LMFDB - Embedded newform 324.2.p.a.47.40

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			47.40
Character	$\chi$	$=$	324.47
Dual form			324.2.p.a.131.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.991400 + 1.00853i) q^{2} +(0.670223 - 1.59712i) q^{3} +(-0.0342526 + 1.99971i) q^{4} +(-0.331581 + 0.0193124i) q^{5} +(2.27520 - 0.907450i) q^{6} +(1.21429 - 5.12351i) q^{7} +(-2.05072 + 1.94796i) q^{8} +(-2.10160 - 2.14086i) q^{9} +O(q^{10})$	\(q+(0.991400 + 1.00853i) q^{2} +(0.670223 - 1.59712i) q^{3} +(-0.0342526 + 1.99971i) q^{4} +(-0.331581 + 0.0193124i) q^{5} +(2.27520 - 0.907450i) q^{6} +(1.21429 - 5.12351i) q^{7} +(-2.05072 + 1.94796i) q^{8} +(-2.10160 - 2.14086i) q^{9} +(-0.348206 - 0.315262i) q^{10} +(3.72834 + 2.45217i) q^{11} +(3.17082 + 1.39495i) q^{12} +(4.04366 + 0.472636i) q^{13} +(6.37105 - 3.85480i) q^{14} +(-0.191389 + 0.542519i) q^{15} +(-3.99765 - 0.136990i) q^{16} +(1.32228 + 1.57583i) q^{17} +(0.0755821 - 4.24197i) q^{18} +(-1.89483 + 2.25818i) q^{19} +(-0.0272616 - 0.663726i) q^{20} +(-7.36902 - 5.37327i) q^{21} +(1.22320 + 6.19121i) q^{22} +(-5.76932 + 1.36735i) q^{23} +(1.73670 + 4.58082i) q^{24} +(-4.85662 + 0.567657i) q^{25} +(3.53222 + 4.54671i) q^{26} +(-4.82775 + 1.92167i) q^{27} +(10.2039 + 2.60372i) q^{28} +(1.29951 - 0.967451i) q^{29} +(-0.736888 + 0.344833i) q^{30} +(-0.754795 - 0.225971i) q^{31} +(-3.82511 - 4.16755i) q^{32} +(6.41523 - 4.31112i) q^{33} +(-0.278360 + 2.89583i) q^{34} +(-0.303689 + 1.72231i) q^{35} +(4.35307 - 4.12926i) q^{36} +(0.491685 + 2.78848i) q^{37} +(-4.15597 + 0.327764i) q^{38} +(3.46501 - 6.14146i) q^{39} +(0.642358 - 0.685512i) q^{40} +(4.71784 - 2.03508i) q^{41} +(-1.88657 - 12.7589i) q^{42} +(0.199085 + 0.396410i) q^{43} +(-5.03132 + 7.37159i) q^{44} +(0.738196 + 0.669280i) q^{45} +(-7.09871 - 4.46292i) q^{46} +(2.48181 + 8.28982i) q^{47} +(-2.89811 + 6.29293i) q^{48} +(-18.5204 - 9.30129i) q^{49} +(-5.38735 - 4.33525i) q^{50} +(3.40301 - 1.05568i) q^{51} +(-1.08364 + 8.06995i) q^{52} +(-3.62150 + 2.09088i) q^{53} +(-6.72429 - 2.96378i) q^{54} +(-1.28360 - 0.741089i) q^{55} +(7.49024 + 12.8723i) q^{56} +(2.33662 + 4.53976i) q^{57} +(2.26404 + 0.351462i) q^{58} +(-3.28860 + 2.16295i) q^{59} +(-1.07832 - 0.401304i) q^{60} +(7.27938 - 7.71569i) q^{61} +(-0.520406 - 0.985258i) q^{62} +(-13.5207 + 8.16795i) q^{63} +(0.410871 - 7.98944i) q^{64} +(-1.34993 - 0.0786244i) q^{65} +(10.7079 + 2.19589i) q^{66} +(-5.77580 - 4.29993i) q^{67} +(-3.19649 + 2.59019i) q^{68} +(-1.68290 + 10.1307i) q^{69} +(-2.03807 + 1.40122i) q^{70} +(11.0971 + 4.03902i) q^{71} +(8.48010 + 0.296441i) q^{72} +(-6.53205 + 2.37747i) q^{73} +(-2.32480 + 3.26038i) q^{74} +(-2.34840 + 8.13707i) q^{75} +(-4.45079 - 3.86646i) q^{76} +(17.0910 - 16.1245i) q^{77} +(9.62904 - 2.59408i) q^{78} +(0.652750 + 0.281569i) q^{79} +(1.32819 - 0.0317808i) q^{80} +(-0.166531 + 8.99846i) q^{81} +(6.72969 + 2.74049i) q^{82} +(-3.61779 + 8.38699i) q^{83} +(10.9974 - 14.5518i) q^{84} +(-0.468875 - 0.496978i) q^{85} +(-0.202418 + 0.593783i) q^{86} +(-0.674175 - 2.72389i) q^{87} +(-12.4225 + 2.23397i) q^{88} +(-0.902508 - 2.47962i) q^{89} +(0.0568609 + 1.40801i) q^{90} +(7.33175 - 20.1438i) q^{91} +(-2.53669 - 11.5838i) q^{92} +(-0.866784 + 1.05405i) q^{93} +(-5.90004 + 10.7215i) q^{94} +(0.584680 - 0.785362i) q^{95} +(-9.21977 + 3.31599i) q^{96} +(-0.958928 + 16.4642i) q^{97} +(-8.98052 - 27.8996i) q^{98} +(-2.58575 - 13.1353i) 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{54}\right)$

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 $

$2$	0.991400	+	1.00853i	0.701026	+	0.713136i
$2$	0.991400	+	1.00853i	0.701026	+	0.713136i
$3$	0.670223	−	1.59712i	0.386953	−	0.922099i
$3$	0.670223	−	1.59712i	0.386953	−	0.922099i
$4$	−0.0342526	+	1.99971i	−0.0171263	+	0.999853i
$5$	−0.331581	+	0.0193124i	−0.148287	+	0.00863676i	−0.132128	−	0.991233i	$-0.542181\pi$
$5$	−0.331581	+	0.0193124i	−0.148287	+	0.00863676i	−0.0161595	+	0.999869i	$0.505144\pi$
$6$	2.27520	−	0.907450i	0.928847	−	0.370465i
$7$	1.21429	−	5.12351i	0.458960	−	1.93650i	0.133021	−	0.991113i	$-0.457532\pi$
$7$	1.21429	−	5.12351i	0.458960	−	1.93650i	0.325939	−	0.945391i	$-0.394320\pi$
$8$	−2.05072	+	1.94796i	−0.725038	+	0.688709i
$9$	−2.10160	−	2.14086i	−0.700534	−	0.713619i
$10$	−0.348206	−	0.315262i	−0.110112	−	0.0996946i
$11$	3.72834	+	2.45217i	1.12414	+	0.739356i	0.968637	−	0.248479i	$-0.0799309\pi$
$11$	3.72834	+	2.45217i	1.12414	+	0.739356i	0.155500	+	0.987836i	$0.450301\pi$
$12$	3.17082	+	1.39495i	0.915337	+	0.402689i
$13$	4.04366	+	0.472636i	1.12151	+	0.131086i	0.656576	−	0.754260i	$-0.272004\pi$
$13$	4.04366	+	0.472636i	1.12151	+	0.131086i	0.464934	+	0.885345i	$0.346078\pi$
$14$	6.37105	−	3.85480i	1.70273	−	1.03024i
$15$	−0.191389	+	0.542519i	−0.0494164	+	0.140078i
$16$	−3.99765	−	0.136990i	−0.999413	−	0.0342476i
$17$	1.32228	+	1.57583i	0.320699	+	0.382194i	0.902176	−	0.431369i	$-0.141969\pi$
$17$	1.32228	+	1.57583i	0.320699	+	0.382194i	−0.581476	+	0.813563i	$0.697525\pi$
$18$	0.0755821	−	4.24197i	0.0178149	−	0.999841i
$19$	−1.89483	+	2.25818i	−0.434705	+	0.518061i	−0.938274	−	0.345894i	$-0.887576\pi$
$19$	−1.89483	+	2.25818i	−0.434705	+	0.518061i	0.503569	+	0.863955i	$0.332020\pi$
$20$	−0.0272616	−	0.663726i	−0.00609588	−	0.148414i
$21$	−7.36902	−	5.37327i	−1.60805	−	1.17254i
$22$	1.22320	+	6.19121i	0.260787	+	1.31997i
$23$	−5.76932	+	1.36735i	−1.20299	+	0.285113i	−0.782770	−	0.622311i	$-0.786194\pi$
$23$	−5.76932	+	1.36735i	−1.20299	+	0.285113i	−0.420216	+	0.907424i	$0.638046\pi$
$24$	1.73670	+	4.58082i	0.354503	+	0.935055i
$25$	−4.85662	+	0.567657i	−0.971324	+	0.113531i
$26$	3.53222	+	4.54671i	0.692725	+	0.891684i
$27$	−4.82775	+	1.92167i	−0.929101	+	0.369825i
$28$	10.2039	+	2.60372i	1.92836	+	0.492058i
$29$	1.29951	−	0.967451i	0.241313	−	0.179651i	−0.469707	−	0.882822i	$-0.655641\pi$
$29$	1.29951	−	0.967451i	0.241313	−	0.179651i	0.711021	+	0.703171i	$0.248233\pi$
$30$	−0.736888	+	0.344833i	−0.134537	+	0.0629575i
$31$	−0.754795	−	0.225971i	−0.135565	−	0.0405855i	0.218302	−	0.975881i	$-0.429948\pi$
$31$	−0.754795	−	0.225971i	−0.135565	−	0.0405855i	−0.353867	+	0.935296i	$0.615133\pi$
$32$	−3.82511	−	4.16755i	−0.676191	−	0.736726i
$33$	6.41523	−	4.31112i	1.11675	−	0.750469i
$34$	−0.278360	+	2.89583i	−0.0477383	+	0.496630i
$35$	−0.303689	+	1.72231i	−0.0513329	+	0.291123i
$36$	4.35307	−	4.12926i	0.725512	−	0.688210i
$37$	0.491685	+	2.78848i	0.0808325	+	0.458424i	0.998178	+	0.0603326i	$0.0192161\pi$
$37$	0.491685	+	2.78848i	0.0808325	+	0.458424i	−0.917346	+	0.398091i	$0.869673\pi$
$38$	−4.15597	+	0.327764i	−0.674187	+	0.0531703i
$39$	3.46501	−	6.14146i	0.554846	−	0.983420i
$40$	0.642358	−	0.685512i	0.101566	−	0.108389i
$41$	4.71784	−	2.03508i	0.736802	−	0.317825i	0.00559815	−	0.999984i	$-0.498218\pi$
$41$	4.71784	−	2.03508i	0.736802	−	0.317825i	0.731204	+	0.682159i	$0.238959\pi$
$42$	−1.88657	−	12.7589i	−0.291103	−	1.96874i
$43$	0.199085	+	0.396410i	0.0303601	+	0.0604520i	0.908301	−	0.418316i	$-0.137380\pi$
$43$	0.199085	+	0.396410i	0.0303601	+	0.0604520i	−0.877941	+	0.478768i	$0.841083\pi$
$44$	−5.03132	+	7.37159i	−0.758500	+	1.11131i
$45$	0.738196	+	0.669280i	0.110044	+	0.0997704i
$46$	−7.09871	−	4.46292i	−1.04665	−	0.658021i
$47$	2.48181	+	8.28982i	0.362009	+	1.20919i	0.924110	+	0.382126i	$0.124808\pi$
$47$	2.48181	+	8.28982i	0.362009	+	1.20919i	−0.562101	+	0.827068i	$0.690007\pi$
$48$	−2.89811	+	6.29293i	−0.418306	+	0.908306i
$49$	−18.5204	−	9.30129i	−2.64577	−	1.32876i
$50$	−5.38735	−	4.33525i	−0.761886	−	0.613098i
$51$	3.40301	−	1.05568i	0.476517	−	0.147825i
$52$	−1.08364	+	8.06995i	−0.150274	+	1.11910i
$53$	−3.62150	+	2.09088i	−0.497452	+	0.287204i	−0.727661	−	0.685937i	$-0.759392\pi$
$53$	−3.62150	+	2.09088i	−0.497452	+	0.287204i	0.230209	+	0.973141i	$0.426059\pi$
$54$	−6.72429	−	2.96378i	−0.915059	−	0.403319i
$55$	−1.28360	−	0.741089i	−0.173081	−	0.0999284i
$56$	7.49024	+	12.8723i	1.00093	+	1.72013i
$57$	2.33662	+	4.53976i	0.309493	+	0.601307i
$58$	2.26404	+	0.351462i	0.297282	+	0.0461492i
$59$	−3.28860	+	2.16295i	−0.428140	+	0.281592i	−0.745235	−	0.666802i	$-0.767663\pi$
$59$	−3.28860	+	2.16295i	−0.428140	+	0.281592i	0.317096	+	0.948394i	$0.397292\pi$
$60$	−1.07832	−	0.401304i	−0.139211	−	0.0518081i
$61$	7.27938	−	7.71569i	0.932029	−	0.987893i	−0.0679230	−	0.997691i	$-0.521637\pi$
$61$	7.27938	−	7.71569i	0.932029	−	0.987893i	0.999952	+	0.00979751i	$0.00311869\pi$
$62$	−0.520406	−	0.985258i	−0.0660916	−	0.125128i
$63$	−13.5207	+	8.16795i	−1.70344	+	1.02907i
$64$	0.410871	−	7.98944i	0.0513588	−	0.998680i
$65$	−1.34993	−	0.0786244i	−0.167438	−	0.00975216i
$66$	10.7079	+	2.19589i	1.31806	+	0.270296i
$67$	−5.77580	−	4.29993i	−0.705627	−	0.525320i	0.183478	−	0.983024i	$-0.441264\pi$
$67$	−5.77580	−	4.29993i	−0.705627	−	0.525320i	−0.889104	+	0.457704i	$0.848672\pi$
$68$	−3.19649	+	2.59019i	−0.387631	+	0.314107i
$69$	−1.68290	+	10.1307i	−0.202597	+	1.21960i
$70$	−2.03807	+	1.40122i	−0.243596	+	0.167477i
$71$	11.0971	+	4.03902i	1.31699	+	0.479344i	0.902491	−	0.430708i	$-0.141736\pi$
$71$	11.0971	+	4.03902i	1.31699	+	0.479344i	0.414495	+	0.910052i	$0.363958\pi$
$72$	8.48010	+	0.296441i	0.999390	+	0.0349359i
$73$	−6.53205	+	2.37747i	−0.764519	+	0.278262i	−0.694702	−	0.719298i	$-0.744464\pi$
$73$	−6.53205	+	2.37747i	−0.764519	+	0.278262i	−0.0698170	+	0.997560i	$0.522242\pi$
$74$	−2.32480	+	3.26038i	−0.270253	+	0.379011i
$75$	−2.34840	+	8.13707i	−0.271170	+	0.939588i
