LMFDB - Embedded newform 276.2.e.a.91.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(91,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("276.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.e (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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.9
Character	$\chi$	$=$	276.91
Dual form			276.2.e.a.91.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.279557 - 1.38631i) q^{2} +1.00000i q^{3} +(-1.84370 + 0.775104i) q^{4} -1.27568i q^{5} +(1.38631 - 0.279557i) q^{6} +2.49131 q^{7} +(1.58995 + 2.33924i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.279557 - 1.38631i) q^{2} +1.00000i q^{3} +(-1.84370 + 0.775104i) q^{4} -1.27568i q^{5} +(1.38631 - 0.279557i) q^{6} +2.49131 q^{7} +(1.58995 + 2.33924i) q^{8} -1.00000 q^{9} +(-1.76848 + 0.356624i) q^{10} +5.92184 q^{11} +(-0.775104 - 1.84370i) q^{12} -2.46678 q^{13} +(-0.696464 - 3.45372i) q^{14} +1.27568 q^{15} +(2.79843 - 2.85811i) q^{16} -6.74152i q^{17} +(0.279557 + 1.38631i) q^{18} -2.53999 q^{19} +(0.988782 + 2.35196i) q^{20} +2.49131i q^{21} +(-1.65549 - 8.20949i) q^{22} +(4.75259 - 0.642542i) q^{23} +(-2.33924 + 1.58995i) q^{24} +3.37265 q^{25} +(0.689606 + 3.41972i) q^{26} -1.00000i q^{27} +(-4.59322 + 1.93103i) q^{28} +5.45110 q^{29} +(-0.356624 - 1.76848i) q^{30} +3.02410i q^{31} +(-4.74454 - 3.08047i) q^{32} +5.92184i q^{33} +(-9.34581 + 1.88464i) q^{34} -3.17811i q^{35} +(1.84370 - 0.775104i) q^{36} +4.92988i q^{37} +(0.710072 + 3.52121i) q^{38} -2.46678i q^{39} +(2.98411 - 2.02826i) q^{40} -9.26643 q^{41} +(3.45372 - 0.696464i) q^{42} -10.1120 q^{43} +(-10.9181 + 4.59004i) q^{44} +1.27568i q^{45} +(-2.21938 - 6.40893i) q^{46} +9.93569i q^{47} +(2.85811 + 2.79843i) q^{48} -0.793365 q^{49} +(-0.942849 - 4.67553i) q^{50} +6.74152 q^{51} +(4.54799 - 1.91201i) q^{52} +2.08399i q^{53} +(-1.38631 + 0.279557i) q^{54} -7.55435i q^{55} +(3.96106 + 5.82778i) q^{56} -2.53999i q^{57} +(-1.52389 - 7.55690i) q^{58} +7.43825i q^{59} +(-2.35196 + 0.988782i) q^{60} +2.14403i q^{61} +(4.19233 - 0.845409i) q^{62} -2.49131 q^{63} +(-2.94411 + 7.43856i) q^{64} +3.14681i q^{65} +(8.20949 - 1.65549i) q^{66} +3.96649 q^{67} +(5.22538 + 12.4293i) q^{68} +(0.642542 + 4.75259i) q^{69} +(-4.40583 + 0.888462i) q^{70} -12.1146i q^{71} +(-1.58995 - 2.33924i) q^{72} -4.45034 q^{73} +(6.83433 - 1.37818i) q^{74} +3.37265i q^{75} +(4.68297 - 1.96876i) q^{76} +14.7532 q^{77} +(-3.41972 + 0.689606i) q^{78} +3.65421 q^{79} +(-3.64602 - 3.56988i) q^{80} +1.00000 q^{81} +(2.59050 + 12.8461i) q^{82} -3.03863 q^{83} +(-1.93103 - 4.59322i) q^{84} -8.59999 q^{85} +(2.82688 + 14.0184i) q^{86} +5.45110i q^{87} +(9.41544 + 13.8526i) q^{88} -5.81313i q^{89} +(1.76848 - 0.356624i) q^{90} -6.14552 q^{91} +(-8.26430 + 4.86841i) q^{92} -3.02410 q^{93} +(13.7739 - 2.77759i) q^{94} +3.24020i q^{95} +(3.08047 - 4.74454i) q^{96} -4.52256i q^{97} +(0.221791 + 1.09985i) q^{98} -5.92184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9	$ 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9} + 8 q^{16} - 4 q^{18} - 4 q^{24} - 24 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} + 16 q^{41} - 32 q^{48} + 40 q^{49} - 12 q^{50} - 40 q^{52} - 4 q^{54} + 24 q^{58} - 40 q^{62} + 48 q^{64} + 16 q^{69} + 72 q^{70} - 4 q^{72} + 16 q^{77} + 24 q^{81} - 40 q^{82} - 64 q^{85} + 44 q^{92} + 16 q^{93} + 72 q^{94} + 44 q^{96} - 52 q^{98}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9 + 8 * q^16 - 4 * q^18 - 4 * q^24 - 24 * q^25 + 40 * q^26 - 32 * q^29 - 36 * q^32 + 16 * q^41 - 32 * q^48 + 40 * q^49 - 12 * q^50 - 40 * q^52 - 4 * q^54 + 24 * q^58 - 40 * q^62 + 48 * q^64 + 16 * q^69 + 72 * q^70 - 4 * q^72 + 16 * q^77 + 24 * q^81 - 40 * q^82 - 64 * q^85 + 44 * q^92 + 16 * q^93 + 72 * q^94 + 44 * q^96 - 52 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−0.279557	−	1.38631i	−0.197677	−	0.980267i
$2$	−0.279557	−	1.38631i	−0.197677	−	0.980267i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−1.84370	+	0.775104i	−0.921848	+	0.387552i
$5$		−	1.27568i		−	0.570499i	−0.958453	−	0.285250i	$-0.907923\pi$
$5$		−	1.27568i		−	0.570499i	0.958453	−	0.285250i	$-0.0920765\pi$
$6$	1.38631	−	0.279557i	0.565958	−	0.114129i
$7$	2.49131			0.941627			0.470814	−	0.882233i	$-0.343960\pi$
$7$	2.49131			0.941627			0.470814	+	0.882233i	$0.343960\pi$
$8$	1.58995	+	2.33924i	0.562133	+	0.827047i
$9$	−1.00000			−0.333333
$10$	−1.76848	+	0.356624i	−0.559242	+	0.112774i
$11$	5.92184			1.78550			0.892751	−	0.450550i	$-0.148772\pi$
$11$	5.92184			1.78550			0.892751	+	0.450550i	$0.148772\pi$
$12$	−0.775104	−	1.84370i	−0.223753	−	0.532229i
$13$	−2.46678			−0.684162			−0.342081	−	0.939670i	$-0.611132\pi$
$13$	−2.46678			−0.684162			−0.342081	+	0.939670i	$0.611132\pi$
$14$	−0.696464	−	3.45372i	−0.186138	−	0.923047i
$15$	1.27568			0.329378
$16$	2.79843	−	2.85811i	0.699607	−	0.714528i
$17$		−	6.74152i		−	1.63506i	−0.575887	−	0.817529i	$-0.695343\pi$
$17$		−	6.74152i		−	1.63506i	0.575887	−	0.817529i	$-0.304657\pi$
$18$	0.279557	+	1.38631i	0.0658923	+	0.326756i
$19$	−2.53999			−0.582714			−0.291357	−	0.956614i	$-0.594107\pi$
$19$	−2.53999			−0.582714			−0.291357	+	0.956614i	$0.594107\pi$
$20$	0.988782	+	2.35196i	0.221098	+	0.525914i
$21$			2.49131i			0.543649i
$22$	−1.65549	−	8.20949i	−0.352952	−	1.75027i
$23$	4.75259	−	0.642542i	0.990984	−	0.133979i
$23$	4.75259	−	0.642542i	0.990984	−	0.133979i
$24$	−2.33924	+	1.58995i	−0.477496	+	0.324547i
$25$	3.37265			0.674530
$26$	0.689606	+	3.41972i	0.135243	+	0.670662i
$27$		−	1.00000i		−	0.192450i
$28$	−4.59322	+	1.93103i	−0.868037	+	0.364930i
$29$	5.45110			1.01224			0.506122	−	0.862462i	$-0.331079\pi$
$29$	5.45110			1.01224			0.506122	+	0.862462i	$0.331079\pi$
$30$	−0.356624	−	1.76848i	−0.0651104	−	0.322878i
$31$			3.02410i			0.543144i	0.962418	+	0.271572i	$0.0875436\pi$
$31$			3.02410i			0.543144i	−0.962418	+	0.271572i	$0.912456\pi$
$32$	−4.74454	−	3.08047i	−0.838725	−	0.544556i
$33$			5.92184i			1.03086i
$34$	−9.34581	+	1.88464i	−1.60279	+	0.323213i
$35$		−	3.17811i		−	0.537198i
$36$	1.84370	−	0.775104i	0.307283	−	0.129184i
$37$			4.92988i			0.810468i	0.914213	+	0.405234i	$0.132810\pi$
$37$			4.92988i			0.810468i	−0.914213	+	0.405234i	$0.867190\pi$
$38$	0.710072	+	3.52121i	0.115189	+	0.571215i
$39$		−	2.46678i		−	0.395001i
$40$	2.98411	−	2.02826i	0.471830	−	0.320696i
$41$	−9.26643			−1.44717			−0.723587	−	0.690233i	$-0.757508\pi$
$41$	−9.26643			−1.44717			−0.723587	+	0.690233i	$0.757508\pi$
$42$	3.45372	−	0.696464i	0.532921	−	0.107467i
$43$	−10.1120			−1.54207			−0.771033	−	0.636795i	$-0.780260\pi$
$43$	−10.1120			−1.54207			−0.771033	+	0.636795i	$0.780260\pi$
$44$	−10.9181	+	4.59004i	−1.64596	+	0.691975i
$45$			1.27568i			0.190166i
$46$	−2.21938	−	6.40893i	−0.327230	−	0.944945i
$47$			9.93569i			1.44927i	0.689133	+	0.724635i	$0.257992\pi$
$47$			9.93569i			1.44927i	−0.689133	+	0.724635i	$0.742008\pi$
$48$	2.85811	+	2.79843i	0.412533	+	0.403918i
$49$	−0.793365			−0.113338
$50$	−0.942849	−	4.67553i	−0.133339	−	0.661220i
$51$	6.74152			0.944001
$52$	4.54799	−	1.91201i	0.630693	−	0.265148i
$53$			2.08399i			0.286258i	0.989704	+	0.143129i	$0.0457164\pi$
$53$			2.08399i			0.286258i	−0.989704	+	0.143129i	$0.954284\pi$
$54$	−1.38631	+	0.279557i	−0.188653	+	0.0380429i
$55$		−	7.55435i		−	1.01863i
$56$	3.96106	+	5.82778i	0.529319	+	0.778770i
$57$		−	2.53999i		−	0.336430i
$58$	−1.52389	−	7.55690i	−0.200097	−	0.992269i
$59$			7.43825i			0.968378i	0.874963	+	0.484189i	$0.160885\pi$
$59$			7.43825i			0.968378i	−0.874963	+	0.484189i	$0.839115\pi$
$60$	−2.35196	+	0.988782i	−0.303636	+	0.127651i
$61$			2.14403i			0.274515i	0.990535	+	0.137257i	$0.0438287\pi$
$61$			2.14403i			0.274515i	−0.990535	+	0.137257i	$0.956171\pi$
$62$	4.19233	−	0.845409i	0.532427	−	0.107367i
$63$	−2.49131			−0.313876
$64$	−2.94411	+	7.43856i	−0.368014	+	0.929820i
$65$			3.14681i			0.390314i
$66$	8.20949	−	1.65549i	1.01052	−	0.203777i
$67$	3.96649			0.484584			0.242292	−	0.970203i	$-0.422101\pi$
