LMFDB - Embedded newform 169.2.h.a.12.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("169.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			12.4
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24935 + 0.862366i) q^{2} +(-1.71162 - 0.898326i) q^{3} +(0.107998 - 0.284768i) q^{4} +(0.371060 + 0.418840i) q^{5} +(2.91310 - 0.353715i) q^{6} +(-0.356102 - 1.44476i) q^{7} +(-0.615953 - 2.49902i) q^{8} +(0.418452 + 0.606232i) q^{9} +O(q^{10})$	\(q+(-1.24935 + 0.862366i) q^{2} +(-1.71162 - 0.898326i) q^{3} +(0.107998 - 0.284768i) q^{4} +(0.371060 + 0.418840i) q^{5} +(2.91310 - 0.353715i) q^{6} +(-0.356102 - 1.44476i) q^{7} +(-0.615953 - 2.49902i) q^{8} +(0.418452 + 0.606232i) q^{9} +(-0.824778 - 0.203290i) q^{10} +(3.96719 + 2.73835i) q^{11} +(-0.440666 + 0.390396i) q^{12} +(2.06554 - 2.95525i) q^{13} +(1.69081 + 1.49793i) q^{14} +(-0.258858 - 1.05023i) q^{15} +(3.38055 + 2.99490i) q^{16} +(7.61181 - 1.87614i) q^{17} +(-1.04559 - 0.396539i) q^{18} -5.51308i q^{19} +(0.159346 - 0.0604319i) q^{20} +(-0.688358 + 2.79278i) q^{21} -7.31788 q^{22} -6.37662 q^{23} +(-1.19066 + 4.83070i) q^{24} +(0.564942 - 4.65271i) q^{25} +(-0.0320826 + 5.47341i) q^{26} +(0.527370 + 4.34328i) q^{27} +(-0.449880 - 0.0546254i) q^{28} +(1.15185 + 1.66874i) q^{29} +(1.22909 + 1.08887i) q^{30} +(-3.06058 + 0.371622i) q^{31} +(-1.69611 - 0.205945i) q^{32} +(-4.33037 - 8.25084i) q^{33} +(-7.89191 + 8.90813i) q^{34} +(0.472990 - 0.685244i) q^{35} +(0.217827 - 0.0536896i) q^{36} +(-6.28396 + 0.763011i) q^{37} +(4.75429 + 6.88778i) q^{38} +(-6.19021 + 3.20273i) q^{39} +(0.818134 - 1.18527i) q^{40} +(-1.57560 + 3.00206i) q^{41} +(-1.54840 - 4.08278i) q^{42} +(1.14959 - 9.46773i) q^{43} +(1.20824 - 0.833990i) q^{44} +(-0.0986435 + 0.400213i) q^{45} +(7.96666 - 5.49899i) q^{46} +(0.734847 - 0.278691i) q^{47} +(-3.09580 - 8.16296i) q^{48} +(4.23766 - 2.22410i) q^{49} +(3.30653 + 6.30007i) q^{50} +(-14.7139 - 3.62665i) q^{51} +(-0.618486 - 0.907362i) q^{52} +(9.64825 - 2.37808i) q^{53} +(-4.40437 - 4.97151i) q^{54} +(0.325133 + 2.67771i) q^{55} +(-3.39115 + 1.77981i) q^{56} +(-4.95254 + 9.43628i) q^{57} +(-2.87813 - 1.09153i) q^{58} +(-0.709790 - 0.801187i) q^{59} +(-0.327027 - 0.0397083i) q^{60} +(5.70686 + 1.40661i) q^{61} +(3.50327 - 3.10363i) q^{62} +(0.726850 - 0.820444i) q^{63} +(-5.70144 + 2.99235i) q^{64} +(2.00422 - 0.231444i) q^{65} +(12.5254 + 6.57384i) q^{66} +(-1.44145 + 0.546670i) q^{67} +(0.287796 - 2.37022i) q^{68} +(10.9143 + 5.72829i) q^{69} +1.26400i q^{70} +(-2.49253 + 4.74913i) q^{71} +(1.25724 - 1.41913i) q^{72} +(4.52280 + 3.12187i) q^{73} +(7.19289 - 6.37235i) q^{74} +(-5.14662 + 7.45617i) q^{75} +(-1.56995 - 0.595402i) q^{76} +(2.54355 - 6.70678i) q^{77} +(4.97182 - 9.33957i) q^{78} +(0.523916 + 1.38145i) q^{79} +2.52720i q^{80} +(3.78266 - 9.97406i) q^{81} +(-0.620390 - 5.10937i) q^{82} +(-1.23021 - 2.34397i) q^{83} +(0.720952 + 0.497637i) q^{84} +(3.61024 + 2.49197i) q^{85} +(6.72841 + 12.8199i) q^{86} +(-0.472451 - 3.89099i) q^{87} +(4.39959 - 11.6008i) q^{88} +15.8350i q^{89} +(-0.221889 - 0.585074i) q^{90} +(-5.00519 - 1.93185i) q^{91} +(-0.688664 + 1.81586i) q^{92} +(5.57238 + 2.11332i) q^{93} +(-0.677750 + 0.981890i) q^{94} +(2.30910 - 2.04568i) q^{95} +(2.71808 + 1.87616i) q^{96} +(-2.04793 + 2.31164i) q^{97} +(-3.37635 + 6.43310i) q^{98} +3.55090i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9}+O(q^{10}) $ 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9	\( 168 q - 13 q^{2} - 13 q^{3} + q^{4} - 13 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} - 27 q^{9} - 9 q^{10} - 13 q^{11} - 9 q^{12} + 52 q^{13} - 15 q^{14} + 39 q^{15} - 31 q^{16} - 11 q^{17} + 26 q^{18} - 13 q^{20} - 13 q^{21} - 6 q^{22} - 102 q^{23} - 91 q^{24} + 3 q^{25} - 13 q^{26} - 19 q^{27} - 13 q^{28} - 17 q^{29} + 23 q^{30} + 39 q^{31} - 13 q^{33} + 52 q^{34} - 21 q^{35} + 11 q^{36} - 13 q^{37} - 40 q^{38} - 65 q^{39} + 53 q^{40} - 13 q^{41} + 101 q^{42} - 3 q^{43} - 39 q^{44} - 78 q^{45} - 39 q^{46} - 39 q^{47} + 8 q^{48} + 85 q^{49} - 13 q^{50} + 62 q^{51} - 78 q^{52} + 18 q^{53} + 65 q^{54} - 103 q^{55} + 3 q^{56} + 65 q^{57} + 39 q^{58} + 91 q^{59} - 117 q^{60} - 23 q^{61} - 64 q^{62} - 78 q^{63} + 15 q^{64} - 13 q^{65} + 134 q^{66} - 65 q^{67} + 40 q^{68} - 40 q^{69} + 26 q^{71} + 156 q^{72} - 13 q^{73} - 53 q^{74} + 35 q^{75} + 221 q^{76} + 3 q^{77} - 143 q^{78} - 23 q^{79} - 43 q^{81} - 129 q^{82} + 117 q^{83} + 234 q^{84} + 26 q^{85} - 91 q^{86} + 79 q^{87} + 95 q^{88} + 17 q^{90} + 39 q^{91} - 89 q^{92} + 52 q^{93} - 61 q^{94} + 122 q^{95} - 182 q^{96} - 91 q^{97} - 13 q^{98}+O(q^{100}) \) 168 * q - 13 * q^2 - 13 * q^3 + q^4 - 13 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 - 27 * q^9 - 9 * q^10 - 13 * q^11 - 9 * q^12 + 52 * q^13 - 15 * q^14 + 39 * q^15 - 31 * q^16 - 11 * q^17 + 26 * q^18 - 13 * q^20 - 13 * q^21 - 6 * q^22 - 102 * q^23 - 91 * q^24 + 3 * q^25 - 13 * q^26 - 19 * q^27 - 13 * q^28 - 17 * q^29 + 23 * q^30 + 39 * q^31 - 13 * q^33 + 52 * q^34 - 21 * q^35 + 11 * q^36 - 13 * q^37 - 40 * q^38 - 65 * q^39 + 53 * q^40 - 13 * q^41 + 101 * q^42 - 3 * q^43 - 39 * q^44 - 78 * q^45 - 39 * q^46 - 39 * q^47 + 8 * q^48 + 85 * q^49 - 13 * q^50 + 62 * q^51 - 78 * q^52 + 18 * q^53 + 65 * q^54 - 103 * q^55 + 3 * q^56 + 65 * q^57 + 39 * q^58 + 91 * q^59 - 117 * q^60 - 23 * q^61 - 64 * q^62 - 78 * q^63 + 15 * q^64 - 13 * q^65 + 134 * q^66 - 65 * q^67 + 40 * q^68 - 40 * q^69 + 26 * q^71 + 156 * q^72 - 13 * q^73 - 53 * q^74 + 35 * q^75 + 221 * q^76 + 3 * q^77 - 143 * q^78 - 23 * q^79 - 43 * q^81 - 129 * q^82 + 117 * q^83 + 234 * q^84 + 26 * q^85 - 91 * q^86 + 79 * q^87 + 95 * q^88 + 17 * q^90 + 39 * q^91 - 89 * q^92 + 52 * q^93 - 61 * q^94 + 122 * q^95 - 182 * q^96 - 91 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.24935	+	0.862366i	−0.883426	+	0.609785i	−0.921023	−	0.389508i	$-0.872645\pi$
$2$	−1.24935	+	0.862366i	−0.883426	+	0.609785i	0.0375970	+	0.999293i	$0.488030\pi$
$3$	−1.71162	−	0.898326i	−0.988203	−	0.518649i	−0.108461	−	0.994101i	$-0.534592\pi$
$3$	−1.71162	−	0.898326i	−0.988203	−	0.518649i	−0.879742	+	0.475452i	$0.842285\pi$
$4$	0.107998	−	0.284768i	0.0539991	−	0.142384i
$5$	0.371060	+	0.418840i	0.165943	+	0.187311i	0.825600	−	0.564256i	$-0.190837\pi$
$5$	0.371060	+	0.418840i	0.165943	+	0.187311i	−0.659657	+	0.751567i	$0.729298\pi$
$6$	2.91310	−	0.353715i	1.18927	−	0.144403i
$7$	−0.356102	−	1.44476i	−0.134594	−	0.546069i	−0.999059	−	0.0433759i	$-0.986189\pi$
$7$	−0.356102	−	1.44476i	−0.134594	−	0.546069i	0.864465	−	0.502693i	$-0.167657\pi$
$8$	−0.615953	−	2.49902i	−0.217772	−	0.883537i
$9$	0.418452	+	0.606232i	0.139484	+	0.202077i
$10$	−0.824778	−	0.203290i	−0.260818	−	0.0642858i
$11$	3.96719	+	2.73835i	1.19615	+	0.825644i	0.988301	−	0.152517i	$-0.0487377\pi$
$11$	3.96719	+	2.73835i	1.19615	+	0.825644i	0.207851	+	0.978161i	$0.433353\pi$
$12$	−0.440666	+	0.390396i	−0.127209	+	0.112698i
$13$	2.06554	−	2.95525i	0.572879	−	0.819640i
$13$	2.06554	−	2.95525i	0.572879	−	0.819640i
$14$	1.69081	+	1.49793i	0.451889	+	0.400338i
$15$	−0.258858	−	1.05023i	−0.0668368	−	0.271167i
$16$	3.38055	+	2.99490i	0.845136	+	0.748725i
$17$	7.61181	−	1.87614i	1.84613	−	0.455031i	0.848847	−	0.528638i	$-0.177297\pi$
$17$	7.61181	−	1.87614i	1.84613	−	0.455031i	0.997287	+	0.0736071i	$0.0234511\pi$
$18$	−1.04559	−	0.396539i	−0.246447	−	0.0934652i
$19$		−	5.51308i		−	1.26479i	−0.774648	−	0.632393i	$-0.782073\pi$
$19$		−	5.51308i		−	1.26479i	0.774648	−	0.632393i	$-0.217927\pi$
$20$	0.159346	−	0.0604319i	0.0356308	−	0.0135130i
$21$	−0.688358	+	2.79278i	−0.150212	+	0.609434i
$22$	−7.31788			−1.56018
