LMFDB - Embedded newform 324.2.p.a.23.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			23.44
Character	$\chi$	$=$	324.23
Dual form			324.2.p.a.155.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17322 + 0.789650i) q^{2} +(-1.69483 + 0.357122i) q^{3} +(0.752907 + 1.85287i) q^{4} +(1.62384 - 2.46892i) q^{5} +(-2.27042 - 0.919342i) q^{6} +(1.06207 - 1.00201i) q^{7} +(-0.579791 + 2.76836i) q^{8} +(2.74493 - 1.21053i) q^{9} +O(q^{10})$	\(q+(1.17322 + 0.789650i) q^{2} +(-1.69483 + 0.357122i) q^{3} +(0.752907 + 1.85287i) q^{4} +(1.62384 - 2.46892i) q^{5} +(-2.27042 - 0.919342i) q^{6} +(1.06207 - 1.00201i) q^{7} +(-0.579791 + 2.76836i) q^{8} +(2.74493 - 1.21053i) q^{9} +(3.85471 - 1.61434i) q^{10} +(4.08084 + 2.04948i) q^{11} +(-1.93775 - 2.87143i) q^{12} +(0.0903180 - 0.209381i) q^{13} +(2.03729 - 0.336921i) q^{14} +(-1.87043 + 4.76432i) q^{15} +(-2.86626 + 2.79008i) q^{16} +(-3.16597 + 3.77306i) q^{17} +(4.17630 + 0.747315i) q^{18} +(-0.207391 - 0.247159i) q^{19} +(5.79719 + 1.14989i) q^{20} +(-1.44220 + 2.07754i) q^{21} +(3.16937 + 5.62693i) q^{22} +(-0.349819 + 0.370786i) q^{23} +(-0.00599347 - 4.89898i) q^{24} +(-1.47834 - 3.42718i) q^{25} +(0.271301 - 0.174331i) q^{26} +(-4.21989 + 3.03191i) q^{27} +(2.65624 + 1.21346i) q^{28} +(0.447794 - 3.83112i) q^{29} +(-5.95658 + 4.11264i) q^{30} +(2.18333 - 9.21220i) q^{31} +(-5.56595 + 1.01004i) q^{32} +(-7.64826 - 2.01616i) q^{33} +(-6.69378 + 1.92663i) q^{34} +(-0.749263 - 4.24928i) q^{35} +(4.30962 + 4.17458i) q^{36} +(-0.158732 + 0.900213i) q^{37} +(-0.0481471 - 0.453740i) q^{38} +(-0.0782996 + 0.387120i) q^{39} +(5.89339 + 5.92683i) q^{40} +(0.900548 - 0.670433i) q^{41} +(-3.33254 + 1.29859i) q^{42} +(8.72158 - 0.507974i) q^{43} +(-0.724922 + 9.10434i) q^{44} +(1.46862 - 8.74271i) q^{45} +(-0.703207 + 0.158781i) q^{46} +(-12.3347 + 2.92337i) q^{47} +(3.86144 - 5.75233i) q^{48} +(-0.283047 + 4.85974i) q^{49} +(0.971846 - 5.18821i) q^{50} +(4.01835 - 7.52534i) q^{51} +(0.455957 + 0.00970353i) q^{52} +(-4.09629 - 2.36499i) q^{53} +(-7.34503 + 0.224876i) q^{54} +(11.6866 - 6.74727i) q^{55} +(2.15816 + 3.52116i) q^{56} +(0.439760 + 0.344830i) q^{57} +(3.55061 - 4.14116i) q^{58} +(-5.59648 + 2.81066i) q^{59} +(-10.2359 + 0.121431i) q^{60} +(3.39394 - 11.3365i) q^{61} +(9.83595 - 9.08390i) q^{62} +(1.70235 - 4.03612i) q^{63} +(-7.32768 - 3.21015i) q^{64} +(-0.370283 - 0.562988i) q^{65} +(-7.38106 - 8.40486i) q^{66} +(0.746744 + 6.38880i) q^{67} +(-9.37466 - 3.02537i) q^{68} +(0.460469 - 0.753350i) q^{69} +(2.47639 - 5.57701i) q^{70} +(-14.0951 + 5.13019i) q^{71} +(1.75969 + 8.30081i) q^{72} +(-11.6460 - 4.23881i) q^{73} +(-0.897081 + 0.930809i) q^{74} +(3.72946 + 5.28055i) q^{75} +(0.301808 - 0.570357i) q^{76} +(6.38775 - 1.91237i) q^{77} +(-0.397552 + 0.392349i) q^{78} +(-7.56539 - 5.63223i) q^{79} +(2.23415 + 11.6072i) q^{80} +(6.06926 - 6.64561i) q^{81} +(1.58595 - 0.0754505i) q^{82} +(2.24764 - 3.01910i) q^{83} +(-4.93525 - 1.10801i) q^{84} +(4.17437 + 13.9434i) q^{85} +(10.6335 + 6.29103i) q^{86} +(0.609242 + 6.65304i) q^{87} +(-8.03973 + 10.1090i) q^{88} +(-1.73568 + 4.76873i) q^{89} +(8.62670 - 9.09746i) q^{90} +(-0.113878 - 0.312877i) q^{91} +(-0.950400 - 0.369002i) q^{92} +(-0.410506 + 16.3929i) q^{93} +(-16.7798 - 6.31030i) q^{94} +(-0.946987 + 0.110687i) q^{95} +(9.07266 - 3.69958i) q^{96} +(1.90027 - 1.24982i) q^{97} +(-4.16957 + 5.47805i) q^{98} +(13.6826 + 0.685700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{54}\right)$

Coefficient data

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

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

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

$2$	1.17322	+	0.789650i	0.829594	+	0.558367i
$2$	1.17322	+	0.789650i	0.829594	+	0.558367i
$3$	−1.69483	+	0.357122i	−0.978513	+	0.206184i
$3$	−1.69483	+	0.357122i	−0.978513	+	0.206184i
$4$	0.752907	+	1.85287i	0.376453	+	0.926436i
$5$	1.62384	−	2.46892i	0.726202	−	1.10414i	−0.264004	−	0.964522i	$-0.585043\pi$
$5$	1.62384	−	2.46892i	0.726202	−	1.10414i	0.990206	−	0.139615i	$-0.0445864\pi$
$6$	−2.27042	−	0.919342i	−0.926895	−	0.375320i
$7$	1.06207	−	1.00201i	0.401426	−	0.378725i	−0.458885	−	0.888496i	$-0.651751\pi$
$7$	1.06207	−	1.00201i	0.401426	−	0.378725i	0.860311	+	0.509770i	$0.170270\pi$
$8$	−0.579791	+	2.76836i	−0.204987	+	0.978765i
$9$	2.74493	−	1.21053i	0.914976	−	0.403508i
$10$	3.85471	−	1.61434i	1.21897	−	0.510498i
$11$	4.08084	+	2.04948i	1.23042	+	0.617940i	0.940722	−	0.339178i	$-0.110149\pi$
$11$	4.08084	+	2.04948i	1.23042	+	0.617940i	0.289698	+	0.957118i	$0.406445\pi$
$12$	−1.93775	−	2.87143i	−0.559381	−	0.828911i
$13$	0.0903180	−	0.209381i	0.0250497	−	0.0580718i	−0.905232	−	0.424918i	$-0.860303\pi$
$13$	0.0903180	−	0.209381i	0.0250497	−	0.0580718i	0.930282	+	0.366846i	$0.119562\pi$
$14$	2.03729	−	0.336921i	0.544488	−	0.0900458i
$15$	−1.87043	+	4.76432i	−0.482942	+	1.23014i
$16$	−2.86626	+	2.79008i	−0.716566	+	0.697520i
$17$	−3.16597	+	3.77306i	−0.767860	+	0.915100i	−0.998318	−	0.0579822i	$-0.981533\pi$
$17$	−3.16597	+	3.77306i	−0.767860	+	0.915100i	0.230457	+	0.973082i	$0.425978\pi$
$18$	4.17630	+	0.747315i	0.984364	+	0.176144i
$19$	−0.207391	−	0.247159i	−0.0475788	−	0.0567022i	0.741730	−	0.670698i	$-0.234005\pi$
$19$	−0.207391	−	0.247159i	−0.0475788	−	0.0567022i	−0.789309	+	0.613996i	$0.789561\pi$
$20$	5.79719	+	1.14989i	1.29629	+	0.257123i
$21$	−1.44220	+	2.07754i	−0.314713	+	0.453356i
$22$	3.16937	+	5.62693i	0.675712	+	1.19967i
$23$	−0.349819	+	0.370786i	−0.0729423	+	0.0773143i	−0.762817	−	0.646615i	$-0.776184\pi$
$23$	−0.349819	+	0.370786i	−0.0729423	+	0.0773143i	0.689875	+	0.723929i	$0.257666\pi$
$24$	−0.00599347	−	4.89898i	−0.00122341	−	0.999999i
$25$	−1.47834	−	3.42718i	−0.295668	−	0.685435i
$26$	0.271301	−	0.174331i	0.0532064	−	0.0341891i
$27$	−4.21989	+	3.03191i	−0.812119	+	0.583492i
$28$	2.65624	+	1.21346i	0.501983	+	0.229322i
$29$	0.447794	−	3.83112i	0.0831533	−	0.711422i	−0.885781	−	0.464104i	$-0.846377\pi$
$29$	0.447794	−	3.83112i	0.0831533	−	0.711422i	0.968934	−	0.247318i	$-0.0795494\pi$
$30$	−5.95658	+	4.11264i	−1.08752	+	0.750861i
$31$	2.18333	−	9.21220i	0.392138	−	1.65456i	−0.316204	−	0.948691i	$-0.602409\pi$
$31$	2.18333	−	9.21220i	0.392138	−	1.65456i	0.708342	−	0.705869i	$-0.249443\pi$
$32$	−5.56595	+	1.01004i	−0.983931	+	0.178552i
$33$	−7.64826	−	2.01616i	−1.33139	−	0.350969i
$34$	−6.69378	+	1.92663i	−1.14797	+	0.330414i
$35$	−0.749263	−	4.24928i	−0.126649	−	0.718260i
$36$	4.30962	+	4.17458i	0.718270	+	0.695764i
$37$	−0.158732	+	0.900213i	−0.0260954	+	0.147994i	−0.995071	−	0.0991602i	$-0.968384\pi$
$37$	−0.158732	+	0.900213i	−0.0260954	+	0.147994i	0.968976	+	0.247154i	$0.0794955\pi$
$38$	−0.0481471	−	0.453740i	−0.00781048	−	0.0736063i
$39$	−0.0782996	+	0.387120i	−0.0125380	+	0.0619889i
$40$	5.89339	+	5.92683i	0.931827	+	0.937114i
$41$	0.900548	−	0.670433i	0.140642	−	0.104704i	−0.524538	−	0.851387i	$-0.675762\pi$
$41$	0.900548	−	0.670433i	0.140642	−	0.104704i	0.665180	+	0.746683i	$0.268355\pi$
$42$	−3.33254	+	1.29859i	−0.514223	+	0.200376i
$43$	8.72158	−	0.507974i	1.33003	−	0.0774653i	0.621648	−	0.783296i	$-0.286463\pi$
$43$	8.72158	−	0.507974i	1.33003	−	0.0774653i	0.708380	+	0.705831i	$0.249426\pi$
$44$	−0.724922	+	9.10434i	−0.109286	+	1.37253i
$45$	1.46862	−	8.74271i	0.218929	−	1.30329i
$46$	−0.703207	+	0.158781i	−0.103682	+	0.0234110i
$47$	−12.3347	+	2.92337i	−1.79920	+	0.426418i	−0.987495	−	0.157653i	$-0.949607\pi$
$47$	−12.3347	+	2.92337i	−1.79920	+	0.426418i	−0.811703	+	0.584071i	$0.801459\pi$
$48$	3.86144	−	5.75233i	0.557351	−	0.830277i
$49$	−0.283047	+	4.85974i	−0.0404353	+	0.694248i
$50$	0.971846	−	5.18821i	0.137440	−	0.733724i
$51$	4.01835	−	7.52534i	0.562682	−	1.05376i
$52$	0.455957	+	0.00970353i	0.0632298	+	0.00134564i
$53$	−4.09629	−	2.36499i	−0.562669	−	0.324857i	0.191547	−	0.981483i	$-0.438649\pi$
$53$	−4.09629	−	2.36499i	−0.562669	−	0.324857i	−0.754216	+	0.656626i	$0.771983\pi$
$54$	−7.34503	+	0.224876i	−0.999532	+	0.0306017i
$55$	11.6866	−	6.74727i	1.57582	−	0.909802i
$56$	2.15816	+	3.52116i	0.288396	+	0.470535i
$57$	0.439760	+	0.344830i	0.0582476	+	0.0456739i
$58$	3.55061	−	4.14116i	0.466218	−	0.543762i
$59$	−5.59648	+	2.81066i	−0.728599	+	0.365916i	−0.774113	−	0.633047i	$-0.781804\pi$
$59$	−5.59648	+	2.81066i	−0.728599	+	0.365916i	0.0455139	+	0.998964i	$0.485507\pi$
$60$	−10.2359	+	0.121431i	−1.32145	+	0.0156767i
$61$	3.39394	−	11.3365i	0.434549	−	1.45150i	−0.408053	−	0.912958i	$-0.633792\pi$
$61$	3.39394	−	11.3365i	0.434549	−	1.45150i	0.842602	−	0.538537i	$-0.181023\pi$
$62$	9.83595	−	9.08390i	1.24917	−	1.15366i
$63$	1.70235	−	4.03612i	0.214476	−	0.508503i
$64$	−7.32768	−	3.21015i	−0.915960	−	0.401268i
$65$	−0.370283	−	0.562988i	−0.0459280	−	0.0698301i
$66$	−7.38106	−	8.40486i	−0.908546	−	1.03457i
$67$	0.746744	+	6.38880i	0.0912293	+	0.780516i	0.958972	+	0.283502i	$0.0914963\pi$
$67$	0.746744	+	6.38880i	0.0912293	+	0.780516i	−0.867742	+	0.497014i	$0.834430\pi$
$68$	−9.37466	−	3.02537i	−1.13685	−	0.366881i
$69$	0.460469	−	0.753350i	0.0554340	−	0.0906926i
$70$	2.47639	−	5.57701i	0.295985	−	0.666580i
$71$	−14.0951	+	5.13019i	−1.67278	+	0.608842i	−0.992292	−	0.123919i	$-0.960454\pi$
$71$	−14.0951	+	5.13019i	−1.67278	+	0.608842i	−0.680486	+	0.732761i	$0.738231\pi$
$72$	1.75969	+	8.30081i	0.207381	+	0.978260i
$73$	−11.6460	−	4.23881i	−1.36306	−	0.496115i	−0.446064	−	0.895001i	$-0.647174\pi$
$73$	−11.6460	−	4.23881i	−1.36306	−	0.496115i	−0.917000	+	0.398887i	$0.869397\pi$
