LMFDB - Embedded newform 189.2.w.a.25.12

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			25.12
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0303128 - 0.0110329i) q^{2} +(0.919170 + 1.46804i) q^{3} +(-1.53129 + 1.28491i) q^{4} +(-3.70820 - 1.34968i) q^{5} +(0.0440593 + 0.0343591i) q^{6} +(-2.47092 + 0.945798i) q^{7} +(-0.0644996 + 0.111717i) q^{8} +(-1.31025 + 2.69875i) q^{9} +O(q^{10})$	\(q+(0.0303128 - 0.0110329i) q^{2} +(0.919170 + 1.46804i) q^{3} +(-1.53129 + 1.28491i) q^{4} +(-3.70820 - 1.34968i) q^{5} +(0.0440593 + 0.0343591i) q^{6} +(-2.47092 + 0.945798i) q^{7} +(-0.0644996 + 0.111717i) q^{8} +(-1.31025 + 2.69875i) q^{9} -0.127297 q^{10} +(2.52713 - 0.919799i) q^{11} +(-3.29380 - 1.06694i) q^{12} +(0.841596 + 4.77293i) q^{13} +(-0.0644656 + 0.0559313i) q^{14} +(-1.42710 - 6.68435i) q^{15} +(0.693509 - 3.93308i) q^{16} +1.66370 q^{17} +(-0.00994232 + 0.0962625i) q^{18} -0.753482 q^{19} +(7.41255 - 2.69795i) q^{20} +(-3.65966 - 2.75805i) q^{21} +(0.0664561 - 0.0557633i) q^{22} +(0.770659 + 4.37062i) q^{23} +(-0.223290 + 0.00799880i) q^{24} +(8.09892 + 6.79580i) q^{25} +(0.0781705 + 0.135395i) q^{26} +(-5.16620 + 0.557106i) q^{27} +(2.56844 - 4.62320i) q^{28} +(0.0179486 - 0.101792i) q^{29} +(-0.117007 - 0.186876i) q^{30} +(-6.79480 + 5.70151i) q^{31} +(-0.0671723 - 0.380953i) q^{32} +(3.67316 + 2.86446i) q^{33} +(0.0504314 - 0.0183555i) q^{34} +(10.4392 - 0.172267i) q^{35} +(-1.46125 - 5.81612i) q^{36} +(-0.656616 + 1.13729i) q^{37} +(-0.0228401 + 0.00831312i) q^{38} +(-6.23325 + 5.62262i) q^{39} +(0.389959 - 0.327214i) q^{40} +(-0.311924 - 1.76901i) q^{41} +(-0.141364 - 0.0432274i) q^{42} +(2.26024 + 1.89657i) q^{43} +(-2.68791 + 4.65560i) q^{44} +(8.50112 - 8.23908i) q^{45} +(0.0715817 + 0.123983i) q^{46} +(-5.41229 - 4.54145i) q^{47} +(6.41136 - 2.59708i) q^{48} +(5.21093 - 4.67399i) q^{49} +(0.320478 + 0.116645i) q^{50} +(1.52922 + 2.44237i) q^{51} +(-7.42149 - 6.22737i) q^{52} +(1.43735 - 2.48957i) q^{53} +(-0.150455 + 0.0738858i) q^{54} -10.6125 q^{55} +(0.0537122 - 0.337047i) q^{56} +(-0.692577 - 1.10614i) q^{57} +(-0.000578989 - 0.00328361i) q^{58} +(-2.04118 - 11.5761i) q^{59} +(10.7741 + 8.40201i) q^{60} +(6.31104 + 5.29559i) q^{61} +(-0.143065 + 0.247795i) q^{62} +(0.685069 - 7.90763i) q^{63} +(3.98752 + 6.90658i) q^{64} +(3.32109 - 18.8349i) q^{65} +(0.142947 + 0.0463040i) q^{66} +(3.44392 + 1.25348i) q^{67} +(-2.54761 + 2.13770i) q^{68} +(-5.70786 + 5.14870i) q^{69} +(0.314541 - 0.120397i) q^{70} +(2.95503 + 5.11826i) q^{71} +(-0.216984 - 0.320445i) q^{72} +(-2.08581 - 3.61273i) q^{73} +(-0.00735617 + 0.0417189i) q^{74} +(-2.53219 + 18.1360i) q^{75} +(1.15380 - 0.968153i) q^{76} +(-5.37439 + 4.66291i) q^{77} +(-0.126913 + 0.239208i) q^{78} +(8.24914 - 3.00244i) q^{79} +(-7.88006 + 13.6487i) q^{80} +(-5.56647 - 7.07209i) q^{81} +(-0.0289726 - 0.0501821i) q^{82} +(-3.12320 + 17.7126i) q^{83} +(9.14785 - 0.478939i) q^{84} +(-6.16935 - 2.24546i) q^{85} +(0.0894389 + 0.0325531i) q^{86} +(0.165931 - 0.0672145i) q^{87} +(-0.0602419 + 0.341649i) q^{88} -9.24903 q^{89} +(0.166791 - 0.343542i) q^{90} +(-6.59374 - 10.9976i) q^{91} +(-6.79595 - 5.70248i) q^{92} +(-14.6156 - 4.73435i) q^{93} +(-0.214167 - 0.0779504i) q^{94} +(2.79406 + 1.01696i) q^{95} +(0.497509 - 0.448772i) q^{96} +(4.56635 + 3.83162i) q^{97} +(0.106390 - 0.199174i) q^{98} +(-0.828875 + 8.02525i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.0303128	−	0.0110329i	0.0214344	−	0.00780147i	−0.331281	−	0.943532i	$-0.607481\pi$
$2$	0.0303128	−	0.0110329i	0.0214344	−	0.00780147i	0.352715	+	0.935731i	$0.385258\pi$
$3$	0.919170	+	1.46804i	0.530683	+	0.847571i
$3$	0.919170	+	1.46804i	0.530683	+	0.847571i
$4$	−1.53129	+	1.28491i	−0.765646	+	0.642453i
$5$	−3.70820	−	1.34968i	−1.65836	−	0.603593i	−0.668255	−	0.743932i	$-0.732959\pi$
$5$	−3.70820	−	1.34968i	−1.65836	−	0.603593i	−0.990104	+	0.140339i	$0.955181\pi$
$6$	0.0440593	+	0.0343591i	0.0179871	+	0.0140270i
$7$	−2.47092	+	0.945798i	−0.933921	+	0.357478i
$7$	−2.47092	+	0.945798i	−0.933921	+	0.357478i
$8$	−0.0644996	+	0.111717i	−0.0228040	+	0.0394978i
$9$	−1.31025	+	2.69875i	−0.436752	+	0.899582i
$10$	−0.127297			−0.0402548
$11$	2.52713	−	0.919799i	0.761958	−	0.277330i	0.0683291	−	0.997663i	$-0.478233\pi$
$11$	2.52713	−	0.919799i	0.761958	−	0.277330i	0.693628	+	0.720333i	$0.256011\pi$
$12$	−3.29380	−	1.06694i	−0.950839	−	0.308000i
$13$	0.841596	+	4.77293i	0.233417	+	1.32377i	0.845923	+	0.533306i	$0.179050\pi$
$13$	0.841596	+	4.77293i	0.233417	+	1.32377i	−0.612506	+	0.790466i	$0.709838\pi$
$14$	−0.0644656	+	0.0559313i	−0.0172292	+	0.0149483i
$15$	−1.42710	−	6.68435i	−0.368475	−	1.72589i
$16$	0.693509	−	3.93308i	0.173377	−	0.983271i
$17$	1.66370			0.403507			0.201754	−	0.979436i	$-0.435336\pi$
$17$	1.66370			0.403507			0.201754	+	0.979436i	$0.435336\pi$
$18$	−0.00994232	+	0.0962625i	−0.00234343	+	0.0226893i
$19$	−0.753482			−0.172861			−0.0864303	−	0.996258i	$-0.527546\pi$
$19$	−0.753482			−0.172861			−0.0864303	+	0.996258i	$0.527546\pi$
$20$	7.41255	−	2.69795i	1.65750	−	0.603279i
$21$	−3.65966	−	2.75805i	−0.798604	−	0.601857i
$22$	0.0664561	−	0.0557633i	0.0141685	−	0.0118888i
$23$	0.770659	+	4.37062i	0.160694	+	0.911338i	0.953394	+	0.301727i	$0.0975632\pi$
$23$	0.770659	+	4.37062i	0.160694	+	0.911338i	−0.792701	+	0.609611i	$0.791326\pi$
$24$	−0.223290	+	0.00799880i	−0.0455789	+	0.00163275i
$25$	8.09892	+	6.79580i	1.61978	+	1.35916i
$26$	0.0781705	+	0.135395i	0.0153305	+	0.0265532i
$27$	−5.16620	+	0.557106i	−0.994236	+	0.107215i
$28$	2.56844	−	4.62320i	0.485390	−	0.873703i
$29$	0.0179486	−	0.101792i	0.00333297	−	0.0189022i	−0.983096	−	0.183091i	$-0.941390\pi$
$29$	0.0179486	−	0.101792i	0.00333297	−	0.0189022i	0.986429	+	0.164189i	$0.0525007\pi$
$30$	−0.117007	−	0.186876i	−0.0213625	−	0.0341188i
$31$	−6.79480	+	5.70151i	−1.22038	+	1.02402i	−0.221577	+	0.975143i	$0.571120\pi$
$31$	−6.79480	+	5.70151i	−1.22038	+	1.02402i	−0.998805	+	0.0488790i	$0.984435\pi$
$32$	−0.0671723	−	0.380953i	−0.0118745	−	0.0673436i
$33$	3.67316	+	2.86446i	0.639414	+	0.498639i
$34$	0.0504314	−	0.0183555i	0.00864892	−	0.00314795i
$35$	10.4392	−	0.172267i	1.76455	−	0.0291184i
$36$	−1.46125	−	5.81612i	−0.243542	−	0.969354i
$37$	−0.656616	+	1.13729i	−0.107947	+	0.186970i	−0.914938	−	0.403593i	$-0.867761\pi$
$37$	−0.656616	+	1.13729i	−0.107947	+	0.186970i	0.806991	+	0.590563i	$0.201094\pi$
$38$	−0.0228401	+	0.00831312i	−0.00370516	+	0.00134857i
$39$	−6.23325	+	5.62262i	−0.998119	+	0.900340i
$40$	0.389959	−	0.327214i	0.0616579	−	0.0517371i
$41$	−0.311924	−	1.76901i	−0.0487143	−	0.276272i	0.950714	−	0.310068i	$-0.100352\pi$
$41$	−0.311924	−	1.76901i	−0.0487143	−	0.276272i	−0.999429	+	0.0337952i	$0.989241\pi$
$42$	−0.141364	−	0.0432274i	−0.0218129	−	0.00667013i
$43$	2.26024	+	1.89657i	0.344684	+	0.289224i	0.798651	−	0.601794i	$-0.205547\pi$
$43$	2.26024	+	1.89657i	0.344684	+	0.289224i	−0.453967	+	0.891018i	$0.649992\pi$
$44$	−2.68791	+	4.65560i	−0.405218	+	0.701859i
$45$	8.50112	−	8.23908i	1.26727	−	1.22821i
$46$	0.0715817	+	0.123983i	0.0105541	+	0.0182803i
$47$	−5.41229	−	4.54145i	−0.789463	−	0.662438i	0.156149	−	0.987733i	$-0.450092\pi$
$47$	−5.41229	−	4.54145i	−0.789463	−	0.662438i	−0.945613	+	0.325295i	$0.894536\pi$
$48$	6.41136	−	2.59708i	0.925400	−	0.374856i
$49$	5.21093	−	4.67399i	0.744419	−	0.667713i
$50$	0.320478	+	0.116645i	0.0453225	+	0.0164960i
$51$	1.52922	+	2.44237i	0.214134	+	0.342001i
$52$	−7.42149	−	6.22737i	−1.02918	−	0.863581i
$53$	1.43735	−	2.48957i	0.197436	−	0.341968i	−0.750261	−	0.661142i	$-0.770072\pi$
$53$	1.43735	−	2.48957i	0.197436	−	0.341968i	0.947696	+	0.319174i	$0.103405\pi$
$54$	−0.150455	+	0.0738858i	−0.0204744	+	0.0100546i
$55$	−10.6125			−1.43099
$56$	0.0537122	−	0.337047i	0.00717760	−	0.0450398i
$57$	−0.692577	−	1.10614i	−0.0917341	−	0.146511i
$58$	−0.000578989	−	0.00328361i	−7.60250e−5	−	0.000431159i
$59$	−2.04118	−	11.5761i	−0.265739	−	1.50708i	−0.766922	−	0.641740i	$-0.778213\pi$
$59$	−2.04118	−	11.5761i	−0.265739	−	1.50708i	0.501183	−	0.865341i	$-0.332898\pi$
$60$	10.7741	+	8.40201i	1.39093	+	1.08469i
$61$	6.31104	+	5.29559i	0.808046	+	0.678031i	0.950141	−	0.311822i	$-0.100939\pi$
$61$	6.31104	+	5.29559i	0.808046	+	0.678031i	−0.142095	+	0.989853i	$0.545384\pi$
$62$	−0.143065	+	0.247795i	−0.0181692	+	0.0314700i
$63$	0.685069	−	7.90763i	0.0863106	−	0.996268i
$64$	3.98752	+	6.90658i	0.498440	+	0.863323i
$65$	3.32109	−	18.8349i	0.411931	−	2.33618i
$66$	0.142947	+	0.0463040i	0.0175956	+	0.00569963i
$67$	3.44392	+	1.25348i	0.420742	+	0.153138i	0.543710	−	0.839273i	$-0.317019\pi$
$67$	3.44392	+	1.25348i	0.420742	+	0.153138i	−0.122968	+	0.992411i	$0.539241\pi$
$68$	−2.54761	+	2.13770i	−0.308944	+	0.259234i
$69$	−5.70786	+	5.14870i	−0.687146	+	0.619831i
$70$	0.314541	−	0.120397i	0.0375948	−	0.0143902i
$71$	2.95503	+	5.11826i	0.350698	+	0.607426i	0.986372	−	0.164531i	$-0.0526112\pi$
$71$	2.95503	+	5.11826i	0.350698	+	0.607426i	−0.635674	+	0.771957i	$0.719278\pi$
$72$	−0.216984	−	0.320445i	−0.0255718	−	0.0377648i
$73$	−2.08581	−	3.61273i	−0.244126	−	0.422838i	0.717760	−	0.696291i	$-0.245168\pi$
$73$	−2.08581	−	3.61273i	−0.244126	−	0.422838i	−0.961885	+	0.273453i	$0.911834\pi$
$74$	−0.00735617	+	0.0417189i	−0.000855138	+	0.00484973i
$75$	−2.53219	+	18.1360i	−0.292393	+	2.09416i
$76$	1.15380	−	0.968153i	0.132350	−	0.111055i
$77$	−5.37439	+	4.66291i	−0.612469	+	0.531388i
$78$	−0.126913	+	0.239208i	−0.0143701	+	0.0270850i
