LMFDB - Embedded newform 57.2.j.b.32.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(2,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("57.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.j (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			32.1
Character	$\chi$	$=$	57.32
Dual form			57.2.j.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49833 + 1.25725i) q^{2} +(1.40671 + 1.01052i) q^{3} +(0.317026 - 1.79794i) q^{4} +(-0.487091 + 0.0858872i) q^{5} +(-3.37821 + 0.254491i) q^{6} +(-0.969730 + 1.67962i) q^{7} +(-0.170480 - 0.295279i) q^{8} +(0.957685 + 2.84303i) q^{9} +O(q^{10})$	\(q+(-1.49833 + 1.25725i) q^{2} +(1.40671 + 1.01052i) q^{3} +(0.317026 - 1.79794i) q^{4} +(-0.487091 + 0.0858872i) q^{5} +(-3.37821 + 0.254491i) q^{6} +(-0.969730 + 1.67962i) q^{7} +(-0.170480 - 0.295279i) q^{8} +(0.957685 + 2.84303i) q^{9} +(0.621842 - 0.741083i) q^{10} +(3.99257 - 2.30511i) q^{11} +(2.26283 - 2.20883i) q^{12} +(-1.79223 - 4.92410i) q^{13} +(-0.658727 - 3.73582i) q^{14} +(-0.771988 - 0.371398i) q^{15} +(4.05783 + 1.47693i) q^{16} +(1.61629 + 1.92622i) q^{17} +(-5.00934 - 3.05576i) q^{18} +(2.80139 - 3.33949i) q^{19} +0.902990i q^{20} +(-3.06143 + 1.38281i) q^{21} +(-3.08409 + 8.47347i) q^{22} +(-3.35200 - 0.591048i) q^{23} +(0.0585708 - 0.587647i) q^{24} +(-4.46858 + 1.62643i) q^{25} +(8.87617 + 5.12466i) q^{26} +(-1.52576 + 4.96710i) q^{27} +(2.71243 + 2.27600i) q^{28} +(-0.872266 - 0.731918i) q^{29} +(1.62363 - 0.414105i) q^{30} +(-1.31458 - 0.758971i) q^{31} +(-7.29606 + 2.65555i) q^{32} +(7.94576 + 0.791954i) q^{33} +(-4.84348 - 0.854036i) q^{34} +(0.328088 - 0.901415i) q^{35} +(5.41522 - 0.820548i) q^{36} +3.28109i q^{37} +(0.00115627 + 8.52572i) q^{38} +(2.45477 - 8.73788i) q^{39} +(0.108400 + 0.129186i) q^{40} +(-9.40408 - 3.42281i) q^{41} +(2.84850 - 5.92089i) q^{42} +(-0.829591 - 4.70484i) q^{43} +(-2.87871 - 7.90919i) q^{44} +(-0.710660 - 1.30256i) q^{45} +(5.76551 - 3.32872i) q^{46} +(3.82673 - 4.56052i) q^{47} +(4.21573 + 6.17815i) q^{48} +(1.61925 + 2.80462i) q^{49} +(4.65059 - 8.05506i) q^{50} +(0.327167 + 4.34294i) q^{51} +(-9.42143 + 1.66125i) q^{52} +(-1.71646 + 9.73455i) q^{53} +(-3.95878 - 9.36063i) q^{54} +(-1.74676 + 1.46571i) q^{55} +0.661277 q^{56} +(7.31539 - 1.86683i) q^{57} +2.22715 q^{58} +(0.172251 - 0.144536i) q^{59} +(-0.912492 + 1.27025i) q^{60} +(-1.90402 + 10.7982i) q^{61} +(2.92389 - 0.515560i) q^{62} +(-5.70391 - 1.14843i) q^{63} +(3.27498 - 5.67243i) q^{64} +(1.29589 + 2.24455i) q^{65} +(-12.9011 + 8.80320i) q^{66} +(0.266197 - 0.317241i) q^{67} +(3.97564 - 2.29534i) q^{68} +(-4.11804 - 4.21871i) q^{69} +(0.641719 + 1.76311i) q^{70} +(-0.540928 - 3.06775i) q^{71} +(0.676224 - 0.767464i) q^{72} +(-0.118214 - 0.0430264i) q^{73} +(-4.12516 - 4.91617i) q^{74} +(-7.92956 - 2.22768i) q^{75} +(-5.11610 - 6.09545i) q^{76} +8.94133i q^{77} +(7.30764 + 16.1785i) q^{78} +(4.94012 - 13.5729i) q^{79} +(-2.10338 - 0.370883i) q^{80} +(-7.16568 + 5.44546i) q^{81} +(18.3938 - 6.69478i) q^{82} +(6.05130 + 3.49372i) q^{83} +(1.51566 + 5.94266i) q^{84} +(-0.952717 - 0.799425i) q^{85} +(7.15817 + 6.00642i) q^{86} +(-0.487408 - 1.91104i) q^{87} +(-1.36130 - 0.785948i) q^{88} +(5.32595 - 1.93849i) q^{89} +(2.70245 + 1.05819i) q^{90} +(10.0086 + 1.76478i) q^{91} +(-2.12534 + 5.83933i) q^{92} +(-1.08227 - 2.39606i) q^{93} +11.6443i q^{94} +(-1.07771 + 1.86724i) q^{95} +(-12.9470 - 3.63724i) q^{96} +(-4.49760 - 5.36003i) q^{97} +(-5.95229 - 2.16645i) q^{98} +(10.3771 + 9.14343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−1.49833	+	1.25725i	−1.05948	+	0.889010i	−0.994058	−	0.108847i	$-0.965284\pi$
$2$	−1.49833	+	1.25725i	−1.05948	+	0.889010i	−0.0654227	+	0.997858i	$0.520840\pi$
$3$	1.40671	+	1.01052i	0.812166	+	0.583426i
$3$	1.40671	+	1.01052i	0.812166	+	0.583426i
$4$	0.317026	−	1.79794i	0.158513	−	0.898972i
$5$	−0.487091	+	0.0858872i	−0.217834	+	0.0384099i	−0.281500	−	0.959561i	$-0.590832\pi$
$5$	−0.487091	+	0.0858872i	−0.217834	+	0.0384099i	0.0636661	+	0.997971i	$0.479721\pi$
$6$	−3.37821	+	0.254491i	−1.37915	+	0.103895i
$7$	−0.969730	+	1.67962i	−0.366523	+	0.634837i	−0.989019	−	0.147786i	$-0.952785\pi$
$7$	−0.969730	+	1.67962i	−0.366523	+	0.634837i	0.622496	+	0.782623i	$0.286119\pi$
$8$	−0.170480	−	0.295279i	−0.0602737	−	0.104397i
$9$	0.957685	+	2.84303i	0.319228	+	0.947678i
$10$	0.621842	−	0.741083i	0.196644	−	0.234351i
$11$	3.99257	−	2.30511i	1.20380	−	0.695016i	0.242405	−	0.970175i	$-0.422064\pi$
$11$	3.99257	−	2.30511i	1.20380	−	0.695016i	0.961399	+	0.275159i	$0.0887304\pi$
$12$	2.26283	−	2.20883i	0.653222	−	0.637634i
$13$	−1.79223	−	4.92410i	−0.497074	−	1.36570i	−0.894090	−	0.447887i	$-0.852177\pi$
$13$	−1.79223	−	4.92410i	−0.497074	−	1.36570i	0.397016	−	0.917812i	$-0.370046\pi$
$14$	−0.658727	−	3.73582i	−0.176052	−	0.998441i
$15$	−0.771988	−	0.371398i	−0.199326	−	0.0958945i
$16$	4.05783	+	1.47693i	1.01446	+	0.369232i
$17$	1.61629	+	1.92622i	0.392008	+	0.467177i	0.925566	−	0.378587i	$-0.123590\pi$
$17$	1.61629	+	1.92622i	0.392008	+	0.467177i	−0.533558	+	0.845764i	$0.679145\pi$
$18$	−5.00934	−	3.05576i	−1.18071	−	0.720250i
$19$	2.80139	−	3.33949i	0.642684	−	0.766132i
$19$	2.80139	−	3.33949i	0.642684	−	0.766132i
$20$			0.902990i			0.201915i
$21$	−3.06143	+	1.38281i	−0.668058	+	0.301754i
$22$	−3.08409	+	8.47347i	−0.657531	+	1.80655i
$23$	−3.35200	−	0.591048i	−0.698940	−	0.123242i	−0.187123	−	0.982336i	$-0.559916\pi$
$23$	−3.35200	−	0.591048i	−0.698940	−	0.123242i	−0.511817	+	0.859094i	$0.671027\pi$
$24$	0.0585708	−	0.587647i	0.0119557	−	0.119953i
$25$	−4.46858	+	1.62643i	−0.893716	+	0.325286i
$26$	8.87617	+	5.12466i	1.74076	+	1.00503i
$27$	−1.52576	+	4.96710i	−0.293633	+	0.955918i
$28$	2.71243	+	2.27600i	0.512602	+	0.430124i
$29$	−0.872266	−	0.731918i	−0.161976	−	0.135914i	0.558197	−	0.829708i	$-0.311493\pi$
$29$	−0.872266	−	0.731918i	−0.161976	−	0.135914i	−0.720173	+	0.693794i	$0.755938\pi$
$30$	1.62363	−	0.414105i	0.296434	−	0.0756048i
$31$	−1.31458	−	0.758971i	−0.236105	−	0.136315i	0.377280	−	0.926099i	$-0.376859\pi$
$31$	−1.31458	−	0.758971i	−0.236105	−	0.136315i	−0.613385	+	0.789784i	$0.710193\pi$
$32$	−7.29606	+	2.65555i	−1.28977	+	0.469439i
$33$	7.94576	+	0.791954i	1.38318	+	0.137861i
$34$	−4.84348	−	0.854036i	−0.830650	−	0.146466i
$35$	0.328088	−	0.901415i	0.0554570	−	0.152367i
$36$	5.41522	−	0.820548i	0.902537	−	0.136758i
$37$			3.28109i			0.539408i	0.962943	+	0.269704i	$0.0869259\pi$
$37$			3.28109i			0.539408i	−0.962943	+	0.269704i	$0.913074\pi$
$38$	0.00115627	+	8.52572i	0.000187572	+	1.38305i
$39$	2.45477	−	8.73788i	0.393078	−	1.39918i
$40$	0.108400	+	0.129186i	0.0171395	+	0.0204261i
$41$	−9.40408	−	3.42281i	−1.46867	−	0.534552i	−0.520932	−	0.853598i	$-0.674415\pi$
$41$	−9.40408	−	3.42281i	−1.46867	−	0.534552i	−0.947739	+	0.319046i	$0.896638\pi$
$42$	2.84850	−	5.92089i	0.439533	−	0.913613i
$43$	−0.829591	−	4.70484i	−0.126511	−	0.717482i	−0.980399	−	0.197024i	$-0.936872\pi$
$43$	−0.829591	−	4.70484i	−0.126511	−	0.717482i	0.853887	−	0.520458i	$-0.174239\pi$
$44$	−2.87871	−	7.90919i	−0.433982	−	1.19235i
$45$	−0.710660	−	1.30256i	−0.105939	−	0.194174i
$46$	5.76551	−	3.32872i	0.850078	−	0.490793i
$47$	3.82673	−	4.56052i	0.558186	−	0.665220i	−0.410976	−	0.911646i	$-0.634812\pi$
$47$	3.82673	−	4.56052i	0.558186	−	0.665220i	0.969162	+	0.246426i	$0.0792563\pi$
$48$	4.21573	+	6.17815i	0.608489	+	0.891739i
$49$	1.61925	+	2.80462i	0.231321	+	0.400660i
$50$	4.65059	−	8.05506i	0.657693	−	1.13916i
$51$	0.327167	+	4.34294i	0.0458125	+	0.608133i
$52$	−9.42143	+	1.66125i	−1.30652	+	0.230374i
$53$	−1.71646	+	9.73455i	−0.235774	+	1.33714i	0.605202	+	0.796072i	$0.293092\pi$
$53$	−1.71646	+	9.73455i	−0.235774	+	1.33714i	−0.840977	+	0.541071i	$0.818019\pi$
$54$	−3.95878	−	9.36063i	−0.538722	−	1.27382i
$55$	−1.74676	+	1.46571i	−0.235533	+	0.197636i
$56$	0.661277			0.0883668
$57$	7.31539	−	1.86683i	0.968947	−	0.247268i
$58$	2.22715			0.292439
$59$	0.172251	−	0.144536i	0.0224252	−	0.0188170i	−0.631506	−	0.775371i	$-0.717563\pi$
$59$	0.172251	−	0.144536i	0.0224252	−	0.0188170i	0.653931	+	0.756554i	$0.273119\pi$
$60$	−0.912492	+	1.27025i	−0.117802	+	0.163988i
$61$	−1.90402	+	10.7982i	−0.243785	+	1.38257i	0.579513	+	0.814963i	$0.303243\pi$
$61$	−1.90402	+	10.7982i	−0.243785	+	1.38257i	−0.823298	+	0.567610i	$0.807868\pi$
$62$	2.92389	−	0.515560i	0.371334	−	0.0654762i
$63$	−5.70391	−	1.14843i	−0.718626	−	0.144688i
$64$	3.27498	−	5.67243i	0.409372	−	0.709054i
$65$	1.29589	+	2.24455i	0.160736	+	0.278402i
$66$	−12.9011	+	8.80320i	−1.58801	+	1.08360i
$67$	0.266197	−	0.317241i	0.0325211	−	0.0387572i	−0.749539	−	0.661960i	$-0.769725\pi$
$67$	0.266197	−	0.317241i	0.0325211	−	0.0387572i	0.782060	+	0.623203i	$0.214169\pi$
$68$	3.97564	−	2.29534i	0.482117	−	0.278350i
$69$	−4.11804	−	4.21871i	−0.495753	−	0.507873i
$70$	0.641719	+	1.76311i	0.0767001	+	0.210732i
$71$	−0.540928	−	3.06775i	−0.0641963	−	0.364075i	−0.999935	−	0.0113819i	$-0.996377\pi$
$71$	−0.540928	−	3.06775i	−0.0641963	−	0.364075i	0.935739	−	0.352694i	$-0.114734\pi$
$72$	0.676224	−	0.767464i	0.0796937	−	0.0904465i
$73$	−0.118214	−	0.0430264i	−0.0138359	−	0.00503586i	0.335093	−	0.942185i	$-0.391232\pi$
$73$	−0.118214	−	0.0430264i	−0.0138359	−	0.00503586i	−0.348929	+	0.937149i	$0.613455\pi$
$74$	−4.12516	−	4.91617i	−0.479540	−	0.571493i
