LMFDB - Embedded newform 2106.2.e.e.1405.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2106,2,Mod(703,2106)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2106, 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("2106.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2106 = 2 \cdot 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2106.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:	$16.8164946657$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1405.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2106.1405
Dual form			2106.2.e.e.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{19} +(-1.00000 - 1.73205i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{26} -2.00000 q^{28} +(-4.00000 - 6.92820i) q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.00000 q^{35} +6.00000 q^{37} +(3.00000 + 5.19615i) q^{38} +(-1.00000 + 1.73205i) q^{40} +(3.00000 - 5.19615i) q^{41} +(4.00000 + 6.92820i) q^{43} +4.00000 q^{44} -4.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} -12.0000 q^{53} +8.00000 q^{55} +(1.00000 + 1.73205i) q^{56} +(-4.00000 + 6.92820i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{70} +16.0000 q^{71} +14.0000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(3.00000 - 5.19615i) q^{76} +(4.00000 - 6.92820i) q^{77} +(2.00000 + 3.46410i) q^{79} +2.00000 q^{80} -6.00000 q^{82} +(-6.00000 - 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{86} +(-2.00000 - 3.46410i) q^{88} +6.00000 q^{89} +2.00000 q^{91} +(2.00000 + 3.46410i) q^{92} +(4.00000 - 6.92820i) q^{94} +(6.00000 - 10.3923i) q^{95} +(5.00000 + 8.66025i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{8} + 4 q^{10} - 4 q^{11} + q^{13} + 2 q^{14} - q^{16} - 12 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23} + q^{25} - 2 q^{26} - 4 q^{28} - 8 q^{29} + 2 q^{31} - q^{32} - 8 q^{35} + 12 q^{37} + 6 q^{38} - 2 q^{40} + 6 q^{41} + 8 q^{43} + 8 q^{44} - 8 q^{46} + 8 q^{47} + 3 q^{49} + q^{50} + q^{52} - 24 q^{53} + 16 q^{55} + 2 q^{56} - 8 q^{58} + 4 q^{59} - 10 q^{61} - 4 q^{62} + 2 q^{64} + 2 q^{65} + 2 q^{67} + 4 q^{70} + 32 q^{71} + 28 q^{73} - 6 q^{74} + 6 q^{76} + 8 q^{77} + 4 q^{79} + 4 q^{80} - 12 q^{82} - 12 q^{83} + 8 q^{86} - 4 q^{88} + 12 q^{89} + 4 q^{91} + 4 q^{92} + 8 q^{94} + 12 q^{95} + 10 q^{97} - 6 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 + 2 * q^8 + 4 * q^10 - 4 * q^11 + q^13 + 2 * q^14 - q^16 - 12 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 + q^25 - 2 * q^26 - 4 * q^28 - 8 * q^29 + 2 * q^31 - q^32 - 8 * q^35 + 12 * q^37 + 6 * q^38 - 2 * q^40 + 6 * q^41 + 8 * q^43 + 8 * q^44 - 8 * q^46 + 8 * q^47 + 3 * q^49 + q^50 + q^52 - 24 * q^53 + 16 * q^55 + 2 * q^56 - 8 * q^58 + 4 * q^59 - 10 * q^61 - 4 * q^62 + 2 * q^64 + 2 * q^65 + 2 * q^67 + 4 * q^70 + 32 * q^71 + 28 * q^73 - 6 * q^74 + 6 * q^76 + 8 * q^77 + 4 * q^79 + 4 * q^80 - 12 * q^82 - 12 * q^83 + 8 * q^86 - 4 * q^88 + 12 * q^89 + 4 * q^91 + 4 * q^92 + 8 * q^94 + 12 * q^95 + 10 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2106\mathbb{Z}\right)^\times$.

