LMFDB - Embedded newform 169.2.h.a.12.2

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			12.2
Character	$\chi$	$=$	169.12
Dual form			169.2.h.a.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08715 + 1.44065i) q^{2} +(-1.12364 - 0.589730i) q^{3} +(1.57149 - 4.14367i) q^{4} +(-2.16703 - 2.44607i) q^{5} +(3.19479 - 0.387918i) q^{6} +(1.08188 + 4.38937i) q^{7} +(1.47582 + 5.98765i) q^{8} +(-0.789415 - 1.14367i) q^{9} +O(q^{10})$	\(q+(-2.08715 + 1.44065i) q^{2} +(-1.12364 - 0.589730i) q^{3} +(1.57149 - 4.14367i) q^{4} +(-2.16703 - 2.44607i) q^{5} +(3.19479 - 0.387918i) q^{6} +(1.08188 + 4.38937i) q^{7} +(1.47582 + 5.98765i) q^{8} +(-0.789415 - 1.14367i) q^{9} +(8.04684 + 1.98337i) q^{10} +(3.32000 + 2.29163i) q^{11} +(-4.20943 + 3.72923i) q^{12} +(1.49453 + 3.28122i) q^{13} +(-8.58159 - 7.60263i) q^{14} +(0.992433 + 4.02646i) q^{15} +(-5.07210 - 4.49349i) q^{16} +(-2.12143 + 0.522885i) q^{17} +(3.29525 + 1.24972i) q^{18} +1.05650i q^{19} +(-13.5412 + 5.13548i) q^{20} +(1.37290 - 5.57007i) q^{21} -10.2308 q^{22} +3.61172 q^{23} +(1.87281 - 7.59828i) q^{24} +(-0.684560 + 5.63786i) q^{25} +(-7.84639 - 4.69528i) q^{26} +(0.671443 + 5.52983i) q^{27} +(19.8882 + 2.41487i) q^{28} +(3.38752 + 4.90767i) q^{29} +(-7.87208 - 6.97405i) q^{30} +(0.311167 - 0.0377825i) q^{31} +(4.81598 + 0.584766i) q^{32} +(-2.37903 - 4.53286i) q^{33} +(3.67443 - 4.14758i) q^{34} +(8.39223 - 12.1582i) q^{35} +(-5.97952 + 1.47382i) q^{36} +(10.3500 - 1.25672i) q^{37} +(-1.52205 - 2.20507i) q^{38} +(0.255728 - 4.56827i) q^{39} +(11.4481 - 16.5854i) q^{40} +(-1.87980 + 3.58166i) q^{41} +(5.15910 + 13.6034i) q^{42} +(0.189699 - 1.56231i) q^{43} +(14.7131 - 10.1557i) q^{44} +(-1.08680 + 4.40932i) q^{45} +(-7.53819 + 5.20324i) q^{46} +(-6.60753 + 2.50591i) q^{47} +(3.04925 + 8.04022i) q^{48} +(-11.8979 + 6.24449i) q^{49} +(-6.69342 - 12.7532i) q^{50} +(2.69208 + 0.663537i) q^{51} +(15.9449 - 1.03643i) q^{52} +(-2.83732 + 0.699337i) q^{53} +(-9.36796 - 10.5742i) q^{54} +(-1.58905 - 13.0870i) q^{55} +(-24.6853 + 12.9559i) q^{56} +(0.623052 - 1.18713i) q^{57} +(-14.1405 - 5.36278i) q^{58} +(5.02059 + 5.66707i) q^{59} +(18.2439 + 2.21521i) q^{60} +(-1.29766 - 0.319844i) q^{61} +(-0.595019 + 0.527140i) q^{62} +(4.16591 - 4.70234i) q^{63} +(1.10604 - 0.580495i) q^{64} +(4.78741 - 10.7662i) q^{65} +(11.4957 + 6.03339i) q^{66} +(-5.61892 + 2.13098i) q^{67} +(-1.16713 + 9.61220i) q^{68} +(-4.05827 - 2.12994i) q^{69} +37.4663i q^{70} +(2.89052 - 5.50742i) q^{71} +(5.68283 - 6.41459i) q^{72} +(-2.50797 - 1.73113i) q^{73} +(-19.7915 + 17.5337i) q^{74} +(4.09402 - 5.93121i) q^{75} +(4.37780 + 1.66028i) q^{76} +(-6.46695 + 17.0520i) q^{77} +(6.04754 + 9.90305i) q^{78} +(-5.57461 - 14.6990i) q^{79} +22.1442i q^{80} +(1.02831 - 2.71144i) q^{81} +(-1.23651 - 10.1836i) q^{82} +(4.29364 + 8.18084i) q^{83} +(-20.9231 - 14.4421i) q^{84} +(5.87621 + 4.05605i) q^{85} +(1.85482 + 3.53406i) q^{86} +(-0.912141 - 7.51216i) q^{87} +(-8.82174 + 23.2610i) q^{88} +11.6712i q^{89} +(-4.08399 - 10.7686i) q^{90} +(-12.7856 + 10.1099i) q^{91} +(5.67578 - 14.9658i) q^{92} +(-0.371920 - 0.141051i) q^{93} +(10.1807 - 14.7493i) q^{94} +(2.58428 - 2.28947i) q^{95} +(-5.06657 - 3.49720i) q^{96} +(-6.62836 + 7.48187i) q^{97} +(15.8365 - 30.1739i) q^{98} -5.60601i 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 $

$2$	−2.08715	+	1.44065i	−1.47583	+	1.01870i	−0.486397	+	0.873738i	$0.661689\pi$
$2$	−2.08715	+	1.44065i	−1.47583	+	1.01870i	−0.989438	+	0.144957i	$0.953696\pi$
$3$	−1.12364	−	0.589730i	−0.648732	−	0.340481i	0.108052	−	0.994145i	$-0.465539\pi$
$3$	−1.12364	−	0.589730i	−0.648732	−	0.340481i	−0.756785	+	0.653664i	$0.773231\pi$
$4$	1.57149	−	4.14367i	0.785743	−	2.07183i
$5$	−2.16703	−	2.44607i	−0.969125	−	1.09392i	−0.995547	−	0.0942647i	$-0.969950\pi$
$5$	−2.16703	−	2.44607i	−0.969125	−	1.09392i	0.0264226	−	0.999651i	$-0.491588\pi$
$6$	3.19479	−	0.387918i	1.30427	−	0.158367i
$7$	1.08188	+	4.38937i	0.408913	+	1.65902i	0.709073	+	0.705136i	$0.249114\pi$
$7$	1.08188	+	4.38937i	0.408913	+	1.65902i	−0.300160	+	0.953889i	$0.597040\pi$
$8$	1.47582	+	5.98765i	0.521782	+	2.11695i
$9$	−0.789415	−	1.14367i	−0.263138	−	0.381222i
$10$	8.04684	+	1.98337i	2.54463	+	0.627196i
$11$	3.32000	+	2.29163i	1.00102	+	0.690952i	0.951445	−	0.307819i	$-0.0995990\pi$
$11$	3.32000	+	2.29163i	1.00102	+	0.690952i	0.0495718	+	0.998771i	$0.484214\pi$
$12$	−4.20943	+	3.72923i	−1.21516	+	1.07654i
$13$	1.49453	+	3.28122i	0.414507	+	0.910046i
$13$	1.49453	+	3.28122i	0.414507	+	0.910046i
$14$	−8.58159	−	7.60263i	−2.29353	−	2.03189i
$15$	0.992433	+	4.02646i	0.256245	+	1.03963i
$16$	−5.07210	−	4.49349i	−1.26802	−	1.12337i
$17$	−2.12143	+	0.522885i	−0.514522	+	0.126818i	−0.488023	−	0.872831i	$-0.662282\pi$
$17$	−2.12143	+	0.522885i	−0.514522	+	0.126818i	−0.0264984	+	0.999649i	$0.508436\pi$
$18$	3.29525	+	1.24972i	0.776697	+	0.294562i
$19$			1.05650i			0.242378i	0.992629	+	0.121189i	$0.0386708\pi$
$19$			1.05650i			0.242378i	−0.992629	+	0.121189i	$0.961329\pi$
$20$	−13.5412	+	5.13548i	−3.02789	+	1.14833i
$21$	1.37290	−	5.57007i	0.299591	−	1.21549i
$22$	−10.2308			−2.18120
$23$	3.61172			0.753097			0.376548	−	0.926397i	$-0.377111\pi$
$23$	3.61172			0.753097			0.376548	+	0.926397i	$0.377111\pi$
$24$	1.87281	−	7.59828i	0.382286	−	1.55099i
$25$	−0.684560	+	5.63786i	−0.136912	+	1.12757i
$26$	−7.84639	−	4.69528i	−1.53880	−	0.920821i
$27$	0.671443	+	5.52983i	0.129219	+	1.06422i
$28$	19.8882	+	2.41487i	3.75852	+	0.456367i
$29$	3.38752	+	4.90767i	0.629046	+	0.911331i	0.999849	−	0.0173809i	$-0.00553279\pi$
$29$	3.38752	+	4.90767i	0.629046	+	0.911331i	−0.370803	+	0.928712i	$0.620917\pi$
$30$	−7.87208	−	6.97405i	−1.43724	−	1.27328i
$31$	0.311167	−	0.0377825i	0.0558872	−	0.00678593i	−0.0925453	−	0.995708i	$-0.529500\pi$
$31$	0.311167	−	0.0377825i	0.0558872	−	0.00678593i	0.148433	+	0.988923i	$0.452577\pi$
$32$	4.81598	+	0.584766i	0.851354	+	0.103373i
$33$	−2.37903	−	4.53286i	−0.414136	−	0.789070i
$34$	3.67443	−	4.14758i	0.630160	−	0.711303i
$35$	8.39223	−	12.1582i	1.41855	−	2.05512i
$36$	−5.97952	+	1.47382i	−0.996587	+	0.245637i
$37$	10.3500	−	1.25672i	1.70153	−	0.206603i	0.788653	−	0.614838i	$-0.210779\pi$
$37$	10.3500	−	1.25672i	1.70153	−	0.206603i	0.912877	+	0.408235i	$0.133856\pi$
$38$	−1.52205	−	2.20507i	−0.246910	−	0.357710i
$39$	0.255728	−	4.56827i	0.0409492	−	0.731508i
$40$	11.4481	−	16.5854i	1.81010	−	2.62238i
$41$	−1.87980	+	3.58166i	−0.293576	+	0.559362i	−0.986913	−	0.161251i	$-0.948447\pi$
$41$	−1.87980	+	3.58166i	−0.293576	+	0.559362i	0.693338	+	0.720613i	$0.256139\pi$
$42$	5.15910	+	13.6034i	0.796066	+	2.09905i
$43$	0.189699	−	1.56231i	0.0289288	−	0.238250i	−0.971071	−	0.238791i	$-0.923249\pi$
$43$	0.189699	−	1.56231i	0.0289288	−	0.238250i	1.00000		0.000540492i	$0.000172044\pi$
$44$	14.7131	−	10.1557i	2.21808	−	1.53103i
$45$	−1.08680	+	4.40932i	−0.162011	+	0.657303i
$46$	−7.53819	+	5.20324i	−1.11145	+	0.767176i
$47$	−6.60753	+	2.50591i	−0.963808	+	0.365524i	−0.785783	−	0.618502i	$-0.787740\pi$
$47$	−6.60753	+	2.50591i	−0.963808	+	0.365524i	−0.178024	+	0.984026i	$0.556971\pi$
$48$	3.04925	+	8.04022i	0.440122	+	1.16051i
$49$	−11.8979	+	6.24449i	−1.69970	+	0.892070i
$50$	−6.69342	−	12.7532i	−0.946593	−	1.80358i