$75$	−7.92956	−	2.22768i	−0.915627	−	0.257231i
$76$	−5.11610	−	6.09545i	−0.586857	−	0.699196i
$77$			8.94133i			1.01896i
$78$	7.30764	+	16.1785i	0.827427	+	1.83186i
$79$	4.94012	−	13.5729i	0.555807	−	1.52707i	−0.269854	−	0.962901i	$-0.586975\pi$
$79$	4.94012	−	13.5729i	0.555807	−	1.52707i	0.825661	−	0.564167i	$-0.190802\pi$
$80$	−2.10338	−	0.370883i	−0.235165	−	0.0414660i
$81$	−7.16568	+	5.44546i	−0.796187	+	0.605051i
$82$	18.3938	−	6.69478i	2.03125	−	0.739315i
$83$	6.05130	+	3.49372i	0.664217	+	0.383486i	0.793882	−	0.608072i	$-0.208057\pi$
$83$	6.05130	+	3.49372i	0.664217	+	0.383486i	−0.129665	+	0.991558i	$0.541390\pi$
$84$	1.51566	+	5.94266i	0.165372	+	0.648397i
$85$	−0.952717	−	0.799425i	−0.103337	−	0.0867098i
$86$	7.15817	+	6.00642i	0.771885	+	0.647689i
$87$	−0.487408	−	1.91104i	−0.0522556	−	0.204885i
$88$	−1.36130	−	0.785948i	−0.145115	−	0.0837824i
$89$	5.32595	−	1.93849i	0.564549	−	0.205479i	−0.0439498	−	0.999034i	$-0.513994\pi$
$89$	5.32595	−	1.93849i	0.564549	−	0.205479i	0.608499	+	0.793555i	$0.291772\pi$
$90$	2.70245	+	1.05819i	0.284863	+	0.111543i
$91$	10.0086	+	1.76478i	1.04919	+	0.185000i
$92$	−2.12534	+	5.83933i	−0.221582	+	0.608792i
$93$	−1.08227	−	2.39606i	−0.112227	−	0.248460i
$94$			11.6443i			1.20102i
$95$	−1.07771	+	1.86724i	−0.110571	+	0.191575i
$96$	−12.9470	−	3.63724i	−1.32139	−	0.371224i
$97$	−4.49760	−	5.36003i	−0.456662	−	0.544229i	0.487754	−	0.872981i	$-0.337816\pi$
$97$	−4.49760	−	5.36003i	−0.456662	−	0.544229i	−0.944416	+	0.328752i	$0.893372\pi$
$98$	−5.95229	−	2.16645i	−0.601272	−	0.218845i
$99$	10.3771	+	9.14343i	1.04294	+	0.918949i
$100$	1.50757	+	8.54988i	0.150757	+	0.854988i
$101$	−3.72167	−	10.2252i	−0.370320	−	1.01745i	−0.975238	−	0.221158i	$-0.929016\pi$
$101$	−3.72167	−	10.2252i	−0.370320	−	1.01745i	0.604918	−	0.796288i	$-0.293206\pi$
$102$	−5.95036	−	6.09583i	−0.589174	−	0.603578i
$103$	−2.06571	+	1.19264i	−0.203540	+	0.117514i	−0.598306	−	0.801268i	$-0.704159\pi$
$103$	−2.06571	+	1.19264i	−0.203540	+	0.117514i	0.394766	+	0.918782i	$0.370826\pi$
$104$	−1.14845	+	1.36867i	−0.112614	+	0.134209i
$105$	1.37243	−	0.936492i	0.133935	−	0.0913922i
$106$	−9.66693	−	16.7436i	−0.938935	−	1.62628i
$107$	−4.30693	+	7.45983i	−0.416367	+	0.721169i	−0.995571	−	0.0940139i	$-0.970030\pi$
$107$	−4.30693	+	7.45983i	−0.416367	+	0.721169i	0.579204	+	0.815183i	$0.303364\pi$
$108$	8.44685	+	4.31794i	0.812799	+	0.415494i
$109$	−4.49188	+	0.792039i	−0.430244	+	0.0758636i	−0.384576	−	0.923093i	$-0.625652\pi$
$109$	−4.49188	+	0.792039i	−0.430244	+	0.0758636i	−0.0456672	+	0.998957i	$0.514541\pi$
$110$	0.774469	−	4.39223i	0.0738428	−	0.418783i
$111$	−3.31562	+	4.61556i	−0.314705	+	0.438089i
$112$	−6.41568	+	5.38339i	−0.606225	+	0.508683i
$113$	8.90791			0.837985			0.418993	−	0.907990i	$-0.362383\pi$
$113$	8.90791			0.837985			0.418993	+	0.907990i	$0.362383\pi$
$114$	−8.61381	+	11.9944i	−0.806758	+	1.12338i
$115$	1.68349			0.156986
$116$	−1.59248	+	1.33625i	−0.147858	+	0.124067i
$117$	12.2830	−	9.81109i	1.13556	−	0.907036i
$118$	−0.0763718	+	0.433126i	−0.00703059	+	0.0398725i
$119$	−4.80268	+	0.846843i	−0.440261	+	0.0776299i
$120$	0.0219421	+	0.291268i	0.00200303	+	0.0265890i
$121$	5.12705	−	8.88031i	0.466096	−	0.807301i
$122$	−10.7232	−	18.5732i	−0.970836	−	1.68154i
$123$	−9.77002	−	14.3180i	−0.880933	−	1.29101i
$124$	−1.78134	+	2.12292i	−0.159969	+	0.190644i
$125$	4.17862	−	2.41253i	0.373747	−	0.215783i
$126$	9.99022	−	5.45052i	0.890000	−	0.485571i
$127$	2.91821	+	8.01772i	0.258949	+	0.711458i	0.999233	+	0.0391627i	$0.0124691\pi$
$127$	2.91821	+	8.01772i	0.258949	+	0.711458i	−0.740283	+	0.672295i	$0.765309\pi$
$128$	−0.471857	−	2.67603i	−0.0417066	−	0.236530i
$129$	3.58736	−	7.45669i	0.315849	−	0.656525i
$130$	−4.76364	−	1.73382i	−0.417799	−	0.152066i
$131$	9.62927	+	11.4757i	0.841313	+	1.00264i	0.999883	+	0.0152905i	$0.00486732\pi$
$131$	9.62927	+	11.4757i	0.841313	+	1.00264i	−0.158570	+	0.987348i	$0.550688\pi$
$132$	3.94290	−	14.0350i	0.343185	−	1.22159i
$133$	2.89248	+	7.94368i	0.250810	+	0.688805i
$134$			0.810009i			0.0699741i
$135$	0.316575	−	2.55047i	0.0272465	−	0.219509i
$136$	0.293228	−	0.805638i	0.0251441	−	0.0690829i
$137$	−1.81606	−	0.320220i	−0.155157	−	0.0273583i	0.0955303	−	0.995427i	$-0.469545\pi$
$137$	−1.81606	−	0.320220i	−0.155157	−	0.0273583i	−0.250687	+	0.968068i	$0.580656\pi$
$138$	11.4742	+	1.14363i	0.976746	+	0.0973522i
$139$	3.82337	−	1.39159i	0.324294	−	0.118033i	−0.174743	−	0.984614i	$-0.555909\pi$
$139$	3.82337	−	1.39159i	0.324294	−	0.118033i	0.499037	+	0.866581i	$0.333687\pi$
$140$	−1.51668	−	0.875656i	−0.128183	−	0.0740064i
$141$	9.99162	−	2.54834i	0.841446	−	0.214609i
$142$	4.66743	+	3.91643i	0.391682	+	0.328660i
$143$	−18.5062	−	15.5285i	−1.54756	−	1.29856i
$144$	−0.312837	+	12.9510i	−0.0260698	+	1.07925i
$145$	0.487735	+	0.281594i	0.0405042	+	0.0233851i
$146$	0.231219	−	0.0841568i	0.0191358	−	0.00696486i
$147$	−0.556317	+	5.58159i	−0.0458842	+	0.460362i
$148$	5.89922	+	1.04019i	0.484913	+	0.0855032i
$149$	−1.40291	+	3.85446i	−0.114931	+	0.315770i	−0.983799	−	0.179273i	$-0.942625\pi$
$149$	−1.40291	+	3.85446i	−0.114931	+	0.315770i	0.868869	+	0.495043i	$0.164848\pi$
$150$	14.6819	−	6.63163i	1.19877	−	0.541470i
$151$			21.1107i			1.71796i	0.512006	+	0.858982i	$0.328902\pi$
$151$			21.1107i			1.71796i	−0.512006	+	0.858982i	$0.671098\pi$
$152$	−1.46366	−	0.257879i	−0.118719	−	0.0209167i
$153$	−3.92841	+	6.43988i	−0.317593	+	0.520633i
$154$	−11.2415	−	13.3971i	−0.905865	−	1.07957i
$155$	0.705503	+	0.256782i	0.0566674	+	0.0206252i
$156$	−14.9320	−	7.18367i	−1.19552	−	0.575154i
$157$	−1.07553	−	6.09962i	−0.0858364	−	0.486803i	−0.997173	−	0.0751405i	$-0.976059\pi$
$157$	−1.07553	−	6.09962i	−0.0858364	−	0.486803i	0.911337	−	0.411662i	$-0.135052\pi$
$158$	9.66256	+	26.5477i	0.768712	+	2.11202i
$159$	−12.2516	+	11.9592i	−0.971612	+	0.948425i
$160$	3.32576	−	1.92013i	0.262925	−	0.151800i
$161$	4.24327	−	5.05693i	0.334417	−	0.398542i
$162$	3.89026	−	17.1682i	0.305648	−	1.34886i
$163$	−0.853080	−	1.47758i	−0.0668184	−	0.115733i	0.830681	−	0.556749i	$-0.187951\pi$
$163$	−0.853080	−	1.47758i	−0.0668184	−	0.115733i	−0.897499	+	0.441016i	$0.854618\pi$
$164$	−9.13535	+	15.8229i	−0.713351	+	1.23556i
$165$	−3.93832	+	0.296686i	−0.306598	+	0.0230970i
$166$	−13.4593	+	2.37325i	−1.04465	+	0.184200i
$167$	0.922825	−	5.23360i	0.0714104	−	0.404988i	−0.928060	−	0.372432i	$-0.878524\pi$
$167$	0.922825	−	5.23360i	0.0714104	−	0.404988i	0.999470	−	0.0325564i	$-0.0103649\pi$
$168$	0.930227	+	0.668236i	0.0717685	+	0.0515555i
$169$	−11.0761	+	9.29394i	−0.852007	+	0.714919i
$170$	2.43256			0.186569
$171$	12.1771	+	4.76628i	0.931209	+	0.364486i
$172$	−8.72204			−0.665049
$173$	8.83296	−	7.41174i	0.671558	−	0.563504i	−0.241968	−	0.970284i	$-0.577793\pi$
$173$	8.83296	−	7.41174i	0.671558	−	0.563504i	0.913526	+	0.406780i	$0.133349\pi$
$174$	3.13296	+	2.25059i	0.237509	+	0.170616i
$175$	1.60153	−	9.08272i	0.121064	−	0.686589i
$176$	19.6056	−	3.45700i	1.47783	−	0.260581i
$177$	0.388365	−	0.0292567i	0.0291913	−	0.00219907i
$178$	−5.54288	+	9.60055i	−0.415456	+	0.719591i
$179$	8.87880	+	15.3785i	0.663633	+	1.14945i	0.979654	+	0.200694i	$0.0643196\pi$
$179$	8.87880	+	15.3785i	0.663633	+	1.14945i	−0.316021	+	0.948752i	$0.602347\pi$
$180$	−2.56723	+	0.864780i	−0.191350	+	0.0644569i
$181$	−7.50836	+	8.94811i	−0.558092	+	0.665108i	−0.969142	−	0.246505i	$-0.920718\pi$
$181$	−7.50836	+	8.94811i	−0.558092	+	0.665108i	0.411050	+	0.911613i	$0.365162\pi$
$182$	−17.2150	+	9.93907i	−1.27606	+	0.736733i
$183$	−13.5903	+	13.2660i	−1.00462	+	0.980649i
$184$	0.396924	+	1.09054i	0.0292616	+	0.0803956i
$185$	−0.281804	−	1.59819i	−0.0207186	−	0.117501i
$186$	4.63406	+	2.22941i	0.339786	+	0.163468i
$187$	10.8933	+	3.96483i	0.796596	+	0.289937i
$188$	−6.98638	−	8.32605i	−0.509534	−	0.607239i
$189$	−6.86326	−	7.37944i	−0.499229	−	0.536776i
$190$	−0.732814	−	4.15270i	−0.0531639	−	0.301268i
$191$		−	2.85848i		−	0.206833i	−0.994638	−	0.103416i	$-0.967023\pi$
$191$		−	2.85848i		−	0.206833i	0.994638	−	0.103416i	$-0.0329774\pi$
$192$	10.3391	−	4.67004i	0.746159	−	0.337031i
$193$	−2.56804	+	7.05562i	−0.184851	+	0.507875i	−0.997157	−	0.0753578i	$-0.975990\pi$
$193$	−2.56804	+	7.05562i	−0.184851	+	0.507875i	0.812305	+	0.583232i	$0.198212\pi$
$194$	13.4778	+	2.37650i	0.967650	+	0.170623i
$195$	−0.445223	+	4.46697i	−0.0318831	+	0.319887i
$196$	5.55590	−	2.02218i	0.396850	−	0.144441i
$197$	−13.9117	−	8.03191i	−0.991165	−	0.572250i	−0.0855430	−	0.996334i	$-0.527263\pi$
$197$	−13.9117	−	8.03191i	−0.991165	−	0.572250i	−0.905622	+	0.424085i	$0.860596\pi$
$198$	−27.0440	−	0.653260i	−1.92193	−	0.0464252i
$199$	4.85208	+	4.07138i	0.343955	+	0.288612i	0.798357	−	0.602184i	$-0.205703\pi$
$199$	4.85208	+	4.07138i	0.343955	+	0.288612i	−0.454402	+	0.890797i	$0.650147\pi$
$200$	1.24205	+	1.04221i	0.0878265	+	0.0736952i
$201$	0.695042	−	0.177269i	0.0490245	−	0.0125036i
$202$	18.4319	+	10.6417i	1.29687	+	0.748746i
$203$	2.07521	−	0.755313i	0.145651	−	0.0530126i
$204$	7.91208	+	0.788596i	0.553956	+	0.0552128i
$205$	4.87462	+	0.859526i	0.340458	+	0.0600319i
$206$	1.59567	−	4.38407i	0.111176	−	0.305453i
$207$	−1.52979	−	10.0959i	−0.106328	−	0.701713i
$208$		−	22.6281i		−	1.56898i
$209$	3.48686	−	19.7906i	0.241191	−	1.36895i
