LMFDB - Embedded newform 690.2.h.b.689.4

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			689.4
Character	$\chi$	$=$	690.689
Dual form			690.2.h.b.689.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.68494 + 0.401202i) q^{3} +1.00000 q^{4} +(1.83064 + 1.28404i) q^{5} +(-1.68494 + 0.401202i) q^{6} +1.73603 q^{7} +1.00000 q^{8} +(2.67807 - 1.35201i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.68494 + 0.401202i) q^{3} +1.00000 q^{4} +(1.83064 + 1.28404i) q^{5} +(-1.68494 + 0.401202i) q^{6} +1.73603 q^{7} +1.00000 q^{8} +(2.67807 - 1.35201i) q^{9} +(1.83064 + 1.28404i) q^{10} -1.14414 q^{11} +(-1.68494 + 0.401202i) q^{12} +5.69546i q^{13} +1.73603 q^{14} +(-3.59969 - 1.42908i) q^{15} +1.00000 q^{16} -5.08878i q^{17} +(2.67807 - 1.35201i) q^{18} -4.40298i q^{19} +(1.83064 + 1.28404i) q^{20} +(-2.92511 + 0.696499i) q^{21} -1.14414 q^{22} +(-1.88614 + 4.40936i) q^{23} +(-1.68494 + 0.401202i) q^{24} +(1.70249 + 4.70123i) q^{25} +5.69546i q^{26} +(-3.96998 + 3.35251i) q^{27} +1.73603 q^{28} +4.89756i q^{29} +(-3.59969 - 1.42908i) q^{30} +8.30726 q^{31} +1.00000 q^{32} +(1.92781 - 0.459031i) q^{33} -5.08878i q^{34} +(3.17805 + 2.22913i) q^{35} +(2.67807 - 1.35201i) q^{36} +11.5412 q^{37} -4.40298i q^{38} +(-2.28503 - 9.59653i) q^{39} +(1.83064 + 1.28404i) q^{40} +5.25409i q^{41} +(-2.92511 + 0.696499i) q^{42} -3.19770 q^{43} -1.14414 q^{44} +(6.63862 + 0.963712i) q^{45} +(-1.88614 + 4.40936i) q^{46} -2.36731 q^{47} +(-1.68494 + 0.401202i) q^{48} -3.98620 q^{49} +(1.70249 + 4.70123i) q^{50} +(2.04163 + 8.57431i) q^{51} +5.69546i q^{52} -7.04209i q^{53} +(-3.96998 + 3.35251i) q^{54} +(-2.09451 - 1.46912i) q^{55} +1.73603 q^{56} +(1.76649 + 7.41878i) q^{57} +4.89756i q^{58} +1.33343i q^{59} +(-3.59969 - 1.42908i) q^{60} +7.49227i q^{61} +8.30726 q^{62} +(4.64921 - 2.34712i) q^{63} +1.00000 q^{64} +(-7.31319 + 10.4263i) q^{65} +(1.92781 - 0.459031i) q^{66} -15.5358 q^{67} -5.08878i q^{68} +(1.40900 - 8.18625i) q^{69} +(3.17805 + 2.22913i) q^{70} -13.2029i q^{71} +(2.67807 - 1.35201i) q^{72} -4.45169i q^{73} +11.5412 q^{74} +(-4.75474 - 7.23826i) q^{75} -4.40298i q^{76} -1.98626 q^{77} +(-2.28503 - 9.59653i) q^{78} -10.6999i q^{79} +(1.83064 + 1.28404i) q^{80} +(5.34415 - 7.24155i) q^{81} +5.25409i q^{82} -4.09978i q^{83} +(-2.92511 + 0.696499i) q^{84} +(6.53419 - 9.31573i) q^{85} -3.19770 q^{86} +(-1.96491 - 8.25211i) q^{87} -1.14414 q^{88} +2.58317 q^{89} +(6.63862 + 0.963712i) q^{90} +9.88749i q^{91} +(-1.88614 + 4.40936i) q^{92} +(-13.9973 + 3.33289i) q^{93} -2.36731 q^{94} +(5.65360 - 8.06028i) q^{95} +(-1.68494 + 0.401202i) q^{96} -4.22932 q^{97} -3.98620 q^{98} +(-3.06409 + 1.54688i) 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
$3$	−1.68494	+	0.401202i	−0.972803	+	0.231634i
$3$	−1.68494	+	0.401202i	−0.972803	+	0.231634i
$4$	1.00000			0.500000
$5$	1.83064	+	1.28404i	0.818687	+	0.574240i
$5$	1.83064	+	1.28404i	0.818687	+	0.574240i
$6$	−1.68494	+	0.401202i	−0.687876	+	0.163790i
$7$	1.73603			0.656157			0.328079	−	0.944650i	$-0.393599\pi$
$7$	1.73603			0.656157			0.328079	+	0.944650i	$0.393599\pi$
$8$	1.00000			0.353553
$9$	2.67807	−	1.35201i	0.892691	−	0.450669i
$10$	1.83064	+	1.28404i	0.578899	+	0.406049i
$11$	−1.14414			−0.344971			−0.172485	−	0.985012i	$-0.555180\pi$
$11$	−1.14414			−0.344971			−0.172485	+	0.985012i	$0.555180\pi$
$12$	−1.68494	+	0.401202i	−0.486401	+	0.115817i
$13$			5.69546i			1.57964i	0.613341	+	0.789818i	$0.289825\pi$
$13$			5.69546i			1.57964i	−0.613341	+	0.789818i	$0.710175\pi$
$14$	1.73603			0.463973
$15$	−3.59969	−	1.42908i	−0.929435	−	0.368986i
$16$	1.00000			0.250000
$17$		−	5.08878i		−	1.23421i	−0.786881	−	0.617105i	$-0.788305\pi$
$17$		−	5.08878i		−	1.23421i	0.786881	−	0.617105i	$-0.211695\pi$
$18$	2.67807	−	1.35201i	0.631228	−	0.318671i
$19$		−	4.40298i		−	1.01011i	−0.863086	−	0.505057i	$-0.831472\pi$
$19$		−	4.40298i		−	1.01011i	0.863086	−	0.505057i	$-0.168528\pi$
$20$	1.83064	+	1.28404i	0.409344	+	0.287120i
$21$	−2.92511	+	0.696499i	−0.638312	+	0.151989i
$22$	−1.14414			−0.243931
$23$	−1.88614	+	4.40936i	−0.393288	+	0.919415i
$23$	−1.88614	+	4.40936i	−0.393288	+	0.919415i
$24$	−1.68494	+	0.401202i	−0.343938	+	0.0818951i
$25$	1.70249	+	4.70123i	0.340498	+	0.940245i
$26$			5.69546i			1.11697i
$27$	−3.96998	+	3.35251i	−0.764022	+	0.645190i
$28$	1.73603			0.328079
$29$			4.89756i			0.909453i	0.890631	+	0.454727i	$0.150263\pi$
$29$			4.89756i			0.909453i	−0.890631	+	0.454727i	$0.849737\pi$
$30$	−3.59969	−	1.42908i	−0.657210	−	0.260912i
$31$	8.30726			1.49203			0.746014	−	0.665930i	$-0.231965\pi$
$31$	8.30726			1.49203			0.746014	+	0.665930i	$0.231965\pi$
$32$	1.00000			0.176777
$33$	1.92781	−	0.459031i	0.335589	−	0.0799071i
$34$		−	5.08878i		−	0.872719i
$35$	3.17805	+	2.22913i	0.537188	+	0.376792i
$36$	2.67807	−	1.35201i	0.446346	−	0.225334i
$37$	11.5412			1.89736			0.948681	−	0.316233i	$-0.102418\pi$
$37$	11.5412			1.89736			0.948681	+	0.316233i	$0.102418\pi$
$38$		−	4.40298i		−	0.714258i
$39$	−2.28503	−	9.59653i	−0.365898	−	1.53668i
$40$	1.83064	+	1.28404i	0.289450	+	0.203024i
$41$			5.25409i			0.820551i	0.911962	+	0.410276i	$0.134568\pi$
$41$			5.25409i			0.820551i	−0.911962	+	0.410276i	$0.865432\pi$
$42$	−2.92511	+	0.696499i	−0.451355	+	0.107472i
$43$	−3.19770			−0.487644			−0.243822	−	0.969820i	$-0.578401\pi$
$43$	−3.19770			−0.487644			−0.243822	+	0.969820i	$0.578401\pi$
$44$	−1.14414			−0.172485
$45$	6.63862	+	0.963712i	0.989627	+	0.143662i
$46$	−1.88614	+	4.40936i	−0.278097	+	0.650125i
$47$	−2.36731			−0.345307			−0.172654	−	0.984983i	$-0.555234\pi$
$47$	−2.36731			−0.345307			−0.172654	+	0.984983i	$0.555234\pi$
$48$	−1.68494	+	0.401202i	−0.243201	+	0.0579086i
$49$	−3.98620			−0.569457
$50$	1.70249	+	4.70123i	0.240768	+	0.664854i
$51$	2.04163	+	8.57431i	0.285885	+	1.20064i
$52$			5.69546i			0.789818i
$53$		−	7.04209i		−	0.967305i	−0.875260	−	0.483653i	$-0.839310\pi$
$53$		−	7.04209i		−	0.967305i	0.875260	−	0.483653i	$-0.160690\pi$
$54$	−3.96998	+	3.35251i	−0.540245	+	0.456218i
$55$	−2.09451	−	1.46912i	−0.282423	−	0.198096i
$56$	1.73603			0.231987
$57$	1.76649	+	7.41878i	0.233977	+	0.982642i
$58$			4.89756i			0.643081i
$59$			1.33343i			0.173598i	0.996226	+	0.0867988i	$0.0276637\pi$
$59$			1.33343i			0.173598i	−0.996226	+	0.0867988i	$0.972336\pi$
$60$	−3.59969	−	1.42908i	−0.464717	−	0.184493i
$61$			7.49227i			0.959287i	0.877463	+	0.479644i	$0.159234\pi$
$61$			7.49227i			0.959287i	−0.877463	+	0.479644i	$0.840766\pi$
$62$	8.30726			1.05502
$63$	4.64921	−	2.34712i	0.585746	−	0.295710i
$64$	1.00000			0.125000
$65$	−7.31319	+	10.4263i	−0.907090	+	1.29323i
$66$	1.92781	−	0.459031i	0.237297	−	0.0565028i
$67$	−15.5358			−1.89800			−0.949000	−	0.315275i	$-0.897903\pi$
$67$	−15.5358			−1.89800			−0.949000	+	0.315275i	$0.897903\pi$
$68$		−	5.08878i		−	0.617105i
$69$	1.40900	−	8.18625i	0.169624	−	0.985509i
$70$	3.17805	+	2.22913i	0.379849	+	0.266432i
$71$		−	13.2029i		−	1.56689i	−0.621459	−	0.783447i	$-0.713460\pi$
$71$		−	13.2029i		−	1.56689i	0.621459	−	0.783447i	$-0.286540\pi$
$72$	2.67807	−	1.35201i	0.315614	−	0.159336i
$73$		−	4.45169i		−	0.521031i	−0.965470	−	0.260515i	$-0.916108\pi$
$73$		−	4.45169i		−	0.521031i	0.965470	−	0.260515i	$-0.0838924\pi$
$74$	11.5412			1.34164
$75$	−4.75474	−	7.23826i	−0.549030	−	0.835803i
$76$		−	4.40298i		−	0.505057i
$77$	−1.98626			−0.226355
$78$	−2.28503	−	9.59653i	−0.258729	−	1.08659i
$79$		−	10.6999i		−	1.20383i	−0.798560	−	0.601915i	$-0.794405\pi$
$79$		−	10.6999i		−	1.20383i	0.798560	−	0.601915i	$-0.205595\pi$
