LMFDB - Embedded newform 225.2.q.a.211.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			211.19
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.825259 + 0.367429i) q^{2} +(-0.453689 - 1.67158i) q^{3} +(-0.792213 - 0.879842i) q^{4} +(-1.78097 + 1.35209i) q^{5} +(0.239774 - 1.54618i) q^{6} +(-1.53265 - 2.65463i) q^{7} +(-0.888808 - 2.73547i) q^{8} +(-2.58833 + 1.51675i) q^{9} +O(q^{10})$	\(q+(0.825259 + 0.367429i) q^{2} +(-0.453689 - 1.67158i) q^{3} +(-0.792213 - 0.879842i) q^{4} +(-1.78097 + 1.35209i) q^{5} +(0.239774 - 1.54618i) q^{6} +(-1.53265 - 2.65463i) q^{7} +(-0.888808 - 2.73547i) q^{8} +(-2.58833 + 1.51675i) q^{9} +(-1.96656 + 0.461443i) q^{10} +(-1.20016 - 0.534345i) q^{11} +(-1.11130 + 1.72342i) q^{12} +(4.56466 - 2.03232i) q^{13} +(-0.289446 - 2.75390i) q^{14} +(3.06813 + 2.36360i) q^{15} +(0.0240823 - 0.229128i) q^{16} +(1.36059 + 4.18745i) q^{17} +(-2.69334 + 0.300684i) q^{18} +(-1.05356 - 3.24253i) q^{19} +(2.60053 + 0.495830i) q^{20} +(-3.74207 + 3.76632i) q^{21} +(-0.794108 - 0.881946i) q^{22} +(-0.595839 - 5.66903i) q^{23} +(-4.16930 + 2.72676i) q^{24} +(1.34371 - 4.81606i) q^{25} +4.51376 q^{26} +(3.70966 + 3.63846i) q^{27} +(-1.12147 + 3.45152i) q^{28} +(6.43584 - 1.36798i) q^{29} +(1.66354 + 3.07790i) q^{30} +(-5.33344 - 1.13366i) q^{31} +(-2.77218 + 4.80156i) q^{32} +(-0.348700 + 2.24858i) q^{33} +(-0.415756 + 3.95565i) q^{34} +(6.31890 + 2.65554i) q^{35} +(3.38501 + 1.07573i) q^{36} +(5.90992 + 4.29381i) q^{37} +(0.321938 - 3.06303i) q^{38} +(-5.46811 - 6.70813i) q^{39} +(5.28154 + 3.67004i) q^{40} +(1.45477 - 0.647706i) q^{41} +(-4.47203 + 1.73324i) q^{42} +(-2.24167 - 3.88268i) q^{43} +(0.480642 + 1.47926i) q^{44} +(2.55896 - 6.20095i) q^{45} +(1.59124 - 4.89734i) q^{46} +(6.49659 - 1.38089i) q^{47} +(-0.393930 + 0.0636974i) q^{48} +(-1.19804 + 2.07507i) q^{49} +(2.87847 - 3.48078i) q^{50} +(6.38236 - 4.17412i) q^{51} +(-5.40430 - 2.40615i) q^{52} +(-2.18021 + 6.70999i) q^{53} +(1.72456 + 4.36571i) q^{54} +(2.85993 - 0.671068i) q^{55} +(-5.89943 + 6.55198i) q^{56} +(-4.94214 + 3.23221i) q^{57} +(5.81387 + 1.23578i) q^{58} +(-3.22129 + 1.43421i) q^{59} +(-0.351016 - 4.57194i) q^{60} +(-11.2015 - 4.98723i) q^{61} +(-3.98493 - 2.89522i) q^{62} +(7.99343 + 4.54641i) q^{63} +(-4.42478 + 3.21479i) q^{64} +(-5.38165 + 9.79132i) q^{65} +(-1.11396 + 1.72754i) q^{66} +(-5.39308 - 1.14633i) q^{67} +(2.60642 - 4.51446i) q^{68} +(-9.20588 + 3.56797i) q^{69} +(4.23901 + 4.51325i) q^{70} +(-2.00148 + 6.15992i) q^{71} +(6.44956 + 5.73220i) q^{72} +(5.08449 - 3.69410i) q^{73} +(3.29954 + 5.71498i) q^{74} +(-8.66004 - 0.0611220i) q^{75} +(-2.01827 + 3.49574i) q^{76} +(0.420936 + 4.00494i) q^{77} +(-2.04784 - 7.54509i) q^{78} +(-2.76067 + 0.586798i) q^{79} +(0.266911 + 0.440631i) q^{80} +(4.39893 - 7.85171i) q^{81} +1.43855 q^{82} +(8.07261 - 8.96554i) q^{83} +(6.27828 + 0.308700i) q^{84} +(-8.08497 - 5.61810i) q^{85} +(-0.423346 - 4.02787i) q^{86} +(-5.20655 - 10.1374i) q^{87} +(-0.394974 + 3.75793i) q^{88} +(5.99213 - 4.35354i) q^{89} +(4.39021 - 4.17715i) q^{90} +(-12.3911 - 9.00265i) q^{91} +(-4.51581 + 5.01532i) q^{92} +(0.524729 + 9.42958i) q^{93} +(5.86875 + 1.24744i) q^{94} +(6.26055 + 4.35034i) q^{95} +(9.28387 + 2.45550i) q^{96} +(16.6509 - 3.53925i) q^{97} +(-1.75113 + 1.27227i) q^{98} +(3.91688 - 0.437280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.825259	+	0.367429i	0.583546	+	0.259811i	0.677207	−	0.735793i	$-0.263190\pi$
$2$	0.825259	+	0.367429i	0.583546	+	0.259811i	−0.0936607	+	0.995604i	$0.529857\pi$
$3$	−0.453689	−	1.67158i	−0.261938	−	0.965085i
$3$	−0.453689	−	1.67158i	−0.261938	−	0.965085i
$4$	−0.792213	−	0.879842i	−0.396106	−	0.439921i
$5$	−1.78097	+	1.35209i	−0.796474	+	0.604673i
$5$	−1.78097	+	1.35209i	−0.796474	+	0.604673i
$6$	0.239774	−	1.54618i	0.0978875	−	0.631226i
$7$	−1.53265	−	2.65463i	−0.579288	−	1.00336i	−0.995561	−	0.0941164i	$-0.969997\pi$
$7$	−1.53265	−	2.65463i	−0.579288	−	1.00336i	0.416273	−	0.909239i	$-0.363336\pi$
$8$	−0.888808	−	2.73547i	−0.314241	−	0.967134i
$9$	−2.58833	+	1.51675i	−0.862777	+	0.505584i
$10$	−1.96656	+	0.461443i	−0.621880	+	0.145921i
$11$	−1.20016	−	0.534345i	−0.361861	−	0.161111i	0.217749	−	0.976005i	$-0.430129\pi$
$11$	−1.20016	−	0.534345i	−0.361861	−	0.161111i	−0.579610	+	0.814894i	$0.696795\pi$
$12$	−1.11130	+	1.72342i	−0.320806	+	0.497508i
$13$	4.56466	−	2.03232i	1.26601	−	0.563663i	0.339737	−	0.940520i	$-0.389662\pi$
$13$	4.56466	−	2.03232i	1.26601	−	0.563663i	0.926271	+	0.376857i	$0.122995\pi$
$14$	−0.289446	−	2.75390i	−0.0773578	−	0.736010i
$15$	3.06813	+	2.36360i	0.792187	+	0.610279i
$16$	0.0240823	−	0.229128i	0.00602058	−	0.0572820i
$17$	1.36059	+	4.18745i	0.329991	+	1.01561i	0.969137	+	0.246522i	$0.0792877\pi$
$17$	1.36059	+	4.18745i	0.329991	+	1.01561i	−0.639147	+	0.769085i	$0.720712\pi$
$18$	−2.69334	+	0.300684i	−0.634827	+	0.0708720i
$19$	−1.05356	−	3.24253i	−0.241703	−	0.743887i	−0.996161	−	0.0875381i	$-0.972100\pi$
$19$	−1.05356	−	3.24253i	−0.241703	−	0.743887i	0.754458	−	0.656349i	$-0.227900\pi$
$20$	2.60053	+	0.495830i	0.581497	+	0.110871i
$21$	−3.74207	+	3.76632i	−0.816586	+	0.821878i
$22$	−0.794108	−	0.881946i	−0.169304	−	0.188032i
$23$	−0.595839	−	5.66903i	−0.124241	−	1.18207i	−0.861964	−	0.506970i	$-0.830766\pi$
$23$	−0.595839	−	5.66903i	−0.124241	−	1.18207i	0.737723	−	0.675104i	$-0.235901\pi$
$24$	−4.16930	+	2.72676i	−0.851055	+	0.556598i
$25$	1.34371	−	4.81606i	0.268742	−	0.963212i
$26$	4.51376			0.885221
$27$	3.70966	+	3.63846i	0.713925	+	0.700222i
$28$	−1.12147	+	3.45152i	−0.211937	+	0.652277i
$29$	6.43584	−	1.36798i	1.19511	−	0.254027i	0.432948	−	0.901419i	$-0.357473\pi$
$29$	6.43584	−	1.36798i	1.19511	−	0.254027i	0.762158	+	0.647392i	$0.224140\pi$
$30$	1.66354	+	3.07790i	0.303720	+	0.561945i
$31$	−5.33344	−	1.13366i	−0.957915	−	0.203611i	−0.297676	−	0.954667i	$-0.596212\pi$
$31$	−5.33344	−	1.13366i	−0.957915	−	0.203611i	−0.660239	+	0.751056i	$0.729545\pi$
$32$	−2.77218	+	4.80156i	−0.490057	+	0.848803i
$33$	−0.348700	+	2.24858i	−0.0607008	+	0.391428i
$34$	−0.415756	+	3.95565i	−0.0713015	+	0.678389i
$35$	6.31890	+	2.65554i	1.06809	+	0.448868i
$36$	3.38501	+	1.07573i	0.564169	+	0.179289i
$37$	5.90992	+	4.29381i	0.971584	+	0.705897i	0.955812	−	0.293978i	$-0.0949793\pi$
$37$	5.90992	+	4.29381i	0.971584	+	0.705897i	0.0157722	+	0.999876i	$0.494979\pi$
$38$	0.321938	−	3.06303i	0.0522252	−	0.496890i
$39$	−5.46811	−	6.70813i	−0.875598	−	1.07416i
$40$	5.28154	+	3.67004i	0.835084	+	0.580285i
$41$	1.45477	−	0.647706i	0.227197	−	0.101155i	−0.289981	−	0.957032i	$-0.593649\pi$
$41$	1.45477	−	0.647706i	0.227197	−	0.101155i	0.517178	+	0.855878i	$0.326982\pi$
$42$	−4.47203	+	1.73324i	−0.690049	+	0.267445i
$43$	−2.24167	−	3.88268i	−0.341851	−	0.592103i	0.642926	−	0.765929i	$-0.277720\pi$
$43$	−2.24167	−	3.88268i	−0.341851	−	0.592103i	−0.984776	+	0.173826i	$0.944387\pi$
$44$	0.480642	+	1.47926i	0.0724595	+	0.223008i
$45$	2.55896	−	6.20095i	0.381467	−	0.924382i
$46$	1.59124	−	4.89734i	0.234616	−	0.722074i
$47$	6.49659	−	1.38089i	0.947624	−	0.201424i	0.291921	−	0.956442i	$-0.405706\pi$
$47$	6.49659	−	1.38089i	0.947624	−	0.201424i	0.655703	+	0.755019i	$0.272372\pi$
$48$	−0.393930	+	0.0636974i	−0.0568590	+	0.00919393i
$49$	−1.19804	+	2.07507i	−0.171149	+	0.296438i
$50$	2.87847	−	3.48078i	0.407077	−	0.492256i
$51$	6.38236	−	4.17412i	0.893710	−	0.584494i
