LMFDB - Embedded newform 57.2.j.b.41.1

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			41.1
Character	$\chi$	$=$	57.41
Dual form			57.2.j.b.32.1

$q$-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 $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

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	−0.0654227	−	0.997858i	$-0.520840\pi$
$2$	−1.49833	−	1.25725i	−1.05948	−	0.889010i	−0.994058	+	0.108847i	$0.965284\pi$
$3$	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	0.0636661	−	0.997971i	$-0.479721\pi$
$5$	−0.487091	−	0.0858872i	−0.217834	−	0.0384099i	−0.281500	+	0.959561i	$0.590832\pi$
$6$	−3.37821	−	0.254491i	−1.37915	−	0.103895i
$7$	−0.969730	−	1.67962i	−0.366523	−	0.634837i	0.622496	−	0.782623i	$-0.286119\pi$
$7$	−0.969730	−	1.67962i	−0.366523	−	0.634837i	−0.989019	+	0.147786i	$0.952785\pi$
$8$	−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	0.961399	−	0.275159i	$-0.0887304\pi$
$11$	3.99257	+	2.30511i	1.20380	+	0.695016i	0.242405	+	0.970175i	$0.422064\pi$
$12$	2.26283	+	2.20883i	0.653222	+	0.637634i
$13$	−1.79223	+	4.92410i	−0.497074	+	1.36570i	0.397016	+	0.917812i	$0.370046\pi$
$13$	−1.79223	+	4.92410i	−0.497074	+	1.36570i	−0.894090	+	0.447887i	$0.852177\pi$
$14$	−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	−0.533558	−	0.845764i	$-0.679145\pi$
$17$	1.61629	−	1.92622i	0.392008	−	0.467177i	0.925566	+	0.378587i	$0.123590\pi$
$18$	−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	−0.511817	−	0.859094i	$-0.671027\pi$
$23$	−3.35200	+	0.591048i	−0.698940	+	0.123242i	−0.187123	+	0.982336i	$0.559916\pi$
$24$	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	−0.720173	−	0.693794i	$-0.755938\pi$
$29$	−0.872266	+	0.731918i	−0.161976	+	0.135914i	0.558197	+	0.829708i	$0.311493\pi$
$30$	1.62363	+	0.414105i	0.296434	+	0.0756048i
$31$	−1.31458	+	0.758971i	−0.236105	+	0.136315i	−0.613385	−	0.789784i	$-0.710193\pi$
$31$	−1.31458	+	0.758971i	−0.236105	+	0.136315i	0.377280	+	0.926099i	$0.376859\pi$
$32$	−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	$-0.913074\pi$
$37$		−	3.28109i		−	0.539408i	0.962943	−	0.269704i	$-0.0869259\pi$
$38$	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	−0.947739	−	0.319046i	$-0.896638\pi$
$41$	−9.40408	+	3.42281i	−1.46867	+	0.534552i	−0.520932	+	0.853598i	$0.674415\pi$
$42$	2.84850	+	5.92089i	0.439533	+	0.913613i
$43$	−0.829591	+	4.70484i	−0.126511	+	0.717482i	0.853887	+	0.520458i	$0.174239\pi$
$43$	−0.829591	+	4.70484i	−0.126511	+	0.717482i	−0.980399	+	0.197024i	$0.936872\pi$
$44$	−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	0.969162	−	0.246426i	$-0.0792563\pi$
$47$	3.82673	+	4.56052i	0.558186	+	0.665220i	−0.410976	+	0.911646i	$0.634812\pi$
$48$	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	−0.840977	−	0.541071i	$-0.818019\pi$
$53$	−1.71646	−	9.73455i	−0.235774	−	1.33714i	0.605202	−	0.796072i	$-0.293092\pi$
$54$	−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	0.653931	−	0.756554i	$-0.273119\pi$
$59$	0.172251	+	0.144536i	0.0224252	+	0.0188170i	−0.631506	+	0.775371i	$0.717563\pi$
$60$	−0.912492	−	1.27025i	−0.117802	−	0.163988i
$61$	−1.90402	−	10.7982i	−0.243785	−	1.38257i	−0.823298	−	0.567610i	$-0.807868\pi$
$61$	−1.90402	−	10.7982i	−0.243785	−	1.38257i	0.579513	−	0.814963i	$-0.303243\pi$
$62$	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	0.782060	−	0.623203i	$-0.214169\pi$
$67$	0.266197	+	0.317241i	0.0325211	+	0.0387572i	−0.749539	+	0.661960i	$0.769725\pi$
$68$	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	0.935739	+	0.352694i	$0.114734\pi$
$71$	−0.540928	+	3.06775i	−0.0641963	+	0.364075i	−0.999935	+	0.0113819i	$0.996377\pi$
$72$	0.676224	+	0.767464i	0.0796937	+	0.0904465i
$73$	−0.118214	+	0.0430264i	−0.0138359	+	0.00503586i	−0.348929	−	0.937149i	$-0.613455\pi$
