LMFDB - Embedded newform 572.2.bk.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(31,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 12, 15]))

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

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

chi := DirichletCharacter("572.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bk (of order $20$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	572.31
Dual form			572.2.bk.a.203.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37530 - 0.329478i) q^{2} +(1.80222 + 2.48055i) q^{3} +(1.78289 + 0.906260i) q^{4} +(1.79602 + 0.915119i) q^{5} +(-1.66131 - 4.00528i) q^{6} +(-0.175107 + 0.0277342i) q^{7} +(-2.15341 - 1.83380i) q^{8} +(-1.97806 + 6.08783i) q^{9} +O(q^{10})$	\(q+(-1.37530 - 0.329478i) q^{2} +(1.80222 + 2.48055i) q^{3} +(1.78289 + 0.906260i) q^{4} +(1.79602 + 0.915119i) q^{5} +(-1.66131 - 4.00528i) q^{6} +(-0.175107 + 0.0277342i) q^{7} +(-2.15341 - 1.83380i) q^{8} +(-1.97806 + 6.08783i) q^{9} +(-2.16855 - 1.85031i) q^{10} +(3.01773 - 1.37597i) q^{11} +(0.965142 + 6.05582i) q^{12} +(-3.28860 + 1.47820i) q^{13} +(0.249962 + 0.0195510i) q^{14} +(0.966837 + 6.10437i) q^{15} +(2.35738 + 3.23152i) q^{16} +(-1.77439 + 0.576534i) q^{17} +(4.72622 - 7.72086i) q^{18} +(5.42174 + 0.858719i) q^{19} +(2.37277 + 3.25922i) q^{20} +(-0.384378 - 0.384378i) q^{21} +(-4.60363 + 0.898093i) q^{22} +1.79412 q^{23} +(0.667902 - 8.64655i) q^{24} +(-0.550673 - 0.757937i) q^{25} +(5.00985 - 0.949448i) q^{26} +(-9.91788 + 3.22251i) q^{27} +(-0.337330 - 0.109245i) q^{28} +(1.69781 + 1.23353i) q^{29} +(0.681565 - 8.71387i) q^{30} +(-3.33316 + 1.69833i) q^{31} +(-2.17739 - 5.22101i) q^{32} +(8.85179 + 5.00582i) q^{33} +(2.63027 - 0.208284i) q^{34} +(-0.339876 - 0.110432i) q^{35} +(-9.04381 + 9.06129i) q^{36} +(-1.58880 - 10.0313i) q^{37} +(-7.17357 - 2.96734i) q^{38} +(-9.59355 - 5.49349i) q^{39} +(-2.18943 - 5.26417i) q^{40} +(0.954216 - 6.02469i) q^{41} +(0.401990 + 0.655278i) q^{42} -2.10032 q^{43} +(6.62727 + 0.281650i) q^{44} +(-9.12372 + 9.12372i) q^{45} +(-2.46745 - 0.591123i) q^{46} +(-1.18011 + 7.45092i) q^{47} +(-3.76741 + 11.6715i) q^{48} +(-6.62750 + 2.15341i) q^{49} +(0.507616 + 1.22382i) q^{50} +(-4.62797 - 3.36241i) q^{51} +(-7.20285 - 0.344859i) q^{52} +(-0.0574194 + 0.176719i) q^{53} +(14.7018 - 1.16420i) q^{54} +(6.67909 + 0.290312i) q^{55} +(0.427936 + 0.261388i) q^{56} +(7.64109 + 14.9965i) q^{57} +(-1.92858 - 2.25587i) q^{58} +(14.5405 - 2.30299i) q^{59} +(-3.80838 + 11.7596i) q^{60} +(-2.07381 - 6.38252i) q^{61} +(5.14365 - 1.23751i) q^{62} +(0.177530 - 1.12088i) q^{63} +(1.27435 + 7.89785i) q^{64} +(-7.25914 - 0.354578i) q^{65} +(-10.5245 - 9.80096i) q^{66} +(-2.92487 - 2.92487i) q^{67} +(-3.68603 - 0.580163i) q^{68} +(3.23341 + 4.45040i) q^{69} +(0.431046 + 0.263859i) q^{70} +(-1.11058 + 2.17964i) q^{71} +(15.4234 - 9.48224i) q^{72} +(0.460974 + 2.91048i) q^{73} +(-1.12001 + 14.3195i) q^{74} +(0.887662 - 2.73194i) q^{75} +(8.88813 + 6.44450i) q^{76} +(-0.490264 + 0.324636i) q^{77} +(11.3840 + 10.7160i) q^{78} +(6.17518 + 2.00644i) q^{79} +(1.27669 + 7.96117i) q^{80} +(-10.3320 - 7.50662i) q^{81} +(-3.29733 + 7.97134i) q^{82} +(3.78571 - 7.42987i) q^{83} +(-0.336956 - 1.03365i) q^{84} +(-3.71444 - 0.588310i) q^{85} +(2.88857 + 0.692010i) q^{86} +6.43461i q^{87} +(-9.02167 - 2.57089i) q^{88} +(11.2816 + 11.2816i) q^{89} +(15.5539 - 9.54177i) q^{90} +(0.534860 - 0.350050i) q^{91} +(3.19872 + 1.62594i) q^{92} +(-10.2199 - 5.20729i) q^{93} +(4.07792 - 9.85841i) q^{94} +(8.95173 + 6.50381i) q^{95} +(9.02682 - 14.8106i) q^{96} +(-1.94104 - 3.80951i) q^{97} +(9.82429 - 0.777960i) q^{98} +(2.40743 + 21.0932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	$ 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) $ 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.37530	−	0.329478i	−0.972482	−	0.232976i
$2$	−1.37530	−	0.329478i	−0.972482	−	0.232976i
$3$	1.80222	+	2.48055i	1.04051	+	1.43214i	0.896753	+	0.442532i	$0.145920\pi$
$3$	1.80222	+	2.48055i	1.04051	+	1.43214i	0.143762	+	0.989612i	$0.454080\pi$
$4$	1.78289	+	0.906260i	0.891444	+	0.453130i
$5$	1.79602	+	0.915119i	0.803206	+	0.409254i	0.806862	−	0.590740i	$-0.201164\pi$
$5$	1.79602	+	0.915119i	0.803206	+	0.409254i	−0.00365668	+	0.999993i	$0.501164\pi$
$6$	−1.66131	−	4.00528i	−0.678226	−	1.63515i
$7$	−0.175107	+	0.0277342i	−0.0661842	+	0.0104825i	−0.189439	−	0.981893i	$-0.560667\pi$
$7$	−0.175107	+	0.0277342i	−0.0661842	+	0.0104825i	0.123255	+	0.992375i	$0.460667\pi$
$8$	−2.15341	−	1.83380i	−0.761346	−	0.648346i
$9$	−1.97806	+	6.08783i	−0.659352	+	2.02928i
$10$	−2.16855	−	1.85031i	−0.685757	−	0.585120i
$11$	3.01773	−	1.37597i	0.909880	−	0.414871i
$11$	3.01773	−	1.37597i	0.909880	−	0.414871i
$12$	0.965142	+	6.05582i	0.278612	+	1.74817i
$13$	−3.28860	+	1.47820i	−0.912095	+	0.409980i
$13$	−3.28860	+	1.47820i	−0.912095	+	0.409980i
$14$	0.249962	+	0.0195510i	0.0668051	+	0.00522523i
$15$	0.966837	+	6.10437i	0.249636	+	1.57614i
$16$	2.35738	+	3.23152i	0.589346	+	0.807881i
$17$	−1.77439	+	0.576534i	−0.430353	+	0.139830i	−0.516180	−	0.856480i	$-0.672647\pi$
$17$	−1.77439	+	0.576534i	−0.430353	+	0.139830i	0.0858276	+	0.996310i	$0.472647\pi$
$18$	4.72622	−	7.72086i	1.11398	−	1.81982i
$19$	5.42174	+	0.858719i	1.24383	+	0.197004i	0.743444	−	0.668798i	$-0.233191\pi$
$19$	5.42174	+	0.858719i	1.24383	+	0.197004i	0.500388	+	0.865802i	$0.333191\pi$
$20$	2.37277	+	3.25922i	0.530568	+	0.728784i
$21$	−0.384378	−	0.384378i	−0.0838781	−	0.0838781i
$22$	−4.60363	+	0.898093i	−0.981498	+	0.191474i
$23$	1.79412			0.374100			0.187050	−	0.982350i	$-0.440107\pi$
$23$	1.79412			0.374100			0.187050	+	0.982350i	$0.440107\pi$
$24$	0.667902	−	8.64655i	0.136335	−	1.76497i
$25$	−0.550673	−	0.757937i	−0.110135	−	0.151587i
$26$	5.00985	−	0.949448i	0.982511	−	0.186202i
$27$	−9.91788	+	3.22251i	−1.90870	+	0.620173i
$28$	−0.337330	−	0.109245i	−0.0637495	−	0.0206454i
$29$	1.69781	+	1.23353i	0.315276	+	0.229061i	0.734157	−	0.678980i	$-0.237578\pi$
$29$	1.69781	+	1.23353i	0.315276	+	0.229061i	−0.418881	+	0.908041i	$0.637578\pi$
$30$	0.681565	−	8.71387i	0.124436	−	1.59093i
$31$	−3.33316	+	1.69833i	−0.598653	+	0.305029i	−0.726932	−	0.686709i	$-0.759055\pi$
$31$	−3.33316	+	1.69833i	−0.598653	+	0.305029i	0.128279	+	0.991738i	$0.459055\pi$
$32$	−2.17739	−	5.22101i	−0.384912	−	0.922953i
$33$	8.85179	+	5.00582i	1.54090	+	0.871402i
$34$	2.63027	−	0.208284i	0.451088	−	0.0357204i
$35$	−0.339876	−	0.110432i	−0.0574495	−	0.0186665i
$36$	−9.04381	+	9.06129i	−1.50730	+	1.51022i
$37$	−1.58880	−	10.0313i	−0.261197	−	1.64914i	−0.674305	−	0.738453i	$-0.735557\pi$
$37$	−1.58880	−	10.0313i	−0.261197	−	1.64914i	0.413108	−	0.910682i	$-0.364443\pi$
$38$	−7.17357	−	2.96734i	−1.16371	−	0.481365i
$39$	−9.59355	−	5.49349i	−1.53620	−	0.879662i
$40$	−2.18943	−	5.26417i	−0.346179	−	0.832339i
$41$	0.954216	−	6.02469i	0.149024	−	0.940898i	−0.793939	−	0.607998i	$-0.791973\pi$
$41$	0.954216	−	6.02469i	0.149024	−	0.940898i	0.942962	−	0.332900i	$-0.108027\pi$
$42$	0.401990	+	0.655278i	0.0620284	+	0.101112i
$43$	−2.10032			−0.320296			−0.160148	−	0.987093i	$-0.551197\pi$
$43$	−2.10032			−0.320296			−0.160148	+	0.987093i	$0.551197\pi$
$44$	6.62727	+	0.281650i	0.999098	+	0.0424603i
$45$	−9.12372	+	9.12372i	−1.36008	+	1.36008i
$46$	−2.46745	−	0.591123i	−0.363806	−	0.0871563i
$47$	−1.18011	+	7.45092i	−0.172137	+	1.08683i	0.738692	+	0.674043i	$0.235444\pi$
$47$	−1.18011	+	7.45092i	−0.172137	+	1.08683i	−0.910828	+	0.412785i	$0.864556\pi$
$48$	−3.76741	+	11.6715i	−0.543779	+	1.68464i
$49$	−6.62750	+	2.15341i	−0.946786	+	0.307629i
$50$	0.507616	+	1.22382i	0.0717878	+	0.173075i
$51$	−4.62797	−	3.36241i	−0.648045	−	0.470832i
$52$	−7.20285	−	0.344859i	−0.998856	−	0.0478233i
$53$	−0.0574194	+	0.176719i	−0.00788716	+	0.0242742i	−0.954923	−	0.296855i	$-0.904062\pi$
$53$	−0.0574194	+	0.176719i	−0.00788716	+	0.0242742i	0.947035	+	0.321129i	$0.104062\pi$
$54$	14.7018	−	1.16420i	2.00066	−	0.158427i
$55$	6.67909	+	0.290312i	0.900608	+	0.0391456i
$56$	0.427936	+	0.261388i	0.0571853	+	0.0349294i
$57$	7.64109	+	14.9965i	1.01209	+	1.98633i
$58$	−1.92858	−	2.25587i	−0.253234	−	0.296210i
$59$	14.5405	−	2.30299i	1.89301	−	0.299824i	0.901805	−	0.432144i	$-0.142243\pi$
$59$	14.5405	−	2.30299i	1.89301	−	0.299824i	0.991207	+	0.132321i	$0.0422428\pi$
$60$	−3.80838	+	11.7596i	−0.491660	+	1.51816i
$61$	−2.07381	−	6.38252i	−0.265524	−	0.817198i	−0.991572	−	0.129554i	$-0.958645\pi$
$61$	−2.07381	−	6.38252i	−0.265524	−	0.817198i	0.726049	−	0.687643i	$-0.241355\pi$
$62$	5.14365	−	1.23751i	0.653244	−	0.157164i
$63$	0.177530	−	1.12088i	0.0223667	−	0.141218i
$64$	1.27435	+	7.89785i	0.159294	+	0.987231i
$65$	−7.25914	−	0.354578i	−0.900385	−	0.0439799i
$66$	−10.5245	−	9.80096i	−1.29548	−	1.20642i
$67$	−2.92487	−	2.92487i	−0.357330	−	0.357330i	0.505498	−	0.862828i	$-0.331309\pi$
$67$	−2.92487	−	2.92487i	−0.357330	−	0.357330i	−0.862828	+	0.505498i	$0.831309\pi$
$68$	−3.68603	−	0.580163i	−0.446997	−	0.0703551i
$69$	3.23341	+	4.45040i	0.389256	+	0.535765i
$70$	0.431046	+	0.263859i	0.0515198	+	0.0315372i
$71$	−1.11058	+	2.17964i	−0.131802	+	0.258676i	−0.947470	−	0.319844i	$-0.896370\pi$
$71$	−1.11058	+	2.17964i	−0.131802	+	0.258676i	0.815668	+	0.578520i	$0.196370\pi$
$72$	15.4234	−	9.48224i	1.81767	−	1.11749i
$73$	0.460974	+	2.91048i	0.0539529	+	0.340646i	0.999868	+	0.0162318i	$0.00516698\pi$
$73$	0.460974	+	2.91048i	0.0539529	+	0.340646i	−0.945915	+	0.324414i	$0.894833\pi$
$74$	−1.12001	+	14.3195i	−0.130199	+	1.66461i
