LMFDB - Embedded newform 585.2.c.c.469.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(469,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 16x^{8} + 90x^{6} + 208x^{4} + 169x^{2} + 16 $ x^10 + 16x^8 + 90x^6 + 208x^4 + 169x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.5
Root			$-0.329386i$ of defining polynomial
Character	$\chi$	$=$	585.469
Dual form			585.2.c.c.469.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.329386i q^{2} +1.89150 q^{4} +(-2.08591 + 0.805596i) q^{5} -3.70203i q^{7} -1.28181i q^{8} +O(q^{10})$	\(q-0.329386i q^{2} +1.89150 q^{4} +(-2.08591 + 0.805596i) q^{5} -3.70203i q^{7} -1.28181i q^{8} +(0.265352 + 0.687069i) q^{10} +3.31322 q^{11} +1.00000i q^{13} -1.21940 q^{14} +3.36080 q^{16} -4.36080i q^{17} -5.21940 q^{19} +(-3.94551 + 1.52379i) q^{20} -1.09133i q^{22} -4.92143i q^{23} +(3.70203 - 3.36080i) q^{25} +0.329386 q^{26} -7.00241i q^{28} +7.78301 q^{29} +0.0981475 q^{31} -3.67061i q^{32} -1.43639 q^{34} +(2.98234 + 7.72209i) q^{35} +2.92143i q^{37} +1.71920i q^{38} +(1.03262 + 2.67373i) q^{40} +0.749608 q^{41} -3.78301i q^{43} +6.26698 q^{44} -1.62105 q^{46} +5.67402i q^{47} -6.70502 q^{49} +(-1.10700 - 1.21940i) q^{50} +1.89150i q^{52} +2.19982i q^{53} +(-6.91108 + 2.66912i) q^{55} -4.74529 q^{56} -2.56361i q^{58} +0.108987 q^{59} +12.1438 q^{61} -0.0323284i q^{62} +5.51255 q^{64} +(-0.805596 - 2.08591i) q^{65} -12.4418i q^{67} -8.24848i q^{68} +(2.54355 - 0.982341i) q^{70} -12.0348 q^{71} +9.56602i q^{73} +0.962276 q^{74} -9.87251 q^{76} -12.2656i q^{77} -14.6093 q^{79} +(-7.01032 + 2.70745i) q^{80} -0.246910i q^{82} +16.7001i q^{83} +(3.51305 + 9.09623i) q^{85} -1.24607 q^{86} -4.24691i q^{88} -3.59403 q^{89} +3.70203 q^{91} -9.30890i q^{92} +1.86894 q^{94} +(10.8872 - 4.20473i) q^{95} +4.10467i q^{97} +2.20854i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) $ 10 * q - 12 * q^4 + 2 * q^5	$ 10 q - 12 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{11} + 24 q^{14} - 16 q^{19} - 32 q^{20} + 10 q^{25} + 16 q^{29} + 24 q^{31} - 40 q^{34} - 12 q^{35} + 36 q^{40} - 10 q^{41} + 36 q^{44} - 24 q^{46} - 44 q^{49} - 40 q^{50} + 2 q^{55} + 16 q^{59} + 26 q^{61} + 32 q^{64} + 56 q^{70} - 10 q^{71} + 24 q^{74} - 2 q^{79} + 12 q^{80} - 4 q^{85} + 38 q^{89} + 10 q^{91} + 24 q^{94} + 48 q^{95}+O(q^{100}) $ 10 * q - 12 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^11 + 24 * q^14 - 16 * q^19 - 32 * q^20 + 10 * q^25 + 16 * q^29 + 24 * q^31 - 40 * q^34 - 12 * q^35 + 36 * q^40 - 10 * q^41 + 36 * q^44 - 24 * q^46 - 44 * q^49 - 40 * q^50 + 2 * q^55 + 16 * q^59 + 26 * q^61 + 32 * q^64 + 56 * q^70 - 10 * q^71 + 24 * q^74 - 2 * q^79 + 12 * q^80 - 4 * q^85 + 38 * q^89 + 10 * q^91 + 24 * q^94 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	0.329386i		−	0.232911i	−0.993196	−	0.116456i	$-0.962847\pi$
$2$		−	0.329386i		−	0.232911i	0.993196	−	0.116456i	$-0.0371532\pi$
$3$		0			0
$3$		0			0
$4$	1.89150			0.945752
$5$	−2.08591	+	0.805596i	−0.932847	+	0.360274i
$5$	−2.08591	+	0.805596i	−0.932847	+	0.360274i
$6$		0			0
$7$		−	3.70203i		−	1.39924i	−0.714517	−	0.699618i	$-0.753354\pi$
$7$		−	3.70203i		−	1.39924i	0.714517	−	0.699618i	$-0.246646\pi$
$8$		−	1.28181i		−	0.453187i
$9$		0			0
$10$	0.265352	+	0.687069i	0.0839117	+	0.217270i
$11$	3.31322			0.998974			0.499487	−	0.866321i	$-0.333522\pi$
$11$	3.31322			0.998974			0.499487	+	0.866321i	$0.333522\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−1.21940			−0.325897
$15$		0			0
$16$	3.36080			0.840200
$17$		−	4.36080i		−	1.05765i	−0.848731	−	0.528825i	$-0.822633\pi$
$17$		−	4.36080i		−	1.05765i	0.848731	−	0.528825i	$-0.177367\pi$
$18$		0			0
$19$	−5.21940			−1.19741			−0.598706	−	0.800969i	$-0.704318\pi$
$19$	−5.21940			−1.19741			−0.598706	+	0.800969i	$0.704318\pi$
$20$	−3.94551	+	1.52379i	−0.882242	+	0.340730i
$21$		0			0
$22$		−	1.09133i		−	0.232672i
$23$		−	4.92143i		−	1.02619i	−0.858332	−	0.513094i	$-0.828499\pi$
$23$		−	4.92143i		−	1.02619i	0.858332	−	0.513094i	$-0.171501\pi$
$24$		0			0
$25$	3.70203	−	3.36080i	0.740406	−	0.672160i
$26$	0.329386			0.0645979
$27$		0			0
$28$		−	7.00241i		−	1.32333i
$29$	7.78301			1.44527			0.722634	−	0.691231i	$-0.242931\pi$
$29$	7.78301			1.44527			0.722634	+	0.691231i	$0.242931\pi$
$30$		0			0
$31$	0.0981475			0.0176278			0.00881390	−	0.999961i	$-0.497194\pi$
$31$	0.0981475			0.0176278			0.00881390	+	0.999961i	$0.497194\pi$
$32$		−	3.67061i		−	0.648879i
$33$		0			0
$34$	−1.43639			−0.246338
$35$	2.98234	+	7.72209i	0.504108	+	1.30527i
$36$		0			0
$37$			2.92143i			0.480279i	0.970738	+	0.240140i	$0.0771932\pi$
$37$			2.92143i			0.480279i	−0.970738	+	0.240140i	$0.922807\pi$
$38$			1.71920i			0.278890i
$39$		0			0
$40$	1.03262	+	2.67373i	0.163271	+	0.422754i
$41$	0.749608			0.117069			0.0585345	−	0.998285i	$-0.481357\pi$
$41$	0.749608			0.117069			0.0585345	+	0.998285i	$0.481357\pi$
$42$		0			0
$43$		−	3.78301i		−	0.576904i	−0.957494	−	0.288452i	$-0.906859\pi$
$43$		−	3.78301i		−	0.576904i	0.957494	−	0.288452i	$-0.0931405\pi$
$44$	6.26698			0.944782
$45$		0			0
$46$	−1.62105			−0.239010
$47$			5.67402i			0.827641i	0.910358	+	0.413821i	$0.135806\pi$
$47$			5.67402i			0.827641i	−0.910358	+	0.413821i	$0.864194\pi$
$48$		0			0
$49$	−6.70502			−0.957860
$50$	−1.10700	−	1.21940i	−0.156553	−	0.172449i
$51$		0			0
$52$			1.89150i			0.262305i
$53$			2.19982i			0.302169i	0.988521	+	0.151085i	$0.0482766\pi$
$53$			2.19982i			0.302169i	−0.988521	+	0.151085i	$0.951723\pi$
$54$		0			0
$55$	−6.91108	+	2.66912i	−0.931889	+	0.359904i
$56$	−4.74529			−0.634116
$57$		0			0
$58$		−	2.56361i		−	0.336619i
$59$	0.108987			0.0141890			0.00709448	−	0.999975i	$-0.497742\pi$
$59$	0.108987			0.0141890			0.00709448	+	0.999975i	$0.497742\pi$
$60$		0			0
$61$	12.1438			1.55486			0.777428	−	0.628972i	$-0.216524\pi$
$61$	12.1438			1.55486			0.777428	+	0.628972i	$0.216524\pi$
$62$		−	0.0323284i		−	0.00410571i
$63$		0			0
$64$	5.51255			0.689069
$65$	−0.805596	−	2.08591i	−0.0999219	−	0.258725i
$66$		0			0
$67$		−	12.4418i		−	1.52001i	−0.649920	−	0.760003i	$-0.725198\pi$
$67$		−	12.4418i		−	1.52001i	0.649920	−	0.760003i	$-0.274802\pi$
