LMFDB - Embedded newform 552.2.n.a.91.4

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			91.4
Character	$\chi$	$=$	552.91
Dual form			552.2.n.a.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39844 + 0.210663i) q^{2} +1.00000 q^{3} +(1.91124 - 0.589197i) q^{4} +0.707233 q^{5} +(-1.39844 + 0.210663i) q^{6} +4.06441 q^{7} +(-2.54863 + 1.22658i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.39844 + 0.210663i) q^{2} +1.00000 q^{3} +(1.91124 - 0.589197i) q^{4} +0.707233 q^{5} +(-1.39844 + 0.210663i) q^{6} +4.06441 q^{7} +(-2.54863 + 1.22658i) q^{8} +1.00000 q^{9} +(-0.989020 + 0.148988i) q^{10} -4.77165i q^{11} +(1.91124 - 0.589197i) q^{12} -6.61936i q^{13} +(-5.68382 + 0.856221i) q^{14} +0.707233 q^{15} +(3.30569 - 2.25220i) q^{16} +5.50614i q^{17} +(-1.39844 + 0.210663i) q^{18} +4.69480i q^{19} +(1.35169 - 0.416699i) q^{20} +4.06441 q^{21} +(1.00521 + 6.67284i) q^{22} +(-3.15417 - 3.61265i) q^{23} +(-2.54863 + 1.22658i) q^{24} -4.49982 q^{25} +(1.39445 + 9.25674i) q^{26} +1.00000 q^{27} +(7.76808 - 2.39474i) q^{28} -1.90010i q^{29} +(-0.989020 + 0.148988i) q^{30} -1.05745i q^{31} +(-4.14835 + 3.84594i) q^{32} -4.77165i q^{33} +(-1.15994 - 7.69998i) q^{34} +2.87449 q^{35} +(1.91124 - 0.589197i) q^{36} +1.73027 q^{37} +(-0.989020 - 6.56537i) q^{38} -6.61936i q^{39} +(-1.80247 + 0.867479i) q^{40} -2.21480 q^{41} +(-5.68382 + 0.856221i) q^{42} +4.15938i q^{43} +(-2.81144 - 9.11977i) q^{44} +0.707233 q^{45} +(5.17195 + 4.38759i) q^{46} +4.75707i q^{47} +(3.30569 - 2.25220i) q^{48} +9.51946 q^{49} +(6.29271 - 0.947945i) q^{50} +5.50614i q^{51} +(-3.90010 - 12.6512i) q^{52} +12.2549 q^{53} +(-1.39844 + 0.210663i) q^{54} -3.37467i q^{55} +(-10.3587 + 4.98533i) q^{56} +4.69480i q^{57} +(0.400281 + 2.65717i) q^{58} -3.11385 q^{59} +(1.35169 - 0.416699i) q^{60} +5.49700 q^{61} +(0.222766 + 1.47878i) q^{62} +4.06441 q^{63} +(4.99100 - 6.25220i) q^{64} -4.68143i q^{65} +(1.00521 + 6.67284i) q^{66} +9.05690i q^{67} +(3.24420 + 10.5236i) q^{68} +(-3.15417 - 3.61265i) q^{69} +(-4.01979 + 0.605548i) q^{70} +9.05745i q^{71} +(-2.54863 + 1.22658i) q^{72} +9.00798 q^{73} +(-2.41967 + 0.364504i) q^{74} -4.49982 q^{75} +(2.76616 + 8.97290i) q^{76} -19.3939i q^{77} +(1.39445 + 9.25674i) q^{78} -1.51857 q^{79} +(2.33790 - 1.59283i) q^{80} +1.00000 q^{81} +(3.09725 - 0.466576i) q^{82} -7.12390i q^{83} +(7.76808 - 2.39474i) q^{84} +3.89412i q^{85} +(-0.876226 - 5.81662i) q^{86} -1.90010i q^{87} +(5.85281 + 12.1611i) q^{88} +7.05000i q^{89} +(-0.989020 + 0.148988i) q^{90} -26.9038i q^{91} +(-8.15694 - 5.04622i) q^{92} -1.05745i q^{93} +(-1.00214 - 6.65245i) q^{94} +3.32032i q^{95} +(-4.14835 + 3.84594i) q^{96} -5.21685i q^{97} +(-13.3123 + 2.00540i) q^{98} -4.77165i 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 $

$2$	−1.39844	+	0.210663i	−0.988843	+	0.148961i
$2$	−1.39844	+	0.210663i	−0.988843	+	0.148961i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.91124	−	0.589197i	0.955621	−	0.294598i
$5$	0.707233			0.316284			0.158142	−	0.987416i	$-0.449450\pi$
$5$	0.707233			0.316284			0.158142	+	0.987416i	$0.449450\pi$
$6$	−1.39844	+	0.210663i	−0.570909	+	0.0860027i
$7$	4.06441			1.53620			0.768102	−	0.640328i	$-0.221201\pi$
$7$	4.06441			1.53620			0.768102	+	0.640328i	$0.221201\pi$
$8$	−2.54863	+	1.22658i	−0.901076	+	0.433662i
$9$	1.00000			0.333333
$10$	−0.989020	+	0.148988i	−0.312756	+	0.0471141i
$11$		−	4.77165i		−	1.43871i	−0.694645	−	0.719353i	$-0.744438\pi$
$11$		−	4.77165i		−	1.43871i	0.694645	−	0.719353i	$-0.255562\pi$
$12$	1.91124	−	0.589197i	0.551728	−	0.170086i
$13$		−	6.61936i		−	1.83588i	−0.396721	−	0.917939i	$-0.629852\pi$
$13$		−	6.61936i		−	1.83588i	0.396721	−	0.917939i	$-0.370148\pi$
$14$	−5.68382	+	0.856221i	−1.51906	+	0.228835i
$15$	0.707233			0.182607
$16$	3.30569	−	2.25220i	0.826424	−	0.563049i
$17$			5.50614i			1.33543i	0.744415	+	0.667717i	$0.232729\pi$
$17$			5.50614i			1.33543i	−0.744415	+	0.667717i	$0.767271\pi$
$18$	−1.39844	+	0.210663i	−0.329614	+	0.0496537i
$19$			4.69480i			1.07706i	0.842606	+	0.538530i	$0.181020\pi$
$19$			4.69480i			1.07706i	−0.842606	+	0.538530i	$0.818980\pi$
$20$	1.35169	−	0.416699i	0.302248	−	0.0931768i
$21$	4.06441			0.886928
$22$	1.00521	+	6.67284i	0.214311	+	1.42265i
$23$	−3.15417	−	3.61265i	−0.657689	−	0.753289i
$23$	−3.15417	−	3.61265i	−0.657689	−	0.753289i
$24$	−2.54863	+	1.22658i	−0.520236	+	0.250375i
$25$	−4.49982			−0.899964
$26$	1.39445	+	9.25674i	0.273475	+	1.81540i
$27$	1.00000			0.192450
$28$	7.76808	−	2.39474i	1.46803	−	0.452563i
$29$		−	1.90010i		−	0.352840i	−0.984315	−	0.176420i	$-0.943548\pi$
$29$		−	1.90010i		−	0.352840i	0.984315	−	0.176420i	$-0.0564517\pi$
$30$	−0.989020	+	0.148988i	−0.180569	+	0.0272013i
$31$		−	1.05745i		−	0.189924i	−0.995481	−	0.0949619i	$-0.969727\pi$
$31$		−	1.05745i		−	0.189924i	0.995481	−	0.0949619i	$-0.0302729\pi$
$32$	−4.14835	+	3.84594i	−0.733331	+	0.679872i
$33$		−	4.77165i		−	0.830637i
$34$	−1.15994	−	7.69998i	−0.198928	−	1.32054i
$35$	2.87449			0.485877
$36$	1.91124	−	0.589197i	0.318540	−	0.0981994i
$37$	1.73027			0.284455			0.142228	−	0.989834i	$-0.454574\pi$
$37$	1.73027			0.284455			0.142228	+	0.989834i	$0.454574\pi$
$38$	−0.989020	−	6.56537i	−0.160440	−	1.06504i
$39$		−	6.61936i		−	1.05995i
$40$	−1.80247	+	0.867479i	−0.284996	+	0.137160i
$41$	−2.21480			−0.345894			−0.172947	−	0.984931i	$-0.555329\pi$
$41$	−2.21480			−0.345894			−0.172947	+	0.984931i	$0.555329\pi$
$42$	−5.68382	+	0.856221i	−0.877032	+	0.132118i
$43$			4.15938i			0.634299i	0.948376	+	0.317149i	$0.102726\pi$
$43$			4.15938i			0.634299i	−0.948376	+	0.317149i	$0.897274\pi$
$44$	−2.81144	−	9.11977i	−0.423840	−	1.37486i
$45$	0.707233			0.105428
$46$	5.17195	+	4.38759i	0.762562	+	0.646915i
$47$			4.75707i			0.693890i	0.937886	+	0.346945i	$0.112781\pi$
$47$			4.75707i			0.693890i	−0.937886	+	0.346945i	$0.887219\pi$
$48$	3.30569	−	2.25220i	0.477136	−	0.325076i
$49$	9.51946			1.35992
$50$	6.29271	−	0.947945i	0.889923	−	0.134060i
$51$			5.50614i			0.771014i
$52$	−3.90010	−	12.6512i	−0.540847	−	1.75440i
$53$	12.2549			1.68334			0.841672	−	0.539989i	$-0.181571\pi$
$53$	12.2549			1.68334			0.841672	+	0.539989i	$0.181571\pi$
$54$	−1.39844	+	0.210663i	−0.190303	+	0.0286676i
$55$		−	3.37467i		−	0.455040i
$56$	−10.3587	+	4.98533i	−1.38424	+	0.666193i
$57$			4.69480i			0.621841i
$58$	0.400281	+	2.65717i	0.0525595	+	0.348903i
$59$	−3.11385			−0.405389			−0.202695	−	0.979242i	$-0.564970\pi$
$59$	−3.11385			−0.405389			−0.202695	+	0.979242i	$0.564970\pi$
$60$	1.35169	−	0.416699i	0.174503	−	0.0537957i
$61$	5.49700			0.703818			0.351909	−	0.936034i	$-0.385533\pi$
$61$	5.49700			0.703818			0.351909	+	0.936034i	$0.385533\pi$
$62$	0.222766	+	1.47878i	0.0282913	+	0.187805i
$63$	4.06441			0.512068
$64$	4.99100	−	6.25220i	0.623875	−	0.781524i
$65$		−	4.68143i		−	0.580660i
$66$	1.00521	+	6.67284i	0.123733	+	0.821370i
$67$			9.05690i			1.10648i	0.833023	+	0.553238i	$0.186608\pi$
$67$			9.05690i			1.10648i	−0.833023	+	0.553238i	$0.813392\pi$
$68$	3.24420	+	10.5236i	0.393417	+	1.27617i
$69$	−3.15417	−	3.61265i	−0.379717	−	0.434912i
$70$	−4.01979	+	0.605548i	−0.480456	+	0.0723768i
$71$			9.05745i			1.07492i	0.843289	+	0.537461i	$0.180616\pi$
$71$			9.05745i			1.07492i	−0.843289	+	0.537461i	$0.819384\pi$
$72$	−2.54863	+	1.22658i	−0.300359	+	0.144554i
$73$	9.00798			1.05430			0.527152	−	0.849771i	$-0.323260\pi$
$73$	9.00798			1.05430			0.527152	+	0.849771i	$0.323260\pi$
$74$	−2.41967	+	0.364504i	−0.281282	+	0.0423728i
$75$	−4.49982			−0.519595
$76$	2.76616	+	8.97290i	0.317300	+	1.02926i
$77$		−	19.3939i		−	2.21015i
$78$	1.39445	+	9.25674i	0.157891	+	1.04812i
$79$	−1.51857			−0.170853			−0.0854264	−	0.996344i	$-0.527225\pi$