$76$	−4.45079	−	3.86646i	−0.510540	−	0.443514i
$77$	17.0910	−	16.1245i	1.94770	−	1.83756i
$78$	9.62904	−	2.59408i	1.09027	−	0.293722i
$79$	0.652750	+	0.281569i	0.0734401	+	0.0316790i	0.432483	−	0.901642i	$-0.357638\pi$
$79$	0.652750	+	0.281569i	0.0734401	+	0.0316790i	−0.359043	+	0.933321i	$0.616897\pi$
$80$	1.32819	−	0.0317808i	0.148496	−	0.00355321i
$81$	−0.166531	+	8.99846i	−0.0185034	+	0.999829i
$82$	6.72969	+	2.74049i	0.743170	+	0.302636i
$83$	−3.61779	+	8.38699i	−0.397104	+	0.920591i	0.595960	+	0.803014i	$0.296772\pi$
$83$	−3.61779	+	8.38699i	−0.397104	+	0.920591i	−0.993064	+	0.117577i	$0.962487\pi$
$84$	10.9974	−	14.5518i	1.19991	−	1.58774i
$85$	−0.468875	−	0.496978i	−0.0508566	−	0.0539048i
$86$	−0.202418	+	0.593783i	−0.0218273	+	0.0640293i
$87$	−0.674175	−	2.72389i	−0.0722792	−	0.292031i
$88$	−12.4225	+	2.23397i	−1.32424	+	0.238142i
$89$	−0.902508	−	2.47962i	−0.0956657	−	0.262839i	0.882625	−	0.470078i	$-0.155774\pi$
$89$	−0.902508	−	2.47962i	−0.0956657	−	0.262839i	−0.978290	+	0.207239i	$0.933552\pi$
$90$	0.0568609	+	1.40801i	0.00599367	+	0.148418i
$91$	7.33175	−	20.1438i	0.768576	−	2.11165i
$92$	−2.53669	−	11.5838i	−0.264468	−	1.20769i
$93$	−0.866784	+	1.05405i	−0.0898813	+	0.109300i
$94$	−5.90004	+	10.7215i	−0.608543	+	1.10584i
$95$	0.584680	−	0.785362i	0.0599869	−	0.0805764i
$96$	−9.21977	+	3.31599i	−0.940989	+	0.338437i
$97$	−0.958928	+	16.4642i	−0.0973644	+	1.67168i	0.497202	+	0.867635i	$0.334361\pi$
$97$	−0.958928	+	16.4642i	−0.0973644	+	1.67168i	−0.594566	+	0.804047i	$0.702676\pi$
$98$	−8.98052	−	27.8996i	−0.907169	−	2.81829i
$99$	−2.58575	−	13.1353i	−0.259878	−	1.32015i
$100$	−0.968796	−	9.73126i	−0.0968796	−	0.973126i
$101$	−4.39125	−	4.14293i	−0.436945	−	0.412237i	0.436083	−	0.899907i	$-0.356366\pi$
$101$	−4.39125	−	4.14293i	−0.436945	−	0.412237i	−0.873028	+	0.487670i	$0.837847\pi$
$102$	4.43843	+	2.38542i	0.439470	+	0.236192i
$103$	−1.27562	−	1.93948i	−0.125690	−	0.191103i	0.767161	−	0.641455i	$-0.221669\pi$
$103$	−1.27562	−	1.93948i	−0.125690	−	0.191103i	−0.892851	+	0.450352i	$0.851298\pi$
$104$	−9.21308	+	6.90767i	−0.903417	+	0.677353i
$105$	2.54720	+	1.63936i	0.248581	+	0.159985i
$106$	−5.69906	−	1.57949i	−0.553542	−	0.153414i
$107$	−0.350758	+	0.607531i	−0.0339091	+	0.0587323i	−0.882482	−	0.470346i	$-0.844129\pi$
$107$	−0.350758	+	0.607531i	−0.0339091	+	0.0587323i	0.848573	+	0.529079i	$0.177462\pi$
$108$	−3.67741	−	9.71991i	−0.353859	−	0.935299i
$109$	−2.14413	−	3.71375i	−0.205371	−	0.355713i	0.744880	−	0.667198i	$-0.232507\pi$
$109$	−2.14413	−	3.71375i	−0.205371	−	0.355713i	−0.950251	+	0.311486i	$0.899173\pi$
$110$	−0.525156	−	2.02926i	−0.0500717	−	0.193483i
$111$	4.78309	+	1.08362i	0.453991	+	0.102853i
$112$	−5.55620	+	20.3157i	−0.525011	+	1.91965i
$113$	−4.52154	+	9.00313i	−0.425351	+	0.846943i	0.574250	+	0.818680i	$0.305294\pi$
$113$	−4.52154	+	9.00313i	−0.425351	+	0.846943i	−0.999601	+	0.0282628i	$0.991002\pi$
$114$	−2.26195	+	6.85727i	−0.211851	+	0.642242i
$115$	1.88659	−	0.564807i	0.175925	−	0.0526686i
$116$	1.89011	+	2.63178i	0.175492	+	0.244355i
$117$	−7.48633	−	9.65020i	−0.692111	−	0.892161i
$118$	−5.44171	−	1.17230i	−0.500950	−	0.107919i
$119$	9.67940	−	4.86118i	0.887309	−	0.445623i
$120$	−0.664324	−	1.48537i	−0.0606442	−	0.135595i
$121$	3.53052	+	8.18466i	0.320956	+	0.744060i
$122$	14.9983	−	0.307886i	1.35788	−	0.0278747i
$123$	−0.0882649	−	8.89892i	−0.00795858	−	0.802388i
$124$	0.477729	−	1.50163i	0.0429013	−	0.134850i
$125$	3.23488	−	0.570397i	0.289337	−	0.0510179i
$126$	−21.6420	−	5.53824i	−1.92802	−	0.493386i
$127$	17.8156	+	3.14137i	1.58088	+	0.278752i	0.894016	−	0.448034i	$-0.147876\pi$
$127$	17.8156	+	3.14137i	1.58088	+	0.278752i	0.686864	+	0.726786i	$0.258987\pi$
$128$	8.46490	−	7.50636i	0.748199	−	0.663475i
$129$	0.766547	−	0.0522796i	0.0674907	−	0.00460296i
$130$	−1.25902	−	1.43939i	−0.110424	−	0.126243i
$131$	5.99370	−	20.0203i	0.523672	−	1.74919i	−0.129101	−	0.991631i	$-0.541209\pi$
$131$	5.99370	−	20.0203i	0.523672	−	1.74919i	0.652773	−	0.757554i	$-0.273606\pi$
$132$	8.40123	+	12.9762i	0.731234	+	1.12944i
$133$	9.26890	+	12.4503i	0.803715	+	1.07958i
$134$	−1.38954	−	10.0880i	−0.120038	−	0.871470i
$135$	1.56368	−	0.730424i	0.134580	−	0.0628649i
$136$	−5.78127	−	0.655828i	−0.495740	−	0.0562368i
$137$	0.869672	+	7.44052i	0.0743011	+	0.635686i	0.978160	+	0.207855i	$0.0666482\pi$
$137$	0.869672	+	7.44052i	0.0743011	+	0.635686i	−0.903859	+	0.427831i	$0.859278\pi$
$138$	−11.8855	+	8.34637i	−1.01176	+	0.710490i
$139$	0.767714	+	3.23924i	0.0651166	+	0.274749i	0.995857	−	0.0909317i	$-0.0289845\pi$
$139$	0.767714	+	3.23924i	0.0651166	+	0.274749i	−0.930740	+	0.365680i	$0.880836\pi$
$140$	−3.43371	−	0.666283i	−0.290201	−	0.0563112i
$141$	14.9032	+	1.59227i	1.25508	+	0.134093i
$142$	6.92822	+	15.1960i	0.581403	+	1.27522i
$143$	13.9172	+	11.6779i	1.16381	+	0.976554i
$144$	8.10820	+	8.84630i	0.675684	+	0.737192i
$145$	−0.412209	+	0.345885i	−0.0342321	+	0.0287242i
$146$	−8.87362	−	4.23072i	−0.734386	−	0.350137i
$147$	−27.2681	+	23.3454i	−2.24904	+	1.92550i
$148$	−5.59299	+	0.887712i	−0.459741	+	0.0729695i
$149$	2.00909	−	17.1889i	0.164591	−	1.40817i	−0.618267	−	0.785969i	$-0.712165\pi$
$149$	2.00909	−	17.1889i	0.164591	−	1.40817i	0.782858	−	0.622201i	$-0.213761\pi$
$150$	−10.5347	+	5.69867i	−0.860151	+	0.465295i
$151$	8.19415	−	12.4586i	0.666830	−	1.01387i	−0.330707	−	0.943733i	$-0.607287\pi$
$151$	8.19415	−	12.4586i	0.666830	−	1.01387i	0.997538	−	0.0701328i	$-0.0223423\pi$
$152$	−0.513079	−	8.32195i	−0.0416162	−	0.674999i
$153$	0.594721	−	6.14257i	0.0480803	−	0.496597i
$154$	33.2060	+	1.25088i	2.67582	+	0.100799i
$155$	0.254640	+	0.0603507i	0.0204531	+	0.00484748i
$156$	12.1624	+	7.13937i	0.973773	+	0.571607i
$157$	−0.731309	−	12.5561i	−0.0583648	−	1.00208i	−0.892650	−	0.450751i	$-0.851156\pi$
$157$	−0.731309	−	12.5561i	−0.0583648	−	1.00208i	0.834285	−	0.551334i	$-0.185881\pi$
$158$	0.363167	+	0.937464i	0.0288920	+	0.0745806i
$159$	0.912172	+	7.18534i	0.0723399	+	0.569835i
$160$	1.34882	+	1.30801i	0.106634	+	0.103407i
$161$			31.2195i			2.46044i
$162$	−9.24029	+	8.75312i	−0.725985	+	0.687710i
$163$		−	12.1831i		−	0.954254i	−0.878834	−	0.477127i	$-0.841678\pi$
$163$		−	12.1831i		−	0.954254i	0.878834	−	0.477127i	$-0.158322\pi$
$164$	3.90796	+	9.50399i	0.305160	+	0.742137i
$165$	−2.04391	+	1.55338i	−0.159118	+	0.120930i
$166$	−12.0452	+	4.66622i	−0.934887	+	0.362169i
$167$	0.549577	+	9.43588i	0.0425276	+	0.730170i	0.950420	+	0.310968i	$0.100653\pi$
$167$	0.549577	+	9.43588i	0.0425276	+	0.730170i	−0.907893	+	0.419202i	$0.862310\pi$
$168$	25.5787	−	3.33555i	1.97344	−	0.257343i
$169$	3.47824	+	0.824359i	0.267557	+	0.0634122i
$170$	0.0363735	−	0.965577i	0.00278972	−	0.0740564i
$171$	8.81662	−	0.689221i	0.674224	−	0.0527060i
$172$	−0.799523	+	0.384533i	−0.0609631	+	0.0293204i
$173$	−7.81954	+	11.8890i	−0.594509	+	0.903906i	−0.999948	−	0.0102156i	$-0.996748\pi$
$173$	−7.81954	+	11.8890i	−0.594509	+	0.903906i	0.405439	+	0.914122i	$0.367119\pi$
$174$	2.07874	−	3.38039i	0.157589	−	0.256266i
$175$	−2.98896	+	25.5722i	−0.225945	+	1.93308i
$176$	−14.5687	−	10.3137i	−1.09816	−	0.777422i
$177$	1.25040	+	6.70196i	0.0939856	+	0.503750i
$178$	1.60602	−	3.36850i	0.120376	−	0.252480i
$179$	−7.29901	+	6.12460i	−0.545554	+	0.457774i	−0.873432	−	0.486946i	$-0.838111\pi$
$179$	−7.29901	+	6.12460i	−0.545554	+	0.457774i	0.327878	+	0.944720i	$0.393666\pi$
$180$	−1.36365	+	1.45325i	−0.101640	+	0.108319i
$181$	12.7593	+	10.7063i	0.948391	+	0.795795i	0.979026	−	0.203736i	$-0.0653084\pi$
$181$	12.7593	+	10.7063i	0.948391	+	0.795795i	−0.0306346	+	0.999531i	$0.509753\pi$
$182$	27.5843	−	12.5763i	2.04468	−	0.932218i
$183$	−7.44410	−	16.7973i	−0.550284	−	1.24169i
$184$	9.16767	−	14.0425i	0.675850	−	1.03523i
$185$	−0.216886	−	0.915112i	−0.0159457	−	0.0672804i
$186$	−1.92237	+	0.170810i	−0.140955	+	0.0125244i
$187$	1.06570	+	9.11767i	0.0779319	+	0.666750i
$188$	−16.6622	+	4.67894i	−1.21522	+	0.341247i
$189$	3.98337	+	27.0685i	0.289747	+	1.96894i
$190$	1.37171	−	0.188942i	0.0995143	−	0.0137073i
$191$	−11.2808	−	15.1527i	−0.816248	−	1.09641i	−0.993677	−	0.112278i	$-0.964185\pi$
$191$	−11.2808	−	15.1527i	−0.816248	−	1.09641i	0.177428	−	0.984134i	$-0.443222\pi$
$192$	−12.4847	−	6.01092i	−0.901009	−	0.433801i
$193$	7.13575	−	23.8351i	0.513642	−	1.71568i	−0.169618	−	0.985510i	$-0.554253\pi$
$193$	7.13575	−	23.8351i	0.513642	−	1.71568i	0.683260	−	0.730175i	$-0.260561\pi$
$194$	−17.5552	+	15.3555i	−1.26039	+	1.10246i
$195$	−1.03033	+	2.10331i	−0.0737832	+	0.150621i
$196$	19.2342	−	36.7168i	1.37387	−	2.62263i
$197$	4.70118	+	0.828945i	0.334945	+	0.0590599i	0.338591	−	0.940933i	$-0.390050\pi$
$197$	4.70118	+	0.828945i	0.334945	+	0.0590599i	−0.00364633	+	0.999993i	$0.501161\pi$
$198$	10.6838	−	15.6302i	0.759265	−	1.11079i
$199$	−14.1271	+	2.49099i	−1.00144	+	0.176581i	−0.650248	−	0.759722i	$-0.725335\pi$
$199$	−14.1271	+	2.49099i	−1.00144	+	0.176581i	−0.351194	+	0.936303i	$0.614224\pi$
$200$	8.85377	−	10.6246i	0.626056	−	0.751274i
$201$	−10.7386	+	6.34276i	−0.757441	+	0.447384i
$202$	−0.175228	−	8.53599i	−0.0123290	−	0.600590i
$203$	−3.37875	−	7.83283i	−0.237142	−	0.549757i
$204$	1.99449	+	6.84118i	0.139642	+	0.478979i
$205$	−1.52504	+	0.765905i	−0.106514	+	0.0534931i
$206$	0.691372	−	3.20929i	0.0481701	−	0.223602i
$207$	15.0521	+	9.47764i	1.04619	+	0.658742i
$208$	−16.1004	−	2.44338i	−1.11636	−	0.169418i
$209$	−12.6020	+	3.77280i	−0.871700	+	0.260970i
