LMFDB - Embedded newform 552.2.f.c.277.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(277,552)]

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([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("552.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.f (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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{16} - 2 x^{15} + 5 x^{14} + 2 x^{13} + 6 x^{12} + 24 x^{11} - 12 x^{10} - 88 x^{9} + \cdots + 512 $ x^18 - 4x^16 - 2x^15 + 5x^14 + 2x^13 + 6x^12 + 24x^11 - 12x^10 - 88x^9 - 24x^8 + 96x^7 + 48x^6 + 32x^5 + 160x^4 - 128x^3 - 512*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			277.16
Root			$-1.06785 + 0.927201i$ of defining polynomial
Character	$\chi$	$=$	552.277
Dual form			552.2.f.c.277.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.927201 + 1.06785i) q^{2} -1.00000i q^{3} +(-0.280598 + 1.98022i) q^{4} +0.619156i q^{5} +(1.06785 - 0.927201i) q^{6} -1.72166 q^{7} +(-2.37474 + 1.53642i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.927201 + 1.06785i) q^{2} -1.00000i q^{3} +(-0.280598 + 1.98022i) q^{4} +0.619156i q^{5} +(1.06785 - 0.927201i) q^{6} -1.72166 q^{7} +(-2.37474 + 1.53642i) q^{8} -1.00000 q^{9} +(-0.661164 + 0.574082i) q^{10} +3.94444i q^{11} +(1.98022 + 0.280598i) q^{12} +4.44686i q^{13} +(-1.59633 - 1.83848i) q^{14} +0.619156 q^{15} +(-3.84253 - 1.11129i) q^{16} +2.82574 q^{17} +(-0.927201 - 1.06785i) q^{18} +3.61479i q^{19} +(-1.22606 - 0.173734i) q^{20} +1.72166i q^{21} +(-4.21206 + 3.65729i) q^{22} -1.00000 q^{23} +(1.53642 + 2.37474i) q^{24} +4.61665 q^{25} +(-4.74856 + 4.12313i) q^{26} +1.00000i q^{27} +(0.483095 - 3.40927i) q^{28} -2.64590i q^{29} +(0.574082 + 0.661164i) q^{30} -1.31143 q^{31} +(-2.37611 - 5.13363i) q^{32} +3.94444 q^{33} +(2.62003 + 3.01746i) q^{34} -1.06598i q^{35} +(0.280598 - 1.98022i) q^{36} +2.06396i q^{37} +(-3.86004 + 3.35163i) q^{38} +4.44686 q^{39} +(-0.951286 - 1.47034i) q^{40} +8.00925 q^{41} +(-1.83848 + 1.59633i) q^{42} -9.70511i q^{43} +(-7.81086 - 1.10680i) q^{44} -0.619156i q^{45} +(-0.927201 - 1.06785i) q^{46} -5.19474 q^{47} +(-1.11129 + 3.84253i) q^{48} -4.03587 q^{49} +(4.28056 + 4.92988i) q^{50} -2.82574i q^{51} +(-8.80575 - 1.24778i) q^{52} -5.88085i q^{53} +(-1.06785 + 0.927201i) q^{54} -2.44222 q^{55} +(4.08851 - 2.64521i) q^{56} +3.61479 q^{57} +(2.82541 - 2.45328i) q^{58} -6.15925i q^{59} +(-0.173734 + 1.22606i) q^{60} +7.23701i q^{61} +(-1.21596 - 1.40041i) q^{62} +1.72166 q^{63} +(3.27880 - 7.29722i) q^{64} -2.75330 q^{65} +(3.65729 + 4.21206i) q^{66} +14.6270i q^{67} +(-0.792896 + 5.59558i) q^{68} +1.00000i q^{69} +(1.13830 - 0.988376i) q^{70} -6.25759 q^{71} +(2.37474 - 1.53642i) q^{72} +14.4583 q^{73} +(-2.20399 + 1.91370i) q^{74} -4.61665i q^{75} +(-7.15807 - 1.01430i) q^{76} -6.79101i q^{77} +(4.12313 + 4.74856i) q^{78} +10.2232 q^{79} +(0.688061 - 2.37912i) q^{80} +1.00000 q^{81} +(7.42618 + 8.55266i) q^{82} -7.59392i q^{83} +(-3.40927 - 0.483095i) q^{84} +1.74957i q^{85} +(10.3636 - 8.99859i) q^{86} -2.64590 q^{87} +(-6.06034 - 9.36703i) q^{88} +1.16936 q^{89} +(0.661164 - 0.574082i) q^{90} -7.65599i q^{91} +(0.280598 - 1.98022i) q^{92} +1.31143i q^{93} +(-4.81657 - 5.54719i) q^{94} -2.23812 q^{95} +(-5.13363 + 2.37611i) q^{96} -3.55425 q^{97} +(-3.74206 - 4.30970i) q^{98} -3.94444i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	$ 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) $ 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.927201	+	1.06785i	0.655630	+	0.755082i
$2$	0.927201	+	1.06785i	0.655630	+	0.755082i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.280598	+	1.98022i	−0.140299	+	0.990109i
$5$			0.619156i			0.276895i	0.990370	+	0.138447i	$0.0442112\pi$
$5$			0.619156i			0.276895i	−0.990370	+	0.138447i	$0.955789\pi$
$6$	1.06785	−	0.927201i	0.435947	−	0.378528i
$7$	−1.72166			−0.650728			−0.325364	−	0.945589i	$-0.605487\pi$
$7$	−1.72166			−0.650728			−0.325364	+	0.945589i	$0.605487\pi$
$8$	−2.37474	+	1.53642i	−0.839598	+	0.543208i
$9$	−1.00000			−0.333333
$10$	−0.661164	+	0.574082i	−0.209078	+	0.181541i
$11$			3.94444i			1.18929i	0.803987	+	0.594647i	$0.202708\pi$
$11$			3.94444i			1.18929i	−0.803987	+	0.594647i	$0.797292\pi$
$12$	1.98022	+	0.280598i	0.571640	+	0.0810016i
$13$			4.44686i			1.23334i	0.787223	+	0.616668i	$0.211518\pi$
$13$			4.44686i			1.23334i	−0.787223	+	0.616668i	$0.788482\pi$
$14$	−1.59633	−	1.83848i	−0.426637	−	0.491353i
$15$	0.619156			0.159865
$16$	−3.84253	−	1.11129i	−0.960632	−	0.277822i
$17$	2.82574			0.685343			0.342671	−	0.939455i	$-0.388668\pi$
$17$	2.82574			0.685343			0.342671	+	0.939455i	$0.388668\pi$
$18$	−0.927201	−	1.06785i	−0.218543	−	0.251694i
$19$			3.61479i			0.829289i	0.909983	+	0.414645i	$0.136094\pi$
$19$			3.61479i			0.829289i	−0.909983	+	0.414645i	$0.863906\pi$
$20$	−1.22606	−	0.173734i	−0.274156	−	0.0388480i
$21$			1.72166i			0.375698i
$22$	−4.21206	+	3.65729i	−0.898015	+	0.779737i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	1.53642	+	2.37474i	0.313621	+	0.484742i
$25$	4.61665			0.923329
$26$	−4.74856	+	4.12313i	−0.931270	+	0.808612i
$27$			1.00000i			0.192450i
$28$	0.483095	−	3.40927i	0.0912964	−	0.644292i
$29$		−	2.64590i		−	0.491331i	−0.969355	−	0.245665i	$-0.920994\pi$
$29$		−	2.64590i		−	0.491331i	0.969355	−	0.245665i	$-0.0790064\pi$
$30$	0.574082	+	0.661164i	0.104812	+	0.120711i
$31$	−1.31143			−0.235541			−0.117770	−	0.993041i	$-0.537575\pi$
$31$	−1.31143			−0.235541			−0.117770	+	0.993041i	$0.537575\pi$
$32$	−2.37611	−	5.13363i	−0.420041	−	0.907505i
$33$	3.94444			0.686639
$34$	2.62003	+	3.01746i	0.449331	+	0.517490i
$35$		−	1.06598i		−	0.180183i
$36$	0.280598	−	1.98022i	0.0467663	−	0.330036i
$37$			2.06396i			0.339312i	0.985503	+	0.169656i	$0.0542657\pi$
$37$			2.06396i			0.339312i	−0.985503	+	0.169656i	$0.945734\pi$
$38$	−3.86004	+	3.35163i	−0.626182	+	0.543707i
$39$	4.44686			0.712067
$40$	−0.951286	−	1.47034i	−0.150412	−	0.232480i
$41$	8.00925			1.25083			0.625417	−	0.780290i	$-0.284929\pi$
$41$	8.00925			1.25083			0.625417	+	0.780290i	$0.284929\pi$
$42$	−1.83848	+	1.59633i	−0.283683	+	0.246319i
$43$		−	9.70511i		−	1.48002i	−0.672598	−	0.740008i	$-0.734822\pi$
$43$		−	9.70511i		−	1.48002i	0.672598	−	0.740008i	$-0.265178\pi$
$44$	−7.81086	−	1.10680i	−1.17753	−	0.166857i
$45$		−	0.619156i		−	0.0922983i
$46$	−0.927201	−	1.06785i	−0.136708	−	0.157446i
$47$	−5.19474			−0.757731			−0.378865	−	0.925452i	$-0.623686\pi$
$47$	−5.19474			−0.757731			−0.378865	+	0.925452i	$0.623686\pi$
$48$	−1.11129	+	3.84253i	−0.160401	+	0.554621i
$49$	−4.03587			−0.576553
$50$	4.28056	+	4.92988i	0.605362	+	0.697190i
$51$		−	2.82574i		−	0.395683i
$52$	−8.80575	−	1.24778i	−1.22114	−	0.173036i
$53$		−	5.88085i		−	0.807797i	−0.914804	−	0.403898i	$-0.867655\pi$
$53$		−	5.88085i		−	0.807797i	0.914804	−	0.403898i	$-0.132345\pi$
$54$	−1.06785	+	0.927201i	−0.145316	+	0.126176i
$55$	−2.44222			−0.329309
$56$	4.08851	−	2.64521i	0.546350	−	0.353481i
$57$	3.61479			0.478790
$58$	2.82541	−	2.45328i	0.370995	−	0.322131i
$59$		−	6.15925i		−	0.801866i	−0.916107	−	0.400933i	$-0.868686\pi$
$59$		−	6.15925i		−	0.801866i	0.916107	−	0.400933i	$-0.131314\pi$
$60$	−0.173734	+	1.22606i	−0.0224289	+	0.158284i
$61$			7.23701i			0.926604i	0.886201	+	0.463302i	$0.153335\pi$
$61$			7.23701i			0.926604i	−0.886201	+	0.463302i	$0.846665\pi$
$62$	−1.21596	−	1.40041i	−0.154427	−	0.177853i
$63$	1.72166			0.216909
$64$	3.27880	−	7.29722i	0.409850	−	0.912153i
$65$	−2.75330			−0.341504
$66$	3.65729	+	4.21206i	0.450181	+	0.518469i
$67$			14.6270i			1.78698i	0.449088	+	0.893488i	$0.351749\pi$
$67$			14.6270i			1.78698i	−0.449088	+	0.893488i	$0.648251\pi$
$68$	−0.792896	+	5.59558i	−0.0961528	+	0.678564i
$69$			1.00000i			0.120386i
$70$	1.13830	−	0.988376i	0.136053	−	0.118134i
$71$	−6.25759			−0.742639			−0.371320	−	0.928505i	$-0.621095\pi$
$71$	−6.25759			−0.742639			−0.371320	+	0.928505i	$0.621095\pi$