$23$	−6.37662			−1.32962			−0.664809	−	0.747013i	$-0.731487\pi$
$23$	−6.37662			−1.32962			−0.664809	+	0.747013i	$0.731487\pi$
$24$	−1.19066	+	4.83070i	−0.243042	+	0.986062i
$25$	0.564942	−	4.65271i	0.112988	−	0.930543i
$26$	−0.0320826	+	5.47341i	−0.00629191	+	1.07342i
$27$	0.527370	+	4.34328i	0.101492	+	0.835865i
$28$	−0.449880	−	0.0546254i	−0.0850194	−	0.0103232i
$29$	1.15185	+	1.66874i	0.213893	+	0.309878i	0.915214	−	0.402968i	$-0.132021\pi$
$29$	1.15185	+	1.66874i	0.213893	+	0.309878i	−0.701321	+	0.712846i	$0.747406\pi$
$30$	1.22909	+	1.08887i	0.224399	+	0.198800i
$31$	−3.06058	+	0.371622i	−0.549696	+	0.0667452i	−0.390673	−	0.920530i	$-0.627758\pi$
$31$	−3.06058	+	0.371622i	−0.549696	+	0.0667452i	−0.159023	+	0.987275i	$0.550835\pi$
$32$	−1.69611	−	0.205945i	−0.299833	−	0.0364063i
$33$	−4.33037	−	8.25084i	−0.753821	−	1.43629i
$34$	−7.89191	+	8.90813i	−1.35345	+	1.52773i
$35$	0.472990	−	0.685244i	0.0799498	−	0.115827i
$36$	0.217827	−	0.0536896i	0.0363045	−	0.00894827i
$37$	−6.28396	+	0.763011i	−1.03308	+	0.125438i	−0.619473	−	0.785018i	$-0.712653\pi$
$37$	−6.28396	+	0.763011i	−1.03308	+	0.125438i	−0.413605	+	0.910457i	$0.635730\pi$
$38$	4.75429	+	6.88778i	0.771248	+	1.11735i
$39$	−6.19021	+	3.20273i	−0.991226	+	0.512848i
$40$	0.818134	−	1.18527i	0.129358	−	0.187408i
$41$	−1.57560	+	3.00206i	−0.246068	+	0.468843i	−0.976895	−	0.213720i	$-0.931442\pi$
$41$	−1.57560	+	3.00206i	−0.246068	+	0.468843i	0.730827	+	0.682562i	$0.239134\pi$
$42$	−1.54840	−	4.08278i	−0.238923	−	0.629987i
$43$	1.14959	−	9.46773i	0.175311	−	1.44382i	−0.593755	−	0.804646i	$-0.702355\pi$
$43$	1.14959	−	9.46773i	0.175311	−	1.44382i	0.769066	−	0.639170i	$-0.220722\pi$
$44$	1.20824	−	0.833990i	0.182149	−	0.125729i
$45$	−0.0986435	+	0.400213i	−0.0147049	+	0.0596602i
$46$	7.96666	−	5.49899i	1.17462	−	0.810781i
$47$	0.734847	−	0.278691i	0.107188	−	0.0406512i	−0.300428	−	0.953805i	$-0.597129\pi$
$47$	0.734847	−	0.278691i	0.107188	−	0.0406512i	0.407616	+	0.913153i	$0.366360\pi$
$48$	−3.09580	−	8.16296i	−0.446841	−	1.17822i
$49$	4.23766	−	2.22410i	0.605380	−	0.317728i
$50$	3.30653	+	6.30007i	0.467614	+	0.890965i
$51$	−14.7139	−	3.62665i	−2.06036	−	0.507832i
$52$	−0.618486	−	0.907362i	−0.0857686	−	0.125829i
$53$	9.64825	−	2.37808i	1.32529	−	0.326654i	0.487727	−	0.872996i	$-0.337826\pi$
$53$	9.64825	−	2.37808i	1.32529	−	0.326654i	0.837562	+	0.546342i	$0.183980\pi$
$54$	−4.40437	−	4.97151i	−0.599359	−	0.676536i
$55$	0.325133	+	2.67771i	0.0438409	+	0.361062i
$56$	−3.39115	+	1.77981i	−0.453162	+	0.237838i
$57$	−4.95254	+	9.43628i	−0.655980	+	1.24987i
$58$	−2.87813	−	1.09153i	−0.377917	−	0.143325i
$59$	−0.709790	−	0.801187i	−0.0924068	−	0.104306i	0.700488	−	0.713664i	$-0.252966\pi$
$59$	−0.709790	−	0.801187i	−0.0924068	−	0.104306i	−0.792895	+	0.609358i	$0.791427\pi$
$60$	−0.327027	−	0.0397083i	−0.0422190	−	0.00512631i
$61$	5.70686	+	1.40661i	0.730688	+	0.180098i	0.587072	−	0.809535i	$-0.300281\pi$
$61$	5.70686	+	1.40661i	0.730688	+	0.180098i	0.143616	+	0.989633i	$0.454127\pi$
$62$	3.50327	−	3.10363i	0.444916	−	0.394161i
$63$	0.726850	−	0.820444i	0.0915745	−	0.103366i
$64$	−5.70144	+	2.99235i	−0.712680	+	0.374043i
$65$	2.00422	−	0.231444i	0.248593	−	0.0287071i
$66$	12.5254	+	6.57384i	1.54177	+	0.809184i
$67$	−1.44145	+	0.546670i	−0.176101	+	0.0667863i	−0.441080	−	0.897468i	$-0.645404\pi$
$67$	−1.44145	+	0.546670i	−0.176101	+	0.0667863i	0.264979	+	0.964254i	$0.414635\pi$
$68$	0.287796	−	2.37022i	0.0349004	−	0.287431i
$69$	10.9143	+	5.72829i	1.31393	+	0.689605i
$70$			1.26400i			0.151077i
$71$	−2.49253	+	4.74913i	−0.295809	+	0.563618i	−0.987319	−	0.158750i	$-0.949254\pi$
$71$	−2.49253	+	4.74913i	−0.295809	+	0.563618i	0.691509	+	0.722367i	$0.256946\pi$
$72$	1.25724	−	1.41913i	0.148167	−	0.167246i
$73$	4.52280	+	3.12187i	0.529354	+	0.365387i	0.802562	−	0.596568i	$-0.203469\pi$
$73$	4.52280	+	3.12187i	0.529354	+	0.365387i	−0.273208	+	0.961955i	$0.588085\pi$
$74$	7.19289	−	6.37235i	0.836157	−	0.740770i
$75$	−5.14662	+	7.45617i	−0.594281	+	0.860964i
$76$	−1.56995	−	0.595402i	−0.180085	−	0.0682973i
$77$	2.54355	−	6.70678i	0.289864	−	0.764308i
$78$	4.97182	−	9.33957i	0.562948	−	1.05750i
$79$	0.523916	+	1.38145i	0.0589452	+	0.155426i	0.961254	−	0.275665i	$-0.0888981\pi$
$79$	0.523916	+	1.38145i	0.0589452	+	0.155426i	−0.902309	+	0.431091i	$0.858129\pi$
$80$			2.52720i			0.282549i
$81$	3.78266	−	9.97406i	0.420296	−	1.10823i
$82$	−0.620390	−	5.10937i	−0.0685107	−	0.564236i
$83$	−1.23021	−	2.34397i	−0.135033	−	0.257284i	0.808545	−	0.588435i	$-0.200256\pi$
$83$	−1.23021	−	2.34397i	−0.135033	−	0.257284i	−0.943578	+	0.331150i	$0.892563\pi$
$84$	0.720952	+	0.497637i	0.0786623	+	0.0542967i
$85$	3.61024	+	2.49197i	0.391586	+	0.270292i
$86$	6.72841	+	12.8199i	0.725543	+	1.38241i
$87$	−0.472451	−	3.89099i	−0.0506521	−	0.417157i
$88$	4.39959	−	11.6008i	0.468998	−	1.23665i
$89$			15.8350i			1.67851i	0.543742	+	0.839253i	$0.317007\pi$
$89$			15.8350i			1.67851i	−0.543742	+	0.839253i	$0.682993\pi$
$90$	−0.221889	−	0.585074i	−0.0233892	−	0.0616722i
$91$	−5.00519	−	1.93185i	−0.524686	−	0.202513i
$92$	−0.688664	+	1.81586i	−0.0717981	+	0.189316i
$93$	5.57238	+	2.11332i	0.577829	+	0.219142i
$94$	−0.677750	+	0.981890i	−0.0699046	+	0.101274i
$95$	2.30910	−	2.04568i	0.236908	−	0.209882i
$96$	2.71808	+	1.87616i	0.277413	+	0.191485i
$97$	−2.04793	+	2.31164i	−0.207936	+	0.234711i	−0.843222	−	0.537566i	$-0.819344\pi$
$97$	−2.04793	+	2.31164i	−0.207936	+	0.234711i	0.635286	+	0.772277i	$0.280882\pi$
$98$	−3.37635	+	6.43310i	−0.341063	+	0.649841i
$99$			3.55090i			0.356879i
$100$	−1.26393	−	0.663362i	−0.126393	−	0.0663362i
$101$	1.05828	−	8.71576i	0.105303	−	0.867250i	−0.840343	−	0.542054i	$-0.817647\pi$
$101$	1.05828	−	8.71576i	0.105303	−	0.867250i	0.945647	−	0.325196i	$-0.105430\pi$
$102$	21.5104	−	8.15780i	2.12984	−	0.807743i
$103$	−2.76538	−	1.45138i	−0.272481	−	0.143009i	0.322949	−	0.946416i	$-0.395326\pi$
$103$	−2.76538	−	1.45138i	−0.272481	−	0.143009i	−0.595430	+	0.803407i	$0.703018\pi$
$104$	−8.65752	−	3.34154i	−0.848940	−	0.327665i
$105$	−1.42515	+	0.747976i	−0.139080	+	0.0729950i
$106$	−10.0033	+	11.2914i	−0.971606	+	1.09672i
$107$	7.87952	−	6.98065i	0.761742	−	0.674845i	−0.189986	−	0.981787i	$-0.560844\pi$
$107$	7.87952	−	6.98065i	0.761742	−	0.674845i	0.951728	+	0.306942i	$0.0993058\pi$
$108$	1.29378	+	0.318888i	0.124494	+	0.0306851i
$109$	−14.8706	−	1.80562i	−1.42435	−	0.172947i	−0.628200	−	0.778052i	$-0.716208\pi$
$109$	−14.8706	−	1.80562i	−1.42435	−	0.172947i	−0.796146	+	0.605105i	$0.793131\pi$
$110$	−2.71537	−	3.06502i	−0.258901	−	0.292238i
$111$	11.4412	+	4.33907i	1.08595	+	0.411846i
$112$	3.12311	−	5.95058i	0.295106	−	0.562277i
$113$	−13.3211	+	6.99145i	−1.25314	+	0.657700i	−0.954939	−	0.296802i	$-0.904080\pi$
$113$	−13.3211	+	6.99145i	−1.25314	+	0.657700i	−0.298204	+	0.954502i	$0.596387\pi$
$114$	−1.95006	−	16.0602i	−0.182639	−	1.50417i
$115$	−2.36611	−	2.67079i	−0.220641	−	0.249052i
$116$	0.599601	−	0.147788i	0.0556716	−	0.0137218i
$117$	2.65590	+	0.0155676i	0.245538	+	0.00143923i
$118$	1.57769	+	0.388867i	0.145239	+	0.0357981i
$119$	−5.42116	−	10.3292i	−0.496957	−	0.946873i
$120$	−2.46509	+	1.29378i	−0.225031	+	0.118106i
$121$	4.33935	+	11.4419i	0.394486	+	1.04017i
$122$	−8.34290	+	3.16404i	−0.755330	+	0.286459i
$123$	5.39365	−	3.72297i	0.486329	−	0.335689i
$124$	−0.224711	+	0.911688i	−0.0201796	+	0.0818720i
$125$	4.46093	−	3.07916i	0.398998	−	0.275408i
$126$	−0.200569	+	1.65184i	−0.0178681	+	0.147157i
$127$	4.68084	+	12.3424i	0.415358	+	1.09521i	0.965561	+	0.260177i	$0.0837811\pi$
$127$	4.68084	+	12.3424i	0.415358	+	1.09521i	−0.550203	+	0.835031i	$0.685450\pi$
