LMFDB - Embedded newform 495.2.c.a.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(199,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("495.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	495.199
Dual form			495.2.c.a.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.52434i q^{2} -4.37228 q^{4} +(-0.686141 - 2.12819i) q^{5} -3.46410i q^{7} +5.98844i q^{8} +(-5.37228 + 1.73205i) q^{10} +1.00000 q^{11} -8.74456 q^{14} +6.37228 q^{16} +1.58457i q^{17} -4.00000 q^{19} +(3.00000 + 9.30506i) q^{20} -2.52434i q^{22} -0.792287i q^{23} +(-4.05842 + 2.92048i) q^{25} +15.1460i q^{28} +8.74456 q^{29} +3.37228 q^{31} -4.10891i q^{32} +4.00000 q^{34} +(-7.37228 + 2.37686i) q^{35} +1.08724i q^{37} +10.0974i q^{38} +(12.7446 - 4.10891i) q^{40} -8.74456 q^{41} +3.46410i q^{43} -4.37228 q^{44} -2.00000 q^{46} -6.63325i q^{47} -5.00000 q^{49} +(7.37228 + 10.2448i) q^{50} -10.0974i q^{53} +(-0.686141 - 2.12819i) q^{55} +20.7446 q^{56} -22.0742i q^{58} -7.37228 q^{59} -0.744563 q^{61} -8.51278i q^{62} +2.37228 q^{64} -9.30506i q^{67} -6.92820i q^{68} +(6.00000 + 18.6101i) q^{70} +10.1168 q^{71} -6.92820i q^{73} +2.74456 q^{74} +17.4891 q^{76} -3.46410i q^{77} -1.25544 q^{79} +(-4.37228 - 13.5615i) q^{80} +22.0742i q^{82} -6.63325i q^{83} +(3.37228 - 1.08724i) q^{85} +8.74456 q^{86} +5.98844i q^{88} +1.37228 q^{89} +3.46410i q^{92} -16.7446 q^{94} +(2.74456 + 8.51278i) q^{95} -5.84096i q^{97} +12.6217i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{4} + 3 q^{5} - 10 q^{10} + 4 q^{11} - 12 q^{14} + 14 q^{16} - 16 q^{19} + 12 q^{20} + q^{25} + 12 q^{29} + 2 q^{31} + 16 q^{34} - 18 q^{35} + 28 q^{40} - 12 q^{41} - 6 q^{44} - 8 q^{46} - 20 q^{49}+ \cdots - 12 q^{95}+O(q^{100}) $ 4 * q - 6 * q^4 + 3 * q^5 - 10 * q^10 + 4 * q^11 - 12 * q^14 + 14 * q^16 - 16 * q^19 + 12 * q^20 + q^25 + 12 * q^29 + 2 * q^31 + 16 * q^34 - 18 * q^35 + 28 * q^40 - 12 * q^41 - 6 * q^44 - 8 * q^46 - 20 * q^49 + 18 * q^50 + 3 * q^55 + 60 * q^56 - 18 * q^59 + 20 * q^61 - 2 * q^64 + 24 * q^70 + 6 * q^71 - 12 * q^74 + 24 * q^76 - 28 * q^79 - 6 * q^80 + 2 * q^85 + 12 * q^86 - 6 * q^89 - 44 * q^94 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	2.52434i		−	1.78498i	−0.451071	−	0.892488i	$-0.648958\pi$
$2$		−	2.52434i		−	1.78498i	0.451071	−	0.892488i	$-0.351042\pi$
$3$		0			0
$3$		0			0
$4$	−4.37228			−2.18614
$5$	−0.686141	−	2.12819i	−0.306851	−	0.951757i
$5$	−0.686141	−	2.12819i	−0.306851	−	0.951757i
$6$		0			0
$7$		−	3.46410i		−	1.30931i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$		−	3.46410i		−	1.30931i	0.755929	−	0.654654i	$-0.227186\pi$
$8$			5.98844i			2.11723i
$9$		0			0
$10$	−5.37228	+	1.73205i	−1.69886	+	0.547723i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−8.74456			−2.33708
$15$		0			0
$16$	6.37228			1.59307
$17$			1.58457i			0.384316i	0.981364	+	0.192158i	$0.0615486\pi$
$17$			1.58457i			0.384316i	−0.981364	+	0.192158i	$0.938451\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	3.00000	+	9.30506i	0.670820	+	2.08068i
$21$		0			0
$22$		−	2.52434i		−	0.538191i
$23$		−	0.792287i		−	0.165203i	−0.996583	−	0.0826016i	$-0.973677\pi$
$23$		−	0.792287i		−	0.165203i	0.996583	−	0.0826016i	$-0.0263229\pi$
$24$		0			0
$25$	−4.05842	+	2.92048i	−0.811684	+	0.584096i
$26$		0			0
$27$		0			0
$28$			15.1460i			2.86233i
$29$	8.74456			1.62382			0.811912	−	0.583779i	$-0.198427\pi$
$29$	8.74456			1.62382			0.811912	+	0.583779i	$0.198427\pi$
$30$		0			0
$31$	3.37228			0.605680			0.302840	−	0.953041i	$-0.402065\pi$
$31$	3.37228			0.605680			0.302840	+	0.953041i	$0.402065\pi$
$32$		−	4.10891i		−	0.726360i
$33$		0			0
$34$	4.00000			0.685994
$35$	−7.37228	+	2.37686i	−1.24614	+	0.401763i
$36$		0			0
$37$			1.08724i			0.178741i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$			1.08724i			0.178741i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$			10.0974i			1.63801i
$39$		0			0
$40$	12.7446	−	4.10891i	2.01509	−	0.649676i
$41$	−8.74456			−1.36567			−0.682836	−	0.730572i	$-0.739253\pi$
$41$	−8.74456			−1.36567			−0.682836	+	0.730572i	$0.739253\pi$
$42$		0			0
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$	−4.37228			−0.659146
$45$		0			0
$46$	−2.00000			−0.294884
$47$		−	6.63325i		−	0.967559i	−0.875190	−	0.483779i	$-0.839264\pi$
$47$		−	6.63325i		−	0.967559i	0.875190	−	0.483779i	$-0.160736\pi$
$48$		0			0
$49$	−5.00000			−0.714286
$50$	7.37228	+	10.2448i	1.04260	+	1.44884i
$51$		0			0
$52$		0			0
$53$		−	10.0974i		−	1.38698i	−0.720467	−	0.693489i	$-0.756073\pi$
$53$		−	10.0974i		−	1.38698i	0.720467	−	0.693489i	$-0.243927\pi$
$54$		0			0
$55$	−0.686141	−	2.12819i	−0.0925192	−	0.286966i
$56$	20.7446			2.77211
$57$		0			0
$58$		−	22.0742i		−	2.89849i
$59$	−7.37228			−0.959789			−0.479895	−	0.877326i	$-0.659325\pi$
$59$	−7.37228			−0.959789			−0.479895	+	0.877326i	$0.659325\pi$
$60$		0			0
$61$	−0.744563			−0.0953315			−0.0476657	−	0.998863i	$-0.515178\pi$
$61$	−0.744563			−0.0953315			−0.0476657	+	0.998863i	$0.515178\pi$
$62$		−	8.51278i		−	1.08112i
$63$		0			0
$64$	2.37228			0.296535
$65$		0			0
$66$		0			0
$67$		−	9.30506i		−	1.13679i	−0.822754	−	0.568397i	$-0.807564\pi$
$67$		−	9.30506i		−	1.13679i	0.822754	−	0.568397i	$-0.192436\pi$
$68$		−	6.92820i		−	0.840168i
$69$		0			0
$70$	6.00000	+	18.6101i	0.717137	+	2.22434i
$71$	10.1168			1.20065			0.600324	−	0.799757i	$-0.295038\pi$
$71$	10.1168			1.20065			0.600324	+	0.799757i	$0.295038\pi$
$72$		0			0
$73$		−	6.92820i		−	0.810885i	−0.914121	−	0.405442i	$-0.867117\pi$
$73$		−	6.92820i		−	0.810885i	0.914121	−	0.405442i	$-0.132883\pi$
$74$	2.74456			0.319049
$75$		0			0
$76$	17.4891			2.00614
$77$		−	3.46410i		−	0.394771i
$78$		0			0
$79$	−1.25544			−0.141248			−0.0706239	−	0.997503i	$-0.522499\pi$
$79$	−1.25544			−0.141248			−0.0706239	+	0.997503i	$0.522499\pi$
$80$	−4.37228	−	13.5615i	−0.488836	−	1.51622i
$81$		0			0
$82$			22.0742i			2.43769i
$83$		−	6.63325i		−	0.728094i	−0.931381	−	0.364047i	$-0.881395\pi$