$51$	2.69208	+	0.663537i	0.376966	+	0.0929138i
$52$	15.9449	−	1.03643i	2.21116	−	0.143728i
$53$	−2.83732	+	0.699337i	−0.389736	+	0.0960614i	−0.429314	−	0.903155i	$-0.641245\pi$
$53$	−2.83732	+	0.699337i	−0.389736	+	0.0960614i	0.0395781	+	0.999216i	$0.487399\pi$
$54$	−9.36796	−	10.5742i	−1.27482	−	1.43897i
$55$	−1.58905	−	13.0870i	−0.214267	−	1.76465i
$56$	−24.6853	+	12.9559i	−3.29871	+	1.73130i
$57$	0.623052	−	1.18713i	0.0825252	−	0.157239i
$58$	−14.1405	−	5.36278i	−1.85674	−	0.704167i
$59$	5.02059	+	5.66707i	0.653625	+	0.737790i	0.978107	−	0.208102i	$-0.0667285\pi$
$59$	5.02059	+	5.66707i	0.653625	+	0.737790i	−0.324482	+	0.945892i	$0.605190\pi$
$60$	18.2439	+	2.21521i	2.35528	+	0.285982i
$61$	−1.29766	−	0.319844i	−0.166148	−	0.0409518i	0.155364	−	0.987857i	$-0.450345\pi$
$61$	−1.29766	−	0.319844i	−0.166148	−	0.0409518i	−0.321512	+	0.946905i	$0.604191\pi$
$62$	−0.595019	+	0.527140i	−0.0755674	+	0.0669469i
$63$	4.16591	−	4.70234i	0.524856	−	0.592439i
$64$	1.10604	−	0.580495i	0.138255	−	0.0725618i
$65$	4.78741	−	10.7662i	0.593805	−	1.33538i
$66$	11.4957	+	6.03339i	1.41502	+	0.742659i
$67$	−5.61892	+	2.13098i	−0.686461	+	0.260340i	−0.673079	−	0.739570i	$-0.735029\pi$
$67$	−5.61892	+	2.13098i	−0.686461	+	0.260340i	−0.0133814	+	0.999910i	$0.504260\pi$
$68$	−1.16713	+	9.61220i	−0.141536	+	1.16565i
$69$	−4.05827	−	2.12994i	−0.488558	−	0.256415i
$70$			37.4663i			4.47808i
$71$	2.89052	−	5.50742i	0.343041	−	0.653611i	−0.651420	−	0.758718i	$-0.725826\pi$
$71$	2.89052	−	5.50742i	0.343041	−	0.653611i	0.994461	+	0.105107i	$0.0335185\pi$
$72$	5.68283	−	6.41459i	0.669728	−	0.755966i
$73$	−2.50797	−	1.73113i	−0.293536	−	0.202613i	0.412191	−	0.911098i	$-0.364764\pi$
$73$	−2.50797	−	1.73113i	−0.293536	−	0.202613i	−0.705726	+	0.708485i	$0.749379\pi$
$74$	−19.7915	+	17.5337i	−2.30071	+	2.03825i
$75$	4.09402	−	5.93121i	0.472736	−	0.684877i
$76$	4.37780	+	1.66028i	0.502168	+	0.190447i
$77$	−6.46695	+	17.0520i	−0.736978	+	1.94325i
$78$	6.04754	+	9.90305i	0.684749	+	1.12130i
$79$	−5.57461	−	14.6990i	−0.627192	−	1.65377i	−0.750078	−	0.661349i	$-0.769984\pi$
$79$	−5.57461	−	14.6990i	−0.627192	−	1.65377i	0.122886	−	0.992421i	$-0.460785\pi$
$80$			22.1442i			2.47580i
$81$	1.02831	−	2.71144i	0.114257	−	0.301271i
$82$	−1.23651	−	10.1836i	−0.136550	−	1.12459i
$83$	4.29364	+	8.18084i	0.471288	+	0.897964i	0.998826	+	0.0484327i	$0.0154226\pi$
$83$	4.29364	+	8.18084i	0.471288	+	0.897964i	−0.527539	+	0.849531i	$0.676885\pi$
$84$	−20.9231	−	14.4421i	−2.28289	−	1.57577i
$85$	5.87621	+	4.05605i	0.637364	+	0.439941i
$86$	1.85482	+	3.53406i	0.200010	+	0.381088i
$87$	−0.912141	−	7.51216i	−0.0977918	−	0.805388i
$88$	−8.82174	+	23.2610i	−0.940401	+	2.47963i
$89$			11.6712i			1.23714i	0.785728	+	0.618572i	$0.212289\pi$
$89$			11.6712i			1.23714i	−0.785728	+	0.618572i	$0.787711\pi$
$90$	−4.08399	−	10.7686i	−0.430490	−	1.13511i
$91$	−12.7856	+	10.1099i	−1.34029	+	1.05981i
$92$	5.67578	−	14.9658i	0.591740	−	1.56029i
$93$	−0.371920	−	0.141051i	−0.0385663	−	0.0146263i
$94$	10.1807	−	14.7493i	1.05006	−	1.52128i
$95$	2.58428	−	2.28947i	0.265141	−	0.234895i
$96$	−5.06657	−	3.49720i	−0.517104	−	0.356931i
$97$	−6.62836	+	7.48187i	−0.673008	+	0.759669i	−0.981480	−	0.191564i	$-0.938644\pi$
$97$	−6.62836	+	7.48187i	−0.673008	+	0.759669i	0.308472	+	0.951233i	$0.400182\pi$
$98$	15.8365	−	30.1739i	1.59972	−	3.04802i
$99$		−	5.60601i		−	0.563425i
$100$	22.2856	+	11.6964i	2.22856	+	1.16964i
$101$	0.442420	−	3.64365i	0.0440224	−	0.362557i	−0.954006	−	0.299788i	$-0.903084\pi$
$101$	0.442420	−	3.64365i	0.0440224	−	0.362557i	0.998028	−	0.0627686i	$-0.0199930\pi$
$102$	−6.57468	+	2.49345i	−0.650990	+	0.246888i
$103$	−2.07723	−	1.09022i	−0.204676	−	0.107422i	0.359271	−	0.933233i	$-0.383025\pi$
$103$	−2.07723	−	1.09022i	−0.204676	−	0.107422i	−0.563947	+	0.825811i	$0.690718\pi$
$104$	−17.4411	+	13.7912i	−1.71024	+	1.35234i
$105$	−16.5999	+	8.71230i	−1.61998	+	0.850234i
$106$	4.91440	−	5.54722i	0.477329	−	0.538793i
$107$	7.96086	−	7.05271i	0.769605	−	0.681811i	−0.183981	−	0.982930i	$-0.558899\pi$
$107$	7.96086	−	7.05271i	0.769605	−	0.681811i	0.953587	+	0.301119i	$0.0973601\pi$
$108$	23.9689	+	5.90781i	2.30641	+	0.568480i
$109$	−2.95191	−	0.358426i	−0.282741	−	0.0343310i	−0.0220626	−	0.999757i	$-0.507023\pi$
$109$	−2.95191	−	0.358426i	−0.282741	−	0.0343310i	−0.260679	+	0.965426i	$0.583946\pi$
$110$	22.1703	+	25.0251i	2.11386	+	2.38605i
$111$	−12.3708	−	4.69162i	−1.17418	−	0.445309i
$112$	14.2361	−	27.1247i	1.34519	−	2.56304i
$113$	4.24363	−	2.22723i	0.399207	−	0.209520i	−0.253158	−	0.967425i	$-0.581469\pi$
$113$	4.24363	−	2.22723i	0.399207	−	0.209520i	0.652365	+	0.757905i	$0.273777\pi$
$114$	0.409836	+	3.37531i	0.0383847	+	0.316126i
$115$	−7.82671	−	8.83453i	−0.729844	−	0.823824i
$116$	25.6592	−	6.32442i	2.38240	−	0.587208i
$117$	2.57281	−	4.29948i	0.237857	−	0.397487i
$118$	−18.6430	−	4.59508i	−1.71623	−	0.423012i
$119$	−4.59027	−	8.74602i	−0.420789	−	0.801746i
$120$	−22.6444	+	11.8847i	−2.06714	+	1.08492i
$121$	1.87017	+	4.93122i	0.170015	+	0.448293i
$122$	3.16918	−	1.20191i	0.286924	−	0.108816i
$123$	4.22443	−	2.91591i	0.380904	−	0.262919i
$124$	0.332436	−	1.34875i	0.0298536	−	0.121121i
$125$	1.82685	−	1.26099i	0.163399	−	0.112786i
$126$	−1.92042	+	15.8161i	−0.171085	+	1.40901i
$127$	3.32053	+	8.75552i	0.294649	+	0.776926i	0.997826	+	0.0659108i	$0.0209953\pi$
$127$	3.32053	+	8.75552i	0.294649	+	0.776926i	−0.703176	+	0.711016i	$0.748235\pi$
$128$	−5.98125	+	11.3963i	−0.528673	+	1.00730i
$129$	−1.13450	+	1.64360i	−0.0998868	+	0.144711i
$130$	5.51835	+	29.3676i	0.483992	+	2.57571i
$131$	3.39091	+	4.91258i	0.296265	+	0.429214i	0.942643	−	0.333804i	$-0.108332\pi$
$131$	3.39091	+	4.91258i	0.296265	+	0.429214i	−0.646377	+	0.763018i	$0.723717\pi$
$132$	−22.5213	+	2.73458i	−1.96023	+	0.238015i
$133$	−4.63738	+	1.14301i	−0.402112	+	0.0991116i
$134$	8.65751	−	12.5426i	0.747895	−	1.08351i
$135$	12.0713	−	13.6257i	1.03893	−	1.17271i
$136$	−6.26170	−	11.9307i	−0.536936	−	1.02305i
$137$	−11.3377	−	1.37665i	−0.968645	−	0.117615i	−0.379105	−	0.925354i	$-0.623768\pi$
$137$	−11.3377	−	1.37665i	−0.968645	−	0.117615i	−0.589540	+	0.807739i	$0.700691\pi$
$138$	11.5387	−	1.40105i	0.982240	−	0.119266i
$139$	7.79404	+	6.90491i	0.661082	+	0.585667i	0.925503	−	0.378740i	$-0.123643\pi$
$139$	7.79404	+	6.90491i	0.661082	+	0.585667i	−0.264422	+	0.964407i	$0.585181\pi$
$140$	−37.1914	−	53.8811i	−3.14325	−	4.55379i
$141$	8.90228	+	1.08093i	0.749707	+	0.0910309i
$142$	1.90135	+	15.6590i	0.159558	+	1.31408i
$143$	−2.55751	+	14.3185i	−0.213870	+	1.19738i
$144$	−1.13505	+	9.34801i	−0.0945878	+	0.779000i
$145$	4.66365	−	18.9212i	0.387295	−	1.57132i
$146$	7.72845			0.639611
$147$	17.0515			1.40638
$148$	11.0575	−	44.8619i	0.908918	−	3.68763i
$149$	15.0501	−	5.70774i	1.23295	−	0.467596i	0.349860	−	0.936802i	$-0.386229\pi$
$149$	15.0501	−	5.70774i	1.23295	−	0.467596i	0.883089	+	0.469206i	$0.155460\pi$
$150$			18.2773i			1.49234i
$151$	−2.53250	−	0.960451i	−0.206092	−	0.0781604i	0.249399	−	0.968401i	$-0.419767\pi$
$151$	−2.53250	−	0.960451i	−0.206092	−	0.0781604i	−0.455491	+	0.890240i	$0.650536\pi$
$152$	−6.32597	+	1.55921i	−0.513104	+	0.126469i
$153$	2.27269	+	2.01343i	0.183736	+	0.162776i