$73$	−0.118214	+	0.0430264i	−0.0138359	+	0.00503586i	0.335093	+	0.942185i	$0.391232\pi$
$74$	−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	0.825661	+	0.564167i	$0.190802\pi$
$79$	4.94012	+	13.5729i	0.555807	+	1.52707i	−0.269854	+	0.962901i	$0.586975\pi$
$80$	−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	−0.129665	−	0.991558i	$-0.541390\pi$
$83$	6.05130	−	3.49372i	0.664217	−	0.383486i	0.793882	+	0.608072i	$0.208057\pi$
$84$	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	0.608499	−	0.793555i	$-0.291772\pi$
$89$	5.32595	+	1.93849i	0.564549	+	0.205479i	−0.0439498	+	0.999034i	$0.513994\pi$
$90$	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	−0.944416	−	0.328752i	$-0.893372\pi$
$97$	−4.49760	+	5.36003i	−0.456662	+	0.544229i	0.487754	+	0.872981i	$0.337816\pi$
$98$	−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	0.604918	+	0.796288i	$0.293206\pi$
$101$	−3.72167	+	10.2252i	−0.370320	+	1.01745i	−0.975238	+	0.221158i	$0.929016\pi$
$102$	−5.95036	+	6.09583i	−0.589174	+	0.603578i
$103$	−2.06571	−	1.19264i	−0.203540	−	0.117514i	0.394766	−	0.918782i	$-0.370826\pi$
$103$	−2.06571	−	1.19264i	−0.203540	−	0.117514i	−0.598306	+	0.801268i	$0.704159\pi$
$104$	−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	0.579204	−	0.815183i	$-0.303364\pi$
$107$	−4.30693	−	7.45983i	−0.416367	−	0.721169i	−0.995571	+	0.0940139i	$0.970030\pi$
$108$	8.44685	−	4.31794i	0.812799	−	0.415494i
$109$	−4.49188	−	0.792039i	−0.430244	−	0.0758636i	−0.0456672	−	0.998957i	$-0.514541\pi$
$109$	−4.49188	−	0.792039i	−0.430244	−	0.0758636i	−0.384576	+	0.923093i	$0.625652\pi$
$110$	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	−0.740283	−	0.672295i	$-0.765309\pi$
$127$	2.91821	−	8.01772i	0.258949	−	0.711458i	0.999233	−	0.0391627i	$-0.0124691\pi$
$128$	−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	−0.158570	−	0.987348i	$-0.550688\pi$
$131$	9.62927	−	11.4757i	0.841313	−	1.00264i	0.999883	−	0.0152905i	$-0.00486732\pi$
$132$	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	−0.250687	−	0.968068i	$-0.580656\pi$
$137$	−1.81606	+	0.320220i	−0.155157	+	0.0273583i	0.0955303	+	0.995427i	$0.469545\pi$
$138$	11.4742	−	1.14363i	0.976746	−	0.0973522i
$139$	3.82337	+	1.39159i	0.324294	+	0.118033i	0.499037	−	0.866581i	$-0.333687\pi$
$139$	3.82337	+	1.39159i	0.324294	+	0.118033i	−0.174743	+	0.984614i	$0.555909\pi$
$140$	−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	0.868869	−	0.495043i	$-0.164848\pi$
$149$	−1.40291	−	3.85446i	−0.114931	−	0.315770i	−0.983799	+	0.179273i	$0.942625\pi$
$150$	14.6819	+	6.63163i	1.19877	+	0.541470i
$151$		−	21.1107i		−	1.71796i	−0.512006	−	0.858982i	$-0.671098\pi$
$151$		−	21.1107i		−	1.71796i	0.512006	−	0.858982i	$-0.328902\pi$
$152$	−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	0.911337	+	0.411662i	$0.135052\pi$
$157$	−1.07553	+	6.09962i	−0.0858364	+	0.486803i	−0.997173	+	0.0751405i	$0.976059\pi$
$158$	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	−0.897499	−	0.441016i	$-0.854618\pi$
$163$	−0.853080	+	1.47758i	−0.0668184	+	0.115733i	0.830681	+	0.556749i	$0.187951\pi$
$164$	−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	0.999470	+	0.0325564i	$0.0103649\pi$
$167$	0.922825	+	5.23360i	0.0714104	+	0.404988i	−0.928060	+	0.372432i	$0.878524\pi$
$168$	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	0.913526	−	0.406780i	$-0.133349\pi$
$173$	8.83296	+	7.41174i	0.671558	+	0.563504i	−0.241968	+	0.970284i	$0.577793\pi$
$174$	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	−0.316021	−	0.948752i	$-0.602347\pi$
$179$	8.87880	−	15.3785i	0.663633	−	1.14945i	0.979654	−	0.200694i	$-0.0643196\pi$
$180$	−2.56723	−	0.864780i	−0.191350	−	0.0644569i
$181$	−7.50836	−	8.94811i	−0.558092	−	0.665108i	0.411050	−	0.911613i	$-0.365162\pi$
$181$	−7.50836	−	8.94811i	−0.558092	−	0.665108i	−0.969142	+	0.246505i	$0.920718\pi$
