LMFDB - Embedded newform 169.2.h.a.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	169.25
Dual form			169.2.h.a.142.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49527 - 0.567082i) q^{2} +(1.18578 + 1.71790i) q^{3} +(0.417236 + 0.369639i) q^{4} +(-2.96326 - 0.359805i) q^{5} +(-0.798874 - 3.24116i) q^{6} +(1.24562 + 2.37332i) q^{7} +(1.07210 + 2.04271i) q^{8} +(-0.481287 + 1.26905i) q^{9} +O(q^{10})$	\(q+(-1.49527 - 0.567082i) q^{2} +(1.18578 + 1.71790i) q^{3} +(0.417236 + 0.369639i) q^{4} +(-2.96326 - 0.359805i) q^{5} +(-0.798874 - 3.24116i) q^{6} +(1.24562 + 2.37332i) q^{7} +(1.07210 + 2.04271i) q^{8} +(-0.481287 + 1.26905i) q^{9} +(4.22684 + 2.21842i) q^{10} +(-4.01299 + 1.52193i) q^{11} +(-0.140252 + 1.15508i) q^{12} +(-1.01665 + 3.45925i) q^{13} +(-0.516666 - 4.25513i) q^{14} +(-2.89566 - 5.51722i) q^{15} +(-0.579073 - 4.76910i) q^{16} +(-3.38159 + 1.77479i) q^{17} +(1.43931 - 1.62464i) q^{18} +3.49861i q^{19} +(-1.10338 - 1.24546i) q^{20} +(-2.60010 + 4.95408i) q^{21} +6.86357 q^{22} +6.33211 q^{23} +(-2.23790 + 4.26397i) q^{24} +(3.79672 + 0.935808i) q^{25} +(3.48185 - 4.59600i) q^{26} +(3.32944 - 0.820634i) q^{27} +(-0.357557 + 1.45066i) q^{28} +(-1.14319 + 3.01434i) q^{29} +(1.20109 + 9.89183i) q^{30} +(-1.63386 - 6.62883i) q^{31} +(-0.734413 + 2.97963i) q^{32} +(-7.37304 - 5.08924i) q^{33} +(6.06285 - 0.736163i) q^{34} +(-2.83715 - 7.48094i) q^{35} +(-0.669900 + 0.351591i) q^{36} +(0.694875 + 2.81922i) q^{37} +(1.98400 - 5.23137i) q^{38} +(-7.14816 + 2.35541i) q^{39} +(-2.44193 - 6.43883i) q^{40} +(6.02013 - 4.15540i) q^{41} +(6.69723 - 5.93322i) q^{42} +(7.11200 + 1.75295i) q^{43} +(-2.23693 - 0.848356i) q^{44} +(1.88279 - 3.58735i) q^{45} +(-9.46823 - 3.59083i) q^{46} +(-6.61375 - 7.46538i) q^{47} +(7.50617 - 6.64989i) q^{48} +(-0.104644 + 0.151603i) q^{49} +(-5.14646 - 3.55234i) q^{50} +(-7.05873 - 3.70471i) q^{51} +(-1.70286 + 1.06753i) q^{52} +(-5.07487 + 2.66350i) q^{53} +(-5.44379 - 0.660996i) q^{54} +(12.4391 - 3.06597i) q^{55} +(-3.51259 + 5.08887i) q^{56} +(-6.01025 + 4.14858i) q^{57} +(3.41876 - 3.85898i) q^{58} +(13.8480 + 1.68145i) q^{59} +(0.831206 - 3.37234i) q^{60} +(-1.93527 - 1.01571i) q^{61} +(-1.31602 + 10.8384i) q^{62} +(-3.61136 + 0.438498i) q^{63} +(-2.67027 + 3.86855i) q^{64} +(4.25725 - 9.88486i) q^{65} +(8.13869 + 11.7909i) q^{66} +(3.89831 + 4.40029i) q^{67} +(-2.06695 - 0.509458i) q^{68} +(7.50849 + 10.8779i) q^{69} +12.7949i q^{70} +(-6.65436 + 4.59318i) q^{71} +(-3.10829 + 0.377415i) q^{72} +(1.17549 - 0.445804i) q^{73} +(0.559701 - 4.60955i) q^{74} +(2.89445 + 7.63205i) q^{75} +(-1.29322 + 1.45975i) q^{76} +(-8.61067 - 7.62838i) q^{77} +(12.0242 + 0.531614i) q^{78} +(-8.90005 + 7.88476i) q^{79} +14.3404i q^{80} +(8.40549 + 7.44662i) q^{81} +(-11.3582 + 2.79954i) q^{82} +(-1.30947 - 0.903865i) q^{83} +(-2.91608 + 1.10592i) q^{84} +(10.6591 - 4.04246i) q^{85} +(-9.64032 - 6.65423i) q^{86} +(-6.53390 + 1.61046i) q^{87} +(-7.41119 - 6.56574i) q^{88} +12.0431i q^{89} +(-4.84960 + 4.29637i) q^{90} +(-9.47627 + 1.89606i) q^{91} +(2.64199 + 2.34060i) q^{92} +(9.45025 - 10.6671i) q^{93} +(5.65587 + 14.9133i) q^{94} +(1.25881 - 10.3673i) q^{95} +(-5.98955 + 2.27154i) q^{96} +(9.94763 - 1.20786i) q^{97} +(0.242442 - 0.167346i) q^{98} -5.82517i 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 $

$2$	−1.49527	−	0.567082i	−1.05732	−	0.400988i	−0.236175	−	0.971711i	$-0.575894\pi$
$2$	−1.49527	−	0.567082i	−1.05732	−	0.400988i	−0.821143	+	0.570723i	$0.806663\pi$
$3$	1.18578	+	1.71790i	0.684610	+	0.991829i	0.999094	+	0.0425661i	$0.0135533\pi$
$3$	1.18578	+	1.71790i	0.684610	+	0.991829i	−0.314483	+	0.949263i	$0.601831\pi$
$4$	0.417236	+	0.369639i	0.208618	+	0.184820i
$5$	−2.96326	−	0.359805i	−1.32521	−	0.160909i	−0.572848	−	0.819661i	$-0.694162\pi$
$5$	−2.96326	−	0.359805i	−1.32521	−	0.160909i	−0.752360	+	0.658752i	$0.771085\pi$
$6$	−0.798874	−	3.24116i	−0.326139	−	1.32320i
$7$	1.24562	+	2.37332i	0.470798	+	0.897031i	0.998856	+	0.0478226i	$0.0152282\pi$
$7$	1.24562	+	2.37332i	0.470798	+	0.897031i	−0.528058	+	0.849209i	$0.677079\pi$
$8$	1.07210	+	2.04271i	0.379044	+	0.722208i
$9$	−0.481287	+	1.26905i	−0.160429	+	0.423016i
$10$	4.22684	+	2.21842i	1.33664	+	0.701525i
$11$	−4.01299	+	1.52193i	−1.20996	+	0.458878i	−0.875356	−	0.483479i	$-0.839373\pi$
$11$	−4.01299	+	1.52193i	−1.20996	+	0.458878i	−0.334607	+	0.942358i	$0.608604\pi$
$12$	−0.140252	+	1.15508i	−0.0404873	+	0.333443i
$13$	−1.01665	+	3.45925i	−0.281968	+	0.959424i
$13$	−1.01665	+	3.45925i	−0.281968	+	0.959424i
$14$	−0.516666	−	4.25513i	−0.138085	−	1.13723i
$15$	−2.89566	−	5.51722i	−0.747657	−	1.42454i
$16$	−0.579073	−	4.76910i	−0.144768	−	1.19227i
$17$	−3.38159	+	1.77479i	−0.820155	+	0.430451i	−0.821958	−	0.569548i	$-0.807118\pi$
$17$	−3.38159	+	1.77479i	−0.820155	+	0.430451i	0.00180312	+	0.999998i	$0.499426\pi$
$18$	1.43931	−	1.62464i	0.339249	−	0.382932i
$19$			3.49861i			0.802635i	0.915939	+	0.401318i	$0.131448\pi$
$19$			3.49861i			0.802635i	−0.915939	+	0.401318i	$0.868552\pi$
$20$	−1.10338	−	1.24546i	−0.246723	−	0.278493i
$21$	−2.60010	+	4.95408i	−0.567388	+	1.08107i
$22$	6.86357			1.46332
$23$	6.33211			1.32034			0.660168	−	0.751118i	$-0.270485\pi$
$23$	6.33211			1.32034			0.660168	+	0.751118i	$0.270485\pi$
$24$	−2.23790	+	4.26397i	−0.456810	+	0.870378i
$25$	3.79672	+	0.935808i	0.759345	+	0.187162i
$26$	3.48185	−	4.59600i	0.682846	−	0.901350i
$27$	3.32944	−	0.820634i	0.640751	−	0.157931i
$28$	−0.357557	+	1.45066i	−0.0675718	+	0.274150i
$29$	−1.14319	+	3.01434i	−0.212285	+	0.559749i	−0.998289	−	0.0584720i	$-0.981377\pi$
$29$	−1.14319	+	3.01434i	−0.212285	+	0.559749i	0.786004	+	0.618221i	$0.212146\pi$
$30$	1.20109	+	9.89183i	0.219287	+	1.80599i
$31$	−1.63386	−	6.62883i	−0.293450	−	1.19057i	−0.913773	−	0.406226i	$-0.866845\pi$
$31$	−1.63386	−	6.62883i	−0.293450	−	1.19057i	0.620323	−	0.784346i	$-0.287002\pi$
$32$	−0.734413	+	2.97963i	−0.129827	+	0.526729i
$33$	−7.37304	−	5.08924i	−1.28348	−	0.885923i
$34$	6.06285	−	0.736163i	1.03977	−	0.126251i
$35$	−2.83715	−	7.48094i	−0.479565	−	1.26451i
$36$	−0.669900	+	0.351591i	−0.111650	+	0.0585985i
$37$	0.694875	+	2.81922i	0.114237	+	0.463477i	1.00000		0.000661049i	$-0.000210419\pi$
$37$	0.694875	+	2.81922i	0.114237	+	0.463477i	−0.885763	+	0.464138i	$0.846364\pi$
$38$	1.98400	−	5.23137i	0.321847	−	0.848640i
$39$	−7.14816	+	2.35541i	−1.14462	+	0.377168i
$40$	−2.44193	−	6.43883i	−0.386103	−	1.01807i
$41$	6.02013	−	4.15540i	0.940187	−	0.648964i	0.00382221	−	0.999993i	$-0.498783\pi$
$41$	6.02013	−	4.15540i	0.940187	−	0.648964i	0.936365	+	0.351028i	$0.114168\pi$
$42$	6.69723	−	5.93322i	1.03340	−	0.915516i
$43$	7.11200	+	1.75295i	1.08457	+	0.267323i	0.740796	−	0.671730i	$-0.234448\pi$
$43$	7.11200	+	1.75295i	1.08457	+	0.267323i	0.343774	+	0.939052i	$0.388295\pi$
$44$	−2.23693	−	0.848356i	−0.337230	−	0.127894i
$45$	1.88279	−	3.58735i	0.280669	−	0.534770i
$46$	−9.46823	−	3.59083i	−1.39601	−	0.529439i
$47$	−6.61375	−	7.46538i	−0.964714	−	1.08894i	−0.995993	−	0.0894267i	$-0.971497\pi$
$47$	−6.61375	−	7.46538i	−0.964714	−	1.08894i	0.0312791	−	0.999511i	$-0.490042\pi$
$48$	7.50617	−	6.64989i	1.08342	−	0.959829i
$49$	−0.104644	+	0.151603i	−0.0149491	+	0.0216575i
$50$	−5.14646	−	3.55234i	−0.727819	−	0.502377i
