LMFDB - Embedded newform 690.2.h.a.689.1

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			689.1
Character	$\chi$	$=$	690.689
Dual form			690.2.h.a.689.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.65921 - 0.497008i) q^{3} +1.00000 q^{4} +(-1.15459 + 1.91492i) q^{5} +(1.65921 + 0.497008i) q^{6} -3.15825 q^{7} -1.00000 q^{8} +(2.50597 + 1.64928i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.65921 - 0.497008i) q^{3} +1.00000 q^{4} +(-1.15459 + 1.91492i) q^{5} +(1.65921 + 0.497008i) q^{6} -3.15825 q^{7} -1.00000 q^{8} +(2.50597 + 1.64928i) q^{9} +(1.15459 - 1.91492i) q^{10} -2.63765 q^{11} +(-1.65921 - 0.497008i) q^{12} +3.37824i q^{13} +3.15825 q^{14} +(2.86744 - 2.60342i) q^{15} +1.00000 q^{16} +0.331367i q^{17} +(-2.50597 - 1.64928i) q^{18} -2.06750i q^{19} +(-1.15459 + 1.91492i) q^{20} +(5.24020 + 1.56967i) q^{21} +2.63765 q^{22} +(2.19771 - 4.26263i) q^{23} +(1.65921 + 0.497008i) q^{24} +(-2.33385 - 4.42189i) q^{25} -3.37824i q^{26} +(-3.33822 - 3.98199i) q^{27} -3.15825 q^{28} +6.73889i q^{29} +(-2.86744 + 2.60342i) q^{30} +2.38669 q^{31} -1.00000 q^{32} +(4.37642 + 1.31093i) q^{33} -0.331367i q^{34} +(3.64647 - 6.04780i) q^{35} +(2.50597 + 1.64928i) q^{36} +2.62847 q^{37} +2.06750i q^{38} +(1.67901 - 5.60521i) q^{39} +(1.15459 - 1.91492i) q^{40} -6.92322i q^{41} +(-5.24020 - 1.56967i) q^{42} -7.19407 q^{43} -2.63765 q^{44} +(-6.05161 + 2.89449i) q^{45} +(-2.19771 + 4.26263i) q^{46} +11.0631 q^{47} +(-1.65921 - 0.497008i) q^{48} +2.97452 q^{49} +(2.33385 + 4.42189i) q^{50} +(0.164692 - 0.549807i) q^{51} +3.37824i q^{52} -13.7812i q^{53} +(3.33822 + 3.98199i) q^{54} +(3.04540 - 5.05090i) q^{55} +3.15825 q^{56} +(-1.02756 + 3.43041i) q^{57} -6.73889i q^{58} -12.0898i q^{59} +(2.86744 - 2.60342i) q^{60} +0.685298i q^{61} -2.38669 q^{62} +(-7.91446 - 5.20884i) q^{63} +1.00000 q^{64} +(-6.46906 - 3.90047i) q^{65} +(-4.37642 - 1.31093i) q^{66} +0.468752 q^{67} +0.331367i q^{68} +(-5.76504 + 5.98033i) q^{69} +(-3.64647 + 6.04780i) q^{70} -5.57976i q^{71} +(-2.50597 - 1.64928i) q^{72} -7.91723i q^{73} -2.62847 q^{74} +(1.67464 + 8.49680i) q^{75} -2.06750i q^{76} +8.33036 q^{77} +(-1.67901 + 5.60521i) q^{78} +6.81084i q^{79} +(-1.15459 + 1.91492i) q^{80} +(3.55974 + 8.26609i) q^{81} +6.92322i q^{82} -4.16761i q^{83} +(5.24020 + 1.56967i) q^{84} +(-0.634541 - 0.382592i) q^{85} +7.19407 q^{86} +(3.34928 - 11.1813i) q^{87} +2.63765 q^{88} -7.02620 q^{89} +(6.05161 - 2.89449i) q^{90} -10.6693i q^{91} +(2.19771 - 4.26263i) q^{92} +(-3.96003 - 1.18620i) q^{93} -11.0631 q^{94} +(3.95909 + 2.38711i) q^{95} +(1.65921 + 0.497008i) q^{96} +18.2042 q^{97} -2.97452 q^{98} +(-6.60987 - 4.35023i) 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} + 14 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 + 14 * 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
$3$	−1.65921	−	0.497008i	−0.957946	−	0.286948i
$3$	−1.65921	−	0.497008i	−0.957946	−	0.286948i
$4$	1.00000			0.500000
$5$	−1.15459	+	1.91492i	−0.516347	+	0.856379i
$5$	−1.15459	+	1.91492i	−0.516347	+	0.856379i
$6$	1.65921	+	0.497008i	0.677370	+	0.202903i
$7$	−3.15825			−1.19371			−0.596853	−	0.802351i	$-0.703582\pi$
$7$	−3.15825			−1.19371			−0.596853	+	0.802351i	$0.703582\pi$
$8$	−1.00000			−0.353553
$9$	2.50597	+	1.64928i	0.835322	+	0.549761i
$10$	1.15459	−	1.91492i	0.365113	−	0.605552i
$11$	−2.63765			−0.795282			−0.397641	−	0.917541i	$-0.630171\pi$
$11$	−2.63765			−0.795282			−0.397641	+	0.917541i	$0.630171\pi$
$12$	−1.65921	−	0.497008i	−0.478973	−	0.143474i
$13$			3.37824i			0.936955i	0.883475	+	0.468477i	$0.155197\pi$
$13$			3.37824i			0.936955i	−0.883475	+	0.468477i	$0.844803\pi$
$14$	3.15825			0.844077
$15$	2.86744	−	2.60342i	0.740369	−	0.672201i
$16$	1.00000			0.250000
$17$			0.331367i			0.0803682i	0.999192	+	0.0401841i	$0.0127944\pi$
$17$			0.331367i			0.0803682i	−0.999192	+	0.0401841i	$0.987206\pi$
$18$	−2.50597	−	1.64928i	−0.590662	−	0.388740i
$19$		−	2.06750i		−	0.474316i	−0.971471	−	0.237158i	$-0.923784\pi$
$19$		−	2.06750i		−	0.474316i	0.971471	−	0.237158i	$-0.0762159\pi$
$20$	−1.15459	+	1.91492i	−0.258174	+	0.428190i
$21$	5.24020	+	1.56967i	1.14351	+	0.342531i
$22$	2.63765			0.562349
$23$	2.19771	−	4.26263i	0.458255	−	0.888821i
$23$	2.19771	−	4.26263i	0.458255	−	0.888821i
$24$	1.65921	+	0.497008i	0.338685	+	0.101451i
$25$	−2.33385	−	4.42189i	−0.466771	−	0.884378i
$26$		−	3.37824i		−	0.662527i
$27$	−3.33822	−	3.98199i	−0.642441	−	0.766335i
$28$	−3.15825			−0.596853
$29$			6.73889i			1.25138i	0.780071	+	0.625691i	$0.215183\pi$
$29$			6.73889i			1.25138i	−0.780071	+	0.625691i	$0.784817\pi$
$30$	−2.86744	+	2.60342i	−0.523520	+	0.475318i
$31$	2.38669			0.428662			0.214331	−	0.976761i	$-0.431243\pi$
$31$	2.38669			0.428662			0.214331	+	0.976761i	$0.431243\pi$
$32$	−1.00000			−0.176777
$33$	4.37642	+	1.31093i	0.761837	+	0.228204i
$34$		−	0.331367i		−	0.0568289i
$35$	3.64647	−	6.04780i	0.616367	−	1.02226i
$36$	2.50597	+	1.64928i	0.417661	+	0.274880i
$37$	2.62847			0.432118			0.216059	−	0.976380i	$-0.430680\pi$
$37$	2.62847			0.432118			0.216059	+	0.976380i	$0.430680\pi$
$38$			2.06750i			0.335392i
$39$	1.67901	−	5.60521i	0.268857	−	0.897552i
$40$	1.15459	−	1.91492i	0.182556	−	0.302776i
$41$		−	6.92322i		−	1.08122i	−0.841272	−	0.540612i	$-0.818193\pi$
$41$		−	6.92322i		−	1.08122i	0.841272	−	0.540612i	$-0.181807\pi$
$42$	−5.24020	−	1.56967i	−0.808580	−	0.242206i
$43$	−7.19407			−1.09709			−0.548543	−	0.836122i	$-0.684817\pi$
$43$	−7.19407			−1.09709			−0.548543	+	0.836122i	$0.684817\pi$
$44$	−2.63765			−0.397641
$45$	−6.05161	+	2.89449i	−0.902120	+	0.431485i
$46$	−2.19771	+	4.26263i	−0.324035	+	0.628491i
$47$	11.0631			1.61372			0.806862	−	0.590740i	$-0.201164\pi$
$47$	11.0631			1.61372			0.806862	+	0.590740i	$0.201164\pi$
$48$	−1.65921	−	0.497008i	−0.239487	−	0.0717369i
$49$	2.97452			0.424932
$50$	2.33385	+	4.42189i	0.330057	+	0.625350i
$51$	0.164692	−	0.549807i	0.0230615	−	0.0769884i
$52$			3.37824i			0.468477i
$53$		−	13.7812i		−	1.89300i	−0.322706	−	0.946499i	$-0.604593\pi$
$53$		−	13.7812i		−	1.89300i	0.322706	−	0.946499i	$-0.395407\pi$
$54$	3.33822	+	3.98199i	0.454275	+	0.541881i
$55$	3.04540	−	5.05090i	0.410642	−	0.681063i
$56$	3.15825			0.422039
$57$	−1.02756	+	3.43041i	−0.136104	+	0.454369i
$58$		−	6.73889i		−	0.884860i
$59$		−	12.0898i		−	1.57396i	−0.616978	−	0.786981i	$-0.711643\pi$
$59$		−	12.0898i		−	1.57396i	0.616978	−	0.786981i	$-0.288357\pi$
$60$	2.86744	−	2.60342i	0.370185	−	0.336100i
$61$			0.685298i			0.0877435i	0.999037	+	0.0438717i	$0.0139693\pi$
$61$			0.685298i			0.0877435i	−0.999037	+	0.0438717i	$0.986031\pi$
$62$	−2.38669			−0.303110
$63$	−7.91446	−	5.20884i	−0.997128	−	0.656252i
$64$	1.00000			0.125000
$65$	−6.46906	−	3.90047i	−0.802389	−	0.483794i
$66$	−4.37642	−	1.31093i	−0.538700	−	0.161365i
$67$	0.468752			0.0572672			0.0286336	−	0.999590i	$-0.490884\pi$
$67$	0.468752			0.0572672			0.0286336	+	0.999590i	$0.490884\pi$
$68$			0.331367i			0.0401841i
$69$	−5.76504	+	5.98033i	−0.694029	+	0.719947i
$70$	−3.64647	+	6.04780i	−0.435837	+	0.722850i
$71$		−	5.57976i		−	0.662196i	−0.943596	−	0.331098i	$-0.892581\pi$
$71$		−	5.57976i		−	0.662196i	0.943596	−	0.331098i	$-0.107419\pi$
$72$	−2.50597	−	1.64928i	−0.295331	−	0.194370i
$73$		−	7.91723i		−	0.926642i	−0.886191	−	0.463321i	$-0.846658\pi$
$73$		−	7.91723i		−	0.926642i	0.886191	−	0.463321i	$-0.153342\pi$
$74$	−2.62847			−0.305553
$75$	1.67464	+	8.49680i	0.193371	+	0.981126i
$76$		−	2.06750i		−	0.237158i
$77$	8.33036			0.949332
$78$	−1.67901	+	5.60521i	−0.190111	+	0.634665i
$79$			6.81084i			0.766280i	0.923690	+	0.383140i	$0.125157\pi$
$79$			6.81084i			0.766280i	−0.923690	+	0.383140i	$0.874843\pi$
$80$	−1.15459	+	1.91492i	−0.129087	+	0.214095i