$128$	6.13064	−	11.6809i	0.541877	−	1.03246i
$129$	−10.4728	+	15.1724i	−0.922076	+	1.33586i
$130$	−2.30439	+	2.01753i	−0.202108	+	0.176949i
$131$	−6.50029	−	9.41730i	−0.567933	−	0.822793i	0.428814	−	0.903393i	$-0.358932\pi$
$131$	−6.50029	−	9.41730i	−0.567933	−	0.822793i	−0.996747	+	0.0806001i	$0.974316\pi$
$132$	−2.81725	+	0.342076i	−0.245210	+	0.0297739i
$133$	−7.96509	+	1.96322i	−0.690661	+	0.170233i
$134$	1.32945	−	1.92604i	0.114847	−	0.166385i
$135$	−1.62345	+	1.83250i	−0.139725	+	0.157717i
$136$	−9.37703	−	17.8664i	−0.804074	−	1.53204i
$137$	7.44324	+	0.903773i	0.635919	+	0.0772146i	0.432146	−	0.901804i	$-0.357756\pi$
$137$	7.44324	+	0.903773i	0.635919	+	0.0772146i	0.203773	+	0.979018i	$0.434680\pi$
$138$	−18.5758	+	2.25551i	−1.58127	+	0.192001i
$139$	17.1607	+	15.2031i	1.45555	+	1.28951i	0.882772	+	0.469802i	$0.155675\pi$
$139$	17.1607	+	15.2031i	1.45555	+	1.28951i	0.572783	+	0.819707i	$0.305864\pi$
$140$	−0.144053	−	0.208697i	−0.0121747	−	0.0176381i
$141$	−1.50813	−	0.183120i	−0.127008	−	0.0154215i
$142$	−0.981431	−	8.08282i	−0.0823599	−	0.678295i
$143$	16.2869	−	6.06786i	1.36198	−	0.507420i
$144$	−0.401010	+	3.30262i	−0.0334175	+	0.275218i
$145$	−0.271531	+	1.10164i	−0.0225494	+	0.0914865i
$146$	−8.34277			−0.690453
$147$	−9.25122			−0.763028
$148$	−0.461375	+	1.87187i	−0.0379248	+	0.153867i
$149$	5.09453	−	1.93210i	0.417360	−	0.158284i	−0.136981	−	0.990574i	$-0.543740\pi$
$149$	5.09453	−	1.93210i	0.417360	−	0.158284i	0.554340	+	0.832290i	$0.312971\pi$
$150$		−	13.7537i		−	1.12298i
$151$	5.58413	+	2.11778i	0.454430	+	0.172342i	0.571190	−	0.820818i	$-0.306482\pi$
$151$	5.58413	+	2.11778i	0.454430	+	0.172342i	−0.116761	+	0.993160i	$0.537251\pi$
$152$	−13.7773	+	3.39580i	−1.11749	+	0.275435i
$153$	4.32255	+	3.82944i	0.349457	+	0.309592i
$154$	2.60591	+	10.5726i	0.209990	+	0.851965i
$155$	−1.29131	−	1.14400i	−0.103720	−	0.0918882i
$156$	0.243504	+	2.10866i	0.0194960	+	0.168828i
$157$	−8.52910	+	7.55612i	−0.680696	+	0.603044i	−0.930955	−	0.365135i	$-0.881023\pi$
$157$	−8.52910	+	7.55612i	−0.680696	+	0.603044i	0.250258	+	0.968179i	$0.419484\pi$
$158$	−1.84588	−	1.27412i	−0.146850	−	0.101363i
$159$	−18.6504	−	4.59691i	−1.47907	−	0.364559i
$160$	−0.543100	−	0.786816i	−0.0429358	−	0.0622033i
$161$	2.27073	+	9.21271i	0.178959	+	0.726063i
$162$	3.87541	+	15.7232i	0.304481	+	1.23533i
$163$	−7.21625	+	0.876211i	−0.565220	+	0.0686301i	−0.398159	−	0.917316i	$-0.630351\pi$
$163$	−7.21625	+	0.876211i	−0.565220	+	0.0686301i	−0.167061	+	0.985947i	$0.553428\pi$
$164$	0.684727	+	0.772897i	0.0534682	+	0.0603531i
$165$	1.84895	−	4.87529i	0.143941	−	0.379541i
$166$	3.55833	+	1.86756i	0.276180	+	0.144950i
$167$	−17.2321	+	11.8944i	−1.33346	+	0.920419i	−0.999752	−	0.0222579i	$-0.992915\pi$
$167$	−17.2321	+	11.8944i	−1.33346	+	0.920419i	−0.333706	+	0.942677i	$0.608299\pi$
$168$	7.40321			0.571170
$169$	−4.46706	−	12.2084i	−0.343620	−	0.939109i
$170$	−6.65945			−0.510757
$171$	3.34220	−	2.30696i	0.255585	−	0.176417i
$172$	−2.57195	−	1.34986i	−0.196109	−	0.102926i
$173$	−5.24454	+	13.8287i	−0.398735	+	1.05138i	0.573876	+	0.818942i	$0.305439\pi$
$173$	−5.24454	+	13.8287i	−0.398735	+	1.05138i	−0.972612	+	0.232436i	$0.925330\pi$
$174$	3.94571	+	4.45379i	0.299124	+	0.337641i
$175$	−6.92325	+	0.840635i	−0.523348	+	0.0635460i
$176$	5.21016	+	21.1385i	0.392731	+	1.59337i
$177$	0.495161	+	2.00895i	0.0372186	+	0.151002i
$178$	−13.6556	−	19.7835i	−1.02353	−	1.48284i
$179$	7.96042	+	1.96207i	0.594990	+	0.146652i	0.525300	−	0.850917i	$-0.323953\pi$
$179$	7.96042	+	1.96207i	0.594990	+	0.146652i	0.0696894	+	0.997569i	$0.477799\pi$
$180$	0.103314	+	0.0713127i	0.00770059	+	0.00531534i
$181$	14.4635	−	12.8135i	1.07506	−	0.952420i	0.0760590	−	0.997103i	$-0.475766\pi$
$181$	14.4635	−	12.8135i	1.07506	−	0.952420i	0.999001	+	0.0446830i	$0.0142278\pi$
$182$	7.91921	−	1.90274i	0.587011	−	0.141041i
$183$	−8.50436	−	7.53421i	−0.628660	−	0.556945i
$184$	3.92770	+	15.9353i	0.289554	+	1.17477i
$185$	−2.65131	−	2.34885i	−0.194928	−	0.172691i
$186$	−8.78433	+	2.16514i	−0.644098	+	0.158756i
$187$	35.3350	+	13.4008i	2.58395	+	0.979963i
$188$		−	0.239359i		−	0.0174570i
$189$	6.08722	−	2.30858i	0.442780	−	0.167924i
$190$	−1.12075	+	4.54707i	−0.0813078	+	0.329879i
$191$	−9.67777			−0.700259			−0.350130	−	0.936701i	$-0.613862\pi$
$191$	−9.67777			−0.700259			−0.350130	+	0.936701i	$0.613862\pi$
$192$	12.4468			0.898270
$193$	2.43340	−	9.87270i	0.175160	−	0.710653i	−0.816008	−	0.578041i	$-0.803817\pi$
$193$	2.43340	−	9.87270i	0.175160	−	0.710653i	0.991168	−	0.132612i	$-0.0423364\pi$
$194$	0.565112	−	4.65412i	0.0405727	−	0.334146i
$195$	−3.63837	−	1.40430i	−0.260549	−	0.100564i
$196$	−0.175691	−	1.44695i	−0.0125494	−	0.103353i
$197$	−19.1013	−	2.31932i	−1.36091	−	0.165245i	−0.592692	−	0.805429i	$-0.701935\pi$
$197$	−19.1013	−	2.31932i	−1.36091	−	0.165245i	−0.768221	+	0.640184i	$0.778858\pi$
$198$	−3.06218	−	4.43633i	−0.217620	−	0.315276i
$199$	0.597329	+	0.529187i	0.0423435	+	0.0375131i	0.684029	−	0.729455i	$-0.260226\pi$
$199$	0.597329	+	0.529187i	0.0423435	+	0.0375131i	−0.641686	+	0.766968i	$0.721765\pi$
$200$	−11.9752	+	1.45405i	−0.846775	+	0.102817i
$201$	2.95830	+	0.359203i	0.208662	+	0.0253362i
$202$	6.19401	+	11.8017i	0.435809	+	0.830364i
$203$	2.00076	−	2.25839i	0.140426	−	0.158508i
$204$	−2.62183	+	3.79837i	−0.183565	+	0.265939i
$205$	−1.84202	+	0.454018i	−0.128653	+	0.0317100i
$206$	4.70656	−	0.571480i	0.327922	−	0.0398169i
$207$	−2.66831	−	3.86571i	−0.185460	−	0.268686i
$208$	15.8334	−	3.80427i	1.09785	−	0.263779i
$209$	15.0967	−	21.8714i	1.04426	−	1.51288i
$210$	1.13549	−	2.16349i	0.0783560	−	0.149295i
$211$	4.20143	+	11.0783i	0.289239	+	0.762659i	0.998342	+	0.0575553i	$0.0183306\pi$
$211$	4.20143	+	11.0783i	0.289239	+	0.762659i	−0.709104	+	0.705104i	$0.750900\pi$
$212$	0.364793	−	3.00434i	0.0250541	−	0.206339i
$213$	8.53253	−	5.88958i	0.584640	−	0.403548i
$214$	−3.82443	+	15.5163i	−0.261433	+	1.06067i
$215$	4.39203	−	3.03160i	0.299534	−	0.206753i
$216$	10.5291	−	3.99317i	0.716415	−	0.271701i
$217$	1.62678	+	4.28948i	0.110433	+	0.291189i
$218$	20.1357	−	10.5681i	1.36376	−	0.715759i
$219$	−4.93686	−	9.40639i	−0.333602	−	0.635625i
$220$	0.797639	+	0.196600i	0.0537768	+	0.0132548i
$221$	10.1780	−	26.3701i	0.684650	−	1.77384i
$222$	−18.0359	+	4.44546i	−1.21049	+	0.298360i
$223$	2.89345	+	3.26603i	0.193760	+	0.218709i	0.837359	−	0.546653i	$-0.184098\pi$
$223$	2.89345	+	3.26603i	0.193760	+	0.218709i	−0.643600	+	0.765362i	$0.722560\pi$
$224$	0.306446	+	2.52381i	0.0204753	+	0.168629i
$225$	3.05702	−	1.60445i	0.203802	−	0.106963i
$226$	10.6136	−	20.2224i	0.706003	−	1.34518i
$227$	−6.51269	−	2.46994i	−0.432262	−	0.163935i	0.128870	−	0.991661i	$-0.458865\pi$
$227$	−6.51269	−	2.46994i	−0.432262	−	0.163935i	−0.561132	+	0.827726i	$0.689634\pi$
$228$	2.15228	+	2.42942i	0.142538	+	0.160893i
$229$	16.8176	+	2.04203i	1.11134	+	0.134941i	0.655554	−	0.755148i	$-0.272435\pi$
$229$	16.8176	+	2.04203i	1.11134	+	0.134941i	0.455786	+	0.890089i	$0.349358\pi$
$230$	5.25930	+	1.29630i	0.346788	+	0.0854756i
$231$	−10.3785	+	9.19451i	−0.682852	+	0.604954i
$232$	3.46073	−	3.90636i	0.227208	−	0.256465i
$233$	−16.6669	+	8.74744i	−1.09188	+	0.573064i	−0.911819	−	0.410591i	$-0.865322\pi$
$233$	−16.6669	+	8.74744i	−1.09188	+	0.573064i	−0.180062	+	0.983655i	$0.557630\pi$
$234$	−3.33158	+	2.27091i	−0.217792	+	0.148454i
$235$	0.389399	+	0.204372i	0.0254016	+	0.0133318i
$236$	−0.304808	+	0.115599i	−0.0198413	+	0.00752482i
$237$	0.344252	−	2.83517i	0.0223616	−	0.184164i
$238$	15.6805	+	8.22974i	1.01641	+	0.533455i
$239$			12.6253i			0.816662i	0.912834	+	0.408331i	$0.133889\pi$