$51$	−7.05873	−	3.70471i	−0.988420	−	0.518763i
$52$	−1.70286	+	1.06753i	−0.236144	+	0.148040i
$53$	−5.07487	+	2.66350i	−0.697087	+	0.365860i	−0.775749	−	0.631042i	$-0.782628\pi$
$53$	−5.07487	+	2.66350i	−0.697087	+	0.365860i	0.0786616	+	0.996901i	$0.474935\pi$
$54$	−5.44379	−	0.660996i	−0.740806	−	0.0899501i
$55$	12.4391	−	3.06597i	1.67729	−	0.413415i
$56$	−3.51259	+	5.08887i	−0.469390	+	0.680029i
$57$	−6.01025	+	4.14858i	−0.796077	+	0.549492i
$58$	3.41876	−	3.85898i	0.448905	−	0.506709i
$59$	13.8480	+	1.68145i	1.80286	+	0.218906i	0.951916	−	0.306358i	$-0.0991104\pi$
$59$	13.8480	+	1.68145i	1.80286	+	0.218906i	0.850939	+	0.525264i	$0.176033\pi$
$60$	0.831206	−	3.37234i	0.107308	−	0.435367i
$61$	−1.93527	−	1.01571i	−0.247785	−	0.130048i	0.336259	−	0.941770i	$-0.390838\pi$
$61$	−1.93527	−	1.01571i	−0.247785	−	0.130048i	−0.584044	+	0.811722i	$0.698531\pi$
$62$	−1.31602	+	10.8384i	−0.167135	+	1.37648i
$63$	−3.61136	+	0.438498i	−0.454988	+	0.0552456i
$64$	−2.67027	+	3.86855i	−0.333783	+	0.483569i
$65$	4.25725	−	9.88486i	0.528046	−	1.22607i
$66$	8.13869	+	11.7909i	1.00180	+	1.45136i
$67$	3.89831	+	4.40029i	0.476255	+	0.537581i	0.936712	−	0.350102i	$-0.113853\pi$
$67$	3.89831	+	4.40029i	0.476255	+	0.537581i	−0.460457	+	0.887682i	$0.652314\pi$
$68$	−2.06695	−	0.509458i	−0.250655	−	0.0617809i
$69$	7.50849	+	10.8779i	0.903916	+	1.30955i
$70$			12.7949i			1.52929i
$71$	−6.65436	+	4.59318i	−0.789728	+	0.545110i	−0.893273	−	0.449515i	$-0.851597\pi$
$71$	−6.65436	+	4.59318i	−0.789728	+	0.545110i	0.103545	+	0.994625i	$0.466981\pi$
$72$	−3.10829	+	0.377415i	−0.366316	+	0.0444788i
$73$	1.17549	−	0.445804i	0.137581	−	0.0521775i	−0.284854	−	0.958571i	$-0.591945\pi$
$73$	1.17549	−	0.445804i	0.137581	−	0.0521775i	0.422434	+	0.906394i	$0.361176\pi$
$74$	0.559701	−	4.60955i	0.0650639	−	0.535849i
$75$	2.89445	+	7.63205i	0.334223	+	0.881273i
$76$	−1.29322	+	1.45975i	−0.148343	+	0.167444i
$77$	−8.61067	−	7.62838i	−0.981276	−	0.869335i
$78$	12.0242	+	0.531614i	1.36147	+	0.0601935i
$79$	−8.90005	+	7.88476i	−1.00133	+	0.887105i	−0.993610	−	0.112866i	$-0.963997\pi$
$79$	−8.90005	+	7.88476i	−1.00133	+	0.887105i	−0.00772390	+	0.999970i	$0.502459\pi$
$80$			14.3404i			1.60331i
$81$	8.40549	+	7.44662i	0.933944	+	0.827402i
$82$	−11.3582	+	2.79954i	−1.25430	+	0.309158i
$83$	−1.30947	−	0.903865i	−0.143733	−	0.0992120i	0.494028	−	0.869446i	$-0.335524\pi$
$83$	−1.30947	−	0.903865i	−0.143733	−	0.0992120i	−0.637761	+	0.770234i	$0.720139\pi$
$84$	−2.91608	+	1.10592i	−0.318170	+	0.120666i
$85$	10.6591	−	4.04246i	1.15614	−	0.438466i
$86$	−9.64032	−	6.65423i	−1.03954	−	0.717544i
$87$	−6.53390	+	1.61046i	−0.700508	+	0.172660i
$88$	−7.41119	−	6.56574i	−0.790035	−	0.699910i
$89$			12.0431i			1.27656i	0.769804	+	0.638281i	$0.220354\pi$
$89$			12.0431i			1.27656i	−0.769804	+	0.638281i	$0.779646\pi$
$90$	−4.84960	+	4.29637i	−0.511193	+	0.452877i
$91$	−9.47627	+	1.89606i	−0.993383	+	0.198761i
$92$	2.64199	+	2.34060i	0.275446	+	0.244024i
$93$	9.45025	−	10.6671i	0.979945	−	1.10613i
$94$	5.65587	+	14.9133i	0.583359	+	1.53819i
$95$	1.25881	−	10.3673i	0.129152	−	1.06366i
$96$	−5.98955	+	2.27154i	−0.611306	+	0.231838i
$97$	9.94763	−	1.20786i	1.01003	−	0.122640i	0.401241	−	0.915973i	$-0.368579\pi$
$97$	9.94763	−	1.20786i	1.01003	−	0.122640i	0.608788	+	0.793333i	$0.291656\pi$
$98$	0.242442	−	0.167346i	0.0244904	−	0.0169045i
$99$		−	5.82517i		−	0.585451i
$100$	1.23822	+	1.79387i	0.123822	+	0.179387i
$101$	14.4463	+	3.56068i	1.43746	+	0.354301i	0.879631	−	0.475657i	$-0.157790\pi$
$101$	14.4463	+	3.56068i	1.43746	+	0.354301i	0.557825	+	0.829958i	$0.311636\pi$
$102$	8.45385	+	9.54243i	0.837056	+	0.944841i
$103$	−6.80853	−	9.86386i	−0.670865	−	0.971915i	−0.999622	−	0.0275007i	$-0.991245\pi$
$103$	−6.80853	−	9.86386i	−0.670865	−	0.971915i	0.328757	−	0.944414i	$-0.393370\pi$
$104$	−8.15621	+	1.63194i	−0.799782	+	0.160025i
$105$	9.48726	−	13.7447i	0.925862	−	1.34134i
$106$	9.09874	−	1.10479i	0.883748	−	0.107306i
$107$	−0.465077	+	3.83026i	−0.0449607	+	0.370285i	0.952811	+	0.303564i	$0.0981767\pi$
$107$	−0.465077	+	3.83026i	−0.0449607	+	0.370285i	−0.997772	+	0.0667207i	$0.978746\pi$
$108$	1.69250	+	0.888294i	0.162861	+	0.0854761i
$109$	−0.648777	+	2.63219i	−0.0621415	+	0.252118i	−0.993795	−	0.111231i	$-0.964521\pi$
$109$	−0.648777	+	2.63219i	−0.0621415	+	0.252118i	0.931653	+	0.363349i	$0.118367\pi$
$110$	−20.3385	−	2.46955i	−1.93920	−	0.235462i
$111$	−4.01916	+	4.53670i	−0.381482	+	0.430604i
$112$	10.5973	−	7.31479i	1.00135	−	0.691182i
$113$	0.494926	−	0.717024i	0.0465587	−	0.0674520i	−0.799013	−	0.601314i	$-0.794644\pi$
$113$	0.494926	−	0.717024i	0.0465587	−	0.0674520i	0.845572	+	0.533862i	$0.179260\pi$
$114$	11.3395	−	2.79495i	1.06205	−	0.261771i
$115$	−18.7637	−	2.27832i	−1.74972	−	0.212455i
$116$	−1.59120	+	0.835125i	−0.147739	+	0.0775394i
$117$	−3.90066	−	2.95507i	−0.360616	−	0.273196i
$118$	−19.7530	−	10.3672i	−1.81841	−	0.954376i
$119$	−8.42431	−	5.81488i	−0.772255	−	0.533049i
$120$	8.16567	−	11.8300i	0.745420	−	1.07993i
$121$	5.55423	−	4.92061i	0.504930	−	0.447329i
$122$	2.31776	+	2.61621i	0.209840	+	0.236861i
$123$	14.2771	+	5.41459i	1.28732	+	0.488217i
$124$	1.76857	−	3.36972i	0.158822	−	0.302610i
$125$	3.04126	+	1.15340i	0.272018	+	0.103163i
$126$	5.64863	+	1.39226i	0.503220	+	0.124033i
$127$	−10.9539	+	9.70434i	−0.972005	+	0.861121i	−0.990333	−	0.138711i	$-0.955704\pi$
$127$	−10.9539	+	9.70434i	−0.972005	+	0.861121i	0.0183282	+	0.999832i	$0.494166\pi$
$128$	11.2377	−	7.75683i	0.993283	−	0.685614i
$129$	5.42188	+	14.2963i	0.477370	+	1.25872i
$130$	−11.9713	+	12.3663i	−1.04995	+	1.08460i
$131$	0.293503	−	0.773904i	0.0256435	−	0.0676163i	−0.921583	−	0.388181i	$-0.873103\pi$
$131$	0.293503	−	0.773904i	0.0256435	−	0.0676163i	0.947227	+	0.320565i	$0.103873\pi$
$132$	−1.19512	−	4.84878i	−0.104022	−	0.422032i
$133$	−8.30332	+	4.35792i	−0.719989	+	0.377879i
$134$	−3.33372	−	8.79029i	−0.287989	−	0.759365i
$135$	−10.1613	+	1.23380i	−0.874542	+	0.106189i
$136$	−7.25079	−	5.00486i	−0.621750	−	0.429163i
$137$	−2.54507	+	10.3258i	−0.217440	+	0.882190i	0.756244	+	0.654290i	$0.227032\pi$
$137$	−2.54507	+	10.3258i	−0.217440	+	0.882190i	−0.973684	+	0.227901i	$0.926814\pi$
$138$	−5.05856	−	20.5234i	−0.430613	−	1.74707i
$139$	1.92737	+	15.8733i	0.163477	+	1.34636i	0.811329	+	0.584590i	$0.198745\pi$
$139$	1.92737	+	15.8733i	0.163477	+	1.34636i	−0.647851	+	0.761767i	$0.724332\pi$
$140$	1.58149	−	4.17004i	0.133660	−	0.352433i
$141$	4.98231	−	20.2140i	0.419586	−	1.70233i
$142$	12.5548	−	3.09448i	1.05357	−	0.259683i
$143$	−1.18493	−	15.4292i	−0.0990885	−	1.29026i
$144$	6.33092	+	1.56043i	0.527576	+	0.130036i
$145$	4.47214	−	8.52094i	0.371391	−	0.707626i
$146$	−2.01049			−0.166389
$147$	−0.384522			−0.0317149
$148$	−0.752166	+	1.43313i	−0.0618277	+	0.117803i
$149$	−9.27077	−	10.4645i	−0.759491	−	0.857288i	0.233877	−	0.972266i	$-0.424859\pi$
$149$	−9.27077	−	10.4645i	−0.759491	−	0.857288i	−0.993368	+	0.114978i	$0.963320\pi$
$150$		−	13.0534i		−	1.06580i
$151$	3.63854	−	4.10706i	0.296100	−	0.334228i	−0.581567	−	0.813498i	$-0.697560\pi$
$151$	3.63854	−	4.10706i	0.296100	−	0.334228i	0.877667	+	0.479270i	$0.159099\pi$
$152$	−7.14665	+	3.75085i	−0.579670	+	0.304234i
$153$	−0.624787	−	5.14558i	−0.0505110	−	0.415996i