$79$	−1.51857			−0.170853			−0.0854264	+	0.996344i	$0.527225\pi$
$80$	2.33790	−	1.59283i	0.261385	−	0.178083i
$81$	1.00000			0.111111
$82$	3.09725	−	0.466576i	0.342034	−	0.0515247i
$83$		−	7.12390i		−	0.781950i	−0.920401	−	0.390975i	$-0.872138\pi$
$83$		−	7.12390i		−	0.781950i	0.920401	−	0.390975i	$-0.127862\pi$
$84$	7.76808	−	2.39474i	0.847567	−	0.261287i
$85$			3.89412i			0.422377i
$86$	−0.876226	−	5.81662i	−0.0944859	−	0.627222i
$87$		−	1.90010i		−	0.203712i
$88$	5.85281	+	12.1611i	0.623912	+	1.29638i
$89$			7.05000i			0.747299i	0.927570	+	0.373649i	$0.121894\pi$
$89$			7.05000i			0.747299i	−0.927570	+	0.373649i	$0.878106\pi$
$90$	−0.989020	+	0.148988i	−0.104252	+	0.0157047i
$91$		−	26.9038i		−	2.82028i
$92$	−8.15694	−	5.04622i	−0.850420	−	0.526105i
$93$		−	1.05745i		−	0.109653i
$94$	−1.00214	−	6.65245i	−0.103363	−	0.686148i
$95$			3.32032i			0.340657i
$96$	−4.14835	+	3.84594i	−0.423389	+	0.392524i
$97$		−	5.21685i		−	0.529691i	−0.964291	−	0.264845i	$-0.914679\pi$
$97$		−	5.21685i		−	0.529691i	0.964291	−	0.264845i	$-0.0853210\pi$
$98$	−13.3123	+	2.00540i	−1.34475	+	0.202576i
$99$		−	4.77165i		−	0.479569i
$100$	−8.60025	+	2.65128i	−0.860025	+	0.265128i
$101$		−	2.30636i		−	0.229492i	−0.993395	−	0.114746i	$-0.963395\pi$
$101$		−	2.30636i		−	0.229492i	0.993395	−	0.114746i	$-0.0366053\pi$
$102$	−1.15994	−	7.69998i	−0.114851	−	0.762412i
$103$	−17.9455			−1.76822			−0.884112	−	0.467275i	$-0.845236\pi$
$103$	−17.9455			−1.76822			−0.884112	+	0.467275i	$0.845236\pi$
$104$	8.11918	+	16.8703i	0.796151	+	1.65427i
$105$	2.87449			0.280521
$106$	−17.1377	+	2.58166i	−1.66456	+	0.250753i
$107$			15.8013i			1.52757i	0.645471	+	0.763785i	$0.276661\pi$
$107$			15.8013i			1.52757i	−0.645471	+	0.763785i	$0.723339\pi$
$108$	1.91124	−	0.589197i	0.183909	−	0.0566955i
$109$	−6.41593			−0.614534			−0.307267	−	0.951623i	$-0.599415\pi$
$109$	−6.41593			−0.614534			−0.307267	+	0.951623i	$0.599415\pi$
$110$	0.710917	+	4.71925i	0.0677833	+	0.449963i
$111$	1.73027			0.164230
$112$	13.4357	−	9.15385i	1.26956	−	0.864958i
$113$		−	5.88965i		−	0.554052i	−0.960862	−	0.277026i	$-0.910651\pi$
$113$		−	5.88965i		−	0.554052i	0.960862	−	0.277026i	$-0.0893487\pi$
$114$	−0.989020	−	6.56537i	−0.0926302	−	0.614904i
$115$	−2.23073	−	2.55498i	−0.208017	−	0.238254i
$116$	−1.11953	−	3.63156i	−0.103946	−	0.337181i
$117$		−	6.61936i		−	0.611960i
$118$	4.35452	−	0.655973i	0.400866	−	0.0603872i
$119$			22.3792i			2.05150i
$120$	−1.80247	+	0.867479i	−0.164543	+	0.0791896i
$121$	−11.7686			−1.06987
$122$	−7.68719	+	1.15801i	−0.695966	+	0.104842i
$123$	−2.21480			−0.199702
$124$	−0.623047	−	2.02104i	−0.0559512	−	0.181495i
$125$	−6.71859			−0.600929
$126$	−5.68382	+	0.856221i	−0.506355	+	0.0762782i
$127$			21.4710i			1.90525i	0.304154	+	0.952623i	$0.401626\pi$
$127$			21.4710i			1.90525i	−0.304154	+	0.952623i	$0.598374\pi$
$128$	−5.66248	+	9.79471i	−0.500497	+	0.865738i
$129$			4.15938i			0.366213i
$130$	0.986203	+	6.54667i	0.0864957	+	0.574181i
$131$	5.33844			0.466422			0.233211	−	0.972426i	$-0.425077\pi$
$131$	5.33844			0.466422			0.233211	+	0.972426i	$0.425077\pi$
$132$	−2.81144	−	9.11977i	−0.244704	−	0.793774i
$133$			19.0816i			1.65459i
$134$	−1.90795	−	12.6655i	−0.164822	−	1.09413i
$135$	0.707233			0.0608689
$136$	−6.75373	−	14.0331i	−0.579127	−	1.20333i
$137$			9.08294i			0.776008i	0.921658	+	0.388004i	$0.126835\pi$
$137$			9.08294i			0.776008i	−0.921658	+	0.388004i	$0.873165\pi$
$138$	5.17195	+	4.38759i	0.440266	+	0.373496i
$139$	−10.3826			−0.880644			−0.440322	−	0.897840i	$-0.645136\pi$
$139$	−10.3826			−0.880644			−0.440322	+	0.897840i	$0.645136\pi$
$140$	5.49384	−	1.69364i	0.464314	−	0.143139i
$141$			4.75707i			0.400617i
$142$	−1.90807	−	12.6663i	−0.160122	−	1.06293i
$143$	−31.5852			−2.64129
$144$	3.30569	−	2.25220i	0.275475	−	0.187683i
$145$		−	1.34382i		−	0.111598i
$146$	−12.5971	+	1.89765i	−1.04254	+	0.157050i
$147$	9.51946			0.785152
$148$	3.30697	−	1.01947i	0.271831	−	0.0838000i
$149$	12.7678			1.04598			0.522991	−	0.852338i	$-0.324816\pi$
$149$	12.7678			1.04598			0.522991	+	0.852338i	$0.324816\pi$
$150$	6.29271	−	0.947945i	0.513798	−	0.0773994i
$151$			9.49209i			0.772455i	0.922404	+	0.386228i	$0.126222\pi$
$151$			9.49209i			0.772455i	−0.922404	+	0.386228i	$0.873778\pi$
$152$	−5.75855	−	11.9653i	−0.467080	−	0.970513i
$153$			5.50614i			0.445145i
$154$	4.08558	+	27.1212i	0.329226	+	2.18549i
$155$		−	0.747864i		−	0.0600699i
$156$	−3.90010	−	12.6512i	−0.312258	−	1.01291i
$157$	17.7700			1.41820			0.709102	−	0.705106i	$-0.249101\pi$
$157$	17.7700			1.41820			0.709102	+	0.705106i	$0.249101\pi$
$158$	2.12363	−	0.319907i	0.168947	−	0.0254504i
$159$	12.2549			0.971880
$160$	−2.93385	+	2.71997i	−0.231941	+	0.215033i
$161$	−12.8198	−	14.6833i	−1.01034	−	1.15721i
$162$	−1.39844	+	0.210663i	−0.109871	+	0.0165512i
$163$	−4.80484			−0.376344			−0.188172	−	0.982136i	$-0.560256\pi$
$163$	−4.80484			−0.376344			−0.188172	+	0.982136i	$0.560256\pi$
$164$	−4.23302	+	1.30495i	−0.330543	+	0.101900i
$165$		−	3.37467i		−	0.262717i
$166$	1.50074	+	9.96232i	0.116480	+	0.773226i
$167$		−	10.3203i		−	0.798606i	−0.916819	−	0.399303i	$-0.869252\pi$
$167$		−	10.3203i		−	0.798606i	0.916819	−	0.399303i	$-0.130748\pi$
$168$	−10.3587	+	4.98533i	−0.799189	+	0.384627i
$169$	−30.8159			−2.37045
$170$	−0.820347	−	5.44568i	−0.0629178	−	0.417665i
$171$			4.69480i			0.359020i
$172$	2.45069	+	7.94958i	0.186863	+	0.606149i
$173$		−	9.29934i		−	0.707015i	−0.935432	−	0.353508i	$-0.884989\pi$
$173$		−	9.29934i		−	0.707015i	0.935432	−	0.353508i	$-0.115011\pi$
$174$	0.400281	+	2.65717i	0.0303452	+	0.201440i
$175$	−18.2891			−1.38253
$176$	−10.7467	−	15.7736i	−0.810062	−	1.18898i
$177$	−3.11385			−0.234052
$178$	−1.48517	−	9.85897i	−0.111318	−	0.738961i
$179$	−13.1531			−0.983111			−0.491555	−	0.870846i	$-0.663571\pi$
$179$	−13.1531			−0.983111			−0.491555	+	0.870846i	$0.663571\pi$
$180$	1.35169	−	0.416699i	0.100749	−	0.0310589i
$181$	−26.0882			−1.93912			−0.969561	−	0.244848i	$-0.921262\pi$
$181$	−26.0882			−1.93912			−0.969561	+	0.244848i	$0.921262\pi$
$182$	5.66763	+	37.6232i	0.420113	+	2.78882i
$183$	5.49700			0.406350
$184$	12.4700	+	5.33845i	0.919301	+	0.393556i
$185$	1.22371			0.0899687
$186$	0.222766	+	1.47878i	0.0163340	+	0.108429i
$187$	26.2734			1.92130
$188$	2.80285	+	9.09191i	0.204419	+	0.663096i
$189$	4.06441			0.295643
$190$	−0.699468	−	4.64325i	−0.0507447	−	0.336857i
$191$	−6.97316			−0.504560			−0.252280	−	0.967654i	$-0.581180\pi$
$191$	−6.97316			−0.504560			−0.252280	+	0.967654i	$0.581180\pi$
$192$	4.99100	−	6.25220i	0.360194	−	0.451213i
$193$	11.7701			0.847232			0.423616	−	0.905842i	$-0.360761\pi$
$193$	11.7701			0.847232			0.423616	+	0.905842i	$0.360761\pi$
$194$	1.09900	+	7.29543i	0.0789034	+	0.523781i
$195$		−	4.68143i		−	0.335244i
$196$	18.1940	−	5.60883i	1.29957	−	0.400631i
$197$		−	13.5963i		−	0.968696i	−0.874875	−	0.484348i	$-0.839057\pi$
$197$		−	13.5963i		−	0.968696i	0.874875	−	0.484348i	$-0.160943\pi$
$198$	1.00521	+	6.67284i	0.0714371	+	0.474218i
$199$	−3.34329			−0.237000			−0.118500	−	0.992954i	$-0.537809\pi$
$199$	−3.34329			−0.237000			−0.118500	+	0.992954i	$0.537809\pi$
$200$	11.4684	−	5.51940i	0.810936	−	0.390280i
$201$			9.05690i			0.638825i
$202$	0.485865	+	3.22530i	0.0341853	+	0.226931i
$203$		−	7.72280i		−	0.542034i
$204$	3.24420	+	10.5236i	0.227139	+	0.736797i
$205$	−1.56638			−0.109401
$206$	25.0956	−	3.78045i	1.74850	−	0.263397i
$207$	−3.15417	−	3.61265i	−0.219230	−	0.251096i
$208$	−14.9081	−	21.8816i	−1.03369	−	1.51721i
$209$	22.4019			1.54957
$210$	−4.01979	+	0.605548i	−0.277392	+	0.0417868i
$211$	−16.9365			−1.16595			−0.582977	−	0.812489i	$-0.698112\pi$
$211$	−16.9365			−1.16595			−0.582977	+	0.812489i	$0.698112\pi$