$210$	−0.878948	+	3.12866i	−0.0606532	+	0.215898i
$211$	−7.05933	−	8.41298i	−0.485984	−	0.579174i	0.466207	−	0.884676i	$-0.345620\pi$
$211$	−7.05933	−	8.41298i	−0.485984	−	0.579174i	−0.952191	+	0.305502i	$0.901176\pi$
$212$	16.9580	+	6.17221i	1.16468	+	0.423909i
$213$	2.33911	−	4.86207i	0.160273	−	0.333144i
$214$	−2.92565	−	16.5922i	−0.199994	−	1.13422i
$215$	0.808172	+	2.22043i	0.0551168	+	0.151432i
$216$	1.72679	−	0.396262i	0.117493	−	0.0269622i
$217$	2.54957	−	1.47199i	0.173076	−	0.0999254i
$218$	5.73453	−	6.83415i	0.388392	−	0.462867i
$219$	−0.122814	−	0.179984i	−0.00829900	−	0.0121622i
$220$	2.08149	+	3.60525i	0.140334	+	0.243066i
$221$	6.58814	−	11.4110i	0.443166	−	0.767586i
$222$	−0.835007	−	11.0842i	−0.0560420	−	0.743923i
$223$	23.0897	−	4.07134i	1.54620	−	0.272637i	0.665532	−	0.746369i	$-0.268205\pi$
$223$	23.0897	−	4.07134i	1.54620	−	0.272637i	0.880669	+	0.473732i	$0.157093\pi$
$224$	2.61489	−	14.8298i	0.174715	−	0.990856i
$225$	−8.90349	−	11.1467i	−0.593566	−	0.743115i
$226$	−13.3470	+	11.1995i	−0.887830	+	0.744978i
$227$	−0.844414			−0.0560457			−0.0280229	−	0.999607i	$-0.508921\pi$
$227$	−0.844414			−0.0560457			−0.0280229	+	0.999607i	$0.508921\pi$
$228$	−1.03729	−	13.7445i	−0.0686962	−	0.910251i
$229$	6.53705			0.431981			0.215990	−	0.976395i	$-0.430702\pi$
$229$	6.53705			0.431981			0.215990	+	0.976395i	$0.430702\pi$
$230$	−2.52243	+	2.11657i	−0.166324	+	0.139563i
$231$	−9.03542	+	12.5779i	−0.594487	+	0.827564i
$232$	−0.0674167	+	0.382339i	−0.00442613	+	0.0251018i
$233$	−26.4558	+	4.66487i	−1.73318	+	0.305606i	−0.949081	−	0.315033i	$-0.897984\pi$
$233$	−26.4558	+	4.66487i	−1.73318	+	0.305606i	−0.784096	+	0.620639i	$0.786873\pi$
$234$	−6.06901	+	30.1431i	−0.396743	+	1.97051i
$235$	−1.47227	+	2.55005i	−0.0960406	+	0.166347i
$236$	−0.205259	−	0.355519i	−0.0133612	−	0.0231423i
$237$	20.6650	−	14.1010i	1.34234	−	0.915961i
$238$	6.13132	−	7.30703i	0.397435	−	0.473644i
$239$	−19.6545	+	11.3476i	−1.27135	+	0.734012i	−0.975241	−	0.221143i	$-0.929021\pi$
$239$	−19.6545	+	11.3476i	−1.27135	+	0.734012i	−0.296105	+	0.955155i	$0.595688\pi$
$240$	−2.58407	−	2.64724i	−0.166801	−	0.170879i
$241$	−8.49003	−	23.3262i	−0.546891	−	1.50257i	−0.837885	−	0.545846i	$-0.816208\pi$
$241$	−8.49003	−	23.3262i	−0.546891	−	1.50257i	0.290994	−	0.956725i	$-0.406014\pi$
$242$	3.48275	+	19.7517i	0.223880	+	1.26968i
$243$	−15.5828	+	0.419115i	−0.999638	+	0.0268862i
$244$	18.8110	+	6.84664i	1.20425	+	0.438312i
$245$	−1.02960	−	1.22703i	−0.0657789	−	0.0783922i
$246$	32.6400	+	9.16969i	2.08105	+	0.584638i
$247$	−21.4647	−	7.80922i	−1.36577	−	0.496889i
$248$			0.517556i			0.0328649i
$249$	4.98196	+	11.0296i	0.315719	+	0.698975i
$250$	−3.22781	+	8.86833i	−0.204145	+	0.560883i
$251$	−15.8837	−	2.80072i	−1.00257	−	0.176780i	−0.351815	−	0.936070i	$-0.614435\pi$
$251$	−15.8837	−	2.80072i	−1.00257	−	0.176780i	−0.650753	+	0.759290i	$0.725547\pi$
$252$	−3.87309	+	9.89123i	−0.243982	+	0.623089i
$253$	−14.7455	+	5.36693i	−0.927042	+	0.337416i
$254$	−14.4527	−	8.34429i	−0.906845	−	0.523567i
$255$	−0.532363	−	2.08730i	−0.0333378	−	0.130712i
$256$	14.1066	+	11.8368i	0.881660	+	0.739801i
$257$	10.9469	+	9.18557i	0.682851	+	0.572980i	0.916838	−	0.399260i	$-0.130733\pi$
$257$	10.9469	+	9.18557i	0.682851	+	0.572980i	−0.233987	+	0.972240i	$0.575177\pi$
$258$	3.99987	+	15.6828i	0.249021	+	0.976369i
$259$	−5.51099	−	3.18177i	−0.342436	−	0.197706i
$260$	4.44641	−	1.61836i	0.275755	−	0.100366i
$261$	1.24551	−	3.18083i	0.0770952	−	0.196888i
$262$	−28.8557	−	5.08804i	−1.78271	−	0.314340i
$263$	4.39828	−	12.0842i	0.271209	−	0.745141i	−0.727073	−	0.686560i	$-0.759120\pi$
$263$	4.39828	−	12.0842i	0.271209	−	0.745141i	0.998283	−	0.0585816i	$-0.0186578\pi$
$264$	−1.12074	−	2.48123i	−0.0689770	−	0.152709i
$265$		−	4.88903i		−	0.300331i
$266$	−14.3211	−	8.26570i	−0.878083	−	0.506803i
$267$	9.45097	+	2.65510i	0.578390	+	0.162489i
$268$	−0.485990	−	0.579180i	−0.0296866	−	0.0353791i
$269$	26.5458	+	9.66190i	1.61853	+	0.589096i	0.983101	−	0.183064i	$-0.0586015\pi$
$269$	26.5458	+	9.66190i	1.61853	+	0.589096i	0.635428	+	0.772160i	$0.280824\pi$
$270$	2.73224	+	4.21947i	0.166279	+	0.256789i
$271$	−0.00607291	−	0.0344412i	−0.000368903	−	0.00209215i	0.984623	−	0.174694i	$-0.0558937\pi$
$271$	−0.00607291	−	0.0344412i	−0.000368903	−	0.00209215i	−0.984992	+	0.172602i	$0.944783\pi$
$272$	3.71374	+	10.2034i	0.225179	+	0.618673i
$273$	12.2959	+	12.5965i	0.744179	+	0.762373i
$274$	3.12366	−	1.80345i	0.188707	−	0.108950i
$275$	−14.0920	+	16.7942i	−0.849780	+	1.01273i
$276$	−8.89053	+	6.06656i	−0.535147	+	0.365164i
$277$	6.22597	+	10.7837i	0.374082	+	0.647929i	0.990189	−	0.139733i	$-0.0446245\pi$
$277$	6.22597	+	10.7837i	0.374082	+	0.647929i	−0.616107	+	0.787662i	$0.711291\pi$
$278$	−3.97910	+	6.89201i	−0.238651	+	0.413355i
$279$	0.898830	−	4.46424i	0.0538115	−	0.267267i
$280$	−0.322102	+	0.0567952i	−0.0192493	+	0.00339416i
$281$	−5.22472	+	29.6308i	−0.311680	+	1.76763i	0.278579	+	0.960413i	$0.410137\pi$
$281$	−5.22472	+	29.6308i	−0.311680	+	1.76763i	−0.590259	+	0.807214i	$0.700974\pi$
$282$	−11.7669	+	16.3802i	−0.700707	+	0.975429i
$283$	21.0118	−	17.6310i	1.24902	−	1.04805i	0.252259	−	0.967660i	$-0.418827\pi$
$283$	21.0118	−	17.6310i	1.24902	−	1.04805i	0.996763	−	0.0803941i	$-0.0256179\pi$
$284$	−5.68714			−0.337469
$285$	−3.40292	+	1.53761i	−0.201572	+	0.0910804i
$286$	47.2516			2.79405
$287$	14.8684	−	12.4761i	0.877656	−	0.736441i
$288$	−14.5371	−	18.1998i	−0.856609	−	1.07243i
$289$	1.85409	−	10.5151i	0.109064	−	0.618534i
$290$	−1.08482	+	0.191284i	−0.0637030	+	0.0112326i
$291$	−0.910397	−	12.0850i	−0.0533684	−	0.708433i
$292$	−0.114836	+	0.198902i	−0.00672026	+	0.0116398i
$293$	−4.44167	−	7.69320i	−0.259485	−	0.449442i	0.706619	−	0.707594i	$-0.250220\pi$
$293$	−4.44167	−	7.69320i	−0.259485	−	0.449442i	−0.966104	+	0.258153i	$0.916886\pi$
$294$	−6.18391	−	9.06251i	−0.360653	−	0.528536i
$295$	−0.0714881	+	0.0851963i	−0.00416220	+	0.00496032i
$296$	0.968839	−	0.559360i	0.0563126	−	0.0325121i
$297$	5.35798	+	23.3485i	0.310902	+	1.35482i
$298$	−2.74400	−	7.53907i	−0.158956	−	0.436727i
$299$	3.09716	+	17.5649i	0.179113	+	1.01580i
$300$	−6.51913	+	13.5507i	−0.376382	+	0.782348i
$301$	8.70683	+	3.16903i	0.501853	+	0.182660i
$302$	−26.5414	−	31.6308i	−1.52729	−	1.82015i
$303$	5.09748	−	18.1448i	0.292843	−	1.04239i
$304$	16.2998	−	9.41363i	0.934856	−	0.539908i
$305$		−	5.42325i		−	0.310535i
$306$	−2.21047	−	14.5881i	−0.126364	−	0.833945i
$307$	−7.84228	+	21.5465i	−0.447582	+	1.22972i	0.486820	+	0.873503i	$0.338157\pi$
$307$	−7.84228	+	21.5465i	−0.447582	+	1.22972i	−0.934402	+	0.356220i	$0.884065\pi$
$308$	16.0760	+	2.83463i	0.916015	+	0.161518i
$309$	−4.11104	−	0.409747i	−0.233869	−	0.0233097i
$310$	−1.37992	+	0.502249i	−0.0783741	+	0.0285258i
$311$	−12.5985	−	7.27375i	−0.714396	−	0.412457i	0.0982907	−	0.995158i	$-0.468662\pi$
$311$	−12.5985	−	7.27375i	−0.714396	−	0.412457i	−0.812687	+	0.582701i	$0.801996\pi$
$312$	−2.99860	+	0.764788i	−0.169763	+	0.0432976i
$313$	−13.4333	−	11.2718i	−0.759292	−	0.637122i	0.178650	−	0.983913i	$-0.442827\pi$
$313$	−13.4333	−	11.2718i	−0.759292	−	0.637122i	−0.937943	+	0.346791i	$0.887271\pi$
$314$	9.28025	+	7.78705i	0.523715	+	0.439449i
$315$	2.87696	+	0.0694943i	0.162098	+	0.00391556i
$316$	−22.8371	−	13.1850i	−1.28469	−	0.741715i
$317$	16.5955	−	6.04028i	0.932098	−	0.339256i	0.169057	−	0.985606i	$-0.445928\pi$
$317$	16.5955	−	6.04028i	0.932098	−	0.339256i	0.763041	+	0.646351i	$0.223706\pi$
$318$	3.32121	−	33.3221i	0.186244	−	1.86861i
$319$	−5.16973	−	0.911563i	−0.289449	−	0.0510377i
$320$	−1.10802	+	3.04427i	−0.0619403	+	0.170180i
$321$	−13.5970	+	6.14158i	−0.758908	+	0.342790i
$322$			12.9118i			0.719548i
$323$	10.9605	−	0.00148648i	0.609856	−	8.27097e-5i
$324$	7.51892	+	14.6098i	0.417718	+	0.811658i
$325$	16.0174	+	19.0888i	0.888486	+	1.05886i
$326$	3.13588	+	1.14137i	0.173681	+	0.0632146i
$327$	−7.11916	−	3.42497i	−0.393690	−	0.189401i
$328$	0.592520	+	3.36035i	0.0327165	+	0.185544i
$329$	3.94905	+	10.8499i	0.217718	+	0.598176i
$330$	5.52791	−	5.39599i	0.304302	−	0.297040i
$331$	−3.69737	+	2.13468i	−0.203226	+	0.117332i	−0.598159	−	0.801377i	$-0.704101\pi$
$331$	−3.69737	+	2.13468i	−0.203226	+	0.117332i	0.394933	+	0.918710i	$0.370768\pi$
$332$	8.19993	−	9.77230i	0.450030	−	0.536325i
$333$	−9.32826	+	3.14225i	−0.511185	+	0.172194i
$334$	5.19725	+	9.00190i	0.284381	+	0.492562i
$335$	−0.102415	+	0.177388i	−0.00559553	+	0.00969174i
$336$	−14.4651	+	1.08970i	−0.789134	+	0.0594479i
$337$	−20.0909	+	3.54257i	−1.09442	+	0.192976i	−0.691585	−	0.722295i	$-0.743087\pi$
$337$	−20.0909	+	3.54257i	−1.09442	+	0.192976i	−0.402837	+	0.915272i	$0.631976\pi$
$338$	4.91085	−	27.8508i	0.267115	−	1.51489i
$339$	12.5309	+	9.00165i	0.680583	+	0.488902i
$340$	−1.73936	+	1.45949i	−0.0943299	+	0.0791521i
$341$	−6.99804			−0.378965
$342$	−24.2378	+	8.16824i	−1.31063	+	0.441688i
$343$	−19.8571			−1.07219
$344$	−1.24781	+	1.04704i	−0.0672777	+	0.0564527i
$345$	2.36819	+	1.70121i	0.127499	+	0.0915899i
$346$	−3.91631	+	22.2105i	−0.210542	+	1.19404i
$347$	26.1493	−	4.61083i	1.40377	−	0.247522i	0.580078	−	0.814561i	$-0.303022\pi$
$347$	26.1493	−	4.61083i	1.40377	−	0.247522i	0.823691	+	0.567039i	$0.191911\pi$
$348$	−3.59047	+	0.270481i	−0.192469	+	0.0144993i