$83$		−	6.63325i		−	0.728094i	0.931381	−	0.364047i	$-0.118605\pi$
$84$		0			0
$85$	3.37228	−	1.08724i	0.365775	−	0.117928i
$86$	8.74456			0.942950
$87$		0			0
$88$			5.98844i			0.638370i
$89$	1.37228			0.145462			0.0727308	−	0.997352i	$-0.476829\pi$
$89$	1.37228			0.145462			0.0727308	+	0.997352i	$0.476829\pi$
$90$		0			0
$91$		0			0
$92$			3.46410i			0.361158i
$93$		0			0
$94$	−16.7446			−1.72707
$95$	2.74456	+	8.51278i	0.281586	+	0.873393i
$96$		0			0
$97$		−	5.84096i		−	0.593060i	−0.955024	−	0.296530i	$-0.904171\pi$
$97$		−	5.84096i		−	0.593060i	0.955024	−	0.296530i	$-0.0958295\pi$
$98$			12.6217i			1.27498i
$99$		0			0
$100$	17.7446	−	12.7692i	1.77446	−	1.27692i
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$		0			0
$103$		−	10.3923i		−	1.02398i	−0.858990	−	0.511992i	$-0.828908\pi$
$103$		−	10.3923i		−	1.02398i	0.858990	−	0.511992i	$-0.171092\pi$
$104$		0			0
$105$		0			0
$106$	−25.4891			−2.47572
$107$		−	6.63325i		−	0.641260i	−0.947204	−	0.320630i	$-0.896105\pi$
$107$		−	6.63325i		−	0.641260i	0.947204	−	0.320630i	$-0.103895\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−5.37228	+	1.73205i	−0.512227	+	0.165145i
$111$		0			0
$112$		−	22.0742i		−	2.08582i
$113$			0.497333i			0.0467852i	0.999726	+	0.0233926i	$0.00744677\pi$
$113$			0.497333i			0.0467852i	−0.999726	+	0.0233926i	$0.992553\pi$
$114$		0			0
$115$	−1.68614	+	0.543620i	−0.157233	+	0.0506929i
$116$	−38.2337			−3.54991
$117$		0			0
$118$			18.6101i			1.71320i
$119$	5.48913			0.503187
$120$		0			0
$121$	1.00000			0.0909091
$122$			1.87953i			0.170164i
$123$		0			0
$124$	−14.7446			−1.32410
$125$	9.00000	+	6.63325i	0.804984	+	0.593296i
$126$		0			0
$127$			8.21782i			0.729214i	0.931162	+	0.364607i	$0.118797\pi$
$127$			8.21782i			0.729214i	−0.931162	+	0.364607i	$0.881203\pi$
$128$		−	14.2063i		−	1.25567i
$129$		0			0
$130$		0			0
$131$	2.74456			0.239794			0.119897	−	0.992786i	$-0.461744\pi$
$131$	2.74456			0.239794			0.119897	+	0.992786i	$0.461744\pi$
$132$		0			0
$133$			13.8564i			1.20150i
$134$	−23.4891			−2.02915
$135$		0			0
$136$	−9.48913			−0.813686
$137$			14.3537i			1.22632i	0.789958	+	0.613161i	$0.210102\pi$
$137$			14.3537i			1.22632i	−0.789958	+	0.613161i	$0.789898\pi$
$138$		0			0
$139$	16.2337			1.37692			0.688462	−	0.725273i	$-0.258286\pi$
$139$	16.2337			1.37692			0.688462	+	0.725273i	$0.258286\pi$
$140$	32.2337	−	10.3923i	2.72424	−	0.878310i
$141$		0			0
$142$		−	25.5383i		−	2.14313i
$143$		0			0
$144$		0			0
$145$	−6.00000	−	18.6101i	−0.498273	−	1.54549i
$146$	−17.4891			−1.44741
$147$		0			0
$148$		−	4.75372i		−	0.390754i
$149$	−11.4891			−0.941226			−0.470613	−	0.882340i	$-0.655967\pi$
$149$	−11.4891			−0.941226			−0.470613	+	0.882340i	$0.655967\pi$
$150$		0			0
$151$	−12.2337			−0.995563			−0.497782	−	0.867302i	$-0.665852\pi$
$151$	−12.2337			−0.995563			−0.497782	+	0.867302i	$0.665852\pi$
$152$		−	23.9538i		−	1.94291i
$153$		0			0
$154$	−8.74456			−0.704657
$155$	−2.31386	−	7.17687i	−0.185854	−	0.576460i
$156$		0			0
$157$			24.4511i			1.95141i	0.219090	+	0.975705i	$0.429691\pi$
$157$			24.4511i			1.95141i	−0.219090	+	0.975705i	$0.570309\pi$
$158$			3.16915i			0.252124i
$159$		0			0
$160$	−8.74456	+	2.81929i	−0.691318	+	0.222885i
$161$	−2.74456			−0.216302
$162$		0			0
$163$		−	3.46410i		−	0.271329i	−0.990755	−	0.135665i	$-0.956683\pi$
$163$		−	3.46410i		−	0.271329i	0.990755	−	0.135665i	$-0.0433170\pi$
$164$	38.2337			2.98555
$165$		0			0
$166$	−16.7446			−1.29963
$167$		−	15.7359i		−	1.21768i	−0.793292	−	0.608842i	$-0.791635\pi$
$167$		−	15.7359i		−	1.21768i	0.793292	−	0.608842i	$-0.208365\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$	−2.74456	−	8.51278i	−0.210498	−	0.652900i
$171$		0			0
$172$		−	15.1460i		−	1.15487i
$173$			8.51278i			0.647214i	0.946192	+	0.323607i	$0.104896\pi$
$173$			8.51278i			0.647214i	−0.946192	+	0.323607i	$0.895104\pi$
$174$		0			0
$175$	10.1168	+	14.0588i	0.764762	+	1.06274i
$176$	6.37228			0.480329
$177$		0			0
$178$		−	3.46410i		−	0.259645i
$179$	12.8614			0.961307			0.480653	−	0.876911i	$-0.340400\pi$
$179$	12.8614			0.961307			0.480653	+	0.876911i	$0.340400\pi$
$180$		0			0
$181$	24.1168			1.79259			0.896295	−	0.443457i	$-0.146248\pi$
$181$	24.1168			1.79259			0.896295	+	0.443457i	$0.146248\pi$
$182$		0			0
$183$		0			0
$184$	4.74456			0.349774
$185$	2.31386	−	0.746000i	0.170118	−	0.0548470i
$186$		0			0
$187$			1.58457i			0.115876i
$188$			29.0024i			2.11522i
$189$		0			0
$190$	21.4891	−	6.92820i	1.55899	−	0.502625i
$191$	19.3723			1.40173			0.700865	−	0.713294i	$-0.252798\pi$
$191$	19.3723			1.40173			0.700865	+	0.713294i	$0.252798\pi$
$192$		0			0
$193$		−	16.4356i		−	1.18306i	−0.806282	−	0.591532i	$-0.798523\pi$
$193$		−	16.4356i		−	1.18306i	0.806282	−	0.591532i	$-0.201477\pi$
$194$	−14.7446			−1.05860
$195$		0			0
$196$	21.8614			1.56153
$197$			8.51278i			0.606510i	0.952909	+	0.303255i	$0.0980734\pi$
$197$			8.51278i			0.606510i	−0.952909	+	0.303255i	$0.901927\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−17.4891	−	24.3036i	−1.23667	−	1.71853i
$201$		0			0
$202$			15.1460i			1.06567i
$203$		−	30.2921i		−	2.12609i
$204$		0			0
$205$	6.00000	+	18.6101i	0.419058	+	1.29979i
$206$	−26.2337			−1.82779
$207$		0			0
$208$		0			0
$209$	−4.00000			−0.276686
$210$		0			0
$211$	1.48913			0.102516			0.0512578	−	0.998685i	$-0.483677\pi$
$211$	1.48913			0.102516			0.0512578	+	0.998685i	$0.483677\pi$
$212$			44.1485i			3.03213i
$213$		0			0
$214$	−16.7446			−1.14463
$215$	7.37228	−	2.37686i	0.502785	−	0.162101i
$216$		0			0
$217$		−	11.6819i		−	0.793021i
$218$			25.2434i			1.70970i
$219$		0			0
$220$	3.00000	+	9.30506i	0.202260	+	0.627347i
$221$		0			0
$222$		0			0
$223$		−	2.37686i		−	0.159166i	−0.996828	−	0.0795832i	$-0.974641\pi$
$223$		−	2.37686i		−	0.159166i	0.996828	−	0.0795832i	$-0.0253589\pi$
$224$	−14.2337			−0.951028
$225$		0			0
$226$	1.25544			0.0835105
$227$			16.7306i			1.11045i	0.831701	+	0.555224i	$0.187368\pi$