$154$	8.54937	+	16.2895i	0.688928	+	1.31264i
$155$	2.45646	+	20.2308i	0.197308	+	1.62498i
$156$	−3.85313	−	1.65948i	−0.308497	−	0.132865i
$157$	1.10817	−	9.12662i	0.0884418	−	0.728384i	−0.879270	−	0.476324i	$-0.841969\pi$
$157$	1.10817	−	9.12662i	0.0884418	−	0.728384i	0.967712	−	0.252060i	$-0.0811080\pi$
$158$	17.7793	−	6.74280i	1.41445	−	0.536429i
$159$	−10.5933	−	5.55979i	−0.840103	−	0.440920i
$160$	3.24834	−	8.56516i	0.256804	−	0.677135i
$161$	7.88737	+	15.0281i	0.621612	+	1.18438i
$162$	−8.34566	−	15.9013i	−0.655697	−	1.24933i
$163$	−2.58193	−	10.4753i	−0.202232	−	0.820488i	−0.981132	−	0.193340i	$-0.938068\pi$
$163$	−2.58193	−	10.4753i	−0.202232	−	0.820488i	0.778900	−	0.627148i	$-0.215778\pi$
$164$	4.04782	+	0.491494i	0.316081	+	0.0383792i
$165$	20.0171	+	17.7336i	1.55833	+	1.38056i
$166$	1.44545	+	2.09410i	0.112189	+	0.162534i
$167$	20.8249	+	7.89785i	1.61148	+	0.611154i	0.985650	−	0.168804i	$-0.0539906\pi$
$167$	20.8249	+	7.89785i	1.61148	+	0.611154i	0.625831	+	0.779958i	$0.284760\pi$
$168$	−12.9073			−0.995822
$169$	−10.9329	−	7.03369i	−0.840988	−	0.541053i
$170$	−18.2306			−1.39823
$171$	−4.43990	−	1.68383i	−0.339528	−	0.128766i
$172$	2.31943	+	3.36027i	0.176855	+	0.256218i
$173$	10.8240	+	9.58923i	0.822933	+	0.729055i	0.965408	−	0.260743i	$-0.0839676\pi$
$173$	10.8240	+	9.58923i	0.822933	+	0.729055i	−0.142475	+	0.989798i	$0.545506\pi$
$174$	10.6832	+	1.29718i	0.809893	+	0.0983389i
$175$	2.50828	+	10.1765i	0.189608	+	0.769271i
$176$	9.58203	+	18.2570i	0.722273	+	1.37618i
$177$	13.5321	+	25.7833i	1.01714	+	1.93799i
$178$	6.82940	−	18.0077i	0.511885	−	1.34973i
$179$	−9.29134	−	4.87647i	−0.694467	−	0.364484i	0.0802655	−	0.996774i	$-0.474423\pi$
$179$	−9.29134	−	4.87647i	−0.694467	−	0.364484i	−0.774733	+	0.632289i	$0.782115\pi$
$180$	2.11159	−	0.800821i	0.157389	−	0.0596897i
$181$	−0.755983	+	6.22608i	−0.0561918	+	0.462781i	0.937269	+	0.348607i	$0.113345\pi$
$181$	−0.755983	+	6.22608i	−0.0561918	+	0.462781i	−0.993461	+	0.114174i	$0.963578\pi$
$182$	15.2448	+	2.53869i	1.13002	+	0.188180i
$183$	−0.549920	−	4.52899i	−0.0406512	−	0.334793i
$184$	6.78865	+	12.9347i	0.500466	+	0.953558i
$185$	−1.04473	−	8.60409i	−0.0768097	−	0.632585i
$186$	−20.1798	+	10.5912i	−1.47966	+	0.776584i
$187$	10.8692	−	12.2688i	0.794833	−	0.897181i
$188$		−	5.55953i		−	0.405470i
$189$	6.09483	+	6.87964i	0.443334	+	0.500420i
$190$	−7.76136	+	14.7880i	−0.563069	+	1.07284i
$191$	−4.04418			−0.292626			−0.146313	−	0.989238i	$-0.546741\pi$
$191$	−4.04418			−0.292626			−0.146313	+	0.989238i	$0.546741\pi$
$192$	−9.81212			−0.708129
$193$	1.56003	−	2.97239i	0.112293	−	0.213957i	−0.822823	−	0.568298i	$-0.807602\pi$
$193$	1.56003	−	2.97239i	0.112293	−	0.213957i	0.935117	+	0.354340i	$0.115295\pi$
$194$	−15.5594	−	3.83504i	−1.11710	−	0.275340i
$195$	22.0293	−	4.40775i	1.57755	−	0.315645i
$196$	−0.0996995	+	0.0245737i	−0.00712139	+	0.00175527i
$197$	5.02080	−	20.3702i	0.357717	−	1.45131i	−0.466238	−	0.884659i	$-0.654391\pi$
$197$	5.02080	−	20.3702i	0.357717	−	1.45131i	0.823955	−	0.566655i	$-0.191763\pi$
$198$	−3.30335	+	8.71021i	−0.234759	+	0.619008i
$199$	−2.93058	−	24.1355i	−0.207743	−	1.71092i	−0.607520	−	0.794305i	$-0.707835\pi$
$199$	−2.93058	−	24.1355i	−0.207743	−	1.71092i	0.399777	−	0.916613i	$-0.369088\pi$
$200$	2.15887	+	8.75890i	0.152655	+	0.619348i
$201$	−2.93670	+	11.9147i	−0.207139	+	0.840396i
$202$	−19.5819	−	13.5164i	−1.37778	−	0.951010i
$203$	−8.57797	+	1.04155i	−0.602056	+	0.0731028i
$204$	−1.57575	−	4.15492i	−0.110325	−	0.290903i
$205$	−19.3343	+	10.1474i	−1.35037	+	0.708728i
$206$	4.58699	+	18.6102i	0.319591	+	1.29663i
$207$	−3.04756	+	8.03576i	−0.211820	+	0.558524i
$208$	17.0862	+	2.84534i	1.18472	+	0.197289i
$209$	−5.32462	−	14.0399i	−0.368312	−	0.971159i
$210$	−21.9804	+	15.1720i	−1.51679	+	1.04697i
$211$	−7.36589	+	6.52561i	−0.507089	+	0.449241i	−0.877465	−	0.479640i	$-0.840767\pi$
$211$	−7.36589	+	6.52561i	−0.507089	+	0.449241i	0.370377	+	0.928882i	$0.379229\pi$
$212$	−3.10195	−	0.764563i	−0.213043	−	0.0525104i
$213$	−15.7812	−	5.98503i	−1.08131	−	0.410087i
$214$	2.86749	−	5.46354i	0.196017	−	0.373480i
$215$	−20.4440	−	7.75338i	−1.39427	−	0.528776i
$216$	5.24581	+	5.92130i	0.356932	+	0.402893i
$217$	13.6972	−	12.1346i	0.929825	−	0.823753i
$218$	2.46277	−	3.56793i	0.166800	−	0.241651i
$219$	2.15972	+	1.49075i	0.145940	+	0.100735i
$220$	6.32336	+	3.31875i	0.426321	+	0.223750i
$221$	−2.70157	−	13.5021i	−0.181727	−	0.908250i
$222$	8.58242	−	4.50440i	0.576014	−	0.302316i
$223$	8.47385	+	1.02891i	0.567451	+	0.0689010i	0.399234	−	0.916849i	$-0.369276\pi$
$223$	8.47385	+	1.02891i	0.567451	+	0.0689010i	0.168217	+	0.985750i	$0.446199\pi$
$224$	−7.98641	+	1.96847i	−0.533615	+	0.131524i
$225$	−3.01490	+	4.36783i	−0.200993	+	0.291189i
$226$	−1.14666	+	0.791483i	−0.0762748	+	0.0526487i
$227$	5.85929	−	6.61378i	0.388895	−	0.438972i	−0.521160	−	0.853459i	$-0.674501\pi$
$227$	5.85929	−	6.61378i	0.388895	−	0.438972i	0.910055	+	0.414487i	$0.136039\pi$
$228$	−4.04117	−	0.490687i	−0.267633	−	0.0324965i
$229$	2.53343	−	10.2785i	0.167414	−	0.679225i	−0.825903	−	0.563812i	$-0.809334\pi$
$229$	2.53343	−	10.2785i	0.167414	−	0.679225i	0.993317	−	0.115414i	$-0.0368194\pi$
$230$	26.7648	+	14.0473i	1.76482	+	0.926249i
$231$	2.89444	−	23.8378i	0.190440	−	1.56841i
$232$	−7.38305	+	0.896464i	−0.484721	+	0.0588558i
$233$	3.13657	−	4.54410i	0.205483	−	0.297694i	−0.706670	−	0.707544i	$-0.749803\pi$
$233$	3.13657	−	4.54410i	0.205483	−	0.297694i	0.912153	+	0.409849i	$0.134419\pi$
$234$	4.15678	+	6.63063i	0.271737	+	0.433458i
$235$	16.9122	+	24.5015i	1.10323	+	1.59830i
$236$	5.15636	+	5.82032i	0.335650	+	0.378871i
$237$	−24.0987	−	5.93980i	−1.56538	−	0.385831i
$238$	9.29912	+	13.4721i	0.602773	+	0.873267i
$239$			7.16043i			0.463170i	0.972815	+	0.231585i	$0.0743911\pi$
$239$			7.16043i			0.463170i	−0.972815	+	0.231585i	$0.925609\pi$
$240$	−24.6354	+	17.0046i	−1.59021	+	1.09764i
$241$	2.00613	−	0.243588i	0.129226	−	0.0156909i	−0.0556680	−	0.998449i	$-0.517729\pi$
$241$	2.00613	−	0.243588i	0.129226	−	0.0156909i	0.184894	+	0.982758i	$0.440806\pi$
$242$	−11.0955	+	4.20796i	−0.713244	+	0.270498i
$243$	−1.58548	+	13.0576i	−0.101708	+	0.837644i
$244$	−0.432019	−	1.13914i	−0.0276572	−	0.0729259i
$245$	0.364634	−	0.411586i	0.0232956	−	0.0262953i
$246$	−18.2776	−	16.1926i	−1.16534	−	1.03240i
$247$	−12.1026	−	3.55685i	−0.770068	−	0.226317i
$248$	11.7891	−	10.4443i	0.748611	−	0.663211i
$249$		−	3.32133i		−	0.210481i
$250$	−3.89344	−	3.44929i	−0.246243	−	0.218152i
$251$	25.2050	−	6.21248i	1.59093	−	0.392128i	0.658237	−	0.752810i	$-0.271302\pi$
$251$	25.2050	−	6.21248i	1.59093	−	0.392128i	0.932689	+	0.360682i	$0.117456\pi$
$252$	−1.66888	−	1.15194i	−0.105129	−	0.0725655i
$253$	−25.4107	+	9.63701i	−1.59756	+	0.605874i
$254$	21.8823	−	8.29885i	1.37302	−	0.520716i
$255$	19.5839	+	13.5178i	1.22639	+	0.846515i
$256$	−12.0741	+	2.97600i	−0.754632	+	0.186000i
$257$	8.26837	+	7.32513i	0.515766	+	0.456929i	0.880407	−	0.474219i	$-0.157270\pi$
$257$	8.26837	+	7.32513i	0.515766	+	0.456929i	−0.364640	+	0.931148i	$0.618808\pi$
$258$		−	24.4515i		−	1.52229i
$259$	−5.82536	+	5.16082i	−0.361971	+	0.320678i
$260$	5.43011	−	2.55068i	0.336761	−	0.158186i
$261$	−3.27514	−	2.90152i	−0.202726	−	0.179600i