$74$	−0.897081	+	0.930809i	−0.104284	+	0.108204i
$75$	3.72946	+	5.28055i	0.430641	+	0.609745i
$76$	0.301808	−	0.570357i	0.0346198	−	0.0654245i
$77$	6.38775	−	1.91237i	0.727952	−	0.217934i
$78$	−0.397552	+	0.392349i	−0.0450139	+	0.0444248i
$79$	−7.56539	−	5.63223i	−0.851173	−	0.633675i	0.0805876	−	0.996748i	$-0.474320\pi$
$79$	−7.56539	−	5.63223i	−0.851173	−	0.633675i	−0.931761	+	0.363072i	$0.881728\pi$
$80$	2.23415	+	11.6072i	0.249785	+	1.29773i
$81$	6.06926	−	6.64561i	0.674362	−	0.738401i
$82$	1.58595	−	0.0754505i	0.175139	−	0.00833211i
$83$	2.24764	−	3.01910i	0.246710	−	0.331390i	−0.661468	−	0.749974i	$-0.730066\pi$
$83$	2.24764	−	3.01910i	0.246710	−	0.331390i	0.908178	+	0.418584i	$0.137474\pi$
$84$	−4.93525	−	1.10801i	−0.538479	−	0.120894i
$85$	4.17437	+	13.9434i	0.452774	+	1.51237i
$86$	10.6335	+	6.29103i	1.14664	+	0.678379i
$87$	0.609242	+	6.65304i	0.0653176	+	0.713281i
$88$	−8.03973	+	10.1090i	−0.857038	+	1.07762i
$89$	−1.73568	+	4.76873i	−0.183981	+	0.505485i	−0.997056	−	0.0766746i	$-0.975570\pi$
$89$	−1.73568	+	4.76873i	−0.183981	+	0.505485i	0.813075	+	0.582159i	$0.197792\pi$
$90$	8.62670	−	9.09746i	0.909334	−	0.958957i
$91$	−0.113878	−	0.312877i	−0.0119377	−	0.0327985i
$92$	−0.950400	−	0.369002i	−0.0990861	−	0.0384711i
$93$	−0.410506	+	16.3929i	−0.0425675	+	1.69986i
$94$	−16.7798	−	6.31030i	−1.73070	−	0.650858i
$95$	−0.946987	+	0.110687i	−0.0971588	+	0.0113562i
$96$	9.07266	−	3.69958i	0.925974	−	0.377586i
$97$	1.90027	−	1.24982i	0.192943	−	0.126900i	−0.449362	−	0.893350i	$-0.648349\pi$
$97$	1.90027	−	1.24982i	0.192943	−	0.126900i	0.642305	+	0.766449i	$0.277978\pi$
$98$	−4.16957	+	5.47805i	−0.421190	+	0.553366i
$99$	13.6826	+	0.685700i	1.37515	+	0.0689154i
$100$	5.23706	−	5.31952i	0.523706	−	0.531952i
$101$	−11.6220	−	3.47940i	−1.15643	−	0.346213i	−0.349546	−	0.936919i	$-0.613664\pi$
$101$	−11.6220	−	3.47940i	−1.15643	−	0.346213i	−0.806887	+	0.590706i	$0.798849\pi$
$102$	10.6568	−	5.65582i	1.05518	−	0.560009i
$103$	−2.08240	−	4.14639i	−0.205185	−	0.408556i	0.767379	−	0.641194i	$-0.221561\pi$
$103$	−2.08240	−	4.14639i	−0.205185	−	0.408556i	−0.972563	+	0.232638i	$0.925264\pi$
$104$	0.527277	+	0.371430i	0.0517037	+	0.0364217i
$105$	2.78739	+	6.93425i	0.272021	+	0.676713i
$106$	−2.93835	−	6.00930i	−0.285397	−	0.583675i
$107$	8.12334	+	14.0700i	0.785313	+	1.36020i	0.928812	+	0.370551i	$0.120831\pi$
$107$	8.12334	+	14.0700i	0.785313	+	1.36020i	−0.143499	+	0.989650i	$0.545835\pi$
$108$	−8.79493	−	5.53617i	−0.846293	−	0.532718i
$109$	−0.887598	+	1.53736i	−0.0850164	+	0.147253i	−0.905398	−	0.424563i	$-0.860428\pi$
$109$	−0.887598	+	1.53736i	−0.0850164	+	0.147253i	0.820382	+	0.571816i	$0.193761\pi$
$110$	19.0390	+	1.31228i	1.81530	+	0.125121i
$111$	−0.0524617	−	1.58240i	−0.00497945	−	0.150195i
$112$	−0.248483	+	5.83530i	−0.0234794	+	0.551384i
$113$	14.1121	+	0.821939i	1.32756	+	0.0773215i	0.707210	−	0.707004i	$-0.249954\pi$
$113$	14.1121	+	0.821939i	1.32756	+	0.0773215i	0.620350	+	0.784325i	$0.286991\pi$
$114$	0.243642	+	0.751819i	0.0228191	+	0.0704143i
$115$	0.347394	+	1.46577i	0.0323947	+	0.136684i
$116$	7.43573	−	2.05477i	0.690390	−	0.190781i
$117$	−0.00554423	−	0.684067i	−0.000512565	−	0.0632420i
$118$	−8.78535	−	1.12173i	−0.808757	−	0.103263i
$119$	0.418164	+	7.17960i	0.0383330	+	0.658153i
$120$	−12.1049	−	7.94034i	−1.10502	−	0.724850i
$121$	5.88417	+	7.90382i	0.534925	+	0.718529i
$122$	12.9337	−	10.6203i	1.17097	−	0.961515i
$123$	−1.28685	+	1.45788i	−0.116032	+	0.131453i
$124$	18.7129	−	2.89050i	1.68047	−	0.259574i
$125$	3.68885	+	0.650444i	0.329941	+	0.0581775i
$126$	5.18436	−	3.39101i	0.461859	−	0.302095i
$127$	−12.5834	+	2.21879i	−1.11660	+	0.196886i	−0.701346	−	0.712821i	$-0.747417\pi$
$127$	−12.5834	+	2.21879i	−1.11660	+	0.196886i	−0.415251	+	0.909707i	$0.636306\pi$
$128$	−6.06212	−	9.55252i	−0.535821	−	0.844332i
$129$	−14.6002	+	3.97560i	−1.28548	+	0.350032i
$130$	0.0101386	−	0.952905i	0.000889212	−	0.0835753i
$131$	3.44093	+	0.815515i	0.300635	+	0.0712519i	0.378165	−	0.925738i	$-0.376555\pi$
$131$	3.44093	+	0.815515i	0.300635	+	0.0712519i	−0.0775297	+	0.996990i	$0.524703\pi$
$132$	−2.02274	−	15.6892i	−0.176057	−	1.36557i
$133$	−0.467922	−	0.0546922i	−0.0405739	−	0.00474241i
$134$	−4.16882	+	8.08516i	−0.360131	+	0.698451i
$135$	0.633149	+	15.3419i	0.0544928	+	1.32042i
$136$	−8.60959	−	10.9521i	−0.738266	−	0.939138i
$137$	−20.9770	+	9.04859i	−1.79219	+	0.773073i	−0.809671	+	0.586884i	$0.800355\pi$
$137$	−20.9770	+	9.04859i	−1.79219	+	0.773073i	−0.982514	+	0.186189i	$0.940386\pi$
$138$	1.13512	−	0.520238i	0.0966274	−	0.0442856i
$139$	7.33929	+	6.92426i	0.622510	+	0.587308i	0.931493	−	0.363760i	$-0.118507\pi$
$139$	7.33929	+	6.92426i	0.622510	+	0.587308i	−0.308983	+	0.951068i	$0.599988\pi$
$140$	7.30925	−	4.58760i	0.617744	−	0.387723i
$141$	19.8612	−	9.35962i	1.67262	−	0.788222i
$142$	−20.5877	−	5.11132i	−1.72768	−	0.428932i
$143$	0.797694	−	0.669345i	0.0667066	−	0.0559734i
$144$	−4.49022	+	11.1282i	−0.374185	+	0.927354i
$145$	−8.73161	−	7.32669i	−0.725121	−	0.608448i
$146$	−10.3162	−	14.1693i	−0.853776	−	1.17266i
$147$	−1.25580	−	8.33753i	−0.103577	−	0.687668i
$148$	−1.78749	+	0.383667i	−0.146931	+	0.0315372i
$149$	16.9523	+	7.31249i	1.38878	+	0.599063i	0.953544	−	0.301252i	$-0.0974047\pi$
$149$	16.9523	+	7.31249i	1.38878	+	0.599063i	0.435239	+	0.900315i	$0.356664\pi$
$150$	0.205707	+	9.14023i	0.0167959	+	0.746297i
$151$	6.52618	−	12.9947i	0.531093	−	1.05749i	−0.454875	−	0.890555i	$-0.650316\pi$
$151$	6.52618	−	12.9947i	0.531093	−	1.05749i	0.985968	−	0.166937i	$-0.0533877\pi$
$152$	0.804471	−	0.430834i	0.0652512	−	0.0349452i
$153$	−4.12298	+	14.1892i	−0.333323	+	1.14713i
$154$	9.00436	+	2.80045i	0.725592	+	0.225667i
$155$	−19.1988	−	20.3496i	−1.54209	−	1.63452i
$156$	−0.776236	+	0.146386i	−0.0621486	+	0.0117203i
$157$	14.6505	+	9.63579i	1.16924	+	0.769020i	0.977190	−	0.212366i	$-0.0681169\pi$
$157$	14.6505	+	9.63579i	1.16924	+	0.769020i	0.192047	+	0.981386i	$0.438487\pi$
$158$	−4.42841	−	12.5819i	−0.352305	−	1.00096i
$159$	7.78713	+	2.54540i	0.617559	+	0.201863i
$160$	−6.54448	+	15.3821i	−0.517387	+	1.21606i
$161$			0.744325i			0.0586610i
$162$	12.3683	−	3.00420i	0.971745	−	0.236032i
$163$		−	21.1308i		−	1.65509i	−0.561396	−	0.827547i	$-0.689735\pi$
$163$		−	21.1308i		−	1.65509i	0.561396	−	0.827547i	$-0.310265\pi$
$164$	1.92026	+	1.16383i	0.149947	+	0.0908796i
$165$	−17.3973	+	15.6091i	−1.35438	+	1.21516i
$166$	5.02102	−	1.76723i	0.389706	−	0.137164i
$167$	−1.66347	−	1.09408i	−0.128723	−	0.0846625i	0.483515	−	0.875336i	$-0.339360\pi$
$167$	−1.66347	−	1.09408i	−0.128723	−	0.0846625i	−0.612238	+	0.790674i	$0.709730\pi$
$168$	−4.91520	−	5.19706i	−0.379216	−	0.400962i
$169$	8.88546	+	9.41804i	0.683497	+	0.724464i
$170$	−6.11290	+	19.6550i	−0.468838	+	1.50747i
$171$	−0.868467	−	0.427382i	−0.0664133	−	0.0326827i
$172$	7.50775	+	15.7775i	0.572460	+	1.20302i
$173$	−4.20119	+	8.36525i	−0.319410	+	0.635998i	−0.994843	−	0.101423i	$-0.967660\pi$
$173$	−4.20119	+	8.36525i	−0.319410	+	0.635998i	0.675433	+	0.737421i	$0.263957\pi$
$174$	−4.53879	+	8.28659i	−0.344085	+	0.628205i
$175$	−5.00418	−	2.15859i	−0.378280	−	0.163174i
$176$	−17.4150	+	5.51153i	−1.31270	+	0.415447i
$177$	8.48135	−	6.76222i	0.637498	−	0.508280i
$178$	−5.80196	+	4.22421i	−0.434876	+	0.316618i
$179$	−17.7226	−	14.8710i	−1.32465	−	1.11151i	−0.985296	−	0.170854i	$-0.945347\pi$
$179$	−17.7226	−	14.8710i	−1.32465	−	1.11151i	−0.339354	−	0.940659i	$-0.610208\pi$
$180$	17.3049	−	3.86128i	1.28983	−	0.287803i
$181$	3.98951	−	3.34760i	0.296538	−	0.248825i	−0.482363	−	0.875971i	$-0.660222\pi$
$181$	3.98951	−	3.34760i	0.296538	−	0.248825i	0.778902	+	0.627146i	$0.215777\pi$
$182$	0.113459	−	0.456999i	0.00841015	−	0.0338750i
$183$	−1.70363	+	20.4256i	−0.125936	+	1.50990i
$184$	−0.823650	−	1.18340i	−0.0607203	−	0.0872418i
$185$	1.96480	+	1.85370i	0.144455	+	0.136286i
$186$	−13.4262	+	18.9083i	−0.984460	+	1.38643i
$187$	−20.6526	+	8.90866i	−1.51027	+	0.651466i
$188$	−14.7035	−	20.6535i	−1.07236	−	1.50631i
$189$	−1.44381	+	7.44850i	−0.105022	+	0.541799i
$190$	−1.19843	−	0.617928i	−0.0869434	−	0.0448292i
$191$	14.3645	+	1.67897i	1.03938	+	0.121486i	0.618624	−	0.785687i	$-0.287690\pi$
$191$	14.3645	+	1.67897i	1.03938	+	0.121486i	0.420757	+	0.907173i	$0.361764\pi$
$192$	13.5656	+	2.82379i	0.979015	+	0.203790i
$193$	3.18369	+	0.754549i	0.229167	+	0.0543136i	0.343595	−	0.939118i	$-0.388355\pi$
$193$	3.18369	+	0.754549i	0.229167	+	0.0543136i	−0.114428	+	0.993432i	$0.536503\pi$
$194$	3.21636	+	0.0342209i	0.230921	+	0.00245692i
$195$	0.828625	+	0.821936i	0.0593390	+	0.0588601i
$196$	−9.21757	+	3.13448i	−0.658398	+	0.223891i
$197$	11.7906	−	2.07900i	0.840045	−	0.148123i	0.262960	−	0.964807i	$-0.415301\pi$
$197$	11.7906	−	2.07900i	0.840045	−	0.148123i	0.577085	+	0.816684i	$0.304190\pi$
$198$	15.5112	+	11.6089i	1.10234	+	0.825009i
$199$	12.4968	+	2.20353i	0.885877	+	0.156204i	0.598031	−	0.801473i	$-0.295950\pi$
$199$	12.4968	+	2.20353i	0.885877	+	0.156204i	0.287846	+	0.957677i	$0.407061\pi$
$200$	10.3448	−	2.10554i	0.731488	−	0.148884i
$201$	−3.54719	−	10.5613i	−0.250199	−	0.744935i
$202$	−10.8877	−	13.2594i	−0.766056	−	0.932930i
$203$	−3.36325	−	4.51763i	−0.236054	−	0.317075i
$204$	16.9689	+	1.77961i	1.18806	+	0.124598i
$205$	−0.192906	−	3.31206i	−0.0134731	−	0.231324i
$206$	0.831081	−	6.50901i	0.0579041	−	0.453504i
$207$	−0.511381	+	1.44125i	−0.0355435	+	0.100174i