$81$	3.55974	+	8.26609i	0.395526	+	0.918455i
$82$			6.92322i			0.764541i
$83$		−	4.16761i		−	0.457455i	−0.973490	−	0.228728i	$-0.926544\pi$
$83$		−	4.16761i		−	0.457455i	0.973490	−	0.228728i	$-0.0734565\pi$
$84$	5.24020	+	1.56967i	0.571753	+	0.171265i
$85$	−0.634541	−	0.382592i	−0.0688257	−	0.0414979i
$86$	7.19407			0.775757
$87$	3.34928	−	11.1813i	0.359081	−	1.19876i
$88$	2.63765			0.281175
$89$	−7.02620			−0.744775			−0.372388	−	0.928077i	$-0.621461\pi$
$89$	−7.02620			−0.744775			−0.372388	+	0.928077i	$0.621461\pi$
$90$	6.05161	−	2.89449i	0.637895	−	0.305106i
$91$		−	10.6693i		−	1.11845i
$92$	2.19771	−	4.26263i	0.229128	−	0.444410i
$93$	−3.96003	−	1.18620i	−0.410636	−	0.123004i
$94$	−11.0631			−1.14108
$95$	3.95909	+	2.38711i	0.406195	+	0.244912i
$96$	1.65921	+	0.497008i	0.169343	+	0.0507256i
$97$	18.2042			1.84836			0.924181	−	0.381956i	$-0.124749\pi$
$97$	18.2042			1.84836			0.924181	+	0.381956i	$0.124749\pi$
$98$	−2.97452			−0.300472
$99$	−6.60987	−	4.35023i	−0.664317	−	0.437215i
$100$	−2.33385	−	4.42189i	−0.233385	−	0.442189i
$101$		−	2.07347i		−	0.206318i	−0.994665	−	0.103159i	$-0.967105\pi$
$101$		−	2.07347i		−	0.206318i	0.994665	−	0.103159i	$-0.0328951\pi$
$102$	−0.164692	+	0.549807i	−0.0163069	+	0.0544390i
$103$	2.39866			0.236347			0.118174	−	0.992993i	$-0.462296\pi$
$103$	2.39866			0.236347			0.118174	+	0.992993i	$0.462296\pi$
$104$		−	3.37824i		−	0.331264i
$105$	−9.05607	+	8.22225i	−0.883782	+	0.802409i
$106$			13.7812i			1.33855i
$107$			10.4463i			1.00988i	0.863154	+	0.504941i	$0.168486\pi$
$107$			10.4463i			1.00988i	−0.863154	+	0.504941i	$0.831514\pi$
$108$	−3.33822	−	3.98199i	−0.321221	−	0.383167i
$109$			3.63460i			0.348132i	0.984734	+	0.174066i	$0.0556906\pi$
$109$			3.63460i			0.348132i	−0.984734	+	0.174066i	$0.944309\pi$
$110$	−3.04540	+	5.05090i	−0.290368	+	0.481584i
$111$	−4.36119	−	1.30637i	−0.413946	−	0.123995i
$112$	−3.15825			−0.298426
$113$		−	0.586991i		−	0.0552195i	−0.999619	−	0.0276097i	$-0.991210\pi$
$113$		−	0.586991i		−	0.0552195i	0.999619	−	0.0276097i	$-0.00878957\pi$
$114$	1.02756	−	3.43041i	0.0962400	−	0.321288i
$115$	5.62516	+	9.13004i	0.524549	+	0.851381i
$116$			6.73889i			0.625691i
$117$	−5.57167	+	8.46575i	−0.515101	+	0.782659i
$118$			12.0898i			1.11296i
$119$		−	1.04654i		−	0.0959359i
$120$	−2.86744	+	2.60342i	−0.261760	+	0.237659i
$121$	−4.04279			−0.367527
$122$		−	0.685298i		−	0.0620440i
$123$	−3.44089	+	11.4871i	−0.310255	+	1.03576i
$124$	2.38669			0.214331
$125$	11.1622	+	0.636316i	0.998379	+	0.0569138i
$126$	7.91446	+	5.20884i	0.705076	+	0.464040i
$127$		−	5.94678i		−	0.527692i	−0.964565	−	0.263846i	$-0.915009\pi$
$127$		−	5.94678i		−	0.527692i	0.964565	−	0.263846i	$-0.0849910\pi$
$128$	−1.00000			−0.0883883
$129$	11.9365	+	3.57551i	1.05095	+	0.314806i
$130$	6.46906	+	3.90047i	0.567374	+	0.342094i
$131$			6.85575i			0.598990i	0.954098	+	0.299495i	$0.0968182\pi$
$131$			6.85575i			0.598990i	−0.954098	+	0.299495i	$0.903182\pi$
$132$	4.37642	+	1.31093i	0.380919	+	0.114102i
$133$			6.52967i			0.566194i
$134$	−0.468752			−0.0404940
$135$	11.4795	−	1.79487i	0.987996	−	0.154478i
$136$		−	0.331367i		−	0.0284144i
$137$			14.8092i			1.26523i	0.774466	+	0.632616i	$0.218019\pi$
$137$			14.8092i			1.26523i	−0.774466	+	0.632616i	$0.781981\pi$
$138$	5.76504	−	5.98033i	0.490753	−	0.509080i
$139$	0.241417			0.0204767			0.0102384	−	0.999948i	$-0.496741\pi$
$139$	0.241417			0.0204767			0.0102384	+	0.999948i	$0.496741\pi$
$140$	3.64647	−	6.04780i	0.308183	−	0.511132i
$141$	−18.3561	−	5.49847i	−1.54586	−	0.463054i
$142$			5.57976i			0.468243i
$143$		−	8.91062i		−	0.745143i
$144$	2.50597	+	1.64928i	0.208831	+	0.137440i
$145$	−12.9045	−	7.78065i	−1.07166	−	0.646148i
$146$			7.91723i			0.655235i
$147$	−4.93537	−	1.47836i	−0.407062	−	0.121933i
$148$	2.62847			0.216059
$149$	21.2344			1.73959			0.869795	−	0.493412i	$-0.164251\pi$
$149$	21.2344			1.73959			0.869795	+	0.493412i	$0.164251\pi$
$150$	−1.67464	−	8.49680i	−0.136734	−	0.693761i
$151$	−16.3816			−1.33311			−0.666556	−	0.745455i	$-0.732232\pi$
$151$	−16.3816			−1.33311			−0.666556	+	0.745455i	$0.732232\pi$
$152$			2.06750i			0.167696i
$153$	−0.546517	+	0.830394i	−0.0441833	+	0.0671333i
$154$	−8.33036			−0.671279
$155$	−2.75565	+	4.57033i	−0.221339	+	0.367098i
$156$	1.67901	−	5.60521i	0.134428	−	0.448776i
$157$	−9.20113			−0.734330			−0.367165	−	0.930156i	$-0.619672\pi$
$157$	−9.20113			−0.734330			−0.367165	+	0.930156i	$0.619672\pi$
$158$		−	6.81084i		−	0.541841i
$159$	−6.84938	+	22.8660i	−0.543191	+	1.81339i
$160$	1.15459	−	1.91492i	0.0912782	−	0.151388i
$161$	−6.94093	+	13.4625i	−0.547022	+	1.06099i
$162$	−3.55974	−	8.26609i	−0.279679	−	0.649446i
$163$			23.6263i			1.85056i	0.379288	+	0.925279i	$0.376169\pi$
$163$			23.6263i			1.85056i	−0.379288	+	0.925279i	$0.623831\pi$
$164$		−	6.92322i		−	0.540612i
$165$	−7.56330	+	6.86692i	−0.588802	+	0.534589i
$166$			4.16761i			0.323470i
$167$	9.99301			0.773282			0.386641	−	0.922230i	$-0.373635\pi$
$167$	9.99301			0.773282			0.386641	+	0.922230i	$0.373635\pi$
$168$	−5.24020	−	1.56967i	−0.404290	−	0.121103i
$169$	1.58751			0.122116
$170$	0.634541	+	0.382592i	0.0486671	+	0.0293435i
$171$	3.40989	−	5.18108i	0.260760	−	0.396207i
$172$	−7.19407			−0.548543
$173$	−13.4215			−1.02042			−0.510208	−	0.860051i	$-0.670432\pi$
$173$	−13.4215			−1.02042			−0.510208	+	0.860051i	$0.670432\pi$
$174$	−3.34928	+	11.1813i	−0.253909	+	0.847649i
$175$	7.37089	+	13.9654i	0.557187	+	1.05569i
$176$	−2.63765			−0.198820
$177$	−6.00874	+	20.0596i	−0.451644	+	1.50777i
$178$	7.02620			0.526636
$179$			1.35729i			0.101448i	0.998713	+	0.0507242i	$0.0161530\pi$
$179$			1.35729i			0.101448i	−0.998713	+	0.0507242i	$0.983847\pi$
$180$	−6.05161	+	2.89449i	−0.451060	+	0.215742i
$181$		−	12.6059i		−	0.936988i	−0.883467	−	0.468494i	$-0.844797\pi$
$181$		−	12.6059i		−	0.936988i	0.883467	−	0.468494i	$-0.155203\pi$
$182$			10.6693i			0.790862i
$183$	0.340599	−	1.13705i	0.0251778	−	0.0840535i
$184$	−2.19771	+	4.26263i	−0.162018	+	0.314246i
$185$	−3.03480	+	5.03332i	−0.223123	+	0.370057i
$186$	3.96003	+	1.18620i	0.290363	+	0.0869767i
$187$		−	0.874030i		−	0.0639154i
$188$	11.0631			0.806862
$189$	10.5429	+	12.5761i	0.766885	+	0.914778i
$190$	−3.95909	−	2.38711i	−0.287223	−	0.173179i
$191$	−23.4458			−1.69648			−0.848239	−	0.529614i	$-0.822337\pi$
$191$	−23.4458			−1.69648			−0.848239	+	0.529614i	$0.822337\pi$
$192$	−1.65921	−	0.497008i	−0.119743	−	0.0358684i
$193$		−	18.6555i		−	1.34286i	−0.741070	−	0.671428i	$-0.765681\pi$
$193$		−	18.6555i		−	1.34286i	0.741070	−	0.671428i	$-0.234319\pi$
$194$	−18.2042			−1.30699
$195$	8.79498	+	9.68689i	0.629822	+	0.693692i
$196$	2.97452			0.212466
$197$	4.98294			0.355019			0.177510	−	0.984119i	$-0.443196\pi$
$197$	4.98294			0.355019			0.177510	+	0.984119i	$0.443196\pi$
$198$	6.60987	+	4.35023i	0.469743	+	0.309158i
$199$		−	14.6734i		−	1.04017i	−0.854115	−	0.520084i	$-0.825901\pi$
$199$		−	14.6734i		−	1.04017i	0.854115	−	0.520084i	$-0.174099\pi$
$200$	2.33385	+	4.42189i	0.165028	+	0.312675i
$201$	−0.777759	−	0.232973i	−0.0548589	−	0.0164327i
$202$			2.07347i			0.145889i
$203$		−	21.2831i		−	1.49378i
$204$	0.164692	−	0.549807i	0.0115307	−	0.0384942i
$205$	13.2574	+	7.99346i	0.925938	+	0.558288i
$206$	−2.39866			−0.167123
$207$	12.5377	−	7.05737i	0.871429	−	0.490521i
$208$			3.37824i			0.234239i
$209$			5.45334i			0.377215i
$210$	9.05607	−	8.22225i	0.624929	−	0.567389i
$211$	4.05994			0.279498			0.139749	−	0.990187i	$-0.455370\pi$
$211$	4.05994			0.279498			0.139749	+	0.990187i	$0.455370\pi$
$212$		−	13.7812i		−	0.946499i
$213$	−2.77319	+	9.25801i	−0.190016	+	0.634348i
$214$		−	10.4463i		−	0.714095i
$215$	8.30619	−	13.7761i	0.566477	−	0.939521i