$182$	−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	$0.0329774\pi$
$191$			2.85848i			0.206833i	−0.994638	+	0.103416i	$0.967023\pi$
$192$	10.3391	+	4.67004i	0.746159	+	0.337031i
$193$	−2.56804	−	7.05562i	−0.184851	−	0.507875i	0.812305	−	0.583232i	$-0.198212\pi$
$193$	−2.56804	−	7.05562i	−0.184851	−	0.507875i	−0.997157	+	0.0753578i	$0.975990\pi$
$194$	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	−0.905622	−	0.424085i	$-0.860596\pi$
$197$	−13.9117	+	8.03191i	−0.991165	+	0.572250i	−0.0855430	+	0.996334i	$0.527263\pi$
$198$	−27.0440	+	0.653260i	−1.92193	+	0.0464252i
$199$	4.85208	−	4.07138i	0.343955	−	0.288612i	−0.454402	−	0.890797i	$-0.650147\pi$
$199$	4.85208	−	4.07138i	0.343955	−	0.288612i	0.798357	+	0.602184i	$0.205703\pi$
$200$	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	−0.952191	−	0.305502i	$-0.901176\pi$
$211$	−7.05933	+	8.41298i	−0.485984	+	0.579174i	0.466207	+	0.884676i	$0.345620\pi$
$212$	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	0.880669	−	0.473732i	$-0.157093\pi$
$223$	23.0897	+	4.07134i	1.54620	+	0.272637i	0.665532	+	0.746369i	$0.268205\pi$
$224$	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	−0.784096	−	0.620639i	$-0.786873\pi$
$233$	−26.4558	−	4.66487i	−1.73318	−	0.305606i	−0.949081	+	0.315033i	$0.897984\pi$
$234$	−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	−0.296105	−	0.955155i	$-0.595688\pi$
$239$	−19.6545	−	11.3476i	−1.27135	−	0.734012i	−0.975241	+	0.221143i	$0.929021\pi$
$240$	−2.58407	+	2.64724i	−0.166801	+	0.170879i
$241$	−8.49003	+	23.3262i	−0.546891	+	1.50257i	0.290994	+	0.956725i	$0.406014\pi$
$241$	−8.49003	+	23.3262i	−0.546891	+	1.50257i	−0.837885	+	0.545846i	$0.816208\pi$
$242$	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	−0.650753	−	0.759290i	$-0.725547\pi$
$251$	−15.8837	+	2.80072i	−1.00257	+	0.176780i	−0.351815	+	0.936070i	$0.614435\pi$
$252$	−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	−0.233987	−	0.972240i	$-0.575177\pi$
$257$	10.9469	−	9.18557i	0.682851	−	0.572980i	0.916838	+	0.399260i	$0.130733\pi$
$258$	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	0.998283	+	0.0585816i	$0.0186578\pi$
$263$	4.39828	+	12.0842i	0.271209	+	0.745141i	−0.727073	+	0.686560i	$0.759120\pi$
$264$	−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	0.635428	−	0.772160i	$-0.280824\pi$
$269$	26.5458	−	9.66190i	1.61853	−	0.589096i	0.983101	+	0.183064i	$0.0586015\pi$
$270$	2.73224	−	4.21947i	0.166279	−	0.256789i
$271$	−0.00607291	+	0.0344412i	−0.000368903	+	0.00209215i	−0.984992	−	0.172602i	$-0.944783\pi$
$271$	−0.00607291	+	0.0344412i	−0.000368903	+	0.00209215i	0.984623	+	0.174694i	$0.0558937\pi$
$272$	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	−0.616107	−	0.787662i	$-0.711291\pi$
$277$	6.22597	−	10.7837i	0.374082	−	0.647929i	0.990189	+	0.139733i	$0.0446245\pi$
$278$	−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	−0.590259	−	0.807214i	$-0.700974\pi$
$281$	−5.22472	−	29.6308i	−0.311680	−	1.76763i	0.278579	−	0.960413i	$-0.410137\pi$
$282$	−11.7669	−	16.3802i	−0.700707	−	0.975429i
$283$	21.0118	+	17.6310i	1.24902	+	1.04805i	0.996763	+	0.0803941i	$0.0256179\pi$
$283$	21.0118	+	17.6310i	1.24902	+	1.04805i	0.252259	+	0.967660i	$0.418827\pi$
$284$	−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	−0.966104	−	0.258153i	$-0.916886\pi$
$293$	−4.44167	+	7.69320i	−0.259485	+	0.449442i	0.706619	+	0.707594i	$0.250220\pi$
$294$	−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	−0.934402	−	0.356220i	$-0.884065\pi$
$307$	−7.84228	−	21.5465i	−0.447582	−	1.22972i	0.486820	−	0.873503i	$-0.338157\pi$
$308$	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	−0.812687	−	0.582701i	$-0.801996\pi$
$311$	−12.5985	+	7.27375i	−0.714396	+	0.412457i	0.0982907	+	0.995158i	$0.468662\pi$
$312$	−2.99860	−	0.764788i	−0.169763	−	0.0432976i