$212$	23.4221	−	7.22057i	1.60864	−	0.495911i
$213$			9.05745i			0.620606i
$214$	−3.32875	−	22.0971i	−0.227548	−	1.51053i
$215$			2.94165i			0.200619i
$216$	−2.54863	+	1.22658i	−0.173412	+	0.0834583i
$217$		−	4.29792i		−	0.291762i
$218$	8.97226	−	1.35160i	0.607678	−	0.0915417i
$219$	9.00798			0.608703
$220$	−1.98834	−	6.44981i	−0.134054	−	0.434846i
$221$	36.4471			2.45170
$222$	−2.41967	+	0.364504i	−0.162398	+	0.0244639i
$223$			6.73080i			0.450728i	0.974275	+	0.225364i	$0.0723571\pi$
$223$			6.73080i			0.450728i	−0.974275	+	0.225364i	$0.927643\pi$
$224$	−16.8606	+	15.6315i	−1.12655	+	1.04442i
$225$	−4.49982			−0.299988
$226$	1.24073	+	8.23629i	0.0825321	+	0.547870i
$227$		−	17.8632i		−	1.18562i	−0.805341	−	0.592812i	$-0.798018\pi$
$227$		−	17.8632i		−	1.18562i	0.805341	−	0.592812i	$-0.201982\pi$
$228$	2.76616	+	8.97290i	0.183193	+	0.594245i
$229$	−21.3486			−1.41076			−0.705378	−	0.708831i	$-0.749223\pi$
$229$	−21.3486			−1.41076			−0.705378	+	0.708831i	$0.749223\pi$
$230$	3.65777	+	3.10305i	0.241186	+	0.204609i
$231$		−	19.3939i		−	1.27603i
$232$	2.33063	+	4.84265i	0.153013	+	0.317936i
$233$	21.7195			1.42289			0.711447	−	0.702740i	$-0.248040\pi$
$233$	21.7195			1.42289			0.711447	+	0.702740i	$0.248040\pi$
$234$	1.39445	+	9.25674i	0.0911582	+	0.605132i
$235$			3.36436i			0.219466i
$236$	−5.95133	+	1.83467i	−0.387399	+	0.119427i
$237$	−1.51857			−0.0986419
$238$	−4.71447	−	31.2959i	−0.305594	−	2.02861i
$239$			11.8993i			0.769702i	0.922979	+	0.384851i	$0.125747\pi$
$239$			11.8993i			0.769702i	−0.922979	+	0.384851i	$0.874253\pi$
$240$	2.33790	−	1.59283i	0.150911	−	0.102817i
$241$			29.7933i			1.91915i	0.281449	+	0.959576i	$0.409185\pi$
$241$			29.7933i			1.91915i	−0.281449	+	0.959576i	$0.590815\pi$
$242$	16.4576	−	2.47921i	1.05794	−	0.159370i
$243$	1.00000			0.0641500
$244$	10.5061	−	3.23881i	0.672583	−	0.207344i
$245$	6.73248			0.430122
$246$	3.09725	−	0.466576i	0.197474	−	0.0297478i
$247$	31.0765			1.97735
$248$	1.29705	+	2.69505i	0.0823627	+	0.171136i
$249$		−	7.12390i		−	0.451459i
$250$	9.39551	−	1.41536i	0.594224	−	0.0895150i
$251$			1.00549i			0.0634661i	0.999496	+	0.0317331i	$0.0101026\pi$
$251$			1.00549i			0.0634661i	−0.999496	+	0.0317331i	$0.989897\pi$
$252$	7.76808	−	2.39474i	0.489343	−	0.150854i
$253$	−17.2383	+	15.0506i	−1.08376	+	0.946221i
$254$	−4.52315	−	30.0258i	−0.283808	−	1.88399i
$255$			3.89412i			0.243860i
$256$	5.85523	−	14.8901i	0.365952	−	0.930634i
$257$	12.8015			0.798537			0.399268	−	0.916834i	$-0.369264\pi$
$257$	12.8015			0.798537			0.399268	+	0.916834i	$0.369264\pi$
$258$	−0.876226	−	5.81662i	−0.0545514	−	0.362127i
$259$	7.03255			0.436981
$260$	−2.75828	−	8.94734i	−0.171061	−	0.554891i
$261$		−	1.90010i		−	0.117613i
$262$	−7.46547	+	1.12461i	−0.461218	+	0.0694787i
$263$	20.9795			1.29365			0.646827	−	0.762637i	$-0.276096\pi$
$263$	20.9795			1.29365			0.646827	+	0.762637i	$0.276096\pi$
$264$	5.85281	+	12.1611i	0.360216	+	0.748467i
$265$	8.66710			0.532415
$266$	−4.01979	−	26.6844i	−0.246469	−	1.63612i
$267$			7.05000i			0.431453i
$268$	5.33630	+	17.3099i	0.325966	+	1.05737i
$269$			16.8439i			1.02699i	0.858092	+	0.513497i	$0.171650\pi$
$269$			16.8439i			1.02699i	−0.858092	+	0.513497i	$0.828350\pi$
$270$	−0.989020	+	0.148988i	−0.0601898	+	0.00906711i
$271$		−	14.4197i		−	0.875933i	−0.898991	−	0.437966i	$-0.855699\pi$
$271$		−	14.4197i		−	0.875933i	0.898991	−	0.437966i	$-0.144301\pi$
$272$	12.4009	+	18.2016i	0.751915	+	1.10363i
$273$		−	26.9038i		−	1.62829i
$274$	−1.91344	−	12.7019i	−0.115595	−	0.767350i
$275$			21.4716i			1.29478i
$276$	−8.15694	−	5.04622i	−0.490990	−	0.303747i
$277$		−	20.1542i		−	1.21095i	−0.795865	−	0.605473i	$-0.792984\pi$
$277$		−	20.1542i		−	1.21095i	0.795865	−	0.605473i	$-0.207016\pi$
$278$	14.5195	−	2.18724i	0.870819	−	0.131182i
$279$		−	1.05745i		−	0.0633079i
$280$	−7.32600	+	3.52579i	−0.437812	+	0.210706i
$281$		−	10.9391i		−	0.652571i	−0.945271	−	0.326286i	$-0.894203\pi$
$281$		−	10.9391i		−	0.652571i	0.945271	−	0.326286i	$-0.105797\pi$
$282$	−1.00214	−	6.65245i	−0.0596764	−	0.396148i
$283$			10.4920i			0.623685i	0.950134	+	0.311843i	$0.100946\pi$
$283$			10.4920i			0.623685i	−0.950134	+	0.311843i	$0.899054\pi$
$284$	5.33662	+	17.3110i	0.316670	+	1.02722i
$285$			3.32032i			0.196679i
$286$	44.1699	−	6.65383i	2.61182	−	0.393449i
$287$	−9.00186			−0.531363
$288$	−4.14835	+	3.84594i	−0.244444	+	0.226624i
$289$	−13.3176			−0.783386
$290$	0.283092	+	1.87924i	0.0166237	+	0.110353i
$291$		−	5.21685i		−	0.305817i
$292$	17.2164	−	5.30747i	1.00752	−	0.310596i
$293$	−5.75301			−0.336095			−0.168047	−	0.985779i	$-0.553746\pi$
$293$	−5.75301			−0.336095			−0.168047	+	0.985779i	$0.553746\pi$
$294$	−13.3123	+	2.00540i	−0.776392	+	0.116957i
$295$	−2.20222			−0.128218
$296$	−4.40982	+	2.12232i	−0.256316	+	0.123357i
$297$		−	4.77165i		−	0.276879i
$298$	−17.8550	+	2.68971i	−1.03431	+	0.155811i
$299$	−23.9134	+	20.8786i	−1.38295	+	1.20744i
$300$	−8.60025	+	2.65128i	−0.496536	+	0.153072i
$301$			16.9054i			0.974412i
$302$	−1.99963	−	13.2741i	−0.115066	−	0.763837i
$303$		−	2.30636i		−	0.132497i
$304$	10.5736	+	15.5196i	0.606438	+	0.890109i
$305$	3.88766			0.222607
$306$	−1.15994	−	7.69998i	−0.0663093	−	0.440179i
$307$	−13.6474			−0.778896			−0.389448	−	0.921048i	$-0.627334\pi$
$307$	−13.6474			−0.778896			−0.389448	+	0.921048i	$0.627334\pi$
$308$	−11.4268	−	37.0665i	−0.651105	−	2.11206i
$309$	−17.9455			−1.02088
$310$	0.157547	+	1.04584i	0.00894808	+	0.0593997i
$311$		−	14.5540i		−	0.825279i	−0.910894	−	0.412639i	$-0.864607\pi$
$311$		−	14.5540i		−	0.825279i	0.910894	−	0.412639i	$-0.135393\pi$
$312$	8.11918	+	16.8703i	0.459658	+	0.955091i
$313$		−	16.5347i		−	0.934599i	−0.884099	−	0.467299i	$-0.845227\pi$
$313$		−	16.5347i		−	0.934599i	0.884099	−	0.467299i	$-0.154773\pi$
$314$	−24.8503	+	3.74349i	−1.40238	+	0.211257i
$315$	2.87449			0.161959
$316$	−2.90236	+	0.894738i	−0.163271	+	0.0503330i
$317$		−	26.7678i		−	1.50343i	−0.659487	−	0.751716i	$-0.729226\pi$
$317$		−	26.7678i		−	1.50343i	0.659487	−	0.751716i	$-0.270774\pi$
$318$	−17.1377	+	2.58166i	−0.961036	+	0.144772i
$319$	−9.06662			−0.507633
$320$	3.52980	−	4.42176i	0.197322	−	0.247184i
$321$			15.8013i			0.881943i
$322$	21.0209	+	17.8330i	1.17145	+	0.993793i
$323$	−25.8502			−1.43834
$324$	1.91124	−	0.589197i	0.106180	−	0.0327331i
$325$			29.7859i			1.65223i
$326$	6.71925	−	1.01220i	0.372145	−	0.0560606i
$327$	−6.41593			−0.354802
$328$	5.64470	−	2.71663i	0.311676	−	0.150001i
$329$			19.3347i			1.06596i
$330$	0.710917	+	4.71925i	0.0391347	+	0.259786i
$331$	14.6892			0.807390			0.403695	−	0.914894i	$-0.367726\pi$
$331$	14.6892			0.807390			0.403695	+	0.914894i	$0.367726\pi$
$332$	−4.19738	−	13.6155i	−0.230361	−	0.747248i
$333$	1.73027			0.0948184
$334$	2.17410	+	14.4322i	0.118961	+	0.789696i
$335$			6.40534i			0.349961i
$336$	13.4357	−	9.15385i	0.732978	−	0.499384i
$337$		−	21.8726i		−	1.19148i	−0.803178	−	0.595739i	$-0.796859\pi$
$337$		−	21.8726i		−	1.19148i	0.803178	−	0.595739i	$-0.203141\pi$
$338$	43.0940	−	6.49176i	2.34400	−	0.353105i
$339$		−	5.88965i		−	0.319882i
$340$	2.29441	+	7.44261i	0.124432	+	0.403632i
$341$	−5.04578			−0.273244
$342$	−0.989020	−	6.56537i	−0.0534801	−	0.355015i
$343$	10.2401			0.552914
$344$	−5.10181	−	10.6007i	−0.275071	−	0.571551i
$345$	−2.23073	−	2.55498i	−0.120099	−	0.137556i
$346$	1.95902	+	13.0045i	0.105318	+	0.699127i
$347$	5.48691			0.294553			0.147276	−	0.989095i	$-0.452949\pi$
$347$	5.48691			0.294553			0.147276	+	0.989095i	$0.452949\pi$
$348$	−1.11953	−	3.63156i	−0.0600133	−	0.194672i
$349$		−	12.9858i		−	0.695112i	−0.937659	−	0.347556i	$-0.887012\pi$
$349$		−	12.9858i		−	0.695112i	0.937659	−	0.347556i	$-0.112988\pi$
