LMFDB - Embedded newform 552.2.n.a.91.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(91,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("552.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.11
Character	$\chi$	$=$	552.91
Dual form			552.2.n.a.91.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.695292 + 1.23149i) q^{2} +1.00000 q^{3} +(-1.03314 - 1.71249i) q^{4} -1.12657 q^{5} +(-0.695292 + 1.23149i) q^{6} -2.04137 q^{7} +(2.82725 - 0.0816198i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.695292 + 1.23149i) q^{2} +1.00000 q^{3} +(-1.03314 - 1.71249i) q^{4} -1.12657 q^{5} +(-0.695292 + 1.23149i) q^{6} -2.04137 q^{7} +(2.82725 - 0.0816198i) q^{8} +1.00000 q^{9} +(0.783294 - 1.38736i) q^{10} +3.16794i q^{11} +(-1.03314 - 1.71249i) q^{12} +0.675694i q^{13} +(1.41935 - 2.51393i) q^{14} -1.12657 q^{15} +(-1.86525 + 3.53848i) q^{16} +7.33548i q^{17} +(-0.695292 + 1.23149i) q^{18} -0.636053i q^{19} +(1.16390 + 1.92924i) q^{20} -2.04137 q^{21} +(-3.90129 - 2.20264i) q^{22} +(-4.34899 - 2.02145i) q^{23} +(2.82725 - 0.0816198i) q^{24} -3.73084 q^{25} +(-0.832110 - 0.469804i) q^{26} +1.00000 q^{27} +(2.10902 + 3.49583i) q^{28} +3.15712i q^{29} +(0.783294 - 1.38736i) q^{30} +8.08308i q^{31} +(-3.06071 - 4.75731i) q^{32} +3.16794i q^{33} +(-9.03357 - 5.10030i) q^{34} +2.29974 q^{35} +(-1.03314 - 1.71249i) q^{36} -8.85157 q^{37} +(0.783294 + 0.442243i) q^{38} +0.675694i q^{39} +(-3.18509 + 0.0919503i) q^{40} +11.0090 q^{41} +(1.41935 - 2.51393i) q^{42} +0.447706i q^{43} +(5.42506 - 3.27292i) q^{44} -1.12657 q^{45} +(5.51322 - 3.95024i) q^{46} +4.96200i q^{47} +(-1.86525 + 3.53848i) q^{48} -2.83281 q^{49} +(2.59403 - 4.59450i) q^{50} +7.33548i q^{51} +(1.15712 - 0.698085i) q^{52} +12.4606 q^{53} +(-0.695292 + 1.23149i) q^{54} -3.56890i q^{55} +(-5.77146 + 0.166616i) q^{56} -0.636053i q^{57} +(-3.88796 - 2.19512i) q^{58} -7.81196 q^{59} +(1.16390 + 1.92924i) q^{60} +0.726453 q^{61} +(-9.95424 - 5.62010i) q^{62} -2.04137 q^{63} +(7.98668 - 0.461519i) q^{64} -0.761215i q^{65} +(-3.90129 - 2.20264i) q^{66} -14.2968i q^{67} +(12.5619 - 7.57856i) q^{68} +(-4.34899 - 2.02145i) q^{69} +(-1.59899 + 2.83211i) q^{70} -0.0830819i q^{71} +(2.82725 - 0.0816198i) q^{72} +1.54805 q^{73} +(6.15442 - 10.9006i) q^{74} -3.73084 q^{75} +(-1.08924 + 0.657131i) q^{76} -6.46693i q^{77} +(-0.832110 - 0.469804i) q^{78} -6.84496 q^{79} +(2.10133 - 3.98634i) q^{80} +1.00000 q^{81} +(-7.65450 + 13.5575i) q^{82} -8.66322i q^{83} +(2.10902 + 3.49583i) q^{84} -8.26391i q^{85} +(-0.551345 - 0.311286i) q^{86} +3.15712i q^{87} +(0.258567 + 8.95655i) q^{88} +14.5262i q^{89} +(0.783294 - 1.38736i) q^{90} -1.37934i q^{91} +(1.03139 + 9.53605i) q^{92} +8.08308i q^{93} +(-6.11066 - 3.45004i) q^{94} +0.716558i q^{95} +(-3.06071 - 4.75731i) q^{96} +0.322544i q^{97} +(1.96963 - 3.48858i) q^{98} +3.16794i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9	$ 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) $ 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 4 * q^24 + 24 * q^25 + 24 * q^27 - 4 * q^32 + 4 * q^36 + 4 * q^46 + 4 * q^48 - 8 * q^49 - 44 * q^50 - 4 * q^54 + 48 * q^58 - 40 * q^62 + 4 * q^64 - 4 * q^72 - 32 * q^73 + 24 * q^75 + 24 * q^81 - 40 * q^82 - 52 * q^92 + 40 * q^94 - 4 * q^96 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	−0.695292	+	1.23149i	−0.491646	+	0.870795i
$2$	−0.695292	+	1.23149i	−0.491646	+	0.870795i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.03314	−	1.71249i	−0.516569	−	0.856245i
$5$	−1.12657			−0.503817			−0.251908	−	0.967751i	$-0.581058\pi$
$5$	−1.12657			−0.503817			−0.251908	+	0.967751i	$0.581058\pi$
$6$	−0.695292	+	1.23149i	−0.283852	+	0.502754i
$7$	−2.04137			−0.771565			−0.385782	−	0.922590i	$-0.626068\pi$
$7$	−2.04137			−0.771565			−0.385782	+	0.922590i	$0.626068\pi$
$8$	2.82725	−	0.0816198i	0.999584	−	0.0288570i
$9$	1.00000			0.333333
$10$	0.783294	−	1.38736i	0.247699	−	0.438721i
$11$			3.16794i			0.955169i	0.878586	+	0.477585i	$0.158488\pi$
$11$			3.16794i			0.955169i	−0.878586	+	0.477585i	$0.841512\pi$
$12$	−1.03314	−	1.71249i	−0.298241	−	0.494353i
$13$			0.675694i			0.187404i	0.995600	+	0.0937019i	$0.0298700\pi$
$13$			0.675694i			0.187404i	−0.995600	+	0.0937019i	$0.970130\pi$
$14$	1.41935	−	2.51393i	0.379336	−	0.671875i
$15$	−1.12657			−0.290879
$16$	−1.86525	+	3.53848i	−0.466312	+	0.884620i
$17$			7.33548i			1.77911i	0.456824	+	0.889557i	$0.348987\pi$
$17$			7.33548i			1.77911i	−0.456824	+	0.889557i	$0.651013\pi$
$18$	−0.695292	+	1.23149i	−0.163882	+	0.290265i
$19$		−	0.636053i		−	0.145921i	−0.997335	−	0.0729603i	$-0.976755\pi$
$19$		−	0.636053i		−	0.145921i	0.997335	−	0.0729603i	$-0.0232446\pi$
$20$	1.16390	+	1.92924i	0.260256	+	0.431391i
$21$	−2.04137			−0.445463
$22$	−3.90129	−	2.20264i	−0.831757	−	0.469605i
$23$	−4.34899	−	2.02145i	−0.906827	−	0.421502i
$23$	−4.34899	−	2.02145i	−0.906827	−	0.421502i
$24$	2.82725	−	0.0816198i	0.577110	−	0.0166606i
$25$	−3.73084			−0.746169
$26$	−0.832110	−	0.469804i	−0.163190	−	0.0921362i
$27$	1.00000			0.192450
$28$	2.10902	+	3.49583i	0.398567	+	0.660649i
$29$			3.15712i			0.586262i	0.956072	+	0.293131i	$0.0946973\pi$
$29$			3.15712i			0.586262i	−0.956072	+	0.293131i	$0.905303\pi$
$30$	0.783294	−	1.38736i	0.143009	−	0.253296i
$31$			8.08308i			1.45176i	0.687819	+	0.725882i	$0.258568\pi$
$31$			8.08308i			1.45176i	−0.687819	+	0.725882i	$0.741432\pi$
$32$	−3.06071	−	4.75731i	−0.541063	−	0.840982i
$33$			3.16794i			0.551467i
$34$	−9.03357	−	5.10030i	−1.54924	−	0.874694i
$35$	2.29974			0.388727
$36$	−1.03314	−	1.71249i	−0.172190	−	0.285415i
$37$	−8.85157			−1.45519			−0.727594	−	0.686008i	$-0.759362\pi$
$37$	−8.85157			−1.45519			−0.727594	+	0.686008i	$0.759362\pi$
$38$	0.783294	+	0.442243i	0.127067	+	0.0717412i
$39$			0.675694i			0.108198i
$40$	−3.18509	+	0.0919503i	−0.503607	+	0.0145386i
$41$	11.0090			1.71932			0.859662	−	0.510863i	$-0.170674\pi$
$41$	11.0090			1.71932			0.859662	+	0.510863i	$0.170674\pi$
$42$	1.41935	−	2.51393i	0.219010	−	0.387907i
$43$			0.447706i			0.0682745i	0.999417	+	0.0341372i	$0.0108683\pi$
$43$			0.447706i			0.0682745i	−0.999417	+	0.0341372i	$0.989132\pi$
$44$	5.42506	−	3.27292i	0.817859	−	0.493411i
$45$	−1.12657			−0.167939
$46$	5.51322	−	3.95024i	0.812880	−	0.582431i
$47$			4.96200i			0.723782i	0.932220	+	0.361891i	$0.117869\pi$
$47$			4.96200i			0.723782i	−0.932220	+	0.361891i	$0.882131\pi$
$48$	−1.86525	+	3.53848i	−0.269226	+	0.510736i
$49$	−2.83281			−0.404688
$50$	2.59403	−	4.59450i	0.366851	−	0.649760i
$51$			7.33548i			1.02717i
$52$	1.15712	−	0.698085i	0.160464	−	0.0968070i
$53$	12.4606			1.71160			0.855799	−	0.517308i	$-0.173066\pi$
$53$	12.4606			1.71160			0.855799	+	0.517308i	$0.173066\pi$
$54$	−0.695292	+	1.23149i	−0.0946172	+	0.167585i
$55$		−	3.56890i		−	0.481230i
$56$	−5.77146	+	0.166616i	−0.771244	+	0.0222650i
$57$		−	0.636053i		−	0.0842473i
$58$	−3.88796	−	2.19512i	−0.510515	−	0.288233i
$59$	−7.81196			−1.01703			−0.508515	−	0.861053i	$-0.669806\pi$
$59$	−7.81196			−1.01703			−0.508515	+	0.861053i	$0.669806\pi$
$60$	1.16390	+	1.92924i	0.150259	+	0.249064i
$61$	0.726453			0.0930128			0.0465064	−	0.998918i	$-0.485191\pi$
$61$	0.726453			0.0930128			0.0465064	+	0.998918i	$0.485191\pi$
$62$	−9.95424	−	5.62010i	−1.26419	−	0.713753i
$63$	−2.04137			−0.257188
$64$	7.98668	−	0.461519i	0.998335	−	0.0576899i
$65$		−	0.761215i		−	0.0944171i
$66$	−3.90129	−	2.20264i	−0.480215	−	0.271126i
$67$		−	14.2968i		−	1.74663i	−0.487153	−	0.873317i	$-0.661965\pi$
$67$		−	14.2968i		−	1.74663i	0.487153	−	0.873317i	$-0.338035\pi$
$68$	12.5619	−	7.57856i	1.52336	−	0.919036i
$69$	−4.34899	−	2.02145i	−0.523557	−	0.243355i
$70$	−1.59899	+	2.83211i	−0.191116	+	0.338502i
$71$		−	0.0830819i		−	0.00986001i	−0.999988	−	0.00493001i	$-0.998431\pi$
$71$		−	0.0830819i		−	0.00986001i	0.999988	−	0.00493001i	$-0.00156928\pi$
$72$	2.82725	−	0.0816198i	0.333195	−	0.00961899i
