LMFDB - Embedded newform 169.2.h.a.25.3

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			25.3
Character	$\chi$	$=$	169.25
Dual form			169.2.h.a.142.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.68720 - 0.639871i) q^{2} +(0.0407127 + 0.0589826i) q^{3} +(0.940192 + 0.832938i) q^{4} +(0.654244 + 0.0794397i) q^{5} +(-0.0309493 - 0.125566i) q^{6} +(-0.153151 - 0.291806i) q^{7} +(0.623830 + 1.18861i) q^{8} +(1.06199 - 2.80025i) q^{9} +O(q^{10})$	\(q+(-1.68720 - 0.639871i) q^{2} +(0.0407127 + 0.0589826i) q^{3} +(0.940192 + 0.832938i) q^{4} +(0.654244 + 0.0794397i) q^{5} +(-0.0309493 - 0.125566i) q^{6} +(-0.153151 - 0.291806i) q^{7} +(0.623830 + 1.18861i) q^{8} +(1.06199 - 2.80025i) q^{9} +(-1.05301 - 0.552663i) q^{10} +(3.29754 - 1.25059i) q^{11} +(-0.0108510 + 0.0893661i) q^{12} +(-3.47540 - 0.959994i) q^{13} +(0.0716793 + 0.590332i) q^{14} +(0.0219505 + 0.0418232i) q^{15} +(-0.594779 - 4.89844i) q^{16} +(4.33713 - 2.27630i) q^{17} +(-3.58359 + 4.04504i) q^{18} -4.67024i q^{19} +(0.548947 + 0.619633i) q^{20} +(0.0109762 - 0.0209135i) q^{21} -6.36384 q^{22} +3.76934 q^{23} +(-0.0447094 + 0.0851866i) q^{24} +(-4.43298 - 1.09263i) q^{25} +(5.24943 + 3.84351i) q^{26} +(0.417162 - 0.102821i) q^{27} +(0.0990641 - 0.401919i) q^{28} +(1.37597 - 3.62813i) q^{29} +(-0.0102735 - 0.0846097i) q^{30} +(1.62148 + 6.57861i) q^{31} +(-1.48836 + 6.03852i) q^{32} +(0.208015 + 0.143583i) q^{33} +(-8.77415 + 1.06537i) q^{34} +(-0.0770175 - 0.203078i) q^{35} +(3.33091 - 1.74820i) q^{36} +(2.40265 + 9.74795i) q^{37} +(-2.98835 + 7.87963i) q^{38} +(-0.0848701 - 0.244072i) q^{39} +(0.313715 + 0.827197i) q^{40} +(-8.11133 + 5.59885i) q^{41} +(-0.0319010 + 0.0282618i) q^{42} +(2.63216 + 0.648770i) q^{43} +(4.14199 + 1.57085i) q^{44} +(0.917254 - 1.74768i) q^{45} +(-6.35963 - 2.41189i) q^{46} +(5.36429 + 6.05503i) q^{47} +(0.264708 - 0.234511i) q^{48} +(3.91476 - 5.67151i) q^{49} +(6.78019 + 4.68003i) q^{50} +(0.310838 + 0.163141i) q^{51} +(-2.46793 - 3.79737i) q^{52} +(-5.64437 + 2.96240i) q^{53} +(-0.769629 - 0.0934498i) q^{54} +(2.25675 - 0.556238i) q^{55} +(0.251302 - 0.364074i) q^{56} +(0.275463 - 0.190138i) q^{57} +(-4.64307 + 5.24095i) q^{58} +(4.72673 + 0.573928i) q^{59} +(-0.0141984 + 0.0576053i) q^{60} +(-4.77126 - 2.50415i) q^{61} +(1.47370 - 12.1370i) q^{62} +(-0.979773 + 0.118966i) q^{63} +(0.768897 - 1.11394i) q^{64} +(-2.19750 - 0.904155i) q^{65} +(-0.259089 - 0.375356i) q^{66} +(-7.79129 - 8.79455i) q^{67} +(5.97375 + 1.47240i) q^{68} +(0.153460 + 0.222325i) q^{69} +0.391916i q^{70} +(-1.05635 + 0.729146i) q^{71} +(3.99090 - 0.484583i) q^{72} +(-4.91959 + 1.86575i) q^{73} +(2.18367 - 17.9841i) q^{74} +(-0.116033 - 0.305953i) q^{75} +(3.89002 - 4.39092i) q^{76} +(-0.869954 - 0.770712i) q^{77} +(-0.0129817 + 0.466105i) q^{78} +(1.45245 - 1.28676i) q^{79} -3.25203i q^{80} +(-6.70201 - 5.93747i) q^{81} +(17.2680 - 4.25618i) q^{82} +(2.13161 + 1.47134i) q^{83} +(0.0277394 - 0.0105202i) q^{84} +(3.01837 - 1.14472i) q^{85} +(-4.02586 - 2.77885i) q^{86} +(0.270016 - 0.0665530i) q^{87} +(3.54357 + 3.13933i) q^{88} +3.65402i q^{89} +(-2.66588 + 2.36177i) q^{90} +(0.252131 + 1.16117i) q^{91} +(3.54390 + 3.13962i) q^{92} +(-0.322008 + 0.363472i) q^{93} +(-5.17620 - 13.6485i) q^{94} +(0.371002 - 3.05548i) q^{95} +(-0.416762 + 0.158057i) q^{96} +(-4.73020 + 0.574351i) q^{97} +(-10.2340 + 7.06403i) q^{98} -10.5621i 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{26}\right)$

Coefficient data

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

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

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

$2$	−1.68720	−	0.639871i	−1.19303	−	0.452457i	−0.323449	−	0.946245i	$-0.604843\pi$
$2$	−1.68720	−	0.639871i	−1.19303	−	0.452457i	−0.869582	+	0.493788i	$0.835612\pi$
$3$	0.0407127	+	0.0589826i	0.0235055	+	0.0340536i	0.834560	−	0.550916i	$-0.185722\pi$
$3$	0.0407127	+	0.0589826i	0.0235055	+	0.0340536i	−0.811055	+	0.584970i	$0.801106\pi$
$4$	0.940192	+	0.832938i	0.470096	+	0.416469i
$5$	0.654244	+	0.0794397i	0.292587	+	0.0355265i	0.265514	−	0.964107i	$-0.414458\pi$
$5$	0.654244	+	0.0794397i	0.292587	+	0.0355265i	0.0270729	+	0.999633i	$0.491381\pi$
$6$	−0.0309493	−	0.125566i	−0.0126350	−	0.0512622i
$7$	−0.153151	−	0.291806i	−0.0578858	−	0.110292i	0.854794	−	0.518967i	$-0.173683\pi$
$7$	−0.153151	−	0.291806i	−0.0578858	−	0.110292i	−0.912680	+	0.408675i	$0.865991\pi$
$8$	0.623830	+	1.18861i	0.220557	+	0.420237i
$9$	1.06199	−	2.80025i	0.353998	−	0.933415i
$10$	−1.05301	−	0.552663i	−0.332991	−	0.174767i
$11$	3.29754	−	1.25059i	0.994247	−	0.377068i	0.196791	−	0.980445i	$-0.436948\pi$
$11$	3.29754	−	1.25059i	0.994247	−	0.377068i	0.797456	+	0.603377i	$0.206179\pi$
$12$	−0.0108510	+	0.0893661i	−0.00313242	+	0.0257978i
$13$	−3.47540	−	0.959994i	−0.963903	−	0.266254i
$13$	−3.47540	−	0.959994i	−0.963903	−	0.266254i
$14$	0.0716793	+	0.590332i	0.0191571	+	0.157773i
$15$	0.0219505	+	0.0418232i	0.00566760	+	0.0107987i
$16$	−0.594779	−	4.89844i	−0.148695	−	1.22461i
$17$	4.33713	−	2.27630i	1.05191	−	0.552084i	0.152098	−	0.988365i	$-0.451397\pi$
$17$	4.33713	−	2.27630i	1.05191	−	0.552084i	0.899810	+	0.436281i	$0.143705\pi$
$18$	−3.58359	+	4.04504i	−0.844661	+	0.953425i
$19$		−	4.67024i		−	1.07143i	−0.844400	−	0.535713i	$-0.820043\pi$
$19$		−	4.67024i		−	1.07143i	0.844400	−	0.535713i	$-0.179957\pi$
$20$	0.548947	+	0.619633i	0.122748	+	0.138554i
$21$	0.0109762	−	0.0209135i	0.00239521	−	0.00456369i
$22$	−6.36384			−1.35678
$23$	3.76934			0.785961			0.392980	−	0.919547i	$-0.371444\pi$
$23$	3.76934			0.785961			0.392980	+	0.919547i	$0.371444\pi$
$24$	−0.0447094	+	0.0851866i	−0.00912626	+	0.0173886i
$25$	−4.43298	−	1.09263i	−0.886597	−	0.218526i
$26$	5.24943	+	3.84351i	1.02950	+	0.753775i
$27$	0.417162	−	0.102821i	0.0802829	−	0.0197879i
$28$	0.0990641	−	0.401919i	0.0187214	−	0.0759555i
$29$	1.37597	−	3.62813i	0.255511	−	0.673727i	−0.744470	−	0.667655i	$-0.767298\pi$
$29$	1.37597	−	3.62813i	0.255511	−	0.673727i	0.999982	−	0.00607198i	$-0.00193278\pi$
$30$	−0.0102735	−	0.0846097i	−0.00187567	−	0.0154475i
$31$	1.62148	+	6.57861i	0.291227	+	1.18155i	0.916140	+	0.400859i	$0.131288\pi$
$31$	1.62148	+	6.57861i	0.291227	+	1.18155i	−0.624913	+	0.780694i	$0.714866\pi$
$32$	−1.48836	+	6.03852i	−0.263108	+	1.06747i
$33$	0.208015	+	0.143583i	0.0362108	+	0.0249945i
$34$	−8.77415	+	1.06537i	−1.50475	+	0.182710i
$35$	−0.0770175	−	0.203078i	−0.0130183	−	0.0343265i
$36$	3.33091	−	1.74820i	0.555151	−	0.291366i
$37$	2.40265	+	9.74795i	0.394994	+	1.60255i	0.745843	+	0.666121i	$0.232047\pi$
$37$	2.40265	+	9.74795i	0.394994	+	1.60255i	−0.350850	+	0.936432i	$0.614107\pi$
$38$	−2.98835	+	7.87963i	−0.484774	+	1.27825i
$39$	−0.0848701	−	0.244072i	−0.0135901	−	0.0390828i
$40$	0.313715	+	0.827197i	0.0496026	+	0.130791i
$41$	−8.11133	+	5.59885i	−1.26678	+	0.874393i	−0.996096	−	0.0882764i	$-0.971864\pi$
$41$	−8.11133	+	5.59885i	−1.26678	+	0.874393i	−0.270681	+	0.962669i	$0.587249\pi$
$42$	−0.0319010	+	0.0282618i	−0.00492244	+	0.00436090i
$43$	2.63216	+	0.648770i	0.401401	+	0.0989365i	0.434848	−	0.900504i	$-0.356802\pi$
$43$	2.63216	+	0.648770i	0.401401	+	0.0989365i	−0.0334467	+	0.999441i	$0.510648\pi$
$44$	4.14199	+	1.57085i	0.624429	+	0.236815i
$45$	0.917254	−	1.74768i	0.136736	−	0.260529i
$46$	−6.35963	−	2.41189i	−0.937676	−	0.355614i
$47$	5.36429	+	6.05503i	0.782462	+	0.883217i	0.995590	−	0.0938070i	$-0.0299037\pi$
