LMFDB - Embedded newform 1638.2.j.k.1171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(235,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1638.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.j (of order $3$, degree $2$, 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:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1171.1
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1638.1171
Dual form			1638.2.j.k.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +(-1.82288 - 3.15731i) q^{10} +(0.322876 + 0.559237i) q^{11} +1.00000 q^{13} +(1.32288 + 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.32288 - 5.75539i) q^{17} +(-2.50000 + 4.33013i) q^{19} +3.64575 q^{20} -0.645751 q^{22} +(-1.17712 + 2.03884i) q^{23} +(-4.14575 - 7.18065i) q^{25} +(-0.500000 + 0.866025i) q^{26} -2.64575 q^{28} -4.29150 q^{29} +(-1.64575 - 2.85052i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.64575 q^{34} +(4.82288 + 8.35347i) q^{35} +(-2.82288 + 4.88936i) q^{37} +(-2.50000 - 4.33013i) q^{38} +(-1.82288 + 3.15731i) q^{40} +2.35425 q^{41} -5.29150 q^{43} +(0.322876 - 0.559237i) q^{44} +(-1.17712 - 2.03884i) q^{46} +(1.50000 - 2.59808i) q^{47} +(-3.50000 - 6.06218i) q^{49} +8.29150 q^{50} +(-0.500000 - 0.866025i) q^{52} +(-1.50000 - 2.59808i) q^{53} -2.35425 q^{55} +(1.32288 - 2.29129i) q^{56} +(2.14575 - 3.71655i) q^{58} +(-3.96863 - 6.87386i) q^{59} +(5.96863 - 10.3380i) q^{61} +3.29150 q^{62} +1.00000 q^{64} +(-1.82288 + 3.15731i) q^{65} +(-3.79150 - 6.56708i) q^{67} +(-3.32288 + 5.75539i) q^{68} -9.64575 q^{70} -16.2915 q^{71} +(6.82288 + 11.8176i) q^{73} +(-2.82288 - 4.88936i) q^{74} +5.00000 q^{76} +1.70850 q^{77} +(5.00000 - 8.66025i) q^{79} +(-1.82288 - 3.15731i) q^{80} +(-1.17712 + 2.03884i) q^{82} +13.2915 q^{83} +24.2288 q^{85} +(2.64575 - 4.58258i) q^{86} +(0.322876 + 0.559237i) q^{88} +(8.46863 - 14.6681i) q^{89} +(1.32288 - 2.29129i) q^{91} +2.35425 q^{92} +(1.50000 + 2.59808i) q^{94} +(-9.11438 - 15.7866i) q^{95} +0.937254 q^{97} +7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8} - 2 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{16} - 8 q^{17} - 10 q^{19} + 4 q^{20} + 8 q^{22} - 10 q^{23} - 6 q^{25} - 2 q^{26} + 4 q^{29} + 4 q^{31} - 2 q^{32} + 16 q^{34} + 14 q^{35} - 6 q^{37} - 10 q^{38} - 2 q^{40} + 20 q^{41} - 4 q^{44} - 10 q^{46} + 6 q^{47} - 14 q^{49} + 12 q^{50} - 2 q^{52} - 6 q^{53} - 20 q^{55} - 2 q^{58} + 8 q^{61} - 8 q^{62} + 4 q^{64} - 2 q^{65} + 6 q^{67} - 8 q^{68} - 28 q^{70} - 44 q^{71} + 22 q^{73} - 6 q^{74} + 20 q^{76} + 28 q^{77} + 20 q^{79} - 2 q^{80} - 10 q^{82} + 32 q^{83} + 44 q^{85} - 4 q^{88} + 18 q^{89} + 20 q^{92} + 6 q^{94} - 10 q^{95} - 28 q^{97} + 28 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^8 - 2 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^16 - 8 * q^17 - 10 * q^19 + 4 * q^20 + 8 * q^22 - 10 * q^23 - 6 * q^25 - 2 * q^26 + 4 * q^29 + 4 * q^31 - 2 * q^32 + 16 * q^34 + 14 * q^35 - 6 * q^37 - 10 * q^38 - 2 * q^40 + 20 * q^41 - 4 * q^44 - 10 * q^46 + 6 * q^47 - 14 * q^49 + 12 * q^50 - 2 * q^52 - 6 * q^53 - 20 * q^55 - 2 * q^58 + 8 * q^61 - 8 * q^62 + 4 * q^64 - 2 * q^65 + 6 * q^67 - 8 * q^68 - 28 * q^70 - 44 * q^71 + 22 * q^73 - 6 * q^74 + 20 * q^76 + 28 * q^77 + 20 * q^79 - 2 * q^80 - 10 * q^82 + 32 * q^83 + 44 * q^85 - 4 * q^88 + 18 * q^89 + 20 * q^92 + 6 * q^94 - 10 * q^95 - 28 * q^97 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.82288	+	3.15731i	−0.815215	+	1.41199i	0.0939588	+	0.995576i	$0.470048\pi$
$5$	−1.82288	+	3.15731i	−0.815215	+	1.41199i	−0.909174	+	0.416417i	$0.863286\pi$
$6$		0			0
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.82288	−	3.15731i	−0.576444	−	0.998430i
$11$	0.322876	+	0.559237i	0.0973507	+	0.168616i	0.910587	−	0.413317i	$-0.135630\pi$
$11$	0.322876	+	0.559237i	0.0973507	+	0.168616i	−0.813237	+	0.581933i	$0.802296\pi$
$12$		0			0
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	1.32288	+	2.29129i	0.353553	+	0.612372i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.32288	−	5.75539i	−0.805916	−	1.39589i	−0.915671	−	0.401928i	$-0.868340\pi$
$17$	−3.32288	−	5.75539i	−0.805916	−	1.39589i	0.109755	−	0.993959i	$-0.464993\pi$
$18$		0			0
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$	3.64575			0.815215
$21$		0			0
$22$	−0.645751			−0.137675
$23$	−1.17712	+	2.03884i	−0.245447	+	0.425127i	−0.962257	−	0.272141i	$-0.912268\pi$
$23$	−1.17712	+	2.03884i	−0.245447	+	0.425127i	0.716810	+	0.697269i	$0.245602\pi$
$24$		0			0
$25$	−4.14575	−	7.18065i	−0.829150	−	1.43613i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$		0			0
$28$	−2.64575			−0.500000
$29$	−4.29150			−0.796912			−0.398456	−	0.917187i	$-0.630454\pi$
$29$	−4.29150			−0.796912			−0.398456	+	0.917187i	$0.630454\pi$
$30$		0			0
$31$	−1.64575	−	2.85052i	−0.295586	−	0.511969i	0.679535	−	0.733643i	$-0.262181\pi$
$31$	−1.64575	−	2.85052i	−0.295586	−	0.511969i	−0.975121	+	0.221673i	$0.928848\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	6.64575			1.13974
$35$	4.82288	+	8.35347i	0.815215	+	1.41199i
$36$		0			0
$37$	−2.82288	+	4.88936i	−0.464078	+	0.803806i	−0.999159	−	0.0409939i	$-0.986948\pi$
$37$	−2.82288	+	4.88936i	−0.464078	+	0.803806i	0.535081	+	0.844800i	$0.320281\pi$
$38$	−2.50000	−	4.33013i	−0.405554	−	0.702439i
$39$		0			0
$40$	−1.82288	+	3.15731i	−0.288222	+	0.499215i
$41$	2.35425			0.367672			0.183836	−	0.982957i	$-0.441148\pi$
$41$	2.35425			0.367672			0.183836	+	0.982957i	$0.441148\pi$
$42$		0			0
$43$	−5.29150			−0.806947			−0.403473	−	0.914991i	$-0.632197\pi$
$43$	−5.29150			−0.806947			−0.403473	+	0.914991i	$0.632197\pi$
