LMFDB - Embedded newform 1638.2.bj.b.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.b.1135.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.366025 + 0.633975i) q^{10} +(-1.50000 + 0.866025i) q^{11} +(1.59808 + 3.23205i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.86603 + 3.23205i) q^{17} +(0.866025 + 0.500000i) q^{19} +(0.633975 + 0.366025i) q^{20} +(-0.866025 + 1.50000i) q^{22} +(1.73205 + 3.00000i) q^{23} +4.46410 q^{25} +(3.00000 + 2.00000i) q^{26} +(0.866025 - 0.500000i) q^{28} +(3.23205 + 5.59808i) q^{29} -2.19615i q^{31} +(-0.866025 - 0.500000i) q^{32} +3.73205i q^{34} +(-0.366025 + 0.633975i) q^{35} +(5.83013 - 3.36603i) q^{37} +1.00000 q^{38} +0.732051 q^{40} +(-2.59808 + 1.50000i) q^{41} +(1.63397 - 2.83013i) q^{43} +1.73205i q^{44} +(3.00000 + 1.73205i) q^{46} +2.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(3.86603 - 2.23205i) q^{50} +(3.59808 + 0.232051i) q^{52} -7.00000 q^{53} +(-0.633975 - 1.09808i) q^{55} +(0.500000 - 0.866025i) q^{56} +(5.59808 + 3.23205i) q^{58} +(-0.803848 - 0.464102i) q^{59} +(-2.59808 + 4.50000i) q^{61} +(-1.09808 - 1.90192i) q^{62} -1.00000 q^{64} +(-2.36603 + 1.16987i) q^{65} +(7.73205 - 4.46410i) q^{67} +(1.86603 + 3.23205i) q^{68} +0.732051i q^{70} +(1.90192 + 1.09808i) q^{71} +5.46410i q^{73} +(3.36603 - 5.83013i) q^{74} +(0.866025 - 0.500000i) q^{76} -1.73205 q^{77} +2.07180 q^{79} +(0.633975 - 0.366025i) q^{80} +(-1.50000 + 2.59808i) q^{82} +0.196152i q^{83} +(-2.36603 - 1.36603i) q^{85} -3.26795i q^{86} +(0.866025 + 1.50000i) q^{88} +(9.06218 - 5.23205i) q^{89} +(-0.232051 + 3.59808i) q^{91} +3.46410 q^{92} +(1.23205 + 2.13397i) q^{94} +(-0.366025 + 0.633975i) q^{95} +(13.5622 + 7.83013i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 6 q^{29} + 2 q^{35} + 6 q^{37} + 4 q^{38} - 4 q^{40} + 10 q^{43} + 12 q^{46} + 2 q^{49} + 12 q^{50} + 4 q^{52} - 28 q^{53} - 6 q^{55} + 2 q^{56} + 12 q^{58} - 24 q^{59} + 6 q^{62} - 4 q^{64} - 6 q^{65} + 24 q^{67} + 4 q^{68} + 18 q^{71} + 10 q^{74} + 36 q^{79} + 6 q^{80} - 6 q^{82} - 6 q^{85} + 12 q^{89} + 6 q^{91} - 2 q^{94} + 2 q^{95} + 30 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 - 2 * q^10 - 6 * q^11 - 4 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 6 * q^20 + 4 * q^25 + 12 * q^26 + 6 * q^29 + 2 * q^35 + 6 * q^37 + 4 * q^38 - 4 * q^40 + 10 * q^43 + 12 * q^46 + 2 * q^49 + 12 * q^50 + 4 * q^52 - 28 * q^53 - 6 * q^55 + 2 * q^56 + 12 * q^58 - 24 * q^59 + 6 * q^62 - 4 * q^64 - 6 * q^65 + 24 * q^67 + 4 * q^68 + 18 * q^71 + 10 * q^74 + 36 * q^79 + 6 * q^80 - 6 * q^82 - 6 * q^85 + 12 * q^89 + 6 * q^91 - 2 * q^94 + 2 * q^95 + 30 * 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
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	−0.708787	−	0.705422i	$-0.750757\pi$