$67$	3.96649			0.484584			0.242292	+	0.970203i	$0.422101\pi$
$68$	5.22538	+	12.4293i	0.633670	+	1.50727i
$69$	0.642542	+	4.75259i	0.0773529	+	0.572145i
$70$	−4.40583	+	0.888462i	−0.526598	+	0.106192i
$71$		−	12.1146i		−	1.43773i	−0.695148	−	0.718867i	$-0.744661\pi$
$71$		−	12.1146i		−	1.43773i	0.695148	−	0.718867i	$-0.255339\pi$
$72$	−1.58995	−	2.33924i	−0.187378	−	0.275682i
$73$	−4.45034			−0.520873			−0.260436	−	0.965491i	$-0.583866\pi$
$73$	−4.45034			−0.520873			−0.260436	+	0.965491i	$0.583866\pi$
$74$	6.83433	−	1.37818i	0.794475	−	0.160211i
$75$			3.37265i			0.389440i
$76$	4.68297	−	1.96876i	0.537173	−	0.225832i
$77$	14.7532			1.68128
$78$	−3.41972	+	0.689606i	−0.387207	+	0.0780825i
$79$	3.65421			0.411131			0.205565	−	0.978643i	$-0.434097\pi$
$79$	3.65421			0.411131			0.205565	+	0.978643i	$0.434097\pi$
$80$	−3.64602	−	3.56988i	−0.407638	−	0.399125i
$81$	1.00000			0.111111
$82$	2.59050	+	12.8461i	0.286073	+	1.41862i
$83$	−3.03863			−0.333533			−0.166766	−	0.985996i	$-0.553333\pi$
$83$	−3.03863			−0.333533			−0.166766	+	0.985996i	$0.553333\pi$
$84$	−1.93103	−	4.59322i	−0.210692	−	0.501161i
$85$	−8.59999			−0.932800
$86$	2.82688	+	14.0184i	0.304831	+	1.51164i
$87$			5.45110i			0.584419i
$88$	9.41544	+	13.8526i	1.00369	+	1.47669i
$89$		−	5.81313i		−	0.616190i	−0.951356	−	0.308095i	$-0.900309\pi$
$89$		−	5.81313i		−	0.616190i	0.951356	−	0.308095i	$-0.0996915\pi$
$90$	1.76848	−	0.356624i	0.186414	−	0.0375915i
$91$	−6.14552			−0.644226
$92$	−8.26430	+	4.86841i	−0.861613	+	0.507566i
$93$	−3.02410			−0.313585
$94$	13.7739	−	2.77759i	1.42067	−	0.286487i
$95$			3.24020i			0.332438i
$96$	3.08047	−	4.74454i	0.314400	−	0.484238i
$97$		−	4.52256i		−	0.459197i	−0.973285	−	0.229598i	$-0.926259\pi$
$97$		−	4.52256i		−	0.459197i	0.973285	−	0.229598i	$-0.0737412\pi$
$98$	0.221791	+	1.09985i	0.0224042	+	0.111101i
$99$	−5.92184			−0.595168
$100$	−6.21814	+	2.61416i	−0.621814	+	0.261416i
$101$	−9.44751			−0.940062			−0.470031	−	0.882650i	$-0.655757\pi$
$101$	−9.44751			−0.940062			−0.470031	+	0.882650i	$0.655757\pi$
$102$	−1.88464	−	9.34581i	−0.186607	−	0.925373i
$103$	−1.68300			−0.165831			−0.0829154	−	0.996557i	$-0.526423\pi$
$103$	−1.68300			−0.165831			−0.0829154	+	0.996557i	$0.526423\pi$
$104$	−3.92206	−	5.77040i	−0.384590	−	0.565834i
$105$	3.17811			0.310151
$106$	2.88905	−	0.582594i	0.280609	−	0.0565865i
$107$	−14.4223			−1.39425			−0.697126	−	0.716949i	$-0.745538\pi$
$107$	−14.4223			−1.39425			−0.697126	+	0.716949i	$0.745538\pi$
$108$	0.775104	+	1.84370i	0.0745844	+	0.177410i
$109$			11.3390i			1.08608i	0.839707	+	0.543040i	$0.182727\pi$
$109$			11.3390i			1.08608i	−0.839707	+	0.543040i	$0.817273\pi$
$110$	−10.4726	+	2.11187i	−0.998528	+	0.201359i
$111$	−4.92988			−0.467924
$112$	6.97175	−	7.12045i	0.658769	−	0.672819i
$113$		−	17.9670i		−	1.69019i	−0.534612	−	0.845097i	$-0.679542\pi$
$113$		−	17.9670i		−	1.69019i	0.534612	−	0.845097i	$-0.320458\pi$
$114$	−3.52121	+	0.710072i	−0.329791	+	0.0665044i
$115$	−0.819675	−	6.06277i	−0.0764351	−	0.565356i
$116$	−10.0502	+	4.22517i	−0.933135	+	0.392297i
$117$	2.46678			0.228054
$118$	10.3117	−	2.07942i	0.949269	−	0.191426i
$119$		−	16.7952i		−	1.53962i
$120$	2.02826	+	2.98411i	0.185154	+	0.272411i
$121$	24.0682			2.18802
$122$	2.97228	−	0.599378i	0.269098	−	0.0542652i
$123$		−	9.26643i		−	0.835526i
$124$	−2.34399	−	5.57552i	−0.210497	−	0.500696i
$125$		−	10.6808i		−	0.955319i
$126$	0.696464	+	3.45372i	0.0620460	+	0.307682i
$127$			0.555947i			0.0493323i	0.999696	+	0.0246662i	$0.00785228\pi$
$127$			0.555947i			0.0493323i	−0.999696	+	0.0246662i	$0.992148\pi$
$128$	11.1352	+	2.00194i	0.984220	+	0.176948i
$129$		−	10.1120i		−	0.890313i
$130$	4.36245	−	0.879714i	0.382612	−	0.0771560i
$131$			0.593855i			0.0518854i	0.999663	+	0.0259427i	$0.00825874\pi$
$131$			0.593855i			0.0518854i	−0.999663	+	0.0259427i	$0.991741\pi$
$132$	−4.59004	−	10.9181i	−0.399512	−	0.950296i
$133$	−6.32791			−0.548699
$134$	−1.10886	−	5.49877i	−0.0957909	−	0.475021i
$135$	−1.27568			−0.109793
$136$	15.7700	−	10.7187i	1.35227	−	0.919119i
$137$		−	12.1761i		−	1.04027i	−0.854083	−	0.520136i	$-0.825881\pi$
$137$		−	12.1761i		−	1.04027i	0.854083	−	0.520136i	$-0.174119\pi$
$138$	6.40893	−	2.21938i	0.545564	−	0.188926i
$139$			12.5827i			1.06725i	0.845721	+	0.533626i	$0.179171\pi$
$139$			12.5827i			1.06725i	−0.845721	+	0.533626i	$0.820829\pi$
$140$	2.46336	+	5.85946i	0.208192	+	0.495215i
$141$	−9.93569			−0.836736
$142$	−16.7945	+	3.38671i	−1.40936	+	0.284206i
$143$	−14.6079			−1.22157
$144$	−2.79843	+	2.85811i	−0.233202	+	0.238176i
$145$		−	6.95383i		−	0.577485i
$146$	1.24412	+	6.16954i	0.102964	+	0.510595i
$147$		−	0.793365i		−	0.0654356i
$148$	−3.82117	−	9.08921i	−0.314099	−	0.747128i
$149$			17.4838i			1.43233i	0.697932	+	0.716164i	$0.254104\pi$
$149$			17.4838i			1.43233i	−0.697932	+	0.716164i	$0.745896\pi$
$150$	4.67553	−	0.942849i	0.381756	−	0.0769833i
$151$			22.2343i			1.80940i	0.426046	+	0.904701i	$0.359906\pi$
$151$			22.2343i			1.80940i	−0.426046	+	0.904701i	$0.640094\pi$
$152$	−4.03846	−	5.94165i	−0.327562	−	0.481932i
$153$			6.74152i			0.545019i
$154$	−4.12435	−	20.4524i	−0.332350	−	1.64810i
$155$	3.85777			0.309864
$156$	1.91201	+	4.54799i	0.153084	+	0.364131i
$157$		−	18.2974i		−	1.46029i	−0.683290	−	0.730147i	$-0.739452\pi$
$157$		−	18.2974i		−	1.46029i	0.683290	−	0.730147i	$-0.260548\pi$
$158$	−1.02156	−	5.06586i	−0.0812710	−	0.403018i
$159$	−2.08399			−0.165271
$160$	−3.92969	+	6.05250i	−0.310669	+	0.478492i
$161$	11.8402	−	1.60077i	0.933138	−	0.126158i
$162$	−0.279557	−	1.38631i	−0.0219641	−	0.108919i
$163$			2.10553i			0.164918i	0.996594	+	0.0824591i	$0.0262774\pi$
$163$			2.10553i			0.164918i	−0.996594	+	0.0824591i	$0.973723\pi$
$164$	17.0845	−	7.18245i	1.33407	−	0.560855i
$165$	7.55435			0.588105
$166$	0.849471	+	4.21247i	0.0659317	+	0.326951i
$167$			4.43024i			0.342823i	0.985200	+	0.171411i	$0.0548327\pi$
$167$			4.43024i			0.342823i	−0.985200	+	0.171411i	$0.945167\pi$
$168$	−5.82778	+	3.96106i	−0.449623	+	0.305603i
$169$	−6.91499			−0.531922
$170$	2.40419	+	11.9222i	0.184393	+	0.914393i
$171$	2.53999			0.194238
$172$	18.6435	−	7.83786i	1.42155	−	0.597631i
$173$	−5.29846			−0.402835			−0.201417	−	0.979505i	$-0.564555\pi$
$173$	−5.29846			−0.402835			−0.201417	+	0.979505i	$0.564555\pi$
$174$	7.55690	−	1.52389i	0.572887	−	0.115526i
$175$	8.40233			0.635156
$176$	16.5718	−	16.9253i	1.24915	−	1.27579i
$177$	−7.43825			−0.559093
$178$	−8.05878	+	1.62510i	−0.604031	+	0.121806i
$179$			6.37775i			0.476696i	0.971180	+	0.238348i	$0.0766058\pi$
$179$			6.37775i			0.476696i	−0.971180	+	0.238348i	$0.923394\pi$
$180$	−0.988782	−	2.35196i	−0.0736994	−	0.175305i
$181$			20.8442i			1.54934i	0.632368	+	0.774668i	$0.282083\pi$
$181$			20.8442i			1.54934i	−0.632368	+	0.774668i	$0.717917\pi$
$182$	1.71802	+	8.51958i	0.127348	+	0.631513i
$183$	−2.14403			−0.158491
$184$	9.05945	+	10.0959i	0.667872	+	0.744277i
$185$	6.28893			0.462372
$186$	0.845409	+	4.19233i	0.0619884	+	0.307397i
$187$		−	39.9222i		−	2.91940i
$188$	−7.70120	−	18.3184i	−0.561668	−	1.33601i
$189$		−	2.49131i		−	0.181216i
$190$	4.49192	−	0.905822i	0.325878	−	0.0657152i
$191$	0.120078			0.00868856			0.00434428	−	0.999991i	$-0.498617\pi$
$191$	0.120078			0.00868856			0.00434428	+	0.999991i	$0.498617\pi$
$192$	−7.43856	−	2.94411i	−0.536832	−	0.212473i
$193$	−5.99420			−0.431472			−0.215736	−	0.976452i	$-0.569215\pi$
$193$	−5.99420			−0.431472			−0.215736	+	0.976452i	$0.569215\pi$
$194$	−6.26966	+	1.26431i	−0.450135	+	0.0907725i
$195$	−3.14681			−0.225348
$196$	1.46272	−	0.614940i	0.104480	−	0.0439243i
$197$	−12.4182			−0.884761			−0.442380	−	0.896827i	$-0.645866\pi$
$197$	−12.4182			−0.884761			−0.442380	+	0.896827i	$0.645866\pi$
$198$	1.65549	+	8.20949i	0.117651	+	0.583423i
$199$	9.56523			0.678061			0.339030	−	0.940775i	$-0.389901\pi$
$199$	9.56523			0.678061			0.339030	+	0.940775i	$0.389901\pi$
$200$	5.36235	+	7.88945i	0.379175	+	0.557868i
