LMFDB - Embedded newform 57.2.j.b.41.4

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			41.4
Character	$\chi$	$=$	57.41
Dual form			57.2.j.b.32.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49833 + 1.25725i) q^{2} +(-1.72716 + 0.130112i) q^{3} +(0.317026 + 1.79794i) q^{4} +(0.487091 + 0.0858872i) q^{5} +(-2.75144 - 1.97652i) q^{6} +(-0.969730 - 1.67962i) q^{7} +(0.170480 - 0.295279i) q^{8} +(2.96614 - 0.449448i) q^{9} +O(q^{10})$	\(q+(1.49833 + 1.25725i) q^{2} +(-1.72716 + 0.130112i) q^{3} +(0.317026 + 1.79794i) q^{4} +(0.487091 + 0.0858872i) q^{5} +(-2.75144 - 1.97652i) q^{6} +(-0.969730 - 1.67962i) q^{7} +(0.170480 - 0.295279i) q^{8} +(2.96614 - 0.449448i) q^{9} +(0.621842 + 0.741083i) q^{10} +(-3.99257 - 2.30511i) q^{11} +(-0.781488 - 3.06408i) q^{12} +(-1.79223 + 4.92410i) q^{13} +(0.658727 - 3.73582i) q^{14} +(-0.852457 - 0.0849643i) 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} +(1.89341 + 2.77480i) q^{21} +(-3.08409 - 8.47347i) q^{22} +(3.35200 - 0.591048i) q^{23} +(-0.256026 + 0.532175i) q^{24} +(-4.46858 - 1.62643i) q^{25} +(-8.87617 + 5.12466i) q^{26} +(-5.06451 + 1.16220i) q^{27} +(2.71243 - 2.27600i) q^{28} +(0.872266 - 0.731918i) q^{29} +(-1.17044 - 1.19906i) q^{30} +(-1.31458 + 0.758971i) q^{31} +(7.29606 + 2.65555i) q^{32} +(7.19571 + 3.46180i) q^{33} +(-4.84348 + 0.854036i) q^{34} +(-0.328088 - 0.901415i) q^{35} +(1.74843 + 5.19047i) 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} +(-0.651648 + 6.53806i) q^{42} +(-0.829591 + 4.70484i) q^{43} +(2.87871 - 7.90919i) q^{44} +(1.48338 + 0.0358318i) q^{45} +(5.76551 + 3.32872i) q^{46} +(-3.82673 - 4.56052i) q^{47} +(-6.81634 + 3.07886i) q^{48} +(1.61925 - 2.80462i) q^{49} +(-4.65059 - 8.05506i) q^{50} +(2.54096 - 3.53718i) q^{51} +(-9.42143 - 1.66125i) q^{52} +(1.71646 + 9.73455i) q^{53} +(-9.04950 - 4.62600i) q^{54} +(-1.74676 - 1.46571i) q^{55} -0.661277 q^{56} +(-5.27295 - 5.40333i) q^{57} +2.22715 q^{58} +(-0.172251 - 0.144536i) q^{59} +(-0.117490 - 1.55961i) q^{60} +(-1.90402 - 10.7982i) q^{61} +(-2.92389 - 0.515560i) q^{62} +(-3.63126 - 4.54615i) q^{63} +(3.27498 + 5.67243i) q^{64} +(-1.29589 + 2.24455i) q^{65} +(6.42921 + 14.2337i) q^{66} +(0.266197 + 0.317241i) q^{67} +(-3.97564 - 2.29534i) q^{68} +(-5.71253 + 1.45697i) q^{69} +(0.641719 - 1.76311i) q^{70} +(0.540928 - 3.06775i) q^{71} +(0.372954 - 0.952462i) 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} +(14.6638 - 10.0060i) q^{78} +(4.94012 + 13.5729i) q^{79} +(2.10338 - 0.370883i) q^{80} +(8.59599 - 2.66625i) q^{81} +(18.3938 + 6.69478i) q^{82} +(-6.05130 + 3.49372i) q^{83} +(-4.38866 + 4.28393i) q^{84} +(-0.952717 + 0.799425i) q^{85} +(-7.15817 + 6.00642i) q^{86} +(-1.41131 + 1.37763i) q^{87} +(-1.36130 + 0.785948i) q^{88} +(-5.32595 - 1.93849i) q^{89} +(2.17755 + 1.91867i) q^{90} +(10.0086 - 1.76478i) q^{91} +(2.12534 + 5.83933i) q^{92} +(2.17173 - 1.48190i) 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} +(-12.8785 - 5.04283i) 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	0.994058	−	0.108847i	$-0.0347160\pi$
$2$	1.49833	+	1.25725i	1.05948	+	0.889010i	0.0654227	+	0.997858i	$0.479160\pi$
$3$	−1.72716	+	0.130112i	−0.997174	+	0.0751202i
$3$	−1.72716	+	0.130112i	−0.997174	+	0.0751202i
$4$	0.317026	+	1.79794i	0.158513	+	0.898972i
$5$	0.487091	+	0.0858872i	0.217834	+	0.0384099i	0.281500	−	0.959561i	$-0.409168\pi$
$5$	0.487091	+	0.0858872i	0.217834	+	0.0384099i	−0.0636661	+	0.997971i	$0.520279\pi$
$6$	−2.75144	−	1.97652i	−1.12327	−	0.806910i
$7$	−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
$9$	2.96614	−	0.449448i	0.988714	−	0.149816i
$10$	0.621842	+	0.741083i	0.196644	+	0.234351i
$11$	−3.99257	−	2.30511i	−1.20380	−	0.695016i	−0.242405	−	0.970175i	$-0.577936\pi$
$11$	−3.99257	−	2.30511i	−1.20380	−	0.695016i	−0.961399	+	0.275159i	$0.911270\pi$
$12$	−0.781488	−	3.06408i	−0.225596	−	0.884524i
$13$	−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
$15$	−0.852457	−	0.0849643i	−0.220103	−	0.0219377i
$16$	4.05783	−	1.47693i	1.01446	−	0.369232i
$17$	−1.61629	+	1.92622i	−0.392008	+	0.467177i	−0.925566	−	0.378587i	$-0.876410\pi$
$17$	−1.61629	+	1.92622i	−0.392008	+	0.467177i	0.533558	+	0.845764i	$0.320855\pi$
$18$	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
$21$	1.89341	+	2.77480i	0.413177	+	0.605510i
$22$	−3.08409	−	8.47347i	−0.657531	−	1.80655i
$23$	3.35200	−	0.591048i	0.698940	−	0.123242i	0.187123	−	0.982336i	$-0.440084\pi$
$23$	3.35200	−	0.591048i	0.698940	−	0.123242i	0.511817	+	0.859094i	$0.328973\pi$
$24$	−0.256026	+	0.532175i	−0.0522610	+	0.108630i
$25$	−4.46858	−	1.62643i	−0.893716	−	0.325286i
$26$	−8.87617	+	5.12466i	−1.74076	+	1.00503i
$27$	−5.06451	+	1.16220i	−0.974666	+	0.223665i
$28$	2.71243	−	2.27600i	0.512602	−	0.430124i
$29$	0.872266	−	0.731918i	0.161976	−	0.135914i	−0.558197	−	0.829708i	$-0.688507\pi$
$29$	0.872266	−	0.731918i	0.161976	−	0.135914i	0.720173	+	0.693794i	$0.244062\pi$
$30$	−1.17044	−	1.19906i	−0.213693	−	0.218917i
$31$	−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
$33$	7.19571	+	3.46180i	1.25261	+	0.602623i
$34$	−4.84348	+	0.854036i	−0.830650	+	0.146466i
$35$	−0.328088	−	0.901415i	−0.0554570	−	0.152367i
$36$	1.74843	+	5.19047i	0.291404	+	0.865078i
$37$		−	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	0.520932	−	0.853598i	$-0.325585\pi$
$41$	9.40408	−	3.42281i	1.46867	−	0.534552i	0.947739	+	0.319046i	$0.103362\pi$
$42$	−0.651648	+	6.53806i	−0.100552	+	1.00884i
$43$	−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
$45$	1.48338	+	0.0358318i	0.221129	+	0.00534149i
$46$	5.76551	+	3.32872i	0.850078	+	0.490793i
$47$	−3.82673	−	4.56052i	−0.558186	−	0.665220i	0.410976	−	0.911646i	$-0.365188\pi$
$47$	−3.82673	−	4.56052i	−0.558186	−	0.665220i	−0.969162	+	0.246426i	$0.920744\pi$
$48$	−6.81634	+	3.07886i	−0.983854	+	0.444395i
$49$	1.61925	−	2.80462i	0.231321	−	0.400660i
$50$	−4.65059	−	8.05506i	−0.657693	−	1.13916i
$51$	2.54096	−	3.53718i	0.355806	−	0.495305i
$52$	−9.42143	−	1.66125i	−1.30652	−	0.230374i
$53$	1.71646	+	9.73455i	0.235774	+	1.33714i	0.840977	+	0.541071i	$0.181981\pi$
$53$	1.71646	+	9.73455i	0.235774	+	1.33714i	−0.605202	+	0.796072i	$0.706908\pi$
$54$	−9.04950	−	4.62600i	−1.23148	−	0.629519i
$55$	−1.74676	−	1.46571i	−0.235533	−	0.197636i
$56$	−0.661277			−0.0883668
$57$	−5.27295	−	5.40333i	−0.698420	−	0.715688i
$58$	2.22715			0.292439
$59$	−0.172251	−	0.144536i	−0.0224252	−	0.0188170i	0.631506	−	0.775371i	$-0.282437\pi$
$59$	−0.172251	−	0.144536i	−0.0224252	−	0.0188170i	−0.653931	+	0.756554i	$0.726881\pi$
$60$	−0.117490	−	1.55961i	−0.0151679	−	0.201344i
$61$	−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
$63$	−3.63126	−	4.54615i	−0.457495	−	0.572761i
$64$	3.27498	+	5.67243i	0.409372	+	0.709054i
$65$	−1.29589	+	2.24455i	−0.160736	+	0.278402i
$66$	6.42921	+	14.2337i	0.791381	+	1.75205i
$67$	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
$69$	−5.71253	+	1.45697i	−0.687708	+	0.175398i
