LMFDB - Embedded newform 1638.2.bj.d.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

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.bj (of order $6$, 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 $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.d.1135.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.366025 + 0.633975i) q^{10} +(3.23205 - 1.86603i) q^{11} +(-0.866025 + 3.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.133975 + 0.232051i) q^{17} +(3.86603 + 2.23205i) q^{19} +(0.633975 + 0.366025i) q^{20} +(1.86603 - 3.23205i) q^{22} +(-1.73205 - 3.00000i) q^{23} +4.46410 q^{25} +(1.00000 + 3.46410i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +7.66025i q^{31} +(-0.866025 - 0.500000i) q^{32} +0.267949i q^{34} +(-0.366025 + 0.633975i) q^{35} +(1.09808 - 0.633975i) q^{37} +4.46410 q^{38} +0.732051 q^{40} +(6.06218 - 3.50000i) q^{41} +(0.366025 - 0.633975i) q^{43} -3.73205i q^{44} +(-3.00000 - 1.73205i) q^{46} +4.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(3.86603 - 2.23205i) q^{50} +(2.59808 + 2.50000i) q^{52} +10.4641 q^{53} +(1.36603 + 2.36603i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-2.59808 - 1.50000i) q^{58} +(-0.803848 - 0.464102i) q^{59} +(5.86603 - 10.1603i) q^{61} +(3.83013 + 6.63397i) q^{62} -1.00000 q^{64} +(-2.56218 - 0.633975i) q^{65} +(-11.1962 + 6.46410i) q^{67} +(0.133975 + 0.232051i) q^{68} +0.732051i q^{70} +(-1.90192 - 1.09808i) q^{71} -6.53590i q^{73} +(0.633975 - 1.09808i) q^{74} +(3.86603 - 2.23205i) q^{76} +3.73205 q^{77} +10.8564 q^{79} +(0.633975 - 0.366025i) q^{80} +(3.50000 - 6.06218i) q^{82} -5.66025i q^{83} +(-0.169873 - 0.0980762i) q^{85} -0.732051i q^{86} +(-1.86603 - 3.23205i) q^{88} +(-5.59808 + 3.23205i) q^{89} +(-2.50000 + 2.59808i) q^{91} -3.46410 q^{92} +(2.23205 + 3.86603i) q^{94} +(-1.63397 + 2.83013i) q^{95} +(0.633975 + 0.366025i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} - 2 q^{10} + 6 q^{11} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 12 q^{19} + 6 q^{20} + 4 q^{22} + 4 q^{25} + 4 q^{26} - 6 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{38} - 4 q^{40} - 2 q^{43} - 12 q^{46} + 2 q^{49} + 12 q^{50} + 28 q^{53} + 2 q^{55} + 2 q^{56} - 24 q^{59} + 20 q^{61} - 2 q^{62} - 4 q^{64} + 14 q^{65} - 24 q^{67} + 4 q^{68} - 18 q^{71} + 6 q^{74} + 12 q^{76} + 8 q^{77} - 12 q^{79} + 6 q^{80} + 14 q^{82} - 18 q^{85} - 4 q^{88} - 12 q^{89} - 10 q^{91} + 2 q^{94} - 10 q^{95} + 6 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 + 6 * q^11 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 12 * q^19 + 6 * q^20 + 4 * q^22 + 4 * q^25 + 4 * q^26 - 6 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^38 - 4 * q^40 - 2 * q^43 - 12 * q^46 + 2 * q^49 + 12 * q^50 + 28 * q^53 + 2 * q^55 + 2 * q^56 - 24 * q^59 + 20 * q^61 - 2 * q^62 - 4 * q^64 + 14 * q^65 - 24 * q^67 + 4 * q^68 - 18 * q^71 + 6 * q^74 + 12 * q^76 + 8 * q^77 - 12 * q^79 + 6 * q^80 + 14 * q^82 - 18 * q^85 - 4 * q^88 - 12 * q^89 - 10 * q^91 + 2 * q^94 - 10 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			0.732051i			0.327383i	0.986512	+	0.163692i	$0.0523402\pi$
$5$			0.732051i			0.327383i	−0.986512	+	0.163692i	$0.947660\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.366025	+	0.633975i	0.115747	+	0.200480i
$11$	3.23205	−	1.86603i	0.974500	−	0.562628i	0.0738948	−	0.997266i	$-0.476457\pi$
$11$	3.23205	−	1.86603i	0.974500	−	0.562628i	0.900605	+	0.434638i	$0.143124\pi$
$12$		0			0
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$13$	−0.866025	+	3.50000i	−0.240192	+	0.970725i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.133975	+	0.232051i	−0.0324936	+	0.0562806i	−0.881815	−	0.471596i	$-0.843678\pi$
$17$	−0.133975	+	0.232051i	−0.0324936	+	0.0562806i	0.849321	+	0.527876i	$0.177012\pi$
$18$		0			0
$19$	3.86603	+	2.23205i	0.886927	+	0.512068i	0.872936	−	0.487835i	$-0.162213\pi$
$19$	3.86603	+	2.23205i	0.886927	+	0.512068i	0.0139909	+	0.999902i	$0.495546\pi$
$20$	0.633975	+	0.366025i	0.141761	+	0.0818458i
$21$		0			0
$22$	1.86603	−	3.23205i	0.397838	−	0.689076i
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	0.626994	−	0.779024i	$-0.284285\pi$
$23$	−1.73205	−	3.00000i	−0.361158	−	0.625543i	−0.988152	+	0.153481i	$0.950952\pi$
$24$		0			0
$25$	4.46410			0.892820
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$			7.66025i			1.37582i	0.725795	+	0.687911i	$0.241472\pi$
$31$			7.66025i			1.37582i	−0.725795	+	0.687911i	$0.758528\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			0.267949i			0.0459529i
$35$	−0.366025	+	0.633975i	−0.0618696	+	0.107161i
$36$		0			0
$37$	1.09808	−	0.633975i	0.180523	−	0.104225i	−0.407016	−	0.913421i	$-0.633431\pi$
$37$	1.09808	−	0.633975i	0.180523	−	0.104225i	0.587538	+	0.809196i	$0.300097\pi$
$38$	4.46410			0.724173
$39$		0			0
$40$	0.732051			0.115747
$41$	6.06218	−	3.50000i	0.946753	−	0.546608i	0.0546823	−	0.998504i	$-0.482585\pi$
$41$	6.06218	−	3.50000i	0.946753	−	0.546608i	0.892071	+	0.451896i	$0.149252\pi$
$42$		0			0
$43$	0.366025	−	0.633975i	0.0558184	−	0.0966802i	−0.836766	−	0.547561i	$-0.815557\pi$
$43$	0.366025	−	0.633975i	0.0558184	−	0.0966802i	0.892584	+	0.450880i	$0.148890\pi$
$44$		−	3.73205i		−	0.562628i
$45$		0			0
$46$	−3.00000	−	1.73205i	−0.442326	−	0.255377i
$47$			4.46410i			0.651156i	0.945515	+	0.325578i	$0.105559\pi$
$47$			4.46410i			0.651156i	−0.945515	+	0.325578i	$0.894441\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	3.86603	−	2.23205i	0.546739	−	0.315660i
$51$		0			0
$52$	2.59808	+	2.50000i	0.360288	+	0.346688i
$53$	10.4641			1.43735			0.718677	−	0.695344i	$-0.244748\pi$
$53$	10.4641			1.43735			0.718677	+	0.695344i	$0.244748\pi$
$54$		0			0
