LMFDB - Embedded newform 189.2.w.a.184.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			184.17
Character	$\chi$	$=$	189.184
Dual form			189.2.w.a.151.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.306313 + 1.73719i) q^{2} +(1.49260 - 0.878725i) q^{3} +(-1.04461 + 0.380207i) q^{4} +(-0.723302 + 4.10205i) q^{5} +(1.98371 + 2.32376i) q^{6} +(-1.55501 - 2.14055i) q^{7} +(0.783518 + 1.35709i) q^{8} +(1.45569 - 2.62316i) q^{9} +O(q^{10})$	\(q+(0.306313 + 1.73719i) q^{2} +(1.49260 - 0.878725i) q^{3} +(-1.04461 + 0.380207i) q^{4} +(-0.723302 + 4.10205i) q^{5} +(1.98371 + 2.32376i) q^{6} +(-1.55501 - 2.14055i) q^{7} +(0.783518 + 1.35709i) q^{8} +(1.45569 - 2.62316i) q^{9} -7.34759 q^{10} +(-0.428940 - 2.43264i) q^{11} +(-1.22508 + 1.48542i) q^{12} +(0.108160 + 0.0907572i) q^{13} +(3.24222 - 3.35702i) q^{14} +(2.52498 + 6.75829i) q^{15} +(-3.82067 + 3.20592i) q^{16} +0.702677 q^{17} +(5.00282 + 1.72529i) q^{18} +6.46502 q^{19} +(-0.804060 - 4.56005i) q^{20} +(-4.20195 - 1.82855i) q^{21} +(4.09457 - 1.49030i) q^{22} +(-4.27608 - 3.58805i) q^{23} +(2.36199 + 1.33709i) q^{24} +(-11.6052 - 4.22394i) q^{25} +(-0.124532 + 0.215695i) q^{26} +(-0.132287 - 5.19447i) q^{27} +(2.43823 + 1.64481i) q^{28} +(0.100910 - 0.0846735i) q^{29} +(-10.9670 + 6.45651i) q^{30} +(4.35670 - 1.58571i) q^{31} +(-4.33878 - 3.64067i) q^{32} +(-2.77786 - 3.25403i) q^{33} +(0.215239 + 1.22068i) q^{34} +(9.90538 - 4.83046i) q^{35} +(-0.523280 + 3.29365i) q^{36} +(-0.387945 - 0.671941i) q^{37} +(1.98032 + 11.2310i) q^{38} +(0.241190 + 0.0404208i) q^{39} +(-6.13358 + 2.23244i) q^{40} +(-2.52108 - 2.11544i) q^{41} +(1.88942 - 7.85969i) q^{42} +(-5.66175 - 2.06071i) q^{43} +(1.37298 + 2.37808i) q^{44} +(9.70744 + 7.86863i) q^{45} +(4.92331 - 8.52742i) q^{46} +(5.59334 + 2.03581i) q^{47} +(-2.88560 + 8.14247i) q^{48} +(-2.16389 + 6.65714i) q^{49} +(3.78296 - 21.4542i) q^{50} +(1.04881 - 0.617460i) q^{51} +(-0.147492 - 0.0536827i) q^{52} +(1.85992 + 3.22148i) q^{53} +(8.98325 - 1.82094i) q^{54} +10.2891 q^{55} +(1.68654 - 3.78745i) q^{56} +(9.64966 - 5.68097i) q^{57} +(0.178004 + 0.149363i) q^{58} +(-2.78047 - 2.33309i) q^{59} +(-5.20717 - 6.09977i) q^{60} +(0.205027 + 0.0746237i) q^{61} +(4.08919 + 7.08269i) q^{62} +(-7.87861 + 0.963077i) q^{63} +(0.00796973 - 0.0138040i) q^{64} +(-0.450523 + 0.378034i) q^{65} +(4.80197 - 5.82242i) q^{66} +(2.66458 - 15.1116i) q^{67} +(-0.734024 + 0.267163i) q^{68} +(-9.53537 - 1.59802i) q^{69} +(11.4256 + 15.7279i) q^{70} +(-7.04066 + 12.1948i) q^{71} +(4.70043 - 0.0797938i) q^{72} +(-6.36370 + 11.0222i) q^{73} +(1.04845 - 0.879758i) q^{74} +(-21.0335 + 3.89313i) q^{75} +(-6.75343 + 2.45805i) q^{76} +(-4.54018 + 4.70095i) q^{77} +(0.00366121 + 0.431374i) q^{78} +(1.00160 + 5.68035i) q^{79} +(-10.3874 - 17.9914i) q^{80} +(-4.76196 - 7.63700i) q^{81} +(2.90267 - 5.02758i) q^{82} +(-1.84338 + 1.54678i) q^{83} +(5.08463 + 0.312508i) q^{84} +(-0.508248 + 2.88242i) q^{85} +(1.84557 - 10.4667i) q^{86} +(0.0762131 - 0.215055i) q^{87} +(2.96524 - 2.48813i) q^{88} +0.904179 q^{89} +(-10.6958 + 19.2739i) q^{90} +(0.0260800 - 0.372651i) q^{91} +(5.83104 + 2.12233i) q^{92} +(5.10939 - 6.19517i) q^{93} +(-1.82327 + 10.3403i) q^{94} +(-4.67616 + 26.5198i) q^{95} +(-9.67519 - 1.62145i) q^{96} +(-1.73081 - 0.629965i) q^{97} +(-12.2275 - 1.71991i) q^{98} +(-7.00562 - 2.41598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.306313	+	1.73719i	0.216596	+	1.22838i	0.878115	+	0.478449i	$0.158801\pi$
$2$	0.306313	+	1.73719i	0.216596	+	1.22838i	−0.661519	+	0.749928i	$0.730088\pi$
$3$	1.49260	−	0.878725i	0.861751	−	0.507332i
$3$	1.49260	−	0.878725i	0.861751	−	0.507332i
$4$	−1.04461	+	0.380207i	−0.522305	+	0.190104i
$5$	−0.723302	+	4.10205i	−0.323471	+	1.83449i	0.196741	+	0.980455i	$0.436964\pi$
$5$	−0.723302	+	4.10205i	−0.323471	+	1.83449i	−0.520212	+	0.854037i	$0.674147\pi$
$6$	1.98371	+	2.32376i	0.809847	+	0.948669i
$7$	−1.55501	−	2.14055i	−0.587738	−	0.809051i
$7$	−1.55501	−	2.14055i	−0.587738	−	0.809051i
$8$	0.783518	+	1.35709i	0.277015	+	0.479805i
$9$	1.45569	−	2.62316i	0.485229	−	0.874387i
$10$	−7.34759			−2.32351
$11$	−0.428940	−	2.43264i	−0.129330	−	0.733469i	−0.978641	−	0.205576i	$-0.934093\pi$
$11$	−0.428940	−	2.43264i	−0.129330	−	0.733469i	0.849311	−	0.527893i	$-0.177018\pi$
$12$	−1.22508	+	1.48542i	−0.353651	+	0.428804i
$13$	0.108160	+	0.0907572i	0.0299983	+	0.0251715i	0.657664	−	0.753312i	$-0.271545\pi$
$13$	0.108160	+	0.0907572i	0.0299983	+	0.0251715i	−0.627665	+	0.778483i	$0.715989\pi$
$14$	3.24222	−	3.35702i	0.866518	−	0.897202i
$15$	2.52498	+	6.75829i	0.651946	+	1.74498i
$16$	−3.82067	+	3.20592i	−0.955168	+	0.801481i
$17$	0.702677			0.170424			0.0852121	−	0.996363i	$-0.472843\pi$
$17$	0.702677			0.170424			0.0852121	+	0.996363i	$0.472843\pi$
$18$	5.00282	+	1.72529i	1.17918	+	0.406655i
$19$	6.46502			1.48318			0.741588	−	0.670855i	$-0.234073\pi$
$19$	6.46502			1.48318			0.741588	+	0.670855i	$0.234073\pi$
$20$	−0.804060	−	4.56005i	−0.179793	−	1.01966i
$21$	−4.20195	−	1.82855i	−0.916941	−	0.399022i
$22$	4.09457	−	1.49030i	0.872965	−	0.317733i
$23$	−4.27608	−	3.58805i	−0.891624	−	0.748161i	0.0769115	−	0.997038i	$-0.475494\pi$
$23$	−4.27608	−	3.58805i	−0.891624	−	0.748161i	−0.968535	+	0.248877i	$0.919939\pi$
$24$	2.36199	+	1.33709i	0.482138	+	0.272933i
$25$	−11.6052	−	4.22394i	−2.32104	−	0.844789i
$26$	−0.124532	+	0.215695i	−0.0244226	+	0.0423012i
$27$	−0.132287	−	5.19447i	−0.0254586	−	0.999676i
$28$	2.43823	+	1.64481i	0.460783	+	0.310841i
$29$	0.100910	−	0.0846735i	0.0187385	−	0.0157235i	−0.633370	−	0.773849i	$-0.718329\pi$
$29$	0.100910	−	0.0846735i	0.0187385	−	0.0157235i	0.652109	+	0.758125i	$0.273885\pi$
$30$	−10.9670	+	6.45651i	−2.00229	+	1.17879i
$31$	4.35670	−	1.58571i	0.782487	−	0.284802i	0.0802776	−	0.996773i	$-0.474419\pi$
$31$	4.35670	−	1.58571i	0.782487	−	0.284802i	0.702209	+	0.711971i	$0.252197\pi$
$32$	−4.33878	−	3.64067i	−0.766995	−	0.643586i
$33$	−2.77786	−	3.25403i	−0.483563	−	0.566454i
$34$	0.215239	+	1.22068i	0.0369132	+	0.209345i
$35$	9.90538	−	4.83046i	1.67431	−	0.816498i
$36$	−0.523280	+	3.29365i	−0.0872133	+	0.548941i
$37$	−0.387945	−	0.671941i	−0.0637778	−	0.110466i	0.832373	−	0.554215i	$-0.186982\pi$
$37$	−0.387945	−	0.671941i	−0.0637778	−	0.110466i	−0.896151	+	0.443749i	$0.853648\pi$
$38$	1.98032	+	11.2310i	0.321250	+	1.82190i
$39$	0.241190	+	0.0404208i	0.0386213	+	0.00647251i
$40$	−6.13358	+	2.23244i	−0.969804	+	0.352980i
$41$	−2.52108	−	2.11544i	−0.393727	−	0.330376i	0.424336	−	0.905505i	$-0.360507\pi$
$41$	−2.52108	−	2.11544i	−0.393727	−	0.330376i	−0.818063	+	0.575129i	$0.804952\pi$
$42$	1.88942	−	7.85969i	0.291544	−	1.21278i
$43$	−5.66175	−	2.06071i	−0.863409	−	0.314255i	−0.127914	−	0.991785i	$-0.540828\pi$
$43$	−5.66175	−	2.06071i	−0.863409	−	0.314255i	−0.735495	+	0.677530i	$0.763050\pi$
$44$	1.37298	+	2.37808i	0.206985	+	0.358509i
$45$	9.70744	+	7.86863i	1.44710	+	1.17299i
$46$	4.92331	−	8.52742i	0.725902	−	1.25730i
$47$	5.59334	+	2.03581i	0.815873	+	0.296953i	0.716048	−	0.698052i	$-0.245949\pi$
$47$	5.59334	+	2.03581i	0.815873	+	0.296953i	0.0998253	+	0.995005i	$0.468172\pi$
$48$	−2.88560	+	8.14247i	−0.416500	+	1.17526i
$49$	−2.16389	+	6.65714i	−0.309127	+	0.951021i
$50$	3.78296	−	21.4542i	0.534992	−	3.03409i
$51$	1.04881	−	0.617460i	0.146863	−	0.0864617i
$52$	−0.147492	−	0.0536827i	−0.0204535	−	0.00744445i
$53$	1.85992	+	3.22148i	0.255480	+	0.442504i	0.965026	−	0.262155i	$-0.0844332\pi$
$53$	1.85992	+	3.22148i	0.255480	+	0.442504i	−0.709546	+	0.704659i	$0.751100\pi$
$54$	8.98325	−	1.82094i	1.22247	−	0.247799i
$55$	10.2891			1.38738
$56$	1.68654	−	3.78745i	0.225374	−	0.506119i
$57$	9.64966	−	5.68097i	1.27813	−	0.752463i
$58$	0.178004	+	0.149363i	0.0233731	+	0.0196123i
$59$	−2.78047	−	2.33309i	−0.361986	−	0.303742i	0.443596	−	0.896227i	$-0.353703\pi$
$59$	−2.78047	−	2.33309i	−0.361986	−	0.303742i	−0.805582	+	0.592485i	$0.798147\pi$
$60$	−5.20717	−	6.09977i	−0.672242	−	0.787476i
$61$	0.205027	+	0.0746237i	0.0262510	+	0.00955458i	0.355112	−	0.934824i	$-0.384443\pi$
$61$	0.205027	+	0.0746237i	0.0262510	+	0.00955458i	−0.328861	+	0.944378i	$0.606665\pi$
$62$	4.08919	+	7.08269i	0.519328	+	0.899502i
$63$	−7.87861	+	0.963077i	−0.992611	+	0.121336i
$64$	0.00796973	−	0.0138040i	0.000996216	−	0.00172550i
$65$	−0.450523	+	0.378034i	−0.0558805	+	0.0468893i
$66$	4.80197	−	5.82242i	0.591082	−	0.716690i
$67$	2.66458	−	15.1116i	0.325530	−	1.84617i	−0.180395	−	0.983594i	$-0.557738\pi$
$67$	2.66458	−	15.1116i	0.325530	−	1.84617i	0.505925	−	0.862578i	$-0.331151\pi$
$68$	−0.734024	+	0.267163i	−0.0890135	+	0.0323983i
$69$	−9.53537	−	1.59802i	−1.14792	−	0.192379i
$70$	11.4256	+	15.7279i	1.36562	+	1.87984i
$71$	−7.04066	+	12.1948i	−0.835573	+	1.44725i	0.0579909	+	0.998317i	$0.481531\pi$
$71$	−7.04066	+	12.1948i	−0.835573	+	1.44725i	−0.893563	+	0.448937i	$0.851803\pi$
$72$	4.70043	−	0.0797938i	0.553951	−	0.00940379i
$73$	−6.36370	+	11.0222i	−0.744815	+	1.29006i	0.205467	+	0.978664i	$0.434129\pi$
$73$	−6.36370	+	11.0222i	−0.744815	+	1.29006i	−0.950281	+	0.311393i	$0.899205\pi$
$74$	1.04845	−	0.879758i	0.121880	−	0.102270i
$75$	−21.0335	+	3.89313i	−2.42874	+	0.449539i
$76$	−6.75343	+	2.45805i	−0.774671	+	0.281957i
$77$	−4.54018	+	4.70095i	−0.517402	+	0.535723i