$349$	−1.37375	+	2.37941i	−0.0735352	+	0.127367i	−0.900448	−	0.434963i	$-0.856761\pi$
$349$	−1.37375	+	2.37941i	−0.0735352	+	0.127367i	0.826913	+	0.562330i	$0.190095\pi$
$350$	9.01963	+	15.6225i	0.482120	+	0.835056i
$351$	27.1930	−	1.38914i	1.45145	−	0.0741470i
$352$	−23.0087	+	27.4207i	−1.22637	+	1.46153i
$353$	21.0798	−	12.1704i	1.12197	−	0.647767i	0.180063	−	0.983655i	$-0.442370\pi$
$353$	21.0798	−	12.1704i	1.12197	−	0.647767i	0.941902	+	0.335888i	$0.109036\pi$
$354$	−0.545117	+	0.532108i	−0.0289726	+	0.0282812i
$355$	0.526962	+	1.44782i	0.0279682	+	0.0768421i
$356$	−1.79683	−	10.1903i	−0.0952315	−	0.540085i
$357$	−7.61175	−	3.66196i	−0.402857	−	0.193811i
$358$	−32.6381	−	11.8793i	−1.72498	−	0.627840i
$359$	19.5952	+	23.3526i	1.03419	+	1.23251i	0.972132	+	0.234433i	$0.0753234\pi$
$359$	19.5952	+	23.3526i	1.03419	+	1.23251i	0.0620627	+	0.998072i	$0.480232\pi$
$360$	−0.263467	+	0.431903i	−0.0138859	+	0.0227633i
$361$	−3.30439	−	18.7105i	−0.173915	−	0.984761i
$362$		−	22.8471i		−	1.20082i
$363$	16.1861	−	7.31105i	0.849548	−	0.383731i
$364$	6.34597	−	17.4354i	0.332619	−	0.913863i
$365$	0.0612763	+	0.0108047i	0.00320735	+	0.000565542i
$366$	3.68412	−	36.9632i	0.192572	−	1.93210i
$367$	11.0315	−	4.01514i	0.575839	−	0.209588i	−0.0376505	−	0.999291i	$-0.511987\pi$
$367$	11.0315	−	4.01514i	0.575839	−	0.209588i	0.613490	+	0.789703i	$0.289765\pi$
$368$	−12.7289	−	7.34904i	−0.663541	−	0.383095i
$369$	0.725005	−	30.0141i	0.0377423	−	1.56247i
$370$	2.43156	+	2.04032i	0.126411	+	0.106071i
$371$	−14.6858	−	12.3229i	−0.762451	−	0.639772i
$372$	−4.65110	+	1.18625i	−0.241148	+	0.0615043i
$373$	21.0815	+	12.1714i	1.09156	+	0.630212i	0.933991	−	0.357297i	$-0.116302\pi$
$373$	21.0815	+	12.1714i	1.09156	+	0.630212i	0.157567	+	0.987508i	$0.449635\pi$
$374$	−21.3066	+	7.75495i	−1.10174	+	0.400999i
$375$	8.31603	+	0.828858i	0.429438	+	0.0428021i
$376$	−1.99901	−	0.352479i	−0.103091	−	0.0181777i
$377$	−2.04074	+	5.60688i	−0.105103	+	0.288769i
$378$	19.5613	+	2.42803i	1.00612	+	0.124884i
$379$		−	5.14415i		−	0.264237i	−0.991234	−	0.132119i	$-0.957822\pi$
$379$		−	5.14415i		−	0.264237i	0.991234	−	0.132119i	$-0.0421780\pi$
$380$	3.01553	+	2.52963i	0.154693	+	0.129767i
$381$	−3.99701	+	14.2276i	−0.204773	+	0.728900i
$382$	3.59383	+	4.28296i	0.183876	+	0.219135i
$383$	−10.8810	−	3.96036i	−0.555993	−	0.202365i	0.0487143	−	0.998813i	$-0.484488\pi$
$383$	−10.8810	−	3.96036i	−0.555993	−	0.202365i	−0.604707	+	0.796448i	$0.706710\pi$
$384$	2.04043	−	4.24123i	0.104125	−	0.216434i
$385$	−0.767946	−	4.35524i	−0.0391381	−	0.221963i
$386$	−5.02291	−	13.8003i	−0.255659	−	0.702418i
$387$	12.5815	−	6.86431i	0.639556	−	0.348933i
$388$	−11.0629	+	6.38716i	−0.561633	+	0.324259i
$389$	−15.4791	+	18.4473i	−0.784821	+	0.935314i	−0.999141	−	0.0414499i	$-0.986802\pi$
$389$	−15.4791	+	18.4473i	−0.784821	+	0.935314i	0.214319	+	0.976764i	$0.431247\pi$
$390$	−4.94901	−	7.25277i	−0.250603	−	0.367258i
$391$	−4.27932	−	7.41199i	−0.216414	−	0.374841i
$392$	0.552098	−	0.956262i	0.0278852	−	0.0482985i
$393$	1.94914	+	25.8737i	0.0983212	+	1.30515i
$394$	30.9424	−	5.45599i	1.55886	−	0.274869i
$395$	−1.24055	+	7.03551i	−0.0624189	+	0.353995i
$396$	19.7292	−	15.7588i	0.991429	−	0.791908i
$397$	9.61123	−	8.06478i	0.482374	−	0.404760i	−0.368910	−	0.929465i	$-0.620269\pi$
$397$	9.61123	−	8.06478i	0.482374	−	0.404760i	0.851284	+	0.524705i	$0.175825\pi$
$398$	−12.3888			−0.620993
$399$	−3.95838	+	14.0974i	−0.198167	+	0.705753i
$400$	−20.5349			−1.02674
$401$	−16.8863	+	14.1693i	−0.843264	+	0.707583i	−0.958295	−	0.285779i	$-0.907748\pi$
$401$	−16.8863	+	14.1693i	−0.843264	+	0.707583i	0.115031	+	0.993362i	$0.463303\pi$
$402$	−0.818533	+	1.13945i	−0.0408247	+	0.0568306i
$403$	−1.38123	+	7.83334i	−0.0688040	+	0.390207i
$404$	−19.5642	+	3.44970i	−0.973355	+	0.171629i
$405$	3.02264	−	3.26787i	0.150196	−	0.162382i
$406$	−2.15973	+	3.74077i	−0.107186	+	0.185651i
$407$	7.56327	+	13.1000i	0.374898	+	0.649342i
$408$	1.22660	−	0.836988i	0.0607260	−	0.0414371i
$409$	8.66466	−	10.3261i	0.428440	−	0.510595i	−0.508031	−	0.861338i	$-0.669627\pi$
$409$	8.66466	−	10.3261i	0.428440	−	0.510595i	0.936472	+	0.350743i	$0.114071\pi$
$410$	−8.38444	+	4.84076i	−0.414078	+	0.239068i
$411$	−2.23109	−	2.28563i	−0.110051	−	0.112742i
$412$	1.48941	+	4.09212i	0.0733779	+	0.201604i
$413$	0.0757285	+	0.429477i	0.00372635	+	0.0211332i
$414$	14.9852	+	13.2037i	0.736482	+	0.648925i
$415$	−3.24760	−	1.18203i	−0.159418	−	0.0580235i
$416$	26.1524	+	31.1672i	1.28222	+	1.52810i
$417$	6.78463	+	1.90603i	0.332245	+	0.0933389i
$418$	19.6573	+	34.0368i	0.961471	+	1.66480i
$419$		−	35.6982i		−	1.74397i	−0.489530	−	0.871986i	$-0.662832\pi$
$419$		−	35.6982i		−	1.74397i	0.489530	−	0.871986i	$-0.337168\pi$
$420$	−1.24866	−	2.76444i	−0.0609286	−	0.134891i
$421$	0.543107	−	1.49217i	0.0264694	−	0.0727241i	−0.925754	−	0.378126i	$-0.876569\pi$
$421$	0.543107	−	1.49217i	0.0264694	−	0.0727241i	0.952224	+	0.305402i	$0.0987908\pi$
$422$	21.1545	+	3.73010i	1.02978	+	0.181578i
$423$	16.6305	+	6.51198i	0.808603	+	0.316623i
$424$	3.16703	−	1.15271i	0.153805	−	0.0559803i
$425$	−10.3554	−	5.97869i	−0.502310	−	0.290009i
$426$	2.60808	+	10.2258i	0.126362	+	0.495444i
$427$	−16.2906	−	13.6694i	−0.788356	−	0.661509i
$428$	12.0469	+	10.1086i	0.582311	+	0.488617i
$429$	−10.3409	−	40.5451i	−0.499265	−	1.95753i
$430$	−4.00255	−	2.31087i	−0.193020	−	0.111440i
$431$	8.42816	−	3.06760i	0.405970	−	0.147761i	−0.130960	−	0.991388i	$-0.541806\pi$
$431$	8.42816	−	3.06760i	0.405970	−	0.147761i	0.536930	+	0.843627i	$0.319584\pi$
$432$	−13.5273	+	17.9022i	−0.650835	+	0.861320i
$433$	12.5463	+	2.21225i	0.602936	+	0.106314i	0.466780	−	0.884374i	$-0.345414\pi$
$433$	12.5463	+	2.21225i	0.602936	+	0.106314i	0.136156	+	0.990687i	$0.456525\pi$
$434$	−1.96943	+	5.41098i	−0.0945359	+	0.259735i
$435$	0.401546	+	0.888989i	0.0192527	+	0.0426238i
$436$			8.32724i			0.398802i
$437$	−11.3641	+	9.53822i	−0.543617	+	0.456275i
$438$	0.410301	+	0.115268i	0.0196049	+	0.00550770i
$439$	−3.08365	−	3.67495i	−0.147175	−	0.175396i	0.687421	−	0.726259i	$-0.258743\pi$
$439$	−3.08365	−	3.67495i	−0.147175	−	0.175396i	−0.834595	+	0.550864i	$0.814298\pi$
$440$	0.730580	+	0.265910i	0.0348291	+	0.0126767i
$441$	−6.42290	+	7.28952i	−0.305853	+	0.347120i
$442$	4.47525	+	25.3804i	0.212866	+	1.20722i
$443$	−2.89248	−	7.94702i	−0.137426	−	0.377574i	0.851820	−	0.523834i	$-0.175499\pi$
$443$	−2.89248	−	7.94702i	−0.137426	−	0.377574i	−0.989246	+	0.146260i	$0.953277\pi$
$444$	7.24737	+	7.42455i	0.343945	+	0.352354i
$445$	−2.42773	+	1.40165i	−0.115085	+	0.0664445i
$446$	−29.4774	+	35.1298i	−1.39579	+	1.66344i
$447$	−5.86852	+	4.00445i	−0.277571	+	0.189404i
$448$	6.35169	+	11.0014i	0.300089	+	0.519770i
$449$	2.29293	−	3.97148i	0.108210	−	0.187426i	−0.806835	−	0.590777i	$-0.798821\pi$
$449$	2.29293	−	3.97148i	0.108210	−	0.187426i	0.915045	+	0.403351i	$0.132155\pi$
$450$	27.3546	+	5.50758i	1.28951	+	0.259630i
$451$	−45.4363	+	8.01165i	−2.13951	+	0.377254i
$452$	2.82404	−	16.0159i	0.132832	−	0.753325i
$453$	−21.3328	+	29.6967i	−1.00230	+	1.39527i
$454$	1.26521	−	1.06164i	0.0593794	−	0.0498252i
$455$	−5.02666			−0.235654
$456$	−1.79836	−	1.84183i	−0.0842160	−	0.0862515i
$457$	−8.38932			−0.392436			−0.196218	−	0.980560i	$-0.562866\pi$
$457$	−8.38932			−0.392436			−0.196218	+	0.980560i	$0.562866\pi$
$458$	−9.79468	+	8.21871i	−0.457675	+	0.384035i
$459$	−12.0338	+	5.08931i	−0.561689	+	0.237549i
$460$	0.533710	−	3.02682i	0.0248844	−	0.141126i
$461$	−24.7397	+	4.36228i	−1.15224	+	0.203171i	−0.716955	−	0.697120i	$-0.754465\pi$
$461$	−24.7397	+	4.36228i	−1.15224	+	0.203171i	−0.435288	+	0.900291i	$0.643353\pi$
$462$	−2.27548	−	30.2056i	−0.105865	−	1.40529i
$463$	5.36106	−	9.28562i	0.249149	−	0.431539i	−0.714141	−	0.700002i	$-0.753182\pi$
$463$	5.36106	−	9.28562i	0.249149	−	0.431539i	0.963290	+	0.268463i	$0.0865157\pi$
$464$	−2.45852	−	4.25827i	−0.114134	−	0.197685i
$465$	0.732956	+	1.07415i	0.0339900	+	0.0498124i
$466$	33.7747	−	40.2511i	1.56458	−	1.86460i
$467$	2.86340	−	1.65318i	0.132502	−	0.0765002i	−0.432284	−	0.901738i	$-0.642292\pi$
$467$	2.86340	−	1.65318i	0.132502	−	0.0765002i	0.564786	+	0.825237i	$0.308959\pi$
$468$	−13.7458	−	25.1945i	−0.635398	−	1.16462i
$469$	0.274706	+	0.754748i	0.0126847	+	0.0348510i
$470$	−1.00010	−	5.67185i	−0.0461311	−	0.261623i
$471$	4.65085	−	9.66726i	0.214300	−	0.445444i
$472$	−0.0720438	−	0.0262218i	−0.00331608	−	0.00120696i
$473$	−14.1574	−	16.8721i	−0.650956	−	0.775780i
$474$	−13.2346	+	47.1092i	−0.607884	+	2.16380i
$475$	−7.08681	+	19.4791i	−0.325165	+	0.893761i
$476$			8.90342i			0.408088i
$477$	−29.3195	+	4.44267i	−1.34245	+	0.203416i
$478$	15.1823	−	41.7131i	0.694423	−	1.90791i
$479$	−5.99987	−	1.05794i	−0.274141	−	0.0483385i	0.0348874	−	0.999391i	$-0.488893\pi$
$479$	−5.99987	−	1.05794i	−0.274141	−	0.0483385i	−0.309028	+	0.951053i	$0.600004\pi$
$480$	6.61873	+	0.659689i	0.302102	+	0.0301105i
$481$	16.1564	−	5.88046i	0.736669	−	0.268126i
$482$	42.0477	+	24.2763i	1.91522	+	1.10575i
$483$	11.0792	−	2.82573i	0.504122	−	0.128575i
$484$	−14.3409	−	12.0334i	−0.651859	−	0.546974i
$485$	2.65110	+	2.22453i	0.120380	+	0.101011i
$486$	22.8213	−	20.2195i	1.03520	−	0.917174i
$487$	1.88147	+	1.08627i	0.0852575	+	0.0492234i	0.542023	−	0.840364i	$-0.317659\pi$
$487$	1.88147	+	1.08627i	0.0852575	+	0.0492234i	−0.456765	+	0.889587i	$0.650992\pi$
