LMFDB - Embedded newform 1617.2.c.b.538.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(538,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("1617.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.c (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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			538.11
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.b.538.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.89228i q^{2} -1.00000i q^{3} -1.58073 q^{4} -1.86532i q^{5} -1.89228 q^{6} -0.793378i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.89228i q^{2} -1.00000i q^{3} -1.58073 q^{4} -1.86532i q^{5} -1.89228 q^{6} -0.793378i q^{8} -1.00000 q^{9} -3.52970 q^{10} +(-1.71180 + 2.84073i) q^{11} +1.58073i q^{12} +0.900357 q^{13} -1.86532 q^{15} -4.66275 q^{16} -4.81348 q^{17} +1.89228i q^{18} -0.291062 q^{19} +2.94856i q^{20} +(5.37546 + 3.23920i) q^{22} -3.81383 q^{23} -0.793378 q^{24} +1.52060 q^{25} -1.70373i q^{26} +1.00000i q^{27} +3.00775i q^{29} +3.52970i q^{30} -2.50172i q^{31} +7.23649i q^{32} +(2.84073 + 1.71180i) q^{33} +9.10847i q^{34} +1.58073 q^{36} -7.22078 q^{37} +0.550771i q^{38} -0.900357i q^{39} -1.47990 q^{40} -3.97302 q^{41} +8.50684i q^{43} +(2.70589 - 4.49043i) q^{44} +1.86532i q^{45} +7.21685i q^{46} -11.5117i q^{47} +4.66275i q^{48} -2.87740i q^{50} +4.81348i q^{51} -1.42322 q^{52} -10.1695 q^{53} +1.89228 q^{54} +(5.29886 + 3.19304i) q^{55} +0.291062i q^{57} +5.69150 q^{58} -8.44197i q^{59} +2.94856 q^{60} +2.88794 q^{61} -4.73395 q^{62} +4.36796 q^{64} -1.67945i q^{65} +(3.23920 - 5.37546i) q^{66} +1.24149 q^{67} +7.60881 q^{68} +3.81383i q^{69} -2.01019 q^{71} +0.793378i q^{72} +10.4505 q^{73} +13.6637i q^{74} -1.52060i q^{75} +0.460090 q^{76} -1.70373 q^{78} +1.26616i q^{79} +8.69751i q^{80} +1.00000 q^{81} +7.51808i q^{82} -10.3852 q^{83} +8.97867i q^{85} +16.0973 q^{86} +3.00775 q^{87} +(2.25377 + 1.35810i) q^{88} -12.5588i q^{89} +3.52970 q^{90} +6.02864 q^{92} -2.50172 q^{93} -21.7835 q^{94} +0.542923i q^{95} +7.23649 q^{96} -7.48439i q^{97} +(1.71180 - 2.84073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 64 q^{4} - 48 q^{9}+O(q^{10}) $ 48 * q - 64 * q^4 - 48 * q^9	$ 48 q - 64 q^{4} - 48 q^{9} - 16 q^{11} + 64 q^{16} + 16 q^{22} + 32 q^{23} - 80 q^{25} + 64 q^{36} - 96 q^{37} - 32 q^{44} + 64 q^{53} + 48 q^{58} - 48 q^{60} - 240 q^{64} + 96 q^{67} - 32 q^{71} + 48 q^{78} + 48 q^{81} - 96 q^{86} - 48 q^{88} - 32 q^{92} + 96 q^{93} + 16 q^{99}+O(q^{100}) $ 48 * q - 64 * q^4 - 48 * q^9 - 16 * q^11 + 64 * q^16 + 16 * q^22 + 32 * q^23 - 80 * q^25 + 64 * q^36 - 96 * q^37 - 32 * q^44 + 64 * q^53 + 48 * q^58 - 48 * q^60 - 240 * q^64 + 96 * q^67 - 32 * q^71 + 48 * q^78 + 48 * q^81 - 96 * q^86 - 48 * q^88 - 32 * q^92 + 96 * q^93 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1617\mathbb{Z}\right)^\times$.

$n$	$199$	$442$	$1079$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.89228i		−	1.33805i	−0.743242	−	0.669023i	$-0.766713\pi$
$2$		−	1.89228i		−	1.33805i	0.743242	−	0.669023i	$-0.233287\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.58073			−0.790365
$5$		−	1.86532i		−	0.834195i	−0.908862	−	0.417097i	$-0.863047\pi$
$5$		−	1.86532i		−	0.834195i	0.908862	−	0.417097i	$-0.136953\pi$
$6$	−1.89228			−0.772521
$7$		0			0
$7$		0			0
$8$		−	0.793378i		−	0.280502i
$9$	−1.00000			−0.333333
$10$	−3.52970			−1.11619
$11$	−1.71180	+	2.84073i	−0.516126	+	0.856513i
$11$	−1.71180	+	2.84073i	−0.516126	+	0.856513i
$12$			1.58073i			0.456317i
$13$	0.900357			0.249714			0.124857	−	0.992175i	$-0.460153\pi$
$13$	0.900357			0.249714			0.124857	+	0.992175i	$0.460153\pi$
$14$		0			0
$15$	−1.86532			−0.481623
$16$	−4.66275			−1.16569
$17$	−4.81348			−1.16744			−0.583721	−	0.811955i	$-0.698404\pi$
$17$	−4.81348			−1.16744			−0.583721	+	0.811955i	$0.698404\pi$
$18$			1.89228i			0.446015i
$19$	−0.291062			−0.0667742			−0.0333871	−	0.999442i	$-0.510629\pi$
$19$	−0.291062			−0.0667742			−0.0333871	+	0.999442i	$0.510629\pi$
$20$			2.94856i			0.659318i
$21$		0			0
$22$	5.37546	+	3.23920i	1.14605	+	0.690600i
$23$	−3.81383			−0.795239			−0.397620	−	0.917550i	$-0.630164\pi$
$23$	−3.81383			−0.795239			−0.397620	+	0.917550i	$0.630164\pi$
$24$	−0.793378			−0.161948
$25$	1.52060			0.304119
$26$		−	1.70373i		−	0.334129i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			3.00775i			0.558525i	0.960215	+	0.279262i	$0.0900899\pi$
$29$			3.00775i			0.558525i	−0.960215	+	0.279262i	$0.909910\pi$
$30$			3.52970i			0.644433i
$31$		−	2.50172i		−	0.449321i	−0.974437	−	0.224661i	$-0.927873\pi$
$31$		−	2.50172i		−	0.449321i	0.974437	−	0.224661i	$-0.0721274\pi$
$32$			7.23649i			1.27924i
$33$	2.84073	+	1.71180i	0.494508	+	0.297985i
$34$			9.10847i			1.56209i
$35$		0			0
$36$	1.58073			0.263455
$37$	−7.22078			−1.18709			−0.593544	−	0.804801i	$-0.702272\pi$
$37$	−7.22078			−1.18709			−0.593544	+	0.804801i	$0.702272\pi$
$38$			0.550771i			0.0893469i
$39$		−	0.900357i		−	0.144173i
$40$	−1.47990			−0.233993
$41$	−3.97302			−0.620482			−0.310241	−	0.950658i	$-0.600410\pi$
$41$	−3.97302			−0.620482			−0.310241	+	0.950658i	$0.600410\pi$
$42$		0			0
$43$			8.50684i			1.29728i	0.761095	+	0.648640i	$0.224662\pi$
$43$			8.50684i			1.29728i	−0.761095	+	0.648640i	$0.775338\pi$
$44$	2.70589	−	4.49043i	0.407928	−	0.676957i
$45$			1.86532i			0.278065i
$46$			7.21685i			1.06407i
$47$		−	11.5117i		−	1.67916i	−0.543236	−	0.839580i	$-0.682801\pi$
$47$		−	11.5117i		−	1.67916i	0.543236	−	0.839580i	$-0.317199\pi$
$48$			4.66275i			0.673011i
$49$		0			0
$50$		−	2.87740i		−	0.406925i
$51$			4.81348i			0.674022i
$52$	−1.42322			−0.197365
$53$	−10.1695			−1.39689			−0.698445	−	0.715664i	$-0.746124\pi$
$53$	−10.1695			−1.39689			−0.698445	+	0.715664i	$0.746124\pi$
$54$	1.89228			0.257507
$55$	5.29886	+	3.19304i	0.714498	+	0.430550i
$56$		0			0
$57$			0.291062i			0.0385521i
$58$	5.69150			0.747331
$59$		−	8.44197i		−	1.09905i	−0.835477	−	0.549526i	$-0.814808\pi$
$59$		−	8.44197i		−	1.09905i	0.835477	−	0.549526i	$-0.185192\pi$
$60$	2.94856			0.380657
$61$	2.88794			0.369762			0.184881	−	0.982761i	$-0.440810\pi$
$61$	2.88794			0.369762			0.184881	+	0.982761i	$0.440810\pi$
$62$	−4.73395			−0.601212
$63$		0			0
$64$	4.36796			0.545995
$65$		−	1.67945i		−	0.208310i
$66$	3.23920	−	5.37546i	0.398718	−	0.661674i