$239$			12.6253i			0.816662i	−0.912834	+	0.408331i	$0.866111\pi$
$240$	2.27025	−	4.32559i	0.146544	−	0.279216i
$241$	−9.94782	+	11.2288i	−0.640795	+	0.723308i	−0.975741	−	0.218929i	$-0.929744\pi$
$241$	−9.94782	+	11.2288i	−0.640795	+	0.723308i	0.334945	+	0.942238i	$0.391282\pi$
$242$	−15.2885	−	10.5529i	−0.982782	−	0.678366i
$243$	−5.60983	+	4.96987i	−0.359871	+	0.318817i
$244$	1.01689	−	1.47322i	0.0650996	−	0.0943131i
$245$	2.50397	+	0.949629i	0.159973	+	0.0606696i
$246$	−3.52802	+	9.30261i	−0.224938	+	0.593113i
$247$	−16.2925	−	11.3875i	−1.03667	−	0.724569i
$248$	2.81386	+	7.41955i	0.178680	+	0.471142i
$249$			5.11712i			0.324284i
$250$	−2.91792	+	7.69392i	−0.184545	+	0.486606i
$251$	−1.53775	−	12.6645i	−0.0970619	−	0.799376i	−0.957222	−	0.289353i	$-0.906560\pi$
$251$	−1.53775	−	12.6645i	−0.0970619	−	0.799376i	0.860161	−	0.510023i	$-0.170363\pi$
$252$	−0.155138	−	0.295590i	−0.00977275	−	0.0186204i
$253$	−25.2973	−	17.4614i	−1.59042	−	1.09779i
$254$	−16.4917	−	11.3834i	−1.03478	−	0.714257i
$255$	−3.94075	−	7.50847i	−0.246779	−	0.470199i
$256$	0.861659	+	7.09640i	0.0538537	+	0.443525i
$257$	−6.21499	+	16.3876i	−0.387681	+	1.02223i	0.589114	+	0.808050i	$0.299477\pi$
$257$	−6.21499	+	16.3876i	−0.387681	+	1.02223i	−0.976794	+	0.214180i	$0.931292\pi$
$258$		−	27.9871i		−	1.74240i
$259$	3.34010	+	8.80713i	0.207544	+	0.547248i
$260$	0.150544	−	0.595733i	0.00933636	−	0.0369458i
$261$	−0.529651	+	1.39658i	−0.0327846	+	0.0864458i
$262$	16.2423	+	6.15990i	1.00345	+	0.380560i
$263$	10.2318	−	14.8234i	0.630922	−	0.914048i	−0.368959	−	0.929445i	$-0.620286\pi$
$263$	10.2318	−	14.8234i	0.630922	−	0.914048i	0.999881	+	0.0153972i	$0.00490128\pi$
$264$	−17.9517	+	15.9038i	−1.10485	+	0.978813i
$265$	4.57611	+	3.15866i	0.281108	+	0.194035i
$266$	8.25820	−	9.32158i	0.506343	−	0.571543i
$267$	14.2250	−	27.1034i	0.870555	−	1.65870i
$268$			0.469518i			0.0286804i
$269$	11.6657	+	6.12264i	0.711271	+	0.373304i	0.781228	−	0.624246i	$-0.214594\pi$
$269$	11.6657	+	6.12264i	0.711271	+	0.373304i	−0.0699564	+	0.997550i	$0.522286\pi$
$270$	0.447981	−	3.68945i	0.0272632	−	0.224533i
$271$	−8.12446	+	3.08120i	−0.493526	+	0.187170i	−0.588796	−	0.808282i	$-0.700398\pi$
$271$	−8.12446	+	3.08120i	−0.493526	+	0.187170i	0.0952702	+	0.995451i	$0.469629\pi$
$272$	31.3509	+	16.4542i	1.90093	+	0.997684i
$273$	6.83154	+	7.80288i	0.413463	+	0.472252i
$274$	−10.0786	+	5.28967i	−0.608872	+	0.319561i
$275$	14.9820	−	16.9112i	0.903448	−	1.01978i
$276$	2.80996	−	2.48941i	0.169140	−	0.149845i
$277$	5.01187	+	1.23531i	0.301134	+	0.0742228i	0.386988	−	0.922085i	$-0.373516\pi$
$277$	5.01187	+	1.23531i	0.301134	+	0.0742228i	−0.0858537	+	0.996308i	$0.527362\pi$
$278$	−34.5505	−	4.19518i	−2.07220	−	0.251610i
$279$	−1.50599	−	1.69991i	−0.0901614	−	0.101771i
$280$	−2.00378	−	0.759932i	−0.119749	−	0.0454146i
$281$	1.85763	−	3.53942i	0.110817	−	0.211144i	−0.823731	−	0.566980i	$-0.808112\pi$
$281$	1.85763	−	3.53942i	0.110817	−	0.211144i	0.934548	+	0.355836i	$0.115804\pi$
$282$	2.04211	−	1.07178i	0.121606	−	0.0638236i
$283$	−0.421394	−	3.47050i	−0.0250493	−	0.206300i	0.974811	−	0.223034i	$-0.0715961\pi$
$283$	−0.421394	−	3.47050i	−0.0250493	−	0.206300i	−0.999860	+	0.0167344i	$0.994673\pi$
$284$	1.08321	+	1.22269i	0.0642766	+	0.0725533i
$285$	−5.78998	+	1.42710i	−0.342969	+	0.0845342i
$286$	−15.1154	+	21.6262i	−0.893792	+	1.27878i
$287$	4.89834	+	1.20733i	0.289140	+	0.0712665i
$288$	−0.584889	−	1.11441i	−0.0344649	−	0.0656674i
$289$	39.3670	−	20.6614i	2.31570	−	1.21537i
$290$	−0.610783	−	1.61050i	−0.0358664	−	0.0945719i
$291$	5.58188	−	2.11693i	0.327216	−	0.124097i
$292$	1.37746	−	0.950793i	0.0806098	−	0.0556409i
$293$	−4.08796	+	16.5855i	−0.238821	+	0.968935i	0.722028	+	0.691864i	$0.243210\pi$
$293$	−4.08796	+	16.5855i	−0.238821	+	0.968935i	−0.960849	+	0.277071i	$0.910636\pi$
$294$	11.5580	−	7.97794i	0.674079	−	0.465283i
$295$	0.0721947	−	0.594577i	0.00420334	−	0.0346176i
$296$	5.77741	+	15.2338i	0.335805	+	0.885445i
$297$	−9.80126	+	18.6747i	−0.568727	+	1.08362i
$298$	−4.69869	+	6.80722i	−0.272188	+	0.394332i
$299$	−13.1712	+	18.8445i	−0.761710	+	1.08981i
$300$	1.56745	+	2.27084i	0.0904968	+	0.131107i
$301$	−14.0880	+	1.71059i	−0.812019	+	0.0985970i
$302$	−8.80285	+	2.16971i	−0.506547	+	0.124853i
$303$	−9.64098	+	13.9674i	−0.553860	+	0.802404i
$304$	16.5111	−	18.6372i	0.946978	−	1.06892i
$305$	1.52844	+	2.91220i	0.0875182	+	0.166752i
$306$	−8.70278	−	1.05671i	−0.497505	−	0.0604080i
$307$	−3.19463	+	0.387899i	−0.182327	+	0.0221385i	−0.211191	−	0.977445i	$-0.567734\pi$
$307$	−3.19463	+	0.387899i	−0.182327	+	0.0221385i	0.0288637	+	0.999583i	$0.490811\pi$
$308$	−1.63518	−	1.44864i	−0.0931728	−	0.0825439i
$309$	3.42946	+	4.96843i	0.195095	+	0.282644i
$310$	2.59985	+	0.315678i	0.147661	+	0.0179293i
$311$	3.04057	+	25.0414i	0.172415	+	1.41996i	0.780034	+	0.625737i	$0.215202\pi$
$311$	3.04057	+	25.0414i	0.172415	+	1.41996i	−0.607619	+	0.794228i	$0.707875\pi$
$312$	11.8166	+	13.4967i	0.668982	+	0.764101i
$313$	−2.07347	+	17.0765i	−0.117199	+	0.965223i	0.808901	+	0.587945i	$0.200063\pi$
$313$	−2.07347	+	17.0765i	−0.117199	+	0.965223i	−0.926100	+	0.377278i	$0.876860\pi$
$314$	4.13971	−	16.7955i	0.233618	−	0.947823i
$315$	0.613340			0.0345578
$316$	0.449975			0.0253131
$317$	7.35763	−	29.8511i	0.413246	−	1.67660i	−0.283252	−	0.959045i	$-0.591413\pi$
$317$	7.35763	−	29.8511i	0.413246	−	1.67660i	0.696498	−	0.717559i	$-0.254740\pi$
$318$	27.2652	−	10.3403i	1.52896	−	0.579856i
$319$			9.77438i			0.547260i
$320$	−3.36889	−	1.27765i	−0.188327	−	0.0714229i
$321$	−19.7576	+	4.86982i	−1.10276	+	0.271807i
$322$	−10.7817	−	9.55173i	−0.600839	−	0.532297i
$323$	−10.3433	−	41.9645i	−0.575517	−	2.33497i
$324$	−2.43177	−	2.15436i	−0.135098	−	0.119687i
$325$	−12.5830	−	11.2799i	−0.697982	−	0.625698i
$326$	8.26003	−	7.31774i	0.457480	−	0.405292i
$327$	23.8308	+	16.4492i	1.31784	+	0.909642i
$328$	8.47270	+	2.08833i	0.467826	+	0.115309i
$329$	−0.664323	−	0.962438i	−0.0366253	−	0.0530609i
$330$	1.89429	+	7.68543i	0.104277	+	0.423069i
$331$	3.08159	+	12.5025i	0.169380	+	0.687201i	0.992802	+	0.119771i	$0.0382160\pi$
$331$	3.08159	+	12.5025i	0.169380	+	0.687201i	−0.823422	+	0.567430i	$0.807938\pi$
$332$	−0.800348	+	0.0971798i	−0.0439248	+	0.00533344i
$333$	−3.09210	−	3.49025i	−0.169446	−	0.191265i
$334$	11.2716	−	29.7207i	0.616753	−	1.62625i
$335$	−0.763831	−	0.400890i	−0.0417326	−	0.0219029i
$336$	−10.6911	+	7.37955i	−0.583249	+	0.402588i
$337$	−15.8912			−0.865650			−0.432825	−	0.901478i	$-0.642483\pi$
$337$	−15.8912			−0.865650			−0.432825	+	0.901478i	$0.642483\pi$
$338$	16.1091	+	11.4004i	0.876217	+	0.620099i
$339$	29.0812			1.57947
$340$	1.09953	−	0.758952i	0.0596305	−	0.0411599i
$341$	−13.1595	−	6.90665i	−0.712628	−	0.374016i
$342$	−2.18615	+	5.76440i	−0.118213	+	0.311703i
$343$	−11.6294	−	13.1269i	−0.627930	−	0.708786i
$344$	−24.3681	+	2.95883i	−1.31384	+	0.159529i
$345$	1.65064	+	6.69690i	0.0888674	+	0.360549i
$346$	−5.37314	−	21.7997i	−0.288862	−	1.17196i
$347$	11.2323	+	16.2728i	0.602983	+	0.873572i	0.999002	−	0.0446705i	$-0.0142238\pi$
$347$	11.2323	+	16.2728i	0.602983	+	0.873572i	−0.396019	+	0.918242i	$0.629608\pi$
$348$	−1.15905	−	0.285680i	−0.0621317	−	0.0153141i
$349$	−0.116668	−	0.0805304i	−0.00624512	−	0.00431070i	0.564938	−	0.825133i	$-0.308900\pi$
$349$	−0.116668	−	0.0805304i	−0.00624512	−	0.00431070i	−0.571183	+	0.820823i	$0.693515\pi$
$350$	7.92465	−	7.02063i	0.423590	−	0.375268i
$351$	13.9248	+	7.41273i	0.743251	+	0.395662i
$352$	−6.16483	−	5.46156i	−0.328587	−	0.291102i
$353$	3.55905	+	14.4396i	0.189429	+	0.768544i	0.986378	+	0.164497i	$0.0526000\pi$