$313$	−13.4333	+	11.2718i	−0.759292	+	0.637122i	−0.937943	−	0.346791i	$-0.887271\pi$
$313$	−13.4333	+	11.2718i	−0.759292	+	0.637122i	0.178650	+	0.983913i	$0.442827\pi$
$314$	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	0.763041	−	0.646351i	$-0.223706\pi$
$317$	16.5955	+	6.04028i	0.932098	+	0.339256i	0.169057	+	0.985606i	$0.445928\pi$
$318$	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	0.394933	−	0.918710i	$-0.370768\pi$
$331$	−3.69737	−	2.13468i	−0.203226	−	0.117332i	−0.598159	+	0.801377i	$0.704101\pi$
$332$	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	−0.402837	−	0.915272i	$-0.631976\pi$
$337$	−20.0909	−	3.54257i	−1.09442	−	0.192976i	−0.691585	+	0.722295i	$0.743087\pi$
$338$	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	0.823691	−	0.567039i	$-0.191911\pi$
$347$	26.1493	+	4.61083i	1.40377	+	0.247522i	0.580078	+	0.814561i	$0.303022\pi$
$348$	−3.59047	−	0.270481i	−0.192469	−	0.0144993i
$349$	−1.37375	−	2.37941i	−0.0735352	−	0.127367i	0.826913	−	0.562330i	$-0.190095\pi$
$349$	−1.37375	−	2.37941i	−0.0735352	−	0.127367i	−0.900448	+	0.434963i	$0.856761\pi$
$350$	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	0.941902	−	0.335888i	$-0.109036\pi$
$353$	21.0798	+	12.1704i	1.12197	+	0.647767i	0.180063	+	0.983655i	$0.442370\pi$
$354$	−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	0.0620627	−	0.998072i	$-0.480232\pi$
$359$	19.5952	−	23.3526i	1.03419	−	1.23251i	0.972132	−	0.234433i	$-0.0753234\pi$
$360$	−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	0.613490	−	0.789703i	$-0.289765\pi$
$367$	11.0315	+	4.01514i	0.575839	+	0.209588i	−0.0376505	+	0.999291i	$0.511987\pi$
$368$	−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	0.157567	−	0.987508i	$-0.449635\pi$
$373$	21.0815	−	12.1714i	1.09156	−	0.630212i	0.933991	+	0.357297i	$0.116302\pi$
$374$	−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	$0.0421780\pi$
$379$			5.14415i			0.264237i	−0.991234	+	0.132119i	$0.957822\pi$
$380$	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	−0.604707	−	0.796448i	$-0.706710\pi$
$383$	−10.8810	+	3.96036i	−0.555993	+	0.202365i	0.0487143	+	0.998813i	$0.484488\pi$
$384$	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	0.214319	−	0.976764i	$-0.431247\pi$
$389$	−15.4791	−	18.4473i	−0.784821	−	0.935314i	−0.999141	+	0.0414499i	$0.986802\pi$
$390$	−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	0.851284	−	0.524705i	$-0.175825\pi$
$397$	9.61123	+	8.06478i	0.482374	+	0.404760i	−0.368910	+	0.929465i	$0.620269\pi$
$398$	−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	0.115031	−	0.993362i	$-0.463303\pi$
$401$	−16.8863	−	14.1693i	−0.843264	−	0.707583i	−0.958295	+	0.285779i	$0.907748\pi$
$402$	−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	0.936472	−	0.350743i	$-0.114071\pi$
$409$	8.66466	+	10.3261i	0.428440	+	0.510595i	−0.508031	+	0.861338i	$0.669627\pi$
$410$	−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	$0.337168\pi$
$419$			35.6982i			1.74397i	−0.489530	+	0.871986i	$0.662832\pi$
$420$	−1.24866	+	2.76444i	−0.0609286	+	0.134891i
$421$	0.543107	+	1.49217i	0.0264694	+	0.0727241i	0.952224	−	0.305402i	$-0.0987908\pi$
$421$	0.543107	+	1.49217i	0.0264694	+	0.0727241i	−0.925754	+	0.378126i	$0.876569\pi$
$422$	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	0.536930	−	0.843627i	$-0.319584\pi$
$431$	8.42816	+	3.06760i	0.405970	+	0.147761i	−0.130960	+	0.991388i	$0.541806\pi$
$432$	−13.5273	−	17.9022i	−0.650835	−	0.861320i
$433$	12.5463	−	2.21225i	0.602936	−	0.106314i	0.136156	−	0.990687i	$-0.456525\pi$
$433$	12.5463	−	2.21225i	0.602936	−	0.106314i	0.466780	+	0.884374i	$0.345414\pi$
$434$	−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	−0.834595	−	0.550864i	$-0.814298\pi$
$439$	−3.08365	+	3.67495i	−0.147175	+	0.175396i	0.687421	+	0.726259i	$0.258743\pi$