$52$	−5.40430	−	2.40615i	−0.749441	−	0.333673i
$53$	−2.18021	+	6.70999i	−0.299475	+	0.921688i	0.682207	+	0.731159i	$0.261020\pi$
$53$	−2.18021	+	6.70999i	−0.299475	+	0.921688i	−0.981682	+	0.190529i	$0.938980\pi$
$54$	1.72456	+	4.36571i	0.234683	+	0.594098i
$55$	2.85993	−	0.671068i	0.385633	−	0.0904868i
$56$	−5.89943	+	6.55198i	−0.788344	+	0.875545i
$57$	−4.94214	+	3.23221i	−0.654603	+	0.428116i
$58$	5.81387	+	1.23578i	0.763398	+	0.162265i
$59$	−3.22129	+	1.43421i	−0.419377	+	0.186719i	−0.605566	−	0.795795i	$-0.707053\pi$
$59$	−3.22129	+	1.43421i	−0.419377	+	0.186719i	0.186189	+	0.982514i	$0.440386\pi$
$60$	−0.351016	−	4.57194i	−0.0453160	−	0.590235i
$61$	−11.2015	−	4.98723i	−1.43420	−	0.638549i	−0.465113	−	0.885251i	$-0.653986\pi$
$61$	−11.2015	−	4.98723i	−1.43420	−	0.638549i	−0.969091	+	0.246702i	$0.920653\pi$
$62$	−3.98493	−	2.89522i	−0.506087	−	0.367694i
$63$	7.99343	+	4.54641i	1.00708	+	0.572794i
$64$	−4.42478	+	3.21479i	−0.553097	+	0.401848i
$65$	−5.38165	+	9.79132i	−0.667511	+	1.21446i
$66$	−1.11396	+	1.72754i	−0.137119	+	0.212646i
$67$	−5.39308	−	1.14633i	−0.658869	−	0.140047i	−0.133669	−	0.991026i	$-0.542676\pi$
$67$	−5.39308	−	1.14633i	−0.658869	−	0.140047i	−0.525200	+	0.850979i	$0.676009\pi$
$68$	2.60642	−	4.51446i	0.316075	−	0.547458i
$69$	−9.20588	+	3.56797i	−1.10826	+	0.429533i
$70$	4.23901	+	4.51325i	0.506659	+	0.539437i
$71$	−2.00148	+	6.15992i	−0.237532	+	0.731048i	0.759244	+	0.650807i	$0.225569\pi$
$71$	−2.00148	+	6.15992i	−0.237532	+	0.731048i	−0.996775	+	0.0802415i	$0.974431\pi$
$72$	6.44956	+	5.73220i	0.760087	+	0.675547i
$73$	5.08449	−	3.69410i	0.595094	−	0.432361i	−0.249040	−	0.968493i	$-0.580115\pi$
$73$	5.08449	−	3.69410i	0.595094	−	0.432361i	0.844134	+	0.536132i	$0.180115\pi$
$74$	3.29954	+	5.71498i	0.383564	+	0.664352i
$75$	−8.66004	−	0.0611220i	−0.999975	−	0.00705776i
$76$	−2.01827	+	3.49574i	−0.231511	+	0.400989i
$77$	0.420936	+	4.00494i	0.0479702	+	0.456406i
$78$	−2.04784	−	7.54509i	−0.231872	−	0.854313i
$79$	−2.76067	+	0.586798i	−0.310599	+	0.0660199i	−0.360574	−	0.932731i	$-0.617419\pi$
$79$	−2.76067	+	0.586798i	−0.310599	+	0.0660199i	0.0499748	+	0.998750i	$0.484086\pi$
$80$	0.266911	+	0.440631i	0.0298416	+	0.0492641i
$81$	4.39893	−	7.85171i	0.488770	−	0.872413i
$82$	1.43855			0.158861
$83$	8.07261	−	8.96554i	0.886084	−	0.984096i	−0.113872	−	0.993495i	$-0.536325\pi$
$83$	8.07261	−	8.96554i	0.886084	−	0.984096i	0.999956	+	0.00939965i	$0.00299205\pi$
$84$	6.27828	+	0.308700i	0.685017	+	0.0336820i
$85$	−8.08497	−	5.61810i	−0.876938	−	0.609368i
$86$	−0.423346	−	4.02787i	−0.0456506	−	0.434336i
$87$	−5.20655	−	10.1374i	−0.558201	−	1.08684i
$88$	−0.394974	+	3.75793i	−0.0421044	+	0.400596i
$89$	5.99213	−	4.35354i	0.635164	−	0.461474i	−0.223021	−	0.974814i	$-0.571592\pi$
$89$	5.99213	−	4.35354i	0.635164	−	0.461474i	0.858185	+	0.513340i	$0.171592\pi$
$90$	4.39021	−	4.17715i	0.462769	−	0.440310i
$91$	−12.3911	−	9.00265i	−1.29894	−	0.943734i
$92$	−4.51581	+	5.01532i	−0.470806	+	0.522883i
$93$	0.524729	+	9.42958i	0.0544118	+	0.977802i
$94$	5.86875	+	1.24744i	0.605315	+	0.128664i
$95$	6.26055	+	4.35034i	0.642318	+	0.446335i
$96$	9.28387	+	2.45550i	0.947531	+	0.250613i
$97$	16.6509	−	3.53925i	1.69064	−	0.359357i	0.740712	−	0.671823i	$-0.234488\pi$
$97$	16.6509	−	3.53925i	1.69064	−	0.359357i	0.949929	+	0.312466i	$0.101155\pi$
$98$	−1.75113	+	1.27227i	−0.176891	+	0.128519i
$99$	3.91688	−	0.437280i	0.393661	−	0.0439483i
$100$	−5.30188	+	2.63309i	−0.530188	+	0.263309i
$101$	−6.32691	−	10.9585i	−0.629551	−	1.09042i	−0.987642	−	0.156728i	$-0.949905\pi$
$101$	−6.32691	−	10.9585i	−0.629551	−	1.09042i	0.358090	−	0.933687i	$-0.383428\pi$
$102$	6.80080	−	1.09967i	0.673379	−	0.108883i
$103$	12.4211	+	13.7950i	1.22389	+	1.35926i	0.912551	+	0.408962i	$0.134109\pi$
$103$	12.4211	+	13.7950i	1.22389	+	1.35926i	0.311334	+	0.950300i	$0.399224\pi$
$104$	−9.61644	−	10.6801i	−0.942970	−	1.04727i
$105$	1.57211	−	11.7673i	0.153423	−	1.14837i
$106$	−4.26468	+	4.73641i	−0.414222	+	0.460041i
$107$	−12.3221			−1.19122			−0.595611	−	0.803273i	$-0.703090\pi$
$107$	−12.3221			−1.19122			−0.595611	+	0.803273i	$0.703090\pi$
$108$	0.262426	−	6.14635i	0.0252519	−	0.591433i
$109$	−0.372310	−	0.270499i	−0.0356608	−	0.0259091i	0.569812	−	0.821775i	$-0.307016\pi$
$109$	−0.372310	−	0.270499i	−0.0356608	−	0.0259091i	−0.605473	+	0.795866i	$0.707016\pi$
$110$	2.60675	+	0.497016i	0.248544	+	0.0473886i
$111$	4.49616	−	11.8269i	0.426756	−	1.12256i
$112$	−0.645159	+	0.287244i	−0.0609618	+	0.0271420i
$113$	−10.8046	+	4.81051i	−1.01641	+	0.452535i	−0.846196	−	0.532872i	$-0.821113\pi$
$113$	−10.8046	+	4.81051i	−1.01641	+	0.452535i	−0.170214	+	0.985407i	$0.554446\pi$
$114$	−5.26615	+	0.851521i	−0.493220	+	0.0797523i
$115$	8.72620	+	9.29074i	0.813722	+	0.866366i
$116$	−6.30216	−	4.57879i	−0.585141	−	0.425130i
$117$	−8.73233	+	12.1838i	−0.807305	+	1.12639i
$118$	−3.18537			−0.293237
$119$	9.03084	−	10.0298i	0.827855	−	0.919427i
$120$	3.73858	−	10.4935i	0.341284	−	0.957926i
$121$	−6.20558	−	6.89200i	−0.564144	−	0.626545i
$122$	−7.41168	−	8.23151i	−0.671022	−	0.745246i
$123$	−1.74270	−	2.13791i	−0.157134	−	0.192768i
$124$	3.22778	+	5.59068i	0.289863	+	0.502058i
$125$	4.11863	+	10.3941i	0.368382	+	0.929675i
$126$	4.92616	+	6.68898i	0.438857	+	0.595902i
$127$	14.1647	−	10.2913i	1.25691	−	0.913201i	0.258311	−	0.966062i	$-0.416834\pi$
$127$	14.1647	−	10.2913i	1.25691	−	0.913201i	0.998602	+	0.0528609i	$0.0168340\pi$
$128$	6.01361	−	1.27823i	0.531533	−	0.112981i
$129$	−5.47317	+	5.50864i	−0.481886	+	0.485009i
$130$	−8.03887	+	6.10300i	−0.705055	+	0.535269i
$131$	5.13306	+	1.09107i	0.448478	+	0.0953269i	0.426613	−	0.904434i	$-0.359707\pi$
$131$	5.13306	+	1.09107i	0.448478	+	0.0953269i	0.0218643	+	0.999761i	$0.493040\pi$
$132$	2.25464	−	1.47456i	0.196241	−	0.128344i
$133$	−6.99297	+	7.76648i	−0.606367	+	0.673439i
$134$	−4.02949	−	2.92759i	−0.348095	−	0.252906i
$135$	−11.5263	−	1.46420i	−0.992028	−	0.126018i
$136$	10.2453	−	7.44368i	0.878531	−	0.638290i
$137$	0.190067	−	1.80837i	0.0162385	−	0.154499i	−0.983398	−	0.181462i	$-0.941917\pi$
$137$	0.190067	−	1.80837i	0.0162385	−	0.154499i	0.999636	+	0.0269631i	$0.00858365\pi$
$138$	−8.90821	−	0.438013i	−0.758317	−	0.0372861i
$139$	1.07343	+	10.2130i	0.0910470	+	0.866254i	0.940775	+	0.339032i	$0.110100\pi$
$139$	1.07343	+	10.2130i	0.0910470	+	0.866254i	−0.849728	+	0.527222i	$0.823234\pi$
$140$	−2.66946	−	7.66338i	−0.225611	−	0.647674i
$141$	−5.25570	−	10.2330i	−0.442609	−	0.861778i
$142$	−3.91507	+	4.34813i	−0.328546	+	0.364887i
$143$	−6.56427			−0.548932
$144$	0.285197	+	0.629586i	0.0237664	+	0.0524655i
$145$	−9.61241	+	11.1382i	−0.798267	+	0.924974i
$146$	5.55334	−	1.18040i	0.459598	−	0.0976905i
$147$	4.01217	+	1.06118i	0.330918	+	0.0875247i
$148$	−0.904043	−	8.60140i	−0.0743119	−	0.707031i
$149$	−3.40851	+	5.90371i	−0.279236	+	0.483651i	−0.971195	−	0.238286i	$-0.923415\pi$
$149$	−3.40851	+	5.90371i	−0.279236	+	0.483651i	0.691959	+	0.721937i	$0.256748\pi$
$150$	−7.12432	−	3.23239i	−0.581698	−	0.263924i
$151$	9.80375	+	16.9806i	0.797818	+	1.38186i	0.921034	+	0.389482i	$0.127346\pi$
$151$	9.80375	+	16.9806i	0.797818	+	1.38186i	−0.123216	+	0.992380i	$0.539321\pi$
$152$	−7.93342	+	5.76397i	−0.643485	+	0.467519i
$153$	−9.87298	−	8.77485i	−0.798183	−	0.709405i
$154$	−1.12415	+	3.45978i	−0.0905866	+	0.278797i