$80$	1.83064	+	1.28404i	0.204672	+	0.143560i
$81$	5.34415	−	7.24155i	0.593795	−	0.804616i
$82$			5.25409i			0.580217i
$83$		−	4.09978i		−	0.450009i	−0.974358	−	0.225005i	$-0.927760\pi$
$83$		−	4.09978i		−	0.450009i	0.974358	−	0.225005i	$-0.0722397\pi$
$84$	−2.92511	+	0.696499i	−0.319156	+	0.0759943i
$85$	6.53419	−	9.31573i	0.708733	−	1.01043i
$86$	−3.19770			−0.344817
$87$	−1.96491	−	8.25211i	−0.210661	−	0.884719i
$88$	−1.14414			−0.121966
$89$	2.58317			0.273816			0.136908	−	0.990584i	$-0.456284\pi$
$89$	2.58317			0.273816			0.136908	+	0.990584i	$0.456284\pi$
$90$	6.63862	+	0.963712i	0.699772	+	0.101584i
$91$			9.88749i			1.03649i
$92$	−1.88614	+	4.40936i	−0.196644	+	0.459708i
$93$	−13.9973	+	3.33289i	−1.45145	+	0.345605i
$94$	−2.36731			−0.244169
$95$	5.65360	−	8.06028i	0.580047	−	0.826967i
$96$	−1.68494	+	0.401202i	−0.171969	+	0.0409475i
$97$	−4.22932			−0.429422			−0.214711	−	0.976678i	$-0.568881\pi$
$97$	−4.22932			−0.429422			−0.214711	+	0.976678i	$0.568881\pi$
$98$	−3.98620			−0.402667
$99$	−3.06409	+	1.54688i	−0.307952	+	0.155468i
$100$	1.70249	+	4.70123i	0.170249	+	0.470123i
$101$			4.51147i			0.448908i	0.974485	+	0.224454i	$0.0720598\pi$
$101$			4.51147i			0.448908i	−0.974485	+	0.224454i	$0.927940\pi$
$102$	2.04163	+	8.57431i	0.202152	+	0.848983i
$103$	7.94596			0.782939			0.391469	−	0.920191i	$-0.371967\pi$
$103$	7.94596			0.782939			0.391469	+	0.920191i	$0.371967\pi$
$104$			5.69546i			0.558486i
$105$	−6.24916	−	2.48092i	−0.609856	−	0.242113i
$106$		−	7.04209i		−	0.683988i
$107$			1.31378i			0.127008i	0.997982	+	0.0635041i	$0.0202276\pi$
$107$			1.31378i			0.127008i	−0.997982	+	0.0635041i	$0.979772\pi$
$108$	−3.96998	+	3.35251i	−0.382011	+	0.322595i
$109$		−	8.13301i		−	0.779001i	−0.921026	−	0.389501i	$-0.872648\pi$
$109$		−	8.13301i		−	0.779001i	0.921026	−	0.389501i	$-0.127352\pi$
$110$	−2.09451	−	1.46912i	−0.199703	−	0.140075i
$111$	−19.4463	+	4.63036i	−1.84576	+	0.439494i
$112$	1.73603			0.164039
$113$		−	16.3907i		−	1.54190i	−0.636893	−	0.770952i	$-0.719781\pi$
$113$		−	16.3907i		−	1.54190i	0.636893	−	0.770952i	$-0.280219\pi$
$114$	1.76649	+	7.41878i	0.165447	+	0.694833i
$115$	−9.11464	+	5.65007i	−0.849945	+	0.526872i
$116$			4.89756i			0.454727i
$117$	7.70030	+	15.2529i	0.711893	+	1.41013i
$118$			1.33343i			0.122752i
$119$		−	8.83427i		−	0.809836i
$120$	−3.59969	−	1.42908i	−0.328605	−	0.130456i
$121$	−9.69095			−0.880995
$122$			7.49227i			0.678318i
$123$	−2.10795	−	8.85285i	−0.190068	−	0.798235i
$124$	8.30726			0.746014
$125$	−2.91991	+	10.7923i	−0.261165	+	0.965294i
$126$	4.64921	−	2.34712i	0.414185	−	0.209098i
$127$		−	22.3450i		−	1.98280i	−0.130882	−	0.991398i	$-0.541781\pi$
$127$		−	22.3450i		−	1.98280i	0.130882	−	0.991398i	$-0.458219\pi$
$128$	1.00000			0.0883883
$129$	5.38794	−	1.28292i	0.474382	−	0.112955i
$130$	−7.31319	+	10.4263i	−0.641409	+	0.914451i
$131$			7.79764i			0.681283i	0.940193	+	0.340642i	$0.110644\pi$
$131$			7.79764i			0.681283i	−0.940193	+	0.340642i	$0.889356\pi$
$132$	1.92781	−	0.459031i	0.167794	−	0.0399535i
$133$		−	7.64371i		−	0.662794i
$134$	−15.5358			−1.34209
$135$	−11.5723	+	1.03963i	−0.995989	+	0.0894770i
$136$		−	5.08878i		−	0.436359i
$137$		−	0.151371i		−	0.0129325i	−0.999979	−	0.00646626i	$-0.997942\pi$
$137$		−	0.151371i		−	0.0129325i	0.999979	−	0.00646626i	$-0.00205829\pi$
$138$	1.40900	−	8.18625i	0.119942	−	0.696860i
$139$	−12.5121			−1.06126			−0.530630	−	0.847604i	$-0.678044\pi$
$139$	−12.5121			−1.06126			−0.530630	+	0.847604i	$0.678044\pi$
$140$	3.17805	+	2.22913i	0.268594	+	0.188396i
$141$	3.98878	−	0.949770i	0.335916	−	0.0799850i
$142$		−	13.2029i		−	1.10796i
$143$		−	6.51640i		−	0.544929i
$144$	2.67807	−	1.35201i	0.223173	−	0.112667i
$145$	−6.28865	+	8.96567i	−0.522244	+	0.744558i
$146$		−	4.45169i		−	0.368424i
$147$	6.71653	−	1.59927i	0.553970	−	0.131906i
$148$	11.5412			0.948681
$149$	10.3539			0.848225			0.424112	−	0.905610i	$-0.360586\pi$
$149$	10.3539			0.848225			0.424112	+	0.905610i	$0.360586\pi$
$150$	−4.75474	−	7.23826i	−0.388223	−	0.591002i
$151$	−0.997420			−0.0811689			−0.0405844	−	0.999176i	$-0.512922\pi$
$151$	−0.997420			−0.0811689			−0.0405844	+	0.999176i	$0.512922\pi$
$152$		−	4.40298i		−	0.357129i
$153$	−6.88007	−	13.6281i	−0.556220	−	1.10177i
$154$	−1.98626			−0.160057
$155$	15.2076	+	10.6668i	1.22150	+	0.856782i
$156$	−2.28503	−	9.59653i	−0.182949	−	0.768338i
$157$	−16.8463			−1.34448			−0.672239	−	0.740334i	$-0.734667\pi$
$157$	−16.8463			−1.34448			−0.672239	+	0.740334i	$0.734667\pi$
$158$		−	10.6999i		−	0.851236i
$159$	2.82530	+	11.8655i	0.224061	+	0.940997i
$160$	1.83064	+	1.28404i	0.144725	+	0.101512i
$161$	−3.27440	+	7.65478i	−0.258059	+	0.603281i
$162$	5.34415	−	7.24155i	0.419876	−	0.568950i
$163$		−	18.0136i		−	1.41093i	−0.708744	−	0.705466i	$-0.750738\pi$
$163$		−	18.0136i		−	1.41093i	0.708744	−	0.705466i	$-0.249262\pi$
$164$			5.25409i			0.410276i
$165$	4.11854	+	1.63506i	0.320628	+	0.127289i
$166$		−	4.09978i		−	0.318205i
$167$	−5.37749			−0.416123			−0.208062	−	0.978116i	$-0.566715\pi$
$167$	−5.37749			−0.416123			−0.208062	+	0.978116i	$0.566715\pi$
$168$	−2.92511	+	0.696499i	−0.225677	+	0.0537361i
$169$	−19.4383			−1.49525
$170$	6.53419	−	9.31573i	0.501150	−	0.714484i
$171$	−5.95286	−	11.7915i	−0.455227	−	0.901720i
$172$	−3.19770			−0.243822
$173$	4.94205			0.375737			0.187869	−	0.982194i	$-0.439842\pi$
$173$	4.94205			0.375737			0.187869	+	0.982194i	$0.439842\pi$
$174$	−1.96491	−	8.25211i	−0.148960	−	0.625591i
$175$	2.95557	+	8.16147i	0.223420	+	0.616949i
$176$	−1.14414			−0.0862427
$177$	−0.534975	−	2.24675i	−0.0402111	−	0.168876i
$178$	2.58317			0.193617
$179$			6.84787i			0.511834i	0.966699	+	0.255917i	$0.0823774\pi$
$179$			6.84787i			0.511834i	−0.966699	+	0.255917i	$0.917623\pi$
$180$	6.63862	+	0.963712i	0.494813	+	0.0718308i
$181$			16.4617i			1.22359i	0.791017	+	0.611794i	$0.209552\pi$
$181$			16.4617i			1.22359i	−0.791017	+	0.611794i	$0.790448\pi$
$182$			9.88749i			0.732909i
$183$	−3.00592	−	12.6241i	−0.222204	−	0.933197i
$184$	−1.88614	+	4.40936i	−0.139048	+	0.325062i
$185$	21.1278	+	14.8194i	1.55335	+	1.08954i
$186$	−13.9973	+	3.33289i	−1.02633	+	0.244379i
$187$			5.82227i			0.425767i
$188$	−2.36731			−0.172654
$189$	−6.89199	+	5.82005i	−0.501319	+	0.423346i
$190$	5.65360	−	8.06028i	0.410155	−	0.584754i
$191$	−7.61075			−0.550694			−0.275347	−	0.961345i	$-0.588793\pi$
$191$	−7.61075			−0.550694			−0.275347	+	0.961345i	$0.588793\pi$
$192$	−1.68494	+	0.401202i	−0.121600	+	0.0289543i
$193$		−	15.7578i		−	1.13427i	−0.823624	−	0.567136i	$-0.808051\pi$
$193$		−	15.7578i		−	1.13427i	0.823624	−	0.567136i	$-0.191949\pi$
$194$	−4.22932			−0.303647
$195$	8.13925	−	20.5019i	0.582864	−	1.46817i
$196$	−3.98620			−0.284729
$197$	16.6660			1.18740			0.593701	−	0.804686i	$-0.297666\pi$
$197$	16.6660			1.18740			0.593701	+	0.804686i	$0.297666\pi$
$198$	−3.06409	+	1.54688i	−0.217755	+	0.109932i
$199$			12.0587i			0.854819i	0.904058	+	0.427410i	$0.140574\pi$
$199$			12.0587i			0.854819i	−0.904058	+	0.427410i	$0.859426\pi$
$200$	1.70249	+	4.70123i	0.120384	+	0.332427i
$201$	26.1770	−	6.23300i	1.84638	−	0.439642i
$202$			4.51147i			0.317426i
$203$			8.50230i			0.596745i
$204$	2.04163	+	8.57431i	0.142943	+	0.600322i
$205$	−6.74646	+	9.61835i	−0.471193	+	0.671775i
$206$	7.94596			0.553621
$207$	0.910257	+	14.3587i	0.0632673	+	0.997997i
$208$			5.69546i			0.394909i
$209$			5.03763i			0.348460i
$210$	−6.24916	−	2.48092i	−0.431233	−	0.171200i
$211$	−11.5238			−0.793332			−0.396666	−	0.917963i	$-0.629833\pi$