$79$	8.24914	−	3.00244i	0.928101	−	0.337801i	0.166644	−	0.986017i	$-0.446707\pi$
$79$	8.24914	−	3.00244i	0.928101	−	0.337801i	0.761457	+	0.648216i	$0.224485\pi$
$80$	−7.88006	+	13.6487i	−0.881017	+	1.52597i
$81$	−5.56647	−	7.07209i	−0.618496	−	0.785788i
$82$	−0.0289726	−	0.0501821i	−0.00319949	−	0.00554168i
$83$	−3.12320	+	17.7126i	−0.342816	+	1.94421i	−0.0137360	+	0.999906i	$0.504372\pi$
$83$	−3.12320	+	17.7126i	−0.342816	+	1.94421i	−0.329080	+	0.944302i	$0.606739\pi$
$84$	9.14785	−	0.478939i	0.998113	−	0.0522565i
$85$	−6.16935	−	2.24546i	−0.669160	−	0.243554i
$86$	0.0894389	+	0.0325531i	0.00964445	+	0.00351029i
$87$	0.165931	−	0.0672145i	0.0177897	−	0.00720615i
$88$	−0.0602419	+	0.341649i	−0.00642180	+	0.0364199i
$89$	−9.24903			−0.980395			−0.490198	−	0.871611i	$-0.663075\pi$
$89$	−9.24903			−0.980395			−0.490198	+	0.871611i	$0.663075\pi$
$90$	0.166791	−	0.343542i	0.0175813	−	0.0362125i
$91$	−6.59374	−	10.9976i	−0.691212	−	1.15286i
$92$	−6.79595	−	5.70248i	−0.708527	−	0.594524i
$93$	−14.6156	−	4.73435i	−1.51557	−	0.490929i
$94$	−0.214167	−	0.0779504i	−0.0220896	−	0.00803997i
$95$	2.79406	+	1.01696i	0.286665	+	0.104337i
$96$	0.497509	−	0.448772i	0.0507768	−	0.0458026i
$97$	4.56635	+	3.83162i	0.463642	+	0.389042i	0.844469	−	0.535604i	$-0.179916\pi$
$97$	4.56635	+	3.83162i	0.463642	+	0.389042i	−0.380827	+	0.924646i	$0.624361\pi$
$98$	0.106390	−	0.199174i	0.0107470	−	0.0201196i
$99$	−0.828875	+	8.02525i	−0.0833051	+	0.806568i
$100$	−21.1338			−2.11338
$101$	−2.59079	+	14.6931i	−0.257793	+	1.46202i	0.531007	+	0.847367i	$0.321814\pi$
$101$	−2.59079	+	14.6931i	−0.257793	+	1.46202i	−0.788800	+	0.614650i	$0.789297\pi$
$102$	0.0733016	+	0.0571633i	0.00725794	+	0.00566001i
$103$	2.03908	+	0.742165i	0.200917	+	0.0731277i	0.440518	−	0.897744i	$-0.354795\pi$
$103$	2.03908	+	0.742165i	0.200917	+	0.0731277i	−0.239602	+	0.970871i	$0.577017\pi$
$104$	−0.587497	−	0.213832i	−0.0576089	−	0.0209679i
$105$	9.84830	+	15.1668i	0.961095	+	1.48013i
$106$	0.0161029	−	0.0913240i	0.00156405	−	0.00887017i
$107$	6.90622	+	11.9619i	0.667649	+	1.15640i	0.978560	+	0.205963i	$0.0660328\pi$
$107$	6.90622	+	11.9619i	0.667649	+	1.15640i	−0.310910	+	0.950439i	$0.600634\pi$
$108$	7.19513	−	7.49118i	0.692352	−	0.720839i
$109$	4.72436	−	8.18284i	0.452512	−	0.783774i	−0.546029	−	0.837766i	$-0.683861\pi$
$109$	4.72436	−	8.18284i	0.452512	−	0.783774i	0.998541	+	0.0539923i	$0.0171946\pi$
$110$	−0.321695	+	0.117087i	−0.0306724	+	0.0111639i
$111$	−2.27313	+	0.0814291i	−0.215756	+	0.00772891i
$112$	2.00630	+	10.3743i	0.189577	+	0.980276i
$113$	7.33190	−	6.15220i	0.689727	−	0.578750i	−0.229103	−	0.973402i	$-0.573579\pi$
$113$	7.33190	−	6.15220i	0.689727	−	0.578750i	0.918831	+	0.394652i	$0.129135\pi$
$114$	−0.0331979	−	0.0258889i	−0.00310927	−	0.00242472i
$115$	3.04116	−	17.2473i	0.283590	−	1.60832i
$116$	0.103308	+	0.178935i	0.00959191	+	0.0166137i
$117$	−13.9836	−	3.98249i	−1.29279	−	0.368182i
$118$	−0.189592	−	0.328384i	−0.0174534	−	0.0302302i
$119$	−4.11088	+	1.57353i	−0.376844	+	0.144245i
$120$	0.838800	+	0.271708i	0.0765716	+	0.0248034i
$121$	−2.88615	+	2.42176i	−0.262377	+	0.220160i
$122$	0.249731	+	0.0908947i	0.0226096	+	0.00822922i
$123$	2.31025	−	2.08393i	0.208309	−	0.187902i
$124$	3.07891	−	17.4614i	0.276494	−	1.56808i
$125$	−10.9948	−	19.0436i	−0.983409	−	1.70331i
$126$	−0.0664782	−	0.247261i	−0.00592235	−	0.0220277i
$127$	2.18105	−	3.77770i	0.193537	−	0.335216i	−0.752883	−	0.658155i	$-0.771337\pi$
$127$	2.18105	−	3.77770i	0.193537	−	0.335216i	0.946420	+	0.322938i	$0.104671\pi$
$128$	0.789730	+	0.662662i	0.0698029	+	0.0585716i
$129$	−0.706683	+	5.06138i	−0.0622200	+	0.445630i
$130$	−0.107132	−	0.607578i	−0.00939614	−	0.0532881i
$131$	−0.752768	−	4.26916i	−0.0657696	−	0.372998i	−0.999872	−	0.0159930i	$-0.994909\pi$
$131$	−0.752768	−	4.26916i	−0.0657696	−	0.372998i	0.934102	−	0.357005i	$-0.116202\pi$
$132$	−9.30524	+	0.333337i	−0.809917	+	0.0290132i
$133$	1.86180	−	0.712642i	0.161438	−	0.0617939i
$134$	0.118224			0.0102130
$135$	19.9092	+	4.90683i	1.71351	+	0.422313i
$136$	−0.107308	+	0.185863i	−0.00920159	+	0.0159376i
$137$	0.386077	+	0.323957i	0.0329848	+	0.0276775i	0.659131	−	0.752028i	$-0.270924\pi$
$137$	0.386077	+	0.323957i	0.0329848	+	0.0276775i	−0.626146	+	0.779706i	$0.715369\pi$
$138$	−0.116216	+	0.219046i	−0.00989295	+	0.0186464i
$139$	9.66255	+	3.51688i	0.819567	+	0.298298i	0.717570	−	0.696487i	$-0.245255\pi$
$139$	9.66255	+	3.51688i	0.819567	+	0.298298i	0.101997	+	0.994785i	$0.467477\pi$
$140$	−15.7641	+	13.6772i	−1.33231	+	1.15593i
$141$	1.69220	−	12.1198i	0.142509	−	1.02067i
$142$	0.146045	+	0.122546i	0.0122558	+	0.0102838i
$143$	6.51695	+	11.2877i	0.544975	+	0.943924i
$144$	9.70572	+	7.02494i	0.808810	+	0.585412i
$145$	−0.203943	+	0.353239i	−0.0169365	+	0.0293349i
$146$	−0.103086	−	0.0864993i	−0.00853144	−	0.00715873i
$147$	11.6513	+	3.35364i	0.960984	+	0.276603i
$148$	−0.455844	−	2.58522i	−0.0374701	−	0.212504i
$149$	−11.9811	+	10.0533i	−0.981530	+	0.823602i	−0.984320	−	0.176394i	$-0.943557\pi$
$149$	−11.9811	+	10.0533i	−0.981530	+	0.823602i	0.00278917	+	0.999996i	$0.499112\pi$
$150$	0.123336	+	0.577690i	0.0100703	+	0.0471682i
$151$	−8.93852	+	3.25336i	−0.727407	+	0.264754i	−0.679067	−	0.734077i	$-0.737615\pi$
$151$	−8.93852	+	3.25336i	−0.727407	+	0.264754i	−0.0483399	+	0.998831i	$0.515393\pi$
$152$	0.0485992	−	0.0841764i	0.00394192	−	0.00682760i
$153$	−2.17987	+	4.48991i	−0.176232	+	0.362988i
$154$	−0.111467	+	0.200641i	−0.00898228	+	0.0161681i
$155$	32.8917	−	11.9716i	2.64192	−	0.961581i
$156$	2.32039	−	16.6190i	0.185780	−	1.33059i
$157$	1.38639	+	7.86263i	0.110646	+	0.627506i	0.988814	+	0.149153i	$0.0476548\pi$
$157$	1.38639	+	7.86263i	0.110646	+	0.627506i	−0.878168	+	0.478353i	$0.841234\pi$
$158$	0.216929	−	0.182025i	0.0172579	−	0.0144811i
$159$	4.97594	−	0.178251i	0.394618	−	0.0141362i
$160$	−0.265074	+	1.50331i	−0.0209560	+	0.118847i
$161$	−6.03797	−	10.0706i	−0.475859	−	0.793674i
$162$	−0.246761	−	0.152960i	−0.0193874	−	0.0120177i
$163$	10.4429	+	18.0876i	0.817952	+	1.41673i	0.907189	+	0.420723i	$0.138224\pi$
$163$	10.4429	+	18.0876i	0.817952	+	1.41673i	−0.0892373	+	0.996010i	$0.528443\pi$
$164$	2.75065	+	2.30807i	0.214790	+	0.180230i
$165$	−9.75472	−	15.5796i	−0.759404	−	1.21287i
$166$	0.100749	+	0.571375i	0.00781963	+	0.0443473i
$167$	−3.51101	+	2.94608i	−0.271690	+	0.227975i	−0.768445	−	0.639916i	$-0.778969\pi$
$167$	−3.51101	+	2.94608i	−0.271690	+	0.227975i	0.496755	+	0.867891i	$0.334525\pi$
$168$	0.544167	−	0.230952i	0.0419834	−	0.0178183i
$169$	−9.85653	+	3.58749i	−0.758195	+	0.275960i
$170$	−0.211784			−0.0162431
$171$	0.987253	−	2.03346i	0.0754971	−	0.155502i
$172$	−5.89800			−0.449718
$173$	2.57715	−	14.6157i	0.195937	−	1.11121i	−0.715141	−	0.698980i	$-0.753638\pi$
$173$	2.57715	−	14.6157i	0.195937	−	1.11121i	0.911078	−	0.412234i	$-0.135251\pi$
$174$	0.00428826	−	0.00386817i	0.000325092	−	0.000293245i
$175$	−26.4393	−	9.13196i	−1.99862	−	0.690312i
$176$	−1.86506	−	10.5773i	−0.140584	−	0.797293i
$177$	15.1179	−	13.6369i	1.13633	−	1.02501i
$178$	−0.280364	+	0.102044i	−0.0210141	+	0.00764852i
$179$	−5.11532			−0.382337			−0.191168	−	0.981557i	$-0.561228\pi$
$179$	−5.11532			−0.382337			−0.191168	+	0.981557i	$0.561228\pi$
$180$	−2.43125	+	23.5396i	−0.181215	+	1.75454i
$181$	9.84429	−	17.0508i	0.731720	−	1.26738i	−0.224427	−	0.974491i	$-0.572051\pi$
$181$	9.84429	−	17.0508i	0.731720	−	1.26738i	0.956147	−	0.292886i	$-0.0946155\pi$
$182$	−0.321210	−	0.260618i	−0.0238097	−	0.0193183i
$183$	−1.97320	+	14.1324i	−0.145863	+	1.04470i
$184$	−0.537978	−	0.195808i	−0.0396603	−	0.0144352i
$185$	3.96984	−	3.33109i	0.291869	−	0.244907i
$186$	−0.495273	+	0.0177419i	−0.0363152	+	0.00130090i
$187$	4.20439	−	1.53027i	0.307455	−	0.111905i
$188$	14.1231			1.03003
$189$	12.2384	−	6.26275i	0.890211	−	0.455548i
$190$	0.0959158			0.00695846
$191$	−8.82949	+	3.21367i	−0.638879	+	0.232533i	−0.641091	−	0.767465i	$-0.721518\pi$
$191$	−8.82949	+	3.21367i	−0.638879	+	0.232533i	0.00221224	+	0.999998i	$0.499296\pi$
$192$	−6.47390	+	12.2021i	−0.467214	+	0.880614i
$193$	8.08871	−	6.78724i	0.582238	−	0.488556i	−0.303443	−	0.952850i	$-0.598136\pi$
$193$	8.08871	−	6.78724i	0.582238	−	0.488556i	0.885681	+	0.464294i	$0.153692\pi$
$194$	0.180693	+	0.0657668i	0.0129730	+	0.00472178i
$195$	30.7029	−	12.4369i	2.19868	−	0.890628i
$196$	−1.97381	+	13.8528i	−0.140987	+	0.989486i
$197$	1.56004	−	2.70208i	0.111149	−	0.192515i	−0.805085	−	0.593159i	$-0.797880\pi$
$197$	1.56004	−	2.70208i	0.111149	−	0.192515i	0.916234	+	0.400644i	$0.131214\pi$
$198$	0.0634166	+	0.252412i	0.00450682	+	0.0179382i
$199$	8.82336			0.625471			0.312736	−	0.949840i	$-0.398755\pi$
$199$	8.82336			0.625471			0.312736	+	0.949840i	$0.398755\pi$
$200$	−1.28158	+	0.466457i	−0.0906214	+	0.0329835i
$201$	1.32539	+	6.20796i	0.0934856	+	0.437876i
$202$	0.0835741	+	0.473972i	0.00588025	+	0.0333486i
$203$	0.0519246	+	0.268495i	0.00364440	+	0.0188446i
$204$	−5.47991	−	1.77508i	−0.383670	−	0.124280i
$205$	−1.23091	+	6.98083i	−0.0859704	+	0.487562i
$206$	0.0699985			0.00487702
$207$	−12.8050	−	3.64682i	−0.890007	−	0.253471i
$208$	19.3560			1.34210
$209$	−1.90414	+	0.693052i	−0.131712	+	0.0479394i
$210$	0.465863	+	0.351092i	0.0321476	+	0.0242276i
$211$	−18.1592	+	15.2374i	−1.25013	+	1.04898i	−0.253468	+	0.967344i	$0.581571\pi$
$211$	−18.1592	+	15.2374i	−1.25013	+	1.04898i	−0.996662	+	0.0816394i	$0.973984\pi$