$55$	1.36603	+	2.36603i	0.184195	+	0.319035i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	−2.59808	−	1.50000i	−0.341144	−	0.196960i
$59$	−0.803848	−	0.464102i	−0.104652	−	0.0604209i	0.446760	−	0.894654i	$-0.352578\pi$
$59$	−0.803848	−	0.464102i	−0.104652	−	0.0604209i	−0.551413	+	0.834233i	$0.685911\pi$
$60$		0			0
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	−0.196238	−	0.980556i	$-0.562873\pi$
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	0.947306	−	0.320331i	$-0.103794\pi$
$62$	3.83013	+	6.63397i	0.486427	+	0.842516i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.56218	−	0.633975i	−0.317799	−	0.0786349i
$66$		0			0
$67$	−11.1962	+	6.46410i	−1.36783	+	0.789716i	−0.990650	−	0.136425i	$-0.956439\pi$
$67$	−11.1962	+	6.46410i	−1.36783	+	0.789716i	−0.377177	+	0.926141i	$0.623105\pi$
$68$	0.133975	+	0.232051i	0.0162468	+	0.0281403i
$69$		0			0
$70$			0.732051i			0.0874968i
$71$	−1.90192	−	1.09808i	−0.225717	−	0.130318i	0.382878	−	0.923799i	$-0.374933\pi$
$71$	−1.90192	−	1.09808i	−0.225717	−	0.130318i	−0.608595	+	0.793481i	$0.708266\pi$
$72$		0			0
$73$		−	6.53590i		−	0.764969i	−0.923962	−	0.382485i	$-0.875069\pi$
$73$		−	6.53590i		−	0.764969i	0.923962	−	0.382485i	$-0.124931\pi$
$74$	0.633975	−	1.09808i	0.0736980	−	0.127649i
$75$		0			0
$76$	3.86603	−	2.23205i	0.443464	−	0.256034i
$77$	3.73205			0.425307
$78$		0			0
$79$	10.8564			1.22144			0.610721	−	0.791846i	$-0.290880\pi$
$79$	10.8564			1.22144			0.610721	+	0.791846i	$0.290880\pi$
$80$	0.633975	−	0.366025i	0.0708805	−	0.0409229i
$81$		0			0
$82$	3.50000	−	6.06218i	0.386510	−	0.669456i
$83$		−	5.66025i		−	0.621294i	−0.950525	−	0.310647i	$-0.899454\pi$
$83$		−	5.66025i		−	0.621294i	0.950525	−	0.310647i	$-0.100546\pi$
$84$		0			0
$85$	−0.169873	−	0.0980762i	−0.0184253	−	0.0106379i
$86$		−	0.732051i		−	0.0789391i
$87$		0			0
$88$	−1.86603	−	3.23205i	−0.198919	−	0.344538i
$89$	−5.59808	+	3.23205i	−0.593395	+	0.342597i	−0.766439	−	0.642317i	$-0.777973\pi$
$89$	−5.59808	+	3.23205i	−0.593395	+	0.342597i	0.173044	+	0.984914i	$0.444640\pi$
$90$		0			0
$91$	−2.50000	+	2.59808i	−0.262071	+	0.272352i
$92$	−3.46410			−0.361158
$93$		0			0
$94$	2.23205	+	3.86603i	0.230218	+	0.398750i
$95$	−1.63397	+	2.83013i	−0.167642	+	0.290365i
$96$		0			0
$97$	0.633975	+	0.366025i	0.0643704	+	0.0371642i	0.531840	−	0.846845i	$-0.321501\pi$
$97$	0.633975	+	0.366025i	0.0643704	+	0.0371642i	−0.467469	+	0.884009i	$0.654834\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$		0			0
$100$	2.23205	−	3.86603i	0.223205	−	0.386603i
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$		0			0
$103$	12.1962			1.20172			0.600861	−	0.799353i	$-0.294824\pi$
$103$	12.1962			1.20172			0.600861	+	0.799353i	$0.294824\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$		0			0
$106$	9.06218	−	5.23205i	0.880197	−	0.508182i
$107$	−0.767949	−	1.33013i	−0.0742405	−	0.128588i	0.826515	−	0.562914i	$-0.190320\pi$
$107$	−0.767949	−	1.33013i	−0.0742405	−	0.128588i	−0.900756	+	0.434326i	$0.856987\pi$
$108$		0			0
$109$			3.66025i			0.350589i	0.984516	+	0.175294i	$0.0560877\pi$
$109$			3.66025i			0.350589i	−0.984516	+	0.175294i	$0.943912\pi$
$110$	2.36603	+	1.36603i	0.225592	+	0.130245i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	−5.09808	+	8.83013i	−0.479587	+	0.830668i	−0.999726	−	0.0234130i	$-0.992547\pi$
$113$	−5.09808	+	8.83013i	−0.479587	+	0.830668i	0.520139	+	0.854081i	$0.325880\pi$
$114$		0			0
$115$	2.19615	−	1.26795i	0.204792	−	0.118237i
$116$	−3.00000			−0.278543
$117$		0			0
$118$	−0.928203			−0.0854480
$119$	−0.232051	+	0.133975i	−0.0212721	+	0.0122814i
$120$		0			0
$121$	1.46410	−	2.53590i	0.133100	−	0.230536i
$122$		−	11.7321i		−	1.06217i
$123$		0			0
$124$	6.63397	+	3.83013i	0.595749	+	0.343956i
$125$			6.92820i			0.619677i
$126$		0			0
$127$	−6.26795	−	10.8564i	−0.556191	−	0.963350i	−0.997810	−	0.0661478i	$-0.978929\pi$
$127$	−6.26795	−	10.8564i	−0.556191	−	0.963350i	0.441619	−	0.897203i	$-0.354404\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.53590	+	0.732051i	−0.222413	+	0.0642051i
$131$	−18.9282			−1.65376			−0.826882	−	0.562375i	$-0.809888\pi$
$131$	−18.9282			−1.65376			−0.826882	+	0.562375i	$0.809888\pi$
$132$		0			0
$133$	2.23205	+	3.86603i	0.193543	+	0.335227i
$134$	−6.46410	+	11.1962i	−0.558413	+	0.967200i
$135$		0			0
$136$	0.232051	+	0.133975i	0.0198982	+	0.0114882i
$137$	−13.3923	−	7.73205i	−1.14418	−	0.660594i	−0.196719	−	0.980460i	$-0.563029\pi$
$137$	−13.3923	−	7.73205i	−1.14418	−	0.660594i	−0.947463	+	0.319866i	$0.896362\pi$
$138$		0			0
$139$	9.06218	−	15.6962i	0.768644	−	1.33133i	−0.169655	−	0.985504i	$-0.554265\pi$
$139$	9.06218	−	15.6962i	0.768644	−	1.33133i	0.938298	−	0.345827i	$-0.112401\pi$
$140$	0.366025	+	0.633975i	0.0309348	+	0.0535806i
$141$		0			0
$142$	−2.19615			−0.184297
$143$	3.73205	+	12.9282i	0.312090	+	1.08111i
$144$		0			0
$145$	1.90192	−	1.09808i	0.157946	−	0.0911903i
$146$	−3.26795	−	5.66025i	−0.270457	−	0.468446i
$147$		0			0
$148$		−	1.26795i		−	0.104225i
$149$	16.3923	+	9.46410i	1.34291	+	0.775329i	0.987233	−	0.159280i	$-0.0509172\pi$
$149$	16.3923	+	9.46410i	1.34291	+	0.775329i	0.355676	+	0.934609i	$0.384251\pi$
$150$		0			0
$151$		−	13.1962i		−	1.07389i	−0.843618	−	0.536944i	$-0.819579\pi$
$151$		−	13.1962i		−	1.07389i	0.843618	−	0.536944i	$-0.180421\pi$
$152$	2.23205	−	3.86603i	0.181043	−	0.313576i
$153$		0			0
$154$	3.23205	−	1.86603i	0.260446	−	0.150369i
$155$	−5.60770			−0.450421
$156$		0			0
$157$	−15.4641			−1.23417			−0.617085	−	0.786897i	$-0.711686\pi$
$157$	−15.4641			−1.23417			−0.617085	+	0.786897i	$0.711686\pi$
$158$	9.40192	−	5.42820i	0.747977	−	0.431845i
$159$		0			0
$160$	0.366025	−	0.633975i	0.0289368	−	0.0501201i
$161$		−	3.46410i		−	0.273009i
$162$		0			0
$163$	−6.75833	−	3.90192i	−0.529353	−	0.305622i	0.211400	−	0.977400i	$-0.432198\pi$