$350$	25.5762	−	3.85284i	1.36710	−	0.205943i
$351$		−	6.61936i		−	0.353315i
$352$	18.3514	+	19.7944i	0.978136	+	1.05505i
$353$	−23.3979			−1.24535			−0.622673	−	0.782482i	$-0.713953\pi$
$353$	−23.3979			−1.24535			−0.622673	+	0.782482i	$0.713953\pi$
$354$	4.35452	−	0.655973i	0.231440	−	0.0348646i
$355$			6.40573i			0.339981i
$356$	4.15384	+	13.4743i	0.220153	+	0.714135i
$357$			22.3792i			1.18443i
$358$	18.3938	−	2.77088i	0.972142	−	0.146445i
$359$	6.29096			0.332024			0.166012	−	0.986124i	$-0.446911\pi$
$359$	6.29096			0.332024			0.166012	+	0.986124i	$0.446911\pi$
$360$	−1.80247	+	0.867479i	−0.0949987	+	0.0457202i
$361$	−3.04114			−0.160060
$362$	36.4827	−	5.49582i	1.91749	−	0.288854i
$363$	−11.7686			−0.617692
$364$	−15.8516	−	51.4197i	−0.830851	−	2.69512i
$365$	6.37074			0.333460
$366$	−7.68719	+	1.15801i	−0.401816	+	0.0605303i
$367$	2.84353			0.148431			0.0742156	−	0.997242i	$-0.476355\pi$
$367$	2.84353			0.148431			0.0742156	+	0.997242i	$0.476355\pi$
$368$	−18.5631	−	4.83851i	−0.967669	−	0.252225i
$369$	−2.21480			−0.115298
$370$	−1.71127	+	0.257790i	−0.0889649	+	0.0134018i
$371$	49.8091			2.58596
$372$	−0.623047	−	2.02104i	−0.0323035	−	0.104786i
$373$	4.48855			0.232409			0.116204	−	0.993225i	$-0.462927\pi$
$373$	4.48855			0.232409			0.116204	+	0.993225i	$0.462927\pi$
$374$	−36.7416	+	5.53482i	−1.89986	+	0.286199i
$375$	−6.71859			−0.346946
$376$	−5.83493	−	12.1240i	−0.300914	−	0.625247i
$377$	−12.5775			−0.647772
$378$	−5.68382	+	0.856221i	−0.292344	+	0.0440393i
$379$		−	24.6072i		−	1.26398i	−0.774975	−	0.631992i	$-0.782237\pi$
$379$		−	24.6072i		−	1.26398i	0.774975	−	0.631992i	$-0.217763\pi$
$380$	1.95632	+	6.34593i	0.100357	+	0.325539i
$381$			21.4710i			1.09999i
$382$	9.75151	−	1.46898i	0.498930	−	0.0751598i
$383$	15.6974			0.802098			0.401049	−	0.916057i	$-0.368646\pi$
$383$	15.6974			0.802098			0.401049	+	0.916057i	$0.368646\pi$
$384$	−5.66248	+	9.79471i	−0.288962	+	0.499834i
$385$		−	13.7160i		−	0.699034i
$386$	−16.4598	+	2.47953i	−0.837780	+	0.126205i
$387$			4.15938i			0.211433i
$388$	−3.07375	−	9.97067i	−0.156046	−	0.506184i
$389$	−26.2382			−1.33033			−0.665166	−	0.746696i	$-0.731639\pi$
$389$	−26.2382			−1.33033			−0.665166	+	0.746696i	$0.731639\pi$
$390$	0.986203	+	6.54667i	0.0499383	+	0.331504i
$391$	19.8917	−	17.3673i	1.00597	−	0.878301i
$392$	−24.2615	+	11.6764i	−1.22539	+	0.589747i
$393$	5.33844			0.269289
$394$	2.86424	+	19.0135i	0.144298	+	0.957889i
$395$	−1.07399			−0.0540381
$396$	−2.81144	−	9.11977i	−0.141280	−	0.458286i
$397$			8.30576i			0.416854i	0.978038	+	0.208427i	$0.0668344\pi$
$397$			8.30576i			0.416854i	−0.978038	+	0.208427i	$0.933166\pi$
$398$	4.67538	−	0.704308i	0.234356	−	0.0353038i
$399$			19.0816i			0.955275i
$400$	−14.8750	+	10.1345i	−0.743752	+	0.506724i
$401$			35.9292i			1.79422i	0.441807	+	0.897110i	$0.354338\pi$
$401$			35.9292i			1.79422i	−0.441807	+	0.897110i	$0.645662\pi$
$402$	−1.90795	−	12.6655i	−0.0951601	−	0.631697i
$403$	−6.99964			−0.348677
$404$	−1.35890	−	4.40802i	−0.0676078	−	0.219307i
$405$	0.707233			0.0351427
$406$	1.62691	+	10.7998i	0.0807420	+	0.535987i
$407$		−	8.25625i		−	0.409247i
$408$	−6.75373	−	14.0331i	−0.334359	−	0.694742i
$409$	11.2914			0.558323			0.279162	−	0.960244i	$-0.409943\pi$
$409$	11.2914			0.558323			0.279162	+	0.960244i	$0.409943\pi$
$410$	2.19048	−	0.329978i	0.108180	−	0.0162965i
$411$			9.08294i			0.448028i
$412$	−34.2982	+	10.5734i	−1.68975	+	0.520916i
$413$	−12.6560			−0.622761
$414$	5.17195	+	4.38759i	0.254187	+	0.215638i
$415$		−	5.03826i		−	0.247318i
$416$	25.4576	+	27.4594i	1.24816	+	1.34631i
$417$	−10.3826			−0.508440
$418$	−31.3276	+	4.71925i	−1.53228	+	0.230826i
$419$		−	11.6838i		−	0.570792i	−0.958410	−	0.285396i	$-0.907875\pi$
$419$		−	11.6838i		−	0.570792i	0.958410	−	0.285396i	$-0.0921251\pi$
$420$	5.49384	−	1.69364i	0.268072	−	0.0826411i
$421$	−24.7806			−1.20773			−0.603867	−	0.797085i	$-0.706374\pi$
$421$	−24.7806			−1.20773			−0.603867	+	0.797085i	$0.706374\pi$
$422$	23.6845	−	3.56788i	1.15295	−	0.173682i
$423$			4.75707i			0.231297i
$424$	−31.2333	+	15.0317i	−1.51682	+	0.730003i
$425$		−	24.7766i		−	1.20184i
$426$	−1.90807	−	12.6663i	−0.0924462	−	0.613682i
$427$	22.3421			1.08121
$428$	9.31007	+	30.2001i	0.450019	+	1.45978i
$429$	−31.5852			−1.52495
$430$	−0.619696	−	4.11371i	−0.0298844	−	0.198380i
$431$	−13.7723			−0.663390			−0.331695	−	0.943387i	$-0.607621\pi$
$431$	−13.7723			−0.663390			−0.331695	+	0.943387i	$0.607621\pi$
$432$	3.30569	−	2.25220i	0.159045	−	0.108359i
$433$			17.2835i			0.830591i	0.909687	+	0.415295i	$0.136322\pi$
$433$			17.2835i			0.830591i	−0.909687	+	0.415295i	$0.863678\pi$
$434$	0.905411	+	6.01036i	0.0434611	+	0.288506i
$435$		−	1.34382i		−	0.0644310i
$436$	−12.2624	+	3.78024i	−0.587262	+	0.181041i
$437$	16.9607	−	14.8082i	0.811338	−	0.708371i
$438$	−12.5971	+	1.89765i	−0.601912	+	0.0906731i
$439$		−	38.9937i		−	1.86107i	−0.366205	−	0.930534i	$-0.619343\pi$
$439$		−	38.9937i		−	1.86107i	0.366205	−	0.930534i	$-0.380657\pi$
$440$	4.13930	+	8.60077i	0.197334	+	0.410025i
$441$	9.51946			0.453307
$442$	−50.9689	+	7.67805i	−2.42434	+	0.365207i
$443$	31.7281			1.50745			0.753723	−	0.657192i	$-0.228256\pi$
$443$	31.7281			1.50745			0.753723	+	0.657192i	$0.228256\pi$
$444$	3.30697	−	1.01947i	0.156942	−	0.0483820i
$445$			4.98600i			0.236359i
$446$	−1.41793	−	9.41258i	−0.0671409	−	0.445699i
$447$	12.7678			0.603898
$448$	20.2855	−	25.4115i	0.958399	−	1.20058i
$449$	−38.7315			−1.82785			−0.913926	−	0.405881i	$-0.866965\pi$
$449$	−38.7315			−1.82785			−0.913926	+	0.405881i	$0.866965\pi$
$450$	6.29271	−	0.947945i	0.296641	−	0.0446866i
$451$			10.5682i			0.497639i
$452$	−3.47016	−	11.2565i	−0.163223	−	0.529463i
$453$			9.49209i			0.445977i
$454$	3.76311	+	24.9805i	0.176612	+	1.17240i
$455$		−	19.0273i		−	0.892012i
$456$	−5.75855	−	11.9653i	−0.269669	−	0.560326i
$457$			6.73265i			0.314940i	0.987524	+	0.157470i	$0.0503338\pi$
$457$			6.73265i			0.314940i	−0.987524	+	0.157470i	$0.949666\pi$
$458$	29.8547	−	4.49736i	1.39502	−	0.210148i
$459$			5.50614i			0.257005i
$460$	−5.76886	−	3.56886i	−0.268974	−	0.166399i
$461$			19.7534i			0.920008i	0.887917	+	0.460004i	$0.152152\pi$
$461$			19.7534i			0.920008i	−0.887917	+	0.460004i	$0.847848\pi$
$462$	4.08558	+	27.1212i	0.190079	+	1.26179i
$463$			29.3453i			1.36379i	0.731450	+	0.681895i	$0.238844\pi$
$463$			29.3453i			1.36379i	−0.731450	+	0.681895i	$0.761156\pi$
$464$	−4.27940	−	6.28116i	−0.198666	−	0.291595i
$465$		−	0.747864i		−	0.0346814i
$466$	−30.3734	+	4.57550i	−1.40702	+	0.211956i
$467$		−	20.2814i		−	0.938513i	−0.883062	−	0.469256i	$-0.844522\pi$
$467$		−	20.2814i		−	0.938513i	0.883062	−	0.469256i	$-0.155478\pi$
$468$	−3.90010	−	12.6512i	−0.180282	−	0.584802i
$469$			36.8110i			1.69977i
$470$	−0.708745	−	4.70483i	−0.0326920	−	0.217018i
$471$	17.7700			0.818800
$472$	7.93605	−	3.81940i	0.365286	−	0.175802i
$473$	19.8471			0.912569
$474$	2.12363	−	0.319907i	0.0975414	−	0.0146938i
$475$		−	21.1258i		−	0.969316i
$476$	13.1858	+	42.7721i	0.604369	+	1.96046i
$477$	12.2549			0.561115
$478$	−2.50674	−	16.6404i	−0.114656	−	0.761114i
$479$	−35.5698			−1.62523			−0.812613	−	0.582803i	$-0.801956\pi$
$479$	−35.5698			−1.62523			−0.812613	+	0.582803i	$0.801956\pi$
$480$	−2.93385	+	2.71997i	−0.133911	+	0.124149i
$481$		−	11.4533i		−	0.522225i
$482$	−6.27633	−	41.6639i	−0.285879	−	1.89774i
$483$	−12.8198	−	14.6833i	−0.583323	−	0.668113i
$484$	−22.4927	+	6.93403i	−1.02239	+	0.315183i
$485$		−	3.68953i		−	0.167533i
$486$	−1.39844	+	0.210663i	−0.0634343	+	0.00955586i
$487$		−	36.2640i		−	1.64328i	−0.570009	−	0.821638i	$-0.693060\pi$
$487$		−	36.2640i		−	1.64328i	0.570009	−	0.821638i	$-0.306940\pi$
