LMFDB - Embedded newform 110.2.k.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, 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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	110.7
Dual form			110.2.k.a.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 - 0.156434i) q^{2} +(-1.07350 - 2.10686i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.91408 + 1.15599i) q^{5} +(-1.38987 - 1.91299i) q^{6} +(-3.37294 - 1.71860i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-1.52312 + 2.09639i) q^{9} +O(q^{10})$	\(q+(0.987688 - 0.156434i) q^{2} +(-1.07350 - 2.10686i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.91408 + 1.15599i) q^{5} +(-1.38987 - 1.91299i) q^{6} +(-3.37294 - 1.71860i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-1.52312 + 2.09639i) q^{9} +(2.07135 + 0.842332i) q^{10} +(2.91083 + 1.58968i) q^{11} +(-1.67202 - 1.67202i) q^{12} +(0.378122 + 2.38737i) q^{13} +(-3.60026 - 1.16980i) q^{14} +(0.380754 - 5.27366i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.299513 + 1.89105i) q^{17} +(-1.17642 + 2.30885i) q^{18} +(-1.20339 + 3.70365i) q^{19} +(2.17761 + 0.507931i) q^{20} +8.95124i q^{21} +(3.12367 + 1.11476i) q^{22} +(-2.12916 + 2.12916i) q^{23} +(-1.91299 - 1.38987i) q^{24} +(2.32737 + 4.42531i) q^{25} +(0.746934 + 2.29883i) q^{26} +(-0.954548 - 0.151186i) q^{27} +(-3.73893 - 0.592189i) q^{28} +(-2.45671 - 7.56098i) q^{29} +(-0.448915 - 5.26829i) q^{30} +(3.04687 + 2.21368i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.224473 - 7.83924i) q^{33} +1.91462i q^{34} +(-4.46938 - 7.18861i) q^{35} +(-0.800751 + 2.46446i) q^{36} +(2.80375 - 5.50267i) q^{37} +(-0.609195 + 3.84631i) q^{38} +(4.62395 - 3.35950i) q^{39} +(2.23026 + 0.161024i) q^{40} +(-10.5998 - 3.44408i) q^{41} +(1.40028 + 8.84104i) q^{42} +(0.0971873 + 0.0971873i) q^{43} +(3.25960 + 0.612384i) q^{44} +(-5.33877 + 2.25194i) q^{45} +(-1.76987 + 2.43602i) q^{46} +(8.25770 - 4.20751i) q^{47} +(-2.10686 - 1.07350i) q^{48} +(4.30864 + 5.93034i) q^{49} +(2.99099 + 4.00674i) q^{50} +(4.30571 - 1.39901i) q^{51} +(1.09735 + 2.15368i) q^{52} +(1.27169 - 0.201417i) q^{53} -0.966447 q^{54} +(3.73388 + 6.40766i) q^{55} -3.78554 q^{56} +(9.09493 - 1.44050i) q^{57} +(-3.60926 - 7.08358i) q^{58} +(-13.8564 + 4.50221i) q^{59} +(-1.26753 - 5.13320i) q^{60} +(-2.01494 - 2.77333i) q^{61} +(3.35566 + 1.70979i) q^{62} +(8.74024 - 4.45338i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-2.03602 + 5.00671i) q^{65} +(-1.00462 - 7.77784i) q^{66} +(-7.14861 - 7.14861i) q^{67} +(0.299513 + 1.89105i) q^{68} +(6.77149 + 2.20019i) q^{69} +(-5.53890 - 6.40095i) q^{70} +(10.0775 - 7.32173i) q^{71} +(-0.405366 + 2.55938i) q^{72} +(-4.54499 + 8.92005i) q^{73} +(1.90843 - 5.87353i) q^{74} +(6.82509 - 9.65403i) q^{75} +3.89425i q^{76} +(-7.08601 - 10.3644i) q^{77} +(4.04148 - 4.04148i) q^{78} +(3.21092 + 2.33287i) q^{79} +(2.22799 - 0.189849i) q^{80} +(3.10843 + 9.56677i) q^{81} +(-11.0080 - 1.74350i) q^{82} +(-0.615229 - 0.0974427i) q^{83} +(2.76609 + 8.51314i) q^{84} +(-2.75932 + 3.27337i) q^{85} +(0.111194 + 0.0807873i) q^{86} +(-13.2927 + 13.2927i) q^{87} +(3.31527 + 0.0949311i) q^{88} -2.93819i q^{89} +(-4.92076 + 3.05939i) q^{90} +(2.82755 - 8.70230i) q^{91} +(-1.36700 + 2.68289i) q^{92} +(1.39311 - 8.79574i) q^{93} +(7.49783 - 5.44749i) q^{94} +(-6.58477 + 5.69796i) q^{95} +(-2.24886 - 0.730698i) q^{96} +(0.904231 + 5.70909i) q^{97} +(5.18331 + 5.18331i) q^{98} +(-7.76613 + 3.68096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$3$	−1.07350	−	2.10686i	−0.619786	−	1.21640i	−0.961035	−	0.276426i	$-0.910850\pi$
$3$	−1.07350	−	2.10686i	−0.619786	−	1.21640i	0.341249	−	0.939973i	$-0.389150\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	1.91408	+	1.15599i	0.856001	+	0.516975i
$5$	1.91408	+	1.15599i	0.856001	+	0.516975i
$6$	−1.38987	−	1.91299i	−0.567412	−	0.780976i
$7$	−3.37294	−	1.71860i	−1.27485	−	0.649569i	−0.320215	−	0.947345i	$-0.603755\pi$
$7$	−3.37294	−	1.71860i	−1.27485	−	0.649569i	−0.954636	+	0.297776i	$0.903755\pi$
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$	−1.52312	+	2.09639i	−0.507706	+	0.698797i
$10$	2.07135	+	0.842332i	0.655017	+	0.266369i
$11$	2.91083	+	1.58968i	0.877647	+	0.479308i
$11$	2.91083	+	1.58968i	0.877647	+	0.479308i
$12$	−1.67202	−	1.67202i	−0.482670	−	0.482670i
$13$	0.378122	+	2.38737i	0.104872	+	0.662138i	0.982985	+	0.183684i	$0.0588024\pi$
$13$	0.378122	+	2.38737i	0.104872	+	0.662138i	−0.878113	+	0.478453i	$0.841198\pi$
$14$	−3.60026	−	1.16980i	−0.962210	−	0.312641i
$15$	0.380754	−	5.27366i	0.0983104	−	1.36165i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−0.299513	+	1.89105i	−0.0726425	+	0.458647i	0.924376	+	0.381483i	$0.124586\pi$
$17$	−0.299513	+	1.89105i	−0.0726425	+	0.458647i	−0.997018	+	0.0771638i	$0.975414\pi$
$18$	−1.17642	+	2.30885i	−0.277284	+	0.544201i
$19$	−1.20339	+	3.70365i	−0.276076	+	0.849676i	0.712856	+	0.701310i	$0.247401\pi$
$19$	−1.20339	+	3.70365i	−0.276076	+	0.849676i	−0.988933	+	0.148366i	$0.952599\pi$
$20$	2.17761	+	0.507931i	0.486929	+	0.113577i
$21$			8.95124i			1.95332i
$22$	3.12367	+	1.11476i	0.665969	+	0.237667i
$23$	−2.12916	+	2.12916i	−0.443960	+	0.443960i	−0.893340	−	0.449381i	$-0.851645\pi$
$23$	−2.12916	+	2.12916i	−0.443960	+	0.443960i	0.449381	+	0.893340i	$0.351645\pi$
$24$	−1.91299	−	1.38987i	−0.390488	−	0.283706i
$25$	2.32737	+	4.42531i	0.465474	+	0.885062i
$26$	0.746934	+	2.29883i	0.146486	+	0.450837i
$27$	−0.954548	−	0.151186i	−0.183703	−	0.0290957i
$28$	−3.73893	−	0.592189i	−0.706592	−	0.111913i
$29$	−2.45671	−	7.56098i	−0.456200	−	1.40404i	−0.869721	−	0.493544i	$-0.835701\pi$
$29$	−2.45671	−	7.56098i	−0.456200	−	1.40404i	0.413521	−	0.910495i	$-0.364299\pi$
$30$	−0.448915	−	5.26829i	−0.0819602	−	0.961854i
$31$	3.04687	+	2.21368i	0.547234	+	0.397589i	0.826765	−	0.562548i	$-0.190179\pi$
$31$	3.04687	+	2.21368i	0.547234	+	0.397589i	−0.279530	+	0.960137i	$0.590179\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.224473	−	7.83924i	0.0390757	−	1.36464i
$34$			1.91462i			0.328355i
$35$	−4.46938	−	7.18861i	−0.755462	−	1.21510i
$36$	−0.800751	+	2.46446i	−0.133458	+	0.410743i
$37$	2.80375	−	5.50267i	0.460934	−	0.904634i	−0.537193	−	0.843459i	$-0.680515\pi$
$37$	2.80375	−	5.50267i	0.460934	−	0.904634i	0.998127	−	0.0611748i	$-0.0194847\pi$
$38$	−0.609195	+	3.84631i	−0.0988245	+	0.623953i
$39$	4.62395	−	3.35950i	0.740425	−	0.537950i
$40$	2.23026	+	0.161024i	0.352635	+	0.0254601i
$41$	−10.5998	−	3.44408i	−1.65541	−	0.537874i	−0.675505	−	0.737356i	$-0.736074\pi$
$41$	−10.5998	−	3.44408i	−1.65541	−	0.537874i	−0.979902	+	0.199481i	$0.936074\pi$
$42$	1.40028	+	8.84104i	0.216068	+	1.36420i
$43$	0.0971873	+	0.0971873i	0.0148209	+	0.0148209i	0.714478	−	0.699657i	$-0.246664\pi$
$43$	0.0971873	+	0.0971873i	0.0148209	+	0.0148209i	−0.699657	+	0.714478i	$0.746664\pi$
$44$	3.25960	+	0.612384i	0.491403	+	0.0923204i
$45$	−5.33877	+	2.25194i	−0.795857	+	0.335700i
$46$	−1.76987	+	2.43602i	−0.260953	+	0.359171i
$47$	8.25770	−	4.20751i	1.20451	−	0.613728i	0.267677	−	0.963509i	$-0.413744\pi$
$47$	8.25770	−	4.20751i	1.20451	−	0.613728i	0.936832	+	0.349781i	$0.113744\pi$
$48$	−2.10686	−	1.07350i	−0.304100	−	0.154947i
$49$	4.30864	+	5.93034i	0.615520	+	0.847191i
$50$	2.99099	+	4.00674i	0.422989	+	0.566639i
$51$	4.30571	−	1.39901i	0.602920	−	0.195901i
$52$	1.09735	+	2.15368i	0.152176	+	0.298661i
$53$	1.27169	−	0.201417i	0.174681	−	0.0276667i	−0.0684813	−	0.997652i	$-0.521815\pi$
$53$	1.27169	−	0.201417i	0.174681	−	0.0276667i	0.243162	+	0.969986i	$0.421815\pi$
$54$	−0.966447			−0.131517
$55$	3.73388	+	6.40766i	0.503476	+	0.864009i
$56$	−3.78554			−0.505864
$57$	9.09493	−	1.44050i	1.20465	−	0.190798i
$58$	−3.60926	−	7.08358i	−0.473919	−	0.930119i
$59$	−13.8564	+	4.50221i	−1.80395	+	0.586138i	−0.999964	−	0.00851320i	$-0.997290\pi$
$59$	−13.8564	+	4.50221i	−1.80395	+	0.586138i	−0.803984	+	0.594651i	$0.797290\pi$
$60$	−1.26753	−	5.13320i	−0.163637	−	0.662694i
$61$	−2.01494	−	2.77333i	−0.257986	−	0.355088i	0.660302	−	0.751000i	$-0.270428\pi$
$61$	−2.01494	−	2.77333i	−0.257986	−	0.355088i	−0.918288	+	0.395912i	$0.870428\pi$
$62$	3.35566	+	1.70979i	0.426169	+	0.217144i
$63$	8.74024	−	4.45338i	1.10117	−	0.561073i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−2.03602	+	5.00671i	−0.252538	+	0.621006i
$66$	−1.00462	−	7.77784i	−0.123660	−	0.957386i
$67$	−7.14861	−	7.14861i	−0.873342	−	0.873342i	0.119493	−	0.992835i	$-0.461873\pi$
$67$	−7.14861	−	7.14861i	−0.873342	−	0.873342i	−0.992835	+	0.119493i	$0.961873\pi$
$68$	0.299513	+	1.89105i	0.0363212	+	0.229323i
$69$	6.77149	+	2.20019i	0.815192	+	0.264872i
$70$	−5.53890	−	6.40095i	−0.662025	−	0.765059i
$71$	10.0775	−	7.32173i	1.19598	−	0.868929i	0.202095	−	0.979366i	$-0.435225\pi$
$71$	10.0775	−	7.32173i	1.19598	−	0.868929i	0.993883	+	0.110437i	$0.0352250\pi$
$72$	−0.405366	+	2.55938i	−0.0477728	+	0.301626i
$73$	−4.54499	+	8.92005i	−0.531951	+	1.04401i	0.456106	+	0.889925i	$0.349244\pi$
$73$	−4.54499	+	8.92005i	−0.531951	+	1.04401i	−0.988057	+	0.154087i	$0.950756\pi$
$74$	1.90843	−	5.87353i	0.221850	−	0.682784i
$75$	6.82509	−	9.65403i	0.788094	−	1.11475i
$76$			3.89425i			0.446701i
$77$	−7.08601	−	10.3644i	−0.807526	−	1.18114i
$78$	4.04148	−	4.04148i	0.457608	−	0.457608i
$79$	3.21092	+	2.33287i	0.361257	+	0.262469i	0.753576	−	0.657361i	$-0.228327\pi$
