007	+	0.0678884i
$461$	1.75721	−	1.21292i	0.0818415	−	0.0564911i	−0.526441	−	0.850211i	$-0.676474\pi$
$461$	1.75721	−	1.21292i	0.0818415	−	0.0564911i	0.608283	+	0.793720i	$0.291859\pi$
$462$	0.0879403	−	0.356788i	0.00409135	−	0.0165993i
$463$	−9.26139	+	6.39267i	−0.430413	+	0.297093i	−0.763505	−	0.645802i	$-0.776523\pi$
$463$	−9.26139	+	6.39267i	−0.430413	+	0.297093i	0.333092	+	0.942894i	$0.391908\pi$
$464$	−0.790351	+	6.50913i	−0.0366911	+	0.302179i
$465$	8.29291	+	21.8666i	0.384575	+	1.01404i
$466$	1.45368	−	2.76976i	0.0673404	−	0.128306i
$467$	0.651226	−	0.943463i	0.0301351	−	0.0436583i	−0.807627	−	0.589694i	$-0.799248\pi$
$467$	0.651226	−	0.943463i	0.0301351	−	0.0436583i	0.837762	+	0.546036i	$0.183864\pi$
$468$	6.40599	−	1.33689i	0.296117	−	0.0617977i
$469$	22.9876	+	33.3033i	1.06147	+	1.53780i
$470$	−26.0567	+	3.16385i	−1.20191	+	0.145938i
$471$	−18.0297	+	4.44392i	−0.830764	+	0.204765i
$472$	2.99581	−	4.34018i	0.137893	−	0.199773i
$473$	−0.278471	+	0.314329i	−0.0128041	+	0.0144529i
$474$	−4.85126	−	9.24330i	−0.222826	−	0.424559i
$475$	−12.0125	−	1.45858i	−0.551169	−	0.0669241i
$476$	2.52553	−	0.306654i	0.115757	−	0.0140555i
$477$	4.29489	+	3.80494i	0.196650	+	0.174216i
$478$	−7.83487	−	11.3508i	−0.358359	−	0.519172i
$479$	−21.3639	−	2.59405i	−0.976141	−	0.118525i	−0.383109	−	0.923703i	$-0.625146\pi$
$479$	−21.3639	−	2.59405i	−0.976141	−	0.118525i	−0.593033	+	0.805178i	$0.702070\pi$
$480$	−3.64780	−	30.0423i	−0.166498	−	1.37124i
$481$	24.6567	−	2.09865i	1.12425	−	0.0956900i
$482$	0.900493	−	7.41623i	0.0410163	−	0.337800i
$483$	0.790137	−	3.20571i	0.0359525	−	0.145865i
$484$	15.0821			0.685549
$485$	−31.8546			−1.44644
$486$	2.37766	−	9.64654i	0.107853	−	0.437576i
$487$	26.8190	−	10.1711i	1.21528	−	0.460897i	0.338128	−	0.941100i	$-0.390206\pi$
$487$	26.8190	−	10.1711i	1.21528	−	0.460897i	0.877157	+	0.480203i	$0.159437\pi$
$488$		−	1.38138i		−	0.0625320i
$489$	−10.6719	−	4.04732i	−0.482600	−	0.183026i
$490$	14.2035	−	3.50085i	0.641650	−	0.158152i
$491$	5.67577	+	5.02829i	0.256144	+	0.226924i	0.781416	−	0.624011i	$-0.214498\pi$
$491$	5.67577	+	5.02829i	0.256144	+	0.226924i	−0.525272	+	0.850935i	$0.676036\pi$
$492$	−4.64310	−	18.8378i	−0.209327	−	0.849274i
$493$	−4.24601	−	3.76163i	−0.191231	−	0.169415i
$494$	1.69068	+	2.64798i	0.0760671	+	0.119138i
$495$	0.416064	−	0.368600i	0.0187007	−	0.0165674i
$496$	−2.33530	−	1.61194i	−0.104858	−	0.0723783i
$497$	−3.35013	−	0.825734i	−0.150274	−	0.0370392i
$498$	−7.74151	−	11.2155i	−0.346906	−	0.502579i
$499$	3.14528	+	12.7609i	0.140802	+	0.571256i	0.998380	+	0.0569016i	$0.0181221\pi$
$499$	3.14528	+	12.7609i	0.140802	+	0.571256i	−0.857578	+	0.514354i	$0.828032\pi$
$500$	7.88454	+	31.9889i	0.352608	+	1.43059i
$501$	−15.9725	+	1.93942i	−0.713600	+	0.0866467i
$502$	−0.976978	−	1.10278i	−0.0436047	−	0.0492195i
$503$	7.01238	−	18.4901i	0.312667	−	0.824434i	−0.682912	−	0.730501i	$-0.739287\pi$