$70$	0.641719	−	1.76311i	0.0767001	−	0.210732i
$71$	0.540928	−	3.06775i	0.0641963	−	0.364075i	−0.935739	−	0.352694i	$-0.885266\pi$
$71$	0.540928	−	3.06775i	0.0641963	−	0.364075i	0.999935	−	0.0113819i	$-0.00362306\pi$
$72$	0.372954	−	0.952462i	0.0439531	−	0.112249i
$73$	−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
$78$	14.6638	−	10.0060i	1.66034	−	1.13296i
$79$	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
$81$	8.59599	−	2.66625i	0.955110	−	0.296250i
$82$	18.3938	+	6.69478i	2.03125	+	0.739315i
$83$	−6.05130	+	3.49372i	−0.664217	+	0.383486i	−0.793882	−	0.608072i	$-0.791943\pi$
$83$	−6.05130	+	3.49372i	−0.664217	+	0.383486i	0.129665	+	0.991558i	$0.458610\pi$
$84$	−4.38866	+	4.28393i	−0.478842	+	0.467415i
$85$	−0.952717	+	0.799425i	−0.103337	+	0.0867098i
$86$	−7.15817	+	6.00642i	−0.771885	+	0.647689i
$87$	−1.41131	+	1.37763i	−0.151308	+	0.147697i
$88$	−1.36130	+	0.785948i	−0.145115	+	0.0837824i
$89$	−5.32595	−	1.93849i	−0.564549	−	0.205479i	0.0439498	−	0.999034i	$-0.486006\pi$
$89$	−5.32595	−	1.93849i	−0.564549	−	0.205479i	−0.608499	+	0.793555i	$0.708228\pi$
$90$	2.17755	+	1.91867i	0.229534	+	0.202246i
$91$	10.0086	−	1.76478i	1.04919	−	0.185000i
$92$	2.12534	+	5.83933i	0.221582	+	0.608792i
$93$	2.17173	−	1.48190i	0.225198	−	0.153666i
$94$		−	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
$99$	−12.8785	−	5.04283i	−1.29434	−	0.506823i
$100$	1.50757	−	8.54988i	0.150757	−	0.854988i
$101$	3.72167	−	10.2252i	0.370320	−	1.01745i	−0.604918	−	0.796288i	$-0.706794\pi$
$101$	3.72167	−	10.2252i	0.370320	−	1.01745i	0.975238	−	0.221158i	$-0.0709836\pi$
$102$	8.25433	−	2.10525i	0.817300	−	0.208451i
$103$	−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
$105$	0.683945	+	1.51420i	0.0667462	+	0.147770i
$106$	−9.66693	+	16.7436i	−0.938935	+	1.62628i
$107$	4.30693	+	7.45983i	0.416367	+	0.721169i	0.995571	−	0.0940139i	$-0.0299698\pi$
$107$	4.30693	+	7.45983i	0.416367	+	0.721169i	−0.579204	+	0.815183i	$0.696636\pi$
$108$	−3.69515	−	8.73726i	−0.355566	−	0.840743i
$109$	−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
$111$	0.426910	+	5.66696i	0.0405205	+	0.537884i
$112$	−6.41568	−	5.38339i	−0.606225	−	0.508683i
$113$	−8.90791			−0.837985			−0.418993	−	0.907990i	$-0.637617\pi$
$113$	−8.90791			−0.837985			−0.418993	+	0.907990i	$0.637617\pi$
$114$	−1.10730	−	14.7254i	−0.103708	−	1.37916i
$115$	1.68349			0.156986
$116$	1.59248	+	1.33625i	0.147858	+	0.124067i
$117$	−3.10287	+	15.4111i	−0.286860	+	1.42476i
$118$	−0.0763718	−	0.433126i	−0.00703059	−	0.0398725i
$119$	4.80268	+	0.846843i	0.440261	+	0.0776299i
$120$	−0.170415	+	0.237228i	−0.0155567	+	0.0216559i
$121$	5.12705	+	8.88031i	0.466096	+	0.807301i
$122$	10.7232	−	18.5732i	0.970836	−	1.68154i
$123$	−15.7970	+	7.13531i	−1.42437	+	0.643369i
$124$	−1.78134	−	2.12292i	−0.159969	−	0.190644i
$125$	−4.17862	−	2.41253i	−0.373747	−	0.215783i
$126$	0.274818	−	11.3770i	0.0244827	−	1.01355i
$127$	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
$129$	0.820676	−	8.23394i	0.0722565	−	0.724958i
$130$	−4.76364	+	1.73382i	−0.417799	+	0.152066i
$131$	−9.62927	+	11.4757i	−0.841313	+	1.00264i	0.158570	+	0.987348i	$0.449312\pi$
$131$	−9.62927	+	11.4757i	−0.841313	+	1.00264i	−0.999883	+	0.0152905i	$0.995133\pi$
$132$	−3.94290	+	14.0350i	−0.343185	+	1.22159i
$133$	2.89248	−	7.94368i	0.250810	−	0.688805i
$134$			0.810009i			0.0699741i
$135$	−2.56669	+	0.131119i	−0.220906	+	0.0112849i
$136$	0.293228	+	0.805638i	0.0251441	+	0.0690829i
$137$	1.81606	−	0.320220i	0.155157	−	0.0273583i	−0.0955303	−	0.995427i	$-0.530455\pi$
$137$	1.81606	−	0.320220i	0.155157	−	0.0273583i	0.250687	+	0.968068i	$0.419344\pi$
$138$	−10.3910	−	4.99906i	−0.884544	−	0.425548i
$139$	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
$141$	7.20274	+	7.37883i	0.606580	+	0.621409i
$142$	4.66743	−	3.91643i	0.391682	−	0.328660i
$143$	18.5062	−	15.5285i	1.54756	−	1.29856i
$144$	11.3723	−	6.20457i	0.947691	−	0.517047i
$145$	0.487735	−	0.281594i	0.0405042	−	0.0233851i
$146$	−0.231219	−	0.0841568i	−0.0191358	−	0.00696486i
$147$	−2.43178	+	5.05471i	−0.200570	+	0.416905i
$148$	5.89922	−	1.04019i	0.484913	−	0.0855032i
$149$	1.40291	+	3.85446i	0.114931	+	0.315770i	0.983799	−	0.179273i	$-0.0573746\pi$
$149$	1.40291	+	3.85446i	0.114931	+	0.315770i	−0.868869	+	0.495043i	$0.835152\pi$
$150$	9.08036	+	13.3073i	0.741409	+	1.08653i
$151$		−	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
$156$	16.4884	+	1.64340i	1.32013	+	0.131577i
$157$	−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
$159$	−4.23118	−	16.5898i	−0.335555	−	1.31565i
$160$	3.32576	+	1.92013i	0.262925	+	0.151800i
$161$	−4.24327	−	5.05693i	−0.334417	−	0.398542i
$162$	16.2318	+	6.81238i	1.27529	+	0.535231i
$163$	−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
$165$	3.20764	+	2.30423i	0.249714	+	0.179384i
$166$	−13.4593	−	2.37325i	−1.04465	−	0.184200i
$167$	−0.922825	−	5.23360i	−0.0714104	−	0.404988i	−0.999470	−	0.0325564i	$-0.989635\pi$
$167$	−0.922825	−	5.23360i	−0.0714104	−	0.404988i	0.928060	−	0.372432i	$-0.121476\pi$
$168$	1.14213	−	0.0860401i	0.0881171	−	0.00663814i
$169$	−11.0761	−	9.29394i	−0.852007	−	0.714919i
$170$	−2.43256			−0.186569
$171$	9.81026	+	8.64632i	0.750209	+	0.661201i
$172$	−8.72204			−0.665049
$173$	−8.83296	−	7.41174i	−0.671558	−	0.563504i	0.241968	−	0.970284i	$-0.422207\pi$
$173$	−8.83296	−	7.41174i	−0.671558	−	0.563504i	−0.913526	+	0.406780i	$0.866651\pi$
$174$	−3.84663	+	0.289779i	−0.291613	+	0.0219681i
$175$	1.60153	+	9.08272i	0.121064	+	0.686589i
$176$	−19.6056	−	3.45700i	−1.47783	−	0.260581i
$177$	0.316311	+	0.227224i	0.0237754	+	0.0170792i
$178$	−5.54288	−	9.60055i	−0.415456	−	0.719591i
$179$	−8.87880	+	15.3785i	−0.663633	+	1.14945i	0.316021	+	0.948752i	$0.397653\pi$
$179$	−8.87880	+	15.3785i	−0.663633	+	1.14945i	−0.979654	+	0.200694i	$0.935680\pi$
$180$	0.405847	+	2.67840i	0.0302500	+	0.199636i
$181$	−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
$183$	4.69352	+	18.4025i	0.346955	+	1.36035i
$184$	0.396924	−	1.09054i	0.0292616	−	0.0803956i
$185$	0.281804	−	1.59819i	0.0207186	−	0.117501i
$186$	5.11709	+	0.510020i	0.375203	+	0.0373965i
$187$	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	$-0.0329774\pi$
$192$	−6.39445	−	9.37106i	−0.461480	−	0.676298i
$193$	−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
$195$	1.94617	−	4.04531i	0.139368	−	0.289690i
$196$	5.55590	+	2.02218i	0.396850	+	0.144441i
$197$	13.9117	−	8.03191i	0.991165	−	0.572250i	0.0855430	−	0.996334i	$-0.472737\pi$
$197$	13.9117	−	8.03191i	0.991165	−	0.572250i	0.905622	+	0.424085i	$0.139404\pi$
$198$	−12.9562	−	23.7474i	−0.920760	−	1.68765i
$199$	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
$201$	−0.501041	−	0.513290i	−0.0353407	−	0.0362047i
$202$	18.4319	−	10.6417i	1.29687	−	0.748746i
$203$	−2.07521	−	0.755313i	−0.145651	−	0.0530126i
$204$	7.16520	+	3.44713i	0.501665	+	0.241347i
$205$	4.87462	−	0.859526i	0.340458	−	0.0600319i
$206$	−1.59567	−	4.38407i	−0.111176	−	0.305453i