$75$	0.887662	−	2.73194i	0.102498	−	0.315457i
$76$	8.88813	+	6.44450i	1.01954	+	0.739235i
$77$	−0.490264	+	0.324636i	−0.0558708	+	0.0369957i
$78$	11.3840	+	10.7160i	1.28899	+	1.21335i
$79$	6.17518	+	2.00644i	0.694762	+	0.225742i	0.635047	−	0.772473i	$-0.280981\pi$
$79$	6.17518	+	2.00644i	0.694762	+	0.225742i	0.0597154	+	0.998215i	$0.480981\pi$
$80$	1.27669	+	7.96117i	0.142738	+	0.890086i
$81$	−10.3320	−	7.50662i	−1.14800	−	0.834069i
$82$	−3.29733	+	7.97134i	−0.364129	+	0.880288i
$83$	3.78571	−	7.42987i	0.415535	−	0.815534i	−0.584456	−	0.811425i	$-0.698692\pi$
$83$	3.78571	−	7.42987i	0.415535	−	0.815534i	0.999992	−	0.00410887i	$-0.00130790\pi$
$84$	−0.336956	−	1.03365i	−0.0367650	−	0.112780i
$85$	−3.71444	−	0.588310i	−0.402888	−	0.0638111i
$86$	2.88857	+	0.692010i	0.311482	+	0.0746213i
$87$			6.43461i			0.689862i
$88$	−9.02167	−	2.57089i	−0.961713	−	0.274058i
$89$	11.2816	+	11.2816i	1.19585	+	1.19585i	0.975398	+	0.220452i	$0.0707533\pi$
$89$	11.2816	+	11.2816i	1.19585	+	1.19585i	0.220452	+	0.975398i	$0.429247\pi$
$90$	15.5539	−	9.54177i	1.63953	−	1.00579i
$91$	0.534860	−	0.350050i	0.0560686	−	0.0366953i
$92$	3.19872	+	1.62594i	0.333489	+	0.169516i
$93$	−10.2199	−	5.20729i	−1.05975	−	0.539971i
$94$	4.07792	−	9.85841i	0.420605	−	1.01682i
$95$	8.95173	+	6.50381i	0.918428	+	0.667277i
$96$	9.02682	−	14.8106i	0.921296	−	1.51160i
$97$	−1.94104	−	3.80951i	−0.197083	−	0.386797i	0.771223	−	0.636565i	$-0.219645\pi$
$97$	−1.94104	−	3.80951i	−0.197083	−	0.386797i	−0.968306	+	0.249768i	$0.919645\pi$
$98$	9.82429	−	0.777960i	0.992403	−	0.0785858i
$99$	2.40743	+	21.0932i	0.241956	+	2.11995i
$100$	−0.294901	−	1.85037i	−0.0294901	−	0.185037i
$101$	−11.7881	−	3.83018i	−1.17296	−	0.381117i	−0.343212	−	0.939258i	$-0.611515\pi$
$101$	−11.7881	−	3.83018i	−1.17296	−	0.381117i	−0.829746	+	0.558141i	$0.811515\pi$
$102$	5.25699	+	6.14913i	0.520520	+	0.608855i
$103$	−11.9955	−	8.71523i	−1.18195	−	0.858737i	−0.189560	−	0.981869i	$-0.560706\pi$
$103$	−11.9955	−	8.71523i	−1.18195	−	0.858737i	−0.992390	+	0.123132i	$0.960706\pi$
$104$	9.79244	+	2.84746i	0.960228	+	0.279217i
$105$	−0.338600	−	1.04210i	−0.0330439	−	0.101699i
$106$	0.137194	−	0.224122i	0.0133254	−	0.0217687i
$107$	2.43835	+	3.35611i	0.235725	+	0.324447i	0.910448	−	0.413624i	$-0.135737\pi$
$107$	2.43835	+	3.35611i	0.235725	+	0.324447i	−0.674723	+	0.738071i	$0.735737\pi$
$108$	−20.6029	−	3.24280i	−1.98252	−	0.312038i
$109$	−13.3604	+	13.3604i	−1.27970	+	1.27970i	−0.338860	+	0.940837i	$0.610041\pi$
$109$	−13.3604	+	13.3604i	−1.27970	+	1.27970i	−0.940837	+	0.338860i	$0.889959\pi$
$110$	−9.09009	−	2.59988i	−0.866706	−	0.247889i
$111$	22.0197	−	22.0197i	2.09002	−	2.09002i
$112$	−0.502418	−	0.500482i	−0.0474740	−	0.0472911i
$113$	15.1786	−	11.0279i	1.42788	−	1.03742i	0.437479	−	0.899229i	$-0.355871\pi$
$113$	15.1786	−	11.0279i	1.42788	−	1.03742i	0.990406	−	0.138191i	$-0.0441286\pi$
$114$	−5.56776	−	23.1422i	−0.521469	−	2.16747i
$115$	3.22228	+	1.64183i	0.300479	+	0.153102i
$116$	1.90911	+	3.73791i	0.177256	+	0.347056i
$117$	−2.49401	−	22.9444i	−0.230571	−	2.12121i
$118$	−20.7563	−	1.62348i	−1.91077	−	0.149453i
$119$	0.294718	−	0.150166i	0.0270168	−	0.0137657i
$120$	9.11219	−	14.9182i	0.831826	−	1.36184i
$121$	7.21341	−	8.30462i	0.655765	−	0.754965i
$122$	0.749203	+	9.46114i	0.0678296	+	0.856571i
$123$	16.6642	−	8.49085i	1.50256	−	0.765594i
$124$	−7.48178	+	0.00722240i	−0.671884	+	0.000648591i
$125$	−1.87206	−	11.8197i	−0.167442	−	1.05719i
$126$	−0.613462	+	1.48305i	−0.0546516	+	0.132121i
$127$	0.233358	+	0.718203i	0.0207072	+	0.0637302i	0.960876	−	0.276978i	$-0.0893330\pi$
$127$	0.233358	+	0.718203i	0.0207072	+	0.0637302i	−0.940169	+	0.340709i	$0.889333\pi$
$128$	0.849551	−	11.2818i	0.0750904	−	0.997177i
$129$	−3.78525	−	5.20995i	−0.333273	−	0.458711i
$130$	9.86665	+	2.87937i	0.865363	+	0.252538i
$131$			9.42680i			0.823623i	0.911269	+	0.411812i	$0.135104\pi$
$131$			9.42680i			0.823623i	−0.911269	+	0.411812i	$0.864896\pi$
$132$	11.2452	+	16.9468i	0.978766	+	1.47503i
$133$	−0.973199			−0.0843871
$134$	3.05889	+	4.98625i	0.264248	+	0.430746i
$135$	−20.7617	−	3.28833i	−1.78688	−	0.283015i
$136$	4.87824	+	2.01236i	0.418305	+	0.172559i
$137$	3.90047	−	7.65510i	0.333240	−	0.654020i	−0.662209	−	0.749319i	$-0.730381\pi$
$137$	3.90047	−	7.65510i	0.333240	−	0.654020i	0.995449	+	0.0952996i	$0.0303809\pi$
$138$	−2.98059	−	7.18596i	−0.253724	−	0.611710i
$139$	−7.47881	+	10.2937i	−0.634344	+	0.873100i	−0.998298	−	0.0583169i	$-0.981427\pi$
$139$	−7.47881	+	10.2937i	−0.634344	+	0.873100i	0.363954	+	0.931417i	$0.381427\pi$
$140$	−0.505880	−	0.504905i	−0.0427547	−	0.0426722i
$141$	−20.6092	+	10.5009i	−1.73561	+	0.884336i
$142$	2.24553	−	2.63175i	0.188440	−	0.220851i
$143$	−7.89016	+	8.98584i	−0.659808	+	0.751434i
$144$	−24.3360	+	7.95922i	−2.02800	+	0.663269i
$145$	1.92048	+	3.76915i	0.159487	+	0.313011i
$146$	0.324961	−	4.15465i	0.0268939	−	0.343842i
$147$	−17.2859	−	12.5589i	−1.42571	−	1.03584i
$148$	6.25831	−	19.3246i	0.514430	−	1.58847i
$149$	3.24978	+	1.65584i	0.266232	+	0.135652i	0.582011	−	0.813181i	$-0.302266\pi$
$149$	3.24978	+	1.65584i	0.266232	+	0.135652i	−0.315779	+	0.948833i	$0.602266\pi$
$150$	−2.12091	+	3.46477i	−0.173172	+	0.282897i
$151$	2.56764	−	16.2114i	0.208951	−	1.31927i	−0.630652	−	0.776066i	$-0.717212\pi$
$151$	2.56764	−	16.2114i	0.208951	−	1.31927i	0.839603	−	0.543200i	$-0.182788\pi$
$152$	−10.1005	−	11.7916i	−0.819259	−	0.956422i
$153$		−	11.9426i		−	0.965502i
$154$	0.781220	−	0.284940i	0.0629525	−	0.0229611i
$155$	−7.54060			−0.605676
$156$	−12.1257	−	18.4885i	−0.970834	−	1.48027i
$157$	−6.74228	+	4.89855i	−0.538092	+	0.390947i	−0.823376	−	0.567496i	$-0.807912\pi$
$157$	−6.74228	+	4.89855i	−0.538092	+	0.390947i	0.285284	+	0.958443i	$0.407912\pi$
$158$	−7.83164	−	4.79404i	−0.623052	−	0.381393i
$159$	−0.541842	+	0.176055i	−0.0429708	+	0.0139621i
$160$	0.867206	−	11.3696i	0.0685586	−	0.898848i
$161$	−0.314163	+	0.0497585i	−0.0247595	+	0.00392152i
$162$	11.7363	+	13.7280i	0.922089	+	1.07857i
$163$	−6.72346	−	13.1955i	−0.526622	−	1.03355i	−0.989144	−	0.146947i	$-0.953055\pi$
$163$	−6.72346	−	13.1955i	−0.526622	−	1.03355i	0.462522	−	0.886608i	$-0.346945\pi$
$164$	7.16120	−	9.87658i	0.559195	−	0.771231i
$165$	11.3171	+	17.0910i	0.881033	+	1.33053i
$166$	−7.65445	+	8.97098i	−0.594101	+	0.696283i
$167$	−3.81590	−	7.48913i	−0.295283	−	0.579526i	0.694932	−	0.719076i	$-0.255435\pi$
$167$	−3.81590	−	7.48913i	−0.295283	−	0.579526i	−0.990215	+	0.139550i	$0.955435\pi$
$168$	0.122851	+	1.53259i	0.00947816	+	0.118242i
$169$	8.62983	−	9.72245i	0.663833	−	0.747881i
$170$	4.91463	+	2.03293i	0.376935	+	0.155918i
$171$	−15.9522	+	31.3080i	−1.21990	+	2.39418i
$172$	−3.74464	−	1.90344i	−0.285526	−	0.145136i
$173$	8.69945	+	11.9738i	0.661407	+	0.910348i	0.999527	−	0.0307547i	$-0.00979107\pi$
$173$	8.69945	+	11.9738i	0.661407	+	0.910348i	−0.338120	+	0.941103i	$0.609791\pi$
$174$	2.12006	−	8.84950i	0.160721	−	0.670879i
$175$	0.117447	+	0.117447i	0.00887819	+	0.00887819i
$176$	11.5604	+	6.50818i	0.871400	+	0.490573i
$177$	31.9179	+	31.9179i	2.39910	+	2.39910i
$178$	−11.7986	−	19.2326i	−0.884339	−	1.44155i
$179$	17.5057	−	12.7186i	1.30844	−	0.950635i	0.308437	−	0.951245i	$-0.400194\pi$
$179$	17.5057	−	12.7186i	1.30844	−	0.950635i	1.00000		0.000609355i	$0.000193964\pi$
$180$	−24.5351	+	7.99811i	−1.82873	+	0.596144i
$181$	4.02551	−	1.30797i	0.299214	−	0.0972204i	−0.155563	−	0.987826i	$-0.549719\pi$
$181$	4.02551	−	1.30797i	0.299214	−	0.0972204i	0.454777	+	0.890606i	$0.349719\pi$
$182$	−0.850926	+	0.305199i	−0.0630748	+	0.0226229i
$183$	12.0947	−	16.6469i	0.894064	−	1.23057i
$184$	−3.86348	−	3.29006i	−0.284819	−	0.242546i
$185$	6.32631	−	19.4704i	0.465119	−	1.43149i
$186$	12.3397	+	10.5288i	0.904791	+	0.772009i
$187$	−4.56134	+	4.18133i	−0.333558	+	0.305769i
$188$	−8.85648	+	12.2147i	−0.645925	+	0.890847i
$189$	1.64731	−	0.839349i	0.119825	−	0.0610536i
$190$	−10.1684	−	11.8941i	−0.737696	−	0.862887i
$191$	−4.82366	+	6.63920i	−0.349028	+	0.480395i	−0.947051	−	0.321083i	$-0.895953\pi$
$191$	−4.82366	+	6.63920i	−0.349028	+	0.480395i	0.598023	+	0.801479i	$0.295953\pi$
$192$	−17.2943	+	17.3948i	−1.24811	+	1.25536i
$193$	−8.37867	+	16.4441i	−0.603110	+	1.18367i	0.364497	+	0.931205i	$0.381241\pi$
$193$	−8.37867	+	16.4441i	−0.603110	+	1.18367i	−0.967606	+	0.252464i	$0.918759\pi$
$194$	1.41436	+	5.87874i	0.101545	+	0.422069i
$195$	−12.2030	−	18.6457i	−0.873878	−	1.33524i
$196$	−13.7676	−	2.16696i	−0.983403	−	0.154783i
$197$	19.0444	−	19.0444i	1.35685	−	1.35685i	0.479087	−	0.877768i	$-0.340968\pi$
$197$	19.0444	−	19.0444i	1.35685	−	1.35685i	0.877768	−	0.479087i	$-0.159032\pi$
$198$	3.63881	−	29.8026i	0.258599	−	2.11798i
$199$	15.5845			1.10476			0.552379	−	0.833593i	$-0.313720\pi$
$199$	15.5845			1.10476			0.552379	+	0.833593i	$0.313720\pi$
$200$	−0.204079	+	2.64197i	−0.0144306	+	0.186816i
$201$	1.98401	−	12.5266i	0.139941	−	0.883555i
$202$	14.9502	+	9.15155i	1.05189	+	0.643901i
$203$	−0.331510	−	0.168913i	−0.0232674	−	0.0118553i
$204$	−5.20393	−	10.1890i	−0.364348	−	0.713369i
$205$	7.22710	−	9.94725i	0.504762	−	0.694746i
$206$	13.6259	+	15.9383i	0.949361	+	1.11047i
$207$	−3.54887	+	10.9223i	−0.246664	+	0.759152i
$208$	−12.5294	−	7.14250i	−0.868754	−	0.495244i
$209$	17.5429	−	4.86876i	1.21347	−	0.336779i
$210$	0.122326	+	1.54476i	0.00844127	+	0.106599i
$211$	24.6916	+	8.02277i	1.69984	+	0.552310i	0.988590	−	0.150632i	$-0.0481309\pi$
$211$	24.6916	+	8.02277i	1.69984	+	0.552310i	0.711247	+	0.702942i	$0.248131\pi$
$212$	−0.262526	+	0.263033i	−0.0180303	+	0.0180652i