$78$	0.00366121	+	0.431374i	0.000414551	+	0.0488435i
$79$	1.00160	+	5.68035i	0.112689	+	0.639090i	0.987869	+	0.155292i	$0.0496319\pi$
$79$	1.00160	+	5.68035i	0.112689	+	0.639090i	−0.875180	+	0.483798i	$0.839257\pi$
$80$	−10.3874	−	17.9914i	−1.16134	−	2.01150i
$81$	−4.76196	−	7.63700i	−0.529106	−	0.848555i
$82$	2.90267	−	5.02758i	0.320547	−	0.555203i
$83$	−1.84338	+	1.54678i	−0.202337	+	0.169781i	−0.738326	−	0.674444i	$-0.764383\pi$
$83$	−1.84338	+	1.54678i	−0.202337	+	0.169781i	0.535989	+	0.844225i	$0.319939\pi$
$84$	5.08463	+	0.312508i	0.554779	+	0.0340974i
$85$	−0.508248	+	2.88242i	−0.0551272	+	0.312642i
$86$	1.84557	−	10.4667i	0.199013	−	1.12866i
$87$	0.0762131	−	0.215055i	0.00817090	−	0.0230564i
$88$	2.96524	−	2.48813i	0.316095	−	0.265236i
$89$	0.904179			0.0958428			0.0479214	−	0.998851i	$-0.484740\pi$
$89$	0.904179			0.0958428			0.0479214	+	0.998851i	$0.484740\pi$
$90$	−10.6958	+	19.2739i	−1.12743	+	2.03165i
$91$	0.0260800	−	0.372651i	0.00273392	−	0.0390644i
$92$	5.83104	+	2.12233i	0.607928	+	0.221268i
$93$	5.10939	−	6.19517i	0.529819	−	0.642409i
$94$	−1.82327	+	10.3403i	−0.188056	+	1.06652i
$95$	−4.67616	+	26.5198i	−0.479764	+	2.72088i
$96$	−9.67519	−	1.62145i	−0.987470	−	0.165489i
$97$	−1.73081	−	0.629965i	−0.175737	−	0.0639632i	0.252653	−	0.967557i	$-0.418697\pi$
$97$	−1.73081	−	0.629965i	−0.175737	−	0.0639632i	−0.428390	+	0.903594i	$0.640919\pi$
$98$	−12.2275	−	1.71991i	−1.23517	−	0.173738i
$99$	−7.00562	−	2.41598i	−0.704091	−	0.242815i
$100$	13.7289			1.37289
$101$	−6.23114	+	5.22855i	−0.620021	+	0.520260i	−0.897810	−	0.440382i	$-0.854843\pi$
$101$	−6.23114	+	5.22855i	−0.620021	+	0.520260i	0.277789	+	0.960642i	$0.410398\pi$
$102$	1.39391	+	1.63285i	0.138018	+	0.161676i
$103$	−1.11235	+	6.30845i	−0.109603	+	0.621590i	0.879678	+	0.475569i	$0.157758\pi$
$103$	−1.11235	+	6.30845i	−0.109603	+	0.621590i	−0.989281	+	0.146021i	$0.953353\pi$
$104$	−0.0384205	+	0.217893i	−0.00376744	+	0.0213662i
$105$	10.5401	−	15.9140i	1.02861	−	1.55305i
$106$	−5.02660	+	4.21781i	−0.488226	+	0.409670i
$107$	−5.96628	+	10.3339i	−0.576782	+	0.999016i	0.419063	+	0.907957i	$0.362358\pi$
$107$	−5.96628	+	10.3339i	−0.576782	+	0.999016i	−0.995846	+	0.0910589i	$0.970975\pi$
$108$	2.11316	+	5.37590i	0.203339	+	0.517296i
$109$	−0.160232	−	0.277531i	−0.0153475	−	0.0265826i	0.858250	−	0.513232i	$-0.171552\pi$
$109$	−0.160232	−	0.277531i	−0.0153475	−	0.0265826i	−0.873597	+	0.486650i	$0.838219\pi$
$110$	3.15168	+	17.8741i	0.300501	+	1.70422i
$111$	−1.16950	−	0.662039i	−0.111004	−	0.0628380i
$112$	12.8036	+	3.19309i	1.20983	+	0.301718i
$113$	1.98832	−	0.723688i	0.187045	−	0.0680789i	−0.246799	−	0.969067i	$-0.579379\pi$
$113$	1.98832	−	0.723688i	0.187045	−	0.0680789i	0.433845	+	0.900988i	$0.357157\pi$
$114$	12.8247	+	15.0231i	1.20115	+	1.40704i
$115$	17.8113	−	14.9454i	1.66091	−	1.39367i
$116$	−0.0732182	+	0.126818i	−0.00679814	+	0.0117747i
$117$	0.395518	−	0.151608i	0.0365657	−	0.0140162i
$118$	3.20132	−	5.54485i	0.294705	−	0.510445i
$119$	−1.09267	−	1.50411i	−0.100165	−	0.137882i
$120$	−7.19326	+	8.72186i	−0.656652	+	0.796193i
$121$	4.60286	−	1.67530i	0.418442	−	0.152300i
$122$	−0.0668330	+	0.379029i	−0.00605077	+	0.0343156i
$123$	−5.62184	−	0.942158i	−0.506905	−	0.0849516i
$124$	−3.94816	+	3.31290i	−0.354555	+	0.297507i
$125$	15.3076	−	26.5135i	1.36915	−	2.37144i
$126$	−4.08637	−	13.3916i	−0.364043	−	1.19302i
$127$	−5.21371	−	9.03041i	−0.462642	−	0.801320i	0.536450	−	0.843932i	$-0.319765\pi$
$127$	−5.21371	−	9.03041i	−0.462642	−	0.801320i	−0.999092	+	0.0426127i	$0.986432\pi$
$128$	−10.6182	−	3.86470i	−0.938524	−	0.341595i
$129$	−10.2615	+	1.89931i	−0.903475	+	0.167225i
$130$	−0.794717	−	0.666847i	−0.0697013	−	0.0584864i
$131$	4.62719	+	3.88267i	0.404279	+	0.339231i	0.822145	−	0.569278i	$-0.192777\pi$
$131$	4.62719	+	3.88267i	0.404279	+	0.339231i	−0.417866	+	0.908509i	$0.637222\pi$
$132$	4.13899	+	2.34303i	0.360253	+	0.203935i
$133$	−10.0532	−	13.8387i	−0.871720	−	1.19997i
$134$	27.0678			2.33831
$135$	21.4037	+	3.21452i	1.84213	+	0.276662i
$136$	0.550560	+	0.953598i	0.0472101	+	0.0817703i
$137$	2.40899	+	0.876802i	0.205814	+	0.0749103i	0.442870	−	0.896586i	$-0.353960\pi$
$137$	2.40899	+	0.876802i	0.205814	+	0.0749103i	−0.237056	+	0.971496i	$0.576182\pi$
$138$	−0.144745	−	17.0542i	−0.0123215	−	1.45175i
$139$	−0.548284	+	3.10947i	−0.0465048	+	0.263742i	−0.999191	−	0.0402133i	$-0.987196\pi$
$139$	−0.548284	+	3.10947i	−0.0465048	+	0.263742i	0.952686	+	0.303955i	$0.0983074\pi$
$140$	−8.51069	+	8.81205i	−0.719284	+	0.744754i
$141$	10.1375	−	1.87637i	0.853733	−	0.158019i
$142$	−23.3413	−	8.49553i	−1.95876	−	0.712929i
$143$	0.174386	−	0.302045i	0.0145829	−	0.0252582i
$144$	2.84796	+	14.6891i	0.237330	+	1.22409i
$145$	0.274347	+	0.475182i	0.0227832	+	0.0394617i
$146$	−21.0970	−	7.67868i	−1.74600	−	0.635492i
$147$	2.61998	+	11.8379i	0.216093	+	0.976373i
$148$	0.660728	+	0.554417i	0.0543115	+	0.0455728i
$149$	11.8471	−	4.31199i	0.970551	−	0.353252i	0.192392	−	0.981318i	$-0.438376\pi$
$149$	11.8471	−	4.31199i	0.970551	−	0.353252i	0.778160	+	0.628066i	$0.216153\pi$
$150$	−13.2059	−	35.3467i	−1.07826	−	2.88605i
$151$	2.81699	+	15.9759i	0.229243	+	1.30010i	0.854405	+	0.519607i	$0.173922\pi$
$151$	2.81699	+	15.9759i	0.229243	+	1.30010i	−0.625162	+	0.780495i	$0.714967\pi$
$152$	5.06546	+	8.77363i	0.410863	+	0.711635i
$153$	1.02288	−	1.84324i	0.0826947	−	0.149017i
$154$	−9.55715	−	6.44719i	−0.770137	−	0.519529i
$155$	3.35345	+	19.0184i	0.269356	+	1.52759i
$156$	−0.267318	+	0.0494783i	−0.0214026	+	0.00396143i
$157$	6.45448	+	5.41595i	0.515124	+	0.432240i	0.862928	−	0.505327i	$-0.168628\pi$
$157$	6.45448	+	5.41595i	0.515124	+	0.432240i	−0.347804	+	0.937567i	$0.613073\pi$
$158$	−9.56104	+	3.47994i	−0.760636	+	0.276849i
$159$	5.60690	+	3.17401i	0.444656	+	0.251715i
$160$	18.0725	−	15.1646i	1.42875	−	1.19887i
$161$	−1.03106	+	14.7326i	−0.0812590	+	1.16109i
$162$	11.8083	−	10.6117i	0.927744	−	0.833736i
$163$	4.06419	−	7.03938i	0.318332	−	0.551367i	−0.661808	−	0.749673i	$-0.730211\pi$
$163$	4.06419	−	7.03938i	0.318332	−	0.551367i	0.980140	+	0.198306i	$0.0635440\pi$
$164$	3.43785	+	1.25128i	0.268451	+	0.0977083i
$165$	15.3574	−	9.04126i	1.19557	−	0.703861i
$166$	−3.25169	−	2.72849i	−0.252380	−	0.211772i
$167$	−18.8324	+	6.85444i	−1.45730	+	0.530412i	−0.944619	−	0.328169i	$-0.893568\pi$
$167$	−18.8324	+	6.85444i	−1.45730	+	0.530412i	−0.512677	+	0.858582i	$0.671346\pi$
$168$	−0.810796	−	7.13514i	−0.0625543	−	0.550488i
$169$	−2.25396	−	12.7829i	−0.173382	−	0.983298i
$170$	−5.16299			−0.395983
$171$	9.41103	−	16.9588i	0.719680	−	1.29687i
$172$	6.69782			0.510704
$173$	−19.8173	+	16.6287i	−1.50668	+	1.26426i	−0.636772	+	0.771052i	$0.719731\pi$
$173$	−19.8173	+	16.6287i	−1.50668	+	1.26426i	−0.869913	+	0.493206i	$0.835825\pi$
$174$	0.396937	+	0.0665222i	0.0300917	+	0.00504303i
$175$	9.00463	+	31.4097i	0.680686	+	2.37435i
$176$	9.43771	+	7.91918i	0.711394	+	0.596931i
$177$	−6.20026	−	1.03909i	−0.466040	−	0.0781031i
$178$	0.276962	+	1.57073i	0.0207592	+	0.117731i
$179$	19.5468			1.46100			0.730499	−	0.682914i	$-0.239288\pi$
$179$	19.5468			1.46100			0.730499	+	0.682914i	$0.239288\pi$
$180$	−13.1322	−	4.52882i	−0.978817	−	0.337558i
$181$	1.41161	+	2.44499i	0.104924	+	0.181734i	0.913707	−	0.406373i	$-0.133207\pi$
$181$	1.41161	+	2.44499i	0.104924	+	0.181734i	−0.808783	+	0.588107i	$0.799873\pi$
$182$	0.655353	−	0.0688420i	0.0485780	−	0.00510291i
$183$	0.371596	−	0.0687792i	0.0274692	−	0.00508430i
$184$	1.51894	−	8.61434i	0.111978	−	0.635057i
$185$	3.03694	−	1.10535i	0.223280	−	0.0812673i
$186$	12.3272	+	6.97832i	0.903878	+	0.511675i
$187$	−0.301407	−	1.70936i	−0.0220410	−	0.125001i
$188$	−6.61690			−0.482587
$189$	−10.9133	+	8.36061i	−0.793826	+	0.608145i
$190$	−47.5023			−3.44618
$191$	−1.41634	−	8.03246i	−0.102483	−	0.581208i	−0.992196	−	0.124688i	$-0.960207\pi$
$191$	−1.41634	−	8.03246i	−0.102483	−	0.581208i	0.889713	−	0.456520i	$-0.150904\pi$
$192$	−0.000234309	−	0.0276069i	−1.69098e−5	−	0.00199236i
$193$	−2.78662	+	1.01425i	−0.200585	+	0.0730071i	−0.440359	−	0.897822i	$-0.645149\pi$
$193$	−2.78662	+	1.01425i	−0.200585	+	0.0730071i	0.239774	+	0.970829i	$0.422927\pi$
$194$	0.564196	−	3.19972i	0.0405069	−	0.229726i
$195$	−0.340261	+	0.960138i	−0.0243666	+	0.0687569i
$196$	−0.270672	−	7.77685i	−0.0193337	−	0.555489i
$197$	−8.95897	−	15.5174i	−0.638300	−	1.10557i	−0.985806	−	0.167891i	$-0.946304\pi$
$197$	−8.95897	−	15.5174i	−0.638300	−	1.10557i	0.347505	−	0.937678i	$-0.387029\pi$
$198$	2.05110	−	12.9101i	0.145766	−	0.917483i
$199$	11.7675			0.834176			0.417088	−	0.908866i	$-0.363051\pi$
$199$	11.7675			0.834176			0.417088	+	0.908866i	$0.363051\pi$
$200$	−3.36059	−	19.0588i	−0.237629	−	1.34766i
$201$	−9.30177	−	24.8969i	−0.656096	−	1.75609i
$202$	−10.9916	−	9.22309i	−0.773370	−	0.648934i
$203$	−0.338164	−	0.0843345i	−0.0237344	−	0.00591912i
$204$	−0.860839	+	1.04377i	−0.0602708	+	0.0730786i
$205$	10.5011	−	8.81150i	0.733431	−	0.615422i
$206$	−11.2997			−0.787287
$207$	−15.6367	+	5.99376i	−1.08682	+	0.416595i
$208$	−0.704206			−0.0488279
$209$	−2.77311	−	15.7271i	−0.191820	−	1.08786i
$210$	30.8742	+	13.4354i	2.13052	+	0.927132i
$211$	4.57923	−	1.66670i	0.315247	−	0.114741i	−0.179550	−	0.983749i	$-0.557464\pi$