$11$	−1.50000	+	0.866025i	−0.452267	+	0.261116i	0.256520	+	0.966539i	$0.417424\pi$
$12$		0			0
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.86603	+	3.23205i	−0.452578	+	0.783887i	−0.998545	−	0.0539188i	$-0.982829\pi$
$17$	−1.86603	+	3.23205i	−0.452578	+	0.783887i	0.545968	+	0.837806i	$0.316162\pi$
$18$		0			0
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i	0.596040	−	0.802955i	$-0.296740\pi$
$19$	0.866025	+	0.500000i	0.198680	+	0.114708i	−0.397360	+	0.917663i	$0.630073\pi$
$20$	0.633975	+	0.366025i	0.141761	+	0.0818458i
$21$		0			0
$22$	−0.866025	+	1.50000i	−0.184637	+	0.319801i
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$		0			0
$25$	4.46410			0.892820
$26$	3.00000	+	2.00000i	0.588348	+	0.392232i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	3.23205	+	5.59808i	0.600177	+	1.03954i	0.992794	+	0.119835i	$0.0382364\pi$
$29$	3.23205	+	5.59808i	0.600177	+	1.03954i	−0.392617	+	0.919702i	$0.628430\pi$
$30$		0			0
$31$		−	2.19615i		−	0.394441i	−0.980359	−	0.197220i	$-0.936809\pi$
$31$		−	2.19615i		−	0.394441i	0.980359	−	0.197220i	$-0.0631914\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$			3.73205i			0.640041i
$35$	−0.366025	+	0.633975i	−0.0618696	+	0.107161i
$36$		0			0
$37$	5.83013	−	3.36603i	0.958467	−	0.553371i	0.0627661	−	0.998028i	$-0.480008\pi$
$37$	5.83013	−	3.36603i	0.958467	−	0.553371i	0.895701	+	0.444657i	$0.146674\pi$
$38$	1.00000			0.162221
$39$		0			0
$40$	0.732051			0.115747
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	−0.688963	−	0.724797i	$-0.741934\pi$
$41$	−2.59808	+	1.50000i	−0.405751	+	0.234261i	0.283211	+	0.959058i	$0.408600\pi$
$42$		0			0
$43$	1.63397	−	2.83013i	0.249179	−	0.431590i	−0.714119	−	0.700024i	$-0.753173\pi$
$43$	1.63397	−	2.83013i	0.249179	−	0.431590i	0.963298	+	0.268434i	$0.0865060\pi$
$44$			1.73205i			0.261116i
$45$		0			0
$46$	3.00000	+	1.73205i	0.442326	+	0.255377i
$47$			2.46410i			0.359426i	0.983719	+	0.179713i	$0.0575169\pi$
$47$			2.46410i			0.359426i	−0.983719	+	0.179713i	$0.942483\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	3.86603	−	2.23205i	0.546739	−	0.315660i
$51$		0			0
$52$	3.59808	+	0.232051i	0.498963	+	0.0321797i
$53$	−7.00000			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$53$	−7.00000			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$54$		0			0
$55$	−0.633975	−	1.09808i	−0.0854851	−	0.148065i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	5.59808	+	3.23205i	0.735063	+	0.424389i
$59$	−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
$61$	−2.59808	+	4.50000i	−0.332650	+	0.576166i	−0.983030	−	0.183442i	$-0.941276\pi$
$61$	−2.59808	+	4.50000i	−0.332650	+	0.576166i	0.650381	+	0.759608i	$0.274609\pi$
$62$	−1.09808	−	1.90192i	−0.139456	−	0.241545i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.36603	+	1.16987i	−0.293469	+	0.145105i