$216$	3.33822	+	3.98199i	0.227137	+	0.270940i
$217$	−7.53776			−0.511697
$218$		−	3.63460i		−	0.246166i
$219$	−3.93493	+	13.1364i	−0.265898	+	0.887673i
$220$	3.04540	−	5.05090i	0.205321	−	0.340531i
$221$	−1.11944			−0.0753014
$222$	4.36119	+	1.30637i	0.292704	+	0.0876778i
$223$		−	26.8510i		−	1.79808i	−0.437871	−	0.899038i	$-0.644267\pi$
$223$		−	26.8510i		−	1.79808i	0.437871	−	0.899038i	$-0.355733\pi$
$224$	3.15825			0.211019
$225$	1.44439	−	14.9303i	0.0962927	−	0.995353i
$226$			0.586991i			0.0390461i
$227$			16.3101i			1.08254i	0.840850	+	0.541268i	$0.182056\pi$
$227$			16.3101i			1.08254i	−0.840850	+	0.541268i	$0.817944\pi$
$228$	−1.02756	+	3.43041i	−0.0680520	+	0.227185i
$229$		−	13.0346i		−	0.861349i	−0.902507	−	0.430675i	$-0.858276\pi$
$229$		−	13.0346i		−	0.861349i	0.902507	−	0.430675i	$-0.141724\pi$
$230$	−5.62516	−	9.13004i	−0.370912	−	0.602017i
$231$	−13.8218	−	4.14025i	−0.909409	−	0.272409i
$232$		−	6.73889i		−	0.442430i
$233$	−18.3561			−1.20255			−0.601274	−	0.799043i	$-0.705340\pi$
$233$	−18.3561			−1.20255			−0.601274	+	0.799043i	$0.705340\pi$
$234$	5.57167	−	8.46575i	0.364231	−	0.553424i
$235$	−12.7734	+	21.1850i	−0.833242	+	1.38196i
$236$		−	12.0898i		−	0.786981i
$237$	3.38504	−	11.3006i	0.219882	−	0.734055i
$238$			1.04654i			0.0678370i
$239$		−	7.83756i		−	0.506970i	−0.967339	−	0.253485i	$-0.918423\pi$
$239$		−	7.83756i		−	0.506970i	0.967339	−	0.253485i	$-0.0815768\pi$
$240$	2.86744	−	2.60342i	0.185092	−	0.168050i
$241$		−	16.8965i		−	1.08840i	−0.838956	−	0.544199i	$-0.816834\pi$
$241$		−	16.8965i		−	1.08840i	0.838956	−	0.544199i	$-0.183166\pi$
$242$	4.04279			0.259881
$243$	−1.79804	−	15.4844i	−0.115344	−	0.993326i
$244$			0.685298i			0.0438717i
$245$	−3.43435	+	5.69598i	−0.219413	+	0.363903i
$246$	3.44089	−	11.4871i	0.219383	−	0.732390i
$247$	6.98450			0.444413
$248$	−2.38669			−0.151555
$249$	−2.07134	+	6.91495i	−0.131266	+	0.438217i
$250$	−11.1622	−	0.636316i	−0.705961	−	0.0402442i
$251$	26.2859			1.65915			0.829577	−	0.558392i	$-0.188582\pi$
$251$	26.2859			1.65915			0.829577	+	0.558392i	$0.188582\pi$
$252$	−7.91446	−	5.20884i	−0.498564	−	0.328126i
$253$	−5.79681	+	11.2433i	−0.364442	+	0.706863i
$254$			5.94678i			0.373134i
$255$	0.862687	+	0.950173i	0.0540236	+	0.0595021i
$256$	1.00000			0.0625000
$257$	2.32061			0.144756			0.0723780	−	0.997377i	$-0.476941\pi$
$257$	2.32061			0.144756			0.0723780	+	0.997377i	$0.476941\pi$
$258$	−11.9365	−	3.57551i	−0.743133	−	0.222602i
$259$	−8.30136			−0.515821
$260$	−6.46906	−	3.90047i	−0.401194	−	0.241897i
$261$	−11.1143	+	16.8874i	−0.687960	+	1.04531i
$262$		−	6.85575i		−	0.423550i
$263$		−	31.4516i		−	1.93939i	−0.244327	−	0.969693i	$-0.578567\pi$
$263$		−	31.4516i		−	1.93939i	0.244327	−	0.969693i	$-0.421433\pi$
$264$	−4.37642	−	1.31093i	−0.269350	−	0.0806824i
$265$	26.3900	+	15.9117i	1.62112	+	0.977445i
$266$		−	6.52967i		−	0.400359i
$267$	11.6579	+	3.49207i	0.713455	+	0.213712i
$268$	0.468752			0.0286336
$269$			10.7521i			0.655570i	0.944752	+	0.327785i	$0.106302\pi$
$269$			10.7521i			0.655570i	−0.944752	+	0.327785i	$0.893698\pi$
$270$	−11.4795	+	1.79487i	−0.698619	+	0.109233i
$271$	7.09113			0.430755			0.215378	−	0.976531i	$-0.430902\pi$
$271$	7.09113			0.430755			0.215378	+	0.976531i	$0.430902\pi$
$272$			0.331367i			0.0200920i
$273$	−5.30273	+	17.7026i	−0.320936	+	1.07141i
$274$		−	14.8092i		−	0.894654i
$275$	6.15589	+	11.6634i	0.371214	+	0.703330i
$276$	−5.76504	+	5.98033i	−0.347014	+	0.359974i
$277$			10.1872i			0.612092i	0.952017	+	0.306046i	$0.0990061\pi$
$277$			10.1872i			0.612092i	−0.952017	+	0.306046i	$0.900994\pi$
$278$	−0.241417			−0.0144792
$279$	5.98097	+	3.93633i	0.358071	+	0.235662i
$280$	−3.64647	+	6.04780i	−0.217919	+	0.361425i
$281$	16.0901			0.959853			0.479926	−	0.877309i	$-0.340663\pi$
$281$	16.0901			0.959853			0.479926	+	0.877309i	$0.340663\pi$
$282$	18.3561	+	5.49847i	1.09309	+	0.327429i
$283$	−28.1303			−1.67217			−0.836086	−	0.548598i	$-0.815162\pi$
$283$	−28.1303			−1.67217			−0.836086	+	0.548598i	$0.815162\pi$
$284$		−	5.57976i		−	0.331098i
$285$	−5.38257	−	5.92842i	−0.318836	−	0.351169i
$286$			8.91062i			0.526896i
$287$			21.8652i			1.29066i
$288$	−2.50597	−	1.64928i	−0.147665	−	0.0971849i
$289$	16.8902			0.993541
$290$	12.9045	+	7.78065i	0.757776	+	0.456895i
$291$	−30.2047	−	9.04765i	−1.77063	−	0.530383i
$292$		−	7.91723i		−	0.463321i
$293$			10.7652i			0.628910i	0.949272	+	0.314455i	$0.101822\pi$
$293$			10.7652i			0.628910i	−0.949272	+	0.314455i	$0.898178\pi$
$294$	4.93537	+	1.47836i	0.287836	+	0.0862198i
$295$	23.1511	+	13.9588i	1.34791	+	0.812711i
$296$	−2.62847			−0.152777
$297$	8.80507	+	10.5031i	0.510922	+	0.609452i
$298$	−21.2344			−1.23008
$299$	14.4002	+	7.42440i	0.832785	+	0.429364i
$300$	1.67464	+	8.49680i	0.0966855	+	0.490563i
$301$	22.7207			1.30960
$302$	16.3816			0.942653
$303$	−1.03053	+	3.44033i	−0.0592025	+	0.197642i
$304$		−	2.06750i		−	0.118579i
$305$	−1.31229	−	0.791237i	−0.0751417	−	0.0453061i
$306$	0.546517	−	0.830394i	0.0312423	−	0.0474704i
$307$		−	21.1061i		−	1.20459i	−0.798274	−	0.602295i	$-0.794253\pi$
$307$		−	21.1061i		−	1.20459i	0.798274	−	0.602295i	$-0.205747\pi$
$308$	8.33036			0.474666
$309$	−3.97989	−	1.19215i	−0.226408	−	0.0678193i
$310$	2.75565	−	4.57033i	0.156510	−	0.259577i
$311$		−	15.5206i		−	0.880092i	−0.897975	−	0.440046i	$-0.854962\pi$
$311$		−	15.5206i		−	0.880092i	0.897975	−	0.440046i	$-0.145038\pi$
$312$	−1.67901	+	5.60521i	−0.0950553	+	0.317333i
$313$	0.701429			0.0396471			0.0198236	−	0.999803i	$-0.493690\pi$
$313$	0.701429			0.0396471			0.0198236	+	0.999803i	$0.493690\pi$
$314$	9.20113			0.519250
$315$	19.1125	−	9.14151i	1.07687	−	0.515066i
$316$			6.81084i			0.383140i
$317$	−26.6487			−1.49674			−0.748370	−	0.663281i	$-0.769163\pi$
$317$	−26.6487			−1.49674			−0.748370	+	0.663281i	$0.769163\pi$
$318$	6.84938	−	22.8660i	0.384094	−	1.28226i
$319$		−	17.7749i		−	0.995201i
$320$	−1.15459	+	1.91492i	−0.0645434	+	0.107047i
$321$	5.19190	−	17.3326i	0.289783	−	0.967413i
$322$	6.94093	−	13.4625i	0.386803	−	0.750233i
$323$	0.685099			0.0381199
$324$	3.55974	+	8.26609i	0.197763	+	0.459227i
$325$	14.9382	−	7.88431i	0.828623	−	0.437343i
$326$		−	23.6263i		−	1.30854i
$327$	1.80643	−	6.03058i	0.0998956	−	0.333492i
$328$			6.92322i			0.382271i
$329$	−34.9401			−1.92631
$330$	7.56330	−	6.86692i	0.416346	−	0.378012i
$331$	−12.0090			−0.660074			−0.330037	−	0.943968i	$-0.607061\pi$
$331$	−12.0090			−0.660074			−0.330037	+	0.943968i	$0.607061\pi$
$332$		−	4.16761i		−	0.228728i
$333$	6.58686	+	4.33509i	0.360958	+	0.237561i
$334$	−9.99301			−0.546793
$335$	−0.541215	+	0.897624i	−0.0295698	+	0.0490424i
$336$	5.24020	+	1.56967i	0.285876	+	0.0856327i
$337$	−32.5953			−1.77558			−0.887789	−	0.460252i	$-0.847759\pi$
$337$	−32.5953			−1.77558			−0.887789	+	0.460252i	$0.847759\pi$
$338$	−1.58751			−0.0863489
$339$	−0.291739	+	0.973942i	−0.0158451	+	0.0528973i
$340$	−0.634541	−	0.382592i	−0.0344128	−	0.0207490i
$341$	−6.29526			−0.340907
$342$	−3.40989	+	5.18108i	−0.184385	+	0.280161i
$343$	12.7134			0.686462
$344$	7.19407			0.387878
$345$	−4.79563	−	17.9444i	−0.258188	−	0.966095i
$346$	13.4215			0.721544
$347$	14.3932			0.772666			0.386333	−	0.922359i	$-0.373742\pi$
$347$	14.3932			0.772666			0.386333	+	0.922359i	$0.373742\pi$
$348$	3.34928	−	11.1813i	0.179540	−	0.599378i
$349$	−0.672923			−0.0360207			−0.0180104	−	0.999838i	$-0.505733\pi$
$349$	−0.672923			−0.0360207			−0.0180104	+	0.999838i	$0.505733\pi$
$350$	−7.37089	−	13.9654i	−0.393990	−	0.746484i
$351$	13.4521	−	11.2773i	0.718021	−	0.601938i
$352$	2.63765			0.140587
$353$	−25.3608			−1.34982			−0.674909	−	0.737901i	$-0.735817\pi$
$353$	−25.3608			−1.34982			−0.674909	+	0.737901i	$0.735817\pi$