$211$	4.57923	−	1.66670i	0.315247	−	0.114741i	0.494798	+	0.869008i	$0.335242\pi$
$212$	−3.16772	−	2.65804i	−0.217560	−	0.182555i
$213$	0.206995	+	24.3887i	0.0141830	+	1.67108i
$214$	−19.7795	−	7.19914i	−1.35210	−	0.492123i
$215$	12.5483	−	21.7343i	0.855786	−	1.48226i
$216$	6.94572	−	4.24948i	0.472597	−	0.289141i
$217$	−10.1690	−	6.85994i	−0.690317	−	0.465683i
$218$	0.433042	−	0.363365i	0.0293293	−	0.0246102i
$219$	0.187092	+	22.0437i	0.0126425	+	1.48958i
$220$	−10.7481	+	3.91198i	−0.724635	+	0.263746i
$221$	0.0760018	+	0.0637730i	0.00511243	+	0.00428984i
$222$	0.791854	−	2.23443i	0.0531458	−	0.149965i
$223$	3.39420	+	19.2495i	0.227292	+	1.28904i	0.858254	+	0.513225i	$0.171549\pi$
$223$	3.39420	+	19.2495i	0.227292	+	1.28904i	−0.630962	+	0.775814i	$0.717339\pi$
$224$	−1.04618	+	14.9486i	−0.0699009	+	0.998798i
$225$	−27.9736	+	24.2936i	−1.86491	+	1.61957i
$226$	1.86623	+	3.23241i	0.124140	+	0.215017i
$227$	−2.13798	−	12.1251i	−0.141902	−	0.804769i	−0.969802	−	0.243893i	$-0.921576\pi$
$227$	−2.13798	−	12.1251i	−0.141902	−	0.804769i	0.827900	−	0.560876i	$-0.189536\pi$
$228$	−7.92019	+	9.60328i	−0.524528	+	0.635992i
$229$	24.0912	−	8.76849i	1.59199	−	0.579438i	0.614225	−	0.789131i	$-0.289469\pi$
$229$	24.0912	−	8.76849i	1.59199	−	0.579438i	0.977767	+	0.209693i	$0.0672465\pi$
$230$	31.4189	+	26.3636i	2.07170	+	1.73836i
$231$	−2.64581	+	11.0062i	−0.174082	+	0.724154i
$232$	0.193975	+	0.0706009i	0.0127351	+	0.00463518i
$233$	−3.66677	−	6.35103i	−0.240218	−	0.416070i	0.720558	−	0.693395i	$-0.243886\pi$
$233$	−3.66677	−	6.35103i	−0.240218	−	0.416070i	−0.960776	+	0.277324i	$0.910552\pi$
$234$	0.384524	+	0.640650i	0.0251371	+	0.0418806i
$235$	−12.3967	+	21.4717i	−0.808670	+	1.40066i
$236$	3.79156	+	1.38002i	0.246810	+	0.0898314i
$237$	6.48645	+	7.59834i	0.421340	+	0.493565i
$238$	2.27823	−	2.35890i	0.147676	−	0.152905i
$239$	2.57748	−	14.6176i	0.166723	−	0.945536i	−0.780546	−	0.625098i	$-0.785059\pi$
$239$	2.57748	−	14.6176i	0.166723	−	0.945536i	0.947270	−	0.320438i	$-0.103830\pi$
$240$	−31.3137	−	17.7263i	−2.02129	−	1.14423i
$241$	16.4437	+	5.98501i	1.05923	+	0.385529i	0.812139	−	0.583464i	$-0.198303\pi$
$241$	16.4437	+	5.98501i	1.05923	+	0.385529i	0.247092	+	0.968992i	$0.420525\pi$
$242$	4.32024	+	7.48287i	0.277715	+	0.481017i
$243$	−13.8185	−	7.21450i	−0.886457	−	0.462811i
$244$	−0.242546			−0.0155274
$245$	−25.7428	−	13.6915i	−1.64465	−	0.874719i
$246$	−0.0853383	−	10.0548i	−0.00544097	−	0.641070i
$247$	0.699258	+	0.586747i	0.0444927	+	0.0373338i
$248$	5.56551	+	4.67002i	0.353410	+	0.296546i
$249$	−1.39223	+	3.92853i	−0.0882287	+	0.248961i
$250$	50.7478	+	18.4707i	3.20957	+	1.16819i
$251$	−6.62373	−	11.4726i	−0.418086	−	0.724147i	0.577661	−	0.816277i	$-0.303966\pi$
$251$	−6.62373	−	11.4726i	−0.418086	−	0.724147i	−0.995747	+	0.0921303i	$0.970632\pi$
$252$	7.86391	−	4.00155i	0.495380	−	0.252074i
$253$	−6.89427	+	11.9412i	−0.433439	+	0.750738i
$254$	14.0905	−	11.8233i	0.884117	−	0.741862i
$255$	1.77424	+	4.74889i	0.111107	+	0.297387i
$256$	3.46676	−	19.6610i	0.216673	−	1.22881i
$257$	20.3970	−	7.42389i	1.27233	−	0.463090i	0.384441	−	0.923150i	$-0.374394\pi$
$257$	20.3970	−	7.42389i	1.27233	−	0.463090i	0.887888	+	0.460060i	$0.152172\pi$
$258$	−6.44270	−	17.2444i	−0.401105	−	1.07359i
$259$	−0.835063	+	1.87529i	−0.0518883	+	0.116525i
$260$	0.326890	−	0.566191i	0.0202729	−	0.0351136i
$261$	−0.0752192	−	0.387961i	−0.00465595	−	0.0240142i
$262$	−5.32756	+	9.22761i	−0.329138	+	0.570084i
$263$	8.30629	−	6.96981i	0.512188	−	0.429777i	−0.349710	−	0.936858i	$-0.613720\pi$
$263$	8.30629	−	6.96981i	0.512188	−	0.429777i	0.861898	+	0.507081i	$0.169276\pi$
$264$	2.23952	−	6.31940i	0.137833	−	0.388932i
$265$	−14.5599	+	5.29939i	−0.894410	+	0.325539i
$266$	20.9610	−	21.7032i	1.28520	−	1.33071i
$267$	1.34957	−	0.794525i	0.0825926	−	0.0486241i
$268$	2.96208	+	16.7988i	0.180938	+	1.02615i
$269$	−6.69178	−	11.5905i	−0.408005	−	0.706686i	0.586661	−	0.809833i	$-0.300442\pi$
$269$	−6.69178	−	11.5905i	−0.408005	−	0.706686i	−0.994666	+	0.103147i	$0.967109\pi$
$270$	0.971989	+	38.1668i	0.0591534	+	2.32276i
$271$	10.7152	−	18.5593i	0.650904	−	1.12740i	−0.332000	−	0.943279i	$-0.607723\pi$
$271$	10.7152	−	18.5593i	0.650904	−	1.12740i	0.982904	−	0.184120i	$-0.0589433\pi$
$272$	−2.68470	+	2.25273i	−0.162784	+	0.136592i
$273$	−0.288530	−	0.579134i	−0.0174627	−	0.0350508i
$274$	−0.785264	+	4.45345i	−0.0474395	+	0.269043i
$275$	−5.29741	+	30.0431i	−0.319446	+	1.81167i
$276$	10.5683	−	1.95611i	0.636139	−	0.117744i
$277$	4.19055	−	3.51628i	0.251785	−	0.211273i	−0.508155	−	0.861265i	$-0.669672\pi$
$277$	4.19055	−	3.51628i	0.251785	−	0.211273i	0.759941	+	0.649992i	$0.225228\pi$
$278$	−5.56969			−0.334048
$279$	2.18242	−	13.7366i	0.130658	−	0.822391i
$280$	14.3164	+	9.65776i	0.855570	+	0.577161i
$281$	13.4765	+	4.90506i	0.803942	+	0.292611i	0.711119	−	0.703072i	$-0.248189\pi$
$281$	13.4765	+	4.90506i	0.803942	+	0.292611i	0.0928232	+	0.995683i	$0.470411\pi$
$282$	6.36486	+	17.0360i	0.379022	+	1.01448i
$283$	−1.38317	+	7.84435i	−0.0822209	+	0.466298i	0.915701	+	0.401861i	$0.131636\pi$
$283$	−1.38317	+	7.84435i	−0.0822209	+	0.466298i	−0.997922	+	0.0644373i	$0.979475\pi$
$284$	2.71821	−	15.4157i	0.161296	−	0.914754i
$285$	16.3240	+	43.6924i	0.966951	+	2.58812i
$286$	0.578125	+	0.210420i	0.0341853	+	0.0124424i
$287$	−0.607891	+	8.68602i	−0.0358827	+	0.512720i
$288$	−15.8660	+	6.08166i	−0.934911	+	0.358365i
$289$	−16.5062			−0.970956
$290$	−0.741445	+	0.622146i	−0.0435392	+	0.0365337i
$291$	−3.13697	+	0.580626i	−0.183892	+	0.0340369i
$292$	2.45685	−	13.9335i	0.143776	−	0.815396i
$293$	3.09426	−	17.5484i	0.180768	−	1.02519i	−0.750504	−	0.660866i	$-0.770189\pi$
$293$	3.09426	−	17.5484i	0.180768	−	1.02519i	0.931273	−	0.364323i	$-0.118700\pi$
$294$	−19.7621	+	8.17751i	−1.15255	+	0.476922i
$295$	11.5816	−	9.71809i	0.674305	−	0.565809i
$296$	0.607924	−	1.05295i	0.0353348	−	0.0612018i
$297$	−12.5795	+	2.54992i	−0.729939	+	0.147962i
$298$	11.1197	+	19.2598i	0.644144	+	1.11569i
$299$	−0.136860	−	0.776170i	−0.00791480	−	0.0448871i
$300$	20.4917	−	12.0639i	1.18309	−	0.696510i
$301$	4.39303	+	15.3237i	0.253210	+	0.883241i
$302$	−26.8903	+	9.78727i	−1.54736	+	0.563194i
$303$	−4.70612	+	13.2796i	−0.270359	+	0.762891i
$304$	−24.7007	+	20.7264i	−1.41668	+	1.18874i
$305$	−0.454406	+	0.787055i	−0.0260192	+	0.0450666i
$306$	3.51537	+	1.21232i	0.200960	+	0.0693039i
$307$	−0.753447	+	1.30501i	−0.0430015	+	0.0744808i	−0.886725	−	0.462297i	$-0.847025\pi$
$307$	−0.753447	+	1.30501i	−0.0430015	+	0.0744808i	0.843724	+	0.536778i	$0.180359\pi$
$308$	2.95539	−	6.63687i	0.168399	−	0.378171i
$309$	3.88310	+	10.3934i	0.220902	+	0.591261i
$310$	−32.0113	+	11.6511i	−1.81812	+	0.661741i
$311$	−1.01822	+	5.77462i	−0.0577380	+	0.327449i	−0.999972	−	0.00750727i	$-0.997610\pi$
$311$	−1.01822	+	5.77462i	−0.0577380	+	0.327449i	0.942234	+	0.334956i	$0.108721\pi$
$312$	0.134122	+	0.358988i	0.00759316	+	0.0203237i
$313$	−1.42966	+	1.19963i	−0.0808090	+	0.0678068i	−0.682297	−	0.731075i	$-0.739019\pi$
$313$	−1.42966	+	1.19963i	−0.0808090	+	0.0678068i	0.601488	+	0.798882i	$0.294575\pi$
$314$	−7.43144	+	12.8716i	−0.419380	+	0.726388i
$315$	1.74802	−	33.0150i	0.0984899	−	1.86019i
$316$	−3.20599	−	5.55294i	−0.180351	−	0.312378i
$317$	9.31341	+	3.38980i	0.523093	+	0.190390i	0.590052	−	0.807365i	$-0.299107\pi$
$317$	9.31341	+	3.38980i	0.523093	+	0.190390i	−0.0669586	+	0.997756i	$0.521330\pi$
$318$	−3.79638	+	10.7125i	−0.212890	+	0.600726i
$319$	−0.249265	−	0.209158i	−0.0139561	−	0.0117106i
$320$	0.0508601	+	0.0426767i	0.00284316	+	0.00238570i
$321$	0.175408	+	20.6671i	0.00979031	+	1.15352i
$322$	−25.9091	+	2.72164i	−1.44386	+	0.151671i
$323$	4.54282			0.252769
$324$	7.87804	+	6.16716i	0.437669	+	0.342620i
$325$	−0.871867	−	1.51012i	−0.0483625	−	0.0837662i
$326$	13.4737	+	4.90401i	0.746236	+	0.271608i
$327$	−0.483035	−	0.273441i	−0.0267119	−	0.0151213i
$328$	0.895534	−	5.07882i	0.0494476	−	0.280431i
$329$	−4.33995	−	15.1385i	−0.239269	−	0.834614i
$330$	20.4106	+	23.9093i	1.12356	+	1.31616i
$331$	−9.12572	−	3.32149i	−0.501595	−	0.182566i	0.0788163	−	0.996889i	$-0.474886\pi$
$331$	−9.12572	−	3.32149i	−0.501595	−	0.182566i	−0.580411	+	0.814324i	$0.697108\pi$
$332$	1.33752	−	2.31664i	0.0734057	−	0.127142i
$333$	−2.32734	+	0.0395085i	−0.127537	+	0.00216505i
$334$	−17.6761	−	30.6159i	−0.967192	−	1.67522i
$335$	60.0611	+	21.8605i	3.28149	+	1.19436i
$336$	21.9165	−	6.48487i	1.19564	−	0.353778i
$337$	−16.7483	−	14.0535i	−0.912339	−	0.765543i	0.0602239	−	0.998185i	$-0.480819\pi$
$337$	−16.7483	−	14.0535i	−0.912339	−	0.765543i	−0.972562	+	0.232642i	$0.925263\pi$
$338$	21.5158	−	7.83112i	1.17031	−	0.425957i
$339$	2.33183	−	2.82736i	0.126648	−	0.153561i
$340$	−0.564995	−	3.20424i	−0.0306411	−	0.173775i
$341$	−5.72623	−	9.91812i	−0.310093	−	0.537096i
$342$	32.3433	+	11.1540i	1.74893	+	0.603141i
$343$	17.6148	−	5.72001i	0.951110	−	0.308852i
$344$	−1.63951	−	9.29812i	−0.0883964	−	0.501321i
$345$	13.4521	−	37.9587i	0.724238	−	2.04363i
$346$	−34.9575	−	29.3329i	−1.87933	−	1.57694i
$347$	−9.34786	+	3.40234i	−0.501819	+	0.182647i	−0.580512	−	0.814252i	$-0.697148\pi$
$347$	−9.34786	+	3.40234i	−0.501819	+	0.182647i	0.0786928	+	0.996899i	$0.474925\pi$
$348$	0.00215260	+	0.253626i	0.000115392	+	0.0135958i