$262$	−0.877734	+	0.990757i	−0.0542266	+	0.0612092i
$263$	2.71745	+	7.16532i	0.167565	+	0.441833i	0.992326	−	0.123649i	$-0.0394596\pi$
$263$	2.71745	+	7.16532i	0.167565	+	0.441833i	−0.824761	+	0.565481i	$0.808690\pi$
$264$	2.49124	−	20.5172i	0.153325	−	1.26275i
$265$	15.9965	−	6.06667i	0.982656	−	0.372672i
$266$	14.8870	−	1.80761i	0.912782	−	0.110832i
$267$	−20.6888	+	14.2804i	−1.26613	+	0.873947i
$268$			3.27693i			0.200170i
$269$	8.35662	+	12.1067i	0.509512	+	0.738156i	0.990340	−	0.138659i	$-0.0442793\pi$
$269$	8.35662	+	12.1067i	0.509512	+	0.738156i	−0.480828	+	0.876815i	$0.659664\pi$
$270$	15.8935	+	3.91740i	0.967249	+	0.238405i
$271$	−14.4745	−	16.3384i	−0.879264	−	0.992484i	0.120736	−	0.992685i	$-0.461475\pi$
$271$	−14.4745	−	16.3384i	−0.879264	−	0.992484i	−1.00000		0.000200502i	$0.999936\pi$
$272$	10.4223	+	15.0994i	0.631948	+	0.915534i
$273$	−14.4940	−	14.0310i	−0.877217	−	0.849192i
$274$	9.66114	−	13.9966i	0.583651	−	0.845564i
$275$	−16.6605	+	2.02295i	−1.00466	+	0.121988i
$276$	−0.888092	+	7.31410i	−0.0534569	+	0.440257i
$277$	−8.15082	−	4.27788i	−0.489735	−	0.257033i	0.201732	−	0.979441i	$-0.435343\pi$
$277$	−8.15082	−	4.27788i	−0.489735	−	0.257033i	−0.691467	+	0.722408i	$0.743035\pi$
$278$	6.11953	−	24.8279i	0.367025	−	1.48908i
$279$	9.19866	+	1.11692i	0.550709	+	0.0668682i
$280$	12.2397	−	13.8158i	0.731463	−	0.825651i
$281$	4.44211	−	3.06617i	0.264994	−	0.182912i	−0.428157	−	0.903704i	$-0.640837\pi$
$281$	4.44211	−	3.06617i	0.264994	−	0.182912i	0.693151	+	0.720792i	$0.256222\pi$
$282$	−18.9129	+	27.4001i	−1.12625	+	1.63165i
$283$	−14.6174	+	3.60288i	−0.868917	+	0.214169i	−0.648479	−	0.761232i	$-0.724595\pi$
$283$	−14.6174	+	3.60288i	−0.868917	+	0.214169i	−0.220438	+	0.975401i	$0.570749\pi$
$284$	−4.47426	−	0.543273i	−0.265498	−	0.0322373i
$285$	19.3026	−	10.1308i	1.14339	−	0.600096i
$286$	−6.97784	+	23.7428i	−0.412609	+	1.40394i
$287$	17.3609	+	9.11169i	1.02478	+	0.537846i
$288$	−3.42783	−	2.36606i	−0.201987	−	0.139422i
$289$	−1.37187	+	1.98749i	−0.0806981	+	0.116911i
$290$	−11.5191	+	10.2051i	−0.676427	+	0.599262i
$291$	13.8707	+	15.6568i	0.813114	+	0.917816i
$292$	0.655244	+	0.248501i	0.0383452	+	0.0145424i
$293$	−9.22898	+	17.5843i	−0.539163	+	1.02729i	0.451669	+	0.892186i	$0.350829\pi$
$293$	−9.22898	+	17.5843i	−0.539163	+	1.02729i	−0.990832	+	0.135103i	$0.956863\pi$
$294$	0.574966	+	0.218056i	0.0335327	+	0.0127173i
$295$	−40.4302	−	9.96514i	−2.35394	−	0.580193i
$296$	−5.01388	+	4.44191i	−0.291426	+	0.258181i
$297$	−12.1121	+	8.36036i	−0.702814	+	0.485118i
$298$	7.92808	+	20.9046i	0.459261	+	1.21097i
$299$	−6.43753	+	21.9044i	−0.372292	+	1.26676i
$300$	−1.61343	+	4.25427i	−0.0931515	+	0.245620i
$301$	4.69850	+	19.0626i	0.270817	+	1.09875i
$302$	−7.76965	+	4.07783i	−0.447093	+	0.234653i
$303$	11.0132	+	29.0394i	0.632691	+	1.66827i
$304$	16.6852	−	2.02595i	0.956962	−	0.116196i
$305$	5.36924	+	3.70612i	0.307442	+	0.212212i
$306$	−1.98374	+	8.04835i	−0.113403	+	0.460094i
$307$	−5.76642	−	23.3953i	−0.329107	−	1.33524i	−0.869544	−	0.493855i	$-0.835587\pi$
$307$	−5.76642	−	23.3953i	−0.329107	−	1.33524i	0.540437	−	0.841384i	$-0.318259\pi$
$308$	−0.772933	−	6.36568i	−0.0440420	−	0.362718i
$309$	8.87169	−	23.3927i	0.504693	−	1.33077i
$310$	7.79943	−	31.6435i	0.442978	−	1.79723i
$311$	14.5747	−	3.59234i	0.826456	−	0.203703i	0.196668	−	0.980470i	$-0.436988\pi$
$311$	14.5747	−	3.59234i	0.826456	−	0.203703i	0.629788	+	0.776767i	$0.283142\pi$
$312$	−12.4750	−	12.0764i	−0.706256	−	0.683693i
$313$	10.8295	+	2.66924i	0.612122	+	0.150874i	0.533176	−	0.846004i	$-0.320998\pi$
$313$	10.8295	+	2.66924i	0.612122	+	0.150874i	0.0789458	+	0.996879i	$0.474845\pi$
$314$	−6.83256	+	13.0184i	−0.385584	+	0.734669i
$315$	10.8592			0.611844
$316$	−6.62794			−0.372851
$317$	−15.5732	+	29.6722i	−0.874677	+	1.66656i	−0.137874	+	0.990450i	$0.544027\pi$
$317$	−15.5732	+	29.6722i	−0.874677	+	1.66656i	−0.736803	+	0.676107i	$0.763666\pi$
$318$	12.6870	+	14.3207i	0.711452	+	0.803063i
$319$		−	13.8364i		−	0.774688i
$320$	9.30461	−	10.5027i	0.520143	−	0.587120i
$321$	−7.13147	+	3.74289i	−0.398040	+	0.208907i
$322$	−3.27159	−	26.9439i	−0.182318	−	1.50153i
$323$	−6.20930	−	11.8308i	−0.345495	−	0.658286i
$324$	0.754516	+	6.21400i	0.0419175	+	0.345222i
$325$	−7.09713	+	12.1824i	−0.393678	+	0.675760i
$326$	−2.07966	+	17.1276i	−0.115182	+	0.948609i
$327$	−5.29114	+	2.00667i	−0.292601	+	0.110969i
$328$	14.9425	+	7.84241i	0.825060	+	0.433025i
$329$	9.47956	−	24.9955i	0.522625	−	1.37805i
$330$	−19.8746	−	37.8679i	−1.09406	−	2.08456i
$331$	8.42087	+	16.0446i	0.462853	+	0.881893i	0.999280	+	0.0379460i	$0.0120815\pi$
$331$	8.42087	+	16.0446i	0.462853	+	0.881893i	−0.536427	+	0.843947i	$0.680226\pi$
$332$	−0.212256	−	0.861158i	−0.0116491	−	0.0472622i
$333$	−3.91216	−	0.475022i	−0.214385	−	0.0260311i
$334$	−26.6602	−	23.6189i	−1.45878	−	1.29237i
$335$	−9.96846	−	14.4418i	−0.544635	−	0.789040i
$336$	25.1321	+	9.53136i	1.37107	+	0.519978i
$337$	15.6888			0.854621			0.427311	−	0.904105i	$-0.359461\pi$
$337$	15.6888			0.854621			0.427311	+	0.904105i	$0.359461\pi$
$338$	12.3589	+	16.7171i	0.672236	+	0.909291i
$339$	1.81865			0.0987754
$340$	5.94161	+	2.25335i	0.322229	+	0.122205i
$341$	16.6453	+	24.1148i	0.901391	+	1.30589i
$342$	5.68399	+	5.03558i	0.307355	+	0.272293i
$343$	18.1354	+	2.20204i	0.979221	+	0.118899i
$344$	4.04399	+	16.4071i	0.218037	+	0.884613i
$345$	−18.3357	−	34.9357i	−0.987159	−	1.88087i
$346$	−10.7469	−	20.4766i	−0.577760	−	1.10083i
$347$	8.17307	−	21.5506i	0.438753	−	1.15690i	−0.515234	−	0.857050i	$-0.672295\pi$
$347$	8.17307	−	21.5506i	0.438753	−	1.15690i	0.953987	−	0.299847i	$-0.0969358\pi$
$348$	−3.32147	−	1.74324i	−0.178050	−	0.0934476i
$349$	−32.7792	+	12.4315i	−1.75463	+	0.665443i	−0.754673	+	0.656101i	$0.772205\pi$
$349$	−32.7792	+	12.4315i	−1.75463	+	0.665443i	−0.999956	+	0.00934238i	$0.997026\pi$
$350$	2.02035	−	16.6390i	0.107992	−	0.889394i
$351$	−0.546094	+	12.3517i	−0.0291483	+	0.659284i
$352$	−1.58759	−	13.0750i	−0.0846186	−	0.696897i
$353$	8.77688	+	16.7230i	0.467146	+	0.890073i	0.999063	+	0.0432765i	$0.0137796\pi$
$353$	8.77688	+	16.7230i	0.467146	+	0.890073i	−0.531917	+	0.846797i	$0.678528\pi$
$354$	−5.61296	−	46.2268i	−0.298325	−	2.45693i
$355$	21.3712	−	11.2165i	1.13427	−	0.595309i
$356$	−4.45159	+	5.02480i	−0.235934	+	0.266314i
$357$		−	21.3673i		−	1.13088i
$358$	11.1277	+	12.5606i	0.588118	+	0.663848i
$359$	−2.82673	+	5.38588i	−0.149189	+	0.284256i	−0.948569	−	0.316570i	$-0.897469\pi$
$359$	−2.82673	+	5.38588i	−0.149189	+	0.284256i	0.799380	+	0.600825i	$0.205161\pi$
$360$	9.34646			0.492602
$361$	6.75975			0.355776
$362$	4.66110	−	8.88099i	0.244982	−	0.466774i
$363$	15.0392	+	3.70683i	0.789353	+	0.194558i
$364$	−4.65470	−	2.71169i	−0.243973	−	0.142131i
$365$	−3.64368	+	0.898087i	−0.190719	+	0.0470080i
$366$	−1.74603	+	7.08393i	−0.0912666	+	0.370283i
$367$	−2.30840	+	6.08676i	−0.120498	+	0.317726i	−0.981670	−	0.190586i	$-0.938961\pi$
$367$	−2.30840	+	6.08676i	−0.120498	+	0.317726i	0.861173	+	0.508312i	$0.169730\pi$
$368$	−3.66676	−	30.1985i	−0.191143	−	1.57420i
$369$	2.37599	+	9.63978i	0.123689	+	0.501827i
$370$	−3.31707	+	13.4579i	−0.172447	+	0.699643i
$371$	−12.6427	−	8.72661i	−0.656375	−	0.453063i
$372$	7.88598	−	0.957531i	0.408869	−	0.0496457i