$440$	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	−0.989246	−	0.146260i	$-0.953277\pi$
$443$	−2.89248	+	7.94702i	−0.137426	+	0.377574i	0.851820	+	0.523834i	$0.175499\pi$
$444$	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	0.915045	−	0.403351i	$-0.132155\pi$
$449$	2.29293	+	3.97148i	0.108210	+	0.187426i	−0.806835	+	0.590777i	$0.798821\pi$
$450$	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	−0.435288	−	0.900291i	$-0.643353\pi$
$461$	−24.7397	−	4.36228i	−1.15224	−	0.203171i	−0.716955	+	0.697120i	$0.754465\pi$
$462$	−2.27548	+	30.2056i	−0.105865	+	1.40529i
$463$	5.36106	+	9.28562i	0.249149	+	0.431539i	0.963290	−	0.268463i	$-0.0865157\pi$
$463$	5.36106	+	9.28562i	0.249149	+	0.431539i	−0.714141	+	0.700002i	$0.753182\pi$
$464$	−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	0.564786	−	0.825237i	$-0.308959\pi$
$467$	2.86340	+	1.65318i	0.132502	+	0.0765002i	−0.432284	+	0.901738i	$0.642292\pi$
$468$	−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	−0.309028	−	0.951053i	$-0.600004\pi$
$479$	−5.99987	+	1.05794i	−0.274141	+	0.0483385i	0.0348874	+	0.999391i	$0.488893\pi$
$480$	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	−0.456765	−	0.889587i	$-0.650992\pi$
$487$	1.88147	−	1.08627i	0.0852575	−	0.0492234i	0.542023	+	0.840364i	$0.317659\pi$
$488$	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	0.891082	+	0.453842i	$0.149947\pi$
$491$	11.0836	+	30.4521i	0.500198	+	1.37428i	−0.390884	+	0.920440i	$0.627831\pi$
$492$	−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	−0.854579	−	0.519321i	$-0.826185\pi$
$499$	2.81643	−	15.9728i	0.126081	−	0.715039i	0.980660	−	0.195719i	$-0.0627039\pi$
$500$	−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	0.946120	−	0.323815i	$-0.104966\pi$
$503$	10.3825	+	12.3734i	0.462933	+	0.551702i	−0.483188	+	0.875517i	$0.660521\pi$
$504$	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	0.871860	+	0.489756i	$0.162914\pi$
$509$	4.96536	+	28.1600i	0.220086	+	1.24817i	−0.651774	+	0.758413i	$0.725975\pi$
$510$	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	−0.877910	−	0.478827i	$-0.841062\pi$
$521$	−0.554173	+	0.959856i	−0.0242788	+	0.0420521i	0.853631	+	0.520879i	$0.174396\pi$
$522$	2.13291	−	6.33186i	0.0933548	−	0.277138i
$523$	8.07045	+	9.61798i	0.352896	+	0.420565i	0.913065	−	0.407813i	$-0.133708\pi$
$523$	8.07045	+	9.61798i	0.352896	+	0.420565i	−0.560170	+	0.828378i	$0.689264\pi$
$524$	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	−0.119540	−	0.992829i	$-0.538142\pi$
$541$	19.4785	−	16.3444i	0.837448	−	0.702702i	0.956988	+	0.290127i	$0.0936975\pi$
$542$	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	0.572144	−	0.820153i	$-0.306112\pi$
$547$	32.5162	−	5.73349i	1.39029	−	0.245146i	0.818149	+	0.575007i	$0.195001\pi$
$548$	−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	0.353123	+	0.935577i	$0.385120\pi$
$557$	−12.2432	+	33.6380i	−0.518762	+	1.42529i	−0.871885	+	0.489710i	$0.837103\pi$
$558$	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	0.999262	−	0.0384008i	$-0.0122264\pi$
$563$	11.0660	+	19.1668i	0.466375	+	0.807785i	−0.532887	+	0.846186i	$0.678893\pi$
$564$	−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	0.979592	−	0.200996i	$-0.0644179\pi$
$577$	7.58405	+	13.1360i	0.315728	+	0.546857i	−0.663864	+	0.747853i	$0.731085\pi$
$578$	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	−0.846257	−	0.532775i	$-0.821149\pi$
$587$	−4.23083	+	5.04211i	−0.174625	+	0.208110i	0.671632	+	0.740885i	$0.265594\pi$
$588$	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	−0.289288	−	0.957242i	$-0.593419\pi$
$593$	−5.69179	+	1.00362i	−0.233734	+	0.0412136i	0.0555543	+	0.998456i	$0.482307\pi$
$594$	−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	0.134447	−	0.990921i	$-0.457074\pi$
$599$	27.7457	−	23.2814i	1.13366	−	0.951254i	0.999213	+	0.0396667i	$0.0126296\pi$