$66$		0			0
$67$	7.73205	−	4.46410i	0.944620	−	0.545377i	0.0532147	−	0.998583i	$-0.483053\pi$
$67$	7.73205	−	4.46410i	0.944620	−	0.545377i	0.891406	+	0.453206i	$0.149720\pi$
$68$	1.86603	+	3.23205i	0.226289	+	0.391944i
$69$		0			0
$70$			0.732051i			0.0874968i
$71$	1.90192	+	1.09808i	0.225717	+	0.130318i	0.608595	−	0.793481i	$-0.291734\pi$
$71$	1.90192	+	1.09808i	0.225717	+	0.130318i	−0.382878	+	0.923799i	$0.625067\pi$
$72$		0			0
$73$			5.46410i			0.639525i	0.947498	+	0.319762i	$0.103603\pi$
$73$			5.46410i			0.639525i	−0.947498	+	0.319762i	$0.896397\pi$
$74$	3.36603	−	5.83013i	0.391293	−	0.677738i
$75$		0			0
$76$	0.866025	−	0.500000i	0.0993399	−	0.0573539i
$77$	−1.73205			−0.197386
$78$		0			0
$79$	2.07180			0.233095			0.116548	−	0.993185i	$-0.462817\pi$
$79$	2.07180			0.233095			0.116548	+	0.993185i	$0.462817\pi$
$80$	0.633975	−	0.366025i	0.0708805	−	0.0409229i
$81$		0			0
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$			0.196152i			0.0215305i	0.999942	+	0.0107653i	$0.00342676\pi$
$83$			0.196152i			0.0215305i	−0.999942	+	0.0107653i	$0.996573\pi$
$84$		0			0
$85$	−2.36603	−	1.36603i	−0.256631	−	0.148166i
$86$		−	3.26795i		−	0.352392i
$87$		0			0
$88$	0.866025	+	1.50000i	0.0923186	+	0.159901i
$89$	9.06218	−	5.23205i	0.960589	−	0.554596i	0.0642347	−	0.997935i	$-0.479539\pi$
$89$	9.06218	−	5.23205i	0.960589	−	0.554596i	0.896354	+	0.443339i	$0.146206\pi$
$90$		0			0
$91$	−0.232051	+	3.59808i	−0.0243255	+	0.377181i
$92$	3.46410			0.361158
$93$		0			0
$94$	1.23205	+	2.13397i	0.127076	+	0.220103i
$95$	−0.366025	+	0.633975i	−0.0375534	+	0.0650444i
$96$		0			0
$97$	13.5622	+	7.83013i	1.37703	+	0.795029i	0.991801	−	0.127792i	$-0.0407889\pi$
$97$	13.5622	+	7.83013i	1.37703	+	0.795029i	0.385230	+	0.922821i	$0.374122\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$		0			0
$100$	2.23205	−	3.86603i	0.223205	−	0.386603i
$101$	−1.53590	−	2.66025i	−0.152828	−	0.264705i	0.779438	−	0.626479i	$-0.215505\pi$
$101$	−1.53590	−	2.66025i	−0.152828	−	0.264705i	−0.932266	+	0.361774i	$0.882171\pi$
$102$		0			0
$103$	−14.7321			−1.45159			−0.725796	−	0.687910i	$-0.758528\pi$
$103$	−14.7321			−1.45159			−0.725796	+	0.687910i	$0.758528\pi$
$104$	3.23205	−	1.59808i	0.316929	−	0.156704i
$105$		0			0
$106$	−6.06218	+	3.50000i	−0.588811	+	0.339950i
$107$	5.42820	+	9.40192i	0.524764	+	0.908918i	0.999584	+	0.0288353i	$0.00917984\pi$
$107$	5.42820	+	9.40192i	0.524764	+	0.908918i	−0.474820	+	0.880083i	$0.657487\pi$
$108$		0			0
$109$		−	4.73205i		−	0.453248i	−0.973982	−	0.226624i	$-0.927231\pi$
$109$		−	4.73205i		−	0.453248i	0.973982	−	0.226624i	$-0.0727689\pi$
$110$	−1.09808	−	0.633975i	−0.104697	−	0.0604471i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	7.63397	−	13.2224i	0.718144	−	1.24386i	−0.243590	−	0.969878i	$-0.578325\pi$