$72$	2.37474	−	1.53642i	0.279866	−	0.181069i
$73$	14.4583			1.69222			0.846110	−	0.533009i	$-0.178939\pi$
$73$	14.4583			1.69222			0.846110	+	0.533009i	$0.178939\pi$
$74$	−2.20399	+	1.91370i	−0.256209	+	0.222463i
$75$		−	4.61665i		−	0.533084i
$76$	−7.15807	−	1.01430i	−0.821087	−	0.116348i
$77$		−	6.79101i		−	0.773907i
$78$	4.12313	+	4.74856i	0.466852	+	0.537669i
$79$	10.2232			1.15020			0.575098	−	0.818085i	$-0.304964\pi$
$79$	10.2232			1.15020			0.575098	+	0.818085i	$0.304964\pi$
$80$	0.688061	−	2.37912i	0.0769276	−	0.265994i
$81$	1.00000			0.111111
$82$	7.42618	+	8.55266i	0.820085	+	0.944483i
$83$		−	7.59392i		−	0.833542i	−0.909012	−	0.416771i	$-0.863162\pi$
$83$		−	7.59392i		−	0.833542i	0.909012	−	0.416771i	$-0.136838\pi$
$84$	−3.40927	−	0.483095i	−0.371982	−	0.0527100i
$85$			1.74957i			0.189768i
$86$	10.3636	−	8.99859i	1.11753	−	0.970343i
$87$	−2.64590			−0.283670
$88$	−6.06034	−	9.36703i	−0.646034	−	0.998529i
$89$	1.16936			0.123952			0.0619758	−	0.998078i	$-0.480260\pi$
$89$	1.16936			0.123952			0.0619758	+	0.998078i	$0.480260\pi$
$90$	0.661164	−	0.574082i	0.0696928	−	0.0605135i
$91$		−	7.65599i		−	0.802566i
$92$	0.280598	−	1.98022i	0.0292543	−	0.206452i
$93$			1.31143i			0.135989i
$94$	−4.81657	−	5.54719i	−0.496791	−	0.572149i
$95$	−2.23812			−0.229626
$96$	−5.13363	+	2.37611i	−0.523948	+	0.242511i
$97$	−3.55425			−0.360880			−0.180440	−	0.983586i	$-0.557752\pi$
$97$	−3.55425			−0.360880			−0.180440	+	0.983586i	$0.557752\pi$
$98$	−3.74206	−	4.30970i	−0.378005	−	0.435345i
$99$		−	3.94444i		−	0.396431i
$100$	−1.29542	+	9.14197i	−0.129542	+	0.914197i
$101$		−	12.0597i		−	1.19999i	−0.800005	−	0.599993i	$-0.795170\pi$
$101$		−	12.0597i		−	1.19999i	0.800005	−	0.599993i	$-0.204830\pi$
$102$	3.01746	−	2.62003i	0.298773	−	0.259421i
$103$	2.87114			0.282902			0.141451	−	0.989945i	$-0.454823\pi$
$103$	2.87114			0.282902			0.141451	+	0.989945i	$0.454823\pi$
$104$	−6.83226	−	10.5601i	−0.669958	−	1.03551i
$105$	−1.06598			−0.104029
$106$	6.27985	−	5.45273i	0.609953	−	0.529616i
$107$		−	7.06779i		−	0.683269i	−0.939833	−	0.341635i	$-0.889019\pi$
$107$		−	7.06779i		−	0.683269i	0.939833	−	0.341635i	$-0.110981\pi$
$108$	−1.98022	−	0.280598i	−0.190547	−	0.0270005i
$109$			16.3200i			1.56318i	0.623795	+	0.781588i	$0.285590\pi$
$109$			16.3200i			1.56318i	−0.623795	+	0.781588i	$0.714410\pi$
$110$	−2.26443	−	2.60792i	−0.215905	−	0.248656i
$111$	2.06396			0.195902
$112$	6.61555	+	1.91327i	0.625110	+	0.180787i
$113$	7.41855			0.697878			0.348939	−	0.937145i	$-0.386542\pi$
$113$	7.41855			0.697878			0.348939	+	0.937145i	$0.386542\pi$
$114$	3.35163	+	3.86004i	0.313909	+	0.361526i
$115$		−	0.619156i		−	0.0577366i
$116$	5.23945	+	0.742432i	0.486471	+	0.0689331i
$117$		−	4.44686i		−	0.411112i
$118$	6.57714	−	5.71086i	0.605475	−	0.525728i
$119$	−4.86498			−0.445972
$120$	−1.47034	+	0.951286i	−0.134223	+	0.0868401i
$121$	−4.55863			−0.414420
$122$	−7.72802	+	6.71016i	−0.699662	+	0.607509i
$123$		−	8.00925i		−	0.722170i
$124$	0.367985	−	2.59693i	0.0330461	−	0.233211i
$125$			5.95420i			0.532560i
$126$	1.59633	+	1.83848i	0.142212	+	0.163784i
$127$	8.34063			0.740112			0.370056	−	0.929010i	$-0.379339\pi$
$127$	8.34063			0.740112			0.370056	+	0.929010i	$0.379339\pi$
$128$	10.8324	−	3.26473i	0.957461	−	0.288564i
$129$	−9.70511			−0.854488
$130$	−2.55286	−	2.94010i	−0.223900	−	0.257864i
$131$		−	8.79783i		−	0.768670i	−0.923194	−	0.384335i	$-0.874431\pi$
$131$		−	8.79783i		−	0.768670i	0.923194	−	0.384335i	$-0.125569\pi$
$132$	−1.10680	+	7.81086i	−0.0963347	+	0.679848i
$133$		−	6.22345i		−	0.539642i
$134$	−15.6194	+	13.5622i	−1.34931	+	1.17159i
$135$	−0.619156			−0.0532884
$136$	−6.71040	+	4.34154i	−0.575412	+	0.372284i
$137$	14.7845			1.26313			0.631563	−	0.775324i	$-0.282414\pi$
$137$	14.7845			1.26313			0.631563	+	0.775324i	$0.282414\pi$
$138$	−1.06785	+	0.927201i	−0.0909012	+	0.0789286i
$139$			0.0202659i			0.00171893i	1.00000		0.000859467i	$0.000273577\pi$
$139$			0.0202659i			0.00171893i	−1.00000		0.000859467i	$0.999726\pi$
$140$	2.11087	+	0.299111i	0.178401	+	0.0252795i
$141$			5.19474i			0.437476i
$142$	−5.80204	−	6.68215i	−0.486896	−	0.560754i
$143$	−17.5404			−1.46680
$144$	3.84253	+	1.11129i	0.320211	+	0.0926075i
$145$	1.63822			0.136047
$146$	13.4058	+	15.4393i	1.10947	+	1.27776i
$147$			4.03587i			0.332873i
$148$	−4.08708	−	0.579141i	−0.335956	−	0.0476051i
$149$			17.7424i			1.45351i	0.686895	+	0.726757i	$0.258973\pi$
$149$			17.7424i			1.45351i	−0.686895	+	0.726757i	$0.741027\pi$
$150$	4.92988	−	4.28056i	0.402523	−	0.349506i
$151$	16.9502			1.37939			0.689693	−	0.724102i	$-0.257745\pi$
$151$	16.9502			1.37939			0.689693	+	0.724102i	$0.257745\pi$
$152$	−5.55385	−	8.58419i	−0.450477	−	0.696270i
$153$	−2.82574			−0.228448
$154$	7.25176	−	6.29663i	0.584364	−	0.507397i
$155$		−	0.811982i		−	0.0652200i
$156$	−1.24778	+	8.80575i	−0.0999022	+	0.705024i
$157$			6.88850i			0.549762i	0.961478	+	0.274881i	$0.0886385\pi$
$157$			6.88850i			0.549762i	−0.961478	+	0.274881i	$0.911361\pi$
$158$	9.47892	+	10.9168i	0.754103	+	0.868492i
$159$	−5.88085			−0.466382
$160$	3.17851	−	1.47118i	0.251284	−	0.116307i
$161$	1.72166			0.135686
$162$	0.927201	+	1.06785i	0.0728478	+	0.0838980i
$163$		−	5.87271i		−	0.459986i	−0.973192	−	0.229993i	$-0.926130\pi$
$163$		−	5.87271i		−	0.459986i	0.973192	−	0.229993i	$-0.0738704\pi$
$164$	−2.24738	+	15.8601i	−0.175491	+	1.23846i
$165$			2.44222i			0.190127i
$166$	8.10916	−	7.04109i	0.629393	−	0.546495i
$167$	−17.7225			−1.37141			−0.685704	−	0.727881i	$-0.740506\pi$
$167$	−17.7225			−1.37141			−0.685704	+	0.727881i	$0.740506\pi$
$168$	−2.64521	−	4.08851i	−0.204082	−	0.315435i
$169$	−6.77452			−0.521117
$170$	−1.86828	+	1.62221i	−0.143290	+	0.124417i
$171$		−	3.61479i		−	0.276430i
$172$	19.2182	+	2.72323i	1.46538	+	0.207645i
$173$		−	14.0857i		−	1.07091i	−0.844563	−	0.535456i	$-0.820140\pi$
$173$		−	14.0857i		−	1.07091i	0.844563	−	0.535456i	$-0.179860\pi$
$174$	−2.45328	−	2.82541i	−0.185982	−	0.214194i
$175$	−7.94832			−0.600836
$176$	4.38342	−	15.1566i	0.330413	−	1.14247i
$177$	−6.15925			−0.462958
$178$	1.08423	+	1.24870i	0.0812664	+	0.0935937i
$179$			8.84963i			0.661452i	0.943727	+	0.330726i	$0.107294\pi$
$179$			8.84963i			0.661452i	−0.943727	+	0.330726i	$0.892706\pi$
$180$	1.22606	+	0.173734i	0.0913854	+	0.0129493i
$181$			14.9793i			1.11340i	0.830713	+	0.556702i	$0.187933\pi$
$181$			14.9793i			1.11340i	−0.830713	+	0.556702i	$0.812067\pi$
$182$	8.17543	−	7.09864i	0.606004	−	0.526186i
$183$	7.23701			0.534975
$184$	2.37474	−	1.53642i	0.175068	−	0.113267i
$185$	−1.27791			−0.0939538
$186$	−1.40041	+	1.21596i	−0.102683	+	0.0891587i
$187$			11.1460i			0.815074i
$188$	1.45763	−	10.2867i	0.106309	−	0.750236i
$189$		−	1.72166i		−	0.125233i
$190$	−2.07518	−	2.38997i	−0.150550	−	0.173386i
$191$	17.3337			1.25422			0.627111	−	0.778930i	$-0.284237\pi$
$191$	17.3337			1.25422			0.627111	+	0.778930i	$0.284237\pi$
$192$	−7.29722	−	3.27880i	−0.526632	−	0.236627i
$193$	18.9291			1.36254			0.681272	−	0.732030i	$-0.261427\pi$
$193$	18.9291			1.36254			0.681272	+	0.732030i	$0.261427\pi$
$194$	−3.29551	−	3.79540i	−0.236604	−	0.272494i
$195$			2.75330i			0.197168i
$196$	1.13246	−	7.99191i	0.0808897	−	0.570851i
$197$			5.04050i			0.359121i	0.983747	+	0.179560i	$0.0574676\pi$
$197$			5.04050i			0.359121i	−0.983747	+	0.179560i	$0.942532\pi$
$198$	4.21206	−	3.65729i	0.299338	−	0.259912i
$199$	−14.5956			−1.03465			−0.517326	−	0.855789i	$-0.673072\pi$
$199$	−14.5956			−1.03465			−0.517326	+	0.855789i	$0.673072\pi$
$200$	−10.9633	+	7.09313i	−0.775226	+	0.501560i
$201$	14.6270			1.03171
$202$	12.8779	−	11.1818i	0.906089	−	0.786747i
$203$			4.55535i			0.319723i
$204$	5.59558	+	0.792896i	0.391769	+	0.0555138i
$205$			4.95897i			0.346350i
$206$	2.66213	+	3.06594i	0.185479	+	0.213614i
$207$	1.00000			0.0695048
$208$	4.94174	−	17.0872i	0.342648	−	1.18478i