$600$	0.694039	−	2.72121i	0.0283340	−	0.111093i
$601$	6.07461	−	3.50718i	0.247789	−	0.143061i	−0.370963	−	0.928648i	$-0.620972\pi$
$601$	6.07461	−	3.50718i	0.247789	−	0.143061i	0.618751	+	0.785587i	$0.287639\pi$
$602$	−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	$-0.906459\pi$
$607$		−	14.2728i		−	0.579314i	0.957130	−	0.289657i	$-0.0935413\pi$
$608$	−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	−0.838235	−	0.545310i	$-0.816412\pi$
$613$	3.36609	−	19.0901i	0.135955	−	0.771040i	0.974190	−	0.225730i	$-0.0724768\pi$
$614$	−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	0.707397	−	0.706817i	$-0.249869\pi$
$617$	−2.77009	−	3.30127i	−0.111520	−	0.132904i	−0.818917	+	0.573913i	$0.805425\pi$
$618$	6.67486	+	4.55467i	0.268502	+	0.183216i
$619$	4.18376	−	7.24648i	0.168159	−	0.291261i	−0.769613	−	0.638510i	$-0.779551\pi$
$619$	4.18376	−	7.24648i	0.168159	−	0.291261i	0.937773	+	0.347250i	$0.112884\pi$
$620$	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	0.947406	+	0.320034i	$0.103694\pi$
$631$	4.18478	+	23.7331i	0.166593	+	0.944799i	−0.780813	+	0.624765i	$0.785195\pi$
$632$	−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	−0.982149	−	0.188103i	$-0.939766\pi$
$641$	0.129228	−	0.732886i	0.00510418	−	0.0289473i	0.987253	+	0.159156i	$0.0508772\pi$
$642$	12.6513	+	26.2969i	0.499305	+	1.03786i
$643$	−36.8973	+	13.4295i	−1.45509	+	0.529608i	−0.944007	−	0.329926i	$-0.892976\pi$
$643$	−36.8973	+	13.4295i	−1.45509	+	0.529608i	−0.511079	+	0.859534i	$0.670754\pi$
$644$	−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	$0.0632226\pi$
$647$			10.0379i			0.394633i	−0.980340	+	0.197316i	$0.936777\pi$
$648$	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	0.0495780	−	0.998770i	$-0.484212\pi$
$653$	24.0034	−	13.8584i	0.939327	−	0.542321i	0.889749	+	0.456449i	$0.150879\pi$
$654$	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	−0.527688	−	0.849438i	$-0.676941\pi$
$659$	−37.9399	−	13.8090i	−1.47793	−	0.537922i	−0.950241	+	0.311516i	$0.899163\pi$
$660$	−0.715126	−	7.17494i	−0.0278362	−	0.279284i
$661$	−28.3986	+	5.00744i	−1.10458	+	0.194767i	−0.696060	−	0.717984i	$-0.745065\pi$
$661$	−28.3986	+	5.00744i	−1.10458	+	0.194767i	−0.408517	+	0.912751i	$0.633954\pi$
$662$	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	0.152596	−	0.988289i	$-0.451237\pi$
$673$	−16.2655	−	9.39089i	−0.626989	−	0.361992i	−0.779585	+	0.626296i	$0.784570\pi$
$674$	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	0.948676	−	0.316251i	$-0.102424\pi$
$677$	5.21572	+	9.03390i	0.200457	+	0.347201i	−0.748219	+	0.663452i	$0.769091\pi$
$678$	−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	0.856609	−	0.515967i	$-0.172567\pi$
$691$	−0.487247	−	0.843937i	−0.0185358	−	0.0321049i	−0.875145	+	0.483862i	$0.839234\pi$
$692$	−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	−0.545799	−	0.837916i	$-0.683774\pi$
$701$	9.90651	−	11.8061i	0.374164	−	0.445911i	0.919963	+	0.392005i	$0.128218\pi$
$702$	−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	−0.300558	−	0.953763i	$-0.597173\pi$
$709$	−30.4578	−	11.0857i	−1.14387	−	0.416333i	−0.843308	+	0.537430i	$0.819395\pi$
$710$	−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	−0.966583	−	0.256354i	$-0.917479\pi$
$719$	−10.4822	−	28.7995i	−0.390919	−	1.07404i	0.575664	−	0.817686i	$-0.304743\pi$
$720$	−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	0.512213	+	0.858859i	$0.328826\pi$
$727$	−7.08739	+	40.1946i	−0.262857	+	1.49073i	−0.775069	+	0.631876i	$0.782285\pi$
$728$	−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	−0.386093	−	0.922460i	$-0.626176\pi$
$733$	16.4021	−	28.4094i	0.605827	−	1.04932i	0.991920	−	0.126864i	$-0.0404910\pi$
$734$	−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	0.762119	−	0.647437i	$-0.224159\pi$