$488$	3.51310	−	1.27866i	0.159030	−	0.0578823i
$489$	0.293088	−	2.94059i	0.0132539	−	0.132978i
$490$	3.08537	+	0.544035i	0.139383	+	0.0245770i
$491$	11.0836	−	30.4521i	0.500198	−	1.37428i	−0.390884	−	0.920440i	$-0.627831\pi$
$491$	11.0836	−	30.4521i	0.500198	−	1.37428i	0.891082	−	0.453842i	$-0.149947\pi$
$492$	−28.8402	+	13.0268i	−1.30022	+	0.587293i
$493$		−	2.86317i		−	0.128951i
$494$	41.9794	−	15.2857i	1.88874	−	0.687736i
$495$	−5.83990	−	3.56242i	−0.262484	−	0.160119i
$496$	−4.21338	−	5.02131i	−0.189186	−	0.225463i
$497$	5.67722	+	2.06634i	0.254658	+	0.0926879i
$498$	−21.3317	−	10.2625i	−0.955895	−	0.459874i
$499$	2.81643	+	15.9728i	0.126081	+	0.715039i	0.980660	+	0.195719i	$0.0627039\pi$
$499$	2.81643	+	15.9728i	0.126081	+	0.715039i	−0.854579	+	0.519321i	$0.826185\pi$
$500$	−3.01285	−	8.27775i	−0.134739	−	0.370192i
$501$	6.58683	−	6.42964i	0.294278	−	0.287255i
$502$	27.3202	−	15.7733i	1.21936	−	0.703998i
$503$	10.3825	−	12.3734i	0.462933	−	0.551702i	−0.483188	−	0.875517i	$-0.660521\pi$
$503$	10.3825	−	12.3734i	0.462933	−	0.551702i	0.946120	+	0.323815i	$0.104966\pi$
$504$	0.633295	+	1.88003i	0.0282092	+	0.0837433i
$505$	2.69100	+	4.66096i	0.119748	+	0.207410i
$506$	15.3461	−	26.5802i	0.682218	−	1.18164i
$507$	−24.9726	+	1.88127i	−1.10907	+	0.0835499i
$508$	15.3406	−	2.70495i	0.680627	−	0.120013i
$509$	4.96536	−	28.1600i	0.220086	−	1.24817i	−0.651774	−	0.758413i	$-0.725975\pi$
$509$	4.96536	−	28.1600i	0.220086	−	1.24817i	0.871860	−	0.489756i	$-0.162914\pi$
$510$	3.42192	+	2.45816i	0.151525	+	0.108849i
$511$	0.186904	−	0.156831i	0.00826813	−	0.00693778i
$512$	−30.5835			−1.35161
$513$	12.3133	+	19.0101i	0.543646	+	0.839315i
$514$	−27.9507			−1.23285
$515$	0.903754	−	0.758339i	0.0398241	−	0.0334164i
$516$	−12.2694	−	8.81383i	−0.540131	−	0.388007i
$517$	4.76598	−	27.0292i	0.209607	−	1.18874i
$518$	12.2576	−	2.16134i	0.538567	−	0.0949639i
$519$	19.9152	−	1.50027i	0.874179	−	0.0658546i
$520$	0.441847	−	0.765301i	0.0193763	−	0.0335607i
$521$	−0.554173	−	0.959856i	−0.0242788	−	0.0420521i	0.853631	−	0.520879i	$-0.174396\pi$
$521$	−0.554173	−	0.959856i	−0.0242788	−	0.0420521i	−0.877910	+	0.478827i	$0.841062\pi$
$522$	2.13291	+	6.33186i	0.0933548	+	0.277138i
$523$	8.07045	−	9.61798i	0.352896	−	0.420565i	−0.560170	−	0.828378i	$-0.689264\pi$
$523$	8.07045	−	9.61798i	0.352896	−	0.420565i	0.913065	+	0.407813i	$0.133708\pi$
$524$	23.6854	−	13.6748i	1.03470	−	0.597386i
$525$	11.4312	−	11.1584i	0.498898	−	0.486993i
$526$	8.60274	+	23.6358i	0.375097	+	1.03057i
$527$	−0.662792	−	3.75888i	−0.0288717	−	0.163739i
$528$	31.0729	+	14.9489i	1.35227	+	0.650569i
$529$	−10.7264	−	3.90408i	−0.466363	−	0.169742i
$530$	6.14673	+	7.32539i	0.266997	+	0.318195i
$531$	0.575883	+	0.351296i	0.0249912	+	0.0152449i
$532$	15.1993	−	2.68217i	0.658972	−	0.116287i
$533$			52.4411i			2.27147i
$534$	−17.4988	+	7.90401i	−0.757248	+	0.342040i
$535$	1.45716	−	4.00352i	0.0629987	−	0.173087i
$536$	−0.139056	−	0.0245193i	−0.00600630	−	0.00105907i
$537$	−3.05044	+	30.6054i	−0.131636	+	1.32072i
$538$	−51.9219	+	18.8980i	−2.23851	+	0.814752i
$539$	12.9299	+	7.46509i	0.556931	+	0.321544i
$540$	−4.48524	−	1.37775i	−0.193014	−	0.0592889i
$541$	19.4785	+	16.3444i	0.837448	+	0.702702i	0.956988	−	0.290127i	$-0.0936975\pi$
$541$	19.4785	+	16.3444i	0.837448	+	0.702702i	−0.119540	+	0.992829i	$0.538142\pi$
$542$	0.0524004	+	0.0439692i	0.00225079	+	0.00188864i
$543$	−19.6044	+	5.00006i	−0.841305	+	0.214573i
$544$	−16.9077	−	9.76167i	−0.724912	−	0.418528i
$545$	2.11992	−	0.771589i	0.0908076	−	0.0330513i
$546$	−34.2602	−	3.41471i	−1.46620	−	0.146136i
$547$	32.5162	+	5.73349i	1.39029	+	0.245146i	0.818149	−	0.575007i	$-0.195001\pi$
$547$	32.5162	+	5.73349i	1.39029	+	0.245146i	0.572144	+	0.820153i	$0.306112\pi$
$548$	−1.15148	+	3.16366i	−0.0491886	+	0.135145i
$549$	−32.5232	+	4.92812i	−1.38806	+	0.210327i
$550$		−	42.8805i		−	1.82843i
$551$	−4.88779	+	0.862533i	−0.208227	+	0.0367451i
$552$	−0.543657	+	1.93518i	−0.0231396	+	0.0823665i
$553$	18.0067	+	21.4596i	0.765723	+	0.912553i
$554$	−22.8864	−	8.32996i	−0.972349	−	0.353906i
$555$	1.21859	−	2.53296i	0.0517263	−	0.107518i
$556$	−1.28990	−	7.31538i	−0.0547039	−	0.310241i
$557$	−12.2432	−	33.6380i	−0.518762	−	1.42529i	−0.871885	−	0.489710i	$-0.837103\pi$
$557$	−12.2432	−	33.6380i	−0.518762	−	1.42529i	0.353123	−	0.935577i	$-0.385120\pi$
$558$	4.26592	+	7.81897i	0.180591	+	0.331003i
$559$	−21.6803	+	12.5171i	−0.916979	+	0.529418i
$560$	2.66265	−	3.17323i	0.112518	−	0.134093i
$561$	11.3172	+	16.5853i	0.477812	+	0.700232i
$562$	−29.4250	−	50.9656i	−1.24122	−	2.14986i
$563$	11.0660	−	19.1668i	0.466375	−	0.807785i	−0.532887	−	0.846186i	$-0.678893\pi$
$563$	11.0660	−	19.1668i	0.466375	−	0.807785i	0.999262	+	0.0384008i	$0.0122264\pi$
$564$	−1.41417	−	18.7723i	−0.0595474	−	0.790455i
$565$	−4.33896	+	0.765075i	−0.182541	+	0.0321870i
$566$	−9.31609	+	52.8342i	−0.391585	+	2.22079i
$567$	−2.19754	−	17.3162i	−0.0922879	−	0.727214i
$568$	−0.813628	+	0.682715i	−0.0341391	+	0.0286461i
$569$	3.68640			0.154542			0.0772710	−	0.997010i	$-0.475379\pi$
$569$	3.68640			0.154542			0.0772710	+	0.997010i	$0.475379\pi$
$570$	3.16554	−	6.58218i	0.132590	−	0.275697i
$571$	−7.83713			−0.327974			−0.163987	−	0.986463i	$-0.552435\pi$
$571$	−7.83713			−0.327974			−0.163987	+	0.986463i	$0.552435\pi$
$572$	−33.7863	+	28.3501i	−1.41268	+	1.18538i
$573$	2.88856	−	4.02107i	0.120672	−	0.167982i
$574$	−6.59228	+	37.3867i	−0.275157	+	1.56049i
$575$	15.9400	−	2.81065i	0.664744	−	0.117212i
$576$	19.2633	+	3.87848i	0.802638	+	0.161603i
$577$	7.58405	−	13.1360i	0.315728	−	0.546857i	−0.663864	−	0.747853i	$-0.731085\pi$
$577$	7.58405	−	13.1360i	0.315728	−	0.546857i	0.979592	+	0.200996i	$0.0644179\pi$
$578$	10.4420	+	18.0861i	0.434331	+	0.752284i
$579$	−10.7424	+	7.33018i	−0.446437	+	0.304632i
$580$	0.660914	−	0.787647i	0.0274430	−	0.0327053i
$581$	−11.7363	+	6.77593i	−0.486902	+	0.281113i
$582$	16.5579	+	16.9627i	0.686347	+	0.703126i
$583$	15.5861	+	42.8224i	0.645510	+	1.77352i
$584$	0.00744828	+	0.0422413i	0.000308212	+	0.00174796i
$585$	−5.14028	+	5.83384i	−0.212524	+	0.241200i
$586$	16.3274	+	5.94268i	0.674478	+	0.245490i
$587$	−4.23083	−	5.04211i	−0.174625	−	0.208110i	0.671632	−	0.740885i	$-0.265594\pi$
$587$	−4.23083	−	5.04211i	−0.174625	−	0.208110i	−0.846257	+	0.532775i	$0.821149\pi$
$588$	9.85901	+	2.76973i	0.406579	+	0.114222i
$589$	−6.21722	+	2.26384i	−0.256176	+	0.0932798i
$590$		−	0.217531i		−	0.00895560i
$591$	−11.4533	−	25.3567i	−0.471126	−	1.04303i
$592$	−4.84594	+	13.3141i	−0.199167	+	0.547207i
$593$	−5.69179	−	1.00362i	−0.233734	−	0.0412136i	0.0555543	−	0.998456i	$-0.482307\pi$
$593$	−5.69179	−	1.00362i	−0.233734	−	0.0412136i	−0.289288	+	0.957242i	$0.593419\pi$
$594$	−37.3830	−	28.2475i	−1.53384	−	1.15901i
$595$	2.26661	−	0.824978i	0.0929219	−	0.0338208i
$596$	6.48535	+	3.74432i	0.265650	+	0.153373i
$597$	2.71126	+	10.6304i	0.110965	+	0.435073i
$598$	−26.7240	−	22.4241i	−1.09283	−	0.916990i
$599$	27.7457	+	23.2814i	1.13366	+	0.951254i	0.999213	−	0.0396667i	$-0.0126296\pi$
$599$	27.7457	+	23.2814i	1.13366	+	0.951254i	0.134447	+	0.990921i	$0.457074\pi$
$600$	0.694039	+	2.72121i	0.0283340	+	0.111093i
$601$	6.07461	+	3.50718i	0.247789	+	0.143061i	0.618751	−	0.785587i	$-0.287639\pi$
$601$	6.07461	+	3.50718i	0.247789	+	0.143061i	−0.370963	+	0.928648i	$0.620972\pi$
$602$	−17.0300	+	6.19841i	−0.694091	+	0.252628i
$603$	1.15686	+	0.452990i	0.0471110	+	0.0184472i
$604$	37.9558	+	6.69264i	1.54440	+	0.272319i
$605$	−1.73463	+	4.76587i	−0.0705229	+	0.193760i
$606$	15.1748	+	33.5957i	0.616433	+	1.36473i
$607$			14.2728i			0.579314i	0.957130	+	0.289657i	$0.0935413\pi$
$607$			14.2728i			0.579314i	−0.957130	+	0.289657i	$0.906459\pi$
$608$	−11.5710	+	31.8043i	−0.469264	+	1.28984i
$609$	3.68248	+	1.03454i	0.149222	+	0.0419215i
$610$	6.81839	+	8.12584i	0.276068	+	0.329006i
$611$	−29.3148	−	10.6697i	−1.18595	−	0.431650i
$612$	10.3331	+	9.10467i	0.417692	+	0.368034i
$613$	3.36609	+	19.0901i	0.135955	+	0.771040i	0.974190	+	0.225730i	$0.0724768\pi$
$613$	3.36609	+	19.0901i	0.135955	+	0.771040i	−0.838235	+	0.545310i	$0.816412\pi$
$614$	−15.3390	−	42.1435i	−0.619031	−	1.70077i
$615$	5.98861	+	6.13502i	0.241484	+	0.247388i
$616$	2.64019	−	1.52431i	0.106376	−	0.0614164i
$617$	−2.77009	+	3.30127i	−0.111520	+	0.132904i	−0.818917	−	0.573913i	$-0.805425\pi$
$617$	−2.77009	+	3.30127i	−0.111520	+	0.132904i	0.707397	+	0.706817i	$0.249869\pi$
$618$	6.67486	−	4.55467i	0.268502	−	0.183216i
$619$	4.18376	+	7.24648i	0.168159	+	0.291261i	0.937773	−	0.347250i	$-0.112884\pi$
$619$	4.18376	+	7.24648i	0.168159	+	0.291261i	−0.769613	+	0.638510i	$0.779551\pi$
$620$	0.685343	−	1.18705i	0.0275240	−	0.0476730i
$621$	8.05015	−	15.7479i	0.323042	−	0.631942i
$622$	28.0217	−	4.94098i	1.12357	−	0.198115i
$623$	−1.90881	+	10.8254i	−0.0764747	+	0.433710i
$624$	22.8663	−	31.8313i	0.915383	−	1.27427i
$625$	16.3859	−	13.7494i	0.655438	−	0.549978i
$626$	34.2990			1.37086
$627$	24.9039	−	24.3162i	0.994567	−	0.971096i
$628$	−11.3077			−0.451228
$629$	−6.32010	+	5.30320i	−0.251999	+	0.211452i
$630$	−4.39801	+	3.51293i	−0.175221	+	0.139959i
$631$	4.18478	−	23.7331i	0.166593	−	0.944799i	−0.780813	−	0.624765i	$-0.785195\pi$
$631$	4.18478	−	23.7331i	0.166593	−	0.944799i	0.947406	−	0.320034i	$-0.103694\pi$
