LMFDB - Embedded newform 225.2.q.a.16.19

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			16.19
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.19

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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	−0.0936607	−	0.995604i	$-0.529857\pi$
$2$	0.825259	−	0.367429i	0.583546	−	0.259811i	0.677207	+	0.735793i	$0.263190\pi$
$3$	−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	0.416273	+	0.909239i	$0.363336\pi$
$7$	−1.53265	+	2.65463i	−0.579288	+	1.00336i	−0.995561	+	0.0941164i	$0.969997\pi$
$8$	−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	−0.579610	−	0.814894i	$-0.696795\pi$
$11$	−1.20016	+	0.534345i	−0.361861	+	0.161111i	0.217749	+	0.976005i	$0.430129\pi$
$12$	−1.11130	−	1.72342i	−0.320806	−	0.497508i
$13$	4.56466	+	2.03232i	1.26601	+	0.563663i	0.926271	−	0.376857i	$-0.122995\pi$
$13$	4.56466	+	2.03232i	1.26601	+	0.563663i	0.339737	+	0.940520i	$0.389662\pi$
$14$	−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	−0.639147	−	0.769085i	$-0.720712\pi$
$17$	1.36059	−	4.18745i	0.329991	−	1.01561i	0.969137	−	0.246522i	$-0.0792877\pi$
$18$	−2.69334	−	0.300684i	−0.634827	−	0.0708720i
$19$	−1.05356	+	3.24253i	−0.241703	+	0.743887i	0.754458	+	0.656349i	$0.227900\pi$
$19$	−1.05356	+	3.24253i	−0.241703	+	0.743887i	−0.996161	+	0.0875381i	$0.972100\pi$
$20$	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	0.737723	+	0.675104i	$0.235901\pi$
$23$	−0.595839	+	5.66903i	−0.124241	+	1.18207i	−0.861964	+	0.506970i	$0.830766\pi$
$24$	−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	0.762158	−	0.647392i	$-0.224140\pi$
$29$	6.43584	+	1.36798i	1.19511	+	0.254027i	0.432948	+	0.901419i	$0.357473\pi$
$30$	1.66354	−	3.07790i	0.303720	−	0.561945i
$31$	−5.33344	+	1.13366i	−0.957915	+	0.203611i	−0.660239	−	0.751056i	$-0.729545\pi$
$31$	−5.33344	+	1.13366i	−0.957915	+	0.203611i	−0.297676	+	0.954667i	$0.596212\pi$
$32$	−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	0.0157722	−	0.999876i	$-0.494979\pi$
$37$	5.90992	−	4.29381i	0.971584	−	0.705897i	0.955812	+	0.293978i	$0.0949793\pi$
$38$	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	0.517178	−	0.855878i	$-0.326982\pi$
$41$	1.45477	+	0.647706i	0.227197	+	0.101155i	−0.289981	+	0.957032i	$0.593649\pi$
$42$	−4.47203	−	1.73324i	−0.690049	−	0.267445i
$43$	−2.24167	+	3.88268i	−0.341851	+	0.592103i	−0.984776	−	0.173826i	$-0.944387\pi$
$43$	−2.24167	+	3.88268i	−0.341851	+	0.592103i	0.642926	+	0.765929i	$0.277720\pi$
$44$	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	0.655703	−	0.755019i	$-0.272372\pi$
$47$	6.49659	+	1.38089i	0.947624	+	0.201424i	0.291921	+	0.956442i	$0.405706\pi$
$48$	−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	−0.981682	−	0.190529i	$-0.938980\pi$
$53$	−2.18021	−	6.70999i	−0.299475	−	0.921688i	0.682207	−	0.731159i	$-0.261020\pi$
$54$	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	0.186189	−	0.982514i	$-0.440386\pi$
$59$	−3.22129	−	1.43421i	−0.419377	−	0.186719i	−0.605566	+	0.795795i	$0.707053\pi$
$60$	−0.351016	+	4.57194i	−0.0453160	+	0.590235i
$61$	−11.2015	+	4.98723i	−1.43420	+	0.638549i	−0.969091	−	0.246702i	$-0.920653\pi$
$61$	−11.2015	+	4.98723i	−1.43420	+	0.638549i	−0.465113	+	0.885251i	$0.653986\pi$
$62$	−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	−0.525200	−	0.850979i	$-0.676009\pi$
$67$	−5.39308	+	1.14633i	−0.658869	+	0.140047i	−0.133669	+	0.991026i	$0.542676\pi$
$68$	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	−0.996775	−	0.0802415i	$-0.974431\pi$
$71$	−2.00148	−	6.15992i	−0.237532	−	0.731048i	0.759244	−	0.650807i	$-0.225569\pi$
$72$	6.44956	−	5.73220i	0.760087	−	0.675547i
$73$	5.08449	+	3.69410i	0.595094	+	0.432361i	0.844134	−	0.536132i	$-0.180115\pi$
$73$	5.08449	+	3.69410i	0.595094	+	0.432361i	−0.249040	+	0.968493i	$0.580115\pi$
$74$	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	0.0499748	−	0.998750i	$-0.484086\pi$
$79$	−2.76067	−	0.586798i	−0.310599	−	0.0660199i	−0.360574	+	0.932731i	$0.617419\pi$
$80$	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	0.999956	−	0.00939965i	$-0.00299205\pi$
$83$	8.07261	+	8.96554i	0.886084	+	0.984096i	−0.113872	+	0.993495i	$0.536325\pi$
$84$	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	0.858185	−	0.513340i	$-0.171592\pi$
$89$	5.99213	+	4.35354i	0.635164	+	0.461474i	−0.223021	+	0.974814i	$0.571592\pi$
$90$	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	0.949929	−	0.312466i	$-0.101155\pi$
$97$	16.6509	+	3.53925i	1.69064	+	0.359357i	0.740712	+	0.671823i	$0.234488\pi$
$98$	−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	0.358090	+	0.933687i	$0.383428\pi$
$101$	−6.32691	+	10.9585i	−0.629551	+	1.09042i	−0.987642	+	0.156728i	$0.949905\pi$
$102$	6.80080	+	1.09967i	0.673379	+	0.108883i
$103$	12.4211	−	13.7950i	1.22389	−	1.35926i	0.311334	−	0.950300i	$-0.399224\pi$
$103$	12.4211	−	13.7950i	1.22389	−	1.35926i	0.912551	−	0.408962i	$-0.134109\pi$