$503$	7.01238	−	18.4901i	0.312667	−	0.824434i	0.995578	−	0.0939336i	$-0.0299441\pi$
$504$	−10.6619	−	5.59581i	−0.474920	−	0.249257i
$505$	−58.9607	+	40.6977i	−2.62372	+	1.81102i
$506$	0.0622568			0.00276765
$507$	−14.3090	−	8.87491i	−0.635486	−	0.394149i
$508$	−27.4161			−1.21639
$509$	22.1454	−	15.2859i	0.981577	−	0.677534i	0.0347901	−	0.999395i	$-0.488924\pi$
$509$	22.1454	−	15.2859i	0.981577	−	0.677534i	0.946787	+	0.321861i	$0.104308\pi$
$510$	1.97645	+	1.03732i	0.0875187	+	0.0459334i
$511$	−3.78126	+	9.97037i	−0.167273	+	0.441063i
$512$	4.66235	+	5.26270i	0.206049	+	0.232581i
$513$	−6.11318	+	0.742274i	−0.269903	+	0.0327722i
$514$	3.42741	+	13.9055i	0.151176	+	0.613347i
$515$	−1.74022	−	7.06035i	−0.0766832	−	0.311116i
$516$	−4.03563	−	5.84662i	−0.177659	−	0.257383i
$517$	−0.845128	−	0.208305i	−0.0371687	−	0.00916126i
$518$	−15.2502	−	10.5264i	−0.670054	−	0.462505i
$519$	−0.886856	+	0.785686i	−0.0389287	+	0.0344878i
$520$	23.0128	−	30.9038i	1.00918	−	1.35522i
$521$	−27.5248	−	24.3848i	−1.20588	−	1.06832i	−0.995886	−	0.0906166i	$-0.971116\pi$
$521$	−27.5248	−	24.3848i	−1.20588	−	1.06832i	−0.209997	−	0.977702i	$-0.567345\pi$
$522$	2.61486	+	10.6089i	0.114449	+	0.464339i
$523$	4.38641	+	3.88602i	0.191805	+	0.169924i	0.753560	−	0.657380i	$-0.228335\pi$
$523$	4.38641	+	3.88602i	0.191805	+	0.169924i	−0.561755	+	0.827304i	$0.689874\pi$
$524$	−9.87824	+	2.43477i	−0.431533	+	0.106363i
$525$	−45.4081	−	17.2210i	−1.98177	−	0.751587i
$526$		−	3.06298i		−	0.133552i
$527$	2.29537	−	0.870518i	0.0999877	−	0.0379203i
$528$	0.0204758	−	0.0830735i	0.000891094	−	0.00361531i
$529$	−22.4406			−0.975679
$530$	13.7492			0.597226
$531$	−0.624727	+	2.53462i	−0.0271109	+	0.109993i
$532$	−0.620209	+	5.10788i	−0.0268895	+	0.221455i
$533$	19.5271	−	34.1648i	0.845812	−	1.47984i
$534$	−0.349136	−	2.87539i	−0.0151086	−	0.124431i
$535$	67.5331	+	8.20000i	2.91971	+	0.354517i
$536$	−18.0185	−	26.1044i	−0.778282	−	1.12754i
$537$	0.801920	+	0.710439i	0.0346054	+	0.0306577i
$538$	−4.48067	+	0.544051i	−0.193175	+	0.0234557i
$539$	0.481567	+	0.0584728i	0.0207426	+	0.00251860i
$540$	14.2837	+	27.2154i	0.614675	+	1.17116i
$541$	4.27914	−	4.83016i	0.183975	−	0.207665i	−0.649287	−	0.760544i	$-0.724932\pi$
$541$	4.27914	−	4.83016i	0.183975	−	0.207665i	0.833261	+	0.552879i	$0.186471\pi$
$542$	3.90937	−	5.66369i	0.167922	−	0.243277i
$543$	20.2635	−	4.99451i	0.869591	−	0.214335i
$544$	−3.15358	+	0.382914i	−0.135209	+	0.0164173i
$545$	9.80398	+	14.2035i	0.419956	+	0.608412i
$546$	4.04481	+	11.9422i	0.173102	+	0.511080i
$547$	−24.8063	+	35.9381i	−1.06064	+	1.53660i	−0.235337	+	0.971914i	$0.575619\pi$
$547$	−24.8063	+	35.9381i	−1.06064	+	1.53660i	−0.825303	+	0.564690i	$0.808996\pi$
$548$	−6.15774	+	11.7326i	−0.263046	+	0.501192i
$549$	0.242471	+	0.639343i	0.0103484	+	0.0272865i
$550$	0.110380	−	0.909058i	0.00470660	−	0.0387624i
$551$	9.44198	−	6.51733i	0.402242	−	0.277647i