$211$	−11.5238			−0.793332			−0.396666	+	0.917963i	$0.629833\pi$
$212$		−	7.04209i		−	0.483653i
$213$	5.29702	+	22.2461i	0.362946	+	1.52428i
$214$			1.31378i			0.0898084i
$215$	−5.85383	−	4.10597i	−0.399228	−	0.280025i
$216$	−3.96998	+	3.35251i	−0.270123	+	0.228109i
$217$	14.4216			0.979005
$218$		−	8.13301i		−	0.550837i
$219$	1.78603	+	7.50084i	0.120689	+	0.506860i
$220$	−2.09451	−	1.46912i	−0.141212	−	0.0990480i
$221$	28.9830			1.94960
$222$	−19.4463	+	4.63036i	−1.30515	+	0.310769i
$223$			15.1762i			1.01627i	0.861277	+	0.508136i	$0.169665\pi$
$223$			15.1762i			1.01627i	−0.861277	+	0.508136i	$0.830335\pi$
$224$	1.73603			0.115993
$225$	10.9155	+	10.2885i	0.727699	+	0.685897i
$226$		−	16.3907i		−	1.09029i
$227$		−	25.7362i		−	1.70817i	−0.520132	−	0.854086i	$-0.674117\pi$
$227$		−	25.7362i		−	1.70817i	0.520132	−	0.854086i	$-0.325883\pi$
$228$	1.76649	+	7.41878i	0.116988	+	0.491321i
$229$		−	24.8194i		−	1.64011i	−0.572285	−	0.820055i	$-0.693943\pi$
$229$		−	24.8194i		−	1.64011i	0.572285	−	0.820055i	$-0.306057\pi$
$230$	−9.11464	+	5.65007i	−0.601002	+	0.372555i
$231$	3.34673	−	0.796891i	0.220199	−	0.0524316i
$232$			4.89756i			0.321540i
$233$	−3.98878			−0.261314			−0.130657	−	0.991428i	$-0.541709\pi$
$233$	−3.98878			−0.261314			−0.130657	+	0.991428i	$0.541709\pi$
$234$	7.70030	+	15.2529i	0.503384	+	0.997111i
$235$	−4.33369	−	3.03972i	−0.282699	−	0.198289i
$236$			1.33343i			0.0867988i
$237$	4.29281	+	18.0287i	0.278848	+	1.17109i
$238$		−	8.83427i		−	0.572641i
$239$			1.46024i			0.0944551i	0.998884	+	0.0472275i	$0.0150386\pi$
$239$			1.46024i			0.0944551i	−0.998884	+	0.0472275i	$0.984961\pi$
$240$	−3.59969	−	1.42908i	−0.232359	−	0.0922465i
$241$		−	4.88957i		−	0.314965i	−0.987522	−	0.157483i	$-0.949662\pi$
$241$		−	4.88957i		−	0.314965i	0.987522	−	0.157483i	$-0.0503378\pi$
$242$	−9.69095			−0.622958
$243$	−6.09928	+	14.3457i	−0.391269	+	0.920276i
$244$			7.49227i			0.479644i
$245$	−7.29730	−	5.11844i	−0.466208	−	0.327005i
$246$	−2.10795	−	8.85285i	−0.134398	−	0.564437i
$247$	25.0770			1.59561
$248$	8.30726			0.527512
$249$	1.64484	+	6.90790i	0.104238	+	0.437770i
$250$	−2.91991	+	10.7923i	−0.184672	+	0.682566i
$251$	16.3660			1.03301			0.516507	−	0.856283i	$-0.327232\pi$
$251$	16.3660			1.03301			0.516507	+	0.856283i	$0.327232\pi$
$252$	4.64921	−	2.34712i	0.292873	−	0.147855i
$253$	2.15801	−	5.04492i	0.135673	−	0.317172i
$254$		−	22.3450i		−	1.40205i
$255$	−7.27226	+	18.3180i	−0.455406	+	1.14712i
$256$	1.00000			0.0625000
$257$	12.9124			0.805454			0.402727	−	0.915320i	$-0.368062\pi$
$257$	12.9124			0.805454			0.402727	+	0.915320i	$0.368062\pi$
$258$	5.38794	−	1.28292i	0.335439	−	0.0798713i
$259$	20.0359			1.24497
$260$	−7.31319	+	10.4263i	−0.453545	+	0.646614i
$261$	6.62153	+	13.1160i	0.409862	+	0.811861i
$262$			7.79764i			0.481740i
$263$			18.6670i			1.15106i	0.817781	+	0.575529i	$0.195204\pi$
$263$			18.6670i			1.15106i	−0.817781	+	0.575529i	$0.804796\pi$
$264$	1.92781	−	0.459031i	0.118649	−	0.0282514i
$265$	9.04231	−	12.8915i	0.555465	−	0.791920i
$266$		−	7.64371i		−	0.468666i
$267$	−4.35251	+	1.03638i	−0.266369	+	0.0634252i
$268$	−15.5358			−0.949000
$269$			13.9987i			0.853516i	0.904366	+	0.426758i	$0.140344\pi$
$269$			13.9987i			0.853516i	−0.904366	+	0.426758i	$0.859656\pi$
$270$	−11.5723	+	1.03963i	−0.704270	+	0.0632698i
$271$	4.95580			0.301043			0.150522	−	0.988607i	$-0.451905\pi$
$271$	4.95580			0.301043			0.150522	+	0.988607i	$0.451905\pi$
$272$		−	5.08878i		−	0.308553i
$273$	−3.96688	−	16.6599i	−0.240087	−	1.00830i
$274$		−	0.151371i		−	0.00914467i
$275$	−1.94788	−	5.37886i	−0.117462	−	0.324357i
$276$	1.40900	−	8.18625i	0.0848118	−	0.492754i
$277$			9.05451i			0.544033i	0.962293	+	0.272017i	$0.0876905\pi$
$277$			9.05451i			0.544033i	−0.962293	+	0.272017i	$0.912309\pi$
$278$	−12.5121			−0.750424
$279$	22.2475	−	11.2315i	1.33192	−	0.672411i
$280$	3.17805	+	2.22913i	0.189925	+	0.133216i
$281$	−27.7262			−1.65401			−0.827004	−	0.562196i	$-0.809957\pi$
$281$	−27.7262			−1.65401			−0.827004	+	0.562196i	$0.809957\pi$
$282$	3.98878	−	0.949770i	0.237529	−	0.0565580i
$283$	−1.11965			−0.0665560			−0.0332780	−	0.999446i	$-0.510595\pi$
$283$	−1.11965			−0.0665560			−0.0332780	+	0.999446i	$0.510595\pi$
$284$		−	13.2029i		−	0.783447i
$285$	−6.29220	+	15.8494i	−0.372718	+	0.938835i
$286$		−	6.51640i		−	0.385323i
$287$			9.12126i			0.538411i
$288$	2.67807	−	1.35201i	0.157807	−	0.0796678i
$289$	−8.89569			−0.523276
$290$	−6.28865	+	8.96567i	−0.369282	+	0.526482i
$291$	7.12616	−	1.69681i	0.417743	−	0.0994688i
$292$		−	4.45169i		−	0.260515i
$293$		−	4.32973i		−	0.252945i	−0.991970	−	0.126473i	$-0.959634\pi$
$293$		−	4.32973i		−	0.252945i	0.991970	−	0.126473i	$-0.0403656\pi$
$294$	6.71653	−	1.59927i	0.391716	−	0.0932715i
$295$	−1.71217	+	2.44103i	−0.0996866	+	0.142122i
$296$	11.5412			0.670819
$297$	4.54220	−	3.83573i	0.263565	−	0.222572i
$298$	10.3539			0.599785
$299$	−25.1133	−	10.7425i	−1.45234	−	0.621252i
$300$	−4.75474	−	7.23826i	−0.274515	−	0.417901i
$301$	−5.55130			−0.319971
$302$	−0.997420			−0.0573951
$303$	−1.81001	−	7.60157i	−0.103982	−	0.436699i
$304$		−	4.40298i		−	0.252528i
$305$	−9.62037	+	13.7157i	−0.550861	+	0.785356i
$306$	−6.88007	−	13.6281i	−0.393307	−	0.779068i
$307$			11.0810i			0.632428i	0.948688	+	0.316214i	$0.102412\pi$
$307$			11.0810i			0.632428i	−0.948688	+	0.316214i	$0.897588\pi$
$308$	−1.98626			−0.113178
$309$	−13.3885	+	3.18794i	−0.761645	+	0.181355i
$310$	15.2076	+	10.6668i	0.863734	+	0.605836i
$311$		−	1.00298i		−	0.0568737i	−0.999596	−	0.0284369i	$-0.990947\pi$
$311$		−	1.00298i		−	0.0568737i	0.999596	−	0.0284369i	$-0.00905295\pi$
$312$	−2.28503	−	9.59653i	−0.129364	−	0.543297i
$313$	19.4627			1.10010			0.550050	−	0.835132i	$-0.314609\pi$
$313$	19.4627			1.10010			0.550050	+	0.835132i	$0.314609\pi$
$314$	−16.8463			−0.950690
$315$	11.5248	+	1.67303i	0.649351	+	0.0942647i
$316$		−	10.6999i		−	0.601915i
$317$	−17.4897			−0.982318			−0.491159	−	0.871070i	$-0.663427\pi$
$317$	−17.4897			−0.982318			−0.491159	+	0.871070i	$0.663427\pi$
$318$	2.82530	+	11.8655i	0.158435	+	0.665386i
$319$		−	5.60349i		−	0.313735i
$320$	1.83064	+	1.28404i	0.102336	+	0.0717800i
$321$	−0.527093	−	2.21365i	−0.0294195	−	0.123554i
$322$	−3.27440	+	7.65478i	−0.182475	+	0.426584i
$323$	−22.4058			−1.24669
$324$	5.34415	−	7.24155i	0.296897	−	0.402308i
$325$	−26.7757	+	9.69646i	−1.48525	+	0.537863i
$326$		−	18.0136i		−	0.997680i
$327$	3.26298	+	13.7037i	0.180443	+	0.757815i
$328$			5.25409i			0.290109i
$329$	−4.10972			−0.226576
$330$	4.11854	+	1.63506i	0.226718	+	0.0900072i
$331$	17.4962			0.961679			0.480840	−	0.876809i	$-0.340332\pi$
$331$	17.4962			0.961679			0.480840	+	0.876809i	$0.340332\pi$
$332$		−	4.09978i		−	0.225005i
$333$	30.9082	−	15.6038i	1.69376	−	0.855083i
$334$	−5.37749			−0.294243
$335$	−28.4405	−	19.9486i	−1.55387	−	1.08991i
$336$	−2.92511	+	0.696499i	−0.159578	+	0.0379971i
$337$	−33.5694			−1.82864			−0.914320	−	0.404992i	$-0.867274\pi$
$337$	−33.5694			−1.82864			−0.914320	+	0.404992i	$0.867274\pi$
$338$	−19.4383			−1.05730
$339$	6.57597	+	27.6174i	0.357158	+	1.49997i
$340$	6.53419	−	9.31573i	0.354366	−	0.505216i
$341$	−9.50466			−0.514706
$342$	−5.95286	−	11.7915i	−0.321894	−	0.637612i
$343$	−19.0724			−1.02981
$344$	−3.19770			−0.172408
$345$	13.0908	−	13.1769i	0.704787	−	0.709419i
$346$	4.94205			0.265687
$347$	8.79124			0.471939			0.235969	−	0.971761i	$-0.424174\pi$
$347$	8.79124			0.471939			0.235969	+	0.971761i	$0.424174\pi$