$73$	1.54805			0.181185			0.0905927	−	0.995888i	$-0.471124\pi$
$73$	1.54805			0.181185			0.0905927	+	0.995888i	$0.471124\pi$
$74$	6.15442	−	10.9006i	0.715437	−	1.26717i
$75$	−3.73084			−0.430801
$76$	−1.08924	+	0.657131i	−0.124944	+	0.0753781i
$77$		−	6.46693i		−	0.736975i
$78$	−0.832110	−	0.469804i	−0.0942180	−	0.0531949i
$79$	−6.84496			−0.770118			−0.385059	−	0.922892i	$-0.625819\pi$
$79$	−6.84496			−0.770118			−0.385059	+	0.922892i	$0.625819\pi$
$80$	2.10133	−	3.98634i	0.234936	−	0.445686i
$81$	1.00000			0.111111
$82$	−7.65450	+	13.5575i	−0.845298	+	1.49718i
$83$		−	8.66322i		−	0.950912i	−0.879740	−	0.475456i	$-0.842283\pi$
$83$		−	8.66322i		−	0.950912i	0.879740	−	0.475456i	$-0.157717\pi$
$84$	2.10902	+	3.49583i	0.230113	+	0.381426i
$85$		−	8.26391i		−	0.896347i
$86$	−0.551345	−	0.311286i	−0.0594531	−	0.0335668i
$87$			3.15712i			0.338479i
$88$	0.258567	+	8.95655i	0.0275633	+	0.954771i
$89$			14.5262i			1.53977i	0.638183	+	0.769885i	$0.279687\pi$
$89$			14.5262i			1.53977i	−0.638183	+	0.769885i	$0.720313\pi$
$90$	0.783294	−	1.38736i	0.0825664	−	0.146240i
$91$		−	1.37934i		−	0.144594i
$92$	1.03139	+	9.53605i	0.107530	+	0.994202i
$93$			8.08308i			0.838177i
$94$	−6.11066	−	3.45004i	−0.630266	−	0.355844i
$95$			0.716558i			0.0735173i
$96$	−3.06071	−	4.75731i	−0.312383	−	0.485541i
$97$			0.322544i			0.0327494i	0.999866	+	0.0163747i	$0.00521246\pi$
$97$			0.322544i			0.0327494i	−0.999866	+	0.0163747i	$0.994788\pi$
$98$	1.96963	−	3.48858i	0.198963	−	0.352400i
$99$			3.16794i			0.318390i
$100$	3.85448	+	6.38904i	0.385448	+	0.638904i
$101$		−	0.0617136i		−	0.00614074i	−0.999995	−	0.00307037i	$-0.999023\pi$
$101$		−	0.0617136i		−	0.00614074i	0.999995	−	0.00307037i	$-0.000977330\pi$
$102$	−9.03357	−	5.10030i	−0.894457	−	0.505005i
$103$	7.53041			0.741993			0.370997	−	0.928634i	$-0.379016\pi$
$103$	7.53041			0.741993			0.370997	+	0.928634i	$0.379016\pi$
$104$	0.0551500	+	1.91035i	0.00540790	+	0.187326i
$105$	2.29974			0.224432
$106$	−8.66377	+	15.3451i	−0.841500	+	1.49045i
$107$		−	9.36246i		−	0.905103i	−0.891738	−	0.452552i	$-0.850514\pi$
$107$		−	9.36246i		−	0.905103i	0.891738	−	0.452552i	$-0.149486\pi$
$108$	−1.03314	−	1.71249i	−0.0994138	−	0.164784i
$109$	16.0966			1.54178			0.770889	−	0.636969i	$-0.219812\pi$
$109$	16.0966			1.54178			0.770889	+	0.636969i	$0.219812\pi$
$110$	4.39506	+	2.48143i	0.419053	+	0.236595i
$111$	−8.85157			−0.840154
$112$	3.80766	−	7.22334i	0.359790	−	0.682542i
$113$			8.40386i			0.790569i	0.918559	+	0.395284i	$0.129354\pi$
$113$			8.40386i			0.790569i	−0.918559	+	0.395284i	$0.870646\pi$
$114$	0.783294	+	0.442243i	0.0733622	+	0.0414198i
$115$	4.89944	+	2.27731i	0.456875	+	0.212360i
$116$	5.40654	−	3.26174i	0.501984	−	0.302845i
$117$			0.675694i			0.0624679i
$118$	5.43159	−	9.62036i	0.500019	−	0.885626i
$119$		−	14.9744i		−	1.37270i
$120$	−3.18509	+	0.0919503i	−0.290758	+	0.00839388i
$121$	0.964173			0.0876521
$122$	−0.505097	+	0.894620i	−0.0457293	+	0.0809951i
$123$	11.0090			0.992652
$124$	13.8422	−	8.35094i	1.24307	−	0.749937i
$125$	9.83589			0.879749
$126$	1.41935	−	2.51393i	0.126445	−	0.223958i
$127$		−	12.1798i		−	1.08078i	−0.841414	−	0.540392i	$-0.818276\pi$
$127$		−	12.1798i		−	1.08078i	0.841414	−	0.540392i	$-0.181724\pi$
$128$	−4.98471	+	10.1564i	−0.440591	+	0.897708i
$129$			0.447706i			0.0394183i
$130$	0.937429	+	0.529267i	0.0822180	+	0.0464198i
$131$	−8.84066			−0.772412			−0.386206	−	0.922412i	$-0.626215\pi$
$131$	−8.84066			−0.772412			−0.386206	+	0.922412i	$0.626215\pi$
$132$	5.42506	−	3.27292i	0.472191	−	0.284871i
$133$			1.29842i			0.112587i
$134$	17.6064	+	9.94046i	1.52096	+	0.858725i
$135$	−1.12657			−0.0969596
$136$	0.598720	+	20.7392i	0.0513398	+	1.77837i
$137$			11.9353i			1.01971i	0.860262	+	0.509853i	$0.170300\pi$
$137$			11.9353i			1.01971i	−0.860262	+	0.509853i	$0.829700\pi$
$138$	5.51322	−	3.95024i	0.469316	−	0.336267i
$139$	−3.11695			−0.264376			−0.132188	−	0.991225i	$-0.542200\pi$
$139$	−3.11695			−0.264376			−0.132188	+	0.991225i	$0.542200\pi$
$140$	−2.37595	−	3.93829i	−0.200805	−	0.332846i
$141$			4.96200i			0.417876i
$142$	0.102315	+	0.0577662i	0.00858605	+	0.00484763i
$143$	−2.14056			−0.179002
$144$	−1.86525	+	3.53848i	−0.155437	+	0.294873i
$145$		−	3.55671i		−	0.295369i
$146$	−1.07635	+	1.90641i	−0.0890790	+	0.157775i
$147$	−2.83281			−0.233646
$148$	9.14490	+	15.1582i	0.751706	+	1.24600i
$149$	6.16511			0.505066			0.252533	−	0.967588i	$-0.418736\pi$
$149$	6.16511			0.505066			0.252533	+	0.967588i	$0.418736\pi$
$150$	2.59403	−	4.59450i	0.211801	−	0.375139i
$151$			8.90664i			0.724812i	0.932020	+	0.362406i	$0.118045\pi$
$151$			8.90664i			0.724812i	−0.932020	+	0.362406i	$0.881955\pi$
$152$	−0.0519146	−	1.79828i	−0.00421083	−	0.145860i
$153$			7.33548i			0.593038i
$154$	7.96396	+	4.49640i	0.641754	+	0.362330i
$155$		−	9.10614i		−	0.731423i
$156$	1.15712	−	0.698085i	0.0926437	−	0.0558916i
$157$	18.2080			1.45316			0.726580	−	0.687082i	$-0.241109\pi$
$157$	18.2080			1.45316			0.726580	+	0.687082i	$0.241109\pi$
$158$	4.75924	−	8.42951i	0.378625	−	0.670615i
$159$	12.4606			0.988192
$160$	3.44810	+	5.35944i	0.272596	+	0.423701i
$161$	8.87789	+	4.12653i	0.699676	+	0.325216i
$162$	−0.695292	+	1.23149i	−0.0546273	+	0.0967550i
$163$	−6.44539			−0.504842			−0.252421	−	0.967618i	$-0.581227\pi$
$163$	−6.44539			−0.504842			−0.252421	+	0.967618i	$0.581227\pi$
$164$	−11.3739	−	18.8529i	−0.888150	−	1.47216i
$165$		−	3.56890i		−	0.277838i
$166$	10.6687	+	6.02347i	0.828050	+	0.467512i
$167$			17.8849i			1.38397i	0.721910	+	0.691987i	$0.243265\pi$
$167$			17.8849i			1.38397i	−0.721910	+	0.691987i	$0.756735\pi$
$168$	−5.77146	+	0.166616i	−0.445278	+	0.0128547i
$169$	12.5434			0.964880
$170$	10.1769	+	5.74583i	0.780535	+	0.440685i
$171$		−	0.636053i		−	0.0486402i
$172$	0.766692	−	0.462542i	0.0584597	−	0.0352685i
$173$		−	22.9330i		−	1.74357i	−0.489891	−	0.871784i	$-0.662964\pi$
$173$		−	22.9330i		−	1.74357i	0.489891	−	0.871784i	$-0.337036\pi$
$174$	−3.88796	−	2.19512i	−0.294746	−	0.166412i
$175$	7.61603			0.575718
$176$	−11.2097	−	5.90899i	−0.844962	−	0.445407i
$177$	−7.81196			−0.587183
$178$	−17.8888	−	10.0999i	−1.34082	−	0.757021i
$179$	5.31535			0.397288			0.198644	−	0.980072i	$-0.436346\pi$
$179$	5.31535			0.397288			0.198644	+	0.980072i	$0.436346\pi$
$180$	1.16390	+	1.92924i	0.0867521	+	0.143797i
$181$	−1.41410			−0.105109			−0.0525547	−	0.998618i	$-0.516736\pi$
$181$	−1.41410			−0.105109			−0.0525547	+	0.998618i	$0.516736\pi$
$182$	1.69864	+	0.959044i	0.125912	+	0.0710891i
$183$	0.726453			0.0537009
$184$	−12.4607	−	5.36019i	−0.918613	−	0.395159i
$185$	9.97190			0.733148
$186$	−9.95424	−	5.62010i	−0.729880	−	0.412086i
$187$	−23.2383			−1.69935
$188$	8.49738	−	5.12643i	0.619735	−	0.373884i
$189$	−2.04137			−0.148488
$190$	−0.882434	−	0.498217i	−0.0640185	−	0.0361444i
$191$	−17.0580			−1.23428			−0.617138	−	0.786855i	$-0.711708\pi$
$191$	−17.0580			−1.23428			−0.617138	+	0.786855i	$0.711708\pi$
$192$	7.98668	−	0.461519i	0.576389	−	0.0333073i
$193$	−0.970609			−0.0698660			−0.0349330	−	0.999390i	$-0.511122\pi$
$193$	−0.970609			−0.0698660			−0.0349330	+	0.999390i	$0.511122\pi$
$194$	−0.397210	−	0.224262i	−0.0285180	−	0.0161011i
$195$		−	0.761215i		−	0.0545117i
$196$	2.92669	+	4.85117i	0.209049	+	0.346512i
$197$			12.2034i			0.869456i	0.900562	+	0.434728i	$0.143155\pi$
$197$			12.2034i			0.869456i	−0.900562	+	0.434728i	$0.856845\pi$
$198$	−3.90129	−	2.20264i	−0.277252	−	0.156535i
$199$	13.9421			0.988326			0.494163	−	0.869369i	$-0.335475\pi$
$199$	13.9421			0.988326			0.494163	+	0.869369i	$0.335475\pi$
$200$	−10.5480	+	0.304511i	−0.745858	+	0.0215322i
$201$		−	14.2968i		−	1.00842i
$202$	0.0759998	+	0.0429090i	0.00534733	+	0.00301907i
$203$		−	6.44485i		−	0.452339i
$204$	12.5619	−	7.57856i	0.879511	−	0.530606i
$205$	−12.4024			−0.866224
$206$	−5.23583	+	9.27363i	−0.364798	+	0.646124i
$207$	−4.34899	−	2.02145i	−0.302276	−	0.140501i
$208$	−2.39093	−	1.26034i	−0.165781	−	0.0873887i