$210$	0.871954	+	4.19418i	0.0601705	+	0.289426i
$211$	5.26200	−	10.4775i	0.362251	−	0.721301i	−0.636500	−	0.771277i	$-0.719618\pi$
$211$	5.26200	−	10.4775i	0.362251	−	0.721301i	0.998750	+	0.0499765i	$0.0159146\pi$
$212$	−4.05709	−	7.31356i	−0.278642	−	0.502298i
$213$	13.8884	−	15.0164i	0.951614	−	1.02891i
$214$	−0.960453	+	0.248557i	−0.0656552	+	0.0169910i
$215$	−0.0736683	−	0.127597i	−0.00502414	−	0.00870206i
$216$	6.15701	−	13.3451i	0.418931	−	0.908018i
$217$	−2.07431	+	3.59280i	−0.140813	+	0.243895i
$218$	1.61972	−	5.84423i	0.109701	−	0.395821i
$219$	−0.580814	+	12.0259i	−0.0392478	+	0.812637i
$220$	1.52593	−	2.54145i	0.102878	−	0.171344i
$221$	4.60205	+	6.99707i	0.309567	+	0.470674i
$222$	3.64909	+	5.89818i	0.244911	+	0.395860i
$223$	3.45046	+	3.25534i	0.231060	+	0.217994i	0.793060	−	0.609143i	$-0.208487\pi$
$223$	3.45046	+	3.25534i	0.231060	+	0.217994i	−0.562000	+	0.827137i	$0.689968\pi$
$224$	−25.9973	+	14.5374i	−1.73702	+	0.971319i
$225$	11.4220	+	9.20433i	0.761464	+	0.613622i
$226$	−13.5625	+	4.36560i	−0.902167	+	0.290396i
$227$	0.0125832	−	0.216046i	0.000835180	−	0.0143395i	−0.997865	−	0.0653131i	$-0.979195\pi$
$227$	0.0125832	−	0.216046i	0.000835180	−	0.0143395i	0.998700	+	0.0509736i	$0.0162324\pi$
$228$	−9.15823	+	4.51706i	−0.606519	+	0.299150i
$229$	10.7560	−	14.4478i	0.710774	−	0.954735i	−0.289223	−	0.957262i	$-0.593397\pi$
$229$	10.7560	−	14.4478i	0.710774	−	0.954735i	0.999997	+	0.00252695i	$0.000804355\pi$
$230$	2.43999	+	1.34272i	0.160888	+	0.0885366i
$231$	−14.2981	−	38.1035i	−0.940744	−	2.50702i
$232$	−0.780370	+	4.51537i	−0.0512338	+	0.296448i
$233$	3.29413	−	9.05054i	0.215805	−	0.592921i	−0.783800	−	0.621014i	$-0.786721\pi$
$233$	3.29413	−	9.05054i	0.215805	−	0.592921i	0.999605	+	0.0280929i	$0.00894342\pi$
$234$	2.31054	−	17.1174i	0.151045	−	1.11900i
$235$	−0.983016	−	2.70082i	−0.0641249	−	0.176182i
$236$	−4.21262	−	6.65033i	−0.274218	−	0.432899i
$237$	0.887188	−	0.853808i	0.0576291	−	0.0554608i
$238$	14.4988	+	4.94256i	0.939817	+	0.320379i
$239$	9.09059	+	9.63546i	0.588021	+	0.623266i	0.951245	−	0.308436i	$-0.0998055\pi$
$239$	9.09059	+	9.63546i	0.588021	+	0.623266i	−0.363224	+	0.931702i	$0.618324\pi$
$240$	0.839426	−	2.14258i	0.0541847	−	0.138303i
$241$	1.34433	−	3.11651i	0.0865960	−	0.200752i	−0.869415	−	0.494082i	$-0.835504\pi$
$241$	1.34433	−	3.11651i	0.0865960	−	0.200752i	0.956011	+	0.293330i	$0.0947635\pi$
$242$	−4.75429	+	11.6749i	−0.305617	+	0.750490i
$243$	14.2600	+	6.29694i	0.914781	+	0.403949i
$244$	15.1798	+	14.8209i	0.971786	+	0.948811i
$245$	6.32064	+	2.72646i	0.403811	+	0.174187i
$246$	8.88729	−	8.91140i	0.566633	−	0.568170i
$247$	−8.72937	+	8.23574i	−0.555436	+	0.524027i
$248$	1.98805	−	1.00691i	0.126241	−	0.0639390i
$249$	10.9703	+	11.3992i	0.695216	+	0.722395i
$250$	3.78232	+	2.69697i	0.239215	+	0.170572i
$251$	−10.3898	+	3.78157i	−0.655796	+	0.238690i	−0.648420	−	0.761283i	$-0.724570\pi$
$251$	−10.3898	+	3.78157i	−0.655796	+	0.238690i	−0.00737581	+	0.999973i	$0.502348\pi$
$252$	−15.8704	−	27.3171i	−0.999741	−	1.72082i
$253$	−24.8630	−	9.04938i	−1.56312	−	0.568929i
$254$	14.4942	+	21.0819i	0.909450	+	1.32280i
$255$	−1.10799	+	0.415764i	−0.0693848	+	0.0260362i
$256$	15.9625	+	1.09528i	0.997654	+	0.0684550i
$257$	−21.8373	−	16.2573i	−1.36217	−	1.01410i	−0.996520	−	0.0833481i	$-0.973439\pi$
$257$	−21.8373	−	16.2573i	−1.36217	−	1.01410i	−0.365652	−	0.930752i	$-0.619154\pi$
$258$	0.812680	+	0.721253i	0.0505952	+	0.0449033i
$259$	14.8839	+	0.866886i	0.924838	+	0.0538657i
$260$	0.203464	−	2.69677i	0.0126183	−	0.167247i
$261$	−4.80223	−	0.748871i	−0.297251	−	0.0463539i
$262$	26.1332	−	13.8034i	1.61451	−	0.852774i
$263$	16.5045	−	17.4938i	1.01771	−	1.07871i	0.0208312	−	0.999783i	$-0.493369\pi$
$263$	16.5045	−	17.4938i	1.01771	−	1.07871i	0.996880	−	0.0789282i	$-0.0251498\pi$
$264$	−4.75791	+	21.3375i	−0.292829	+	1.31323i
$265$	1.16044	−	0.763234i	0.0712854	−	0.0468851i
$266$	−3.36727	+	21.6911i	−0.206460	+	1.32997i
$267$	−4.56514	−	0.220482i	−0.279382	−	0.0134933i
$268$	8.79643	−	11.4026i	0.537327	−	0.696526i
$269$	−11.6720	−	6.73882i	−0.711653	−	0.410873i	0.100020	−	0.994985i	$-0.468109\pi$
$269$	−11.6720	−	6.73882i	−0.711653	−	0.410873i	−0.811673	+	0.584112i	$0.801443\pi$
$270$	2.28688	+	0.852870i	0.139175	+	0.0519040i
$271$	−7.42746	+	4.28825i	−0.451186	+	0.260493i	−0.708331	−	0.705880i	$-0.750552\pi$
$271$	−7.42746	+	4.28825i	−0.451186	+	0.260493i	0.257145	+	0.966373i	$0.417218\pi$
$272$	−5.07013	−	6.48075i	−0.307422	−	0.392953i
$273$	−27.2583	−	25.2106i	−1.64974	−	1.52581i
$274$	−6.64177	+	8.25362i	−0.401244	+	0.498619i
$275$	−19.4991	−	9.79283i	−1.17584	−	0.590530i
$276$	−20.2009	−	3.71230i	−1.21595	−	0.223454i
$277$	0.863179	+	2.88322i	0.0518634	+	0.173236i	0.979997	−	0.199011i	$-0.0637728\pi$
$277$	0.863179	+	2.88322i	0.0518634	+	0.173236i	−0.928134	+	0.372246i	$0.878588\pi$
$278$	−2.50575	+	3.98564i	−0.150285	+	0.239043i
$279$	1.10251	+	2.09081i	0.0660054	+	0.125173i
$280$	−2.73221	−	4.12354i	−0.163281	−	0.246429i
$281$	−8.59506	−	17.1142i	−0.512738	−	1.02095i	−0.989852	−	0.142104i	$-0.954613\pi$
$281$	−8.59506	−	17.1142i	−0.512738	−	1.02095i	0.477113	−	0.878842i	$-0.341683\pi$
$282$	13.1692	+	16.6089i	0.784215	+	0.989044i
$283$	3.65527	−	1.57673i	0.217283	−	0.0937269i	−0.284656	−	0.958630i	$-0.591879\pi$
$283$	3.65527	−	1.57673i	0.217283	−	0.0937269i	0.501939	+	0.864903i	$0.332620\pi$
$284$	−8.45696	+	22.0526i	−0.501828	+	1.30858i
$285$	−0.862453	−	1.46017i	−0.0510873	−	0.0864932i
$286$	2.02001	+	25.6133i	0.119446	+	1.51455i
$287$	−4.69789	−	26.6430i	−0.277308	−	1.57269i
$288$	−0.883260	+	16.9476i	−0.0520466	+	0.998645i
$289$	2.21720	−	12.5744i	0.130424	−	0.739669i
$290$	−0.757498	−	0.0728141i	−0.0444818	−	0.00427579i
$291$	25.6526	+	12.5662i	1.50378	+	0.736642i
$292$	−4.53051	−	13.1436i	−0.265128	−	0.769172i
$293$	−5.45895	−	1.63430i	−0.318915	−	0.0954769i	0.123345	−	0.992364i	$-0.460638\pi$
$293$	−5.45895	−	1.63430i	−0.318915	−	0.0954769i	−0.442260	+	0.896887i	$0.645823\pi$
$294$	−50.5781	−	4.35597i	−2.94977	−	0.254045i
$295$	1.04867	−	0.780703i	0.0610557	−	0.0454543i
$296$	−6.44017	−	4.76060i	−0.374327	−	0.276704i
$297$	−22.7118	−	4.67383i	−1.31787	−	0.271203i
$298$	19.3273	−	15.0148i	1.11960	−	0.869786i
$299$	−23.9754	+	2.80233i	−1.38654	+	0.162063i
$300$	−16.1913	−	4.97482i	−0.934806	−	0.287222i
$301$	2.27276	−	0.538654i	0.131000	−	0.0310475i
$302$	20.6885	−	4.08743i	1.19049	−	0.235205i
$303$	−9.55988	+	4.23668i	−0.549201	+	0.243391i
$304$	7.88424	−	8.76783i	0.452192	−	0.502870i
$305$	−2.26469	+	2.69896i	−0.129676	+	0.154542i
$306$	6.78455	−	5.48995i	0.387847	−	0.313840i
$307$	16.4349	+	19.5863i	0.937988	+	1.11785i	0.992851	+	0.119357i	$0.0380833\pi$
$307$	16.4349	+	19.5863i	0.937988	+	1.11785i	−0.0548632	+	0.998494i	$0.517472\pi$
$308$	31.6589	+	34.7293i	1.80393	+	1.97889i
$309$	−3.95253	+	0.737431i	−0.224852	+	0.0419510i
$310$	0.191584	+	0.316643i	0.0108813	+	0.0179841i
$311$	−10.1880	−	1.19081i	−0.577709	−	0.0675245i	−0.177779	−	0.984070i	$-0.556891\pi$
$311$	−10.1880	−	1.19081i	−0.577709	−	0.0675245i	−0.399930	+	0.916546i	$0.630965\pi$
$312$	4.85758	+	19.3441i	0.275006	+	1.09514i
$313$	13.3905	+	8.80705i	0.756874	+	0.497804i	0.868343	−	0.495964i	$-0.165185\pi$
$313$	13.3905	+	8.80705i	0.756874	+	0.497804i	−0.111469	+	0.993768i	$0.535556\pi$
$314$	11.9381	−	13.1856i	0.673708	−	0.744109i
$315$	4.32545	−	2.96945i	0.243711	−	0.167310i
$316$	−0.585414	+	1.29566i	−0.0329321	+	0.0728868i
$317$	3.01482	−	12.7205i	0.169329	−	0.714457i	−0.820434	−	0.571741i	$-0.806268\pi$
$317$	3.01482	−	12.7205i	0.169329	−	0.714457i	0.989764	−	0.142716i	$-0.0455836\pi$
$318$	−6.34228	+	8.04349i	−0.355657	+	0.451057i
$319$	7.21737	−	0.420364i	0.404095	−	0.0235359i
$320$	0.0180583	+	2.65708i	0.00100949	+	0.148535i
$321$	0.735216	+	0.967386i	0.0410358	+	0.0539942i
$322$	−31.4857	+	30.9510i	−1.75463	+	1.72483i
$323$	−6.06399			−0.337410
$324$	−17.9886	−	0.641234i	−0.999365	−	0.0356241i
$325$	−19.9068			−1.10423
$326$	12.2870	−	12.0783i	0.680513	−	0.668957i
$327$	−7.36836	+	0.935406i	−0.407471	+	0.0517281i
$328$	−5.71069	+	13.3635i	−0.315320	+	0.737878i
$329$	45.4866	−	2.64929i	2.50776	−	0.146060i
$330$	−3.59296	−	0.521320i	−0.197786	−	0.0286977i
$331$	−4.65105	+	19.6243i	−0.255645	+	1.07865i	0.682082	+	0.731276i	$0.261075\pi$
$331$	−4.65105	+	19.6243i	−0.255645	+	1.07865i	−0.937727	+	0.347374i	$0.887073\pi$
$332$	−16.6476	−	7.52180i	−0.913655	−	0.412812i
$333$	4.93641	−	6.91291i	0.270514	−	0.378825i
$334$	−8.97148	+	9.90899i	−0.490898	+	0.542196i
$335$	1.99819	+	1.31423i	0.109173	+	0.0718040i
$336$	28.7227	+	22.4900i	1.56695	+	1.22693i
$337$	−14.0975	−	1.64777i	−0.767942	−	0.0897595i	−0.276904	−	0.960898i	$-0.589308\pi$
$337$	−14.0975	−	1.64777i	−0.767942	−	0.0897595i	−0.491038	+	0.871138i	$0.663382\pi$
$338$	2.61694	+	4.32517i	0.142343	+	0.235258i
$339$	11.3487	+	13.2556i	0.616375	+	0.719943i
$340$	1.00987	−	0.920589i	0.0547679	−	0.0499260i
$341$	−2.26001	−	2.69338i	−0.122387	−	0.145855i
$342$	9.43589	+	8.20850i	0.510235	+	0.443865i
$343$	−46.4526	+	55.3600i	−2.50820	+	2.98916i
$344$	−1.18046	−	0.425115i	−0.0636461	−	0.0229207i
$345$	0.362368	−	3.39166i	0.0195092	−	0.182601i
$346$	−19.7427	+	3.90057i	−1.06137	+	0.209696i
$347$	11.8414	−	2.80647i	0.635682	−	0.150659i	0.0998751	−	0.995000i	$-0.468156\pi$
$347$	11.8414	−	2.80647i	0.635682	−	0.150659i	0.535807	+	0.844341i	$0.320008\pi$
$348$	5.47007	−	1.25485i	0.293226	−	0.0672671i