$349$	−19.2188	+	16.1265i	−1.02876	+	0.863233i	−0.990703	−	0.136043i	$-0.956562\pi$
$349$	−19.2188	+	16.1265i	−1.02876	+	0.863233i	−0.0380577	+	0.999276i	$0.512117\pi$
$350$	−51.8064	+	25.2639i	−2.76917	+	1.35041i
$351$	0.457127	−	0.573841i	0.0243997	−	0.0306294i
$352$	−6.99537	+	12.1163i	−0.372854	+	0.645803i
$353$	9.30697	+	3.38746i	0.495360	+	0.180296i	0.577606	−	0.816316i	$-0.303987\pi$
$353$	9.30697	+	3.38746i	0.495360	+	0.180296i	−0.0822460	+	0.996612i	$0.526209\pi$
$354$	−0.0941184	−	11.0893i	−0.00500234	−	0.589390i
$355$	−44.9311	−	37.7016i	−2.38469	−	2.00100i
$356$	−0.944515	+	0.343775i	−0.0500592	+	0.0182201i
$357$	−2.95262	−	1.28488i	−0.156269	−	0.0680030i
$358$	5.98745	+	33.9565i	0.316447	+	1.79466i
$359$	−16.5248			−0.872144			−0.436072	−	0.899912i	$-0.643631\pi$
$359$	−16.5248			−0.872144			−0.436072	+	0.899912i	$0.643631\pi$
$360$	−3.07251	+	19.3391i	−0.161936	+	1.01926i
$361$	22.7965			1.19981
$362$	−3.81501	+	3.20117i	−0.200512	+	0.168250i
$363$	5.39808	−	6.54520i	0.283326	−	0.343534i
$364$	0.114441	+	0.399191i	0.00599834	+	0.0209233i
$365$	−40.6109	−	34.0766i	−2.12567	−	1.78365i
$366$	0.233307	+	0.624464i	0.0121952	+	0.0326413i
$367$	−5.50999	−	31.2487i	−0.287619	−	1.63117i	−0.695776	−	0.718259i	$-0.744939\pi$
$367$	−5.50999	−	31.2487i	−0.287619	−	1.63117i	0.408157	−	0.912912i	$-0.366172\pi$
$368$	27.8405			1.45129
$369$	−9.21904	+	3.53379i	−0.479924	+	0.183962i
$370$	2.85046	+	4.93715i	0.148188	+	0.256670i
$371$	4.00353	−	8.99068i	0.207853	−	0.466773i
$372$	−2.98188	+	8.41417i	−0.154603	+	0.436254i
$373$	−4.16072	+	23.5966i	−0.215434	+	1.22179i	0.664718	+	0.747094i	$0.268552\pi$
$373$	−4.16072	+	23.5966i	−0.215434	+	1.22179i	−0.880152	+	0.474692i	$0.842559\pi$
$374$	2.87716	−	1.04720i	0.148774	−	0.0541494i
$375$	−0.450040	−	53.0250i	−0.0232400	−	2.73820i
$376$	1.61970	+	9.18578i	0.0835296	+	0.473720i
$377$	0.0185992			0.000957907
$378$	−17.8669	−	16.3975i	−0.918972	−	0.843396i
$379$	18.5458			0.952632			0.476316	−	0.879274i	$-0.341972\pi$
$379$	18.5458			0.952632			0.476316	+	0.879274i	$0.341972\pi$
$380$	−5.19826	−	29.4808i	−0.266665	−	1.51233i
$381$	−15.7172	−	8.89734i	−0.805217	−	0.455825i
$382$	13.5200	−	4.92090i	0.691746	−	0.251775i
$383$	−3.93094	+	22.2935i	−0.200862	+	1.13914i	0.702959	+	0.711231i	$0.251862\pi$
$383$	−3.93094	+	22.2935i	−0.200862	+	1.13914i	−0.903820	+	0.427912i	$0.859249\pi$
$384$	−19.2447	+	3.56202i	−0.982075	+	0.181774i
$385$	−15.9996	−	22.0243i	−0.815416	−	1.12246i
$386$	−2.61552	−	4.53021i	−0.133126	−	0.230581i
$387$	−13.6473	+	11.8519i	−0.693731	+	0.602468i
$388$	2.04754			0.103948
$389$	1.59902	+	9.06849i	0.0810735	+	0.459791i	0.998135	+	0.0610450i	$0.0194433\pi$
$389$	1.59902	+	9.06849i	0.0810735	+	0.459791i	−0.917061	+	0.398746i	$0.869446\pi$
$390$	−1.77217	−	0.296995i	−0.0897372	−	0.0150389i
$391$	−3.00470	−	2.52124i	−0.151954	−	0.127505i
$392$	−10.7298	+	2.27939i	−0.541937	+	0.115127i
$393$	10.3183	+	1.72924i	0.520490	+	0.0872284i
$394$	24.2124	−	20.3166i	1.21980	−	1.02354i
$395$	−24.0256			−1.20886
$396$	8.23672	−	0.139825i	0.413911	−	0.00702649i
$397$	−16.3534			−0.820753			−0.410376	−	0.911916i	$-0.634603\pi$
$397$	−16.3534			−0.820753			−0.410376	+	0.911916i	$0.634603\pi$
$398$	3.60454	+	20.4424i	0.180679	+	1.02468i
$399$	−27.1657	−	11.8216i	−1.35999	−	0.591820i
$400$	57.8813	−	21.0671i	2.89406	−	1.05335i
$401$	28.0881	+	23.5687i	1.40265	+	1.17697i	0.959906	+	0.280321i	$0.0904410\pi$
$401$	28.0881	+	23.5687i	1.40265	+	1.17697i	0.442748	+	0.896646i	$0.354003\pi$
$402$	40.4013	−	23.7852i	2.01504	−	1.18630i
$403$	0.615137	+	0.223891i	0.0306421	+	0.0111528i
$404$	4.52118	−	7.83092i	0.224937	−	0.389603i
$405$	34.7717	−	14.0099i	1.72782	−	0.696159i
$406$	0.0429209	−	0.613287i	0.00213013	−	0.0304369i
$407$	−1.46819	+	1.23195i	−0.0727753	+	0.0610657i
$408$	1.65971	+	0.939546i	0.0821681	+	0.0465144i
$409$	−1.51858	+	0.552719i	−0.0750891	+	0.0273302i	−0.379292	−	0.925277i	$-0.623832\pi$
$409$	−1.51858	+	0.552719i	−0.0750891	+	0.0273302i	0.304203	+	0.952607i	$0.401610\pi$
$410$	18.5239	+	15.5434i	0.914829	+	0.767633i
$411$	4.36612	−	0.808131i	0.215365	−	0.0398622i
$412$	−1.23655	−	7.01280i	−0.0609203	−	0.345496i
$413$	−0.670435	+	9.57970i	−0.0329900	+	0.471386i
$414$	−15.2020	−	25.3279i	−0.747138	−	1.24480i
$415$	−5.01164	−	8.68041i	−0.246012	−	0.426104i
$416$	−0.138867	−	0.787552i	−0.00680849	−	0.0386129i
$417$	1.91400	+	5.12298i	0.0937292	+	0.250873i
$418$	26.4715	−	9.63482i	1.29476	−	0.471255i
$419$	11.2741	+	9.46013i	0.550778	+	0.462158i	0.875204	−	0.483753i	$-0.160727\pi$
$419$	11.2741	+	9.46013i	0.550778	+	0.462158i	−0.324426	+	0.945911i	$0.605171\pi$
$420$	−4.95965	+	20.6314i	−0.242006	+	1.00671i
$421$	12.7240	+	4.63116i	0.620130	+	0.225709i	0.632930	−	0.774209i	$-0.281852\pi$
$421$	12.7240	+	4.63116i	0.620130	+	0.225709i	−0.0127998	+	0.999918i	$0.504074\pi$
$422$	4.29806	+	7.44446i	0.209226	+	0.362390i
$423$	13.4824	−	11.7087i	0.655537	−	0.569299i
$424$	−2.91456	+	5.04817i	−0.141544	+	0.245161i
$425$	−8.15470	−	2.96807i	−0.395561	−	0.143972i
$426$	−42.3043	+	7.83016i	−2.04965	+	0.379373i
$427$	−0.159083	−	0.554910i	−0.00769858	−	0.0268540i
$428$	2.30342	−	13.0633i	0.111340	−	0.631440i
$429$	−0.00512691	−	0.604068i	−0.000247530	−	0.0291647i
$430$	41.6002	+	15.1412i	2.00614	+	0.730176i
$431$	−10.9091	−	18.8951i	−0.525472	−	0.910145i	−0.999560	−	0.0296670i	$-0.990555\pi$
$431$	−10.9091	−	18.8951i	−0.525472	−	0.910145i	0.474088	−	0.880478i	$-0.342778\pi$
$432$	17.1585	+	19.4223i	0.825539	+	0.934454i
$433$	10.1358			0.487096			0.243548	−	0.969889i	$-0.421689\pi$
$433$	10.1358			0.487096			0.243548	+	0.969889i	$0.421689\pi$
$434$	8.80210	−	19.7668i	0.422514	−	0.948835i
$435$	0.827043	+	0.468180i	0.0396537	+	0.0224475i
$436$	0.272900	+	0.228990i	0.0130695	+	0.0109666i
$437$	−27.6449	−	23.1968i	−1.32244	−	1.10966i
$438$	−38.2368	+	7.07729i	−1.82702	+	0.338166i
$439$	−2.67426	−	0.973350i	−0.127635	−	0.0464554i	0.277413	−	0.960751i	$-0.410523\pi$
$439$	−2.67426	−	0.973350i	−0.127635	−	0.0464554i	−0.405048	+	0.914295i	$0.632745\pi$
$440$	8.06167	+	13.9632i	0.384325	+	0.665671i
$441$	14.3128	+	15.3669i	0.681563	+	0.731759i
$442$	−0.0875055	+	0.151564i	−0.00416221	+	0.00720916i
$443$	−4.88441	+	4.09850i	−0.232065	+	0.194726i	−0.751404	−	0.659843i	$-0.770623\pi$
$443$	−4.88441	+	4.09850i	−0.232065	+	0.194726i	0.519339	+	0.854569i	$0.326178\pi$
$444$	1.47338	+	0.246922i	0.0699236	+	0.0117184i
$445$	−0.653995	+	3.70899i	−0.0310023	+	0.175823i
$446$	−32.4003	+	11.7927i	−1.53420	+	0.558402i
$447$	13.8939	−	16.8464i	0.657157	−	0.796807i
$448$	−0.0419411	+	0.00440573i	−0.00198153	+	0.000208151i
$449$	−2.33757	+	4.04880i	−0.110317	+	0.191074i	−0.915898	−	0.401411i	$-0.868520\pi$
$449$	−2.33757	+	4.04880i	−0.110317	+	0.191074i	0.805581	+	0.592485i	$0.201853\pi$
$450$	−50.7712	−	41.1540i	−2.39338	−	1.94002i
$451$	−4.06471	+	7.04029i	−0.191400	+	0.331514i
$452$	−1.80187	+	1.51195i	−0.0847527	+	0.0711159i
$453$	18.2431	+	21.3702i	0.857134	+	1.00406i
$454$	20.4086	−	7.42813i	0.957824	−	0.348620i
$455$	1.50977	+	0.376520i	0.0707790	+	0.0176515i
$456$	15.2703	+	8.64434i	0.715096	+	0.404808i
$457$	3.33384	+	18.9071i	0.155950	+	0.884438i	0.957912	+	0.287062i	$0.0926787\pi$
$457$	3.33384	+	18.9071i	0.155950	+	0.884438i	−0.801962	+	0.597375i	$0.796210\pi$
$458$	22.6120	+	39.1651i	1.05659	+	1.83006i
$459$	−0.0929549	−	3.65003i	−0.00433876	−	0.170369i
$460$	−12.9235	+	22.3841i	−0.602561	+	1.04367i
$461$	−1.41824	+	1.19004i	−0.0660540	+	0.0554259i	−0.675217	−	0.737619i	$-0.735950\pi$
$461$	−1.41824	+	1.19004i	−0.0660540	+	0.0554259i	0.609163	+	0.793045i	$0.291506\pi$
$462$	−19.9303	−	1.22494i	−0.927240	−	0.0569893i
$463$	−2.62612	+	14.8935i	−0.122046	+	0.692158i	0.860972	+	0.508652i	$0.169856\pi$
$463$	−2.62612	+	14.8935i	−0.122046	+	0.692158i	−0.983019	+	0.183506i	$0.941255\pi$
$464$	−0.114087	+	0.647020i	−0.00529636	+	0.0300371i
$465$	21.7172	+	25.4400i	1.00711	+	1.17975i
$466$	9.90976	−	8.31528i	0.459061	−	0.385198i
$467$	−24.7350			−1.14460			−0.572300	−	0.820044i	$-0.693949\pi$
$467$	−24.7350			−1.14460			−0.572300	+	0.820044i	$0.693949\pi$
$468$	−0.355520	+	0.308750i	−0.0164339	+	0.0142720i
$469$	−36.4905	+	17.7950i	−1.68497	+	0.821696i
$470$	−41.0976	−	14.9583i	−1.89569	−	0.689975i
$471$	14.3931	+	2.41212i	0.663197	+	0.111144i
$472$	0.987672	−	5.60137i	0.0454613	−	0.257824i
$473$	−2.58441	+	14.6569i	−0.118831	+	0.673926i
$474$	−11.2129	+	13.5957i	−0.515024	+	0.624469i
$475$	−75.0277	−	27.3079i	−3.44251	−	1.25297i
$476$	1.71329	+	1.15577i	0.0785285	+	0.0529748i
$477$	11.1579	−	0.189415i	0.510886	−	0.00867273i
$478$	26.1831			1.19759
$479$	24.2765	−	20.3704i	1.10922	−	0.930748i	0.111211	−	0.993797i	$-0.464527\pi$
$479$	24.2765	−	20.3704i	1.10922	−	0.930748i	0.998010	+	0.0630491i	$0.0200825\pi$
$480$	13.6494	−	38.5153i	0.623006	−	1.75798i
$481$	0.0190232	−	0.107886i	0.000867385	−	0.00491918i
$482$	−5.36018	+	30.3991i	−0.244149	+	1.38464i
$483$	11.4069	+	22.8958i	0.519034	+	1.04180i
$484$	−4.17124	+	3.50008i	−0.189602	+	0.159095i
$485$	3.83605	−	6.64423i	0.174186	−	0.301699i
$486$	8.30016	−	26.2152i	0.376503	−	1.18915i
$487$	15.0234	+	26.0213i	0.680775	+	1.17914i	0.974745	+	0.223323i	$0.0716904\pi$