$68$		−	8.24848i		−	1.00027i
$69$		0			0
$70$	2.54355	−	0.982341i	0.304012	−	0.117412i
$71$	−12.0348			−1.42827			−0.714135	−	0.700008i	$-0.753180\pi$
$71$	−12.0348			−1.42827			−0.714135	+	0.700008i	$0.753180\pi$
$72$		0			0
$73$			9.56602i			1.11962i	0.828622	+	0.559809i	$0.189125\pi$
$73$			9.56602i			1.11962i	−0.828622	+	0.559809i	$0.810875\pi$
$74$	0.962276			0.111862
$75$		0			0
$76$	−9.87251			−1.13245
$77$		−	12.2656i		−	1.39780i
$78$		0			0
$79$	−14.6093			−1.64367			−0.821836	−	0.569724i	$-0.807050\pi$
$79$	−14.6093			−1.64367			−0.821836	+	0.569724i	$0.807050\pi$
$80$	−7.01032	+	2.70745i	−0.783778	+	0.302702i
$81$		0			0
$82$		−	0.246910i		−	0.0272667i
$83$			16.7001i			1.83308i	0.399948	+	0.916538i	$0.369028\pi$
$83$			16.7001i			1.83308i	−0.399948	+	0.916538i	$0.630972\pi$
$84$		0			0
$85$	3.51305	+	9.09623i	0.381043	+	0.986625i
$86$	−1.24607			−0.134367
$87$		0			0
$88$		−	4.24691i		−	0.452722i
$89$	−3.59403			−0.380966			−0.190483	−	0.981690i	$-0.561005\pi$
$89$	−3.59403			−0.380966			−0.190483	+	0.981690i	$0.561005\pi$
$90$		0			0
$91$	3.70203			0.388078
$92$		−	9.30890i		−	0.970520i
$93$		0			0
$94$	1.86894			0.192767
$95$	10.8872	−	4.20473i	1.11700	−	0.431396i
$96$		0			0
$97$			4.10467i			0.416766i	0.978047	+	0.208383i	$0.0668200\pi$
$97$			4.10467i			0.416766i	−0.978047	+	0.208383i	$0.933180\pi$
$98$			2.20854i			0.223096i
$99$		0			0
$100$	7.00241	−	6.35697i	0.700241	−	0.635697i
$101$	−2.77761			−0.276383			−0.138191	−	0.990406i	$-0.544129\pi$
$101$	−2.77761			−0.276383			−0.138191	+	0.990406i	$0.544129\pi$
$102$		0			0
$103$			16.5046i			1.62625i	0.582091	+	0.813124i	$0.302235\pi$
$103$			16.5046i			1.62625i	−0.582091	+	0.813124i	$0.697765\pi$
$104$	1.28181			0.125692
$105$		0			0
$106$	0.724591			0.0703785
$107$		−	1.04326i		−	0.100855i	−0.998728	−	0.0504277i	$-0.983942\pi$
$107$		−	1.04326i		−	0.100855i	0.998728	−	0.0504277i	$-0.0160585\pi$
$108$		0			0
$109$	11.0652			1.05986			0.529929	−	0.848042i	$-0.322219\pi$
$109$	11.0652			1.05986			0.529929	+	0.848042i	$0.322219\pi$
$110$	0.879170	+	2.27641i	0.0838256	+	0.217047i
$111$		0			0
$112$		−	12.4418i		−	1.17564i
$113$			15.9647i			1.50183i	0.660398	+	0.750915i	$0.270387\pi$
$113$			15.9647i			1.50183i	−0.660398	+	0.750915i	$0.729613\pi$
$114$		0			0
$115$	3.96468	+	10.2656i	0.369709	+	0.957276i
$116$	14.7216			1.36687
$117$		0			0
$118$		−	0.0358989i		−	0.00330476i
$119$	−16.1438			−1.47990
$120$		0			0
$121$	−0.0225619			−0.00205108
$122$		−	4.00000i		−	0.362143i
$123$		0			0
$124$	0.185646			0.0166715
$125$	−5.01464	+	9.99266i	−0.448523	+	0.893771i
$126$		0			0
$127$			18.9701i			1.68332i	0.540006	+	0.841661i	$0.318422\pi$
$127$			18.9701i			1.68332i	−0.540006	+	0.841661i	$0.681578\pi$
$128$		−	9.15699i		−	0.809371i
$129$		0			0
$130$	−0.687069	+	0.265352i	−0.0602599	+	0.0232729i
$131$	0.539929			0.0471738			0.0235869	−	0.999722i	$-0.492491\pi$
$131$	0.539929			0.0471738			0.0235869	+	0.999722i	$0.492491\pi$
$132$		0			0
$133$			19.3224i			1.67546i
$134$	−4.09815			−0.354026
$135$		0			0
$136$	−5.58970			−0.479313
$137$		−	12.2376i		−	1.04553i	−0.852476	−	0.522766i	$-0.824900\pi$
$137$		−	12.2376i		−	1.04553i	0.852476	−	0.522766i	$-0.175100\pi$
$138$		0			0
$139$	9.70502			0.823169			0.411584	−	0.911372i	$-0.364976\pi$
$139$	9.70502			0.823169			0.411584	+	0.911372i	$0.364976\pi$
$140$	5.64111	+	14.6064i	0.476761	+	1.23446i
$141$		0			0
$142$			3.96410i			0.332660i
$143$			3.31322i			0.277066i
$144$		0			0
$145$	−16.2346	+	6.26996i	−1.34821	+	0.520692i
$146$	3.15091			0.260771
$147$		0			0
$148$			5.52589i			0.454225i
$149$	5.28954			0.433336			0.216668	−	0.976245i	$-0.430481\pi$
$149$	5.28954			0.433336			0.216668	+	0.976245i	$0.430481\pi$
$150$		0			0
$151$	−16.3858			−1.33345			−0.666727	−	0.745302i	$-0.732305\pi$
$151$	−16.3858			−1.33345			−0.666727	+	0.745302i	$0.732305\pi$
$152$			6.69026i			0.542652i
$153$		0			0
$154$	−4.04013			−0.325563
$155$	−0.204727	+	0.0790672i	−0.0164440	+	0.00635083i
$156$		0			0
$157$		−	6.44477i		−	0.514349i	−0.966365	−	0.257174i	$-0.917209\pi$
$157$		−	6.44477i		−	0.514349i	0.966365	−	0.257174i	$-0.0827915\pi$
$158$			4.81209i			0.382829i
$159$		0			0
$160$	2.95703	+	7.65657i	0.233774	+	0.605305i
$161$	−18.2193			−1.43588
$162$		0			0
$163$		−	12.7673i		−	1.00001i	−0.866023	−	0.500005i	$-0.833332\pi$
$163$		−	12.7673i		−	1.00001i	0.866023	−	0.500005i	$-0.166668\pi$
$164$	1.41789			0.110718
$165$		0			0
$166$	5.50078			0.426943
$167$		−	3.98716i		−	0.308535i	−0.988029	−	0.154268i	$-0.950698\pi$
$167$		−	3.98716i		−	0.308535i	0.988029	−	0.154268i	$-0.0493018\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	2.99617	−	1.15715i	0.229796	−	0.0887492i
$171$		0			0
$172$		−	7.15558i		−	0.545608i
$173$			14.8836i			1.13158i	0.824551	+	0.565788i	$0.191428\pi$
$173$			14.8836i			1.13158i	−0.824551	+	0.565788i	$0.808572\pi$
$174$		0			0
$175$	−12.4418	−	13.7050i	−0.940510	−	1.03600i
$176$	11.1351			0.839338
$177$		0			0
$178$			1.18382i			0.0887312i
$179$	4.72160			0.352909			0.176455	−	0.984309i	$-0.443537\pi$
$179$	4.72160			0.352909			0.176455	+	0.984309i	$0.443537\pi$
$180$		0			0
$181$	−11.4614			−0.851916			−0.425958	−	0.904743i	$-0.640063\pi$
$181$	−11.4614			−0.851916			−0.425958	+	0.904743i	$0.640063\pi$
$182$		−	1.21940i		−	0.0903877i
$183$		0			0
$184$	−6.30832			−0.465055
$185$	−2.35349	−	6.09383i	−0.173032	−	0.448027i
$186$		0			0
$187$		−	14.4483i		−	1.05656i
$188$			10.7324i			0.782744i
$189$		0			0
$190$	−1.38498	−	3.58608i	−0.100477	−	0.260162i
$191$	16.9994			1.23003			0.615017	−	0.788514i	$-0.289149\pi$
$191$	16.9994			1.23003			0.615017	+	0.788514i	$0.289149\pi$
$192$		0			0
$193$			8.64459i			0.622252i	0.950369	+	0.311126i	$0.100706\pi$
$193$			8.64459i			0.622252i	−0.950369	+	0.311126i	$0.899294\pi$
$194$	1.35202			0.0970693
$195$		0			0
$196$	−12.6826			−0.905898
$197$			19.4540i			1.38604i	0.720917	+	0.693022i	$0.243721\pi$
$197$			19.4540i			1.38604i	−0.720917	+	0.693022i	$0.756279\pi$
$198$		0			0
$199$	18.2218			1.29171			0.645855	−	0.763460i	$-0.276501\pi$