$739$	6.98259	+	5.85908i	0.256859	+	0.215530i	−0.505260	+	0.862967i	$0.668604\pi$
$740$	−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	0.823216	−	0.567729i	$-0.192178\pi$
$743$	11.0957	+	9.31040i	0.407062	+	0.341565i	−0.416154	+	0.909294i	$0.636622\pi$
$744$	−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	−0.960535	−	0.278160i	$-0.910275\pi$
$751$	−29.2589	−	34.8694i	−1.06767	−	1.27240i	−0.107139	−	0.994244i	$-0.534169\pi$
$752$	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	0.393455	−	0.919344i	$-0.371280\pi$
$757$	35.3771	−	12.8762i	1.28580	−	0.467994i	0.892347	+	0.451350i	$0.149057\pi$
$758$	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	$-0.938868\pi$
$761$		−	10.5310i		−	0.381748i	0.981615	−	0.190874i	$-0.0611322\pi$
$762$	−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	0.216468	−	0.976290i	$-0.430546\pi$
$769$	33.7073	−	28.2837i	1.21551	−	1.01994i	0.999047	−	0.0436483i	$-0.0138981\pi$
$770$	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	0.438003	−	0.898974i	$-0.355686\pi$
$773$	5.44057	+	1.98021i	0.195684	+	0.0712231i	−0.242319	+	0.970197i	$0.577908\pi$
$774$	−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	0.506858	−	0.862030i	$-0.330807\pi$
$787$	0.385641	+	0.222650i	0.0137466	+	0.00793662i	−0.493111	+	0.869966i	$0.664140\pi$
$788$	−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	0.825913	−	0.563797i	$-0.190660\pi$
$809$	21.3495	+	12.3261i	0.750608	+	0.433364i	−0.0753057	+	0.997160i	$0.523993\pi$
$810$	−0.420385	−	8.69658i	−0.0147708	−	0.305567i
$811$	−5.65228	+	15.5295i	−0.198478	+	0.545315i	−0.998506	−	0.0546487i	$-0.982596\pi$
$811$	−5.65228	+	15.5295i	−0.198478	+	0.545315i	0.800027	+	0.599964i	$0.204818\pi$
$812$	−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	−0.00367851	−	0.999993i	$-0.501171\pi$
$821$	9.59543	−	1.69193i	0.334883	−	0.0590488i	0.338561	+	0.940944i	$0.390060\pi$
$822$	6.21652	−	0.619600i	0.216826	−	0.0216110i
$823$	−38.3969	−	13.9753i	−1.33843	−	0.487150i	−0.429114	−	0.903250i	$-0.641174\pi$
$823$	−38.3969	−	13.9753i	−1.33843	−	0.487150i	−0.909318	+	0.416101i	$0.863396\pi$
$824$	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	−0.847074	−	0.531476i	$-0.821638\pi$
$827$	−13.5381	+	11.3598i	−0.470765	+	0.395019i	0.376309	+	0.926494i	$0.377193\pi$
$828$	−18.6368	+	0.450181i	−0.647674	+	0.0156449i
$829$	−24.9946	+	14.4306i	−0.868097	+	0.501196i	−0.866715	−	0.498803i	$-0.833773\pi$
$829$	−24.9946	+	14.4306i	−0.868097	+	0.501196i	−0.00138139	+	0.999999i	$0.500440\pi$
$830$	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	−0.433146	−	0.901324i	$-0.642597\pi$
$839$	−5.37586	+	1.95665i	−0.185595	+	0.0675511i	0.247551	+	0.968875i	$0.420374\pi$
$840$	−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	0.877852	−	0.478932i	$-0.158976\pi$
$853$	16.3156	+	13.6904i	0.558634	+	0.468750i	−0.319218	+	0.947681i	$0.603420\pi$
$854$	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	−0.995278	−	0.0970637i	$-0.969055\pi$
$857$	−36.9941	−	31.0418i	−1.26370	−	1.06037i	−0.268417	−	0.963303i	$-0.586501\pi$
$858$	66.4695	−	47.7489i	2.26923	−	1.63012i
$859$	−6.19245	−	35.1191i	−0.211284	−	1.19825i	−0.887240	−	0.461307i	$-0.847381\pi$
$859$	−6.19245	−	35.1191i	−0.211284	−	1.19825i	0.675957	−	0.736941i	$-0.263731\pi$
$860$	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	−0.877886	−	0.478870i	$-0.841047\pi$
$863$	−0.711785	+	1.23285i	−0.0242294	+	0.0419666i	0.853656	+	0.520837i	$0.174380\pi$
$864$	−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	0.900832	−	0.434169i	$-0.142958\pi$
$877$	−2.02335	−	5.55910i	−0.0683236	−	0.187718i	−0.969155	+	0.246451i	$0.920736\pi$
$878$	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	−0.496700	−	0.867922i	$-0.665455\pi$
$881$	0.195705	−	0.112990i	0.00659346	−	0.00380673i	0.503293	+	0.864116i	$0.332122\pi$
