LMFDB - Embedded newform 165.2.d.c.164.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(164,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("165.164");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.d (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:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 24x^{14} + 244x^{12} - 1224x^{10} + 2880x^{8} - 2208x^{6} + 3976x^{4} + 432x^{2} + 2116 $ x^16 - 24x^14 + 244x^12 - 1224x^10 + 2880x^8 - 2208x^6 + 3976x^4 + 432*x^2 + 2116
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			164.4
Root			$0.896709 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	165.164
Dual form			165.2.d.c.164.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39417i q^{2} +(0.796225 + 1.53819i) q^{3} -3.73205 q^{4} +(2.17533 - 0.517638i) q^{5} +(3.68269 - 1.90630i) q^{6} +3.38587 q^{7} +4.14682i q^{8} +(-1.73205 + 2.44949i) q^{9} +O(q^{10})$	\(q-2.39417i q^{2} +(0.796225 + 1.53819i) q^{3} -3.73205 q^{4} +(2.17533 - 0.517638i) q^{5} +(3.68269 - 1.90630i) q^{6} +3.38587 q^{7} +4.14682i q^{8} +(-1.73205 + 2.44949i) q^{9} +(-1.23931 - 5.20810i) q^{10} +(-2.69591 - 1.93185i) q^{11} +(-2.97155 - 5.74060i) q^{12} -3.38587 q^{13} -8.10634i q^{14} +(2.52828 + 2.93391i) q^{15} +2.46410 q^{16} -1.75265i q^{17} +(5.86450 + 4.14682i) q^{18} +3.81260i q^{19} +(-8.11843 + 1.93185i) q^{20} +(2.69591 + 5.20810i) q^{21} +(-4.62518 + 6.45448i) q^{22} +2.75821 q^{23} +(-6.37860 + 3.30181i) q^{24} +(4.46410 - 2.25207i) q^{25} +8.10634i q^{26} +(-5.14688 - 0.713876i) q^{27} -12.6362 q^{28} -1.97355 q^{29} +(7.02428 - 6.05312i) q^{30} -3.46410 q^{31} +2.39417i q^{32} +(0.824999 - 5.68501i) q^{33} -4.19615 q^{34} +(7.36537 - 1.75265i) q^{35} +(6.46410 - 9.14162i) q^{36} +8.40482i q^{37} +9.12801 q^{38} +(-2.69591 - 5.20810i) q^{39} +(2.14655 + 9.02070i) q^{40} -7.36537 q^{41} +(12.4691 - 6.45448i) q^{42} +8.34312 q^{43} +(10.0613 + 7.20977i) q^{44} +(-2.49983 + 6.22502i) q^{45} -6.60361i q^{46} +1.59245 q^{47} +(1.96198 + 3.79025i) q^{48} +4.46410 q^{49} +(-5.39183 - 10.6878i) q^{50} +(2.69591 - 1.39551i) q^{51} +12.6362 q^{52} -8.70131 q^{53} +(-1.70914 + 12.3225i) q^{54} +(-6.86450 - 2.80690i) q^{55} +14.0406i q^{56} +(-5.86450 + 3.03569i) q^{57} +4.72500i q^{58} -4.89898i q^{59} +(-9.43565 - 10.9495i) q^{60} +10.4162i q^{61} +8.29365i q^{62} +(-5.86450 + 8.29365i) q^{63} +10.6603 q^{64} +(-7.36537 + 1.75265i) q^{65} +(-13.6109 - 1.97519i) q^{66} -13.1298i q^{67} +6.54099i q^{68} +(2.19615 + 4.24264i) q^{69} +(-4.19615 - 17.6340i) q^{70} -3.58630i q^{71} +(-10.1576 - 7.18251i) q^{72} +3.38587 q^{73} +20.1226 q^{74} +(7.01853 + 5.07348i) q^{75} -14.2288i q^{76} +(-9.12801 - 6.54099i) q^{77} +(-12.4691 + 6.45448i) q^{78} -11.4378i q^{79} +(5.36023 - 1.27551i) q^{80} +(-3.00000 - 8.48528i) q^{81} +17.6340i q^{82} +10.0463i q^{83} +(-10.0613 - 19.4369i) q^{84} +(-0.907241 - 3.81260i) q^{85} -19.9749i q^{86} +(-1.57139 - 3.03569i) q^{87} +(8.01105 - 11.1795i) q^{88} +9.52056i q^{89} +(14.9038 + 5.98502i) q^{90} -11.4641 q^{91} -10.2938 q^{92} +(-2.75821 - 5.32844i) q^{93} -3.81260i q^{94} +(1.97355 + 8.29365i) q^{95} +(-3.68269 + 1.90630i) q^{96} -8.40482i q^{97} -10.6878i q^{98} +(9.40151 - 3.25755i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{4}+O(q^{10}) $ 16 * q - 32 * q^4	$ 16 q - 32 q^{4} - 16 q^{16} + 16 q^{25} + 16 q^{34} + 48 q^{36} + 48 q^{45} + 16 q^{49} - 16 q^{55} - 48 q^{60} + 32 q^{64} - 48 q^{66} - 48 q^{69} + 16 q^{70} - 48 q^{81} - 128 q^{91} + 48 q^{99}+O(q^{100}) $ 16 * q - 32 * q^4 - 16 * q^16 + 16 * q^25 + 16 * q^34 + 48 * q^36 + 48 * q^45 + 16 * q^49 - 16 * q^55 - 48 * q^60 + 32 * q^64 - 48 * q^66 - 48 * q^69 + 16 * q^70 - 48 * q^81 - 128 * q^91 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$		−	2.39417i		−	1.69293i	−0.532441	−	0.846467i	$-0.678725\pi$
$2$		−	2.39417i		−	1.69293i	0.532441	−	0.846467i	$-0.321275\pi$
$3$	0.796225	+	1.53819i	0.459701	+	0.888074i
$3$	0.796225	+	1.53819i	0.459701	+	0.888074i
$4$	−3.73205			−1.86603
$5$	2.17533	−	0.517638i	0.972836	−	0.231495i
$5$	2.17533	−	0.517638i	0.972836	−	0.231495i
$6$	3.68269	−	1.90630i	1.50345	−	0.778243i
$7$	3.38587			1.27974			0.639869	−	0.768484i	$-0.278989\pi$
$7$	3.38587			1.27974			0.639869	+	0.768484i	$0.278989\pi$
$8$			4.14682i			1.46612i
$9$	−1.73205	+	2.44949i	−0.577350	+	0.816497i
$10$	−1.23931	−	5.20810i	−0.391905	−	1.64695i
$11$	−2.69591	−	1.93185i	−0.812848	−	0.582475i
$11$	−2.69591	−	1.93185i	−0.812848	−	0.582475i
$12$	−2.97155	−	5.74060i	−0.857813	−	1.65717i
$13$	−3.38587			−0.939071			−0.469535	−	0.882914i	$-0.655579\pi$
$13$	−3.38587			−0.939071			−0.469535	+	0.882914i	$0.655579\pi$
$14$		−	8.10634i		−	2.16651i
$15$	2.52828	+	2.93391i	0.652798	+	0.757532i
$16$	2.46410			0.616025
$17$		−	1.75265i		−	0.425081i	−0.977152	−	0.212541i	$-0.931826\pi$
$17$		−	1.75265i		−	0.425081i	0.977152	−	0.212541i	$-0.0681738\pi$
$18$	5.86450	+	4.14682i	1.38227	+	0.977416i
$19$			3.81260i			0.874670i	0.899299	+	0.437335i	$0.144078\pi$
$19$			3.81260i			0.874670i	−0.899299	+	0.437335i	$0.855922\pi$
$20$	−8.11843	+	1.93185i	−1.81534	+	0.431975i
$21$	2.69591	+	5.20810i	0.588297	+	1.13650i
$22$	−4.62518	+	6.45448i	−0.986092	+	1.37610i
$23$	2.75821			0.575126			0.287563	−	0.957762i	$-0.407155\pi$
$23$	2.75821			0.575126			0.287563	+	0.957762i	$0.407155\pi$
$24$	−6.37860	+	3.30181i	−1.30203	+	0.673978i
$25$	4.46410	−	2.25207i	0.892820	−	0.450413i
$26$			8.10634i			1.58978i
$27$	−5.14688	−	0.713876i	−0.990518	−	0.137386i
$28$	−12.6362			−2.38802
$29$	−1.97355			−0.366478			−0.183239	−	0.983068i	$-0.558658\pi$
$29$	−1.97355			−0.366478			−0.183239	+	0.983068i	$0.558658\pi$
$30$	7.02428	−	6.05312i	1.28245	−	1.10514i
$31$	−3.46410			−0.622171			−0.311086	−	0.950382i	$-0.600693\pi$
$31$	−3.46410			−0.622171			−0.311086	+	0.950382i	$0.600693\pi$
$32$			2.39417i			0.423233i
$33$	0.824999	−	5.68501i	0.143614	−	0.989634i
$34$	−4.19615			−0.719634
$35$	7.36537	−	1.75265i	1.24498	−	0.296253i
$36$	6.46410	−	9.14162i	1.07735	−	1.52360i
$37$			8.40482i			1.38174i	0.722977	+	0.690872i	$0.242773\pi$
$37$			8.40482i			1.38174i	−0.722977	+	0.690872i	$0.757227\pi$
$38$	9.12801			1.48076
$39$	−2.69591	−	5.20810i	−0.431692	−	0.833964i
$40$	2.14655	+	9.02070i	0.339400	+	1.42630i
$41$	−7.36537			−1.15028			−0.575139	−	0.818056i	$-0.695052\pi$
$41$	−7.36537			−1.15028			−0.575139	+	0.818056i	$0.695052\pi$
$42$	12.4691	−	6.45448i	1.92402	−	0.995947i
$43$	8.34312			1.27231			0.636157	−	0.771560i	$-0.280523\pi$
$43$	8.34312			1.27231			0.636157	+	0.771560i	$0.280523\pi$
$44$	10.0613	+	7.20977i	1.51680	+	1.08691i
$45$	−2.49983	+	6.22502i	−0.372653	+	0.927971i
$46$		−	6.60361i		−	0.973650i
$47$	1.59245			0.232283			0.116141	−	0.993233i	$-0.462947\pi$
$47$	1.59245			0.232283			0.116141	+	0.993233i	$0.462947\pi$
$48$	1.96198	+	3.79025i	0.283187	+	0.547076i
$49$	4.46410			0.637729
$50$	−5.39183	−	10.6878i	−0.762519	−	1.51149i
$51$	2.69591	−	1.39551i	0.377503	−	0.195410i
$52$	12.6362			1.75233
$53$	−8.70131			−1.19522			−0.597608	−	0.801788i	$-0.703882\pi$
$53$	−8.70131			−1.19522			−0.597608	+	0.801788i	$0.703882\pi$
$54$	−1.70914	+	12.3225i	−0.232585	+	1.67688i
$55$	−6.86450	−	2.80690i	−0.925608	−	0.378483i
$56$			14.0406i			1.87625i
$57$	−5.86450	+	3.03569i	−0.776771	+	0.402086i
$58$			4.72500i			0.620423i
$59$		−	4.89898i		−	0.637793i	−0.947790	−	0.318896i	$-0.896688\pi$
$59$		−	4.89898i		−	0.637793i	0.947790	−	0.318896i	$-0.103312\pi$
$60$	−9.43565	−	10.9495i	−1.21814	−	1.41357i
$61$			10.4162i			1.33366i	0.745210	+	0.666829i	$0.232349\pi$
$61$			10.4162i			1.33366i	−0.745210	+	0.666829i	$0.767651\pi$
$62$			8.29365i			1.05329i
$63$	−5.86450	+	8.29365i	−0.738857	+	1.04490i
$64$	10.6603			1.33253
$65$	−7.36537	+	1.75265i	−0.913562	+	0.217390i
$66$	−13.6109	−	1.97519i	−1.67538	−	0.243129i
$67$		−	13.1298i		−	1.60406i	−0.597281	−	0.802032i	$-0.703752\pi$