$632$	−4.84998	+	0.855183i	−0.192922	+	0.0340173i
$633$	−1.42894	−	18.9683i	−0.0567952	−	0.753921i
$634$	−17.2715	+	29.9151i	−0.685938	+	1.18808i
$635$	−2.11005	−	3.65472i	−0.0837349	−	0.145033i
$636$	17.6179	+	25.8190i	0.698595	+	1.02379i
$637$	10.9082	−	12.9999i	0.432198	−	0.515073i
$638$	8.89204	−	5.13382i	0.352039	−	0.203250i
$639$	8.20369	−	4.47582i	0.324533	−	0.177061i
$640$	0.459674	+	1.26294i	0.0181702	+	0.0499222i
$641$	0.129228	+	0.732886i	0.00510418	+	0.0289473i	0.987253	−	0.159156i	$-0.0508772\pi$
$641$	0.129228	+	0.732886i	0.00510418	+	0.0289473i	−0.982149	+	0.188103i	$0.939766\pi$
$642$	12.6513	−	26.2969i	0.499305	−	1.03786i
$643$	−36.8973	−	13.4295i	−1.45509	−	0.529608i	−0.511079	−	0.859534i	$-0.670754\pi$
$643$	−36.8973	−	13.4295i	−1.45509	−	0.529608i	−0.944007	+	0.329926i	$0.892976\pi$
$644$	−7.74685	−	9.23234i	−0.305269	−	0.363805i
$645$	−1.10693	+	3.94019i	−0.0435855	+	0.155145i
$646$	−16.4205	+	13.7823i	−0.646057	+	0.542256i
$647$		−	10.0379i		−	0.394633i	−0.980340	−	0.197316i	$-0.936777\pi$
$647$		−	10.0379i		−	0.394633i	0.980340	−	0.197316i	$-0.0632226\pi$
$648$	2.82954	+	1.18754i	0.111155	+	0.0466509i
$649$	0.354553	−	0.974127i	0.0139174	−	0.0382378i
$650$	−47.9988	−	8.46349i	−1.88267	−	0.331965i
$651$	5.07399	+	0.505724i	0.198865	+	0.0198209i
$652$	−2.92705	+	1.06536i	−0.114632	+	0.0417227i
$653$	24.0034	+	13.8584i	0.939327	+	0.542321i	0.889749	−	0.456449i	$-0.150879\pi$
$653$	24.0034	+	13.8584i	0.939327	+	0.542321i	0.0495780	+	0.998770i	$0.484212\pi$
$654$	14.9729	−	3.81881i	0.585487	−	0.149327i
$655$	−5.67595	−	4.76268i	−0.221778	−	0.186093i
$656$	−33.1049	−	27.7783i	−1.29253	−	1.08456i
$657$	0.00911367	−	0.377292i	0.000355558	−	0.0147196i
$658$	−19.5581	−	11.2919i	−0.762453	−	0.440202i
$659$	−37.9399	+	13.8090i	−1.47793	+	0.537922i	−0.950241	−	0.311516i	$-0.899163\pi$
$659$	−37.9399	+	13.8090i	−1.47793	+	0.537922i	−0.527688	+	0.849438i	$0.676941\pi$
$660$	−0.715126	+	7.17494i	−0.0278362	+	0.279284i
$661$	−28.3986	−	5.00744i	−1.10458	−	0.194767i	−0.408517	−	0.912751i	$-0.633954\pi$
$661$	−28.3986	−	5.00744i	−1.10458	−	0.194767i	−0.696060	+	0.717984i	$0.745065\pi$
$662$	2.85607	−	7.84698i	0.111004	−	0.304981i
$663$	20.7987	−	9.39452i	0.807754	−	0.364853i
$664$		−	2.38243i		−	0.0924564i
$665$	−2.09116	−	3.62087i	−0.0810918	−	0.140411i
$666$	10.0262	−	16.4361i	0.388509	−	0.636886i
$667$	2.49124	+	2.96894i	0.0964611	+	0.114958i
$668$	−9.11716	−	3.31838i	−0.352754	−	0.128392i
$669$	36.5948	+	17.6055i	1.41484	+	0.680667i
$670$	−0.0695694	−	0.394548i	−0.00268770	−	0.0152427i
$671$	17.2892	+	47.5017i	0.667442	+	1.83378i
$672$	18.6642	−	18.2188i	0.719988	−	0.702807i
$673$	−16.2655	+	9.39089i	−0.626989	+	0.361992i	−0.779585	−	0.626296i	$-0.784570\pi$
$673$	−16.2655	+	9.39089i	−0.626989	+	0.361992i	0.152596	+	0.988289i	$0.451237\pi$
$674$	25.6490	−	30.5673i	0.987962	−	1.17741i
$675$	−1.26064	−	24.6774i	−0.0485220	−	0.949835i
$676$	13.1986	+	22.8606i	0.507638	+	0.879254i
$677$	5.21572	−	9.03390i	0.200457	−	0.347201i	−0.748219	−	0.663452i	$-0.769091\pi$
$677$	5.21572	−	9.03390i	0.200457	−	0.347201i	0.948676	+	0.316251i	$0.102424\pi$
$678$	−30.0927	+	2.26698i	−1.15570	+	0.0870628i
$679$	13.3643	−	2.35648i	0.512874	−	0.0904335i
$680$	−0.0736348	+	0.417603i	−0.00282376	+	0.0160144i
$681$	−1.18785	−	0.853300i	−0.0455184	−	0.0326985i
$682$	10.4854	−	8.79829i	0.401506	−	0.336904i
$683$	−27.0630			−1.03554			−0.517769	−	0.855520i	$-0.673237\pi$
$683$	−27.0630			−1.03554			−0.517769	+	0.855520i	$0.673237\pi$
$684$	12.4300	−	20.3828i	0.475271	−	0.779355i
$685$	0.912089			0.0348491
$686$	29.7526	−	24.9654i	1.13596	−	0.953184i
$687$	9.19576	+	6.60585i	0.350840	+	0.252029i
$688$	3.58238	−	20.3167i	0.136577	−	0.774567i
$689$	51.0101	−	8.99446i	1.94333	−	0.342662i
$690$	−5.68718	+	0.428433i	−0.216507	+	0.0163102i
$691$	−0.487247	+	0.843937i	−0.0185358	+	0.0321049i	−0.875145	−	0.483862i	$-0.839234\pi$
$691$	−0.487247	+	0.843937i	−0.0185358	+	0.0321049i	0.856609	+	0.515967i	$0.172567\pi$
$692$	−10.5256	−	18.2309i	−0.400123	−	0.693034i
$693$	−25.4205	+	8.56297i	−0.965645	+	0.325281i
$694$	−33.3834	+	39.7848i	−1.26722	+	1.51021i
$695$	−1.74281	+	1.00621i	−0.0661085	+	0.0381678i
$696$	−0.481199	+	0.469716i	−0.0182398	+	0.0178045i
$697$	−8.60665	−	23.6466i	−0.326000	−	0.895678i
$698$	−0.933174	−	5.29229i	−0.0353212	−	0.200316i
$699$	−41.9297	−	20.1721i	−1.58593	−	0.762978i
$700$	−15.8225	−	5.75892i	−0.598034	−	0.217667i
$701$	9.90651	+	11.8061i	0.374164	+	0.445911i	0.919963	−	0.392005i	$-0.128218\pi$
$701$	9.90651	+	11.8061i	0.374164	+	0.445911i	−0.545799	+	0.837916i	$0.683774\pi$
$702$	−38.9976	+	36.2698i	−1.47187	+	1.36891i
$703$	10.9572	+	9.19163i	0.413258	+	0.346669i
$704$		−	30.1967i		−	1.13808i
$705$	−4.64796	+	2.09943i	−0.175052	+	0.0790690i
$706$	−16.2833	+	44.7380i	−0.612830	+	1.68374i
$707$	20.7835	+	3.66469i	0.781643	+	0.137825i
$708$	0.0705198	−	0.707533i	0.00265030	−	0.0265907i
$709$	−30.4578	+	11.0857i	−1.14387	+	0.416333i	−0.843308	−	0.537430i	$-0.819395\pi$
$709$	−30.4578	+	11.0857i	−1.14387	+	0.416333i	−0.300558	+	0.953763i	$0.597173\pi$
$710$	−2.60983	−	1.50679i	−0.0979452	−	0.0565487i
$711$	43.3192	+	1.04640i	1.62460	+	0.0392430i
$712$	−1.48036	−	1.24217i	−0.0554789	−	0.0465523i
$713$	3.95787	+	3.32105i	0.148223	+	0.124374i
$714$	16.0089	−	4.08305i	0.599119	−	0.152804i
$715$	10.3479	+	5.97435i	0.386989	+	0.223428i
$716$	30.4646	−	11.0882i	1.13851	−	0.414385i
$717$	−39.1153	−	3.89862i	−1.46079	−	0.145596i
$718$	−58.7202	−	10.3540i	−2.19142	−	0.386406i
$719$	−10.4822	+	28.7995i	−0.390919	+	1.07404i	0.575664	+	0.817686i	$0.304743\pi$
$719$	−10.4822	+	28.7995i	−0.390919	+	1.07404i	−0.966583	+	0.256354i	$0.917479\pi$
$720$	−0.959944	−	6.33517i	−0.0357750	−	0.236098i
$721$		−	4.62614i		−	0.172286i
$722$	28.4748	+	23.8800i	1.05972	+	0.888723i
$723$	11.6286	−	41.3926i	0.432472	−	1.53941i
$724$	13.7079	+	16.3364i	0.509448	+	0.607137i
$725$	5.08821	+	1.85196i	0.188971	+	0.0687799i
$726$	−15.0603	+	31.3043i	−0.558939	+	1.16181i
$727$	−7.08739	−	40.1946i	−0.262857	−	1.49073i	−0.775069	−	0.631876i	$-0.782285\pi$
$727$	−7.08739	−	40.1946i	−0.262857	−	1.49073i	0.512213	−	0.858859i	$-0.328826\pi$
$728$	−1.18516	−	3.25619i	−0.0439248	−	0.120682i
$729$	−22.3441	−	15.1572i	−0.827559	−	0.561379i
$730$	−0.105397	+	0.0608507i	−0.00390090	+	0.00225219i
$731$	7.72170	−	9.20236i	0.285597	−	0.340362i
$732$	19.5430	+	28.6402i	0.722330	+	1.05857i
$733$	16.4021	+	28.4094i	0.605827	+	1.04932i	0.991920	+	0.126864i	$0.0404910\pi$
$733$	16.4021	+	28.4094i	0.605827	+	1.04932i	−0.386093	+	0.922460i	$0.626176\pi$
$734$	−11.4808	+	19.8854i	−0.423765	+	0.733982i
$735$	−0.208410	−	2.76652i	−0.00768734	−	0.102045i
$736$	26.0259	−	4.58908i	0.959329	−	0.169156i
$737$	0.331533	−	1.88022i	0.0122122	−	0.0692587i
$738$	36.6489	+	45.8826i	1.34907	+	1.68896i
$739$	6.98259	−	5.85908i	0.256859	−	0.215530i	−0.505260	−	0.862967i	$-0.668604\pi$
$739$	6.98259	−	5.85908i	0.256859	−	0.215530i	0.762119	+	0.647437i	$0.224159\pi$
$740$	−2.96279			−0.108914
$741$	−22.3033	−	32.6759i	−0.819332	−	1.20038i
$742$	37.4972			1.37657
$743$	11.0957	−	9.31040i	0.407062	−	0.341565i	−0.416154	−	0.909294i	$-0.636622\pi$
$743$	11.0957	−	9.31040i	0.407062	−	0.341565i	0.823216	+	0.567729i	$0.192178\pi$
$744$	−0.523003	+	0.728053i	−0.0191742	+	0.0266917i
$745$	0.352295	−	1.99796i	0.0129071	−	0.0731997i
$746$	−46.8896	+	8.26790i	−1.71675	+	0.302709i
$747$	−4.13753	+	20.5499i	−0.151384	+	0.751883i
$748$	10.5820	−	18.3286i	0.386916	−	0.670159i
$749$	−8.35312	−	14.4680i	−0.305216	−	0.528650i
$750$	−13.5023	+	9.21343i	−0.493033	+	0.336427i
$751$	−29.2589	+	34.8694i	−1.06767	+	1.27240i	−0.107139	+	0.994244i	$0.534169\pi$
$751$	−29.2589	+	34.8694i	−1.06767	+	1.27240i	−0.960535	+	0.278160i	$0.910275\pi$
$752$	22.2638	−	12.8540i	0.811877	−	0.468737i
$753$	−19.5136	−	19.9906i	−0.711114	−	0.728499i
$754$	−3.99155	−	10.9667i	−0.145364	−	0.399384i
$755$	−1.81314	−	10.2828i	−0.0659869	−	0.374230i
$756$	−15.4437	+	10.0003i	−0.561680	+	0.363707i
$757$	35.3771	+	12.8762i	1.28580	+	0.467994i	0.892347	−	0.451350i	$-0.149057\pi$
$757$	35.3771	+	12.8762i	1.28580	+	0.467994i	0.393455	+	0.919344i	$0.371280\pi$
$758$	6.46749	+	7.70765i	0.234910	+	0.279954i
$759$	−26.1661	−	7.35096i	−0.949770	−	0.266823i
$760$	0.735085		9.96935e-5i	0.0266643		3.61626e-6i
$761$			10.5310i			0.381748i	0.981615	+	0.190874i	$0.0611322\pi$
$761$			10.5310i			0.381748i	−0.981615	+	0.190874i	$0.938868\pi$
$762$	−11.8988	−	26.3428i	−0.431046	−	0.954301i
$763$	3.02558	−	8.31271i	0.109533	−	0.300940i
$764$	−5.13939	−	0.906213i	−0.185937	−	0.0327857i
$765$	1.36039	−	3.47420i	0.0491849	−	0.125610i
$766$	21.2825	−	7.74620i	0.768968	−	0.279882i
$767$	−1.02042	−	0.589141i	−0.0368453	−	0.0212726i
$768$	7.88251	+	30.9060i	0.284436	+	1.11522i
$769$	33.7073	+	28.2837i	1.21551	+	1.01994i	0.999047	+	0.0436483i	$0.0138981\pi$
$769$	33.7073	+	28.2837i	1.21551	+	1.01994i	0.216468	+	0.976290i	$0.430546\pi$
$770$	6.62626	+	5.56009i	0.238794	+	0.200372i
$771$	6.11697	+	23.9836i	0.220297	+	0.863748i
$772$	11.8715	+	6.85400i	0.427264	+	0.246681i
$773$	5.44057	−	1.98021i	0.195684	−	0.0712231i	−0.242319	−	0.970197i	$-0.577908\pi$
$773$	5.44057	−	1.98021i	0.195684	−	0.0712231i	0.438003	+	0.898974i	$0.355686\pi$