$354$	6.00874	−	20.0596i	0.319361	−	1.06615i
$355$	10.6848	+	6.44233i	0.567091	+	0.341923i
$356$	−7.02620			−0.372388
$357$	−0.520137	+	1.73643i	−0.0275286	+	0.0919015i
$358$		−	1.35729i		−	0.0717349i
$359$	18.0914			0.954827			0.477413	−	0.878679i	$-0.341574\pi$
$359$	18.0914			0.954827			0.477413	+	0.878679i	$0.341574\pi$
$360$	6.05161	−	2.89449i	0.318948	−	0.152553i
$361$	14.7255			0.775024
$362$			12.6059i			0.662550i
$363$	6.70785	+	2.00930i	0.352071	+	0.105461i
$364$		−	10.6693i		−	0.559224i
$365$	15.1609	+	9.14114i	0.793557	+	0.478469i
$366$	−0.340599	+	1.13705i	−0.0178034	+	0.0594348i
$367$	−0.368267			−0.0192234			−0.00961170	−	0.999954i	$-0.503060\pi$
$367$	−0.368267			−0.0192234			−0.00961170	+	0.999954i	$0.503060\pi$
$368$	2.19771	−	4.26263i	0.114564	−	0.222205i
$369$	11.4183	−	17.3493i	0.594415	−	0.903171i
$370$	3.03480	−	5.03332i	0.157772	−	0.261670i
$371$			43.5246i			2.25968i
$372$	−3.96003	−	1.18620i	−0.205318	−	0.0615018i
$373$	19.5200			1.01071			0.505353	−	0.862913i	$-0.331362\pi$
$373$	19.5200			1.01071			0.505353	+	0.862913i	$0.331362\pi$
$374$			0.874030i			0.0451950i
$375$	−18.2042	−	6.60349i	−0.940062	−	0.341003i
$376$	−11.0631			−0.570538
$377$	−22.7656			−1.17249
$378$	−10.5429	−	12.5761i	−0.542270	−	0.646846i
$379$		−	33.4418i		−	1.71779i	−0.512153	−	0.858894i	$-0.671152\pi$
$379$		−	33.4418i		−	1.71779i	0.512153	−	0.858894i	$-0.328848\pi$
$380$	3.95909	+	2.38711i	0.203097	+	0.122456i
$381$	−2.95560	+	9.86697i	−0.151420	+	0.505500i
$382$	23.4458			1.19959
$383$		−	17.0408i		−	0.870745i	−0.900250	−	0.435373i	$-0.856617\pi$
$383$		−	17.0408i		−	0.870745i	0.900250	−	0.435373i	$-0.143383\pi$
$384$	1.65921	+	0.497008i	0.0846713	+	0.0253628i
$385$	−9.61813	+	15.9520i	−0.490185	+	0.812988i
$386$			18.6555i			0.949542i
$387$	−18.0281	−	11.8651i	−0.916420	−	0.603135i
$388$	18.2042			0.924181
$389$	0.355884			0.0180440			0.00902201	−	0.999959i	$-0.497128\pi$
$389$	0.355884			0.0180440			0.00902201	+	0.999959i	$0.497128\pi$
$390$	−8.79498	−	9.68689i	−0.445351	−	0.490515i
$391$	1.41249	+	0.728249i	0.0714329	+	0.0368291i
$392$	−2.97452			−0.150236
$393$	3.40736	−	11.3751i	0.171879	−	0.573800i
$394$	−4.98294			−0.251037
$395$	−13.0422	−	7.86372i	−0.656226	−	0.395666i
$396$	−6.60987	−	4.35023i	−0.332158	−	0.218607i
$397$		−	19.0771i		−	0.957450i	−0.877965	−	0.478725i	$-0.841099\pi$
$397$		−	19.0771i		−	0.957450i	0.877965	−	0.478725i	$-0.158901\pi$
$398$			14.6734i			0.735510i
$399$	3.24529	−	10.8341i	0.162468	−	0.542383i
$400$	−2.33385	−	4.42189i	−0.116693	−	0.221095i
$401$	−29.7359			−1.48494			−0.742471	−	0.669879i	$-0.766346\pi$
$401$	−29.7359			−1.48494			−0.742471	+	0.669879i	$0.766346\pi$
$402$	0.777759	+	0.232973i	0.0387911	+	0.0116197i
$403$			8.06281i			0.401637i
$404$		−	2.07347i		−	0.103159i
$405$	−19.9390	−	2.72731i	−0.990774	−	0.135521i
$406$			21.2831i			1.05626i
$407$	−6.93299			−0.343656
$408$	−0.164692	+	0.549807i	−0.00815346	+	0.0272195i
$409$	14.1316			0.698763			0.349382	−	0.936981i	$-0.386392\pi$
$409$	14.1316			0.698763			0.349382	+	0.936981i	$0.386392\pi$
$410$	−13.2574	−	7.99346i	−0.654737	−	0.394769i
$411$	7.36027	−	24.5715i	0.363055	−	1.21202i
$412$	2.39866			0.118174
$413$			38.1827i			1.87885i
$414$	−12.5377	+	7.05737i	−0.616194	+	0.346851i
$415$	7.98066	+	4.81188i	0.391755	+	0.236206i
$416$		−	3.37824i		−	0.165632i
$417$	−0.400561	−	0.119986i	−0.0196156	−	0.00587574i
$418$		−	5.45334i		−	0.266731i
$419$	−16.0060			−0.781943			−0.390972	−	0.920403i	$-0.627861\pi$
$419$	−16.0060			−0.781943			−0.390972	+	0.920403i	$0.627861\pi$
$420$	−9.05607	+	8.22225i	−0.441891	+	0.401205i
$421$		−	26.7513i		−	1.30378i	−0.758315	−	0.651889i	$-0.773977\pi$
$421$		−	26.7513i		−	1.30378i	0.758315	−	0.651889i	$-0.226023\pi$
$422$	−4.05994			−0.197635
$423$	27.7238	+	18.2462i	1.34798	+	0.887162i
$424$			13.7812i			0.669276i
$425$	1.46527	−	0.773361i	0.0710759	−	0.0375135i
$426$	2.77319	−	9.25801i	0.134361	−	0.448552i
$427$		−	2.16434i		−	0.104740i
$428$			10.4463i			0.504941i
$429$	−4.42865	+	14.7846i	−0.213817	+	0.713807i
$430$	−8.30619	+	13.7761i	−0.400560	+	0.664342i
$431$	1.45183			0.0699322			0.0349661	−	0.999388i	$-0.488868\pi$
$431$	1.45183			0.0699322			0.0349661	+	0.999388i	$0.488868\pi$
$432$	−3.33822	−	3.98199i	−0.160610	−	0.191584i
$433$	−14.3432			−0.689289			−0.344645	−	0.938733i	$-0.612001\pi$
$433$	−14.3432			−0.689289			−0.344645	+	0.938733i	$0.612001\pi$
$434$	7.53776			0.361824
$435$	17.5442	+	19.3234i	0.841179	+	0.926484i
$436$			3.63460i			0.174066i
$437$	−8.81298	−	4.54377i	−0.421582	−	0.217358i
$438$	3.93493	−	13.1364i	0.188018	−	0.627680i
$439$	−31.5600			−1.50628			−0.753138	−	0.657863i	$-0.771461\pi$
$439$	−31.5600			−1.50628			−0.753138	+	0.657863i	$0.771461\pi$
$440$	−3.04540	+	5.05090i	−0.145184	+	0.240792i
$441$	7.45406	+	4.90583i	0.354955	+	0.233611i
$442$	1.11944			0.0532461
$443$	−40.5298			−1.92563			−0.962815	−	0.270160i	$-0.912923\pi$
$443$	−40.5298			−1.92563			−0.962815	+	0.270160i	$0.912923\pi$
$444$	−4.36119	−	1.30637i	−0.206973	−	0.0619976i
$445$	8.11236	−	13.4546i	0.384563	−	0.637810i
$446$			26.8510i			1.27143i
$447$	−35.2324	−	10.5537i	−1.66643	−	0.499171i
$448$	−3.15825			−0.149213
$449$			13.0425i			0.615512i	0.951465	+	0.307756i	$0.0995780\pi$
$449$			13.0425i			0.615512i	−0.951465	+	0.307756i	$0.900422\pi$
$450$	−1.44439	+	14.9303i	−0.0680892	+	0.703821i
$451$			18.2610i			0.859879i
$452$		−	0.586991i		−	0.0276097i
$453$	27.1805	+	8.14176i	1.27705	+	0.382533i
$454$		−	16.3101i		−	0.765469i
$455$	20.4309	+	12.3187i	0.957815	+	0.577508i
$456$	1.02756	−	3.43041i	0.0481200	−	0.160644i
$457$	32.9430			1.54101			0.770504	−	0.637435i	$-0.220004\pi$
$457$	32.9430			1.54101			0.770504	+	0.637435i	$0.220004\pi$
$458$			13.0346i			0.609066i
$459$	1.31950	−	1.10618i	0.0615890	−	0.0516318i
$460$	5.62516	+	9.13004i	0.262274	+	0.425690i
$461$		−	18.9180i		−	0.881100i	−0.897728	−	0.440550i	$-0.854784\pi$
$461$		−	18.9180i		−	0.881100i	0.897728	−	0.440550i	$-0.145216\pi$
$462$	13.8218	+	4.14025i	0.643049	+	0.192622i
$463$		−	1.43119i		−	0.0665132i	−0.999447	−	0.0332566i	$-0.989412\pi$
$463$		−	1.43119i		−	0.0665132i	0.999447	−	0.0332566i	$-0.0105879\pi$
$464$			6.73889i			0.312845i
$465$	6.84369	−	6.21356i	0.317368	−	0.288147i
$466$	18.3561			0.850329
$467$		−	36.8872i		−	1.70694i	−0.521144	−	0.853469i	$-0.674495\pi$
$467$		−	36.8872i		−	1.70694i	0.521144	−	0.853469i	$-0.325505\pi$
$468$	−5.57167	+	8.46575i	−0.257550	+	0.391330i
$469$	−1.48043			−0.0683601
$470$	12.7734	−	21.1850i	0.589191	−	0.977193i
$471$	15.2666	+	4.57303i	0.703449	+	0.210714i
$472$			12.0898i			0.556479i
$473$	18.9755			0.872492
$474$	−3.38504	+	11.3006i	−0.155480	+	0.519055i
$475$	−9.14225	+	4.82523i	−0.419475	+	0.221397i
$476$		−	1.04654i		−	0.0479680i
$477$	22.7292	−	34.5353i	1.04070	−	1.58126i
$478$			7.83756i			0.358482i
$479$	−17.8352			−0.814912			−0.407456	−	0.913225i	$-0.633584\pi$
$479$	−17.8352			−0.814912			−0.407456	+	0.913225i	$0.633584\pi$
$480$	−2.86744	+	2.60342i	−0.130880	+	0.118829i
$481$			8.87960i			0.404875i
$482$			16.8965i			0.769613i
$483$	18.2074	−	18.8874i	0.828466	−	0.859405i
$484$	−4.04279			−0.183763
$485$	−21.0184	+	34.8597i	−0.954397	+	1.58290i
$486$	1.79804	+	15.4844i	0.0815609	+	0.702387i
$487$			5.32528i			0.241312i	0.992694	+	0.120656i	$0.0384997\pi$
$487$			5.32528i			0.241312i	−0.992694	+	0.120656i	$0.961500\pi$
$488$		−	0.685298i		−	0.0310220i
$489$	11.7425	−	39.2011i	0.531013	−	1.77273i
$490$	3.43435	−	5.69598i	0.155148	−	0.257318i
$491$		−	27.6023i		−	1.24568i	−0.782351	−	0.622838i	$-0.785979\pi$
$491$		−	27.6023i		−	1.24568i	0.782351	−	0.622838i	$-0.214021\pi$
$492$	−3.44089	+	11.4871i	−0.155127	+	0.517878i