$67$		−	13.1298i		−	1.60406i	0.597281	−	0.802032i	$-0.296248\pi$
$68$			6.54099i			0.793212i
$69$	2.19615	+	4.24264i	0.264386	+	0.510754i
$70$	−4.19615	−	17.6340i	−0.501536	−	2.10766i
$71$		−	3.58630i		−	0.425616i	−0.977094	−	0.212808i	$-0.931739\pi$
$71$		−	3.58630i		−	0.425616i	0.977094	−	0.212808i	$-0.0682608\pi$
$72$	−10.1576	−	7.18251i	−1.19709	−	0.846467i
$73$	3.38587			0.396286			0.198143	−	0.980173i	$-0.436509\pi$
$73$	3.38587			0.396286			0.198143	+	0.980173i	$0.436509\pi$
$74$	20.1226			2.33920
$75$	7.01853	+	5.07348i	0.810430	+	0.585835i
$76$		−	14.2288i		−	1.63216i
$77$	−9.12801	−	6.54099i	−1.04023	−	0.745416i
$78$	−12.4691	+	6.45448i	−1.41185	+	0.730825i
$79$		−	11.4378i		−	1.28685i	−0.765508	−	0.643426i	$-0.777512\pi$
$79$		−	11.4378i		−	1.28685i	0.765508	−	0.643426i	$-0.222488\pi$
$80$	5.36023	−	1.27551i	0.599292	−	0.142607i
$81$	−3.00000	−	8.48528i	−0.333333	−	0.942809i
$82$			17.6340i			1.94734i
$83$			10.0463i			1.10273i	0.834266	+	0.551363i	$0.185892\pi$
$83$			10.0463i			1.10273i	−0.834266	+	0.551363i	$0.814108\pi$
$84$	−10.0613	−	19.4369i	−1.09778	−	2.12074i
$85$	−0.907241	−	3.81260i	−0.0984041	−	0.413534i
$86$		−	19.9749i		−	2.15394i
$87$	−1.57139	−	3.03569i	−0.168470	−	0.325460i
$88$	8.01105	−	11.1795i	0.853981	−	1.19174i
$89$			9.52056i			1.00918i	0.863360	+	0.504589i	$0.168356\pi$
$89$			9.52056i			1.00918i	−0.863360	+	0.504589i	$0.831644\pi$
$90$	14.9038	+	5.98502i	1.57099	+	0.630876i
$91$	−11.4641			−1.20176
$92$	−10.2938			−1.07320
$93$	−2.75821	−	5.32844i	−0.286013	−	0.552534i
$94$		−	3.81260i		−	0.393239i
$95$	1.97355	+	8.29365i	0.202482	+	0.850910i
$96$	−3.68269	+	1.90630i	−0.375863	+	0.194561i
$97$		−	8.40482i		−	0.853380i	−0.904398	−	0.426690i	$-0.859679\pi$
$97$		−	8.40482i		−	0.853380i	0.904398	−	0.426690i	$-0.140321\pi$
$98$		−	10.6878i		−	1.07963i
$99$	9.40151	−	3.25755i	0.944887	−	0.327396i
$100$	−16.6603	+	8.40482i	−1.66603	+	0.840482i
$101$	1.97355			0.196375			0.0981876	−	0.995168i	$-0.468695\pi$
$101$	1.97355			0.196375			0.0981876	+	0.995168i	$0.468695\pi$
$102$	−3.34108	−	6.45448i	−0.330816	−	0.639088i
$103$			0.824313i			0.0812220i	0.999175	+	0.0406110i	$0.0129304\pi$
$103$			0.824313i			0.0812220i	−0.999175	+	0.0406110i	$0.987070\pi$
$104$		−	14.0406i		−	1.37679i
$105$	8.56041	+	9.93383i	0.835410	+	0.969442i
$106$			20.8324i			2.02342i
$107$		−	6.54099i		−	0.632342i	−0.948702	−	0.316171i	$-0.897603\pi$
$107$		−	6.54099i		−	0.632342i	0.948702	−	0.316171i	$-0.102397\pi$
$108$	19.2084	+	2.66422i	1.84833	+	0.256365i
$109$		−	2.79101i		−	0.267331i	−0.991027	−	0.133665i	$-0.957325\pi$
$109$		−	2.79101i		−	0.267331i	0.991027	−	0.133665i	$-0.0426747\pi$
$110$	−6.72020	+	16.4348i	−0.640746	+	1.56699i
$111$	−12.9282	+	6.69213i	−1.22709	+	0.635189i
$112$	8.34312			0.788351
$113$	5.51641			0.518940			0.259470	−	0.965751i	$-0.416452\pi$
$113$	5.51641			0.518940			0.259470	+	0.965751i	$0.416452\pi$
$114$	7.26795	+	14.0406i	0.680706	+	1.31502i
$115$	6.00000	−	1.42775i	0.559503	−	0.133139i
$116$	7.36537			0.683858
$117$	5.86450	−	8.29365i	0.542173	−	0.766748i
$118$	−11.7290			−1.07974
$119$		−	5.93426i		−	0.543992i
$120$	−12.1664	+	10.4843i	−1.11064	+	0.957083i
$121$	3.53590	+	10.4162i	0.321445	+	0.946928i
$122$	24.9382			2.25780
$123$	−5.86450	−	11.3293i	−0.528784	−	1.02153i
$124$	12.9282			1.16099
$125$	8.54513	−	7.20977i	0.764300	−	0.644861i
$126$	19.8564	+	14.0406i	1.76895	+	1.25084i
$127$	16.9293			1.50224			0.751118	−	0.660168i	$-0.229515\pi$
$127$	16.9293			1.50224			0.751118	+	0.660168i	$0.229515\pi$
$128$		−	20.7341i		−	1.83265i
$129$	6.64300	+	12.8333i	0.584884	+	1.12991i
$130$	4.19615	+	17.6340i	0.368027	+	1.54660i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−3.07894	+	21.2168i	−0.267987	+	1.84668i
$133$			12.9090i			1.11935i
$134$	−31.4350			−2.71557
$135$	−11.5657	+	1.11131i	−0.995415	+	0.0956461i
$136$	7.26795			0.623222
$137$	4.35066			0.371702			0.185851	−	0.982578i	$-0.440496\pi$
$137$	4.35066			0.371702			0.185851	+	0.982578i	$0.440496\pi$
$138$	10.1576	−	5.25796i	0.864673	−	0.447588i
$139$		−	1.02158i		−	0.0866495i	−0.999061	−	0.0433247i	$-0.986205\pi$
$139$		−	1.02158i		−	0.0866495i	0.999061	−	0.0433247i	$-0.0137950\pi$
$140$	−27.4879	+	6.54099i	−2.32316	+	0.552815i
$141$	1.26795	+	2.44949i	0.106781	+	0.206284i
$142$	−8.58622			−0.720539
$143$	9.12801	+	6.54099i	0.763322	+	0.546985i
$144$	−4.26795	+	6.03579i	−0.355662	+	0.502983i
$145$	−4.29311	+	1.02158i	−0.356523	+	0.0848378i
$146$		−	8.10634i		−	0.670886i
$147$	3.55443	+	6.86663i	0.293164	+	0.566350i
$148$		−	31.3672i		−	2.57837i
$149$	3.41828			0.280037			0.140018	−	0.990149i	$-0.455284\pi$
$149$	3.41828			0.280037			0.140018	+	0.990149i	$0.455284\pi$
$150$	12.1468	−	16.8036i	0.991780	−	1.37200i
$151$		−	21.8540i		−	1.77845i	−0.457467	−	0.889227i	$-0.651243\pi$
$151$		−	21.8540i		−	1.77845i	0.457467	−	0.889227i	$-0.348757\pi$
$152$	−15.8102			−1.28237
$153$	4.29311	+	3.03569i	0.347077	+	0.245421i
$154$	−15.6603	+	21.8540i	−1.26194	+	1.76105i
$155$	−7.53556	+	1.79315i	−0.605270	+	0.144029i
$156$	10.0613	+	19.4369i	0.805548	+	1.55620i
$157$		−	4.50413i		−	0.359469i	−0.983715	−	0.179734i	$-0.942476\pi$
$157$		−	4.50413i		−	0.359469i	0.983715	−	0.179734i	$-0.0575238\pi$
$158$	−27.3840			−2.17856
$159$	−6.92820	−	13.3843i	−0.549442	−	1.06144i
$160$	1.23931	+	5.20810i	0.0979763	+	0.411737i
$161$	9.33892			0.736010
$162$	−20.3152	+	7.18251i	−1.59611	+	0.564311i
$163$		−	0.824313i		−	0.0645652i	−0.999479	−	0.0322826i	$-0.989722\pi$
$163$		−	0.824313i		−	0.0645652i	0.999479	−	0.0322826i	$-0.0102777\pi$
$164$	27.4879			2.14645
$165$	−1.14814	−	12.7938i	−0.0893823	−	0.995997i
$166$	24.0526			1.86684
$167$		−	12.6124i		−	0.975974i	−0.872851	−	0.487987i	$-0.837731\pi$
$167$		−	12.6124i		−	0.975974i	0.872851	−	0.487987i	$-0.162269\pi$
$168$	−21.5971	+	11.1795i	−1.66625	+	0.862516i
$169$	−1.53590			−0.118146
$170$	−9.12801	+	2.17209i	−0.700086	+	0.166592i
$171$	−9.33892	−	6.60361i	−0.714165	−	0.504991i
$172$	−31.1370			−2.37417
$173$		−	18.3400i		−	1.39436i	−0.716896	−	0.697180i	$-0.754438\pi$
$173$		−	18.3400i		−	1.39436i	0.716896	−	0.697180i	$-0.245562\pi$
$174$	−7.26795	+	3.76217i	−0.550982	+	0.285209i
$175$	15.1149	−	7.62519i	1.14258	−	0.576411i
$176$	−6.64300	−	4.76028i	−0.500735	−	0.358820i
$177$	7.53556	−	3.90069i	0.566407	−	0.293194i
$178$	22.7938			1.70847
$179$			5.17638i			0.386901i	0.981110	+	0.193450i	$0.0619679\pi$
$179$			5.17638i			0.386901i	−0.981110	+	0.193450i	$0.938032\pi$
$180$	9.32949	−	23.2321i	0.695379	−	1.73162i
$181$	−2.53590			−0.188492			−0.0942459	−	0.995549i	$-0.530044\pi$
$181$	−2.53590			−0.188492			−0.0942459	+	0.995549i	$0.530044\pi$
$182$			27.4470i			2.03451i
$183$	−16.0221	+	8.29365i	−1.18439	+	0.613084i
$184$			11.4378i			0.843205i
$185$	4.35066	+	18.2832i	0.319867	+	1.34421i
$186$	−12.7572	+	6.60361i	−0.935403	+	0.484200i
$187$	−3.38587	+	4.72500i	−0.247599	+	0.345527i
$188$	−5.94311			−0.433446
$189$	−17.4267	−	2.41709i	−1.26760	−	0.175817i
$190$	19.8564	−	4.72500i	1.44054	−	0.342788i
$191$			4.62158i			0.334406i	0.985923	+	0.167203i	$0.0534735\pi$
$191$			4.62158i			0.334406i	−0.985923	+	0.167203i	$0.946527\pi$
$192$	8.48796	+	16.3975i	0.612566	+	1.18339i
$193$	16.9293			1.21860			0.609300	−	0.792940i	$-0.291450\pi$
$193$	16.9293			1.21860			0.609300	+	0.792940i	$0.291450\pi$
$194$	−20.1226			−1.44472
$195$	−8.56041	−	9.93383i	−0.613024	−	0.711376i
$196$	−16.6603			−1.19002
$197$			20.9060i			1.48949i	0.667348	+	0.744746i	$0.267429\pi$
$197$			20.9060i			1.48949i	−0.667348	+	0.744746i	$0.732571\pi$
$198$	−7.79912	−	22.5088i	−0.554259	−	1.59963i
$199$	−2.92820			−0.207575			−0.103787	−	0.994600i	$-0.533096\pi$
$199$	−2.92820			−0.207575			−0.103787	+	0.994600i	$0.533096\pi$
$200$	9.33892	+	18.5118i	0.660361	+	1.30899i