$209$	−14.2583			−0.986269
$210$	−0.988376	−	1.13830i	−0.0682044	−	0.0785503i
$211$			13.0601i			0.899097i	0.893256	+	0.449548i	$0.148415\pi$
$211$			13.0601i			0.899097i	−0.893256	+	0.449548i	$0.851585\pi$
$212$	11.6454	+	1.65015i	0.799807	+	0.113333i
$213$			6.25759i			0.428763i
$214$	7.54733	−	6.55326i	0.515925	−	0.447972i
$215$	6.00898			0.409809
$216$	−1.53642	−	2.37474i	−0.104540	−	0.161581i
$217$	2.25785			0.153273
$218$	−17.4273	+	15.1319i	−1.18033	+	1.02486i
$219$		−	14.4583i		−	0.977003i
$220$	0.685282	−	4.83614i	0.0462017	−	0.326052i
$221$			12.5657i			0.845258i
$222$	1.91370	+	2.20399i	0.128439	+	0.147922i
$223$	−4.66323			−0.312273			−0.156137	−	0.987735i	$-0.549904\pi$
$223$	−4.66323			−0.312273			−0.156137	+	0.987735i	$0.549904\pi$
$224$	4.09086	+	8.83838i	0.273332	+	0.590539i
$225$	−4.61665			−0.307776
$226$	6.87848	+	7.92188i	0.457550	+	0.526956i
$227$			3.88192i			0.257652i	0.991667	+	0.128826i	$0.0411209\pi$
$227$			3.88192i			0.257652i	−0.991667	+	0.128826i	$0.958879\pi$
$228$	−1.01430	+	7.15807i	−0.0671737	+	0.474055i
$229$		−	0.275712i		−	0.0182195i	−0.999959	−	0.00910977i	$-0.997100\pi$
$229$		−	0.275712i		−	0.0182195i	0.999959	−	0.00910977i	$-0.00289977\pi$
$230$	0.661164	−	0.574082i	0.0435959	−	0.0378538i
$231$	−6.79101			−0.446815
$232$	4.06522	+	6.28332i	0.266895	+	0.412520i
$233$	−9.89319			−0.648125			−0.324062	−	0.946036i	$-0.605049\pi$
$233$	−9.89319			−0.648125			−0.324062	+	0.946036i	$0.605049\pi$
$234$	4.74856	−	4.12313i	0.310423	−	0.269537i
$235$		−	3.21635i		−	0.209812i
$236$	12.1967	+	1.72827i	0.793935	+	0.112501i
$237$		−	10.2232i		−	0.664066i
$238$	−4.51081	−	5.19505i	−0.292392	−	0.336745i
$239$	−24.0570			−1.55612			−0.778060	−	0.628190i	$-0.783796\pi$
$239$	−24.0570			−1.55612			−0.778060	+	0.628190i	$0.783796\pi$
$240$	−2.37912	−	0.688061i	−0.153572	−	0.0444142i
$241$	−21.8111			−1.40497			−0.702487	−	0.711697i	$-0.747927\pi$
$241$	−21.8111			−1.40497			−0.702487	+	0.711697i	$0.747927\pi$
$242$	−4.22676	−	4.86792i	−0.271706	−	0.312922i
$243$		−	1.00000i		−	0.0641500i
$244$	−14.3309	−	2.03069i	−0.917439	−	0.130001i
$245$		−	2.49883i		−	0.159645i
$246$	8.55266	−	7.42618i	0.545298	−	0.473476i
$247$	−16.0744			−1.02279
$248$	3.11432	−	2.01492i	0.197759	−	0.127948i
$249$	−7.59392			−0.481245
$250$	−6.35818	+	5.52074i	−0.402127	+	0.349162i
$251$			21.4940i			1.35669i	0.734743	+	0.678346i	$0.237303\pi$
$251$			21.4940i			1.35669i	−0.734743	+	0.678346i	$0.762697\pi$
$252$	−0.483095	+	3.40927i	−0.0304321	+	0.214764i
$253$		−	3.94444i		−	0.247985i
$254$	7.73344	+	8.90653i	0.485239	+	0.558845i
$255$	1.74957			0.109563
$256$	13.5301	+	8.54033i	0.845629	+	0.533770i
$257$	1.27342			0.0794336			0.0397168	−	0.999211i	$-0.487354\pi$
$257$	1.27342			0.0794336			0.0397168	+	0.999211i	$0.487354\pi$
$258$	−8.99859	−	10.3636i	−0.560228	−	0.645209i
$259$		−	3.55344i		−	0.220800i
$260$	0.772569	−	5.45213i	0.0479127	−	0.338127i
$261$			2.64590i			0.163777i
$262$	9.39474	−	8.15735i	0.580409	−	0.503963i
$263$	2.85512			0.176054			0.0880271	−	0.996118i	$-0.471944\pi$
$263$	2.85512			0.176054			0.0880271	+	0.996118i	$0.471944\pi$
$264$	−9.36703	+	6.06034i	−0.576501	+	0.372988i
$265$	3.64116			0.223675
$266$	6.64570	−	5.77039i	0.407474	−	0.353805i
$267$		−	1.16936i		−	0.0715635i
$268$	−28.9647	−	4.10431i	−1.76930	−	0.250711i
$269$		−	30.0475i		−	1.83203i	−0.401145	−	0.916015i	$-0.631388\pi$
$269$		−	30.0475i		−	1.83203i	0.401145	−	0.916015i	$-0.368612\pi$
$270$	−0.574082	−	0.661164i	−0.0349375	−	0.0402372i
$271$	−19.4149			−1.17937			−0.589685	−	0.807633i	$-0.700748\pi$
$271$	−19.4149			−1.17937			−0.589685	+	0.807633i	$0.700748\pi$
$272$	−10.8580	−	3.14022i	−0.658362	−	0.190404i
$273$	−7.65599			−0.463362
$274$	13.7082	+	15.7876i	0.828144	+	0.953765i
$275$			18.2101i			1.09811i
$276$	−1.98022	−	0.280598i	−0.119195	−	0.0168900i
$277$		−	25.2571i		−	1.51755i	−0.651351	−	0.758777i	$-0.725797\pi$
$277$		−	25.2571i		−	1.51755i	0.651351	−	0.758777i	$-0.274203\pi$
$278$	−0.0216409	+	0.0187906i	−0.00129794	+	0.00112698i
$279$	1.31143			0.0785135
$280$	1.63780	+	2.53142i	0.0978770	+	0.151282i
$281$	−17.9480			−1.07069			−0.535344	−	0.844634i	$-0.679818\pi$
$281$	−17.9480			−1.07069			−0.535344	+	0.844634i	$0.679818\pi$
$282$	−5.54719	+	4.81657i	−0.330331	+	0.286822i
$283$		−	25.1352i		−	1.49414i	−0.664748	−	0.747068i	$-0.731461\pi$
$283$		−	25.1352i		−	1.49414i	0.664748	−	0.747068i	$-0.268539\pi$
$284$	1.75586	−	12.3914i	0.104191	−	0.735294i
$285$			2.23812i			0.132575i
$286$	−16.2634	−	18.7304i	−0.961677	−	1.10755i
$287$	−13.7892			−0.813953
$288$	2.37611	+	5.13363i	0.140014	+	0.302502i
$289$	−9.01519			−0.530305
$290$	1.51896	+	1.74937i	0.0891964	+	0.102727i
$291$			3.55425i			0.208354i
$292$	−4.05697	+	28.6306i	−0.237416	+	1.67548i
$293$		−	5.59642i		−	0.326947i	−0.986548	−	0.163473i	$-0.947730\pi$
$293$		−	5.59642i		−	0.326947i	0.986548	−	0.163473i	$-0.0522697\pi$
$294$	−4.30970	+	3.74206i	−0.251347	+	0.218242i
$295$	3.81354			0.222033
$296$	−3.17111	−	4.90136i	−0.184317	−	0.284886i
$297$	−3.94444			−0.228880
$298$	−18.9462	+	16.4508i	−1.09752	+	0.952967i
$299$		−	4.44686i		−	0.257168i
$300$	9.14197	+	1.29542i	0.527812	+	0.0747911i
$301$			16.7089i			0.963088i
$302$	15.7162	+	18.1002i	0.904367	+	1.04155i
$303$	−12.0597			−0.692813
$304$	4.01708	−	13.8899i	0.230395	−	0.796642i
$305$	−4.48083			−0.256572
$306$	−2.62003	−	3.01746i	−0.149777	−	0.172497i
$307$			10.0329i			0.572610i	0.958138	+	0.286305i	$0.0924271\pi$
$307$			10.0329i			0.572610i	−0.958138	+	0.286305i	$0.907573\pi$
$308$	13.4477	+	1.90554i	0.766252	+	0.108578i
$309$		−	2.87114i		−	0.163334i
$310$	0.867073	−	0.752870i	0.0492465	−	0.0427602i
$311$	26.9330			1.52723			0.763615	−	0.645672i	$-0.223423\pi$
$311$	26.9330			1.52723			0.763615	+	0.645672i	$0.223423\pi$
$312$	−10.5601	+	6.83226i	−0.597850	+	0.386800i
$313$	−21.2741			−1.20248			−0.601242	−	0.799067i	$-0.705327\pi$
$313$	−21.2741			−1.20248			−0.601242	+	0.799067i	$0.705327\pi$
$314$	−7.35587	+	6.38703i	−0.415116	+	0.360441i
$315$			1.06598i			0.0600611i
$316$	−2.86860	+	20.2441i	−0.161371	+	1.13882i
$317$		−	12.8690i		−	0.722795i	−0.932412	−	0.361398i	$-0.882300\pi$
$317$		−	12.8690i		−	0.722795i	0.932412	−	0.361398i	$-0.117700\pi$
$318$	−5.45273	−	6.27985i	−0.305774	−	0.352157i
$319$	10.4366			0.584337
$320$	4.51812	+	2.03009i	0.252570	+	0.113485i
$321$	−7.06779			−0.394486
$322$	1.59633	+	1.83848i	0.0889599	+	0.102454i
$323$			10.2145i			0.568347i
$324$	−0.280598	+	1.98022i	−0.0155888	+	0.110012i
$325$			20.5296i			1.13878i
$326$	6.27116	−	5.44518i	0.347327	−	0.301581i
$327$	16.3200			0.902500
$328$	−19.0199	+	12.3056i	−1.05020	+	0.679463i
$329$	8.94360			0.493077
$330$	−2.60792	+	2.26443i	−0.143561	+	0.124653i
$331$		−	16.6072i		−	0.912814i	−0.889771	−	0.456407i	$-0.849136\pi$
$331$		−	16.6072i		−	0.912814i	0.889771	−	0.456407i	$-0.150864\pi$
$332$	15.0376	+	2.13084i	0.825297	+	0.116945i
$333$		−	2.06396i		−	0.113104i
$334$	−16.4323	−	18.9249i	−0.899136	−	1.03553i
$335$	−9.05641			−0.494804
$336$	1.91327	−	6.61555i	0.104377	−	0.360908i
$337$	−9.30878			−0.507082			−0.253541	−	0.967325i	$-0.581595\pi$
$337$	−9.30878			−0.507082			−0.253541	+	0.967325i	$0.581595\pi$
$338$	−6.28134	−	7.23416i	−0.341660	−	0.393486i
$339$		−	7.41855i		−	0.402920i
$340$	−3.46454	−	0.490926i	−0.187891	−	0.0266242i
$341$		−	5.17288i		−	0.280127i
$342$	3.86004	−	3.35163i	0.208727	−	0.181236i
$343$	19.0001			1.02591
$344$	14.9112	+	23.0471i	0.803957	+	1.24262i
$345$	−0.619156			−0.0333342
$346$	15.0413	−	13.0602i	0.808627	−	0.702123i
$347$			24.2292i			1.30069i	0.759638	+	0.650346i	$0.225376\pi$
$347$			24.2292i			1.30069i	−0.759638	+	0.650346i	$0.774624\pi$
$348$	0.742432	−	5.23945i	0.0397986	−	0.280864i
$349$			9.76314i			0.522609i	0.965256	+	0.261305i	$0.0841527\pi$
$349$			9.76314i			0.522609i	−0.965256	+	0.261305i	$0.915847\pi$
$350$	−7.36968	−	8.48759i	−0.393926	−	0.453681i