$79$	3.21092	+	2.33287i	0.361257	+	0.262469i	−0.392319	+	0.919829i	$0.628327\pi$
$80$	2.22799	−	0.189849i	0.249097	−	0.0212258i
$81$	3.10843	+	9.56677i	0.345381	+	1.06297i
$82$	−11.0080	−	1.74350i	−1.21564	−	0.192538i
$83$	−0.615229	−	0.0974427i	−0.0675302	−	0.0106957i	0.122578	−	0.992459i	$-0.460884\pi$
$83$	−0.615229	−	0.0974427i	−0.0675302	−	0.0106957i	−0.190108	+	0.981763i	$0.560884\pi$
$84$	2.76609	+	8.51314i	0.301805	+	0.928860i
$85$	−2.75932	+	3.27337i	−0.299291	+	0.355047i
$86$	0.111194	+	0.0807873i	0.0119904	+	0.00871152i
$87$	−13.2927	+	13.2927i	−1.42512	+	1.42512i
$88$	3.31527	+	0.0949311i	0.353409	+	0.0101197i
$89$		−	2.93819i		−	0.311448i	−0.987801	−	0.155724i	$-0.950229\pi$
$89$		−	2.93819i		−	0.311448i	0.987801	−	0.155724i	$-0.0497710\pi$
$90$	−4.92076	+	3.05939i	−0.518694	+	0.322488i
$91$	2.82755	−	8.70230i	0.296408	−	0.912249i
$92$	−1.36700	+	2.68289i	−0.142520	+	0.279711i
$93$	1.39311	−	8.79574i	0.144459	−	0.912075i
$94$	7.49783	−	5.44749i	0.773342	−	0.561866i
$95$	−6.58477	+	5.69796i	−0.675583	+	0.584598i
$96$	−2.24886	−	0.730698i	−0.229523	−	0.0745766i
$97$	0.904231	+	5.70909i	0.0918108	+	0.579670i	0.990111	+	0.140288i	$0.0448028\pi$
$97$	0.904231	+	5.70909i	0.0918108	+	0.579670i	−0.898300	+	0.439383i	$0.855197\pi$
$98$	5.18331	+	5.18331i	0.523593	+	0.523593i
$99$	−7.76613	+	3.68096i	−0.780526	+	0.369950i
$100$	3.58096	+	3.48952i	0.358096	+	0.348952i
$101$	3.24958	−	4.47267i	0.323346	−	0.445047i	−0.616139	−	0.787637i	$-0.711304\pi$
$101$	3.24958	−	4.47267i	0.323346	−	0.445047i	0.939485	+	0.342590i	$0.111304\pi$
$102$	4.03385	−	2.05535i	0.399410	−	0.203510i
$103$	8.58917	+	4.37640i	0.846316	+	0.431219i	0.822682	−	0.568501i	$-0.192477\pi$
$103$	8.58917	+	4.37640i	0.846316	+	0.431219i	0.0236334	+	0.999721i	$0.492477\pi$
$104$	1.42075	+	1.95550i	0.139316	+	0.191752i
$105$	−10.3476	+	17.1334i	−1.00982	+	1.67204i
$106$	1.22453	−	0.397874i	0.118937	−	0.0386449i
$107$	2.80896	+	5.51290i	0.271553	+	0.532952i	0.986002	−	0.166735i	$-0.0533226\pi$
$107$	2.80896	+	5.51290i	0.271553	+	0.532952i	−0.714449	+	0.699688i	$0.753323\pi$
$108$	−0.954548	+	0.151186i	−0.0918514	+	0.0145478i
$109$	−0.930262			−0.0891029			−0.0445515	−	0.999007i	$-0.514186\pi$
$109$	−0.930262			−0.0891029			−0.0445515	+	0.999007i	$0.514186\pi$
$110$	4.69029	+	5.74467i	0.447202	+	0.547732i
$111$	−14.6032			−1.38608
$112$	−3.73893	+	0.592189i	−0.353296	+	0.0559566i
$113$	−3.43706	−	6.74561i	−0.323331	−	0.634574i	0.670934	−	0.741517i	$-0.265894\pi$
$113$	−3.43706	−	6.74561i	−0.323331	−	0.634574i	−0.994265	+	0.106944i	$0.965894\pi$
$114$	8.75762	−	2.84552i	0.820226	−	0.266508i
$115$	−6.53665	+	1.61408i	−0.609546	+	0.150514i
$116$	−4.67294	−	6.43175i	−0.433872	−	0.597173i
$117$	−5.58079	−	2.84356i	−0.515944	−	0.262887i
$118$	−12.9815	+	6.61440i	−1.19504	+	0.608905i
$119$	4.26019	−	5.86365i	0.390531	−	0.537520i
$120$	−2.05493	−	4.87172i	−0.187589	−	0.444725i
$121$	5.94581	+	9.25458i	0.540528	+	0.841326i
$122$	−2.42398	−	2.42398i	−0.219456	−	0.219456i
$123$	4.12267	+	26.0295i	0.371729	+	2.34700i
$124$	3.58181	+	1.16380i	0.321656	+	0.104512i
$125$	−0.660856	+	11.1608i	−0.0591087	+	0.998252i
$126$	7.93597	−	5.76582i	0.706993	−	0.513660i
$127$	−2.58963	+	16.3503i	−0.229793	+	1.45085i	0.555391	+	0.831589i	$0.312569\pi$
$127$	−2.58963	+	16.3503i	−0.229793	+	1.45085i	−0.785183	+	0.619263i	$0.787431\pi$
$128$	0.453990	−	0.891007i	0.0401275	−	0.0787546i
$129$	0.100430	−	0.309091i	0.00884235	−	0.0272140i
$130$	−1.22774	+	5.26358i	−0.107679	+	0.461646i
$131$		−	11.1450i		−	0.973740i	−0.873475	−	0.486870i	$-0.838139\pi$
$131$		−	11.1450i		−	0.973740i	0.873475	−	0.486870i	$-0.161861\pi$
$132$	−2.20897	−	7.52493i	−0.192266	−	0.654961i
$133$	10.4240	−	10.4240i	0.903880	−	0.903880i
$134$	−8.17889	−	5.94231i	−0.706549	−	0.513338i
$135$	−1.65231	−	1.39283i	−0.142208	−	0.119876i
$136$	0.591650	+	1.82091i	0.0507336	+	0.156142i
$137$	5.51251	+	0.873096i	0.470966	+	0.0745936i	0.387406	−	0.921909i	$-0.373371\pi$
$137$	5.51251	+	0.873096i	0.470966	+	0.0745936i	0.0835595	+	0.996503i	$0.473371\pi$
$138$	7.03231	+	1.11381i	0.598630	+	0.0948137i
$139$	0.109716	+	0.337671i	0.00930598	+	0.0286408i	0.955602	−	0.294662i	$-0.0952069\pi$
$139$	0.109716	+	0.337671i	0.00930598	+	0.0286408i	−0.946296	+	0.323302i	$0.895207\pi$
$140$	−6.47203	−	5.45567i	−0.546987	−	0.461088i
$141$	−17.7293	−	12.8811i	−1.49308	−	1.08478i
$142$	8.80805	−	8.80805i	0.739155	−	0.739155i
$143$	−2.69452	+	7.55032i	−0.225327	+	0.631389i
$144$			2.59128i			0.215940i
$145$	4.03809	−	17.3122i	0.335346	−	1.43770i
$146$	−3.09363	+	9.52122i	−0.256031	+	0.787982i
$147$	7.86909	−	15.4440i	0.649031	−	1.27380i
$148$	0.966107	−	6.09976i	0.0794135	−	0.501397i
$149$	14.2232	−	10.3338i	1.16521	−	0.846575i	0.174782	−	0.984607i	$-0.444078\pi$
$149$	14.2232	−	10.3338i	1.16521	−	0.846575i	0.990428	+	0.138033i	$0.0440779\pi$
$150$	5.23084	−	10.6028i	0.427096	−	0.865719i
$151$	0.121851	+	0.0395918i	0.00991610	+	0.00322194i	0.313971	−	0.949433i	$-0.398341\pi$
$151$	0.121851	+	0.0395918i	0.00991610	+	0.00322194i	−0.304055	+	0.952655i	$0.598341\pi$
$152$	0.609195	+	3.84631i	0.0494122	+	0.311977i
$153$	−3.50819	−	3.50819i	−0.283620	−	0.283620i
$154$	−8.62013	−	9.12835i	−0.694630	−	0.735583i
$155$	3.27295	+	7.75931i	0.262889	+	0.623243i
$156$	3.35950	−	4.62395i	0.268975	−	0.370212i
$157$	−11.1086	+	5.66010i	−0.886560	+	0.451725i	−0.837099	−	0.547051i	$-0.815750\pi$
$157$	−11.1086	+	5.66010i	−0.886560	+	0.451725i	−0.0494610	+	0.998776i	$0.515750\pi$
$158$	3.53633	+	1.80185i	0.281336	+	0.143348i
$159$	−1.78952	−	2.46307i	−0.141918	−	0.195334i
$160$	2.17086	−	0.536047i	0.171622	−	0.0423782i
$161$	10.8407	−	3.52235i	0.854365	−	0.277600i
$162$	4.56674	+	8.96272i	0.358797	+	0.704178i
$163$	2.51984	−	0.399103i	0.197369	−	0.0312602i	−0.0569671	−	0.998376i	$-0.518143\pi$
$163$	2.51984	−	0.399103i	0.197369	−	0.0312602i	0.254336	+	0.967116i	$0.418143\pi$
$164$	−11.1453			−0.870299
$165$	9.49175	−	14.7454i	0.738932	−	1.14793i
$166$	−0.622898			−0.0483463
$167$	−0.358992	+	0.0568587i	−0.0277796	+	0.00439986i	−0.170309	−	0.985391i	$-0.554477\pi$
$167$	−0.358992	+	0.0568587i	−0.0277796	+	0.00439986i	0.142529	+	0.989791i	$0.454477\pi$
$168$	4.06378	+	7.97562i	0.313527	+	0.615332i
$169$	6.80717	−	2.21178i	0.523629	−	0.170137i
$170$	−2.21328	+	3.66473i	−0.169751	+	0.281072i
$171$	−5.93140	−	8.16388i	−0.453586	−	0.624307i
$172$	0.122463	+	0.0623981i	0.00933773	+	0.00475781i
$173$	−6.24707	+	3.18304i	−0.474956	+	0.242002i	−0.675046	−	0.737775i	$-0.735876\pi$
$173$	−6.24707	+	3.18304i	−0.474956	+	0.242002i	0.200090	+	0.979777i	$0.435876\pi$
$174$	−11.0496	+	15.2085i	−0.837667	+	1.15295i
$175$	−0.244748	−	18.9261i	−0.0185012	−	1.43068i
$176$	3.28930	−	0.424860i	0.247940	−	0.0320250i
$177$	24.3604	+	24.3604i	1.83104	+	1.83104i
$178$	−0.459635	−	2.90202i	−0.0344511	−	0.217516i
$179$	−5.23603	−	1.70129i	−0.391359	−	0.127160i	0.106726	−	0.994288i	$-0.465963\pi$
$179$	−5.23603	−	1.70129i	−0.391359	−	0.127160i	−0.498085	+	0.867128i	$0.665963\pi$
$180$	−4.38159	+	3.79150i	−0.326584	+	0.282601i
$181$	6.35837	−	4.61963i	0.472614	−	0.343374i	−0.325845	−	0.945423i	$-0.605649\pi$
$181$	6.35837	−	4.61963i	0.472614	−	0.343374i	0.798459	+	0.602049i	$0.205649\pi$
$182$	1.43140	−	9.03748i	0.106102	−	0.669903i
$183$	−3.67998	+	7.22237i	−0.272032	+	0.533893i
$184$	−0.930475	+	2.86371i	−0.0685955	+	0.211115i
$185$	11.7276	−	7.29142i	0.862233	−	0.536076i
$186$		−	8.90538i		−	0.652974i
$187$	−3.87800	+	5.02838i	−0.283587	+	0.367712i
$188$	6.55335	−	6.55335i	0.477952	−	0.477952i
$189$	2.95981	+	2.15042i	0.215294	+	0.156420i
$190$	−5.61234	+	6.65789i	−0.407162	+	0.483014i
$191$	−0.968503	−	2.98075i	−0.0700784	−	0.215679i	0.909884	−	0.414864i	$-0.136171\pi$
$191$	−0.968503	−	2.98075i	−0.0700784	−	0.215679i	−0.979962	+	0.199184i	$0.936171\pi$
$192$	−2.33548	−	0.369903i	−0.168549	−	0.0266955i
$193$	9.21611	+	1.45969i	0.663390	+	0.105071i	0.479044	−	0.877791i	$-0.340983\pi$
$193$	9.21611	+	1.45969i	0.663390	+	0.105071i	0.184346	+	0.982861i	$0.440983\pi$
$194$	1.78620	+	5.49735i	0.128241	+	0.394687i
$195$	12.7341	−	1.08509i	0.911911	−	0.0777046i
$196$	5.93034	+	4.30864i	0.423596	+	0.307760i
$197$	4.64426	−	4.64426i	0.330890	−	0.330890i	−0.522034	−	0.852924i	$-0.674827\pi$
$197$	4.64426	−	4.64426i	0.330890	−	0.330890i	0.852924	+	0.522034i	$0.174827\pi$
$198$	−7.09469	+	4.85053i	−0.504198	+	0.344712i
$199$		−	13.3351i		−	0.945300i	−0.881250	−	0.472650i	$-0.843297\pi$
$199$		−	13.3351i		−	0.945300i	0.881250	−	0.472650i	$-0.156703\pi$
$200$	4.08275	+	2.88637i	0.288694	+	0.204098i
$201$	−7.38712	+	22.7352i	−0.521047	+	1.60362i
$202$	2.50990	−	4.92595i	0.176596	−	0.346588i
$203$	−4.70795	+	29.7248i	−0.330433	+	2.08627i
$204$	3.66266	−	2.66107i	0.256437	−	0.186313i
$205$	−16.3074	−	18.8455i	−1.13896	−	1.31622i
$206$	9.16804	+	2.97888i	0.638768	+	0.207548i
$207$	−1.22059	−	7.70650i	−0.0848369	−	0.535639i
$208$	1.70917	+	1.70917i	0.118510	+	0.118510i
$209$	−9.39049	+	8.86768i	−0.649554	+	0.613390i
$210$	−7.53992	+	18.5411i	−0.520304	+	1.27946i
$211$	−12.3551	+	17.0054i	−0.850561	+	1.17070i	0.133178	+	0.991092i	$0.457482\pi$
$211$	−12.3551	+	17.0054i	−0.850561	+	1.17070i	−0.983739	+	0.179605i	$0.942518\pi$
$212$	1.14721	−	0.584534i	0.0787909	−	0.0401459i