$208$	0.325313	+	0.852135i	0.0225564	+	0.0590849i
$209$	−0.339784	−	1.43366i	−0.0235034	−	0.0991685i
$210$	−2.20540	+	10.3365i	−0.152187	+	0.713285i
$211$	−6.29659	−	0.366735i	−0.433475	−	0.0252471i	−0.159980	−	0.987120i	$-0.551143\pi$
$211$	−6.29659	−	0.366735i	−0.433475	−	0.0252471i	−0.273496	+	0.961873i	$0.588180\pi$
$212$	1.29791	−	9.37052i	0.0891405	−	0.643570i
$213$	22.0567	−	13.7285i	1.51130	−	0.940661i
$214$	−1.57991	+	22.9219i	−0.108000	+	1.56691i
$215$	12.9083	−	22.3578i	0.880337	−	1.52479i
$216$	−5.94679	−	13.4401i	−0.404628	−	0.914482i
$217$	−6.91189	−	11.9718i	−0.469210	−	0.812695i
$218$	−2.25533	+	1.10278i	−0.152750	+	0.0746897i
$219$	21.2519	+	3.02502i	1.43607	+	0.204412i
$220$	21.3008	+	16.5737i	1.43610	+	1.11740i
$221$	0.504061	+	1.00367i	0.0339068	+	0.0675140i
$222$	1.18799	−	1.89793i	0.0797328	−	0.127381i
$223$	13.0851	+	3.91741i	0.876241	+	0.262329i	0.693173	−	0.720771i	$-0.256212\pi$
$223$	13.0851	+	3.91741i	0.876241	+	0.262329i	0.183067	+	0.983100i	$0.441397\pi$
$224$	−4.89937	+	6.64989i	−0.327353	+	0.444315i
$225$	−8.20662	−	7.61778i	−0.547108	−	0.507852i
$226$	15.9077	+	12.1080i	1.05816	+	0.805410i
$227$	10.5315	−	6.92667i	0.699000	−	0.459739i	−0.149619	−	0.988744i	$-0.547805\pi$
$227$	10.5315	−	6.92667i	0.699000	−	0.459739i	0.848619	+	0.529004i	$0.177434\pi$
$228$	−0.307828	+	1.07444i	−0.0203864	+	0.0711568i
$229$	1.79150	−	0.209396i	0.118385	−	0.0138373i	−0.0566939	−	0.998392i	$-0.518056\pi$
$229$	1.79150	−	0.209396i	0.118385	−	0.0138373i	0.175079	+	0.984554i	$0.443982\pi$
$230$	−0.749876	+	1.99400i	−0.0494453	+	0.131480i
$231$	−10.1432	+	5.52235i	−0.667376	+	0.363344i
$232$	10.3463	+	3.46091i	0.679269	+	0.227220i
$233$	−3.33799	−	9.17104i	−0.218679	−	0.600815i	0.781041	−	0.624480i	$-0.214689\pi$
$233$	−3.33799	−	9.17104i	−0.218679	−	0.600815i	−0.999720	+	0.0236645i	$0.992467\pi$
$234$	0.533669	−	0.806942i	0.0348870	−	0.0527514i
$235$	−12.8119	+	35.2005i	−0.835757	+	2.29622i
$236$	−9.42141	−	8.25339i	−0.613281	−	0.537250i
$237$	14.8335	+	6.84392i	0.963538	+	0.444561i
$238$	−5.17877	+	8.75348i	−0.335690	+	0.567404i
$239$	1.08105	+	3.61095i	0.0699272	+	0.233573i	0.985808	−	0.167877i	$-0.0536913\pi$
$239$	1.08105	+	3.61095i	0.0699272	+	0.233573i	−0.915881	+	0.401451i	$0.868506\pi$
$240$	−7.93170	−	18.8744i	−0.511989	−	1.21834i
$241$	−1.40732	+	1.89036i	−0.0906537	+	0.121769i	−0.845136	−	0.534551i	$-0.820481\pi$
$241$	−1.40732	+	1.89036i	−0.0906537	+	0.121769i	0.754482	+	0.656320i	$0.227888\pi$
$242$	0.662204	+	13.9194i	0.0425681	+	0.894772i
$243$	−7.91309	+	13.4307i	−0.507625	+	0.861578i
$244$	23.5605	−	2.24683i	1.50830	−	0.143838i
$245$	11.5387	+	8.59024i	0.737180	+	0.548810i
$246$	−2.66098	+	0.694255i	−0.169658	+	0.0442641i
$247$	−0.0704816	+	0.0211008i	−0.00448464	+	0.00134261i
$248$	24.2369	+	11.3854i	1.53904	+	0.722974i
$249$	−2.73119	+	5.91956i	−0.173082	+	0.375137i
$250$	3.81422	+	3.67602i	0.241233	+	0.232492i
$251$	22.4949	+	8.18746i	1.41986	+	0.516788i	0.934008	−	0.357251i	$-0.116286\pi$
$251$	22.4949	+	8.18746i	1.41986	+	0.516788i	0.485855	+	0.874039i	$0.338508\pi$
$252$	8.76012	+	0.115411i	0.551836	+	0.00727022i
$253$	−2.18747	+	0.796175i	−0.137525	+	0.0500551i
$254$	−16.5152	−	7.33334i	−1.03626	−	0.460135i
$255$	−12.0543	−	22.1409i	−0.754872	−	1.38652i
$256$	0.430929	−	15.9942i	0.0269330	−	0.999637i
$257$	−2.74883	−	23.5177i	−0.171467	−	1.46700i	−0.755437	−	0.655221i	$-0.772575\pi$
$257$	−2.74883	−	23.5177i	−0.171467	−	1.46700i	0.583970	−	0.811775i	$-0.301499\pi$
$258$	−20.2687	−	6.86480i	−1.26187	−	0.427384i
$259$	0.733441	+	1.11514i	0.0455738	+	0.0692916i
$260$	0.764356	−	1.10997i	0.0474034	−	0.0688371i
$261$	−3.40851	−	11.0582i	−0.210982	−	0.684487i
$262$	3.39301	+	3.67391i	0.209621	+	0.226975i
$263$	−0.132660	+	0.443115i	−0.00818016	+	0.0273236i	−0.961982	−	0.273112i	$-0.911947\pi$
$263$	−0.132660	+	0.443115i	−0.00818016	+	0.0273236i	0.953802	+	0.300436i	$0.0971321\pi$
$264$	10.0159	−	20.0042i	0.616434	−	1.23118i
$265$	−12.4907	+	6.27306i	−0.767297	+	0.385351i
$266$	−0.505789	−	0.433660i	−0.0310119	−	0.0265894i
$267$	1.23866	−	8.70206i	0.0758051	−	0.532557i
$268$	−11.2754	+	6.19379i	−0.688755	+	0.378346i
$269$	13.7753	−	7.95320i	0.839897	−	0.484915i	−0.0173321	−	0.999850i	$-0.505517\pi$
$269$	13.7753	−	7.95320i	0.839897	−	0.484915i	0.857229	+	0.514935i	$0.172184\pi$
$270$	−11.3719	+	18.4995i	−0.692073	+	1.12584i
$271$	−10.3923	−	6.00000i	−0.631287	−	0.364474i	0.149963	−	0.988692i	$-0.452085\pi$
$271$	−10.3923	−	6.00000i	−0.631287	−	0.364474i	−0.781250	+	0.624218i	$0.785418\pi$
$272$	−1.45262	−	19.6479i	−0.0880779	−	1.19133i
$273$	0.304740	+	0.489607i	0.0184437	+	0.0296324i
$274$	−31.7559	−	5.94846i	−1.91844	−	0.359359i
$275$	0.991045	−	17.0156i	0.0597623	−	1.02608i
$276$	1.74255	+	0.285988i	0.104889	+	0.0172145i
$277$	−27.7689	+	6.58135i	−1.66847	+	0.395435i	−0.952943	−	0.303150i	$-0.901962\pi$
$277$	−27.7689	+	6.58135i	−1.66847	+	0.395435i	−0.715527	+	0.698585i	$0.753814\pi$
$278$	3.14288	+	13.9192i	0.188498	+	0.834817i
$279$	−5.15852	−	27.9298i	−0.308832	−	1.67211i
$280$	12.1980	+	0.389464i	0.728968	+	0.0232749i
$281$	−13.8458	+	0.806428i	−0.825973	+	0.0481075i	−0.465923	−	0.884825i	$-0.654278\pi$
$281$	−13.8458	+	0.806428i	−0.825973	+	0.0481075i	−0.360050	+	0.932933i	$0.617241\pi$
$282$	30.6925	+	4.70250i	1.82771	+	0.280030i
$283$	−4.92399	+	3.66577i	−0.292701	+	0.217908i	−0.733485	−	0.679705i	$-0.762108\pi$
$283$	−4.92399	+	3.66577i	−0.292701	+	0.217908i	0.440785	+	0.897613i	$0.354700\pi$
$284$	−20.1179	−	22.2538i	−1.19378	−	1.32052i
$285$	1.56546	−	0.525786i	0.0927297	−	0.0311449i
$286$	1.46442	−	0.155392i	0.0865931	−	0.00918853i
$287$	0.284664	−	1.61441i	0.0168032	−	0.0952956i
$288$	−14.0555	+	9.51022i	−0.828226	+	0.560395i
$289$	−1.26056	−	7.14902i	−0.0741509	−	0.420531i
$290$	−4.45861	−	15.4908i	−0.261819	−	0.909649i
$291$	−2.77430	+	2.79687i	−0.162632	+	0.163956i
$292$	−0.914407	−	24.7700i	−0.0535116	−	1.44955i
$293$	−4.75442	+	20.0605i	−0.277756	+	1.17195i	0.637944	+	0.770083i	$0.279785\pi$
$293$	−4.75442	+	20.0605i	−0.277756	+	1.17195i	−0.915700	+	0.401863i	$0.868363\pi$
$294$	5.11039	−	10.7734i	0.298044	−	0.628319i
$295$	−2.14847	+	18.3813i	−0.125089	+	1.07020i
$296$	−2.40009	−	0.961364i	−0.139502	−	0.0558781i
$297$	−23.4345	+	3.72419i	−1.35981	+	0.216100i
$298$	14.1145	+	21.9655i	0.817630	+	1.27243i
$299$	0.0460406	+	0.106734i	0.00266259	+	0.00617259i
$300$	−6.97624	+	10.8860i	−0.402773	+	0.628502i
$301$	8.75395	−	9.27865i	0.504569	−	0.534812i
$302$	17.9179	−	10.0923i	1.03106	−	0.580745i
$303$	20.9400	+	1.74653i	1.20297	+	0.100336i
$304$	1.28403	+	0.129786i	0.0736443	+	0.00744372i
$305$	−22.4779	−	26.7881i	−1.28708	−	1.53388i
$306$	−16.0417	+	13.3915i	−0.917044	+	0.765538i
$307$	−11.1013	+	13.2301i	−0.633587	+	0.755080i	−0.983343	−	0.181761i	$-0.941820\pi$
$307$	−11.1013	+	13.2301i	−0.633587	+	0.755080i	0.349755	+	0.936841i	$0.386265\pi$
$308$	8.35275	+	10.3958i	0.475942	+	0.592358i
$309$	5.01008	+	6.28378i	0.285014	+	0.357471i
$310$	−6.45549	−	39.0350i	−0.366647	−	2.21704i
$311$	−9.36763	+	21.7166i	−0.531189	+	1.23144i	0.415590	+	0.909552i	$0.363575\pi$
$311$	−9.36763	+	21.7166i	−0.531189	+	1.23144i	−0.946779	+	0.321883i	$0.895684\pi$
$312$	−1.02629	−	0.441211i	−0.0581024	−	0.0249787i
$313$	−10.6820	−	5.36471i	−0.603783	−	0.303231i	0.120522	−	0.992711i	$-0.461543\pi$
$313$	−10.6820	−	5.36471i	−0.603783	−	0.303231i	−0.724305	+	0.689479i	$0.757839\pi$
$314$	9.57942	+	22.8737i	0.540598	+	1.29084i
$315$	−7.20054	−	10.7570i	−0.405704	−	0.606086i
$316$	4.73976	−	18.2582i	0.266632	−	1.02711i
$317$	−6.96984	+	6.57571i	−0.391465	+	0.369328i	−0.856661	−	0.515879i	$-0.827465\pi$
$317$	−6.96984	+	6.57571i	−0.391465	+	0.369328i	0.465196	+	0.885208i	$0.345984\pi$
$318$	7.12607	+	9.13542i	0.399610	+	0.512289i
$319$	9.67917	−	14.7165i	0.541930	−	0.823964i
$320$	−19.8246	+	12.8787i	−1.10823	+	0.719943i
$321$	−18.7924	−	20.9454i	−1.04889	−	1.16906i
$322$	−0.587756	+	0.873260i	−0.0327544	+	0.0486649i
$323$	1.58914			0.0884221
$324$	16.8830	+	6.24203i	0.937947	+	0.346779i
$325$	−0.851106			−0.0472108
$326$	16.6860	−	24.7912i	0.924150	−	1.37306i
$327$	0.955304	−	2.92256i	0.0528285	−	0.161618i
$328$	1.33387	+	2.88176i	0.0736509	+	0.159118i
$329$	−10.1711	+	15.4643i	−0.560749	+	0.852577i
$330$	−32.7366	+	4.57515i	−1.80209	+	0.251854i
$331$	2.77131	−	2.61460i	0.152325	−	0.143711i	−0.606307	−	0.795231i	$-0.707350\pi$
$331$	2.77131	−	2.61460i	0.152325	−	0.143711i	0.758632	+	0.651520i	$0.225868\pi$
$332$	7.28627	+	1.89148i	0.399886	+	0.103809i
$333$	0.654024	+	2.66317i	0.0358403	+	0.145941i
$334$	−1.08768	−	2.59716i	−0.0595152	−	0.142110i
$335$	16.9861	+	8.53072i	0.928047	+	0.466083i
$336$	−1.66278	−	9.97860i	−0.0907119	−	0.544377i
$337$	−1.93740	+	4.49140i	−0.105537	+	0.244662i	−0.962799	−	0.270218i	$-0.912904\pi$
$337$	−1.93740	+	4.49140i	−0.105537	+	0.244662i	0.857262	+	0.514880i	$0.172164\pi$
$338$	2.98768	+	18.0659i	0.162508	+	0.982653i
$339$	−24.2113	+	3.64671i	−1.31498	+	0.198062i
$340$	−22.6923	+	18.2326i	−1.23067	+	0.988802i
$341$	27.7900	−	33.1188i	1.50491	−	1.79349i
$342$	−0.681424	−	1.18720i	−0.0368472	−	0.0641964i
$343$	11.1389	+	13.2748i	0.601442	+	0.716770i
$344$	−3.65044	+	24.4390i	−0.196819	+	1.31766i
$345$	−1.11224	−	2.36018i	−0.0598808	−	0.127068i
$346$	−11.5345	+	6.49684i	−0.620101	+	0.349272i
$347$	4.00557	−	4.24566i	0.215030	−	0.227919i	−0.610876	−	0.791726i	$-0.709183\pi$
$347$	4.00557	−	4.24566i	0.215030	−	0.227919i	0.825906	+	0.563808i	$0.190664\pi$