$155$	11.0315	−	5.19228i	0.886072	−	0.417054i
$156$	−1.57019	+	10.1253i	−0.125716	+	0.810676i
$157$	7.62958	−	13.2148i	0.608907	−	1.05466i	−0.382514	−	0.923950i	$-0.624942\pi$
$157$	7.62958	−	13.2148i	0.608907	−	1.05466i	0.991421	−	0.130708i	$-0.0417251\pi$
$158$	−2.49387	−	0.530089i	−0.198402	−	0.0421716i
$159$	12.2054	+	0.600134i	0.967951	+	0.0475937i
$160$	−1.55496	−	12.2997i	−0.122930	−	0.972374i
$161$	−14.1360	+	10.2704i	−1.11407	+	0.809419i
$162$	6.51520	−	4.86340i	0.511883	−	0.382105i
$163$	−0.570284	−	0.414336i	−0.0446681	−	0.0324533i	0.565227	−	0.824935i	$-0.308789\pi$
$163$	−0.570284	−	0.414336i	−0.0446681	−	0.0324533i	−0.609895	+	0.792482i	$0.708789\pi$
$164$	−1.72237	−	0.766848i	−0.134494	−	0.0598808i
$165$	−2.41926	−	4.47613i	−0.188339	−	0.348466i
$166$	9.95619	−	4.43278i	0.772750	−	0.344051i
$167$	4.41742	+	0.938953i	0.341831	+	0.0726583i	0.375628	−	0.926770i	$-0.377427\pi$
$167$	4.41742	+	0.938953i	0.341831	+	0.0726583i	−0.0337978	+	0.999429i	$0.510760\pi$
$168$	13.6286	+	6.88878i	1.05147	+	0.531481i
$169$	8.00710	−	8.89278i	0.615930	−	0.684060i
$170$	−4.60794	−	7.60704i	−0.353413	−	0.583433i
$171$	7.64507	+	6.79475i	0.584633	+	0.519607i
$172$	−1.64027	+	5.04822i	−0.125069	+	0.384923i
$173$	−3.97911	−	1.77162i	−0.302527	−	0.134693i	0.249859	−	0.968282i	$-0.419616\pi$
$173$	−3.97911	−	1.77162i	−0.302527	−	0.134693i	−0.552386	+	0.833589i	$0.686282\pi$
$174$	−0.571995	−	10.2790i	−0.0433629	−	0.779248i
$175$	−14.8443	+	3.81428i	−1.12212	+	0.288333i
$176$	−0.151336	+	0.262122i	−0.0114074	+	0.0197582i
$177$	3.85886	+	4.73395i	0.290050	+	0.355826i
$178$	6.54467	−	1.39111i	0.490544	−	0.104268i
$179$	−0.115016	+	0.353983i	−0.00859671	+	0.0264579i	−0.955263	−	0.295758i	$-0.904428\pi$
$179$	−0.115016	+	0.353983i	−0.00859671	+	0.0264579i	0.946666	+	0.322216i	$0.104428\pi$
$180$	−7.48309	+	2.66099i	−0.557757	+	0.198338i
$181$	1.51210	+	4.65376i	0.112393	+	0.345912i	0.991394	−	0.130908i	$-0.0417894\pi$
$181$	1.51210	+	4.65376i	0.112393	+	0.345912i	−0.879001	+	0.476820i	$0.841789\pi$
$182$	−6.91802	−	11.9824i	−0.512797	−	0.888191i
$183$	−3.25453	+	20.9868i	−0.240582	+	1.55139i
$184$	−14.9779	+	6.66857i	−1.10418	+	0.491614i
$185$	−16.3310	+	0.343591i	−1.20068	+	0.0252613i
$186$	−3.03166	+	7.97465i	−0.222292	+	0.584730i
$187$	0.604626	−	5.75263i	0.0442146	−	0.420674i
$188$	−6.36165	−	4.62201i	−0.463971	−	0.337094i
$189$	3.97315	−	15.4243i	0.289004	−	1.12195i
$190$	3.56813	+	5.89046i	0.258859	+	0.427339i
$191$	−0.438688	+	4.17383i	−0.0317423	+	0.302008i	0.967120	+	0.254321i	$0.0818518\pi$
$191$	−0.438688	+	4.17383i	−0.0317423	+	0.302008i	−0.998862	+	0.0476875i	$0.984815\pi$
$192$	7.38123	+	5.93783i	0.532695	+	0.428526i
$193$	1.47540	−	2.55547i	0.106202	−	0.183946i	−0.808027	−	0.589146i	$-0.799464\pi$
$193$	1.47540	−	2.55547i	0.106202	−	0.183946i	0.914228	+	0.405199i	$0.132798\pi$
$194$	15.0417	+	3.19722i	1.07993	+	0.229547i
$195$	18.8085	+	4.55362i	1.34691	+	0.326092i
$196$	2.77483	−	0.589809i	0.198202	−	0.0421292i
$197$	−2.11764	+	6.51743i	−0.150876	+	0.464348i	−0.997720	−	0.0674935i	$-0.978500\pi$
$197$	−2.11764	+	6.51743i	−0.150876	+	0.464348i	0.846844	+	0.531842i	$0.178500\pi$
$198$	3.39311	+	1.07831i	0.241138	+	0.0766318i
$199$	9.62725			0.682458			0.341229	−	0.939980i	$-0.389157\pi$
$199$	9.62725			0.682458			0.341229	+	0.939980i	$0.389157\pi$
$200$	−14.3685	+	0.604870i	−1.01601	+	0.0427708i
$201$	0.530596	+	9.53501i	0.0374253	+	0.672548i
$202$	−1.19486	−	11.3683i	−0.0840700	−	0.799872i
$203$	−13.4954	−	14.9881i	−0.947190	−	1.05196i
$204$	−8.72876	−	2.30867i	−0.611135	−	0.161639i
$205$	−1.71515	+	3.12053i	−0.119791	+	0.217947i
$206$	5.18192	+	15.9483i	0.361042	+	1.11117i
$207$	10.1407	+	13.7696i	0.704830	+	0.957052i
$208$	−0.355733	−	1.09483i	−0.0246656	−	0.0759130i
$209$	−0.468188	+	4.45451i	−0.0323852	+	0.308125i
$210$	5.62105	−	9.13344i	0.387890	−	0.630267i
$211$	0.649884	+	6.18323i	0.0447398	+	0.425671i	0.993851	+	0.110729i	$0.0353185\pi$
$211$	0.649884	+	6.18323i	0.0447398	+	0.425671i	−0.949111	+	0.314942i	$0.898015\pi$
$212$	7.63092	−	3.39750i	0.524094	−	0.233341i
$213$	11.2048	+	0.550936i	0.767742	+	0.0377495i
$214$	−10.1689	−	4.52749i	−0.695133	−	0.309493i
$215$	9.24207	+	3.88400i	0.630304	+	0.264887i
$216$	6.65572	−	13.3816i	0.452864	−	0.910500i
$217$	5.16487	+	15.8958i	0.350614	+	1.07908i
$218$	−0.207863	−	0.360029i	−0.0140783	−	0.0243842i
$219$	−8.48174	−	6.82314i	−0.573143	−	0.461065i
$220$	−2.85611	−	1.98466i	−0.192559	−	0.133805i
$221$	14.7208	+	16.3492i	0.990231	+	1.09976i
$222$	8.05605	−	8.10826i	0.540687	−	0.544191i
$223$	14.2889	+	6.36182i	0.956854	+	0.426019i	0.824926	−	0.565240i	$-0.191217\pi$
$223$	14.2889	+	6.36182i	0.956854	+	0.426019i	0.131928	+	0.991259i	$0.457883\pi$
$224$	16.9951			1.13554
$225$	3.82679	+	14.5036i	0.255120	+	0.966909i
$226$	−10.6841			−0.710696
$227$	−3.05923	−	1.36206i	−0.203048	−	0.0904029i	0.302693	−	0.953088i	$-0.402114\pi$
$227$	−3.05923	−	1.36206i	−0.203048	−	0.0904029i	−0.505741	+	0.862685i	$0.668781\pi$
$228$	6.75906	+	1.78771i	0.447630	+	0.118394i
$229$	15.8284	+	17.5792i	1.04597	+	1.16167i	0.986554	+	0.163436i	$0.0522576\pi$
$229$	15.8284	+	17.5792i	1.04597	+	1.16167i	0.0594174	+	0.998233i	$0.481076\pi$
$230$	3.78769	+	10.8735i	0.249753	+	0.716979i
$231$	6.50359	−	2.52063i	0.427905	−	0.165845i
$232$	−9.46229	−	16.3892i	−0.621230	−	1.07600i
$233$	−6.81754	−	20.9822i	−0.446632	−	1.37459i	−0.880684	−	0.473704i	$-0.842917\pi$
$233$	−6.81754	−	20.9822i	−0.446632	−	1.37459i	0.434053	−	0.900888i	$-0.357083\pi$
$234$	−11.6831	+	6.84625i	−0.763748	+	0.447553i
$235$	−9.70314	+	11.2433i	−0.632963	+	0.733431i
$236$	3.81383	+	1.69803i	0.248259	+	0.110532i
$237$	2.23336	+	4.34844i	0.145072	+	0.282462i
$238$	11.1380	−	4.95896i	0.721969	−	0.321441i
$239$	1.51232	+	14.3888i	0.0978238	+	0.930731i	0.927837	+	0.372987i	$0.121666\pi$
$239$	1.51232	+	14.3888i	0.0978238	+	0.930731i	−0.830013	+	0.557744i	$0.811667\pi$
$240$	0.615454	−	0.646072i	0.0397274	−	0.0417038i
$241$	−0.931272	+	8.86046i	−0.0599885	+	0.570753i	0.922704	+	0.385509i	$0.125974\pi$
$241$	−0.931272	+	8.86046i	−0.0599885	+	0.570753i	−0.982693	+	0.185244i	$0.940693\pi$
$242$	−2.58889	−	7.96779i	−0.166420	−	0.512189i
$243$	−15.1205	−	3.79091i	−0.969979	−	0.243187i
$244$	4.48600	+	13.8065i	0.287187	+	0.883870i
$245$	−0.672000	−	5.31549i	−0.0429325	−	0.339594i
$246$	−0.652654	−	2.40465i	−0.0416117	−	0.153315i
$247$	−11.3990	−	12.6599i	−0.725300	−	0.805527i
$248$	1.63932	+	15.5971i	0.104097	+	0.990415i
$249$	−18.6490	−	9.42641i	−1.18183	−	0.597374i
$250$	−0.420149	+	10.0911i	−0.0265725	+	0.638218i
$251$	12.4010			0.782742			0.391371	−	0.920233i	$-0.372001\pi$
$251$	12.4010			0.782742			0.391371	+	0.920233i	$0.372001\pi$
$252$	−2.33237	−	10.6347i	−0.146926	−	0.669922i
$253$	−2.31412	+	7.12212i	−0.145487	+	0.447764i
$254$	15.4708	−	3.28843i	0.970727	−	0.206334i
$255$	−5.72301	+	16.0635i	−0.358389	+	1.00594i
$256$	16.1321	+	3.42897i	1.00825	+	0.214311i
$257$	15.6534	−	27.1124i	0.976431	−	1.69123i	0.301301	−	0.953529i	$-0.402579\pi$
$257$	15.6534	−	27.1124i	0.976431	−	1.69123i	0.675130	−	0.737699i	$-0.264088\pi$
$258$	−6.54082	+	2.53505i	−0.407214	+	0.157826i
$259$	2.34062	−	22.2695i	0.145439	−	1.38376i
$260$	12.8782	−	3.02181i	0.798673	−	0.187405i
$261$	−14.5832	+	13.3024i	−0.902678	+	0.823395i
$262$	3.83522	+	2.78645i	0.236940	+	0.172147i