$213$	−26.2441	−	13.3720i	−1.79822	−	0.916236i
$214$	3.63679	+	5.00561i	0.248606	+	0.342176i
$215$	0.0736762	+	0.298371i	0.00502467	+	0.0203488i
$216$	−0.919145	+	0.298648i	−0.0625399	+	0.0203205i
$217$	−6.47248	−	12.7030i	−0.439381	−	0.862333i
$218$	−0.918809	+	0.145525i	−0.0622296	+	0.00985620i
$219$	23.6724			1.59963
$220$	5.53121	+	4.94022i	0.372914	+	0.333069i
$221$	−4.62789			−0.311305
$222$	−14.4234	+	2.28445i	−0.968037	+	0.153322i
$223$	−12.8753	−	25.2691i	−0.862192	−	1.69215i	−0.710475	−	0.703722i	$-0.751520\pi$
$223$	−12.8753	−	25.2691i	−0.862192	−	1.69215i	−0.151716	−	0.988424i	$-0.548480\pi$
$224$	−3.60026	+	1.16980i	−0.240553	+	0.0781603i
$225$	−12.8220	−	1.86119i	−0.854803	−	0.124079i
$226$	−4.44999	−	6.12489i	−0.296009	−	0.407421i
$227$	0.742483	+	0.378314i	0.0492803	+	0.0251096i	0.478457	−	0.878111i	$-0.341196\pi$
$227$	0.742483	+	0.378314i	0.0492803	+	0.0251096i	−0.429177	+	0.903221i	$0.641196\pi$
$228$	8.20466	−	4.18048i	0.543367	−	0.276859i
$229$	−0.375767	+	0.517200i	−0.0248314	+	0.0341775i	−0.821252	−	0.570565i	$-0.806724\pi$
$229$	−0.375767	+	0.517200i	−0.0248314	+	0.0341775i	0.796421	+	0.604743i	$0.206724\pi$
$230$	−6.20367	+	2.61676i	−0.409058	+	0.172544i
$231$	−14.2296	+	26.0555i	−0.936242	+	1.71433i
$232$	−5.62156	−	5.62156i	−0.369073	−	0.369073i
$233$	−2.44827	−	15.4577i	−0.160391	−	1.01267i	−0.928224	−	0.372021i	$-0.878665\pi$
$233$	−2.44827	−	15.4577i	−0.160391	−	1.01267i	0.767833	−	0.640650i	$-0.221335\pi$
$234$	−5.95691	−	1.93552i	−0.389416	−	0.126529i
$235$	20.6697	+	1.49234i	1.34834	+	0.0973494i
$236$	−11.7869	+	8.56372i	−0.767265	+	0.557450i
$237$	1.46812	−	9.26932i	0.0953644	−	0.602107i
$238$	3.29046	−	6.45790i	0.213289	−	0.418603i
$239$	−2.22365	+	6.84370i	−0.143836	+	0.442682i	−0.996859	−	0.0791906i	$-0.974766\pi$
$239$	−2.22365	+	6.84370i	−0.143836	+	0.442682i	0.853023	+	0.521873i	$0.174766\pi$
$240$	−2.79174	−	4.49028i	−0.180206	−	0.289846i
$241$		−	15.1360i		−	0.974996i	−0.873124	−	0.487498i	$-0.837910\pi$
$241$		−	15.1360i		−	0.974996i	0.873124	−	0.487498i	$-0.162090\pi$
$242$	7.32035	+	8.21051i	0.470570	+	0.527792i
$243$	14.7688	−	14.7688i	0.947422	−	0.947422i
$244$	−2.77333	−	2.01494i	−0.177544	−	0.128993i
$245$	1.39165	+	16.3319i	0.0889092	+	1.04340i
$246$	8.14382	+	25.0641i	0.519231	+	1.59803i
$247$	−9.29702	−	1.47250i	−0.591555	−	0.0936931i
$248$	3.71977	+	0.589154i	0.236206	+	0.0374113i
$249$	0.455151	+	1.40081i	0.0288440	+	0.0887727i
$250$	1.09321	+	11.1268i	0.0691408	+	0.703718i
$251$	13.1674	+	9.56671i	0.831122	+	0.603845i	0.919877	−	0.392208i	$-0.128289\pi$
$251$	13.1674	+	9.56671i	0.831122	+	0.603845i	−0.0887546	+	0.996054i	$0.528289\pi$
$252$	6.93630	−	6.93630i	0.436946	−	0.436946i
$253$	−9.58228	+	2.81292i	−0.602433	+	0.176847i
$254$			16.5541i			1.03870i
$255$	9.85870	+	2.29955i	0.617375	+	0.144003i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.78048	+	5.45700i	−0.173442	+	0.340398i	−0.961321	−	0.275432i	$-0.911179\pi$
$257$	−2.78048	+	5.45700i	−0.173442	+	0.340398i	0.787879	+	0.615830i	$0.211179\pi$
$258$	0.0508408	−	0.320996i	0.00316521	−	0.0199844i
$259$	−18.9138	+	13.7417i	−1.17524	+	0.853865i
$260$	−0.389215	+	5.39083i	−0.0241381	+	0.334325i
$261$	19.5926	+	6.36604i	1.21275	+	0.394048i
$262$	−1.74346	−	11.0077i	−0.107711	−	0.680061i
$263$	4.74495	+	4.74495i	0.292586	+	0.292586i	0.838101	−	0.545515i	$-0.183666\pi$
$263$	4.74495	+	4.74495i	0.292586	+	0.292586i	−0.545515	+	0.838101i	$0.683666\pi$
$264$	−3.35893	−	7.08673i	−0.206728	−	0.436158i
$265$	2.66696	+	1.08454i	0.163830	+	0.0666228i
$266$	8.66503	−	11.9264i	0.531287	−	0.731254i
$267$	−6.19037	+	3.15415i	−0.378845	+	0.193031i
$268$	−9.00778	−	4.58969i	−0.550238	−	0.280360i
$269$	4.43761	+	6.10785i	0.270566	+	0.372402i	0.922581	−	0.385804i	$-0.126076\pi$
$269$	4.43761	+	6.10785i	0.270566	+	0.372402i	−0.652015	+	0.758206i	$0.726076\pi$
$270$	−1.84985	−	1.11720i	−0.112578	−	0.0679909i
$271$	2.47006	−	0.802572i	0.150046	−	0.0487528i	−0.233031	−	0.972469i	$-0.574864\pi$
$271$	2.47006	−	0.802572i	0.150046	−	0.0487528i	0.383077	+	0.923716i	$0.374864\pi$
$272$	0.869219	+	1.70594i	0.0527042	+	0.103438i
$273$	−21.3699	+	3.38467i	−1.29337	+	0.204849i
$274$	5.58123			0.337174
$275$	−0.260272	+	16.5811i	−0.0156950	+	0.999877i
$276$	7.11997			0.428572
$277$	1.16334	−	0.184255i	0.0698984	−	0.0110708i	−0.121387	−	0.992605i	$-0.538734\pi$
$277$	1.16334	−	0.184255i	0.0698984	−	0.0110708i	0.191286	+	0.981534i	$0.438734\pi$
$278$	0.161188	+	0.316350i	0.00966744	+	0.0189734i
$279$	−9.28149	+	3.01574i	−0.555668	+	0.180548i
$280$	−7.24581	−	4.37605i	−0.433020	−	0.261519i
$281$	−4.33675	−	5.96902i	−0.258709	−	0.356082i	0.659829	−	0.751416i	$-0.270629\pi$
$281$	−4.33675	−	5.96902i	−0.258709	−	0.356082i	−0.918537	+	0.395334i	$0.870629\pi$
$282$	−19.5261	−	9.94903i	−1.16276	−	0.592456i
$283$	24.9654	−	12.7205i	1.48404	−	0.756154i	0.490692	−	0.871333i	$-0.336744\pi$
$283$	24.9654	−	12.7205i	1.48404	−	0.756154i	0.993345	+	0.115179i	$0.0367440\pi$
$284$	7.32173	−	10.0775i	0.434465	−	0.597989i
$285$	19.0736	+	7.75644i	1.12982	+	0.459452i
$286$	−1.48021	+	7.87887i	−0.0875268	+	0.465888i
$287$	29.8334	+	29.8334i	1.76101	+	1.76101i
$288$	0.405366	+	2.55938i	0.0238864	+	0.150813i
$289$	12.6816	+	4.12050i	0.745977	+	0.242383i
$290$	1.28015	−	17.7308i	0.0751730	−	1.04119i
$291$	11.0576	−	8.03381i	0.648207	−	0.470950i
$292$	−1.56610	+	9.88795i	−0.0916489	+	0.578649i
$293$	5.31674	−	10.4347i	0.310607	−	0.609601i	−0.681948	−	0.731401i	$-0.738867\pi$
$293$	5.31674	−	10.4347i	0.310607	−	0.609601i	0.992555	+	0.121800i	$0.0388668\pi$
$294$	5.35624	−	16.4848i	0.312382	−	0.961414i
$295$	−31.7267	−	7.40028i	−1.84720	−	0.430861i
$296$		−	6.17580i		−	0.358961i
$297$	−2.53819	−	1.95750i	−0.147280	−	0.113586i
$298$	12.4315	−	12.4315i	0.720139	−	0.720139i
$299$	−5.88817	−	4.27800i	−0.340521	−	0.247403i
$300$	3.50779	−	11.2906i	0.202522	−	0.651863i
$301$	−0.160781	−	0.494833i	−0.00926726	−	0.0285217i
$302$	0.126544	+	0.0200427i	0.00728181	+	0.00115333i
$303$	−12.9117	−	2.04502i	−0.741760	−	0.117483i
$304$	1.20339	+	3.70365i	0.0690191	+	0.212419i
$305$	−0.650806	−	7.63760i	−0.0372650	−	0.437328i
$306$	−4.01380	−	2.91619i	−0.229453	−	0.166708i
$307$	−1.13098	+	1.13098i	−0.0645485	+	0.0645485i	−0.738644	−	0.674096i	$-0.764534\pi$
$307$	−1.13098	+	1.13098i	−0.0645485	+	0.0645485i	0.674096	+	0.738644i	$0.264534\pi$
$308$	−9.94199	−	7.66748i	−0.566497	−	0.436895i
$309$		−	22.7943i		−	1.29672i
$310$	4.44647	+	7.15178i	0.252543	+	0.406194i
$311$	−2.17943	+	6.70760i	−0.123584	+	0.380353i	−0.993640	−	0.112599i	$-0.964082\pi$
$311$	−2.17943	+	6.70760i	−0.123584	+	0.380353i	0.870056	+	0.492952i	$0.164082\pi$
$312$	2.59479	−	5.09257i	0.146901	−	0.288310i
$313$	−2.02955	+	12.8141i	−0.114717	+	0.724294i	0.861542	+	0.507686i	$0.169499\pi$
$313$	−2.02955	+	12.8141i	−0.114717	+	0.724294i	−0.976259	+	0.216607i	$0.930501\pi$
$314$	−10.0864	+	7.32818i	−0.569207	+	0.413553i
$315$	21.8775	+	1.57954i	1.23266	+	0.0889973i
$316$	3.77467	+	1.22646i	0.212342	+	0.0689940i
$317$	−3.89292	−	24.5789i	−0.218648	−	1.38049i	−0.815787	−	0.578352i	$-0.803696\pi$
$317$	−3.89292	−	24.5789i	−0.218648	−	1.38049i	0.597139	−	0.802137i	$-0.296304\pi$
$318$	−2.15280	−	2.15280i	−0.120723	−	0.120723i
$319$	4.86851	−	25.9141i	0.272584	−	1.45091i
$320$	2.06028	−	0.869045i	0.115173	−	0.0485811i
$321$	8.59951	−	11.8362i	0.479978	−	0.660633i
$322$	10.1562	−	5.17484i	0.565983	−	0.288383i
$323$	−6.64335	−	3.38496i	−0.369646	−	0.188344i
$324$	5.91259	+	8.13798i	0.328477	+	0.452110i
$325$	−9.68482	+	7.22960i	−0.537217	+	0.401026i
$326$	2.42638	−	0.788380i	0.134385	−	0.0436643i
$327$	0.998637	+	1.95994i	0.0552248	+	0.108385i
$328$	−11.0080	+	1.74350i	−0.607818	+	0.0962688i
$329$	−35.0837			−1.93423
$330$	7.06820	−	16.0487i	0.389092	−	0.883452i
$331$	−27.6212			−1.51820			−0.759099	−	0.650975i	$-0.774360\pi$
$331$	−27.6212			−1.51820			−0.759099	+	0.650975i	$0.774360\pi$
$332$	−0.615229	+	0.0974427i	−0.0337651	+	0.00534787i
$333$	7.26532	+	14.2590i	0.398137	+	0.781388i
$334$	−0.345678	+	0.112317i	−0.0189146	+	0.00614574i
$335$	−5.41925	−	21.9467i	−0.296085	−	1.19908i
$336$	5.26141	+	7.24171i	0.287033	+	0.395068i
$337$	24.5405	+	12.5040i	1.33680	+	0.681136i	0.968604	−	0.248610i	$-0.0799739\pi$
$337$	24.5405	+	12.5040i	1.33680	+	0.681136i	0.368201	+	0.929746i	$0.379974\pi$
$338$	6.37737	−	3.24943i	0.346883	−	0.176746i
$339$	−10.5224	+	14.4828i	−0.571498	+	0.786600i
$340$	−1.61274	+	3.96584i	−0.0874634	+	0.215078i
$341$	5.34986	+	11.2872i	0.289711	+	0.611236i
$342$	−7.13549	−	7.13549i	−0.385843	−	0.385843i
$343$	−0.195601	−	1.23497i	−0.0105614	−	0.0666823i
$344$	0.130717	+	0.0424724i	0.00704777	+	0.00228996i
$345$	10.4177	+	12.0391i	0.560873	+	0.648164i
$346$	−5.67222	+	4.12111i	−0.304941	+	0.221552i
$347$	3.03544	−	19.1650i	0.162951	−	1.02883i	−0.761676	−	0.647959i	$-0.775623\pi$
$347$	3.03544	−	19.1650i	0.162951	−	1.02883i	0.924627	−	0.380875i	$-0.124377\pi$
$348$	−8.53443	+	16.7498i	−0.457493	+	0.897881i
$349$	−10.3261	+	31.7804i	−0.552741	+	1.70116i	0.149093	+	0.988823i	$0.452365\pi$
$349$	−10.3261	+	31.7804i	−0.552741	+	1.70116i	−0.701834	+	0.712340i	$0.747635\pi$
$350$	−3.20243	−	18.6548i	−0.171177	−	0.997142i
$351$		−	2.33603i		−	0.124688i
