LMFDB - Embedded newform 405.2.e.j.271.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(136,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("405.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			271.2
Root			$-0.651388 - 1.12824i$ of defining polynomial
Character	$\chi$	$=$	405.271
Dual form			405.2.e.j.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.30278 - 3.98852i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.30278 - 3.98852i) q^{7} +3.00000 q^{8} +1.30278 q^{10} +(-1.30278 - 2.25647i) q^{11} +(0.302776 - 0.524423i) q^{13} +(3.00000 - 5.19615i) q^{14} +(1.65139 + 2.86029i) q^{16} +5.60555 q^{17} -3.60555 q^{19} +(-0.151388 - 0.262211i) q^{20} +(1.69722 - 2.93968i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.788897 q^{26} -1.39445 q^{28} +(4.30278 + 7.45263i) q^{29} +(-0.802776 + 1.39045i) q^{31} +(0.848612 - 1.46984i) q^{32} +(3.65139 + 6.32439i) q^{34} -4.60555 q^{35} +2.00000 q^{37} +(-2.34861 - 4.06792i) q^{38} +(1.50000 - 2.59808i) q^{40} +(1.30278 - 2.25647i) q^{41} +(3.30278 + 5.72058i) q^{43} -0.788897 q^{44} -3.90833 q^{46} +(2.60555 + 4.51295i) q^{47} +(-7.10555 + 12.3072i) q^{49} +(0.651388 - 1.12824i) q^{50} +(-0.0916731 - 0.158782i) q^{52} +5.60555 q^{53} -2.60555 q^{55} +(-6.90833 - 11.9656i) q^{56} +(-5.60555 + 9.70910i) q^{58} +(-4.30278 + 7.45263i) q^{59} +(-5.10555 - 8.84307i) q^{61} -2.09167 q^{62} +8.81665 q^{64} +(-0.302776 - 0.524423i) q^{65} +(7.60555 - 13.1732i) q^{67} +(0.848612 - 1.46984i) q^{68} +(-3.00000 - 5.19615i) q^{70} -14.6056 q^{71} +5.39445 q^{73} +(1.30278 + 2.25647i) q^{74} +(-0.545837 + 0.945417i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(2.19722 + 3.80570i) q^{79} +3.30278 q^{80} +3.39445 q^{82} +(1.50000 + 2.59808i) q^{83} +(2.80278 - 4.85455i) q^{85} +(-4.30278 + 7.45263i) q^{86} +(-3.90833 - 6.76942i) q^{88} -7.81665 q^{89} -2.78890 q^{91} +(0.454163 + 0.786634i) q^{92} +(-3.39445 + 5.87936i) q^{94} +(-1.80278 + 3.12250i) q^{95} +(-4.00000 - 6.92820i) q^{97} -18.5139 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q - q^2 - 3 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8	$ 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} - 6 q^{13} + 12 q^{14} + 3 q^{16} + 8 q^{17} + 3 q^{20} + 14 q^{22} - 6 q^{23} - 2 q^{25} + 32 q^{26} - 20 q^{28} + 10 q^{29} + 4 q^{31} + 7 q^{32} + 11 q^{34} - 4 q^{35} + 8 q^{37} - 13 q^{38} + 6 q^{40} - 2 q^{41} + 6 q^{43} - 32 q^{44} + 6 q^{46} - 4 q^{47} - 14 q^{49} - q^{50} - 22 q^{52} + 8 q^{53} + 4 q^{55} - 6 q^{56} - 8 q^{58} - 10 q^{59} - 6 q^{61} - 30 q^{62} - 8 q^{64} + 6 q^{65} + 16 q^{67} + 7 q^{68} - 12 q^{70} - 44 q^{71} + 36 q^{73} - 2 q^{74} - 13 q^{76} - 24 q^{77} + 16 q^{79} + 6 q^{80} + 28 q^{82} + 6 q^{83} + 4 q^{85} - 10 q^{86} + 6 q^{88} + 12 q^{89} - 40 q^{91} - 9 q^{92} - 28 q^{94} - 16 q^{97} - 38 q^{98}+O(q^{100}) $ 4 * q - q^2 - 3 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 - 2 * q^10 + 2 * q^11 - 6 * q^13 + 12 * q^14 + 3 * q^16 + 8 * q^17 + 3 * q^20 + 14 * q^22 - 6 * q^23 - 2 * q^25 + 32 * q^26 - 20 * q^28 + 10 * q^29 + 4 * q^31 + 7 * q^32 + 11 * q^34 - 4 * q^35 + 8 * q^37 - 13 * q^38 + 6 * q^40 - 2 * q^41 + 6 * q^43 - 32 * q^44 + 6 * q^46 - 4 * q^47 - 14 * q^49 - q^50 - 22 * q^52 + 8 * q^53 + 4 * q^55 - 6 * q^56 - 8 * q^58 - 10 * q^59 - 6 * q^61 - 30 * q^62 - 8 * q^64 + 6 * q^65 + 16 * q^67 + 7 * q^68 - 12 * q^70 - 44 * q^71 + 36 * q^73 - 2 * q^74 - 13 * q^76 - 24 * q^77 + 16 * q^79 + 6 * q^80 + 28 * q^82 + 6 * q^83 + 4 * q^85 - 10 * q^86 + 6 * q^88 + 12 * q^89 - 40 * q^91 - 9 * q^92 - 28 * q^94 - 16 * q^97 - 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.651388	+	1.12824i	0.460601	+	0.797784i	0.998991	−	0.0449118i	$-0.0143007\pi$
$2$	0.651388	+	1.12824i	0.460601	+	0.797784i	−0.538390	+	0.842696i	$0.680967\pi$
$3$		0			0
$3$		0			0
$4$	0.151388	−	0.262211i	0.0756939	−	0.131106i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−2.30278	−	3.98852i	−0.870367	−	1.50752i	−0.861617	−	0.507559i	$-0.830548\pi$
$7$	−2.30278	−	3.98852i	−0.870367	−	1.50752i	−0.00875026	−	0.999962i	$-0.502785\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$	1.30278			0.411974
$11$	−1.30278	−	2.25647i	−0.392802	−	0.680352i	0.600016	−	0.799988i	$-0.295161\pi$
$11$	−1.30278	−	2.25647i	−0.392802	−	0.680352i	−0.992818	+	0.119635i	$0.961827\pi$
$12$		0			0
$13$	0.302776	−	0.524423i	0.0839749	−	0.145449i	−0.820979	−	0.570958i	$-0.806572\pi$
$13$	0.302776	−	0.524423i	0.0839749	−	0.145449i	0.904954	+	0.425510i	$0.139905\pi$
$14$	3.00000	−	5.19615i	0.801784	−	1.38873i
$15$		0			0
$16$	1.65139	+	2.86029i	0.412847	+	0.715072i
$17$	5.60555			1.35955			0.679773	−	0.733423i	$-0.262078\pi$
$17$	5.60555			1.35955			0.679773	+	0.733423i	$0.262078\pi$
$18$		0			0
$19$	−3.60555			−0.827170			−0.413585	−	0.910465i	$-0.635724\pi$
$19$	−3.60555			−0.827170			−0.413585	+	0.910465i	$0.635724\pi$
$20$	−0.151388	−	0.262211i	−0.0338513	−	0.0586323i
$21$		0			0
$22$	1.69722	−	2.93968i	0.361849	−	0.626742i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.788897			0.154716
$27$		0			0
$28$	−1.39445			−0.263526
$29$	4.30278	+	7.45263i	0.799005	+	1.38392i	0.920264	+	0.391297i	$0.127973\pi$
$29$	4.30278	+	7.45263i	0.799005	+	1.38392i	−0.121259	+	0.992621i	$0.538693\pi$
$30$		0			0
$31$	−0.802776	+	1.39045i	−0.144183	+	0.249732i	−0.929068	−	0.369910i	$-0.879389\pi$
$31$	−0.802776	+	1.39045i	−0.144183	+	0.249732i	0.784885	+	0.619641i	$0.212722\pi$
$32$	0.848612	−	1.46984i	0.150015	−	0.259833i
$33$		0			0
$34$	3.65139	+	6.32439i	0.626208	+	1.08462i
$35$	−4.60555			−0.778480