$209$	2.01498			0.139379
$210$	−1.59899	+	2.83211i	−0.110341	+	0.195434i
$211$	−10.1618			−0.699568			−0.349784	−	0.936830i	$-0.613745\pi$
$211$	−10.1618			−0.699568			−0.349784	+	0.936830i	$0.613745\pi$
$212$	−12.8736	−	21.3387i	−0.884159	−	1.46555i
$213$		−	0.0830819i		−	0.00569268i
$214$	11.5298	+	6.50964i	0.788160	+	0.444990i
$215$		−	0.504371i		−	0.0343978i
$216$	2.82725	−	0.0816198i	0.192370	−	0.00555353i
$217$		−	16.5006i		−	1.12013i
$218$	−11.1919	+	19.8229i	−0.758009	+	1.34257i
$219$	1.54805			0.104607
$220$	−6.11170	+	3.68717i	−0.412051	+	0.248589i
$221$	−4.95653			−0.333413
$222$	6.15442	−	10.9006i	0.413058	−	0.731602i
$223$		−	8.44475i		−	0.565502i	−0.959193	−	0.282751i	$-0.908753\pi$
$223$		−	8.44475i		−	0.565502i	0.959193	−	0.282751i	$-0.0912470\pi$
$224$	6.24805	+	9.71143i	0.417465	+	0.648872i
$225$	−3.73084			−0.248723
$226$	−10.3493	−	5.84314i	−0.688424	−	0.388680i
$227$		−	17.6099i		−	1.16881i	−0.811461	−	0.584406i	$-0.801327\pi$
$227$		−	17.6099i		−	1.16881i	0.811461	−	0.584406i	$-0.198673\pi$
$228$	−1.08924	+	0.657131i	−0.0721364	+	0.0435196i
$229$	−3.08856			−0.204098			−0.102049	−	0.994779i	$-0.532540\pi$
$229$	−3.08856			−0.204098			−0.102049	+	0.994779i	$0.532540\pi$
$230$	−6.21102	+	4.45022i	−0.409542	+	0.293439i
$231$		−	6.46693i		−	0.425493i
$232$	0.257684	+	8.92596i	0.0169178	+	0.586018i
$233$	−28.2832			−1.85289			−0.926447	−	0.376425i	$-0.877153\pi$
$233$	−28.2832			−1.85289			−0.926447	+	0.376425i	$0.877153\pi$
$234$	−0.832110	−	0.469804i	−0.0543968	−	0.0307121i
$235$		−	5.59003i		−	0.364654i
$236$	8.07084	+	13.3779i	0.525367	+	0.870828i
$237$	−6.84496			−0.444628
$238$	18.4408	+	10.4116i	1.19534	+	0.674883i
$239$			22.5449i			1.45831i	0.684351	+	0.729153i	$0.260086\pi$
$239$			22.5449i			1.45831i	−0.684351	+	0.729153i	$0.739914\pi$
$240$	2.10133	−	3.98634i	0.135640	−	0.257317i
$241$		−	7.59261i		−	0.489083i	−0.969639	−	0.244541i	$-0.921363\pi$
$241$		−	7.59261i		−	0.489083i	0.969639	−	0.244541i	$-0.0786374\pi$
$242$	−0.670382	+	1.18737i	−0.0430938	+	0.0763271i
$243$	1.00000			0.0641500
$244$	−0.750526	−	1.24404i	−0.0480475	−	0.0796417i
$245$	3.19136			0.203888
$246$	−7.65450	+	13.5575i	−0.488033	+	0.864397i
$247$	0.429777			0.0273461
$248$	0.659740	+	22.8529i	0.0418935	+	1.45116i
$249$		−	8.66322i		−	0.549009i
$250$	−6.83882	+	12.1128i	−0.432525	+	0.766081i
$251$			4.94339i			0.312024i	0.987755	+	0.156012i	$0.0498638\pi$
$251$			4.94339i			0.312024i	−0.987755	+	0.156012i	$0.950136\pi$
$252$	2.10902	+	3.49583i	0.132856	+	0.220216i
$253$	6.40384	−	13.7773i	0.402606	−	0.866173i
$254$	14.9993	+	8.46852i	0.941141	+	0.531362i
$255$		−	8.26391i		−	0.517506i
$256$	−9.04169	−	13.2003i	−0.565106	−	0.825019i
$257$	12.6435			0.788677			0.394338	−	0.918965i	$-0.370974\pi$
$257$	12.6435			0.788677			0.394338	+	0.918965i	$0.370974\pi$
$258$	−0.551345	−	0.311286i	−0.0343253	−	0.0193798i
$259$	18.0693			1.12277
$260$	−1.30357	+	0.786441i	−0.0808442	+	0.0487730i
$261$			3.15712i			0.195421i
$262$	6.14684	−	10.8872i	0.379753	−	0.672613i
$263$	−5.36863			−0.331044			−0.165522	−	0.986206i	$-0.552931\pi$
$263$	−5.36863			−0.331044			−0.165522	+	0.986206i	$0.552931\pi$
$264$	0.258567	+	8.95655i	0.0159137	+	0.551237i
$265$	−14.0377			−0.862332
$266$	−1.59899	−	0.902780i	−0.0980405	−	0.0553530i
$267$			14.5262i			0.888987i
$268$	−24.4832	+	14.7706i	−1.49555	+	0.902257i
$269$		−	9.32832i		−	0.568758i	−0.958712	−	0.284379i	$-0.908213\pi$
$269$		−	9.32832i		−	0.568758i	0.958712	−	0.284379i	$-0.0917874\pi$
$270$	0.783294	−	1.38736i	0.0476697	−	0.0844319i
$271$		−	5.82454i		−	0.353815i	−0.984227	−	0.176908i	$-0.943391\pi$
$271$		−	5.82454i		−	0.353815i	0.984227	−	0.176908i	$-0.0566094\pi$
$272$	−25.9564	−	13.6825i	−1.57384	−	0.829623i
$273$		−	1.37934i		−	0.0834815i
$274$	−14.6983	−	8.29855i	−0.887955	−	0.501334i
$275$		−	11.8191i		−	0.712717i
$276$	1.03139	+	9.53605i	0.0620823	+	0.574003i
$277$			21.2935i			1.27940i	0.768624	+	0.639701i	$0.220942\pi$
$277$			21.2935i			1.27940i	−0.768624	+	0.639701i	$0.779058\pi$
$278$	2.16719	−	3.83849i	0.129979	−	0.230217i
$279$			8.08308i			0.483921i
$280$	6.50194	−	0.187705i	0.388565	−	0.0112175i
$281$			8.49280i			0.506638i	0.967383	+	0.253319i	$0.0815222\pi$
$281$			8.49280i			0.506638i	−0.967383	+	0.253319i	$0.918478\pi$
$282$	−6.11066	−	3.45004i	−0.363884	−	0.205447i
$283$		−	5.36190i		−	0.318732i	−0.987220	−	0.159366i	$-0.949055\pi$
$283$		−	5.36190i		−	0.318732i	0.987220	−	0.159366i	$-0.0509450\pi$
$284$	−0.142277	+	0.0858352i	−0.00844259	+	0.00509338i
$285$			0.716558i			0.0424452i
$286$	1.48831	−	2.63607i	0.0880056	−	0.155874i
$287$	−22.4735			−1.32657
$288$	−3.06071	−	4.75731i	−0.180354	−	0.280327i
$289$	−36.8092			−2.16525
$290$	4.38006	+	2.47295i	0.257206	+	0.145217i
$291$			0.322544i			0.0189079i
$292$	−1.59935	−	2.65102i	−0.0935948	−	0.155139i
$293$	−24.4801			−1.43014			−0.715072	−	0.699051i	$-0.753606\pi$
$293$	−24.4801			−1.43014			−0.715072	+	0.699051i	$0.753606\pi$
$294$	1.96963	−	3.48858i	0.114871	−	0.203458i
$295$	8.80071			0.512397
$296$	−25.0256	+	0.722464i	−1.45458	+	0.0419923i
$297$			3.16794i			0.183822i
$298$	−4.28655	+	7.59228i	−0.248313	+	0.439809i
$299$	1.36588	−	2.93859i	0.0789911	−	0.169943i
$300$	3.85448	+	6.38904i	0.222538	+	0.368871i
$301$		−	0.913932i		−	0.0526782i
$302$	−10.9684	−	6.19271i	−0.631163	−	0.356351i
$303$		−	0.0617136i		−	0.00354536i
$304$	2.25066	+	1.18640i	0.129084	+	0.0680446i
$305$	−0.818399			−0.0468614
$306$	−9.03357	−	5.10030i	−0.516415	−	0.291565i
$307$	25.7635			1.47040			0.735201	−	0.677850i	$-0.237088\pi$
$307$	25.7635			1.47040			0.735201	+	0.677850i	$0.237088\pi$
$308$	−11.0746	+	6.68123i	−0.631031	+	0.380699i
$309$	7.53041			0.428390
$310$	11.2141	+	6.33143i	0.636920	+	0.359601i
$311$		−	2.84583i		−	0.161372i	−0.996740	−	0.0806860i	$-0.974289\pi$
$311$		−	2.84583i		−	0.161372i	0.996740	−	0.0806860i	$-0.0257111\pi$
$312$	0.0551500	+	1.91035i	0.00312225	+	0.108153i
$313$		−	23.9402i		−	1.35318i	−0.736359	−	0.676591i	$-0.763457\pi$
$313$		−	23.9402i		−	1.35318i	0.736359	−	0.676591i	$-0.236543\pi$
$314$	−12.6599	+	22.4230i	−0.714439	+	1.26540i
$315$	2.29974			0.129576
$316$	7.07179	+	11.7219i	0.397819	+	0.659410i
$317$			10.7507i			0.603818i	0.953337	+	0.301909i	$0.0976238\pi$
$317$			10.7507i			0.603818i	−0.953337	+	0.301909i	$0.902376\pi$
$318$	−8.66377	+	15.3451i	−0.485840	+	0.860513i
$319$	−10.0016			−0.559980
$320$	−8.99754	+	0.519933i	−0.502978	+	0.0290651i
$321$		−	9.36246i		−	0.522561i
$322$	−11.2545	+	8.06390i	−0.627190	+	0.449384i
$323$	4.66575			0.259609
$324$	−1.03314	−	1.71249i	−0.0573966	−	0.0951384i
$325$		−	2.52091i		−	0.139835i
$326$	4.48143	−	7.93744i	0.248203	−	0.439614i
$327$	16.0966			0.890146
$328$	31.1253	−	0.898557i	1.71861	−	0.0496145i
$329$		−	10.1293i		−	0.558445i
$330$	4.39506	+	2.48143i	0.241940	+	0.136598i
$331$	9.82506			0.540034			0.270017	−	0.962856i	$-0.412971\pi$
$331$	9.82506			0.540034			0.270017	+	0.962856i	$0.412971\pi$
$332$	−14.8357	+	8.95031i	−0.814214	+	0.491212i
$333$	−8.85157			−0.485063
$334$	−22.0251	−	12.4352i	−1.20516	−	0.680425i
$335$			16.1063i			0.879983i
$336$	3.80766	−	7.22334i	0.207725	−	0.394066i
$337$		−	14.6863i		−	0.800015i	−0.916512	−	0.400008i	$-0.869008\pi$
$337$		−	14.6863i		−	0.800015i	0.916512	−	0.400008i	$-0.130992\pi$
$338$	−8.72135	+	15.4471i	−0.474379	+	0.840213i
$339$			8.40386i			0.456435i
$340$	−14.1519	+	8.53777i	−0.767493	+	0.463026i
$341$	−25.6067			−1.38668
$342$	0.783294	+	0.442243i	0.0423557	+	0.0239137i
$343$	20.0724			1.08381
$344$	0.0365417	+	1.26578i	0.00197019	+	0.0682460i
$345$	4.89944	+	2.27731i	0.263777	+	0.122606i
$346$	28.2418	+	15.9452i	1.51829	+	0.857217i
$347$	−17.9021			−0.961037			−0.480518	−	0.876985i	$-0.659551\pi$
$347$	−17.9021			−0.961037			−0.480518	+	0.876985i	$0.659551\pi$
$348$	5.40654	−	3.26174i	0.289821	−	0.174848i
$349$			25.9937i			1.39141i	0.718328	+	0.695704i	$0.244908\pi$