$199$	18.2218			1.29171			0.645855	+	0.763460i	$0.276501\pi$
$200$	−4.30790	−	4.74529i	−0.304614	−	0.335542i
$201$		0			0
$202$			0.914907i			0.0643726i
$203$		−	28.8129i		−	2.02227i
$204$		0			0
$205$	−1.56361	+	0.603881i	−0.109208	+	0.0421769i
$206$	5.43639			0.378771
$207$		0			0
$208$			3.36080i			0.233030i
$209$	−17.2930			−1.19618
$210$		0			0
$211$	6.41810			0.441840			0.220920	−	0.975292i	$-0.429094\pi$
$211$	6.41810			0.441840			0.220920	+	0.975292i	$0.429094\pi$
$212$			4.16098i			0.285777i
$213$		0			0
$214$	−0.343634			−0.0234903
$215$	3.04758	+	7.89101i	0.207843	+	0.538163i
$216$		0			0
$217$		−	0.363345i		−	0.0246654i
$218$		−	3.64473i		−	0.246852i
$219$		0			0
$220$	−13.0723	+	5.04865i	−0.881337	+	0.340380i
$221$	4.36080			0.293339
$222$		0			0
$223$		−	2.54292i		−	0.170286i	−0.996369	−	0.0851432i	$-0.972865\pi$
$223$		−	2.54292i		−	0.170286i	0.996369	−	0.0851432i	$-0.0271348\pi$
$224$	−13.5887			−0.907935
$225$		0			0
$226$	5.25854			0.349793
$227$		−	27.9311i		−	1.85386i	−0.375240	−	0.926928i	$-0.622440\pi$
$227$		−	27.9311i		−	1.85386i	0.375240	−	0.926928i	$-0.377560\pi$
$228$		0			0
$229$	−2.58730			−0.170973			−0.0854867	−	0.996339i	$-0.527245\pi$
$229$	−2.58730			−0.170973			−0.0854867	+	0.996339i	$0.527245\pi$
$230$	3.38136	−	1.30591i	0.222960	−	0.0861092i
$231$		0			0
$232$		−	9.97632i		−	0.654977i
$233$			23.2651i			1.52414i	0.647492	+	0.762072i	$0.275818\pi$
$233$			23.2651i			1.52414i	−0.647492	+	0.762072i	$0.724182\pi$
$234$		0			0
$235$	−4.57097	−	11.8355i	−0.298177	−	0.772062i
$236$	0.206150			0.0134192
$237$		0			0
$238$			5.31754i			0.344685i
$239$	15.6008			1.00913			0.504567	−	0.863372i	$-0.331652\pi$
$239$	15.6008			1.00913			0.504567	+	0.863372i	$0.331652\pi$
$240$		0			0
$241$	26.8689			1.73078			0.865390	−	0.501098i	$-0.167071\pi$
$241$	26.8689			1.73078			0.865390	+	0.501098i	$0.167071\pi$
$242$			0.00743158i			0.000477720i
$243$		0			0
$244$	22.9701			1.47051
$245$	13.9861	−	5.40154i	0.893536	−	0.345092i
$246$		0			0
$247$		−	5.21940i		−	0.332102i
$248$		−	0.125806i		−	0.00798869i
$249$		0			0
$250$	3.29144	+	1.65175i	0.208169	+	0.104466i
$251$	2.90426			0.183315			0.0916576	−	0.995791i	$-0.470783\pi$
$251$	2.90426			0.183315			0.0916576	+	0.995791i	$0.470783\pi$
$252$		0			0
$253$		−	16.3058i		−	1.02514i
$254$	6.24848			0.392064
$255$		0			0
$256$	8.00892			0.500558
$257$		−	28.0048i		−	1.74689i	−0.486921	−	0.873446i	$-0.661880\pi$
$257$		−	28.0048i		−	1.74689i	0.486921	−	0.873446i	$-0.338120\pi$
$258$		0			0
$259$	10.8152			0.672024
$260$	−1.52379	−	3.94551i	−0.0945014	−	0.244690i
$261$		0			0
$262$		−	0.177845i		−	0.0109873i
$263$		−	2.74828i		−	0.169466i	−0.996404	−	0.0847330i	$-0.972996\pi$
$263$		−	2.74828i		−	0.169466i	0.996404	−	0.0847330i	$-0.0270037\pi$
$264$		0			0
$265$	−1.77217	−	4.58863i	−0.108864	−	0.281877i
$266$	6.36451			0.390233
$267$		0			0
$268$		−	23.5337i		−	1.43755i
$269$	−27.1224			−1.65368			−0.826841	−	0.562435i	$-0.809865\pi$
$269$	−27.1224			−1.65368			−0.826841	+	0.562435i	$0.809865\pi$
$270$		0			0
$271$	19.6555			1.19399			0.596994	−	0.802246i	$-0.296362\pi$
$271$	19.6555			1.19399			0.596994	+	0.802246i	$0.296362\pi$
$272$		−	14.6558i		−	0.888637i
$273$		0			0
$274$	−4.03090			−0.243516
$275$	12.2656	−	11.1351i	0.739646	−	0.671470i
$276$		0			0
$277$			15.1664i			0.911259i	0.890170	+	0.455630i	$0.150586\pi$
$277$			15.1664i			0.911259i	−0.890170	+	0.455630i	$0.849414\pi$
$278$		−	3.19670i		−	0.191725i
$279$		0			0
$280$	9.89823	−	3.82279i	0.591533	−	0.228455i
$281$	−3.97552			−0.237160			−0.118580	−	0.992945i	$-0.537834\pi$
$281$	−3.97552			−0.237160			−0.118580	+	0.992945i	$0.537834\pi$
$282$		0			0
$283$		−	0.768971i		−	0.0457106i	−0.999739	−	0.0228553i	$-0.992724\pi$
$283$		−	0.768971i		−	0.0457106i	0.999739	−	0.0228553i	$-0.00727570\pi$
$284$	−22.7639			−1.35079
$285$		0			0
$286$	1.09133			0.0645316
$287$		−	2.77507i		−	0.163807i
$288$		0			0
$289$	−2.01658			−0.118623
$290$	2.06524	+	5.34746i	0.121275	+	0.314014i
$291$		0			0
$292$			18.0942i			1.05888i
$293$		−	7.85369i		−	0.458817i	−0.973330	−	0.229409i	$-0.926321\pi$
$293$		−	7.85369i		−	0.458817i	0.973330	−	0.229409i	$-0.0736792\pi$
$294$		0			0
$295$	−0.227338	+	0.0877999i	−0.0132361	+	0.00511191i
$296$	3.74470			0.217656
$297$		0			0
$298$		−	1.74230i		−	0.100929i
$299$	4.92143			0.284613
$300$		0			0
$301$	−14.0048			−0.807224
$302$			5.39724i			0.310576i
$303$		0			0
$304$	−17.5414			−1.00607
$305$	−25.3309	+	9.78301i	−1.45044	+	0.560174i
$306$		0			0
$307$		−	0.893913i		−	0.0510183i	−0.999675	−	0.0255092i	$-0.991879\pi$
$307$		−	0.893913i		−	0.0510183i	0.999675	−	0.0255092i	$-0.00812070\pi$
$308$		−	23.2005i		−	1.32197i
$309$		0			0
$310$	0.0260436	+	0.0674341i	0.00147918	+	0.00383000i
$311$	−34.4340			−1.95257			−0.976286	−	0.216486i	$-0.930541\pi$
$311$	−34.4340			−1.95257			−0.976286	+	0.216486i	$0.930541\pi$
$312$		0			0
$313$		−	20.6008i		−	1.16442i	−0.813037	−	0.582212i	$-0.802187\pi$
$313$		−	20.6008i		−	1.16442i	0.813037	−	0.582212i	$-0.197813\pi$
$314$	−2.12282			−0.119797
$315$		0			0
$316$	−27.6335			−1.55451
$317$			13.1772i			0.740106i	0.929011	+	0.370053i	$0.120660\pi$
$317$			13.1772i			0.740106i	−0.929011	+	0.370053i	$0.879340\pi$
$318$		0			0
$319$	25.7868			1.44379
$320$	−11.4987	+	4.44089i	−0.642796	+	0.248253i
$321$		0			0
$322$			6.00117i			0.334432i
$323$			22.7607i			1.26644i
$324$		0			0
$325$	3.36080	+	3.70203i	0.186424	+	0.205352i
$326$	−4.20536			−0.232913
$327$		0			0
$328$		−	0.960853i		−	0.0530542i
$329$	21.0054			1.15806
$330$		0			0
$331$	−19.0536			−1.04728			−0.523640	−	0.851939i	$-0.675426\pi$
$331$	−19.0536			−1.04728			−0.523640	+	0.851939i	$0.675426\pi$
$332$			31.5883i			1.73364i
$333$		0			0
$334$	−1.31331			−0.0718613
$335$	10.0231	+	25.9524i	0.547618	+	1.41793i
$336$		0			0
$337$		−	11.6525i		−	0.634754i	−0.948299	−	0.317377i	$-0.897198\pi$
$337$		−	11.6525i		−	0.634754i	0.948299	−	0.317377i	$-0.102802\pi$
$338$			0.329386i			0.0179162i
$339$		0			0
$340$	6.64494	+	17.2056i	0.360373	+	0.933103i
$341$	0.325184			0.0176097
$342$		0			0
$343$		−	1.09203i		−	0.0589641i