$353$	3.55905	+	14.4396i	0.189429	+	0.768544i	−0.796949	+	0.604047i	$0.793554\pi$
$354$	−2.35108	−	2.08288i	−0.124959	−	0.110704i
$355$	−2.91400	+	0.718238i	−0.154659	+	0.0381201i
$356$	4.50929	+	1.71015i	0.238992	+	0.0906377i
$357$			22.5496i			1.19345i
$358$	−11.6374	+	4.41348i	−0.615055	+	0.233260i
$359$	3.16392	−	12.8365i	0.166985	−	0.677487i	−0.826442	−	0.563022i	$-0.809639\pi$
$359$	3.16392	−	12.8365i	0.166985	−	0.677487i	0.993427	−	0.114465i	$-0.0365153\pi$
$360$	1.06090			0.0559143
$361$	−11.3940			−0.599684
$362$	−7.02003	+	28.4814i	−0.368965	+	1.49695i
$363$	2.85127	−	23.4823i	0.149653	−	1.23250i
$364$	−1.09068	+	1.21668i	−0.0571671	+	0.0637714i
$365$	0.370669	+	3.05273i	0.0194017	+	0.159787i
$366$	17.1222	+	2.07901i	0.894992	+	0.108672i
$367$	13.0938	+	18.9696i	0.683489	+	0.990205i	0.999145	+	0.0413315i	$0.0131600\pi$
$367$	13.0938	+	18.9696i	0.683489	+	0.990205i	−0.315656	+	0.948874i	$0.602225\pi$
$368$	−21.5565	−	19.0974i	−1.12371	−	0.995519i
$369$	−2.47926	+	0.301036i	−0.129065	+	0.0156713i
$370$	5.33799	+	0.648149i	0.277509	+	0.0336957i
$371$	−6.87153	−	13.0926i	−0.356752	−	0.679734i
$372$	1.20361	−	1.35860i	0.0624044	−	0.0704401i
$373$	0.200544	−	0.290538i	0.0103838	−	0.0150435i	−0.817758	−	0.575563i	$-0.804783\pi$
$373$	0.200544	−	0.290538i	0.0103838	−	0.0150435i	0.828141	+	0.560519i	$0.189398\pi$
$374$	−55.7023	+	13.7294i	−2.88030	+	0.709929i
$375$	−10.4015	+	1.26297i	−0.537131	+	0.0652196i
$376$	−1.14908	−	1.66474i	−0.0592595	−	0.0858523i
$377$	7.31075	+	0.0428522i	0.376523	+	0.00220700i
$378$	−5.61424	+	8.13364i	−0.288766	+	0.418349i
$379$	12.9321	−	24.6401i	0.664278	−	1.26568i	−0.287174	−	0.957878i	$-0.592716\pi$
$379$	12.9321	−	24.6401i	0.664278	−	1.26568i	0.951452	−	0.307797i	$-0.0995918\pi$
$380$	−0.333166	−	0.878486i	−0.0170910	−	0.0450654i
$381$	3.07566	−	25.3303i	0.157571	−	1.29771i
$382$	12.0910	−	8.34579i	0.618627	−	0.427008i
$383$	−7.40981	+	30.0628i	−0.378624	+	1.53614i	0.404657	+	0.914469i	$0.367391\pi$
$383$	−7.40981	+	30.0628i	−0.378624	+	1.53614i	−0.783281	+	0.621668i	$0.786455\pi$
$384$	−20.9866	+	14.4860i	−1.07097	+	0.739236i
$385$	3.75288	−	1.42328i	0.191264	−	0.0725370i
$386$	5.47371	+	14.4330i	0.278604	+	0.734619i
$387$	6.22069	−	3.26487i	0.316215	−	0.165963i
$388$	0.437107	+	0.832837i	0.0221907	+	0.0422809i
$389$	−9.50675	−	2.34320i	−0.482011	−	0.118805i	−0.00917957	−	0.999958i	$-0.502922\pi$
$389$	−9.50675	−	2.34320i	−0.482011	−	0.118805i	−0.472832	+	0.881153i	$0.656768\pi$
$390$	5.75663	−	1.38314i	0.291498	−	0.0700381i
$391$	−48.5376	+	11.9635i	−2.45465	+	0.605018i
$392$	−8.16826	−	9.22006i	−0.412559	−	0.465683i
$393$	2.66621	+	21.9582i	0.134492	+	1.10764i
$394$	25.8644	−	13.5747i	1.30303	−	0.683883i
$395$	−0.384204	+	0.732039i	−0.0193314	+	0.0368329i
$396$	1.01118	+	0.383491i	0.0508138	+	0.0192711i
$397$	3.77725	+	4.26364i	0.189575	+	0.213986i	0.835612	−	0.549320i	$-0.185113\pi$
$397$	3.77725	+	4.26364i	0.189575	+	0.213986i	−0.646037	+	0.763306i	$0.723575\pi$
$398$	−1.20263	−	0.146026i	−0.0602823	−	0.00731960i
$399$	15.3968	+	3.79497i	0.770804	+	0.189986i
$400$	15.8442	−	14.0368i	0.792212	−	0.701838i
$401$	−13.4783	+	15.2138i	−0.673074	+	0.759743i	−0.981491	−	0.191508i	$-0.938662\pi$
$401$	−13.4783	+	15.2138i	−0.673074	+	0.759743i	0.308417	+	0.951251i	$0.400201\pi$
$402$	−4.00573	+	2.10237i	−0.199787	+	0.104857i
$403$	−5.22352	+	9.81239i	−0.260202	+	0.488790i
$404$	−2.36767	−	1.24265i	−0.117796	−	0.0618242i
$405$	5.58113	−	2.11664i	0.277329	−	0.105177i
$406$	−0.552096	+	4.54692i	−0.0274001	+	0.225660i
$407$	−27.0190	−	14.1807i	−1.33928	−	0.702911i
$408$			39.0042i			1.93099i
$409$	12.6089	−	24.0242i	0.623468	−	1.18792i	−0.344958	−	0.938618i	$-0.612107\pi$
$409$	12.6089	−	24.0242i	0.623468	−	1.18792i	0.968426	−	0.249301i	$-0.0802010\pi$
$410$	1.90981	−	2.15573i	0.0943187	−	0.106464i
$411$	−11.9281	−	8.23337i	−0.588370	−	0.406122i
$412$	−0.711964	+	0.630745i	−0.0350759	+	0.0310746i
$413$	−0.904768	+	1.31078i	−0.0445207	+	0.0644994i
$414$	6.66732	+	2.52858i	0.327681	+	0.124273i
$415$	0.525267	−	1.38502i	0.0257843	−	0.0679877i
$416$	−4.11201	+	4.58704i	−0.201608	+	0.224898i
$417$	−15.7153	−	41.4378i	−0.769581	−	2.02922i
$418$			40.3440i			1.97329i
$419$	0.200610	−	0.528964i	0.00980042	−	0.0258416i	−0.930027	−	0.367492i	$-0.880217\pi$
$419$	0.200610	−	0.528964i	0.00980042	−	0.0258416i	0.939827	+	0.341650i	$0.110986\pi$
$420$	0.0590860	+	0.486617i	0.00288310	+	0.0237445i
$421$	−6.11901	−	11.6588i	−0.298222	−	0.568215i	0.689528	−	0.724259i	$-0.257818\pi$
$421$	−6.11901	−	11.6588i	−0.298222	−	0.568215i	−0.987750	+	0.156044i	$0.950126\pi$
$422$	−14.8026	−	10.2175i	−0.720579	−	0.497380i
$423$	0.476449	+	0.328869i	0.0231657	+	0.0159902i
$424$	−11.8857	−	22.6464i	−0.577223	−	1.09981i
$425$	−4.42893	−	36.4755i	−0.214834	−	1.76932i
$426$	−5.58117	+	14.7163i	−0.270409	+	0.713009i
$427$		−	8.74596i		−	0.423246i
$428$	−1.13689	−	2.99773i	−0.0549536	−	0.144901i
$429$	−33.3279	−	4.24511i	−1.60909	−	0.204956i
$430$	−2.87285	+	7.57508i	−0.138541	+	0.365303i
$431$	18.8432	+	7.14627i	0.907643	+	0.344224i	0.763857	−	0.645385i	$-0.223303\pi$
$431$	18.8432	+	7.14627i	0.907643	+	0.344224i	0.143786	+	0.989609i	$0.454072\pi$
$432$	−11.2249	+	16.2621i	−0.540058	+	0.782410i
$433$	23.0956	−	20.4609i	1.10990	−	0.983289i	0.109960	−	0.993936i	$-0.464928\pi$
$433$	23.0956	−	20.4609i	1.10990	−	0.983289i	0.999943	+	0.0106473i	$0.00338921\pi$
$434$	−5.73153	−	3.95619i	−0.275122	−	0.189903i
$435$	1.45439	−	1.64167i	0.0697328	−	0.0787121i
$436$	−2.12018	+	4.03966i	−0.101538	+	0.193465i
$437$			35.1548i			1.68168i
$438$	14.2796	+	7.49453i	0.682307	+	0.358103i
$439$	−0.530641	+	4.37022i	−0.0253261	+	0.208579i	−0.999879	−	0.0155800i	$-0.995041\pi$
$439$	−0.530641	+	4.37022i	−0.0253261	+	0.208579i	0.974553	+	0.224159i	$0.0719636\pi$
$440$	6.49138	−	2.46186i	0.309465	−	0.117364i
$441$	3.12157	+	1.63833i	0.148646	+	0.0780156i
$442$	10.0247	+	41.7228i	0.476826	+	1.98455i
$443$	6.38961	−	3.35353i	0.303580	−	0.159331i	−0.306054	−	0.952014i	$-0.599009\pi$
$443$	6.38961	−	3.35353i	0.303580	−	0.159331i	0.609634	+	0.792683i	$0.291317\pi$
$444$	2.47125	−	2.78947i	0.117280	−	0.132382i
$445$	−6.63233	+	5.87573i	−0.314402	+	0.278536i
$446$	−6.43145	−	1.58521i	−0.304538	−	0.0750619i
$447$	−10.4555	−	1.26953i	−0.494530	−	0.0600468i
$448$	6.35353	+	7.17165i	0.300176	+	0.338829i
$449$	−3.64932	−	1.38400i	−0.172222	−	0.0653152i	0.266987	−	0.963700i	$-0.413972\pi$
$449$	−3.64932	−	1.38400i	−0.172222	−	0.0653152i	−0.439209	+	0.898385i	$0.644741\pi$
$450$	−2.43568	+	4.64080i	−0.114819	+	0.218769i
$451$	−14.4714	+	7.59517i	−0.681431	+	0.357643i
$452$	0.552285	+	4.54848i	0.0259773	+	0.213942i
$453$	−7.65543	−	8.64120i	−0.359684	−	0.405999i
$454$	10.2666	−	2.53050i	0.481837	−	0.118762i
$455$	−1.04809	−	2.81321i	−0.0491351	−	0.131885i
$456$	26.6320	+	6.56420i	1.24716	+	0.307397i
$457$	−10.5225	−	20.0489i	−0.492220	−	0.937846i	−0.997205	−	0.0747182i	$-0.976194\pi$
$457$	−10.5225	−	20.0489i	−0.492220	−	0.937846i	0.504985	−	0.863128i	$-0.331498\pi$
$458$	−22.7721	+	11.9517i	−1.06407	+	0.558468i
$459$	12.1629	+	32.0708i	0.567713	+	1.49694i
$460$	−1.01609	+	0.385352i	−0.0473754	+	0.0179671i
$461$	11.1691	−	7.70944i	0.520195	−	0.359065i	−0.278851	−	0.960334i	$-0.589954\pi$
$461$	11.1691	−	7.70944i	0.520195	−	0.359065i	0.799046	+	0.601270i	$0.205338\pi$
$462$	5.03732	−	20.4372i	0.234357	−	0.950825i
$463$	−16.3933	+	11.3155i	−0.761862	+	0.525876i	−0.884480	−	0.466578i	$-0.845487\pi$
$463$	−16.3933	+	11.3155i	−0.761862	+	0.525876i	0.122617	+	0.992454i	$0.460871\pi$