$104$	−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	−0.605473	−	0.795866i	$-0.707016\pi$
$109$	−0.372310	+	0.270499i	−0.0356608	+	0.0259091i	0.569812	+	0.821775i	$0.307016\pi$
$110$	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	−0.170214	−	0.985407i	$-0.554446\pi$
$113$	−10.8046	−	4.81051i	−1.01641	−	0.452535i	−0.846196	+	0.532872i	$0.821113\pi$
$114$	−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	0.998602	−	0.0528609i	$-0.0168340\pi$
$127$	14.1647	+	10.2913i	1.25691	+	0.913201i	0.258311	+	0.966062i	$0.416834\pi$
$128$	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	0.0218643	−	0.999761i	$-0.493040\pi$
$131$	5.13306	−	1.09107i	0.448478	−	0.0953269i	0.426613	+	0.904434i	$0.359707\pi$
$132$	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	0.999636	−	0.0269631i	$-0.00858365\pi$
$137$	0.190067	+	1.80837i	0.0162385	+	0.154499i	−0.983398	+	0.181462i	$0.941917\pi$
$138$	−8.90821	+	0.438013i	−0.758317	+	0.0372861i
$139$	1.07343	−	10.2130i	0.0910470	−	0.866254i	−0.849728	−	0.527222i	$-0.823234\pi$
$139$	1.07343	−	10.2130i	0.0910470	−	0.866254i	0.940775	−	0.339032i	$-0.110100\pi$
$140$	−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	0.691959	−	0.721937i	$-0.256748\pi$
$149$	−3.40851	−	5.90371i	−0.279236	−	0.483651i	−0.971195	+	0.238286i	$0.923415\pi$
$150$	−7.12432	+	3.23239i	−0.581698	+	0.263924i
$151$	9.80375	−	16.9806i	0.797818	−	1.38186i	−0.123216	−	0.992380i	$-0.539321\pi$
$151$	9.80375	−	16.9806i	0.797818	−	1.38186i	0.921034	−	0.389482i	$-0.127346\pi$
$152$	−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	0.991421	+	0.130708i	$0.0417251\pi$
$157$	7.62958	+	13.2148i	0.608907	+	1.05466i	−0.382514	+	0.923950i	$0.624942\pi$
$158$	−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	−0.609895	−	0.792482i	$-0.708789\pi$
$163$	−0.570284	+	0.414336i	−0.0446681	+	0.0324533i	0.565227	+	0.824935i	$0.308789\pi$
$164$	−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	−0.0337978	−	0.999429i	$-0.510760\pi$
$167$	4.41742	−	0.938953i	0.341831	−	0.0726583i	0.375628	+	0.926770i	$0.377427\pi$
$168$	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	−0.552386	−	0.833589i	$-0.686282\pi$
$173$	−3.97911	+	1.77162i	−0.302527	+	0.134693i	0.249859	+	0.968282i	$0.419616\pi$
$174$	−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	0.946666	−	0.322216i	$-0.104428\pi$
$179$	−0.115016	−	0.353983i	−0.00859671	−	0.0264579i	−0.955263	+	0.295758i	$0.904428\pi$
$180$	−7.48309	−	2.66099i	−0.557757	−	0.198338i
$181$	1.51210	−	4.65376i	0.112393	−	0.345912i	−0.879001	−	0.476820i	$-0.841789\pi$
$181$	1.51210	−	4.65376i	0.112393	−	0.345912i	0.991394	+	0.130908i	$0.0417894\pi$
$182$	−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	−0.998862	−	0.0476875i	$-0.984815\pi$
$191$	−0.438688	−	4.17383i	−0.0317423	−	0.302008i	0.967120	−	0.254321i	$-0.0818518\pi$
$192$	7.38123	−	5.93783i	0.532695	−	0.428526i
$193$	1.47540	+	2.55547i	0.106202	+	0.183946i	0.914228	−	0.405199i	$-0.132798\pi$
$193$	1.47540	+	2.55547i	0.106202	+	0.183946i	−0.808027	+	0.589146i	$0.799464\pi$
$194$	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	0.846844	−	0.531842i	$-0.178500\pi$
$197$	−2.11764	−	6.51743i	−0.150876	−	0.464348i	−0.997720	+	0.0674935i	$0.978500\pi$
$198$	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	−0.949111	−	0.314942i	$-0.898015\pi$
$211$	0.649884	−	6.18323i	0.0447398	−	0.425671i	0.993851	−	0.110729i	$-0.0353185\pi$
$212$	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	0.131928	−	0.991259i	$-0.457883\pi$
$223$	14.2889	−	6.36182i	0.956854	−	0.426019i	0.824926	+	0.565240i	$0.191217\pi$
$224$	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	−0.505741	−	0.862685i	$-0.668781\pi$
$227$	−3.05923	+	1.36206i	−0.203048	+	0.0904029i	0.302693	+	0.953088i	$0.402114\pi$
$228$	6.75906	−	1.78771i	0.447630	−	0.118394i
$229$	15.8284	−	17.5792i	1.04597	−	1.16167i	0.0594174	−	0.998233i	$-0.481076\pi$
$229$	15.8284	−	17.5792i	1.04597	−	1.16167i	0.986554	−	0.163436i	$-0.0522576\pi$
$230$	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	0.434053	+	0.900888i	$0.357083\pi$
$233$	−6.81754	+	20.9822i	−0.446632	+	1.37459i	−0.880684	+	0.473704i	$0.842917\pi$
$234$	−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	−0.830013	−	0.557744i	$-0.811667\pi$
$239$	1.51232	−	14.3888i	0.0978238	−	0.930731i	0.927837	−	0.372987i	$-0.121666\pi$
$240$	0.615454	+	0.646072i	0.0397274	+	0.0417038i
$241$	−0.931272	−	8.86046i	−0.0599885	−	0.570753i	−0.982693	−	0.185244i	$-0.940693\pi$
$241$	−0.931272	−	8.86046i	−0.0599885	−	0.570753i	0.922704	−	0.385509i	$-0.125974\pi$
$242$	−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	0.675130	+	0.737699i	$0.264088\pi$
$257$	15.6534	+	27.1124i	0.976431	+	1.69123i	0.301301	+	0.953529i	$0.402579\pi$
$258$	−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	−0.693244	−	0.720703i	$-0.743819\pi$
$263$	−2.67571	−	25.4577i	−0.164992	−	1.56979i	0.528252	−	0.849087i	$-0.322847\pi$