$113$	7.63397	−	13.2224i	0.718144	−	1.24386i	0.961734	−	0.273984i	$-0.0883414\pi$
$114$		0			0
$115$	−2.19615	+	1.26795i	−0.204792	+	0.118237i
$116$	6.46410			0.600177
$117$		0			0
$118$	−0.928203			−0.0854480
$119$	−3.23205	+	1.86603i	−0.296282	+	0.171058i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$			5.19615i			0.470438i
$123$		0			0
$124$	−1.90192	−	1.09808i	−0.170798	−	0.0986102i
$125$			6.92820i			0.619677i
$126$		0			0
$127$	−7.73205	−	13.3923i	−0.686109	−	1.18837i	−0.973087	−	0.230438i	$-0.925984\pi$
$127$	−7.73205	−	13.3923i	−0.686109	−	1.18837i	0.286978	−	0.957937i	$-0.407349\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.46410	+	2.19615i	−0.128410	+	0.192615i
$131$	13.8564			1.21064			0.605320	−	0.795982i	$-0.293045\pi$
$131$	13.8564			1.21064			0.605320	+	0.795982i	$0.293045\pi$
$132$		0			0
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	4.46410	−	7.73205i	0.385640	−	0.667947i
$135$		0			0
$136$	3.23205	+	1.86603i	0.277146	+	0.160010i
$137$	−12.4641	−	7.19615i	−1.06488	−	0.614809i	−0.138102	−	0.990418i	$-0.544100\pi$
$137$	−12.4641	−	7.19615i	−1.06488	−	0.614809i	−0.926778	+	0.375609i	$0.877433\pi$
$138$		0			0
$139$	−5.79423	+	10.0359i	−0.491460	+	0.851234i	−0.999952	−	0.00983316i	$-0.996870\pi$
$139$	−5.79423	+	10.0359i	−0.491460	+	0.851234i	0.508492	+	0.861067i	$0.330203\pi$
$140$	0.366025	+	0.633975i	0.0309348	+	0.0535806i
$141$		0			0
$142$	2.19615			0.184297
$143$	−5.19615	−	3.46410i	−0.434524	−	0.289683i
$144$		0			0
$145$	−4.09808	+	2.36603i	−0.340327	+	0.196488i
$146$	2.73205	+	4.73205i	0.226106	+	0.391627i
$147$		0			0
$148$		−	6.73205i		−	0.553371i
$149$	−12.0000	−	6.92820i	−0.983078	−	0.567581i	−0.0798802	−	0.996804i	$-0.525454\pi$
$149$	−12.0000	−	6.92820i	−0.983078	−	0.567581i	−0.903198	+	0.429224i	$0.858787\pi$
$150$		0			0
$151$		−	5.19615i		−	0.422857i	−0.977393	−	0.211428i	$-0.932188\pi$
$151$		−	5.19615i		−	0.422857i	0.977393	−	0.211428i	$-0.0678115\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$		0			0
$154$	−1.50000	+	0.866025i	−0.120873	+	0.0697863i
$155$	1.60770			0.129133
$156$		0			0
$157$	−0.535898			−0.0427693			−0.0213847	−	0.999771i	$-0.506807\pi$
$157$	−0.535898			−0.0427693			−0.0213847	+	0.999771i	$0.506807\pi$
$158$	1.79423	−	1.03590i	0.142741	−	0.0824117i
$159$		0			0
$160$	0.366025	−	0.633975i	0.0289368	−	0.0501201i
$161$			3.46410i			0.273009i
$162$		0			0
$163$	2.36603	+	1.36603i	0.185321	+	0.106995i	0.589790	−	0.807556i	$-0.299210\pi$
$163$	2.36603	+	1.36603i	0.185321	+	0.106995i	−0.404469	+	0.914552i	$0.632544\pi$
$164$			3.00000i			0.234261i
$165$		0			0
$166$	0.0980762	+	0.169873i	0.00761219	+	0.0131847i
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.0422232	−	0.999108i	$-0.486556\pi$