$67$	1.24149			0.151672			0.0758359	−	0.997120i	$-0.475837\pi$
$67$	1.24149			0.151672			0.0758359	+	0.997120i	$0.475837\pi$
$68$	7.60881			0.922704
$69$			3.81383i			0.459132i
$70$		0			0
$71$	−2.01019			−0.238566			−0.119283	−	0.992860i	$-0.538060\pi$
$71$	−2.01019			−0.238566			−0.119283	+	0.992860i	$0.538060\pi$
$72$			0.793378i			0.0935005i
$73$	10.4505			1.22313			0.611566	−	0.791193i	$-0.290540\pi$
$73$	10.4505			1.22313			0.611566	+	0.791193i	$0.290540\pi$
$74$			13.6637i			1.58838i
$75$		−	1.52060i		−	0.175583i
$76$	0.460090			0.0527760
$77$		0			0
$78$	−1.70373			−0.192909
$79$			1.26616i			0.142454i	0.997460	+	0.0712269i	$0.0226914\pi$
$79$			1.26616i			0.142454i	−0.997460	+	0.0712269i	$0.977309\pi$
$80$			8.69751i			0.972411i
$81$	1.00000			0.111111
$82$			7.51808i			0.830233i
$83$	−10.3852			−1.13993			−0.569963	−	0.821670i	$-0.693043\pi$
$83$	−10.3852			−1.13993			−0.569963	+	0.821670i	$0.693043\pi$
$84$		0			0
$85$			8.97867i			0.973873i
$86$	16.0973			1.73582
$87$	3.00775			0.322464
$88$	2.25377	+	1.35810i	0.240253	+	0.144774i
$89$		−	12.5588i		−	1.33123i	−0.746297	−	0.665613i	$-0.768170\pi$
$89$		−	12.5588i		−	1.33123i	0.746297	−	0.665613i	$-0.231830\pi$
$90$	3.52970			0.372063
$91$		0			0
$92$	6.02864			0.628529
$93$	−2.50172			−0.259416
$94$	−21.7835			−2.24679
$95$			0.542923i			0.0557027i
$96$	7.23649			0.738571
$97$		−	7.48439i		−	0.759925i	−0.925002	−	0.379962i	$-0.875937\pi$
$97$		−	7.48439i		−	0.759925i	0.925002	−	0.379962i	$-0.124063\pi$
$98$		0			0
$99$	1.71180	−	2.84073i	0.172042	−	0.285504i
$100$	−2.40365			−0.240365
$101$	9.11063			0.906541			0.453271	−	0.891373i	$-0.350257\pi$
$101$	9.11063			0.906541			0.453271	+	0.891373i	$0.350257\pi$
$102$	9.10847			0.901872
$103$			5.61955i			0.553711i	0.960912	+	0.276855i	$0.0892923\pi$
$103$			5.61955i			0.553711i	−0.960912	+	0.276855i	$0.910708\pi$
$104$		−	0.714324i		−	0.0700452i
$105$		0			0
$106$			19.2436i			1.86910i
$107$			15.5448i			1.50278i	0.659861	+	0.751388i	$0.270615\pi$
$107$			15.5448i			1.50278i	−0.659861	+	0.751388i	$0.729385\pi$
$108$		−	1.58073i		−	0.152106i
$109$		−	12.4535i		−	1.19283i	−0.802678	−	0.596413i	$-0.796592\pi$
$109$		−	12.4535i		−	1.19283i	0.802678	−	0.596413i	$-0.203408\pi$
$110$	6.04213	−	10.0269i	0.576095	−	0.956031i
$111$			7.22078i			0.685366i
$112$		0			0
$113$	14.8389			1.39593			0.697964	−	0.716133i	$-0.254090\pi$
$113$	14.8389			1.39593			0.697964	+	0.716133i	$0.254090\pi$
$114$	0.550771			0.0515845
$115$			7.11401i			0.663384i
$116$		−	4.75443i		−	0.441438i
$117$	−0.900357			−0.0832381
$118$	−15.9746			−1.47058
$119$		0			0
$120$			1.47990i			0.135096i
$121$	−5.13951	−	9.72551i	−0.467228	−	0.884137i
$122$		−	5.46479i		−	0.494759i
$123$			3.97302i			0.358236i
$124$			3.95453i			0.355128i
$125$		−	12.1630i		−	1.08789i
$126$		0			0
$127$			6.93333i			0.615234i	0.951510	+	0.307617i	$0.0995315\pi$
$127$			6.93333i			0.615234i	−0.951510	+	0.307617i	$0.900468\pi$
$128$			6.20756i			0.548676i
$129$	8.50684			0.748985
$130$	−3.17799			−0.278729
$131$	−8.38789			−0.732853			−0.366427	−	0.930447i	$-0.619419\pi$
$131$	−8.38789			−0.732853			−0.366427	+	0.930447i	$0.619419\pi$
$132$	−4.49043	−	2.70589i	−0.390842	−	0.235517i
$133$		0			0
$134$		−	2.34924i		−	0.202944i
$135$	1.86532			0.160541
$136$			3.81891i			0.327469i
$137$	11.3137			0.966591			0.483296	−	0.875457i	$-0.339440\pi$
$137$	11.3137			0.966591			0.483296	+	0.875457i	$0.339440\pi$
$138$	7.21685			0.614339
$139$	0.754620			0.0640060			0.0320030	−	0.999488i	$-0.489811\pi$
$139$	0.754620			0.0640060			0.0320030	+	0.999488i	$0.489811\pi$
$140$		0			0
$141$	−11.5117			−0.969463
$142$			3.80385i			0.319212i
$143$	−1.54123	+	2.55767i	−0.128884	+	0.213883i
$144$	4.66275			0.388563
$145$	5.61040			0.465918
$146$		−	19.7752i		−	1.63661i
$147$		0			0
$148$	11.4141			0.938232
$149$		−	21.0369i		−	1.72341i	−0.507412	−	0.861704i	$-0.669398\pi$
$149$		−	21.0369i		−	1.72341i	0.507412	−	0.861704i	$-0.330602\pi$
$150$	−2.87740			−0.234938
$151$		−	20.7068i		−	1.68510i	−0.538619	−	0.842549i	$-0.681054\pi$
$151$		−	20.7068i		−	1.68510i	0.538619	−	0.842549i	$-0.318946\pi$
$152$			0.230922i			0.0187303i
$153$	4.81348			0.389147
$154$		0			0
$155$	−4.66649			−0.374822
$156$			1.42322i			0.113949i
$157$			16.8380i			1.34382i	0.740633	+	0.671909i	$0.234526\pi$
$157$			16.8380i			1.34382i	−0.740633	+	0.671909i	$0.765474\pi$
$158$	2.39593			0.190610
$159$			10.1695i			0.806495i
$160$	13.4983			1.06714
$161$		0			0
$162$		−	1.89228i		−	0.148672i
$163$	4.95538			0.388136			0.194068	−	0.980988i	$-0.437832\pi$
$163$	4.95538			0.388136			0.194068	+	0.980988i	$0.437832\pi$
$164$	6.28028			0.490407
$165$	3.19304	−	5.29886i	0.248578	−	0.412516i
$166$			19.6518i			1.52527i
$167$	−12.5317			−0.969730			−0.484865	−	0.874589i	$-0.661131\pi$
$167$	−12.5317			−0.969730			−0.484865	+	0.874589i	$0.661131\pi$
$168$		0			0
$169$	−12.1894			−0.937643
$170$	16.9902			1.30309
$171$	0.291062			0.0222581
$172$		−	13.4470i		−	1.02532i
$173$	−8.16807			−0.621007			−0.310503	−	0.950572i	$-0.600498\pi$
$173$	−8.16807			−0.621007			−0.310503	+	0.950572i	$0.600498\pi$
$174$		−	5.69150i		−	0.431472i
$175$		0			0
$176$	7.98168	−	13.2456i	0.601642	−	0.998427i
$177$	−8.44197			−0.634538
$178$	−23.7647			−1.78124
$179$	9.70118			0.725100			0.362550	−	0.931964i	$-0.381906\pi$
$179$	9.70118			0.725100			0.362550	+	0.931964i	$0.381906\pi$
$180$		−	2.94856i		−	0.219773i
$181$		−	2.49983i		−	0.185811i	−0.995675	−	0.0929054i	$-0.970385\pi$
$181$		−	2.49983i		−	0.185811i	0.995675	−	0.0929054i	$-0.0296154\pi$
$182$		0			0
$183$		−	2.88794i		−	0.213482i
$184$			3.02581i			0.223066i
$185$			13.4690i			0.990263i
$186$			4.73395i			0.347110i
$187$	8.23970	−	13.6738i	0.602547	−	0.999928i
$188$			18.1969i			1.32715i
$189$		0			0
$190$	1.02736			0.0745327
$191$	−10.5423			−0.762813			−0.381407	−	0.924407i	$-0.624560\pi$
$191$	−10.5423			−0.762813			−0.381407	+	0.924407i	$0.624560\pi$
$192$		−	4.36796i		−	0.315230i
$193$		−	0.969897i		−	0.0698147i	−0.999391	−	0.0349074i	$-0.988886\pi$
$193$		−	0.969897i		−	0.0698147i	0.999391	−	0.0349074i	$-0.0111136\pi$
$194$	−14.1626			−1.01681
$195$	−1.67945			−0.120268
$196$		0			0
$197$			15.8674i			1.13051i	0.824917	+	0.565254i	$0.191222\pi$
$197$			15.8674i			1.13051i	−0.824917	+	0.565254i	$0.808778\pi$