$488$	−14.0098	+	6.74251i	−0.634193	+	0.305219i
$489$	−4.80484			−0.217282
$490$	−9.41493	+	1.41828i	−0.425323	+	0.0640715i
$491$	14.1989			0.640786			0.320393	−	0.947285i	$-0.396185\pi$
$491$	14.1989			0.640786			0.320393	+	0.947285i	$0.396185\pi$
$492$	−4.23302	+	1.30495i	−0.190839	+	0.0588318i
$493$	10.4622			0.471195
$494$	−43.4585	+	6.54667i	−1.95529	+	0.294549i
$495$		−	3.37467i		−	0.151680i
$496$	−2.38159	−	3.49561i	−0.106936	−	0.156957i
$497$			36.8132i			1.65130i
$498$	1.50074	+	9.96232i	0.0672498	+	0.446422i
$499$	−30.1022			−1.34756			−0.673779	−	0.738933i	$-0.735330\pi$
$499$	−30.1022			−1.34756			−0.673779	+	0.738933i	$0.735330\pi$
$500$	−12.8409	+	3.95857i	−0.574260	+	0.177033i
$501$		−	10.3203i		−	0.461075i
$502$	−0.211820	−	1.40612i	−0.00945399	−	0.0627580i
$503$	27.6492			1.23282			0.616409	−	0.787426i	$-0.288587\pi$
$503$	27.6492			1.23282			0.616409	+	0.787426i	$0.288587\pi$
$504$	−10.3587	+	4.98533i	−0.461412	+	0.222064i
$505$		−	1.63114i		−	0.0725846i
$506$	20.9360	−	24.6787i	0.930720	−	1.09710i
$507$	−30.8159			−1.36858
$508$	12.6507	+	41.0363i	0.561282	+	1.82069i
$509$			14.6086i			0.647517i	0.946140	+	0.323758i	$0.104946\pi$
$509$			14.6086i			0.647517i	−0.946140	+	0.323758i	$0.895054\pi$
$510$	−0.820347	−	5.44568i	−0.0363256	−	0.241139i
$511$	36.6122			1.61963
$512$	−5.05136	+	22.0564i	−0.223241	+	0.974763i
$513$			4.69480i			0.207280i
$514$	−17.9021	+	2.69680i	−0.789627	+	0.118951i
$515$	−12.6917			−0.559262
$516$	2.45069	+	7.94958i	0.107886	+	0.349961i
$517$	22.6990			0.998303
$518$	−9.83456	+	1.48150i	−0.432106	+	0.0650932i
$519$		−	9.29934i		−	0.408196i
$520$	5.74215	+	11.9312i	0.251810	+	0.523218i
$521$		−	22.8769i		−	1.00225i	−0.865374	−	0.501127i	$-0.832919\pi$
$521$		−	22.8769i		−	1.00225i	0.865374	−	0.501127i	$-0.167081\pi$
$522$	0.400281	+	2.65717i	0.0175198	+	0.116301i
$523$			17.6456i			0.771588i	0.922585	+	0.385794i	$0.126073\pi$
$523$			17.6456i			0.771588i	−0.922585	+	0.385794i	$0.873927\pi$
$524$	10.2031	−	3.14539i	0.445723	−	0.137407i
$525$	−18.2891			−0.798203
$526$	−29.3385	+	4.41961i	−1.27922	+	0.192704i
$527$	5.82247			0.253631
$528$	−10.7467	−	15.7736i	−0.467689	−	0.686458i
$529$	−3.10246	+	22.7898i	−0.134889	+	0.990861i
$530$	−12.1204	+	1.82584i	−0.526475	+	0.0793092i
$531$	−3.11385			−0.135130
$532$	11.2428	+	36.4696i	0.487438	+	1.58116i
$533$			14.6605i			0.635019i
$534$	−1.48517	−	9.85897i	−0.0642697	−	0.426639i
$535$			11.1752i			0.483146i
$536$	−11.1090	−	23.0827i	−0.479837	−	0.997019i
$537$	−13.1531			−0.567599
$538$	−3.54839	−	23.5552i	−0.152982	−	1.01554i
$539$		−	45.4235i		−	1.95653i
$540$	1.35169	−	0.416699i	0.0581676	−	0.0179319i
$541$		−	29.4325i		−	1.26540i	−0.774397	−	0.632700i	$-0.781947\pi$
$541$		−	29.4325i		−	1.26540i	0.774397	−	0.632700i	$-0.218053\pi$
$542$	3.03769	+	20.1650i	0.130480	+	0.866160i
$543$	−26.0882			−1.11955
$544$	−21.1763	−	22.8414i	−0.907925	−	0.979316i
$545$	−4.53756			−0.194368
$546$	5.66763	+	37.6232i	0.242552	+	1.61013i
$547$	35.5765			1.52114			0.760571	−	0.649255i	$-0.224919\pi$
$547$	35.5765			1.52114			0.760571	+	0.649255i	$0.224919\pi$
$548$	5.35164	+	17.3597i	0.228611	+	0.741569i
$549$	5.49700			0.234606
$550$	−4.52326	−	30.0266i	−0.192872	−	1.28034i
$551$	8.92060			0.380030
$552$	12.4700	+	5.33845i	0.530759	+	0.227220i
$553$	−6.17211			−0.262465
$554$	4.24574	+	28.1843i	0.180384	+	1.19744i
$555$	1.22371			0.0519435
$556$	−19.8438	+	6.11742i	−0.841563	+	0.259436i
$557$	8.06756			0.341833			0.170917	−	0.985285i	$-0.445327\pi$
$557$	8.06756			0.341833			0.170917	+	0.985285i	$0.445327\pi$
$558$	0.222766	+	1.47878i	0.00943042	+	0.0626016i
$559$	27.5324			1.16450
$560$	9.50218	−	6.47391i	0.401540	−	0.273573i
$561$	26.2734			1.10926
$562$	2.30446	+	15.2976i	0.0972078	+	0.645291i
$563$			31.5966i			1.33164i	0.746113	+	0.665820i	$0.231918\pi$
$563$			31.5966i			1.33164i	−0.746113	+	0.665820i	$0.768082\pi$
$564$	2.80285	+	9.09191i	0.118021	+	0.382838i
$565$		−	4.16536i		−	0.175238i
$566$	−2.21028	−	14.6724i	−0.0929048	−	0.616727i
$567$	4.06441			0.170689
$568$	−11.1097	−	23.0841i	−0.466153	−	0.968586i
$569$		−	30.9949i		−	1.29937i	−0.760202	−	0.649687i	$-0.774900\pi$
$569$		−	30.9949i		−	1.29937i	0.760202	−	0.649687i	$-0.225100\pi$
$570$	−0.699468	−	4.64325i	−0.0292975	−	0.194484i
$571$			4.59140i			0.192144i	0.995374	+	0.0960720i	$0.0306279\pi$
$571$			4.59140i			0.192144i	−0.995374	+	0.0960720i	$0.969372\pi$
$572$	−60.3670	+	18.6099i	−2.52407	+	0.778119i
$573$	−6.97316			−0.291308
$574$	12.5885	−	1.89636i	0.525435	−	0.0791524i
$575$	14.1932	+	16.2563i	0.591897	+	0.677933i
$576$	4.99100	−	6.25220i	0.207958	−	0.260508i
$577$	17.3568			0.722572			0.361286	−	0.932455i	$-0.382338\pi$
$577$	17.3568			0.722572			0.361286	+	0.932455i	$0.382338\pi$
$578$	18.6238	−	2.80552i	0.774646	−	0.116694i
$579$	11.7701			0.489150
$580$	−0.791772	−	2.56836i	−0.0328765	−	0.106645i
$581$		−	28.9545i		−	1.20123i
$582$	1.09900	+	7.29543i	0.0455549	+	0.302405i
$583$		−	58.4762i		−	2.42184i
$584$	−22.9580	+	11.0490i	−0.950008	+	0.457212i
$585$		−	4.68143i		−	0.193553i
$586$	8.04522	−	1.21195i	0.332345	−	0.0500650i
$587$	−24.4037			−1.00725			−0.503624	−	0.863923i	$-0.668000\pi$
$587$	−24.4037			−1.00725			−0.503624	+	0.863923i	$0.668000\pi$
$588$	18.1940	−	5.60883i	0.750307	−	0.231304i
$589$	4.96452			0.204559
$590$	3.07966	−	0.463926i	0.126788	−	0.0190995i
$591$		−	13.5963i		−	0.559277i
$592$	5.71975	−	3.89691i	0.235080	−	0.160162i
$593$	−20.0748			−0.824372			−0.412186	−	0.911100i	$-0.635235\pi$
$593$	−20.0748			−0.824372			−0.412186	+	0.911100i	$0.635235\pi$
$594$	1.00521	+	6.67284i	0.0412442	+	0.273790i
$595$			15.8273i			0.648857i
$596$	24.4024	−	7.52277i	0.999563	−	0.308145i
$597$	−3.34329			−0.136832
$598$	29.0430	−	34.2350i	1.18766	−	1.39997i
$599$		−	22.0543i		−	0.901114i	−0.892748	−	0.450557i	$-0.851225\pi$
$599$		−	22.0543i		−	0.901114i	0.892748	−	0.450557i	$-0.148775\pi$
$600$	11.4684	−	5.51940i	0.468194	−	0.225328i
$601$	42.7799			1.74503			0.872514	−	0.488589i	$-0.162488\pi$
$601$	42.7799			1.74503			0.872514	+	0.488589i	$0.162488\pi$
$602$	−3.56134	−	23.6411i	−0.145150	−	0.963541i
$603$			9.05690i			0.368826i
$604$	5.59271	+	18.1417i	0.227564	+	0.738174i
$605$	−8.32315			−0.338384
$606$	0.485865	+	3.22530i	0.0197369	+	0.131019i
$607$		−	10.6180i		−	0.430971i	−0.976507	−	0.215485i	$-0.930867\pi$
$607$		−	10.6180i		−	0.430971i	0.976507	−	0.215485i	$-0.0691334\pi$
$608$	−18.0559	−	19.4757i	−0.732263	−	0.789842i
$609$		−	7.72280i		−	0.312944i
$610$	−5.43664	+	0.818985i	−0.220123	+	0.0331597i
$611$	31.4887			1.27390
$612$	3.24420	+	10.5236i	0.131139	+	0.425390i
$613$	4.65784			0.188128			0.0940642	−	0.995566i	$-0.470014\pi$
$613$	4.65784			0.188128			0.0940642	+	0.995566i	$0.470014\pi$
$614$	19.0850	−	2.87499i	0.770206	−	0.116025i
$615$	−1.56638			−0.0631625
$616$	23.7882	+	49.4279i	0.958456	+	1.99151i
$617$			17.2443i			0.694231i	0.937822	+	0.347115i	$0.112839\pi$
$617$			17.2443i			0.694231i	−0.937822	+	0.347115i	$0.887161\pi$
$618$	25.0956	−	3.78045i	1.00949	−	0.152072i
$619$			18.0162i			0.724131i	0.932153	+	0.362066i	$0.117928\pi$
$619$			18.0162i			0.724131i	−0.932153	+	0.362066i	$0.882072\pi$
$620$	−0.440639	−	1.42935i	−0.0176965	−	0.0574041i
$621$	−3.15417	−	3.61265i	−0.126572	−	0.144971i
$622$	3.06598	+	20.3528i	0.122934	+	0.816071i
$623$			28.6541i			1.14800i
$624$	−14.9081	−	21.8816i	−0.596801	−	0.875964i
$625$	17.7475			0.709900
$626$	3.48325	+	23.1228i	0.139219	+	0.924171i
$627$	22.4019			0.894647
$628$	33.9629	−	10.4701i	1.35527	−	0.417801i
$629$			9.52712i			0.379871i
$630$	−4.01979	+	0.605548i	−0.160152	+	0.0241256i
$631$	3.98228			0.158532			0.0792661	−	0.996853i	$-0.474742\pi$