$213$	−7.40823	+	1.17335i	−0.507603	+	0.0803965i
$214$	−2.24770	−	5.41903i	−0.153650	−	0.370437i
$215$	−3.77223	−	1.92205i	−0.257264	−	0.131082i
$216$	27.2667	+	11.2480i	1.85526	+	0.765330i
$217$	0.536557	−	0.389832i	0.0364239	−	0.0264635i
$218$	22.7765	−	13.9726i	1.54262	−	0.946344i
$219$	−6.38880	+	6.38880i	−0.431715	+	0.431715i
$220$	11.6450	+	6.57059i	0.785104	+	0.442989i
$221$	4.98303	−	4.51890i	0.335195	−	0.303974i
$222$	−37.5387	+	23.0287i	−2.51943	+	1.54558i
$223$	19.3465	+	3.06419i	1.29554	+	0.205193i	0.765862	−	0.643005i	$-0.222313\pi$
$223$	19.3465	+	3.06419i	1.29554	+	0.205193i	0.529679	+	0.848198i	$0.322313\pi$
$224$	0.526077	+	0.853847i	0.0351500	+	0.0570500i
$225$	5.70345	−	1.85316i	0.380230	−	0.123544i
$226$	−24.5086	+	10.1656i	−1.63029	+	0.676209i
$227$	0.355477	+	2.24439i	0.0235938	+	0.148966i	0.996673	−	0.0815062i	$-0.0259730\pi$
$227$	0.355477	+	2.24439i	0.0235938	+	0.148966i	−0.973079	+	0.230472i	$0.925973\pi$
$228$	0.0324949	+	33.6619i	0.00215203	+	2.22931i
$229$	6.75025	−	3.43942i	0.446069	−	0.227284i	−0.216503	−	0.976282i	$-0.569465\pi$
$229$	6.75025	−	3.43942i	0.446069	−	0.227284i	0.662572	+	0.748998i	$0.269465\pi$
$230$	−3.89065	−	3.31968i	−0.256542	−	0.218893i
$231$	−1.68884	−	0.631057i	−0.111118	−	0.0415205i
$232$	−1.39403	−	5.76975i	−0.0915228	−	0.378803i
$233$	−0.622025	−	0.202108i	−0.0407502	−	0.0132405i	0.288571	−	0.957459i	$-0.406820\pi$
$233$	−0.622025	−	0.202108i	−0.0407502	−	0.0132405i	−0.329321	+	0.944218i	$0.606820\pi$
$234$	−4.12968	+	32.3772i	−0.269965	+	2.11656i
$235$	−8.93798	+	12.3021i	−0.583050	+	0.802499i
$236$	28.0112	+	9.07150i	1.82337	+	0.590505i
$237$	6.15199	+	18.9339i	0.399615	+	1.22989i
$238$	−0.454802	+	0.109420i	−0.0294804	+	0.00709267i
$239$	−26.9688	−	4.27144i	−1.74447	−	0.276297i	−0.798839	−	0.601545i	$-0.794552\pi$
$239$	−26.9688	−	4.27144i	−1.74447	−	0.276297i	−0.945629	+	0.325248i	$0.894552\pi$
$240$	−17.4472	+	17.5147i	−1.12621	+	1.13057i
$241$	−6.91524	−	6.91524i	−0.445450	−	0.445450i	0.448389	−	0.893839i	$-0.351998\pi$
$241$	−6.91524	−	6.91524i	−0.445450	−	0.445450i	−0.893839	+	0.448389i	$0.851998\pi$
$242$	−12.6568	+	9.04466i	−0.813609	+	0.581413i
$243$		−	7.87273i		−	0.505036i
$244$	2.08686	−	13.2587i	0.133597	−	0.848803i
$245$	−13.8738	−	2.19739i	−0.886362	−	0.140386i
$246$	−25.7158	+	6.18695i	−1.63958	+	0.394466i
$247$	−19.0993	+	5.19044i	−1.21526	+	0.330260i
$248$	10.2921	+	2.45515i	0.653546	+	0.155902i
$249$	25.2528	−	3.99966i	1.60033	−	0.253468i
$250$	−1.31970	+	16.8725i	−0.0834650	+	1.06711i
$251$	−6.15017	+	18.9283i	−0.388195	+	1.19474i	0.545941	+	0.837824i	$0.316172\pi$
$251$	−6.15017	+	18.9283i	−0.388195	+	1.19474i	−0.934136	+	0.356918i	$0.883828\pi$
$252$	1.33233	−	1.83752i	0.0839287	−	0.115753i
$253$	5.41417	−	2.46866i	0.340386	−	0.155203i
$254$	−0.0843052	−	1.06463i	−0.00528978	−	0.0668008i
$255$	−5.23492	−	10.2741i	−0.327824	−	0.643390i
$256$	−4.88548	+	15.2359i	−0.305342	+	0.952243i
$257$	−4.67536	+	6.43508i	−0.291641	+	0.401410i	−0.929546	−	0.368705i	$-0.879801\pi$
$257$	−4.67536	+	6.43508i	−0.291641	+	0.401410i	0.637905	+	0.770115i	$0.279801\pi$
$258$	3.48928	+	8.41239i	0.217233	+	0.523732i
$259$	0.556420	+	1.71248i	0.0345743	+	0.106409i
$260$	−12.6209	−	7.21084i	−0.782715	−	0.447197i
$261$	−10.8679	+	7.89600i	−0.672707	+	0.488750i
$262$	3.10592	−	12.9647i	0.191884	−	0.800959i
$263$		−	8.79739i		−	0.542471i	−0.962513	−	0.271235i	$-0.912568\pi$
$263$		−	8.79739i		−	0.542471i	0.962513	−	0.271235i	$-0.0874321\pi$
$264$	−9.88185	−	27.0120i	−0.608186	−	1.66247i
$265$	−0.264845	+	0.264845i	−0.0162693	+	0.0162693i
$266$	1.33844	+	0.320648i	0.0820650	+	0.0196602i
$267$	−7.65260	+	48.3166i	−0.468332	+	2.95693i
$268$	−2.56403	−	7.86541i	−0.156623	−	0.480457i
$269$	−6.74110	−	20.7470i	−0.411012	−	1.26497i	−0.915770	−	0.401704i	$-0.868418\pi$
$269$	−6.74110	−	20.7470i	−0.411012	−	1.26497i	0.504758	−	0.863261i	$-0.331582\pi$
$270$	27.4701	+	11.3630i	1.67178	+	0.691528i
$271$	26.4703	−	4.19248i	1.60796	−	0.254675i	0.713110	−	0.701052i	$-0.247286\pi$
$271$	26.4703	−	4.19248i	1.60796	−	0.254675i	0.894845	+	0.446377i	$0.147286\pi$
$272$	−6.04600	−	4.37487i	−0.366593	−	0.265265i
$273$	1.83225	+	0.695877i	0.110893	+	0.0421164i
$274$	−7.88650	+	9.24293i	−0.476441	+	0.558386i
$275$	−2.70468	−	1.52954i	−0.163098	−	0.0922347i
$276$	1.73158	+	10.8649i	0.104229	+	0.653989i
$277$	4.42716	+	1.43847i	0.266003	+	0.0864295i	0.438982	−	0.898496i	$-0.355339\pi$
$277$	4.42716	+	1.43847i	0.266003	+	0.0864295i	−0.172979	+	0.984925i	$0.555339\pi$
$278$	13.6771	−	11.6928i	0.820300	−	0.701288i
$279$	−3.74597	−	23.6511i	−0.224265	−	1.41595i
$280$	0.529381	+	0.861071i	0.0316366	+	0.0514588i
$281$	−4.26284	+	8.36629i	−0.254300	+	0.499091i	−0.982497	−	0.186276i	$-0.940358\pi$
$281$	−4.26284	+	8.36629i	−0.254300	+	0.499091i	0.728198	+	0.685367i	$0.240358\pi$
$282$	31.8036	−	7.65160i	1.89388	−	0.455646i
$283$	9.13582	−	6.63756i	0.543068	−	0.394562i	−0.282155	−	0.959369i	$-0.591049\pi$
$283$	9.13582	−	6.63756i	0.543068	−	0.394562i	0.825223	+	0.564807i	$0.191049\pi$
$284$	−3.95537	+	2.87958i	−0.234708	+	0.170872i
$285$			33.9265i			2.00963i
$286$	13.8120	−	9.75858i	0.816718	−	0.577037i
$287$			1.08143i			0.0638347i
$288$	36.0916	−	2.92813i	2.12672	−	0.172542i
$289$	−10.9372	+	7.94636i	−0.643366	+	0.467433i
$290$	−1.39938	−	5.81646i	−0.0821744	−	0.341554i
$291$	5.95148	−	11.6804i	0.348882	−	0.684719i
$292$	−1.81578	+	5.60682i	−0.106261	+	0.328114i
$293$	0.641418	+	4.04975i	0.0374720	+	0.236589i	0.999315	−	0.0370139i	$-0.0117846\pi$
$293$	0.641418	+	4.04975i	0.0374720	+	0.236589i	−0.961843	+	0.273603i	$0.911785\pi$
$294$	19.6353	+	22.9676i	1.14516	+	1.33950i
$295$	28.2226	+	9.17007i	1.64318	+	0.533902i
$296$	−14.9741	+	24.5150i	−0.870349	+	1.42491i
$297$	−25.4954	+	23.3714i	−1.47939	+	1.35615i
$298$	−3.92385	−	3.34801i	−0.227302	−	0.193945i
$299$	−5.90015	+	2.65208i	−0.341215	+	0.153373i
$300$	4.05845	−	4.06630i	0.234315	−	0.234768i
$301$	0.367781	−	0.0582508i	0.0211985	−	0.00335752i
$302$	−8.87256	+	21.4495i	−0.510559	+	1.23428i
$303$	−11.7438	−	36.1437i	−0.674664	−	2.07640i
$304$	10.0061	+	19.5448i	0.573892	+	1.12097i
$305$	2.11616	−	13.3609i	0.121171	−	0.765044i
$306$	−3.93482	+	16.4246i	−0.224939	+	0.938934i
$307$	−14.9113	+	14.9113i	−0.851034	+	0.851034i	−0.990261	−	0.139227i	$-0.955538\pi$
$307$	−14.9113	+	14.9113i	−0.851034	+	0.851034i	0.139227	+	0.990261i	$0.455538\pi$
$308$	−1.16829	+	0.134483i	−0.0665696	+	0.00766289i
$309$		−	45.4621i		−	2.58625i
$310$	10.3706	+	2.48446i	0.589009	+	0.141108i
$311$	−3.80203	+	2.76234i	−0.215593	+	0.156638i	−0.690341	−	0.723484i	$-0.742539\pi$
$311$	−3.80203	+	2.76234i	−0.215593	+	0.156638i	0.474747	+	0.880122i	$0.342539\pi$
$312$	10.5849	+	29.4224i	0.599252	+	1.66571i
$313$	−2.01825	−	6.21154i	−0.114078	−	0.351097i	0.877675	−	0.479256i	$-0.159093\pi$
$313$	−2.01825	−	6.21154i	−0.114078	−	0.351097i	−0.991754	+	0.128159i	$0.959093\pi$
$314$	10.8866	−	4.51553i	0.614366	−	0.254826i
$315$	1.34459	−	1.85067i	0.0757589	−	0.104273i
$316$	9.19131	+	9.17358i	0.517052	+	0.516054i
$317$	−8.20833	−	16.1097i	−0.461026	−	0.904814i	−0.998120	−	0.0612914i	$-0.980478\pi$
$317$	−8.20833	−	16.1097i	−0.461026	−	0.904814i	0.537094	−	0.843522i	$-0.319522\pi$
$318$	0.803200	−	0.0636033i	0.0450412	−	0.00356670i
$319$	6.82085	+	1.38633i	0.381894	+	0.0776198i
$320$	−4.93871	+	15.3509i	−0.276082	+	0.858141i
$321$	−3.93052	+	12.0969i	−0.219380	+	0.675183i
$322$	0.448462	+	0.0350769i	0.0249918	+	0.00195476i
$323$	−10.1154	+	1.60211i	−0.562833	+	0.0891441i
$324$	−11.6178	−	22.7469i	−0.645434	−	1.26372i
$325$	2.93133	+	1.67855i	0.162601	+	0.0931090i
$326$	4.89913	+	20.3630i	0.271338	+	1.12780i
$327$	−57.2197	−	9.06270i	−3.16425	−	0.501169i
$328$	−13.1029	+	11.2238i	−0.723486	+	0.619729i
$329$		−	1.33744i		−	0.0737353i
$330$	−9.93325	−	27.2340i	−0.546807	−	1.49918i
$331$	−22.1583	−	22.1583i	−1.21793	−	1.21793i	−0.968356	−	0.249574i	$-0.919709\pi$
$331$	−22.1583	−	22.1583i	−1.21793	−	1.21793i	−0.249574	−	0.968356i	$-0.580291\pi$
$332$	13.4829	−	9.81579i	0.739970	−	0.538712i
$333$	64.2116	+	10.1701i	3.51877	+	0.557319i
$334$	2.78050	+	11.5570i	0.152142	+	0.632373i
$335$	−2.57653	−	7.92974i	−0.140771	−	0.433248i
$336$	0.335999	−	2.14825i	0.0183303	−	0.117197i
$337$	−19.5593	+	26.9210i	−1.06546	+	1.46648i	−0.190874	+	0.981615i	$0.561132\pi$
$337$	−19.5593	+	26.9210i	−1.06546	+	1.46648i	−0.874588	+	0.484868i	$0.838868\pi$
$338$	−15.0719	+	10.5279i	−0.819804	+	0.572644i
$339$	54.7105	+	17.7765i	2.97147	+	0.965489i
$340$	−6.08927	−	4.41514i	−0.330237	−	0.239445i
$341$	−7.72173	+	9.71143i	−0.418155	+	0.525903i
$342$	32.2544	−	37.8020i	1.74412	−	2.04410i
$343$	2.20656	−	1.12430i	0.119143	−	0.0607065i
$344$	4.52286	+	3.85157i	0.243856	+	0.207663i
$345$	1.73462	+	10.9520i	0.0933889	+	0.589634i
$346$	−8.01924	−	19.3338i	−0.431117	−	1.03939i
$347$	−12.9648	+	4.21251i	−0.695986	+	0.226140i	−0.635581	−	0.772034i	$-0.719239\pi$
$347$	−12.9648	+	4.21251i	−0.695986	+	0.226140i	−0.0604051	+	0.998174i	$0.519239\pi$
$348$	−5.83143	+	11.4722i	−0.312597	+	0.614974i
$349$	−2.14746	−	0.340124i	−0.114951	−	0.0182064i	0.0986939	−	0.995118i	$-0.468534\pi$
$349$	−2.14746	−	0.340124i	−0.114951	−	0.0182064i	−0.213645	+	0.976911i	$0.568534\pi$
$350$	−0.122829	−	0.200222i	−0.00656548	−	0.0107023i
$351$	27.8524	−	25.2582i	1.48665	−	1.34818i
$352$	−13.7547	−	12.7596i	−0.733130	−	0.680089i
$353$	−9.12036	+	9.12036i	−0.485428	+	0.485428i	−0.906860	−	0.421432i	$-0.861528\pi$