$487$	15.0234	+	26.0213i	0.680775	+	1.17914i	−0.293969	+	0.955815i	$0.594976\pi$
$488$	0.0593709	+	0.336709i	0.00268760	+	0.0152421i
$489$	−0.119487	−	14.0783i	−0.00540337	−	0.636641i
$490$	15.8994	−	48.9140i	0.718261	−	2.20971i
$491$	29.0255	−	10.5644i	1.30990	−	0.476766i	0.409695	−	0.912223i	$-0.365635\pi$
$491$	29.0255	−	10.5644i	1.30990	−	0.476766i	0.900210	+	0.435456i	$0.143413\pi$
$492$	6.23085	−	1.15328i	0.280909	−	0.0519937i
$493$	0.0709071	−	0.0594981i	0.00319350	−	0.00267966i
$494$	−0.805098	+	1.39447i	−0.0362231	+	0.0627402i
$495$	14.9777	−	26.9899i	0.673196	−	1.21311i
$496$	−11.5619	+	20.0257i	−0.519143	+	0.899182i
$497$	37.0518	−	3.89213i	1.66200	−	0.174586i
$498$	−7.25106	−	1.21520i	−0.324928	−	0.0544543i
$499$	−14.5259	+	5.28698i	−0.650267	+	0.236678i	−0.646029	−	0.763313i	$-0.723571\pi$
$499$	−14.5259	+	5.28698i	−0.650267	+	0.236678i	−0.00423824	+	0.999991i	$0.501349\pi$
$500$	−5.90983	+	33.5163i	−0.264295	+	1.49889i
$501$	−22.0860	+	26.7794i	−0.986731	+	1.19642i
$502$	17.9012	−	15.0209i	0.798970	−	0.670415i
$503$	−12.4023	+	21.4813i	−0.552989	+	0.957806i	0.445067	+	0.895497i	$0.353180\pi$
$503$	−12.4023	+	21.4813i	−0.552989	+	0.957806i	−0.998057	+	0.0623088i	$0.980154\pi$
$504$	−7.48001	−	9.93741i	−0.333186	−	0.442648i
$505$	−16.9408	−	29.3423i	−0.753854	−	1.30571i
$506$	−22.8560	−	8.31889i	−1.01607	−	0.369820i
$507$	−14.5969	−	17.0990i	−0.648270	−	0.759395i
$508$	8.87973	+	7.45098i	0.393974	+	0.330584i
$509$	1.04593	+	0.877641i	0.0463601	+	0.0389008i	0.665673	−	0.746243i	$-0.268144\pi$
$509$	1.04593	+	0.877641i	0.0463601	+	0.0389008i	−0.619313	+	0.785144i	$0.712589\pi$
$510$	−7.70625	+	4.53684i	−0.341239	+	0.200895i
$511$	33.4893	−	3.51790i	1.48148	−	0.155623i
$512$	12.6175			0.557620
$513$	−0.855236	−	33.5823i	−0.0377596	−	1.48270i
$514$	19.1446	+	33.1594i	0.844430	+	1.46260i
$515$	−25.0730	−	9.12584i	−1.10485	−	0.402132i
$516$	9.99714	−	5.88554i	0.440100	−	0.259097i
$517$	2.55319	−	14.4798i	0.112289	−	0.636823i
$518$	−3.51352	−	0.876236i	−0.154375	−	0.0384996i
$519$	−14.9672	+	42.2339i	−0.656988	+	1.85386i
$520$	−0.866020	−	0.315205i	−0.0379775	−	0.0138227i
$521$	13.2774	−	22.9971i	0.581693	−	1.00752i	−0.413586	−	0.910465i	$-0.635724\pi$
$521$	13.2774	−	22.9971i	0.581693	−	1.00752i	0.995279	−	0.0970569i	$-0.0309429\pi$
$522$	0.650921	−	0.249507i	0.0284900	−	0.0109206i
$523$	17.0005	+	29.4458i	0.743381	+	1.28757i	0.950947	+	0.309353i	$0.100113\pi$
$523$	17.0005	+	29.4458i	0.743381	+	1.28757i	−0.207566	+	0.978221i	$0.566554\pi$
$524$	−6.30983	−	2.29659i	−0.275646	−	0.100327i
$525$	41.0408	+	38.9694i	1.79117	+	1.70077i
$526$	14.6522	+	12.2947i	0.638866	+	0.536072i
$527$	3.06136	−	1.11424i	0.133355	−	0.0485372i
$528$	21.0455	+	3.52699i	0.915886	+	0.153492i
$529$	1.41679	+	8.03502i	0.0615996	+	0.349349i
$530$	−13.6659	−	23.6701i	−0.593610	−	1.02816i
$531$	−10.1676	+	3.89737i	−0.441234	+	0.169131i
$532$	15.7632	+	10.6337i	0.683422	+	0.461032i
$533$	−0.0806895	−	0.457613i	−0.00349505	−	0.0198214i
$534$	1.79363	+	2.10109i	0.0776180	+	0.0909231i
$535$	−38.0748	−	31.9485i	−1.64612	−	1.38125i
$536$	22.5955	−	8.22410i	0.975979	−	0.355227i
$537$	29.1755	−	17.1763i	1.25902	−	0.741211i
$538$	18.0851	−	15.1752i	0.779705	−	0.654250i
$539$	17.1226	+	2.40845i	0.737524	+	0.103739i
$540$	−23.5807	+	4.77990i	−1.01475	+	0.205694i
$541$	−1.17215	+	2.03023i	−0.0503948	+	0.0872863i	−0.890122	−	0.455722i	$-0.849381\pi$
$541$	−1.17215	+	2.03023i	−0.0503948	+	0.0872863i	0.839728	+	0.543008i	$0.182715\pi$
$542$	35.5233	+	12.9294i	1.52586	+	0.555366i
$543$	4.25544	+	2.40896i	0.182618	+	0.103378i
$544$	−3.04876	−	2.55822i	−0.130715	−	0.109683i
$545$	1.25434	−	0.456543i	0.0537300	−	0.0195561i
$546$	0.917684	−	0.678628i	0.0392732	−	0.0290426i
$547$	3.75899	+	21.3183i	0.160723	+	0.911504i	0.953366	+	0.301818i	$0.0975934\pi$
$547$	3.75899	+	21.3183i	0.160723	+	0.911504i	−0.792643	+	0.609686i	$0.791296\pi$
$548$	−2.84983			−0.121739
$549$	0.494205	−	0.429190i	0.0210921	−	0.0183174i
$550$	−53.8132			−2.29460
$551$	0.652385	−	0.547416i	0.0277925	−	0.0233207i
$552$	−5.30247	−	14.1925i	−0.225688	−	0.604071i
$553$	10.6016	−	10.9770i	0.450825	−	0.466789i
$554$	7.39207	+	6.20268i	0.314059	+	0.263527i
$555$	3.56162	−	4.31848i	0.151182	−	0.183309i
$556$	−0.609501	−	3.45665i	−0.0258486	−	0.146595i
$557$	−9.14873			−0.387644			−0.193822	−	0.981037i	$-0.562088\pi$
$557$	−9.14873			−0.387644			−0.193822	+	0.981037i	$0.562088\pi$
$558$	24.5316	−	0.416445i	1.03851	−	0.0176295i
$559$	−0.425352	−	0.736731i	−0.0179905	−	0.0311604i
$560$	−22.3591	+	50.2115i	−0.944844	+	2.12182i
$561$	−1.95194	−	2.28653i	−0.0824109	−	0.0965375i
$562$	−4.39297	+	24.9138i	−0.185306	+	1.05092i
$563$	−31.8857	+	11.6055i	−1.34382	+	0.489111i	−0.911014	−	0.412374i	$-0.864700\pi$
$563$	−31.8857	+	11.6055i	−1.34382	+	0.489111i	−0.432808	+	0.901486i	$0.642477\pi$
$564$	−9.87635	+	5.81443i	−0.415869	+	0.244832i
$565$	1.53045	+	8.67962i	0.0643866	+	0.365155i
$566$	−14.0508			−0.590599
$567$	−8.94247	+	22.0688i	−0.375548	+	0.926803i
$568$	−22.0659			−0.925866
$569$	3.23972	+	18.3734i	0.135816	+	0.770251i	0.974288	+	0.225306i	$0.0723383\pi$
$569$	3.23972	+	18.3734i	0.135816	+	0.770251i	−0.838472	+	0.544945i	$0.816551\pi$
$570$	−70.9018	+	41.7415i	−2.96975	+	1.74836i
$571$	−3.69402	+	1.34451i	−0.154590	+	0.0562661i	−0.418156	−	0.908375i	$-0.637323\pi$
$571$	−3.69402	+	1.34451i	−0.154590	+	0.0562661i	0.263566	+	0.964641i	$0.415101\pi$
$572$	−0.0673255	+	0.381822i	−0.00281502	+	0.0159648i
$573$	−9.17234	−	10.7446i	−0.383180	−	0.448864i
$574$	−15.2755	+	1.60462i	−0.637585	+	0.0669756i
$575$	34.4689	+	59.7019i	1.43745	+	2.48974i
$576$	−0.0246086	−	0.0410001i	−0.00102536	−	0.00170834i
$577$	7.95004			0.330965			0.165482	−	0.986213i	$-0.447082\pi$
$577$	7.95004			0.330965			0.165482	+	0.986213i	$0.447082\pi$
$578$	−5.05608	−	28.6745i	−0.210305	−	1.19270i
$579$	−3.26805	+	3.96253i	−0.135816	+	0.164677i
$580$	−0.467253	−	0.392072i	−0.0194016	−	0.0162799i
$581$	6.17742	+	1.54058i	0.256282	+	0.0639141i
$582$	−1.96955	−	5.27166i	−0.0816406	−	0.218517i
$583$	7.03891	−	5.90634i	0.291522	−	0.244616i
$584$	−19.9443			−0.825300
$585$	0.335824	+	1.73209i	0.0138846	+	0.0716133i
$586$	31.4327			1.29847
$587$	−3.92585	−	22.2646i	−0.162037	−	0.918958i	−0.952067	−	0.305890i	$-0.901046\pi$
$587$	−3.92585	−	22.2646i	−0.162037	−	0.918958i	0.790030	−	0.613068i	$-0.210065\pi$
$588$	−7.23772	−	11.3699i	−0.298478	−	0.468885i
$589$	28.1662	−	10.2516i	1.16057	−	0.422412i
$590$	20.4297	+	17.1426i	0.841079	+	0.705749i
$591$	−27.0076	−	15.2887i	−1.11095	−	0.628894i
$592$	3.63640	+	1.32354i	0.149455	+	0.0543973i
$593$	−11.6835	+	20.2365i	−0.479785	+	0.831011i	−0.999731	−	0.0231874i	$-0.992619\pi$
$593$	−11.6835	+	20.2365i	−0.479785	+	0.831011i	0.519946	+	0.854199i	$0.325952\pi$
$594$	−8.28298	−	21.0720i	−0.339855	−	0.864593i
$595$	6.96028	−	3.39426i	0.285344	−	0.139151i
$596$	−10.7361	+	9.00870i	−0.439770	+	0.369011i
$597$	17.5641	−	10.3404i	0.718852	−	0.423204i
$598$	1.30643	−	0.475502i	0.0534240	−	0.0194447i
$599$	−25.1192	−	21.0775i	−1.02634	−	0.861204i	−0.0359318	−	0.999354i	$-0.511440\pi$
$599$	−25.1192	−	21.0775i	−1.02634	−	0.861204i	−0.990411	+	0.138150i	$0.955884\pi$
$600$	−21.7635	−	25.4941i	−0.888490	−	1.04079i
$601$	6.43928	+	36.5190i	0.262664	+	1.48964i	0.775606	+	0.631217i	$0.217444\pi$
$601$	6.43928	+	36.5190i	0.262664	+	1.48964i	−0.512943	+	0.858423i	$0.671445\pi$
$602$	−25.2745	+	12.3254i	−1.03011	+	0.502344i
$603$	−35.7613	−	28.9873i	−1.45631	−	1.18045i
$604$	−9.01681	−	15.6176i	−0.366889	−	0.635470i
$605$	3.54292	+	20.0929i	0.144040	+	0.816893i
$606$	−24.5106	−	4.10771i	−0.995677	−	0.166864i
$607$	−14.1208	+	5.13953i	−0.573144	+	0.208607i	−0.612300	−	0.790626i	$-0.709755\pi$
$607$	−14.1208	+	5.13953i	−0.573144	+	0.208607i	0.0391558	+	0.999233i	$0.487533\pi$
$608$	−28.0503	−	23.5370i	−1.13759	−	0.954551i
$609$	−0.578849	+	0.171275i	−0.0234561	+	0.00694043i
$610$	−1.50645	−	0.548304i	−0.0609945	−	0.0222002i
$611$	0.420213	+	0.727830i	0.0170000	+	0.0294449i
$612$	−0.367697	+	2.31437i	−0.0148633	+	0.0935529i
$613$	14.0661	−	24.3632i	0.568125	−	0.984021i	−0.428627	−	0.903482i	$-0.641002\pi$
$613$	14.0661	−	24.3632i	0.568125	−	0.984021i	0.996751	−	0.0805393i	$-0.0256643\pi$
$614$	−2.49784	−	0.909139i	−0.100805	−	0.0366899i
$615$	7.93107	−	22.3796i	0.319812	−	0.902433i
$616$	−9.93693	−	2.47817i	−0.400370	−	0.0998482i
$617$	0.135031	−	0.765797i	0.00543613	−	0.0308298i	−0.981969	−	0.189042i	$-0.939462\pi$
$617$	0.135031	−	0.765797i	0.00543613	−	0.0308298i	0.987405	+	0.158212i	$0.0505729\pi$
$618$	−16.8659	+	9.92933i	−0.678445	+	0.399416i
$619$	10.3239	+	3.75760i	0.414953	+	0.151031i	0.541056	−	0.840987i	$-0.318025\pi$
$619$	10.3239	+	3.75760i	0.414953	+	0.151031i	−0.126103	+	0.992017i	$0.540247\pi$
$620$	−10.7340	−	18.5918i	−0.431087	−	0.746664i
$621$	−18.0724	+	22.6866i	−0.725219	+	0.910382i
$622$	−10.3435			−0.414737
$623$	−1.40601	−	1.93544i	−0.0563305	−	0.0775417i
$624$	−1.05109	+	0.618803i	−0.0420775	+	0.0247719i
$625$	50.3844	+	42.2775i	2.01538	+	1.69110i
$626$	−2.52190	−	2.11612i	−0.100795	−	0.0845773i
$627$	−17.9589	−	21.0374i	−0.717209	−	0.840152i
$628$	−8.80160	−	3.20352i	−0.351222	−	0.127834i
$629$	−0.272600	−	0.472157i	−0.0108693	−	0.0188262i