$264$	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	−0.940922	−	0.338622i	$-0.890039\pi$
$269$	0.317149	−	0.976085i	0.0193369	−	0.0595129i	0.960259	+	0.279109i	$0.0900392\pi$
$270$	−8.97421	+	5.44345i	−0.546153	+	0.331278i
$271$	6.14011	+	18.8973i	0.372985	+	1.14793i	0.944828	+	0.327567i	$0.106229\pi$
$271$	6.14011	+	18.8973i	0.372985	+	1.14793i	−0.571843	+	0.820363i	$0.693771\pi$
$272$	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	0.155456	−	0.987843i	$-0.450315\pi$
$277$	16.5366	−	7.36256i	0.993587	−	0.442373i	0.838131	+	0.545470i	$0.183649\pi$
$278$	−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	−0.990164	−	0.139913i	$-0.955318\pi$
$281$	−17.1957	−	19.0978i	−1.02581	−	1.13928i	−0.0356460	−	0.999364i	$-0.511349\pi$
$282$	−0.577394	+	10.3760i	−0.0343833	+	0.617882i
$283$	−8.60803	+	1.82969i	−0.511694	+	0.108764i	−0.456521	−	0.889713i	$-0.650905\pi$
$283$	−8.60803	+	1.82969i	−0.511694	+	0.108764i	−0.0551737	+	0.998477i	$0.517571\pi$
$284$	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	0.758317	−	0.651886i	$-0.226022\pi$
$293$	−3.17339	−	5.49647i	−0.185391	−	0.321107i	−0.943708	+	0.330779i	$0.892689\pi$
$294$	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	−0.999955	−	0.00950197i	$-0.996975\pi$
$311$	−0.350514	+	3.33492i	−0.0198758	+	0.189106i	0.980079	+	0.198608i	$0.0636421\pi$
$312$	−13.4898	−	20.9201i	−0.763709	−	1.18437i
$313$	0.927483	+	8.82441i	0.0524244	+	0.498785i	0.988957	+	0.148204i	$0.0473492\pi$
$313$	0.927483	+	8.82441i	0.0524244	+	0.498785i	−0.936532	+	0.350581i	$0.885984\pi$
$314$	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	−0.928534	−	0.371249i	$-0.878930\pi$
$317$	−21.3777	−	23.7423i	−1.20069	−	1.33350i	−0.272157	−	0.962253i	$-0.587737\pi$
$318$	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	0.472251	−	0.881464i	$-0.343442\pi$
$331$	−8.25522	−	9.16835i	−0.453748	−	0.503938i	−0.925999	+	0.377526i	$0.876775\pi$
$332$	−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	0.220680	−	0.975346i	$-0.429172\pi$
$337$	−6.54409	−	2.91362i	−0.356479	−	0.158715i	−0.577160	+	0.816631i	$0.695839\pi$
$338$	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	−0.737408	−	0.675448i	$-0.763950\pi$
$347$	0.212737	−	0.236268i	0.0114203	−	0.0126835i	0.748828	+	0.662764i	$0.230617\pi$
$348$	−4.79457	−	12.6119i	−0.257016	−	0.676068i
$349$	−7.13603	+	12.3600i	−0.381983	+	0.661614i	−0.991346	−	0.131278i	$-0.958092\pi$
$349$	−7.13603	+	12.3600i	−0.381983	+	0.661614i	0.609363	+	0.792892i	$0.291425\pi$
$350$	−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	0.578902	−	0.815397i	$-0.303481\pi$
$353$	14.5817	+	3.09943i	0.776104	+	0.164966i	0.197202	+	0.980363i	$0.436815\pi$
$354$	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	−0.213763	−	0.976885i	$-0.568572\pi$
$359$	12.3016	−	8.93763i	0.649253	−	0.471710i	0.863017	+	0.505175i	$0.168572\pi$
$360$	−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	0.872134	−	0.489267i	$-0.162736\pi$
$367$	5.63960	+	6.26341i	0.294385	+	0.326948i	−0.577749	+	0.816214i	$0.696069\pi$
$368$	−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	0.458257	+	0.888820i	$0.348474\pi$
$373$	−3.37560	+	32.1167i	−0.174782	+	1.66294i	−0.633039	+	0.774120i	$0.718193\pi$
$374$	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	0.978705	+	0.205270i	$0.0658072\pi$
$379$	5.98776	+	18.4284i	0.307571	+	0.946605i	−0.671135	+	0.741335i	$0.734193\pi$
$380$	−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	0.507326	−	0.861754i	$-0.330634\pi$
$383$	25.8583	−	5.49635i	1.32130	−	0.280851i	0.813972	+	0.580904i	$0.197301\pi$
$384$	−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	−0.147305	−	0.989091i	$-0.547060\pi$
$389$	9.64786	−	4.29550i	0.489166	−	0.217791i	0.636471	+	0.771300i	$0.280393\pi$
$390$	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	0.928548	−	0.371213i	$-0.121058\pi$
$397$	−0.814060	−	2.50542i	−0.0408565	−	0.125743i	−0.969404	+	0.245469i	$0.921058\pi$
$398$	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	0.944303	−	0.329076i	$-0.106737\pi$
$401$	3.74794	+	6.49163i	0.187163	+	0.324177i	−0.757140	+	0.653253i	$0.773404\pi$
$402$	−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	0.980451	−	0.196766i	$-0.0630438\pi$
$409$	30.1389	+	13.4187i	1.49027	+	0.663513i	0.509824	+	0.860279i	$0.329710\pi$
$410$	−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	−0.619438	−	0.785045i	$-0.712640\pi$
$419$	−17.7269	+	3.76797i	−0.866017	+	0.184078i	−0.246579	+	0.969123i	$0.579306\pi$
$420$	−11.5988	−	7.93901i	−0.565965	−	0.387384i
$421$	−23.5464	−	5.00494i	−1.14758	−	0.243926i	−0.405408	−	0.914136i	$-0.632871\pi$
$421$	−23.5464	−	5.00494i	−1.14758	−	0.243926i	−0.742171	+	0.670210i	$0.766204\pi$
$422$	−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	0.730026	+	0.683419i	$0.239508\pi$
$431$	−5.44510	+	16.7583i	−0.262281	+	0.807218i	−0.992307	+	0.123799i	$0.960492\pi$
