LMFDB - Embedded newform 552.2.n.a.91.10

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			91.10
Character	$\chi$	$=$	552.91
Dual form			552.2.n.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)

$f(q)$	$=$	$q+(-0.695292 - 1.23149i) q^{2} +1.00000 q^{3} +(-1.03314 + 1.71249i) q^{4} +1.12657 q^{5} +(-0.695292 - 1.23149i) q^{6} +2.04137 q^{7} +(2.82725 + 0.0816198i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(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} +(-0.534415 - 6.76124i) 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} +(-7.95483 + 5.35916i) 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	$-0.418942\pi$
$5$	1.12657			0.503817			0.251908	+	0.967751i	$0.418942\pi$
$6$	−0.695292	−	1.23149i	−0.283852	−	0.502754i
$7$	2.04137			0.771565			0.385782	−	0.922590i	$-0.373932\pi$
$7$	2.04137			0.771565			0.385782	+	0.922590i	$0.373932\pi$
$8$	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	$-0.970130\pi$
$13$		−	0.675694i		−	0.187404i	0.995600	−	0.0937019i	$-0.0298700\pi$
$14$	−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	$-0.905303\pi$
$29$		−	3.15712i		−	0.586262i	0.956072	−	0.293131i	$-0.0946973\pi$
$30$	−0.783294	−	1.38736i	−0.143009	−	0.253296i
$31$		−	8.08308i		−	1.45176i	−0.687819	−	0.725882i	$-0.741432\pi$
$31$		−	8.08308i		−	1.45176i	0.687819	−	0.725882i	$-0.258568\pi$
$32$	−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	$-0.240638\pi$
$37$	8.85157			1.45519			0.727594	+	0.686008i	$0.240638\pi$
$38$	−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
$46$	−0.534415	−	6.76124i	−0.0787952	−	0.996891i
$47$		−	4.96200i		−	0.723782i	−0.932220	−	0.361891i	$-0.882131\pi$
$47$		−	4.96200i		−	0.723782i	0.932220	−	0.361891i	$-0.117869\pi$
$48$	−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	$-0.826934\pi$
$53$	−12.4606			−1.71160			−0.855799	+	0.517308i	$0.826934\pi$
$54$	−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	$-0.514809\pi$
$61$	−0.726453			−0.0930128			−0.0465064	+	0.998918i	$0.514809\pi$
$62$	−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	$0.00156928\pi$
$71$			0.0830819i			0.00986001i	−0.999988	+	0.00493001i	$0.998431\pi$
$72$	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	$-0.374181\pi$
$79$	6.84496			0.770118			0.385059	+	0.922892i	$0.374181\pi$
$80$	−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
$92$	−7.95483	+	5.35916i	−0.829349	+	0.558731i
$93$		−	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	$0.000977330\pi$
$101$			0.0617136i			0.00614074i	−0.999995	+	0.00307037i	$0.999023\pi$
$102$	9.03357	−	5.10030i	0.894457	−	0.505005i
$103$	−7.53041			−0.741993			−0.370997	−	0.928634i	$-0.620984\pi$
$103$	−7.53041			−0.741993			−0.370997	+	0.928634i	$0.620984\pi$
$104$	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	$-0.780188\pi$
$109$	−16.0966			−1.54178			−0.770889	+	0.636969i	$0.780188\pi$
$110$	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	$0.181724\pi$
$127$			12.1798i			1.08078i	−0.841414	+	0.540392i	$0.818276\pi$
$128$	−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	$0.829700\pi$
$138$	−0.534415	−	6.76124i	−0.0454925	−	0.575555i
$139$	−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	$-0.581264\pi$
$149$	−6.16511			−0.505066			−0.252533	+	0.967588i	$0.581264\pi$
$150$	2.59403	+	4.59450i	0.211801	+	0.375139i
$151$		−	8.90664i		−	0.724812i	−0.932020	−	0.362406i	$-0.881955\pi$
$151$		−	8.90664i		−	0.724812i	0.932020	−	0.362406i	$-0.118045\pi$
$152$	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	$-0.758891\pi$
$157$	−18.2080			−1.45316			−0.726580	+	0.687082i	$0.758891\pi$
$158$	−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	$-0.756735\pi$
$167$		−	17.8849i		−	1.38397i	0.721910	−	0.691987i	$-0.243265\pi$
$168$	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	$0.337036\pi$
$173$			22.9330i			1.74357i	−0.489891	+	0.871784i	$0.662964\pi$
$174$	−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	$-0.483264\pi$