$n$	$1379$	$1783$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	2.00000			0.632456
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	1.00000	−	1.73205i	0.267261	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$		0			0
$22$	−2.00000	+	3.46410i	−0.426401	+	0.738549i
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.00000			−0.196116
$27$		0			0
$28$	−2.00000			−0.377964
$29$	−4.00000	−	6.92820i	−0.742781	−	1.28654i	−0.951224	−	0.308500i	$-0.900173\pi$
$29$	−4.00000	−	6.92820i	−0.742781	−	1.28654i	0.208443	−	0.978035i	$-0.433160\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$	−4.00000			−0.676123
$36$		0			0
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$	3.00000	+	5.19615i	0.486664	+	0.842927i
$39$		0			0
$40$	−1.00000	+	1.73205i	−0.158114	+	0.273861i
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		0			0
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$	−4.00000			−0.589768
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$		0			0
$58$	−4.00000	+	6.92820i	−0.525226	+	0.909718i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$		0			0
$69$		0			0
$70$	2.00000	+	3.46410i	0.239046	+	0.414039i
$71$	16.0000			1.89885			0.949425	−	0.313993i	$-0.101667\pi$
$71$	16.0000			1.89885			0.949425	+	0.313993i	$0.101667\pi$
$72$		0			0
$73$	14.0000			1.63858			0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000			1.63858			0.819288	+	0.573382i	$0.194369\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$		0			0
$76$	3.00000	−	5.19615i	0.344124	−	0.596040i
$77$	4.00000	−	6.92820i	0.455842	−	0.789542i
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	2.00000			0.223607
$81$		0			0
$82$	−6.00000			−0.662589
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$		0			0
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$	2.00000	+	3.46410i	0.208514	+	0.361158i
$93$		0			0
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$	6.00000	−	10.3923i	0.615587	−	1.06623i
$96$		0			0
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−8.00000	−	13.8564i	−0.796030	−	1.37876i	−0.922183	−	0.386753i	$-0.873597\pi$
$101$	−8.00000	−	13.8564i	−0.796030	−	1.37876i	0.126153	−	0.992011i	$-0.459737\pi$
$102$		0			0
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	0.500000	−	0.866025i	0.0490290	−	0.0849208i
$105$		0			0
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	20.0000			1.93347			0.966736	−	0.255774i	$-0.0823304\pi$
$107$	20.0000			1.93347			0.966736	+	0.255774i	$0.0823304\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$		0			0
$112$	1.00000	−	1.73205i	0.0944911	−	0.163663i
$113$	2.00000	−	3.46410i	0.188144	−	0.325875i	−0.756487	−	0.654008i	$-0.773086\pi$
$113$	2.00000	−	3.46410i	0.188144	−	0.325875i	0.944632	+	0.328133i	$0.106419\pi$
$114$		0			0
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$	8.00000			0.742781
$117$		0			0
$118$	−4.00000			−0.368230
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	−5.00000	+	8.66025i	−0.452679	+	0.784063i
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$		0			0
$133$	−6.00000	−	10.3923i	−0.520266	−	0.901127i
$134$	−2.00000			−0.172774
$135$		0			0
$136$		0			0
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	−0.0346338	−	0.999400i	$-0.511026\pi$
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	0.882823	−	0.469706i	$-0.155640\pi$
$140$	2.00000	−	3.46410i	0.169031	−	0.292770i
$141$		0			0
$142$	−8.00000	−	13.8564i	−0.671345	−	1.16280i
$143$	−4.00000			−0.334497
$144$		0			0
$145$	16.0000			1.32873
$146$	−7.00000	−	12.1244i	−0.579324	−	1.00342i
$147$		0			0
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−9.00000	−	15.5885i	−0.732410	−	1.26857i	−0.955851	−	0.293853i	$-0.905062\pi$
$151$	−9.00000	−	15.5885i	−0.732410	−	1.26857i	0.223441	−	0.974717i	$-0.428271\pi$
$152$	−6.00000			−0.486664
$153$		0			0
$154$	−8.00000			−0.644658
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$		0			0
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	8.00000			0.630488
$162$		0			0
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	3.00000	+	5.19615i	0.234261	+	0.405751i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$		0			0
$172$	−8.00000			−0.609994
$173$	8.00000	+	13.8564i	0.608229	+	1.05348i	0.991532	+	0.129861i	$0.0414530\pi$
$173$	8.00000	+	13.8564i	0.608229	+	1.05348i	−0.383304	+	0.923622i	$0.625214\pi$
$174$		0			0
$175$	−1.00000	+	1.73205i	−0.0755929	+	0.130931i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$		0			0
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$	−1.00000	−	1.73205i	−0.0741249	−	0.128388i