$227$			16.7306i			1.11045i	−0.831701	+	0.555224i	$0.812632\pi$
$228$		0			0
$229$	−14.6277			−0.966627			−0.483313	−	0.875447i	$-0.660567\pi$
$229$	−14.6277			−0.966627			−0.483313	+	0.875447i	$0.660567\pi$
$230$	1.37228	+	4.25639i	0.0904856	+	0.280658i
$231$		0			0
$232$			52.3663i			3.43801i
$233$			3.75906i			0.246264i	0.992390	+	0.123132i	$0.0392938\pi$
$233$			3.75906i			0.246264i	−0.992390	+	0.123132i	$0.960706\pi$
$234$		0			0
$235$	−14.1168	+	4.55134i	−0.920881	+	0.296897i
$236$	32.2337			2.09823
$237$		0			0
$238$		−	13.8564i		−	0.898177i
$239$	−14.7446			−0.953746			−0.476873	−	0.878972i	$-0.658230\pi$
$239$	−14.7446			−0.953746			−0.476873	+	0.878972i	$0.658230\pi$
$240$		0			0
$241$	16.7446			1.07861			0.539306	−	0.842110i	$-0.318687\pi$
$241$	16.7446			1.07861			0.539306	+	0.842110i	$0.318687\pi$
$242$		−	2.52434i		−	0.162271i
$243$		0			0
$244$	3.25544			0.208408
$245$	3.43070	+	10.6410i	0.219180	+	0.679827i
$246$		0			0
$247$		0			0
$248$			20.1947i			1.28236i
$249$		0			0
$250$	16.7446	−	22.7190i	1.05902	−	1.43688i
$251$	22.1168			1.39600			0.698001	−	0.716096i	$-0.254073\pi$
$251$	22.1168			1.39600			0.698001	+	0.716096i	$0.254073\pi$
$252$		0			0
$253$		−	0.792287i		−	0.0498107i
$254$	20.7446			1.30163
$255$		0			0
$256$	−31.1168			−1.94480
$257$			10.6873i			0.666653i	0.942811	+	0.333326i	$0.108171\pi$
$257$			10.6873i			0.666653i	−0.942811	+	0.333326i	$0.891829\pi$
$258$		0			0
$259$	3.76631			0.234027
$260$		0			0
$261$		0			0
$262$		−	6.92820i		−	0.428026i
$263$		−	27.4179i		−	1.69066i	−0.534246	−	0.845329i	$-0.679405\pi$
$263$		−	27.4179i		−	1.69066i	0.534246	−	0.845329i	$-0.320595\pi$
$264$		0			0
$265$	−21.4891	+	6.92820i	−1.32007	+	0.425596i
$266$	34.9783			2.14465
$267$		0			0
$268$			40.6844i			2.48519i
$269$	−11.4891			−0.700504			−0.350252	−	0.936655i	$-0.613904\pi$
$269$	−11.4891			−0.700504			−0.350252	+	0.936655i	$0.613904\pi$
$270$		0			0
$271$	13.4891			0.819406			0.409703	−	0.912219i	$-0.365632\pi$
$271$	13.4891			0.819406			0.409703	+	0.912219i	$0.365632\pi$
$272$			10.0974i			0.612242i
$273$		0			0
$274$	36.2337			2.18896
$275$	−4.05842	+	2.92048i	−0.244732	+	0.176112i
$276$		0			0
$277$			11.6819i			0.701899i	0.936394	+	0.350949i	$0.114141\pi$
$277$			11.6819i			0.701899i	−0.936394	+	0.350949i	$0.885859\pi$
$278$		−	40.9793i		−	2.45778i
$279$		0			0
$280$	−14.2337	−	44.1485i	−0.850626	−	2.63838i
$281$	0.510875			0.0304762			0.0152381	−	0.999884i	$-0.495149\pi$
$281$	0.510875			0.0304762			0.0152381	+	0.999884i	$0.495149\pi$
$282$		0			0
$283$			15.1460i			0.900338i	0.892943	+	0.450169i	$0.148636\pi$
$283$			15.1460i			0.900338i	−0.892943	+	0.450169i	$0.851364\pi$
$284$	−44.2337			−2.62479
$285$		0			0
$286$		0			0
$287$			30.2921i			1.78808i
$288$		0			0
$289$	14.4891			0.852301
$290$	−46.9783	+	15.1460i	−2.75866	+	0.889405i
$291$		0			0
$292$			30.2921i			1.77271i
$293$		−	3.16915i		−	0.185144i	−0.995706	−	0.0925718i	$-0.970491\pi$
$293$		−	3.16915i		−	0.185144i	0.995706	−	0.0925718i	$-0.0295088\pi$
$294$		0			0
$295$	5.05842	+	15.6896i	0.294513	+	0.913487i
$296$	−6.51087			−0.378437
$297$		0			0
$298$			29.0024i			1.68007i
$299$		0			0
$300$		0			0
$301$	12.0000			0.691669
$302$			30.8820i			1.77706i
$303$		0			0
$304$	−25.4891			−1.46190
$305$	0.510875	+	1.58457i	0.0292526	+	0.0907324i
$306$		0			0
$307$		−	31.5817i		−	1.80246i	−0.433340	−	0.901231i	$-0.642665\pi$
$307$		−	31.5817i		−	1.80246i	0.433340	−	0.901231i	$-0.357335\pi$
$308$			15.1460i			0.863025i
$309$		0			0
$310$	−18.1168	+	5.84096i	−1.02897	+	0.331744i
$311$	−5.48913			−0.311260			−0.155630	−	0.987815i	$-0.549741\pi$
$311$	−5.48913			−0.311260			−0.155630	+	0.987815i	$0.549741\pi$
$312$		0			0
$313$		−	21.8719i		−	1.23627i	−0.786072	−	0.618135i	$-0.787888\pi$
$313$		−	21.8719i		−	1.23627i	0.786072	−	0.618135i	$-0.212112\pi$
$314$	61.7228			3.48322
$315$		0			0
$316$	5.48913			0.308787
$317$			32.9639i			1.85144i	0.378215	+	0.925718i	$0.376538\pi$
$317$			32.9639i			1.85144i	−0.378215	+	0.925718i	$0.623462\pi$
$318$		0			0
$319$	8.74456			0.489602
$320$	−1.62772	−	5.04868i	−0.0909922	−	0.282230i
$321$		0			0
$322$			6.92820i			0.386094i
$323$		−	6.33830i		−	0.352672i
$324$		0			0
$325$		0			0
$326$	−8.74456			−0.484317
$327$		0			0
$328$		−	52.3663i		−	2.89144i
$329$	−22.9783			−1.26683
$330$		0			0
$331$	−14.1168			−0.775932			−0.387966	−	0.921674i	$-0.626822\pi$
$331$	−14.1168			−0.775932			−0.387966	+	0.921674i	$0.626822\pi$
$332$			29.0024i			1.59172i
$333$		0			0
$334$	−39.7228			−2.17354
$335$	−19.8030	+	6.38458i	−1.08195	+	0.348827i
$336$		0			0
$337$			32.4665i			1.76856i	0.466952	+	0.884282i	$0.345352\pi$
$337$			32.4665i			1.76856i	−0.466952	+	0.884282i	$0.654648\pi$
$338$		−	32.8164i		−	1.78498i
$339$		0			0
$340$	−14.7446	+	4.75372i	−0.799636	+	0.257807i
$341$	3.37228			0.182619
$342$		0			0
$343$		−	6.92820i		−	0.374088i
$344$	−20.7446			−1.11847
$345$		0			0
$346$	21.4891			1.15526
$347$		−	22.6641i		−	1.21667i	−0.793679	−	0.608337i	$-0.791837\pi$
$347$		−	22.6641i		−	1.21667i	0.793679	−	0.608337i	$-0.208163\pi$
$348$		0			0
$349$	−15.4891			−0.829114			−0.414557	−	0.910023i	$-0.636063\pi$
$349$	−15.4891			−0.829114			−0.414557	+	0.910023i	$0.636063\pi$
$350$	35.4891	−	25.5383i	1.89697	−	1.36508i
$351$		0			0
$352$		−	4.10891i		−	0.219006i
$353$		−	25.0410i		−	1.33280i	−0.745595	−	0.666399i	$-0.767835\pi$
$353$		−	25.0410i		−	1.33280i	0.745595	−	0.666399i	$-0.232165\pi$
$354$		0			0
$355$	−6.94158	−	21.5306i	−0.368421	−	1.14273i
$356$	−6.00000			−0.317999
$357$		0			0
$358$		−	32.4665i		−	1.71591i
$359$	29.4891			1.55638			0.778188	−	0.628031i	$-0.216139\pi$
$359$	29.4891			1.55638			0.778188	+	0.628031i	$0.216139\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$		−	60.8791i		−	3.19973i
$363$		0			0
$364$		0			0
$365$	−14.7446	+	4.75372i	−0.771766	+	0.248821i
$366$		0			0