$44$	0.322876	−	0.559237i	0.0486753	−	0.0843082i
$45$		0			0
$46$	−1.17712	−	2.03884i	−0.173558	−	0.300610i
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	−0.735643	−	0.677369i	$-0.763120\pi$
$47$	1.50000	−	2.59808i	0.218797	−	0.378968i	0.954441	+	0.298401i	$0.0964533\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$	8.29150			1.17260
$51$		0			0
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	−2.35425			−0.317447
$56$	1.32288	−	2.29129i	0.176777	−	0.306186i
$57$		0			0
$58$	2.14575	−	3.71655i	0.281751	−	0.488007i
$59$	−3.96863	−	6.87386i	−0.516671	−	0.894901i	−0.999813	−	0.0193585i	$-0.993838\pi$
$59$	−3.96863	−	6.87386i	−0.516671	−	0.894901i	0.483141	−	0.875542i	$-0.339496\pi$
$60$		0			0
$61$	5.96863	−	10.3380i	0.764204	−	1.32364i	−0.176462	−	0.984307i	$-0.556465\pi$
$61$	5.96863	−	10.3380i	0.764204	−	1.32364i	0.940666	−	0.339333i	$-0.110201\pi$
$62$	3.29150			0.418021
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.82288	+	3.15731i	−0.226100	+	0.391617i
$66$		0			0
$67$	−3.79150	−	6.56708i	−0.463206	−	0.802296i	0.535913	−	0.844273i	$-0.319968\pi$
$67$	−3.79150	−	6.56708i	−0.463206	−	0.802296i	−0.999119	+	0.0419774i	$0.986634\pi$
$68$	−3.32288	+	5.75539i	−0.402958	+	0.697943i
$69$		0			0
$70$	−9.64575			−1.15289
$71$	−16.2915			−1.93345			−0.966723	−	0.255826i	$-0.917653\pi$
$71$	−16.2915			−1.93345			−0.966723	+	0.255826i	$0.917653\pi$
$72$		0			0
$73$	6.82288	+	11.8176i	0.798557	+	1.38314i	0.920556	+	0.390611i	$0.127736\pi$
$73$	6.82288	+	11.8176i	0.798557	+	1.38314i	−0.121998	+	0.992530i	$0.538930\pi$
$74$	−2.82288	−	4.88936i	−0.328153	−	0.568377i
$75$		0			0
$76$	5.00000			0.573539
$77$	1.70850			0.194701
$78$		0			0
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	−1.82288	−	3.15731i	−0.203804	−	0.352998i
$81$		0			0
$82$	−1.17712	+	2.03884i	−0.129992	+	0.225152i
$83$	13.2915			1.45893			0.729466	−	0.684017i	$-0.239769\pi$
$83$	13.2915			1.45893			0.729466	+	0.684017i	$0.239769\pi$
$84$		0			0
$85$	24.2288			2.62798
$86$	2.64575	−	4.58258i	0.285299	−	0.494152i
$87$		0			0
$88$	0.322876	+	0.559237i	0.0344187	+	0.0596149i
$89$	8.46863	−	14.6681i	0.897673	−	1.55481i	0.0672111	−	0.997739i	$-0.478590\pi$
$89$	8.46863	−	14.6681i	0.897673	−	1.55481i	0.830462	−	0.557076i	$-0.188077\pi$
$90$		0			0
$91$	1.32288	−	2.29129i	0.138675	−	0.240192i
$92$	2.35425			0.245447
$93$		0			0
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	−9.11438	−	15.7866i	−0.935115	−	1.61967i
$96$		0			0
$97$	0.937254			0.0951637			0.0475819	−	0.998867i	$-0.484849\pi$
$97$	0.937254			0.0951637			0.0475819	+	0.998867i	$0.484849\pi$
$98$	7.00000			0.707107
$99$		0			0
$100$	−4.14575	+	7.18065i	−0.414575	+	0.718065i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	2.64575	−	4.58258i	0.260694	−	0.451535i	−0.705733	−	0.708478i	$-0.749382\pi$
$103$	2.64575	−	4.58258i	0.260694	−	0.451535i	0.966426	+	0.256943i	$0.0827154\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	3.00000			0.291386
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	0.945769	−	0.324840i	$-0.105310\pi$
$109$	2.00000	+	3.46410i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$110$	1.17712	−	2.03884i	0.112234	−	0.194396i
$111$		0			0
$112$	1.32288	+	2.29129i	0.125000	+	0.216506i
$113$	−15.2288			−1.43260			−0.716300	−	0.697792i	$-0.754166\pi$
$113$	−15.2288			−1.43260			−0.716300	+	0.697792i	$0.754166\pi$
$114$		0			0
$115$	−4.29150	−	7.43310i	−0.400185	−	0.693140i
$116$	2.14575	+	3.71655i	0.199228	+	0.345073i
$117$		0			0
$118$	7.93725			0.730683
$119$	−17.5830			−1.61183
$120$		0			0
$121$	5.29150	−	9.16515i	0.481046	−	0.833196i
$122$	5.96863	+	10.3380i	0.540374	+	0.935955i
$123$		0			0
$124$	−1.64575	+	2.85052i	−0.147793	+	0.255985i
$125$	12.0000			1.07331
$126$		0			0
$127$	−10.2288			−0.907655			−0.453828	−	0.891089i	$-0.649942\pi$
$127$	−10.2288			−0.907655			−0.453828	+	0.891089i	$0.649942\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.82288	−	3.15731i	−0.159877	−	0.276915i
$131$	5.46863	−	9.47194i	0.477796	−	0.827567i	−0.521880	−	0.853019i	$-0.674769\pi$
$131$	5.46863	−	9.47194i	0.477796	−	0.827567i	0.999676	+	0.0254518i	$0.00810242\pi$
$132$		0			0
$133$	6.61438	+	11.4564i	0.573539	+	0.993399i
$134$	7.58301			0.655072
$135$		0			0
$136$	−3.32288	−	5.75539i	−0.284934	−	0.493521i
$137$	−9.76013	−	16.9050i	−0.833864	−	1.44430i	−0.894952	−	0.446163i	$-0.852790\pi$
$137$	−9.76013	−	16.9050i	−0.833864	−	1.44430i	0.0610877	−	0.998132i	$-0.480543\pi$
$138$		0			0
$139$	−22.2288			−1.88542			−0.942709	−	0.333615i	$-0.891731\pi$
$139$	−22.2288			−1.88542			−0.942709	+	0.333615i	$0.891731\pi$
$140$	4.82288	−	8.35347i	0.407607	−	0.705997i
$141$		0			0
$142$	8.14575	−	14.1089i	0.683576	−	1.18399i
$143$	0.322876	+	0.559237i	0.0270002	+	0.0467658i
$144$		0			0
$145$	7.82288	−	13.5496i	0.649654	−	1.12523i
$146$	−13.6458			−1.12933
$147$		0			0
$148$	5.64575			0.464078
$149$	−3.53137	+	6.11652i	−0.289301	+	0.501085i	−0.973643	−	0.228077i	$-0.926756\pi$
$149$	−3.53137	+	6.11652i	−0.289301	+	0.501085i	0.684342	+	0.729161i	$0.260090\pi$
$150$		0			0
$151$	−3.03137	−	5.25049i	−0.246690	−	0.427279i	0.715916	−	0.698187i	$-0.246009\pi$
$151$	−3.03137	−	5.25049i	−0.246690	−	0.427279i	−0.962605	+	0.270908i	$0.912676\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$		0			0
$154$	−0.854249	+	1.47960i	−0.0688373	+	0.119230i
$155$	12.0000			0.963863
$156$		0			0
$157$	−1.32288	−	2.29129i	−0.105577	−	0.182865i	0.808397	−	0.588638i	$-0.200336\pi$
$157$	−1.32288	−	2.29129i	−0.105577	−	0.182865i	−0.913974	+	0.405773i	$0.867002\pi$
