LMFDB - Embedded newform 57.2.j.b.29.1

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			29.1
Character	$\chi$	$=$	57.29
Dual form			57.2.j.b.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.448036 - 2.54094i) q^{2} +(-1.71942 + 0.208799i) q^{3} +(-4.37626 + 1.59283i) q^{4} +(0.533860 - 1.46677i) q^{5} +(1.30091 + 4.27539i) q^{6} +(1.49687 - 2.59266i) q^{7} +(3.42787 + 5.93724i) q^{8} +(2.91281 - 0.718027i) q^{9} +O(q^{10})$	\(q+(-0.448036 - 2.54094i) q^{2} +(-1.71942 + 0.208799i) q^{3} +(-4.37626 + 1.59283i) q^{4} +(0.533860 - 1.46677i) q^{5} +(1.30091 + 4.27539i) q^{6} +(1.49687 - 2.59266i) q^{7} +(3.42787 + 5.93724i) q^{8} +(2.91281 - 0.718027i) q^{9} +(-3.96616 - 0.699341i) q^{10} +(-1.05900 + 0.611412i) q^{11} +(7.19204 - 3.65250i) q^{12} +(0.203530 - 0.242558i) q^{13} +(-7.25845 - 2.64186i) q^{14} +(-0.611669 + 2.63346i) q^{15} +(6.41525 - 5.38303i) q^{16} +(5.00468 - 0.882460i) q^{17} +(-3.12951 - 7.07956i) q^{18} +(-0.461268 + 4.33442i) q^{19} +7.26931i q^{20} +(-2.03241 + 4.77042i) q^{21} +(2.02803 + 2.41691i) q^{22} +(-0.211619 - 0.581418i) q^{23} +(-7.13363 - 9.49287i) q^{24} +(1.96382 + 1.64784i) q^{25} +(-0.707514 - 0.408483i) q^{26} +(-4.85841 + 1.84278i) q^{27} +(-2.42104 + 13.7304i) q^{28} +(-0.204862 + 1.16183i) q^{29} +(6.96552 + 0.374329i) q^{30} +(-4.50103 - 2.59867i) q^{31} +(-6.04864 - 5.07541i) q^{32} +(1.69320 - 1.27239i) q^{33} +(-4.48456 - 12.3212i) q^{34} +(-3.00371 - 3.57969i) q^{35} +(-11.6035 + 7.78187i) q^{36} -3.64847i q^{37} +(11.2202 - 0.769925i) q^{38} +(-0.299308 + 0.459555i) q^{39} +(10.5386 - 1.85823i) q^{40} +(-0.118123 + 0.0991172i) q^{41} +(13.0319 + 3.02691i) q^{42} +(8.99072 + 3.27235i) q^{43} +(3.66057 - 4.36249i) q^{44} +(0.501851 - 4.65574i) q^{45} +(-1.38254 + 0.798207i) q^{46} +(-8.03246 - 1.41634i) q^{47} +(-9.90652 + 10.5952i) q^{48} +(-0.981262 - 1.69960i) q^{49} +(3.30720 - 5.72824i) q^{50} +(-8.42088 + 2.56229i) q^{51} +(-0.504348 + 1.38568i) q^{52} +(-2.88328 + 1.04943i) q^{53} +(6.85915 + 11.5193i) q^{54} +(0.331444 + 1.87971i) q^{55} +20.5243 q^{56} +(-0.111912 - 7.54900i) q^{57} +3.04393 q^{58} +(0.468861 + 2.65904i) q^{59} +(-1.51783 - 12.4990i) q^{60} +(-6.47830 + 2.35791i) q^{61} +(-4.58645 + 12.6012i) q^{62} +(2.49850 - 8.62672i) q^{63} +(-1.81179 + 3.13812i) q^{64} +(-0.247119 - 0.428023i) q^{65} +(-3.99168 - 3.73223i) q^{66} +(8.96745 + 1.58120i) q^{67} +(-20.4962 + 11.8335i) q^{68} +(0.485261 + 0.955515i) q^{69} +(-7.75000 + 9.23609i) q^{70} +(12.9496 + 4.71326i) q^{71} +(14.2478 + 14.8327i) q^{72} +(-0.335304 + 0.281354i) q^{73} +(-9.27055 + 1.63465i) q^{74} +(-3.72070 - 2.42328i) q^{75} +(-4.88536 - 19.7033i) q^{76} +3.66082i q^{77} +(1.30180 + 0.554625i) q^{78} +(-0.940136 - 1.12041i) q^{79} +(-4.47082 - 12.2835i) q^{80} +(7.96887 - 4.18295i) q^{81} +(0.304774 + 0.255736i) q^{82} +(-9.46265 - 5.46326i) q^{83} +(1.29589 - 24.1139i) q^{84} +(1.37743 - 7.81181i) q^{85} +(4.28669 - 24.3110i) q^{86} +(0.109654 - 2.04045i) q^{87} +(-7.26019 - 4.19167i) q^{88} +(6.02351 + 5.05433i) q^{89} +(-12.0548 + 0.810768i) q^{90} +(-0.324211 - 0.890763i) q^{91} +(1.85220 + 2.20736i) q^{92} +(8.28176 + 3.52839i) q^{93} +21.0446i q^{94} +(6.11134 + 2.99055i) q^{95} +(11.4599 + 7.46380i) q^{96} +(-18.2890 + 3.22484i) q^{97} +(-3.87893 + 3.25481i) q^{98} +(-2.64564 + 2.54131i) 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 $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.448036	−	2.54094i	−0.316810	−	1.79672i	−0.561888	−	0.827213i	$-0.689925\pi$
$2$	−0.448036	−	2.54094i	−0.316810	−	1.79672i	0.245078	−	0.969503i	$-0.421186\pi$
$3$	−1.71942	+	0.208799i	−0.992707	+	0.120550i
$3$	−1.71942	+	0.208799i	−0.992707	+	0.120550i
$4$	−4.37626	+	1.59283i	−2.18813	+	0.796414i
$5$	0.533860	−	1.46677i	0.238750	−	0.655959i	−0.761223	−	0.648491i	$-0.775401\pi$
$5$	0.533860	−	1.46677i	0.238750	−	0.655959i	0.999972	−	0.00746821i	$-0.00237723\pi$
$6$	1.30091	+	4.27539i	0.531094	+	1.74542i
$7$	1.49687	−	2.59266i	0.565765	−	0.979934i	−0.431213	−	0.902250i	$-0.641914\pi$
$7$	1.49687	−	2.59266i	0.565765	−	0.979934i	0.996978	−	0.0776837i	$-0.0247524\pi$
$8$	3.42787	+	5.93724i	1.21193	+	2.09913i
$9$	2.91281	−	0.718027i	0.970935	−	0.239342i
$10$	−3.96616	−	0.699341i	−1.25421	−	0.221151i
$11$	−1.05900	+	0.611412i	−0.319299	+	0.184348i	−0.651080	−	0.759009i	$-0.725684\pi$
$11$	−1.05900	+	0.611412i	−0.319299	+	0.184348i	0.331781	+	0.943356i	$0.392351\pi$
$12$	7.19204	−	3.65250i	2.07616	−	1.05439i
$13$	0.203530	−	0.242558i	0.0564491	−	0.0672734i	−0.737081	−	0.675804i	$-0.763796\pi$
$13$	0.203530	−	0.242558i	0.0564491	−	0.0672734i	0.793530	+	0.608531i	$0.208241\pi$
$14$	−7.25845	−	2.64186i	−1.93990	−	0.706067i
$15$	−0.611669	+	2.63346i	−0.157932	+	0.679956i
$16$	6.41525	−	5.38303i	1.60381	−	1.34576i
$17$	5.00468	−	0.882460i	1.21381	−	0.214028i	0.470152	−	0.882585i	$-0.344199\pi$
$17$	5.00468	−	0.882460i	1.21381	−	0.214028i	0.743660	+	0.668558i	$0.233088\pi$
$18$	−3.12951	−	7.07956i	−0.737632	−	1.66867i
$19$	−0.461268	+	4.33442i	−0.105822	+	0.994385i
$19$	−0.461268	+	4.33442i	−0.105822	+	0.994385i
$20$			7.26931i			1.62547i
$21$	−2.03241	+	4.77042i	−0.443508	+	1.04099i
$22$	2.02803	+	2.41691i	0.432377	+	0.515287i
$23$	−0.211619	−	0.581418i	−0.0441256	−	0.121234i	0.915673	−	0.401925i	$-0.131659\pi$
$23$	−0.211619	−	0.581418i	−0.0441256	−	0.121234i	−0.959798	+	0.280691i	$0.909436\pi$
$24$	−7.13363	−	9.49287i	−1.45615	−	1.93772i
$25$	1.96382	+	1.64784i	0.392764	+	0.329568i
$26$	−0.707514	−	0.408483i	−0.138755	−	0.0801102i
$27$	−4.85841	+	1.84278i	−0.935002	+	0.354644i
$28$	−2.42104	+	13.7304i	−0.457534	+	2.59481i
$29$	−0.204862	+	1.16183i	−0.0380420	+	0.215747i	−0.997903	−	0.0647299i	$-0.979381\pi$
$29$	−0.204862	+	1.16183i	−0.0380420	+	0.215747i	0.959861	+	0.280477i	$0.0904925\pi$
$30$	6.96552	+	0.374329i	1.27172	+	0.0683428i
$31$	−4.50103	−	2.59867i	−0.808409	−	0.466735i	0.0379939	−	0.999278i	$-0.487903\pi$
$31$	−4.50103	−	2.59867i	−0.808409	−	0.466735i	−0.846403	+	0.532543i	$0.821237\pi$
$32$	−6.04864	−	5.07541i	−1.06926	−	0.897214i
$33$	1.69320	−	1.27239i	0.294748	−	0.221495i
$34$	−4.48456	−	12.3212i	−0.769095	−	2.11307i
$35$	−3.00371	−	3.57969i	−0.507720	−	0.605077i
$36$	−11.6035	+	7.78187i	−1.93392	+	1.29698i
$37$		−	3.64847i		−	0.599805i	−0.953970	−	0.299902i	$-0.903046\pi$
$37$		−	3.64847i		−	0.599805i	0.953970	−	0.299902i	$-0.0969541\pi$
$38$	11.2202	−	0.769925i	1.82015	−	0.124898i
$39$	−0.299308	+	0.459555i	−0.0479276	+	0.0735878i
$40$	10.5386	−	1.85823i	1.66629	−	0.293812i
$41$	−0.118123	+	0.0991172i	−0.0184477	+	0.0154795i	−0.651965	−	0.758249i	$-0.726055\pi$
$41$	−0.118123	+	0.0991172i	−0.0184477	+	0.0154795i	0.633517	+	0.773729i	$0.281611\pi$
$42$	13.0319	+	3.02691i	2.01087	+	0.467062i
$43$	8.99072	+	3.27235i	1.37107	+	0.499029i	0.919460	−	0.393185i	$-0.128627\pi$
$43$	8.99072	+	3.27235i	1.37107	+	0.499029i	0.451613	+	0.892214i	$0.350849\pi$
$44$	3.66057	−	4.36249i	0.551851	−	0.657671i
$45$	0.501851	−	4.65574i	0.0748115	−	0.694036i
$46$	−1.38254	+	0.798207i	−0.203844	+	0.117689i
$47$	−8.03246	−	1.41634i	−1.17165	−	0.206594i	−0.446244	−	0.894911i	$-0.647239\pi$
$47$	−8.03246	−	1.41634i	−1.17165	−	0.206594i	−0.725410	+	0.688317i	$0.758350\pi$
$48$	−9.90652	+	10.5952i	−1.42988	+	1.52928i
$49$	−0.981262	−	1.69960i	−0.140180	−	0.242799i
$50$	3.30720	−	5.72824i	0.467709	−	0.810095i
$51$	−8.42088	+	2.56229i	−1.17916	+	0.358793i
$52$	−0.504348	+	1.38568i	−0.0699404	+	0.192160i
$53$	−2.88328	+	1.04943i	−0.396048	+	0.144150i	−0.532364	−	0.846516i	$-0.678696\pi$
$53$	−2.88328	+	1.04943i	−0.396048	+	0.144150i	0.136315	+	0.990665i	$0.456474\pi$
$54$	6.85915	+	11.5193i	0.933412	+	1.56758i
$55$	0.331444	+	1.87971i	0.0446919	+	0.253460i
$56$	20.5243			2.74268
$57$	−0.111912	−	7.54900i	−0.0148231	−	0.999890i
$58$	3.04393			0.399688
$59$	0.468861	+	2.65904i	0.0610405	+	0.346178i	0.999998	+	0.00214403i	$0.000682465\pi$
$59$	0.468861	+	2.65904i	0.0610405	+	0.346178i	−0.938957	+	0.344034i	$0.888206\pi$
$60$	−1.51783	−	12.4990i	−0.195951	−	1.61361i
$61$	−6.47830	+	2.35791i	−0.829462	+	0.301899i	−0.721638	−	0.692271i	$-0.756610\pi$
$61$	−6.47830	+	2.35791i	−0.829462	+	0.301899i	−0.107824	+	0.994170i	$0.534388\pi$
$62$	−4.58645	+	12.6012i	−0.582479	+	1.60035i
$63$	2.49850	−	8.62672i	0.314781	−	1.08686i
$64$	−1.81179	+	3.13812i	−0.226474	+	0.392265i
$65$	−0.247119	−	0.428023i	−0.0306514	−	0.0530898i
$66$	−3.99168	−	3.73223i	−0.491342	−	0.459406i
$67$	8.96745	+	1.58120i	1.09555	+	0.193175i	0.692081	−	0.721820i	$-0.256694\pi$
$67$	8.96745	+	1.58120i	1.09555	+	0.193175i	0.403467	+	0.914994i	$0.367805\pi$
$68$	−20.4962	+	11.8335i	−2.48552	+	1.43502i
$69$	0.485261	+	0.955515i	0.0584186	+	0.115031i
$70$	−7.75000	+	9.23609i	−0.926302	+	1.10392i
$71$	12.9496	+	4.71326i	1.53683	+	0.559360i	0.965282	−	0.261208i	$-0.0841209\pi$
$71$	12.9496	+	4.71326i	1.53683	+	0.559360i	0.571548	+	0.820569i	$0.306343\pi$
$72$	14.2478	+	14.8327i	1.67912	+	1.74805i
$73$	−0.335304	+	0.281354i	−0.0392444	+	0.0329300i	−0.662199	−	0.749328i	$-0.730377\pi$
$73$	−0.335304	+	0.281354i	−0.0392444	+	0.0329300i	0.622954	+	0.782258i	$0.285932\pi$
$74$	−9.27055	+	1.63465i	−1.07768	+	0.190024i
$75$	−3.72070	−	2.42328i	−0.429629	−	0.279817i