$367$		−	25.7407i		−	1.34365i	−0.740708	−	0.671827i	$-0.765510\pi$
$367$		−	25.7407i		−	1.34365i	0.740708	−	0.671827i	$-0.234490\pi$
$368$		−	5.04868i		−	0.263180i
$369$		0			0
$370$	−1.88316	−	5.84096i	−0.0979006	−	0.303657i
$371$	−34.9783			−1.81598
$372$		0			0
$373$		−	11.6819i		−	0.604867i	−0.953170	−	0.302434i	$-0.902201\pi$
$373$		−	11.6819i		−	0.604867i	0.953170	−	0.302434i	$-0.0977990\pi$
$374$	4.00000			0.206835
$375$		0			0
$376$	39.7228			2.04855
$377$		0			0
$378$		0			0
$379$	0.627719			0.0322437			0.0161219	−	0.999870i	$-0.494868\pi$
$379$	0.627719			0.0322437			0.0161219	+	0.999870i	$0.494868\pi$
$380$	−12.0000	−	37.2203i	−0.615587	−	1.90936i
$381$		0			0
$382$		−	48.9022i		−	2.50205i
$383$			10.8896i			0.556435i	0.960518	+	0.278217i	$0.0897435\pi$
$383$			10.8896i			0.556435i	−0.960518	+	0.278217i	$0.910256\pi$
$384$		0			0
$385$	−7.37228	+	2.37686i	−0.375726	+	0.121136i
$386$	−41.4891			−2.11174
$387$		0			0
$388$			25.5383i			1.29651i
$389$	18.8614			0.956311			0.478156	−	0.878275i	$-0.341305\pi$
$389$	18.8614			0.956311			0.478156	+	0.878275i	$0.341305\pi$
$390$		0			0
$391$	1.25544			0.0634902
$392$		−	29.9422i		−	1.51231i
$393$		0			0
$394$	21.4891			1.08261
$395$	0.861407	+	2.67181i	0.0433421	+	0.134434i
$396$		0			0
$397$			16.4356i			0.824881i	0.910984	+	0.412441i	$0.135324\pi$
$397$			16.4356i			0.824881i	−0.910984	+	0.412441i	$0.864676\pi$
$398$		−	20.1947i		−	1.01227i
$399$		0			0
$400$	−25.8614	+	18.6101i	−1.29307	+	0.930506i
$401$	11.4891			0.573740			0.286870	−	0.957970i	$-0.407385\pi$
$401$	11.4891			0.573740			0.286870	+	0.957970i	$0.407385\pi$
$402$		0			0
$403$		0			0
$404$	26.2337			1.30517
$405$		0			0
$406$	−76.4674			−3.79501
$407$			1.08724i			0.0538925i
$408$		0			0
$409$	−27.4891			−1.35925			−0.679625	−	0.733560i	$-0.737857\pi$
$409$	−27.4891			−1.35925			−0.679625	+	0.733560i	$0.737857\pi$
$410$	46.9783	−	15.1460i	2.32009	−	0.748009i
$411$		0			0
$412$			45.4381i			2.23857i
$413$			25.5383i			1.25666i
$414$		0			0
$415$	−14.1168	+	4.55134i	−0.692969	+	0.223417i
$416$		0			0
$417$		0			0
$418$			10.0974i			0.493878i
$419$	−22.9783			−1.12256			−0.561280	−	0.827626i	$-0.689691\pi$
$419$	−22.9783			−1.12256			−0.561280	+	0.827626i	$0.689691\pi$
$420$		0			0
$421$	8.51087			0.414795			0.207397	−	0.978257i	$-0.433501\pi$
$421$	8.51087			0.414795			0.207397	+	0.978257i	$0.433501\pi$
$422$		−	3.75906i		−	0.182988i
$423$		0			0
$424$	60.4674			2.93656
$425$	−4.62772	−	6.43087i	−0.224477	−	0.311943i
$426$		0			0
$427$			2.57924i			0.124818i
$428$			29.0024i			1.40189i
$429$		0			0
$430$	−6.00000	−	18.6101i	−0.289346	−	0.897460i
$431$	25.7228			1.23902			0.619512	−	0.784987i	$-0.287330\pi$
$431$	25.7228			1.23902			0.619512	+	0.784987i	$0.287330\pi$
$432$		0			0
$433$			29.2048i			1.40349i	0.712426	+	0.701747i	$0.247596\pi$
$433$			29.2048i			1.40349i	−0.712426	+	0.701747i	$0.752404\pi$
$434$	−29.4891			−1.41552
$435$		0			0
$436$	43.7228			2.09394
$437$			3.16915i			0.151601i
$438$		0			0
$439$	−21.4891			−1.02562			−0.512810	−	0.858502i	$-0.671395\pi$
$439$	−21.4891			−1.02562			−0.512810	+	0.858502i	$0.671395\pi$
$440$	12.7446	−	4.10891i	0.607573	−	0.195885i
$441$		0			0
$442$		0			0
$443$			31.6742i			1.50489i	0.658656	+	0.752444i	$0.271125\pi$
$443$			31.6742i			1.50489i	−0.658656	+	0.752444i	$0.728875\pi$
$444$		0			0
$445$	−0.941578	−	2.92048i	−0.0446351	−	0.138444i
$446$	−6.00000			−0.284108
$447$		0			0
$448$		−	8.21782i		−	0.388256i
$449$	6.86141			0.323810			0.161905	−	0.986806i	$-0.448236\pi$
$449$	6.86141			0.323810			0.161905	+	0.986806i	$0.448236\pi$
$450$		0			0
$451$	−8.74456			−0.411765
$452$		−	2.17448i		−	0.102279i
$453$		0			0
$454$	42.2337			1.98213
$455$		0			0
$456$		0			0
$457$			20.7846i			0.972263i	0.873886	+	0.486132i	$0.161592\pi$
$457$			20.7846i			0.972263i	−0.873886	+	0.486132i	$0.838408\pi$
$458$			36.9253i			1.72541i
$459$		0			0
$460$	7.37228	−	2.37686i	0.343734	−	0.110822i
$461$	−2.23369			−0.104033			−0.0520166	−	0.998646i	$-0.516565\pi$
$461$	−2.23369			−0.104033			−0.0520166	+	0.998646i	$0.516565\pi$
$462$		0			0
$463$		−	30.0897i		−	1.39839i	−0.714933	−	0.699193i	$-0.753543\pi$
$463$		−	30.0897i		−	1.39839i	0.714933	−	0.699193i	$-0.246457\pi$
$464$	55.7228			2.58687
$465$		0			0
$466$	9.48913			0.439575
$467$		−	7.72049i		−	0.357262i	−0.983916	−	0.178631i	$-0.942833\pi$
$467$		−	7.72049i		−	0.357262i	0.983916	−	0.178631i	$-0.0571668\pi$
$468$		0			0
$469$	−32.2337			−1.48841
$470$	11.4891	+	35.6357i	0.529954	+	1.64375i
$471$		0			0
$472$		−	44.1485i		−	2.03210i
$473$			3.46410i			0.159280i
$474$		0			0
$475$	16.2337	−	11.6819i	0.744853	−	0.536003i
$476$	−24.0000			−1.10004
$477$		0			0
$478$			37.2203i			1.70241i
$479$	−5.48913			−0.250805			−0.125402	−	0.992106i	$-0.540022\pi$
$479$	−5.48913			−0.250805			−0.125402	+	0.992106i	$0.540022\pi$
$480$		0			0
$481$		0			0
$482$		−	42.2689i		−	1.92530i
$483$		0			0
$484$	−4.37228			−0.198740
$485$	−12.4307	+	4.00772i	−0.564449	+	0.181981i
$486$		0			0
$487$			7.13058i			0.323118i	0.986863	+	0.161559i	$0.0516521\pi$
$487$			7.13058i			0.323118i	−0.986863	+	0.161559i	$0.948348\pi$
$488$		−	4.45877i		−	0.201839i
$489$		0			0
$490$	26.8614	−	8.66025i	1.21347	−	0.391230i
$491$	−6.51087			−0.293832			−0.146916	−	0.989149i	$-0.546935\pi$
$491$	−6.51087			−0.293832			−0.146916	+	0.989149i	$0.546935\pi$
$492$		0			0
$493$			13.8564i			0.624061i
$494$		0			0
$495$		0			0
$496$	21.4891			0.964890
$497$		−	35.0458i		−	1.57202i
$498$		0			0
$499$	20.0000			0.895323			0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000			0.895323			0.447661	+	0.894203i	$0.352257\pi$
$500$	−39.3505	−	29.0024i	−1.75981	−	1.29703i
$501$		0			0
$502$		−	55.8304i		−	2.49183i
$503$		−	13.5615i		−	0.604675i	−0.953201	−	0.302338i	$-0.902233\pi$
$503$		−	13.5615i		−	0.604675i	0.953201	−	0.302338i	$-0.0977670\pi$
$504$		0			0
$505$	4.11684	+	12.7692i	0.183197	+	0.568220i
$506$	−2.00000			−0.0889108