$630$	57.8888	−	7.07630i	2.30635	−	0.281927i
$631$	21.9799	−	38.0704i	0.875008	−	1.51556i	0.0182532	−	0.999833i	$-0.494190\pi$
$631$	21.9799	−	38.0704i	0.875008	−	1.51556i	0.856755	−	0.515724i	$-0.172477\pi$
$632$	−6.92399	+	5.80992i	−0.275422	+	0.231106i
$633$	5.37037	−	6.51160i	0.213453	−	0.258813i
$634$	−3.03591	+	17.2175i	−0.120571	+	0.683794i
$635$	40.8143	−	14.8552i	1.61967	−	0.589510i
$636$	−7.06381	−	1.18382i	−0.280098	−	0.0469414i
$637$	−0.838231	+	0.523650i	−0.0332119	+	0.0207478i
$638$	0.286994	−	0.497088i	0.0113622	−	0.0196799i
$639$	21.7399	+	36.2206i	0.860017	+	1.43286i
$640$	23.5334	−	40.7610i	0.930238	−	1.61122i
$641$	−25.0939	+	21.0563i	−0.991149	+	0.831673i	−0.985734	−	0.168312i	$-0.946168\pi$
$641$	−25.0939	+	21.0563i	−0.991149	+	0.831673i	−0.00541559	+	0.999985i	$0.501724\pi$
$642$	−35.8488	+	6.63531i	−1.41484	+	0.261875i
$643$	15.9951	−	5.82174i	0.630785	−	0.229587i	−0.00678774	−	0.999977i	$-0.502161\pi$
$643$	15.9951	−	5.82174i	0.630785	−	0.229587i	0.637573	+	0.770390i	$0.279938\pi$
$644$	−4.52439	−	15.7819i	−0.178286	−	0.621892i
$645$	−0.368918	−	43.4670i	−0.0145261	−	1.71151i
$646$	1.39153	+	7.89174i	0.0547489	+	0.310496i
$647$	14.6339	+	25.3466i	0.575317	+	0.996479i	0.996007	+	0.0892745i	$0.0284548\pi$
$647$	14.6339	+	25.3466i	0.575317	+	0.996479i	−0.420690	+	0.907205i	$0.638212\pi$
$648$	6.63303	−	12.4461i	0.260570	−	0.488931i
$649$	−4.48291	+	7.76464i	−0.175970	+	0.304789i
$650$	2.35629	−	1.97717i	0.0924215	−	0.0775508i
$651$	−21.2062	−	1.30336i	−0.831137	−	0.0510827i
$652$	−1.56907	+	8.89865i	−0.0614496	+	0.348498i
$653$	3.95607	−	22.4360i	0.154813	−	0.877988i	−0.804144	−	0.594435i	$-0.797376\pi$
$653$	3.95607	−	22.4360i	0.154813	−	0.877988i	0.958957	−	0.283553i	$-0.0915132\pi$
$654$	0.327058	−	0.922881i	0.0127890	−	0.0360875i
$655$	−19.2738	+	16.1726i	−0.753088	+	0.631916i
$656$	16.4142			0.640865
$657$	19.6496	+	32.7379i	0.766604	+	1.27723i
$658$	24.9691	−	12.1764i	0.973396	−	0.474687i
$659$	−1.59882	−	0.581922i	−0.0622810	−	0.0226684i	0.310692	−	0.950511i	$-0.399439\pi$
$659$	−1.59882	−	0.581922i	−0.0622810	−	0.0226684i	−0.372973	+	0.927842i	$0.621662\pi$
$660$	−12.6050	+	15.2836i	−0.490648	+	0.594914i
$661$	−2.71224	+	15.3819i	−0.105494	+	0.598285i	0.885528	+	0.464586i	$0.153797\pi$
$661$	−2.71224	+	15.3819i	−0.105494	+	0.598285i	−0.991022	+	0.133699i	$0.957314\pi$
$662$	2.97473	−	16.8705i	0.115616	−	0.655691i
$663$	0.169479	+	0.0284028i	0.00658201	+	0.00110307i
$664$	−3.54344	−	1.28971i	−0.137512	−	0.0500503i
$665$	64.0384	−	31.2290i	2.48330	−	1.21101i
$666$	−0.781527	−	4.03092i	−0.0302836	−	0.156195i
$667$	−0.735312			−0.0284714
$668$	17.0664	−	14.3204i	0.660320	−	0.554075i
$669$	21.9811	+	25.7491i	0.849840	+	0.995518i
$670$	−19.5782	+	111.034i	−0.756373	+	4.28960i
$671$	0.0935884	−	0.530766i	0.00361294	−	0.0204900i
$672$	11.5742	+	23.2316i	0.446485	+	0.896178i
$673$	−27.8478	+	23.3671i	−1.07346	+	0.900736i	−0.995361	−	0.0962102i	$-0.969328\pi$
$673$	−27.8478	+	23.3671i	−1.07346	+	0.900736i	−0.0780940	+	0.996946i	$0.524883\pi$
$674$	19.2834	−	33.3997i	0.742767	−	1.28651i
$675$	−20.4059	+	60.8415i	−0.785424	+	2.34179i
$676$	7.21466	+	12.4961i	0.277487	+	0.480621i
$677$	−5.55448	−	31.5010i	−0.213476	−	1.21068i	−0.883531	−	0.468372i	$-0.844841\pi$
$677$	−5.55448	−	31.5010i	−0.213476	−	1.21068i	0.670055	−	0.742311i	$-0.266270\pi$
$678$	5.62592	+	3.18477i	0.216062	+	0.122311i
$679$	1.34296	+	4.68449i	0.0515382	+	0.179774i
$680$	−4.30993	+	1.56869i	−0.165278	+	0.0601563i
$681$	−13.8457	−	16.2191i	−0.530569	−	0.621518i
$682$	15.4756	−	12.9856i	0.592592	−	0.497244i
$683$	0.740434	−	1.28247i	0.0283319	−	0.0490723i	−0.851512	−	0.524335i	$-0.824314\pi$
$683$	0.740434	−	1.28247i	0.0283319	−	0.0490723i	0.879844	+	0.475263i	$0.157647\pi$
$684$	−3.38301	+	21.2935i	−0.129353	+	0.814177i
$685$	−5.33912	+	9.24762i	−0.203997	+	0.353333i
$686$	15.3324	+	28.8481i	0.585393	+	1.10143i
$687$	28.2534	−	34.2574i	1.07793	−	1.30700i
$688$	28.2382	−	10.2779i	1.07657	−	0.391839i
$689$	−0.0912029	+	0.517237i	−0.00347455	+	0.0197052i
$690$	70.0620	+	11.7416i	2.66721	+	0.446995i
$691$	6.74135	−	5.65666i	0.256453	−	0.215190i	−0.505492	−	0.862831i	$-0.668689\pi$
$691$	6.74135	−	5.65666i	0.256453	−	0.215190i	0.761945	+	0.647642i	$0.224245\pi$
$692$	14.3790	−	24.9052i	0.546609	−	0.946755i
$693$	5.72228	+	18.7527i	0.217371	+	0.712357i
$694$	−8.77388	−	15.1968i	−0.333052	−	0.576863i
$695$	−12.3586	−	4.49818i	−0.468790	−	0.170626i
$696$	0.351564	−	0.0650715i	0.0133260	−	0.00246653i
$697$	−1.77151	−	1.48647i	−0.0671006	−	0.0563041i
$698$	−33.9018	−	28.4470i	−1.28320	−	1.07673i
$699$	−11.0538	−	6.25745i	−0.418094	−	0.236678i
$700$	−21.3485	−	29.3873i	−0.806899	−	1.11074i
$701$	1.01529			0.0383469			0.0191734	−	0.999816i	$-0.493897\pi$
$701$	1.01529			0.0383469			0.0191734	+	0.999816i	$0.493897\pi$
$702$	1.13689	+	0.618341i	0.0429093	+	0.0233378i
$703$	−2.50807	−	4.34411i	−0.0945937	−	0.163841i
$704$	−0.0369987	−	0.0134664i	−0.00139444	−	0.000507534i
$705$	0.364461	+	42.9418i	0.0137264	+	1.61728i
$706$	−3.03381	+	17.2056i	−0.114179	+	0.647540i
$707$	20.8814	+	5.20761i	0.785327	+	0.195852i
$708$	6.87193	−	1.27193i	0.258263	−	0.0478022i
$709$	−42.0314	−	15.2982i	−1.57852	−	0.574535i	−0.603639	−	0.797258i	$-0.706283\pi$
$709$	−42.0314	−	15.2982i	−1.57852	−	0.574535i	−0.974882	+	0.222723i	$0.928505\pi$
$710$	51.7319	−	89.6023i	1.94146	−	3.36271i
$711$	16.3585	+	5.64145i	0.613492	+	0.211571i
$712$	0.708440	+	1.22705i	0.0265499	+	0.0459858i
$713$	−24.3192	−	8.85147i	−0.910762	−	0.331490i
$714$	1.32765	−	5.52283i	0.0496861	−	0.206687i
$715$	1.11287	+	0.933808i	0.0416189	+	0.0349224i
$716$	−20.4188	+	7.43184i	−0.763087	+	0.277741i
$717$	−8.99773	−	24.0831i	−0.336027	−	0.899400i
$718$	−5.06175	−	28.7066i	−0.188903	−	1.07132i
$719$	−2.63441	−	4.56292i	−0.0982467	−	0.170168i	0.812712	−	0.582665i	$-0.197990\pi$
$719$	−2.63441	−	4.56292i	−0.0982467	−	0.170168i	−0.910959	+	0.412497i	$0.864657\pi$
$720$	−62.3152	+	1.05785i	−2.32235	+	0.0394239i
$721$	15.2333	−	7.42867i	0.567316	−	0.276658i
$722$	6.98286	+	39.6017i	0.259875	+	1.47382i
$723$	29.8030	−	5.51627i	1.10838	−	0.205152i
$724$	−2.40419	−	2.01735i	−0.0893510	−	0.0749744i
$725$	−1.52874	+	0.556414i	−0.0567758	+	0.0206647i
$726$	13.0238	+	7.37260i	0.483357	+	0.273623i
$727$	31.0047	−	26.0161i	1.14990	−	0.964882i	0.150185	−	0.988658i	$-0.452013\pi$
$727$	31.0047	−	26.0161i	1.14990	−	0.964882i	0.999717	+	0.0237758i	$0.00756878\pi$
$728$	0.526155	−	0.256585i	0.0195006	−	0.00950969i
$729$	−26.9650	+	1.37432i	−0.998704	+	0.0509007i
$730$	46.7579	−	80.9870i	1.73059	−	2.99746i
$731$	−3.97838	−	1.44801i	−0.147146	−	0.0535567i
$732$	−0.362023	+	0.213131i	−0.0133807	+	0.00787755i
$733$	−18.8382	−	15.8071i	−0.695804	−	0.583849i	0.224772	−	0.974411i	$-0.427836\pi$
$733$	−18.8382	−	15.8071i	−0.695804	−	0.583849i	−0.920577	+	0.390562i	$0.872281\pi$
$734$	52.5972	−	19.1438i	1.94140	−	0.706610i
$735$	−50.4547	+	2.18493i	−1.86105	+	0.0805925i
$736$	5.49004	+	31.1356i	0.202366	+	1.14767i
$737$	−37.9040			−1.39621
$738$	−8.96277	−	14.9328i	−0.329924	−	0.549683i
$739$	41.2905			1.51890			0.759448	−	0.650568i	$-0.225469\pi$
$739$	41.2905			1.51890			0.759448	+	0.650568i	$0.225469\pi$
$740$	−2.75215	+	2.30933i	−0.101171	+	0.0848927i
$741$	1.55930	+	0.261321i	0.0572823	+	0.00959987i
$742$	16.8448	+	4.20093i	0.618393	+	0.154221i
$743$	−8.19507	−	6.87648i	−0.300648	−	0.252274i	0.479966	−	0.877287i	$-0.340649\pi$
$743$	−8.19507	−	6.87648i	−0.300648	−	0.252274i	−0.780614	+	0.625013i	$0.785093\pi$
$744$	12.4107	+	2.07990i	0.454999	+	0.0762527i
$745$	9.11896	+	51.7162i	0.334093	+	1.89474i
$746$	−42.2663			−1.54748
$747$	1.37407	+	7.08709i	0.0502745	+	0.259303i
$748$	0.964765	+	1.67102i	0.0352753	+	0.0610986i
$749$	31.3978	−	3.29821i	1.14725	−	0.120514i
$750$	91.9766	−	17.0241i	3.35851	−	0.621631i
$751$	2.25015	−	12.7612i	0.0821092	−	0.465664i	−0.915834	−	0.401557i	$-0.868469\pi$
$751$	2.25015	−	12.7612i	0.0821092	−	0.465664i	0.997943	−	0.0641070i	$-0.0204199\pi$
$752$	−27.8970	+	10.1537i	−1.01730	+	0.370266i
$753$	−19.9679	−	11.3036i	−0.727669	−	0.411925i
$754$	0.00569717	+	0.0323103i	0.000207479	+	0.00117667i
$755$	−67.5716			−2.45918
$756$	8.22139	−	12.8829i	0.299009	−	0.468547i
$757$	28.7036			1.04325			0.521625	−	0.853175i	$-0.325326\pi$
$757$	28.7036			1.04325			0.521625	+	0.853175i	$0.325326\pi$
$758$	5.68081	+	32.2175i	0.206336	+	1.17019i
$759$	0.202691	+	23.8816i	0.00735721	+	0.866847i
$760$	−39.6537	+	14.4328i	−1.43839	+	0.523532i
$761$	−6.50686	+	36.9023i	−0.235874	+	1.33771i	0.604892	+	0.796307i	$0.293216\pi$
$761$	−6.50686	+	36.9023i	−0.235874	+	1.33771i	−0.840766	+	0.541399i	$0.817895\pi$
$762$	10.6420	−	30.0291i	0.385518	−	1.08784i
$763$	−0.344905	+	0.774548i	−0.0124864	+	0.0280405i
$764$	4.53352	+	7.85229i	0.164017	+	0.284086i
$765$	6.82120	+	5.52911i	0.246621	+	0.199905i
$766$	−39.9321			−1.44280
$767$	−0.0889913	−	0.504695i	−0.00321329	−	0.0182235i
$768$	−12.1021	−	32.3923i	−0.436698	−	1.16885i
$769$	−25.1958	−	21.1418i	−0.908584	−	0.762392i	0.0632654	−	0.997997i	$-0.479849\pi$
$769$	−25.1958	−	21.1418i	−0.908584	−	0.762392i	−0.971849	+	0.235605i	$0.924293\pi$
$770$	33.3594	−	34.5407i	1.20219	−	1.24476i
$771$	23.9209	−	29.0042i	0.861490	−	1.04456i
