LMFDB - Embedded newform 690.2.h.b.689.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(689,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("690.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.h (of order $2$, degree $1$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			689.16
Character	$\chi$	$=$	690.689
Dual form			690.2.h.b.689.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.250553 + 1.71383i) q^{3} +1.00000 q^{4} +(0.545034 - 2.16863i) q^{5} +(0.250553 + 1.71383i) q^{6} +1.86244 q^{7} +1.00000 q^{8} +(-2.87445 + 0.858813i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.250553 + 1.71383i) q^{3} +1.00000 q^{4} +(0.545034 - 2.16863i) q^{5} +(0.250553 + 1.71383i) q^{6} +1.86244 q^{7} +1.00000 q^{8} +(-2.87445 + 0.858813i) q^{9} +(0.545034 - 2.16863i) q^{10} +2.81769 q^{11} +(0.250553 + 1.71383i) q^{12} +1.42524i q^{13} +1.86244 q^{14} +(3.85322 + 0.390741i) q^{15} +1.00000 q^{16} -3.10510i q^{17} +(-2.87445 + 0.858813i) q^{18} +3.42893i q^{19} +(0.545034 - 2.16863i) q^{20} +(0.466642 + 3.19192i) q^{21} +2.81769 q^{22} +(4.05141 - 2.56633i) q^{23} +(0.250553 + 1.71383i) q^{24} +(-4.40588 - 2.36395i) q^{25} +1.42524i q^{26} +(-2.19206 - 4.71114i) q^{27} +1.86244 q^{28} +6.01613i q^{29} +(3.85322 + 0.390741i) q^{30} +5.09305 q^{31} +1.00000 q^{32} +(0.705981 + 4.82904i) q^{33} -3.10510i q^{34} +(1.01510 - 4.03895i) q^{35} +(-2.87445 + 0.858813i) q^{36} -1.27090 q^{37} +3.42893i q^{38} +(-2.44262 + 0.357098i) q^{39} +(0.545034 - 2.16863i) q^{40} +1.76178i q^{41} +(0.466642 + 3.19192i) q^{42} -9.25323 q^{43} +2.81769 q^{44} +(0.295774 + 6.70168i) q^{45} +(4.05141 - 2.56633i) q^{46} -2.70892 q^{47} +(0.250553 + 1.71383i) q^{48} -3.53130 q^{49} +(-4.40588 - 2.36395i) q^{50} +(5.32162 - 0.777993i) q^{51} +1.42524i q^{52} -5.16111i q^{53} +(-2.19206 - 4.71114i) q^{54} +(1.53573 - 6.11051i) q^{55} +1.86244 q^{56} +(-5.87661 + 0.859130i) q^{57} +6.01613i q^{58} +5.36568i q^{59} +(3.85322 + 0.390741i) q^{60} +6.07393i q^{61} +5.09305 q^{62} +(-5.35350 + 1.59949i) q^{63} +1.00000 q^{64} +(3.09081 + 0.776803i) q^{65} +(0.705981 + 4.82904i) q^{66} -8.70699 q^{67} -3.10510i q^{68} +(5.41335 + 6.30045i) q^{69} +(1.01510 - 4.03895i) q^{70} +4.56938i q^{71} +(-2.87445 + 0.858813i) q^{72} +1.66588i q^{73} -1.27090 q^{74} +(2.94751 - 8.14323i) q^{75} +3.42893i q^{76} +5.24779 q^{77} +(-2.44262 + 0.357098i) q^{78} -10.4725i q^{79} +(0.545034 - 2.16863i) q^{80} +(7.52488 - 4.93723i) q^{81} +1.76178i q^{82} -6.08785i q^{83} +(0.466642 + 3.19192i) q^{84} +(-6.73380 - 1.69238i) q^{85} -9.25323 q^{86} +(-10.3106 + 1.50736i) q^{87} +2.81769 q^{88} -8.61365 q^{89} +(0.295774 + 6.70168i) q^{90} +2.65443i q^{91} +(4.05141 - 2.56633i) q^{92} +(1.27608 + 8.72864i) q^{93} -2.70892 q^{94} +(7.43607 + 1.86888i) q^{95} +(0.250553 + 1.71383i) q^{96} +7.72840 q^{97} -3.53130 q^{98} +(-8.09929 + 2.41987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 - 2 * q^3 + 24 * q^4 - 2 * q^6 + 24 * q^8 + 6 * q^9	$ 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9} - 2 q^{12} + 24 q^{16} + 6 q^{18} + 4 q^{23} - 2 q^{24} + 12 q^{25} - 2 q^{27} - 28 q^{31} + 24 q^{32} - 8 q^{35} + 6 q^{36} + 4 q^{46} - 16 q^{47} - 2 q^{48} - 4 q^{49} + 12 q^{50} - 2 q^{54} + 4 q^{55} - 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} + 6 q^{72} - 6 q^{75} - 8 q^{77} + 14 q^{81} - 44 q^{85} - 28 q^{87} + 4 q^{92} + 4 q^{93} - 16 q^{94} - 4 q^{95} - 2 q^{96} - 4 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 - 2 * q^3 + 24 * q^4 - 2 * q^6 + 24 * q^8 + 6 * q^9 - 2 * q^12 + 24 * q^16 + 6 * q^18 + 4 * q^23 - 2 * q^24 + 12 * q^25 - 2 * q^27 - 28 * q^31 + 24 * q^32 - 8 * q^35 + 6 * q^36 + 4 * q^46 - 16 * q^47 - 2 * q^48 - 4 * q^49 + 12 * q^50 - 2 * q^54 + 4 * q^55 - 28 * q^62 + 24 * q^64 - 8 * q^69 - 8 * q^70 + 6 * q^72 - 6 * q^75 - 8 * q^77 + 14 * q^81 - 44 * q^85 - 28 * q^87 + 4 * q^92 + 4 * q^93 - 16 * q^94 - 4 * q^95 - 2 * q^96 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.250553	+	1.71383i	0.144657	+	0.989482i
$3$	0.250553	+	1.71383i	0.144657	+	0.989482i
$4$	1.00000			0.500000
$5$	0.545034	−	2.16863i	0.243747	−	0.969839i
$5$	0.545034	−	2.16863i	0.243747	−	0.969839i
$6$	0.250553	+	1.71383i	0.102288	+	0.699669i
$7$	1.86244			0.703938			0.351969	−	0.936012i	$-0.385512\pi$
$7$	1.86244			0.703938			0.351969	+	0.936012i	$0.385512\pi$
$8$	1.00000			0.353553
$9$	−2.87445	+	0.858813i	−0.958149	+	0.286271i
$10$	0.545034	−	2.16863i	0.172355	−	0.685780i
$11$	2.81769			0.849564			0.424782	−	0.905296i	$-0.360351\pi$
$11$	2.81769			0.849564			0.424782	+	0.905296i	$0.360351\pi$
$12$	0.250553	+	1.71383i	0.0723285	+	0.494741i
$13$			1.42524i			0.395290i	0.980274	+	0.197645i	$0.0633293\pi$
$13$			1.42524i			0.395290i	−0.980274	+	0.197645i	$0.936671\pi$
$14$	1.86244			0.497759
$15$	3.85322	+	0.390741i	0.994898	+	0.100889i
$16$	1.00000			0.250000
$17$		−	3.10510i		−	0.753097i	−0.926397	−	0.376548i	$-0.877111\pi$
$17$		−	3.10510i		−	0.753097i	0.926397	−	0.376548i	$-0.122889\pi$
$18$	−2.87445	+	0.858813i	−0.677513	+	0.202424i
$19$			3.42893i			0.786651i	0.919399	+	0.393325i	$0.128675\pi$
$19$			3.42893i			0.786651i	−0.919399	+	0.393325i	$0.871325\pi$
$20$	0.545034	−	2.16863i	0.121873	−	0.484919i
$21$	0.466642	+	3.19192i	0.101830	+	0.696534i
$22$	2.81769			0.600733
$23$	4.05141	−	2.56633i	0.844778	−	0.535116i
$23$	4.05141	−	2.56633i	0.844778	−	0.535116i
$24$	0.250553	+	1.71383i	0.0511440	+	0.349835i
$25$	−4.40588	−	2.36395i	−0.881175	−	0.472790i
$26$			1.42524i			0.279512i
$27$	−2.19206	−	4.71114i	−0.421863	−	0.906660i
$28$	1.86244			0.351969
$29$			6.01613i			1.11717i	0.829448	+	0.558584i	$0.188655\pi$
$29$			6.01613i			1.11717i	−0.829448	+	0.558584i	$0.811345\pi$
$30$	3.85322	+	0.390741i	0.703499	+	0.0713392i
$31$	5.09305			0.914739			0.457370	−	0.889277i	$-0.348792\pi$
$31$	5.09305			0.914739			0.457370	+	0.889277i	$0.348792\pi$
$32$	1.00000			0.176777
$33$	0.705981	+	4.82904i	0.122896	+	0.840628i
$34$		−	3.10510i		−	0.532520i
$35$	1.01510	−	4.03895i	0.171583	−	0.682707i
$36$	−2.87445	+	0.858813i	−0.479074	+	0.143136i
$37$	−1.27090			−0.208934			−0.104467	−	0.994528i	$-0.533314\pi$
$37$	−1.27090			−0.208934			−0.104467	+	0.994528i	$0.533314\pi$
$38$			3.42893i			0.556246i
$39$	−2.44262	+	0.357098i	−0.391132	+	0.0571815i
$40$	0.545034	−	2.16863i	0.0861775	−	0.342890i
$41$			1.76178i			0.275144i	0.990492	+	0.137572i	$0.0439299\pi$
$41$			1.76178i			0.275144i	−0.990492	+	0.137572i	$0.956070\pi$
$42$	0.466642	+	3.19192i	0.0720044	+	0.492524i
$43$	−9.25323			−1.41110			−0.705552	−	0.708658i	$-0.749301\pi$
$43$	−9.25323			−1.41110			−0.705552	+	0.708658i	$0.749301\pi$
$44$	2.81769			0.424782
$45$	0.295774	+	6.70168i	0.0440914	+	0.999028i
$46$	4.05141	−	2.56633i	0.597349	−	0.378384i
$47$	−2.70892			−0.395137			−0.197568	−	0.980289i	$-0.563304\pi$
$47$	−2.70892			−0.395137			−0.197568	+	0.980289i	$0.563304\pi$
$48$	0.250553	+	1.71383i	0.0361643	+	0.247370i
$49$	−3.53130			−0.504471
$50$	−4.40588	−	2.36395i	−0.623085	−	0.334313i
$51$	5.32162	−	0.777993i	0.745176	−	0.108941i
$52$			1.42524i			0.197645i
$53$		−	5.16111i		−	0.708933i	−0.935069	−	0.354467i	$-0.884662\pi$
$53$		−	5.16111i		−	0.708933i	0.935069	−	0.354467i	$-0.115338\pi$
$54$	−2.19206	−	4.71114i	−0.298302	−	0.641105i
$55$	1.53573	−	6.11051i	0.207078	−	0.823941i
$56$	1.86244			0.248880
$57$	−5.87661	+	0.859130i	−0.778377	+	0.113795i
$58$			6.01613i			0.789957i
$59$			5.36568i			0.698552i	0.937020	+	0.349276i	$0.113572\pi$
$59$			5.36568i			0.698552i	−0.937020	+	0.349276i	$0.886428\pi$
$60$	3.85322	+	0.390741i	0.497449	+	0.0504444i
$61$			6.07393i			0.777687i	0.921304	+	0.388843i	$0.127125\pi$
$61$			6.07393i			0.777687i	−0.921304	+	0.388843i	$0.872875\pi$
$62$	5.09305			0.646818
$63$	−5.35350	+	1.59949i	−0.674477	+	0.201517i
$64$	1.00000			0.125000
$65$	3.09081	+	0.776803i	0.383367	+	0.0963505i
$66$	0.705981	+	4.82904i	0.0869002	+	0.594414i