$154$	−11.0685	−	44.9065i	−0.891923	−	3.61867i
$155$	−0.766726	−	0.679260i	−0.0615849	−	0.0545594i
$156$	−18.5275	−	8.23862i	−1.48339	−	0.659618i
$157$	6.33967	−	5.61646i	0.505961	−	0.448242i	−0.371120	−	0.928585i	$-0.621026\pi$
$157$	6.33967	−	5.61646i	0.505961	−	0.448242i	0.877081	+	0.480343i	$0.159488\pi$
$158$	32.8112	+	22.6479i	2.61032	+	1.80177i
$159$	3.60054	+	0.887454i	0.285542	+	0.0703797i
$160$	−9.00600	−	13.0474i	−0.711987	−	1.03149i
$161$	3.90746	+	15.8532i	0.307951	+	1.24941i
$162$	1.76000	+	7.14060i	0.138279	+	0.561019i
$163$	1.95998	−	0.237984i	0.153517	−	0.0186404i	−0.0434172	−	0.999057i	$-0.513824\pi$
$163$	1.95998	−	0.237984i	0.153517	−	0.0186404i	0.196934	+	0.980417i	$0.436901\pi$
$164$	11.8871	+	13.4178i	0.928229	+	1.04775i
$165$	−5.93227	+	15.6421i	−0.461827	+	1.21774i
$166$	−20.7472	−	10.8890i	−1.61029	−	0.845147i
$167$	−6.27653	+	4.33238i	−0.485693	+	0.335250i	−0.785617	−	0.618714i	$-0.787654\pi$
$167$	−6.27653	+	4.33238i	−0.485693	+	0.335250i	0.299924	+	0.953963i	$0.403039\pi$
$168$	35.3778			2.72946
$169$	−8.53278	+	9.80773i	−0.656368	+	0.754441i
$170$	−18.1079			−1.38881
$171$	1.20829	−	0.834019i	0.0923999	−	0.0637790i
$172$	−6.17559	−	3.24120i	−0.470885	−	0.247139i
$173$	−2.64025	+	6.96176i	−0.200734	+	0.529293i	−0.997149	−	0.0754579i	$-0.975958\pi$
$173$	−2.64025	+	6.96176i	−0.200734	+	0.529293i	0.796415	+	0.604751i	$0.206727\pi$
$174$	12.7262	+	14.3649i	0.964769	+	1.08900i
$175$	−25.4872	+	3.09471i	−1.92665	+	0.233938i
$176$	−6.54195	−	26.5417i	−0.493118	−	2.00066i
$177$	−2.29928	−	9.32853i	−0.172824	−	0.701175i
$178$	−16.8141	−	24.3595i	−1.26027	−	1.82582i
$179$	18.1263	+	4.46772i	1.35482	+	0.333933i	0.848857	−	0.528622i	$-0.177291\pi$
$179$	18.1263	+	4.46772i	1.35482	+	0.333933i	0.505963	+	0.862555i	$0.331137\pi$
$180$	16.5629	+	11.4325i	1.23452	+	0.852130i
$181$	10.9966	−	9.74215i	0.817372	−	0.724128i	−0.146869	−	0.989156i	$-0.546920\pi$
$181$	10.9966	−	9.74215i	0.817372	−	0.724128i	0.964241	+	0.265028i	$0.0853811\pi$
$182$	12.1205	−	39.5204i	0.898428	−	2.92945i
$183$	1.26947	+	1.12466i	0.0938423	+	0.0831370i
$184$	5.33027	+	21.6257i	0.392952	+	1.59427i
$185$	−25.5028	−	22.5935i	−1.87500	−	1.66111i
$186$	0.979456	−	0.241414i	0.0718172	−	0.0177013i
$187$	−8.24139	−	3.12555i	−0.602670	−	0.228563i
$188$			31.3174i			2.28406i
$189$	−23.5460	+	8.92983i	−1.71272	+	0.649549i
$190$	−2.09543	+	8.50151i	−0.152019	+	0.616764i
$191$	5.43446			0.393224			0.196612	−	0.980481i	$-0.437006\pi$
$191$	5.43446			0.393224			0.196612	+	0.980481i	$0.437006\pi$
$192$	−1.58512			−0.114396
$193$	1.80581	−	7.32645i	0.129985	−	0.527370i	−0.869458	−	0.494006i	$-0.835532\pi$
$193$	1.80581	−	7.32645i	0.129985	−	0.527370i	0.999443	−	0.0333634i	$-0.0106219\pi$
$194$	3.05557	−	25.1649i	0.219377	−	1.80674i
$195$	−11.7285	+	9.27404i	−0.839893	+	0.664128i
$196$	7.17774	+	59.1140i	0.512696	+	4.22243i
$197$	−24.6410	−	2.99196i	−1.75560	−	0.213169i	−0.821508	−	0.570197i	$-0.806867\pi$
$197$	−24.6410	−	2.99196i	−1.75560	−	0.213169i	−0.934093	+	0.357029i	$0.883790\pi$
$198$	8.07631	+	11.7006i	0.573959	+	0.831523i
$199$	7.84415	+	6.94931i	0.556057	+	0.492623i	0.893709	−	0.448648i	$-0.148094\pi$
$199$	7.84415	+	6.94931i	0.556057	+	0.492623i	−0.337652	+	0.941271i	$0.609633\pi$
$200$	−34.7678	+	4.22158i	−2.45846	+	0.298511i
$201$	7.57033	+	0.919205i	0.533970	+	0.0648357i
$202$	4.32584	+	8.24221i	0.304365	+	0.579920i
$203$	−17.8767	+	20.1786i	−1.25470	+	1.41626i
$204$	6.98004	−	10.1123i	0.488700	−	0.708005i
$205$	12.8346	−	3.16344i	0.896406	−	0.220944i
$206$	5.90611	−	0.717131i	0.411498	−	0.0499649i
$207$	−2.85115	−	4.13060i	−0.198169	−	0.287097i
$208$	7.16372	−	23.3583i	0.496715	−	1.61961i
$209$	−2.42111	+	3.50759i	−0.167472	+	0.242625i
$210$	22.0950	−	42.0985i	1.52470	−	2.90507i
$211$	8.54221	+	22.5240i	0.588070	+	1.55061i	0.816677	+	0.577095i	$0.195814\pi$
$211$	8.54221	+	22.5240i	0.588070	+	1.55061i	−0.228607	+	0.973519i	$0.573417\pi$
$212$	−1.56099	+	12.8559i	−0.107209	+	0.882949i
$213$	−6.49579	+	4.48372i	−0.445084	+	0.307219i
$214$	−6.45497	+	26.1888i	−0.441253	+	1.79023i
$215$	−4.23261	+	2.92156i	−0.288661	+	0.199249i
$216$	−32.1197	+	12.1814i	−2.18547	+	0.828840i
$217$	0.502487	+	1.32495i	0.0341110	+	0.0899434i
$218$	6.67743	−	3.50458i	0.452252	−	0.237360i
$219$	1.79715	+	3.42419i	0.121440	+	0.231385i
$220$	−56.7252	−	13.9815i	−3.82441	−	0.942633i
$221$	−4.88623	−	6.17940i	−0.328683	−	0.415671i
$222$	32.5786	−	8.02990i	2.18653	−	0.538932i
$223$	2.46404	+	2.78132i	0.165004	+	0.186251i	0.825197	−	0.564845i	$-0.191064\pi$
$223$	2.46404	+	2.78132i	0.165004	+	0.186251i	−0.660193	+	0.751096i	$0.729526\pi$
$224$	2.64357	+	21.7718i	0.176631	+	1.45469i
$225$	6.98823	−	3.66770i	0.465882	−	0.244514i
$226$	−5.64841	+	10.7621i	−0.375726	+	0.715887i
$227$	5.26039	+	1.99500i	0.349144	+	0.132413i	0.522942	−	0.852368i	$-0.324835\pi$
$227$	5.26039	+	1.99500i	0.349144	+	0.132413i	−0.173797	+	0.984781i	$0.555604\pi$
$228$	−3.93994	−	4.44727i	−0.260929	−	0.294528i
$229$	−17.8893	−	2.17215i	−1.18216	−	0.143540i	−0.494237	−	0.869327i	$-0.664553\pi$
$229$	−17.8893	−	2.17215i	−1.18216	−	0.143540i	−0.687919	+	0.725787i	$0.741476\pi$
$230$	29.0630	+	7.16338i	1.91636	+	0.472339i
$231$	17.3226	−	15.3465i	1.13974	−	1.00972i
$232$	−24.3860	+	27.5261i	−1.60102	+	1.80718i
$233$	−9.30221	+	4.88217i	−0.609408	+	0.319842i	−0.741044	−	0.671456i	$-0.765669\pi$
$233$	−9.30221	+	4.88217i	−0.609408	+	0.319842i	0.131636	+	0.991298i	$0.457977\pi$
$234$	0.824223	+	12.6802i	0.0538812	+	0.828929i
$235$	20.4483	+	10.7321i	1.33390	+	0.700086i
$236$	31.3723	−	11.8979i	2.04216	−	0.774489i
$237$	−2.40463	+	19.8039i	−0.156197	+	1.28640i
$238$	22.1805	+	11.6412i	1.43775	+	0.754589i
$239$		−	9.48356i		−	0.613441i	−0.951800	−	0.306720i	$-0.900768\pi$
$239$		−	9.48356i		−	0.613441i	0.951800	−	0.306720i	$-0.0992316\pi$
$240$	13.0591	−	24.8821i	0.842962	−	1.60613i
$241$	18.3608	−	20.7251i	1.18272	−	1.33502i	0.252689	−	0.967548i	$-0.418685\pi$
$241$	18.3608	−	20.7251i	1.18272	−	1.33502i	0.930035	−	0.367471i	$-0.119776\pi$
$242$	−11.0075	−	7.59792i	−0.707588	−	0.488413i
$243$	9.75414	−	8.64142i	0.625729	−	0.554347i
$244$	−3.36458	+	4.87443i	−0.215395	+	0.312054i
$245$	41.0575	+	15.5711i	2.62307	+	0.994798i
$246$	−4.61618	+	12.1719i	−0.294317	+	0.776050i
$247$	−3.46662	+	1.57897i	−0.220575	+	0.100468i
$248$	0.685455	+	1.80740i	0.0435264	+	0.114770i
$249$		−	11.7244i		−	0.743003i
$250$	−1.99627	+	5.26372i	−0.126255	+	0.332907i
$251$	−3.16323	−	26.0516i	−0.199661	−	1.64436i	−0.656150	−	0.754630i	$-0.727816\pi$
$251$	−3.16323	−	26.0516i	−0.199661	−	1.64436i	0.456489	−	0.889729i	$-0.349107\pi$
$252$	−12.9383	−	24.6518i	−0.815035	−	1.55292i
$253$	11.9909	+	8.27673i	0.753862	+	0.520354i
$254$	−19.5441	−	13.4903i	−1.22630	−	0.846457i
$255$	−4.21075	−	8.02291i	−0.263687	−	0.502414i
$256$	−3.63327	−	29.9227i	−0.227079	−	1.87017i
$257$	10.5134	−	27.7215i	0.655805	−	1.72922i	−0.0280578	−	0.999606i	$-0.508932\pi$
$257$	10.5134	−	27.7215i	0.655805	−	1.72922i	0.683863	−	0.729610i	$-0.260299\pi$
$258$		−	5.06485i		−	0.315324i
$259$	16.7137	+	44.0703i	1.03854	+	2.73840i
$260$	−37.0883	−	36.7564i	−2.30012	−	2.27953i
$261$	2.93857	−	7.74837i	0.181893	−	0.479612i
$262$	−14.1546	−	5.36815i	−0.874477	−	0.331645i