$349$	11.6674	−	1.36373i	0.624542	−	0.0729985i	0.202065	−	0.979372i	$-0.435235\pi$
$349$	11.6674	−	1.36373i	0.624542	−	0.0729985i	0.422477	+	0.906374i	$0.361161\pi$
$350$	−28.7535	+	22.3379i	−1.53694	+	1.19401i
$351$	−20.4301	+	5.48880i	−1.09048	+	0.292971i
$352$	−4.04179	−	24.9179i	−0.215428	−	1.32813i
$353$	−22.3758	+	16.6582i	−1.19095	+	0.886626i	−0.995563	−	0.0941012i	$-0.970002\pi$
$353$	−22.3758	+	16.6582i	−1.19095	+	0.886626i	−0.195383	+	0.980727i	$0.562595\pi$
$354$	−5.51946	+	7.90538i	−0.293356	+	0.420166i
$355$	−3.75760	−	1.12495i	−0.199432	−	0.0597062i
$356$	4.98943	−	1.71982i	0.264439	−	0.0911502i
$357$	−1.27654	−	18.7173i	−0.0675618	−	0.990623i
$358$	−13.4131	−	1.28932i	−0.708902	−	0.0681428i
$359$	1.83984	−	10.4342i	0.0971028	−	0.550698i	−0.896980	−	0.442071i	$-0.854244\pi$
$359$	1.83984	−	10.4342i	0.0971028	−	0.550698i	0.994083	−	0.108626i	$-0.0346451\pi$
$360$	−2.81756	+	0.0654770i	−0.148499	+	0.00345094i
$361$	1.79035	+	10.1536i	0.0942292	+	0.534400i
$362$	1.85195	+	23.4823i	0.0973365	+	1.23420i
$363$	15.4381	−	0.153125i	0.810292	−	0.00803698i
$364$	40.0306	+	15.3513i	2.09817	+	0.804628i
$365$	2.11999	−	0.914474i	0.110965	−	0.0478658i
$366$	9.56044	−	24.1604i	0.499732	−	1.26288i
$367$	−12.7800	−	25.4471i	−0.667111	−	1.32833i	−0.931440	−	0.363895i	$-0.881447\pi$
$367$	−12.7800	−	25.4471i	−0.667111	−	1.32833i	0.264329	−	0.964433i	$-0.414849\pi$
$368$	23.2510	−	4.67586i	1.21204	−	0.243746i
$369$	−14.2718	−	5.82329i	−0.742961	−	0.303148i
$370$	0.707895	−	1.12598i	0.0368017	−	0.0585367i
$371$	6.31505	+	21.0937i	0.327861	+	1.09513i
$372$	−2.07810	−	1.76942i	−0.107744	−	0.0917400i
$373$	1.46644	+	0.736476i	0.0759296	+	0.0381333i	0.486359	−	0.873759i	$-0.338325\pi$
$373$	1.46644	+	0.736476i	0.0759296	+	0.0381333i	−0.410429	+	0.911892i	$0.634621\pi$
$374$	−8.13888	+	10.1140i	−0.420851	+	0.522985i
$375$	1.25710	−	5.54880i	0.0649163	−	0.286539i
$376$	−21.2378	−	12.1656i	−1.09525	−	0.627392i
$377$	5.71204	−	3.29785i	0.294185	−	0.169848i
$378$	−23.3502	+	30.8530i	−1.20100	+	1.58691i
$379$	7.48181	+	4.31963i	0.384315	+	0.221884i	0.679694	−	0.733496i	$-0.262113\pi$
$379$	7.48181	+	4.31963i	0.384315	+	0.221884i	−0.295379	+	0.955380i	$0.595446\pi$
$380$	1.55047	+	1.19609i	0.0795372	+	0.0613581i
$381$	16.9576	−	26.3483i	0.868764	−	1.34986i
$382$	4.09816	−	26.3994i	0.209680	−	1.35071i
$383$	−16.7826	+	11.0381i	−0.857549	+	0.564019i	−0.900400	−	0.435063i	$-0.856726\pi$
$383$	−16.7826	+	11.0381i	−0.857549	+	0.564019i	0.0428515	+	0.999081i	$0.486356\pi$
$384$	−6.31520	−	18.5504i	−0.322271	−	0.946647i
$385$	−5.35565	+	5.67665i	−0.272949	+	0.289309i
$386$	31.1127	−	16.4335i	1.58359	−	0.836442i
$387$	0.430260	−	1.25931i	0.0218714	−	0.0640142i
$388$	−32.8906	−	2.48151i	−1.66977	−	0.125980i
$389$	−16.6464	−	0.969545i	−0.844008	−	0.0491579i	−0.369310	−	0.929306i	$-0.620406\pi$
$389$	−16.6464	−	0.969545i	−0.844008	−	0.0491579i	−0.474698	+	0.880148i	$0.657443\pi$
$390$	−3.14271	+	1.04611i	−0.159137	+	0.0529717i
$391$	−9.78335	−	7.28343i	−0.494765	−	0.368339i
$392$	56.0987	−	17.0028i	2.83341	−	0.858769i
$393$	−27.9578	−	22.9908i	−1.41029	−	1.15973i
$394$	3.82474	+	5.56308i	0.192687	+	0.280264i
$395$	−0.221877	−	0.0807567i	−0.0111639	−	0.00406331i
$396$	26.3554	−	4.72083i	1.32441	−	0.237230i
$397$	18.3142	−	6.66581i	0.919162	−	0.334548i	0.161257	−	0.986912i	$-0.448445\pi$
$397$	18.3142	−	6.66581i	0.919162	−	0.334548i	0.757905	+	0.652365i	$0.226223\pi$
$398$	−16.5178	−	11.7780i	−0.827963	−	0.590377i
$399$	26.0969	−	6.45910i	1.30648	−	0.323359i
$400$	19.4928	−	1.60399i	0.974642	−	0.0801994i
$401$	−26.5877	+	25.0842i	−1.32773	+	1.25264i	−0.383421	+	0.923574i	$0.625254\pi$
$401$	−26.5877	+	25.0842i	−1.32773	+	1.25264i	−0.944305	+	0.329071i	$0.893264\pi$
$402$	−17.0431	−	4.54194i	−0.850031	−	0.226531i
$403$	−2.94533	−	1.27049i	−0.146718	−	0.0632878i
$404$	8.43505	−	8.63930i	0.419660	−	0.429821i
$405$	−0.118563	−	2.98693i	−0.00589146	−	0.148422i
$406$	4.54992	−	11.1730i	0.225809	−	0.554508i
$407$	−5.00466	+	11.6021i	−0.248072	+	0.575095i
$408$	−4.92218	+	8.79385i	−0.243684	+	0.435360i
$409$	−0.403479	−	0.427663i	−0.0199508	−	0.0211466i	0.717321	−	0.696742i	$-0.245368\pi$
$409$	−0.403479	−	0.427663i	−0.0199508	−	0.0211466i	−0.737272	+	0.675596i	$0.763886\pi$
$410$	−2.28436	−	0.778728i	−0.112817	−	0.0384586i
$411$	12.4663	+	3.59783i	0.614917	+	0.177468i
$412$	3.92208	−	2.48442i	0.193227	−	0.122399i
$413$	7.08855	+	19.4756i	0.348805	+	0.958333i
$414$	5.36421	+	24.5766i	0.263637	+	1.20787i
$415$	1.03762	−	2.85083i	0.0509347	−	0.139942i
$416$	−13.4977	−	18.6601i	−0.661781	−	0.914885i
$417$	5.68800	+	0.944879i	0.278543	+	0.0462709i
$418$	−16.2986	−	8.96912i	−0.797191	−	0.438694i
$419$	11.9116	−	16.0000i	0.581918	−	0.781651i	−0.409510	−	0.912306i	$-0.634300\pi$
$419$	11.9116	−	16.0000i	0.581918	−	0.781651i	0.991428	+	0.130654i	$0.0417078\pi$
$420$	−3.36549	+	5.03750i	−0.164219	+	0.245805i
$421$	1.39043	−	23.8727i	0.0677653	−	1.16349i	−0.777409	−	0.628995i	$-0.783467\pi$
$421$	1.39043	−	23.8727i	0.0677653	−	1.16349i	0.845175	−	0.534490i	$-0.179496\pi$
$422$	15.7836	−	5.08052i	0.768333	−	0.247316i
$423$	12.5315	−	22.7351i	0.609304	−	1.10542i
$424$	3.35372	−	11.3424i	0.162871	−	0.550833i
$425$	−7.31633	−	6.90260i	−0.354894	−	0.334825i
$426$	28.9134	−	0.880498i	1.40086	−	0.0426602i
$427$	−30.6921	−	46.6651i	−1.48530	−	2.25828i
$428$	−1.20287	−	0.722223i	−0.0581429	−	0.0349100i
$429$	27.9786	−	14.4006i	1.35082	−	0.695269i
$430$	0.0556505	−	0.200796i	0.00268371	−	0.00968326i
$431$	7.28587	−	12.6195i	0.350948	−	0.607860i	−0.635468	−	0.772127i	$-0.719193\pi$
$431$	7.28587	−	12.6195i	0.350948	−	0.607860i	0.986416	+	0.164268i	$0.0525261\pi$
$432$	19.5629	−	7.02080i	0.941222	−	0.337789i
$433$	10.3858	+	17.9888i	0.499112	+	0.864487i	0.999999	−	0.00102540i	$-0.000326396\pi$
$433$	10.3858	+	17.9888i	0.499112	+	0.864487i	−0.500888	+	0.865512i	$0.666993\pi$
$434$	−5.67990	+	1.46991i	−0.272644	+	0.0705580i
$435$	0.276148	+	0.890169i	0.0132403	+	0.0426803i
$436$	7.49985	−	4.16043i	0.359178	−	0.199249i
$437$	7.84418	−	15.6190i	0.375238	−	0.747160i
$438$	−12.7043	+	11.3367i	−0.607034	+	0.541690i
$439$	−1.04390	+	0.312523i	−0.0498227	+	0.0149159i	−0.311618	−	0.950208i	$-0.600871\pi$
$439$	−1.04390	+	0.312523i	−0.0498227	+	0.0149159i	0.261795	+	0.965124i	$0.415686\pi$
$440$	4.07592	−	0.980651i	0.194312	−	0.0467507i
$441$	19.0098	+	59.1971i	0.905228	+	2.81891i
$442$	−2.49427	+	11.5782i	−0.118640	+	0.550718i
$443$	16.3634	−	8.21801i	0.777449	−	0.390450i	−0.0153894	−	0.999882i	$-0.504899\pi$
$443$	16.3634	−	8.21801i	0.777449	−	0.390450i	0.792838	+	0.609432i	$0.208602\pi$
$444$	−2.33076	+	9.52766i	−0.110613	+	0.452163i
$445$	0.347142	+	0.804765i	0.0164561	+	0.0381495i
$446$	0.137687	+	6.70722i	0.00651966	+	0.317596i
$447$	−26.1062	−	14.7292i	−1.23478	−	0.696665i
$448$	−40.4351	−	11.8066i	−1.91038	−	0.557811i
$449$	−16.6496	+	2.93578i	−0.785745	+	0.138548i	−0.552104	−	0.833775i	$-0.686175\pi$
$449$	−16.6496	+	2.93578i	−0.785745	+	0.138548i	−0.233641	+	0.972323i	$0.575064\pi$
$450$	2.04091	+	20.6445i	0.0962094	+	0.973192i
$451$	22.5800	+	3.98147i	1.06325	+	0.187480i
$452$	−17.8487	−	9.35013i	−0.839534	−	0.439793i
$453$	−14.4060	−	21.4371i	−0.676853	−	1.00720i
$454$	0.230363	−	0.201497i	0.0108115	−	0.00945674i
$455$	−2.04204	+	6.82090i	−0.0957325	+	0.319769i
$456$	−13.6350	−	4.75811i	−0.638520	−	0.222819i
$457$	12.7659	+	17.1475i	0.597162	+	0.802128i	0.993239	−	0.116089i	$-0.0370359\pi$
$457$	12.7659	+	17.1475i	0.597162	+	0.802128i	−0.396076	+	0.918218i	$0.629628\pi$
$458$	25.2344	−	3.47583i	1.17913	−	0.162415i
$459$	−9.41184	−	5.06673i	−0.439307	−	0.236495i
$460$	1.06483	+	3.79197i	0.0496479	+	0.176801i
$461$	2.83477	+	24.2530i	0.132029	+	1.12958i	0.883043	+	0.469291i	$0.155491\pi$
$461$	2.83477	+	24.2530i	0.132029	+	1.12958i	−0.751015	+	0.660285i	$0.770435\pi$
$462$	24.2532	−	52.1958i	1.12836	−	2.42837i
$463$	−4.09152	−	17.2635i	−0.190149	−	0.802301i	−0.981581	−	0.191045i	$-0.938813\pi$
$463$	−4.09152	−	17.2635i	−0.190149	−	0.802301i	0.791433	−	0.611257i	$-0.209336\pi$
$464$	−5.32753	+	3.68951i	−0.247324	+	0.171281i
$465$	0.267053	−	0.366242i	0.0123843	−	0.0169841i
$466$	12.3935	−	5.65049i	0.574118	−	0.261754i
$467$	10.3241	+	8.66297i	0.477744	+	0.400875i	0.849610	−	0.527412i	$-0.176837\pi$
$467$	10.3241	+	8.66297i	0.477744	+	0.400875i	−0.371866	+	0.928286i	$0.621282\pi$
$468$	19.5540	−	14.6399i	0.903883	−	0.676730i
$469$	−29.0442	+	24.3710i	−1.34114	+	1.12535i
$470$	1.74928	−	3.66899i	0.0806884	−	0.169238i
$471$	−20.5437	−	7.24738i	−0.946606	−	0.333942i
$472$	2.53064	−	10.8417i	0.116482	−	0.499028i
$473$	−0.229809	+	1.96614i	−0.0105666	+	0.0904033i
$474$	1.74065	+	0.0482877i	0.0799506	+	0.00221793i
$475$	7.92062	−	12.0427i	0.363423	−	0.552558i
$476$	9.38939	+	19.5225i	0.430362	+	0.894811i
$477$	12.0872	+	3.35893i	0.553436	+	0.153795i
$478$	−0.705212	+	18.7207i	−0.0322557	+	0.856265i
$479$	0.561962	+	0.133187i	0.0256767	+	0.00608549i	0.243434	−	0.969917i	$-0.421726\pi$
$479$	0.561962	+	0.133187i	0.0256767	+	0.00608549i	−0.217757	+	0.976003i	$0.569874\pi$
$480$	2.99306	−	1.27757i	0.136614	−	0.0583130i
$481$	0.670269	+	11.5081i	0.0305616	+	0.524723i
$482$	4.47585	−	1.73391i	0.203870	−	0.0789776i
$483$	49.8614	+	20.9240i	2.26877	+	0.952076i
$484$	−16.4878	+	6.77965i	−0.749447	+	0.308166i
$485$		−	5.47772i		−	0.248730i
$486$	7.78676	+	20.6244i	0.353215	+	0.935542i
$487$			2.47577i			0.112188i	0.998425	+	0.0560939i	$0.0178646\pi$
