LMFDB - Embedded newform 690.2.h.b.689.15

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			689.15
Character	$\chi$	$=$	690.689
Dual form			690.2.h.b.689.13

$q$-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} +(-3.38316 + 7.58645i) 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	$-0.614488\pi$
$7$	−1.86244			−0.703938			−0.351969	+	0.936012i	$0.614488\pi$
$8$	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	$-0.639649\pi$
$11$	−2.81769			−0.849564			−0.424782	+	0.905296i	$0.639649\pi$
$12$	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	$0.122889\pi$
$17$			3.10510i			0.753097i	−0.926397	+	0.376548i	$0.877111\pi$
$18$	−2.87445	+	0.858813i	−0.677513	+	0.202424i
$19$		−	3.42893i		−	0.786651i	−0.919399	−	0.393325i	$-0.871325\pi$
$19$		−	3.42893i		−	0.786651i	0.919399	−	0.393325i	$-0.128675\pi$
$20$	−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	$-0.466686\pi$
$37$	1.27090			0.208934			0.104467	+	0.994528i	$0.466686\pi$
$38$		−	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	$-0.250699\pi$
$43$	9.25323			1.41110			0.705552	+	0.708658i	$0.250699\pi$
$44$	−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	$0.115338\pi$
$53$			5.16111i			0.708933i	−0.935069	+	0.354467i	$0.884662\pi$
$54$	−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	$-0.872875\pi$
$61$		−	6.07393i		−	0.777687i	0.921304	−	0.388843i	$-0.127125\pi$
$62$	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	$-0.321492\pi$
$67$	8.70699			1.06373			0.531864	+	0.846830i	$0.321492\pi$
$68$			3.10510i			0.376548i
$69$	−3.38316	+	7.58645i	−0.407285	+	0.913301i
$70$	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	$0.200528\pi$
$79$			10.4725i			1.17825i	−0.808042	+	0.589125i	$0.799472\pi$
$80$	−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	$0.108437\pi$
$83$			6.08785i			0.668228i	−0.942533	+	0.334114i	$0.891563\pi$
$84$	−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	$-0.349095\pi$
$89$	8.61365			0.913045			0.456522	+	0.889712i	$0.349095\pi$
$90$	−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	$-0.628338\pi$
$97$	−7.72840			−0.784700			−0.392350	+	0.919816i	$0.628338\pi$
$98$	−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	$-0.238025\pi$
$103$	14.8824			1.46640			0.733202	+	0.680011i	$0.238025\pi$
$104$			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	$0.104652\pi$
$107$			6.67983i			0.645763i	−0.946439	+	0.322882i	$0.895348\pi$
$108$	−2.19206	−	4.71114i	−0.210932	−	0.453330i
$109$		−	5.41472i		−	0.518636i	−0.965792	−	0.259318i	$-0.916502\pi$
$109$		−	5.41472i		−	0.518636i	0.965792	−	0.259318i	$-0.0834978\pi$
$110$	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	$0.0826604\pi$
$113$			5.45914i			0.513553i	−0.966471	+	0.256777i	$0.917340\pi$
$114$	5.87661	−	0.859130i	0.550395	−	0.0804649i
$115$	−7.77356	+	7.38727i	−0.724889	+	0.688866i
$116$			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	$-0.993398\pi$
$137$		−	0.485493i		−	0.0414785i	0.999785	−	0.0207392i	$-0.00660198\pi$
$138$	−3.38316	+	7.58645i	−0.287994	+	0.645802i
$139$	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	$-0.302565\pi$
$149$	14.1900			1.16249			0.581246	+	0.813728i	$0.302565\pi$
$150$	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	$-0.831851\pi$
$157$	−21.6439			−1.72737			−0.863687	+	0.504029i	$0.831851\pi$
$158$			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	$-0.760533\pi$
$181$		−	18.3864i		−	1.36665i	0.730113	−	0.683327i	$-0.239467\pi$
$182$		−	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	$-0.134053\pi$
$191$	25.2254			1.82525			0.912624	+	0.408800i	$0.134053\pi$
$192$	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	$-0.718642\pi$
$199$		−	21.8154i		−	1.54645i	0.634131	−	0.773225i	$-0.281358\pi$
$200$	−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