$67$	−8.70699			−1.06373			−0.531864	−	0.846830i	$-0.678508\pi$
$67$	−8.70699			−1.06373			−0.531864	+	0.846830i	$0.678508\pi$
$68$		−	3.10510i		−	0.376548i
$69$	5.41335	+	6.30045i	0.651691	+	0.758485i
$70$	1.01510	−	4.03895i	0.121327	−	0.482746i
$71$			4.56938i			0.542286i	0.962539	+	0.271143i	$0.0874016\pi$
$71$			4.56938i			0.542286i	−0.962539	+	0.271143i	$0.912598\pi$
$72$	−2.87445	+	0.858813i	−0.338757	+	0.101212i
$73$			1.66588i			0.194977i	0.995237	+	0.0974884i	$0.0310809\pi$
$73$			1.66588i			0.194977i	−0.995237	+	0.0974884i	$0.968919\pi$
$74$	−1.27090			−0.147739
$75$	2.94751	−	8.14323i	0.340349	−	0.940299i
$76$			3.42893i			0.393325i
$77$	5.24779			0.598041
$78$	−2.44262	+	0.357098i	−0.276572	+	0.0404334i
$79$		−	10.4725i		−	1.17825i	−0.808042	−	0.589125i	$-0.799472\pi$
$79$		−	10.4725i		−	1.17825i	0.808042	−	0.589125i	$-0.200528\pi$
$80$	0.545034	−	2.16863i	0.0609367	−	0.242460i
$81$	7.52488	−	4.93723i	0.836098	−	0.548581i
$82$			1.76178i			0.194556i
$83$		−	6.08785i		−	0.668228i	−0.942533	−	0.334114i	$-0.891563\pi$
$83$		−	6.08785i		−	0.668228i	0.942533	−	0.334114i	$-0.108437\pi$
$84$	0.466642	+	3.19192i	0.0509148	+	0.348267i
$85$	−6.73380	−	1.69238i	−0.730383	−	0.183565i
$86$	−9.25323			−0.997802
$87$	−10.3106	+	1.50736i	−1.10542	+	0.161606i
$88$	2.81769			0.300366
$89$	−8.61365			−0.913045			−0.456522	−	0.889712i	$-0.650905\pi$
$89$	−8.61365			−0.913045			−0.456522	+	0.889712i	$0.650905\pi$
$90$	0.295774	+	6.70168i	0.0311773	+	0.706419i
$91$			2.65443i			0.278259i
$92$	4.05141	−	2.56633i	0.422389	−	0.267558i
$93$	1.27608	+	8.72864i	0.132323	+	0.905118i
$94$	−2.70892			−0.279404
$95$	7.43607	+	1.86888i	0.762924	+	0.191743i
$96$	0.250553	+	1.71383i	0.0255720	+	0.174917i
$97$	7.72840			0.784700			0.392350	−	0.919816i	$-0.371662\pi$
$97$	7.72840			0.784700			0.392350	+	0.919816i	$0.371662\pi$
$98$	−3.53130			−0.356715
$99$	−8.09929	+	2.41987i	−0.814009	+	0.243206i
$100$	−4.40588	−	2.36395i	−0.440588	−	0.236395i
$101$		−	17.1560i		−	1.70709i	−0.521019	−	0.853545i	$-0.674448\pi$
$101$		−	17.1560i		−	1.70709i	0.521019	−	0.853545i	$-0.325552\pi$
$102$	5.32162	−	0.777993i	0.526919	−	0.0770328i
$103$	−14.8824			−1.46640			−0.733202	−	0.680011i	$-0.761975\pi$
$103$	−14.8824			−1.46640			−0.733202	+	0.680011i	$0.761975\pi$
$104$			1.42524i			0.139756i
$105$	7.17641	+	0.727733i	0.700346	+	0.0710195i
$106$		−	5.16111i		−	0.501292i
$107$		−	6.67983i		−	0.645763i	−0.946439	−	0.322882i	$-0.895348\pi$
$107$		−	6.67983i		−	0.645763i	0.946439	−	0.322882i	$-0.104652\pi$
$108$	−2.19206	−	4.71114i	−0.210932	−	0.453330i
$109$			5.41472i			0.518636i	0.965792	+	0.259318i	$0.0834978\pi$
$109$			5.41472i			0.518636i	−0.965792	+	0.259318i	$0.916502\pi$
$110$	1.53573	−	6.11051i	0.146427	−	0.582614i
$111$	−0.318428	−	2.17811i	−0.0302238	−	0.206737i
$112$	1.86244			0.175985
$113$		−	5.45914i		−	0.513553i	−0.966471	−	0.256777i	$-0.917340\pi$
$113$		−	5.45914i		−	0.513553i	0.966471	−	0.256777i	$-0.0826604\pi$
$114$	−5.87661	+	0.859130i	−0.550395	+	0.0804649i
$115$	−3.35724	−	10.1847i	−0.313065	−	0.949732i
$116$			6.01613i			0.558584i
$117$	−1.22401	−	4.09677i	−0.113160	−	0.378746i
$118$			5.36568i			0.493951i
$119$		−	5.78307i		−	0.530134i
$120$	3.85322	+	0.390741i	0.351749	+	0.0356696i
$121$	−3.06065			−0.278241
$122$			6.07393i			0.549908i
$123$	−3.01940	+	0.441421i	−0.272250	+	0.0398016i
$124$	5.09305			0.457370
$125$	−7.52788	+	8.26626i	−0.673314	+	0.739357i
$126$	−5.35350	+	1.59949i	−0.476927	+	0.142494i
$127$		−	14.0561i		−	1.24727i	−0.781714	−	0.623637i	$-0.785655\pi$
$127$		−	14.0561i		−	1.24727i	0.781714	−	0.623637i	$-0.214345\pi$
$128$	1.00000			0.0883883
$129$	−2.31843	−	15.8585i	−0.204126	−	1.39626i
$130$	3.09081	+	0.776803i	0.271082	+	0.0681301i
$131$		−	11.5832i		−	1.01203i	−0.862524	−	0.506016i	$-0.831118\pi$
$131$		−	11.5832i		−	1.01203i	0.862524	−	0.506016i	$-0.168882\pi$
$132$	0.705981	+	4.82904i	0.0614478	+	0.420314i
$133$			6.38619i			0.553753i
$134$	−8.70699			−0.752170
$135$	−11.4115	+	2.18604i	−0.982141	+	0.188144i
$136$		−	3.10510i		−	0.266260i
$137$			0.485493i			0.0414785i	0.999785	+	0.0207392i	$0.00660198\pi$
$137$			0.485493i			0.0414785i	−0.999785	+	0.0207392i	$0.993398\pi$
$138$	5.41335	+	6.30045i	0.460815	+	0.536330i
$139$	7.10504			0.602642			0.301321	−	0.953523i	$-0.402572\pi$
$139$	7.10504			0.602642			0.301321	+	0.953523i	$0.402572\pi$
$140$	1.01510	−	4.03895i	0.0857913	−	0.341353i
$141$	−0.678730	−	4.64264i	−0.0571593	−	0.390981i
$142$			4.56938i			0.383454i
$143$			4.01587i			0.335824i
$144$	−2.87445	+	0.858813i	−0.239537	+	0.0715678i
$145$	13.0467	+	3.27900i	1.08347	+	0.272306i
$146$			1.66588i			0.137869i
$147$	−0.884779	−	6.05206i	−0.0729753	−	0.499165i
$148$	−1.27090			−0.104467
$149$	−14.1900			−1.16249			−0.581246	−	0.813728i	$-0.697435\pi$
$149$	−14.1900			−1.16249			−0.581246	+	0.813728i	$0.697435\pi$
$150$	2.94751	−	8.14323i	0.240663	−	0.664892i
$151$	−5.21003			−0.423986			−0.211993	−	0.977271i	$-0.567995\pi$
$151$	−5.21003			−0.423986			−0.211993	+	0.977271i	$0.567995\pi$
$152$			3.42893i			0.278123i
$153$	2.66670	+	8.92544i	0.215590	+	0.721579i
$154$	5.24779			0.422879
$155$	2.77589	−	11.0449i	0.222965	−	0.887150i
$156$	−2.44262	+	0.357098i	−0.195566	+	0.0285907i
$157$	21.6439			1.72737			0.863687	−	0.504029i	$-0.168149\pi$
$157$	21.6439			1.72737			0.863687	+	0.504029i	$0.168149\pi$
$158$		−	10.4725i		−	0.833149i
$159$	8.84529	−	1.29313i	0.701477	−	0.102552i
$160$	0.545034	−	2.16863i	0.0430887	−	0.171445i
$161$	7.54554	−	4.77964i	0.594672	−	0.376689i
$162$	7.52488	−	4.93723i	0.591210	−	0.387905i
$163$			11.2769i			0.883276i	0.897193	+	0.441638i	$0.145602\pi$
$163$			11.2769i			0.883276i	−0.897193	+	0.441638i	$0.854398\pi$
$164$			1.76178i			0.137572i
$165$	10.8572	+	1.10098i	0.845230	+	0.0857115i
$166$		−	6.08785i		−	0.472509i
$167$	21.3073			1.64881			0.824405	−	0.566000i	$-0.191510\pi$
$167$	21.3073			1.64881			0.824405	+	0.566000i	$0.191510\pi$
$168$	0.466642	+	3.19192i	0.0360022	+	0.246262i
$169$	10.9687			0.843746
$170$	−6.73380	−	1.69238i	−0.516459	−	0.129800i
$171$	−2.94481	−	9.85628i	−0.225195	−	0.753728i
$172$	−9.25323			−0.705552
$173$	−21.7694			−1.65509			−0.827547	−	0.561396i	$-0.810264\pi$
$173$	−21.7694			−1.65509			−0.827547	+	0.561396i	$0.810264\pi$
$174$	−10.3106	+	1.50736i	−0.781648	+	0.114273i
$175$	−8.20570	−	4.40273i	−0.620293	−	0.332815i
$176$	2.81769			0.212391
$177$	−9.19588	+	1.34439i	−0.691205	+	0.101051i
$178$	−8.61365			−0.645620
$179$		−	16.2259i		−	1.21278i	−0.795168	−	0.606389i	$-0.792617\pi$
$179$		−	16.2259i		−	1.21278i	0.795168	−	0.606389i	$-0.207383\pi$
$180$	0.295774	+	6.70168i	0.0220457	+	0.499514i
$181$			18.3864i			1.36665i	0.730113	+	0.683327i	$0.239467\pi$
$181$			18.3864i			1.36665i	−0.730113	+	0.683327i	$0.760533\pi$
$182$			2.65443i			0.196759i
$183$	−10.4097	+	1.52184i	−0.769507	+	0.112498i
$184$	4.05141	−	2.56633i	0.298674	−	0.189192i
$185$	−0.692682	+	2.75610i	−0.0509270	+	0.202633i
$186$	1.27608	+	8.72864i	0.0935668	+	0.640015i
$187$		−	8.74919i		−	0.639804i
$188$	−2.70892			−0.197568
$189$	−4.08260	−	8.77424i	−0.296965	−	0.638232i
$190$	7.43607	+	1.86888i	0.539469	+	0.135583i
$191$	−25.2254			−1.82525			−0.912624	−	0.408800i	$-0.865947\pi$
$191$	−25.2254			−1.82525			−0.912624	+	0.408800i	$0.865947\pi$
$192$	0.250553	+	1.71383i	0.0180821	+	0.123685i
$193$			25.9696i			1.86934i	0.355522	+	0.934668i	$0.384303\pi$
$193$			25.9696i			1.86934i	−0.355522	+	0.934668i	$0.615697\pi$
$194$	7.72840			0.554867
$195$	−0.556898	+	5.49176i	−0.0398803	+	0.393273i
$196$	−3.53130			−0.252236
$197$	−1.86587			−0.132938			−0.0664688	−	0.997789i	$-0.521173\pi$
$197$	−1.86587			−0.132938			−0.0664688	+	0.997789i	$0.521173\pi$
$198$	−8.09929	+	2.41987i	−0.575591	+	0.171972i
$199$			21.8154i			1.54645i	0.634131	+	0.773225i	$0.281358\pi$
$199$			21.8154i			1.54645i	−0.634131	+	0.773225i	$0.718642\pi$