$353$	−9.12036	+	9.12036i	−0.485428	+	0.485428i	0.421432	+	0.906860i	$0.361528\pi$
$354$	−33.3804	−	54.4129i	−1.77415	−	2.89201i
$355$	−3.98927	+	2.89837i	−0.211728	+	0.153830i
$356$	9.88979	+	30.3380i	0.524158	+	1.60791i
$357$	0.903643	+	0.460429i	0.0478258	+	0.0243685i
$358$	−28.2661	+	11.7242i	−1.49391	+	0.619642i
$359$	−1.98370	+	0.314187i	−0.104696	+	0.0165822i	−0.208562	−	0.978009i	$-0.566878\pi$
$359$	−1.98370	+	0.314187i	−0.104696	+	0.0165822i	0.103867	+	0.994591i	$0.466878\pi$
$360$	36.3782	−	2.91603i	1.91730	−	0.153689i
$361$	10.5878	+	3.44017i	0.557250	+	0.181062i
$362$	−5.96722	+	0.472529i	−0.313630	+	0.0248356i
$363$	33.6002	+	2.92644i	1.76355	+	0.153598i
$364$	1.27083	−	0.139378i	0.0666098	−	0.00730540i
$365$	−1.83551	+	5.64913i	−0.0960751	+	0.295689i
$366$	−22.1186	+	18.9095i	−1.15616	+	0.988416i
$367$	−3.35165	+	4.61315i	−0.174955	+	0.240805i	−0.887485	−	0.460837i	$-0.847549\pi$
$367$	−3.35165	+	4.61315i	−0.174955	+	0.240805i	0.712530	+	0.701642i	$0.247549\pi$
$368$	4.22943	+	5.79774i	0.220474	+	0.302228i
$369$	34.7898	+	17.7263i	1.81108	+	0.922793i
$370$	−15.1156	+	24.6932i	−0.785823	+	1.28374i
$371$	0.00515338	−	0.0325371i	0.000267550	−	0.00168924i
$372$	−13.5018	−	18.5459i	−0.700033	−	0.961560i
$373$	−7.41338			−0.383850			−0.191925	−	0.981410i	$-0.561473\pi$
$373$	−7.41338			−0.383850			−0.191925	+	0.981410i	$0.561473\pi$
$374$	7.65086	−	4.24772i	0.395616	−	0.219644i
$375$	25.9455	−	25.9455i	1.33982	−	1.33982i
$376$	16.2048	−	13.8808i	0.835697	−	0.715848i
$377$	−7.40684	−	1.54689i	−0.381472	−	0.0796688i
$378$	−2.54210	+	0.611601i	−0.130751	+	0.0314574i
$379$	6.77163	−	13.2901i	0.347835	−	0.682665i	−0.649116	−	0.760689i	$-0.724861\pi$
$379$	6.77163	−	13.2901i	0.347835	−	0.682665i	0.996951	+	0.0780240i	$0.0248611\pi$
$380$	10.0658	+	19.7082i	0.516364	+	1.01101i
$381$	−1.36097	+	1.87322i	−0.0697248	+	0.0959679i
$382$	8.82144	−	7.54158i	0.451344	−	0.385861i
$383$	−16.1764	+	8.24229i	−0.826576	+	0.421161i	−0.815486	−	0.578777i	$-0.803530\pi$
$383$	−16.1764	+	8.24229i	−0.826576	+	0.421161i	−0.0110898	+	0.999939i	$0.503530\pi$
$384$	29.5160	−	18.2249i	1.50623	−	0.930036i
$385$	−1.17761	+	0.134404i	−0.0600164	+	0.00684985i
$386$	16.9411	−	19.8549i	0.862280	−	1.01059i
$387$	4.15456	−	12.7864i	0.211188	−	0.649970i
$388$	−0.00825457	−	8.55102i	−0.000419062	−	0.434112i
$389$	−12.7371	+	17.5311i	−0.645796	+	0.888862i	−0.998908	−	0.0467189i	$-0.985124\pi$
$389$	−12.7371	+	17.5311i	−0.645796	+	0.888862i	0.353112	+	0.935581i	$0.385124\pi$
$390$	10.6395	+	29.6640i	0.538751	+	1.50209i
$391$	−3.18347	+	1.03437i	−0.160995	+	0.0523104i
$392$	18.2206	+	7.51635i	0.920282	+	0.379633i
$393$	−23.3836	+	16.9892i	−1.17955	+	0.856992i
$394$	−32.4664	+	19.9170i	−1.63563	+	1.00340i
$395$	9.25464	+	9.25464i	0.465651	+	0.465651i
$396$	−14.8237	+	39.7886i	−0.744921	+	1.99945i
$397$	−14.4805	−	14.4805i	−0.726753	−	0.726753i	0.243218	−	0.969972i	$-0.421797\pi$
$397$	−14.4805	−	14.4805i	−0.726753	−	0.726753i	−0.969972	+	0.243218i	$0.921797\pi$
$398$	−21.4334	−	5.13476i	−1.07436	−	0.257382i
$399$	−1.75392	−	2.41407i	−0.0878059	−	0.120855i
$400$	1.15114	−	3.56626i	0.0575571	−	0.178313i
$401$	6.37858	−	12.5187i	0.318531	−	0.625152i	−0.675114	−	0.737714i	$-0.735905\pi$
$401$	6.37858	−	12.5187i	0.318531	−	0.625152i	0.993645	+	0.112561i	$0.0359054\pi$
$402$	−6.85583	+	16.5741i	−0.341938	+	0.826639i
$403$	8.45096	−	10.5122i	0.420972	−	0.523651i
$404$	−17.5457	−	17.5119i	−0.872931	−	0.871247i
$405$	−11.6870	−	22.9370i	−0.580732	−	1.13975i
$406$	0.400272	+	0.341530i	0.0198651	+	0.0169499i
$407$	−18.5973	−	28.0856i	−0.921836	−	1.39215i
$408$	3.79992	+	15.7274i	0.188124	+	0.778624i
$409$	−8.07898	−	15.8559i	−0.399480	−	0.784024i	0.600397	−	0.799702i	$-0.295009\pi$
$409$	−8.07898	−	15.8559i	−0.399480	−	0.784024i	−0.999877	+	0.0156783i	$0.995009\pi$
$410$	−13.2168	+	11.2993i	−0.652732	+	0.558031i
$411$	26.0184	−	4.12090i	1.28339	−	0.203269i
$412$	−13.4883	−	26.4093i	−0.664523	−	1.30109i
$413$	−2.48227	+	0.806538i	−0.122144	+	0.0396872i
$414$	8.47941	−	13.8521i	0.416740	−	0.680796i
$415$	13.5984	−	9.87984i	0.667521	−	0.484982i
$416$	14.8783	+	13.9512i	0.729468	+	0.684015i
$417$	−39.0125			−1.91045
$418$	−25.7309	+	0.915996i	−1.25854	+	0.0448028i
$419$			17.2623i			0.843319i	0.906754	+	0.421660i	$0.138552\pi$
$419$			17.2623i			0.843319i	−0.906754	+	0.421660i	$0.861448\pi$
$420$	0.340731	−	2.16481i	0.0166260	−	0.105632i
$421$	−0.931670	+	5.88233i	−0.0454068	+	0.286687i	−0.999935	−	0.0114345i	$-0.996360\pi$
$421$	−0.931670	+	5.88233i	−0.0454068	+	0.286687i	0.954528	+	0.298122i	$0.0963602\pi$
$422$	−31.3149	−	19.1690i	−1.52439	−	0.933133i
$423$	−43.0256	−	21.9226i	−2.09198	−	1.06592i
$424$	0.447714	−	0.275252i	0.0217429	−	0.0133674i
$425$	1.41409	+	1.02739i	0.0685932	+	0.0498359i
$426$	10.5751	+	0.827144i	0.512366	+	0.0400752i
$427$	0.540152	+	1.06011i	0.0261398	+	0.0513022i
$428$	1.30581	+	8.19335i	0.0631186	+	0.396040i
$429$	−36.5096	−	3.37743i	−1.76270	−	0.163064i
$430$	4.55466	+	3.88625i	0.219645	+	0.187412i
$431$	5.94210	−	3.02765i	0.286221	−	0.145837i	−0.304986	−	0.952357i	$-0.598652\pi$
$431$	5.94210	−	3.02765i	0.286221	−	0.145837i	0.591207	+	0.806520i	$0.298652\pi$
$432$	−33.7939	−	24.4531i	−1.62591	−	1.17650i
$433$	4.63210	−	6.37554i	0.222605	−	0.306389i	−0.683078	−	0.730346i	$-0.739359\pi$
$433$	4.63210	−	6.37554i	0.222605	−	0.306389i	0.905683	+	0.423957i	$0.139359\pi$
$434$	−0.866367	+	0.359351i	−0.0415869	+	0.0172494i
$435$	−5.88843	+	11.5567i	−0.282329	+	0.554101i
$436$	−35.9282	+	11.7121i	−1.72065	+	0.560909i
$437$	9.72725	+	1.54064i	0.465317	+	0.0736990i
$438$	10.8915	−	6.68153i	0.520414	−	0.319256i
$439$	−8.64852			−0.412771			−0.206386	−	0.978471i	$-0.566170\pi$
$439$	−8.64852			−0.412771			−0.206386	+	0.978471i	$0.566170\pi$
$440$	−13.8504	−	12.8733i	−0.660294	−	0.613709i
$441$		−	44.6067i		−	2.12413i
$442$	−8.34203	+	4.57304i	−0.396790	+	0.217517i
$443$	−2.27428	−	3.13028i	−0.108054	−	0.148724i	0.751565	−	0.659659i	$-0.229299\pi$
$443$	−2.27428	−	3.13028i	−0.108054	−	0.148724i	−0.859619	+	0.510935i	$0.829299\pi$
$444$	59.2144	−	19.3031i	2.81019	−	0.916086i
$445$	9.93802	+	30.5861i	0.471107	+	1.44992i
$446$	−25.5977	−	10.5884i	−1.21209	−	0.501377i
$447$	1.74942	+	11.0454i	0.0827449	+	0.522431i
$448$	−0.442189	−	1.34762i	−0.0208914	−	0.0636693i
$449$	16.2371	−	8.27321i	0.766276	−	0.390437i	−0.0267368	−	0.999643i	$-0.508512\pi$
$449$	16.2371	−	8.27321i	0.766276	−	0.390437i	0.793012	+	0.609206i	$0.208512\pi$
$450$	−8.45452	+	0.669492i	−0.398550	+	0.0315601i
$451$	−5.41022	−	19.4939i	−0.254757	−	0.917930i
$452$	37.0560	−	5.90576i	1.74297	−	0.277784i
$453$	44.8406	−	22.8474i	2.10680	−	1.07347i
$454$	0.250591	−	3.20383i	0.0117608	−	0.150363i
$455$	1.28096	−	0.139237i	0.0600523	−	0.00652755i
$456$	11.0461	−	46.3058i	0.517283	−	2.16847i
$457$	−20.0533	−	10.2177i	−0.938054	−	0.477962i	−0.0830279	−	0.996547i	$-0.526459\pi$
$457$	−20.0533	−	10.2177i	−0.938054	−	0.477962i	−0.855026	+	0.518585i	$0.826459\pi$
$458$	−10.4168	+	2.50618i	−0.486746	+	0.117106i
$459$	15.7403	−	11.4360i	0.734694	−	0.533786i
$460$	4.25704	+	5.84743i	0.198485	+	0.272638i
$461$	−4.46792	+	4.46792i	−0.208092	+	0.208092i	−0.803456	−	0.595364i	$-0.797008\pi$
$461$	−4.46792	+	4.46792i	−0.208092	+	0.208092i	0.595364	+	0.803456i	$0.297008\pi$
$462$	2.11474	+	1.42433i	0.0983866	+	0.0662657i
$463$	−11.0562	+	11.0562i	−0.513824	+	0.513824i	−0.915696	−	0.401872i	$-0.868360\pi$
$463$	−11.0562	+	11.0562i	−0.513824	+	0.513824i	0.401872	+	0.915696i	$0.368360\pi$
$464$	0.0162068	+	8.39443i	0.000752384	+	0.389702i
$465$	−13.5898	−	18.7048i	−0.630214	−	0.867415i
$466$	0.788879	+	0.482902i	0.0365441	+	0.0223700i
$467$	10.2365	+	31.5046i	0.473687	+	1.45786i	0.847720	+	0.530443i	$0.177975\pi$
$467$	10.2365	+	31.5046i	0.473687	+	1.45786i	−0.374033	+	0.927415i	$0.622025\pi$
$468$	16.3471	−	43.1676i	0.755644	−	1.99542i
$469$	0.593284	+	0.431046i	0.0273953	+	0.0199039i
$470$	16.3457	−	13.9742i	0.753969	−	0.644580i
$471$	−24.3022	−	7.89625i	−1.11978	−	0.363840i
$472$	−35.5349	−	21.7051i	−1.63563	−	0.999058i
$473$	−6.33821	+	2.88998i	−0.291431	+	0.132881i
$474$	−2.22253	−	28.0667i	−0.102084	−	1.28915i
$475$	−2.33475	−	4.58221i	−0.107126	−	0.210246i
$476$	0.661539		0.000638605i	0.0303216		2.92704e-5i
$477$	−0.962255	−	0.699119i	−0.0440586	−	0.0320105i
$478$	35.6828	+	14.7601i	1.63209	+	0.675113i
$479$	−31.4496	−	16.0244i	−1.43697	−	0.732172i	−0.449992	−	0.893033i	$-0.648573\pi$
$479$	−31.4496	−	16.0244i	−1.43697	−	0.732172i	−0.986977	+	0.160861i	$0.948573\pi$
$480$	29.7658	−	18.3395i	1.35862	−	0.837078i
$481$	20.0532	+	30.6404i	0.914349	+	1.39708i
$482$	7.23210	+	11.7889i	0.329413	+	0.536971i
$483$	−0.689620	−	0.689620i	−0.0313788	−	0.0313788i
$484$	20.3869	−	8.26898i	0.926675	−	0.375863i
$485$		−	8.61824i		−	0.391334i
$486$	−2.59389	+	10.8273i	−0.117661	+	0.491138i
$487$	−9.69382	−	1.53535i	−0.439269	−	0.0695734i	−0.0671169	−	0.997745i	$-0.521380\pi$
$487$	−9.69382	−	1.53535i	−0.439269	−	0.0695734i	−0.372152	+	0.928172i	$0.621380\pi$
$488$	−7.23851	+	17.5471i	−0.327672	+	0.794321i
$489$	20.6150	−	40.4592i	0.932242	−	1.82963i
$490$	18.3566	+	7.59316i	0.829265	+	0.343024i
$491$	21.0528	+	15.2958i	0.950102	+	0.690289i	0.950831	−	0.309711i	$-0.100232\pi$
$491$	21.0528	+	15.2958i	0.950102	+	0.690289i	−0.000729363		1.00000i	$0.500232\pi$
$492$	37.4054	−	0.0361086i	1.68637	−	0.00162790i
$493$	−3.72375	−	1.20992i	−0.167709	−	0.0544921i
$494$	27.9774	−	0.845610i	1.25876	−	0.0380458i
$495$	−14.9790	+	40.0869i	−0.673255	+	1.80177i
