LMFDB - Embedded newform 552.2.n.a.91.3

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			91.3
Character	$\chi$	$=$	552.91
Dual form			552.2.n.a.91.1

$q$-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} +(-3.64985 + 5.71652i) 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} +(3.89982 - 8.76307i) 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	$-0.550550\pi$
$5$	−0.707233			−0.316284			−0.158142	+	0.987416i	$0.550550\pi$
$6$	−1.39844	+	0.210663i	−0.570909	+	0.0860027i
$7$	−4.06441			−1.53620			−0.768102	−	0.640328i	$-0.778799\pi$
$7$	−4.06441			−1.53620			−0.768102	+	0.640328i	$0.778799\pi$
$8$	−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	$0.255562\pi$
$11$			4.77165i			1.43871i	−0.694645	+	0.719353i	$0.744438\pi$
$12$	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	$-0.767271\pi$
$17$		−	5.50614i		−	1.33543i	0.744415	−	0.667717i	$-0.232729\pi$
$18$	−1.39844	+	0.210663i	−0.329614	+	0.0496537i
$19$		−	4.69480i		−	1.07706i	−0.842606	−	0.538530i	$-0.818980\pi$
$19$		−	4.69480i		−	1.07706i	0.842606	−	0.538530i	$-0.181020\pi$
$20$	−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	$-0.545426\pi$
$37$	−1.73027			−0.284455			−0.142228	+	0.989834i	$0.545426\pi$
$38$	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	$-0.897274\pi$
$43$		−	4.15938i		−	0.634299i	0.948376	−	0.317149i	$-0.102726\pi$
$44$	2.81144	+	9.11977i	0.423840	+	1.37486i
$45$	−0.707233			−0.105428
$46$	−3.64985	+	5.71652i	−0.538141	+	0.842855i
$47$			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	$-0.818429\pi$
$53$	−12.2549			−1.68334			−0.841672	+	0.539989i	$0.818429\pi$
$54$	−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	$-0.614467\pi$
$61$	−5.49700			−0.703818			−0.351909	+	0.936034i	$0.614467\pi$
$62$	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	$-0.813392\pi$
$67$		−	9.05690i		−	1.10648i	0.833023	−	0.553238i	$-0.186608\pi$
$68$	−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	$-0.472775\pi$
$79$	1.51857			0.170853			0.0854264	+	0.996344i	$0.472775\pi$
$80$	−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	$0.127862\pi$
$83$			7.12390i			0.781950i	−0.920401	+	0.390975i	$0.872138\pi$
$84$	−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	$-0.878106\pi$
$89$		−	7.05000i		−	0.747299i	0.927570	−	0.373649i	$-0.121894\pi$
$90$	0.989020	−	0.148988i	0.104252	−	0.0157047i
$91$			26.9038i			2.82028i
$92$	3.89982	−	8.76307i	0.406584	−	0.913613i
$93$		−	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	$0.0853210\pi$
$97$			5.21685i			0.529691i	−0.964291	+	0.264845i	$0.914679\pi$
$98$	−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	$-0.154764\pi$
$103$	17.9455			1.76822			0.884112	+	0.467275i	$0.154764\pi$
$104$	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	$-0.723339\pi$
$107$		−	15.8013i		−	1.52757i	0.645471	−	0.763785i	$-0.276661\pi$
$108$	1.91124	−	0.589197i	0.183909	−	0.0566955i
$109$	6.41593			0.614534			0.307267	−	0.951623i	$-0.400585\pi$
$109$	6.41593			0.614534			0.307267	+	0.951623i	$0.400585\pi$
$110$	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	$0.0893487\pi$
$113$			5.88965i			0.554052i	−0.960862	+	0.277026i	$0.910651\pi$
$114$	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	$-0.873165\pi$
$137$		−	9.08294i		−	0.776008i	0.921658	−	0.388004i	$-0.126835\pi$
$138$	−3.64985	+	5.71652i	−0.310696	+	0.486623i
$139$	−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	$-0.675184\pi$
$149$	−12.7678			−1.04598			−0.522991	+	0.852338i	$0.675184\pi$
$150$	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	$-0.750899\pi$
$157$	−17.7700			−1.41820			−0.709102	+	0.705106i	$0.750899\pi$
$158$	−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	$-0.0787382\pi$
$181$	26.0882			1.93912			0.969561	+	0.244848i	$0.0787382\pi$
$182$	−5.66763	−	37.6232i	−0.420113	−	2.78882i
$183$	−5.49700			−0.406350
$184$	−3.60759	+	13.0761i	−0.265955	+	0.963985i
$185$	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	$-0.418820\pi$