$351$	−4.44686			−0.237356
$352$	20.2493	−	9.37242i	1.07929	−	0.499552i
$353$	10.2714			0.546689			0.273345	−	0.961916i	$-0.411870\pi$
$353$	10.2714			0.546689			0.273345	+	0.961916i	$0.411870\pi$
$354$	−5.71086	−	6.57714i	−0.303529	−	0.349571i
$355$		−	3.87442i		−	0.205633i
$356$	−0.328119	+	2.31558i	−0.0173903	+	0.122726i
$357$			4.86498i			0.257482i
$358$	−9.45006	+	8.20538i	−0.499451	+	0.433668i
$359$	12.3991			0.654402			0.327201	−	0.944955i	$-0.393895\pi$
$359$	12.3991			0.654402			0.327201	+	0.944955i	$0.393895\pi$
$360$	0.951286	+	1.47034i	0.0501372	+	0.0774935i
$361$	5.93331			0.312279
$362$	−15.9956	+	13.8888i	−0.840711	+	0.729980i
$363$			4.55863i			0.239266i
$364$	15.1605	+	2.14825i	0.794628	+	0.112599i
$365$			8.95196i			0.468567i
$366$	6.71016	+	7.72802i	0.350746	+	0.403950i
$367$	1.97116			0.102894			0.0514468	−	0.998676i	$-0.483617\pi$
$367$	1.97116			0.102894			0.0514468	+	0.998676i	$0.483617\pi$
$368$	3.84253	+	1.11129i	0.200306	+	0.0579300i
$369$	−8.00925			−0.416945
$370$	−1.18488	−	1.36461i	−0.0615990	−	0.0709429i
$371$			10.1248i			0.525656i
$372$	−2.59693	−	0.367985i	−0.134644	−	0.0190792i
$373$			4.97318i			0.257502i	0.991677	+	0.128751i	$0.0410967\pi$
$373$			4.97318i			0.257502i	−0.991677	+	0.128751i	$0.958903\pi$
$374$	−11.9022	+	10.3346i	−0.615448	+	0.534387i
$375$	5.95420			0.307474
$376$	12.3362	−	7.98133i	0.636189	−	0.411605i
$377$	11.7659			0.605976
$378$	1.83848	−	1.59633i	0.0945610	−	0.0821063i
$379$			20.1597i			1.03553i	0.855522	+	0.517766i	$0.173236\pi$
$379$			20.1597i			1.03553i	−0.855522	+	0.517766i	$0.826764\pi$
$380$	0.628010	−	4.43196i	0.0322163	−	0.227355i
$381$		−	8.34063i		−	0.427304i
$382$	16.0718	+	18.5098i	0.822306	+	0.947042i
$383$	30.3516			1.55089			0.775447	−	0.631413i	$-0.217525\pi$
$383$	30.3516			1.55089			0.775447	+	0.631413i	$0.217525\pi$
$384$	−3.26473	−	10.8324i	−0.166603	−	0.552790i
$385$	4.20469			0.214291
$386$	17.5510	+	20.2134i	0.893325	+	1.02883i
$387$			9.70511i			0.493339i
$388$	0.997316	−	7.03820i	0.0506310	−	0.357310i
$389$		−	26.7786i		−	1.35773i	−0.734263	−	0.678866i	$-0.762472\pi$
$389$		−	26.7786i		−	1.35773i	0.734263	−	0.678866i	$-0.237528\pi$
$390$	−2.94010	+	2.55286i	−0.148878	+	0.129269i
$391$	−2.82574			−0.142904
$392$	9.58415	−	6.20081i	0.484073	−	0.313188i
$393$	−8.79783			−0.443792
$394$	−5.38249	+	4.67356i	−0.271166	+	0.235450i
$395$			6.32973i			0.318483i
$396$	7.81086	+	1.10680i	0.392510	+	0.0556189i
$397$		−	16.8280i		−	0.844575i	−0.906462	−	0.422288i	$-0.861227\pi$
$397$		−	16.8280i		−	0.844575i	0.906462	−	0.422288i	$-0.138773\pi$
$398$	−13.5330	−	15.5858i	−0.678348	−	0.781247i
$399$	−6.22345			−0.311562
$400$	−17.7396	−	5.13043i	−0.886980	−	0.256522i
$401$	19.5684			0.977198			0.488599	−	0.872508i	$-0.337508\pi$
$401$	19.5684			0.977198			0.488599	+	0.872508i	$0.337508\pi$
$402$	13.5622	+	15.6194i	0.676420	+	0.779027i
$403$		−	5.83176i		−	0.290501i
$404$	23.8809	+	3.38393i	1.18812	+	0.168357i
$405$			0.619156i			0.0307661i
$406$	−4.86442	+	4.22372i	−0.241417	+	0.209620i
$407$	−8.14116			−0.403542
$408$	4.34154	+	6.71040i	0.214938	+	0.332215i
$409$	−31.8845			−1.57659			−0.788294	−	0.615299i	$-0.789035\pi$
$409$	−31.8845			−1.57659			−0.788294	+	0.615299i	$0.789035\pi$
$410$	−5.29543	+	4.59796i	−0.261523	+	0.227077i
$411$		−	14.7845i		−	0.729267i
$412$	−0.805636	+	5.68549i	−0.0396908	+	0.280104i
$413$			10.6042i			0.521797i
$414$	0.927201	+	1.06785i	0.0455694	+	0.0524819i
$415$	4.70182			0.230803
$416$	22.8285	−	10.5662i	1.11926	−	0.518051i
$417$	0.0202659			0.000992427
$418$	−13.2203	−	15.2257i	−0.646627	−	0.744714i
$419$			7.63011i			0.372755i	0.982478	+	0.186378i	$0.0596748\pi$
$419$			7.63011i			0.372755i	−0.982478	+	0.186378i	$0.940325\pi$
$420$	0.299111	−	2.11087i	0.0145951	−	0.103000i
$421$			5.13113i			0.250076i	0.992152	+	0.125038i	$0.0399053\pi$
$421$			5.13113i			0.250076i	−0.992152	+	0.125038i	$0.960095\pi$
$422$	−13.9462	+	12.1094i	−0.678892	+	0.589475i
$423$	5.19474			0.252577
$424$	9.03548	+	13.9655i	0.438802	+	0.678225i
$425$	13.0454			0.632797
$426$	−6.68215	+	5.80204i	−0.323751	+	0.281110i
$427$		−	12.4597i		−	0.602967i
$428$	13.9958	+	1.98321i	0.676511	+	0.0958619i
$429$			17.5404i			0.846857i
$430$	5.57153	+	6.41667i	0.268683	+	0.309439i
$431$	−5.31890			−0.256202			−0.128101	−	0.991761i	$-0.540888\pi$
$431$	−5.31890			−0.256202			−0.128101	+	0.991761i	$0.540888\pi$
$432$	1.11129	−	3.84253i	0.0534669	−	0.184874i
$433$	31.0864			1.49392			0.746958	−	0.664871i	$-0.231513\pi$
$433$	31.0864			1.49392			0.746958	+	0.664871i	$0.231513\pi$
$434$	2.09348	+	2.41104i	0.100490	+	0.115734i
$435$		−	1.63822i		−	0.0785467i
$436$	−32.3172	−	4.57936i	−1.54771	−	0.219312i
$437$		−	3.61479i		−	0.172919i
$438$	15.4393	−	13.4058i	0.737718	−	0.640552i
$439$	−37.5107			−1.79029			−0.895143	−	0.445778i	$-0.852927\pi$
$439$	−37.5107			−1.79029			−0.895143	+	0.445778i	$0.852927\pi$
$440$	5.79965	−	3.75229i	0.276488	−	0.178884i
$441$	4.03587			0.192184
$442$	−13.4182	+	11.6509i	−0.638239	+	0.554176i
$443$		−	12.9789i		−	0.616648i	−0.951281	−	0.308324i	$-0.900232\pi$
$443$		−	12.9789i		−	0.616648i	0.951281	−	0.308324i	$-0.0997680\pi$
$444$	−0.579141	+	4.08708i	−0.0274848	+	0.193964i
$445$			0.724015i			0.0343216i
$446$	−4.32375	−	4.97962i	−0.204736	−	0.235792i
$447$	17.7424			0.839187
$448$	−5.64499	+	12.5634i	−0.266701	+	0.593563i
$449$	8.86040			0.418148			0.209074	−	0.977900i	$-0.432955\pi$
$449$	8.86040			0.418148			0.209074	+	0.977900i	$0.432955\pi$
$450$	−4.28056	−	4.92988i	−0.201787	−	0.232397i
$451$			31.5920i			1.48761i
$452$	−2.08163	+	14.6903i	−0.0979115	+	0.690976i
$453$		−	16.9502i		−	0.796389i
$454$	−4.14530	+	3.59932i	−0.194549	+	0.168925i
$455$	4.74025			0.222226
$456$	−8.58419	+	5.55385i	−0.401991	+	0.260083i
$457$	−32.9408			−1.54091			−0.770453	−	0.637497i	$-0.779970\pi$
$457$	−32.9408			−1.54091			−0.770453	+	0.637497i	$0.779970\pi$
$458$	0.294418	−	0.255640i	0.0137572	−	0.0119453i
$459$			2.82574i			0.131894i
$460$	1.22606	+	0.173734i	0.0571655	+	0.00810037i
$461$		−	31.9639i		−	1.48871i	−0.667786	−	0.744353i	$-0.732758\pi$
$461$		−	31.9639i		−	1.48871i	0.667786	−	0.744353i	$-0.267242\pi$
$462$	−6.29663	−	7.25176i	−0.292946	−	0.337382i
$463$	29.9044			1.38978			0.694888	−	0.719118i	$-0.255454\pi$
$463$	29.9044			1.38978			0.694888	+	0.719118i	$0.255454\pi$
$464$	−2.94036	+	10.1669i	−0.136503	+	0.471988i
$465$	−0.811982			−0.0376548
$466$	−9.17298	−	10.5644i	−0.424930	−	0.489388i
$467$			22.9172i			1.06048i	0.847847	+	0.530242i	$0.177899\pi$
$467$			22.9172i			1.06048i	−0.847847	+	0.530242i	$0.822101\pi$
$468$	8.80575	+	1.24778i	0.407046	+	0.0576785i
$469$		−	25.1828i		−	1.16283i
$470$	3.43458	−	2.98221i	0.158425	−	0.137559i
$471$	6.88850			0.317406
$472$	9.46322	+	14.6266i	0.435580	+	0.673245i
$473$	38.2813			1.76017
$474$	10.9168	−	9.47892i	0.501424	−	0.435381i
$475$			16.6882i			0.765707i
$476$	1.36510	−	9.63372i	0.0625693	−	0.441561i
$477$			5.88085i			0.269266i
$478$	−22.3057	−	25.6893i	−1.02024	−	1.17500i
$479$	22.9872			1.05031			0.525156	−	0.851006i	$-0.324007\pi$
$479$	22.9872			1.05031			0.525156	+	0.851006i	$0.324007\pi$
$480$	−1.47118	−	3.17851i	−0.0671499	−	0.145079i
$481$	−9.17812			−0.418486
$482$	−20.2232	−	23.2909i	−0.921143	−	1.06087i
$483$		−	1.72166i		−	0.0783384i
$484$	1.27914	−	9.02707i	0.0581427	−	0.410322i
$485$		−	2.20064i		−	0.0999258i
$486$	1.06785	−	0.927201i	0.0484386	−	0.0420587i
$487$	26.7229			1.21093			0.605464	−	0.795872i	$-0.292987\pi$
$487$	26.7229			1.21093			0.605464	+	0.795872i	$0.292987\pi$
$488$	−11.1191	−	17.1860i	−0.503339	−	0.777975i
$489$	−5.87271			−0.265573
$490$	2.66837	−	2.31692i	0.120545	−	0.104668i
$491$		−	15.8895i		−	0.717082i	−0.933514	−	0.358541i	$-0.883274\pi$
$491$		−	15.8895i		−	0.717082i	0.933514	−	0.358541i	$-0.116726\pi$
$492$	15.8601	+	2.24738i	0.715027	+	0.101320i
$493$		−	7.47662i		−	0.336730i