$207$	−13.8496	−	3.89736i	−0.962612	−	0.270885i
$208$			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	$-0.809544\pi$
$227$		−	16.9730i		−	1.12654i	0.826274	−	0.563268i	$-0.190456\pi$
$228$	5.87661	−	0.859130i	0.389188	−	0.0568973i
$229$		−	27.5394i		−	1.81985i	−0.414768	−	0.909927i	$-0.636137\pi$
$229$		−	27.5394i		−	1.81985i	0.414768	−	0.909927i	$-0.363863\pi$
$230$	−7.77356	+	7.38727i	−0.512574	+	0.487102i
$231$	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	$0.279885\pi$
$241$			23.9160i			1.54056i	−0.637703	+	0.770282i	$0.720115\pi$
$242$	−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	$-0.696494\pi$
$251$	−18.3410			−1.15768			−0.578838	+	0.815443i	$0.696494\pi$
$252$	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	$-0.906019\pi$
$263$		−	9.43774i		−	0.581956i	0.956730	−	0.290978i	$-0.0939807\pi$
$264$	−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
$276$	−3.38316	+	7.58645i	−0.203642	+	0.456651i
$277$			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	$-0.782842\pi$
$281$	−26.0221			−1.55235			−0.776174	+	0.630519i	$0.782842\pi$
$282$	−0.678730	−	4.64264i	−0.0404178	−	0.276465i
$283$	−27.1139			−1.61176			−0.805878	−	0.592081i	$-0.798307\pi$
$283$	−27.1139			−1.61176			−0.805878	+	0.592081i	$0.798307\pi$
$284$			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	$0.195148\pi$
$293$			19.6980i			1.15077i	−0.817883	+	0.575385i	$0.804852\pi$
$294$	−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	$-0.293838\pi$
$313$	21.3482			1.20667			0.603336	+	0.797487i	$0.293838\pi$
$314$	−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	$-0.500154\pi$
$337$	−0.0178070			−0.000970010			−0.000485005		1.00000i	$0.500154\pi$
$338$	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
$345$	−14.6082	−	11.4717i	−0.786481	−	0.617615i
$346$	−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	$-0.537161\pi$
$359$	−4.41391			−0.232957			−0.116479	+	0.993193i	$0.537161\pi$
$360$	−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	$-0.240139\pi$
$367$	27.9186			1.45734			0.728669	+	0.684866i	$0.240139\pi$
$368$	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	$-0.516933\pi$
$373$	−2.05388			−0.106346			−0.0531730	+	0.998585i	$0.516933\pi$
$374$		−	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	$0.142883\pi$
$379$			16.8965i			0.867913i	−0.900934	+	0.433957i	$0.857117\pi$
$380$	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	$0.257474\pi$
$383$			28.3189i			1.44703i	−0.690310	+	0.723514i	$0.742526\pi$
$384$	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	$-0.677264\pi$
$389$	−20.8493			−1.05710			−0.528551	+	0.848902i	$0.677264\pi$
$390$	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	$-0.412696\pi$
$401$	10.8474			0.541694			0.270847	+	0.962622i	$0.412696\pi$
$402$	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
$414$	−13.8496	−	3.89736i	−0.680669	−	0.191545i
$415$	−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	$-0.794020\pi$
$419$	−32.6625			−1.59567			−0.797833	+	0.602879i	$0.794020\pi$
$420$	7.17641	+	0.727733i	0.350173	+	0.0355097i
$421$			9.88085i			0.481563i	0.970579	+	0.240782i	$0.0774038\pi$
$421$			9.88085i			0.481563i	−0.970579	+	0.240782i	$0.922596\pi$
$422$	−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	$-0.596670\pi$
$431$	−12.4169			−0.598099			−0.299049	+	0.954238i	$0.596670\pi$
$432$	−2.19206	−	4.71114i	−0.105466	−	0.226665i
$433$	−35.5189			−1.70693			−0.853465	−	0.521151i	$-0.825503\pi$
$433$	−35.5189			−1.70693			−0.853465	+	0.521151i	$0.825503\pi$
$434$	−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	$-0.481497\pi$
$457$	2.48388			0.116191			0.0580955	+	0.998311i	$0.481497\pi$
$458$		−	27.5394i		−	1.28683i
$459$	14.6286	−	6.80658i	0.682803	−	0.317704i
$460$	−7.77356	+	7.38727i	−0.362444	+	0.344433i