$487$			2.47577i			0.112188i	−0.998425	+	0.0560939i	$0.982135\pi$
$488$	0.101952	+	30.0027i	0.00461516	+	1.35816i
$489$	−19.4579	−	8.16539i	−0.879917	−	0.369252i
$490$	3.51658	+	9.07755i	0.158863	+	0.410082i
$491$	1.39586	+	23.9660i	0.0629943	+	1.08157i	0.870646	+	0.491910i	$0.163701\pi$
$491$	1.39586	+	23.9660i	0.0629943	+	1.08157i	−0.807652	+	0.589660i	$0.799262\pi$
$492$	17.7982	+	0.128307i	0.802407	+	0.00578454i
$493$	3.24285	+	0.768570i	0.146051	+	0.0346146i
$494$	−16.9603	−	0.638896i	−0.763078	−	0.0287453i
$495$	1.11106	+	4.30549i	0.0499384	+	0.193517i
$496$	2.98645	+	1.00675i	0.134096	+	0.0452045i
$497$	34.1691	−	51.9516i	1.53269	−	2.33035i
$498$	−0.620433	+	22.3650i	−0.0278023	+	1.00220i
$499$	−3.87334	+	33.1386i	−0.173395	+	1.48349i	0.573863	+	0.818951i	$0.305444\pi$
$499$	−3.87334	+	33.1386i	−0.173395	+	1.48349i	−0.747258	+	0.664534i	$0.768630\pi$
$500$	1.02982	+	6.48835i	0.0460551	+	0.290168i
$501$	15.4386	+	5.44640i	0.689746	+	0.243327i
$502$	−14.1142	−	6.72931i	−0.629949	−	0.300344i
$503$	−18.3653	+	15.4103i	−0.818866	+	0.687110i	−0.952706	−	0.303893i	$-0.901714\pi$
$503$	−18.3653	+	15.4103i	−0.818866	+	0.687110i	0.133840	+	0.991003i	$0.457269\pi$
$504$	11.8162	−	43.0879i	0.526333	−	1.91929i
$505$	1.53606	+	1.28891i	0.0683539	+	0.0573557i
$506$	−15.5226	−	34.0465i	−0.690063	−	1.51355i
$507$	3.64780	−	5.00268i	0.162004	−	0.222177i
$508$	−6.89206	+	35.5184i	−0.305786	+	1.57587i
$509$	−0.567018	−	2.39244i	−0.0251326	−	0.106043i	0.959033	−	0.283295i	$-0.0914274\pi$
$509$	−0.567018	−	2.39244i	−0.0251326	−	0.106043i	−0.984166	+	0.177252i	$0.943279\pi$
$510$	−1.51777	−	0.705244i	−0.0672078	−	0.0312287i
$511$	4.24917	+	36.3540i	0.187972	+	1.60821i
$512$	14.7206	+	17.1844i	0.650563	+	0.759452i
$513$	4.80833	−	14.5432i	0.212293	−	0.642096i
$514$	−5.25360	−	38.1409i	−0.231726	−	1.68232i
$515$	0.460426	+	0.618459i	0.0202888	+	0.0272526i
$516$	0.0782875	+	1.53466i	0.00344642	+	0.0675596i
$517$	−11.0750	+	36.9931i	−0.487078	+	1.62695i
$518$	13.8816	+	15.8702i	0.609922	+	0.697297i
$519$	13.7474	+	20.4571i	0.603444	+	0.897966i
$520$	2.92148	−	2.46838i	0.128115	−	0.108246i
$521$	36.3438	+	6.40840i	1.59225	+	0.280757i	0.898339	−	0.439302i	$-0.144774\pi$
$521$	36.3438	+	6.40840i	1.59225	+	0.280757i	0.693913	+	0.720059i	$0.255885\pi$
$522$	−4.00567	−	5.58561i	−0.175324	−	0.244475i
$523$	11.6835	−	2.06012i	0.510884	−	0.0900826i	0.0877368	−	0.996144i	$-0.472037\pi$
$523$	11.6835	−	2.06012i	0.510884	−	0.0900826i	0.423147	+	0.906061i	$0.360925\pi$
$524$	39.8295	+	12.6714i	1.73996	+	0.553552i
$525$	38.8387	+	21.9128i	1.69506	+	0.956355i
$526$	34.0055	−	0.698069i	1.48271	−	0.0304373i
$527$	−0.641957	−	1.48822i	−0.0279641	−	0.0648280i
$528$	−26.2365	+	16.3555i	−1.14180	+	0.711783i
$529$	10.8618	−	5.45501i	0.472253	−	0.237174i
$530$	1.92020	+	0.413666i	0.0834083	+	0.0179685i
$531$	11.5419	+	2.49477i	0.500876	+	0.108264i
$532$	−25.2144	+	18.1086i	−1.09318	+	0.785108i
$533$	20.0392	−	5.99934i	0.867994	−	0.259860i
$534$	−4.30352	−	4.82265i	−0.186231	−	0.208697i
$535$	0.104572	−	0.208220i	0.00452104	−	0.00900212i
$536$	20.2206	−	2.43313i	0.873398	−	0.105095i
$537$	4.88977	+	15.7623i	0.211009	+	0.680192i
$538$	−4.77532	−	18.4524i	−0.205878	−	0.795538i
$539$	−46.2420	−	80.0935i	−1.99178	−	3.44987i
$540$	1.40707	+	3.15192i	0.0605508	+	0.135637i
$541$	−1.95454	+	3.38536i	−0.0840323	+	0.145548i	−0.904978	−	0.425457i	$-0.860113\pi$
$541$	−1.95454	+	3.38536i	−0.0840323	+	0.145548i	0.820946	+	0.571006i	$0.193447\pi$
$542$	−11.6884	−	3.23943i	−0.502060	−	0.139145i
$543$	25.6509	−	13.2025i	1.10078	−	0.566576i
$544$	1.50949	−	11.5384i	0.0647187	−	0.494704i
$545$	0.782675	+	1.19000i	0.0335261	+	0.0509740i
$546$	−1.59831	−	52.4844i	−0.0684011	−	2.24613i
$547$	−12.7711	−	12.0489i	−0.546054	−	0.515175i	0.363036	−	0.931775i	$-0.381740\pi$
$547$	−12.7711	−	12.0489i	−0.546054	−	0.515175i	−0.909090	+	0.416600i	$0.863222\pi$
$548$	−14.9086	+	1.48423i	−0.636866	+	0.0634032i
$549$	−31.8166	+	0.631214i	−1.35790	+	0.0269396i
$550$	−9.45510	−	29.3740i	−0.403167	−	1.25251i
$551$	−0.277686	+	4.76769i	−0.0118298	+	0.203110i
$552$	−16.2832	−	24.0535i	−0.693058	−	1.02378i
$553$	2.23525	−	3.00246i	0.0950526	−	0.127678i
$554$	−2.05205	+	3.72896i	−0.0871831	+	0.158428i
$555$	−1.60691	−	0.266936i	−0.0682094	−	0.0113308i
$556$	−6.50382	+	1.42425i	−0.275824	+	0.0604017i
$557$	−10.6043	+	29.1351i	−0.449319	+	1.23449i	0.483880	+	0.875134i	$0.339227\pi$
$557$	−10.6043	+	29.1351i	−0.449319	+	1.23449i	−0.933199	+	0.359360i	$0.882995\pi$
$558$	−1.01561	+	3.18474i	−0.0429942	+	0.134821i
$559$	0.617674	+	1.69704i	0.0261248	+	0.0717773i
$560$	1.44998	−	6.84359i	0.0612730	−	0.289194i
$561$	15.2763	+	4.40881i	0.644966	+	0.186140i
$562$	8.73896	−	25.6353i	0.368631	−	1.08136i
$563$	−18.9340	−	20.0688i	−0.797971	−	0.845800i	0.192815	−	0.981235i	$-0.438238\pi$
$563$	−18.9340	−	20.0688i	−0.797971	−	0.845800i	−0.990786	+	0.135435i	$0.956757\pi$
$564$	−3.69455	+	29.7475i	−0.155569	+	1.25260i
$565$	1.32538	−	3.07259i	0.0557593	−	0.129265i
$566$	5.21401	+	2.12327i	0.219161	+	0.0892477i
$567$	45.9015	+	11.7800i	1.92768	+	0.494713i
$568$	−30.6249	+	13.3339i	−1.28499	+	0.559478i
$569$	−6.75878	−	2.91546i	−0.283343	−	0.122222i	0.249665	−	0.968332i	$-0.419679\pi$
$569$	−6.75878	−	2.91546i	−0.283343	−	0.122222i	−0.533008	+	0.846110i	$0.678939\pi$
$570$	0.617588	−	2.31742i	0.0258679	−	0.0970662i
$571$	−0.780524	+	0.736386i	−0.0326639	+	0.0308168i	−0.702401	−	0.711782i	$-0.747888\pi$
$571$	−0.780524	+	0.736386i	−0.0326639	+	0.0308168i	0.669737	+	0.742599i	$0.266407\pi$
$572$	−23.8291	+	27.4303i	−0.996343	+	1.14692i
$573$	−31.7614	+	7.86109i	−1.32685	+	0.328402i
$574$	22.2127	−	31.1519i	0.927142	−	1.30025i
$575$	27.2432	−	9.91571i	1.13612	−	0.413514i
$576$	−17.9677	+	15.9110i	−0.748656	+	0.662959i
$577$	−7.25579	−	2.64089i	−0.302062	−	0.109942i	0.186542	−	0.982447i	$-0.440272\pi$
$577$	−7.25579	−	2.64089i	−0.302062	−	0.109942i	−0.488605	+	0.872505i	$0.662494\pi$
$578$	14.8797	−	10.2301i	0.618915	−	0.425517i
$579$	−33.2850	−	27.3715i	−1.38328	−	1.13752i
$580$	−0.677549	−	0.836145i	−0.0281337	−	0.0347190i
$581$	38.5777	+	28.7201i	1.60047	+	1.19151i
$582$	12.7586	+	38.3294i	0.528863	+	1.58881i
$583$	−18.6294	−	1.08504i	−0.771550	−	0.0449377i
$584$	8.76415	−	17.5997i	0.362663	−	0.728282i
$585$	2.66869	+	3.05524i	0.110337	+	0.126319i
$586$	−3.76376	−	7.12574i	−0.155480	−	0.294362i
$587$	−10.5419	+	11.1738i	−0.435111	+	0.461191i	−0.907409	−	0.420248i	$-0.861943\pi$
$587$	−10.5419	+	11.1738i	−0.435111	+	0.461191i	0.472298	+	0.881439i	$0.343425\pi$
$588$	−45.7500	−	55.3278i	−1.88670	−	2.28168i
$589$	1.94049	−	1.27628i	0.0799566	−	0.0525883i
$590$	1.82701	+	0.283619i	0.0752167	+	0.0116764i
$591$	4.47476	−	6.95278i	0.184067	−	0.285999i
$592$	−1.58359	−	11.2147i	−0.0650851	−	0.460923i
$593$	14.9621	+	8.63835i	0.614418	+	0.354735i	0.774693	−	0.632338i	$-0.217905\pi$
$593$	14.9621	+	8.63835i	0.614418	+	0.354735i	−0.160274	+	0.987073i	$0.551238\pi$
$594$	−17.8027	−	27.5390i	−0.730456	−	1.12994i
$595$	−3.11562	+	1.79881i	−0.127728	+	0.0737439i
$596$	34.3039	+	4.60636i	1.40514	+	0.188684i
$597$	−5.48988	+	24.2322i	−0.224686	+	0.991758i
$598$	−26.5955	−	21.4016i	−1.08757	−	0.875178i
$599$	18.5412	+	9.31176i	0.757575	+	0.380468i	0.785274	−	0.619148i	$-0.212522\pi$
$599$	18.5412	+	9.31176i	0.757575	+	0.380468i	−0.0276996	+	0.999616i	$0.508818\pi$
$600$	−11.0348	−	21.2614i	−0.450495	−	0.867994i
$601$	7.28165	+	24.3224i	0.297025	+	0.992132i	0.968063	+	0.250709i	$0.0806636\pi$
$601$	7.28165	+	24.3224i	0.297025	+	0.992132i	−0.671038	+	0.741423i	$0.734151\pi$
$602$	2.79646	+	1.75812i	0.113975	+	0.0716555i
$603$	2.93292	+	21.4019i	0.119438	+	0.871553i
$604$	24.6329	+	16.8126i	1.00230	+	0.684096i
$605$	−1.32872	−	2.64569i	−0.0540200	−	0.107563i
$606$	−13.7505	−	5.44115i	−0.558574	−	0.221032i
$607$	−27.6209	+	11.9145i	−1.12110	+	0.483595i	−0.874258	−	0.485461i	$-0.838652\pi$
$607$	−27.6209	+	11.9145i	−1.12110	+	0.483595i	−0.246841	+	0.969056i	$0.579393\pi$
$608$	16.6590	−	0.740958i	0.675613	−	0.0300498i
$609$	−14.7745	+	0.146543i	−0.598693	+	0.00593821i
$610$	−4.96719	+	0.391741i	−0.201116	+	0.0158611i
$611$	6.11753	+	34.6942i	0.247489	+	1.40358i
$612$	12.2630	+	1.39967i	0.495701	+	0.0565782i
$613$	−0.00521673	+	0.0295855i	−0.000210702	+	0.00119495i	−0.984913	−	0.173051i	$-0.944638\pi$
$613$	−0.00521673	+	0.0295855i	−0.000210702	+	0.00119495i	0.984702	+	0.174246i	$0.0557487\pi$
$614$	−3.45980	+	35.9929i	−0.139626	+	1.45256i
$615$	0.201126	+	2.94901i	0.00811019	+	0.118915i
$616$	−3.63878	+	66.3595i	−0.146611	+	2.67370i
$617$	−19.4038	−	5.80912i	−0.781168	−	0.233866i	−0.128701	−	0.991683i	$-0.541081\pi$
$617$	−19.4038	−	5.80912i	−0.781168	−	0.233866i	−0.652467	+	0.757817i	$0.726266\pi$
$618$	−4.66226	−	3.25515i	−0.187544	−	0.130941i
$619$	2.15296	−	1.60282i	0.0865349	−	0.0644228i	−0.553022	−	0.833167i	$-0.686525\pi$
$619$	2.15296	−	1.60282i	0.0865349	−	0.0644228i	0.639557	+	0.768744i	$0.279118\pi$
$620$	−0.129406	+	0.507137i	−0.00519706	+	0.0203671i
$621$	25.2252	−	17.6880i	1.01225	−	0.709793i
$622$	−8.89943	−	11.4554i	−0.356835	−	0.459322i
$623$	−13.8003	+	1.61302i	−0.552896	+	0.0646243i
$624$	−14.6932	+	24.0767i	−0.588201	+	0.963841i
$625$	22.7278	−	5.38658i	0.909111	−	0.215463i
$626$	4.39317	+	22.2360i	0.175586	+	0.888728i
$627$	−2.42054	+	22.6556i	−0.0966670	+	0.904777i
$628$	25.1335	−	1.03232i	1.00294	−	0.0411942i
$629$	−3.74403	+	4.46196i	−0.149284	+	0.177910i