$552$	−0.619339	+	2.51276i	−0.0263608	+	0.106950i
$553$	28.5385	−	19.6987i	1.21358	−	0.837675i
$554$	10.3558	−	3.92743i	0.439975	−	0.166861i
$555$	12.6093	+	33.2481i	0.535236	+	1.41130i
$556$	6.39728	−	3.35755i	0.271305	−	0.142392i
$557$	10.7338	+	20.4515i	0.454804	+	0.866556i	0.999608	+	0.0279930i	$0.00891161\pi$
$557$	10.7338	+	20.4515i	0.454804	+	0.866556i	−0.544804	+	0.838563i	$0.683396\pi$
$558$	−4.59114	−	1.13161i	−0.194358	−	0.0479051i
$559$	2.24940	−	14.2325i	0.0951396	−	0.601969i
$560$	8.32167	−	2.05111i	0.351655	−	0.0866751i
$561$	0.0490846	+	0.0554050i	0.00207235	+	0.00233920i
$562$	−0.477399	−	3.93173i	−0.0201379	−	0.165850i
$563$	−9.30082	+	4.88145i	−0.391983	+	0.205728i	−0.649187	−	0.760629i	$-0.724891\pi$
$563$	−9.30082	+	4.88145i	−0.391983	+	0.205728i	0.257205	+	0.966357i	$0.417199\pi$
$564$	6.84306	−	13.0384i	0.288145	−	0.549014i
$565$	−4.48289	−	1.70014i	−0.188597	−	0.0715252i
$566$	−6.51333	−	7.35203i	−0.273776	−	0.309029i
$567$	−11.1112	−	1.34915i	−0.466627	−	0.0566588i
$568$	2.62596	+	0.647241i	0.110183	+	0.0271576i
$569$	−16.4278	+	14.5537i	−0.688689	+	0.610125i	−0.933130	−	0.359539i	$-0.882934\pi$
$569$	−16.4278	+	14.5537i	−0.688689	+	0.610125i	0.244441	+	0.969664i	$0.421395\pi$
$570$	−2.99365	+	3.37914i	−0.125390	+	0.141537i
$571$	−20.1547	+	10.5780i	−0.843450	+	0.442676i	−0.830353	−	0.557238i	$-0.811861\pi$
$571$	−20.1547	+	10.5780i	−0.843450	+	0.442676i	−0.0130966	+	0.999914i	$0.504169\pi$
$572$	0.438278	−	0.279831i	0.0183253	−	0.0117003i
$573$	−18.7503	−	9.84090i	−0.783303	−	0.411109i
$574$	−27.5525	+	10.4493i	−1.15002	+	0.436145i
$575$	0.991753	−	8.16782i	0.0413590	−	0.340622i
$576$	3.94584	+	2.07094i	0.164410	+	0.0862891i
$577$			1.95329i			0.0813165i	0.999173	+	0.0406583i	$0.0129455\pi$
$577$			1.95329i			0.0813165i	−0.999173	+	0.0406583i	$0.987055\pi$
$578$	−6.14944	+	11.7168i	−0.255783	+	0.487354i
$579$	6.33783	−	7.15393i	0.263391	−	0.297307i
$580$	−47.1266	−	32.5291i	−1.95682	−	1.35070i
$581$	33.8849	−	30.0194i	1.40578	−	1.24541i
$582$	−4.64145	+	6.72430i	−0.192394	+	0.278731i
$583$	0.426312	+	0.161679i	0.0176561	+	0.00669606i
$584$	2.96390	−	7.81515i	0.122647	−	0.323393i
$585$	−5.22650	+	18.3426i	−0.216089	+	0.758374i
$586$	3.37129	+	8.88937i	0.139267	+	0.367217i
$587$			7.95369i			0.328284i	0.986437	+	0.164142i	$0.0524855\pi$
$587$			7.95369i			0.328284i	−0.986437	+	0.164142i	$0.947514\pi$
$588$	−2.91009	+	7.67327i	−0.120010	+	0.316440i
$589$	0.598468	+	4.92883i	0.0246594	+	0.203089i
$590$	2.90694	+	5.53871i	0.119677	+	0.228025i
$591$	−8.11258	−	5.59971i	−0.333707	−	0.230341i
$592$	−3.55081	−	2.45095i	−0.145937	−	0.100733i
$593$	9.72876	+	18.5366i	0.399512	+	0.761207i	0.999239	−	0.0389974i	$-0.0124164\pi$
$593$	9.72876	+	18.5366i	0.399512	+	0.761207i	−0.599727	+	0.800205i	$0.704724\pi$
$594$	−0.0561726	−	0.462623i	−0.00230479	−	0.0189816i
$595$	−2.62932	+	6.93295i	−0.107792	+	0.284223i
$596$		−	18.1366i		−	0.742903i
