LMFDB - Embedded newform 160.2.u.a.43.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(43,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.u (of order $8$, degree $4$, 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:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			43.20
Character	$\chi$	$=$	160.43
Dual form			160.2.u.a.67.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30876 + 0.535863i) q^{2} +(0.461737 - 1.11473i) q^{3} +(1.42570 + 1.40263i) q^{4} +(-1.20640 - 1.88271i) q^{5} +(1.20165 - 1.21149i) q^{6} -2.85280i q^{7} +(1.11428 + 2.59969i) q^{8} +(1.09189 + 1.09189i) q^{9} +O(q^{10})$	\(q+(1.30876 + 0.535863i) q^{2} +(0.461737 - 1.11473i) q^{3} +(1.42570 + 1.40263i) q^{4} +(-1.20640 - 1.88271i) q^{5} +(1.20165 - 1.21149i) q^{6} -2.85280i q^{7} +(1.11428 + 2.59969i) q^{8} +(1.09189 + 1.09189i) q^{9} +(-0.570021 - 3.11048i) q^{10} +(-1.27011 + 3.06631i) q^{11} +(2.22186 - 0.941630i) q^{12} +(-2.38019 + 5.74629i) q^{13} +(1.52871 - 3.73363i) q^{14} +(-2.65576 + 0.475502i) q^{15} +(0.0652546 + 3.99947i) q^{16} +(-3.11621 - 3.11621i) q^{17} +(0.843921 + 2.01413i) q^{18} +(0.590480 + 1.42554i) q^{19} +(0.920770 - 4.37632i) q^{20} +(-3.18011 - 1.31724i) q^{21} +(-3.30539 + 3.33246i) q^{22} -5.60544i q^{23} +(3.41246 - 0.0417562i) q^{24} +(-2.08918 + 4.54261i) q^{25} +(-6.19431 + 6.24505i) q^{26} +(5.06553 - 2.09821i) q^{27} +(4.00143 - 4.06725i) q^{28} +(0.202591 + 0.489097i) q^{29} +(-3.73055 - 0.800803i) q^{30} -8.93487i q^{31} +(-2.05776 + 5.26931i) q^{32} +(2.83166 + 2.83166i) q^{33} +(-2.40851 - 5.74823i) q^{34} +(-5.37099 + 3.44163i) q^{35} +(0.0251919 + 3.08824i) q^{36} +(1.58307 + 3.82187i) q^{37} +(0.00889999 + 2.18211i) q^{38} +(5.30655 + 5.30655i) q^{39} +(3.55017 - 5.23414i) q^{40} +(-4.98538 + 4.98538i) q^{41} +(-3.45614 - 3.42806i) q^{42} +(0.171694 - 0.0711182i) q^{43} +(-6.11170 + 2.59016i) q^{44} +(0.738451 - 3.37298i) q^{45} +(3.00375 - 7.33618i) q^{46} +(3.72891 - 3.72891i) q^{47} +(4.48847 + 1.77396i) q^{48} -1.13848 q^{49} +(-5.16845 + 4.82568i) q^{50} +(-4.91261 + 2.03487i) q^{51} +(-11.4534 + 4.85397i) q^{52} +(-3.88110 - 9.36980i) q^{53} +(7.75392 - 0.0316252i) q^{54} +(7.30523 - 1.30797i) q^{55} +(7.41639 - 3.17883i) q^{56} +1.86175 q^{57} +(0.00305354 + 0.748671i) q^{58} +(1.19131 - 2.87607i) q^{59} +(-4.45327 - 3.04712i) q^{60} +(-4.59206 + 1.90209i) q^{61} +(4.78786 - 11.6936i) q^{62} +(3.11496 - 3.11496i) q^{63} +(-5.51674 + 5.79358i) q^{64} +(13.6900 - 2.45114i) q^{65} +(2.18858 + 5.22334i) q^{66} +(3.93702 + 1.63077i) q^{67} +(-0.0718964 - 8.81368i) q^{68} +(-6.24857 - 2.58824i) q^{69} +(-8.87358 + 1.62616i) q^{70} +(-6.22186 + 6.22186i) q^{71} +(-1.62190 + 4.05526i) q^{72} +9.23847 q^{73} +(0.0238608 + 5.85022i) q^{74} +(4.09915 + 4.42637i) q^{75} +(-1.15766 + 2.86063i) q^{76} +(8.74758 + 3.62337i) q^{77} +(4.10141 + 9.78858i) q^{78} +9.03379i q^{79} +(7.45111 - 4.94783i) q^{80} -1.98303i q^{81} +(-9.19614 + 3.85318i) q^{82} +(-3.83575 - 1.58882i) q^{83} +(-2.68628 - 6.33852i) q^{84} +(-2.10750 + 9.62632i) q^{85} +(0.262816 - 0.00107193i) q^{86} +0.638756 q^{87} +(-9.38671 + 0.114859i) q^{88} +(2.19449 - 2.19449i) q^{89} +(2.77391 - 4.01871i) q^{90} +(16.3930 + 6.79021i) q^{91} +(7.86237 - 7.99169i) q^{92} +(-9.95999 - 4.12556i) q^{93} +(6.87843 - 2.88206i) q^{94} +(1.97153 - 2.83148i) q^{95} +(4.92372 + 4.72689i) q^{96} +(6.97515 - 6.97515i) q^{97} +(-1.48999 - 0.610068i) q^{98} +(-4.73491 + 1.96126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	$ 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) $ 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.30876	+	0.535863i	0.925433	+	0.378912i
$2$	1.30876	+	0.535863i	0.925433	+	0.378912i
$3$	0.461737	−	1.11473i	0.266584	−	0.643591i	−0.732734	−	0.680515i	$-0.761756\pi$
$3$	0.461737	−	1.11473i	0.266584	−	0.643591i	0.999318	+	0.0369242i	$0.0117560\pi$
$4$	1.42570	+	1.40263i	0.712851	+	0.701315i
$5$	−1.20640	−	1.88271i	−0.539521	−	0.841972i
$5$	−1.20640	−	1.88271i	−0.539521	−	0.841972i
$6$	1.20165	−	1.21149i	0.490570	−	0.494588i
$7$		−	2.85280i		−	1.07826i	−0.842223	−	0.539129i	$-0.818754\pi$
$7$		−	2.85280i		−	1.07826i	0.842223	−	0.539129i	$-0.181246\pi$
$8$	1.11428	+	2.59969i	0.393959	+	0.919128i
$9$	1.09189	+	1.09189i	0.363965	+	0.363965i
$10$	−0.570021	−	3.11048i	−0.180256	−	0.983620i
$11$	−1.27011	+	3.06631i	−0.382952	+	0.924528i	0.608440	+	0.793600i	$0.291796\pi$
$11$	−1.27011	+	3.06631i	−0.382952	+	0.924528i	−0.991392	+	0.130928i	$0.958204\pi$
$12$	2.22186	−	0.941630i	0.641395	−	0.271825i
$13$	−2.38019	+	5.74629i	−0.660146	+	1.59373i	0.137428	+	0.990512i	$0.456116\pi$
$13$	−2.38019	+	5.74629i	−0.660146	+	1.59373i	−0.797574	+	0.603221i	$0.793884\pi$
$14$	1.52871	−	3.73363i	0.408565	−	0.997855i
$15$	−2.65576	+	0.475502i	−0.685713	+	0.122774i
$16$	0.0652546	+	3.99947i	0.0163136	+	0.999867i
$17$	−3.11621	−	3.11621i	−0.755792	−	0.755792i	0.219762	−	0.975554i	$-0.429472\pi$
$17$	−3.11621	−	3.11621i	−0.755792	−	0.755792i	−0.975554	+	0.219762i	$0.929472\pi$
$18$	0.843921	+	2.01413i	0.198914	+	0.474735i
$19$	0.590480	+	1.42554i	0.135465	+	0.327042i	0.977026	−	0.213120i	$-0.0683627\pi$
$19$	0.590480	+	1.42554i	0.135465	+	0.327042i	−0.841561	+	0.540163i	$0.818363\pi$
$20$	0.920770	−	4.37632i	0.205890	−	0.978575i
$21$	−3.18011	−	1.31724i	−0.693957	−	0.287446i
$22$	−3.30539	+	3.33246i	−0.704711	+	0.710483i
$23$		−	5.60544i		−	1.16882i	−0.811460	−	0.584408i	$-0.801327\pi$
$23$		−	5.60544i		−	1.16882i	0.811460	−	0.584408i	$-0.198673\pi$
$24$	3.41246	−	0.0417562i	0.696566	−	0.00852344i
$25$	−2.08918	+	4.54261i	−0.417835	+	0.908523i
$26$	−6.19431	+	6.24505i	−1.21481	+	1.22476i
$27$	5.06553	−	2.09821i	0.974862	−	0.403801i
$28$	4.00143	−	4.06725i	0.756199	−	0.768637i
$29$	0.202591	+	0.489097i	0.0376202	+	0.0908231i	0.941573	−	0.336809i	$-0.109348\pi$
$29$	0.202591	+	0.489097i	0.0376202	+	0.0908231i	−0.903953	+	0.427632i	$0.859348\pi$
$30$	−3.73055	−	0.800803i	−0.681102	−	0.146206i
$31$		−	8.93487i		−	1.60475i	−0.596820	−	0.802375i	$-0.703569\pi$
$31$		−	8.93487i		−	1.60475i	0.596820	−	0.802375i	$-0.296431\pi$
$32$	−2.05776	+	5.26931i	−0.363765	+	0.931491i
$33$	2.83166	+	2.83166i	0.492929	+	0.492929i
$34$	−2.40851	−	5.74823i	−0.413056	−	0.985813i
$35$	−5.37099	+	3.44163i	−0.907863	+	0.581742i
$36$	0.0251919	+	3.08824i	0.00419865	+	0.514706i
$37$	1.58307	+	3.82187i	0.260255	+	0.628312i	0.998954	−	0.0457236i	$-0.0145593\pi$
$37$	1.58307	+	3.82187i	0.260255	+	0.628312i	−0.738699	+	0.674036i	$0.764559\pi$
$38$	0.00889999	+	2.18211i	0.00144377	+	0.353985i
$39$	5.30655	+	5.30655i	0.849728	+	0.849728i
$40$	3.55017	−	5.23414i	0.561332	−	0.827591i
$41$	−4.98538	+	4.98538i	−0.778585	+	0.778585i	−0.979590	−	0.201005i	$-0.935579\pi$
$41$	−4.98538	+	4.98538i	−0.778585	+	0.778585i	0.201005	+	0.979590i	$0.435579\pi$
$42$	−3.45614	−	3.42806i	−0.533293	−	0.528961i
$43$	0.171694	−	0.0711182i	0.0261832	−	0.0108454i	−0.369553	−	0.929209i	$-0.620489\pi$
$43$	0.171694	−	0.0711182i	0.0261832	−	0.0108454i	0.395737	+	0.918364i	$0.370489\pi$
$44$	−6.11170	+	2.59016i	−0.921373	+	0.390481i
$45$	0.738451	−	3.37298i	0.110082	−	0.502814i
$46$	3.00375	−	7.33618i	0.442878	−	1.08166i
$47$	3.72891	−	3.72891i	0.543917	−	0.543917i	−0.380758	−	0.924675i	$-0.624337\pi$
$47$	3.72891	−	3.72891i	0.543917	−	0.543917i	0.924675	+	0.380758i	$0.124337\pi$
$48$	4.48847	+	1.77396i	0.647854	+	0.256049i
$49$	−1.13848			−0.162640
$50$	−5.16845	+	4.82568i	−0.730929	+	0.682454i
$51$	−4.91261	+	2.03487i	−0.687903	+	0.284939i
$52$	−11.4534	+	4.85397i	−1.58829	+	0.673124i
$53$	−3.88110	−	9.36980i	−0.533110	−	1.28704i	−0.929454	−	0.368939i	$-0.879721\pi$
$53$	−3.88110	−	9.36980i	−0.533110	−	1.28704i	0.396344	−	0.918102i	$-0.370279\pi$
$54$	7.75392	−	0.0316252i	1.05517	−	0.00430365i
$55$	7.30523	−	1.30797i	0.985037	−	0.176367i
$56$	7.41639	−	3.17883i	0.991057	−	0.424789i
$57$	1.86175			0.246594
$58$	0.00305354	+	0.748671i	0.000400950	+	0.0983054i
$59$	1.19131	−	2.87607i	0.155095	−	0.374433i	−0.827164	−	0.561960i	$-0.810047\pi$
$59$	1.19131	−	2.87607i	0.155095	−	0.374433i	0.982259	+	0.187527i	$0.0600474\pi$
$60$	−4.45327	−	3.04712i	−0.574915	−	0.393382i
$61$	−4.59206	+	1.90209i	−0.587953	+	0.243538i	−0.656770	−	0.754091i	$-0.728078\pi$
$61$	−4.59206	+	1.90209i	−0.587953	+	0.243538i	0.0688165	+	0.997629i	$0.478078\pi$
$62$	4.78786	−	11.6936i	0.608059	−	1.48509i
$63$	3.11496	−	3.11496i	0.392448	−	0.392448i
$64$	−5.51674	+	5.79358i	−0.689593	+	0.724197i
$65$	13.6900	−	2.45114i	1.69804	−	0.304027i
$66$	2.18858	+	5.22334i	0.269396	+	0.642949i
$67$	3.93702	+	1.63077i	0.480984	+	0.199230i	0.609983	−	0.792415i	$-0.291176\pi$
$67$	3.93702	+	1.63077i	0.480984	+	0.199230i	−0.128999	+	0.991645i	$0.541176\pi$
$68$	−0.0718964	−	8.81368i	−0.00871872	−	1.06882i
$69$	−6.24857	−	2.58824i	−0.752239	−	0.311588i
$70$	−8.87358	+	1.62616i	−1.06060	+	0.194363i
$71$	−6.22186	+	6.22186i	−0.738398	+	0.738398i	−0.972268	−	0.233869i	$-0.924861\pi$
$71$	−6.22186	+	6.22186i	−0.738398	+	0.738398i	0.233869	+	0.972268i	$0.424861\pi$
$72$	−1.62190	+	4.05526i	−0.191143	+	0.477917i
$73$	9.23847			1.08128			0.540640	−	0.841254i	$-0.318182\pi$
$73$	9.23847			1.08128			0.540640	+	0.841254i	$0.318182\pi$
$74$	0.0238608	+	5.85022i	0.00277376	+	0.680075i
$75$	4.09915	+	4.42637i	0.473329	+	0.511113i
$76$	−1.15766	+	2.86063i	−0.132793	+	0.328137i
$77$	8.74758	+	3.62337i	0.996879	+	0.412921i
$78$	4.10141	+	9.78858i	0.464394	+	1.10834i