$493$	−2.23304			−0.100571
$494$	−6.98450			−0.314247
$495$	15.9620	−	7.63465i	0.717440	−	0.343152i
$496$	2.38669			0.107166
$497$			17.6223i			0.790467i
$498$	2.07134	−	6.91495i	0.0928188	−	0.309866i
$499$	−25.7722			−1.15372			−0.576861	−	0.816843i	$-0.695722\pi$
$499$	−25.7722			−1.15372			−0.576861	+	0.816843i	$0.695722\pi$
$500$	11.1622	+	0.636316i	0.499190	+	0.0284569i
$501$	−16.5805	−	4.96660i	−0.740763	−	0.221891i
$502$	−26.2859			−1.17320
$503$			36.2072i			1.61440i	0.590277	+	0.807201i	$0.299018\pi$
$503$			36.2072i			1.61440i	−0.590277	+	0.807201i	$0.700982\pi$
$504$	7.91446	+	5.20884i	0.352538	+	0.232020i
$505$	3.97054	+	2.39401i	0.176687	+	0.106532i
$506$	5.79681	−	11.2433i	0.257699	−	0.499828i
$507$	−2.63401	−	0.789003i	−0.116980	−	0.0350408i
$508$		−	5.94678i		−	0.263846i
$509$		−	9.39513i		−	0.416432i	−0.978083	−	0.208216i	$-0.933234\pi$
$509$		−	9.39513i		−	0.416432i	0.978083	−	0.208216i	$-0.0667656\pi$
$510$	−0.862687	−	0.950173i	−0.0382004	−	0.0420744i
$511$			25.0046i			1.10614i
$512$	−1.00000			−0.0441942
$513$	−8.23276	+	6.90176i	−0.363485	+	0.304720i
$514$	−2.32061			−0.102358
$515$	−2.76947	+	4.59325i	−0.122037	+	0.202403i
$516$	11.9365	+	3.57551i	0.525475	+	0.157403i
$517$	−29.1807			−1.28337
$518$	8.30136			0.364741
$519$	22.2691	+	6.67058i	0.977504	+	0.292806i
$520$	6.46906	+	3.90047i	0.283687	+	0.171047i
$521$	21.5382			0.943606			0.471803	−	0.881704i	$-0.343603\pi$
$521$	21.5382			0.943606			0.471803	+	0.881704i	$0.343603\pi$
$522$	11.1143	−	16.8874i	0.486461	−	0.739143i
$523$	12.2150			0.534126			0.267063	−	0.963679i	$-0.413947\pi$
$523$	12.2150			0.534126			0.267063	+	0.963679i	$0.413947\pi$
$524$			6.85575i			0.299495i
$525$	−5.28893	−	26.8350i	−0.230828	−	1.17117i
$526$			31.4516i			1.37135i
$527$			0.790870i			0.0344508i
$528$	4.37642	+	1.31093i	0.190459	+	0.0570511i
$529$	−13.3401	−	18.7361i	−0.580004	−	0.814613i
$530$	−26.3900	−	15.9117i	−1.14631	−	0.691158i
$531$	19.9395	−	30.2967i	0.865302	−	1.31476i
$532$			6.52967i			0.283097i
$533$	23.3883			1.01306
$534$	−11.6579	−	3.49207i	−0.504489	−	0.151117i
$535$	−20.0039	−	12.0612i	−0.864843	−	0.521450i
$536$	−0.468752			−0.0202470
$537$	0.674582	−	2.25203i	0.0291104	−	0.0971821i
$538$		−	10.7521i		−	0.463558i
$539$	−7.84576			−0.337941
$540$	11.4795	−	1.79487i	0.493998	−	0.0772391i
$541$	−15.9915			−0.687529			−0.343764	−	0.939056i	$-0.611702\pi$
$541$	−15.9915			−0.687529			−0.343764	+	0.939056i	$0.611702\pi$
$542$	−7.09113			−0.304590
$543$	−6.26522	+	20.9158i	−0.268866	+	0.897584i
$544$		−	0.331367i		−	0.0142072i
$545$	−6.95998	−	4.19647i	−0.298133	−	0.179757i
$546$	5.30273	−	17.7026i	0.226936	−	0.757603i
$547$			42.8762i			1.83325i	0.399745	+	0.916627i	$0.369099\pi$
$547$			42.8762i			1.83325i	−0.399745	+	0.916627i	$0.630901\pi$
$548$			14.8092i			0.632616i
$549$	−1.13025	+	1.71733i	−0.0482379	+	0.0732941i
$550$	−6.15589	−	11.6634i	−0.262488	−	0.497330i
$551$	13.9326			0.593550
$552$	5.76504	−	5.98033i	0.245376	−	0.254540i
$553$		−	21.5103i		−	0.914712i
$554$		−	10.1872i		−	0.432814i
$555$	7.53697	−	6.84302i	0.319927	−	0.290470i
$556$	0.241417			0.0102384
$557$		−	4.49189i		−	0.190328i	−0.995462	−	0.0951638i	$-0.969663\pi$
$557$		−	4.49189i		−	0.190328i	0.995462	−	0.0951638i	$-0.0303375\pi$
$558$	−5.98097	−	3.93633i	−0.253195	−	0.166638i
$559$		−	24.3033i		−	1.02792i
$560$	3.64647	−	6.04780i	0.154092	−	0.255566i
$561$	−0.434400	+	1.45020i	−0.0183404	+	0.0612275i
$562$	−16.0901			−0.678718
$563$			18.8243i			0.793348i	0.917960	+	0.396674i	$0.129836\pi$
$563$			18.8243i			0.793348i	−0.917960	+	0.396674i	$0.870164\pi$
$564$	−18.3561	−	5.49847i	−0.772931	−	0.231527i
$565$	1.12404	+	0.677733i	0.0472888	+	0.0285124i
$566$	28.1303			1.18240
$567$	−11.2425	−	26.1064i	−0.472142	−	1.09636i
$568$			5.57976i			0.234122i
$569$	34.8852			1.46246			0.731231	−	0.682130i	$-0.238946\pi$
$569$	34.8852			1.46246			0.731231	+	0.682130i	$0.238946\pi$
$570$	5.38257	+	5.92842i	0.225451	+	0.248314i
$571$			28.9370i			1.21097i	0.795855	+	0.605487i	$0.207022\pi$
$571$			28.9370i			1.21097i	−0.795855	+	0.605487i	$0.792978\pi$
$572$		−	8.91062i		−	0.372572i
$573$	38.9015	+	11.6527i	1.62513	+	0.486800i
$574$		−	21.8652i		−	0.912637i
$575$	−23.9781	+	0.230305i	−0.999954	+	0.00960438i
$576$	2.50597	+	1.64928i	0.104415	+	0.0687201i
$577$		−	28.8137i		−	1.19953i	−0.800177	−	0.599764i	$-0.795261\pi$
$577$		−	28.8137i		−	1.19953i	0.800177	−	0.599764i	$-0.204739\pi$
$578$	−16.8902			−0.702540
$579$	−9.27195	+	30.9535i	−0.385329	+	1.28638i
$580$	−12.9045	−	7.78065i	−0.535828	−	0.323074i
$581$			13.1624i			0.546066i
$582$	30.2047	+	9.04765i	1.25203	+	0.375037i
$583$			36.3501i			1.50547i
$584$			7.91723i			0.327617i
$585$	−9.77827	−	20.4438i	−0.404282	−	0.845246i
$586$		−	10.7652i		−	0.444707i
$587$	−14.8097			−0.611260			−0.305630	−	0.952150i	$-0.598867\pi$
$587$	−14.8097			−0.611260			−0.305630	+	0.952150i	$0.598867\pi$
$588$	−4.93537	−	1.47836i	−0.203531	−	0.0609666i
$589$		−	4.93448i		−	0.203322i
$590$	−23.1511	−	13.9588i	−0.953115	−	0.574673i
$591$	−8.26774	−	2.47656i	−0.340090	−	0.101872i
$592$	2.62847			0.108029
$593$	2.98454			0.122561			0.0612803	−	0.998121i	$-0.480482\pi$
$593$	2.98454			0.122561			0.0612803	+	0.998121i	$0.480482\pi$
$594$	−8.80507	−	10.5031i	−0.361276	−	0.430948i
$595$	2.00404	+	1.20832i	0.0821575	+	0.0495363i
$596$	21.2344			0.869795
$597$	−7.29278	+	24.3462i	−0.298474	+	0.996425i
$598$	−14.4002	−	7.42440i	−0.588868	−	0.303606i
$599$			5.47578i			0.223734i	0.993723	+	0.111867i	$0.0356831\pi$
$599$			5.47578i			0.223734i	−0.993723	+	0.111867i	$0.964317\pi$
$600$	−1.67464	−	8.49680i	−0.0683670	−	0.346880i
$601$	1.39688			0.0569799			0.0284900	−	0.999594i	$-0.490930\pi$
$601$	1.39688			0.0569799			0.0284900	+	0.999594i	$0.490930\pi$
$602$	−22.7207			−0.926025
$603$	1.17468	+	0.773104i	0.0478365	+	0.0314832i
$604$	−16.3816			−0.666556
$605$	4.66776	−	7.74163i	0.189771	−	0.314742i
$606$	1.03053	−	3.44033i	0.0418625	−	0.139754i
$607$			32.7100i			1.32766i	0.747884	+	0.663830i	$0.231070\pi$
$607$			32.7100i			1.32766i	−0.747884	+	0.663830i	$0.768930\pi$
$608$			2.06750i			0.0838481i
$609$	−10.5779	+	35.3132i	−0.428637	+	1.43096i
$610$	1.31229	+	0.791237i	0.0531332	+	0.0320363i
$611$			37.3739i			1.51199i
$612$	−0.546517	+	0.830394i	−0.0220916	+	0.0335667i
$613$	35.5819			1.43714			0.718569	−	0.695456i	$-0.244798\pi$
$613$	35.5819			1.43714			0.718569	+	0.695456i	$0.244798\pi$
$614$			21.1061i			0.851774i
$615$	−18.0241	−	19.8519i	−0.726800	−	0.800505i
$616$	−8.33036			−0.335640
$617$		−	36.0529i		−	1.45144i	−0.687992	−	0.725718i	$-0.741508\pi$
$617$		−	36.0529i		−	1.45144i	0.687992	−	0.725718i	$-0.258492\pi$
$618$	3.97989	+	1.19215i	0.160095	+	0.0479555i
$619$		−	2.79306i		−	0.112263i	−0.998423	−	0.0561313i	$-0.982123\pi$
$619$		−	2.79306i		−	0.112263i	0.998423	−	0.0561313i	$-0.0178766\pi$
$620$	−2.75565	+	4.57033i	−0.110669	+	0.183549i
$621$	−24.3102	+	5.47834i	−0.975536	+	0.219838i
$622$			15.5206i			0.622319i
$623$	22.1905			0.889042
$624$	1.67901	−	5.60521i	0.0672142	−	0.224388i
$625$	−14.1063	+	20.6401i	−0.564250	+	0.825604i
$626$	−0.701429			−0.0280347
$627$	2.71035	−	9.04824i	0.108241	−	0.361352i
$628$	−9.20113			−0.367165
$629$			0.870987i			0.0347285i
$630$	−19.1125	+	9.14151i	−0.761459	+	0.364207i
$631$			12.2810i			0.488899i	0.969662	+	0.244450i	$0.0786073\pi$
$631$			12.2810i			0.488899i	−0.969662	+	0.244450i	$0.921393\pi$
$632$		−	6.81084i		−	0.270921i
$633$	−6.73630	−	2.01782i	−0.267744	−	0.0802013i
$634$	26.6487			1.05836
$635$	11.3876	+	6.86608i	0.451904	+	0.272472i
$636$	−6.84938	+	22.8660i	−0.271596	+	0.906695i
$637$			10.0487i			0.398142i
$638$			17.7749i			0.703713i