$597$	7.43385	+	19.6014i	0.304247	+	0.802234i
$598$	−1.80048	+	1.14957i	−0.0736273	+	0.0470093i
$599$	1.02144	−	2.69333i	0.0417351	−	0.110046i	−0.912528	−	0.409014i	$-0.865873\pi$
$599$	1.02144	−	2.69333i	0.0417351	−	0.110046i	0.954263	+	0.298967i	$0.0966421\pi$
$600$	35.5926	+	13.4985i	1.45306	+	0.551073i
$601$	−0.862750	+	1.24991i	−0.0351923	+	0.0509848i	−0.840185	−	0.542300i	$-0.817554\pi$
$601$	−0.862750	+	1.24991i	−0.0351923	+	0.0509848i	0.804993	+	0.593285i	$0.202169\pi$
$602$	−8.07637	+	7.15504i	−0.329168	+	0.291618i
$603$	12.9216	+	8.91913i	0.526208	+	0.363215i
$604$	−19.6272	+	22.1546i	−0.798621	+	0.901456i
$605$	−20.4280	+	38.9222i	−0.830515	+	1.58241i
$606$			18.3762i			0.746481i
$607$	15.7322	+	8.25691i	0.638551	+	0.335138i	0.752737	−	0.658322i	$-0.228733\pi$
$607$	15.7322	+	8.25691i	0.638551	+	0.335138i	−0.114185	+	0.993459i	$0.536426\pi$
$608$	0.774444	−	6.37812i	0.0314078	−	0.258667i
$609$	43.0522	−	16.3275i	1.74456	−	0.661625i
$610$	1.45079	+	0.761433i	0.0587407	+	0.0308295i
$611$	28.2877	−	9.58099i	1.14440	−	0.387605i
$612$	0.874029	−	0.458726i	0.0353305	−	0.0185429i
$613$	26.2330	−	29.6109i	1.05954	−	1.19597i	0.0795700	−	0.996829i	$-0.474645\pi$
$613$	26.2330	−	29.6109i	1.05954	−	1.19597i	0.979970	−	0.199144i	$-0.0638163\pi$
$614$	−15.7020	+	13.9108i	−0.633681	+	0.561392i
$615$	54.9034	+	13.5325i	2.21392	+	0.545682i
$616$	−0.949828	−	0.115330i	−0.0382696	−	0.00464678i
$617$	1.11031	+	1.25328i	0.0446994	+	0.0504552i	0.770435	−	0.637518i	$-0.220039\pi$
$617$	1.11031	+	1.25328i	0.0446994	+	0.0504552i	−0.725736	+	0.687973i	$0.758501\pi$
$618$	−1.74396	−	0.661395i	−0.0701522	−	0.0266052i
$619$	21.0964	−	40.1959i	0.847937	−	1.61561i	0.0613600	−	0.998116i	$-0.480456\pi$
$619$	21.0964	−	40.1959i	0.847937	−	1.61561i	0.786577	−	0.617493i	$-0.211851\pi$
$620$	21.9428	−	11.5165i	0.881243	−	0.462512i
$621$	−0.504706	−	4.15663i	−0.0202532	−	0.166800i
$622$	7.80150	+	8.80608i	0.312812	+	0.353091i
$623$	9.34220	−	2.30264i	0.374287	−	0.0922535i
$624$	0.941782	+	2.78059i	0.0377015	+	0.111313i
$625$	−39.8258	−	9.81617i	−1.59303	−	0.392647i
$626$	−7.67993	−	14.6329i	−0.306952	−	0.584848i
$627$	−0.132558	+	0.0695720i	−0.00529387	+	0.00277844i
$628$	6.97753	+	18.3982i	0.278434	+	0.734170i
$629$	3.49009	−	1.32362i	0.139159	−	0.0527761i
$630$	11.7540	−	8.11319i	0.468290	−	0.323237i
$631$	8.28278	−	33.6046i	0.329732	−	1.33778i	−0.538921	−	0.842356i	$-0.681168\pi$
$631$	8.28278	−	33.6046i	0.329732	−	1.33778i	0.868653	−	0.495420i	$-0.164986\pi$
$632$	−22.3696	+	15.4406i	−0.889813	+	0.614194i
$633$	1.31401	−	10.8219i	0.0522274	−	0.430131i
$634$	5.44188	+	14.3491i	0.216125	+	0.569874i
$635$	37.1338	−	70.7525i	1.47361	−	2.80773i
$636$	−4.38160	+	6.34785i	−0.173742	+	0.251709i
$637$	−15.0068	+	7.20106i	−0.594589	+	0.285316i
$638$	0.493207	+	0.714534i	0.0195263	+	0.0282887i
$639$	−1.32898	+	0.161368i	−0.0525738	+	0.00638361i