$79$			9.03379i			1.01638i	0.861245	+	0.508190i	$0.169685\pi$
$79$			9.03379i			1.01638i	−0.861245	+	0.508190i	$0.830315\pi$
$80$	7.45111	−	4.94783i	0.833059	−	0.553184i
$81$		−	1.98303i		−	0.220336i
$82$	−9.19614	+	3.85318i	−1.01554	+	0.425513i
$83$	−3.83575	−	1.58882i	−0.421028	−	0.174395i	0.162103	−	0.986774i	$-0.448172\pi$
$83$	−3.83575	−	1.58882i	−0.421028	−	0.174395i	−0.583131	+	0.812378i	$0.698172\pi$
$84$	−2.68628	−	6.33852i	−0.293097	−	0.691589i
$85$	−2.10750	+	9.62632i	−0.228591	+	1.04412i
$86$	0.262816	−	0.00107193i	0.0283402	−	0.000115589i
$87$	0.638756			0.0684819
$88$	−9.38671	+	0.114859i	−1.00063	+	0.0122441i
$89$	2.19449	−	2.19449i	0.232616	−	0.232616i	−0.581168	−	0.813784i	$-0.697404\pi$
$89$	2.19449	−	2.19449i	0.232616	−	0.232616i	0.813784	+	0.581168i	$0.197404\pi$
$90$	2.77391	−	4.01871i	0.292396	−	0.423610i
$91$	16.3930	+	6.79021i	1.71845	+	0.711807i
$92$	7.86237	−	7.99169i	0.819708	−	0.833192i
$93$	−9.95999	−	4.12556i	−1.03280	−	0.427801i
$94$	6.87843	−	2.88206i	0.709456	−	0.297262i
$95$	1.97153	−	2.83148i	0.202274	−	0.290504i
$96$	4.92372	+	4.72689i	0.502525	+	0.482436i
$97$	6.97515	−	6.97515i	0.708219	−	0.708219i	−0.257941	−	0.966161i	$-0.583044\pi$
$97$	6.97515	−	6.97515i	0.708219	−	0.708219i	0.966161	+	0.257941i	$0.0830442\pi$
$98$	−1.48999	−	0.610068i	−0.150512	−	0.0616261i
$99$	−4.73491	+	1.96126i	−0.475876	+	0.197114i
$100$	−9.35015	+	3.54607i	−0.935015	+	0.354607i
$101$	1.02535	−	2.47541i	0.102026	−	0.246313i	−0.864621	−	0.502424i	$-0.832441\pi$
$101$	1.02535	−	2.47541i	0.102026	−	0.246313i	0.966647	+	0.256112i	$0.0824415\pi$
$102$	−7.51984	+	0.0306705i	−0.744575	+	0.00303683i
$103$	−1.92420			−0.189597			−0.0947986	−	0.995496i	$-0.530221\pi$
$103$	−1.92420			−0.189597			−0.0947986	+	0.995496i	$0.530221\pi$
$104$	−17.5907	+	0.215247i	−1.72491	+	0.0211067i
$105$	1.35651	+	7.57635i	0.132382	+	0.739376i
$106$	−0.0584977	−	14.3425i	−0.00568180	−	1.39307i
$107$	−5.12277	−	12.3675i	−0.495237	−	1.19561i	−0.952022	−	0.306031i	$-0.900999\pi$
$107$	−5.12277	−	12.3675i	−0.495237	−	1.19561i	0.456784	−	0.889577i	$-0.349001\pi$
$108$	10.1650	+	4.11365i	0.978124	+	0.395836i
$109$	10.2082	−	4.22837i	0.977767	−	0.405005i	0.164169	−	0.986432i	$-0.447506\pi$
$109$	10.2082	−	4.22837i	0.977767	−	0.405005i	0.813598	+	0.581428i	$0.197506\pi$
$110$	10.2617	+	2.20278i	0.978413	+	0.210027i
$111$	4.99133			0.473756
$112$	11.4097	−	0.186158i	1.07811	−	0.0175903i
$113$	5.58188	−	5.58188i	0.525099	−	0.525099i	−0.394008	−	0.919107i	$-0.628912\pi$
$113$	5.58188	−	5.58188i	0.525099	−	0.525099i	0.919107	+	0.394008i	$0.128912\pi$
$114$	2.43658	+	0.997641i	0.228207	+	0.0934376i
$115$	−10.5534	+	6.76243i	−0.984111	+	0.630600i
$116$	−0.397189	+	0.981467i	−0.0368780	+	0.0911269i
$117$	−8.87324	+	3.67542i	−0.820332	+	0.339793i
$118$	3.10032	−	3.12571i	0.285407	−	0.287745i
$119$	−8.88993	+	8.88993i	−0.814939	+	0.814939i
$120$	−4.19542	−	6.37429i	−0.382988	−	0.581891i
$121$	−0.0109209	−	0.0109209i	−0.000992805	−	0.000992805i
$122$	−7.02917	+	0.0286693i	−0.636391	+	0.00259559i
$123$	3.25543	+	7.85930i	0.293532	+	0.708649i
$124$	12.5323	−	12.7385i	1.12544	−	1.14395i
$125$	11.0728	−	1.54692i	0.990382	−	0.138361i
$126$	5.74592	−	2.40754i	0.511887	−	0.214481i
$127$	−6.46535	−	6.46535i	−0.573707	−	0.573707i	0.359455	−	0.933162i	$-0.382963\pi$
$127$	−6.46535	−	6.46535i	−0.573707	−	0.573707i	−0.933162	+	0.359455i	$0.882963\pi$
$128$	−10.3247	+	4.62618i	−0.912579	+	0.408901i
$129$		−	0.224231i		−	0.0197425i
$130$	19.2305	+	4.12803i	1.68662	+	0.362052i
$131$	−5.60396	−	13.5291i	−0.489620	−	1.18205i	−0.954912	−	0.296890i	$-0.904051\pi$
$131$	−5.60396	−	13.5291i	−0.489620	−	1.18205i	0.465292	−	0.885157i	$-0.345949\pi$
$132$	0.0653313	+	8.00888i	0.00568636	+	0.697084i
$133$	4.06680	−	1.68452i	0.352636	−	0.146067i
$134$	4.27875	+	4.24398i	0.369627	+	0.366624i
$135$	−10.0614	−	7.00563i	−0.865948	−	0.602948i
$136$	4.62883	−	11.5735i	0.396919	−	0.992421i
$137$			11.3509i			0.969771i	0.874578	+	0.484886i	$0.161139\pi$
$137$			11.3509i			0.969771i	−0.874578	+	0.484886i	$0.838861\pi$
$138$	−6.79093	−	6.73576i	−0.578082	−	0.573386i
$139$	−3.95349	−	1.63759i	−0.335330	−	0.138898i	0.208664	−	0.977987i	$-0.433089\pi$
$139$	−3.95349	−	1.63759i	−0.335330	−	0.138898i	−0.543994	+	0.839089i	$0.683089\pi$
$140$	−12.4848	−	2.62677i	−1.05516	−	0.222003i
$141$	−2.43496	−	5.87851i	−0.205061	−	0.495060i
$142$	−11.4770	+	4.80885i	−0.963126	+	0.403550i
$143$	−14.5968	−	14.5968i	−1.22065	−	1.22065i
$144$	−4.29574	+	4.43824i	−0.357978	+	0.369854i
$145$	0.676421	−	0.971468i	0.0561737	−	0.0806760i
$146$	12.0909	+	4.95055i	1.00065	+	0.409710i
$147$	−0.525678	+	1.26910i	−0.0433572	+	0.104673i
$148$	−3.10369	+	7.66932i	−0.255122	+	0.630414i
$149$	2.47973	−	5.98661i	0.203148	−	0.490442i	−0.789167	−	0.614178i	$-0.789488\pi$
$149$	2.47973	−	5.98661i	0.203148	−	0.490442i	0.992315	+	0.123736i	$0.0394876\pi$
$150$	2.99287	+	7.98963i	0.244367	+	0.652350i
$151$	9.25945	+	9.25945i	0.753523	+	0.753523i	0.975135	−	0.221612i	$-0.0711318\pi$
$151$	9.25945	+	9.25945i	0.753523	+	0.753523i	−0.221612	+	0.975135i	$0.571132\pi$
$152$	−3.04801	+	3.12352i	−0.247226	+	0.253351i
$153$		−	6.80514i		−	0.550163i
$154$	9.50685	+	9.42962i	0.766084	+	0.759860i
$155$	−16.8217	+	10.7791i	−1.35116	+	0.865795i
$156$	0.122431	+	15.0087i	0.00980235	+	1.20166i
$157$	−3.59597	+	8.68144i	−0.286990	+	0.692854i	−0.999965	−	0.00833467i	$-0.997347\pi$
$157$	−3.59597	+	8.68144i	−0.286990	+	0.692854i	0.712976	+	0.701189i	$0.247347\pi$
$158$	−4.84087	+	11.8231i	−0.385119	+	0.940592i
$159$	−12.2369			−0.970447
$160$	12.4031	−	2.48275i	0.980548	−	0.196279i
$161$	−15.9912			−1.26028
$162$	1.06263	−	2.59530i	0.0834880	−	0.203906i
$163$	−5.33308	+	12.8752i	−0.417719	+	1.00846i	0.565288	+	0.824894i	$0.308765\pi$
$163$	−5.33308	+	12.8752i	−0.417719	+	1.00846i	−0.983007	+	0.183569i	$0.941235\pi$
$164$	−14.1003	+	0.115021i	−1.10105	+	0.00898166i
$165$	1.91506	−	8.74732i	0.149087	−	0.680978i
$166$	−4.16868	−	4.13481i	−0.323552	−	0.320924i
$167$			20.1300i			1.55771i	0.627205	+	0.778854i	$0.284199\pi$
$167$			20.1300i			1.55771i	−0.627205	+	0.778854i	$0.715801\pi$
$168$	−0.119122	−	9.73508i	−0.00919047	−	0.751077i
$169$	−18.1621	−	18.1621i	−1.39708	−	1.39708i
$170$	−7.91660	+	11.4692i	−0.607176	+	0.879648i
$171$	−0.911802	+	2.20128i	−0.0697272	+	0.168336i
$172$	0.344538	+	0.139431i	0.0262708	+	0.0106315i
$173$	−8.10217	+	19.5604i	−0.615997	+	1.48715i	0.240318	+	0.970694i	$0.422748\pi$
$173$	−8.10217	+	19.5604i	−0.615997	+	1.48715i	−0.856315	+	0.516454i	$0.827252\pi$
$174$	0.835978	+	0.342286i	0.0633753	+	0.0259486i
$175$	12.9592	+	5.96001i	0.979622	+	0.450534i
$176$	−12.3465	−	4.87967i	−0.930652	−	0.367819i
$177$	−2.65598	−	2.65598i	−0.199636	−	0.199636i
$178$	4.04801	−	1.69612i	0.303411	−	0.127129i
$179$	4.14657	+	10.0107i	0.309929	+	0.748234i	0.999707	+	0.0242135i	$0.00770814\pi$
$179$	4.14657	+	10.0107i	0.309929	+	0.748234i	−0.689778	+	0.724021i	$0.742292\pi$
$180$	5.78386	−	3.77309i	0.431103	−	0.281230i
$181$	−13.0422	−	5.40225i	−0.969419	−	0.401546i	−0.158923	−	0.987291i	$-0.550802\pi$
$181$	−13.0422	−	5.40225i	−0.969419	−	0.401546i	−0.810496	+	0.585745i	$0.800802\pi$
$182$	17.8159	+	17.6712i	1.32060	+	1.30987i
$183$			5.99719i			0.443325i
$184$	14.5724	−	6.24606i	1.07429	−	0.460465i
$185$	5.28565	−	7.59119i	0.388608	−	0.558115i
$186$	−10.8245	−	10.7366i	−0.793690	−	0.787242i
$187$	13.5132	−	5.59735i	0.988183	−	0.409319i
$188$	10.5466	−	0.0860324i	0.769190	−	0.00627456i
$189$	−5.98579	−	14.4510i	−0.435402	−	1.05115i
$190$	4.09754	−	2.64927i	0.297267	−	0.192198i
$191$		−	16.7332i		−	1.21077i	−0.795933	−	0.605385i	$-0.793019\pi$
$191$		−	16.7332i		−	1.21077i	0.795933	−	0.605385i	$-0.206981\pi$
$192$	3.91100	+	8.82480i	0.282252	+	0.636875i
$193$	0.855004	+	0.855004i	0.0615445	+	0.0615445i	0.737209	−	0.675665i	$-0.236143\pi$
$193$	0.855004	+	0.855004i	0.0615445	+	0.0615445i	−0.675665	+	0.737209i	$0.736143\pi$
$194$	12.8665	−	5.39107i	0.923762	−	0.387056i
$195$	3.58883	−	16.3925i	0.257002	−	1.17389i
$196$	−1.62313	−	1.59686i	−0.115938	−	0.114062i
$197$	−3.73648	−	9.02066i	−0.266213	−	0.642695i	0.733086	−	0.680136i	$-0.238079\pi$
$197$	−3.73648	−	9.02066i	−0.266213	−	0.642695i	−0.999299	+	0.0374411i	$0.988079\pi$
$198$	−7.24782	+	0.0295611i	−0.515080	+	0.00210081i
$199$	7.42744	+	7.42744i	0.526517	+	0.526517i	0.919532	−	0.393015i	$-0.128568\pi$
$199$	7.42744	+	7.42744i	0.526517	+	0.526517i	−0.393015	+	0.919532i	$0.628568\pi$
$200$	−14.1373	−	0.369441i	−0.999659	−	0.0261235i
$201$	3.63574	−	3.63574i	0.256445	−	0.256445i
$202$	2.66842	−	2.69027i	0.187749	−	0.189287i
$203$	1.39530	−	0.577951i	0.0979307	−	0.0405642i
$204$	−9.85809	−	3.98946i	−0.690204	−	0.279318i
$205$	15.4004	+	3.37163i	1.07561	+	0.235485i
$206$	−2.51832	−	1.03111i	−0.175459	−	0.0718407i
$207$	6.12055	−	6.12055i	0.425407	−	0.425407i
$208$	−23.1374	−	9.14452i	−1.60429	−	0.634058i
$209$	−5.12114			−0.354237
$210$	−2.28453	+	10.6425i	−0.157648	+	0.734404i
$211$	6.57333	−	2.72276i	0.452527	−	0.187443i	−0.144766	−	0.989466i	$-0.546243\pi$
$211$	6.57333	−	2.72276i	0.452527	−	0.187443i	0.597293	+	0.802023i	$0.296243\pi$
$212$	7.60908	−	18.8023i	0.522594	−	1.29135i
$213$	4.06284	+	9.80857i	0.278381	+	0.672072i
$214$	−0.0772128	−	18.9311i	−0.00527816	−	1.29411i
$215$	−0.341028	−	0.237453i	−0.0232579	−	0.0161942i
$216$	11.0991	+	10.8308i	0.755201	+	0.736942i