$348$	−1.96491	−	8.25211i	−0.105330	−	0.442359i
$349$	28.9759			1.55104			0.775522	−	0.631321i	$-0.217487\pi$
$349$	28.9759			1.55104			0.775522	+	0.631321i	$0.217487\pi$
$350$	2.95557	+	8.16147i	0.157982	+	0.436249i
$351$	−19.0941	−	22.6108i	−1.01917	−	1.20688i
$352$	−1.14414			−0.0609828
$353$	21.7061			1.15530			0.577650	−	0.816285i	$-0.303970\pi$
$353$	21.7061			1.15530			0.577650	+	0.816285i	$0.303970\pi$
$354$	−0.534975	−	2.24675i	−0.0284336	−	0.119414i
$355$	16.9530	−	24.1697i	0.899772	−	1.28280i
$356$	2.58317			0.136908
$357$	3.54433	+	14.8853i	0.187586	+	0.787811i
$358$			6.84787i			0.361921i
$359$	21.4318			1.13113			0.565563	−	0.824705i	$-0.308659\pi$
$359$	21.4318			1.13113			0.565563	+	0.824705i	$0.308659\pi$
$360$	6.63862	+	0.963712i	0.349886	+	0.0507921i
$361$	−0.386266			−0.0203298
$362$			16.4617i			0.865207i
$363$	16.3287	−	3.88803i	0.857035	−	0.204069i
$364$			9.88749i			0.518245i
$365$	5.71614	−	8.14944i	0.299196	−	0.426561i
$366$	−3.00592	−	12.6241i	−0.157122	−	0.659870i
$367$	8.57945			0.447844			0.223922	−	0.974607i	$-0.428114\pi$
$367$	8.57945			0.447844			0.223922	+	0.974607i	$0.428114\pi$
$368$	−1.88614	+	4.40936i	−0.0983220	+	0.229854i
$369$	7.10357	+	14.0708i	0.369797	+	0.732499i
$370$	21.1278	+	14.8194i	1.09838	+	0.770422i
$371$		−	12.2253i		−	0.634704i
$372$	−13.9973	+	3.33289i	−0.725725	+	0.172802i
$373$	−26.7453			−1.38482			−0.692409	−	0.721505i	$-0.743451\pi$
$373$	−26.7453			−1.38482			−0.692409	+	0.721505i	$0.743451\pi$
$374$			5.82227i			0.301063i
$375$	0.589988	−	19.3559i	0.0304668	−	0.999536i
$376$	−2.36731			−0.122085
$377$	−27.8938			−1.43661
$378$	−6.89199	+	5.82005i	−0.354486	+	0.299351i
$379$		−	4.35515i		−	0.223709i	−0.993725	−	0.111854i	$-0.964321\pi$
$379$		−	4.35515i		−	0.223709i	0.993725	−	0.111854i	$-0.0356790\pi$
$380$	5.65360	−	8.06028i	0.290024	−	0.413484i
$381$	8.96485	+	37.6500i	0.459283	+	1.92887i
$382$	−7.61075			−0.389400
$383$			15.1717i			0.775236i	0.921820	+	0.387618i	$0.126702\pi$
$383$			15.1717i			0.775236i	−0.921820	+	0.387618i	$0.873298\pi$
$384$	−1.68494	+	0.401202i	−0.0859844	+	0.0204738i
$385$	−3.63613	−	2.55043i	−0.185314	−	0.129982i
$386$		−	15.7578i		−	0.802052i
$387$	−8.56367	+	4.32331i	−0.435316	+	0.219766i
$388$	−4.22932			−0.214711
$389$	32.7383			1.65990			0.829948	−	0.557840i	$-0.188370\pi$
$389$	32.7383			1.65990			0.829948	+	0.557840i	$0.188370\pi$
$390$	8.13925	−	20.5019i	0.412147	−	1.03815i
$391$	22.4383	+	9.59817i	1.13475	+	0.485400i
$392$	−3.98620			−0.201334
$393$	−3.12843	−	13.1386i	−0.157809	−	0.662754i
$394$	16.6660			0.839620
$395$	13.7391	−	19.5876i	0.691287	−	0.985560i
$396$	−3.06409	+	1.54688i	−0.153976	+	0.0777338i
$397$		−	18.2547i		−	0.916179i	−0.888906	−	0.458089i	$-0.848534\pi$
$397$		−	18.2547i		−	0.916179i	0.888906	−	0.458089i	$-0.151466\pi$
$398$			12.0587i			0.604449i
$399$	3.06667	+	12.8792i	0.153526	+	0.644768i
$400$	1.70249	+	4.70123i	0.0851244	+	0.235061i
$401$	−11.5261			−0.575584			−0.287792	−	0.957693i	$-0.592921\pi$
$401$	−11.5261			−0.575584			−0.287792	+	0.957693i	$0.592921\pi$
$402$	26.1770	−	6.23300i	1.30559	−	0.310874i
$403$			47.3137i			2.35686i
$404$			4.51147i			0.224454i
$405$	19.0817	−	6.39457i	0.948175	−	0.317749i
$406$			8.50230i			0.421962i
$407$	−13.2047			−0.654535
$408$	2.04163	+	8.57431i	0.101076	+	0.424492i
$409$	−24.4078			−1.20689			−0.603443	−	0.797406i	$-0.706205\pi$
$409$	−24.4078			−1.20689			−0.603443	+	0.797406i	$0.706205\pi$
$410$	−6.74646	+	9.61835i	−0.333184	+	0.475017i
$411$	0.0607305	+	0.255052i	0.00299561	+	0.0125808i
$412$	7.94596			0.391469
$413$			2.31487i			0.113907i
$414$	0.910257	+	14.3587i	0.0447367	+	0.705690i
$415$	5.26428	−	7.50522i	0.258413	−	0.368417i
$416$			5.69546i			0.279243i
$417$	21.0821	−	5.01987i	1.03240	−	0.245824i
$418$			5.03763i			0.246398i
$419$	−21.3693			−1.04396			−0.521978	−	0.852959i	$-0.674806\pi$
$419$	−21.3693			−1.04396			−0.521978	+	0.852959i	$0.674806\pi$
$420$	−6.24916	−	2.48092i	−0.304928	−	0.121056i
$421$		−	6.04733i		−	0.294729i	−0.989082	−	0.147364i	$-0.952921\pi$
$421$		−	6.04733i		−	0.294729i	0.989082	−	0.147364i	$-0.0470790\pi$
$422$	−11.5238			−0.560970
$423$	−6.33983	+	3.20062i	−0.308253	+	0.155619i
$424$		−	7.04209i		−	0.341994i
$425$	23.9235	−	8.66359i	1.16046	−	0.420246i
$426$	5.29702	+	22.2461i	0.256642	+	1.07783i
$427$			13.0068i			0.629443i
$428$			1.31378i			0.0635041i
$429$	2.61439	+	10.9798i	0.126224	+	0.530108i
$430$	−5.85383	−	4.10597i	−0.282297	−	0.198007i
$431$	−22.4661			−1.08215			−0.541077	−	0.840973i	$-0.681983\pi$
$431$	−22.4661			−1.08215			−0.541077	+	0.840973i	$0.681983\pi$
$432$	−3.96998	+	3.35251i	−0.191006	+	0.161297i
$433$	−0.979211			−0.0470579			−0.0235289	−	0.999723i	$-0.507490\pi$
$433$	−0.979211			−0.0470579			−0.0235289	+	0.999723i	$0.507490\pi$
$434$	14.4216			0.692261
$435$	6.99898	−	17.6297i	0.335576	−	0.845278i
$436$		−	8.13301i		−	0.389501i
$437$	19.4143	+	8.30466i	0.928714	+	0.397266i
$438$	1.78603	+	7.50084i	0.0853397	+	0.358404i
$439$	5.31334			0.253592			0.126796	−	0.991929i	$-0.459531\pi$
$439$	5.31334			0.253592			0.126796	+	0.991929i	$0.459531\pi$
$440$	−2.09451	−	1.46912i	−0.0998517	−	0.0700375i
$441$	−10.6753	+	5.38937i	−0.508350	+	0.256637i
$442$	28.9830			1.37858
$443$	25.1317			1.19404			0.597021	−	0.802226i	$-0.296351\pi$
$443$	25.1317			1.19404			0.597021	+	0.802226i	$0.296351\pi$
$444$	−19.4463	+	4.63036i	−0.922880	+	0.219747i
$445$	4.72886	+	3.31690i	0.224170	+	0.157236i
$446$			15.1762i			0.718613i
$447$	−17.4457	+	4.15401i	−0.825155	+	0.196478i
$448$	1.73603			0.0820197
$449$		−	38.0365i		−	1.79505i	−0.440961	−	0.897526i	$-0.645362\pi$
$449$		−	38.0365i		−	1.79505i	0.440961	−	0.897526i	$-0.354638\pi$
$450$	10.9155	+	10.2885i	0.514561	+	0.485002i
$451$		−	6.01141i		−	0.283066i
$452$		−	16.3907i		−	0.770952i
$453$	1.68060	−	0.400167i	0.0789613	−	0.0188015i
$454$		−	25.7362i		−	1.20786i
$455$	−12.6959	+	18.1004i	−0.595194	+	0.848561i
$456$	1.76649	+	7.41878i	0.0827233	+	0.347416i
$457$	4.11542			0.192511			0.0962556	−	0.995357i	$-0.469313\pi$
$457$	4.11542			0.192511			0.0962556	+	0.995357i	$0.469313\pi$
$458$		−	24.8194i		−	1.15973i
$459$	17.0602	+	20.2023i	0.796300	+	0.942964i
$460$	−9.11464	+	5.65007i	−0.424972	+	0.263436i
$461$		−	19.2873i		−	0.898298i	−0.893457	−	0.449149i	$-0.851727\pi$
$461$		−	19.2873i		−	0.898298i	0.893457	−	0.449149i	$-0.148273\pi$
$462$	3.34673	−	0.796891i	0.155704	−	0.0370747i
$463$			6.98126i			0.324447i	0.986754	+	0.162223i	$0.0518665\pi$
$463$			6.98126i			0.324447i	−0.986754	+	0.162223i	$0.948134\pi$
$464$			4.89756i			0.227363i
$465$	−29.9035	−	11.8717i	−1.38674	−	0.550537i
$466$	−3.98878			−0.184777
$467$			4.81285i			0.222712i	0.993781	+	0.111356i	$0.0355194\pi$
$467$			4.81285i			0.222712i	−0.993781	+	0.111356i	$0.964481\pi$
$468$	7.70030	+	15.2529i	0.355947	+	0.705064i
$469$	−26.9706			−1.24539
$470$	−4.33369	−	3.03972i	−0.199898	−	0.140212i
$471$	28.3850	−	6.75876i	1.30791	−	0.311427i
$472$			1.33343i			0.0613760i
$473$	3.65861			0.168223
$474$	4.29281	+	18.0287i	0.197175	+	0.828085i
$475$	20.6994	−	7.49603i	0.949755	−	0.343941i
$476$		−	8.83427i		−	0.404918i
$477$	−9.52095	−	18.8592i	−0.435934	−	0.863505i
$478$			1.46024i			0.0667898i
$479$	−30.2089			−1.38028			−0.690140	−	0.723676i	$-0.742451\pi$
$479$	−30.2089			−1.38028			−0.690140	+	0.723676i	$0.742451\pi$
$480$	−3.59969	−	1.42908i	−0.164302	−	0.0652281i
$481$			65.7325i			2.99714i
$482$		−	4.88957i		−	0.222714i
$483$	2.44606	−	14.2116i	0.111300	−	0.646649i