$198$	−5.37546	−	3.23920i	−0.382018	−	0.230200i
$199$			12.3524i			0.875636i	0.899064	+	0.437818i	$0.144249\pi$
$199$			12.3524i			0.875636i	−0.899064	+	0.437818i	$0.855751\pi$
$200$		−	1.20641i		−	0.0853059i
$201$		−	1.24149i		−	0.0875678i
$202$		−	17.2399i		−	1.21299i
$203$		0			0
$204$		−	7.60881i		−	0.532724i
$205$			7.41095i			0.517603i
$206$	10.6338			0.740890
$207$	3.81383			0.265080
$208$	−4.19814			−0.291089
$209$	0.498239	−	0.826829i	0.0344639	−	0.0571930i
$210$		0			0
$211$		−	18.1000i		−	1.24606i	−0.782199	−	0.623029i	$-0.785902\pi$
$211$		−	18.1000i		−	1.24606i	0.782199	−	0.623029i	$-0.214098\pi$
$212$	16.0753			1.10405
$213$			2.01019i			0.137736i
$214$	29.4152			2.01078
$215$	15.8679			1.08218
$216$	0.793378			0.0539826
$217$		0			0
$218$	−23.5655			−1.59606
$219$		−	10.4505i		−	0.706176i
$220$	−8.37607	−	5.04733i	−0.564714	−	0.340291i
$221$	−4.33385			−0.291527
$222$	13.6637			0.917050
$223$			8.47667i			0.567640i	0.958878	+	0.283820i	$0.0916017\pi$
$223$			8.47667i			0.567640i	−0.958878	+	0.283820i	$0.908398\pi$
$224$		0			0
$225$	−1.52060			−0.101373
$226$		−	28.0794i		−	1.86781i
$227$	29.3584			1.94858			0.974291	−	0.225291i	$-0.0723334\pi$
$227$	29.3584			1.94858			0.974291	+	0.225291i	$0.0723334\pi$
$228$		−	0.460090i		−	0.0304702i
$229$		−	3.71748i		−	0.245658i	−0.992428	−	0.122829i	$-0.960803\pi$
$229$		−	3.71748i		−	0.245658i	0.992428	−	0.122829i	$-0.0391967\pi$
$230$	13.4617			0.887638
$231$		0			0
$232$	2.38628			0.156667
$233$		−	22.4024i		−	1.46763i	−0.679348	−	0.733816i	$-0.737737\pi$
$233$		−	22.4024i		−	1.46763i	0.679348	−	0.733816i	$-0.262263\pi$
$234$			1.70373i			0.111376i
$235$	−21.4730			−1.40075
$236$			13.3445i			0.868651i
$237$	1.26616			0.0822457
$238$		0			0
$239$			0.435991i			0.0282019i	0.999901	+	0.0141010i	$0.00448862\pi$
$239$			0.435991i			0.0282019i	−0.999901	+	0.0141010i	$0.995511\pi$
$240$	8.69751			0.561422
$241$	−21.0825			−1.35805			−0.679023	−	0.734117i	$-0.737596\pi$
$241$	−21.0825			−1.35805			−0.679023	+	0.734117i	$0.737596\pi$
$242$	−18.4034	+	9.72540i	−1.18301	+	0.625172i
$243$		−	1.00000i		−	0.0641500i
$244$	−4.56505			−0.292247
$245$		0			0
$246$	7.51808			0.479335
$247$	−0.262060			−0.0166745
$248$	−1.98481			−0.126035
$249$			10.3852i			0.658137i
$250$	−23.0158			−1.45564
$251$		−	19.8562i		−	1.25331i	−0.779297	−	0.626655i	$-0.784424\pi$
$251$		−	19.8562i		−	1.25331i	0.779297	−	0.626655i	$-0.215576\pi$
$252$		0			0
$253$	6.52851	−	10.8341i	0.410444	−	0.681133i
$254$	13.1198			0.823211
$255$	8.97867			0.562266
$256$	20.4824			1.28015
$257$			6.88940i			0.429749i	0.976642	+	0.214874i	$0.0689342\pi$
$257$			6.88940i			0.429749i	−0.976642	+	0.214874i	$0.931066\pi$
$258$		−	16.0973i		−	1.00218i
$259$		0			0
$260$			2.65476i			0.164641i
$261$		−	3.00775i		−	0.186175i
$262$			15.8722i			0.980591i
$263$			0.801816i			0.0494421i	0.999694	+	0.0247211i	$0.00786976\pi$
$263$			0.801816i			0.0494421i	−0.999694	+	0.0247211i	$0.992130\pi$
$264$	1.35810	−	2.25377i	0.0835854	−	0.138710i
$265$			18.9694i			1.16528i
$266$		0			0
$267$	−12.5588			−0.768583
$268$	−1.96246			−0.119876
$269$		−	18.2436i		−	1.11233i	−0.831071	−	0.556166i	$-0.812272\pi$
$269$		−	18.2436i		−	1.11233i	0.831071	−	0.556166i	$-0.187728\pi$
$270$		−	3.52970i		−	0.214811i
$271$	−26.2689			−1.59572			−0.797862	−	0.602840i	$-0.794036\pi$
$271$	−26.2689			−1.59572			−0.797862	+	0.602840i	$0.794036\pi$
$272$	22.4441			1.36087
$273$		0			0
$274$		−	21.4086i		−	1.29334i
$275$	−2.60295	+	4.31960i	−0.156964	+	0.260482i
$276$		−	6.02864i		−	0.362881i
$277$		−	12.1096i		−	0.727598i	−0.931478	−	0.363799i	$-0.881480\pi$
$277$		−	12.1096i		−	0.727598i	0.931478	−	0.363799i	$-0.118520\pi$
$278$		−	1.42795i		−	0.0856429i
$279$			2.50172i			0.149774i
$280$		0			0
$281$		−	17.8968i		−	1.06763i	−0.845601	−	0.533816i	$-0.820758\pi$
$281$		−	17.8968i		−	1.06763i	0.845601	−	0.533816i	$-0.179242\pi$
$282$			21.7835i			1.29719i
$283$	18.6424			1.10817			0.554087	−	0.832458i	$-0.313067\pi$
$283$	18.6424			1.10817			0.554087	+	0.832458i	$0.313067\pi$
$284$	3.17757			0.188554
$285$	0.542923			0.0321600
$286$	4.83984	+	2.91644i	0.286186	+	0.172453i
$287$		0			0
$288$		−	7.23649i		−	0.426414i
$289$	6.16962			0.362919
$290$		−	10.6165i		−	0.623420i
$291$	−7.48439			−0.438743
$292$	−16.5193			−0.966721
$293$	−29.3389			−1.71400			−0.857000	−	0.515317i	$-0.827674\pi$
$293$	−29.3389			−1.71400			−0.857000	+	0.515317i	$0.827674\pi$
$294$		0			0
$295$	−15.7469			−0.916823
$296$			5.72881i			0.332980i
$297$	−2.84073	−	1.71180i	−0.164836	−	0.0993285i
$298$	−39.8077			−2.30600
$299$	−3.43381			−0.198583
$300$			2.40365i			0.138775i
$301$		0			0
$302$	−39.1832			−2.25474
$303$		−	9.11063i		−	0.523392i
$304$	1.35715			0.0778379
$305$		−	5.38691i		−	0.308454i
$306$		−	9.10847i		−	0.520696i
$307$	−29.1807			−1.66543			−0.832714	−	0.553703i	$-0.813214\pi$
$307$	−29.1807			−1.66543			−0.832714	+	0.553703i	$0.813214\pi$
$308$		0			0
$309$	5.61955			0.319685
$310$			8.83031i			0.501528i
$311$		−	1.25309i		−	0.0710561i	−0.999369	−	0.0355281i	$-0.988689\pi$
$311$		−	1.25309i		−	0.0710561i	0.999369	−	0.0355281i	$-0.0113113\pi$
$312$	−0.714324			−0.0404406
$313$			11.8927i			0.672215i	0.941824	+	0.336108i	$0.109111\pi$
$313$			11.8927i			0.672215i	−0.941824	+	0.336108i	$0.890889\pi$
$314$	31.8622			1.79809
$315$		0			0
$316$		−	2.00145i		−	0.112590i
$317$	−33.3231			−1.87161			−0.935807	−	0.352512i	$-0.885328\pi$
$317$	−33.3231			−1.87161			−0.935807	+	0.352512i	$0.885328\pi$
$318$	19.2436			1.07913
$319$	−8.54420	−	5.14865i	−0.478383	−	0.288269i
$320$		−	8.14763i		−	0.455466i
$321$	15.5448			0.867628
$322$		0			0
$323$	1.40102			0.0779550
$324$	−1.58073			−0.0878183
$325$	1.36908			0.0759429
$326$		−	9.37698i		−	0.519343i
$327$	−12.4535			−0.688679
$328$			3.15211i			0.174046i
$329$		0			0
$330$	−10.0269	−	6.04213i	−0.551965	−	0.332608i
$331$	−8.96904			−0.492983			−0.246492	−	0.969145i	$-0.579278\pi$
$331$	−8.96904			−0.492983			−0.246492	+	0.969145i	$0.579278\pi$
$332$	16.4162			0.900957
$333$	7.22078			0.395696
$334$			23.7134i			1.29754i
$335$		−	2.31577i		−	0.126524i
$336$		0			0
$337$			29.8245i			1.62464i	0.583210	+	0.812321i	$0.301796\pi$
$337$			29.8245i			1.62464i	−0.583210	+	0.812321i	$0.698204\pi$
$338$			23.0657i			1.25461i
$339$		−	14.8389i		−	0.805939i