$344$	−4.84909			−0.261445
$345$		0			0
$346$	4.90244			0.263557
$347$		−	18.4680i		−	0.991415i	−0.868490	−	0.495707i	$-0.834909\pi$
$347$		−	18.4680i		−	0.991415i	0.868490	−	0.495707i	$-0.165091\pi$
$348$		0			0
$349$	−18.9309			−1.01335			−0.506675	−	0.862137i	$-0.669126\pi$
$349$	−18.9309			−1.01335			−0.506675	+	0.862137i	$0.669126\pi$
$350$	−4.51424	+	4.09815i	−0.241296	+	0.219055i
$351$		0			0
$352$		−	12.1616i		−	0.648213i
$353$		−	21.9048i		−	1.16587i	−0.812517	−	0.582937i	$-0.801903\pi$
$353$		−	21.9048i		−	1.16587i	0.812517	−	0.582937i	$-0.198097\pi$
$354$		0			0
$355$	25.1035	−	9.69521i	1.33236	−	0.514568i
$356$	−6.79812			−0.360300
$357$		0			0
$358$		−	1.55523i		−	0.0821964i
$359$	23.5630			1.24361			0.621803	−	0.783173i	$-0.286400\pi$
$359$	23.5630			1.24361			0.621803	+	0.783173i	$0.286400\pi$
$360$		0			0
$361$	8.24210			0.433795
$362$			3.77521i			0.198421i
$363$		0			0
$364$	7.00241			0.367026
$365$	−7.70635	−	19.9538i	−0.403369	−	1.04443i
$366$		0			0
$367$		−	19.9450i		−	1.04112i	−0.853825	−	0.520560i	$-0.825723\pi$
$367$		−	19.9450i		−	1.04112i	0.853825	−	0.520560i	$-0.174277\pi$
$368$		−	16.5399i		−	0.862203i
$369$		0			0
$370$	−2.00722	+	0.775206i	−0.104350	+	0.0403011i
$371$	8.14381			0.422806
$372$		0			0
$373$			4.48616i			0.232285i	0.993233	+	0.116142i	$0.0370529\pi$
$373$			4.48616i			0.232285i	−0.993233	+	0.116142i	$0.962947\pi$
$374$	−4.75907			−0.246085
$375$		0			0
$376$	7.27300			0.375076
$377$			7.78301i			0.400845i
$378$		0			0
$379$	−4.65976			−0.239356			−0.119678	−	0.992813i	$-0.538186\pi$
$379$	−4.65976			−0.239356			−0.119678	+	0.992813i	$0.538186\pi$
$380$	20.5932	−	7.95326i	1.05641	−	0.407994i
$381$		0			0
$382$		−	5.59937i		−	0.286489i
$383$		−	4.70011i		−	0.240165i	−0.992764	−	0.120082i	$-0.961684\pi$
$383$		−	4.70011i		−	0.240165i	0.992764	−	0.120082i	$-0.0383158\pi$
$384$		0			0
$385$	9.88116	+	25.5850i	0.503590	+	1.30393i
$386$	2.84741			0.144929
$387$		0			0
$388$			7.76400i			0.394157i
$389$	14.6128			0.740899			0.370449	−	0.928853i	$-0.379204\pi$
$389$	14.6128			0.740899			0.370449	+	0.928853i	$0.379204\pi$
$390$		0			0
$391$	−21.4614			−1.08535
$392$			8.59454i			0.434090i
$393$		0			0
$394$	6.40789			0.322825
$395$	30.4736	−	11.7692i	1.53329	−	0.592172i
$396$		0			0
$397$			22.2911i			1.11876i	0.828911	+	0.559380i	$0.188961\pi$
$397$			22.2911i			1.11876i	−0.828911	+	0.559380i	$0.811039\pi$
$398$		−	6.00200i		−	0.300853i
$399$		0			0
$400$	12.4418	−	11.2950i	0.622089	−	0.564749i
$401$	−3.61021			−0.180285			−0.0901426	−	0.995929i	$-0.528732\pi$
$401$	−3.61021			−0.180285			−0.0901426	+	0.995929i	$0.528732\pi$
$402$		0			0
$403$			0.0981475i			0.00488907i
$404$	−5.25387			−0.261390
$405$		0			0
$406$	−9.49057			−0.471009
$407$			9.67933i			0.479787i
$408$		0			0
$409$	−12.6911			−0.627535			−0.313767	−	0.949500i	$-0.601591\pi$
$409$	−12.6911			−0.627535			−0.313767	+	0.949500i	$0.601591\pi$
$410$	0.198910	+	0.515032i	0.00982347	+	0.0254356i
$411$		0			0
$412$			31.2186i			1.53803i
$413$		−	0.403475i		−	0.0198537i
$414$		0			0
$415$	−13.4536	−	34.8349i	−0.660409	−	1.70998i
$416$	3.67061			0.179967
$417$		0			0
$418$			5.69608i			0.278604i
$419$	2.66078			0.129987			0.0649937	−	0.997886i	$-0.479297\pi$
$419$	2.66078			0.129987			0.0649937	+	0.997886i	$0.479297\pi$
$420$		0			0
$421$	−20.0305			−0.976227			−0.488113	−	0.872780i	$-0.662315\pi$
$421$	−20.0305			−0.976227			−0.488113	+	0.872780i	$0.662315\pi$
$422$		−	2.11403i		−	0.102909i
$423$		0			0
$424$	2.81975			0.136939
$425$	−14.6558	−	16.1438i	−0.710910	−	0.783090i
$426$		0			0
$427$		−	44.9567i		−	2.17561i
$428$		−	1.97333i		−	0.0953843i
$429$		0			0
$430$	2.59919	−	1.00383i	0.125344	−	0.0484090i
$431$	2.79742			0.134747			0.0673736	−	0.997728i	$-0.478538\pi$
$431$	2.79742			0.134747			0.0673736	+	0.997728i	$0.478538\pi$
$432$		0			0
$433$			9.56602i			0.459714i	0.973224	+	0.229857i	$0.0738258\pi$
$433$			9.56602i			0.459714i	−0.973224	+	0.229857i	$0.926174\pi$
$434$	−0.119681			−0.00574485
$435$		0			0
$436$	20.9299			1.00236
$437$			25.6869i			1.22877i
$438$		0			0
$439$	7.45654			0.355881			0.177941	−	0.984041i	$-0.443056\pi$
$439$	7.45654			0.355881			0.177941	+	0.984041i	$0.443056\pi$
$440$	3.42130	+	8.85867i	0.163104	+	0.422320i
$441$		0			0
$442$		−	1.43639i		−	0.0683219i
$443$			7.92201i			0.376386i	0.982132	+	0.188193i	$0.0602630\pi$
$443$			7.92201i			0.376386i	−0.982132	+	0.188193i	$0.939737\pi$
$444$		0			0
$445$	7.49681	−	2.89533i	0.355383	−	0.137252i
$446$	−0.837602			−0.0396616
$447$		0			0
$448$		−	20.4076i		−	0.964170i
$449$	38.7241			1.82750			0.913752	−	0.406273i	$-0.133172\pi$
$449$	38.7241			1.82750			0.913752	+	0.406273i	$0.133172\pi$
$450$		0			0
$451$	2.48362			0.116949
$452$			30.1973i			1.42036i
$453$		0			0
$454$	−9.20012			−0.431783
$455$	−7.72209	+	2.98234i	−0.362017	+	0.139814i
$456$		0			0
$457$		−	12.8322i		−	0.600267i	−0.953897	−	0.300134i	$-0.902969\pi$
$457$		−	12.8322i		−	0.600267i	0.953897	−	0.300134i	$-0.0970313\pi$
$458$			0.852220i			0.0398216i
$459$		0			0
$460$	7.49922	+	19.4175i	0.349653	+	0.905346i
$461$	31.1178			1.44930			0.724649	−	0.689118i	$-0.242002\pi$
$461$	31.1178			1.44930			0.724649	+	0.689118i	$0.242002\pi$
$462$		0			0
$463$			10.2588i			0.476768i	0.971171	+	0.238384i	$0.0766177\pi$
$463$			10.2588i			0.476768i	−0.971171	+	0.238384i	$0.923382\pi$
$464$	26.1571			1.21431
$465$		0			0
$466$	7.66318			0.354990
$467$		−	12.3315i		−	0.570632i	−0.958434	−	0.285316i	$-0.907901\pi$
$467$		−	12.3315i		−	0.570632i	0.958434	−	0.285316i	$-0.0920985\pi$
$468$		0			0
$469$	−46.0598			−2.12685
$470$	−3.89844	+	1.50561i	−0.179822	+	0.0694488i
$471$		0			0
$472$		−	0.139701i		−	0.00643025i
$473$		−	12.5340i		−	0.576312i
$474$		0			0
$475$	−19.3224	+	17.5414i	−0.886570	+	0.804852i
$476$	−30.5361			−1.39962
$477$		0			0
$478$		−	5.13870i		−	0.235039i
$479$	−8.21141			−0.375189			−0.187594	−	0.982247i	$-0.560069\pi$
$479$	−8.21141			−0.375189			−0.187594	+	0.982247i	$0.560069\pi$
$480$		0			0
$481$	−2.92143			−0.133206
$482$		−	8.85025i		−	0.403118i
$483$		0			0