$348$	−11.8685	+	6.13796i	−0.636220	+	0.329029i
$349$	−3.66260	−	8.49087i	−0.196055	−	0.454506i	0.791623	−	0.611010i	$-0.209237\pi$
$349$	−3.66260	−	8.49087i	−0.196055	−	0.454506i	−0.987677	+	0.156505i	$0.949977\pi$
$350$	−4.16649	−	6.48406i	−0.222708	−	0.346588i
$351$	0.253692	+	1.15740i	0.0135411	+	0.0617775i
$352$	−24.7838	−	7.28546i	−1.32098	−	0.388317i
$353$	0.387307	−	3.31362i	0.0206142	−	0.176366i	−0.979009	−	0.203818i	$-0.934665\pi$
$353$	0.387307	−	3.31362i	0.0206142	−	0.176366i	0.999623	+	0.0274514i	$0.00873915\pi$
$354$	15.2903	−	1.23630i	0.812671	−	0.0657085i
$355$	−10.2221	+	43.1303i	−0.542531	+	2.28912i
$356$	−10.1426	+	0.374425i	−0.537559	+	0.0198445i
$357$	−3.27271	−	12.0189i	−0.173210	−	0.636108i
$358$	−9.04967	−	31.4417i	−0.478290	−	1.66175i
$359$	1.17561	+	6.66722i	0.0620464	+	0.351883i	0.999987	+	0.00508686i	$0.00161921\pi$
$359$	1.17561	+	6.66722i	0.0620464	+	0.351883i	−0.937941	+	0.346796i	$0.887270\pi$
$360$	23.3515	+	9.13462i	1.23073	+	0.481437i
$361$	3.28124	−	18.6088i	0.172697	−	0.979412i
$362$	7.32402	−	0.777164i	0.384942	−	0.0408468i
$363$	−12.7953	−	11.2943i	−0.671580	−	0.592797i
$364$	0.493982	−	0.446569i	0.0258917	−	0.0234066i
$365$	−29.3765	+	21.8700i	−1.53764	+	1.14473i
$366$	−18.1278	+	22.6185i	−0.947557	+	1.18229i
$367$	−0.391852	+	0.0228228i	−0.0204545	+	0.00119134i	−0.0683690	−	0.997660i	$-0.521780\pi$
$367$	−0.391852	+	0.0228228i	−0.0204545	+	0.00119134i	0.0479145	+	0.998851i	$0.484742\pi$
$368$	−0.0318499	−	2.03879i	−0.00166029	−	0.106279i
$369$	1.66036	−	2.93043i	0.0864351	−	0.152552i
$370$	0.841383	+	3.72631i	0.0437414	+	0.193721i
$371$	−6.72031	+	1.59274i	−0.348901	+	0.0826911i
$372$	−30.6830	+	11.5817i	−1.59084	+	0.600483i
$373$	0.982467	−	16.8683i	0.0508702	−	0.873408i	−0.872289	−	0.488990i	$-0.837365\pi$
$373$	0.982467	−	16.8683i	0.0508702	−	0.873408i	0.923159	−	0.384417i	$-0.125598\pi$
$374$	−31.2648	−	5.85647i	−1.61667	−	0.302831i
$375$	−6.48428	+	0.214975i	−0.334847	+	0.0111013i
$376$	−0.941420	−	35.8418i	−0.0485500	−	1.84840i
$377$	−0.761720	−	0.439779i	−0.0392306	−	0.0226498i
$378$	−7.57562	+	7.59865i	−0.389648	+	0.390832i
$379$	21.8595	−	12.6206i	1.12285	−	0.648277i	0.180722	−	0.983534i	$-0.442156\pi$
$379$	21.8595	−	12.6206i	1.12285	−	0.648277i	0.942127	+	0.335257i	$0.108823\pi$
$380$	−0.918082	−	1.67131i	−0.0470966	−	0.0857363i
$381$	20.5344	−	8.25430i	1.05201	−	0.422881i
$382$	15.5270	+	13.3128i	0.794431	+	0.681140i
$383$	25.9070	−	13.0110i	1.32379	−	0.664831i	0.360363	−	0.932812i	$-0.382653\pi$
$383$	25.9070	−	13.0110i	1.32379	−	0.664831i	0.963424	+	0.267982i	$0.0863566\pi$
$384$	13.6857	+	14.0250i	0.698396	+	0.715712i
$385$	5.65118	−	18.8762i	0.288011	−	0.962022i
$386$	3.13935	+	3.39926i	0.159789	+	0.173018i
$387$	23.3252	−	11.9520i	1.18569	−	0.607557i
$388$	3.74649	+	2.57995i	0.190199	+	0.130977i
$389$	−8.58324	−	13.0502i	−0.435188	−	0.661671i	0.549601	−	0.835427i	$-0.314780\pi$
$389$	−8.58324	−	13.0502i	−0.435188	−	0.661671i	−0.984789	+	0.173757i	$0.944409\pi$
$390$	0.323120	+	1.61864i	0.0163618	+	0.0819629i
$391$	−0.291482	−	2.49378i	−0.0147409	−	0.126116i
$392$	−13.2894	−	3.60121i	−0.671217	−	0.181889i
$393$	−6.12305	−	0.153332i	−0.308867	−	0.00773456i
$394$	15.4747	+	6.87131i	0.779603	+	0.346171i
$395$	−26.1905	+	9.53256i	−1.31779	+	0.479635i
$396$	9.03117	+	25.8683i	0.453834	+	1.29993i
$397$	12.5501	+	4.56786i	0.629871	+	0.229254i	0.637175	−	0.770719i	$-0.280103\pi$
$397$	12.5501	+	4.56786i	0.629871	+	0.229254i	−0.00730394	+	0.999973i	$0.502325\pi$
$398$	12.9216	+	12.4534i	0.647699	+	0.624230i
$399$	0.812581	−	0.0744109i	0.0406799	−	0.00372520i
$400$	13.7994	+	5.69851i	0.689970	+	0.284925i
$401$	28.7614	−	8.61061i	1.43628	−	0.429993i	0.528317	−	0.849047i	$-0.322823\pi$
$401$	28.7614	−	8.61061i	1.43628	−	0.429993i	0.907961	+	0.419054i	$0.137638\pi$
$402$	4.17807	−	15.1918i	0.208383	−	0.757697i
$403$	−1.73166	−	1.28918i	−0.0862603	−	0.0642184i
$404$	−2.30341	−	24.1538i	−0.114599	−	1.20169i
$405$	−6.55202	−	25.7759i	−0.325573	−	1.28082i
$406$	−0.378499	−	7.95597i	−0.0187846	−	0.394848i
$407$	−2.49273	+	3.34831i	−0.123560	+	0.165970i
$408$	18.5031	+	15.4874i	0.916039	+	0.766740i
$409$	5.65075	+	18.8748i	0.279412	+	0.933300i	0.976355	+	0.216174i	$0.0693577\pi$
$409$	5.65075	+	18.8748i	0.279412	+	0.933300i	−0.696943	+	0.717126i	$0.745457\pi$
$410$	2.38905	−	4.03811i	0.117987	−	0.199428i
$411$	32.3211	−	22.8272i	1.59428	−	1.12598i
$412$	6.11488	−	6.98025i	0.301258	−	0.343892i
$413$	−3.12755	+	8.59286i	−0.153897	+	0.422827i
$414$	−1.73804	+	1.28709i	−0.0854202	+	0.0632571i
$415$	−3.80414	−	10.4518i	−0.186738	−	0.513057i
$416$	−0.291223	+	1.25663i	−0.0142784	+	0.0616113i
$417$	−14.9117	−	9.11446i	−0.730228	−	0.446337i
$418$	0.733448	−	1.95032i	0.0358741	−	0.0953931i
$419$	−8.59571	+	1.00469i	−0.419928	+	0.0490825i	−0.323433	−	0.946251i	$-0.604837\pi$
$419$	−8.59571	+	1.00469i	−0.419928	+	0.0490825i	−0.0964945	+	0.995334i	$0.530763\pi$
$420$	−10.7496	+	10.3855i	−0.524528	+	0.506761i
$421$	18.8861	−	12.4216i	0.920454	−	0.605392i	0.00160396	−	0.999999i	$-0.499489\pi$
$421$	18.8861	−	12.4216i	0.920454	−	0.605392i	0.918850	+	0.394606i	$0.129119\pi$
$422$	−7.09772	−	5.40236i	−0.345511	−	0.262983i
$423$	−30.3190	+	22.9559i	−1.47416	+	1.11615i
$424$	8.92216	−	9.96882i	0.433298	−	0.484129i
$425$	17.6113	+	5.27248i	0.854274	+	0.255753i
$426$	36.7182	+	1.31050i	1.77900	+	0.0634941i
$427$	−7.75476	−	15.4410i	−0.375279	−	0.747242i
$428$	−19.9538	+	25.6449i	−0.964506	+	1.23959i
$429$	−1.11292	+	1.41930i	−0.0537324	+	0.0685246i
$430$	32.7991	−	16.0377i	1.58171	−	0.773405i
$431$	10.8549	+	18.8013i	0.522864	+	0.905627i	0.999646	+	0.0266056i	$0.00846982\pi$
$431$	10.8549	+	18.8013i	0.522864	+	0.905627i	−0.476782	+	0.879022i	$0.658197\pi$
$432$	3.63605	−	20.4641i	0.174939	−	0.984579i
$433$	−7.10360	+	12.3038i	−0.341377	+	0.591283i	−0.984689	−	0.174322i	$-0.944227\pi$
$433$	−7.10360	+	12.3038i	−0.341377	+	0.591283i	0.643312	+	0.765604i	$0.277560\pi$
$434$	1.34429	−	19.5035i	0.0645282	−	0.936199i
$435$	17.4152	+	9.29928i	0.834993	+	0.445866i
$436$	−3.51682	−	0.487112i	−0.168425	−	0.0233284i
$437$	0.164193	+	0.00956314i	0.00785440	+	0.000457467i
$438$	22.5445	+	20.3305i	1.07722	+	0.971431i
$439$	−0.673047	−	2.83981i	−0.0321228	−	0.135537i	0.954621	−	0.297824i	$-0.0962609\pi$
$439$	−0.673047	−	2.83981i	−0.0321228	−	0.135537i	−0.986743	+	0.162288i	$0.948113\pi$
$440$	11.9031	+	36.2648i	0.567458	+	1.72886i
$441$	5.10589	+	13.6823i	0.243138	+	0.651536i
$442$	−0.201170	+	1.57556i	−0.00956868	+	0.0749417i
$443$	0.827007	+	14.1992i	0.0392923	+	0.674622i	0.959242	+	0.282586i	$0.0911922\pi$
$443$	0.827007	+	14.1992i	0.0392923	+	0.674622i	−0.919950	+	0.392036i	$0.871771\pi$
$444$	2.89248	−	1.28860i	0.137271	−	0.0611544i
$445$	8.95518	+	12.0289i	0.424516	+	0.570224i
$446$	12.2583	+	14.9286i	0.580448	+	0.706890i
$447$	−31.3427	−	6.33944i	−1.48246	−	0.299845i
$448$	−10.9991	+	3.93303i	−0.519661	+	0.185818i
$449$	−31.8076	−	5.60854i	−1.50110	−	0.264684i	−0.638123	−	0.769935i	$-0.720289\pi$
$449$	−31.8076	−	5.60854i	−1.50110	−	0.264684i	−0.862972	+	0.505251i	$0.831400\pi$
$450$	−3.61282	−	15.4177i	−0.170310	−	0.726798i
$451$	5.04903	−	0.890281i	0.237750	−	0.0419217i
$452$	9.10218	+	26.7668i	0.428131	+	1.25901i
$453$	−6.42010	+	24.3545i	−0.301643	+	1.14427i
$454$	17.8254	+	0.189656i	0.836589	+	0.00890101i
$455$	−0.957390	−	0.226906i	−0.0448831	−	0.0106375i
$456$	−1.20958	+	1.01749i	−0.0566440	+	0.0476482i
$457$	26.1549	+	3.05707i	1.22347	+	0.143004i	0.703197	−	0.710995i	$-0.251755\pi$
$457$	26.1549	+	3.05707i	1.22347	+	0.143004i	0.520276	+	0.853998i	$0.325829\pi$
$458$	2.26717	+	1.16899i	0.105938	+	0.0546231i
$459$	1.92047	−	25.5208i	0.0896399	−	1.19121i
$460$	−2.45433	+	1.74727i	−0.114434	+	0.0814668i
$461$	−6.10448	+	2.63322i	−0.284314	+	0.122641i	−0.533461	−	0.845824i	$-0.679109\pi$
$461$	−6.10448	+	2.63322i	−0.284314	+	0.122641i	0.249147	+	0.968466i	$0.419850\pi$
$462$	−16.2610	−	1.53065i	−0.756530	−	0.0712121i
$463$	−12.4374	−	11.7340i	−0.578013	−	0.545327i	0.340741	−	0.940157i	$-0.389322\pi$
$463$	−12.4374	−	11.7340i	−0.578013	−	0.545327i	−0.918754	+	0.394830i	$0.870804\pi$
$464$	9.40564	+	12.2304i	0.436646	+	0.567782i
$465$	39.8062	+	27.6329i	1.84597	+	1.28144i
$466$	3.32571	−	13.3955i	0.154060	−	0.620536i
$467$	18.4438	−	15.4762i	0.853479	−	0.716154i	−0.107074	−	0.994251i	$-0.534148\pi$
$467$	18.4438	−	15.4762i	0.853479	−	0.716154i	0.960553	+	0.278097i	$0.0897038\pi$
$468$	1.26331	−	0.525312i	0.0583967	−	0.0242825i
$469$	7.19476	+	6.03712i	0.332223	+	0.278768i
$470$	−42.8273	+	31.1811i	−1.97547	+	1.43828i
$471$	−28.2713	−	11.0990i	−1.30267	−	0.511417i
$472$	−4.53613	−	17.1227i	−0.208792	−	0.788135i
$473$	36.6325	+	15.8017i	1.68436	+	0.726563i
$474$	11.9987	+	19.7427i	0.551118	+	0.906813i
$475$	−0.540464	+	1.07615i	−0.0247982	+	0.0493772i
$476$	−12.9880	+	6.18037i	−0.595306	+	0.283277i
$477$	−14.1069	−	1.53307i	−0.645911	−	0.0701947i
$478$	−1.58308	+	5.09011i	−0.0724083	+	0.232816i
$479$	9.84582	+	10.4360i	0.449867	+	0.476831i	0.912124	−	0.409915i	$-0.134442\pi$
$479$	9.84582	+	10.4360i	0.449867	+	0.476831i	−0.462257	+	0.886746i	$0.652960\pi$
$480$	5.59854	−	28.4072i	0.255537	−	1.29661i
$481$	0.174151	+	0.114541i	0.00794060	+	0.00522262i
$482$	−3.14383	+	1.10653i	−0.143198	+	0.0504009i
$483$	−0.265815	−	1.26151i	−0.0120950	−	0.0574006i
$484$	−10.2145	+	16.8535i	−0.464296	+	0.766066i