$163$	−6.75833	−	3.90192i	−0.529353	−	0.305622i	−0.740753	+	0.671777i	$0.765531\pi$
$164$		−	7.00000i		−	0.546608i
$165$		0			0
$166$	−2.83013	−	4.90192i	−0.219660	−	0.380463i
$167$	−5.07180	+	2.92820i	−0.392467	+	0.226591i	−0.683229	−	0.730204i	$-0.739425\pi$
$167$	−5.07180	+	2.92820i	−0.392467	+	0.226591i	0.290761	+	0.956796i	$0.406091\pi$
$168$		0			0
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$	−0.196152			−0.0150442
$171$		0			0
$172$	−0.366025	−	0.633975i	−0.0279092	−	0.0483401i
$173$	−10.3660	+	17.9545i	−0.788114	+	1.36505i	0.139007	+	0.990291i	$0.455609\pi$
$173$	−10.3660	+	17.9545i	−0.788114	+	1.36505i	−0.927121	+	0.374763i	$0.877724\pi$
$174$		0			0
$175$	3.86603	+	2.23205i	0.292244	+	0.168727i
$176$	−3.23205	−	1.86603i	−0.243625	−	0.140657i
$177$		0			0
$178$	−3.23205	+	5.59808i	−0.242252	+	0.419594i
$179$	−11.1962	−	19.3923i	−0.836840	−	1.44945i	−0.892524	−	0.451000i	$-0.851067\pi$
$179$	−11.1962	−	19.3923i	−0.836840	−	1.44945i	0.0556840	−	0.998448i	$-0.482266\pi$
$180$		0			0
$181$	−1.19615			−0.0889093			−0.0444547	−	0.999011i	$-0.514155\pi$
$181$	−1.19615			−0.0889093			−0.0444547	+	0.999011i	$0.514155\pi$
$182$	−0.866025	+	3.50000i	−0.0641941	+	0.259437i
$183$		0			0
$184$	−3.00000	+	1.73205i	−0.221163	+	0.127688i
$185$	0.464102	+	0.803848i	0.0341214	+	0.0591000i
$186$		0			0
$187$			1.00000i			0.0731272i
$188$	3.86603	+	2.23205i	0.281959	+	0.162789i
$189$		0			0
$190$			3.26795i			0.237082i
$191$	−2.09808	+	3.63397i	−0.151811	+	0.262945i	−0.931893	−	0.362732i	$-0.881844\pi$
$191$	−2.09808	+	3.63397i	−0.151811	+	0.262945i	0.780082	+	0.625677i	$0.215177\pi$
$192$		0			0
$193$	−14.8923	+	8.59808i	−1.07197	+	0.618903i	−0.928719	−	0.370783i	$-0.879089\pi$
$193$	−14.8923	+	8.59808i	−1.07197	+	0.618903i	−0.143252	+	0.989686i	$0.545756\pi$
$194$	0.732051			0.0525582
$195$		0			0
$196$	1.00000			0.0714286
$197$	−1.96410	+	1.13397i	−0.139936	+	0.0807923i	−0.568334	−	0.822798i	$-0.692412\pi$
$197$	−1.96410	+	1.13397i	−0.139936	+	0.0807923i	0.428397	+	0.903591i	$0.359078\pi$
$198$		0			0
$199$	−2.09808	+	3.63397i	−0.148729	+	0.257606i	−0.930758	−	0.365636i	$-0.880851\pi$
$199$	−2.09808	+	3.63397i	−0.148729	+	0.257606i	0.782029	+	0.623242i	$0.214185\pi$
$200$		−	4.46410i		−	0.315660i
$201$		0			0
$202$	8.66025	+	5.00000i	0.609333	+	0.351799i
$203$		−	3.00000i		−	0.210559i
$204$		0			0
$205$	2.56218	+	4.43782i	0.178950	+	0.309951i
$206$	10.5622	−	6.09808i	0.735902	−	0.424873i
$207$		0			0
$208$	3.46410	−	1.00000i	0.240192	−	0.0693375i
$209$	16.6603			1.15241
$210$		0			0
$211$	7.92820	+	13.7321i	0.545800	+	0.945353i	0.998556	+	0.0537189i	$0.0171075\pi$
$211$	7.92820	+	13.7321i	0.545800	+	0.945353i	−0.452756	+	0.891634i	$0.649559\pi$
$212$	5.23205	−	9.06218i	0.359339	−	0.622393i
$213$		0			0
$214$	−1.33013	−	0.767949i	−0.0909256	−	0.0524959i
$215$	0.464102	+	0.267949i	0.0316515	+	0.0182740i
$216$		0			0
$217$	−3.83013	+	6.63397i	−0.260006	+	0.450344i
$218$	1.83013	+	3.16987i	0.123952	+	0.214691i
$219$		0			0
$220$	2.73205			0.184195
$221$	−0.696152	−	0.669873i	−0.0468283	−	0.0450605i
$222$		0			0
$223$	7.26795	−	4.19615i	0.486698	−	0.280995i	−0.236506	−	0.971630i	$-0.576002\pi$
$223$	7.26795	−	4.19615i	0.486698	−	0.280995i	0.723204	+	0.690635i	$0.242669\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$			10.1962i			0.678238i
$227$	−7.39230	−	4.26795i	−0.490645	−	0.283274i	0.234197	−	0.972189i	$-0.424754\pi$
$227$	−7.39230	−	4.26795i	−0.490645	−	0.283274i	−0.724842	+	0.688915i	$0.758087\pi$
$228$		0			0
$229$			10.3205i			0.681998i	0.940064	+	0.340999i	$0.110765\pi$
$229$			10.3205i			0.681998i	−0.940064	+	0.340999i	$0.889235\pi$
$230$	1.26795	−	2.19615i	0.0836061	−	0.144810i
$231$		0			0
$232$	−2.59808	+	1.50000i	−0.170572	+	0.0984798i
$233$	2.19615			0.143875			0.0719374	−	0.997409i	$-0.477082\pi$
$233$	2.19615			0.143875			0.0719374	+	0.997409i	$0.477082\pi$
$234$		0			0
$235$	−3.26795			−0.213177
$236$	−0.803848	+	0.464102i	−0.0523260	+	0.0302104i
$237$		0			0
$238$	−0.133975	+	0.232051i	−0.00868428	+	0.0150416i
$239$		−	13.8038i		−	0.892897i	−0.894809	−	0.446448i	$-0.852689\pi$
$239$		−	13.8038i		−	0.892897i	0.894809	−	0.446448i	$-0.147311\pi$
$240$		0			0
$241$	−11.0718	−	6.39230i	−0.713197	−	0.411765i	0.0990466	−	0.995083i	$-0.468421\pi$
$241$	−11.0718	−	6.39230i	−0.713197	−	0.411765i	−0.812244	+	0.583318i	$0.801754\pi$
$242$		−	2.92820i		−	0.188232i
$243$		0			0
$244$	−5.86603	−	10.1603i	−0.375534	−	0.650444i
$245$	−0.633975	+	0.366025i	−0.0405032	+	0.0233845i
$246$		0			0
$247$	−11.1603	+	11.5981i	−0.710110	+	0.737968i
$248$	7.66025			0.486427
$249$		0			0
$250$	3.46410	+	6.00000i	0.219089	+	0.379473i
$251$	−9.09808	+	15.7583i	−0.574265	+	0.994657i	0.421856	+	0.906663i	$0.361379\pi$
$251$	−9.09808	+	15.7583i	−0.574265	+	0.994657i	−0.996121	+	0.0879939i	$0.971954\pi$
$252$		0			0
$253$	−11.1962	−	6.46410i	−0.703896	−	0.406395i
$254$	−10.8564	−	6.26795i	−0.681192	−	0.393286i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.52628	−	9.57180i	−0.344720	−	0.597072i	0.640583	−	0.767889i	$-0.278693\pi$
$257$	−5.52628	−	9.57180i	−0.344720	−	0.597072i	−0.985303	+	0.170817i	$0.945359\pi$
$258$		0			0
$259$	1.26795			0.0787865
$260$	−1.83013	+	1.90192i	−0.113500	+	0.117952i
$261$		0			0
$262$	−16.3923	+	9.46410i	−1.01272	+	0.584694i
$263$	−9.36603	−	16.2224i	−0.577534	−	1.00032i	−0.995761	−	0.0919756i	$-0.970682\pi$
$263$	−9.36603	−	16.2224i	−0.577534	−	1.00032i	0.418227	−	0.908342i	$-0.362652\pi$
$264$		0			0
$265$			7.66025i			0.470566i
$266$	3.86603	+	2.23205i	0.237041	+	0.136856i
$267$		0			0
$268$			12.9282i			0.789716i
$269$	−11.8564	+	20.5359i	−0.722898	+	1.25210i	0.236936	+	0.971525i	$0.423857\pi$