$484$	−9.69095			−0.440498
$485$	−7.74236	−	5.43061i	−0.351562	−	0.246591i
$486$	−6.09928	+	14.3457i	−0.276669	+	0.650734i
$487$			18.3722i			0.832523i	0.909245	+	0.416261i	$0.136660\pi$
$487$			18.3722i			0.832523i	−0.909245	+	0.416261i	$0.863340\pi$
$488$			7.49227i			0.339159i
$489$	7.22709	+	30.3519i	0.326820	+	1.37256i
$490$	−7.29730	−	5.11844i	−0.329659	−	0.231227i
$491$			28.7601i			1.29793i	0.760820	+	0.648963i	$0.224797\pi$
$491$			28.7601i			1.29793i	−0.760820	+	0.648963i	$0.775203\pi$
$492$	−2.10795	−	8.85285i	−0.0950339	−	0.399117i
$493$	24.9226			1.12246
$494$	25.0770			1.12827
$495$	−7.59550	−	1.10262i	−0.341392	−	0.0495591i
$496$	8.30726			0.373007
$497$		−	22.9206i		−	1.02813i
$498$	1.64484	+	6.90790i	0.0737071	+	0.309550i
$499$	3.39532			0.151996			0.0759978	−	0.997108i	$-0.475786\pi$
$499$	3.39532			0.151996			0.0759978	+	0.997108i	$0.475786\pi$
$500$	−2.91991	+	10.7923i	−0.130582	+	0.482647i
$501$	9.06078	−	2.15746i	0.404806	−	0.0963883i
$502$	16.3660			0.730451
$503$			26.2687i			1.17127i	0.810576	+	0.585633i	$0.199154\pi$
$503$			26.2687i			1.17127i	−0.810576	+	0.585633i	$0.800846\pi$
$504$	4.64921	−	2.34712i	0.207092	−	0.104549i
$505$	−5.79290	+	8.25887i	−0.257781	+	0.367515i
$506$	2.15801	−	5.04492i	0.0959352	−	0.224274i
$507$	32.7524	−	7.79868i	1.45459	−	0.346352i
$508$		−	22.3450i		−	0.991398i
$509$			36.2970i			1.60884i	0.594062	+	0.804419i	$0.297523\pi$
$509$			36.2970i			1.60884i	−0.594062	+	0.804419i	$0.702477\pi$
$510$	−7.27226	+	18.3180i	−0.322021	+	0.811135i
$511$		−	7.72826i		−	0.341878i
$512$	1.00000			0.0441942
$513$	14.7610	+	17.4797i	0.651715	+	0.771749i
$514$	12.9124			0.569542
$515$	14.5462	+	10.2029i	0.640982	+	0.449594i
$516$	5.38794	−	1.28292i	0.237191	−	0.0564776i
$517$	2.70853			0.119121
$518$	20.0359			0.880326
$519$	−8.32709	+	1.98276i	−0.365519	+	0.0870337i
$520$	−7.31319	+	10.4263i	−0.320705	+	0.457225i
$521$	−14.9400			−0.654534			−0.327267	−	0.944932i	$-0.606128\pi$
$521$	−14.9400			−0.654534			−0.327267	+	0.944932i	$0.606128\pi$
$522$	6.62153	+	13.1160i	0.289817	+	0.574072i
$523$	−6.42338			−0.280875			−0.140437	−	0.990090i	$-0.544851\pi$
$523$	−6.42338			−0.280875			−0.140437	+	0.990090i	$0.544851\pi$
$524$			7.79764i			0.340642i
$525$	−8.25437	−	12.5658i	−0.360250	−	0.548418i
$526$			18.6670i			0.813921i
$527$		−	42.2738i		−	1.84148i
$528$	1.92781	−	0.459031i	0.0838972	−	0.0199768i
$529$	−15.8849	−	16.6334i	−0.690649	−	0.723190i
$530$	9.04231	−	12.8915i	0.392773	−	0.559972i
$531$	1.80280	+	3.57102i	0.0782350	+	0.154969i
$532$		−	7.64371i		−	0.331397i
$533$	−29.9245			−1.29617
$534$	−4.35251	+	1.03638i	−0.188351	+	0.0448484i
$535$	−1.68695	+	2.40507i	−0.0729332	+	0.103980i
$536$	−15.5358			−0.671045
$537$	−2.74738	−	11.5383i	−0.118558	−	0.497914i
$538$			13.9987i			0.603527i
$539$	4.56077			0.196446
$540$	−11.5723	+	1.03963i	−0.497994	+	0.0447385i
$541$	0.426269			0.0183267			0.00916336	−	0.999958i	$-0.497083\pi$
$541$	0.426269			0.0183267			0.00916336	+	0.999958i	$0.497083\pi$
$542$	4.95580			0.212870
$543$	−6.60447	−	27.7370i	−0.283425	−	1.19031i
$544$		−	5.08878i		−	0.218180i
$545$	10.4431	−	14.8886i	0.447333	−	0.637758i
$546$	−3.96688	−	16.6599i	−0.169767	−	0.712976i
$547$			4.14315i			0.177148i	0.996070	+	0.0885741i	$0.0282310\pi$
$547$			4.14315i			0.177148i	−0.996070	+	0.0885741i	$0.971769\pi$
$548$		−	0.151371i		−	0.00646626i
$549$	10.1296	+	20.0649i	0.432321	+	0.856347i
$550$	−1.94788	−	5.37886i	−0.0830580	−	0.229355i
$551$	21.5639			0.918651
$552$	1.40900	−	8.18625i	0.0599710	−	0.348430i
$553$		−	18.5753i		−	0.789902i
$554$			9.05451i			0.384689i
$555$	−41.5447	−	16.4933i	−1.76348	−	0.700100i
$556$	−12.5121			−0.530630
$557$			32.9820i			1.39749i	0.715371	+	0.698745i	$0.246258\pi$
$557$			32.9820i			1.39749i	−0.715371	+	0.698745i	$0.753742\pi$
$558$	22.2475	−	11.2315i	0.941810	−	0.475466i
$559$		−	18.2124i		−	0.770301i
$560$	3.17805	+	2.22913i	0.134297	+	0.0941979i
$561$	−2.33591	−	9.81020i	−0.0986222	−	0.414187i
$562$	−27.7262			−1.16956
$563$			24.5497i			1.03464i	0.855791	+	0.517322i	$0.173071\pi$
$563$			24.5497i			1.03464i	−0.855791	+	0.517322i	$0.826929\pi$
$564$	3.98878	−	0.949770i	0.167958	−	0.0399925i
$565$	21.0463	−	30.0054i	0.885423	−	1.26234i
$566$	−1.11965			−0.0470622
$567$	9.27761	−	12.5715i	0.389623	−	0.527955i
$568$		−	13.2029i		−	0.553980i
$569$	−22.5192			−0.944054			−0.472027	−	0.881584i	$-0.656477\pi$
$569$	−22.5192			−0.944054			−0.472027	+	0.881584i	$0.656477\pi$
$570$	−6.29220	+	15.8494i	−0.263551	+	0.663857i
$571$			14.4426i			0.604404i	0.953244	+	0.302202i	$0.0977217\pi$
$571$			14.4426i			0.604404i	−0.953244	+	0.302202i	$0.902278\pi$
$572$		−	6.51640i		−	0.272464i
$573$	12.8237	−	3.05345i	0.535717	−	0.127560i
$574$			9.12126i			0.380714i
$575$	−23.9405	−	1.36030i	−0.998390	−	0.0567283i
$576$	2.67807	−	1.35201i	0.111586	−	0.0563336i
$577$		−	2.27420i		−	0.0946761i	−0.998879	−	0.0473380i	$-0.984926\pi$
$577$		−	2.27420i		−	0.0946761i	0.998879	−	0.0473380i	$-0.0150738\pi$
$578$	−8.89569			−0.370012
$579$	6.32207	+	26.5510i	0.262736	+	1.10342i
$580$	−6.28865	+	8.96567i	−0.261122	+	0.372279i
$581$		−	7.11734i		−	0.295277i
$582$	7.12616	−	1.69681i	0.295389	−	0.0703351i
$583$			8.05713i			0.333692i
$584$		−	4.45169i		−	0.184212i
$585$	−5.48878	+	37.8100i	−0.226933	+	1.56325i
$586$		−	4.32973i		−	0.178859i
$587$	−32.0738			−1.32383			−0.661914	−	0.749580i	$-0.730255\pi$
$587$	−32.0738			−1.32383			−0.661914	+	0.749580i	$0.730255\pi$
$588$	6.71653	−	1.59927i	0.276985	−	0.0659529i
$589$		−	36.5767i		−	1.50712i
$590$	−1.71217	+	2.44103i	−0.0704891	+	0.100496i
$591$	−28.0813	+	6.68643i	−1.15511	+	0.275043i
$592$	11.5412			0.474341
$593$	12.3921			0.508882			0.254441	−	0.967088i	$-0.418109\pi$
$593$	12.3921			0.508882			0.254441	+	0.967088i	$0.418109\pi$
$594$	4.54220	−	3.83573i	0.186369	−	0.157382i
$595$	11.3435	−	16.1724i	0.465040	−	0.663003i
$596$	10.3539			0.424112
$597$	−4.83798	−	20.3183i	−0.198005	−	0.831571i
$598$	−25.1133	−	10.7425i	−1.02696	−	0.439292i
$599$			0.139135i			0.00568490i	0.999996	+	0.00284245i	$0.000904780\pi$
$599$			0.139135i			0.00568490i	−0.999996	+	0.00284245i	$0.999095\pi$
$600$	−4.75474	−	7.23826i	−0.194111	−	0.295501i
$601$	18.8209			0.767720			0.383860	−	0.923391i	$-0.374595\pi$
$601$	18.8209			0.767720			0.383860	+	0.923391i	$0.374595\pi$
$602$	−5.55130			−0.226254
$603$	−41.6060	+	21.0045i	−1.69433	+	0.855370i
$604$	−0.997420			−0.0405844
$605$	−17.7406	−	12.4436i	−0.721259	−	0.505902i
$606$	−1.81001	−	7.60157i	−0.0735267	−	0.308793i
$607$		−	3.92687i		−	0.159387i	−0.996819	−	0.0796933i	$-0.974606\pi$
$607$		−	3.92687i		−	0.159387i	0.996819	−	0.0796933i	$-0.0253941\pi$
$608$		−	4.40298i		−	0.178565i
$609$	−3.41114	−	14.3259i	−0.138226	−	0.580515i
$610$	−9.62037	+	13.7157i	−0.389517	+	0.555331i
$611$		−	13.4829i		−	0.545460i
$612$	−6.88007	−	13.6281i	−0.278110	−	0.550884i
$613$	−0.906632			−0.0366185			−0.0183093	−	0.999832i	$-0.505828\pi$
$613$	−0.906632			−0.0366185			−0.0183093	+	0.999832i	$0.505828\pi$
$614$			11.0810i			0.447194i
$615$	7.50850	−	18.9131i	0.302772	−	0.762649i
$616$	−1.98626			−0.0800286
$617$			15.1168i			0.608578i	0.952580	+	0.304289i	$0.0984189\pi$
$617$			15.1168i			0.608578i	−0.952580	+	0.304289i	$0.901581\pi$
$618$	−13.3885	+	3.18794i	−0.538564	+	0.128238i
$619$			20.8967i			0.839908i	0.907545	+	0.419954i	$0.137954\pi$
$619$			20.8967i			0.839908i	−0.907545	+	0.419954i	$0.862046\pi$
$620$	15.2076	+	10.6668i	0.610752	+	0.428391i