$774$	−10.2212	+	26.1032i	−0.367392	+	0.938259i
$775$	7.10870	+	1.25346i	0.255352	+	0.0450255i
$776$	−0.815958	+	2.24182i	−0.0292912	+	0.0804768i
$777$	−4.53713	−	10.0448i	−0.162769	−	0.360356i
$778$		−	47.1013i		−	1.68866i
$779$	−37.7750	+	21.8162i	−1.35343	+	0.781647i
$780$	7.89022	+	2.21663i	0.282515	+	0.0793681i
$781$	−9.23120	−	11.0013i	−0.330318	−	0.393658i
$782$	15.7306	+	5.72546i	0.562524	+	0.204742i
$783$	4.96638	−	3.21589i	0.177484	−	0.114927i
$784$	2.42841	+	13.7722i	0.0867289	+	0.491864i
$785$	1.04776	+	2.87869i	0.0373961	+	0.102745i
$786$	−35.4501	−	36.3168i	−1.26446	−	1.29538i
$787$	0.385641	−	0.222650i	0.0137466	−	0.00793662i	−0.493111	−	0.869966i	$-0.664140\pi$
$787$	0.385641	−	0.222650i	0.0137466	−	0.00793662i	0.506858	+	0.862030i	$0.330807\pi$
$788$	−18.8513	+	22.4661i	−0.671549	+	0.800321i
$789$	18.3984	−	12.5544i	0.655002	−	0.446948i
$790$	−6.98665	−	12.1012i	−0.248574	−	0.430542i
$791$	−8.63826	+	14.9619i	−0.307141	+	0.531984i
$792$	0.930779	−	4.62292i	0.0330738	−	0.164268i
$793$	56.5840	−	9.97729i	2.00936	−	0.354304i
$794$	−4.26137	+	24.1674i	−0.151230	+	0.857670i
$795$	4.94048	−	6.87746i	0.175221	−	0.243918i
$796$	8.85834	−	7.43303i	0.313976	−	0.263457i
$797$	25.7666			0.912699			0.456349	−	0.889801i	$-0.349157\pi$
$797$	25.7666			0.912699			0.456349	+	0.889801i	$0.349157\pi$
$798$	−11.7930	−	26.0993i	−0.417468	−	0.923904i
$799$	14.9697			0.529589
$800$	28.2840	−	23.7331i	0.999989	−	0.839091i
$801$	10.6118	+	13.2854i	0.374948	+	0.469416i
$802$	7.48697	−	42.4607i	0.264374	−	1.49934i
$803$	−0.571157	+	0.100710i	−0.0201557	+	0.00355400i
$804$	−0.0983734	−	1.30585i	−0.00346936	−	0.0460536i
$805$	−1.63253	+	2.82763i	−0.0575392	+	0.0996608i
$806$	−7.77893	−	13.4735i	−0.274001	−	0.474584i
$807$	27.5788	+	40.4167i	0.970821	+	1.42274i
$808$	−2.38482	+	2.84212i	−0.0838978	+	0.0999855i
$809$	21.3495	−	12.3261i	0.750608	−	0.433364i	−0.0753057	−	0.997160i	$-0.523993\pi$
$809$	21.3495	−	12.3261i	0.750608	−	0.433364i	0.825913	+	0.563797i	$0.190660\pi$
$810$	−0.420385	+	8.69658i	−0.0147708	+	0.305567i
$811$	−5.65228	−	15.5295i	−0.198478	−	0.545315i	0.800027	−	0.599964i	$-0.204818\pi$
$811$	−5.65228	−	15.5295i	−0.198478	−	0.545315i	−0.998506	+	0.0546487i	$0.982596\pi$
$812$	−0.700116	−	3.97056i	−0.0245693	−	0.139339i
$813$	0.0262608	−	0.0545857i	0.000921005	−	0.00191440i
$814$	−27.8023	−	10.1192i	−0.974468	−	0.354678i
$815$	0.542433	+	0.646446i	0.0190006	+	0.0226440i
$816$	−5.08662	+	18.1061i	−0.178067	+	0.633841i
$817$	−18.0358	−	10.4097i	−0.630992	−	0.364189i
$818$			26.3657i			0.921853i
$819$	4.56773	+	30.1449i	0.159610	+	1.05335i
$820$	3.09076	−	8.49179i	0.107934	−	0.296546i
$821$	9.59543	+	1.69193i	0.334883	+	0.0590488i	0.338561	−	0.940944i	$-0.390060\pi$
$821$	9.59543	+	1.69193i	0.334883	+	0.0590488i	−0.00367851	+	0.999993i	$0.501171\pi$
$822$	6.21652	+	0.619600i	0.216826	+	0.0216110i
$823$	−38.3969	+	13.9753i	−1.33843	+	0.487150i	−0.909318	−	0.416101i	$-0.863396\pi$
$823$	−38.3969	+	13.9753i	−1.33843	+	0.487150i	−0.429114	+	0.903250i	$0.641174\pi$
$824$	0.704322	+	0.406640i	0.0245362	+	0.0141660i
$825$	−36.7943	+	9.38432i	−1.28101	+	0.326720i
$826$	−0.653427	−	0.548290i	−0.0227356	−	0.0190775i
$827$	−13.5381	−	11.3598i	−0.470765	−	0.395019i	0.376309	−	0.926494i	$-0.377193\pi$
$827$	−13.5381	−	11.3598i	−0.470765	−	0.395019i	−0.847074	+	0.531476i	$0.821638\pi$
$828$	−18.6368	−	0.450181i	−0.647674	−	0.0156449i
$829$	−24.9946	−	14.4306i	−0.868097	−	0.501196i	−0.00138139	−	0.999999i	$-0.500440\pi$
$829$	−24.9946	−	14.4306i	−0.868097	−	0.501196i	−0.866715	+	0.498803i	$0.833773\pi$
$830$	6.35209	−	2.31197i	0.220484	−	0.0802497i
$831$	−2.13902	+	21.4610i	−0.0742018	+	0.744475i
$832$	−33.8011	−	5.96005i	−1.17184	−	0.206627i
$833$	−2.78514	+	7.65211i	−0.0964994	+	0.265130i
$834$	−12.5620	+	5.67410i	−0.434986	+	0.196478i
$835$			2.62850i			0.0909629i
$836$	−34.4770	−	12.5433i	−1.19241	−	0.433820i
$837$	5.77561	−	5.37161i	0.199634	−	0.185670i
$838$	44.8816	+	53.4878i	1.55041	+	1.84771i
$839$	−5.37586	−	1.95665i	−0.185595	−	0.0675511i	0.247551	−	0.968875i	$-0.420374\pi$
$839$	−5.37586	−	1.95665i	−0.185595	−	0.0675511i	−0.433146	+	0.901324i	$0.642597\pi$
$840$	−0.510498	−	0.245597i	−0.0176138	−	0.00847389i
$841$	−4.81065	−	27.2826i	−0.165885	−	0.940778i
$842$	1.06228	+	2.91859i	0.0366086	+	0.100581i
$843$	−37.2923	+	36.4024i	−1.28442	+	1.25376i
$844$	−17.3641	+	10.0251i	−0.597696	+	0.345080i
$845$	4.59683	−	5.47829i	0.158136	−	0.188459i
$846$	−33.1052	+	11.1516i	−1.13818	+	0.383400i
$847$	9.94371	+	17.2230i	0.341670	+	0.591790i
$848$	−21.3424	+	36.9660i	−0.732900	+	1.26942i
$849$	47.3741	−	3.56884i	1.62588	−	0.122482i
$850$	23.0325	−	4.06126i	0.790009	−	0.139300i
$851$	1.93928	−	10.9982i	0.0664778	−	0.377014i
$852$	−8.00017	−	5.74698i	−0.274081	−	0.196888i
$853$	16.3156	−	13.6904i	0.558634	−	0.468750i	−0.319218	−	0.947681i	$-0.603420\pi$
$853$	16.3156	−	13.6904i	0.558634	−	0.468750i	0.877852	+	0.478932i	$0.158976\pi$
$854$	41.5946			1.42334
$855$	−6.34073	−	1.27575i	−0.216848	−	0.0436297i
$856$	2.93698			0.100384
$857$	−36.9941	+	31.0418i	−1.26370	+	1.06037i	−0.268417	+	0.963303i	$0.586501\pi$
$857$	−36.9941	+	31.0418i	−1.26370	+	1.06037i	−0.995278	+	0.0970637i	$0.969055\pi$
$858$	66.4695	+	47.7489i	2.26923	+	1.63012i
$859$	−6.19245	+	35.1191i	−0.211284	+	1.19825i	0.675957	+	0.736941i	$0.263731\pi$
$859$	−6.19245	+	35.1191i	−0.211284	+	1.19825i	−0.887240	+	0.461307i	$0.847381\pi$
$860$	4.24842	−	0.749112i	0.144870	−	0.0255445i
$861$	33.5230	−	2.52539i	1.14246	−	0.0860651i
$862$	−8.77145	+	15.1926i	−0.298757	+	0.517462i
$863$	−0.711785	−	1.23285i	−0.0242294	−	0.0419666i	0.853656	−	0.520837i	$-0.174380\pi$
$863$	−0.711785	−	1.23285i	−0.0242294	−	0.0419666i	−0.877886	+	0.478870i	$0.841047\pi$
$864$	−2.05830	−	40.2920i	−0.0700248	−	1.37076i
$865$	−3.66588	+	4.36883i	−0.124644	+	0.148545i
$866$	−21.5799	+	12.4591i	−0.733313	+	0.423379i
$867$	13.2339	−	12.9181i	0.449447	−	0.438721i
$868$	−1.83828	−	5.05063i	−0.0623953	−	0.171430i
$869$	−11.5632	−	65.5781i	−0.392254	−	2.22459i
$870$	−1.71933	−	0.827158i	−0.0582908	−	0.0280433i
$871$	−2.03921	−	0.742212i	−0.0690960	−	0.0251489i
$872$	0.999646	+	1.19133i	0.0338523	+	0.0403436i
$873$	10.9315	−	17.9200i	0.369974	−	0.606502i
$874$	5.03524	−	28.5789i	0.170319	−	0.966696i
$875$			9.35799i			0.316358i
$876$	−0.362536	+	0.163753i	−0.0122490	+	0.00553271i
$877$	−2.02335	+	5.55910i	−0.0683236	+	0.187718i	−0.969155	−	0.246451i	$-0.920736\pi$
$877$	−2.02335	+	5.55910i	−0.0683236	+	0.187718i	0.900832	+	0.434169i	$0.142958\pi$
$878$	9.24067	+	1.62938i	0.311857	+	0.0549889i
$879$	1.52600	−	15.3105i	0.0514707	−	0.516412i
$880$	−9.25281	+	3.36775i	−0.311912	+	0.113527i
$881$	0.195705	+	0.112990i	0.00659346	+	0.00380673i	0.503293	−	0.864116i	$-0.332122\pi$
$881$	0.195705	+	0.112990i	0.00659346	+	0.00380673i	−0.496700	+	0.867922i	$0.665455\pi$
$882$	0.458890	−	18.9973i	0.0154516	−	0.639673i
$883$	−0.614505	−	0.515631i	−0.0206797	−	0.0173524i	0.632389	−	0.774651i	$-0.282074\pi$
$883$	−0.614505	−	0.515631i	−0.0206797	−	0.0173524i	−0.653069	+	0.757298i	$0.726519\pi$
$884$	−18.4277	−	15.4627i	−0.619791	−	0.520066i
$885$	−0.186656	+	0.0476063i	−0.00627438	+	0.00160027i
$886$	14.3253	+	8.27071i	0.481268	+	0.277860i
$887$	−42.0903	+	15.3196i	−1.41325	+	0.514382i	−0.932083	−	0.362246i	$-0.882010\pi$
$887$	−42.0903	+	15.3196i	−1.41325	+	0.514382i	−0.481170	+	0.876627i	$0.659788\pi$
$888$	1.92812	+	0.192176i	0.0647036	+	0.00644901i
$889$	−16.2966	−	2.87353i	−0.546571	−	0.0963751i
$890$	1.87532	−	5.15240i	0.0628609	−	0.172709i
$891$	−16.0571	+	38.2590i	−0.537932	+	1.28173i
$892$		−	42.8047i		−	1.43321i
$893$	−4.50963	−	25.5551i	−0.150909	−	0.855170i
$894$	3.75839	−	13.3782i	0.125699	−	0.447434i
$895$	−5.64560	−	6.72817i	−0.188712	−	0.224898i
$896$	4.95229	+	1.80249i	0.165444	+	0.0602169i
$897$	−13.3929	+	27.8385i	−0.447176	+	0.929500i
$898$	1.55756	+	8.83339i	0.0519766	+	0.294774i
$899$	0.591155	+	1.62419i	0.0197161	+	0.0541696i
$900$	−22.8638	+	12.4742i	−0.762127	+	0.415806i
$901$	−21.5252	+	12.4276i	−0.717108	+	0.414022i
$902$	58.0061	−	69.1290i	1.93139	−	2.30174i
$903$	9.04564	+	13.2564i	0.301020	+	0.441144i
$904$	−1.51862	−	2.63032i	−0.0505084	−	0.0874832i
$905$	2.88872	−	5.00341i	0.0960244	−	0.166319i
$906$	−5.37247	−	71.3162i	−0.178488	−	2.36932i
$907$	−20.9386	+	3.69204i	−0.695256	+	0.122592i	−0.510098	−	0.860116i	$-0.670391\pi$
$907$	−20.9386	+	3.69204i	−0.695256	+	0.122592i	−0.185158	+	0.982709i	$0.559280\pi$
$908$	−0.267701	+	1.51821i	−0.00888397	+	0.0503835i
$909$	25.5064	−	20.3734i	0.845994	−	0.675741i
$910$	7.53161	−	6.31977i	0.249671	−	0.209498i
$911$	40.5821			1.34454			0.672272	−	0.740304i	$-0.265319\pi$
$911$	40.5821			1.34454			0.672272	+	0.740304i	$0.265319\pi$
$912$	32.4418	+	3.22903i	1.07426	+	0.106924i
$913$	32.2136			1.06612
$914$	12.5700	−	10.5475i	0.415778	−	0.348880i
$915$	5.48032	−	7.62896i	0.181174	−	0.252206i
$916$	2.07242	−	11.7533i	0.0684745	−	0.388338i
$917$	−28.6127	+	5.04518i	−0.944873	+	0.166607i
$918$	11.6321	−	22.7550i	0.383916	−	0.751026i
$919$	22.2065	−	38.4628i	0.732526	−	1.26877i	−0.223275	−	0.974756i	$-0.571675\pi$
$919$	22.2065	−	38.4628i	0.732526	−	1.26877i	0.955800	−	0.294016i	$-0.0949919\pi$
$920$	−0.287001	−	0.497100i	−0.00946214	−	0.0163889i