$181$	1.41410			0.105109			0.0525547	+	0.998618i	$0.483264\pi$
$182$	−1.69864	+	0.959044i	−0.125912	+	0.0710891i
$183$	−0.726453			−0.0537009
$184$	12.1307	+	6.07012i	0.894286	+	0.447495i
$185$	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	$-0.288292\pi$
$191$	17.0580			1.23428			0.617138	+	0.786855i	$0.288292\pi$
$192$	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	$-0.856845\pi$
$197$		−	12.2034i		−	0.869456i	0.900562	−	0.434728i	$-0.143155\pi$
$198$	3.90129	−	2.20264i	0.277252	−	0.156535i
$199$	−13.9421			−0.988326			−0.494163	−	0.869369i	$-0.664525\pi$
$199$	−13.9421			−0.988326			−0.494163	+	0.869369i	$0.664525\pi$
$200$	−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	$0.0912470\pi$
$223$			8.44475i			0.565502i	−0.959193	+	0.282751i	$0.908753\pi$
$224$	−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	$-0.467460\pi$
$229$	3.08856			0.204098			0.102049	+	0.994779i	$0.467460\pi$
$230$	−0.602055	−	7.61700i	−0.0396984	−	0.502250i
$231$			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	$-0.739914\pi$
$239$		−	22.5449i		−	1.45831i	0.684351	−	0.729153i	$-0.260086\pi$
$240$	−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	$-0.447069\pi$
$263$	5.36863			0.331044			0.165522	+	0.986206i	$0.447069\pi$
$264$	−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	$0.0917874\pi$
$269$			9.32832i			0.568758i	−0.958712	+	0.284379i	$0.908213\pi$
$270$	−0.783294	−	1.38736i	−0.0476697	−	0.0844319i
$271$			5.82454i			0.353815i	0.984227	+	0.176908i	$0.0566094\pi$
$271$			5.82454i			0.353815i	−0.984227	+	0.176908i	$0.943391\pi$
$272$	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
$276$	−7.95483	+	5.35916i	−0.478825	+	0.322584i
$277$		−	21.2935i		−	1.27940i	−0.768624	−	0.639701i	$-0.779058\pi$
$277$		−	21.2935i		−	1.27940i	0.768624	−	0.639701i	$-0.220942\pi$
$278$	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	$-0.246394\pi$
$293$	24.4801			1.43014			0.715072	+	0.699051i	$0.246394\pi$
$294$	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	$0.0257111\pi$
$311$			2.84583i			0.161372i	−0.996740	+	0.0806860i	$0.974289\pi$
$312$	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	$-0.902376\pi$
$317$		−	10.7507i		−	0.603818i	0.953337	−	0.301909i	$-0.0976238\pi$
$318$	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
$322$	−1.09094	−	13.8022i	−0.0607956	−	0.769166i
$323$	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	$-0.755092\pi$
$349$		−	25.9937i		−	1.39141i	0.718328	−	0.695704i	$-0.244908\pi$
$350$	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	$-0.784857\pi$
$359$	−29.5635			−1.56030			−0.780150	+	0.625593i	$0.784857\pi$
$360$	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	$-0.320238\pi$
$367$	20.5057			1.07039			0.535195	+	0.844729i	$0.320238\pi$
$368$	−0.959074	−	19.1593i	−0.0499952	−	0.998749i
$369$	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	$-0.437396\pi$
$373$	7.54799			0.390820			0.195410	+	0.980722i	$0.437396\pi$
$374$	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	$-0.415546\pi$
$383$	10.2635			0.524439			0.262219	+	0.965008i	$0.415546\pi$
$384$	−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	$-0.813503\pi$
$389$	−32.8672			−1.66643			−0.833215	+	0.552948i	$0.813503\pi$
$390$	−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	$0.114936\pi$
$397$			14.0784i			0.706574i	−0.935515	+	0.353287i	$0.885064\pi$
$398$	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
$414$	−0.534415	−	6.76124i	−0.0262651	−	0.332297i
$415$		−	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	$-0.438342\pi$
$421$	7.89931			0.384989			0.192494	+	0.981298i	$0.438342\pi$
$422$	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	$-0.528748\pi$
$431$	−3.74482			−0.180382			−0.0901908	+	0.995925i	$0.528748\pi$
$432$	−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	$0.214866\pi$
$439$			26.1868i			1.24983i	−0.780693	+	0.624914i	$0.785134\pi$