$340$		−	14.1928i		−	0.769715i
$341$	7.10670	+	4.28243i	0.384849	+	0.231906i
$342$		−	0.550771i		−	0.0297823i
$343$		0			0
$344$	6.74914			0.363889
$345$	7.11401			0.383005
$346$			15.4563i			0.830935i
$347$			8.77073i			0.470837i	0.971894	+	0.235419i	$0.0756461\pi$
$347$			8.77073i			0.470837i	−0.971894	+	0.235419i	$0.924354\pi$
$348$	−4.75443			−0.254864
$349$	7.34311			0.393067			0.196534	−	0.980497i	$-0.437031\pi$
$349$	7.34311			0.393067			0.196534	+	0.980497i	$0.437031\pi$
$350$		0			0
$351$			0.900357i			0.0480575i
$352$	−20.5569	−	12.3874i	−1.09569	−	0.660250i
$353$		−	24.2404i		−	1.29019i	−0.764103	−	0.645094i	$-0.776818\pi$
$353$		−	24.2404i		−	1.29019i	0.764103	−	0.645094i	$-0.223182\pi$
$354$			15.9746i			0.849040i
$355$			3.74964i			0.199010i
$356$			19.8520i			1.05215i
$357$		0			0
$358$		−	18.3574i		−	0.970217i
$359$			37.0753i			1.95676i	0.206814	+	0.978380i	$0.433690\pi$
$359$			37.0753i			1.95676i	−0.206814	+	0.978380i	$0.566310\pi$
$360$	1.47990			0.0779977
$361$	−18.9153			−0.995541
$362$	−4.73038			−0.248623
$363$	−9.72551	+	5.13951i	−0.510457	+	0.269754i
$364$		0			0
$365$		−	19.4934i		−	1.02033i
$366$	−5.46479			−0.285649
$367$		−	29.9810i		−	1.56499i	−0.622655	−	0.782497i	$-0.713946\pi$
$367$		−	29.9810i		−	1.56499i	0.622655	−	0.782497i	$-0.286054\pi$
$368$	17.7830			0.927001
$369$	3.97302			0.206827
$370$	25.4872			1.32502
$371$		0			0
$372$	3.95453			0.205033
$373$			21.2178i			1.09862i	0.835620	+	0.549309i	$0.185109\pi$
$373$			21.2178i			1.09862i	−0.835620	+	0.549309i	$0.814891\pi$
$374$	−25.8747	−	15.5918i	−1.33795	−	0.806235i
$375$	−12.1630			−0.628093
$376$	−9.13316			−0.471007
$377$			2.70805i			0.139472i
$378$		0			0
$379$	28.1686			1.44692			0.723462	−	0.690364i	$-0.242550\pi$
$379$	28.1686			1.44692			0.723462	+	0.690364i	$0.242550\pi$
$380$		−	0.858214i		−	0.0440254i
$381$	6.93333			0.355205
$382$			19.9490i			1.02068i
$383$			37.8485i			1.93397i	0.254834	+	0.966985i	$0.417979\pi$
$383$			37.8485i			1.93397i	−0.254834	+	0.966985i	$0.582021\pi$
$384$	6.20756			0.316778
$385$		0			0
$386$	−1.83532			−0.0934152
$387$		−	8.50684i		−	0.432427i
$388$			11.8308i			0.600618i
$389$	3.58172			0.181600			0.0908002	−	0.995869i	$-0.471058\pi$
$389$	3.58172			0.181600			0.0908002	+	0.995869i	$0.471058\pi$
$390$			3.17799i			0.160924i
$391$	18.3578			0.928395
$392$		0			0
$393$			8.38789i			0.423113i
$394$	30.0257			1.51267
$395$	2.36178			0.118834
$396$	−2.70589	+	4.49043i	−0.135976	+	0.225652i
$397$		−	21.5924i		−	1.08369i	−0.840479	−	0.541845i	$-0.817726\pi$
$397$		−	21.5924i		−	1.08369i	0.840479	−	0.541845i	$-0.182274\pi$
$398$	23.3741			1.17164
$399$		0			0
$400$	−7.09016			−0.354508
$401$	−12.6601			−0.632214			−0.316107	−	0.948724i	$-0.602376\pi$
$401$	−12.6601			−0.632214			−0.316107	+	0.948724i	$0.602376\pi$
$402$	−2.34924			−0.117170
$403$		−	2.25244i		−	0.112202i
$404$	−14.4014			−0.716498
$405$		−	1.86532i		−	0.0926883i
$406$		0			0
$407$	12.3605	−	20.5123i	0.612687	−	1.01676i
$408$	3.81891			0.189064
$409$	−32.9108			−1.62734			−0.813668	−	0.581330i	$-0.802533\pi$
$409$	−32.9108			−1.62734			−0.813668	+	0.581330i	$0.802533\pi$
$410$	14.0236			0.692576
$411$		−	11.3137i		−	0.558062i
$412$		−	8.88299i		−	0.437633i
$413$		0			0
$414$		−	7.21685i		−	0.354689i
$415$			19.3717i			0.950921i
$416$			6.51542i			0.319445i
$417$		−	0.754620i		−	0.0369539i
$418$	−1.56459	−	0.942808i	−0.0765268	−	0.0461143i
$419$			21.6747i			1.05888i	0.848348	+	0.529439i	$0.177598\pi$
$419$			21.6747i			1.05888i	−0.848348	+	0.529439i	$0.822402\pi$
$420$		0			0
$421$	−22.7158			−1.10710			−0.553551	−	0.832816i	$-0.686727\pi$
$421$	−22.7158			−1.10710			−0.553551	+	0.832816i	$0.686727\pi$
$422$	−34.2504			−1.66728
$423$			11.5117i			0.559720i
$424$			8.06827i			0.391830i
$425$	−7.31936			−0.355041
$426$	3.80385			0.184297
$427$		0			0
$428$		−	24.5722i		−	1.18774i
$429$	2.55767	+	1.54123i	0.123486	+	0.0744112i
$430$		−	30.0266i		−	1.44801i
$431$		−	18.0018i		−	0.867117i	−0.901125	−	0.433558i	$-0.857258\pi$
$431$		−	18.0018i		−	0.867117i	0.901125	−	0.433558i	$-0.142742\pi$
$432$		−	4.66275i		−	0.224337i
$433$		−	6.83243i		−	0.328345i	−0.986432	−	0.164173i	$-0.947505\pi$
$433$		−	6.83243i		−	0.328345i	0.986432	−	0.164173i	$-0.0524954\pi$
$434$		0			0
$435$		−	5.61040i		−	0.268998i
$436$			19.6856i			0.942768i
$437$	1.11006			0.0531015
$438$	−19.7752			−0.944895
$439$	1.47898			0.0705881			0.0352940	−	0.999377i	$-0.488763\pi$
$439$	1.47898			0.0705881			0.0352940	+	0.999377i	$0.488763\pi$
$440$	2.53329	−	4.20400i	0.120770	−	0.200418i
$441$		0			0
$442$			8.20087i			0.390076i
$443$	13.3647			0.634976			0.317488	−	0.948262i	$-0.397161\pi$
$443$	13.3647			0.634976			0.317488	+	0.948262i	$0.397161\pi$
$444$		−	11.4141i		−	0.541689i
$445$	−23.4261			−1.11050
$446$	16.0402			0.759527
$447$	−21.0369			−0.995010
$448$		0			0
$449$	14.0478			0.662957			0.331478	−	0.943463i	$-0.392453\pi$
$449$	14.0478			0.662957			0.331478	+	0.943463i	$0.392453\pi$
$450$			2.87740i			0.135642i
$451$	6.80101	−	11.2863i	0.320247	−	0.531451i
$452$	−23.4563			−1.10329
$453$	−20.7068			−0.972892
$454$		−	55.5543i		−	2.60729i
$455$		0			0
$456$	0.230922			0.0108139
$457$		−	25.3107i		−	1.18398i	−0.805944	−	0.591992i	$-0.798342\pi$
$457$		−	25.3107i		−	1.18398i	0.805944	−	0.591992i	$-0.201658\pi$
$458$	−7.03453			−0.328702
$459$		−	4.81348i		−	0.224674i
$460$		−	11.2453i		−	0.524316i
$461$	5.13785			0.239294			0.119647	−	0.992817i	$-0.461824\pi$
$461$	5.13785			0.239294			0.119647	+	0.992817i	$0.461824\pi$
$462$		0			0
$463$	−6.89525			−0.320450			−0.160225	−	0.987081i	$-0.551222\pi$
$463$	−6.89525			−0.320450			−0.160225	+	0.987081i	$0.551222\pi$
$464$		−	14.0244i		−	0.651066i
$465$			4.66649i			0.216403i
$466$	−42.3917			−1.96376
$467$		−	5.21936i		−	0.241523i	−0.992682	−	0.120762i	$-0.961466\pi$
$467$		−	5.21936i		−	0.241523i	0.992682	−	0.120762i	$-0.0385337\pi$
$468$	1.42322			0.0657884
$469$		0			0
$470$			40.6330i			1.87426i
$471$	16.8380			0.775854
$472$	−6.69768			−0.308286
$473$	−24.1656	−	14.5620i	−1.11114	−	0.669560i
$474$		−	2.39593i		−	0.110048i
$475$	−0.442588			−0.0203073
$476$		0			0
$477$	10.1695			0.465630
$478$	0.825018			0.0377354
$479$	−26.2295			−1.19846			−0.599229	−	0.800578i	$-0.704526\pi$