$47$	5.36429	+	6.05503i	0.782462	+	0.883217i	−0.213128	+	0.977024i	$0.568365\pi$
$48$	0.264708	−	0.234511i	0.0382073	−	0.0338487i
$49$	3.91476	−	5.67151i	0.559251	−	0.810215i
$50$	6.78019	+	4.68003i	0.958864	+	0.661856i
$51$	0.310838	+	0.163141i	0.0435261	+	0.0228442i
$52$	−2.46793	−	3.79737i	−0.342240	−	0.526601i
$53$	−5.64437	+	2.96240i	−0.775314	+	0.406916i	−0.805476	−	0.592629i	$-0.798090\pi$
$53$	−5.64437	+	2.96240i	−0.775314	+	0.406916i	0.0301615	+	0.999545i	$0.490398\pi$
$54$	−0.769629	−	0.0934498i	−0.104733	−	0.0127169i
$55$	2.25675	−	0.556238i	0.304300	−	0.0750031i
$56$	0.251302	−	0.364074i	0.0335817	−	0.0486515i
$57$	0.275463	−	0.190138i	0.0364859	−	0.0251844i
$58$	−4.64307	+	5.24095i	−0.609666	+	0.688170i
$59$	4.72673	+	0.573928i	0.615367	+	0.0747191i	0.422285	−	0.906463i	$-0.361228\pi$
$59$	4.72673	+	0.573928i	0.615367	+	0.0747191i	0.193083	+	0.981182i	$0.438151\pi$
$60$	−0.0141984	+	0.0576053i	−0.00183301	+	0.00743681i
$61$	−4.77126	−	2.50415i	−0.610897	−	0.320623i	0.130749	−	0.991416i	$-0.458262\pi$
$61$	−4.77126	−	2.50415i	−0.610897	−	0.320623i	−0.741645	+	0.670792i	$0.765954\pi$
$62$	1.47370	−	12.1370i	0.187160	−	1.54140i
$63$	−0.979773	+	0.118966i	−0.123440	+	0.0149883i
$64$	0.768897	−	1.11394i	0.0961122	−	0.139243i
$65$	−2.19750	−	0.904155i	−0.272566	−	0.112147i
$66$	−0.259089	−	0.375356i	−0.0318917	−	0.0462031i
$67$	−7.79129	−	8.79455i	−0.951858	−	1.07443i	−0.997149	−	0.0754513i	$-0.975960\pi$
$67$	−7.79129	−	8.79455i	−0.951858	−	1.07443i	0.0452919	−	0.998974i	$-0.485578\pi$
$68$	5.97375	+	1.47240i	0.724424	+	0.178554i
$69$	0.153460	+	0.222325i	0.0184744	+	0.0267648i
$70$			0.391916i			0.0468429i
$71$	−1.05635	+	0.729146i	−0.125366	+	0.0865337i	−0.629097	−	0.777326i	$-0.716575\pi$
$71$	−1.05635	+	0.729146i	−0.125366	+	0.0865337i	0.503732	+	0.863860i	$0.331960\pi$
$72$	3.99090	−	0.484583i	0.470332	−	0.0571086i
$73$	−4.91959	+	1.86575i	−0.575794	+	0.218370i	−0.625274	−	0.780405i	$-0.715013\pi$
$73$	−4.91959	+	1.86575i	−0.575794	+	0.218370i	0.0494801	+	0.998775i	$0.484244\pi$
$74$	2.18367	−	17.9841i	0.253847	−	2.09061i
$75$	−0.116033	−	0.305953i	−0.0133983	−	0.0353284i
$76$	3.89002	−	4.39092i	0.446215	−	0.503673i
$77$	−0.869954	−	0.770712i	−0.0991404	−	0.0878308i
$78$	−0.0129817	+	0.466105i	−0.00146988	+	0.0527759i
$79$	1.45245	−	1.28676i	0.163413	−	0.144771i	−0.577453	−	0.816424i	$-0.695954\pi$
$79$	1.45245	−	1.28676i	0.163413	−	0.144771i	0.740867	+	0.671652i	$0.234415\pi$
$80$		−	3.25203i		−	0.363588i
$81$	−6.70201	−	5.93747i	−0.744668	−	0.659718i
$82$	17.2680	−	4.25618i	1.90693	−	0.470016i
$83$	2.13161	+	1.47134i	0.233975	+	0.161501i	0.679283	−	0.733876i	$-0.262291\pi$
$83$	2.13161	+	1.47134i	0.233975	+	0.161501i	−0.445309	+	0.895377i	$0.646906\pi$
$84$	0.0277394	−	0.0105202i	0.00302661	−	0.00114784i
$85$	3.01837	−	1.14472i	0.327388	−	0.124162i
$86$	−4.02586	−	2.77885i	−0.434120	−	0.299651i
$87$	0.270016	−	0.0665530i	0.0289488	−	0.00713523i
$88$	3.54357	+	3.13933i	0.377746	+	0.334654i
$89$			3.65402i			0.387325i	0.981068	+	0.193662i	$0.0620367\pi$
$89$			3.65402i			0.387325i	−0.981068	+	0.193662i	$0.937963\pi$
$90$	−2.66588	+	2.36177i	−0.281009	+	0.248952i
$91$	0.252131	+	1.16117i	0.0264305	+	0.121723i
$92$	3.54390	+	3.13962i	0.369477	+	0.327328i
$93$	−0.322008	+	0.363472i	−0.0333907	+	0.0376903i
$94$	−5.17620	−	13.6485i	−0.533884	−	1.40774i
$95$	0.371002	−	3.05548i	0.0380640	−	0.313485i
$96$	−0.416762	+	0.158057i	−0.0425356	+	0.0161316i
$97$	−4.73020	+	0.574351i	−0.480279	+	0.0583165i	−0.357096	−	0.934068i	$-0.616233\pi$
$97$	−4.73020	+	0.574351i	−0.480279	+	0.0583165i	−0.123183	+	0.992384i	$0.539310\pi$
$98$	−10.2340	+	7.06403i	−1.03379	+	0.713575i
$99$		−	10.5621i		−	1.06153i
$100$	−3.25776	−	4.71968i	−0.325776	−	0.471968i
$101$	9.31468	+	2.29586i	0.926846	+	0.228447i	0.673720	−	0.738987i	$-0.264695\pi$
$101$	9.31468	+	2.29586i	0.926846	+	0.228447i	0.253125	+	0.967433i	$0.418541\pi$
$102$	−0.420058	−	0.474148i	−0.0415919	−	0.0469476i
$103$	10.2787	+	14.8913i	1.01279	+	1.46728i	0.879322	+	0.476229i	$0.157997\pi$
$103$	10.2787	+	14.8913i	1.01279	+	1.46728i	0.133470	+	0.991053i	$0.457388\pi$
$104$	−1.02700	−	4.72976i	−0.100706	−	0.463792i
$105$	0.00884250	−	0.0128106i	0.000862939	−	0.00125018i
$106$	11.4187	−	1.38649i	1.10909	−	0.134667i
$107$	0.361820	−	2.97985i	0.0349784	−	0.288073i	−0.964715	−	0.263298i	$-0.915190\pi$
$107$	0.361820	−	2.97985i	0.0349784	−	0.288073i	0.999693	−	0.0247755i	$-0.00788709\pi$
$108$	0.477856	+	0.250798i	0.0459817	+	0.0241331i
$109$	2.02715	−	8.22449i	0.194166	−	0.787763i	−0.790377	−	0.612621i	$-0.790115\pi$
$109$	2.02715	−	8.22449i	0.194166	−	0.787763i	0.984543	−	0.175142i	$-0.0560386\pi$
$110$	−4.16351	−	0.505541i	−0.396975	−	0.0482015i
$111$	−0.477140	+	0.538580i	−0.0452882	+	0.0511198i
$112$	−1.33830	+	0.923763i	−0.126458	+	0.0872874i
$113$	−6.79111	+	9.83862i	−0.638854	+	0.925540i	−0.999976	−	0.00697911i	$-0.997778\pi$
$113$	−6.79111	+	9.83862i	−0.638854	+	0.925540i	0.361122	+	0.932519i	$0.382394\pi$
$114$	−0.586425	+	0.144541i	−0.0549237	+	0.0135375i
$115$	2.46607	+	0.299435i	0.229962	+	0.0279224i
$116$	4.31568	−	2.26505i	0.400701	−	0.210304i
$117$	−6.37907	+	8.71247i	−0.589745	+	0.805468i
$118$	−7.60770	−	3.99283i	−0.700345	−	0.367570i
$119$	−1.32848	−	0.916980i	−0.121781	−	0.0840594i
$120$	−0.0360180	+	0.0521811i	−0.00328798	+	0.00476346i
$121$	1.07619	−	0.953425i	0.0978358	−	0.0866750i
$122$	6.44774	+	7.27799i	0.583751	+	0.658919i
$123$	−0.660468	−	0.250483i	−0.0595524	−	0.0225853i
$124$	−3.95507	+	7.53575i	−0.355175	+	0.676730i
$125$	−5.89457	−	2.23551i	−0.527226	−	0.199950i
$126$	1.72920	+	0.426209i	0.154049	+	0.0379697i
$127$	−8.50787	+	7.53732i	−0.754952	+	0.668829i	−0.950100	−	0.311945i	$-0.899020\pi$
$127$	−8.50787	+	7.53732i	−0.754952	+	0.668829i	0.195149	+	0.980774i	$0.437481\pi$
$128$	8.22660	−	5.67841i	0.727136	−	0.501906i
$129$	0.0688964	+	0.181665i	0.00606599	+	0.0159947i
$130$	3.12908	+	2.93161i	0.274439	+	0.257119i
$131$	−5.04950	+	13.3144i	−0.441177	+	1.16329i	0.511495	+	0.859286i	$0.329092\pi$
$131$	−5.04950	+	13.3144i	−0.441177	+	1.16329i	−0.952672	+	0.304001i	$0.901677\pi$
$132$	0.0759790	+	0.308259i	0.00661312	+	0.0268305i
$133$	−1.36280	+	0.715254i	−0.118170	+	0.0620203i
$134$	7.51810	+	19.8236i	0.649465	+	1.71250i
$135$	0.281094	−	0.0341310i	0.0241927	−	0.00293753i
$136$	5.41126	+	3.73512i	0.464012	+	0.320284i
$137$	−0.316758	+	1.28514i	−0.0270624	+	0.109797i	−0.982920	−	0.184035i	$-0.941084\pi$
$137$	−0.316758	+	1.28514i	−0.0270624	+	0.109797i	0.955857	+	0.293831i	$0.0949303\pi$
$138$	−0.116658	−	0.473302i	−0.00993062	−	0.0402901i
$139$	1.23304	+	10.1550i	0.104585	+	0.861337i	0.946717	+	0.322065i	$0.104377\pi$
$139$	1.23304	+	10.1550i	0.104585	+	0.861337i	−0.842132	+	0.539271i	$0.818700\pi$
$140$	0.0967404	−	0.255084i	0.00817606	−	0.0215585i
$141$	−0.138746	+	0.562916i	−0.0116846	+	0.0474061i
$142$	2.24884	−	0.554288i	0.188718	−	0.0465148i
$143$	−12.6608	+	1.18069i	−1.05875	+	0.0987343i
$144$	−14.3485	−	3.53659i	−1.19571	−	0.294716i
$145$	1.18844	−	2.26438i	0.0986944	−	0.188046i
$146$	9.49417			0.785743
$147$	0.493900			0.0407362
$148$	−5.86048	+	11.1662i	−0.481728	+	0.917856i
$149$	0.0468329	+	0.0528634i	0.00383670	+	0.00433074i	0.750426	−	0.660955i	$-0.229848\pi$
$149$	0.0468329	+	0.0528634i	0.00383670	+	0.00433074i	−0.746589	+	0.665285i	$0.768310\pi$
$150$			0.590450i			0.0482100i
$151$	10.5204	−	11.8751i	0.856136	−	0.966378i	−0.143593	−	0.989637i	$-0.545866\pi$