$217$	−25.4894			−1.73033
$218$	15.6259	−	0.0637320i	1.05832	−	0.00431647i
$219$	4.26574	−	10.2984i	0.288252	−	0.695902i
$220$	12.2497	+	8.38177i	0.825874	+	0.565099i
$221$	25.3238	−	10.4895i	1.70346	−	0.705598i
$222$	6.53245	+	2.67467i	0.438429	+	0.179512i
$223$	−16.4114	+	16.4114i	−1.09899	+	1.09899i	−0.104456	+	0.994529i	$0.533310\pi$
$223$	−16.4114	+	16.4114i	−1.09899	+	1.09899i	−0.994529	+	0.104456i	$0.966690\pi$
$224$	15.0323	+	5.87039i	1.00439	+	0.392232i
$225$	−7.24121	+	2.67889i	−0.482747	+	0.178593i
$226$	10.2965	−	4.31422i	0.684911	−	0.286978i
$227$	7.86906	+	3.25947i	0.522288	+	0.216339i	0.628222	−	0.778034i	$-0.283783\pi$
$227$	7.86906	+	3.25947i	0.522288	+	0.216339i	−0.105934	+	0.994373i	$0.533783\pi$
$228$	2.65430	+	2.61134i	0.175785	+	0.172940i
$229$	18.7237	+	7.75561i	1.23730	+	0.512505i	0.902869	−	0.429916i	$-0.141457\pi$
$229$	18.7237	+	7.75561i	1.23730	+	0.512505i	0.334428	+	0.942421i	$0.391457\pi$
$230$	−17.4356	+	3.19522i	−1.14967	+	0.210686i
$231$	8.07817	−	8.07817i	0.531504	−	0.531504i
$232$	−1.04576	+	1.07167i	−0.0686572	+	0.0703583i
$233$	−2.78989			−0.182772			−0.0913858	−	0.995816i	$-0.529130\pi$
$233$	−2.78989			−0.182772			−0.0913858	+	0.995816i	$0.529130\pi$
$234$	−13.5825	+	0.0553976i	−0.887913	+	0.00362146i
$235$	−11.5190	−	2.52187i	−0.751418	−	0.164509i
$236$	5.73252	−	2.42946i	0.373155	−	0.158144i
$237$	10.0703	+	4.17124i	0.654133	+	0.270951i
$238$	−16.3986	+	6.87100i	−1.06296	+	0.445381i
$239$			5.49746i			0.355601i	0.984067	+	0.177801i	$0.0568982\pi$
$239$			5.49746i			0.355601i	−0.984067	+	0.177801i	$0.943102\pi$
$240$	−2.07505	−	10.5906i	−0.133944	−	0.683619i
$241$			22.1585i			1.42735i	0.700476	+	0.713676i	$0.252971\pi$
$241$			22.1585i			1.42735i	−0.700476	+	0.713676i	$0.747029\pi$
$242$	−0.00844070	−	0.0201449i	−0.000542588	−	0.00129496i
$243$	12.9861	+	5.37900i	0.833056	+	0.345063i
$244$	−9.21485	−	3.72915i	−0.589920	−	0.238734i
$245$	1.37346	+	2.14342i	0.0877474	+	0.136938i
$246$	0.0490673	+	12.0304i	0.00312842	+	0.767030i
$247$	−9.59704			−0.610645
$248$	23.2279	−	9.95598i	1.47497	−	0.632205i
$249$	−3.54221	+	3.54221i	−0.224479	+	0.224479i
$250$	15.3206	+	3.90895i	0.968958	+	0.247224i
$251$	−4.92262	−	2.03902i	−0.310713	−	0.128702i	0.221878	−	0.975075i	$-0.428781\pi$
$251$	−4.92262	−	2.03902i	−0.310713	−	0.128702i	−0.532591	+	0.846373i	$0.678781\pi$
$252$	8.81013	−	0.0718674i	0.554986	−	0.00452722i
$253$	17.1880	+	7.11952i	1.08060	+	0.447600i
$254$	−4.99705	−	11.9261i	−0.313543	−	0.748312i
$255$	9.75766	+	6.79413i	0.611048	+	0.425465i
$256$	−15.9915	+	0.521967i	−0.999468	+	0.0326229i
$257$	5.69134	−	5.69134i	0.355016	−	0.355016i	−0.506956	−	0.861972i	$-0.669229\pi$
$257$	5.69134	−	5.69134i	0.355016	−	0.355016i	0.861972	+	0.506956i	$0.169229\pi$
$258$	0.120157	−	0.293465i	0.00748066	−	0.0182703i
$259$	10.9030	−	4.51619i	0.677482	−	0.280622i
$260$	22.9560	+	15.7075i	1.42367	+	0.974136i
$261$	−0.312835	+	0.755250i	−0.0193640	+	0.0467488i
$262$	−0.0844654	−	20.7093i	−0.00521829	−	1.27943i
$263$	−0.991959			−0.0611668			−0.0305834	−	0.999532i	$-0.509737\pi$
$263$	−0.991959			−0.0611668			−0.0305834	+	0.999532i	$0.509737\pi$
$264$	−4.20616	+	10.5167i	−0.258871	+	0.647259i
$265$	−12.9584	+	18.6107i	−0.796029	+	1.14325i
$266$	6.22513	−	0.0253899i	0.381687	−	0.00155675i
$267$	−1.43299	−	3.45955i	−0.0876977	−	0.211721i
$268$	3.32566	+	7.84718i	0.203147	+	0.479343i
$269$	−5.79006	+	2.39832i	−0.353026	+	0.146228i	−0.552147	−	0.833747i	$-0.686191\pi$
$269$	−5.79006	+	2.39832i	−0.353026	+	0.146228i	0.199121	+	0.979975i	$0.436191\pi$
$270$	−9.41390	−	14.5602i	−0.572912	−	0.886106i
$271$	3.73742			0.227032			0.113516	−	0.993536i	$-0.463789\pi$
$271$	3.73742			0.227032			0.113516	+	0.993536i	$0.463789\pi$
$272$	12.2598	−	12.6665i	0.743362	−	0.768021i
$273$	15.1385	−	15.1385i	0.916225	−	0.916225i
$274$	−6.08251	+	14.8556i	−0.367458	+	0.897458i
$275$	−11.2756	−	12.1757i	−0.679944	−	0.734221i
$276$	−5.27825	−	12.4545i	−0.317713	−	0.749673i
$277$	5.70730	−	2.36404i	0.342918	−	0.142041i	−0.204576	−	0.978851i	$-0.565582\pi$
$277$	5.70730	−	2.36404i	0.342918	−	0.142041i	0.547495	+	0.836809i	$0.315582\pi$
$278$	−4.29664	−	4.26173i	−0.257695	−	0.255602i
$279$	9.75593	−	9.75593i	0.584072	−	0.584072i
$280$	−14.9320	−	10.1279i	−0.892356	−	0.605260i
$281$	13.3626	+	13.3626i	0.797147	+	0.797147i	0.982645	−	0.185498i	$-0.0593898\pi$
$281$	13.3626	+	13.3626i	0.797147	+	0.797147i	−0.185498	+	0.982645i	$0.559390\pi$
$282$	−0.0367008	−	8.99836i	−0.00218550	−	0.535845i
$283$	−9.65114	−	23.2999i	−0.573701	−	1.38504i	−0.898383	−	0.439213i	$-0.855258\pi$
$283$	−9.65114	−	23.2999i	−0.573701	−	1.38504i	0.324683	−	0.945823i	$-0.394742\pi$
$284$	−17.5975	+	0.143549i	−1.04422	+	0.00851807i
$285$	−2.24602	−	3.50513i	−0.133043	−	0.207626i
$286$	−11.2818	−	26.9256i	−0.667108	−	1.59214i
$287$	14.2223	+	14.2223i	0.839515	+	0.839515i
$288$	−8.00038	+	3.50667i	−0.471427	+	0.206632i
$289$			2.42153i			0.142443i
$290$	1.40585	−	0.908950i	0.0825541	−	0.0533754i
$291$	−4.55474	−	10.9961i	−0.267003	−	0.644603i
$292$	13.1713	+	12.9582i	0.770792	+	0.758319i
$293$	−11.6421	+	4.82230i	−0.680137	+	0.281722i	−0.695884	−	0.718154i	$-0.744987\pi$
$293$	−11.6421	+	4.82230i	−0.680137	+	0.281722i	0.0157473	+	0.999876i	$0.494987\pi$
$294$	−1.36805	+	1.37925i	−0.0797862	+	0.0804397i
$295$	−6.85200	+	1.22682i	−0.398939	+	0.0714283i
$296$	−8.17168	+	8.37414i	−0.474969	+	0.486737i
$297$			18.1975i			1.05592i
$298$	6.45338	−	6.50623i	0.373834	−	0.376896i
$299$	32.2105	+	13.3420i	1.86278	+	0.771589i
$300$	−0.364392	+	12.0603i	−0.0210382	+	0.696300i
$301$	−0.202886	−	0.489810i	−0.0116942	−	0.0282322i
$302$	7.15660	+	17.0802i	0.411816	+	0.982854i
$303$	−2.28598	−	2.28598i	−0.131326	−	0.131326i
$304$	−5.66289	+	2.45463i	−0.324789	+	0.140783i
$305$	9.12097	+	6.35082i	0.522265	+	0.363647i
$306$	3.64662	−	8.90629i	0.208463	−	0.509139i
$307$	3.39649	−	8.19985i	0.193848	−	0.467990i	−0.796832	−	0.604201i	$-0.793492\pi$
$307$	3.39649	−	8.19985i	0.193848	−	0.467990i	0.990680	+	0.136211i	$0.0434924\pi$
$308$	7.38920	+	17.4355i	0.421039	+	0.993478i
$309$	−0.888476	+	2.14497i	−0.0505436	+	0.122023i
$310$	−27.7917	+	5.09306i	−1.57846	+	0.289266i
$311$	9.26889	+	9.26889i	0.525591	+	0.525591i	0.919254	−	0.393664i	$-0.128793\pi$
$311$	9.26889	+	9.26889i	0.525591	+	0.525591i	−0.393664	+	0.919254i	$0.628793\pi$
$312$	−7.88236	+	19.7084i	−0.446251	+	1.11577i
$313$		−	12.4634i		−	0.704474i	−0.935911	−	0.352237i	$-0.885421\pi$
$313$		−	12.4634i		−	0.704474i	0.935911	−	0.352237i	$-0.114579\pi$
$314$	−9.35832	+	9.43497i	−0.528120	+	0.532446i
$315$	−9.62245	−	2.10665i	−0.542164	−	0.118697i
$316$	−12.6711	+	12.8795i	−0.712803	+	0.724528i
$317$	−5.24907	+	12.6724i	−0.294817	+	0.711752i	0.705179	+	0.709029i	$0.250867\pi$
$317$	−5.24907	+	12.6724i	−0.294817	+	0.711752i	−0.999996	+	0.00272265i	$0.999133\pi$
$318$	−16.0151	−	6.55728i	−0.898083	−	0.367714i
$319$	−1.75704			−0.0983752
$320$	17.5630	+	3.39701i	0.981804	+	0.189899i
$321$	−16.1518			−0.901505
$322$	−20.9287	−	8.56910i	−1.16631	−	0.477537i
$323$	2.60224	−	6.28236i	0.144792	−	0.349560i
$324$	2.78145	−	2.82720i	0.154525	−	0.157067i
$325$	−21.1305	−	22.8173i	−1.17211	−	1.26568i
$326$	−13.8791	+	13.9927i	−0.768690	+	0.774986i
$327$		−	13.3318i		−	0.737250i
$328$	−18.5155	−	7.40529i	−1.02235	−	0.408889i
$329$	−10.6378	−	10.6378i	−0.586483	−	0.586483i
$330$	7.19372	−	10.4219i	0.396001	−	0.573708i
$331$	7.08741	−	17.1105i	0.389559	−	0.940479i	−0.600474	−	0.799644i	$-0.705021\pi$
$331$	7.08741	−	17.1105i	0.389559	−	0.940479i	0.990033	−	0.140835i	$-0.0449786\pi$
$332$	−3.24011	−	7.64532i	−0.177824	−	0.419591i
$333$	−2.44453	+	5.90163i	−0.133960	+	0.323407i
$334$	−10.7869	+	26.3454i	−0.590235	+	1.44155i
$335$	−1.67938	−	9.37962i	−0.0917544	−	0.512464i
$336$	5.06076	−	12.8047i	0.276087	−	0.698554i
$337$	−18.5925	−	18.5925i	−1.01280	−	1.01280i	−0.999917	−	0.0128814i	$-0.995900\pi$
$337$	−18.5925	−	18.5925i	−1.01280	−	1.01280i	−0.0128814	−	0.999917i	$-0.504100\pi$
$338$	−14.0374	−	33.5022i	−0.763536	−	1.82228i
$339$	−3.64494	−	8.79967i	−0.197966	−	0.477932i
$340$	−16.5068	+	10.7682i	−0.895209	+	0.583989i
$341$	27.3971	+	11.3482i	1.48364	+	0.614542i
$342$	−2.37292	+	2.39235i	−0.128313	+	0.129364i
$343$		−	16.7218i		−	0.902890i
$344$	0.376201	+	0.367106i	0.0202834	+	0.0197930i
$345$	2.66540	+	14.8867i	0.143500	+	0.801473i
$346$	−21.0855	+	21.2582i	−1.13356	+	1.14285i
$347$	−22.1463	+	9.17331i	−1.18888	+	0.492449i	−0.887389	−	0.461021i	$-0.847483\pi$
$347$	−22.1463	+	9.17331i	−1.18888	+	0.492449i	−0.301488	+	0.953470i	$0.597483\pi$
$348$	0.910676	+	0.895939i	0.0488174	+	0.0480274i
$349$	6.86283	+	16.5683i	0.367359	+	0.886883i	0.994181	+	0.107721i	$0.0343552\pi$
$349$	6.86283	+	16.5683i	0.367359	+	0.886883i	−0.626822	+	0.779162i	$0.715645\pi$
$350$	13.7667	+	14.7446i	0.735861	+	0.788129i
$351$			34.1021i			1.82024i
$352$	−13.5438	−	13.0023i	−0.721885	−	0.693027i
$353$	13.2332	+	13.2332i	0.704333	+	0.704333i	0.965338	−	0.261004i	$-0.0840537\pi$
$353$	13.2332	+	13.2332i	0.704333	+	0.704333i	−0.261004	+	0.965338i	$0.584054\pi$
$354$	−2.05280	−	4.89928i	−0.109105	−	0.260394i
$355$	19.2200	+	4.20786i	1.02009	+	0.223330i
$356$	6.20675	−	0.0506307i	0.328957	−	0.00268342i
$357$	5.80508	+	14.0147i	0.307237	+	0.741737i
$358$	0.0624990	+	15.3236i	0.00330317	+	0.809876i
$359$	−1.53937	−	1.53937i	−0.0812451	−	0.0812451i	0.665316	−	0.746561i	$-0.268297\pi$