$432$	0.923010	+	0.762365i	0.0444083	+	0.0366793i
$433$	0.572909	−	1.76323i	0.0275322	−	0.0847355i	−0.936346	−	0.351078i	$-0.885815\pi$
$433$	0.572909	−	1.76323i	0.0275322	−	0.0847355i	0.963878	+	0.266342i	$0.0858152\pi$
$434$	−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	−0.605576	−	0.795788i	$-0.707057\pi$
$439$	−8.78739	+	3.91240i	−0.419399	+	0.186728i	0.186176	+	0.982516i	$0.440390\pi$
$440$	−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	−0.0374398	+	0.999299i	$0.511920\pi$
$443$	−18.6090	+	32.2317i	−0.884138	+	1.53137i	−0.846698	+	0.532073i	$0.821413\pi$
$444$	−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	−0.741663	−	0.670773i	$-0.765962\pi$
$457$	4.49089	−	7.77846i	0.210075	−	0.363861i	0.951738	+	0.306912i	$0.0992958\pi$
$458$	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	−0.639860	−	0.768492i	$-0.721008\pi$
$461$	−10.6691	+	4.75018i	−0.496909	+	0.221238i	0.142951	+	0.989730i	$0.454341\pi$
$462$	6.29330	−	0.309439i	0.292791	−	0.0143964i
$463$	24.8731	+	11.0742i	1.15595	+	0.514662i	0.892960	−	0.450137i	$-0.148625\pi$
$463$	24.8731	+	11.0742i	1.15595	+	0.514662i	0.262990	+	0.964799i	$0.415291\pi$
$464$	−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	−0.980034	−	0.198830i	$-0.936286\pi$
$467$	−1.51920	+	4.67562i	−0.0703002	+	0.216362i	0.909734	+	0.415192i	$0.136286\pi$
$468$	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	−0.651626	−	0.758541i	$-0.725913\pi$
$479$	−34.0425	−	7.23596i	−1.55544	−	0.330619i	−0.903816	+	0.427921i	$0.859246\pi$
$480$	−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	−0.330044	−	0.943966i	$-0.607064\pi$
$487$	10.2778	−	7.46726i	0.465732	−	0.338374i	0.795775	+	0.605592i	$0.207064\pi$
$488$	−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	0.627369	−	0.778722i	$-0.284132\pi$
$491$	10.3803	+	4.62163i	0.468458	+	0.208571i	−0.158911	+	0.987293i	$0.550798\pi$
$492$	−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	0.563630	−	0.826027i	$-0.309404\pi$
$499$	−9.68467	−	16.7743i	−0.433545	−	0.750923i	−0.997176	+	0.0751046i	$0.976071\pi$
$500$	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	0.991780	+	0.127955i	$0.0408413\pi$
$503$	5.93488	+	18.2657i	0.264623	+	0.814427i	−0.727157	+	0.686471i	$0.759159\pi$
$504$	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	0.0936937	−	0.995601i	$-0.470133\pi$
$509$	−13.1641	−	5.86104i	−0.583489	−	0.259786i	−0.677182	+	0.735815i	$0.736799\pi$
$510$	−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	0.999748	+	0.0224375i	$0.00714269\pi$
$521$	4.65920	+	14.3396i	0.204123	+	0.628227i	−0.795625	+	0.605790i	$0.792857\pi$
$522$	−16.9226	−	5.61960i	−0.740682	−	0.245963i
$523$	12.9615	+	9.41708i	0.566767	+	0.411780i	0.833929	−	0.551871i	$-0.186086\pi$
$523$	12.9615	+	9.41708i	0.566767	+	0.411780i	−0.267162	+	0.963652i	$0.586086\pi$
$524$	−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	−0.276586	−	0.960989i	$-0.589203\pi$
$541$	12.8369	−	9.32652i	0.551900	−	0.400979i	0.828485	+	0.560011i	$0.189203\pi$
$542$	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	0.526239	−	0.850337i	$-0.323602\pi$
$547$	15.4623	+	3.28661i	0.661119	+	0.140525i	0.134880	+	0.990862i	$0.456935\pi$
$548$	−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	0.0180307	−	0.999837i	$-0.494260\pi$
$563$	−16.9161	−	7.53153i	−0.712928	−	0.317416i	−0.730959	+	0.682421i	$0.760927\pi$
$564$	−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	0.591814	−	0.806074i	$-0.298412\pi$
$569$	−6.48119	−	7.19809i	−0.271705	−	0.301759i	−0.863520	+	0.504315i	$0.831745\pi$
$570$	8.22753	+	8.63684i	0.344613	+	0.361757i
$571$	−20.0597	+	22.2785i	−0.839471	+	0.932327i	−0.998489	−	0.0549489i	$-0.982500\pi$
$571$	−20.0597	+	22.2785i	−0.839471	+	0.932327i	0.159018	+	0.987276i	$0.449167\pi$
$572$	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	−0.123480	−	0.992347i	$-0.539405\pi$
$577$	−26.5530	−	19.2919i	−1.10542	−	0.803131i	−0.981936	+	0.189216i	$0.939405\pi$
$578$	−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	0.996503	−	0.0835562i	$-0.0266278\pi$
$587$	0.106692	+	1.01511i	0.00440367	+	0.0418981i	−0.992099	+	0.125454i	$0.959961\pi$
$588$	−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	0.761748	−	0.647874i	$-0.224341\pi$
$599$	−4.41032	−	7.63890i	−0.180201	−	0.312117i	−0.941949	+	0.335756i	$0.891008\pi$
$600$	7.52991	−	23.7436i	0.307407	−	0.969328i
$601$	5.73110	−	9.92656i	0.233777	−	0.404913i	−0.725140	−	0.688602i	$-0.758225\pi$
$601$	5.73110	−	9.92656i	0.233777	−	0.404913i	0.958916	+	0.283689i	$0.0915582\pi$
$602$	−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	−0.956327	−	0.292299i	$-0.905580\pi$
$607$	−18.0174	−	31.2070i	−0.731302	−	1.26665i	0.225025	−	0.974353i	$-0.427754\pi$
$608$	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	−0.852139	−	0.523316i	$-0.824695\pi$
$613$	−15.2951	+	11.1125i	−0.617761	+	0.448830i	0.234378	+	0.972146i	$0.424695\pi$