$151$	10.5204	−	11.8751i	0.856136	−	0.966378i	0.999729	+	0.0232586i	$0.00740412\pi$
$152$	5.55109	−	2.91343i	0.450252	−	0.236311i
$153$	−1.76820	−	14.5624i	−0.142951	−	1.17730i
$154$	0.974631	+	1.85700i	0.0785380	+	0.149642i
$155$	0.538243	+	4.43283i	0.0432327	+	0.356053i
$156$	0.123503	−	0.300166i	0.00988811	−	0.0240325i
$157$	0.741200	−	6.10433i	0.0591542	−	0.487179i	−0.932782	−	0.360441i	$-0.882626\pi$
$157$	0.741200	−	6.10433i	0.0591542	−	0.487179i	0.991936	−	0.126738i	$-0.0404506\pi$
$158$	−3.27393	+	1.24164i	−0.260460	+	0.0987794i
$159$	−0.404527	−	0.212312i	−0.0320811	−	0.0168375i
$160$	−1.45345	+	3.83243i	−0.114905	+	0.302980i
$161$	−0.577279	−	1.09991i	−0.0454960	−	0.0866853i
$162$	7.50843	+	14.3061i	0.589918	+	1.12400i
$163$	3.66798	+	14.8816i	0.287299	+	1.16562i	0.920220	+	0.391400i	$0.128009\pi$
$163$	3.66798	+	14.8816i	0.287299	+	1.16562i	−0.632922	+	0.774216i	$0.718145\pi$
$164$	−12.2897	−	1.49224i	−0.959664	−	0.116524i
$165$	0.124687	+	0.110463i	0.00970684	+	0.00859951i
$166$	−2.65499	−	3.84641i	−0.206067	−	0.298539i
$167$	−11.6004	−	4.39946i	−0.897668	−	0.340441i	−0.137756	−	0.990466i	$-0.543989\pi$
$167$	−11.6004	−	4.39946i	−0.897668	−	0.340441i	−0.759912	+	0.650026i	$0.774758\pi$
$168$	0.0317052			0.00244611
$169$	11.1568	+	6.67273i	0.858217	+	0.513287i
$170$	−5.82507			−0.446763
$171$	−13.0778	−	4.95976i	−1.00009	−	0.379282i
$172$	1.93435	+	2.80239i	0.147493	+	0.213681i
$173$	−12.2353	−	10.8395i	−0.930233	−	0.824114i	0.0544417	−	0.998517i	$-0.482662\pi$
$173$	−12.2353	−	10.8395i	−0.930233	−	0.824114i	−0.984674	+	0.174403i	$0.944201\pi$
$174$	−0.498157	−	0.0604872i	−0.0377652	−	0.00458552i
$175$	0.360081	+	1.46091i	0.0272196	+	0.110434i
$176$	−8.08727	−	15.4090i	−0.609601	−	1.16150i
$177$	0.158586	+	0.302161i	0.0119201	+	0.0227118i
$178$	2.33810	−	6.16506i	0.175248	−	0.462091i
$179$	9.41774	+	4.94281i	0.703915	+	0.369443i	0.778391	−	0.627780i	$-0.216036\pi$
$179$	9.41774	+	4.94281i	0.703915	+	0.369443i	−0.0744761	+	0.997223i	$0.523728\pi$
$180$	2.31810	−	0.879141i	0.172781	−	0.0655273i
$181$	−0.789062	+	6.49851i	−0.0586505	+	0.483031i	0.933556	+	0.358430i	$0.116688\pi$
$181$	−0.789062	+	6.49851i	−0.0586505	+	0.483031i	−0.992207	+	0.124600i	$0.960235\pi$
$182$	0.317601	−	2.12045i	0.0235422	−	0.157178i
$183$	−0.0465497	−	0.383372i	−0.00344106	−	0.0283396i
$184$	2.35142	+	4.48026i	0.173349	+	0.330289i
$185$	0.797549	+	6.56841i	0.0586370	+	0.482919i
$186$	0.775868	−	0.407207i	0.0568894	−	0.0298579i
$187$	11.4551	−	12.9302i	0.837683	−	0.945549i
$188$			10.1610i			0.741068i
$189$	−0.0938928	−	0.105983i	−0.00682969	−	0.00770913i
$190$	−2.58107	+	4.91781i	−0.187250	+	0.356776i
$191$	24.9792			1.80743			0.903714	−	0.428137i	$-0.140830\pi$
$191$	24.9792			1.80743			0.903714	+	0.428137i	$0.140830\pi$
$192$	0.0970069			0.00700087
$193$	−8.18622	+	15.5975i	−0.589257	+	1.12274i	0.390133	+	0.920758i	$0.372429\pi$
$193$	−8.18622	+	15.5975i	−0.589257	+	1.12274i	−0.979390	+	0.201977i	$0.935263\pi$
$194$	8.34832	+	2.05768i	0.599374	+	0.147732i
$195$	−0.0361368	−	0.166425i	−0.00258781	−	0.0119179i
$196$	8.40464	−	2.07156i	0.600331	−	0.147968i
$197$	4.27098	−	17.3280i	0.304294	−	1.23457i	−0.597310	−	0.802010i	$-0.703764\pi$
$197$	4.27098	−	17.3280i	0.304294	−	1.23457i	0.901605	−	0.432561i	$-0.142390\pi$
$198$	−6.75835	+	17.8203i	−0.480295	+	1.26643i
$199$	−2.62956	−	21.6564i	−0.186405	−	1.53518i	−0.722706	−	0.691155i	$-0.757102\pi$
$199$	−2.62956	−	21.6564i	−0.186405	−	1.53518i	0.536302	−	0.844026i	$-0.319821\pi$
$200$	−1.46672	−	5.95070i	−0.103712	−	0.420778i
$201$	0.201520	−	0.817600i	0.0142141	−	0.0576691i
$202$	−14.2467	−	9.83378i	−1.00239	−	0.691902i
$203$	−1.26944	+	0.154138i	−0.0890973	+	0.0108184i
$204$	0.156362	+	0.412292i	0.0109475	+	0.0288662i
$205$	−5.75156	+	3.01865i	−0.401706	+	0.210832i
$206$	−7.81375	−	31.7016i	−0.544410	−	2.20876i
$207$	4.00301	−	10.5551i	0.278228	−	0.733628i
$208$	−2.63538	+	17.5950i	−0.182731	+	1.22000i
$209$	−5.84057	−	15.4003i	−0.404001	−	1.06526i
$210$	−0.0231162	+	0.0159559i	−0.00159517	+	0.00110107i
$211$	8.84842	−	7.83902i	0.609151	−	0.539660i	−0.301167	−	0.953571i	$-0.597376\pi$
$211$	8.84842	−	7.83902i	0.609151	−	0.539660i	0.910317	+	0.413911i	$0.135838\pi$
$212$	−7.77429	−	1.91619i	−0.533940	−	0.131604i
$213$	−0.0860138	−	0.0326207i	−0.00589357	−	0.00223514i
$214$	−2.51718	+	4.79609i	−0.172071	+	0.327854i
$215$	1.67054	+	0.633552i	0.113930	+	0.0432079i
$216$	0.382452	+	0.431699i	0.0260226	+	0.0293734i
$217$	1.67134	−	1.48068i	0.113458	−	0.100515i
$218$	−8.68283	+	12.5793i	−0.588076	+	0.851975i
$219$	−0.310337	−	0.214210i	−0.0209706	−	0.0144750i
$220$	2.58509	+	1.35676i	0.174287	+	0.0914726i
$221$	−17.2585	+	3.74744i	−1.16093	+	0.252080i
$222$	1.14965	−	0.603385i	0.0771597	−	0.0404965i
$223$	16.0740	+	1.95174i	1.07640	+	0.130698i	0.639483	−	0.768806i	$-0.279149\pi$
$223$	16.0740	+	1.95174i	1.07640	+	0.130698i	0.436913	+	0.899504i	$0.356072\pi$
$224$	1.99002	−	0.490495i	0.132964	−	0.0327726i
$225$	−7.76744	+	11.2531i	−0.517829	+	0.750205i
$226$	17.7534	−	12.2543i	1.18094	−	0.815144i
$227$	3.74017	−	4.22178i	0.248244	−	0.280209i	−0.611160	−	0.791507i	$-0.709297\pi$
$227$	3.74017	−	4.22178i	0.248244	−	0.280209i	0.859404	+	0.511298i	$0.170835\pi$
$228$	0.417361	+	0.0506768i	0.0276404	+	0.00335615i
$229$	−2.00761	+	8.14520i	−0.132667	+	0.538250i	0.866565	+	0.499064i	$0.166323\pi$
$229$	−2.00761	+	8.14520i	−0.132667	+	0.538250i	−0.999232	+	0.0391860i	$0.987524\pi$
$230$	−3.96915	−	2.08317i	−0.261718	−	0.137360i
$231$	0.0100404	−	0.0826899i	0.000660608	−	0.00544059i
$232$	5.17080	−	0.627849i	0.339480	−	0.0412203i
$233$	4.14167	−	6.00025i	0.271330	−	0.393089i	−0.663505	−	0.748172i	$-0.730932\pi$
$233$	4.14167	−	6.00025i	0.271330	−	0.393089i	0.934835	+	0.355083i	$0.115547\pi$
$234$	16.3376	−	10.6179i	1.06802	−	0.694114i
$235$	3.02855	+	4.38761i	0.197561	+	0.286216i
$236$	3.96598	+	4.47667i	0.258164	+	0.291406i
$237$	0.135029	+	0.0332817i	0.00877109	+	0.00216188i
$238$	1.65466	+	2.39718i	0.107255	+	0.155386i
$239$			15.3967i			0.995929i	0.867197	+	0.497964i	$0.165919\pi$
$239$			15.3967i			0.995929i	−0.867197	+	0.497964i	$0.834081\pi$
$240$	0.191813	−	0.132399i	0.0123815	−	0.00854631i
$241$	−21.5486	+	2.61647i	−1.38806	+	0.168542i	−0.780215	−	0.625511i	$-0.784890\pi$
$241$	−21.5486	+	2.61647i	−1.38806	+	0.168542i	−0.607849	+	0.794053i	$0.707967\pi$
$242$	−2.42583	+	0.919994i	−0.155938	+	0.0591395i
$243$	0.232714	−	1.91657i	0.0149286	−	0.122948i
$244$	−2.40010	−	6.32854i	−0.153651	−	0.405143i
$245$	3.01175	−	3.39956i	0.192414	−	0.217190i
$246$	0.954067	+	0.845229i	0.0608291	+	0.0538899i
$247$	−4.48340	+	16.2309i	−0.285272	+	1.03275i
$248$	−6.80786	+	6.03124i	−0.432300	+	0.382984i
$249$			0.185630i			0.0117638i
$250$	8.51488	+	7.54353i	0.538528	+	0.477095i
$251$	−8.36831	+	2.06260i	−0.528203	+	0.130190i	−0.494394	−	0.869238i	$-0.664610\pi$
$251$	−8.36831	+	2.06260i	−0.528203	+	0.130190i	−0.0338091	+	0.999428i	$0.510764\pi$
$252$	−1.02027	−	0.704239i	−0.0642707	−	0.0443629i
$253$	12.4295	−	4.71391i	0.781439	−	0.296361i
$254$	19.1774	−	7.27303i	1.20330	−	0.456350i
$255$	0.190404	+	0.131427i	0.0119236	+	0.00823026i
$256$	−20.1418	+	4.96451i	−1.25886	+	0.310282i
$257$	17.2091	+	15.2459i	1.07347	+	0.951015i	0.998932	−	0.0462033i	$-0.0147122\pi$
$257$	17.2091	+	15.2459i	1.07347	+	0.951015i	0.0745415	+	0.997218i	$0.476251\pi$
$258$		−	0.350590i		−	0.0218268i