$349$			25.9937i			1.39141i	−0.718328	+	0.695704i	$0.755092\pi$
$350$	−5.29536	+	9.37907i	−0.283049	+	0.501332i
$351$			0.675694i			0.0360659i
$352$	15.0709	−	9.69615i	0.803280	−	0.516806i
$353$	−2.36295			−0.125767			−0.0628835	−	0.998021i	$-0.520030\pi$
$353$	−2.36295			−0.125767			−0.0628835	+	0.998021i	$0.520030\pi$
$354$	5.43159	−	9.62036i	0.288686	−	0.511316i
$355$			0.0935975i			0.00496764i
$356$	24.8759	−	15.0075i	1.31842	−	0.795398i
$357$		−	14.9744i		−	0.792530i
$358$	−3.69572	+	6.54580i	−0.195325	+	0.345956i
$359$	29.5635			1.56030			0.780150	−	0.625593i	$-0.215143\pi$
$359$	29.5635			1.56030			0.780150	+	0.625593i	$0.215143\pi$
$360$	−3.18509	+	0.0919503i	−0.167869	+	0.00484621i
$361$	18.5954			0.978707
$362$	0.983214	−	1.74145i	0.0516766	−	0.0915288i
$363$	0.964173			0.0506060
$364$	−2.36211	+	1.42505i	−0.123808	+	0.0746929i
$365$	−1.74398			−0.0912842
$366$	−0.505097	+	0.894620i	−0.0264018	+	0.0467625i
$367$	−20.5057			−1.07039			−0.535195	−	0.844729i	$-0.679762\pi$
$367$	−20.5057			−1.07039			−0.535195	+	0.844729i	$0.679762\pi$
$368$	15.2648	−	11.6183i	0.795734	−	0.605646i
$369$	11.0090			0.573108
$370$	−6.93338	+	12.2803i	−0.360449	+	0.638422i
$371$	−25.4367			−1.32061
$372$	13.8422	−	8.35094i	0.717685	−	0.432976i
$373$	−7.54799			−0.390820			−0.195410	−	0.980722i	$-0.562604\pi$
$373$	−7.54799			−0.390820			−0.195410	+	0.980722i	$0.562604\pi$
$374$	16.1574	−	28.6178i	0.835480	−	1.47979i
$375$	9.83589			0.507923
$376$	0.404998	+	14.0288i	0.0208862	+	0.723481i
$377$	−2.13325			−0.109868
$378$	1.41935	−	2.51393i	0.0730033	−	0.129302i
$379$			29.5328i			1.51700i	0.651674	+	0.758499i	$0.274067\pi$
$379$			29.5328i			1.51700i	−0.651674	+	0.758499i	$0.725933\pi$
$380$	1.22710	−	0.740303i	0.0629488	−	0.0379768i
$381$		−	12.1798i		−	0.623991i
$382$	11.8603	−	21.0068i	0.606827	−	1.07480i
$383$	−10.2635			−0.524439			−0.262219	−	0.965008i	$-0.584454\pi$
$383$	−10.2635			−0.524439			−0.262219	+	0.965008i	$0.584454\pi$
$384$	−4.98471	+	10.1564i	−0.254375	+	0.518292i
$385$			7.28544i			0.371300i
$386$	0.674856	−	1.19530i	0.0343493	−	0.0608390i
$387$			0.447706i			0.0227582i
$388$	0.552353	−	0.333232i	0.0280415	−	0.0169173i
$389$	32.8672			1.66643			0.833215	−	0.552948i	$-0.186497\pi$
$389$	32.8672			1.66643			0.833215	+	0.552948i	$0.186497\pi$
$390$	0.937429	+	0.529267i	0.0474686	+	0.0268005i
$391$	14.8283	−	31.9019i	0.749901	−	1.61335i
$392$	−8.00907	+	0.231214i	−0.404519	+	0.0116781i
$393$	−8.84066			−0.445952
$394$	−15.0284	−	8.48492i	−0.757118	−	0.427464i
$395$	7.71132			0.387998
$396$	5.42506	−	3.27292i	0.272620	−	0.164470i
$397$		−	14.0784i		−	0.706574i	−0.935515	−	0.353287i	$-0.885064\pi$
$397$		−	14.0784i		−	0.706574i	0.935515	−	0.353287i	$-0.114936\pi$
$398$	−9.69379	+	17.1695i	−0.485906	+	0.860630i
$399$			1.29842i			0.0650023i
$400$	6.95895	−	13.2015i	0.347948	−	0.660076i
$401$			6.26535i			0.312877i	0.987688	+	0.156438i	$0.0500013\pi$
$401$			6.26535i			0.312877i	−0.987688	+	0.156438i	$0.949999\pi$
$402$	17.6064	+	9.94046i	0.878127	+	0.495785i
$403$	−5.46169			−0.272066
$404$	−0.105684	+	0.0637587i	−0.00525798	+	0.00317212i
$405$	−1.12657			−0.0559796
$406$	7.93677	+	4.48105i	0.393895	+	0.222391i
$407$		−	28.0412i		−	1.38995i
$408$	0.598720	+	20.7392i	0.0296411	+	1.02674i
$409$	−11.9951			−0.593117			−0.296559	−	0.955015i	$-0.595839\pi$
$409$	−11.9951			−0.593117			−0.296559	+	0.955015i	$0.595839\pi$
$410$	8.62332	−	15.2735i	0.425875	−	0.754304i
$411$			11.9353i			0.588727i
$412$	−7.77996	−	12.8958i	−0.383291	−	0.635328i
$413$	15.9471			0.784705
$414$	5.51322	−	3.95024i	0.270960	−	0.194144i
$415$			9.75971i			0.479085i
$416$	3.21449	−	2.06810i	0.157603	−	0.101397i
$417$	−3.11695			−0.152638
$418$	−1.40100	+	2.48143i	−0.0685250	+	0.121370i
$419$			33.7213i			1.64739i	0.567030	+	0.823697i	$0.308092\pi$
$419$			33.7213i			1.64739i	−0.567030	+	0.823697i	$0.691908\pi$
$420$	−2.37595	−	3.93829i	−0.115935	−	0.192169i
$421$	−7.89931			−0.384989			−0.192494	−	0.981298i	$-0.561658\pi$
$421$	−7.89931			−0.384989			−0.192494	+	0.981298i	$0.561658\pi$
$422$	7.06543	−	12.5142i	0.343940	−	0.609181i
$423$			4.96200i			0.241261i
$424$	35.2293	−	1.01703i	1.71089	−	0.0493915i
$425$		−	27.3675i		−	1.32752i
$426$	0.102315	+	0.0577662i	0.00495716	+	0.00279878i
$427$	−1.48296			−0.0717654
$428$	−16.0331	+	9.67272i	−0.774990	+	0.467548i
$429$	−2.14056			−0.103347
$430$	0.621128	+	0.350685i	0.0299535	+	0.0169115i
$431$	3.74482			0.180382			0.0901908	−	0.995925i	$-0.471252\pi$
$431$	3.74482			0.180382			0.0901908	+	0.995925i	$0.471252\pi$
$432$	−1.86525	+	3.53848i	−0.0897418	+	0.170245i
$433$		−	20.7565i		−	0.997494i	−0.866748	−	0.498747i	$-0.833794\pi$
$433$		−	20.7565i		−	0.997494i	0.866748	−	0.498747i	$-0.166206\pi$
$434$	20.3203	+	11.4727i	0.975404	+	0.550707i
$435$		−	3.55671i		−	0.170531i
$436$	−16.6301	−	27.5654i	−0.796436	−	1.32014i
$437$	−1.28575	+	2.76619i	−0.0615059	+	0.132325i
$438$	−1.07635	+	1.90641i	−0.0514298	+	0.0910916i
$439$		−	26.1868i		−	1.24983i	−0.780693	−	0.624914i	$-0.785134\pi$
$439$		−	26.1868i		−	1.24983i	0.780693	−	0.624914i	$-0.214866\pi$
$440$	−0.291293	−	10.0902i	−0.0138868	−	0.481030i
$441$	−2.83281			−0.134896
$442$	3.44624	−	6.10393i	0.163921	−	0.290334i
$443$	2.15943			0.102598			0.0512988	−	0.998683i	$-0.483664\pi$
$443$	2.15943			0.102598			0.0512988	+	0.998683i	$0.483664\pi$
$444$	9.14490	+	15.1582i	0.433998	+	0.719378i
$445$		−	16.3647i		−	0.775762i
$446$	10.3996	+	5.87156i	0.492437	+	0.278027i
$447$	6.16511			0.291600
$448$	−16.3038	+	0.942131i	−0.770280	+	0.0445115i
$449$	26.8391			1.26662			0.633308	−	0.773899i	$-0.281696\pi$
$449$	26.8391			1.26662			0.633308	+	0.773899i	$0.281696\pi$
$450$	2.59403	−	4.59450i	0.122284	−	0.216587i
$451$			34.8760i			1.64224i
$452$	14.3915	−	8.68235i	0.676921	−	0.408384i
$453$			8.90664i			0.418470i
$454$	21.6865	+	12.2440i	1.01780	+	0.574642i
$455$			1.55392i			0.0728489i
$456$	−0.0519146	−	1.79828i	−0.00243112	−	0.0842122i
$457$			11.3884i			0.532729i	0.963872	+	0.266364i	$0.0858225\pi$
$457$			11.3884i			0.532729i	−0.963872	+	0.266364i	$0.914178\pi$
$458$	2.14745	−	3.80353i	0.100344	−	0.177727i
$459$			7.33548i			0.342391i
$460$	−1.16193	−	10.7430i	−0.0541752	−	0.500896i
$461$			33.4672i			1.55872i	0.626575	+	0.779361i	$0.284456\pi$
$461$			33.4672i			1.55872i	−0.626575	+	0.779361i	$0.715544\pi$
$462$	7.96396	+	4.49640i	0.370517	+	0.209192i
$463$			21.8710i			1.01643i	0.861229	+	0.508217i	$0.169695\pi$
$463$			21.8710i			1.01643i	−0.861229	+	0.508217i	$0.830305\pi$
$464$	−11.1714	−	5.88881i	−0.518619	−	0.273381i
$465$		−	9.10614i		−	0.422287i
$466$	19.6651	−	34.8305i	0.910967	−	1.61349i
$467$			20.4396i			0.945830i	0.881108	+	0.472915i	$0.156798\pi$
$467$			20.4396i			0.945830i	−0.881108	+	0.472915i	$0.843202\pi$
$468$	1.15712	−	0.698085i	0.0534879	−	0.0322690i
$469$			29.1851i			1.34764i
$470$	6.88407	+	3.88670i	0.317539	+	0.179280i
$471$	18.2080			0.838982
$472$	−22.0864	+	0.637611i	−1.01661	+	0.0293484i
$473$	−1.41830			−0.0652137
$474$	4.75924	−	8.42951i	0.218599	−	0.387180i
$475$			2.37302i			0.108881i
$476$	−25.6435	+	15.4706i	−1.17537	+	0.709096i
$477$	12.4606			0.570533
$478$	−27.7638	−	15.6753i	−1.26989	−	0.716969i
$479$	23.5065			1.07404			0.537020	−	0.843570i	$-0.319550\pi$
$479$	23.5065			1.07404			0.537020	+	0.843570i	$0.319550\pi$
$480$	3.44810	+	5.35944i	0.157384	+	0.244624i
$481$		−	5.98095i		−	0.272708i
$482$	9.35023	+	5.27908i	0.425891	+	0.240455i
$483$	8.87789	+	4.12653i	0.403958	+	0.187764i
$484$	−0.996125	−	1.65114i	−0.0452784	−	0.0750517i
$485$		−	0.363368i		−	0.0164997i
$486$	−0.695292	+	1.23149i	−0.0315391	+	0.0558616i
$487$		−	11.7619i		−	0.532981i	−0.963838	−	0.266490i	$-0.914136\pi$
$487$		−	11.7619i		−	0.532981i	0.963838	−	0.266490i	$-0.0858640\pi$
$488$	2.05386	−	0.0592930i	0.0929740	−	0.00268407i
$489$	−6.44539			−0.291471
$490$	−2.21892	+	3.93013i	−0.100241	+	0.177545i