$201$			3.96649i			0.279774i
$202$	2.64112	+	13.0971i	0.185828	+	0.921512i
$203$	13.5804			0.953157
$204$	−12.4293	+	5.22538i	−0.870225	+	0.365850i
$205$			11.8210i			0.825612i
$206$	0.470494	+	2.33315i	0.0327809	+	0.162558i
$207$	−4.75259	+	0.642542i	−0.330328	+	0.0446597i
$208$	−6.90311	+	7.05034i	−0.478644	+	0.488853i
$209$	−15.0414			−1.04044
$210$	−0.888462	−	4.40583i	−0.0613097	−	0.304031i
$211$		−	2.54447i		−	0.175169i	−0.996157	−	0.0875843i	$-0.972085\pi$
$211$		−	2.54447i		−	0.175169i	0.996157	−	0.0875843i	$-0.0279147\pi$
$212$	−1.61531	−	3.84224i	−0.110940	−	0.263886i
$213$	12.1146			0.830076
$214$	4.03184	+	19.9937i	0.275611	+	1.36674i
$215$			12.8996i			0.879748i
$216$	2.33924	−	1.58995i	0.159165	−	0.108182i
$217$			7.53398i			0.511440i
$218$	15.7193	−	3.16990i	1.06465	−	0.214693i
$219$		−	4.45034i		−	0.300726i
$220$	5.85541	+	13.9279i	0.394772	+	0.939020i
$221$			16.6298i			1.11864i
$222$	1.37818	+	6.83433i	0.0924977	+	0.458691i
$223$			8.25462i			0.552770i	0.961047	+	0.276385i	$0.0891365\pi$
$223$			8.25462i			0.552770i	−0.961047	+	0.276385i	$0.910864\pi$
$224$	−11.8201	−	7.67442i	−0.789766	−	0.512769i
$225$	−3.37265			−0.224843
$226$	−24.9078	+	5.02281i	−1.65684	+	0.334112i
$227$	10.9045			0.723755			0.361877	−	0.932226i	$-0.382136\pi$
$227$	10.9045			0.723755			0.361877	+	0.932226i	$0.382136\pi$
$228$	1.96876	+	4.68297i	0.130384	+	0.310137i
$229$			14.3196i			0.946264i	0.880992	+	0.473132i	$0.156877\pi$
$229$			14.3196i			0.946264i	−0.880992	+	0.473132i	$0.843123\pi$
$230$	−8.17571	+	2.83121i	−0.539090	+	0.186685i
$231$			14.7532i			0.970686i
$232$	8.66698	+	12.7514i	0.569015	+	0.837173i
$233$	10.5570			0.691615			0.345808	−	0.938305i	$-0.387605\pi$
$233$	10.5570			0.691615			0.345808	+	0.938305i	$0.387605\pi$
$234$	−0.689606	−	3.41972i	−0.0450810	−	0.223554i
$235$	12.6747			0.826808
$236$	−5.76542	−	13.7139i	−0.375297	−	0.892697i
$237$			3.65421i			0.237366i
$238$	−23.2833	+	4.69522i	−1.50923	+	0.304346i
$239$		−	4.84386i		−	0.313323i	−0.987652	−	0.156662i	$-0.949927\pi$
$239$		−	4.84386i		−	0.313323i	0.987652	−	0.156662i	$-0.0500732\pi$
$240$	3.56988	−	3.64602i	0.230435	−	0.235350i
$241$		−	22.0218i		−	1.41855i	−0.704933	−	0.709274i	$-0.749023\pi$
$241$		−	22.0218i		−	1.41855i	0.704933	−	0.709274i	$-0.250977\pi$
$242$	−6.72844	−	33.3659i	−0.432521	−	2.14484i
$243$			1.00000i			0.0641500i
$244$	−1.66185	−	3.95294i	−0.106389	−	0.253061i
$245$			1.01208i			0.0646592i
$246$	−12.8461	+	2.59050i	−0.819039	+	0.165164i
$247$	6.26560			0.398671
$248$	−7.07410	+	4.80817i	−0.449206	+	0.305319i
$249$		−	3.03863i		−	0.192565i
$250$	−14.8069	+	2.98589i	−0.936468	+	0.188844i
$251$	−1.49664			−0.0944669			−0.0472334	−	0.998884i	$-0.515040\pi$
$251$	−1.49664			−0.0944669			−0.0472334	+	0.998884i	$0.515040\pi$
$252$	4.59322	−	1.93103i	0.289346	−	0.121643i
$253$	28.1441	−	3.80503i	1.76940	−	0.239220i
$254$	0.770713	−	0.155419i	0.0483588	−	0.00975185i
$255$		−	8.59999i		−	0.538552i
$256$	−0.337613	−	15.9964i	−0.0211008	−	0.999777i
$257$	15.3146			0.955301			0.477650	−	0.878550i	$-0.341489\pi$
$257$	15.3146			0.955301			0.477650	+	0.878550i	$0.341489\pi$
$258$	−14.0184	+	2.82688i	−0.872744	+	0.175994i
$259$			12.2819i			0.763159i
$260$	−2.43911	−	5.80176i	−0.151267	−	0.359810i
$261$	−5.45110			−0.337415
$262$	0.823266	−	0.166016i	0.0508615	−	0.0102565i
$263$	2.19677			0.135458			0.0677292	−	0.997704i	$-0.478425\pi$
$263$	2.19677			0.135458			0.0677292	+	0.997704i	$0.478425\pi$
$264$	−13.8526	+	9.41544i	−0.852570	+	0.579480i
$265$	2.65849			0.163310
$266$	1.76901	+	8.77242i	0.108465	+	0.537872i
$267$	5.81313			0.355757
$268$	−7.31299	+	3.07444i	−0.446712	+	0.187801i
$269$	−8.15180			−0.497024			−0.248512	−	0.968629i	$-0.579942\pi$
$269$	−8.15180			−0.497024			−0.248512	+	0.968629i	$0.579942\pi$
$270$	0.356624	+	1.76848i	0.0217035	+	0.107626i
$271$		−	17.0762i		−	1.03731i	−0.854984	−	0.518654i	$-0.826433\pi$
$271$		−	17.0762i		−	1.03731i	0.854984	−	0.518654i	$-0.173567\pi$
$272$	−19.2680	−	18.8656i	−1.16829	−	1.14390i
$273$		−	6.14552i		−	0.371944i
$274$	−16.8798	+	3.40391i	−1.01975	+	0.205638i
$275$	19.9723			1.20438
$276$	−4.86841	−	8.26430i	−0.293044	−	0.497452i
$277$	13.9801			0.839982			0.419991	−	0.907528i	$-0.362033\pi$
$277$	13.9801			0.839982			0.419991	+	0.907528i	$0.362033\pi$
$278$	17.4435	−	3.51759i	1.04619	−	0.210971i
$279$		−	3.02410i		−	0.181048i
$280$	7.43436	−	5.05303i	0.444288	−	0.301976i
$281$			22.1413i			1.32084i	0.750896	+	0.660420i	$0.229622\pi$
$281$			22.1413i			1.32084i	−0.750896	+	0.660420i	$0.770378\pi$
$282$	2.77759	+	13.7739i	0.165403	+	0.820225i
$283$	−14.2647			−0.847946			−0.423973	−	0.905675i	$-0.639365\pi$
$283$	−14.2647			−0.847946			−0.423973	+	0.905675i	$0.639365\pi$
$284$	9.39004	+	22.3356i	0.557197	+	1.32537i
$285$	−3.24020			−0.191933
$286$	4.08374	+	20.2510i	0.241477	+	1.19747i
$287$	−23.0856			−1.36270
$288$	4.74454	+	3.08047i	0.279575	+	0.181519i
$289$	−28.4481			−1.67341
$290$	−9.64015	+	1.94399i	−0.566089	+	0.114155i
$291$	4.52256			0.265117
$292$	8.20507	−	3.44948i	0.480166	−	0.201865i
$293$		−	9.44315i		−	0.551675i	−0.961204	−	0.275837i	$-0.911045\pi$
$293$		−	9.44315i		−	0.551675i	0.961204	−	0.275837i	$-0.0889552\pi$
$294$	−1.09985	+	0.221791i	−0.0641444	+	0.0129351i
$295$	9.48880			0.552459
$296$	−11.5322	+	7.83827i	−0.670295	+	0.455590i
$297$		−	5.92184i		−	0.343620i
$298$	24.2379	−	4.88772i	1.40407	−	0.283138i
$299$	−11.7236	+	1.58501i	−0.677994	+	0.0916635i
$300$	−2.61416	−	6.21814i	−0.150928	−	0.359005i
$301$	−25.1922			−1.45205
$302$	30.8236	−	6.21576i	1.77370	−	0.357677i
$303$		−	9.44751i		−	0.542745i
$304$	−7.10798	+	7.25958i	−0.407670	+	0.416365i
$305$	2.73508			0.156610
$306$	9.34581	−	1.88464i	0.534265	−	0.107738i
$307$			16.9520i			0.967504i	0.875205	+	0.483752i	$0.160726\pi$
$307$			16.9520i			0.967504i	−0.875205	+	0.483752i	$0.839274\pi$
$308$	−27.2003	+	11.4352i	−1.54988	+	0.651583i
$309$		−	1.68300i		−	0.0957424i
$310$	−1.07847	−	5.34805i	−0.0612528	−	0.303749i
$311$		−	19.6873i		−	1.11636i	−0.829719	−	0.558182i	$-0.811499\pi$
$311$		−	19.6873i		−	1.11636i	0.829719	−	0.558182i	$-0.188501\pi$
$312$	5.77040	−	3.92206i	0.326685	−	0.222043i
$313$			1.61663i			0.0913772i	0.998956	+	0.0456886i	$0.0145482\pi$
$313$			1.61663i			0.0913772i	−0.998956	+	0.0456886i	$0.985452\pi$
$314$	−25.3658	+	5.11518i	−1.43148	+	0.288666i
$315$			3.17811i			0.179066i
$316$	−6.73725	+	2.83239i	−0.379000	+	0.159335i
$317$	−24.6211			−1.38286			−0.691430	−	0.722444i	$-0.743019\pi$
$317$	−24.6211			−1.38286			−0.691430	+	0.722444i	$0.743019\pi$
$318$	0.582594	+	2.88905i	0.0326703	+	0.162010i
$319$	32.2806			1.80736
$320$	9.48919	+	3.75573i	0.530462	+	0.209952i
$321$		−	14.4223i		−	0.804972i
$322$	−5.52917	−	15.9666i	−0.308129	−	0.889786i
$323$			17.1234i			0.952771i
$324$	−1.84370	+	0.775104i	−0.102428	+	0.0430613i
$325$	−8.31959			−0.461488
$326$	2.91892	−	0.588617i	0.161664	−	0.0326005i
$327$	−11.3390			−0.627048
$328$	−14.7332	−	21.6764i	−0.813503	−	1.19688i
$329$			24.7529i			1.36467i
$330$	−2.11187	−	10.4726i	−0.116255	−	0.576500i
$331$			24.9576i			1.37179i	0.727699	+	0.685896i	$0.240590\pi$
$331$			24.9576i			1.37179i	−0.727699	+	0.685896i	$0.759410\pi$
$332$	5.60231	−	2.35525i	0.307467	−	0.129261i
$333$		−	4.92988i		−	0.270156i
$334$	6.14168	−	1.23851i	0.336058	−	0.0677681i
$335$		−	5.05995i		−	0.276455i
$336$	7.12045	+	6.97175i	0.388452	+	0.380340i
$337$		−	16.3446i		−	0.890347i	−0.895444	−	0.445173i	$-0.853142\pi$
$337$		−	16.3446i		−	0.890347i	0.895444	−	0.445173i	$-0.146858\pi$
$338$	1.93314	+	9.58630i	0.105149	+	0.521426i
$339$	17.9670			0.975834
$340$	15.8558	−	6.66589i	0.859899	−	0.361508i
$341$			17.9082i			0.969786i
$342$	−0.710072	−	3.52121i	−0.0383963	−	0.190405i
$343$	−19.4157			−1.04835
$344$	−16.0776	−	23.6544i	−0.866846	−	1.27536i
$345$	6.06277	−	0.819675i	0.326408	−	0.0441298i
$346$	1.48122	+	7.34530i	0.0796311	+	0.394886i
$347$		−	18.8134i		−	1.00995i	−0.863133	−	0.504977i	$-0.831501\pi$