$201$	20.1962	−	10.4543i	1.42453	−	0.737389i
$202$		−	4.72500i		−	0.332450i
$203$	−6.68216			−0.468996
$204$	−10.0613	+	5.20810i	−0.704431	+	0.364640i
$205$	−16.0221	+	3.81260i	−1.11903	+	0.266283i
$206$	1.97355			0.137503
$207$	−4.77735	+	6.75620i	−0.332049	+	0.469588i
$208$	−8.34312			−0.578491
$209$	7.36537	−	10.2784i	0.509473	−	0.710974i
$210$	23.7833	−	20.4951i	1.64120	−	1.41429i
$211$			14.2288i			0.979551i	0.871848	+	0.489776i	$0.162921\pi$
$211$			14.2288i			0.979551i	−0.871848	+	0.489776i	$0.837079\pi$
$212$	32.4737			2.23031
$213$	5.51641	−	2.85550i	0.377978	−	0.195656i
$214$	−15.6603			−1.07051
$215$	18.1490	−	4.31872i	1.23775	−	0.294534i
$216$	2.96032	−	21.3432i	0.201424	−	1.45222i
$217$	−11.7290			−0.796216
$218$	−6.68216			−0.452573
$219$	2.69591	+	5.20810i	0.182173	+	0.351931i
$220$	25.6186	+	10.4755i	1.72721	+	0.706258i
$221$			5.93426i			0.399181i
$222$	16.0221	+	30.9523i	1.07533	+	2.07738i
$223$			18.2374i			1.22127i	0.791914	+	0.610633i	$0.209085\pi$
$223$			18.2374i			1.22127i	−0.791914	+	0.610633i	$0.790915\pi$
$224$			8.10634i			0.541628i
$225$	−2.21564	+	14.8355i	−0.147709	+	0.989031i
$226$		−	13.2072i		−	0.878532i
$227$		−	10.0463i		−	0.666797i	−0.942786	−	0.333398i	$-0.891805\pi$
$227$		−	10.0463i		−	0.666797i	0.942786	−	0.333398i	$-0.108195\pi$
$228$	21.8866	−	11.3293i	1.44948	−	0.750304i
$229$	−13.3205			−0.880244			−0.440122	−	0.897938i	$-0.645065\pi$
$229$	−13.3205			−0.880244			−0.440122	+	0.897938i	$0.645065\pi$
$230$	−3.41828	−	14.3650i	−0.225395	−	0.947201i
$231$	2.79334	−	19.2487i	0.183788	−	1.26647i
$232$		−	8.18395i		−	0.537302i
$233$			7.82403i			0.512569i	0.966601	+	0.256285i	$0.0824984\pi$
$233$			7.82403i			0.512569i	−0.966601	+	0.256285i	$0.917502\pi$
$234$	−19.8564	−	14.0406i	−1.29805	−	0.917863i
$235$	3.46410	−	0.824313i	0.225973	−	0.0537723i
$236$			18.2832i			1.19014i
$237$	17.5935	−	9.10706i	1.14282	−	0.591567i
$238$	−14.2076			−0.920943
$239$	24.0697			1.55694			0.778469	−	0.627684i	$-0.215997\pi$
$239$	24.0697			1.55694			0.778469	+	0.627684i	$0.215997\pi$
$240$	6.22993	+	7.22945i	0.402140	+	0.466659i
$241$		−	2.79101i		−	0.179785i	−0.995951	−	0.0898925i	$-0.971348\pi$
$241$		−	2.79101i		−	0.179785i	0.995951	−	0.0898925i	$-0.0286524\pi$
$242$	24.9382	−	8.46554i	1.60309	−	0.544186i
$243$	10.6633	−	11.3708i	0.684050	−	0.729435i
$244$		−	38.8738i		−	2.48864i
$245$	9.71088	−	2.31079i	0.620406	−	0.147631i
$246$	−27.1244	+	14.0406i	−1.72939	+	0.895196i
$247$		−	12.9090i		−	0.821377i
$248$		−	14.3650i		−	0.912180i
$249$	−15.4531	+	7.99912i	−0.979301	+	0.506924i
$250$	−17.2614	−	20.4585i	−1.09171	−	1.29391i
$251$			16.9706i			1.07117i	0.844481	+	0.535586i	$0.179909\pi$
$251$			16.9706i			1.07117i	−0.844481	+	0.535586i	$0.820091\pi$
$252$	21.8866	−	30.9523i	1.37873	−	1.94981i
$253$	−7.43588	−	5.32844i	−0.467490	−	0.334996i
$254$		−	40.5317i		−	2.54319i
$255$	5.14213	−	4.43119i	0.322013	−	0.277492i
$256$	−28.3205			−1.77003
$257$	−12.1986			−0.760926			−0.380463	−	0.924796i	$-0.624235\pi$
$257$	−12.1986			−0.760926			−0.380463	+	0.924796i	$0.624235\pi$
$258$	30.7251	−	15.9045i	1.91286	−	0.990170i
$259$			28.4576i			1.76827i
$260$	27.4879	−	6.54099i	1.70473	−	0.405655i
$261$	3.41828	−	4.83418i	0.211586	−	0.299228i
$262$		0			0
$263$			0.469622i			0.0289582i	0.999895	+	0.0144791i	$0.00460899\pi$
$263$			0.469622i			0.0289582i	−0.999895	+	0.0144791i	$0.995391\pi$
$264$	23.5748	+	3.42112i	1.45093	+	0.210556i
$265$	−18.9282	+	4.50413i	−1.16275	+	0.276687i
$266$	30.9062			1.89498
$267$	−14.6444	+	7.58051i	−0.896224	+	0.463920i
$268$			49.0012i			2.99322i
$269$			8.48528i			0.517357i	0.965964	+	0.258678i	$0.0832870\pi$
$269$			8.48528i			0.517357i	−0.965964	+	0.258678i	$0.916713\pi$
$270$	2.66066	+	27.6902i	0.161923	+	1.68517i
$271$		−	19.8108i		−	1.20342i	−0.798714	−	0.601711i	$-0.794486\pi$
$271$		−	19.8108i		−	1.20342i	0.798714	−	0.601711i	$-0.205514\pi$
$272$		−	4.31872i		−	0.261861i
$273$	−9.12801	−	17.6340i	−0.552452	−	1.06726i
$274$		−	10.4162i		−	0.629266i
$275$	−16.3855	−	2.55261i	−0.988082	−	0.153928i
$276$	−8.19615	−	15.8338i	−0.493350	−	0.953080i
$277$	−20.0721			−1.20602			−0.603008	−	0.797735i	$-0.706031\pi$
$277$	−20.0721			−1.20602			−0.603008	+	0.797735i	$0.706031\pi$
$278$	−2.44584			−0.146692
$279$	6.00000	−	8.48528i	0.359211	−	0.508001i
$280$	7.26795	+	30.5429i	0.434343	+	1.82529i
$281$	−32.8798			−1.96144			−0.980721	−	0.195411i	$-0.937396\pi$
$281$	−32.8798			−1.96144			−0.980721	+	0.195411i	$0.937396\pi$
$282$	5.86450	−	3.03569i	0.349226	−	0.180772i
$283$	6.52864			0.388087			0.194044	−	0.980993i	$-0.437840\pi$
$283$	6.52864			0.388087			0.194044	+	0.980993i	$0.437840\pi$
$284$			13.3843i			0.794210i
$285$	−11.1858	+	9.63930i	−0.662590	+	0.570983i
$286$	15.6603	−	21.8540i	0.926010	−	1.29225i
$287$	−24.9382			−1.47205
$288$	−5.86450	−	4.14682i	−0.345569	−	0.244354i
$289$	13.9282			0.819306
$290$	2.44584	+	10.2784i	0.143625	+	0.603570i
$291$	12.9282	−	6.69213i	0.757865	−	0.392300i
$292$	−12.6362			−0.739479
$293$			1.75265i			0.102391i	0.998689	+	0.0511956i	$0.0163032\pi$
$293$			1.75265i			0.102391i	−0.998689	+	0.0511956i	$0.983697\pi$
$294$	16.4399	−	8.50991i	0.958794	−	0.496308i
$295$	−2.53590	−	10.6569i	−0.147646	−	0.620468i
$296$	−34.8533			−2.02581
$297$	12.4964	+	11.8676i	0.725117	+	0.688626i
$298$		−	8.18395i		−	0.474083i
$299$	−9.33892			−0.540084
$300$	−26.1935	−	18.9345i	−1.51228	−	1.09318i
$301$	28.2487			1.62823
$302$	−52.3222			−3.01080
$303$	1.57139	+	3.03569i	0.0902738	+	0.174396i
$304$			9.39463i			0.538819i
$305$	5.39183	+	22.6587i	0.308735	+	1.29743i
$306$	7.26795	−	10.2784i	0.415481	−	0.587579i
$307$	−8.34312			−0.476167			−0.238084	−	0.971245i	$-0.576519\pi$
$307$	−8.34312			−0.476167			−0.238084	+	0.971245i	$0.576519\pi$
$308$	34.0662	+	24.4113i	1.94110	+	1.39096i
$309$	−1.26795	+	0.656339i	−0.0721311	+	0.0373378i
$310$	4.29311	+	18.0414i	0.243832	+	1.02468i
$311$			14.6969i			0.833387i	0.909047	+	0.416693i	$0.136811\pi$
$311$			14.6969i			0.833387i	−0.909047	+	0.416693i	$0.863189\pi$
$312$	21.5971	−	11.1795i	1.22269	−	0.632913i
$313$			15.7645i			0.891060i	0.895267	+	0.445530i	$0.146985\pi$
$313$			15.7645i			0.891060i	−0.895267	+	0.445530i	$0.853015\pi$
$314$	−10.7837			−0.608557
$315$	−8.46409	+	21.0771i	−0.476897	+	1.18756i
$316$			42.6864i			2.40130i
$317$	−0.853392			−0.0479312			−0.0239656	−	0.999713i	$-0.507629\pi$
$317$	−0.853392			−0.0479312			−0.0239656	+	0.999713i	$0.507629\pi$
$318$	−32.0442	+	16.5873i	−1.79695	+	0.930169i
$319$	5.32051	+	3.81260i	0.297891	+	0.213464i
$320$	23.1895	−	5.51815i	1.29634	−	0.308474i
$321$	10.0613	−	5.20810i	0.561566	−	0.290688i
$322$		−	22.3590i		−	1.24602i
$323$	6.68216			0.371806
$324$	11.1962	+	31.6675i	0.622008	+	1.75931i
$325$	−15.1149	+	7.62519i	−0.838421	+	0.422970i
$326$	−1.97355			−0.109305
$327$	4.29311	−	2.22228i	0.237409	−	0.122892i
$328$		−	30.5429i		−	1.68645i
$329$	5.39183			0.297261
$330$	−30.6306	+	2.74884i	−1.68616	+	0.151318i
$331$	15.4641			0.849984			0.424992	−	0.905197i	$-0.360277\pi$
$331$	15.4641			0.849984			0.424992	+	0.905197i	$0.360277\pi$
$332$		−	37.4933i		−	2.05771i
$333$	−20.5875	−	14.5576i	−1.12819	−	0.797750i
$334$	−30.1962			−1.65226
$335$	−6.79650	−	28.5617i	−0.371332	−	1.56049i
$336$	6.64300	+	12.8333i	0.362406	+	0.700114i
$337$	20.0721			1.09340			0.546699	−	0.837329i	$-0.315884\pi$
$337$	20.0721			1.09340			0.546699	+	0.837329i	$0.315884\pi$
$338$			3.67720i			0.200013i
$339$	4.39230	+	8.48528i	0.238557	+	0.460857i
$340$	3.38587	+	14.2288i	0.183624	+	0.771665i
$341$	9.33892	+	6.69213i	0.505731	+	0.362399i
$342$	−15.8102	+	22.3590i	−0.854916	+	1.20903i
$343$	−8.58622			−0.463612
$344$			34.5975i			1.86537i
$345$	6.97350	+	8.09232i	0.375441	+	0.435676i
$346$	−43.9090			−2.36056
$347$			18.6837i			1.00300i	0.865159	+	0.501498i	$0.167217\pi$