$491$	31.2017			1.40811			0.704057	−	0.710143i	$-0.251370\pi$
$491$	31.2017			1.40811			0.704057	+	0.710143i	$0.251370\pi$
$492$	−11.3739	−	18.8529i	−0.512774	−	0.849954i
$493$	−23.1590			−1.04303
$494$	−0.298821	+	0.529267i	−0.0134446	+	0.0238128i
$495$		−	3.56890i		−	0.160410i
$496$	−28.6018	−	15.0770i	−1.28426	−	0.676976i
$497$			0.169601i			0.00760764i
$498$	10.6687	+	6.02347i	0.478075	+	0.269918i
$499$	27.1663			1.21613			0.608064	−	0.793888i	$-0.291946\pi$
$499$	27.1663			1.21613			0.608064	+	0.793888i	$0.291946\pi$
$500$	−10.1618	−	16.8439i	−0.454451	−	0.753281i
$501$			17.8849i			0.799038i
$502$	−6.08773	−	3.43710i	−0.271709	−	0.153405i
$503$	−1.22757			−0.0547347			−0.0273673	−	0.999625i	$-0.508712\pi$
$503$	−1.22757			−0.0547347			−0.0273673	+	0.999625i	$0.508712\pi$
$504$	−5.77146	+	0.166616i	−0.257081	+	0.00742168i
$505$			0.0695246i			0.00309381i
$506$	12.5141	+	17.4655i	0.556320	+	0.776438i
$507$	12.5434			0.557074
$508$	−20.8578	+	12.5834i	−0.925416	+	0.558300i
$509$		−	16.4650i		−	0.729798i	−0.931047	−	0.364899i	$-0.881103\pi$
$509$		−	16.4650i		−	0.729798i	0.931047	−	0.364899i	$-0.118897\pi$
$510$	10.1769	+	5.74583i	0.450642	+	0.254430i
$511$	−3.16014			−0.139796
$512$	22.5427	−	1.95670i	0.996254	−	0.0864748i
$513$		−	0.636053i		−	0.0280824i
$514$	−8.79089	+	15.5703i	−0.387750	+	0.686776i
$515$	−8.48352			−0.373829
$516$	0.766692	−	0.462542i	0.0337517	−	0.0203623i
$517$	−15.7193			−0.691334
$518$	−12.5634	+	22.2522i	−0.552006	+	0.977705i
$519$		−	22.9330i		−	1.00665i
$520$	−0.0621303	−	2.15214i	−0.00272459	−	0.0943778i
$521$			20.6812i			0.906062i	0.891495	+	0.453031i	$0.149657\pi$
$521$			20.6812i			0.906062i	−0.891495	+	0.453031i	$0.850343\pi$
$522$	−3.88796	−	2.19512i	−0.170172	−	0.0960778i
$523$			3.83784i			0.167817i	0.996473	+	0.0839085i	$0.0267403\pi$
$523$			3.83784i			0.167817i	−0.996473	+	0.0839085i	$0.973260\pi$
$524$	9.13363	+	15.1396i	0.399005	+	0.661374i
$525$	7.61603			0.332391
$526$	3.73277	−	6.61142i	0.162756	−	0.288272i
$527$	−59.2933			−2.58285
$528$	−11.2097	−	5.90899i	−0.487839	−	0.257156i
$529$	14.8274	+	17.5826i	0.644671	+	0.764460i
$530$	9.76033	−	17.2874i	0.423962	−	0.750915i
$531$	−7.81196			−0.339010
$532$	2.22353	−	1.34145i	0.0964023	−	0.0581591i
$533$			7.43874i			0.322208i
$534$	−17.8888	−	10.0999i	−0.774126	−	0.437066i
$535$			10.5474i			0.456006i
$536$	−1.16690	−	40.4206i	−0.0504026	−	1.74591i
$537$	5.31535			0.229374
$538$	11.4877	+	6.48590i	0.495272	+	0.279627i
$539$		−	8.97417i		−	0.386545i
$540$	1.16390	+	1.92924i	0.0500863	+	0.0830212i
$541$		−	4.87351i		−	0.209529i	−0.994497	−	0.104764i	$-0.966591\pi$
$541$		−	4.87351i		−	0.209529i	0.994497	−	0.104764i	$-0.0334088\pi$
$542$	7.17286	+	4.04975i	0.308101	+	0.173952i
$543$	−1.41410			−0.0606849
$544$	34.8972	−	22.4518i	1.49620	−	0.962613i
$545$	−18.1340			−0.776774
$546$	1.69864	+	0.959044i	0.0726953	+	0.0410433i
$547$	−13.0557			−0.558220			−0.279110	−	0.960259i	$-0.590039\pi$
$547$	−13.0557			−0.558220			−0.279110	+	0.960259i	$0.590039\pi$
$548$	20.4392	−	12.3309i	0.873118	−	0.526749i
$549$	0.726453			0.0310043
$550$	14.5551	+	8.21771i	0.620631	+	0.350404i
$551$	2.00810			0.0855478
$552$	−12.4607	−	5.36019i	−0.530361	−	0.228145i
$553$	13.9731			0.594196
$554$	−26.2227	−	14.8052i	−1.11410	−	0.629012i
$555$	9.97190			0.423283
$556$	3.22024	+	5.33774i	0.136568	+	0.226371i
$557$	−25.5035			−1.08062			−0.540309	−	0.841467i	$-0.681693\pi$
$557$	−25.5035			−1.08062			−0.540309	+	0.841467i	$0.681693\pi$
$558$	−9.95424	−	5.62010i	−0.421397	−	0.237918i
$559$	−0.302512			−0.0127949
$560$	−4.28959	+	8.13759i	−0.181268	+	0.343876i
$561$	−23.2383			−0.981123
$562$	−10.4588	−	5.90497i	−0.441178	−	0.249086i
$563$		−	10.5410i		−	0.444249i	−0.975018	−	0.222124i	$-0.928701\pi$
$563$		−	10.5410i		−	0.444249i	0.975018	−	0.222124i	$-0.0712991\pi$
$564$	8.49738	−	5.12643i	0.357804	−	0.215862i
$565$		−	9.46752i		−	0.398302i
$566$	6.60314	+	3.72809i	0.277550	+	0.156703i
$567$	−2.04137			−0.0857294
$568$	−0.00678113	−	0.234893i	−0.000284530	−	0.00985591i
$569$			6.72139i			0.281775i	0.990026	+	0.140888i	$0.0449956\pi$
$569$			6.72139i			0.281775i	−0.990026	+	0.140888i	$0.955004\pi$
$570$	−0.882434	−	0.498217i	−0.0369611	−	0.0208680i
$571$			35.6940i			1.49375i	0.664967	+	0.746873i	$0.268446\pi$
$571$			35.6940i			1.49375i	−0.664967	+	0.746873i	$0.731554\pi$
$572$	2.21149	+	3.66568i	0.0924671	+	0.153270i
$573$	−17.0580			−0.712610
$574$	15.6257	−	27.6759i	0.652202	−	1.15517i
$575$	16.2254	+	7.54173i	0.676646	+	0.314512i
$576$	7.98668	−	0.461519i	0.332778	−	0.0192300i
$577$	17.9584			0.747617			0.373809	−	0.927506i	$-0.378052\pi$
$577$	17.9584			0.747617			0.373809	+	0.927506i	$0.378052\pi$
$578$	25.5931	−	45.3302i	1.06453	−	1.88549i
$579$	−0.970609			−0.0403371
$580$	−6.09083	+	3.67458i	−0.252908	+	0.152578i
$581$			17.6848i			0.733690i
$582$	−0.397210	−	0.224262i	−0.0164649	−	0.00929596i
$583$			39.4745i			1.63487i
$584$	4.37672	−	0.126351i	0.181110	−	0.00522846i
$585$		−	0.761215i		−	0.0314724i
$586$	17.0208	−	30.1471i	0.703124	−	1.24536i
$587$	22.7426			0.938686			0.469343	−	0.883016i	$-0.344491\pi$
$587$	22.7426			0.938686			0.469343	+	0.883016i	$0.344491\pi$
$588$	2.92669	+	4.85117i	0.120695	+	0.200059i
$589$	5.14127			0.211842
$590$	−6.11906	+	10.8380i	−0.251918	+	0.446193i
$591$			12.2034i			0.501981i
$592$	16.5104	−	31.3211i	0.678572	−	1.28729i
$593$	−8.20562			−0.336965			−0.168482	−	0.985705i	$-0.553887\pi$
$593$	−8.20562			−0.336965			−0.168482	+	0.985705i	$0.553887\pi$
$594$	−3.90129	−	2.20264i	−0.160072	−	0.0903754i
$595$			16.8697i			0.691590i
$596$	−6.36941	−	10.5577i	−0.260901	−	0.432460i
$597$	13.9421			0.570610
$598$	2.66915	+	3.72525i	0.109150	+	0.152337i
$599$		−	37.7477i		−	1.54233i	−0.636635	−	0.771165i	$-0.719674\pi$
$599$		−	37.7477i		−	1.54233i	0.636635	−	0.771165i	$-0.280326\pi$
$600$	−10.5480	+	0.304511i	−0.430621	+	0.0124316i
$601$	−41.7041			−1.70115			−0.850573	−	0.525857i	$-0.823745\pi$
$601$	−41.7041			−1.70115			−0.850573	+	0.525857i	$0.823745\pi$
$602$	1.12550	+	0.635450i	0.0458719	+	0.0258990i
$603$		−	14.2968i		−	0.582211i
$604$	15.2525	−	9.20179i	0.620617	−	0.374416i
$605$	−1.08621			−0.0441606
$606$	0.0759998	+	0.0429090i	0.00308728	+	0.00174306i
$607$			32.2348i			1.30837i	0.756334	+	0.654186i	$0.226989\pi$
$607$			32.2348i			1.30837i	−0.756334	+	0.654186i	$0.773011\pi$
$608$	−3.02591	+	1.94678i	−0.122717	+	0.0789522i
$609$		−	6.44485i		−	0.261158i
$610$	0.569026	−	1.00785i	0.0230392	−	0.0408067i
$611$	−3.35279			−0.135639
$612$	12.5619	−	7.57856i	0.507786	−	0.306345i
$613$	−13.7579			−0.555676			−0.277838	−	0.960628i	$-0.589618\pi$
$613$	−13.7579			−0.555676			−0.277838	+	0.960628i	$0.589618\pi$
$614$	−17.9132	+	31.7275i	−0.722916	+	1.28042i
$615$	−12.4024			−0.500115
$616$	−0.527830	−	18.2836i	−0.0212669	−	0.736668i
$617$			43.5902i			1.75487i	0.479692	+	0.877437i	$0.340748\pi$
$617$			43.5902i			1.75487i	−0.479692	+	0.877437i	$0.659252\pi$
$618$	−5.23583	+	9.27363i	−0.210616	+	0.373040i
$619$			9.46626i			0.380481i	0.981738	+	0.190240i	$0.0609268\pi$
$619$			9.46626i			0.380481i	−0.981738	+	0.190240i	$0.939073\pi$
$620$	−15.5942	+	9.40791i	−0.626278	+	0.377831i
$621$	−4.34899	−	2.02145i	−0.174519	−	0.0811182i
$622$	3.50461	+	1.97868i	0.140522	+	0.0793379i
$623$		−	29.6533i		−	1.18803i
$624$	−2.39093	−	1.26034i	−0.0957138	−	0.0504539i
$625$	7.57341			0.302937
$626$	29.4822	+	16.6454i	1.17834	+	0.665285i
$627$	2.01498			0.0804704
$628$	−18.8114	−	31.1811i	−0.750658	−	1.24426i
$629$		−	64.9305i		−	2.58895i
$630$	−1.59899	+	2.83211i	−0.0637053	+	0.112834i
$631$	31.2961			1.24588			0.622938	−	0.782271i	$-0.285939\pi$
$631$	31.2961			1.24588			0.622938	+	0.782271i	$0.285939\pi$
$632$	−19.3524	+	0.558685i	−0.769798	+	0.0222233i
$633$	−10.1618			−0.403896
$634$	−13.2394	−	7.47485i	−0.525802	−	0.296864i
$635$			13.7214i			0.544517i
$636$	−12.8736	−	21.3387i	−0.510470	−	0.846135i