$158$	5.00000	+	8.66025i	0.397779	+	0.688973i
$159$		0			0
$160$	3.64575			0.288222
$161$	3.11438	+	5.39426i	0.245447	+	0.425127i
$162$		0			0
$163$	−1.20850	+	2.09318i	−0.0946568	+	0.163950i	−0.909465	−	0.415780i	$-0.863509\pi$
$163$	−1.20850	+	2.09318i	−0.0946568	+	0.163950i	0.814809	+	0.579730i	$0.196842\pi$
$164$	−1.17712	−	2.03884i	−0.0919180	−	0.159207i
$165$		0			0
$166$	−6.64575	+	11.5108i	−0.515810	+	0.893410i
$167$	6.87451			0.531965			0.265983	−	0.963978i	$-0.414304\pi$
$167$	6.87451			0.531965			0.265983	+	0.963978i	$0.414304\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−12.1144	+	20.9827i	−0.929130	+	1.60930i
$171$		0			0
$172$	2.64575	+	4.58258i	0.201737	+	0.349418i
$173$	−11.1458	+	19.3050i	−0.847396	+	1.46773i	0.0361285	+	0.999347i	$0.488497\pi$
$173$	−11.1458	+	19.3050i	−0.847396	+	1.46773i	−0.883524	+	0.468385i	$0.844836\pi$
$174$		0			0
$175$	−21.9373			−1.65830
$176$	−0.645751			−0.0486753
$177$		0			0
$178$	8.46863	+	14.6681i	0.634750	+	1.09942i
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$	14.6458			1.08861			0.544305	−	0.838887i	$-0.316793\pi$
$181$	14.6458			1.08861			0.544305	+	0.838887i	$0.316793\pi$
$182$	1.32288	+	2.29129i	0.0980581	+	0.169842i
$183$		0			0
$184$	−1.17712	+	2.03884i	−0.0867788	+	0.150305i
$185$	−10.2915	−	17.8254i	−0.756646	−	1.31055i
$186$		0			0
$187$	2.14575	−	3.71655i	0.156913	−	0.271781i
$188$	−3.00000			−0.218797
$189$		0			0
$190$	18.2288			1.32245
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	−9.46863	−	16.4001i	−0.681567	−	1.18051i	−0.974503	−	0.224376i	$-0.927966\pi$
$193$	−9.46863	−	16.4001i	−0.681567	−	1.18051i	0.292936	−	0.956132i	$-0.405368\pi$
$194$	−0.468627	+	0.811686i	−0.0336455	+	0.0582756i
$195$		0			0
$196$	−3.50000	+	6.06218i	−0.250000	+	0.433013i
$197$	26.8118			1.91026			0.955129	−	0.296189i	$-0.0957157\pi$
$197$	26.8118			1.91026			0.955129	+	0.296189i	$0.0957157\pi$
$198$		0			0
$199$	11.1144	+	19.2507i	0.787877	+	1.36464i	0.927265	+	0.374406i	$0.122153\pi$
$199$	11.1144	+	19.2507i	0.787877	+	1.36464i	−0.139388	+	0.990238i	$0.544513\pi$
$200$	−4.14575	−	7.18065i	−0.293149	−	0.507749i
$201$		0			0
$202$		0			0
$203$	−5.67712	+	9.83307i	−0.398456	+	0.690146i
$204$		0			0
$205$	−4.29150	+	7.43310i	−0.299732	+	0.519150i
$206$	2.64575	+	4.58258i	0.184338	+	0.319283i
$207$		0			0
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−3.22876			−0.223338
$210$		0			0
$211$	−6.35425			−0.437445			−0.218722	−	0.975787i	$-0.570189\pi$
$211$	−6.35425			−0.437445			−0.218722	+	0.975787i	$0.570189\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	9.64575	−	16.7069i	0.657835	−	1.13940i
$216$		0			0
$217$	−8.70850			−0.591171
$218$	−4.00000			−0.270914
$219$		0			0
$220$	1.17712	+	2.03884i	0.0793617	+	0.137459i
$221$	−3.32288	−	5.75539i	−0.223521	−	0.387149i
$222$		0			0
$223$	−20.5203			−1.37414			−0.687069	−	0.726592i	$-0.741103\pi$
$223$	−20.5203			−1.37414			−0.687069	+	0.726592i	$0.741103\pi$
$224$	−2.64575			−0.176777
$225$		0			0
$226$	7.61438	−	13.1885i	0.506501	−	0.877285i
$227$	−2.35425	−	4.07768i	−0.156257	−	0.270645i	0.777259	−	0.629181i	$-0.216609\pi$
$227$	−2.35425	−	4.07768i	−0.156257	−	0.270645i	−0.933516	+	0.358536i	$0.883276\pi$
$228$		0			0
$229$	−13.2288	+	22.9129i	−0.874181	+	1.51413i	−0.0165480	+	0.999863i	$0.505268\pi$
$229$	−13.2288	+	22.9129i	−0.874181	+	1.51413i	−0.857633	+	0.514263i	$0.828066\pi$
$230$	8.58301			0.565947
$231$		0			0
$232$	−4.29150			−0.281751
$233$	0.322876	−	0.559237i	0.0211523	−	0.0366368i	−0.855256	−	0.518207i	$-0.826600\pi$
$233$	0.322876	−	0.559237i	0.0211523	−	0.0366368i	0.876408	+	0.481570i	$0.159933\pi$
$234$		0			0
$235$	5.46863	+	9.47194i	0.356734	+	0.617881i
$236$	−3.96863	+	6.87386i	−0.258336	+	0.447450i
$237$		0			0
$238$	8.79150	−	15.2273i	0.569868	−	0.987041i
$239$	−3.00000			−0.194054			−0.0970269	−	0.995282i	$-0.530933\pi$
$239$	−3.00000			−0.194054			−0.0970269	+	0.995282i	$0.530933\pi$
$240$		0			0
$241$	6.93725	+	12.0157i	0.446868	+	0.773998i	0.998180	−	0.0603011i	$-0.0192061\pi$
$241$	6.93725	+	12.0157i	0.446868	+	0.773998i	−0.551312	+	0.834299i	$0.685873\pi$
$242$	5.29150	+	9.16515i	0.340151	+	0.589158i
$243$		0			0
$244$	−11.9373			−0.764204
$245$	25.5203			1.63043
$246$		0			0
$247$	−2.50000	+	4.33013i	−0.159071	+	0.275519i
$248$	−1.64575	−	2.85052i	−0.104505	−	0.181009i
$249$		0			0
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	13.2915			0.838952			0.419476	−	0.907766i	$-0.362214\pi$
$251$	13.2915			0.838952			0.419476	+	0.907766i	$0.362214\pi$
$252$		0			0
$253$	−1.52026			−0.0955779
$254$	5.11438	−	8.85836i	0.320905	−	0.555823i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.93725	+	13.7477i	−0.495112	+	0.857560i	−0.999984	−	0.00563467i	$-0.998206\pi$
$257$	−7.93725	+	13.7477i	−0.495112	+	0.857560i	0.504872	+	0.863194i	$0.331540\pi$
$258$		0			0
$259$	7.46863	+	12.9360i	0.464078	+	0.803806i
$260$	3.64575			0.226100
$261$		0			0
$262$	5.46863	+	9.47194i	0.337853	+	0.585178i
$263$	−1.82288	−	3.15731i	−0.112403	−	0.194688i	0.804335	−	0.594175i	$-0.202522\pi$
$263$	−1.82288	−	3.15731i	−0.112403	−	0.194688i	−0.916739	+	0.399487i	$0.869188\pi$
$264$		0			0
$265$	10.9373			0.671870
$266$	−13.2288			−0.811107
$267$		0			0
$268$	−3.79150	+	6.56708i	−0.231603	+	0.401148i
$269$	3.43725	+	5.95350i	0.209573	+	0.362991i	0.951580	−	0.307401i	$-0.0994593\pi$
$269$	3.43725	+	5.95350i	0.209573	+	0.362991i	−0.742007	+	0.670392i	$0.766126\pi$
$270$		0			0
$271$	11.3229	−	19.6118i	0.687816	−	1.19133i	−0.284727	−	0.958609i	$-0.591903\pi$
$271$	11.3229	−	19.6118i	0.687816	−	1.19133i	0.972543	−	0.232723i	$-0.0747636\pi$