$347$			18.6837i			1.00300i	−0.865159	+	0.501498i	$0.832783\pi$
$348$	5.86450	+	11.3293i	0.314370	+	0.607316i
$349$		−	5.58203i		−	0.298799i	−0.988777	−	0.149400i	$-0.952266\pi$
$349$		−	5.58203i		−	0.298799i	0.988777	−	0.149400i	$-0.0477341\pi$
$350$	−18.2560	−	36.1875i	−0.975825	−	1.93431i
$351$	17.4267	+	2.41709i	0.930166	+	0.129015i
$352$	4.62518	−	6.45448i	0.246523	−	0.344025i
$353$	−11.8862			−0.632639			−0.316320	−	0.948653i	$-0.602447\pi$
$353$	−11.8862			−0.632639			−0.316320	+	0.948653i	$0.602447\pi$
$354$	−9.33892	−	18.0414i	−0.496358	−	0.958890i
$355$	−1.85641	−	7.80138i	−0.0985278	−	0.414054i
$356$		−	35.5312i		−	1.88315i
$357$	9.12801	−	4.72500i	0.483105	−	0.250074i
$358$	12.3931			0.654998
$359$	−20.1226			−1.06203			−0.531014	−	0.847363i	$-0.678189\pi$
$359$	−20.1226			−1.06203			−0.531014	+	0.847363i	$0.678189\pi$
$360$	−25.8141	−	10.3664i	−1.36052	−	0.546355i
$361$	4.46410			0.234953
$362$			6.07137i			0.319104i
$363$	−13.2067	+	13.7325i	−0.693173	+	0.720771i
$364$	42.7846			2.24252
$365$	7.36537	−	1.75265i	0.385521	−	0.0917381i
$366$	19.8564	+	38.3596i	1.03791	+	2.00509i
$367$		−	35.0470i		−	1.82944i	−0.404088	−	0.914720i	$-0.632411\pi$
$367$		−	35.0470i		−	1.82944i	0.404088	−	0.914720i	$-0.367589\pi$
$368$	6.79650			0.354292
$369$	12.7572	−	18.0414i	0.664113	−	0.939198i
$370$	43.7732	−	10.4162i	2.27566	−	0.541513i
$371$	−29.4615			−1.52956
$372$	10.2938	+	19.8860i	0.533707	+	1.03104i
$373$	−8.34312			−0.431991			−0.215995	−	0.976394i	$-0.569300\pi$
$373$	−8.34312			−0.431991			−0.215995	+	0.976394i	$0.569300\pi$
$374$	11.3125	+	8.10634i	0.584954	+	0.419169i
$375$	17.8938	+	7.40342i	0.924034	+	0.382311i
$376$			6.60361i			0.340555i
$377$	6.68216			0.344149
$378$	−5.78692	+	41.7224i	−0.297647	+	2.14597i
$379$	10.9282			0.561344			0.280672	−	0.959804i	$-0.409443\pi$
$379$	10.9282			0.561344			0.280672	+	0.959804i	$0.409443\pi$
$380$	−7.36537	−	30.9523i	−0.377836	−	1.58782i
$381$	13.4796	+	26.0405i	0.690579	+	1.33410i
$382$	11.0648			0.566127
$383$	27.3840			1.39926			0.699629	−	0.714506i	$-0.253349\pi$
$383$	27.3840			1.39926			0.699629	+	0.714506i	$0.253349\pi$
$384$	31.8930	−	16.5090i	1.62753	−	0.842473i
$385$	−23.2423	−	9.50380i	−1.18454	−	0.484359i
$386$		−	40.5317i		−	2.06301i
$387$	−14.4507	+	20.4364i	−0.734571	+	1.03884i
$388$			31.3672i			1.59243i
$389$		−	37.8792i		−	1.92055i	−0.279056	−	0.960275i	$-0.590022\pi$
$389$		−	37.8792i		−	1.92055i	0.279056	−	0.960275i	$-0.409978\pi$
$390$	−23.7833	+	20.4951i	−1.20431	+	1.03781i
$391$		−	4.83418i		−	0.244475i
$392$			18.5118i			0.934989i
$393$		0			0
$394$	50.0526			2.52161
$395$	−5.92064	−	24.8809i	−0.297900	−	1.25190i
$396$	−35.0869	+	12.1573i	−1.76318	+	0.610929i
$397$			20.7103i			1.03942i	0.854342	+	0.519711i	$0.173960\pi$
$397$			20.7103i			1.03942i	−0.854342	+	0.519711i	$0.826040\pi$
$398$			7.01062i			0.351410i
$399$	−19.8564	+	10.2784i	−0.994064	+	0.514565i
$400$	11.0000	−	5.54932i	0.550000	−	0.277466i
$401$			11.0363i			0.551127i	0.961283	+	0.275563i	$0.0888644\pi$
$401$			11.0363i			0.551127i	−0.961283	+	0.275563i	$0.911136\pi$
$402$	−25.0294	−	48.3530i	−1.24835	−	2.41163i
$403$	11.7290			0.584263
$404$	−7.36537			−0.366441
$405$	−10.9183	−	16.9054i	−0.542534	−	0.840034i
$406$			15.9982i			0.793979i
$407$	16.2369	−	22.6587i	0.804832	−	1.12315i
$408$	5.78692	+	11.1795i	0.286495	+	0.553467i
$409$			23.6234i			1.16810i	0.811716	+	0.584052i	$0.198534\pi$
$409$			23.6234i			1.16810i	−0.811716	+	0.584052i	$0.801466\pi$
$410$	9.12801	+	38.3596i	0.450800	+	1.89445i
$411$	3.46410	+	6.69213i	0.170872	+	0.330098i
$412$		−	3.07638i		−	0.151562i
$413$		−	16.5873i		−	0.816208i
$414$	16.1755	+	11.4378i	0.794981	+	0.562137i
$415$	5.20035	+	21.8540i	0.255275	+	1.07277i
$416$		−	8.10634i		−	0.397446i
$417$	1.57139	−	0.813410i	0.0769511	−	0.0398328i
$418$	−24.6083	−	17.6340i	−1.20363	−	0.862505i
$419$			35.5312i			1.73581i	0.496728	+	0.867906i	$0.334535\pi$
$419$			35.5312i			1.73581i	−0.496728	+	0.867906i	$0.665465\pi$
$420$	−31.9479	−	37.0735i	−1.55890	−	1.80900i
$421$	−32.7846			−1.59782			−0.798912	−	0.601448i	$-0.794591\pi$
$421$	−32.7846			−1.59782			−0.798912	+	0.601448i	$0.794591\pi$
$422$	34.0662			1.65832
$423$	−2.75821	+	3.90069i	−0.134109	+	0.189658i
$424$		−	36.0828i		−	1.75234i
$425$	−3.94709	−	7.82403i	−0.191462	−	0.379521i
$426$	−6.83656	−	13.2072i	−0.331233	−	0.639892i
$427$			35.2679i			1.70673i
$428$			24.4113i			1.17997i
$429$	−2.79334	+	19.2487i	−0.134864	+	0.929336i
$430$	−10.3397	−	43.4519i	−0.498627	−	2.09543i
$431$	−16.1755			−0.779145			−0.389573	−	0.920996i	$-0.627377\pi$
$431$	−16.1755			−0.779145			−0.389573	+	0.920996i	$0.627377\pi$
$432$	−12.6824	−	1.75906i	−0.610184	−	0.0846330i
$433$			19.5035i			0.937276i	0.883390	+	0.468638i	$0.155255\pi$
$433$			19.5035i			0.937276i	−0.883390	+	0.468638i	$0.844745\pi$
$434$			28.0812i			1.34794i
$435$	−4.98967	−	5.79020i	−0.239236	−	0.277619i
$436$			10.4162i			0.498846i
$437$			10.5159i			0.503045i
$438$	12.4691	−	6.45448i	0.595796	−	0.308407i
$439$			6.60361i			0.315173i	0.987505	+	0.157587i	$0.0503713\pi$
$439$			6.60361i			0.315173i	−0.987505	+	0.157587i	$0.949629\pi$
$440$	11.6397	−	28.4659i	0.554903	−	1.35706i
$441$	−7.73205	+	10.9348i	−0.368193	+	0.520703i
$442$	14.2076			0.675787
$443$	−1.28009			−0.0608188			−0.0304094	−	0.999538i	$-0.509681\pi$
$443$	−1.28009			−0.0608188			−0.0304094	+	0.999538i	$0.509681\pi$
$444$	48.2487	−	24.9754i	2.28978	−	1.18528i
$445$	4.92820	+	20.7103i	0.233619	+	0.981764i
$446$	43.6634			2.06752
$447$	2.72172	+	5.25796i	0.128733	+	0.248693i
$448$	36.0942			1.70529
$449$		−	18.5606i		−	0.875931i	−0.898992	−	0.437965i	$-0.855699\pi$
$449$		−	18.5606i		−	0.875931i	0.898992	−	0.437965i	$-0.144301\pi$
$450$	35.5186	+	5.30462i	1.67436	+	0.250062i
$451$	19.8564	+	14.2288i	0.935002	+	0.670008i
$452$	−20.5875			−0.968356
$453$	33.6156	−	17.4007i	1.57940	−	0.817557i
$454$	−24.0526			−1.12884
$455$	−24.9382	+	5.93426i	−1.16912	+	0.278202i
$456$	−12.5885	−	24.3190i	−0.589509	−	1.13884i
$457$	−28.6583			−1.34058			−0.670290	−	0.742099i	$-0.733830\pi$
$457$	−28.6583			−1.34058			−0.670290	+	0.742099i	$0.733830\pi$
$458$			31.8916i			1.49019i
$459$	−1.25118	+	9.02070i	−0.0584000	+	0.421050i
$460$	−22.3923	+	5.32844i	−1.04405	+	0.248440i
$461$	31.4350			1.46408			0.732038	−	0.681264i	$-0.238569\pi$
$461$	31.4350			1.46408			0.732038	+	0.681264i	$0.238569\pi$
$462$	−46.0847	−	6.68772i	−2.14405	−	0.311141i
$463$		−	7.58051i		−	0.352296i	−0.984364	−	0.176148i	$-0.943636\pi$
$463$		−	7.58051i		−	0.352296i	0.984364	−	0.176148i	$-0.0563637\pi$
$464$	−4.86302			−0.225760
$465$	−8.75821	−	10.1634i	−0.406152	−	0.471314i
$466$	18.7321			0.867745
$467$	29.7155			1.37507			0.687535	−	0.726151i	$-0.258693\pi$
$467$	29.7155			1.37507			0.687535	+	0.726151i	$0.258693\pi$
$468$	−21.8866	+	30.9523i	−1.01171	+	1.43077i
$469$		−	44.4559i		−	2.05278i
$470$	−1.97355	−	8.29365i	−0.0910329	−	0.382557i
$471$	6.92820	−	3.58630i	0.319235	−	0.165248i
$472$	20.3152			0.935083
$473$	−22.4923	−	16.1177i	−1.03420	−	0.741091i
$474$	−21.8038	−	42.1218i	−1.00148	−	1.93472i
$475$	8.58622	+	17.0198i	0.393963	+	0.780923i
$476$			22.1469i			1.01510i
$477$	15.0711	−	21.3138i	0.690059	−	0.975891i
$478$		−	57.6269i		−	2.63579i
$479$	−1.44474			−0.0660117			−0.0330058	−	0.999455i	$-0.510508\pi$
$479$	−1.44474			−0.0660117			−0.0330058	+	0.999455i	$0.510508\pi$
$480$	−7.02428	+	6.05312i	−0.320613	+	0.276286i
$481$		−	28.4576i		−	1.29756i
$482$	−6.68216			−0.304364
$483$	7.43588	+	14.3650i	0.338344	+	0.653631i
$484$	−13.1962	−	38.8738i	−0.599825	−	1.76699i
$485$	−4.35066	−	18.2832i	−0.197553	−	0.830199i
$486$	−27.2235	−	25.5297i	−1.23488	−	1.15805i
$487$			12.6881i			0.574952i	0.957788	+	0.287476i	$0.0928161\pi$
$487$			12.6881i			0.574952i	−0.957788	+	0.287476i	$0.907184\pi$
$488$	−43.1942			−1.95531