$640$	−35.0046	+	8.62785i	−1.38368	+	0.341046i
$641$	−14.8935	+	21.5769i	−0.588257	+	0.852237i	−0.998206	−	0.0598710i	$-0.980931\pi$
$641$	−14.8935	+	21.5769i	−0.588257	+	0.852237i	0.409949	+	0.912108i	$0.365546\pi$
$642$	11.5710	−	13.0610i	0.456672	−	0.515476i
$643$	14.6399	+	27.8940i	0.577341	+	1.10003i	0.982583	+	0.185822i	$0.0594947\pi$
$643$	14.6399	+	27.8940i	0.577341	+	1.10003i	−0.405243	+	0.914209i	$0.632813\pi$
$644$	−3.47308	−	0.421709i	−0.136859	−	0.0166177i
$645$	20.5544	−	2.49575i	0.809328	−	0.0982702i
$646$	0.354712	+	0.314248i	0.0139560	+	0.0123639i
$647$	0.830344	+	1.20296i	0.0326442	+	0.0472933i	0.838966	−	0.544184i	$-0.183160\pi$
$647$	0.830344	+	1.20296i	0.0326442	+	0.0472933i	−0.806322	+	0.591477i	$0.798545\pi$
$648$	8.70939	+	1.05751i	0.342137	+	0.0415430i
$649$	0.0250030	+	0.205919i	0.000981455	+	0.00808301i
$650$	13.5935	+	28.3284i	0.533181	+	1.11113i
$651$	−2.40185	+	19.7810i	−0.0941358	+	0.775278i
$652$	−2.89438	+	11.7430i	−0.113353	+	0.459891i
$653$	25.9954			1.01728			0.508640	−	0.860979i	$-0.330148\pi$
$653$	25.9954			1.01728			0.508640	+	0.860979i	$0.330148\pi$
$654$	4.42678			0.173101
$655$	7.09622	−	28.7905i	0.277272	−	1.12494i
$656$	−6.41526	+	2.43299i	−0.250474	+	0.0949922i
$657$			4.13734i			0.161413i
$658$	−20.9113	−	7.93059i	−0.815206	−	0.309167i
$659$	12.4111	−	3.05907i	0.483468	−	0.119164i	0.00995425	−	0.999950i	$-0.496831\pi$
$659$	12.4111	−	3.05907i	0.483468	−	0.119164i	0.473514	+	0.880786i	$0.342985\pi$
$660$	0.559295	+	0.495492i	0.0217705	+	0.0192870i
$661$	2.51762	+	10.2144i	0.0979240	+	0.397293i	0.999366	−	0.0356068i	$-0.0113364\pi$
$661$	2.51762	+	10.2144i	0.0979240	+	0.397293i	−0.901442	+	0.432900i	$0.857490\pi$
$662$	−18.9198	−	16.7615i	−0.735338	−	0.651453i
$663$	−2.44259	−	0.695986i	−0.0948624	−	0.0270298i
$664$	−26.5603	+	23.5303i	−1.03074	+	0.913154i
$665$	−12.3418	−	8.51895i	−0.478595	−	0.330351i
$666$	−6.98080	−	1.72061i	−0.270501	−	0.0666724i
$667$	4.43143	+	6.42003i	0.171586	+	0.248585i
$668$	4.08024	+	16.5542i	0.157869	+	0.640500i
$669$	5.47223	+	22.2017i	0.211569	+	0.858367i
$670$	37.3481	−	4.53488i	1.44288	−	0.175198i
$671$	0.0360299	+	0.0406694i	0.00139092	+	0.00157002i
$672$	9.14365	−	24.1098i	0.352724	−	0.930057i
$673$	−38.9104	−	20.4218i	−1.49989	−	0.787201i	−0.502867	−	0.864364i	$-0.667721\pi$
$673$	−38.9104	−	20.4218i	−1.49989	−	0.787201i	−0.997018	+	0.0771630i	$0.975414\pi$
$674$	19.5630	−	13.5033i	0.753538	−	0.520130i
$675$	−61.5889			−2.37056
$676$	−7.50808	+	16.1856i	−0.288772	+	0.622522i
$677$	22.4753			0.863795			0.431898	−	0.901923i	$-0.357844\pi$
$677$	22.4753			0.863795			0.431898	+	0.901923i	$0.357844\pi$
$678$	−1.01208	+	0.698586i	−0.0388686	+	0.0268290i
$679$	−24.0327	−	12.6133i	−0.922291	−	0.484056i
$680$	2.06096	−	5.43431i	0.0790343	−	0.208396i
$681$	16.7042	+	18.8551i	0.640105	+	0.722529i
$682$	−0.372996	+	0.0452899i	−0.0142827	+	0.00173424i