$772$	2.52531	−	2.11899i	0.0908879	−	0.0762640i
$773$	−18.3980			−0.661731			−0.330866	−	0.943678i	$-0.607341\pi$
$773$	−18.3980			−0.661731			−0.330866	+	0.943678i	$0.607341\pi$
$774$	−24.7694	−	20.0775i	−0.890318	−	0.721672i
$775$	−57.2583			−2.05678
$776$	−0.501203	−	2.84246i	−0.0179921	−	0.102038i
$777$	0.401452	+	3.53284i	0.0144020	+	0.126740i
$778$	−15.2639	+	5.55560i	−0.547237	+	0.199178i
$779$	−16.2988	−	13.6763i	−0.583966	−	0.490006i
$780$	−0.00961053	−	1.13234i	−0.000344112	−	0.0405443i
$781$	32.6856	+	11.8966i	1.16958	+	0.425693i
$782$	3.45950	−	5.99202i	0.123711	−	0.214274i
$783$	−0.453183	−	0.512972i	−0.0161954	−	0.0183321i
$784$	−13.0748	−	32.3720i	−0.466957	−	1.15614i
$785$	−26.8850	+	22.5592i	−0.959568	+	0.805174i
$786$	0.156630	+	18.4546i	0.00558680	+	0.658252i
$787$	33.4128	−	12.1613i	1.19104	−	0.433503i	0.330951	−	0.943648i	$-0.392631\pi$
$787$	33.4128	−	12.1613i	1.19104	−	0.433503i	0.860088	+	0.510145i	$0.170408\pi$
$788$	15.2585	+	12.8034i	0.543560	+	0.456101i
$789$	6.27340	−	17.7021i	0.223339	−	0.630210i
$790$	−7.35935	−	41.7369i	−0.261834	−	1.48493i
$791$	−4.64094	−	3.13075i	−0.165013	−	0.111317i
$792$	−2.21031	−	11.4002i	−0.0785401	−	0.405090i
$793$	0.0154031	+	0.0266790i	0.000546981	+	0.000947399i
$794$	−5.00926	−	28.4089i	−0.177772	−	1.00819i
$795$	−17.0754	+	20.7040i	−0.605603	+	0.734296i
$796$	−12.2925	+	4.47409i	−0.435695	+	0.158580i
$797$	−7.71007	−	6.46952i	−0.273105	−	0.229162i	0.495940	−	0.868357i	$-0.334823\pi$
$797$	−7.71007	−	6.46952i	−0.273105	−	0.229162i	−0.769045	+	0.639194i	$0.779268\pi$
$798$	12.2151	−	50.8131i	0.432411	−	1.79876i
$799$	3.93031	+	1.43052i	0.139045	+	0.0506081i
$800$	34.9744	+	60.5774i	1.23653	+	2.14174i
$801$	1.31620	−	2.37181i	0.0465057	−	0.0838037i
$802$	−32.3396	+	56.0138i	−1.14195	+	1.97792i
$803$	29.5428	+	10.7527i	1.04254	+	0.379455i
$804$	19.1827	+	22.4710i	0.676522	+	0.792490i
$805$	−59.6881	−	14.8856i	−2.10373	−	0.524648i
$806$	−0.200517	+	1.13719i	−0.00706292	+	0.0400558i
$807$	−20.1730	−	11.4197i	−0.710123	−	0.401993i
$808$	−11.9778	−	4.35957i	−0.421378	−	0.153369i
$809$	14.1884	+	24.5750i	0.498838	+	0.864012i	0.999999	−	0.00134173i	$-0.000427087\pi$
$809$	14.1884	+	24.5750i	0.498838	+	0.864012i	−0.501162	+	0.865354i	$0.667094\pi$
$810$	34.9889	+	56.1135i	1.22939	+	1.97163i
$811$	−24.0856			−0.845758			−0.422879	−	0.906186i	$-0.638981\pi$
$811$	−24.0856			−0.845758			−0.422879	+	0.906186i	$0.638981\pi$
$812$	0.385314	−	0.0404756i	0.0135219	−	0.00142041i
$813$	−0.315027	−	37.1173i	−0.0110485	−	1.30176i
$814$	−2.58986	−	2.17315i	−0.0907746	−	0.0761689i
$815$	25.9363	+	21.7631i	0.908508	+	0.762329i
$816$	−2.02764	+	5.72153i	−0.0709817	+	0.200294i
$817$	−36.6033	−	13.3225i	−1.28059	−	0.466096i
$818$	−1.42534	−	2.46876i	−0.0498358	−	0.0863182i
$819$	−0.939559	−	0.610874i	−0.0328308	−	0.0213457i
$820$	−7.61941	+	13.1972i	−0.266081	+	0.460866i
$821$	−21.4922	+	18.0341i	−0.750083	+	0.629394i	−0.935525	−	0.353261i	$-0.885073\pi$
$821$	−21.4922	+	18.0341i	−0.750083	+	0.629394i	0.185442	+	0.982655i	$0.440628\pi$
$822$	2.74128	+	7.33724i	0.0956130	+	0.255915i
$823$	4.95932	−	28.1257i	0.172871	−	0.980401i	−0.767701	−	0.640808i	$-0.778599\pi$
$823$	4.95932	−	28.1257i	0.172871	−	0.980401i	0.940572	−	0.339593i	$-0.110289\pi$
$824$	−9.43270	+	3.43322i	−0.328604	+	0.119602i
$825$	18.4927	+	49.4972i	0.643834	+	1.72327i
$826$	−16.8471	+	1.76972i	−0.586186	+	0.0615763i
$827$	19.8973	−	34.4632i	0.691897	−	1.19840i	−0.279318	−	0.960199i	$-0.590108\pi$
$827$	19.8973	−	34.4632i	0.691897	−	1.19840i	0.971215	−	0.238203i	$-0.0765582\pi$
$828$	14.0554	−	12.2063i	0.488458	−	0.424199i
$829$	−17.7672	+	30.7737i	−0.617081	+	1.06882i	0.372935	+	0.927858i	$0.378352\pi$
$829$	−17.7672	+	30.7737i	−0.617081	+	1.06882i	−0.990016	+	0.140958i	$0.954982\pi$
$830$	13.5444	−	11.3651i	0.470132	−	0.394488i
$831$	3.16494	−	8.93073i	0.109791	−	0.309804i
$832$	0.00211482		0.000769731i	7.33181e−5		2.66856e-5i
$833$	−1.52052	+	4.67782i	−0.0526828	+	0.162077i
$834$	−8.31329	+	4.89422i	−0.287866	+	0.169473i
$835$	−14.4957	−	82.2093i	−0.501645	−	2.84497i
$836$	8.87637	+	15.3743i	0.306996	+	0.531732i
$837$	−8.81325	−	22.4210i	−0.304631	−	0.774983i
$838$	−12.9806	+	22.4831i	−0.448408	+	0.776665i
$839$	6.42785	−	5.39360i	0.221914	−	0.186208i	−0.525052	−	0.851070i	$-0.675954\pi$
$839$	6.42785	−	5.39360i	0.221914	−	0.186208i	0.746966	+	0.664862i	$0.231510\pi$
$840$	29.8551	+	1.83493i	1.03010	+	0.0633112i
$841$	−5.03278	+	28.5423i	−0.173544	+	0.984218i
$842$	−4.14766	+	23.5226i	−0.142938	+	0.810642i
$843$	24.4252	−	4.52089i	0.841249	−	0.155708i
$844$	−4.14982	+	3.48212i	−0.142843	+	0.119859i
$845$	54.0663			1.85994
$846$	24.4701	+	19.8349i	0.841301	+	0.681939i
$847$	−10.7436	−	7.24753i	−0.369153	−	0.249028i
$848$	−17.4340	−	6.34544i	−0.598685	−	0.217903i
$849$	4.82851	+	12.9239i	0.165714	+	0.443546i
$850$	2.65820	−	15.0754i	0.0911756	−	0.517082i
$851$	−0.752077	+	4.26524i	−0.0257809	+	0.146210i
$852$	−9.48898	−	25.3980i	−0.325087	−	0.870121i
$853$	53.3397	+	19.4141i	1.82632	+	0.664725i	0.993861	+	0.110633i	$0.0352878\pi$
$853$	53.3397	+	19.4141i	1.82632	+	0.664725i	0.832456	+	0.554092i	$0.186934\pi$
$854$	0.915255	−	0.446334i	0.0313194	−	0.0152732i
$855$	62.7588	+	50.8709i	2.14631	+	1.73975i
$856$	−18.6987			−0.639110
$857$	16.0477	−	13.4657i	0.548181	−	0.459978i	−0.326144	−	0.945320i	$-0.605749\pi$
$857$	16.0477	−	13.4657i	0.548181	−	0.459978i	0.874324	+	0.485342i	$0.161305\pi$
$858$	1.04781	−	0.193940i	0.0357716	−	0.00662101i
$859$	4.95940	−	28.1262i	0.169213	−	0.959652i	−0.775401	−	0.631469i	$-0.782452\pi$
$859$	4.95940	−	28.1262i	0.169213	−	0.959652i	0.944614	−	0.328184i	$-0.106436\pi$
$860$	−4.84455	+	27.4748i	−0.165198	+	0.936883i
$861$	6.72529	+	13.4989i	0.229197	+	0.460041i
$862$	29.4827	−	24.7390i	1.00419	−	0.842612i
$863$	23.8019	−	41.2262i	0.810228	−	1.40336i	−0.102477	−	0.994735i	$-0.532677\pi$
$863$	23.8019	−	41.2262i	0.810228	−	1.40336i	0.912705	−	0.408620i	$-0.133990\pi$
$864$	−18.3374	+	23.0193i	−0.623850	+	0.783132i
$865$	−53.8779	−	93.3193i	−1.83190	−	3.17295i
$866$	3.10473	+	17.6078i	0.105503	+	0.598338i
$867$	−24.6372	+	14.5044i	−0.836722	+	0.492597i
$868$	13.2308	+	3.29963i	0.449084	+	0.111997i
$869$	13.3886	−	4.87307i	0.454179	−	0.165307i
$870$	−0.559983	+	1.58014i	−0.0189852	+	0.0535717i
$871$	1.65969	−	1.39264i	0.0562363	−	0.0471879i
$872$	0.251090	−	0.434900i	0.00850297	−	0.0147276i
$873$	−4.17202	+	3.62317i	−0.141201	+	0.122626i
$874$	31.8293	−	55.1299i	1.07664	−	1.86480i
$875$	−80.5567	+	8.46214i	−2.72331	+	0.286072i
$876$	−8.57662	−	22.9560i	−0.289777	−	0.775610i
$877$	−47.5513	+	17.3072i	−1.60569	+	0.584424i	−0.980582	−	0.196112i	$-0.937168\pi$
$877$	−47.5513	+	17.3072i	−1.60569	+	0.584424i	−0.625111	+	0.780536i	$0.714946\pi$
$878$	0.871732	−	4.94384i	0.0294195	−	0.166846i
$879$	−10.8017	−	28.9117i	−0.364334	−	0.975167i
$880$	−39.3112	+	32.9860i	−1.32518	+	1.11196i
$881$	−10.1196	+	17.5276i	−0.340937	+	0.590519i	−0.984607	−	0.174783i	$-0.944077\pi$
$881$	−10.1196	+	17.5276i	−0.340937	+	0.590519i	0.643670	+	0.765303i	$0.277411\pi$
$882$	−22.3111	+	29.5712i	−0.751253	+	0.995713i
$883$	2.54791	+	4.41312i	0.0857441	+	0.148513i	0.905708	−	0.423902i	$-0.139340\pi$
$883$	2.54791	+	4.41312i	0.0857441	+	0.148513i	−0.819964	+	0.572415i	$0.806007\pi$
$884$	−0.103639	−	0.0377216i	−0.00348576	−	0.00126871i
$885$	8.74707	−	24.6822i	0.294030	−	0.829682i
$886$	−8.61603	−	7.22971i	−0.289461	−	0.242887i
$887$	−0.672255	−	0.564089i	−0.0225721	−	0.0189403i	0.631432	−	0.775431i	$-0.282468\pi$
$887$	−0.672255	−	0.564089i	−0.0225721	−	0.0189403i	−0.654004	+	0.756491i	$0.726912\pi$
$888$	−0.0178729	−	2.10583i	−0.000599775	−	0.0706672i
$889$	−11.2227	+	25.2026i	−0.376396	+	0.845267i
$890$	−6.64354			−0.222692
$891$	−16.5355	+	14.8600i	−0.553960	+	0.497827i
$892$	−10.8644	−	18.8177i	−0.363767	−	0.630063i
$893$	36.1611	+	13.1615i	1.21008	+	0.440434i
$894$	33.5212	+	18.9760i	1.12112	+	0.634652i
$895$	−14.1383	+	80.1820i	−0.472590	+	2.68019i
$896$	8.23880	+	28.7384i	0.275239	+	0.960082i
$897$	−0.886316	−	1.03825i	−0.0295932	−	0.0346660i
$898$	−7.74955	−	2.82061i	−0.258606	−	0.0941248i
$899$	0.305367	−	0.528911i	0.0101846	−	0.0176402i
$900$	19.9849	−	36.0131i	0.666164	−	1.20044i
$901$	1.30692	+	2.26366i	0.0435400	+	0.0754134i
$902$	−13.4754	−	4.90464i	−0.448681	−	0.163307i
$903$	20.0223	+	19.0118i	0.666301	+	0.632672i
$904$	2.53999	+	2.13131i	0.0844789	+	0.0708862i
$905$	−11.0505	+	4.02205i	−0.367330	+	0.133697i
$906$	−31.5360	+	38.2376i	−1.04771	+	1.27036i
$907$	−1.74063	−	9.87160i	−0.0577966	−	0.327781i	0.942176	−	0.335117i	$-0.108776\pi$
$907$	−1.74063	−	9.87160i	−0.0577966	−	0.327781i	−0.999973	+	0.00733616i	$0.997665\pi$
$908$	6.84339	+	11.8531i	0.227106	+	0.393359i
$909$	4.64474	+	23.9564i	0.154056	+	0.794584i
$910$	−0.191625	+	2.73808i	−0.00635230	+	0.0907666i
$911$	1.74967	+	9.92289i	0.0579693	+	0.328760i	0.999977	−	0.00683209i	$-0.00217474\pi$
$911$	1.74967	+	9.92289i	0.0579693	+	0.328760i	−0.942007	+	0.335592i	$0.891064\pi$
$912$	−18.6554	+	52.6412i	−0.617743	+	1.74312i
$913$	4.55345	+	3.82080i	0.150697	+	0.126450i
$914$	−31.8240	+	11.5830i	−1.05265	+	0.383132i
$915$	0.0133595	+	1.57405i	0.000441651	+	0.0520366i
$916$	−21.8321	+	18.3193i	−0.721353	+	0.605287i