$489$	1.26795	−	0.656339i	0.0573386	−	0.0296807i
$490$	−5.53242	−	23.2495i	−0.249929	−	1.05031i
$491$	16.1755			0.729989			0.364995	−	0.931010i	$-0.381071\pi$
$491$	16.1755			0.729989			0.364995	+	0.931010i	$0.381071\pi$
$492$	21.8866	+	42.2817i	0.986724	+	1.90620i
$493$			3.45894i			0.155783i
$494$	−30.9062			−1.39054
$495$	18.7651	−	11.9528i	0.843430	−	0.537239i
$496$	−8.53590			−0.383273
$497$		−	12.1427i		−	0.544677i
$498$	19.1513	+	36.9974i	0.858188	+	1.65789i
$499$	−10.9282			−0.489214			−0.244607	−	0.969622i	$-0.578659\pi$
$499$	−10.9282			−0.489214			−0.244607	+	0.969622i	$0.578659\pi$
$500$	−31.8909	+	26.9072i	−1.42620	+	1.20333i
$501$	19.4002	−	10.0423i	0.866737	−	0.448656i
$502$	40.6304			1.81342
$503$			17.0569i			0.760530i	0.924877	+	0.380265i	$0.124167\pi$
$503$			17.0569i			0.760530i	−0.924877	+	0.380265i	$0.875833\pi$
$504$	−34.3923	−	24.3190i	−1.53196	−	1.08326i
$505$	4.29311	−	1.02158i	0.191041	−	0.0454598i
$506$	−12.7572	+	17.8028i	−0.567127	+	0.791430i
$507$	−1.22292	−	2.36250i	−0.0543118	−	0.104922i
$508$	−63.1812			−2.80321
$509$			2.62536i			0.116367i	0.998306	+	0.0581834i	$0.0185308\pi$
$509$			2.62536i			0.116367i	−0.998306	+	0.0581834i	$0.981469\pi$
$510$	−10.6090	−	12.3111i	−0.469776	−	0.545146i
$511$	11.4641			0.507142
$512$			26.3359i			1.16389i
$513$	2.72172	−	19.6230i	0.120167	−	0.866376i
$514$			29.2055i			1.28820i
$515$	0.426696	+	1.79315i	0.0188025	+	0.0790157i
$516$	−24.7920	−	47.8945i	−1.09141	−	2.10844i
$517$	−4.29311	−	3.07638i	−0.188811	−	0.135299i
$518$	68.1324			2.99356
$519$	28.2103	−	14.6027i	1.23830	−	0.640989i
$520$	−7.26795	−	30.5429i	−0.318721	−	1.33940i
$521$		−	26.4911i		−	1.16060i	−0.814404	−	0.580299i	$-0.802936\pi$
$521$		−	26.4911i		−	1.16060i	0.814404	−	0.580299i	$-0.197064\pi$
$522$	−11.5738	−	8.18395i	−0.506574	−	0.358202i
$523$	−28.6583			−1.25314			−0.626571	−	0.779365i	$-0.715542\pi$
$523$	−28.6583			−1.25314			−0.626571	+	0.779365i	$0.715542\pi$
$524$		0			0
$525$	23.7638	+	17.1781i	1.03714	+	0.749715i
$526$	1.12436			0.0490242
$527$			6.07137i			0.264473i
$528$	2.03288	−	14.0085i	0.0884698	−	0.609640i
$529$	−15.3923			−0.669231
$530$	10.7837	+	45.3173i	0.468412	+	1.96846i
$531$	12.0000	+	8.48528i	0.520756	+	0.368230i
$532$		−	48.1769i		−	2.08873i
$533$	24.9382			1.08019
$534$	18.1490	+	35.0612i	0.785385	+	1.51725i
$535$	−3.38587	−	14.2288i	−0.146384	−	0.615165i
$536$	54.4471			2.35176
$537$	−7.96225	+	4.12157i	−0.343597	+	0.177859i
$538$	20.3152			0.875851
$539$	−12.0348	−	8.62398i	−0.518377	−	0.371461i
$540$	43.1637	−	4.14746i	1.85747	−	0.178478i
$541$		−	20.8324i		−	0.895656i	−0.894120	−	0.447828i	$-0.852198\pi$
$541$		−	20.8324i		−	0.895656i	0.894120	−	0.447828i	$-0.147802\pi$
$542$	−47.4305			−2.03732
$543$	−2.01915	−	3.90069i	−0.0866499	−	0.167395i
$544$	4.19615			0.179909
$545$	−1.44474	−	6.07137i	−0.0618857	−	0.260069i
$546$	−42.2187	+	21.8540i	−1.80679	+	0.935265i
$547$	6.52864			0.279145			0.139572	−	0.990212i	$-0.455427\pi$
$547$	6.52864			0.279145			0.139572	+	0.990212i	$0.455427\pi$
$548$	−16.2369			−0.693605
$549$	−25.5144	−	18.0414i	−1.08893	−	0.769988i
$550$	−6.11138	+	39.2296i	−0.260590	+	1.67276i
$551$		−	7.52433i		−	0.320547i
$552$	−17.5935	+	9.10706i	−0.748828	+	0.387622i
$553$		−	38.7269i		−	1.64683i
$554$			48.0561i			2.04171i
$555$	−24.6590	+	21.2497i	−1.04672	+	0.902000i
$556$			3.81260i			0.161690i
$557$			1.75265i			0.0742623i	0.999310	+	0.0371312i	$0.0118219\pi$
$557$			1.75265i			0.0742623i	−0.999310	+	0.0371312i	$0.988178\pi$
$558$	−20.3152	−	14.3650i	−0.860011	−	0.608120i
$559$	−28.2487			−1.19479
$560$	18.1490	−	4.31872i	0.766936	−	0.182499i
$561$	−9.96386	−	1.44594i	−0.420675	−	0.0610475i
$562$			78.7198i			3.32059i
$563$			28.2604i			1.19103i	0.803342	+	0.595517i	$0.203053\pi$
$563$			28.2604i			1.19103i	−0.803342	+	0.595517i	$0.796947\pi$
$564$	−4.73205	−	9.14162i	−0.199255	−	0.384932i
$565$	12.0000	−	2.85550i	0.504844	−	0.120132i
$566$		−	15.6307i		−	0.657006i
$567$	−10.1576	−	28.7300i	−0.426579	−	1.20655i
$568$	14.8718			0.624005
$569$	−7.36537			−0.308772			−0.154386	−	0.988011i	$-0.549340\pi$
$569$	−7.36537			−0.308772			−0.154386	+	0.988011i	$0.549340\pi$
$570$	23.0781	+	26.7807i	0.966636	+	1.12172i
$571$			32.2702i			1.35047i	0.737604	+	0.675233i	$0.235957\pi$
$571$			32.2702i			1.35047i	−0.737604	+	0.675233i	$0.764043\pi$
$572$	−34.0662	−	24.4113i	−1.42438	−	1.02069i
$573$	−7.10886	+	3.67982i	−0.296977	+	0.153727i
$574$			59.7062i			2.49209i
$575$	12.3129	−	6.21166i	0.513484	−	0.259044i
$576$	−18.4641	+	26.1122i	−0.769338	+	1.08801i
$577$		−	4.94588i		−	0.205900i	−0.994687	−	0.102950i	$-0.967172\pi$
$577$		−	4.94588i		−	0.205900i	0.994687	−	0.102950i	$-0.0328281\pi$
$578$		−	33.3465i		−	1.38703i
$579$	13.4796	+	26.0405i	0.560192	+	1.08221i
$580$	16.0221	−	3.81260i	0.665281	−	0.158309i
$581$			34.0155i			1.41120i
$582$	−16.0221	−	30.9523i	−0.664137	−	1.28301i
$583$	23.4580	+	16.8096i	0.971530	+	0.696184i
$584$			14.0406i			0.581004i
$585$	8.46409	−	21.0771i	0.349947	−	0.871430i
$586$	4.19615			0.173341
$587$	21.0142			0.867350			0.433675	−	0.901069i	$-0.357217\pi$
$587$	21.0142			0.867350			0.433675	+	0.901069i	$0.357217\pi$
$588$	−13.2653	−	25.6266i	−0.547052	−	1.05682i
$589$		−	13.2072i		−	0.544194i
$590$	−25.5144	+	6.07137i	−1.05041	+	0.249954i
$591$	−32.1574	+	16.6459i	−1.32278	+	0.684721i
$592$			20.7103i			0.851189i
$593$		−	43.5647i		−	1.78899i	−0.447081	−	0.894494i	$-0.647536\pi$
$593$		−	43.5647i		−	1.78899i	0.447081	−	0.894494i	$-0.352464\pi$
$594$	28.4130	−	29.9186i	1.16580	−	1.22758i
$595$	−3.07180	−	12.9090i	−0.125931	−	0.529215i
$596$	−12.7572			−0.522555
$597$	−2.33151	−	4.50413i	−0.0954223	−	0.184342i
$598$			22.3590i			0.914326i
$599$		−	13.1069i		−	0.535532i	−0.963484	−	0.267766i	$-0.913715\pi$
$599$		−	13.1069i		−	0.535532i	0.963484	−	0.267766i	$-0.0862854\pi$
$600$	−21.0388	+	29.1046i	−0.858907	+	1.18819i
$601$		−	10.4162i		−	0.424886i	−0.977173	−	0.212443i	$-0.931858\pi$
$601$		−	10.4162i		−	0.424886i	0.977173	−	0.212443i	$-0.0681420\pi$
$602$		−	67.6322i		−	2.75648i
$603$	32.1614	+	22.7415i	1.30971	+	0.926106i
$604$			81.5602i			3.31864i
$605$	13.0836	+	20.8284i	0.531923	+	0.846793i
$606$	7.26795	−	3.76217i	0.295240	−	0.152828i
$607$	25.5156			1.03564			0.517822	−	0.855488i	$-0.326743\pi$
$607$	25.5156			1.03564			0.517822	+	0.855488i	$0.326743\pi$
$608$	−9.12801			−0.370190
$609$	−5.32051	−	10.2784i	−0.215598	−	0.416503i
$610$	54.2487	−	12.9090i	2.19647	−	0.522668i
$611$	−5.39183			−0.218130
$612$	−16.0221	−	11.3293i	−0.647655	−	0.457961i
$613$	2.05758			0.0831047			0.0415523	−	0.999136i	$-0.486770\pi$
$613$	2.05758			0.0831047			0.0415523	+	0.999136i	$0.486770\pi$
$614$			19.9749i			0.806120i
$615$	−18.6217	−	21.6093i	−0.750899	−	0.871372i
$616$	27.1244	−	37.8522i	1.09287	−	1.52511i
$617$	38.8435			1.56378			0.781891	−	0.623415i	$-0.214255\pi$
$617$	38.8435			1.56378			0.781891	+	0.623415i	$0.214255\pi$
$618$	1.57139	+	3.03569i	0.0632104	+	0.122113i
$619$	22.3923			0.900023			0.450011	−	0.893023i	$-0.351420\pi$
$619$	22.3923			0.900023			0.450011	+	0.893023i	$0.351420\pi$
$620$	28.1231	−	6.69213i	1.12945	−	0.268762i
$621$	−14.1962	−	1.96902i	−0.569672	−	0.0790139i
$622$	35.1870			1.41087
$623$			32.2354i			1.29148i
$624$	−6.64300	−	12.8333i	−0.265933	−	0.513743i
$625$	14.8564	−	20.1069i	0.594256	−	0.804276i
$626$	37.7428			1.50851
$627$	21.6747	+	3.14539i	0.865603	+	0.125615i
$628$			16.8096i			0.670778i
$629$	14.7307			0.587353
$630$	50.4621	+	20.2645i	2.01046	+	0.807356i
$631$	−30.6410			−1.21980			−0.609900	−	0.792479i	$-0.708790\pi$
$631$	−30.6410			−1.21980			−0.609900	+	0.792479i	$0.708790\pi$
$632$	47.4305			1.88668
$633$	−21.8866	+	11.3293i	−0.869914	+	0.450301i
$634$			2.04316i			0.0811444i
$635$	36.8269	−	8.76327i	1.46143	−	0.347760i
$636$	25.8564	+	49.9507i	1.02527	+	1.98068i