$630$	7.28302	+	1.41842i	0.290163	+	0.0565111i
$631$	−17.5646	−	20.9326i	−0.699234	−	0.833314i	0.293206	−	0.956049i	$-0.405278\pi$
$631$	−17.5646	−	20.9326i	−0.699234	−	0.833314i	−0.992439	+	0.122735i	$0.960833\pi$
$632$	−1.88709	+	0.694116i	−0.0750645	+	0.0276105i
$633$	−13.2071	−	15.4263i	−0.524937	−	0.613141i
$634$	15.8179	−	9.57061i	0.628209	−	0.380098i
$635$	−5.96799	−	0.697557i	−0.236832	−	0.0276817i
$636$	−14.3998	+	1.57796i	−0.570990	+	0.0625702i
$637$	−70.4941	−	46.3647i	−2.79308	−	1.83704i
$638$	7.57925	+	6.86217i	0.300065	+	0.271676i
$639$	−14.6748	−	32.2458i	−0.580525	−	1.27562i
$640$	−2.66183	+	2.65244i	−0.105218	+	0.104847i
$641$	0.603889	−	2.54801i	0.0238522	−	0.100640i	−0.959817	−	0.280627i	$-0.909457\pi$
$641$	0.603889	−	2.54801i	0.0238522	−	0.100640i	0.983669	+	0.179987i	$0.0576056\pi$
$642$	−0.246741	+	1.70055i	−0.00973810	+	0.0671154i
$643$	25.0196	−	1.45723i	0.986678	−	0.0574675i	0.442790	−	0.896625i	$-0.353989\pi$
$643$	25.0196	−	1.45723i	0.986678	−	0.0574675i	0.543888	+	0.839158i	$0.316952\pi$
$644$	−62.4299	−	1.06935i	−2.46008	−	0.0421383i
$645$	−0.253163	+	0.0321388i	−0.00996827	+	0.00126546i
$646$	−6.01184	−	6.11570i	−0.236533	−	0.240619i
$647$	25.9251			1.01922			0.509611	−	0.860405i	$-0.329789\pi$
$647$	25.9251			1.01922			0.509611	+	0.860405i	$0.329789\pi$
$648$	−17.1872	−	18.7777i	−0.675176	−	0.737657i
$649$	−17.5649			−0.689484
$650$	−19.7356	−	20.0766i	−0.774095	−	0.787468i
$651$	4.34790	+	5.72090i	0.170408	+	0.224220i
$652$	24.3626	+	0.417303i	0.954114	+	0.0163429i
$653$	−36.3056	+	2.11456i	−1.42075	+	0.0827491i	−0.751226	−	0.660045i	$-0.770537\pi$
$653$	−36.3056	+	2.11456i	−1.42075	+	0.0827491i	−0.669520	+	0.742794i	$0.733500\pi$
$654$	−8.24837	−	6.50383i	−0.322537	−	0.254320i
$655$	−1.60075	+	6.75411i	−0.0625467	+	0.263905i
$656$	−19.1391	+	7.48923i	−0.747255	+	0.292405i
$657$	18.8176	+	8.98768i	0.734145	+	0.350643i
$658$	47.7673	+	43.2479i	1.86216	+	1.68598i
$659$	−15.3480	−	10.0946i	−0.597874	−	0.393228i	0.214193	−	0.976791i	$-0.431288\pi$
$659$	−15.3480	−	10.0946i	−0.597874	−	0.393228i	−0.812068	+	0.583563i	$0.801658\pi$
$660$	−3.03629	−	4.14043i	−0.118187	−	0.161166i
$661$	18.2245	+	2.13013i	0.708849	+	0.0828526i	0.462875	−	0.886424i	$-0.346818\pi$
$661$	18.2245	+	2.13013i	0.708849	+	0.0828526i	0.245975	+	0.969276i	$0.420892\pi$
$662$	−24.4027	+	14.7648i	−0.948438	+	0.573852i
$663$	14.2596	−	2.66044i	0.553796	−	0.103323i
$664$	−8.91848	−	24.2467i	−0.346104	−	0.940953i
$665$	−3.31383	−	3.94927i	−0.128505	−	0.153146i
$666$	11.8658	−	1.87495i	0.459791	−	0.0726529i
$667$	−6.17445	+	7.35842i	−0.239076	+	0.284919i
$668$	−18.8878	+	0.775790i	−0.730791	+	0.0300162i
$669$	7.51176	−	3.32900i	0.290421	−	0.128707i
$670$	0.655568	+	3.31815i	0.0253268	+	0.128191i
$671$	46.0602	−	10.9165i	1.77813	−	0.421425i
$672$	5.79398	+	51.2642i	0.223508	+	1.97756i
$673$	−6.82541	+	0.797776i	−0.263100	+	0.0307520i	−0.246620	−	0.969112i	$-0.579320\pi$
$673$	−6.82541	+	0.797776i	−0.263100	+	0.0307520i	−0.0164800	+	0.999864i	$0.505246\pi$
$674$	−12.3145	−	15.8513i	−0.474336	−	0.610571i
$675$	22.3557	−	12.0733i	0.860472	−	0.464702i
$676$	−1.76761	+	6.92723i	−0.0679852	+	0.266432i
$677$	−27.9166	+	20.7831i	−1.07292	+	0.798761i	−0.980413	−	0.196951i	$-0.936896\pi$
$677$	−27.9166	+	20.7831i	−1.07292	+	0.798761i	−0.0925087	+	0.995712i	$0.529489\pi$
$678$	−2.11752	+	24.5870i	−0.0813230	+	0.944257i
$679$	83.1898	+	24.9054i	3.19253	+	0.955781i
$680$	1.92962	+	0.105810i	0.0739977	+	0.00405762i
$681$	−0.336618	−	0.164896i	−0.0128992	−	0.00631883i
$682$	0.475768	−	4.94950i	0.0182181	−	0.189526i
$683$	−4.58120	+	25.9813i	−0.175295	+	0.994146i	0.762508	+	0.646978i	$0.223968\pi$
$683$	−4.58120	+	25.9813i	−0.175295	+	0.994146i	−0.937803	+	0.347168i	$0.887144\pi$
$684$	1.07625	+	17.6543i	0.0411513	+	0.675028i
$685$	−0.432061	−	2.45034i	−0.0165082	−	0.0936226i
$686$	−101.885	+	8.03525i	−3.88999	+	0.306787i
$687$	−15.8660	−	26.8618i	−0.605324	−	1.02484i
$688$	−0.741567	−	1.61198i	−0.0282720	−	0.0614563i
$689$	−15.6324	+	6.74314i	−0.595546	+	0.256893i
$690$	3.77983	−	2.99703i	0.143896	−	0.114095i
$691$	−12.7173	−	25.3222i	−0.483789	−	0.963303i	−0.994617	−	0.103620i	$-0.966957\pi$
$691$	−12.7173	−	25.3222i	−0.483789	−	0.963303i	0.510828	−	0.859683i	$-0.329339\pi$
$692$	−23.5067	−	16.0440i	−0.893592	−	0.609902i
$693$	−70.4388	−	2.70202i	−2.67575	−	0.102641i
$694$	14.5700	+	9.16008i	0.553070	+	0.347712i
$695$	−0.317117	−	1.05924i	−0.0120289	−	0.0401794i
$696$	6.68858	+	4.27265i	0.253530	+	0.161954i
$697$	9.44521	+	4.74356i	0.357763	+	0.179675i
$698$	12.9424	+	10.4149i	0.489878	+	0.394210i
$699$	−12.2470	−	11.3270i	−0.463225	−	0.428427i
$700$	−51.0346	−	6.85297i	−1.92893	−	0.259018i
$701$	35.5930	−	20.5496i	1.34433	−	0.776150i	0.356891	−	0.934146i	$-0.383837\pi$
$701$	35.5930	−	20.5496i	1.34433	−	0.776150i	0.987440	+	0.157997i	$0.0505035\pi$
$702$	−25.7900	−	15.1627i	−0.973379	−	0.572278i
$703$	−7.22855	−	4.17340i	−0.272630	−	0.157403i
$704$	21.1233	−	28.7798i	0.796115	−	1.08468i
$705$	−4.97237	−	0.240150i	−0.187270	−	0.00904457i
$706$	−38.9836	−	6.05170i	−1.46717	−	0.227759i
$707$	−26.5586	+	17.4679i	−0.998839	+	0.656946i
$708$	−13.4448	+	2.27087i	−0.505286	+	0.0853444i
$709$	19.7083	−	20.8895i	0.740159	−	0.784523i	−0.242459	−	0.970162i	$-0.577954\pi$
$709$	19.7083	−	20.8895i	0.740159	−	0.784523i	0.982618	+	0.185639i	$0.0594354\pi$
$710$	−2.59074	−	4.90491i	−0.0972286	−	0.184078i
$711$	−0.769023	−	1.98919i	−0.0288406	−	0.0746005i
$712$	6.68100	+	3.32694i	0.250381	+	0.124682i
$713$	4.66363	+	0.271626i	0.174654	+	0.0101725i
$714$	17.6113	−	19.8437i	0.659086	−	0.742633i
$715$	−4.84019	−	3.60339i	−0.181013	−	0.134759i
$716$	−11.9974	−	14.8057i	−0.448363	−	0.553314i
$717$	21.4817	−	8.06088i	0.802250	−	0.301039i
$718$	12.3472	−	8.48897i	0.460794	−	0.316806i
$719$	7.65583	+	2.78650i	0.285514	+	0.103919i	0.480807	−	0.876826i	$-0.340344\pi$
$719$	7.65583	+	2.78650i	0.285514	+	0.103919i	−0.195293	+	0.980745i	$0.562566\pi$
$720$	−2.85937	−	2.77668i	−0.106562	−	0.103481i
$721$	−11.4859	+	4.18053i	−0.427758	+	0.155691i
$722$	−8.46523	+	11.8719i	−0.315043	+	0.441827i
$723$	−4.07645	−	4.23582i	−0.151605	−	0.157532i
$724$	−21.8465	+	25.1481i	−0.811920	+	0.934623i
$725$	−5.76205	+	5.43622i	−0.213997	+	0.201896i
$726$	15.4598	+	15.4180i	0.573767	+	0.572214i
$727$	−0.734115	−	0.316666i	−0.0272268	−	0.0117445i	0.382423	−	0.923987i	$-0.375090\pi$
$727$	−0.734115	−	0.316666i	−0.0272268	−	0.0117445i	−0.409650	+	0.912243i	$0.634349\pi$
$728$	24.2041	+	55.5912i	0.897064	+	2.06035i
$729$	19.6144	−	18.5547i	0.726459	−	0.687210i
$730$	3.02403	+	1.23146i	0.111924	+	0.0455782i
$731$	−0.361429	+	0.837887i	−0.0133679	+	0.0309904i
$732$	33.8446	−	14.3107i	1.25093	−	0.528937i
$733$	10.1768	+	10.7868i	0.375889	+	0.398419i	0.887507	−	0.460794i	$-0.152435\pi$
$733$	10.1768	+	10.7868i	0.375889	+	0.398419i	−0.511618	+	0.859213i	$0.670954\pi$
$734$	12.9940	−	38.1172i	0.479616	−	1.40693i
$735$	8.59073	−	8.26750i	0.316874	−	0.304952i
$736$	27.7668	+	18.8137i	1.02350	+	0.693480i
$737$	−10.9900	−	30.1948i	−0.404822	−	1.11224i
$738$	−8.27614	−	20.1667i	−0.304649	−	0.742347i
$739$	6.11149	−	16.7912i	0.224815	−	0.617674i	−0.775084	−	0.631858i	$-0.782293\pi$
$739$	6.11149	−	16.7912i	0.224815	−	0.617674i	0.999899	+	0.0141837i	$0.00451495\pi$
$740$	1.83738	−	0.402362i	0.0675436	−	0.0147911i
$741$	7.30286	+	19.4617i	0.268277	+	0.714942i
$742$	−15.0129	+	27.2812i	−0.551140	+	1.00153i
$743$	11.7385	−	15.7675i	0.430644	−	0.578455i	−0.532842	−	0.846215i	$-0.678876\pi$
$743$	11.7385	−	15.7675i	0.430644	−	0.578455i	0.963486	+	0.267760i	$0.0862834\pi$
$744$	−0.275723	−	3.85002i	−0.0101085	−	0.141149i
$745$	−0.334218	+	5.73831i	−0.0122448	+	0.210235i
$746$	0.711077	+	2.20909i	0.0260344	+	0.0808806i
$747$	25.5585	−	9.88094i	0.935136	−	0.361525i
$748$	−18.2692	+	1.81879i	−0.667987	+	0.0665015i
$749$	2.68677	+	2.53484i	0.0981724	+	0.0926209i
$750$	6.84240	−	4.23326i	0.249849	−	0.154577i
$751$	6.31709	+	9.60467i	0.230514	+	0.350480i	0.932160	−	0.362046i	$-0.117922\pi$
$751$	6.31709	+	9.60467i	0.230514	+	0.350480i	−0.701646	+	0.712525i	$0.747551\pi$
$752$	−8.78579	−	33.4798i	−0.320385	−	1.22088i
$753$	−0.923833	+	19.1282i	−0.0336663	+	0.697071i
$754$	8.98888	+	2.49126i	0.327356	+	0.0907263i
$755$	−2.47642	+	4.28928i	−0.0901260	+	0.156103i
$756$	−54.2655	+	7.03840i	−1.97362	+	0.255984i
$757$	−4.53120	−	7.84826i	−0.164689	−	0.285250i	0.771856	−	0.635798i	$-0.219329\pi$
$757$	−4.53120	−	7.84826i	−0.164689	−	0.285250i	−0.936545	+	0.350548i	$0.885995\pi$
$758$	3.06101	+	11.8281i	0.111181	+	0.429616i
$759$	−31.1167	+	33.6441i	−1.12946	+	1.22120i
$760$	0.330844	+	2.74949i	0.0120010	+	0.0997345i
$761$	3.53505	−	7.03887i	0.128146	−	0.255159i	−0.820406	−	0.571781i	$-0.806253\pi$
$761$	3.53505	−	7.03887i	0.128146	−	0.255159i	0.948552	+	0.316623i	$0.102549\pi$
$762$	43.3847	−	9.01952i	1.57166	−	0.326743i
$763$	−21.6310	+	6.47591i	−0.783096	+	0.234444i
$764$	30.6874	−	22.0392i	1.11023	−	0.797351i
$765$	−0.0785703	+	2.04824i	−0.00284072	+	0.0740544i
$766$	−27.7704	−	5.98253i	−1.00339	−	0.216157i
$767$	−14.3203	+	7.19192i	−0.517076	+	0.259685i
$768$	12.4477	−	24.7599i	0.449168	−	0.893447i
$769$	−1.82966	−	4.24163i	−0.0659792	−	0.152957i	0.882036	−	0.471182i	$-0.156173\pi$
$769$	−1.82966	−	4.24163i	−0.0659792	−	0.152957i	−0.948015	+	0.318225i	$0.896913\pi$
$770$	−11.0346	+	0.226521i	−0.397661	+	0.00816324i