$352$	3.18234	−	0.934189i	0.169619	−	0.0497924i
$353$	−24.1739	+	24.1739i	−1.28665	+	1.28665i	−0.349836	+	0.936811i	$0.613763\pi$
$353$	−24.1739	+	24.1739i	−1.28665	+	1.28665i	−0.936811	+	0.349836i	$0.886237\pi$
$354$	27.8713	+	20.2497i	1.48134	+	1.07626i
$355$	27.7529	−	2.36485i	1.47297	−	0.125513i
$356$	−0.907952	−	2.79439i	−0.0481213	−	0.148102i
$357$	−16.9272	−	2.68101i	−0.895884	−	0.141894i
$358$	−5.43771	−	0.861248i	−0.287392	−	0.0455184i
$359$	3.23291	+	9.94988i	0.170627	+	0.525135i	0.999407	−	0.0344397i	$-0.0109647\pi$
$359$	3.23291	+	9.94988i	0.170627	+	0.525135i	−0.828780	+	0.559574i	$0.810965\pi$
$360$	−3.73452	+	4.43025i	−0.196827	+	0.233495i
$361$	3.10243	+	2.25405i	0.163286	+	0.118634i
$362$	5.55742	−	5.55742i	0.292092	−	0.292092i
$363$	13.1153	−	22.4618i	0.688376	−	1.17894i
$364$		−	9.15014i		−	0.479598i
$365$	−19.0110	+	11.8197i	−0.995079	+	0.618670i
$366$	−2.50485	+	7.70913i	−0.130930	+	0.402963i
$367$	−13.7429	+	26.9720i	−0.717375	+	1.40793i	0.187506	+	0.982263i	$0.439960\pi$
$367$	−13.7429	+	26.9720i	−0.717375	+	1.40793i	−0.904881	+	0.425664i	$0.860040\pi$
$368$	−0.471037	+	2.97401i	−0.0245545	+	0.155031i
$369$	23.3648	−	16.9756i	1.21633	−	0.883712i
$370$	10.4426	−	9.03626i	0.542886	−	0.469773i
$371$	−4.63550	−	1.50617i	−0.240663	−	0.0781963i
$372$	−1.39311	−	8.79574i	−0.0722293	−	0.456038i
$373$	−12.0888	−	12.0888i	−0.625934	−	0.625934i	0.321108	−	0.947043i	$-0.395945\pi$
$373$	−12.0888	−	12.0888i	−0.625934	−	0.625934i	−0.947043	+	0.321108i	$0.895945\pi$
$374$	−3.04364	+	5.57313i	−0.157383	+	0.288179i
$375$	24.2237	−	10.5888i	1.25091	−	0.546803i
$376$	5.44749	−	7.49783i	0.280933	−	0.386671i
$377$	17.1219	−	8.72406i	0.881824	−	0.449312i
$378$	3.25977	+	1.66093i	0.167664	+	0.0854292i
$379$	−2.27211	−	3.12729i	−0.116710	−	0.160638i	0.746665	−	0.665200i	$-0.231654\pi$
$379$	−2.27211	−	3.12729i	−0.116710	−	0.160638i	−0.863375	+	0.504562i	$0.831654\pi$
$380$	−4.50172	+	7.45389i	−0.230933	+	0.382376i
$381$	37.2278	−	12.0960i	1.90724	−	0.619699i
$382$	−1.42287	−	2.79254i	−0.0728004	−	0.142879i
$383$	3.60856	−	0.571540i	0.184389	−	0.0292043i	−0.0635570	−	0.997978i	$-0.520244\pi$
$383$	3.60856	−	0.571540i	0.184389	−	0.0292043i	0.247946	+	0.968774i	$0.420244\pi$
$384$	−2.36459			−0.120667
$385$	−1.58195	−	28.0297i	−0.0806238	−	1.42853i
$386$	9.33099			0.474935
$387$	−0.351770	+	0.0557150i	−0.0178815	+	0.00283215i
$388$	2.62418	+	5.15025i	0.133223	+	0.261464i
$389$	−15.2843	+	4.96616i	−0.774944	+	0.251795i	−0.669680	−	0.742650i	$-0.733569\pi$
$389$	−15.2843	+	4.96616i	−0.774944	+	0.251795i	−0.105264	+	0.994444i	$0.533569\pi$
$390$	12.4076	−	3.06378i	0.628284	−	0.155141i
$391$	−3.38863	−	4.66404i	−0.171370	−	0.235871i
$392$	6.53135	+	3.32789i	0.329883	+	0.168084i
$393$	−23.4809	+	11.9641i	−1.18446	+	0.603510i
$394$	3.86056	−	5.31361i	0.194492	−	0.267696i
$395$	3.44917	+	8.17709i	0.173547	+	0.411434i
$396$	−6.24855	+	5.90067i	−0.314002	+	0.296520i
$397$	0.712041	+	0.712041i	0.0357363	+	0.0357363i	0.724749	−	0.689013i	$-0.241956\pi$
$397$	0.712041	+	0.712041i	0.0357363	+	0.0357363i	−0.689013	+	0.724749i	$0.741956\pi$
$398$	−2.08607	−	13.1709i	−0.104565	−	0.660199i
$399$	−33.1523	−	10.7718i	−1.65969	−	0.539266i
$400$	4.48401	+	2.21216i	0.224201	+	0.110608i
$401$	−25.1330	+	18.2602i	−1.25508	+	0.911872i	−0.998505	−	0.0546520i	$-0.982595\pi$
$401$	−25.1330	+	18.2602i	−1.25508	+	0.911872i	−0.256578	+	0.966524i	$0.582595\pi$
$402$	−3.73960	+	23.6109i	−0.186514	+	1.17760i
$403$	−4.13279	+	8.11105i	−0.205869	+	0.404040i
$404$	1.70841	−	5.25794i	0.0849964	−	0.261592i
$405$	−5.10933	+	21.9048i	−0.253885	+	1.08846i
$406$			30.0954i			1.49361i
$407$	16.9087	−	11.5602i	0.838135	−	0.573020i
$408$	3.20128	−	3.20128i	0.158487	−	0.158487i
$409$	−3.09808	−	2.25088i	−0.153190	−	0.111299i	0.508550	−	0.861032i	$-0.330182\pi$
$409$	−3.09808	−	2.25088i	−0.153190	−	0.111299i	−0.661740	+	0.749733i	$0.730182\pi$
$410$	−19.0548	−	16.0624i	−0.941047	−	0.793265i
$411$	−4.07819	−	12.5514i	−0.201162	−	0.619114i
$412$	9.52117	+	1.50800i	0.469074	+	0.0742941i
$413$	54.4742	+	8.62787i	2.68050	+	0.424550i
$414$	−2.41112	−	7.42068i	−0.118500	−	0.364707i
$415$	−1.06495	−	0.897712i	−0.0522765	−	0.0440670i
$416$	1.95550	+	1.42075i	0.0958762	+	0.0696582i
$417$	0.593646	−	0.593646i	0.0290710	−	0.0290710i
$418$	−7.88767	+	10.2275i	−0.385798	+	0.500243i
$419$		−	25.9429i		−	1.26739i	−0.773582	−	0.633697i	$-0.781537\pi$
$419$		−	25.9429i		−	1.26739i	0.773582	−	0.633697i	$-0.218463\pi$
$420$	−4.54661	+	19.4924i	−0.221852	+	0.951130i
$421$	−7.27446	+	22.3885i	−0.354535	+	1.09115i	0.601743	+	0.798690i	$0.294473\pi$
$421$	−7.27446	+	22.3885i	−0.354535	+	1.09115i	−0.956278	+	0.292458i	$0.905527\pi$
$422$	−9.54278	+	18.7288i	−0.464535	+	0.911702i
$423$	−3.75686	+	23.7199i	−0.182665	+	1.15330i
$424$	1.04165	−	0.756801i	0.0505868	−	0.0367535i
$425$	−9.06555	+	3.07573i	−0.439744	+	0.149195i
$426$	−28.0128	−	9.10192i	−1.35723	−	0.440989i
$427$	2.03003	+	12.8171i	0.0982402	+	0.620264i
$428$	4.37506	+	4.37506i	0.211477	+	0.211477i
$429$	18.8001	−	2.42829i	0.907675	−	0.117239i
$430$	0.119445	+	0.283172i	0.00576013	+	0.0136558i
$431$	4.68163	−	6.44372i	0.225506	−	0.310383i	−0.681239	−	0.732061i	$-0.738559\pi$
$431$	4.68163	−	6.44372i	0.225506	−	0.310383i	0.906746	+	0.421678i	$0.138559\pi$
$432$	−0.861110	+	0.438758i	−0.0414302	+	0.0211097i
$433$	34.1350	+	17.3926i	1.64042	+	0.835837i	0.997557	+	0.0698566i	$0.0222542\pi$
$433$	34.1350	+	17.3926i	1.64042	+	0.835837i	0.642864	+	0.765980i	$0.277746\pi$
$434$	−8.37998	−	11.5340i	−0.402252	−	0.553652i
$435$	−40.8094	+	10.0770i	−1.95666	+	0.483154i
$436$	−0.884732	+	0.287467i	−0.0423710	+	0.0137672i
$437$	−5.32345	−	10.4479i	−0.254655	−	0.499789i
$438$	23.3809	−	3.70318i	1.11718	−	0.176945i
$439$	26.1459			1.24788			0.623938	−	0.781474i	$-0.285532\pi$
$439$	26.1459			1.24788			0.623938	+	0.781474i	$0.285532\pi$
$440$	6.23593	+	4.01412i	0.297286	+	0.191366i
$441$	−18.9949			−0.904518
$442$	−4.57091	+	0.723961i	−0.217416	+	0.0344353i
$443$	4.13411	+	8.11366i	0.196418	+	0.385491i	0.968118	−	0.250495i	$-0.0805934\pi$
$443$	4.13411	+	8.11366i	0.196418	+	0.385491i	−0.771700	+	0.635987i	$0.780593\pi$
$444$	−13.8885	+	4.51264i	−0.659119	+	0.214161i
$445$	3.39652	−	5.62392i	0.161011	−	0.266600i
$446$	−16.6697	−	22.9439i	−0.789334	−	1.08642i
$447$	−37.0405	−	18.8731i	−1.75195	−	0.892665i
$448$	−3.37294	+	1.71860i	−0.159356	+	0.0811961i
$449$	2.63455	−	3.62615i	0.124332	−	0.171129i	−0.742313	−	0.670053i	$-0.766271\pi$
$449$	2.63455	−	3.62615i	0.124332	−	0.171129i	0.866646	+	0.498924i	$0.166271\pi$
$450$	−12.9553	+	0.167536i	−0.610720	+	0.00789770i
$451$	−25.3791	−	26.8754i	−1.19506	−	1.26551i
$452$	−5.35335	−	5.35335i	−0.251800	−	0.251800i
$453$	−0.0473927	−	0.299226i	−0.00222670	−	0.0140588i
$454$	0.792523	+	0.257506i	0.0371949	+	0.0120854i
$455$	15.4719	−	13.3882i	0.725335	−	0.627650i
$456$	7.44967	−	5.41250i	0.348863	−	0.253464i
$457$	−0.824706	+	5.20699i	−0.0385781	+	0.243573i	−0.999440	−	0.0334544i	$-0.989349\pi$
$457$	−0.824706	+	5.20699i	−0.0385781	+	0.243573i	0.960862	+	0.277027i	$0.0893491\pi$
$458$	−0.290233	+	0.569615i	−0.0135617	+	0.0266164i
$459$	0.571798	−	1.75981i	0.0266893	−	0.0821411i
$460$	−5.71795	+	3.55502i	−0.266601	+	0.165754i
$461$			1.13643i			0.0529290i	0.999650	+	0.0264645i	$0.00842490\pi$
$461$			1.13643i			0.0529290i	−0.999650	+	0.0264645i	$0.991575\pi$
$462$	−9.97847	+	27.9607i	−0.464241	+	1.30085i
$463$	−12.8865	+	12.8865i	−0.598886	+	0.598886i	−0.940016	−	0.341130i	$-0.889190\pi$
$463$	−12.8865	+	12.8865i	−0.598886	+	0.598886i	0.341130	+	0.940016i	$0.389190\pi$
$464$	−6.43175	−	4.67294i	−0.298587	−	0.216936i
$465$	12.8343	−	15.2253i	0.595177	−	0.706055i
$466$	−4.83625	−	14.8844i	−0.224035	−	0.689508i
$467$	9.39003	+	1.48723i	0.434519	+	0.0688210i	0.369862	−	0.929087i	$-0.379405\pi$
$467$	9.39003	+	1.48723i	0.434519	+	0.0688210i	0.0646565	+	0.997908i	$0.479405\pi$
$468$	−6.18635	−	0.979822i	−0.285964	−	0.0452923i
$469$	11.8262	+	36.3974i	0.546085	+	1.68068i
$470$	20.6487	−	1.75949i	0.952452	−	0.0811591i
$471$	23.8501	+	17.3281i	1.09896	+	0.798438i
$472$	−10.3022	+	10.3022i	−0.474196	+	0.474196i
$473$	0.128398	+	0.437392i	0.00590376	+	0.0201113i
$474$		−	9.38486i		−	0.431061i
$475$	−19.1905	+	3.29440i	−0.880522	+	0.151157i
$476$	2.23971	−	6.89313i	0.102657	−	0.315946i
$477$	−1.51469	+	2.97275i	−0.0693530	+	0.136113i
$478$	−1.12569	+	7.10730i	−0.0514877	+	0.325080i
$479$	15.9973	−	11.6227i	0.730935	−	0.531055i	−0.158924	−	0.987291i	$-0.550802\pi$
$479$	15.9973	−	11.6227i	0.730935	−	0.531055i	0.889859	+	0.456235i	$0.150802\pi$
$480$	−3.45980	−	3.99827i	−0.157918	−	0.182495i
$481$	14.1971	+	4.61291i	0.647331	+	0.210331i
$482$	−2.36779	−	14.9497i	−0.107850	−	0.680939i
$483$	−19.0586	−	19.0586i	−0.867196	−	0.867196i
$484$	8.51463	+	6.96427i	0.387029	+	0.316558i
$485$	−4.86889	+	11.9729i	−0.221085	+	0.543662i
$486$	12.2767	−	16.8974i	0.556881	−	0.766480i
$487$	3.81579	−	1.94424i	0.172910	−	0.0881020i	−0.365393	−	0.930853i	$-0.619066\pi$
$487$	3.81579	−	1.94424i	0.172910	−	0.0881020i	0.538303	+	0.842751i	$0.319066\pi$
$488$	−3.05439	−	1.55629i	−0.138266	−	0.0704498i
$489$	−3.54591	−	4.88052i	−0.160352	−	0.220705i
$490$	3.92938	+	15.9131i	0.177511	+	0.718880i
$491$	−8.68765	+	2.82279i	−0.392068	+	0.127391i	−0.498415	−	0.866938i	$-0.666085\pi$