$212$	0.997855	+	5.65912i	0.0685330	+	0.388670i
$213$	−4.79761	+	9.04264i	−0.328727	+	0.619591i
$214$	0.341322	+	0.286403i	0.0233323	+	0.0195781i
$215$	−5.82168	−	10.0835i	−0.397035	−	0.687686i
$216$	0.270980	−	0.613083i	0.0184378	−	0.0417150i
$217$	11.3969	−	20.5145i	0.773675	−	1.39262i
$218$	0.0529277	−	0.300168i	0.00358472	−	0.0203300i
$219$	3.38640	−	6.38276i	0.228832	−	0.431307i
$220$	16.2509	−	13.6361i	1.09563	−	0.919346i
$221$	1.40016	+	7.94073i	0.0941853	+	0.534151i
$222$	−0.0680064	+	0.0275476i	−0.00456429	+	0.00184888i
$223$	−0.334278	+	0.121667i	−0.0223849	+	0.00814745i	−0.353188	−	0.935552i	$-0.614903\pi$
$223$	−0.334278	+	0.121667i	−0.0223849	+	0.00814745i	0.330803	+	0.943700i	$0.392680\pi$
$224$	0.526282	+	0.877774i	0.0351637	+	0.0586487i
$225$	−28.9518	+	12.9527i	−1.93012	+	0.863514i
$226$	0.154373	−	0.267383i	0.0102688	−	0.0177860i
$227$	−11.0233	+	4.01214i	−0.731639	+	0.266295i	−0.680859	−	0.732415i	$-0.738393\pi$
$227$	−11.0233	+	4.01214i	−0.731639	+	0.266295i	−0.0507807	+	0.998710i	$0.516171\pi$
$228$	2.48182	+	0.803922i	0.164363	+	0.0532410i
$229$	13.9724	−	11.7242i	0.923323	−	0.774760i	−0.0512835	−	0.998684i	$-0.516331\pi$
$229$	13.9724	−	11.7242i	0.923323	−	0.774760i	0.974607	+	0.223924i	$0.0718868\pi$
$230$	−0.0981024	−	0.556367i	−0.00646868	−	0.0366857i
$231$	−11.7853	−	3.60380i	−0.775415	−	0.237113i
$232$	0.0102141	+	0.00857066i	0.000670590	+	0.000562692i
$233$	13.3533	−	23.1286i	0.874803	−	1.51520i	0.0178301	−	0.999841i	$-0.494324\pi$
$233$	13.3533	−	23.1286i	0.874803	−	1.51520i	0.856973	−	0.515362i	$-0.172342\pi$
$234$	−0.467821	+	0.0335601i	−0.0305824	+	0.00219389i
$235$	13.9404	+	24.1454i	0.909370	+	1.57507i
$236$	17.9999	+	15.1037i	1.17169	+	0.983166i
$237$	11.9900	+	9.35028i	0.778837	+	0.607366i
$238$	−0.107252	+	0.0930531i	−0.00695209	+	0.00603174i
$239$	−9.78283	−	3.56066i	−0.632799	−	0.230320i	0.00565038	−	0.999984i	$-0.498201\pi$
$239$	−9.78283	−	3.56066i	−0.632799	−	0.230320i	−0.638449	+	0.769664i	$0.720424\pi$
$240$	−27.2798	+	0.977231i	−1.76090	+	0.0630800i
$241$	−9.42034	−	7.90460i	−0.606817	−	0.509180i	0.286811	−	0.957987i	$-0.407405\pi$
$241$	−9.42034	−	7.90460i	−0.606817	−	0.509180i	−0.893629	+	0.448807i	$0.851849\pi$
$242$	−0.0607679	+	0.105253i	−0.00390631	+	0.00676593i
$243$	5.26555	−	14.6722i	0.337785	−	0.941223i
$244$	−16.4684			−1.05428
$245$	−25.6316	+	10.2990i	−1.63754	+	0.657982i
$246$	0.0470383	−	0.0886587i	0.00299905	−	0.00565267i
$247$	−0.634127	−	3.59631i	−0.0403485	−	0.228828i
$248$	−0.198692	−	1.12684i	−0.0126169	−	0.0715542i
$249$	−28.8734	+	11.6959i	−1.82978	+	0.741197i
$250$	−0.543392	−	0.455960i	−0.0343671	−	0.0288374i
$251$	−7.54312	+	13.0651i	−0.476118	+	0.824660i	−0.999626	−	0.0273608i	$-0.991290\pi$
$251$	−7.54312	+	13.0651i	−0.476118	+	0.824660i	0.523508	+	0.852021i	$0.324623\pi$
$252$	9.11153	+	12.9891i	0.573972	+	0.818239i
$253$	5.96765	+	10.3363i	0.375183	+	0.649836i
$254$	0.0244347	−	0.138576i	0.00153317	−	0.00869503i
$255$	−2.37426	−	11.1208i	−0.148682	−	0.696410i
$256$	−14.9569	−	5.44387i	−0.934807	−	0.340242i
$257$	8.27056	−	6.93982i	0.515903	−	0.432894i	−0.347297	−	0.937755i	$-0.612901\pi$
$257$	8.27056	−	6.93982i	0.515903	−	0.432894i	0.863201	+	0.504861i	$0.168456\pi$
$258$	0.0344204	+	0.161221i	0.00214292	+	0.0100372i
$259$	0.546799	−	3.43119i	0.0339765	−	0.213204i
$260$	19.1155	+	33.1090i	1.18549	+	2.05333i
$261$	0.251192	+	0.181811i	0.0155484	+	0.0112538i
$262$	−0.0699199	−	0.121105i	−0.00431966	−	0.00748188i
$263$	2.69620	−	15.2909i	0.166255	−	0.942877i	−0.781507	−	0.623897i	$-0.785549\pi$
$263$	2.69620	−	15.2909i	0.166255	−	0.942877i	0.947761	−	0.318980i	$-0.103340\pi$
$264$	−0.556925	+	0.225596i	−0.0342763	+	0.0138845i
$265$	−8.69010	+	7.29186i	−0.533829	+	0.447936i
$266$	0.0485737	−	0.0421432i	0.00297824	−	0.00258397i
$267$	−8.50143	−	13.5779i	−0.520279	−	0.830954i
$268$	−6.88426	+	2.50567i	−0.420523	+	0.153058i
$269$	5.78363	−	10.0175i	0.352634	−	0.610780i	−0.634076	−	0.773271i	$-0.718619\pi$
$269$	5.78363	−	10.0175i	0.352634	−	0.610780i	0.986710	+	0.162491i	$0.0519528\pi$
$270$	0.657641	−	0.0709178i	0.0400228	−	0.00431592i
$271$	−4.43407	−	7.68004i	−0.269351	−	0.466529i	0.699344	−	0.714786i	$-0.253476\pi$
$271$	−4.43407	−	7.68004i	−0.269351	−	0.466529i	−0.968694	+	0.248257i	$0.920142\pi$
$272$	1.15379	−	6.54348i	0.0699589	−	0.396757i
$273$	10.0840	−	19.7885i	0.610313	−	1.19765i
$274$	0.0152773	+	0.00556047i	0.000922933	+	0.000335920i
$275$	26.7178	+	9.72448i	1.61114	+	0.586408i
$276$	2.12481	−	15.2182i	0.127898	−	0.916030i
$277$	0.367346	−	2.08332i	0.0220717	−	0.125175i	−0.971781	−	0.235884i	$-0.924201\pi$
$277$	0.367346	−	2.08332i	0.0220717	−	0.125175i	0.993853	+	0.110710i	$0.0353124\pi$
$278$	0.331700			0.0198941
$279$	−6.48402	−	25.8079i	−0.388188	−	1.54508i
$280$	−0.654079	+	1.17734i	−0.0390887	+	0.0703597i
$281$	1.89531	+	1.59035i	0.113065	+	0.0948724i	0.697567	−	0.716519i	$-0.254266\pi$
$281$	1.89531	+	1.59035i	0.113065	+	0.0948724i	−0.584503	+	0.811392i	$0.698710\pi$
$282$	−0.0824218	−	0.386054i	−0.00490815	−	0.0229892i
$283$	14.8229	+	5.39510i	0.881130	+	0.320705i	0.742666	−	0.669662i	$-0.233561\pi$
$283$	14.8229	+	5.39510i	0.881130	+	0.320705i	0.138465	+	0.990367i	$0.455783\pi$
$284$	−11.1015	−	4.04062i	−0.658753	−	0.239766i
$285$	1.07529	+	5.03654i	0.0636947	+	0.298339i
$286$	0.322083	+	0.270260i	0.0190452	+	0.0159808i
$287$	2.44386	+	4.07606i	0.144257	+	0.240602i
$288$	1.11611	+	0.317864i	0.0657673	+	0.0187303i
$289$	−14.2321			−0.837182
$290$	−0.00228480	+	0.0129577i	−0.000134168	+	0.000760904i
$291$	−1.42771	+	10.2255i	−0.0836936	+	0.599427i
$292$	7.83601	+	2.85207i	0.458568	+	0.166905i
$293$	24.9842	+	9.09352i	1.45959	+	0.531249i	0.945254	−	0.326337i	$-0.105814\pi$
$293$	24.9842	+	9.09352i	1.45959	+	0.531249i	0.514341	+	0.857586i	$0.328036\pi$
$294$	0.390184	−	0.0268902i	0.0227560	−	0.00156827i
$295$	−8.05488	+	45.6815i	−0.468973	+	2.65968i
$296$	−0.0847030	−	0.146710i	−0.00492326	−	0.00852734i
$297$	−12.5432	+	6.15974i	−0.727832	+	0.357425i
$298$	−0.252263	+	0.436932i	−0.0146132	+	0.0253108i
$299$	−20.2121	+	7.35660i	−1.16890	+	0.425443i
$300$	−19.4255	−	31.0251i	−1.12153	−	1.79124i
$301$	−7.37866	−	2.54854i	−0.425299	−	0.146896i
$302$	−0.235057	+	0.197236i	−0.0135260	+	0.0113497i
$303$	−23.9513	+	9.70207i	−1.37597	+	0.557370i
$304$	−0.522546	+	2.96351i	−0.0299701	+	0.169969i
$305$	−16.2553	−	28.1550i	−0.930775	−	1.61215i
$306$	−0.0165411	+	0.160152i	−0.000945590	+	0.00915529i
$307$	5.29520	+	9.17155i	0.302213	+	0.523448i	0.976637	−	0.214896i	$-0.0689413\pi$
$307$	5.29520	+	9.17155i	0.302213	+	0.523448i	−0.674424	+	0.738344i	$0.735608\pi$
$308$	2.23837	−	14.0459i	0.127543	−	0.800337i
$309$	0.784737	+	3.67562i	0.0446421	+	0.209099i
$310$	0.864956	−	0.725784i	0.0491262	−	0.0412218i
$311$	17.6456	+	6.42249i	1.00059	+	0.364186i	0.789813	−	0.613348i	$-0.210178\pi$
$311$	17.6456	+	6.42249i	1.00059	+	0.364186i	0.210780	+	0.977534i	$0.432400\pi$
$312$	−0.226097	−	1.05901i	−0.0128002	−	0.0599549i
$313$	−5.57157	+	31.5979i	−0.314924	+	1.78602i	0.257724	+	0.966219i	$0.417027\pi$
$313$	−5.57157	+	31.5979i	−0.314924	+	1.78602i	−0.572648	+	0.819802i	$0.694084\pi$
$314$	0.128773	+	0.223042i	0.00726710	+	0.0125870i
$315$	−13.2131	+	28.3985i	−0.744475	+	1.60007i
$316$	−8.77398	+	15.1970i	−0.493575	+	0.854897i
$317$	5.25691	+	4.41107i	0.295257	+	0.247750i	0.778367	−	0.627810i	$-0.216048\pi$
$317$	5.25691	+	4.41107i	0.295257	+	0.247750i	−0.483110	+	0.875560i	$0.660493\pi$
$318$	0.148868	−	0.0603026i	0.00834811	−	0.00338160i
$319$	−0.0482694	−	0.273749i	−0.00270257	−	0.0153270i
$320$	−5.46488	−	30.9929i	−0.305496	−	1.73255i
$321$	−11.2125	+	21.1336i	−0.625823	+	1.17956i
$322$	−0.294136	−	0.238651i	−0.0163916	−	0.0132995i
$323$	−1.25357			−0.0697505
$324$	17.6109	+	3.67705i	0.978381	+	0.204280i
$325$	−25.6198	+	44.3749i	−1.42113	+	2.46147i
$326$	0.516114	+	0.433071i	0.0285849	+	0.0239856i
$327$	16.3552	−	0.585884i	0.904444	−	0.0323994i
$328$	0.217746	+	0.0792532i	0.0120230	+	0.00437602i
$329$	17.6686	+	6.10264i	0.974104	+	0.336449i
$330$	−0.467581	−	0.364637i	−0.0257395	−	0.0200726i
$331$	2.02724	+	1.70106i	0.111427	+	0.0934985i	0.696799	−	0.717266i	$-0.254607\pi$
$331$	2.02724	+	1.70106i	0.111427	+	0.0934985i	−0.585372	+	0.810765i	$0.699051\pi$
$332$	−17.9765	−	31.1361i	−0.986586	−	1.70882i
$333$	−2.20893	−	3.26218i	−0.121049	−	0.178767i
$334$	−0.0739244	+	0.128041i	−0.00404496	+	0.00700608i
$335$	−11.0790	−	9.29635i	−0.605308	−	0.507914i
$336$	−13.3857	+	12.4810i	−0.730248	+	0.680896i
$337$	−1.96653	−	11.1527i	−0.107123	−	0.607527i	−0.990351	−	0.138582i	$-0.955745\pi$
$337$	−1.96653	−	11.1527i	−0.107123	−	0.607527i	0.883227	−	0.468945i	$-0.155366\pi$
$338$	−0.259198	+	0.217493i	−0.0140985	+	0.0118301i
$339$	15.7709	+	5.10858i	0.856558	+	0.277460i
$340$	12.3323	−	4.48858i	0.668811	−	0.243427i
$341$	−11.9271	+	20.6583i	−0.645887	+	1.11871i
$342$	0.00749136	−	0.0725320i	0.000405086	−	0.00392208i
$343$	−8.45516	+	16.4776i	−0.456536	+	0.889705i
$344$	−0.357663	+	0.130179i	−0.0192839	+	0.00701876i
$345$	28.1150	−	11.3887i	1.51366	−	0.613145i
$346$	−0.0831341	−	0.471477i	−0.00446932	−	0.0253468i
$347$	18.3420	−	15.3908i	0.984652	−	0.826221i	−0.000132581	−	1.00000i	$-0.500042\pi$
$347$	18.3420	−	15.3908i	0.984652	−	0.826221i	0.984785	+	0.173779i	$0.0555978\pi$
$348$	−0.167725	+	0.316131i	−0.00899100	+	0.0169464i