$637$	−15.1149			−0.598872
$638$	9.12801	−	12.7382i	0.361381	−	0.504310i
$639$	8.78461	+	6.21166i	0.347514	+	0.245729i
$640$	−10.7328	−	45.1035i	−0.424250	−	1.78287i
$641$		−	27.8038i		−	1.09818i	−0.835762	−	0.549092i	$-0.814974\pi$
$641$		−	27.8038i		−	1.09818i	0.835762	−	0.549092i	$-0.185026\pi$
$642$	−12.4691	−	24.0884i	−0.492116	−	0.950695i
$643$			4.12157i			0.162539i	0.996692	+	0.0812693i	$0.0258974\pi$
$643$			4.12157i			0.162539i	−0.996692	+	0.0812693i	$0.974103\pi$
$644$	−34.8533			−1.37341
$645$	21.0937	+	24.4780i	0.830564	+	0.963819i
$646$		−	15.9982i		−	0.629442i
$647$	−44.7866			−1.76074			−0.880372	−	0.474283i	$-0.842707\pi$
$647$	−44.7866			−1.76074			−0.880372	+	0.474283i	$0.842707\pi$
$648$	35.1870	−	12.4405i	1.38227	−	0.488708i
$649$	−9.46410	+	13.2072i	−0.371498	+	0.518429i
$650$	18.2560	+	36.1875i	0.716060	+	1.41939i
$651$	−9.33892	−	18.0414i	−0.366021	−	0.707098i
$652$			3.07638i			0.120480i
$653$	−25.7916			−1.00930			−0.504651	−	0.863323i	$-0.668379\pi$
$653$	−25.7916			−1.00930			−0.504651	+	0.863323i	$0.668379\pi$
$654$	−5.32051	−	10.2784i	−0.208048	−	0.401919i
$655$		0			0
$656$	−18.1490			−0.708600
$657$	−5.86450	+	8.29365i	−0.228796	+	0.323566i
$658$		−	12.9090i		−	0.503243i
$659$	−36.2981			−1.41397			−0.706986	−	0.707228i	$-0.749945\pi$
$659$	−36.2981			−1.41397			−0.706986	+	0.707228i	$0.749945\pi$
$660$	4.28491	+	47.7472i	0.166790	+	1.85856i
$661$	−11.4641			−0.445902			−0.222951	−	0.974830i	$-0.571569\pi$
$661$	−11.4641			−0.445902			−0.222951	+	0.974830i	$0.571569\pi$
$662$		−	37.0237i		−	1.43897i
$663$	−9.12801	+	4.72500i	−0.354502	+	0.183504i
$664$	−41.6603			−1.61673
$665$	6.68216	+	28.0812i	0.259123	+	1.08894i
$666$	−34.8533	+	49.2900i	−1.35054	+	1.90995i
$667$	−5.44344			−0.210771
$668$			47.0700i			1.82119i
$669$	−28.0526	+	14.5211i	−1.08457	+	0.561417i
$670$	−68.3815	+	16.2720i	−2.64181	+	0.628641i
$671$	20.1226	−	28.0812i	0.776823	−	1.08406i
$672$	−12.4691	+	6.45448i	−0.481006	+	0.248987i
$673$	8.82931			0.340345			0.170172	−	0.985414i	$-0.445568\pi$
$673$	8.82931			0.340345			0.170172	+	0.985414i	$0.445568\pi$
$674$		−	48.0561i		−	1.85105i
$675$	−24.5839	+	8.40429i	−0.946235	+	0.323481i
$676$	5.73205			0.220463
$677$			30.4827i			1.17155i	0.810475	+	0.585773i	$0.199209\pi$
$677$			30.4827i			1.17155i	−0.810475	+	0.585773i	$0.800791\pi$
$678$	20.3152	−	10.5159i	0.780201	−	0.403862i
$679$		−	28.4576i		−	1.09210i
$680$	15.8102	−	3.76217i	0.606292	−	0.144273i
$681$	15.4531	−	7.99912i	0.592165	−	0.306527i
$682$	16.0221	−	22.3590i	0.613518	−	0.856169i
$683$	−37.2511			−1.42537			−0.712687	−	0.701483i	$-0.752522\pi$
$683$	−37.2511			−1.42537			−0.712687	+	0.701483i	$0.752522\pi$
$684$	34.8533	+	24.6450i	1.33265	+	0.942326i
$685$	9.46410	−	2.25207i	0.361605	−	0.0860470i
$686$			20.5569i			0.784865i
$687$	−10.6061	−	20.4895i	−0.404649	−	0.781722i
$688$	20.5583			0.783778
$689$	29.4615			1.12239
$690$	19.3744	−	16.6958i	0.737571	−	0.635597i
$691$	−2.14359			−0.0815461			−0.0407731	−	0.999168i	$-0.512982\pi$
$691$	−2.14359			−0.0815461			−0.0407731	+	0.999168i	$0.512982\pi$
$692$			68.4456i			2.60191i
$693$	31.8323	−	11.0296i	1.20921	−	0.418981i
$694$	44.7321			1.69801
$695$	−0.528810	−	2.22228i	−0.0200589	−	0.0842958i
$696$	12.5885	−	6.51626i	0.477164	−	0.246998i
$697$			12.9090i			0.488961i
$698$	−13.3643			−0.505847
$699$	−12.0348	+	6.22969i	−0.455199	+	0.235628i
$700$	−56.4094	+	28.4576i	−2.13208	+	1.07560i
$701$	−43.6634			−1.64914			−0.824572	−	0.565756i	$-0.808584\pi$
$701$	−43.6634			−1.64914			−0.824572	+	0.565756i	$0.808584\pi$
$702$	5.78692	−	41.7224i	0.218413	−	1.57471i
$703$	−32.0442			−1.20857
$704$	−28.7391	−	20.5940i	−1.08315	−	0.776167i
$705$	4.02615	+	4.67210i	0.151634	+	0.175962i
$706$			28.4576i			1.07102i
$707$	6.68216			0.251309
$708$	−28.1231	+	14.5576i	−1.05693	+	0.547107i
$709$	−42.9282			−1.61220			−0.806101	−	0.591778i	$-0.798426\pi$
$709$	−42.9282			−1.61220			−0.806101	+	0.591778i	$0.798426\pi$
$710$	−18.6778	+	4.44455i	−0.700967	+	0.166801i
$711$	28.0168	+	19.8108i	1.05071	+	0.742964i
$712$	−39.4801			−1.47958
$713$	−9.55470			−0.357826
$714$	−11.3125	−	21.8540i	−0.423358	−	0.817865i
$715$	23.2423	+	9.50380i	0.869212	+	0.355422i
$716$		−	19.3185i		−	0.721967i
$717$	19.1649	+	37.0237i	0.715725	+	1.38268i
$718$			48.1769i			1.79794i
$719$			37.6018i			1.40231i	0.713009	+	0.701154i	$0.247332\pi$
$719$			37.6018i			1.40231i	−0.713009	+	0.701154i	$0.752668\pi$
$720$	−6.15983	+	15.3391i	−0.229563	+	0.571654i
$721$			2.79101i			0.103943i
$722$		−	10.6878i		−	0.397759i
$723$	4.29311	−	2.22228i	0.159662	−	0.0826474i
$724$	9.46410			0.351731
$725$	−8.81011	+	4.44455i	−0.327199	+	0.165067i
$726$	32.8780	+	31.6192i	1.22022	+	1.17350i
$727$		−	18.6791i		−	0.692771i	−0.938092	−	0.346386i	$-0.887409\pi$
$727$		−	18.6791i		−	0.692771i	0.938092	−	0.346386i	$-0.112591\pi$
$728$		−	47.5396i		−	1.76194i
$729$	25.9808	+	7.34847i	0.962250	+	0.272166i
$730$	−4.19615	−	17.6340i	−0.155307	−	0.652662i
$731$		−	14.6226i		−	0.540837i
$732$	59.7953	−	30.9523i	2.21010	−	1.14403i
$733$	3.38587			0.125060			0.0625299	−	0.998043i	$-0.480083\pi$
$733$	3.38587			0.125060			0.0625299	+	0.998043i	$0.480083\pi$
$734$	−83.9086			−3.09712
$735$	11.2865	+	13.0973i	0.416308	+	0.483100i
$736$			6.60361i			0.243412i
$737$	−25.3649	+	35.3969i	−0.934327	+	1.30386i
$738$	−43.1942	−	30.5429i	−1.59000	−	1.12430i
$739$		−	4.56045i		−	0.167759i	−0.996476	−	0.0838794i	$-0.973269\pi$
$739$		−	4.56045i		−	0.167759i	0.996476	−	0.0838794i	$-0.0267310\pi$
$740$	−16.2369	−	68.2340i	−0.596879	−	2.50833i
$741$	19.8564	−	10.2784i	0.729443	−	0.377588i
$742$			70.5358i			2.58945i
$743$		−	22.1890i		−	0.814037i	−0.913420	−	0.407019i	$-0.866568\pi$
$743$		−	22.1890i		−	0.814037i	0.913420	−	0.407019i	$-0.133432\pi$
$744$	22.0961	−	11.4378i	0.810083	−	0.419330i
$745$	7.43588	−	1.76943i	0.272430	−	0.0648270i
$746$			19.9749i			0.731331i
$747$	−24.6083	−	17.4007i	−0.900371	−	0.636659i
$748$	12.6362	−	17.6340i	0.462026	−	0.644761i
$749$		−	22.1469i		−	0.809232i
$750$	17.7251	−	42.8409i	0.647228	−	1.56433i
$751$	23.7128			0.865293			0.432646	−	0.901564i	$-0.357580\pi$
$751$	23.7128			0.865293			0.432646	+	0.901564i	$0.357580\pi$
$752$	3.92396			0.143092
$753$	−26.1039	+	13.5124i	−0.951280	+	0.492419i
$754$		−	15.9982i		−	0.582622i
$755$	−11.3125	−	47.5396i	−0.411703	−	1.73014i
$756$	65.0372	+	9.02070i	2.36538	+	0.328080i
$757$			27.4665i			0.998288i	0.866519	+	0.499144i	$0.166352\pi$
$757$			27.4665i			0.998288i	−0.866519	+	0.499144i	$0.833648\pi$
$758$		−	26.1640i		−	0.950318i
$759$	2.27552	−	15.6804i	0.0825960	−	0.569164i
$760$	−34.3923	+	8.18395i	−1.24754	+	0.296863i
$761$	−24.5985			−0.891694			−0.445847	−	0.895109i	$-0.647097\pi$
$761$	−24.5985			−0.891694			−0.445847	+	0.895109i	$0.647097\pi$
$762$	62.3454	−	32.2724i	2.25854	−	1.16910i
$763$		−	9.45001i		−	0.342113i
$764$		−	17.2480i		−	0.624009i
$765$	10.9103	+	4.38134i	0.394463	+	0.158408i
$766$		−	65.5620i		−	2.36885i
$767$			16.5873i			0.598933i
$768$	−22.5495	−	43.5623i	−0.813685	−	1.57192i
$769$		−	9.66836i		−	0.348650i	−0.984688	−	0.174325i	$-0.944226\pi$
$769$		−	9.66836i		−	0.348650i	0.984688	−	0.174325i	$-0.0557743\pi$
$770$	−22.7537	+	55.6460i	−0.819987	+	2.00534i
$771$	−9.71281	−	18.7637i	−0.349798	−	0.675759i
$772$	−63.1812			−2.27394
$773$	8.38895			0.301729			0.150865	−	0.988554i	$-0.451794\pi$
$773$	8.38895			0.301729			0.150865	+	0.988554i	$0.451794\pi$
$774$	48.9282	+	34.5975i	1.75869	+	1.24358i
$775$	−15.4641	+	7.80138i	−0.555487	+	0.280234i
$776$	34.8533			1.25116
$777$	−43.7732	+	22.6587i	−1.57035	+	0.812875i
$778$	−90.6892			−3.25136
$779$		−	28.0812i		−	1.00611i
$780$	31.9479	+	37.0735i	1.14392	+	1.32745i
$781$	−6.92820	+	9.66836i	−0.247911	+	0.345961i
$782$	−11.5738			−0.413880
$783$	10.1576	+	1.40887i	0.363003	+	0.0503488i