$191$	6.97316			0.504560			0.252280	+	0.967654i	$0.418820\pi$
$192$	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	$-0.462191\pi$
$199$	3.34329			0.237000			0.118500	+	0.992954i	$0.462191\pi$
$200$	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	$0.201982\pi$
$227$			17.8632i			1.18562i	−0.805341	+	0.592812i	$0.798018\pi$
$228$	−2.76616	−	8.97290i	−0.183193	−	0.594245i
$229$	21.3486			1.41076			0.705378	−	0.708831i	$-0.250777\pi$
$229$	21.3486			1.41076			0.705378	+	0.708831i	$0.250777\pi$
$230$	2.58129	−	4.04291i	0.170205	−	0.266582i
$231$		−	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	$-0.590815\pi$
$241$		−	29.7933i		−	1.91915i	0.281449	−	0.959576i	$-0.409185\pi$
$242$	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	$-0.989897\pi$
$251$		−	1.00549i		−	0.0634661i	0.999496	−	0.0317331i	$-0.0101026\pi$
$252$	−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	$-0.723904\pi$
$263$	−20.9795			−1.29365			−0.646827	+	0.762637i	$0.723904\pi$
$264$	−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
$276$	3.89982	−	8.76307i	0.234741	−	0.527475i
$277$		−	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	$0.105797\pi$
$281$			10.9391i			0.652571i	−0.945271	+	0.326286i	$0.894203\pi$
$282$	−1.00214	−	6.65245i	−0.0596764	−	0.396148i
$283$		−	10.4920i		−	0.623685i	−0.950134	−	0.311843i	$-0.899054\pi$
$283$		−	10.4920i		−	0.623685i	0.950134	−	0.311843i	$-0.100946\pi$
$284$	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	$-0.446254\pi$
$293$	5.75301			0.336095			0.168047	+	0.985779i	$0.446254\pi$
$294$	−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	$0.154773\pi$
$313$			16.5347i			0.934599i	−0.884099	+	0.467299i	$0.845227\pi$
$314$	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
$322$	14.8345	−	23.2343i	0.826694	−	1.29480i
$323$	−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	$0.203141\pi$
$337$			21.8726i			1.19148i	−0.803178	+	0.595739i	$0.796859\pi$
$338$	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	$-0.553089\pi$
$359$	−6.29096			−0.332024			−0.166012	+	0.986124i	$0.553089\pi$
$360$	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	$-0.523645\pi$
$367$	−2.84353			−0.148431			−0.0742156	+	0.997242i	$0.523645\pi$
$368$	2.29032	−	19.0461i	0.119391	−	0.992847i
$369$	−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	$-0.537073\pi$
$373$	−4.48855			−0.232409			−0.116204	+	0.993225i	$0.537073\pi$
$374$	−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	$0.217763\pi$
$379$			24.6072i			1.26398i	−0.774975	+	0.631992i	$0.782237\pi$
$380$	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	$-0.631354\pi$
$383$	−15.6974			−0.802098			−0.401049	+	0.916057i	$0.631354\pi$
$384$	−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	$-0.268361\pi$
$389$	26.2382			1.33033			0.665166	+	0.746696i	$0.268361\pi$
$390$	−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	$-0.645662\pi$
$401$		−	35.9292i		−	1.79422i	0.441807	−	0.897110i	$-0.354338\pi$
$402$	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
$414$	−3.64985	+	5.71652i	−0.179380	+	0.280952i
$415$		−	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	$0.0921251\pi$
$419$			11.6838i			0.570792i	−0.958410	+	0.285396i	$0.907875\pi$
$420$	5.49384	−	1.69364i	0.268072	−	0.0826411i
$421$	24.7806			1.20773			0.603867	−	0.797085i	$-0.293626\pi$
$421$	24.7806			1.20773			0.603867	+	0.797085i	$0.293626\pi$
$422$	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	$-0.392379\pi$
$431$	13.7723			0.663390			0.331695	+	0.943387i	$0.392379\pi$
$432$	3.30569	−	2.25220i	0.159045	−	0.108359i
$433$		−	17.2835i		−	0.830591i	−0.909687	−	0.415295i	$-0.863678\pi$
$433$		−	17.2835i		−	0.830591i	0.909687	−	0.415295i	$-0.136322\pi$
$434$	−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	$-0.949666\pi$
$457$		−	6.73265i		−	0.314940i	0.987524	−	0.157470i	$-0.0503338\pi$
$458$	−29.8547	+	4.49736i	−1.39502	+	0.210148i
$459$		−	5.50614i		−	0.257005i