$484$	−0.0426760			−0.00193982
$485$	−3.30670	−	8.56196i	−0.150150	−	0.388778i
$486$		0			0
$487$			23.4860i			1.06425i	0.846665	+	0.532127i	$0.178607\pi$
$487$			23.4860i			1.06425i	−0.846665	+	0.532127i	$0.821393\pi$
$488$		−	15.5660i		−	0.704641i
$489$		0			0
$490$	−1.77919	−	4.60681i	−0.0803756	−	0.208114i
$491$	−1.21739			−0.0549401			−0.0274701	−	0.999623i	$-0.508745\pi$
$491$	−1.21739			−0.0549401			−0.0274701	+	0.999623i	$0.508745\pi$
$492$		0			0
$493$		−	33.9402i		−	1.52859i
$494$	−1.71920			−0.0773503
$495$		0			0
$496$	0.329854			0.0148109
$497$			44.5533i			1.99849i
$498$		0			0
$499$	1.60334			0.0717755			0.0358877	−	0.999356i	$-0.488574\pi$
$499$	1.60334			0.0717755			0.0358877	+	0.999356i	$0.488574\pi$
$500$	−9.48523	+	18.9012i	−0.424192	+	0.845286i
$501$		0			0
$502$		−	0.956622i		−	0.0426961i
$503$			27.4355i			1.22329i	0.791132	+	0.611645i	$0.209492\pi$
$503$			27.4355i			1.22329i	−0.791132	+	0.611645i	$0.790508\pi$
$504$		0			0
$505$	5.79385	−	2.23764i	0.257823	−	0.0995735i
$506$	−5.37089			−0.238765
$507$		0			0
$508$			35.8820i			1.59201i
$509$	11.4124			0.505844			0.252922	−	0.967487i	$-0.418608\pi$
$509$	11.4124			0.505844			0.252922	+	0.967487i	$0.418608\pi$
$510$		0			0
$511$	35.4137			1.56661
$512$		−	20.9520i		−	0.925956i
$513$		0			0
$514$	−9.22439			−0.406870
$515$	−13.2961	−	34.4271i	−0.585894	−	1.51704i
$516$		0			0
$517$			18.7993i			0.826792i
$518$		−	3.56237i		−	0.156522i
$519$		0			0
$520$	−2.67373	+	1.03262i	−0.117251	+	0.0452833i
$521$	−30.6274			−1.34181			−0.670906	−	0.741542i	$-0.734095\pi$
$521$	−30.6274			−1.34181			−0.670906	+	0.741542i	$0.734095\pi$
$522$		0			0
$523$		−	24.9956i		−	1.09298i	−0.837465	−	0.546490i	$-0.815964\pi$
$523$		−	24.9956i		−	1.09298i	0.837465	−	0.546490i	$-0.184036\pi$
$524$	1.02128			0.0446148
$525$		0			0
$526$	−0.905243			−0.0394705
$527$		−	0.428002i		−	0.0186440i
$528$		0			0
$529$	−1.22042			−0.0530620
$530$	−1.51143	+	0.583728i	−0.0656523	+	0.0253555i
$531$		0			0
$532$			36.5483i			1.58457i
$533$			0.749608i			0.0324691i
$534$		0			0
$535$	0.840444	+	2.17614i	0.0363356	+	0.0940827i
$536$	−15.9480			−0.688847
$537$		0			0
$538$			8.93374i			0.385161i
$539$	−22.2152			−0.956877
$540$		0			0
$541$	−0.131461			−0.00565193			−0.00282596	−	0.999996i	$-0.500900\pi$
$541$	−0.131461			−0.00565193			−0.00282596	+	0.999996i	$0.500900\pi$
$542$		−	6.47425i		−	0.278093i
$543$		0			0
$544$	−16.0068			−0.686287
$545$	−23.0811	+	8.91411i	−0.988684	+	0.381839i
$546$		0			0
$547$			21.5955i			0.923358i	0.887047	+	0.461679i	$0.152753\pi$
$547$			21.5955i			0.923358i	−0.887047	+	0.461679i	$0.847247\pi$
$548$		−	23.1475i		−	0.988814i
$549$		0			0
$550$	−3.66774	−	4.04013i	−0.156393	−	0.172272i
$551$	−40.6226			−1.73058
$552$		0			0
$553$			54.0840i			2.29988i
$554$	4.99559			0.212242
$555$		0			0
$556$	18.3571			0.778514
$557$			40.1776i			1.70238i	0.524858	+	0.851190i	$0.324119\pi$
$557$			40.1776i			1.70238i	−0.524858	+	0.851190i	$0.675881\pi$
$558$		0			0
$559$	3.78301			0.160004
$560$	10.0231	+	25.9524i	0.423551	+	1.09669i
$561$		0			0
$562$			1.30948i			0.0552371i
$563$			3.57240i			0.150559i	0.997162	+	0.0752793i	$0.0239848\pi$
$563$			3.57240i			0.150559i	−0.997162	+	0.0752793i	$0.976015\pi$
$564$		0			0
$565$	−12.8611	−	33.3009i	−0.541070	−	1.40098i
$566$	−0.253288			−0.0106465
$567$		0			0
$568$			15.4263i			0.647274i
$569$	0.744448			0.0312089			0.0156044	−	0.999878i	$-0.495033\pi$
$569$	0.744448			0.0312089			0.0156044	+	0.999878i	$0.495033\pi$
$570$		0			0
$571$	17.4234			0.729145			0.364573	−	0.931175i	$-0.381215\pi$
$571$	17.4234			0.729145			0.364573	+	0.931175i	$0.381215\pi$
$572$			6.26698i			0.262035i
$573$		0			0
$574$	−0.914069			−0.0381525
$575$	−16.5399	−	18.2193i	−0.689763	−	0.759796i
$576$		0			0
$577$			40.6582i			1.69262i	0.532687	+	0.846312i	$0.321182\pi$
$577$			40.6582i			1.69262i	−0.532687	+	0.846312i	$0.678818\pi$
$578$			0.664234i			0.0276285i
$579$		0			0
$580$	−30.7079	+	11.8597i	−1.27508	+	0.492446i
$581$	61.8243			2.56490
$582$		0			0
$583$			7.28850i			0.301859i
$584$	12.2618			0.507396
$585$		0			0
$586$	−2.58689			−0.106864
$587$		−	5.24004i		−	0.216280i	−0.994136	−	0.108140i	$-0.965511\pi$
$587$		−	5.24004i		−	0.216280i	0.994136	−	0.108140i	$-0.0344894\pi$
$588$		0			0
$589$	−0.512270			−0.0211077
$590$	0.0289200	+	0.0748819i	0.00119062	+	0.00308284i
$591$		0			0
$592$			9.81833i			0.403531i
$593$			4.71557i			0.193645i	0.995302	+	0.0968227i	$0.0308680\pi$
$593$			4.71557i			0.193645i	−0.995302	+	0.0968227i	$0.969132\pi$
$594$		0			0
$595$	33.6745	−	13.0054i	1.38052	−	0.533169i
$596$	10.0052			0.409828
$597$		0			0
$598$		−	1.62105i		−	0.0662896i
$599$	−17.6268			−0.720213			−0.360107	−	0.932911i	$-0.617260\pi$
$599$	−17.6268			−0.720213			−0.360107	+	0.932911i	$0.617260\pi$
$600$		0			0
$601$	−4.38747			−0.178969			−0.0894844	−	0.995988i	$-0.528522\pi$
$601$	−4.38747			−0.178969			−0.0894844	+	0.995988i	$0.528522\pi$
$602$			4.61299i			0.188011i
$603$		0			0
$604$	−30.9938			−1.26112
$605$	0.0470621	−	0.0181758i	0.00191335	−	0.000738952i
$606$		0			0
$607$			25.4225i			1.03187i	0.856628	+	0.515934i	$0.172555\pi$
$607$			25.4225i			1.03187i	−0.856628	+	0.515934i	$0.827445\pi$
$608$			19.1584i			0.776975i
$609$		0			0
$610$	3.22239	+	8.34363i	0.130471	+	0.337824i
$611$	−5.67402			−0.229546
$612$		0			0
$613$			15.8464i			0.640029i	0.947413	+	0.320015i	$0.103688\pi$
$613$			15.8464i			0.640029i	−0.947413	+	0.320015i	$0.896312\pi$
$614$	−0.294442			−0.0118827
$615$		0			0
$616$	−15.7222			−0.633465
$617$			9.43461i			0.379823i	0.981801	+	0.189912i	$0.0608201\pi$
$617$			9.43461i			0.379823i	−0.981801	+	0.189912i	$0.939180\pi$
$618$		0			0
$619$	19.0899			0.767288			0.383644	−	0.923481i	$-0.374669\pi$
$619$	19.0899			0.767288			0.383644	+	0.923481i	$0.374669\pi$
$620$	−0.387241	+	0.149556i	−0.0155520	+	0.00600632i
$621$		0			0
$622$			11.3421i			0.454775i
$623$			13.3052i			0.533061i
$624$		0			0
$625$	2.41004	−	24.8836i	0.0964015	−	0.995343i
$626$	−6.78560			−0.271207
$627$		0			0
$628$		−	12.1903i		−	0.486447i