$269$	−11.8564	+	20.5359i	−0.722898	+	1.25210i	−0.959833	+	0.280570i	$0.909476\pi$
$270$		0			0
$271$	18.6340	−	10.7583i	1.13193	−	0.653522i	0.187513	−	0.982262i	$-0.439957\pi$
$271$	18.6340	−	10.7583i	1.13193	−	0.653522i	0.944420	+	0.328740i	$0.106624\pi$
$272$	0.267949			0.0162468
$273$		0			0
$274$	−15.4641			−0.934221
$275$	14.4282	−	8.33013i	0.870053	−	0.502326i
$276$		0			0
$277$	−13.1962	+	22.8564i	−0.792880	+	1.37331i	0.131297	+	0.991343i	$0.458086\pi$
$277$	−13.1962	+	22.8564i	−0.792880	+	1.37331i	−0.924177	+	0.381965i	$0.875247\pi$
$278$		−	18.1244i		−	1.08703i
$279$		0			0
$280$	0.633975	+	0.366025i	0.0378872	+	0.0218742i
$281$			18.1962i			1.08549i	0.839897	+	0.542746i	$0.182615\pi$
$281$			18.1962i			1.08549i	−0.839897	+	0.542746i	$0.817385\pi$
$282$		0			0
$283$	−11.4641	−	19.8564i	−0.681470	−	1.18034i	−0.974532	−	0.224247i	$-0.928008\pi$
$283$	−11.4641	−	19.8564i	−0.681470	−	1.18034i	0.293062	−	0.956093i	$-0.405326\pi$
$284$	−1.90192	+	1.09808i	−0.112858	+	0.0651588i
$285$		0			0
$286$	9.69615	+	9.33013i	0.573346	+	0.551702i
$287$	7.00000			0.413197
$288$		0			0
$289$	8.46410	+	14.6603i	0.497888	+	0.862368i
$290$	1.09808	−	1.90192i	0.0644813	−	0.111685i
$291$		0			0
$292$	−5.66025	−	3.26795i	−0.331241	−	0.191242i
$293$	11.0718	+	6.39230i	0.646821	+	0.373442i	0.787237	−	0.616650i	$-0.211511\pi$
$293$	11.0718	+	6.39230i	0.646821	+	0.373442i	−0.140416	+	0.990093i	$0.544844\pi$
$294$		0			0
$295$	0.339746	−	0.588457i	0.0197808	−	0.0342613i
$296$	−0.633975	−	1.09808i	−0.0368490	−	0.0638244i
$297$		0			0
$298$	18.9282			1.09648
$299$	12.0000	−	3.46410i	0.693978	−	0.200334i
$300$		0			0
$301$	0.633975	−	0.366025i	0.0365417	−	0.0210974i
$302$	−6.59808	−	11.4282i	−0.379677	−	0.657619i
$303$		0			0
$304$		−	4.46410i		−	0.256034i
$305$	7.43782	+	4.29423i	0.425888	+	0.245887i
$306$		0			0
$307$			33.7846i			1.92819i	0.265558	+	0.964095i	$0.414444\pi$
$307$			33.7846i			1.92819i	−0.265558	+	0.964095i	$0.585556\pi$
$308$	1.86603	−	3.23205i	0.106327	−	0.184163i
$309$		0			0
$310$	−4.85641	+	2.80385i	−0.275825	+	0.159248i
$311$	−19.1962			−1.08851			−0.544257	−	0.838919i	$-0.683188\pi$
$311$	−19.1962			−1.08851			−0.544257	+	0.838919i	$0.683188\pi$
$312$		0			0
$313$	1.80385			0.101959			0.0509797	−	0.998700i	$-0.483766\pi$
$313$	1.80385			0.101959			0.0509797	+	0.998700i	$0.483766\pi$
$314$	−13.3923	+	7.73205i	−0.755771	+	0.436345i
$315$		0			0
$316$	5.42820	−	9.40192i	0.305360	−	0.528900i
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$		0			0
$319$	−9.69615	−	5.59808i	−0.542880	−	0.313432i
$320$		−	0.732051i		−	0.0409229i
$321$		0			0
$322$	−1.73205	−	3.00000i	−0.0965234	−	0.167183i
$323$	−1.03590	+	0.598076i	−0.0576389	+	0.0332779i
$324$		0			0
$325$	−3.86603	+	15.6244i	−0.214449	+	0.866683i
$326$	−7.80385			−0.432215
$327$		0			0
$328$	−3.50000	−	6.06218i	−0.193255	−	0.334728i
$329$	−2.23205	+	3.86603i	−0.123057	+	0.213141i
$330$		0			0
$331$	−14.6603	−	8.46410i	−0.805800	−	0.465229i	0.0396949	−	0.999212i	$-0.487361\pi$
$331$	−14.6603	−	8.46410i	−0.805800	−	0.465229i	−0.845495	+	0.533983i	$0.820695\pi$
$332$	−4.90192	−	2.83013i	−0.269028	−	0.155323i
$333$		0			0
$334$	−2.92820	+	5.07180i	−0.160224	+	0.277516i
$335$	−4.73205	−	8.19615i	−0.258540	−	0.447804i
$336$		0			0
$337$	−27.7846			−1.51352			−0.756762	−	0.653690i	$-0.773220\pi$
$337$	−27.7846			−1.51352			−0.756762	+	0.653690i	$0.773220\pi$
$338$	−12.9904	+	0.500000i	−0.706584	+	0.0271964i
$339$		0			0
$340$	−0.169873	+	0.0980762i	−0.00921266	+	0.00531893i
$341$	14.2942	+	24.7583i	0.774076	+	1.34074i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−0.633975	−	0.366025i	−0.0341816	−	0.0197348i
$345$		0			0
$346$			20.7321i			1.11456i
$347$	11.4282	−	19.7942i	0.613498	−	1.06261i	−0.377148	−	0.926153i	$-0.623095\pi$
$347$	11.4282	−	19.7942i	0.613498	−	1.06261i	0.990646	−	0.136457i	$-0.0435715\pi$
$348$		0			0
$349$	20.5359	−	11.8564i	1.09926	−	0.634659i	0.163235	−	0.986587i	$-0.447807\pi$
$349$	20.5359	−	11.8564i	1.09926	−	0.634659i	0.936027	+	0.351928i	$0.114474\pi$
$350$	4.46410			0.238616
$351$		0			0
$352$	−3.73205			−0.198919
$353$	1.26795	−	0.732051i	0.0674861	−	0.0389631i	−0.465877	−	0.884849i	$-0.654261\pi$
$353$	1.26795	−	0.732051i	0.0674861	−	0.0389631i	0.533363	+	0.845886i	$0.320928\pi$
$354$		0			0
$355$	0.803848	−	1.39230i	0.0426638	−	0.0738959i
$356$			6.46410i			0.342597i
$357$		0			0
$358$	−19.3923	−	11.1962i	−1.02492	−	0.591735i
$359$			15.8038i			0.834095i	0.908885	+	0.417048i	$0.136935\pi$
$359$			15.8038i			0.834095i	−0.908885	+	0.417048i	$0.863065\pi$
$360$		0			0
$361$	0.464102	+	0.803848i	0.0244264	+	0.0423078i
$362$	−1.03590	+	0.598076i	−0.0544456	+	0.0314342i
$363$		0			0
$364$	1.00000	+	3.46410i	0.0524142	+	0.181568i
$365$	4.78461			0.250438
$366$		0			0
$367$	−8.12436	−	14.0718i	−0.424088	−	0.734542i	0.572247	−	0.820081i	$-0.306072\pi$
$367$	−8.12436	−	14.0718i	−0.424088	−	0.734542i	−0.996335	+	0.0855396i	$0.972739\pi$
$368$	−1.73205	+	3.00000i	−0.0902894	+	0.156386i
$369$		0			0
$370$	0.803848	+	0.464102i	0.0417900	+	0.0241275i
$371$	9.06218	+	5.23205i	0.470485	+	0.271635i
$372$		0			0
$373$	10.2942	−	17.8301i	0.533015	−	0.923209i	−0.466242	−	0.884657i	$-0.654392\pi$
$373$	10.2942	−	17.8301i	0.533015	−	0.923209i	0.999257	−	0.0385516i	$-0.0122744\pi$
$374$	0.500000	+	0.866025i	0.0258544	+	0.0447811i
$375$		0			0
$376$	4.46410			0.230218
$377$	10.3923	−	3.00000i	0.535231	−	0.154508i
$378$		0			0
$379$	−12.6340	+	7.29423i	−0.648964	+	0.374679i	−0.788059	−	0.615600i	$-0.788914\pi$
$379$	−12.6340	+	7.29423i	−0.648964	+	0.374679i	0.139095	+	0.990279i	$0.455581\pi$
$380$	1.63397	+	2.83013i	0.0838211	+	0.145182i
$381$		0			0
$382$			4.19615i			0.214694i