$614$	−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	0.311476	−	0.950254i	$-0.399177\pi$
$617$	24.4055	−	5.18754i	0.982527	−	0.208842i	0.671051	+	0.741412i	$0.265843\pi$
$618$	24.3078	+	15.8976i	0.977805	+	0.639493i
$619$	−8.91589	−	9.90210i	−0.358360	−	0.397999i	0.536825	−	0.843693i	$-0.319623\pi$
$619$	−8.91589	−	9.90210i	−0.358360	−	0.397999i	−0.895185	+	0.445695i	$0.852957\pi$
$620$	−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	−0.274986	−	0.961448i	$-0.588673\pi$
$631$	12.8766	−	39.6300i	0.512608	−	1.57764i	0.787593	−	0.616195i	$-0.211327\pi$
$632$	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	0.987215	+	0.159397i	$0.0509549\pi$
$641$	1.38523	+	13.1796i	0.0547135	+	0.520564i	−0.932501	+	0.361167i	$0.882378\pi$
$642$	−2.95452	−	19.0522i	−0.116606	−	0.751930i
$643$	−18.9481	−	32.8190i	−0.747239	−	1.29426i	−0.949141	−	0.314851i	$-0.898046\pi$
$643$	−18.9481	−	32.8190i	−0.747239	−	1.29426i	0.201902	−	0.979406i	$-0.435288\pi$
$644$	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	0.985178	−	0.171533i	$-0.0548720\pi$
$647$	2.22129	+	6.83642i	0.0873278	+	0.268767i	−0.897851	+	0.440300i	$0.854872\pi$
$648$	−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	−0.0453968	+	0.998969i	$0.514455\pi$
$653$	−26.4265	+	29.3496i	−1.03415	+	1.14854i	−0.988751	+	0.149569i	$0.952211\pi$
$654$	−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	0.999517	+	0.0310641i	$0.00988960\pi$
$659$	0.726501	+	6.91219i	0.0283004	+	0.269261i	−0.971217	+	0.238197i	$0.923444\pi$
$660$	−2.02172	−	5.67462i	−0.0786953	−	0.220884i
$661$	3.40322	−	32.3795i	0.132370	−	1.25942i	−0.703582	−	0.710614i	$-0.748417\pi$
$661$	3.40322	−	32.3795i	0.132370	−	1.25942i	0.835952	−	0.548803i	$-0.184916\pi$
$662$	−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	−0.536612	−	0.843829i	$-0.680296\pi$
$673$	−6.96780	+	3.10226i	−0.268589	+	0.119583i	0.268023	+	0.963412i	$0.413630\pi$
$674$	−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	−0.505358	−	0.862910i	$-0.668639\pi$
$677$	−5.26216	+	2.34286i	−0.202241	+	0.0900436i	0.303117	+	0.952953i	$0.401973\pi$
$678$	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	−0.685932	−	0.727665i	$-0.740605\pi$
$683$	7.75429	−	23.8652i	0.296709	−	0.913178i	0.982642	−	0.185513i	$-0.0593946\pi$
$684$	−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	−0.825918	−	0.563791i	$-0.809342\pi$
$691$	−3.55575	−	33.8307i	−0.135267	−	1.28698i	0.690651	−	0.723188i	$-0.257324\pi$
$692$	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	0.985711	−	0.168447i	$-0.0538751\pi$
$709$	−0.358984	−	3.41550i	−0.0134819	−	0.128272i	−0.999193	+	0.0401750i	$0.987208\pi$
$710$	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	−0.992937	−	0.118642i	$-0.962146\pi$
$719$	−3.21496	+	9.89464i	−0.119898	+	0.369008i	0.873039	+	0.487650i	$0.162146\pi$
$720$	−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	−0.776934	−	0.629582i	$-0.783226\pi$
$727$	−22.3505	+	9.95109i	−0.828934	+	0.369065i	−0.0520001	+	0.998647i	$0.516560\pi$
$728$	−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	0.245721	−	0.969341i	$-0.420975\pi$
$733$	23.4045	−	4.97477i	0.864464	−	0.183747i	0.618743	+	0.785593i	$0.287642\pi$
$734$	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	0.998915	−	0.0465793i	$-0.0148320\pi$
$739$	34.3422	+	24.9510i	1.26330	+	0.917839i	0.264382	+	0.964418i	$0.414832\pi$
$740$	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	0.729160	−	0.684343i	$-0.239911\pi$
$743$	−6.21697	−	10.7681i	−0.228079	−	0.395044i	−0.957239	+	0.289300i	$0.906578\pi$
$744$	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	−0.935533	−	0.353240i	$-0.885080\pi$
$751$	−21.2022	−	36.7234i	−0.773681	−	1.34005i	0.161852	−	0.986815i	$-0.448253\pi$
$752$	−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	0.811610	+	0.584199i	$0.198591\pi$
$761$	−2.86142	+	27.2246i	−0.103726	+	0.986890i	−0.915336	+	0.402690i	$0.868075\pi$
$762$	−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	−0.0572712	+	1.02919i
$769$	−22.8442	+	4.85569i	−0.823783	+	0.175101i	−0.600471	−	0.799646i	$-0.705020\pi$
$769$	−22.8442	+	4.85569i	−0.823783	+	0.175101i	−0.223312	+	0.974747i	$0.571687\pi$
$770$	−2.67585	+	7.68171i	−0.0964309	+	0.276830i
$771$	−52.4223	+	13.8652i	−1.88794	+	0.499343i
$772$	−3.41724	−	0.726356i	−0.122989	−	0.0261421i
$773$	1.17568	+	0.854182i	0.0422863	+	0.0307228i	0.608728	−	0.793379i	$-0.291680\pi$
$773$	1.17568	+	0.854182i	0.0422863	+	0.0307228i	−0.566441	+	0.824102i	$0.691680\pi$
$774$	7.20503	−	9.78335i	0.258980	−	0.351655i
$775$	−12.6264	−	24.1629i	−0.453553	−	0.867956i
$776$	−24.4810	+	42.4023i	−0.878815	+	1.52215i
$777$	−38.2872	−	6.19092i	−1.37354	−	0.222098i
$778$	6.38369	−	7.08980i	0.228866	−	0.254182i
$779$	−3.63290	+	4.03474i	−0.130162	+	0.144560i
$780$	−10.8939	+	20.1560i	−0.390064	+	0.721699i
$781$	5.69362	+	6.32340i	0.203734	+	0.226269i
$782$	22.6724			0.810764