$494$	−14.9042	−	17.1651i	−0.670573	−	0.772292i
$495$	2.44222			0.109770
$496$	5.03923	+	1.45738i	0.226268	+	0.0654384i
$497$	10.7735			0.483256
$498$	−7.04109	−	8.10916i	−0.315519	−	0.363380i
$499$			18.3961i			0.823522i	0.911292	+	0.411761i	$0.135086\pi$
$499$			18.3961i			0.823522i	−0.911292	+	0.411761i	$0.864914\pi$
$500$	−11.7906	−	1.67074i	−0.527293	−	0.0747176i
$501$			17.7225i			0.791783i
$502$	−22.9524	+	19.9293i	−1.02441	+	0.889487i
$503$	−25.6432			−1.14337			−0.571687	−	0.820472i	$-0.693711\pi$
$503$	−25.6432			−1.14337			−0.571687	+	0.820472i	$0.693711\pi$
$504$	−4.08851	+	2.64521i	−0.182117	+	0.117827i
$505$	7.46684			0.332270
$506$	4.21206	−	3.65729i	0.187249	−	0.162586i
$507$			6.77452i			0.300867i
$508$	−2.34036	+	16.5163i	−0.103837	+	0.732791i
$509$		−	19.5780i		−	0.867779i	−0.900966	−	0.433890i	$-0.857141\pi$
$509$		−	19.5780i		−	0.867779i	0.900966	−	0.433890i	$-0.142859\pi$
$510$	1.62221	+	1.86828i	0.0718325	+	0.0827287i
$511$	−24.8924			−1.10117
$512$	3.42532	+	22.3667i	0.151379	+	0.988476i
$513$	−3.61479			−0.159597
$514$	1.18071	+	1.35982i	0.0520791	+	0.0599789i
$515$			1.77768i			0.0783341i
$516$	2.72323	−	19.2182i	0.119884	−	0.846036i
$517$		−	20.4904i		−	0.901165i
$518$	3.79453	−	3.29475i	0.166722	−	0.144763i
$519$	−14.0857			−0.618292
$520$	6.53837	−	4.23023i	0.286726	−	0.185508i
$521$	15.0324			0.658581			0.329290	−	0.944229i	$-0.393190\pi$
$521$	15.0324			0.658581			0.329290	+	0.944229i	$0.393190\pi$
$522$	−2.82541	+	2.45328i	−0.123665	+	0.107377i
$523$		−	25.5484i		−	1.11715i	−0.829453	−	0.558577i	$-0.811348\pi$
$523$		−	25.5484i		−	1.11715i	0.829453	−	0.558577i	$-0.188652\pi$
$524$	17.4216	+	2.46865i	0.761067	+	0.107844i
$525$			7.94832i			0.346893i
$526$	2.64727	+	3.04883i	0.115426	+	0.132935i
$527$	−3.70577			−0.161426
$528$	−15.1566	−	4.38342i	−0.659608	−	0.190764i
$529$	1.00000			0.0434783
$530$	3.37609	+	3.88821i	0.146648	+	0.168893i
$531$			6.15925i			0.267289i
$532$	12.3238	+	1.74629i	0.534304	+	0.0757111i
$533$			35.6160i			1.54270i
$534$	1.24870	−	1.08423i	0.0540364	−	0.0469192i
$535$	4.37606			0.189194
$536$	−22.4733	−	34.7354i	−0.970699	−	1.50034i
$537$	8.84963			0.381890
$538$	32.0862	−	27.8601i	1.38333	−	1.20113i
$539$		−	15.9193i		−	0.685691i
$540$	0.173734	−	1.22606i	0.00747631	−	0.0527614i
$541$		−	46.1889i		−	1.98582i	−0.118880	−	0.992909i	$-0.537930\pi$
$541$		−	46.1889i		−	1.98582i	0.118880	−	0.992909i	$-0.462070\pi$
$542$	−18.0015	−	20.7321i	−0.773231	−	0.890522i
$543$	14.9793			0.642824
$544$	−6.71427	−	14.5063i	−0.287872	−	0.621952i
$545$	−10.1046			−0.432835
$546$	−7.09864	−	8.17543i	−0.303794	−	0.349876i
$547$		−	19.5998i		−	0.838026i	−0.907980	−	0.419013i	$-0.862376\pi$
$547$		−	19.5998i		−	0.838026i	0.907980	−	0.419013i	$-0.137624\pi$
$548$	−4.14850	+	29.2766i	−0.177215	+	1.25063i
$549$		−	7.23701i		−	0.308868i
$550$	−19.4456	+	16.8844i	−0.829164	+	0.719954i
$551$	9.56435			0.407455
$552$	−1.53642	−	2.37474i	−0.0653946	−	0.101076i
$553$	−17.6009			−0.748464
$554$	26.9708	−	23.4184i	1.14588	−	0.994954i
$555$			1.27791i			0.0542443i
$556$	−0.0401310	−	0.00568657i	−0.00170193	−	0.000241164i
$557$			12.0286i			0.509668i	0.966985	+	0.254834i	$0.0820209\pi$
$557$			12.0286i			0.509668i	−0.966985	+	0.254834i	$0.917979\pi$
$558$	1.21596	+	1.40041i	0.0514758	+	0.0592842i
$559$	43.1572			1.82536
$560$	−1.18461	+	4.09605i	−0.0500589	+	0.173090i
$561$	11.1460			0.470583
$562$	−16.6414	−	19.1657i	−0.701975	−	0.808458i
$563$			31.2069i			1.31522i	0.753361	+	0.657608i	$0.228432\pi$
$563$			31.2069i			1.31522i	−0.753361	+	0.657608i	$0.771568\pi$
$564$	−10.2867	−	1.45763i	−0.433149	−	0.0613774i
$565$			4.59324i			0.193239i
$566$	26.8406	−	23.3054i	1.12820	−	0.979600i
$567$	−1.72166			−0.0723031
$568$	14.8602	−	9.61431i	0.623518	−	0.403408i
$569$	8.49470			0.356116			0.178058	−	0.984020i	$-0.443018\pi$
$569$	8.49470			0.356116			0.178058	+	0.984020i	$0.443018\pi$
$570$	−2.38997	+	2.07518i	−0.100105	+	0.0869199i
$571$		−	22.8478i		−	0.956152i	−0.878319	−	0.478076i	$-0.841334\pi$
$571$		−	22.8478i		−	0.956152i	0.878319	−	0.478076i	$-0.158666\pi$
$572$	4.92179	−	34.7338i	0.205790	−	1.45229i
$573$		−	17.3337i		−	0.724126i
$574$	−12.7854	−	14.7248i	−0.533652	−	0.614602i
$575$	−4.61665			−0.192527
$576$	−3.27880	+	7.29722i	−0.136617	+	0.304051i
$577$	−0.659661			−0.0274620			−0.0137310	−	0.999906i	$-0.504371\pi$
$577$	−0.659661			−0.0274620			−0.0137310	+	0.999906i	$0.504371\pi$
$578$	−8.35889	−	9.62685i	−0.347684	−	0.400424i
$579$		−	18.9291i		−	0.786665i
$580$	−0.459681	+	3.24404i	−0.0190872	+	0.134701i
$581$			13.0742i			0.542409i
$582$	−3.79540	+	3.29551i	−0.157324	+	0.136603i
$583$	23.1967			0.960708
$584$	−34.3348	+	22.2141i	−1.42078	+	0.919227i
$585$	2.75330			0.113835
$586$	5.97613	−	5.18901i	0.246872	−	0.214356i
$587$		−	8.14929i		−	0.336357i	−0.985757	−	0.168179i	$-0.946211\pi$
$587$		−	8.14929i		−	0.336357i	0.985757	−	0.168179i	$-0.0537885\pi$
$588$	−7.99191	−	1.13246i	−0.329581	−	0.0467017i
$589$		−	4.74056i		−	0.195331i
$590$	3.53591	+	4.07228i	0.145571	+	0.167653i
$591$	5.04050			0.207339
$592$	2.29365	−	7.93081i	0.0942686	−	0.325954i
$593$	−22.4830			−0.923266			−0.461633	−	0.887071i	$-0.652736\pi$
$593$	−22.4830			−0.923266			−0.461633	+	0.887071i	$0.652736\pi$
$594$	−3.65729	−	4.21206i	−0.150060	−	0.172823i
$595$		−	3.01218i		−	0.123487i
$596$	−35.1338	−	4.97848i	−1.43914	−	0.203926i
$597$			14.5956i			0.597356i
$598$	4.74856	−	4.12313i	0.194183	−	0.168607i
$599$	40.3090			1.64698			0.823490	−	0.567331i	$-0.192024\pi$
$599$	40.3090			1.64698			0.823490	+	0.567331i	$0.192024\pi$
$600$	7.09313	+	10.9633i	0.289576	+	0.447577i
$601$	−39.1633			−1.59751			−0.798753	−	0.601659i	$-0.794507\pi$
$601$	−39.1633			−1.59751			−0.798753	+	0.601659i	$0.794507\pi$
$602$	−17.8426	+	15.4925i	−0.727211	+	0.631429i
$603$		−	14.6270i		−	0.595658i
$604$	−4.75618	+	33.5651i	−0.193526	+	1.36574i
$605$		−	2.82250i		−	0.114751i
$606$	−11.1818	−	12.8779i	−0.454229	−	0.523131i
$607$	47.4922			1.92765			0.963824	−	0.266539i	$-0.0858800\pi$
$607$	47.4922			1.92765			0.963824	+	0.266539i	$0.0858800\pi$
$608$	18.5570	−	8.58913i	0.752584	−	0.348335i
$609$	4.55535			0.184592
$610$	−4.15463	−	4.78485i	−0.168216	−	0.193733i
$611$		−	23.1003i		−	0.934537i
$612$	0.792896	−	5.59558i	0.0320509	−	0.226188i
$613$		−	3.08961i		−	0.124788i	−0.998052	−	0.0623940i	$-0.980126\pi$
$613$		−	3.08961i		−	0.124788i	0.998052	−	0.0623940i	$-0.0198735\pi$
$614$	−10.7137	+	9.30255i	−0.432368	+	0.375420i
$615$	4.95897			0.199965
$616$	10.4339	+	16.1269i	0.420392	+	0.649771i
$617$	−19.3907			−0.780641			−0.390320	−	0.920679i	$-0.627636\pi$
$617$	−19.3907			−0.780641			−0.390320	+	0.920679i	$0.627636\pi$
$618$	3.06594	−	2.66213i	0.123330	−	0.107086i
$619$		−	7.59263i		−	0.305174i	−0.988290	−	0.152587i	$-0.951240\pi$
$619$		−	7.59263i		−	0.305174i	0.988290	−	0.152587i	$-0.0487604\pi$
$620$	1.60790	+	0.227840i	0.0645749	+	0.00915029i
$621$		−	1.00000i		−	0.0401286i
$622$	24.9723	+	28.7603i	1.00130	+	1.15318i
$623$	−2.01324			−0.0806588
$624$	−17.0872	−	4.94174i	−0.684034	−	0.197828i
$625$	19.3967			0.775866
$626$	−19.7254	−	22.7175i	−0.788385	−	0.907975i
$627$			14.2583i			0.569423i
$628$	−13.6407	−	1.93290i	−0.544325	−	0.0771310i
$629$			5.83220i			0.232545i
$630$	−1.13830	+	0.988376i	−0.0453511	+	0.0393778i
$631$	−12.0377			−0.479215			−0.239607	−	0.970870i	$-0.577019\pi$
$631$	−12.0377			−0.479215			−0.239607	+	0.970870i	$0.577019\pi$
$632$	−24.2774	+	15.7071i	−0.965702	+	0.624795i
$633$	13.0601			0.519094
$634$	13.7421	−	11.9321i	0.545770	−	0.473886i
$635$			5.16415i			0.204933i
$636$	1.65015	−	11.6454i	0.0654328	−	0.461769i
$637$		−	17.9469i		−	0.711084i
$638$	9.67681	+	11.1447i	0.383109	+	0.441222i
$639$	6.25759			0.247546
$640$	2.02138	+	6.70696i	0.0799019	+	0.265116i
$641$	−46.6358			−1.84200			−0.921002	−	0.389558i	$-0.872628\pi$