$207$	9.67686	−	3.25968i	0.672589	−	0.226564i
$208$			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
$213$	−0.535115	+	5.36887i	−0.0366655	+	0.367869i
$214$	−2.92565	+	16.5922i	−0.199994	+	1.13422i
$215$	−0.808172	+	2.22043i	−0.0551168	+	0.151432i
$216$	−0.520223	+	1.69358i	−0.0353967	+	0.115233i
$217$	2.54957	+	1.47199i	0.173076	+	0.0999254i
$218$	−5.73453	−	6.83415i	−0.388392	−	0.462867i
$219$	0.198576	−	0.0896944i	0.0134185	−	0.00606098i
$220$	2.08149	−	3.60525i	0.140334	−	0.243066i
$221$	−6.58814	−	11.4110i	−0.443166	−	0.767586i
$222$	−6.48514	+	9.02773i	−0.435254	+	0.605901i
$223$	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
$225$	−13.9854	−	2.81583i	−0.932363	−	0.187722i
$226$	−13.3470	−	11.1995i	−0.887830	−	0.744978i
$227$	0.844414			0.0560457			0.0280229	−	0.999607i	$-0.491079\pi$
$227$	0.844414			0.0560457			0.0280229	+	0.999607i	$0.491079\pi$
$228$	8.04322	−	11.1935i	0.532675	−	0.741306i
$229$	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
$231$	−1.16337	−	15.4431i	−0.0765444	−	1.01608i
$232$	−0.0674167	−	0.382339i	−0.00442613	−	0.0251018i
$233$	26.4558	+	4.66487i	1.73318	+	0.305606i	0.949081	−	0.315033i	$-0.102016\pi$
$233$	26.4558	+	4.66487i	1.73318	+	0.305606i	0.784096	+	0.620639i	$0.213127\pi$
$234$	−24.0247	+	19.1898i	−1.57055	+	1.25448i
$235$	−1.47227	−	2.55005i	−0.0960406	−	0.166347i
$236$	0.205259	−	0.355519i	0.0133612	−	0.0231423i
$237$	−10.2984	−	22.7997i	−0.668951	−	1.48100i
$238$	6.13132	+	7.30703i	0.397435	+	0.473644i
$239$	19.6545	+	11.3476i	1.27135	+	0.734012i	0.975241	−	0.221143i	$-0.0709789\pi$
$239$	19.6545	+	11.3476i	1.27135	+	0.734012i	0.296105	+	0.955155i	$0.404312\pi$
$240$	−3.58461	+	0.914248i	−0.231386	+	0.0590144i
$241$	−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
$243$	−14.4997	+	5.72348i	−0.930157	+	0.367161i
$244$	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
$249$	9.99697	−	6.82155i	0.633532	−	0.432298i
$250$	−3.22781	−	8.86833i	−0.204145	−	0.560883i
$251$	15.8837	−	2.80072i	1.00257	−	0.176780i	0.351815	−	0.936070i	$-0.385565\pi$
$251$	15.8837	−	2.80072i	1.00257	−	0.176780i	0.650753	+	0.759290i	$0.274453\pi$
$252$	7.02252	−	7.97004i	0.442377	−	0.502066i
$253$	−14.7455	−	5.36693i	−0.927042	−	0.337416i
$254$	14.4527	−	8.34429i	0.906845	−	0.523567i
$255$	1.54148	−	1.50469i	0.0965311	−	0.0942275i
$256$	14.1066	−	11.8368i	0.881660	−	0.739801i
$257$	−10.9469	+	9.18557i	−0.682851	+	0.572980i	−0.916838	−	0.399260i	$-0.869267\pi$
$257$	−10.9469	+	9.18557i	−0.682851	+	0.572980i	0.233987	+	0.972240i	$0.424823\pi$
$258$	11.5818	−	11.3054i	0.721050	−	0.703843i
$259$	−5.51099	+	3.18177i	−0.342436	+	0.197706i
$260$	−4.44641	−	1.61836i	−0.275755	−	0.100366i
$261$	2.25831	−	2.56301i	0.139786	−	0.158646i
$262$	−28.8557	+	5.08804i	−1.78271	+	0.314340i
$263$	−4.39828	−	12.0842i	−0.271209	−	0.745141i	−0.998283	−	0.0585816i	$-0.981342\pi$
$263$	−4.39828	−	12.0842i	−0.271209	−	0.745141i	0.727073	−	0.686560i	$-0.240880\pi$
$264$	2.24892	−	1.53458i	0.138412	−	0.0944467i
$265$			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	$-0.941399\pi$
$269$	−26.5458	+	9.66190i	−1.61853	+	0.589096i	−0.635428	+	0.772160i	$0.719176\pi$
$270$	−4.01061	−	3.03052i	−0.244078	−	0.184432i
$271$	−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
$273$	−17.0568	+	4.35030i	−1.03232	+	0.263292i
$274$	3.12366	+	1.80345i	0.188707	+	0.108950i
$275$	14.0920	+	16.7942i	0.849780	+	1.01273i
$276$	−4.43057	−	9.80891i	−0.266689	−	0.590427i
$277$	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
$279$	−3.55810	+	2.84205i	−0.213018	+	0.170149i
$280$	−0.322102	−	0.0567952i	−0.0192493	−	0.00339416i
$281$	5.22472	+	29.6308i	0.311680	+	1.76763i	0.590259	+	0.807214i	$0.299026\pi$
$281$	5.22472	+	29.6308i	0.311680	+	1.76763i	−0.278579	+	0.960413i	$0.589863\pi$
$282$	1.51507	+	20.1116i	0.0902210	+	1.19763i
$283$	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
$285$	−2.10433	−	3.08479i	−0.124650	−	0.182727i
$286$	47.2516			2.79405
$287$	−14.8684	−	12.4761i	−0.877656	−	0.736441i
$288$	22.8347	+	4.59753i	1.34555	+	0.270912i
$289$	1.85409	+	10.5151i	0.109064	+	0.618534i
$290$	1.08482	+	0.191284i	0.0637030	+	0.0112326i
$291$	7.07066	−	9.84281i	0.414489	−	0.576995i
$292$	−0.114836	−	0.198902i	−0.00672026	−	0.0116398i
$293$	4.44167	−	7.69320i	0.259485	−	0.449442i	−0.706619	−	0.707594i	$-0.749780\pi$
$293$	4.44167	−	7.69320i	0.259485	−	0.449442i	0.966104	+	0.258153i	$0.0831138\pi$
$294$	−9.99865	+	4.51627i	−0.583133	+	0.263394i
$295$	−0.0714881	−	0.0851963i	−0.00416220	−	0.00496032i
$296$	−0.968839	−	0.559360i	−0.0563126	−	0.0325121i
$297$	22.8994	+	7.03410i	1.32876	+	0.408160i
$298$	−2.74400	+	7.53907i	−0.158956	+	0.436727i
$299$	−3.09716	+	17.5649i	−0.179113	+	1.01580i
$300$	−1.49138	+	14.9631i	−0.0861046	+	0.863897i
$301$	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
$306$	−13.9826	+	4.71008i	−0.799332	+	0.269258i
$307$	−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
$309$	3.72297	+	1.79110i	0.211793	+	0.101892i
$310$	−1.37992	−	0.502249i	−0.0783741	−	0.0285258i
$311$	12.5985	−	7.27375i	0.714396	−	0.412457i	−0.0982907	−	0.995158i	$-0.531338\pi$
$311$	12.5985	−	7.27375i	0.714396	−	0.412457i	0.812687	+	0.582701i	$0.198004\pi$
$312$	−2.16163	−	2.21447i	−0.122378	−	0.125370i
$313$	−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
$315$	−1.37830	−	2.52627i	−0.0776581	−	0.142339i
$316$	−22.8371	+	13.1850i	−1.28469	+	0.741715i
$317$	−16.5955	−	6.04028i	−0.932098	−	0.339256i	−0.169057	−	0.985606i	$-0.554072\pi$
$317$	−16.5955	−	6.04028i	−0.932098	−	0.339256i	−0.763041	+	0.646351i	$0.776294\pi$
$318$	14.5178	−	30.1766i	0.814115	−	1.69222i
$319$	−5.16973	+	0.911563i	−0.289449	+	0.0510377i
$320$	1.10802	+	3.04427i	0.0619403	+	0.170180i
$321$	−8.40936	−	12.3239i	−0.469365	−	0.687854i
$322$		−	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
$327$	7.86123	+	0.783528i	0.434727	+	0.0433292i
$328$	0.592520	−	3.36035i	0.0327165	−	0.185544i
$329$	−3.94905	+	10.8499i	−0.217718	+	0.598176i
$330$	1.90911	+	7.48531i	0.105093	+	0.412053i
$331$	−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
$333$	−1.47468	−	9.73219i	−0.0808120	−	0.533320i
$334$	5.19725	−	9.00190i	0.284381	−	0.492562i
$335$	0.102415	+	0.177388i	0.00559553	+	0.00969174i
$336$	11.7813	+	8.46321i	0.642724	+	0.461706i
$337$	−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
$339$	15.3854	−	1.15903i	0.835618	−	0.0629497i
$340$	−1.73936	−	1.45949i	−0.0943299	−	0.0791521i
$341$	6.99804			0.378965
$342$	3.82844	+	25.2890i	0.207018	+	1.36747i
$343$	−19.8571			−1.07219
$344$	1.24781	+	1.04704i	0.0672777	+	0.0564527i
$345$	−2.90765	+	0.219043i	−0.156543	+	0.0117929i
$346$	−3.91631	−	22.2105i	−0.210542	−	1.19404i
$347$	−26.1493	−	4.61083i	−1.40377	−	0.247522i	−0.580078	−	0.814561i	$-0.696978\pi$
$347$	−26.1493	−	4.61083i	−1.40377	−	0.247522i	−0.823691	+	0.567039i	$0.808089\pi$
$348$	−2.92432	−	2.10071i	−0.156760	−	0.112610i
$349$	−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