$637$		−	1.91411i		−	0.0758399i
$638$	6.95400	−	12.3168i	0.275311	−	0.487628i
$639$		−	0.0830819i		−	0.00328667i
$640$	5.61562	−	11.4419i	0.221977	−	0.452280i
$641$		−	36.4806i		−	1.44090i	−0.693509	−	0.720448i	$-0.743936\pi$
$641$		−	36.4806i		−	1.44090i	0.693509	−	0.720448i	$-0.256064\pi$
$642$	11.5298	+	6.50964i	0.455044	+	0.256915i
$643$			21.2410i			0.837662i	0.908064	+	0.418831i	$0.137560\pi$
$643$			21.2410i			0.837662i	−0.908064	+	0.418831i	$0.862440\pi$
$644$	−2.10544	−	19.4666i	−0.0829661	−	0.767091i
$645$		−	0.504371i		−	0.0198596i
$646$	−3.24406	+	5.74583i	−0.127636	+	0.226067i
$647$			26.5742i			1.04474i	0.852720	+	0.522369i	$0.174952\pi$
$647$			26.5742i			1.04474i	−0.852720	+	0.522369i	$0.825048\pi$
$648$	2.82725	−	0.0816198i	0.111065	−	0.00320633i
$649$		−	24.7478i		−	0.971436i
$650$	3.10447	+	1.75277i	0.121767	+	0.0687492i
$651$		−	16.5006i		−	0.646708i
$652$	6.65898	+	11.0377i	0.260786	+	0.432268i
$653$			39.2816i			1.53721i	0.639725	+	0.768603i	$0.279048\pi$
$653$			39.2816i			1.53721i	−0.639725	+	0.768603i	$0.720952\pi$
$654$	−11.1919	+	19.8229i	−0.437637	+	0.775135i
$655$	9.95961			0.389154
$656$	−20.5346	+	38.9553i	−0.801742	+	1.52095i
$657$	1.54805			0.0603951
$658$	12.4741	+	7.04280i	0.486291	+	0.274557i
$659$		−	20.9971i		−	0.817929i	−0.912550	−	0.408965i	$-0.865890\pi$
$659$		−	20.9971i		−	0.817929i	0.912550	−	0.408965i	$-0.134110\pi$
$660$	−6.11170	+	3.68717i	−0.237898	+	0.143523i
$661$	−13.1757			−0.512477			−0.256238	−	0.966614i	$-0.582483\pi$
$661$	−13.1757			−0.512477			−0.256238	+	0.966614i	$0.582483\pi$
$662$	−6.83128	+	12.0995i	−0.265505	+	0.470259i
$663$	−4.95653			−0.192496
$664$	−0.707091	−	24.4931i	−0.0274404	−	0.950516i
$665$		−	1.46276i		−	0.0567233i
$666$	6.15442	−	10.9006i	0.238479	−	0.422391i
$667$	6.38197	−	13.7303i	0.247111	−	0.531639i
$668$	30.6277	−	18.4776i	1.18502	−	0.714919i
$669$		−	8.44475i		−	0.326493i
$670$	−19.8348	−	11.1986i	−0.766285	−	0.432640i
$671$			2.30136i			0.0888429i
$672$	6.24805	+	9.71143i	0.241024	+	0.374627i
$673$	32.2831			1.24442			0.622211	−	0.782849i	$-0.286234\pi$
$673$	32.2831			1.24442			0.622211	+	0.782849i	$0.286234\pi$
$674$	18.0861	+	10.2113i	0.696649	+	0.393324i
$675$	−3.73084			−0.143600
$676$	−12.9591	−	21.4805i	−0.498427	−	0.826174i
$677$	9.09250			0.349453			0.174727	−	0.984617i	$-0.444096\pi$
$677$	9.09250			0.349453			0.174727	+	0.984617i	$0.444096\pi$
$678$	−10.3493	−	5.84314i	−0.397462	−	0.224404i
$679$		−	0.658431i		−	0.0252683i
$680$	−0.674499	−	23.3641i	−0.0258659	−	0.895974i
$681$		−	17.6099i		−	0.674814i
$682$	17.8041	−	31.5344i	0.681755	−	1.20751i
$683$	−16.1991			−0.619840			−0.309920	−	0.950763i	$-0.600302\pi$
$683$	−16.1991			−0.619840			−0.309920	+	0.950763i	$0.600302\pi$
$684$	−1.08924	+	0.657131i	−0.0416480	+	0.0251260i
$685$		−	13.4460i		−	0.513745i
$686$	−13.9562	+	24.7190i	−0.532849	+	0.943775i
$687$	−3.08856			−0.117836
$688$	−1.58420	−	0.835082i	−0.0603970	−	0.0318372i
$689$			8.41956i			0.320760i
$690$	−6.21102	+	4.45022i	−0.236449	+	0.169417i
$691$	20.4558			0.778174			0.389087	−	0.921201i	$-0.372791\pi$
$691$	20.4558			0.778174			0.389087	+	0.921201i	$0.372791\pi$
$692$	−39.2726	+	23.6930i	−1.49292	+	0.900673i
$693$		−	6.46693i		−	0.245658i
$694$	12.4472	−	22.0463i	0.472489	−	0.836866i
$695$	3.51145			0.133197
$696$	0.257684	+	8.92596i	0.00976747	+	0.338338i
$697$			80.7566i			3.05887i
$698$	−32.0109	−	18.0732i	−1.21163	−	0.684080i
$699$	−28.2832			−1.06977
$700$	−7.86841	−	13.0424i	−0.297398	−	0.492956i
$701$	7.80036			0.294616			0.147308	−	0.989091i	$-0.452939\pi$
$701$	7.80036			0.294616			0.147308	+	0.989091i	$0.452939\pi$
$702$	−0.832110	−	0.469804i	−0.0314060	−	0.0177316i
$703$			5.63007i			0.212342i
$704$	1.46206	+	25.3013i	0.0551036	+	0.953578i
$705$		−	5.59003i		−	0.210533i
$706$	1.64294	−	2.90995i	0.0618328	−	0.109517i
$707$			0.125980i			0.00473798i
$708$	8.07084	+	13.3779i	0.303321	+	0.502773i
$709$	−35.0186			−1.31515			−0.657576	−	0.753388i	$-0.728418\pi$
$709$	−35.0186			−1.31515			−0.657576	+	0.753388i	$0.728418\pi$
$710$	−0.115264	−	0.0650776i	−0.00432580	−	0.00244232i
$711$	−6.84496			−0.256706
$712$	1.18562	+	41.0691i	0.0444331	+	1.53913i
$713$	16.3396	−	35.1532i	0.611922	−	1.31650i
$714$	18.4408	+	10.4116i	0.690131	+	0.389644i
$715$	2.41148			0.0901843
$716$	−5.49149	−	9.10249i	−0.205227	−	0.340176i
$717$			22.5449i			0.841953i
$718$	−20.5552	+	36.4071i	−0.767114	+	1.35870i
$719$			29.8119i			1.11180i	0.831250	+	0.555899i	$0.187626\pi$
$719$			29.8119i			1.11180i	−0.831250	+	0.555899i	$0.812374\pi$
$720$	2.10133	−	3.98634i	0.0783120	−	0.148562i
$721$	−15.3723			−0.572496
$722$	−12.9293	+	22.9001i	−0.481177	+	0.852254i
$723$		−	7.59261i		−	0.282372i
$724$	1.46096	+	2.42164i	0.0542963	+	0.0899994i
$725$		−	11.7787i		−	0.437451i
$726$	−0.670382	+	1.18737i	−0.0248802	+	0.0440674i
$727$	−38.9023			−1.44281			−0.721403	−	0.692515i	$-0.756503\pi$
$727$	−38.9023			−1.44281			−0.721403	+	0.692515i	$0.756503\pi$
$728$	−0.112582	−	3.89974i	−0.00417255	−	0.144534i
$729$	1.00000			0.0370370
$730$	1.21258	−	2.14770i	0.0448795	−	0.0794899i
$731$	−3.28413			−0.121468
$732$	−0.750526	−	1.24404i	−0.0277403	−	0.0459812i
$733$	28.0442			1.03583			0.517917	−	0.855431i	$-0.326707\pi$
$733$	28.0442			1.03583			0.517917	+	0.855431i	$0.326707\pi$
$734$	14.2575	−	25.2526i	0.526252	−	0.932091i
$735$	3.19136			0.117715
$736$	3.69432	+	26.8766i	0.136175	+	0.990685i
$737$	45.2914			1.66833
$738$	−7.65450	+	13.5575i	−0.281766	+	0.499060i
$739$	7.06291			0.259813			0.129907	−	0.991526i	$-0.458532\pi$
$739$	7.06291			0.259813			0.129907	+	0.991526i	$0.458532\pi$
$740$	−10.3024	−	17.0768i	−0.378722	−	0.627755i
$741$	0.429777			0.0157883
$742$	17.6860	−	31.3251i	0.649272	−	1.14998i
$743$	31.3186			1.14897			0.574485	−	0.818515i	$-0.305203\pi$
$743$	31.3186			1.14897			0.574485	+	0.818515i	$0.305203\pi$
$744$	0.659740	+	22.8529i	0.0241872	+	0.837827i
$745$	−6.94542			−0.254460
$746$	5.24806	−	9.29528i	0.192145	−	0.340325i
$747$		−	8.66322i		−	0.316971i
$748$	24.0084	+	39.7954i	0.877835	+	1.45506i
$749$			19.1122i			0.698346i
$750$	−6.83882	+	12.1128i	−0.249718	+	0.442297i
$751$	−31.9328			−1.16524			−0.582622	−	0.812743i	$-0.697973\pi$
$751$	−31.9328			−1.16524			−0.582622	+	0.812743i	$0.697973\pi$
$752$	−17.5579	−	9.25537i	−0.640272	−	0.337508i
$753$			4.94339i			0.180147i
$754$	1.48323	−	2.62707i	0.0540160	−	0.0956723i
$755$		−	10.0339i		−	0.365172i
$756$	2.10902	+	3.49583i	0.0767042	+	0.127142i
$757$	3.70021			0.134486			0.0672431	−	0.997737i	$-0.478580\pi$
$757$	3.70021			0.134486			0.0672431	+	0.997737i	$0.478580\pi$
$758$	−36.3694	−	20.5339i	−1.32100	−	0.745825i
$759$	6.40384	−	13.7773i	0.232445	−	0.500085i
$760$	0.0584853	+	2.02589i	0.00212149	+	0.0734866i
$761$	−29.3796			−1.06501			−0.532504	−	0.846428i	$-0.678749\pi$
$761$	−29.3796			−1.06501			−0.532504	+	0.846428i	$0.678749\pi$
$762$	14.9993	+	8.46852i	0.543368	+	0.306782i
$763$	−32.8592			−1.18958
$764$	17.6233	+	29.2117i	0.637590	+	1.05684i
$765$		−	8.26391i		−	0.298782i
$766$	7.13611	−	12.6394i	0.257838	−	0.456679i
$767$		−	5.27849i		−	0.190595i
$768$	−9.04169	−	13.2003i	−0.326264	−	0.476325i
$769$			37.9659i			1.36908i	0.728974	+	0.684542i	$0.239998\pi$
$769$			37.9659i			1.36908i	−0.728974	+	0.684542i	$0.760002\pi$
$770$	−8.97195	−	5.06550i	−0.323327	−	0.182548i
$771$	12.6435			0.455343
$772$	1.00277	+	1.66216i	0.0360906	+	0.0598224i
$773$	25.8178			0.928603			0.464301	−	0.885677i	$-0.346305\pi$
$773$	25.8178			0.928603			0.464301	+	0.885677i	$0.346305\pi$
$774$	−0.551345	−	0.311286i	−0.0198177	−	0.0111889i
$775$		−	30.1567i		−	1.08326i
$776$	0.0263260	+	0.911912i	0.000945047	+	0.0327357i
$777$	18.0693			0.648233
$778$	−22.8523	+	40.4756i	−0.819293	+	1.45112i
$779$		−	7.00234i		−	0.250885i
$780$	−1.30357	+	0.786441i	−0.0466754	+	0.0281591i
$781$	0.263198			0.00941798
$782$	28.9769	+	40.4421i	1.03621	+	1.44621i