$347$		−	18.8134i		−	1.00995i	0.863133	−	0.504977i	$-0.168499\pi$
$348$	−4.22517	−	10.0502i	−0.226493	−	0.538746i
$349$	13.5829			0.727078			0.363539	−	0.931579i	$-0.381568\pi$
$349$	13.5829			0.727078			0.363539	+	0.931579i	$0.381568\pi$
$350$	−2.34893	−	11.6482i	−0.125556	−	0.622623i
$351$			2.46678i			0.131667i
$352$	−28.0964	−	18.2421i	−1.49754	−	0.972306i
$353$	31.5063			1.67691			0.838456	−	0.544969i	$-0.183459\pi$
$353$	31.5063			1.67691			0.838456	+	0.544969i	$0.183459\pi$
$354$	2.07942	+	10.3117i	0.110520	+	0.548061i
$355$	−15.4542			−0.820226
$356$	4.50578	+	10.7176i	0.238806	+	0.568033i
$357$	16.7952			0.888897
$358$	8.84152	−	1.78295i	0.467289	−	0.0942316i
$359$	18.4884			0.975779			0.487890	−	0.872905i	$-0.337767\pi$
$359$	18.4884			0.975779			0.487890	+	0.872905i	$0.337767\pi$
$360$	−2.98411	+	2.02826i	−0.157277	+	0.106899i
$361$	−12.5485			−0.660445
$362$	28.8965	−	5.82714i	1.51876	−	0.306268i
$363$			24.0682i			1.26325i
$364$	11.3305	−	4.76342i	0.593878	−	0.249671i
$365$			5.67719i			0.297158i
$366$	0.599378	+	2.97228i	0.0313300	+	0.155364i
$367$	3.17955			0.165971			0.0829855	−	0.996551i	$-0.473554\pi$
$367$	3.17955			0.165971			0.0829855	+	0.996551i	$0.473554\pi$
$368$	11.4633	−	15.3816i	0.597567	−	0.801819i
$369$	9.26643			0.482391
$370$	−1.75812	−	8.71839i	−0.0914001	−	0.453248i
$371$			5.19187i			0.269548i
$372$	5.57552	−	2.34399i	0.289077	−	0.121530i
$373$		−	17.7910i		−	0.921186i	−0.887612	−	0.460593i	$-0.847637\pi$
$373$		−	17.7910i		−	0.921186i	0.887612	−	0.460593i	$-0.152363\pi$
$374$	−55.3444	+	11.1605i	−2.86179	+	0.577098i
$375$	10.6808			0.551553
$376$	−23.2420	+	15.7973i	−1.19861	+	0.814682i
$377$	−13.4467			−0.692539
$378$	−3.45372	+	0.696464i	−0.177640	+	0.0358222i
$379$	13.2435			0.680273			0.340136	−	0.940376i	$-0.389527\pi$
$379$	13.2435			0.680273			0.340136	+	0.940376i	$0.389527\pi$
$380$	−2.51150	−	5.97395i	−0.128837	−	0.306457i
$381$	−0.555947			−0.0284820
$382$	−0.0335687	−	0.166465i	−0.00171753	−	0.00851711i
$383$	9.71405			0.496365			0.248182	−	0.968713i	$-0.420167\pi$
$383$	9.71405			0.496365			0.248182	+	0.968713i	$0.420167\pi$
$384$	−2.00194	+	11.1352i	−0.102161	+	0.568240i
$385$		−	18.8202i		−	0.959168i
$386$	1.67572	+	8.30980i	0.0852920	+	0.422958i
$387$	10.1120			0.514022
$388$	3.50546	+	8.33823i	0.177963	+	0.423309i
$389$			27.6072i			1.39974i	0.714271	+	0.699870i	$0.246759\pi$
$389$			27.6072i			1.39974i	−0.714271	+	0.699870i	$0.753241\pi$
$390$	0.879714	+	4.36245i	0.0445460	+	0.220901i
$391$	−4.33171	−	32.0397i	−0.219064	−	1.62032i
$392$	−1.26141	−	1.85587i	−0.0637109	−	0.0937357i
$393$	−0.593855			−0.0299560
$394$	3.47160	+	17.2155i	0.174897	+	0.867302i
$395$		−	4.66159i		−	0.234550i
$396$	10.9181	−	4.59004i	0.548654	−	0.230658i
$397$	12.2838			0.616508			0.308254	−	0.951304i	$-0.400255\pi$
$397$	12.2838			0.616508			0.308254	+	0.951304i	$0.400255\pi$
$398$	−2.67403	−	13.2603i	−0.134037	−	0.664681i
$399$		−	6.32791i		−	0.316792i
$400$	9.43812	−	9.63942i	0.471906	−	0.481971i
$401$			17.1714i			0.857499i	0.903423	+	0.428750i	$0.141046\pi$
$401$			17.1714i			0.857499i	−0.903423	+	0.428750i	$0.858954\pi$
$402$	5.49877	−	1.10886i	0.274254	−	0.0553049i
$403$		−	7.45979i		−	0.371599i
$404$	17.4183	−	7.32280i	0.866594	−	0.364323i
$405$		−	1.27568i		−	0.0633888i
$406$	−3.79650	−	18.8266i	−0.188417	−	0.934348i
$407$			29.1940i			1.44709i
$408$	10.7187	+	15.7700i	0.530654	+	0.780734i
$409$	24.7976			1.22616			0.613082	−	0.790019i	$-0.289930\pi$
$409$	24.7976			1.22616			0.613082	+	0.790019i	$0.289930\pi$
$410$	16.3875	−	3.30463i	0.809320	−	0.163204i
$411$	12.1761			0.600602
$412$	3.10294	−	1.30450i	0.152871	−	0.0642681i
$413$			18.5310i			0.911851i
$414$	2.21938	+	6.40893i	0.109077	+	0.314982i
$415$			3.87631i			0.190280i
$416$	11.7037	+	7.59885i	0.573823	+	0.372564i
$417$	−12.5827			−0.616178
$418$	4.20494	+	20.8520i	0.205670	+	1.01991i
$419$	14.3462			0.700856			0.350428	−	0.936590i	$-0.386036\pi$
$419$	14.3462			0.700856			0.350428	+	0.936590i	$0.386036\pi$
$420$	−5.85946	+	2.46336i	−0.285912	+	0.120200i
$421$		−	34.0216i		−	1.65811i	−0.559166	−	0.829056i	$-0.688879\pi$
$421$		−	34.0216i		−	1.65811i	0.559166	−	0.829056i	$-0.311121\pi$
$422$	−3.52742	+	0.711325i	−0.171712	+	0.0346267i
$423$		−	9.93569i		−	0.483090i
$424$	−4.87496	+	3.31344i	−0.236749	+	0.160915i
$425$		−	22.7368i		−	1.10290i
$426$	−3.38671	−	16.7945i	−0.164087	−	0.813696i
$427$			5.34144i			0.258491i
$428$	26.5902	−	11.1787i	1.28529	−	0.540345i
$429$		−	14.6079i		−	0.705275i
$430$	17.8829	−	3.60619i	0.862388	−	0.173906i
$431$	−24.1892			−1.16515			−0.582575	−	0.812777i	$-0.697955\pi$
$431$	−24.1892			−1.16515			−0.582575	+	0.812777i	$0.697955\pi$
$432$	−2.85811	−	2.79843i	−0.137511	−	0.134639i
$433$			26.3588i			1.26672i	0.773856	+	0.633362i	$0.218325\pi$
$433$			26.3588i			1.26672i	−0.773856	+	0.633362i	$0.781675\pi$
$434$	10.4444	−	2.10618i	0.501347	−	0.101100i
$435$	6.95383			0.333411
$436$	−8.78891	−	20.9057i	−0.420912	−	1.00120i
$437$	−12.0715	+	1.63205i	−0.577460	+	0.0780715i
$438$	−6.16954	+	1.24412i	−0.294792	+	0.0594466i
$439$			3.36175i			0.160448i	0.996777	+	0.0802238i	$0.0255635\pi$
$439$			3.36175i			0.160448i	−0.996777	+	0.0802238i	$0.974437\pi$
$440$	17.6715	−	12.0110i	0.842454	−	0.572604i
$441$	0.793365			0.0377793
$442$	23.0541	−	4.64899i	1.09657	−	0.221130i
$443$		−	24.2964i		−	1.15436i	−0.816618	−	0.577179i	$-0.804154\pi$
$443$		−	24.2964i		−	1.15436i	0.816618	−	0.577179i	$-0.195846\pi$
$444$	9.08921	−	3.82117i	0.431355	−	0.181345i
$445$	−7.41566			−0.351536
$446$	11.4434	−	2.30764i	0.541862	−	0.109270i
$447$	−17.4838			−0.826955
$448$	−7.33470	+	18.5318i	−0.346532	+	0.875544i
$449$	−2.97429			−0.140365			−0.0701826	−	0.997534i	$-0.522358\pi$
$449$	−2.97429			−0.140365			−0.0701826	+	0.997534i	$0.522358\pi$
$450$	0.942849	+	4.67553i	0.0444463	+	0.220407i
$451$	−54.8744			−2.58393
$452$	13.9263	+	33.1257i	0.655039	+	1.55810i
$453$	−22.2343			−1.04466
$454$	−3.04842	−	15.1169i	−0.143070	−	0.709473i
$455$			7.83969i			0.367530i
$456$	5.94165	−	4.03846i	0.278243	−	0.189118i
$457$		−	30.9823i		−	1.44929i	−0.689123	−	0.724644i	$-0.742004\pi$
$457$		−	30.9823i		−	1.44929i	0.689123	−	0.724644i	$-0.257996\pi$
$458$	19.8513	−	4.00314i	0.927592	−	0.187054i
$459$	−6.74152			−0.314667
$460$	6.21051	+	10.5426i	0.289566	+	0.491550i
$461$	42.5845			1.98336			0.991679	−	0.128738i	$-0.0410925\pi$
$461$	42.5845			1.98336			0.991679	+	0.128738i	$0.0410925\pi$
$462$	20.4524	−	4.12435i	0.951532	−	0.191882i
$463$		−	28.2192i		−	1.31146i	−0.754997	−	0.655728i	$-0.772362\pi$
$463$		−	28.2192i		−	1.31146i	0.754997	−	0.655728i	$-0.227638\pi$
$464$	15.2545	−	15.5799i	0.708173	−	0.723277i
$465$			3.85777i			0.178900i
$466$	−2.95130	−	14.6353i	−0.136716	−	0.677968i
$467$	16.9236			0.783130			0.391565	−	0.920150i	$-0.371934\pi$
$467$	16.9236			0.783130			0.391565	+	0.920150i	$0.371934\pi$
$468$	−4.54799	+	1.91201i	−0.210231	+	0.0883828i
$469$	9.88176			0.456297
$470$	−3.54331	−	17.5711i	−0.163441	−	0.810492i
$471$	18.2974			0.843101
$472$	−17.3999	+	11.8265i	−0.800894	+	0.544357i
$473$	−59.8817			−2.75336
$474$	5.06586	−	1.02156i	0.232683	−	0.0469218i
$475$	−8.56650			−0.393058
$476$	13.0180	+	30.9653i	0.596681	+	1.41929i
$477$		−	2.08399i		−	0.0954193i
$478$	−6.71508	+	1.35414i	−0.307141	+	0.0619368i
$479$	−25.7641			−1.17719			−0.588595	−	0.808428i	$-0.700319\pi$
$479$	−25.7641			−1.17719			−0.588595	+	0.808428i	$0.700319\pi$
$480$	−6.05250	−	3.92969i	−0.276257	−	0.179365i
$481$		−	12.1609i		−	0.554491i
$482$	−30.5290	+	6.15635i	−1.39056	+	0.280414i
$483$	1.60077	+	11.8402i	0.0728376	+	0.538747i
$484$	−44.3745	+	18.6554i	−2.01702	+	0.847972i
$485$	−5.76932			−0.261971
$486$	1.38631	−	0.279557i	0.0628842	−	0.0126810i
$487$			21.2924i			0.964850i	0.875937	+	0.482425i	$0.160244\pi$
$487$			21.2924i			0.964850i	−0.875937	+	0.482425i	$0.839756\pi$
$488$	−5.01540	+	3.40890i	−0.227037	+	0.154314i