$272$	6.64575			0.402958
$273$		0			0
$274$	19.5203			1.17926
$275$	2.67712	−	4.63692i	0.161437	−	0.279617i
$276$		0			0
$277$	−9.26013	−	16.0390i	−0.556387	−	0.963691i	−0.997794	−	0.0663840i	$-0.978854\pi$
$277$	−9.26013	−	16.0390i	−0.556387	−	0.963691i	0.441407	−	0.897307i	$-0.354480\pi$
$278$	11.1144	−	19.2507i	0.666596	−	1.15458i
$279$		0			0
$280$	4.82288	+	8.35347i	0.288222	+	0.499215i
$281$	2.58301			0.154089			0.0770446	−	0.997028i	$-0.475452\pi$
$281$	2.58301			0.154089			0.0770446	+	0.997028i	$0.475452\pi$
$282$		0			0
$283$	5.53137	+	9.58062i	0.328806	+	0.569509i	0.982275	−	0.187444i	$-0.0600204\pi$
$283$	5.53137	+	9.58062i	0.328806	+	0.569509i	−0.653469	+	0.756953i	$0.726687\pi$
$284$	8.14575	+	14.1089i	0.483361	+	0.837207i
$285$		0			0
$286$	−0.645751			−0.0381841
$287$	3.11438	−	5.39426i	0.183836	−	0.318413i
$288$		0			0
$289$	−13.5830	+	23.5265i	−0.799000	+	1.38391i
$290$	7.82288	+	13.5496i	0.459375	+	0.795661i
$291$		0			0
$292$	6.82288	−	11.8176i	0.399279	−	0.691571i
$293$	−7.52026			−0.439338			−0.219669	−	0.975574i	$-0.570498\pi$
$293$	−7.52026			−0.439338			−0.219669	+	0.975574i	$0.570498\pi$
$294$		0			0
$295$	28.9373			1.68479
$296$	−2.82288	+	4.88936i	−0.164076	+	0.284189i
$297$		0			0
$298$	−3.53137	−	6.11652i	−0.204567	−	0.354320i
$299$	−1.17712	+	2.03884i	−0.0680749	+	0.117909i
$300$		0			0
$301$	−7.00000	+	12.1244i	−0.403473	+	0.698836i
$302$	6.06275			0.348872
$303$		0			0
$304$	−2.50000	−	4.33013i	−0.143385	−	0.248350i
$305$	21.7601	+	37.6897i	1.24598	+	2.15810i
$306$		0			0
$307$	−9.58301			−0.546931			−0.273465	−	0.961882i	$-0.588170\pi$
$307$	−9.58301			−0.546931			−0.273465	+	0.961882i	$0.588170\pi$
$308$	−0.854249	−	1.47960i	−0.0486753	−	0.0843082i
$309$		0			0
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−0.531373	−	0.920365i	−0.0301314	−	0.0521891i	0.850566	−	0.525868i	$-0.176259\pi$
$311$	−0.531373	−	0.920365i	−0.0301314	−	0.0521891i	−0.880698	+	0.473678i	$0.842926\pi$
$312$		0			0
$313$	−6.58301	+	11.4021i	−0.372093	+	0.644485i	−0.989887	−	0.141855i	$-0.954693\pi$
$313$	−6.58301	+	11.4021i	−0.372093	+	0.644485i	0.617794	+	0.786340i	$0.288027\pi$
$314$	2.64575			0.149308
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−6.64575	+	11.5108i	−0.373263	+	0.646510i	−0.990065	−	0.140608i	$-0.955094\pi$
$317$	−6.64575	+	11.5108i	−0.373263	+	0.646510i	0.616803	+	0.787118i	$0.288428\pi$
$318$		0			0
$319$	−1.38562	−	2.39997i	−0.0775799	−	0.134372i
$320$	−1.82288	+	3.15731i	−0.101902	+	0.176499i
$321$		0			0
$322$	−6.22876			−0.347115
$323$	33.2288			1.84890
$324$		0			0
$325$	−4.14575	−	7.18065i	−0.229965	−	0.398311i
$326$	−1.20850	−	2.09318i	−0.0669325	−	0.115930i
$327$		0			0
$328$	2.35425			0.129992
$329$	−3.96863	−	6.87386i	−0.218797	−	0.378968i
$330$		0			0
$331$	−5.70850	+	9.88741i	−0.313767	+	0.543461i	−0.979175	−	0.203019i	$-0.934925\pi$
$331$	−5.70850	+	9.88741i	−0.313767	+	0.543461i	0.665407	+	0.746480i	$0.268258\pi$
$332$	−6.64575	−	11.5108i	−0.364733	−	0.631736i
$333$		0			0
$334$	−3.43725	+	5.95350i	−0.188078	+	0.325761i
$335$	27.6458			1.51045
$336$		0			0
$337$	−15.5830			−0.848860			−0.424430	−	0.905461i	$-0.639526\pi$
$337$	−15.5830			−0.848860			−0.424430	+	0.905461i	$0.639526\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$		0			0
$340$	−12.1144	−	20.9827i	−0.656994	−	1.13795i
$341$	1.06275	−	1.84073i	0.0575509	−	0.0996811i
$342$		0			0
$343$	−18.5203			−1.00000
$344$	−5.29150			−0.285299
$345$		0			0
$346$	−11.1458	−	19.3050i	−0.599199	−	1.03784i
$347$	0.114378	+	0.198109i	0.00614015	+	0.0106350i	0.869079	−	0.494673i	$-0.164712\pi$
$347$	0.114378	+	0.198109i	0.00614015	+	0.0106350i	−0.862939	+	0.505308i	$0.831379\pi$
$348$		0			0
$349$	18.9373			1.01369			0.506844	−	0.862038i	$-0.330812\pi$
$349$	18.9373			1.01369			0.506844	+	0.862038i	$0.330812\pi$
$350$	10.9686	−	18.9982i	0.586298	−	1.01550i
$351$		0			0
$352$	0.322876	−	0.559237i	0.0172093	−	0.0298074i
$353$	−10.2915	−	17.8254i	−0.547761	−	0.948751i	−0.998428	−	0.0560580i	$-0.982147\pi$
$353$	−10.2915	−	17.8254i	−0.547761	−	0.948751i	0.450666	−	0.892693i	$-0.351187\pi$
$354$		0			0
$355$	29.6974	−	51.4374i	1.57617	−	2.73001i
$356$	−16.9373			−0.897673
$357$		0			0
$358$	6.00000			0.317110
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	−0.934268	−	0.356572i	$-0.883946\pi$
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	0.775934	+	0.630814i	$0.217279\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−7.32288	+	12.6836i	−0.384882	+	0.666635i
$363$		0			0
$364$	−2.64575			−0.138675
$365$	−49.7490			−2.60398
$366$		0			0
$367$	0.291503	+	0.504897i	0.0152163	+	0.0263554i	0.873533	−	0.486764i	$-0.161823\pi$
$367$	0.291503	+	0.504897i	0.0152163	+	0.0263554i	−0.858317	+	0.513120i	$0.828490\pi$
$368$	−1.17712	−	2.03884i	−0.0613618	−	0.106282i
$369$		0			0
$370$	20.5830			1.07006
$371$	−7.93725			−0.412082
$372$		0			0
$373$	−7.32288	+	12.6836i	−0.379164	+	0.656732i	−0.990941	−	0.134299i	$-0.957122\pi$
$373$	−7.32288	+	12.6836i	−0.379164	+	0.656732i	0.611777	+	0.791030i	$0.290455\pi$
$374$	2.14575	+	3.71655i	0.110954	+	0.192178i
$375$		0			0
$376$	1.50000	−	2.59808i	0.0773566	−	0.133986i
$377$	−4.29150			−0.221024
$378$		0			0
$379$	−9.16601			−0.470826			−0.235413	−	0.971895i	$-0.575644\pi$
$379$	−9.16601			−0.470826			−0.235413	+	0.971895i	$0.575644\pi$
$380$	−9.11438	+	15.7866i	−0.467558	+	0.809834i
$381$		0			0
$382$		0			0
$383$	12.8745	−	22.2993i	0.657857	−	1.13944i	−0.323313	−	0.946292i	$-0.604797\pi$
$383$	12.8745	−	22.2993i	0.657857	−	1.13944i	0.981169	−	0.193149i	$-0.0618701\pi$