$263$	−2.67571	+	25.4577i	−0.164992	+	1.56979i	0.528252	+	0.849087i	$0.322847\pi$
$263$	−2.67571	+	25.4577i	−0.164992	+	1.56979i	−0.693244	+	0.720703i	$0.743819\pi$
$264$	6.46086	−	1.04470i	0.397638	−	0.0642969i
$265$	−5.18962	−	14.8981i	−0.318796	−	0.915185i
$266$	−8.62464	+	3.83994i	−0.528810	+	0.235442i
$267$	−9.99583	−	8.04115i	−0.611735	−	0.492110i
$268$	3.26387	+	5.65319i	0.199373	+	0.345324i
$269$	0.317149	+	0.976085i	0.0193369	+	0.0595129i	0.960259	−	0.279109i	$-0.0900392\pi$
$269$	0.317149	+	0.976085i	0.0193369	+	0.0595129i	−0.940922	+	0.338622i	$0.890039\pi$
$270$	−8.97421	−	5.44345i	−0.546153	−	0.331278i
$271$	6.14011	−	18.8973i	0.372985	−	1.14793i	−0.571843	−	0.820363i	$-0.693771\pi$
$271$	6.14011	−	18.8973i	0.372985	−	1.14793i	0.944828	−	0.327567i	$-0.106229\pi$
$272$	0.992228	−	0.210905i	0.0601627	−	0.0127880i
$273$	−9.42691	+	24.7970i	−0.570543	+	1.50078i
$274$	0.821301	−	1.42253i	0.0496166	−	0.0859384i
$275$	−4.18611	+	5.06203i	−0.252432	+	0.305252i
$276$	10.4323	+	5.27313i	0.627948	+	0.317405i
$277$	16.5366	+	7.36256i	0.993587	+	0.442373i	0.838131	−	0.545470i	$-0.183649\pi$
$277$	16.5366	+	7.36256i	0.993587	+	0.442373i	0.155456	+	0.987843i	$0.450315\pi$
$278$	−2.86669	+	8.82276i	−0.171933	+	0.529154i
$279$	15.5242	−	5.15522i	0.929410	−	0.308635i
$280$	1.64785	−	19.6454i	0.0984778	−	1.17404i
$281$	−17.1957	+	19.0978i	−1.02581	+	1.13928i	−0.0356460	+	0.999364i	$0.511349\pi$
$281$	−17.1957	+	19.0978i	−1.02581	+	1.13928i	−0.990164	+	0.139913i	$0.955318\pi$
$282$	−0.577394	−	10.3760i	−0.0343833	−	0.617882i
$283$	−8.60803	−	1.82969i	−0.511694	−	0.108764i	−0.0551737	−	0.998477i	$-0.517571\pi$
$283$	−8.60803	−	1.82969i	−0.511694	−	0.108764i	−0.456521	+	0.889713i	$0.650905\pi$
$284$	7.00535	−	3.11898i	0.415691	−	0.185078i
$285$	4.43158	−	12.4387i	0.262504	−	0.736804i
$286$	−5.41722	−	2.41190i	−0.320327	−	0.142619i
$287$	−3.94908	−	2.86917i	−0.233107	−	0.169362i
$288$	−0.107445	−	16.6327i	−0.00633125	−	0.980093i
$289$	−1.93028	+	1.40243i	−0.113546	+	0.0824960i
$290$	−12.0252	+	5.65999i	−0.706145	+	0.332366i
$291$	−13.4705	−	26.2275i	−0.789652	−	1.53748i
$292$	−7.27822	−	1.54703i	−0.425926	−	0.0905333i
$293$	−3.17339	+	5.49647i	−0.185391	+	0.321107i	−0.943708	−	0.330779i	$-0.892689\pi$
$293$	−3.17339	+	5.49647i	−0.185391	+	0.321107i	0.758317	+	0.651886i	$0.226022\pi$
$294$	2.92117	+	2.34994i	0.170366	+	0.137051i
$295$	3.79785	−	6.90977i	0.221119	−	0.402302i
$296$	6.49279	−	19.9828i	0.377386	−	1.16147i
$297$	−2.50799	−	6.34897i	−0.145528	−	0.368405i
$298$	−4.98210	+	3.61971i	−0.288605	+	0.209684i
$299$	−14.2411	−	24.6662i	−0.823582	−	1.42649i
$300$	6.80682	+	7.66788i	0.392992	+	0.442705i
$301$	−6.87138	+	11.9016i	−0.396060	+	0.685996i
$302$	1.85147	+	17.6156i	0.106540	+	1.01366i
$303$	−15.4476	+	15.5477i	−0.887440	+	0.893191i
$304$	−0.768325	+	0.163313i	−0.0440665	+	0.00936662i
$305$	26.6927	−	6.26331i	1.52842	−	0.358636i
$306$	−4.92363	−	10.8691i	−0.281465	−	0.621347i
$307$	−25.8730			−1.47665			−0.738325	−	0.674445i	$-0.764383\pi$
$307$	−25.8730			−1.47665			−0.738325	+	0.674445i	$0.764383\pi$
$308$	3.19024	−	3.54312i	0.181781	−	0.201888i
$309$	17.4241	−	27.0214i	0.991222	−	1.53720i
$310$	11.0116	−	0.231676i	0.625419	−	0.0131583i
$311$	−0.350514	−	3.33492i	−0.0198758	−	0.189106i	0.980079	−	0.198608i	$-0.0636421\pi$
$311$	−0.350514	−	3.33492i	−0.0198758	−	0.189106i	−0.999955	+	0.00950197i	$0.996975\pi$
$312$	−13.4898	+	20.9201i	−0.763709	+	1.18437i
$313$	0.927483	−	8.82441i	0.0524244	−	0.498785i	−0.936532	−	0.350581i	$-0.885984\pi$
$313$	0.927483	−	8.82441i	0.0524244	−	0.498785i	0.988957	−	0.148204i	$-0.0473492\pi$
$314$	11.1519	−	8.10232i	0.629338	−	0.457241i
$315$	−20.3832	+	2.71079i	−1.14846	+	0.152736i
$316$	2.70333	+	1.96408i	0.152074	+	0.110488i
$317$	−21.3777	+	23.7423i	−1.20069	+	1.33350i	−0.272157	+	0.962253i	$0.587737\pi$
$317$	−21.3777	+	23.7423i	−1.20069	+	1.33350i	−0.928534	+	0.371249i	$0.878930\pi$
$318$	9.85210	+	4.97988i	0.552478	+	0.279258i
$319$	−8.45500	−	1.79717i	−0.473389	−	0.100622i
$320$	3.53372	−	11.7081i	0.197541	−	0.654504i
$321$	5.59040	+	20.5973i	0.312026	+	1.14963i
$322$	−15.4395	+	3.28176i	−0.860407	+	0.182885i
$323$	12.1445	−	8.82347i	0.675736	−	0.490951i
$324$	−10.3932	+	2.34987i	−0.577397	+	0.130548i
$325$	−3.65418	−	24.7145i	−0.202697	−	1.37091i
$326$	−0.318393	−	0.551473i	−0.0176342	−	0.0305433i
$327$	−0.283247	+	0.745067i	−0.0156636	+	0.0412023i
$328$	−3.06479	−	3.40380i	−0.169225	−	0.187943i
$329$	−13.6228	−	15.1296i	−0.751047	−	0.834122i
$330$	−0.351856	−	4.58287i	−0.0193690	−	0.252279i
$331$	−8.25522	+	9.16835i	−0.453748	+	0.503938i	−0.925999	−	0.377526i	$-0.876775\pi$
$331$	−8.25522	+	9.16835i	−0.453748	+	0.503938i	0.472251	+	0.881464i	$0.343442\pi$
$332$	−14.2835			−0.783908
$333$	−21.8095	−	2.14992i	−1.19515	−	0.117815i
$334$	3.30052	+	2.39797i	0.180596	+	0.131211i
$335$	11.1549	−	5.25033i	0.609455	−	0.286856i
$336$	0.772851	+	0.948114i	0.0421625	+	0.0517239i
$337$	−6.54409	+	2.91362i	−0.356479	+	0.158715i	−0.577160	−	0.816631i	$-0.695839\pi$
$337$	−6.54409	+	2.91362i	−0.356479	+	0.158715i	0.220680	+	0.975346i	$0.429172\pi$
$338$	9.87539	−	4.39681i	0.537151	−	0.239155i
$339$	12.9431	+	15.8782i	0.702970	+	0.862386i
$340$	1.46198	+	11.5642i	0.0792872	+	0.627158i
$341$	5.79521	+	4.21047i	0.313828	+	0.228010i
$342$	3.81258	+	8.41645i	0.206161	+	0.455109i
$343$	−14.1124			−0.761998
$344$	−8.62854	+	9.58296i	−0.465219	+	0.516679i
$345$	11.5712	−	18.8016i	0.622972	−	1.01224i
$346$	−2.63286	−	2.92408i	−0.141543	−	0.157200i
$347$	0.212737	+	0.236268i	0.0114203	+	0.0126835i	0.748828	−	0.662764i	$-0.230617\pi$
$347$	0.212737	+	0.236268i	0.0114203	+	0.0126835i	−0.737408	+	0.675448i	$0.763950\pi$
$348$	−4.79457	+	12.6119i	−0.257016	+	0.676068i
$349$	−7.13603	−	12.3600i	−0.381983	−	0.661614i	0.609363	−	0.792892i	$-0.291425\pi$
$349$	−7.13603	−	12.3600i	−0.381983	−	0.661614i	−0.991346	+	0.131278i	$0.958092\pi$
$350$	−13.6519	−	2.30645i	−0.729723	−	0.123285i
$351$	24.3279	+	9.06912i	1.29852	+	0.484074i
$352$	5.89274	−	4.28133i	0.314084	−	0.228196i
$353$	14.5817	−	3.09943i	0.776104	−	0.164966i	0.197202	−	0.980363i	$-0.436815\pi$
$353$	14.5817	−	3.09943i	0.776104	−	0.164966i	0.578902	+	0.815397i	$0.303481\pi$
$354$	1.44517	+	5.32459i	0.0768099	+	0.282999i
$355$	−4.76418	−	13.6768i	−0.252857	−	0.725890i
$356$	−8.57746	−	1.82320i	−0.454605	−	0.0966292i
$357$	−20.8627	−	10.5453i	−1.10417	−	0.558118i
$358$	−0.224982	+	0.249868i	−0.0118907	+	0.0132059i
$359$	12.3016	+	8.93763i	0.649253	+	0.471710i	0.863017	−	0.505175i	$-0.168572\pi$
$359$	12.3016	+	8.93763i	0.649253	+	0.471710i	−0.213763	+	0.976885i	$0.568572\pi$
$360$	−19.2369	−	1.48851i	−1.01387	−	0.0784514i
$361$	5.96733	−	4.33552i	0.314070	−	0.228185i
$362$	−0.462054	+	4.39615i	−0.0242850	+	0.231057i
$363$	−8.70509	+	13.4999i	−0.456899	+	0.708562i
$364$	1.89547	+	18.0342i	0.0993497	+	0.945249i
$365$	−4.06058	+	13.4538i	−0.212540	+	0.704202i
$366$	−10.3970	+	16.1237i	−0.543460	+	0.842801i
$367$	5.63960	−	6.26341i	0.294385	−	0.326948i	−0.577749	−	0.816214i	$-0.696069\pi$
$367$	5.63960	−	6.26341i	0.294385	−	0.326948i	0.872134	+	0.489267i	$0.162736\pi$
$368$	−1.31328			−0.0684595
$369$	−2.78302	+	3.88301i	−0.144878	+	0.202141i
$370$	−13.6035	−	5.71693i	−0.707215	−	0.297209i
$371$	21.1540	−	4.49643i	1.09826	−	0.233443i
$372$	7.88084	−	7.93192i	0.408603	−	0.411251i