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−6.00000	+	10.3923i	−0.441129	+	0.764057i
$186$		0			0
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−12.0000			−0.870572
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$		0			0
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$		0			0
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$		0			0
$202$	−8.00000	+	13.8564i	−0.562878	+	0.974933i
$203$	8.00000	−	13.8564i	0.561490	−	0.972529i
$204$		0			0
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$	4.00000			0.278693
$207$		0			0
$208$	−1.00000			−0.0693375
$209$	12.0000	+	20.7846i	0.830057	+	1.43770i
$210$		0			0
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$		0			0
$214$	−10.0000	−	17.3205i	−0.683586	−	1.18401i
$215$	−16.0000			−1.09119
$216$		0			0
$217$	4.00000			0.271538
$218$	−5.00000	−	8.66025i	−0.338643	−	0.586546i
$219$		0			0
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$		0			0
$222$		0			0
$223$	−3.00000	−	5.19615i	−0.200895	−	0.347960i	0.747922	−	0.663786i	$-0.231052\pi$
$223$	−3.00000	−	5.19615i	−0.200895	−	0.347960i	−0.948817	+	0.315826i	$0.897718\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$	−4.00000			−0.266076
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$		0			0
$229$	15.0000	−	25.9808i	0.991228	−	1.71686i	0.381157	−	0.924510i	$-0.375526\pi$
$229$	15.0000	−	25.9808i	0.991228	−	1.71686i	0.610071	−	0.792347i	$-0.291141\pi$
$230$	4.00000	−	6.92820i	0.263752	−	0.456832i
$231$		0			0
$232$	−4.00000	−	6.92820i	−0.262613	−	0.454859i
$233$	−20.0000			−1.31024			−0.655122	−	0.755523i	$-0.727383\pi$
$233$	−20.0000			−1.31024			−0.655122	+	0.755523i	$0.727383\pi$
$234$		0			0
$235$	−16.0000			−1.04372
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$		0			0
$238$		0			0
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$		0			0
$241$	−3.00000	−	5.19615i	−0.193247	−	0.334714i	0.753077	−	0.657932i	$-0.228569\pi$
$241$	−3.00000	−	5.19615i	−0.193247	−	0.334714i	−0.946324	+	0.323218i	$0.895235\pi$
$242$	5.00000			0.321412
$243$		0			0
$244$	10.0000			0.640184
$245$	3.00000	+	5.19615i	0.191663	+	0.331970i
$246$		0			0
$247$	−3.00000	+	5.19615i	−0.190885	+	0.330623i
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$		0			0
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−16.0000			−1.00591
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	−0.615948	−	0.787787i	$-0.711227\pi$
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	0.990217	+	0.139533i	$0.0445601\pi$
$258$		0			0
$259$	6.00000	+	10.3923i	0.372822	+	0.645746i
$260$	−2.00000			−0.124035
$261$		0			0
$262$	−4.00000			−0.247121
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	12.0000	−	20.7846i	0.737154	−	1.27679i
$266$	−6.00000	+	10.3923i	−0.367884	+	0.637193i
$267$		0			0
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$	22.0000			1.33640			0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000			1.33640			0.668202	+	0.743980i	$0.267064\pi$
$272$		0			0
$273$		0			0
$274$	−9.00000	+	15.5885i	−0.543710	+	0.941733i
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	3.00000	+	5.19615i	0.180253	+	0.312207i	0.941966	−	0.335707i	$-0.108975\pi$
$277$	3.00000	+	5.19615i	0.180253	+	0.312207i	−0.761714	+	0.647913i	$0.775642\pi$
$278$	−20.0000			−1.19952
$279$		0			0
$280$	−4.00000			−0.239046
$281$	−5.00000	−	8.66025i	−0.298275	−	0.516627i	0.677466	−	0.735554i	$-0.263078\pi$
$281$	−5.00000	−	8.66025i	−0.298275	−	0.516627i	−0.975741	+	0.218926i	$0.929745\pi$
$282$		0			0
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$	−8.00000	+	13.8564i	−0.474713	+	0.822226i
$285$		0			0
$286$	2.00000	+	3.46410i	0.118262	+	0.204837i
$287$	12.0000			0.708338
$288$		0			0
$289$	−17.0000			−1.00000
$290$	−8.00000	−	13.8564i	−0.469776	−	0.813676i
$291$		0			0
$292$	−7.00000	+	12.1244i	−0.409644	+	0.709524i
$293$	1.00000	−	1.73205i	0.0584206	−	0.101187i	−0.835336	−	0.549740i	$-0.814727\pi$
$293$	1.00000	−	1.73205i	0.0584206	−	0.101187i	0.893757	+	0.448552i	$0.148060\pi$
$294$		0			0
$295$	4.00000	+	6.92820i	0.232889	+	0.403376i
$296$	6.00000			0.348743
$297$		0			0
$298$	6.00000			0.347571
$299$	−2.00000	−	3.46410i	−0.115663	−	0.200334i
$300$		0			0
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$	−9.00000	+	15.5885i	−0.517892	+	0.897015i
$303$		0			0
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$	20.0000			1.14520
$306$		0			0
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	4.00000	+	6.92820i	0.227921	+	0.394771i