$76$	−4.88536	−	19.7033i	−0.560390	−	2.26012i
$77$			3.66082i			0.417190i
$78$	1.30180	+	0.554625i	0.147400	+	0.0627990i
$79$	−0.940136	−	1.12041i	−0.105774	−	0.126056i	0.710560	−	0.703636i	$-0.248442\pi$
$79$	−0.940136	−	1.12041i	−0.105774	−	0.126056i	−0.816334	+	0.577580i	$0.803997\pi$
$80$	−4.47082	−	12.2835i	−0.499852	−	1.37333i
$81$	7.96887	−	4.18295i	0.885430	−	0.464772i
$82$	0.304774	+	0.255736i	0.0336567	+	0.0282413i
$83$	−9.46265	−	5.46326i	−1.03866	−	0.599671i	−0.119207	−	0.992869i	$-0.538035\pi$
$83$	−9.46265	−	5.46326i	−1.03866	−	0.599671i	−0.919454	+	0.393198i	$0.871369\pi$
$84$	1.29589	−	24.1139i	0.141393	−	2.63104i
$85$	1.37743	−	7.81181i	0.149404	−	0.847310i
$86$	4.28669	−	24.3110i	0.462246	−	2.62153i
$87$	0.109654	−	2.04045i	0.0117562	−	0.218759i
$88$	−7.26019	−	4.19167i	−0.773939	−	0.446834i
$89$	6.02351	+	5.05433i	0.638491	+	0.535758i	0.903554	−	0.428473i	$-0.140948\pi$
$89$	6.02351	+	5.05433i	0.638491	+	0.535758i	−0.265063	+	0.964231i	$0.585393\pi$
$90$	−12.0548	+	0.810768i	−1.27069	+	0.0854624i
$91$	−0.324211	−	0.890763i	−0.0339866	−	0.0933773i
$92$	1.85220	+	2.20736i	0.193105	+	0.230134i
$93$	8.28176	+	3.52839i	0.858779	+	0.365877i
$94$			21.0446i			2.17058i
$95$	6.11134	+	2.99055i	0.627011	+	0.306824i
$96$	11.4599	+	7.46380i	1.16962	+	0.761771i
$97$	−18.2890	+	3.22484i	−1.85697	+	0.327433i	−0.986367	−	0.164561i	$-0.947379\pi$
$97$	−18.2890	+	3.22484i	−1.85697	+	0.327433i	−0.870599	+	0.491994i	$0.836268\pi$
$98$	−3.87893	+	3.25481i	−0.391831	+	0.328786i
$99$	−2.64564	+	2.54131i	−0.265897	+	0.255411i
$100$	−11.2189	−	4.08335i	−1.12189	−	0.408335i
$101$	−9.92594	+	11.8293i	−0.987668	+	1.17706i	−0.00346803	+	0.999994i	$0.501104\pi$
$101$	−9.92594	+	11.8293i	−0.987668	+	1.17706i	−0.984200	+	0.177062i	$0.943341\pi$
$102$	10.2835	+	20.2490i	1.01822	+	2.00495i
$103$	6.42425	−	3.70904i	0.633000	−	0.365463i	−0.148913	−	0.988850i	$-0.547577\pi$
$103$	6.42425	−	3.70904i	0.633000	−	0.365463i	0.781913	+	0.623387i	$0.214244\pi$
$104$	2.13780	+	0.376951i	0.209628	+	0.0369631i
$105$	5.91208	+	5.52781i	0.576960	+	0.539459i
$106$	3.95834	+	6.85605i	0.384468	+	0.665919i
$107$	−6.82023	+	11.8130i	−0.659337	+	1.14200i	0.321451	+	0.946926i	$0.395829\pi$
$107$	−6.82023	+	11.8130i	−0.659337	+	1.14200i	−0.980788	+	0.195078i	$0.937504\pi$
$108$	18.3264	−	15.8031i	1.76346	−	1.52065i
$109$	−0.443482	+	1.21846i	−0.0424778	+	0.116707i	−0.959118	−	0.283007i	$-0.908668\pi$
$109$	−0.443482	+	1.21846i	−0.0424778	+	0.116707i	0.916640	+	0.399714i	$0.130890\pi$
$110$	4.62773	−	1.68436i	0.441237	−	0.160597i
$111$	0.761799	+	6.27325i	0.0723067	+	0.595431i
$112$	−4.35356	−	24.6903i	−0.411373	−	2.33301i
$113$	6.86179			0.645503			0.322752	−	0.946484i	$-0.395392\pi$
$113$	6.86179			0.645503			0.322752	+	0.946484i	$0.395392\pi$
$114$	−19.1314	+	3.66659i	−1.79182	+	0.343408i
$115$	−0.965781			−0.0900595
$116$	−0.954068	−	5.41079i	−0.0885830	−	0.502379i
$117$	0.418680	−	0.852664i	0.0387070	−	0.0788288i
$118$	6.54641	−	2.38270i	0.602646	−	0.219345i
$119$	5.20345	−	14.2964i	0.477000	−	1.31055i
$120$	−17.7322	+	5.39552i	−1.61872	+	0.492542i
$121$	−4.75235	+	8.23131i	−0.432032	+	0.748301i
$122$	8.89382	+	15.4046i	0.805209	+	1.39466i
$123$	0.182408	−	0.195088i	0.0164472	−	0.0175905i
$124$	23.8369	+	4.20309i	2.14062	+	0.377449i
$125$	10.2243	−	5.90301i	0.914490	−	0.527981i
$126$	−23.0394	−	2.48346i	−2.05251	−	0.221244i
$127$	−2.00315	+	2.38726i	−0.177751	+	0.211835i	−0.847562	−	0.530696i	$-0.821931\pi$
$127$	−2.00315	+	2.38726i	−0.177751	+	0.211835i	0.669811	+	0.742531i	$0.266375\pi$
$128$	−6.05398	−	2.20347i	−0.535101	−	0.194761i
$129$	−16.1421	−	3.74929i	−1.42123	−	0.330107i
$130$	−0.976864	+	0.819686i	−0.0856766	+	0.0718912i
$131$	3.61069	−	0.636662i	0.315467	−	0.0556254i	−0.0136728	−	0.999907i	$-0.504352\pi$
$131$	3.61069	−	0.636662i	0.315467	−	0.0556254i	0.329140	+	0.944281i	$0.393241\pi$
$132$	−5.38316	+	8.26528i	−0.468544	+	0.719400i
$133$	10.5472	+	7.68400i	0.914561	+	0.666287i
$134$		−	23.4942i		−	2.02959i
$135$	0.109224	+	8.10995i	0.00940049	+	0.697994i
$136$	22.3947	+	26.6890i	1.92033	+	2.28856i
$137$	−5.40504	−	14.8502i	−0.461784	−	1.26874i	−0.924143	−	0.382048i	$-0.875219\pi$
$137$	−5.40504	−	14.8502i	−0.461784	−	1.26874i	0.462359	−	0.886693i	$-0.347003\pi$
$138$	2.21049	−	1.66113i	0.188170	−	0.141404i
$139$	−5.59691	−	4.69637i	−0.474724	−	0.398341i	0.373790	−	0.927513i	$-0.378058\pi$
$139$	−5.59691	−	4.69637i	−0.474724	−	0.398341i	−0.848514	+	0.529173i	$0.822502\pi$
$140$	18.8469	+	10.8812i	1.59285	+	0.919632i
$141$	14.1069	+	0.758108i	1.18801	+	0.0638442i
$142$	6.17423	−	35.0158i	0.518130	−	2.93846i
$143$	−0.0672349	+	0.381308i	−0.00562247	+	0.0318866i
$144$	14.8212	−	20.2860i	1.23510	−	1.69050i
$145$	1.59477	+	0.920741i	0.132439	+	0.0764634i
$146$	0.865132	+	0.725932i	0.0715988	+	0.0600786i
$147$	2.04208	+	2.71743i	0.168428	+	0.224130i
$148$	5.81139	+	15.9667i	0.477693	+	1.31245i
$149$	3.59311	+	4.28210i	0.294359	+	0.350803i	0.892873	−	0.450309i	$-0.148686\pi$
$149$	3.59311	+	4.28210i	0.294359	+	0.350803i	−0.598514	+	0.801113i	$0.704242\pi$
$150$	−4.49041	+	10.5398i	−0.366641	+	0.860570i
$151$		−	19.1657i		−	1.55968i	−0.625980	−	0.779839i	$-0.715301\pi$
$151$		−	19.1657i		−	1.55968i	0.625980	−	0.779839i	$-0.284699\pi$
$152$	−27.3157	+	12.1192i	−2.21559	+	0.982994i
$153$	13.9440	−	6.16393i	1.12731	−	0.498324i
$154$	9.30194	−	1.64018i	0.749572	−	0.132170i
$155$	−6.21457	+	5.21465i	−0.499167	+	0.418850i
$156$	0.577855	−	2.48788i	0.0462654	−	0.199190i
$157$	−13.5243	−	4.92243i	−1.07935	−	0.392853i	−0.259687	−	0.965693i	$-0.583619\pi$
$157$	−13.5243	−	4.92243i	−1.07935	−	0.392853i	−0.819667	+	0.572840i	$0.805842\pi$
$158$	−2.42568	+	2.89081i	−0.192977	+	0.229981i
$159$	4.73844	−	2.40643i	0.375783	−	0.190842i
$160$	−10.6736	+	6.16239i	−0.843820	+	0.487180i
$161$	−1.82419	−	0.321653i	−0.143766	−	0.0253498i
$162$	−14.1990	−	18.3743i	−1.11558	−	1.44362i
$163$	−0.951823	−	1.64861i	−0.0745525	−	0.129129i	0.826339	−	0.563173i	$-0.190420\pi$
$163$	−0.951823	−	1.64861i	−0.0745525	−	0.129129i	−0.900892	+	0.434044i	$0.857086\pi$
$164$	0.359061	−	0.621912i	0.0280380	−	0.0485632i
$165$	−0.962373	−	3.16281i	−0.0749206	−	0.246224i
$166$	−9.64222	+	26.4918i	−0.748381	+	2.05616i
$167$	12.4088	−	4.51642i	0.960220	−	0.349491i	0.186100	−	0.982531i	$-0.440415\pi$
$167$	12.4088	−	4.51642i	0.960220	−	0.349491i	0.774120	+	0.633039i	$0.218193\pi$
$168$	−35.2899	+	4.28547i	−2.72268	+	0.330631i
$169$	2.24002	+	12.7038i	0.172309	+	0.977213i
$170$	−20.4665			−1.56971
$171$	1.76865	+	12.9565i	0.135252	+	0.990811i
$172$	−44.5580			−3.39752
$173$	−2.37910	−	13.4925i	−0.180880	−	1.02582i	−0.931136	−	0.364672i	$-0.881181\pi$
$173$	−2.37910	−	13.4925i	−0.180880	−	1.02582i	0.750256	−	0.661147i	$-0.229930\pi$
$174$	−5.23380	+	0.635571i	−0.396773	+	0.0481825i
$175$	7.21188	−	2.62491i	0.545167	−	0.198424i
$176$	−3.50247	+	9.62296i	−0.264009	+	0.725358i
$177$	−1.36138	−	4.47411i	−0.102327	−	0.336295i
$178$	10.1440	−	17.5699i	0.760325	−	1.31692i
$179$	−9.56990	−	16.5756i	−0.715288	−	1.23892i	−0.962848	−	0.270043i	$-0.912962\pi$
$179$	−9.56990	−	16.5756i	−0.715288	−	1.23892i	0.247560	−	0.968873i	$-0.420371\pi$
$180$	5.21956	+	21.1741i	0.389043	+	1.57822i
$181$	6.05191	+	1.06712i	0.449835	+	0.0793181i	0.393976	−	0.919121i	$-0.371099\pi$
$181$	6.05191	+	1.06712i	0.449835	+	0.0793181i	0.0558589	+	0.998439i	$0.482210\pi$
$182$	−2.11812	+	1.22290i	−0.157005	+	0.0906471i
$183$	10.6466	−	5.40690i	0.787018	−	0.399690i
$184$	2.72662	−	3.24946i	0.201009	−	0.239553i
$185$	−5.35146	−	1.94777i	−0.393447	−	0.143203i
$186$	5.25491	−	22.6243i	0.385309	−	1.65890i
$187$	−4.76039	+	3.99444i	−0.348114	+	0.292102i
$188$	37.4081	−	6.59606i	2.72827	−	0.481067i
$189$	−2.49472	+	15.3546i	−0.181464	+	1.11688i
$190$	4.86070	−	16.8684i	0.352633	−	1.22377i
$191$			26.3867i			1.90927i	0.297773	+	0.954637i	$0.403756\pi$
$191$			26.3867i			1.90927i	−0.297773	+	0.954637i	$0.596244\pi$
$192$	2.45999	−	5.77404i	0.177535	−	0.416705i
$193$	−5.01339	−	5.97472i	−0.360871	−	0.430070i	0.554809	−	0.831978i	$-0.312792\pi$
$193$	−5.01339	−	5.97472i	−0.360871	−	0.430070i	−0.915680	+	0.401908i	$0.868347\pi$
$194$	16.3883	+	45.0264i	1.17661	+	3.23271i
$195$	0.514273	+	0.684353i	0.0368279	+	0.0490076i
$196$	7.00142	+	5.87489i	0.500102	+	0.419635i
$197$	−20.9467	−	12.0936i	−1.49239	−	0.861630i	−0.492426	−	0.870355i	$-0.663890\pi$
$197$	−20.9467	−	12.0936i	−1.49239	−	0.861630i	−0.999962	+	0.00872425i	$0.997223\pi$
$198$	7.64267	+	5.58381i	0.543141	+	0.396824i
$199$	−0.711595	+	4.03566i	−0.0504437	+	0.286080i	−0.999586	−	0.0287666i	$-0.990842\pi$
$199$	−0.711595	+	4.03566i	−0.0504437	+	0.286080i	0.949142	+	0.314847i	$0.101953\pi$
$200$	−3.05191	+	17.3082i	−0.215803	+	1.22388i
$201$	−15.7490	−	0.846353i	−1.11085	−	0.0596972i
$202$	34.5047	+	19.9213i	2.42774	+	1.40166i
$203$	2.70558	+	2.27025i	0.189895	+	0.159341i
$204$	32.7707	−	24.6263i	2.29441	−	1.72418i
$205$	0.0823207	+	0.226174i	0.00574952	+	0.0157967i
$206$	−12.3028	−	14.6619i	−0.857174	−	1.02154i
$207$	−1.03388	−	1.54161i	−0.0718595	−	0.107149i
$208$		−	2.65168i		−	0.183861i
$209$	−2.16164	−	4.87216i	−0.149524	−	0.337015i
$210$	11.3970	−	17.4989i	0.786468	−	1.20754i
$211$	9.83078	−	1.73343i	0.676779	−	0.119334i	0.175314	−	0.984512i	$-0.443906\pi$