$263$	2.23291	−	3.23493i	0.137687	−	0.199474i	−0.748074	−	0.663615i	$-0.769021\pi$
$263$	2.23291	−	3.23493i	0.137687	−	0.199474i	0.885762	+	0.464141i	$0.153637\pi$
$264$	23.6302	−	20.9345i	1.45434	−	1.28843i
$265$	7.85919	+	5.42481i	0.482786	+	0.333243i
$266$	8.03220	−	9.06648i	0.492486	−	0.555901i
$267$	6.88286	−	13.1142i	0.421224	−	0.802575i
$268$			26.6318i			1.62679i
$269$	−12.2557	−	6.43227i	−0.747241	−	0.392182i	0.0477059	−	0.998861i	$-0.484809\pi$
$269$	−12.2557	−	6.43227i	−0.747241	−	0.392182i	−0.794947	+	0.606679i	$0.792501\pi$
$270$	−5.56469	+	45.8294i	−0.338656	+	2.78909i
$271$	−18.0214	+	6.83460i	−1.09472	+	0.415172i	−0.834854	−	0.550472i	$-0.814448\pi$
$271$	−18.0214	+	6.83460i	−1.09472	+	0.415172i	−0.259866	+	0.965645i	$0.583678\pi$
$272$	13.1097	+	6.88048i	0.794890	+	0.417190i
$273$	20.3285	−	3.81984i	1.23033	−	0.231187i
$274$	25.6467	−	13.4604i	1.54937	−	0.813174i
$275$	−15.1926	+	17.1489i	−0.916149	+	1.03412i
$276$	−15.2033	+	13.4689i	−0.915131	+	0.810735i
$277$	−15.5133	−	3.82368i	−0.932103	−	0.229743i	−0.256107	−	0.966648i	$-0.582440\pi$
$277$	−15.5133	−	3.82368i	−0.932103	−	0.229743i	−0.675996	+	0.736906i	$0.736286\pi$
$278$	−26.2149	−	3.18306i	−1.57226	−	0.190907i
$279$	−0.288850	−	0.326044i	−0.0172930	−	0.0195198i
$280$	85.1847	+	32.3063i	5.09076	+	1.93067i
$281$	11.3344	−	21.5959i	0.676155	−	1.28830i	−0.269459	−	0.963012i	$-0.586845\pi$
$281$	11.3344	−	21.5959i	0.676155	−	1.28830i	0.945613	−	0.325293i	$-0.105463\pi$
$282$	−20.1376	+	10.5690i	−1.19918	+	0.629376i
$283$	−2.00640	−	16.5242i	−0.119268	−	0.982260i	−0.922340	−	0.386378i	$-0.873726\pi$
$283$	−2.00640	−	16.5242i	−0.119268	−	0.982260i	0.803072	−	0.595881i	$-0.203197\pi$
$284$	−18.2785	−	20.6322i	−1.08463	−	1.22429i
$285$	−4.25396	+	1.04851i	−0.251983	+	0.0621082i
$286$	−15.2901	−	33.5693i	−0.904125	−	1.98500i
$287$	−17.7549	−	4.37620i	−1.04804	−	0.258319i
$288$	−3.13303	−	5.96950i	−0.184616	−	0.351756i
$289$	−10.8257	+	5.68177i	−0.636806	+	0.334222i
$290$	17.5251	+	46.2099i	1.02911	+	2.71354i
$291$	11.8602	−	4.49797i	0.695255	−	0.263675i
$292$	−11.1145	+	7.67176i	−0.650425	+	0.448956i
$293$	1.44135	−	5.84777i	0.0842043	−	0.341630i	−0.913696	−	0.406398i	$-0.866785\pi$
$293$	1.44135	−	5.84777i	0.0842043	−	0.341630i	0.997900	+	0.0647679i	$0.0206307\pi$
$294$	−35.5889	+	24.5652i	−2.07559	+	1.43267i
$295$	2.98230	−	24.5614i	0.173636	−	1.43002i
$296$	22.7996	+	60.1175i	1.32520	+	3.49426i
$297$	−10.4431	+	19.8977i	−0.605972	+	1.15458i
$298$	−23.1888	+	33.5948i	−1.34329	+	1.94609i
$299$	5.39782	+	11.8509i	0.312164	+	0.685353i
$300$	−18.1433	−	26.2850i	−1.04750	−	1.51757i
$301$	7.06279	−	0.857578i	0.407093	−	0.0494300i
$302$	6.66937	−	1.64385i	0.383779	−	0.0945931i
$303$	−2.64589	+	3.83324i	−0.152003	+	0.220214i
$304$	4.74738	−	5.35868i	0.272281	−	0.307342i
$305$	2.02970	+	3.86727i	0.116220	+	0.221439i
$306$	−7.64409	−	0.928160i	−0.436983	−	0.0530594i
$307$	22.3992	−	2.71976i	1.27839	−	0.155225i	0.546971	−	0.837152i	$-0.315781\pi$
$307$	22.3992	−	2.71976i	1.27839	−	0.155225i	0.731420	+	0.681927i	$0.238858\pi$
$308$	60.4949	+	53.5938i	3.44702	+	3.05379i
$309$	1.69112	+	2.45001i	0.0962046	+	0.139376i
$310$	2.57884	+	0.313128i	0.146469	+	0.0177845i
$311$	−0.827340	−	6.81376i	−0.0469142	−	0.386373i	−0.997187	−	0.0749543i	$-0.976119\pi$
$311$	−0.827340	−	6.81376i	−0.0469142	−	0.386373i	0.950273	−	0.311419i	$-0.100804\pi$
$312$	27.7306	−	5.21074i	1.56994	−	0.295000i
$313$	−2.16036	+	17.7921i	−0.122111	+	1.00567i	0.794881	+	0.606765i	$0.207533\pi$
$313$	−2.16036	+	17.7921i	−0.122111	+	1.00567i	−0.916992	+	0.398906i	$0.869390\pi$
$314$	−5.14045	+	20.8556i	−0.290093	+	1.17695i
$315$	−20.5299			−1.15673
$316$	−69.6683			−3.91915
$317$	3.63805	−	14.7601i	0.204333	−	0.829012i	−0.775850	−	0.630917i	$-0.782679\pi$
$317$	3.63805	−	14.7601i	0.204333	−	0.829012i	0.980183	−	0.198094i	$-0.0634752\pi$
$318$	−8.79337	+	3.33489i	−0.493108	+	0.187011i
$319$			24.0564i			1.34690i
$320$	−3.81675	−	1.44750i	−0.213363	−	0.0809178i
$321$	−13.1043	+	3.22992i	−0.731411	+	0.180277i
$322$	−30.9944	−	27.4586i	−1.72725	−	1.53021i
$323$	−0.552429	−	2.24129i	−0.0307380	−	0.124709i
$324$	−9.61932	−	8.52197i	−0.534407	−	0.473443i
$325$	−19.5221	+	6.17974i	−1.08289	+	0.342790i
$326$	−3.74790	+	3.32035i	−0.207577	+	0.183897i
$327$	3.10550	+	2.14357i	0.171734	+	0.118540i
$328$	−24.2200	−	5.96969i	−1.33732	−	0.329621i
$329$	−18.1479	−	26.2918i	−1.00053	−	1.44951i
$330$	−10.1533	−	41.1937i	−0.558923	−	2.26764i
$331$	−8.40186	−	34.0877i	−0.461808	−	1.87363i	−0.486065	−	0.873923i	$-0.661568\pi$
$331$	−8.40186	−	34.0877i	−0.461808	−	1.87363i	0.0242567	−	0.999706i	$-0.492278\pi$
$332$	40.6461	−	4.93533i	2.23074	−	0.270861i
$333$	−9.60771	−	10.8449i	−0.526499	−	0.594295i
$334$	6.85859	−	18.0846i	0.375285	−	0.989546i
$335$	17.3889	+	9.12639i	0.950056	+	0.498628i
$336$	−31.9925	+	22.0828i	−1.74534	+	1.20472i
$337$	17.8241			0.970941			0.485470	−	0.874253i	$-0.338648\pi$
$337$	17.8241			0.970941			0.485470	+	0.874253i	$0.338648\pi$
$338$	3.67962	−	32.7629i	0.200145	−	1.78207i
$339$	−6.08176			−0.330316
$340$	26.0413	−	17.9750i	1.41229	−	0.974832i
$341$	1.11966	+	0.587641i	0.0606328	+	0.0318225i
$342$	−1.32034	+	3.48144i	−0.0713956	+	0.188255i
$343$	−19.2968	−	21.7816i	−1.04193	−	1.17610i
$344$	9.63454	−	1.16984i	0.519460	−	0.0630738i
$345$	3.58439	+	14.5425i	0.192977	+	0.782940i
$346$	−4.51890	−	18.3339i	−0.242938	−	0.985636i
$347$	−3.11548	−	4.51355i	−0.167248	−	0.242300i	0.730394	−	0.683026i	$-0.239336\pi$
$347$	−3.11548	−	4.51355i	−0.167248	−	0.242300i	−0.897642	+	0.440726i	$0.854721\pi$
$348$	−32.5613	−	8.02564i	−1.74547	−	0.430220i
$349$	12.9358	+	8.92893i	0.692437	+	0.477955i	0.861570	−	0.507639i	$-0.169481\pi$
$349$	12.9358	+	8.92893i	0.692437	+	0.477955i	−0.169133	+	0.985593i	$0.554097\pi$
$350$	48.7372	−	43.1774i	2.60511	−	2.30793i
$351$	−17.1411	+	10.4676i	−0.914923	+	0.558721i
$352$	14.6490	+	12.9779i	0.780794	+	0.691723i
$353$	1.40183	+	5.68743i	0.0746117	+	0.302711i	0.996378	−	0.0850343i	$-0.0271000\pi$
$353$	1.40183	+	5.68743i	0.0746117	+	0.302711i	−0.921766	+	0.387746i	$0.873254\pi$
$354$	18.2381	+	16.1575i	0.969344	+	0.858764i
$355$	−19.7354	+	4.86433i	−1.04744	+	0.258172i
$356$	48.3616	+	18.3411i	2.56316	+	0.972077i
$357$			12.5344i			0.663390i
$358$	−44.2686	+	16.7889i	−2.33967	+	0.887319i
$359$	−4.40190	+	17.8592i	−0.232323	+	0.942572i	0.732730	+	0.680519i	$0.238246\pi$
$359$	−4.40190	+	17.8592i	−0.232323	+	0.942572i	−0.965053	+	0.262053i	$0.915600\pi$
$360$	−28.0054			−1.47601
$361$	17.8838			0.941253
$362$	−8.91648	+	36.1756i	−0.468640	+	1.90135i
$363$	0.806704	−	6.64380i	0.0423410	−	0.348709i
$364$	21.7998	+	68.8667i	1.14262	+	3.60960i
$365$	1.20039	+	9.88607i	0.0628311	+	0.517461i
$366$	−4.26982	−	0.518450i	−0.223187	−	0.0270998i
$367$	−5.09446	−	7.38061i	−0.265929	−	0.385264i	0.667158	−	0.744917i	$-0.267511\pi$
$367$	−5.09446	−	7.38061i	−0.265929	−	0.385264i	−0.933086	+	0.359652i	$0.882895\pi$
$368$	−18.3190	−	16.2292i	−0.954945	−	0.846007i
$369$	5.58016	−	0.677555i	0.290492	−	0.0352721i
$370$	85.7773	+	10.4153i	4.45935	+	0.541463i
$371$	−6.13930	−	11.6975i	−0.318736	−	0.607301i
$372$	−1.16893	+	1.31945i	−0.0606064	+	0.0684105i