$309$		0			0
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$		0			0
$313$	−13.0000	−	22.5167i	−0.734803	−	1.27272i	−0.954810	−	0.297218i	$-0.903941\pi$
$313$	−13.0000	−	22.5167i	−0.734803	−	1.27272i	0.220006	−	0.975499i	$-0.429392\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	−4.00000			−0.225018
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$		0			0
$319$	−16.0000	+	27.7128i	−0.895828	+	1.55162i
$320$	−1.00000	+	1.73205i	−0.0559017	+	0.0968246i
$321$		0			0
$322$	−4.00000	−	6.92820i	−0.222911	−	0.386094i
$323$		0			0
$324$		0			0
$325$	1.00000			0.0554700
$326$	5.00000	+	8.66025i	0.276924	+	0.479647i
$327$		0			0
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	−8.00000	+	13.8564i	−0.441054	+	0.763928i
$330$		0			0
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	0.970091	−	0.242742i	$-0.0780468\pi$
$331$	5.00000	+	8.66025i	0.274825	+	0.476011i	−0.695266	+	0.718752i	$0.744713\pi$
$332$	12.0000			0.658586
$333$		0			0
$334$		0			0
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$		0			0
$337$	17.0000	−	29.4449i	0.926049	−	1.60396i	0.136184	−	0.990684i	$-0.456516\pi$
$337$	17.0000	−	29.4449i	0.926049	−	1.60396i	0.789865	−	0.613280i	$-0.210150\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$		0			0
$340$		0			0
$341$	−8.00000			−0.433224
$342$		0			0
$343$	20.0000			1.07990
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	8.00000	−	13.8564i	0.430083	−	0.744925i
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	0.340293	+	0.940319i	$0.389474\pi$
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	−0.984487	+	0.175457i	$0.943860\pi$
$348$		0			0
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	−0.994388	−	0.105797i	$-0.966261\pi$
$349$	−11.0000	−	19.0526i	−0.588817	−	1.01986i	0.405571	−	0.914063i	$-0.367073\pi$
$350$	2.00000			0.106904
$351$		0			0
$352$	4.00000			0.213201
$353$	7.00000	+	12.1244i	0.372572	+	0.645314i	0.989960	−	0.141344i	$-0.0451425\pi$
$353$	7.00000	+	12.1244i	0.372572	+	0.645314i	−0.617388	+	0.786659i	$0.711809\pi$
$354$		0			0
$355$	−16.0000	+	27.7128i	−0.849192	+	1.47084i
$356$	−3.00000	+	5.19615i	−0.159000	+	0.275396i
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	9.00000	+	15.5885i	0.473029	+	0.819311i
$363$		0			0
$364$	−1.00000	+	1.73205i	−0.0524142	+	0.0907841i
$365$	−14.0000	+	24.2487i	−0.732793	+	1.26924i
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$	12.0000			0.623850
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$		0			0
$376$	4.00000	+	6.92820i	0.206284	+	0.357295i
$377$	−8.00000			−0.412021
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	6.00000	+	10.3923i	0.307794	+	0.533114i
$381$		0			0
$382$	−2.00000	+	3.46410i	−0.102329	+	0.177239i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$	8.00000	+	13.8564i	0.407718	+	0.706188i
$386$	2.00000			0.101797
$387$		0			0
$388$	−10.0000			−0.507673
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	0.672874	−	0.739758i	$-0.265060\pi$
$389$	−6.00000	−	10.3923i	−0.304212	−	0.526911i	−0.977086	+	0.212847i	$0.931726\pi$
$390$		0			0
$391$		0			0
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$		0			0
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	−8.00000			−0.402524
$396$		0			0
$397$	−10.0000			−0.501886			−0.250943	−	0.968002i	$-0.580741\pi$
$397$	−10.0000			−0.501886			−0.250943	+	0.968002i	$0.580741\pi$
$398$	−4.00000	−	6.92820i	−0.200502	−	0.347279i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$		0			0
$403$	−1.00000	−	1.73205i	−0.0498135	−	0.0862796i
$404$	16.0000			0.796030
$405$		0			0
$406$	−16.0000			−0.794067
$407$	−12.0000	−	20.7846i	−0.594818	−	1.03025i
$408$		0			0
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$	6.00000	−	10.3923i	0.296319	−	0.513239i
$411$		0			0
$412$	−2.00000	−	3.46410i	−0.0985329	−	0.170664i
$413$	8.00000			0.393654
$414$		0			0
$415$	24.0000			1.17811
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$		0			0
$418$	12.0000	−	20.7846i	0.586939	−	1.01661i
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.0273103	−	0.999627i	$-0.491306\pi$
$419$	18.0000	−	31.1769i	0.879358	−	1.52309i	0.852047	−	0.523465i	$-0.175361\pi$
$420$		0			0
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	0.718076	−	0.695965i	$-0.245023\pi$
$421$	−5.00000	−	8.66025i	−0.243685	−	0.422075i	−0.961761	+	0.273890i	$0.911690\pi$
$422$	8.00000			0.389434
$423$		0			0
$424$	−12.0000			−0.582772
$425$		0			0
$426$		0			0
$427$	10.0000	−	17.3205i	0.483934	−	0.838198i