$631$	3.98228			0.158532			0.0792661	+	0.996853i	$0.474742\pi$
$632$	3.87028	−	1.86265i	0.153951	−	0.0740924i
$633$	−16.9365			−0.673164
$634$	5.63899	+	37.4331i	0.223953	+	1.48666i
$635$			15.1850i			0.602599i
$636$	23.4221	−	7.22057i	0.928749	−	0.286314i
$637$		−	63.0127i		−	2.49665i
$638$	12.6791	−	1.91000i	0.501969	−	0.0756176i
$639$			9.05745i			0.358307i
$640$	−4.00469	+	6.92714i	−0.158299	+	0.273819i
$641$			29.4471i			1.16309i	0.813514	+	0.581545i	$0.197552\pi$
$641$			29.4471i			1.16309i	−0.813514	+	0.581545i	$0.802448\pi$
$642$	−3.32875	−	22.0971i	−0.131375	−	0.872103i
$643$			28.1113i			1.10860i	0.832316	+	0.554301i	$0.187014\pi$
$643$			28.1113i			1.10860i	−0.832316	+	0.554301i	$0.812986\pi$
$644$	−33.1532	−	20.5099i	−1.30642	−	0.808205i
$645$			2.94165i			0.115827i
$646$	36.1499	−	5.44568i	1.42230	−	0.214257i
$647$			31.7123i			1.24674i	0.781927	+	0.623370i	$0.214237\pi$
$647$			31.7123i			1.24674i	−0.781927	+	0.623370i	$0.785763\pi$
$648$	−2.54863	+	1.22658i	−0.100120	+	0.0481847i
$649$			14.8582i			0.583236i
$650$	−6.27479	−	41.6537i	−0.246117	−	1.63379i
$651$		−	4.29792i		−	0.168449i
$652$	−9.18321	+	2.83099i	−0.359642	+	0.110870i
$653$		−	23.1253i		−	0.904963i	−0.891774	−	0.452482i	$-0.850539\pi$
$653$		−	23.1253i		−	0.904963i	0.891774	−	0.452482i	$-0.149461\pi$
$654$	8.97226	−	1.35160i	0.350843	−	0.0528517i
$655$	3.77552			0.147522
$656$	−7.32145	+	4.98816i	−0.285855	+	0.194755i
$657$	9.00798			0.351435
$658$	−4.07310	−	27.0383i	−0.158786	−	1.05406i
$659$			17.6062i			0.685840i	0.939365	+	0.342920i	$0.111416\pi$
$659$			17.6062i			0.685840i	−0.939365	+	0.342920i	$0.888584\pi$
$660$	−1.98834	−	6.44981i	−0.0773961	−	0.251058i
$661$	−30.0716			−1.16965			−0.584825	−	0.811159i	$-0.698837\pi$
$661$	−30.0716			−1.16965			−0.584825	+	0.811159i	$0.698837\pi$
$662$	−20.5419	+	3.09446i	−0.798382	+	0.120270i
$663$	36.4471			1.41549
$664$	8.73804	+	18.1562i	0.339102	+	0.704596i
$665$			13.4951i			0.523319i
$666$	−2.41967	+	0.364504i	−0.0937605	+	0.0141243i
$667$	−6.86440	+	5.99324i	−0.265791	+	0.232059i
$668$	−6.08067	−	19.7245i	−0.235268	−	0.763165i
$669$			6.73080i			0.260228i
$670$	−1.34937	−	8.95746i	−0.0521306	−	0.346057i
$671$		−	26.2297i		−	1.01259i
$672$	−16.8606	+	15.6315i	−0.650412	+	0.602997i
$673$	−1.80969			−0.0697586			−0.0348793	−	0.999392i	$-0.511105\pi$
$673$	−1.80969			−0.0697586			−0.0348793	+	0.999392i	$0.511105\pi$
$674$	4.60775	+	30.5875i	0.177484	+	1.17819i
$675$	−4.49982			−0.173198
$676$	−58.8966	+	18.1566i	−2.26525	+	0.698331i
$677$	8.31892			0.319722			0.159861	−	0.987140i	$-0.448895\pi$
$677$	8.31892			0.319722			0.159861	+	0.987140i	$0.448895\pi$
$678$	1.24073	+	8.23629i	0.0476500	+	0.316313i
$679$		−	21.2034i		−	0.813713i
$680$	−4.77646	−	9.92467i	−0.183169	−	0.380594i
$681$		−	17.8632i		−	0.684520i
$682$	7.05620	−	1.06296i	0.270196	−	0.0407028i
$683$	−33.8876			−1.29667			−0.648336	−	0.761354i	$-0.724535\pi$
$683$	−33.8876			−1.29667			−0.648336	+	0.761354i	$0.724535\pi$
$684$	2.76616	+	8.97290i	0.105767	+	0.343087i
$685$			6.42375i			0.245439i
$686$	−14.3201	+	2.15721i	−0.546745	+	0.0823627i
$687$	−21.3486			−0.814501
$688$	9.36773	+	13.7496i	0.357141	+	0.524200i
$689$		−	81.1198i		−	3.09042i
$690$	3.65777	+	3.10305i	0.139249	+	0.118131i
$691$	−11.6171			−0.441935			−0.220967	−	0.975281i	$-0.570921\pi$
$691$	−11.6171			−0.441935			−0.220967	+	0.975281i	$0.570921\pi$
$692$	−5.47914	−	17.7733i	−0.208286	−	0.675639i
$693$		−	19.3939i		−	0.736715i
$694$	−7.67309	+	1.15589i	−0.291267	+	0.0438769i
$695$	−7.34295			−0.278534
$696$	2.33063	+	4.84265i	0.0883423	+	0.183560i
$697$		−	12.1950i		−	0.461918i
$698$	2.73562	+	18.1598i	0.103545	+	0.687357i
$699$	21.7195			0.821508
$700$	−34.9550	+	10.7759i	−1.32117	+	0.407291i
$701$	−4.60701			−0.174004			−0.0870022	−	0.996208i	$-0.527729\pi$
$701$	−4.60701			−0.174004			−0.0870022	+	0.996208i	$0.527729\pi$
$702$	1.39445	+	9.25674i	0.0526302	+	0.349373i
$703$			8.12329i			0.306376i
$704$	−29.8333	−	23.8153i	−1.12438	−	0.897572i
$705$			3.36436i			0.126709i
$706$	32.7205	−	4.92907i	1.23145	−	0.185508i
$707$		−	9.37401i		−	0.352546i
$708$	−5.95133	+	1.83467i	−0.223665	+	0.0689512i
$709$	34.7022			1.30327			0.651634	−	0.758534i	$-0.274084\pi$
$709$	34.7022			1.30327			0.651634	+	0.758534i	$0.274084\pi$
$710$	−1.34945	−	8.95800i	−0.0506439	−	0.336188i
$711$	−1.51857			−0.0569509
$712$	−8.64740	−	17.9678i	−0.324075	−	0.673373i
$713$	−3.82020	+	3.33538i	−0.143068	+	0.124911i
$714$	−4.71447	−	31.2959i	−0.176435	−	1.17122i
$715$	−22.3381			−0.835398
$716$	−25.1388	+	7.74978i	−0.939482	+	0.289623i
$717$			11.8993i			0.444387i
$718$	−8.79750	+	1.32527i	−0.328320	+	0.0494587i
$719$			21.8256i			0.813958i	0.913438	+	0.406979i	$0.133418\pi$
$719$			21.8256i			0.813958i	−0.913438	+	0.406979i	$0.866582\pi$
$720$	2.33790	−	1.59283i	0.0871283	−	0.0593612i
$721$	−72.9380			−2.71635
$722$	4.25284	−	0.640655i	0.158274	−	0.0238427i
$723$			29.7933i			1.10802i
$724$	−49.8609	+	15.3711i	−1.85307	+	0.571262i
$725$			8.55012i			0.317543i
$726$	16.4576	−	2.47921i	0.610800	−	0.0920121i
$727$	−4.07669			−0.151196			−0.0755981	−	0.997138i	$-0.524087\pi$
$727$	−4.07669			−0.151196			−0.0755981	+	0.997138i	$0.524087\pi$
$728$	32.9997	+	68.5677i	1.22305	+	2.54129i
$729$	1.00000			0.0370370
$730$	−8.90907	+	1.34208i	−0.329739	+	0.0496726i
$731$	−22.9021			−0.847065
$732$	10.5061	−	3.23881i	0.388316	−	0.119710i
$733$	17.3134			0.639486			0.319743	−	0.947504i	$-0.396403\pi$
$733$	17.3134			0.639486			0.319743	+	0.947504i	$0.396403\pi$
$734$	−3.97650	+	0.599027i	−0.146775	+	0.0221105i
$735$	6.73248			0.248331
$736$	26.9786	+	2.85579i	0.994444	+	0.105266i
$737$	43.2163			1.59189
$738$	3.09725	−	0.466576i	0.114011	−	0.0171749i
$739$	39.4205			1.45011			0.725054	−	0.688692i	$-0.241815\pi$
$739$	39.4205			1.45011			0.725054	+	0.688692i	$0.241815\pi$
$740$	2.33880	−	0.721004i	0.0859760	−	0.0265046i
$741$	31.0765			1.14163
$742$	−69.6548	+	10.4929i	−2.55711	+	0.385208i
$743$	−16.5094			−0.605672			−0.302836	−	0.953043i	$-0.597933\pi$
$743$	−16.5094			−0.605672			−0.302836	+	0.953043i	$0.597933\pi$
$744$	1.29705	+	2.69505i	0.0475521	+	0.0988052i
$745$	9.02984			0.330828
$746$	−6.27695	+	0.945572i	−0.229816	+	0.0346198i
$747$		−	7.12390i		−	0.260650i
$748$	50.2147	−	15.4802i	1.83603	−	0.566011i
$749$			64.2230i			2.34666i
$750$	9.39551	−	1.41536i	0.343076	−	0.0516815i
$751$	−13.8860			−0.506708			−0.253354	−	0.967374i	$-0.581534\pi$
$751$	−13.8860			−0.506708			−0.253354	+	0.967374i	$0.581534\pi$
$752$	10.7138	+	15.7254i	0.390694	+	0.573447i
$753$			1.00549i			0.0366422i
$754$	17.5888	−	2.64960i	0.640545	−	0.0964928i
$755$			6.71312i			0.244315i
$756$	7.76808	−	2.39474i	0.282522	−	0.0870958i
$757$	11.5324			0.419151			0.209575	−	0.977792i	$-0.432792\pi$
$757$	11.5324			0.419151			0.209575	+	0.977792i	$0.432792\pi$
$758$	5.18381	+	34.4115i	0.188285	+	1.24988i
$759$	−17.2383	+	15.0506i	−0.625710	+	0.546301i
$760$	−4.07264	−	8.46225i	−0.147730	−	0.306958i
$761$	17.3262			0.628074			0.314037	−	0.949411i	$-0.398318\pi$
$761$	17.3262			0.628074			0.314037	+	0.949411i	$0.398318\pi$
$762$	−4.52315	−	30.0258i	−0.163856	−	1.08772i
$763$	−26.0770			−0.944050
$764$	−13.3274	+	4.10856i	−0.482168	+	0.148642i
$765$			3.89412i			0.140792i
$766$	−21.9517	+	3.30685i	−0.793149	+	0.119481i
$767$			20.6117i			0.744246i
$768$	5.85523	−	14.8901i	0.211283	−	0.537302i
$769$		−	14.8399i		−	0.535141i	−0.963538	−	0.267571i	$-0.913779\pi$
$769$		−	14.8399i		−	0.535141i	0.963538	−	0.267571i	$-0.0862209\pi$
$770$	2.88946	+	19.1810i	0.104129	+	0.691235i
$771$	12.8015			0.461035
$772$	22.4956	−	6.93492i	0.809633	−	0.249593i
$773$	−26.2957			−0.945792			−0.472896	−	0.881118i	$-0.656791\pi$