$351$	3.35397	−	27.0211i	0.179022	−	1.44228i
$352$	−23.0087	−	27.4207i	−1.22637	−	1.46153i
$353$	−21.0798	−	12.1704i	−1.12197	−	0.647767i	−0.180063	−	0.983655i	$-0.557630\pi$
$353$	−21.0798	−	12.1704i	−1.12197	−	0.647767i	−0.941902	+	0.335888i	$0.890964\pi$
$354$	0.188261	+	0.738139i	0.0100060	+	0.0392317i
$355$	0.526962	−	1.44782i	0.0279682	−	0.0768421i
$356$	1.79683	−	10.1903i	0.0952315	−	0.540085i
$357$	−8.40517	−	0.837743i	−0.444849	−	0.0443381i
$358$	−32.6381	+	11.8793i	−1.72498	+	0.627840i
$359$	−19.5952	+	23.3526i	−1.03419	+	1.23251i	−0.0620627	+	0.998072i	$0.519768\pi$
$359$	−19.5952	+	23.3526i	−1.03419	+	1.23251i	−0.972132	+	0.234433i	$0.924677\pi$
$360$	0.263467	−	0.431903i	0.0138859	−	0.0227633i
$361$	−3.30439	+	18.7105i	−0.173915	+	0.984761i
$362$		−	22.8471i		−	1.20082i
$363$	−10.0107	−	14.6706i	−0.525423	−	0.770007i
$364$	6.34597	+	17.4354i	0.332619	+	0.913863i
$365$	−0.0612763	+	0.0108047i	−0.00320735	+	0.000565542i
$366$	−16.1041	+	33.4740i	−0.841776	+	1.74972i
$367$	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
$369$	26.3555	−	14.3792i	1.37201	−	0.748550i
$370$	2.43156	−	2.04032i	0.126411	−	0.106071i
$371$	14.6858	−	12.3229i	0.762451	−	0.639772i
$372$	3.35287	+	3.43484i	0.173838	+	0.178088i
$373$	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
$375$	7.53102	+	3.62312i	0.388900	+	0.187097i
$376$	−1.99901	+	0.352479i	−0.103091	+	0.0181777i
$377$	2.04074	+	5.60688i	0.105103	+	0.288769i
$378$	1.00564	+	19.6857i	0.0517244	+	1.01252i
$379$			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	−0.0487143	−	0.998813i	$-0.515512\pi$
$383$	10.8810	−	3.96036i	0.555993	−	0.202365i	0.604707	+	0.796448i	$0.293290\pi$
$384$	−0.466786	+	4.68332i	−0.0238206	+	0.238995i
$385$	−0.767946	+	4.35524i	−0.0391381	+	0.221963i
$386$	5.02291	−	13.8003i	0.255659	−	0.702418i
$387$	−0.346102	+	14.3281i	−0.0175934	+	0.728338i
$388$	−11.0629	−	6.38716i	−0.561633	−	0.324259i
$389$	15.4791	+	18.4473i	0.784821	+	0.935314i	0.999141	−	0.0414499i	$-0.0131977\pi$
$389$	15.4791	+	18.4473i	0.784821	+	0.935314i	−0.214319	+	0.976764i	$0.568753\pi$
$390$	8.00197	−	3.61439i	0.405195	−	0.183022i
$391$	−4.27932	+	7.41199i	−0.216414	+	0.374841i
$392$	−0.552098	−	0.956262i	−0.0278852	−	0.0482985i
$393$	15.1381	−	21.0733i	0.763618	−	1.06301i
$394$	30.9424	+	5.45599i	1.55886	+	0.274869i
$395$	1.24055	+	7.03551i	0.0624189	+	0.353995i
$396$	4.98389	−	24.7536i	0.250450	−	1.24391i
$397$	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
$399$	−3.96220	+	14.0963i	−0.198358	+	0.705699i
$400$	−20.5349			−1.02674
$401$	16.8863	+	14.1693i	0.843264	+	0.707583i	0.958295	−	0.285779i	$-0.0922524\pi$
$401$	16.8863	+	14.1693i	0.843264	+	0.707583i	−0.115031	+	0.993362i	$0.536697\pi$
$402$	−0.105392	−	1.39901i	−0.00525647	−	0.0697764i
$403$	−1.38123	−	7.83334i	−0.0688040	−	0.390207i
$404$	19.5642	+	3.44970i	0.973355	+	0.171629i
$405$	4.41602	−	0.560421i	0.219434	−	0.0278475i
$406$	−2.15973	−	3.74077i	−0.107186	−	0.185651i
$407$	−7.56327	+	13.1000i	−0.374898	+	0.649342i
$408$	−0.611275	−	1.35331i	−0.0302626	−	0.0669989i
$409$	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
$411$	−3.09496	+	0.789362i	−0.152663	+	0.0389364i
$412$	1.48941	−	4.09212i	0.0733779	−	0.201604i
$413$	−0.0757285	+	0.429477i	−0.00372635	+	0.0211332i
$414$	18.5974	+	7.28215i	0.914012	+	0.357898i
$415$	−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	$-0.337168\pi$
$420$	−2.50561	+	1.70973i	−0.122261	+	0.0834265i
$421$	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
$423$	−13.4003	−	11.8072i	−0.651547	−	0.574087i
$424$	3.16703	+	1.15271i	0.153805	+	0.0559803i
$425$	10.3554	−	5.97869i	0.502310	−	0.290009i
$426$	−7.55180	+	7.37159i	−0.365886	+	0.357154i
$427$	−16.2906	+	13.6694i	−0.788356	+	0.661509i
$428$	−12.0469	+	10.1086i	−0.582311	+	0.488617i
$429$	−29.9426	+	29.2280i	−1.44564	+	1.41114i
$430$	−4.00255	+	2.31087i	−0.193020	+	0.111440i
$431$	−8.42816	−	3.06760i	−0.405970	−	0.147761i	0.130960	−	0.991388i	$-0.458194\pi$
$431$	−8.42816	−	3.06760i	−0.405970	−	0.147761i	−0.536930	+	0.843627i	$0.680416\pi$
$432$	−18.8345	+	12.1959i	−0.906173	+	0.586777i
$433$	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
$435$	−0.805756	+	0.549817i	−0.0386330	+	0.0263617i
$436$		−	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
$441$	3.54239	−	9.04667i	0.168685	−	0.430794i
$442$	4.47525	−	25.3804i	0.212866	−	1.20722i
$443$	2.89248	−	7.94702i	0.137426	−	0.377574i	−0.851820	−	0.523834i	$-0.824501\pi$
$443$	2.89248	−	7.94702i	0.137426	−	0.377574i	0.989246	+	0.146260i	$0.0467235\pi$
$444$	−10.0535	+	2.56413i	−0.477120	+	0.121688i
$445$	−2.42773	−	1.40165i	−0.115085	−	0.0664445i
$446$	29.4774	+	35.1298i	1.39579	+	1.66344i
$447$	−2.92456	−	6.47472i	−0.138327	−	0.306244i
$448$	6.35169	−	11.0014i	0.300089	−	0.519770i
$449$	−2.29293	−	3.97148i	−0.108210	−	0.187426i	0.806835	−	0.590777i	$-0.201179\pi$
$449$	−2.29293	−	3.97148i	−0.108210	−	0.187426i	−0.915045	+	0.403351i	$0.867845\pi$
$450$	−17.4146	−	21.8023i	−0.820934	−	1.02777i
$451$	−45.4363	−	8.01165i	−2.13951	−	0.377254i
$452$	−2.82404	−	16.0159i	−0.132832	−	0.753325i
$453$	2.74676	+	36.4615i	0.129054	+	1.71311i
$454$	1.26521	+	1.06164i	0.0593794	+	0.0498252i
$455$	5.02666			0.235654
$456$	−2.49442	+	0.635837i	−0.116812	+	0.0297758i
$457$	−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
$459$	5.94707	−	11.6338i	0.277586	−	0.543020i
$460$	0.533710	+	3.02682i	0.0248844	+	0.141126i
$461$	24.7397	+	4.36228i	1.15224	+	0.203171i	0.716955	−	0.697120i	$-0.245535\pi$
$461$	24.7397	+	4.36228i	1.15224	+	0.203171i	0.435288	+	0.900291i	$0.356647\pi$
$462$	17.6727	−	24.6015i	0.822208	−	1.14457i
$463$	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
$465$	1.18510	−	0.535298i	0.0549579	−	0.0248238i
$466$	33.7747	+	40.2511i	1.56458	+	1.86460i
$467$	−2.86340	−	1.65318i	−0.132502	−	0.0765002i	0.432284	−	0.901738i	$-0.357708\pi$
$467$	−2.86340	−	1.65318i	−0.132502	−	0.0765002i	−0.564786	+	0.825237i	$0.691041\pi$
$468$	−28.6919	−	0.693068i	−1.32629	−	0.0320371i
$469$	0.274706	−	0.754748i	0.0126847	−	0.0348510i
$470$	1.00010	−	5.67185i	0.0461311	−	0.261623i
$471$	1.06397	−	10.6749i	0.0490252	−	0.491875i
$472$	−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
$477$	9.46644	+	28.1026i	0.433439	+	1.28673i
$478$	15.1823	+	41.7131i	0.694423	+	1.90791i
$479$	5.99987	−	1.05794i	0.274141	−	0.0483385i	−0.0348874	−	0.999391i	$-0.511107\pi$
$479$	5.99987	−	1.05794i	0.274141	−	0.0483385i	0.309028	+	0.951053i	$0.399996\pi$
$480$	−5.99395	−	2.88364i	−0.273585	−	0.131620i
$481$	16.1564	+	5.88046i	0.736669	+	0.268126i
$482$	−42.0477	+	24.2763i	−1.91522	+	1.10575i
$483$	7.98676	+	8.18202i	0.363410	+	0.372295i
$484$	−14.3409	+	12.0334i	−0.651859	+	0.546974i
$485$	−2.65110	+	2.22453i	−0.120380	+	0.101011i
$486$	−28.9212	−	9.65410i	−1.31189	−	0.437919i
$487$	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
$489$	1.28115	−	2.66301i	0.0579357	−	0.120425i