$200$	−4.40588	−	2.36395i	−0.311542	−	0.167157i
$201$	−2.18157	−	14.9223i	−0.153876	−	1.05254i
$202$		−	17.1560i		−	1.20709i
$203$			11.2047i			0.786417i
$204$	5.32162	−	0.777993i	0.372588	−	0.0544704i
$205$	3.82065	+	0.960232i	0.266846	+	0.0670655i
$206$	−14.8824			−1.03690
$207$	−9.44158	+	10.8562i	−0.656235	+	0.754557i
$208$			1.42524i			0.0988224i
$209$			9.66165i			0.668310i
$210$	7.17641	+	0.727733i	0.495220	+	0.0502183i
$211$	−8.73807			−0.601553			−0.300777	−	0.953695i	$-0.597246\pi$
$211$	−8.73807			−0.601553			−0.300777	+	0.953695i	$0.597246\pi$
$212$		−	5.16111i		−	0.354467i
$213$	−7.83115	+	1.14487i	−0.536582	+	0.0784455i
$214$		−	6.67983i		−	0.456624i
$215$	−5.04333	+	20.0668i	−0.343952	+	1.36854i
$216$	−2.19206	−	4.71114i	−0.149151	−	0.320553i
$217$	9.48553			0.643920
$218$			5.41472i			0.366731i
$219$	−2.85504	+	0.417393i	−0.192926	+	0.0282048i
$220$	1.53573	−	6.11051i	0.103539	−	0.411970i
$221$	4.42550			0.297691
$222$	−0.318428	−	2.17811i	−0.0213715	−	0.146185i
$223$			7.02715i			0.470573i	0.971926	+	0.235286i	$0.0756028\pi$
$223$			7.02715i			0.470573i	−0.971926	+	0.235286i	$0.924397\pi$
$224$	1.86244			0.124440
$225$	14.6946	+	3.01122i	0.979643	+	0.200748i
$226$		−	5.45914i		−	0.363137i
$227$			16.9730i			1.12654i	0.826274	+	0.563268i	$0.190456\pi$
$227$			16.9730i			1.12654i	−0.826274	+	0.563268i	$0.809544\pi$
$228$	−5.87661	+	0.859130i	−0.389188	+	0.0568973i
$229$			27.5394i			1.81985i	0.414768	+	0.909927i	$0.363863\pi$
$229$			27.5394i			1.81985i	−0.414768	+	0.909927i	$0.636137\pi$
$230$	−3.35724	−	10.1847i	−0.221370	−	0.671562i
$231$	1.31485	+	8.99383i	0.0865108	+	0.591750i
$232$			6.01613i			0.394978i
$233$	0.678730			0.0444651			0.0222325	−	0.999753i	$-0.492923\pi$
$233$	0.678730			0.0444651			0.0222325	+	0.999753i	$0.492923\pi$
$234$	−1.22401	−	4.09677i	−0.0800162	−	0.267814i
$235$	−1.47645	+	5.87464i	−0.0963133	+	0.383219i
$236$			5.36568i			0.349276i
$237$	17.9481	−	2.62393i	1.16586	−	0.170442i
$238$		−	5.78307i		−	0.374861i
$239$		−	4.80875i		−	0.311052i	−0.987832	−	0.155526i	$-0.950293\pi$
$239$		−	4.80875i		−	0.311052i	0.987832	−	0.155526i	$-0.0497072\pi$
$240$	3.85322	+	0.390741i	0.248724	+	0.0252222i
$241$		−	23.9160i		−	1.54056i	−0.637703	−	0.770282i	$-0.720115\pi$
$241$		−	23.9160i		−	1.54056i	0.637703	−	0.770282i	$-0.279885\pi$
$242$	−3.06065			−0.196746
$243$	10.3470	+	11.6593i	0.663758	+	0.747947i
$244$			6.07393i			0.388843i
$245$	−1.92468	+	7.65807i	−0.122963	+	0.489256i
$246$	−3.01940	+	0.441421i	−0.192510	+	0.0281440i
$247$	−4.88704			−0.310955
$248$	5.09305			0.323409
$249$	10.4336	−	1.52533i	0.661200	−	0.0966640i
$250$	−7.52788	+	8.26626i	−0.476105	+	0.522804i
$251$	18.3410			1.15768			0.578838	−	0.815443i	$-0.303506\pi$
$251$	18.3410			1.15768			0.578838	+	0.815443i	$0.303506\pi$
$252$	−5.35350	+	1.59949i	−0.337239	+	0.100759i
$253$	11.4156	−	7.23110i	0.717694	−	0.454616i
$254$		−	14.0561i		−	0.881955i
$255$	1.21329	−	11.9646i	0.0759790	−	0.749254i
$256$	1.00000			0.0625000
$257$	1.66764			0.104025			0.0520124	−	0.998646i	$-0.483436\pi$
$257$	1.66764			0.104025			0.0520124	+	0.998646i	$0.483436\pi$
$258$	−2.31843	−	15.8585i	−0.144339	−	0.987307i
$259$	−2.36698			−0.147077
$260$	3.09081	+	0.776803i	0.191684	+	0.0481753i
$261$	−5.16673	−	17.2930i	−0.319813	−	1.07041i
$262$		−	11.5832i		−	0.715614i
$263$			9.43774i			0.581956i	0.956730	+	0.290978i	$0.0939807\pi$
$263$			9.43774i			0.581956i	−0.956730	+	0.290978i	$0.906019\pi$
$264$	0.705981	+	4.82904i	0.0434501	+	0.297207i
$265$	−11.1925	−	2.81298i	−0.687551	−	0.172800i
$266$			6.38619i			0.391563i
$267$	−2.15818	−	14.7624i	−0.132078	−	0.903441i
$268$	−8.70699			−0.531864
$269$			5.27030i			0.321336i	0.987009	+	0.160668i	$0.0513648\pi$
$269$			5.27030i			0.321336i	−0.987009	+	0.160668i	$0.948635\pi$
$270$	−11.4115	+	2.18604i	−0.694479	+	0.133038i
$271$	−14.5216			−0.882123			−0.441062	−	0.897477i	$-0.645398\pi$
$271$	−14.5216			−0.882123			−0.441062	+	0.897477i	$0.645398\pi$
$272$		−	3.10510i		−	0.188274i
$273$	−4.54924	+	0.665076i	−0.275333	+	0.0402522i
$274$			0.485493i			0.0293297i
$275$	−12.4144	−	6.66087i	−0.748615	−	0.401665i
$276$	5.41335	+	6.30045i	0.325846	+	0.379242i
$277$			1.92030i			0.115380i	0.998335	+	0.0576899i	$0.0183735\pi$
$277$			1.92030i			0.115380i	−0.998335	+	0.0576899i	$0.981627\pi$
$278$	7.10504			0.426132
$279$	−14.6397	+	4.37398i	−0.876456	+	0.261863i
$280$	1.01510	−	4.03895i	0.0606636	−	0.241373i
$281$	26.0221			1.55235			0.776174	−	0.630519i	$-0.217158\pi$
$281$	26.0221			1.55235			0.776174	+	0.630519i	$0.217158\pi$
$282$	−0.678730	−	4.64264i	−0.0404178	−	0.276465i
$283$	27.1139			1.61176			0.805878	−	0.592081i	$-0.201693\pi$
$283$	27.1139			1.61176			0.805878	+	0.592081i	$0.201693\pi$
$284$			4.56938i			0.271143i
$285$	−1.33982	+	13.2124i	−0.0793642	+	0.782637i
$286$			4.01587i			0.237463i
$287$			3.28122i			0.193684i
$288$	−2.87445	+	0.858813i	−0.169378	+	0.0506061i
$289$	7.35837			0.432845
$290$	13.0467	+	3.27900i	0.766131	+	0.192549i
$291$	1.93638	+	13.2452i	0.113512	+	0.776447i
$292$			1.66588i			0.0974884i
$293$		−	19.6980i		−	1.15077i	−0.817883	−	0.575385i	$-0.804852\pi$
$293$		−	19.6980i		−	1.15077i	0.817883	−	0.575385i	$-0.195148\pi$
$294$	−0.884779	−	6.05206i	−0.0516014	−	0.352963i
$295$	11.6362	+	2.92448i	0.677483	+	0.170270i
$296$	−1.27090			−0.0738694
$297$	−6.17655	−	13.2745i	−0.358400	−	0.770266i
$298$	−14.1900			−0.822006
$299$	3.65763	+	5.77423i	0.211526	+	0.333932i
$300$	2.94751	−	8.14323i	0.170174	−	0.470150i
$301$	−17.2336			−0.993330
$302$	−5.21003			−0.299803
$303$	29.4026	−	4.29851i	1.68913	−	0.246943i
$304$			3.42893i			0.196663i
$305$	13.1721	+	3.31050i	0.754231	+	0.189559i
$306$	2.66670	+	8.92544i	0.152445	+	0.510233i
$307$			4.43868i			0.253329i	0.991946	+	0.126665i	$0.0404272\pi$
$307$			4.43868i			0.253329i	−0.991946	+	0.126665i	$0.959573\pi$
$308$	5.24779			0.299020
$309$	−3.72883	−	25.5059i	−0.212126	−	1.45098i
$310$	2.77589	−	11.0449i	0.157660	−	0.627309i
$311$			4.43551i			0.251515i	0.992061	+	0.125757i	$0.0401361\pi$
$311$			4.43551i			0.251515i	−0.992061	+	0.125757i	$0.959864\pi$
$312$	−2.44262	+	0.357098i	−0.138286	+	0.0202167i
$313$	−21.3482			−1.20667			−0.603336	−	0.797487i	$-0.706162\pi$
$313$	−21.3482			−1.20667			−0.603336	+	0.797487i	$0.706162\pi$
$314$	21.6439			1.22144
$315$	0.550863	+	12.4815i	0.0310376	+	0.703253i
$316$		−	10.4725i		−	0.589125i
$317$	18.2416			1.02455			0.512275	−	0.858822i	$-0.328803\pi$
$317$	18.2416			1.02455			0.512275	+	0.858822i	$0.328803\pi$
$318$	8.84529	−	1.29313i	0.496019	−	0.0725154i
$319$			16.9516i			0.949106i
$320$	0.545034	−	2.16863i	0.0304683	−	0.121230i
$321$	11.4481	−	1.67365i	0.638971	−	0.0934142i
$322$	7.54554	−	4.77964i	0.420496	−	0.266359i
$323$	10.6472			0.592424
$324$	7.52488	−	4.93723i	0.418049	−	0.274290i
$325$	3.36919	−	6.27942i	0.186889	−	0.348319i
$326$			11.2769i			0.624571i
$327$	−9.27993	+	1.35668i	−0.513181	+	0.0750244i
$328$			1.76178i			0.0972782i
$329$	−5.04522			−0.278152
$330$	10.8572	+	1.10098i	0.597668	+	0.0606072i
$331$	13.8007			0.758553			0.379277	−	0.925283i	$-0.376173\pi$
$331$	13.8007			0.758553			0.379277	+	0.925283i	$0.376173\pi$
$332$		−	6.08785i		−	0.334114i
$333$	3.65312	−	1.09146i	0.200190	−	0.0598118i
$334$	21.3073			1.16588
$335$	−4.74561	+	18.8822i	−0.259280	+	1.03165i
$336$	0.466642	+	3.19192i	0.0254574	+	0.174133i
$337$	0.0178070			0.000970010			0.000485005	−	1.00000i	$-0.499846\pi$
$337$	0.0178070			0.000970010			0.000485005		1.00000i	$0.499846\pi$
$338$	10.9687			0.596619
$339$	9.35606	−	1.36781i	0.508151	−	0.0742891i
$340$	−6.73380	−	1.69238i	−0.365191	−	0.0917824i
$341$	14.3506			0.777130
$342$	−2.94481	−	9.85628i	−0.159237	−	0.532966i
$343$	−19.6140			−1.05905
$344$	−9.25323			−0.498901
$345$	16.6138	−	8.30558i	0.894455	−	0.447157i
$346$	−21.7694			−1.17033
$347$	−11.0542			−0.593420			−0.296710	−	0.954968i	$-0.595889\pi$