$211$	9.83078	−	1.73343i	0.676779	−	0.119334i	0.501465	+	0.865178i	$0.332795\pi$
$212$	10.9464	−	9.18513i	0.751802	−	0.630837i
$213$	−23.2499	−	5.40020i	−1.59305	−	0.370016i
$214$	33.0718	+	12.0372i	2.26074	+	0.822843i
$215$	9.59958	−	11.4403i	0.654686	−	0.780224i
$216$	−27.5950	−	22.5287i	−1.87760	−	1.53289i
$217$	−13.4750	+	7.77977i	−0.914740	+	0.528125i
$218$	3.29472	+	0.580948i	0.223147	+	0.0393468i
$219$	0.517782	−	0.553777i	0.0349885	−	0.0374208i
$220$	−4.44454	−	7.69817i	−0.299651	−	0.519010i
$221$	0.804555	−	1.39353i	0.0541202	−	0.0937390i
$222$	15.5986	−	4.74633i	1.04691	−	0.318553i
$223$	3.65141	−	10.0322i	0.244516	−	0.671803i	−0.755348	−	0.655324i	$-0.772532\pi$
$223$	3.65141	−	10.0322i	0.244516	−	0.671803i	0.999864	−	0.0164789i	$-0.00524564\pi$
$224$	−22.2129	+	8.08482i	−1.48416	+	0.540190i
$225$	6.90342	+	3.38976i	0.460228	+	0.225984i
$226$	−3.07433	−	17.4354i	−0.204502	−	1.15979i
$227$	0.519141			0.0344566			0.0172283	−	0.999852i	$-0.494516\pi$
$227$	0.519141			0.0344566			0.0172283	+	0.999852i	$0.494516\pi$
$228$	12.5140	+	32.8581i	0.828761	+	2.17608i
$229$	−3.84464			−0.254061			−0.127030	−	0.991899i	$-0.540545\pi$
$229$	−3.84464			−0.254061			−0.127030	+	0.991899i	$0.540545\pi$
$230$	0.432705	+	2.45399i	0.0285317	+	0.161811i
$231$	−0.764378	−	6.29449i	−0.0502924	−	0.414147i
$232$	−7.60031	+	2.76629i	−0.498985	+	0.181616i
$233$	−6.29055	+	17.2831i	−0.412107	+	1.13226i	0.543960	+	0.839111i	$0.316924\pi$
$233$	−6.29055	+	17.2831i	−0.412107	+	1.13226i	−0.956068	+	0.293145i	$0.905298\pi$
$234$	−2.35415	−	0.681818i	−0.153896	−	0.0445718i
$235$	−6.36565	+	11.0256i	−0.415249	+	0.719233i
$236$	−6.28726	−	10.8899i	−0.409266	−	0.708869i
$237$	1.85043	+	1.73016i	0.120198	+	0.112386i
$238$	−38.6576	−	6.81637i	−2.50580	−	0.441840i
$239$	14.2757	−	8.24205i	0.923415	−	0.533134i	0.0386922	−	0.999251i	$-0.487681\pi$
$239$	14.2757	−	8.24205i	0.923415	−	0.533134i	0.884723	+	0.466117i	$0.154347\pi$
$240$	10.2520	+	20.1869i	0.661763	+	1.30306i
$241$	−7.68280	+	9.15600i	−0.494893	+	0.589790i	−0.954455	−	0.298356i	$-0.903562\pi$
$241$	−7.68280	+	9.15600i	−0.494893	+	0.589790i	0.459562	+	0.888146i	$0.348006\pi$
$242$	23.0445	+	8.38752i	1.48136	+	0.539170i
$243$	−12.8284	+	8.85614i	−0.822945	+	0.568122i
$244$	24.5950	−	20.6376i	1.57453	−	1.32119i
$245$	−3.01677	+	0.531938i	−0.192734	+	0.0339843i
$246$	−0.577432	−	0.376081i	−0.0368157	−	0.0239780i
$247$	0.957466	+	0.994070i	0.0609221	+	0.0632511i
$248$		−	35.6316i		−	2.26261i
$249$	17.4110	+	7.41784i	1.10338	+	0.470087i
$250$	−19.5801	−	23.3346i	−1.23835	−	1.47581i
$251$	3.07435	+	8.44670i	0.194051	+	0.533151i	0.998114	−	0.0613939i	$-0.0195546\pi$
$251$	3.07435	+	8.44670i	0.194051	+	0.533151i	−0.804063	+	0.594545i	$0.797332\pi$
$252$	2.80679	+	41.7324i	0.176811	+	2.62890i
$253$	0.579589	+	0.486333i	0.0364385	+	0.0305755i
$254$	6.96338	+	4.02031i	0.436921	+	0.252257i
$255$	−0.737284	+	13.7194i	−0.0461705	+	0.859141i
$256$	−4.14494	+	23.5071i	−0.259059	+	1.46919i
$257$	−2.19345	+	12.4397i	−0.136824	+	0.775965i	0.836749	+	0.547587i	$0.184453\pi$
$257$	−2.19345	+	12.4397i	−0.136824	+	0.775965i	−0.973572	+	0.228378i	$0.926658\pi$
$258$	−2.29449	+	42.6959i	−0.142849	+	2.65813i
$259$	−9.45925	−	5.46130i	−0.587769	−	0.339349i
$260$	1.76323	+	1.47952i	0.109351	+	0.0917561i
$261$	0.237503	+	3.53129i	0.0147011	+	0.218581i
$262$	−3.23544	−	8.88930i	−0.199886	−	0.549183i
$263$	−0.255221	−	0.304161i	−0.0157376	−	0.0187553i	0.758118	−	0.652117i	$-0.226119\pi$
$263$	−0.255221	−	0.304161i	−0.0157376	−	0.0187553i	−0.773856	+	0.633362i	$0.781675\pi$
$264$	13.3585	+	5.69132i	0.822161	+	0.350277i
$265$			4.78935i			0.294207i
$266$	14.7990	−	30.2426i	0.907387	−	1.85429i
$267$	−11.4123	−	7.43280i	−0.698421	−	0.454880i
$268$	−41.7625	+	7.36385i	−2.55105	+	0.449819i
$269$	14.7929	−	12.4127i	0.901936	−	0.756814i	−0.0686317	−	0.997642i	$-0.521863\pi$
$269$	14.7929	−	12.4127i	0.901936	−	0.756814i	0.970568	+	0.240828i	$0.0774189\pi$
$270$	20.5580	−	3.91109i	1.25112	−	0.238021i
$271$	−0.628030	−	0.228584i	−0.0381501	−	0.0138855i	0.322875	−	0.946442i	$-0.395351\pi$
$271$	−0.628030	−	0.228584i	−0.0381501	−	0.0138855i	−0.361025	+	0.932556i	$0.617573\pi$
$272$	27.3559	−	32.6015i	1.65870	−	1.97676i
$273$	0.743446	+	1.46390i	0.0449954	+	0.0885992i
$274$	−35.3119	+	20.3873i	−2.13327	+	1.23164i
$275$	−3.08718	−	0.544354i	−0.186164	−	0.0328258i
$276$	−3.64560	−	3.40865i	−0.219439	−	0.205176i
$277$	9.43326	+	16.3389i	0.566790	+	0.981709i	0.996881	+	0.0789232i	$0.0251482\pi$
$277$	9.43326	+	16.3389i	0.566790	+	0.981709i	−0.430091	+	0.902786i	$0.641518\pi$
$278$	−9.42557	+	16.3256i	−0.565308	+	0.979143i
$279$	−14.9766	−	4.33756i	−0.896623	−	0.259683i
$280$	10.9571	−	30.1045i	0.654813	−	1.79909i
$281$	−12.1777	+	4.43233i	−0.726463	+	0.264411i	−0.678667	−	0.734446i	$-0.737442\pi$
$281$	−12.1777	+	4.43233i	−0.726463	+	0.264411i	−0.0477960	+	0.998857i	$0.515220\pi$
$282$	−4.39409	−	36.1844i	−0.261665	−	2.15475i
$283$	−2.29514	−	13.0164i	−0.136432	−	0.773742i	−0.973852	−	0.227183i	$-0.927048\pi$
$283$	−2.29514	−	13.0164i	−0.136432	−	0.773742i	0.837420	−	0.546559i	$-0.184063\pi$
$284$	−64.1780			−3.80827
$285$	−11.1324	−	3.86596i	−0.659426	−	0.229000i
$286$	0.999006			0.0590724
$287$	0.0801617	+	0.454619i	0.00473179	+	0.0268353i
$288$	−21.2628	−	10.4406i	−1.25292	−	0.615218i
$289$	8.29328	−	3.01851i	0.487840	−	0.177559i
$290$	1.62503	−	4.46474i	0.0954253	−	0.262179i
$291$	30.7731	−	9.36359i	1.80395	−	0.548903i
$292$	1.01923	−	1.76536i	0.0596460	−	0.103310i
$293$	−2.19757	−	3.80631i	−0.128384	−	0.222367i	0.794667	−	0.607046i	$-0.207646\pi$
$293$	−2.19757	−	3.80631i	−0.128384	−	0.222367i	−0.923051	+	0.384679i	$0.874312\pi$
$294$	5.98991	−	6.40630i	0.349339	−	0.373623i
$295$	4.15051	+	0.731847i	0.241652	+	0.0426098i
$296$	21.6618	−	12.5065i	1.25907	−	0.726924i
$297$	4.01834	−	4.92199i	0.233168	−	0.285603i
$298$	9.27072	−	11.0484i	0.537038	−	0.640017i
$299$	−0.184098	−	0.0670063i	−0.0106467	−	0.00387507i
$300$	20.1426	+	4.67849i	1.16293	+	0.270112i
$301$	21.9421	−	18.4116i	1.26472	−	1.06123i
$302$	−48.6988	+	8.58691i	−2.80230	+	0.494121i
$303$	14.5969	−	22.4120i	0.838570	−	1.28754i
$304$	20.3732	+	30.2894i	1.16848	+	1.73722i
$305$			10.7610i			0.616171i
$306$	−21.9096	−	32.6693i	−1.25249	−	1.86758i
$307$	15.1110	+	18.0086i	0.862431	+	1.02781i	0.999307	+	0.0372172i	$0.0118493\pi$
$307$	15.1110	+	18.0086i	0.862431	+	1.02781i	−0.136876	+	0.990588i	$0.543706\pi$
$308$	−5.83106	−	16.0207i	−0.332256	−	0.912865i
$309$	−10.2715	+	7.71878i	−0.584327	+	0.439106i
$310$	16.0345	+	13.4545i	0.910696	+	0.764165i
$311$	8.52818	+	4.92375i	0.483589	+	0.279200i	0.721911	−	0.691986i	$-0.243264\pi$
$311$	8.52818	+	4.92375i	0.483589	+	0.279200i	−0.238322	+	0.971186i	$0.576597\pi$
$312$	−3.75448	−	0.201767i	−0.212555	−	0.0114228i
$313$	−1.00653	+	5.70833i	−0.0568926	+	0.322654i	−0.999950	−	0.00997537i	$-0.996825\pi$
$313$	−1.00653	+	5.70833i	−0.0568926	+	0.322654i	0.943058	+	0.332629i	$0.107936\pi$
$314$	−6.44824	+	36.5698i	−0.363895	+	2.06375i
$315$	−11.3195	−	8.27018i	−0.637784	−	0.465972i
$316$	5.89890	+	3.40573i	0.331839	+	0.191587i
$317$	4.09664	+	3.43749i	0.230090	+	0.193069i	0.750543	−	0.660822i	$-0.229792\pi$
$317$	4.09664	+	3.43749i	0.230090	+	0.193069i	−0.520452	+	0.853891i	$0.674237\pi$
$318$	−8.23759	−	10.9619i	−0.461941	−	0.614714i
$319$	−0.493409	−	1.35563i	−0.0276256	−	0.0759007i
$320$	3.63565	+	4.33280i	0.203239	+	0.242211i
$321$	9.26029	−	21.7355i	0.516859	−	1.21316i
$322$			4.77926i			0.266338i
$323$	1.51646	+	22.0994i	0.0843779	+	1.22965i
$324$	−28.2111	+	30.9987i	−1.56729	+	1.72215i
$325$	0.799392	−	0.140954i	0.0443423	−	0.00781875i
$326$	−3.76256	+	3.15716i	−0.208389	+	0.174859i
$327$	0.508118	−	2.18764i	0.0280990	−	0.120977i
$328$	−0.993393	−	0.361565i	−0.0548509	−	0.0199641i
$329$	−15.6957	+	18.7054i	−0.865330	+	1.03126i
$330$	−7.60532	+	3.86239i	−0.418659	+	0.212617i
$331$	−4.46270	+	2.57654i	−0.245292	+	0.141620i	−0.617607	−	0.786487i	$-0.711898\pi$
$331$	−4.46270	+	2.57654i	−0.245292	+	0.141620i	0.372314	+	0.928107i	$0.378564\pi$
$332$	50.1130	+	8.83628i	2.75031	+	0.484954i
$333$	−2.61970	−	10.6273i	−0.143559	−	0.582372i
$334$	−17.0355	−	29.5064i	−0.932144	−	1.61452i
$335$	7.10662	−	12.3090i	0.388276	−	0.672514i
$336$	12.6409	+	41.5439i	0.689618	+	2.26641i
$337$	10.8959	−	29.9364i	0.593540	−	1.63074i	−0.170344	−	0.985385i	$-0.554488\pi$
$337$	10.8959	−	29.9364i	0.593540	−	1.63074i	0.763884	−	0.645353i	$-0.223290\pi$
$338$	31.2759	−	11.3835i	1.70119	−	0.619181i
$339$	−11.7983	+	1.43274i	−0.640796	+	0.0778157i
$340$	6.41487	+	36.3805i	0.347895	+	1.97301i
$341$	6.35543			0.344166
$342$	32.1294	−	10.2990i	1.73736	−	0.556908i
$343$	15.0809			0.814294
$344$	11.3902	+	64.5973i	0.614121	+	3.48285i
$345$	1.66058	−	0.201654i	0.0894027	−	0.0108567i
$346$	−33.2178	+	12.0903i	−1.78580	+	0.649979i
$347$	4.16813	−	11.4518i	0.223757	−	0.614767i	−0.776118	−	0.630588i	$-0.782814\pi$
$347$	4.16813	−	11.4518i	0.223757	−	0.614767i	0.999875	+	0.0158208i	$0.00503613\pi$
$348$	2.77021	+	9.10420i	0.148499	+	0.488037i
$349$	7.60525	−	13.1727i	0.407100	−	0.705117i	−0.587464	−	0.809250i	$-0.699874\pi$