$490$	3.08537	−	0.544035i	0.139383	−	0.0245770i
$491$	−11.0836	−	30.4521i	−0.500198	−	1.37428i	−0.891082	−	0.453842i	$-0.850053\pi$
$491$	−11.0836	−	30.4521i	−0.500198	−	1.37428i	0.390884	−	0.920440i	$-0.372169\pi$
$492$	−17.8369	−	26.1400i	−0.804151	−	1.17848i
$493$			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
$498$	23.5552	+	2.34774i	1.05553	+	0.105205i
$499$	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
$501$	2.27482	+	8.91918i	0.101631	+	0.398480i
$502$	27.3202	+	15.7733i	1.21936	+	0.703998i
$503$	−10.3825	−	12.3734i	−0.462933	−	0.551702i	0.483188	−	0.875517i	$-0.339479\pi$
$503$	−10.3825	−	12.3734i	−0.462933	−	0.551702i	−0.946120	+	0.323815i	$0.895034\pi$
$504$	−1.96144	+	0.297209i	−0.0873695	+	0.0132388i
$505$	2.69100	−	4.66096i	0.119748	−	0.207410i
$506$	−15.3461	−	26.5802i	−0.682218	−	1.18164i
$507$	20.3394	+	14.6110i	0.903304	+	0.648896i
$508$	15.3406	+	2.70495i	0.680627	+	0.120013i
$509$	−4.96536	−	28.1600i	−0.220086	−	1.24817i	−0.871860	−	0.489756i	$-0.837086\pi$
$509$	−4.96536	−	28.1600i	−0.220086	−	1.24817i	0.651774	−	0.758413i	$-0.274025\pi$
$510$	4.20142	−	0.316506i	0.186042	−	0.0140151i
$511$	0.186904	+	0.156831i	0.00826813	+	0.00693778i
$512$	30.5835			1.35161
$513$	−18.0688	−	13.6571i	−0.797759	−	0.602977i
$514$	−27.9507			−1.23285
$515$	−0.903754	−	0.758339i	−0.0398241	−	0.0334164i
$516$	15.0643	−	1.13484i	0.663170	−	0.0499587i
$517$	4.76598	+	27.0292i	0.209607	+	1.18874i
$518$	−12.2576	−	2.16134i	−0.538567	−	0.0949639i
$519$	16.2203	+	11.6520i	0.711991	+	0.511464i
$520$	0.441847	+	0.765301i	0.0193763	+	0.0335607i
$521$	0.554173	−	0.959856i	0.0242788	−	0.0420521i	−0.853631	−	0.520879i	$-0.825604\pi$
$521$	0.554173	−	0.959856i	0.0242788	−	0.0420521i	0.877910	+	0.478827i	$0.158938\pi$
$522$	6.60604	−	1.00099i	0.289138	−	0.0438120i
$523$	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
$525$	−3.94786	−	15.4789i	−0.172299	−	0.675555i
$526$	8.60274	−	23.6358i	0.375097	−	1.03057i
$527$	0.662792	−	3.75888i	0.0288717	−	0.163739i
$528$	34.3118	+	3.41986i	1.49323	+	0.148830i
$529$	−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
$534$	10.8226	+	15.8605i	0.468338	+	0.686349i
$535$	1.45716	+	4.00352i	0.0629987	+	0.173087i
$536$	0.139056	−	0.0245193i	0.00600630	−	0.00105907i
$537$	13.3342	−	27.7164i	0.575411	−	1.19605i
$538$	−51.9219	−	18.8980i	−2.23851	−	0.814752i
$539$	−12.9299	+	7.46509i	−0.556931	+	0.321544i
$540$	−1.04945	−	4.57320i	−0.0451613	−	0.196799i
$541$	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
$543$	14.1324	+	14.4779i	0.606478	+	0.621305i
$544$	−16.9077	+	9.76167i	−0.724912	+	0.418528i
$545$	−2.11992	−	0.771589i	−0.0908076	−	0.0330513i
$546$	−31.0262	−	14.9265i	−1.32780	−	0.638793i
$547$	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
$549$	−10.5008	−	31.1734i	−0.448165	−	1.33045i
$550$			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
$555$	−0.278776	+	2.79699i	−0.0118334	+	0.118726i
$556$	−1.28990	+	7.31538i	−0.0547039	+	0.310241i
$557$	12.2432	−	33.6380i	0.518762	−	1.42529i	−0.353123	−	0.935577i	$-0.614880\pi$
$557$	12.2432	−	33.6380i	0.518762	−	1.42529i	0.871885	−	0.489710i	$-0.162897\pi$
$558$	−8.90438	−	0.215090i	−0.376953	−	0.00910547i
$559$	−21.6803	−	12.5171i	−0.916979	−	0.529418i
$560$	−2.66265	−	3.17323i	−0.112518	−	0.134093i
$561$	−18.2985	+	8.26524i	−0.772565	+	0.348959i
$562$	−29.4250	+	50.9656i	−1.24122	+	2.14986i
$563$	−11.0660	−	19.1668i	−0.466375	−	0.807785i	0.532887	−	0.846186i	$-0.321107\pi$
$563$	−11.0660	−	19.1668i	−0.466375	−	0.807785i	−0.999262	+	0.0384008i	$0.987774\pi$
$564$	−10.9833	+	15.2894i	−0.462479	+	0.643800i
$565$	−4.33896	−	0.765075i	−0.182541	−	0.0321870i
$566$	9.31609	+	52.8342i	0.391585	+	2.22079i
$567$	−12.8141	−	11.8525i	−0.538141	−	0.497757i
$568$	−0.813628	−	0.682715i	−0.0341391	−	0.0286461i
$569$	−3.68640			−0.154542			−0.0772710	−	0.997010i	$-0.524621\pi$
$569$	−3.68640			−0.154542			−0.0772710	+	0.997010i	$0.524621\pi$
$570$	0.725368	−	7.26771i	0.0303823	−	0.304411i
$571$	−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
$573$	0.371923	+	4.93705i	0.0155373	+	0.206248i
$574$	−6.59228	−	37.3867i	−0.275157	−	1.56049i
$575$	−15.9400	−	2.81065i	−0.664744	−	0.117212i
$576$	12.2635	+	15.3533i	0.510980	+	0.639721i
$577$	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
$579$	5.35342	+	11.8520i	0.222481	+	0.492554i
$580$	0.660914	+	0.787647i	0.0274430	+	0.0327053i
$581$	11.7363	+	6.77593i	0.486902	+	0.281113i
$582$	22.9691	−	5.85821i	0.952098	−	0.242831i
$583$	15.5861	−	42.8224i	0.645510	−	1.77352i
$584$	−0.00744828	+	0.0422413i	−0.000308212	+	0.00174796i
$585$	−2.83499	+	7.24010i	−0.117213	+	0.299341i
$586$	16.3274	−	5.94268i	0.674478	−	0.245490i
$587$	4.23083	−	5.04211i	0.174625	−	0.208110i	−0.671632	−	0.740885i	$-0.734406\pi$
$587$	4.23083	−	5.04211i	0.174625	−	0.208110i	0.846257	+	0.532775i	$0.178851\pi$
$588$	−9.85901	−	2.76973i	−0.406579	−	0.114222i
$589$	−6.21722	−	2.26384i	−0.256176	−	0.0932798i
$590$		−	0.217531i		−	0.00895560i
$591$	−22.9826	+	15.6824i	−0.945377	+	0.645089i
$592$	−4.84594	−	13.3141i	−0.199167	−	0.547207i
$593$	5.69179	−	1.00362i	0.233734	−	0.0412136i	−0.0555543	−	0.998456i	$-0.517693\pi$
$593$	5.69179	−	1.00362i	0.233734	−	0.0412136i	0.289288	+	0.957242i	$0.406581\pi$
$594$	25.4673	+	39.3297i	1.04494	+	1.61372i
$595$	2.26661	+	0.824978i	0.0929219	+	0.0338208i
$596$	−6.48535	+	3.74432i	−0.265650	+	0.153373i
$597$	−7.85057	+	7.66322i	−0.321302	+	0.313635i
$598$	−26.7240	+	22.4241i	−1.09283	+	0.916990i
$599$	−27.7457	+	23.2814i	−1.13366	+	0.951254i	−0.999213	−	0.0396667i	$-0.987370\pi$
$599$	−27.7457	+	23.2814i	−1.13366	+	0.951254i	−0.134447	+	0.990921i	$0.542926\pi$
$600$	2.00962	−	1.96166i	0.0820423	−	0.0800845i
$601$	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
$603$	0.932161	+	0.821340i	0.0379605	+	0.0334476i
$604$	37.9558	−	6.69264i	1.54440	−	0.272319i
$605$	1.73463	+	4.76587i	0.0705229	+	0.193760i
$606$	−30.4502	+	20.7781i	−1.23696	+	0.844052i
$607$		−	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
$612$	−12.8239	−	5.02145i	−0.518377	−	0.202980i
$613$	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
$615$	−8.30739	+	2.11878i	−0.334986	+	0.0854376i
$616$	2.64019	+	1.52431i	0.106376	+	0.0614164i
$617$	2.77009	+	3.30127i	0.111520	+	0.132904i	0.818917	−	0.573913i	$-0.194575\pi$
$617$	2.77009	+	3.30127i	0.111520	+	0.132904i	−0.707397	+	0.706817i	$0.750131\pi$
$618$	3.32640	+	7.36437i	0.133807	+	0.296238i
$619$	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
$621$	−16.2893	+	6.88906i	−0.653669	+	0.276448i
$622$	28.0217	+	4.94098i	1.12357	+	0.198115i
$623$	1.90881	+	10.8254i	0.0764747	+	0.433710i
$624$	−2.94419	−	39.0824i	−0.117862	−	1.56455i
$625$	16.3859	+	13.7494i	0.655438	+	0.549978i
$626$	−34.2990			−1.37086
$627$	8.59735	+	33.7279i	0.343345	+	1.34696i
$628$	−11.3077			−0.451228
$629$	6.32010	+	5.30320i	0.251999	+	0.211452i
$630$	1.11100	−	5.51805i	0.0442635	−	0.219844i