$485$		−	6.72112i		−	0.305190i
$486$	−19.8894	+	9.50861i	−0.902199	+	0.431319i
$487$		−	4.60903i		−	0.208855i	−0.994532	−	0.104428i	$-0.966699\pi$
$487$		−	4.60903i		−	0.208855i	0.994532	−	0.104428i	$-0.0333011\pi$
$488$	29.4159	+	15.9685i	1.33160	+	0.722859i
$489$	7.54629	+	35.8133i	0.341255	+	1.61953i
$490$	6.75419	+	19.1898i	0.305123	+	0.866907i
$491$	15.4786	+	10.1805i	0.698541	+	0.459438i	0.848459	−	0.529261i	$-0.177531\pi$
$491$	15.4786	+	10.1805i	0.698541	+	0.459438i	−0.149918	+	0.988698i	$0.547901\pi$
$492$	−3.67014	−	1.28673i	−0.165463	−	0.0580102i
$493$	13.0373	+	13.8188i	0.587172	+	0.622366i
$494$	−0.0993529	−	0.0308998i	−0.00447010	−	0.00139025i
$495$	23.9112	−	32.6677i	1.07473	−	1.46831i
$496$	19.4448	+	32.4963i	0.873095	+	1.45913i
$497$	−9.82948	+	19.5721i	−0.440912	+	0.877928i
$498$	−7.87867	+	4.78829i	−0.353052	+	0.214568i
$499$	8.99756	+	3.88117i	0.402786	+	0.173745i	0.587828	−	0.808986i	$-0.299983\pi$
$499$	8.99756	+	3.88117i	0.402786	+	0.173745i	−0.185042	+	0.982731i	$0.559242\pi$
$500$	1.57217	+	7.32469i	0.0703097	+	0.327570i
$501$	3.21002	+	1.26022i	0.143413	+	0.0563027i
$502$	19.9263	+	27.3688i	0.889353	+	1.22153i
$503$	9.65616	+	8.10248i	0.430547	+	0.361272i	0.832158	−	0.554539i	$-0.187105\pi$
$503$	9.65616	+	8.10248i	0.430547	+	0.361272i	−0.401611	+	0.915810i	$0.631550\pi$
$504$	10.1864	+	7.05283i	0.453740	+	0.314158i
$505$	−27.4626	+	23.0439i	−1.22207	+	1.02544i
$506$	−3.19509	−	0.793246i	−0.142039	−	0.0352641i
$507$	−18.4228	−	12.7888i	−0.818184	−	0.567971i
$508$	−13.5853	−	21.6449i	−0.602749	−	0.960337i
$509$	−9.73251	−	9.18215i	−0.431386	−	0.406992i	0.439683	−	0.898153i	$-0.355091\pi$
$509$	−9.73251	−	9.18215i	−0.431386	−	0.406992i	−0.871068	+	0.491162i	$0.836572\pi$
$510$	3.34114	−	35.4950i	0.147948	−	1.57174i
$511$	−16.6163	+	7.16755i	−0.735060	+	0.317074i
$512$	13.1354	−	18.4245i	0.580508	−	0.814255i
$513$	1.62454	+	0.414193i	0.0717250	+	0.0182871i
$514$	15.3458	−	29.7622i	0.676874	−	1.31275i
$515$	−13.6186	−	1.59178i	−0.600107	−	0.0701424i
$516$	−18.3589	−	24.0591i	−0.808205	−	1.05914i
$517$	−56.3272	−	13.3498i	−2.47727	−	0.587124i
$518$	−0.0200820	+	1.88747i	−0.000882354	+	0.0829308i
$519$	4.13290	−	15.6781i	0.181414	−	0.688190i
$520$	1.77324	−	0.698663i	0.0777619	−	0.0306384i
$521$	21.7133	−	3.82864i	0.951276	−	0.167736i	0.323586	−	0.946199i	$-0.395112\pi$
$521$	21.7133	−	3.82864i	0.951276	−	0.167736i	0.627690	+	0.778463i	$0.284000\pi$
$522$	4.73318	−	15.6653i	0.207166	−	0.685652i
$523$	−25.5054	−	4.49728i	−1.11527	−	0.196652i	−0.414508	−	0.910046i	$-0.636046\pi$
$523$	−25.5054	−	4.49728i	−1.11527	−	0.196652i	−0.700764	+	0.713393i	$0.747157\pi$
$524$	1.07965	+	6.98961i	0.0471649	+	0.305342i
$525$	9.25214	+	1.87135i	0.403796	+	0.0816726i
$526$	−0.505545	+	0.415118i	−0.0220428	+	0.0181000i
$527$	27.8458	+	37.4034i	1.21298	+	1.62932i
$528$	27.5472	−	15.5604i	1.19884	−	0.677179i
$529$	1.32222	+	22.7017i	0.0574879	+	0.987029i
$530$	−19.6079	−	2.50357i	−0.851713	−	0.108748i
$531$	−11.9596	+	14.4897i	−0.519000	+	0.628800i
$532$	−0.250964	−	0.908176i	−0.0108807	−	0.0393744i
$533$	−0.0590401	−	0.249110i	−0.00255731	−	0.0107901i
$534$	8.32481	−	9.23135i	0.360250	−	0.399480i
$535$	47.9288	+	2.79154i	2.07214	+	0.120689i
$536$	−18.1195	−	1.63691i	−0.782643	−	0.0707039i
$537$	35.3477	+	18.8748i	1.52536	+	0.814508i
$538$	22.4418	+	1.54682i	0.967534	+	0.0666880i
$539$	−11.1150	+	19.2517i	−0.478756	+	0.829230i
$540$	−27.9499	+	12.7242i	−1.20277	+	0.547562i
$541$	7.60674	+	13.1753i	0.327039	+	0.566449i	0.981923	−	0.189281i	$-0.0606157\pi$
$541$	7.60674	+	13.1753i	0.327039	+	0.566449i	−0.654884	+	0.755730i	$0.727282\pi$
$542$	−7.45460	−	15.2456i	−0.320202	−	0.654855i
$543$	−5.56606	+	7.09837i	−0.238863	+	0.304620i
$544$	13.8107	−	24.1984i	0.592128	−	1.03750i
$545$	2.35432	+	4.68784i	0.100848	+	0.200805i
$546$	−0.0290901	+	0.815056i	−0.00124494	+	0.0348812i
$547$	−1.00380	−	0.300517i	−0.0429192	−	0.0128492i	0.265272	−	0.964174i	$-0.414538\pi$
$547$	−1.00380	−	0.300517i	−0.0429192	−	0.0128492i	−0.308191	+	0.951325i	$0.599724\pi$
$548$	−32.5596	−	32.0549i	−1.39088	−	1.36932i
$549$	−4.40706	−	35.2264i	−0.188089	−	1.50343i
$550$	14.5991	−	19.1805i	0.622506	−	0.817860i
$551$	−1.03977	+	0.683865i	−0.0442956	+	0.0291336i
$552$	1.81857	+	1.71153i	0.0774035	+	0.0728476i
$553$	−13.6786	+	1.59879i	−0.581672	+	0.0679877i
$554$	−37.7761	−	14.2063i	−1.60495	−	0.603568i
$555$	−3.99201	−	2.44003i	−0.169451	−	0.103574i
$556$	−7.30397	+	18.8121i	−0.309757	+	0.797810i
$557$	8.61563	+	23.6712i	0.365056	+	1.00298i	0.977216	+	0.212249i	$0.0680787\pi$
$557$	8.61563	+	23.6712i	0.365056	+	1.00298i	−0.612160	+	0.790734i	$0.709699\pi$
$558$	16.0027	−	36.8413i	0.677447	−	1.55962i
$559$	0.681356	−	1.87201i	0.0288183	−	0.0791776i
$560$	14.0034	+	10.0891i	0.591752	+	0.426340i
$561$	31.8213	−	22.4742i	1.34349	−	0.948862i
$562$	−16.8811	−	9.98724i	−0.712084	−	0.421286i
$563$	−12.2671	−	40.9750i	−0.516997	−	1.72689i	−0.673475	−	0.739210i	$-0.735199\pi$
$563$	−12.2671	−	40.9750i	−0.516997	−	1.72689i	0.156477	−	0.987682i	$-0.449986\pi$
$564$	32.2958	+	29.7534i	1.35990	+	1.25284i
$565$	24.9451	−	33.5071i	1.04945	−	1.40966i
$566$	−8.67161	+	0.412545i	−0.364495	+	0.0173406i
$567$	−0.213002	−	13.1396i	−0.00894523	−	0.551811i
$568$	−6.03003	−	41.9948i	−0.253014	−	1.76206i
$569$	−6.09566	−	4.53805i	−0.255543	−	0.190245i	0.461762	−	0.887004i	$-0.347217\pi$
$569$	−6.09566	−	4.53805i	−0.255543	−	0.190245i	−0.717306	+	0.696759i	$0.754625\pi$
$570$	2.25182	+	0.619299i	0.0943183	+	0.0259396i
$571$	−26.3160	+	7.87849i	−1.10129	+	0.329705i	−0.785336	−	0.619070i	$-0.787510\pi$
$571$	−26.3160	+	7.87849i	−1.10129	+	0.329705i	−0.315954	+	0.948774i	$0.602325\pi$
$572$	1.84080	+	0.974071i	0.0769677	+	0.0407279i
$573$	−24.9451	+	2.28431i	−1.04210	+	0.0954284i
$574$	1.60879	−	1.66928i	0.0671497	−	0.0696744i
$575$	1.78790	+	0.650743i	0.0745606	+	0.0271379i
$576$	−23.9999	+	0.0587237i	−0.999997	+	0.00244682i
$577$	−19.8683	+	7.23147i	−0.827128	+	0.301050i	−0.720680	−	0.693268i	$-0.756170\pi$
$577$	−19.8683	+	7.23147i	−0.827128	+	0.301050i	−0.106448	+	0.994318i	$0.533948\pi$
$578$	4.16630	−	9.38280i	0.173295	−	0.390273i
$579$	−5.66530	−	0.141869i	−0.235442	−	0.00589587i
$580$	7.00133	−	21.6949i	0.290714	−	0.900830i
$581$	−0.638027	−	5.45867i	−0.0264698	−	0.226464i
$582$	−5.46342	+	1.09063i	−0.226466	+	0.0452082i
$583$	−11.8693	−	18.0464i	−0.491577	−	0.747406i
$584$	18.4868	−	29.7828i	0.764990	−	1.23242i
$585$	−1.69791	−	1.09713i	−0.0702001	−	0.0453605i
$586$	−21.4188	+	19.7811i	−0.884801	+	0.817150i
$587$	9.22036	−	30.7982i	0.380565	−	1.27118i	−0.526496	−	0.850178i	$-0.676495\pi$
$587$	9.22036	−	30.7982i	0.380565	−	1.27118i	0.907061	−	0.420999i	$-0.138320\pi$
$588$	14.5029	−	8.60422i	0.598088	−	0.354832i
$589$	−2.72969	+	1.37090i	−0.112475	+	0.0564869i
$590$	−17.0354	+	19.8689i	−0.701338	+	0.817988i
$591$	−19.2406	+	7.73424i	−0.791454	+	0.318144i
$592$	−2.05670	−	3.02312i	−0.0845298	−	0.124250i
$593$	−10.6719	+	6.16144i	−0.438244	+	0.253020i	−0.702852	−	0.711336i	$-0.748091\pi$
$593$	−10.6719	+	6.16144i	−0.438244	+	0.253020i	0.264609	+	0.964356i	$0.414757\pi$
$594$	−30.4348	−	14.1358i	−1.24875	−	0.579998i
$595$	18.4049	+	10.6261i	0.754528	+	0.435627i
$596$	−0.785635	+	36.9160i	−0.0321808	+	1.51214i
$597$	−21.9670	+	0.728278i	−0.899049	+	0.0298064i
$598$	−0.0302666	+	0.161579i	−0.00123769	+	0.00660745i
$599$	−0.822872	+	14.1282i	−0.0336217	+	0.577262i	0.938862	+	0.344292i	$0.111881\pi$
$599$	−0.822872	+	14.1282i	−0.0336217	+	0.577262i	−0.972484	+	0.232969i	$0.925156\pi$
$600$	−16.7808	+	7.26289i	−0.685073	+	0.296506i
$601$	25.5548	−	6.05659i	1.04240	−	0.247054i	0.326458	−	0.945212i	$-0.394145\pi$
$601$	25.5548	−	6.05659i	1.04240	−	0.247054i	0.715943	+	0.698158i	$0.245997\pi$
$602$	17.5972	−	3.97337i	0.717209	−	0.161942i
$603$	9.78356	+	16.6328i	0.398418	+	0.677342i
$604$	28.9911	+	2.30838i	1.17963	+	0.0939266i
$605$	29.0689	−	1.69307i	1.18182	−	0.0688330i
$606$	23.1881	+	18.5843i	0.941952	+	0.754936i
$607$	−27.1053	+	20.1791i	−1.10017	+	0.819045i	−0.984699	−	0.174266i	$-0.944245\pi$
$607$	−27.1053	+	20.1791i	−1.10017	+	0.819045i	−0.115470	+	0.993311i	$0.536837\pi$
$608$	1.40397	+	1.16620i	0.0569386	+	0.0472958i
$609$	7.31349	+	6.45554i	0.296358	+	0.261592i
$610$	−5.21836	−	49.1780i	−0.211285	−	1.99116i
$611$	−0.501946	+	2.84668i	−0.0203066	+	0.115164i
$612$	−29.3951	+	3.04383i	−1.18823	+	0.123040i
$613$	1.75561	+	9.95655i	0.0709083	+	0.402141i	0.999517	+	0.0310803i	$0.00989476\pi$
$613$	1.75561	+	9.95655i	0.0709083	+	0.402141i	−0.928609	+	0.371061i	$0.878994\pi$
$614$	−23.4715	+	6.75565i	−0.947232	+	0.272636i
$615$	1.50975	+	5.54450i	0.0608791	+	0.223576i
$616$	1.59057	+	18.7924i	0.0640857	+	0.757167i
$617$	0.0943090	−	0.397921i	0.00379674	−	0.0160197i	−0.971114	−	0.238618i	$-0.923306\pi$
$617$	0.0943090	−	0.397921i	0.00379674	−	0.0160197i	0.974910	+	0.222598i	$0.0714538\pi$
$618$	0.915965	+	11.3285i	0.0368455	+	0.455698i
$619$	−3.95716	+	33.8557i	−0.159052	+	1.36078i	0.644073	+	0.764964i	$0.277243\pi$
$619$	−3.95716	+	33.8557i	−0.159052	+	1.36078i	−0.803125	+	0.595811i	$0.796831\pi$
$620$	23.2502	−	50.8943i	0.933752	−	2.04397i
$621$	0.352006	−	2.62530i	0.0141255	−	0.105350i
$622$	−28.1388	+	18.0813i	−1.12826	+	0.724993i
$623$	2.93492	+	6.80391i	0.117585	+	0.272593i
$624$	−0.855668	−	1.32805i	−0.0342542	−	0.0531646i
$625$	20.4027	−	21.6256i	0.816109	−	0.865025i
$626$	−8.29615	−	14.7291i	−0.331581	−	0.588691i