$383$	−12.6506	−	7.30385i	−0.646417	−	0.373209i	0.140665	−	0.990057i	$-0.455076\pi$
$383$	−12.6506	−	7.30385i	−0.646417	−	0.373209i	−0.787082	+	0.616848i	$0.788409\pi$
$384$		0			0
$385$			2.73205i			0.139238i
$386$	−8.59808	+	14.8923i	−0.437631	+	0.757998i
$387$		0			0
$388$	0.633975	−	0.366025i	0.0321852	−	0.0185821i
$389$	−33.1769			−1.68214			−0.841068	−	0.540929i	$-0.818073\pi$
$389$	−33.1769			−1.68214			−0.841068	+	0.540929i	$0.818073\pi$
$390$		0			0
$391$	0.928203			0.0469413
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$		0			0
$394$	−1.13397	+	1.96410i	−0.0571288	+	0.0989500i
$395$			7.94744i			0.399879i
$396$		0			0
$397$	−14.2583	−	8.23205i	−0.715605	−	0.413155i	0.0975279	−	0.995233i	$-0.468906\pi$
$397$	−14.2583	−	8.23205i	−0.715605	−	0.413155i	−0.813133	+	0.582078i	$0.802240\pi$
$398$			4.19615i			0.210334i
$399$		0			0
$400$	−2.23205	−	3.86603i	−0.111603	−	0.193301i
$401$	8.66025	−	5.00000i	0.432472	−	0.249688i	−0.267927	−	0.963439i	$-0.586339\pi$
$401$	8.66025	−	5.00000i	0.432472	−	0.249688i	0.700399	+	0.713751i	$0.253005\pi$
$402$		0			0
$403$	−26.8109	−	6.63397i	−1.33555	−	0.330462i
$404$	10.0000			0.497519
$405$		0			0
$406$	−1.50000	−	2.59808i	−0.0744438	−	0.128940i
$407$	2.36603	−	4.09808i	0.117280	−	0.203134i
$408$		0			0
$409$	11.4904	+	6.63397i	0.568163	+	0.328029i	0.756415	−	0.654092i	$-0.226949\pi$
$409$	11.4904	+	6.63397i	0.568163	+	0.328029i	−0.188252	+	0.982121i	$0.560282\pi$
$410$	4.43782	+	2.56218i	0.219168	+	0.126537i
$411$		0			0
$412$	6.09808	−	10.5622i	0.300431	−	0.520361i
$413$	−0.464102	−	0.803848i	−0.0228369	−	0.0395548i
$414$		0			0
$415$	4.14359			0.203401
$416$	2.50000	−	2.59808i	0.122573	−	0.127381i
$417$		0			0
$418$	14.4282	−	8.33013i	0.705706	−	0.407440i
$419$	−3.09808	−	5.36603i	−0.151351	−	0.262147i	0.780373	−	0.625314i	$-0.215029\pi$
$419$	−3.09808	−	5.36603i	−0.151351	−	0.262147i	−0.931724	+	0.363166i	$0.881696\pi$
$420$		0			0
$421$			14.3923i			0.701438i	0.936481	+	0.350719i	$0.114063\pi$
$421$			14.3923i			0.701438i	−0.936481	+	0.350719i	$0.885937\pi$
$422$	13.7321	+	7.92820i	0.668466	+	0.385939i
$423$		0			0
$424$		−	10.4641i		−	0.508182i
$425$	−0.598076	+	1.03590i	−0.0290110	+	0.0502485i
$426$		0			0
$427$	10.1603	−	5.86603i	0.491689	−	0.283877i
$428$	−1.53590			−0.0742405
$429$		0			0
$430$	0.535898			0.0258433
$431$	−18.2942	+	10.5622i	−0.881202	+	0.508762i	−0.871055	−	0.491186i	$-0.836563\pi$
$431$	−18.2942	+	10.5622i	−0.881202	+	0.508762i	−0.0101474	+	0.999949i	$0.503230\pi$
$432$		0			0
$433$	4.46410	−	7.73205i	0.214531	−	0.371579i	−0.738596	−	0.674148i	$-0.764511\pi$
$433$	4.46410	−	7.73205i	0.214531	−	0.371579i	0.953127	+	0.302569i	$0.0978444\pi$
$434$			7.66025i			0.367704i
$435$		0			0
$436$	3.16987	+	1.83013i	0.151809	+	0.0876472i
$437$		−	15.4641i		−	0.739748i
$438$		0			0
$439$	−8.19615	−	14.1962i	−0.391181	−	0.677545i	0.601425	−	0.798930i	$-0.294600\pi$
$439$	−8.19615	−	14.1962i	−0.391181	−	0.677545i	−0.992606	+	0.121384i	$0.961267\pi$
$440$	2.36603	−	1.36603i	0.112796	−	0.0651227i
$441$		0			0
$442$	−0.937822	−	0.232051i	−0.0446077	−	0.0110375i
$443$	31.3923			1.49149			0.745747	−	0.666230i	$-0.232093\pi$
$443$	31.3923			1.49149			0.745747	+	0.666230i	$0.232093\pi$
$444$		0			0
$445$	−2.36603	−	4.09808i	−0.112160	−	0.194267i
$446$	4.19615	−	7.26795i	0.198694	−	0.344147i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	9.29423	+	5.36603i	0.438622	+	0.253238i	0.703013	−	0.711177i	$-0.251838\pi$
$449$	9.29423	+	5.36603i	0.438622	+	0.253238i	−0.264391	+	0.964416i	$0.585171\pi$
$450$		0			0
$451$	13.0622	−	22.6244i	0.615074	−	1.06534i
$452$	5.09808	+	8.83013i	0.239793	+	0.415334i
$453$		0			0
$454$	−8.53590			−0.400610
$455$	−1.90192	−	1.83013i	−0.0891636	−	0.0857977i
$456$		0			0
$457$	5.87564	−	3.39230i	0.274851	−	0.158685i	−0.356239	−	0.934395i	$-0.615941\pi$
$457$	5.87564	−	3.39230i	0.274851	−	0.158685i	0.631090	+	0.775710i	$0.282608\pi$
$458$	5.16025	+	8.93782i	0.241123	+	0.417637i
$459$		0			0
$460$		−	2.53590i		−	0.118237i
$461$	24.0000	+	13.8564i	1.11779	+	0.645357i	0.940836	−	0.338862i	$-0.110042\pi$
$461$	24.0000	+	13.8564i	1.11779	+	0.645357i	0.176955	+	0.984219i	$0.443375\pi$
$462$		0			0
$463$			1.19615i			0.0555899i	0.999614	+	0.0277950i	$0.00884855\pi$
$463$			1.19615i			0.0555899i	−0.999614	+	0.0277950i	$0.991151\pi$
$464$	−1.50000	+	2.59808i	−0.0696358	+	0.120613i
$465$		0			0
$466$	1.90192	−	1.09808i	0.0881049	−	0.0508674i
$467$	−9.85641			−0.456100			−0.228050	−	0.973649i	$-0.573235\pi$
$467$	−9.85641			−0.456100			−0.228050	+	0.973649i	$0.573235\pi$
$468$		0			0
$469$	−12.9282			−0.596969
$470$	−2.83013	+	1.63397i	−0.130544	+	0.0753696i
$471$		0			0
$472$	−0.464102	+	0.803848i	−0.0213620	+	0.0370001i
$473$		−	2.73205i		−	0.125620i
$474$		0			0
$475$	17.2583	+	9.96410i	0.791866	+	0.457184i
$476$			0.267949i			0.0122814i
$477$		0			0
$478$	−6.90192	−	11.9545i	−0.315687	−	0.546785i
$479$	−27.1865	+	15.6962i	−1.24218	+	0.717176i	−0.969539	−	0.244939i	$-0.921232\pi$
$479$	−27.1865	+	15.6962i	−1.24218	+	0.717176i	−0.272646	+	0.962114i	$0.587899\pi$
$480$		0			0
$481$	1.26795	+	4.39230i	0.0578135	+	0.200272i
$482$	−12.7846			−0.582323
$483$		0			0
$484$	−1.46410	−	2.53590i	−0.0665501	−	0.115268i
$485$	−0.267949	+	0.464102i	−0.0121669	+	0.0210738i
$486$		0			0
$487$	18.3564	+	10.5981i	0.831808	+	0.480245i	0.854471	−	0.519498i	$-0.173881\pi$
$487$	18.3564	+	10.5981i	0.831808	+	0.480245i	−0.0226632	+	0.999743i	$0.507215\pi$
$488$	−10.1603	−	5.86603i	−0.459933	−	0.265542i
$489$		0			0
$490$	−0.366025	+	0.633975i	−0.0165353	+	0.0286401i
$491$	−18.1244	−	31.3923i	−0.817941	−	1.41671i	−0.907197	−	0.420706i	$-0.861782\pi$
$491$	−18.1244	−	31.3923i	−0.817941	−	1.41671i	0.0892562	−	0.996009i	$-0.471551\pi$