$639$	9.20261	−	13.9827i	0.364049	−	0.553147i
$640$	1.15459	−	1.91492i	0.0456391	−	0.0756939i
$641$	13.5240			0.534164			0.267082	−	0.963674i	$-0.413940\pi$
$641$	13.5240			0.534164			0.267082	+	0.963674i	$0.413940\pi$
$642$	−5.19190	+	17.3326i	−0.204908	+	0.684065i
$643$	22.1920			0.875167			0.437584	−	0.899178i	$-0.355834\pi$
$643$	22.1920			0.875167			0.437584	+	0.899178i	$0.355834\pi$
$644$	−6.94093	+	13.4625i	−0.273511	+	0.530495i
$645$	−20.6285	+	18.7292i	−0.812248	+	0.737462i
$646$	−0.685099			−0.0269549
$647$	−8.05146			−0.316535			−0.158268	−	0.987396i	$-0.550591\pi$
$647$	−8.05146			−0.316535			−0.158268	+	0.987396i	$0.550591\pi$
$648$	−3.55974	−	8.26609i	−0.139840	−	0.324723i
$649$			31.8888i			1.25174i
$650$	−14.9382	+	7.88431i	−0.585925	+	0.309248i
$651$	12.5067	+	3.74633i	0.490178	+	0.146830i
$652$			23.6263i			0.925279i
$653$	36.1968			1.41649			0.708246	−	0.705966i	$-0.249487\pi$
$653$	36.1968			1.41649			0.708246	+	0.705966i	$0.249487\pi$
$654$	−1.80643	+	6.03058i	−0.0706369	+	0.235814i
$655$	−13.1282	−	7.91557i	−0.512962	−	0.309287i
$656$		−	6.92322i		−	0.270306i
$657$	13.0578	−	19.8403i	0.509431	−	0.774045i
$658$	34.9401			1.36211
$659$	−27.2539			−1.06166			−0.530831	−	0.847478i	$-0.678120\pi$
$659$	−27.2539			−1.06166			−0.530831	+	0.847478i	$0.678120\pi$
$660$	−7.56330	+	6.86692i	−0.294401	+	0.267295i
$661$			23.7666i			0.924412i	0.886773	+	0.462206i	$0.152942\pi$
$661$			23.7666i			0.924412i	−0.886773	+	0.462206i	$0.847058\pi$
$662$	12.0090			0.466743
$663$	1.85738	+	0.556368i	0.0721347	+	0.0216075i
$664$			4.16761i			0.161735i
$665$	−12.5038	−	7.53907i	−0.484877	−	0.292353i
$666$	−6.58686	−	4.33509i	−0.255236	−	0.167981i
$667$	28.7254	+	14.8102i	1.11225	+	0.573452i
$668$	9.99301			0.386641
$669$	−13.3452	+	44.5515i	−0.515954	+	1.72246i
$670$	0.541215	−	0.897624i	0.0209090	−	0.0346782i
$671$		−	1.80758i		−	0.0697808i
$672$	−5.24020	−	1.56967i	−0.202145	−	0.0605515i
$673$			14.3957i			0.554912i	0.960738	+	0.277456i	$0.0894914\pi$
$673$			14.3957i			0.554912i	−0.960738	+	0.277456i	$0.910509\pi$
$674$	32.5953			1.25552
$675$	−9.81702	+	24.0546i	−0.377857	+	0.925864i
$676$	1.58751			0.0610579
$677$		−	31.0852i		−	1.19470i	−0.801981	−	0.597350i	$-0.796220\pi$
$677$		−	31.0852i		−	1.19470i	0.801981	−	0.597350i	$-0.203780\pi$
$678$	0.291739	−	0.973942i	0.0112042	−	0.0374040i
$679$	−57.4935			−2.20640
$680$	0.634541	+	0.382592i	0.0243335	+	0.0146717i
$681$	8.10622	−	27.0618i	0.310631	−	1.03701i
$682$	6.29526			0.241058
$683$	−3.72271			−0.142446			−0.0712228	−	0.997460i	$-0.522690\pi$
$683$	−3.72271			−0.142446			−0.0712228	+	0.997460i	$0.522690\pi$
$684$	3.40989	−	5.18108i	0.130380	−	0.198103i
$685$	−28.3584	−	17.0985i	−1.08352	−	0.653299i
$686$	−12.7134			−0.485402
$687$	−6.47829	+	21.6271i	−0.247162	+	0.825126i
$688$	−7.19407			−0.274271
$689$	46.5563			1.77365
$690$	4.79563	+	17.9444i	0.182566	+	0.683132i
$691$	−37.6228			−1.43124			−0.715619	−	0.698491i	$-0.753855\pi$
$691$	−37.6228			−1.43124			−0.715619	+	0.698491i	$0.753855\pi$
$692$	−13.4215			−0.510208
$693$	20.8756	+	13.7391i	0.792998	+	0.521906i
$694$	−14.3932			−0.546357
$695$	−0.278737	+	0.462294i	−0.0105731	+	0.0175358i
$696$	−3.34928	+	11.1813i	−0.126954	+	0.423824i
$697$	2.29412			0.0868961
$698$	0.672923			0.0254705
$699$	30.4566	+	9.12312i	1.15198	+	0.345068i
$700$	7.37089	+	13.9654i	0.278593	+	0.527844i
$701$	−12.0462			−0.454979			−0.227489	−	0.973781i	$-0.573052\pi$
$701$	−12.0462			−0.454979			−0.227489	+	0.973781i	$0.573052\pi$
$702$	−13.4521	+	11.2773i	−0.507718	+	0.425635i
$703$		−	5.43435i		−	0.204961i
$704$	−2.63765			−0.0994102
$705$	31.7228	−	28.8020i	1.19475	−	1.08475i
$706$	25.3608			0.954465
$707$			6.54854i			0.246283i
$708$	−6.00874	+	20.0596i	−0.225822	+	0.753885i
$709$			49.3481i			1.85331i	0.375915	+	0.926654i	$0.377328\pi$
$709$			49.3481i			1.85331i	−0.375915	+	0.926654i	$0.622672\pi$
$710$	−10.6848	−	6.44233i	−0.400994	−	0.241776i
$711$	−11.2330	+	17.0677i	−0.421270	+	0.640090i
$712$	7.02620			0.263318
$713$	5.24527	−	10.1736i	0.196437	−	0.381004i
$714$	0.520137	−	1.73643i	0.0194656	−	0.0649842i
$715$	17.0631	+	10.2881i	0.638125	+	0.384753i
$716$			1.35729i			0.0507242i
$717$	−3.89533	+	13.0042i	−0.145474	+	0.485650i
$718$	−18.0914			−0.675164
$719$			12.1521i			0.453198i	0.973988	+	0.226599i	$0.0727608\pi$
$719$			12.1521i			0.453198i	−0.973988	+	0.226599i	$0.927239\pi$
$720$	−6.05161	+	2.89449i	−0.225530	+	0.107871i
$721$	−7.57557			−0.282129
$722$	−14.7255			−0.548025
$723$	−8.39768	+	28.0348i	−0.312313	+	1.04263i
$724$		−	12.6059i		−	0.468494i
$725$	29.7987	−	15.7276i	1.10669	−	0.584108i
$726$	−6.70785	−	2.00930i	−0.248952	−	0.0745721i
$727$	−12.7421			−0.472578			−0.236289	−	0.971683i	$-0.575931\pi$
$727$	−12.7421			−0.472578			−0.236289	+	0.971683i	$0.575931\pi$
$728$			10.6693i			0.395431i
$729$	−4.71254	+	26.5856i	−0.174539	+	0.984650i
$730$	−15.1609	−	9.14114i	−0.561129	−	0.338329i
$731$		−	2.38387i		−	0.0881708i
$732$	0.340599	−	1.13705i	0.0125889	−	0.0420268i
$733$	−7.41403			−0.273844			−0.136922	−	0.990582i	$-0.543721\pi$
$733$	−7.41403			−0.273844			−0.136922	+	0.990582i	$0.543721\pi$
$734$	0.368267			0.0135930
$735$	8.52926	−	7.74394i	0.314607	−	0.285640i
$736$	−2.19771	+	4.26263i	−0.0810088	+	0.157123i
$737$	−1.23640			−0.0455435
$738$	−11.4183	+	17.3493i	−0.420315	+	0.638638i
$739$	−19.5512			−0.719202			−0.359601	−	0.933106i	$-0.617087\pi$
$739$	−19.5512			−0.719202			−0.359601	+	0.933106i	$0.617087\pi$
$740$	−3.03480	+	5.03332i	−0.111561	+	0.185028i
$741$	−11.5888	−	3.47135i	−0.425724	−	0.127523i
$742$		−	43.5246i		−	1.59784i
$743$		−	41.8808i		−	1.53646i	−0.640176	−	0.768228i	$-0.721139\pi$
$743$		−	41.8808i		−	1.53646i	0.640176	−	0.768228i	$-0.278861\pi$
$744$	3.96003	+	1.18620i	0.145182	+	0.0434884i
$745$	−24.5170	+	40.6622i	−0.898233	+	1.48975i
$746$	−19.5200			−0.714676
$747$	6.87357	−	10.4439i	0.251491	−	0.382122i
$748$		−	0.874030i		−	0.0319577i
$749$		−	32.9920i		−	1.20550i
$750$	18.2042	+	6.60349i	0.664724	+	0.241125i
$751$		−	19.1550i		−	0.698975i	−0.936941	−	0.349488i	$-0.886356\pi$
$751$		−	19.1550i		−	0.698975i	0.936941	−	0.349488i	$-0.113644\pi$
$752$	11.0631			0.403431
$753$	−43.6139	−	13.0643i	−1.58938	−	0.476090i
$754$	22.7656			0.829074
$755$	18.9140	−	31.3694i	0.688349	−	1.14165i
$756$	10.5429	+	12.5761i	0.383443	+	0.457389i
$757$	−38.7480			−1.40832			−0.704160	−	0.710042i	$-0.748676\pi$
$757$	−38.7480			−1.40832			−0.704160	+	0.710042i	$0.748676\pi$
$758$			33.4418i			1.21466i
$759$	15.2062	−	15.7740i	0.551949	−	0.572561i
$760$	−3.95909	−	2.38711i	−0.143611	−	0.0865895i
$761$		−	31.4000i		−	1.13825i	−0.822252	−	0.569124i	$-0.807282\pi$
$761$		−	31.4000i		−	1.13825i	0.822252	−	0.569124i	$-0.192718\pi$
$762$	2.95560	−	9.86697i	0.107070	−	0.357443i
$763$		−	11.4790i		−	0.415567i
$764$	−23.4458			−0.848239
$765$	−0.959137	−	2.00530i	−0.0346777	−	0.0725018i
$766$			17.0408i			0.615710i
$767$	40.8423			1.47473
$768$	−1.65921	−	0.497008i	−0.0598716	−	0.0179342i
$769$		−	44.1018i		−	1.59035i	−0.606380	−	0.795175i	$-0.707379\pi$
$769$		−	44.1018i		−	1.59035i	0.606380	−	0.795175i	$-0.292621\pi$
$770$	9.61813	−	15.9520i	0.346613	−	0.574870i
$771$	−3.85039	−	1.15336i	−0.138668	−	0.0415374i
$772$		−	18.6555i		−	0.671428i
$773$			38.2289i			1.37500i	0.726185	+	0.687499i	$0.241292\pi$
$773$			38.2289i			1.37500i	−0.726185	+	0.687499i	$0.758708\pi$
$774$	18.0281	+	11.8651i	0.648007	+	0.426481i
$775$	−5.57019	−	10.5537i	−0.200087	−	0.379100i
$776$	−18.2042			−0.653494
$777$	13.7737	+	4.12584i	0.494129	+	0.148014i
$778$	−0.355884			−0.0127591
$779$	−14.3137			−0.512842
$780$	8.79498	+	9.68689i	0.314911	+	0.346846i
$781$			14.7175i			0.526633i