$373$	−3.37560	−	32.1167i	−0.174782	−	1.66294i	−0.633039	−	0.774120i	$-0.718193\pi$
$373$	−3.37560	−	32.1167i	−0.174782	−	1.66294i	0.458257	−	0.888820i	$-0.348474\pi$
$374$	2.61266	−	4.52525i	0.135097	−	0.233995i
$375$	15.5059	−	11.6003i	0.800722	−	0.599036i
$376$	−9.55160	−	16.5439i	−0.492586	−	0.853184i
$377$	26.5972	−	19.3240i	1.36983	−	0.995238i
$378$	8.94620	−	11.2692i	0.460143	−	0.579624i
$379$	5.98776	−	18.4284i	0.307571	−	0.946605i	−0.671135	−	0.741335i	$-0.734193\pi$
$379$	5.98776	−	18.4284i	0.307571	−	0.946605i	0.978705	−	0.205270i	$-0.0658072\pi$
$380$	−1.13208	−	8.95468i	−0.0580744	−	0.459365i
$381$	−23.6290	−	19.0083i	−1.21055	−	0.973826i
$382$	−1.89562	+	3.28331i	−0.0969883	+	0.167989i
$383$	25.8583	+	5.49635i	1.32130	+	0.280851i	0.813972	−	0.580904i	$-0.197301\pi$
$383$	25.8583	+	5.49635i	1.32130	+	0.280851i	0.507326	+	0.861754i	$0.330634\pi$
$384$	−4.86497	−	9.47229i	−0.248265	−	0.483381i
$385$	−6.16471	−	6.56354i	−0.314183	−	0.334509i
$386$	2.15654	−	1.56682i	0.109765	−	0.0797489i
$387$	11.6912	+	6.64961i	0.594299	+	0.338019i
$388$	−16.3050	−	11.8463i	−0.827762	−	0.601405i
$389$	9.64786	+	4.29550i	0.489166	+	0.217791i	0.636471	−	0.771300i	$-0.280393\pi$
$389$	9.64786	+	4.29550i	0.489166	+	0.217791i	−0.147305	+	0.989091i	$0.547060\pi$
$390$	13.8488	+	10.6687i	0.701260	+	0.540231i
$391$	22.9281	−	10.2082i	1.15952	−	0.516253i
$392$	6.74111	+	1.43287i	0.340477	+	0.0723707i
$393$	−0.505014	−	9.07531i	−0.0254746	−	0.457789i
$394$	−4.14230	+	4.60049i	−0.208686	+	0.231769i
$395$	4.12326	−	4.77774i	0.207464	−	0.240394i
$396$	−3.48774	−	3.09981i	−0.175265	−	0.155772i
$397$	−0.814060	+	2.50542i	−0.0408565	+	0.125743i	−0.969404	−	0.245469i	$-0.921058\pi$
$397$	−0.814060	+	2.50542i	−0.0408565	+	0.125743i	0.928548	+	0.371213i	$0.121058\pi$
$398$	7.94498	+	3.53733i	0.398246	+	0.177310i
$399$	16.1549	+	8.16571i	0.808756	+	0.408797i
$400$	−1.07113	−	0.423864i	−0.0535567	−	0.0211932i
$401$	3.74794	−	6.49163i	0.187163	−	0.324177i	−0.757140	−	0.653253i	$-0.773404\pi$
$401$	3.74794	−	6.49163i	0.187163	−	0.324177i	0.944303	+	0.329076i	$0.106737\pi$
$402$	−3.06556	+	8.06381i	−0.152896	+	0.402186i
$403$	−26.6493	+	5.66448i	−1.32750	+	0.282168i
$404$	−4.62951	+	14.2482i	−0.230327	+	0.708873i
$405$	2.78185	+	19.9314i	0.138231	+	0.990400i
$406$	−5.63011	−	17.3277i	−0.279417	−	0.859959i
$407$	−4.79846	−	8.31118i	−0.237851	−	0.411970i
$408$	−17.0909	−	13.7488i	−0.846125	−	0.680665i
$409$	30.1389	−	13.4187i	1.49027	−	0.663513i	0.509824	−	0.860279i	$-0.329710\pi$
$409$	30.1389	−	13.4187i	1.49027	−	0.663513i	0.980451	+	0.196766i	$0.0630438\pi$
$410$	−2.56201	+	1.94505i	−0.126529	+	0.0960590i
$411$	−3.10905	+	0.502725i	−0.153358	+	0.0247976i
$412$	2.29728	−	21.8572i	0.113179	−	1.07683i
$413$	8.74443	+	6.35320i	0.430285	+	0.312620i
$414$	3.30939	+	15.0895i	0.162647	+	0.741607i
$415$	−2.25487	+	26.8822i	−0.110687	+	1.31960i
$416$	−2.89577	+	27.5514i	−0.141977	+	1.35082i
$417$	16.5848	−	6.42784i	0.812160	−	0.314772i
$418$	−2.02309	+	3.50410i	−0.0989527	+	0.171391i
$419$	−17.7269	−	3.76797i	−0.866017	−	0.184078i	−0.246579	−	0.969123i	$-0.579306\pi$
$419$	−17.7269	−	3.76797i	−0.866017	−	0.184078i	−0.619438	+	0.785045i	$0.712640\pi$
$420$	−11.5988	+	7.93901i	−0.565965	+	0.387384i
$421$	−23.5464	+	5.00494i	−1.14758	+	0.243926i	−0.742171	−	0.670210i	$-0.766204\pi$
$421$	−23.5464	+	5.00494i	−1.14758	+	0.243926i	−0.405408	+	0.914136i	$0.632871\pi$
$422$	−1.73558	+	5.34155i	−0.0844865	+	0.260023i
$423$	−14.7209	+	13.4279i	−0.715752	+	0.652888i
$424$	20.2928			0.985503
$425$	21.9953	−	0.925935i	1.06693	−	0.0449145i
$426$	9.04445	+	4.57164i	0.438205	+	0.221497i
$427$	3.92875	+	37.3795i	0.190125	+	1.80892i
$428$	9.76172	+	10.8415i	0.471851	+	0.524043i
$429$	2.97814	+	10.9727i	0.143786	+	0.529766i
$430$	6.20000	+	6.60111i	0.298991	+	0.318334i
$431$	−5.44510	−	16.7583i	−0.262281	−	0.807218i	−0.992307	−	0.123799i	$-0.960492\pi$
$431$	−5.44510	−	16.7583i	−0.262281	−	0.807218i	0.730026	−	0.683419i	$-0.239508\pi$
$432$	0.923010	−	0.762365i	0.0444083	−	0.0366793i
$433$	0.572909	+	1.76323i	0.0275322	+	0.0847355i	0.963878	−	0.266342i	$-0.0858152\pi$
$433$	0.572909	+	1.76323i	0.0275322	+	0.0847355i	−0.936346	+	0.351078i	$0.885815\pi$
$434$	−1.57823	+	15.0159i	−0.0757576	+	0.720786i
$435$	22.9793	+	11.0146i	1.10177	+	0.528110i
$436$	0.0569525	+	0.541866i	0.00272753	+	0.0259507i
$437$	−17.7542	+	7.90469i	−0.849299	+	0.378132i
$438$	−4.49261	−	8.74729i	−0.214665	−	0.417962i
$439$	−8.78739	−	3.91240i	−0.419399	−	0.186728i	0.186176	−	0.982516i	$-0.440390\pi$
$439$	−8.78739	−	3.91240i	−0.419399	−	0.186728i	−0.605576	+	0.795788i	$0.707057\pi$
$440$	−4.37761	−	7.22680i	−0.208695	−	0.344524i
$441$	−0.0464339	−	7.18809i	−0.00221114	−	0.342290i
$442$	6.14136	+	18.9011i	0.292114	+	0.899036i
$443$	−18.6090	−	32.2317i	−0.884138	−	1.53137i	−0.846698	−	0.532073i	$-0.821413\pi$
$443$	−18.6090	−	32.2317i	−0.884138	−	1.53137i	−0.0374398	−	0.999299i	$-0.511920\pi$
$444$	−13.9677	+	5.41354i	−0.662879	+	0.256915i
$445$	−4.78544	+	15.8554i	−0.226851	+	0.751618i
$446$	9.45451	+	10.5003i	0.447684	+	0.497203i
$447$	11.4149	+	3.01913i	0.539907	+	0.142800i
$448$	15.3157	+	6.81899i	0.723599	+	0.322167i
$449$	−27.8383			−1.31377			−0.656885	−	0.753991i	$-0.728126\pi$
$449$	−27.8383			−1.31377			−0.656885	+	0.753991i	$0.728126\pi$
$450$	−2.17096	+	13.3753i	−0.102340	+	0.630519i
$451$	−2.09206			−0.0985111
$452$	12.7920	+	5.69537i	0.601686	+	0.267888i
$453$	23.9365	−	24.0916i	1.12464	−	1.13192i
$454$	−2.02420	−	2.24810i	−0.0950003	−	0.105509i
$455$	34.2405	−	0.720393i	1.60522	−	0.0337725i
$456$	13.2342	+	10.6463i	0.619749	+	0.498557i
$457$	4.49089	+	7.77846i	0.210075	+	0.363861i	0.951738	−	0.306912i	$-0.0992958\pi$
$457$	4.49089	+	7.77846i	0.210075	+	0.363861i	−0.741663	+	0.670773i	$0.765962\pi$
$458$	6.60342	+	20.3232i	0.308558	+	0.949643i
$459$	−10.1886	+	20.4845i	−0.475562	+	0.956134i
$460$	1.26137	−	15.0379i	0.0588119	−	0.701147i
$461$	−10.6691	−	4.75018i	−0.496909	−	0.221238i	0.142951	−	0.989730i	$-0.454341\pi$
$461$	−10.6691	−	4.75018i	−0.496909	−	0.221238i	−0.639860	+	0.768492i	$0.721008\pi$
$462$	6.29330	+	0.309439i	0.292791	+	0.0143964i
$463$	24.8731	−	11.0742i	1.15595	−	0.514662i	0.262990	−	0.964799i	$-0.415291\pi$
$463$	24.8731	−	11.0742i	1.15595	−	0.514662i	0.892960	+	0.450137i	$0.148625\pi$
$464$	−0.158452	−	1.50757i	−0.00735597	−	0.0699874i
$465$	−13.6842	−	16.0843i	−0.634588	−	0.745893i
$466$	2.08324	−	19.8207i	0.0965043	−	0.918177i
$467$	−1.51920	−	4.67562i	−0.0703002	−	0.216362i	0.909734	−	0.415192i	$-0.136286\pi$
$467$	−1.51920	−	4.67562i	−0.0703002	−	0.216362i	−0.980034	+	0.198830i	$0.936286\pi$
$468$	17.6377	−	1.96907i	0.815301	−	0.0910201i
$469$	5.22261	+	16.0736i	0.241158	+	0.742208i
$470$	−12.1387	+	5.71341i	−0.559917	+	0.263540i
$471$	−25.5510	−	6.75801i	−1.17733	−	0.311392i
$472$	6.78636	+	7.53701i	0.312367	+	0.346919i
$473$	0.615664	+	5.85765i	0.0283083	+	0.269335i
$474$	0.245359	+	4.40919i	0.0112697	+	0.202521i
$475$	−17.0319	+	0.716992i	−0.781477	+	0.0328978i
$476$	−15.9789			−0.732394
$477$	−4.53428	−	20.6745i	−0.207611	−	0.946621i
$478$	−4.03879	+	12.4301i	−0.184730	+	0.568541i
$479$	−34.0425	+	7.23596i	−1.55544	+	0.330619i	−0.903816	−	0.427921i	$-0.859246\pi$
$479$	−34.0425	+	7.23596i	−1.55544	+	0.330619i	−0.651626	+	0.758541i	$0.725913\pi$
$480$	−19.8544	+	8.17946i	−0.906223	+	0.373339i