$349$	7.60525	−	13.1727i	0.407100	−	0.705117i	0.994563	+	0.104133i	$0.0332069\pi$
$350$	−9.90092	−	17.1489i	−0.529227	−	0.916647i
$351$	−0.541852	+	1.55351i	−0.0289219	+	0.0829200i
$352$	9.50864	+	1.67663i	0.506812	+	0.0893647i
$353$	11.6828	−	6.74506i	0.621812	−	0.359003i	−0.155762	−	0.987795i	$-0.549783\pi$
$353$	11.6828	−	6.74506i	0.621812	−	0.359003i	0.777574	+	0.628791i	$0.216450\pi$
$354$	−10.7585	+	5.46374i	−0.571809	+	0.290395i
$355$	13.8265	−	16.4778i	0.733835	−	0.874550i
$356$	−34.4111	−	12.5246i	−1.82379	−	0.663804i
$357$	−5.96184	+	25.6679i	−0.315534	+	1.35849i
$358$	−37.8299	+	31.7430i	−1.99937	+	1.67767i
$359$	−17.2391	+	3.03973i	−0.909847	+	0.160431i	−0.608934	−	0.793221i	$-0.708403\pi$
$359$	−17.2391	+	3.03973i	−0.909847	+	0.160431i	−0.300913	+	0.953652i	$0.597291\pi$
$360$	29.3625	−	12.9796i	1.54754	−	0.684087i
$361$	−18.5745	−	3.99866i	−0.977603	−	0.210456i
$362$		−	15.8557i		−	0.833355i
$363$	6.45259	−	15.1454i	0.338673	−	0.794926i
$364$	2.83766	+	3.38180i	0.148734	+	0.177254i
$365$	0.233675	+	0.642018i	0.0122311	+	0.0336047i
$366$	−18.5087	−	24.6299i	−0.967464	−	1.28742i
$367$	−0.400474	−	0.336037i	−0.0209046	−	0.0175410i	0.632275	−	0.774744i	$-0.282121\pi$
$367$	−0.400474	−	0.336037i	−0.0209046	−	0.0175410i	−0.653180	+	0.757203i	$0.726566\pi$
$368$	−4.48738	−	2.59079i	−0.233921	−	0.135054i
$369$	−0.272901	+	0.373525i	−0.0142067	+	0.0194449i
$370$	−2.55153	+	14.4704i	−0.132648	+	0.752281i
$371$	−1.59509	+	9.04622i	−0.0828131	+	0.469656i
$372$	−41.8633	−	2.24974i	−2.17051	−	0.116644i
$373$	2.06421	+	1.19177i	0.106881	+	0.0617078i	0.552488	−	0.833521i	$-0.313679\pi$
$373$	2.06421	+	1.19177i	0.106881	+	0.0617078i	−0.445607	+	0.895229i	$0.647012\pi$
$374$	12.2825	+	10.3062i	0.635111	+	0.532921i
$375$	−16.3473	+	12.2846i	−0.844173	+	0.634373i
$376$	−19.1251	−	52.5456i	−0.986299	−	2.70983i
$377$	0.240116	+	0.286159i	0.0123666	+	0.0147379i
$378$	40.1329	−	0.540505i	2.06421	−	0.0278006i
$379$			18.6924i			0.960166i	0.877223	+	0.480083i	$0.159393\pi$
$379$			18.6924i			0.960166i	−0.877223	+	0.480083i	$0.840607\pi$
$380$	−31.5083	−	3.35310i	−1.61634	−	0.172010i
$381$	2.94580	−	4.52296i	0.150918	−	0.231718i
$382$	67.0470	−	11.8222i	3.43042	−	0.604876i
$383$	−25.4328	+	21.3407i	−1.29956	+	1.09046i	−0.309334	+	0.950953i	$0.600106\pi$
$383$	−25.4328	+	21.3407i	−1.29956	+	1.09046i	−0.990222	+	0.139503i	$0.955449\pi$
$384$	10.8694	+	2.52462i	0.554677	+	0.128834i
$385$	5.36958	+	1.95437i	0.273659	+	0.0996038i
$386$	−12.9352	+	15.4156i	−0.658386	+	0.784634i
$387$	28.5379	+	3.07615i	1.45066	+	0.156369i
$388$	74.9007	−	43.2440i	3.80251	−	2.19538i
$389$	20.5469	+	3.62298i	1.04177	+	0.183692i	0.668255	−	0.743932i	$-0.267041\pi$
$389$	20.5469	+	3.62298i	1.04177	+	0.183692i	0.373515	+	0.927624i	$0.378153\pi$
$390$	1.50849	−	1.61335i	0.0763853	−	0.0816953i
$391$	−1.57216	−	2.72306i	−0.0795076	−	0.137711i
$392$	6.72727	−	11.6520i	0.339779	−	0.588514i
$393$	−6.07535	+	1.84860i	−0.306461	+	0.0932494i
$394$	−21.3442	+	58.6426i	−1.07530	+	2.95437i
$395$	−2.14528	+	0.780820i	−0.107941	+	0.0392873i
$396$	7.53013	−	15.3355i	0.378403	−	0.770637i
$397$	−4.74235	−	26.8952i	−0.238012	−	1.34983i	−0.836177	−	0.548460i	$-0.815214\pi$
$397$	−4.74235	−	26.8952i	−0.238012	−	1.34983i	0.598165	−	0.801373i	$-0.295897\pi$
$398$	10.5732			0.529986
$399$	−19.7395	−	11.0098i	−0.988213	−	0.551177i
$400$	21.4688			1.07344
$401$	−3.70169	−	20.9933i	−0.184853	−	1.04836i	−0.926144	−	0.377171i	$-0.876897\pi$
$401$	−3.70169	−	20.9933i	−0.184853	−	1.04836i	0.741290	−	0.671185i	$-0.234214\pi$
$402$	4.90557	+	40.3964i	0.244668	+	2.01479i
$403$	−1.54642	+	0.562852i	−0.0770328	+	0.0280377i
$404$	24.5965	−	67.5783i	1.22372	−	3.36214i
$405$	−1.88115	−	13.9216i	−0.0934753	−	0.691770i
$406$	4.55638	−	7.89189i	0.226129	−	0.391668i
$407$	2.23072	+	3.86372i	0.110573	+	0.191517i
$408$	−44.0786	−	41.2136i	−2.18222	−	2.04038i
$409$	−27.5154	−	4.85171i	−1.36055	−	0.239902i	−0.554714	−	0.832041i	$-0.687172\pi$
$409$	−27.5154	−	4.85171i	−1.36055	−	0.239902i	−0.805836	+	0.592139i	$0.798283\pi$
$410$	0.537812	−	0.310506i	0.0265607	−	0.0153348i
$411$	12.3943	+	24.4052i	0.611363	+	1.20382i
$412$	−22.2063	+	26.4645i	−1.09403	+	1.30381i
$413$	7.59583	+	2.76466i	0.373766	+	0.136040i
$414$	−3.45392	+	3.31772i	−0.169751	+	0.163057i
$415$	−13.0651	+	10.9629i	−0.641339	+	0.538147i
$416$	−2.46216	+	0.434145i	−0.120717	+	0.0212857i
$417$	10.6040	+	6.90639i	0.519282	+	0.338208i
$418$	−11.4114	+	7.67550i	−0.558149	+	0.375421i
$419$		−	18.7147i		−	0.914272i	−0.889397	−	0.457136i	$-0.848875\pi$
$419$		−	18.7147i		−	0.914272i	0.889397	−	0.457136i	$-0.151125\pi$
$420$	−34.6776	−	14.7742i	−1.69210	−	0.720907i
$421$	7.28959	+	8.68740i	0.355273	+	0.423398i	0.913848	−	0.406056i	$-0.133096\pi$
$421$	7.28959	+	8.68740i	0.355273	+	0.423398i	−0.558575	+	0.829454i	$0.688652\pi$
$422$	−8.80910	−	24.2028i	−0.428820	−	1.17817i
$423$	−24.4140	+	1.64201i	−1.18705	+	0.0798370i
$424$	−16.1142	−	13.5214i	−0.782574	−	0.656657i
$425$	11.2824	+	6.51391i	0.547278	+	0.315971i
$426$	−3.30481	+	61.4960i	−0.160119	+	2.97949i
$427$	−3.58394	+	20.3255i	−0.173439	+	0.983622i
$428$	11.0310	−	62.5602i	0.533206	−	3.02396i
$429$	0.0359881	−	0.669667i	0.00173752	−	0.0323319i
$430$	−33.3702	−	19.2663i	−1.60925	−	0.929102i
$431$	0.337025	+	0.282798i	0.0162339	+	0.0136219i	0.650868	−	0.759190i	$-0.274405\pi$
$431$	0.337025	+	0.282798i	0.0162339	+	0.0136219i	−0.634635	+	0.772812i	$0.718849\pi$
$432$	−21.2481	+	37.9749i	−1.02230	+	1.82707i
$433$	11.3377	+	31.1501i	0.544856	+	1.49698i	0.840570	+	0.541704i	$0.182220\pi$
$433$	11.3377	+	31.1501i	0.544856	+	1.49698i	−0.295713	+	0.955277i	$0.595557\pi$
$434$	25.8052	+	30.7534i	1.23869	+	1.47621i
$435$	−2.93433	−	1.25015i	−0.140690	−	0.0599403i
$436$		−	6.03867i		−	0.289200i
$437$	2.61773	−	0.649056i	0.125223	−	0.0310486i
$438$	−1.63910	−	1.06754i	−0.0783192	−	0.0510092i
$439$	5.42779	−	0.957066i	0.259054	−	0.0456783i	−0.0426125	−	0.999092i	$-0.513568\pi$
$439$	5.42779	−	0.957066i	0.259054	−	0.0456783i	0.301667	+	0.953413i	$0.402457\pi$
$440$	−10.0241	+	8.41126i	−0.477882	+	0.400991i
$441$	−4.07858	−	4.24602i	−0.194218	−	0.202191i
$442$	−3.90135	−	1.41997i	−0.185568	−	0.0675413i
$443$	−4.10597	+	4.89330i	−0.195080	+	0.232488i	−0.854714	−	0.519100i	$-0.826267\pi$
$443$	−4.10597	+	4.89330i	−0.195080	+	0.232488i	0.659633	+	0.751588i	$0.270712\pi$
$444$	−13.3260	−	26.2400i	−0.632426	−	1.24529i
$445$	10.6292	−	6.13680i	0.503875	−	0.290912i
$446$	−27.1271	−	4.78324i	−1.28450	−	0.226493i
$447$	−7.07216	−	6.61248i	−0.334502	−	0.312760i
$448$	5.42405	+	9.39473i	0.256262	+	0.443859i
$449$	11.0074	−	19.0653i	0.519470	−	0.899749i	−0.480274	−	0.877119i	$-0.659463\pi$
$449$	11.0074	−	19.0653i	0.519470	−	0.899749i	0.999744	−	0.0226300i	$-0.00720396\pi$
$450$	5.52020	−	19.0599i	0.260225	−	0.898493i
$451$	0.0644906	−	0.177187i	0.00303675	−	0.00834339i
$452$	−30.0290	+	10.9297i	−1.41244	+	0.514088i
$453$	4.00178	+	32.9538i	0.188020	+	1.54830i
$454$	−0.232594	−	1.31911i	−0.0109162	−	0.0619087i
$455$	−1.47963			−0.0693660
$456$	44.4366	−	26.5414i	2.08094	−	1.24292i
$457$	6.66744			0.311890			0.155945	−	0.987766i	$-0.450158\pi$
$457$	6.66744			0.311890			0.155945	+	0.987766i	$0.450158\pi$
$458$	1.72254	+	9.76899i	0.0804889	+	0.456475i
$459$	−22.6886	+	13.5099i	−1.05901	+	0.630587i
$460$	4.22651	−	1.53832i	0.197062	−	0.0717247i
$461$	−5.50703	+	15.1304i	−0.256488	+	0.704695i	0.742890	+	0.669414i	$0.233455\pi$
$461$	−5.50703	+	15.1304i	−0.256488	+	0.704695i	−0.999377	+	0.0352807i	$0.988767\pi$
$462$	−15.6515	+	4.76240i	−0.728172	+	0.221567i
$463$	−19.1725	+	33.2078i	−0.891023	+	1.54330i	−0.0523713	+	0.998628i	$0.516678\pi$
$463$	−19.1725	+	33.2078i	−0.891023	+	1.54330i	−0.838651	+	0.544669i	$0.816655\pi$
$464$	4.93994	+	8.55622i	0.229331	+	0.397212i
$465$	9.59664	−	10.2638i	0.445034	−	0.475971i
$466$	46.7338	+	8.24043i	2.16490	+	0.381731i
$467$	18.0289	−	10.4090i	0.834277	−	0.481670i	−0.0210381	−	0.999779i	$-0.506697\pi$
$467$	18.0289	−	10.4090i	0.834277	−	0.481670i	0.855315	+	0.518109i	$0.173364\pi$
$468$	−0.474108	+	4.39836i	−0.0219156	+	0.203314i
$469$	17.5227	−	20.8827i	0.809121	−	0.964273i
$470$	30.8675	+	11.2349i	1.42381	+	0.518225i
$471$	24.2817	+	5.63987i	1.11884	+	0.259871i
$472$	−14.1802	+	11.8986i	−0.652696	+	0.547677i
$473$	−11.5219	+	2.03162i	−0.529777	+	0.0934140i
$474$	3.56716	−	5.47700i	0.163845	−	0.251567i
$475$	−8.04828	+	7.75193i	−0.369280	+	0.355683i
$476$			70.8528i			3.24753i
$477$	−7.64491	+	5.12705i	−0.350036	+	0.234751i
$478$	−27.3386	−	32.5809i	−1.25044	−	1.49021i
$479$	−2.82297	−	7.75604i	−0.128985	−	0.354383i	0.858343	−	0.513076i	$-0.171494\pi$
$479$	−2.82297	−	7.75604i	−0.128985	−	0.354383i	−0.987328	+	0.158693i	$0.949272\pi$
$480$	17.0656	−	12.8244i	0.778937	−	0.585350i
$481$	−0.884965	−	0.742574i	−0.0403509	−	0.0338584i
$482$	26.7070	+	15.4193i	1.21647	+	0.702331i
$483$	3.20370	+	0.172168i	0.145774	+	0.00783391i
$484$	7.68645	−	43.5920i	0.349384	−	1.98146i
$485$	−5.03366	+	28.5473i	−0.228567	+	1.29627i
$486$	28.2505	+	28.6284i	1.28147	+	1.29861i
$487$	−22.5542	−	13.0217i	−1.02203	−	0.590069i	−0.107338	−	0.994223i	$-0.534233\pi$
$487$	−22.5542	−	13.0217i	−1.02203	−	0.590069i	−0.914691	+	0.404154i	$0.867566\pi$