$428$	−10.0000	+	17.3205i	−0.483368	+	0.837218i
$429$		0			0
$430$	8.00000	+	13.8564i	0.385794	+	0.668215i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$	−2.00000	−	3.46410i	−0.0960031	−	0.166282i
$435$		0			0
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	−12.0000	+	20.7846i	−0.574038	+	0.994263i
$438$		0			0
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	0.909798	−	0.415051i	$-0.136236\pi$
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	−0.814344	+	0.580383i	$0.802903\pi$
$440$	8.00000			0.381385
$441$		0			0
$442$		0			0
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	0.876454	+	0.481486i	$0.159903\pi$
$443$	18.0000	+	31.1769i	0.855206	+	1.48126i	−0.0212481	+	0.999774i	$0.506764\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	−3.00000	+	5.19615i	−0.142054	+	0.246045i
$447$		0			0
$448$	1.00000	+	1.73205i	0.0472456	+	0.0818317i
$449$	−26.0000			−1.22702			−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000			−1.22702			−0.613508	+	0.789689i	$0.710242\pi$
$450$		0			0
$451$	−24.0000			−1.13012
$452$	2.00000	+	3.46410i	0.0940721	+	0.162938i
$453$		0			0
$454$	6.00000	−	10.3923i	0.281594	−	0.487735i
$455$	−2.00000	+	3.46410i	−0.0937614	+	0.162400i
$456$		0			0
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	0.888466	−	0.458942i	$-0.151771\pi$
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	−0.841688	+	0.539964i	$0.818438\pi$
$458$	−30.0000			−1.40181
$459$		0			0
$460$	−8.00000			−0.373002
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$	−11.0000	+	19.0526i	−0.511213	+	0.885448i	0.488702	+	0.872451i	$0.337470\pi$
$463$	−11.0000	+	19.0526i	−0.511213	+	0.885448i	−0.999916	+	0.0129968i	$0.995863\pi$
$464$	−4.00000	+	6.92820i	−0.185695	+	0.321634i
$465$		0			0
$466$	10.0000	+	17.3205i	0.463241	+	0.802357i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	4.00000			0.184703
$470$	8.00000	+	13.8564i	0.369012	+	0.639148i
$471$		0			0
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	16.0000	−	27.7128i	0.735681	−	1.27424i
$474$		0			0
$475$	−3.00000	−	5.19615i	−0.137649	−	0.238416i
$476$		0			0
$477$		0			0
$478$	24.0000			1.09773
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$	3.00000	−	5.19615i	0.136788	−	0.236924i
$482$	−3.00000	+	5.19615i	−0.136646	+	0.236678i
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−20.0000			−0.908153
$486$		0			0
$487$	38.0000			1.72194			0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000			1.72194			0.860972	+	0.508652i	$0.169856\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$		0			0
$490$	3.00000	−	5.19615i	0.135526	−	0.234738i
$491$	−8.00000	+	13.8564i	−0.361035	+	0.625331i	−0.988131	−	0.153611i	$-0.950910\pi$
$491$	−8.00000	+	13.8564i	−0.361035	+	0.625331i	0.627096	+	0.778942i	$0.284243\pi$
$492$		0			0
$493$		0			0
$494$	6.00000			0.269953
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	16.0000	+	27.7128i	0.717698	+	1.24309i
$498$		0			0
$499$	−11.0000	+	19.0526i	−0.492428	+	0.852910i	−0.999962	−	0.00872186i	$-0.997224\pi$
$499$	−11.0000	+	19.0526i	−0.492428	+	0.852910i	0.507534	+	0.861632i	$0.330557\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$		0			0
$502$		0			0
$503$	−32.0000			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$504$		0			0
$505$	32.0000			1.42398
$506$	8.00000	+	13.8564i	0.355643	+	0.615992i
$507$		0			0
$508$	4.00000	−	6.92820i	0.177471	−	0.307389i
$509$	−5.00000	+	8.66025i	−0.221621	+	0.383859i	−0.955300	−	0.295637i	$-0.904468\pi$
$509$	−5.00000	+	8.66025i	−0.221621	+	0.383859i	0.733679	+	0.679496i	$0.237801\pi$
$510$		0			0
$511$	14.0000	+	24.2487i	0.619324	+	1.07270i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−12.0000			−0.529297
$515$	−4.00000	−	6.92820i	−0.176261	−	0.305293i
$516$		0			0
$517$	16.0000	−	27.7128i	0.703679	−	1.21881i
$518$	6.00000	−	10.3923i	0.263625	−	0.456612i
$519$		0			0
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	36.0000			1.57719			0.788594	−	0.614914i	$-0.210809\pi$
$521$	36.0000			1.57719			0.788594	+	0.614914i	$0.210809\pi$
$522$		0			0
$523$	−12.0000			−0.524723			−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000			−0.524723			−0.262362	+	0.964970i	$0.584501\pi$
$524$	2.00000	+	3.46410i	0.0873704	+	0.151330i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−24.0000			−1.04249
$531$		0			0
$532$	12.0000			0.520266
$533$	−3.00000	−	5.19615i	−0.129944	−	0.225070i
$534$		0			0
$535$	−20.0000	+	34.6410i	−0.864675	+	1.49766i
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$		0			0
$538$		0			0