$359$	−1.53937	−	1.53937i	−0.0812451	−	0.0812451i	−0.746561	+	0.665316i	$0.768297\pi$
$360$	9.59154	−	1.83872i	0.505519	−	0.0969090i
$361$	11.7515	−	11.7515i	0.618501	−	0.618501i
$362$	−14.1742	−	14.0591i	−0.744981	−	0.738929i
$363$	−0.0172164	+	0.00713127i	−0.000903627	+	0.000374294i
$364$	13.8474	+	32.6742i	0.725801	+	1.71259i
$365$	−11.1453	−	17.3933i	−0.583373	−	0.910409i
$366$	−3.21367	+	7.84888i	−0.167981	+	0.410267i
$367$	−23.1242	+	23.1242i	−1.20707	+	1.20707i	−0.235103	+	0.971970i	$0.575543\pi$
$367$	−23.1242	+	23.1242i	−1.20707	+	1.20707i	−0.971970	+	0.235103i	$0.924457\pi$
$368$	22.4188	−	0.365781i	1.16866	−	0.0190676i
$369$	−10.8870			−0.566755
$370$	10.9855	−	7.10266i	0.571108	−	0.369250i
$371$	−26.7302	+	11.0720i	−1.38776	+	0.574830i
$372$	−8.41334	−	19.8520i	−0.436211	−	1.02928i
$373$	5.83903	+	14.0967i	0.302333	+	0.729897i	0.999910	+	0.0133874i	$0.00426147\pi$
$373$	5.83903	+	14.0967i	0.302333	+	0.729897i	−0.697577	+	0.716510i	$0.745739\pi$
$374$	20.6849	−	0.0843658i	1.06959	−	0.00436245i
$375$	3.38832	−	13.0575i	0.174972	−	0.674286i
$376$	13.8491	+	5.53893i	0.714211	+	0.285649i
$377$	−3.29270			−0.169583
$378$	−0.0902205	−	22.1204i	−0.00464044	−	1.13775i
$379$	8.06350	−	19.4670i	0.414194	−	0.999953i	−0.569805	−	0.821780i	$-0.692981\pi$
$379$	8.06350	−	19.4670i	0.414194	−	0.999953i	0.983999	−	0.178173i	$-0.0570186\pi$
$380$	6.78234	−	1.27153i	0.347927	−	0.0652282i
$381$	−10.1924	+	4.22184i	−0.522174	+	0.216292i
$382$	8.96668	−	21.8997i	0.458775	−	1.12049i
$383$	14.4872	−	14.4872i	0.740262	−	0.740262i	−0.232366	−	0.972628i	$-0.574647\pi$
$383$	14.4872	−	14.4872i	0.740262	−	0.740262i	0.972628	+	0.232366i	$0.0746467\pi$
$384$	0.389681	+	13.6453i	0.0198858	+	0.696334i
$385$	−3.73138	−	20.8404i	−0.190169	−	1.06212i
$386$	0.660830	+	1.57716i	0.0336353	+	0.0802753i
$387$	0.265126	+	0.109819i	0.0134771	+	0.00558239i
$388$	19.7280	−	0.160929i	1.00154	−	0.00816992i
$389$	24.3436	+	10.0834i	1.23427	+	0.511251i	0.901919	−	0.431905i	$-0.142158\pi$
$389$	24.3436	+	10.0834i	1.23427	+	0.511251i	0.332350	+	0.943156i	$0.392158\pi$
$390$	13.4811	−	19.5307i	0.682640	−	0.988978i
$391$	−17.4677	+	17.4677i	−0.883382	+	0.883382i
$392$	−1.26859	−	2.95969i	−0.0640733	−	0.149487i
$393$	−17.6689			−0.891280
$394$	−0.0563179	−	13.8081i	−0.00283726	−	0.695642i
$395$	17.0080	−	10.8984i	0.855764	−	0.548358i
$396$	−9.50150	−	3.84515i	−0.477468	−	0.193226i
$397$	−30.5493	−	12.6539i	−1.53323	−	0.635083i	−0.553039	−	0.833155i	$-0.686532\pi$
$397$	−30.5493	−	12.6539i	−1.53323	−	0.635083i	−0.980188	+	0.198072i	$0.936532\pi$
$398$	5.74065	+	13.7008i	0.287753	+	0.686760i
$399$		−	5.31120i		−	0.265892i
$400$	−18.3044	−	8.05917i	−0.915218	−	0.402958i
$401$			5.82175i			0.290724i	0.989379	+	0.145362i	$0.0464347\pi$
$401$			5.82175i			0.290724i	−0.989379	+	0.145362i	$0.953565\pi$
$402$	6.70656	−	2.81005i	0.334493	−	0.140153i
$403$	51.3423	+	21.2667i	2.55754	+	1.05937i
$404$	4.93393	−	2.09102i	0.245472	−	0.104032i
$405$	−3.73346	+	2.39233i	−0.185517	+	0.118876i
$406$	2.13581	−	0.00871115i	0.105999	−	0.000432327i
$407$	−13.7297			−0.680557
$408$	−10.7641	−	10.5038i	−0.532901	−	0.520017i
$409$	17.1699	−	17.1699i	0.848998	−	0.848998i	−0.141010	−	0.990008i	$-0.545035\pi$
$409$	17.1699	−	17.1699i	0.848998	−	0.848998i	0.990008	+	0.141010i	$0.0450350\pi$
$410$	18.3487	+	12.6651i	0.906177	+	0.625487i
$411$	12.6532	+	5.24112i	0.624136	+	0.258526i
$412$	−2.74334	−	2.69894i	−0.135155	−	0.132967i
$413$	−8.20487	−	3.39857i	−0.403735	−	0.167233i
$414$	11.2901	−	4.73055i	0.554878	−	0.232494i
$415$	1.63618	+	9.13835i	0.0803170	+	0.448584i
$416$	−25.3811	−	24.3664i	−1.24441	−	1.19466i
$417$	−3.65094	+	3.65094i	−0.178787	+	0.178787i
$418$	−6.70234	−	2.74423i	−0.327822	−	0.134225i
$419$	−32.5858	+	13.4975i	−1.59192	+	0.659396i	−0.990244	−	0.139342i	$-0.955501\pi$
$419$	−32.5858	+	13.4975i	−1.59192	+	0.659396i	−0.601678	+	0.798738i	$0.705501\pi$
$420$	−8.69283	+	12.7043i	−0.424167	+	0.619907i
$421$	−8.21979	+	19.8443i	−0.400608	+	0.967154i	0.586910	+	0.809652i	$0.300344\pi$
$421$	−8.21979	+	19.8443i	−0.400608	+	0.967154i	−0.987519	+	0.157502i	$0.949656\pi$
$422$	10.0619	−	0.0410388i	0.489808	−	0.00199774i
$423$	8.14314			0.395933
$424$	20.0339	−	20.5303i	0.972932	−	0.997037i
$425$	20.6661	−	7.64543i	1.00245	−	0.370858i
$426$	0.0612370	+	15.0142i	0.00296694	+	0.727439i
$427$	5.42630	+	13.1002i	0.262597	+	0.633965i
$428$	10.0434	−	24.8177i	0.485468	−	1.19961i
$429$	−23.0114	+	9.53164i	−1.11100	+	0.460192i
$430$	−0.319081	−	0.493513i	−0.0153874	−	0.0237993i
$431$	31.1195			1.49897			0.749486	−	0.662021i	$-0.230301\pi$
$431$	31.1195			1.49897			0.749486	+	0.662021i	$0.230301\pi$
$432$	8.72228	+	20.1225i	0.419651	+	0.968145i
$433$	−13.1890	+	13.1890i	−0.633823	+	0.633823i	−0.949025	−	0.315202i	$-0.897928\pi$
$433$	−13.1890	+	13.1890i	−0.633823	+	0.633823i	0.315202	+	0.949025i	$0.397928\pi$
$434$	−33.3595	−	13.6588i	−1.60131	−	0.655644i
$435$	−0.770598	−	1.20259i	−0.0369474	−	0.0576598i
$436$	20.4847	+	8.28992i	0.981039	+	0.397015i
$437$	7.99081	−	3.30990i	0.382252	−	0.158334i
$438$	11.1014	−	11.1923i	0.530444	−	0.534789i
$439$	−1.66123	+	1.66123i	−0.0792864	+	0.0792864i	−0.745638	−	0.666351i	$-0.767855\pi$
$439$	−1.66123	+	1.66123i	−0.0792864	+	0.0792864i	0.666351	+	0.745638i	$0.267855\pi$
$440$	11.5404	+	17.5339i	0.550168	+	0.835894i
$441$	−1.24310	−	1.24310i	−0.0591951	−	0.0591951i
$442$	38.7637	−	0.158102i	1.84380	−	0.00752015i
$443$	10.4258	+	25.1701i	0.495344	+	1.19587i	0.951966	+	0.306205i	$0.0990592\pi$
$443$	10.4258	+	25.1701i	0.495344	+	1.19587i	−0.456622	+	0.889661i	$0.650941\pi$
$444$	7.11615	+	7.00099i	0.337718	+	0.332252i
$445$	−6.77903	−	1.48414i	−0.321357	−	0.0703551i
$446$	−30.2728	+	12.6843i	−1.43346	+	0.600618i
$447$	−5.52848	−	5.52848i	−0.261488	−	0.261488i
$448$	16.5279	+	15.7382i	0.780871	+	0.743559i
$449$			12.5920i			0.594251i	0.954838	+	0.297126i	$0.0960280\pi$
$449$			12.5920i			0.594251i	−0.954838	+	0.297126i	$0.903972\pi$
$450$	−10.9125	−	0.374267i	−0.514421	−	0.0176431i
$451$	−8.95475	−	21.6187i	−0.421663	−	1.01798i
$452$	15.7874	−	0.128784i	0.742578	−	0.00605748i
$453$	14.5972	−	6.04637i	0.685838	−	0.284083i
$454$	8.55208	+	8.48260i	0.401369	+	0.398108i
$455$	−6.99263	−	39.0550i	−0.327819	−	1.83093i
$456$	2.07452	+	4.83996i	0.0971481	+	0.226652i
$457$		−	27.3753i		−	1.28056i	−0.768140	−	0.640282i	$-0.778818\pi$
$457$		−	27.3753i		−	1.28056i	0.768140	−	0.640282i	$-0.221182\pi$
$458$	20.3489	+	20.1836i	0.950841	+	0.943116i
$459$	−22.3237	−	9.24680i	−1.04198	−	0.431603i
$460$	−24.5312	−	5.16132i	−1.14377	−	0.240648i
$461$	−9.56985	−	23.1037i	−0.445712	−	1.07605i	−0.973912	−	0.226925i	$-0.927133\pi$
$461$	−9.56985	−	23.1037i	−0.445712	−	1.07605i	0.528200	−	0.849120i	$-0.322867\pi$
$462$	14.9012	−	6.24359i	0.693265	−	0.290478i
$463$	−13.2724	−	13.2724i	−0.616821	−	0.616821i	0.327894	−	0.944715i	$-0.393661\pi$
$463$	−13.2724	−	13.2724i	−0.616821	−	0.616821i	−0.944715	+	0.327894i	$0.893661\pi$
$464$	−1.94291	+	0.842171i	−0.0901973	+	0.0390968i
$465$	4.24855	+	23.7288i	0.197022	+	1.10040i
$466$	−3.65129	−	1.49500i	−0.169143	−	0.0692544i
$467$	10.2311	−	24.7001i	0.473439	−	1.14298i	−0.489194	−	0.872175i	$-0.662709\pi$
$467$	10.2311	−	24.7001i	0.473439	−	1.14298i	0.962633	−	0.270808i	$-0.0872909\pi$
$468$	−17.8059	−	7.20583i	−0.823076	−	0.333090i
$469$	4.65226	−	11.2315i	0.214821	−	0.518624i
$470$	−13.7242	−	9.47314i	−0.633052	−	0.436963i
$471$	8.01708	+	8.01708i	0.369408	+	0.369408i
$472$	8.80434	−	0.107733i	0.405253	−	0.00495883i
$473$			0.616797i			0.0283603i
$474$	10.9443	+	10.8554i	0.502690	+	0.498606i
$475$	−7.70932	−	0.295891i	−0.353728	−	0.0135764i
$476$	−25.1437	+	0.205106i	−1.15246	+	0.00940102i
$477$	5.99308	−	14.4686i	0.274404	−	0.662470i
$478$	−2.94589	+	7.19486i	−0.134742	+	0.329085i
$479$	3.15265			0.144048			0.0720241	−	0.997403i	$-0.477054\pi$
$479$	3.15265			0.144048			0.0720241	+	0.997403i	$0.477054\pi$
$480$	2.95935	−	14.9725i	0.135075	−	0.683397i
$481$	−25.7296			−1.17317
$482$	−11.8739	+	29.0001i	−0.540841	+	1.32092i
$483$	−7.38374	+	17.8259i	−0.335972	+	0.811108i
$484$	−0.000251963	−	0.0308878i	−1.14529e−5	−	0.00140399i
$485$	−21.5470	−	4.71731i	−0.978400	−	0.214202i
$486$	14.1132	+	13.9986i	0.640189	+	0.634988i
$487$		−	30.6930i		−	1.39083i	−0.718608	−	0.695416i	$-0.755220\pi$
$487$		−	30.6930i		−	1.39083i	0.718608	−	0.695416i	$-0.244780\pi$
$488$	−10.0617	−	9.81845i	−0.455472	−	0.444460i
$489$	11.8899	+	11.8899i	0.537681	+	0.537681i
$490$	0.648956	+	3.54121i	0.0293168	+	0.159976i
$491$	−12.0379	+	29.0621i	−0.543263	+	1.31155i	0.379145	+	0.925337i	$0.376218\pi$
$491$	−12.0379	+	29.0621i	−0.543263	+	1.31155i	−0.922408	+	0.386216i	$0.873782\pi$
$492$	−6.38242	+	15.7712i	−0.287742	+	0.711020i
$493$	0.892815	−	2.15545i	0.0402103	−	0.0970764i
$494$	−12.5602	−	5.14270i	−0.565111	−	0.231381i
$495$	9.40470	+	6.54837i	0.422710	+	0.294327i
$496$	35.7347	−	0.583041i	1.60454	−	0.0261793i
$497$	17.7497	+	17.7497i	0.796184	+	0.796184i
$498$	−6.53405	+	2.73777i	−0.292798	+	0.122682i
$499$	−16.7101	−	40.3418i	−0.748047	−	1.80595i	−0.569454	−	0.822023i	$-0.692845\pi$
$499$	−16.7101	−	40.3418i	−0.748047	−	1.80595i	−0.178593	−	0.983923i	$-0.557155\pi$
$500$	17.9563	+	13.3256i	0.803030	+	0.595939i
$501$	22.4396	+	9.29478i	1.00253	+	0.415260i
$502$	−5.34989	−	5.30643i	−0.238777	−	0.236838i
$503$			11.1328i			0.496387i	0.968710	+	0.248193i	$0.0798369\pi$