$461$			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	$-0.688295\pi$
$467$		−	35.8763i		−	1.66016i	0.557646	−	0.830079i	$-0.311705\pi$
$468$	−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	$-0.590168\pi$
$479$	−12.2342			−0.558997			−0.279498	+	0.960146i	$0.590168\pi$
$480$	−3.85322	−	0.390741i	−0.175875	−	0.0178348i
$481$			1.81133i			0.0825895i
$482$			23.9160i			1.08934i
$483$	6.30095	−	14.1293i	0.286703	−	0.642907i
$484$	−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	$-0.783577\pi$
$503$		−	28.2017i		−	1.25745i	0.777627	−	0.628726i	$-0.216423\pi$
$504$	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	$-0.490362\pi$
$521$	1.38200			0.0605463			0.0302732	+	0.999542i	$0.490362\pi$
$522$	−5.16673	−	17.2930i	−0.226142	−	0.756896i
$523$	−6.79504			−0.297126			−0.148563	−	0.988903i	$-0.547465\pi$
$523$	−6.79504			−0.297126			−0.148563	+	0.988903i	$0.547465\pi$
$524$		−	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
$552$	−3.38316	+	7.58645i	−0.143997	+	0.322901i
$553$		−	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	$-0.601073\pi$
$557$		−	44.8421i		−	1.90002i	0.312220	−	0.950010i	$-0.398927\pi$
$558$	−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	$0.0339440\pi$
$563$			5.05096i			0.212873i	−0.994320	+	0.106436i	$0.966056\pi$
$564$	−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	$-0.289928\pi$
$569$	29.2487			1.22617			0.613085	+	0.790017i	$0.289928\pi$
$570$	−1.33982	+	13.2124i	−0.0561190	+	0.553408i
$571$			12.9387i			0.541468i	0.962654	+	0.270734i	$0.0872663\pi$
$571$			12.9387i			0.541468i	−0.962654	+	0.270734i	$0.912734\pi$
$572$		−	4.01587i		−	0.167912i
$573$	6.32032	+	43.2322i	0.264035	+	1.80605i
$574$		−	3.28122i		−	0.136956i
$575$	−11.7834	−	20.8843i	−0.491400	−	0.870934i
$576$	−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	$-0.624491\pi$
$613$	−18.8764			−0.762411			−0.381205	+	0.924490i	$0.624491\pi$
$614$			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	$0.245304\pi$
$617$			34.6063i			1.39320i	−0.717461	+	0.696599i	$0.754696\pi$
$618$	3.72883	+	25.5059i	0.149995	+	1.02600i
$619$			15.1407i			0.608554i	0.952584	+	0.304277i	$0.0984149\pi$
$619$			15.1407i			0.608554i	−0.952584	+	0.304277i	$0.901585\pi$
$620$	−2.77589	+	11.0449i	−0.111482	+	0.443575i
$621$	3.20937	−	24.7123i	0.128787	−	0.991672i
$622$			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	$-0.915744\pi$
$631$		−	13.1436i		−	0.523238i	0.965171	−	0.261619i	$-0.0842565\pi$
$632$			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	$-0.437980\pi$
$641$	9.80368			0.387222			0.193611	+	0.981078i	$0.437980\pi$
$642$	−11.4481	+	1.67365i	−0.451821	+	0.0660538i
$643$	23.8063			0.938829			0.469415	−	0.882978i	$-0.344465\pi$
$643$	23.8063			0.938829			0.469415	+	0.882978i	$0.344465\pi$
$644$	−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	$-0.272035\pi$
$659$	33.7062			1.31301			0.656504	+	0.754323i	$0.272035\pi$
$660$	10.8572	+	1.10098i	0.422615	+	0.0428558i
$661$		−	28.8662i		−	1.12276i	−0.827557	−	0.561382i	$-0.810270\pi$
$661$		−	28.8662i		−	1.12276i	0.827557	−	0.561382i	$-0.189730\pi$
$662$	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	$-0.898061\pi$
$677$		−	16.3820i		−	0.629611i	0.949156	−	0.314806i	$-0.101939\pi$
$678$	−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
$690$	−14.6082	−	11.4717i	−0.556126	−	0.436719i
$691$	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	$-0.238957\pi$
$701$	38.7195			1.46242			0.731208	+	0.682155i	$0.238957\pi$
$702$	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	$-0.818217\pi$
$709$		−	28.7863i		−	1.08109i	0.841314	−	0.540547i	$-0.181783\pi$
$710$	−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	$-0.203101\pi$
$727$	43.3161			1.60650			0.803252	+	0.595640i	$0.203101\pi$
$728$		−	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	$-0.284907\pi$