$496$	−13.3457	−	6.76756i	−0.599241	−	0.303873i
$497$	0.134020	−	0.412472i	0.00601163	−	0.0185019i
$498$	−36.0480	−	2.81953i	−1.61535	−	0.126346i
$499$	1.73285	+	10.9408i	0.0775732	+	0.489778i	0.995634	+	0.0933391i	$0.0297541\pi$
$499$	1.73285	+	10.9408i	0.0775732	+	0.489778i	−0.918061	+	0.396439i	$0.870246\pi$
$500$	7.37408	−	22.7698i	0.329779	−	1.01830i
$501$	11.7000	−	22.9626i	0.522719	−	1.02589i
$502$	14.6948	−	24.0057i	0.655859	−	1.07143i
$503$	14.6631	+	20.1821i	0.653796	+	0.899874i	0.999256	−	0.0385599i	$-0.0122771\pi$
$503$	14.6631	+	20.1821i	0.653796	+	0.899874i	−0.345460	+	0.938434i	$0.612277\pi$
$504$	−2.43777	+	2.08816i	−0.108587	+	0.0930141i
$505$	−17.6666	−	17.6666i	−0.786153	−	0.786153i
$506$	−8.25947	+	1.61129i	−0.367178	+	0.0716304i
$507$	39.6699	+	3.88467i	1.76180	+	0.172524i
$508$	−0.234827	+	1.49196i	−0.0104188	+	0.0661950i
$509$	5.59208	−	35.3070i	0.247865	−	1.56496i	−0.478776	−	0.877937i	$-0.658919\pi$
$509$	5.59208	−	35.3070i	0.247865	−	1.56496i	0.726640	−	0.687018i	$-0.241081\pi$
$510$	3.81448	+	15.8548i	0.168908	+	0.702060i
$511$	−0.161439	−	0.496860i	−0.00714166	−	0.0219798i
$512$	11.7389	−	19.3442i	0.518790	−	0.854902i
$513$	−56.5394	+	8.95495i	−2.49627	+	0.395371i
$514$	8.55023	−	7.30973i	0.377135	−	0.322418i
$515$	−13.5687	−	26.6300i	−0.597908	−	1.17346i
$516$	−2.02711	−	12.7192i	−0.0892385	−	0.559931i
$517$	6.69099	+	24.1087i	0.294269	+	1.06030i
$518$	−0.201018	−	2.53851i	−0.00883221	−	0.111536i
$519$	−14.0231	+	43.1588i	−0.615547	+	1.89446i
$520$	14.9817	+	14.0754i	0.656990	+	0.617245i
$521$	−20.3861	−	14.8113i	−0.893129	−	0.648896i	0.0435629	−	0.999051i	$-0.486129\pi$
$521$	−20.3861	−	14.8113i	−0.893129	−	0.648896i	−0.936692	+	0.350154i	$0.886129\pi$
$522$	17.5482	−	7.27861i	0.768062	−	0.318576i
$523$	10.4024	−	3.37994i	0.454865	−	0.147794i	−0.0726188	−	0.997360i	$-0.523136\pi$
$523$	10.4024	−	3.37994i	0.454865	−	0.147794i	0.527484	+	0.849565i	$0.323136\pi$
$524$	−8.54313	+	16.8069i	−0.373209	+	0.734214i
$525$	−0.0796674	+	0.503000i	−0.00347697	+	0.0219527i
$526$	−2.89855	+	12.0990i	−0.126383	+	0.527543i
$527$	4.93518	−	4.93518i	0.214980	−	0.214980i
$528$	4.69063	+	40.4054i	0.204133	+	1.75842i
$529$	−19.7811			−0.860049
$530$	0.451502	−	0.276980i	0.0196120	−	0.0120313i
$531$	−14.7417	+	93.0755i	−0.639736	+	4.03913i
$532$	−1.73511	−	0.881972i	−0.0752264	−	0.0382383i
$533$	5.76767	+	21.2233i	0.249826	+	0.919284i
$534$	26.4439	−	63.9284i	1.14434	−	2.76645i
$535$	1.30810	+	8.25903i	0.0565542	+	0.357069i
$536$	0.934819	+	11.6621i	0.0403780	+	0.503725i
$537$	63.0983	+	20.5019i	2.72289	+	0.884722i
$538$	2.43535	+	30.7543i	0.104996	+	1.32591i
$539$	−17.0370	+	15.6176i	−0.733836	+	0.672700i
$540$	−34.0357	−	24.6782i	−1.46466	−	1.06198i
$541$	−22.6203	+	11.5256i	−0.972524	+	0.495526i	−0.866684	−	0.498857i	$-0.833753\pi$
$541$	−22.6203	+	11.5256i	−0.972524	+	0.495526i	−0.105840	+	0.994383i	$0.533753\pi$
$542$	−37.7859	−	2.95546i	−1.62304	−	0.126948i
$543$	10.4993	+	7.62822i	0.450570	+	0.327358i
$544$	6.87363	+	8.00877i	0.294705	+	0.343373i
$545$	−36.2220	+	11.7692i	−1.55158	+	0.504139i
$546$	−2.29062	−	1.56073i	−0.0980295	−	0.0667929i
$547$	−11.8687	−	16.3359i	−0.507469	−	0.698471i	0.476021	−	0.879434i	$-0.342079\pi$
$547$	−11.8687	−	16.3359i	−0.507469	−	0.698471i	−0.983490	+	0.180963i	$0.942079\pi$
$548$	13.8916	−	10.1134i	0.593421	−	0.432021i
$549$	42.9578			1.83339
$550$	3.21579	+	2.99471i	0.137122	+	0.127695i
$551$	8.14583	+	8.14583i	0.347024	+	0.347024i
$552$	1.19830	−	15.5130i	0.0510029	−	0.660275i
$553$	−1.13696	−	0.180077i	−0.0483486	−	0.00765767i
$554$	−5.61473	−	3.43698i	−0.238547	−	0.146023i
$555$	59.6986	−	19.3973i	2.53407	−	0.823368i
$556$	−22.6627	+	11.5748i	−0.961111	+	0.490880i
$557$	6.30678	+	39.8195i	0.267227	+	1.68720i	0.647290	+	0.762244i	$0.275902\pi$
$557$	6.30678	+	39.8195i	0.267227	+	1.68720i	−0.380063	+	0.924961i	$0.624098\pi$
$558$	−2.64069	+	33.7615i	−0.111789	+	1.42924i
$559$	6.90713	−	3.10470i	0.292140	−	0.131315i
$560$	−0.444353	−	1.35865i	−0.0187774	−	0.0574134i
$561$	−18.5925	−	3.77892i	−0.784978	−	0.159546i
$562$	8.61918	−	10.1016i	0.363578	−	0.426112i
$563$	−5.60507	+	17.2506i	−0.236226	+	0.727028i	0.760731	+	0.649067i	$0.224841\pi$
$563$	−5.60507	+	17.2506i	−0.236226	+	0.727028i	−0.996956	+	0.0779603i	$0.975159\pi$
$564$	−46.2604	+	0.0446567i	−1.94792	+	0.00188039i
$565$	37.3530	−	5.91613i	1.57145	−	0.248894i
$566$	−14.7514	+	6.11857i	−0.620048	+	0.257183i
$567$	2.01739	+	1.02791i	0.0847224	+	0.0431682i
$568$	6.38857	−	2.65708i	0.268059	−	0.111489i
$569$	−8.70484	−	11.9812i	−0.364926	−	0.502278i	0.586587	−	0.809886i	$-0.300471\pi$
$569$	−8.70484	−	11.9812i	−0.364926	−	0.502278i	−0.951513	+	0.307609i	$0.900471\pi$
$570$	11.1780	−	46.6591i	0.468196	−	1.95433i
$571$	−3.76332			−0.157490			−0.0787450	−	0.996895i	$-0.525091\pi$
$571$	−3.76332			−0.157490			−0.0787450	+	0.996895i	$0.525091\pi$
$572$	−22.2108	+	8.87021i	−0.928680	+	0.370882i
$573$	−25.1622			−1.05116
$574$	0.356307	−	1.48729i	0.0148720	−	0.0620781i
$575$	−0.987974	−	1.35983i	−0.0412014	−	0.0567088i
$576$	−50.6015	−	7.86434i	−2.10840	−	0.327681i
$577$	19.4061	+	9.88788i	0.807885	+	0.411638i	0.808598	−	0.588362i	$-0.200227\pi$
$577$	19.4061	+	9.88788i	0.807885	+	0.411638i	−0.000713009		1.00000i	$0.500227\pi$
$578$	17.6601	−	7.32504i	0.734563	−	0.304681i
$579$	−55.8905	+	8.85218i	−2.32273	+	0.367884i
$580$	0.00816713	+	8.46043i	0.000339122	+	0.351300i
$581$	−0.456842	+	1.40601i	−0.0189530	+	0.0583313i
$582$	−12.0335	+	14.1032i	−0.498804	+	0.584596i
$583$	0.0698833	+	0.612297i	0.00289427	+	0.0253588i
$584$	4.34457	−	7.11279i	0.179779	−	0.294329i
$585$	16.5176	−	43.4910i	0.682918	−	1.79813i
$586$	0.452163	−	5.78095i	0.0186787	−	0.238809i
$587$	−2.31103	−	14.5913i	−0.0953865	−	0.602247i	−0.988359	−	0.152136i	$-0.951385\pi$
$587$	−2.31103	−	14.5913i	−0.0953865	−	0.602247i	0.892973	−	0.450110i	$-0.148615\pi$
$588$	−19.4371	−	38.0566i	−0.801574	−	1.56943i
$589$	−19.5299	+	6.34565i	−0.804715	+	0.261468i
$590$	−35.7931	−	21.9103i	−1.47358	−	0.902032i
$591$	81.5626	+	12.9182i	3.35504	+	0.531386i
$592$	28.6710	−	28.7819i	1.17837	−	1.18293i
$593$	−18.9874	−	18.9874i	−0.779720	−	0.779720i	0.200063	−	0.979783i	$-0.435885\pi$
$593$	−18.9874	−	18.9874i	−0.779720	−	0.779720i	−0.979783	+	0.200063i	$0.935885\pi$
$594$	42.7641	−	23.7424i	1.75463	−	0.974164i
$595$	0.666740			0.0273337
$596$	4.29337	+	5.89733i	0.175863	+	0.241564i
$597$	28.0868	+	38.6582i	1.14952	+	1.58217i
$598$	8.98827	−	1.70342i	0.367558	−	0.0696582i
$599$	−38.9593	+	12.6586i	−1.59183	+	0.517218i	−0.965070	−	0.261992i	$-0.915621\pi$
$599$	−38.9593	+	12.6586i	−1.59183	+	0.517218i	−0.626763	+	0.779210i	$0.715621\pi$
$600$	−6.92134	+	4.25520i	−0.282562	+	0.173718i
$601$	23.8147	+	17.3024i	0.971420	+	0.705778i	0.955775	−	0.294100i	$-0.0950197\pi$
$601$	23.8147	+	17.3024i	0.971420	+	0.705778i	0.0156453	+	0.999878i	$0.495020\pi$
$602$	−0.525001	−	0.0410635i	−0.0213974	−	0.00167362i
$603$	23.5917	−	12.0206i	0.960728	−	0.489515i
$604$	19.2696	−	26.5762i	0.784067	−	1.08137i
$605$	20.5552	−	8.31414i	0.835686	−	0.338018i
$606$	4.24268	+	53.5777i	0.172347	+	2.17645i
$607$	27.9032	+	9.06631i	1.13256	+	0.367990i	0.814547	−	0.580097i	$-0.196985\pi$
$607$	27.9032	+	9.06631i	1.13256	+	0.367990i	0.318010	+	0.948087i	$0.396985\pi$
$608$	−7.32186	−	30.1767i	−0.296941	−	1.22383i
$609$	−0.178459	−	1.12674i	−0.00723151	−	0.0456580i
$610$	−7.31248	+	17.6780i	−0.296074	+	0.715762i
$611$	−7.13306	−	26.2476i	−0.288573	−	1.06186i
$612$	10.8231	−	21.2923i	0.437498	−	0.860691i
$613$	−2.23090	+	14.0854i	−0.0901052	+	0.568902i	0.900789	+	0.434258i	$0.142989\pi$
$613$	−2.23090	+	14.0854i	−0.0901052	+	0.568902i	−0.990894	+	0.134644i	$0.957011\pi$
$614$	25.4205	−	15.5946i	1.02589	−	0.629345i
$615$	37.6995			1.52019
$616$	1.65106	+	0.199972i	0.0665230	+	0.00805709i
$617$	−22.3320	+	22.3320i	−0.899053	+	0.899053i	−0.995352	−	0.0962997i	$-0.969299\pi$
$617$	−22.3320	+	22.3320i	−0.899053	+	0.899053i	0.0962997	+	0.995352i	$0.469299\pi$
$618$	−14.9788	+	62.5240i	−0.602534	+	2.51508i
$619$	−4.53786	+	28.6509i	−0.182392	+	1.15158i	0.711297	+	0.702892i	$0.248108\pi$
$619$	−4.53786	+	28.6509i	−0.182392	+	1.15158i	−0.893689	+	0.448687i	$0.851892\pi$
$620$	−13.4441	−	6.83375i	−0.539926	−	0.274450i
$621$	−17.7939	+	5.78158i	−0.714043	+	0.232007i
$622$	6.13905	−	2.54635i	0.246154	−	0.102099i
$623$	−2.28838	−	1.66260i	−0.0916819	−	0.0666108i
$624$	−4.86337	−	43.9520i	−0.194691	−	1.75949i
$625$	6.00667	−	18.4866i	0.240267	−	0.739465i
$626$	0.729133	+	9.20769i	0.0291420	+	0.368013i
$627$	43.6935	+	34.7414i	1.74495	+	1.38744i
$628$	−16.4601	+	2.62331i	−0.656829	+	0.104682i
$629$	8.60254	+	16.8834i	0.343006	+	0.673187i
$630$	−2.45896	+	2.10221i	−0.0979674	+	0.0837539i
$631$	14.0466	−	2.22476i	0.559185	−	0.0885661i	0.129556	−	0.991572i	$-0.458645\pi$
$631$	14.0466	−	2.22476i	0.559185	−	0.0885661i	0.429628	+	0.903006i	$0.358645\pi$
$632$	−9.61830	−	15.6447i	−0.382595	−	0.622314i
$633$	24.5988	+	75.7074i	0.977715	+	3.00910i
$634$	5.98109	+	24.8602i	0.237539	+	0.987323i
$635$	−0.238125	+	1.50346i	−0.00944968	+	0.0596630i
$636$	−1.12560	−	0.177163i	−0.0446327	−	0.00702497i
$637$	18.6121	−	16.8785i	0.737437	−	0.668750i
$638$	−8.92393	−	4.15394i	−0.353302	−	0.164456i
$639$	−11.0725	−	11.0725i	−0.438021	−	0.438021i
$640$	11.8500	−	19.4849i	0.468411	−	0.770207i
$641$	−10.4698	−	14.4105i	−0.413534	−	0.569181i	0.550542	−	0.834808i	$-0.314421\pi$
$641$	−10.4698	−	14.4105i	−0.413534	−	0.569181i	−0.964076	+	0.265627i	$0.914421\pi$
$642$	9.39130	−	15.3418i	0.370645	−	0.605494i