$503$			11.1328i			0.496387i	−0.968710	+	0.248193i	$0.920163\pi$
$504$	11.5689	+	4.62696i	0.515318	+	0.206101i
$505$	−5.89747	+	1.05592i	−0.262434	+	0.0469876i
$506$	18.6799	+	18.5282i	0.830424	+	0.823677i
$507$	−28.6320	+	11.8598i	−1.27159	+	0.526711i
$508$	−0.149167	−	18.2862i	−0.00661821	−	0.811318i
$509$	1.02850	+	2.48303i	0.0455876	+	0.110058i	0.945033	−	0.326975i	$-0.106029\pi$
$509$	1.02850	+	2.48303i	0.0455876	+	0.110058i	−0.899445	+	0.437033i	$0.856029\pi$
$510$	9.12971	+	14.1207i	0.404270	+	0.625273i
$511$		−	26.3555i		−	1.16590i
$512$	−21.2087	−	7.88611i	−0.937301	−	0.348520i
$513$	5.98219	+	5.98219i	0.264120	+	0.264120i
$514$	10.4984	−	4.39882i	0.463063	−	0.194023i
$515$	2.32137	+	3.62271i	0.102292	+	0.159636i
$516$	0.314514	−	0.319687i	0.0138457	−	0.0140734i
$517$	6.69788	+	16.1701i	0.294572	+	0.711161i
$518$	16.6895	−	0.0680701i	0.733296	−	0.00299083i
$519$	18.0635	+	18.0635i	0.792900	+	0.792900i
$520$	21.6268	+	32.8586i	0.948398	+	1.44094i
$521$	28.4382	−	28.4382i	1.24590	−	1.24590i	0.288386	−	0.957514i	$-0.406881\pi$
$521$	28.4382	−	28.4382i	1.24590	−	1.24590i	0.957514	−	0.288386i	$-0.0931187\pi$
$522$	−0.814135	+	0.820804i	−0.0356337	+	0.0359256i
$523$	−6.44490	+	2.66957i	−0.281816	+	0.116732i	−0.519114	−	0.854705i	$-0.673738\pi$
$523$	−6.44490	+	2.66957i	−0.281816	+	0.116732i	0.237298	+	0.971437i	$0.423738\pi$
$524$	10.9868	−	27.1488i	0.479962	−	1.18600i
$525$	12.6275	−	11.6941i	0.551111	−	0.510370i
$526$	−1.29824	−	0.531554i	−0.0566058	−	0.0231769i
$527$	−27.8429	+	27.8429i	−1.21286	+	1.21286i
$528$	−11.1404	+	11.5099i	−0.484822	+	0.500905i
$529$	−8.42100			−0.366130
$530$	−26.9323	+	17.4131i	−1.16986	+	0.756375i
$531$	4.44115	−	1.83958i	0.192729	−	0.0798311i
$532$	8.16080	+	3.30259i	0.353816	+	0.143185i
$533$	−16.7813	−	40.5135i	−0.726877	−	1.75484i
$534$	−0.0215987	−	5.29560i	−0.000934668	−	0.229163i
$535$	−17.1042	+	24.5649i	−0.739479	+	1.06203i
$536$	0.147475	+	12.0522i	0.00636994	+	0.520574i
$537$	13.0739			0.564179
$538$	−8.86297	+	0.0361486i	−0.382110	+	0.00155848i
$539$	1.44599	−	3.49093i	0.0622832	−	0.150365i
$540$	−4.51826	−	24.1004i	−0.194435	−	1.03711i
$541$	−19.0655	+	7.89720i	−0.819691	+	0.339527i	−0.752813	−	0.658234i	$-0.771304\pi$
$541$	−19.0655	+	7.89720i	−0.819691	+	0.339527i	−0.0668778	+	0.997761i	$0.521304\pi$
$542$	4.89139	+	2.00275i	0.210103	+	0.0860253i
$543$	−12.0441	+	12.0441i	−0.516863	+	0.516863i
$544$	22.8327	−	10.0079i	0.978944	−	0.429083i
$545$	−20.2760	−	14.1179i	−0.868528	−	0.604745i
$546$	27.9249	−	11.7005i	1.19507	−	0.500736i
$547$	28.7870	+	11.9240i	1.23084	+	0.509832i	0.900842	−	0.434148i	$-0.142950\pi$
$547$	28.7870	+	11.9240i	1.23084	+	0.509832i	0.330003	+	0.943980i	$0.392950\pi$
$548$	−15.9211	+	16.1830i	−0.680115	+	0.691302i
$549$	−7.09093	−	2.93716i	−0.302633	−	0.125355i
$550$	−8.23255	−	21.9772i	−0.351037	−	0.937111i
$551$	−0.577604	+	0.577604i	−0.0246068	+	0.0246068i
$552$	−0.234062	−	19.1284i	−0.00996234	−	0.814157i
$553$	25.7716			1.09592
$554$	8.73628	−	0.0356319i	0.371169	−	0.00151386i
$555$	−6.02156	−	9.39721i	−0.255601	−	0.398890i
$556$	−3.33956	−	7.87999i	−0.141629	−	0.334186i
$557$	17.2197	+	7.13265i	0.729624	+	0.302220i	0.716397	−	0.697692i	$-0.245790\pi$
$557$	17.2197	+	7.13265i	0.729624	+	0.302220i	0.0132265	+	0.999913i	$0.495790\pi$
$558$	17.9960	−	7.54032i	0.761831	−	0.319207i
$559$			1.15588i			0.0488885i
$560$	−14.1152	−	21.2565i	−0.596475	−	0.898252i
$561$		−	17.6481i		−	0.745103i
$562$	10.3279	+	24.6490i	0.435657	+	1.03975i
$563$	−26.0393	−	10.7858i	−1.09743	−	0.454569i	−0.240836	−	0.970566i	$-0.577422\pi$
$563$	−26.0393	−	10.7858i	−1.09743	−	0.454569i	−0.856591	+	0.515997i	$0.827422\pi$
$564$	4.77385	−	11.7964i	0.201015	−	0.496716i
$565$	−17.2431	−	3.77505i	−0.725421	−	0.158817i
$566$	−0.145466	−	35.6657i	−0.00611441	−	1.49914i
$567$	−5.65718			−0.237579
$568$	−23.1078	−	9.24196i	−0.969581	−	0.387784i
$569$	−23.4090	+	23.4090i	−0.981358	+	0.981358i	−0.999829	−	0.0184715i	$-0.994120\pi$
$569$	−23.4090	+	23.4090i	−0.981358	+	0.981358i	0.0184715	+	0.999829i	$0.494120\pi$
$570$	−1.06123	−	5.79093i	−0.0444502	−	0.242555i
$571$	−17.2596	−	7.14917i	−0.722293	−	0.299184i	−0.00891231	−	0.999960i	$-0.502837\pi$
$571$	−17.2596	−	7.14917i	−0.722293	−	0.299184i	−0.713381	+	0.700777i	$0.752837\pi$
$572$	−0.336774	−	41.2846i	−0.0140812	−	1.72620i
$573$	−18.6530	−	7.72632i	−0.779240	−	0.322772i
$574$	10.9924	+	26.2348i	0.458812	+	1.09502i
$575$	25.4634	+	11.7108i	1.06190	+	0.488372i
$576$	−12.3497	+	0.302276i	−0.514569	+	0.0125948i
$577$	−2.45829	+	2.45829i	−0.102340	+	0.102340i	−0.756423	−	0.654083i	$-0.773055\pi$
$577$	−2.45829	+	2.45829i	−0.102340	+	0.102340i	0.654083	+	0.756423i	$0.273055\pi$
$578$	−1.29761	+	3.16920i	−0.0539734	+	0.131821i
$579$	1.34789	−	0.558313i	0.0560163	−	0.0232027i
$580$	2.32699	−	0.436256i	0.0966228	−	0.0181145i
$581$	−4.53258	+	10.9426i	−0.188043	+	0.453976i
$582$	−0.0686511	−	16.8320i	−0.00284568	−	0.697708i
$583$	33.6601			1.39406
$584$	10.2943	+	24.0171i	0.425980	+	0.993835i
$585$	17.6245	+	12.2717i	0.728682	+	0.507372i
$586$	−17.8208	+	0.0726840i	−0.736169	+	0.00300255i
$587$	3.88067	+	9.36876i	0.160172	+	0.386690i	0.983508	−	0.180864i	$-0.0578895\pi$
$587$	3.88067	+	9.36876i	0.160172	+	0.386690i	−0.823336	+	0.567555i	$0.807890\pi$
$588$	−2.52954	+	1.07202i	−0.104316	+	0.0442095i
$589$	12.7371	−	5.27586i	0.524821	−	0.217388i
$590$	−9.62503	−	2.06612i	−0.396256	−	0.0850608i
$591$	−11.7809			−0.484601
$592$	−15.1822	+	6.58084i	−0.623983	+	0.270471i
$593$	2.49306	−	2.49306i	0.102378	−	0.102378i	−0.654063	−	0.756440i	$-0.726937\pi$
$593$	2.49306	−	2.49306i	0.102378	−	0.102378i	0.756440	+	0.654063i	$0.226937\pi$
$594$	−9.75134	+	23.8161i	−0.400102	+	0.977187i
$595$	27.4620	+	6.01229i	1.12583	+	0.246480i
$596$	11.9324	−	5.05697i	0.488769	−	0.207142i
$597$	11.7091	−	4.85008i	0.479223	−	0.198501i
$598$	35.0063	+	34.7219i	1.43151	+	1.41988i
$599$	−4.69333	+	4.69333i	−0.191764	+	0.191764i	−0.796458	−	0.604694i	$-0.793296\pi$
$599$	−4.69333	+	4.69333i	−0.191764	+	0.191764i	0.604694	+	0.796458i	$0.293296\pi$
$600$	−6.93955	+	15.5887i	−0.283306	+	0.636407i
$601$	4.79610	+	4.79610i	0.195637	+	0.195637i	0.798127	−	0.602490i	$-0.205825\pi$
$601$	4.79610	+	4.79610i	0.195637	+	0.195637i	−0.602490	+	0.798127i	$0.705825\pi$
$602$	−0.00305799	−	0.749763i	−0.000124634	−	0.0305581i
$603$	2.51818	+	6.07943i	0.102548	+	0.247574i
$604$	0.213632	+	26.1888i	0.00869254	+	1.06561i
$605$	−0.00738581	+	0.0337358i	−0.000300276	+	0.00137155i
$606$	−1.76683	−	4.21677i	−0.0717725	−	0.171295i
$607$	17.0112	+	17.0112i	0.690465	+	0.690465i	0.962334	−	0.271869i	$-0.0876418\pi$
$607$	17.0112	+	17.0112i	0.690465	+	0.690465i	−0.271869	+	0.962334i	$0.587642\pi$
$608$	−8.72670	+	0.177988i	−0.353915	+	0.00721836i
$609$		−	1.82224i		−	0.0738411i
$610$	8.53399	+	13.1993i	0.345531	+	0.534423i
$611$	12.5519	+	30.3029i	0.507794	+	1.22592i
$612$	9.54510	−	9.70210i	0.385838	−	0.392184i
$613$	−2.30499	+	0.954758i	−0.0930976	+	0.0385623i	−0.428746	−	0.903425i	$-0.641045\pi$
$613$	−2.30499	+	0.954758i	−0.0930976	+	0.0385623i	0.335649	+	0.941987i	$0.391045\pi$
$614$	8.83918	−	8.91158i	0.356720	−	0.359642i
$615$	10.8694	−	15.6105i	0.438296	−	0.629476i
$616$	0.327671	+	26.7784i	0.0132022	+	1.07893i
$617$		−	17.8586i		−	0.718961i	−0.933153	−	0.359481i	$-0.882954\pi$
$617$		−	17.8586i		−	0.718961i	0.933153	−	0.359481i	$-0.117046\pi$
$618$	−2.31221	+	2.33115i	−0.0930107	+	0.0937726i
$619$	−13.7857	−	5.71022i	−0.554094	−	0.229513i	0.0880251	−	0.996118i	$-0.471944\pi$
$619$	−13.7857	−	5.71022i	−0.554094	−	0.229513i	−0.642119	+	0.766605i	$0.721944\pi$
$620$	−39.1019	−	8.22696i	−1.57037	−	0.330402i
$621$	−11.7614	−	28.3946i	−0.471969	−	1.13943i
$622$	7.16390	+	17.0976i	0.287246	+	0.685551i
$623$	−6.26045	−	6.26045i	−0.250820	−	0.250820i
$624$	−20.8771	+	21.5696i	−0.835752	+	0.863477i
$625$	−16.2707	−	18.9806i	−0.650827	−	0.759226i
$626$	6.67868	−	16.3116i	0.266934	−	0.651943i
$627$	−2.36462	+	5.70870i	−0.0944338	+	0.227983i
$628$	−17.3036	+	7.33333i	−0.690490	+	0.292632i
$629$	6.97658	−	16.8429i	0.278174	−	0.671572i
$630$	−11.4646	−	7.91341i	−0.456760	−	0.315278i
$631$	−35.0175	−	35.0175i	−1.39403	−	1.39403i	−0.816062	−	0.577965i	$-0.803847\pi$
$631$	−35.0175	−	35.0175i	−1.39403	−	1.39403i	−0.577965	−	0.816062i	$-0.696153\pi$
$632$	−23.4850	+	10.0662i	−0.934184	+	0.400412i
$633$		−	8.58471i		−	0.341212i
$634$	−13.6604	+	13.7723i	−0.542525	+	0.546969i
$635$	−4.37254	+	19.9722i	−0.173519	+	0.792572i
$636$	−17.4461	−	17.1638i	−0.691784	−	0.680589i
$637$	2.70979	−	6.54202i	0.107366	−	0.259204i
$638$	−2.29954	−	0.941531i	−0.0910396	−	0.0372756i
$639$	−13.5872			−0.537502
$640$	21.1655	+	13.8572i	0.836638	+	0.547756i
$641$	23.8169			0.940713			0.470356	−	0.882477i	$-0.344125\pi$
$641$	23.8169			0.940713			0.470356	+	0.882477i	$0.344125\pi$
$642$	−21.1388	−	8.65514i	−0.834282	−	0.341591i
$643$	−9.23548	+	22.2964i	−0.364212	+	0.879285i	0.630463	+	0.776220i	$0.282865\pi$
$643$	−9.23548	+	22.2964i	−0.364212	+	0.879285i	−0.994675	+	0.103066i	$0.967135\pi$
$644$	−22.7987	−	22.4298i	−0.898395	−	0.883857i
$645$	−0.422162	+	0.270514i	−0.0166226	+	0.0106515i
$646$	6.77218	−	6.82765i	0.266448	−	0.268630i
$647$		−	12.3627i		−	0.486028i	−0.970023	−	0.243014i	$-0.921864\pi$
$647$		−	12.3627i		−	0.486028i	0.970023	−	0.243014i	$-0.0781361\pi$
$648$	5.15524	−	2.20965i	0.202517	−	0.0868034i