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−2.34861	−	4.06792i	−0.380995	−	0.659903i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	1.30278	−	2.25647i	0.203459	−	0.352402i	−0.746181	−	0.665743i	$-0.768115\pi$
$41$	1.30278	−	2.25647i	0.203459	−	0.352402i	0.949641	+	0.313341i	$0.101448\pi$
$42$		0			0
$43$	3.30278	+	5.72058i	0.503669	+	0.872380i	0.999991	+	0.00424128i	$0.00135005\pi$
$43$	3.30278	+	5.72058i	0.503669	+	0.872380i	−0.496322	+	0.868138i	$0.665317\pi$
$44$	−0.788897			−0.118931
$45$		0			0
$46$	−3.90833			−0.576251
$47$	2.60555	+	4.51295i	0.380059	+	0.658281i	0.991070	−	0.133341i	$-0.0425704\pi$
$47$	2.60555	+	4.51295i	0.380059	+	0.658281i	−0.611012	+	0.791622i	$0.709237\pi$
$48$		0			0
$49$	−7.10555	+	12.3072i	−1.01508	+	1.75817i
$50$	0.651388	−	1.12824i	0.0921201	−	0.159557i
$51$		0			0
$52$	−0.0916731	−	0.158782i	−0.0127128	−	0.0220192i
$53$	5.60555			0.769982			0.384991	−	0.922920i	$-0.374205\pi$
$53$	5.60555			0.769982			0.384991	+	0.922920i	$0.374205\pi$
$54$		0			0
$55$	−2.60555			−0.351332
$56$	−6.90833	−	11.9656i	−0.923164	−	1.59897i
$57$		0			0
$58$	−5.60555	+	9.70910i	−0.736045	+	1.27487i
$59$	−4.30278	+	7.45263i	−0.560174	+	0.970249i	0.437307	+	0.899312i	$0.355932\pi$
$59$	−4.30278	+	7.45263i	−0.560174	+	0.970249i	−0.997481	+	0.0709370i	$0.977401\pi$
$60$		0			0
$61$	−5.10555	−	8.84307i	−0.653699	−	1.13224i	−0.982218	−	0.187742i	$-0.939883\pi$
$61$	−5.10555	−	8.84307i	−0.653699	−	1.13224i	0.328519	−	0.944497i	$-0.393450\pi$
$62$	−2.09167			−0.265643
$63$		0			0
$64$	8.81665			1.10208
$65$	−0.302776	−	0.524423i	−0.0375547	−	0.0650466i
$66$		0			0
$67$	7.60555	−	13.1732i	0.929166	−	1.60936i	0.144446	−	0.989513i	$-0.453860\pi$
$67$	7.60555	−	13.1732i	0.929166	−	1.60936i	0.784720	−	0.619850i	$-0.212807\pi$
$68$	0.848612	−	1.46984i	0.102909	−	0.178244i
$69$		0			0
$70$	−3.00000	−	5.19615i	−0.358569	−	0.621059i
$71$	−14.6056			−1.73336			−0.866680	−	0.498864i	$-0.833751\pi$
$71$	−14.6056			−1.73336			−0.866680	+	0.498864i	$0.833751\pi$
$72$		0			0
$73$	5.39445			0.631372			0.315686	−	0.948864i	$-0.397765\pi$
$73$	5.39445			0.631372			0.315686	+	0.948864i	$0.397765\pi$
$74$	1.30278	+	2.25647i	0.151445	+	0.262310i
$75$		0			0
$76$	−0.545837	+	0.945417i	−0.0626117	+	0.108447i
$77$	−6.00000	+	10.3923i	−0.683763	+	1.18431i
$78$		0			0
$79$	2.19722	+	3.80570i	0.247207	+	0.428175i	0.962750	−	0.270394i	$-0.0871539\pi$
$79$	2.19722	+	3.80570i	0.247207	+	0.428175i	−0.715543	+	0.698569i	$0.753821\pi$
$80$	3.30278			0.369262
$81$		0			0
$82$	3.39445			0.374854
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	0.936530	−	0.350588i	$-0.114018\pi$
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	−0.771883	+	0.635764i	$0.780685\pi$
$84$		0			0
$85$	2.80278	−	4.85455i	0.304004	−	0.526550i
$86$	−4.30278	+	7.45263i	−0.463980	+	0.803637i
$87$		0			0
$88$	−3.90833	−	6.76942i	−0.416629	−	0.721623i
$89$	−7.81665			−0.828564			−0.414282	−	0.910149i	$-0.635967\pi$
$89$	−7.81665			−0.828564			−0.414282	+	0.910149i	$0.635967\pi$
$90$		0			0
$91$	−2.78890			−0.292356
$92$	0.454163	+	0.786634i	0.0473498	+	0.0820123i
$93$		0			0
$94$	−3.39445	+	5.87936i	−0.350111	+	0.606409i
$95$	−1.80278	+	3.12250i	−0.184961	+	0.320362i
$96$		0			0
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	0.588315	−	0.808632i	$-0.299792\pi$
$97$	−4.00000	−	6.92820i	−0.406138	−	0.703452i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	−18.5139			−1.87018
$99$		0			0
$100$	−0.302776			−0.0302776
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	0.993258	+	0.115924i	$0.0369830\pi$
$101$	6.00000	+	10.3923i	0.597022	+	1.03407i	−0.396236	+	0.918149i	$0.629684\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	0.908327	−	1.57327i	0.0890688	−	0.154272i
$105$		0			0
$106$	3.65139	+	6.32439i	0.354654	+	0.614279i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$	−1.69722	−	2.93968i	−0.161824	−	0.280287i
$111$		0			0
$112$	7.60555	−	13.1732i	0.718657	−	1.24475i
$113$	−0.394449	+	0.683205i	−0.0371066	+	0.0642705i	−0.883982	−	0.467520i	$-0.845147\pi$
$113$	−0.394449	+	0.683205i	−0.0371066	+	0.0642705i	0.846876	+	0.531791i	$0.178481\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$	2.60555			0.241919
$117$		0			0
$118$	−11.2111			−1.03207
$119$	−12.9083	−	22.3579i	−1.18330	−	2.04954i
$120$		0			0
$121$	2.10555	−	3.64692i	0.191414	−	0.331538i
$122$	6.65139	−	11.5205i	0.602188	−	1.04302i
$123$		0			0
$124$	0.243061	+	0.420994i	0.0218275	+	0.0378064i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−4.78890			−0.424946			−0.212473	−	0.977167i	$-0.568152\pi$
$127$	−4.78890			−0.424946			−0.212473	+	0.977167i	$0.568152\pi$
$128$	4.04584	+	7.00759i	0.357605	+	0.619390i
$129$		0			0
$130$	0.394449	−	0.683205i	0.0345954	−	0.0599211i
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$		0			0
$133$	8.30278	+	14.3808i	0.719942	+	1.24698i
$134$	19.8167			1.71190
$135$		0			0
$136$	16.8167			1.44202
$137$	−2.40833	−	4.17134i	−0.205757	−	0.356382i	0.744616	−	0.667493i	$-0.232632\pi$
$137$	−2.40833	−	4.17134i	−0.205757	−	0.356382i	−0.950374	+	0.311111i	$0.899299\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	−0.697224	+	1.20763i	−0.0589262	+	0.102063i
$141$		0			0
$142$	−9.51388	−	16.4785i	−0.798387	−	1.38285i
$143$	−1.57779			−0.131942
$144$		0			0
$145$	8.60555			0.714652
$146$	3.51388	+	6.08622i	0.290811	+	0.503699i
$147$		0			0
$148$	0.302776	−	0.524423i	0.0248880	−	0.0431073i
$149$	−6.51388	+	11.2824i	−0.533638	+	0.924288i	0.465590	+	0.885000i	$0.345842\pi$
$149$	−6.51388	+	11.2824i	−0.533638	+	0.924288i	−0.999228	+	0.0392872i	$0.987491\pi$
$150$		0			0
$151$	7.21110	+	12.4900i	0.586831	+	1.01642i	0.994644	+	0.103356i	$0.0329581\pi$