$347$	−11.0542			−0.593420			−0.296710	+	0.954968i	$0.595889\pi$
$348$	−10.3106	+	1.50736i	−0.552709	+	0.0808031i
$349$	−3.76193			−0.201371			−0.100686	−	0.994918i	$-0.532104\pi$
$349$	−3.76193			−0.201371			−0.100686	+	0.994918i	$0.532104\pi$
$350$	−8.20570	−	4.40273i	−0.438613	−	0.235336i
$351$	6.71449	−	3.12421i	0.358393	−	0.166758i
$352$	2.81769			0.150183
$353$	−23.7727			−1.26529			−0.632647	−	0.774441i	$-0.718031\pi$
$353$	−23.7727			−1.26529			−0.632647	+	0.774441i	$0.718031\pi$
$354$	−9.19588	+	1.34439i	−0.488756	+	0.0714535i
$355$	9.90927	+	2.49047i	0.525930	+	0.132180i
$356$	−8.61365			−0.456522
$357$	9.91122	−	1.44897i	0.524558	−	0.0766876i
$358$		−	16.2259i		−	0.857564i
$359$	4.41391			0.232957			0.116479	−	0.993193i	$-0.462839\pi$
$359$	4.41391			0.232957			0.116479	+	0.993193i	$0.462839\pi$
$360$	0.295774	+	6.70168i	0.0155887	+	0.353210i
$361$	7.24243			0.381181
$362$			18.3864i			0.966370i
$363$	−0.766855	−	5.24544i	−0.0402495	−	0.275314i
$364$			2.65443i			0.139130i
$365$	3.61268	+	0.907963i	0.189096	+	0.0475250i
$366$	−10.4097	+	1.52184i	−0.544124	+	0.0795480i
$367$	−27.9186			−1.45734			−0.728669	−	0.684866i	$-0.759861\pi$
$367$	−27.9186			−1.45734			−0.728669	+	0.684866i	$0.759861\pi$
$368$	4.05141	−	2.56633i	0.211195	−	0.133779i
$369$	−1.51304	−	5.06415i	−0.0787659	−	0.263629i
$370$	−0.692682	+	2.75610i	−0.0360108	+	0.143283i
$371$		−	9.61229i		−	0.499045i
$372$	1.27608	+	8.72864i	0.0661617	+	0.452559i
$373$	2.05388			0.106346			0.0531730	−	0.998585i	$-0.483067\pi$
$373$	2.05388			0.106346			0.0531730	+	0.998585i	$0.483067\pi$
$374$		−	8.74919i		−	0.452410i
$375$	−16.0531	−	10.8304i	−0.828980	−	0.559278i
$376$	−2.70892			−0.139702
$377$	−8.57442			−0.441605
$378$	−4.08260	−	8.77424i	−0.209986	−	0.451298i
$379$		−	16.8965i		−	0.867913i	−0.900934	−	0.433957i	$-0.857117\pi$
$379$		−	16.8965i		−	0.867913i	0.900934	−	0.433957i	$-0.142883\pi$
$380$	7.43607	+	1.86888i	0.381462	+	0.0958717i
$381$	24.0897	−	3.52179i	1.23415	−	0.180427i
$382$	−25.2254			−1.29064
$383$		−	28.3189i		−	1.44703i	−0.690310	−	0.723514i	$-0.742526\pi$
$383$		−	28.3189i		−	1.44703i	0.690310	−	0.723514i	$-0.257474\pi$
$384$	0.250553	+	1.71383i	0.0127860	+	0.0874587i
$385$	2.86022	−	11.3805i	0.145770	−	0.580003i
$386$			25.9696i			1.32182i
$387$	26.5979	−	7.94680i	1.35205	−	0.403959i
$388$	7.72840			0.392350
$389$	20.8493			1.05710			0.528551	−	0.848902i	$-0.322736\pi$
$389$	20.8493			1.05710			0.528551	+	0.848902i	$0.322736\pi$
$390$	−0.556898	+	5.49176i	−0.0281996	+	0.278086i
$391$	−7.96870	−	12.5800i	−0.402994	−	0.636200i
$392$	−3.53130			−0.178358
$393$	19.8517	−	2.90222i	1.00139	−	0.146398i
$394$	−1.86587			−0.0940011
$395$	−22.7110	−	5.70788i	−1.14271	−	0.287195i
$396$	−8.09929	+	2.41987i	−0.407004	+	0.121603i
$397$			36.6485i			1.83934i	0.392696	+	0.919668i	$0.371542\pi$
$397$			36.6485i			1.83934i	−0.392696	+	0.919668i	$0.628458\pi$
$398$			21.8154i			1.09351i
$399$	−10.9449	+	1.60008i	−0.547929	+	0.0801043i
$400$	−4.40588	−	2.36395i	−0.220294	−	0.118197i
$401$	−10.8474			−0.541694			−0.270847	−	0.962622i	$-0.587304\pi$
$401$	−10.8474			−0.541694			−0.270847	+	0.962622i	$0.587304\pi$
$402$	−2.18157	−	14.9223i	−0.108807	−	0.744258i
$403$			7.25881i			0.361587i
$404$		−	17.1560i		−	0.853545i
$405$	−6.60568	−	19.0096i	−0.328239	−	0.944595i
$406$			11.2047i			0.556081i
$407$	−3.58099			−0.177503
$408$	5.32162	−	0.777993i	0.263459	−	0.0385164i
$409$	11.4634			0.566829			0.283415	−	0.958997i	$-0.408533\pi$
$409$	11.4634			0.566829			0.283415	+	0.958997i	$0.408533\pi$
$410$	3.82065	+	0.960232i	0.188688	+	0.0474225i
$411$	−0.832054	+	0.121642i	−0.0410422	+	0.00600015i
$412$	−14.8824			−0.733202
$413$			9.99329i			0.491737i
$414$	−9.44158	+	10.8562i	−0.464028	+	0.533552i
$415$	−13.2023	−	3.31809i	−0.648074	−	0.162878i
$416$			1.42524i			0.0698780i
$417$	1.78019	+	12.1769i	0.0871764	+	0.596303i
$418$			9.66165i			0.472567i
$419$	32.6625			1.59567			0.797833	−	0.602879i	$-0.205980\pi$
$419$	32.6625			1.59567			0.797833	+	0.602879i	$0.205980\pi$
$420$	7.17641	+	0.727733i	0.350173	+	0.0355097i
$421$		−	9.88085i		−	0.481563i	−0.970579	−	0.240782i	$-0.922596\pi$
$421$		−	9.88085i		−	0.481563i	0.970579	−	0.240782i	$-0.0774038\pi$
$422$	−8.73807			−0.425362
$423$	7.78665	−	2.32646i	0.378600	−	0.113116i
$424$		−	5.16111i		−	0.250646i
$425$	−7.34030	+	13.6807i	−0.356057	+	0.663610i
$426$	−7.83115	+	1.14487i	−0.379421	+	0.0554693i
$427$			11.3124i			0.547443i
$428$		−	6.67983i		−	0.322882i
$429$	−6.88253	+	1.00619i	−0.332292	+	0.0485793i
$430$	−5.04333	+	20.0668i	−0.243211	+	0.967707i
$431$	12.4169			0.598099			0.299049	−	0.954238i	$-0.403330\pi$
$431$	12.4169			0.598099			0.299049	+	0.954238i	$0.403330\pi$
$432$	−2.19206	−	4.71114i	−0.105466	−	0.226665i
$433$	35.5189			1.70693			0.853465	−	0.521151i	$-0.174497\pi$
$433$	35.5189			1.70693			0.853465	+	0.521151i	$0.174497\pi$
$434$	9.48553			0.455320
$435$	−2.35075	+	23.1815i	−0.112710	+	1.11147i
$436$			5.41472i			0.259318i
$437$	8.79976	+	13.8920i	0.420950	+	0.664545i
$438$	−2.85504	+	0.417393i	−0.136419	+	0.0199438i
$439$	38.9261			1.85784			0.928922	−	0.370277i	$-0.120737\pi$
$439$	38.9261			1.85784			0.928922	+	0.370277i	$0.120737\pi$
$440$	1.53573	−	6.11051i	0.0732133	−	0.291307i
$441$	10.1505	−	3.03273i	0.483358	−	0.144416i
$442$	4.42550			0.210500
$443$	−26.2942			−1.24928			−0.624638	−	0.780915i	$-0.714753\pi$
$443$	−26.2942			−1.24928			−0.624638	+	0.780915i	$0.714753\pi$
$444$	−0.318428	−	2.17811i	−0.0151119	−	0.103368i
$445$	−4.69473	+	18.6798i	−0.222552	+	0.885507i
$446$			7.02715i			0.332745i
$447$	−3.55536	−	24.3193i	−0.168163	−	1.15027i
$448$	1.86244			0.0879923
$449$			13.2479i			0.625205i	0.949884	+	0.312602i	$0.101201\pi$
$449$			13.2479i			0.625205i	−0.949884	+	0.312602i	$0.898799\pi$
$450$	14.6946	+	3.01122i	0.692712	+	0.141950i
$451$			4.96415i			0.233753i
$452$		−	5.45914i		−	0.256777i
$453$	−1.30539	−	8.92912i	−0.0613326	−	0.419527i
$454$			16.9730i			0.796581i
$455$	5.75646	+	1.44675i	0.269867	+	0.0678248i
$456$	−5.87661	+	0.859130i	−0.275198	+	0.0402325i
$457$	−2.48388			−0.116191			−0.0580955	−	0.998311i	$-0.518503\pi$
$457$	−2.48388			−0.116191			−0.0580955	+	0.998311i	$0.518503\pi$
$458$			27.5394i			1.28683i
$459$	−14.6286	+	6.80658i	−0.682803	+	0.317704i
$460$	−3.35724	−	10.1847i	−0.156532	−	0.474866i
$461$			13.6575i			0.636094i	0.948075	+	0.318047i	$0.103027\pi$
$461$			13.6575i			0.636094i	−0.948075	+	0.318047i	$0.896973\pi$
$462$	1.31485	+	8.99383i	0.0611724	+	0.418431i
$463$		−	32.8123i		−	1.52492i	−0.647037	−	0.762459i	$-0.723992\pi$
$463$		−	32.8123i		−	1.52492i	0.647037	−	0.762459i	$-0.276008\pi$
$464$			6.01613i			0.279292i
$465$	19.6247	+	1.99006i	0.910072	+	0.0922869i
$466$	0.678730			0.0314415
$467$			35.8763i			1.66016i	0.557646	+	0.830079i	$0.311705\pi$
$467$			35.8763i			1.66016i	−0.557646	+	0.830079i	$0.688295\pi$
$468$	−1.22401	−	4.09677i	−0.0565800	−	0.189373i
$469$	−16.2163			−0.748799
$470$	−1.47645	+	5.87464i	−0.0681038	+	0.270977i
$471$	5.42296	+	37.0941i	0.249877	+	1.70921i
$472$			5.36568i			0.246976i
$473$	−26.0727			−1.19882
$474$	17.9481	−	2.62393i	0.824386	−	0.120521i
$475$	8.10582	−	15.1074i	0.371921	−	0.693177i
$476$		−	5.78307i		−	0.265067i
$477$	4.43243	+	14.8353i	0.202947	+	0.679264i
$478$		−	4.80875i		−	0.219947i
$479$	12.2342			0.558997			0.279498	−	0.960146i	$-0.409832\pi$
$479$	12.2342			0.558997			0.279498	+	0.960146i	$0.409832\pi$
$480$	3.85322	+	0.390741i	0.175875	+	0.0178348i
$481$		−	1.81133i		−	0.0825895i
$482$		−	23.9160i		−	1.08934i
$483$	10.0821	+	11.7342i	0.458750	+	0.533926i
$484$	−3.06065			−0.139120
$485$	4.21224	−	16.7600i	0.191268	−	0.761033i
$486$	10.3470	+	11.6593i	0.469348	+	0.528879i
$487$		−	29.9618i		−	1.35770i	−0.734277	−	0.678850i	$-0.762479\pi$
$487$		−	29.9618i		−	1.35770i	0.734277	−	0.678850i	$-0.237521\pi$