$491$	−8.68765	+	2.82279i	−0.392068	+	0.127391i	0.106347	+	0.994329i	$0.466085\pi$
$492$	11.9645	+	23.4816i	0.539399	+	1.05863i
$493$	15.0340	−	2.38115i	0.677097	−	0.107242i
$494$	−9.41291			−0.423507
$495$	−19.1201	−	1.93195i	−0.859385	−	0.0868347i
$496$	3.76614			0.169105
$497$	−46.5739	+	7.37658i	−2.08912	+	0.330885i
$498$	0.668682	+	1.31236i	0.0299644	+	0.0588084i
$499$	−1.27310	+	0.413655i	−0.0569917	+	0.0185177i	−0.337374	−	0.941371i	$-0.609539\pi$
$499$	−1.27310	+	0.413655i	−0.0569917	+	0.0185177i	0.280382	+	0.959888i	$0.409539\pi$
$500$	2.82036	+	10.8188i	0.126130	+	0.483830i
$501$	0.505172	+	0.695310i	0.0225694	+	0.0310641i
$502$	14.5019	+	7.38909i	0.647251	+	0.329791i
$503$	34.7508	−	17.7064i	1.54946	−	0.789490i	0.550489	−	0.834842i	$-0.314441\pi$
$503$	34.7508	−	17.7064i	1.54946	−	0.789490i	0.998971	+	0.0453526i	$0.0144411\pi$
$504$	5.76582	−	7.93597i	0.256830	−	0.353496i
$505$	11.3903	−	4.80453i	0.506862	−	0.213799i
$506$	−9.02427	+	4.27729i	−0.401178	+	0.190149i
$507$	−11.9674	−	11.9674i	−0.531493	−	0.531493i
$508$	2.58963	+	16.3503i	0.114896	+	0.725426i
$509$	15.4337	+	5.01473i	0.684089	+	0.222274i	0.630385	−	0.776283i	$-0.282897\pi$
$509$	15.4337	+	5.01473i	0.684089	+	0.222274i	0.0537041	+	0.998557i	$0.482897\pi$
$510$	10.0970	+	0.729000i	0.447105	+	0.0322807i
$511$	30.6600	−	22.2758i	1.35632	−	0.985422i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$	1.70863	−	3.35338i	0.0754379	−	0.148055i
$514$	−1.89259	+	5.82478i	−0.0834784	+	0.256920i
$515$	11.3812	+	18.3058i	0.501517	+	0.806648i
$516$		−	0.324998i		−	0.0143072i
$517$	30.7253	+	0.879805i	1.35130	+	0.0386938i
$518$	−16.5312	+	16.5312i	−0.726341	+	0.726341i
$519$	13.4125	+	9.74473i	0.588742	+	0.427746i
$520$	0.458889	+	5.38535i	0.0201236	+	0.236163i
$521$	−10.2283	−	31.4795i	−0.448110	−	1.37914i	−0.879037	−	0.476754i	$-0.841813\pi$
$521$	−10.2283	−	31.4795i	−0.448110	−	1.37914i	0.430927	−	0.902387i	$-0.358187\pi$
$522$	20.3473	+	3.22269i	0.890577	+	0.141054i
$523$	5.72096	+	0.906110i	0.250160	+	0.0396214i	0.280255	−	0.959926i	$-0.409581\pi$
$523$	5.72096	+	0.906110i	0.250160	+	0.0396214i	−0.0300950	+	0.999547i	$0.509581\pi$
$524$	−3.44398	−	10.5995i	−0.150451	−	0.463041i
$525$	−39.6120	+	20.8329i	−1.72881	+	0.909220i
$526$	5.42881	+	3.94426i	0.236707	+	0.171978i
$527$	−5.09875	+	5.09875i	−0.222105	+	0.222105i
$528$	−4.42619	−	6.47402i	−0.192625	−	0.281746i
$529$			13.9334i			0.605800i
$530$	2.80378	+	0.653985i	0.121788	+	0.0284073i
$531$	11.6665	−	35.9058i	0.506283	−	1.55818i
$532$	6.69265	−	13.1351i	0.290163	−	0.569477i
$533$	4.21427	−	26.6079i	0.182540	−	1.15251i
$534$	−5.62074	+	4.08371i	−0.243233	+	0.176719i
$535$	−0.996296	+	13.7992i	−0.0430736	+	0.596593i
$536$	−9.61486	−	3.12406i	−0.415299	−	0.134939i
$537$	2.03650	+	12.8579i	0.0878814	+	0.554861i
$538$	5.33846	+	5.33846i	0.230157	+	0.230157i
$539$	3.11435	+	24.1116i	0.134144	+	1.03856i
$540$	−2.00185	−	0.814069i	−0.0861457	−	0.0350319i
$541$	6.86569	−	9.44981i	0.295179	−	0.406279i	−0.635509	−	0.772094i	$-0.719210\pi$
$541$	6.86569	−	9.44981i	0.295179	−	0.406279i	0.930688	+	0.365815i	$0.119210\pi$
$542$	2.31410	−	1.17909i	0.0993992	−	0.0506464i
$543$	−16.5586	−	8.43705i	−0.710600	−	0.362069i
$544$	1.12539	+	1.54896i	0.0482505	+	0.0664111i
$545$	−1.78059	−	1.07537i	−0.0762722	−	0.0460640i
$546$	−20.5774	+	6.68599i	−0.880630	+	0.286134i
$547$	−8.31127	−	16.3118i	−0.355364	−	0.697442i	0.642249	−	0.766496i	$-0.278002\pi$
$547$	−8.31127	−	16.3118i	−0.355364	−	0.697442i	−0.997613	+	0.0690547i	$0.978002\pi$
$548$	5.51251	−	0.873096i	0.235483	−	0.0372968i
$549$	8.88297			0.379116
$550$	2.33678	+	16.4177i	0.0996408	+	0.700051i
$551$	30.9596			1.31892
$552$	7.03231	−	1.11381i	0.299315	−	0.0474068i
$553$	−6.82098	−	13.3869i	−0.290057	−	0.569270i
$554$	1.12019	−	0.363973i	0.0475925	−	0.0154637i
$555$	−27.9517	−	16.8812i	−1.18648	−	0.716567i
$556$	0.208692	+	0.287240i	0.00885051	+	0.0121817i
$557$	−24.2640	−	12.3631i	−1.02810	−	0.523843i	−0.143234	−	0.989689i	$-0.545750\pi$
$557$	−24.2640	−	12.3631i	−1.02810	−	0.523843i	−0.884866	+	0.465845i	$0.845750\pi$
$558$	−8.69545	+	4.43056i	−0.368108	+	0.187560i
$559$	−0.195273	+	0.268771i	−0.00825918	+	0.0113678i
$560$	−7.84116	−	3.18868i	−0.331350	−	0.134746i
$561$	14.7572	+	2.77244i	0.623047	+	0.117053i
$562$	−5.21711	−	5.21711i	−0.220071	−	0.220071i
$563$	−5.99604	−	37.8575i	−0.252703	−	1.59550i	−0.708692	−	0.705518i	$-0.750715\pi$
$563$	−5.99604	−	37.8575i	−0.252703	−	1.59550i	0.455990	−	0.889985i	$-0.349285\pi$
$564$	−20.8420	−	6.77199i	−0.877608	−	0.285152i
$565$	1.21907	−	16.8848i	0.0512868	−	0.710350i
$566$	22.6681	−	16.4693i	0.952810	−	0.692257i
$567$	5.95689	−	37.6103i	0.250166	−	1.57948i
$568$	5.65512	−	11.0988i	0.237283	−	0.465695i
$569$	11.5547	−	35.5616i	0.484397	−	1.49082i	−0.348454	−	0.937326i	$-0.613293\pi$
$569$	11.5547	−	35.5616i	0.484397	−	1.49082i	0.832852	−	0.553496i	$-0.186707\pi$
$570$	20.0521	+	4.67718i	0.839891	+	0.195906i
$571$			6.62261i			0.277148i	0.990352	+	0.138574i	$0.0442518\pi$
$571$			6.62261i			0.277148i	−0.990352	+	0.138574i	$0.955748\pi$
$572$	−0.229461	+	8.01343i	−0.00959423	+	0.335058i
$573$	−5.24034	+	5.24034i	−0.218918	+	0.218918i
$574$	34.1331	+	24.7991i	1.42469	+	1.03510i
$575$	−14.3775	−	4.46684i	−0.599583	−	0.186280i
$576$	0.800751	+	2.46446i	0.0333646	+	0.102686i
$577$	10.6777	+	1.69119i	0.444520	+	0.0704051i	0.374682	−	0.927153i	$-0.377752\pi$
$577$	10.6777	+	1.69119i	0.444520	+	0.0704051i	0.0698378	+	0.997558i	$0.477752\pi$
$578$	13.1701	+	2.08593i	0.547802	+	0.0867634i
$579$	−6.81814	−	20.9841i	−0.283352	−	0.872069i
$580$	−1.50932	−	17.7127i	−0.0626709	−	0.735482i
$581$	1.90767	+	1.38600i	0.0791433	+	0.0575010i
$582$	9.66469	−	9.66469i	0.400614	−	0.400614i
$583$	4.02187	+	1.43530i	0.166569	+	0.0594442i
$584$			10.0112i			0.414267i
$585$	−7.39493	−	11.8941i	−0.305743	−	0.491761i
$586$	3.61894	−	11.1379i	0.149497	−	0.460104i
$587$	−8.56193	+	16.8037i	−0.353389	+	0.693565i	−0.997447	−	0.0714120i	$-0.977249\pi$
$587$	−8.56193	+	16.8037i	−0.353389	+	0.693565i	0.644058	+	0.764977i	$0.277249\pi$
$588$	2.71150	−	17.1198i	0.111820	−	0.706007i
$589$	−11.8653	+	8.62063i	−0.488900	+	0.355207i
$590$	−32.4937	−	2.34603i	−1.33775	−	0.0965844i
$591$	−14.7705	−	4.79921i	−0.607575	−	0.197413i
$592$	−0.966107	−	6.09976i	−0.0397068	−	0.250699i
$593$	3.18852	+	3.18852i	0.130937	+	0.130937i	0.769538	−	0.638601i	$-0.220487\pi$
$593$	3.18852	+	3.18852i	0.130937	+	0.130937i	−0.638601	+	0.769538i	$0.720487\pi$
$594$	−2.81316	−	1.53634i	−0.115425	−	0.0630370i
$595$	14.9327	−	6.29872i	0.612179	−	0.258223i
$596$	10.3338	−	14.2232i	0.423287	−	0.582605i
$597$	−28.0953	+	14.3152i	−1.14986	+	0.585884i
$598$	−6.48490	−	3.30422i	−0.265187	−	0.135120i
$599$	17.2599	+	23.7562i	0.705220	+	0.970652i	0.999887	+	0.0150521i	$0.00479142\pi$
$599$	17.2599	+	23.7562i	0.705220	+	0.970652i	−0.294667	+	0.955600i	$0.595209\pi$
$600$	1.69837	−	11.7003i	0.0693355	−	0.477664i
$601$	−31.9450	+	10.3796i	−1.30306	+	0.423391i	−0.876646	−	0.481136i	$-0.840224\pi$
$601$	−31.9450	+	10.3796i	−1.30306	+	0.423391i	−0.426417	+	0.904527i	$0.640224\pi$
$602$	−0.236210	−	0.463589i	−0.00962721	−	0.0188945i
$603$	25.8745	−	4.09812i	1.05369	−	0.166888i
$604$	0.128122			0.00521320
$605$	0.682520	+	24.5873i	0.0277484	+	0.999615i
$606$	−13.0727			−0.531041
$607$	22.0445	−	3.49151i	0.894759	−	0.141716i	0.307913	−	0.951414i	$-0.400369\pi$
$607$	22.0445	−	3.49151i	0.894759	−	0.141716i	0.586846	+	0.809699i	$0.300369\pi$
$608$	1.76795	+	3.46980i	0.0716999	+	0.140719i
$609$	67.6802	−	21.9906i	2.74254	−	0.891105i
$610$	−1.83758	−	7.44176i	−0.0744013	−	0.301308i
$611$	13.1673	+	18.1232i	0.532692	+	0.733187i
$612$	−4.42057	−	2.25239i	−0.178691	−	0.0910476i
$613$	−24.8621	+	12.6679i	−1.00417	+	0.511651i	−0.877133	−	0.480247i	$-0.840547\pi$
$613$	−24.8621	+	12.6679i	−1.00417	+	0.511651i	−0.127038	+	0.991898i	$0.540547\pi$
$614$	−0.940132	+	1.29398i	−0.0379407	+	0.0522208i
$615$	−22.1988	+	54.5882i	−0.895141	+	2.20121i
$616$	−11.0190	−	6.01781i	−0.443970	−	0.242464i
$617$	−0.417706	−	0.417706i	−0.0168162	−	0.0168162i	0.698649	−	0.715465i	$-0.253785\pi$
$617$	−0.417706	−	0.417706i	−0.0168162	−	0.0168162i	−0.715465	+	0.698649i	$0.753785\pi$
$618$	−3.56581	−	22.5136i	−0.143438	−	0.905632i
$619$	−21.6610	−	7.03808i	−0.870628	−	0.282884i	−0.160568	−	0.987025i	$-0.551332\pi$
$619$	−21.6610	−	7.03808i	−0.870628	−	0.282884i	−0.710061	+	0.704141i	$0.751332\pi$
$620$	5.51051	+	6.36815i	0.221308	+	0.255751i
$621$	2.35428	−	1.71048i	0.0944740	−	0.0686394i
$622$	−1.10330	+	6.96595i	−0.0442383	+	0.279309i
$623$	−5.04957	+	9.91035i	−0.202307	+	0.397050i
$624$	1.76619	−	5.43578i	0.0707043	−	0.217605i
$625$	−14.1667	+	20.5987i	−0.566668	+	0.823946i
$626$			12.9738i			0.518537i
$627$	28.7637	+	10.2650i	1.14871	+	0.409946i
$628$	−8.81581	+	8.81581i	−0.351789	+	0.351789i
$629$	9.56606	+	6.95015i	0.381424	+	0.277121i
$630$	21.8553	−	1.86230i	0.870736	−	0.0741960i
$631$	9.23349	+	28.4178i	0.367580	+	1.13129i	0.948350	+	0.317226i	$0.102751\pi$
$631$	9.23349	+	28.4178i	0.367580	+	1.13129i	−0.580770	+	0.814067i	$0.697249\pi$
$632$	3.92005	+	0.620876i	0.155931	+	0.0246971i
$633$	49.0912	+	7.77529i	1.95120	+	0.309040i
$634$	−7.68998	−	23.6673i	−0.305408	−	0.939949i