$481$	35.7031	+	7.58893i	1.62792	+	0.346026i
$482$	−4.02413	+	6.97000i	−0.183294	+	0.317475i
$483$	23.5810	+	18.9698i	1.07297	+	0.863154i
$484$	−1.14772	+	10.9199i	−0.0521692	+	0.496357i
$485$	−24.8693	+	28.8168i	−1.12926	+	1.30850i
$486$	−11.0854	−	8.68418i	−0.502845	−	0.393923i
$487$	10.2778	+	7.46726i	0.465732	+	0.338374i	0.795775	−	0.605592i	$-0.207064\pi$
$487$	10.2778	+	7.46726i	0.465732	+	0.338374i	−0.330044	+	0.943966i	$0.607064\pi$
$488$	−3.68643	+	35.0740i	−0.166877	+	1.58773i
$489$	−0.433862	+	1.14125i	−0.0196199	+	0.0516092i
$490$	1.39849	−	4.63357i	0.0631774	−	0.209323i
$491$	10.3803	−	4.62163i	0.468458	−	0.208571i	−0.158911	−	0.987293i	$-0.550798\pi$
$491$	10.3803	−	4.62163i	0.468458	−	0.208571i	0.627369	+	0.778722i	$0.284132\pi$
$492$	−0.500425	+	3.22698i	−0.0225609	+	0.145484i
$493$	14.4849	+	25.0885i	0.652366	+	1.12993i
$494$	−4.75552	−	14.6360i	−0.213961	−	0.658504i
$495$	−6.38460	+	6.07475i	−0.286967	+	0.273040i
$496$	−0.388194	+	1.19474i	−0.0174304	+	0.0536454i
$497$	19.4199	−	4.12782i	0.871101	−	0.185158i
$498$	−11.9267	−	14.6314i	−0.534450	−	0.655650i
$499$	−9.68467	+	16.7743i	−0.433545	+	0.750923i	−0.997176	−	0.0751046i	$-0.976071\pi$
$499$	−9.68467	+	16.7743i	−0.433545	+	0.750923i	0.563630	+	0.826027i	$0.309404\pi$
$500$	5.88231	−	11.8581i	0.263065	−	0.530309i
$501$	−0.434607	−	7.81005i	−0.0194168	−	0.348927i
$502$	10.2340	+	4.55647i	0.456766	+	0.203365i
$503$	5.93488	−	18.2657i	0.264623	−	0.814427i	−0.727157	−	0.686471i	$-0.759159\pi$
$503$	5.93488	−	18.2657i	0.264623	−	0.814427i	0.991780	−	0.127955i	$-0.0408413\pi$
$504$	5.33196	−	25.9067i	0.237504	−	1.15397i
$505$	26.0850	+	10.9623i	1.16077	+	0.487815i
$506$	−4.52662	+	5.02732i	−0.201233	+	0.223491i
$507$	−18.4977	−	9.34991i	−0.821511	−	0.415244i
$508$	−20.2761	−	4.30982i	−0.899607	−	0.191217i
$509$	−13.1641	+	5.86104i	−0.583489	+	0.259786i	−0.677182	−	0.735815i	$-0.736799\pi$
$509$	−13.1641	+	5.86104i	−0.583489	+	0.259786i	0.0936937	+	0.995601i	$0.470133\pi$
$510$	−10.6252	+	11.1538i	−0.470490	+	0.493897i
$511$	−17.5992	−	7.83567i	−0.778543	−	0.346630i
$512$	2.10561	+	1.52982i	0.0930558	+	0.0676090i
$513$	7.88945	−	15.8620i	0.348328	−	0.700325i
$514$	22.8800	−	16.6233i	1.00919	−	0.733222i
$515$	−40.7737	−	7.77410i	−1.79670	−	0.342568i
$516$	9.18265	+	0.451507i	0.404244	+	0.0198765i
$517$	−8.53481	−	1.81413i	−0.375360	−	0.0797853i
$518$	10.1141	−	17.5181i	0.444388	−	0.769703i
$519$	−1.15611	+	7.45516i	−0.0507476	+	0.327245i
$520$	31.5671	+	6.01873i	1.38431	+	0.263939i
$521$	4.65920	−	14.3396i	0.204123	−	0.628227i	−0.795625	−	0.605790i	$-0.792857\pi$
$521$	4.65920	−	14.3396i	0.204123	−	0.628227i	0.999748	−	0.0224375i	$-0.00714269\pi$
$522$	−16.9226	+	5.61960i	−0.740682	+	0.245963i
$523$	12.9615	−	9.41708i	0.566767	−	0.411780i	−0.267162	−	0.963652i	$-0.586086\pi$
$523$	12.9615	−	9.41708i	0.566767	−	0.411780i	0.833929	+	0.551871i	$0.186086\pi$
$524$	−3.10651	−	5.38064i	−0.135709	−	0.235054i
$525$	13.1106	+	23.0829i	0.572192	+	1.00742i
$526$	−11.5621	+	20.0261i	−0.504130	+	0.873178i
$527$	−2.50947	−	23.8760i	−0.109314	−	1.04005i
$528$	0.506816	+	0.134048i	0.0220563	+	0.00583368i
$529$	−9.28544	+	1.97368i	−0.403715	+	0.0858122i
$530$	1.19123	−	14.2016i	0.0517436	−	0.616879i
$531$	6.16244	−	8.59812i	0.267427	−	0.373127i
$532$	12.3732			0.536446
$533$	5.32419	−	5.91312i	0.230616	−	0.256126i
$534$	−5.29460	−	10.3088i	−0.229120	−	0.446105i
$535$	21.9453	−	16.6606i	0.948778	−	0.720299i
$536$	1.65765	+	15.7715i	0.0715995	+	0.681223i
$537$	0.643891	+	0.0316599i	0.0277860	+	0.00136622i
$538$	−0.0969116	+	0.922052i	−0.00417816	+	0.0397525i
$539$	2.54664	−	1.85024i	0.109692	−	0.0796956i
$540$	7.84304	+	11.3013i	0.337511	+	0.486330i
$541$	12.8369	+	9.32652i	0.551900	+	0.400979i	0.828485	−	0.560011i	$-0.189203\pi$
$541$	12.8369	+	9.32652i	0.551900	+	0.400979i	−0.276586	+	0.960989i	$0.589203\pi$
$542$	12.0106	−	13.3391i	0.515900	−	0.572964i
$543$	7.09310	−	4.63895i	0.304394	−	0.199076i
$544$	−23.8781	−	5.07544i	−1.02376	−	0.217608i
$545$	1.02881	−	0.0216454i	0.0440694	−	0.000927186i
$546$	−16.8908	+	17.0003i	−0.722859	+	0.727544i
$547$	15.4623	−	3.28661i	0.661119	−	0.140525i	0.134880	−	0.990862i	$-0.456935\pi$
$547$	15.4623	−	3.28661i	0.661119	−	0.140525i	0.526239	+	0.850337i	$0.323602\pi$
$548$	−1.74165	+	1.26538i	−0.0743996	+	0.0540545i
$549$	36.5576	−	4.08128i	1.56024	−	0.174185i
$550$	−5.31456	+	2.63939i	−0.226614	+	0.112544i
$551$	−11.2163	−	19.4271i	−0.477829	−	0.827624i
$552$	17.9423	+	22.0112i	0.763676	+	0.936858i
$553$	5.78887	+	6.42919i	0.246168	+	0.273397i
$554$	10.9417	+	12.1520i	0.464870	+	0.516290i
$555$	7.98353	+	27.1426i	0.338882	+	1.15214i
$556$	8.13542	−	9.03530i	0.345019	−	0.383182i
$557$	32.3933			1.37255			0.686273	−	0.727344i	$-0.259245\pi$
$557$	32.3933			1.37255			0.686273	+	0.727344i	$0.259245\pi$
$558$	14.7057	+	1.44965i	0.622540	+	0.0613685i
$559$	−18.1233	−	13.1673i	−0.766533	−	0.556919i
$560$	0.760631	−	1.38389i	0.0321425	−	0.0584798i
$561$	−9.89027	+	1.59923i	−0.417568	+	0.0675195i
$562$	−21.2080	+	9.44240i	−0.894605	+	0.398304i
$563$	−16.9161	+	7.53153i	−0.712928	+	0.317416i	−0.730959	−	0.682421i	$-0.760927\pi$
$563$	−16.9161	+	7.53153i	−0.712928	+	0.317416i	0.0180307	+	0.999837i	$0.494260\pi$
$564$	−4.83983	+	12.7309i	−0.203793	+	0.536069i
$565$	12.7384	−	23.1761i	0.535909	−	0.975027i
$566$	−6.43157	−	4.67281i	−0.270339	−	0.196413i
$567$	−27.5854	+	0.356410i	−1.15848	+	0.0149678i
$568$	18.6292			0.781664
$569$	−6.48119	+	7.19809i	−0.271705	+	0.301759i	−0.863520	−	0.504315i	$-0.831745\pi$
$569$	−6.48119	+	7.19809i	−0.271705	+	0.301759i	0.591814	+	0.806074i	$0.298412\pi$
$570$	8.22753	−	8.63684i	0.344613	−	0.361757i
$571$	−20.0597	−	22.2785i	−0.839471	−	0.932327i	0.159018	−	0.987276i	$-0.449167\pi$
$571$	−20.0597	−	22.2785i	−0.839471	−	0.932327i	−0.998489	+	0.0549489i	$0.982500\pi$
$572$	5.20030	+	5.77552i	0.217436	+	0.241487i
$573$	7.17591	−	1.16032i	0.299778	−	0.0484732i
$574$	−2.20480	−	3.81882i	−0.0920264	−	0.159394i
$575$	−28.1030	−	4.74794i	−1.17198	−	0.198003i
$576$	6.57676	−	15.0322i	0.274032	−	0.626343i
$577$	−26.5530	+	19.2919i	−1.10542	+	0.803131i	−0.981936	−	0.189216i	$-0.939405\pi$
$577$	−26.5530	+	19.2919i	−1.10542	+	0.803131i	−0.123480	+	0.992347i	$0.539405\pi$
$578$	−2.10828	+	0.448128i	−0.0876928	+	0.0186397i
$579$	−4.94103	−	1.30685i	−0.205342	−	0.0543110i
$580$	17.4149	−	0.366395i	0.723114	−	0.0152137i
$581$	−36.1727	−	7.68874i	−1.50070	−	0.318983i
$582$	−1.47987	−	26.5939i	−0.0613427	−	1.10235i
$583$	6.20205	−	6.88807i	0.256862	−	0.285275i
$584$	−14.6242	−	10.6251i	−0.605155	−	0.439671i
$585$	−0.921503	−	33.5058i	−0.0380995	−	1.38529i
$586$	−4.63843	+	3.37002i	−0.191612	+	0.139214i
$587$	0.106692	−	1.01511i	0.00440367	−	0.0418981i	−0.992099	−	0.125454i	$-0.959961\pi$
$587$	0.106692	−	1.01511i	0.00440367	−	0.0418981i	0.996503	+	0.0835562i	$0.0266278\pi$
$588$	−2.24482	−	4.37076i	−0.0925749	−	0.180247i
$589$	1.94319	+	18.4882i	0.0800677	+	0.761793i
$590$	5.67306	−	4.30691i	0.233556	−	0.177313i
$591$	11.8551	+	0.582912i	0.487655	+	0.0239778i
$592$	1.12615	−	1.25072i	0.0462847	−	0.0514043i
$593$	4.83840			0.198689			0.0993446	−	0.995053i	$-0.468325\pi$
$593$	4.83840			0.198689			0.0993446	+	0.995053i	$0.468325\pi$
$594$	0.263053	−	6.16105i	0.0107932	−	0.252791i
$595$	−2.52253	+	30.0732i	−0.103413	+	1.23288i