$649$	7.30585	+	7.30585i	0.286780	+	0.286780i
$650$	−15.4278	−	41.1854i	−0.605130	−	1.61542i
$651$	−11.7694	+	28.4139i	−0.461280	+	1.11363i
$652$	−25.6625	+	10.8759i	−1.00502	+	0.425931i
$653$	−2.46905	+	5.96081i	−0.0966213	+	0.233265i	−0.964799	−	0.262990i	$-0.915292\pi$
$653$	−2.46905	+	5.96081i	−0.0966213	+	0.233265i	0.868177	+	0.496254i	$0.165292\pi$
$654$	7.14401	−	17.4481i	0.279353	−	0.682275i
$655$	−18.7108	+	26.8722i	−0.731091	+	1.04998i
$656$	−20.2642	−	19.6135i	−0.791183	−	0.765780i
$657$	10.0874	+	10.0874i	0.393548	+	0.393548i
$658$	−8.22195	−	19.6228i	−0.320525	−	0.764976i
$659$	11.6543	+	28.1360i	0.453988	+	1.09602i	0.970793	+	0.239921i	$0.0771214\pi$
$659$	11.6543	+	28.1360i	0.453988	+	1.09602i	−0.516804	+	0.856103i	$0.672879\pi$
$660$	14.9996	−	9.78495i	0.583857	−	0.380879i
$661$	15.2017	+	6.29677i	0.591279	+	0.244916i	0.658201	−	0.752842i	$-0.271318\pi$
$661$	15.2017	+	6.29677i	0.591279	+	0.244916i	−0.0669216	+	0.997758i	$0.521318\pi$
$662$	18.4446	−	18.5957i	0.716870	−	0.722741i
$663$		−	33.0726i		−	1.28443i
$664$	−0.143681	−	11.7421i	−0.00557591	−	0.455683i
$665$	−8.07767	−	5.62437i	−0.313238	−	0.218104i
$666$	−6.36177	+	6.41387i	−0.246513	+	0.248533i
$667$	2.74161	−	1.13561i	0.106155	−	0.0439710i
$668$	−28.2350	+	28.6994i	−1.09244	+	1.11041i
$669$	10.7165	+	25.8720i	0.414325	+	1.00027i
$670$	2.82828	−	13.1756i	0.109266	−	0.509017i
$671$		−	16.4966i		−	0.636843i
$672$	13.4849	−	14.0464i	0.520191	−	0.541852i
$673$	3.09274	+	3.09274i	0.119216	+	0.119216i	0.764198	−	0.644982i	$-0.223135\pi$
$673$	3.09274	+	3.09274i	0.119216	+	0.119216i	−0.644982	+	0.764198i	$0.723135\pi$
$674$	−14.3701	−	34.2962i	−0.553515	−	1.32104i
$675$	−1.05142	+	27.3943i	−0.0404692	+	1.05441i
$676$	−0.419031	−	51.3685i	−0.0161166	−	1.97571i
$677$	−3.25254	−	7.85233i	−0.125005	−	0.301790i	0.848971	−	0.528439i	$-0.177223\pi$
$677$	−3.25254	−	7.85233i	−0.125005	−	0.301790i	−0.973976	+	0.226650i	$0.927223\pi$
$678$	−0.0549383	−	13.4698i	−0.00210989	−	0.517306i
$679$	−19.8987	−	19.8987i	−0.763643	−	0.763643i
$680$	−27.3738	+	5.24761i	−1.04974	+	0.201237i
$681$	7.26688	−	7.26688i	0.278467	−	0.278467i
$682$	29.7751	+	29.5332i	1.14015	+	1.13089i
$683$	5.55915	−	2.30268i	0.212715	−	0.0881095i	−0.273782	−	0.961792i	$-0.588275\pi$
$683$	5.55915	−	2.30268i	0.212715	−	0.0881095i	0.486497	+	0.873682i	$0.338275\pi$
$684$	−4.38755	+	1.85946i	−0.167762	+	0.0710980i
$685$	21.3704	−	13.6938i	0.816520	−	0.523211i
$686$	8.96057	−	21.8848i	0.342116	−	0.835564i
$687$	17.2909	−	17.2909i	0.659687	−	0.659687i
$688$	0.295639	+	0.682046i	0.0112711	+	0.0260027i
$689$	63.0793			2.40313
$690$	−4.48886	+	20.9114i	−0.170888	+	0.796083i
$691$	−16.5713	+	6.86406i	−0.630403	+	0.261121i	−0.674924	−	0.737887i	$-0.735824\pi$
$691$	−16.5713	+	6.86406i	−0.630403	+	0.261121i	0.0445215	+	0.999008i	$0.485824\pi$
$692$	−38.9873	+	16.5229i	−1.48207	+	0.628107i
$693$	5.59510	+	13.5078i	0.212540	+	0.513117i
$694$	−33.8999	+	0.138264i	−1.28682	+	0.00524844i
$695$	1.68640	+	9.41885i	0.0639690	+	0.357277i
$696$	0.711756	+	1.66057i	0.0269790	+	0.0629436i
$697$	31.0710			1.17690
$698$	0.103440	+	25.3615i	0.00391525	+	0.959947i
$699$	−1.28819	+	3.10998i	−0.0487240	+	0.117630i
$700$	10.1162	+	26.6741i	0.382358	+	1.00819i
$701$	4.40983	−	1.82661i	0.166557	−	0.0689901i	−0.297847	−	0.954614i	$-0.596269\pi$
$701$	4.40983	−	1.82661i	0.166557	−	0.0689901i	0.464404	+	0.885623i	$0.346269\pi$
$702$	−18.2741	+	44.6315i	−0.689710	+	1.68451i
$703$	−4.51348	+	4.51348i	−0.170229	+	0.170229i
$704$	−10.7581	−	24.2745i	−0.405460	−	0.914881i
$705$	−8.12997	+	11.6762i	−0.306192	+	0.439750i
$706$	10.2279	+	24.4103i	0.384933	+	0.918693i
$707$	−7.06186	−	2.92512i	−0.265589	−	0.110010i
$708$	−0.0612781	−	7.51200i	−0.00230297	−	0.282318i
$709$	37.4804	+	15.5249i	1.40761	+	0.583049i	0.951714	−	0.306986i	$-0.0993206\pi$
$709$	37.4804	+	15.5249i	1.40761	+	0.583049i	0.455891	+	0.890035i	$0.349321\pi$
$710$	22.8995	+	15.8064i	0.859404	+	0.593202i
$711$	−9.86393	+	9.86393i	−0.369926	+	0.369926i
$712$	8.15028	+	3.25970i	0.305445	+	0.122163i
$713$	−50.0839			−1.87566
$714$	0.0874969	+	21.4526i	0.00327449	+	0.802843i
$715$	−9.87187	+	45.0912i	−0.369187	+	1.68631i
$716$	−8.12954	+	20.0884i	−0.303815	+	0.750738i
$717$	6.12820	+	2.53838i	0.228862	+	0.0947977i
$718$	−1.18978	−	2.83956i	−0.0444021	−	0.105972i
$719$		−	49.3502i		−	1.84045i	−0.391386	−	0.920226i	$-0.628004\pi$
$719$		−	49.3502i		−	1.84045i	0.391386	−	0.920226i	$-0.371996\pi$
$720$	13.5383	+	2.73331i	0.504543	+	0.101864i
$721$			5.48937i			0.204435i
$722$	21.6771	−	9.08271i	0.806738	−	0.338023i
$723$	24.7007	+	10.2314i	0.918630	+	0.380509i
$724$	−11.0169	−	25.9954i	−0.409441	−	0.966111i
$725$	−2.64503	−	0.101519i	−0.0982339	−	0.00377032i
$726$	−0.0263535		0.000107486i	−0.000978070		3.98917e-6i
$727$	−1.88680			−0.0699775			−0.0349888	−	0.999388i	$-0.511140\pi$
$727$	−1.88680			−0.0699775			−0.0349888	+	0.999388i	$0.511140\pi$
$728$	0.614057	+	50.1829i	0.0227585	+	1.85990i
$729$	16.1989	−	16.1989i	0.599960	−	0.599960i
$730$	−5.26612	−	28.7360i	−0.194908	−	1.06357i
$731$	−0.756655	−	0.313417i	−0.0279859	−	0.0115921i
$732$	−8.41184	+	8.55020i	−0.310911	+	0.316025i
$733$	−24.5778	−	10.1805i	−0.907803	−	0.376024i	−0.120588	−	0.992703i	$-0.538478\pi$
$733$	−24.5778	−	10.1805i	−0.907803	−	0.376024i	−0.787215	+	0.616678i	$0.788478\pi$
$734$	−42.6554	+	17.8726i	−1.57444	+	0.659690i
$735$	3.02352	−	0.541348i	0.111524	−	0.0199679i
$736$	29.5368	+	11.5347i	1.08874	+	0.425174i
$737$	−10.0009	+	10.0009i	−0.368387	+	0.368387i
$738$	−14.2485	−	5.83394i	−0.524493	−	0.214750i
$739$	18.2668	−	7.56635i	0.671954	−	0.278333i	−0.0205048	−	0.999790i	$-0.506527\pi$
$739$	18.2668	−	7.56635i	0.671954	−	0.278333i	0.692459	+	0.721457i	$0.256527\pi$
$740$	18.1834	−	3.40897i	0.668435	−	0.125316i
$741$	−4.43131	+	10.6981i	−0.162788	+	0.393006i
$742$	−40.9164	+	0.166882i	−1.50209	+	0.00612644i
$743$	12.5162			0.459176			0.229588	−	0.973288i	$-0.426262\pi$
$743$	12.5162			0.459176			0.229588	+	0.973288i	$0.426262\pi$
$744$	−0.373086	−	30.4899i	−0.0136780	−	1.11781i
$745$	−14.2626	+	2.55366i	−0.522541	+	0.0935588i
$746$	0.0880085	+	21.5780i	0.00322222	+	0.790028i
$747$	−2.45341	−	5.92305i	−0.0897654	−	0.216713i
$748$	27.1168	+	10.9739i	0.991489	+	0.401244i
$749$	−35.2819	+	14.6143i	−1.28917	+	0.533993i
$750$	11.4315	−	15.2734i	0.417420	−	0.557707i
$751$	36.0130			1.31413			0.657067	−	0.753832i	$-0.271797\pi$
$751$	36.0130			1.31413			0.657067	+	0.753832i	$0.271797\pi$
$752$	15.1570	+	14.6703i	0.552718	+	0.534972i
$753$	−4.54591	+	4.54591i	−0.165662	+	0.165662i
$754$	−4.30935	−	1.76443i	−0.156937	−	0.0642569i
$755$	6.26219	−	28.6035i	0.227905	−	1.04099i
$756$	11.7354	−	28.9986i	0.426813	−	1.05467i
$757$	3.48710	−	1.44440i	0.126741	−	0.0524977i	−0.318412	−	0.947952i	$-0.603149\pi$
$757$	3.48710	−	1.44440i	0.126741	−	0.0524977i	0.445153	+	0.895455i	$0.353149\pi$
$758$	20.9848	−	21.1567i	0.762203	−	0.768446i
$759$	15.8727	−	15.8727i	0.576143	−	0.576143i
$760$	9.55781	+	1.97027i	0.346698	+	0.0714693i
$761$	33.9805	+	33.9805i	1.23179	+	1.23179i	0.963274	+	0.268519i	$0.0865342\pi$
$761$	33.9805	+	33.9805i	1.23179	+	1.23179i	0.268519	+	0.963274i	$0.413466\pi$
$762$	−15.6018	+	0.0636336i	−0.565192	+	0.00230520i
$763$	−12.0627	−	29.1219i	−0.436699	−	1.05429i
$764$	23.4704	−	23.8565i	0.849131	−	0.863098i
$765$	−12.8121	+	8.20975i	−0.463222	+	0.296824i
$766$	26.7234	−	11.1971i	0.965557	−	0.404569i
$767$	13.6912	+	13.6912i	0.494360	+	0.494360i
$768$	−6.80201	+	18.0672i	−0.245446	+	0.651945i
$769$			33.3956i			1.20428i	0.798392	+	0.602138i	$0.205684\pi$
$769$			33.3956i			1.20428i	−0.798392	+	0.602138i	$0.794316\pi$
$770$	6.28410	−	29.2746i	0.226463	−	1.05498i
$771$	−3.71641	−	8.97222i	−0.133843	−	0.323127i
$772$	0.0197264	+	2.41824i	0.000709970	+	0.0870342i
$773$	−18.7580	+	7.76983i	−0.674679	+	0.279461i	−0.693601	−	0.720360i	$-0.743977\pi$
$773$	−18.7580	+	7.76983i	−0.674679	+	0.279461i	0.0189214	+	0.999821i	$0.493977\pi$
$774$	0.288138	+	0.285797i	0.0103569	+	0.0102728i
$775$	40.5877	+	18.6665i	1.45795	+	0.670521i
$776$	25.9055	+	10.3609i	0.929953	+	0.371935i
$777$		−	14.2393i		−	0.510831i
$778$	26.4566	+	26.2416i	0.948514	+	0.940808i
$779$	−10.0506	−	4.16311i	−0.360102	−	0.149159i
$780$	28.1093	−	18.3370i	1.00647	−	0.656572i
$781$	−11.1757	−	26.9806i	−0.399899	−	0.965441i
$782$	−32.2214	+	13.5008i	−1.15223	+	0.482786i
$783$	2.05246	+	2.05246i	0.0733489	+	0.0733489i
$784$	−0.0742909	−	4.55330i	−0.00265324	−	0.162618i
$785$	20.6828	−	3.70317i	0.738201	−	0.132172i
$786$	−23.1244	−	9.46812i	−0.824819	−	0.337717i
$787$	0.428092	−	1.03350i	0.0152598	−	0.0368405i	−0.916066	−	0.401028i	$-0.868653\pi$
$787$	0.428092	−	1.03350i	0.0152598	−	0.0368405i	0.931326	+	0.364187i	$0.118653\pi$
$788$	7.32554	−	18.1017i	0.260962	−	0.644845i
$789$	−0.458025	+	1.10577i	−0.0163061	+	0.0393664i
$790$	28.0994	−	5.14944i	0.999732	−	0.183209i
$791$	−15.9240	−	15.9240i	−0.566192	−	0.566192i
$792$	−10.3747	−	10.1239i	−0.368649	−	0.359736i
$793$		−	30.9146i		−	1.09781i
$794$	−33.2009	−	32.9312i	−1.17826	−	1.16869i
$795$	14.7626	+	23.0384i	0.523576	+	0.817089i
$796$	0.171364	+	21.0073i	0.00607384	+	0.744583i
$797$	2.33727	−	5.64266i	0.0827903	−	0.199873i	−0.877063	−	0.480375i	$-0.840501\pi$
$797$	2.33727	−	5.64266i	0.0827903	−	0.199873i	0.959854	+	0.280501i	$0.0905007\pi$
$798$	2.84607	−	6.95108i	0.100750	−	0.246066i