$151$	7.21110	+	12.4900i	0.586831	+	1.01642i	−0.407813	+	0.913065i	$0.633709\pi$
$152$	−10.8167			−0.877346
$153$		0			0
$154$	−15.6333			−1.25977
$155$	0.802776	+	1.39045i	0.0644805	+	0.111683i
$156$		0			0
$157$	−1.90833	+	3.30532i	−0.152301	+	0.263793i	−0.932073	−	0.362270i	$-0.882002\pi$
$157$	−1.90833	+	3.30532i	−0.152301	+	0.263793i	0.779772	+	0.626064i	$0.215335\pi$
$158$	−2.86249	+	4.95798i	−0.227728	+	0.394436i
$159$		0			0
$160$	−0.848612	−	1.46984i	−0.0670887	−	0.116201i
$161$	13.8167			1.08890
$162$		0			0
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$	−0.394449	−	0.683205i	−0.0308013	−	0.0533494i
$165$		0			0
$166$	−1.95416	+	3.38471i	−0.151672	+	0.262704i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$		0			0
$169$	6.31665	+	10.9408i	0.485896	+	0.841597i
$170$	7.30278			0.560097
$171$		0			0
$172$	2.00000			0.152499
$173$	5.40833	+	9.36750i	0.411187	+	0.712198i	0.995020	−	0.0996766i	$-0.0317808\pi$
$173$	5.40833	+	9.36750i	0.411187	+	0.712198i	−0.583832	+	0.811874i	$0.698447\pi$
$174$		0			0
$175$	−2.30278	+	3.98852i	−0.174073	+	0.301504i
$176$	4.30278	−	7.45263i	0.324334	−	0.561763i
$177$		0			0
$178$	−5.09167	−	8.81904i	−0.381637	−	0.661015i
$179$	6.78890			0.507426			0.253713	−	0.967280i	$-0.418348\pi$
$179$	6.78890			0.507426			0.253713	+	0.967280i	$0.418348\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	−1.81665	−	3.14654i	−0.134659	−	0.233237i
$183$		0			0
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$		0			0
$187$	−7.30278	−	12.6488i	−0.534032	−	0.924970i
$188$	1.57779			0.115073
$189$		0			0
$190$	−4.69722			−0.340772
$191$	8.21110	+	14.2220i	0.594135	+	1.02907i	0.993668	+	0.112353i	$0.0358387\pi$
$191$	8.21110	+	14.2220i	0.594135	+	1.02907i	−0.399534	+	0.916718i	$0.630828\pi$
$192$		0			0
$193$	−10.9083	+	18.8938i	−0.785199	+	1.36000i	0.143682	+	0.989624i	$0.454106\pi$
$193$	−10.9083	+	18.8938i	−0.785199	+	1.36000i	−0.928880	+	0.370380i	$0.879228\pi$
$194$	5.21110	−	9.02589i	0.374135	−	0.648021i
$195$		0			0
$196$	2.15139	+	3.72631i	0.153671	+	0.266165i
$197$	1.18335			0.0843099			0.0421550	−	0.999111i	$-0.486578\pi$
$197$	1.18335			0.0843099			0.0421550	+	0.999111i	$0.486578\pi$
$198$		0			0
$199$	13.2111			0.936510			0.468255	−	0.883593i	$-0.344883\pi$
$199$	13.2111			0.936510			0.468255	+	0.883593i	$0.344883\pi$
$200$	−1.50000	−	2.59808i	−0.106066	−	0.183712i
$201$		0			0
$202$	−7.81665	+	13.5388i	−0.549978	+	0.952590i
$203$	19.8167	−	34.3235i	1.39086	−	2.40903i
$204$		0			0
$205$	−1.30278	−	2.25647i	−0.0909898	−	0.157599i
$206$	5.21110			0.363075
$207$		0			0
$208$	2.00000			0.138675
$209$	4.69722	+	8.13583i	0.324914	+	0.562767i
$210$		0			0
$211$	−6.40833	+	11.0995i	−0.441167	+	0.764124i	−0.997776	−	0.0666502i	$-0.978769\pi$
$211$	−6.40833	+	11.0995i	−0.441167	+	0.764124i	0.556609	+	0.830775i	$0.312102\pi$
$212$	0.848612	−	1.46984i	0.0582829	−	0.100949i
$213$		0			0
$214$		0			0
$215$	6.60555			0.450495
$216$		0			0
$217$	7.39445			0.501968
$218$	−4.55971	−	7.89766i	−0.308823	−	0.534897i
$219$		0			0
$220$	−0.394449	+	0.683205i	−0.0265937	+	0.0460617i
$221$	1.69722	−	2.93968i	0.114168	−	0.197744i
$222$		0			0
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$	−7.81665			−0.522272
$225$		0			0
$226$	−1.02776			−0.0683653
$227$	−13.1056	−	22.6995i	−0.869846	−	1.50662i	−0.862154	−	0.506647i	$-0.830885\pi$
$227$	−13.1056	−	22.6995i	−0.869846	−	1.50662i	−0.00769242	−	0.999970i	$-0.502449\pi$
$228$		0			0
$229$	3.10555	−	5.37897i	0.205221	−	0.355453i	−0.744982	−	0.667084i	$-0.767542\pi$
$229$	3.10555	−	5.37897i	0.205221	−	0.355453i	0.950203	+	0.311632i	$0.100875\pi$
$230$	−1.95416	+	3.38471i	−0.128854	+	0.223181i
$231$		0			0
$232$	12.9083	+	22.3579i	0.847473	+	1.46787i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	5.21110			0.339935
$236$	1.30278	+	2.25647i	0.0848035	+	0.146884i
$237$		0			0
$238$	16.8167	−	29.1273i	1.09006	−	1.88804i
$239$	−0.394449	+	0.683205i	−0.0255148	+	0.0441929i	−0.878501	−	0.477741i	$-0.841456\pi$
$239$	−0.394449	+	0.683205i	−0.0255148	+	0.0441929i	0.852986	+	0.521934i	$0.174789\pi$
$240$		0			0
$241$	−14.1056	−	24.4315i	−0.908618	−	1.57377i	−0.815985	−	0.578073i	$-0.803805\pi$
$241$	−14.1056	−	24.4315i	−0.908618	−	1.57377i	−0.0926334	−	0.995700i	$-0.529528\pi$
$242$	5.48612			0.352661
$243$		0			0
$244$	−3.09167			−0.197924
$245$	7.10555	+	12.3072i	0.453957	+	0.786277i
$246$		0			0
$247$	−1.09167	+	1.89083i	−0.0694615	+	0.120311i
$248$	−2.40833	+	4.17134i	−0.152929	+	0.264881i
$249$		0			0
$250$	−0.651388	−	1.12824i	−0.0411974	−	0.0713560i
$251$	15.6333			0.986766			0.493383	−	0.869812i	$-0.335760\pi$
$251$	15.6333			0.986766			0.493383	+	0.869812i	$0.335760\pi$
$252$		0			0
$253$	7.81665			0.491429
$254$	−3.11943	−	5.40301i	−0.195730	−	0.339015i
$255$		0			0
$256$	3.54584	−	6.14157i	0.221615	−	0.383848i
$257$	11.4083	−	19.7598i	0.711632	−	1.23258i	−0.252612	−	0.967568i	$-0.581290\pi$
$257$	11.4083	−	19.7598i	0.711632	−	1.23258i	0.964244	−	0.265015i	$-0.0853769\pi$
$258$		0			0
$259$	−4.60555	−	7.97705i	−0.286175	−	0.495670i
$260$	−0.183346			−0.0113706
$261$		0			0
$262$	7.81665			0.482914
$263$	−8.60555	−	14.9053i	−0.530641	−	0.919097i	−0.999361	−	0.0357503i	$-0.988618\pi$
$263$	−8.60555	−	14.9053i	−0.530641	−	0.919097i	0.468720	−	0.883347i	$-0.344715\pi$
$264$		0			0
$265$	2.80278	−	4.85455i	0.172173	−	0.298213i
$266$	−10.8167	+	18.7350i	−0.663212	+	1.14872i
$267$		0			0
$268$	−2.30278	−	3.98852i	−0.140664	−	0.243638i
$269$	−11.2111			−0.683553			−0.341776	−	0.939781i	$-0.611029\pi$
$269$	−11.2111			−0.683553			−0.341776	+	0.939781i	$0.611029\pi$