$479$	−26.2295			−1.19846			−0.599229	+	0.800578i	$0.704526\pi$
$480$		−	13.4983i		−	0.616112i
$481$	−6.50128			−0.296433
$482$			39.8941i			1.81713i
$483$		0			0
$484$	8.12417	+	15.3734i	0.369281	+	0.698790i
$485$	−13.9608			−0.633925
$486$	−1.89228			−0.0858356
$487$	−3.28038			−0.148648			−0.0743242	−	0.997234i	$-0.523680\pi$
$487$	−3.28038			−0.148648			−0.0743242	+	0.997234i	$0.523680\pi$
$488$		−	2.29123i		−	0.103719i
$489$		−	4.95538i		−	0.224090i
$490$		0			0
$491$		−	12.2540i		−	0.553014i	−0.961012	−	0.276507i	$-0.910823\pi$
$491$		−	12.2540i		−	0.553014i	0.961012	−	0.276507i	$-0.0891769\pi$
$492$		−	6.28028i		−	0.283137i
$493$		−	14.4777i		−	0.652045i
$494$			0.495891i			0.0223112i
$495$	−5.29886	−	3.19304i	−0.238166	−	0.143517i
$496$			11.6649i			0.523769i
$497$		0			0
$498$	19.6518			0.880617
$499$	24.9826			1.11838			0.559188	−	0.829041i	$-0.311113\pi$
$499$	24.9826			1.11838			0.559188	+	0.829041i	$0.311113\pi$
$500$			19.2264i			0.859829i
$501$			12.5317i			0.559874i
$502$	−37.5734			−1.67698
$503$	9.82296			0.437984			0.218992	−	0.975727i	$-0.429723\pi$
$503$	9.82296			0.437984			0.218992	+	0.975727i	$0.429723\pi$
$504$		0			0
$505$		−	16.9942i		−	0.756232i
$506$	−20.5011	−	12.3538i	−0.911386	−	0.549192i
$507$			12.1894i			0.541348i
$508$		−	10.9597i		−	0.486259i
$509$			13.4187i			0.594773i	0.954757	+	0.297386i	$0.0961149\pi$
$509$			13.4187i			0.594773i	−0.954757	+	0.297386i	$0.903885\pi$
$510$		−	16.9902i		−	0.752337i
$511$		0			0
$512$		−	26.3433i		−	1.16422i
$513$		−	0.291062i		−	0.0128507i
$514$	13.0367			0.575023
$515$	10.4822			0.461903
$516$	−13.4470			−0.591972
$517$	32.7018	+	19.7057i	1.43822	+	0.866658i
$518$		0			0
$519$			8.16807i			0.358538i
$520$	−1.33244			−0.0584314
$521$		−	25.5403i		−	1.11894i	−0.828850	−	0.559470i	$-0.811005\pi$
$521$		−	25.5403i		−	1.11894i	0.828850	−	0.559470i	$-0.188995\pi$
$522$	−5.69150			−0.249110
$523$	39.6024			1.73169			0.865846	−	0.500310i	$-0.166781\pi$
$523$	39.6024			1.73169			0.865846	+	0.500310i	$0.166781\pi$
$524$	13.2590			0.579221
$525$		0			0
$526$	1.51726			0.0661558
$527$			12.0420i			0.524556i
$528$	−13.2456	−	7.98168i	−0.576442	−	0.347358i
$529$	−8.45467			−0.367594
$530$	35.8954			1.55920
$531$			8.44197i			0.366350i
$532$		0			0
$533$	−3.57714			−0.154943
$534$			23.7647i			1.02840i
$535$	28.9960			1.25361
$536$		−	0.984969i		−	0.0425442i
$537$		−	9.70118i		−	0.418637i
$538$	−34.5220			−1.48835
$539$		0			0
$540$	−2.94856			−0.126886
$541$		−	16.5705i		−	0.712423i	−0.934405	−	0.356211i	$-0.884068\pi$
$541$		−	16.5705i		−	0.712423i	0.934405	−	0.356211i	$-0.115932\pi$
$542$			49.7082i			2.13515i
$543$	−2.49983			−0.107278
$544$		−	34.8327i		−	1.49344i
$545$	−23.2297			−0.995049
$546$		0			0
$547$			27.2457i			1.16494i	0.812852	+	0.582470i	$0.197914\pi$
$547$			27.2457i			1.16494i	−0.812852	+	0.582470i	$0.802086\pi$
$548$	−17.8838			−0.763960
$549$	−2.88794			−0.123254
$550$	8.17391	+	4.92551i	0.348537	+	0.210025i
$551$		−	0.875441i		−	0.0372950i
$552$	3.02581			0.128787
$553$		0			0
$554$	−22.9148			−0.973558
$555$	13.4690			0.571728
$556$	−1.19285			−0.0505881
$557$		−	15.3235i		−	0.649279i	−0.945838	−	0.324640i	$-0.894757\pi$
$557$		−	15.3235i		−	0.649279i	0.945838	−	0.324640i	$-0.105243\pi$
$558$	4.73395			0.200404
$559$			7.65919i			0.323949i
$560$		0			0
$561$	−13.6738	−	8.23970i	−0.577309	−	0.347880i
$562$	−33.8657			−1.42854
$563$	−14.5303			−0.612379			−0.306190	−	0.951971i	$-0.599054\pi$
$563$	−14.5303			−0.612379			−0.306190	+	0.951971i	$0.599054\pi$
$564$	18.1969			0.766229
$565$		−	27.6793i		−	1.16448i
$566$		−	35.2766i		−	1.48279i
$567$		0			0
$568$			1.59484i			0.0669181i
$569$		−	16.5065i		−	0.691990i	−0.938236	−	0.345995i	$-0.887541\pi$
$569$		−	16.5065i		−	0.691990i	0.938236	−	0.345995i	$-0.112459\pi$
$570$		−	1.02736i		−	0.0430315i
$571$		−	0.0805235i		−	0.00336981i	−0.999999	−	0.00168490i	$-0.999464\pi$
$571$		−	0.0805235i		−	0.00336981i	0.999999	−	0.00168490i	$-0.000536321\pi$
$572$	2.43626	−	4.04299i	0.101865	−	0.169046i
$573$			10.5423i			0.440410i
$574$		0			0
$575$	−5.79930			−0.241848
$576$	−4.36796			−0.181998
$577$			43.7298i			1.82049i	0.414065	+	0.910247i	$0.364109\pi$
$577$			43.7298i			1.82049i	−0.414065	+	0.910247i	$0.635891\pi$
$578$		−	11.6747i		−	0.485602i
$579$	−0.969897			−0.0403075
$580$	−8.86852			−0.368245
$581$		0			0
$582$			14.1626i			0.587058i
$583$	17.4081	−	28.8889i	0.720971	−	1.19645i
$584$		−	8.29116i		−	0.343091i
$585$			1.67945i			0.0694368i
$586$			55.5175i			2.29341i
$587$			30.4516i			1.25687i	0.777861	+	0.628436i	$0.216305\pi$
$587$			30.4516i			1.25687i	−0.777861	+	0.628436i	$0.783695\pi$
$588$		0			0
$589$			0.728154i			0.0300031i
$590$			29.7977i			1.22675i
$591$	15.8674			0.652699
$592$	33.6687			1.38377
$593$	23.7822			0.976616			0.488308	−	0.872671i	$-0.337614\pi$
$593$	23.7822			0.976616			0.488308	+	0.872671i	$0.337614\pi$
$594$	−3.23920	+	5.37546i	−0.132906	+	0.220558i
$595$		0			0
$596$			33.2536i			1.36212i
$597$	12.3524			0.505549
$598$			6.49774i			0.265712i
$599$	36.3159			1.48383			0.741914	−	0.670495i	$-0.233918\pi$
$599$	36.3159			1.48383			0.741914	+	0.670495i	$0.233918\pi$
$600$	−1.20641			−0.0492514
$601$	27.7374			1.13143			0.565716	−	0.824600i	$-0.308600\pi$
$601$	27.7374			1.13143			0.565716	+	0.824600i	$0.308600\pi$
$602$		0			0
$603$	−1.24149			−0.0505573
$604$			32.7319i			1.33184i
$605$	−18.1411	+	9.58681i	−0.737542	+	0.389759i
$606$	−17.2399			−0.700322
$607$	−4.34093			−0.176193			−0.0880965	−	0.996112i	$-0.528078\pi$
$607$	−4.34093			−0.176193			−0.0880965	+	0.996112i	$0.528078\pi$
$608$		−	2.10627i		−	0.0854204i
$609$		0			0
$610$	−10.1936			−0.412725
$611$		−	10.3647i		−	0.419310i
$612$	−7.60881			−0.307568
$613$		−	14.1419i		−	0.571186i	−0.958351	−	0.285593i	$-0.907810\pi$
$613$		−	14.1419i		−	0.571186i	0.958351	−	0.285593i	$-0.0921905\pi$
$614$			55.2180i			2.22842i
$615$	7.41095			0.298838
$616$		0			0
$617$	−29.2862			−1.17902			−0.589509	−	0.807762i	$-0.700679\pi$
$617$	−29.2862			−1.17902			−0.589509	+	0.807762i	$0.700679\pi$
$618$		−	10.6338i		−	0.427753i
$619$		−	26.8245i		−	1.07817i	−0.842252	−	0.539083i	$-0.818771\pi$
$619$		−	26.8245i		−	1.07817i	0.842252	−	0.539083i	$-0.181229\pi$
$620$	7.37646			0.296246
$621$		−	3.81383i		−	0.153044i
$622$	−2.37120			−0.0950763
$623$		0			0