$507$		0			0
$508$		−	35.9306i		−	1.59416i
$509$	22.6277			1.00296			0.501478	−	0.865170i	$-0.332790\pi$
$509$	22.6277			1.00296			0.501478	+	0.865170i	$0.332790\pi$
$510$		0			0
$511$	−24.0000			−1.06170
$512$			50.1369i			2.21576i
$513$		0			0
$514$	26.9783			1.18996
$515$	−22.1168	+	7.13058i	−0.974585	+	0.314211i
$516$		0			0
$517$		−	6.63325i		−	0.291730i
$518$		−	9.50744i		−	0.417733i
$519$		0			0
$520$		0			0
$521$	21.6060			0.946575			0.473287	−	0.880908i	$-0.343067\pi$
$521$	21.6060			0.946575			0.473287	+	0.880908i	$0.343067\pi$
$522$		0			0
$523$			29.0024i			1.26819i	0.773256	+	0.634094i	$0.218627\pi$
$523$			29.0024i			1.26819i	−0.773256	+	0.634094i	$0.781373\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	−69.2119			−3.01778
$527$			5.34363i			0.232772i
$528$		0			0
$529$	22.3723			0.972708
$530$	17.4891	+	54.2458i	0.759679	+	2.35629i
$531$		0			0
$532$		−	60.5841i		−	2.62665i
$533$		0			0
$534$		0			0
$535$	−14.1168	+	4.55134i	−0.610324	+	0.196772i
$536$	55.7228			2.40686
$537$		0			0
$538$			29.0024i			1.25038i
$539$	−5.00000			−0.215365
$540$		0			0
$541$	34.2337			1.47182			0.735911	−	0.677079i	$-0.236754\pi$
$541$	34.2337			1.47182			0.735911	+	0.677079i	$0.236754\pi$
$542$		−	34.0511i		−	1.46262i
$543$		0			0
$544$	6.51087			0.279151
$545$	6.86141	+	21.2819i	0.293910	+	0.911618i
$546$		0			0
$547$			29.0024i			1.24005i	0.784580	+	0.620027i	$0.212878\pi$
$547$			29.0024i			1.24005i	−0.784580	+	0.620027i	$0.787122\pi$
$548$		−	62.7586i		−	2.68091i
$549$		0			0
$550$	7.37228	+	10.2448i	0.314355	+	0.436841i
$551$	−34.9783			−1.49012
$552$		0			0
$553$			4.34896i			0.184937i
$554$	29.4891			1.25287
$555$		0			0
$556$	−70.9783			−3.01015
$557$		−	0.994667i		−	0.0421454i	−0.999778	−	0.0210727i	$-0.993292\pi$
$557$		−	0.994667i		−	0.0421454i	0.999778	−	0.0210727i	$-0.00670814\pi$
$558$		0			0
$559$		0			0
$560$	−46.9783	+	15.1460i	−1.98519	+	0.640036i
$561$		0			0
$562$		−	1.28962i		−	0.0543994i
$563$			18.9051i			0.796754i	0.917222	+	0.398377i	$0.130426\pi$
$563$			18.9051i			0.796754i	−0.917222	+	0.398377i	$0.869574\pi$
$564$		0			0
$565$	1.05842	−	0.341241i	0.0445281	−	0.0143561i
$566$	38.2337			1.60708
$567$		0			0
$568$			60.5841i			2.54205i
$569$	−27.2554			−1.14261			−0.571304	−	0.820739i	$-0.693562\pi$
$569$	−27.2554			−1.14261			−0.571304	+	0.820739i	$0.693562\pi$
$570$		0			0
$571$	1.48913			0.0623180			0.0311590	−	0.999514i	$-0.490080\pi$
$571$	1.48913			0.0623180			0.0311590	+	0.999514i	$0.490080\pi$
$572$		0			0
$573$		0			0
$574$	76.4674			3.19169
$575$	2.31386	+	3.21543i	0.0964946	+	0.134093i
$576$		0			0
$577$		−	21.8719i		−	0.910537i	−0.890354	−	0.455269i	$-0.849543\pi$
$577$		−	21.8719i		−	0.910537i	0.890354	−	0.455269i	$-0.150457\pi$
$578$		−	36.5754i		−	1.52134i
$579$		0			0
$580$	26.2337	+	81.3687i	1.08929	+	3.37865i
$581$	−22.9783			−0.953298
$582$		0			0
$583$		−	10.0974i		−	0.418190i
$584$	41.4891			1.71683
$585$		0			0
$586$	−8.00000			−0.330477
$587$		−	41.2743i		−	1.70357i	−0.523890	−	0.851786i	$-0.675520\pi$
$587$		−	41.2743i		−	1.70357i	0.523890	−	0.851786i	$-0.324480\pi$
$588$		0			0
$589$	−13.4891			−0.555810
$590$	39.6060	−	12.7692i	1.63055	−	0.525698i
$591$		0			0
$592$			6.92820i			0.284747i
$593$			22.7739i			0.935214i	0.883937	+	0.467607i	$0.154884\pi$
$593$			22.7739i			0.935214i	−0.883937	+	0.467607i	$0.845116\pi$
$594$		0			0
$595$	−3.76631	−	11.6819i	−0.154404	−	0.478912i
$596$	50.2337			2.05765
$597$		0			0
$598$		0			0
$599$	10.9783			0.448559			0.224280	−	0.974525i	$-0.427997\pi$
$599$	10.9783			0.448559			0.224280	+	0.974525i	$0.427997\pi$
$600$		0			0
$601$	−38.4674			−1.56912			−0.784558	−	0.620055i	$-0.787110\pi$
$601$	−38.4674			−1.56912			−0.784558	+	0.620055i	$0.787110\pi$
$602$		−	30.2921i		−	1.23461i
$603$		0			0
$604$	53.4891			2.17644
$605$	−0.686141	−	2.12819i	−0.0278956	−	0.0865234i
$606$		0			0
$607$		−	3.46410i		−	0.140604i	−0.997526	−	0.0703018i	$-0.977604\pi$
$607$		−	3.46410i		−	0.140604i	0.997526	−	0.0703018i	$-0.0223962\pi$
$608$			16.4356i			0.666554i
$609$		0			0
$610$	4.00000	−	1.28962i	0.161955	−	0.0522152i
$611$		0			0
$612$		0			0
$613$		−	4.34896i		−	0.175653i	−0.996136	−	0.0878265i	$-0.972008\pi$
$613$		−	4.34896i		−	0.175653i	0.996136	−	0.0878265i	$-0.0279921\pi$
$614$	−79.7228			−3.21735
$615$		0			0
$616$	20.7446			0.835822
$617$		−	17.0256i		−	0.685423i	−0.939441	−	0.342712i	$-0.888655\pi$
$617$		−	17.0256i		−	0.685423i	0.939441	−	0.342712i	$-0.111345\pi$
$618$		0			0
$619$	−14.1168			−0.567404			−0.283702	−	0.958913i	$-0.591563\pi$
$619$	−14.1168			−0.567404			−0.283702	+	0.958913i	$0.591563\pi$
$620$	10.1168	+	31.3793i	0.406302	+	1.26022i
$621$		0			0
$622$			13.8564i			0.555591i
$623$		−	4.75372i		−	0.190454i
$624$		0			0
$625$	7.94158	−	23.7051i	0.317663	−	0.948204i
$626$	−55.2119			−2.20671
$627$		0			0
$628$		−	106.907i		−	4.26606i
$629$	−1.72281			−0.0686931
$630$		0			0
$631$	23.6060			0.939739			0.469869	−	0.882736i	$-0.344301\pi$
$631$	23.6060			0.939739			0.469869	+	0.882736i	$0.344301\pi$
$632$		−	7.51811i		−	0.299054i
$633$		0			0
$634$	83.2119			3.30477
$635$	17.4891	−	5.63858i	0.694035	−	0.223760i
$636$		0			0
$637$		0			0
$638$		−	22.0742i		−	0.873927i
$639$		0			0
$640$	−30.2337	+	9.74749i	−1.19509	+	0.385304i
$641$	25.3723			1.00214			0.501072	−	0.865405i	$-0.332939\pi$
$641$	25.3723			1.00214			0.501072	+	0.865405i	$0.332939\pi$
$642$		0			0
$643$		−	30.4944i		−	1.20258i	−0.799030	−	0.601292i	$-0.794653\pi$
$643$		−	30.4944i		−	1.20258i	0.799030	−	0.601292i	$-0.205347\pi$
$644$	12.0000			0.472866
$645$		0			0
$646$	−16.0000			−0.629512
$647$		−	21.9817i		−	0.864188i	−0.901829	−	0.432094i	$-0.857775\pi$
$647$		−	21.9817i		−	0.864188i	0.901829	−	0.432094i	$-0.142225\pi$
$648$		0			0
$649$	−7.37228			−0.289387
$650$		0			0
$651$		0			0
$652$			15.1460i			0.593164i
$653$			30.7894i			1.20488i	0.798163	+	0.602441i	$0.205805\pi$