$259$	2.47654	−	2.19402i	0.153885	−	0.136330i
$260$	−1.31297	−	2.68046i	−0.0814268	−	0.166235i
$261$	−8.69839	−	7.70611i	−0.538417	−	0.476996i
$262$	17.0390	−	19.2331i	1.05268	−	1.18823i
$263$	3.22143	+	8.49420i	0.198642	+	0.523775i	0.996912	−	0.0785241i	$-0.0250208\pi$
$263$	3.22143	+	8.49420i	0.198642	+	0.523775i	−0.798271	+	0.602299i	$0.794252\pi$
$264$	−0.0408973	+	0.336820i	−0.00251706	+	0.0207298i
$265$	−3.92813	+	1.48974i	−0.241303	+	0.0915142i
$266$	2.75699	−	0.334759i	0.169042	−	0.0205254i
$267$	−0.215523	+	0.148765i	−0.0131898	+	0.00910426i
$268$		−	14.7582i		−	0.901502i
$269$	6.52433	+	9.45212i	0.397795	+	0.576306i	0.969787	−	0.243953i	$-0.0784444\pi$
$269$	6.52433	+	9.45212i	0.397795	+	0.576306i	−0.571992	+	0.820259i	$0.693829\pi$
$270$	−0.496102	−	0.122278i	−0.0301918	−	0.00744161i
$271$	14.5947	+	16.4740i	0.886564	+	1.00072i	0.999974	+	0.00717530i	$0.00228399\pi$
$271$	14.5947	+	16.4740i	0.886564	+	1.00072i	−0.113411	+	0.993548i	$0.536178\pi$
$272$	−13.7300	−	19.8913i	−0.832501	−	1.20609i
$273$	−0.0582236	+	0.0621455i	−0.00352385	+	0.00376122i
$274$	1.35676	−	1.96560i	0.0819646	−	0.118746i
$275$	−15.9844	+	1.94086i	−0.963896	+	0.117038i
$276$	−0.0409011	+	0.336851i	−0.00246196	+	0.0202760i
$277$	−26.3640	−	13.8369i	−1.58406	−	0.831379i	−0.999804	−	0.0198090i	$-0.993694\pi$
$277$	−26.3640	−	13.8369i	−1.58406	−	0.831379i	−0.584256	−	0.811570i	$-0.698614\pi$
$278$	4.41751	−	17.9225i	0.264944	−	1.07492i
$279$	20.1437	+	2.44589i	1.20597	+	0.146432i
$280$	0.193335	−	0.218230i	0.0115540	−	0.0130417i
$281$	22.8197	−	15.7513i	1.36131	−	0.939643i	0.361333	−	0.932437i	$-0.382322\pi$
$281$	22.8197	−	15.7513i	1.36131	−	0.939643i	0.999974	−	0.00720608i	$-0.00229379\pi$
$282$	0.594287	−	0.860973i	0.0353893	−	0.0512702i
$283$	−17.0550	+	4.20369i	−1.01382	+	0.249883i	−0.711020	−	0.703172i	$-0.751766\pi$
$283$	−17.0550	+	4.20369i	−1.01382	+	0.249883i	−0.302796	+	0.953055i	$0.597920\pi$
$284$	−1.60051	−	0.194337i	−0.0949725	−	0.0115318i
$285$	0.195324	−	0.102514i	0.0115700	−	0.00607241i
$286$	22.1169	+	6.10925i	1.30780	+	0.361247i
$287$	2.87604	+	1.50946i	0.169767	+	0.0891006i
$288$	15.3287	+	10.5806i	0.903253	+	0.623470i
$289$	3.97205	−	5.75450i	0.233650	−	0.338500i
$290$	−3.45404	+	3.06002i	−0.202828	+	0.179690i
$291$	−0.226456	−	0.255616i	−0.0132751	−	0.0149845i
$292$	−6.17941	−	2.34354i	−0.361623	−	0.137145i
$293$	−4.89485	+	9.32635i	−0.285960	+	0.544851i	−0.985486	−	0.169756i	$-0.945702\pi$
$293$	−4.89485	+	9.32635i	−0.285960	+	0.544851i	0.699526	+	0.714607i	$0.253394\pi$
$294$	−0.833309	−	0.316033i	−0.0485996	−	0.0184314i
$295$	3.04684	+	0.750979i	0.177394	+	0.0437237i
$296$	−10.0876	+	8.93688i	−0.586333	+	0.519445i
$297$	1.24702	−	0.860758i	0.0723596	−	0.0499462i
$298$	−0.0451907	−	0.119158i	−0.00261783	−	0.00690265i
$299$	−13.1000	−	3.61854i	−0.757590	−	0.209266i
$300$	0.145747	−	0.384302i	0.00841468	−	0.0221877i
$301$	−0.213805	−	0.867440i	−0.0123235	−	0.0499984i
$302$	−25.3485	+	13.3039i	−1.45864	+	0.765555i
$303$	0.243810	+	0.642875i	0.0140065	+	0.0369322i
$304$	−22.8769	+	2.77776i	−1.31208	+	0.159315i
$305$	−2.92264	−	2.01735i	−0.167350	−	0.115513i
$306$	−6.33478	+	25.7012i	−0.362135	+	1.46924i
$307$	−7.01209	−	28.4492i	−0.400201	−	1.62368i	−0.732683	−	0.680570i	$-0.761732\pi$
$307$	−7.01209	−	28.4492i	−0.400201	−	1.62368i	0.332483	−	0.943109i	$-0.392114\pi$
$308$	−0.175969	−	1.44923i	−0.0100268	−	0.0825778i
$309$	−0.459852	+	1.21253i	−0.0261600	+	0.0689784i
$310$	1.92831	−	7.82348i	0.109521	−	0.444344i
$311$	−8.53462	+	2.10359i	−0.483954	+	0.119284i	−0.473742	−	0.880664i	$-0.657097\pi$
$311$	−8.53462	+	2.10359i	−0.483954	+	0.119284i	−0.0102124	+	0.999948i	$0.503251\pi$
$312$	0.237162	−	0.253137i	0.0134266	−	0.0143310i
$313$	18.3809	+	4.53050i	1.03895	+	0.256079i	0.721659	−	0.692249i	$-0.243380\pi$
$313$	18.3809	+	4.53050i	1.03895	+	0.256079i	0.317293	+	0.948327i	$0.397226\pi$
$314$	−5.15654	+	9.82496i	−0.291000	+	0.554455i
$315$	−0.650462			−0.0366494
$316$	2.43737			0.137113
$317$	10.2424	−	19.5153i	0.575271	−	1.09609i	−0.407835	−	0.913055i	$-0.633716\pi$
$317$	10.2424	−	19.5153i	0.575271	−	1.09609i	0.983107	−	0.183033i	$-0.0585914\pi$
$318$	0.546667	+	0.617059i	0.0306555	+	0.0346030i
$319$		−	13.6847i		−	0.766196i
$320$	0.591538	−	0.667708i	0.0330680	−	0.0373260i
$321$	0.190490	−	0.0999769i	0.0106321	−	0.00558016i
$322$	0.270183	+	2.22516i	0.0150567	+	0.124003i
$323$	−10.6309	−	20.2554i	−0.591517	−	1.12704i
$324$	−1.35564	−	11.1647i	−0.0753135	−	0.620262i
$325$	14.3575	+	8.05297i	0.796409	+	0.446699i
$326$	3.33367	−	27.4553i	0.184635	−	1.52061i
$327$	0.567632	−	0.215275i	0.0313901	−	0.0119047i
$328$	−11.7149	−	6.14847i	−0.646849	−	0.339492i
$329$	0.945344	−	2.49267i	0.0521185	−	0.137425i
$330$	−0.139690	−	0.266156i	−0.00768966	−	0.0146514i
$331$	−10.0418	−	19.1331i	−0.551949	−	1.05165i	−0.988393	−	0.151919i	$-0.951455\pi$
$331$	−10.0418	−	19.1331i	−0.551949	−	1.05165i	0.436444	−	0.899731i	$-0.356238\pi$
$332$	0.778585	+	3.15885i	0.0427304	+	0.173364i
$333$	29.8483	+	3.62423i	1.63567	+	0.198607i
$334$	16.7572	+	14.8456i	0.916911	+	0.812313i
$335$	−4.39877	−	6.37272i	−0.240331	−	0.348179i
$336$	−0.108972	−	0.0413276i	−0.00594490	−	0.00225460i
$337$	4.82536			0.262854			0.131427	−	0.991326i	$-0.458044\pi$
$337$	4.82536			0.262854			0.131427	+	0.991326i	$0.458044\pi$
$338$	−14.5541	−	18.3972i	−0.791640	−	1.00067i
$339$	−0.856791			−0.0465345
$340$	3.79133	+	1.43786i	0.205614	+	0.0779789i
$341$	13.5741	+	19.6654i	0.735077	+	1.06494i
$342$	18.8913	+	16.7362i	1.02152	+	0.904992i
$343$	−4.54459	−	0.551813i	−0.245385	−	0.0297951i
$344$	0.870888	+	3.53333i	0.0469551	+	0.190505i
$345$	0.0827389	+	0.157646i	0.00445451	+	0.00848736i
$346$	13.7075	+	26.1175i	0.736921	+	1.40408i
$347$	1.10386	−	2.91065i	0.0592585	−	0.156252i	−0.902117	−	0.431491i	$-0.857988\pi$
$347$	1.10386	−	2.91065i	0.0592585	−	0.156252i	0.961376	+	0.275239i	$0.0887570\pi$
$348$	0.309301	+	0.162334i	0.0165803	+	0.00870201i
$349$	−27.3443	+	10.3703i	−1.46371	+	0.555112i	−0.952552	−	0.304376i	$-0.901552\pi$
$349$	−27.3443	+	10.3703i	−1.46371	+	0.555112i	−0.511157	+	0.859487i	$0.670783\pi$
$350$	0.327263	−	2.69525i	0.0174929	−	0.144067i
$351$	−1.54851	−	0.0431282i	−0.0826535	−	0.00230201i
$352$	2.64380	+	21.7736i	0.140915	+	1.16054i
$353$	0.0347175	+	0.0661486i	0.00184782	+	0.00352074i	0.886378	−	0.462962i	$-0.153213\pi$
$353$	0.0347175	+	0.0661486i	0.00184782	+	0.00352074i	−0.884530	+	0.466483i	$0.845521\pi$
$354$	−0.0742229	−	0.611280i	−0.00394490	−	0.0324892i
$355$	−0.749034	+	0.393124i	−0.0397546	+	0.0208648i
$356$	−3.04357	+	3.43548i	−0.161309	+	0.182080i
$357$		−	0.115690i		−	0.00612294i
$358$	−12.7269	−	14.3657i	−0.672636	−	0.759249i
$359$	−14.2617	+	27.1734i	−0.752703	+	1.43416i	0.143102	+	0.989708i	$0.454292\pi$
$359$	−14.2617	+	27.1734i	−0.752703	+	1.43416i	−0.895805	+	0.444448i	$0.853400\pi$
$360$	2.64952			0.139642
$361$	−2.81112			−0.147954
$362$	5.48952	−	10.4594i	0.288523	−	0.549734i
$363$	0.100050	+	0.0246602i	0.00525127	+	0.00129432i
$364$	−0.730127	+	1.30173i	−0.0382691	+	0.0682291i
$365$	−3.36683	+	0.829848i	−0.176228	+	0.0434362i
$366$	−0.166770	+	0.676611i	−0.00871719	+	0.0353670i
$367$	−5.66750	+	14.9440i	−0.295841	+	0.780069i	0.701861	+	0.712314i	$0.252353\pi$
$367$	−5.66750	+	14.9440i	−0.295841	+	0.780069i	−0.997702	+	0.0677552i	$0.978416\pi$
$368$	−2.24192	−	18.4639i	−0.116868	−	0.962496i
$369$	7.06397	+	28.6597i	0.367736	+	1.49196i