$624$			4.19814i			0.168060i
$625$	−15.0848			−0.603392
$626$	22.5043			0.899454
$627$	−0.826829	−	0.498239i	−0.0330204	−	0.0198977i
$628$		−	26.6163i		−	1.06211i
$629$	34.7571			1.38586
$630$		0			0
$631$	33.7168			1.34225			0.671123	−	0.741346i	$-0.265812\pi$
$631$	33.7168			1.34225			0.671123	+	0.741346i	$0.265812\pi$
$632$	1.00454			0.0399585
$633$	−18.1000			−0.719412
$634$			63.0568i			2.50430i
$635$	12.9329			0.513225
$636$		−	16.0753i		−	0.637425i
$637$		0			0
$638$	−9.74269	+	16.1680i	−0.385717	+	0.640099i
$639$	2.01019			0.0795220
$640$	11.5791			0.457703
$641$	22.3914			0.884408			0.442204	−	0.896915i	$-0.354197\pi$
$641$	22.3914			0.884408			0.442204	+	0.896915i	$0.354197\pi$
$642$		−	29.4152i		−	1.16092i
$643$		−	11.5175i		−	0.454205i	−0.973871	−	0.227103i	$-0.927075\pi$
$643$		−	11.5175i		−	0.454205i	0.973871	−	0.227103i	$-0.0729253\pi$
$644$		0			0
$645$		−	15.8679i		−	0.624800i
$646$		−	2.65113i		−	0.104307i
$647$			6.78080i			0.266581i	0.991077	+	0.133290i	$0.0425543\pi$
$647$			6.78080i			0.266581i	−0.991077	+	0.133290i	$0.957446\pi$
$648$		−	0.793378i		−	0.0311668i
$649$	23.9814	+	14.4509i	0.941351	+	0.567249i
$650$		−	2.59068i		−	0.101615i
$651$		0			0
$652$	−7.83312			−0.306769
$653$	−0.898983			−0.0351799			−0.0175900	−	0.999845i	$-0.505599\pi$
$653$	−0.898983			−0.0351799			−0.0175900	+	0.999845i	$0.505599\pi$
$654$			23.5655i			0.921483i
$655$			15.6461i			0.611342i
$656$	18.5252			0.723289
$657$	−10.4505			−0.407711
$658$		0			0
$659$			25.5184i			0.994056i	0.867735	+	0.497028i	$0.165575\pi$
$659$			25.5184i			0.994056i	−0.867735	+	0.497028i	$0.834425\pi$
$660$	−5.04733	+	8.37607i	−0.196467	+	0.326038i
$661$			13.4429i			0.522867i	0.965221	+	0.261434i	$0.0841953\pi$
$661$			13.4429i			0.522867i	−0.965221	+	0.261434i	$0.915805\pi$
$662$			16.9719i			0.659633i
$663$			4.33385i			0.168313i
$664$			8.23941i			0.319751i
$665$		0			0
$666$		−	13.6637i		−	0.529459i
$667$		−	11.4710i		−	0.444161i
$668$	19.8092			0.766440
$669$	8.47667			0.327727
$670$	−4.38208			−0.169295
$671$	−4.94356	+	8.20385i	−0.190844	+	0.316706i
$672$		0			0
$673$		−	34.1336i		−	1.31575i	−0.753125	−	0.657877i	$-0.771455\pi$
$673$		−	34.1336i		−	1.31575i	0.753125	−	0.657877i	$-0.228545\pi$
$674$	56.4363			2.17384
$675$			1.52060i			0.0585278i
$676$	19.2681			0.741080
$677$	34.0026			1.30683			0.653414	−	0.757001i	$-0.273336\pi$
$677$	34.0026			1.30683			0.653414	+	0.757001i	$0.273336\pi$
$678$	−28.0794			−1.07838
$679$		0			0
$680$	7.12348			0.273173
$681$		−	29.3584i		−	1.12501i
$682$	8.10356	−	13.4479i	0.310301	−	0.514946i
$683$	−12.1953			−0.466639			−0.233320	−	0.972400i	$-0.574959\pi$
$683$	−12.1953			−0.466639			−0.233320	+	0.972400i	$0.574959\pi$
$684$	−0.460090			−0.0175920
$685$		−	21.1036i		−	0.806326i
$686$		0			0
$687$	−3.71748			−0.141831
$688$		−	39.6653i		−	1.51223i
$689$	−9.15620			−0.348823
$690$		−	13.4617i		−	0.512478i
$691$		−	40.8753i		−	1.55497i	−0.628902	−	0.777485i	$-0.716495\pi$
$691$		−	40.8753i		−	1.55497i	0.628902	−	0.777485i	$-0.283505\pi$
$692$	12.9115			0.490822
$693$		0			0
$694$	16.5967			0.630002
$695$		−	1.40760i		−	0.0533935i
$696$		−	2.38628i		−	0.0904518i
$697$	19.1241			0.724376
$698$		−	13.8952i		−	0.525942i
$699$	−22.4024			−0.847338
$700$		0			0
$701$		−	27.5002i		−	1.03867i	−0.854571	−	0.519335i	$-0.826180\pi$
$701$		−	27.5002i		−	1.03867i	0.854571	−	0.519335i	$-0.173820\pi$
$702$	1.70373			0.0643031
$703$	2.10169			0.0792669
$704$	−7.47706	+	12.4082i	−0.281802	+	0.467652i
$705$			21.4730i			0.808721i
$706$	−45.8697			−1.72633
$707$		0			0
$708$	13.3445			0.501516
$709$	51.7170			1.94227			0.971136	−	0.238526i	$-0.0766643\pi$
$709$	51.7170			1.94227			0.971136	+	0.238526i	$0.0766643\pi$
$710$	7.09538			0.266285
$711$		−	1.26616i		−	0.0474846i
$712$	−9.96384			−0.373411
$713$			9.54113i			0.357318i
$714$		0			0
$715$	4.77087	+	2.87488i	0.178420	+	0.107514i
$716$	−15.3349			−0.573093
$717$	0.435991			0.0162824
$718$	70.1569			2.61823
$719$			26.2537i			0.979098i	0.871976	+	0.489549i	$0.162839\pi$
$719$			26.2537i			0.979098i	−0.871976	+	0.489549i	$0.837161\pi$
$720$		−	8.69751i		−	0.324137i
$721$		0			0
$722$			35.7930i			1.33208i
$723$			21.0825i			0.784068i
$724$			3.95155i			0.146858i
$725$			4.57357i			0.169858i
$726$	9.72540	+	18.4034i	0.360943	+	0.683014i
$727$		−	24.8656i		−	0.922214i	−0.887345	−	0.461107i	$-0.847452\pi$
$727$		−	24.8656i		−	0.922214i	0.887345	−	0.461107i	$-0.152548\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−36.8870			−1.36525
$731$		−	40.9475i		−	1.51450i
$732$			4.56505i			0.168729i
$733$	30.3022			1.11924			0.559618	−	0.828751i	$-0.310948\pi$
$733$	30.3022			1.11924			0.559618	+	0.828751i	$0.310948\pi$
$734$	−56.7324			−2.09403
$735$		0			0
$736$		−	27.5988i		−	1.01730i
$737$	−2.12517	+	3.52673i	−0.0782818	+	0.129909i
$738$		−	7.51808i		−	0.276744i
$739$		−	11.0419i		−	0.406184i	−0.979160	−	0.203092i	$-0.934901\pi$
$739$		−	11.0419i		−	0.406184i	0.979160	−	0.203092i	$-0.0650990\pi$
$740$		−	21.2909i		−	0.782669i
$741$			0.262060i			0.00962701i
$742$		0			0
$743$			3.86918i			0.141946i	0.997478	+	0.0709732i	$0.0226105\pi$
$743$			3.86918i			0.141946i	−0.997478	+	0.0709732i	$0.977390\pi$
$744$			1.98481i			0.0727665i
$745$	−39.2404			−1.43766
$746$	40.1501			1.47000
$747$	10.3852			0.379975
$748$	−13.0247	+	21.6146i	−0.476232	+	0.790308i
$749$		0			0
$750$			23.0158i			0.840417i
$751$	41.9163			1.52955			0.764774	−	0.644299i	$-0.222851\pi$
$751$	41.9163			1.52955			0.764774	+	0.644299i	$0.222851\pi$
$752$			53.6764i			1.95738i
$753$	−19.8562			−0.723599
$754$	5.12439			0.186619
$755$	−38.6248			−1.40570
$756$		0			0
$757$	18.7452			0.681306			0.340653	−	0.940189i	$-0.389352\pi$
$757$	18.7452			0.681306			0.340653	+	0.940189i	$0.389352\pi$
$758$		−	53.3029i		−	1.93605i
$759$	−10.8341	−	6.52851i	−0.393252	−	0.236970i
$760$	0.430743			0.0156247
$761$	−37.7789			−1.36949			−0.684743	−	0.728785i	$-0.740085\pi$
$761$	−37.7789			−1.36949			−0.684743	+	0.728785i	$0.740085\pi$
$762$		−	13.1198i		−	0.475281i
$763$		0			0
$764$	16.6645			0.602901
$765$		−	8.97867i		−	0.324624i
$766$	71.6201			2.58774
$767$		−	7.60079i		−	0.274449i
$768$		−	20.4824i		−	0.739094i
$769$	−24.6420			−0.888613			−0.444307	−	0.895875i	$-0.646550\pi$
$769$	−24.6420			−0.888613			−0.444307	+	0.895875i	$0.646550\pi$