$488$	−36.2062	−	30.3806i	−1.63898	−	1.37527i
$489$	1.98081	+	2.63590i	0.0895754	+	0.119200i
$490$	2.70325	+	7.42711i	0.122120	+	0.335523i
$491$	−24.6341	−	29.3577i	−1.11172	−	1.32490i	−0.940550	−	0.339654i	$-0.889690\pi$
$491$	−24.6341	−	29.3577i	−1.11172	−	1.32490i	−0.171169	−	0.985242i	$-0.554755\pi$
$492$	−0.487522	+	1.14430i	−0.0219792	+	0.0515890i
$493$			5.99538i			0.270018i
$494$	2.09689	−	2.87824i	0.0943437	−	0.129498i
$495$	2.31511	+	5.23725i	0.104057	+	0.235397i
$496$	−42.8640	+	7.55807i	−1.92465	+	0.339368i
$497$	31.6037	−	26.5187i	1.41762	−	1.18953i
$498$	11.0475	−	47.5638i	0.495052	−	2.13138i
$499$	−22.9331	−	8.34698i	−1.02663	−	0.373662i	−0.226832	−	0.973934i	$-0.572837\pi$
$499$	−22.9331	−	8.34698i	−1.02663	−	0.373662i	−0.799796	+	0.600272i	$0.795059\pi$
$500$	−35.3418	+	42.1187i	−1.58053	+	1.88360i
$501$	−20.3929	+	10.3566i	−0.911086	+	0.462697i
$502$	20.0851	−	11.5962i	0.896443	−	0.517562i
$503$	−39.5690	−	6.97708i	−1.76429	−	0.311093i	−0.804953	−	0.593339i	$-0.797809\pi$
$503$	−39.5690	−	6.97708i	−1.76429	−	0.311093i	−0.959342	+	0.282246i	$0.908921\pi$
$504$	59.7834	−	14.7370i	2.66296	−	0.656440i
$505$	12.0517	+	20.8742i	0.536295	+	0.928891i
$506$	0.976067	−	1.69060i	0.0433915	−	0.0751562i
$507$	−6.50407	−	21.3754i	−0.288856	−	0.949314i
$508$	4.96381	−	13.6380i	0.220233	−	0.605086i
$509$	33.9250	−	12.3477i	1.50370	−	0.547302i	0.546685	−	0.837338i	$-0.315889\pi$
$509$	33.9250	−	12.3477i	1.50370	−	0.547302i	0.957016	+	0.290036i	$0.0936672\pi$
$510$	35.1905	−	4.27339i	1.55826	−	0.189229i
$511$	0.227547	+	1.29048i	0.0100661	+	0.0570876i
$512$	48.7022			2.15236
$513$	−5.74637	−	21.9084i	−0.253709	−	0.967281i
$514$	32.5912			1.43754
$515$	−2.01066	−	11.4030i	−0.0886001	−	0.502476i
$516$	76.6139	−	9.30369i	3.37274	−	0.409572i
$517$	9.37231	−	3.41124i	0.412194	−	0.150026i
$518$	−9.63875	+	26.4823i	−0.423502	+	1.16356i
$519$	6.90791	+	22.7026i	0.303223	+	0.996533i
$520$	1.69418	−	2.93441i	0.0742949	−	0.128683i
$521$	−8.36859	−	14.4948i	−0.366635	−	0.635030i	0.622402	−	0.782697i	$-0.286157\pi$
$521$	−8.36859	−	14.4948i	−0.366635	−	0.635030i	−0.989037	+	0.147668i	$0.952823\pi$
$522$	8.86638	−	2.18563i	0.388071	−	0.0956623i
$523$	−3.12791	−	0.551534i	−0.136774	−	0.0241169i	0.104842	−	0.994489i	$-0.466566\pi$
$523$	−3.12791	−	0.551534i	−0.136774	−	0.0241169i	−0.241616	+	0.970372i	$0.577677\pi$
$524$	−14.7872	+	8.53740i	−0.645982	+	0.372958i
$525$	−11.8522	+	6.01916i	−0.517271	+	0.262697i
$526$	−0.658506	+	0.784777i	−0.0287122	+	0.0342179i
$527$	−24.8194	−	9.03354i	−1.08115	−	0.393507i
$528$	4.01295	−	17.2772i	0.174641	−	0.751895i
$529$	17.3258	−	14.5380i	0.753294	−	0.632089i
$530$	12.1694	−	2.14580i	0.528607	−	0.0932077i
$531$	3.27497	+	7.40862i	0.142122	+	0.321507i
$532$	−58.3967	−	16.8272i	−2.53182	−	0.729553i
$533$			0.0488250i			0.00211485i
$534$	−13.7732	+	32.3281i	−0.596025	+	1.39897i
$535$	13.6859	+	16.3102i	0.591692	+	0.705151i
$536$	21.3512	+	58.6620i	0.922233	+	2.53381i
$537$	19.9156	+	26.5021i	0.859424	+	1.14365i
$538$	−38.1676	−	32.0264i	−1.64552	−	1.38076i
$539$	2.07831	+	1.19991i	0.0895190	+	0.0516838i
$540$	−13.3958	−	35.3173i	−0.576461	−	1.51981i
$541$	0.328535	−	1.86322i	0.0141248	−	0.0801059i	−0.976931	−	0.213557i	$-0.931495\pi$
$541$	0.328535	−	1.86322i	0.0141248	−	0.0801059i	0.991055	+	0.133452i	$0.0426061\pi$
$542$	−0.299439	+	1.69820i	−0.0128620	+	0.0729440i
$543$	−10.6286	−	0.571183i	−0.456117	−	0.0245118i
$544$	−34.7503	−	20.0631i	−1.48991	−	0.860198i
$545$	1.55044	+	1.30097i	0.0664134	+	0.0557274i
$546$	3.38659	−	2.54493i	0.144933	−	0.108913i
$547$	−9.41432	−	25.8656i	−0.402527	−	1.10593i	−0.961033	−	0.276434i	$-0.910847\pi$
$547$	−9.41432	−	25.8656i	−0.402527	−	1.10593i	0.558506	−	0.829501i	$-0.311375\pi$
$548$	47.3077	+	56.3791i	2.02089	+	2.40840i
$549$	−17.1770	+	11.5197i	−0.733096	+	0.491650i
$550$			8.08824i			0.344884i
$551$	−4.94138	−	1.42388i	−0.210510	−	0.0606592i
$552$	−4.00971	+	6.15649i	−0.170665	+	0.262038i
$553$	−4.31211	+	0.760341i	−0.183370	+	0.0323330i
$554$	37.2897	−	31.2898i	1.58429	−	1.32938i
$555$	9.60810	+	2.23166i	0.407841	+	0.0947285i
$556$	31.9740	+	11.6376i	1.35600	+	0.493544i
$557$	4.41474	−	5.26128i	0.187058	−	0.222928i	−0.664363	−	0.747410i	$-0.731297\pi$
$557$	4.41474	−	5.26128i	0.187058	−	0.222928i	0.851421	+	0.524483i	$0.175741\pi$
$558$	−4.31145	+	39.9979i	−0.182518	+	1.69325i
$559$	2.62362	−	1.51475i	0.110967	−	0.0640669i
$560$	−38.5391	−	6.79549i	−1.62858	−	0.287162i
$561$	7.35106	−	7.86208i	0.310362	−	0.331937i
$562$	16.7184	+	28.9571i	0.705222	+	1.22148i
$563$	−8.11401	+	14.0539i	−0.341965	+	0.592301i	−0.984798	−	0.173706i	$-0.944426\pi$
$563$	−8.11401	+	14.0539i	−0.341965	+	0.592301i	0.642833	+	0.766007i	$0.277759\pi$
$564$	−62.9430	+	19.1522i	−2.65038	+	0.806452i
$565$	3.66324	−	10.0647i	0.154114	−	0.423424i
$566$	−32.0455	+	11.6636i	−1.34697	+	0.490258i
$567$	1.08343	−	26.9219i	0.0454996	−	1.13062i
$568$	16.4056	+	93.0411i	0.688366	+	3.90392i
$569$	−23.4699			−0.983911			−0.491956	−	0.870620i	$-0.663718\pi$
$569$	−23.4699			−0.983911			−0.491956	+	0.870620i	$0.663718\pi$
$570$	−4.83547	+	30.0188i	−0.202535	+	1.25735i
$571$	−12.3766			−0.517944			−0.258972	−	0.965885i	$-0.583384\pi$
$571$	−12.3766			−0.517944			−0.258972	+	0.965885i	$0.583384\pi$
$572$	−0.313121	−	1.77580i	−0.0130922	−	0.0742498i
$573$	−5.50952	−	45.3698i	−0.230164	−	1.89535i
$574$	1.11925	−	0.407372i	0.0467164	−	0.0170034i
$575$	0.542503	−	1.49051i	0.0226239	−	0.0621587i
$576$	−3.02415	+	10.4416i	−0.126006	+	0.435068i
$577$	−7.38649	+	12.7938i	−0.307504	+	0.532612i	−0.977816	−	0.209467i	$-0.932827\pi$
$577$	−7.38649	+	12.7938i	−0.307504	+	0.532612i	0.670312	+	0.742079i	$0.266160\pi$
$578$	−11.3855	−	19.7203i	−0.473576	−	0.820258i
$579$	9.86763	+	9.22626i	0.410085	+	0.383430i
$580$	−8.44571	−	1.48921i	−0.350689	−	0.0618360i
$581$	−28.3288	+	16.3556i	−1.17528	+	0.678546i
$582$	−37.5798	−	73.9974i	−1.55773	−	3.06729i
$583$	2.41175	−	2.87421i	0.0998843	−	0.119037i
$584$	−2.81984	−	1.02634i	−0.116686	−	0.0424702i
$585$	−1.02714	−	1.06931i	−0.0424672	−	0.0442105i
$586$	−8.68702	+	7.28927i	−0.358857	+	0.301117i
$587$	16.0113	−	2.82322i	0.660857	−	0.116527i	0.166847	−	0.985983i	$-0.446642\pi$
$587$	16.0113	−	2.82322i	0.660857	−	0.116527i	0.494010	+	0.869456i	$0.335530\pi$
$588$	−13.2651	−	8.63951i	−0.547042	−	0.356287i
$589$	13.3399	−	18.3107i	0.549662	−	0.754479i
$590$		−	10.8741i		−	0.447679i
$591$	38.5412	+	16.4202i	1.58537	+	0.675439i
$592$	−19.6398	−	23.4058i	−0.807192	−	0.961974i
$593$	1.06316	+	2.92101i	0.0436587	+	0.119951i	0.959606	−	0.281347i	$-0.0907812\pi$
$593$	1.06316	+	2.92101i	0.0436587	+	0.119951i	−0.915947	+	0.401299i	$0.868559\pi$
$594$	−14.3068	−	8.00513i	−0.587017	−	0.328455i
$595$	−18.1915	−	15.2645i	−0.745781	−	0.625784i
$596$	−22.5450	−	13.0164i	−0.923480	−	0.533171i
$597$	0.380888	−	7.08757i	0.0155887	−	0.290075i
$598$	−0.0877763	+	0.497804i	−0.00358944	+	0.0203567i
$599$	1.76308	−	9.99893i	0.0720375	−	0.408545i	−0.927371	−	0.374144i	$-0.877937\pi$
$599$	1.76308	−	9.99893i	0.0720375	−	0.408545i	0.999408	−	0.0344010i	$-0.0109523\pi$
$600$	1.63356	−	30.3973i	0.0666899	−	1.24097i
$601$	8.56591	+	4.94553i	0.349411	+	0.201732i	0.664426	−	0.747354i	$-0.268676\pi$
$601$	8.56591	+	4.94553i	0.349411	+	0.201732i	−0.315015	+	0.949087i	$0.602010\pi$
$602$	−56.6136	−	47.5045i	−2.30740	−	1.93614i
$603$	27.2558	−	1.83314i	1.10994	−	0.0746511i
$604$	30.5276	+	83.8739i	1.24215	+	3.41278i
$605$	9.53634	+	11.3650i	0.387707	+	0.462052i
$606$	−63.4875	−	27.0485i	−2.57900	−	1.09877i
$607$			16.5025i			0.669817i	0.942251	+	0.334908i	$0.108705\pi$
$607$			16.5025i			0.669817i	−0.942251	+	0.334908i	$0.891295\pi$
$608$	24.7890	−	23.8762i	1.00533	−	0.968309i
$609$	−5.12606	−	3.33860i	−0.207718	−	0.135287i
$610$	27.3430	−	4.82130i	1.10708	−	0.195209i
$611$	−1.97839	+	1.66007i	−0.0800371	+	0.0671591i
$612$	−51.2046	+	49.1854i	−2.06982	+	1.98820i
$613$	−13.2779	−	4.83276i	−0.536289	−	0.195193i	0.0596550	−	0.998219i	$-0.481000\pi$
$613$	−13.2779	−	4.83276i	−0.536289	−	0.195193i	−0.595944	+	0.803026i	$0.703222\pi$
$614$	38.9885	−	46.4647i	1.57345	−	1.87516i
$615$	−0.188769	−	0.371700i	−0.00761189	−	0.0149884i
$616$	−21.7352	+	12.5488i	−0.875736	+	0.505606i
$617$	10.3704	+	1.82858i	0.417496	+	0.0736158i	0.378450	−	0.925622i	$-0.376457\pi$
$617$	10.3704	+	1.82858i	0.417496	+	0.0736158i	0.0390458	+	0.999237i	$0.487568\pi$
$618$	24.2150	+	22.6411i	0.974070	+	0.910757i
$619$	−7.21587	−	12.4983i	−0.290030	−	0.502347i	0.683786	−	0.729682i	$-0.260332\pi$
$619$	−7.21587	−	12.4983i	−0.290030	−	0.502347i	−0.973817	+	0.227335i	$0.926999\pi$
$620$	18.8905	−	32.7194i	0.758663	−	1.31404i
$621$	2.09956	+	2.43480i	0.0842524	+	0.0977052i
$622$	8.69001	−	23.8756i	0.348438	−	0.957325i
$623$	22.1206	−	8.05124i	0.886243	−	0.322566i
$624$	0.553668	+	4.55934i	0.0221645	+	0.182520i
$625$	−0.974188	−	5.52490i	−0.0389675	−	0.220996i
$626$	14.9555			0.597742
$627$	4.73406	+	7.92594i	0.189060	+	0.316532i
$628$	67.0263			2.67464
$629$	−3.21963	−	18.2594i	−0.128375	−	0.728051i
$630$	−15.9425	+	32.4676i	−0.635163	+	1.29354i
$631$	6.27530	−	2.28402i	0.249816	−	0.0909254i	−0.214077	−	0.976817i	$-0.568674\pi$
$631$	6.27530	−	2.28402i	0.249816	−	0.0909254i	0.463893	+	0.885891i	$0.346452\pi$