$489$	−2.10553			−0.0952156
$490$	1.40305	−	0.282933i	0.0633833	−	0.0127816i
$491$			7.54351i			0.340434i	0.985407	+	0.170217i	$0.0544468\pi$
$491$			7.54351i			0.340434i	−0.985407	+	0.170217i	$0.945553\pi$
$492$	7.18245	+	17.0845i	0.323810	+	0.770228i
$493$		−	36.7487i		−	1.65508i
$494$	−1.75159	−	8.68605i	−0.0788079	−	0.390804i
$495$			7.55435i			0.339543i
$496$	8.64322	+	8.46272i	0.388092	+	0.379987i
$497$		−	30.1811i		−	1.35381i
$498$	−4.21247	+	0.849471i	−0.188765	+	0.0380657i
$499$		−	18.4954i		−	0.827970i	−0.910284	−	0.413985i	$-0.864137\pi$
$499$		−	18.4954i		−	0.827970i	0.910284	−	0.413985i	$-0.135863\pi$
$500$	8.27872	+	19.6921i	0.370236	+	0.880658i
$501$	−4.43024			−0.197929
$502$	0.418395	+	2.07480i	0.0186739	+	0.0926028i
$503$	−41.5195			−1.85126			−0.925632	−	0.378425i	$-0.876466\pi$
$503$	−41.5195			−1.85126			−0.925632	+	0.378425i	$0.876466\pi$
$504$	−3.96106	−	5.82778i	−0.176440	−	0.259590i
$505$			12.0520i			0.536305i
$506$	−13.1428	−	37.9527i	−0.584270	−	1.68720i
$507$		−	6.91499i		−	0.307106i
$508$	−0.430917	−	1.02500i	−0.0191188	−	0.0454769i
$509$	−0.524721			−0.0232579			−0.0116289	−	0.999932i	$-0.503702\pi$
$509$	−0.524721			−0.0232579			−0.0116289	+	0.999932i	$0.503702\pi$
$510$	−11.9222	+	2.40419i	−0.527925	+	0.106459i
$511$	−11.0872			−0.490468
$512$	−22.0816	+	4.93995i	−0.975878	+	0.218317i
$513$			2.53999i			0.112143i
$514$	−4.28131	−	21.2308i	−0.188841	−	0.936450i
$515$			2.14696i			0.0946064i
$516$	7.83786	+	18.6435i	0.345043	+	0.820733i
$517$			58.8376i			2.58767i
$518$	17.0265	−	3.43349i	0.748100	−	0.150859i
$519$		−	5.29846i		−	0.232577i
$520$	−7.36116	+	5.00328i	−0.322808	+	0.219408i
$521$			14.1174i			0.618493i	0.950982	+	0.309247i	$0.100077\pi$
$521$			14.1174i			0.618493i	−0.950982	+	0.309247i	$0.899923\pi$
$522$	1.52389	+	7.55690i	0.0666990	+	0.330756i
$523$	−26.2501			−1.14784			−0.573918	−	0.818913i	$-0.694577\pi$
$523$	−26.2501			−1.14784			−0.573918	+	0.818913i	$0.694577\pi$
$524$	−0.460300	−	1.09489i	−0.0201083	−	0.0478304i
$525$			8.40233i			0.366708i
$526$	−0.614122	−	3.04539i	−0.0267770	−	0.132786i
$527$	20.3870			0.888072
$528$	16.9253	+	16.5718i	0.736579	+	0.721197i
$529$	22.1743	−	6.10748i	0.964099	−	0.265543i
$530$	−0.743201	−	3.68549i	−0.0322826	−	0.160087i
$531$		−	7.43825i		−	0.322793i
$532$	11.6667	−	4.90479i	0.505817	−	0.212650i
$533$	22.8583			0.990101
$534$	−1.62510	−	8.05878i	−0.0703250	−	0.348737i
$535$			18.3981i			0.795420i
$536$	6.30652	+	9.27858i	0.272400	+	0.400773i
$537$	−6.37775			−0.275220
$538$	2.27889	+	11.3009i	0.0982501	+	0.487216i
$539$	−4.69818			−0.202365
$540$	2.35196	−	0.988782i	0.101212	−	0.0425504i
$541$	22.3639			0.961498			0.480749	−	0.876858i	$-0.340365\pi$
$541$	22.3639			0.961498			0.480749	+	0.876858i	$0.340365\pi$
$542$	−23.6729	+	4.77378i	−1.01684	+	0.205052i
$543$	−20.8442			−0.894510
$544$	−20.7671	+	31.9854i	−0.890381	+	1.37136i
$545$	14.4649			0.619608
$546$	−8.51958	+	1.71802i	−0.364604	+	0.0735247i
$547$		−	20.2548i		−	0.866033i	−0.901386	−	0.433017i	$-0.857449\pi$
$547$		−	20.2548i		−	0.866033i	0.901386	−	0.433017i	$-0.142551\pi$
$548$	9.43773	+	22.4490i	0.403160	+	0.958973i
$549$		−	2.14403i		−	0.0915049i
$550$	−5.58340	−	27.6878i	−0.238077	−	1.18061i
$551$	−13.8457			−0.589848
$552$	−10.0959	+	9.05945i	−0.429708	+	0.385596i
$553$	9.10378			0.387132
$554$	−3.90823	−	19.3807i	−0.166045	−	0.823407i
$555$			6.28893i			0.266950i
$556$	−9.75291	−	23.1987i	−0.413616	−	0.983843i
$557$		−	28.8162i		−	1.22098i	−0.792023	−	0.610491i	$-0.790972\pi$
$557$		−	28.8162i		−	1.22098i	0.792023	−	0.610491i	$-0.209028\pi$
$558$	−4.19233	+	0.845409i	−0.177476	+	0.0357890i
$559$	24.9441			1.05502
$560$	−9.08338	−	8.89370i	−0.383843	−	0.375827i
$561$	39.9222			1.68552
$562$	30.6947	−	6.18977i	1.29478	−	0.261100i
$563$	−20.5741			−0.867095			−0.433548	−	0.901131i	$-0.642738\pi$
$563$	−20.5741			−0.867095			−0.433548	+	0.901131i	$0.642738\pi$
$564$	18.3184	−	7.70120i	0.771343	−	0.324279i
$565$	−22.9201			−0.964255
$566$	3.98779	+	19.7752i	0.167619	+	0.831214i
$567$	2.49131			0.104625
$568$	28.3389	−	19.2616i	1.18907	−	0.808197i
$569$			33.7758i			1.41596i	0.706234	+	0.707979i	$0.250393\pi$
$569$			33.7758i			1.41596i	−0.706234	+	0.707979i	$0.749607\pi$
$570$	0.905822	+	4.49192i	0.0379407	+	0.188146i
$571$	−34.0122			−1.42337			−0.711684	−	0.702500i	$-0.752067\pi$
$571$	−34.0122			−1.42337			−0.711684	+	0.702500i	$0.752067\pi$
$572$	26.9325	−	11.3226i	1.12610	−	0.473423i
$573$			0.120078i			0.00501634i
$574$	6.45374	+	32.0037i	0.269374	+	1.33581i
$575$	16.0288	−	2.16707i	0.668449	−	0.0903730i
$576$	2.94411	−	7.43856i	0.122671	−	0.309940i
$577$	−32.4491			−1.35088			−0.675438	−	0.737417i	$-0.736045\pi$
$577$	−32.4491			−1.35088			−0.675438	+	0.737417i	$0.736045\pi$
$578$	7.95286	+	39.4377i	0.330795	+	1.64039i
$579$		−	5.99420i		−	0.249110i
$580$	5.38995	+	12.8208i	0.223805	+	0.532353i
$581$	−7.57017			−0.314064
$582$	−1.26431	−	6.26966i	−0.0524075	−	0.259886i
$583$			12.3411i			0.511114i
$584$	−7.07582	−	10.4104i	−0.292800	−	0.430787i
$585$		−	3.14681i		−	0.130105i
$586$	−13.0911	+	2.63990i	−0.540789	+	0.109053i
$587$		−	4.92756i		−	0.203382i	−0.994816	−	0.101691i	$-0.967575\pi$
$587$		−	4.92756i		−	0.203382i	0.994816	−	0.101691i	$-0.0324254\pi$
$588$	0.614940	+	1.46272i	0.0253597	+	0.0603217i
$589$		−	7.68118i		−	0.316498i
$590$	−2.65266	−	13.1544i	−0.109208	−	0.541558i
$591$		−	12.4182i		−	0.510817i
$592$	14.0902	+	13.7959i	0.579102	+	0.567009i
$593$	−19.1860			−0.787875			−0.393938	−	0.919137i	$-0.628887\pi$
$593$	−19.1860			−0.787875			−0.393938	+	0.919137i	$0.628887\pi$
$594$	−8.20949	+	1.65549i	−0.336840	+	0.0679257i
$595$	−21.4253			−0.878350
$596$	−13.5518	−	32.2348i	−0.555102	−	1.32039i
$597$			9.56523i			0.391479i
$598$	5.47473	+	15.8094i	0.223878	+	0.646495i
$599$			35.3094i			1.44270i	0.692568	+	0.721352i	$0.256479\pi$
$599$			35.3094i			1.44270i	−0.692568	+	0.721352i	$0.743521\pi$
$600$	−7.88945	+	5.36235i	−0.322085	+	0.218917i
$601$	−35.4004			−1.44401			−0.722006	−	0.691887i	$-0.756780\pi$
$601$	−35.4004			−1.44401			−0.722006	+	0.691887i	$0.756780\pi$
$602$	7.04265	+	34.9241i	0.287037	+	1.42340i
$603$	−3.96649			−0.161528
$604$	−17.2339	−	40.9933i	−0.701238	−	1.66799i
$605$		−	30.7032i		−	1.24826i
$606$	−13.0971	+	2.64112i	−0.532035	+	0.107288i
$607$			41.3927i			1.68008i	0.542525	+	0.840039i	$0.317468\pi$
$607$			41.3927i			1.68008i	−0.542525	+	0.840039i	$0.682532\pi$
$608$	12.0511	+	7.82437i	0.488736	+	0.317320i
$609$			13.5804i			0.550305i
$610$	−0.764612	−	3.79167i	−0.0309583	−	0.153520i
$611$		−	24.5092i		−	0.991535i
$612$	−5.22538	−	12.4293i	−0.211223	−	0.502425i
$613$			21.8461i			0.882354i	0.897420	+	0.441177i	$0.145439\pi$
$613$			21.8461i			0.882354i	−0.897420	+	0.441177i	$0.854561\pi$
$614$	23.5007	−	4.73906i	0.948413	−	0.191253i
$615$	−11.8210			−0.476667
$616$	23.4568	+	34.5112i	0.945101	+	1.39050i
$617$		−	23.4324i		−	0.943354i	−0.881771	−	0.471677i	$-0.843649\pi$
$617$		−	23.4324i		−	0.943354i	0.881771	−	0.471677i	$-0.156351\pi$
$618$	−2.33315	+	0.470494i	−0.0938532	+	0.0189261i
$619$	18.8898			0.759247			0.379624	−	0.925141i	$-0.376054\pi$
$619$	18.8898			0.759247			0.379624	+	0.925141i	$0.376054\pi$
$620$	−7.11255	+	2.99017i	−0.285647	+	0.120088i
$621$	−0.642542	−	4.75259i	−0.0257843	−	0.190715i
$622$	−27.2926	+	5.50372i	−1.09433	+	0.220679i
$623$		−	14.4823i		−	0.580221i
$624$	−7.05034	−	6.90311i	−0.282239	−	0.276345i
$625$	3.23804			0.129522
$626$	2.24114	−	0.451940i	0.0895741	−	0.0180631i
$627$		−	15.0414i		−	0.600696i
$628$	14.1824	+	33.7349i	0.565940	+	1.34617i
$629$	33.2349			1.32516
$630$	4.40583	−	0.888462i	0.175533	−	0.0353972i
$631$	17.4008			0.692717			0.346358	−	0.938102i	$-0.387418\pi$
$631$	17.4008			0.692717			0.346358	+	0.938102i	$0.387418\pi$
$632$	5.81001	+	8.54808i	0.231110	+	0.340024i
$633$	2.54447			0.101134
$634$	6.88301	+	34.1324i	0.273359	+	1.35557i
$635$	0.709208			0.0281441
$636$	3.84224	−	1.61531i	0.152355	−	0.0640512i