$784$	11.0000			0.392857
$785$	−2.33151	−	9.79796i	−0.0832151	−	0.349704i
$786$		0			0
$787$	−11.9721			−0.426759			−0.213379	−	0.976969i	$-0.568447\pi$
$787$	−11.9721			−0.426759			−0.213379	+	0.976969i	$0.568447\pi$
$788$		−	78.0223i		−	2.77943i
$789$	−0.722368	+	0.373925i	−0.0257170	+	0.0133121i
$790$	−59.5692	+	14.1750i	−2.11938	+	0.504324i
$791$	18.6778			0.664107
$792$	13.5085	+	38.9864i	0.480003	+	1.38532i
$793$		−	35.2679i		−	1.25240i
$794$	49.5841			1.75967
$795$	−21.9993	−	25.5289i	−0.780235	−	0.905415i
$796$	10.9282			0.387340
$797$	7.22319			0.255859			0.127929	−	0.991783i	$-0.459167\pi$
$797$	7.22319			0.255859			0.127929	+	0.991783i	$0.459167\pi$
$798$	24.6083	+	47.5396i	0.871125	+	1.68288i
$799$		−	2.79101i		−	0.0987390i
$800$	5.39183	+	10.6878i	0.190630	+	0.377871i
$801$	−23.3205	−	16.4901i	−0.823990	−	0.582649i
$802$	26.4228			0.933021
$803$	−9.12801	−	6.54099i	−0.322120	−	0.230827i
$804$	−75.3731	+	39.0160i	−2.65820	+	1.37599i
$805$	20.3152	−	4.83418i	0.716017	−	0.170382i
$806$		−	28.0812i		−	0.989118i
$807$	−13.0520	+	6.75620i	−0.459451	+	0.237829i
$808$			8.18395i			0.287910i
$809$	53.0023			1.86346			0.931732	−	0.363148i	$-0.118298\pi$
$809$	53.0023			1.86346			0.931732	+	0.363148i	$0.118298\pi$
$810$	−40.4743	+	26.1402i	−1.42212	+	0.918474i
$811$			22.6019i			0.793658i	0.917892	+	0.396829i	$0.129889\pi$
$811$			22.6019i			0.793658i	−0.917892	+	0.396829i	$0.870111\pi$
$812$	24.9382			0.875158
$813$	30.4728	−	15.7739i	1.06873	−	0.553214i
$814$	−54.2487	−	38.8738i	−1.90142	−	1.36253i
$815$	−0.426696	−	1.79315i	−0.0149465	−	0.0628113i
$816$	6.64300	−	3.43867i	0.232552	−	0.120378i
$817$			31.8090i			1.11285i
$818$	56.5585			1.97752
$819$	19.8564	−	28.0812i	0.693839	−	0.981237i
$820$	59.7953	−	14.2288i	2.08814	−	0.496891i
$821$	−24.9856			−0.872003			−0.436002	−	0.899946i	$-0.643606\pi$
$821$	−24.9856			−0.872003			−0.436002	+	0.899946i	$0.643606\pi$
$822$	16.0221	−	8.29365i	0.558835	−	0.289274i
$823$		−	31.1463i		−	1.08569i	−0.839832	−	0.542847i	$-0.817346\pi$
$823$		−	31.1463i		−	1.08569i	0.839832	−	0.542847i	$-0.182654\pi$
$824$	−3.41828			−0.119081
$825$	−9.12014	−	27.2364i	−0.317523	−	0.948251i
$826$	−39.7128			−1.38179
$827$			10.9855i			0.382005i	0.981590	+	0.191002i	$0.0611738\pi$
$827$			10.9855i			0.382005i	−0.981590	+	0.191002i	$0.938826\pi$
$828$	17.8293	−	25.2145i	0.619612	−	0.876263i
$829$	32.1051			1.11506			0.557528	−	0.830158i	$-0.311750\pi$
$829$	32.1051			1.11506			0.557528	+	0.830158i	$0.311750\pi$
$830$	52.3222	−	12.4505i	1.81613	−	0.432164i
$831$	−15.9819	−	30.8747i	−0.554407	−	1.07103i
$832$	−36.0942			−1.25134
$833$		−	7.82403i		−	0.271086i
$834$	−1.94744	−	3.76217i	−0.0674344	−	0.130273i
$835$	−6.52864	−	27.4360i	−0.225933	−	0.949463i
$836$	−27.4879	+	38.3596i	−0.950690	+	1.32670i
$837$	17.8293	+	2.47294i	0.616271	+	0.0854773i
$838$	85.0677			2.93862
$839$			38.8401i			1.34091i	0.741950	+	0.670455i	$0.233901\pi$
$839$			38.8401i			1.34091i	−0.741950	+	0.670455i	$0.766099\pi$
$840$	−41.1938	+	35.4985i	−1.42132	+	1.22482i
$841$	−25.1051			−0.865694
$842$			78.4919i			2.70501i
$843$	−26.1797	−	50.5753i	−0.901677	−	1.74191i
$844$		−	53.1026i		−	1.82787i
$845$	−3.34108	+	0.795040i	−0.114937	+	0.0273502i
$846$	9.33892	+	6.60361i	0.321079	+	0.227037i
$847$	11.9721	+	35.2679i	0.411366	+	1.21182i
$848$	−21.4409			−0.736284
$849$	5.19827	+	10.0423i	0.178404	+	0.344650i
$850$	−18.7321	+	9.45001i	−0.642504	+	0.324133i
$851$			23.1822i			0.794676i
$852$	−20.5875	+	10.6569i	−0.705317	+	0.365099i
$853$	0.243094			0.00832339			0.00416170	−	0.999991i	$-0.498675\pi$
$853$	0.243094			0.00832339			0.00416170	+	0.999991i	$0.498675\pi$
$854$	84.4374			2.88939
$855$	−23.7335	−	9.53084i	−0.811668	−	0.325948i
$856$	27.1244			0.927091
$857$		−	2.69190i		−	0.0919535i	−0.998943	−	0.0459768i	$-0.985360\pi$
$857$		−	2.69190i		−	0.0919535i	0.998943	−	0.0459768i	$-0.0146400\pi$
$858$	46.0847	+	6.68772i	1.57330	+	0.228315i
$859$	32.5359			1.11011			0.555055	−	0.831813i	$-0.312697\pi$
$859$	32.5359			1.11011			0.555055	+	0.831813i	$0.312697\pi$
$860$	−67.7331	+	16.1177i	−2.30968	+	0.549608i
$861$	−19.8564	−	38.3596i	−0.676705	−	1.30729i
$862$			38.7269i			1.31904i
$863$	29.7155			1.01153			0.505764	−	0.862672i	$-0.331211\pi$
$863$	29.7155			1.01153			0.505764	+	0.862672i	$0.331211\pi$
$864$	1.70914	−	12.3225i	0.0581461	−	0.419220i
$865$	−9.49346	−	39.8954i	−0.322787	−	1.35648i
$866$	46.6946			1.58675
$867$	11.0900	+	21.4242i	0.376636	+	0.727604i
$868$	43.7732			1.48576
$869$	−22.0961	+	30.8353i	−0.749559	+	1.04602i
$870$	−13.8627	+	11.9461i	−0.469991	+	0.405011i
$871$			44.4559i			1.50633i
$872$	11.5738			0.391940
$873$	20.5875	+	14.5576i	0.696782	+	0.492699i
$874$	25.1769			0.851622
$875$	28.9327	−	24.4113i	0.978103	−	0.825253i
$876$	−10.0613	−	19.4369i	−0.339939	−	0.656712i
$877$	23.2149			0.783911			0.391956	−	0.919984i	$-0.371799\pi$
$877$	23.2149			0.783911			0.391956	+	0.919984i	$0.371799\pi$
$878$	15.8102			0.533567
$879$	−2.69591	+	1.39551i	−0.0909309	+	0.0470693i
$880$	−16.9148	−	6.91649i	−0.570198	−	0.233155i
$881$			45.0518i			1.51783i	0.651188	+	0.758916i	$0.274271\pi$
$881$			45.0518i			1.51783i	−0.651188	+	0.758916i	$0.725729\pi$
$882$	26.1797	+	18.5118i	0.881516	+	0.623326i
$883$		−	12.0846i		−	0.406680i	−0.979108	−	0.203340i	$-0.934820\pi$
$883$		−	12.0846i		−	0.406680i	0.979108	−	0.203340i	$-0.0651797\pi$
$884$		−	22.1469i		−	0.744882i
$885$	14.3732	−	12.3860i	0.483148	−	0.416350i
$886$			3.06475i			0.102962i
$887$		−	10.0463i		−	0.337322i	−0.985674	−	0.168661i	$-0.946056\pi$
$887$		−	10.0463i		−	0.337322i	0.985674	−	0.168661i	$-0.0539443\pi$
$888$	−27.7511	−	53.6110i	−0.931266	−	1.79907i
$889$	57.3205			1.92247
$890$	49.5841	−	11.7990i	1.66206	−	0.395502i
$891$	−8.30456	+	28.6711i	−0.278213	+	0.960519i
$892$		−	68.0629i		−	2.27891i
$893$			6.07137i			0.203171i
$894$	12.5885	−	6.51626i	0.421021	−	0.217937i
$895$	2.67949	+	11.2603i	0.0895655	+	0.376391i
$896$		−	70.2030i		−	2.34532i
$897$	−7.43588	−	14.3650i	−0.248277	−	0.479634i
$898$	−44.4373			−1.48289
$899$	6.83656			0.228012
$900$	8.26888	−	55.3667i	0.275629	−	1.84556i
$901$			15.2504i			0.508064i
$902$	34.0662	−	47.5396i	1.13428	−	1.58290i
$903$	22.4923	+	43.4519i	0.748498	+	1.44599i
$904$			22.8756i			0.760831i
$905$	−5.51641	+	1.31268i	−0.183372	+	0.0436349i
$906$	−41.6603	−	80.4814i	−1.38407	−	2.67382i
$907$		−	31.7498i		−	1.05423i	−0.849793	−	0.527117i	$-0.823273\pi$
$907$		−	31.7498i		−	1.05423i	0.849793	−	0.527117i	$-0.176727\pi$
$908$			37.4933i			1.24426i
$909$	−3.41828	+	4.83418i	−0.113377	+	0.160340i
$910$	14.2076	+	59.7062i	0.470978	+	1.97924i
$911$		−	28.7647i		−	0.953019i	−0.879169	−	0.476509i	$-0.841902\pi$
$911$		−	28.7647i		−	0.953019i	0.879169	−	0.476509i	$-0.158098\pi$
$912$	−14.4507	+	7.48024i	−0.478511	+	0.247695i
$913$	19.4080	−	27.0840i	0.642310	−	0.896348i
$914$			68.6129i			2.26951i
$915$	−30.5602	+	26.3351i	−1.01029	+	0.870610i
$916$	49.7128			1.64256
$917$		0			0
$918$	21.5971	+	2.99553i	0.712810	+	0.0988673i
$919$			19.8108i			0.653499i	0.945111	+	0.326750i	$0.105953\pi$
$919$			19.8108i			0.653499i	−0.945111	+	0.326750i	$0.894047\pi$
$920$	5.92064	+	24.8809i	0.195198	+	0.820301i
$921$	−6.64300	−	12.8333i	−0.218894	−	0.422872i
$922$		−	75.2608i		−	2.47858i
$923$			12.1427i			0.399683i
$924$	−10.4249	+	71.8371i	−0.342953	+	2.36327i
$925$	18.9282	+	37.5200i	0.622355	+	1.23365i
$926$	−18.1490			−0.596414
$927$	−2.01915	−	1.42775i	−0.0663175	−	0.0468935i
$928$		−	4.72500i		−	0.155106i
$929$			41.4655i			1.36044i	0.733009	+	0.680219i	$0.238115\pi$
$929$			41.4655i			1.36044i	−0.733009	+	0.680219i	$0.761885\pi$
$930$	−24.3328	+	20.9686i	−0.797904	+	0.687589i
$931$			17.0198i			0.557802i
$932$		−	29.1997i		−	0.956467i
$933$	−22.6067	+	11.7021i	−0.740109	+	0.383109i
$934$		−	71.1440i		−	2.32790i