$643$	−17.8326	+	34.9984i	−0.703249	+	1.38020i	0.211982	+	0.977274i	$0.432008\pi$
$643$	−17.8326	+	34.9984i	−0.703249	+	1.38020i	−0.915231	+	0.402930i	$0.867992\pi$
$644$	−0.605212	−	0.195999i	−0.0238487	−	0.00772346i
$645$	−2.03067	−	12.8211i	−0.0799575	−	0.504832i
$646$	14.4395	+	1.12940i	0.568114	+	0.0444356i
$647$	−6.34343	+	19.5231i	−0.249386	+	0.767531i	0.745498	+	0.666508i	$0.232212\pi$
$647$	−6.34343	+	19.5231i	−0.249386	+	0.767531i	−0.994884	+	0.101023i	$0.967788\pi$
$648$	8.48334	+	35.1116i	0.333257	+	1.37931i
$649$	40.7105	−	26.9571i	1.59803	−	1.05816i
$650$	−3.47841	−	3.27431i	−0.136434	−	0.128429i
$651$	1.93399	+	0.628392i	0.0757991	+	0.0246286i
$652$	−0.0285925	−	29.6194i	−0.00111977	−	1.15998i
$653$	−17.2509	−	12.5335i	−0.675080	−	0.490475i	0.196642	−	0.980475i	$-0.436996\pi$
$653$	−17.2509	−	12.5335i	−0.675080	−	0.490475i	−0.871722	+	0.490001i	$0.836996\pi$
$654$	75.7081	+	31.3165i	2.96042	+	1.22457i
$655$	−8.62664	+	16.9307i	−0.337071	+	0.661539i
$656$	21.7184	−	11.1189i	0.847960	−	0.434121i
$657$	−18.6303	−	2.95075i	−0.726838	−	0.115120i
$658$	−0.440656	+	1.83937i	−0.0171785	+	0.0717063i
$659$		−	47.6969i		−	1.85801i	−0.370070	−	0.929004i	$-0.620666\pi$
$659$		−	47.6969i		−	1.85801i	0.370070	−	0.929004i	$-0.379334\pi$
$660$	4.68819	+	40.7276i	0.182488	+	1.58532i
$661$	−8.84025	−	8.84025i	−0.343846	−	0.343846i	0.513965	−	0.857811i	$-0.328176\pi$
$661$	−8.84025	−	8.84025i	−0.343846	−	0.343846i	−0.857811	+	0.513965i	$0.828176\pi$
$662$	23.1736	+	37.7749i	0.900667	+	1.46816i
$663$	20.1899	+	4.21657i	0.784110	+	0.163758i
$664$	−21.7771	+	9.05733i	−0.845115	+	0.351492i
$665$	−1.74789	−	0.890593i	−0.0677802	−	0.0345357i
$666$	−84.9592	−	35.1432i	−3.29210	−	1.36177i
$667$	3.04608	+	2.21311i	0.117945	+	0.0856918i
$668$	−0.0162277	−	16.8105i	−0.000627868	−	0.650417i
$669$	27.2659	+	53.5124i	1.05416	+	2.06891i
$670$	0.930821	+	11.7547i	0.0359608	+	0.454122i
$671$	−15.0403	−	16.4072i	−0.580626	−	0.633394i
$672$	−1.16990	+	2.84378i	−0.0451299	+	0.109701i
$673$	38.4564	+	12.4952i	1.48238	+	0.481656i	0.934824	−	0.355110i	$-0.115557\pi$
$673$	38.4564	+	12.4952i	1.48238	+	0.481656i	0.547560	+	0.836766i	$0.315557\pi$
$674$	35.7697	−	30.5801i	1.37780	−	1.17790i
$675$	7.90397	+	5.74257i	0.304224	+	0.221032i
$676$	24.1971	−	9.51318i	0.930658	−	0.365891i
$677$	4.53333	+	13.9521i	0.174230	+	0.536224i	0.999597	−	0.0283714i	$-0.00903210\pi$
$677$	4.53333	+	13.9521i	0.174230	+	0.536224i	−0.825368	+	0.564596i	$0.809032\pi$
$678$	−69.3863	−	42.4739i	−2.66477	−	1.63120i
$679$	0.445543	+	0.613238i	0.0170984	+	0.0235339i
$680$	6.91987	+	8.07841i	0.265365	+	0.309793i
$681$	−4.92668	+	4.92668i	−0.188791	+	0.188791i
$682$	13.8194	−	10.8120i	0.529171	−	0.414012i
$683$	−8.27841	+	8.27841i	−0.316764	+	0.316764i	−0.847523	−	0.530759i	$-0.821907\pi$
$683$	−8.27841	+	8.27841i	−0.316764	+	0.316764i	0.530759	+	0.847523i	$0.321907\pi$
$684$	−56.8143	+	41.3618i	−2.17235	+	1.58151i
$685$	14.0107	−	10.1793i	0.535320	−	0.388933i
$686$	−3.40511	+	0.819233i	−0.130008	+	0.0312785i
$687$	20.6971	+	10.5457i	0.789644	+	0.402344i
$688$	−4.95127	−	6.78724i	−0.188765	−	0.258761i
$689$	−0.0723966	−	0.666035i	−0.00275809	−	0.0253739i
$690$	1.22281	−	15.6337i	0.0465516	−	0.595166i
$691$	−10.8932	+	5.55035i	−0.414396	+	0.211145i	−0.648743	−	0.761008i	$-0.724705\pi$
$691$	−10.8932	+	5.55035i	−0.414396	+	0.211145i	0.234347	+	0.972153i	$0.424705\pi$
$692$	4.65880	+	29.2318i	0.177101	+	1.11123i
$693$	−1.00656	−	3.62679i	−0.0382361	−	0.137771i
$694$	19.2184	−	1.52185i	0.729519	−	0.0577687i
$695$	−22.8521	+	11.6437i	−0.866828	+	0.441671i
$696$	11.7998	−	13.8563i	0.447270	−	0.525223i
$697$	1.78029	+	11.2403i	0.0674331	+	0.425756i
$698$	2.84134	+	1.17531i	0.107546	+	0.0444863i
$699$	−0.619689	−	1.90721i	−0.0234388	−	0.0721371i
$700$	0.102958	+	0.315834i	0.00389144	+	0.0119374i
$701$	−20.8453	−	28.6911i	−0.787315	−	1.08365i	−0.994437	−	0.105331i	$-0.966410\pi$
$701$	−20.8453	−	28.6911i	−0.787315	−	1.08365i	0.207122	−	0.978315i	$-0.433590\pi$
$702$	−46.6274	+	25.5608i	−1.75984	+	0.964730i
$703$		−	55.7514i		−	2.10270i
$704$	14.7129	+	22.0801i	0.554512	+	0.832176i
$705$	−46.6241			−1.75597
$706$	15.5482	−	9.53826i	0.585163	−	0.358977i
$707$	2.17040	+	0.343758i	0.0816263	+	0.0129283i
$708$	27.9801	+	85.8320i	1.05156	+	3.22576i
$709$	−10.7034	+	21.0067i	−0.401976	+	0.788922i	−0.999920	−	0.0126155i	$-0.995984\pi$
$709$	−10.7034	+	21.0067i	−0.401976	+	0.788922i	0.597945	+	0.801537i	$0.295984\pi$
$710$	6.44138	−	2.67175i	0.241741	−	0.100269i
$711$	−24.4297	+	33.6246i	−0.916186	+	1.26102i
$712$	−3.60572	−	44.9822i	−0.135130	−	1.68578i
$713$	−5.98009	+	3.04701i	−0.223956	+	0.114111i
$714$	−1.09108	−	0.930957i	−0.0408325	−	0.0348402i
$715$	−22.3940	+	8.91833i	−0.837489	+	0.333527i
$716$	42.7371	−	6.81119i	1.59716	−	0.254546i
$717$	−38.0083	−	74.5955i	−1.41945	−	2.78582i
$718$	2.83169	+	0.221484i	0.105678	+	0.00826571i
$719$	−12.0025	−	8.72030i	−0.447616	−	0.325212i	0.341038	−	0.940050i	$-0.389222\pi$
$719$	−12.0025	−	8.72030i	−0.447616	−	0.325212i	−0.788654	+	0.614837i	$0.789222\pi$
$720$	−50.9916	−	7.97540i	−1.90035	−	0.297225i
$721$	2.34220	+	1.19341i	0.0872281	+	0.0444450i
$722$	−13.4279	−	8.21969i	−0.499733	−	0.305905i
$723$	4.69078	−	29.6164i	0.174452	−	1.10145i
$724$	8.36239	+	1.31620i	0.310786	+	0.0489162i
$725$		−	1.96611i		−	0.0730194i
$726$	−45.2461	−	15.0952i	−1.67924	−	0.560237i
$727$	−28.0451			−1.04013			−0.520067	−	0.854125i	$-0.674093\pi$
$727$	−28.0451			−1.04013			−0.520067	+	0.854125i	$0.674093\pi$
$728$	−1.79370	−	0.227025i	−0.0664788	−	0.00841410i
$729$	−11.4672	+	8.33144i	−0.424713	+	0.308572i
$730$	4.38564	−	7.16447i	0.162320	−	0.265169i
$731$	3.72679	−	1.21091i	0.137840	−	0.0447870i
$732$	36.6499	−	18.7186i	1.35462	−	0.691861i
$733$	−49.4099	+	7.82576i	−1.82500	+	0.289051i	−0.972365	−	0.233464i	$-0.924994\pi$
$733$	−49.4099	+	7.82576i	−1.82500	+	0.289051i	−0.852630	+	0.522515i	$0.824994\pi$
$734$	6.12945	−	5.24017i	0.226242	−	0.193418i
$735$	−19.5529	−	38.3747i	−0.721219	−	1.41547i
$736$	−3.90650	−	9.36713i	−0.143996	−	0.345277i
$737$	−12.8510	−	4.80194i	−0.473373	−	0.176882i
$738$	−42.0059	−	35.8414i	−1.54626	−	1.31934i
$739$	−8.22711	−	16.1466i	−0.302639	−	0.593963i	0.688737	−	0.725012i	$-0.258166\pi$
$739$	−8.22711	−	16.1466i	−0.302639	−	0.593963i	−0.991376	+	0.131049i	$0.958166\pi$
$740$	28.9243	−	28.9802i	1.06328	−	1.06533i
$741$	−47.2964	−	38.0224i	−1.73747	−	1.39679i
$742$	−0.0178077	+	0.0430503i	−0.000653741	+	0.00158043i
$743$	−17.6179	+	34.5771i	−0.646339	+	1.26851i	0.302620	+	0.953111i	$0.402139\pi$
$743$	−17.6179	+	34.5771i	−0.646339	+	1.26851i	−0.948959	+	0.315400i	$0.897861\pi$
$744$	12.4585	+	29.9547i	0.456750	+	1.09819i
$745$	4.32138	+	5.94787i	0.158323	+	0.217913i
$746$	10.1956	+	2.44254i	0.373288	+	0.0894279i
$747$	37.7434	+	37.7434i	1.38096	+	1.38096i
$748$	−11.9217	+	3.32109i	−0.435902	+	0.121431i
$749$	−0.520052	−	0.520052i	−0.0190023	−	0.0190023i
$750$	−44.2313	+	27.1344i	−1.61510	+	0.990807i
$751$	2.90512	−	2.11069i	0.106009	−	0.0770203i	−0.533518	−	0.845789i	$-0.679130\pi$
$751$	2.90512	−	2.11069i	0.106009	−	0.0770203i	0.639527	+	0.768769i	$0.279130\pi$
$752$	−26.8598	+	13.7511i	−0.979476	+	0.501452i
$753$	−58.0364	+	18.8572i	−2.11497	+	0.687194i
$754$	9.67695	+	4.56782i	0.352414	+	0.166350i
$755$	19.4469	−	26.7664i	0.707745	−	0.974128i
$756$	3.69765	−	0.00356946i	0.134482	−	0.000129820i
$757$	−2.28463	+	7.03137i	−0.0830363	+	0.255559i	−0.983952	−	0.178436i	$-0.942896\pi$
$757$	−2.28463	+	7.03137i	−0.0830363	+	0.255559i	0.900915	+	0.433995i	$0.142896\pi$
$758$	−13.6918	+	16.0467i	−0.497308	+	0.582843i
$759$	15.8812	+	8.98105i	0.576450	+	0.325991i
$760$	−7.35006	−	30.4211i	−0.266615	−	1.10349i
$761$	6.90954	−	3.52059i	0.250471	−	0.127621i	−0.324248	−	0.945972i	$-0.605111\pi$
$761$	6.90954	−	3.52059i	0.250471	−	0.127621i	0.574719	+	0.818351i	$0.305111\pi$
$762$	2.48893	−	2.12782i	0.0901643	−	0.0770829i
$763$	1.96896	−	2.71004i	0.0712812	−	0.0981102i
$764$	−14.6169	+	7.46546i	−0.528820	+	0.270091i
$765$	10.9289	−	21.4492i	0.395135	−	0.775497i
$766$	24.9630	−	6.00584i	0.901951	−	0.217000i
$767$	−44.4136	+	29.0674i	−1.60368	+	1.04956i
$768$	−46.5981	+	15.3398i	−1.68146	+	0.553527i
$769$	7.13839	−	7.13839i	0.257417	−	0.257417i	−0.566586	−	0.824003i	$-0.691736\pi$
$769$	7.13839	−	7.13839i	0.257417	−	0.257417i	0.824003	+	0.566586i	$0.191736\pi$
$770$	1.66384	+	0.203150i	0.0599607	+	0.00732102i
$771$	−24.3886			−0.878333
$772$	−29.8408	+	21.7247i	−1.07399	+	0.781888i
$773$	−4.62192	+	29.1816i	−0.166239	+	1.04959i	0.753611	+	0.657320i	$0.228310\pi$
$773$	−4.62192	+	29.1816i	−0.166239	+	1.04959i	−0.919850	+	0.392270i	$0.871690\pi$
$774$	−9.92659	+	16.2163i	−0.356804	+	0.582882i
$775$	3.12271	+	1.59110i	0.112171	+	0.0571540i
$776$	−2.80602	+	11.7629i	−0.100730	+	0.422264i
$777$	−3.24511	+	4.46651i	−0.116418	+	0.160235i
$778$	23.2934	−	19.9139i	0.835109	−	0.713948i
$779$	10.3470	−	31.8449i	0.370720	−	1.14096i
$780$	−4.85884	−	44.3023i	−0.173974	−	1.58628i
$781$	−0.352321	+	8.10571i	−0.0126070	+	0.290045i
$782$	4.71902	−	0.373687i	0.168752	−	0.0133630i
$783$	−20.8138	−	6.76280i	−0.743823	−	0.241683i
$784$	−22.5824	−	16.3405i	−0.806513	−	0.583590i
$785$	−16.5920	+	2.62792i	−0.592195	+	0.0937945i
$786$	37.7570	−	15.6608i	1.34675	−	0.558603i
$787$	1.20435	+	0.613645i	0.0429303	+	0.0218741i	0.475324	−	0.879811i	$-0.342331\pi$
$787$	1.20435	+	0.613645i	0.0429303	+	0.0218741i	−0.432394	+	0.901685i	$0.642331\pi$
$788$	51.2131	−	16.6948i	1.82439	−	0.594728i