$733$	33.8680			1.25094			0.625471	+	0.780248i	$0.284907\pi$
$734$	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	$0.0718238\pi$
$743$			12.1969i			0.447462i	−0.974651	+	0.223731i	$0.928176\pi$
$744$	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	$0.385836\pi$
$751$			51.3212i			1.87274i	−0.351017	+	0.936369i	$0.614164\pi$
$752$	−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	$-0.282947\pi$
$757$	34.6816			1.26053			0.630263	+	0.776382i	$0.282947\pi$
$758$			16.8965i			0.613707i
$759$	9.53268	−	21.3762i	0.346014	−	0.775908i
$760$	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	$-0.980135\pi$
$769$		−	3.45905i		−	0.124737i	0.998053	−	0.0623683i	$-0.0198654\pi$
$770$	−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	$0.0168177\pi$
$773$			2.93653i			0.105620i	−0.998605	+	0.0528099i	$0.983182\pi$
$774$	−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	$-0.743004\pi$
$787$	−38.7922			−1.38279			−0.691397	+	0.722475i	$0.743004\pi$
$788$	−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	$0.0576548\pi$
$797$			10.1711i			0.360278i	−0.983641	+	0.180139i	$0.942345\pi$
$798$	−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
$805$	14.4778	−	13.7584i	0.510277	−	0.484919i
$806$			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	$-0.983546\pi$
$827$		−	2.97165i		−	0.103334i	0.998664	−	0.0516672i	$-0.0164535\pi$
$828$	−13.8496	−	3.89736i	−0.481306	−	0.135443i
$829$	−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	$-0.725127\pi$
$839$	−37.6408			−1.29951			−0.649753	+	0.760146i	$0.725127\pi$
$840$	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	$-0.673712\pi$
$881$	−30.8121			−1.03809			−0.519043	+	0.854748i	$0.673712\pi$
$882$	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
$897$	−10.8125	−	4.82181i	−0.361019	−	0.160995i
$898$			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	$-0.674412\pi$
$907$	−31.3767			−1.04185			−0.520923	+	0.853604i	$0.674412\pi$
$908$		−	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	$-0.419818\pi$
$911$	15.0457			0.498486			0.249243	+	0.968441i	$0.419818\pi$
$912$	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	$0.0841108\pi$
$919$			15.8352i			0.522355i	−0.965291	+	0.261177i	$0.915889\pi$
$920$	−7.77356	+	7.38727i	−0.256287	+	0.243551i
$921$	−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	$-0.416854\pi$
$937$	15.8104			0.516502			0.258251	+	0.966078i	$0.416854\pi$
$938$	−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	$-0.840234\pi$
$941$	−53.7844			−1.75332			−0.876661	+	0.481108i	$0.840234\pi$
$942$	−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	$-0.853685\pi$
$953$		−	27.3913i		−	0.887292i	0.896202	−	0.443646i	$-0.146315\pi$
$954$	−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
$966$	6.30095	−	14.1293i	0.202730	−	0.454604i
$967$			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	$-0.612342\pi$
$971$	−21.5416			−0.691304			−0.345652	+	0.938363i	$0.612342\pi$
$972$	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	$0.365620\pi$
$977$			57.0255i			1.82441i	−0.409737	+	0.912204i	$0.634380\pi$
$978$	−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	$0.0915782\pi$
$983$			17.7927i			0.567498i	−0.958899	+	0.283749i	$0.908422\pi$
$984$	−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.689.15	yes	24
3.2	odd	2		690.2.h.a.689.12	yes	24
5.4	even	2		690.2.h.a.689.9	✓	24
15.14	odd	2	inner	690.2.h.b.689.14	yes	24
23.22	odd	2	inner	690.2.h.b.689.16	yes	24
69.68	even	2		690.2.h.a.689.11	yes	24
115.114	odd	2		690.2.h.a.689.10	yes	24
345.344	even	2	inner	690.2.h.b.689.13	yes	24

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

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} +(-3.38316 + 7.58645i) 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

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