$384$		0			0
$385$	−3.11438	+	5.39426i	−0.158723	+	0.274917i
$386$	18.9373			0.963881
$387$		0			0
$388$	−0.468627	−	0.811686i	−0.0237909	−	0.0412071i
$389$	3.85425	+	6.67575i	0.195418	+	0.338474i	0.947038	−	0.321123i	$-0.104060\pi$
$389$	3.85425	+	6.67575i	0.195418	+	0.338474i	−0.751619	+	0.659597i	$0.770727\pi$
$390$		0			0
$391$	15.6458			0.791240
$392$	−3.50000	−	6.06218i	−0.176777	−	0.306186i
$393$		0			0
$394$	−13.4059	+	23.2197i	−0.675379	+	1.16979i
$395$	18.2288	+	31.5731i	0.917188	+	1.58862i
$396$		0			0
$397$	7.46863	−	12.9360i	0.374840	−	0.649241i	−0.615463	−	0.788165i	$-0.711031\pi$
$397$	7.46863	−	12.9360i	0.374840	−	0.649241i	0.990303	+	0.138924i	$0.0443644\pi$
$398$	−22.2288			−1.11423
$399$		0			0
$400$	8.29150			0.414575
$401$	−9.11438	+	15.7866i	−0.455150	+	0.788343i	−0.998697	−	0.0510356i	$-0.983748\pi$
$401$	−9.11438	+	15.7866i	−0.455150	+	0.788343i	0.543547	+	0.839379i	$0.317081\pi$
$402$		0			0
$403$	−1.64575	−	2.85052i	−0.0819807	−	0.141995i
$404$		0			0
$405$		0			0
$406$	−5.67712	−	9.83307i	−0.281751	−	0.488007i
$407$	−3.64575			−0.180713
$408$		0			0
$409$	13.4686	+	23.3283i	0.665981	+	1.15351i	0.979018	+	0.203772i	$0.0653201\pi$
$409$	13.4686	+	23.3283i	0.665981	+	1.15351i	−0.313038	+	0.949741i	$0.601347\pi$
$410$	−4.29150	−	7.43310i	−0.211942	−	0.367095i
$411$		0			0
$412$	−5.29150			−0.260694
$413$	−21.0000			−1.03334
$414$		0			0
$415$	−24.2288	+	41.9654i	−1.18934	+	2.06000i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$	1.61438	−	2.79619i	0.0789618	−	0.136766i
$419$	−30.4575			−1.48795			−0.743973	−	0.668209i	$-0.767061\pi$
$419$	−30.4575			−1.48795			−0.743973	+	0.668209i	$0.767061\pi$
$420$		0			0
$421$	−24.3542			−1.18695			−0.593477	−	0.804851i	$-0.702245\pi$
$421$	−24.3542			−1.18695			−0.593477	+	0.804851i	$0.702245\pi$
$422$	3.17712	−	5.50294i	0.154660	−	0.267879i
$423$		0			0
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$	−27.5516	+	47.7208i	−1.33645	+	2.31480i
$426$		0			0
$427$	−15.7915	−	27.3517i	−0.764204	−	1.32364i
$428$	12.0000			0.580042
$429$		0			0
$430$	9.64575	+	16.7069i	0.465159	+	0.805680i
$431$	10.2915	+	17.8254i	0.495724	+	0.858620i	0.999988	−	0.00493021i	$-0.00156934\pi$
$431$	10.2915	+	17.8254i	0.495724	+	0.858620i	−0.504264	+	0.863550i	$0.668236\pi$
$432$		0			0
$433$	−33.5830			−1.61390			−0.806948	−	0.590622i	$-0.798882\pi$
$433$	−33.5830			−1.61390			−0.806948	+	0.590622i	$0.798882\pi$
$434$	4.35425	−	7.54178i	0.209011	−	0.362017i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	−5.88562	−	10.1942i	−0.281547	−	0.487655i
$438$		0			0
$439$	−11.8229	+	20.4778i	−0.564275	+	0.977353i	0.432842	+	0.901470i	$0.357511\pi$
$439$	−11.8229	+	20.4778i	−0.564275	+	0.977353i	−0.997117	+	0.0758831i	$0.975822\pi$
$440$	−2.35425			−0.112234
$441$		0			0
$442$	6.64575			0.316106
$443$	9.53137	−	16.5088i	0.452849	−	0.784358i	−0.545713	−	0.837972i	$-0.683741\pi$
$443$	9.53137	−	16.5088i	0.452849	−	0.784358i	0.998562	+	0.0536147i	$0.0170743\pi$
$444$		0			0
$445$	30.8745	+	53.4762i	1.46359	+	2.53502i
$446$	10.2601	−	17.7711i	0.485831	−	0.841484i
$447$		0			0
$448$	1.32288	−	2.29129i	0.0625000	−	0.108253i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$	0.760130	+	1.31658i	0.0357931	+	0.0619955i
$452$	7.61438	+	13.1885i	0.358150	+	0.620334i
$453$		0			0
$454$	4.70850			0.220981
$455$	4.82288	+	8.35347i	0.226100	+	0.391617i
$456$		0			0
$457$	−16.1144	+	27.9109i	−0.753799	+	1.30562i	0.192170	+	0.981362i	$0.438447\pi$
$457$	−16.1144	+	27.9109i	−0.753799	+	1.30562i	−0.945969	+	0.324256i	$0.894886\pi$
$458$	−13.2288	−	22.9129i	−0.618139	−	1.07065i
$459$		0			0
$460$	−4.29150	+	7.43310i	−0.200092	+	0.346570i
$461$	36.4575			1.69800			0.848998	−	0.528396i	$-0.177206\pi$
$461$	36.4575			1.69800			0.848998	+	0.528396i	$0.177206\pi$
$462$		0			0
$463$	25.1660			1.16956			0.584782	−	0.811191i	$-0.301180\pi$
$463$	25.1660			1.16956			0.584782	+	0.811191i	$0.301180\pi$
$464$	2.14575	−	3.71655i	0.0996140	−	0.172537i
$465$		0			0
$466$	0.322876	+	0.559237i	0.0149569	+	0.0259062i
$467$	−18.7601	+	32.4935i	−0.868115	+	1.50362i	−0.00419497	+	0.999991i	$0.501335\pi$
$467$	−18.7601	+	32.4935i	−0.868115	+	1.50362i	−0.863920	+	0.503629i	$0.831998\pi$
$468$		0			0
$469$	−20.0627			−0.926412
$470$	−10.9373			−0.504498
$471$		0			0
$472$	−3.96863	−	6.87386i	−0.182671	−	0.316395i
$473$	−1.70850	−	2.95920i	−0.0785568	−	0.136064i
$474$		0			0
$475$	41.4575			1.90220
$476$	8.79150	+	15.2273i	0.402958	+	0.697943i
$477$		0			0
$478$	1.50000	−	2.59808i	0.0686084	−	0.118833i
$479$	−17.3745	−	30.0935i	−0.793862	−	1.37501i	−0.923560	−	0.383455i	$-0.874734\pi$
$479$	−17.3745	−	30.0935i	−0.793862	−	1.37501i	0.129698	−	0.991554i	$-0.458599\pi$
$480$		0			0
$481$	−2.82288	+	4.88936i	−0.128712	+	0.222936i
$482$	−13.8745			−0.631967
$483$		0			0
$484$	−10.5830			−0.481046
$485$	−1.70850	+	2.95920i	−0.0775789	+	0.134371i
$486$		0			0
$487$	11.9686	+	20.7303i	0.542350	+	0.939378i	0.998769	+	0.0496129i	$0.0157987\pi$
$487$	11.9686	+	20.7303i	0.542350	+	0.939378i	−0.456418	+	0.889765i	$0.650868\pi$
$488$	5.96863	−	10.3380i	0.270187	−	0.467978i
$489$		0			0
$490$	−12.7601	+	22.1012i	−0.576444	+	0.998430i
$491$	−11.1660			−0.503915			−0.251957	−	0.967738i	$-0.581074\pi$
$491$	−11.1660			−0.503915			−0.251957	+	0.967738i	$0.581074\pi$
$492$		0			0
$493$	14.2601	+	24.6993i	0.642244	+	1.11240i
$494$	−2.50000	−	4.33013i	−0.112480	−	0.194822i
$495$		0			0
$496$	3.29150			0.147793
$497$	−21.5516	+	37.3285i	−0.966723	+	1.67441i
$498$		0			0
$499$	14.6458	−	25.3672i	0.655634	−	1.13559i	−0.326101	−	0.945335i	$-0.605735\pi$