$631$	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
$633$	11.0979	−	15.4490i	0.441104	−	0.614044i
$634$	−17.2715	−	29.9151i	−0.685938	−	1.18808i
$635$	2.11005	−	3.65472i	0.0837349	−	0.145033i
$636$	28.4860	−	12.8668i	1.12955	−	0.510202i
$637$	10.9082	+	12.9999i	0.432198	+	0.515073i
$638$	−8.89204	−	5.13382i	−0.352039	−	0.203250i
$639$	0.225673	−	9.34251i	0.00892748	−	0.369584i
$640$	0.459674	−	1.26294i	0.0181702	−	0.0499222i
$641$	−0.129228	+	0.732886i	−0.00510418	+	0.0289473i	−0.987253	−	0.159156i	$-0.949123\pi$
$641$	−0.129228	+	0.732886i	−0.00510418	+	0.0289473i	0.982149	+	0.188103i	$0.0602339\pi$
$642$	2.89422	−	29.0380i	0.114226	−	1.14604i
$643$	−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	$-0.936777\pi$
$647$		−	10.0379i		−	0.394633i	0.980340	−	0.197316i	$-0.0632226\pi$
$648$	0.678153	−	2.99276i	0.0266403	−	0.117567i
$649$	0.354553	+	0.974127i	0.0139174	+	0.0382378i
$650$	47.9988	−	8.46349i	1.88267	−	0.331965i
$651$	−4.59502	−	2.21063i	−0.180093	−	0.0866415i
$652$	−2.92705	−	1.06536i	−0.114632	−	0.0417227i
$653$	−24.0034	+	13.8584i	−0.939327	+	0.542321i	−0.889749	−	0.456449i	$-0.849121\pi$
$653$	−24.0034	+	13.8584i	−0.939327	+	0.542321i	−0.0495780	+	0.998770i	$0.515788\pi$
$654$	10.7936	+	11.0575i	0.422065	+	0.432383i
$655$	−5.67595	+	4.76268i	−0.221778	+	0.186093i
$656$	33.1049	−	27.7783i	1.29253	−	1.08456i
$657$	−0.331301	+	0.180753i	−0.0129253	+	0.00705186i
$658$	−19.5581	+	11.2919i	−0.762453	+	0.440202i
$659$	37.9399	+	13.8090i	1.47793	+	0.537922i	0.950241	−	0.311516i	$-0.100837\pi$
$659$	37.9399	+	13.8090i	1.47793	+	0.537922i	0.527688	+	0.849438i	$0.323059\pi$
$660$	−3.12597	+	6.49765i	−0.121678	+	0.252921i
$661$	−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
$663$	12.8635	+	18.8514i	0.499575	+	0.732127i
$664$			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
$669$	−40.4093	−	4.02759i	−1.56231	−	0.155716i
$670$	−0.0695694	+	0.394548i	−0.00268770	+	0.0152427i
$671$	−17.2892	+	47.5017i	−0.667442	+	1.83378i
$672$	6.44586	+	25.2731i	0.248654	+	0.974932i
$673$	−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
$675$	24.5214	+	3.04370i	0.943830	+	0.117152i
$676$	13.1986	−	22.8606i	0.507638	−	0.879254i
$677$	−5.21572	−	9.03390i	−0.200457	−	0.347201i	0.748219	−	0.663452i	$-0.230909\pi$
$677$	−5.21572	−	9.03390i	−0.200457	−	0.347201i	−0.948676	+	0.316251i	$0.897576\pi$
$678$	24.5096	+	17.6066i	0.941284	+	0.676179i
$679$	13.3643	+	2.35648i	0.512874	+	0.0904335i
$680$	0.0736348	+	0.417603i	0.00282376	+	0.0160144i
$681$	−1.45844	+	0.109868i	−0.0558874	+	0.00421017i
$682$	10.4854	+	8.79829i	0.401506	+	0.336904i
$683$	27.0630			1.03554			0.517769	−	0.855520i	$-0.326763\pi$
$683$	27.0630			1.03554			0.517769	+	0.855520i	$0.326763\pi$
$684$	−12.4355	+	20.3794i	−0.475483	+	0.779226i
$685$	0.912089			0.0348491
$686$	−29.7526	−	24.9654i	−1.13596	−	0.953184i
$687$	−11.2905	+	0.850550i	−0.430760	+	0.0324505i
$688$	3.58238	+	20.3167i	0.136577	+	0.774567i
$689$	−51.0101	−	8.99446i	−1.94333	−	0.342662i
$690$	−4.63202	−	3.32745i	−0.176338	−	0.126674i
$691$	−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
$693$	4.01866	+	26.5212i	0.152656	+	1.00746i
$694$	−33.3834	−	39.7848i	−1.26722	−	1.51021i
$695$	1.74281	+	1.00621i	0.0661085	+	0.0381678i
$696$	0.166186	+	0.651588i	0.00629927	+	0.0246984i
$697$	−8.60665	+	23.6466i	−0.326000	+	0.895678i
$698$	0.933174	−	5.29229i	0.0353212	−	0.200316i
$699$	−46.3003	−	4.61475i	−1.75124	−	0.174546i
$700$	−15.8225	+	5.75892i	−0.598034	+	0.217667i
$701$	−9.90651	+	11.8061i	−0.374164	+	0.445911i	−0.919963	−	0.392005i	$-0.871782\pi$
$701$	−9.90651	+	11.8061i	−0.374164	+	0.445911i	0.545799	+	0.837916i	$0.316226\pi$
$702$	38.9976	−	36.2698i	1.47187	−	1.36891i
$703$	10.9572	−	9.19163i	0.413258	−	0.346669i
$704$		−	30.1967i		−	1.13808i
$705$	2.87464	+	4.21278i	0.108265	+	0.158663i
$706$	−16.2833	−	44.7380i	−0.612830	−	1.68374i
$707$	−20.7835	+	3.66469i	−0.781643	+	0.137825i
$708$	−0.308258	+	0.640745i	−0.0115850	+	0.0240807i
$709$	−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
$711$	20.7534	+	38.0388i	0.778314	+	1.42656i
$712$	−1.48036	+	1.24217i	−0.0554789	+	0.0465523i
$713$	−3.95787	+	3.32105i	−0.148223	+	0.124374i
$714$	−11.5405	−	11.8226i	−0.431892	−	0.442451i
$715$	10.3479	−	5.97435i	0.386989	−	0.223428i
$716$	−30.4646	−	11.0882i	−1.13851	−	0.414385i
$717$	−35.4229	−	17.0417i	−1.32289	−	0.636434i
$718$	−58.7202	+	10.3540i	−2.19142	+	0.386406i
$719$	10.4822	+	28.7995i	0.390919	+	1.07404i	0.966583	+	0.256354i	$0.0825212\pi$
$719$	10.4822	+	28.7995i	0.390919	+	1.07404i	−0.575664	+	0.817686i	$0.695257\pi$
$720$	6.07223	−	2.04545i	0.226299	−	0.0762294i
$721$			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
$726$	3.44533	−	34.5674i	0.127868	−	1.28291i
$727$	−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
$729$	24.2986	−	11.7719i	0.899948	−	0.435998i
$730$	−0.105397	−	0.0608507i	−0.00390090	−	0.00225219i
$731$	−7.72170	−	9.20236i	−0.285597	−	0.340362i
$732$	−31.5987	+	14.2728i	−1.16792	+	0.527537i
$733$	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
$735$	−1.61863	+	2.25324i	−0.0597042	+	0.0831120i
$736$	26.0259	+	4.58908i	0.959329	+	0.169156i
$737$	−0.331533	−	1.88022i	−0.0122122	−	0.0692587i
$738$	57.5675	+	11.5906i	2.11909	+	0.426657i
$739$	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
$741$	36.0568	−	16.2806i	1.32458	−	0.598081i
$742$	37.4972			1.37657
$743$	−11.0957	−	9.31040i	−0.407062	−	0.341565i	0.416154	−	0.909294i	$-0.363378\pi$
$743$	−11.0957	−	9.31040i	−0.407062	−	0.341565i	−0.823216	+	0.567729i	$0.807822\pi$
$744$	−0.0673403	−	0.893901i	−0.00246882	−	0.0327720i
$745$	0.352295	+	1.99796i	0.0129071	+	0.0731997i
$746$	46.8896	+	8.26790i	1.71675	+	0.302709i
$747$	−16.3788	+	13.0826i	−0.599268	+	0.478668i
$748$	10.5820	+	18.3286i	0.386916	+	0.670159i
$749$	8.35312	−	14.4680i	0.305216	−	0.528650i
$750$	6.72881	+	14.8970i	0.245701	+	0.543962i
$751$	−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
$753$	−27.0692	+	6.90393i	−0.986455	+	0.251593i
$754$	−3.99155	+	10.9667i	−0.145364	+	0.399384i
$755$	1.81314	−	10.2828i	0.0659869	−	0.374230i
$756$	−11.0920	+	14.6792i	−0.403412	+	0.533878i
$757$	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	$0.0611322\pi$
$761$			10.5310i			0.381748i	−0.981615	+	0.190874i	$0.938868\pi$
$762$	−23.8764	+	16.2924i	−0.864952	+	0.590210i
$763$	3.02558	+	8.31271i	0.109533	+	0.300940i
$764$	5.13939	−	0.906213i	0.185937	−	0.0327857i
$765$	−2.46659	+	2.79940i	−0.0891799	+	0.101213i
$766$	21.2825	+	7.74620i	0.768968	+	0.279882i
$767$	1.02042	−	0.589141i	0.0368453	−	0.0212726i
$768$	−22.8241	+	22.2795i	−0.823595	+	0.803941i
$769$	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
$771$	17.7119	−	17.2893i	0.637879	−	0.622657i
$772$	11.8715	−	6.85400i	0.427264	−	0.246681i
$773$	−5.44057	−	1.98021i	−0.195684	−	0.0712231i	0.242319	−	0.970197i	$-0.422092\pi$
$773$	−5.44057	−	1.98021i	−0.195684	−	0.0712231i	−0.438003	+	0.898974i	$0.644314\pi$