$370$	2.85731	−	11.5926i	0.148544	−	0.602668i
$371$	1.72889	+	1.19336i	0.0897594	+	0.0619564i
$372$	−0.605499	+	0.0735209i	−0.0313937	+	0.00381188i
$373$	0.145322	+	0.383181i	0.00752447	+	0.0198404i	0.938726	−	0.344665i	$-0.112007\pi$
$373$	0.145322	+	0.383181i	0.00752447	+	0.0198404i	−0.931201	+	0.364505i	$0.881238\pi$
$374$	−27.6008	+	14.4860i	−1.42720	+	0.749054i
$375$	−0.108127	−	0.438690i	−0.00558368	−	0.0226539i
$376$	−3.85066	+	10.1534i	−0.198583	+	0.523619i
$377$	−8.26503	+	11.2883i	−0.425671	+	0.581377i
$378$	0.0906005	+	0.238894i	0.00465999	+	0.0122874i
$379$	−13.5587	+	9.35891i	−0.696465	+	0.480735i	−0.862937	−	0.505311i	$-0.831378\pi$
$379$	−13.5587	+	9.35891i	−0.696465	+	0.480735i	0.166472	+	0.986046i	$0.446762\pi$
$380$	2.89383	−	2.56371i	0.148451	−	0.131516i
$381$	−0.790949	−	0.194951i	−0.0405215	−	0.00998766i
$382$	−42.1449	−	15.9834i	−2.15632	−	0.817784i
$383$	−1.57355	+	2.99815i	−0.0804047	+	0.153198i	−0.922339	−	0.386382i	$-0.873725\pi$
$383$	−1.57355	+	2.99815i	−0.0804047	+	0.153198i	0.841934	+	0.539580i	$0.181417\pi$
$384$	0.669855	+	0.254042i	0.0341834	+	0.0129640i
$385$	−0.507937	−	0.573343i	−0.0258869	−	0.0292202i
$386$	23.7922	−	21.0781i	1.21099	−	1.07285i
$387$	4.61205	−	6.68171i	0.234444	−	0.339651i
$388$	−4.92570	−	3.39996i	−0.250064	−	0.172607i
$389$	22.9003	+	12.0190i	1.16109	+	0.609389i	0.931444	−	0.363885i	$-0.118550\pi$
$389$	22.9003	+	12.0190i	1.16109	+	0.609389i	0.229649	+	0.973273i	$0.426242\pi$
$390$	−0.0455204	+	0.303915i	−0.00230501	+	0.0153893i
$391$	16.3481	−	8.58014i	0.826759	−	0.433916i
$392$	9.18334	+	1.11506i	0.463829	+	0.0563190i
$393$	−0.990898	+	0.244235i	−0.0499842	+	0.0123200i
$394$	−18.2937	+	26.5030i	−0.921624	+	1.33520i
$395$	1.05248	−	0.726471i	0.0529558	−	0.0365527i
$396$	8.79753	−	9.93036i	0.442093	−	0.499019i
$397$	24.5311	+	2.97862i	1.23118	+	0.149493i	0.710154	−	0.704047i	$-0.248625\pi$
$397$	24.5311	+	2.97862i	1.23118	+	0.149493i	0.521028	+	0.853539i	$0.325549\pi$
$398$	−9.42070	+	38.2213i	−0.472217	+	1.91586i
$399$	−0.0976708	−	0.0512616i	−0.00488966	−	0.00256629i
$400$	−2.71555	+	22.3646i	−0.135778	+	1.11823i
$401$	−6.52706	+	0.792528i	−0.325946	+	0.0395770i	−0.281874	−	0.959451i	$-0.590956\pi$
$401$	−6.52706	+	0.792528i	−0.325946	+	0.0395770i	−0.0440716	+	0.999028i	$0.514033\pi$
$402$	−0.863164	+	1.25051i	−0.0430507	+	0.0623697i
$403$	0.680128	−	24.4199i	0.0338796	−	1.21644i
$404$	6.84528	+	9.91710i	0.340565	+	0.493394i
$405$	−3.91309	−	4.41696i	−0.194443	−	0.219481i
$406$	2.24043	+	0.552217i	0.111191	+	0.0274061i
$407$	20.1136	+	29.1395i	0.996993	+	1.44439i
$408$			0.471237i			0.0233297i
$409$	5.90260	−	4.07427i	0.291865	−	0.201460i	−0.413130	−	0.910672i	$-0.635565\pi$
$409$	5.90260	−	4.07427i	0.291865	−	0.201460i	0.704995	+	0.709212i	$0.250949\pi$
$410$	11.6356	−	1.41282i	0.574641	−	0.0697740i
$411$	−0.0886967	+	0.0336382i	−0.00437508	+	0.00165925i
$412$	−2.73955	+	22.5622i	−0.134968	+	1.11156i
$413$	−0.556429	−	1.46718i	−0.0273801	−	0.0721954i
$414$	−13.5078	+	15.2471i	−0.663870	+	0.749355i
$415$	1.27771	+	1.13195i	0.0627204	+	0.0555654i
$416$	10.9696	−	19.5575i	0.537829	−	0.958883i
$417$	−0.548768	+	0.486166i	−0.0268733	+	0.0238076i
$418$			29.7206i			1.45368i
$419$	−0.597549	−	0.529382i	−0.0291922	−	0.0258620i	0.648400	−	0.761299i	$-0.275438\pi$
$419$	−0.597549	−	0.529382i	−0.0291922	−	0.0258620i	−0.677593	+	0.735437i	$0.736977\pi$
$420$	0.0189840	−	0.00467915i	0.000926327	−	0.000228319i
$421$	−6.34030	−	4.37639i	−0.309007	−	0.213292i	0.403461	−	0.914997i	$-0.367807\pi$
$421$	−6.34030	−	4.37639i	−0.309007	−	0.213292i	−0.712468	+	0.701705i	$0.752423\pi$
$422$	−19.9450	+	7.56415i	−0.970909	+	0.368217i
$423$	22.6524	−	8.59093i	1.10140	−	0.417705i
$424$	−7.04226	−	4.86092i	−0.342002	−	0.236067i
$425$	−21.7136	+	5.35192i	−1.05326	+	0.259606i
$426$	0.124250	+	0.110075i	0.00601991	+	0.00533317i
$427$			1.77579i			0.0859367i
$428$	2.82221	−	2.50026i	0.136417	−	0.120855i
$429$	−0.585098	−	0.698700i	−0.0282488	−	0.0337336i
$430$	−2.41314	−	2.13786i	−0.116372	−	0.103097i
$431$	−15.5599	+	17.5635i	−0.749495	+	0.846005i	−0.992273	−	0.124077i	$-0.960403\pi$
$431$	−15.5599	+	17.5635i	−0.749495	+	0.846005i	0.242778	+	0.970082i	$0.421941\pi$
$432$	−0.751783	−	1.98229i	−0.0361702	−	0.0953729i
$433$	4.26993	−	35.1660i	0.205200	−	1.68997i	−0.418428	−	0.908250i	$-0.637419\pi$
$433$	4.26993	−	35.1660i	0.205200	−	1.68997i	0.623628	−	0.781721i	$-0.285658\pi$
$434$	−3.76734	+	1.42876i	−0.180838	+	0.0685828i
$435$	0.181943	−	0.0220919i	0.00872352	−	0.00105923i
$436$	8.75640	−	6.04411i	0.419356	−	0.289460i
$437$		−	17.6037i		−	0.842099i
$438$	0.386534	+	0.559991i	0.0184693	+	0.0267574i
$439$	15.2356	+	3.75523i	0.727154	+	0.179227i	0.585481	−	0.810686i	$-0.300906\pi$
$439$	15.2356	+	3.75523i	0.727154	+	0.179227i	0.141673	+	0.989914i	$0.454752\pi$
$440$	2.06898	+	2.33539i	0.0986345	+	0.111335i
$441$	−11.7242	−	16.9854i	−0.558294	−	0.808828i
$442$	31.5164	+	4.72053i	1.49908	+	0.224533i
$443$	3.60396	−	5.22124i	0.171229	−	0.248068i	−0.727969	−	0.685610i	$-0.759535\pi$
$443$	3.60396	−	5.22124i	0.171229	−	0.248068i	0.899198	+	0.437542i	$0.144151\pi$
$444$	−0.897207	+	0.108941i	−0.0425796	+	0.00517010i
$445$	−0.290274	+	2.39062i	−0.0137603	+	0.113326i
$446$	−25.8712	−	13.5783i	−1.22504	−	0.642950i
$447$	−0.00121132	+	0.00491453i	−5.72936e−5	+	0.000232449i
$448$	−0.442812	−	0.0537671i	−0.0209209	−	0.00254026i
$449$	23.9249	−	27.0056i	1.12909	−	1.27447i	0.171864	−	0.985121i	$-0.445021\pi$
$449$	23.9249	−	27.0056i	1.12909	−	1.27447i	0.957222	−	0.289354i	$-0.0934405\pi$
$450$	20.3058	−	14.0160i	0.957222	−	0.660723i
$451$	−19.7456	+	28.6064i	−0.929783	+	1.34702i
$452$	−14.5799	+	3.59362i	−0.685781	+	0.169030i
$453$	1.12873	+	0.137053i	0.0530326	+	0.00643932i
$454$	−9.01182	+	4.72977i	−0.422946	+	0.221979i
$455$	0.0727126	+	0.779716i	0.00340882	+	0.0365536i
$456$	0.397842	+	0.208803i	0.0186306	+	0.00977811i
$457$	9.67187	+	6.67601i	0.452431	+	0.312291i	0.772399	−	0.635138i	$-0.219057\pi$
$457$	9.67187	+	6.67601i	0.452431	+	0.312291i	−0.319968	+	0.947428i	$0.603672\pi$
$458$	8.59912	−	12.4580i	0.401810	−	0.582123i
$459$	1.57523	−	1.39554i	0.0735256	−	0.0651380i
$460$	2.06917	+	2.33561i	0.0964754	+	0.108898i
$461$	−1.41283	−	0.535814i	−0.0658019	−	0.0249554i	0.321484	−	0.946915i	$-0.395818\pi$
$461$	−1.41283	−	0.535814i	−0.0658019	−	0.0249554i	−0.387286	+	0.921960i	$0.626587\pi$
$462$	−0.0698510	+	0.133090i	−0.00324976	+	0.00619190i
$463$	−4.09867	−	1.55442i	−0.190481	−	0.0722401i	0.257520	−	0.966273i	$-0.417095\pi$
$463$	−4.09867	−	1.55442i	−0.190481	−	0.0722401i	−0.448001	+	0.894033i	$0.647864\pi$
$464$	−18.5906	−	4.58217i	−0.863047	−	0.212722i
$465$	−0.239546	+	0.212219i	−0.0111087	+	0.00984144i
$466$	−10.8272	+	7.47349i	−0.501561	+	0.346203i
$467$	−6.05640	−	15.9694i	−0.280257	−	0.738977i	−0.999043	−	0.0437453i	$-0.986071\pi$
$467$	−6.05640	−	15.9694i	−0.280257	−	0.738977i	0.718786	−	0.695232i	$-0.244698\pi$
$468$	−13.2545	+	2.87803i	−0.612689	+	0.133037i
$469$	−1.37305	+	3.62044i	−0.0634016	+	0.167176i
$470$	−2.30227	−	9.34066i	−0.106196	−	0.430852i
$471$	0.390225	−	0.204806i	0.0179806	−	0.00943696i
$472$	2.26650	+	5.97626i	0.104324	+	0.275080i
$473$	9.49102	−	1.15242i	0.436397	−	0.0529882i
$474$	−0.206526	−	0.142554i	−0.00948603	−	0.00654774i
$475$	−5.10285	+	20.7031i	−0.234135	+	0.949923i
$476$	−0.485235	−	1.96867i	−0.0222407	−	0.0902340i
$477$	2.30115	+	18.9517i	0.105362	+	0.867738i