$621$	−7.29446	−	23.8284i	−0.292717	−	0.956199i
$622$		−	1.00298i		−	0.0402158i
$623$	4.48447			0.179666
$624$	−2.28503	−	9.59653i	−0.0914745	−	0.384169i
$625$	−19.2031	+	16.0076i	−0.768123	+	0.640303i
$626$	19.4627			0.777888
$627$	−2.02111	−	8.48812i	−0.0807152	−	0.338983i
$628$	−16.8463			−0.672239
$629$		−	58.7307i		−	2.34175i
$630$	11.5248	+	1.67303i	0.459160	+	0.0666552i
$631$			20.9270i			0.833091i	0.909115	+	0.416545i	$0.136759\pi$
$631$			20.9270i			0.833091i	−0.909115	+	0.416545i	$0.863241\pi$
$632$		−	10.6999i		−	0.425618i
$633$	19.4170	−	4.62338i	0.771756	−	0.183763i
$634$	−17.4897			−0.694604
$635$	28.6918	−	40.9056i	1.13860	−	1.62329i
$636$	2.82530	+	11.8655i	0.112031	+	0.470499i
$637$		−	22.7033i		−	0.899536i
$638$		−	5.60349i		−	0.221844i
$639$	−17.8504	−	35.3583i	−0.706150	−	1.39875i
$640$	1.83064	+	1.28404i	0.0723624	+	0.0507561i
$641$	14.5326			0.574003			0.287002	−	0.957930i	$-0.407341\pi$
$641$	14.5326			0.574003			0.287002	+	0.957930i	$0.407341\pi$
$642$	−0.527093	−	2.21365i	−0.0208027	−	0.0873659i
$643$	17.8860			0.705353			0.352677	−	0.935745i	$-0.385272\pi$
$643$	17.8860			0.705353			0.352677	+	0.935745i	$0.385272\pi$
$644$	−3.27440	+	7.65478i	−0.129029	+	0.301641i
$645$	11.5107	+	4.56975i	0.453234	+	0.179934i
$646$	−22.4058			−0.881545
$647$	−23.9501			−0.941575			−0.470787	−	0.882247i	$-0.656030\pi$
$647$	−23.9501			−0.941575			−0.470787	+	0.882247i	$0.656030\pi$
$648$	5.34415	−	7.24155i	0.209938	−	0.284475i
$649$		−	1.52563i		−	0.0598861i
$650$	−26.7757	+	9.69646i	−1.05023	+	0.380326i
$651$	−24.2997	+	5.78600i	−0.952379	+	0.226771i
$652$		−	18.0136i		−	0.705466i
$653$	14.0531			0.549941			0.274970	−	0.961453i	$-0.411332\pi$
$653$	14.0531			0.549941			0.274970	+	0.961453i	$0.411332\pi$
$654$	3.26298	+	13.7037i	0.127593	+	0.535856i
$655$	−10.0125	+	14.2747i	−0.391220	+	0.557758i
$656$			5.25409i			0.205138i
$657$	−6.01871	−	11.9219i	−0.234812	−	0.465119i
$658$	−4.10972			−0.160213
$659$	−4.68941			−0.182674			−0.0913368	−	0.995820i	$-0.529114\pi$
$659$	−4.68941			−0.182674			−0.0913368	+	0.995820i	$0.529114\pi$
$660$	4.11854	+	1.63506i	0.160314	+	0.0636447i
$661$			29.5090i			1.14777i	0.818937	+	0.573883i	$0.194564\pi$
$661$			29.5090i			1.14777i	−0.818937	+	0.573883i	$0.805436\pi$
$662$	17.4962			0.680010
$663$	−48.8347	+	11.6280i	−1.89658	+	0.451595i
$664$		−	4.09978i		−	0.159102i
$665$	9.81482	−	13.9929i	0.380602	−	0.542621i
$666$	30.9082	−	15.6038i	1.19767	−	0.604635i
$667$	−21.5951	−	9.23749i	−0.836165	−	0.357677i
$668$	−5.37749			−0.208062
$669$	−6.08872	−	25.5710i	−0.235403	−	0.988632i
$670$	−28.4405	−	19.9486i	−1.09875	−	0.770681i
$671$		−	8.57220i		−	0.330926i
$672$	−2.92511	+	0.696499i	−0.112839	+	0.0268680i
$673$		−	3.86927i		−	0.149150i	−0.997215	−	0.0745748i	$-0.976240\pi$
$673$		−	3.86927i		−	0.149150i	0.997215	−	0.0745748i	$-0.0237599\pi$
$674$	−33.5694			−1.29304
$675$	−22.5197	−	12.9562i	−0.866785	−	0.498683i
$676$	−19.4383			−0.747626
$677$			16.8183i			0.646378i	0.946334	+	0.323189i	$0.104755\pi$
$677$			16.8183i			0.646378i	−0.946334	+	0.323189i	$0.895245\pi$
$678$	6.57597	+	27.6174i	0.252549	+	1.06064i
$679$	−7.34222			−0.281768
$680$	6.53419	−	9.31573i	0.250575	−	0.357242i
$681$	10.3254	+	43.3641i	0.395671	+	1.66172i
$682$	−9.50466			−0.363952
$683$	−15.6624			−0.599306			−0.299653	−	0.954048i	$-0.596871\pi$
$683$	−15.6624			−0.599306			−0.299653	+	0.954048i	$0.596871\pi$
$684$	−5.95286	−	11.7915i	−0.227613	−	0.450860i
$685$	0.194367	−	0.277106i	0.00742637	−	0.0105877i
$686$	−19.0724			−0.728186
$687$	9.95759	+	41.8192i	0.379906	+	1.59550i
$688$	−3.19770			−0.121911
$689$	40.1079			1.52799
$690$	13.0908	−	13.1769i	0.498360	−	0.501635i
$691$	16.0908			0.612124			0.306062	−	0.952012i	$-0.400988\pi$
$691$	16.0908			0.612124			0.306062	+	0.952012i	$0.400988\pi$
$692$	4.94205			0.187869
$693$	−5.31935	+	2.68544i	−0.202065	+	0.102011i
$694$	8.79124			0.333711
$695$	−22.9051	−	16.0660i	−0.868839	−	0.609417i
$696$	−1.96491	−	8.25211i	−0.0744798	−	0.312795i
$697$	26.7369			1.01273
$698$	28.9759			1.09675
$699$	6.72088	−	1.60031i	0.254207	−	0.0605292i
$700$	2.95557	+	8.16147i	0.111710	+	0.308474i
$701$	−17.8010			−0.672335			−0.336167	−	0.941802i	$-0.609131\pi$
$701$	−17.8010			−0.672335			−0.336167	+	0.941802i	$0.609131\pi$
$702$	−19.0941	−	22.6108i	−0.720659	−	0.853391i
$703$		−	50.8158i		−	1.91655i
$704$	−1.14414			−0.0431214
$705$	8.52157	+	3.38306i	0.320941	+	0.127414i
$706$	21.7061			0.816920
$707$			7.83204i			0.294554i
$708$	−0.534975	−	2.24675i	−0.0201056	−	0.0844381i
$709$		−	22.3078i		−	0.837788i	−0.908035	−	0.418894i	$-0.862418\pi$
$709$		−	22.3078i		−	0.837788i	0.908035	−	0.418894i	$-0.137582\pi$
$710$	16.9530	−	24.1697i	0.636235	−	0.907073i
$711$	−14.4663	−	28.6550i	−0.542529	−	1.07465i
$712$	2.58317			0.0968086
$713$	−15.6687	+	36.6297i	−0.586797	+	1.37179i
$714$	3.54433	+	14.8853i	0.132643	+	0.557067i
$715$	8.36731	−	11.9292i	0.312920	−	0.446126i
$716$			6.84787i			0.255917i
$717$	−0.585852	−	2.46042i	−0.0218790	−	0.0918862i
$718$	21.4318			0.799828
$719$		−	44.9337i		−	1.67574i	−0.545867	−	0.837872i	$-0.683799\pi$
$719$		−	44.9337i		−	1.67574i	0.545867	−	0.837872i	$-0.316201\pi$
$720$	6.63862	+	0.963712i	0.247407	+	0.0359154i
$721$	13.7944			0.513731
$722$	−0.386266			−0.0143753
$723$	1.96171	+	8.23866i	0.0729567	+	0.306399i
$724$			16.4617i			0.611794i
$725$	−23.0245	+	8.33803i	−0.855109	+	0.309667i
$726$	16.3287	−	3.88803i	0.606015	−	0.144298i
$727$	21.8671			0.811005			0.405503	−	0.914094i	$-0.367096\pi$
$727$	21.8671			0.811005			0.405503	+	0.914094i	$0.367096\pi$
$728$			9.88749i			0.366455i
$729$	4.52142	−	26.6187i	0.167460	−	0.985879i
$730$	5.71614	−	8.14944i	0.211564	−	0.301624i
$731$			16.2724i			0.601856i
$732$	−3.00592	−	12.6241i	−0.111102	−	0.466599i
$733$	30.5063			1.12677			0.563387	−	0.826193i	$-0.309498\pi$
$733$	30.5063			1.12677			0.563387	+	0.826193i	$0.309498\pi$
$734$	8.57945			0.316673
$735$	14.3491	+	5.69659i	0.529274	+	0.210122i
$736$	−1.88614	+	4.40936i	−0.0695241	+	0.162531i
$737$	17.7751			0.654755
$738$	7.10357	+	14.0708i	0.261486	+	0.517955i
$739$	36.2277			1.33266			0.666329	−	0.745658i	$-0.267865\pi$
$739$	36.2277			1.33266			0.666329	+	0.745658i	$0.267865\pi$
$740$	21.1278	+	14.8194i	0.776673	+	0.544770i
$741$	−42.2534	+	10.0610i	−1.55222	+	0.369599i
$742$		−	12.2253i		−	0.448804i
$743$			33.8173i			1.24064i	0.784351	+	0.620318i	$0.212996\pi$
$743$			33.8173i			1.24064i	−0.784351	+	0.620318i	$0.787004\pi$
$744$	−13.9973	+	3.33289i	−0.513165	+	0.122190i
$745$	18.9543	+	13.2948i	0.694431	+	0.487084i
$746$	−26.7453			−0.979215
$747$	−5.54293	−	10.9795i	−0.202805	−	0.401719i
$748$			5.82227i			0.212883i
$749$			2.28077i			0.0833374i
$750$	0.589988	−	19.3559i	0.0215433	−	0.706779i
$751$		−	14.0015i		−	0.510922i	−0.966819	−	0.255461i	$-0.917773\pi$
$751$		−	14.0015i		−	0.510922i	0.966819	−	0.255461i	$-0.0822272\pi$
$752$	−2.36731			−0.0863269
$753$	−27.5758	+	6.56608i	−1.00492	+	0.239281i
$754$	−27.8938			−1.01583
$755$	−1.82592	−	1.28073i	−0.0664519	−	0.0466104i
$756$	−6.89199	+	5.82005i	−0.250659	+	0.211673i
$757$	−27.6891			−1.00638			−0.503189	−	0.864176i	$-0.667840\pi$
$757$	−27.6891			−1.00638			−0.503189	+	0.864176i	$0.667840\pi$
$758$		−	4.35515i		−	0.158186i
$759$	−1.61209	+	9.36621i	−0.0585152	+	0.339972i
$760$	5.65360	−	8.06028i	0.205078	−	0.292377i
$761$		−	19.8854i		−	0.720844i	−0.932789	−	0.360422i	$-0.882633\pi$
$761$		−	19.8854i		−	0.720844i	0.932789	−	0.360422i	$-0.117367\pi$