$783$	28.8521	−	18.3418i	1.03109	−	0.655483i
$784$	0.446604	−	0.324477i	0.0159501	−	0.0115885i
$785$	4.27956	−	33.8511i	0.152744	−	1.20820i
$786$	2.91776	+	7.67503i	0.104073	+	0.273759i
$787$	−6.62348	−	2.94896i	−0.236102	−	0.105119i	0.285276	−	0.958446i	$-0.407915\pi$
$787$	−6.62348	−	2.94896i	−0.236102	−	0.105119i	−0.521377	+	0.853326i	$0.674582\pi$
$788$	7.41193	+	3.30001i	0.264039	+	0.117558i
$789$	43.7685	+	7.07723i	1.55820	+	0.251956i
$790$	5.15824	+	2.42786i	0.183522	+	0.0863795i
$791$	29.3298	−	21.3093i	1.04285	−	0.757673i
$792$	−4.67752	+	10.3258i	−0.166208	+	0.366913i
$793$	−61.2666			−2.17564
$794$	−1.59237	−	1.76851i	−0.0565112	−	0.0627621i
$795$	−22.5489	−	15.4340i	−0.799726	−	0.547386i
$796$	−7.62684	+	8.47046i	−0.270326	+	0.300227i
$797$	−2.86572	+	3.18271i	−0.101509	+	0.112737i	−0.791758	−	0.610834i	$-0.790834\pi$
$797$	−2.86572	+	3.18271i	−0.101509	+	0.112737i	0.690249	+	0.723572i	$0.257501\pi$
$798$	10.3316	−	12.6746i	0.365736	−	0.448676i
$799$	14.6216	−	25.3253i	0.517275	−	0.895946i
$800$	19.3996	−	19.8029i	0.685879	−	0.700138i
$801$	−8.90639	−	20.3570i	−0.314692	−	0.719278i
$802$	5.47824	+	3.98017i	0.193443	+	0.140545i
$803$	−8.07612	−	1.71663i	−0.285000	−	0.0605786i
$804$	7.96896	+	8.02060i	0.281043	+	0.282865i
$805$	11.2893	+	37.4043i	0.397894	+	1.31833i
$806$	−24.0739	+	5.11706i	−0.847966	+	0.180241i
$807$	1.48771	+	0.972978i	0.0523700	+	0.0342504i
$808$	−24.3533	−	27.0471i	−0.856747	−	0.951514i
$809$	20.0966	−	14.6011i	0.706560	−	0.513346i	−0.175502	−	0.984479i	$-0.556155\pi$
$809$	20.0966	−	14.6011i	0.706560	−	0.513346i	0.882062	+	0.471133i	$0.156155\pi$
$810$	−5.02763	−	17.4707i	−0.176653	−	0.613858i
$811$	−18.6705	−	13.5649i	−0.655610	−	0.476329i	0.209567	−	0.977794i	$-0.432794\pi$
$811$	−18.6705	−	13.5649i	−0.655610	−	0.476329i	−0.865178	+	0.501465i	$0.832794\pi$
$812$	−2.49597	−	23.7476i	−0.0875915	−	0.833377i
$813$	−34.3740	+	1.69015i	−1.20555	+	0.0592763i
$814$	−0.906206	+	8.62197i	−0.0317625	+	0.302200i
$815$	1.57588	+	0.0331552i	0.0552006	+	0.00116138i
$816$	−0.802706	+	1.56290i	−0.0281003	+	0.0547124i
$817$	−10.2280	−	11.3593i	−0.357831	−	0.397412i
$818$	29.8029			1.04203
$819$	45.7270	−	4.50765i	1.59783	−	0.157510i
$820$	4.10433	+	0.963062i	0.143330	+	0.0336316i
$821$	38.0717	+	8.09238i	1.32871	+	0.282426i	0.816953	−	0.576704i	$-0.195661\pi$
$821$	38.0717	+	8.09238i	1.32871	+	0.282426i	0.511757	+	0.859130i	$0.328995\pi$
$822$	−2.75049	+	0.727478i	−0.0959343	+	0.0253737i
$823$	3.43227	−	32.6558i	0.119641	−	1.13831i	−0.755738	−	0.654874i	$-0.772722\pi$
$823$	3.43227	−	32.6558i	0.119641	−	1.13831i	0.875379	−	0.483437i	$-0.160612\pi$
$824$	26.6959	+	46.2386i	0.929994	+	1.61080i
$825$	10.3608	−	4.70081i	0.360715	−	0.163661i
$826$	4.88207	−	8.45599i	0.169869	−	0.294221i
$827$	3.02903	+	2.20072i	0.105330	+	0.0765264i	0.639203	−	0.769038i	$-0.279264\pi$
$827$	3.02903	+	2.20072i	0.105330	+	0.0765264i	−0.533874	+	0.845564i	$0.679264\pi$
$828$	4.08143	+	19.8307i	0.141840	+	0.689164i
$829$	−8.58235	−	26.4138i	−0.298077	−	0.917388i	−0.982170	−	0.187993i	$-0.939802\pi$
$829$	−8.58235	−	26.4138i	−0.298077	−	0.917388i	0.684093	−	0.729395i	$-0.260198\pi$
$830$	−11.7382	−	21.3563i	−0.407438	−	0.741288i
$831$	4.80461	+	30.9825i	0.166670	+	1.07477i
$832$	−13.6641	−	23.6670i	−0.473718	−	0.820504i
$833$	−10.3193	+	2.19343i	−0.357542	+	0.0759979i
$834$	16.0485	−	0.789098i	0.555714	−	0.0273242i
$835$	−9.13685	−	4.30050i	−0.316194	−	0.148825i
$836$	4.29017	+	3.11699i	0.148379	+	0.107803i
$837$	−15.6605	+	23.6110i	−0.541306	+	0.816116i
$838$	−13.2448	+	9.62294i	−0.457535	+	0.332419i
$839$	−19.6893	+	8.76624i	−0.679750	+	0.302644i	−0.717415	−	0.696646i	$-0.754675\pi$
$839$	−19.6893	+	8.76624i	−0.679750	+	0.302644i	0.0376648	+	0.999290i	$0.488008\pi$
$840$	−33.5864	−	6.15841i	−1.15884	−	0.212485i
$841$	13.0558	+	5.81284i	0.450201	+	0.200443i
$842$	−21.2708	+	4.52125i	−0.733041	+	0.155813i
$843$	39.7249	−	20.0795i	1.36820	−	0.691574i
$844$	4.92542	+	5.47023i	0.169540	+	0.188293i
$845$	−2.23657	−	26.6641i	−0.0769404	−	0.917272i
$846$	−17.0823	−	5.67264i	−0.587302	−	0.195029i
$847$	−8.78471	−	27.0365i	−0.301846	−	0.928987i
$848$	1.48494	−	0.661138i	0.0509931	−	0.0227036i
$849$	0.846898	−	15.2191i	0.0290655	−	0.522318i
$850$	18.4920	−	7.31756i	0.634270	−	0.250990i
$851$	20.8203	+	36.0619i	0.713712	+	1.23619i
$852$	−8.39187	+	10.2949i	−0.287501	+	0.352699i
$853$	45.2681	+	9.62204i	1.54995	+	0.329452i	0.901832	−	0.432086i	$-0.142222\pi$
$853$	45.2681	+	9.62204i	1.54995	+	0.329452i	0.648119	+	0.761539i	$0.275556\pi$
$854$	−10.4921	−	32.2913i	−0.359032	−	1.10499i
$855$	−22.8028	+	1.76443i	−0.779838	+	0.0603421i
$856$	10.9520	−	33.7067i	0.374331	−	1.15207i
$857$	11.5451	−	19.9968i	0.394375	−	0.683077i	−0.598646	−	0.801013i	$-0.704295\pi$
$857$	11.5451	−	19.9968i	0.394375	−	0.683077i	0.993021	+	0.117936i	$0.0376279\pi$
$858$	−1.57394	−	10.1496i	−0.0537336	−	0.346500i
$859$	38.2129	+	17.0135i	1.30381	+	0.580493i	0.936846	−	0.349743i	$-0.113731\pi$