$770$		0			0
$771$	6.88940			0.248116
$772$			1.53314i			0.0551791i
$773$			30.5712i			1.09957i	0.835306	+	0.549785i	$0.185291\pi$
$773$			30.5712i			1.09957i	−0.835306	+	0.549785i	$0.814709\pi$
$774$	−16.0973			−0.578607
$775$		−	3.80410i		−	0.136647i
$776$	−5.93795			−0.213160
$777$		0			0
$778$		−	6.77762i		−	0.242989i
$779$	1.15640			0.0414322
$780$	2.65476			0.0950556
$781$	3.44104	−	5.71041i	0.123130	−	0.204335i
$782$		−	34.7382i		−	1.24223i
$783$	−3.00775			−0.107488
$784$		0			0
$785$	31.4082			1.12101
$786$	15.8722			0.566144
$787$	50.4683			1.79900			0.899501	−	0.436919i	$-0.143930\pi$
$787$	50.4683			1.79900			0.899501	+	0.436919i	$0.143930\pi$
$788$		−	25.0821i		−	0.893514i
$789$	0.801816			0.0285454
$790$		−	4.46916i		−	0.159006i
$791$		0			0
$792$	−2.25377	−	1.35810i	−0.0800844	−	0.0482580i
$793$	2.60017			0.0923349
$794$	−40.8588			−1.45003
$795$	18.9694			0.672774
$796$		−	19.5257i		−	0.692072i
$797$		−	28.4246i		−	1.00685i	−0.864039	−	0.503425i	$-0.832073\pi$
$797$		−	28.4246i		−	1.00685i	0.864039	−	0.503425i	$-0.167927\pi$
$798$		0			0
$799$			55.4116i			1.96032i
$800$			11.0038i			0.389042i
$801$			12.5588i			0.443742i
$802$			23.9564i			0.845931i
$803$	−17.8890	+	29.6869i	−0.631290	+	1.04763i
$804$			1.96246i			0.0692105i
$805$		0			0
$806$	−4.26225			−0.150131
$807$	−18.2436			−0.642205
$808$		−	7.22818i		−	0.254286i
$809$			17.6721i			0.621317i	0.950522	+	0.310658i	$0.100550\pi$
$809$			17.6721i			0.621317i	−0.950522	+	0.310658i	$0.899450\pi$
$810$	−3.52970			−0.124021
$811$	12.9104			0.453347			0.226673	−	0.973971i	$-0.427215\pi$
$811$	12.9104			0.453347			0.226673	+	0.973971i	$0.427215\pi$
$812$		0			0
$813$			26.2689i			0.921292i
$814$	−38.8150	−	23.3895i	−1.36047	−	0.819803i
$815$		−	9.24336i		−	0.323781i
$816$		−	22.4441i		−	0.785700i
$817$		−	2.47602i		−	0.0866249i
$818$			62.2766i			2.17745i
$819$		0			0
$820$		−	11.7147i		−	0.409095i
$821$		−	0.556628i		−	0.0194265i	−0.999953	−	0.00971323i	$-0.996908\pi$
$821$		−	0.556628i		−	0.0194265i	0.999953	−	0.00971323i	$-0.00309187\pi$
$822$	−21.4086			−0.746712
$823$	13.9163			0.485092			0.242546	−	0.970140i	$-0.422017\pi$
$823$	13.9163			0.485092			0.242546	+	0.970140i	$0.422017\pi$
$824$	4.45843			0.155317
$825$	4.31960	+	2.60295i	0.150389	+	0.0906231i
$826$		0			0
$827$			21.0494i			0.731961i	0.930623	+	0.365980i	$0.119266\pi$
$827$			21.0494i			0.731961i	−0.930623	+	0.365980i	$0.880734\pi$
$828$	−6.02864			−0.209510
$829$		−	5.33390i		−	0.185254i	−0.995701	−	0.0926270i	$-0.970474\pi$
$829$		−	5.33390i		−	0.185254i	0.995701	−	0.0926270i	$-0.0295264\pi$
$830$	36.6568			1.27237
$831$	−12.1096			−0.420079
$832$	3.93273			0.136343
$833$		0			0
$834$	−1.42795			−0.0494460
$835$			23.3755i			0.808943i
$836$	−0.787581	+	1.30699i	−0.0272390	+	0.0452033i
$837$	2.50172			0.0864719
$838$	41.0146			1.41683
$839$		−	54.9109i		−	1.89574i	−0.318665	−	0.947868i	$-0.603234\pi$
$839$		−	54.9109i		−	1.89574i	0.318665	−	0.947868i	$-0.396766\pi$
$840$		0			0
$841$	19.9535			0.688050
$842$			42.9847i			1.48135i
$843$	−17.8968			−0.616397
$844$			28.6113i			0.984840i
$845$			22.7370i			0.782177i
$846$	21.7835			0.748930
$847$		0			0
$848$	47.4179			1.62834
$849$		−	18.6424i		−	0.639805i
$850$			13.8503i			0.475061i
$851$	27.5388			0.944019
$852$		−	3.17757i		−	0.108862i
$853$	−14.7057			−0.503514			−0.251757	−	0.967791i	$-0.581008\pi$
$853$	−14.7057			−0.503514			−0.251757	+	0.967791i	$0.581008\pi$
$854$		0			0
$855$		−	0.542923i		−	0.0185676i
$856$	12.3329			0.421531
$857$	32.2496			1.10163			0.550813	−	0.834629i	$-0.314318\pi$
$857$	32.2496			1.10163			0.550813	+	0.834629i	$0.314318\pi$
$858$	2.91644	−	4.83984i	0.0995655	−	0.165229i
$859$			27.8732i			0.951021i	0.879710	+	0.475511i	$0.157737\pi$
$859$			27.8732i			0.951021i	−0.879710	+	0.475511i	$0.842263\pi$
$860$	−25.0829			−0.855321
$861$		0			0
$862$	−34.0645			−1.16024
$863$	27.3785			0.931975			0.465987	−	0.884791i	$-0.345699\pi$
$863$	27.3785			0.931975			0.465987	+	0.884791i	$0.345699\pi$
$864$	−7.23649			−0.246190
$865$			15.2360i			0.518040i
$866$	−12.9289			−0.439341
$867$		−	6.16962i		−	0.209531i
$868$		0			0
$869$	−3.59681	−	2.16740i	−0.122013	−	0.0735241i
$870$	−10.6165			−0.359931
$871$	1.11778			0.0378746
$872$	−9.88032			−0.334590
$873$			7.48439i			0.253308i
$874$		−	2.10055i		−	0.0710522i
$875$		0			0
$876$			16.5193i			0.558137i
$877$			33.7526i			1.13975i	0.821733	+	0.569873i	$0.193008\pi$
$877$			33.7526i			1.13975i	−0.821733	+	0.569873i	$0.806992\pi$
$878$		−	2.79865i		−	0.0944500i
$879$			29.3389i			0.989578i
$880$	−24.7073	−	14.8884i	−0.832882	−	0.501887i
$881$		−	13.1011i		−	0.441386i	−0.975343	−	0.220693i	$-0.929168\pi$
$881$		−	13.1011i		−	0.441386i	0.975343	−	0.220693i	$-0.0708320\pi$
$882$		0			0
$883$	−13.1303			−0.441869			−0.220935	−	0.975289i	$-0.570911\pi$
$883$	−13.1303			−0.441869			−0.220935	+	0.975289i	$0.570911\pi$
$884$	6.85065			0.230412
$885$			15.7469i			0.529328i
$886$		−	25.2898i		−	0.849627i
$887$	−40.1470			−1.34800			−0.674002	−	0.738729i	$-0.735426\pi$
$887$	−40.1470			−1.34800			−0.674002	+	0.738729i	$0.735426\pi$
$888$	5.72881			0.192246
$889$		0			0
$890$			44.3287i			1.48590i
$891$	−1.71180	+	2.84073i	−0.0573473	+	0.0951681i
$892$		−	13.3993i		−	0.448642i
$893$			3.35063i			0.112125i
$894$			39.8077i			1.33137i
$895$		−	18.0958i		−	0.604875i
$896$		0			0
$897$			3.43381i			0.114652i
$898$		−	26.5824i		−	0.887066i
$899$	7.52453			0.250957
$900$	2.40365			0.0801217
$901$	48.9508			1.63079
$902$	−21.3568	−	12.8694i	−0.711105	−	0.428505i
$903$		0			0
$904$		−	11.7729i		−	0.391560i
$905$	−4.66297			−0.155002
$906$			39.1832i			1.30177i
$907$	53.5448			1.77793			0.888963	−	0.457978i	$-0.151426\pi$
$907$	53.5448			1.77793			0.888963	+	0.457978i	$0.151426\pi$
$908$	−46.4076			−1.54009
$909$	−9.11063			−0.302180
$910$		0			0
$911$	45.3624			1.50292			0.751462	−	0.659777i	$-0.229349\pi$
$911$	45.3624			1.50292			0.751462	+	0.659777i	$0.229349\pi$
$912$		−	1.35715i		−	0.0449397i
$913$	17.7774	−	29.5016i	0.588346	−	0.976361i
$914$	−47.8949			−1.58422
$915$	−5.38691			−0.178086
$916$			5.87634i			0.194160i
$917$		0			0
$918$	−9.10847			−0.300624
$919$			22.8198i			0.752755i	0.926466	+	0.376377i	$0.122830\pi$
$919$			22.8198i			0.752755i	−0.926466	+	0.376377i	$0.877170\pi$