$488$			6.07393i			0.274954i
$489$	−19.3267	+	2.82547i	−0.873986	+	0.127772i
$490$	−1.92468	+	7.65807i	−0.0869481	+	0.345956i
$491$		−	22.6758i		−	1.02335i	−0.859180	−	0.511673i	$-0.829026\pi$
$491$		−	22.6758i		−	1.02335i	0.859180	−	0.511673i	$-0.170974\pi$
$492$	−3.01940	+	0.441421i	−0.136125	+	0.0199008i
$493$	18.6807			0.841336
$494$	−4.88704			−0.219878
$495$	0.833398	+	18.8832i	0.0374585	+	0.848738i
$496$	5.09305			0.228685
$497$			8.51022i			0.381735i
$498$	10.4336	−	1.52533i	0.467539	−	0.0683518i
$499$	30.3689			1.35950			0.679749	−	0.733445i	$-0.262089\pi$
$499$	30.3689			1.35950			0.679749	+	0.733445i	$0.262089\pi$
$500$	−7.52788	+	8.26626i	−0.336657	+	0.369678i
$501$	5.33862	+	36.5172i	0.238512	+	1.63147i
$502$	18.3410			0.818600
$503$			28.2017i			1.25745i	0.777627	+	0.628726i	$0.216423\pi$
$503$			28.2017i			1.25745i	−0.777627	+	0.628726i	$0.783577\pi$
$504$	−5.35350	+	1.59949i	−0.238464	+	0.0712471i
$505$	−37.2050	−	9.35063i	−1.65560	−	0.416097i
$506$	11.4156	−	7.23110i	0.507486	−	0.321462i
$507$	2.74825	+	18.7985i	0.122054	+	0.834871i
$508$		−	14.0561i		−	0.623637i
$509$			21.9925i			0.974800i	0.873179	+	0.487400i	$0.162055\pi$
$509$			21.9925i			0.974800i	−0.873179	+	0.487400i	$0.837945\pi$
$510$	1.21329	−	11.9646i	0.0537253	−	0.529803i
$511$			3.10262i			0.137252i
$512$	1.00000			0.0441942
$513$	16.1542	−	7.51644i	0.713224	−	0.331859i
$514$	1.66764			0.0735566
$515$	−8.11140	+	32.2743i	−0.357431	+	1.42217i
$516$	−2.31843	−	15.8585i	−0.102063	−	0.698131i
$517$	−7.63289			−0.335694
$518$	−2.36698			−0.103999
$519$	−5.45439	−	37.3091i	−0.239421	−	1.63769i
$520$	3.09081	+	0.776803i	0.135541	+	0.0340651i
$521$	−1.38200			−0.0605463			−0.0302732	−	0.999542i	$-0.509638\pi$
$521$	−1.38200			−0.0605463			−0.0302732	+	0.999542i	$0.509638\pi$
$522$	−5.16673	−	17.2930i	−0.226142	−	0.756896i
$523$	6.79504			0.297126			0.148563	−	0.988903i	$-0.452535\pi$
$523$	6.79504			0.297126			0.148563	+	0.988903i	$0.452535\pi$
$524$		−	11.5832i		−	0.506016i
$525$	5.48957	−	15.1663i	0.239585	−	0.661912i
$526$			9.43774i			0.411505i
$527$		−	15.8144i		−	0.688887i
$528$	0.705981	+	4.82904i	0.0307239	+	0.210157i
$529$	9.82793	−	20.7945i	0.427301	−	0.904109i
$530$	−11.1925	−	2.81298i	−0.486172	−	0.122188i
$531$	−4.60812	−	15.4234i	−0.199975	−	0.669317i
$532$			6.38619i			0.276877i
$533$	−2.51096			−0.108762
$534$	−2.15818	−	14.7624i	−0.0933936	−	0.638830i
$535$	−14.4860	−	3.64073i	−0.626286	−	0.157403i
$536$	−8.70699			−0.376085
$537$	27.8084	−	4.06545i	1.20002	−	0.175437i
$538$			5.27030i			0.227219i
$539$	−9.95009			−0.428581
$540$	−11.4115	+	2.18604i	−0.491071	+	0.0940720i
$541$	−20.5911			−0.885280			−0.442640	−	0.896699i	$-0.645958\pi$
$541$	−20.5911			−0.885280			−0.442640	+	0.896699i	$0.645958\pi$
$542$	−14.5216			−0.623755
$543$	−31.5113	+	4.60679i	−1.35228	+	0.197696i
$544$		−	3.10510i		−	0.133130i
$545$	11.7425	+	2.95121i	0.502994	+	0.126416i
$546$	−4.54924	+	0.665076i	−0.194690	+	0.0284626i
$547$			9.29346i			0.397360i	0.980064	+	0.198680i	$0.0636654\pi$
$547$			9.29346i			0.397360i	−0.980064	+	0.198680i	$0.936335\pi$
$548$			0.485493i			0.0207392i
$549$	−5.21637	−	17.4592i	−0.222629	−	0.745140i
$550$	−12.4144	−	6.66087i	−0.529351	−	0.284020i
$551$	−20.6289			−0.878821
$552$	5.41335	+	6.30045i	0.230408	+	0.268165i
$553$		−	19.5045i		−	0.829415i
$554$			1.92030i			0.0815859i
$555$	−4.89705	−	0.496591i	−0.207868	−	0.0210791i
$556$	7.10504			0.301321
$557$			44.8421i			1.90002i	0.312220	+	0.950010i	$0.398927\pi$
$557$			44.8421i			1.90002i	−0.312220	+	0.950010i	$0.601073\pi$
$558$	−14.6397	+	4.37398i	−0.619748	+	0.185165i
$559$		−	13.1881i		−	0.557795i
$560$	1.01510	−	4.03895i	0.0428956	−	0.170677i
$561$	14.9947	−	2.19214i	0.633075	−	0.0925522i
$562$	26.0221			1.09768
$563$		−	5.05096i		−	0.212873i	−0.994320	−	0.106436i	$-0.966056\pi$
$563$		−	5.05096i		−	0.212873i	0.994320	−	0.106436i	$-0.0339440\pi$
$564$	−0.678730	−	4.64264i	−0.0285797	−	0.195490i
$565$	−11.8388	−	2.97542i	−0.498064	−	0.125177i
$566$	27.1139			1.13968
$567$	14.0147	−	9.19531i	0.588561	−	0.386167i
$568$			4.56938i			0.191727i
$569$	−29.2487			−1.22617			−0.613085	−	0.790017i	$-0.710072\pi$
$569$	−29.2487			−1.22617			−0.613085	+	0.790017i	$0.710072\pi$
$570$	−1.33982	+	13.2124i	−0.0561190	+	0.553408i
$571$		−	12.9387i		−	0.541468i	−0.962654	−	0.270734i	$-0.912734\pi$
$571$		−	12.9387i		−	0.541468i	0.962654	−	0.270734i	$-0.0872663\pi$
$572$			4.01587i			0.167912i
$573$	−6.32032	−	43.2322i	−0.264035	−	1.80605i
$574$			3.28122i			0.136956i
$575$	−23.9167	+	1.72958i	−0.997395	+	0.0721284i
$576$	−2.87445	+	0.858813i	−0.119769	+	0.0357839i
$577$			6.02880i			0.250982i	0.992095	+	0.125491i	$0.0400507\pi$
$577$			6.02880i			0.250982i	−0.992095	+	0.125491i	$0.959949\pi$
$578$	7.35837			0.306068
$579$	−44.5076	+	6.50678i	−1.84967	+	0.270413i
$580$	13.0467	+	3.27900i	0.541736	+	0.136153i
$581$		−	11.3383i		−	0.470391i
$582$	1.93638	+	13.2452i	0.0802654	+	0.549031i
$583$		−	14.5424i		−	0.602285i
$584$			1.66588i			0.0689347i
$585$	−9.55148	+	0.421548i	−0.394905	+	0.0174289i
$586$		−	19.6980i		−	0.813718i
$587$	29.1084			1.20143			0.600715	−	0.799463i	$-0.294883\pi$
$587$	29.1084			1.20143			0.600715	+	0.799463i	$0.294883\pi$
$588$	−0.884779	−	6.05206i	−0.0364877	−	0.249583i
$589$			17.4637i			0.719580i
$590$	11.6362	+	2.92448i	0.479053	+	0.120399i
$591$	−0.467500	−	3.19779i	−0.0192304	−	0.131539i
$592$	−1.27090			−0.0522335
$593$	−27.8950			−1.14551			−0.572754	−	0.819727i	$-0.694125\pi$
$593$	−27.8950			−1.14551			−0.572754	+	0.819727i	$0.694125\pi$
$594$	−6.17655	−	13.2745i	−0.253427	−	0.544660i
$595$	−12.5413	−	3.15197i	−0.514144	−	0.129218i
$596$	−14.1900			−0.581246
$597$	−37.3879	+	5.46592i	−1.53018	+	0.223705i
$598$	3.65763	+	5.77423i	0.149571	+	0.236126i
$599$		−	34.0771i		−	1.39235i	−0.717871	−	0.696177i	$-0.754883\pi$
$599$		−	34.0771i		−	1.39235i	0.717871	−	0.696177i	$-0.245117\pi$
$600$	2.94751	−	8.14323i	0.120331	−	0.332446i
$601$	39.8474			1.62541			0.812704	−	0.582677i	$-0.197995\pi$
$601$	39.8474			1.62541			0.812704	+	0.582677i	$0.197995\pi$
$602$	−17.2336			−0.702391
$603$	25.0278	−	7.47768i	1.01921	−	0.304515i
$604$	−5.21003			−0.211993
$605$	−1.66816	+	6.63740i	−0.0678202	+	0.269848i
$606$	29.4026	−	4.29851i	1.19440	−	0.174615i
$607$		−	22.8823i		−	0.928765i	−0.885635	−	0.464383i	$-0.846276\pi$
$607$		−	22.8823i		−	0.928765i	0.885635	−	0.464383i	$-0.153724\pi$
$608$			3.42893i			0.139062i
$609$	−19.2030	+	2.80738i	−0.778145	+	0.113761i
$610$	13.1721	+	3.31050i	0.533322	+	0.134038i
$611$		−	3.86086i		−	0.156194i
$612$	2.66670	+	8.92544i	0.107795	+	0.360789i
$613$	18.8764			0.762411			0.381205	−	0.924490i	$-0.375509\pi$
$613$	18.8764			0.762411			0.381205	+	0.924490i	$0.375509\pi$
$614$			4.43868i			0.179131i
$615$	−0.688400	+	6.78854i	−0.0277590	+	0.273740i
$616$	5.24779			0.211439
$617$		−	34.6063i		−	1.39320i	−0.717461	−	0.696599i	$-0.754696\pi$
$617$		−	34.6063i		−	1.39320i	0.717461	−	0.696599i	$-0.245304\pi$
$618$	−3.72883	−	25.5059i	−0.149995	−	1.02600i
$619$		−	15.1407i		−	0.608554i	−0.952584	−	0.304277i	$-0.901585\pi$
$619$		−	15.1407i		−	0.608554i	0.952584	−	0.304277i	$-0.0984149\pi$
$620$	2.77589	−	11.0449i	0.111482	−	0.443575i
$621$	−20.9713	−	13.4612i	−0.841549	−	0.540181i
$622$			4.43551i			0.177848i
$623$	−16.0424			−0.642727
$624$	−2.44262	+	0.357098i	−0.0977830	+	0.0142954i
$625$	13.8235	+	20.8305i	0.552939	+	0.833222i
$626$	−21.3482			−0.853246
$627$	−16.5585	+	2.42076i	−0.661281	+	0.0966758i
$628$	21.6439			0.863687
$629$			3.94626i			0.157348i
$630$	0.550863	+	12.4815i	0.0219469	+	0.497275i
$631$			13.1436i			0.523238i	0.965171	+	0.261619i	$0.0842565\pi$
$631$			13.1436i			0.523238i	−0.965171	+	0.261619i	$0.915744\pi$
$632$		−	10.4725i		−	0.416574i
$633$	−2.18935	−	14.9756i	−0.0870190	−	0.595226i
$634$	18.2416			0.724466
$635$	−30.4823	−	7.66103i	−1.20965	−	0.304019i