$629$	12.7398			0.507967
$630$		0			0
$631$	−6.58431			−0.262117			−0.131059	−	0.991375i	$-0.541838\pi$
$631$	−6.58431			−0.262117			−0.131059	+	0.991375i	$0.541838\pi$
$632$			18.7263i			0.744891i
$633$		0			0
$634$	4.34039			0.172379
$635$	−15.2822	−	39.5698i	−0.606457	−	1.57028i
$636$		0			0
$637$		−	6.70502i		−	0.265662i
$638$		−	8.49382i		−	0.336274i
$639$		0			0
$640$	7.37683	+	19.1006i	0.291595	+	0.755019i
$641$	−20.5606			−0.812096			−0.406048	−	0.913852i	$-0.633093\pi$
$641$	−20.5606			−0.812096			−0.406048	+	0.913852i	$0.633093\pi$
$642$		0			0
$643$			14.7084i			0.580043i	0.957020	+	0.290022i	$0.0936625\pi$
$643$			14.7084i			0.580043i	−0.957020	+	0.290022i	$0.906338\pi$
$644$	−34.4618			−1.35799
$645$		0			0
$646$	7.49707			0.294968
$647$		−	30.1145i		−	1.18392i	−0.805967	−	0.591961i	$-0.798354\pi$
$647$		−	30.1145i		−	1.18392i	0.805967	−	0.591961i	$-0.201646\pi$
$648$		0			0
$649$	0.361099			0.0141744
$650$	1.21940	−	1.10700i	0.0478287	−	0.0434201i
$651$		0			0
$652$		−	24.1493i		−	0.945761i
$653$			23.8527i			0.933427i	0.884409	+	0.466713i	$0.154562\pi$
$653$			23.8527i			0.933427i	−0.884409	+	0.466713i	$0.845438\pi$
$654$		0			0
$655$	−1.12624	+	0.434965i	−0.0440059	+	0.0169955i
$656$	2.51928			0.0983615
$657$		0			0
$658$		−	6.91888i		−	0.269726i
$659$	−26.4789			−1.03147			−0.515736	−	0.856747i	$-0.672482\pi$
$659$	−26.4789			−1.03147			−0.515736	+	0.856747i	$0.672482\pi$
$660$		0			0
$661$	14.7579			0.574016			0.287008	−	0.957928i	$-0.407339\pi$
$661$	14.7579			0.574016			0.287008	+	0.957928i	$0.407339\pi$
$662$			6.27599i			0.243923i
$663$		0			0
$664$	21.4063			0.830726
$665$	−15.5660	−	40.3047i	−0.603624	−	1.56295i
$666$		0			0
$667$		−	38.3035i		−	1.48312i
$668$		−	7.54172i		−	0.291798i
$669$		0			0
$670$	8.54836	−	3.30145i	0.330252	−	0.127546i
$671$	40.2351			1.55326
$672$		0			0
$673$		−	11.2784i		−	0.434750i	−0.976088	−	0.217375i	$-0.930251\pi$
$673$		−	11.2784i		−	0.434750i	0.976088	−	0.217375i	$-0.0697495\pi$
$674$	−3.83818			−0.147841
$675$		0			0
$676$	−1.89150			−0.0727502
$677$			29.1052i			1.11861i	0.828963	+	0.559303i	$0.188931\pi$
$677$			29.1052i			1.11861i	−0.828963	+	0.559303i	$0.811069\pi$
$678$		0			0
$679$	15.1956			0.583153
$680$	11.6596	−	4.50305i	0.447126	−	0.172684i
$681$		0			0
$682$		−	0.107111i		−	0.00410150i
$683$		−	1.84463i		−	0.0705827i	−0.999377	−	0.0352914i	$-0.988764\pi$
$683$		−	1.84463i		−	0.0705827i	0.999377	−	0.0352914i	$-0.0112359\pi$
$684$		0			0
$685$	9.85860	+	25.5266i	0.376678	+	0.975321i
$686$	−0.359700			−0.0137334
$687$		0			0
$688$		−	12.7139i		−	0.484715i
$689$	−2.19982			−0.0838066
$690$		0			0
$691$	−30.4103			−1.15686			−0.578431	−	0.815731i	$-0.696335\pi$
$691$	−30.4103			−1.15686			−0.578431	+	0.815731i	$0.696335\pi$
$692$			28.1523i			1.07019i
$693$		0			0
$694$	−6.08310			−0.230911
$695$	−20.2438	+	7.81833i	−0.767890	+	0.296566i
$696$		0			0
$697$		−	3.26889i		−	0.123818i
$698$			6.23558i			0.236020i
$699$		0			0
$700$	−23.5337	−	25.9231i	−0.889490	−	0.979801i
$701$	48.8119			1.84360			0.921801	−	0.387664i	$-0.126718\pi$
$701$	48.8119			1.84360			0.921801	+	0.387664i	$0.126718\pi$
$702$		0			0
$703$		−	15.2481i		−	0.575092i
$704$	18.2643			0.688362
$705$		0			0
$706$	−7.21513			−0.271545
$707$			10.2828i			0.386725i
$708$		0			0
$709$	−6.74926			−0.253474			−0.126737	−	0.991936i	$-0.540450\pi$
$709$	−6.74926			−0.253474			−0.126737	+	0.991936i	$0.540450\pi$
$710$	−3.19347	−	8.26875i	−0.119849	−	0.310321i
$711$		0			0
$712$			4.60685i			0.172649i
$713$		−	0.483025i		−	0.0180894i
$714$		0			0
$715$	−2.66912	−	6.91108i	−0.0998194	−	0.258460i
$716$	8.93093			0.333765
$717$		0			0
$718$		−	7.76131i		−	0.289650i
$719$	0.286459			0.0106831			0.00534156	−	0.999986i	$-0.498300\pi$
$719$	0.286459			0.0106831			0.00534156	+	0.999986i	$0.498300\pi$
$720$		0			0
$721$	61.1005			2.27550
$722$		−	2.71483i		−	0.101036i
$723$		0			0
$724$	−21.6792			−0.805701
$725$	28.8129	−	26.1571i	1.07009	−	0.971452i
$726$		0			0
$727$			15.1967i			0.563614i	0.959471	+	0.281807i	$0.0909338\pi$
$727$			15.1967i			0.563614i	−0.959471	+	0.281807i	$0.909066\pi$
$728$		−	4.74529i		−	0.175872i
$729$		0			0
$730$	−6.57251	+	2.53836i	−0.243260	+	0.0939490i
$731$	−16.4970			−0.610162
$732$		0			0
$733$		−	8.90456i		−	0.328897i	−0.986386	−	0.164449i	$-0.947416\pi$
$733$		−	8.90456i		−	0.328897i	0.986386	−	0.164449i	$-0.0525845\pi$
$734$	−6.56959			−0.242488
$735$		0			0
$736$	−18.0647			−0.665872
$737$		−	41.2224i		−	1.51845i
$738$		0			0
$739$	31.4422			1.15662			0.578310	−	0.815817i	$-0.303713\pi$
$739$	31.4422			1.15662			0.578310	+	0.815817i	$0.303713\pi$
$740$	−4.45164	−	11.5265i	−0.163645	−	0.423723i
$741$		0			0
$742$		−	2.68246i		−	0.0984761i
$743$		−	41.3314i		−	1.51630i	−0.652080	−	0.758150i	$-0.726103\pi$
$743$		−	41.3314i		−	1.51630i	0.652080	−	0.758150i	$-0.273897\pi$
$744$		0			0
$745$	−11.0335	+	4.26123i	−0.404236	+	0.156119i
$746$	1.47768			0.0541016
$747$		0			0
$748$		−	27.3290i		−	0.999248i
$749$	−3.86217			−0.141121
$750$		0			0
$751$	−50.8813			−1.85668			−0.928342	−	0.371726i	$-0.878766\pi$
$751$	−50.8813			−1.85668			−0.928342	+	0.371726i	$0.878766\pi$
$752$			19.0693i			0.695384i
$753$		0			0
$754$	2.56361			0.0933613
$755$	34.1792	−	13.2003i	1.24391	−	0.480409i
$756$		0			0
$757$		−	45.8173i		−	1.66526i	−0.553830	−	0.832630i	$-0.686834\pi$
$757$		−	45.8173i		−	1.66526i	0.553830	−	0.832630i	$-0.313166\pi$
$758$			1.53486i			0.0557486i
$759$		0			0
$760$	−5.38965	−	13.9553i	−0.195503	−	0.506211i
$761$	10.9129			0.395591			0.197795	−	0.980243i	$-0.436622\pi$
$761$	10.9129			0.395591			0.197795	+	0.980243i	$0.436622\pi$
$762$		0			0
$763$		−	40.9638i		−	1.48299i
$764$	32.1545			1.16331
$765$		0			0
$766$	−1.54815			−0.0559370
$767$			0.108987i			0.00393531i
$768$		0			0
$769$	−28.9338			−1.04338			−0.521689	−	0.853136i	$-0.674698\pi$
$769$	−28.9338			−1.04338			−0.521689	+	0.853136i	$0.674698\pi$
$770$	8.42734	−	3.25471i	0.303700	−	0.117292i
$771$		0			0
$772$			16.3513i			0.588496i
$773$		−	6.42314i		−	0.231024i	−0.993306	−	0.115512i	$-0.963149\pi$