$920$	5.64410			0.186080
$921$			29.1807i			0.961536i
$922$		−	9.72227i		−	0.320186i
$923$	−1.80989			−0.0595733
$924$		0			0
$925$	−10.9799			−0.361016
$926$			13.0478i			0.428776i
$927$		−	5.61955i		−	0.184570i
$928$	−21.7655			−0.714488
$929$			7.74550i			0.254122i	0.991895	+	0.127061i	$0.0405543\pi$
$929$			7.74550i			0.254122i	−0.991895	+	0.127061i	$0.959446\pi$
$930$	8.83031			0.289557
$931$		0			0
$932$			35.4122i			1.15996i
$933$	−1.25309			−0.0410243
$934$	−9.87650			−0.323169
$935$	−25.5060	−	15.3696i	−0.834135	−	0.502641i
$936$			0.714324i			0.0233484i
$937$	−49.2391			−1.60857			−0.804286	−	0.594243i	$-0.797452\pi$
$937$	−49.2391			−1.60857			−0.804286	+	0.594243i	$0.797452\pi$
$938$		0			0
$939$	11.8927			0.388104
$940$	33.9431			1.10710
$941$	−48.3583			−1.57644			−0.788218	−	0.615396i	$-0.788996\pi$
$941$	−48.3583			−1.57644			−0.788218	+	0.615396i	$0.788996\pi$
$942$		−	31.8622i		−	1.03813i
$943$	15.1525			0.493432
$944$			39.3628i			1.28115i
$945$		0			0
$946$	−27.5554	+	45.7282i	−0.895902	+	1.48675i
$947$	6.36836			0.206944			0.103472	−	0.994632i	$-0.467005\pi$
$947$	6.36836			0.206944			0.103472	+	0.994632i	$0.467005\pi$
$948$	−2.00145			−0.0650041
$949$	9.40914			0.305434
$950$			0.837500i			0.0271721i
$951$			33.3231i			1.08058i
$952$		0			0
$953$			0.126055i			0.00408332i	0.999998	+	0.00204166i	$0.000649881\pi$
$953$			0.126055i			0.00408332i	−0.999998	+	0.00204166i	$0.999350\pi$
$954$		−	19.2436i		−	0.623034i
$955$			19.6647i			0.636335i
$956$		−	0.689184i		−	0.0222898i
$957$	−5.14865	+	8.54420i	−0.166432	+	0.276195i
$958$			49.6337i			1.60359i
$959$		0			0
$960$	−8.14763			−0.262964
$961$	24.7414			0.798110
$962$			12.3022i			0.396640i
$963$		−	15.5448i		−	0.500925i
$964$	33.3258			1.07335
$965$	−1.80916			−0.0582391
$966$		0			0
$967$			14.6847i			0.472227i	0.971725	+	0.236114i	$0.0758737\pi$
$967$			14.6847i			0.472227i	−0.971725	+	0.236114i	$0.924126\pi$
$968$	−7.71600	+	4.07757i	−0.248002	+	0.131058i
$969$		−	1.40102i		−	0.0450073i
$970$			26.4177i			0.848221i
$971$			1.40638i			0.0451330i	0.999745	+	0.0225665i	$0.00718374\pi$
$971$			1.40638i			0.0451330i	−0.999745	+	0.0225665i	$0.992816\pi$
$972$			1.58073i			0.0507019i
$973$		0			0
$974$			6.20741i			0.198898i
$975$		−	1.36908i		−	0.0438456i
$976$	−13.4657			−0.431028
$977$	36.5575			1.16958			0.584789	−	0.811186i	$-0.301177\pi$
$977$	36.5575			1.16958			0.584789	+	0.811186i	$0.301177\pi$
$978$	−9.37698			−0.299843
$979$	35.6761	+	21.4980i	1.14021	+	0.687080i
$980$		0			0
$981$			12.4535i			0.397609i
$982$	−23.1880			−0.739958
$983$		−	22.1831i		−	0.707530i	−0.935334	−	0.353765i	$-0.884901\pi$
$983$		−	22.1831i		−	0.707530i	0.935334	−	0.353765i	$-0.115099\pi$
$984$	3.15211			0.100486
$985$	29.5978			0.943064
$986$	−27.3960			−0.872465
$987$		0			0
$988$	0.414246			0.0131789
$989$		−	32.4437i		−	1.03165i
$990$	−6.04213	+	10.0269i	−0.192032	+	0.318677i
$991$	−47.0998			−1.49618			−0.748088	−	0.663600i	$-0.769028\pi$
$991$	−47.0998			−1.49618			−0.748088	+	0.663600i	$0.769028\pi$
$992$	18.1036			0.574791
$993$			8.96904i			0.284624i
$994$		0			0
$995$	23.0411			0.730451
$996$		−	16.4162i		−	0.520168i
$997$	−23.6307			−0.748393			−0.374197	−	0.927349i	$-0.622081\pi$
$997$	−23.6307			−0.748393			−0.374197	+	0.927349i	$0.622081\pi$
$998$		−	47.2742i		−	1.49644i
$999$		−	7.22078i		−	0.228455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.b.538.11	✓	48
7.6	odd	2	inner	1617.2.c.b.538.12	yes	48
11.10	odd	2	inner	1617.2.c.b.538.37	yes	48
77.76	even	2	inner	1617.2.c.b.538.38	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.c.b.538.11	✓	48	1.1	even	1	trivial
1617.2.c.b.538.12	yes	48	7.6	odd	2	inner
1617.2.c.b.538.37	yes	48	11.10	odd	2	inner
1617.2.c.b.538.38	yes	48	77.76	even	2	inner

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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.89228i q^{2} -1.00000i q^{3} -1.58073 q^{4} -1.86532i q^{5} -1.89228 q^{6} -0.793378i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.89228i q^{2} -1.00000i q^{3} -1.58073 q^{4} -1.86532i q^{5} -1.89228 q^{6} -0.793378i q^{8} -1.00000 q^{9} -3.52970 q^{10} +(-1.71180 + 2.84073i) q^{11} +1.58073i q^{12} +0.900357 q^{13} -1.86532 q^{15} -4.66275 q^{16} -4.81348 q^{17} +1.89228i q^{18} -0.291062 q^{19} +2.94856i q^{20} +(5.37546 + 3.23920i) q^{22} -3.81383 q^{23} -0.793378 q^{24} +1.52060 q^{25} -1.70373i q^{26} +1.00000i q^{27} +3.00775i q^{29} +3.52970i q^{30} -2.50172i q^{31} +7.23649i q^{32} +(2.84073 + 1.71180i) q^{33} +9.10847i q^{34} +1.58073 q^{36} -7.22078 q^{37} +0.550771i q^{38} -0.900357i q^{39} -1.47990 q^{40} -3.97302 q^{41} +8.50684i q^{43} +(2.70589 - 4.49043i) q^{44} +1.86532i q^{45} +7.21685i q^{46} -11.5117i q^{47} +4.66275i q^{48} -2.87740i q^{50} +4.81348i q^{51} -1.42322 q^{52} -10.1695 q^{53} +1.89228 q^{54} +(5.29886 + 3.19304i) q^{55} +0.291062i q^{57} +5.69150 q^{58} -8.44197i q^{59} +2.94856 q^{60} +2.88794 q^{61} -4.73395 q^{62} +4.36796 q^{64} -1.67945i q^{65} +(3.23920 - 5.37546i) q^{66} +1.24149 q^{67} +7.60881 q^{68} +3.81383i q^{69} -2.01019 q^{71} +0.793378i q^{72} +10.4505 q^{73} +13.6637i q^{74} -1.52060i q^{75} +0.460090 q^{76} -1.70373 q^{78} +1.26616i q^{79} +8.69751i q^{80} +1.00000 q^{81} +7.51808i q^{82} -10.3852 q^{83} +8.97867i q^{85} +16.0973 q^{86} +3.00775 q^{87} +(2.25377 + 1.35810i) q^{88} -12.5588i q^{89} +3.52970 q^{90} +6.02864 q^{92} -2.50172 q^{93} -21.7835 q^{94} +0.542923i q^{95} +7.23649 q^{96} -7.48439i q^{97} +(1.71180 - 2.84073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 64 q^{4} - 48 q^{9}+O(q^{10}) \) 48 * q - 64 * q^4 - 48 * q^9	\( 48 q - 64 q^{4} - 48 q^{9} - 16 q^{11} + 64 q^{16} + 16 q^{22} + 32 q^{23} - 80 q^{25} + 64 q^{36} - 96 q^{37} - 32 q^{44} + 64 q^{53} + 48 q^{58} - 48 q^{60} - 240 q^{64} + 96 q^{67} - 32 q^{71} + 48 q^{78} + 48 q^{81} - 96 q^{86} - 48 q^{88} - 32 q^{92} + 96 q^{93} + 16 q^{99}+O(q^{100}) \) 48 * q - 64 * q^4 - 48 * q^9 - 16 * q^11 + 64 * q^16 + 16 * q^22 + 32 * q^23 - 80 * q^25 + 64 * q^36 - 96 * q^37 - 32 * q^44 + 64 * q^53 + 48 * q^58 - 48 * q^60 - 240 * q^64 + 96 * q^67 - 32 * q^71 + 48 * q^78 + 48 * q^81 - 96 * q^86 - 48 * q^88 - 32 * q^92 + 96 * q^93 + 16 * q^99

Introduction

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