$636$	8.84529	−	1.29313i	0.350738	−	0.0512761i
$637$		−	5.03294i		−	0.199412i
$638$			16.9516i			0.671119i
$639$	−3.92424	−	13.1344i	−0.155241	−	0.519590i
$640$	0.545034	−	2.16863i	0.0215444	−	0.0857225i
$641$	−9.80368			−0.387222			−0.193611	−	0.981078i	$-0.562020\pi$
$641$	−9.80368			−0.387222			−0.193611	+	0.981078i	$0.562020\pi$
$642$	11.4481	−	1.67365i	0.451821	−	0.0660538i
$643$	−23.8063			−0.938829			−0.469415	−	0.882978i	$-0.655535\pi$
$643$	−23.8063			−0.938829			−0.469415	+	0.882978i	$0.655535\pi$
$644$	7.54554	−	4.77964i	0.297336	−	0.188344i
$645$	−35.6548	−	3.61561i	−1.40391	−	0.142365i
$646$	10.6472			0.418907
$647$	−0.146971			−0.00577802			−0.00288901	−	0.999996i	$-0.500920\pi$
$647$	−0.146971			−0.00577802			−0.00288901	+	0.999996i	$0.500920\pi$
$648$	7.52488	−	4.93723i	0.295605	−	0.193953i
$649$			15.1188i			0.593465i
$650$	3.36919	−	6.27942i	0.132150	−	0.246299i
$651$	2.37663	+	16.2566i	0.0931475	+	0.637147i
$652$			11.2769i			0.441638i
$653$	39.9239			1.56234			0.781172	−	0.624316i	$-0.214622\pi$
$653$	39.9239			1.56234			0.781172	+	0.624316i	$0.214622\pi$
$654$	−9.27993	+	1.35668i	−0.362874	+	0.0530503i
$655$	−25.1197	−	6.31326i	−0.981508	−	0.246679i
$656$			1.76178i			0.0687861i
$657$	−1.43068	−	4.78849i	−0.0558162	−	0.186817i
$658$	−5.04522			−0.196683
$659$	−33.7062			−1.31301			−0.656504	−	0.754323i	$-0.727965\pi$
$659$	−33.7062			−1.31301			−0.656504	+	0.754323i	$0.727965\pi$
$660$	10.8572	+	1.10098i	0.422615	+	0.0428558i
$661$			28.8662i			1.12276i	0.827557	+	0.561382i	$0.189730\pi$
$661$			28.8662i			1.12276i	−0.827557	+	0.561382i	$0.810270\pi$
$662$	13.8007			0.536378
$663$	1.10882	+	7.58457i	0.0430632	+	0.294560i
$664$		−	6.08785i		−	0.236254i
$665$	13.8493	+	3.48069i	0.537052	+	0.134976i
$666$	3.65312	−	1.09146i	0.141556	−	0.0422933i
$667$	15.4394	+	24.3738i	0.597815	+	0.943759i
$668$	21.3073			0.824405
$669$	−12.0434	+	1.76068i	−0.465623	+	0.0680717i
$670$	−4.74561	+	18.8822i	−0.183339	+	0.729483i
$671$			17.1144i			0.660695i
$672$	0.466642	+	3.19192i	0.0180011	+	0.123131i
$673$		−	50.5859i		−	1.94994i	−0.222331	−	0.974971i	$-0.571367\pi$
$673$		−	50.5859i		−	1.94994i	0.222331	−	0.974971i	$-0.428633\pi$
$674$	0.0178070			0.000685900
$675$	−1.47894	+	25.9386i	−0.0569243	+	0.998378i
$676$	10.9687			0.421873
$677$			16.3820i			0.629611i	0.949156	+	0.314806i	$0.101939\pi$
$677$			16.3820i			0.629611i	−0.949156	+	0.314806i	$0.898061\pi$
$678$	9.35606	−	1.36781i	0.359317	−	0.0525303i
$679$	14.3937			0.552380
$680$	−6.73380	−	1.69238i	−0.258229	−	0.0649000i
$681$	−29.0889	+	4.25264i	−1.11469	+	0.162961i
$682$	14.3506			0.549514
$683$	37.1299			1.42074			0.710368	−	0.703830i	$-0.248529\pi$
$683$	37.1299			1.42074			0.710368	+	0.703830i	$0.248529\pi$
$684$	−2.94481	−	9.85628i	−0.112598	−	0.376864i
$685$	1.05285	+	0.264610i	0.0402274	+	0.0101102i
$686$	−19.6140			−0.748865
$687$	−47.1979	+	6.90009i	−1.80071	+	0.263255i
$688$	−9.25323			−0.352776
$689$	7.35581			0.280234
$690$	16.6138	−	8.30558i	0.632475	−	0.316188i
$691$	22.6242			0.860664			0.430332	−	0.902671i	$-0.358397\pi$
$691$	22.6242			0.860664			0.430332	+	0.902671i	$0.358397\pi$
$692$	−21.7694			−0.827547
$693$	−15.0845	+	4.50687i	−0.573012	+	0.171202i
$694$	−11.0542			−0.419611
$695$	3.87249	−	15.4082i	0.146892	−	0.584466i
$696$	−10.3106	+	1.50736i	−0.390824	+	0.0571364i
$697$	5.47051			0.207210
$698$	−3.76193			−0.142391
$699$	0.170058	+	1.16323i	0.00643219	+	0.0439974i
$700$	−8.20570	−	4.40273i	−0.310146	−	0.166407i
$701$	−38.7195			−1.46242			−0.731208	−	0.682155i	$-0.761043\pi$
$701$	−38.7195			−1.46242			−0.731208	+	0.682155i	$0.761043\pi$
$702$	6.71449	−	3.12421i	0.253422	−	0.117916i
$703$		−	4.35782i		−	0.164358i
$704$	2.81769			0.106196
$705$	−10.4381	−	1.05849i	−0.393121	−	0.0398649i
$706$	−23.7727			−0.894697
$707$		−	31.9522i		−	1.20169i
$708$	−9.19588	+	1.34439i	−0.345602	+	0.0505253i
$709$			28.7863i			1.08109i	0.841314	+	0.540547i	$0.181783\pi$
$709$			28.7863i			1.08109i	−0.841314	+	0.540547i	$0.818217\pi$
$710$	9.90927	+	2.49047i	0.371888	+	0.0934656i
$711$	8.99394	+	30.1027i	0.337299	+	1.12894i
$712$	−8.61365			−0.322810
$713$	20.6341	−	13.0704i	0.772752	−	0.489492i
$714$	9.91122	−	1.44897i	0.370918	−	0.0542263i
$715$	8.70892	+	2.18879i	0.325695	+	0.0818560i
$716$		−	16.2259i		−	0.606389i
$717$	8.24139	−	1.20485i	0.307780	−	0.0449959i
$718$	4.41391			0.164725
$719$		−	28.5972i		−	1.06649i	−0.845959	−	0.533247i	$-0.820972\pi$
$719$		−	28.5972i		−	1.06649i	0.845959	−	0.533247i	$-0.179028\pi$
$720$	0.295774	+	6.70168i	0.0110228	+	0.249757i
$721$	−27.7176			−1.03226
$722$	7.24243			0.269535
$723$	40.9880	−	5.99223i	1.52436	−	0.222854i
$724$			18.3864i			0.683327i
$725$	14.2218	−	26.5063i	0.528186	−	0.984420i
$726$	−0.766855	−	5.24544i	−0.0284607	−	0.194676i
$727$	−43.3161			−1.60650			−0.803252	−	0.595640i	$-0.796899\pi$
$727$	−43.3161			−1.60650			−0.803252	+	0.595640i	$0.796899\pi$
$728$			2.65443i			0.0983796i
$729$	−17.3897	+	20.6543i	−0.644063	+	0.764972i
$730$	3.61268	+	0.907963i	0.133711	+	0.0336052i
$731$			28.7322i			1.06270i
$732$	−10.4097	+	1.52184i	−0.384753	+	0.0562490i
$733$	−33.8680			−1.25094			−0.625471	−	0.780248i	$-0.715093\pi$
$733$	−33.8680			−1.25094			−0.625471	+	0.780248i	$0.715093\pi$
$734$	−27.9186			−1.03049
$735$	−13.6069	−	1.37982i	−0.501897	−	0.0508955i
$736$	4.05141	−	2.56633i	0.149337	−	0.0945961i
$737$	−24.5336			−0.903706
$738$	−1.51304	−	5.06415i	−0.0556959	−	0.186414i
$739$	−23.8692			−0.878042			−0.439021	−	0.898477i	$-0.644675\pi$
$739$	−23.8692			−0.878042			−0.439021	+	0.898477i	$0.644675\pi$
$740$	−0.692682	+	2.75610i	−0.0254635	+	0.101316i
$741$	−1.22446	−	8.37557i	−0.0449818	−	0.307684i
$742$		−	9.61229i		−	0.352878i
$743$		−	12.1969i		−	0.447462i	−0.974651	−	0.223731i	$-0.928176\pi$
$743$		−	12.1969i		−	0.447462i	0.974651	−	0.223731i	$-0.0718238\pi$
$744$	1.27608	+	8.72864i	0.0467834	+	0.320007i
$745$	−7.73405	+	30.7729i	−0.283354	+	1.12743i
$746$	2.05388			0.0751979
$747$	5.22833	+	17.4992i	0.191295	+	0.640262i
$748$		−	8.74919i		−	0.319902i
$749$		−	12.4408i		−	0.454577i
$750$	−16.0531	−	10.8304i	−0.586177	−	0.395470i
$751$		−	51.3212i		−	1.87274i	−0.351017	−	0.936369i	$-0.614164\pi$
$751$		−	51.3212i		−	1.87274i	0.351017	−	0.936369i	$-0.385836\pi$
$752$	−2.70892			−0.0987842
$753$	4.59541	+	31.4335i	0.167466	+	1.14550i
$754$	−8.57442			−0.312262
$755$	−2.83964	+	11.2986i	−0.103345	+	0.411198i
$756$	−4.08260	−	8.77424i	−0.148483	−	0.319116i
$757$	−34.6816			−1.26053			−0.630263	−	0.776382i	$-0.717053\pi$
$757$	−34.6816			−1.26053			−0.630263	+	0.776382i	$0.717053\pi$
$758$		−	16.8965i		−	0.613707i
$759$	15.2531	+	17.7527i	0.553653	+	0.644381i
$760$	7.43607	+	1.86888i	0.269735	+	0.0677916i
$761$		−	15.6935i		−	0.568888i	−0.958693	−	0.284444i	$-0.908191\pi$
$761$		−	15.6935i		−	0.568888i	0.958693	−	0.284444i	$-0.0918090\pi$
$762$	24.0897	−	3.52179i	0.872679	−	0.127581i
$763$			10.0846i			0.365088i
$764$	−25.2254			−0.912624
$765$	20.8094	−	0.918407i	0.752365	−	0.0332051i
$766$		−	28.3189i		−	1.02320i
$767$	−7.64737			−0.276131
$768$	0.250553	+	1.71383i	0.00904107	+	0.0618426i
$769$			3.45905i			0.124737i	0.998053	+	0.0623683i	$0.0198654\pi$
$769$			3.45905i			0.124737i	−0.998053	+	0.0623683i	$0.980135\pi$
$770$	2.86022	−	11.3805i	0.103075	−	0.410124i
$771$	0.417834	+	2.85806i	0.0150479	+	0.102931i
$772$			25.9696i			0.934668i
$773$		−	2.93653i		−	0.105620i	−0.998605	−	0.0528099i	$-0.983182\pi$
$773$		−	2.93653i		−	0.105620i	0.998605	−	0.0528099i	$-0.0168177\pi$
$774$	26.5979	−	7.94680i	0.956042	−	0.285642i
$775$	−22.4394	−	12.0397i	−0.806045	−	0.432479i
$776$	7.72840			0.277433
$777$	−0.593054	−	4.05660i	−0.0212757	−	0.145530i
$778$	20.8493			0.747484
$779$	−6.04103			−0.216442
$780$	−0.556898	+	5.49176i	−0.0199402	+	0.196636i
$781$			12.8751i			0.460706i
$782$	−7.96870	−	12.5800i	−0.284960	−	0.449861i