$464$	−1.10384	+	9.09093i	−0.0512444	+	0.422036i
$465$	1.18254	+	3.11811i	0.0548390	+	0.144599i
$466$	13.2793	−	25.3016i	0.615151	−	1.17207i
$467$	12.8806	−	18.6607i	0.596041	−	0.863514i	−0.402614	−	0.915370i	$-0.631898\pi$
$467$	12.8806	−	18.6607i	0.596041	−	0.863514i	0.998655	+	0.0518557i	$0.0165136\pi$
$468$	0.291265	−	0.754633i	0.0134637	−	0.0348829i
$469$	1.30311	+	1.88788i	0.0601721	+	0.0871744i
$470$	−0.662741	+	0.0804713i	−0.0305700	+	0.00371186i
$471$	21.3864	−	5.27128i	0.985434	−	0.242888i
$472$	−1.56499	+	2.26727i	−0.0720343	+	0.104360i
$473$	30.4866	−	34.4123i	1.40178	−	1.58228i
$474$	2.01486	+	3.83900i	0.0925457	+	0.176331i
$475$	−25.6508	−	3.11457i	−1.17694	−	0.142906i
$476$	−3.52689	+	0.428242i	−0.161655	+	0.0196284i
$477$	5.47899	+	4.85397i	0.250866	+	0.222248i
$478$	−10.8876	−	15.7735i	−0.497989	−	0.721461i
$479$	19.0488	+	2.31294i	0.870361	+	0.105681i	0.543518	−	0.839398i	$-0.317092\pi$
$479$	19.0488	+	2.31294i	0.870361	+	0.105681i	0.326843	+	0.945079i	$0.394015\pi$
$480$	0.222762	+	1.83461i	0.0101676	+	0.0837381i
$481$	−10.7249	+	20.1467i	−0.489014	+	0.918612i
$482$	2.74503	−	22.6074i	0.125033	−	1.02974i
$483$	4.38940	−	17.8085i	0.199725	−	0.810315i
$484$	3.72693			0.169406
$485$	−1.72811			−0.0784695
$486$	2.72280	−	11.0469i	0.123509	−	0.501095i
$487$	36.8108	−	13.9605i	1.66806	−	0.632611i	0.673731	−	0.738977i	$-0.264691\pi$
$487$	36.8108	−	13.9605i	1.66806	−	0.632611i	0.994327	+	0.106366i	$0.0339215\pi$
$488$		−	15.1280i		−	0.684811i
$489$	13.1386	+	4.98281i	0.594147	+	0.225330i
$490$	−3.94727	+	0.972914i	−0.178319	+	0.0439518i
$491$	5.38199	+	4.76803i	0.242886	+	0.215178i	0.775779	−	0.631004i	$-0.217357\pi$
$491$	5.38199	+	4.76803i	0.242886	+	0.215178i	−0.532894	+	0.846182i	$0.678895\pi$
$492$	−0.477677	−	1.93801i	−0.0215354	−	0.0873724i
$493$	11.8985	+	10.5411i	0.535879	+	0.474748i
$494$	30.1753	+	0.176874i	1.35765	+	0.00795792i
$495$	−1.48726	+	1.31760i	−0.0668474	+	0.0592216i
$496$	−11.4594	−	7.90985i	−0.514542	−	0.355163i
$497$	7.74896	+	1.90995i	0.347588	+	0.0856729i
$498$	−4.41283	−	6.39308i	−0.197744	−	0.286481i
$499$	−5.38343	−	21.8414i	−0.240995	−	0.977757i	−0.959381	−	0.282112i	$-0.908965\pi$
$499$	−5.38343	−	21.8414i	−0.240995	−	0.977757i	0.718386	−	0.695645i	$-0.244881\pi$
$500$	−0.395073	−	1.60287i	−0.0176682	−	0.0716827i
$501$	40.1798	−	4.87871i	1.79510	−	0.217965i
$502$	12.8426	+	14.4963i	0.573195	+	0.647003i
$503$	−3.26795	+	8.61688i	−0.145711	+	0.384208i	−0.987925	−	0.154936i	$-0.950483\pi$
$503$	−3.26795	+	8.61688i	−0.145711	+	0.384208i	0.842214	+	0.539144i	$0.181252\pi$
$504$	−2.49801	−	1.31106i	−0.111270	−	0.0583992i
$505$	4.04320	−	2.79082i	0.179920	−	0.124190i
$506$	46.6634			2.07444
$507$	−3.32125	+	24.9090i	−0.147502	+	1.10625i
$508$	4.02023			0.178369
$509$	12.3474	−	8.52277i	0.547288	−	0.377765i	−0.262100	−	0.965041i	$-0.584415\pi$
$509$	12.3474	−	8.52277i	0.547288	−	0.377765i	0.809387	+	0.587276i	$0.199799\pi$
$510$	11.3984	+	5.98236i	0.504732	+	0.264904i
$511$	2.89978	−	7.64608i	0.128279	−	0.338243i
$512$	10.2996	+	11.6259i	0.455184	+	0.513796i
$513$	23.9448	−	2.90743i	1.05719	−	0.128366i
$514$	−6.36738	−	25.8335i	−0.280853	−	1.13947i
$515$	−0.418224	−	1.69680i	−0.0184292	−	0.0747701i
$516$	3.18958	+	4.62090i	0.140413	+	0.203424i
$517$	3.67843	+	0.906651i	0.161777	+	0.0398745i
$518$	−11.7679	−	8.12282i	−0.517054	−	0.356896i
$519$	21.3994	−	18.9582i	0.939328	−	0.832172i
$520$	−1.81289	−	4.86603i	−0.0795004	−	0.213389i
$521$	−15.6697	−	13.8821i	−0.686500	−	0.608186i	0.246037	−	0.969260i	$-0.420872\pi$
$521$	−15.6697	−	13.8821i	−0.686500	−	0.608186i	−0.932537	+	0.361075i	$0.882410\pi$
$522$	−0.542638	−	2.20157i	−0.0237506	−	0.0963601i
$523$	11.3099	+	10.0197i	0.494547	+	0.438131i	0.873167	−	0.487422i	$-0.162063\pi$
$523$	11.3099	+	10.0197i	0.494547	+	0.438131i	−0.378619	+	0.925552i	$0.623601\pi$
$524$	−3.38376	+	0.834022i	−0.147820	+	0.0364344i
$525$	12.6051	+	4.78049i	0.550133	+	0.208638i
$526$			27.3432i			1.19222i
$527$	−22.5993	+	8.57079i	−0.984442	+	0.373350i
$528$	10.0714	−	40.8614i	0.438303	−	1.77826i
$529$	17.6613			0.767884
$530$	−8.44111			−0.366658
$531$	0.188692	−	0.765555i	0.00818855	−	0.0332223i
$532$	−0.301154	+	2.48022i	−0.0130567	+	0.107531i
$533$	5.61737	+	10.8572i	0.243315	+	0.470277i
$534$	5.60107	+	46.1289i	0.242382	+	1.99619i
$535$	5.84755	+	0.710021i	0.252812	+	0.0306969i
$536$	2.25400	+	3.26549i	0.0973582	+	0.141048i
$537$	−11.8626	−	10.5094i	−0.511910	−	0.453513i
$538$	−19.8546	+	2.41078i	−0.855991	+	0.103936i
$539$	22.9019	+	2.78080i	0.986456	+	0.119777i
$540$	0.346507	+	0.660214i	0.0149113	+	0.0284111i
$541$	−17.1681	+	19.3788i	−0.738114	+	0.833158i	−0.990933	−	0.134355i	$-0.957104\pi$
$541$	−17.1681	+	19.3788i	−0.738114	+	0.833158i	0.252820	+	0.967513i	$0.418642\pi$
$542$	7.49319	−	10.8558i	0.321860	−	0.466295i
$543$	−36.2666	+	8.93892i	−1.55635	+	0.383606i
$544$	−13.2968	+	1.61453i	−0.570097	+	0.0692223i
$545$	−4.76162	−	6.89840i	−0.203965	−	0.295495i
$546$	−15.2639	−	3.85727i	−0.653237	−	0.165076i
$547$	18.9847	−	27.5040i	0.811725	−	1.17599i	−0.169955	−	0.985452i	$-0.554362\pi$
$547$	18.9847	−	27.5040i	0.811725	−	1.17599i	0.981680	−	0.190535i	$-0.0610224\pi$
$548$	1.06122	−	2.02199i	0.0453332	−	0.0863751i
$549$	1.53531	+	4.04828i	0.0655254	+	0.172776i
$550$	−4.13418	+	34.0480i	−0.176282	+	1.45181i
$551$	9.19990	−	6.35023i	0.391929	−	0.270529i
$552$	7.59239	−	30.8035i	0.323153	−	1.31109i
$553$	1.80931	−	1.24887i	0.0769395	−	0.0531075i
$554$	−7.32689	+	2.77872i	−0.311290	+	0.118057i
$555$	2.42799	+	6.40208i	0.103062	+	0.271753i
$556$	6.18268	−	3.24492i	0.262204	−	0.137615i
$557$	21.0303	+	40.0699i	0.891083	+	1.69782i	0.697309	+	0.716771i	$0.254381\pi$
$557$	21.0303	+	40.0699i	0.891083	+	1.69782i	0.193774	+	0.981046i	$0.437927\pi$
$558$	3.34747	+	0.825076i	0.141710	+	0.0349283i
$559$	−25.6050	−	22.9534i	−1.08298	−	0.970823i
$560$	3.65120	−	0.899940i	0.154291	−	0.0380294i
$561$	−48.4417	−	54.6794i	−2.04521	−	2.30857i
$562$	0.731439	+	6.02394i	0.0308539	+	0.254105i
$563$	−12.8602	+	6.74958i	−0.541995	+	0.284461i	−0.713420	−	0.700736i	$-0.752855\pi$
$563$	−12.8602	+	6.74958i	−0.541995	+	0.284461i	0.171426	+	0.985197i	$0.445163\pi$
$564$	−0.215022	+	0.409691i	−0.00905407	+	0.0172511i
$565$	−7.87122	−	2.98516i	−0.331145	−	0.125587i
$566$	3.51931	+	3.97248i	0.147928	+	0.166976i
$567$	−15.7572	−	1.91327i	−0.661739	−	0.0803497i
$568$	13.4035	+	3.30365i	0.562396	+	0.138618i
$569$	−26.8751	+	23.8092i	−1.12666	+	0.998135i	−0.126681	+	0.991943i	$0.540432\pi$
$569$	−26.8751	+	23.8092i	−1.12666	+	0.998135i	−0.999981	+	0.00619191i	$0.998029\pi$
$570$	6.00305	−	6.77604i	0.251440	−	0.283817i
$571$	−27.3178	+	14.3375i	−1.14322	+	0.600006i	−0.926524	−	0.376235i	$-0.877219\pi$
$571$	−27.3178	+	14.3375i	−1.14322	+	0.600006i	−0.216691	+	0.976240i	$0.569526\pi$
$572$	0.0310269	−	5.29331i	0.00129730	−	0.221324i
$573$	16.5647	+	8.69380i	0.691998	+	0.363189i
$574$	−7.16092	+	2.71578i	−0.298891	+	0.113354i
$575$	−3.60242	+	29.6686i	−0.150231	+	1.23727i
$576$	−4.19983	−	2.20424i	−0.174993	−	0.0918434i
$577$			23.4543i			0.976415i	0.872728	+	0.488207i	$0.162349\pi$
$577$			23.4543i			0.976415i	−0.872728	+	0.488207i	$0.837651\pi$
$578$	−31.3656	+	59.7621i	−1.30464	+	2.48577i
$579$	−13.0340	+	14.7123i	−0.541673	+	0.611423i
$580$	0.284388	+	0.196299i	0.0118086	+	0.00815086i
$581$	−2.94840	+	2.61206i	−0.122320	+	0.108366i
$582$	−5.14817	+	7.45842i	−0.213399	+	0.309161i
$583$	44.7884	+	16.9860i	1.85495	+	0.703489i
$584$	5.01577	−	13.2255i	0.207554	−	0.547275i
$585$	0.978977	+	1.11817i	0.0404757	+	0.0462308i
$586$	−9.19547	−	24.2465i	−0.379861	−	1.00161i