$349$	4.47083	−	25.3553i	0.239318	−	1.35724i	−0.594008	−	0.804459i	$-0.702455\pi$
$349$	4.47083	−	25.3553i	0.239318	−	1.35724i	0.833326	−	0.552781i	$-0.186433\pi$
$350$	−0.902200	+	0.0148880i	−0.0482246	+	0.000795798i
$351$	−7.00688	−	24.1890i	−0.373999	−	1.29112i
$352$	−0.520153	−	0.900931i	−0.0277242	−	0.0480198i
$353$	19.1986	+	16.1095i	1.02184	+	0.857423i	0.989857	−	0.142065i	$-0.0453743\pi$
$353$	19.1986	+	16.1095i	1.02184	+	0.857423i	0.0319799	+	0.999489i	$0.489819\pi$
$354$	0.307811	−	0.580169i	0.0163600	−	0.0308356i
$355$	−4.04986	−	22.9679i	−0.214944	−	1.21901i
$356$	14.1630	−	11.8841i	0.750635	−	0.629858i
$357$	−6.08859	−	4.58858i	−0.322242	−	0.242854i
$358$	−0.155059	+	0.0564370i	−0.00819515	+	0.00298279i
$359$	8.42993			0.444915			0.222457	−	0.974942i	$-0.428592\pi$
$359$	8.42993			0.444915			0.222457	+	0.974942i	$0.428592\pi$
$360$	0.372123	+	1.48113i	0.0196126	+	0.0780626i
$361$	−18.4323			−0.970119
$362$	0.110287	−	0.625469i	0.00579656	−	0.0328739i
$363$	−6.20809	−	2.01095i	−0.325840	−	0.105548i
$364$	24.2278	+	8.36812i	1.26988	+	0.438609i
$365$	2.85860	+	16.2119i	0.149626	+	0.848570i
$366$	0.0961087	+	0.450162i	0.00502368	+	0.0235303i
$367$	−13.2149	+	4.80983i	−0.689813	+	0.251071i	−0.663055	−	0.748571i	$-0.730740\pi$
$367$	−13.2149	+	4.80983i	−0.689813	+	0.251071i	−0.0267577	+	0.999642i	$0.508518\pi$
$368$	17.7245			0.923953
$369$	5.18280	+	1.47605i	0.269806	+	0.0768399i
$370$	0.0835852	−	0.144774i	0.00434539	−	0.00752643i
$371$	−1.19696	+	7.51098i	−0.0621431	+	0.389951i
$372$	28.4639	−	11.5300i	1.47579	−	0.597803i
$373$	−7.08308	−	2.57803i	−0.366748	−	0.133485i	0.152071	−	0.988370i	$-0.451406\pi$
$373$	−7.08308	−	2.57803i	−0.366748	−	0.133485i	−0.518819	+	0.854884i	$0.673628\pi$
$374$	0.110563	−	0.0927736i	0.00571709	−	0.00479721i
$375$	17.8506	−	33.6452i	0.921801	−	1.73743i
$376$	0.856445	−	0.311720i	0.0441678	−	0.0160758i
$377$	0.500949			0.0258002
$378$	0.301883	−	0.324867i	0.0155272	−	0.0167093i
$379$	28.7753			1.47809			0.739044	−	0.673657i	$-0.235278\pi$
$379$	28.7753			1.47809			0.739044	+	0.673657i	$0.235278\pi$
$380$	−5.58522	+	2.03285i	−0.286516	+	0.104283i
$381$	7.55055	−	0.270480i	0.386827	−	0.0138571i
$382$	−0.232190	+	0.194830i	−0.0118799	+	0.00996840i
$383$	7.01885	+	2.55465i	0.358646	+	0.130537i	0.515058	−	0.857155i	$-0.327770\pi$
$383$	7.01885	+	2.55465i	0.358646	+	0.130537i	−0.156412	+	0.987692i	$0.549993\pi$
$384$	−0.246916	+	1.76845i	−0.0126004	+	0.0902459i
$385$	26.2228	−	10.0373i	1.33644	−	0.511549i
$386$	0.170308	−	0.294982i	0.00866845	−	0.0150142i
$387$	−8.07985	+	3.61483i	−0.410722	+	0.183752i
$388$	−11.9157			−0.604927
$389$	−19.8965	+	7.24173i	−1.00879	+	0.367170i	−0.792969	−	0.609262i	$-0.791466\pi$
$389$	−19.8965	+	7.24173i	−1.00879	+	0.367170i	−0.215823	+	0.976433i	$0.569243\pi$
$390$	0.793473	−	0.715742i	0.0401791	−	0.0362430i
$391$	1.28215	+	7.27142i	0.0648410	+	0.367731i
$392$	0.186059	+	0.883618i	0.00939742	+	0.0446294i
$393$	5.57535	−	5.02917i	0.281239	−	0.253688i
$394$	0.0174774	−	0.0991193i	0.000880499	−	0.00499356i
$395$	−34.6418			−1.74302
$396$	−9.04244	−	13.3540i	−0.454400	−	0.671065i
$397$	27.8419			1.39735			0.698673	−	0.715441i	$-0.253774\pi$
$397$	27.8419			1.39735			0.698673	+	0.715441i	$0.253774\pi$
$398$	0.267460	−	0.0973476i	0.0134066	−	0.00487960i
$399$	2.75749	+	2.07814i	0.138047	+	0.104037i
$400$	32.3451	−	27.1408i	1.61726	−	1.35704i
$401$	−4.18351	−	23.7258i	−0.208914	−	1.18481i	−0.891160	−	0.453689i	$-0.850108\pi$
$401$	−4.18351	−	23.7258i	−0.208914	−	1.18481i	0.682246	−	0.731123i	$-0.261003\pi$
$402$	0.108668	+	0.173558i	0.00541988	+	0.00865627i
$403$	−32.9314	−	27.6327i	−1.64043	−	1.37648i
$404$	−14.9120	−	25.8283i	−0.741899	−	1.28501i
$405$	11.0966	+	33.7377i	0.551392	+	1.67644i
$406$	0.00453627	+	0.00756594i	0.000225131	+	0.000375491i
$407$	−0.613272	+	3.47804i	−0.0303988	+	0.172400i
$408$	−0.371488	+	0.0133076i	−0.0183914	+	0.000658826i
$409$	12.7810	−	10.7245i	0.631978	−	0.530292i	−0.269565	−	0.962982i	$-0.586880\pi$
$409$	12.7810	−	10.7245i	0.631978	−	0.530292i	0.901543	+	0.432690i	$0.142436\pi$
$410$	0.0397069	+	0.225189i	0.00196098	+	0.0111213i
$411$	−0.120710	+	0.864546i	−0.00595419	+	0.0426449i
$412$	−4.07604	+	1.48356i	−0.200812	+	0.0730896i
$413$	15.9923	+	26.6731i	0.786928	+	1.31250i
$414$	−0.428389	+	0.0307314i	−0.0210542	+	0.00151036i
$415$	35.4877	−	61.4665i	1.74202	−	3.01727i
$416$	1.76173	−	0.641216i	0.0863758	−	0.0314382i
$417$	3.71862	+	17.4176i	0.182101	+	0.852942i
$418$	−0.0500735	+	0.0420166i	−0.00244917	+	0.00205510i
$419$	−3.30513	−	18.7443i	−0.161466	−	0.915721i	−0.952633	−	0.304121i	$-0.901637\pi$
$419$	−3.30513	−	18.7443i	−0.161466	−	0.915721i	0.791167	−	0.611600i	$-0.209474\pi$
$420$	−34.5685	−	10.5706i	−1.68677	−	0.515794i
$421$	5.08767	+	4.26906i	0.247958	+	0.208061i	0.758292	−	0.651915i	$-0.226034\pi$
$421$	5.08767	+	4.26906i	0.247958	+	0.208061i	−0.510334	+	0.859976i	$0.670478\pi$
$422$	−0.382342	+	0.662236i	−0.0186121	+	0.0322371i
$423$	19.3477	−	8.65594i	0.940717	−	0.420866i
$424$	0.185417	+	0.321152i	0.00900466	+	0.0155965i
$425$	13.4742	+	11.3062i	0.653595	+	0.548431i
$426$	−0.0456621	+	0.327039i	−0.00221233	+	0.0158451i
$427$	−20.6027	−	7.11603i	−0.997033	−	0.344369i
$428$	−25.9454	−	9.44335i	−1.25412	−	0.456461i
$429$	−10.5805	+	19.9424i	−0.510834	+	0.962829i
$430$	−0.287722	−	0.241427i	−0.0138752	−	0.0116426i
$431$	−0.575323	+	0.996489i	−0.0277123	+	0.0479992i	−0.879549	−	0.475808i	$-0.842156\pi$
$431$	−0.575323	+	0.996489i	−0.0277123	+	0.0479992i	0.851837	+	0.523808i	$0.175489\pi$
$432$	−1.39166	+	20.7055i	−0.0669563	+	0.996192i
$433$	−10.6968			−0.514055			−0.257028	−	0.966404i	$-0.582743\pi$
$433$	−10.6968			−0.514055			−0.257028	+	0.966404i	$0.582743\pi$
$434$	0.119138	−	0.747594i	0.00571879	−	0.0358856i
$435$	−0.706025	+	0.0252916i	−0.0338513	+	0.00121264i
$436$	3.27980	+	18.6007i	0.157074	+	0.890811i
$437$	−0.580677	−	3.29319i	−0.0277776	−	0.157534i
$438$	0.0322306	−	0.230841i	0.00154004	−	0.0110300i
$439$	−19.5171	−	16.3768i	−0.931503	−	0.781624i	0.0445839	−	0.999006i	$-0.485804\pi$
$439$	−19.5171	−	16.3768i	−0.931503	−	0.781624i	−0.976087	+	0.217382i	$0.930248\pi$
$440$	0.684504	−	1.18560i	0.0326324	−	0.0565210i
$441$	5.78627	+	20.1871i	0.275537	+	0.961291i
$442$	0.130053	+	0.225258i	0.00618597	+	0.0107144i
$443$	−5.83349	+	33.0834i	−0.277157	+	1.57184i	0.454867	+	0.890559i	$0.349687\pi$
$443$	−5.83349	+	33.0834i	−0.277157	+	1.57184i	−0.732024	+	0.681278i	$0.761424\pi$
$444$	3.37619	−	3.04545i	0.160227	−	0.144531i
$445$	34.2973	+	12.4832i	1.62585	+	0.591760i
$446$	−0.00879056	+	0.00737615i	−0.000416245	+	0.000349271i
$447$	−25.7713	−	8.34796i	−1.21894	−	0.394845i
$448$	−16.3851	−	13.2943i	−0.774123	−	0.628095i
$449$	−11.0779	−	19.1875i	−0.522800	−	0.905516i	−0.999648	−	0.0265304i	$-0.991554\pi$
$449$	−11.0779	−	19.1875i	−0.522800	−	0.905516i	0.476848	−	0.878986i	$-0.341779\pi$
$450$	−0.734703	+	0.712056i	−0.0346342	+	0.0335666i
$451$	−2.41540	−	4.18360i	−0.113737	−	0.196998i
$452$	−3.32228	+	18.8416i	−0.156267	+	0.886235i
$453$	−12.9921	−	10.1317i	−0.610420	−	0.476028i
$454$	−0.289880	+	0.243238i	−0.0136047	+	0.0114157i
$455$	9.60781	+	49.6806i	0.450421	+	2.32906i
$456$	0.168245	−	0.00602695i	0.00787878	−	0.000282238i
$457$	9.55339	−	3.47715i	0.446889	−	0.162654i	−0.108766	−	0.994067i	$-0.534690\pi$
$457$	9.55339	−	3.47715i	0.446889	−	0.162654i	0.555655	+	0.831413i	$0.312468\pi$
$458$	0.294190	−	0.509551i	0.0137466	−	0.0238098i
$459$	−8.59502	+	0.926858i	−0.401181	+	0.0432620i
$460$	17.5043	+	30.3183i	0.816140	+	1.41360i
$461$	0.142962	−	0.810775i	0.00665838	−	0.0377616i	−0.981298	−	0.192497i	$-0.938341\pi$
$461$	0.142962	−	0.810775i	0.00665838	−	0.0377616i	0.987956	+	0.154735i	$0.0494525\pi$
$462$	−0.397005	+	0.0207854i	−0.0184704	+	0.000967022i
$463$	−10.3711	−	3.77477i	−0.481985	−	0.175428i	0.0895886	−	0.995979i	$-0.471445\pi$
$463$	−10.3711	−	3.77477i	−0.481985	−	0.175428i	−0.571574	+	0.820551i	$0.693667\pi$
$464$	−0.387907	−	0.141187i	−0.0180081	−	0.00655442i
$465$	47.8078	+	37.2822i	2.21703	+	1.72892i
$466$	0.149599	−	0.848417i	0.00693003	−	0.0393022i
$467$	19.6268			0.908218			0.454109	−	0.890946i	$-0.349958\pi$
$467$	19.6268			0.908218			0.454109	+	0.890946i	$0.349958\pi$
$468$	26.5301	−	11.8693i	1.22636	−	0.548658i
$469$	−9.69521	+	0.159989i	−0.447683	+	0.00738762i
$470$	0.688967	+	0.578112i	0.0317797	+	0.0266663i
$471$	−10.2683	+	9.26236i	−0.473138	+	0.426787i
$472$	1.42490	+	0.518621i	0.0655863	+	0.0238714i
$473$	7.45638	+	2.71390i	0.342845	+	0.124785i
$474$	0.466613	+	0.151147i	0.0214322	+	0.00694242i
$475$	−6.10239	−	5.12051i	−0.279997	−	0.234945i
$476$	4.27313	−	7.69163i	0.195858	−	0.352545i
$477$	4.83542	+	7.14102i	0.221398	+	0.326965i
$478$	−0.335829			−0.0153605
$479$	−1.97315	+	11.1903i	−0.0901556	+	0.511298i	0.905969	+	0.423344i	$0.139144\pi$
$479$	−1.97315	+	11.1903i	−0.0901556	+	0.511298i	−0.996125	+	0.0879538i	$0.971967\pi$
$480$	−2.45056	+	0.992659i	−0.111852	+	0.0453085i
$481$	−5.98082	−	2.17684i	−0.272702	−	0.0992554i
$482$	−0.372768	−	0.135676i	−0.0169791	−	0.00617989i
$483$	9.23407	−	18.1205i	0.420165	−	0.824513i
$484$	1.30779	−	7.41686i	0.0594451	−	0.337130i
$485$	−11.7615	−	20.3715i	−0.534062	−	0.925023i
$486$	−0.00226435	−	0.502850i	−0.000102713	−	0.0228097i
$487$	2.67544	−	4.63401i	0.121236	−	0.209987i	−0.799019	−	0.601305i	$-0.794648\pi$
$487$	2.67544	−	4.63401i	0.121236	−	0.209987i	0.920255	+	0.391318i	$0.127981\pi$