$773$	−26.2957			−0.945792			−0.472896	+	0.881118i	$0.656791\pi$
$774$	−0.876226	−	5.81662i	−0.0314953	−	0.209074i
$775$			4.75834i			0.170925i
$776$	6.39889	+	13.2958i	0.229707	+	0.477292i
$777$	7.03255			0.252291
$778$	36.6925	−	5.52742i	1.31549	−	0.198168i
$779$		−	10.3980i		−	0.372548i
$780$	−2.75828	−	8.94734i	−0.0987623	−	0.320366i
$781$	43.2190			1.54650
$782$	−24.1587	+	28.4775i	−0.863912	+	1.01835i
$783$		−	1.90010i		−	0.0679041i
$784$	31.4684	−	21.4397i	1.12387	−	0.765703i
$785$	12.5676			0.448556
$786$	−7.46547	+	1.12461i	−0.266284	+	0.0401136i
$787$		−	46.7539i		−	1.66659i	−0.552825	−	0.833297i	$-0.686450\pi$
$787$		−	46.7539i		−	1.66659i	0.552825	−	0.833297i	$-0.313550\pi$
$788$	−8.01089	−	25.9858i	−0.285376	−	0.925707i
$789$	20.9795			0.746891
$790$	1.50190	−	0.226249i	0.0534352	−	0.00804957i
$791$		−	23.9380i		−	0.851136i
$792$	5.85281	+	12.1611i	0.207971	+	0.432128i
$793$		−	36.3866i		−	1.29212i
$794$	−1.74972	−	11.6151i	−0.0620951	−	0.412204i
$795$	8.66710			0.307390
$796$	−6.38984	+	1.96986i	−0.226482	+	0.0698197i
$797$	6.06463			0.214820			0.107410	−	0.994215i	$-0.465744\pi$
$797$	6.06463			0.214820			0.107410	+	0.994215i	$0.465744\pi$
$798$	−4.01979	−	26.6844i	−0.142299	−	0.944617i
$799$	−26.1931			−0.926644
$800$	18.6668	−	17.3060i	0.659972	−	0.611860i
$801$			7.05000i			0.249100i
$802$	−7.56895	−	50.2447i	−0.267269	−	1.77420i
$803$		−	42.9829i		−	1.51683i
$804$	5.33630	+	17.3099i	0.188197	+	0.610474i
$805$	−9.06662	−	10.3845i	−0.319556	−	0.366006i
$806$	9.78855	−	1.47456i	0.344787	−	0.0519393i
$807$			16.8439i			0.592935i
$808$	2.82894	+	5.87805i	0.0995217	+	0.206789i
$809$	34.6645			1.21874			0.609370	−	0.792886i	$-0.291422\pi$
$809$	34.6645			1.21874			0.609370	+	0.792886i	$0.291422\pi$
$810$	−0.989020	+	0.148988i	−0.0347506	+	0.00523490i
$811$	−17.1291			−0.601483			−0.300742	−	0.953706i	$-0.597234\pi$
$811$	−17.1291			−0.601483			−0.300742	+	0.953706i	$0.597234\pi$
$812$	−4.55025	−	14.7601i	−0.159682	−	0.517980i
$813$		−	14.4197i		−	0.505720i
$814$	1.73929	+	11.5458i	0.0609619	+	0.404681i
$815$	−3.39814			−0.119032
$816$	12.4009	+	18.2016i	0.434118	+	0.637184i
$817$	−19.5274			−0.683179
$818$	−15.7903	+	2.37868i	−0.552094	+	0.0831685i
$819$		−	26.9038i		−	0.940095i
$820$	−2.99373	+	0.922906i	−0.104546	+	0.0322293i
$821$		−	6.26971i		−	0.218814i	−0.993997	−	0.109407i	$-0.965105\pi$
$821$		−	6.26971i		−	0.218814i	0.993997	−	0.109407i	$-0.0348952\pi$
$822$	−1.91344	−	12.7019i	−0.0667388	−	0.443030i
$823$			39.4914i			1.37658i	0.725434	+	0.688291i	$0.241639\pi$
$823$			39.4914i			1.37658i	−0.725434	+	0.688291i	$0.758361\pi$
$824$	45.7364	−	22.0116i	1.59330	−	0.766811i
$825$			21.4716i			0.747544i
$826$	17.6986	−	2.66615i	0.615813	−	0.0927671i
$827$			25.6532i			0.892050i	0.895021	+	0.446025i	$0.147161\pi$
$827$			25.6532i			0.892050i	−0.895021	+	0.446025i	$0.852839\pi$
$828$	−8.15694	−	5.04622i	−0.283473	−	0.175368i
$829$		−	17.3454i		−	0.602430i	−0.953556	−	0.301215i	$-0.902608\pi$
$829$		−	17.3454i		−	0.602430i	0.953556	−	0.301215i	$-0.0973921\pi$
$830$	1.06137	+	7.04568i	0.0368408	+	0.244559i
$831$		−	20.1542i		−	0.699141i
$832$	−41.3855	−	33.0372i	−1.43478	−	1.14536i
$833$			52.4155i			1.81609i
$834$	14.5195	−	2.18724i	0.502768	−	0.0757378i
$835$		−	7.29883i		−	0.252587i
$836$	42.8155	−	13.1991i	1.48081	−	0.456502i
$837$		−	1.05745i		−	0.0365508i
$838$	2.46135	+	16.3391i	0.0850258	+	0.564424i
$839$	−16.1675			−0.558163			−0.279082	−	0.960267i	$-0.590030\pi$
$839$	−16.1675			−0.558163			−0.279082	+	0.960267i	$0.590030\pi$
$840$	−7.32600	+	3.52579i	−0.252771	+	0.121651i
$841$	25.3896			0.875504
$842$	34.6541	−	5.22036i	1.19426	−	0.179906i
$843$		−	10.9391i		−	0.376762i
$844$	−32.3697	+	9.97891i	−1.11421	+	0.343488i
$845$	−21.7940			−0.749736
$846$	−1.00214	−	6.65245i	−0.0344542	−	0.228716i
$847$	−47.8325			−1.64354
$848$	40.5111	−	27.6005i	1.39116	−	0.947805i
$849$			10.4920i			0.360085i
$850$	5.21952	+	34.6485i	0.179028	+	1.18843i
$851$	−5.45757	−	6.25087i	−0.187083	−	0.214277i
$852$	5.33662	+	17.3110i	0.182830	+	0.593065i
$853$			8.35448i			0.286052i	0.989719	+	0.143026i	$0.0456833\pi$
$853$			8.35448i			0.286052i	−0.989719	+	0.143026i	$0.954317\pi$
$854$	−31.2439	+	4.70664i	−1.06915	+	0.161058i
$855$			3.32032i			0.113552i
$856$	−19.3816	−	40.2716i	−0.662449	−	1.37646i
$857$	−12.1448			−0.414859			−0.207430	−	0.978250i	$-0.566510\pi$
$857$	−12.1448			−0.414859			−0.207430	+	0.978250i	$0.566510\pi$
$858$	44.1699	−	6.65383i	1.50794	−	0.227158i
$859$	27.8503			0.950241			0.475120	−	0.879921i	$-0.342405\pi$
$859$	27.8503			0.950241			0.475120	+	0.879921i	$0.342405\pi$
$860$	1.73321	+	5.62220i	0.0591020	+	0.191716i
$861$	−9.00186			−0.306783
$862$	19.2597	−	2.90132i	0.655989	−	0.0988194i
$863$		−	29.6847i		−	1.01048i	−0.862979	−	0.505239i	$-0.831404\pi$
$863$		−	29.6847i		−	1.01048i	0.862979	−	0.505239i	$-0.168596\pi$
$864$	−4.14835	+	3.84594i	−0.141130	+	0.130841i
$865$		−	6.57680i		−	0.223618i
$866$	−3.64098	−	24.1698i	−0.123726	−	0.821324i
$867$	−13.3176			−0.452288
$868$	−2.53232	−	8.21436i	−0.0859525	−	0.278814i
$869$			7.24609i			0.245807i
$870$	0.283092	+	1.87924i	0.00959772	+	0.0637122i
$871$	59.9509			2.03136
$872$	16.3518	−	7.86966i	0.553742	−	0.266500i
$873$		−	5.21685i		−	0.176564i
$874$	−20.5989	+	24.2813i	−0.696767	+	0.821326i
$875$	−27.3071			−0.923149
$876$	17.2164	−	5.30747i	0.581689	−	0.179323i
$877$		−	17.8807i		−	0.603787i	−0.953342	−	0.301893i	$-0.902381\pi$
$877$		−	17.8807i		−	0.603787i	0.953342	−	0.301893i	$-0.0976187\pi$
$878$	8.21453	+	54.5302i	0.277227	+	1.84030i
$879$	−5.75301			−0.194044
$880$	−7.60041	−	11.1556i	−0.256210	−	0.376056i
$881$		−	20.4097i		−	0.687622i	−0.939039	−	0.343811i	$-0.888282\pi$
$881$		−	20.4097i		−	0.687622i	0.939039	−	0.343811i	$-0.111718\pi$
$882$	−13.3123	+	2.00540i	−0.448250	+	0.0675252i
$883$	16.7990			0.565333			0.282666	−	0.959218i	$-0.408781\pi$
$883$	16.7990			0.565333			0.282666	+	0.959218i	$0.408781\pi$
$884$	69.6592	−	21.4745i	2.34289	−	0.722266i
$885$	−2.20222			−0.0740269
$886$	−44.3697	+	6.68393i	−1.49063	+	0.224551i
$887$		−	16.4325i		−	0.551750i	−0.961194	−	0.275875i	$-0.911032\pi$
$887$		−	16.4325i		−	0.551750i	0.961194	−	0.275875i	$-0.0889675\pi$
$888$	−4.40982	+	2.12232i	−0.147984	+	0.0712204i
$889$			87.2672i			2.92685i
$890$	−1.05036	−	6.97259i	−0.0352083	−	0.233722i
$891$		−	4.77165i		−	0.159856i
$892$	3.96576	+	12.8642i	0.132784	+	0.430725i
$893$	−22.3335			−0.747361
$894$	−17.8550	+	2.68971i	−0.597161	+	0.0899574i
$895$	−9.30233			−0.310943
$896$	−23.0147	+	39.8097i	−0.768866	+	1.32995i
$897$	−23.9134	+	20.8786i	−0.798445	+	0.697115i
$898$	54.1635	−	8.15929i	1.80746	−	0.272279i
$899$	−2.00926			−0.0670127
$900$	−8.60025	+	2.65128i	−0.286675	+	0.0883760i
$901$			67.4774i			2.24800i
$902$	−2.22634	−	14.7790i	−0.0741289	−	0.492087i
$903$			16.9054i			0.562577i
$904$	7.22413	+	15.0105i	0.240271	+	0.499242i
$905$	−18.4505			−0.613314
$906$	−1.99963	−	13.2741i	−0.0664333	−	0.441001i
$907$		−	23.2224i		−	0.771088i	−0.922690	−	0.385544i	$-0.874014\pi$
$907$		−	23.2224i		−	0.771088i	0.922690	−	0.385544i	$-0.125986\pi$
$908$	−10.5249	−	34.1409i	−0.349283	−	1.13301i
$909$		−	2.30636i		−	0.0764972i
$910$	4.00834	+	26.6084i	0.132875	+	0.882059i
$911$	−30.7469			−1.01869			−0.509345	−	0.860563i	$-0.670112\pi$
$911$	−30.7469			−1.01869			−0.509345	+	0.860563i	$0.670112\pi$
$912$	10.5736	+	15.5196i	0.350127	+	0.513904i
$913$	−33.9927			−1.12500
$914$	−1.41832	−	9.41517i	−0.0469138	−	0.311426i
$915$	3.88766			0.128522
$916$	−40.8024	+	12.5785i	−1.34815	+	0.415607i
$917$	21.6976			0.716519
$918$	−1.15994	−	7.69998i	−0.0382837	−	0.254137i