$683$	−3.13572	−	12.7221i	−0.119985	−	0.486798i	−0.999931	−	0.0117248i	$-0.996268\pi$
$683$	−3.13572	−	12.7221i	−0.119985	−	0.486798i	0.879946	−	0.475073i	$-0.157578\pi$
$684$	0.477770	+	1.93839i	0.0182680	+	0.0741162i
$685$	−21.9379	−	31.7825i	−0.838202	−	1.21435i
$686$	−6.24827	−	1.54006i	−0.238560	−	0.0587997i
$687$	−12.7453	−	8.79747i	−0.486265	−	0.335644i
$688$	−1.88048	+	1.66596i	−0.0716927	+	0.0635142i
$689$	−15.3145	+	3.19603i	−0.583435	+	0.121759i
$690$	−2.29763	−	2.03552i	−0.0874693	−	0.0774911i
$691$	−9.90273	−	40.1770i	−0.376718	−	1.52840i	−0.787294	−	0.616577i	$-0.788519\pi$
$691$	−9.90273	−	40.1770i	−0.376718	−	1.52840i	0.410577	−	0.911826i	$-0.365327\pi$
$692$	0.939757	+	0.832552i	0.0357242	+	0.0316489i
$693$	0.459853	−	0.113344i	0.0174684	−	0.00430557i
$694$	9.44195	+	3.58086i	0.358412	+	0.135928i
$695$			21.0571i			0.798740i
$696$	−33.7459	+	12.7981i	−1.27914	+	0.485112i
$697$	1.42052	−	5.76328i	0.0538061	−	0.218300i
$698$	−1.32599			−0.0501893
$699$	−5.11449			−0.193448
$700$	−12.3154	+	49.9654i	−0.465477	+	1.88852i
$701$	−1.29461	+	10.6621i	−0.0488967	+	0.402700i	0.947626	+	0.319381i	$0.103475\pi$
$701$	−1.29461	+	10.6621i	−0.0488967	+	0.402700i	−0.996523	+	0.0833189i	$0.973448\pi$
$702$	10.1668	+	12.3420i	0.383722	+	0.465817i
$703$	0.909967	+	7.49425i	0.0343201	+	0.282651i
$704$	0.351519	+	0.0426822i	0.0132484	+	0.00160864i
$705$	24.3794	+	35.3196i	0.918181	+	1.33021i
$706$	4.86759	+	4.31231i	0.183194	+	0.162296i
$707$	−60.5979	+	7.35791i	−2.27902	+	0.276723i
$708$	−3.48355	−	0.422980i	−0.130920	−	0.0158965i
$709$	0.960847	+	1.83074i	0.0360854	+	0.0687549i	0.902831	−	0.429995i	$-0.141485\pi$
$709$	0.960847	+	1.83074i	0.0360854	+	0.0687549i	−0.866746	+	0.498750i	$0.833792\pi$
$710$	−2.12723	+	2.40114i	−0.0798334	+	0.0901133i
$711$	7.64305	−	11.0729i	0.286637	−	0.415265i
$712$	−7.32276	+	1.80490i	−0.274432	+	0.0676415i
$713$	−3.35134	+	0.406926i	−0.125509	+	0.0152395i
$714$	1.08039	+	1.56521i	0.0404326	+	0.0585767i
$715$	0.128530	+	1.51008i	0.00480674	+	0.0564737i
$716$	0.644901	−	0.934301i	0.0241011	−	0.0349165i
$717$	−10.4799	+	19.9677i	−0.391378	+	0.745708i
$718$	1.25456	+	3.30800i	0.0468197	+	0.123453i
$719$	−4.09358	+	33.7137i	−0.152665	+	1.25731i	0.691955	+	0.721941i	$0.256750\pi$
$719$	−4.09358	+	33.7137i	−0.152665	+	1.25731i	−0.844620	+	0.535367i	$0.820173\pi$
$720$	2.73677	−	1.88905i	0.101993	−	0.0704009i
$721$	1.48275	−	6.01575i	0.0552205	−	0.224038i
$722$	11.5980	−	8.00555i	0.431634	−	0.297936i
$723$	−11.4211	+	4.33145i	−0.424755	+	0.161088i
$724$	−7.84203	−	20.6777i	−0.291447	−	0.768482i
$725$	101.601	−	53.3241i	3.77335	−	1.98041i
$726$	5.23972	+	9.98346i	0.194464	+	0.370521i
$727$	35.8557	+	8.83763i	1.32981	+	0.327770i	0.839302	−	0.543665i	$-0.182964\pi$
$727$	35.8557	+	8.83763i	1.32981	+	0.327770i	0.490511	+	0.871435i	$0.336810\pi$
$728$	29.5989	−	14.2031i	1.09701	−	0.526403i
$729$	−25.3382	+	6.24529i	−0.938450	+	0.231307i