$488$	−0.998665	+	0.363484i	−0.0452074	+	0.0164542i
$489$	−16.9545	+	31.9562i	−0.766709	+	1.44511i
$490$	−0.663335	+	0.594984i	−0.0299664	+	0.0268786i
$491$	−24.6086	+	20.6490i	−1.11057	+	0.931878i	−0.998090	−	0.0617756i	$-0.980324\pi$
$491$	−24.6086	+	20.6490i	−1.11057	+	0.931878i	−0.112479	+	0.993654i	$0.535879\pi$
$492$	−0.860015	+	6.15957i	−0.0387725	+	0.277695i
$493$	0.0298611	−	0.169351i	0.00134488	−	0.00762718i
$494$	−0.0589001	−	0.102018i	−0.00265004	−	0.00459000i
$495$	13.9051	−	28.6405i	0.624989	−	1.28730i
$496$	17.7123	+	30.6786i	0.795305	+	1.37751i
$497$	−12.1425	−	9.85197i	−0.544665	−	0.441921i
$498$	−0.746194	+	0.673094i	−0.0334377	+	0.0301621i
$499$	−24.0547	+	20.1843i	−1.07684	+	0.903575i	−0.995654	−	0.0931244i	$-0.970315\pi$
$499$	−24.0547	+	20.1843i	−1.07684	+	0.903575i	−0.0811839	+	0.996699i	$0.525870\pi$
$500$	41.3056	+	15.0340i	1.84724	+	0.672341i
$501$	−7.55217	−	2.44633i	−0.337406	−	0.109294i
$502$	−0.0845067	+	0.479261i	−0.00377172	+	0.0213905i
$503$	−6.05814	−	10.4930i	−0.270119	−	0.467860i	0.698773	−	0.715343i	$-0.253730\pi$
$503$	−6.05814	−	10.4930i	−0.270119	−	0.467860i	−0.968892	+	0.247484i	$0.920396\pi$
$504$	0.839227	+	0.586573i	0.0373821	+	0.0261280i
$505$	29.4381	−	50.9882i	1.30998	−	2.26895i
$506$	0.294936	+	0.247480i	0.0131115	+	0.0110018i
$507$	−14.3264	−	11.1722i	−0.636257	−	0.496176i
$508$	1.51416	+	8.58721i	0.0671798	+	0.380996i
$509$	3.20646	+	18.1847i	0.142124	+	0.806024i	0.969632	+	0.244570i	$0.0786468\pi$
$509$	3.20646	+	18.1847i	0.142124	+	0.806024i	−0.827508	+	0.561454i	$0.810242\pi$
$510$	−0.194665	−	0.310906i	−0.00861993	−	0.0137672i
$511$	8.57080	+	6.95403i	0.379150	+	0.307628i
$512$	−2.57529			−0.113813
$513$	3.89264	−	0.419769i	0.171864	−	0.0185333i
$514$	0.174137	−	0.301614i	0.00768085	−	0.0133036i
$515$	−6.55964	−	5.50420i	−0.289052	−	0.242544i
$516$	−5.42126	−	8.65847i	−0.238658	−	0.381168i
$517$	−17.8548	−	6.49860i	−0.785251	−	0.285808i
$518$	−0.0212811	−	0.110042i	−0.000935040	−	0.00483496i
$519$	23.8252	−	9.65099i	1.04581	−	0.423632i
$520$	1.88996	+	1.58586i	0.0828801	+	0.0695446i
$521$	−13.1082	−	22.7040i	−0.574279	−	0.994680i	−0.996120	−	0.0880100i	$-0.971949\pi$
$521$	−13.1082	−	22.7040i	−0.574279	−	0.994680i	0.421841	−	0.906670i	$-0.361384\pi$
$522$	0.00962025	+	0.00273982i	0.000421067	+	0.000119919i
$523$	−15.4813	+	26.8143i	−0.676948	+	1.17251i	0.298948	+	0.954270i	$0.403364\pi$
$523$	−15.4813	+	26.8143i	−0.676948	+	1.17251i	−0.975895	+	0.218238i	$0.929969\pi$
$524$	6.63817	+	5.57009i	0.289990	+	0.243330i
$525$	−10.8961	−	47.2076i	−0.475546	−	2.06031i
$526$	−0.0869744	−	0.493256i	−0.00379226	−	0.0215070i
$527$	−11.3045	+	9.48562i	−0.492433	+	0.413200i
$528$	13.8135	−	12.4603i	0.601157	−	0.542265i
$529$	3.10448	−	1.12994i	0.134978	−	0.0491278i
$530$	−0.182970	+	0.316914i	−0.00794773	+	0.0137659i
$531$	33.9155	+	9.65902i	1.47181	+	0.419166i
$532$	−1.93527	+	3.48350i	−0.0839048	+	0.151029i
$533$	8.18083	−	2.97758i	0.354351	−	0.128973i
$534$	−0.407506	−	0.317788i	−0.0176345	−	0.0137520i
$535$	−9.46495	−	53.6784i	−0.409205	−	2.32072i
$536$	−0.362166	+	0.303894i	−0.0156432	+	0.0131262i
$537$	−4.70185	−	7.50947i	−0.202900	−	0.324057i
$538$	0.0647948	−	0.367470i	0.00279350	−	0.0158427i
$539$	8.86955	−	16.6048i	0.382039	−	0.715219i
$540$	−36.7917	+	18.0677i	−1.58326	+	0.777510i
$541$	−10.8185	−	18.7381i	−0.465122	−	0.805615i	0.534085	−	0.845431i	$-0.320656\pi$
$541$	−10.8185	−	18.7381i	−0.465122	−	0.805615i	−0.999207	+	0.0398159i	$0.987323\pi$
$542$	−0.219142	−	0.183882i	−0.00941298	−	0.00789842i
$543$	34.0798	−	1.22082i	1.46250	−	0.0523905i
$544$	−0.111755	−	0.633792i	−0.00479144	−	0.0271736i
$545$	−28.5631	+	23.9673i	−1.22351	+	1.02664i
$546$	0.0873498	−	0.711100i	0.00373823	−	0.0304323i
$547$	−27.7409	+	10.0969i	−1.18612	+	0.431711i	−0.858358	−	0.513051i	$-0.828515\pi$
$547$	−27.7409	+	10.0969i	−1.18612	+	0.431711i	−0.327758	+	0.944762i	$0.606293\pi$
$548$	−1.00745			−0.0430362
$549$	−22.5605	+	10.0933i	−0.962860	+	0.430773i
$550$	0.917180			0.0391087
$551$	−0.0135239	+	0.0766980i	−0.000576139	+	0.00326745i
$552$	−0.207040	−	0.969752i	−0.00881221	−	0.0412754i
$553$	−17.5433	+	15.2208i	−0.746017	+	0.647255i
$554$	−0.0118499	−	0.0672042i	−0.000503454	−	0.00285523i
$555$	8.53912	+	2.76603i	0.362466	+	0.117411i
$556$	−19.3150	+	7.03010i	−0.819140	+	0.298143i
$557$	23.2458			0.984957			0.492479	−	0.870325i	$-0.336091\pi$
$557$	23.2458			0.984957			0.492479	+	0.870325i	$0.336091\pi$
$558$	−0.481286	−	0.710770i	−0.0203744	−	0.0300893i
$559$	−7.14997	+	12.3841i	−0.302411	+	0.523792i
$560$	6.56214	−	41.1777i	0.277301	−	1.74008i
$561$	6.11104	+	4.76561i	0.258008	+	0.201204i
$562$	0.0749983	+	0.0272971i	0.00316361	+	0.00115146i
$563$	−22.4743	+	18.8582i	−0.947179	+	0.794777i	−0.978820	−	0.204722i	$-0.934371\pi$
$563$	−22.4743	+	18.8582i	−0.947179	+	0.794777i	0.0316415	+	0.999499i	$0.489927\pi$
$564$	12.9815	+	20.7332i	0.546622	+	0.873027i
$565$	−35.4916	+	12.9179i	−1.49314	+	0.543460i
$566$	0.508847			0.0213884
$567$	20.4431	+	12.2098i	0.858529	+	0.512765i
$568$	−0.762393			−0.0319893
$569$	−39.0561	+	14.2153i	−1.63732	+	0.595935i	−0.986567	−	0.163356i	$-0.947768\pi$
$569$	−39.0561	+	14.2153i	−1.63732	+	0.595935i	−0.650751	+	0.759291i	$0.725546\pi$
$570$	0.0881629	+	0.140808i	0.00369274	+	0.00589779i
$571$	−9.70179	+	8.14077i	−0.406007	+	0.340681i	−0.822810	−	0.568316i	$-0.807595\pi$
$571$	−9.70179	+	8.14077i	−0.406007	+	0.340681i	0.416803	+	0.908997i	$0.363151\pi$
$572$	−24.4830	−	8.91108i	−1.02368	−	0.372591i
$573$	−12.8336	−	10.0081i	−0.536130	−	0.418094i
$574$	0.119051	+	0.0965938i	0.00496910	+	0.00403175i
$575$	−23.4604	+	40.6346i	−0.978366	+	1.69458i
$576$	−23.8638	+	1.71192i	−0.994324	+	0.0713299i
$577$	−17.8669			−0.743808			−0.371904	−	0.928271i	$-0.621295\pi$
$577$	−17.8669			−0.743808			−0.371904	+	0.928271i	$0.621295\pi$
$578$	−0.431414	+	0.157022i	−0.0179445	+	0.00653125i
$579$	17.3988	+	5.63589i	0.723069	+	0.234220i
$580$	−0.141583	−	0.802959i	−0.00587893	−	0.0333410i
$581$	−9.03532	−	46.7203i	−0.374848	−	1.93829i
$582$	0.0695393	+	0.325714i	0.00288250	+	0.0135013i
$583$	1.34247	−	7.61353i	0.0555995	−	0.315320i
$584$	0.538136			0.0222682
$585$	46.4790	+	33.6412i	1.92167	+	1.39089i
$586$	0.857670			0.0354300
$587$	−14.7437	+	5.36628i	−0.608539	+	0.221490i	−0.627864	−	0.778323i	$-0.716071\pi$
$587$	−14.7437	+	5.36628i	−0.608539	+	0.221490i	0.0193246	+	0.999813i	$0.493848\pi$
$588$	−22.1507	+	9.83545i	−0.913478	+	0.405607i
$589$	5.11976	−	4.29598i	0.210956	−	0.177013i
$590$	0.259836	+	1.47360i	0.0106973	+	0.0606672i
$591$	5.40069	−	0.193466i	0.222155	−	0.00795813i
$592$	4.01770	+	3.37125i	0.165126	+	0.138558i
$593$	16.1429	+	27.9602i	0.662908	+	1.14819i	0.979848	+	0.199744i	$0.0640111\pi$
$593$	16.1429	+	27.9602i	0.662908	+	1.14819i	−0.316940	+	0.948445i	$0.602656\pi$
$594$	−0.312260	+	0.325108i	−0.0128122	+	0.0133393i
$595$	17.3677	−	0.286601i	0.712008	−	0.0117495i
$596$	5.42897	−	30.7892i	0.222379	−	1.26117i
$597$	8.11016	+	12.9530i	0.331927	+	0.530131i
$598$	−0.531519	+	0.445998i	−0.0217354	+	0.0182382i
$599$	−3.83043	−	21.7234i	−0.156507	−	0.887596i	−0.957395	−	0.288782i	$-0.906750\pi$
$599$	−3.83043	−	21.7234i	−0.156507	−	0.887596i	0.800888	−	0.598814i	$-0.204361\pi$
$600$	−1.86277	−	1.45265i	−0.0760471	−	0.0593043i
$601$	34.2549	−	12.4678i	1.39729	−	0.508571i	0.469915	−	0.882712i	$-0.344285\pi$
$601$	34.2549	−	12.4678i	1.39729	−	0.508571i	0.927372	+	0.374141i	$0.122062\pi$
$602$	−0.251785	+	0.00415494i	−0.0102620	+	0.000169343i
$603$	−7.89525	+	7.65189i	−0.321519	+	0.311609i
$604$	9.50723	−	16.4670i	0.386844	−	0.670033i
$605$	13.9710	−	5.08503i	0.568002	−	0.206736i
$606$	−0.618989	+	0.558351i	−0.0251447	+	0.0226814i
$607$	3.43140	−	2.87928i	0.139276	−	0.116867i	−0.570488	−	0.821306i	$-0.693246\pi$
$607$	3.43140	−	2.87928i	0.139276	−	0.116867i	0.709764	+	0.704439i	$0.248801\pi$
$608$	0.0506131	+	0.287041i	0.00205263	+	0.0116410i
$609$	−0.346432	+	0.323020i	−0.0140381	+	0.0130894i
$610$	−0.803375	−	0.674112i	−0.0325277	−	0.0272940i
$611$	17.1210	−	29.6545i	0.692643	−	1.19969i
$612$	−2.43109	−	9.67630i	−0.0982711	−	0.391141i
$613$	0.737367	+	1.27716i	0.0297820	+	0.0515839i	0.880532	−	0.473986i	$-0.157185\pi$
$613$	0.737367	+	1.27716i	0.0297820	+	0.0515839i	−0.850750	+	0.525570i	$0.823852\pi$
$614$	0.261701	+	0.219594i	0.0105614	+	0.00886207i
$615$	−11.3795	+	4.60955i	−0.458867	+	0.185875i
$616$	−0.174278	−	0.901164i	−0.00702184	−	0.0363089i
$617$	−35.4677	−	12.9092i	−1.42788	−	0.519705i	−0.491555	−	0.870847i	$-0.663571\pi$
$617$	−35.4677	−	12.9092i	−1.42788	−	0.519705i	−0.936322	+	0.351142i	$0.885793\pi$
$618$	0.0643405	+	0.102760i	0.00258815	+	0.00413362i
$619$	9.28915	+	7.79452i	0.373362	+	0.313288i	0.810090	−	0.586306i	$-0.199418\pi$
$619$	9.28915	+	7.79452i	0.373362	+	0.313288i	−0.436728	+	0.899594i	$0.643863\pi$
$620$	−34.9844	+	60.5947i	−1.40501	+	2.43354i
$621$	−6.41628	−	22.1502i	−0.257476	−	0.888856i
$622$	0.605747			0.0242883
$623$	22.8536	−	8.74772i	0.915612	−	0.350470i
$624$	17.7914	+	28.4152i	0.712227	+	1.13752i
$625$	5.88902	+	33.3983i	0.235561	+	1.33593i
$626$	0.179729	+	1.01929i	0.00718340	+	0.0407391i
$627$	−2.76766	−	2.15832i	−0.110530	−	0.0861949i
$628$	−12.2257	−	10.2586i	−0.487859	−	0.409362i
$629$	−1.09241	+	1.89212i	−0.0435574	+	0.0754437i
$630$	−0.0872071	+	1.00662i	−0.00347442	+	0.0401046i