$637$	1.95706			0.0775414
$638$	−9.02426	−	44.7508i	−0.357274	−	1.77170i
$639$			12.1146i			0.479244i
$640$	2.55383	−	14.2049i	0.100949	−	0.561497i
$641$		−	7.29894i		−	0.288291i	−0.989557	−	0.144145i	$-0.953957\pi$
$641$		−	7.29894i		−	0.288291i	0.989557	−	0.144145i	$-0.0460433\pi$
$642$	−19.9937	+	4.03184i	−0.789087	+	0.159124i
$643$	6.74160			0.265863			0.132931	−	0.991125i	$-0.457561\pi$
$643$	6.74160			0.265863			0.132931	+	0.991125i	$0.457561\pi$
$644$	−20.5889	+	12.1287i	−0.811318	+	0.477938i
$645$	−12.8996			−0.507923
$646$	23.7383	−	4.78697i	0.933970	−	0.188341i
$647$		−	4.47981i		−	0.176120i	−0.996115	−	0.0880598i	$-0.971933\pi$
$647$		−	4.47981i		−	0.176120i	0.996115	−	0.0880598i	$-0.0280667\pi$
$648$	1.58995	+	2.33924i	0.0624592	+	0.0918941i
$649$			44.0482i			1.72904i
$650$	2.32580	+	11.5335i	0.0912255	+	0.452382i
$651$	−7.53398			−0.295280
$652$	−1.63201	−	3.88196i	−0.0639144	−	0.152029i
$653$	0.978338			0.0382853			0.0191427	−	0.999817i	$-0.493906\pi$
$653$	0.978338			0.0382853			0.0191427	+	0.999817i	$0.493906\pi$
$654$	3.16990	+	15.7193i	0.123953	+	0.614675i
$655$	0.757567			0.0296006
$656$	−25.9314	+	26.4845i	−1.01245	+	1.03405i
$657$	4.45034			0.173624
$658$	34.3151	−	6.91985i	1.33774	−	0.269764i
$659$	33.2279			1.29437			0.647187	−	0.762331i	$-0.275945\pi$
$659$	33.2279			1.29437			0.647187	+	0.762331i	$0.275945\pi$
$660$	−13.9279	+	5.85541i	−0.542144	+	0.227921i
$661$			10.6444i			0.414021i	0.978339	+	0.207010i	$0.0663734\pi$
$661$			10.6444i			0.414021i	−0.978339	+	0.207010i	$0.933627\pi$
$662$	34.5989	−	6.97707i	1.34472	−	0.271172i
$663$	−16.6298			−0.645850
$664$	−4.83127	−	7.10809i	−0.187490	−	0.275847i
$665$			8.07236i			0.313033i
$666$	−6.83433	+	1.37818i	−0.264825	+	0.0534036i
$667$	25.9069	−	3.50256i	1.00312	−	0.135620i
$668$	−3.43390	−	8.16802i	−0.132862	−	0.316030i
$669$	−8.25462			−0.319142
$670$	−7.01465	+	1.41455i	−0.270999	+	0.0546487i
$671$			12.6966i			0.490147i
$672$	7.67442	−	11.8201i	0.296047	−	0.455972i
$673$	15.5105			0.597885			0.298943	−	0.954271i	$-0.403366\pi$
$673$	15.5105			0.597885			0.298943	+	0.954271i	$0.403366\pi$
$674$	−22.6586	+	4.56925i	−0.872778	+	0.176001i
$675$		−	3.37265i		−	0.129813i
$676$	12.7491	−	5.35984i	0.490352	−	0.206148i
$677$			10.7034i			0.411365i	0.978619	+	0.205683i	$0.0659415\pi$
$677$			10.7034i			0.411365i	−0.978619	+	0.205683i	$0.934059\pi$
$678$	−5.02281	−	24.9078i	−0.192900	−	0.956579i
$679$		−	11.2671i		−	0.432392i
$680$	−13.6736	−	20.1175i	−0.524357	−	0.771469i
$681$			10.9045i			0.417860i
$682$	24.8263	−	5.00638i	0.950649	−	0.191704i
$683$		−	36.5249i		−	1.39759i	−0.715324	−	0.698793i	$-0.753721\pi$
$683$		−	36.5249i		−	1.39759i	0.715324	−	0.698793i	$-0.246279\pi$
$684$	−4.68297	+	1.96876i	−0.179058	+	0.0752773i
$685$	−15.5327			−0.593475
$686$	5.42780	+	26.9161i	0.207234	+	1.02766i
$687$	−14.3196			−0.546326
$688$	−28.2977	+	28.9013i	−1.07884	+	1.10185i
$689$		−	5.14075i		−	0.195847i
$690$	−2.83121	−	8.17571i	−0.107782	−	0.311244i
$691$		−	47.9613i		−	1.82453i	−0.409596	−	0.912267i	$-0.634330\pi$
$691$		−	47.9613i		−	1.82453i	0.409596	−	0.912267i	$-0.365670\pi$
$692$	9.76876	−	4.10686i	0.371352	−	0.156119i
$693$	−14.7532			−0.560426
$694$	−26.0811	+	5.25941i	−0.990025	+	0.199645i
$695$	16.0515			0.608866
$696$	−12.7514	+	8.66698i	−0.483342	+	0.328521i
$697$			62.4698i			2.36621i
$698$	−3.79721	−	18.8301i	−0.143726	−	0.712731i
$699$			10.5570i			0.399304i
$700$	−15.4913	+	6.51268i	−0.585517	+	0.246156i
$701$		−	35.8504i		−	1.35405i	−0.735960	−	0.677025i	$-0.763269\pi$
$701$		−	35.8504i		−	1.35405i	0.735960	−	0.677025i	$-0.236731\pi$
$702$	3.41972	−	0.689606i	0.129069	−	0.0260275i
$703$		−	12.5219i		−	0.472271i
$704$	−17.4346	+	44.0500i	−0.657090	+	1.66020i
$705$			12.6747i			0.477358i
$706$	−8.80782	−	43.6774i	−0.331486	−	1.64382i
$707$	−23.5367			−0.885188
$708$	13.7139	−	5.76542i	0.515399	−	0.216678i
$709$		−	18.1038i		−	0.679902i	−0.940443	−	0.339951i	$-0.889590\pi$
$709$		−	18.1038i		−	0.679902i	0.940443	−	0.339951i	$-0.110410\pi$
$710$	4.32034	+	21.4243i	0.162140	+	0.804041i
$711$	−3.65421			−0.137044
$712$	13.5983	−	9.24258i	0.509618	−	0.346380i
$713$	1.94311	+	14.3723i	0.0727700	+	0.538247i
$714$	−4.69522	−	23.2833i	−0.175714	−	0.871357i
$715$			18.6349i			0.696907i
$716$	−4.94342	−	11.7586i	−0.184744	−	0.439441i
$717$	4.84386			0.180897
$718$	−5.16856	−	25.6306i	−0.192889	−	0.956525i
$719$		−	4.13110i		−	0.154064i	−0.997029	−	0.0770319i	$-0.975456\pi$
$719$		−	4.13110i		−	0.154064i	0.997029	−	0.0770319i	$-0.0245443\pi$
$720$	3.64602	+	3.56988i	0.135879	+	0.133042i
$721$	−4.19287			−0.156151
$722$	3.50801	+	17.3960i	0.130555	+	0.647412i
$723$	22.0218			0.818999
$724$	−16.1564	−	38.4303i	−0.600449	−	1.42825i
$725$	18.3847			0.682789
$726$	33.3659	−	6.72844i	1.23833	−	0.249716i
$727$	47.9031			1.77663			0.888314	−	0.459237i	$-0.151877\pi$
$727$	47.9031			1.77663			0.888314	+	0.459237i	$0.151877\pi$
$728$	−9.77108	−	14.3759i	−0.362140	−	0.532805i
$729$	−1.00000			−0.0370370
$730$	7.87033	−	1.58710i	0.291294	−	0.0587412i
$731$			68.1703i			2.52137i
$732$	3.95294	−	1.66185i	0.146105	−	0.0614236i
$733$			15.5853i			0.575657i	0.957682	+	0.287829i	$0.0929334\pi$
$733$			15.5853i			0.575657i	−0.957682	+	0.287829i	$0.907067\pi$
$734$	−0.888865	−	4.40783i	−0.0328086	−	0.162696i
$735$	−1.01208			−0.0373310
$736$	−24.5282	−	11.5917i	−0.904122	−	0.427275i
$737$	23.4889			0.865225
$738$	−2.59050	−	12.8461i	−0.0953575	−	0.472872i
$739$		−	1.51685i		−	0.0557982i	−0.999611	−	0.0278991i	$-0.991118\pi$
$739$		−	1.51685i		−	0.0557982i	0.999611	−	0.0278991i	$-0.00888172\pi$
$740$	−11.5949	+	4.87458i	−0.426236	+	0.179193i
$741$			6.26560i			0.230173i
$742$	7.19752	−	1.45142i	0.264229	−	0.0532834i
$743$	−13.3402			−0.489406			−0.244703	−	0.969598i	$-0.578690\pi$
$743$	−13.3402			−0.489406			−0.244703	+	0.969598i	$0.578690\pi$
$744$	−4.80817	−	7.07410i	−0.176276	−	0.259349i
$745$	22.3037			0.817143
$746$	−24.6639	+	4.97362i	−0.903008	+	0.182097i
$747$	3.03863			0.111178
$748$	30.9439	+	73.6044i	1.13142	+	2.69124i
$749$	−35.9303			−1.31287
$750$	−2.98589	−	14.8069i	−0.109029	−	0.540670i
$751$	2.46508			0.0899519			0.0449760	−	0.998988i	$-0.485679\pi$
$751$	2.46508			0.0899519			0.0449760	+	0.998988i	$0.485679\pi$
$752$	28.3973	+	27.8043i	1.03554	+	1.01392i
$753$		−	1.49664i		−	0.0545405i
$754$	3.75911	+	18.6412i	0.136899	+	0.678873i
$755$	28.3638			1.03226
$756$	1.93103	+	4.59322i	0.0702308	+	0.167054i
$757$			4.61509i			0.167738i	0.996477	+	0.0838692i	$0.0267278\pi$
$757$			4.61509i			0.167738i	−0.996477	+	0.0838692i	$0.973272\pi$
$758$	−3.70231	−	18.3596i	−0.134474	−	0.666849i
$759$	3.80503	+	28.1441i	0.138114	+	1.02157i
$760$	−7.57962	+	5.15176i	−0.274942	+	0.186874i
$761$	−35.9097			−1.30172			−0.650862	−	0.759196i	$-0.725592\pi$
$761$	−35.9097			−1.30172			−0.650862	+	0.759196i	$0.725592\pi$
$762$	0.155419	+	0.770713i	0.00563023	+	0.0279200i
$763$			28.2490i			1.02268i
$764$	−0.221388	+	0.0930732i	−0.00800953	+	0.00336727i
$765$	8.59999			0.310933
$766$	−2.71563	−	13.4667i	−0.0981198	−	0.486570i
$767$		−	18.3485i		−	0.662527i
$768$	15.9964	−	0.337613i	0.577222	−	0.0121826i
$769$			22.0207i			0.794087i	0.917800	+	0.397044i	$0.129964\pi$
$769$			22.0207i			0.794087i	−0.917800	+	0.397044i	$0.870036\pi$
$770$	−26.0906	+	5.26133i	−0.940241	+	0.189605i
$771$			15.3146i			0.551543i
$772$	11.0515	−	4.64613i	0.397751	−	0.167218i
$773$		−	26.2098i		−	0.942700i	−0.881946	−	0.471350i	$-0.843767\pi$
$773$		−	26.2098i		−	0.942700i	0.881946	−	0.471350i	$-0.156233\pi$
$774$	−2.82688	−	14.0184i	−0.101610	−	0.503879i
$775$			10.1992i			0.366367i
$776$	10.5794	−	7.19065i	0.379777	−	0.258129i
$777$	−12.2819			−0.440610
$778$	38.2720	−	7.71778i	1.37212	−	0.276696i
$779$	23.5366			0.843288
$780$	5.80176	−	2.43911i	0.207736	−	0.0873341i
$781$		−	71.7405i		−	2.56708i
$782$	−43.2059	+	14.9620i	−1.54504	+	0.535040i
$783$		−	5.45110i		−	0.194806i