$373$	5.84708	−	8.47095i	0.302750	−	0.438609i	−0.641851	−	0.766829i	$-0.721833\pi$
$373$	5.84708	−	8.47095i	0.302750	−	0.438609i	0.944601	+	0.328220i	$0.106449\pi$
$374$	21.7038	−	5.34951i	1.12228	−	0.276616i
$375$	−2.79636	+	0.339540i	−0.144404	+	0.0175338i
$376$	−24.7560	−	35.8653i	−1.27670	−	1.84961i
$377$	−11.0404	+	18.4498i	−0.568609	+	0.950214i
$378$	36.2792	−	52.5595i	1.86600	−	2.70337i
$379$	−1.19735	+	2.28137i	−0.0615040	+	0.117186i	−0.914267	−	0.405112i	$-0.867233\pi$
$379$	−1.19735	+	2.28137i	−0.0615040	+	0.117186i	0.852763	+	0.522298i	$0.174925\pi$
$380$	−5.42565	−	14.3063i	−0.278330	−	0.733896i
$381$	1.43232	−	11.7962i	0.0733801	−	0.604340i
$382$	−11.3425	+	7.82917i	−0.580333	+	0.400575i
$383$	5.70627	−	23.1513i	0.291577	−	1.18297i	−0.624193	−	0.781270i	$-0.714572\pi$
$383$	5.70627	−	23.1513i	0.291577	−	1.18297i	0.915770	−	0.401704i	$-0.131582\pi$
$384$	13.4415	−	9.27801i	0.685934	−	0.473466i
$385$	55.7243	−	21.1335i	2.83998	−	1.07706i
$386$	6.78589	+	17.8929i	0.345393	+	0.910725i
$387$	−1.93651	+	1.01636i	−0.0984385	+	0.0516645i
$388$	20.5860	+	39.2234i	1.04510	+	1.99127i
$389$	21.9652	+	5.41395i	1.11368	+	0.274498i	0.752889	−	0.658148i	$-0.228660\pi$
$389$	21.9652	+	5.41395i	1.11368	+	0.274498i	0.360793	+	0.932646i	$0.382506\pi$
$390$	11.1184	−	36.2529i	0.563000	−	1.83574i
$391$	−7.66201	+	1.88852i	−0.387485	+	0.0955064i
$392$	−54.9490	−	62.0246i	−2.77534	−	3.13271i
$393$	−0.913055	−	7.51968i	−0.0460575	−	0.379318i
$394$	55.7398	−	29.2545i	2.80813	−	1.47382i
$395$	−23.8745	+	45.4891i	−1.20126	+	2.28880i
$396$	−23.2295	−	8.80977i	−1.16732	−	0.442708i
$397$	−23.2522	−	26.2463i	−1.16699	−	1.31726i	−0.939127	−	0.343571i	$-0.888363\pi$
$397$	−23.2522	−	26.2463i	−1.16699	−	1.31726i	−0.227867	−	0.973692i	$-0.573175\pi$
$398$	−26.3834	−	3.20353i	−1.32248	−	0.160578i
$399$	5.88480	+	1.45047i	0.294608	+	0.0726145i
$400$	28.8058	−	25.5197i	1.44029	−	1.27599i
$401$	−9.43276	+	10.6474i	−0.471049	+	0.531705i	−0.935232	−	0.354034i	$-0.884810\pi$
$401$	−9.43276	+	10.6474i	−0.471049	+	0.531705i	0.464183	+	0.885739i	$0.346348\pi$
$402$	−17.1246	+	8.98771i	−0.854100	+	0.448266i
$403$	0.589019	+	0.964539i	0.0293411	+	0.0480471i
$404$	−14.4028	−	7.55919i	−0.716568	−	0.376084i
$405$	−8.86075	+	3.36044i	−0.440294	+	0.166982i
$406$	8.24087	−	67.8696i	0.408987	−	3.36831i
$407$	37.2419	+	19.5461i	1.84601	+	0.968862i
$408$			17.0985i			0.846500i
$409$	−16.0734	+	30.6252i	−0.794776	+	1.51432i	0.0616781	+	0.998096i	$0.480355\pi$
$409$	−16.0734	+	30.6252i	−0.794776	+	1.51432i	−0.856454	+	0.516223i	$0.827338\pi$
$410$	−22.2302	+	25.0927i	−1.09787	+	1.23924i
$411$	11.9276	+	8.23304i	0.588346	+	0.406106i
$412$	−7.78184	+	6.89410i	−0.383384	+	0.339648i
$413$	−19.4432	+	28.1683i	−0.956736	+	1.38607i
$414$	11.9015	+	4.51365i	0.584928	+	0.221834i
$415$	10.7065	−	28.2306i	0.525560	−	1.38579i
$416$	5.27887	+	16.6762i	0.258818	+	0.817620i
$417$	−4.68563	−	12.3550i	−0.229456	−	0.605027i
$418$		−	10.8088i		−	0.528677i
$419$	−0.299663	+	0.790146i	−0.0146395	+	0.0386012i	−0.942137	−	0.335229i	$-0.891186\pi$
$419$	−0.299663	+	0.790146i	−0.0146395	+	0.0386012i	0.927497	+	0.373830i	$0.121956\pi$
$420$	10.0144	+	82.4758i	0.488651	+	4.02441i
$421$	5.96064	+	11.3571i	0.290504	+	0.553509i	0.986346	−	0.164686i	$-0.0526610\pi$
$421$	5.96064	+	11.3571i	0.290504	+	0.553509i	−0.695842	+	0.718195i	$0.744969\pi$
$422$	−50.2780	−	34.7044i	−2.44750	−	1.68939i
$423$	8.08200	+	5.57860i	0.392960	+	0.271241i
$424$	−8.37477	−	15.9568i	−0.406715	−	0.774931i
$425$	−1.49571	−	12.3183i	−0.0725524	−	0.597523i
$426$	7.09817	−	18.7163i	0.343908	−	0.906810i
$427$		−	6.04193i		−	0.292389i
$428$	−16.7137	−	44.0704i	−0.807887	−	2.13022i
$429$	11.3178	−	14.5806i	0.546428	−	0.703958i
$430$	4.62512	−	12.1954i	0.223043	−	0.588116i
$431$	35.6530	+	13.5214i	1.71734	+	0.651303i	0.999014	−	0.0443995i	$-0.0141375\pi$
$431$	35.6530	+	13.5214i	1.71734	+	0.651303i	0.718330	+	0.695702i	$0.244907\pi$
$432$	21.4426	−	31.0649i	1.03166	−	1.49461i
$433$	−27.2456	+	24.1375i	−1.30934	+	1.15997i	−0.333192	+	0.942859i	$0.608126\pi$
$433$	−27.2456	+	24.1375i	−1.30934	+	1.15997i	−0.976146	+	0.217113i	$0.930336\pi$
$434$	−2.95755	−	2.04145i	−0.141967	−	0.0979928i
$435$	−16.3986	+	18.5102i	−0.786254	+	0.887497i
$436$	−6.12408	+	11.6685i	−0.293290	+	0.558818i
$437$			3.81580i			0.182534i
$438$	−8.68398	−	4.55770i	−0.414936	−	0.217775i
$439$	2.71002	−	22.3190i	0.129342	−	1.06523i	−0.773060	−	0.634334i	$-0.781275\pi$
$439$	2.71002	−	22.3190i	0.129342	−	1.06523i	0.902402	−	0.430896i	$-0.141802\pi$
$440$	76.0150	−	28.8287i	3.62387	−	1.37435i
$441$	16.5340	+	8.67770i	0.787332	+	0.413224i
$442$	19.1006	+	5.85795i	0.908524	+	0.278634i
$443$	−34.7850	+	18.2566i	−1.65268	+	0.867395i	−0.659386	+	0.751805i	$0.729184\pi$
$443$	−34.7850	+	18.2566i	−1.65268	+	0.867395i	−0.993297	+	0.115590i	$0.963124\pi$
$444$	−38.8810	+	43.8876i	−1.84521	+	2.08281i
$445$	28.5486	−	25.2918i	1.35333	−	1.19895i
$446$	−9.14972	−	2.25520i	−0.433252	−	0.106787i
$447$	−20.2768	−	2.46205i	−0.959062	−	0.116451i
$448$	3.74461	+	4.22679i	0.176916	+	0.199697i
$449$	1.21196	+	0.459636i	0.0571960	+	0.0216916i	0.383037	−	0.923733i	$-0.374878\pi$
$449$	1.21196	+	0.459636i	0.0571960	+	0.0216916i	−0.325841	+	0.945425i	$0.605647\pi$
$450$	−9.30156	+	17.7226i	−0.438480	+	0.835453i
$451$	−14.4488	+	7.58330i	−0.680366	+	0.357084i
$452$	−2.56009	−	21.0842i	−0.120417	−	0.991719i
$453$	2.27921	+	2.57269i	0.107086	+	0.120876i
$454$	−13.8533	+	3.41453i	−0.650168	+	0.160252i
$455$	52.4362	+	9.36591i	2.45825	+	0.439081i
$456$	8.02761	+	1.97863i	0.375927	+	0.0926577i
$457$	5.86972	+	11.1838i	0.274574	+	0.523157i	0.983224	−	0.182404i	$-0.0583877\pi$
$457$	5.86972	+	11.1838i	0.274574	+	0.523157i	−0.708650	+	0.705560i	$0.750695\pi$
$458$	40.4668	−	21.2386i	1.89089	−	0.992416i
$459$	−4.31588	−	11.3800i	−0.201448	−	0.531175i
$460$	−48.9069	+	18.5480i	−2.28030	+	0.864803i
$461$	10.8881	−	7.51553i	0.507111	−	0.350033i	−0.286877	−	0.957968i	$-0.592617\pi$
$461$	10.8881	−	7.51553i	0.507111	−	0.350033i	0.793987	+	0.607934i	$0.208002\pi$
$462$	−14.0458	+	56.9861i	−0.653470	+	2.65123i
$463$	20.2963	−	14.0095i	0.943248	−	0.651077i	0.00608952	−	0.999981i	$-0.498062\pi$
$463$	20.2963	−	14.0095i	0.943248	−	0.651077i	0.937158	+	0.348905i	$0.113446\pi$
$464$	4.87071	−	40.1139i	0.226117	−	1.86224i
$465$	0.460942	+	1.21540i	0.0213757	+	0.0563630i
$466$	12.3815	−	23.5911i	0.573564	−	1.09283i
$467$	−3.50539	+	5.07843i	−0.162210	+	0.235002i	−0.895658	−	0.444744i	$-0.853295\pi$
$467$	−3.50539	+	5.07843i	−0.162210	+	0.235002i	0.733448	+	0.679746i	$0.237910\pi$
$468$	−13.7725	−	17.4175i	−0.636633	−	0.805122i
$469$	−15.4326	−	22.3581i	−0.712613	−	1.03240i
$470$	−58.1399	+	7.05946i	−2.68179	+	0.325629i
$471$	−10.4357	+	2.57217i	−0.480851	+	0.118519i
$472$	−26.5230	+	38.4251i	−1.22082	+	1.76866i
$473$	4.21004	−	4.75215i	0.193578	−	0.218504i
$474$	−23.5117	−	44.7978i	−1.07993	−	2.05763i
$475$	−5.95641	−	0.723240i	−0.273299	−	0.0331845i
$476$	−43.4542	+	5.27629i	−1.99172	+	0.241838i
$477$	3.03963	+	2.69288i	0.139175	+	0.123299i
$478$	13.6625	+	19.7936i	0.624909	+	0.905337i
$479$	−0.994422	−	0.120745i	−0.0454363	−	0.00551697i	0.0977870	−	0.995207i	$-0.468824\pi$