$799$	−23.2401			−0.822177
$800$	−19.6374	−	20.3561i	−0.694287	−	0.719698i
$801$	4.79230			0.169328
$802$	−3.11966	+	7.61927i	−0.110159	+	0.269046i
$803$	−11.7338	+	28.3280i	−0.414079	+	0.999674i
$804$	10.2831	−	0.0838828i	0.362656	−	0.00295832i
$805$	19.2919	+	30.1068i	0.679949	+	1.06112i
$806$	55.7987	+	55.3454i	1.96543	+	1.94946i
$807$			7.56177i			0.266187i
$808$	7.57783	−	0.0927252i	0.266587	−	0.00326206i
$809$	−23.1009	−	23.1009i	−0.812186	−	0.812186i	0.172776	−	0.984961i	$-0.444726\pi$
$809$	−23.1009	−	23.1009i	−0.812186	−	0.812186i	−0.984961	+	0.172776i	$0.944726\pi$
$810$	−6.16816	+	1.13037i	−0.216727	+	0.0397170i
$811$	14.0560	−	33.9342i	0.493573	−	1.19159i	−0.459317	−	0.888272i	$-0.651906\pi$
$811$	14.0560	−	33.9342i	0.493573	−	1.19159i	0.952890	−	0.303317i	$-0.0980942\pi$
$812$	2.79993	+	1.13310i	0.0982583	+	0.0397640i
$813$	1.72571	−	4.16623i	0.0605232	−	0.146116i
$814$	−17.9689	−	7.35725i	−0.629810	−	0.257871i
$815$	30.6741	−	5.49206i	1.07447	−	0.192379i
$816$	−8.45897	−	19.5150i	−0.296123	−	0.683163i
$817$	0.202764	+	0.202764i	0.00709382	+	0.00709382i
$818$	31.6720	−	13.2706i	1.10739	−	0.463995i
$819$	10.4852	+	25.3136i	0.366384	+	0.884529i
$820$	17.2272	+	26.4080i	0.601601	+	0.922207i
$821$	−27.2377	−	11.2822i	−0.950602	−	0.393752i	−0.147145	−	0.989115i	$-0.547008\pi$
$821$	−27.2377	−	11.2822i	−0.950602	−	0.393752i	−0.803457	+	0.595363i	$0.797008\pi$
$822$	13.7515	+	13.6397i	0.479637	+	0.475741i
$823$		−	22.3084i		−	0.777622i	−0.921318	−	0.388811i	$-0.872886\pi$
$823$		−	22.3084i		−	0.777622i	0.921318	−	0.388811i	$-0.127114\pi$
$824$	−2.14411	−	5.00232i	−0.0746935	−	0.174264i
$825$	−18.7790	+	6.94730i	−0.653800	+	0.241874i
$826$	−8.91703	−	8.84459i	−0.310263	−	0.307743i
$827$	11.9572	−	4.95283i	0.415792	−	0.172227i	−0.164973	−	0.986298i	$-0.552754\pi$
$827$	11.9572	−	4.95283i	0.415792	−	0.172227i	0.580765	+	0.814071i	$0.302754\pi$
$828$	17.3109	−	0.141212i	0.601597	−	0.00490744i
$829$	−6.35979	−	15.3539i	−0.220885	−	0.533262i	0.774126	−	0.633031i	$-0.218190\pi$
$829$	−6.35979	−	15.3539i	−0.220885	−	0.533262i	−0.995011	+	0.0997690i	$0.968190\pi$
$830$	−2.75553	+	12.8367i	−0.0956458	+	0.445567i
$831$		−	7.45368i		−	0.258565i
$832$	−20.1607	−	45.4906i	−0.698945	−	1.57710i
$833$	3.54774	+	3.54774i	0.122922	+	0.122922i
$834$	−6.73461	+	2.82180i	−0.233200	+	0.0977110i
$835$	37.8990	−	24.2850i	1.31155	−	0.840416i
$836$	−7.30122	−	7.18307i	−0.252518	−	0.248432i
$837$	−18.7473	−	45.2599i	−0.648000	−	1.56441i
$838$	−49.8798	+	0.203441i	−1.72307	+	0.00702774i
$839$	−2.21827	−	2.21827i	−0.0765832	−	0.0765832i	0.667778	−	0.744361i	$-0.267246\pi$
$839$	−2.21827	−	2.21827i	−0.0765832	−	0.0765832i	−0.744361	+	0.667778i	$0.767246\pi$
$840$	−18.1846	+	11.9687i	−0.627428	+	0.412960i
$841$	20.3079	−	20.3079i	0.700273	−	0.700273i
$842$	−21.3916	+	21.5668i	−0.737202	+	0.743241i
$843$	21.0658	−	8.72572i	0.725543	−	0.300530i
$844$	13.1906	+	5.33811i	0.454041	+	0.183745i
$845$	−12.2831	+	56.1048i	−0.422551	+	1.93006i
$846$	10.6574	+	4.36361i	0.366409	+	0.150024i
$847$	−0.0311550	+	0.0311550i	−0.00107050	+	0.00107050i
$848$	37.2210	−	16.1337i	1.27817	−	0.554035i
$849$	−30.4294			−1.04434
$850$	31.1438	+	1.06814i	1.06822	+	0.0366369i
$851$	21.4233	−	8.87382i	0.734381	−	0.304191i
$852$	−7.96539	+	19.6828i	−0.272890	+	0.674320i
$853$	−5.79560	−	13.9918i	−0.198437	−	0.479070i	0.793068	−	0.609133i	$-0.208482\pi$
$853$	−5.79560	−	13.9918i	−0.198437	−	0.479070i	−0.991506	+	0.130062i	$0.958482\pi$
$854$	0.0817877	+	20.0528i	0.00279872	+	0.686193i
$855$	5.24438	−	0.938983i	0.179354	−	0.0321125i
$856$	26.4433	−	27.0985i	0.903814	−	0.926207i
$857$	−33.3396			−1.13886			−0.569430	−	0.822040i	$-0.692836\pi$
$857$	−33.3396			−1.13886			−0.569430	+	0.822040i	$0.692836\pi$
$858$	−35.2241	+	0.143665i	−1.20253	+	0.00490465i
$859$	−3.32977	+	8.03877i	−0.113610	+	0.274279i	−0.970449	−	0.241304i	$-0.922425\pi$
$859$	−3.32977	+	8.03877i	−0.113610	+	0.274279i	0.856839	+	0.515583i	$0.172425\pi$
$860$	−0.153145	−	0.816874i	−0.00522220	−	0.0278552i
$861$	22.4210	−	9.28709i	0.764106	−	0.316503i
$862$	40.7279	+	16.6758i	1.38720	+	0.567978i
$863$	−20.8688	+	20.8688i	−0.710384	+	0.710384i	−0.966615	−	0.256232i	$-0.917519\pi$
$863$	−20.8688	+	20.8688i	−0.710384	+	0.710384i	0.256232	+	0.966615i	$0.417519\pi$
$864$	0.632463	+	31.0095i	0.0215168	+	1.05496i
$865$	46.6010	−	8.34370i	1.58448	−	0.283694i
$866$	−24.3287	+	10.1937i	−0.826724	+	0.346397i
$867$	2.69936	+	1.11811i	0.0916750	+	0.0379730i
$868$	−36.3403	−	35.7522i	−1.23347	−	1.21351i
$869$	−27.7004	−	11.4739i	−0.939672	−	0.389225i
$870$	−0.364104	−	1.98684i	−0.0123443	−	0.0673601i
$871$	−18.7417	+	18.7417i	−0.635039	+	0.635039i
$872$	22.3673	+	21.8265i	0.757451	+	0.739138i
$873$	15.2322			0.515533
$874$	12.2317	−	0.0498884i	0.413743	−	0.00168750i
$875$	−4.41306	−	31.5885i	−0.149189	−	1.06789i
$876$	20.5266	−	8.69921i	0.693528	−	0.293919i
$877$	29.2461	+	12.1141i	0.987571	+	0.409065i	0.817225	−	0.576319i	$-0.195511\pi$
$877$	29.2461	+	12.1141i	0.987571	+	0.409065i	0.170346	+	0.985384i	$0.445511\pi$
$878$	−3.06435	+	1.28396i	−0.103417	+	0.0433316i
$879$			15.2044i			0.512833i
$880$	5.70789	+	29.1317i	0.192413	+	0.982029i
$881$		−	19.8623i		−	0.669177i	−0.942364	−	0.334589i	$-0.891403\pi$
$881$		−	19.8623i		−	0.669177i	0.942364	−	0.334589i	$-0.108597\pi$
$882$	−0.960785	−	2.29304i	−0.0323513	−	0.0772108i
$883$	−51.1935	−	21.2050i	−1.72280	−	0.713606i	−0.999740	−	0.0228200i	$-0.992736\pi$
$883$	−51.1935	−	21.2050i	−1.72280	−	0.713606i	−0.723059	−	0.690786i	$-0.757264\pi$
$884$	50.8170	+	20.5651i	1.70916	+	0.691679i
$885$	−1.79625	+	8.20462i	−0.0603802	+	0.275795i
$886$	0.157142	+	38.5283i	0.00527930	+	1.29438i
$887$	8.37787			0.281301			0.140651	−	0.990059i	$-0.455081\pi$
$887$	8.37787			0.281301			0.140651	+	0.990059i	$0.455081\pi$
$888$	5.56176	+	12.9759i	0.186640	+	0.435442i
$889$	−18.4444	+	18.4444i	−0.618604	+	0.618604i
$890$	−8.07682	−	5.57501i	−0.270736	−	0.186875i
$891$	6.08057	+	2.51866i	0.203707	+	0.0843782i
$892$	−46.4168	+	0.378639i	−1.55415	+	0.0126778i
$893$	7.51757	+	3.11388i	0.251566	+	0.104202i
$894$	−4.27294	−	10.1980i	−0.142909	−	0.341071i
$895$	13.8448	−	19.8837i	0.462780	−	0.664639i
$896$	13.1976	+	29.4542i	0.440900	+	0.983995i
$897$	29.7456	−	29.7456i	0.993175	−	0.993175i
$898$	−6.74756	+	16.4798i	−0.225169	+	0.549940i
$899$	4.37002	−	1.81012i	0.145748	−	0.0603709i
$900$	−14.0813	−	6.33744i	−0.469377	−	0.211248i
$901$	−17.1039	+	41.2926i	−0.569815	+	1.37566i
$902$	−0.134970	−	33.0922i	−0.00449402	−	1.10185i
$903$	−0.639687			−0.0212875
$904$	20.7310	+	8.29134i	0.689501	+	0.275766i
$905$	5.56330	+	31.0719i	0.184930	+	1.03287i
$906$	22.3443	−	0.0911337i	0.742339	−	0.00302772i
$907$	1.62441	+	3.92168i	0.0539378	+	0.130217i	0.948551	−	0.316623i	$-0.102549\pi$
$907$	1.62441	+	3.92168i	0.0539378	+	0.130217i	−0.894614	+	0.446841i	$0.852549\pi$
$908$	6.64711	+	15.6844i	0.220592	+	0.520506i
$909$	3.82246	−	1.58332i	0.126783	−	0.0525152i
$910$	11.7764	−	54.8607i	0.390385	−	1.81861i
$911$	−55.0295			−1.82321			−0.911604	−	0.411069i	$-0.865156\pi$
$911$	−55.0295			−1.82321			−0.911604	+	0.411069i	$0.865156\pi$
$912$	0.121488	+	7.44600i	0.00402285	+	0.246562i
$913$	9.74362	−	9.74362i	0.322467	−	0.322467i
$914$	14.6694	−	35.8277i	0.485221	−	1.18508i
$915$	11.2910	−	7.23503i	0.373267	−	0.239183i
$916$	15.8162	+	37.3196i	0.522581	+	1.23308i
$917$	−38.5960	+	15.9870i	−1.27455	+	0.527936i
$918$	−24.2614	−	24.0643i	−0.800745	−	0.794240i
$919$	−15.9859	+	15.9859i	−0.527328	+	0.527328i	−0.919775	−	0.392447i	$-0.871629\pi$
$919$	−15.9859	+	15.9859i	−0.527328	+	0.527328i	0.392447	+	0.919775i	$0.371629\pi$
$920$	−29.3397	−	19.9003i	−0.967301	−	0.656093i
$921$	−7.57235	−	7.57235i	−0.249518	−	0.249518i
$922$	−0.144241	−	35.3653i	−0.00475033	−	1.16469i
$923$	−20.9434	−	50.5618i	−0.689359	−	1.66426i
$924$	22.8477	−	0.186377i	0.751636	−	0.00613136i
$925$	−20.6686	−	0.793283i	−0.679580	−	0.0260830i
$926$	−10.2582	−	24.4826i	−0.337105	−	0.804547i
$927$	−2.10102	−	2.10102i	−0.0690067	−	0.0690067i
$928$	−2.99409	+	0.0610668i	−0.0982858	+	0.00200461i
$929$			54.2796i			1.78086i	0.455124	+	0.890428i	$0.349595\pi$
$929$			54.2796i			1.78086i	−0.455124	+	0.890428i	$0.650405\pi$
$930$	−7.15507	+	33.3320i	−0.234624	+	1.09300i
$931$	−0.672248	−	1.62295i	−0.0220320	−	0.0531901i
$932$	−3.97755	−	3.91318i	−0.130289	−	0.128180i
$933$	14.6121	−	6.05254i	0.478380	−	0.198151i
$934$	26.6259	−	26.8440i	0.871226	−	0.878362i
$935$	−26.8406	−	18.6887i	−0.877780	−	0.611187i
$936$	−19.4423	−	18.9722i	−0.635490	−	0.620126i
$937$		−	9.11875i		−	0.297897i	−0.988845	−	0.148948i	$-0.952411\pi$
$937$		−	9.11875i		−	0.297897i	0.988845	−	0.148948i	$-0.0475888\pi$
$938$	12.1072	−	12.2064i	0.395316	−	0.398554i
$939$	−13.8934	−	5.75482i	−0.453393	−	0.187802i
$940$	−12.8854	−	19.7524i	−0.420277	−	0.644251i
$941$	−12.1119	−	29.2406i	−0.394835	−	0.953217i	−0.988871	−	0.148778i	$-0.952466\pi$
$941$	−12.1119	−	29.2406i	−0.394835	−	0.953217i	0.594035	−	0.804439i	$-0.297534\pi$
$942$	6.19638	+	14.7885i	0.201889	+	0.481835i
$943$	27.9453	+	27.9453i	0.910023	+	0.910023i
$944$	11.5805	+	4.57692i	0.376913	+	0.148966i
$945$	−19.9857	+	28.7032i	−0.650134	+	0.933715i
$946$	−0.330518	+	0.807238i	−0.0107461	+	0.0262456i
$947$	4.04701	−	9.77034i	0.131510	−	0.317493i	−0.844384	−	0.535739i	$-0.820033\pi$
$947$	4.04701	−	9.77034i	0.131510	−	0.317493i	0.975894	+	0.218245i	$0.0700333\pi$