$773$		−	6.42314i		−	0.231024i	0.993306	−	0.115512i	$-0.0368509\pi$
$774$		0			0
$775$	0.363345	−	0.329854i	0.0130517	−	0.0118487i
$776$	5.26139			0.188873
$777$		0			0
$778$		−	4.81325i		−	0.172563i
$779$	−3.91250			−0.140180
$780$		0			0
$781$	−39.8740			−1.42681
$782$			7.06907i			0.252789i
$783$		0			0
$784$	−22.5342			−0.804794
$785$	5.19188	+	13.4432i	0.185306	+	0.479808i
$786$		0			0
$787$		−	34.8040i		−	1.24063i	−0.784354	−	0.620314i	$-0.787005\pi$
$787$		−	34.8040i		−	1.24063i	0.784354	−	0.620314i	$-0.212995\pi$
$788$			36.7974i			1.31085i
$789$		0			0
$790$	−3.87660	−	10.0376i	−0.137923	−	0.357121i
$791$	59.1017			2.10142
$792$		0			0
$793$			12.1438i			0.431239i
$794$	7.34239			0.260572
$795$		0			0
$796$	34.4666			1.22164
$797$			1.30902i			0.0463679i	0.999731	+	0.0231839i	$0.00738034\pi$
$797$			1.30902i			0.0463679i	−0.999731	+	0.0231839i	$0.992620\pi$
$798$		0			0
$799$	24.7433			0.875354
$800$	−12.3362	−	13.5887i	−0.436151	−	0.480434i
$801$		0			0
$802$			1.18915i			0.0419904i
$803$			31.6943i			1.11847i
$804$		0			0
$805$	38.0037	−	14.6774i	1.33945	−	0.517309i
$806$	0.0323284			0.00113872
$807$		0			0
$808$			3.56037i			0.125253i
$809$	17.2262			0.605641			0.302821	−	0.953048i	$-0.402072\pi$
$809$	17.2262			0.605641			0.302821	+	0.953048i	$0.402072\pi$
$810$		0			0
$811$	−6.97289			−0.244851			−0.122426	−	0.992478i	$-0.539067\pi$
$811$	−6.97289			−0.244851			−0.122426	+	0.992478i	$0.539067\pi$
$812$		−	54.4998i		−	1.91257i
$813$		0			0
$814$	3.18823			0.111748
$815$	10.2853	+	26.6313i	0.360277	+	0.932855i
$816$		0			0
$817$			19.7450i			0.690791i
$818$			4.18027i			0.146160i
$819$		0			0
$820$	−2.95758	+	1.14224i	−0.103283	+	0.0398889i
$821$	−35.4054			−1.23566			−0.617828	−	0.786313i	$-0.711987\pi$
$821$	−35.4054			−1.23566			−0.617828	+	0.786313i	$0.711987\pi$
$822$		0			0
$823$			33.3942i			1.16405i	0.813172	+	0.582024i	$0.197739\pi$
$823$			33.3942i			1.16405i	−0.813172	+	0.582024i	$0.802261\pi$
$824$	21.1557			0.736995
$825$		0			0
$826$	−0.132899			−0.00462414
$827$		−	17.9643i		−	0.624680i	−0.949970	−	0.312340i	$-0.898887\pi$
$827$		−	17.9643i		−	0.624680i	0.949970	−	0.312340i	$-0.101113\pi$
$828$		0			0
$829$	−33.6052			−1.16716			−0.583578	−	0.812057i	$-0.698348\pi$
$829$	−33.6052			−1.16716			−0.583578	+	0.812057i	$0.698348\pi$
$830$	−11.4741	+	4.43141i	−0.398273	+	0.153816i
$831$		0			0
$832$			5.51255i			0.191113i
$833$			29.2392i			1.01308i
$834$		0			0
$835$	3.21204	+	8.31684i	0.111157	+	0.287816i
$836$	−32.7098			−1.13129
$837$		0			0
$838$		−	0.876422i		−	0.0302755i
$839$	−47.1755			−1.62868			−0.814340	−	0.580389i	$-0.802901\pi$
$839$	−47.1755			−1.62868			−0.814340	+	0.580389i	$0.802901\pi$
$840$		0			0
$841$	31.5752			1.08880
$842$			6.59776i			0.227374i
$843$		0			0
$844$	12.1399			0.417871
$845$	2.08591	−	0.805596i	0.0717574	−	0.0277134i
$846$		0			0
$847$			0.0835249i			0.00286995i
$848$			7.39317i			0.253882i
$849$		0			0
$850$	−5.31754	+	4.82741i	−0.182390	+	0.165579i
$851$	14.3776			0.492857
$852$		0			0
$853$		−	2.89307i		−	0.0990569i	−0.998773	−	0.0495284i	$-0.984228\pi$
$853$		−	2.89307i		−	0.0990569i	0.998773	−	0.0495284i	$-0.0157718\pi$
$854$	−14.8081			−0.506723
$855$		0			0
$856$	−1.33725			−0.0457064
$857$			25.7442i			0.879404i	0.898144	+	0.439702i	$0.144916\pi$
$857$			25.7442i			0.879404i	−0.898144	+	0.439702i	$0.855084\pi$
$858$		0			0
$859$	30.0417			1.02501			0.512505	−	0.858684i	$-0.328718\pi$
$859$	30.0417			1.02501			0.512505	+	0.858684i	$0.328718\pi$
$860$	5.76451	+	14.9259i	0.196568	+	0.508969i
$861$		0			0
$862$		−	0.921432i		−	0.0313841i
$863$		−	23.2852i		−	0.792636i	−0.918113	−	0.396318i	$-0.870288\pi$
$863$		−	23.2852i		−	0.792636i	0.918113	−	0.396318i	$-0.129712\pi$
$864$		0			0
$865$	−11.9901	−	31.0458i	−0.407677	−	1.05559i
$866$	3.15091			0.107072
$867$		0			0
$868$		−	0.687268i		−	0.0233274i
$869$	−48.4038			−1.64199
$870$		0			0
$871$	12.4418			0.421574
$872$		−	14.1835i		−	0.480314i
$873$		0			0
$874$	8.46089			0.286194
$875$	36.9931	+	18.5644i	1.25060	+	0.627590i
$876$		0			0
$877$			23.5946i			0.796731i	0.917227	+	0.398366i	$0.130423\pi$
$877$			23.5946i			0.796731i	−0.917227	+	0.398366i	$0.869577\pi$
$878$		−	2.45608i		−	0.0828887i
$879$		0			0
$880$	−23.2268	+	8.97038i	−0.782974	+	0.302391i
$881$	−54.7266			−1.84379			−0.921893	−	0.387445i	$-0.873358\pi$
$881$	−54.7266			−1.84379			−0.921893	+	0.387445i	$0.873358\pi$
$882$		0			0
$883$			2.10978i			0.0709998i	0.999370	+	0.0354999i	$0.0113023\pi$
$883$			2.10978i			0.0709998i	−0.999370	+	0.0354999i	$0.988698\pi$
$884$	8.24848			0.277426
$885$		0			0
$886$	2.60940			0.0876644
$887$		−	9.66363i		−	0.324473i	−0.986752	−	0.162236i	$-0.948129\pi$
$887$		−	9.66363i		−	0.324473i	0.986752	−	0.162236i	$-0.0518707\pi$
$888$		0			0
$889$	70.2278			2.35536
$890$	−0.953682	−	2.46934i	−0.0319675	−	0.0827726i
$891$		0			0
$892$		−	4.80994i		−	0.161049i
$893$		−	29.6150i		−	0.991027i
$894$		0			0
$895$	−9.84883	+	3.80371i	−0.329210	+	0.127144i
$896$	−33.8994			−1.13250
$897$		0			0
$898$		−	12.7552i		−	0.425646i
$899$	0.763883			0.0254769
$900$		0			0
$901$	9.59299			0.319589
$902$		−	0.818069i		−	0.0272387i
$903$		0			0
$904$	20.4636			0.680611
$905$	23.9073	−	9.23323i	0.794707	−	0.306923i
$906$		0			0
$907$			12.3350i			0.409577i	0.978806	+	0.204788i	$0.0656506\pi$
$907$			12.3350i			0.409577i	−0.978806	+	0.204788i	$0.934349\pi$
$908$		−	52.8319i		−	1.75329i
$909$		0			0
$910$	0.982341	+	2.54355i	0.0325643	+	0.0843178i
$911$	4.24151			0.140528			0.0702638	−	0.997528i	$-0.477616\pi$
$911$	4.24151			0.140528			0.0702638	+	0.997528i	$0.477616\pi$
$912$		0			0
$913$			55.3312i			1.83119i
$914$	−4.22676			−0.139809
$915$		0			0
$916$	−4.89389			−0.161699
$917$		−	1.99883i		−	0.0660073i
$918$		0			0
$919$	9.01009			0.297215			0.148608	−	0.988896i	$-0.452521\pi$
$919$	9.01009			0.297215			0.148608	+	0.988896i	$0.452521\pi$
$920$	13.1586	−	5.08196i	0.433825	−	0.167547i
$921$		0			0
$922$		−	10.2498i		−	0.337558i
$923$		−	12.0348i		−	0.396131i
$924$		0			0
$925$	9.81833	+	10.8152i	0.322825	+	0.355602i
$926$	3.37911			0.111045
$927$		0			0