$771$	−40.6007	+	23.9808i	−1.46220	+	0.863649i
$772$	47.4187	+	15.0858i	1.70664	+	0.542950i
$773$	42.9176	−	7.56753i	1.54364	−	0.272185i	0.663965	−	0.747764i	$-0.268872\pi$
$773$	42.9176	−	7.56753i	1.54364	−	0.272185i	0.879673	+	0.475579i	$0.157761\pi$
$774$	1.69661	−	0.814549i	0.0609833	−	0.0292784i
$775$	3.79403	+	0.668989i	0.136285	+	0.0240308i
$776$	−30.1051	−	35.6313i	−1.08071	−	1.27909i
$777$	11.3600	−	23.1904i	0.407539	−	0.831949i
$778$	−15.5255	−	17.7496i	−0.556615	−	0.636354i
$779$	−4.34396	+	14.5098i	−0.155638	+	0.519869i
$780$	−4.17071	−	2.13239i	−0.149335	−	0.0763519i
$781$	31.4695	+	42.2708i	1.12607	+	1.51257i
$782$	−2.35367	−	17.0876i	−0.0841672	−	0.611050i
$783$	−4.41460	+	7.16784i	−0.157765	+	0.256158i
$784$	72.7640	+	39.7205i	2.59871	+	1.41859i
$785$	0.484976	+	4.14923i	0.0173095	+	0.148093i
$786$	−4.53059	−	50.9893i	−0.161601	−	1.81873i
$787$	3.65369	+	15.4161i	0.130240	+	0.549525i	0.998566	+	0.0535318i	$0.0170479\pi$
$787$	3.65369	+	15.4161i	0.130240	+	0.549525i	−0.868326	+	0.495993i	$0.834804\pi$
$788$	−1.81867	+	9.37258i	−0.0647876	+	0.333885i
$789$	−16.8780	−	38.0844i	−0.600872	−	1.35584i
$790$	−0.138524	−	0.303831i	−0.00492845	−	0.0108098i
$791$	40.6371	+	34.0986i	1.44489	+	1.21241i
$792$	30.8898	+	21.8999i	1.09762	+	0.778178i
$793$	33.0821	−	27.7592i	1.17478	−	0.985757i
$794$	24.8793	+	11.8618i	0.882934	+	0.420961i
$795$	−0.441225	−	2.36490i	−0.0156486	−	0.0838745i
$796$	−4.49735	−	28.3353i	−0.159404	−	1.00432i
$797$	−4.47780	+	38.3100i	−0.158612	+	1.35701i	0.646058	+	0.763288i	$0.276416\pi$
$797$	−4.47780	+	38.3100i	−0.158612	+	1.35701i	−0.804670	+	0.593722i	$0.797658\pi$
$798$	32.3866	+	19.9158i	1.14647	+	0.705013i
$799$	−9.78169	+	14.8723i	−0.346051	+	0.526146i
$800$	20.9429	+	18.0689i	0.740442	+	0.638831i
$801$	−3.41180	+	7.14332i	−0.120550	+	0.252397i
$802$	−51.6571	−	1.94593i	−1.82408	−	0.0687133i
$803$	−30.1837	−	7.15366i	−1.06516	−	0.252447i
$804$	−12.3158	−	21.6913i	−0.434346	−	0.764992i
$805$	−0.602923	−	10.3518i	−0.0212503	−	0.364853i
$806$	−1.63868	−	4.23002i	−0.0577200	−	0.148996i
$807$	−18.5855	+	14.1251i	−0.654242	+	0.497226i
$808$	17.0755	−	0.0580243i	0.600713	−	0.00204129i
$809$			31.2517i			1.09875i	0.835576	+	0.549375i	$0.185134\pi$
$809$			31.2517i			1.09875i	−0.835576	+	0.549375i	$0.814866\pi$
$810$	2.89486	−	3.08082i	0.101715	−	0.108249i
$811$		−	43.1596i		−	1.51554i	−0.652523	−	0.757769i	$-0.726290\pi$
$811$		−	43.1596i		−	1.51554i	0.652523	−	0.757769i	$-0.273710\pi$
$812$	15.7791	−	6.48822i	0.553737	−	0.227692i
$813$	1.87080	+	14.7367i	0.0656120	+	0.516837i
$814$	−16.6627	+	6.45499i	−0.584026	+	0.226247i
$815$	0.235285	+	4.03968i	0.00824167	+	0.141504i
$816$	−13.7487	+	3.75407i	−0.481300	+	0.131419i
$817$	−1.27240	−	0.301564i	−0.0445155	−	0.0105504i
$818$	0.0313003	−	0.830905i	0.00109439	−	0.0290519i
$819$	−58.5335	+	26.6381i	−2.04532	+	0.930810i
$820$	−1.47935	−	3.07587i	−0.0516611	−	0.107414i
$821$	−19.9348	+	30.3094i	−0.695730	+	1.05781i	0.298897	+	0.954285i	$0.403381\pi$
$821$	−19.9348	+	30.3094i	−0.695730	+	1.05781i	−0.994627	+	0.103521i	$0.966989\pi$
$822$	8.73057	+	16.1395i	0.304514	+	0.562929i
$823$	−2.46426	+	21.0831i	−0.0858987	+	0.734911i	0.879818	+	0.475311i	$0.157665\pi$
$823$	−2.46426	+	21.0831i	−0.0858987	+	0.734911i	−0.965716	+	0.259599i	$0.916410\pi$
$824$	6.39396	+	1.49247i	0.222744	+	0.0519926i
$825$	−28.7091	+	24.5791i	−0.999523	+	0.855735i
$826$	−12.6141	+	26.4571i	−0.438901	+	0.920562i
$827$	17.8383	−	14.9681i	0.620300	−	0.520493i	−0.277598	−	0.960697i	$-0.589538\pi$
$827$	17.8383	−	14.9681i	0.620300	−	0.520493i	0.897898	+	0.440204i	$0.145094\pi$
$828$	−19.4681	+	29.7752i	−0.676563	+	1.03476i
$829$	32.0840	+	26.9217i	1.11432	+	0.935028i	0.998304	−	0.0582191i	$-0.0185422\pi$
$829$	32.0840	+	26.9217i	1.11432	+	0.935028i	0.116019	+	0.993247i	$0.462987\pi$
$830$	3.90383	−	1.77985i	0.135504	−	0.0617795i
$831$	5.18337	+	0.553796i	0.179809	+	0.0192110i
$832$	5.43752	−	32.1124i	0.188512	−	1.11330i
$833$	−9.83185	−	41.4839i	−0.340654	−	1.43733i
$834$	4.68615	+	6.67326i	0.162268	+	0.231076i
$835$	−0.364459	−	3.11814i	−0.0126126	−	0.107908i
$836$	−7.11283	−	25.3296i	−0.246002	−	0.876041i
$837$	4.07820	−	0.359534i	0.140963	−	0.0124273i
$838$	27.9456	−	3.84927i	0.965363	−	0.132971i
$839$	−18.5923	−	24.9738i	−0.641878	−	0.862191i	0.355492	−	0.934679i	$-0.384313\pi$
$839$	−18.5923	−	24.9738i	−0.641878	−	0.862191i	−0.997369	+	0.0724882i	$0.976906\pi$
$840$	−8.41699	+	1.59999i	−0.290414	+	0.0552049i
$841$	−7.56452	+	25.2673i	−0.260846	+	0.871285i
$842$	25.4548	−	22.2651i	0.877229	−	0.767307i
$843$	−33.0940	+	2.25706i	−1.13982	+	0.0777373i
$844$	20.7717	+	10.8813i	0.714991	+	0.374551i
$845$	−1.16924	−	0.206168i	−0.0402231	−	0.00709241i
$846$	35.3527	−	9.90119i	1.21545	−	0.340410i
$847$	46.2212	−	8.15005i	1.58818	−	0.280039i
$848$	14.7639	−	7.86249i	0.506996	−	0.269999i
$849$	−0.0683857	−	6.89468i	−0.00234699	−	0.236625i
$850$	−0.291950	−	14.2219i	−0.0100138	−	0.487809i
$851$	−6.64953	−	15.4153i	−0.227943	−	0.528431i
$852$	29.5527	+	28.2870i	1.01246	+	0.969096i
$853$	0.982223	−	0.493291i	0.0336307	−	0.0168900i	−0.431904	−	0.901919i	$-0.642158\pi$
$853$	0.982223	−	0.493291i	0.0336307	−	0.0168900i	0.465535	+	0.885029i	$0.345862\pi$
$854$	16.6348	−	77.2176i	0.569232	−	2.64233i
$855$	−2.91011	+	0.398802i	−0.0995237	+	0.0136388i
$856$	−0.464144	−	1.92914i	−0.0158641	−	0.0659366i
$857$	4.15400	−	1.24362i	0.141898	−	0.0424814i	−0.215067	−	0.976599i	$-0.568997\pi$
$857$	4.15400	−	1.24362i	0.141898	−	0.0424814i	0.356964	+	0.934118i	$0.383812\pi$
$858$	42.2614	+	13.9404i	1.44278	+	0.475918i
$859$	11.1841	−	22.2694i	0.381598	−	0.759824i	−0.618056	−	0.786134i	$-0.712080\pi$
$859$	11.1841	−	22.2694i	0.381598	−	0.759824i	0.999654	+	0.0263104i	$0.00837584\pi$
$860$	0.257680	−	0.142944i	0.00878683	−	0.00487437i
$861$	−45.7009	−	10.3537i	−1.55748	−	0.352852i
$862$	19.9503	−	5.16297i	0.679510	−	0.175851i
$863$	−3.00733	−	5.20885i	−0.102371	−	0.177311i	0.810290	−	0.586029i	$-0.199309\pi$
$863$	−3.00733	−	5.20885i	−0.102371	−	0.177311i	−0.912661	+	0.408717i	$0.865976\pi$
$864$	26.4754	+	12.7693i	0.900710	+	0.434421i
$865$	2.36320	−	4.09319i	0.0803514	−	0.139173i
$866$	−7.84567	+	28.3085i	−0.266607	+	0.961962i
$867$	−18.5968	−	11.9688i	−0.631580	−	0.406481i
$868$	−7.11350	−	4.27107i	−0.241448	−	0.144969i
$869$	1.74322	+	2.65044i	0.0591347	+	0.0899100i
$870$	−0.623986	+	1.16102i	−0.0211551	+	0.0393621i
$871$	−21.3231	−	20.1173i	−0.722506	−	0.681649i
$872$	11.6313	+	3.43915i	0.393884	+	0.116464i
$873$	37.2627	−	32.5482i	1.26115	−	1.10159i
$874$	23.5289	−	7.57365i	0.795878	−	0.256183i
$875$	1.00566	−	17.2666i	0.0339976	−	0.583717i
$876$	−24.0284	−	1.57338i	−0.811845	−	0.0531595i
$877$	23.6782	−	31.8053i	0.799555	−	1.07399i	−0.196073	−	0.980589i	$-0.562819\pi$
$877$	23.6782	−	31.8053i	0.799555	−	1.07399i	0.995629	−	0.0934000i	$-0.0297735\pi$
$878$	−1.35011	−	0.742967i	−0.0455641	−	0.0250739i
$879$	−6.26889	+	7.62326i	−0.211444	+	0.257126i
$880$	5.02988	+	3.13846i	0.169557	+	0.105797i
$881$	−3.77591	+	10.3742i	−0.127214	+	0.349517i	−0.986906	−	0.161295i	$-0.948433\pi$
$881$	−3.77591	+	10.3742i	−0.127214	+	0.349517i	0.859693	+	0.510812i	$0.170655\pi$
$882$	−40.8556	+	77.8599i	−1.37568	+	2.62168i
$883$	7.13289	+	19.5974i	0.240041	+	0.659506i	0.999955	+	0.00948318i	$0.00301864\pi$
$883$	7.13289	+	19.5974i	0.240041	+	0.659506i	−0.759914	+	0.650023i	$0.774759\pi$
$884$	−14.1497	+	8.96308i	−0.475907	+	0.301461i
$885$	−0.544039	−	2.19809i	−0.0182877	−	0.0738881i
$886$	24.5108	+	8.35560i	0.823455	+	0.280712i
$887$	−8.02743	−	8.50858i	−0.269535	−	0.285690i	0.578442	−	0.815723i	$-0.303661\pi$
$887$	−8.02743	−	8.50858i	−0.269535	−	0.285690i	−0.847977	+	0.530033i	$0.822179\pi$
$888$	−11.9196	+	7.09508i	−0.399996	+	0.238095i
$889$	37.7283	−	87.4639i	1.26536	−	2.93345i
$890$	−0.467471	+	1.14795i	−0.0156697	+	0.0384792i
$891$	−22.6866	+	33.1410i	−0.760030	+	1.11026i
$892$	−6.62791	+	6.78840i	−0.221919	+	0.227293i
$893$	−23.4225	−	10.1035i	−0.783804	−	0.338100i
$894$	−11.0270	−	40.9313i	−0.368797	−	1.36895i
$895$	2.30193	−	2.17176i	0.0769451	−	0.0725939i
$896$	−28.1800	−	52.4849i	−0.941428	−	1.75340i
$897$	−11.5932	+	40.1699i	−0.387086	+	1.34123i
$898$	−19.4673	−	13.8811i	−0.649631	−	0.463217i
$899$	−1.19948	+	0.436575i	−0.0400049	+	0.0145606i
$900$	−18.7972	+	22.5253i	−0.626573	+	0.750843i
$901$	−8.08349	−	2.94215i	−0.269300	−	0.0980173i
$902$	18.3704	+	26.7198i	0.611668	+	0.889672i
$903$	0.662958	−	3.99089i	0.0220619	−	0.132809i
$904$	−8.26537	−	27.2707i	−0.274902	−	0.907008i
$905$	−4.43750	−	3.30360i	−0.147508	−	0.109815i
$906$	7.33777	−	35.7816i	0.243781	−	1.18876i
$907$	22.8197	+	1.32910i	0.757717	+	0.0441320i	0.432654	−	0.901560i	$-0.357577\pi$
$907$	22.8197	+	1.32910i	0.757717	+	0.0441320i	0.325064	+	0.945692i	$0.394614\pi$
$908$	0.431598	+	0.0325630i	0.0143231	+	0.00108064i
$909$	0.359244	+	18.1078i	0.0119154	+	0.600598i
$910$	−8.90354	+	4.70278i	−0.295150	+	0.155896i
$911$	−23.4737	+	24.8807i	−0.777719	+	0.824334i	−0.988185	−	0.153268i	$-0.951020\pi$
$911$	−23.4737	+	24.8807i	−0.777719	+	0.824334i	0.210466	+	0.977601i	$0.432502\pi$
$912$	−8.71911	−	18.4685i	−0.288718	−	0.611553i
$913$	−34.0547	+	22.3981i	−1.12704	+	0.741269i
$914$	−4.63767	+	29.8748i	−0.153401	+	0.988171i
$915$	2.79272	+	5.42590i	0.0923244	+	0.179375i
$916$	28.5229	+	22.0036i	0.942422	+	0.727021i
$917$	−95.2963	−	55.0193i	−3.14696	−	1.81690i
$918$	−4.22096	−	14.5153i	−0.139313	−	0.479075i