$774$	−18.5326	+	21.0331i	−0.666139	+	0.756019i
$775$	7.10870	−	1.25346i	0.255352	−	0.0450255i
$776$	0.815958	+	2.24182i	0.0292912	+	0.0804768i
$777$	9.10436	−	6.21247i	0.326617	−	0.222871i
$778$			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
$783$	−3.56697	+	4.72055i	−0.127473	+	0.168699i
$784$	2.42841	−	13.7722i	0.0867289	−	0.491864i
$785$	−1.04776	+	2.87869i	−0.0373961	+	0.102745i
$786$	49.1763	−	12.5423i	1.75406	−	0.447370i
$787$	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
$789$	9.16881	+	20.2990i	0.326418	+	0.722663i
$790$	−6.98665	+	12.1012i	−0.248574	+	0.430542i
$791$	8.63826	+	14.9619i	0.307141	+	0.531984i
$792$	−3.68457	+	2.94307i	−0.130926	+	0.104577i
$793$	56.5840	+	9.97729i	2.00936	+	0.354304i
$794$	4.26137	+	24.1674i	0.151230	+	0.857670i
$795$	−0.636122	−	8.44412i	−0.0225609	−	0.299482i
$796$	8.85834	+	7.43303i	0.313976	+	0.263457i
$797$	−25.7666			−0.912699			−0.456349	−	0.889801i	$-0.650843\pi$
$797$	−25.7666			−0.912699			−0.456349	+	0.889801i	$0.650843\pi$
$798$	−23.6593	+	16.1395i	−0.837531	+	0.571332i
$799$	14.9697			0.529589
$800$	−28.2840	−	23.7331i	−0.999989	−	0.839091i
$801$	−16.6688	−	3.35609i	−0.588962	−	0.118582i
$802$	7.48697	+	42.4607i	0.264374	+	1.49934i
$803$	0.571157	+	0.100710i	0.0201557	+	0.00355400i
$804$	0.764023	−	1.06357i	0.0269450	−	0.0375092i
$805$	−1.63253	−	2.82763i	−0.0575392	−	0.0996608i
$806$	7.77893	−	13.4735i	0.274001	−	0.474584i
$807$	44.5917	−	20.1416i	1.56970	−	0.709016i
$808$	−2.38482	−	2.84212i	−0.0838978	−	0.0999855i
$809$	−21.3495	−	12.3261i	−0.750608	−	0.433364i	0.0753057	−	0.997160i	$-0.476007\pi$
$809$	−21.3495	−	12.3261i	−0.750608	−	0.433364i	−0.825913	+	0.563797i	$0.809340\pi$
$810$	7.32126	+	4.71235i	0.257243	+	0.165575i
$811$	−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
$813$	0.00600765	−	0.0602755i	0.000210698	−	0.00211395i
$814$	−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
$819$	28.8937	−	9.73294i	1.00963	−	0.340097i
$820$	3.09076	+	8.49179i	0.107934	+	0.296546i
$821$	−9.59543	+	1.69193i	−0.334883	+	0.0590488i	−0.338561	−	0.940944i	$-0.609940\pi$
$821$	−9.59543	+	1.69193i	−0.334883	+	0.0590488i	0.00367851	+	0.999993i	$0.498829\pi$
$822$	−5.62970	−	2.70841i	−0.196358	−	0.0944666i
$823$	−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
$825$	−26.5242	−	27.1727i	−0.923455	−	0.946031i
$826$	−0.653427	+	0.548290i	−0.0227356	+	0.0190775i
$827$	13.5381	−	11.3598i	0.470765	−	0.395019i	−0.376309	−	0.926494i	$-0.622807\pi$
$827$	13.5381	−	11.3598i	0.470765	−	0.395019i	0.847074	+	0.531476i	$0.178362\pi$
$828$	8.92854	+	16.3650i	0.310288	+	0.568725i
$829$	−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
$831$	−9.35013	+	19.4352i	−0.324352	+	0.674199i
$832$	−33.8011	+	5.96005i	−1.17184	+	0.206627i
$833$	2.78514	+	7.65211i	0.0964994	+	0.265130i
$834$	−7.76927	−	11.3858i	−0.269028	−	0.394260i
$835$		−	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	$-0.579626\pi$
$839$	5.37586	−	1.95665i	0.185595	−	0.0675511i	0.433146	+	0.901324i	$0.357403\pi$
$840$	0.563710	+	0.0561849i	0.0194498	+	0.00193856i
$841$	−4.81065	+	27.2826i	−0.165885	+	0.940778i
$842$	−1.06228	+	2.91859i	−0.0366086	+	0.100581i
$843$	−12.8792	−	50.4973i	−0.443584	−	1.73922i
$844$	−17.3641	−	10.0251i	−0.597696	−	0.345080i
$845$	−4.59683	−	5.47829i	−0.158136	−	0.188459i
$846$	−5.23352	−	34.5387i	−0.179932	−	1.18747i
$847$	9.94371	−	17.2230i	0.341670	−	0.591790i
$848$	21.3424	+	36.9660i	0.732900	+	1.26942i
$849$	−38.5847	−	27.7176i	−1.32422	−	0.951266i
$850$	23.0325	+	4.06126i	0.790009	+	0.139300i
$851$	−1.93928	−	10.9982i	−0.0664778	−	0.377014i
$852$	−9.82258	+	0.739965i	−0.336516	+	0.0253508i
$853$	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
$855$	4.03588	+	5.05412i	0.138024	+	0.172847i
$856$	2.93698			0.100384
$857$	36.9941	+	31.0418i	1.26370	+	1.06037i	0.995278	+	0.0970637i	$0.0309451\pi$
$857$	36.9941	+	31.0418i	1.26370	+	1.06037i	0.268417	+	0.963303i	$0.413499\pi$
$858$	−81.6109	+	6.14800i	−2.78615	+	0.209889i
$859$	−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
$861$	27.3034	+	19.6136i	0.930498	+	0.668430i
$862$	−8.77145	−	15.1926i	−0.298757	−	0.517462i
$863$	0.711785	−	1.23285i	0.0242294	−	0.0419666i	−0.853656	−	0.520837i	$-0.825620\pi$
$863$	0.711785	−	1.23285i	0.0242294	−	0.0419666i	0.877886	+	0.478870i	$0.158953\pi$
$864$	−40.0372	−	4.96959i	−1.36209	−	0.169069i
$865$	−3.66588	−	4.36883i	−0.124644	−	0.148545i
$866$	21.5799	+	12.4591i	0.733313	+	0.423379i
$867$	−4.57044	−	17.9199i	−0.155220	−	0.608593i
$868$	−1.83828	+	5.05063i	−0.0623953	+	0.171430i
$869$	11.5632	−	65.5781i	0.392254	−	2.22459i
$870$	−1.89855	−	0.189228i	−0.0643668	−	0.00641544i
$871$	−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
$876$	0.224219	+	0.328593i	0.00757566	+	0.0111021i
$877$	−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
$879$	−6.67048	+	13.8653i	−0.224990	+	0.467664i
$880$	−9.25281	−	3.36775i	−0.311912	−	0.113527i
$881$	−0.195705	+	0.112990i	−0.00659346	+	0.00380673i	−0.503293	−	0.864116i	$-0.667878\pi$
$881$	−0.195705	+	0.112990i	−0.00659346	+	0.00380673i	0.496700	+	0.867922i	$0.334545\pi$
$882$	16.6816	−	9.10125i	0.561699	−	0.306455i
$883$	−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
$885$	0.134556	+	0.137846i	0.00452306	+	0.00463364i
$886$	14.3253	−	8.27071i	0.481268	−	0.277860i
$887$	42.0903	+	15.3196i	1.41325	+	0.514382i	0.932083	−	0.362246i	$-0.117990\pi$
$887$	42.0903	+	15.3196i	1.41325	+	0.514382i	0.481170	+	0.876627i	$0.340212\pi$
$888$	1.74612	+	0.840044i	0.0585958	+	0.0281900i
$889$	−16.2966	+	2.87353i	−0.546571	+	0.0963751i
$890$	−1.87532	−	5.15240i	−0.0628609	−	0.172709i
$891$	−40.4661	−	9.16951i	−1.35566	−	0.307190i
$892$			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
$897$	3.06388	−	30.7403i	0.102300	−	1.02639i
$898$	1.55756	−	8.83339i	0.0519766	−	0.294774i
$899$	−0.591155	+	1.62419i	−0.0197161	+	0.0541696i
$900$	0.628954	−	26.0377i	0.0209651	−	0.867924i
$901$	−21.5252	−	12.4276i	−0.717108	−	0.414022i
$902$	−58.0061	−	69.1290i	−1.93139	−	2.30174i
$903$	−14.6257	+	6.60627i	−0.486714	+	0.219843i
$904$	−1.51862	+	2.63032i	−0.0505084	+	0.0874832i
$905$	−2.88872	−	5.00341i	−0.0960244	−	0.166319i
$906$	−41.7256	+	58.0848i	−1.38624	+	1.92974i
$907$	−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
$909$	6.44330	−	32.0021i	0.213711	−	1.06144i
$910$	7.53161	+	6.31977i	0.249671	+	0.209498i
$911$	−40.5821			−1.34454			−0.672272	−	0.740304i	$-0.734681\pi$
$911$	−40.5821			−1.34454			−0.672272	+	0.740304i	$0.734681\pi$
$912$	−29.3771	−	14.1380i	−0.972773	−	0.468156i
$913$	32.2136			1.06612
$914$	−12.5700	−	10.5475i	−0.415778	−	0.348880i
$915$	0.705631	+	9.36681i	0.0233274	+	0.309657i
$916$	2.07242	+	11.7533i	0.0684745	+	0.388338i
$917$	28.6127	+	5.04518i	0.944873	+	0.166607i
$918$	23.5373	−	9.95436i	0.776847	−	0.328543i
$919$	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
$921$	16.3483	+	36.1938i	0.538695	+	1.19263i