$653$			30.7894i			1.20488i	−0.798163	+	0.602441i	$0.794195\pi$
$654$		0			0
$655$	−1.88316	−	5.84096i	−0.0735810	−	0.228225i
$656$	−55.7228			−2.17561
$657$		0			0
$658$			58.0049i			2.26127i
$659$	21.2554			0.827994			0.413997	−	0.910278i	$-0.364132\pi$
$659$	21.2554			0.827994			0.413997	+	0.910278i	$0.364132\pi$
$660$		0			0
$661$	−16.3505			−0.635962			−0.317981	−	0.948097i	$-0.603005\pi$
$661$	−16.3505			−0.635962			−0.317981	+	0.948097i	$0.603005\pi$
$662$			35.6357i			1.38502i
$663$		0			0
$664$	39.7228			1.54154
$665$	29.4891	−	9.50744i	1.14354	−	0.368683i
$666$		0			0
$667$		−	6.92820i		−	0.268261i
$668$			68.8019i			2.66203i
$669$		0			0
$670$	16.1168	+	49.9894i	0.622648	+	1.93126i
$671$	−0.744563			−0.0287435
$672$		0			0
$673$			18.6101i			0.717368i	0.933459	+	0.358684i	$0.116774\pi$
$673$			18.6101i			0.717368i	−0.933459	+	0.358684i	$0.883226\pi$
$674$	81.9565			3.15685
$675$		0			0
$676$	−56.8397			−2.18614
$677$			50.0820i			1.92481i	0.271623	+	0.962404i	$0.412440\pi$
$677$			50.0820i			1.92481i	−0.271623	+	0.962404i	$0.587560\pi$
$678$		0			0
$679$	−20.2337			−0.776498
$680$	6.51087	+	20.1947i	0.249681	+	0.774431i
$681$		0			0
$682$		−	8.51278i		−	0.325971i
$683$		−	17.9104i		−	0.685323i	−0.939459	−	0.342661i	$-0.888672\pi$
$683$		−	17.9104i		−	0.685323i	0.939459	−	0.342661i	$-0.111328\pi$
$684$		0			0
$685$	30.5475	−	9.84868i	1.16716	−	0.376299i
$686$	−17.4891			−0.667738
$687$		0			0
$688$			22.0742i			0.841572i
$689$		0			0
$690$		0			0
$691$	44.8614			1.70661			0.853304	−	0.521413i	$-0.174595\pi$
$691$	44.8614			1.70661			0.853304	+	0.521413i	$0.174595\pi$
$692$		−	37.2203i		−	1.41490i
$693$		0			0
$694$	−57.2119			−2.17174
$695$	−11.1386	−	34.5484i	−0.422511	−	1.31050i
$696$		0			0
$697$		−	13.8564i		−	0.524849i
$698$			39.0998i			1.47995i
$699$		0			0
$700$	−44.2337	−	61.4690i	−1.67188	−	2.32331i
$701$	12.5109			0.472529			0.236265	−	0.971689i	$-0.424077\pi$
$701$	12.5109			0.472529			0.236265	+	0.971689i	$0.424077\pi$
$702$		0			0
$703$		−	4.34896i		−	0.164024i
$704$	2.37228			0.0894087
$705$		0			0
$706$	−63.2119			−2.37901
$707$			20.7846i			0.781686i
$708$		0			0
$709$	−23.8832			−0.896951			−0.448475	−	0.893795i	$-0.648033\pi$
$709$	−23.8832			−0.896951			−0.448475	+	0.893795i	$0.648033\pi$
$710$	−54.3505	+	17.5229i	−2.03974	+	0.657622i
$711$		0			0
$712$			8.21782i			0.307976i
$713$		−	2.67181i		−	0.100060i
$714$		0			0
$715$		0			0
$716$	−56.2337			−2.10155
$717$		0			0
$718$		−	74.4405i		−	2.77810i
$719$	−30.3505			−1.13188			−0.565942	−	0.824445i	$-0.691487\pi$
$719$	−30.3505			−1.13188			−0.565942	+	0.824445i	$0.691487\pi$
$720$		0			0
$721$	−36.0000			−1.34071
$722$			7.57301i			0.281838i
$723$		0			0
$724$	−105.446			−3.91886
$725$	−35.4891	+	25.5383i	−1.31803	+	0.948470i
$726$		0			0
$727$		−	14.0588i		−	0.521412i	−0.965418	−	0.260706i	$-0.916045\pi$
$727$		−	14.0588i		−	0.521412i	0.965418	−	0.260706i	$-0.0839552\pi$
$728$		0			0
$729$		0			0
$730$	12.0000	+	37.2203i	0.444140	+	1.37758i
$731$	−5.48913			−0.203023
$732$		0			0
$733$		−	9.50744i		−	0.351165i	−0.984465	−	0.175583i	$-0.943819\pi$
$733$		−	9.50744i		−	0.351165i	0.984465	−	0.175583i	$-0.0561809\pi$
$734$	−64.9783			−2.39839
$735$		0			0
$736$	−3.25544			−0.119997
$737$		−	9.30506i		−	0.342756i
$738$		0			0
$739$	10.7446			0.395245			0.197623	−	0.980278i	$-0.436678\pi$
$739$	10.7446			0.395245			0.197623	+	0.980278i	$0.436678\pi$
$740$	−10.1168	+	3.26172i	−0.371903	+	0.119903i
$741$		0			0
$742$			88.2969i			3.24148i
$743$		−	11.3870i		−	0.417747i	−0.977943	−	0.208874i	$-0.933020\pi$
$743$		−	11.3870i		−	0.417747i	0.977943	−	0.208874i	$-0.0669798\pi$
$744$		0			0
$745$	7.88316	+	24.4511i	0.288816	+	0.895819i
$746$	−29.4891			−1.07967
$747$		0			0
$748$		−	6.92820i		−	0.253320i
$749$	−22.9783			−0.839607
$750$		0			0
$751$	27.3723			0.998829			0.499414	−	0.866363i	$-0.333549\pi$
$751$	27.3723			0.998829			0.499414	+	0.866363i	$0.333549\pi$
$752$		−	42.2689i		−	1.54139i
$753$		0			0
$754$		0			0
$755$	8.39403	+	26.0357i	0.305490	+	0.947535i
$756$		0			0
$757$		−	39.7995i		−	1.44654i	−0.690567	−	0.723269i	$-0.742639\pi$
$757$		−	39.7995i		−	1.44654i	0.690567	−	0.723269i	$-0.257361\pi$
$758$		−	1.58457i		−	0.0575543i
$759$		0			0
$760$	−50.9783	+	16.4356i	−1.84918	+	0.596184i
$761$	−32.7446			−1.18699			−0.593495	−	0.804838i	$-0.702252\pi$
$761$	−32.7446			−1.18699			−0.593495	+	0.804838i	$0.702252\pi$
$762$		0			0
$763$			34.6410i			1.25409i
$764$	−84.7011			−3.06438
$765$		0			0
$766$	27.4891			0.993222
$767$		0			0
$768$		0			0
$769$	−29.2119			−1.05341			−0.526705	−	0.850048i	$-0.676573\pi$
$769$	−29.2119			−1.05341			−0.526705	+	0.850048i	$0.676573\pi$
$770$	6.00000	+	18.6101i	0.216225	+	0.670662i
$771$		0			0
$772$			71.8613i			2.58634i
$773$			17.6155i			0.633584i	0.948495	+	0.316792i	$0.102606\pi$
$773$			17.6155i			0.633584i	−0.948495	+	0.316792i	$0.897394\pi$
$774$		0			0
$775$	−13.6861	+	9.84868i	−0.491621	+	0.353775i
$776$	34.9783			1.25565
$777$		0			0
$778$		−	47.6126i		−	1.70699i
$779$	34.9783			1.25323
$780$		0			0
$781$	10.1168			0.362009
$782$		−	3.16915i		−	0.113328i
$783$		0			0
$784$	−31.8614			−1.13791
$785$	52.0367	−	16.7769i	1.85727	−	0.598793i
$786$		0			0
$787$			15.1460i			0.539898i	0.962875	+	0.269949i	$0.0870068\pi$
$787$			15.1460i			0.539898i	−0.962875	+	0.269949i	$0.912993\pi$
$788$		−	37.2203i		−	1.32592i
$789$		0			0
$790$	6.74456	−	2.17448i	0.239961	−	0.0773646i
$791$	1.72281			0.0612562
$792$		0			0
$793$		0			0
$794$	41.4891			1.47239
$795$		0			0
$796$	−34.9783			−1.23977
$797$			5.25106i			0.186002i	0.995666	+	0.0930010i	$0.0296460\pi$
$797$			5.25106i			0.186002i	−0.995666	+	0.0930010i	$0.970354\pi$
$798$		0			0
$799$	10.5109			0.371848
$800$	12.0000	+	16.6757i	0.424264	+	0.589575i
$801$		0			0
$802$		−	29.0024i		−	1.02411i
$803$		−	6.92820i		−	0.244491i
$804$		0			0
$805$	1.88316	+	5.84096i	0.0663725	+	0.205867i