$919$	18.6535			0.615322			0.307661	−	0.951496i	$-0.400454\pi$
$919$	18.6535			0.615322			0.307661	+	0.951496i	$0.400454\pi$
$920$	8.81920	+	3.77553i	0.290760	+	0.124476i
$921$	−13.6474			−0.449696
$922$	−4.16131	−	27.6239i	−0.137045	−	0.909744i
$923$	59.9545			1.97343
$924$	−11.4268	−	37.0665i	−0.375916	−	1.21940i
$925$	−7.78592			−0.255999
$926$	−6.18196	−	41.0374i	−0.203152	−	1.34857i
$927$	−17.9455			−0.589408
$928$	7.30767	+	7.88228i	0.239886	+	0.258749i
$929$	18.3221			0.601128			0.300564	−	0.953762i	$-0.402825\pi$
$929$	18.3221			0.601128			0.300564	+	0.953762i	$0.402825\pi$
$930$	0.157547	+	1.04584i	0.00516618	+	0.0342944i
$931$			44.6919i			1.46472i
$932$	41.5113	−	12.7971i	1.35975	−	0.419182i
$933$		−	14.5540i		−	0.476475i
$934$	4.27255	+	28.3623i	0.139802	+	0.928042i
$935$	18.5814			0.607676
$936$	8.11918	+	16.8703i	0.265384	+	0.551422i
$937$			19.8701i			0.649128i	0.945864	+	0.324564i	$0.105218\pi$
$937$			19.8701i			0.649128i	−0.945864	+	0.324564i	$0.894782\pi$
$938$	−7.75471	−	51.4778i	−0.253200	−	1.68081i
$939$		−	16.5347i		−	0.539591i
$940$	1.98227	+	6.43010i	0.0646544	+	0.209727i
$941$	−37.1524			−1.21114			−0.605568	−	0.795794i	$-0.707054\pi$
$941$	−37.1524			−1.21114			−0.605568	+	0.795794i	$0.707054\pi$
$942$	−24.8503	+	3.74349i	−0.809665	+	0.121969i
$943$	6.98585	+	8.00129i	0.227491	+	0.260558i
$944$	−10.2935	+	7.01301i	−0.335023	+	0.228254i
$945$	2.87449			0.0935071
$946$	−27.7548	+	4.18104i	−0.902388	+	0.135937i
$947$	−52.5957			−1.70913			−0.854566	−	0.519343i	$-0.826177\pi$
$947$	−52.5957			−1.70913			−0.854566	+	0.519343i	$0.826177\pi$
$948$	−2.90236	+	0.894738i	−0.0942643	+	0.0290597i
$949$		−	59.6270i		−	1.93557i
$950$	4.45041	+	29.5430i	0.144390	+	0.958502i
$951$		−	26.7678i		−	0.868007i
$952$	−27.4499	−	57.0363i	−0.889658	−	1.84856i
$953$		−	15.9812i		−	0.517682i	−0.965920	−	0.258841i	$-0.916659\pi$
$953$		−	15.9812i		−	0.517682i	0.965920	−	0.258841i	$-0.0833406\pi$
$954$	−17.1377	+	2.58166i	−0.554855	+	0.0835843i
$955$	−4.93165			−0.159584
$956$	7.01103	+	22.7424i	0.226753	+	0.735543i
$957$	−9.06662			−0.293082
$958$	49.7421	−	7.49324i	1.60709	−	0.242096i
$959$			36.9168i			1.19211i
$960$	3.52980	−	4.42176i	0.113924	−	0.142712i
$961$	29.8818			0.963929
$962$	2.41278	+	16.0167i	0.0777913	+	0.516399i
$963$			15.8013i			0.509190i
$964$	17.5541	+	56.9421i	0.565379	+	1.83398i
$965$	8.32422			0.267966
$966$	21.0209	+	17.8330i	0.676338	+	0.573767i
$967$			38.2253i			1.22924i	0.788822	+	0.614622i	$0.210691\pi$
$967$			38.2253i			1.22924i	−0.788822	+	0.614622i	$0.789309\pi$
$968$	29.9938	−	14.4352i	0.964037	−	0.463964i
$969$	−25.8502			−0.830429
$970$	0.777247	+	5.15957i	0.0249559	+	0.165664i
$971$			9.44782i			0.303195i	0.988442	+	0.151597i	$0.0484417\pi$
$971$			9.44782i			0.303195i	−0.988442	+	0.151597i	$0.951558\pi$
$972$	1.91124	−	0.589197i	0.0613031	−	0.0188985i
$973$	−42.1994			−1.35285
$974$	7.63947	+	50.7128i	0.244784	+	1.62494i
$975$			29.7859i			0.953913i
$976$	18.1714	−	12.3803i	0.581652	−	0.396284i
$977$		−	0.445730i		−	0.0142602i	−0.999975	−	0.00713008i	$-0.997730\pi$
$977$		−	0.445730i		−	0.0142602i	0.999975	−	0.00713008i	$-0.00226959\pi$
$978$	6.71925	−	1.01220i	0.214858	−	0.0323666i
$979$	33.6401			1.07514
$980$	12.8674	−	3.96675i	0.411034	−	0.126713i
$981$	−6.41593			−0.204845
$982$	−19.8562	+	2.99118i	−0.633637	+	0.0954523i
$983$	−23.6354			−0.753851			−0.376925	−	0.926244i	$-0.623019\pi$
$983$	−23.6354			−0.753851			−0.376925	+	0.926244i	$0.623019\pi$
$984$	5.64470	−	2.71663i	0.179946	−	0.0866030i
$985$		−	9.61575i		−	0.306383i
$986$	−14.6307	+	2.20400i	−0.465938	+	0.0701897i
$987$			19.3347i			0.615430i
$988$	59.3948	−	18.3102i	1.88960	−	0.582525i
$989$	15.0264	−	13.1194i	0.477811	−	0.417172i
$990$	0.710917	+	4.71925i	0.0225944	+	0.149988i
$991$		−	8.87816i		−	0.282024i	−0.990008	−	0.141012i	$-0.954964\pi$
$991$		−	8.87816i		−	0.282024i	0.990008	−	0.141012i	$-0.0450356\pi$
$992$	4.06689	+	4.38667i	0.129124	+	0.139277i
$993$	14.6892			0.466147
$994$	−7.75518	−	51.4809i	−0.245979	−	1.63288i
$995$	−2.36449			−0.0749593
$996$	−4.19738	−	13.6155i	−0.132999	−	0.431424i
$997$		−	25.8021i		−	0.817161i	−0.912722	−	0.408581i	$-0.866024\pi$
$997$		−	25.8021i		−	0.817161i	0.912722	−	0.408581i	$-0.133976\pi$
$998$	42.0960	−	6.34141i	1.33252	−	0.200734i
$999$	1.73027			0.0547434

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.a.91.4	yes	24
4.3	odd	2		2208.2.n.a.367.13		24
8.3	odd	2	inner	552.2.n.a.91.1	✓	24
8.5	even	2		2208.2.n.a.367.11		24
23.22	odd	2	inner	552.2.n.a.91.3	yes	24
92.91	even	2		2208.2.n.a.367.12		24
184.45	odd	2		2208.2.n.a.367.14		24
184.91	even	2	inner	552.2.n.a.91.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.a.91.1	✓	24	8.3	odd	2	inner
552.2.n.a.91.2	yes	24	184.91	even	2	inner
552.2.n.a.91.3	yes	24	23.22	odd	2	inner
552.2.n.a.91.4	yes	24	1.1	even	1	trivial
2208.2.n.a.367.11		24	8.5	even	2
2208.2.n.a.367.12		24	92.91	even	2
2208.2.n.a.367.13		24	4.3	odd	2
2208.2.n.a.367.14		24	184.45	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)

\(f(q)\)	\(=\)	\(q+(-1.39844 + 0.210663i) q^{2} +1.00000 q^{3} +(1.91124 - 0.589197i) q^{4} +0.707233 q^{5} +(-1.39844 + 0.210663i) q^{6} +4.06441 q^{7} +(-2.54863 + 1.22658i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.39844 + 0.210663i) q^{2} +1.00000 q^{3} +(1.91124 - 0.589197i) q^{4} +0.707233 q^{5} +(-1.39844 + 0.210663i) q^{6} +4.06441 q^{7} +(-2.54863 + 1.22658i) q^{8} +1.00000 q^{9} +(-0.989020 + 0.148988i) q^{10} -4.77165i q^{11} +(1.91124 - 0.589197i) q^{12} -6.61936i q^{13} +(-5.68382 + 0.856221i) q^{14} +0.707233 q^{15} +(3.30569 - 2.25220i) q^{16} +5.50614i q^{17} +(-1.39844 + 0.210663i) q^{18} +4.69480i q^{19} +(1.35169 - 0.416699i) q^{20} +4.06441 q^{21} +(1.00521 + 6.67284i) q^{22} +(-3.15417 - 3.61265i) q^{23} +(-2.54863 + 1.22658i) q^{24} -4.49982 q^{25} +(1.39445 + 9.25674i) q^{26} +1.00000 q^{27} +(7.76808 - 2.39474i) q^{28} -1.90010i q^{29} +(-0.989020 + 0.148988i) q^{30} -1.05745i q^{31} +(-4.14835 + 3.84594i) q^{32} -4.77165i q^{33} +(-1.15994 - 7.69998i) q^{34} +2.87449 q^{35} +(1.91124 - 0.589197i) q^{36} +1.73027 q^{37} +(-0.989020 - 6.56537i) q^{38} -6.61936i q^{39} +(-1.80247 + 0.867479i) q^{40} -2.21480 q^{41} +(-5.68382 + 0.856221i) q^{42} +4.15938i q^{43} +(-2.81144 - 9.11977i) q^{44} +0.707233 q^{45} +(5.17195 + 4.38759i) q^{46} +4.75707i q^{47} +(3.30569 - 2.25220i) q^{48} +9.51946 q^{49} +(6.29271 - 0.947945i) q^{50} +5.50614i q^{51} +(-3.90010 - 12.6512i) q^{52} +12.2549 q^{53} +(-1.39844 + 0.210663i) q^{54} -3.37467i q^{55} +(-10.3587 + 4.98533i) q^{56} +4.69480i q^{57} +(0.400281 + 2.65717i) q^{58} -3.11385 q^{59} +(1.35169 - 0.416699i) q^{60} +5.49700 q^{61} +(0.222766 + 1.47878i) q^{62} +4.06441 q^{63} +(4.99100 - 6.25220i) q^{64} -4.68143i q^{65} +(1.00521 + 6.67284i) q^{66} +9.05690i q^{67} +(3.24420 + 10.5236i) q^{68} +(-3.15417 - 3.61265i) q^{69} +(-4.01979 + 0.605548i) q^{70} +9.05745i q^{71} +(-2.54863 + 1.22658i) q^{72} +9.00798 q^{73} +(-2.41967 + 0.364504i) q^{74} -4.49982 q^{75} +(2.76616 + 8.97290i) q^{76} -19.3939i q^{77} +(1.39445 + 9.25674i) q^{78} -1.51857 q^{79} +(2.33790 - 1.59283i) q^{80} +1.00000 q^{81} +(3.09725 - 0.466576i) q^{82} -7.12390i q^{83} +(7.76808 - 2.39474i) q^{84} +3.89412i q^{85} +(-0.876226 - 5.81662i) q^{86} -1.90010i q^{87} +(5.85281 + 12.1611i) q^{88} +7.05000i q^{89} +(-0.989020 + 0.148988i) q^{90} -26.9038i q^{91} +(-8.15694 - 5.04622i) q^{92} -1.05745i q^{93} +(-1.00214 - 6.65245i) q^{94} +3.32032i q^{95} +(-4.14835 + 3.84594i) q^{96} -5.21685i q^{97} +(-13.3123 + 2.00540i) q^{98} -4.77165i 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

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