$539$	−12.0000			−0.516877
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$	−11.0000	−	19.0526i	−0.472490	−	0.818377i
$543$		0			0
$544$		0			0
$545$	−10.0000	+	17.3205i	−0.428353	+	0.741929i
$546$		0			0
$547$	10.0000	+	17.3205i	0.427569	+	0.740571i	0.996657	−	0.0817056i	$-0.0260367\pi$
$547$	10.0000	+	17.3205i	0.427569	+	0.740571i	−0.569087	+	0.822277i	$0.692703\pi$
$548$	18.0000			0.768922
$549$		0			0
$550$	−4.00000			−0.170561
$551$	24.0000	+	41.5692i	1.02243	+	1.77091i
$552$		0			0
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	3.00000	−	5.19615i	0.127458	−	0.220763i
$555$		0			0
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	−18.0000			−0.762684			−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000			−0.762684			−0.381342	+	0.924434i	$0.624538\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	2.00000	+	3.46410i	0.0845154	+	0.146385i
$561$		0			0
$562$	−5.00000	+	8.66025i	−0.210912	+	0.365311i
$563$	−10.0000	+	17.3205i	−0.421450	+	0.729972i	−0.996082	−	0.0884397i	$-0.971812\pi$
$563$	−10.0000	+	17.3205i	−0.421450	+	0.729972i	0.574632	+	0.818412i	$0.305145\pi$
$564$		0			0
$565$	4.00000	+	6.92820i	0.168281	+	0.291472i
$566$	−20.0000			−0.840663
$567$		0			0
$568$	16.0000			0.671345
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$		0			0
$571$	−18.0000	+	31.1769i	−0.753277	+	1.30471i	0.192950	+	0.981209i	$0.438194\pi$
$571$	−18.0000	+	31.1769i	−0.753277	+	1.30471i	−0.946227	+	0.323505i	$0.895139\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$		0			0
$574$	−6.00000	−	10.3923i	−0.250435	−	0.433766i
$575$	4.00000			0.166812
$576$		0			0
$577$	−30.0000			−1.24892			−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000			−1.24892			−0.624458	+	0.781058i	$0.714680\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$		0			0
$580$	−8.00000	+	13.8564i	−0.332182	+	0.575356i
$581$	12.0000	−	20.7846i	0.497844	−	0.862291i
$582$		0			0
$583$	24.0000	+	41.5692i	0.993978	+	1.72162i
$584$	14.0000			0.579324
$585$		0			0
$586$	−2.00000			−0.0826192
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	0.995726	+	0.0923513i	$0.0294383\pi$
$587$	14.0000	+	24.2487i	0.577842	+	1.00085i	−0.417885	+	0.908500i	$0.637228\pi$
$588$		0			0
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$	4.00000	−	6.92820i	0.164677	−	0.285230i
$591$		0			0
$592$	−3.00000	−	5.19615i	−0.123299	−	0.213561i
$593$	38.0000			1.56047			0.780236	−	0.625485i	$-0.215099\pi$
$593$	38.0000			1.56047			0.780236	+	0.625485i	$0.215099\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	−2.00000	+	3.46410i	−0.0817861	+	0.141658i
$599$	−20.0000	+	34.6410i	−0.817178	+	1.41539i	0.0905757	+	0.995890i	$0.471129\pi$
$599$	−20.0000	+	34.6410i	−0.817178	+	1.41539i	−0.907754	+	0.419504i	$0.862204\pi$
$600$		0			0
$601$	−5.00000	−	8.66025i	−0.203954	−	0.353259i	0.745845	−	0.666120i	$-0.232046\pi$
$601$	−5.00000	−	8.66025i	−0.203954	−	0.353259i	−0.949799	+	0.312861i	$0.898713\pi$
$602$	16.0000			0.652111
$603$		0			0
$604$	18.0000			0.732410
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$		0			0
$607$	−12.0000	+	20.7846i	−0.487065	+	0.843621i	−0.999889	−	0.0148722i	$-0.995266\pi$
$607$	−12.0000	+	20.7846i	−0.487065	+	0.843621i	0.512824	+	0.858494i	$0.328599\pi$
$608$	3.00000	−	5.19615i	0.121666	−	0.210732i
$609$		0			0
$610$	−10.0000	−	17.3205i	−0.404888	−	0.701287i
$611$	8.00000			0.323645
$612$		0			0
$613$	−34.0000			−1.37325			−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000			−1.37325			−0.686624	+	0.727013i	$0.740908\pi$
$614$	−1.00000	−	1.73205i	−0.0403567	−	0.0698999i
$615$		0			0
$616$	4.00000	−	6.92820i	0.161165	−	0.279145i
$617$	7.00000	−	12.1244i	0.281809	−	0.488108i	−0.690021	−	0.723789i	$-0.742399\pi$
$617$	7.00000	−	12.1244i	0.281809	−	0.488108i	0.971830	+	0.235681i	$0.0757321\pi$
$618$		0			0
$619$	−17.0000	−	29.4449i	−0.683288	−	1.18349i	−0.973972	−	0.226670i	$-0.927216\pi$
$619$	−17.0000	−	29.4449i	−0.683288	−	1.18349i	0.290684	−	0.956819i	$-0.406117\pi$
$620$	−4.00000			−0.160644
$621$		0			0
$622$	12.0000			0.481156
$623$	6.00000	+	10.3923i	0.240385	+	0.416359i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−13.0000	+	22.5167i	−0.519584	+	0.899947i
$627$		0			0
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$		0			0
$630$		0			0
$631$	−14.0000			−0.557331			−0.278666	−	0.960388i	$-0.589892\pi$
$631$	−14.0000			−0.557331			−0.278666	+	0.960388i	$0.589892\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$		0			0
$634$	3.00000	−	5.19615i	0.119145	−	0.206366i