$928$		−	28.5684i		−	0.937805i
$929$	17.1130			0.561458			0.280729	−	0.959787i	$-0.409424\pi$
$929$	17.1130			0.561458			0.280729	+	0.959787i	$0.409424\pi$
$930$		0			0
$931$	34.9961			1.14695
$932$			44.0060i			1.44146i
$933$		0			0
$934$	−4.06181			−0.132906
$935$	11.6395	+	30.1378i	0.380652	+	0.985612i
$936$		0			0
$937$		−	15.6965i		−	0.512782i	−0.966573	−	0.256391i	$-0.917467\pi$
$937$		−	15.6965i		−	0.512782i	0.966573	−	0.256391i	$-0.0825335\pi$
$938$			15.1715i			0.495366i
$939$		0			0
$940$	−8.64602	−	22.3869i	−0.282002	−	0.730180i
$941$	−2.53477			−0.0826311			−0.0413156	−	0.999146i	$-0.513155\pi$
$941$	−2.53477			−0.0826311			−0.0413156	+	0.999146i	$0.513155\pi$
$942$		0			0
$943$		−	3.68914i		−	0.120135i
$944$	0.366285			0.0119216
$945$		0			0
$946$	−4.12851			−0.134229
$947$		−	4.66480i		−	0.151586i	−0.997124	−	0.0757928i	$-0.975851\pi$
$947$		−	4.66480i		−	0.151586i	0.997124	−	0.0757928i	$-0.0241488\pi$
$948$		0			0
$949$	−9.56602			−0.310526
$950$	5.77787	+	6.36451i	0.187459	+	0.206492i
$951$		0			0
$952$			20.6932i			0.670672i
$953$		−	41.4489i		−	1.34266i	−0.741158	−	0.671330i	$-0.765723\pi$
$953$		−	41.4489i		−	1.34266i	0.741158	−	0.671330i	$-0.234277\pi$
$954$		0			0
$955$	−35.4592	+	13.6947i	−1.14743	+	0.443149i
$956$	29.5091			0.954392
$957$		0			0
$958$			2.70472i			0.0873856i
$959$	−45.3041			−1.46295
$960$		0			0
$961$	−30.9904			−0.999689
$962$			0.962276i			0.0310250i
$963$		0			0
$964$	50.8227			1.63689
$965$	−6.96405	−	18.0318i	−0.224181	−	0.580465i
$966$		0			0
$967$		−	40.1592i		−	1.29143i	−0.763578	−	0.645716i	$-0.776559\pi$
$967$		−	40.1592i		−	1.29143i	0.763578	−	0.645716i	$-0.223441\pi$
$968$			0.0289200i			0.000929525i
$969$		0			0
$970$	−2.82019	+	1.08918i	−0.0905508	+	0.0349715i
$971$	3.79988			0.121944			0.0609719	−	0.998139i	$-0.480580\pi$
$971$	3.79988			0.121944			0.0609719	+	0.998139i	$0.480580\pi$
$972$		0			0
$973$		−	35.9283i		−	1.15181i
$974$	7.73597			0.247876
$975$		0			0
$976$	40.8129			1.30639
$977$			53.7828i			1.72066i	0.509734	+	0.860332i	$0.329744\pi$
$977$			53.7828i			1.72066i	−0.509734	+	0.860332i	$0.670256\pi$
$978$		0			0
$979$	−11.9078			−0.380575
$980$	26.4547	−	10.2170i	0.845064	−	0.326371i
$981$		0			0
$982$			0.400992i			0.0127962i
$983$			25.6007i			0.816536i	0.912862	+	0.408268i	$0.133867\pi$
$983$			25.6007i			0.816536i	−0.912862	+	0.408268i	$0.866133\pi$
$984$		0			0
$985$	−15.6721	−	40.5794i	−0.499355	−	1.29297i
$986$	−11.1794			−0.356025
$987$		0			0
$988$		−	9.87251i		−	0.314086i
$989$	−18.6178			−0.592012
$990$		0			0
$991$	−51.0382			−1.62128			−0.810640	−	0.585544i	$-0.800881\pi$
$991$	−51.0382			−1.62128			−0.810640	+	0.585544i	$0.800881\pi$
$992$		−	0.360261i		−	0.0114383i
$993$		0			0
$994$	14.6752			0.465470
$995$	−38.0090	+	14.6794i	−1.20497	+	0.465369i
$996$		0			0
$997$		−	6.08651i		−	0.192762i	−0.995345	−	0.0963809i	$-0.969273\pi$
$997$		−	6.08651i		−	0.192762i	0.995345	−	0.0963809i	$-0.0307267\pi$
$998$		−	0.528118i		−	0.0167173i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.c.c.469.5		10
3.2	odd	2		195.2.c.b.79.6	yes	10
5.2	odd	4		2925.2.a.bm.1.3		5
5.3	odd	4		2925.2.a.bl.1.3		5
5.4	even	2	inner	585.2.c.c.469.6		10
12.11	even	2		3120.2.l.p.1249.5		10
15.2	even	4		975.2.a.s.1.3		5
15.8	even	4		975.2.a.r.1.3		5
15.14	odd	2		195.2.c.b.79.5	✓	10
60.59	even	2		3120.2.l.p.1249.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.c.b.79.5	✓	10	15.14	odd	2
195.2.c.b.79.6	yes	10	3.2	odd	2
585.2.c.c.469.5		10	1.1	even	1	trivial
585.2.c.c.469.6		10	5.4	even	2	inner
975.2.a.r.1.3		5	15.8	even	4
975.2.a.s.1.3		5	15.2	even	4
2925.2.a.bl.1.3		5	5.3	odd	4
2925.2.a.bm.1.3		5	5.2	odd	4
3120.2.l.p.1249.5		10	12.11	even	2
3120.2.l.p.1249.10		10	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.329386i q^{2} +1.89150 q^{4} +(-2.08591 + 0.805596i) q^{5} -3.70203i q^{7} -1.28181i q^{8} +O(q^{10})\)	\(q-0.329386i q^{2} +1.89150 q^{4} +(-2.08591 + 0.805596i) q^{5} -3.70203i q^{7} -1.28181i q^{8} +(0.265352 + 0.687069i) q^{10} +3.31322 q^{11} +1.00000i q^{13} -1.21940 q^{14} +3.36080 q^{16} -4.36080i q^{17} -5.21940 q^{19} +(-3.94551 + 1.52379i) q^{20} -1.09133i q^{22} -4.92143i q^{23} +(3.70203 - 3.36080i) q^{25} +0.329386 q^{26} -7.00241i q^{28} +7.78301 q^{29} +0.0981475 q^{31} -3.67061i q^{32} -1.43639 q^{34} +(2.98234 + 7.72209i) q^{35} +2.92143i q^{37} +1.71920i q^{38} +(1.03262 + 2.67373i) q^{40} +0.749608 q^{41} -3.78301i q^{43} +6.26698 q^{44} -1.62105 q^{46} +5.67402i q^{47} -6.70502 q^{49} +(-1.10700 - 1.21940i) q^{50} +1.89150i q^{52} +2.19982i q^{53} +(-6.91108 + 2.66912i) q^{55} -4.74529 q^{56} -2.56361i q^{58} +0.108987 q^{59} +12.1438 q^{61} -0.0323284i q^{62} +5.51255 q^{64} +(-0.805596 - 2.08591i) q^{65} -12.4418i q^{67} -8.24848i q^{68} +(2.54355 - 0.982341i) q^{70} -12.0348 q^{71} +9.56602i q^{73} +0.962276 q^{74} -9.87251 q^{76} -12.2656i q^{77} -14.6093 q^{79} +(-7.01032 + 2.70745i) q^{80} -0.246910i q^{82} +16.7001i q^{83} +(3.51305 + 9.09623i) q^{85} -1.24607 q^{86} -4.24691i q^{88} -3.59403 q^{89} +3.70203 q^{91} -9.30890i q^{92} +1.86894 q^{94} +(10.8872 - 4.20473i) q^{95} +4.10467i q^{97} +2.20854i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} + 2 q^{5}+O(q^{10}) \) 10 * q - 12 * q^4 + 2 * q^5	\( 10 q - 12 q^{4} + 2 q^{5} + 4 q^{10} - 10 q^{11} + 24 q^{14} - 16 q^{19} - 32 q^{20} + 10 q^{25} + 16 q^{29} + 24 q^{31} - 40 q^{34} - 12 q^{35} + 36 q^{40} - 10 q^{41} + 36 q^{44} - 24 q^{46} - 44 q^{49} - 40 q^{50} + 2 q^{55} + 16 q^{59} + 26 q^{61} + 32 q^{64} + 56 q^{70} - 10 q^{71} + 24 q^{74} - 2 q^{79} + 12 q^{80} - 4 q^{85} + 38 q^{89} + 10 q^{91} + 24 q^{94} + 48 q^{95}+O(q^{100}) \) 10 * q - 12 * q^4 + 2 * q^5 + 4 * q^10 - 10 * q^11 + 24 * q^14 - 16 * q^19 - 32 * q^20 + 10 * q^25 + 16 * q^29 + 24 * q^31 - 40 * q^34 - 12 * q^35 + 36 * q^40 - 10 * q^41 + 36 * q^44 - 24 * q^46 - 44 * q^49 - 40 * q^50 + 2 * q^55 + 16 * q^59 + 26 * q^61 + 32 * q^64 + 56 * q^70 - 10 * q^71 + 24 * q^74 - 2 * q^79 + 12 * q^80 - 4 * q^85 + 38 * q^89 + 10 * q^91 + 24 * q^94 + 48 * q^95

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