$922$	31.5838	+	37.6401i	1.04016	+	1.23961i
$923$	14.1365	+	8.16169i	0.465307	+	0.268645i
$924$	27.3970	−	6.98754i	0.901294	−	0.229873i
$925$	−5.33647	+	14.6618i	−0.175462	+	0.482078i
$926$	−3.64171	+	20.6531i	−0.119674	+	0.678704i
$927$	−6.66320	−	2.60910i	−0.218848	−	0.0856941i
$928$	8.30774	−	3.02377i	0.272715	−	0.0992602i
$929$	38.4969	−	45.8788i	1.26304	−	1.50524i	0.488724	−	0.872438i	$-0.337462\pi$
$929$	38.4969	−	45.8788i	1.26304	−	1.50524i	0.774318	−	0.632797i	$-0.218093\pi$
$930$	2.44868	+	0.687919i	0.0802955	+	0.0225578i
$931$	13.9022	−	2.44938i	0.455625	−	0.0802753i
$932$			49.0449i			1.60652i
$933$	−20.8132	+	14.2021i	−0.681393	+	0.464957i
$934$	−2.21186	−	6.07702i	−0.0723741	−	0.198846i
$935$	5.64655	−	0.995639i	0.184662	−	0.0325609i
$936$	4.02160	+	3.54349i	0.131450	+	0.115823i
$937$	−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
$939$	21.7347	−	21.2161i	0.709286	−	0.692360i
$940$	4.11810	−	3.45550i	0.134318	−	0.112706i
$941$	−6.76374	+	5.67545i	−0.220492	+	0.185014i	−0.746342	−	0.665563i	$-0.768192\pi$
$941$	−6.76374	+	5.67545i	−0.220492	+	0.185014i	0.525850	+	0.850577i	$0.323747\pi$
$942$	15.0153	−	14.6569i	0.489223	−	0.477549i
$943$	29.4994	−	17.0315i	0.960634	−	0.554622i
$944$	−0.912435	−	0.332099i	−0.0296972	−	0.0108089i
$945$	2.70923	+	4.18392i	0.0881312	+	0.136103i
$946$	42.4249	−	7.48065i	1.37935	−	0.243217i
$947$	7.64505	+	21.0046i	0.248431	+	0.682558i	0.999744	+	0.0226124i	$0.00719837\pi$
$947$	7.64505	+	21.0046i	0.248431	+	0.682558i	−0.751314	+	0.659945i	$0.770579\pi$
$948$	37.7278	−	25.7440i	1.22534	−	0.836125i
$949$		−	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	$-0.569934\pi$
$953$	7.48437	−	2.72409i	0.242443	−	0.0882419i	0.460384	+	0.887720i	$0.347712\pi$
$954$	−21.1481	+	54.0087i	−0.684695	+	1.74860i
$955$	0.245507	−	1.39234i	0.00794443	−	0.0450551i
$956$	−14.1713	+	38.9352i	−0.458331	+	1.25925i
$957$	8.81033	−	2.24706i	0.284797	−	0.0726370i
$958$	10.3199	+	5.95819i	0.333421	+	0.192501i
$959$	−2.29894	−	2.73977i	−0.0742365	−	0.0884716i
$960$	−2.30982	−	5.11376i	−0.0745493	−	0.165046i
$961$	−14.3479	+	24.8513i	−0.462836	+	0.801656i
$962$	16.8145	+	29.1235i	0.542121	+	0.938981i
$963$	16.1278	+	20.1912i	0.519711	+	0.650651i
$964$	−44.6307	−	7.86960i	−1.43746	−	0.253463i
$965$	−0.644879	−	3.65729i	−0.0207594	−	0.117732i
$966$	1.67998	+	22.3007i	0.0540526	+	0.717515i
$967$	−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
$969$	18.9306	−	1.42352i	0.608139	−	0.0457301i
$970$	−6.76902			−0.217340
$971$	−35.3393	−	29.6532i	−1.13409	−	0.951616i	−0.134862	−	0.990864i	$-0.543059\pi$
$971$	−35.3393	−	29.6532i	−1.13409	−	0.951616i	−0.999229	+	0.0392486i	$0.987504\pi$
$972$	−14.8873	−	24.2552i	−0.477510	−	0.777985i
$973$	−1.37029	−	7.77129i	−0.0439294	−	0.249136i
$974$	4.18477	+	0.737889i	0.134089	+	0.0236435i
$975$	−25.1809	+	35.0534i	−0.806434	+	1.12261i
$976$	−23.6744	−	41.0053i	−0.757800	−	1.31255i
$977$	19.4513	−	33.6907i	0.622303	−	1.07786i	−0.366753	−	0.930318i	$-0.619531\pi$
$977$	19.4513	−	33.6907i	0.622303	−	1.07786i	0.989056	−	0.147541i	$-0.0471360\pi$
$978$	5.26766	−	2.37934i	0.168441	−	0.0760829i
$979$	16.7958	+	20.0164i	0.536795	+	0.639727i
$980$	2.53254	+	1.46217i	0.0808992	+	0.0467072i
$981$	−13.6795	−	0.330435i	−0.436753	−	0.0105500i
$982$	21.6789	−	59.5622i	0.691801	−	1.90071i
$983$	−1.40399	+	7.96240i	−0.0447802	+	0.253961i	−0.998977	−	0.0452181i	$-0.985602\pi$
$983$	−1.40399	+	7.96240i	−0.0447802	+	0.253961i	0.954197	+	0.299179i	$0.0967128\pi$
$984$	−0.586154	+	5.88095i	−0.0186859	+	0.187478i
$985$	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
$990$	−4.27127	−	12.6799i	−0.135750	−	0.402994i
$991$	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
$993$	6.66368	+	3.20585i	0.211466	+	0.101735i
$994$	−11.1043	−	4.04162i	−0.352206	−	0.128192i
$995$	2.71308	−	1.56640i	0.0860105	−	0.0496582i
$996$	15.4341	+	15.8114i	0.489047	+	0.501003i
$997$	−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
$999$	3.81328	+	16.6171i	0.120647	+	0.525743i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(1.49833 + 1.25725i) q^{2} +(-1.72716 + 0.130112i) q^{3} +(0.317026 + 1.79794i) q^{4} +(0.487091 + 0.0858872i) q^{5} +(-2.75144 - 1.97652i) q^{6} +(-0.969730 - 1.67962i) q^{7} +(0.170480 - 0.295279i) q^{8} +(2.96614 - 0.449448i) q^{9} +O(q^{10})\)	\(q+(1.49833 + 1.25725i) q^{2} +(-1.72716 + 0.130112i) q^{3} +(0.317026 + 1.79794i) q^{4} +(0.487091 + 0.0858872i) q^{5} +(-2.75144 - 1.97652i) q^{6} +(-0.969730 - 1.67962i) q^{7} +(0.170480 - 0.295279i) q^{8} +(2.96614 - 0.449448i) q^{9} +(0.621842 + 0.741083i) q^{10} +(-3.99257 - 2.30511i) q^{11} +(-0.781488 - 3.06408i) q^{12} +(-1.79223 + 4.92410i) q^{13} +(0.658727 - 3.73582i) q^{14} +(-0.852457 - 0.0849643i) 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} +(1.89341 + 2.77480i) q^{21} +(-3.08409 - 8.47347i) q^{22} +(3.35200 - 0.591048i) q^{23} +(-0.256026 + 0.532175i) q^{24} +(-4.46858 - 1.62643i) q^{25} +(-8.87617 + 5.12466i) q^{26} +(-5.06451 + 1.16220i) q^{27} +(2.71243 - 2.27600i) q^{28} +(0.872266 - 0.731918i) q^{29} +(-1.17044 - 1.19906i) q^{30} +(-1.31458 + 0.758971i) q^{31} +(7.29606 + 2.65555i) q^{32} +(7.19571 + 3.46180i) q^{33} +(-4.84348 + 0.854036i) q^{34} +(-0.328088 - 0.901415i) q^{35} +(1.74843 + 5.19047i) 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} +(-0.651648 + 6.53806i) q^{42} +(-0.829591 + 4.70484i) q^{43} +(2.87871 - 7.90919i) q^{44} +(1.48338 + 0.0358318i) q^{45} +(5.76551 + 3.32872i) q^{46} +(-3.82673 - 4.56052i) q^{47} +(-6.81634 + 3.07886i) q^{48} +(1.61925 - 2.80462i) q^{49} +(-4.65059 - 8.05506i) q^{50} +(2.54096 - 3.53718i) q^{51} +(-9.42143 - 1.66125i) q^{52} +(1.71646 + 9.73455i) q^{53} +(-9.04950 - 4.62600i) q^{54} +(-1.74676 - 1.46571i) q^{55} -0.661277 q^{56} +(-5.27295 - 5.40333i) q^{57} +2.22715 q^{58} +(-0.172251 - 0.144536i) q^{59} +(-0.117490 - 1.55961i) q^{60} +(-1.90402 - 10.7982i) q^{61} +(-2.92389 - 0.515560i) q^{62} +(-3.63126 - 4.54615i) q^{63} +(3.27498 + 5.67243i) q^{64} +(-1.29589 + 2.24455i) q^{65} +(6.42921 + 14.2337i) q^{66} +(0.266197 + 0.317241i) q^{67} +(-3.97564 - 2.29534i) q^{68} +(-5.71253 + 1.45697i) q^{69} +(0.641719 - 1.76311i) q^{70} +(0.540928 - 3.06775i) q^{71} +(0.372954 - 0.952462i) 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} +(14.6638 - 10.0060i) q^{78} +(4.94012 + 13.5729i) q^{79} +(2.10338 - 0.370883i) q^{80} +(8.59599 - 2.66625i) q^{81} +(18.3938 + 6.69478i) q^{82} +(-6.05130 + 3.49372i) q^{83} +(-4.38866 + 4.28393i) q^{84} +(-0.952717 + 0.799425i) q^{85} +(-7.15817 + 6.00642i) q^{86} +(-1.41131 + 1.37763i) q^{87} +(-1.36130 + 0.785948i) q^{88} +(-5.32595 - 1.93849i) q^{89} +(2.17755 + 1.91867i) q^{90} +(10.0086 - 1.76478i) q^{91} +(2.12534 + 5.83933i) q^{92} +(2.17173 - 1.48190i) 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} +(-12.8785 - 5.04283i) 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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