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.886365	+	0.462988i	$0.153223\pi$
$168$		0			0
$169$	−7.89230	+	10.3301i	−0.607100	+	0.794625i
$170$	−2.73205			−0.209539
$171$		0			0
$172$	−1.63397	−	2.83013i	−0.124589	−	0.215795i
$173$	4.56218	−	7.90192i	0.346856	−	0.600772i	−0.638833	−	0.769345i	$-0.720583\pi$
$173$	4.56218	−	7.90192i	0.346856	−	0.600772i	0.985689	+	0.168573i	$0.0539159\pi$
$174$		0			0
$175$	3.86603	+	2.23205i	0.292244	+	0.168727i
$176$	1.50000	+	0.866025i	0.113067	+	0.0652791i
$177$		0			0
$178$	5.23205	−	9.06218i	0.392159	−	0.679239i
$179$	−5.73205	−	9.92820i	−0.428434	−	0.742069i	0.568301	−	0.822821i	$-0.307601\pi$
$179$	−5.73205	−	9.92820i	−0.428434	−	0.742069i	−0.996734	+	0.0807523i	$0.974268\pi$
$180$		0			0
$181$	2.66025			0.197735			0.0988676	−	0.995101i	$-0.468478\pi$
$181$	2.66025			0.197735			0.0988676	+	0.995101i	$0.468478\pi$
$182$	1.59808	+	3.23205i	0.118457	+	0.239576i
$183$		0			0
$184$	3.00000	−	1.73205i	0.221163	−	0.127688i
$185$	2.46410	+	4.26795i	0.181164	+	0.313786i
$186$		0			0
$187$		−	6.46410i		−	0.472702i
$188$	2.13397	+	1.23205i	0.155636	+	0.0898565i
$189$		0			0
$190$			0.732051i			0.0531085i
$191$	11.5622	−	20.0263i	0.836610	−	1.44905i	−0.0561031	−	0.998425i	$-0.517868\pi$
$191$	11.5622	−	20.0263i	0.836610	−	1.44905i	0.892713	−	0.450626i	$-0.148799\pi$
$192$		0			0
$193$	−1.03590	+	0.598076i	−0.0745656	+	0.0430505i	−0.536819	−	0.843697i	$-0.680374\pi$
$193$	−1.03590	+	0.598076i	−0.0745656	+	0.0430505i	0.462254	+	0.886748i	$0.347041\pi$
$194$	15.6603			1.12434
$195$		0			0
$196$	1.00000			0.0714286
$197$	−23.0885	+	13.3301i	−1.64498	+	0.949732i	−0.665961	+	0.745987i	$0.731978\pi$
$197$	−23.0885	+	13.3301i	−1.64498	+	0.949732i	−0.979024	+	0.203745i	$0.934689\pi$
$198$		0			0
$199$	−8.09808	+	14.0263i	−0.574057	+	0.994297i	0.422086	+	0.906556i	$0.361298\pi$
$199$	−8.09808	+	14.0263i	−0.574057	+	0.994297i	−0.996143	+	0.0877408i	$0.972035\pi$
$200$		−	4.46410i		−	0.315660i
$201$		0			0
$202$	−2.66025	−	1.53590i	−0.187175	−	0.108065i
$203$			6.46410i			0.453691i
$204$		0			0
$205$	−1.09808	−	1.90192i	−0.0766930	−	0.132836i
$206$	−12.7583	+	7.36603i	−0.888915	+	0.513215i
$207$		0			0
$208$	2.00000	−	3.00000i	0.138675	−	0.208013i
$209$	−1.73205			−0.119808
$210$		0			0
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.833858	−	0.551979i	$-0.813873\pi$
$211$	−13.0000	−	22.5167i	−0.894957	−	1.55011i	−0.0610990	−	0.998132i	$-0.519461\pi$
$212$	−3.50000	+	6.06218i	−0.240381	+	0.416352i
$213$		0			0
$214$	9.40192	+	5.42820i	0.642702	+	0.371064i
$215$	2.07180	+	1.19615i	0.141295	+	0.0815769i
$216$		0			0
$217$	1.09808	−	1.90192i	0.0745423	−	0.129111i
$218$	−2.36603	−	4.09808i	−0.160247	−	0.277557i
$219$		0			0