$789$	21.8224	−	15.8549i	0.776896	−	0.564448i
$790$	−9.67868	−	15.7771i	−0.344352	−	0.561323i
$791$	−2.35203	+	2.35203i	−0.0836286	+	0.0836286i
$792$	33.4965	−	49.8370i	1.19025	−	1.77088i
$793$	16.2546	+	17.9241i	0.577217	+	0.636502i
$794$	15.1440	+	24.6859i	0.537439	+	0.876071i
$795$	−1.13427	−	0.179651i	−0.0402284	−	0.00637156i
$796$	27.7855	+	14.1236i	0.984830	+	0.500599i
$797$	−2.95829	+	0.961207i	−0.104788	+	0.0340477i	−0.360942	−	0.932588i	$-0.617545\pi$
$797$	−2.95829	+	0.961207i	−0.104788	+	0.0340477i	0.256154	+	0.966636i	$0.417545\pi$
$798$	1.61678	+	3.89794i	0.0572335	+	0.137986i
$799$	−2.20174	−	13.9012i	−0.0778918	−	0.491789i
$800$	−2.75817	+	4.52540i	−0.0975159	+	0.159997i
$801$	−90.9963	+	46.3649i	−3.21520	+	1.63822i
$802$	−12.8971	+	15.1153i	−0.455411	+	0.533740i
$803$	5.39582	+	8.14875i	0.190415	+	0.287563i
$804$	14.8896	−	20.5354i	0.525115	−	0.724228i
$805$	−0.609778	−	0.198129i	−0.0214919	−	0.00698313i
$806$	−15.0861	+	11.6730i	−0.531386	+	0.411165i
$807$	39.3149	−	54.1123i	1.38395	−	1.90484i
$808$	18.3608	+	29.8649i	0.645930	+	1.05064i
$809$	−10.0679	−	30.9857i	−0.353968	−	1.08940i	−0.956606	−	0.291386i	$-0.905884\pi$
$809$	−10.0679	−	30.9857i	−0.353968	−	1.08940i	0.602638	−	0.798015i	$-0.294116\pi$
$810$	8.51587	+	35.3959i	0.299217	+	1.24368i
$811$	38.7800	+	6.14214i	1.36175	+	0.215680i	0.794198	−	0.607659i	$-0.207891\pi$
$811$	38.7800	+	6.14214i	1.36175	+	0.215680i	0.567550	+	0.823339i	$0.307891\pi$
$812$	−0.437966	−	0.601586i	−0.0153696	−	0.0211115i
$813$	58.1050	+	58.1050i	2.03783	+	2.03783i
$814$	16.3233	+	44.7535i	0.572131	+	1.56861i
$815$		−	29.8523i		−	1.04568i
$816$	−0.0441773	−	22.8819i	−0.00154651	−	0.801026i
$817$	−11.3874	−	1.80359i	−0.398395	−	0.0630995i
$818$	5.88684	+	24.4684i	0.205829	+	0.855519i
$819$	1.07306	+	3.94856i	0.0374959	+	0.137974i
$820$	21.8999	−	11.1852i	0.764778	−	0.390604i
$821$	35.8298	−	5.67489i	1.25047	−	0.198055i	0.504135	−	0.863625i	$-0.331811\pi$
$821$	35.8298	−	5.67489i	1.25047	−	0.198055i	0.746335	+	0.665570i	$0.231811\pi$
$822$	−37.1408	−	2.90500i	−1.29543	−	0.101324i
$823$	0.402427	−	1.23854i	0.0140277	−	0.0431729i	−0.943798	−	0.330524i	$-0.892775\pi$
$823$	0.402427	−	1.23854i	0.0140277	−	0.0431729i	0.957825	+	0.287351i	$0.0927746\pi$
$824$	9.84921	+	40.7648i	0.343113	+	1.42011i
$825$	−1.08034	−	9.46567i	−0.0376128	−	0.329552i
$826$	3.67960	−	0.291378i	0.128030	−	0.0101383i
$827$	−18.4827	−	36.2743i	−0.642706	−	1.26138i	−0.950735	−	0.310005i	$-0.899669\pi$
$827$	−18.4827	−	36.2743i	−0.642706	−	1.26138i	0.308029	−	0.951377i	$-0.400331\pi$
$828$	−16.2257	+	16.2570i	−0.563882	+	0.564971i
$829$	−16.4772	+	22.6789i	−0.572276	+	0.787670i	−0.992822	−	0.119601i	$-0.961838\pi$
$829$	−16.4772	+	22.6789i	−0.572276	+	0.787670i	0.420546	+	0.907271i	$0.361838\pi$
$830$	−21.9571	+	9.10734i	−0.762141	+	0.316120i
$831$	4.41054	+	13.5742i	0.153000	+	0.470885i
$832$	−15.8655	−	24.0891i	−0.550036	−	0.835141i
$833$	10.5183	−	7.64196i	0.364436	−	0.264778i
$834$	53.6538	+	12.8538i	1.85788	+	0.445089i
$835$		−	16.9426i		−	0.586324i
$836$	35.6894	+	7.21799i	1.23435	+	0.249639i
$837$	27.5850	−	27.5850i	0.953476	−	0.953476i
$838$	5.68755	−	23.7408i	0.196473	−	0.820113i
$839$	6.12795	−	38.6904i	0.211560	−	1.33574i	−0.621872	−	0.783119i	$-0.713628\pi$
$839$	6.12795	−	38.6904i	0.211560	−	1.33574i	0.833433	−	0.552621i	$-0.186372\pi$
$840$	−1.18186	+	2.86500i	−0.0407782	+	0.0988518i
$841$	−7.60053	−	23.3920i	−0.262087	−	0.806622i
$842$	3.21942	−	7.78300i	0.110949	−	0.268220i
$843$	−28.4356	+	4.50375i	−0.979373	+	0.155117i
$844$	36.7516	+	36.6807i	1.26504	+	1.26260i
$845$	24.3966	−	9.56442i	0.839267	−	0.329026i
$846$	51.9500	+	44.3262i	1.78608	+	1.52396i
$847$	−1.03280	+	1.65425i	−0.0354873	+	0.0568408i
$848$	−0.706430	+	0.231042i	−0.0242589	+	0.00793401i
$849$	32.9296	+	10.6995i	1.13014	+	0.367205i
$850$	−1.60629	−	1.87888i	−0.0550951	−	0.0644451i
$851$	−2.85050	−	17.9974i	−0.0977139	−	0.616941i
$852$	−14.2714	−	4.62183i	−0.488930	−	0.158341i
$853$	5.26836	−	10.3397i	0.180385	−	0.354026i	−0.783054	−	0.621954i	$-0.786339\pi$
$853$	5.26836	−	10.3397i	0.180385	−	0.354026i	0.963439	+	0.267928i	$0.0863390\pi$
$854$	−0.393588	−	1.63593i	−0.0134683	−	0.0559804i
$855$	−57.3011	+	41.6317i	−1.95966	+	1.42377i
$856$	0.903652	−	11.6985i	0.0308862	−	0.399848i
$857$		−	6.63707i		−	0.226718i	−0.993554	−	0.113359i	$-0.963839\pi$
$857$		−	6.63707i		−	0.226718i	0.993554	−	0.113359i	$-0.0361610\pi$
$858$	49.0988	+	16.6741i	1.67621	+	0.569244i
$859$			4.63070i			0.157998i	0.996875	+	0.0789988i	$0.0251723\pi$
$859$			4.63070i			0.157998i	−0.996875	+	0.0789988i	$0.974828\pi$
$860$	−4.98359	−	6.84541i	−0.169939	−	0.233427i
$861$	−2.68253	+	1.94898i	−0.0914205	+	0.0664209i
$862$	−9.16970	+	2.20613i	−0.312321	+	0.0751412i
$863$	17.8164	−	34.9667i	0.606478	−	1.19028i	−0.359860	−	0.933006i	$-0.617176\pi$
$863$	17.8164	−	34.9667i	0.606478	−	1.19028i	0.966338	−	0.257274i	$-0.0828244\pi$
$864$	38.4199	+	44.7647i	1.30707	+	1.52293i
$865$	4.66698	+	29.4662i	0.158682	+	1.00188i
$866$	−8.47112	+	7.24209i	−0.287860	+	0.246096i
$867$	−39.4226	−	12.8092i	−1.33886	−	0.435023i
$868$	1.30991	−	0.208766i	0.0444613	−	0.00708598i
$869$	21.3958	−	2.44197i	0.725804	−	0.0828382i
$870$	11.9060	−	13.9538i	0.403652	−	0.473078i
$871$	13.9423	+	5.29519i	0.472417	+	0.179421i
$872$	53.2708	−	4.27013i	1.80398	−	0.144605i
$873$	27.0311	−	4.28131i	0.914865	−	0.144900i
$874$	−12.8703	−	5.32376i	−0.435343	−	0.180079i
$875$	0.655622	+	2.01780i	0.0221641	+	0.0682140i
$876$	−17.1804	+	5.60060i	−0.580473	+	0.189227i
$877$	−5.84247	+	36.8879i	−0.197286	+	1.24562i	0.667933	+	0.744221i	$0.267179\pi$
$877$	−5.84247	+	36.8879i	−0.197286	+	1.24562i	−0.865219	+	0.501394i	$0.832821\pi$
$878$	11.8943	+	2.84949i	0.401413	+	0.0961658i
$879$	−8.88963	+	8.88963i	−0.299840	+	0.299840i
$880$	14.8070	+	22.2680i	0.499145	+	0.750654i
$881$			19.6329i			0.661448i	0.943728	+	0.330724i	$0.107293\pi$
$881$			19.6329i			0.661448i	−0.943728	+	0.330724i	$0.892707\pi$
$882$	−14.6969	+	61.3475i	−0.494871	+	2.06568i
$883$	−11.7220	+	8.51652i	−0.394476	+	0.286604i	−0.767287	−	0.641304i	$-0.778394\pi$
$883$	−11.7220	+	8.51652i	−0.394476	+	0.286604i	0.372811	+	0.927907i	$0.378394\pi$
$884$	12.9795	−	3.54078i	0.436547	−	0.119089i
$885$	28.1166	+	86.5339i	0.945128	+	2.90881i
$886$	2.09646	+	5.05439i	0.0704318	+	0.169806i
$887$	27.5725	−	37.9502i	0.925792	−	1.27424i	−0.0356859	−	0.999363i	$-0.511362\pi$
$887$	27.5725	−	37.9502i	0.925792	−	1.27424i	0.961478	−	0.274881i	$-0.0886384\pi$
$888$	−87.7973	+	7.03773i	−2.94629	+	0.236171i
$889$	−0.0607814	−	0.119290i	−0.00203854	−	0.00400087i
$890$	−3.59030	−	45.3393i	−0.120347	−	1.51978i
$891$	−41.5080	−	8.43648i	−1.39057	−	0.282633i
$892$	31.7158	+	22.9961i	1.06192	+	0.769967i
$893$	−12.7965	+	39.3835i	−0.428218	+	1.31792i
$894$	1.23324	−	15.7672i	0.0412459	−	0.527333i
$895$	43.0797	−	6.82315i	1.44000	−	0.228073i
$896$	0.164129	+	1.99908i	0.00548315	+	0.0667845i
$897$	−17.2120	−	9.85597i	−0.574692	−	0.329081i
$898$	−25.0567	+	6.02837i	−0.836152	+	0.201169i
$899$	−7.75402	−	1.22812i	−0.258611	−	0.0409600i
$900$	11.8481	+	1.86483i	0.394936	+	0.0621609i
$901$		−	0.346672i		−	0.0115493i
$902$	1.01786	+	28.5924i	0.0338912	+	0.952023i
$903$	0.807317	+	0.807317i	0.0268658	+	0.0268658i
$904$	−52.9088	−	4.08694i	−1.75972	−	0.135929i
$905$	8.42685	+	1.33468i	0.280118	+	0.0443663i
$906$	−69.1969	+	16.6480i	−2.29891	+	0.553094i
$907$	−2.74343	−	8.44340i	−0.0910940	−	0.280359i	0.895122	−	0.445821i	$-0.147088\pi$
$907$	−2.74343	−	8.44340i	−0.0910940	−	0.280359i	−0.986216	+	0.165463i	$0.947088\pi$
$908$	−1.40023	+	4.32366i	−0.0464682	+	0.143486i
$909$	46.6350	−	64.1875i	1.54678	−	2.12897i
$910$	−1.80758	−	0.230555i	−0.0599205	−	0.00764281i
$911$	31.9557	+	10.3831i	1.05874	+	0.344006i	0.786093	−	0.618108i	$-0.212101\pi$
$911$	31.9557	+	10.3831i	1.05874	+	0.344006i	0.272648	+	0.962114i	$0.412101\pi$
$912$	−30.4485	+	60.0448i	−1.00825	+	1.98828i
$913$	1.20098	−	27.6304i	0.0397465	−	0.914432i
$914$	24.2128	+	20.6595i	0.800887	+	0.683354i
$915$	36.9562	−	18.8301i	1.22173	−	0.622505i
$916$	15.1520	−	0.0146267i	0.500635	−	0.000483279i
$917$	−0.261445	−	1.65070i	−0.00863367	−	0.0545108i
$918$	−25.4155	+	10.5418i	−0.838836	+	0.347932i
$919$	23.6897	−	7.69725i	0.781451	−	0.253909i	0.108992	−	0.994043i	$-0.465238\pi$
$919$	23.6897	−	7.69725i	0.781451	−	0.253909i	0.672460	+	0.740134i	$0.265238\pi$
$920$	−3.92810	−	9.44456i	−0.129506	−	0.311378i
$921$	−63.8618	−	10.1147i	−2.10432	−	0.333291i
$922$	7.61680	−	4.67264i	0.250846	−	0.153885i
$923$	0.430314	−	8.80965i	0.0141639	−	0.289973i
$924$	−2.43911	−	2.65563i	−0.0802409	−	0.0873639i
$925$	−6.72818	+	6.72818i	−0.221221	+	0.221221i
$926$	18.8483	−	11.5628i	0.619393	−	0.379976i
$927$	76.7846	−	55.7873i	2.52194	−	1.83229i
$928$	2.74349	−	11.5502i	0.0900594	−	0.379153i
$929$	16.2597	+	8.28472i	0.533463	+	0.271813i	0.699902	−	0.714239i	$-0.253227\pi$
$929$	16.2597	+	8.28472i	0.533463	+	0.271813i	−0.166439	+	0.986052i	$0.553227\pi$
$930$	12.5273	+	30.2023i	0.410785	+	0.990371i
$931$	−37.7817	+	5.98404i	−1.23825	+	0.196119i
$932$	−0.925838	−	0.924052i	−0.0303268	−	0.0302683i
$933$	−13.7042	−	4.45277i	−0.448656	−	0.145777i
$934$	−3.69812	−	46.7009i	−0.121006	−	1.52810i
$935$	−12.0187	+	3.33560i	−0.393053	+	0.109086i
$936$	−36.7049	+	53.9823i	−1.19974	+	1.76447i
$937$	16.1818	−	49.8025i	0.528637	−	1.62698i	−0.228374	−	0.973573i	$-0.573341\pi$
$937$	16.1818	−	49.8025i	0.528637	−	1.62698i	0.757011	−	0.653403i	$-0.226659\pi$