$440$	−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
$460$	−8.96166	+	6.03746i	−0.417840	+	0.281498i
$461$		−	33.4672i		−	1.55872i	−0.626575	−	0.779361i	$-0.715544\pi$
$461$		−	33.4672i		−	1.55872i	0.626575	−	0.779361i	$-0.284456\pi$
$462$	7.96396	−	4.49640i	0.370517	−	0.209192i
$463$		−	21.8710i		−	1.01643i	−0.861229	−	0.508217i	$-0.830305\pi$
$463$		−	21.8710i		−	1.01643i	0.861229	−	0.508217i	$-0.169695\pi$
$464$	−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	$-0.680450\pi$
$479$	−23.5065			−1.07404			−0.537020	+	0.843570i	$0.680450\pi$
$480$	−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	$0.0858640\pi$
$487$			11.7619i			0.532981i	−0.963838	+	0.266490i	$0.914136\pi$
$488$	−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	$-0.491288\pi$
$503$	1.22757			0.0547347			0.0273673	+	0.999625i	$0.491288\pi$
$504$	5.77146	+	0.166616i	0.257081	+	0.00742168i
$505$			0.0695246i			0.00309381i
$506$	21.4192	−	1.69299i	0.952199	−	0.0752628i
$507$	12.5434			0.557074
$508$	−20.8578	−	12.5834i	−0.925416	−	0.558300i
$509$			16.4650i			0.729798i	0.931047	+	0.364899i	$0.118897\pi$
$509$			16.4650i			0.729798i	−0.931047	+	0.364899i	$0.881103\pi$
$510$	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	$0.0334088\pi$
$541$			4.87351i			0.209529i	−0.994497	+	0.104764i	$0.966591\pi$
$542$	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
$552$	12.1307	+	6.07012i	0.516316	+	0.258361i
$553$	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	$-0.318307\pi$
$557$	25.5035			1.08062			0.540309	+	0.841467i	$0.318307\pi$
$558$	−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
$598$	−4.56853	+	0.361101i	−0.186821	+	0.0147665i
$599$			37.7477i			1.54233i	0.636635	+	0.771165i	$0.280326\pi$
$599$			37.7477i			1.54233i	−0.636635	+	0.771165i	$0.719674\pi$
$600$	−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	$-0.773011\pi$
$607$		−	32.2348i		−	1.30837i	0.756334	−	0.654186i	$-0.226989\pi$
$608$	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	$-0.410382\pi$
$613$	13.7579			0.555676			0.277838	+	0.960628i	$0.410382\pi$
$614$	−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	$-0.714061\pi$
$631$	−31.2961			−1.24588			−0.622938	+	0.782271i	$0.714061\pi$
$632$	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	$0.862440\pi$
$644$	−16.2387	+	10.9400i	−0.639896	+	0.431098i
$645$			0.504371i			0.0198596i
$646$	−3.24406	−	5.74583i	−0.127636	−	0.226067i
$647$		−	26.5742i		−	1.04474i	−0.852720	−	0.522369i	$-0.825048\pi$
$647$		−	26.5742i		−	1.04474i	0.852720	−	0.522369i	$-0.174952\pi$
$648$	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	$-0.720952\pi$
$653$		−	39.2816i		−	1.53721i	0.639725	−	0.768603i	$-0.279048\pi$
$654$	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	$-0.417517\pi$
$661$	13.1757			0.512477			0.256238	+	0.966614i	$0.417517\pi$
$662$	−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	$-0.555904\pi$
$677$	−9.09250			−0.349453			−0.174727	+	0.984617i	$0.555904\pi$
$678$	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
$690$	−0.602055	−	7.61700i	−0.0229199	−	0.289974i
$691$	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	$-0.547061\pi$
$701$	−7.80036			−0.294616			−0.147308	+	0.989091i	$0.547061\pi$
$702$	−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	$-0.271582\pi$
$709$	35.0186			1.31515			0.657576	+	0.753388i	$0.271582\pi$
$710$	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	$-0.812374\pi$
$719$		−	29.8119i		−	1.11180i	0.831250	−	0.555899i	$-0.187626\pi$
$720$	−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	$-0.243497\pi$
$727$	38.9023			1.44281			0.721403	+	0.692515i	$0.243497\pi$
$728$	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	$-0.673293\pi$
$733$	−28.0442			−1.03583			−0.517917	+	0.855431i	$0.673293\pi$
$734$	−14.2575	−	25.2526i	−0.526252	−	0.932091i
$735$	−3.19136			−0.117715
$736$	−22.9277	+	14.5024i	−0.845127	+	0.534566i
$737$	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	$-0.694797\pi$