$806$		0			0
$807$		0			0
$808$		−	35.9306i		−	1.26404i
$809$	−32.7446			−1.15124			−0.575619	−	0.817718i	$-0.695239\pi$
$809$	−32.7446			−1.15124			−0.575619	+	0.817718i	$0.695239\pi$
$810$		0			0
$811$	−0.233688			−0.00820589			−0.00410295	−	0.999992i	$-0.501306\pi$
$811$	−0.233688			−0.00820589			−0.00410295	+	0.999992i	$0.501306\pi$
$812$			132.445i			4.64792i
$813$		0			0
$814$	2.74456			0.0961969
$815$	−7.37228	+	2.37686i	−0.258240	+	0.0832578i
$816$		0			0
$817$		−	13.8564i		−	0.484774i
$818$			69.3918i			2.42623i
$819$		0			0
$820$	−26.2337	−	81.3687i	−0.916120	−	2.84152i
$821$	18.0000			0.628204			0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000			0.628204			0.314102	+	0.949389i	$0.398297\pi$
$822$		0			0
$823$			56.0328i			1.95318i	0.215111	+	0.976590i	$0.430989\pi$
$823$			56.0328i			1.95318i	−0.215111	+	0.976590i	$0.569011\pi$
$824$	62.2337			2.16801
$825$		0			0
$826$	64.4674			2.24311
$827$			28.4125i			0.988000i	0.869462	+	0.494000i	$0.164466\pi$
$827$			28.4125i			0.988000i	−0.869462	+	0.494000i	$0.835534\pi$
$828$		0			0
$829$	20.3505			0.706803			0.353402	−	0.935472i	$-0.385025\pi$
$829$	20.3505			0.706803			0.353402	+	0.935472i	$0.385025\pi$
$830$	11.4891	+	35.6357i	0.398793	+	1.23693i
$831$		0			0
$832$		0			0
$833$		−	7.92287i		−	0.274511i
$834$		0			0
$835$	−33.4891	+	10.7971i	−1.15894	+	0.373648i
$836$	17.4891			0.604874
$837$		0			0
$838$			58.0049i			2.00374i
$839$	−10.1168			−0.349272			−0.174636	−	0.984633i	$-0.555875\pi$
$839$	−10.1168			−0.349272			−0.174636	+	0.984633i	$0.555875\pi$
$840$		0			0
$841$	47.4674			1.63681
$842$		−	21.4843i		−	0.740399i
$843$		0			0
$844$	−6.51087			−0.224114
$845$	−8.91983	−	27.6665i	−0.306851	−	0.951757i
$846$		0			0
$847$		−	3.46410i		−	0.119028i
$848$		−	64.3432i		−	2.20955i
$849$		0			0
$850$	−16.2337	+	11.6819i	−0.556811	+	0.400687i
$851$	0.861407			0.0295286
$852$		0			0
$853$			35.0458i			1.19994i	0.800021	+	0.599972i	$0.204822\pi$
$853$			35.0458i			1.19994i	−0.800021	+	0.599972i	$0.795178\pi$
$854$	6.51087			0.222798
$855$		0			0
$856$	39.7228			1.35770
$857$		−	23.9538i		−	0.818245i	−0.912480	−	0.409122i	$-0.865835\pi$
$857$		−	23.9538i		−	0.818245i	0.912480	−	0.409122i	$-0.134165\pi$
$858$		0			0
$859$	6.11684			0.208704			0.104352	−	0.994540i	$-0.466723\pi$
$859$	6.11684			0.208704			0.104352	+	0.994540i	$0.466723\pi$
$860$	−32.2337	+	10.3923i	−1.09916	+	0.354375i
$861$		0			0
$862$		−	64.9331i		−	2.21163i
$863$			2.87419i			0.0978387i	0.998803	+	0.0489194i	$0.0155777\pi$
$863$			2.87419i			0.0978387i	−0.998803	+	0.0489194i	$0.984422\pi$
$864$		0			0
$865$	18.1168	−	5.84096i	0.615991	−	0.198599i
$866$	73.7228			2.50520
$867$		0			0
$868$			51.0767i			1.73365i
$869$	−1.25544			−0.0425878
$870$		0			0
$871$		0			0
$872$		−	59.8844i		−	2.02794i
$873$		0			0
$874$	8.00000			0.270604
$875$	22.9783	−	31.1769i	0.776807	−	1.05397i
$876$		0			0
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$			54.2458i			1.83071i
$879$		0			0
$880$	−4.37228	−	13.5615i	−0.147390	−	0.457156i
$881$	6.86141			0.231167			0.115583	−	0.993298i	$-0.463126\pi$
$881$	6.86141			0.231167			0.115583	+	0.993298i	$0.463126\pi$
$882$		0			0
$883$			24.2487i			0.816034i	0.912974	+	0.408017i	$0.133780\pi$
$883$			24.2487i			0.816034i	−0.912974	+	0.408017i	$0.866220\pi$
$884$		0			0
$885$		0			0
$886$	79.9565			2.68619
$887$		−	27.4179i		−	0.920602i	−0.887763	−	0.460301i	$-0.847742\pi$
$887$		−	27.4179i		−	0.920602i	0.887763	−	0.460301i	$-0.152258\pi$
$888$		0			0
$889$	28.4674			0.954765
$890$	−7.37228	+	2.37686i	−0.247119	+	0.0796726i
$891$		0			0
$892$			10.3923i			0.347960i
$893$			26.5330i			0.887893i
$894$		0			0
$895$	−8.82473	−	27.3716i	−0.294978	−	0.914931i
$896$	−49.2119			−1.64406
$897$		0			0
$898$		−	17.3205i		−	0.577993i
$899$	29.4891			0.983517
$900$		0			0
$901$	16.0000			0.533037
$902$			22.0742i			0.734991i
$903$		0			0
$904$	−2.97825			−0.0990551
$905$	−16.5475	−	51.3253i	−0.550059	−	1.70611i
$906$		0			0
$907$			19.8997i			0.660760i	0.943848	+	0.330380i	$0.107177\pi$
$907$			19.8997i			0.660760i	−0.943848	+	0.330380i	$0.892823\pi$
$908$		−	73.1509i		−	2.42760i
$909$		0			0
$910$		0			0
$911$	53.4891			1.77217			0.886087	−	0.463519i	$-0.153413\pi$
$911$	53.4891			1.77217			0.886087	+	0.463519i	$0.153413\pi$
$912$		0			0
$913$		−	6.63325i		−	0.219529i
$914$	52.4674			1.73547
$915$		0			0
$916$	63.9565			2.11318
$917$		−	9.50744i		−	0.313963i
$918$		0			0
$919$	28.2337			0.931343			0.465672	−	0.884958i	$-0.345813\pi$
$919$	28.2337			0.931343			0.465672	+	0.884958i	$0.345813\pi$
$920$	−3.25544	−	10.0974i	−0.107329	−	0.332900i
$921$		0			0
$922$			5.63858i			0.185697i
$923$		0			0
$924$		0			0
$925$	−3.17527	−	4.41248i	−0.104402	−	0.145081i
$926$	−75.9565			−2.49609
$927$		0			0
$928$		−	35.9306i		−	1.17948i
$929$	−7.02175			−0.230376			−0.115188	−	0.993344i	$-0.536747\pi$
$929$	−7.02175			−0.230376			−0.115188	+	0.993344i	$0.536747\pi$
$930$		0			0
$931$	20.0000			0.655474
$932$		−	16.4356i		−	0.538368i
$933$		0			0
$934$	−19.4891			−0.637704
$935$	3.37228	−	1.08724i	0.110285	−	0.0355566i
$936$		0			0
$937$		−	53.6559i		−	1.75286i	−0.481527	−	0.876431i	$-0.659918\pi$
$937$		−	53.6559i		−	1.75286i	0.481527	−	0.876431i	$-0.340082\pi$
$938$			81.3687i			2.65678i
$939$		0			0
$940$	61.7228	−	19.8997i	2.01318	−	0.649058i
$941$	58.4674			1.90598			0.952991	−	0.302999i	$-0.0979878\pi$
$941$	58.4674			1.90598			0.952991	+	0.302999i	$0.0979878\pi$
$942$		0			0
$943$			6.92820i			0.225613i
$944$	−46.9783			−1.52901
$945$		0			0
$946$	8.74456			0.284310
$947$		−	26.7354i		−	0.868783i	−0.900724	−	0.434392i	$-0.856963\pi$
$947$		−	26.7354i		−	0.868783i	0.900724	−	0.434392i	$-0.143037\pi$
$948$		0			0
$949$		0			0
$950$	−29.4891	−	40.9793i	−0.956754	−	1.32954i
$951$		0			0
$952$			32.8713i			1.06536i
$953$		−	31.2867i		−	1.01348i	−0.862100	−	0.506738i	$-0.830851\pi$
$953$		−	31.2867i		−	1.01348i	0.862100	−	0.506738i	$-0.169149\pi$