$596$	7.89460	−	1.67805i	0.323375	−	0.0687355i
$597$	−4.36778	−	16.0927i	−0.178761	−	0.658630i
$598$	−2.68947	−	25.5886i	−0.109981	−	1.04640i
$599$	−4.41032	+	7.63890i	−0.180201	+	0.312117i	−0.941949	−	0.335756i	$-0.891008\pi$
$599$	−4.41032	+	7.63890i	−0.180201	+	0.312117i	0.761748	+	0.647874i	$0.224341\pi$
$600$	7.52991	+	23.7436i	0.307407	+	0.969328i
$601$	5.73110	+	9.92656i	0.233777	+	0.404913i	0.958916	−	0.283689i	$-0.0915582\pi$
$601$	5.73110	+	9.92656i	0.233777	+	0.404913i	−0.725140	+	0.688602i	$0.758225\pi$
$602$	−10.0437	+	7.29714i	−0.409349	+	0.297409i
$603$	15.6978	−	5.21286i	0.639263	−	0.212284i
$604$	7.17358	−	22.0780i	0.291889	−	0.898341i
$605$	20.3705	+	3.88394i	0.828180	+	0.157905i
$606$	−18.4609	+	7.15498i	−0.749924	+	0.290651i
$607$	−18.0174	+	31.2070i	−0.731302	+	1.26665i	0.225025	+	0.974353i	$0.427754\pi$
$607$	−18.0174	+	31.2070i	−0.731302	+	1.26665i	−0.956327	+	0.292299i	$0.905580\pi$
$608$	18.4898	+	3.93014i	0.749862	+	0.159388i
$609$	−18.9311	+	29.3585i	−0.767127	+	1.18967i
$610$	24.3297	+	4.63882i	0.985082	+	0.187820i
$611$	26.8483	−	19.5064i	1.08617	−	0.789145i
$612$	0.101020	+	15.6382i	0.00408350	+	0.632137i
$613$	−15.2951	−	11.1125i	−0.617761	−	0.448830i	0.234378	−	0.972146i	$-0.424695\pi$
$613$	−15.2951	−	11.1125i	−0.617761	−	0.448830i	−0.852139	+	0.523316i	$0.824695\pi$
$614$	−21.3519	−	9.50648i	−0.861693	−	0.383651i
$615$	5.99434	+	1.45125i	0.241715	+	0.0585202i
$616$	10.5813	−	4.71108i	0.426331	−	0.189815i
$617$	24.4055	+	5.18754i	0.982527	+	0.208842i	0.671051	−	0.741412i	$-0.265843\pi$
$617$	24.4055	+	5.18754i	0.982527	+	0.208842i	0.311476	+	0.950254i	$0.399177\pi$
$618$	24.3078	−	15.8976i	0.977805	−	0.639493i
$619$	−8.91589	+	9.90210i	−0.358360	+	0.397999i	−0.895185	−	0.445695i	$-0.852957\pi$
$619$	−8.91589	+	9.90210i	−0.358360	+	0.397999i	0.536825	+	0.843693i	$0.319623\pi$
$620$	−13.3077	−	5.59259i	−0.534450	−	0.224604i
$621$	18.4162	−	23.1981i	0.739015	−	0.930908i
$622$	0.936081	−	2.88096i	0.0375334	−	0.115516i
$623$	−20.7409	−	9.23443i	−0.830965	−	0.369970i
$624$	−1.66870	+	1.09135i	−0.0668017	+	0.0436889i
$625$	−21.3889	−	12.9428i	−0.855555	−	0.517712i
$626$	4.00776	−	6.94164i	0.160182	−	0.277444i
$627$	7.65847	−	1.23835i	0.305850	−	0.0494550i
$628$	−17.6712	+	3.75613i	−0.705158	+	0.149886i
$629$	−9.93916	+	30.5896i	−0.396300	+	1.21969i
$630$	−17.8174	−	5.25228i	−0.709864	−	0.209256i
$631$	12.8766	+	39.6300i	0.512608	+	1.57764i	0.787593	+	0.616195i	$0.211327\pi$
$631$	12.8766	+	39.6300i	0.512608	+	1.57764i	−0.274986	+	0.961448i	$0.588673\pi$
$632$	4.05887	+	7.03017i	0.161453	+	0.279645i
$633$	10.0409	−	3.89159i	0.399090	−	0.154677i
$634$	−26.3657	+	11.7388i	−1.04712	+	0.466207i
$635$	−11.3122	+	37.4803i	−0.448911	+	1.48736i
$636$	−9.14125	−	11.2142i	−0.362474	−	0.444674i
$637$	−1.25145	+	11.9068i	−0.0495843	+	0.471763i
$638$	−6.31724	−	4.58974i	−0.250102	−	0.181710i
$639$	−4.16257	−	18.9797i	−0.164669	−	0.750824i
$640$	−8.98178	+	10.4074i	−0.355036	+	0.411390i
$641$	1.38523	−	13.1796i	0.0547135	−	0.520564i	−0.932501	−	0.361167i	$-0.882378\pi$
$641$	1.38523	−	13.1796i	0.0547135	−	0.520564i	0.987215	−	0.159397i	$-0.0509549\pi$
$642$	−2.95452	+	19.0522i	−0.116606	+	0.751930i
$643$	−18.9481	+	32.8190i	−0.747239	+	1.29426i	0.201902	+	0.979406i	$0.435288\pi$
$643$	−18.9481	+	32.8190i	−0.747239	+	1.29426i	−0.949141	+	0.314851i	$0.898046\pi$
$644$	20.2350	+	4.30108i	0.797370	+	0.169486i
$645$	2.29938	−	17.2109i	0.0905382	−	0.677680i
$646$	13.2643	−	2.81942i	0.521878	−	0.110929i
$647$	2.22129	−	6.83642i	0.0873278	−	0.268767i	−0.897851	−	0.440300i	$-0.854872\pi$
$647$	2.22129	−	6.83642i	0.0873278	−	0.268767i	0.985178	+	0.171533i	$0.0548720\pi$
$648$	−25.3879	−	5.05447i	−0.997332	−	0.198558i
$649$	4.63243			0.181839
$650$	6.06519	−	21.7385i	0.237896	−	0.852655i
$651$	24.2278	−	15.8452i	0.949563	−	0.621023i
$652$	0.0872367	+	0.830002i	0.00341645	+	0.0325054i
$653$	−26.4265	−	29.3496i	−1.03415	−	1.14854i	−0.988751	−	0.149569i	$-0.952211\pi$
$653$	−26.4265	−	29.3496i	−1.03415	−	1.14854i	−0.0453968	−	0.998969i	$-0.514455\pi$
$654$	−0.507511	+	0.510800i	−0.0198452	+	0.0199739i
$655$	−10.6170	+	4.99720i	−0.414842	+	0.195257i
$656$	−0.113373	−	0.348927i	−0.00442648	−	0.0136233i
$657$	−7.55732	+	17.2735i	−0.294839	+	0.673902i
$658$	−5.68325	−	17.4912i	−0.221556	−	0.681879i
$659$	0.726501	−	6.91219i	0.0283004	−	0.269261i	−0.971217	−	0.238197i	$-0.923444\pi$
$659$	0.726501	−	6.91219i	0.0283004	−	0.269261i	0.999517	−	0.0310641i	$-0.00988960\pi$
$660$	−2.02172	+	5.67462i	−0.0786953	+	0.220884i
$661$	3.40322	+	32.3795i	0.132370	+	1.25942i	0.835952	+	0.548803i	$0.184916\pi$
$661$	3.40322	+	32.3795i	0.132370	+	1.25942i	−0.703582	+	0.710614i	$0.748417\pi$
$662$	−10.1814	+	4.53306i	−0.395712	+	0.176182i
$663$	20.6502	−	32.0244i	0.801986	−	1.24373i
$664$	−31.6999	−	14.1137i	−1.23020	−	0.547719i
$665$	1.95330	−	23.2870i	0.0757458	−	0.903030i
$666$	−17.2085	−	9.78767i	−0.666816	−	0.379265i
$667$	−11.5898	−	35.6698i	−0.448760	−	1.38114i
$668$	−2.67341	−	4.63048i	−0.103437	−	0.179159i
$669$	4.15156	−	26.7712i	0.160508	−	1.03504i
$670$	11.1348	−	0.234267i	0.430174	−	0.00905051i
$671$	10.7787	+	11.9709i	0.416106	+	0.462133i
$672$	−7.71051	−	28.4087i	−0.297439	−	1.09589i
$673$	−6.96780	−	3.10226i	−0.268589	−	0.119583i	0.268023	−	0.963412i	$-0.413630\pi$
$673$	−6.96780	−	3.10226i	−0.268589	−	0.119583i	−0.536612	+	0.843829i	$0.680296\pi$
$674$	−6.47112			−0.249258
$675$	22.5078	−	12.9769i	0.866324	−	0.499482i
$676$	−14.1676			−0.544906
$677$	−5.26216	−	2.34286i	−0.202241	−	0.0900436i	0.303117	−	0.952953i	$-0.401973\pi$
$677$	−5.26216	−	2.34286i	−0.202241	−	0.0900436i	−0.505358	+	0.862910i	$0.668639\pi$
$678$	4.84726	+	17.8593i	0.186158	+	0.685882i
$679$	−34.9154	−	38.7775i	−1.33993	−	1.48814i
$680$	−8.18214	+	27.1096i	−0.313771	+	1.03961i
$681$	−0.888842	+	5.73169i	−0.0340605	+	0.219639i
$682$	3.23550	+	5.60406i	0.123894	+	0.214590i
$683$	7.75429	+	23.8652i	0.296709	+	0.913178i	0.982642	+	0.185513i	$0.0593946\pi$
$683$	7.75429	+	23.8652i	0.296709	+	0.913178i	−0.685932	+	0.727665i	$0.740605\pi$
$684$	−0.0782244	−	12.1093i	−0.00299099	−	0.463012i
$685$	2.10657	+	3.47763i	0.0804878	+	0.132874i
$686$	−11.6464	−	5.18531i	−0.444661	−	0.197976i
$687$	22.2039	−	34.4339i	0.847130	−	1.31374i
$688$	−0.943614	+	0.420124i	−0.0359750	+	0.0160171i
$689$	3.68492	+	35.0597i	0.140384	+	1.33567i
$690$	16.4575	−	11.2646i	0.626526	−	0.428836i
$691$	−3.55575	+	33.8307i	−0.135267	+	1.28698i	0.690651	+	0.723188i	$0.257324\pi$
$691$	−3.55575	+	33.8307i	−0.135267	+	1.28698i	−0.825918	+	0.563791i	$0.809342\pi$
$692$	1.59356	+	4.90449i	0.0605782	+	0.186441i
$693$	−7.16403	−	9.72767i	−0.272139	−	0.369523i
$694$	0.0887512	+	0.273148i	0.00336895	+	0.0103686i
$695$	−15.7206	−	16.7377i	−0.596316	−	0.634895i
$696$	−23.1028	+	23.2525i	−0.875709	+	0.881385i
$697$	4.69158	+	5.21053i	0.177706	+	0.197363i
$698$	−1.34766	−	12.8222i	−0.0510098	−	0.485326i
$699$	−31.9803	+	20.9154i	−1.20961	+	0.791095i
$700$	15.1158	+	10.0389i	0.571324	+	0.379435i
$701$	−43.0578			−1.62627			−0.813135	−	0.582076i	$-0.802241\pi$
$701$	−43.0578			−1.62627			−0.813135	+	0.582076i	$0.802241\pi$
$702$	16.7445	+	16.4231i	0.631981	+	0.619851i
$703$	7.69632	−	23.6868i	0.290272	−	0.893366i
$704$	7.02824	−	1.49390i	0.264887	−	0.0563034i
$705$	23.1962	+	11.1186i	0.873620	+	0.418750i