$730$	6.57411	+	7.42064i	0.243319	+	0.274650i
$731$	−0.261982	−	2.15762i	−0.00968977	−	0.0798024i
$732$	−0.813885	+	0.427160i	−0.0300820	+	0.0157883i
$733$	11.5115	−	21.9333i	0.425186	−	0.810124i	−0.574781	−	0.818307i	$-0.694913\pi$
$733$	11.5115	−	21.9333i	0.425186	−	0.810124i	0.999967	+	0.00818381i	$0.00260502\pi$
$734$	9.11775	+	3.45791i	0.336542	+	0.127634i
$735$	−15.8608	−	17.9031i	−0.585033	−	0.660366i
$736$	4.33678	+	0.526580i	0.159856	+	0.0194100i
$737$	1.21136	+	0.298573i	0.0446209	+	0.0109981i
$738$	−8.55794	+	7.58167i	−0.315022	+	0.279085i
$739$	−2.85202	+	3.21926i	−0.104913	+	0.118422i	−0.798622	−	0.601833i	$-0.794437\pi$
$739$	−2.85202	+	3.21926i	−0.104913	+	0.118422i	0.693709	+	0.720256i	$0.255976\pi$
$740$	33.3639	−	17.5107i	1.22648	−	0.643707i
$741$	2.54898	−	4.45972i	0.0936392	−	0.163832i
$742$	10.3731	+	5.44421i	0.380807	+	0.199863i
$743$	−27.9539	+	10.6015i	−1.02553	+	0.388931i	−0.809290	−	0.587409i	$-0.800148\pi$
$743$	−27.9539	+	10.6015i	−1.02553	+	0.388931i	−0.216238	+	0.976341i	$0.569379\pi$
$744$	1.88266	−	15.5051i	0.0690216	−	0.568444i
$745$	46.8049	+	24.5651i	1.71480	+	0.899996i
$746$			15.8227i			0.579311i
$747$	8.16266	−	15.5526i	0.298656	−	0.569041i
$748$	0.0520124	−	0.0587099i	0.00190176	−	0.00214665i
$749$	47.7035	+	32.9273i	1.74305	+	1.20314i
$750$	−18.4356	+	16.3325i	−0.673171	+	0.596378i
$751$	−6.38113	+	9.24466i	−0.232851	+	0.337342i	−0.921939	−	0.387335i	$-0.873396\pi$
$751$	−6.38113	+	9.24466i	−0.232851	+	0.337342i	0.689088	+	0.724677i	$0.258011\pi$
$752$	−4.86892	−	1.84654i	−0.177551	−	0.0673363i
$753$	−0.854208	+	2.25236i	−0.0311291	+	0.0820806i
$754$	−27.4575	−	11.5575i	−0.999944	−	0.420899i
$755$	−30.5900	−	80.6591i	−1.11328	−	2.93549i
$756$			26.1886i			0.952469i
$757$	−9.72412	+	25.6404i	−0.353429	+	0.931916i	0.633926	+	0.773393i	$0.281442\pi$
$757$	−9.72412	+	25.6404i	−0.353429	+	0.931916i	−0.987355	+	0.158522i	$0.949327\pi$
$758$	−2.44924	−	20.1713i	−0.0889603	−	0.732654i
$759$	−0.0473052	−	0.0901325i	−0.00171707	−	0.00327160i
$760$	9.67399	+	6.67747i	0.350912	+	0.242217i
$761$	26.7764	+	18.4824i	0.970644	+	0.669987i	0.944100	−	0.329661i	$-0.106934\pi$
$761$	26.7764	+	18.4824i	0.970644	+	0.669987i	0.0265443	+	0.999648i	$0.491550\pi$
$762$	−9.52473	−	18.1479i	−0.345045	−	0.657427i
$763$	1.77250	+	14.5979i	0.0641690	+	0.528479i
$764$	−7.95696	+	20.9808i	−0.287873	+	0.759058i
$765$			2.87692i			0.104015i
$766$	6.53540	+	17.2324i	0.236134	+	0.622634i
$767$	−4.52537	−	5.49355i

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)