$631$	−0.847811	−	1.46845i	−0.0337508	−	0.0584581i	0.848657	−	0.528944i	$-0.177412\pi$
$631$	−0.847811	−	1.46845i	−0.0337508	−	0.0584581i	−0.882407	+	0.470486i	$0.844079\pi$
$632$	−0.196644	+	1.11522i	−0.00782207	+	0.0443611i
$633$	−39.0603	−	12.6526i	−1.55251	−	0.502896i
$634$	0.208019	+	0.0757126i	0.00826147	+	0.00300693i
$635$	−13.1865	+	11.0648i	−0.523289	+	0.439091i
$636$	−7.39059	+	6.66658i	−0.293056	+	0.264347i
$637$	26.6941	+	20.9378i	1.05766	+	0.829585i
$638$	−0.00448344	−	0.00776554i	−0.000177501	−	0.000307441i
$639$	−17.6847	+	1.26865i	−0.699597	+	0.0501870i
$640$	−2.03410	−	3.52317i	−0.0804049	−	0.139265i
$641$	−5.96752	+	33.8435i	−0.235703	+	1.33674i	0.605426	+	0.795902i	$0.293003\pi$
$641$	−5.96752	+	33.8435i	−0.235703	+	1.33674i	−0.841129	+	0.540835i	$0.818108\pi$
$642$	−0.106717	+	0.764326i	−0.00421179	+	0.0301655i
$643$	22.7195	−	19.0639i	0.895969	−	0.751807i	−0.0734294	−	0.997300i	$-0.523394\pi$
$643$	22.7195	−	19.0639i	0.895969	−	0.751807i	0.969398	+	0.245493i	$0.0789499\pi$
$644$	22.1857	+	7.66279i	0.874238	+	0.301956i
$645$	9.45175	−	17.8148i	0.372162	−	0.701458i
$646$	−0.0379992	+	0.0138306i	−0.00149506	+	0.000544156i
$647$	−1.88069	+	3.25746i	−0.0739377	+	0.128064i	−0.900624	−	0.434599i	$-0.856890\pi$
$647$	−1.88069	+	3.25746i	−0.0739377	+	0.128064i	0.826686	+	0.562663i	$0.190223\pi$
$648$	1.14910	−	0.165720i	0.0451411	−	0.00651008i
$649$	−15.8060	−	27.3768i	−0.620441	−	1.07463i
$650$	−0.287023	+	1.62779i	−0.0112580	+	0.0638471i
$651$	40.5918	−	2.12520i	1.59092	−	0.0832930i
$652$	−39.2321	−	14.2793i	−1.53645	−	0.559221i
$653$	16.7177	+	6.08474i	0.654213	+	0.238114i	0.647736	−	0.761865i	$-0.275716\pi$
$653$	16.7177	+	6.08474i	0.654213	+	0.238114i	0.00647719	+	0.999979i	$0.497938\pi$
$654$	0.489307	−	0.198206i	0.0191334	−	0.00775045i
$655$	−2.97056	+	16.8469i	−0.116069	+	0.658263i
$656$	−7.17397			−0.280097
$657$	12.4828	−	0.895479i	0.487000	−	0.0349359i
$658$	0.602916	−	0.00994925i	0.0235041	−	0.000387862i
$659$	19.8663	+	16.6698i	0.773883	+	0.649365i	0.941700	−	0.336453i	$-0.109227\pi$
$659$	19.8663	+	16.6698i	0.773883	+	0.649365i	−0.167817	+	0.985818i	$0.553672\pi$
$660$	34.9556	+	11.3230i	1.36064	+	0.440746i
$661$	20.6360	+	7.51089i	0.802647	+	0.292140i	0.710583	−	0.703613i	$-0.248431\pi$
$661$	20.6360	+	7.51089i	0.802647	+	0.292140i	0.0920643	+	0.995753i	$0.470653\pi$
$662$	0.0802190	+	0.0291973i	0.00311780	+	0.00113479i
$663$	−10.3703	+	9.35437i	−0.402748	+	0.363294i
$664$	−1.77734	−	1.49137i	−0.0689743	−	0.0578763i
$665$	−7.86575	+	0.129800i	−0.305021	+	0.00503342i
$666$	−0.102950	−	0.0745148i	−0.00398924	−	0.00288739i
$667$	0.458725			0.0177619
$668$	1.59093	−	9.02263i	0.0615550	−	0.349096i
$669$	−0.485871	−	0.378900i	−0.0187848	−	0.0146491i
$670$	−0.438400	−	0.159565i	−0.0169369	−	0.00616452i
$671$	20.8197	+	7.57775i	0.803735	+	0.292536i
$672$	−0.804861	+	1.57942i	−0.0310482	+	0.0609276i
$673$	0.0952584	−	0.540237i	0.00367194	−	0.0208246i	−0.982917	−	0.184051i	$-0.941079\pi$
$673$	0.0952584	−	0.540237i	0.00367194	−	0.0208246i	0.986589	+	0.163226i	$0.0521900\pi$
$674$	−0.182658	−	0.316373i	−0.00703573	−	0.0121862i
$675$	−45.6266	−	30.5965i	−1.75617	−	1.17766i
$676$	10.4836	−	18.1582i	0.403217	−	0.698393i
$677$	40.3843	−	14.6987i	1.55209	−	0.564916i	0.583186	−	0.812339i	$-0.301806\pi$
$677$	40.3843	−	14.6987i	1.55209	−	0.564916i	0.968908	+	0.247423i	$0.0795837\pi$
$678$	0.534422	−	0.0191443i	0.0205244	−	0.000735234i
$679$	−14.9070	−	5.14880i	−0.572080	−	0.197593i
$680$	0.648775	−	0.544387i	0.0248794	−	0.0208763i
$681$	−16.0222	−	12.4947i	−0.613972	−	0.478798i
$682$	−0.133621	+	0.757801i	−0.00511660	+	0.0290177i
$683$	3.14418	+	5.44587i	0.120309	+	0.208380i	0.919889	−	0.392178i	$-0.128278\pi$
$683$	3.14418	+	5.44587i	0.120309	+	0.208380i	−0.799581	+	0.600559i	$0.794945\pi$
$684$	1.10103	+	4.38234i	0.0420989	+	0.167563i
$685$	−0.994415	−	1.72238i	−0.0379946	−	0.0658087i
$686$	−0.0745032	+	0.592766i	−0.00284455	+	0.0226319i
$687$	30.0546	+	9.73542i	1.14666	+	0.371430i
$688$	9.02686	−	7.57443i	0.344146	−	0.288773i
$689$	13.0922	+	4.76517i	0.498773	+	0.181538i
$690$	0.726593	−	0.655413i	0.0276609	−	0.0249511i
$691$	3.88895	−	22.0553i	0.147943	−	0.839025i	−0.817014	−	0.576617i	$-0.804372\pi$
$691$	3.88895	−	22.0553i	0.147943	−	0.839025i	0.964957	−	0.262408i	$-0.0845165\pi$
$692$	14.8335	+	25.6923i	0.563884	+	0.976676i
$693$	−5.54218	−	20.6137i	−0.210530	−	0.783051i
$694$	0.386192	−	0.668904i	0.0146597	−	0.0253913i
$695$	−31.0840	−	26.0826i	−1.17908	−	0.989370i
$696$	−0.00319353	+	0.0228726i	−0.000121050	+	0.000866983i
$697$	−0.518948	−	2.94310i	−0.0196566	−	0.111478i
$698$	−0.144221	−	0.817917i	−0.00545884	−	0.0309586i
$699$	46.2275	−	1.65598i	1.74848	−	0.0626351i
$700$	52.2200	−	19.9883i	1.97373	−	0.755487i
$701$	34.7809			1.31366			0.656828	−	0.754040i	$-0.271898\pi$
$701$	34.7809			1.31366			0.656828	+	0.754040i	$0.271898\pi$
$702$	−0.479274	−	0.655930i	−0.0180890	−	0.0247565i
$703$	0.494748	−	0.856929i	0.0186598	−	0.0323197i
$704$	16.4296	+	13.7861i	0.619215	+	0.519583i
$705$	−22.6328	+	42.6587i	−0.852400	+	1.60662i
$706$	0.759698	+	0.276507i	0.0285916	+	0.0104065i
$707$	−7.49506	−	38.7559i	−0.281881	−	1.45756i
$708$	−5.62780	+	40.3073i	−0.211506	+	1.51484i
$709$	21.3878	+	17.9465i	0.803235	+	0.673994i	0.948983	−	0.315328i	$-0.102114\pi$
$709$	21.3878	+	17.9465i	0.803235	+	0.673994i	−0.145748	+	0.989322i	$0.546559\pi$
$710$	−0.376166	−	0.651538i	−0.0141173	−	0.0244518i
$711$	−2.70565	+	26.1963i	−0.101470	+	0.982438i
$712$	0.596558	−	1.03327i	0.0223570	−	0.0387234i
$713$	−30.1556	−	25.3036i	−1.12934	−	0.947627i
$714$	−0.235188	−	0.0719175i	−0.00880168	−	0.00269145i
$715$	−8.93146	−	50.6528i	−0.334018	−	1.89431i
$716$	7.83305	−	6.57271i	0.292735	−	0.245634i
$717$	−3.76491	−	17.6344i	−0.140603	−	0.658568i
$718$	0.255535	−	0.0930070i	0.00953647	−	0.00347099i
$719$	−20.6505	+	35.7678i	−0.770135	+	1.33391i	0.167353	+	0.985897i	$0.446478\pi$
$719$	−20.6505	+	35.7678i	−0.770135	+	1.33391i	−0.937488	+	0.348017i	$0.886855\pi$
$720$	−26.5094	−	39.1495i	−0.987947	−	1.45902i
$721$	−5.74035	+	0.0947267i	−0.213782	+	0.00352781i
$722$	−0.558733	+	0.203362i	−0.0207939	+	0.00756836i
$723$	2.94535	−	21.0951i	0.109539	−	0.784534i
$724$	6.83421	+	38.7587i	0.253992	+	1.44046i
$725$	0.837119	−	0.702426i	0.0310898	−	0.0260875i
$726$	−0.210371	+	0.00753602i	−0.00780761	+	0.000279688i
$727$	−2.47910	+	14.0597i	−0.0919447	+	0.521444i	0.903696	+	0.428174i	$0.140843\pi$
$727$	−2.47910	+	14.0597i	−0.0919447	+	0.521444i	−0.995641	+	0.0932699i	$0.970268\pi$
$728$	1.65390	−	0.0272925i	0.0612977	−	0.00101153i
$729$	26.3793	−	5.75624i	0.977010	−	0.213194i
$730$	0.265517	+	0.459889i	0.00982723	+	0.0170213i
$731$	3.76037	+	3.15532i	0.139082	+	0.116704i
$732$	−15.1372	−	24.1762i	−0.559488	−	0.893577i
$733$	3.41036	+	19.3411i	0.125965	+	0.714381i	0.980730	+	0.195367i	$0.0625897\pi$
$733$	3.41036	+	19.3411i	0.125965	+	0.714381i	−0.854766	+	0.519014i	$0.826299\pi$
$734$	−0.347514	+	0.291599i	−0.0128270	+	0.0107631i
$735$	−38.6791	−	28.1615i	−1.42670	−	1.03875i
$736$	1.61324	−	0.587170i	0.0594646	−	0.0216434i
$737$	9.85618			0.363057
$738$	0.173390	−	0.0124385i	0.00638258	−	0.000457868i
$739$	1.77314			0.0652262			0.0326131	−	0.999468i	$-0.489617\pi$
$739$	1.77314			0.0652262			0.0326131	+	0.999468i	$0.489617\pi$
$740$	−1.79884	+	10.2018i	−0.0661268	+	0.375024i
$741$	4.69664	−	4.23654i	0.172535	−	0.155633i
$742$	0.0465851	+	0.240885i	0.00171019	+	0.00884315i
$743$	−6.26135	−	35.5099i	−0.229707	−	1.30273i	−0.853480	−	0.521126i	$-0.825512\pi$
$743$	−6.26135	−	35.5099i	−0.229707	−	1.30273i	0.623773	−	0.781605i	$-0.285599\pi$
$744$	1.47160	−	1.32744i	0.0539516	−	0.0486663i
$745$	57.9971	−	21.1092i	2.12485	−	0.773382i
$746$	−0.243151			−0.00890239
$747$	−43.7096	−	31.6367i	−1.59925	−	1.15753i
$748$	−4.47189	+	7.74554i	−0.163508	+	0.283205i
$749$	−28.3783	−	23.0251i	−1.03692	−	0.841319i
$750$	0.169896	−	1.21682i	0.00620372	−	0.0444321i
$751$	31.2937	+	11.3900i	1.14192	+	0.415626i	0.842607	−	0.538529i	$-0.181020\pi$
$751$	31.2937	+	11.3900i	1.14192	+	0.415626i	0.299315	+	0.954154i	$0.403242\pi$
$752$	−21.6154	+	18.1374i	−0.788231	+	0.661404i
$753$	−26.1134	+	0.935447i	−0.951625	+	0.0340896i
$754$	0.0151851	−	0.00552694i	0.000553010	−	0.000201279i
$755$	37.5368			1.36610
$756$	−10.6935	+	25.3153i	−0.388918	+	0.920708i
$757$	3.07203			0.111655			0.0558274	−	0.998440i	$-0.482220\pi$
$757$	3.07203			0.111655			0.0558274	+	0.998440i	$0.482220\pi$
$758$	0.872259	−	0.317476i	0.0316819	−	0.0115313i
$759$	−9.68873	+	18.2615i	−0.351679	+	0.662851i
$760$	−0.293827	+	0.246550i	−0.0106582	+	0.00894330i
$761$	21.0629	+	7.66628i	0.763531	+	0.277902i	0.694288	−	0.719697i	$-0.255719\pi$
$761$	21.0629	+	7.66628i	0.763531	+	0.277902i	0.0692427	+	0.997600i	$0.477942\pi$
$762$	0.225894	−	0.0915038i	0.00818328	−	0.00331483i
$763$	−3.93423	+	24.6875i	−0.142429	+	0.893746i
$764$	9.39125	−	16.2661i	0.339764	−	0.588488i
$765$	14.1433	−	13.7074i	0.511353	−	0.495591i
$766$	0.240946			0.00870574
$767$	53.5341	−	19.4848i	1.93300	−	0.703556i
$768$	−5.75615	−	26.9611i	−0.207707	−	0.972876i
$769$	−1.89903	−	10.7699i	−0.0684806	−	0.388373i	−0.999713	−	0.0239475i	$-0.992377\pi$
$769$	−1.89903	−	10.7699i	−0.0684806	−	0.388373i	0.931233	−	0.364425i	$-0.118735\pi$
$770$	0.684143	−	0.593573i	0.0246548	−	0.0213909i
$771$	17.7900	+	5.76260i	0.640690	+	0.207535i
$772$	−3.66522	+	20.7865i	−0.131914	+	0.748122i