$460$	−2.75808	+	6.19753i	−0.128596	+	0.288962i
$461$			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	$0.155478\pi$
$467$			20.2814i			0.938513i	−0.883062	+	0.469256i	$0.844522\pi$
$468$	−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	$-0.198044\pi$
$479$	35.5698			1.62523			0.812613	+	0.582803i	$0.198044\pi$
$480$	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	$-0.711413\pi$
$503$	−27.6492			−1.23282			−0.616409	+	0.787426i	$0.711413\pi$
$504$	10.3587	−	4.98533i	0.461412	−	0.222064i
$505$			1.63114i			0.0725846i
$506$	−27.2772	−	17.4158i	−1.21262	−	0.774226i
$507$	−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	$0.167081\pi$
$521$			22.8769i			1.00225i	−0.865374	+	0.501127i	$0.832919\pi$
$522$	0.400281	+	2.65717i	0.0175198	+	0.116301i
$523$		−	17.6456i		−	0.771588i	−0.922585	−	0.385794i	$-0.873927\pi$
$523$		−	17.6456i		−	0.771588i	0.922585	−	0.385794i	$-0.126073\pi$
$524$	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
$552$	−3.60759	+	13.0761i	−0.153549	+	0.556557i
$553$	−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	$-0.554673\pi$
$557$	−8.06756			−0.341833			−0.170917	+	0.985285i	$0.554673\pi$
$558$	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	$-0.768082\pi$
$563$		−	31.5966i		−	1.33164i	0.746113	−	0.665820i	$-0.231918\pi$
$564$	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	$0.225100\pi$
$569$			30.9949i			1.29937i	−0.760202	+	0.649687i	$0.774900\pi$
$570$	−0.699468	−	4.64325i	−0.0292975	−	0.194484i
$571$		−	4.59140i		−	0.192144i	−0.995374	−	0.0960720i	$-0.969372\pi$
$571$		−	4.59140i		−	0.192144i	0.995374	−	0.0960720i	$-0.0306279\pi$
$572$	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
$598$	37.8397	+	24.1596i	1.54738	+	0.987961i
$599$		−	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	$-0.529986\pi$
$613$	−4.65784			−0.188128			−0.0940642	+	0.995566i	$0.529986\pi$
$614$	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	$-0.887161\pi$
$617$		−	17.2443i		−	0.694231i	0.937822	−	0.347115i	$-0.112839\pi$
$618$	−25.0956	+	3.78045i	−1.00949	+	0.152072i
$619$		−	18.0162i		−	0.724131i	−0.932153	−	0.362066i	$-0.882072\pi$
$619$		−	18.0162i		−	0.724131i	0.932153	−	0.362066i	$-0.117928\pi$
$620$	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	$-0.525258\pi$
$631$	−3.98228			−0.158532			−0.0792661	+	0.996853i	$0.525258\pi$
$632$	−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	$-0.802448\pi$
$641$		−	29.4471i		−	1.16309i	0.813514	−	0.581545i	$-0.197552\pi$
$642$	3.32875	+	22.0971i	0.131375	+	0.872103i
$643$		−	28.1113i		−	1.10860i	−0.832316	−	0.554301i	$-0.812986\pi$
$643$		−	28.1113i		−	1.10860i	0.832316	−	0.554301i	$-0.187014\pi$
$644$	−15.8505	+	35.6167i	−0.624596	+	1.40350i
$645$			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	$-0.888584\pi$
$659$		−	17.6062i		−	0.685840i	0.939365	−	0.342920i	$-0.111416\pi$
$660$	−1.98834	−	6.44981i	−0.0773961	−	0.251058i
$661$	30.0716			1.16965			0.584825	−	0.811159i	$-0.301163\pi$
$661$	30.0716			1.16965			0.584825	+	0.811159i	$0.301163\pi$
$662$	−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	$-0.551105\pi$
$677$	−8.31892			−0.319722			−0.159861	+	0.987140i	$0.551105\pi$
$678$	−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
$690$	2.58129	−	4.04291i	0.0982682	−	0.153911i
$691$	−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	$-0.472271\pi$
$701$	4.60701			0.174004			0.0870022	+	0.996208i	$0.472271\pi$
$702$	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	$-0.725916\pi$
$709$	−34.7022			−1.30327			−0.651634	+	0.758534i	$0.725916\pi$
$710$	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	$-0.475913\pi$
$727$	4.07669			0.151196			0.0755981	+	0.997138i	$0.475913\pi$
$728$	−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	$-0.603597\pi$
$733$	−17.3134			−0.639486			−0.319743	+	0.947504i	$0.603597\pi$
$734$	3.97650	−	0.599027i	0.146775	−	0.0221105i
$735$	−6.73248			−0.248331
$736$	0.809439	+	27.1172i	0.0298363	+	0.999555i