$706$	13.1725	+	2.79990i	0.495753	+	0.105375i
$707$	−19.3939	+	33.5912i	−0.729383	+	1.26333i
$708$	1.10809	−	7.14549i	0.0416445	−	0.268544i
$709$	−0.358984	+	3.41550i	−0.0134819	+	0.128272i	−0.999193	−	0.0401750i	$-0.987208\pi$
$709$	−0.358984	+	3.41550i	−0.0134819	+	0.128272i	0.985711	+	0.168447i	$0.0538751\pi$
$710$	1.09357	−	13.0374i	0.0410410	−	0.489285i
$711$	6.25550	−	5.70607i	0.234600	−	0.213995i
$712$	−17.2348	−	12.5218i	−0.645902	−	0.469275i
$713$	−3.24887	+	30.9109i	−0.121671	+	1.15762i
$714$	−13.3425	−	16.3682i	−0.499329	−	0.612564i
$715$	11.6908	−	8.87548i	0.437210	−	0.331924i
$716$	0.402566	−	0.179234i	0.0150446	−	0.00669829i
$717$	23.3658	−	9.05598i	0.872611	−	0.338202i
$718$	6.86806	+	11.8958i	0.256314	+	0.443948i
$719$	−3.21496	−	9.89464i	−0.119898	−	0.369008i	0.873039	−	0.487650i	$-0.162146\pi$
$719$	−3.21496	−	9.89464i	−0.119898	−	0.369008i	−0.992937	+	0.118642i	$0.962146\pi$
$720$	−1.35918	−	0.735662i	−0.0506538	−	0.0274165i
$721$	17.5835	−	54.1163i	0.654842	−	2.01540i
$722$	6.51759	−	1.38536i	0.242560	−	0.0515576i
$723$	15.2334	−	2.46320i	0.566538	−	0.0916075i
$724$	2.89667	−	5.01718i	0.107654	−	0.186462i
$725$	2.05964	−	32.8336i	0.0764930	−	1.21941i
$726$	−12.1442	+	7.94243i	−0.450714	+	0.294771i
$727$	−22.3505	−	9.95109i	−0.828934	−	0.369065i	−0.0520001	−	0.998647i	$-0.516560\pi$
$727$	−22.3505	−	9.95109i	−0.828934	−	0.369065i	−0.776934	+	0.629582i	$0.783226\pi$
$728$	−13.6132	+	41.8970i	−0.504538	+	1.55281i
$729$	0.523207	+	26.9949i	0.0193780	+	0.999812i
$730$	−8.29433	+	9.61086i	−0.306987	+	0.355714i
$731$	13.2086	−	14.6696i	0.488536	−	0.542574i
$732$	21.0433	−	13.7625i	0.777785	−	0.508678i
$733$	23.4045	+	4.97477i	0.864464	+	0.183747i	0.618743	−	0.785593i	$-0.287642\pi$
$733$	23.4045	+	4.97477i	0.864464	+	0.183747i	0.245721	+	0.969341i	$0.420975\pi$
$734$	6.95549	−	3.09678i	0.256732	−	0.114304i
$735$	−8.58037	+	3.53488i	−0.316492	+	0.130386i
$736$	28.8719	+	12.8546i	1.06423	+	0.473827i
$737$	5.86001	+	4.25755i	0.215856	+	0.156829i
$738$	−3.72345	+	2.18192i	−0.137062	+	0.0803177i
$739$	34.3422	−	24.9510i	1.26330	−	0.917839i	0.264382	−	0.964418i	$-0.414832\pi$
$739$	34.3422	−	24.9510i	1.26330	−	0.917839i	0.998915	+	0.0465793i	$0.0148320\pi$
$740$	13.2399	+	14.0965i	0.486710	+	0.518197i
$741$	−15.9903	+	24.7979i	−0.587419	+	0.910974i
$742$	19.1097	+	4.06189i	0.701538	+	0.149117i
$743$	−6.21697	+	10.7681i	−0.228079	+	0.395044i	−0.957239	−	0.289300i	$-0.906578\pi$
$743$	−6.21697	+	10.7681i	−0.228079	+	0.395044i	0.729160	+	0.684343i	$0.239911\pi$
$744$	25.3279	−	9.81647i	0.928568	−	0.359889i
$745$	−1.91189	−	15.1229i	−0.0700462	−	0.554062i
$746$	9.01486	−	27.7449i	0.330058	−	1.01581i
$747$	−7.29610	+	35.4499i	−0.266950	+	1.29705i
$748$	−5.54040	+	4.02533i	−0.202577	+	0.147181i
$749$	18.8855	+	32.7106i	0.690060	+	1.19522i
$750$	17.0587	−	3.87592i	0.622895	−	0.141528i
$751$	−21.2022	+	36.7234i	−0.773681	+	1.34005i	0.161852	+	0.986815i	$0.448253\pi$
$751$	−21.2022	+	36.7234i	−0.773681	+	1.34005i	−0.935533	+	0.353240i	$0.885080\pi$
$752$	−0.159948	−	1.52180i	−0.00583270	−	0.0554945i
$753$	−5.62618	−	20.7291i	−0.205029	−	0.755412i
$754$	29.0498	−	6.17473i	1.05793	−	0.224870i
$755$	−40.4195	−	16.9864i	−1.47102	−	0.618198i
$756$	−16.7185	+	8.72357i	−0.608046	+	0.317273i
$757$	28.4481			1.03397			0.516983	−	0.855996i	$-0.327055\pi$
$757$	28.4481			1.03397			0.516983	+	0.855996i	$0.327055\pi$
$758$	11.7126	−	13.0082i	0.425421	−	0.472478i
$759$	12.9550	+	0.636994i	0.470238	+	0.0231214i
$760$	6.33579	−	20.9921i	0.229823	−	0.761465i
$761$	−2.86142	−	27.2246i	−0.103726	−	0.986890i	−0.915336	−	0.402690i	$-0.868075\pi$
$761$	−2.86142	−	27.2246i	−0.103726	−	0.986890i	0.811610	−	0.584199i	$-0.198591\pi$
$762$	−12.5158	−	24.3688i	−0.453400	−	0.882787i
$763$	−0.147453	+	1.40293i	−0.00533817	+	0.0507893i
$764$	4.01985	−	2.92059i	0.145433	−	0.105663i
$765$	29.4479	+	2.27861i	1.06469	+	0.0823833i
$766$	19.3203	+	14.0370i	0.698070	+	0.507178i
$767$	−11.7893	+	13.0934i	−0.425688	+	0.472775i
$768$	−1.58715	−	28.5216i

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.825259 + 0.367429i) q^{2} +(-0.453689 - 1.67158i) q^{3} +(-0.792213 - 0.879842i) q^{4} +(-1.78097 + 1.35209i) q^{5} +(0.239774 - 1.54618i) q^{6} +(-1.53265 - 2.65463i) q^{7} +(-0.888808 - 2.73547i) q^{8} +(-2.58833 + 1.51675i) q^{9} +O(q^{10})\)	\(q+(0.825259 + 0.367429i) q^{2} +(-0.453689 - 1.67158i) q^{3} +(-0.792213 - 0.879842i) q^{4} +(-1.78097 + 1.35209i) q^{5} +(0.239774 - 1.54618i) q^{6} +(-1.53265 - 2.65463i) q^{7} +(-0.888808 - 2.73547i) q^{8} +(-2.58833 + 1.51675i) q^{9} +(-1.96656 + 0.461443i) q^{10} +(-1.20016 - 0.534345i) q^{11} +(-1.11130 + 1.72342i) q^{12} +(4.56466 - 2.03232i) q^{13} +(-0.289446 - 2.75390i) q^{14} +(3.06813 + 2.36360i) q^{15} +(0.0240823 - 0.229128i) q^{16} +(1.36059 + 4.18745i) q^{17} +(-2.69334 + 0.300684i) q^{18} +(-1.05356 - 3.24253i) q^{19} +(2.60053 + 0.495830i) q^{20} +(-3.74207 + 3.76632i) q^{21} +(-0.794108 - 0.881946i) q^{22} +(-0.595839 - 5.66903i) q^{23} +(-4.16930 + 2.72676i) q^{24} +(1.34371 - 4.81606i) q^{25} +4.51376 q^{26} +(3.70966 + 3.63846i) q^{27} +(-1.12147 + 3.45152i) q^{28} +(6.43584 - 1.36798i) q^{29} +(1.66354 + 3.07790i) q^{30} +(-5.33344 - 1.13366i) q^{31} +(-2.77218 + 4.80156i) q^{32} +(-0.348700 + 2.24858i) q^{33} +(-0.415756 + 3.95565i) q^{34} +(6.31890 + 2.65554i) q^{35} +(3.38501 + 1.07573i) q^{36} +(5.90992 + 4.29381i) q^{37} +(0.321938 - 3.06303i) q^{38} +(-5.46811 - 6.70813i) q^{39} +(5.28154 + 3.67004i) q^{40} +(1.45477 - 0.647706i) q^{41} +(-4.47203 + 1.73324i) q^{42} +(-2.24167 - 3.88268i) q^{43} +(0.480642 + 1.47926i) q^{44} +(2.55896 - 6.20095i) q^{45} +(1.59124 - 4.89734i) q^{46} +(6.49659 - 1.38089i) q^{47} +(-0.393930 + 0.0636974i) q^{48} +(-1.19804 + 2.07507i) q^{49} +(2.87847 - 3.48078i) q^{50} +(6.38236 - 4.17412i) q^{51} +(-5.40430 - 2.40615i) q^{52} +(-2.18021 + 6.70999i) q^{53} +(1.72456 + 4.36571i) q^{54} +(2.85993 - 0.671068i) q^{55} +(-5.89943 + 6.55198i) q^{56} +(-4.94214 + 3.23221i) q^{57} +(5.81387 + 1.23578i) q^{58} +(-3.22129 + 1.43421i) q^{59} +(-0.351016 - 4.57194i) q^{60} +(-11.2015 - 4.98723i) q^{61} +(-3.98493 - 2.89522i) q^{62} +(7.99343 + 4.54641i) q^{63} +(-4.42478 + 3.21479i) q^{64} +(-5.38165 + 9.79132i) q^{65} +(-1.11396 + 1.72754i) q^{66} +(-5.39308 - 1.14633i) q^{67} +(2.60642 - 4.51446i) q^{68} +(-9.20588 + 3.56797i) q^{69} +(4.23901 + 4.51325i) q^{70} +(-2.00148 + 6.15992i) q^{71} +(6.44956 + 5.73220i) q^{72} +(5.08449 - 3.69410i) q^{73} +(3.29954 + 5.71498i) q^{74} +(-8.66004 - 0.0611220i) q^{75} +(-2.01827 + 3.49574i) q^{76} +(0.420936 + 4.00494i) q^{77} +(-2.04784 - 7.54509i) q^{78} +(-2.76067 + 0.586798i) q^{79} +(0.266911 + 0.440631i) q^{80} +(4.39893 - 7.85171i) q^{81} +1.43855 q^{82} +(8.07261 - 8.96554i) q^{83} +(6.27828 + 0.308700i) q^{84} +(-8.08497 - 5.61810i) q^{85} +(-0.423346 - 4.02787i) q^{86} +(-5.20655 - 10.1374i) q^{87} +(-0.394974 + 3.75793i) q^{88} +(5.99213 - 4.35354i) q^{89} +(4.39021 - 4.17715i) q^{90} +(-12.3911 - 9.00265i) q^{91} +(-4.51581 + 5.01532i) q^{92} +(0.524729 + 9.42958i) q^{93} +(5.86875 + 1.24744i) q^{94} +(6.26055 + 4.35034i) q^{95} +(9.28387 + 2.45550i) q^{96} +(16.6509 - 3.53925i) q^{97} +(-1.75113 + 1.27227i) q^{98} +(3.91688 - 0.437280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

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