$635$	−23.8575	+	28.3021i	−0.946757	+	1.12313i
$636$	−2.46307	−	1.78952i	−0.0976670	−	0.0709592i
$637$	−12.5287	+	12.5287i	−0.496406	+	0.496406i
$638$	0.754710	−	26.3566i	0.0298793	−	1.04347i
$639$			32.2782i			1.27691i
$640$	1.89897	−	1.18064i	0.0750633	−	0.0466691i
$641$	−3.25266	+	10.0107i	−0.128472	+	0.395397i	−0.994518	−	0.104568i	$-0.966654\pi$
$641$	−3.25266	+	10.0107i	−0.128472	+	0.395397i	0.866045	+	0.499965i	$0.166654\pi$
$642$	6.64204	−	13.0357i	0.262141	−	0.514480i
$643$	0.252761	−	1.59587i	0.00996791	−	0.0629349i	−0.982203	−	0.187823i	$-0.939857\pi$
$643$	0.252761	−	1.59587i	0.00996791	−	0.0629349i	0.992171	+	0.124888i	$0.0398570\pi$
$644$	9.22163	−	6.69991i	0.363383	−	0.264013i
$645$	0.549537	−	0.475528i	0.0216380	−	0.0187239i
$646$	−7.09109	−	2.30403i	−0.278995	−	0.0906510i
$647$	2.21420	+	13.9799i	0.0870492	+	0.549607i	0.992214	+	0.124546i	$0.0397474\pi$
$647$	2.21420	+	13.9799i	0.0870492	+	0.549607i	−0.905165	+	0.425061i	$0.860253\pi$
$648$	7.11286	+	7.11286i	0.279419	+	0.279419i
$649$	−47.4906	−	8.92211i	−1.86417	−	0.350223i
$650$	−8.43463	+	8.65563i	−0.330833	+	0.339502i
$651$	−19.8152	+	27.2733i	−0.776619	+	1.06892i
$652$	2.27318	−	1.15824i	0.0890246	−	0.0453603i
$653$	−35.1755	−	17.9228i	−1.37652	−	0.701374i	−0.399947	−	0.916538i	$-0.630971\pi$
$653$	−35.1755	−	17.9228i	−1.37652	−	0.701374i	−0.976578	+	0.215164i	$0.930971\pi$
$654$	1.29294	+	1.77958i	0.0505581	+	0.0695873i
$655$	12.8835	−	21.3323i	0.503399	−	0.833522i
$656$	−10.5998	+	3.44408i	−0.413852	+	0.134469i
$657$	−11.7774	−	23.1144i	−0.459479	−	0.901778i
$658$	−34.6518	+	5.48830i	−1.35087	+	0.213956i
$659$	24.5190			0.955123			0.477562	−	0.878598i	$-0.341521\pi$
$659$	24.5190			0.955123			0.477562	+	0.878598i	$0.341521\pi$
$660$	4.47061	−	16.9568i	0.174018	−	0.660044i
$661$	−48.3034			−1.87879			−0.939393	−	0.342843i	$-0.888610\pi$
$661$	−48.3034			−1.87879			−0.939393	+	0.342843i	$0.888610\pi$
$662$	−27.2811	+	4.32090i	−1.06031	+	0.167937i
$663$	4.96804	+	9.75033i	0.192943	+	0.378671i
$664$	−0.592411	+	0.192486i	−0.0229900	+	0.00746991i
$665$	32.0025	−	7.90231i	1.24100	−	0.306438i
$666$	9.40647	+	12.9469i	0.364493	+	0.501682i
$667$	21.3292	+	10.8678i	0.825871	+	0.420802i
$668$	−0.323851	+	0.165011i	−0.0125302	+	0.00638445i
$669$	−39.4170	+	54.2529i	−1.52395	+	2.09754i
$670$	−8.78576	−	20.8288i	−0.339423	−	0.804685i
$671$	−1.45643	−	11.2758i	−0.0562247	−	0.435297i
$672$	6.32949	+	6.32949i	0.244165	+	0.244165i
$673$	7.11215	+	44.9043i	0.274153	+	1.73093i	0.612991	+	0.790090i	$0.289966\pi$
$673$	7.11215	+	44.9043i	0.274153	+	1.73093i	−0.338838	+	0.940845i	$0.610034\pi$
$674$	26.1944	+	8.51107i	1.00897	+	0.327834i
$675$	−1.55254	−	4.57603i	−0.0597574	−	0.176132i
$676$	5.79053	−	4.20706i	0.222713	−	0.161810i
$677$	−5.72547	+	36.1492i	−0.220048	+	1.38933i	0.592095	+	0.805868i	$0.298301\pi$
$677$	−5.72547	+	36.1492i	−0.220048	+	1.38933i	−0.812142	+	0.583459i	$0.801699\pi$
$678$	−8.12724	+	15.9506i	−0.312125	+	0.612579i
$679$	6.76172	−	20.8104i	0.259491	−	0.798631i
$680$	−0.972495	+	4.16931i	−0.0372935	+	0.159886i
$681$		−	1.97043i		−	0.0755071i
$682$	7.04970	+	10.3113i	0.269947	+	0.394841i
$683$	−2.98080	+	2.98080i	−0.114057	+	0.114057i	−0.761832	−	0.647775i	$-0.775700\pi$
$683$	−2.98080	+	2.98080i	−0.114057	+	0.114057i	0.647775	+	0.761832i	$0.275700\pi$
$684$	−8.16388	−	5.93140i	−0.312154	−	0.226793i
$685$	9.54207	+	8.04359i	0.364584	+	0.307330i
$686$	−0.386385	−	1.18917i	−0.0147522	−	0.0454027i
$687$	1.49306	+	0.236477i	0.0569636	+	0.00902216i
$688$	0.135751	+	0.0215009i	0.00517547	+	0.000819715i
$689$	0.961712	+	2.95985i	0.0366383	+	0.112761i
$690$	12.1728	+	10.2612i	0.463411	+	0.390637i
$691$	26.6374	+	19.3532i	1.01333	+	0.736230i	0.964906	−	0.262597i	$-0.0845789\pi$
$691$	26.6374	+	19.3532i	1.01333	+	0.736230i	0.0484278	+	0.998827i	$0.484579\pi$
$692$	−4.95770	+	4.95770i	−0.188464	+	0.188464i
$693$	32.5208	+	0.931217i	1.23536	+	0.0353740i
$694$		−	19.4039i		−	0.736563i
$695$	−0.180340	+	0.773158i	−0.00684068	+	0.0293275i
$696$	−5.80911	+	17.8786i	−0.220194	+	0.677687i
$697$	9.68768	−	19.0131i	0.366947	−	0.720174i
$698$	−5.22739	+	33.0044i	−0.197860	+	1.24924i
$699$	−29.9392	+	21.7521i	−1.13240	+	0.822739i
$700$	−6.08126	−	17.9242i	−0.229850	−	0.677470i
$701$	13.3104	+	4.32482i	0.502728	+	0.163346i	0.549392	−	0.835565i	$-0.314859\pi$
$701$	13.3104	+	4.32482i	0.502728	+	0.163346i	−0.0466648	+	0.998911i	$0.514859\pi$
$702$	−0.365435	−	2.30727i	−0.0137925	−	0.0870822i
$703$	17.0060	+	17.0060i	0.641393	+	0.641393i
$704$	2.99702	−	1.42052i	0.112954	−	0.0535377i
$705$	−19.0448	−	45.1503i	−0.717268	−	1.70046i
$706$	−20.0946	+	27.6579i	−0.756272	+	1.04092i
$707$	−18.6474	+	9.50131i	−0.701306	+	0.357333i
$708$	30.6959	+	15.6403i	1.15362	+	0.587800i
$709$	−30.3403	−	41.7598i	−1.13945	−	1.56832i	−0.768723	−	0.639582i	$-0.779107\pi$
$709$	−30.3403	−	41.7598i	−1.13945	−	1.56832i	−0.370730	−	0.928741i	$-0.620893\pi$
$710$	27.0413	−	6.67725i	1.01484	−	0.250593i
$711$	−9.78123	+	3.17811i	−0.366825	+	0.119189i
$712$	−1.33391	−	2.61795i	−0.0499905	−	0.0981118i
$713$	−11.2005	+	1.77399i	−0.419463	+	0.0664365i
$714$	−17.1382			−0.641382
$715$	−13.8856	+	11.3370i	−0.519292	+	0.423981i
$716$	−5.50549			−0.205750
$717$	16.8058	−	2.66178i	0.627626	−	0.0994061i
$718$	4.74961	+	9.32164i	0.177254	+	0.347881i
$719$	−25.2857	+	8.21582i	−0.942997	+	0.306398i	−0.739867	−	0.672753i	$-0.765111\pi$
$719$	−25.2857	+	8.21582i	−0.942997	+	0.306398i	−0.203130	+	0.979152i	$0.565111\pi$
$720$	−2.99550	+	4.95991i	−0.111636	+	0.184845i
$721$	−21.4495	−	29.5227i	−0.798820	−	1.09948i
$722$	3.41685	+	1.74097i	0.127162	+	0.0647922i
$723$	−31.8895	+	16.2485i	−1.18598	+	0.604289i
$724$	4.61963	−	6.35837i	0.171687	−	0.236307i
$725$	27.7420	−	28.4689i	1.03031	−	1.05731i
$726$	9.44004	−	24.2370i	0.350353	−	0.899518i
$727$	−7.00349	−	7.00349i	−0.259745	−	0.259745i	0.565205	−	0.824950i	$-0.308797\pi$
$727$	−7.00349	−	7.00349i	−0.259745	−	0.259745i	−0.824950	+	0.565205i	$0.808797\pi$
$728$	−1.43140	−	9.03748i	−0.0530511	−	0.334951i
$729$	−18.2700	−	5.93629i	−0.676667	−	0.219863i
$730$	−16.9279	+	14.6481i	−0.626529	+	0.542151i
$731$	−0.212895	+	0.154677i	−0.00787419	+	0.00572094i
$732$	−1.26804	+	8.00606i	−0.0468679	+	0.295912i
$733$	16.8229	−	33.0168i	0.621368	−	1.21950i	−0.339005	−	0.940785i	$-0.610090\pi$
$733$	16.8229	−	33.0168i	0.621368	−	1.21950i	0.960373	−	0.278719i	$-0.0899097\pi$
$734$	−9.35438	+	28.7898i	−0.345276	+	1.06265i
$735$	32.9151	−	20.4643i	1.21409	−	0.754837i
$736$			3.01108i			0.110990i
$737$	−9.44434	−	32.1724i	−0.347887	−	1.18509i
$738$	20.4216	−	20.4216i	0.751730	−	0.751730i
$739$	−7.51881	−	5.46274i	−0.276584	−	0.200950i	0.440842	−	0.897585i	$-0.354680\pi$
$739$	−7.51881	−	5.46274i	−0.276584	−	0.200950i	−0.717426	+	0.696635i	$0.754680\pi$
$740$	8.90047	−	10.5586i	0.327188	−	0.388142i
$741$	6.87800	+	21.1683i	0.252669	+	0.777637i
$742$	−4.81405	−	0.762470i	−0.176729	−	0.0279912i
$743$	−38.2835	−	6.06352i	−1.40449	−	0.222449i	−0.592239	−	0.805762i	$-0.701756\pi$
$743$	−38.2835	−	6.06352i	−1.40449	−	0.222449i	−0.812247	+	0.583313i	$0.801756\pi$
$744$	−2.75191	−	8.46952i	−0.100890	−	0.310507i
$745$	39.1700	−	3.33770i	1.43508	−	0.122284i
$746$	−13.8311	−	10.0489i	−0.506392	−	0.367915i
$747$	1.14135	−	1.14135i	0.0417596	−	0.0417596i
$748$	−2.13434	+	5.98064i	−0.0780392	+	0.218674i
$749$		−	23.4222i		−	0.855827i
$750$	22.2690	−	14.2478i	0.813150	−	0.520258i
$751$	4.09184	−	12.5934i	0.149313	−	0.459539i	−0.848227	−	0.529633i	$-0.822330\pi$
$751$	4.09184	−	12.5934i	0.149313	−	0.459539i	0.997540	+	0.0700937i	$0.0223298\pi$
$752$	4.20751	−	8.25770i	0.153432	−	0.301127i
$753$	6.02049	−	38.0119i	0.219399	−	1.38523i
$754$	15.5464	−	11.2951i	0.566166	−	0.411344i
$755$	0.187464	+	0.216640i	0.00682253	+	0.00788435i
$756$	3.47946	+	1.13055i	0.126547	+	0.0411175i
$757$	−0.0635739	−	0.401390i	−0.00231063	−	0.0145888i	0.986506	−	0.163725i	$-0.0523508\pi$
$757$	−0.0635739	−	0.401390i	−0.00231063	−	0.0145888i	−0.988817	+	0.149136i	$0.952351\pi$
$758$	−2.73335	−	2.73335i	−0.0992797	−	0.0992797i
$759$	16.2130	+	17.1689i	0.588496	+	0.623192i
$760$	−3.28025	+	8.06634i	−0.118987	+	0.292597i
$761$	−13.8009	+	18.9953i	−0.500281	+	0.688577i	−0.982243	−	0.187615i	$-0.939924\pi$
$761$	−13.8009	+	18.9953i	−0.500281	+	0.688577i	0.481962	+	0.876192i	$0.339924\pi$
$762$	34.8772	−	17.7708i	1.26347	−	0.643769i
$763$	3.13772	+	1.59875i	0.113593	+	0.0578785i
$764$	−1.84220	−	2.53557i	−0.0666486	−	0.0917339i
$765$	−2.65950	−	10.7704i	−0.0961545	−	0.389403i
$766$	3.47473	−	1.12901i	0.125547	−	0.0407927i
$767$	−15.9879	−	31.3779i	−0.577288	−	1.13299i
$768$	−2.33548	+	0.369903i	−0.0842743	+	0.0133477i
$769$	−23.6278			−0.852040			−0.426020	−	0.904714i	$-0.640085\pi$
$769$	−23.6278			−0.852040			−0.426020	+	0.904714i	$0.640085\pi$
$770$	−5.94729	−	27.4371i	−0.214325	−	0.988766i
$771$	14.4820			0.521557
$772$	9.21611	−	1.45969i	0.331695	−	0.0525354i
$773$	−2.54428	−	4.99343i	−0.0915114	−	0.179601i	0.840714	−	0.541479i	$-0.182136\pi$
$773$	−2.54428	−	4.99343i	−0.0915114	−	0.179601i	−0.932225	+	0.361878i	$0.882136\pi$
$774$	−0.338724	+	0.110058i	−0.0121752	+	0.00395595i
$775$	−2.70503	+	18.6354i	−0.0971675	+	0.669403i
$776$	3.39755	+	4.67633i	0.121965	+	0.167870i
$777$	49.2558	+	25.0971i	1.76704	+	0.900353i