$479$	−0.994422	−	0.120745i	−0.0454363	−	0.00551697i	−0.143223	+	0.989690i	$0.545747\pi$
$480$	2.42500	+	19.9717i	0.110686	+	0.911579i
$481$	19.5919	+	32.0824i	0.893315	+	1.46283i
$482$	−8.46406	+	69.7078i	−0.385527	+	3.17510i
$483$	4.95854	−	20.1176i	0.225621	−	0.915381i
$484$	23.3723			1.06238
$485$	32.6650			1.48324
$486$	−7.90904	+	32.0882i	−0.358761	+	1.45555i
$487$	9.99546	−	3.79078i	0.452938	−	0.171777i	−0.117577	−	0.993064i	$-0.537513\pi$
$487$	9.99546	−	3.79078i	0.452938	−	0.171777i	0.570515	+	0.821287i	$0.306744\pi$
$488$		−	8.24195i		−	0.373096i
$489$	−2.34265	−	0.888450i	−0.105938	−	0.0401771i
$490$	−108.125	+	26.6505i	−4.88461	+	1.20395i
$491$	18.5849	+	16.4648i	0.838725	+	0.743045i	0.968637	−	0.248480i	$-0.0799311\pi$
$491$	18.5849	+	16.4648i	0.838725	+	0.743045i	−0.129912	+	0.991526i	$0.541470\pi$
$492$	−5.44394	−	22.0870i	−0.245432	−	0.995757i
$493$	−9.75252	−	8.63997i	−0.439231	−	0.389125i
$494$	4.96058	−	8.28973i	0.223187	−	0.372973i
$495$	−13.7127	+	12.1484i	−0.616340	+	0.546029i
$496$	−1.74804	−	1.20659i	−0.0784894	−	0.0541773i
$497$	27.3013	+	6.72916i	1.22463	+	0.301844i
$498$	16.8908	+	24.4705i	0.756893	+	1.09655i
$499$	−2.87551	−	11.6664i	−0.128726	−	0.522261i	−0.999531	−	0.0306322i	$-0.990248\pi$
$499$	−2.87551	−	11.6664i	−0.128726	−	0.522261i	0.870805	−	0.491629i	$-0.163598\pi$
$500$	−2.35423	−	9.55150i	−0.105284	−	0.427156i
$501$	9.60749	−	1.16656i	0.429231	−	0.0521181i
$502$	44.1334	+	49.8163i	1.96977	+	2.22341i
$503$	9.27902	−	24.4668i	0.413731	−	1.09092i	−0.552561	−	0.833472i	$-0.686349\pi$
$503$	9.27902	−	24.4668i	0.413731	−	1.09092i	0.966292	−	0.257447i	$-0.0828813\pi$
$504$	34.3041	+	18.0042i	1.52803	+	0.801971i
$505$	−9.87137	+	6.81371i	−0.439270	+	0.303206i
$506$	−36.9507			−1.64266
$507$	15.3717	−	5.98830i	0.682680	−	0.265950i
$508$	41.4981			1.84118
$509$	−19.5537	+	13.4970i	−0.866703	+	0.598242i	−0.916285	−	0.400528i	$-0.868827\pi$
$509$	−19.5537	+	13.4970i	−0.866703	+	0.598242i	0.0495811	+	0.998770i	$0.484211\pi$
$510$	20.3467	+	10.6788i	0.900965	+	0.472863i
$511$	4.88522	−	12.8813i	0.216110	−	0.569834i
$512$	33.6218	+	37.9511i	1.48589	+	1.67722i
$513$	−5.84228	+	0.709381i	−0.257943	+	0.0313199i
$514$	17.9941	+	73.0048i	0.793684	+	3.22010i
$515$	1.83468	+	7.44358i	0.0808456	+	0.328004i
$516$	5.02769	+	7.28387i	0.221332	+	0.320655i
$517$	−27.6796	−	6.82241i	−1.21735	−	0.300049i
$518$	−98.3739	−	67.9026i	−4.32230	−	2.98347i
$519$	7.07225	−	6.26546i	0.310437	−	0.275023i
$520$	71.5296	+	12.7763i	3.13678	+	0.560277i
$521$	8.91445	+	7.89751i	0.390549	+	0.345996i	0.835433	−	0.549592i	$-0.185217\pi$
$521$	8.91445	+	7.89751i	0.390549	+	0.345996i	−0.444884	+	0.895588i	$0.646755\pi$
$522$	5.02949	+	20.4054i	0.220135	+	0.893122i
$523$	6.23027	+	5.51954i	0.272431	+	0.241353i	0.788265	−	0.615336i	$-0.210980\pi$
$523$	6.23027	+	5.51954i	0.272431	+	0.241353i	−0.515834	+	0.856688i	$0.672518\pi$
$524$	25.6849	−	6.33076i	1.12205	−	0.276560i
$525$	30.4635	+	11.5533i	1.32953	+	0.504226i
$526$			9.96861i			0.434652i
$527$	−0.640362	+	0.242857i	−0.0278946	+	0.0105790i
$528$	−8.30168	+	33.6813i	−0.361284	+	1.46579i
$529$	−9.95545			−0.432845
$530$	−24.2185			−1.05199
$531$	2.51791	−	10.2155i	0.109268	−	0.443317i
$532$	−2.55132	+	21.0120i	−0.110614	+	0.910985i
$533$	−14.5616	−	0.815148i	−0.630734	−	0.0353080i
$534$	4.52746	+	37.2870i	0.195923	+	1.61357i
$535$	−34.5028	−	4.18940i	−1.49169	−	0.181124i
$536$	−21.0521	−	30.4992i	−0.909311	−	1.31736i
$537$	−17.7326	−	15.7097i	−0.765218	−	0.677924i
$538$	34.8460	−	4.23107i	1.50232	−	0.182414i
$539$	−53.8110	−	6.53383i	−2.31780	−	0.281432i
$540$	−37.4905	−	71.4321i	−1.61333	−	3.07395i
$541$	−12.0641	+	13.6175i	−0.518675	+	0.585463i	−0.948233	−	0.317576i	$-0.897131\pi$
$541$	−12.0641	+	13.6175i	−0.518675	+	0.585463i	0.429558	+	0.903039i	$0.358670\pi$
$542$	27.7669	−	40.2273i	1.19269	−	1.72791i
$543$	−18.1015	+	4.46161i	−0.776808	+	0.191466i
$544$	−10.5225	+	1.27767i	−0.451150	+	0.0547795i
$545$	5.52013	+	7.99729i	0.236456	+	0.342566i
$546$	−36.9254	+	37.2588i	−1.58026	+	1.59453i
$547$	−2.57808	+	3.73500i	−0.110231	+	0.159697i	−0.874217	−	0.485536i	$-0.838624\pi$
$547$	−2.57808	+	3.73500i	−0.110231	+	0.159697i	0.763986	+	0.645233i	$0.223240\pi$
$548$	−23.5214	+	44.8163i	−1.00478	+	1.91446i
$549$	0.658596	+	1.73658i	0.0281082	+	0.0741152i
$550$	7.00357	−	57.6796i	0.298633	−	2.45947i
$551$	−5.18496	+	3.57892i	−0.220887	+	0.152467i
$552$	6.76407	−	27.4429i	0.287898	−	1.16805i
$553$	58.4884	−	40.3716i	2.48718	−	1.71677i
$554$	37.8871	−	14.3687i	1.60967	−	0.610466i
$555$	15.3318	+	40.4266i	0.650799	+	1.71602i
$556$	40.8599	−	21.4449i	1.73285	−	0.909468i
$557$	1.18616	+	2.26005i	0.0502594	+	0.0957613i	0.909290	−	0.416163i	$-0.136625\pi$
$557$	1.18616	+	2.26005i	0.0502594	+	0.0957613i	−0.859031	+	0.511924i	$0.828933\pi$
$558$	1.07259	+	0.264369i	0.0454063	+	0.0111917i
$559$	5.40980	−	1.71247i	0.228810	−	0.0724299i
$560$	−97.1991	+	23.9574i	−4.10741	+	1.01239i
$561$	7.41710	+	8.37218i	0.313150	+	0.353474i
$562$	7.45565	+	61.4028i	0.314497	+	2.59012i
$563$	−5.22213	+	2.74078i	−0.220086	+	0.115510i	−0.571164	−	0.820836i	$-0.693508\pi$
$563$	−5.22213	+	2.74078i	−0.220086	+	0.115510i	0.351077	+	0.936347i	$0.385816\pi$
$564$	18.4688	−	35.1894i	0.777678	−	1.48174i
$565$	−14.6440	−	5.55374i	−0.616078	−	0.233648i
$566$	27.9932	+	31.5978i	1.17664	+	1.32816i
$567$	13.0140	+	1.58019i	0.546537	+	0.0663616i
$568$	37.2424	+	9.17943i	1.56266	+	0.385160i
$569$	−29.9105	+	26.4984i	−1.25391	+	1.11087i	−0.264708	+	0.964329i	$0.585276\pi$
$569$	−29.9105	+	26.4984i	−1.25391	+	1.11087i	−0.989205	+	0.146541i	$0.953186\pi$
$570$	7.36810	−	8.31687i	0.308616	−	0.348355i
$571$	−11.0784	+	5.81437i	−0.463615	+	0.243324i	−0.680323	−	0.732913i	$-0.738160\pi$
$571$	−11.0784	+	5.81437i	−0.463615	+	0.243324i	0.216708	+	0.976236i	$0.430468\pi$
$572$	55.3122	+	33.0988i	2.31272	+	1.38393i
$573$	−6.10636	−	3.20487i	−0.255097	−	0.133885i
$574$	43.3617	−	16.4449i	1.80988	−	0.686398i
$575$	−2.47244	+	20.3624i	−0.103108	+	0.849171i
$576$	−1.53702	−	0.806688i	−0.0640423	−	0.0336120i
$577$		−	22.7952i		−	0.948976i	−0.880262	−	0.474488i	$-0.842633\pi$
$577$		−	22.7952i		−	0.948976i	0.880262	−	0.474488i	$-0.157367\pi$
$578$	14.4094	−	27.4548i	0.599351	−	1.14197i
$579$	−6.34971	+	7.16734i	−0.263885	+	0.297864i
$580$	−71.0741	−	49.0589i	−2.95119	−	2.03706i
$581$	−31.2635	+	27.6970i	−1.29703	+	1.14907i
$582$	−18.2739	+	26.4743i	−0.757476	+	1.09739i
$583$	−11.0225	−	4.18029i	−0.456506	−	0.173130i
$584$	6.66406	−	17.5717i	0.275761	−	0.727122i
$585$	−16.0922	+	3.02382i	−0.665330	+	0.125020i
$586$	5.41631	+	14.2816i	0.223746	+	0.589968i
$587$		−	29.2514i		−	1.20733i	−0.797236	−	0.603667i	$-0.793706\pi$
$587$		−	29.2514i		−	1.20733i	0.797236	−	0.603667i	$-0.206294\pi$
$588$	26.7961	−	70.6556i	1.10505	−	2.91379i
$589$	0.0399173	+	0.328748i	0.00164476	+	0.0135458i
$590$	29.1600	+	55.5597i	1.20050	+	2.28736i
$591$	25.9231	+	17.8935i	1.06634	+	0.736038i
$592$	−58.1433	−	40.1334i	−2.38967	−	1.64947i
$593$	−3.78380	−	7.20943i	−0.155382	−	0.296056i	0.795304	−	0.606211i	$-0.207311\pi$
$593$	−3.78380	−	7.20943i	−0.155382	−	0.296056i	−0.950686	+	0.310155i	$0.899619\pi$
$594$	−6.86937	−	56.5743i	−0.281854	−	2.32127i
$595$	−11.4461	+	30.1810i	−0.469246	+	1.23730i