$373$	−7.00773	−	18.4779i	−0.362847	−	0.956748i	−0.984800	−	0.173693i	$-0.944430\pi$
$373$	−7.00773	−	18.4779i	−0.362847	−	0.956748i	0.621953	−	0.783054i	$-0.286339\pi$
$374$	−23.2098	+	12.1814i	−1.20015	+	0.629887i
$375$	1.62484	+	6.59225i	0.0839065	+	0.340422i
$376$	8.15904	−	21.5136i	0.420770	−	1.10948i
$377$	−9.26514	−	7.01910i	−0.477179	−	0.361502i
$378$	−5.21211	−	13.7432i	−0.268082	−	0.706874i
$379$	−8.18135	+	5.64718i	−0.420247	+	0.290076i	−0.759361	−	0.650670i	$-0.774488\pi$
$379$	−8.18135	+	5.64718i	−0.420247	+	0.290076i	0.339113	+	0.940745i	$0.389873\pi$
$380$	4.35737	−	3.86029i	0.223528	−	0.198029i
$381$	−29.6600	−	7.31054i	−1.51953	−	0.374530i
$382$	6.04715	+	2.29338i	0.309399	+	0.117340i
$383$	5.64400	−	10.7537i	0.288395	−	0.549491i	−0.697555	−	0.716531i	$-0.745729\pi$
$383$	5.64400	−	10.7537i	0.288395	−	0.549491i	0.985950	+	0.167041i	$0.0534211\pi$
$384$	26.6509	+	10.1074i	1.36002	+	0.515789i
$385$	22.7709	+	25.7030i	1.16051	+	1.30995i
$386$	−4.01826	+	3.55987i	−0.204524	+	0.181192i
$387$	−5.64749	+	8.18181i	−0.287078	+	0.415905i
$388$	4.59699	+	3.17307i	0.233377	+	0.161088i
$389$	−22.2427	−	11.6739i	−1.12775	−	0.591888i	−0.205566	−	0.978643i	$-0.565904\pi$
$389$	−22.2427	−	11.6739i	−1.12775	−	0.591888i	−0.922182	+	0.386755i	$0.873596\pi$
$390$	−35.4394	−	5.90166i	−1.79454	−	0.298842i
$391$	−21.4126	+	11.2382i	−1.08288	+	0.568340i
$392$	−0.421869	−	0.0512242i	−0.0213076	−	0.00258721i
$393$	1.67752	−	0.413471i	0.0846196	−	0.0208569i
$394$	−19.0590	+	27.6118i	−0.960179	+	1.39106i
$395$	29.2101	−	20.1623i	1.46972	−	1.01447i
$396$	2.15321	−	2.43047i	0.108203	−	0.122136i
$397$	20.9301	+	2.54138i	1.05045	+	0.127548i	0.627510	−	0.778608i	$-0.284074\pi$
$397$	20.9301	+	2.54138i	1.05045	+	0.127548i	0.422942	+	0.906157i	$0.360997\pi$
$398$	−9.30478	+	37.7510i	−0.466406	+	1.89228i
$399$	−17.3324	−	9.09673i	−0.867704	−	0.455406i
$400$	2.26438	−	18.6488i	0.113219	−	0.932442i
$401$	−14.1859	+	1.72248i	−0.708409	+	0.0860164i	−0.466807	−	0.884359i	$-0.654596\pi$
$401$	−14.1859	+	1.72248i	−0.708409	+	0.0860164i	−0.241602	+	0.970376i	$0.577673\pi$
$402$	11.1478	−	16.1503i	0.556000	−	0.805505i
$403$	24.5918	+	1.08726i	1.22501	+	0.0541602i
$404$	4.71133	+	6.82554i	0.234398	+	0.339584i
$405$	−22.2283	−	25.0906i	−1.10453	−	1.24676i
$406$	13.4171	+	3.30701i	0.665877	+	0.164124i
$407$	−7.07917	−	10.2560i	−0.350902	−	0.508369i
$408$		−	18.3908i		−	0.910479i
$409$	32.3164	−	22.3064i	1.59794	−	1.10298i	0.662750	−	0.748841i	$-0.269389\pi$
$409$	32.3164	−	22.3064i	1.59794	−	1.10298i	0.935193	−	0.354139i	$-0.115226\pi$
$410$	34.6645	−	4.20904i	1.71196	−	0.207869i
$411$	−20.7565	+	7.87191i	−1.02384	+	0.388293i
$412$	0.805302	−	6.63226i	0.0396744	−	0.326748i
$413$	13.2587	+	34.9602i	0.652416	+	1.72028i
$414$	9.11387	−	10.2874i	0.447922	−	0.505600i
$415$	3.55509	+	3.14954i	0.174513	+	0.154605i
$416$	−9.56065	−	5.56975i	−0.468749	−	0.273080i
$417$	−24.9833	+	22.1333i	−1.22344	+	1.08387i
$418$			24.0129i			1.17451i
$419$	−23.9613	−	21.2278i	−1.17058	−	1.03705i	−0.998650	−	0.0519390i	$-0.983460\pi$
$419$	−23.9613	−	21.2278i	−1.17058	−	1.03705i	−0.171934	−	0.985108i	$-0.555002\pi$
$420$	9.03900	−	2.22791i	0.441058	−	0.108711i
$421$	−2.27803	−	1.57241i	−0.111025	−	0.0766347i	0.511259	−	0.859427i	$-0.329179\pi$
$421$	−2.27803	−	1.57241i	−0.111025	−	0.0766347i	−0.622283	+	0.782792i	$0.713795\pi$
$422$	14.7146	−	5.58050i	0.716294	−	0.271654i
$423$	12.6570	−	4.80018i	0.615406	−	0.233393i
$424$	−10.8815	−	7.51098i	−0.528454	−	0.364765i
$425$	−14.4998	+	3.57388i	−0.703344	+	0.173359i
$426$	20.2032	+	17.8985i	0.978849	+	0.867185i
$427$		−	5.85819i		−	0.283498i
$428$	−1.60986	+	1.42621i	−0.0778155	+	0.0689385i
$429$	25.1008	−	20.3312i	1.21188	−	0.981601i
$430$	26.1725	+	23.1868i	1.26215	+	1.11817i
$431$	8.49682	−	9.59093i	0.409278	−	0.461979i	−0.507339	−	0.861747i	$-0.669371\pi$
$431$	8.49682	−	9.59093i	0.409278	−	0.461979i	0.916616	+	0.399768i	$0.130909\pi$
$432$	−5.84167	−	15.4032i	−0.281058	−	0.741088i
$433$	−0.382386	+	3.14923i	−0.0183763	+	0.151342i	−0.999009	−	0.0445148i	$-0.985826\pi$
$433$	−0.382386	+	3.14923i	−0.0183763	+	0.151342i	0.980632	+	0.195857i	$0.0627489\pi$
$434$	−27.3623	+	10.3772i	−1.31343	+	0.498120i
$435$	19.9411	−	2.42129i	0.956102	−	0.116092i
$436$	−1.24365	+	0.858432i	−0.0595602	+	0.0411114i
$437$			22.1536i			1.05975i
$438$	−2.38399	−	3.45381i	−0.113912	−	0.165029i
$439$	21.9973	+	5.42186i	1.04988	+	0.258771i	0.726262	−	0.687418i	$-0.241256\pi$
$439$	21.9973	+	5.42186i	1.04988	+	0.258771i	0.323614	+	0.946189i	$0.395102\pi$
$440$	19.5989	+	22.1225i	0.934339	+	1.05465i
$441$	−0.142028	−	0.205762i	−0.00676322	−	0.00979821i
$442$	−3.61721	+	21.7213i	−0.172053	+	1.03318i
$443$	−5.50468	+	7.97490i	−0.261535	+	0.378899i	−0.931649	−	0.363359i	$-0.881630\pi$
$443$	−5.50468	+	7.97490i	−0.261535	+	0.378899i	0.670114	+	0.742258i	$0.266245\pi$
$444$	−3.35388	+	0.407235i	−0.159168	+	0.0193265i
$445$	4.33315	−	35.6867i	0.205411	−	1.69171i
$446$	−12.0872	−	6.34387i	−0.572347	−	0.300391i
$447$	6.98392	−	28.3349i	0.330328	−	1.34019i
$448$	−12.5074	−	1.51868i	−0.590921	−	0.0717508i
$449$	−1.31155	+	1.48043i	−0.0618956	+	0.0698657i	−0.778643	−	0.627467i	$-0.784092\pi$
$449$	−1.31155	+	1.48043i	−0.0618956	+	0.0698657i	0.716747	+	0.697333i	$0.245630\pi$
$450$	6.98502	−	4.82141i	0.329277	−	0.227283i
$451$	−17.8345	+	25.8378i	−0.839796	+	1.21665i
$452$	0.471541	−	0.116225i	0.0221794	−	0.00546674i
$453$	11.3700	+	1.38057i	0.534210	+	0.0648649i
$454$	−12.5118	+	6.56670i	−0.587208	+	0.308190i
$455$	28.7628	−	2.20892i	1.34842	−	0.103556i
$456$	−14.9179	−	7.82954i	−0.698596	−	0.366652i
$457$	33.8787	+	23.3848i	1.58478	+	1.09389i	0.945838	+	0.324639i	$0.105243\pi$
$457$	33.8787	+	23.3848i	1.58478	+	1.09389i	0.638942	+	0.769255i	$0.279373\pi$
$458$	−9.61695	+	13.9326i	−0.449371	+	0.651026i
$459$	−9.80234	+	8.68411i	−0.457534	+	0.405340i
$460$	−6.98673	−	7.88639i	−0.325758	−	0.367705i
$461$	−19.4481	−	7.37569i	−0.905788	−	0.343520i	−0.142663	−	0.989771i	$-0.545567\pi$
$461$	−19.4481	−	7.37569i	−0.905788	−	0.343520i	−0.763125	+	0.646251i	$0.776336\pi$
$462$	−17.8460	+	34.0027i	−0.830270	+	1.58195i
$463$	1.54081	+	0.584352i	0.0716075	+	0.0271571i	0.390149	−	0.920752i	$-0.372424\pi$
$463$	1.54081	+	0.584352i	0.0716075	+	0.0271571i	−0.318541	+	0.947909i	$0.603193\pi$
$464$	15.0377	+	3.70645i	0.698107	+	0.172068i
$465$	−31.8416	+	28.2092i	−1.47662	+	1.30817i
$466$	−7.26690	+	5.01598i	−0.336633	+	0.232361i
$467$	−5.16556	−	13.6205i	−0.239033	−	0.630279i	0.760791	−	0.648996i	$-0.224811\pi$
$467$	−5.16556	−	13.6205i	−0.239033	−	0.630279i	−0.999825	+	0.0187172i	$0.994042\pi$
$468$	−0.535188	−	2.67480i	−0.0247391	−	0.123643i
$469$	−5.58749	+	14.7330i	−0.258007	+	0.680307i
$470$	−11.3939	−	46.2270i	−0.525563	−	2.13229i
$471$	16.9927	−	8.91844i	0.782980	−	0.410940i
$472$	11.4117	+	30.0902i	0.525266	+	1.38501i
$473$	−31.2083	+	3.78937i	−1.43496	+	0.174235i
$474$	32.6658	+	22.5476i	1.50039	+	1.03564i
$475$	−3.27403	+	13.2832i	−0.150223	+	0.609477i
$476$	−1.36552	−	5.54013i	−0.0625885	−	0.253932i
$477$	−0.937641	−	7.72217i	−0.0429316	−	0.353574i
$478$	4.06055	−	10.7068i	0.185725	−	0.489717i
$479$	7.18259	−	29.1409i	0.328181	−	1.33148i	−0.542675	−	0.839943i	$-0.682588\pi$