$859$	38.2129	+	17.0135i	1.30381	+	0.580493i	0.366962	+	0.930236i	$0.380398\pi$
$860$	−3.90438	+	11.2085i	−0.133138	+	0.382207i
$861$	−3.00439	−	7.90290i	−0.102389	−	0.269330i
$862$	1.66386	+	15.8306i	0.0566714	+	0.539193i
$863$	8.30540	−	6.03422i	0.282719	−	0.205407i	−0.437383	−	0.899275i	$-0.644095\pi$
$863$	8.30540	−	6.03422i	0.282719	−	0.205407i	0.720102	+	0.693868i	$0.244095\pi$
$864$	−27.7541	−	7.72569i	−0.944215	−	0.262833i
$865$	9.48207	+	2.22492i	0.322400	+	0.0756496i
$866$	−0.175064	−	1.66563i	−0.00594893	−	0.0566003i
$867$	3.22002	−	2.59035i	0.109358	−	0.0879728i
$868$	9.89413	+	17.1371i	0.335829	+	0.581672i
$869$	3.62679	−	0.770898i	0.123030	−	0.0261509i
$870$	14.9168	−	17.5332i	0.505727	−	0.594430i
$871$	−26.9473	−	5.72782i	−0.913073	−	0.194080i
$872$	−0.409030	−	1.25886i	−0.0138515	−	0.0426305i
$873$	−37.7299	−	34.4160i	−1.27696	−	1.16481i
$874$	−17.5562			−0.593849
$875$	21.2800	+	26.8639i	0.719396	+	0.908167i
$876$	0.716065	−	12.8680i	0.0241936	−	0.434768i
$877$	−1.59498	+	15.1752i	−0.0538585	+	0.512430i	0.934022	+	0.357215i	$0.116274\pi$
$877$	−1.59498	+	15.1752i	−0.0538585	+	0.512430i	−0.987881	+	0.155215i	$0.950393\pi$
$878$	−5.81434	+	6.45748i	−0.196225	+	0.217929i
$879$	10.6275	−	2.81087i	0.358457	−	0.0948083i
$880$	−0.0848868	+	0.671450i	−0.00286153	+	0.0226346i
$881$	7.88976	−	24.2822i	0.265813	−	0.818088i	−0.725692	−	0.688019i	$-0.758480\pi$
$881$	7.88976	−	24.2822i	0.265813	−	0.818088i	0.991505	−	0.130068i	$-0.0415196\pi$
$882$	2.60279	+	5.94910i	0.0876406	+	0.200317i
$883$	−7.07144	+	21.7636i	−0.237973	+	0.732405i	0.758740	+	0.651393i	$0.225815\pi$
$883$	−7.07144	+	21.7636i	−0.237973	+	0.732405i	−0.996713	+	0.0810118i	$0.974185\pi$
$884$	2.72262	+	25.9040i	0.0915717	+	0.871246i
$885$	−13.2732	+	3.21350i	−0.446175	+	0.108021i
$886$	−3.51436	+	33.4369i	−0.118067	+	1.12334i
$887$	26.6020	+	11.8440i	0.893209	+	0.397682i	0.801424	−	0.598097i	$-0.204076\pi$
$887$	26.6020	+	11.8440i	0.893209	+	0.397682i	0.0917847	+	0.995779i	$0.470743\pi$
$888$	−36.3484	+	1.78724i	−1.21977	+	0.0599757i
$889$	−49.0290	+	21.8291i	−1.64438	+	0.732125i
$890$	−9.77496	−	11.3265i	−0.327657	−	0.379665i
$891$	−9.47494	−	7.07276i	−0.317422	−	0.236946i
$892$	−5.72244	+	17.6119i	−0.191602	+	0.589689i
$893$	−11.3221	+	19.6105i	−0.378881	+	0.656240i
$894$	8.31094	−	6.68573i	0.277959	−	0.223604i
$895$	−0.273776	+	0.785946i	−0.00915134	+	0.0262713i
$896$	−12.6100	+	14.0048i	−0.421271	+	0.467869i
$897$	−34.7705	−	34.9958i	−1.16095	−	1.16848i
$898$	−22.9738	+	10.2286i	−0.766645	+	0.341333i
$899$	−35.8760			−1.19653
$900$	9.72927	+	14.8569i	0.324309	+	0.495232i
$901$	−31.0641			−1.03490
$902$	−1.72649	+	0.768682i	−0.0574858	+	0.0255943i
$903$	23.0119	−	6.08642i	0.765787	−	0.202543i
$904$	22.7622	−	25.2800i	0.757060	−	0.840800i
$905$	−8.98531	+	6.24372i	−0.298682	+	0.207548i
$906$	28.6058	+	11.0869i	0.950363	+	0.368336i
$907$	6.18003	−	10.7041i	0.205204	−	0.355425i	−0.744993	−	0.667072i	$-0.767547\pi$
$907$	6.18003	−	10.7041i	0.205204	−	0.355425i	0.950198	+	0.311647i	$0.100881\pi$
$908$	1.22517	−	3.77068i	0.0406586	−	0.125134i
$909$	32.9975	−	18.7680i	1.09446	−	0.622495i
$910$	28.5220	−	11.9864i	0.945495	−	0.397347i
$911$	49.5174	−	22.0466i	1.64058	−	0.730435i	0.641265	−	0.767319i	$-0.278410\pi$
$911$	49.5174	−	22.0466i	1.64058	−	0.730435i	0.999320	+	0.0368838i	$0.0117431\pi$
$912$	0.621570	−	1.21022i	0.0205822	−	0.0400744i
$913$	−14.4791	−	6.44651i	−0.479188	−	0.213348i
$914$	0.848120	−	8.06933i	0.0280533	−	0.266910i
$915$	−22.5798	+	41.7773i	−0.746465	+	1.38111i
$916$	2.92747	+	27.8530i	0.0967263	+	0.920289i
$917$	−4.97082	+	15.2986i	−0.164151	+	0.505204i
$918$	−15.9348	−	13.1614i	−0.525927	−	0.434392i
$919$	−0.890312	+	2.74010i	−0.0293687	+	0.0903875i	−0.964666	−	0.263474i	$-0.915132\pi$
$919$	−0.890312	+	2.74010i	−0.0293687	+	0.0903875i	0.935298	+	0.353862i	$0.115132\pi$
$920$	17.6586	+	32.1279i	0.582188	+	1.05923i
$921$	11.7383	−	43.2487i	0.386790	−	1.42509i
$922$	−7.05940	+	7.84026i	−0.232489	+	0.258205i
$923$	3.38284	−	32.1856i	0.111348	−	1.05940i
$924$	−7.36998	+	3.72526i	−0.242455	+	0.122552i
$925$	28.6205	+	22.6929i	0.941035	+	0.746137i
$926$	24.5957			0.808265
$927$	−53.0735	+	16.8664i	−1.74316	+	0.553964i
$928$	−11.2729	−	34.6943i	−0.370050	−	1.13890i
$929$	49.4771	+	10.5167i	1.62329	+	0.345041i	0.927680	−	0.373376i	$-0.121800\pi$
$929$	49.4771	+	10.5167i	1.62329	+	0.345041i	0.695612	+	0.718418i	$0.255133\pi$
$930$	−5.38313	+	18.3017i	−0.176520	+	0.600136i
$931$	7.99067	−	1.69847i	0.261884	−	0.0556651i
$932$	−13.0601	−	22.6207i	−0.427798	−	0.740967i
$933$	−5.41555	−	2.09893i	−0.177297	−	0.0687158i
$934$	0.464224	+	4.41679i	0.0151899	+	0.144522i
$935$	6.70125	−	11.0628i	0.219154	−	0.361791i
$936$	41.0897	−	13.0580i	1.34306	−	0.426814i
$937$	41.9653	−	30.4896i	1.37095	−	0.996051i	0.373283	−	0.927717i	$-0.378232\pi$