$641$	−46.6358			−1.84200			−0.921002	+	0.389558i	$0.872628\pi$
$642$	−6.55326	−	7.54733i	−0.258637	−	0.297869i
$643$		−	10.3591i		−	0.408522i	−0.978917	−	0.204261i	$-0.934521\pi$
$643$		−	10.3591i		−	0.408522i	0.978917	−	0.204261i	$-0.0654791\pi$
$644$	−0.483095	+	3.40927i	−0.0190366	+	0.134344i
$645$		−	6.00898i		−	0.236603i
$646$	−10.9075	+	9.47085i	−0.429149	+	0.372625i
$647$	−22.4871			−0.884061			−0.442030	−	0.897000i	$-0.645742\pi$
$647$	−22.4871			−0.884061			−0.442030	+	0.897000i	$0.645742\pi$
$648$	−2.37474	+	1.53642i	−0.0932887	+	0.0603564i
$649$	24.2948			0.953655
$650$	−21.9224	+	19.0350i	−0.859869	+	0.746615i
$651$		−	2.25785i		−	0.0884921i
$652$	11.6292	+	1.64787i	0.455437	+	0.0645355i
$653$			9.76763i			0.382237i	0.981567	+	0.191119i	$0.0612115\pi$
$653$			9.76763i			0.382237i	−0.981567	+	0.191119i	$0.938789\pi$
$654$	15.1319	+	17.4273i	0.591706	+	0.681462i
$655$	5.44723			0.212841
$656$	−30.7758	−	8.90059i	−1.20159	−	0.347510i
$657$	−14.4583			−0.564073
$658$	8.29251	+	9.55040i	0.323276	+	0.372314i
$659$			26.6057i			1.03641i	0.855256	+	0.518206i	$0.173400\pi$
$659$			26.6057i			1.03641i	−0.855256	+	0.518206i	$0.826600\pi$
$660$	−4.83614	−	0.685282i	−0.188246	−	0.0266746i
$661$		−	0.158545i		−	0.00616669i	−0.999995	−	0.00308334i	$-0.999019\pi$
$661$		−	0.158545i		−	0.00616669i	0.999995	−	0.00308334i	$-0.000981460\pi$
$662$	17.7340	−	15.3982i	0.689250	−	0.598468i
$663$	12.5657			0.488010
$664$	11.6675	+	18.0336i	0.452786	+	0.699840i
$665$	3.85329			0.149424
$666$	2.20399	−	1.91370i	0.0854029	−	0.0741544i
$667$			2.64590i			0.102450i
$668$	4.97289	−	35.0944i	0.192407	−	1.35784i
$669$			4.66323i			0.180291i
$670$	−8.39711	−	9.67086i	−0.324408	−	0.373618i
$671$	−28.5460			−1.10200
$672$	8.83838	−	4.09086i	0.340948	−	0.157808i
$673$	35.1007			1.35303			0.676516	−	0.736428i	$-0.263489\pi$
$673$	35.1007			1.35303			0.676516	+	0.736428i	$0.263489\pi$
$674$	−8.63111	−	9.94036i	−0.332458	−	0.382888i
$675$			4.61665i			0.177695i
$676$	1.90092	−	13.4150i	0.0731121	−	0.515963i
$677$		−	35.7938i		−	1.37567i	−0.725867	−	0.687835i	$-0.758561\pi$
$677$		−	35.7938i		−	1.37567i	0.725867	−	0.687835i	$-0.241439\pi$
$678$	7.92188	−	6.87848i	0.304238	−	0.264167i
$679$	6.11923			0.234835
$680$	−2.68809	−	4.15479i	−0.103083	−	0.159329i
$681$	3.88192			0.148756
$682$	5.52385	−	4.79630i	0.211519	−	0.183660i
$683$		−	5.86741i		−	0.224510i	−0.993679	−	0.112255i	$-0.964193\pi$
$683$		−	5.86741i		−	0.224510i	0.993679	−	0.112255i	$-0.0358074\pi$
$684$	7.15807	+	1.01430i	0.273696	+	0.0387828i
$685$			9.15392i			0.349753i
$686$	17.6169	+	20.2892i	0.672615	+	0.774644i
$687$	−0.275712			−0.0105191
$688$	−10.7852	+	37.2922i	−0.411182	+	1.42175i
$689$	26.1513			0.996285
$690$	−0.574082	−	0.661164i	−0.0218549	−	0.0251701i
$691$		−	18.5354i		−	0.705121i	−0.935789	−	0.352560i	$-0.885311\pi$
$691$		−	18.5354i		−	0.705121i	0.935789	−	0.352560i	$-0.114689\pi$
$692$	27.8927	+	3.95240i	1.06032	+	0.150248i
$693$			6.79101i			0.257969i
$694$	−25.8731	+	22.4653i	−0.982129	+	0.852772i
$695$	−0.0125478			−0.000475964
$696$	6.28332	−	4.06522i	0.238169	−	0.154092i
$697$	22.6321			0.857250
$698$	−10.4256	+	9.05239i	−0.394613	+	0.342638i
$699$			9.89319i			0.374195i
$700$	2.23028	−	15.7394i	0.0842966	−	0.594893i
$701$			41.3408i			1.56142i	0.624893	+	0.780710i	$0.285143\pi$
$701$			41.3408i			1.56142i	−0.624893	+	0.780710i	$0.714857\pi$
$702$	−4.12313	−	4.74856i	−0.155617	−	0.179223i
$703$	−7.46076			−0.281388
$704$	28.7835	+	12.9330i	1.08482	+	0.487432i
$705$	−3.21635			−0.121135
$706$	9.52361	+	10.9683i	0.358426	+	0.412796i
$707$			20.7628i			0.780865i
$708$	1.72827	−	12.1967i	0.0649524	−	0.458379i
$709$			25.7806i			0.968209i	0.875010	+	0.484105i	$0.160855\pi$
$709$			25.7806i			0.968209i	−0.875010	+	0.484105i	$0.839145\pi$
$710$	4.13729	−	3.59237i	0.155270	−	0.134819i
$711$	−10.2232			−0.383399
$712$	−2.77692	+	1.79663i	−0.104070	+	0.0673315i
$713$	1.31143			0.0491136
$714$	−5.19505	+	4.51081i	−0.194420	+	0.168813i
$715$		−	10.8602i		−	0.406149i
$716$	−17.5242	−	2.48319i	−0.654910	−	0.0928010i
$717$			24.0570i			0.898426i
$718$	11.4965	+	13.2404i	0.429045	+	0.494127i
$719$	20.5853			0.767703			0.383851	−	0.923395i	$-0.374598\pi$
$719$	20.5853			0.767703			0.383851	+	0.923395i	$0.374598\pi$
$720$	−0.688061	+	2.37912i	−0.0256425	+	0.0886647i
$721$	−4.94314			−0.184092
$722$	5.50137	+	6.33587i	0.204740	+	0.235797i
$723$			21.8111i			0.811162i
$724$	−29.6623	−	4.20316i	−1.10239	−	0.156209i
$725$		−	12.2152i		−	0.453660i
$726$	−4.86792	+	4.22676i	−0.180665	+	0.156870i
$727$	9.69635			0.359618			0.179809	−	0.983702i	$-0.442452\pi$
$727$	9.69635			0.359618			0.179809	+	0.983702i	$0.442452\pi$
$728$	11.7629	+	18.1810i	0.435960	+	0.673833i
$729$	−1.00000			−0.0370370
$730$	−9.55933	+	8.30026i	−0.353807	+	0.307206i
$731$		−	27.4241i		−	1.01432i
$732$	−2.03069	+	14.3309i	−0.0750564	+	0.529684i
$733$		−	33.0479i		−	1.22065i	−0.792151	−	0.610325i	$-0.791039\pi$
$733$		−	33.0479i		−	1.22065i	0.792151	−	0.610325i	$-0.208961\pi$
$734$	1.82766	+	2.10490i	0.0674601	+	0.0776931i
$735$	−2.49883			−0.0921708
$736$	2.37611	+	5.13363i	0.0875845	+	0.189228i
$737$	−57.6955			−2.12524
$738$	−7.42618	−	8.55266i	−0.273362	−	0.314828i
$739$			32.4267i			1.19284i	0.802674	+	0.596419i	$0.203410\pi$
$739$			32.4267i			1.19284i	−0.802674	+	0.596419i	$0.796590\pi$
$740$	0.358579	−	2.53054i	0.0131816	−	0.0930246i
$741$			16.0744i			0.590509i
$742$	−10.8118	+	9.38777i	−0.396914	+	0.344636i
$743$	21.0863			0.773581			0.386790	−	0.922168i	$-0.373584\pi$
$743$	21.0863			0.773581			0.386790	+	0.922168i	$0.373584\pi$
$744$	−2.01492	−	3.11432i	−0.0738705	−	0.114176i
$745$	−10.9853			−0.402471
$746$	−5.31060	+	4.61114i	−0.194435	+	0.168826i
$747$			7.59392i			0.277847i
$748$	−22.0715	−	3.12753i	−0.807012	−	0.114354i
$749$			12.1684i			0.444623i
$750$	5.52074	+	6.35818i	0.201589	+	0.232168i
$751$	−3.66352			−0.133684			−0.0668419	−	0.997764i	$-0.521292\pi$
$751$	−3.66352			−0.133684			−0.0668419	+	0.997764i	$0.521292\pi$
$752$	19.9609	+	5.77286i	0.727901	+	0.210515i
$753$	21.4940			0.783286
$754$	10.9094	+	12.5642i	0.397296	+	0.457561i
$755$			10.4948i			0.381945i
$756$	3.40927	+	0.483095i	0.123994	+	0.0175700i
$757$		−	11.3833i		−	0.413734i	−0.978369	−	0.206867i	$-0.933673\pi$
$757$		−	11.3833i		−	0.413734i	0.978369	−	0.206867i	$-0.0663268\pi$
$758$	−21.5275	+	18.6921i	−0.781913	+	0.678926i
$759$	−3.94444			−0.143174
$760$	5.31495	−	3.43870i	0.192793	−	0.124735i
$761$	17.9155			0.649436			0.324718	−	0.945811i	$-0.394731\pi$
$761$	17.9155			0.649436			0.324718	+	0.945811i	$0.394731\pi$
$762$	8.90653	−	7.73344i	0.322649	−	0.280153i
$763$		−	28.0976i		−	1.01720i
$764$	−4.86380	+	34.3245i	−0.175966	+	1.24182i
$765$		−	1.74957i		−	0.0632560i
$766$	28.1420	+	32.4109i	1.01681	+	1.17105i
$767$	27.3893			0.988970
$768$	8.54033	−	13.5301i	0.308172	−	0.488224i
$769$	−5.92264			−0.213576			−0.106788	−	0.994282i	$-0.534057\pi$
$769$	−5.92264			−0.213576			−0.106788	+	0.994282i	$0.534057\pi$
$770$	3.89859	+	4.48997i	0.140495	+	0.161807i
$771$		−	1.27342i		−	0.0458610i
$772$	−5.31145	+	37.4837i	−0.191163	+	1.34907i
$773$		−	38.7979i		−	1.39546i	−0.716359	−	0.697732i	$-0.754193\pi$
$773$		−	38.7979i		−	1.39546i	0.716359	−	0.697732i	$-0.245807\pi$
$774$	−10.3636	+	8.99859i	−0.372511	+	0.323448i
$775$	−6.05443			−0.217482
$776$	8.44044	−	5.46084i	0.302994	−	0.196033i
$777$	−3.55344			−0.127479
$778$	28.5955	−	24.8292i	1.02520	−	0.890169i
$779$			28.9517i			1.03730i
$780$	−5.45213	−	0.772569i	−0.195217	−	0.0276624i
$781$		−	24.6827i		−	0.883216i
$782$	−2.62003	−	3.01746i	−0.0936920	−	0.107904i
$783$	2.64590			0.0945566
$784$	15.5080	+	4.48502i	0.553856	+	0.160179i
$785$	−4.26506			−0.152226
$786$	−8.15735	−	9.39474i	−0.290963	−	0.335099i
$787$			15.1528i			0.540137i	0.962841	+	0.270069i	$0.0870464\pi$
$787$			15.1528i			0.540137i	−0.962841	+	0.270069i	$0.912954\pi$