$270$		0			0
$271$	−19.2389			−1.16868			−0.584339	−	0.811510i	$-0.698646\pi$
$271$	−19.2389			−1.16868			−0.584339	+	0.811510i	$0.698646\pi$
$272$	9.25694	+	16.0335i	0.561284	+	0.972173i
$273$		0			0
$274$	3.13751	−	5.43433i	0.189544	−	0.328300i
$275$	−1.30278	+	2.25647i	−0.0785603	+	0.136070i
$276$		0			0
$277$	14.5139	+	25.1388i	0.872054	+	1.51044i	0.859868	+	0.510517i	$0.170546\pi$
$277$	14.5139	+	25.1388i	0.872054	+	1.51044i	0.0121867	+	0.999926i	$0.496121\pi$
$278$	5.21110			0.312541
$279$		0			0
$280$	−13.8167			−0.825703
$281$	0.908327	+	1.57327i	0.0541862	+	0.0938533i	0.891846	−	0.452339i	$-0.149410\pi$
$281$	0.908327	+	1.57327i	0.0541862	+	0.0938533i	−0.837660	+	0.546192i	$0.816077\pi$
$282$		0			0
$283$	−5.30278	+	9.18468i	−0.315217	+	0.545972i	−0.979484	−	0.201524i	$-0.935411\pi$
$283$	−5.30278	+	9.18468i	−0.315217	+	0.545972i	0.664266	+	0.747496i	$0.268744\pi$
$284$	−2.21110	+	3.82974i	−0.131205	+	0.227253i
$285$		0			0
$286$	−1.02776	−	1.78013i	−0.0607725	−	0.105261i
$287$	−12.0000			−0.708338
$288$		0			0
$289$	14.4222			0.848365
$290$	5.60555	+	9.70910i	0.329169	+	0.570138i
$291$		0			0
$292$	0.816654	−	1.41449i	0.0477911	−	0.0827765i
$293$	−14.4083	+	24.9560i	−0.841743	+	1.45794i	0.0466761	+	0.998910i	$0.485137\pi$
$293$	−14.4083	+	24.9560i	−0.841743	+	1.45794i	−0.888420	+	0.459032i	$0.848196\pi$
$294$		0			0
$295$	4.30278	+	7.45263i	0.250517	+	0.433909i
$296$	6.00000			0.348743
$297$		0			0
$298$	−16.9722			−0.983176
$299$	0.908327	+	1.57327i	0.0525299	+	0.0909845i
$300$		0			0
$301$	15.2111	−	26.3464i	0.876753	−	1.51858i
$302$	−9.39445	+	16.2717i	−0.540590	+	0.936329i
$303$		0			0
$304$	−5.95416	−	10.3129i	−0.341495	−	0.591486i
$305$	−10.2111			−0.584686
$306$		0			0
$307$	−20.4222			−1.16556			−0.582778	−	0.812631i	$-0.698034\pi$
$307$	−20.4222			−1.16556			−0.582778	+	0.812631i	$0.698034\pi$
$308$	1.81665	+	3.14654i	0.103513	+	0.179291i
$309$		0			0
$310$	−1.04584	+	1.81144i	−0.0593995	+	0.102883i
$311$	6.90833	−	11.9656i	0.391735	−	0.678505i	−0.600943	−	0.799292i	$-0.705208\pi$
$311$	6.90833	−	11.9656i	0.391735	−	0.678505i	0.992679	+	0.120786i	$0.0385416\pi$
$312$		0			0
$313$	−11.8167	−	20.4670i	−0.667917	−	1.15687i	−0.978486	−	0.206315i	$-0.933853\pi$
$313$	−11.8167	−	20.4670i	−0.667917	−	1.15687i	0.310569	−	0.950551i	$-0.399480\pi$
$314$	−4.97224			−0.280600
$315$		0			0
$316$	1.33053			0.0748483
$317$	−0.197224	−	0.341603i	−0.0110772	−	0.0191863i	0.860434	−	0.509562i	$-0.170193\pi$
$317$	−0.197224	−	0.341603i	−0.0110772	−	0.0191863i	−0.871511	+	0.490376i	$0.836859\pi$
$318$		0			0
$319$	11.2111	−	19.4182i	0.627701	−	1.08721i
$320$	4.40833	−	7.63545i	0.246433	−	0.426834i
$321$		0			0
$322$	9.00000	+	15.5885i	0.501550	+	0.868711i
$323$	−20.2111			−1.12458
$324$		0			0
$325$	−0.605551			−0.0335899
$326$	1.30278	+	2.25647i	0.0721541	+	0.124975i
$327$		0			0
$328$	3.90833	−	6.76942i	0.215801	−	0.373779i
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	−7.39445	−	12.8076i	−0.406436	−	0.703967i	0.588052	−	0.808823i	$-0.299895\pi$
$331$	−7.39445	−	12.8076i	−0.406436	−	0.703967i	−0.994487	+	0.104856i	$0.966562\pi$
$332$	0.908327			0.0498509
$333$		0			0
$334$	−3.90833			−0.213854
$335$	−7.60555	−	13.1732i	−0.415536	−	0.719729i
$336$		0			0
$337$	0.302776	−	0.524423i	0.0164932	−	0.0285671i	−0.857661	−	0.514216i	$-0.828083\pi$
$337$	0.302776	−	0.524423i	0.0164932	−	0.0285671i	0.874154	+	0.485648i	$0.161416\pi$
$338$	−8.22918	+	14.2534i	−0.447609	+	0.775281i
$339$		0			0
$340$	−0.848612	−	1.46984i	−0.0460225	−	0.0797132i
$341$	4.18335			0.226541
$342$		0			0
$343$	33.2111			1.79323
$344$	9.90833	+	17.1617i	0.534221	+	0.925298i
$345$		0			0
$346$	−7.04584	+	12.2037i	−0.378787	+	0.656077i
$347$	0.788897	−	1.36641i	0.0423502	−	0.0733528i	−0.844073	−	0.536228i	$-0.819849\pi$
$347$	0.788897	−	1.36641i	0.0423502	−	0.0733528i	0.886424	+	0.462875i	$0.153182\pi$
$348$		0			0
$349$	−12.9222	−	22.3819i	−0.691710	−	1.19808i	−0.971277	−	0.237950i	$-0.923524\pi$
$349$	−12.9222	−	22.3819i	−0.691710	−	1.19808i	0.279568	−	0.960126i	$-0.409809\pi$
$350$	−6.00000			−0.320713
$351$		0			0
$352$	−4.42221			−0.235704
$353$	−10.8167	−	18.7350i	−0.575712	−	0.997163i	−0.995964	−	0.0897554i	$-0.971391\pi$
$353$	−10.8167	−	18.7350i	−0.575712	−	0.997163i	0.420251	−	0.907408i	$-0.361942\pi$
$354$		0			0
$355$	−7.30278	+	12.6488i	−0.387591	+	0.671327i
$356$	−1.18335	+	2.04962i	−0.0627172	+	0.108629i
$357$		0			0
$358$	4.42221	+	7.65948i	0.233721	+	0.404816i
$359$	−33.6333			−1.77510			−0.887549	−	0.460713i	$-0.847594\pi$
$359$	−33.6333			−1.77510			−0.887549	+	0.460713i	$0.847594\pi$
$360$		0			0
$361$	−6.00000			−0.315789
$362$	−4.55971	−	7.89766i	−0.239653	−	0.415092i
$363$		0			0
$364$	−0.422205	+	0.731281i	−0.0221296	+	0.0383295i
$365$	2.69722	−	4.67173i	0.141179	−	0.244530i
$366$		0			0
$367$	−2.30278	−	3.98852i	−0.120204	−	0.208199i	0.799644	−	0.600474i	$-0.205022\pi$
$367$	−2.30278	−	3.98852i	−0.120204	−	0.208199i	−0.919848	+	0.392275i	$0.871688\pi$
$368$	−9.90833			−0.516507
$369$		0			0
$370$	2.60555			0.135456
$371$	−12.9083	−	22.3579i	−0.670167	−	1.16076i
$372$		0			0
$373$	5.39445	−	9.34346i	0.279314	−	0.483786i	−0.691900	−	0.721993i	$-0.743226\pi$
$373$	5.39445	−	9.34346i	0.279314	−	0.483786i	0.971214	+	0.238207i	$0.0765596\pi$
$374$	9.51388	−	16.4785i	0.491951	−	0.852084i
$375$		0			0
$376$	7.81665	+	13.5388i	0.403113	+	0.698212i
$377$	5.21110			0.268385
$378$		0			0
$379$	14.3944			0.739393			0.369697	−	0.929153i	$-0.379462\pi$
$379$	14.3944			0.739393			0.369697	+	0.929153i	$0.379462\pi$
$380$	0.545837	+	0.945417i	0.0280008	+	0.0484988i
$381$		0			0