$773$	−8.52859			−0.306752			−0.153376	−	0.988168i	$-0.549015\pi$
$773$	−8.52859			−0.306752			−0.153376	+	0.988168i	$0.549015\pi$
$774$	−0.205040	+	0.198720i	−0.00737002	+	0.00714285i
$775$	−93.7769			−3.36857
$776$	−0.722583	+	0.262999i	−0.0259392	+	0.00944110i
$777$	5.53971	−	2.35113i	0.198736	−	0.0843462i
$778$	−0.523220	+	0.439034i	−0.0187583	+	0.0157401i
$779$	0.235029	+	1.33291i	0.00842078	+	0.0477566i
$780$	−31.0348	+	58.4949i	−1.11122	+	2.09445i
$781$	12.1755	+	10.2165i	0.435674	+	0.365574i
$782$	0.119091	+	0.206271i	0.00425867	+	0.00737624i
$783$	−0.0360174	+	0.535875i	−0.00128716	+	0.0191506i
$784$	−14.7694	−	23.7365i	−0.527478	−	0.847731i
$785$	5.47097	−	31.0274i	0.195267	−	1.10742i
$786$	0.113518	−	0.213961i	0.00404905	−	0.00763172i
$787$	13.3134	−	11.1713i	0.474573	−	0.398214i	−0.373886	−	0.927475i	$-0.621975\pi$
$787$	13.3134	−	11.1713i	0.474573	−	0.398214i	0.848459	+	0.529260i	$0.177531\pi$
$788$	1.08303	+	6.14218i	0.0385814	+	0.218806i
$789$	24.9258	−	10.0968i	0.887383	−	0.359456i
$790$	−1.05009	+	0.382201i	−0.0373605	+	0.0135981i
$791$	−12.2978	+	22.1361i	−0.437261	+	0.787069i
$792$	−0.843091	−	0.610224i	−0.0299579	−	0.0216834i
$793$	−19.9641	+	34.5789i	−0.708947	+	1.22793i
$794$	0.843966	−	0.307179i	0.0299512	−	0.0109014i
$795$	−18.6924	−	6.05492i	−0.662951	−	0.214746i
$796$	−13.5111	+	11.3372i	−0.478889	+	0.401836i
$797$	3.90230	+	22.1311i	0.138227	+	0.783922i	0.972558	+	0.232659i	$0.0747428\pi$
$797$	3.90230	+	22.1311i	0.138227	+	0.783922i	−0.834332	+	0.551263i	$0.814146\pi$
$798$	0.106515	+	0.0325710i	0.00377060	+	0.00115300i
$799$	−9.00443	−	7.55562i	−0.318554	−	0.267299i
$800$	2.04486	−	3.54180i	0.0722966	−	0.125221i
$801$	12.1186	−	24.9608i	0.428189	−	0.881946i
$802$	−0.388580	−	0.673040i	−0.0137212	−	0.0237659i
$803$	−8.59410	−	7.21131i	−0.303279	−	0.254481i
$804$	−10.0062	−	7.80320i	−0.352892	−	0.275198i
$805$	8.79798	+	45.4931i	0.310088	+	1.60342i
$806$	−1.30311	−	0.474294i	−0.0459001	−	0.0167063i
$807$	20.0222	−	0.717246i	0.704816	−	0.0252483i
$808$	−1.47436	−	1.23713i	−0.0518677	−	0.0435222i
$809$	2.39080	−	4.14099i	0.0840561	−	0.145589i	−0.820933	−	0.571025i	$-0.806546\pi$
$809$	2.39080	−	4.14099i	0.0840561	−	0.145589i	0.904989	+	0.425436i	$0.139879\pi$
$810$	0.708593	+	0.900254i	0.0248974	+	0.0316317i
$811$	20.5917			0.723074			0.361537	−	0.932358i	$-0.382252\pi$
$811$	20.5917			0.723074			0.361537	+	0.932358i	$0.382252\pi$
$812$	−0.424503	−	0.344426i	−0.0148971	−	0.0120870i
$813$	7.19890	−	13.5686i	0.252477	−	0.475873i
$814$	0.0197830	+	0.112195i	0.000693395	+	0.00393244i
$815$	−14.3120	−	81.1672i	−0.501326	−	2.84316i
$816$	10.6666	−	4.32076i	0.373405	−	0.151257i
$817$	−1.70305	−	1.42903i	−0.0595822	−	0.0499954i
$818$	0.269103	−	0.466101i	0.00940898	−	0.0162968i
$819$	38.3191	−	3.38524i	1.33898	−	0.118290i
$820$	−7.08483	−	12.2713i	−0.247413	−	0.428532i
$821$	1.92106	−	10.8949i	0.0670454	−	0.380233i	−0.932760	−	0.360498i	$-0.882607\pi$
$821$	1.92106	−	10.8949i	0.0670454	−	0.380233i	0.999805	−	0.0197349i	$-0.00628223\pi$
$822$	0.00587943	+	0.0275386i	0.000205069	+	0.000960518i
$823$	−8.55766	−	3.11473i	−0.298301	−	0.108573i	0.188534	−	0.982067i	$-0.439626\pi$
$823$	−8.55766	−	3.11473i	−0.298301	−	0.108573i	−0.486835	+	0.873494i	$0.661849\pi$
$824$	−0.214432	+	0.179930i	−0.00747009	+	0.00626815i
$825$	10.2823	+	48.1611i	0.357984	+	1.67675i
$826$	0.779053	+	0.632095i	0.0271067	+	0.0219934i
$827$	10.6567	+	18.4580i	0.370570	+	0.641846i	0.989653	−	0.143479i	$-0.0458290\pi$
$827$	10.6567	+	18.4580i	0.370570	+	0.641846i	−0.619083	+	0.785325i	$0.712496\pi$
$828$	24.2940	−	10.8688i	0.844274	−	0.377718i
$829$	18.2668	+	31.6389i	0.634431	+	1.09887i	0.986635	+	0.162943i	$0.0520987\pi$
$829$	18.2668	+	31.6389i	0.634431	+	1.09887i	−0.352205	+	0.935923i	$0.614568\pi$
$830$	0.397574	−	2.25475i	0.0138000	−	0.0782637i
$831$	3.39604	−	1.37565i	0.117807	−	0.0477207i
$832$	−29.6087	+	24.8447i	−1.02650	+	0.861334i
$833$	8.66944	−	7.77613i	0.300378	−	0.269427i
$834$	0.304889	+	0.486948i	0.0105574	+	0.0168616i
$835$	16.9958	−	6.18596i	0.588163	−	0.214074i
$836$	2.02529	−	3.50791i	0.0700462	−	0.121324i
$837$	31.9269	−	33.2406i	1.10356	−	1.14896i
$838$	−0.306993	−	0.531728i	−0.0106049	−	0.0183682i
$839$	0.629449	−	3.56978i	0.0217310	−	0.123243i	−0.972012	−	0.234929i	$-0.924514\pi$
$839$	0.629449	−	3.56978i	0.0217310	−	0.123243i	0.993743	+	0.111687i	$0.0356253\pi$
$840$	−2.32959	+	0.121967i	−0.0803785	+	0.00420825i
$841$	27.2410	+	9.91493i	0.939346	+	0.341894i
$842$	0.201322	+	0.0732751i	0.00693801	+	0.00252523i
$843$	−0.592583	+	4.24418i	−0.0204097	+	0.146177i
$844$	8.22842	−	46.6657i	0.283234	−	1.60630i
$845$	41.3920			1.42393
$846$	0.490982	−	0.475847i	0.0168803	−	0.0163600i
$847$	4.84095	−	8.71371i	0.166337	−	0.299407i
$848$	−8.79486	−	7.37977i	−0.302017	−	0.253422i
$849$	5.70457	+	26.7196i	0.195780	+	0.917013i
$850$	0.533181	+	0.194062i	0.0182880	+	0.00665627i
$851$	−5.47671	−	1.99336i	−0.187739	−	0.0683315i
$852$	−4.27240	−	20.0114i	−0.146370	−	0.685579i
$853$	−28.5745	−	23.9768i	−0.978372	−	0.820951i	0.00547111	−	0.999985i	$-0.498258\pi$
$853$	−28.5745	−	23.9768i	−0.978372	−	0.820951i	−0.983843	+	0.179034i	$0.942703\pi$
$854$	−0.703035	+	0.0116014i	−0.0240574	+	0.000396992i
$855$	−6.40544	+	6.20800i	−0.219061	+	0.212309i
$856$	−1.78179			−0.0609004
$857$	0.179304	−	1.01688i	0.00612490	−	0.0347361i	−0.981592	−	0.190989i	$-0.938830\pi$
$857$	0.179304	−	1.01688i	0.00612490	−	0.0347361i	0.987717	+	0.156253i	$0.0499416\pi$
$858$	−0.100702	+	0.721245i	−0.00343791	+	0.0246229i
$859$	−7.62616	−	2.77570i	−0.260201	−	0.0947055i	0.208626	−	0.977996i	$-0.433101\pi$
$859$	−7.62616	−	2.77570i	−0.260201	−	0.0947055i	−0.468827	+	0.883290i	$0.655323\pi$
$860$	21.8710	+	7.96039i	0.745794	+	0.271447i
$861$	−3.73748	+	7.33427i	−0.127373	+	0.249951i
$862$	−0.00644543	+	0.0365539i	−0.000219532	+	0.00124503i
$863$	−3.95244	−	6.84583i	−0.134543	−	0.233035i	0.790880	−	0.611971i	$-0.209623\pi$
$863$	−3.95244	−	6.84583i	−0.134543	−	0.233035i	−0.925423	+	0.378937i	$0.876290\pi$
$864$	0.559256	+	1.93066i	0.0190263	+	0.0656823i
$865$	−29.2831	+	50.7198i	−0.995655	+	1.72452i
$866$	−0.324250	+	0.118017i	−0.0110185	+	0.00401039i
$867$	−13.0817	−	20.8932i	−0.444278	−	0.709571i
$868$	8.90718	+	46.0577i	0.302329	+	1.56330i
$869$	18.0850	−	15.1751i	0.613491	−	0.514780i
$870$	−0.0211225	+	0.00855619i	−0.000716121	+	0.000290082i
$871$	−3.08440	+	17.4925i	−0.104511	+	0.592711i
$872$	0.609439	+	1.05558i	0.0206382	+	0.0357464i
$873$	−16.3236	+	7.30302i	−0.552472	+	0.247170i
$874$	−0.0539355	−	0.0934190i	−0.00182439	−	0.00315994i
$875$	45.1789	+	36.6565i	1.52732	+	1.23921i
$876$	3.01568	+	14.1251i	0.101890	+	0.477242i
$877$	−30.5229	+	25.6118i	−1.03069	+	0.864848i	−0.990932	−	0.134361i	$-0.957102\pi$
$877$	−30.5229	+	25.6118i	−1.03069	+	0.864848i	−0.0397535	+	0.999210i	$0.512657\pi$
$878$	−0.772304	−	0.281096i	−0.0260640	−	0.00948651i
$879$	9.61515	+	45.0362i	0.324311	+	1.51903i
$880$	−7.35988	+	41.7400i	−0.248102	+	1.40705i
$881$	−19.8806	−	34.4342i	−0.669794	−	1.16012i	−0.977962	−	0.208785i	$-0.933049\pi$
$881$	−19.8806	−	34.4342i	−0.669794	−	1.16012i	0.308168	−	0.951332i	$-0.400284\pi$
$882$	0.398121	+	0.548087i	0.0134054	+	0.0184551i
$883$	−3.57561	+	6.19315i	−0.120329	+	0.208416i	−0.919897	−	0.392159i	$-0.871728\pi$
$883$	−3.57561	+	6.19315i	−0.120329	+	0.208416i	0.799568	+	0.600575i	$0.205062\pi$
$884$	−12.3472	−	10.3605i	−0.415280	−	0.348461i
$885$	−74.4658	+	30.1642i	−2.50314	+	1.01396i
$886$	0.188178	+	1.06721i	0.00632195	+	0.0358536i
$887$	−1.21324	−	6.88062i	−0.0407366	−	0.231029i	0.957641	−	0.287964i	$-0.0929783\pi$
$887$	−1.21324	−	6.88062i	−0.0407366	−	0.231029i	−0.998378	+	0.0569351i	$0.981867\pi$
$888$	0.137519	−	0.259198i	0.00461483	−	0.00869812i
$889$	−1.81628	+	11.3972i	−0.0609161	+	0.382251i
$890$	1.17737			0.0394656
$891$	−20.5721	−	12.7520i	−0.689190	−	0.427209i
$892$	0.355547	−	0.615825i	0.0119046	−	0.0206193i
$893$	4.07806	+	3.42190i	0.136467	+	0.114509i
$894$	−0.873303	+	0.0312839i	−0.0292076	+	0.00104629i
$895$	18.9686	+	6.90402i	0.634052	+	0.230776i
$896$	−2.57811	−	0.890463i	−0.0861285	−	0.0297483i
$897$	−29.3781	−	22.9101i	−0.980905	−	0.764946i
$898$	−0.547498	−	0.459405i	−0.0182702	−	0.0153306i
$899$	0.458409	+	0.793987i	0.0152888	+	0.0264809i
$900$	27.6906	−	57.0347i	0.923021	−	1.90116i
$901$	2.39133	−	4.14190i	0.0796667	−	0.137987i
$902$	−0.119375	−	0.100167i	−0.00397475	−	0.00333521i
$903$	−3.04089	−	13.1747i	−0.101194	−	0.438426i
$904$	0.214398	+	1.21591i	0.00713075	+	0.0404405i
$905$	−59.5177	+	49.9413i	−1.97843	+	1.66010i
$906$	−0.505608	−	0.163779i	−0.0167977	−	0.00544118i
$907$	2.70663	−	0.985132i	0.0898721	−	0.0327108i	−0.296693	−	0.954973i	$-0.595884\pi$
$907$	2.70663	−	0.985132i	0.0898721	−	0.0327108i	0.386565	+	0.922262i	$0.373662\pi$
$908$	11.7246	−	20.3076i	0.389095	−	0.673932i
$909$	−36.2583	−	26.2436i	−1.20261	−	0.870444i
$910$	0.839363	+	1.39995i	0.0278246	+	0.0464080i
$911$	2.02689	−	0.737729i	0.0671540	−	0.0244421i	−0.308225	−	0.951314i	$-0.599735\pi$
$911$	2.02689	−	0.737729i	0.0671540	−	0.0244421i	0.375379	+	0.926872i	$0.377513\pi$
$912$	−4.83084	+	1.95685i	−0.159965	+	0.0647977i
$913$	8.39927	+	47.6347i	0.277975	+	1.57648i
$914$	0.251227	−	0.210804i	0.00830984	−	0.00697278i
$915$	26.3911	−	49.7425i	0.872464	−	1.64444i
$916$	−6.33128	+	35.9065i	−0.209191	+	1.18638i
$917$	5.89779	+	9.83680i	0.194762	+	0.324840i