$935$	−4.91953	+	12.0311i	−0.160886	+	0.393459i
$936$	34.3923	+	24.3190i	1.12415	+	0.794892i
$937$	46.6729			1.52474			0.762368	−	0.647144i	$-0.224037\pi$
$937$	46.6729			1.52474			0.762368	+	0.647144i	$0.224037\pi$
$938$	−106.435			−3.47522
$939$	−24.2487	+	12.5521i	−0.791327	+	0.409621i
$940$	−12.9282	+	3.07638i	−0.421671	+	0.100340i
$941$	−46.1658			−1.50496			−0.752481	−	0.658614i	$-0.771143\pi$
$941$	−46.1658			−1.50496			−0.752481	+	0.658614i	$0.771143\pi$
$942$	−8.58622	−	16.5873i	−0.279754	−	0.540443i
$943$	−20.3152			−0.661554
$944$		−	12.0716i		−	0.392897i
$945$	−39.1599	+	3.76274i	−1.27387	+	0.122402i
$946$	−38.5885	+	53.8505i	−1.25462	+	1.75083i
$947$	−23.6581			−0.768785			−0.384392	−	0.923170i	$-0.625589\pi$
$947$	−23.6581			−0.768785			−0.384392	+	0.923170i	$0.625589\pi$
$948$	−65.6598	+	33.9880i	−2.13253	+	1.10388i
$949$	−11.4641			−0.372140
$950$	40.7483	−	20.5569i	1.32205	−	0.666953i
$951$	−0.679492	−	1.31268i	−0.0220340	−	0.0425665i
$952$	24.6083			0.797560
$953$			10.3901i			0.336568i	0.985739	+	0.168284i	$0.0538226\pi$
$953$			10.3901i			0.336568i	−0.985739	+	0.168284i	$0.946177\pi$
$954$	−51.0288	−	36.0828i	−1.65212	−	1.16822i
$955$	2.39230	+	10.0534i	0.0774132	+	0.325322i
$956$	−89.8292			−2.90528
$957$	−1.62817	+	11.2196i	−0.0526313	+	0.362679i
$958$			3.45894i			0.111753i
$959$	14.7307			0.475681
$960$	26.9521	+	31.2762i	0.869874	+	1.00944i
$961$	−19.0000			−0.612903
$962$	−68.1324			−2.19668
$963$	16.0221	+	11.3293i	0.516305	+	0.365083i
$964$			10.4162i			0.335484i
$965$	36.8269	−	8.76327i	1.18550	−	0.282100i
$966$	34.3923	−	17.8028i	1.10655	−	0.572795i
$967$	8.34312			0.268297			0.134148	−	0.990961i	$-0.457170\pi$
$967$	8.34312			0.268297			0.134148	+	0.990961i	$0.457170\pi$
$968$	−43.1942	+	14.6627i	−1.38831	+	0.471279i
$969$	5.32051	+	10.2784i	0.170919	+	0.330191i
$970$	−43.7732	+	10.4162i	−1.40547	+	0.334444i
$971$			50.2281i			1.61190i	0.591985	+	0.805949i	$0.298344\pi$
$971$			50.2281i			1.61190i	−0.591985	+	0.805949i	$0.701656\pi$
$972$	−39.7959	+	42.4363i	−1.27646	+	1.36114i
$973$		−	3.45894i		−	0.110889i
$974$	30.3774			0.973355
$975$	−23.7638	−	17.1781i	−0.761051	−	0.550141i
$976$			25.6666i			0.821568i
$977$	39.1559			1.25271			0.626354	−	0.779539i	$-0.284546\pi$
$977$	39.1559			1.25271			0.626354	+	0.779539i	$0.284546\pi$
$978$	−1.57139	−	3.03569i	−0.0502474	−	0.0970705i
$979$	18.3923	−	25.6666i	0.587821	−	0.820308i
$980$	−36.2415	+	8.62398i	−1.15769	+	0.275483i
$981$	6.83656	+	4.83418i	0.218275	+	0.154343i
$982$		−	38.7269i		−	1.23582i
$983$	−8.27462			−0.263919			−0.131960	−	0.991255i	$-0.542127\pi$
$983$	−8.27462			−0.263919			−0.131960	+	0.991255i	$0.542127\pi$
$984$	46.9808	−	24.3190i	1.49769	−	0.775262i
$985$	10.8217	+	45.4774i	0.344810	+	1.44903i
$986$	8.28130			0.263730
$987$	4.29311	+	8.29365i	0.136651	+	0.263990i
$988$			48.1769i			1.53271i
$989$	23.0120			0.731740
$990$	−28.6171	−	44.9269i	−0.909510	−	1.42787i
$991$	−48.2487			−1.53267			−0.766335	−	0.642441i	$-0.777922\pi$
$991$	−48.2487			−1.53267			−0.766335	+	0.642441i	$0.777922\pi$
$992$		−	8.29365i		−	0.263324i
$993$	12.3129	+	23.7867i	0.390738	+	0.754848i
$994$	−29.0718			−0.922101
$995$	−6.36980	+	1.51575i	−0.201936	+	0.0480525i
$996$	57.6718	−	29.8531i	1.82740	−	0.945932i
$997$	−29.9866			−0.949686			−0.474843	−	0.880071i	$-0.657495\pi$
$997$	−29.9866			−0.949686			−0.474843	+	0.880071i	$0.657495\pi$
$998$			26.1640i			0.828206i
$999$	6.00000	−	43.2586i	0.189832	−	1.36864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.d.c.164.4	yes	16
3.2	odd	2	inner	165.2.d.c.164.14	yes	16
5.2	odd	4		825.2.f.f.626.15		16
5.3	odd	4		825.2.f.f.626.2		16
5.4	even	2	inner	165.2.d.c.164.13	yes	16
11.10	odd	2	inner	165.2.d.c.164.16	yes	16
15.2	even	4		825.2.f.f.626.4		16
15.8	even	4		825.2.f.f.626.13		16
15.14	odd	2	inner	165.2.d.c.164.3	yes	16
33.32	even	2	inner	165.2.d.c.164.2	yes	16
55.32	even	4		825.2.f.f.626.3		16
55.43	even	4		825.2.f.f.626.14		16
55.54	odd	2	inner	165.2.d.c.164.1	✓	16
165.32	odd	4		825.2.f.f.626.16		16
165.98	odd	4		825.2.f.f.626.1		16
165.164	even	2	inner	165.2.d.c.164.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.d.c.164.1	✓	16	55.54	odd	2	inner
165.2.d.c.164.2	yes	16	33.32	even	2	inner
165.2.d.c.164.3	yes	16	15.14	odd	2	inner
165.2.d.c.164.4	yes	16	1.1	even	1	trivial
165.2.d.c.164.13	yes	16	5.4	even	2	inner
165.2.d.c.164.14	yes	16	3.2	odd	2	inner
165.2.d.c.164.15	yes	16	165.164	even	2	inner
165.2.d.c.164.16	yes	16	11.10	odd	2	inner
825.2.f.f.626.1		16	165.98	odd	4
825.2.f.f.626.2		16	5.3	odd	4
825.2.f.f.626.3		16	55.32	even	4
825.2.f.f.626.4		16	15.2	even	4
825.2.f.f.626.13		16	15.8	even	4
825.2.f.f.626.14		16	55.43	even	4
825.2.f.f.626.15		16	5.2	odd	4
825.2.f.f.626.16		16	165.32	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.39417i q^{2} +(0.796225 + 1.53819i) q^{3} -3.73205 q^{4} +(2.17533 - 0.517638i) q^{5} +(3.68269 - 1.90630i) q^{6} +3.38587 q^{7} +4.14682i q^{8} +(-1.73205 + 2.44949i) q^{9} +O(q^{10})\)	\(q-2.39417i q^{2} +(0.796225 + 1.53819i) q^{3} -3.73205 q^{4} +(2.17533 - 0.517638i) q^{5} +(3.68269 - 1.90630i) q^{6} +3.38587 q^{7} +4.14682i q^{8} +(-1.73205 + 2.44949i) q^{9} +(-1.23931 - 5.20810i) q^{10} +(-2.69591 - 1.93185i) q^{11} +(-2.97155 - 5.74060i) q^{12} -3.38587 q^{13} -8.10634i q^{14} +(2.52828 + 2.93391i) q^{15} +2.46410 q^{16} -1.75265i q^{17} +(5.86450 + 4.14682i) q^{18} +3.81260i q^{19} +(-8.11843 + 1.93185i) q^{20} +(2.69591 + 5.20810i) q^{21} +(-4.62518 + 6.45448i) q^{22} +2.75821 q^{23} +(-6.37860 + 3.30181i) q^{24} +(4.46410 - 2.25207i) q^{25} +8.10634i q^{26} +(-5.14688 - 0.713876i) q^{27} -12.6362 q^{28} -1.97355 q^{29} +(7.02428 - 6.05312i) q^{30} -3.46410 q^{31} +2.39417i q^{32} +(0.824999 - 5.68501i) q^{33} -4.19615 q^{34} +(7.36537 - 1.75265i) q^{35} +(6.46410 - 9.14162i) q^{36} +8.40482i q^{37} +9.12801 q^{38} +(-2.69591 - 5.20810i) q^{39} +(2.14655 + 9.02070i) q^{40} -7.36537 q^{41} +(12.4691 - 6.45448i) q^{42} +8.34312 q^{43} +(10.0613 + 7.20977i) q^{44} +(-2.49983 + 6.22502i) q^{45} -6.60361i q^{46} +1.59245 q^{47} +(1.96198 + 3.79025i) q^{48} +4.46410 q^{49} +(-5.39183 - 10.6878i) q^{50} +(2.69591 - 1.39551i) q^{51} +12.6362 q^{52} -8.70131 q^{53} +(-1.70914 + 12.3225i) q^{54} +(-6.86450 - 2.80690i) q^{55} +14.0406i q^{56} +(-5.86450 + 3.03569i) q^{57} +4.72500i q^{58} -4.89898i q^{59} +(-9.43565 - 10.9495i) q^{60} +10.4162i q^{61} +8.29365i q^{62} +(-5.86450 + 8.29365i) q^{63} +10.6603 q^{64} +(-7.36537 + 1.75265i) q^{65} +(-13.6109 - 1.97519i) q^{66} -13.1298i q^{67} +6.54099i q^{68} +(2.19615 + 4.24264i) q^{69} +(-4.19615 - 17.6340i) q^{70} -3.58630i q^{71} +(-10.1576 - 7.18251i) q^{72} +3.38587 q^{73} +20.1226 q^{74} +(7.01853 + 5.07348i) q^{75} -14.2288i q^{76} +(-9.12801 - 6.54099i) q^{77} +(-12.4691 + 6.45448i) q^{78} -11.4378i q^{79} +(5.36023 - 1.27551i) q^{80} +(-3.00000 - 8.48528i) q^{81} +17.6340i q^{82} +10.0463i q^{83} +(-10.0613 - 19.4369i) q^{84} +(-0.907241 - 3.81260i) q^{85} -19.9749i q^{86} +(-1.57139 - 3.03569i) q^{87} +(8.01105 - 11.1795i) q^{88} +9.52056i q^{89} +(14.9038 + 5.98502i) q^{90} -11.4641 q^{91} -10.2938 q^{92} +(-2.75821 - 5.32844i) q^{93} -3.81260i q^{94} +(1.97355 + 8.29365i) q^{95} +(-3.68269 + 1.90630i) q^{96} -8.40482i q^{97} -10.6878i q^{98} +(9.40151 - 3.25755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{4}+O(q^{10}) \) 16 * q - 32 * q^4	\( 16 q - 32 q^{4} - 16 q^{16} + 16 q^{25} + 16 q^{34} + 48 q^{36} + 48 q^{45} + 16 q^{49} - 16 q^{55} - 48 q^{60} + 32 q^{64} - 48 q^{66} - 48 q^{69} + 16 q^{70} - 48 q^{81} - 128 q^{91} + 48 q^{99}+O(q^{100}) \) 16 * q - 32 * q^4 - 16 * q^16 + 16 * q^25 + 16 * q^34 + 48 * q^36 + 48 * q^45 + 16 * q^49 - 16 * q^55 - 48 * q^60 + 32 * q^64 - 48 * q^66 - 48 * q^69 + 16 * q^70 - 48 * q^81 - 128 * q^91 + 48 * q^99

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