$499$	14.6458	−	25.3672i	0.655634	−	1.13559i	0.981734	−	0.190256i	$-0.0609318\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$		0			0
$502$	−6.64575	+	11.5108i	−0.296614	+	0.513751i
$503$	−36.4575			−1.62556			−0.812780	−	0.582571i	$-0.802047\pi$
$503$	−36.4575			−1.62556			−0.812780	+	0.582571i	$0.802047\pi$
$504$		0			0
$505$		0			0
$506$	0.760130	−	1.31658i	0.0337919	−	0.0585293i
$507$		0			0
$508$	5.11438	+	8.85836i	0.226914	+	0.393026i
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$		0			0
$511$	36.1033			1.59711
$512$	1.00000			0.0441942
$513$		0			0
$514$	−7.93725	−	13.7477i	−0.350097	−	0.606386i
$515$	9.64575	+	16.7069i	0.425043	+	0.736195i
$516$		0			0
$517$	1.93725			0.0852003
$518$	−14.9373			−0.656305
$519$		0			0
$520$	−1.82288	+	3.15731i	−0.0799384	+	0.138457i
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	0.993011	−	0.118020i	$-0.0376547\pi$
$521$	9.00000	+	15.5885i	0.394297	+	0.682943i	−0.598714	+	0.800963i	$0.704321\pi$
$522$		0			0
$523$	13.3542	−	23.1302i	0.583941	−	1.01141i	−0.411066	−	0.911606i	$-0.634843\pi$
$523$	13.3542	−	23.1302i	0.583941	−	1.01141i	0.995007	−	0.0998091i	$-0.0318232\pi$
$524$	−10.9373			−0.477796
$525$		0			0
$526$	3.64575			0.158962
$527$	−10.9373	+	18.9439i	−0.476434	+	0.825208i
$528$		0			0
$529$	8.72876	+	15.1186i	0.379511	+	0.657333i
$530$	−5.46863	+	9.47194i	−0.237542	+	0.411435i
$531$		0			0
$532$	6.61438	−	11.4564i	0.286770	−	0.496700i
$533$	2.35425			0.101974
$534$		0			0
$535$	−21.8745	−	37.8878i	−0.945717	−	1.63803i
$536$	−3.79150	−	6.56708i	−0.163768	−	0.283654i
$537$		0			0
$538$	−6.87451			−0.296381
$539$	2.26013	−	3.91466i	0.0973507	−	0.168616i
$540$		0			0
$541$	−20.8229	+	36.0663i	−0.895245	+	1.55061i	−0.0617447	+	0.998092i	$0.519666\pi$
$541$	−20.8229	+	36.0663i	−0.895245	+	1.55061i	−0.833501	+	0.552518i	$0.813667\pi$
$542$	11.3229	+	19.6118i	0.486359	+	0.842399i
$543$		0			0
$544$	−3.32288	+	5.75539i	−0.142467	+	0.246760i
$545$	−14.5830			−0.624667
$546$		0			0
$547$	−20.9373			−0.895212			−0.447606	−	0.894231i	$-0.647723\pi$
$547$	−20.9373			−0.895212			−0.447606	+	0.894231i	$0.647723\pi$
$548$	−9.76013	+	16.9050i	−0.416932	+	0.722148i
$549$		0			0
$550$	2.67712	+	4.63692i	0.114153	+	0.197719i
$551$	10.7288	−	18.5828i	0.457060	−	0.791652i
$552$		0			0
$553$	−13.2288	−	22.9129i	−0.562544	−	0.974355i
$554$	18.5203			0.786850
$555$		0			0
$556$	11.1144	+	19.2507i	0.471355	+	0.816410i
$557$	5.58301	+	9.67005i	0.236560	+	0.409733i	0.959725	−	0.280942i	$-0.0906468\pi$
$557$	5.58301	+	9.67005i	0.236560	+	0.409733i	−0.723165	+	0.690675i	$0.757314\pi$
$558$		0			0
$559$	−5.29150			−0.223807
$560$	−9.64575			−0.407607
$561$		0			0
$562$	−1.29150	+	2.23695i	−0.0544788	+	0.0943600i
$563$	−13.5203	−	23.4178i	−0.569811	−	0.986942i	−0.996584	−	0.0825829i	$-0.973683\pi$
$563$	−13.5203	−	23.4178i	−0.569811	−	0.986942i	0.426773	−	0.904359i	$-0.359650\pi$
$564$		0			0
$565$	27.7601	−	48.0820i	1.16788	−	2.02282i
$566$	−11.0627			−0.465002
$567$		0			0
$568$	−16.2915			−0.683576
$569$	−16.6144	+	28.7769i	−0.696511	+	1.20639i	0.273158	+	0.961969i	$0.411932\pi$
$569$	−16.6144	+	28.7769i	−0.696511	+	1.20639i	−0.969669	+	0.244423i	$0.921401\pi$
$570$		0			0
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	0.983444	−	0.181210i	$-0.0580014\pi$
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	−0.648655	+	0.761083i	$0.724668\pi$
$572$	0.322876	−	0.559237i	0.0135001	−	0.0233829i
$573$		0			0
$574$	3.11438	+	5.39426i	0.129992	+	0.225152i
$575$	19.5203			0.814051
$576$		0			0
$577$	6.29150	+	10.8972i	0.261919	+	0.453656i	0.966752	−	0.255717i	$-0.0823114\pi$
$577$	6.29150	+	10.8972i	0.261919	+	0.453656i	−0.704833	+	0.709373i	$0.748978\pi$
$578$	−13.5830	−	23.5265i	−0.564979	−	0.978572i
$579$		0			0
$580$	−15.6458			−0.649654
$581$	17.5830	−	30.4547i	0.729466	−	1.26347i
$582$		0			0
$583$	0.968627	−	1.67771i	0.0401164	−	0.0694837i
$584$	6.82288	+	11.8176i	0.282333	+	0.489014i
$585$		0			0
$586$	3.76013	−	6.51274i	0.155330	−	0.269039i
$587$	−31.9373			−1.31819			−0.659096	−	0.752059i	$-0.729061\pi$
$587$	−31.9373			−1.31819			−0.659096	+	0.752059i	$0.729061\pi$
$588$		0			0
$589$	16.4575			0.678120
$590$	−14.4686	+	25.0604i	−0.595664	+	1.03172i
$591$		0			0
$592$	−2.82288	−	4.88936i	−0.116019	−	0.200952i
$593$	21.7601	−	37.6897i	0.893581	−	1.54773i	0.0580309	−	0.998315i	$-0.481518\pi$
$593$	21.7601	−	37.6897i	0.893581	−	1.54773i	0.835551	−	0.549414i	$-0.185149\pi$
$594$		0			0
$595$	32.0516	−	55.5151i	1.31399	−	2.27590i
$596$	7.06275			0.289301
$597$		0			0
$598$	−1.17712	−	2.03884i	−0.0481362	−	0.0833743i
$599$	−16.4059	−	28.4158i	−0.670326	−	1.16104i	−0.977812	−	0.209486i	$-0.932821\pi$
$599$	−16.4059	−	28.4158i	−0.670326	−	1.16104i	0.307485	−	0.951553i	$-0.400512\pi$
$600$		0			0
$601$	14.8745			0.606744			0.303372	−	0.952872i	$-0.401888\pi$
$601$	14.8745			0.606744			0.303372	+	0.952872i	$0.401888\pi$
$602$	−7.00000	−	12.1244i	−0.285299	−	0.494152i
$603$		0			0
$604$	−3.03137	+	5.25049i	−0.123345	+	0.213639i
$605$	19.2915	+	33.4139i	0.784311	+	1.35847i
$606$		0			0
$607$	−8.40588	+	14.5594i	−0.341184	+	0.590948i	−0.984653	−	0.174524i	$-0.944161\pi$
$607$	−8.40588	+	14.5594i	−0.341184	+	0.590948i	0.643469	+	0.765472i	$0.277495\pi$
$608$	5.00000			0.202777
$609$		0			0
$610$	−43.5203			−1.76208
$611$	1.50000	−	2.59808i	0.0606835	−	0.105107i
$612$		0			0
$613$	−20.9373	−	36.2644i	−0.845648	−	1.46470i	−0.885058	−	0.465482i	$-0.845881\pi$
$613$	−20.9373	−	36.2644i	−0.845648	−	1.46470i	0.0394098	−	0.999223i	$-0.487452\pi$
$614$	4.79150	−	8.29913i	0.193369	−	0.334925i