$917$	1.11572	−	15.9423i	0.0368444	−	0.526461i
$918$	6.31232	−	1.27953i	0.208338	−	0.0422309i
$919$	−22.4955	+	38.9634i	−0.742059	+	1.28528i	0.209498	+	0.977809i	$0.432817\pi$
$919$	−22.4955	+	38.9634i	−0.742059	+	1.28528i	−0.951556	+	0.307474i	$0.900516\pi$
$920$	34.2378	+	12.4615i	1.12879	+	0.410845i
$921$	0.0221513	+	2.60992i	0.000729909	+	0.0859999i
$922$	−2.50176	−	2.09922i	−0.0823910	−	0.0691342i
$923$	−1.86828	+	0.680000i	−0.0614953	+	0.0223825i
$924$	−1.42079	−	12.5031i	−0.0467404	−	0.411323i
$925$	1.66394	+	9.43666i	0.0547099	+	0.310275i
$926$	−26.6772			−0.876666
$927$	14.9289	+	12.1010i	0.490328	+	0.397449i
$928$	−0.746095			−0.0244918
$929$	19.2024	−	16.1127i	0.630009	−	0.528640i	−0.270923	−	0.962601i	$-0.587329\pi$
$929$	19.2024	−	16.1127i	0.630009	−	0.528640i	0.900932	+	0.433961i	$0.142884\pi$
$930$	−37.5417	+	45.5196i	−1.23104	+	1.49265i
$931$	−13.9896	+	43.0386i	−0.458490	+	1.41053i
$932$	6.24506	+	5.24023i	0.204564	+	0.171649i
$933$	3.55451	+	9.51391i	0.116369	+	0.311472i
$934$	−7.57666	−	42.9694i	−0.247916	−	1.40600i
$935$	7.22990			0.236443
$936$	0.515641	+	0.417967i	0.0168543	+	0.0136617i
$937$	25.9068	+	44.8718i	0.846337	+	1.46590i	0.884455	+	0.466625i	$0.154530\pi$
$937$	25.9068	+	44.8718i	0.846337	+	1.46590i	−0.0381183	+	0.999273i	$0.512136\pi$
$938$	−42.0907	−	57.9400i	−1.37431	−	1.89181i
$939$	−1.07976	+	3.04683i	−0.0352367	+	0.0994296i
$940$	4.78602	−	27.1428i	0.156103	−	0.885302i
$941$	10.7417	−	3.90966i	0.350169	−	0.127451i	−0.160946	−	0.986963i	$-0.551455\pi$
$941$	10.7417	−	3.90966i	0.350169	−	0.127451i	0.511116	+	0.859512i	$0.329232\pi$
$942$	0.218483	+	25.7423i	0.00711857	+	0.838730i
$943$	3.19003	+	18.0916i	0.103882	+	0.589142i
$944$	18.1030			0.589201
$945$	−26.4020	−	50.8142i	−0.858859	−	1.65298i
$946$	−26.2535			−0.853575
$947$	3.19378	+	18.1128i	0.103784	+	0.588587i	0.991699	+	0.128580i	$0.0410420\pi$
$947$	3.19378	+	18.1128i	0.103784	+	0.588587i	−0.887915	+	0.460007i	$0.847847\pi$
$948$	−9.66476	−	5.47112i	−0.313897	−	0.177694i
$949$	−1.68865	+	0.614618i	−0.0548158	+	0.0199513i
$950$	24.4569	−	138.702i	0.793487	−	4.50009i
$951$	16.8799	−	3.12432i	0.547367	−	0.101313i
$952$	1.18510	−	2.66135i	0.0384092	−	0.0862550i
$953$	−1.96945	−	3.41119i	−0.0637968	−	0.110499i	0.832363	−	0.554231i	$-0.186988\pi$
$953$	−1.96945	−	3.41119i	−0.0637968	−	0.110499i	−0.896160	+	0.443732i	$0.853654\pi$
$954$	3.74687	+	19.3254i	0.121309	+	0.625682i
$955$	33.9740			1.09937
$956$	2.86526	+	16.2497i	0.0926692	+	0.525553i
$957$	−0.555844	−	0.0931532i	−0.0179679	−	0.00301122i
$958$	42.8235	+	35.9331i	1.38356	+	1.16095i
$959$	−1.86917	−	6.52000i	−0.0603587	−	0.210542i
$960$	0.113415	+	0.0190070i	0.00366044	+	0.000613449i
$961$	−7.28100	+	6.10948i	−0.234871	+	0.197080i
$962$	0.193246			0.00623049
$963$	18.4225	+	30.6934i	0.593656	+	0.989082i
$964$	−19.4528			−0.626533
$965$	−2.14492	−	12.1645i	−0.0690475	−	0.391588i
$966$	−36.2803	+	26.8293i	−1.16730	+	0.863219i
$967$	5.07490	−	1.84711i	0.163198	−	0.0593991i	−0.259129	−	0.965843i	$-0.583436\pi$
$967$	5.07490	−	1.84711i	0.163198	−	0.0593991i	0.422327	+	0.906444i	$0.361213\pi$
$968$	5.87997	+	4.93388i	0.188989	+	0.158581i
$969$	6.78060	−	3.99189i	0.217824	−	0.128238i
$970$	12.7173	+	4.62872i	0.408328	+	0.148619i
$971$	23.7078	−	41.0631i	0.760819	−	1.31778i	−0.181610	−	0.983371i	$-0.558131\pi$
$971$	23.7078	−	41.0631i	0.760819	−	1.31778i	0.942429	−	0.334407i	$-0.108536\pi$
$972$	17.1780	+	2.28245i	0.550983	+	0.0732098i
$973$	7.50856	−	3.66163i	0.240713	−	0.117387i
$974$	−40.6020	+	34.0692i	−1.30097	+	1.09165i
$975$	−2.62832	−	1.48786i	−0.0841737	−	0.0476498i
$976$	−1.02258	+	0.372188i	−0.0327319	+	0.0119135i
$977$	−44.2452	−	37.1261i	−1.41553	−	1.18777i	−0.953685	−	0.300809i	$-0.902743\pi$
$977$	−44.2452	−	37.1261i	−1.41553	−	1.18777i	−0.461844	−	0.886961i	$-0.652812\pi$
$978$	24.4200	−	4.51993i	0.780865	−	0.144531i
$979$	−0.387839	−	2.19954i	−0.0123954	−	0.0702977i
$980$	32.0968	+	4.51471i	1.02530	+	0.144217i
$981$	−0.961255	+	0.0163181i	−0.0306905	+	0.000520998i
$982$	27.2433	+	47.1868i	0.869369	+	1.50579i
$983$	7.20854	+	40.8817i	0.229917	+	1.30392i	0.853059	+	0.521814i	$0.174745\pi$
$983$	7.20854	+	40.8817i	0.229917	+	1.30392i	−0.623142	+	0.782109i	$0.714144\pi$
$984$	−3.12622	−	8.36756i	−0.0996602	−	0.266748i
$985$	70.1332	−	25.5264i	2.23463	−	0.813338i
$986$	0.125079	+	0.104954i	0.00398334	+	0.00334242i
$987$	−19.7804	−	18.7821i	−0.629617	−	0.597840i
$988$	−0.953538	−	0.347059i	−0.0303361	−	0.0110414i
$989$	16.8161	+	29.1264i	0.534722	+	0.926166i
$990$	51.4744	+	17.7516i	1.63596	+	0.564184i
$991$	25.3701	−	43.9423i	0.805908	−	1.39587i	−0.109768	−	0.993957i	$-0.535011\pi$
$991$	25.3701	−	43.9423i	0.805908	−	1.39587i	0.915676	−	0.401917i	$-0.131656\pi$
$992$	−24.6758	−	8.98127i	−0.783458	−	0.285155i
$993$	−16.5397	+	3.06135i	−0.524871	+	0.0971491i
$994$	18.1108	+	63.1738i	0.574440	+	2.00375i
$995$	−8.51146	+	48.2709i	−0.269831	+	1.53029i
$996$	−0.0393228	−	4.63312i	−0.00124599	−	0.146806i
$997$	−30.2743	−	11.0190i	−0.958798	−	0.348974i	−0.185236	−	0.982694i	$-0.559305\pi$
$997$	−30.2743	−	11.0190i	−0.958798	−	0.348974i	−0.773562	+	0.633720i	$0.781527\pi$
$998$	−13.6339	−	23.6147i	−0.431575	−	0.747510i
$999$	−3.43905	+	2.10406i	−0.108807	+	0.0665694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.184.17	yes	132
3.2	odd	2		567.2.w.a.37.6		132
7.4	even	3		189.2.u.a.130.6	yes	132
21.11	odd	6		567.2.u.a.361.17		132
27.11	odd	18		567.2.u.a.289.17		132
27.16	even	9		189.2.u.a.16.6	✓	132
189.11	odd	18		567.2.w.a.46.6		132
189.151	even	9	inner	189.2.w.a.151.17	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.6	✓	132	27.16	even	9
189.2.u.a.130.6	yes	132	7.4	even	3
189.2.w.a.151.17	yes	132	189.151	even	9	inner
189.2.w.a.184.17	yes	132	1.1	even	1	trivial
567.2.u.a.289.17		132	27.11	odd	18
567.2.u.a.361.17		132	21.11	odd	6
567.2.w.a.37.6		132	3.2	odd	2
567.2.w.a.46.6		132	189.11	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.306313 + 1.73719i) q^{2} +(1.49260 - 0.878725i) q^{3} +(-1.04461 + 0.380207i) q^{4} +(-0.723302 + 4.10205i) q^{5} +(1.98371 + 2.32376i) q^{6} +(-1.55501 - 2.14055i) q^{7} +(0.783518 + 1.35709i) q^{8} +(1.45569 - 2.62316i) q^{9} +O(q^{10})\)	\(q+(0.306313 + 1.73719i) q^{2} +(1.49260 - 0.878725i) q^{3} +(-1.04461 + 0.380207i) q^{4} +(-0.723302 + 4.10205i) q^{5} +(1.98371 + 2.32376i) q^{6} +(-1.55501 - 2.14055i) q^{7} +(0.783518 + 1.35709i) q^{8} +(1.45569 - 2.62316i) q^{9} -7.34759 q^{10} +(-0.428940 - 2.43264i) q^{11} +(-1.22508 + 1.48542i) q^{12} +(0.108160 + 0.0907572i) q^{13} +(3.24222 - 3.35702i) q^{14} +(2.52498 + 6.75829i) q^{15} +(-3.82067 + 3.20592i) q^{16} +0.702677 q^{17} +(5.00282 + 1.72529i) q^{18} +6.46502 q^{19} +(-0.804060 - 4.56005i) q^{20} +(-4.20195 - 1.82855i) q^{21} +(4.09457 - 1.49030i) q^{22} +(-4.27608 - 3.58805i) q^{23} +(2.36199 + 1.33709i) q^{24} +(-11.6052 - 4.22394i) q^{25} +(-0.124532 + 0.215695i) q^{26} +(-0.132287 - 5.19447i) q^{27} +(2.43823 + 1.64481i) q^{28} +(0.100910 - 0.0846735i) q^{29} +(-10.9670 + 6.45651i) q^{30} +(4.35670 - 1.58571i) q^{31} +(-4.33878 - 3.64067i) q^{32} +(-2.77786 - 3.25403i) q^{33} +(0.215239 + 1.22068i) q^{34} +(9.90538 - 4.83046i) q^{35} +(-0.523280 + 3.29365i) q^{36} +(-0.387945 - 0.671941i) q^{37} +(1.98032 + 11.2310i) q^{38} +(0.241190 + 0.0404208i) q^{39} +(-6.13358 + 2.23244i) q^{40} +(-2.52108 - 2.11544i) q^{41} +(1.88942 - 7.85969i) q^{42} +(-5.66175 - 2.06071i) q^{43} +(1.37298 + 2.37808i) q^{44} +(9.70744 + 7.86863i) q^{45} +(4.92331 - 8.52742i) q^{46} +(5.59334 + 2.03581i) q^{47} +(-2.88560 + 8.14247i) q^{48} +(-2.16389 + 6.65714i) q^{49} +(3.78296 - 21.4542i) q^{50} +(1.04881 - 0.617460i) q^{51} +(-0.147492 - 0.0536827i) q^{52} +(1.85992 + 3.22148i) q^{53} +(8.98325 - 1.82094i) q^{54} +10.2891 q^{55} +(1.68654 - 3.78745i) q^{56} +(9.64966 - 5.68097i) q^{57} +(0.178004 + 0.149363i) q^{58} +(-2.78047 - 2.33309i) q^{59} +(-5.20717 - 6.09977i) q^{60} +(0.205027 + 0.0746237i) q^{61} +(4.08919 + 7.08269i) q^{62} +(-7.87861 + 0.963077i) q^{63} +(0.00796973 - 0.0138040i) q^{64} +(-0.450523 + 0.378034i) q^{65} +(4.80197 - 5.82242i) q^{66} +(2.66458 - 15.1116i) q^{67} +(-0.734024 + 0.267163i) q^{68} +(-9.53537 - 1.59802i) q^{69} +(11.4256 + 15.7279i) q^{70} +(-7.04066 + 12.1948i) q^{71} +(4.70043 - 0.0797938i) q^{72} +(-6.36370 + 11.0222i) q^{73} +(1.04845 - 0.879758i) q^{74} +(-21.0335 + 3.89313i) q^{75} +(-6.75343 + 2.45805i) q^{76} +(-4.54018 + 4.70095i) q^{77} +(0.00366121 + 0.431374i) q^{78} +(1.00160 + 5.68035i) q^{79} +(-10.3874 - 17.9914i) q^{80} +(-4.76196 - 7.63700i) q^{81} +(2.90267 - 5.02758i) q^{82} +(-1.84338 + 1.54678i) q^{83} +(5.08463 + 0.312508i) q^{84} +(-0.508248 + 2.88242i) q^{85} +(1.84557 - 10.4667i) q^{86} +(0.0762131 - 0.215055i) q^{87} +(2.96524 - 2.48813i) q^{88} +0.904179 q^{89} +(-10.6958 + 19.2739i) q^{90} +(0.0260800 - 0.372651i) q^{91} +(5.83104 + 2.12233i) q^{92} +(5.10939 - 6.19517i) q^{93} +(-1.82327 + 10.3403i) q^{94} +(-4.67616 + 26.5198i) q^{95} +(-9.67519 - 1.62145i) q^{96} +(-1.73081 - 0.629965i) q^{97} +(-12.2275 - 1.71991i) q^{98} +(-7.00562 - 2.41598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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