$782$	−1.41249	−	0.728249i	−0.0505107	−	0.0260421i
$783$	26.8342	−	22.4959i	0.958977	−	0.803939i
$784$	2.97452			0.106233
$785$	10.6235	−	17.6194i	0.379169	−	0.628865i
$786$	−3.40736	+	11.3751i	−0.121537	+	0.405738i
$787$	41.9228			1.49439			0.747193	−	0.664607i	$-0.231401\pi$
$787$	41.9228			1.49439			0.747193	+	0.664607i	$0.231401\pi$
$788$	4.98294			0.177510
$789$	−15.6317	+	52.1848i	−0.556502	+	1.85783i
$790$	13.0422	+	7.86372i	0.464022	+	0.279778i
$791$			1.85386i			0.0659158i
$792$	6.60987	+	4.35023i	0.234871	+	0.154579i
$793$	−2.31510			−0.0822116
$794$			19.0771i			0.677019i
$795$	−35.8784	−	39.5168i	−1.27247	−	1.40152i
$796$		−	14.6734i		−	0.520084i
$797$			0.345464i			0.0122370i	0.999981	+	0.00611848i	$0.00194758\pi$
$797$			0.345464i			0.0122370i	−0.999981	+	0.00611848i	$0.998052\pi$
$798$	−3.24529	+	10.8341i	−0.114882	+	0.383523i
$799$			3.66595i			0.129692i
$800$	2.33385	+	4.42189i	0.0825142	+	0.156337i
$801$	−17.6074	−	11.5882i	−0.622127	−	0.409448i
$802$	29.7359			1.05001
$803$			20.8829i			0.736942i
$804$	−0.777759	−	0.232973i	−0.0274294	−	0.00821634i
$805$	−17.7656	−	28.8349i	−0.626156	−	1.01630i
$806$		−	8.06281i		−	0.284000i
$807$	5.34390	−	17.8401i	0.188114	−	0.628000i
$808$			2.07347i			0.0729445i
$809$		−	39.9547i		−	1.40473i	−0.711816	−	0.702366i	$-0.752127\pi$
$809$		−	39.9547i		−	1.40473i	0.711816	−	0.702366i	$-0.247873\pi$
$810$	19.9390	+	2.72731i	0.700583	+	0.0958280i
$811$	30.4786			1.07025			0.535124	−	0.844774i	$-0.320265\pi$
$811$	30.4786			1.07025			0.535124	+	0.844774i	$0.320265\pi$
$812$		−	21.2831i		−	0.746890i
$813$	−11.7657	−	3.52435i	−0.412641	−	0.123604i
$814$	6.93299			0.243001
$815$	−45.2426	−	27.2787i	−1.58478	−	0.955531i
$816$	0.164692	−	0.549807i	0.00576537	−	0.0192471i
$817$			14.8737i			0.520365i
$818$	−14.1316			−0.494100
$819$	17.5967	−	26.7369i	0.614879	−	0.934264i
$820$	13.2574	+	7.99346i	0.462969	+	0.279144i
$821$			12.0374i			0.420106i	0.977690	+	0.210053i	$0.0673637\pi$
$821$			12.0374i			0.420106i	−0.977690	+	0.210053i	$0.932636\pi$
$822$	−7.36027	+	24.5715i	−0.256719	+	0.857031i
$823$		−	10.6364i		−	0.370760i	−0.982667	−	0.185380i	$-0.940648\pi$
$823$		−	10.6364i		−	0.370760i	0.982667	−	0.185380i	$-0.0593516\pi$
$824$	−2.39866			−0.0835614
$825$	−4.41712	−	22.4116i	−0.153784	−	0.780272i
$826$		−	38.1827i		−	1.32854i
$827$			36.9079i			1.28341i	0.766950	+	0.641707i	$0.221773\pi$
$827$			36.9079i			1.28341i	−0.766950	+	0.641707i	$0.778227\pi$
$828$	12.5377	−	7.05737i	0.435715	−	0.245260i
$829$	49.8365			1.73089			0.865446	−	0.501002i	$-0.167035\pi$
$829$	49.8365			1.73089			0.865446	+	0.501002i	$0.167035\pi$
$830$	−7.98066	−	4.81188i	−0.277013	−	0.167023i
$831$	5.06314	−	16.9028i	0.175638	−	0.586351i
$832$			3.37824i			0.117119i
$833$			0.985658i			0.0341510i
$834$	0.400561	+	0.119986i	0.0138703	+	0.00415478i
$835$	−11.5378	+	19.1358i	−0.399282	+	0.662223i
$836$			5.45334i			0.188608i
$837$	−7.96731	−	9.50379i	−0.275390	−	0.328499i
$838$	16.0060			0.552917
$839$	0.622041			0.0214752			0.0107376	−	0.999942i	$-0.496582\pi$
$839$	0.622041			0.0214752			0.0107376	+	0.999942i	$0.496582\pi$
$840$	9.05607	−	8.22225i	0.312464	−	0.283695i
$841$	−16.4127			−0.565955
$842$			26.7513i			0.921910i
$843$	−26.6968	−	7.99689i	−0.919487	−	0.275427i
$844$	4.05994			0.139749
$845$	−1.83291	+	3.03995i	−0.0630542	+	0.104577i
$846$	−27.7238	−	18.2462i	−0.953166	−	0.627318i
$847$	12.7681			0.438718
$848$		−	13.7812i		−	0.473250i
$849$	46.6741	+	13.9810i	1.60185	+	0.479826i
$850$	−1.46527	+	0.773361i	−0.0502582	+	0.0265261i
$851$	5.77663	−	11.2042i	0.198020	−	0.384075i
$852$	−2.77319	+	9.25801i	−0.0950078	+	0.317174i
$853$		−	53.1589i		−	1.82013i	−0.414468	−	0.910064i	$-0.636032\pi$
$853$		−	53.1589i		−	1.82013i	0.414468	−	0.910064i	$-0.363968\pi$
$854$			2.16434i			0.0740622i
$855$	5.98435	+	12.5117i	0.204660	+	0.427890i
$856$		−	10.4463i		−	0.357047i
$857$	43.2814			1.47847			0.739233	−	0.673450i	$-0.235188\pi$
$857$	43.2814			1.47847			0.739233	+	0.673450i	$0.235188\pi$
$858$	4.42865	−	14.7846i	0.151191	−	0.504738i
$859$	14.1473			0.482701			0.241351	−	0.970438i	$-0.422410\pi$
$859$	14.1473			0.482701			0.241351	+	0.970438i	$0.422410\pi$
$860$	8.30619	−	13.7761i	0.283239	−	0.469761i
$861$	10.8672	−	36.2790i	0.370353	−	1.23639i
$862$	−1.45183			−0.0494496
$863$	13.3566			0.454664			0.227332	−	0.973817i	$-0.427000\pi$
$863$	13.3566			0.454664			0.227332	+	0.973817i	$0.427000\pi$
$864$	3.33822	+	3.98199i	0.113569	+	0.135470i
$865$	15.4963	−	25.7011i	0.526890	−	0.873864i
$866$	14.3432			0.487401
$867$	−28.0244	−	8.39456i	−0.951759	−	0.285094i
$868$	−7.53776			−0.255848
$869$		−	17.9646i		−	0.609408i
$870$	−17.5442	−	19.3234i	−0.594804	−	0.655123i
$871$			1.58356i			0.0536567i
$872$		−	3.63460i		−	0.123083i
$873$	45.6192	+	30.0239i	1.54398	+	1.01616i
$874$	8.81298	+	4.54377i	0.298104	+	0.153695i
$875$	−35.2530	−	2.00964i	−1.19177	−	0.0679383i
$876$	−3.93493	+	13.1364i	−0.132949	+	0.443837i
$877$			6.59780i			0.222792i	0.993776	+	0.111396i	$0.0355322\pi$
$877$			6.59780i			0.222792i	−0.993776	+	0.111396i	$0.964468\pi$
$878$	31.5600			1.06510
$879$	5.35039	−	17.8618i	0.180464	−	0.602462i
$880$	3.04540	−	5.05090i	0.102660	−	0.170266i
$881$	−22.5045			−0.758196			−0.379098	−	0.925357i	$-0.623766\pi$
$881$	−22.5045			−0.758196			−0.379098	+	0.925357i	$0.623766\pi$
$882$	−7.45406	−	4.90583i	−0.250991	−	0.165188i
$883$			8.29422i			0.279123i	0.990213	+	0.139561i	$0.0445692\pi$
$883$			8.29422i			0.279123i	−0.990213	+	0.139561i	$0.955431\pi$
$884$	−1.11944			−0.0376507
$885$	−31.4749	−	34.6668i	−1.05802	−	1.16531i
$886$	40.5298			1.36163
$887$	48.1455			1.61657			0.808283	−	0.588794i	$-0.200397\pi$
$887$	48.1455			1.61657			0.808283	+	0.588794i	$0.200397\pi$
$888$	4.36119	+	1.30637i	0.146352	+	0.0438389i
$889$			18.7814i			0.629908i
$890$	−8.11236	+	13.4546i	−0.271927	+	0.451000i
$891$	−9.38934	−	21.8031i	−0.314555	−	0.730430i
$892$		−	26.8510i		−	0.899038i
$893$		−	22.8730i		−	0.765416i
$894$	35.2324	+	10.5537i	1.17835	+	0.352968i
$895$	−2.59910	−	1.56711i	−0.0868783	−	0.0523826i
$896$	3.15825			0.105510
$897$	−20.2030	−	19.4757i	−0.674558	−	0.650274i
$898$		−	13.0425i		−	0.435233i
$899$			16.0837i			0.536420i
$900$	1.44439	−	14.9303i	0.0481463	−	0.497677i
$901$	4.56664			0.152137
$902$		−	18.2610i		−	0.608026i
$903$	−37.6984	−	11.2923i	−1.25452	−	0.375786i
$904$			0.586991i			0.0195230i
$905$	24.1393	+	14.5546i	0.802417	+	0.483811i
$906$	−27.1805	−	8.14176i	−0.903011	−	0.270492i
$907$	−24.1181			−0.800828			−0.400414	−	0.916334i	$-0.631134\pi$
$907$	−24.1181			−0.800828			−0.400414	+	0.916334i	$0.631134\pi$
$908$			16.3101i			0.541268i
$909$	3.41974	−	5.19605i	0.113426	−	0.172342i
$910$	−20.4309	−	12.3187i	−0.677278	−	0.408360i
$911$	5.60483			0.185696			0.0928481	−	0.995680i	$-0.470403\pi$
$911$	5.60483			0.185696			0.0928481	+	0.995680i	$0.470403\pi$
$912$	−1.02756	+	3.43041i	−0.0340260	+	0.113592i
$913$			10.9927i			0.363806i
$914$	−32.9430			−1.08966
$915$	1.78412	+	1.96505i	0.0589812	+	0.0649625i
$916$		−	13.0346i		−	0.430675i
$917$		−	21.6522i		−	0.715017i
$918$	−1.31950	+	1.10618i	−0.0435500	+	0.0365092i
$919$			3.54435i			0.116917i	0.998290	+	0.0584587i	$0.0186186\pi$
$919$			3.54435i			0.116917i	−0.998290	+	0.0584587i	$0.981381\pi$
$920$	−5.62516	−	9.13004i	−0.185456	−	0.301008i
$921$	−10.4899	+	35.0195i	−0.345654	+	1.15393i
$922$			18.9180i			0.623032i
$923$	18.8498			0.620448
$924$	−13.8218	−	4.14025i	−0.454705	−	0.136204i
$925$	−6.13446	−	11.6228i	−0.201700	−	0.382156i
$926$			1.43119i			0.0470319i
$927$	6.01097	+	3.95607i	0.197426	+	0.129935i
$928$		−	6.73889i		−	0.221215i
$929$		−	14.1130i		−	0.463033i	−0.972831	−	0.231517i	$-0.925631\pi$