$627$	1.08787	+	2.30847i	0.0434453	+	0.0921916i
$628$	−6.82341	+	34.4003i	−0.272284	+	1.37272i
$629$	−2.89401	−	3.44895i	−0.115392	−	0.137519i
$630$	0.0463993	−	18.3062i	0.00184859	−	0.729338i
$631$	4.66128	−	5.55510i	0.185563	−	0.221145i	−0.665241	−	0.746629i	$-0.731671\pi$
$631$	4.66128	−	5.55510i	0.185563	−	0.221145i	0.850804	+	0.525484i	$0.176116\pi$
$632$	19.9784	−	17.6783i	0.794698	−	0.703203i
$633$	10.8026	−	1.62710i	0.429367	−	0.0646713i
$634$	−13.3697	+	2.21104i	−0.530978	+	0.0878116i
$635$	−14.9554	+	34.6704i	−0.593486	+	1.37585i
$636$	1.14668	+	16.3450i	0.0454690	+	0.648121i
$637$	0.991971	+	0.498187i	0.0393033	+	0.0197389i
$638$	22.9767	−	9.62255i	0.909656	−	0.380960i
$639$	−32.4798	+	31.1445i	−1.28488	+	1.23206i
$640$	−33.4283	−	0.544832i	−1.32137	−	0.0215364i
$641$	−10.6643	+	10.0612i	−0.421213	+	0.397394i	−0.867453	−	0.497519i	$-0.834244\pi$
$641$	−10.6643	+	10.0612i	−0.421213	+	0.397394i	0.446240	+	0.894914i	$0.352763\pi$
$642$	−5.50823	−	39.4130i	−0.217392	−	1.55551i
$643$	23.3660	−	35.5263i	0.921466	−	1.40102i	0.00540417	−	0.999985i	$-0.498280\pi$
$643$	23.3660	−	35.5263i	0.921466	−	1.40102i	0.916062	−	0.401036i	$-0.131350\pi$
$644$	−1.37914	+	0.560407i	−0.0543457	+	0.0220831i
$645$	−13.8929	+	42.5026i	−0.547034	+	1.67354i
$646$	1.86442	+	1.25486i	0.0733545	+	0.0493720i
$647$	38.8708			1.52817			0.764085	−	0.645116i	$-0.223191\pi$
$647$	38.8708			1.52817			0.764085	+	0.645116i	$0.223191\pi$
$648$	14.8786	+	20.6550i	0.584485	+	0.811404i
$649$	−28.5987			−1.12260
$650$	−0.998537	−	0.672075i	−0.0391658	−	0.0263610i
$651$	15.9899	+	17.8217i	0.626693	+	0.698489i
$652$	39.1527	−	15.9095i	1.53334	−	0.623066i
$653$	−7.39217	+	11.2392i	−0.289278	+	0.439826i	−0.950665	−	0.310219i	$-0.899598\pi$
$653$	−7.39217	+	11.2392i	−0.289278	+	0.439826i	0.661387	+	0.750045i	$0.269968\pi$
$654$	3.42858	−	2.67446i	0.134068	−	0.104580i
$655$	7.60095	−	7.17113i	0.296994	−	0.280199i
$656$	−0.710647	+	4.43424i	−0.0277461	+	0.173128i
$657$	−37.0987	+	2.46259i	−1.44736	+	0.0960749i
$658$	−24.1443	+	10.1116i	−0.941244	+	0.394190i
$659$	15.8813	+	7.97587i	0.618646	+	0.310696i	0.730378	−	0.683043i	$-0.239344\pi$
$659$	15.8813	+	7.97587i	0.618646	+	0.310696i	−0.111733	+	0.993738i	$0.535640\pi$
$660$	−42.0201	−	20.4828i	−1.63563	−	0.797290i
$661$	5.49351	−	12.7354i	0.213673	−	0.495349i	−0.777346	−	0.629073i	$-0.783434\pi$
$661$	5.49351	−	12.7354i	0.213673	−	0.495349i	0.991019	+	0.133725i	$0.0426937\pi$
$662$	5.31599	−	0.879142i	0.206612	−	0.0341688i
$663$	−1.21273	−	1.52104i	−0.0470986	−	0.0590723i
$664$	7.05481	+	7.97273i	0.273780	+	0.309402i
$665$	−0.894859	+	1.06645i	−0.0347011	+	0.0413552i
$666$	−1.33566	+	3.64094i	−0.0517556	+	0.141084i
$667$	1.26388	+	1.50624i	0.0489377	+	0.0583217i
$668$	0.774754	−	3.90593i	0.0299761	−	0.151125i
$669$	−23.5760	−	1.96640i	−0.911501	−	0.0760253i
$670$	13.1922	+	23.4215i	0.509658	+	0.904850i
$671$	37.0841	−	39.3068i	1.43162	−	1.51742i
$672$	5.92879	−	13.0201i	0.228708	−	0.502263i
$673$	9.59860	+	22.2521i	0.369999	+	0.857754i	0.996902	+	0.0786563i	$0.0250630\pi$
$673$	9.59860	+	22.2521i	0.369999	+	0.857754i	−0.626903	+	0.779097i	$0.715678\pi$
$674$	−5.81964	+	3.73955i	−0.224164	+	0.144042i
$675$	16.6293	+	9.98012i	0.640064	+	0.384135i
$676$	−10.7605	+	23.5545i	−0.413865	+	0.905943i
$677$	−0.492799	+	4.21617i	−0.0189398	+	0.162040i	−0.999398	−	0.0346858i	$-0.988957\pi$
$677$	−0.492799	+	4.21617i	−0.0189398	+	0.162040i	0.980458	+	0.196726i	$0.0630310\pi$
$678$	−31.2849	−	14.8400i	−1.20149	−	0.569928i
$679$	0.765878	−	3.23149i	0.0293917	−	0.124013i
$680$	−41.0206	+	3.47193i	−1.57307	+	0.133143i
$681$	−15.3755	+	15.5006i	−0.589189	+	0.593984i
$682$	58.7562	−	16.9114i	2.24989	−	0.647572i
$683$	−4.21456	−	23.9019i	−0.161266	−	0.914582i	−0.952832	−	0.303499i	$-0.901845\pi$
$683$	−4.21456	−	23.9019i	−0.161266	−	0.914582i	0.791566	−	0.611083i	$-0.209266\pi$
$684$	0.138009	−	1.93094i	0.00527692	−	0.0738312i
$685$	−11.7229	+	66.4840i	−0.447910	+	2.54022i
$686$	2.58595	+	24.3701i	0.0987319	+	0.930453i
$687$	−2.96151	+	0.994674i	−0.112989	+	0.0379492i
$688$	−23.5811	+	25.7899i	−0.899019	+	0.983230i
$689$	−0.865153	+	0.644083i	−0.0329597	+	0.0245376i
$690$	0.558814	−	3.64729i	0.0212737	−	0.138850i
$691$	12.2925	−	0.715957i	0.467629	−	0.0272363i	0.177287	−	0.984159i	$-0.443268\pi$
$691$	12.2925	−	0.715957i	0.467629	−	0.0272363i	0.290342	+	0.956923i	$0.406231\pi$
$692$	−18.6628	−	1.48601i	−0.709455	−	0.0564894i
$693$	15.2189	−	12.9818i	0.578120	−	0.493139i
$694$	8.05202	−	1.81811i	0.305650	−	0.0690144i
$695$	29.0133	−	6.87627i	1.10054	−	0.260832i
$696$	−18.7713	−	2.17077i	−0.711523	−	0.0822829i
$697$	−0.321526	+	5.52039i	−0.0121787	+	0.209100i
$698$	2.40776	−	12.8539i	0.0911351	−	0.486526i
$699$	8.93252	+	14.3513i	0.337859	+	0.542817i
$700$	0.231913	−	10.8973i	0.00876550	−	0.411880i
$701$	−15.5709	−	8.98989i	−0.588106	−	0.339543i	0.176242	−	0.984347i	$-0.443606\pi$
$701$	−15.5709	−	8.98989i	−0.588106	−	0.339543i	−0.764348	+	0.644804i	$0.776939\pi$
$702$	−0.616304	+	1.55822i	−0.0232609	+	0.0588111i
$703$	0.255416	−	0.147464i	0.00963319	−	0.00556172i
$704$	−23.3240	−	28.1180i	−0.879056	−	1.05974i
$705$	9.14322	−	64.2344i	0.344354	−	2.41921i
$706$	3.07100	−	3.58178i	0.115578	−	0.134802i
$707$	−15.8298	+	7.95003i	−0.595342	+	0.298992i
$708$	18.9152	+	10.6235i	0.710876	+	0.399257i
$709$	4.49073	−	15.0001i	0.168653	−	0.563340i	−0.831319	−	0.555796i	$-0.812413\pi$
$709$	4.49073	−	15.0001i	0.168653	−	0.563340i	0.999972	−	0.00754389i	$-0.00240132\pi$
$710$	−46.0506	+	42.5296i	−1.72825	+	1.59611i
$711$	−27.5844	−	6.30195i	−1.03450	−	0.236342i
$712$	−12.1953	−	7.56985i	−0.457037	−	0.283692i
$713$	2.65199	+	4.03215i	0.0993177	+	0.151005i
$714$	5.65110	−	16.6851i	0.211487	−	0.624426i
$715$	−0.357236	−	3.05635i	−0.0133599	−	0.114301i
$716$	14.2106	−	44.0342i	0.531077	−	1.64564i
$717$	−3.12175	−	5.73390i	−0.116584	−	0.214137i
$718$	−3.88552	+	8.75047i	−0.145006	+	0.326564i
$719$	−21.5415	+	7.84045i	−0.803361	+	0.292399i	−0.710878	−	0.703315i	$-0.751702\pi$
$719$	−21.5415	+	7.84045i	−0.803361	+	0.292399i	−0.0924823	+	0.995714i	$0.529480\pi$
$720$	20.1834	+	29.1565i	0.752191	+	1.08660i
$721$	−6.36639	−	2.31718i	−0.237097	−	0.0862962i
$722$	18.5441	−	19.2413i	0.690139	−	0.716087i
$723$	1.71009	−	3.70644i	0.0635989	−	0.137844i
$724$	9.20640	+	4.87162i	0.342153	+	0.181052i
$725$	−13.7919	+	4.12903i	−0.512220	+	0.153348i
$726$	−6.09324	−	23.3546i	−0.226141	−	0.866769i
$727$	29.7678	+	22.1613i	1.10403	+	0.821917i	0.985270	−	0.171006i	$-0.0547017\pi$
$727$	29.7678	+	22.1613i	1.10403	+	0.821917i	0.118757	+	0.992923i	$0.462109\pi$
$728$	0.932184	−	0.133852i	0.0345490	−	0.00496090i
$729$	8.61499	−	25.5887i	0.319074	−	0.947730i
$730$	−51.7349	+	2.46125i	−1.91479	+	0.0910949i
$731$	−25.6956	+	34.5152i	−0.950388	+	1.27659i
$732$	−39.1287	+	12.2220i	−1.44624	+	0.451737i
$733$	0.779023	+	2.60212i	0.0287739	+	0.0961114i	0.971170	−	0.238386i	$-0.0766185\pi$
$733$	0.779023	+	2.60212i	0.0287739	+	0.0961114i	−0.942397	+	0.334498i	$0.891433\pi$
$734$	−0.477751	−	0.282649i	−0.0176341	−	0.0104328i
$735$	−22.6239	−	10.4383i	−0.834497	−	0.385023i
$736$	1.57257	−	2.41711i	0.0579655	−	0.0890959i
$737$	−10.0464	+	27.6021i	−0.370062	+	1.01674i
$738$	4.26199	−	2.12694i	0.156886	−	0.0782938i
$739$	−12.8921	−	35.4207i	−0.474242	−	1.30297i	−0.914313	−	0.405007i	$-0.867269\pi$
$739$	−12.8921	−	35.4207i	−0.474242	−	1.30297i	0.440071	−	0.897963i	$-0.354953\pi$
$740$	−1.95535	+	5.03619i	−0.0718800	+	0.185134i
$741$	0.111919	−	0.0609329i	0.00411145	−	0.00223843i
$742$	−9.14214	−	3.43805i	−0.335618	−	0.126215i
$743$	−22.0175	+	2.57348i	−0.807744	+	0.0944117i	−0.509934	−	0.860214i	$-0.670330\pi$
$743$	−22.0175	+	2.57348i	−0.807744	+	0.0944117i	−0.297810	+	0.954625i	$0.596256\pi$
$744$	−45.1434	−	10.6409i	−1.65504	−	0.390113i
$745$	45.5817	−	29.9795i	1.66998	−	1.09837i
$746$	14.4727	−	19.0145i	0.529884	−	0.696170i
$747$	2.51490	−	11.0080i	0.0920155	−	0.402763i
$748$	−32.0561	−	31.5592i	−1.17209	−	1.15392i
$749$	22.7259	+	6.80370i	0.830388	+	0.248602i
$750$	−7.77727	−	4.86810i	−0.283986	−	0.177758i
$751$	1.58048	+	3.14700i	0.0576727	+	0.114836i	0.920622	−	0.390454i	$-0.127682\pi$
$751$	1.58048	+	3.14700i	0.0576727	+	0.114836i	−0.862950	+	0.505290i	$0.831386\pi$
$752$	27.1980	−	42.7939i	0.991809	−	1.56053i
$753$	−41.0490	−	5.84298i	−1.49591	−	0.212930i
$754$	−0.546396	−	1.11745i	−0.0198986	−	0.0406952i
$755$	−21.4854	−	37.2139i	−0.781935	−	1.35435i
$756$	−14.8882	+	2.93283i	−0.541477	+	0.106666i
$757$	16.7730	−	29.0517i	0.609625	−	1.05590i	−0.381678	−	0.924296i	$-0.624654\pi$
$757$	16.7730	−	29.0517i	0.609625	−	1.05590i	0.991302	−	0.131605i	$-0.0420132\pi$
$758$	35.6120	+	2.45458i	1.29349	+	0.0891544i
$759$	3.42307	−	2.13058i	0.124250	−	0.0773351i
$760$	0.242633	−	2.68578i	0.00880123	−	0.0974235i
$761$	9.10383	+	0.530238i	0.330014	+	0.0192211i	0.222352	−	0.974966i	$-0.428627\pi$
$761$	9.10383	+	0.530238i	0.330014	+	0.0192211i	0.107662	+	0.994188i	$0.465664\pi$
$762$	30.6095	+	6.53085i	1.10886	+	0.236588i
$763$	0.597767	+	2.52218i	0.0216406	+	0.0913089i
$764$	7.70423	+	27.8797i	0.278729	+	1.00865i
$765$	28.3371	+	33.2203i	1.02453	+	1.20108i
$766$	40.6688	+	5.19267i	1.46943	+	0.187619i
$767$	0.0830345	+	1.42565i	0.00299820	+	0.0514771i
$768$	4.98153	+	27.2614i	0.179755	+	0.983711i
$769$	−17.9951	−	24.1716i	−0.648919	−	0.871650i	0.348933	−	0.937148i	$-0.386544\pi$
$769$	−17.9951	−	24.1716i	−0.648919	−	0.871650i	−0.997853	+	0.0654976i	$0.979137\pi$