$479$	7.18259	−	29.1409i	0.328181	−	1.33148i	0.870855	−	0.491539i	$-0.163566\pi$
$480$	18.5659	−	4.57608i	0.847413	−	0.208869i
$481$	−10.4588	−	0.462407i	−0.476882	−	0.0210840i
$482$	−3.13785	−	0.773410i	−0.142925	−	0.0352279i
$483$	−16.4641	+	31.3698i	−0.749143	+	1.42737i
$484$	4.13628			0.188013
$485$	−29.9120			−1.35823
$486$	9.77544	−	18.6255i	0.443423	−	0.844872i
$487$	1.11248	+	1.25573i	0.0504112	+	0.0569025i	0.773175	−	0.634192i	$-0.218667\pi$
$487$	1.11248	+	1.25573i	0.0504112	+	0.0569025i	−0.722764	+	0.691095i	$0.757129\pi$
$488$		−	5.04213i		−	0.228247i
$489$	14.9339	−	16.8569i	0.675334	−	0.762294i
$490$	−0.778630	+	0.408657i	−0.0351749	+	0.0184612i
$491$	−4.51584	−	37.1913i	−0.203797	−	1.67842i	−0.632179	−	0.774822i	$-0.717839\pi$
$491$	−4.51584	−	37.1913i	−0.203797	−	1.67842i	0.428382	−	0.903598i	$-0.359084\pi$
$492$	3.95548	+	7.53654i	0.178327	+	0.339773i
$493$	−1.48404	−	12.2222i	−0.0668378	−	0.550459i
$494$	16.0796	+	12.1816i	0.723455	+	0.548077i
$495$	−2.09592	+	17.2615i	−0.0942047	+	0.775845i
$496$	−30.6674	+	11.6306i	−1.37701	+	0.522230i
$497$	−19.1899	−	10.0716i	−0.860783	−	0.451774i
$498$	−1.88347	+	4.96629i	−0.0844001	+	0.222545i
$499$	−5.47945	−	10.4402i	−0.245294	−	0.467369i	0.731416	−	0.681931i	$-0.238860\pi$
$499$	−5.47945	−	10.4402i	−0.245294	−	0.467369i	−0.976710	+	0.214563i	$0.931167\pi$
$500$	0.842582	+	1.60541i	0.0376814	+	0.0717960i
$501$	11.1261	+	45.1402i	0.497076	+	2.01672i
$502$	−41.2113	−	5.00396i	−1.83935	−	0.223338i
$503$	−5.57077	−	4.93527i	−0.248388	−	0.220053i	0.529737	−	0.848162i	$-0.322291\pi$
$503$	−5.57077	−	4.93527i	−0.248388	−	0.220053i	−0.778125	+	0.628109i	$0.783829\pi$
$504$	−4.76746	−	6.90686i	−0.212360	−	0.307656i
$505$	−41.5268	−	15.7490i	−1.84792	−	0.700823i
$506$	43.4609			1.93207
$507$	−0.880788	−	27.1219i	−0.0391172	−	1.20453i
$508$	−8.15748			−0.361930
$509$	−24.2504	−	9.19697i	−1.07488	−	0.407649i	−0.247267	−	0.968947i	$-0.579533\pi$
$509$	−24.2504	−	9.19697i	−1.07488	−	0.407649i	−0.827613	+	0.561299i	$0.810302\pi$
$510$	−21.6175	−	31.3184i	−0.957240	−	1.38680i
$511$	2.52224	+	2.23451i	0.111578	+	0.0988491i
$512$	−7.36884	−	0.894739i	−0.325660	−	0.0395422i
$513$	2.87107	+	11.6484i	0.126761	+	0.514290i
$514$	−8.20951	−	15.6419i	−0.362106	−	0.689935i
$515$	16.6264	+	31.6789i	0.732645	+	1.39594i
$516$	−3.02227	+	7.96908i	−0.133048	+	0.350819i
$517$	37.9027	+	19.8929i	1.66696	+	0.874887i
$518$	11.6371	−	4.41338i	0.511306	−	0.193913i
$519$	−3.63844	+	29.9652i	−0.159710	+	1.31533i
$520$	24.7561	−	1.90121i	1.08563	−	0.0833736i
$521$	−0.331168	−	2.72742i	−0.0145088	−	0.119490i	0.983655	−	0.180063i	$-0.0576303\pi$
$521$	−0.331168	−	2.72742i	−0.0145088	−	0.119490i	−0.998164	+	0.0605730i	$0.980707\pi$
$522$	3.25183	+	6.19585i	0.142329	+	0.271185i
$523$	2.77086	+	22.8200i	0.121161	+	0.997851i	0.918802	+	0.394719i	$0.129158\pi$
$523$	2.77086	+	22.8200i	0.121161	+	0.997851i	−0.797641	+	0.603132i	$0.793919\pi$
$524$	0.408525	−	0.214411i	0.0178465	−	0.00936657i
$525$	−14.5079	+	16.3761i	−0.633178	+	0.714710i
$526$		−	12.2551i		−	0.534349i
$527$	17.2898	+	19.5162i	0.753157	+	0.850138i
$528$	−20.0016	+	38.1098i	−0.870456	+	1.65852i
$529$	17.0956			0.743289
$530$	−27.3594			−1.18842
$531$	−8.79870	+	16.7645i	−0.381831	+	0.727518i
$532$	−5.07530	−	1.25095i	−0.220042	−	0.0542355i
$533$	8.25421	+	25.0497i	0.357529	+	1.08502i
$534$	39.0335	−	9.62089i	1.68914	−	0.416337i
$535$	2.75629	−	11.1827i	0.119165	−	0.483470i
$536$	−4.80915	+	12.6807i	−0.207724	+	0.547722i
$537$	−2.64020	−	21.7440i	−0.113933	−	0.938322i
$538$	−5.62996	−	22.8416i	−0.242725	−	0.984773i
$539$	0.189206	−	0.767641i	0.00814970	−	0.0330646i
$540$	−4.69571	−	3.24121i	−0.202071	−	0.139480i
$541$	5.16069	−	0.626622i	0.221876	−	0.0269406i	−0.00884385	−	0.999961i	$-0.502815\pi$
$541$	5.16069	−	0.626622i	0.221876	−	0.0269406i	0.230719	+	0.973020i	$0.425892\pi$
$542$	12.3782	+	32.6385i	0.531688	+	1.40194i
$543$	−11.5922	+	6.08406i	−0.497469	+	0.261092i
$544$	−2.80475	−	11.3793i	−0.120253	−	0.487884i
$545$	2.86957	−	7.56642i	0.122919	−	0.324110i
$546$	13.7158	+	29.1994i	0.586982	+	1.24962i
$547$	7.41221	+	19.5444i	0.316923	+	0.835658i	0.994927	+	0.100599i	$0.0320760\pi$
$547$	7.41221	+	19.5444i	0.316923	+	0.835658i	−0.678004	+	0.735058i	$0.737155\pi$
$548$	−4.87871	+	3.36753i	−0.208408	+	0.143854i
$549$	2.22040	−	1.96710i	0.0947643	−	0.0839539i
$550$	26.0591	+	6.42299i	1.11116	+	0.273877i
$551$	−10.5460	−	3.99957i	−0.449274	−	0.170387i
$552$	−14.1706	+	26.9999i	−0.603143	+	1.14919i
$553$	−29.7991	−	11.3013i	−1.26719	−	0.480581i
$554$	9.76179	+	11.0188i	0.414739	+	0.468143i
$555$	13.5421	−	11.9973i	0.574832	−	0.509256i
$556$	−5.06323	+	7.33535i	−0.214729	+	0.311088i
$557$	36.0381	+	24.8753i	1.52699	+	1.05400i	0.975548	+	0.219785i	$0.0705357\pi$
$557$	36.0381	+	24.8753i	1.52699	+	1.05400i	0.551437	+	0.834216i	$0.314080\pi$
$558$	−13.1211	−	6.88649i	−0.555461	−	0.291528i
$559$	−13.2943	+	22.8201i	−0.562289	+	0.965186i
$560$	−34.0344	+	17.8626i	−1.43822	+	0.754834i
$561$	33.9649	+	4.12409i	1.43400	+	0.174119i
$562$	−8.38094	+	2.06572i	−0.353529	+	0.0871370i
$563$	−4.00372	+	5.80039i	−0.168737	+	0.244457i	−0.898225	−	0.439536i	$-0.855143\pi$
$563$	−4.00372	+	5.80039i	−0.168737	+	0.244457i	0.729488	+	0.683993i	$0.239758\pi$
$564$	9.55070	−	6.59237i	0.402157	−	0.277589i
$565$	−1.72458	+	1.94665i	−0.0725537	+	0.0818962i
$566$	23.9002	+	2.90201i	1.00460	+	0.121981i
$567$	−7.20321	+	29.2246i	−0.302506	+	1.22732i
$568$	−16.5167	−	8.66862i	−0.693024	−	0.363727i
$569$	−3.04680	+	25.0926i	−0.127728	+	1.05194i	0.778055	+	0.628196i	$0.216207\pi$
$569$	−3.04680	+	25.0926i	−0.127728	+	1.05194i	−0.905783	+	0.423741i	$0.860717\pi$
$570$	−34.6076	+	4.20213i	−1.44955	+	0.176008i
$571$	−5.61872	+	8.14012i	−0.235136	+	0.340654i	−0.922733	−	0.385439i	$-0.874050\pi$
$571$	−5.61872	+	8.14012i	−0.235136	+	0.340654i	0.687597	+	0.726092i	$0.258666\pi$
$572$	5.20885	−	6.87562i	0.217793	−	0.287484i
$573$	−4.79550	−	6.94748i	−0.200335	−	0.290235i
$574$	−20.7922	−	23.4695i	−0.867848	−	0.979598i
$575$	24.0413	+	5.92564i	1.00259	+	0.247116i
$576$	−3.62421	−	5.25058i	−0.151009	−	0.218774i
$577$			5.35677i			0.223005i	0.993764	+	0.111503i	$0.0355663\pi$
$577$			5.35677i			0.223005i	−0.993764	+	0.111503i	$0.964434\pi$
$578$	3.17839	−	2.19388i	0.132203	−	0.0912535i
$579$	6.95612	−	0.844625i	0.289086	−	0.0351014i
$580$	5.01561	−	1.90217i	0.208262	−	0.0789833i
$581$	0.514061	−	4.23367i	0.0213268	−	0.175642i
$582$	−11.8618	−	31.2769i	−0.491687	−	1.29647i
$583$	16.3118	−	18.4122i	0.675564	−	0.762555i
$584$	2.17089	+	1.92324i	0.0898322	+	0.0795843i
$585$	10.4954	+	10.1601i	0.433932	+	0.420069i
$586$	23.7716	−	21.0598i	0.981996	−	0.869973i
$587$		−	32.7230i		−	1.35062i	−0.737533	−	0.675312i	$-0.764009\pi$
$587$		−	32.7230i		−	1.35062i	0.737533	−	0.675312i	$-0.235991\pi$
$588$	−0.160437	−	0.142135i	−0.00661630	−	0.00586153i
$589$	23.1917	−	5.71623i	0.955595	−	0.235533i
$590$	54.8031	+	37.8278i	2.25621	+	1.55735i
$591$	40.9474	−	15.5293i	1.68435	−	0.638791i
$592$	13.0427	−	4.94646i	0.536053	−	0.203298i
$593$	−34.0214	−	23.4832i	−1.39709	−	0.964341i	−0.998893	−	0.0470414i	$-0.985021\pi$
$593$	−34.0214	−	23.4832i	−1.39709	−	0.964341i	−0.398197	−	0.917300i	$-0.630364\pi$
$594$	22.8519	−	5.63248i	0.937624	−	0.231103i