$784$	−2.22017	+	2.26753i	−0.0792919	+	0.0809830i
$785$	−23.3416			−0.833097
$786$	0.166016	+	0.823266i	0.00592161	+	0.0293649i
$787$	−30.7607			−1.09650			−0.548250	−	0.836315i	$-0.684706\pi$
$787$	−30.7607			−1.09650			−0.548250	+	0.836315i	$0.684706\pi$
$788$	22.8954	−	9.62541i	0.815615	−	0.342891i
$789$			2.19677i			0.0782070i
$790$	−6.46239	+	1.30318i	−0.229922	+	0.0463650i
$791$		−	44.7614i		−	1.59153i
$792$	−9.41544	−	13.8526i	−0.334563	−	0.492232i
$793$		−	5.28885i		−	0.187813i
$794$	−3.43403	−	17.0292i	−0.121869	−	0.604343i
$795$			2.65849i			0.0942871i
$796$	−17.6354	+	7.41405i	−0.625069	+	0.262784i
$797$		−	54.7924i		−	1.94085i	−0.241408	−	0.970424i	$-0.577609\pi$
$797$		−	54.7924i		−	1.94085i	0.241408	−	0.970424i	$-0.422391\pi$
$798$	−8.77242	+	1.76901i	−0.310540	+	0.0626223i
$799$	66.9816			2.36964
$800$	−16.0017	−	10.3894i	−0.565745	−	0.367320i
$801$			5.81313i			0.205397i
$802$	23.8048	−	4.80039i	0.840578	−	0.169508i
$803$	−26.3542			−0.930020
$804$	−3.07444	−	7.31299i	−0.108427	−	0.257909i
$805$	−2.04207	−	15.1042i	−0.0719734	−	0.532355i
$806$	−10.3416	+	2.08544i	−0.364266	+	0.0734564i
$807$		−	8.15180i		−	0.286957i
$808$	−15.0211	−	22.1000i	−0.528440	−	0.777476i
$809$	42.9727			1.51084			0.755421	−	0.655240i	$-0.227433\pi$
$809$	42.9727			1.51084			0.755421	+	0.655240i	$0.227433\pi$
$810$	−1.76848	+	0.356624i	−0.0621380	+	0.0125305i
$811$			1.35261i			0.0474966i	0.999718	+	0.0237483i	$0.00756003\pi$
$811$			1.35261i			0.0474966i	−0.999718	+	0.0237483i	$0.992440\pi$
$812$	−25.0381	+	10.5262i	−0.878665	+	0.369398i
$813$	17.0762			0.598890
$814$	40.4719	−	8.16139i	1.41854	−	0.286057i
$815$	2.68598			0.0940857
$816$	18.8656	−	19.2680i	0.660430	−	0.674515i
$817$	25.6844			0.898583
$818$	−6.93235	−	34.3771i	−0.242384	−	1.20197i
$819$	6.14552			0.214742
$820$	−9.16248	−	21.7943i	−0.319968	−	0.761088i
$821$	−8.46867			−0.295559			−0.147779	−	0.989020i	$-0.547213\pi$
$821$	−8.46867			−0.295559			−0.147779	+	0.989020i	$0.547213\pi$
$822$	−3.40391	−	16.8798i	−0.118725	−	0.588750i
$823$		−	28.1188i		−	0.980160i	−0.871677	−	0.490080i	$-0.836967\pi$
$823$		−	28.1188i		−	0.980160i	0.871677	−	0.490080i	$-0.163033\pi$
$824$	−2.67588	−	3.93694i	−0.0932189	−	0.137150i
$825$			19.9723i			0.695347i
$826$	25.6897	−	5.18047i	0.893858	−	0.180252i
$827$	9.58345			0.333249			0.166625	−	0.986020i	$-0.446713\pi$
$827$	9.58345			0.333249			0.166625	+	0.986020i	$0.446713\pi$
$828$	8.26430	−	4.86841i	0.287204	−	0.169189i
$829$	−16.3484			−0.567803			−0.283902	−	0.958853i	$-0.591629\pi$
$829$	−16.3484			−0.567803			−0.283902	+	0.958853i	$0.591629\pi$
$830$	5.37375	−	1.08365i	0.186526	−	0.0376140i
$831$			13.9801i			0.484964i
$832$	7.26248	−	18.3493i	0.251781	−	0.636148i
$833$			5.34848i			0.185314i
$834$	3.51759	+	17.4435i	0.121804	+	0.604019i
$835$	5.65155			0.195580
$836$	27.7318	−	11.6587i	0.959124	−	0.403223i
$837$	3.02410			0.104528
$838$	−4.01057	−	19.8882i	−0.138543	−	0.687026i
$839$	46.3381			1.59977			0.799884	−	0.600155i	$-0.204894\pi$
$839$	46.3381			1.59977			0.799884	+	0.600155i	$0.204894\pi$
$840$	5.05303	+	7.43436i	0.174346	+	0.256510i
$841$	0.714489			0.0246376
$842$	−47.1644	+	9.51098i	−1.62539	+	0.327770i
$843$	−22.1413			−0.762588
$844$	1.97223	+	4.69123i	0.0678869	+	0.161479i
$845$			8.82129i			0.303461i
$846$	−13.7739	+	2.77759i	−0.473557	+	0.0954956i
$847$	59.9614			2.06030
$848$	5.95628	+	5.83189i	0.204539	+	0.200268i
$849$		−	14.2647i		−	0.489562i
$850$	−31.5202	+	6.35623i	−1.08113	+	0.218017i
$851$	3.16766	+	23.4297i	0.108586	+	0.803161i
$852$	−22.3356	+	9.39004i	−0.765204	+	0.321698i
$853$	−22.0557			−0.755173			−0.377587	−	0.925974i	$-0.623246\pi$
$853$	−22.0557			−0.755173			−0.377587	+	0.925974i	$0.623246\pi$
$854$	7.40488	−	1.49324i	0.253390	−	0.0510976i
$855$		−	3.24020i		−	0.110813i
$856$	−22.9307	−	33.7371i	−0.783754	−	1.15311i
$857$	44.6464			1.52509			0.762546	−	0.646935i	$-0.223949\pi$
$857$	44.6464			1.52509			0.762546	+	0.646935i	$0.223949\pi$
$858$	−20.2510	+	4.08374i	−0.691358	+	0.139417i
$859$			28.3561i			0.967496i	0.875207	+	0.483748i	$0.160725\pi$
$859$			28.3561i			0.967496i	−0.875207	+	0.483748i	$0.839275\pi$
$860$	−9.99857	−	23.7830i	−0.340948	−	0.810994i
$861$		−	23.0856i		−	0.786754i
$862$	6.76225	+	33.5336i	0.230323	+	1.14216i
$863$			48.0292i			1.63493i	0.575975	+	0.817467i	$0.304623\pi$
$863$			48.0292i			1.63493i	−0.575975	+	0.817467i	$0.695377\pi$
$864$	−3.08047	+	4.74454i	−0.104800	+	0.161413i
$865$			6.75912i			0.229817i
$866$	36.5414	−	7.36879i	1.24173	−	0.250402i
$867$		−	28.4481i		−	0.966146i
$868$	−5.83962	−	13.8904i	−0.198209	−	0.471469i
$869$	21.6397			0.734075
$870$	−1.94399	−	9.64015i	−0.0659076	−	0.326832i
$871$	−9.78445			−0.331534
$872$	−26.5247	+	18.0285i	−0.898239	+	0.610521i
$873$			4.52256i			0.153066i
$874$	5.63721	+	16.2786i	0.190681	+	0.550632i
$875$		−	26.6092i		−	0.899554i
$876$	3.44948	+	8.20507i	0.116547	+	0.277224i
$877$	−36.8661			−1.24488			−0.622440	−	0.782668i	$-0.713858\pi$
$877$	−36.8661			−1.24488			−0.622440	+	0.782668i	$0.713858\pi$
$878$	4.66042	−	0.939801i	0.157281	−	0.0317167i
$879$	9.44315			0.318510
$880$	−21.5912	−	21.1403i	−0.727839	−	0.712639i
$881$		−	39.9739i		−	1.34675i	−0.739299	−	0.673377i	$-0.764843\pi$
$881$		−	39.9739i		−	1.34675i	0.739299	−	0.673377i	$-0.235157\pi$
$882$	−0.221791	−	1.09985i	−0.00746808	−	0.0370338i
$883$			27.9445i			0.940406i	0.882558	+	0.470203i	$0.155819\pi$
$883$			27.9445i			0.940406i	−0.882558	+	0.470203i	$0.844181\pi$
$884$	−12.8899	−	30.6604i	−0.433533	−	1.03122i
$885$			9.48880i			0.318962i
$886$	−33.6823	+	6.79223i	−1.13158	+	0.228190i
$887$		−	20.8547i		−	0.700233i	−0.936706	−	0.350117i	$-0.886142\pi$
$887$		−	20.8547i		−	0.700233i	0.936706	−	0.350117i	$-0.113858\pi$
$888$	−7.83827	−	11.5322i	−0.263035	−	0.386995i
$889$			1.38504i			0.0464526i
$890$	2.07310	+	10.2804i	0.0694905	+	0.344599i
$891$	5.92184			0.198389
$892$	−6.39819	−	15.2190i	−0.214227	−	0.509570i
$893$		−	25.2366i		−	0.844509i
$894$	4.88772	+	24.2379i	0.163470	+	0.810637i
$895$	8.13594			0.271955
$896$	27.7412	+	4.98746i	0.926769	+	0.166619i
$897$	−1.58501	−	11.7236i	−0.0529219	−	0.391440i
$898$	0.831483	+	4.12327i	0.0277469	+	0.137595i
$899$			16.4847i			0.549794i
$900$	6.21814	−	2.61416i	0.207271	−	0.0871386i
$901$	14.0492			0.468048
$902$	15.3405	+	76.0727i	0.510783	+	2.53294i
$903$		−	25.1922i		−	0.838343i
$904$	42.0292	−	28.5667i	1.39787	−	0.950114i
$905$	26.5904			0.883896
$906$	6.21576	+	30.8236i	0.206505	+	1.02405i
$907$	12.8699			0.427337			0.213669	−	0.976906i	$-0.431459\pi$
$907$	12.8699			0.427337			0.213669	+	0.976906i	$0.431459\pi$
$908$	−20.1045	+	8.45210i	−0.667192	+	0.280493i
$909$	9.44751			0.313354
$910$	10.8682	−	2.19164i	0.360278	−	0.0726522i
$911$	−12.5529			−0.415896			−0.207948	−	0.978140i	$-0.566678\pi$
$911$	−12.5529			−0.415896			−0.207948	+	0.978140i	$0.566678\pi$
$912$	−7.25958	−	7.10798i	−0.240389	−	0.235369i
$913$	−17.9943			−0.595524
$914$	−42.9509	+	8.66131i	−1.42069	+	0.286491i
$915$			2.73508i			0.0904191i
$916$	−11.0992	−	26.4009i	−0.366727	−	0.872311i
$917$			1.47948i			0.0488567i
$918$	1.88464	+	9.34581i	0.0622024	+	0.308458i
$919$	−25.9215			−0.855070			−0.427535	−	0.903999i	$-0.640618\pi$
$919$	−25.9215			−0.855070			−0.427535	+	0.903999i	$0.640618\pi$
$920$	12.8790	−	11.5569i	0.424609	−	0.381020i
$921$	−16.9520			−0.558589
$922$	−11.9048	−	59.0352i	−0.392064	−	1.94422i
$923$			29.8840i			0.983643i
$924$	−11.4352	−	27.2003i	−0.376192	−	0.894825i
$925$			16.6268i			0.546685i
$926$	−39.1204	+	7.88887i	−1.28558	+	0.259244i
$927$	1.68300			0.0552769
$928$	−25.8630	−	16.7920i	−0.848994	−	0.551223i
$929$	−40.8765			−1.34111			−0.670557	−	0.741858i	$-0.733945\pi$
$929$	−40.8765			−1.34111			−0.670557	+	0.741858i	$0.733945\pi$
$930$	5.34805	−	1.07847i	0.175370	−	0.0353643i
$931$	2.01514			0.0660435
$932$	−19.4640	+	8.18281i	−0.637564	+	0.268037i
$933$	19.6873			0.644533
$934$	−4.73111	−	23.4613i	−0.154807	−	0.767676i