$783$	28.3428	−	13.1878i	1.01289	−	0.471292i
$784$	−3.53130			−0.126118
$785$	11.7967	−	46.9376i	0.421042	−	1.67527i
$786$	19.8517	−	2.90222i	0.708087	−	0.103519i
$787$	38.7922			1.38279			0.691397	−	0.722475i	$-0.256996\pi$
$787$	38.7922			1.38279			0.691397	+	0.722475i	$0.256996\pi$
$788$	−1.86587			−0.0664688
$789$	−16.1747	+	2.36466i	−0.575835	+	0.0841841i
$790$	−22.7110	−	5.70788i	−0.808020	−	0.203077i
$791$		−	10.1674i		−	0.361510i
$792$	−8.09929	+	2.41987i	−0.287796	+	0.0859862i
$793$	−8.65679			−0.307412
$794$			36.6485i			1.30061i
$795$	2.01666	−	19.8869i	0.0715234	−	0.705316i
$796$			21.8154i			0.773225i
$797$		−	10.1711i		−	0.360278i	−0.983641	−	0.180139i	$-0.942345\pi$
$797$		−	10.1711i		−	0.360278i	0.983641	−	0.180139i	$-0.0576548\pi$
$798$	−10.9449	+	1.60008i	−0.387444	+	0.0566423i
$799$			8.41147i			0.297576i
$800$	−4.40588	−	2.36395i	−0.155771	−	0.0835783i
$801$	24.7595	−	7.39752i	0.874833	−	0.261378i
$802$	−10.8474			−0.383036
$803$			4.69394i			0.165645i
$804$	−2.18157	−	14.9223i	−0.0769379	−	0.526270i
$805$	−6.25268	−	18.9685i	−0.220378	−	0.668552i
$806$			7.25881i			0.255681i
$807$	−9.03241	+	1.32049i	−0.317956	+	0.0464835i
$808$		−	17.1560i		−	0.603547i
$809$			43.9894i			1.54659i	0.634049	+	0.773293i	$0.281392\pi$
$809$			43.9894i			1.54659i	−0.634049	+	0.773293i	$0.718608\pi$
$810$	−6.60568	−	19.0096i	−0.232100	−	0.667929i
$811$	20.8474			0.732052			0.366026	−	0.930605i	$-0.380718\pi$
$811$	20.8474			0.732052			0.366026	+	0.930605i	$0.380718\pi$
$812$			11.2047i			0.393208i
$813$	−3.63843	−	24.8876i	−0.127605	−	0.872845i
$814$	−3.58099			−0.125514
$815$	24.4554	+	6.14630i	0.856636	+	0.215296i
$816$	5.32162	−	0.777993i	0.186294	−	0.0272352i
$817$		−	31.7287i		−	1.11005i
$818$	11.4634			0.400809
$819$	−2.27966	−	7.63000i	−0.0796576	−	0.266614i
$820$	3.82065	+	0.960232i	0.133423	+	0.0335327i
$821$		−	22.2545i		−	0.776688i	−0.921514	−	0.388344i	$-0.873047\pi$
$821$		−	22.2545i		−	0.776688i	0.921514	−	0.388344i	$-0.126953\pi$
$822$	−0.832054	+	0.121642i	−0.0290212	+	0.00424275i
$823$		−	7.63593i		−	0.266172i	−0.991104	−	0.133086i	$-0.957511\pi$
$823$		−	7.63593i		−	0.266172i	0.991104	−	0.133086i	$-0.0424886\pi$
$824$	−14.8824			−0.518452
$825$	8.30515	−	22.9451i	0.289148	−	0.798845i
$826$			9.99329i			0.347711i
$827$			2.97165i			0.103334i	0.998664	+	0.0516672i	$0.0164535\pi$
$827$			2.97165i			0.103334i	−0.998664	+	0.0516672i	$0.983546\pi$
$828$	−9.44158	+	10.8562i	−0.328117	+	0.377278i
$829$	−0.893404			−0.0310292			−0.0155146	−	0.999880i	$-0.504939\pi$
$829$	−0.893404			−0.0310292			−0.0155146	+	0.999880i	$0.504939\pi$
$830$	−13.2023	−	3.31809i	−0.458257	−	0.115172i
$831$	−3.29108	+	0.481139i	−0.114166	+	0.0166905i
$832$			1.42524i			0.0494112i
$833$			10.9650i			0.379916i
$834$	1.78019	+	12.1769i	0.0616430	+	0.421650i
$835$	11.6132	−	46.2076i	0.401892	−	1.59908i
$836$			9.66165i			0.334155i
$837$	−11.1643	−	23.9941i	−0.385895	−	0.829357i
$838$	32.6625			1.12831
$839$	37.6408			1.29951			0.649753	−	0.760146i	$-0.274873\pi$
$839$	37.6408			1.29951			0.649753	+	0.760146i	$0.274873\pi$
$840$	7.17641	+	0.727733i	0.247610	+	0.0251092i
$841$	−7.19384			−0.248064
$842$		−	9.88085i		−	0.340517i
$843$	6.51992	+	44.5975i	0.224558	+	1.53602i
$844$	−8.73807			−0.300777
$845$	5.97831	−	23.7870i	0.205660	−	0.818298i
$846$	7.78665	−	2.32646i	0.267710	−	0.0799853i
$847$	−5.70028			−0.195864
$848$		−	5.16111i		−	0.177233i
$849$	6.79349	+	46.4688i	0.233152	+	1.59480i
$850$	−7.34030	+	13.6807i	−0.251770	+	0.469243i
$851$	−5.14893	+	3.26154i	−0.176503	+	0.111804i
$852$	−7.83115	+	1.14487i	−0.268291	+	0.0392227i
$853$		−	30.1134i		−	1.03106i	−0.856871	−	0.515531i	$-0.827595\pi$
$853$		−	30.1134i		−	1.03106i	0.856871	−	0.515531i	$-0.172405\pi$
$854$			11.3124i			0.387101i
$855$	−22.9796	+	1.01419i	−0.785886	+	0.0346845i
$856$		−	6.67983i		−	0.228312i
$857$	−20.9765			−0.716544			−0.358272	−	0.933617i	$-0.616634\pi$
$857$	−20.9765			−0.716544			−0.358272	+	0.933617i	$0.616634\pi$
$858$	−6.88253	+	1.00619i	−0.234966	+	0.0343508i
$859$	27.5748			0.940842			0.470421	−	0.882442i	$-0.344102\pi$
$859$	27.5748			0.940842			0.470421	+	0.882442i	$0.344102\pi$
$860$	−5.04333	+	20.0668i	−0.171976	+	0.684272i
$861$	−5.62347	+	0.822122i	−0.191647	+	0.0280178i
$862$	12.4169			0.422920
$863$	−26.0803			−0.887785			−0.443892	−	0.896080i	$-0.646403\pi$
$863$	−26.0803			−0.887785			−0.443892	+	0.896080i	$0.646403\pi$
$864$	−2.19206	−	4.71114i	−0.0745756	−	0.160276i
$865$	−11.8650	+	47.2096i	−0.403424	+	1.60517i
$866$	35.5189			1.20698
$867$	1.84366	+	12.6110i	0.0626141	+	0.428292i
$868$	9.48553			0.321960
$869$		−	29.5083i		−	1.00100i
$870$	−2.35075	+	23.1815i	−0.0796978	+	0.785926i
$871$		−	12.4095i		−	0.420481i
$872$			5.41472i			0.183366i
$873$	−22.2149	+	6.63726i	−0.751860	+	0.224637i
$874$	8.79976	+	13.8920i	0.297656	+	0.469905i
$875$	−14.0203	+	15.3955i	−0.473971	+	0.520462i
$876$	−2.85504	+	0.417393i	−0.0964630	+	0.0141024i
$877$			36.4162i			1.22969i	0.788649	+	0.614844i	$0.210781\pi$
$877$			36.4162i			1.22969i	−0.788649	+	0.614844i	$0.789219\pi$
$878$	38.9261			1.31369
$879$	33.7591	−	4.93541i	1.13867	−	0.166467i
$880$	1.53573	−	6.11051i	0.0517696	−	0.205985i
$881$	30.8121			1.03809			0.519043	−	0.854748i	$-0.326288\pi$
$881$	30.8121			1.03809			0.519043	+	0.854748i	$0.326288\pi$
$882$	10.1505	−	3.03273i	0.341786	−	0.102117i
$883$		−	4.89341i		−	0.164676i	−0.996604	−	0.0823382i	$-0.973761\pi$
$883$		−	4.89341i		−	0.164676i	0.996604	−	0.0823382i	$-0.0262388\pi$
$884$	4.42550			0.148846
$885$	−2.09659	+	20.6752i	−0.0704761	+	0.694988i
$886$	−26.2942			−0.883371
$887$	14.4052			0.483679			0.241840	−	0.970316i	$-0.422249\pi$
$887$	14.4052			0.483679			0.241840	+	0.970316i	$0.422249\pi$
$888$	−0.318428	−	2.17811i	−0.0106857	−	0.0730924i
$889$		−	26.1786i		−	0.878003i
$890$	−4.69473	+	18.6798i	−0.157368	+	0.626148i
$891$	21.2027	−	13.9116i	0.710319	−	0.466054i
$892$			7.02715i			0.235286i
$893$		−	9.28870i		−	0.310835i
$894$	−3.55536	−	24.3193i	−0.118909	−	0.813360i
$895$	−35.1878	−	8.84365i	−1.17620	−	0.295611i
$896$	1.86244			0.0622199
$897$	−8.97963	+	7.71531i	−0.299821	+	0.257607i
$898$			13.2479i			0.442087i
$899$			30.6405i			1.02192i
$900$	14.6946	+	3.01122i	0.489821	+	0.100374i
$901$	−16.0258			−0.533896
$902$			4.96415i			0.165288i
$903$	−4.31795	−	29.5356i	−0.143692	−	0.982882i
$904$		−	5.45914i		−	0.181568i
$905$	39.8733	+	10.0212i	1.32543	+	0.333117i
$906$	−1.30539	−	8.92912i	−0.0433687	−	0.296650i
$907$	31.3767			1.04185			0.520923	−	0.853604i	$-0.325588\pi$
$907$	31.3767			1.04185			0.520923	+	0.853604i	$0.325588\pi$
$908$			16.9730i			0.563268i
$909$	14.7338	+	49.3141i	0.488691	+	1.63565i
$910$	5.75646	+	1.44675i	0.190825	+	0.0479594i
$911$	−15.0457			−0.498486			−0.249243	−	0.968441i	$-0.580182\pi$
$911$	−15.0457			−0.498486			−0.249243	+	0.968441i	$0.580182\pi$
$912$	−5.87661	+	0.859130i	−0.194594	+	0.0284487i
$913$		−	17.1537i		−	0.567703i
$914$	−2.48388			−0.0821594
$915$	−2.37333	+	23.4042i	−0.0784599	+	0.773719i
$916$			27.5394i			0.909927i
$917$		−	21.5731i		−	0.712408i
$918$	−14.6286	+	6.80658i	−0.482814	+	0.224651i
$919$		−	15.8352i		−	0.522355i	−0.965291	−	0.261177i	$-0.915889\pi$
$919$		−	15.8352i		−	0.522355i	0.965291	−	0.261177i	$-0.0841108\pi$
$920$	−3.35724	−	10.1847i	−0.110685	−	0.335781i
$921$	−7.60716	+	1.11213i	−0.250665	+	0.0366459i
$922$			13.6575i			0.449786i
$923$	−6.51245			−0.214360
$924$	1.31485	+	8.99383i	0.0432554	+	0.295875i
$925$	5.59941	+	3.00434i	0.184108	+	0.0987820i
$926$		−	32.8123i		−	1.07828i
$927$	42.7786	−	12.7812i	1.40503	−	0.419789i
$928$			6.01613i			0.197489i
$929$			16.2436i			0.532934i	0.963844	+	0.266467i	$0.0858563\pi$
$929$			16.2436i			0.532934i	−0.963844	+	0.266467i	$0.914144\pi$
$930$	19.6247	+	1.99006i	0.643518	+	0.0652567i
$931$		−	12.1086i		−	0.396843i
$932$	0.678730			0.0222325
$933$	−7.60172	+	1.11133i	−0.248869	+	0.0363834i