$635$	8.00000	−	13.8564i	0.317470	−	0.549875i
$636$		0			0
$637$	−1.50000	−	2.59808i	−0.0594322	−	0.102940i
$638$	32.0000			1.26689
$639$		0			0
$640$	2.00000			0.0790569
$641$	−20.0000	−	34.6410i	−0.789953	−	1.36824i	−0.925995	−	0.377535i	$-0.876772\pi$
$641$	−20.0000	−	34.6410i	−0.789953	−	1.36824i	0.136043	−	0.990703i	$-0.456562\pi$
$642$		0			0
$643$	5.00000	−	8.66025i	0.197181	−	0.341527i	−0.750432	−	0.660947i	$-0.770155\pi$
$643$	5.00000	−	8.66025i	0.197181	−	0.341527i	0.947613	+	0.319420i	$0.103488\pi$
$644$	−4.00000	+	6.92820i	−0.157622	+	0.273009i
$645$		0			0
$646$		0			0
$647$	−8.00000			−0.314512			−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000			−0.314512			−0.157256	+	0.987558i	$0.550265\pi$
$648$		0			0
$649$	−16.0000			−0.628055
$650$	−0.500000	−	0.866025i	−0.0196116	−	0.0339683i
$651$		0			0
$652$	5.00000	−	8.66025i	0.195815	−	0.339162i
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$		0			0
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$	−6.00000			−0.234261
$657$		0			0
$658$	16.0000			0.623745
$659$	−24.0000	−	41.5692i	−0.934907	−	1.61931i	−0.774799	−	0.632207i	$-0.782149\pi$
$659$	−24.0000	−	41.5692i	−0.934907	−	1.61931i	−0.160108	−	0.987099i	$-0.551184\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	5.00000	−	8.66025i	0.194331	−	0.336590i
$663$		0			0
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	24.0000			0.930680
$666$		0			0
$667$	−32.0000			−1.23904
$668$		0			0
$669$		0			0
$670$	2.00000	−	3.46410i	0.0772667	−	0.133830i
$671$	−20.0000	+	34.6410i	−0.772091	+	1.33730i
$672$		0			0
$673$	−11.0000	−	19.0526i	−0.424019	−	0.734422i	0.572309	−	0.820038i	$-0.306048\pi$
$673$	−11.0000	−	19.0526i	−0.424019	−	0.734422i	−0.996328	+	0.0856156i	$0.972714\pi$
$674$	−34.0000			−1.30963
$675$		0			0
$676$	1.00000			0.0384615
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	0.727386	−	0.686229i	$-0.240735\pi$
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$678$		0			0
$679$	−10.0000	+	17.3205i	−0.383765	+	0.664700i
$680$		0			0
$681$		0			0
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	4.00000			0.153056			0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000			0.153056			0.0765279	+	0.997067i	$0.475617\pi$
$684$		0			0
$685$	36.0000			1.37549
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$		0			0
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	13.0000	+	22.5167i	0.494543	+	0.856574i	0.999980	−	0.00628943i	$-0.00200200\pi$
$691$	13.0000	+	22.5167i	0.494543	+	0.856574i	−0.505437	+	0.862864i	$0.668669\pi$
$692$	−16.0000			−0.608229
$693$		0			0
$694$	24.0000			0.911028
$695$	20.0000	+	34.6410i	0.758643	+	1.31401i
$696$		0			0
$697$		0			0
$698$	−11.0000	+	19.0526i	−0.416356	+	0.721150i
$699$		0			0
$700$	−1.00000	−	1.73205i	−0.0377964	−	0.0654654i
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		0			0
$703$	−36.0000			−1.35777
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$		0			0
$706$	7.00000	−	12.1244i	0.263448	−	0.456306i
$707$	16.0000	−	27.7128i	0.601742	−	1.04225i
$708$		0			0
$709$	11.0000	+	19.0526i	0.413114	+	0.715534i	0.995228	−	0.0975728i	$-0.0311079\pi$
$709$	11.0000	+	19.0526i	0.413114	+	0.715534i	−0.582115	+	0.813107i	$0.697775\pi$
$710$	32.0000			1.20094
$711$		0			0
$712$	6.00000			0.224860
$713$	−4.00000	−	6.92820i	−0.149801	−	0.259463i
$714$		0			0
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$		0			0
$719$	−28.0000			−1.04422			−0.522112	−	0.852877i	$-0.674856\pi$
$719$	−28.0000			−1.04422			−0.522112	+	0.852877i	$0.674856\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	−8.50000	−	14.7224i	−0.316337	−	0.547912i
$723$		0			0
$724$	9.00000	−	15.5885i	0.334482	−	0.579340i
$725$	4.00000	−	6.92820i	0.148556	−	0.257307i
$726$		0			0
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$	2.00000			0.0741249
$729$		0			0
$730$	28.0000			1.03633
$731$		0			0
$732$		0			0
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$		0			0
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$	−8.00000			−0.294684
$738$		0			0
$739$	−54.0000			−1.98642			−0.993211	−	0.116326i	$-0.962888\pi$
$739$	−54.0000			−1.98642			−0.993211	+	0.116326i	$0.962888\pi$
$740$	−6.00000	−	10.3923i	−0.220564	−	0.382029i
$741$		0			0
$742$	−12.0000	+	20.7846i	−0.440534	+	0.763027i
$743$	−20.0000	+	34.6410i	−0.733729	+	1.27086i	0.221550	+	0.975149i	$0.428888\pi$
$743$	−20.0000	+	34.6410i	−0.733729	+	1.27086i	−0.955279	+	0.295707i	$0.904445\pi$
$744$		0			0
$745$	−6.00000	−	10.3923i	−0.219823	−	0.380745i
$746$	−10.0000			−0.366126