$954$		0			0
$955$	−13.2921	−	41.2280i	−0.430123	−	1.33411i
$956$	64.4674			2.08502
$957$		0			0
$958$			13.8564i			0.447680i
$959$	49.7228			1.60563
$960$		0			0
$961$	−19.6277			−0.633152
$962$		0			0
$963$		0			0
$964$	−73.2119			−2.35800
$965$	−34.9783	+	11.2772i	−1.12599	+	0.363025i
$966$		0			0
$967$			26.4232i			0.849713i	0.905261	+	0.424856i	$0.139675\pi$
$967$			26.4232i			0.849713i	−0.905261	+	0.424856i	$0.860325\pi$
$968$			5.98844i			0.192476i
$969$		0			0
$970$	10.1168	+	31.3793i	0.324832	+	1.00753i
$971$	9.09509			0.291875			0.145938	−	0.989294i	$-0.453380\pi$
$971$	9.09509			0.291875			0.145938	+	0.989294i	$0.453380\pi$
$972$		0			0
$973$		−	56.2351i		−	1.80282i
$974$	18.0000			0.576757
$975$		0			0
$976$	−4.74456			−0.151870
$977$		−	50.5793i		−	1.61818i	−0.587687	−	0.809088i	$-0.699962\pi$
$977$		−	50.5793i		−	1.61818i	0.587687	−	0.809088i	$-0.300038\pi$
$978$		0			0
$979$	1.37228			0.0438583
$980$	−15.0000	−	46.5253i	−0.479157	−	1.48620i
$981$		0			0
$982$			16.4356i			0.524483i
$983$			24.7460i			0.789276i	0.918837	+	0.394638i	$0.129130\pi$
$983$			24.7460i			0.789276i	−0.918837	+	0.394638i	$0.870870\pi$
$984$		0			0
$985$	18.1168	−	5.84096i	0.577251	−	0.186109i
$986$	34.9783			1.11393
$987$		0			0
$988$		0			0
$989$	2.74456			0.0872720
$990$		0			0
$991$	18.9783			0.602864			0.301432	−	0.953488i	$-0.402535\pi$
$991$	18.9783			0.602864			0.301432	+	0.953488i	$0.402535\pi$
$992$		−	13.8564i		−	0.439941i
$993$		0			0
$994$	−88.4674			−2.80601
$995$	−5.48913	−	17.0256i	−0.174017	−	0.539746i
$996$		0			0
$997$		−	2.17448i		−	0.0688665i	−0.999407	−	0.0344333i	$-0.989037\pi$
$997$		−	2.17448i		−	0.0688665i	0.999407	−	0.0344333i	$-0.0109626\pi$
$998$		−	50.4868i		−	1.59813i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.c.a.199.1		4
3.2	odd	2		55.2.b.a.34.4	yes	4
5.2	odd	4		2475.2.a.bi.1.4		4
5.3	odd	4		2475.2.a.bi.1.1		4
5.4	even	2	inner	495.2.c.a.199.4		4
12.11	even	2		880.2.b.h.529.3		4
15.2	even	4		275.2.a.h.1.1		4
15.8	even	4		275.2.a.h.1.4		4
15.14	odd	2		55.2.b.a.34.1	✓	4
33.2	even	10		605.2.j.j.444.1		16
33.5	odd	10		605.2.j.i.124.1		16
33.8	even	10		605.2.j.j.9.1		16
33.14	odd	10		605.2.j.i.9.4		16
33.17	even	10		605.2.j.j.124.4		16
33.20	odd	10		605.2.j.i.444.4		16
33.26	odd	10		605.2.j.i.269.1		16
33.29	even	10		605.2.j.j.269.4		16
33.32	even	2		605.2.b.c.364.1		4
60.23	odd	4		4400.2.a.cc.1.2		4
60.47	odd	4		4400.2.a.cc.1.3		4
60.59	even	2		880.2.b.h.529.2		4
165.14	odd	10		605.2.j.i.9.1		16
165.29	even	10		605.2.j.j.269.1		16
165.32	odd	4		3025.2.a.ba.1.4		4
165.59	odd	10		605.2.j.i.269.4		16
165.74	even	10		605.2.j.j.9.4		16
165.98	odd	4		3025.2.a.ba.1.1		4
165.104	odd	10		605.2.j.i.124.4		16
165.119	odd	10		605.2.j.i.444.1		16
165.134	even	10		605.2.j.j.444.4		16
165.149	even	10		605.2.j.j.124.1		16
165.164	even	2		605.2.b.c.364.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.b.a.34.1	✓	4	15.14	odd	2
55.2.b.a.34.4	yes	4	3.2	odd	2
275.2.a.h.1.1		4	15.2	even	4
275.2.a.h.1.4		4	15.8	even	4
495.2.c.a.199.1		4	1.1	even	1	trivial
495.2.c.a.199.4		4	5.4	even	2	inner
605.2.b.c.364.1		4	33.32	even	2
605.2.b.c.364.4		4	165.164	even	2
605.2.j.i.9.1		16	165.14	odd	10
605.2.j.i.9.4		16	33.14	odd	10
605.2.j.i.124.1		16	33.5	odd	10
605.2.j.i.124.4		16	165.104	odd	10
605.2.j.i.269.1		16	33.26	odd	10
605.2.j.i.269.4		16	165.59	odd	10
605.2.j.i.444.1		16	165.119	odd	10
605.2.j.i.444.4		16	33.20	odd	10
605.2.j.j.9.1		16	33.8	even	10
605.2.j.j.9.4		16	165.74	even	10
605.2.j.j.124.1		16	165.149	even	10
605.2.j.j.124.4		16	33.17	even	10
605.2.j.j.269.1		16	165.29	even	10
605.2.j.j.269.4		16	33.29	even	10
605.2.j.j.444.1		16	33.2	even	10
605.2.j.j.444.4		16	165.134	even	10
880.2.b.h.529.2		4	60.59	even	2
880.2.b.h.529.3		4	12.11	even	2
2475.2.a.bi.1.1		4	5.3	odd	4
2475.2.a.bi.1.4		4	5.2	odd	4
3025.2.a.ba.1.1		4	165.98	odd	4
3025.2.a.ba.1.4		4	165.32	odd	4
4400.2.a.cc.1.2		4	60.23	odd	4
4400.2.a.cc.1.3		4	60.47	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.52434i q^{2} -4.37228 q^{4} +(-0.686141 - 2.12819i) q^{5} -3.46410i q^{7} +5.98844i q^{8} +(-5.37228 + 1.73205i) q^{10} +1.00000 q^{11} -8.74456 q^{14} +6.37228 q^{16} +1.58457i q^{17} -4.00000 q^{19} +(3.00000 + 9.30506i) q^{20} -2.52434i q^{22} -0.792287i q^{23} +(-4.05842 + 2.92048i) q^{25} +15.1460i q^{28} +8.74456 q^{29} +3.37228 q^{31} -4.10891i q^{32} +4.00000 q^{34} +(-7.37228 + 2.37686i) q^{35} +1.08724i q^{37} +10.0974i q^{38} +(12.7446 - 4.10891i) q^{40} -8.74456 q^{41} +3.46410i q^{43} -4.37228 q^{44} -2.00000 q^{46} -6.63325i q^{47} -5.00000 q^{49} +(7.37228 + 10.2448i) q^{50} -10.0974i q^{53} +(-0.686141 - 2.12819i) q^{55} +20.7446 q^{56} -22.0742i q^{58} -7.37228 q^{59} -0.744563 q^{61} -8.51278i q^{62} +2.37228 q^{64} -9.30506i q^{67} -6.92820i q^{68} +(6.00000 + 18.6101i) q^{70} +10.1168 q^{71} -6.92820i q^{73} +2.74456 q^{74} +17.4891 q^{76} -3.46410i q^{77} -1.25544 q^{79} +(-4.37228 - 13.5615i) q^{80} +22.0742i q^{82} -6.63325i q^{83} +(3.37228 - 1.08724i) q^{85} +8.74456 q^{86} +5.98844i q^{88} +1.37228 q^{89} +3.46410i q^{92} -16.7446 q^{94} +(2.74456 + 8.51278i) q^{95} -5.84096i q^{97} +12.6217i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} + 3 q^{5} - 10 q^{10} + 4 q^{11} - 12 q^{14} + 14 q^{16} - 16 q^{19} + 12 q^{20} + q^{25} + 12 q^{29} + 2 q^{31} + 16 q^{34} - 18 q^{35} + 28 q^{40} - 12 q^{41} - 6 q^{44} - 8 q^{46} - 20 q^{49}+ \cdots - 12 q^{95}+O(q^{100}) \) 4 * q - 6 * q^4 + 3 * q^5 - 10 * q^10 + 4 * q^11 - 12 * q^14 + 14 * q^16 - 16 * q^19 + 12 * q^20 + q^25 + 12 * q^29 + 2 * q^31 + 16 * q^34 - 18 * q^35 + 28 * q^40 - 12 * q^41 - 6 * q^44 - 8 * q^46 - 20 * q^49 + 18 * q^50 + 3 * q^55 + 60 * q^56 - 18 * q^59 + 20 * q^61 - 2 * q^64 + 24 * q^70 + 6 * q^71 - 12 * q^74 + 24 * q^76 - 28 * q^79 - 6 * q^80 + 2 * q^85 + 12 * q^86 - 6 * q^89 - 44 * q^94 - 12 * q^95

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