$778$	−14.3192	+	7.29601i	−0.513369	+	0.261575i
$779$	25.5113	−	35.1133i	0.914038	−	1.25806i
$780$	11.7756	−	4.96704i	0.421633	−	0.177849i
$781$	40.9731	−	5.29225i	1.46613	−	0.189372i
$782$	−4.07652	−	4.07652i	−0.145776	−	0.145776i
$783$	1.20194	+	7.58874i	0.0429538	+	0.271199i
$784$	6.97153	+	2.26519i	0.248983	+	0.0808996i
$785$	−27.8057	−	2.00755i	−0.992427	−	0.0716526i
$786$	−21.3202	+	15.4901i	−0.760467	+	0.552512i
$787$	2.55027	−	16.1018i	0.0909074	−	0.573966i	−0.899622	−	0.436669i	$-0.856158\pi$
$787$	2.55027	−	16.1018i	0.0909074	−	0.573966i	0.990530	−	0.137298i	$-0.0438418\pi$
$788$	2.98180	−	5.85211i	0.106222	−	0.208473i
$789$	4.90326	−	15.0907i	0.174561	−	0.537242i
$790$	4.68588	+	7.53685i	0.166716	+	0.268149i
$791$			28.6595i			1.01901i
$792$	−5.24855	+	6.80551i	−0.186499	+	0.241823i
$793$	5.85906	−	5.85906i	0.208061	−	0.208061i
$794$	0.814663	+	0.591887i	0.0289113	+	0.0210053i
$795$	−0.577999	−	6.78317i	−0.0204995	−	0.240574i
$796$	−4.12077	−	12.6824i	−0.146057	−	0.449517i
$797$	17.8602	+	2.82878i	0.632641	+	0.100200i	0.464515	−	0.885565i	$-0.346229\pi$
$797$	17.8602	+	2.82878i	0.632641	+	0.100200i	0.168126	+	0.985766i	$0.446229\pi$
$798$	−34.4292	−	5.45305i	−1.21878	−	0.193036i
$799$	5.48331	+	16.8759i	0.193986	+	0.597027i
$800$	4.77486	+	1.48347i	0.168817	+	0.0524485i
$801$	6.15961	+	4.47522i	0.217639	+	0.158124i
$802$	−21.9671	+	21.9671i	−0.775684	+	0.775684i
$803$	−27.4097	+	18.7396i	−0.967268	+	0.661306i
$804$			23.9052i			0.843072i
$805$	24.8217	+	5.78968i	0.874849	+	0.204060i
$806$	−2.81306	+	8.65770i	−0.0990858	+	0.304955i
$807$	8.10463	−	15.9062i	0.285296	−	0.559926i
$808$	0.864851	−	5.46046i	0.0304254	−	0.192098i
$809$	−39.0029	+	28.3373i	−1.37127	+	0.996285i	−0.373632	+	0.927577i	$0.621888\pi$
$809$	−39.0029	+	28.3373i	−1.37127	+	0.996285i	−0.997637	+	0.0687081i	$0.978112\pi$
$810$	−1.61975	+	22.4344i	−0.0569123	+	0.788266i
$811$	18.0347	+	5.85984i	0.633285	+	0.205767i	0.608030	−	0.793914i	$-0.291960\pi$
$811$	18.0347	+	5.85984i	0.633285	+	0.205767i	0.0252553	+	0.999681i	$0.491960\pi$
$812$	4.70795	+	29.7248i	0.165217	+	1.04314i
$813$	−4.34252	−	4.34252i	−0.152299	−	0.152299i
$814$	14.8922	−	14.0630i	0.521970	−	0.492909i
$815$	5.28452	+	2.14900i	0.185109	+	0.0752761i
$816$	2.66107	−	3.66266i	0.0931563	−	0.128219i
$817$	−0.476902	+	0.242994i	−0.0166847	+	0.00850127i
$818$	−3.41205	−	1.73853i	−0.119300	−	0.0607861i
$819$	13.9367	+	19.1823i	0.486989	+	0.670283i
$820$	−21.3329	−	12.8838i	−0.744976	−	0.449923i
$821$	41.1233	−	13.3618i	1.43521	−	0.466329i	0.514812	−	0.857303i	$-0.327862\pi$
$821$	41.1233	−	13.3618i	1.43521	−	0.466329i	0.920402	+	0.390974i	$0.127862\pi$
$822$	−5.99145	−	11.7589i	−0.208976	−	0.410138i
$823$	−33.7267	+	5.34178i	−1.17564	+	0.186203i	−0.713533	−	0.700622i	$-0.752906\pi$
$823$	−33.7267	+	5.34178i	−1.17564	+	0.186203i	−0.462106	+	0.886825i	$0.652906\pi$
$824$	9.63985			0.335820
$825$	35.2135	−	17.2515i	1.22598	−	0.600618i
$826$	55.1533			1.91903
$827$	23.1114	−	3.66049i	0.803663	−	0.127288i	0.258929	−	0.965896i	$-0.416631\pi$
$827$	23.1114	−	3.66049i	0.803663	−	0.127288i	0.544734	+	0.838609i	$0.316631\pi$
$828$	−3.54229	−	6.95214i	−0.123103	−	0.241603i
$829$	−5.46037	+	1.77418i	−0.189647	+	0.0616199i	−0.402301	−	0.915508i	$-0.631789\pi$
$829$	−5.46037	+	1.77418i	−0.189647	+	0.0616199i	0.212654	+	0.977128i	$0.431789\pi$
$830$	−1.19227	−	0.720065i	−0.0413844	−	0.0249938i
$831$	−1.63705	−	2.25320i	−0.0567886	−	0.0781628i
$832$	2.15368	+	1.09735i	0.0746654	+	0.0380439i
$833$	−12.5050	+	6.37164i	−0.433274	+	0.220764i
$834$	0.493471	−	0.679204i	0.0170875	−	0.0235189i
$835$	−0.752866	−	0.306160i	−0.0260540	−	0.0105951i
$836$	−6.19062	+	11.3355i	−0.214107	+	0.392046i
$837$	−2.57371	−	2.57371i	−0.0889604	−	0.0889604i
$838$	−4.05836	−	25.6235i	−0.140194	−	0.885149i
$839$	31.4060	+	10.2044i	1.08425	+	0.352296i	0.796024	−	0.605265i	$-0.206933\pi$
$839$	31.4060	+	10.2044i	1.08425	+	0.352296i	0.288231	+	0.957561i	$0.406933\pi$
$840$	−1.44136	+	19.9636i	−0.0497317	+	0.688811i
$841$	−27.6715	+	20.1045i	−0.954190	+	0.693260i
$842$	−3.68257	+	23.2508i	−0.126910	+	0.801276i
$843$	−7.92041	+	15.5447i	−0.272793	+	0.535387i
$844$	−6.49547	+	19.9910i	−0.223583	+	0.688119i
$845$	15.5862	+	3.63551i	0.536183	+	0.125065i
$846$			24.0156i			0.825672i
$847$	−4.14996	−	41.4336i	−0.142594	−	1.42368i
$848$	0.910433	−	0.910433i	0.0312644	−	0.0312644i
$849$	−53.6007	−	38.9432i	−1.83957	−	1.33653i
$850$	−8.47278	+	4.45603i	−0.290614	+	0.152841i
$851$	5.74643	+	17.6857i	0.196985	+	0.606257i
$852$	−29.0918	−	4.60769i	−0.996668	−	0.157857i
$853$	−13.6706	−	2.16521i	−0.468071	−	0.0741352i	−0.0820564	−	0.996628i	$-0.526149\pi$
$853$	−13.6706	−	2.16521i	−0.468071	−	0.0741352i	−0.386015	+	0.922492i	$0.626149\pi$
$854$	4.01008	+	12.3418i	0.137222	+	0.422326i
$855$	−1.91579	−	22.4829i	−0.0655185	−	0.768900i
$856$	5.00561	+	3.63679i	0.171088	+	0.124303i
$857$	14.0941	−	14.0941i	0.481446	−	0.481446i	−0.424147	−	0.905593i	$-0.639426\pi$
$857$	14.0941	−	14.0941i	0.481446	−	0.481446i	0.905593	+	0.424147i	$0.139426\pi$
$858$	18.1887	−	5.33937i	0.620953	−	0.182283i
$859$			15.9608i			0.544576i	0.962216	+	0.272288i	$0.0877803\pi$
$859$			15.9608i			0.544576i	−0.962216	+	0.272288i	$0.912220\pi$
$860$	0.162272	+	0.261001i	0.00553343	+	0.00890006i
$861$	30.8288	−	94.8812i	1.05064	−	3.23354i
$862$	3.61598	−	7.09675i	0.123161	−	0.241716i
$863$	2.96283	−	18.7066i	0.100856	−	0.636779i	−0.884535	−	0.466473i	$-0.845524\pi$
$863$	2.96283	−	18.7066i	0.100856	−	0.636779i	0.985391	−	0.170306i	$-0.0544756\pi$
$864$	−0.781872	+	0.568063i	−0.0265998	+	0.0193259i
$865$	−15.6369	−	1.12898i	−0.531672	−	0.0383863i
$866$	36.4355	+	11.8386i	1.23813	+	0.402293i
$867$	−4.93238	−	31.1418i	−0.167512	−	1.05763i
$868$	−10.0811	−	10.0811i	−0.342176	−	0.342176i
$869$	5.63791	+	11.8949i	0.191253	+	0.403508i
$870$	−38.7306	+	16.3369i	−1.31309	+	0.553873i
$871$	14.3633	−	19.7694i	0.486683	−	0.669862i
$872$	−0.828870	+	0.422330i	−0.0280691	+	0.0143019i
$873$	−13.3457	−	6.80000i	−0.451685	−	0.230145i
$874$	−6.89231	−	9.48645i	−0.233136	−	0.320884i
$875$	21.4099	−	36.5089i	0.723788	−	1.23423i
$876$	22.5138	−	7.31517i	0.760670	−	0.247157i
$877$	11.6388	+	22.8424i	0.393014	+	0.771333i	0.999722	−	0.0235918i	$-0.00751018\pi$
$877$	11.6388	+	22.8424i	0.393014	+	0.771333i	−0.606708	+	0.794925i	$0.707510\pi$
$878$	25.8240	−	4.09012i	0.871517	−	0.138035i
$879$	−27.6920			−0.934028
$880$	6.78710	+	2.98919i	0.228793	+	0.100766i
$881$	−37.2681			−1.25559			−0.627797	−	0.778377i	$-0.716043\pi$
$881$	−37.2681			−1.25559			−0.627797	+	0.778377i	$0.716043\pi$
$882$	−18.7610	+	2.97146i	−0.631717	+	0.100054i
$883$	−1.66521	−	3.26816i	−0.0560388	−	0.109982i	0.861289	−	0.508116i	$-0.169658\pi$
$883$	−1.66521	−	3.26816i	−0.0560388	−	0.109982i	−0.917327	+	0.398134i	$0.869658\pi$
$884$	−4.40138	+	1.43010i	−0.148034	+	0.0480993i
$885$	18.4672	+	74.7880i	0.620769	+	2.51397i
$886$	5.35247	+	7.36705i	0.179820	+	0.247501i
$887$	5.37918	+	2.74083i	0.180615	+	0.0920280i	0.541960	−	0.840404i	$-0.317682\pi$
$887$	5.37918	+	2.74083i	0.180615	+	0.0920280i	−0.361345	+	0.932432i	$0.617682\pi$
$888$	−13.0116	+	6.62972i	−0.436640	+	0.222479i
$889$	36.8342	−	50.6980i	1.23538	−	1.70036i
$890$	2.47493	−	6.08602i	0.0829599	−	0.204004i
$891$	−6.16003	+	32.7886i	−0.206369	+	1.09846i
$892$	−20.0537	−	20.0537i	−0.671447	−	0.671447i
$893$	5.64591	+	35.6469i	0.188933	+	1.19288i
$894$	−39.5368	−	12.8463i	−1.32231	−	0.429644i
$895$	−8.05548	−	9.30920i	−0.269265	−	0.311172i
$896$	−3.06256	+	2.22508i	−0.102313	+	0.0743348i
$897$	−2.69222	+	16.9980i	−0.0898906	+	0.567547i
$898$	2.03486	−	3.99364i	0.0679042	−	0.133270i
$899$	9.25232	−	28.4757i	0.308582	−	0.949718i
$900$	−12.7696	+	2.19213i	−0.425654	+	0.0730711i
$901$			2.46516i			0.0821265i
$902$	−29.2709	−	22.5743i	−0.974614	−	0.751643i
$903$	−0.869947	+	0.869947i	−0.0289500	+	0.0289500i
$904$	−6.12489	−	4.44999i	−0.203711	−	0.148004i
$905$	17.5106	−	1.49209i	0.582074	−	0.0495989i
$906$	−0.0936184	−	0.288128i	−0.00311026	−	0.00957240i
$907$	−40.7763	−	6.45833i	−1.35396	−	0.214445i	−0.563070	−	0.826409i	$-0.690380\pi$
$907$	−40.7763	−	6.45833i	−1.35396	−	0.214445i	−0.790886	+	0.611964i	$0.790380\pi$
$908$	0.823048	+	0.130358i	0.0273138	+	0.00432608i
$909$	4.42697	+	13.6248i	0.146833	+	0.451906i
$910$	13.1871	−	15.6437i	0.437147	−	0.518585i
$911$	−42.3267	−	30.7522i	−1.40235	−	1.01887i	−0.994380	−	0.105869i	$-0.966238\pi$
$911$	−42.3267	−	30.7522i	−1.40235	−	1.01887i	−0.407967	−	0.912997i	$-0.633762\pi$
$912$	6.51125	−	6.51125i	0.215609	−	0.215609i
$913$	−1.63592	−	1.26166i	−0.0541411	−	0.0417548i
$914$			5.27189i			0.174379i
$915$	−15.3928	+	9.57014i	−0.508869	+	0.316379i
$916$	−0.197553	+	0.608004i	−0.00652732	+	0.0200890i
$917$	−19.1537	+	37.5913i	−0.632511	+	1.24137i
$918$	0.289463	−	1.82760i	0.00955370	−	0.0603197i
$919$	−6.74707	+	4.90203i	−0.222565	+	0.161703i	−0.693481	−	0.720475i	$-0.743924\pi$
$919$	−6.74707	+	4.90203i	−0.222565	+	0.161703i	0.470915	+	0.882178i	$0.343924\pi$
$920$	−5.09142	+	4.40573i	−0.167859	+	0.145253i
$921$	3.59693	+	1.16871i	0.118523	+	0.0385104i
$922$	0.177778	+	1.12244i	0.00585479	+	0.0369657i
$923$	21.2902	+	21.2902i	0.700776	+	0.700776i
$924$	−5.48160	+	29.1775i	−0.180331	+	0.959868i
$925$	30.8764	−	0.399287i	1.01521	−	0.0131285i