$587$		−	2.44599i		−	0.100957i	−0.998725	−	0.0504783i	$-0.983925\pi$
$587$		−	2.44599i		−	0.100957i	0.998725	−	0.0504783i	$-0.0160746\pi$
$588$	−0.999115	+	2.63445i	−0.0412028	+	0.108643i
$589$	2.04878	+	16.8732i	0.0844184	+	0.695248i
$590$	0.422546	+	0.805095i	0.0173960	+	0.0331452i
$591$	30.6107	+	21.1290i	1.25916	+	0.869132i
$592$	−23.5284	−	16.2405i	−0.967010	−	0.667479i
$593$	5.29149	+	10.0821i	0.217295	+	0.414022i	0.969565	−	0.244833i	$-0.0787333\pi$
$593$	5.29149	+	10.0821i	0.217295	+	0.414022i	−0.752270	+	0.658855i	$0.771041\pi$
$594$	−3.85923	−	31.7836i	−0.158346	−	1.30410i
$595$	2.31469	−	6.10334i	0.0948931	−	0.250212i
$596$		−	1.65942i		−	0.0679725i
$597$	−0.547016	−	1.44236i	−0.0223879	−	0.0590320i
$598$	0.204578	−	34.9019i	0.00836583	−	1.42724i
$599$	4.48897	−	11.8364i	0.183414	−	0.483624i	−0.811499	−	0.584353i	$-0.801348\pi$
$599$	4.48897	−	11.8364i	0.183414	−	0.483624i	0.994914	+	0.100729i	$0.0321175\pi$
$600$	21.8032	+	8.26886i	0.890112	+	0.337575i
$601$	−0.593535	+	0.859883i	−0.0242108	+	0.0350754i	−0.834902	−	0.550398i	$-0.814476\pi$
$601$	−0.593535	+	0.859883i	−0.0242108	+	0.0350754i	0.810692	+	0.585473i	$0.199091\pi$
$602$	16.1257	−	14.2862i	0.657236	−	0.582260i
$603$	−0.934586	−	0.645098i	−0.0380593	−	0.0262704i
$604$	1.20615	−	1.36146i	0.0490776	−	0.0553971i
$605$	−3.18218	+	6.06313i	−0.129374	+	0.246501i
$606$		−	25.7642i		−	1.04660i
$607$	−1.83294	−	0.961999i	−0.0743965	−	0.0390463i	0.427115	−	0.904197i	$-0.359530\pi$
$607$	−1.83294	−	0.961999i	−0.0743965	−	0.0390463i	−0.501511	+	0.865151i	$0.667222\pi$
$608$	−1.13539	+	9.35078i	−0.0460461	+	0.379224i
$609$	−5.45331	+	2.06817i	−0.220979	+	0.0838064i
$610$	−4.42094	−	2.32029i	−0.178999	−	0.0939458i
$611$	0.694257	−	2.74731i	0.0280866	−	0.111144i
$612$	1.55733	−	0.817350i	0.0629513	−	0.0330394i
$613$	−24.6459	+	27.8194i	−0.995437	+	1.12362i	−0.00310709	+	0.999995i	$0.500989\pi$
$613$	−24.6459	+	27.8194i	−0.995437	+	1.12362i	−0.992330	+	0.123621i	$0.960549\pi$
$614$	3.65671	−	3.23957i	0.147573	−	0.130738i
$615$	3.56070	+	0.877633i	0.143581	+	0.0353896i
$616$	−18.3271	−	2.22531i	−0.738419	−	0.0896603i
$617$	−9.69535	−	10.9438i	−0.390320	−	0.440580i	0.520200	−	0.854044i	$-0.325857\pi$
$617$	−9.69535	−	10.9438i	−0.390320	−	0.440580i	−0.910521	+	0.413464i	$0.864319\pi$
$618$	−8.56921	−	3.24987i	−0.344704	−	0.130729i
$619$	6.55445	−	12.4885i	0.263446	−	0.501954i	−0.717420	−	0.696641i	$-0.754677\pi$
$619$	6.55445	−	12.4885i	0.263446	−	0.501954i	0.980865	+	0.194688i	$0.0623693\pi$
$620$	−0.465233	+	0.244173i	−0.0186842	+	0.00980623i
$621$	−3.36284	−	27.6955i	−0.134946	−	1.11138i
$622$	−25.3936	−	28.6634i	−1.01819	−	1.14930i
$623$	22.8778	−	5.63887i	0.916580	−	0.225917i
$624$	−30.5181	−	7.71207i	−1.22170	−	0.308730i
$625$	−19.8085	−	4.88236i	−0.792341	−	0.195295i
$626$	−12.1357	−	23.1227i	−0.485041	−	0.924169i
$627$	−45.4875	+	23.8737i	−1.81660	+	0.953423i
$628$	1.23061	+	3.24486i	0.0491068	+	0.129484i
$629$	−46.4008	+	17.5975i	−1.85012	+	0.701658i
$630$	−0.766278	+	0.528923i	−0.0305292	+	0.0210728i
$631$	−3.46494	+	14.0578i	−0.137937	+	0.559633i	0.860779	+	0.508979i	$0.169977\pi$
$631$	−3.46494	+	14.0578i	−0.137937	+	0.559633i	−0.998716	+	0.0506543i	$0.983869\pi$
$632$	3.12957	−	2.16019i	0.124488	−	0.0859277i
$633$	2.76065	−	22.7360i	0.109726	−	0.903676i
$634$	16.5503	+	43.6395i	0.657296	+	1.73315i
$635$	−3.43261	+	6.54028i	−0.136219	+	0.259543i
$636$	−3.32326	+	4.81458i	−0.131776	+	0.190910i
$637$	2.18031	−	17.1173i	0.0863868	−	0.678213i
$638$	−8.42909	−	12.2117i	−0.333711	−	0.483464i
$639$	−3.92208	+	0.476226i	−0.155155	+	0.0188392i
$640$	7.16728	−	1.76658i	0.283312	−	0.0698301i
$641$	−2.64723	+	3.83517i	−0.104559	+	0.151480i	−0.871771	−	0.489914i	$-0.837028\pi$
$641$	−2.64723	+	3.83517i	−0.104559	+	0.151480i	0.767212	+	0.641394i	$0.221644\pi$
$642$	20.4847	−	23.1224i	0.808466	−	0.912570i
$643$	20.9121	+	39.8446i	0.824692	+	1.57132i	0.820723	+	0.571327i	$0.193571\pi$
$643$	20.9121	+	39.8446i	0.824692	+	1.57132i	0.00396936	+	0.999992i	$0.498737\pi$
$644$	2.86872	+	0.348325i	0.113043	+	0.0137259i
$645$	−10.2408	+	1.24346i	−0.403233	+	0.0489614i
$646$	49.1112	+	43.5087i	1.93225	+	1.71183i
$647$	−5.03830	−	7.29924i	−0.198076	−	0.286963i	0.711342	−	0.702846i	$-0.248088\pi$
$647$	−5.03830	−	7.29924i	−0.198076	−	0.286963i	−0.909418	+	0.415884i	$0.863472\pi$
$648$	−27.2553	−	3.30940i	−1.07069	−	0.130005i
$649$	−0.621937	−	5.12211i	−0.0244132	−	0.201060i
$650$	25.4481	+	3.24143i	0.998157	+	0.127139i
$651$	1.06892	−	8.80333i	0.0418942	−	0.345030i
$652$	−0.529825	+	2.14958i	−0.0207495	+	0.0841842i
$653$	−16.3219			−0.638726			−0.319363	−	0.947632i	$-0.603469\pi$
$653$	−16.3219			−0.638726			−0.319363	+	0.947632i	$0.603469\pi$
$654$	−43.9583			−1.71890
$655$	1.53234	−	6.21696i	0.0598736	−	0.242917i
$656$	−14.3173	+	5.42982i	−0.558995	+	0.211999i
$657$			4.04822i			0.157936i
$658$	1.65995	+	0.629535i	0.0647115	+	0.0245418i
$659$	30.7304	−	7.57435i	1.19708	−	0.295055i	0.410108	−	0.912037i	$-0.365491\pi$
$659$	30.7304	−	7.57435i	1.19708	−	0.295055i	0.786977	+	0.616982i	$0.211645\pi$
$660$	−1.18864	−	1.05304i	−0.0462678	−	0.0409897i
$661$	−1.95324	−	7.92460i	−0.0759722	−	0.308231i	0.920646	−	0.390397i	$-0.127662\pi$
$661$	−1.95324	−	7.92460i	−0.0759722	−	0.308231i	−0.996619	+	0.0821661i	$0.973816\pi$
$662$	−14.6318	−	12.9626i	−0.568679	−	0.503806i
$663$	−41.1099	+	35.9923i	−1.59657	+	1.39782i
$664$	−5.09988	+	4.51810i	−0.197914	+	0.175336i
$665$	−3.77780	−	2.60763i	−0.146497	−	0.101119i
$666$	6.87300	+	1.69404i	0.266323	+	0.0656428i
$667$	−7.34491	−	10.6409i	−0.284396	−	0.412019i
$668$	1.52612	+	6.19172i	0.0590474	+	0.239565i
$669$	−2.01852	−	8.18945i	−0.0780404	−	0.316622i
$670$	1.30001	−	0.157850i	0.0502237	−	0.00609826i
$671$	18.7884	+	21.2077i	0.725317	+	0.818713i
$672$	1.74269	−	4.59509i	0.0672257	−	0.177260i
$673$	−22.4534	−	11.7844i	−0.865513	−	0.454257i	−0.0273182	−	0.999627i	$-0.508697\pi$
$673$	−22.4534	−	11.7844i	−0.865513	−	0.454257i	−0.838195	+	0.545370i	$0.816389\pi$
$674$	19.8538	−	13.7041i	0.764738	−	0.527861i
$675$	20.5060			0.789276
$676$	−3.95900	−	0.0464131i	−0.152269	−	0.00178512i
$677$	−0.693109			−0.0266384			−0.0133192	−	0.999911i	$-0.504240\pi$
$677$	−0.693109			−0.0266384			−0.0133192	+	0.999911i	$0.504240\pi$
$678$	−36.3327	+	25.0787i	−1.39535	+	0.963140i
$679$	4.06904	+	2.13560i	0.156155	+	0.0819567i
$680$	4.00374	−	10.5570i	0.153536	−	0.404842i
$681$	8.92842	+	10.0781i	0.342138	+	0.386194i
$682$	22.3969	−	2.71948i	0.857623	−	0.104134i
$683$	6.82528	+	27.6913i	0.261162	+	1.05958i	0.944247	+	0.329238i	$0.106792\pi$
$683$	6.82528	+	27.6913i	0.261162	+	1.05958i	−0.683085	+	0.730339i	$0.739362\pi$
$684$	−0.295995	−	1.20090i	−0.0113176	−	0.0459175i
$685$	2.38335	+	3.45288i	0.0910632	+	0.131928i
$686$	25.8495	+	6.37132i	0.986937	+	0.243258i
$687$	−26.9510	−	18.6029i	−1.02824	−	0.709745i
$688$	32.2412	−	28.5632i	1.22918	−	1.08896i
$689$	12.9011	−	33.4251i	0.491491	−	1.27339i
$690$	−7.83741	−	6.94334i	−0.298365	−	0.264329i
$691$	5.50740	+	22.3444i	0.209512	+	0.850022i	0.977736	+	0.209841i	$0.0672945\pi$
$691$	5.50740	+	22.3444i	0.209512	+	0.850022i	−0.768224	+	0.640181i	$0.778859\pi$
$692$	3.37157	+	2.98695i	0.128168	+	0.113547i
$693$	5.13021	−	1.26448i	0.194881	−	0.0480338i
$694$	−28.0663	−	10.6441i	−1.06538	−	0.404046i
$695$			12.8289i			0.486626i
$696$	−9.43264	+	3.57733i	−0.357543	+	0.135598i
$697$	−6.36089	+	25.8071i	−0.240936	+	0.977515i
$698$	0.215207			0.00814570
$699$	36.3853			1.37622
$700$	−0.508313	+	2.06231i	−0.0192124	+	0.0779478i
$701$	−3.88840	+	32.0238i	−0.146863	+	1.20952i	0.713801	+	0.700349i	$0.246972\pi$