$595$	22.8712	+	20.2621i	0.937627	+	0.830665i
$596$		−	7.79302i		−	0.319215i
$597$	37.9872	−	33.6538i	1.55471	−	1.37736i
$598$	22.0474	−	29.1024i	0.901587	−	1.19009i
$599$	−29.6689	−	26.2844i	−1.21224	−	1.07395i	−0.995208	−	0.0977848i	$-0.968824\pi$
$599$	−29.6689	−	26.2844i	−1.21224	−	1.07395i	−0.217031	−	0.976165i	$-0.569637\pi$
$600$	−12.4869	+	14.0948i	−0.509777	+	0.575420i
$601$	−8.27338	−	21.8151i	−0.337478	−	0.889857i	−0.991110	−	0.133044i	$-0.957525\pi$
$601$	−8.27338	−	21.8151i	−0.337478	−	0.889857i	0.653632	−	0.756813i	$-0.273244\pi$
$602$	3.78450	−	31.1682i	0.154245	−	1.27032i
$603$	−7.46038	+	2.82935i	−0.303810	+	0.115220i
$604$	3.03626	−	0.368669i	0.123544	−	0.0150009i
$605$	−18.2291	+	12.5826i	−0.741117	+	0.511556i
$606$		−	49.6672i		−	2.01759i
$607$	−0.715194	−	1.03614i	−0.0290288	−	0.0420555i	0.808201	−	0.588907i	$-0.200442\pi$
$607$	−0.715194	−	1.03614i	−0.0290288	−	0.0420555i	−0.837230	+	0.546852i	$0.815826\pi$
$608$	−10.4246	−	2.56942i	−0.422771	−	0.104204i
$609$	−11.9609	−	13.5010i	−0.484679	−	0.547089i
$610$	−5.92680	−	8.58645i	−0.239969	−	0.347655i
$611$	32.5485	−	15.2890i	1.31677	−	0.618525i
$612$	1.64132	−	2.37787i	0.0663466	−	0.0961197i
$613$	−20.7097	+	2.51462i	−0.836459	+	0.101564i	−0.527547	−	0.849526i	$-0.676888\pi$
$613$	−20.7097	+	2.51462i	−0.836459	+	0.101564i	−0.308912	+	0.951091i	$0.599965\pi$
$614$	−4.64468	+	38.2524i	−0.187444	+	1.54374i
$615$	−40.3585	−	21.1818i	−1.62741	−	0.854132i
$616$	6.35112	−	25.7675i	0.255894	−	1.03820i
$617$	−22.9906	−	2.79157i	−0.925567	−	0.112384i	−0.356146	−	0.934430i	$-0.615909\pi$
$617$	−22.9906	−	2.79157i	−0.925567	−	0.112384i	−0.569421	+	0.822046i	$0.692833\pi$
$618$	−26.5312	+	29.9475i	−1.06724	+	1.20467i
$619$	32.1571	−	22.1964i	1.29250	−	0.892150i	0.294520	−	0.955645i	$-0.404840\pi$
$619$	32.1571	−	22.1964i	1.29250	−	0.892150i	0.997982	+	0.0634958i	$0.0202249\pi$
$620$	−6.45316	+	9.34902i	−0.259165	+	0.375466i
$621$	21.0824	−	5.19634i	0.846007	−	0.208522i
$622$	−23.8303	−	2.89352i	−0.955509	−	0.116020i
$623$	−28.5821	+	15.0010i	−1.14512	+	0.601003i
$624$	15.3725	+	32.7263i	0.615392	+	1.31010i
$625$	−25.9092	−	13.5982i	−1.03637	−	0.543929i
$626$	−14.6794	−	10.1325i	−0.586708	−	0.404975i
$627$	17.8053	−	25.7954i	0.711074	−	1.03017i
$628$	3.83593	−	3.39833i	0.153070	−	0.135608i
$629$	−7.35331	−	8.30017i	−0.293196	−	0.330950i
$630$	−16.2374	−	6.15803i	−0.646913	−	0.245342i
$631$	−16.3856	+	31.2202i	−0.652302	+	1.24286i	0.304609	+	0.952478i	$0.401474\pi$
$631$	−16.3856	+	31.2202i	−0.652302	+	1.24286i	−0.956911	+	0.290381i	$0.906218\pi$
$632$	−25.6480	−	9.72702i	−1.02022	−	0.386920i
$633$	−19.9446	−	4.91591i	−0.792729	−	0.195390i
$634$	40.1127	−	35.5368i	1.59308	−	1.41135i
$635$	35.9510	−	24.8152i	1.42667	−	0.984760i
$636$	−2.36479	−	6.23544i	−0.0937701	−	0.247251i
$637$	−0.418046	−	0.516116i	−0.0165636	−	0.0204493i
$638$	−7.84636	+	20.6892i	−0.310640	+	0.819091i
$639$	−2.62631	−	10.6553i	−0.103895	−	0.421519i
$640$	−36.0912	+	18.9421i	−1.42663	+	0.748753i
$641$	−0.874882	−	2.30687i	−0.0345558	−	0.0911161i	0.916628	−	0.399742i	$-0.130900\pi$
$641$	−0.874882	−	2.30687i	−0.0345558	−	0.0911161i	−0.951184	+	0.308626i	$0.900131\pi$
$642$	12.7860	−	1.55250i	0.504624	−	0.0612724i
$643$	−1.59243	−	1.09917i	−0.0627992	−	0.0433472i	0.536252	−	0.844058i	$-0.319840\pi$
$643$	−1.59243	−	1.09917i	−0.0627992	−	0.0433472i	−0.599051	+	0.800711i	$0.704455\pi$
$644$	−2.26409	+	9.18577i	−0.0892176	+	0.361970i
$645$	−10.9225	−	44.3145i	−0.430074	−	1.74488i
$646$	2.57554	+	21.2115i	0.101333	+	0.834556i
$647$	10.5842	−	27.9083i	0.416109	−	1.09719i	−0.549110	−	0.835750i	$-0.685033\pi$
$647$	10.5842	−	27.9083i	0.416109	−	1.09719i	0.965220	−	0.261440i	$-0.0841974\pi$
$648$	−6.19979	+	25.1535i	−0.243551	+	0.988124i
$649$	−58.1309	+	14.3280i	−2.28184	+	0.562423i
$650$	17.5206	−	14.1914i	0.687214	−	0.556633i
$651$	37.0879	+	9.14135i	1.45359	+	0.358278i
$652$	2.79480	−	5.32505i	0.109453	−	0.208545i
$653$	15.2608			0.597202			0.298601	−	0.954378i	$-0.403480\pi$
$653$	15.2608			0.597202			0.298601	+	0.954378i	$0.403480\pi$
$654$	9.04964			0.353869
$655$	−1.14818	+	2.18767i	−0.0448631	+	0.0854795i
$656$	−23.3036	−	26.3043i	−0.909853	−	1.02701i
$657$			1.70631i			0.0665696i
$658$	−28.3490	+	31.9995i	−1.10516	+	1.24747i
$659$	10.3649	−	5.43992i	0.403760	−	0.211909i	−0.250604	−	0.968090i	$-0.580629\pi$
$659$	10.3649	−	5.43992i	0.403760	−	0.211909i	0.654363	+	0.756180i	$0.272937\pi$
$660$	1.79683	+	14.7982i	0.0699413	+	0.576019i
$661$	11.6001	+	22.1022i	0.451193	+	0.859676i	0.999723	+	0.0235450i	$0.00749531\pi$
$661$	11.6001	+	22.1022i	0.451193	+	0.859676i	−0.548530	+	0.836131i	$0.684812\pi$
$662$	−3.49288	−	28.7664i	−0.135755	−	1.11804i
$663$	19.9918	−	20.6515i	0.776416	−	0.802039i
$664$	0.442451	−	3.64391i	0.0171704	−	0.141411i
$665$	26.1729	−	9.92606i	1.01494	−	0.384916i
$666$	5.58037	+	2.92880i	0.216235	+	0.113489i
$667$	−7.23880	+	19.0871i	−0.280287	+	0.739057i
$668$	5.76956	+	10.9930i	0.223231	+	0.425331i
$669$	8.28055	+	15.7773i	0.320144	+	0.609984i
$670$	6.71587	+	27.2474i	0.259457	+	1.05266i
$671$	9.31204	+	1.13069i	0.359487	+	0.0436497i
$672$	−12.8518	−	11.3857i	−0.495768	−	0.439212i
$673$	−5.68629	−	8.23802i	−0.219191	−	0.317552i	0.697927	−	0.716169i	$-0.254106\pi$
$673$	−5.68629	−	8.23802i	−0.219191	−	0.317552i	−0.917118	+	0.398616i	$0.869491\pi$
$674$	−23.4590	−	8.89682i	−0.903606	−	0.342693i
$675$	13.4089			0.516110
$676$	−1.96166	−	6.97592i	−0.0754483	−	0.268305i
$677$	30.1174			1.15751			0.578753	−	0.815503i	$-0.303539\pi$
$677$	30.1174			1.15751			0.578753	+	0.815503i	$0.303539\pi$
$678$	−2.71937	−	1.03132i	−0.104437	−	0.0396077i
$679$	15.2576	+	22.1044i	0.585532	+	0.848289i
$680$	19.6852	+	17.4395i	0.754892	+	0.668776i
$681$	18.3096	+	2.22319i	0.701626	+	0.0851929i
$682$	−11.2141	−	45.4974i	−0.429411	−	1.74219i
$683$	−2.17489	−	4.14390i	−0.0832197	−	0.158562i	0.840290	−	0.542138i	$-0.182385\pi$
$683$	−2.17489	−	4.14390i	−0.0832197	−	0.158562i	−0.923509	+	0.383576i	$0.874693\pi$
$684$	−1.23008	−	2.34372i	−0.0470332	−	0.0896143i
$685$	11.2570	−	29.6822i	0.430107	−	1.13410i
$686$	−25.8687	−	13.5769i	−0.987670	−	0.518369i
$687$	20.6616	−	7.83591i	0.788289	−	0.298959i
$688$	4.24162	−	34.9329i	0.161710	−	1.33181i
$689$	−4.05435	−	20.2631i	−0.154458	−	0.771963i
$690$	7.60541	+	62.6362i	0.289533	+	2.38452i
$691$	−19.1533	−	36.4935i	−0.728626	−	1.38828i	−0.914042	−	0.405620i	$-0.867056\pi$
$691$	−19.1533	−	36.4935i	−0.728626	−	1.38828i	0.185416	−	0.982660i	$-0.440637\pi$
$692$	0.971612	+	8.00195i	0.0369351	+	0.304188i
$693$	13.8250	−	7.25591i	0.525168	−	0.275629i
$694$	−24.4419	+	27.5892i	−0.927803	+	1.04727i
$695$		−	47.7302i		−	1.81051i
$696$	−10.2947	−	11.6203i	−0.390220	−	0.440467i
$697$	−12.9826	+	24.7363i	−0.491752	+	0.936955i
$698$	56.0635			2.12203
$699$	11.5256			0.435938
$700$	−2.71509	+	5.17316i	−0.102621	+	0.195527i
$701$	19.1873	+	4.72923i	0.724693	+	0.178621i	0.584373	−	0.811485i	$-0.301341\pi$
$701$	19.1873	+	4.72923i	0.724693	+	0.178621i	0.140320	+	0.990106i	$0.455187\pi$
$702$	7.82097	−	18.1594i	0.295184	−	0.685384i
$703$	−9.86334	+	2.43109i	−0.372003	+	0.0916905i
$704$	4.82811	−	19.5884i	0.181966	−	0.738266i
$705$	−22.0370	+	58.1067i	−0.829961	+	2.18843i