$747$		0			0
$748$		0			0
$749$	20.0000	+	34.6410i	0.730784	+	1.26576i
$750$		0			0
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	−0.735542	−	0.677479i	$-0.763072\pi$
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	0.954485	+	0.298259i	$0.0964058\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$		0			0
$754$	4.00000	+	6.92820i	0.145671	+	0.252310i
$755$	36.0000			1.31017
$756$		0			0
$757$	−18.0000			−0.654221			−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000			−0.654221			−0.327111	+	0.944986i	$0.606075\pi$
$758$	−5.00000	−	8.66025i	−0.181608	−	0.314555i
$759$		0			0
$760$	6.00000	−	10.3923i	0.217643	−	0.376969i
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$		0			0
$763$	10.0000	+	17.3205i	0.362024	+	0.627044i
$764$	4.00000			0.144715
$765$		0			0
$766$		0			0
$767$	−2.00000	−	3.46410i	−0.0722158	−	0.125081i
$768$		0			0
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	−0.457938	−	0.888984i	$-0.651412\pi$
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	0.998852	−	0.0479061i	$-0.0152548\pi$
$770$	8.00000	−	13.8564i	0.288300	−	0.499350i
$771$		0			0
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	14.0000			0.503545			0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000			0.503545			0.251773	+	0.967786i	$0.418987\pi$
$774$		0			0
$775$	2.00000			0.0718421
$776$	5.00000	+	8.66025i	0.179490	+	0.310885i
$777$		0			0
$778$	−6.00000	+	10.3923i	−0.215110	+	0.372582i
$779$	−18.0000	+	31.1769i	−0.644917	+	1.11703i
$780$		0			0
$781$	−32.0000	−	55.4256i	−1.14505	−	1.98328i
$782$		0			0
$783$		0			0
$784$	−3.00000			−0.107143
$785$	−2.00000	−	3.46410i	−0.0713831	−	0.123639i
$786$		0			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:	\( N \)	\(=\)	\( 2106 = 2 \cdot 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2106.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +2.00000 q^{10} +(-2.00000 - 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{19} +(-1.00000 - 1.73205i) q^{20} +(-2.00000 + 3.46410i) q^{22} +(2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{26} -2.00000 q^{28} +(-4.00000 - 6.92820i) q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} -4.00000 q^{35} +6.00000 q^{37} +(3.00000 + 5.19615i) q^{38} +(-1.00000 + 1.73205i) q^{40} +(3.00000 - 5.19615i) q^{41} +(4.00000 + 6.92820i) q^{43} +4.00000 q^{44} -4.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.500000 + 0.866025i) q^{52} -12.0000 q^{53} +8.00000 q^{55} +(1.00000 + 1.73205i) q^{56} +(-4.00000 + 6.92820i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(1.00000 - 1.73205i) q^{67} +(2.00000 + 3.46410i) q^{70} +16.0000 q^{71} +14.0000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(3.00000 - 5.19615i) q^{76} +(4.00000 - 6.92820i) q^{77} +(2.00000 + 3.46410i) q^{79} +2.00000 q^{80} -6.00000 q^{82} +(-6.00000 - 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{86} +(-2.00000 - 3.46410i) q^{88} +6.00000 q^{89} +2.00000 q^{91} +(2.00000 + 3.46410i) q^{92} +(4.00000 - 6.92820i) q^{94} +(6.00000 - 10.3923i) q^{95} +(5.00000 + 8.66025i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{8} + 4 q^{10} - 4 q^{11} + q^{13} + 2 q^{14} - q^{16} - 12 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23} + q^{25} - 2 q^{26} - 4 q^{28} - 8 q^{29} + 2 q^{31} - q^{32} - 8 q^{35} + 12 q^{37} + 6 q^{38} - 2 q^{40} + 6 q^{41} + 8 q^{43} + 8 q^{44} - 8 q^{46} + 8 q^{47} + 3 q^{49} + q^{50} + q^{52} - 24 q^{53} + 16 q^{55} + 2 q^{56} - 8 q^{58} + 4 q^{59} - 10 q^{61} - 4 q^{62} + 2 q^{64} + 2 q^{65} + 2 q^{67} + 4 q^{70} + 32 q^{71} + 28 q^{73} - 6 q^{74} + 6 q^{76} + 8 q^{77} + 4 q^{79} + 4 q^{80} - 12 q^{82} - 12 q^{83} + 8 q^{86} - 4 q^{88} + 12 q^{89} + 4 q^{91} + 4 q^{92} + 8 q^{94} + 12 q^{95} + 10 q^{97} - 6 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 + 2 * q^8 + 4 * q^10 - 4 * q^11 + q^13 + 2 * q^14 - q^16 - 12 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 + q^25 - 2 * q^26 - 4 * q^28 - 8 * q^29 + 2 * q^31 - q^32 - 8 * q^35 + 12 * q^37 + 6 * q^38 - 2 * q^40 + 6 * q^41 + 8 * q^43 + 8 * q^44 - 8 * q^46 + 8 * q^47 + 3 * q^49 + q^50 + q^52 - 24 * q^53 + 16 * q^55 + 2 * q^56 - 8 * q^58 + 4 * q^59 - 10 * q^61 - 4 * q^62 + 2 * q^64 + 2 * q^65 + 2 * q^67 + 4 * q^70 + 32 * q^71 + 28 * q^73 - 6 * q^74 + 6 * q^76 + 8 * q^77 + 4 * q^79 + 4 * q^80 - 12 * q^82 - 12 * q^83 + 8 * q^86 - 4 * q^88 + 12 * q^89 + 4 * q^91 + 4 * q^92 + 8 * q^94 + 12 * q^95 + 10 * q^97 - 6 * q^98

Introduction

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