$770$	21.5357	−	17.6836i	0.776093	−	0.637273i
$771$	13.0575	+	38.8770i	0.470255	+	1.40012i
$772$	0.998942	+	6.46708i	0.0359527	+	0.232755i
$773$	−31.8189	−	5.61053i	−1.14445	−	0.201797i	−0.430896	−	0.902402i	$-0.641802\pi$
$773$	−31.8189	−	5.61053i	−1.14445	−	0.201797i	−0.713549	+	0.700605i	$0.752914\pi$
$774$	36.8036	+	4.39631i	1.32288	+	0.158022i
$775$	−34.7995	+	6.13610i	−1.25004	+	0.220415i
$776$	2.35821	+	5.98526i	0.0846549	+	0.214858i
$777$	−1.64130	−	1.62805i	−0.0588814	−	0.0584061i
$778$	0.235014	−	22.0885i	0.00842567	−	0.791913i
$779$	−0.352470	−	0.0835369i	−0.0126285	−	0.00299302i
$780$	−0.899064	+	2.15418i	−0.0321917	+	0.0771319i
$781$	−68.0340	−	7.95203i	−2.43445	−	0.284546i
$782$	1.62724	−	3.15593i	0.0581901	−	0.112856i
$783$	9.72600	+	17.5246i	0.347579	+	0.626278i
$784$	−12.7478	−	14.7190i	−0.455277	−	0.525679i
$785$	47.5800	−	20.5240i	1.69820	−	0.732534i
$786$	−7.06262	−	5.01495i	−0.251915	−	0.178877i
$787$	9.02807	+	8.51755i	0.321816	+	0.303618i	0.830148	−	0.557544i	$-0.188256\pi$
$787$	9.02807	+	8.51755i	0.321816	+	0.303618i	−0.508332	+	0.861161i	$0.669738\pi$
$788$	12.7293	+	20.2812i	0.453464	+	0.722486i
$789$	0.0665905	−	0.798383i	0.00237068	−	0.0284232i
$790$	−38.2547	−	9.49750i	−1.36104	−	0.337906i
$791$	15.8117	−	13.2676i	0.562200	−	0.471742i
$792$	−9.83130	+	37.4807i	−0.349340	+	1.33182i
$793$	−2.06712	−	1.73452i	−0.0734056	−	0.0615946i
$794$	11.1171	+	15.2693i	0.394530	+	0.541887i
$795$	18.9294	−	15.0925i	0.671357	−	0.535276i
$796$	5.32609	+	24.8141i	0.188778	+	0.879511i
$797$	−36.1598	−	15.5978i	−1.28084	−	0.552502i	−0.356583	−	0.934263i	$-0.616058\pi$
$797$	−36.1598	−	15.5978i	−1.28084	−	0.552502i	−0.924261	+	0.381761i	$0.875318\pi$
$798$	1.01210	+	0.554354i	0.0358279	+	0.0196239i
$799$	28.0212	−	55.7947i	0.991317	−	1.97388i
$800$	11.6900	+	17.5823i	0.413302	+	0.621629i
$801$	1.00836	+	15.1909i	0.0356288	+	0.536744i
$802$	40.5430	+	12.6093i	1.43162	+	0.445250i
$803$	−38.8382	−	41.1661i	−1.37057	−	1.45272i
$804$	16.8980	−	14.5241i	0.595946	−	0.512227i
$805$	1.83768	+	1.20866i	0.0647698	+	0.0425997i
$806$	−1.01363	−	2.87990i	−0.0357036	−	0.101440i
$807$	−20.5067	+	18.3988i	−0.721869	+	0.647669i
$808$	16.3706	−	30.1566i	0.575915	−	1.06091i
$809$			27.2554i			0.958249i	0.877747	+	0.479124i	$0.159046\pi$
$809$			27.2554i			0.958249i	−0.877747	+	0.479124i	$0.840954\pi$
$810$	12.6670	−	35.4147i	0.445072	−	1.24435i
$811$			38.0529i			1.33622i	0.744064	+	0.668109i	$0.232896\pi$
$811$			38.0529i			1.33622i	−0.744064	+	0.668109i	$0.767104\pi$
$812$	5.83837	−	9.63302i	0.204887	−	0.338053i
$813$	19.7560	+	6.45768i	0.692872	+	0.226481i
$814$	−5.56852	+	1.95994i	−0.195176	+	0.0686958i
$815$	−52.1704	−	34.3130i	−1.82745	−	1.20193i
$816$	9.47863	+	32.7811i	0.331819	+	1.14757i
$817$	−1.93433	−	2.05027i	−0.0676737	−	0.0717299i
$818$	−8.27491	+	26.6065i	−0.289325	+	0.930274i
$819$	−0.691333	−	0.720973i	−0.0241571	−	0.0251929i
$820$	5.99158	−	2.85110i	0.209235	−	0.0995648i
$821$	15.1224	−	30.1112i	0.527776	−	1.05089i	−0.458945	−	0.888465i	$-0.651773\pi$
$821$	15.1224	−	30.1112i	0.527776	−	1.05089i	0.986721	−	0.162424i	$-0.0519311\pi$
$822$	55.9453	−	1.25909i	1.95132	−	0.0439158i
$823$	13.6638	+	5.89399i	0.476290	+	0.205452i	0.620672	−	0.784071i	$-0.286860\pi$
$823$	13.6638	+	5.89399i	0.476290	+	0.205452i	−0.144381	+	0.989522i	$0.546119\pi$
$824$	12.6861	−	3.36079i	0.441940	−	0.117079i
$825$	4.39698	+	29.1925i	0.153083	+	1.01635i
$826$	−10.4547	+	7.61168i	−0.363764	+	0.264844i
$827$	−14.1961	−	11.9119i	−0.493647	−	0.414219i	0.361684	−	0.932301i	$-0.382202\pi$
$827$	−14.1961	−	11.9119i	−0.493647	−	0.414219i	−0.855331	+	0.518082i	$0.826646\pi$
$828$	−3.05547	+	0.137600i	−0.106185	+	0.00478195i
$829$	15.4399	−	12.9556i	0.536249	−	0.449966i	−0.334004	−	0.942572i	$-0.608400\pi$
$829$	15.4399	−	12.9556i	0.536249	−	0.449966i	0.870253	+	0.492606i	$0.163955\pi$
$830$	3.79014	−	15.2662i	0.131558	−	0.529898i
$831$	44.7133	−	21.0712i	1.55109	−	0.730951i
$832$	−1.33397	+	1.24434i	−0.0462469	+	0.0431398i
$833$	−17.4399	−	16.4537i	−0.604258	−	0.570088i
$834$	−10.2975	−	22.4683i	−0.356574	−	0.778014i
$835$	−5.40240	+	2.33037i	−0.186958	+	0.0806457i
$836$	2.40056	−	1.70899i	0.0830253	−	0.0591066i
$837$	18.7172	+	45.4942i	0.646960	+	1.57251i
$838$	−10.8780	−	5.60887i	−0.375776	−	0.193755i
$839$	−19.3121	−	2.25726i	−0.666728	−	0.0779293i	−0.224005	−	0.974588i	$-0.571913\pi$
$839$	−19.3121	−	2.25726i	−0.666728	−	0.0779293i	−0.442723	+	0.896659i	$0.645987\pi$
$840$	−20.8126	+	3.69609i	−0.718104	+	0.127527i
$841$	13.7413	+	3.25675i	0.473838	+	0.112302i
$842$	31.9664	+	0.340111i	1.10163	+	0.0117210i
$843$	23.1784	−	6.31141i	0.798307	−	0.217377i
$844$	−4.06123	−	11.9429i	−0.139793	−	0.411091i
$845$	37.6809	−	6.64417i	1.29626	−	0.228566i
$846$	−53.6980	+	2.99101i	−1.84618	+	0.102833i
$847$	14.1691	+	2.49840i	0.486858	+	0.0858461i
$848$	18.3396	−	4.65027i	0.629783	−	0.159691i
$849$	7.03621	−	7.97134i	0.241482	−	0.273576i
$850$	16.4986	+	20.0926i	0.565897	+	0.689169i
$851$	−0.278259	−	0.373767i	−0.00953861	−	0.0128126i
$852$	42.0438	+	30.5320i	1.44040	+	1.04601i
$853$	2.57491	+	44.2095i	0.0881633	+	1.51371i	0.695076	+	0.718936i	$0.255371\pi$
$853$	2.57491	+	44.2095i	0.0881633	+	1.51371i	−0.606913	+	0.794769i	$0.707592\pi$
$854$	3.09491	−	24.2393i	0.105906	−	0.829451i
$855$	−2.46542	+	1.45018i	−0.0843157	+	0.0495951i
$856$	−43.6608	+	14.3307i	−1.49230	+	0.489812i
$857$	−3.44994	−	14.5564i	−0.117848	−	0.497239i	−0.999671	−	0.0256583i	$-0.991832\pi$
$857$	−3.44994	−	14.5564i	−0.117848	−	0.497239i	0.881823	−	0.471581i	$-0.156316\pi$
$858$	−2.42646	+	0.786341i	−0.0828379	+	0.0268453i
$859$	25.1816	+	1.46666i	0.859186	+	0.0500419i	0.482079	−	0.876128i	$-0.339882\pi$
$859$	25.1816	+	1.46666i	0.859186	+	0.0500419i	0.377107	+	0.926170i	$0.376919\pi$
$860$	51.1448	+	7.08404i	1.74402	+	0.241564i
$861$	0.0940830	+	2.83782i	0.00320634	+	0.0967126i
$862$	−2.11118	+	30.6297i	−0.0719070	+	1.04325i
$863$	2.56243	−	4.43825i	0.0872260	−	0.151080i	−0.819112	−	0.573634i	$-0.805533\pi$
$863$	2.56243	−	4.43825i	0.0872260	−	0.151080i	0.906338	+	0.422554i	$0.138866\pi$
$864$	20.4254	−	21.1378i	0.694885	−	0.719121i
$865$	13.8311	+	23.9562i	0.470272	+	0.814536i
$866$	−18.0498	+	8.82574i	−0.613357	+	0.299911i
$867$	4.68952	+	11.6662i	0.159264	+	0.396206i
$868$	16.9781	−	21.8205i	0.576274	−	0.740635i
$869$	−19.3301	−	38.4893i	−0.655727	−	1.30566i
$870$	13.0887	+	24.6620i	0.443748	+	0.836120i
$871$	1.40514	+	0.420670i	0.0476112	+	0.0142539i
$872$	−3.74136	−	3.34854i	−0.126699	−	0.113396i
$873$	3.70315	−	5.73100i	0.125333	−	0.193965i
$874$	0.185083	+	0.140874i	0.00626053	+	0.00476515i
$875$	4.56958	−	3.00546i	0.154480	−	0.101603i
$876$	10.3957	+	41.6545i	0.351238	+	1.40738i
$877$	−26.2096	+	3.06346i	−0.885036	+	0.103446i	−0.546452	−	0.837490i	$-0.684022\pi$
$877$	−26.2096	+	3.06346i	−0.885036	+	0.103446i	−0.338584	+	0.940936i	$0.609948\pi$
$878$	1.45282	−	3.86320i	0.0490302	−	0.130377i
$879$	0.893918	−	35.6971i	0.0301511	−	1.20403i
$880$	−14.6715	+	51.9460i	−0.494576	+	1.75110i
$881$	7.94369	+	21.8251i	0.267630	+	0.735306i	0.998600	+	0.0528970i	$0.0168455\pi$
$881$	7.94369	+	21.8251i	0.267630	+	0.735306i	−0.730970	+	0.682409i	$0.760932\pi$
$882$	−4.81384	+	20.0842i	−0.162091	+	0.676271i
$883$	−11.9481	+	32.8273i	−0.402087	+	1.10473i	0.559165	+	0.829056i	$0.311122\pi$
$883$	−11.9481	+	32.8273i	−0.402087	+	1.10473i	−0.961252	+	0.275669i	$0.911100\pi$
$884$	−1.48016	+	1.68963i	−0.0497831	+	0.0568284i
$885$	−2.92308	−	31.9206i	−0.0982581	−	1.07300i
$886$	−10.2421	+	17.3118i	−0.344090	+	0.581602i
$887$	−4.96260	−	16.5762i	−0.166628	−	0.556575i	−0.999993	−	0.00385214i	$-0.998774\pi$
$887$	−4.96260	−	16.5762i	−0.166628	−	0.556575i	0.833365	−	0.552723i	$-0.186411\pi$
$888$	4.41107	+	0.772228i	0.148026	+	0.0259143i
$889$	−11.1412	+	14.9653i	−0.373665	+	0.501919i
$890$	1.00781	+	21.1840i	0.0337820	+	0.710090i
$891$	38.3877	−	14.6809i	1.28604	−	0.491828i
$892$	2.59337	+	27.1944i	0.0868326	+	0.910535i
$893$	3.28064	+	2.44235i	0.109783	+	0.0817301i
$894$	−31.7661	−	32.1874i	−1.06242	−	1.07651i
$895$	−65.4941	+	19.6076i	−2.18923	+	0.655411i
$896$	−16.0102	−	4.07115i	−0.534862	−	0.136007i
$897$	−0.116148	−	0.164454i	−0.00387808	−	0.00549097i
$898$	−32.8887	−	31.6970i	−1.09751	−	1.05774i
$899$	−34.3154	−	12.4898i	−1.14448	−	0.416558i
$900$	7.93595	−	20.9413i	0.264532	−	0.698043i
$901$	21.8920	−	7.96803i	0.729328	−	0.265454i
$902$	6.62665	+	2.94247i	0.220643	+	0.0979735i
$903$	−11.5229	+	18.8520i	−0.383458	+	0.627355i
$904$	−10.4575	+	38.5910i	−0.347812	+	1.28352i
$905$	−1.78665	−	15.2858i	−0.0593902	−	0.508116i
$906$	−26.7637	+	23.5036i	−0.889165	+	0.780855i
$907$	−7.28929	−	11.0828i	−0.242037	−	0.367999i	0.693956	−	0.720017i	$-0.255866\pi$
$907$	−7.28929	−	11.0828i	−0.242037	−	0.367999i	−0.935993	+	0.352018i	$0.885496\pi$
$908$	20.7635	+	14.2984i	0.689060	+	0.474508i
$909$	−36.1135	+	4.51803i	−1.19781	+	0.149854i
$910$	−0.944056	−	1.02221i	−0.0312952	−	0.0338860i
$911$	10.5242	−	35.1532i	0.348681	−	1.16468i	−0.586334	−	0.810070i	$-0.699429\pi$
$911$	10.5242	−	35.1532i	0.348681	−	1.16468i	0.935015	−	0.354608i	$-0.115386\pi$
$912$	−2.22257	+	0.238591i	−0.0735967	+	0.00790053i
$913$	15.3598	−	7.71400i	0.508336	−	0.255296i
$914$	28.2715	+	24.2398i	0.935138	+	0.801782i
$915$	47.6629	+	37.3740i	1.57569	+	1.23555i
$916$	1.73681	+	3.16176i	0.0573859	+	0.104467i
$917$	4.47167	−	2.58172i	0.147668	−	0.0852560i