$706$	−3.64055	−	29.9826i	−0.137014	−	1.12841i
$707$	9.54383	+	38.7208i	0.358933	+	1.45625i
$708$	−3.88442	+	15.7597i	−0.145985	+	0.592286i
$709$	32.6361	+	22.5271i	1.22567	+	0.846022i	0.991993	−	0.126291i	$-0.0403074\pi$
$709$	32.6361	+	22.5271i	1.22567	+	0.846022i	0.233681	+	0.972313i	$0.424923\pi$
$710$	−38.3165	+	4.65246i	−1.43799	+	0.174604i
$711$	−5.72267	−	15.0894i	−0.214617	−	0.565898i
$712$	−24.6005	+	12.9114i	−0.921944	+	0.483873i
$713$	−10.3458	−	41.9745i	−0.387452	−	1.57196i
$714$	−12.1170	+	31.9499i	−0.453467	+	1.19569i
$715$	−2.04026	+	46.1471i	−0.0763015	+	1.72580i
$716$	−2.07415	−	5.46908i	−0.0775146	−	0.204389i
$717$	−12.3009	+	8.49069i	−0.459385	+	0.317091i
$718$	7.28096	−	6.45037i	0.271723	−	0.240726i
$719$	−3.92686	−	0.967885i	−0.146447	−	0.0360960i	0.165411	−	0.986225i	$-0.447105\pi$
$719$	−3.92686	−	0.967885i	−0.146447	−	0.0360960i	−0.311858	+	0.950129i	$0.600951\pi$
$720$	−18.1987	−	6.90185i	−0.678225	−	0.257217i
$721$	14.9293	−	28.4454i	0.555996	−	1.05936i
$722$	−10.1077	−	3.83333i	−0.376168	−	0.142662i
$723$	2.79729	+	3.15749i	0.104032	+	0.117428i
$724$	−2.61683	+	2.31831i	−0.0972536	+	0.0861592i
$725$	−7.16122	+	10.3748i	−0.265961	+	0.385311i
$726$	−20.3856	−	14.0712i	−0.756582	−	0.522231i
$727$	−1.70346	−	0.894047i	−0.0631780	−	0.0331584i	0.432838	−	0.901472i	$-0.357512\pi$
$727$	−1.70346	−	0.894047i	−0.0631780	−	0.0331584i	−0.496016	+	0.868313i	$0.665204\pi$
$728$	−14.0326	−	17.3245i	−0.520083	−	0.642090i
$729$	5.51839	−	2.89627i	0.204385	−	0.107269i
$730$	5.95758	+	0.723382i	0.220500	+	0.0267736i
$731$	−27.1610	+	6.69458i	−1.00459	+	0.247608i
$732$	1.44465	−	2.09293i	0.0533957	−	0.0773570i
$733$	18.9425	−	13.0750i	0.699655	−	0.482937i	−0.164361	−	0.986400i	$-0.552556\pi$
$733$	18.9425	−	13.0750i	0.699655	−	0.482937i	0.864017	+	0.503463i	$0.167941\pi$
$734$	6.90338	−	7.79230i	0.254808	−	0.287619i
$735$	1.13944	+	0.138353i	0.0420288	+	0.00510322i
$736$	−4.65038	+	18.8673i	−0.171415	+	0.695460i
$737$	−22.3408	−	11.7254i	−0.822935	−	0.431909i
$738$	1.91379	−	15.7615i	0.0704476	−	0.580188i
$739$	7.24267	−	0.879420i	0.266426	−	0.0323500i	0.0137665	−	0.999905i	$-0.495618\pi$
$739$	7.24267	−	0.879420i	0.266426	−	0.0323500i	0.252659	+	0.967555i	$0.418695\pi$
$740$	2.74451	−	3.97611i	0.100890	−	0.146165i
$741$	−8.24066	−	25.0086i	−0.302728	−	0.918715i
$742$	13.9555	+	20.2181i	0.512324	+	0.742229i
$743$	7.08098	+	7.99277i	0.259776	+	0.293226i	0.863899	−	0.503664i	$-0.168015\pi$
$743$	7.08098	+	7.99277i	0.259776	+	0.293226i	−0.604124	+	0.796891i	$0.706477\pi$
$744$	31.9215	+	7.86794i	1.17030	+	0.288453i
$745$	23.7065	+	34.3448i	0.868538	+	1.25830i
$746$			31.6034i			1.15708i
$747$	1.77728	−	1.22677i	0.0650273	−	0.0448851i
$748$	9.07003	−	1.10130i	0.331633	−	0.0402675i
$749$	−9.66974	+	3.66725i	−0.353325	+	0.133998i
$750$	1.30876	−	10.7786i	0.0477892	−	0.393580i
$751$	−17.2606	−	45.5126i	−0.629850	−	1.66078i	−0.744704	−	0.667395i	$-0.767409\pi$
$751$	−17.2606	−	45.5126i	−0.629850	−	1.66078i	0.114854	−	0.993382i	$-0.463360\pi$
$752$	−31.7733	+	35.8646i	−1.15865	+	1.30785i
$753$	40.5600	+	35.9330i	1.47809	+	1.30947i
$754$	9.87351	+	15.7496i	0.359572	+	0.573566i
$755$	−12.2597	+	10.8611i	−0.446175	+	0.395277i
$756$			5.12332i			0.186333i
$757$	14.3633	+	12.7248i	0.522043	+	0.462490i	0.882518	−	0.470279i	$-0.155847\pi$
$757$	14.3633	+	12.7248i	0.522043	+	0.462490i	−0.360475	+	0.932769i	$0.617385\pi$
$758$	15.4358	−	3.80457i	0.560652	−	0.138188i
$759$	−46.6869	−	32.2257i	−1.69463	−	1.16972i
$760$	22.5269	−	8.54334i	0.817138	−	0.309900i
$761$	36.1128	−	13.6958i	1.30909	−	0.496471i	0.401317	−	0.915939i	$-0.368553\pi$
$761$	36.1128	−	13.6958i	1.30909	−	0.496471i	0.907770	+	0.419468i	$0.137783\pi$
$762$	40.2041	+	27.7509i	1.45644	+	1.00531i
$763$	−7.05516	+	1.73894i	−0.255414	+	0.0629539i
$764$	−1.68738	−	1.49489i	−0.0610472	−	0.0540831i
$765$			15.4725i			0.559409i
$766$	−14.5376	+	12.8792i	−0.525264	+	0.465343i
$767$	−19.8951	+	46.1943i

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)

\(f(q)\)	\(=\)	\(q+(-1.49527 - 0.567082i) q^{2} +(1.18578 + 1.71790i) q^{3} +(0.417236 + 0.369639i) q^{4} +(-2.96326 - 0.359805i) q^{5} +(-0.798874 - 3.24116i) q^{6} +(1.24562 + 2.37332i) q^{7} +(1.07210 + 2.04271i) q^{8} +(-0.481287 + 1.26905i) q^{9} +O(q^{10})\)	\(q+(-1.49527 - 0.567082i) q^{2} +(1.18578 + 1.71790i) q^{3} +(0.417236 + 0.369639i) q^{4} +(-2.96326 - 0.359805i) q^{5} +(-0.798874 - 3.24116i) q^{6} +(1.24562 + 2.37332i) q^{7} +(1.07210 + 2.04271i) q^{8} +(-0.481287 + 1.26905i) q^{9} +(4.22684 + 2.21842i) q^{10} +(-4.01299 + 1.52193i) q^{11} +(-0.140252 + 1.15508i) q^{12} +(-1.01665 + 3.45925i) q^{13} +(-0.516666 - 4.25513i) q^{14} +(-2.89566 - 5.51722i) q^{15} +(-0.579073 - 4.76910i) q^{16} +(-3.38159 + 1.77479i) q^{17} +(1.43931 - 1.62464i) q^{18} +3.49861i q^{19} +(-1.10338 - 1.24546i) q^{20} +(-2.60010 + 4.95408i) q^{21} +6.86357 q^{22} +6.33211 q^{23} +(-2.23790 + 4.26397i) q^{24} +(3.79672 + 0.935808i) q^{25} +(3.48185 - 4.59600i) q^{26} +(3.32944 - 0.820634i) q^{27} +(-0.357557 + 1.45066i) q^{28} +(-1.14319 + 3.01434i) q^{29} +(1.20109 + 9.89183i) q^{30} +(-1.63386 - 6.62883i) q^{31} +(-0.734413 + 2.97963i) q^{32} +(-7.37304 - 5.08924i) q^{33} +(6.06285 - 0.736163i) q^{34} +(-2.83715 - 7.48094i) q^{35} +(-0.669900 + 0.351591i) q^{36} +(0.694875 + 2.81922i) q^{37} +(1.98400 - 5.23137i) q^{38} +(-7.14816 + 2.35541i) q^{39} +(-2.44193 - 6.43883i) q^{40} +(6.02013 - 4.15540i) q^{41} +(6.69723 - 5.93322i) q^{42} +(7.11200 + 1.75295i) q^{43} +(-2.23693 - 0.848356i) q^{44} +(1.88279 - 3.58735i) q^{45} +(-9.46823 - 3.59083i) q^{46} +(-6.61375 - 7.46538i) q^{47} +(7.50617 - 6.64989i) q^{48} +(-0.104644 + 0.151603i) q^{49} +(-5.14646 - 3.55234i) q^{50} +(-7.05873 - 3.70471i) q^{51} +(-1.70286 + 1.06753i) q^{52} +(-5.07487 + 2.66350i) q^{53} +(-5.44379 - 0.660996i) q^{54} +(12.4391 - 3.06597i) q^{55} +(-3.51259 + 5.08887i) q^{56} +(-6.01025 + 4.14858i) q^{57} +(3.41876 - 3.85898i) q^{58} +(13.8480 + 1.68145i) q^{59} +(0.831206 - 3.37234i) q^{60} +(-1.93527 - 1.01571i) q^{61} +(-1.31602 + 10.8384i) q^{62} +(-3.61136 + 0.438498i) q^{63} +(-2.67027 + 3.86855i) q^{64} +(4.25725 - 9.88486i) q^{65} +(8.13869 + 11.7909i) q^{66} +(3.89831 + 4.40029i) q^{67} +(-2.06695 - 0.509458i) q^{68} +(7.50849 + 10.8779i) q^{69} +12.7949i q^{70} +(-6.65436 + 4.59318i) q^{71} +(-3.10829 + 0.377415i) q^{72} +(1.17549 - 0.445804i) q^{73} +(0.559701 - 4.60955i) q^{74} +(2.89445 + 7.63205i) q^{75} +(-1.29322 + 1.45975i) q^{76} +(-8.61067 - 7.62838i) q^{77} +(12.0242 + 0.531614i) q^{78} +(-8.90005 + 7.88476i) q^{79} +14.3404i q^{80} +(8.40549 + 7.44662i) q^{81} +(-11.3582 + 2.79954i) q^{82} +(-1.30947 - 0.903865i) q^{83} +(-2.91608 + 1.10592i) q^{84} +(10.6591 - 4.04246i) q^{85} +(-9.64032 - 6.65423i) q^{86} +(-6.53390 + 1.61046i) q^{87} +(-7.41119 - 6.56574i) q^{88} +12.0431i q^{89} +(-4.84960 + 4.29637i) q^{90} +(-9.47627 + 1.89606i) q^{91} +(2.64199 + 2.34060i) q^{92} +(9.45025 - 10.6671i) q^{93} +(5.65587 + 14.9133i) q^{94} +(1.25881 - 10.3673i) q^{95} +(-5.98955 + 2.27154i) q^{96} +(9.94763 - 1.20786i) q^{97} +(0.242442 - 0.167346i) q^{98} -5.82517i 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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