$788$	−9.98130	−	1.41435i	−0.355569	−	0.0503843i
$789$		−	2.85512i		−	0.101645i
$790$	−6.75919	+	5.86893i	−0.240481	+	0.208807i
$791$	−12.7722			−0.454129
$792$	6.06034	+	9.36703i	0.215345	+	0.332843i
$793$	−32.1819			−1.14281
$794$	17.9698	−	15.6030i	0.637724	−	0.553729i
$795$		−	3.64116i		−	0.129139i
$796$	4.09548	−	28.9024i	0.145160	−	1.02442i
$797$		−	23.9779i		−	0.849339i	−0.905348	−	0.424670i	$-0.860390\pi$
$797$		−	23.9779i		−	0.849339i	0.905348	−	0.424670i	$-0.139610\pi$
$798$	−5.77039	−	6.64570i	−0.204270	−	0.235255i
$799$	−14.6790			−0.519305
$800$	−10.9697	−	23.7001i	−0.387836	−	0.837926i
$801$	−1.16936			−0.0413172
$802$	18.1438	+	20.8960i	0.640680	+	0.737865i
$803$			57.0300i			2.01255i
$804$	−4.10431	+	28.9647i	−0.144748	+	1.02151i
$805$			1.06598i			0.0375708i
$806$	6.22743	−	5.40721i	0.219352	−	0.190461i
$807$	−30.0475			−1.05772
$808$	18.5288	+	28.6387i	0.651842	+	1.00751i
$809$	−27.2651			−0.958591			−0.479296	−	0.877654i	$-0.659108\pi$
$809$	−27.2651			−0.958591			−0.479296	+	0.877654i	$0.659108\pi$
$810$	−0.661164	+	0.574082i	−0.0232309	+	0.0201712i
$811$			7.66818i			0.269266i	0.990896	+	0.134633i	$0.0429856\pi$
$811$			7.66818i			0.269266i	−0.990896	+	0.134633i	$0.957014\pi$
$812$	−9.02058	−	1.27822i	−0.316560	−	0.0448567i
$813$			19.4149i			0.680910i
$814$	−7.54849	−	8.69352i	−0.264574	−	0.304708i
$815$	3.63612			0.127368
$816$	−3.14022	+	10.8580i	−0.109930	+	0.380106i
$817$	35.0819			1.22736
$818$	−29.5633	−	34.0478i	−1.03366	−	1.19045i
$819$			7.65599i			0.267522i
$820$	−9.81985	−	1.39148i	−0.342924	−	0.0485925i
$821$			39.6774i			1.38475i	0.721538	+	0.692375i	$0.243436\pi$
$821$			39.6774i			1.38475i	−0.721538	+	0.692375i	$0.756564\pi$
$822$	15.7876	−	13.7082i	0.550656	−	0.478129i
$823$	−17.4632			−0.608730			−0.304365	−	0.952555i	$-0.598444\pi$
$823$	−17.4632			−0.608730			−0.304365	+	0.952555i	$0.598444\pi$
$824$	−6.81822	+	4.41129i	−0.237524	+	0.153675i
$825$	18.2101			0.633994
$826$	−11.3236	+	9.83219i	−0.394000	+	0.342106i
$827$		−	45.2033i		−	1.57187i	−0.618306	−	0.785937i	$-0.712181\pi$
$827$		−	45.2033i		−	1.57187i	0.618306	−	0.785937i	$-0.287819\pi$
$828$	−0.280598	+	1.98022i	−0.00975144	+	0.0688173i
$829$			4.23533i			0.147099i	0.997292	+	0.0735495i	$0.0234327\pi$
$829$			4.23533i			0.147099i	−0.997292	+	0.0735495i	$0.976567\pi$
$830$	4.35953	+	5.02083i	0.151322	+	0.174276i
$831$	−25.2571			−0.876160
$832$	32.4497	+	14.5804i	1.12499	+	0.505483i
$833$	−11.4043			−0.395136
$834$	0.0187906	+	0.0216409i	0.000650665	+	0.000749364i
$835$		−	10.9730i		−	0.379736i
$836$	4.00085	−	28.2346i	0.138372	−	0.976514i
$837$		−	1.31143i		−	0.0453298i
$838$	−8.14779	+	7.07464i	−0.281461	+	0.244389i
$839$	−47.1004			−1.62609			−0.813044	−	0.582202i	$-0.802191\pi$
$839$	−47.1004			−1.62609			−0.813044	+	0.582202i	$0.802191\pi$
$840$	2.53142	−	1.63780i	0.0873424	−	0.0565093i
$841$	21.9992			0.758594
$842$	−5.47926	+	4.75759i	−0.188828	+	0.163957i
$843$			17.9480i			0.618162i
$844$	−25.8619	−	3.66464i	−0.890204	−	0.126142i
$845$		−	4.19449i		−	0.144295i
$846$	4.81657	+	5.54719i	0.165597	+	0.190716i
$847$	7.84842			0.269675
$848$	−6.53533	+	22.5973i	−0.224424	+	0.775996i
$849$	−25.1352			−0.862639
$850$	12.0957	+	13.9305i	0.414881	+	0.477814i
$851$		−	2.06396i		−	0.0707515i
$852$	−12.3914	−	1.75586i	−0.424522	−	0.0601549i
$853$			28.9662i			0.991782i	0.868385	+	0.495891i	$0.165159\pi$
$853$			28.9662i			0.991782i	−0.868385	+	0.495891i	$0.834841\pi$
$854$	13.3051	−	11.5526i	0.455290	−	0.395323i
$855$	2.23812			0.0765420
$856$	10.8591	+	16.7842i	0.371157	+	0.573672i
$857$	−7.31949			−0.250029			−0.125014	−	0.992155i	$-0.539898\pi$
$857$	−7.31949			−0.250029			−0.125014	+	0.992155i	$0.539898\pi$
$858$	−18.7304	+	16.2634i	−0.639447	+	0.555225i
$859$		−	5.41487i		−	0.184753i	−0.995724	−	0.0923765i	$-0.970554\pi$
$859$		−	5.41487i		−	0.184753i	0.995724	−	0.0923765i	$-0.0294463\pi$
$860$	−1.68611	+	11.8991i	−0.0574957	+	0.405755i
$861$			13.7892i			0.469936i
$862$	−4.93169	−	5.67977i	−0.167974	−	0.193454i
$863$	28.8289			0.981348			0.490674	−	0.871343i	$-0.336751\pi$
$863$	28.8289			0.981348			0.490674	+	0.871343i	$0.336751\pi$
$864$	5.13363	−	2.37611i	0.174649	−	0.0808368i
$865$	8.72122			0.296530
$866$	28.8233	+	33.1955i	0.979456	+	1.12803i
$867$			9.01519i			0.306172i
$868$	−0.633548	+	4.47104i	−0.0215040	+	0.151757i
$869$			40.3247i			1.36792i
$870$	1.74937	−	1.51896i	0.0593092	−	0.0514976i
$871$	−65.0443			−2.20394
$872$	−25.0745	−	38.7559i	−0.849129	−	1.31244i
$873$	3.55425			0.120293
$874$	3.86004	−	3.35163i	0.130568	−	0.113371i
$875$		−	10.2511i		−	0.346552i
$876$	28.6306	+	4.05697i	0.967340	+	0.137072i
$877$			18.7572i			0.633387i	0.948528	+	0.316693i	$0.102573\pi$
$877$			18.7572i			0.633387i	−0.948528	+	0.316693i	$0.897427\pi$
$878$	−34.7799	−	40.0557i	−1.17377	−	1.35181i
$879$	−5.59642			−0.188763
$880$	9.38432	+	2.71402i	0.316345	+	0.0914895i
$881$	−46.9623			−1.58220			−0.791100	−	0.611687i	$-0.790491\pi$
$881$	−46.9623			−1.58220			−0.791100	+	0.611687i	$0.790491\pi$
$882$	3.74206	+	4.30970i	0.126002	+	0.145115i
$883$		−	4.69775i		−	0.158092i	−0.996871	−	0.0790459i	$-0.974813\pi$
$883$		−	4.69775i		−	0.158092i	0.996871	−	0.0790459i	$-0.0251874\pi$
$884$	−24.8827	−	3.52590i	−0.836897	−	0.118589i
$885$		−	3.81354i		−	0.128191i
$886$	13.8595	−	12.0341i	0.465620	−	0.404293i
$887$	−33.4104			−1.12181			−0.560906	−	0.827879i	$-0.689547\pi$
$887$	−33.4104			−1.12181			−0.560906	+	0.827879i	$0.689547\pi$
$888$	−4.90136	+	3.17111i	−0.164479	+	0.106416i
$889$	−14.3598			−0.481611
$890$	−0.773137	+	0.671307i	−0.0259156	+	0.0225023i
$891$			3.94444i			0.132144i
$892$	1.30849	−	9.23422i	0.0438116	−	0.309184i
$893$		−	18.7779i		−	0.628378i
$894$	16.4508	+	18.9462i	0.550196	+	0.633655i
$895$	−5.47930			−0.183153
$896$	−18.6498	+	5.62077i	−0.623046	+	0.187777i
$897$	−4.44686			−0.148476
$898$	8.21536	+	9.46155i	0.274150	+	0.315736i
$899$			3.46992i			0.115728i
$900$	1.29542	−	9.14197i	0.0431807	−	0.304732i
$901$		−	16.6178i		−	0.553618i
$902$	−33.7355	+	29.2921i	−1.12327	+	0.975322i
$903$	16.7089			0.556039
$904$	−17.6171	+	11.3980i	−0.585937	+	0.379093i
$905$	−9.27452			−0.308296
$906$	18.1002	−	15.7162i	0.601339	−	0.522136i
$907$		−	26.9548i		−	0.895020i	−0.894279	−	0.447510i	$-0.852311\pi$
$907$		−	26.9548i		−	0.895020i	0.894279	−	0.447510i	$-0.147689\pi$
$908$	−7.68706	−	1.08926i	−0.255104	−	0.0361483i
$909$			12.0597i			0.399996i
$910$	4.39516	+	5.06187i	0.145698	+	0.167799i
$911$	−34.9043			−1.15643			−0.578215	−	0.815885i	$-0.696250\pi$
$911$	−34.9043			−1.15643			−0.578215	+	0.815885i	$0.696250\pi$
$912$	−13.8899	−	4.01708i	−0.459942	−	0.133019i
$913$	29.9538			0.991326
$914$	−30.5427	−	35.1758i	−1.01026	−	1.16351i
$915$			4.48083i			0.148132i
$916$	0.545969	+	0.0773640i	0.0180393	+	0.00255618i
$917$			15.1469i			0.500195i
$918$	−3.01746	+	2.62003i	−0.0995910	+	0.0864738i
$919$	36.6999			1.21062			0.605308	−	0.795991i	$-0.293050\pi$
$919$	36.6999			1.21062			0.605308	+	0.795991i	$0.293050\pi$
$920$	0.951286	+	1.47034i	0.0313630	+	0.0484755i
$921$	10.0329			0.330597
$922$	34.1326	−	29.6369i	1.12410	−	0.976040i
$923$		−	27.8266i		−	0.915923i
$924$	1.90554	−	13.4477i	0.0626877	−	0.442396i
$925$			9.52856i			0.313297i
$926$	27.7274	+	31.9334i	0.911179	+	1.04940i
$927$	−2.87114			−0.0943007
$928$	−13.5830	+	6.28694i	−0.445885	+	0.206379i
$929$	19.7566			0.648192			0.324096	−	0.946024i	$-0.394940\pi$
$929$	19.7566			0.648192			0.324096	+	0.946024i	$0.394940\pi$
$930$	−0.752870	−	0.867073i	−0.0246876	−	0.0284325i
$931$		−	14.5888i		−	0.478129i
$932$	2.77601	−	19.5907i	0.0909311	−	0.641714i
$933$		−	26.9330i		−	0.881746i
$934$	−24.4721	+	21.2489i	−0.800752	+	0.695285i
$935$	−6.90109			−0.225690
$936$	6.83226	+	10.5601i	0.223319	+	0.345169i
$937$	43.8304			1.43188			0.715938	−	0.698163i	$-0.245999\pi$
$937$	43.8304			1.43188			0.715938	+	0.698163i	$0.245999\pi$