$492$		0			0
$493$	0.803848			0.0362035
$494$	−3.86603	+	15.6244i	−0.173941	+	0.702973i
$495$		0			0
$496$	6.63397	−	3.83013i	0.297874	−	0.171978i
$497$	−1.09808	−	1.90192i	−0.0492554	−	0.0853129i
$498$		0			0
$499$			12.9808i			0.581099i	0.956860	+	0.290549i	$0.0938380\pi$
$499$			12.9808i			0.581099i	−0.956860	+	0.290549i	$0.906162\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$		0			0
$502$			18.1962i			0.812134i
$503$	−11.8564	+	20.5359i	−0.528651	+	0.915650i	0.470791	+	0.882245i	$0.343969\pi$
$503$	−11.8564	+	20.5359i	−0.528651	+	0.915650i	−0.999442	+	0.0334056i	$0.989365\pi$
$504$		0			0
$505$	−6.33975	+	3.66025i	−0.282115	+	0.162879i
$506$	−12.9282			−0.574729
$507$		0			0
$508$	−12.5359			−0.556191
$509$	22.5622	−	13.0263i	1.00005	−	0.577380i	0.0917876	−	0.995779i	$-0.470742\pi$
$509$	22.5622	−	13.0263i	1.00005	−	0.577380i	0.908263	+	0.418399i	$0.137409\pi$
$510$		0			0
$511$	3.26795	−	5.66025i	0.144566	−	0.250395i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−9.57180	−	5.52628i	−0.422194	−	0.243754i
$515$			8.92820i			0.393424i
$516$		0			0
$517$	8.33013	+	14.4282i	0.366359	+	0.634552i
$518$	1.09808	−	0.633975i	0.0482467	−	0.0278552i
$519$		0			0
$520$	−0.633975	+	2.56218i	−0.0278016	+	0.112359i
$521$	2.26795			0.0993607			0.0496803	−	0.998765i	$-0.484180\pi$
$521$	2.26795			0.0993607			0.0496803	+	0.998765i	$0.484180\pi$
$522$		0			0
$523$	9.40192	+	16.2846i	0.411117	+	0.712076i	0.995012	−	0.0997531i	$-0.0318053\pi$
$523$	9.40192	+	16.2846i	0.411117	+	0.712076i	−0.583895	+	0.811829i	$0.698472\pi$
$524$	−9.46410	+	16.3923i	−0.413441	+	0.716101i
$525$		0			0
$526$	−16.2224	−	9.36603i	−0.707332	−	0.408378i
$527$	−1.77757	−	1.02628i	−0.0774321	−	0.0447054i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	3.83013	+	6.63397i	0.166370	+	0.288161i
$531$		0			0
$532$	4.46410			0.193543
$533$	7.00000	+	24.2487i	0.303204	+	1.05033i
$534$		0			0
$535$	0.973721	−	0.562178i	0.0420976	−	0.0243051i
$536$	6.46410	+	11.1962i	0.279207	+	0.483600i
$537$		0			0
$538$			23.7128i			1.02233i
$539$	3.23205	+	1.86603i	0.139214	+	0.0803754i
$540$		0			0
$541$		−	30.1962i		−	1.29823i	−0.760689	−	0.649117i	$-0.775139\pi$
$541$		−	30.1962i		−	1.29823i	0.760689	−	0.649117i	$-0.224861\pi$
$542$	10.7583	−	18.6340i	0.462110	−	0.800398i
$543$		0			0
$544$	0.232051	−	0.133975i	0.00994910	−	0.00574411i
$545$	−2.67949			−0.114777
$546$		0			0
$547$	−12.8756			−0.550523			−0.275261	−	0.961369i	$-0.588764\pi$
$547$	−12.8756			−0.550523			−0.275261	+	0.961369i	$0.588764\pi$
$548$	−13.3923	+	7.73205i	−0.572091	+	0.330297i
$549$		0			0
$550$	8.33013	−	14.4282i	0.355198	−	0.615221i
$551$		−	13.3923i		−	0.570531i
$552$		0			0
$553$	9.40192	+	5.42820i	0.399810	+	0.230831i
$554$			26.3923i			1.12130i
$555$		0			0
$556$	−9.06218	−	15.6962i	−0.384322	−	0.665665i
$557$	−31.7487	+	18.3301i	−1.34524	+	0.776672i	−0.987570	−	0.157177i	$-0.949761\pi$
$557$	−31.7487	+	18.3301i	−1.34524	+	0.776672i	−0.357666	+	0.933850i	$0.616427\pi$
$558$		0			0
$559$	1.90192	+	1.83013i	0.0804428	+	0.0774061i
$560$	0.732051			0.0309348
$561$		0			0
$562$	9.09808	+	15.7583i	0.383779	+	0.664725i
$563$	16.6340	−	28.8109i	0.701038	−	1.21423i	−0.267064	−	0.963679i	$-0.586053\pi$
$563$	16.6340	−	28.8109i	0.701038	−	1.21423i	0.968102	−	0.250555i	$-0.0806132\pi$
$564$		0			0
$565$	−6.46410	−	3.73205i	−0.271947	−	0.157009i
$566$	−19.8564	−	11.4641i	−0.834627	−	0.481872i
$567$		0			0
$568$	−1.09808	+	1.90192i	−0.0460743	+	0.0798029i
$569$	−11.3660	−	19.6865i	−0.476489	−	0.825302i	0.523149	−	0.852242i	$-0.324757\pi$
$569$	−11.3660	−	19.6865i	−0.476489	−	0.825302i	−0.999637	+	0.0269391i	$0.991424\pi$
$570$		0			0
$571$	−19.8038			−0.828765			−0.414383	−	0.910103i	$-0.636002\pi$
$571$	−19.8038			−0.828765			−0.414383	+	0.910103i	$0.636002\pi$
$572$	13.0622	+	3.23205i	0.546157	+	0.135139i
$573$		0			0
$574$	6.06218	−	3.50000i	0.253030	−	0.146087i
$575$	−7.73205	−	13.3923i	−0.322449	−	0.558498i
$576$		0			0
$577$			13.2679i			0.552352i	0.961107	+	0.276176i	$0.0890673\pi$
$577$			13.2679i			0.552352i	−0.961107	+	0.276176i	$0.910933\pi$
$578$	14.6603	+	8.46410i	0.609786	+	0.352060i
$579$		0			0
$580$		−	2.19615i		−	0.0911903i
$581$	2.83013	−	4.90192i	0.117413	−	0.203366i
$582$		0			0
$583$	33.8205	−	19.5263i	1.40070	−	0.808696i
$584$	−6.53590			−0.270457
$585$		0			0
$586$	12.7846			0.528127
$587$	27.1699	−	15.6865i	1.12142	−	0.647453i	0.179657	−	0.983729i	$-0.442501\pi$
$587$	27.1699	−	15.6865i	1.12142	−	0.647453i	0.941763	+	0.336277i	$0.109168\pi$
$588$		0			0
$589$	−17.0981	+	29.6147i	−0.704514	+	1.22025i
$590$		−	0.679492i		−	0.0279742i
$591$		0			0
$592$	−1.09808	−	0.633975i	−0.0451307	−	0.0260562i
$593$			13.6795i			0.561749i	0.959744	+	0.280875i	$0.0906245\pi$
$593$			13.6795i			0.561749i	−0.959744	+	0.280875i	$0.909375\pi$
$594$		0			0
$595$	−0.0980762	−	0.169873i	−0.00402073	−	0.00696411i
$596$	16.3923	−	9.46410i	0.671455	−	0.387665i
$597$		0			0
$598$	8.66025	−	9.00000i	0.354144	−	0.368037i
$599$	21.7128			0.887161			0.443581	−	0.896234i	$-0.353708\pi$
$599$	21.7128			0.887161			0.443581	+	0.896234i	$0.353708\pi$
$600$		0			0
$601$	6.43782	+	11.1506i	0.262604	+	0.454844i	0.966933	−	0.255030i	$-0.0820853\pi$
$601$	6.43782	+	11.1506i	0.262604	+	0.454844i	−0.704329	+	0.709874i	$0.748752\pi$
$602$	0.366025	−	0.633975i	0.0149181	−	0.0258389i
$603$		0			0
$604$	−11.4282	−	6.59808i	−0.465007	−	0.268472i
$605$	1.85641	+	1.07180i	0.0754737	+	0.0435747i
$606$		0			0
$607$	−19.9545	+	34.5622i	−0.809927	+	1.40284i	0.102986	+	0.994683i	$0.467160\pi$
$607$	−19.9545	+	34.5622i	−0.809927	+	1.40284i	−0.912914	+	0.408153i	$0.866173\pi$
$608$	−2.23205	−	3.86603i	−0.0905216	−	0.156788i
$609$		0			0
$610$	8.58846			0.347736