$882$	0.458890	+	18.9973i	0.0154516	+	0.639673i
$883$	−0.614505	+	0.515631i	−0.0206797	+	0.0173524i	−0.653069	−	0.757298i	$-0.726519\pi$
$883$	−0.614505	+	0.515631i	−0.0206797	+	0.0173524i	0.632389	+	0.774651i	$0.282074\pi$
$884$	−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	−0.481170	−	0.876627i	$-0.659788\pi$
$887$	−42.0903	−	15.3196i	−1.41325	−	0.514382i	−0.932083	+	0.362246i	$0.882010\pi$
$888$	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	−0.185158	−	0.982709i	$-0.559280\pi$
$907$	−20.9386	−	3.69204i	−0.695256	−	0.122592i	−0.510098	+	0.860116i	$0.670391\pi$
$908$	−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	0.955800	+	0.294016i	$0.0949919\pi$
$919$	22.2065	+	38.4628i	0.732526	+	1.26877i	−0.223275	+	0.974756i	$0.571675\pi$
$920$	−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	−0.488724	+	0.872438i	$0.662538\pi$
$929$	−38.4969	+	45.8788i	−1.26304	+	1.50524i	−0.774318	+	0.632797i	$0.781907\pi$
$930$	−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	−0.0391088	−	0.999235i	$-0.512452\pi$
$937$	−21.7752	−	7.92551i	−0.711364	−	0.258915i	−0.672255	+	0.740320i	$0.734674\pi$
$938$	−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	−0.525850	−	0.850577i	$-0.676253\pi$
$941$	6.76374	−	5.67545i	0.220492	−	0.185014i	0.746342	+	0.665563i	$0.231808\pi$
$942$	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	−0.999744	−	0.0226124i	$-0.992802\pi$
$947$	−7.64505	−	21.0046i	−0.248431	−	0.682558i	0.751314	−	0.659945i	$-0.229421\pi$
$948$	−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	−0.460384	−	0.887720i	$-0.652288\pi$
$953$	−7.48437	+	2.72409i	−0.242443	+	0.0882419i	0.217941	+	0.975962i	$0.430066\pi$
$954$	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	−0.126776	−	0.991931i	$-0.540463\pi$
$967$	−35.0040	−	29.3718i	−1.12565	−	0.944534i	−0.998876	+	0.0473972i	$0.984907\pi$
$968$	−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	0.999229	−	0.0392486i	$-0.0124964\pi$
$971$	35.3393	+	29.6532i	1.13409	+	0.951616i	0.134862	+	0.990864i	$0.456941\pi$
$972$	−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	0.366753	+	0.930318i	$0.380469\pi$
$977$	−19.4513	+	33.6907i	−0.622303	+	1.07786i	−0.989056	+	0.147541i	$0.952864\pi$
$978$	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	−0.954197	−	0.299179i	$-0.903287\pi$
$983$	1.40399	−	7.96240i	0.0447802	−	0.253961i	0.998977	+	0.0452181i	$0.0143983\pi$
$984$	−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	0.965361	+	0.260918i	$0.0840253\pi$
$991$	12.3895	+	34.0400i	0.393567	+	1.08132i	−0.571794	+	0.820397i	$0.693752\pi$
$992$	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	−0.905314	−	0.424742i	$-0.860365\pi$
$997$	−20.3418	+	17.0688i	−0.644231	+	0.540574i	0.261083	+	0.965316i	$0.415920\pi$
$998$	−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.41.1	yes	24
3.2	odd	2	inner	57.2.j.b.41.4	yes	24
4.3	odd	2		912.2.cc.e.497.1		24
12.11	even	2		912.2.cc.e.497.4		24
19.5	even	9		1083.2.d.d.1082.5		24
19.13	odd	18	inner	57.2.j.b.32.4	yes	24
19.14	odd	18		1083.2.d.d.1082.19		24
57.5	odd	18		1083.2.d.d.1082.20		24
57.14	even	18		1083.2.d.d.1082.6		24
57.32	even	18	inner	57.2.j.b.32.1	✓	24
76.51	even	18		912.2.cc.e.545.4		24
228.203	odd	18		912.2.cc.e.545.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.32.1	✓	24	57.32	even	18	inner
57.2.j.b.32.4	yes	24	19.13	odd	18	inner
57.2.j.b.41.1	yes	24	1.1	even	1	trivial
57.2.j.b.41.4	yes	24	3.2	odd	2	inner
912.2.cc.e.497.1		24	4.3	odd	2
912.2.cc.e.497.4		24	12.11	even	2
912.2.cc.e.545.1		24	228.203	odd	18
912.2.cc.e.545.4		24	76.51	even	18
1083.2.d.d.1082.5		24	19.5	even	9
1083.2.d.d.1082.6		24	57.14	even	18
1083.2.d.d.1082.19		24	19.14	odd	18
1083.2.d.d.1082.20		24	57.5	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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