$478$	9.85189	−	25.9773i	0.450615	−	1.18817i
$479$	−0.537860	+	2.18218i	−0.0245755	+	0.0997066i	−0.981949	−	0.189147i	$-0.939428\pi$
$479$	−0.537860	+	2.18218i	−0.0245755	+	0.0997066i	0.957373	+	0.288853i	$0.0932740\pi$
$480$	−0.285221	+	0.0703005i	−0.0130185	+	0.00320877i
$481$	1.00779	−	36.1846i	0.0459513	−	1.64987i
$482$	38.0309	+	9.37379i	1.73226	+	0.426964i
$483$	0.0413731	−	0.0788298i	0.00188254	−	0.00358688i
$484$	1.80597			0.0820897
$485$	−3.14034			−0.142595
$486$	−1.61900	+	3.08474i	−0.0734392	+	0.139927i
$487$	−22.0288	−	24.8653i	−0.998219	−	1.12676i	−0.991931	−	0.126776i	$-0.959537\pi$
$487$	−22.0288	−	24.8653i	−0.998219	−	1.12676i	−0.00628722	−	0.999980i	$-0.502001\pi$
$488$		−	7.23332i		−	0.327437i
$489$	−0.728421	+	0.822217i	−0.0329403	+	0.0371819i
$490$	−7.25671	+	3.80862i	−0.327825	+	0.172056i
$491$	−4.38877	−	36.1448i	−0.198062	−	1.63119i	−0.664959	−	0.746879i	$-0.731551\pi$
$491$	−4.38877	−	36.1448i	−0.198062	−	1.63119i	0.466897	−	0.884312i	$-0.345372\pi$
$492$	−0.412331	−	0.785631i	−0.0185893	−	0.0354190i
$493$	−2.29097	−	18.8678i	−0.103180	−	0.849763i
$494$	17.9501	−	24.5161i	0.807614	−	1.10303i
$495$	0.839046	−	6.91017i	0.0377123	−	0.310589i
$496$	31.2605	−	11.8556i	1.40364	−	0.532330i
$497$	0.374550	+	0.196579i	0.0168009	+	0.00881778i
$498$	0.118779	−	0.313196i	0.00532263	−	0.0140346i
$499$	−6.95200	−	13.2459i	−0.311214	−	0.592969i	0.678737	−	0.734382i	$-0.262528\pi$
$499$	−6.95200	−	13.2459i	−0.311214	−	0.592969i	−0.989951	+	0.141413i	$0.954836\pi$
$500$	−3.67998	−	7.01162i	−0.164574	−	0.313569i
$501$	−0.212793	−	0.863337i	−0.00950691	−	0.0385710i
$502$	15.4388	+	1.87461i	0.689068	+	0.0836681i
$503$	20.8999	+	18.5157i	0.931881	+	0.825575i	0.984919	−	0.173018i	$-0.0553518\pi$
$503$	20.8999	+	18.5157i	0.931881	+	0.825575i	−0.0530374	+	0.998593i	$0.516890\pi$
$504$	−0.752616	−	1.09035i	−0.0335242	−	0.0485682i
$505$	5.91170	+	2.24201i	0.263067	+	0.0997682i
$506$	−23.9874			−1.06637
$507$	0.0606499	+	0.929723i	0.00269356	+	0.0412904i
$508$	−14.2771			−0.633446
$509$	−5.28161	−	2.00305i	−0.234103	−	0.0887837i	0.234764	−	0.972052i	$-0.424568\pi$
$509$	−5.28161	−	2.00305i	−0.234103	−	0.0887837i	−0.468867	+	0.883269i	$0.655338\pi$
$510$	−0.237155	−	0.343578i	−0.0105014	−	0.0152139i
$511$	1.29788	+	1.14982i	0.0574148	+	0.0508650i
$512$	17.3136	+	2.10225i	0.765158	+	0.0929070i
$513$	−0.480199	−	1.94825i	−0.0212013	−	0.0860172i
$514$	−19.2798	−	36.7345i	−0.850394	−	1.62029i
$515$	5.54183	+	10.5591i	0.244202	+	0.465288i
$516$	−0.0865396	+	0.228186i	−0.00380969	+	0.0100453i
$517$	25.2614	+	13.2582i	1.11099	+	0.583094i
$518$	−5.58231	+	2.11709i	−0.245272	+	0.0930196i
$519$	0.141211	−	1.16298i	0.00619847	−	0.0510490i
$520$	−0.296179	−	3.17601i	−0.0129883	−	0.139277i
$521$	5.24338	+	43.1831i	0.229717	+	1.89189i	0.415959	+	0.909383i	$0.363446\pi$
$521$	5.24338	+	43.1831i	0.229717	+	1.89189i	−0.186243	+	0.982504i	$0.559631\pi$
$522$	9.74503	+	18.5676i	0.426528	+	0.812682i
$523$	−4.38425	−	36.1076i	−0.191710	−	1.57887i	−0.697736	−	0.716355i	$-0.745809\pi$
$523$	−4.38425	−	36.1076i	−0.191710	−	1.57887i	0.506026	−	0.862518i	$-0.331114\pi$
$524$	−15.8376	+	8.31221i	−0.691869	+	0.363121i
$525$	−0.0715082	+	0.0807160i	−0.00312087	+	0.00352274i
$526$		−	16.3927i		−	0.714757i
$527$	22.0075	+	24.8413i	0.958660	+	1.08210i
$528$	0.579608	−	1.10435i	0.0252242	−	0.0480607i
$529$	−8.79211			−0.382266
$530$	7.58079			0.329289
$531$	6.62689	−	12.6265i	0.287583	−	0.547943i
$532$	−1.87706	−	0.462653i	−0.0813807	−	0.0200586i
$533$	33.5650	−	11.6714i	1.45386	−	0.505545i
$534$	0.458821	−	0.113089i	0.0198551	−	0.00489385i
$535$	0.473437	−	1.92081i	0.0204685	−	0.0830438i
$536$	5.59284	−	14.7471i	0.241574	−	0.636978i
$537$	0.0918821	+	0.756718i	0.00396501	+	0.0326548i
$538$	−4.95972	−	20.1224i	−0.213829	−	0.867537i
$539$	5.81634	−	23.5978i	0.250527	−	1.01643i
$540$	0.292711	+	0.202044i	0.0125963	+	0.00869459i
$541$	−12.9920	+	1.57751i	−0.558570	+	0.0678227i	−0.394953	−	0.918701i	$-0.629239\pi$
$541$	−12.9920	+	1.57751i	−0.558570	+	0.0678227i	−0.163617	+	0.986524i	$0.552316\pi$
$542$	−14.0829	−	37.1336i	−0.604914	−	1.59503i
$543$	−0.415424	+	0.218031i	−0.0178275	+	0.00935661i
$544$	7.29027	+	29.5778i	0.312568	+	1.26814i
$545$	1.97961	−	5.21979i	0.0847970	−	0.223591i
$546$	0.138000	−	0.0675964i	0.00590586	−	0.00289286i
$547$	−7.21929	−	19.0357i	−0.308674	−	0.813907i	−0.996147	−	0.0876973i	$-0.972049\pi$
$547$	−7.21929	−	19.0357i	−0.308674	−	0.813907i	0.687473	−	0.726210i	$-0.258720\pi$
$548$	−1.36825	+	0.944436i	−0.0584488	+	0.0403443i
$549$	−12.0793	+	10.7013i	−0.515531	+	0.456721i
$550$	28.2108	+	6.95334i	1.20291	+	0.296491i
$551$	−16.9442	−	6.42610i	−0.721849	−	0.273761i
$552$	−0.168525	+	0.321097i	−0.00717288	+	0.0136668i
$553$	−0.597927	−	0.226764i	−0.0254265	−	0.00964298i
$554$	35.6276	+	40.2152i	1.51367	+	1.70858i
$555$	−0.354951	+	0.314459i	−0.0150668	+	0.0133480i
$556$	−7.29919	+	10.5747i	−0.309555	+	0.448467i
$557$	−12.5398	−	8.65558i	−0.531327	−	0.366749i	0.271990	−	0.962300i	$-0.412318\pi$
$557$	−12.5398	−	8.65558i	−0.531327	−	0.366749i	−0.803317	+	0.595552i	$0.796934\pi$
$558$	−32.4215	−	17.0161i	−1.37251	−	0.720349i
$559$	−8.52500	−	4.78160i	−0.360569	−	0.202240i
$560$	−0.948960	+	0.498053i	−0.0401009	+	0.0210466i
$561$	1.22903	+	0.149231i	0.0518895	+	0.00630053i
$562$	−48.5802	+	11.9739i	−2.04923	+	0.505090i
$563$	−20.2500	+	29.3372i	−0.853436	+	1.23642i	0.116532	+	0.993187i	$0.462822\pi$
$563$	−20.2500	+	29.3372i	−0.853436	+	1.23642i	−0.969969	+	0.243229i	$0.921793\pi$
$564$	−0.599322	+	0.413682i	−0.0252360	+	0.0174192i
$565$	−5.22462	+	5.89738i	−0.219801	+	0.248105i
$566$	31.4651	+	3.82055i	1.32258	+	0.160590i
$567$	−0.706163	+	2.86502i	−0.0296561	+	0.120319i
$568$	−1.52565	−	0.800724i	−0.0640149	−	0.0335976i
$569$	5.24552	−	43.2007i	0.219903	−	1.81107i	−0.296839	−	0.954927i	$-0.595933\pi$
$569$	5.24552	−	43.2007i	0.219903	−	1.81107i	0.516743	−	0.856141i	$-0.327144\pi$
$570$	−0.395147	+	0.0479796i	−0.0165509	+	0.00200964i
$571$	−9.07445	+	13.1466i	−0.379754	+	0.550168i	−0.965526	−	0.260308i	$-0.916176\pi$
$571$	−9.07445	+	13.1466i	−0.379754	+	0.550168i	0.585772	+	0.810476i	$0.300791\pi$
$572$	−12.8871	−	9.43562i	−0.538836	−	0.394523i
$573$	1.01697	+	1.47333i	0.0424845	+	0.0615494i
$574$	−3.88659	−	4.38706i	−0.162223	−	0.183112i
$575$	−16.7094	−	4.11850i	−0.696830	−	0.171753i
$576$	−2.30274	−	3.33610i	−0.0959476	−	0.139004i
$577$			9.17968i			0.382155i	0.981575	+	0.191078i	$0.0611982\pi$
$577$			9.17968i			0.382155i	−0.981575	+	0.191078i	$0.938802\pi$
$578$	−10.3838	+	7.16741i	−0.431908	+	0.298125i
$579$	−1.25327	+	0.152174i	−0.0520839	+	0.00632414i
$580$	3.00345	−	1.13906i	0.124711	−	0.0472968i
$581$	0.102887	−	0.847355i	0.00426849	−	0.0351542i
$582$	0.218516	+	0.576179i	0.00905777	+	0.0238834i
$583$	−14.9078	+	16.8274i	−0.617419	+	0.696922i
$584$	−5.28663	−	4.68355i	−0.218762	−	0.193807i
$585$	−4.86559	+	5.19333i	−0.201167	+	0.214718i
$586$	14.2263	−	12.6034i	0.587681	−	0.520640i
$587$			22.2638i			0.918924i	0.888197	+	0.459462i	$0.151958\pi$
$587$			22.2638i			0.918924i	−0.888197	+	0.459462i	$0.848042\pi$
$588$	0.464361	+	0.411388i	0.0191499	+	0.0169654i
$589$	30.7237	−	7.57270i	1.26595	−	0.312028i
$590$	−4.66011	−	3.21664i	−0.191854	−	0.132427i
$591$	1.19593	−	0.453558i	0.0491942	−	0.0186569i
$592$	46.3207	−	17.5671i	1.90377	−	0.722005i
$593$	9.13330	+	6.30426i	0.375060	+	0.258885i	0.740650	−	0.671891i	$-0.234518\pi$