$382$	−10.6972	+	18.5281i	−0.547318	+	0.947982i
$383$	−9.31665	+	16.1369i	−0.476059	+	0.824558i	−0.999624	−	0.0274277i	$-0.991268\pi$
$383$	−9.31665	+	16.1369i	−0.476059	+	0.824558i	0.523565	+	0.851986i	$0.324602\pi$
$384$		0			0
$385$	6.00000	+	10.3923i	0.305788	+	0.529641i
$386$	−28.4222			−1.44665
$387$		0			0
$388$	−2.42221			−0.122969
$389$	2.09167	+	3.62288i	0.106052	+	0.183688i	0.914168	−	0.405337i	$-0.132846\pi$
$389$	2.09167	+	3.62288i	0.106052	+	0.183688i	−0.808116	+	0.589024i	$0.799512\pi$
$390$		0			0
$391$	−8.40833	+	14.5636i	−0.425227	+	0.736515i
$392$	−21.3167	+	36.9215i	−1.07665	+	1.86482i
$393$		0			0
$394$	0.770817	+	1.33509i	0.0388332	+	0.0672611i
$395$	4.39445			0.221109
$396$		0			0
$397$	−12.6056			−0.632654			−0.316327	−	0.948650i	$-0.602450\pi$
$397$	−12.6056			−0.632654			−0.316327	+	0.948650i	$0.602450\pi$
$398$	8.60555	+	14.9053i	0.431357	+	0.747133i
$399$		0			0
$400$	1.65139	−	2.86029i	0.0825694	−	0.143014i
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$		0			0
$403$	0.486122	+	0.841988i	0.0242155	+	0.0419424i
$404$	3.63331			0.180764
$405$		0			0
$406$	51.6333			2.56252
$407$	−2.60555	−	4.51295i	−0.129152	−	0.223698i
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$	1.69722	−	2.93968i	0.0838199	−	0.145180i
$411$		0			0
$412$	−0.605551	−	1.04885i	−0.0298334	−	0.0516729i
$413$	39.6333			1.95023
$414$		0			0
$415$	3.00000			0.147264
$416$	−0.513878	−	0.890063i	−0.0251950	−	0.0436389i
$417$		0			0
$418$	−6.11943	+	10.5992i	−0.299311	+	0.518422i
$419$	−6.51388	+	11.2824i	−0.318224	+	0.551180i	−0.980118	−	0.198418i	$-0.936420\pi$
$419$	−6.51388	+	11.2824i	−0.318224	+	0.551180i	0.661894	+	0.749598i	$0.269753\pi$
$420$		0			0
$421$	11.7111	+	20.2842i	0.570764	+	0.988593i	0.996488	+	0.0837393i	$0.0266863\pi$
$421$	11.7111	+	20.2842i	0.570764	+	0.988593i	−0.425723	+	0.904853i	$0.639980\pi$
$422$	−16.6972			−0.812808
$423$		0			0
$424$	16.8167			0.816689
$425$	−2.80278	−	4.85455i	−0.135955	−	0.235480i
$426$		0			0
$427$	−23.5139	+	40.7272i	−1.13792	+	1.97093i
$428$		0			0
$429$		0			0
$430$	4.30278	+	7.45263i	0.207498	+	0.359398i
$431$	−25.8167			−1.24354			−0.621772	−	0.783198i	$-0.713587\pi$
$431$	−25.8167			−1.24354			−0.621772	+	0.783198i	$0.713587\pi$
$432$		0			0
$433$	−28.2389			−1.35707			−0.678536	−	0.734567i	$-0.737385\pi$
$433$	−28.2389			−1.35707			−0.678536	+	0.734567i	$0.737385\pi$
$434$	4.81665	+	8.34269i	0.231207	+	0.400462i
$435$		0			0
$436$	−1.05971	+	1.83548i	−0.0507511	+	0.0879035i
$437$	5.40833	−	9.36750i	0.258715	−	0.448108i
$438$		0			0
$439$	−10.1972	−	17.6621i	−0.486687	−	0.842967i	0.513196	−	0.858271i	$-0.328461\pi$
$439$	−10.1972	−	17.6621i	−0.486687	−	0.842967i	−0.999883	+	0.0153049i	$0.995128\pi$
$440$	−7.81665			−0.372644
$441$		0			0
$442$	4.42221			0.210343
$443$	9.31665	+	16.1369i	0.442648	+	0.766688i	0.997885	−	0.0650038i	$-0.0207059\pi$
$443$	9.31665	+	16.1369i	0.442648	+	0.766688i	−0.555237	+	0.831692i	$0.687373\pi$
$444$		0			0
$445$	−3.90833	+	6.76942i	−0.185272	+	0.320901i
$446$	−6.51388	+	11.2824i	−0.308441	+	0.534236i
$447$		0			0
$448$	−20.3028	−	35.1654i	−0.959216	−	1.66141i
$449$	12.2389			0.577587			0.288794	−	0.957391i	$-0.406746\pi$
$449$	12.2389			0.577587			0.288794	+	0.957391i	$0.406746\pi$
$450$		0			0
$451$	−6.78890			−0.319677
$452$	0.119429	+	0.206858i	0.00561749	+	0.00972978i
$453$		0			0
$454$	17.0736	−	29.5723i	0.801303	−	1.38790i
$455$	−1.39445	+	2.41526i	−0.0653728	+	0.113229i
$456$		0			0
$457$	−0.605551	−	1.04885i	−0.0283265	−	0.0490629i	0.851515	−	0.524331i	$-0.175684\pi$
$457$	−0.605551	−	1.04885i	−0.0283265	−	0.0490629i	−0.879841	+	0.475268i	$0.842351\pi$
$458$	8.09167			0.378099
$459$		0			0
$460$	0.908327			0.0423510
$461$	−10.8167	−	18.7350i	−0.503782	−	0.872576i	−0.999990	−	0.00437236i	$-0.998608\pi$
$461$	−10.8167	−	18.7350i	−0.503782	−	0.872576i	0.496209	−	0.868203i	$-0.334725\pi$
$462$		0			0
$463$	7.60555	−	13.1732i	0.353460	−	0.612211i	−0.633393	−	0.773830i	$-0.718338\pi$
$463$	7.60555	−	13.1732i	0.353460	−	0.612211i	0.986853	+	0.161620i	$0.0516717\pi$
$464$	−14.2111	+	24.6144i	−0.659734	+	1.14269i
$465$		0			0
$466$	11.7250	+	20.3083i	0.543149	+	0.940762i
$467$	2.21110			0.102318			0.0511588	−	0.998691i	$-0.483709\pi$
$467$	2.21110			0.102318			0.0511588	+	0.998691i	$0.483709\pi$
$468$		0			0
$469$	−70.0555			−3.23486
$470$	3.39445	+	5.87936i	0.156574	+	0.271195i
$471$		0			0
$472$	−12.9083	+	22.3579i	−0.594154	+	1.02910i
$473$	8.60555	−	14.9053i	0.395684	−	0.685344i
$474$		0			0
$475$	1.80278	+	3.12250i	0.0827170	+	0.143270i
$476$	−7.81665			−0.358276
$477$		0			0
$478$	−1.02776			−0.0470085
$479$	−8.09167	−	14.0152i	−0.369718	−	0.640370i	0.619803	−	0.784757i	$-0.287212\pi$
$479$	−8.09167	−	14.0152i	−0.369718	−	0.640370i	−0.989521	+	0.144387i	$0.953879\pi$
$480$		0			0
$481$	0.605551	−	1.04885i	0.0276108	−	0.0478232i
$482$	18.3764	−	31.8288i	0.837021	−	1.44976i
$483$		0			0
$484$	−0.637510	−	1.10420i	−0.0289777	−	0.0501909i
$485$	−8.00000			−0.363261
$486$		0			0
$487$	−8.18335			−0.370823			−0.185411	−	0.982661i	$-0.559362\pi$
$487$	−8.18335			−0.370823			−0.185411	+	0.982661i	$0.559362\pi$
$488$	−15.3167	−	26.5292i	−0.693352	−	1.20092i
$489$		0			0
$490$	−9.25694	+	16.0335i	−0.418186	+	0.724319i
$491$	6.39445	−	11.0755i	0.288577	−	0.499831i	−0.684893	−	0.728644i	$-0.740151\pi$
$491$	6.39445	−	11.0755i	0.288577	−	0.499831i	0.973470	+	0.228813i	$0.0734844\pi$
$492$		0			0
$493$	24.1194	+	41.7761i	1.08628	+	1.88150i
$494$	−2.84441			−0.127976
$495$		0			0
$496$	−5.30278			−0.238102
$497$	33.6333	+	58.2546i	1.50866	+	2.61308i
$498$		0			0