$632$	3.42948	−	9.42243i	0.136418	−	0.374804i
$633$	−16.5413	+	5.03316i	−0.657458	+	0.200050i
$634$	6.89901	−	11.9494i	0.273995	−	0.474573i
$635$	2.43216	+	4.21262i	0.0965173	+	0.167173i
$636$	−16.9036	+	18.0787i	−0.670272	+	0.716867i
$637$	−0.611967	−	0.107906i	−0.0242470	−	0.00427540i
$638$	−3.22351	+	1.86110i	−0.127620	+	0.0736815i
$639$	41.1038	+	4.43065i	1.62604	+	0.175274i
$640$	−6.46396	+	7.70344i	−0.255510	+	0.304505i
$641$	24.7334	+	9.00224i	0.976912	+	0.355567i	0.780639	−	0.624982i	$-0.214894\pi$
$641$	24.7334	+	9.00224i	0.976912	+	0.355567i	0.196273	+	0.980549i	$0.437116\pi$
$642$	−59.3777	−	13.7915i	−2.34345	−	0.544309i
$643$	−3.88657	+	3.26122i	−0.153272	+	0.128610i	−0.716199	−	0.697896i	$-0.754120\pi$
$643$	−3.88657	+	3.26122i	−0.153272	+	0.128610i	0.562927	+	0.826506i	$0.309675\pi$
$644$	8.49545	−	1.49798i	0.334768	−	0.0590286i
$645$	−14.1170	+	21.6751i	−0.555855	+	0.853456i
$646$	55.4739	−	13.7546i	2.18259	−	0.541167i
$647$			15.3275i			0.602585i	0.953532	+	0.301293i	$0.0974181\pi$
$647$			15.3275i			0.602585i	−0.953532	+	0.301293i	$0.902582\pi$
$648$	52.1514	+	32.9745i	2.04870	+	1.29536i
$649$	−2.12229	−	2.52925i	−0.0833073	−	0.0992818i
$650$	−0.716314	−	1.96806i	−0.0280961	−	0.0771935i
$651$	21.5447	−	16.1902i	0.844403	−	0.634546i
$652$	6.79137	+	5.69864i	0.265971	+	0.223176i
$653$	−6.35742	−	3.67046i	−0.248785	−	0.143636i	0.370423	−	0.928863i	$-0.379213\pi$
$653$	−6.35742	−	3.67046i	−0.248785	−	0.143636i	−0.619208	+	0.785227i	$0.712546\pi$
$654$	−5.78631	−	0.310958i	−0.226263	−	0.0121594i
$655$	0.993767	−	5.63593i	0.0388297	−	0.220214i
$656$	−0.224239	+	1.27172i	−0.00875506	+	0.0496524i
$657$	−0.774657	+	1.06029i	−0.0302222	+	0.0413657i
$658$	54.5615	+	31.5011i	2.12703	+	1.22804i
$659$	17.2736	+	14.4942i	0.672882	+	0.564615i	0.913917	−	0.405901i	$-0.133042\pi$
$659$	17.2736	+	14.4942i	0.672882	+	0.564615i	−0.241035	+	0.970517i	$0.577487\pi$
$660$	9.24940	+	12.3084i	0.360032	+	0.479102i
$661$	−4.78873	−	13.1569i	−0.186260	−	0.511746i	0.811055	−	0.584969i	$-0.198893\pi$
$661$	−4.78873	−	13.1569i	−0.186260	−	0.511746i	−0.997316	+	0.0732238i	$0.976671\pi$
$662$	8.54630	+	10.1851i	0.332161	+	0.395854i
$663$	−1.09240	+	2.56405i	−0.0424253	+	0.0995796i
$664$		−	74.9093i		−	2.90705i
$665$	16.9014	−	11.3682i	0.655408	−	0.440839i
$666$	−25.8296	+	11.4179i	−1.00088	+	0.442435i
$667$	0.718863	−	0.126755i	0.0278345	−	0.00490797i
$668$	−47.1101	+	39.5301i	−1.82274	+	1.52946i
$669$	−4.18359	+	18.0119i	−0.161747	+	0.696380i
$670$	−34.4605	−	12.5426i	−1.33133	−	0.484563i
$671$	5.41884	−	6.45793i	0.209192	−	0.249305i
$672$	36.5051	−	18.5392i	1.40822	−	0.715166i
$673$	−29.2421	+	16.8829i	−1.12720	+	0.650789i	−0.943229	−	0.332143i	$-0.892228\pi$
$673$	−29.2421	+	16.8829i	−1.12720	+	0.650789i	−0.183970	+	0.982932i	$0.558895\pi$
$674$	−80.9483	−	14.2734i	−3.11801	−	0.549790i
$675$	−12.5776	−	4.38699i	−0.484114	−	0.168855i
$676$	−30.0378	−	52.0270i	−1.15530	−	2.00104i
$677$	−20.9506	+	36.2875i	−0.805197	+	1.39464i	0.110961	+	0.993825i	$0.464607\pi$
$677$	−20.9506	+	36.2875i	−0.805197	+	1.39464i	−0.916158	+	0.400817i	$0.868726\pi$
$678$	8.92657	+	29.3369i	0.342823	+	1.12668i
$679$	−19.0154	+	52.2443i	−0.729743	+	2.00495i
$680$	51.1023	−	18.5997i	1.95968	−	0.713266i
$681$	−0.892620	+	0.108396i	−0.0342053	+	0.00415375i
$682$	−2.84747	−	16.1488i	−0.109035	−	0.618369i
$683$	37.5667			1.43745			0.718725	−	0.695295i	$-0.244726\pi$
$683$	37.5667			1.43745			0.718725	+	0.695295i	$0.244726\pi$
$684$	−28.3776	−	53.8840i	−1.08505	−	2.06031i
$685$	−24.6674			−0.942492
$686$	−6.75681	−	38.3198i	−0.257976	−	1.46305i
$687$	6.61054	−	0.802758i	0.252208	−	0.0306271i
$688$	75.2929	−	27.4044i	2.87051	−	1.04478i
$689$	−0.332287	+	0.912951i	−0.0126591	+	0.0347807i
$690$	−1.25639	−	4.12909i	−0.0478301	−	0.157192i
$691$	−2.67694	+	4.63659i	−0.101835	+	0.176384i	−0.912441	−	0.409209i	$-0.865805\pi$
$691$	−2.67694	+	4.63659i	−0.101835	+	0.176384i	0.810605	+	0.585593i	$0.199138\pi$
$692$	31.9029	+	55.2574i	1.21277	+	2.10057i
$693$	2.62857	+	10.6633i	0.0998512	+	0.405064i
$694$	−30.9659	−	5.46013i	−1.17545	−	0.207264i
$695$	−9.87645	+	5.70217i	−0.374635	+	0.216296i
$696$	12.4905	−	6.34335i	0.473452	−	0.240444i
$697$	−0.503702	+	0.600288i	−0.0190791	+	0.0227375i
$698$	−36.8784	−	13.4226i	−1.39587	−	0.508055i
$699$	7.20738	−	31.0304i	0.272608	−	1.17368i
$700$	−27.3800	+	22.9746i	−1.03487	+	0.868357i
$701$	−23.4648	+	4.13747i	−0.886251	+	0.156270i	−0.598202	−	0.801345i	$-0.704118\pi$
$701$	−23.4648	+	4.13747i	−0.886251	+	0.156270i	−0.288050	+	0.957616i	$0.593007\pi$
$702$	4.19014	+	0.680785i	0.158147	+	0.0256946i
$703$	15.8140	+	1.68292i	0.596437	+	0.0634726i
$704$		−	4.43100i		−	0.167000i
$705$	8.64308	−	20.2868i	0.325517	−	0.764046i
$706$	−22.3731	−	26.6632i	−0.842023	−	1.00348i
$707$	15.8114	+	43.4415i	0.594650	+	1.63379i
$708$	13.0842	+	17.4114i	0.491735	+	0.654362i
$709$	33.4374	+	28.0573i	1.25577	+	1.05371i	0.996120	+	0.0880094i	$0.0280505\pi$
$709$	33.4374	+	28.0573i	1.25577	+	1.05371i	0.259647	+	0.965704i	$0.416394\pi$
$710$	−48.0639	−	27.7497i	−1.80381	−	1.04143i
$711$	−3.54292	−	2.58849i	−0.132870	−	0.0970761i
$712$	−9.36095	+	53.0886i	−0.350817	+	1.98958i
$713$	−0.558412	+	3.16691i	−0.0209127	+	0.118602i
$714$	67.8918	+	3.64852i	2.54079	+	0.136543i
$715$	0.523397	+	0.302183i	0.0195739	+	0.0113010i
$716$	68.2824	+	57.2957i	2.55183	+	2.14124i
$717$	−22.8249	+	17.1523i	−0.852411	+	0.640564i
$718$	15.4475	+	42.4417i	0.576497	+	1.58391i
$719$	−9.49121	−	11.3112i	−0.353962	−	0.421836i	0.559455	−	0.828861i	$-0.311011\pi$
$719$	−9.49121	−	11.3112i	−0.353962	−	0.421836i	−0.913417	+	0.407025i	$0.866566\pi$
$720$	−21.8425	−	32.5692i	−0.814021	−	1.21378i
$721$		−	22.2079i		−	0.827065i
$722$	−1.83833	+	48.9882i	−0.0684154	+	1.82315i
$723$	11.2982	−	17.3472i	0.420184	−	0.645148i
$724$	−28.1845	+	4.96968i	−1.04747	+	0.184697i
$725$	−2.31683	+	1.94405i	−0.0860447	+	0.0722001i
$726$	−41.3745	−	9.60998i	−1.53555	−	0.356660i
$727$	−29.6234	−	10.7820i	−1.09867	−	0.399884i	−0.271845	−	0.962341i	$-0.587634\pi$
$727$	−29.6234	−	10.7820i	−1.09867	−	0.399884i	−0.826826	+	0.562457i	$0.809856\pi$
$728$	4.17732	−	4.97834i	0.154822	−	0.184509i
$729$	20.2083	−	17.9060i	0.748456	−	0.663185i
$730$	1.52663	−	0.881402i	0.0565033	−	0.0326222i
$731$	47.8834	+	8.44313i	1.77103	+	0.312280i
$732$	−37.9800	+	40.6202i	−1.40378	+	1.50137i
$733$	0.100159	+	0.173480i	0.00369944	+	0.00640762i	0.867869	−	0.496793i	$-0.165489\pi$
$733$	0.100159	+	0.173480i	0.00369944	+	0.00640762i	−0.864170	+	0.503200i	$0.832156\pi$
$734$	−0.674424	+	1.16814i	−0.0248934	+	0.0431167i
$735$	5.07603	−	1.54453i	0.187232	−	0.0569707i
$736$	−1.67093	+	4.59084i	−0.0615912	+	0.169221i
$737$	−10.4633	+	3.80831i	−0.385419	+	0.140281i
$738$	1.07137	+	0.526073i	0.0394378	+	0.0193650i
$739$	2.98492	+	16.9283i	0.109802	+	0.622719i	0.989193	+	0.146619i	$0.0468390\pi$
$739$	2.98492	+	16.9283i	0.109802	+	0.622719i	−0.879391	+	0.476100i	$0.842050\pi$
$740$	26.5219			0.974963
$741$	−1.85385	−	1.50930i	−0.0681028	−	0.0554457i
$742$	23.7006			0.870075
$743$	7.10350	+	40.2860i	0.260602	+	1.47795i	0.781272	+	0.624191i	$0.214571\pi$
$743$	7.10350	+	40.2860i	0.260602	+	1.47795i	−0.520670	+	0.853758i	$0.674318\pi$
$744$	7.43986	+	61.2657i	0.272758	+	2.24611i
$745$	8.19907	−	2.98422i	0.300391	−	0.109333i
$746$	2.10339	−	5.77901i	0.0770104	−	0.211584i
$747$	−31.4856	−	9.11898i	−1.15200	−	0.333646i
$748$	14.4702	−	25.0632i	0.529084	−	0.916400i
$749$	20.4181	+	35.3651i	0.746059	+	1.29221i
$750$	38.5386	+	36.0337i	1.40723	+	1.31576i
$751$	9.89135	+	1.74411i	0.360941	+	0.0636436i	0.351178	−	0.936309i	$-0.385781\pi$
$751$	9.89135	+	1.74411i	0.360941	+	0.0636436i	0.00976278	+	0.999952i	$0.496892\pi$
$752$	−59.1544	+	34.1528i	−2.15714	+	1.24542i
$753$	−7.04975	−	13.8815i	−0.256907	−	0.505870i
$754$	0.619532	−	0.738329i	0.0225620	−	0.0268884i
$755$	−28.1116	−	10.2318i	−1.02309	−	0.372373i
$756$	−13.5398	−	71.1695i	−0.492436	−	2.58841i
$757$	30.7487	−	25.8012i	1.11758	−	0.937760i	0.119099	−	0.992882i	$-0.461999\pi$
$757$	30.7487	−	25.8012i	1.11758	−	0.937760i	0.998480	+	0.0551222i	$0.0175548\pi$
$758$	47.4964	−	8.37489i	1.72515	−	0.304190i
$759$	−1.09810	−	0.715193i	−0.0398586	−	0.0259599i
$760$	3.19327	+	46.5357i	0.115832	+	1.68803i
$761$		−	13.1199i		−	0.475596i	−0.971315	−	0.237798i	$-0.923574\pi$
$761$		−	13.1199i		−	0.475596i	0.971315	−	0.237798i	$-0.0764257\pi$
$762$	−12.8124	−	5.45864i	−0.464144	−	0.197746i
$763$	2.49521	+	2.97367i	0.0903326	+	0.107654i
$764$	−42.0294	−	115.475i	−1.52057	−	4.17774i
$765$	−1.59690	−	23.7433i	−0.0577361	−	0.858442i
$766$	65.6202	+	55.0619i	2.37095	+	1.98947i
$767$	0.740399	+	0.427470i	0.0267343	+	0.0154350i
$768$	2.21862	−	41.2840i	0.0800574	−	1.48971i
$769$	2.89735	−	16.4317i	0.104481	−	0.592541i	−0.886945	−	0.461874i	$-0.847177\pi$
$769$	2.89735	−	16.4317i	0.104481	−	0.592541i	0.991426	−	0.130667i	$-0.0417118\pi$
$770$	2.56017	−	14.5194i	0.0922620	−	0.523244i
$771$	1.17406	−	21.8470i	0.0422829	−	0.786800i
$772$	31.4566	+	18.1615i	1.13215	+	0.653645i
$773$	−24.3598	−	20.4403i	−0.876161	−	0.735187i	0.0892248	−	0.996012i	$-0.471561\pi$
$773$	−24.3598	−	20.4403i	−0.876161	−	0.735187i	−0.965386	+	0.260825i	$0.916005\pi$