$919$	10.5287	−	6.07875i	0.347310	−	0.200520i	−0.316190	−	0.948696i	$-0.602404\pi$
$919$	10.5287	−	6.07875i	0.347310	−	0.200520i	0.663500	+	0.748176i	$0.269070\pi$
$920$	−2.76863	+	4.83327i	−0.0912791	+	0.159348i
$921$	42.2968	−	13.1213i	1.39373	−	0.432362i
$922$	−21.6494	+	26.9034i	−0.712987	+	0.886017i
$923$	42.9640	+	21.5773i	1.41418	+	0.710227i
$924$	76.6855	−	27.2868i	2.52277	−	0.897670i
$925$	−3.97083	−	13.2635i	−0.130560	−	0.436101i
$926$	13.3543	−	21.2414i	0.438851	−	0.698036i
$927$	−1.47131	+	6.80692i	−0.0483241	+	0.223569i
$928$	−9.00268	−	1.71517i	−0.295528	−	0.0563034i
$929$	0.236191	+	0.470296i	0.00774919	+	0.0154299i	0.897474	−	0.441068i	$-0.145400\pi$
$929$	0.236191	+	0.470296i	0.00774919	+	0.0154299i	−0.889725	+	0.456497i	$0.849104\pi$
$930$	0.634121	−	0.0937627i	0.0207937	−	0.00307460i
$931$	56.0971	−	24.1979i	1.83851	−	0.793054i
$932$	17.9856	+	6.89729i	0.589138	+	0.225928i
$933$	−8.73010	+	15.4734i	−0.285811	+	0.506576i
$934$	1.49850	+	19.0006i	0.0490324	+	0.621720i
$935$	−0.529451	−	3.00266i	−0.0173149	−	0.0981976i
$936$	34.1506	+	5.20671i	1.11625	+	0.170187i
$937$	1.60530	−	9.10408i	0.0524427	−	0.297417i	−0.947294	−	0.320366i	$-0.896194\pi$
$937$	1.60530	−	9.10408i	0.0524427	−	0.297417i	0.999737	+	0.0229483i	$0.00730532\pi$
$938$	−53.3732	−	5.13047i	−1.74270	−	0.167516i
$939$	23.0405	−	15.4835i	0.751900	−	0.505286i
$940$	5.43451	−	1.87323i	0.177254	−	0.0610982i
$941$	21.8777	+	6.54976i	0.713194	+	0.213516i	0.622790	−	0.782389i	$-0.285999\pi$
$941$	21.8777	+	6.54976i	0.713194	+	0.213516i	0.0904036	+	0.995905i	$0.471184\pi$
$942$	−13.0579	−	27.9040i	−0.425449	−	0.909161i
$943$	−24.4360	+	18.1919i	−0.795746	+	0.592411i
$944$	13.4430	−	8.19621i	0.437532	−	0.266764i
$945$	−1.84357	−	8.89847i	−0.0599712	−	0.289467i
$946$	−2.21074	+	1.71746i	−0.0718773	+	0.0558396i
$947$	−7.47691	+	0.873926i	−0.242967	+	0.0283988i	−0.236705	−	0.971582i	$-0.576067\pi$
$947$	−7.47691	+	0.873926i	−0.242967	+	0.0283988i	−0.00626225	+	0.999980i	$0.501993\pi$
$948$	1.67698	+	1.80336i	0.0544657	+	0.0585705i
$949$	−27.5371	+	6.52641i	−0.893892	+	0.211856i
$950$	19.9979	−	3.95099i	0.648818	−	0.128187i
$951$	−18.2957	−	13.3406i	−0.593278	−	0.432600i
$952$	−10.3803	+	28.8240i	−0.336427	+	0.934192i
$953$	6.93552	−	8.26543i	0.224663	−	0.267743i	−0.641924	−	0.766768i	$-0.721864\pi$
$953$	6.93552	−	8.26543i	0.224663	−	0.267743i	0.866588	+	0.499024i	$0.166308\pi$
$954$	8.59571	+	15.5203i	0.278296	+	0.502489i
$955$	4.03312	+	4.80649i	0.130509	+	0.155534i
$956$	−19.5795	+	17.8485i	−0.633245	+	0.577261i
$957$	4.16587	−	11.8088i	0.134664	−	0.381723i
$958$	0.422806	+	0.698795i	0.0136602	+	0.0225771i
$959$	39.1776	+	4.57920i	1.26511	+	0.147870i
$960$	4.25579	+	1.75199i	0.137355	+	0.0565454i
$961$	−25.3815	−	16.6937i	−0.818757	−	0.538505i
$962$	−10.9417	+	12.0851i	−0.352774	+	0.389639i
$963$	2.03779	−	0.525866i	0.0656669	−	0.0169458i
$964$	6.18606	+	2.79502i	0.199240	+	0.0900214i
$965$	−1.90577	+	8.04106i	−0.0613488	+	0.258851i
$966$	28.3301	+	71.0306i	0.911507	+	2.28537i
$967$	−27.4274	+	1.59747i	−0.882006	+	0.0513710i	−0.493167	−	0.869935i	$-0.664161\pi$
$967$	−27.4274	+	1.59747i	−0.882006	+	0.0513710i	−0.388839	+	0.921306i	$0.627124\pi$
$968$	−23.1835	−	9.90709i	−0.745146	−	0.318426i
$969$	−4.06423	+	9.68494i	−0.130562	+	0.311125i
$970$	5.52443	−	5.43061i	0.177379	−	0.174366i
$971$	48.3888			1.55287			0.776435	−	0.630197i	$-0.217026\pi$
$971$	48.3888			1.55287			0.776435	+	0.630197i	$0.217026\pi$
$972$	−13.0805	+	28.3002i	−0.419557	+	0.907729i
$973$	17.5285			0.561938
$974$	−2.49688	+	2.45448i	−0.0800052	+	0.0786465i
$975$	−13.3420	+	31.7936i	−0.427286	+	1.01821i
$976$	−30.1574	+	29.8475i	−0.965315	+	0.955394i
$977$	6.14529	−	0.357922i	0.196605	−	0.0114510i	0.0404404	−	0.999182i	$-0.487124\pi$
$977$	6.14529	−	0.357922i	0.196605	−	0.0114510i	0.156165	+	0.987731i	$0.450087\pi$
$978$	−11.0556	−	27.7190i	−0.353518	−	0.886356i
$979$	2.71559	−	11.4580i	0.0867906	−	0.366198i
$980$	−5.66861	+	12.5460i	−0.181077	+	0.400768i
$981$	−3.44448	+	12.3951i	−0.109974	+	0.395745i
$982$	−22.7865	+	25.1676i	−0.727146	+	0.803132i
$983$	41.4449	+	27.2588i	1.32189	+	0.869419i	0.997080	−	0.0763610i	$-0.0243301\pi$
$983$	41.4449	+	27.2588i	1.32189	+	0.869419i	0.324807	+	0.945780i	$0.394701\pi$
$984$	17.5158	+	18.0772i	0.558383	+	0.576280i
$985$	−1.57483	−	0.184071i	−0.0501783	−	0.00586500i
$986$	2.43984	+	4.03246i	0.0777003	+	0.128420i
$987$	26.2549	−	74.4233i	0.835703	−	2.36892i
$988$	−16.1701	−	17.7383i	−0.514438	−	0.564330i
$989$	−1.69062	−	2.01480i	−0.0537584	−	0.0640668i
$990$	−3.24069	+	5.38899i	−0.102996	+	0.171273i
$991$	34.5244	−	41.1446i	1.09670	−	1.30700i	0.148649	−	0.988890i	$-0.452508\pi$
$991$	34.5244	−	41.1446i	1.09670	−	1.30700i	0.948054	−	0.318110i	$-0.103048\pi$
$992$	1.94543	+	4.01001i	0.0617675	+	0.127318i
$993$	28.2252	+	20.5810i	0.895700	+	0.653117i
$994$	86.2699	−	17.0444i	2.73631	−	0.540614i
$995$	4.63616	−	1.09879i	0.146976	−	0.0348340i
$996$	−23.1708	+	21.5470i	−0.734196	+	0.682742i
$997$	−52.1200	+	6.09195i	−1.65066	+	0.192934i	−0.889917	−	0.456123i	$-0.849238\pi$
$997$	−52.1200	+	6.09195i	−1.65066	+	0.192934i	−0.760740	+	0.649057i	$0.775164\pi$
$998$	−37.2611	+	28.9472i	−1.17948	+	0.916307i
$999$	−7.73227	−	12.5173i	−0.244638	−	0.396028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.47.40	✓	936
3.2	odd	2		972.2.p.a.791.13		936
4.3	odd	2	inner	324.2.p.a.47.52	yes	936
12.11	even	2		972.2.p.a.791.1		936
81.31	even	27		972.2.p.a.827.1		936
81.50	odd	54	inner	324.2.p.a.131.52	yes	936
324.31	odd	54		972.2.p.a.827.13		936
324.131	even	54	inner	324.2.p.a.131.40	yes	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.47.40	✓	936	1.1	even	1	trivial
324.2.p.a.47.52	yes	936	4.3	odd	2	inner
324.2.p.a.131.40	yes	936	324.131	even	54	inner
324.2.p.a.131.52	yes	936	81.50	odd	54	inner
972.2.p.a.791.1		936	12.11	even	2
972.2.p.a.791.13		936	3.2	odd	2
972.2.p.a.827.1		936	81.31	even	27
972.2.p.a.827.13		936	324.31	odd	54

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)

\(f(q)\)	\(=\)	\(q+(0.991400 + 1.00853i) q^{2} +(0.670223 - 1.59712i) q^{3} +(-0.0342526 + 1.99971i) q^{4} +(-0.331581 + 0.0193124i) q^{5} +(2.27520 - 0.907450i) q^{6} +(1.21429 - 5.12351i) q^{7} +(-2.05072 + 1.94796i) q^{8} +(-2.10160 - 2.14086i) q^{9} +O(q^{10})\)	\(q+(0.991400 + 1.00853i) q^{2} +(0.670223 - 1.59712i) q^{3} +(-0.0342526 + 1.99971i) q^{4} +(-0.331581 + 0.0193124i) q^{5} +(2.27520 - 0.907450i) q^{6} +(1.21429 - 5.12351i) q^{7} +(-2.05072 + 1.94796i) q^{8} +(-2.10160 - 2.14086i) q^{9} +(-0.348206 - 0.315262i) q^{10} +(3.72834 + 2.45217i) q^{11} +(3.17082 + 1.39495i) q^{12} +(4.04366 + 0.472636i) q^{13} +(6.37105 - 3.85480i) q^{14} +(-0.191389 + 0.542519i) q^{15} +(-3.99765 - 0.136990i) q^{16} +(1.32228 + 1.57583i) q^{17} +(0.0755821 - 4.24197i) q^{18} +(-1.89483 + 2.25818i) q^{19} +(-0.0272616 - 0.663726i) q^{20} +(-7.36902 - 5.37327i) q^{21} +(1.22320 + 6.19121i) q^{22} +(-5.76932 + 1.36735i) q^{23} +(1.73670 + 4.58082i) q^{24} +(-4.85662 + 0.567657i) q^{25} +(3.53222 + 4.54671i) q^{26} +(-4.82775 + 1.92167i) q^{27} +(10.2039 + 2.60372i) q^{28} +(1.29951 - 0.967451i) q^{29} +(-0.736888 + 0.344833i) q^{30} +(-0.754795 - 0.225971i) q^{31} +(-3.82511 - 4.16755i) q^{32} +(6.41523 - 4.31112i) q^{33} +(-0.278360 + 2.89583i) q^{34} +(-0.303689 + 1.72231i) q^{35} +(4.35307 - 4.12926i) q^{36} +(0.491685 + 2.78848i) q^{37} +(-4.15597 + 0.327764i) q^{38} +(3.46501 - 6.14146i) q^{39} +(0.642358 - 0.685512i) q^{40} +(4.71784 - 2.03508i) q^{41} +(-1.88657 - 12.7589i) q^{42} +(0.199085 + 0.396410i) q^{43} +(-5.03132 + 7.37159i) q^{44} +(0.738196 + 0.669280i) q^{45} +(-7.09871 - 4.46292i) q^{46} +(2.48181 + 8.28982i) q^{47} +(-2.89811 + 6.29293i) q^{48} +(-18.5204 - 9.30129i) q^{49} +(-5.38735 - 4.33525i) q^{50} +(3.40301 - 1.05568i) q^{51} +(-1.08364 + 8.06995i) q^{52} +(-3.62150 + 2.09088i) q^{53} +(-6.72429 - 2.96378i) q^{54} +(-1.28360 - 0.741089i) q^{55} +(7.49024 + 12.8723i) q^{56} +(2.33662 + 4.53976i) q^{57} +(2.26404 + 0.351462i) q^{58} +(-3.28860 + 2.16295i) q^{59} +(-1.07832 - 0.401304i) q^{60} +(7.27938 - 7.71569i) q^{61} +(-0.520406 - 0.985258i) q^{62} +(-13.5207 + 8.16795i) q^{63} +(0.410871 - 7.98944i) q^{64} +(-1.34993 - 0.0786244i) q^{65} +(10.7079 + 2.19589i) q^{66} +(-5.77580 - 4.29993i) q^{67} +(-3.19649 + 2.59019i) q^{68} +(-1.68290 + 10.1307i) q^{69} +(-2.03807 + 1.40122i) q^{70} +(11.0971 + 4.03902i) q^{71} +(8.48010 + 0.296441i) q^{72} +(-6.53205 + 2.37747i) q^{73} +(-2.32480 + 3.26038i) q^{74} +(-2.34840 + 8.13707i) q^{75} +(-4.45079 - 3.86646i) q^{76} +(17.0910 - 16.1245i) q^{77} +(9.62904 - 2.59408i) q^{78} +(0.652750 + 0.281569i) q^{79} +(1.32819 - 0.0317808i) q^{80} +(-0.166531 + 8.99846i) q^{81} +(6.72969 + 2.74049i) q^{82} +(-3.61779 + 8.38699i) q^{83} +(10.9974 - 14.5518i) q^{84} +(-0.468875 - 0.496978i) q^{85} +(-0.202418 + 0.593783i) q^{86} +(-0.674175 - 2.72389i) q^{87} +(-12.4225 + 2.23397i) q^{88} +(-0.902508 - 2.47962i) q^{89} +(0.0568609 + 1.40801i) q^{90} +(7.33175 - 20.1438i) q^{91} +(-2.53669 - 11.5838i) q^{92} +(-0.866784 + 1.05405i) q^{93} +(-5.90004 + 10.7215i) q^{94} +(0.584680 - 0.785362i) q^{95} +(-9.21977 + 3.31599i) q^{96} +(-0.958928 + 16.4642i) q^{97} +(-8.98052 - 27.8996i) q^{98} +(-2.58575 - 13.1353i) 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

L-functions

Modular forms

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