\(f(q)\)	\(=\)	\(q+(0.651938 - 0.450000i) q^{2} +(-1.14686 - 0.601918i) q^{3} +(-0.486687 + 1.28329i) q^{4} +(-2.65258 - 2.99414i) q^{5} +(-1.01854 + 0.123674i) q^{6} +(-0.815660 - 3.30926i) q^{7} +(0.639345 + 2.59392i) q^{8} +(-0.751216 - 1.08832i) q^{9} +O(q^{10})\)	\(q+(0.651938 - 0.450000i) q^{2} +(-1.14686 - 0.601918i) q^{3} +(-0.486687 + 1.28329i) q^{4} +(-2.65258 - 2.99414i) q^{5} +(-1.01854 + 0.123674i) q^{6} +(-0.815660 - 3.30926i) q^{7} +(0.639345 + 2.59392i) q^{8} +(-0.751216 - 1.08832i) q^{9} +(-3.07668 - 0.758333i) q^{10} +(-0.0864794 - 0.0596924i) q^{11} +(1.33059 - 1.17880i) q^{12} +(3.60323 + 0.129485i) q^{13} +(-2.02093 - 1.79039i) q^{14} +(1.23990 + 5.03049i) q^{15} +(-0.470548 - 0.416869i) q^{16} +(0.528057 - 0.130154i) q^{17} +(-0.979492 - 0.371472i) q^{18} +1.09996i q^{19} +(5.13332 - 1.94681i) q^{20} +(-1.05646 + 4.28621i) q^{21} -0.0832408 q^{22} -0.747912 q^{23} +(0.828090 - 3.35969i) q^{24} +(-1.32603 + 10.9208i) q^{25} +(2.40735 - 1.53704i) q^{26} +(0.674820 + 5.55764i) q^{27} +(4.64371 + 0.563848i) q^{28} +(-5.92507 - 8.58394i) q^{29} +(3.07206 + 2.72161i) q^{30} +(4.48092 - 0.544083i) q^{31} +(-5.79851 - 0.704066i) q^{32} +(0.0632497 + 0.120512i) q^{33} +(0.285691 - 0.322478i) q^{34} +(-7.74479 + 11.2203i) q^{35} +(1.76224 - 0.434353i) q^{36} +(6.81322 - 0.827274i) q^{37} +(0.494981 + 0.717104i) q^{38} +(-4.05445 - 2.31735i) q^{39} +(6.07066 - 8.79487i) q^{40} +(5.07205 - 9.66399i) q^{41} +(1.24005 + 3.26975i) q^{42} +(0.481709 - 3.96723i) q^{43} +(0.118691 - 0.0819264i) q^{44} +(-1.26594 + 5.13611i) q^{45} +(-0.487592 + 0.336561i) q^{46} +(7.74511 - 2.93733i) q^{47} +(0.288731 + 0.761320i) q^{48} +(-4.08772 + 2.14540i) q^{49} +(4.04989 + 7.71642i) q^{50} +(-0.683948 - 0.168578i) q^{51} +(-1.91981 + 4.56096i) q^{52} +(-4.21290 + 1.03839i) q^{53} +(2.94088 + 3.31957i) q^{54} +(0.0506658 + 0.417270i) q^{55} +(8.06248 - 4.23152i) q^{56} +(0.662084 - 1.26150i) q^{57} +(-7.72555 - 2.92992i) q^{58} +(-1.30902 - 1.47758i) q^{59} +(-7.05901 - 0.857119i) q^{60} +(-0.502044 - 0.123743i) q^{61} +(2.67645 - 2.37112i) q^{62} +(-2.98881 + 3.37367i) q^{63} +(-2.98382 + 1.56603i) q^{64} +(-9.17014 - 11.1320i) q^{65} +(0.0954654 + 0.0501041i) q^{66} +(-11.1014 + 4.21020i) q^{67} +(-0.0899728 + 0.740993i) q^{68} +(0.857749 + 0.450181i) q^{69} +10.8001i q^{70} +(0.470463 - 0.896392i) q^{71} +(2.34274 - 2.64441i) q^{72} +(-2.57481 - 1.77726i) q^{73} +(4.06952 - 3.60528i) q^{74} +(8.09421 - 11.7265i) q^{75} +(-1.41156 - 0.535335i) q^{76} +(-0.127000 + 0.334871i) q^{77} +(-3.68606 + 0.313737i) q^{78} +(3.60784 + 9.51309i) q^{79} +2.51466i q^{80} +(1.16452 - 3.07059i) q^{81} +(-1.04213 - 8.58275i) q^{82} +(6.17255 + 11.7608i) q^{83} +(-4.98628 - 3.44178i) q^{84} +(-1.79041 - 1.23583i) q^{85} +(-1.47121 - 2.80316i) q^{86} +(1.62839 + 13.4110i) q^{87} +(0.0995474 - 0.262485i) q^{88} +2.82305i q^{89} +(1.48594 + 3.91809i) q^{90} +(-2.51051 - 12.0296i) q^{91} +(0.363999 - 0.959787i) q^{92} +(-5.46648 - 2.07316i) q^{93} +(3.72753 - 5.40026i) q^{94} +(3.29343 - 2.91772i) q^{95} +(6.22628 + 4.29769i) q^{96} +(5.28070 - 5.96068i) q^{97} +(-1.69951 + 3.23814i) q^{98} +0.138959i 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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