$929$		−	14.1130i		−	0.463033i	0.972831	−	0.231517i	$-0.0743688\pi$
$930$	−6.84369	+	6.21356i	−0.224413	+	0.203751i
$931$		−	6.14982i		−	0.201552i
$932$	−18.3561			−0.601274
$933$	−7.71385	+	25.7519i	−0.252540	+	0.843081i
$934$			36.8872i			1.20699i
$935$	1.67370	+	1.00914i	0.0547358	+	0.0330025i
$936$	5.57167	−	8.46575i	0.182116	−	0.276712i
$937$	0.752217			0.0245739			0.0122869	−	0.999925i	$-0.496089\pi$
$937$	0.752217			0.0245739			0.0122869	+	0.999925i	$0.496089\pi$
$938$	1.48043			0.0483379
$939$	−1.16382	−	0.348616i	−0.0379798	−	0.0113766i
$940$	−12.7734	+	21.1850i	−0.416621	+	0.690980i
$941$	−16.4726			−0.536991			−0.268495	−	0.963281i	$-0.586526\pi$
$941$	−16.4726			−0.536991			−0.268495	+	0.963281i	$0.586526\pi$
$942$	−15.2666	−	4.57303i	−0.497413	−	0.148997i
$943$	−29.5111	−	15.2153i	−0.961015	−	0.495477i
$944$		−	12.0898i		−	0.393490i
$945$	−36.2550	+	5.66866i	−1.17938	+	0.184401i
$946$	−18.9755			−0.616945
$947$	−25.2263			−0.819743			−0.409872	−	0.912143i	$-0.634427\pi$
$947$	−25.2263			−0.819743			−0.409872	+	0.912143i	$0.634427\pi$
$948$	3.38504	−	11.3006i	0.109941	−	0.367027i
$949$	26.7463			0.868222
$950$	9.14225	−	4.82523i	0.296614	−	0.156551i
$951$	44.2158	+	13.2446i	1.43380	+	0.429486i
$952$			1.04654i			0.0339185i
$953$		−	7.11142i		−	0.230362i	−0.993345	−	0.115181i	$-0.963255\pi$
$953$		−	7.11142i		−	0.230362i	0.993345	−	0.115181i	$-0.0367447\pi$
$954$	−22.7292	+	34.5353i	−0.735883	+	1.11812i
$955$	27.0702	−	44.8969i	0.875972	−	1.45283i
$956$		−	7.83756i		−	0.253485i
$957$	−8.83424	+	29.4923i	−0.285571	+	0.953349i
$958$	17.8352			0.576230
$959$		−	46.7710i		−	1.51031i
$960$	2.86744	−	2.60342i	0.0925461	−	0.0840251i
$961$	−25.3037			−0.816249
$962$		−	8.87960i		−	0.286290i
$963$	−17.2289	+	26.1781i	−0.555194	+	0.843577i
$964$		−	16.8965i		−	0.544199i
$965$	35.7239	+	21.5395i	1.14999	+	0.693380i
$966$	−18.2074	+	18.8874i	−0.585814	+	0.607691i
$967$		−	39.3623i		−	1.26581i	−0.774231	−	0.632903i	$-0.781863\pi$
$967$		−	39.3623i		−	1.26581i	0.774231	−	0.632903i	$-0.218137\pi$
$968$	4.04279			0.129940
$969$	−1.13672	−	0.340500i	−0.0365169	−	0.0109384i
$970$	21.0184	−	34.8597i	0.674860	−	1.11928i
$971$	−13.1049			−0.420555			−0.210277	−	0.977642i	$-0.567437\pi$
$971$	−13.1049			−0.420555			−0.210277	+	0.977642i	$0.567437\pi$
$972$	−1.79804	−	15.4844i	−0.0576722	−	0.496663i
$973$	−0.762454			−0.0244431
$974$		−	5.32528i		−	0.170633i
$975$	−28.7042	+	5.65734i	−0.919270	+	0.181180i
$976$			0.685298i			0.0219359i
$977$		−	2.33181i		−	0.0746011i	−0.999304	−	0.0373006i	$-0.988124\pi$
$977$		−	2.33181i		−	0.0746011i	0.999304	−	0.0373006i	$-0.0118759\pi$
$978$	−11.7425	+	39.2011i	−0.375483	+	1.25351i
$979$	18.5327			0.592306
$980$	−3.43435	+	5.69598i	−0.109706	+	0.181952i
$981$	−5.99449	+	9.10820i	−0.191389	+	0.290802i
$982$			27.6023i			0.880826i
$983$			5.68571i			0.181346i	0.995881	+	0.0906730i	$0.0289018\pi$
$983$			5.68571i			0.181346i	−0.995881	+	0.0906730i	$0.971098\pi$
$984$	3.44089	−	11.4871i	0.109692	−	0.366195i
$985$	−5.75324	+	9.54193i	−0.183313	+	0.304031i
$986$	2.23304			0.0711146
$987$	57.9731	+	17.3655i	1.84530	+	0.552750i
$988$	6.98450			0.222206
$989$	−15.8105	+	30.6657i	−0.502745	+	0.975112i
$990$	−15.9620	+	7.63465i	−0.507307	+	0.242645i
$991$	31.5258			1.00145			0.500724	−	0.865607i	$-0.333067\pi$
$991$	31.5258			1.00145			0.500724	+	0.865607i	$0.333067\pi$
$992$	−2.38669			−0.0757775
$993$	19.9255	+	5.96856i	0.632315	+	0.189407i
$994$		−	17.6223i		−	0.558945i
$995$	28.0984	+	16.9417i	0.890778	+	0.537088i
$996$	−2.07134	+	6.91495i	−0.0656328	+	0.219109i
$997$		−	17.7313i		−	0.561555i	−0.959773	−	0.280778i	$-0.909408\pi$
$997$		−	17.7313i		−	0.561555i	0.959773	−	0.280778i	$-0.0905924\pi$
$998$	25.7722			0.815804
$999$	−8.77442	−	10.4666i	−0.277610	−	0.331147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.h.a.689.1	✓	24
3.2	odd	2		690.2.h.b.689.22	yes	24
5.4	even	2		690.2.h.b.689.23	yes	24
15.14	odd	2	inner	690.2.h.a.689.4	yes	24
23.22	odd	2	inner	690.2.h.a.689.2	yes	24
69.68	even	2		690.2.h.b.689.21	yes	24
115.114	odd	2		690.2.h.b.689.24	yes	24
345.344	even	2	inner	690.2.h.a.689.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.h.a.689.1	✓	24	1.1	even	1	trivial
690.2.h.a.689.2	yes	24	23.22	odd	2	inner
690.2.h.a.689.3	yes	24	345.344	even	2	inner
690.2.h.a.689.4	yes	24	15.14	odd	2	inner
690.2.h.b.689.21	yes	24	69.68	even	2
690.2.h.b.689.22	yes	24	3.2	odd	2
690.2.h.b.689.23	yes	24	5.4	even	2
690.2.h.b.689.24	yes	24	115.114	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.65921 - 0.497008i) q^{3} +1.00000 q^{4} +(-1.15459 + 1.91492i) q^{5} +(1.65921 + 0.497008i) q^{6} -3.15825 q^{7} -1.00000 q^{8} +(2.50597 + 1.64928i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.65921 - 0.497008i) q^{3} +1.00000 q^{4} +(-1.15459 + 1.91492i) q^{5} +(1.65921 + 0.497008i) q^{6} -3.15825 q^{7} -1.00000 q^{8} +(2.50597 + 1.64928i) q^{9} +(1.15459 - 1.91492i) q^{10} -2.63765 q^{11} +(-1.65921 - 0.497008i) q^{12} +3.37824i q^{13} +3.15825 q^{14} +(2.86744 - 2.60342i) q^{15} +1.00000 q^{16} +0.331367i q^{17} +(-2.50597 - 1.64928i) q^{18} -2.06750i q^{19} +(-1.15459 + 1.91492i) q^{20} +(5.24020 + 1.56967i) q^{21} +2.63765 q^{22} +(2.19771 - 4.26263i) q^{23} +(1.65921 + 0.497008i) q^{24} +(-2.33385 - 4.42189i) q^{25} -3.37824i q^{26} +(-3.33822 - 3.98199i) q^{27} -3.15825 q^{28} +6.73889i q^{29} +(-2.86744 + 2.60342i) q^{30} +2.38669 q^{31} -1.00000 q^{32} +(4.37642 + 1.31093i) q^{33} -0.331367i q^{34} +(3.64647 - 6.04780i) q^{35} +(2.50597 + 1.64928i) q^{36} +2.62847 q^{37} +2.06750i q^{38} +(1.67901 - 5.60521i) q^{39} +(1.15459 - 1.91492i) q^{40} -6.92322i q^{41} +(-5.24020 - 1.56967i) q^{42} -7.19407 q^{43} -2.63765 q^{44} +(-6.05161 + 2.89449i) q^{45} +(-2.19771 + 4.26263i) q^{46} +11.0631 q^{47} +(-1.65921 - 0.497008i) q^{48} +2.97452 q^{49} +(2.33385 + 4.42189i) q^{50} +(0.164692 - 0.549807i) q^{51} +3.37824i q^{52} -13.7812i q^{53} +(3.33822 + 3.98199i) q^{54} +(3.04540 - 5.05090i) q^{55} +3.15825 q^{56} +(-1.02756 + 3.43041i) q^{57} -6.73889i q^{58} -12.0898i q^{59} +(2.86744 - 2.60342i) q^{60} +0.685298i q^{61} -2.38669 q^{62} +(-7.91446 - 5.20884i) q^{63} +1.00000 q^{64} +(-6.46906 - 3.90047i) q^{65} +(-4.37642 - 1.31093i) q^{66} +0.468752 q^{67} +0.331367i q^{68} +(-5.76504 + 5.98033i) q^{69} +(-3.64647 + 6.04780i) q^{70} -5.57976i q^{71} +(-2.50597 - 1.64928i) q^{72} -7.91723i q^{73} -2.62847 q^{74} +(1.67464 + 8.49680i) q^{75} -2.06750i q^{76} +8.33036 q^{77} +(-1.67901 + 5.60521i) q^{78} +6.81084i q^{79} +(-1.15459 + 1.91492i) q^{80} +(3.55974 + 8.26609i) q^{81} +6.92322i q^{82} -4.16761i q^{83} +(5.24020 + 1.56967i) q^{84} +(-0.634541 - 0.382592i) q^{85} +7.19407 q^{86} +(3.34928 - 11.1813i) q^{87} +2.63765 q^{88} -7.02620 q^{89} +(6.05161 - 2.89449i) q^{90} -10.6693i q^{91} +(2.19771 - 4.26263i) q^{92} +(-3.96003 - 1.18620i) q^{93} -11.0631 q^{94} +(3.95909 + 2.38711i) q^{95} +(1.65921 + 0.497008i) q^{96} +18.2042 q^{97} -2.97452 q^{98} +(-6.60987 - 4.35023i) 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	\( 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9} + 2 q^{12} + 24 q^{16} - 6 q^{18} - 4 q^{23} - 2 q^{24} + 12 q^{25} + 2 q^{27} - 28 q^{31} - 24 q^{32} + 8 q^{35} + 6 q^{36} + 4 q^{46} + 16 q^{47} + 2 q^{48} - 4 q^{49} - 12 q^{50} - 2 q^{54} + 4 q^{55} + 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} - 6 q^{72} + 14 q^{75} + 8 q^{77} + 14 q^{81} - 44 q^{85} + 28 q^{87} - 4 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} - 2 q^{96} + 4 q^{98}+O(q^{100}) \) 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 + 14 * 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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