$948$	8.50648	+	20.0718i	0.276278	+	0.651901i
$949$	−21.9893	+	53.0869i	−0.713803	+	1.72327i
$950$	−9.93108	−	4.51839i	−0.322207	−	0.146596i
$951$	11.7026	+	11.7026i	0.379484	+	0.379484i
$952$	−33.0169	−	13.2051i	−1.07009	−	0.427981i
$953$			26.1916i			0.848430i	0.905561	+	0.424215i	$0.139450\pi$
$953$			26.1916i			0.848430i	−0.905561	+	0.424215i	$0.860550\pi$
$954$	15.5967	−	15.7244i	0.504961	−	0.509097i
$955$	−31.5037	+	20.1870i	−1.01943	+	0.653235i
$956$	−7.71091	+	7.83775i	−0.249389	+	0.253491i
$957$	−0.811289	+	1.95863i	−0.0262253	+	0.0633134i
$958$	4.12606	+	1.68939i	0.133307	+	0.0545816i
$959$	32.3818			1.04566
$960$	11.8963	−	18.0096i	0.383950	−	0.581256i
$961$	−48.8319			−1.57522
$962$	−33.6738	−	13.7875i	−1.08569	−	0.444528i
$963$	7.91044	−	19.0975i	0.254910	−	0.615408i
$964$	−31.0801	+	31.5914i	−1.00102	+	1.01749i
$965$	0.578242	−	2.64120i	0.0186143	−	0.0850233i
$966$	−19.2158	+	19.3732i	−0.618258	+	0.623322i
$967$			25.0714i			0.806243i	0.915146	+	0.403121i	$0.132075\pi$
$967$			25.0714i			0.806243i	−0.915146	+	0.403121i	$0.867925\pi$
$968$	0.0162219	−	0.0405597i	0.000521391	−	0.00130364i
$969$	−5.80160	−	5.80160i	−0.186374	−	0.186374i
$970$	−25.6720	−	17.7201i	−0.824279	−	0.568957i
$971$	8.75256	−	21.1306i	0.280883	−	0.678112i	−0.718974	−	0.695037i	$-0.755388\pi$
$971$	8.75256	−	21.1306i	0.280883	−	0.678112i	0.999857	+	0.0169256i	$0.00538785\pi$
$972$	10.9695	+	25.8835i	0.351847	+	0.830214i
$973$	−4.67171	+	11.2785i	−0.149768	+	0.361572i
$974$	16.4472	−	40.1697i	0.527003	−	1.28712i
$975$	−35.1919	+	13.0193i	−1.12704	+	0.416951i
$976$	−7.90702	−	18.2417i	−0.253097	−	0.583902i
$977$	6.85206	+	6.85206i	0.219217	+	0.219217i	0.808168	−	0.588952i	$-0.200459\pi$
$977$	6.85206	+	6.85206i	0.219217	+	0.219217i	−0.588952	+	0.808168i	$0.700459\pi$
$978$	9.18968	+	21.9324i	0.293853	+	0.701321i
$979$	3.94175	+	9.51624i	0.125979	+	0.304140i
$980$	−1.04828	+	4.98234i	−0.0334859	+	0.159155i
$981$	15.7632	+	6.52933i	0.503280	+	0.208465i
$982$	−31.3280	+	31.5846i	−0.999717	+	1.00791i
$983$			58.8468i			1.87692i	0.345387	+	0.938460i	$0.387747\pi$
$983$			58.8468i			1.87692i	−0.345387	+	0.938460i	$0.612253\pi$
$984$	−16.8042	+	17.2206i	−0.535699	+	0.548972i
$985$	−12.4756	+	17.9173i	−0.397504	+	0.570891i
$986$	2.32350	−	2.34253i	0.0739954	−	0.0746014i
$987$	−16.7702	+	6.94646i	−0.533802	+	0.221108i
$988$	−13.6825	−	13.4611i	−0.435299	−	0.428255i
$989$	−0.398649	−	0.962424i	−0.0126763	−	0.0306033i
$990$	8.79946	+	13.6099i	0.279665	+	0.432550i
$991$			1.38483i			0.0439907i	0.999758	+	0.0219954i	$0.00700190\pi$
$991$			1.38483i			0.0439907i	−0.999758	+	0.0219954i	$0.992998\pi$
$992$	47.0806	+	18.3858i	1.49481	+	0.583751i
$993$	−15.8011	−	15.8011i	−0.501433	−	0.501433i
$994$	13.7187	+	32.7415i	0.435131	+	1.03850i
$995$	5.02320	−	22.9442i	0.159246	−	0.727380i
$996$	−10.0186	+	0.0817250i	−0.317450	+	0.00258956i
$997$	−18.3437	−	44.2856i	−0.580950	−	1.40254i	−0.891953	−	0.452129i	$-0.850665\pi$
$997$	−18.3437	−	44.2856i	−0.580950	−	1.40254i	0.311002	−	0.950409i	$-0.399335\pi$
$998$	−0.251863	−	61.7520i	−0.00797257	−	1.95473i
$999$	16.0382	+	16.0382i	0.507426	+	0.507426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.u.a.43.20	✓	88
4.3	odd	2		640.2.u.a.463.8		88
5.2	odd	4		160.2.ba.a.107.9	yes	88
5.3	odd	4		800.2.bb.b.107.14		88
5.4	even	2		800.2.v.b.43.3		88
20.7	even	4		640.2.ba.a.207.15		88
32.3	odd	8		160.2.ba.a.3.9	yes	88
32.29	even	8		640.2.ba.a.303.15		88
160.3	even	8		800.2.v.b.707.3		88
160.67	even	8	inner	160.2.u.a.67.20	yes	88
160.99	odd	8		800.2.bb.b.643.14		88
160.157	odd	8		640.2.u.a.47.8		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.u.a.43.20	✓	88	1.1	even	1	trivial
160.2.u.a.67.20	yes	88	160.67	even	8	inner
160.2.ba.a.3.9	yes	88	32.3	odd	8
160.2.ba.a.107.9	yes	88	5.2	odd	4
640.2.u.a.47.8		88	160.157	odd	8
640.2.u.a.463.8		88	4.3	odd	2
640.2.ba.a.207.15		88	20.7	even	4
640.2.ba.a.303.15		88	32.29	even	8
800.2.v.b.43.3		88	5.4	even	2
800.2.v.b.707.3		88	160.3	even	8
800.2.bb.b.107.14		88	5.3	odd	4
800.2.bb.b.643.14		88	160.99	odd	8

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30876 + 0.535863i) q^{2} +(0.461737 - 1.11473i) q^{3} +(1.42570 + 1.40263i) q^{4} +(-1.20640 - 1.88271i) q^{5} +(1.20165 - 1.21149i) q^{6} -2.85280i q^{7} +(1.11428 + 2.59969i) q^{8} +(1.09189 + 1.09189i) q^{9} +O(q^{10})\)	\(q+(1.30876 + 0.535863i) q^{2} +(0.461737 - 1.11473i) q^{3} +(1.42570 + 1.40263i) q^{4} +(-1.20640 - 1.88271i) q^{5} +(1.20165 - 1.21149i) q^{6} -2.85280i q^{7} +(1.11428 + 2.59969i) q^{8} +(1.09189 + 1.09189i) q^{9} +(-0.570021 - 3.11048i) q^{10} +(-1.27011 + 3.06631i) q^{11} +(2.22186 - 0.941630i) q^{12} +(-2.38019 + 5.74629i) q^{13} +(1.52871 - 3.73363i) q^{14} +(-2.65576 + 0.475502i) q^{15} +(0.0652546 + 3.99947i) q^{16} +(-3.11621 - 3.11621i) q^{17} +(0.843921 + 2.01413i) q^{18} +(0.590480 + 1.42554i) q^{19} +(0.920770 - 4.37632i) q^{20} +(-3.18011 - 1.31724i) q^{21} +(-3.30539 + 3.33246i) q^{22} -5.60544i q^{23} +(3.41246 - 0.0417562i) q^{24} +(-2.08918 + 4.54261i) q^{25} +(-6.19431 + 6.24505i) q^{26} +(5.06553 - 2.09821i) q^{27} +(4.00143 - 4.06725i) q^{28} +(0.202591 + 0.489097i) q^{29} +(-3.73055 - 0.800803i) q^{30} -8.93487i q^{31} +(-2.05776 + 5.26931i) q^{32} +(2.83166 + 2.83166i) q^{33} +(-2.40851 - 5.74823i) q^{34} +(-5.37099 + 3.44163i) q^{35} +(0.0251919 + 3.08824i) q^{36} +(1.58307 + 3.82187i) q^{37} +(0.00889999 + 2.18211i) q^{38} +(5.30655 + 5.30655i) q^{39} +(3.55017 - 5.23414i) q^{40} +(-4.98538 + 4.98538i) q^{41} +(-3.45614 - 3.42806i) q^{42} +(0.171694 - 0.0711182i) q^{43} +(-6.11170 + 2.59016i) q^{44} +(0.738451 - 3.37298i) q^{45} +(3.00375 - 7.33618i) q^{46} +(3.72891 - 3.72891i) q^{47} +(4.48847 + 1.77396i) q^{48} -1.13848 q^{49} +(-5.16845 + 4.82568i) q^{50} +(-4.91261 + 2.03487i) q^{51} +(-11.4534 + 4.85397i) q^{52} +(-3.88110 - 9.36980i) q^{53} +(7.75392 - 0.0316252i) q^{54} +(7.30523 - 1.30797i) q^{55} +(7.41639 - 3.17883i) q^{56} +1.86175 q^{57} +(0.00305354 + 0.748671i) q^{58} +(1.19131 - 2.87607i) q^{59} +(-4.45327 - 3.04712i) q^{60} +(-4.59206 + 1.90209i) q^{61} +(4.78786 - 11.6936i) q^{62} +(3.11496 - 3.11496i) q^{63} +(-5.51674 + 5.79358i) q^{64} +(13.6900 - 2.45114i) q^{65} +(2.18858 + 5.22334i) q^{66} +(3.93702 + 1.63077i) q^{67} +(-0.0718964 - 8.81368i) q^{68} +(-6.24857 - 2.58824i) q^{69} +(-8.87358 + 1.62616i) q^{70} +(-6.22186 + 6.22186i) q^{71} +(-1.62190 + 4.05526i) q^{72} +9.23847 q^{73} +(0.0238608 + 5.85022i) q^{74} +(4.09915 + 4.42637i) q^{75} +(-1.15766 + 2.86063i) q^{76} +(8.74758 + 3.62337i) q^{77} +(4.10141 + 9.78858i) q^{78} +9.03379i q^{79} +(7.45111 - 4.94783i) q^{80} -1.98303i q^{81} +(-9.19614 + 3.85318i) q^{82} +(-3.83575 - 1.58882i) q^{83} +(-2.68628 - 6.33852i) q^{84} +(-2.10750 + 9.62632i) q^{85} +(0.262816 - 0.00107193i) q^{86} +0.638756 q^{87} +(-9.38671 + 0.114859i) q^{88} +(2.19449 - 2.19449i) q^{89} +(2.77391 - 4.01871i) q^{90} +(16.3930 + 6.79021i) q^{91} +(7.86237 - 7.99169i) q^{92} +(-9.95999 - 4.12556i) q^{93} +(6.87843 - 2.88206i) q^{94} +(1.97153 - 2.83148i) q^{95} +(4.92372 + 4.72689i) q^{96} +(6.97515 - 6.97515i) q^{97} +(-1.48999 - 0.610068i) q^{98} +(-4.73491 + 1.96126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8}+O(q^{10}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8	\( 88 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 16 q^{8} - 16 q^{10} - 8 q^{11} - 20 q^{12} - 4 q^{13} + 16 q^{14} - 8 q^{15} - 8 q^{16} + 4 q^{18} + 16 q^{19} + 24 q^{20} - 8 q^{21} - 20 q^{22} - 32 q^{24} - 4 q^{25} - 8 q^{26} - 16 q^{27} + 12 q^{28} + 8 q^{30} - 24 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 8 q^{36} - 4 q^{37} - 60 q^{38} + 16 q^{40} - 8 q^{41} + 60 q^{42} - 36 q^{43} + 16 q^{44} - 4 q^{45} - 8 q^{46} - 8 q^{47} - 24 q^{48} - 40 q^{49} - 12 q^{50} + 8 q^{51} - 56 q^{52} - 4 q^{53} - 56 q^{54} - 36 q^{55} + 40 q^{56} - 8 q^{57} - 36 q^{58} + 12 q^{60} - 40 q^{61} + 40 q^{62} + 56 q^{63} + 48 q^{64} - 8 q^{65} + 72 q^{66} + 20 q^{67} + 8 q^{68} + 24 q^{69} + 60 q^{70} + 24 q^{71} + 24 q^{72} - 8 q^{73} + 8 q^{75} + 56 q^{76} + 24 q^{77} + 32 q^{78} - 8 q^{80} + 84 q^{82} - 44 q^{83} + 56 q^{84} - 4 q^{85} + 24 q^{86} - 120 q^{87} + 104 q^{88} + 148 q^{90} - 8 q^{91} + 124 q^{92} + 8 q^{93} - 32 q^{94} + 24 q^{96} - 8 q^{97} - 16 q^{98}+O(q^{100}) \) 88 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 16 * q^8 - 16 * q^10 - 8 * q^11 - 20 * q^12 - 4 * q^13 + 16 * q^14 - 8 * q^15 - 8 * q^16 + 4 * q^18 + 16 * q^19 + 24 * q^20 - 8 * q^21 - 20 * q^22 - 32 * q^24 - 4 * q^25 - 8 * q^26 - 16 * q^27 + 12 * q^28 + 8 * q^30 - 24 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 8 * q^36 - 4 * q^37 - 60 * q^38 + 16 * q^40 - 8 * q^41 + 60 * q^42 - 36 * q^43 + 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 - 24 * q^48 - 40 * q^49 - 12 * q^50 + 8 * q^51 - 56 * q^52 - 4 * q^53 - 56 * q^54 - 36 * q^55 + 40 * q^56 - 8 * q^57 - 36 * q^58 + 12 * q^60 - 40 * q^61 + 40 * q^62 + 56 * q^63 + 48 * q^64 - 8 * q^65 + 72 * q^66 + 20 * q^67 + 8 * q^68 + 24 * q^69 + 60 * q^70 + 24 * q^71 + 24 * q^72 - 8 * q^73 + 8 * q^75 + 56 * q^76 + 24 * q^77 + 32 * q^78 - 8 * q^80 + 84 * q^82 - 44 * q^83 + 56 * q^84 - 4 * q^85 + 24 * q^86 - 120 * q^87 + 104 * q^88 + 148 * q^90 - 8 * q^91 + 124 * q^92 + 8 * q^93 - 32 * q^94 + 24 * q^96 - 8 * q^97 - 16 * q^98

Introduction

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