$762$	8.96485	+	37.6500i	0.324762	+	1.36392i
$763$		−	14.1191i		−	0.511147i
$764$	−7.61075			−0.275347
$765$	4.90412	−	33.7825i	0.177309	−	1.22141i
$766$			15.1717i			0.548174i
$767$	−7.59449			−0.274221
$768$	−1.68494	+	0.401202i	−0.0608002	+	0.0144771i
$769$		−	46.5122i		−	1.67727i	−0.544693	−	0.838636i	$-0.683354\pi$
$769$		−	46.5122i		−	1.67727i	0.544693	−	0.838636i	$-0.316646\pi$
$770$	−3.63613	−	2.55043i	−0.131037	−	0.0919112i
$771$	−21.7567	+	5.18049i	−0.783548	+	0.186571i
$772$		−	15.7578i		−	0.567136i
$773$		−	8.87729i		−	0.319294i	−0.987174	−	0.159647i	$-0.948964\pi$
$773$		−	8.87729i		−	0.319294i	0.987174	−	0.159647i	$-0.0510356\pi$
$774$	−8.56367	+	4.32331i	−0.307815	+	0.155398i
$775$	14.1430	+	39.0543i	0.508032	+	1.40287i
$776$	−4.22932			−0.151824
$777$	−33.7593	+	8.03844i	−1.21111	+	0.288377i
$778$	32.7383			1.17372
$779$	23.1337			0.828850
$780$	8.13925	−	20.5019i	0.291432	−	0.734085i
$781$			15.1059i			0.540532i
$782$	22.4383	+	9.59817i	0.802391	+	0.343230i
$783$	−16.4191	−	19.4432i	−0.586770	−	0.694843i
$784$	−3.98620			−0.142364
$785$	−30.8395	−	21.6313i	−1.10071	−	0.772053i
$786$	−3.12843	−	13.1386i	−0.111587	−	0.468638i
$787$	−19.8370			−0.707113			−0.353556	−	0.935413i	$-0.615028\pi$
$787$	−19.8370			−0.707113			−0.353556	+	0.935413i	$0.615028\pi$
$788$	16.6660			0.593701
$789$	−7.48925	−	31.4529i	−0.266624	−	1.11975i
$790$	13.7391	−	19.5876i	0.488813	−	0.696896i
$791$		−	28.4547i		−	1.01173i
$792$	−3.06409	+	1.54688i	−0.108878	+	0.0549661i
$793$	−42.6719			−1.51532
$794$		−	18.2547i		−	0.647836i
$795$	−10.0637	+	25.3493i	−0.356922	+	0.899047i
$796$			12.0587i			0.427410i
$797$			13.3280i			0.472102i	0.971741	+	0.236051i	$0.0758532\pi$
$797$			13.3280i			0.472102i	−0.971741	+	0.236051i	$0.924147\pi$
$798$	3.06667	+	12.8792i	0.108559	+	0.455920i
$799$			12.0467i			0.426182i
$800$	1.70249	+	4.70123i	0.0601921	+	0.166213i
$801$	6.91793	−	3.49247i	0.244433	−	0.123400i
$802$	−11.5261			−0.406999
$803$			5.09335i			0.179740i
$804$	26.1770	−	6.23300i	0.923190	−	0.219821i
$805$	−15.8233	+	9.80869i	−0.557697	+	0.345711i
$806$			47.3137i			1.66655i
$807$	−5.61631	−	23.5870i	−0.197704	−	0.830303i
$808$			4.51147i			0.158713i
$809$			6.62271i			0.232842i	0.993200	+	0.116421i	$0.0371422\pi$
$809$			6.62271i			0.232842i	−0.993200	+	0.116421i	$0.962858\pi$
$810$	19.0817	−	6.39457i	0.670461	−	0.224682i
$811$	−1.32885			−0.0466624			−0.0233312	−	0.999728i	$-0.507427\pi$
$811$	−1.32885			−0.0466624			−0.0233312	+	0.999728i	$0.507427\pi$
$812$			8.50230i			0.298372i
$813$	−8.35024	+	1.98828i	−0.292856	+	0.0697319i
$814$	−13.2047			−0.462826
$815$	23.1301	−	32.9764i	0.810213	−	1.15511i
$816$	2.04163	+	8.57431i	0.0714714	+	0.300161i
$817$			14.0794i			0.492576i
$818$	−24.4078			−0.853397
$819$	13.3679	+	26.4794i	0.467114	+	0.925266i
$820$	−6.74646	+	9.61835i	−0.235597	+	0.335887i
$821$			4.08413i			0.142537i	0.997457	+	0.0712685i	$0.0227047\pi$
$821$			4.08413i			0.142537i	−0.997457	+	0.0712685i	$0.977295\pi$
$822$	0.0607305	+	0.255052i	0.00211822	+	0.00889596i
$823$			50.6325i			1.76494i	0.470370	+	0.882469i	$0.344120\pi$
$823$			50.6325i			1.76494i	−0.470370	+	0.882469i	$0.655880\pi$
$824$	7.94596			0.276811
$825$	5.44008	+	8.28158i	0.189399	+	0.288328i
$826$			2.31487i			0.0805447i
$827$		−	34.8361i		−	1.21137i	−0.795704	−	0.605686i	$-0.792899\pi$
$827$		−	34.8361i		−	1.21137i	0.795704	−	0.605686i	$-0.207101\pi$
$828$	0.910257	+	14.3587i	0.0316336	+	0.498998i
$829$	−46.1526			−1.60295			−0.801474	−	0.598030i	$-0.795950\pi$
$829$	−46.1526			−1.60295			−0.801474	+	0.598030i	$0.795950\pi$
$830$	5.26428	−	7.50522i	0.182726	−	0.260510i
$831$	−3.63269	−	15.2564i	−0.126017	−	0.529237i
$832$			5.69546i			0.197455i
$833$			20.2849i			0.702831i
$834$	21.0821	−	5.01987i	0.730014	−	0.173824i
$835$	−9.84426	−	6.90491i	−0.340675	−	0.238954i
$836$			5.03763i			0.174230i
$837$	−32.9796	+	27.8501i	−1.13994	+	0.962641i
$838$	−21.3693			−0.738189
$839$	−42.5749			−1.46985			−0.734924	−	0.678150i	$-0.762782\pi$
$839$	−42.5749			−1.46985			−0.734924	+	0.678150i	$0.762782\pi$
$840$	−6.24916	−	2.48092i	−0.215617	−	0.0855998i
$841$	5.01394			0.172894
$842$		−	6.04733i		−	0.208405i
$843$	46.7171	−	11.1238i	1.60902	−	0.383125i
$844$	−11.5238			−0.396666
$845$	−35.5845	−	24.9595i	−1.22414	−	0.858633i
$846$	−6.33983	+	3.20062i	−0.217968	+	0.110039i
$847$	−16.8238			−0.578071
$848$		−	7.04209i		−	0.241826i
$849$	1.88654	−	0.449204i	0.0647459	−	0.0154166i
$850$	23.9235	−	8.66359i	0.820570	−	0.297159i
$851$	−21.7684	+	50.8894i	−0.746210	+	1.74446i
$852$	5.29702	+	22.2461i	0.181473	+	0.762139i
$853$			47.5842i			1.62925i	0.579986	+	0.814626i	$0.303058\pi$
$853$			47.5842i			1.62925i	−0.579986	+	0.814626i	$0.696942\pi$
$854$			13.0068i			0.445084i
$855$	4.24321	−	29.2297i	0.145115	−	0.999636i
$856$			1.31378i			0.0449042i
$857$	20.1057			0.686796			0.343398	−	0.939190i	$-0.388422\pi$
$857$	20.1057			0.686796			0.343398	+	0.939190i	$0.388422\pi$
$858$	2.61439	+	10.9798i	0.0892539	+	0.374843i
$859$	−26.3202			−0.898034			−0.449017	−	0.893523i	$-0.648226\pi$
$859$	−26.3202			−0.898034			−0.449017	+	0.893523i	$0.648226\pi$
$860$	−5.85383	−	4.10597i	−0.199614	−	0.140012i
$861$	−3.65947	−	15.3688i	−0.124714	−	0.523768i
$862$	−22.4661			−0.765198
$863$	49.2546			1.67665			0.838323	−	0.545175i	$-0.183537\pi$
$863$	49.2546			1.67665			0.838323	+	0.545175i	$0.183537\pi$
$864$	−3.96998	+	3.35251i	−0.135061	+	0.114055i
$865$	9.04713	+	6.34579i	0.307611	+	0.215763i
$866$	−0.979211			−0.0332750
$867$	14.9887	−	3.56897i	0.509044	−	0.121209i
$868$	14.4216			0.489503
$869$			12.2421i			0.415286i
$870$	6.99898	−	17.6297i	0.237288	−	0.597702i
$871$		−	88.4836i		−	2.99815i
$872$		−	8.13301i		−	0.275419i
$873$	−11.3264	+	5.71806i	−0.383341	+	0.193527i
$874$	19.4143	+	8.30466i	0.656700	+	0.280909i
$875$	−5.06905	+	18.7358i	−0.171365	+	0.633385i
$876$	1.78603	+	7.50084i	0.0603443	+	0.253430i
$877$		−	10.9019i		−	0.368132i	−0.982914	−	0.184066i	$-0.941074\pi$
$877$		−	10.9019i		−	0.368132i	0.982914	−	0.184066i	$-0.0589260\pi$
$878$	5.31334			0.179317
$879$	1.73710	+	7.29535i	0.0585908	+	0.246066i
$880$	−2.09451	−	1.46912i	−0.0706058	−	0.0495240i
$881$	−8.66459			−0.291918			−0.145959	−	0.989291i	$-0.546627\pi$
$881$	−8.66459			−0.291918			−0.145959	+	0.989291i	$0.546627\pi$
$882$	−10.6753	+	5.38937i	−0.359457	+	0.181470i
$883$			11.5104i			0.387357i	0.981065	+	0.193679i	$0.0620419\pi$
$883$			11.5104i			0.387357i	−0.981065	+	0.193679i	$0.937958\pi$
$884$	28.9830			0.974802
$885$	1.90557	−	4.79992i	0.0640551	−	0.161348i
$886$	25.1317			0.844315
$887$	55.2764			1.85600			0.928000	−	0.372581i	$-0.121527\pi$
$887$	55.2764			1.85600			0.928000	+	0.372581i	$0.121527\pi$
$888$	−19.4463	+	4.63036i	−0.652575	+	0.155385i
$889$		−	38.7915i		−	1.30103i
$890$	4.72886	+	3.31690i	0.158512	+	0.111183i
$891$	−6.11446	+	8.28534i	−0.204842	+	0.277569i
$892$			15.1762i			0.508136i
$893$			10.4232i			0.348800i
$894$	−17.4457	+	4.15401i	−0.583473	+	0.138931i
$895$	−8.79294	+	12.5360i	−0.293915	+	0.419032i
$896$	1.73603			0.0579967
$897$	46.6245	+	8.02490i	1.55675	+	0.267944i
$898$		−	38.0365i		−	1.26929i
$899$			40.6853i			1.35693i
$900$	10.9155	+	10.2885i	0.363849	+	0.342948i
$901$	−35.8356			−1.19386
$902$		−	6.01141i		−	0.200158i
$903$	9.35362	−	2.22719i	0.311269	−	0.0741163i
$904$		−	16.3907i		−	0.545146i
$905$	−21.1375	+	30.1354i	−0.702633	+	1.00174i
$906$	1.68060	−	0.400167i	0.0558341	−	0.0132947i
$907$	0.798692			0.0265201			0.0132601	−	0.999912i	$-0.495779\pi$