$921$	−32.8051	+	22.3849i	−1.08096	+	0.737608i
$922$	31.5838	−	37.6401i	1.04016	−	1.23961i
$923$	−14.1365	+	8.16169i	−0.465307	+	0.268645i
$924$	19.7499	+	20.2327i	0.649723	+	0.665607i
$925$	−5.33647	−	14.6618i	−0.175462	−	0.482078i
$926$	3.64171	+	20.6531i	0.119674	+	0.678704i
$927$	−5.36900	−	4.73070i	−0.176341	−	0.155377i
$928$	8.30774	+	3.02377i	0.272715	+	0.0992602i
$929$	−38.4969	−	45.8788i	−1.26304	−	1.50524i	−0.774318	−	0.632797i	$-0.781907\pi$
$929$	−38.4969	−	45.8788i	−1.26304	−	1.50524i	−0.488724	−	0.872438i	$-0.662538\pi$
$930$	−2.44868	−	0.687919i	−0.0802955	−	0.0225578i
$931$	13.9022	+	2.44938i	0.455625	+	0.0802753i
$932$			49.0449i			1.60652i
$933$	−10.3722	−	22.9632i	−0.339570	−	0.751780i
$934$	−2.21186	+	6.07702i	−0.0723741	+	0.198846i
$935$	−5.64655	−	0.995639i	−0.184662	−	0.0325609i
$936$	−4.99101	−	1.95432i	−0.163136	−	0.0638790i
$937$	−21.7752	+	7.92551i	−0.711364	+	0.258915i	−0.672255	−	0.740320i	$-0.734674\pi$
$937$	−21.7752	+	7.92551i	−0.711364	+	0.258915i	−0.0391088	+	0.999235i	$0.512452\pi$
$938$	−1.36051	−	0.785489i	−0.0444221	−	0.0256471i
$939$	−7.50628	−	29.4309i	−0.244958	−	0.960440i
$940$	4.11810	+	3.45550i	0.134318	+	0.112706i
$941$	6.76374	+	5.67545i	0.220492	+	0.185014i	0.746342	−	0.665563i	$-0.231808\pi$
$941$	6.76374	+	5.67545i	0.220492	+	0.185014i	−0.525850	+	0.850577i	$0.676253\pi$
$942$	5.18565	+	20.3321i	0.168958	+	0.662454i
$943$	29.4994	+	17.0315i	0.960634	+	0.554622i
$944$	0.912435	−	0.332099i	0.0296972	−	0.0108089i
$945$	3.97683	+	3.00499i	0.129366	+	0.0977524i
$946$	42.4249	+	7.48065i	1.37935	+	0.243217i
$947$	−7.64505	+	21.0046i	−0.248431	+	0.682558i	0.751314	+	0.659945i	$0.229421\pi$
$947$	−7.64505	+	21.0046i	−0.248431	+	0.682558i	−0.999744	+	0.0226124i	$0.992802\pi$
$948$	−18.8015	−	41.6250i	−0.610645	−	1.35192i
$949$			0.659210i			0.0213989i
$950$	−13.8717	−	38.0960i	−0.450056	−	1.23600i
$951$	29.4490	+	8.27323i	0.954949	+	0.268278i
$952$	1.06881	+	1.27376i	0.0346405	+	0.0412829i
$953$	−7.48437	−	2.72409i	−0.242443	−	0.0882419i	0.217941	−	0.975962i	$-0.430066\pi$
$953$	−7.48437	−	2.72409i	−0.242443	−	0.0882419i	−0.460384	+	0.887720i	$0.652288\pi$
$954$	38.3448	−	43.5185i	1.24146	−	1.40896i
$955$	0.245507	+	1.39234i	0.00794443	+	0.0450551i
$956$	14.1713	+	38.9352i	0.458331	+	1.25925i
$957$	−6.35117	−	6.50644i	−0.205304	−	0.210323i
$958$	10.3199	−	5.95819i	0.333421	−	0.192501i
$959$	2.29894	−	2.73977i	0.0742365	−	0.0884716i
$960$	−4.63497	+	3.16273i	−0.149593	+	0.102077i
$961$	−14.3479	−	24.8513i	−0.462836	−	0.801656i
$962$	−16.8145	+	29.1235i	−0.542121	+	0.938981i
$963$	−25.3332	−	5.10059i	−0.816352	−	0.164364i
$964$	−44.6307	+	7.86960i	−1.43746	+	0.253463i
$965$	0.644879	−	3.65729i	0.0207594	−	0.117732i
$966$	−13.0477	+	18.1632i	−0.419803	+	0.584392i
$967$	−35.0040	+	29.3718i	−1.12565	+	0.944534i	−0.998876	−	0.0473972i	$-0.984907\pi$
$967$	−35.0040	+	29.3718i	−1.12565	+	0.944534i	−0.126776	+	0.991931i	$0.540463\pi$
$968$	−3.49623			−0.112373
$969$	15.4197	+	11.0737i	0.495353	+	0.355739i
$970$	−6.76902			−0.217340
$971$	35.3393	−	29.6532i	1.13409	−	0.951616i	0.134862	−	0.990864i	$-0.456941\pi$
$971$	35.3393	−	29.6532i	1.13409	−	0.951616i	0.999229	+	0.0392486i	$0.0124964\pi$
$972$	−4.18661	+	28.1499i	−0.134286	+	0.902909i
$973$	−1.37029	+	7.77129i	−0.0439294	+	0.249136i
$974$	−4.18477	+	0.737889i	−0.134089	+	0.0236435i
$975$	3.24222	+	43.0384i	0.103834	+	1.37833i
$976$	−23.6744	+	41.0053i	−0.757800	+	1.31255i
$977$	−19.4513	−	33.6907i	−0.622303	−	1.07786i	−0.989056	−	0.147541i	$-0.952864\pi$
$977$	−19.4513	−	33.6907i	−0.622303	−	1.07786i	0.366753	−	0.930318i	$-0.380469\pi$
$978$	3.25791	+	4.77446i	0.104177	+	0.152671i
$979$	16.7958	−	20.0164i	0.536795	−	0.639727i
$980$	−2.53254	+	1.46217i	−0.0808992	+	0.0467072i
$981$	−6.55359	−	12.0120i	−0.209240	−	0.383515i
$982$	21.6789	+	59.5622i	0.691801	+	1.90071i
$983$	1.40399	+	7.96240i	0.0447802	+	0.253961i	0.998977	−	0.0452181i	$-0.0143983\pi$
$983$	1.40399	+	7.96240i	0.0447802	+	0.253961i	−0.954197	+	0.299179i	$0.903287\pi$
$984$	−2.56221	+	5.32581i	−0.0816802	+	0.169780i
$985$	7.46608	+	2.71743i	0.237889	+	0.0865846i
$986$	3.59972	+	4.28998i	0.114638	+	0.136621i
$987$	−5.40892	+	19.2533i	−0.172168	+	0.612841i
$988$	−20.8454	+	36.1166i	−0.663180	+	1.14902i
$989$			16.2610i			0.517069i
$990$	13.2290	−	2.00453i	0.420444	−	0.0637083i
$991$	12.3895	−	34.0400i	0.393567	−	1.08132i	−0.571794	−	0.820397i	$-0.693752\pi$
$991$	12.3895	−	34.0400i	0.393567	−	1.08132i	0.965361	−	0.260918i	$-0.0840253\pi$
$992$	11.6067	+	2.04657i	0.368513	+	0.0649788i
$993$	−7.35828	−	0.733399i	−0.233508	−	0.0232737i
$994$	−11.1043	+	4.04162i	−0.352206	+	0.128192i
$995$	−2.71308	−	1.56640i	−0.0860105	−	0.0496582i
$996$	21.4101	−	5.46060i	0.678405	−	0.173026i
$997$	−20.3418	−	17.0688i	−0.644231	−	0.540574i	0.261083	−	0.965316i	$-0.415920\pi$
$997$	−20.3418	−	17.0688i	−0.644231	−	0.540574i	−0.905314	+	0.424742i	$0.860365\pi$
$998$	−24.3017	−	20.3916i	−0.769258	−	0.645484i
$999$	−16.2975	−	5.00617i	−0.515630	−	0.158388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.32.1	✓	24
3.2	odd	2	inner	57.2.j.b.32.4	yes	24
4.3	odd	2		912.2.cc.e.545.1		24
12.11	even	2		912.2.cc.e.545.4		24
19.3	odd	18	inner	57.2.j.b.41.4	yes	24
19.4	even	9		1083.2.d.d.1082.6		24
19.15	odd	18		1083.2.d.d.1082.20		24
57.23	odd	18		1083.2.d.d.1082.19		24
57.41	even	18	inner	57.2.j.b.41.1	yes	24
57.53	even	18		1083.2.d.d.1082.5		24
76.3	even	18		912.2.cc.e.497.4		24
228.155	odd	18		912.2.cc.e.497.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.32.1	✓	24	1.1	even	1	trivial
57.2.j.b.32.4	yes	24	3.2	odd	2	inner
57.2.j.b.41.1	yes	24	57.41	even	18	inner
57.2.j.b.41.4	yes	24	19.3	odd	18	inner
912.2.cc.e.497.1		24	228.155	odd	18
912.2.cc.e.497.4		24	76.3	even	18
912.2.cc.e.545.1		24	4.3	odd	2
912.2.cc.e.545.4		24	12.11	even	2
1083.2.d.d.1082.5		24	57.53	even	18
1083.2.d.d.1082.6		24	19.4	even	9
1083.2.d.d.1082.19		24	57.23	odd	18
1083.2.d.d.1082.20		24	19.15	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49833 + 1.25725i) q^{2} +(1.40671 + 1.01052i) q^{3} +(0.317026 - 1.79794i) q^{4} +(-0.487091 + 0.0858872i) q^{5} +(-3.37821 + 0.254491i) q^{6} +(-0.969730 + 1.67962i) q^{7} +(-0.170480 - 0.295279i) q^{8} +(0.957685 + 2.84303i) q^{9} +O(q^{10})\)	\(q+(-1.49833 + 1.25725i) q^{2} +(1.40671 + 1.01052i) q^{3} +(0.317026 - 1.79794i) q^{4} +(-0.487091 + 0.0858872i) q^{5} +(-3.37821 + 0.254491i) q^{6} +(-0.969730 + 1.67962i) q^{7} +(-0.170480 - 0.295279i) q^{8} +(0.957685 + 2.84303i) q^{9} +(0.621842 - 0.741083i) q^{10} +(3.99257 - 2.30511i) q^{11} +(2.26283 - 2.20883i) q^{12} +(-1.79223 - 4.92410i) q^{13} +(-0.658727 - 3.73582i) q^{14} +(-0.771988 - 0.371398i) q^{15} +(4.05783 + 1.47693i) q^{16} +(1.61629 + 1.92622i) q^{17} +(-5.00934 - 3.05576i) q^{18} +(2.80139 - 3.33949i) q^{19} +0.902990i q^{20} +(-3.06143 + 1.38281i) q^{21} +(-3.08409 + 8.47347i) q^{22} +(-3.35200 - 0.591048i) q^{23} +(0.0585708 - 0.587647i) q^{24} +(-4.46858 + 1.62643i) q^{25} +(8.87617 + 5.12466i) q^{26} +(-1.52576 + 4.96710i) q^{27} +(2.71243 + 2.27600i) q^{28} +(-0.872266 - 0.731918i) q^{29} +(1.62363 - 0.414105i) q^{30} +(-1.31458 - 0.758971i) q^{31} +(-7.29606 + 2.65555i) q^{32} +(7.94576 + 0.791954i) q^{33} +(-4.84348 - 0.854036i) q^{34} +(0.328088 - 0.901415i) q^{35} +(5.41522 - 0.820548i) q^{36} +3.28109i q^{37} +(0.00115627 + 8.52572i) q^{38} +(2.45477 - 8.73788i) q^{39} +(0.108400 + 0.129186i) q^{40} +(-9.40408 - 3.42281i) q^{41} +(2.84850 - 5.92089i) q^{42} +(-0.829591 - 4.70484i) q^{43} +(-2.87871 - 7.90919i) q^{44} +(-0.710660 - 1.30256i) q^{45} +(5.76551 - 3.32872i) q^{46} +(3.82673 - 4.56052i) q^{47} +(4.21573 + 6.17815i) q^{48} +(1.61925 + 2.80462i) q^{49} +(4.65059 - 8.05506i) q^{50} +(0.327167 + 4.34294i) q^{51} +(-9.42143 + 1.66125i) q^{52} +(-1.71646 + 9.73455i) q^{53} +(-3.95878 - 9.36063i) q^{54} +(-1.74676 + 1.46571i) q^{55} +0.661277 q^{56} +(7.31539 - 1.86683i) q^{57} +2.22715 q^{58} +(0.172251 - 0.144536i) q^{59} +(-0.912492 + 1.27025i) q^{60} +(-1.90402 + 10.7982i) q^{61} +(2.92389 - 0.515560i) q^{62} +(-5.70391 - 1.14843i) q^{63} +(3.27498 - 5.67243i) q^{64} +(1.29589 + 2.24455i) q^{65} +(-12.9011 + 8.80320i) q^{66} +(0.266197 - 0.317241i) q^{67} +(3.97564 - 2.29534i) q^{68} +(-4.11804 - 4.21871i) q^{69} +(0.641719 + 1.76311i) q^{70} +(-0.540928 - 3.06775i) q^{71} +(0.676224 - 0.767464i) q^{72} +(-0.118214 - 0.0430264i) q^{73} +(-4.12516 - 4.91617i) q^{74} +(-7.92956 - 2.22768i) q^{75} +(-5.11610 - 6.09545i) q^{76} +8.94133i q^{77} +(7.30764 + 16.1785i) q^{78} +(4.94012 - 13.5729i) q^{79} +(-2.10338 - 0.370883i) q^{80} +(-7.16568 + 5.44546i) q^{81} +(18.3938 - 6.69478i) q^{82} +(6.05130 + 3.49372i) q^{83} +(1.51566 + 5.94266i) q^{84} +(-0.952717 - 0.799425i) q^{85} +(7.15817 + 6.00642i) q^{86} +(-0.487408 - 1.91104i) q^{87} +(-1.36130 - 0.785948i) q^{88} +(5.32595 - 1.93849i) q^{89} +(2.70245 + 1.05819i) q^{90} +(10.0086 + 1.76478i) q^{91} +(-2.12534 + 5.83933i) q^{92} +(-1.08227 - 2.39606i) q^{93} +11.6443i q^{94} +(-1.07771 + 1.86724i) q^{95} +(-12.9470 - 3.63724i) q^{96} +(-4.49760 - 5.36003i) q^{97} +(-5.95229 - 2.16645i) q^{98} +(10.3771 + 9.14343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

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