$596$		−	71.3321i		−	2.92188i
$597$	−4.71576	−	12.4344i	−0.193003	−	0.508907i
$598$	−28.3390	−	16.9581i	−1.15887	−	0.693467i
$599$	14.8492	−	39.1542i	0.606723	−	1.59980i	−0.180806	−	0.983519i	$-0.557870\pi$
$599$	14.8492	−	39.1542i	0.606723	−	1.59980i	0.787529	−	0.616278i	$-0.211360\pi$
$600$	41.5560	+	15.7601i	1.69652	+	0.643404i
$601$	5.59308	−	8.10298i	0.228147	−	0.330527i	−0.692147	−	0.721757i	$-0.743335\pi$
$601$	5.59308	−	8.10298i	0.228147	−	0.330527i	0.920293	+	0.391230i	$0.127950\pi$
$602$	−13.5056	+	11.9649i	−0.550447	+	0.487654i
$603$	6.87279	+	4.74394i	0.279882	+	0.193188i
$604$	−7.95958	+	8.98451i	−0.323871	+	0.365574i
$605$	8.00941	−	15.2607i	0.325629	−	0.620434i
$606$		−	11.8123i		−	0.479843i
$607$	25.9914	+	13.6413i	1.05496	+	0.553684i	0.900743	−	0.434353i	$-0.143023\pi$
$607$	25.9914	+	13.6413i	1.05496	+	0.553684i	0.154214	+	0.988037i	$0.450715\pi$
$608$	−0.617807	+	5.08810i	−0.0250554	+	0.206350i
$609$	31.9868	−	12.1310i	1.29617	−	0.491573i
$610$	−9.80767	−	5.14746i	−0.397101	−	0.208415i
$611$	−18.0976	−	17.9356i	−0.732149	−	0.725597i
$612$	11.9145	−	6.25321i	0.481615	−	0.252771i
$613$	10.7644	−	12.1505i	0.434770	−	0.490754i	−0.489763	−	0.871856i	$-0.662917\pi$
$613$	10.7644	−	12.1505i	0.434770	−	0.490754i	0.924533	+	0.381102i	$0.124455\pi$
$614$	−42.8322	+	37.9460i	−1.72857	+	1.53138i
$615$	−16.2870	−	4.01438i	−0.656755	−	0.161875i
$616$	−111.645	−	13.5562i	−4.49831	−	0.546194i
$617$	−3.60302	−	4.06697i	−0.145052	−	0.163730i	0.671494	−	0.741010i	$-0.265653\pi$
$617$	−3.60302	−	4.06697i	−0.145052	−	0.163730i	−0.816547	+	0.577280i	$0.804114\pi$
$618$	−7.05924	−	2.67722i	−0.283964	−	0.107693i
$619$	−17.6554	+	33.6395i	−0.709629	+	1.35209i	0.217024	+	0.976166i	$0.430365\pi$
$619$	−17.6554	+	33.6395i	−0.709629	+	1.35209i	−0.926653	+	0.375919i	$0.877327\pi$
$620$	−4.01953	+	2.10961i	−0.161428	+	0.0847240i
$621$	2.42507	+	19.9722i	0.0973146	+	0.801458i
$622$	11.5430	+	13.0294i	0.462834	+	0.522431i
$623$	−51.2291	+	12.6269i	−2.05245	+	0.505884i
$624$	−21.8245	+	22.0216i	−0.873680	+	0.881569i
$625$	20.5279	+	5.05967i	0.821116	+	0.202387i
$626$	−21.1233	−	40.2471i	−0.844258	−	1.60860i
$627$	4.78898	−	2.51345i	0.191254	−	0.100378i
$628$	−13.3100	−	35.0957i	−0.531129	−	1.40047i
$629$	−21.2997	+	8.07789i	−0.849273	+	0.322087i
$630$	42.8489	−	29.5765i	1.70714	−	1.17835i
$631$	−2.67268	+	10.8435i	−0.106398	+	0.431672i	−0.999847	−	0.0174918i	$-0.994432\pi$
$631$	−2.67268	+	10.8435i	−0.106398	+	0.431672i	0.893449	+	0.449164i	$0.148278\pi$
$632$	79.7855	−	55.0719i	3.17370	−	2.19064i
$633$	3.68472	−	30.3464i	0.146454	−	1.20616i
$634$	13.6711	+	36.0477i	0.542948	+	1.43164i
$635$	14.2209	−	27.0957i	0.564340	−	1.07526i
$636$	9.33552	−	13.5248i	0.370177	−	0.536295i
$637$	−38.2712	−	29.7070i	−1.51636	−	1.17703i
$638$	−34.6569	−	50.2091i	−1.37208	−	1.98780i
$639$	−8.58046	+	1.04186i	−0.339438	+	0.0412152i
$640$	40.8377	−	10.0656i	1.61425	−	0.397878i
$641$	−3.38476	+	4.90367i	−0.133690	+	0.193683i	−0.884111	−	0.467276i	$-0.845235\pi$
$641$	−3.38476	+	4.90367i	−0.133690	+	0.193683i	0.750421	+	0.660960i	$0.229851\pi$
$642$	22.6974	−	25.6201i	0.895795	−	1.01114i
$643$	−4.65804	−	8.87516i	−0.183695	−	0.350002i	0.776143	−	0.630558i	$-0.217174\pi$
$643$	−4.65804	−	8.87516i	−0.183695	−	0.350002i	−0.959838	+	0.280555i	$0.909481\pi$
$644$	71.8309	+	8.72184i	2.83053	+	0.343689i
$645$	6.47885	−	0.786674i	0.255104	−	0.0309753i
$646$	4.38192	+	3.88205i	0.172405	+	0.152737i
$647$	−10.3001	−	14.9223i	−0.404938	−	0.586654i	0.566466	−	0.824085i	$-0.308310\pi$
$647$	−10.3001	−	14.9223i	−0.404938	−	0.586654i	−0.971404	+	0.237431i	$0.923695\pi$
$648$	17.7527	+	2.15557i	0.697394	+	0.0846789i
$649$	3.68151	+	30.3200i	0.144512	+	1.19016i
$650$	31.8427	−	41.0226i	1.24897	−	1.60904i
$651$	0.216750	−	1.78509i	0.00849508	−	0.0699633i
$652$	2.09395	−	8.49548i	0.0820053	−	0.332709i
$653$	0.0295751			0.00115736			0.000578682	−	1.00000i	$-0.499816\pi$
$653$	0.0295751			0.00115736			0.000578682		1.00000i	$0.499816\pi$
$654$	−9.56977			−0.374207
$655$	4.66832	−	18.9401i	0.182406	−	0.740051i
$656$	25.6287	−	9.71967i	1.00063	−	0.379489i
$657$			4.23486i			0.165218i
$658$	75.7546	+	28.7299i	2.95322	+	1.12001i
$659$	42.9704	−	10.5913i	1.67389	−	0.412577i	0.715632	−	0.698478i	$-0.246139\pi$
$659$	42.9704	−	10.5913i	1.67389	−	0.412577i	0.958259	+	0.285901i	$0.0922928\pi$
$660$	55.4933	+	49.1627i	2.16007	+	1.91366i
$661$	−10.4381	−	42.3492i	−0.405997	−	1.64719i	−0.717213	−	0.696854i	$-0.754582\pi$
$661$	−10.4381	−	42.3492i	−0.405997	−	1.64719i	0.311216	−	0.950339i	$-0.399264\pi$
$662$	66.6444	+	59.0418i	2.59021	+	2.29472i
$663$	1.84617	+	9.82496i	0.0716993	+	0.381570i
$664$	−42.6473	+	37.7823i	−1.65504	+	1.46624i
$665$	12.8452	+	8.86641i	0.498116	+	0.343825i
$666$	35.6764	+	8.79344i	1.38243	+	0.340739i
$667$	12.2348	+	17.7251i	0.473733	+	0.686320i
$668$	8.08846	+	32.8162i	0.312952	+	1.26970i
$669$	−1.12845	−	4.57831i	−0.0436285	−	0.177008i
$670$	−49.4411	+	6.00323i	−1.91008	+	0.231925i
$671$	−3.57526	−	4.03563i	−0.138021	−	0.155794i
$672$	9.86906	−	26.0226i	0.380707	−	1.00384i
$673$	0.595279	+	0.312426i	0.0229463	+	0.0120431i	0.476157	−	0.879360i	$-0.342029\pi$
$673$	0.595279	+	0.312426i	0.0229463	+	0.0120431i	−0.453211	+	0.891403i	$0.649722\pi$
$674$	−37.2015	+	25.6783i	−1.43295	+	0.989093i
$675$	−31.6360			−1.21767
$676$	27.2309	+	50.7697i	1.04734	+	1.95268i
$677$	−2.61448			−0.100483			−0.0502413	−	0.998737i	$-0.515999\pi$
$677$	−2.61448			−0.100483			−0.0502413	+	0.998737i	$0.515999\pi$
$678$	12.6935	−	8.76170i	0.487492	−	0.336491i
$679$	−40.0118	−	20.9998i	−1.53551	−	0.805898i
$680$	−15.6140	+	41.1707i	−0.598769	+	1.57882i
$681$	−4.73426	−	5.34387i	−0.181417	−	0.204778i
$682$	−3.18347	+	0.386543i	−0.121901	+	0.0148015i
$683$	10.2731	+	41.6796i	0.393089	+	1.59483i	0.750494	+	0.660877i	$0.229815\pi$
$683$	10.2731	+	41.6796i	0.393089	+	1.59483i	−0.357405	+	0.933950i	$0.616338\pi$
$684$	−1.55710	−	6.31738i	−0.0595370	−	0.241551i
$685$	21.2017	+	30.7160i	0.810077	+	1.17360i
$686$	71.6551	+	17.6614i	2.73580	+	0.674315i
$687$	18.8201	+	12.9906i	0.718031	+	0.495621i
$688$	−7.98240	+	7.07179i	−0.304326	+	0.269609i
$689$	−6.53513	−	8.26470i	−0.248969	−	0.314860i
$690$	−28.4318	−	25.1884i	−1.08238	−	0.958904i
$691$	−0.376207	−	1.52633i	−0.0143116	−	0.0580644i	0.963352	−	0.268241i	$-0.0864423\pi$
$691$	−0.376207	−	1.52633i	−0.0143116	−	0.0580644i	−0.977663	+	0.210176i	$0.932596\pi$
$692$	24.6981	+	21.8806i	0.938882	+	0.831777i
$693$	24.6068	−	6.06504i	0.934737	−	0.230392i
$694$	13.0049	+	4.93211i	0.493660	+	0.187220i
$695$		−	34.0279i		−	1.29075i
$696$	43.6340	−	16.5482i	1.65394	−	0.627258i
$697$	2.11506	−	8.58115i	0.0801138	−	0.325034i
$698$	−39.8624			−1.50881
$699$	13.3315			0.504243
$700$	−27.2294	+	110.474i	−1.02917	+	4.17552i
$701$	5.37817	−	44.2932i	0.203131	−	1.67293i	−0.433034	−	0.901378i	$-0.642557\pi$
$701$	5.37817	−	44.2932i	0.203131	−	1.67293i	0.636165	−	0.771553i	$-0.280520\pi$
$702$	20.6957	−	46.5418i	0.781110	−	1.75661i
$703$	1.32773	+	10.9348i	0.0500761	+	0.412414i
$704$	5.00233	+	0.607393i	0.188532	+	0.0228920i
$705$	−16.6475	−	24.1180i	−0.626980	−	0.908337i
$706$	−11.1194	−	9.85095i	−0.418485	−	0.370745i