$611$	−15.6244	−	3.86603i	−0.632094	−	0.156403i
$612$		0			0
$613$	36.2487	−	20.9282i	1.46407	−	0.845282i	0.464876	−	0.885376i	$-0.346099\pi$
$613$	36.2487	−	20.9282i	1.46407	−	0.845282i	0.999196	+	0.0400938i	$0.0127657\pi$
$614$	16.8923	+	29.2583i	0.681718	+	1.18077i
$615$		0			0
$616$		−	3.73205i		−	0.150369i
$617$	−35.9545	−	20.7583i	−1.44747	−	0.835699i	−0.449143	−	0.893460i	$-0.648270\pi$
$617$	−35.9545	−	20.7583i	−1.44747	−	0.835699i	−0.998330	+	0.0577612i	$0.981604\pi$
$618$		0			0
$619$		−	2.32051i		−	0.0932691i	−0.998912	−	0.0466345i	$-0.985150\pi$
$619$		−	2.32051i		−	0.0932691i	0.998912	−	0.0466345i	$-0.0148496\pi$
$620$	−2.80385	+	4.85641i	−0.112605	+	0.195038i
$621$		0			0
$622$	−16.6244	+	9.59808i	−0.666576	+	0.384848i
$623$	−6.46410			−0.258979
$624$		0			0
$625$	17.2487			0.689948
$626$	1.56218	−	0.901924i	0.0624372	−	0.0360481i
$627$		0			0
$628$	−7.73205	+	13.3923i	−0.308542	+	0.534411i
$629$			0.339746i			0.0135466i
$630$		0			0
$631$	−13.8397	−	7.99038i	−0.550952	−	0.318092i	0.198554	−	0.980090i	$-0.436375\pi$
$631$	−13.8397	−	7.99038i	−0.550952	−	0.318092i	−0.749506	+	0.661998i	$0.769709\pi$
$632$		−	10.8564i		−	0.431845i
$633$		0			0
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	7.94744	−	4.58846i	0.315385	−	0.182087i
$636$		0			0
$637$	−3.46410	+	1.00000i	−0.137253	+	0.0396214i
$638$	−11.1962			−0.443260
$639$		0			0
$640$	−0.366025	−	0.633975i	−0.0144684	−	0.0250600i
$641$	8.12436	−	14.0718i	0.320893	−	0.555803i	−0.659780	−	0.751459i	$-0.729350\pi$
$641$	8.12436	−	14.0718i	0.320893	−	0.555803i	0.980672	+	0.195656i	$0.0626838\pi$
$642$		0			0
$643$	1.45448	+	0.839746i	0.0573592	+	0.0331163i	0.528405	−	0.848992i	$-0.322790\pi$
$643$	1.45448	+	0.839746i	0.0573592	+	0.0331163i	−0.471046	+	0.882109i	$0.656123\pi$
$644$	−3.00000	−	1.73205i	−0.118217	−	0.0682524i
$645$		0			0
$646$	−0.598076	+	1.03590i	−0.0235310	+	0.0407569i
$647$	−0.866025	−	1.50000i	−0.0340470	−	0.0589711i	0.848500	−	0.529196i	$-0.177506\pi$
$647$	−0.866025	−	1.50000i	−0.0340470	−	0.0589711i	−0.882547	+	0.470225i	$0.844173\pi$
$648$		0			0
$649$	−3.46410			−0.135978
$650$	4.46410	+	15.4641i	0.175096	+	0.606552i
$651$		0			0
$652$	−6.75833	+	3.90192i	−0.264677	+	0.152811i
$653$	5.83975	+	10.1147i	0.228527	+	0.395820i	0.957372	−	0.288859i	$-0.0932758\pi$
$653$	5.83975	+	10.1147i	0.228527	+	0.395820i	−0.728845	+	0.684679i	$0.759942\pi$
$654$		0			0
$655$		−	13.8564i		−	0.541415i
$656$	−6.06218	−	3.50000i	−0.236688	−	0.136652i
$657$		0			0
$658$			4.46410i			0.174029i
$659$	16.9641	−	29.3827i	0.660828	−	1.14459i	−0.319571	−	0.947562i	$-0.603539\pi$
$659$	16.9641	−	29.3827i	0.660828	−	1.14459i	0.980399	−	0.197025i	$-0.0631279\pi$
$660$		0			0
$661$	23.9090	−	13.8038i	0.929951	−	0.536907i	0.0431549	−	0.999068i	$-0.486259\pi$
$661$	23.9090	−	13.8038i	0.929951	−	0.536907i	0.886796	+	0.462161i	$0.152926\pi$
$662$	−16.9282			−0.657933
$663$		0			0
$664$	−5.66025			−0.219660
$665$	−2.83013	+	1.63397i	−0.109748	+	0.0633628i
$666$		0			0
$667$	−5.19615	+	9.00000i	−0.201196	+	0.348481i
$668$			5.85641i			0.226591i
$669$		0			0
$670$	−8.19615	−	4.73205i	−0.316645	−	0.182815i
$671$		−	43.7846i		−	1.69029i
$672$		0			0
$673$	−23.9641	−	41.5070i	−0.923748	−	1.59998i	−0.793562	−	0.608489i	$-0.791776\pi$
$673$	−23.9641	−	41.5070i	−0.923748	−	1.59998i	−0.130186	−	0.991490i	$-0.541557\pi$
$674$	−24.0622	+	13.8923i	−0.926840	+	0.535112i
$675$		0			0
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	47.7654			1.83577			0.917886	−	0.396844i	$-0.129895\pi$
$677$	47.7654			1.83577			0.917886	+	0.396844i	$0.129895\pi$
$678$		0			0
$679$	0.366025	+	0.633975i	0.0140468	+	0.0243297i
$680$	−0.0980762	+	0.169873i	−0.00376105	+	0.00651433i
$681$		0			0
$682$	24.7583	+	14.2942i	0.948045	+	0.547354i
$683$	22.8564	+	13.1962i	0.874576	+	0.504937i	0.868866	−	0.495047i	$-0.164849\pi$
$683$	22.8564	+	13.1962i	0.874576	+	0.504937i	0.00570987	+	0.999984i	$0.498182\pi$
$684$		0			0
$685$	5.66025	−	9.80385i	0.216267	−	0.374586i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−0.732051			−0.0279092
$689$	−9.06218	+	36.6244i	−0.345241	+	1.39528i
$690$		0			0
$691$	35.3205	−	20.3923i	1.34366	−	0.775760i	0.356314	−	0.934366i	$-0.384033\pi$
$691$	35.3205	−	20.3923i	1.34366	−	0.775760i	0.987342	+	0.158607i	$0.0507002\pi$
$692$	10.3660	+	17.9545i	0.394057	+	0.682527i
$693$		0			0
$694$		−	22.8564i		−	0.867617i
$695$	11.4904	+	6.63397i	0.435855	+	0.251641i
$696$		0			0
$697$			1.87564i			0.0710451i
$698$	11.8564	−	20.5359i	0.448772	−	0.777295i
$699$		0			0
$700$	3.86603	−	2.23205i	0.146122	−	0.0843636i
$701$	14.3205			0.540878			0.270439	−	0.962737i	$-0.412831\pi$
$701$	14.3205			0.540878			0.270439	+	0.962737i	$0.412831\pi$
$702$		0			0
$703$	5.66025			0.213481
$704$	−3.23205	+	1.86603i	−0.121812	+	0.0703285i
$705$		0			0
$706$	0.732051	−	1.26795i	0.0275511	−	0.0477199i
$707$			10.0000i			0.376089i
$708$		0			0
$709$	20.8301	+	12.0263i	0.782292	+	0.451656i	0.837242	−	0.546833i	$-0.184167\pi$
$709$	20.8301	+	12.0263i	0.782292	+	0.451656i	−0.0549501	+	0.998489i	$0.517500\pi$
$710$		−	1.60770i		−	0.0603357i
$711$		0			0
$712$	3.23205	+	5.59808i	0.121126	+	0.209797i
$713$	22.9808	−	13.2679i	0.860636	−	0.496889i
$714$		0			0
$715$	−9.46410	+	2.73205i	−0.353937	+	0.102173i
$716$	−22.3923			−0.836840
$717$		0			0
$718$	7.90192	+	13.6865i	0.294897	+	0.510777i
$719$	−1.52628	+	2.64359i	−0.0569206	+	0.0985894i	−0.893082	−	0.449895i	$-0.851462\pi$
$719$	−1.52628	+	2.64359i	−0.0569206	+	0.0985894i	0.836161	+	0.548484i	$0.184795\pi$
$720$		0			0
$721$	10.5622	+	6.09808i	0.393356	+	0.227104i
$722$	0.803848	+	0.464102i	0.0299161	+	0.0172721i
$723$		0			0
$724$	−0.598076	+	1.03590i	−0.0222273	+	0.0384989i
$725$	−6.69615	−	11.5981i	−0.248689	−	0.430742i