$499$	13.8028	−	23.9071i	0.617897	−	1.07023i	−0.371972	−	0.928244i	$-0.621318\pi$
$499$	13.8028	−	23.9071i	0.617897	−	1.07023i	0.989869	−	0.141985i	$-0.0453485\pi$
$500$	−0.151388	+	0.262211i	−0.00677027	+	0.0117265i
$501$		0			0
$502$	10.1833	+	17.6381i	0.454505	+	0.787226i
$503$	−31.4222			−1.40105			−0.700523	−	0.713629i	$-0.747050\pi$
$503$	−31.4222			−1.40105			−0.700523	+	0.713629i	$0.747050\pi$
$504$		0			0
$505$	12.0000			0.533993
$506$	5.09167	+	8.81904i	0.226352	+	0.392054i
$507$		0			0
$508$	−0.724981	+	1.25570i	−0.0321658	+	0.0557128i
$509$	16.4222	−	28.4441i	0.727901	−	1.26076i	−0.229867	−	0.973222i	$-0.573829\pi$
$509$	16.4222	−	28.4441i	0.727901	−	1.26076i	0.957769	−	0.287540i	$-0.0928375\pi$
$510$		0			0
$511$	−12.4222	−	21.5159i	−0.549526	−	0.951807i
$512$	25.4222			1.12351
$513$		0			0
$514$	29.7250			1.31111
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$		0			0
$517$	6.78890	−	11.7587i	0.298575	−	0.517148i
$518$	6.00000	−	10.3923i	0.263625	−	0.456612i
$519$		0			0
$520$	−0.908327	−	1.57327i	−0.0398328	−	0.0689924i
$521$	21.3944			0.937308			0.468654	−	0.883382i	$-0.344739\pi$
$521$	21.3944			0.937308			0.468654	+	0.883382i	$0.344739\pi$
$522$		0			0
$523$	23.3944			1.02297			0.511484	−	0.859293i	$-0.329096\pi$
$523$	23.3944			1.02297			0.511484	+	0.859293i	$0.329096\pi$
$524$	−0.908327	−	1.57327i	−0.0396804	−	0.0687285i
$525$		0			0
$526$	11.2111	−	19.4182i	0.488827	−	0.846674i
$527$	−4.50000	+	7.79423i	−0.196023	+	0.339522i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	7.30278			0.317212
$531$		0			0
$532$	5.02776			0.217981
$533$	−0.788897	−	1.36641i	−0.0341709	−	0.0591858i
$534$		0			0
$535$		0			0
$536$	22.8167	−	39.5196i	0.985529	−	1.70699i
$537$		0			0
$538$	−7.30278	−	12.6488i	−0.314845	−	0.545328i
$539$	37.0278			1.59490
$540$		0			0
$541$	−11.5778			−0.497768			−0.248884	−	0.968533i	$-0.580064\pi$
$541$	−11.5778			−0.497768			−0.248884	+	0.968533i	$0.580064\pi$
$542$	−12.5320	−	21.7060i	−0.538294	−	0.932352i
$543$		0			0
$544$	4.75694	−	8.23926i	0.203952	−	0.353255i
$545$	−3.50000	+	6.06218i	−0.149924	+	0.259675i
$546$		0			0
$547$	3.30278	+	5.72058i	0.141216	+	0.244594i	0.927955	−	0.372692i	$-0.121565\pi$
$547$	3.30278	+	5.72058i	0.141216	+	0.244594i	−0.786738	+	0.617286i	$0.788232\pi$
$548$	−1.45837			−0.0622983
$549$		0			0
$550$	−3.39445			−0.144740
$551$	−15.5139	−	26.8708i	−0.660913	−	1.14474i
$552$		0			0
$553$	10.1194	−	17.5274i	0.430322	−	0.745339i
$554$	−18.9083	+	32.7502i	−0.803338	+	1.39142i
$555$		0			0
$556$	−0.605551	−	1.04885i	−0.0256811	−	0.0444810i
$557$	33.6333			1.42509			0.712544	−	0.701627i	$-0.247543\pi$
$557$	33.6333			1.42509			0.712544	+	0.701627i	$0.247543\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$	−7.60555	−	13.1732i	−0.321393	−	0.556669i
$561$		0			0
$562$	−1.18335	+	2.04962i	−0.0499164	+	0.0864578i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$	0.394449	+	0.683205i	0.0165946	+	0.0287427i
$566$	−13.8167			−0.580757
$567$		0			0
$568$	−43.8167			−1.83851
$569$	18.9083	+	32.7502i	0.792678	+	1.37296i	0.924303	+	0.381659i	$0.124647\pi$
$569$	18.9083	+	32.7502i	0.792678	+	1.37296i	−0.131625	+	0.991300i	$0.542019\pi$
$570$		0			0
$571$	18.2250	−	31.5666i	0.762692	−	1.32102i	−0.178767	−	0.983891i	$-0.557211\pi$
$571$	18.2250	−	31.5666i	0.762692	−	1.32102i	0.941458	−	0.337129i	$-0.109456\pi$
$572$	−0.238859	+	0.413716i	−0.00998719	+	0.0172983i
$573$		0			0
$574$	−7.81665	−	13.5388i	−0.326261	−	0.565100i
$575$	3.00000			0.125109
$576$		0			0
$577$	27.8167			1.15802			0.579011	−	0.815320i	$-0.303439\pi$
$577$	27.8167			1.15802			0.579011	+	0.815320i	$0.303439\pi$
$578$	9.39445	+	16.2717i	0.390758	+	0.676812i
$579$		0			0
$580$	1.30278	−	2.25647i	0.0540948	−	0.0936950i
$581$	6.90833	−	11.9656i	0.286606	−	0.496416i
$582$		0			0
$583$	−7.30278	−	12.6488i	−0.302450	−	0.523859i
$584$	16.1833			0.669672
$585$		0			0
$586$	−37.5416			−1.55083
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	0.997162	−	0.0752860i	$-0.0239870\pi$
$587$	10.5000	+	18.1865i	0.433381	+	0.750639i	−0.563781	+	0.825925i	$0.690654\pi$
$588$		0			0
$589$	2.89445	−	5.01333i	0.119264	−	0.206571i
$590$	−5.60555	+	9.70910i	−0.230777	+	0.399717i
$591$		0			0
$592$	3.30278	+	5.72058i	0.135743	+	0.235114i
$593$	−21.2389			−0.872175			−0.436088	−	0.899904i	$-0.643636\pi$
$593$	−21.2389			−0.872175			−0.436088	+	0.899904i	$0.643636\pi$
$594$		0			0
$595$	−25.8167			−1.05838
$596$	1.97224	+	3.41603i	0.0807862	+	0.139926i
$597$		0			0
$598$	−1.18335	+	2.04962i	−0.0483906	+	0.0838150i
$599$	−7.69722	+	13.3320i	−0.314500	+	0.544730i	−0.979331	−	0.202264i	$-0.935170\pi$
$599$	−7.69722	+	13.3320i	−0.314500	+	0.544730i	0.664831	+	0.746994i	$0.268504\pi$
$600$		0			0
$601$	−16.3167	−	28.2613i	−0.665570	−	1.15280i	−0.979130	−	0.203233i	$-0.934855\pi$
$601$	−16.3167	−	28.2613i	−0.665570	−	1.15280i	0.313560	−	0.949568i	$-0.398478\pi$
$602$	39.6333			1.61533
$603$		0			0
$604$	4.36669			0.177678
$605$	−2.10555	−	3.64692i	−0.0856028	−	0.148268i
$606$		0			0
$607$	−8.69722	+	15.0640i	−0.353009	+	0.611430i	−0.986775	−	0.162095i	$-0.948175\pi$
$607$	−8.69722	+	15.0640i	−0.353009	+	0.611430i	0.633766	+	0.773525i	$0.281508\pi$
$608$	−3.05971	+	5.29958i	−0.124088	+	0.214926i
$609$		0			0
$610$	−6.65139	−	11.5205i	−0.269307	−	0.466453i
$611$	3.15559			0.127661
$612$		0			0
$613$	28.8444			1.16501			0.582507	−	0.812825i	$-0.302072\pi$
$613$	28.8444			1.16501			0.582507	+	0.812825i	$0.302072\pi$
$614$	−13.3028	−	23.0411i	−0.536856	−	0.929862i
$615$		0			0
$616$	−18.0000	+	31.1769i	−0.725241	+	1.25615i
$617$	−13.2250	+	22.9063i	−0.532418	+	0.922174i	0.466866	+	0.884328i	$0.345383\pi$