$707$	16.4720	−	2.00006i	0.619492	−	0.0752200i
$708$	−42.2676	−	5.13222i	−1.58851	−	0.192881i
$709$	−14.7541	−	28.1116i	−0.554103	−	1.05575i	−0.987951	−	0.154769i	$-0.950537\pi$
$709$	−14.7541	−	28.1116i	−0.554103	−	1.05575i	0.433848	−	0.900986i	$-0.357156\pi$
$710$	34.1828	−	38.5844i	1.28286	−	1.44805i
$711$	−12.4101	+	17.9791i	−0.465415	+	0.674270i
$712$	−69.8830	+	17.2246i	−2.61898	+	0.645520i
$713$	1.12385	−	0.136460i	0.0420884	−	0.00511046i
$714$	−18.0577	−	26.1611i	−0.675792	−	0.979053i
$715$	40.5663	−	24.7728i	1.51709	−	0.926451i
$716$	46.9979	−	68.0883i	1.75640	−	2.54458i
$717$	−5.59275	+	10.6561i	−0.208865	+	0.397959i
$718$	−16.5415	−	43.6163i	−0.617323	−	1.62775i
$719$	−2.47863	+	20.4134i	−0.0924374	+	0.761291i	0.870613	+	0.491969i	$0.163723\pi$
$719$	−2.47863	+	20.4134i	−0.0924374	+	0.761291i	−0.963050	+	0.269322i	$0.913200\pi$
$720$	25.3256	−	17.4810i	0.943828	−	0.651477i
$721$	2.53804	−	10.2972i	0.0945214	−	0.383488i
$722$	−37.3261	+	25.7643i	−1.38913	+	0.958849i
$723$	−32.8531	+	12.4595i	−1.22182	+	0.463375i
$724$	−23.0872	−	60.8760i	−0.858030	−	2.26244i
$725$	−29.9877	+	15.7388i	−1.11372	+	0.584523i
$726$	7.88770	+	15.0288i	0.292740	+	0.557770i
$727$	−35.9185	−	8.85312i	−1.33214	−	0.328344i	−0.491947	−	0.870625i	$-0.663715\pi$
$727$	−35.9185	−	8.85312i	−1.33214	−	0.328344i	−0.840197	+	0.542281i	$0.817561\pi$
$728$	−79.4039	−	61.6350i	−2.94290	−	2.28435i
$729$	−24.5031	+	6.03947i	−0.907521	+	0.223684i
$730$	−16.7478	−	18.9043i	−0.619863	−	0.699681i
$731$	0.414477	+	3.41352i	0.0153300	+	0.126254i
$732$	6.65517	−	3.49290i	0.245982	−	0.129101i
$733$	8.19602	−	15.6162i	0.302727	−	0.576798i	−0.685809	−	0.727781i	$-0.740552\pi$
$733$	8.19602	−	15.6162i	0.302727	−	0.576798i	0.988536	+	0.150983i	$0.0482439\pi$
$734$	21.2658	+	8.06504i	0.784934	+	0.297686i
$735$	−36.9510	−	41.7091i	−1.36296	−	1.53846i
$736$	17.3940	+	2.11202i	0.641152	+	0.0778499i
$737$	−23.5382	−	5.80165i	−0.867041	−	0.213707i
$738$	−10.6705	+	9.45323i	−0.392786	+	0.347978i
$739$	−25.4694	+	28.7490i	−0.936906	+	1.05755i	0.0613270	+	0.998118i	$0.480467\pi$
$739$	−25.4694	+	28.7490i	−0.936906	+	1.05755i	−0.998232	+	0.0594300i	$0.981072\pi$
$740$	−133.697	+	70.1697i	−4.91481	+	2.57949i
$741$	4.82639	+	0.270177i	0.177302	+	0.00992521i
$742$	29.6656	+	15.5697i	1.08906	+	0.571581i
$743$	−25.1278	+	9.52972i	−0.921850	+	0.349611i	−0.769450	−	0.638708i	$-0.779469\pi$
$743$	−25.1278	+	9.52972i	−0.921850	+	0.349611i	−0.152400	+	0.988319i	$0.548700\pi$
$744$	0.295674	−	2.43509i	0.0108399	−	0.0892748i
$745$	−46.5754	−	24.4447i	−1.70639	−	0.895584i
$746$			26.1037i			0.955725i
$747$	5.96668	−	11.3686i	0.218309	−	0.415954i
$748$	−25.9025	+	29.2378i	−0.947088	+	1.06904i
$749$	39.5696	+	27.3129i	1.44584	+	0.997993i
$750$	5.34726	−	4.73725i	0.195254	−	0.172980i
$751$	−0.267879	+	0.388090i	−0.00977505	+	0.0141616i	−0.827841	−	0.560963i	$-0.810431\pi$
$751$	−0.267879	+	0.388090i	−0.00977505	+	0.0141616i	0.818066	+	0.575125i	$0.195046\pi$
$752$	44.7743	+	16.9806i	1.63275	+	0.619221i
$753$	−11.8091	+	31.1380i	−0.430346	+	1.13473i
$754$	−3.53689	−	54.4128i	−0.128806	−	1.98160i
$755$	3.13867	+	8.27600i	0.114228	+	0.301194i
$756$			111.600i			4.05885i
$757$	0.0741439	−	0.195501i	0.00269481	−	0.00710562i	−0.933662	−	0.358155i	$-0.883406\pi$
$757$	0.0741439	−	0.195501i	0.00269481	−	0.00710562i	0.936357	+	0.351050i	$0.114175\pi$
$758$	−0.787606	−	6.48652i	−0.0286071	−	0.235601i
$759$	−8.59240	−	16.3715i	−0.311884	−	0.594246i
$760$	17.5225	+	12.0949i	0.635608	+	0.438728i
$761$	21.0116	+	14.5033i	0.761670	+	0.525743i	0.884418	−	0.466695i	$-0.154556\pi$
$761$	21.0116	+	14.5033i	0.761670	+	0.525743i	−0.122749	+	0.992438i	$0.539171\pi$
$762$	14.0048	+	26.6840i	0.507341	+	0.966658i
$763$	−1.62035	−	13.3448i	−0.0586606	−	0.483113i
$764$	8.54018	−	22.5186i	0.308973	−	0.814695i
$765$		−	9.92232i		−	0.358742i
$766$	21.4431	+	56.5408i	0.774771	+	2.04290i
$767$	−11.0915	+	24.9432i	−0.400491	+	0.900648i

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)

\(f(q)\)	\(=\)	\(q+(-2.08715 + 1.44065i) q^{2} +(-1.12364 - 0.589730i) q^{3} +(1.57149 - 4.14367i) q^{4} +(-2.16703 - 2.44607i) q^{5} +(3.19479 - 0.387918i) q^{6} +(1.08188 + 4.38937i) q^{7} +(1.47582 + 5.98765i) q^{8} +(-0.789415 - 1.14367i) q^{9} +O(q^{10})\)	\(q+(-2.08715 + 1.44065i) q^{2} +(-1.12364 - 0.589730i) q^{3} +(1.57149 - 4.14367i) q^{4} +(-2.16703 - 2.44607i) q^{5} +(3.19479 - 0.387918i) q^{6} +(1.08188 + 4.38937i) q^{7} +(1.47582 + 5.98765i) q^{8} +(-0.789415 - 1.14367i) q^{9} +(8.04684 + 1.98337i) q^{10} +(3.32000 + 2.29163i) q^{11} +(-4.20943 + 3.72923i) q^{12} +(1.49453 + 3.28122i) q^{13} +(-8.58159 - 7.60263i) q^{14} +(0.992433 + 4.02646i) q^{15} +(-5.07210 - 4.49349i) q^{16} +(-2.12143 + 0.522885i) q^{17} +(3.29525 + 1.24972i) q^{18} +1.05650i q^{19} +(-13.5412 + 5.13548i) q^{20} +(1.37290 - 5.57007i) q^{21} -10.2308 q^{22} +3.61172 q^{23} +(1.87281 - 7.59828i) q^{24} +(-0.684560 + 5.63786i) q^{25} +(-7.84639 - 4.69528i) q^{26} +(0.671443 + 5.52983i) q^{27} +(19.8882 + 2.41487i) q^{28} +(3.38752 + 4.90767i) q^{29} +(-7.87208 - 6.97405i) q^{30} +(0.311167 - 0.0377825i) q^{31} +(4.81598 + 0.584766i) q^{32} +(-2.37903 - 4.53286i) q^{33} +(3.67443 - 4.14758i) q^{34} +(8.39223 - 12.1582i) q^{35} +(-5.97952 + 1.47382i) q^{36} +(10.3500 - 1.25672i) q^{37} +(-1.52205 - 2.20507i) q^{38} +(0.255728 - 4.56827i) q^{39} +(11.4481 - 16.5854i) q^{40} +(-1.87980 + 3.58166i) q^{41} +(5.15910 + 13.6034i) q^{42} +(0.189699 - 1.56231i) q^{43} +(14.7131 - 10.1557i) q^{44} +(-1.08680 + 4.40932i) q^{45} +(-7.53819 + 5.20324i) q^{46} +(-6.60753 + 2.50591i) q^{47} +(3.04925 + 8.04022i) q^{48} +(-11.8979 + 6.24449i) q^{49} +(-6.69342 - 12.7532i) q^{50} +(2.69208 + 0.663537i) q^{51} +(15.9449 - 1.03643i) q^{52} +(-2.83732 + 0.699337i) q^{53} +(-9.36796 - 10.5742i) q^{54} +(-1.58905 - 13.0870i) q^{55} +(-24.6853 + 12.9559i) q^{56} +(0.623052 - 1.18713i) q^{57} +(-14.1405 - 5.36278i) q^{58} +(5.02059 + 5.66707i) q^{59} +(18.2439 + 2.21521i) q^{60} +(-1.29766 - 0.319844i) q^{61} +(-0.595019 + 0.527140i) q^{62} +(4.16591 - 4.70234i) q^{63} +(1.10604 - 0.580495i) q^{64} +(4.78741 - 10.7662i) q^{65} +(11.4957 + 6.03339i) q^{66} +(-5.61892 + 2.13098i) q^{67} +(-1.16713 + 9.61220i) q^{68} +(-4.05827 - 2.12994i) q^{69} +37.4663i q^{70} +(2.89052 - 5.50742i) q^{71} +(5.68283 - 6.41459i) q^{72} +(-2.50797 - 1.73113i) q^{73} +(-19.7915 + 17.5337i) q^{74} +(4.09402 - 5.93121i) q^{75} +(4.37780 + 1.66028i) q^{76} +(-6.46695 + 17.0520i) q^{77} +(6.04754 + 9.90305i) q^{78} +(-5.57461 - 14.6990i) q^{79} +22.1442i q^{80} +(1.02831 - 2.71144i) q^{81} +(-1.23651 - 10.1836i) q^{82} +(4.29364 + 8.18084i) q^{83} +(-20.9231 - 14.4421i) q^{84} +(5.87621 + 4.05605i) q^{85} +(1.85482 + 3.53406i) q^{86} +(-0.912141 - 7.51216i) q^{87} +(-8.82174 + 23.2610i) q^{88} +11.6712i q^{89} +(-4.08399 - 10.7686i) q^{90} +(-12.7856 + 10.1099i) q^{91} +(5.67578 - 14.9658i) q^{92} +(-0.371920 - 0.141051i) q^{93} +(10.1807 - 14.7493i) q^{94} +(2.58428 - 2.28947i) q^{95} +(-5.06657 - 3.49720i) q^{96} +(-6.62836 + 7.48187i) q^{97} +(15.8365 - 30.1739i) q^{98} -5.60601i 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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