$737$	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	$-0.402067\pi$
$743$	16.5094			0.605672			0.302836	+	0.953043i	$0.402067\pi$
$744$	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	$-0.418466\pi$
$751$	13.8860			0.506708			0.253354	+	0.967374i	$0.418466\pi$
$752$	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	$-0.567208\pi$
$757$	−11.5324			−0.419151			−0.209575	+	0.977792i	$0.567208\pi$
$758$	−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	$0.0862209\pi$
$769$			14.8399i			0.535141i	−0.963538	+	0.267571i	$0.913779\pi$
$770$	−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	$-0.343209\pi$
$773$	26.2957			0.945792			0.472896	+	0.881118i	$0.343209\pi$
$774$	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
$782$	31.4760	+	20.0966i	1.12558	+	0.718652i
$783$		−	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	$0.313550\pi$
$787$			46.7539i			1.66659i	−0.552825	+	0.833297i	$0.686450\pi$
$788$	−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	$-0.534256\pi$
$797$	−6.06463			−0.214820			−0.107410	+	0.994215i	$0.534256\pi$
$798$	−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	$-0.852839\pi$
$827$		−	25.6532i		−	0.892050i	0.895021	−	0.446025i	$-0.147161\pi$
$828$	3.89982	−	8.76307i	0.135528	−	0.304538i
$829$		−	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	$-0.409970\pi$
$839$	16.1675			0.558163			0.279082	+	0.960267i	$0.409970\pi$
$840$	−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
$874$	26.8379	+	17.1353i	0.907806	+	0.579610i
$875$	−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	$0.111718\pi$
$881$			20.4097i			0.687622i	−0.939039	+	0.343811i	$0.888282\pi$
$882$	−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	$0.125986\pi$
$907$			23.2224i			0.771088i	−0.922690	+	0.385544i	$0.874014\pi$
$908$	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	$-0.329888\pi$
$911$	30.7469			1.01869			0.509345	+	0.860563i	$0.329888\pi$
$912$	−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	$-0.599546\pi$
$919$	−18.6535			−0.615322			−0.307661	+	0.951496i	$0.599546\pi$
$920$	2.55141	−	9.24788i	0.0841174	−	0.304893i
$921$	−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	$-0.894782\pi$
$937$		−	19.8701i		−	0.649128i	0.945864	−	0.324564i	$-0.105218\pi$
$938$	−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	$-0.292946\pi$
$941$	37.1524			1.21114			0.605568	+	0.795794i	$0.292946\pi$
$942$	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	$0.0833406\pi$
$953$			15.9812i			0.517682i	−0.965920	+	0.258841i	$0.916659\pi$
$954$	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
$966$	14.8345	−	23.2343i	0.477292	−	0.747551i
$967$			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	$-0.951558\pi$
$971$		−	9.44782i		−	0.303195i	0.988442	−	0.151597i	$-0.0484417\pi$
$972$	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	$0.00226959\pi$
$977$			0.445730i			0.0142602i	−0.999975	+	0.00713008i	$0.997730\pi$
$978$	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	$-0.376981\pi$
$983$	23.6354			0.753851			0.376925	+	0.926244i	$0.376981\pi$
$984$	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.91.3	yes	24
4.3	odd	2		2208.2.n.a.367.12		24
8.3	odd	2	inner	552.2.n.a.91.2	yes	24
8.5	even	2		2208.2.n.a.367.14		24
23.22	odd	2	inner	552.2.n.a.91.4	yes	24
92.91	even	2		2208.2.n.a.367.13		24
184.45	odd	2		2208.2.n.a.367.11		24
184.91	even	2	inner	552.2.n.a.91.1	✓	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39844 + 0.210663i) q^{2} +1.00000 q^{3} +(1.91124 - 0.589197i) q^{4} -0.707233 q^{5} +(-1.39844 + 0.210663i) q^{6} -4.06441 q^{7} +(-2.54863 + 1.22658i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(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} +(-3.64985 + 5.71652i) 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} +(3.89982 - 8.76307i) 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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