$593$	9.13330	+	6.30426i	0.375060	+	0.258885i	−0.365591	+	0.930776i	$0.619133\pi$
$594$	−2.65475	+	0.654338i	−0.108926	+	0.0268478i
$595$	−0.796303	−	0.705463i	−0.0326452	−	0.0289212i
$596$			0.0887106i			0.00363373i
$597$	1.17029	−	1.03679i	0.0478969	−	0.0424330i
$598$	19.7869	+	14.4875i	0.809145	+	0.592437i
$599$	20.9579	+	18.5671i	0.856315	+	0.758629i	0.972081	−	0.234647i	$-0.0753935\pi$
$599$	20.9579	+	18.5671i	0.856315	+	0.758629i	−0.115765	+	0.993277i	$0.536932\pi$
$600$	0.291273	−	0.328780i	0.0118912	−	0.0134224i
$601$	9.65153	+	25.4490i	0.393694	+	1.03809i	0.974568	+	0.224092i	$0.0719418\pi$
$601$	9.65153	+	25.4490i	0.393694	+	1.03809i	−0.580874	+	0.813994i	$0.697289\pi$
$602$	−0.194318	+	1.60035i	−0.00791981	+	0.0652255i
$603$	−32.9012	+	12.4778i	−1.33984	+	0.508134i
$604$	19.7824	−	2.40201i	0.804933	−	0.0977365i
$605$	0.779834	−	0.538280i	0.0317048	−	0.0218842i
$606$		−	1.24067i		−	0.0503986i
$607$	−21.2694	−	30.8140i	−0.863298	−	1.25070i	−0.966661	−	0.256060i	$-0.917576\pi$
$607$	−21.2694	−	30.8140i	−0.863298	−	1.25070i	0.103363	−	0.994644i	$-0.467040\pi$
$608$	28.2013	+	6.95100i	1.14371	+	0.281900i
$609$	−0.0607739	−	0.0685995i	−0.00246268	−	0.00277979i
$610$	3.64024	+	5.27379i	0.147389	+	0.213530i
$611$	−12.8303	−	26.1934i	−0.519057	−	1.05967i
$612$	10.4672	−	15.1643i	0.423110	−	0.612980i
$613$	−6.70832	+	0.814538i	−0.270947	+	0.0328989i	−0.254882	−	0.966972i	$-0.582037\pi$
$613$	−6.70832	+	0.814538i	−0.270947	+	0.0328989i	−0.0160643	+	0.999871i	$0.505114\pi$
$614$	−6.37299	+	52.4863i	−0.257193	+	2.11817i
$615$	−0.412210	−	0.216344i	−0.0166219	−	0.00872384i
$616$	0.373371	−	1.51483i	0.0150436	−	0.0610341i
$617$	−44.1267	−	5.35795i	−1.77648	−	0.215703i	−0.834413	−	0.551140i	$-0.814193\pi$
$617$	−44.1267	−	5.35795i	−1.77648	−	0.215703i	−0.942063	+	0.335437i	$0.891116\pi$
$618$	1.55172	−	1.75153i	0.0624195	−	0.0704571i
$619$	−5.52087	+	3.81078i	−0.221902	+	0.153168i	−0.673830	−	0.738886i	$-0.735352\pi$
$619$	−5.52087	+	3.81078i	−0.221902	+	0.153168i	0.451927	+	0.892055i	$0.350737\pi$
$620$	−3.18622	+	4.61603i	−0.127962	+	0.185384i
$621$	1.57242	−	0.387568i	0.0630992	−	0.0155526i
$622$	15.7457	+	1.91187i	0.631343	+	0.0766589i
$623$	1.06626	−	0.559618i	0.0427189	−	0.0224206i
$624$	−1.14509	+	0.560900i	−0.0458404	+	0.0224540i
$625$	16.5345	+	8.67799i	0.661381	+	0.347120i
$626$	−28.1134	−	19.4053i	−1.12364	−	0.775591i
$627$	0.670564	−	0.971480i	0.0267798	−	0.0387972i
$628$	5.78140	−	5.12187i	0.230703	−	0.204385i
$629$	32.6099	+	36.8090i	1.30024	+	1.46767i
$630$	1.09746	+	0.416212i	0.0437239	+	0.0165823i
$631$	−13.1080	+	24.9751i	−0.521820	+	0.994244i	0.471826	+	0.881692i	$0.343595\pi$
$631$	−13.1080	+	24.9751i	−0.521820	+	0.994244i	−0.993646	+	0.112553i	$0.964097\pi$
$632$	2.43553	+	0.923675i	0.0968802	+	0.0367418i
$633$	0.822609	+	0.202755i	0.0326958	+	0.00805878i
$634$	−29.7683	+	26.3724i	−1.18225	+	1.04738i
$635$	−6.16499	+	4.25538i	−0.244650	+	0.168870i
$636$	−0.203491	−	0.536560i	−0.00806893	−	0.0212760i
$637$	−19.0500	+	15.9526i	−0.754787	+	0.632066i
$638$	−8.75645	+	23.0889i	−0.346671	+	0.914097i
$639$	0.919951	+	3.73239i	0.0363927	+	0.147651i
$640$	5.83330	−	3.06155i	0.230581	−	0.121018i
$641$	7.65645	+	20.1884i	0.302411	+	0.797393i	0.996958	+	0.0779453i	$0.0248360\pi$
$641$	7.65645	+	20.1884i	0.302411	+	0.797393i	−0.694546	+	0.719448i	$0.744395\pi$
$642$	−0.385367	+	0.0467921i	−0.0152092	+	0.00184674i
$643$	−7.88819	−	5.44482i	−0.311080	−	0.214723i	0.402287	−	0.915513i	$-0.368215\pi$
$643$	−7.88819	−	5.44482i	−0.311080	−	0.214723i	−0.713367	+	0.700791i	$0.752831\pi$
$644$	0.373406	−	1.51497i	0.0147143	−	0.0596981i
$645$	0.0306437	+	0.124326i	0.00120659	+	0.00489534i
$646$	4.97555	+	40.9774i	0.195761	+	1.61223i
$647$	−11.8038	+	31.1241i	−0.464056	+	1.22361i	0.475041	+	0.879963i	$0.342433\pi$
$647$	−11.8038	+	31.1241i	−0.464056	+	1.22361i	−0.939097	+	0.343651i	$0.888336\pi$
$648$	2.87641	−	11.6700i	0.112996	−	0.458443i
$649$	16.3043	−	4.01866i	0.640001	−	0.157746i
$650$	−19.0711	−	22.7739i	−0.748030	−	0.893267i
$651$	0.155379	+	0.0382975i	0.00608979	+	0.00150100i
$652$	−8.94683	+	17.0468i	−0.350385	+	0.667602i
$653$	31.3330			1.22616			0.613078	−	0.790022i	$-0.289931\pi$
$653$	31.3330			1.22616			0.613078	+	0.790022i	$0.289931\pi$
$654$	−1.09546			−0.0428358
$655$	−4.36130	+	8.30977i	−0.170410	+	0.324689i
$656$	32.2501	+	36.4028i	1.25915	+	1.42129i
$657$			15.7575i			0.614757i
$658$	−3.18997	+	3.60073i	−0.124358	+	0.140371i
$659$	−3.29907	+	1.73148i	−0.128513	+	0.0674490i	−0.527755	−	0.849397i	$-0.676966\pi$
$659$	−3.29907	+	1.73148i	−0.128513	+	0.0674490i	0.399241	+	0.916846i	$0.369274\pi$
$660$	0.0252208	+	0.207712i	0.000981720	+	0.00808519i
$661$	7.00117	+	13.3396i	0.272314	+	0.518851i	0.982757	−	0.184904i	$-0.0591975\pi$
$661$	7.00117	+	13.3396i	0.272314	+	0.518851i	−0.710443	+	0.703755i	$0.751505\pi$
$662$	4.69987	+	38.7069i	0.182666	+	1.50439i
$663$	−0.923674	−	0.865382i	−0.0358725	−	0.0336086i
$664$	−0.419090	+	3.45152i	−0.0162639	+	0.133945i
$665$	−0.948425	+	0.359690i	−0.0367783	+	0.0139482i
$666$	−48.0410	−	25.2139i	−1.86155	−	0.977017i
$667$	5.18649	−	13.6756i	0.200822	−	0.529523i
$668$	−7.24215	−	13.7988i	−0.280207	−	0.533890i
$669$	0.539298	+	1.02755i	0.0208505	+	0.0397273i
$670$	3.34389	+	13.5667i	0.129186	+	0.524128i
$671$	−18.8651	−	2.29064i	−0.728279	−	0.0884291i
$672$	0.109950	+	0.0974070i	0.00424140	+	0.00375755i
$673$	2.19947	+	3.18648i	0.0847832	+	0.122830i	0.863081	−	0.505066i	$-0.168532\pi$
$673$	2.19947	+	3.18648i	0.0847832	+	0.122830i	−0.778298	+	0.627896i	$0.783916\pi$
$674$	−8.14136	−	3.08761i	−0.313593	−	0.118930i
$675$	−1.96162			−0.0755027
$676$	4.93159	+	15.5666i	0.189677	+	0.598715i
$677$	7.14945			0.274776			0.137388	−	0.990517i	$-0.456129\pi$
$677$	7.14945			0.274776			0.137388	+	0.990517i	$0.456129\pi$
$678$	1.44558	+	0.548236i	0.0555172	+	0.0210549i
$679$	0.892036	+	1.29234i	0.0342332	+	0.0495954i
$680$	3.24357	+	2.87355i	0.124385	+	0.110196i
$681$	0.401284	+	0.0487247i	0.0153772	+	0.00186713i
$682$	−10.3188	−	41.8652i	−0.395129	−	1.60310i
$683$	−20.0208	−	38.1464i	−0.766075	−	1.45963i	−0.884435	−	0.466663i	$-0.845456\pi$
$683$	−20.0208	−	38.1464i	−0.766075	−	1.45963i	0.118361	−	0.992971i	$-0.462236\pi$
$684$	−8.16449	−	15.5561i	−0.312177	−	0.594804i
$685$	−0.309328	+	0.815630i	−0.0118188	+	0.0311636i
$686$	7.31454	+	3.83897i	0.279271	+	0.146573i
$687$	−0.562160	+	0.213199i	−0.0214477	+	0.00813405i
$688$	1.61241	−	13.2794i	0.0614725	−	0.506271i
$689$	22.4603	−	4.87695i	0.855671	−	0.185797i
$690$	−0.0387242	−	0.318922i	−0.00147420	−	0.0121412i
$691$	17.1746	+	32.7235i	0.653354	+	1.24486i	0.956448	+	0.291902i	$0.0942880\pi$
$691$	17.1746	+	32.7235i	0.653354	+	1.24486i	−0.303094	+	0.952961i	$0.598020\pi$
$692$	−2.47488	−	20.3825i	−0.0940809	−	0.774826i
$693$	−3.08207	+	1.61759i	−0.117078	+	0.0614473i
$694$	−3.72488	+	4.20452i	−0.141394	+	0.159601i
$695$			6.74181i			0.255731i
$696$	0.247549	+	0.279426i	0.00938334	+	0.0105916i
$697$	−22.4352	+	42.7467i	−0.849795	+	1.61915i
$698$	52.7711			1.99742
$699$	0.522528			0.0197638
$700$	−0.878299	+	1.67346i	−0.0331966	+	0.0632508i
$701$	−18.8590	−	4.64832i	−0.712293	−	0.175565i	−0.133512	−	0.991047i	$-0.542625\pi$
$701$	−18.8590	−	4.64832i	−0.712293	−	0.175565i	−0.578782	+	0.815483i	$0.696472\pi$
$702$	2.58506	+	1.06361i	0.0975667	+	0.0401435i
$703$	45.5252	−	11.2210i	1.71702	−	0.423207i
$704$	1.14239	−	4.63484i	0.0430553	−	0.174682i