$935$	−50.9278			−1.66552
$936$	3.92206	+	5.77040i	0.128197	+	0.188611i
$937$		−	14.6250i		−	0.477778i	−0.971047	−	0.238889i	$-0.923217\pi$
$937$		−	14.6250i		−	0.477778i	0.971047	−	0.238889i	$-0.0767832\pi$
$938$	−2.76252	−	13.6992i	−0.0901993	−	0.447293i
$939$	−1.61663			−0.0527566
$940$	−23.3683	+	9.82423i	−0.762191	+	0.320431i
$941$		−	6.12552i		−	0.199686i	−0.995003	−	0.0998431i	$-0.968166\pi$
$941$		−	6.12552i		−	0.199686i	0.995003	−	0.0998431i	$-0.0318341\pi$
$942$	−5.11518	−	25.3658i	−0.166661	−	0.826464i
$943$	−44.0396	+	5.95407i	−1.43413	+	0.193891i
$944$	21.2594	+	20.8154i	0.691933	+	0.677484i
$945$	−3.17811			−0.103384
$946$	16.7404	+	83.0145i	0.544276	+	2.69903i
$947$			6.15274i			0.199937i	0.994991	+	0.0999686i	$0.0318742\pi$
$947$			6.15274i			0.199937i	−0.994991	+	0.0999686i	$0.968126\pi$
$948$	−2.83239	−	6.73725i	−0.0919918	−	0.218816i
$949$	10.9780			0.356361
$950$	2.39483	+	11.8758i	0.0776984	+	0.385302i
$951$		−	24.6211i		−	0.798394i
$952$	39.2881	−	26.7036i	1.27333	−	0.865468i
$953$			10.5440i			0.341552i	0.985310	+	0.170776i	$0.0546275\pi$
$953$			10.5440i			0.341552i	−0.985310	+	0.170776i	$0.945373\pi$
$954$	−2.88905	+	0.582594i	−0.0935364	+	0.0188622i
$955$		−	0.153181i		−	0.00495682i
$956$	3.75450	+	8.93061i	0.121429	+	0.288837i
$957$			32.2806i			1.04348i
$958$	7.20253	+	35.7169i	0.232703	+	1.15396i
$959$		−	30.3344i		−	0.979549i
$960$	−3.75573	+	9.48919i	−0.121216	+	0.306262i
$961$	21.8548			0.704994
$962$	−16.8588	+	3.39968i	−0.543550	+	0.109610i
$963$	14.4223			0.464751
$964$	17.0692	+	40.6015i	0.549761	+	1.30769i
$965$			7.64665i			0.246154i
$966$	15.9666	−	5.52917i	0.513718	−	0.177898i
$967$		−	13.7270i		−	0.441430i	−0.975338	−	0.220715i	$-0.929161\pi$
$967$		−	13.7270i		−	0.441430i	0.975338	−	0.220715i	$-0.0708391\pi$
$968$	38.2673	+	56.3014i	1.22996	+	1.80960i
$969$	−17.1234			−0.550082
$970$	1.61286	+	7.99805i	0.0517857	+	0.256802i
$971$	4.43428			0.142303			0.0711514	−	0.997466i	$-0.477333\pi$
$971$	4.43428			0.142303			0.0711514	+	0.997466i	$0.477333\pi$
$972$	−0.775104	−	1.84370i	−0.0248615	−	0.0591366i
$973$			31.3475i			1.00495i
$974$	29.5178	−	5.95244i	0.945811	−	0.190728i
$975$		−	8.31959i		−	0.266440i
$976$	6.12787	+	5.99991i	0.196148	+	0.192052i
$977$			7.21336i			0.230776i	0.993321	+	0.115388i	$0.0368111\pi$
$977$			7.21336i			0.230776i	−0.993321	+	0.115388i	$0.963189\pi$
$978$	0.588617	+	2.91892i	0.0188219	+	0.0933367i
$979$		−	34.4244i		−	1.10021i
$980$	−0.784464	−	1.86596i	−0.0250588	−	0.0596059i
$981$		−	11.3390i		−	0.362027i
$982$	10.4576	−	2.10884i	0.333716	−	0.0672959i
$983$	51.7339			1.65006			0.825028	−	0.565092i	$-0.191159\pi$
$983$	51.7339			1.65006			0.825028	+	0.565092i	$0.191159\pi$
$984$	21.6764	−	14.7332i	0.691020	−	0.469676i
$985$			15.8416i			0.504756i
$986$	−50.9450	+	10.2734i	−1.62242	+	0.327170i
$987$	−24.7529			−0.787894
$988$	−11.5519	+	4.85649i	−0.367514	+	0.154506i
$989$	−48.0583	+	6.49739i	−1.52816	+	0.206605i
$990$	10.4726	−	2.11187i	0.332843	−	0.0671197i
$991$			5.11827i			0.162587i	0.996690	+	0.0812936i	$0.0259051\pi$
$991$			5.11827i			0.162587i	−0.996690	+	0.0812936i	$0.974095\pi$
$992$	9.31566	−	14.3480i	0.295772	−	0.455548i
$993$	−24.9576			−0.792005
$994$	−41.8403	+	8.43735i	−1.32709	+	0.267617i
$995$		−	12.2021i		−	0.386833i
$996$	2.35525	+	5.60231i	0.0746291	+	0.177516i
$997$	30.9514			0.980242			0.490121	−	0.871654i	$-0.336953\pi$
$997$	30.9514			0.980242			0.490121	+	0.871654i	$0.336953\pi$
$998$	−25.6404	+	5.17053i	−0.811632	+	0.163670i
$999$	4.92988			0.155975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.e.a.91.9	✓	24
3.2	odd	2		828.2.e.f.91.16		24
4.3	odd	2	inner	276.2.e.a.91.11	yes	24
8.3	odd	2		4416.2.i.d.1471.11		24
8.5	even	2		4416.2.i.d.1471.10		24
12.11	even	2		828.2.e.f.91.14		24
23.22	odd	2	inner	276.2.e.a.91.10	yes	24
69.68	even	2		828.2.e.f.91.15		24
92.91	even	2	inner	276.2.e.a.91.12	yes	24
184.45	odd	2		4416.2.i.d.1471.9		24
184.91	even	2		4416.2.i.d.1471.12		24
276.275	odd	2		828.2.e.f.91.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.e.a.91.9	✓	24	1.1	even	1	trivial
276.2.e.a.91.10	yes	24	23.22	odd	2	inner
276.2.e.a.91.11	yes	24	4.3	odd	2	inner
276.2.e.a.91.12	yes	24	92.91	even	2	inner
828.2.e.f.91.13		24	276.275	odd	2
828.2.e.f.91.14		24	12.11	even	2
828.2.e.f.91.15		24	69.68	even	2
828.2.e.f.91.16		24	3.2	odd	2
4416.2.i.d.1471.9		24	184.45	odd	2
4416.2.i.d.1471.10		24	8.5	even	2
4416.2.i.d.1471.11		24	8.3	odd	2
4416.2.i.d.1471.12		24	184.91	even	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.279557 - 1.38631i) q^{2} +1.00000i q^{3} +(-1.84370 + 0.775104i) q^{4} -1.27568i q^{5} +(1.38631 - 0.279557i) q^{6} +2.49131 q^{7} +(1.58995 + 2.33924i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.279557 - 1.38631i) q^{2} +1.00000i q^{3} +(-1.84370 + 0.775104i) q^{4} -1.27568i q^{5} +(1.38631 - 0.279557i) q^{6} +2.49131 q^{7} +(1.58995 + 2.33924i) q^{8} -1.00000 q^{9} +(-1.76848 + 0.356624i) q^{10} +5.92184 q^{11} +(-0.775104 - 1.84370i) q^{12} -2.46678 q^{13} +(-0.696464 - 3.45372i) q^{14} +1.27568 q^{15} +(2.79843 - 2.85811i) q^{16} -6.74152i q^{17} +(0.279557 + 1.38631i) q^{18} -2.53999 q^{19} +(0.988782 + 2.35196i) q^{20} +2.49131i q^{21} +(-1.65549 - 8.20949i) q^{22} +(4.75259 - 0.642542i) q^{23} +(-2.33924 + 1.58995i) q^{24} +3.37265 q^{25} +(0.689606 + 3.41972i) q^{26} -1.00000i q^{27} +(-4.59322 + 1.93103i) q^{28} +5.45110 q^{29} +(-0.356624 - 1.76848i) q^{30} +3.02410i q^{31} +(-4.74454 - 3.08047i) q^{32} +5.92184i q^{33} +(-9.34581 + 1.88464i) q^{34} -3.17811i q^{35} +(1.84370 - 0.775104i) q^{36} +4.92988i q^{37} +(0.710072 + 3.52121i) q^{38} -2.46678i q^{39} +(2.98411 - 2.02826i) q^{40} -9.26643 q^{41} +(3.45372 - 0.696464i) q^{42} -10.1120 q^{43} +(-10.9181 + 4.59004i) q^{44} +1.27568i q^{45} +(-2.21938 - 6.40893i) q^{46} +9.93569i q^{47} +(2.85811 + 2.79843i) q^{48} -0.793365 q^{49} +(-0.942849 - 4.67553i) q^{50} +6.74152 q^{51} +(4.54799 - 1.91201i) q^{52} +2.08399i q^{53} +(-1.38631 + 0.279557i) q^{54} -7.55435i q^{55} +(3.96106 + 5.82778i) q^{56} -2.53999i q^{57} +(-1.52389 - 7.55690i) q^{58} +7.43825i q^{59} +(-2.35196 + 0.988782i) q^{60} +2.14403i q^{61} +(4.19233 - 0.845409i) q^{62} -2.49131 q^{63} +(-2.94411 + 7.43856i) q^{64} +3.14681i q^{65} +(8.20949 - 1.65549i) q^{66} +3.96649 q^{67} +(5.22538 + 12.4293i) q^{68} +(0.642542 + 4.75259i) q^{69} +(-4.40583 + 0.888462i) q^{70} -12.1146i q^{71} +(-1.58995 - 2.33924i) q^{72} -4.45034 q^{73} +(6.83433 - 1.37818i) q^{74} +3.37265i q^{75} +(4.68297 - 1.96876i) q^{76} +14.7532 q^{77} +(-3.41972 + 0.689606i) q^{78} +3.65421 q^{79} +(-3.64602 - 3.56988i) q^{80} +1.00000 q^{81} +(2.59050 + 12.8461i) q^{82} -3.03863 q^{83} +(-1.93103 - 4.59322i) q^{84} -8.59999 q^{85} +(2.82688 + 14.0184i) q^{86} +5.45110i q^{87} +(9.41544 + 13.8526i) q^{88} -5.81313i q^{89} +(1.76848 - 0.356624i) q^{90} -6.14552 q^{91} +(-8.26430 + 4.86841i) q^{92} -3.02410 q^{93} +(13.7739 - 2.77759i) q^{94} +3.24020i q^{95} +(3.08047 - 4.74454i) q^{96} -4.52256i q^{97} +(0.221791 + 1.09985i) q^{98} -5.92184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9	\( 24 q + 4 q^{2} + 4 q^{6} + 4 q^{8} - 24 q^{9} + 8 q^{16} - 4 q^{18} - 4 q^{24} - 24 q^{25} + 40 q^{26} - 32 q^{29} - 36 q^{32} + 16 q^{41} - 32 q^{48} + 40 q^{49} - 12 q^{50} - 40 q^{52} - 4 q^{54} + 24 q^{58} - 40 q^{62} + 48 q^{64} + 16 q^{69} + 72 q^{70} - 4 q^{72} + 16 q^{77} + 24 q^{81} - 40 q^{82} - 64 q^{85} + 44 q^{92} + 16 q^{93} + 72 q^{94} + 44 q^{96} - 52 q^{98}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^6 + 4 * q^8 - 24 * q^9 + 8 * q^16 - 4 * q^18 - 4 * q^24 - 24 * q^25 + 40 * q^26 - 32 * q^29 - 36 * q^32 + 16 * q^41 - 32 * q^48 + 40 * q^49 - 12 * q^50 - 40 * q^52 - 4 * q^54 + 24 * q^58 - 40 * q^62 + 48 * q^64 + 16 * q^69 + 72 * q^70 - 4 * q^72 + 16 * q^77 + 24 * q^81 - 40 * q^82 - 64 * q^85 + 44 * q^92 + 16 * q^93 + 72 * q^94 + 44 * q^96 - 52 * q^98

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