$701$	−3.88840	+	32.0238i	−0.146863	+	1.20952i	−0.860664	+	0.509174i	$0.829951\pi$
$702$	−23.7895	+	2.74717i	−0.897876	+	0.103685i
$703$	4.20654	+	34.6440i	0.158653	+	1.30662i
$704$	−30.8128	−	3.74135i	−1.16130	−	0.141007i
$705$	−0.482909	−	0.699615i	−0.0181874	−	0.0263490i
$706$	−16.8988	−	14.9710i	−0.635993	−	0.563441i
$707$	−12.9691	+	1.57473i	−0.487752	+	0.0592238i
$708$	0.625560	+	0.0759568i	0.0235100	+	0.00285463i
$709$	−12.9825	−	24.7360i	−0.487566	−	0.928980i	−0.997628	−	0.0688421i	$-0.978070\pi$
$709$	−12.9825	−	24.7360i	−0.487566	−	0.928980i	0.510061	−	0.860138i	$-0.329623\pi$
$710$	3.02124	−	3.41027i	0.113385	−	0.127985i
$711$	−0.618248	+	0.895686i	−0.0231861	+	0.0335909i
$712$	39.5720	−	9.75361i	1.48302	−	0.365532i
$713$	19.5162	−	2.36969i	0.730886	−	0.0887456i
$714$	−19.4460	−	28.1724i	−0.727747	−	1.05432i
$715$	8.58489	+	4.57008i	0.321057	+	0.170911i
$716$	1.41844	−	2.05497i	0.0530097	−	0.0767979i
$717$	11.3416	−	21.6097i	0.423561	−	0.807028i
$718$	7.11694	+	18.7658i	0.265602	+	0.700335i
$719$	2.01341	−	16.5820i	0.0750877	−	0.618403i	−0.905783	−	0.423742i	$-0.860716\pi$
$719$	2.01341	−	16.5820i	0.0750877	−	0.618403i	0.980871	−	0.194661i	$-0.0623606\pi$
$720$	−1.53207	+	1.05751i	−0.0570967	+	0.0394110i
$721$	−1.11215	+	4.51216i	−0.0414186	+	0.168042i
$722$	14.2351	−	9.82580i	0.529777	−	0.365678i
$723$	27.1140	−	10.2830i	1.00838	−	0.382428i
$724$	−2.08685	−	5.50256i	−0.0775570	−	0.204501i
$725$	8.41491	−	4.41648i	0.312522	−	0.164024i
$726$	16.6881	+	31.7966i	0.619355	+	1.18008i
$727$	−44.7588	−	11.0321i	−1.66001	−	0.409156i	−0.705830	−	0.708382i	$-0.749426\pi$
$727$	−44.7588	−	11.0321i	−1.66001	−	0.409156i	−0.954183	+	0.299225i	$0.903272\pi$
$728$	−1.74477	+	13.6980i	−0.0646655	+	0.507681i
$729$	−17.0054	+	4.19146i	−0.629830	+	0.155239i
$730$	−3.09567	−	3.49429i	−0.114576	−	0.129329i
$731$	−9.01235	−	74.2234i	−0.333334	−	2.74525i
$732$	−3.06395	+	1.60809i	−0.113247	+	0.0594366i
$733$	−13.3709	+	25.4762i	−0.493867	+	0.940984i	0.503180	+	0.864182i	$0.332163\pi$
$733$	−13.3709	+	25.4762i	−0.493867	+	0.940984i	−0.997046	+	0.0768026i	$0.975529\pi$
$734$	−32.7175	−	12.4081i	−1.20762	−	0.457992i
$735$	−3.43276	−	3.87478i	−0.126619	−	0.142923i
$736$	10.8154	+	1.31323i	0.398663	+	0.0484064i
$737$	−7.21547	−	1.77845i	−0.265785	−	0.0655102i
$738$	2.83786	−	2.51413i	0.104463	−	0.0925463i
$739$	19.0837	−	21.5410i	0.702004	−	0.792399i	−0.284052	−	0.958809i	$-0.591679\pi$
$739$	19.0837	−	21.5410i	0.702004	−	0.792399i	0.986057	+	0.166410i	$0.0532174\pi$
$740$	−0.955214	+	0.501335i	−0.0351144	+	0.0184294i
$741$	17.6569	+	34.1271i	0.648643	+	1.25369i
$742$	19.8756	+	10.4315i	0.729656	+	0.382953i
$743$	29.7663	−	11.2889i	1.09202	−	0.414148i	0.258146	−	0.966106i	$-0.416888\pi$
$743$	29.7663	−	11.2889i	1.09202	−	0.414148i	0.833872	+	0.551958i	$0.186119\pi$
$744$	1.84892	−	15.2272i	0.0677846	−	0.558256i
$745$	2.69961	+	1.41687i	0.0989062	+	0.0519100i
$746$			0.535926i			0.0196217i
$747$	0.906206	−	1.72663i	0.0331564	−	0.0631742i
$748$	7.63223	−	8.61501i	0.279062	−	0.314996i
$749$	−12.8913	−	8.89822i	−0.471038	−	0.325134i
$750$	11.9060	−	10.5478i	0.434746	−	0.385151i
$751$	4.57027	−	6.62117i	0.166771	−	0.241610i	−0.730683	−	0.682716i	$-0.760798\pi$
$751$	4.57027	−	6.62117i	0.166771	−	0.241610i	0.897455	+	0.441106i	$0.145414\pi$
$752$	3.31883	+	1.25867i	0.121025	+	0.0458989i
$753$	−8.74482	+	23.0582i	−0.318679	+	0.840287i
$754$	−9.17067	+	6.25101i	−0.333976	+	0.227648i
$755$	1.18503	+	3.12468i	0.0431278	+	0.113719i
$756$		−	1.98276i		−	0.0721125i
$757$	−13.4500	+	35.4646i	−0.488847	+	1.28898i	0.432988	+	0.901400i	$0.357459\pi$
$757$	−13.4500	+	35.4646i	−0.488847	+	1.28898i	−0.921835	+	0.387584i	$0.873310\pi$
$758$	5.09200	+	41.9364i	0.184950	+	1.52320i
$759$	27.6132	+	52.6125i	1.00229	+	1.90971i
$760$	−6.53449	−	4.51044i	−0.237031	−	0.163611i
$761$	30.5291	+	21.0727i	1.10668	+	0.763885i	0.973836	−	0.227252i	$-0.0729743\pi$
$761$	30.5291	+	21.0727i	1.10668	+	0.763885i	0.132842	+	0.991137i	$0.457590\pi$
$762$	18.0015	+	34.2989i	0.652124	+	1.24252i
$763$	2.68676	+	22.1275i	0.0972674	+	0.801069i
$764$	−1.04518	+	2.75592i	−0.0378134	+	0.0997056i
$765$			3.23141i			0.116832i
$766$	−16.6677	−	43.9490i	−0.602227	−	1.58794i
$767$	−3.83381	+	0.442722i	−0.138431

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)

\(f(q)\)	\(=\)	\(q+(-1.24935 + 0.862366i) q^{2} +(-1.71162 - 0.898326i) q^{3} +(0.107998 - 0.284768i) q^{4} +(0.371060 + 0.418840i) q^{5} +(2.91310 - 0.353715i) q^{6} +(-0.356102 - 1.44476i) q^{7} +(-0.615953 - 2.49902i) q^{8} +(0.418452 + 0.606232i) q^{9} +O(q^{10})\)	\(q+(-1.24935 + 0.862366i) q^{2} +(-1.71162 - 0.898326i) q^{3} +(0.107998 - 0.284768i) q^{4} +(0.371060 + 0.418840i) q^{5} +(2.91310 - 0.353715i) q^{6} +(-0.356102 - 1.44476i) q^{7} +(-0.615953 - 2.49902i) q^{8} +(0.418452 + 0.606232i) q^{9} +(-0.824778 - 0.203290i) q^{10} +(3.96719 + 2.73835i) q^{11} +(-0.440666 + 0.390396i) q^{12} +(2.06554 - 2.95525i) q^{13} +(1.69081 + 1.49793i) q^{14} +(-0.258858 - 1.05023i) q^{15} +(3.38055 + 2.99490i) q^{16} +(7.61181 - 1.87614i) q^{17} +(-1.04559 - 0.396539i) q^{18} -5.51308i q^{19} +(0.159346 - 0.0604319i) q^{20} +(-0.688358 + 2.79278i) q^{21} -7.31788 q^{22} -6.37662 q^{23} +(-1.19066 + 4.83070i) q^{24} +(0.564942 - 4.65271i) q^{25} +(-0.0320826 + 5.47341i) q^{26} +(0.527370 + 4.34328i) q^{27} +(-0.449880 - 0.0546254i) q^{28} +(1.15185 + 1.66874i) q^{29} +(1.22909 + 1.08887i) q^{30} +(-3.06058 + 0.371622i) q^{31} +(-1.69611 - 0.205945i) q^{32} +(-4.33037 - 8.25084i) q^{33} +(-7.89191 + 8.90813i) q^{34} +(0.472990 - 0.685244i) q^{35} +(0.217827 - 0.0536896i) q^{36} +(-6.28396 + 0.763011i) q^{37} +(4.75429 + 6.88778i) q^{38} +(-6.19021 + 3.20273i) q^{39} +(0.818134 - 1.18527i) q^{40} +(-1.57560 + 3.00206i) q^{41} +(-1.54840 - 4.08278i) q^{42} +(1.14959 - 9.46773i) q^{43} +(1.20824 - 0.833990i) q^{44} +(-0.0986435 + 0.400213i) q^{45} +(7.96666 - 5.49899i) q^{46} +(0.734847 - 0.278691i) q^{47} +(-3.09580 - 8.16296i) q^{48} +(4.23766 - 2.22410i) q^{49} +(3.30653 + 6.30007i) q^{50} +(-14.7139 - 3.62665i) q^{51} +(-0.618486 - 0.907362i) q^{52} +(9.64825 - 2.37808i) q^{53} +(-4.40437 - 4.97151i) q^{54} +(0.325133 + 2.67771i) q^{55} +(-3.39115 + 1.77981i) q^{56} +(-4.95254 + 9.43628i) q^{57} +(-2.87813 - 1.09153i) q^{58} +(-0.709790 - 0.801187i) q^{59} +(-0.327027 - 0.0397083i) q^{60} +(5.70686 + 1.40661i) q^{61} +(3.50327 - 3.10363i) q^{62} +(0.726850 - 0.820444i) q^{63} +(-5.70144 + 2.99235i) q^{64} +(2.00422 - 0.231444i) q^{65} +(12.5254 + 6.57384i) q^{66} +(-1.44145 + 0.546670i) q^{67} +(0.287796 - 2.37022i) q^{68} +(10.9143 + 5.72829i) q^{69} +1.26400i q^{70} +(-2.49253 + 4.74913i) q^{71} +(1.25724 - 1.41913i) q^{72} +(4.52280 + 3.12187i) q^{73} +(7.19289 - 6.37235i) q^{74} +(-5.14662 + 7.45617i) q^{75} +(-1.56995 - 0.595402i) q^{76} +(2.54355 - 6.70678i) q^{77} +(4.97182 - 9.33957i) q^{78} +(0.523916 + 1.38145i) q^{79} +2.52720i q^{80} +(3.78266 - 9.97406i) q^{81} +(-0.620390 - 5.10937i) q^{82} +(-1.23021 - 2.34397i) q^{83} +(0.720952 + 0.497637i) q^{84} +(3.61024 + 2.49197i) q^{85} +(6.72841 + 12.8199i) q^{86} +(-0.472451 - 3.89099i) q^{87} +(4.39959 - 11.6008i) q^{88} +15.8350i q^{89} +(-0.221889 - 0.585074i) q^{90} +(-5.00519 - 1.93185i) q^{91} +(-0.688664 + 1.81586i) q^{92} +(5.57238 + 2.11332i) q^{93} +(-0.677750 + 0.981890i) q^{94} +(2.30910 - 2.04568i) q^{95} +(2.71808 + 1.87616i) q^{96} +(-2.04793 + 2.31164i) q^{97} +(-3.37635 + 6.43310i) q^{98} +3.55090i 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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