$918$	22.4057	−	28.4251i	0.739497	−	0.938170i
$919$	14.9150	+	8.61118i	0.492000	+	0.284057i	0.725404	−	0.688323i	$-0.241653\pi$
$919$	14.9150	+	8.61118i	0.492000	+	0.284057i	−0.233404	+	0.972380i	$0.574986\pi$
$920$	−4.25921	+	0.111872i	−0.140422	+	0.00368832i
$921$	14.0902	−	26.3873i	0.464288	−	0.869491i
$922$	−9.24124	−	1.73105i	−0.304344	−	0.0570092i
$923$	−0.198877	+	3.41459i	−0.00654612	+	0.112393i
$924$	−17.8691	−	14.6363i	−0.587851	−	0.481498i
$925$	3.31985	−	0.786819i	0.109156	−	0.0258704i
$926$	−5.32602	−	23.5878i	−0.175024	−	0.775144i
$927$	−10.7353	−	8.86075i	−0.352595	−	0.291025i
$928$	1.37719	+	21.7761i	0.0452086	+	0.714837i
$929$	7.54881	−	0.439668i	0.247669	−	0.0144251i	0.0661385	−	0.997810i	$-0.478932\pi$
$929$	7.54881	−	0.439668i	0.247669	−	0.0144251i	0.181530	+	0.983385i	$0.441895\pi$
$930$	24.8812	+	63.8524i	0.815888	+	2.09380i
$931$	1.25983	−	0.937909i	0.0412893	−	0.0307387i
$932$	14.4796	−	13.0898i	0.474294	−	0.428771i
$933$	8.12110	−	40.1514i	0.265873	−	1.31450i
$934$	33.8595	−	3.59289i	1.10792	−	0.117563i
$935$	−11.5416	+	65.4559i	−0.377452	+	2.14064i
$936$	1.89696	+	0.381268i	0.0620041	+	0.0124621i
$937$	−1.68470	−	9.55441i	−0.0550368	−	0.312129i	0.944845	−	0.327518i	$-0.106212\pi$
$937$	−1.68470	−	9.55441i	−0.0550368	−	0.312129i	−0.999882	+	0.0153893i	$0.995101\pi$
$938$	3.67385	+	12.7642i	0.119955	+	0.416767i
$939$	20.0201	+	5.27751i	0.653331	+	0.172225i
$940$	−74.8681	+	2.76382i	−2.44193	+	0.0901460i
$941$	0.494496	−	2.08644i	0.0161201	−	0.0680161i	−0.964390	−	0.264483i	$-0.914799\pi$
$941$	0.494496	−	2.08644i	0.0161201	−	0.0680161i	0.980510	+	0.196467i	$0.0629468\pi$
$942$	−24.4042	−	35.3461i	−0.795133	−	1.15164i
$943$	−0.0664413	+	0.568441i	−0.00216363	+	0.0185110i
$944$	8.19902	−	23.6707i	0.266855	−	0.770415i
$945$	16.0453	+	15.6598i	0.521953	+	0.509414i
$946$	30.5003	+	47.4658i	0.991649	+	1.54324i
$947$	14.4750	+	33.5569i	0.470375	+	1.09045i	0.974004	+	0.226532i	$0.0727388\pi$
$947$	14.4750	+	33.5569i	0.470375	+	1.09045i	−0.503628	+	0.863920i	$0.668002\pi$
$948$	−1.51268	+	32.6374i	−0.0491296	+	1.06001i
$949$	−1.93937	+	2.05561i	−0.0629546	+	0.0667280i
$950$	−1.48387	+	0.835790i	−0.0481430	+	0.0271166i
$951$	9.46440	−	13.6338i	0.306904	−	0.442107i
$952$	−20.1182	−	3.00504i	−0.652035	−	0.0973939i
$953$	−10.0127	−	11.9326i	−0.324342	−	0.386536i	0.579093	−	0.815262i	$-0.303407\pi$
$953$	−10.0127	−	11.9326i	−0.324342	−	0.386536i	−0.903434	+	0.428726i	$0.858963\pi$
$954$	−15.3400	−	12.9382i	−0.496650	−	0.418888i
$955$	27.4709	−	32.7386i	0.888938	−	1.05939i
$956$	−5.87670	+	4.72176i	−0.190066	+	0.152712i
$957$	−11.1490	+	28.3986i	−0.360397	+	0.917997i
$958$	3.31059	+	20.0185i	0.106960	+	0.646767i
$959$	−13.2123	+	30.6295i	−0.426646	+	0.989077i
$960$	29.0001	−	28.9071i	0.935974	−	0.932973i
$961$	−52.3951	−	26.3138i	−1.69016	−	0.848833i
$962$	0.113871	+	0.271900i	0.00367134	+	0.00876642i
$963$	39.3301	+	28.7877i	1.26740	+	0.927671i
$964$	−4.56218	−	1.18432i	−0.146938	−	0.0381445i
$965$	7.03272	−	6.63503i	0.226391	−	0.213589i
$966$	0.684289	−	1.68993i	0.0220166	−	0.0543726i
$967$	16.2281	−	24.6736i	0.521859	−	0.793448i	−0.474359	−	0.880331i	$-0.657320\pi$
$967$	16.2281	−	24.6736i	0.521859	−	0.793448i	0.996219	+	0.0868831i	$0.0276907\pi$
$968$	−25.2922	+	11.7070i	−0.812923	+	0.376276i
$969$	−2.69333	+	0.567517i	−0.0865222	+	0.0182313i
$970$	5.30733	−	7.88538i	0.170408	−	0.253184i
$971$	−15.3181			−0.491580			−0.245790	−	0.969323i	$-0.579047\pi$
$971$	−15.3181			−0.491580			−0.245790	+	0.969323i	$0.579047\pi$
$972$	−30.8431	−	4.54990i	−0.989294	−	0.145938i
$973$	14.7331			0.472320
$974$	3.63952	−	5.40743i	0.116618	−	0.173265i
$975$	1.44248	−	0.303949i	0.0461964	−	0.00973414i
$976$	21.9019	+	41.9629i	0.701063	+	1.34320i
$977$	19.1423	−	29.1044i	0.612415	−	0.931132i	−0.387542	−	0.921852i	$-0.626676\pi$
$977$	19.1423	−	29.1044i	0.612415	−	0.931132i	0.999957	−	0.00927957i	$-0.00295382\pi$
$978$	−19.4265	+	47.9759i	−0.621190	+	1.53410i
$979$	−16.8564	+	15.9032i	−0.538733	+	0.508269i
$980$	−7.22905	+	27.8474i	−0.230923	+	0.889551i
$981$	−0.575373	+	5.29441i	−0.0183702	+	0.169038i
$982$	10.1209	+	24.1667i	0.322971	+	0.771189i
$983$	−15.2030	−	7.63522i	−0.484900	−	0.243526i	0.189516	−	0.981878i	$-0.439308\pi$
$983$	−15.2030	−	7.63522i	−0.484900	−	0.243526i	−0.674416	+	0.738352i	$0.735604\pi$
$984$	−3.28983	−	4.40775i	−0.104876	−	0.140514i
$985$	14.0131	−	32.4860i	0.446495	−	1.03509i
$986$	4.38372	+	26.5074i	0.139606	+	0.844169i
$987$	11.7156	−	29.8418i	0.372912	−	0.949875i
$988$	−0.0921631	−	0.114706i	−0.00293210	−	0.00364930i
$989$	−2.86262	+	3.41154i	−0.0910261	+	0.108481i
$990$	53.8492	−	19.4451i	1.71144	−	0.618005i
$991$	−18.6985	−	22.2840i	−0.593977	−	0.707874i	0.382388	−	0.924002i	$-0.375102\pi$
$991$	−18.6985	−	22.2840i	−0.593977	−	0.707874i	−0.976365	+	0.216128i	$0.930657\pi$
$992$	−2.84762	+	53.4799i	−0.0904119	+	1.69799i
$993$	−3.76319	+	5.42101i	−0.119421	+	0.172030i
$994$	−26.9873	+	15.2006i	−0.855984	+	0.482134i
$995$	25.7332	−	27.2756i	0.815796	−	0.864693i
$996$	−13.0245	−	0.603662i	−0.412697	−	0.0191278i
$997$	3.45765	+	8.01573i	0.109505	+	0.253861i	0.964153	−	0.265347i	$-0.0854865\pi$
$997$	3.45765	+	8.01573i	0.109505	+	0.253861i	−0.854648	+	0.519207i	$0.826227\pi$
$998$	7.49138	+	11.6584i	0.237136	+	0.369040i
$999$	−2.05954	−	4.28007i	−0.0651609	−	0.135415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.23.44	yes	936
3.2	odd	2		972.2.p.a.503.9		936
4.3	odd	2	inner	324.2.p.a.23.40	✓	936
12.11	even	2		972.2.p.a.503.13		936
81.7	even	27		972.2.p.a.143.13		936
81.74	odd	54	inner	324.2.p.a.155.40	yes	936
324.7	odd	54		972.2.p.a.143.9		936
324.155	even	54	inner	324.2.p.a.155.44	yes	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.23.40	✓	936	4.3	odd	2	inner
324.2.p.a.23.44	yes	936	1.1	even	1	trivial
324.2.p.a.155.40	yes	936	81.74	odd	54	inner
324.2.p.a.155.44	yes	936	324.155	even	54	inner
972.2.p.a.143.9		936	324.7	odd	54
972.2.p.a.143.13		936	81.7	even	27
972.2.p.a.503.9		936	3.2	odd	2
972.2.p.a.503.13		936	12.11	even	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17322 + 0.789650i) q^{2} +(-1.69483 + 0.357122i) q^{3} +(0.752907 + 1.85287i) q^{4} +(1.62384 - 2.46892i) q^{5} +(-2.27042 - 0.919342i) q^{6} +(1.06207 - 1.00201i) q^{7} +(-0.579791 + 2.76836i) q^{8} +(2.74493 - 1.21053i) q^{9} +O(q^{10})\)	\(q+(1.17322 + 0.789650i) q^{2} +(-1.69483 + 0.357122i) q^{3} +(0.752907 + 1.85287i) q^{4} +(1.62384 - 2.46892i) q^{5} +(-2.27042 - 0.919342i) q^{6} +(1.06207 - 1.00201i) q^{7} +(-0.579791 + 2.76836i) q^{8} +(2.74493 - 1.21053i) q^{9} +(3.85471 - 1.61434i) q^{10} +(4.08084 + 2.04948i) q^{11} +(-1.93775 - 2.87143i) q^{12} +(0.0903180 - 0.209381i) q^{13} +(2.03729 - 0.336921i) q^{14} +(-1.87043 + 4.76432i) q^{15} +(-2.86626 + 2.79008i) q^{16} +(-3.16597 + 3.77306i) q^{17} +(4.17630 + 0.747315i) q^{18} +(-0.207391 - 0.247159i) q^{19} +(5.79719 + 1.14989i) q^{20} +(-1.44220 + 2.07754i) q^{21} +(3.16937 + 5.62693i) q^{22} +(-0.349819 + 0.370786i) q^{23} +(-0.00599347 - 4.89898i) q^{24} +(-1.47834 - 3.42718i) q^{25} +(0.271301 - 0.174331i) q^{26} +(-4.21989 + 3.03191i) q^{27} +(2.65624 + 1.21346i) q^{28} +(0.447794 - 3.83112i) q^{29} +(-5.95658 + 4.11264i) q^{30} +(2.18333 - 9.21220i) q^{31} +(-5.56595 + 1.01004i) q^{32} +(-7.64826 - 2.01616i) q^{33} +(-6.69378 + 1.92663i) q^{34} +(-0.749263 - 4.24928i) q^{35} +(4.30962 + 4.17458i) q^{36} +(-0.158732 + 0.900213i) q^{37} +(-0.0481471 - 0.453740i) q^{38} +(-0.0782996 + 0.387120i) q^{39} +(5.89339 + 5.92683i) q^{40} +(0.900548 - 0.670433i) q^{41} +(-3.33254 + 1.29859i) q^{42} +(8.72158 - 0.507974i) q^{43} +(-0.724922 + 9.10434i) q^{44} +(1.46862 - 8.74271i) q^{45} +(-0.703207 + 0.158781i) q^{46} +(-12.3347 + 2.92337i) q^{47} +(3.86144 - 5.75233i) q^{48} +(-0.283047 + 4.85974i) q^{49} +(0.971846 - 5.18821i) q^{50} +(4.01835 - 7.52534i) q^{51} +(0.455957 + 0.00970353i) q^{52} +(-4.09629 - 2.36499i) q^{53} +(-7.34503 + 0.224876i) q^{54} +(11.6866 - 6.74727i) q^{55} +(2.15816 + 3.52116i) q^{56} +(0.439760 + 0.344830i) q^{57} +(3.55061 - 4.14116i) q^{58} +(-5.59648 + 2.81066i) q^{59} +(-10.2359 + 0.121431i) q^{60} +(3.39394 - 11.3365i) q^{61} +(9.83595 - 9.08390i) q^{62} +(1.70235 - 4.03612i) q^{63} +(-7.32768 - 3.21015i) q^{64} +(-0.370283 - 0.562988i) q^{65} +(-7.38106 - 8.40486i) q^{66} +(0.746744 + 6.38880i) q^{67} +(-9.37466 - 3.02537i) q^{68} +(0.460469 - 0.753350i) q^{69} +(2.47639 - 5.57701i) q^{70} +(-14.0951 + 5.13019i) q^{71} +(1.75969 + 8.30081i) q^{72} +(-11.6460 - 4.23881i) q^{73} +(-0.897081 + 0.930809i) q^{74} +(3.72946 + 5.28055i) q^{75} +(0.301808 - 0.570357i) q^{76} +(6.38775 - 1.91237i) q^{77} +(-0.397552 + 0.392349i) q^{78} +(-7.56539 - 5.63223i) q^{79} +(2.23415 + 11.6072i) q^{80} +(6.06926 - 6.64561i) q^{81} +(1.58595 - 0.0754505i) q^{82} +(2.24764 - 3.01910i) q^{83} +(-4.93525 - 1.10801i) q^{84} +(4.17437 + 13.9434i) q^{85} +(10.6335 + 6.29103i) q^{86} +(0.609242 + 6.65304i) q^{87} +(-8.03973 + 10.1090i) q^{88} +(-1.73568 + 4.76873i) q^{89} +(8.62670 - 9.09746i) q^{90} +(-0.113878 - 0.312877i) q^{91} +(-0.950400 - 0.369002i) q^{92} +(-0.410506 + 16.3929i) q^{93} +(-16.7798 - 6.31030i) q^{94} +(-0.946987 + 0.110687i) q^{95} +(9.07266 - 3.69958i) q^{96} +(1.90027 - 1.24982i) q^{97} +(-4.16957 + 5.47805i) q^{98} +(13.6826 + 0.685700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

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