$926$	−10.7120	+	14.7437i	−0.352017	+	0.484509i
$927$	−22.2570	+	11.3405i	−0.731015	+	0.372471i
$928$	−7.08358	−	3.60926i	−0.232530	−	0.118480i
$929$	15.6662	+	21.5626i	0.513990	+	0.707447i	0.984586	−	0.174902i	$-0.0559610\pi$
$929$	15.6662	+	21.5626i	0.513990	+	0.707447i	−0.470596	+	0.882349i	$0.655961\pi$
$930$	10.2945	−	17.0456i	0.337571	−	0.558946i
$931$	−27.1489	+	8.82121i	−0.889769	+	0.289103i
$932$	−7.10514	−	13.9446i	−0.232737	−	0.456772i
$933$	16.4716	−	2.60885i	0.539257	−	0.0854099i
$934$	9.50708			0.311081
$935$	−13.2355	+	5.14177i	−0.432849	+	0.168154i
$936$	−6.26347			−0.204728
$937$	41.1341	−	6.51500i	1.34379	−	0.212836i	0.557236	−	0.830354i	$-0.311862\pi$
$937$	41.1341	−	6.51500i	1.34379	−	0.212836i	0.786557	+	0.617518i	$0.211862\pi$
$938$	17.3745	+	34.0993i	0.567296	+	1.11338i
$939$	29.1762	−	9.47993i	0.952130	−	0.309366i
$940$	20.1192	−	4.96799i	0.656216	−	0.162038i
$941$	27.5497	+	37.9190i	0.898096	+	1.23612i	0.971072	+	0.238789i	$0.0767504\pi$
$941$	27.5497	+	37.9190i	0.898096	+	1.23612i	−0.0729759	+	0.997334i	$0.523250\pi$
$942$	26.2672	+	13.3838i	0.855832	+	0.436068i
$943$	29.9015	−	15.2356i	0.973728	−	0.496139i
$944$	−8.56372	+	11.7869i	−0.278725	+	0.383632i
$945$	3.17942	+	7.53758i	0.103427	+	0.245198i
$946$	0.195241	+	0.411921i	0.00634782	+	0.0133927i
$947$	−7.34005	−	7.34005i	−0.238519	−	0.238519i	0.577717	−	0.816237i	$-0.303944\pi$
$947$	−7.34005	−	7.34005i	−0.238519	−	0.238519i	−0.816237	+	0.577717i	$0.803944\pi$
$948$	−1.46812	−	9.26932i	−0.0476822	−	0.301054i
$949$	−23.0140	−	7.47771i	−0.747067	−	0.242737i
$950$	−18.4389	+	6.25590i	−0.598237	+	0.202968i
$951$	−47.6054	+	34.5873i	−1.54371	+	1.12157i
$952$	1.13382	−	7.15864i	0.0367472	−	0.232013i
$953$	17.4051	−	34.1594i	0.563806	−	1.10653i	−0.416517	−	0.909128i	$-0.636749\pi$
$953$	17.4051	−	34.1594i	0.563806	−	1.10653i	0.980322	−	0.197403i	$-0.0632507\pi$
$954$	−1.03100	+	3.17310i	−0.0333800	+	0.102733i
$955$	1.59193	−	6.82495i	0.0515136	−	0.220850i
$956$			7.19589i			0.232732i
$957$	−59.8238	+	17.5615i	−1.93383	+	0.567683i
$958$	13.9822	−	13.9822i	0.451743	−	0.451743i
$959$	−17.0929	−	12.4187i	−0.551957	−	0.401021i
$960$	−4.04268	−	3.40781i	−0.130477	−	0.109987i
$961$	−5.19649	−	15.9931i	−0.167629	−	0.515908i
$962$	14.7439	+	2.33521i	0.475363	+	0.0752901i
$963$	−15.8356	−	2.50811i	−0.510295	−	0.0808227i
$964$	−4.67729	−	14.3952i	−0.150645	−	0.463638i
$965$	15.9529	+	13.4477i	0.513544	+	0.432897i
$966$	−21.8054	−	15.8425i	−0.701576	−	0.509725i
$967$	−32.4979	+	32.4979i	−1.04506	+	1.04506i	−0.0461256	+	0.998936i	$0.514687\pi$
$967$	−32.4979	+	32.4979i	−1.04506	+	1.04506i	−0.998936	+	0.0461256i	$0.985313\pi$
$968$	9.49925	+	5.54655i	0.305317	+	0.178273i
$969$			17.6304i			0.566370i
$970$	−2.93597	+	12.5872i	−0.0942684	+	0.404150i
$971$	−5.30721	+	16.3339i	−0.170316	+	0.524180i	−0.999389	−	0.0349616i	$-0.988869\pi$
$971$	−5.30721	+	16.3339i	−0.170316	+	0.524180i	0.829072	+	0.559141i	$0.188869\pi$
$972$	9.48218	−	18.6098i	0.304141	−	0.596911i
$973$	0.210255	−	1.32750i	0.00674048	−	0.0425577i
$974$	3.46466	−	2.51722i	0.111015	−	0.0806571i
$975$	25.6285	+	12.6436i	0.820768	+	0.404920i
$976$	−3.26024	−	1.05932i	−0.104358	−	0.0339079i
$977$	−0.384764	−	2.42931i	−0.0123097	−	0.0777204i	0.980769	−	0.195174i	$-0.0625270\pi$
$977$	−0.384764	−	2.42931i	−0.0123097	−	0.0777204i	−0.993078	+	0.117453i	$0.962527\pi$
$978$	−4.26573	−	4.26573i	−0.136403	−	0.136403i
$979$	4.67080	−	8.55257i	0.149279	−	0.273341i
$980$	6.37036	+	15.1025i	0.203494	+	0.482431i
$981$	1.41690	−	1.95019i	0.0452381	−	0.0622649i
$982$	−8.13911	+	4.14708i	−0.259729	+	0.132339i
$983$	−9.83630	−	5.01184i	−0.313729	−	0.159853i	0.290035	−	0.957016i	$-0.406333\pi$
$983$	−9.83630	−	5.01184i	−0.313729	−	0.159853i	−0.603764	+	0.797163i	$0.706333\pi$
$984$	15.4905	+	21.3208i	0.493818	+	0.679683i
$985$	14.2582	−	3.52074i	0.454304	−	0.112180i
$986$	14.4764	−	4.70367i	0.461023	−	0.149795i
$987$	37.6624	+	73.9167i	1.19881	+	2.35279i
$988$	−9.29702	+	1.47250i	−0.295778	+	0.0468466i
$989$	−0.413854			−0.0131598
$990$	−19.1869	+	1.08288i	−0.609801	+	0.0344162i
$991$	29.5223			0.937807			0.468903	−	0.883250i	$-0.344649\pi$
$991$	29.5223			0.937807			0.468903	+	0.883250i	$0.344649\pi$
$992$	3.71977	−	0.589154i	0.118103	−	0.0187057i
$993$	29.6514	+	58.1941i	0.940958	+	1.84673i
$994$	−44.8465	+	14.5715i	−1.42245	+	0.462181i
$995$	15.4153	−	25.5244i	0.488697	−	0.809178i
$996$	0.865748	+	1.19160i	0.0274323	+	0.0377573i
$997$	−54.1640	−	27.5979i	−1.71539	−	0.874036i	−0.980671	−	0.195666i	$-0.937313\pi$
$997$	−54.1640	−	27.5979i	−1.71539	−	0.874036i	−0.734721	−	0.678370i	$-0.762687\pi$
$998$	−1.19271	+	0.607718i	−0.0377547	+	0.0192370i
$999$	−3.50824	+	4.82868i	−0.110996	+	0.152773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.7.4	✓	48
3.2	odd	2		990.2.bh.c.667.1		48
4.3	odd	2		880.2.cm.c.337.5		48
5.2	odd	4		550.2.bh.b.293.4		48
5.3	odd	4	inner	110.2.k.a.73.3	yes	48
5.4	even	2		550.2.bh.b.7.3		48
11.8	odd	10	inner	110.2.k.a.107.3	yes	48
15.8	even	4		990.2.bh.c.73.6		48
20.3	even	4		880.2.cm.c.513.2		48
33.8	even	10		990.2.bh.c.217.6		48
44.19	even	10		880.2.cm.c.657.2		48
55.8	even	20	inner	110.2.k.a.63.4	yes	48
55.19	odd	10		550.2.bh.b.107.4		48
55.52	even	20		550.2.bh.b.393.3		48
165.8	odd	20		990.2.bh.c.613.1		48
220.63	odd	20		880.2.cm.c.833.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.4	✓	48	1.1	even	1	trivial
110.2.k.a.63.4	yes	48	55.8	even	20	inner
110.2.k.a.73.3	yes	48	5.3	odd	4	inner
110.2.k.a.107.3	yes	48	11.8	odd	10	inner
550.2.bh.b.7.3		48	5.4	even	2
550.2.bh.b.107.4		48	55.19	odd	10
550.2.bh.b.293.4		48	5.2	odd	4
550.2.bh.b.393.3		48	55.52	even	20
880.2.cm.c.337.5		48	4.3	odd	2
880.2.cm.c.513.2		48	20.3	even	4
880.2.cm.c.657.2		48	44.19	even	10
880.2.cm.c.833.5		48	220.63	odd	20
990.2.bh.c.73.6		48	15.8	even	4
990.2.bh.c.217.6		48	33.8	even	10
990.2.bh.c.613.1		48	165.8	odd	20
990.2.bh.c.667.1		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 - 0.156434i) q^{2} +(-1.07350 - 2.10686i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.91408 + 1.15599i) q^{5} +(-1.38987 - 1.91299i) q^{6} +(-3.37294 - 1.71860i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-1.52312 + 2.09639i) q^{9} +O(q^{10})\)	\(q+(0.987688 - 0.156434i) q^{2} +(-1.07350 - 2.10686i) q^{3} +(0.951057 - 0.309017i) q^{4} +(1.91408 + 1.15599i) q^{5} +(-1.38987 - 1.91299i) q^{6} +(-3.37294 - 1.71860i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-1.52312 + 2.09639i) q^{9} +(2.07135 + 0.842332i) q^{10} +(2.91083 + 1.58968i) q^{11} +(-1.67202 - 1.67202i) q^{12} +(0.378122 + 2.38737i) q^{13} +(-3.60026 - 1.16980i) q^{14} +(0.380754 - 5.27366i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-0.299513 + 1.89105i) q^{17} +(-1.17642 + 2.30885i) q^{18} +(-1.20339 + 3.70365i) q^{19} +(2.17761 + 0.507931i) q^{20} +8.95124i q^{21} +(3.12367 + 1.11476i) q^{22} +(-2.12916 + 2.12916i) q^{23} +(-1.91299 - 1.38987i) q^{24} +(2.32737 + 4.42531i) q^{25} +(0.746934 + 2.29883i) q^{26} +(-0.954548 - 0.151186i) q^{27} +(-3.73893 - 0.592189i) q^{28} +(-2.45671 - 7.56098i) q^{29} +(-0.448915 - 5.26829i) q^{30} +(3.04687 + 2.21368i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.224473 - 7.83924i) q^{33} +1.91462i q^{34} +(-4.46938 - 7.18861i) q^{35} +(-0.800751 + 2.46446i) q^{36} +(2.80375 - 5.50267i) q^{37} +(-0.609195 + 3.84631i) q^{38} +(4.62395 - 3.35950i) q^{39} +(2.23026 + 0.161024i) q^{40} +(-10.5998 - 3.44408i) q^{41} +(1.40028 + 8.84104i) q^{42} +(0.0971873 + 0.0971873i) q^{43} +(3.25960 + 0.612384i) q^{44} +(-5.33877 + 2.25194i) q^{45} +(-1.76987 + 2.43602i) q^{46} +(8.25770 - 4.20751i) q^{47} +(-2.10686 - 1.07350i) q^{48} +(4.30864 + 5.93034i) q^{49} +(2.99099 + 4.00674i) q^{50} +(4.30571 - 1.39901i) q^{51} +(1.09735 + 2.15368i) q^{52} +(1.27169 - 0.201417i) q^{53} -0.966447 q^{54} +(3.73388 + 6.40766i) q^{55} -3.78554 q^{56} +(9.09493 - 1.44050i) q^{57} +(-3.60926 - 7.08358i) q^{58} +(-13.8564 + 4.50221i) q^{59} +(-1.26753 - 5.13320i) q^{60} +(-2.01494 - 2.77333i) q^{61} +(3.35566 + 1.70979i) q^{62} +(8.74024 - 4.45338i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-2.03602 + 5.00671i) q^{65} +(-1.00462 - 7.77784i) q^{66} +(-7.14861 - 7.14861i) q^{67} +(0.299513 + 1.89105i) q^{68} +(6.77149 + 2.20019i) q^{69} +(-5.53890 - 6.40095i) q^{70} +(10.0775 - 7.32173i) q^{71} +(-0.405366 + 2.55938i) q^{72} +(-4.54499 + 8.92005i) q^{73} +(1.90843 - 5.87353i) q^{74} +(6.82509 - 9.65403i) q^{75} +3.89425i q^{76} +(-7.08601 - 10.3644i) q^{77} +(4.04148 - 4.04148i) q^{78} +(3.21092 + 2.33287i) q^{79} +(2.22799 - 0.189849i) q^{80} +(3.10843 + 9.56677i) q^{81} +(-11.0080 - 1.74350i) q^{82} +(-0.615229 - 0.0974427i) q^{83} +(2.76609 + 8.51314i) q^{84} +(-2.75932 + 3.27337i) q^{85} +(0.111194 + 0.0807873i) q^{86} +(-13.2927 + 13.2927i) q^{87} +(3.31527 + 0.0949311i) q^{88} -2.93819i q^{89} +(-4.92076 + 3.05939i) q^{90} +(2.82755 - 8.70230i) q^{91} +(-1.36700 + 2.68289i) q^{92} +(1.39311 - 8.79574i) q^{93} +(7.49783 - 5.44749i) q^{94} +(-6.58477 + 5.69796i) q^{95} +(-2.24886 - 0.730698i) q^{96} +(0.904231 + 5.70909i) q^{97} +(5.18331 + 5.18331i) q^{98} +(-7.76613 + 3.68096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

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