$615$		0			0
$616$	1.70850			0.0688373
$617$	10.7085			0.431108			0.215554	−	0.976492i	$-0.430844\pi$
$617$	10.7085			0.431108			0.215554	+	0.976492i	$0.430844\pi$
$618$		0			0
$619$	20.8745	+	36.1557i	0.839017	+	1.45322i	0.890717	+	0.454558i	$0.150203\pi$
$619$	20.8745	+	36.1557i	0.839017	+	1.45322i	−0.0516999	+	0.998663i	$0.516464\pi$
$620$	−6.00000	−	10.3923i	−0.240966	−	0.417365i
$621$		0			0
$622$	1.06275			0.0426122
$623$	−22.4059	−	38.8081i	−0.897673	−	1.55481i
$624$		0			0
$625$	−1.14575	+	1.98450i	−0.0458301	+	0.0793800i
$626$	−6.58301	−	11.4021i	−0.263110	−	0.455720i
$627$		0			0
$628$	−1.32288	+	2.29129i	−0.0527885	+	0.0914323i
$629$	37.5203			1.49603
$630$		0			0
$631$	14.4575			0.575545			0.287772	−	0.957699i	$-0.407085\pi$
$631$	14.4575			0.575545			0.287772	+	0.957699i	$0.407085\pi$
$632$	5.00000	−	8.66025i	0.198889	−	0.344486i
$633$		0			0
$634$	−6.64575	−	11.5108i	−0.263937	−	0.457151i
$635$	18.6458	−	32.2954i	0.739934	−	1.28160i
$636$		0			0
$637$	−3.50000	−	6.06218i	−0.138675	−	0.240192i
$638$	2.77124			0.109715
$639$		0			0
$640$	−1.82288	−	3.15731i	−0.0720555	−	0.124804i
$641$	−10.7085	−	18.5477i	−0.422960	−	0.732589i	0.573267	−	0.819368i	$-0.305676\pi$
$641$	−10.7085	−	18.5477i	−0.422960	−	0.732589i	−0.996228	+	0.0867798i	$0.972342\pi$
$642$		0			0
$643$	−10.8745			−0.428849			−0.214424	−	0.976741i	$-0.568788\pi$
$643$	−10.8745			−0.428849			−0.214424	+	0.976741i	$0.568788\pi$
$644$	3.11438	−	5.39426i	0.122724	−	0.212564i
$645$		0			0
$646$	−16.6144	+	28.7769i	−0.653684	+	1.13221i
$647$	12.8745	+	22.2993i	0.506149	+	0.876676i	0.999975	+	0.00711502i	$0.00226480\pi$
$647$	12.8745	+	22.2993i	0.506149	+	0.876676i	−0.493826	+	0.869561i	$0.664402\pi$
$648$		0			0
$649$	2.56275	−	4.43881i	0.100597	−	0.174238i
$650$	8.29150			0.325219
$651$		0			0
$652$	2.41699			0.0946568
$653$	6.00000	−	10.3923i	0.234798	−	0.406682i	−0.724416	−	0.689363i	$-0.757890\pi$
$653$	6.00000	−	10.3923i	0.234798	−	0.406682i	0.959214	+	0.282681i	$0.0912238\pi$
$654$		0			0
$655$	19.9373	+	34.5323i	0.779013	+	1.34929i
$656$	−1.17712	+	2.03884i	−0.0459590	+	0.0796033i
$657$		0			0
$658$	7.93725			0.309426
$659$	16.9373			0.659782			0.329891	−	0.944019i	$-0.392988\pi$
$659$	16.9373			0.659782			0.329891	+	0.944019i	$0.392988\pi$
$660$		0			0
$661$	−7.76013	−	13.4409i	−0.301834	−	0.522792i	0.674717	−	0.738076i	$-0.264266\pi$
$661$	−7.76013	−	13.4409i	−0.301834	−	0.522792i	−0.976551	+	0.215284i	$0.930932\pi$
$662$	−5.70850	−	9.88741i	−0.221867	−	0.384285i
$663$		0			0
$664$	13.2915			0.515810
$665$	−48.2288			−1.87023
$666$		0			0
$667$	5.05163	−	8.74968i	0.195600	−	0.338789i
$668$	−3.43725	−	5.95350i	−0.132991	−	0.230348i
$669$		0			0
$670$	−13.8229	+	23.9419i	−0.534024	+	0.924957i
$671$	7.70850			0.297583
$672$		0			0
$673$	−6.58301			−0.253756			−0.126878	−	0.991918i	$-0.540496\pi$
$673$	−6.58301			−0.253756			−0.126878	+	0.991918i	$0.540496\pi$
$674$	7.79150	−	13.4953i	0.300117	−	0.519819i
$675$		0			0
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	10.0830	−	17.4643i	0.387521	−	0.671207i	−0.604594	−	0.796534i	$-0.706665\pi$
$677$	10.0830	−	17.4643i	0.387521	−	0.671207i	0.992115	+	0.125327i	$0.0399980\pi$
$678$		0			0
$679$	1.23987	−	2.14752i	0.0475819	−	0.0824142i
$680$	24.2288			0.929130
$681$		0			0
$682$	1.06275	+	1.84073i	0.0406947	+	0.0704852i
$683$	9.64575	+	16.7069i	0.369084	+	0.639273i	0.989423	−	0.145061i	$-0.0463380\pi$
$683$	9.64575	+	16.7069i	0.369084	+	0.639273i	−0.620338	+	0.784334i	$0.713005\pi$
$684$		0			0
$685$	71.1660			2.71911
$686$	9.26013	−	16.0390i	0.353553	−	0.612372i
$687$		0			0
$688$	2.64575	−	4.58258i	0.100868	−	0.174709i
$689$	−1.50000	−	2.59808i	−0.0571454	−	0.0989788i
$690$		0			0
$691$	20.0203	−	34.6761i	0.761607	−	1.31914i	−0.180416	−	0.983590i	$-0.557744\pi$
$691$	20.0203	−	34.6761i	0.761607	−	1.31914i	0.942022	−	0.335551i	$-0.108922\pi$
$692$	22.2915			0.847396
$693$		0			0
$694$	−0.228757			−0.00868348
$695$	40.5203	−	70.1831i	1.53702	−	2.66220i
$696$		0			0
$697$	−7.82288	−	13.5496i	−0.296313	−	0.513228i
$698$	−9.46863	+	16.4001i	−0.358393	+	0.620755i
$699$		0			0
$700$	10.9686	+	18.9982i	0.414575	+	0.718065i
$701$	−12.0000			−0.453234			−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000			−0.453234			−0.226617	+	0.973984i	$0.572767\pi$
$702$		0			0
$703$	−14.1144	−	24.4468i	−0.532334	−	0.922029i
$704$	0.322876	+	0.559237i	0.0121688	+	0.0210770i
$705$		0			0
$706$	20.5830			0.774652
$707$		0			0
$708$		0			0
$709$	−3.23987	+	5.61162i	−0.121676	+	0.210749i	−0.920429	−	0.390911i	$-0.872160\pi$
$709$	−3.23987	+	5.61162i	−0.121676	+	0.210749i	0.798753	+	0.601659i	$0.205494\pi$
$710$	29.6974	+	51.4374i	1.11452	+	1.93041i
$711$		0			0
$712$	8.46863	−	14.6681i	0.317375	−	0.549710i
$713$	7.74902			0.290203
$714$		0			0
$715$	−2.35425			−0.0880439
$716$	−3.00000	+	5.19615i	−0.112115	+	0.194189i
$717$		0			0
$718$	−3.00000	−	5.19615i	−0.111959	−	0.193919i
$719$	22.2915	−	38.6100i	0.831333	−	1.43991i	−0.0656489	−	0.997843i	$-0.520912\pi$
$719$	22.2915	−	38.6100i	0.831333	−	1.43991i	0.896982	−	0.442068i	$-0.145755\pi$
$720$		0			0
$721$	−7.00000	−	12.1244i	−0.260694	−	0.451535i
$722$	6.00000			0.223297
$723$		0			0
$724$	−7.32288	−	12.6836i	−0.272153	−	0.471382i
$725$	17.7915	+	30.8158i	0.660760	+	1.14447i
$726$		0			0
$727$	−16.4575			−0.610375			−0.305188	−	0.952292i	$-0.598719\pi$
$727$	−16.4575			−0.610375			−0.305188	+	0.952292i	$0.598719\pi$
$728$	1.32288	−	2.29129i	0.0490290	−	0.0849208i
$729$		0			0
$730$	24.8745	−	43.0839i	0.920647	−	1.59461i
$731$	17.5830	+	30.4547i	0.650331	+	1.12641i