$783$			3.15712i			0.112826i
$784$	5.28390	−	10.0239i	0.188711	−	0.357995i
$785$	−20.5126			−0.732126
$786$	6.14684	−	10.8872i	0.219251	−	0.388333i
$787$		−	28.7742i		−	1.02569i	−0.858481	−	0.512845i	$-0.828592\pi$
$787$		−	28.7742i		−	1.02569i	0.858481	−	0.512845i	$-0.171408\pi$
$788$	20.8982	−	12.6078i	0.744468	−	0.449134i
$789$	−5.36863			−0.191128
$790$	−5.36161	+	9.49641i	−0.190758	+	0.337867i
$791$		−	17.1554i		−	0.609975i
$792$	0.258567	+	8.95655i	0.00918776	+	0.318257i
$793$			0.490860i			0.0174309i
$794$	17.3374	+	9.78859i	0.615281	+	0.347384i
$795$	−14.0377			−0.497868
$796$	−14.4041	−	23.8756i	−0.510539	−	0.846249i
$797$	6.34630			0.224798			0.112399	−	0.993663i	$-0.464147\pi$
$797$	6.34630			0.224798			0.112399	+	0.993663i	$0.464147\pi$
$798$	−1.59899	−	0.902780i	−0.0566037	−	0.0319581i
$799$	−36.3986			−1.28769
$800$	11.4190	+	17.7488i	0.403724	+	0.627515i
$801$			14.5262i			0.513257i
$802$	−7.71572	−	4.35625i	−0.272452	−	0.153824i
$803$			4.90412i			0.173063i
$804$	−24.4832	+	14.7706i	−0.863454	+	0.520918i
$805$	−10.0016	−	4.64882i	−0.352509	−	0.163849i
$806$	3.79747	−	6.72602i	0.133760	−	0.236914i
$807$		−	9.32832i		−	0.328372i
$808$	−0.00503706	−	0.174480i	−0.000177203	−	0.00613818i
$809$	−1.67875			−0.0590218			−0.0295109	−	0.999564i	$-0.509395\pi$
$809$	−1.67875			−0.0590218			−0.0295109	+	0.999564i	$0.509395\pi$
$810$	0.783294	−	1.38736i	0.0275221	−	0.0487468i
$811$	48.9995			1.72060			0.860302	−	0.509785i	$-0.170275\pi$
$811$	48.9995			1.72060			0.860302	+	0.509785i	$0.170275\pi$
$812$	−11.0367	+	6.65842i	−0.387314	+	0.233665i
$813$		−	5.82454i		−	0.204275i
$814$	34.5325	+	19.4968i	1.21036	+	0.683363i
$815$	7.26117			0.254348
$816$	−25.9564	−	13.6825i	−0.908657	−	0.478983i
$817$	0.284765			0.00996265
$818$	8.34006	−	14.7718i	0.291603	−	0.516484i
$819$		−	1.37934i		−	0.0481980i
$820$	12.8134	+	21.2391i	0.447465	+	0.741700i
$821$		−	47.1044i		−	1.64396i	−0.569520	−	0.821978i	$-0.692871\pi$
$821$		−	47.1044i		−	1.64396i	0.569520	−	0.821978i	$-0.307129\pi$
$822$	−14.6983	−	8.29855i	−0.512661	−	0.289445i
$823$			35.8300i			1.24896i	0.781042	+	0.624478i	$0.214688\pi$
$823$			35.8300i			1.24896i	−0.781042	+	0.624478i	$0.785312\pi$
$824$	21.2903	−	0.614631i	0.741684	−	0.0214117i
$825$		−	11.8191i		−	0.411488i
$826$	−11.0879	+	19.6387i	−0.385797	+	0.683318i
$827$		−	17.6215i		−	0.612761i	−0.951909	−	0.306380i	$-0.900882\pi$
$827$		−	17.6215i		−	0.612761i	0.951909	−	0.306380i	$-0.0991179\pi$
$828$	1.03139	+	9.53605i	0.0358432	+	0.331401i
$829$		−	18.6855i		−	0.648975i	−0.945890	−	0.324487i	$-0.894808\pi$
$829$		−	18.6855i		−	0.648975i	0.945890	−	0.324487i	$-0.105192\pi$
$830$	−12.0190	−	6.78585i	−0.417185	−	0.235540i
$831$			21.2935i			0.738663i
$832$	0.311846	+	5.39655i	0.0108113	+	0.187092i
$833$		−	20.7800i		−	0.719985i
$834$	2.16719	−	3.83849i	0.0750436	−	0.132916i
$835$		−	20.1486i		−	0.697270i
$836$	−2.08175	−	3.45063i	−0.0719989	−	0.119343i
$837$			8.08308i			0.279392i
$838$	−41.5275	−	23.4462i	−1.43454	−	0.809934i
$839$	23.7780			0.820908			0.410454	−	0.911881i	$-0.365370\pi$
$839$	23.7780			0.820908			0.410454	+	0.911881i	$0.365370\pi$
$840$	6.50194	−	0.187705i	0.224338	−	0.00647642i
$841$	19.0326			0.656297
$842$	5.49232	−	9.72793i	0.189278	−	0.335246i
$843$			8.49280i			0.292508i
$844$	10.4986	+	17.4020i	0.361376	+	0.599002i
$845$	−14.1310			−0.486123
$846$	−6.11066	−	3.45004i	−0.210089	−	0.118615i
$847$	−1.96823			−0.0676293
$848$	−23.2422	+	44.0917i	−0.798139	+	1.51411i
$849$		−	5.36190i		−	0.184020i
$850$	33.7028	+	19.0284i	1.15600	+	0.652669i
$851$	38.4954	+	17.8930i	1.31960	+	0.613366i
$852$	−0.142277	+	0.0858352i	−0.00487433	+	0.00294066i
$853$			5.19183i			0.177765i	0.996042	+	0.0888825i	$0.0283296\pi$
$853$			5.19183i			0.177765i	−0.996042	+	0.0888825i	$0.971670\pi$
$854$	1.03109	−	1.82625i	0.0352831	−	0.0624930i
$855$			0.716558i			0.0245058i
$856$	−0.764162	−	26.4700i	−0.0261185	−	0.904726i
$857$	−28.1642			−0.962071			−0.481035	−	0.876701i	$-0.659739\pi$
$857$	−28.1642			−0.962071			−0.481035	+	0.876701i	$0.659739\pi$
$858$	1.48831	−	2.63607i	0.0508101	−	0.0899941i
$859$	25.6237			0.874268			0.437134	−	0.899396i	$-0.355993\pi$
$859$	25.6237			0.874268			0.437134	+	0.899396i	$0.355993\pi$
$860$	−0.863731	+	0.521085i	−0.0294530	+	0.0177689i
$861$	−22.4735			−0.765896
$862$	−2.60374	+	4.61171i	−0.0886839	+	0.157076i
$863$		−	0.866384i		−	0.0294921i	−0.999891	−	0.0147460i	$-0.995306\pi$
$863$		−	0.866384i		−	0.0294921i	0.999891	−	0.0147460i	$-0.00469398\pi$
$864$	−3.06071	−	4.75731i	−0.104128	−	0.161847i
$865$			25.8356i			0.878438i
$866$	25.5614	+	14.4318i	0.868613	+	0.490413i
$867$	−36.8092			−1.25011
$868$	−28.2570	+	17.0474i	−0.959107	+	0.578625i
$869$		−	21.6844i		−	0.735593i
$870$	4.38006	+	2.47295i	0.148498	+	0.0838409i
$871$	9.66027			0.327326
$872$	45.5092	−	1.31381i	1.54114	−	0.0444911i
$873$			0.322544i			0.0109165i
$874$	−2.51256	−	3.50670i	−0.0849887	−	0.118616i
$875$	−20.0787			−0.678783
$876$	−1.59935	−	2.65102i	−0.0540370	−	0.0895696i
$877$			51.6475i			1.74401i	0.489495	+	0.872006i	$0.337181\pi$
$877$			51.6475i			1.74401i	−0.489495	+	0.872006i	$0.662819\pi$
$878$	32.2488	+	18.2075i	1.08835	+	0.614473i
$879$	−24.4801			−0.825694
$880$	12.6285	+	6.65688i	0.425706	+	0.224404i
$881$		−	31.3452i		−	1.05605i	−0.849230	−	0.528024i	$-0.822933\pi$
$881$		−	31.3452i		−	1.05605i	0.849230	−	0.528024i	$-0.177067\pi$
$882$	1.96963	−	3.48858i	0.0663209	−	0.117467i
$883$	−41.3489			−1.39150			−0.695751	−	0.718283i	$-0.744928\pi$
$883$	−41.3489			−1.39150			−0.695751	+	0.718283i	$0.744928\pi$
$884$	5.12079	+	8.48802i	0.172231	+	0.285483i
$885$	8.80071			0.295833
$886$	−1.50143	+	2.65932i	−0.0504416	+	0.0893415i
$887$			35.3559i			1.18714i	0.804784	+	0.593568i	$0.202281\pi$
$887$			35.3559i			1.18714i	−0.804784	+	0.593568i	$0.797719\pi$
$888$	−25.0256	+	0.722464i	−0.839804	+	0.0242443i
$889$			24.8635i			0.833895i
$890$	20.1530	+	11.3783i	0.675530	+	0.381400i
$891$			3.16794i			0.106130i
$892$	−14.4616	+	8.72460i	−0.484209	+	0.292121i
$893$	3.15610			0.105615
$894$	−4.28655	+	7.59228i	−0.143364	+	0.253924i
$895$	−5.98811			−0.200160
$896$	10.1756	−	20.7330i	0.339944	−	0.692640i
$897$	1.36588	−	2.93859i	0.0456055	−	0.0981165i
$898$	−18.6610	+	33.0521i	−0.622727	+	1.10296i
$899$	−25.5193			−0.851115
$900$	3.85448	+	6.38904i	0.128483	+	0.212968i
$901$			91.4046i			3.04513i
$902$	−42.9494	−	24.2490i	−1.43006	−	0.807402i
$903$		−	0.913932i		−	0.0304138i
$904$	0.685922	+	23.7598i	0.0228134	+	0.790240i
$905$	1.59308			0.0529559
$906$	−10.9684	−	6.19271i	−0.364402	−	0.205739i
$907$			46.2848i			1.53686i	0.639932	+	0.768431i	$0.278962\pi$
$907$			46.2848i			1.53686i	−0.639932	+	0.768431i	$0.721038\pi$
$908$	−30.1569	+	18.1935i	−1.00079	+	0.603773i
$909$		−	0.0617136i		−	0.00204691i
$910$	−1.91364	−	1.08043i	−0.0634365	−	0.0358159i
$911$	−48.9141			−1.62060			−0.810298	−	0.586018i	$-0.800695\pi$
$911$	−48.9141			−1.62060			−0.810298	+	0.586018i	$0.800695\pi$
$912$	2.25066	+	1.18640i	0.0745269	+	0.0392856i
$913$	27.4445			0.908282
$914$	−14.0248	−	7.91829i	−0.463898	−	0.261914i
$915$	−0.818399			−0.0270554
$916$	3.19091	+	5.28913i	0.105431	+	0.174758i
$917$	18.0471			0.595966
$918$	−9.03357	−	5.10030i	−0.298152	−	0.168335i
$919$	17.2295			0.568347			0.284174	−	0.958773i	$-0.408281\pi$
$919$	17.2295			0.568347			0.284174	+	0.958773i	$0.408281\pi$
$920$	14.0378	+	6.03862i	0.462813	+	0.199087i
$921$	25.7635			0.848937
$922$	−41.2145	−	23.2695i	−1.35733	−	0.766339i
$923$	0.0561379			0.00184780
$924$	−11.0746	+	6.68123i	−0.364326	+	0.219796i
$925$	33.0238			1.08582
$926$	−26.9340	−	15.2068i	−0.885106	−	0.499725i
$927$	7.53041			0.247331
$928$	15.0194	−	9.66304i	0.493036	−	0.317205i
$929$	4.54239			0.149031			0.0745154	−	0.997220i	$-0.476259\pi$
$929$	4.54239			0.149031			0.0745154	+	0.997220i	$0.476259\pi$
$930$	11.2141	+	6.33143i	0.367726	+	0.207616i