$617$	−13.2250	+	22.9063i	−0.532418	+	0.922174i	−0.999284	+	0.0378463i	$0.987950\pi$
$618$		0			0
$619$	3.81665	+	6.61064i	0.153404	+	0.265704i	0.932477	−	0.361230i	$-0.117643\pi$
$619$	3.81665	+	6.61064i	0.153404	+	0.265704i	−0.779073	+	0.626934i	$0.784310\pi$
$620$	0.486122			0.0195231
$621$		0			0
$622$	18.0000			0.721734
$623$	18.0000	+	31.1769i	0.721155	+	1.24908i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	15.3944	−	26.6640i	0.615286	−	1.06571i
$627$		0			0
$628$	0.577795	+	1.00077i	0.0230565	+	0.0399351i
$629$	11.2111			0.447016
$630$		0			0
$631$	30.0278			1.19539			0.597693	−	0.801725i	$-0.296084\pi$
$631$	30.0278			1.19539			0.597693	+	0.801725i	$0.296084\pi$
$632$	6.59167	+	11.4171i	0.262203	+	0.454148i
$633$		0			0
$634$	0.256939	−	0.445032i	0.0102044	−	0.0176745i
$635$	−2.39445	+	4.14731i	−0.0950208	+	0.164581i
$636$		0			0
$637$	4.30278	+	7.45263i	0.170482	+	0.295284i
$638$	29.2111			1.15648
$639$		0			0
$640$	8.09167			0.319851
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$		0			0
$643$	11.5139	−	19.9426i	0.454063	−	0.786460i	−0.544571	−	0.838715i	$-0.683307\pi$
$643$	11.5139	−	19.9426i	0.454063	−	0.786460i	0.998634	+	0.0522547i	$0.0166408\pi$
$644$	2.09167	−	3.62288i	0.0824235	−	0.142762i
$645$		0			0
$646$	−13.1653	−	22.8029i	−0.517980	−	0.897168i
$647$	−38.2111			−1.50223			−0.751117	−	0.660169i	$-0.770484\pi$
$647$	−38.2111			−1.50223			−0.751117	+	0.660169i	$0.770484\pi$
$648$		0			0
$649$	22.4222			0.880149
$650$	−0.394449	−	0.683205i	−0.0154716	−	0.0267975i
$651$		0			0
$652$	0.302776	−	0.524423i	0.0118576	−	0.0205380i
$653$	13.6194	−	23.5895i	0.532969	−	0.923130i	−0.466289	−	0.884632i	$-0.654409\pi$
$653$	13.6194	−	23.5895i	0.532969	−	0.923130i	0.999259	−	0.0384979i	$-0.0122573\pi$
$654$		0			0
$655$	−3.00000	−	5.19615i	−0.117220	−	0.203030i
$656$	8.60555			0.335990
$657$		0			0
$658$	31.2666			1.21890
$659$	−10.3028	−	17.8449i	−0.401339	−	0.695140i	0.592549	−	0.805535i	$-0.298122\pi$
$659$	−10.3028	−	17.8449i	−0.401339	−	0.695140i	−0.993888	+	0.110395i	$0.964788\pi$
$660$		0			0
$661$	−11.4222	+	19.7838i	−0.444272	+	0.769502i	−0.998001	−	0.0631948i	$-0.979871\pi$
$661$	−11.4222	+	19.7838i	−0.444272	+	0.769502i	0.553729	+	0.832697i	$0.313204\pi$
$662$	9.63331	−	16.6854i	0.374409	−	0.648496i
$663$		0			0
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$	16.6056			0.643936
$666$		0			0
$667$	−25.8167			−0.999625
$668$	0.454163	+	0.786634i	0.0175721	+	0.0304358i
$669$		0			0
$670$	9.90833	−	17.1617i	0.382792	−	0.663015i
$671$	−13.3028	+	23.0411i	−0.513548	+	0.889491i
$672$		0			0
$673$	5.51388	+	9.55032i	0.212544	+	0.368138i	0.952510	−	0.304507i	$-0.0984917\pi$
$673$	5.51388	+	9.55032i	0.212544	+	0.368138i	−0.739966	+	0.672645i	$0.765158\pi$
$674$	0.788897			0.0303872
$675$		0			0
$676$	3.82506			0.147118
$677$	−10.8167	−	18.7350i	−0.415718	−	0.720044i	0.579786	−	0.814769i	$-0.303136\pi$
$677$	−10.8167	−	18.7350i	−0.415718	−	0.720044i	−0.995504	+	0.0947247i	$0.969803\pi$
$678$		0			0
$679$	−18.4222	+	31.9082i	−0.706979	+	1.22452i
$680$	8.40833	−	14.5636i	0.322445	−	0.558490i
$681$		0			0
$682$	2.72498	+	4.71981i	0.104345	+	0.180731i
$683$	9.00000			0.344375			0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000			0.344375			0.172188	+	0.985064i	$0.444916\pi$
$684$		0			0
$685$	−4.81665			−0.184035
$686$	21.6333	+	37.4700i	0.825964	+	1.43061i
$687$		0			0
$688$	−10.9083	+	18.8938i	−0.415876	+	0.720318i
$689$	1.69722	−	2.93968i	0.0646591	−	0.111993i
$690$		0			0
$691$	−1.19722	−	2.07365i	−0.0455446	−	0.0788855i	0.842354	−	0.538924i	$-0.181169\pi$
$691$	−1.19722	−	2.07365i	−0.0455446	−	0.0788855i	−0.887899	+	0.460038i	$0.847836\pi$
$692$	3.27502			0.124498
$693$		0			0
$694$	2.05551			0.0780262
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$		0			0
$697$	7.30278	−	12.6488i	0.276612	−	0.479107i
$698$	16.8347	−	29.1586i	0.637204	−	1.10367i
$699$		0			0
$700$	0.697224	+	1.20763i	0.0263526	+	0.0456440i
$701$	−40.4222			−1.52673			−0.763363	−	0.645970i	$-0.776453\pi$
$701$	−40.4222			−1.52673			−0.763363	+	0.645970i	$0.776453\pi$
$702$		0			0
$703$	−7.21110			−0.271972
$704$	−11.4861	−	19.8945i	−0.432900	−	0.749804i
$705$		0			0
$706$	14.0917	−	24.4075i	0.530347	−	0.918588i
$707$	27.6333	−	47.8623i	1.03926	−	1.80005i
$708$		0			0
$709$	−17.4222	−	30.1761i	−0.654305	−	1.13329i	−0.982068	−	0.188529i	$-0.939628\pi$
$709$	−17.4222	−	30.1761i	−0.654305	−	1.13329i	0.327763	−	0.944760i	$-0.393705\pi$
$710$	−19.0278			−0.714099
$711$		0			0
$712$	−23.4500			−0.878824
$713$	−2.40833	−	4.17134i	−0.0901926	−	0.156218i
$714$		0			0
$715$	−0.788897	+	1.36641i	−0.0295031	+	0.0511009i
$716$	1.02776	−	1.78013i	0.0384091	−	0.0665264i
$717$		0			0
$718$	−21.9083	−	37.9463i	−0.817611	−	1.41614i
$719$	49.2666			1.83733			0.918667	−	0.395032i	$-0.129267\pi$
$719$	49.2666			1.83733			0.918667	+	0.395032i	$0.129267\pi$
$720$		0			0
$721$	−18.4222			−0.686079
$722$	−3.90833	−	6.76942i	−0.145453	−	0.251932i
$723$		0			0
$724$	−1.05971	+	1.83548i	−0.0393840	+	0.0682151i
$725$	4.30278	−	7.45263i	0.159801	−	0.276784i
$726$		0			0
$727$	3.81665	+	6.61064i	0.141552	+	0.245175i	0.928081	−	0.372378i	$-0.121457\pi$
$727$	3.81665	+	6.61064i	0.141552	+	0.245175i	−0.786529	+	0.617553i	$0.788124\pi$
$728$	−8.36669			−0.310090
$729$		0			0
$730$	7.02776			0.260109
$731$	18.5139	+	32.0670i	0.684761	+	1.18604i
$732$		0			0
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	3.00000	−	5.19615i	0.110732	−	0.191793i
$735$		0			0
$736$	2.54584	+	4.40952i	0.0938408	+	0.162537i
$737$	−39.6333			−1.45991
$738$		0			0