$743$	−31.3186			−1.14897			−0.574485	+	0.818515i	$0.694797\pi$
$744$	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	$-0.302027\pi$
$751$	31.9328			1.16524			0.582622	+	0.812743i	$0.302027\pi$
$752$	−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	$-0.521420\pi$
$757$	−3.70021			−0.134486			−0.0672431	+	0.997737i	$0.521420\pi$
$758$	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	$-0.653695\pi$
$773$	−25.8178			−0.928603			−0.464301	+	0.885677i	$0.653695\pi$
$774$	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
$782$	49.5969	−	3.92019i	1.77358	−	0.140186i
$783$		−	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	$-0.535853\pi$
$797$	−6.34630			−0.224798			−0.112399	+	0.993663i	$0.535853\pi$
$798$	−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	$0.307129\pi$
$821$			47.1044i			1.64396i	−0.569520	+	0.821978i	$0.692871\pi$
$822$	14.6983	−	8.29855i	0.512661	−	0.289445i
$823$		−	35.8300i		−	1.24896i	−0.781042	−	0.624478i	$-0.785312\pi$
$823$		−	35.8300i		−	1.24896i	0.781042	−	0.624478i	$-0.214688\pi$
$824$	−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	$-0.0991179\pi$
$828$	−7.95483	+	5.35916i	−0.276450	+	0.186244i
$829$			18.6855i			0.648975i	0.945890	+	0.324487i	$0.105192\pi$
$829$			18.6855i			0.648975i	−0.945890	+	0.324487i	$0.894808\pi$
$830$	−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	$-0.634630\pi$
$839$	−23.7780			−0.820908			−0.410454	+	0.911881i	$0.634630\pi$
$840$	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	$-0.971670\pi$
$853$		−	5.19183i		−	0.177765i	0.996042	−	0.0888825i	$-0.0283296\pi$
$854$	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	$0.00469398\pi$
$863$			0.866384i			0.0294921i	−0.999891	+	0.0147460i	$0.995306\pi$
$864$	−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
$874$	−4.30051	+	0.339917i	−0.145467	+	0.0114979i
$875$	−20.0787			−0.678783
$876$	−1.59935	+	2.65102i	−0.0540370	+	0.0895696i
$877$		−	51.6475i		−	1.74401i	−0.489495	−	0.872006i	$-0.662819\pi$
$877$		−	51.6475i		−	1.74401i	0.489495	−	0.872006i	$-0.337181\pi$
$878$	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	$-0.797719\pi$
$887$		−	35.3559i		−	1.18714i	0.804784	−	0.593568i	$-0.202281\pi$
$888$	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	$-0.199305\pi$
$911$	48.9141			1.62060			0.810298	+	0.586018i	$0.199305\pi$
$912$	−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	$-0.591719\pi$
$919$	−17.2295			−0.568347			−0.284174	+	0.958773i	$0.591719\pi$
$920$	13.6661	+	6.83840i	0.450556	+	0.225456i
$921$	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	$-0.500554\pi$
$941$	−0.106814			−0.00348203			−0.00174102	+	0.999998i	$0.500554\pi$
$942$	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
$966$	−1.09094	−	13.8022i	−0.0351004	−	0.444078i
$967$			45.6575i			1.46825i	0.679016	+	0.734124i	$0.262407\pi$
$967$			45.6575i			1.46825i	−0.679016	+	0.734124i	$0.737593\pi$
$968$	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	$-0.824442\pi$
$983$	−53.4079			−1.70345			−0.851723	+	0.523992i	$0.824442\pi$
$984$	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	$0.125904\pi$
$991$			24.2589i			0.770609i	−0.922789	+	0.385305i	$0.874096\pi$
$992$	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	$0.211419\pi$
$997$			38.9275i			1.23285i	−0.787415	+	0.616423i	$0.788581\pi$
$998$	−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.91.10	yes	24
4.3	odd	2		2208.2.n.a.367.16		24
8.3	odd	2	inner	552.2.n.a.91.11	yes	24
8.5	even	2		2208.2.n.a.367.10		24
23.22	odd	2	inner	552.2.n.a.91.9	✓	24
92.91	even	2		2208.2.n.a.367.9		24
184.45	odd	2		2208.2.n.a.367.15		24
184.91	even	2	inner	552.2.n.a.91.12	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
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} +(-0.534415 - 6.76124i) 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} +(-7.95483 + 5.35916i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more