$918$	−0.250313	+	0.122924i	−0.00826156	+	0.00405710i
$919$	−23.8878	−	41.3749i	−0.787986	−	1.36483i	−0.927199	−	0.374570i	$-0.877790\pi$
$919$	−23.8878	−	41.3749i	−0.787986	−	1.36483i	0.139212	−	0.990263i	$-0.455543\pi$
$920$	1.73066	+	1.45219i	0.0570580	+	0.0478774i
$921$	−8.59698	+	16.2037i	−0.283280	+	0.533932i
$922$	−0.00461168	−	0.0261541i	−0.000151878	−	0.000861341i
$923$	−21.9421	+	18.4116i	−0.722234	+	0.606027i
$924$	22.6773	−	9.62453i	0.746027	−	0.316624i
$925$	−13.0467	+	4.74861i	−0.428973	+	0.156133i
$926$	−0.356023			−0.0116997
$927$	−4.67463	+	4.53054i	−0.153535	+	0.148802i
$928$	−0.0399834			−0.00131252
$929$	−8.36754	+	47.4547i	−0.274530	+	1.55694i	0.465920	+	0.884827i	$0.345723\pi$
$929$	−8.36754	+	47.4547i	−0.274530	+	1.55694i	−0.740450	+	0.672111i	$0.765388\pi$
$930$	1.86052	+	0.602667i	0.0610088	+	0.0197622i
$931$	−3.92634	+	3.52177i	−0.128681	+	0.115421i
$932$	9.27027	+	52.5743i	0.303658	+	1.72213i
$933$	6.79090	+	31.8078i	0.222324	+	1.04134i
$934$	0.594942	−	0.216541i	0.0194671	−	0.00708544i
$935$	−17.6561			−0.577416
$936$	1.34685	−	1.30533i	0.0440231	−	0.0426661i
$937$	15.2256	−	26.3715i	0.497398	−	0.861519i	−0.502598	−	0.864521i	$-0.667622\pi$
$937$	15.2256	−	26.3715i	0.497398	−	0.861519i	0.999995	+	0.00300197i	$0.000955559\pi$
$938$	−0.292124	+	0.111816i	−0.00953817	+	0.00365094i
$939$	−51.5081	+	20.8646i	−1.68090	+	0.680890i
$940$	−52.3714	−	19.0616i	−1.70817	−	0.621722i
$941$	35.4628	−	29.7568i	1.15605	−	0.970044i	0.156209	−	0.987724i	$-0.450073\pi$
$941$	35.4628	−	29.7568i	1.15605	−	0.970044i	0.999844	+	0.0176803i	$0.00562810\pi$
$942$	−0.209069	+	0.394057i	−0.00681184	+	0.0128391i
$943$	7.49128	−	2.72660i	0.243950	−	0.0887904i
$944$	−46.9454			−1.52794
$945$	−53.8351	+	6.70571i	−1.75126	+	0.218137i
$946$	0.255966			0.00832217
$947$	34.5084	−	12.5600i	1.12137	−	0.408147i	0.286220	−	0.958164i	$-0.407601\pi$
$947$	34.5084	−	12.5600i	1.12137	−	0.408147i	0.835153	+	0.550017i	$0.185379\pi$
$948$	−30.3745	+	1.08809i	−0.986518	+	0.0353395i
$949$	15.4879	−	12.9959i	0.502758	−	0.421864i
$950$	−0.241475	−	0.0878896i	−0.00783447	−	0.00285151i
$951$	−1.64362	+	11.7718i	−0.0532979	+	0.381728i
$952$	0.0893612	−	0.560745i	0.00289621	−	0.0181739i
$953$	−5.62515	+	9.74305i	−0.182217	+	0.315608i	−0.942635	−	0.333825i	$-0.891661\pi$
$953$	−5.62515	+	9.74305i	−0.182217	+	0.315608i	0.760418	+	0.649433i	$0.224994\pi$
$954$	0.225361	+	0.163115i	0.00729634	+	0.00528105i
$955$	37.0789			1.19985
$956$	19.5555	−	7.11761i	0.632469	−	0.230200i
$957$	0.357506	−	0.322483i	0.0115565	−	0.0104244i
$958$	0.0636503	+	0.360979i	0.00205645	+	0.0116627i
$959$	−1.26037	−	0.435322i	−0.0406993	−	0.0140573i
$960$	40.4755	−	36.5103i	1.30634	−	1.17837i
$961$	8.27894	−	46.9522i	0.267063	−	1.51459i
$962$	−0.205312			−0.00661953
$963$	−41.3311	+	2.96497i	−1.33188	+	0.0955449i
$964$	24.5820			0.791732
$965$	−39.1552	+	14.2513i	−1.26045	+	0.458766i
$966$	0.0799873	−	0.651163i	0.00257355	−	0.0209508i
$967$	−17.6244	+	14.7886i	−0.566762	+	0.475570i	−0.880570	−	0.473917i	$-0.842840\pi$
$967$	−17.6244	+	14.7886i	−0.566762	+	0.475570i	0.313808	+	0.949487i	$0.398395\pi$
$968$	−0.0843959	−	0.478633i	−0.00271259	−	0.0153839i
$969$	−1.15224	−	1.84028i	−0.0370154	−	0.0591184i
$970$	−0.581281	−	0.487753i	−0.0186638	−	0.0156608i
$971$	16.5858	+	28.7275i	0.532265	+	0.921910i	0.999290	+	0.0376660i	$0.0119923\pi$
$971$	16.5858	+	28.7275i	0.532265	+	0.921910i	−0.467025	+	0.884244i	$0.654674\pi$
$972$	10.7893	+	29.2332i	0.346068	+	0.937655i
$973$	−27.2017	+	0.448879i	−0.872046	+	0.0143904i
$974$	0.0299734	−	0.169988i	0.000960410	−	0.00544675i
$975$	−88.6928	+	3.17720i	−2.84044	+	0.101752i
$976$	25.2048	−	21.1493i	0.806785	−	0.676973i
$977$	7.62420	+	43.2390i	0.243920	+	1.38334i	0.822988	+	0.568058i	$0.192305\pi$
$977$	7.62420	+	43.2390i	0.243920	+	1.38334i	−0.579069	+	0.815279i	$0.696584\pi$
$978$	−0.161367	+	1.15574i	−0.00515995	+	0.0369564i
$979$	−23.3735	+	8.50725i	−0.747019	+	0.271893i
$980$	26.0161	−	48.7050i	0.831053	−	1.55582i
$981$	15.8933	+	23.4715i	0.507434	+	0.749386i
$982$	−0.518134	+	0.897435i	−0.0165343	+	0.0286383i
$983$	25.8810	−	9.41993i	0.825477	−	0.300449i	0.105476	−	0.994422i	$-0.466363\pi$
$983$	25.8810	−	9.41993i	0.825477	−	0.300449i	0.720001	+	0.693973i	$0.244141\pi$
$984$	0.0837993	+	0.392506i	0.00267142	+	0.0125126i
$985$	−9.43188	+	7.91429i	−0.300525	+	0.252170i
$986$	−0.000963265	−	0.00546295i	−3.06766e−5	−	0.000173976i
$987$	7.28159	+	31.5475i	0.231776	+	1.00417i
$988$	5.59196	+	4.69221i	0.177904	+	0.149279i
$989$	−6.54731	+	11.3403i	−0.208192	+	0.360600i
$990$	0.105513	−	1.02159i	0.00335343	−	0.0324682i
$991$	−6.09712	−	10.5605i	−0.193681	−	0.335466i	0.752786	−	0.658265i	$-0.228709\pi$
$991$	−6.09712	−	10.5605i	−0.193681	−	0.335466i	−0.946467	+	0.322799i	$0.895376\pi$
$992$	2.62843	+	2.20551i	0.0834527	+	0.0700251i
$993$	−0.633833	+	4.53962i	−0.0201141	+	0.144061i
$994$	−0.476769	−	0.164673i	−0.0151222	−	0.00522311i
$995$	−32.7188	−	11.9087i	−1.03726	−	0.377530i
$996$	29.1855	−	55.0095i	0.924779	−	1.74304i
$997$	−2.38312	−	1.99967i	−0.0754740	−	0.0633302i	0.604270	−	0.796779i	$-0.293465\pi$
$997$	−2.38312	−	1.99967i	−0.0754740	−	0.0633302i	−0.679744	+	0.733449i	$0.737909\pi$
$998$	−0.506473	+	0.877238i	−0.0160321	+	0.0277685i
$999$	2.75862	−	6.24129i	0.0872789	−	0.197466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.12	yes	132
3.2	odd	2		567.2.w.a.235.11		132
7.2	even	3		189.2.u.a.79.11	yes	132
21.2	odd	6		567.2.u.a.478.12		132
27.13	even	9		189.2.u.a.67.11	✓	132
27.14	odd	18		567.2.u.a.172.12		132
189.121	even	9	inner	189.2.w.a.121.12	yes	132
189.149	odd	18		567.2.w.a.415.11		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.11	✓	132	27.13	even	9
189.2.u.a.79.11	yes	132	7.2	even	3
189.2.w.a.25.12	yes	132	1.1	even	1	trivial
189.2.w.a.121.12	yes	132	189.121	even	9	inner
567.2.u.a.172.12		132	27.14	odd	18
567.2.u.a.478.12		132	21.2	odd	6
567.2.w.a.235.11		132	3.2	odd	2
567.2.w.a.415.11		132	189.149	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)

\(f(q)\)	\(=\)	\(q+(0.0303128 - 0.0110329i) q^{2} +(0.919170 + 1.46804i) q^{3} +(-1.53129 + 1.28491i) q^{4} +(-3.70820 - 1.34968i) q^{5} +(0.0440593 + 0.0343591i) q^{6} +(-2.47092 + 0.945798i) q^{7} +(-0.0644996 + 0.111717i) q^{8} +(-1.31025 + 2.69875i) q^{9} +O(q^{10})\)	\(q+(0.0303128 - 0.0110329i) q^{2} +(0.919170 + 1.46804i) q^{3} +(-1.53129 + 1.28491i) q^{4} +(-3.70820 - 1.34968i) q^{5} +(0.0440593 + 0.0343591i) q^{6} +(-2.47092 + 0.945798i) q^{7} +(-0.0644996 + 0.111717i) q^{8} +(-1.31025 + 2.69875i) q^{9} -0.127297 q^{10} +(2.52713 - 0.919799i) q^{11} +(-3.29380 - 1.06694i) q^{12} +(0.841596 + 4.77293i) q^{13} +(-0.0644656 + 0.0559313i) q^{14} +(-1.42710 - 6.68435i) q^{15} +(0.693509 - 3.93308i) q^{16} +1.66370 q^{17} +(-0.00994232 + 0.0962625i) q^{18} -0.753482 q^{19} +(7.41255 - 2.69795i) q^{20} +(-3.65966 - 2.75805i) q^{21} +(0.0664561 - 0.0557633i) q^{22} +(0.770659 + 4.37062i) q^{23} +(-0.223290 + 0.00799880i) q^{24} +(8.09892 + 6.79580i) q^{25} +(0.0781705 + 0.135395i) q^{26} +(-5.16620 + 0.557106i) q^{27} +(2.56844 - 4.62320i) q^{28} +(0.0179486 - 0.101792i) q^{29} +(-0.117007 - 0.186876i) q^{30} +(-6.79480 + 5.70151i) q^{31} +(-0.0671723 - 0.380953i) q^{32} +(3.67316 + 2.86446i) q^{33} +(0.0504314 - 0.0183555i) q^{34} +(10.4392 - 0.172267i) q^{35} +(-1.46125 - 5.81612i) q^{36} +(-0.656616 + 1.13729i) q^{37} +(-0.0228401 + 0.00831312i) q^{38} +(-6.23325 + 5.62262i) q^{39} +(0.389959 - 0.327214i) q^{40} +(-0.311924 - 1.76901i) q^{41} +(-0.141364 - 0.0432274i) q^{42} +(2.26024 + 1.89657i) q^{43} +(-2.68791 + 4.65560i) q^{44} +(8.50112 - 8.23908i) q^{45} +(0.0715817 + 0.123983i) q^{46} +(-5.41229 - 4.54145i) q^{47} +(6.41136 - 2.59708i) q^{48} +(5.21093 - 4.67399i) q^{49} +(0.320478 + 0.116645i) q^{50} +(1.52922 + 2.44237i) q^{51} +(-7.42149 - 6.22737i) q^{52} +(1.43735 - 2.48957i) q^{53} +(-0.150455 + 0.0738858i) q^{54} -10.6125 q^{55} +(0.0537122 - 0.337047i) q^{56} +(-0.692577 - 1.10614i) q^{57} +(-0.000578989 - 0.00328361i) q^{58} +(-2.04118 - 11.5761i) q^{59} +(10.7741 + 8.40201i) q^{60} +(6.31104 + 5.29559i) q^{61} +(-0.143065 + 0.247795i) q^{62} +(0.685069 - 7.90763i) q^{63} +(3.98752 + 6.90658i) q^{64} +(3.32109 - 18.8349i) q^{65} +(0.142947 + 0.0463040i) q^{66} +(3.44392 + 1.25348i) q^{67} +(-2.54761 + 2.13770i) q^{68} +(-5.70786 + 5.14870i) q^{69} +(0.314541 - 0.120397i) q^{70} +(2.95503 + 5.11826i) q^{71} +(-0.216984 - 0.320445i) q^{72} +(-2.08581 - 3.61273i) q^{73} +(-0.00735617 + 0.0417189i) q^{74} +(-2.53219 + 18.1360i) q^{75} +(1.15380 - 0.968153i) q^{76} +(-5.37439 + 4.66291i) q^{77} +(-0.126913 + 0.239208i) q^{78} +(8.24914 - 3.00244i) q^{79} +(-7.88006 + 13.6487i) q^{80} +(-5.56647 - 7.07209i) q^{81} +(-0.0289726 - 0.0501821i) q^{82} +(-3.12320 + 17.7126i) q^{83} +(9.14785 - 0.478939i) q^{84} +(-6.16935 - 2.24546i) q^{85} +(0.0894389 + 0.0325531i) q^{86} +(0.165931 - 0.0672145i) q^{87} +(-0.0602419 + 0.341649i) q^{88} -9.24903 q^{89} +(0.166791 - 0.343542i) q^{90} +(-6.59374 - 10.9976i) q^{91} +(-6.79595 - 5.70248i) q^{92} +(-14.6156 - 4.73435i) q^{93} +(-0.214167 - 0.0779504i) q^{94} +(2.79406 + 1.01696i) q^{95} +(0.497509 - 0.448772i) q^{96} +(4.56635 + 3.83162i) q^{97} +(0.106390 - 0.199174i) q^{98} +(-0.828875 + 8.02525i) 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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