$931$			1.80182i			0.0590523i
$932$	29.2205	+	48.4347i	0.957148	+	1.58653i
$933$		−	2.84583i		−	0.0931682i
$934$	−25.1711	−	14.2115i	−0.823624	−	0.465013i
$935$	26.1796			0.856163
$936$	0.0551500	+	1.91035i	0.00180263	+	0.0624419i
$937$		−	11.2130i		−	0.366314i	−0.983084	−	0.183157i	$-0.941368\pi$
$937$		−	11.2130i		−	0.366314i	0.983084	−	0.183157i	$-0.0586316\pi$
$938$	−35.9411	−	20.2921i	−1.17352	−	0.662562i
$939$		−	23.9402i		−	0.781259i
$940$	−9.57288	+	5.77528i	−0.312233	+	0.188369i
$941$	0.106814			0.00348203			0.00174102	−	0.999998i	$-0.499446\pi$
$941$	0.106814			0.00348203			0.00174102	+	0.999998i	$0.499446\pi$
$942$	−12.6599	+	22.4230i	−0.412482	+	0.730582i
$943$	−47.8782	−	22.2543i	−1.55913	−	0.724699i
$944$	14.5713	−	27.6425i	0.474254	−	0.899686i
$945$	2.29974			0.0748106
$946$	0.986135	−	1.74663i	0.0320620	−	0.0567877i
$947$	−43.9497			−1.42817			−0.714087	−	0.700056i	$-0.753158\pi$
$947$	−43.9497			−1.42817			−0.714087	+	0.700056i	$0.753158\pi$
$948$	7.07179	+	11.7219i	0.229681	+	0.380711i
$949$			1.04601i			0.0339548i
$950$	−2.92235	−	1.64994i	−0.0948134	−	0.0535311i
$951$			10.7507i			0.348614i
$952$	−1.22221	−	42.3364i	−0.0396120	−	1.37213i
$953$		−	42.8095i		−	1.38674i	−0.720583	−	0.693368i	$-0.756126\pi$
$953$		−	42.8095i		−	1.38674i	0.720583	−	0.693368i	$-0.243874\pi$
$954$	−8.66377	+	15.3451i	−0.280500	+	0.496817i
$955$	19.2171			0.621849
$956$	38.6079	−	23.2920i	1.24867	−	0.753316i
$957$	−10.0016			−0.323304
$958$	−16.3439	+	28.9480i	−0.528047	+	0.935269i
$959$		−	24.3644i		−	0.786769i
$960$	−8.99754	+	0.519933i	−0.290394	+	0.0167808i
$961$	−34.3362			−1.10762
$962$	7.36548	+	4.15850i	0.237473	+	0.134076i
$963$		−	9.36246i		−	0.301701i
$964$	−13.0023	+	7.84422i	−0.418775	+	0.252645i
$965$	1.09346			0.0351996
$966$	−11.2545	+	8.06390i	−0.362108	+	0.259452i
$967$		−	45.6575i		−	1.46825i	−0.679016	−	0.734124i	$-0.737593\pi$
$967$		−	45.6575i		−	1.46825i	0.679016	−	0.734124i	$-0.262407\pi$
$968$	2.72596	−	0.0786957i	0.0876156	−	0.00252937i
$969$	4.66575			0.149886
$970$	0.447484	+	0.252647i	0.0143678	+	0.00811199i
$971$		−	23.2495i		−	0.746111i	−0.927809	−	0.373055i	$-0.878310\pi$
$971$		−	23.2495i		−	0.746111i	0.927809	−	0.373055i	$-0.121690\pi$
$972$	−1.03314	−	1.71249i	−0.0331379	−	0.0549282i
$973$	6.36284			0.203983
$974$	14.4846	+	8.17792i	0.464117	+	0.262038i
$975$		−	2.52091i		−	0.0807337i
$976$	−1.35502	+	2.57054i	−0.0433730	+	0.0822810i
$977$			57.1849i			1.82951i	0.404012	+	0.914754i	$0.367615\pi$
$977$			57.1849i			1.82951i	−0.404012	+	0.914754i	$0.632385\pi$
$978$	4.48143	−	7.93744i	0.143300	−	0.253811i
$979$	−46.0180			−1.47074
$980$	−3.29711	−	5.46517i	−0.105322	−	0.174578i
$981$	16.0966			0.513926
$982$	−21.6943	+	38.4247i	−0.692293	+	1.22618i
$983$	53.4079			1.70345			0.851723	−	0.523992i	$-0.175558\pi$
$983$	53.4079			1.70345			0.851723	+	0.523992i	$0.175558\pi$
$984$	31.1253	−	0.898557i	0.992239	−	0.0286449i
$985$		−	13.7480i		−	0.438046i
$986$	16.1022	−	28.5201i	0.512800	−	0.908264i
$987$		−	10.1293i		−	0.322418i
$988$	−0.444019	−	0.735990i	−0.0141261	−	0.0234149i
$989$	0.905016	−	1.94707i	0.0287778	−	0.0619131i
$990$	4.39506	+	2.48143i	0.139684	+	0.0788649i
$991$		−	24.2589i		−	0.770609i	−0.922789	−	0.385305i	$-0.874096\pi$
$991$		−	24.2589i		−	0.770609i	0.922789	−	0.385305i	$-0.125904\pi$
$992$	38.4538	−	24.7400i	1.22091	−	0.785496i
$993$	9.82506			0.311789
$994$	−0.208862	−	0.117922i	−0.00662470	−	0.00374026i
$995$	−15.7067			−0.497935
$996$	−14.8357	+	8.95031i	−0.470087	+	0.283601i
$997$		−	38.9275i		−	1.23285i	−0.787415	−	0.616423i	$-0.788581\pi$
$997$		−	38.9275i		−	1.23285i	0.787415	−	0.616423i	$-0.211419\pi$
$998$	−18.8885	+	33.4550i	−0.597904	+	1.05900i
$999$	−8.85157			−0.280051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.a.91.11	yes	24
4.3	odd	2		2208.2.n.a.367.10		24
8.3	odd	2	inner	552.2.n.a.91.10	yes	24
8.5	even	2		2208.2.n.a.367.16		24
23.22	odd	2	inner	552.2.n.a.91.12	yes	24
92.91	even	2		2208.2.n.a.367.15		24
184.45	odd	2		2208.2.n.a.367.9		24
184.91	even	2	inner	552.2.n.a.91.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.a.91.9	✓	24	184.91	even	2	inner
552.2.n.a.91.10	yes	24	8.3	odd	2	inner
552.2.n.a.91.11	yes	24	1.1	even	1	trivial
552.2.n.a.91.12	yes	24	23.22	odd	2	inner
2208.2.n.a.367.9		24	184.45	odd	2
2208.2.n.a.367.10		24	4.3	odd	2
2208.2.n.a.367.15		24	92.91	even	2
2208.2.n.a.367.16		24	8.5	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.695292 + 1.23149i) q^{2} +1.00000 q^{3} +(-1.03314 - 1.71249i) q^{4} -1.12657 q^{5} +(-0.695292 + 1.23149i) q^{6} -2.04137 q^{7} +(2.82725 - 0.0816198i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.695292 + 1.23149i) q^{2} +1.00000 q^{3} +(-1.03314 - 1.71249i) q^{4} -1.12657 q^{5} +(-0.695292 + 1.23149i) q^{6} -2.04137 q^{7} +(2.82725 - 0.0816198i) q^{8} +1.00000 q^{9} +(0.783294 - 1.38736i) q^{10} +3.16794i q^{11} +(-1.03314 - 1.71249i) q^{12} +0.675694i q^{13} +(1.41935 - 2.51393i) q^{14} -1.12657 q^{15} +(-1.86525 + 3.53848i) q^{16} +7.33548i q^{17} +(-0.695292 + 1.23149i) q^{18} -0.636053i q^{19} +(1.16390 + 1.92924i) q^{20} -2.04137 q^{21} +(-3.90129 - 2.20264i) q^{22} +(-4.34899 - 2.02145i) q^{23} +(2.82725 - 0.0816198i) q^{24} -3.73084 q^{25} +(-0.832110 - 0.469804i) q^{26} +1.00000 q^{27} +(2.10902 + 3.49583i) q^{28} +3.15712i q^{29} +(0.783294 - 1.38736i) q^{30} +8.08308i q^{31} +(-3.06071 - 4.75731i) q^{32} +3.16794i q^{33} +(-9.03357 - 5.10030i) q^{34} +2.29974 q^{35} +(-1.03314 - 1.71249i) q^{36} -8.85157 q^{37} +(0.783294 + 0.442243i) q^{38} +0.675694i q^{39} +(-3.18509 + 0.0919503i) q^{40} +11.0090 q^{41} +(1.41935 - 2.51393i) q^{42} +0.447706i q^{43} +(5.42506 - 3.27292i) q^{44} -1.12657 q^{45} +(5.51322 - 3.95024i) q^{46} +4.96200i q^{47} +(-1.86525 + 3.53848i) q^{48} -2.83281 q^{49} +(2.59403 - 4.59450i) q^{50} +7.33548i q^{51} +(1.15712 - 0.698085i) q^{52} +12.4606 q^{53} +(-0.695292 + 1.23149i) q^{54} -3.56890i q^{55} +(-5.77146 + 0.166616i) q^{56} -0.636053i q^{57} +(-3.88796 - 2.19512i) q^{58} -7.81196 q^{59} +(1.16390 + 1.92924i) q^{60} +0.726453 q^{61} +(-9.95424 - 5.62010i) q^{62} -2.04137 q^{63} +(7.98668 - 0.461519i) q^{64} -0.761215i q^{65} +(-3.90129 - 2.20264i) q^{66} -14.2968i q^{67} +(12.5619 - 7.57856i) q^{68} +(-4.34899 - 2.02145i) q^{69} +(-1.59899 + 2.83211i) q^{70} -0.0830819i q^{71} +(2.82725 - 0.0816198i) q^{72} +1.54805 q^{73} +(6.15442 - 10.9006i) q^{74} -3.73084 q^{75} +(-1.08924 + 0.657131i) q^{76} -6.46693i q^{77} +(-0.832110 - 0.469804i) q^{78} -6.84496 q^{79} +(2.10133 - 3.98634i) q^{80} +1.00000 q^{81} +(-7.65450 + 13.5575i) q^{82} -8.66322i q^{83} +(2.10902 + 3.49583i) q^{84} -8.26391i q^{85} +(-0.551345 - 0.311286i) q^{86} +3.15712i q^{87} +(0.258567 + 8.95655i) q^{88} +14.5262i q^{89} +(0.783294 - 1.38736i) q^{90} -1.37934i q^{91} +(1.03139 + 9.53605i) q^{92} +8.08308i q^{93} +(-6.11066 - 3.45004i) q^{94} +0.716558i q^{95} +(-3.06071 - 4.75731i) q^{96} +0.322544i q^{97} +(1.96963 - 3.48858i) q^{98} +3.16794i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9	\( 24 q - 4 q^{2} + 24 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 24 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 4 q^{24} + 24 q^{25} + 24 q^{27} - 4 q^{32} + 4 q^{36} + 4 q^{46} + 4 q^{48} - 8 q^{49} - 44 q^{50} - 4 q^{54} + 48 q^{58} - 40 q^{62} + 4 q^{64} - 4 q^{72} - 32 q^{73} + 24 q^{75} + 24 q^{81} - 40 q^{82} - 52 q^{92} + 40 q^{94} - 4 q^{96} - 20 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 24 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 24 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 4 * q^24 + 24 * q^25 + 24 * q^27 - 4 * q^32 + 4 * q^36 + 4 * q^46 + 4 * q^48 - 8 * q^49 - 44 * q^50 - 4 * q^54 + 48 * q^58 - 40 * q^62 + 4 * q^64 - 4 * q^72 - 32 * q^73 + 24 * q^75 + 24 * q^81 - 40 * q^82 - 52 * q^92 + 40 * q^94 - 4 * q^96 - 20 * q^98

Introduction

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