$739$	30.0278			1.10459			0.552294	−	0.833649i	$-0.313752\pi$
$739$	30.0278			1.10459			0.552294	+	0.833649i	$0.313752\pi$
$740$	−0.302776	−	0.524423i	−0.0111303	−	0.0192782i
$741$		0			0
$742$	16.8167	−	29.1273i	0.617359	−	1.06930i
$743$	−17.2111	+	29.8105i	−0.631414	+	1.09364i	0.355849	+	0.934544i	$0.384192\pi$
$743$	−17.2111	+	29.8105i	−0.631414	+	1.09364i	−0.987263	+	0.159098i	$0.949141\pi$
$744$		0			0
$745$	6.51388	+	11.2824i	0.238650	+	0.413354i
$746$	14.0555			0.514609
$747$		0			0
$748$	−4.42221			−0.161692
$749$		0			0
$750$		0			0
$751$	−3.01388	+	5.22019i	−0.109978	+	0.190487i	−0.915761	−	0.401723i	$-0.868411\pi$
$751$	−3.01388	+	5.22019i	−0.109978	+	0.190487i	0.805783	+	0.592211i	$0.201745\pi$
$752$	−8.60555	+	14.9053i	−0.313812	+	0.543539i
$753$		0			0
$754$	3.39445	+	5.87936i	0.123619	+	0.214114i
$755$	14.4222			0.524878
$756$		0			0
$757$	31.2111			1.13439			0.567193	−	0.823585i	$-0.308029\pi$
$757$	31.2111			1.13439			0.567193	+	0.823585i	$0.308029\pi$
$758$	9.37637	+	16.2403i	0.340565	+	0.589876i
$759$		0			0
$760$	−5.40833	+	9.36750i	−0.196181	+	0.339795i
$761$	−26.7250	+	46.2890i	−0.968780	+	1.67798i	−0.269682	+	0.962949i	$0.586919\pi$
$761$	−26.7250	+	46.2890i	−0.968780	+	1.67798i	−0.699097	+	0.715027i	$0.746415\pi$
$762$		0			0
$763$	16.1194	+	27.9197i	0.583563	+	1.01076i
$764$	4.97224			0.179889
$765$		0			0
$766$	−24.2750			−0.877092
$767$	2.60555	+	4.51295i	0.0940810	+	0.162953i
$768$		0			0
$769$	−20.5000	+	35.5070i	−0.739249	+	1.28042i	0.213585	+	0.976924i	$0.431486\pi$
$769$	−20.5000	+	35.5070i	−0.739249	+	1.28042i	−0.952834	+	0.303492i	$0.901847\pi$
$770$	−7.81665	+	13.5388i	−0.281693	+	0.487906i
$771$		0			0
$772$	3.30278	+	5.72058i	0.118869	+	0.205888i
$773$	−16.8167			−0.604853			−0.302426	−	0.953173i	$-0.597797\pi$
$773$	−16.8167			−0.604853			−0.302426	+	0.953173i	$0.597797\pi$
$774$		0			0
$775$	1.60555			0.0576731
$776$	−12.0000	−	20.7846i	−0.430775	−	0.746124i
$777$		0			0
$778$	−2.72498	+	4.71981i	−0.0976953	+	0.169213i
$779$	−4.69722	+	8.13583i	−0.168296	+	0.291496i
$780$		0			0
$781$	19.0278	+	32.9570i	0.680867	+	1.17930i
$782$	−21.9083			−0.783440
$783$		0			0
$784$	−46.9361			−1.67629
$785$	1.90833	+	3.30532i

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.30278 - 3.98852i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+(0.651388 + 1.12824i) q^{2} +(0.151388 - 0.262211i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.30278 - 3.98852i) q^{7} +3.00000 q^{8} +1.30278 q^{10} +(-1.30278 - 2.25647i) q^{11} +(0.302776 - 0.524423i) q^{13} +(3.00000 - 5.19615i) q^{14} +(1.65139 + 2.86029i) q^{16} +5.60555 q^{17} -3.60555 q^{19} +(-0.151388 - 0.262211i) q^{20} +(1.69722 - 2.93968i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +0.788897 q^{26} -1.39445 q^{28} +(4.30278 + 7.45263i) q^{29} +(-0.802776 + 1.39045i) q^{31} +(0.848612 - 1.46984i) q^{32} +(3.65139 + 6.32439i) q^{34} -4.60555 q^{35} +2.00000 q^{37} +(-2.34861 - 4.06792i) q^{38} +(1.50000 - 2.59808i) q^{40} +(1.30278 - 2.25647i) q^{41} +(3.30278 + 5.72058i) q^{43} -0.788897 q^{44} -3.90833 q^{46} +(2.60555 + 4.51295i) q^{47} +(-7.10555 + 12.3072i) q^{49} +(0.651388 - 1.12824i) q^{50} +(-0.0916731 - 0.158782i) q^{52} +5.60555 q^{53} -2.60555 q^{55} +(-6.90833 - 11.9656i) q^{56} +(-5.60555 + 9.70910i) q^{58} +(-4.30278 + 7.45263i) q^{59} +(-5.10555 - 8.84307i) q^{61} -2.09167 q^{62} +8.81665 q^{64} +(-0.302776 - 0.524423i) q^{65} +(7.60555 - 13.1732i) q^{67} +(0.848612 - 1.46984i) q^{68} +(-3.00000 - 5.19615i) q^{70} -14.6056 q^{71} +5.39445 q^{73} +(1.30278 + 2.25647i) q^{74} +(-0.545837 + 0.945417i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(2.19722 + 3.80570i) q^{79} +3.30278 q^{80} +3.39445 q^{82} +(1.50000 + 2.59808i) q^{83} +(2.80278 - 4.85455i) q^{85} +(-4.30278 + 7.45263i) q^{86} +(-3.90833 - 6.76942i) q^{88} -7.81665 q^{89} -2.78890 q^{91} +(0.454163 + 0.786634i) q^{92} +(-3.39445 + 5.87936i) q^{94} +(-1.80278 + 3.12250i) q^{95} +(-4.00000 - 6.92820i) q^{97} -18.5139 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q - q^2 - 3 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8	\( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} - 6 q^{13} + 12 q^{14} + 3 q^{16} + 8 q^{17} + 3 q^{20} + 14 q^{22} - 6 q^{23} - 2 q^{25} + 32 q^{26} - 20 q^{28} + 10 q^{29} + 4 q^{31} + 7 q^{32} + 11 q^{34} - 4 q^{35} + 8 q^{37} - 13 q^{38} + 6 q^{40} - 2 q^{41} + 6 q^{43} - 32 q^{44} + 6 q^{46} - 4 q^{47} - 14 q^{49} - q^{50} - 22 q^{52} + 8 q^{53} + 4 q^{55} - 6 q^{56} - 8 q^{58} - 10 q^{59} - 6 q^{61} - 30 q^{62} - 8 q^{64} + 6 q^{65} + 16 q^{67} + 7 q^{68} - 12 q^{70} - 44 q^{71} + 36 q^{73} - 2 q^{74} - 13 q^{76} - 24 q^{77} + 16 q^{79} + 6 q^{80} + 28 q^{82} + 6 q^{83} + 4 q^{85} - 10 q^{86} + 6 q^{88} + 12 q^{89} - 40 q^{91} - 9 q^{92} - 28 q^{94} - 16 q^{97} - 38 q^{98}+O(q^{100}) \) 4 * q - q^2 - 3 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 - 2 * q^10 + 2 * q^11 - 6 * q^13 + 12 * q^14 + 3 * q^16 + 8 * q^17 + 3 * q^20 + 14 * q^22 - 6 * q^23 - 2 * q^25 + 32 * q^26 - 20 * q^28 + 10 * q^29 + 4 * q^31 + 7 * q^32 + 11 * q^34 - 4 * q^35 + 8 * q^37 - 13 * q^38 + 6 * q^40 - 2 * q^41 + 6 * q^43 - 32 * q^44 + 6 * q^46 - 4 * q^47 - 14 * q^49 - q^50 - 22 * q^52 + 8 * q^53 + 4 * q^55 - 6 * q^56 - 8 * q^58 - 10 * q^59 - 6 * q^61 - 30 * q^62 - 8 * q^64 + 6 * q^65 + 16 * q^67 + 7 * q^68 - 12 * q^70 - 44 * q^71 + 36 * q^73 - 2 * q^74 - 13 * q^76 - 24 * q^77 + 16 * q^79 + 6 * q^80 + 28 * q^82 + 6 * q^83 + 4 * q^85 - 10 * q^86 + 6 * q^88 + 12 * q^89 - 40 * q^91 - 9 * q^92 - 28 * q^94 - 16 * q^97 - 38 * q^98

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