$732$		0			0
$733$	−7.11438	+	12.3225i	−0.262776	+	0.455141i	−0.966978	−	0.254858i	$-0.917971\pi$
$733$	−7.11438	+	12.3225i	−0.262776	+	0.455141i	0.704203	+	0.709999i	$0.251305\pi$
$734$	−0.583005			−0.0215191
$735$		0			0
$736$	2.35425			0.0867788
$737$	2.44837	−	4.24070i	0.0901868	−	0.156208i
$738$		0			0
$739$	8.64575	+	14.9749i	0.318039	+	0.550860i	0.980079	−	0.198609i	$-0.0636423\pi$
$739$	8.64575	+	14.9749i	0.318039	+	0.550860i	−0.662040	+	0.749469i	$0.730309\pi$
$740$	−10.2915	+	17.8254i	−0.378323	+	0.655275i
$741$		0			0
$742$	3.96863	−	6.87386i	0.145693	−	0.252347i
$743$	51.4575			1.88779			0.943897	−	0.330241i	$-0.107130\pi$
$743$	51.4575			1.88779			0.943897	+	0.330241i	$0.107130\pi$
$744$		0			0
$745$	−12.8745	−	22.2993i	−0.471685	−	0.816983i
$746$	−7.32288	−	12.6836i	−0.268110	−	0.464379i
$747$		0			0
$748$	−4.29150			−0.156913
$749$	15.8745	+	27.4955i	0.580042	+	1.00466i
$750$		0			0
$751$	16.5830	−	28.7226i	0.605122	−	1.04810i	−0.386910	−	0.922118i	$-0.626457\pi$
$751$	16.5830	−	28.7226i	0.605122	−	1.04810i	0.992032	−	0.125985i	$-0.0402092\pi$
$752$	1.50000	+	2.59808i	0.0546994	+	0.0947421i
$753$		0			0
$754$	2.14575	−	3.71655i	0.0781437	−	0.135349i
$755$	22.1033			0.804420
$756$		0			0
$757$	26.6458			0.968456			0.484228	−	0.874942i	$-0.339100\pi$
$757$	26.6458			0.968456			0.484228	+	0.874942i	$0.339100\pi$
$758$	4.58301	−	7.93800i	0.166462	−	0.288321i
$759$		0			0
$760$	−9.11438	−	15.7866i	−0.330613	−	0.572639i
$761$	3.64575	−	6.31463i	0.132158	−	0.228905i	−0.792350	−	0.610067i	$-0.791143\pi$
$761$	3.64575	−	6.31463i	0.132158	−	0.228905i	0.924508	+	0.381162i	$0.124476\pi$
$762$		0			0
$763$	10.5830			0.383131
$764$		0			0
$765$		0			0
$766$	12.8745	+	22.2993i	0.465175	+	0.805707i
$767$	−3.96863	−	6.87386i	−0.143299	−	0.248201i
$768$		0			0
$769$	5.64575			0.203591			0.101795	−	0.994805i	$-0.467541\pi$
$769$	5.64575			0.203591			0.101795	+	0.994805i	$0.467541\pi$
$770$	−3.11438	−	5.39426i	−0.112234	−	0.194396i
$771$		0			0
$772$	−9.46863	+	16.4001i	−0.340783	+	0.590254i
$773$	20.1660	+	34.9286i	0.725321	+	1.25629i	0.958842	+	0.283941i	$0.0916420\pi$
$773$	20.1660	+	34.9286i	0.725321	+	1.25629i	−0.233521	+	0.972352i	$0.575025\pi$
$774$		0			0
$775$	−13.6458	+	23.6351i	−0.490170	+	0.848999i
$776$	0.937254			0.0336455
$777$		0			0
$778$	−7.70850			−0.276363
$779$	−5.88562	+	10.1942i	−0.210874	+	0.365245i
$780$		0			0
$781$	−5.26013	−	9.11081i	−0.188222	−	0.326010i
$782$	−7.82288	+	13.5496i	−0.279745	+	0.484533i
$783$		0			0
$784$	7.00000			0.250000
$785$	9.64575			0.344272
$786$		0

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +(1.32288 - 2.29129i) q^{7} +1.00000 q^{8} +(-1.82288 - 3.15731i) q^{10} +(0.322876 + 0.559237i) q^{11} +1.00000 q^{13} +(1.32288 + 2.29129i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.32288 - 5.75539i) q^{17} +(-2.50000 + 4.33013i) q^{19} +3.64575 q^{20} -0.645751 q^{22} +(-1.17712 + 2.03884i) q^{23} +(-4.14575 - 7.18065i) q^{25} +(-0.500000 + 0.866025i) q^{26} -2.64575 q^{28} -4.29150 q^{29} +(-1.64575 - 2.85052i) q^{31} +(-0.500000 - 0.866025i) q^{32} +6.64575 q^{34} +(4.82288 + 8.35347i) q^{35} +(-2.82288 + 4.88936i) q^{37} +(-2.50000 - 4.33013i) q^{38} +(-1.82288 + 3.15731i) q^{40} +2.35425 q^{41} -5.29150 q^{43} +(0.322876 - 0.559237i) q^{44} +(-1.17712 - 2.03884i) q^{46} +(1.50000 - 2.59808i) q^{47} +(-3.50000 - 6.06218i) q^{49} +8.29150 q^{50} +(-0.500000 - 0.866025i) q^{52} +(-1.50000 - 2.59808i) q^{53} -2.35425 q^{55} +(1.32288 - 2.29129i) q^{56} +(2.14575 - 3.71655i) q^{58} +(-3.96863 - 6.87386i) q^{59} +(5.96863 - 10.3380i) q^{61} +3.29150 q^{62} +1.00000 q^{64} +(-1.82288 + 3.15731i) q^{65} +(-3.79150 - 6.56708i) q^{67} +(-3.32288 + 5.75539i) q^{68} -9.64575 q^{70} -16.2915 q^{71} +(6.82288 + 11.8176i) q^{73} +(-2.82288 - 4.88936i) q^{74} +5.00000 q^{76} +1.70850 q^{77} +(5.00000 - 8.66025i) q^{79} +(-1.82288 - 3.15731i) q^{80} +(-1.17712 + 2.03884i) q^{82} +13.2915 q^{83} +24.2288 q^{85} +(2.64575 - 4.58258i) q^{86} +(0.322876 + 0.559237i) q^{88} +(8.46863 - 14.6681i) q^{89} +(1.32288 - 2.29129i) q^{91} +2.35425 q^{92} +(1.50000 + 2.59808i) q^{94} +(-9.11438 - 15.7866i) q^{95} +0.937254 q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{8} - 2 q^{10} - 4 q^{11} + 4 q^{13} - 2 q^{16} - 8 q^{17} - 10 q^{19} + 4 q^{20} + 8 q^{22} - 10 q^{23} - 6 q^{25} - 2 q^{26} + 4 q^{29} + 4 q^{31} - 2 q^{32} + 16 q^{34} + 14 q^{35} - 6 q^{37} - 10 q^{38} - 2 q^{40} + 20 q^{41} - 4 q^{44} - 10 q^{46} + 6 q^{47} - 14 q^{49} + 12 q^{50} - 2 q^{52} - 6 q^{53} - 20 q^{55} - 2 q^{58} + 8 q^{61} - 8 q^{62} + 4 q^{64} - 2 q^{65} + 6 q^{67} - 8 q^{68} - 28 q^{70} - 44 q^{71} + 22 q^{73} - 6 q^{74} + 20 q^{76} + 28 q^{77} + 20 q^{79} - 2 q^{80} - 10 q^{82} + 32 q^{83} + 44 q^{85} - 4 q^{88} + 18 q^{89} + 20 q^{92} + 6 q^{94} - 10 q^{95} - 28 q^{97} + 28 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 + 4 * q^8 - 2 * q^10 - 4 * q^11 + 4 * q^13 - 2 * q^16 - 8 * q^17 - 10 * q^19 + 4 * q^20 + 8 * q^22 - 10 * q^23 - 6 * q^25 - 2 * q^26 + 4 * q^29 + 4 * q^31 - 2 * q^32 + 16 * q^34 + 14 * q^35 - 6 * q^37 - 10 * q^38 - 2 * q^40 + 20 * q^41 - 4 * q^44 - 10 * q^46 + 6 * q^47 - 14 * q^49 + 12 * q^50 - 2 * q^52 - 6 * q^53 - 20 * q^55 - 2 * q^58 + 8 * q^61 - 8 * q^62 + 4 * q^64 - 2 * q^65 + 6 * q^67 - 8 * q^68 - 28 * q^70 - 44 * q^71 + 22 * q^73 - 6 * q^74 + 20 * q^76 + 28 * q^77 + 20 * q^79 - 2 * q^80 - 10 * q^82 + 32 * q^83 + 44 * q^85 - 4 * q^88 + 18 * q^89 + 20 * q^92 + 6 * q^94 - 10 * q^95 - 28 * q^97 + 28 * q^98

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