$937$	41.9653	−	30.4896i	1.37095	−	0.996051i	0.997663	−	0.0683333i	$-0.0217681\pi$
$938$	−1.59588	−	15.1838i	−0.0521073	−	0.495768i
$939$	−15.1715	−	2.45318i	−0.495102	−	0.0800565i
$940$	17.5793	+	0.369854i	0.573372	+	0.0120633i
$941$	−30.6626	−	13.6519i	−0.999573	−	0.445039i	−0.159317	−	0.987228i	$-0.550929\pi$
$941$	−30.6626	−	13.6519i	−0.999573	−	0.445039i	−0.840257	+	0.542189i	$0.817596\pi$
$942$	−18.6031	+	14.9653i	−0.606123	+	0.487596i
$943$	−4.53867	+	7.86121i	−0.147800	+	0.255996i
$944$	0.251042	−	0.772628i	0.00817072	−	0.0251469i
$945$	13.7789	−	32.8422i	0.448229	−	1.06836i
$946$	−1.64419	−	5.06029i	−0.0534572	−	0.164524i
$947$	−15.8754	−	3.37442i	−0.515880	−	0.109654i	−0.0573878	−	0.998352i	$-0.518277\pi$
$947$	−15.8754	−	3.37442i	−0.515880	−	0.109654i	−0.458493	+	0.888698i	$0.651610\pi$
$948$	2.05664	+	5.40990i	0.0667966	+	0.175705i
$949$	15.7014	+	27.1956i	0.509688	+	0.882806i
$950$	−14.3192	+	5.66630i	−0.464575	+	0.183839i
$951$	49.3859	−	24.9628i	1.60145	−	0.809474i
$952$	−35.4628	+	15.7890i	−1.14935	+	0.511726i
$953$	0.829618	+	2.55330i	0.0268740	+	0.0827096i	0.963594	−	0.267370i	$-0.0861546\pi$
$953$	0.829618	+	2.55330i	0.0268740	+	0.0827096i	−0.936720	+	0.350080i	$0.886155\pi$
$954$	3.85446	+	18.7279i	0.124793	+	0.606337i
$955$	−4.86211	+	8.02662i	−0.157334	+	0.259735i
$956$	11.4618	+	12.7296i	0.370700	+	0.411704i
$957$	0.831842	−	14.9485i	0.0268896	−	0.483217i
$958$	−30.7526	+	6.53666i	−0.993571	+	0.211190i
$959$	−5.09185	−	2.26704i	−0.164424	−	0.0732065i
$960$	−21.1742	+	0.595024i	−0.683396	+	0.0192043i
$961$	−1.15948	+	0.516233i	−0.0374025	+	0.0166527i
$962$	26.6759	−	19.3812i	0.860066	−	0.624875i
$963$	31.8937	+	18.6896i	1.02776	+	0.602263i
$964$	8.53357	+	6.20000i	0.274848	+	0.199689i
$965$	0.827575	−	6.54608i	0.0266406	−	0.210726i
$966$	12.4904	−	24.3193i	0.401873	−	0.782461i
$967$	4.01563	−	0.853548i	0.129134	−	0.0274483i	−0.142891	−	0.989738i	$-0.545640\pi$
$967$	4.01563	−	0.853548i	0.129134	−	0.0274483i	0.272025	+	0.962290i	$0.412307\pi$
$968$	−13.3373	−	23.1008i	−0.428676	−	0.742489i
$969$	−20.2589	+	16.2973i	−0.650810	+	0.523544i
$970$	−31.1118	−	14.6436i	−0.998939	−	0.470177i
$971$	−0.954719	−	2.93832i	−0.0306384	−	0.0942953i	0.934568	−	0.355785i	$-0.115786\pi$
$971$	−0.954719	−	2.93832i	−0.0306384	−	0.0942953i	−0.965206	+	0.261489i	$0.915786\pi$
$972$	8.64324	−	16.3068i	0.277232	−	0.523042i
$973$	25.4665	+	18.5025i	0.816419	+	0.593163i
$974$	5.73816	−	9.93878i	0.183862	−	0.318459i
$975$	−39.6543	−	17.3209i	−1.26996	−	0.554714i
$976$	−1.41247	−	2.44647i	−0.0452121	−	0.0783096i
$977$	−2.68758	+	25.5707i	−0.0859834	+	0.818078i	0.863519	+	0.504317i	$0.168256\pi$
$977$	−2.68758	+	25.5707i	−0.0859834	+	0.818078i	−0.949502	+	0.313761i	$0.898411\pi$
$978$	−0.777377	−	0.782415i	−0.0248578	−	0.0250189i
$979$	−9.51780	−	2.02307i	−0.304190	−	0.0646576i
$980$	−4.14442	−	4.80225i	−0.132389	−	0.153402i
$981$	1.37394	−	0.135440i	0.0438666	−	0.00432426i
$982$	10.2646			0.327556
$983$	−27.1300	−	30.1309i	−0.865311	−	0.961026i	0.134241	−	0.990949i	$-0.457140\pi$
$983$	−27.1300	−	30.1309i	−0.865311	−	0.961026i	−0.999552	+	0.0299231i	$0.990474\pi$
$984$	−4.29924	−	6.66730i	−0.137055	−	0.212546i
$985$	−5.04069	+	14.4706i	−0.160610	+	0.461072i
$986$	2.73551	−	26.0267i	0.0871165	−	0.828859i
$987$	−19.1098	−	29.6356i	−0.608271	−	0.943312i
$988$	−2.10824	−	20.0586i	−0.0670722	−	0.638149i
$989$	−20.6753	−	15.0215i	−0.657437	−	0.477656i
$990$	−7.50099	−	2.66735i	−0.238397	−	0.0847741i
$991$	−4.89581	+	3.55701i	−0.155520	+	0.112992i	−0.662824	−	0.748775i	$-0.730642\pi$
$991$	−4.89581	+	3.55701i	−0.155520	+	0.112992i	0.507304	+	0.861767i	$0.330642\pi$
$992$	20.2286	+	22.4661i	0.642258	+	0.713300i
$993$	19.0709	−	9.63965i	0.605197	−	0.305905i
$994$	17.5431	−	3.72890i	0.556434	−	0.118274i
$995$	−17.1459	−	13.0169i	−0.543560	−	0.412664i
$996$	6.48026	−	23.8759i	0.205335	−	0.756537i
$997$	30.1668	+	6.41216i	0.955393	+	0.203075i	0.659128	−	0.752031i	$-0.270926\pi$
$997$	30.1668	+	6.41216i	0.955393	+	0.203075i	0.296265	+	0.955106i	$0.404259\pi$
$998$	−14.1557	−	10.2847i	−0.448092	−	0.325558i
$999$	6.30096	−	37.4316i	0.199354	−	1.18428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.19	✓	224
3.2	odd	2		675.2.r.a.316.10		224
9.4	even	3	inner	225.2.q.a.166.10	yes	224
9.5	odd	6		675.2.r.a.91.19		224
25.11	even	5	inner	225.2.q.a.61.10	yes	224
75.11	odd	10		675.2.r.a.586.19		224
225.86	odd	30		675.2.r.a.361.10		224
225.211	even	15	inner	225.2.q.a.211.19	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.19	✓	224	1.1	even	1	trivial
225.2.q.a.61.10	yes	224	25.11	even	5	inner
225.2.q.a.166.10	yes	224	9.4	even	3	inner
225.2.q.a.211.19	yes	224	225.211	even	15	inner
675.2.r.a.91.19		224	9.5	odd	6
675.2.r.a.316.10		224	3.2	odd	2
675.2.r.a.361.10		224	225.86	odd	30
675.2.r.a.586.19		224	75.11	odd	10

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

Introduction

L-functions

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