$726$		0			0
$727$	−1.46410			−0.0543005			−0.0271503	−	0.999631i	$-0.508643\pi$
$727$	−1.46410			−0.0543005			−0.0271503	+	0.999631i	$0.508643\pi$
$728$	2.59808	+	2.50000i	0.0962911	+	0.0926562i
$729$		0			0
$730$	4.14359	−	2.39230i	0.153361	−	0.0885432i
$731$	0.0980762	+	0.169873i	0.00362748	+	0.00628298i
$732$		0			0
$733$			6.85641i			0.253247i	0.991951	+	0.126624i	$0.0404140\pi$
$733$			6.85641i			0.253247i	−0.991951	+	0.126624i	$0.959586\pi$
$734$	−14.0718	−	8.12436i	−0.519399	−	0.299875i
$735$		0			0
$736$			3.46410i			0.127688i
$737$	−24.1244	+	41.7846i	−0.888632	+	1.53916i
$738$		0			0
$739$	5.53590	−	3.19615i	0.203641	−	0.117572i	−0.394712	−	0.918805i	$-0.629155\pi$
$739$	5.53590	−	3.19615i	0.203641	−	0.117572i	0.598353	+	0.801233i	$0.295822\pi$
$740$	0.928203			0.0341214
$741$		0			0
$742$	10.4641			0.384149
$743$	16.9019	−	9.75833i	0.620071	−	0.357998i	−0.156825	−	0.987626i	$-0.550126\pi$
$743$	16.9019	−	9.75833i	0.620071	−	0.357998i	0.776897	+	0.629628i	$0.216793\pi$
$744$		0			0
$745$	−6.92820	+	12.0000i	−0.253830	+	0.439646i
$746$		−	20.5885i		−	0.753797i
$747$		0			0
$748$	0.866025	+	0.500000i	0.0316650	+	0.0182818i
$749$		−	1.53590i		−	0.0561205i
$750$		0			0
$751$	−3.42820	−	5.93782i	−0.125097	−	0.216674i	0.796674	−	0.604409i	$-0.206591\pi$
$751$	−3.42820	−	5.93782i	−0.125097	−	0.216674i	−0.921771	+	0.387735i	$0.873258\pi$
$752$	3.86603	−	2.23205i	0.140979	−	0.0813945i
$753$		0			0
$754$	7.50000	−	7.79423i	0.273134	−	0.283849i
$755$	9.66025			0.351573
$756$		0			0
$757$	19.0263	+	32.9545i	0.691522	+	1.19775i	0.971339	+	0.237698i	$0.0763928\pi$
$757$	19.0263	+	32.9545i	0.691522	+	1.19775i	−0.279817	+	0.960053i	$0.590274\pi$
$758$	−7.29423	+	12.6340i	−0.264938	+	0.458887i
$759$		0			0
$760$	2.83013	+	1.63397i	0.102659	+	0.0592705i
$761$	0.588457	+	0.339746i	0.0213316	+	0.0123158i	0.510628	−	0.859802i	$-0.329413\pi$
$761$	0.588457	+	0.339746i	0.0213316	+	0.0123158i	−0.489296	+	0.872118i	$0.662746\pi$
$762$		0			0
$763$	−1.83013	+	3.16987i	−0.0662550	+	0.114757i
$764$	2.09808	+	3.63397i	0.0759057	+	0.131473i
$765$		0			0
$766$	−14.6077			−0.527797
$767$	2.32051	−	2.41154i	0.0837887	−	0.0870758i
$768$		0			0
$769$	21.1699	−	12.2224i	0.763405	−	0.440752i	−0.0671118	−	0.997745i	$-0.521378\pi$
$769$	21.1699	−	12.2224i	0.763405	−	0.440752i	0.830517	+	0.556993i	$0.188045\pi$
$770$	1.36603	+	2.36603i	0.0492281	+	0.0852656i
$771$		0			0
$772$			17.1962i			0.618903i
$773$	−36.7128	−	21.1962i	−1.32047	−	0.762373i	−0.336665	−	0.941625i	$-0.609299\pi$
$773$	−36.7128	−	21.1962i	−1.32047	−	0.762373i	−0.983803	+	0.179252i	$0.942632\pi$
$774$		0			0
$775$			34.1962i			1.22836i
$776$	0.366025	−	0.633975i	0.0131395	−	0.0227584i
$777$		0			0
$778$	−28.7321	+	16.5885i	−1.03009	+	0.594725i
$779$	31.2487			1.11960
$780$		0			0
$781$	−8.19615			−0.293281
$782$	0.803848	−	0.464102i	0.0287455	−	0.0165962i
$783$		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.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.366025 + 0.633975i) q^{10} +(3.23205 - 1.86603i) q^{11} +(-0.866025 + 3.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.133975 + 0.232051i) q^{17} +(3.86603 + 2.23205i) q^{19} +(0.633975 + 0.366025i) q^{20} +(1.86603 - 3.23205i) q^{22} +(-1.73205 - 3.00000i) q^{23} +4.46410 q^{25} +(1.00000 + 3.46410i) q^{26} +(0.866025 - 0.500000i) q^{28} +(-1.50000 - 2.59808i) q^{29} +7.66025i q^{31} +(-0.866025 - 0.500000i) q^{32} +0.267949i q^{34} +(-0.366025 + 0.633975i) q^{35} +(1.09808 - 0.633975i) q^{37} +4.46410 q^{38} +0.732051 q^{40} +(6.06218 - 3.50000i) q^{41} +(0.366025 - 0.633975i) q^{43} -3.73205i q^{44} +(-3.00000 - 1.73205i) q^{46} +4.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(3.86603 - 2.23205i) q^{50} +(2.59808 + 2.50000i) q^{52} +10.4641 q^{53} +(1.36603 + 2.36603i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-2.59808 - 1.50000i) q^{58} +(-0.803848 - 0.464102i) q^{59} +(5.86603 - 10.1603i) q^{61} +(3.83013 + 6.63397i) q^{62} -1.00000 q^{64} +(-2.56218 - 0.633975i) q^{65} +(-11.1962 + 6.46410i) q^{67} +(0.133975 + 0.232051i) q^{68} +0.732051i q^{70} +(-1.90192 - 1.09808i) q^{71} -6.53590i q^{73} +(0.633975 - 1.09808i) q^{74} +(3.86603 - 2.23205i) q^{76} +3.73205 q^{77} +10.8564 q^{79} +(0.633975 - 0.366025i) q^{80} +(3.50000 - 6.06218i) q^{82} -5.66025i q^{83} +(-0.169873 - 0.0980762i) q^{85} -0.732051i q^{86} +(-1.86603 - 3.23205i) q^{88} +(-5.59808 + 3.23205i) q^{89} +(-2.50000 + 2.59808i) q^{91} -3.46410 q^{92} +(2.23205 + 3.86603i) q^{94} +(-1.63397 + 2.83013i) q^{95} +(0.633975 + 0.366025i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} + 6 q^{11} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 12 q^{19} + 6 q^{20} + 4 q^{22} + 4 q^{25} + 4 q^{26} - 6 q^{29} + 2 q^{35} - 6 q^{37} + 4 q^{38} - 4 q^{40} - 2 q^{43} - 12 q^{46} + 2 q^{49} + 12 q^{50} + 28 q^{53} + 2 q^{55} + 2 q^{56} - 24 q^{59} + 20 q^{61} - 2 q^{62} - 4 q^{64} + 14 q^{65} - 24 q^{67} + 4 q^{68} - 18 q^{71} + 6 q^{74} + 12 q^{76} + 8 q^{77} - 12 q^{79} + 6 q^{80} + 14 q^{82} - 18 q^{85} - 4 q^{88} - 12 q^{89} - 10 q^{91} + 2 q^{94} - 10 q^{95} + 6 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 + 6 * q^11 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 12 * q^19 + 6 * q^20 + 4 * q^22 + 4 * q^25 + 4 * q^26 - 6 * q^29 + 2 * q^35 - 6 * q^37 + 4 * q^38 - 4 * q^40 - 2 * q^43 - 12 * q^46 + 2 * q^49 + 12 * q^50 + 28 * q^53 + 2 * q^55 + 2 * q^56 - 24 * q^59 + 20 * q^61 - 2 * q^62 - 4 * q^64 + 14 * q^65 - 24 * q^67 + 4 * q^68 - 18 * q^71 + 6 * q^74 + 12 * q^76 + 8 * q^77 - 12 * q^79 + 6 * q^80 + 14 * q^82 - 18 * q^85 - 4 * q^88 - 12 * q^89 - 10 * q^91 + 2 * q^94 - 10 * q^95 + 6 * q^97

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