$705$	−0.135492	+	0.357263i	−0.00510292	+	0.0134553i
$706$	−0.0162488	−	0.133821i	−0.000611531	−	0.00503641i
$707$	−0.756611	−	3.06969i	−0.0284553	−	0.115448i
$708$	−0.102579	+	0.416181i	−0.00385517	+	0.0156411i
$709$	−42.2805	−	29.1841i	−1.58788	−	1.09603i	−0.943523	−	0.331308i	$-0.892510\pi$
$709$	−42.2805	−	29.1841i	−1.58788	−	1.09603i	−0.644356	−	0.764725i	$-0.722875\pi$
$710$	1.51532	−	0.183993i	0.0568690	−	0.00690514i
$711$	−2.06075	−	5.43374i	−0.0772840	−	0.203781i
$712$	−4.34319	+	2.27948i	−0.162768	+	0.0854273i
$713$	6.11191	+	24.7970i	0.228893	+	0.928654i
$714$	−0.0740264	+	0.195192i	−0.00277037	+	0.00730486i
$715$	−8.37708	−	0.233313i	−0.313285	−	0.00872542i
$716$	4.73743	+	12.4916i	0.177046	+	0.466832i
$717$	−0.908136	+	0.626841i	−0.0339150	+	0.0234098i
$718$	41.4498	−	36.7213i	1.54689	−	1.37043i
$719$	−42.9134	−	10.5772i	−1.60040	−	0.394463i	−0.664656	−	0.747149i	$-0.731422\pi$
$719$	−42.9134	−	10.5772i	−1.60040	−	0.394463i	−0.935742	+	0.352686i	$0.885268\pi$
$720$	−9.10648	−	3.45363i	−0.339378	−	0.128709i
$721$	2.77116	−	5.28001i	0.103203	−	0.196638i
$722$	4.74293	+	1.79876i	0.176514	+	0.0669428i
$723$	−1.03163	−	1.16447i	−0.0383666	−	0.0433069i
$724$	−6.15472	+	5.45261i	−0.228739	+	0.202645i
$725$	−10.0639	+	14.5800i	−0.373763	+	0.541489i
$726$	−0.153026	−	0.105626i	−0.00567931	−	0.00392015i
$727$	−18.2408	−	9.57350i	−0.676513	−	0.355062i	0.0912202	−	0.995831i	$-0.470923\pi$
$727$	−18.2408	−	9.57350i	−0.676513	−	0.355062i	−0.767734	+	0.640769i	$0.778616\pi$
$728$	−1.22289	+	1.02405i	−0.0453231	+	0.0379540i
$729$	−23.6621	+	12.4188i	−0.876373	+	0.459956i
$730$	6.21151	+	0.754214i	0.229898	+	0.0279147i
$731$	12.8928	−	3.17780i	0.476858	−	0.117535i
$732$	0.275559	−	0.399216i	0.0101850	−	0.0147554i
$733$	5.84606	−	4.03524i	0.215929	−	0.149045i	−0.455191	−	0.890394i	$-0.650429\pi$
$733$	5.84606	−	4.03524i	0.215929	−	0.149045i	0.671120	+	0.741349i	$0.265814\pi$
$734$	19.1244	−	21.5870i	0.705896	−	0.796792i
$735$	0.323132	+	0.0392353i	0.0119189	+	0.00144721i
$736$	−5.61013	+	22.7612i	−0.206792	+	0.838989i
$737$	−36.6905	−	19.2567i	−1.35151	−	0.709329i
$738$	6.42014	−	52.8746i	0.236329	−	1.94634i
$739$	11.1160	−	1.34973i	0.408909	−	0.0496505i	0.0865020	−	0.996252i	$-0.472431\pi$
$739$	11.1160	−	1.34973i	0.408909	−	0.0496505i	0.322407	+	0.946601i	$0.395508\pi$
$740$	−4.72122	+	6.83987i	−0.173556	+	0.251439i
$741$	−1.13987	+	0.396364i	−0.0418743	+	0.0145608i
$742$	−2.15338	−	3.11971i	−0.0790531	−	0.114528i
$743$	−17.4377	−	19.6832i	−0.639729	−	0.722105i	0.335810	−	0.941930i	$-0.390990\pi$
$743$	−17.4377	−	19.6832i	−0.639729	−	0.722105i	−0.975539	+	0.219825i	$0.929451\pi$
$744$	−0.632904	−	0.155997i	−0.0232034	−	0.00571912i
$745$	0.0264407	+	0.0383060i	0.000968712	+	0.00140342i
$746$		−	0.739491i		−	0.0270747i
$747$	6.38388	−	4.40648i	0.233574	−	0.161225i
$748$	21.5401	−	2.61544i	0.787583	−	0.0956299i
$749$	−0.924951	+	0.350788i	−0.0337970	+	0.0128175i
$750$	−0.0982725	+	0.809347i	−0.00358840	+	0.0295532i
$751$	−6.03822	−	15.9215i	−0.220338	−	0.580983i	0.778578	−	0.627548i	$-0.215942\pi$
$751$	−6.03822	−	15.9215i	−0.220338	−	0.580983i	−0.998915	+	0.0465658i	$0.985172\pi$
$752$	26.4697	−	29.8781i	0.965250	−	1.08954i
$753$	−0.462354	−	0.409610i	−0.0168491	−	0.0149270i
$754$	21.1678	−	13.7571i	0.770887	−	0.501003i
$755$	7.82625	−	6.93345i	0.284826	−	0.252334i
$756$		−	0.177851i		−	0.00646839i
$757$	3.27955	+	2.90543i	0.119197	+	0.105600i	0.720616	−	0.693335i	$-0.243859\pi$
$757$	3.27955	+	2.90543i	0.119197	+	0.105600i	−0.601419	+	0.798934i	$0.705398\pi$
$758$	28.8648	−	7.11453i	1.04842	−	0.258411i
$759$	0.784079	+	0.541211i	0.0284603	+	0.0196447i
$760$	3.86321	−	1.46512i	0.140133	−	0.0531456i
$761$	23.5689	−	8.93852i	0.854373	−	0.324021i	0.111755	−	0.993736i	$-0.464353\pi$
$761$	23.5689	−	8.93852i	0.854373	−	0.324021i	0.742618	+	0.669715i	$0.233584\pi$
$762$	1.20975	+	0.835027i	0.0438245	+	0.0302499i
$763$	−2.71041	+	0.668057i	−0.0981236	+	0.0241853i
$764$	23.4852	+	20.8061i	0.849665	+	0.752737i
$765$		−	9.66787i		−	0.349542i
$766$	4.57333	−	4.05161i	0.165241	−	0.146391i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.68720 - 0.639871i) q^{2} +(0.0407127 + 0.0589826i) q^{3} +(0.940192 + 0.832938i) q^{4} +(0.654244 + 0.0794397i) q^{5} +(-0.0309493 - 0.125566i) q^{6} +(-0.153151 - 0.291806i) q^{7} +(0.623830 + 1.18861i) q^{8} +(1.06199 - 2.80025i) q^{9} +O(q^{10})\)	\(q+(-1.68720 - 0.639871i) q^{2} +(0.0407127 + 0.0589826i) q^{3} +(0.940192 + 0.832938i) q^{4} +(0.654244 + 0.0794397i) q^{5} +(-0.0309493 - 0.125566i) q^{6} +(-0.153151 - 0.291806i) q^{7} +(0.623830 + 1.18861i) q^{8} +(1.06199 - 2.80025i) q^{9} +(-1.05301 - 0.552663i) q^{10} +(3.29754 - 1.25059i) q^{11} +(-0.0108510 + 0.0893661i) q^{12} +(-3.47540 - 0.959994i) q^{13} +(0.0716793 + 0.590332i) q^{14} +(0.0219505 + 0.0418232i) q^{15} +(-0.594779 - 4.89844i) q^{16} +(4.33713 - 2.27630i) q^{17} +(-3.58359 + 4.04504i) q^{18} -4.67024i q^{19} +(0.548947 + 0.619633i) q^{20} +(0.0109762 - 0.0209135i) q^{21} -6.36384 q^{22} +3.76934 q^{23} +(-0.0447094 + 0.0851866i) q^{24} +(-4.43298 - 1.09263i) q^{25} +(5.24943 + 3.84351i) q^{26} +(0.417162 - 0.102821i) q^{27} +(0.0990641 - 0.401919i) q^{28} +(1.37597 - 3.62813i) q^{29} +(-0.0102735 - 0.0846097i) q^{30} +(1.62148 + 6.57861i) q^{31} +(-1.48836 + 6.03852i) q^{32} +(0.208015 + 0.143583i) q^{33} +(-8.77415 + 1.06537i) q^{34} +(-0.0770175 - 0.203078i) q^{35} +(3.33091 - 1.74820i) q^{36} +(2.40265 + 9.74795i) q^{37} +(-2.98835 + 7.87963i) q^{38} +(-0.0848701 - 0.244072i) q^{39} +(0.313715 + 0.827197i) q^{40} +(-8.11133 + 5.59885i) q^{41} +(-0.0319010 + 0.0282618i) q^{42} +(2.63216 + 0.648770i) q^{43} +(4.14199 + 1.57085i) q^{44} +(0.917254 - 1.74768i) q^{45} +(-6.35963 - 2.41189i) q^{46} +(5.36429 + 6.05503i) q^{47} +(0.264708 - 0.234511i) q^{48} +(3.91476 - 5.67151i) q^{49} +(6.78019 + 4.68003i) q^{50} +(0.310838 + 0.163141i) q^{51} +(-2.46793 - 3.79737i) q^{52} +(-5.64437 + 2.96240i) q^{53} +(-0.769629 - 0.0934498i) q^{54} +(2.25675 - 0.556238i) q^{55} +(0.251302 - 0.364074i) q^{56} +(0.275463 - 0.190138i) q^{57} +(-4.64307 + 5.24095i) q^{58} +(4.72673 + 0.573928i) q^{59} +(-0.0141984 + 0.0576053i) q^{60} +(-4.77126 - 2.50415i) q^{61} +(1.47370 - 12.1370i) q^{62} +(-0.979773 + 0.118966i) q^{63} +(0.768897 - 1.11394i) q^{64} +(-2.19750 - 0.904155i) q^{65} +(-0.259089 - 0.375356i) q^{66} +(-7.79129 - 8.79455i) q^{67} +(5.97375 + 1.47240i) q^{68} +(0.153460 + 0.222325i) q^{69} +0.391916i q^{70} +(-1.05635 + 0.729146i) q^{71} +(3.99090 - 0.484583i) q^{72} +(-4.91959 + 1.86575i) q^{73} +(2.18367 - 17.9841i) q^{74} +(-0.116033 - 0.305953i) q^{75} +(3.89002 - 4.39092i) q^{76} +(-0.869954 - 0.770712i) q^{77} +(-0.0129817 + 0.466105i) q^{78} +(1.45245 - 1.28676i) q^{79} -3.25203i q^{80} +(-6.70201 - 5.93747i) q^{81} +(17.2680 - 4.25618i) q^{82} +(2.13161 + 1.47134i) q^{83} +(0.0277394 - 0.0105202i) q^{84} +(3.01837 - 1.14472i) q^{85} +(-4.02586 - 2.77885i) q^{86} +(0.270016 - 0.0665530i) q^{87} +(3.54357 + 3.13933i) q^{88} +3.65402i q^{89} +(-2.66588 + 2.36177i) q^{90} +(0.252131 + 1.16117i) q^{91} +(3.54390 + 3.13962i) q^{92} +(-0.322008 + 0.363472i) q^{93} +(-5.17620 - 13.6485i) q^{94} +(0.371002 - 3.05548i) q^{95} +(-0.416762 + 0.158057i) q^{96} +(-4.73020 + 0.574351i) q^{97} +(-10.2340 + 7.06403i) q^{98} -10.5621i 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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