$774$	−4.96969	−	73.8913i	−0.178632	−	2.65597i
$775$	−4.55702	−	12.5203i	−0.163693	−	0.449742i
$776$	−81.8389	−	97.5318i	−2.93784	−	3.50119i
$777$	17.4047	+	7.41518i	0.624391	+	0.266018i
$778$		−	53.8317i		−	1.92996i
$779$	−0.375129	−	0.557716i	−0.0134404	−	0.0199822i
$780$	−3.34065	−	2.17576i	−0.119614	−	0.0779047i
$781$	−16.5953	+	2.92619i	−0.593826	+	0.104707i
$782$	−6.21476	+	5.21480i	−0.222239	+	0.186481i
$783$	−1.14570	−	6.02217i	−0.0409439	−	0.215215i
$784$	−15.4440	−	5.62116i	−0.551572	−	0.200756i
$785$	−14.4401	+	17.2091i	−0.515391	+	0.614219i
$786$	7.41916	+	14.6089i	0.264633	+	0.521081i
$787$	35.4572	−	20.4712i	1.26391	−	0.729721i	0.290084	−	0.957001i	$-0.406317\pi$
$787$	35.4572	−	20.4712i	1.26391	−	0.729721i	0.973829	+	0.227280i	$0.0729833\pi$
$788$	110.931	+	19.5601i	3.95175	+	0.696800i
$789$	0.502341	+	0.469690i	0.0178838	+	0.0167214i
$790$	2.94518	+	5.10120i	0.104785	+	0.181493i
$791$	10.2712	−	17.7903i	0.365203	−	0.632550i
$792$	−24.1573	−	6.99652i	−0.858391	−	0.248610i
$793$	−0.746600	+	2.05127i	−0.0265126	+	0.0728427i
$794$	−66.2144	+	24.1001i	−2.34986	+	0.855280i
$795$	−1.00001	−	8.23489i	−0.0354668	−	0.292062i
$796$	−3.31398	−	18.7945i	−0.117461	−	0.666155i
$797$	−33.9496			−1.20256			−0.601278	−	0.799040i	$-0.705342\pi$
$797$	−33.9496			−1.20256			−0.601278	+	0.799040i	$0.705342\pi$
$798$	−19.1311	+	55.0898i	−0.677234	+	1.95016i
$799$	−41.4497			−1.46639
$800$	−3.51497	−	19.9344i	−0.124273	−	0.704786i
$801$	21.1745	+	10.3972i	0.748163	+	0.367368i
$802$	−51.6843	+	18.8115i	−1.82504	+	0.664259i
$803$	0.183063	−	0.502962i	0.00646016	−	0.0177491i
$804$	70.2696	−	21.3815i	2.47822	−	0.754068i
$805$	−1.44565	+	2.50394i	−0.0509525	+	0.0882524i
$806$	2.12303	+	3.67719i	0.0747805	+	0.129524i
$807$	−22.8434	+	24.4313i	−0.804124	+	0.860024i
$808$	−104.258	−	18.3835i	−3.66778	−	0.646729i
$809$	−34.8389	+	20.1142i	−1.22487	+	0.707179i	−0.965952	−	0.258720i	$-0.916699\pi$
$809$	−34.8389	+	20.1142i	−1.22487	+	0.707179i	−0.258918	+	0.965899i	$0.583366\pi$
$810$	−34.5311	+	11.0173i	−1.21330	+	0.387108i
$811$	3.57962	−	4.26603i	0.125698	−	0.149801i	−0.699525	−	0.714608i	$-0.746605\pi$
$811$	3.57962	−	4.26603i	0.125698	−	0.149801i	0.825223	+	0.564807i	$0.191050\pi$
$812$	−15.4565	−	5.62569i	−0.542415	−	0.197423i
$813$	1.12758	+	0.261900i	0.0395458	+	0.00918523i
$814$	8.81803	−	7.39921i	0.309072	−	0.259342i
$815$	−2.92626	+	0.515979i	−0.102503	+	0.0180740i
$816$	−40.2291	+	61.7676i	−1.40830	+	2.16230i
$817$	−18.3309	+	37.4602i	−0.641317	+	1.31057i
$818$			72.0888i			2.52053i
$819$	−1.58396	−	2.36183i	−0.0553479	−	0.0825289i
$820$	−0.720513	−	0.858674i	−0.0251614	−	0.0299862i
$821$	−14.7571	−	40.5449i	−0.515027	−	1.41503i	−0.875937	−	0.482425i	$-0.839756\pi$
$821$	−14.7571	−	40.5449i	−0.515027	−	1.41503i	0.360910	−	0.932600i	$-0.382466\pi$
$822$	56.4591	−	42.4275i	1.96924	−	1.47983i
$823$	−12.3611	−	10.3722i	−0.430882	−	0.361553i	0.401402	−	0.915902i	$-0.368523\pi$
$823$	−12.3611	−	10.3722i	−0.430882	−	0.361553i	−0.832284	+	0.554349i	$0.812967\pi$
$824$	44.0430	+	25.4282i	1.53431	+	0.885834i
$825$	5.42183	+	0.291370i	0.188764	+	0.0101442i
$826$	3.62162	−	20.5392i	0.126012	−	0.714651i
$827$	4.52142	−	25.6422i	0.157225	−	0.891668i	−0.799498	−	0.600668i	$-0.794901\pi$
$827$	4.52142	−	25.6422i	0.157225	−	0.891668i	0.956723	−	0.290999i	$-0.0939877\pi$
$828$	6.98004	+	5.09969i	0.242573	+	0.177227i
$829$	2.64421	+	1.52664i	0.0918373	+	0.0530223i	0.545215	−	0.838296i	$-0.316448\pi$
$829$	2.64421	+	1.52664i	0.0918373	+	0.0530223i	−0.453378	+	0.891318i	$0.649781\pi$
$830$	33.7097	+	28.2858i	1.17008	+	0.981814i
$831$	−19.6313	−	26.1237i	−0.681002	−	0.906223i
$832$	0.392420	+	1.07817i	0.0136047	+	0.0373787i
$833$	−6.41073	−	7.64001i	−0.222119	−	0.264711i
$834$	12.7977	−	30.0386i	0.443150	−	1.04015i
$835$		−	20.6119i		−	0.713305i
$836$	17.2204	+	17.8787i	0.595580	+	0.618349i
$837$	26.6567	+	4.33099i	0.921389	+	0.149701i
$838$	−47.5529	+	8.38486i	−1.64269	+	0.289650i
$839$	−15.6775	+	13.1550i	−0.541248	+	0.454161i	−0.871964	−	0.489569i	$-0.837154\pi$
$839$	−15.6775	+	13.1550i	−0.541248	+	0.454161i	0.330717	+	0.943730i	$0.392710\pi$
$840$	−12.5541	+	54.0500i	−0.433158	+	1.86490i
$841$	25.9432	+	9.44255i	0.894593	+	0.325605i
$842$	18.8082	−	22.4147i	0.648172	−	0.772461i
$843$	20.0132	−	10.1637i	0.689290	−	0.350058i
$844$	−40.2610	+	23.2447i	−1.38584	+	0.800116i
$845$	19.8293	+	3.49645i	0.682150	+	0.120281i
$846$	15.1106	+	61.2988i	0.519513	+	2.10749i
$847$	14.2273	+	24.6425i	0.488857	+	0.846726i
$848$	−12.8478	+	22.2531i	−0.441196	+	0.764174i
$849$	6.66411	+	21.9014i	0.228712	+	0.751653i
$850$	11.4965	−	31.5865i	0.394328	−	1.08341i
$851$	−2.12129	+	0.772085i	−0.0727168	+	0.0264667i
$852$	110.349	−	13.4003i	3.78049	−	0.459088i
$853$	3.67736	+	20.8553i	0.125910	+	0.714074i	0.980763	+	0.195203i	$0.0625364\pi$
$853$	3.67736	+	20.8553i	0.125910	+	0.714074i	−0.854853	+	0.518871i	$0.826352\pi$
$854$	53.2517			1.82224
$855$	19.9485	+	4.32278i	0.682223	+	0.147836i
$856$	−93.5154			−3.19629
$857$	−3.52925	−	20.0154i	−0.120557	−	0.683713i	−0.983848	−	0.179006i	$-0.942712\pi$
$857$	−3.52925	−	20.0154i	−0.120557	−	0.683713i	0.863291	−	0.504707i	$-0.168399\pi$
$858$	−1.71771	+	0.208592i	−0.0586416	+	0.00712121i
$859$	31.7891	−	11.5703i	1.08463	−	0.394774i	0.263002	−	0.964795i	$-0.415287\pi$
$859$	31.7891	−	11.5703i	1.08463	−	0.394774i	0.821630	+	0.570022i	$0.193065\pi$
$860$	−23.7878	+	65.3563i	−0.811156	+	2.22863i
$861$	−0.232756	−	0.764944i	−0.00793230	−	0.0260692i
$862$	0.567573	−	0.983065i	0.0193316	−	0.0334833i
$863$	14.5264	+	25.1605i	0.494484	+	0.856472i	0.999980	−	0.00635715i	$-0.00202356\pi$
$863$	14.5264	+	25.1605i	0.494484	+	0.856472i	−0.505495	+	0.862829i	$0.668690\pi$
$864$	38.7396	+	13.5121i	1.31795	+	0.459691i
$865$	−21.0606	−	3.71354i	−0.716080	−	0.126264i
$866$	74.0710	−	42.7649i	2.51703	−	1.45321i
$867$	−13.6294	+	6.92171i	−0.462877	+	0.235074i
$868$	46.5781	−	55.5096i	1.58096	−	1.88412i
$869$	1.68063	+	0.611700i	0.0570115	+	0.0207505i
$870$	−1.86188	+	8.01607i	−0.0631236	+	0.271770i
$871$	2.20868	−	1.85330i	0.0748382	−	0.0627967i
$872$	−8.75446	+	1.54365i	−0.296463	+	0.0522745i
$873$	−50.9567	+	22.5253i	−1.72462	+	0.762367i
$874$	−2.82205	−	6.36068i	−0.0954573	−	0.215153i
$875$		−	35.3442i		−	1.19485i
$876$	−1.38388	+	3.24821i	−0.0467569	+	0.109747i
$877$	−10.5631	−	12.5886i	−0.356690	−	0.425087i	0.557623	−	0.830094i	$-0.311713\pi$
$877$	−10.5631	−	12.5886i	−0.356690	−	0.425087i	−0.914313	+	0.405007i	$0.867269\pi$
$878$	−4.86370	−	13.3629i	−0.164142	−	0.450976i
$879$	4.57331	+	6.08579i	0.154254	+	0.205269i
$880$	12.2448	+	10.2746i	0.412773	+	0.346358i
$881$	11.4445	+	6.60751i	0.385577	+	0.222613i	0.680242	−	0.732988i	$-0.261875\pi$
$881$	11.4445	+	6.60751i	0.385577	+	0.222613i	−0.294665	+	0.955601i	$0.595208\pi$
$882$	−8.96153	+	12.2658i	−0.301751	+	0.413011i
$883$	3.37508	−	19.1410i	0.113580	−	0.644146i	−0.873863	−	0.486172i	$-0.838393\pi$
$883$	3.37508	−	19.1410i	0.113580	−	0.644146i	0.987443	−	0.157974i	$-0.0504962\pi$
$884$	−1.30129	+	7.37997i	−0.0437670	+	0.248215i
$885$	−7.28928	−	0.391728i	−0.245026	−	0.0131678i
$886$	14.2732	+	8.24064i	0.479518	+	0.276850i
$887$	−10.2659	−	8.61409i	−0.344694	−	0.289233i	0.453961	−	0.891022i	$-0.350011\pi$
$887$	−10.2659	−	8.61409i	−0.344694	−	0.289233i	−0.798655	+	0.601789i	$0.794455\pi$
$888$	−34.6344	+	26.0268i	−1.16226	+	0.873404i
$889$	3.19090	+	8.76692i	0.107019	+	0.294033i
$890$	−20.3555	−	24.2588i	−0.682319	−	0.813156i
$891$	−5.88150	+	9.30199i	−0.197038	+	0.311628i
$892$			49.7194i			1.66473i
$893$	9.84413	−	34.1628i	0.329421	−	1.14321i
$894$	−13.6333	+	20.9326i	−0.455967	+	0.700090i
$895$	−29.4215	+	5.18780i	−0.983452	+	0.173409i
$896$	−14.7749	+	12.3976i	−0.493594	+	0.414175i
$897$	0.330533	+	0.0767723i	0.0110362	+	0.00256335i
$898$	−53.3756	−	19.4271i	−1.78117	−	0.648292i
$899$	3.94131	−	4.69707i	0.131450	−	0.156656i
$900$	−35.6104	−	3.83851i	−1.18701	−	0.127950i
$901$	−13.5038	+	7.79642i	−0.449876	+	0.259736i
$902$	−0.479115	−	0.0844809i	−0.0159528	−	0.00281291i
$903$	−33.8833	+	36.2387i	−1.12757	+	1.20595i
$904$	23.5213	+	40.7401i	0.782307	+	1.35500i
$905$	4.79609	−	8.30707i	0.159427	−	0.276136i
$906$	81.9407	−	24.9328i	2.72230	−	0.828336i
$907$	3.51601	−	9.66017i	0.116747	−	0.320761i	−0.867531	−	0.497382i	$-0.834295\pi$
$907$	3.51601	−	9.66017i	0.116747	−	0.320761i	0.984279	+	0.176622i	$0.0565169\pi$
$908$	−2.27189	+	0.826902i	−0.0753954	+	0.0274417i
$909$	−20.4186	+	41.5835i	−0.677242	+	1.37924i
$910$	0.662927	+	3.75964i	0.0219758	+	0.124631i
$911$	−19.5762			−0.648589			−0.324294	−	0.945956i	$-0.605127\pi$
$911$	−19.5762			−0.648589			−0.324294	+	0.945956i	$0.605127\pi$
$912$	−41.3545	−	47.8263i	−1.36938	−	1.58369i
$913$	13.3612			0.442191
$914$	−2.98726	−	16.9416i	−0.0988097	−	0.560377i
$915$	−2.24688	−	18.5026i	−0.0742797	−	0.611677i
$916$	16.8251	−	6.12384i	0.555918	−	0.202337i
$917$	3.75410	−	10.3143i	0.123971	−	0.340608i
$918$	44.4931	+	51.5975i	1.46849	+	1.70297i
$919$	23.2470	−	40.2651i	0.766849	−	1.32822i	−0.172414	−	0.985024i	$-0.555157\pi$
$919$	23.2470	−	40.2651i	0.766849	−	1.32822i	0.939263	−	0.343197i	$-0.111510\pi$
$920$	−3.31057	−	5.73407i	−0.109146	−	0.189047i