$938$	26.8914	−	23.3495i	0.878036	−	0.762389i
$939$			21.2741i			0.694255i
$940$	6.36908	+	0.902502i	0.207737	+	0.0294364i
$941$			39.7807i			1.29681i	0.761294	+	0.648407i	$0.224565\pi$
$941$			39.7807i			1.29681i	−0.761294	+	0.648407i	$0.775435\pi$
$942$	6.38703	+	7.35587i	0.208101	+	0.239667i
$943$	−8.00925			−0.260817
$944$	−6.84471	+	23.6671i	−0.222776	+	0.770299i
$945$	1.06598			0.0346763
$946$	35.4944	+	40.8786i	1.15402	+	1.32908i
$947$		−	42.3464i		−	1.37607i	−0.725677	−	0.688036i	$-0.758473\pi$
$947$		−	42.3464i		−	1.37607i	0.725677	−	0.688036i	$-0.241527\pi$
$948$	20.2441	+	2.86860i	0.657498	+	0.0931677i
$949$			64.2941i			2.08707i
$950$	−17.8205	+	15.4733i	−0.578172	+	0.502020i
$951$	−12.8690			−0.417306
$952$	11.5531	−	7.47467i	0.374437	−	0.242255i
$953$	48.7119			1.57793			0.788967	−	0.614435i	$-0.210616\pi$
$953$	48.7119			1.57793			0.788967	+	0.614435i	$0.210616\pi$
$954$	−6.27985	+	5.45273i	−0.203318	+	0.176539i
$955$			10.7323i			0.347288i
$956$	6.75035	−	47.6382i	0.218322	−	1.54073i
$957$		−	10.4366i		−	0.337367i
$958$	21.3138	+	24.5468i	0.688616	+	0.793073i
$959$	−25.4540			−0.821952
$960$	2.03009	−	4.51812i	0.0655208	−	0.145822i
$961$	−29.2801			−0.944521
$962$	−8.50996	−	9.80083i	−0.274372	−	0.315991i
$963$			7.06779i			0.227756i
$964$	6.12013	−	43.1907i	0.197116	−	1.39108i
$965$			11.7200i			0.377281i
$966$	1.83848	−	1.59633i	0.0591520	−	0.0513610i
$967$	−3.51886			−0.113159			−0.0565794	−	0.998398i	$-0.518019\pi$
$967$	−3.51886			−0.113159			−0.0565794	+	0.998398i	$0.518019\pi$
$968$	10.8256	−	7.00398i	0.347947	−	0.225117i
$969$	10.2145			0.328135
$970$	2.34995	−	2.04043i	0.0754522	−	0.0655143i
$971$		−	32.3215i		−	1.03725i	−0.855003	−	0.518623i	$-0.826445\pi$
$971$		−	32.3215i		−	1.03725i	0.855003	−	0.518623i	$-0.173555\pi$
$972$	1.98022	+	0.280598i	0.0635155	+	0.00900018i
$973$		−	0.0348911i		−	0.00111856i
$974$	24.7775	+	28.5360i	0.793921	+	0.914351i
$975$	20.5296			0.657472
$976$	8.04241	−	27.8084i	0.257431	−	0.890126i
$977$	−36.1177			−1.15551			−0.577754	−	0.816211i	$-0.696071\pi$
$977$	−36.1177			−1.15551			−0.577754	+	0.816211i	$0.696071\pi$
$978$	−5.44518	−	6.27116i	−0.174118	−	0.200530i
$979$			4.61246i			0.147415i
$980$	4.94824	+	0.701167i	0.158066	+	0.0223980i
$981$		−	16.3200i		−	0.521058i
$982$	16.9675	−	14.7327i	0.541456	−	0.470140i
$983$	6.18076			0.197136			0.0985678	−	0.995130i	$-0.468574\pi$
$983$	6.18076			0.197136			0.0985678	+	0.995130i	$0.468574\pi$
$984$	12.3056	+	19.0199i	0.392288	+	0.606332i
$985$	−3.12086			−0.0994388
$986$	7.98389	−	6.93232i	0.254259	−	0.220770i
$987$		−	8.94360i		−	0.284678i
$988$	4.51045	−	31.8309i	0.143497	−	1.01268i
$989$			9.70511i			0.308605i
$990$	2.26443	+	2.60792i	0.0719684	+	0.0828853i
$991$	−59.8067			−1.89982			−0.949911	−	0.312521i	$-0.898827\pi$
$991$	−59.8067			−1.89982			−0.949911	+	0.312521i	$0.898827\pi$
$992$	3.11611	+	6.73241i	0.0989366	+	0.213754i
$993$	−16.6072			−0.527014
$994$	9.98917	+	11.5044i	0.316837	+	0.364898i
$995$		−	9.03692i		−	0.286490i
$996$	2.13084	−	15.0376i	0.0675182	−	0.476486i
$997$		−	11.7718i		−	0.372817i	−0.982472	−	0.186409i	$-0.940315\pi$
$997$		−	11.7718i		−	0.372817i	0.982472	−	0.186409i	$-0.0596848\pi$
$998$	−19.6442	+	17.0569i	−0.621827	+	0.539926i
$999$	−2.06396			−0.0653007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.f.c.277.16	yes	18
4.3	odd	2		2208.2.f.c.1105.14		18
8.3	odd	2		2208.2.f.c.1105.5		18
8.5	even	2	inner	552.2.f.c.277.15	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.f.c.277.15	✓	18	8.5	even	2	inner
552.2.f.c.277.16	yes	18	1.1	even	1	trivial
2208.2.f.c.1105.5		18	8.3	odd	2
2208.2.f.c.1105.14		18	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.927201 + 1.06785i) q^{2} -1.00000i q^{3} +(-0.280598 + 1.98022i) q^{4} +0.619156i q^{5} +(1.06785 - 0.927201i) q^{6} -1.72166 q^{7} +(-2.37474 + 1.53642i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.927201 + 1.06785i) q^{2} -1.00000i q^{3} +(-0.280598 + 1.98022i) q^{4} +0.619156i q^{5} +(1.06785 - 0.927201i) q^{6} -1.72166 q^{7} +(-2.37474 + 1.53642i) q^{8} -1.00000 q^{9} +(-0.661164 + 0.574082i) q^{10} +3.94444i q^{11} +(1.98022 + 0.280598i) q^{12} +4.44686i q^{13} +(-1.59633 - 1.83848i) q^{14} +0.619156 q^{15} +(-3.84253 - 1.11129i) q^{16} +2.82574 q^{17} +(-0.927201 - 1.06785i) q^{18} +3.61479i q^{19} +(-1.22606 - 0.173734i) q^{20} +1.72166i q^{21} +(-4.21206 + 3.65729i) q^{22} -1.00000 q^{23} +(1.53642 + 2.37474i) q^{24} +4.61665 q^{25} +(-4.74856 + 4.12313i) q^{26} +1.00000i q^{27} +(0.483095 - 3.40927i) q^{28} -2.64590i q^{29} +(0.574082 + 0.661164i) q^{30} -1.31143 q^{31} +(-2.37611 - 5.13363i) q^{32} +3.94444 q^{33} +(2.62003 + 3.01746i) q^{34} -1.06598i q^{35} +(0.280598 - 1.98022i) q^{36} +2.06396i q^{37} +(-3.86004 + 3.35163i) q^{38} +4.44686 q^{39} +(-0.951286 - 1.47034i) q^{40} +8.00925 q^{41} +(-1.83848 + 1.59633i) q^{42} -9.70511i q^{43} +(-7.81086 - 1.10680i) q^{44} -0.619156i q^{45} +(-0.927201 - 1.06785i) q^{46} -5.19474 q^{47} +(-1.11129 + 3.84253i) q^{48} -4.03587 q^{49} +(4.28056 + 4.92988i) q^{50} -2.82574i q^{51} +(-8.80575 - 1.24778i) q^{52} -5.88085i q^{53} +(-1.06785 + 0.927201i) q^{54} -2.44222 q^{55} +(4.08851 - 2.64521i) q^{56} +3.61479 q^{57} +(2.82541 - 2.45328i) q^{58} -6.15925i q^{59} +(-0.173734 + 1.22606i) q^{60} +7.23701i q^{61} +(-1.21596 - 1.40041i) q^{62} +1.72166 q^{63} +(3.27880 - 7.29722i) q^{64} -2.75330 q^{65} +(3.65729 + 4.21206i) q^{66} +14.6270i q^{67} +(-0.792896 + 5.59558i) q^{68} +1.00000i q^{69} +(1.13830 - 0.988376i) q^{70} -6.25759 q^{71} +(2.37474 - 1.53642i) q^{72} +14.4583 q^{73} +(-2.20399 + 1.91370i) q^{74} -4.61665i q^{75} +(-7.15807 - 1.01430i) q^{76} -6.79101i q^{77} +(4.12313 + 4.74856i) q^{78} +10.2232 q^{79} +(0.688061 - 2.37912i) q^{80} +1.00000 q^{81} +(7.42618 + 8.55266i) q^{82} -7.59392i q^{83} +(-3.40927 - 0.483095i) q^{84} +1.74957i q^{85} +(10.3636 - 8.99859i) q^{86} -2.64590 q^{87} +(-6.06034 - 9.36703i) q^{88} +1.16936 q^{89} +(0.661164 - 0.574082i) q^{90} -7.65599i q^{91} +(0.280598 - 1.98022i) q^{92} +1.31143i q^{93} +(-4.81657 - 5.54719i) q^{94} -2.23812 q^{95} +(-5.13363 + 2.37611i) q^{96} -3.55425 q^{97} +(-3.74206 - 4.30970i) q^{98} -3.94444i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9}+O(q^{10}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9	\( 18 q - 8 q^{4} + 8 q^{7} - 6 q^{8} - 18 q^{9} + 12 q^{10} - 4 q^{12} - 14 q^{14} + 8 q^{15} + 12 q^{16} - 8 q^{17} - 16 q^{20} - 30 q^{22} - 18 q^{23} + 6 q^{24} - 22 q^{25} + 8 q^{26} - 2 q^{28} + 4 q^{30} - 44 q^{31} + 10 q^{32} - 24 q^{33} + 18 q^{34} + 8 q^{36} - 20 q^{38} - 8 q^{39} + 40 q^{40} + 28 q^{41} + 6 q^{42} - 26 q^{44} + 42 q^{49} + 60 q^{50} - 36 q^{52} + 40 q^{55} - 2 q^{56} + 12 q^{57} + 52 q^{58} + 16 q^{60} + 24 q^{62} - 8 q^{63} + 16 q^{64} - 104 q^{65} + 2 q^{66} + 54 q^{68} - 48 q^{70} - 24 q^{71} + 6 q^{72} + 12 q^{73} - 22 q^{74} - 4 q^{78} + 8 q^{79} - 32 q^{80} + 18 q^{81} - 20 q^{82} + 34 q^{84} + 12 q^{87} + 10 q^{88} + 24 q^{89} - 12 q^{90} + 8 q^{92} - 56 q^{94} - 16 q^{95} - 30 q^{96} + 12 q^{97} - 48 q^{98}+O(q^{100}) \) 18 * q - 8 * q^4 + 8 * q^7 - 6 * q^8 - 18 * q^9 + 12 * q^10 - 4 * q^12 - 14 * q^14 + 8 * q^15 + 12 * q^16 - 8 * q^17 - 16 * q^20 - 30 * q^22 - 18 * q^23 + 6 * q^24 - 22 * q^25 + 8 * q^26 - 2 * q^28 + 4 * q^30 - 44 * q^31 + 10 * q^32 - 24 * q^33 + 18 * q^34 + 8 * q^36 - 20 * q^38 - 8 * q^39 + 40 * q^40 + 28 * q^41 + 6 * q^42 - 26 * q^44 + 42 * q^49 + 60 * q^50 - 36 * q^52 + 40 * q^55 - 2 * q^56 + 12 * q^57 + 52 * q^58 + 16 * q^60 + 24 * q^62 - 8 * q^63 + 16 * q^64 - 104 * q^65 + 2 * q^66 + 54 * q^68 - 48 * q^70 - 24 * q^71 + 6 * q^72 + 12 * q^73 - 22 * q^74 - 4 * q^78 + 8 * q^79 - 32 * q^80 + 18 * q^81 - 20 * q^82 + 34 * q^84 + 12 * q^87 + 10 * q^88 + 24 * q^89 - 12 * q^90 + 8 * q^92 - 56 * q^94 - 16 * q^95 - 30 * q^96 + 12 * q^97 - 48 * q^98

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