$938$	−0.673922	−	0.788291i	−0.0220043	−	0.0257386i
$939$	11.7707	−	16.2010i	0.384122	−	0.528698i
$940$	−27.0843	+	13.8331i	−0.883393	+	0.451186i
$941$	23.9686	+	12.2126i	0.781352	+	0.398119i	0.798699	−	0.601731i	$-0.205522\pi$
$941$	23.9686	+	12.2126i	0.781352	+	0.398119i	−0.0173467	+	0.999850i	$0.505522\pi$
$942$	30.8211	+	18.8667i	1.00421	+	0.614711i
$943$	1.71198	−	10.8090i	0.0557497	−	0.351990i
$944$	41.7197	+	41.5589i	1.35786	+	1.35263i
$945$	3.72672			0.121230
$946$	9.66911	−	1.88628i	0.314370	−	0.0613284i
$947$	−12.9304	+	12.9304i	−0.420182	+	0.420182i	−0.885267	−	0.465084i	$-0.846024\pi$
$947$	−12.9304	+	12.9304i	−0.420182	+	0.420182i	0.465084	+	0.885267i	$0.346024\pi$
$948$	−6.19071	+	39.3323i	−0.201065	+	1.27745i
$949$	−5.81824	−	8.88999i	−0.188868	−	0.288581i
$950$	1.70124	+	7.07115i	0.0551956	+	0.229418i
$951$	25.1678	−	49.3945i	0.816120	−	1.60173i
$952$	−0.910024	−	0.217084i	−0.0294941	−	0.00703574i
$953$	0.844155	−	1.16188i	0.0273449	−	0.0376370i	−0.795126	−	0.606445i	$-0.792595\pi$
$953$	0.844155	−	1.16188i	0.0273449	−	0.0376370i	0.822471	+	0.568808i	$0.192595\pi$
$954$	1.09304	+	1.27854i	0.0353886	+	0.0413942i
$955$	−14.7391	+	7.50992i	−0.476945	+	0.243015i
$956$	−44.2114	−	32.0563i	−1.42990	−	1.03677i
$957$	8.85382	+	19.4179i	0.286203	+	0.627692i
$958$	37.9729	+	32.4002i	1.22685	+	1.04680i
$959$	−0.470691	+	1.44864i	−0.0151994	+	0.0467789i
$960$	−46.9793	+	15.4151i	−1.51625	+	0.497519i
$961$	−9.99572	+	13.7579i	−0.322442	+	0.443804i
$962$	−17.4838	−	48.7468i	−0.563702	−	1.57166i
$963$	−25.2546	+	8.20572i	−0.813818	+	0.264426i
$964$	−6.06210	−	18.5961i	−0.195247	−	0.598941i
$965$	−30.0965	+	21.8664i	−0.968842	+	0.703905i
$966$	0.721218	+	1.17565i	0.0232048	+	0.0378258i
$967$	−26.0737	−	26.0737i	−0.838473	−	0.838473i	0.150185	−	0.988658i	$-0.452013\pi$
$967$	−26.0737	−	26.0737i	−0.838473	−	0.838473i	−0.988658	+	0.150185i	$0.952013\pi$
$968$	−30.7624	+	4.65529i	−0.988743	+	0.149627i
$969$	−22.2042	−	22.2042i	−0.713303	−	0.713303i
$970$	−2.83952	+	11.8527i	−0.0911715	+	0.380566i
$971$	4.61907	+	6.35760i	0.148233	+	0.204025i	0.876676	−	0.481081i	$-0.159756\pi$
$971$	4.61907	+	6.35760i	0.148233	+	0.204025i	−0.728443	+	0.685106i	$0.759756\pi$
$972$	7.13474	−	14.0362i	0.228847	−	0.450211i
$973$	1.02410	−	2.00992i	0.0328312	−	0.0644350i
$974$	12.8260	+	5.30546i	0.410973	+	0.169998i
$975$	1.11920	+	10.2964i	0.0358430	+	0.329749i
$976$	15.7365	−	21.7476i	0.503713	−	0.696124i
$977$	2.00325	+	3.93160i	0.0640897	+	0.125783i	0.920829	−	0.389967i	$-0.127513\pi$
$977$	2.00325	+	3.93160i	0.0640897	+	0.125783i	−0.856739	+	0.515750i	$0.827513\pi$
$978$	−41.6821	+	48.8513i	−1.33285	+	1.56209i
$979$	49.5681	+	18.5217i	1.58420	+	0.591958i
$980$	−22.7440	−	16.4909i	−0.726530	−	0.526784i
$981$	−54.9084	−	107.764i	−1.75309	−	3.44063i
$982$	−23.9143	−	27.9727i	−0.763136	−	0.892645i
$983$	41.8261	−	6.62461i	1.33405	−	0.211292i	0.551652	−	0.834075i	$-0.313998\pi$
$983$	41.8261	−	6.62461i	1.33405	−	0.211292i	0.782395	+	0.622782i	$0.213998\pi$
$984$	−51.4554	−	12.2746i	−1.64034	−	0.391299i
$985$	51.6319	−	16.7762i	1.64513	−	0.534535i
$986$	4.72263	+	2.89090i	0.150399	+	0.0920649i
$987$	3.31758	−	2.41036i	0.105600	−	0.0767226i
$988$	−38.7558	−	8.05496i	−1.23299	−	0.256262i
$989$	−3.76823			−0.119823
$990$	33.8083	−	50.1962i	1.07450	−	1.59534i
$991$			5.83879i			0.185475i	0.995691	+	0.0927376i	$0.0295618\pi$
$991$			5.83879i			0.185475i	−0.995691	+	0.0927376i	$0.970438\pi$
$992$	16.1246	+	13.7045i	0.511956	+	0.435120i
$993$	15.0305	−	94.8989i	0.476979	−	3.01152i
$994$	−0.320218	+	0.523115i	−0.0101567	+	0.0165922i
$995$	27.9902	+	14.2617i	0.887348	+	0.452126i
$996$	48.6477	+	15.7547i	1.54146	+	0.499207i
$997$	41.1693	+	29.9112i	1.30384	+	0.947298i	0.999985	−	0.00541915i	$-0.00172498\pi$
$997$	41.1693	+	29.9112i	1.30384	+	0.947298i	0.303859	+	0.952717i	$0.401725\pi$
$998$	1.22156	−	15.6178i	0.0386679	−	0.494373i
$999$	48.0835	+	94.3692i	1.52130	+	2.98571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bk.a.31.6	✓	640
4.3	odd	2	inner	572.2.bk.a.31.50	yes	640
11.5	even	5	inner	572.2.bk.a.291.70	yes	640
13.8	odd	4	inner	572.2.bk.a.515.46	yes	640
44.27	odd	10	inner	572.2.bk.a.291.46	yes	640
52.47	even	4	inner	572.2.bk.a.515.70	yes	640
143.60	odd	20	inner	572.2.bk.a.203.50	yes	640
572.203	even	20	inner	572.2.bk.a.203.6	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bk.a.31.6	✓	640	1.1	even	1	trivial
572.2.bk.a.31.50	yes	640	4.3	odd	2	inner
572.2.bk.a.203.6	yes	640	572.203	even	20	inner
572.2.bk.a.203.50	yes	640	143.60	odd	20	inner
572.2.bk.a.291.46	yes	640	44.27	odd	10	inner
572.2.bk.a.291.70	yes	640	11.5	even	5	inner
572.2.bk.a.515.46	yes	640	13.8	odd	4	inner
572.2.bk.a.515.70	yes	640	52.47	even	4	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37530 - 0.329478i) q^{2} +(1.80222 + 2.48055i) q^{3} +(1.78289 + 0.906260i) q^{4} +(1.79602 + 0.915119i) q^{5} +(-1.66131 - 4.00528i) q^{6} +(-0.175107 + 0.0277342i) q^{7} +(-2.15341 - 1.83380i) q^{8} +(-1.97806 + 6.08783i) q^{9} +O(q^{10})\)	\(q+(-1.37530 - 0.329478i) q^{2} +(1.80222 + 2.48055i) q^{3} +(1.78289 + 0.906260i) q^{4} +(1.79602 + 0.915119i) q^{5} +(-1.66131 - 4.00528i) q^{6} +(-0.175107 + 0.0277342i) q^{7} +(-2.15341 - 1.83380i) q^{8} +(-1.97806 + 6.08783i) q^{9} +(-2.16855 - 1.85031i) q^{10} +(3.01773 - 1.37597i) q^{11} +(0.965142 + 6.05582i) q^{12} +(-3.28860 + 1.47820i) q^{13} +(0.249962 + 0.0195510i) q^{14} +(0.966837 + 6.10437i) q^{15} +(2.35738 + 3.23152i) q^{16} +(-1.77439 + 0.576534i) q^{17} +(4.72622 - 7.72086i) q^{18} +(5.42174 + 0.858719i) q^{19} +(2.37277 + 3.25922i) q^{20} +(-0.384378 - 0.384378i) q^{21} +(-4.60363 + 0.898093i) q^{22} +1.79412 q^{23} +(0.667902 - 8.64655i) q^{24} +(-0.550673 - 0.757937i) q^{25} +(5.00985 - 0.949448i) q^{26} +(-9.91788 + 3.22251i) q^{27} +(-0.337330 - 0.109245i) q^{28} +(1.69781 + 1.23353i) q^{29} +(0.681565 - 8.71387i) q^{30} +(-3.33316 + 1.69833i) q^{31} +(-2.17739 - 5.22101i) q^{32} +(8.85179 + 5.00582i) q^{33} +(2.63027 - 0.208284i) q^{34} +(-0.339876 - 0.110432i) q^{35} +(-9.04381 + 9.06129i) q^{36} +(-1.58880 - 10.0313i) q^{37} +(-7.17357 - 2.96734i) q^{38} +(-9.59355 - 5.49349i) q^{39} +(-2.18943 - 5.26417i) q^{40} +(0.954216 - 6.02469i) q^{41} +(0.401990 + 0.655278i) q^{42} -2.10032 q^{43} +(6.62727 + 0.281650i) q^{44} +(-9.12372 + 9.12372i) q^{45} +(-2.46745 - 0.591123i) q^{46} +(-1.18011 + 7.45092i) q^{47} +(-3.76741 + 11.6715i) q^{48} +(-6.62750 + 2.15341i) q^{49} +(0.507616 + 1.22382i) q^{50} +(-4.62797 - 3.36241i) q^{51} +(-7.20285 - 0.344859i) q^{52} +(-0.0574194 + 0.176719i) q^{53} +(14.7018 - 1.16420i) q^{54} +(6.67909 + 0.290312i) q^{55} +(0.427936 + 0.261388i) q^{56} +(7.64109 + 14.9965i) q^{57} +(-1.92858 - 2.25587i) q^{58} +(14.5405 - 2.30299i) q^{59} +(-3.80838 + 11.7596i) q^{60} +(-2.07381 - 6.38252i) q^{61} +(5.14365 - 1.23751i) q^{62} +(0.177530 - 1.12088i) q^{63} +(1.27435 + 7.89785i) q^{64} +(-7.25914 - 0.354578i) q^{65} +(-10.5245 - 9.80096i) q^{66} +(-2.92487 - 2.92487i) q^{67} +(-3.68603 - 0.580163i) q^{68} +(3.23341 + 4.45040i) q^{69} +(0.431046 + 0.263859i) q^{70} +(-1.11058 + 2.17964i) q^{71} +(15.4234 - 9.48224i) q^{72} +(0.460974 + 2.91048i) q^{73} +(-1.12001 + 14.3195i) q^{74} +(0.887662 - 2.73194i) q^{75} +(8.88813 + 6.44450i) q^{76} +(-0.490264 + 0.324636i) q^{77} +(11.3840 + 10.7160i) q^{78} +(6.17518 + 2.00644i) q^{79} +(1.27669 + 7.96117i) q^{80} +(-10.3320 - 7.50662i) q^{81} +(-3.29733 + 7.97134i) q^{82} +(3.78571 - 7.42987i) q^{83} +(-0.336956 - 1.03365i) q^{84} +(-3.71444 - 0.588310i) q^{85} +(2.88857 + 0.692010i) q^{86} +6.43461i q^{87} +(-9.02167 - 2.57089i) q^{88} +(11.2816 + 11.2816i) q^{89} +(15.5539 - 9.54177i) q^{90} +(0.534860 - 0.350050i) q^{91} +(3.19872 + 1.62594i) q^{92} +(-10.2199 - 5.20729i) q^{93} +(4.07792 - 9.85841i) q^{94} +(8.95173 + 6.50381i) q^{95} +(9.02682 - 14.8106i) q^{96} +(-1.94104 - 3.80951i) q^{97} +(9.82429 - 0.777960i) q^{98} +(2.40743 + 21.0932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9}+O(q^{10}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9	\( 640 q - 6 q^{2} - 12 q^{5} - 14 q^{6} - 6 q^{8} + 120 q^{9} - 12 q^{13} + 4 q^{14} - 36 q^{16} - 10 q^{18} - 60 q^{20} - 56 q^{21} - 44 q^{22} - 14 q^{24} + 26 q^{26} - 14 q^{28} - 24 q^{29} - 16 q^{32} - 28 q^{33} + 12 q^{34} - 12 q^{37} + 4 q^{40} - 36 q^{41} - 8 q^{42} + 26 q^{44} - 16 q^{45} - 50 q^{46} + 48 q^{48} + 36 q^{50} - 52 q^{52} - 40 q^{53} + 116 q^{54} - 36 q^{57} - 70 q^{58} + 52 q^{60} - 8 q^{61} - 48 q^{65} - 228 q^{66} - 44 q^{68} - 68 q^{70} - 38 q^{72} - 12 q^{73} - 12 q^{74} + 108 q^{76} + 108 q^{78} + 62 q^{80} - 168 q^{81} - 36 q^{84} - 52 q^{85} - 62 q^{86} + 16 q^{89} - 80 q^{92} - 4 q^{93} - 124 q^{94} - 132 q^{96} - 4 q^{97} - 108 q^{98}+O(q^{100}) \) 640 * q - 6 * q^2 - 12 * q^5 - 14 * q^6 - 6 * q^8 + 120 * q^9 - 12 * q^13 + 4 * q^14 - 36 * q^16 - 10 * q^18 - 60 * q^20 - 56 * q^21 - 44 * q^22 - 14 * q^24 + 26 * q^26 - 14 * q^28 - 24 * q^29 - 16 * q^32 - 28 * q^33 + 12 * q^34 - 12 * q^37 + 4 * q^40 - 36 * q^41 - 8 * q^42 + 26 * q^44 - 16 * q^45 - 50 * q^46 + 48 * q^48 + 36 * q^50 - 52 * q^52 - 40 * q^53 + 116 * q^54 - 36 * q^57 - 70 * q^58 + 52 * q^60 - 8 * q^61 - 48 * q^65 - 228 * q^66 - 44 * q^68 - 68 * q^70 - 38 * q^72 - 12 * q^73 - 12 * q^74 + 108 * q^76 + 108 * q^78 + 62 * q^80 - 168 * q^81 - 36 * q^84 - 52 * q^85 - 62 * q^86 + 16 * q^89 - 80 * q^92 - 4 * q^93 - 124 * q^94 - 132 * q^96 - 4 * q^97 - 108 * q^98

Introduction

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