$921$	−29.7424	−	27.8092i	−0.980044	−	0.916343i
$922$	40.9129	+	7.21405i	1.34739	+	0.237582i
$923$	3.77886	−	2.18173i	0.124383	−	0.0718124i
$924$	13.3712	+	26.3288i	0.439879	+	0.866154i
$925$	6.01209	−	7.16493i	0.197676	−	0.235582i
$926$	92.9690	+	33.8379i	3.05515	+	1.11198i
$927$	16.0494	−	15.4165i	0.527131	−	0.506345i
$928$	7.13591	−	5.98774i	0.234248	−	0.196557i
$929$	30.1221	−	5.31134i	0.988274	−	0.174259i	0.343930	−	0.938995i	$-0.388242\pi$
$929$	30.1221	−	5.31134i	0.988274	−	0.174259i	0.644344	+	0.764736i	$0.277131\pi$
$930$	−30.3793	−	19.7860i	−0.996175	−	0.648807i
$931$	7.81940	−	3.46924i	0.256270	−	0.113700i
$932$		−	85.6552i		−	2.80573i
$933$	−15.6916	−	6.68531i	−0.513720	−	0.218867i
$934$	−34.5262	−	41.1467i	−1.12973	−	1.34636i
$935$	3.31754	+	9.11486i	0.108495	+	0.298088i
$936$	6.49765	−	0.437011i	0.212382	−	0.0142842i
$937$	28.6832	+	24.0681i	0.937039	+	0.786269i	0.977068	−	0.212929i	$-0.0683004\pi$
$937$	28.6832	+	24.0681i	0.937039	+	0.786269i	−0.0400285	+	0.999199i	$0.512745\pi$
$938$	−60.9125	−	35.1678i	−1.98886	−	1.14827i
$939$	0.538756	−	10.0252i	0.0175816	−	0.327159i
$940$	10.2958	−	58.3904i	0.335812	−	1.90448i
$941$	10.4374	−	59.1934i	0.340249	−	1.92965i	−0.0272576	−	0.999628i	$-0.508677\pi$
$941$	10.4374	−	59.1934i	0.340249	−	1.92965i	0.367507	−	0.930021i	$-0.380211\pi$
$942$	3.45148	−	64.2252i	0.112455	−	2.09257i
$943$	0.0826256	+	0.0477039i	0.00269066	+	0.00155345i
$944$	17.3216	+	14.5345i	0.563769	+	0.473059i
$945$	21.1899	+	11.8564i	0.689306	+	0.385689i
$946$	10.3245	+	28.3662i	0.335677	+	0.922265i
$947$	9.17974	+	10.9400i	0.298302	+	0.355502i	0.894287	−	0.447493i	$-0.147683\pi$
$947$	9.17974	+	10.9400i	0.298302	+	0.355502i	−0.595986	+	0.802995i	$0.703239\pi$
$948$	−10.8538	−	4.62419i	−0.352515	−	0.150187i
$949$			0.138595i			0.00449897i
$950$	23.3031	+	16.9771i	0.756053	+	0.550809i
$951$	−7.76159	−	5.05511i	−0.251687	−	0.163923i
$952$	102.718	−	18.1119i	3.32910	−	0.587010i
$953$	−27.9483	+	23.4514i	−0.905334	+	0.759665i	−0.971226	−	0.238162i	$-0.923455\pi$
$953$	−27.9483	+	23.4514i	−0.905334	+	0.759665i	0.0658917	+	0.997827i	$0.479011\pi$
$954$	16.4527	+	17.1281i	0.532676	+	0.554544i
$955$	38.7032	+	14.0868i	1.25240	+	0.455838i
$956$	−49.3458	+	58.8080i	−1.59596	+	1.90199i
$957$	1.13143	+	2.22787i	0.0365740	+	0.0720169i
$958$	−18.4429	+	10.6480i	−0.595861	+	0.344021i
$959$	−46.5923	−	8.21548i	−1.50454	−	0.265292i
$960$	−7.15589	−	6.69077i	−0.230955	−	0.215944i
$961$	−1.99380	−	3.45337i	−0.0643162	−	0.111399i
$962$	−1.49034	+	2.58134i	−0.0480505	+	0.0832258i
$963$	−11.3840	+	39.3061i	−0.366843	+	1.26662i
$964$	19.0380	−	52.3064i	0.613172	−	1.68468i
$965$	−11.4400	+	4.16381i	−0.368266	+	0.134038i
$966$	−0.997907	−	8.21756i	−0.0321071	−	0.264396i
$967$	2.87010	+	16.2772i	0.0922963	+	0.523438i	0.995542	+	0.0943153i	$0.0300662\pi$
$967$	2.87010	+	16.2772i	0.0922963	+	0.523438i	−0.903246	+	0.429123i	$0.858823\pi$
$968$	−65.1617			−2.09438
$969$	−7.22178	−	37.6816i	−0.231997	−	1.21051i
$970$	74.7923			2.40144
$971$	8.86117	+	50.2542i	0.284369	+	1.61273i	0.707532	+	0.706681i	$0.249808\pi$
$971$	8.86117	+	50.2542i	0.284369	+	1.61273i	−0.423164	+	0.906053i	$0.639081\pi$
$972$	42.0343	−	59.1903i	1.34825	−	1.89853i
$973$	−20.5540	+	7.48103i	−0.658930	+	0.239831i
$974$	−22.9822	+	63.1431i	−0.736398	+	2.02324i
$975$	−1.34506	+	0.409272i	−0.0430764	+	0.0131072i
$976$	−28.8672	+	49.9995i	−0.924017	+	1.60044i
$977$	−3.79775	−	6.57789i	−0.121501	−	0.210445i	0.798859	−	0.601518i	$-0.205437\pi$
$977$	−3.79775	−	6.57789i	−0.121501	−	0.210445i	−0.920360	+	0.391073i	$0.872104\pi$
$978$	5.81020	−	6.21410i	0.185790	−	0.198705i
$979$	−9.46915	−	1.66967i	−0.302635	−	0.0533628i
$980$	12.3549	−	7.13310i	0.394662	−	0.227858i
$981$	−0.416891	+	3.86756i	−0.0133103	+	0.123482i
$982$	−63.5593	+	75.7470i	−2.02826	+	2.41719i
$983$	29.7553	+	10.8301i	0.949048	+	0.345425i	0.769733	−	0.638366i	$-0.220390\pi$
$983$	29.7553	+	10.8301i	0.949048	+	0.345425i	0.179315	+	0.983792i	$0.442612\pi$
$984$	1.78355	+	0.414263i	0.0568576	+	0.0132062i
$985$	−28.9210	+	24.2676i	−0.921501	+	0.773231i
$986$	15.2339	−	2.68615i	0.485146	−	0.0855443i
$987$	23.0818	−	35.4396i	0.734700	−	1.12806i
$988$	−5.77350	−	2.82523i	−0.183680	−	0.0898825i
$989$		−	5.91986i		−	0.188241i
$990$	12.2703	−	8.22905i	0.389975	−	0.261536i
$991$	9.88741	+	11.7834i	0.314084	+	0.374311i	0.899872	−	0.436153i	$-0.143659\pi$
$991$	9.88741	+	11.7834i	0.314084	+	0.374311i	−0.585788	+	0.810464i	$0.699215\pi$
$992$	14.0358	+	38.5630i	0.445637	+	1.22438i
$993$	7.13528	−	5.36197i	0.226431	−	0.170157i
$994$	−81.5420	−	68.4219i	−2.58636	−	2.17021i
$995$	5.53948	+	3.19822i	0.175613	+	0.101390i
$996$	−88.0103	−	4.72970i	−2.78871	−	0.149866i
$997$	−5.27918	+	29.9397i	−0.167193	+	0.948201i	0.779581	+	0.626302i	$0.215432\pi$
$997$	−5.27918	+	29.9397i	−0.167193	+	0.948201i	−0.946774	+	0.321899i	$0.895679\pi$
$998$	−10.9343	+	62.0115i	−0.346119	+	1.96294i
$999$	6.72334	+	17.7258i	0.212717	+	0.560818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.29.1	yes	24
3.2	odd	2	inner	57.2.j.b.29.4	yes	24
4.3	odd	2		912.2.cc.e.257.4		24
12.11	even	2		912.2.cc.e.257.2		24
19.2	odd	18	inner	57.2.j.b.2.4	yes	24
19.6	even	9		1083.2.d.d.1082.2		24
19.13	odd	18		1083.2.d.d.1082.24		24
57.2	even	18	inner	57.2.j.b.2.1	✓	24
57.32	even	18		1083.2.d.d.1082.1		24
57.44	odd	18		1083.2.d.d.1082.23		24
76.59	even	18		912.2.cc.e.401.2		24
228.59	odd	18		912.2.cc.e.401.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.2.1	✓	24	57.2	even	18	inner
57.2.j.b.2.4	yes	24	19.2	odd	18	inner
57.2.j.b.29.1	yes	24	1.1	even	1	trivial
57.2.j.b.29.4	yes	24	3.2	odd	2	inner
912.2.cc.e.257.2		24	12.11	even	2
912.2.cc.e.257.4		24	4.3	odd	2
912.2.cc.e.401.2		24	76.59	even	18
912.2.cc.e.401.4		24	228.59	odd	18
1083.2.d.d.1082.1		24	57.32	even	18
1083.2.d.d.1082.2		24	19.6	even	9
1083.2.d.d.1082.23		24	57.44	odd	18
1083.2.d.d.1082.24		24	19.13	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)

\(f(q)\)	\(=\)	\(q+(-0.448036 - 2.54094i) q^{2} +(-1.71942 + 0.208799i) q^{3} +(-4.37626 + 1.59283i) q^{4} +(0.533860 - 1.46677i) q^{5} +(1.30091 + 4.27539i) q^{6} +(1.49687 - 2.59266i) q^{7} +(3.42787 + 5.93724i) q^{8} +(2.91281 - 0.718027i) q^{9} +O(q^{10})\)	\(q+(-0.448036 - 2.54094i) q^{2} +(-1.71942 + 0.208799i) q^{3} +(-4.37626 + 1.59283i) q^{4} +(0.533860 - 1.46677i) q^{5} +(1.30091 + 4.27539i) q^{6} +(1.49687 - 2.59266i) q^{7} +(3.42787 + 5.93724i) q^{8} +(2.91281 - 0.718027i) q^{9} +(-3.96616 - 0.699341i) q^{10} +(-1.05900 + 0.611412i) q^{11} +(7.19204 - 3.65250i) q^{12} +(0.203530 - 0.242558i) q^{13} +(-7.25845 - 2.64186i) q^{14} +(-0.611669 + 2.63346i) q^{15} +(6.41525 - 5.38303i) q^{16} +(5.00468 - 0.882460i) q^{17} +(-3.12951 - 7.07956i) q^{18} +(-0.461268 + 4.33442i) q^{19} +7.26931i q^{20} +(-2.03241 + 4.77042i) q^{21} +(2.02803 + 2.41691i) q^{22} +(-0.211619 - 0.581418i) q^{23} +(-7.13363 - 9.49287i) q^{24} +(1.96382 + 1.64784i) q^{25} +(-0.707514 - 0.408483i) q^{26} +(-4.85841 + 1.84278i) q^{27} +(-2.42104 + 13.7304i) q^{28} +(-0.204862 + 1.16183i) q^{29} +(6.96552 + 0.374329i) q^{30} +(-4.50103 - 2.59867i) q^{31} +(-6.04864 - 5.07541i) q^{32} +(1.69320 - 1.27239i) q^{33} +(-4.48456 - 12.3212i) q^{34} +(-3.00371 - 3.57969i) q^{35} +(-11.6035 + 7.78187i) q^{36} -3.64847i q^{37} +(11.2202 - 0.769925i) q^{38} +(-0.299308 + 0.459555i) q^{39} +(10.5386 - 1.85823i) q^{40} +(-0.118123 + 0.0991172i) q^{41} +(13.0319 + 3.02691i) q^{42} +(8.99072 + 3.27235i) q^{43} +(3.66057 - 4.36249i) q^{44} +(0.501851 - 4.65574i) q^{45} +(-1.38254 + 0.798207i) q^{46} +(-8.03246 - 1.41634i) q^{47} +(-9.90652 + 10.5952i) q^{48} +(-0.981262 - 1.69960i) q^{49} +(3.30720 - 5.72824i) q^{50} +(-8.42088 + 2.56229i) q^{51} +(-0.504348 + 1.38568i) q^{52} +(-2.88328 + 1.04943i) q^{53} +(6.85915 + 11.5193i) q^{54} +(0.331444 + 1.87971i) q^{55} +20.5243 q^{56} +(-0.111912 - 7.54900i) q^{57} +3.04393 q^{58} +(0.468861 + 2.65904i) q^{59} +(-1.51783 - 12.4990i) q^{60} +(-6.47830 + 2.35791i) q^{61} +(-4.58645 + 12.6012i) q^{62} +(2.49850 - 8.62672i) q^{63} +(-1.81179 + 3.13812i) q^{64} +(-0.247119 - 0.428023i) q^{65} +(-3.99168 - 3.73223i) q^{66} +(8.96745 + 1.58120i) q^{67} +(-20.4962 + 11.8335i) q^{68} +(0.485261 + 0.955515i) q^{69} +(-7.75000 + 9.23609i) q^{70} +(12.9496 + 4.71326i) q^{71} +(14.2478 + 14.8327i) q^{72} +(-0.335304 + 0.281354i) q^{73} +(-9.27055 + 1.63465i) q^{74} +(-3.72070 - 2.42328i) q^{75} +(-4.88536 - 19.7033i) q^{76} +3.66082i q^{77} +(1.30180 + 0.554625i) q^{78} +(-0.940136 - 1.12041i) q^{79} +(-4.47082 - 12.2835i) q^{80} +(7.96887 - 4.18295i) q^{81} +(0.304774 + 0.255736i) q^{82} +(-9.46265 - 5.46326i) q^{83} +(1.29589 - 24.1139i) q^{84} +(1.37743 - 7.81181i) q^{85} +(4.28669 - 24.3110i) q^{86} +(0.109654 - 2.04045i) q^{87} +(-7.26019 - 4.19167i) q^{88} +(6.02351 + 5.05433i) q^{89} +(-12.0548 + 0.810768i) q^{90} +(-0.324211 - 0.890763i) q^{91} +(1.85220 + 2.20736i) q^{92} +(8.28176 + 3.52839i) q^{93} +21.0446i q^{94} +(6.11134 + 2.99055i) q^{95} +(11.4599 + 7.46380i) q^{96} +(-18.2890 + 3.22484i) q^{97} +(-3.87893 + 3.25481i) q^{98} +(-2.64564 + 2.54131i) 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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