$934$			35.8763i			1.17391i
$935$	−18.9737	−	4.76861i	−0.620507	−	0.155950i
$936$	−1.22401	−	4.09677i	−0.0400081	−	0.133907i
$937$	−15.8104			−0.516502			−0.258251	−	0.966078i	$-0.583146\pi$
$937$	−15.8104			−0.516502			−0.258251	+	0.966078i	$0.583146\pi$
$938$	−16.2163			−0.529481
$939$	−5.34886	−	36.5872i	−0.174554	−	1.19398i
$940$	−1.47645	+	5.87464i	−0.0481566	+	0.191610i
$941$	53.7844			1.75332			0.876661	−	0.481108i	$-0.159766\pi$
$941$	53.7844			1.75332			0.876661	+	0.481108i	$0.159766\pi$
$942$	5.42296	+	37.0941i	0.176690	+	1.20859i
$943$	4.52131	+	7.13771i	0.147234	+	0.232436i
$944$			5.36568i			0.174638i
$945$	−21.2532	+	4.07137i	−0.691367	+	0.132442i
$946$	−26.0727			−0.847697
$947$	−13.2042			−0.429080			−0.214540	−	0.976715i	$-0.568825\pi$
$947$	−13.2042			−0.429080			−0.214540	+	0.976715i	$0.568825\pi$
$948$	17.9481	−	2.62393i	0.582929	−	0.0852211i
$949$	−2.37428			−0.0770723
$950$	8.10582	−	15.1074i	0.262988	−	0.490150i
$951$	4.57049	+	31.2630i	0.148208	+	1.01377i
$952$		−	5.78307i		−	0.187431i
$953$			27.3913i			0.887292i	0.896202	+	0.443646i	$0.146315\pi$
$953$			27.3913i			0.887292i	−0.896202	+	0.443646i	$0.853685\pi$
$954$	4.43243	+	14.8353i	0.143505	+	0.480312i
$955$	−13.7487	+	54.7045i	−0.444898	+	1.77020i
$956$		−	4.80875i		−	0.155526i
$957$	−29.0522	+	4.24727i	−0.939123	+	0.137295i
$958$	12.2342			0.395270
$959$			0.904204i			0.0291983i
$960$	3.85322	+	0.390741i	0.124362	+	0.0126111i
$961$	−5.06083			−0.163252
$962$		−	1.81133i		−	0.0583996i
$963$	5.73673	+	19.2008i	0.184863	+	0.618737i
$964$		−	23.9160i		−	0.770282i
$965$	56.3184	+	14.1543i	1.81295	+	0.455644i
$966$	10.0821	+	11.7342i	0.324385	+	0.377543i
$967$			34.0128i			1.09378i	0.837205	+	0.546888i	$0.184188\pi$
$967$			34.0128i			1.09378i	−0.837205	+	0.546888i	$0.815812\pi$
$968$	−3.06065			−0.0983729
$969$	2.66768	+	18.2475i	0.0856984	+	0.586193i
$970$	4.21224	−	16.7600i	0.135247	−	0.538132i
$971$	21.5416			0.691304			0.345652	−	0.938363i	$-0.387658\pi$
$971$	21.5416			0.691304			0.345652	+	0.938363i	$0.387658\pi$
$972$	10.3470	+	11.6593i	0.331879	+	0.373974i
$973$	13.2328			0.424223
$974$		−	29.9618i		−	0.960039i
$975$	11.6060	+	4.20090i	0.371691	+	0.134536i
$976$			6.07393i			0.194422i
$977$		−	57.0255i		−	1.82441i	−0.409737	−	0.912204i	$-0.634380\pi$
$977$		−	57.0255i		−	1.82441i	0.409737	−	0.912204i	$-0.365620\pi$
$978$	−19.3267	+	2.82547i	−0.618001	+	0.0903486i
$979$	−24.2706			−0.775690
$980$	−1.92468	+	7.65807i	−0.0614816	+	0.244628i
$981$	−4.65024	−	15.5643i	−0.148471	−	0.496931i
$982$		−	22.6758i		−	0.723615i
$983$		−	17.7927i		−	0.567498i	−0.958899	−	0.283749i	$-0.908422\pi$
$983$		−	17.7927i		−	0.567498i	0.958899	−	0.283749i	$-0.0915782\pi$
$984$	−3.01940	+	0.441421i	−0.0962550	+	0.0140720i
$985$	−1.01696	+	4.04637i	−0.0324031	+	0.128928i
$986$	18.6807			0.594914
$987$	−1.26410	−	8.64666i	−0.0402366	−	0.275226i
$988$	−4.88704			−0.155477
$989$	−37.4887	+	23.7468i	−1.19207	+	0.755105i
$990$	0.833398	+	18.8832i	0.0264871	+	0.600148i
$991$	−30.2616			−0.961290			−0.480645	−	0.876915i	$-0.659597\pi$
$991$	−30.2616			−0.961290			−0.480645	+	0.876915i	$0.659597\pi$
$992$	5.09305			0.161705
$993$	3.45780	+	23.6520i	0.109730	+	0.750575i
$994$			8.51022i			0.269928i
$995$	47.3094	+	11.8901i	1.49981	+	0.376942i
$996$	10.4336	−	1.52533i	0.330600	−	0.0483320i
$997$		−	13.5572i		−	0.429360i	−0.976684	−	0.214680i	$-0.931129\pi$
$997$		−	13.5572i		−	0.429360i	0.976684	−	0.214680i	$-0.0688709\pi$
$998$	30.3689			0.961310
$999$	2.78589	+	5.98738i	0.0881416	+	0.189432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.h.b.689.16	yes	24
3.2	odd	2		690.2.h.a.689.11	yes	24
5.4	even	2		690.2.h.a.689.10	yes	24
15.14	odd	2	inner	690.2.h.b.689.13	yes	24
23.22	odd	2	inner	690.2.h.b.689.15	yes	24
69.68	even	2		690.2.h.a.689.12	yes	24
115.114	odd	2		690.2.h.a.689.9	✓	24
345.344	even	2	inner	690.2.h.b.689.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.h.a.689.9	✓	24	115.114	odd	2
690.2.h.a.689.10	yes	24	5.4	even	2
690.2.h.a.689.11	yes	24	3.2	odd	2
690.2.h.a.689.12	yes	24	69.68	even	2
690.2.h.b.689.13	yes	24	15.14	odd	2	inner
690.2.h.b.689.14	yes	24	345.344	even	2	inner
690.2.h.b.689.15	yes	24	23.22	odd	2	inner
690.2.h.b.689.16	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.250553 + 1.71383i) q^{3} +1.00000 q^{4} +(0.545034 - 2.16863i) q^{5} +(0.250553 + 1.71383i) q^{6} +1.86244 q^{7} +1.00000 q^{8} +(-2.87445 + 0.858813i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.250553 + 1.71383i) q^{3} +1.00000 q^{4} +(0.545034 - 2.16863i) q^{5} +(0.250553 + 1.71383i) q^{6} +1.86244 q^{7} +1.00000 q^{8} +(-2.87445 + 0.858813i) q^{9} +(0.545034 - 2.16863i) q^{10} +2.81769 q^{11} +(0.250553 + 1.71383i) q^{12} +1.42524i q^{13} +1.86244 q^{14} +(3.85322 + 0.390741i) q^{15} +1.00000 q^{16} -3.10510i q^{17} +(-2.87445 + 0.858813i) q^{18} +3.42893i q^{19} +(0.545034 - 2.16863i) q^{20} +(0.466642 + 3.19192i) q^{21} +2.81769 q^{22} +(4.05141 - 2.56633i) q^{23} +(0.250553 + 1.71383i) q^{24} +(-4.40588 - 2.36395i) q^{25} +1.42524i q^{26} +(-2.19206 - 4.71114i) q^{27} +1.86244 q^{28} +6.01613i q^{29} +(3.85322 + 0.390741i) q^{30} +5.09305 q^{31} +1.00000 q^{32} +(0.705981 + 4.82904i) q^{33} -3.10510i q^{34} +(1.01510 - 4.03895i) q^{35} +(-2.87445 + 0.858813i) q^{36} -1.27090 q^{37} +3.42893i q^{38} +(-2.44262 + 0.357098i) q^{39} +(0.545034 - 2.16863i) q^{40} +1.76178i q^{41} +(0.466642 + 3.19192i) q^{42} -9.25323 q^{43} +2.81769 q^{44} +(0.295774 + 6.70168i) q^{45} +(4.05141 - 2.56633i) q^{46} -2.70892 q^{47} +(0.250553 + 1.71383i) q^{48} -3.53130 q^{49} +(-4.40588 - 2.36395i) q^{50} +(5.32162 - 0.777993i) q^{51} +1.42524i q^{52} -5.16111i q^{53} +(-2.19206 - 4.71114i) q^{54} +(1.53573 - 6.11051i) q^{55} +1.86244 q^{56} +(-5.87661 + 0.859130i) q^{57} +6.01613i q^{58} +5.36568i q^{59} +(3.85322 + 0.390741i) q^{60} +6.07393i q^{61} +5.09305 q^{62} +(-5.35350 + 1.59949i) q^{63} +1.00000 q^{64} +(3.09081 + 0.776803i) q^{65} +(0.705981 + 4.82904i) q^{66} -8.70699 q^{67} -3.10510i q^{68} +(5.41335 + 6.30045i) q^{69} +(1.01510 - 4.03895i) q^{70} +4.56938i q^{71} +(-2.87445 + 0.858813i) q^{72} +1.66588i q^{73} -1.27090 q^{74} +(2.94751 - 8.14323i) q^{75} +3.42893i q^{76} +5.24779 q^{77} +(-2.44262 + 0.357098i) q^{78} -10.4725i q^{79} +(0.545034 - 2.16863i) q^{80} +(7.52488 - 4.93723i) q^{81} +1.76178i q^{82} -6.08785i q^{83} +(0.466642 + 3.19192i) q^{84} +(-6.73380 - 1.69238i) q^{85} -9.25323 q^{86} +(-10.3106 + 1.50736i) q^{87} +2.81769 q^{88} -8.61365 q^{89} +(0.295774 + 6.70168i) q^{90} +2.65443i q^{91} +(4.05141 - 2.56633i) q^{92} +(1.27608 + 8.72864i) q^{93} -2.70892 q^{94} +(7.43607 + 1.86888i) q^{95} +(0.250553 + 1.71383i) q^{96} +7.72840 q^{97} -3.53130 q^{98} +(-8.09929 + 2.41987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 - 2 * q^3 + 24 * q^4 - 2 * q^6 + 24 * q^8 + 6 * q^9	\( 24 q + 24 q^{2} - 2 q^{3} + 24 q^{4} - 2 q^{6} + 24 q^{8} + 6 q^{9} - 2 q^{12} + 24 q^{16} + 6 q^{18} + 4 q^{23} - 2 q^{24} + 12 q^{25} - 2 q^{27} - 28 q^{31} + 24 q^{32} - 8 q^{35} + 6 q^{36} + 4 q^{46} - 16 q^{47} - 2 q^{48} - 4 q^{49} + 12 q^{50} - 2 q^{54} + 4 q^{55} - 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} + 6 q^{72} - 6 q^{75} - 8 q^{77} + 14 q^{81} - 44 q^{85} - 28 q^{87} + 4 q^{92} + 4 q^{93} - 16 q^{94} - 4 q^{95} - 2 q^{96} - 4 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 - 2 * q^3 + 24 * q^4 - 2 * q^6 + 24 * q^8 + 6 * q^9 - 2 * q^12 + 24 * q^16 + 6 * q^18 + 4 * q^23 - 2 * q^24 + 12 * q^25 - 2 * q^27 - 28 * q^31 + 24 * q^32 - 8 * q^35 + 6 * q^36 + 4 * q^46 - 16 * q^47 - 2 * q^48 - 4 * q^49 + 12 * q^50 - 2 * q^54 + 4 * q^55 - 28 * q^62 + 24 * q^64 - 8 * q^69 - 8 * q^70 + 6 * q^72 - 6 * q^75 - 8 * q^77 + 14 * q^81 - 44 * q^85 - 28 * q^87 + 4 * q^92 + 4 * q^93 - 16 * q^94 - 4 * q^95 - 2 * q^96 - 4 * q^98

Introduction

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