$907$	0.798692			0.0265201			0.0132601	+	0.999912i	$0.495779\pi$
$908$		−	25.7362i		−	0.854086i
$909$	6.09953	+	12.0820i	0.202309	+	0.400736i
$910$	−12.6959	+	18.1004i	−0.420866	+	0.600023i
$911$	40.2084			1.33216			0.666082	−	0.745878i	$-0.267970\pi$
$911$	40.2084			1.33216			0.666082	+	0.745878i	$0.267970\pi$
$912$	1.76649	+	7.41878i	0.0584942	+	0.245660i
$913$			4.69072i			0.155240i
$914$	4.11542			0.136126
$915$	10.7070	−	26.9698i	0.353963	−	0.891595i
$916$		−	24.8194i		−	0.820055i
$917$			13.5369i			0.447029i
$918$	17.0602	+	20.2023i	0.563069	+	0.666777i
$919$			28.7966i			0.949912i	0.880009	+	0.474956i	$0.157536\pi$
$919$			28.7966i			0.949912i	−0.880009	+	0.474956i	$0.842464\pi$
$920$	−9.11464	+	5.65007i	−0.300501	+	0.186277i
$921$	−4.44573	−	18.6709i	−0.146492	−	0.615227i
$922$		−	19.2873i		−	0.635192i
$923$	75.1965			2.47512
$924$	3.34673	−	0.796891i	0.110099	−	0.0262158i
$925$	19.6488	+	54.2578i	0.646048	+	1.78399i
$926$			6.98126i			0.229418i
$927$	21.2799	−	10.7430i	0.698922	−	0.352846i
$928$			4.89756i			0.160770i
$929$			32.3056i			1.05991i	0.848025	+	0.529956i	$0.177791\pi$
$929$			32.3056i			1.05991i	−0.848025	+	0.529956i	$0.822209\pi$
$930$	−29.9035	−	11.8717i	−0.980575	−	0.389289i
$931$			17.5512i			0.575217i
$932$	−3.98878			−0.130657
$933$	0.402397	+	1.68996i	0.0131739	+	0.0553269i
$934$			4.81285i			0.157481i
$935$	−7.47602	+	10.6585i	−0.244492	+	0.348570i
$936$	7.70030	+	15.2529i	0.251692	+	0.498555i
$937$	4.44768			0.145299			0.0726496	−	0.997358i	$-0.476855\pi$
$937$	4.44768			0.145299			0.0726496	+	0.997358i	$0.476855\pi$
$938$	−26.9706			−0.880622
$939$	−32.7936	+	7.80850i	−1.07018	+	0.254821i
$940$	−4.33369	−	3.03972i	−0.141349	−	0.0991446i
$941$	59.5295			1.94061			0.970303	−	0.241893i	$-0.0777683\pi$
$941$	59.5295			1.94061			0.970303	+	0.241893i	$0.0777683\pi$
$942$	28.3850	−	6.75876i	0.924834	−	0.220212i
$943$	−23.1672	−	9.90997i	−0.754427	−	0.322713i
$944$			1.33343i			0.0433994i
$945$	−20.0899	+	1.80483i	−0.653525	+	0.0587110i
$946$	3.65861			0.118952
$947$	−0.416026			−0.0135190			−0.00675952	−	0.999977i	$-0.502152\pi$
$947$	−0.416026			−0.0135190			−0.00675952	+	0.999977i	$0.502152\pi$
$948$	4.29281	+	18.0287i	0.139424	+	0.585545i
$949$	25.3544			0.823039
$950$	20.6994	−	7.49603i	0.671578	−	0.243203i
$951$	29.4691	−	7.01690i	0.955602	−	0.227539i
$952$		−	8.83427i		−	0.286320i
$953$			12.5044i			0.405058i	0.979276	+	0.202529i	$0.0649160\pi$
$953$			12.5044i			0.405058i	−0.979276	+	0.202529i	$0.935084\pi$
$954$	−9.52095	−	18.8592i	−0.308252	−	0.610590i
$955$	−13.9325	−	9.77250i	−0.450846	−	0.316231i
$956$			1.46024i			0.0472275i
$957$	2.24813	+	9.44156i	0.0726718	+	0.305202i
$958$	−30.2089			−0.976006
$959$		−	0.262785i		−	0.00848577i
$960$	−3.59969	−	1.42908i	−0.116179	−	0.0461232i
$961$	38.0106			1.22615
$962$			65.7325i			2.11930i
$963$	1.77625	+	3.51841i	0.0572387	+	0.113379i
$964$		−	4.88957i		−	0.157483i
$965$	20.2337	−	28.8469i	0.651344	−	0.928615i
$966$	2.44606	−	14.2116i	0.0787008	−	0.457250i
$967$			22.9201i			0.737060i	0.929616	+	0.368530i	$0.120139\pi$
$967$			22.9201i			0.737060i	−0.929616	+	0.368530i	$0.879861\pi$
$968$	−9.69095			−0.311479
$969$	37.7526	−	8.98927i	1.21279	−	0.288777i
$970$	−7.74236	−	5.43061i	−0.248592	−	0.174366i
$971$	39.2670			1.26014			0.630069	−	0.776539i	$-0.283027\pi$
$971$	39.2670			1.26014			0.630069	+	0.776539i	$0.283027\pi$
$972$	−6.09928	+	14.3457i	−0.195634	+	0.460138i
$973$	−21.7213			−0.696353
$974$			18.3722i			0.588683i
$975$	41.2252	−	27.0804i	1.32026	−	0.867268i
$976$			7.49227i			0.239822i
$977$		−	43.3094i		−	1.38559i	−0.721134	−	0.692795i	$-0.756379\pi$
$977$		−	43.3094i		−	1.38559i	0.721134	−	0.692795i	$-0.243621\pi$
$978$	7.22709	+	30.3519i	0.231097	+	0.970546i
$979$	−2.95551			−0.0944585
$980$	−7.29730	−	5.11844i	−0.233104	−	0.163503i
$981$	−10.9959	−	21.7808i	−0.351072	−	0.695408i
$982$			28.7601i			0.917772i
$983$			24.8074i			0.791234i	0.918416	+	0.395617i	$0.129469\pi$
$983$			24.8074i			0.791234i	−0.918416	+	0.395617i	$0.870531\pi$
$984$	−2.10795	−	8.85285i	−0.0671991	−	0.282219i
$985$	30.5094	+	21.3998i	0.972111	+	0.681854i
$986$	24.9226			0.793697
$987$	6.92464	−	1.64883i	0.220414	−	0.0524828i
$988$	25.0770			0.797806
$989$	6.03131	−	14.0998i	0.191785	−	0.448348i
$990$	−7.59550	−	1.10262i	−0.241401	−	0.0350436i
$991$	−5.76457			−0.183117			−0.0915587	−	0.995800i	$-0.529185\pi$
$991$	−5.76457			−0.183117			−0.0915587	+	0.995800i	$0.529185\pi$
$992$	8.30726			0.263756
$993$	−29.4801	+	7.01952i	−0.935524	+	0.222758i
$994$		−	22.9206i		−	0.726997i
$995$	−15.4839	+	22.0752i	−0.490871	+	0.699830i
$996$	1.64484	+	6.90790i	0.0521188	+	0.218885i
$997$			1.94254i			0.0615209i	0.999527	+	0.0307604i	$0.00979290\pi$
$997$			1.94254i			0.0615209i	−0.999527	+	0.0307604i	$0.990207\pi$
$998$	3.39532			0.107477
$999$	−45.8183	+	38.6920i	−1.44963	+	1.22416i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.68494 + 0.401202i) q^{3} +1.00000 q^{4} +(1.83064 + 1.28404i) q^{5} +(-1.68494 + 0.401202i) q^{6} +1.73603 q^{7} +1.00000 q^{8} +(2.67807 - 1.35201i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.68494 + 0.401202i) q^{3} +1.00000 q^{4} +(1.83064 + 1.28404i) q^{5} +(-1.68494 + 0.401202i) q^{6} +1.73603 q^{7} +1.00000 q^{8} +(2.67807 - 1.35201i) q^{9} +(1.83064 + 1.28404i) q^{10} -1.14414 q^{11} +(-1.68494 + 0.401202i) q^{12} +5.69546i q^{13} +1.73603 q^{14} +(-3.59969 - 1.42908i) q^{15} +1.00000 q^{16} -5.08878i q^{17} +(2.67807 - 1.35201i) q^{18} -4.40298i q^{19} +(1.83064 + 1.28404i) q^{20} +(-2.92511 + 0.696499i) q^{21} -1.14414 q^{22} +(-1.88614 + 4.40936i) q^{23} +(-1.68494 + 0.401202i) q^{24} +(1.70249 + 4.70123i) q^{25} +5.69546i q^{26} +(-3.96998 + 3.35251i) q^{27} +1.73603 q^{28} +4.89756i q^{29} +(-3.59969 - 1.42908i) q^{30} +8.30726 q^{31} +1.00000 q^{32} +(1.92781 - 0.459031i) q^{33} -5.08878i q^{34} +(3.17805 + 2.22913i) q^{35} +(2.67807 - 1.35201i) q^{36} +11.5412 q^{37} -4.40298i q^{38} +(-2.28503 - 9.59653i) q^{39} +(1.83064 + 1.28404i) q^{40} +5.25409i q^{41} +(-2.92511 + 0.696499i) q^{42} -3.19770 q^{43} -1.14414 q^{44} +(6.63862 + 0.963712i) q^{45} +(-1.88614 + 4.40936i) q^{46} -2.36731 q^{47} +(-1.68494 + 0.401202i) q^{48} -3.98620 q^{49} +(1.70249 + 4.70123i) q^{50} +(2.04163 + 8.57431i) q^{51} +5.69546i q^{52} -7.04209i q^{53} +(-3.96998 + 3.35251i) q^{54} +(-2.09451 - 1.46912i) q^{55} +1.73603 q^{56} +(1.76649 + 7.41878i) q^{57} +4.89756i q^{58} +1.33343i q^{59} +(-3.59969 - 1.42908i) q^{60} +7.49227i q^{61} +8.30726 q^{62} +(4.64921 - 2.34712i) q^{63} +1.00000 q^{64} +(-7.31319 + 10.4263i) q^{65} +(1.92781 - 0.459031i) q^{66} -15.5358 q^{67} -5.08878i q^{68} +(1.40900 - 8.18625i) q^{69} +(3.17805 + 2.22913i) q^{70} -13.2029i q^{71} +(2.67807 - 1.35201i) q^{72} -4.45169i q^{73} +11.5412 q^{74} +(-4.75474 - 7.23826i) q^{75} -4.40298i q^{76} -1.98626 q^{77} +(-2.28503 - 9.59653i) q^{78} -10.6999i q^{79} +(1.83064 + 1.28404i) q^{80} +(5.34415 - 7.24155i) q^{81} +5.25409i q^{82} -4.09978i q^{83} +(-2.92511 + 0.696499i) q^{84} +(6.53419 - 9.31573i) q^{85} -3.19770 q^{86} +(-1.96491 - 8.25211i) q^{87} -1.14414 q^{88} +2.58317 q^{89} +(6.63862 + 0.963712i) q^{90} +9.88749i q^{91} +(-1.88614 + 4.40936i) q^{92} +(-13.9973 + 3.33289i) q^{93} -2.36731 q^{94} +(5.65360 - 8.06028i) q^{95} +(-1.68494 + 0.401202i) q^{96} -4.22932 q^{97} -3.98620 q^{98} +(-3.06409 + 1.54688i) 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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