$220$	−1.26795			−0.0854851
$221$	−13.4282	−	0.866025i	−0.903279	−	0.0582552i
$222$		0			0
$223$	21.1244	−	12.1962i	1.41459	−	0.816715i	0.418775	−	0.908090i	$-0.362460\pi$
$223$	21.1244	−	12.1962i	1.41459	−	0.816715i	0.995817	+	0.0913753i	$0.0291263\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$		−	15.2679i		−	1.01561i
$227$	−15.9282	−	9.19615i	−1.05719	−	0.610370i	−0.132538	−	0.991178i	$-0.542313\pi$
$227$	−15.9282	−	9.19615i	−1.05719	−	0.610370i	−0.924654	+	0.380808i	$0.875646\pi$
$228$		0			0
$229$			19.9282i			1.31689i	0.752628	+	0.658446i	$0.228786\pi$
$229$			19.9282i			1.31689i	−0.752628	+	0.658446i	$0.771214\pi$
$230$	−1.26795	+	2.19615i	−0.0836061	+	0.144810i
$231$		0			0
$232$	5.59808	−	3.23205i	0.367532	−	0.212195i
$233$	−9.12436			−0.597756			−0.298878	−	0.954291i	$-0.596612\pi$
$233$	−9.12436			−0.597756			−0.298878	+	0.954291i	$0.596612\pi$
$234$		0			0
$235$	−1.80385			−0.117670
$236$	−0.803848	+	0.464102i	−0.0523260	+	0.0302104i
$237$		0			0
$238$	−1.86603	+	3.23205i	−0.120956	+	0.209503i
$239$			0.732051i			0.0473524i	0.999720	+	0.0236762i	$0.00753708\pi$
$239$			0.732051i			0.0473524i	−0.999720	+	0.0236762i	$0.992463\pi$
$240$		0			0
$241$	−6.92820	−	4.00000i	−0.446285	−	0.257663i	0.259975	−	0.965615i	$-0.416286\pi$
$241$	−6.92820	−	4.00000i	−0.446285	−	0.257663i	−0.706260	+	0.707953i	$0.749619\pi$
$242$			8.00000i			0.514259i
$243$		0			0
$244$	2.59808	+	4.50000i	0.166325	+	0.288083i
$245$	−0.633975	+	0.366025i	−0.0405032	+	0.0233845i
$246$		0			0
$247$	−0.232051	+	3.59808i	−0.0147650	+	0.228940i
$248$	−2.19615			−0.139456
$249$		0			0
$250$	3.46410	+	6.00000i	0.219089	+	0.379473i
$251$	−6.56218	+	11.3660i	−0.414201	+	0.717417i	−0.995344	−	0.0963841i	$-0.969272\pi$
$251$	−6.56218	+	11.3660i	−0.414201	+	0.717417i	0.581143	+	0.813801i	$0.302606\pi$
$252$		0			0
$253$	−5.19615	−	3.00000i	−0.326679	−	0.188608i
$254$	−13.3923	−	7.73205i	−0.840308	−	0.485152i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.3301	−	17.8923i	−0.644376	−	1.11609i	−0.984445	−	0.175691i	$-0.943784\pi$
$257$	−10.3301	−	17.8923i	−0.644376	−	1.11609i	0.340070	−	0.940400i	$-0.389549\pi$
$258$		0			0
$259$	6.73205			0.418309
$260$	−0.169873	+	2.63397i	−0.0105351	+	0.163352i
$261$		0			0
$262$	12.0000	−	6.92820i	0.741362	−	0.428026i
$263$	−7.56218	−	13.0981i	−0.466304	−	0.807662i	0.532955	−	0.846143i	$-0.321081\pi$
$263$	−7.56218	−	13.0981i	−0.466304	−	0.807662i	−0.999259	+	0.0384813i	$0.987748\pi$
$264$		0			0
$265$		−	5.12436i		−	0.314787i
$266$	0.866025	+	0.500000i	0.0530994	+	0.0306570i
$267$		0			0
$268$		−	8.92820i		−	0.545377i
$269$	−4.92820	+	8.53590i	−0.300478	+	0.520443i	−0.976244	−	0.216673i	$-0.930479\pi$
$269$	−4.92820	+	8.53590i	−0.300478	+	0.520443i	0.675766	+	0.737116i	$0.263813\pi$
$270$		0			0
$271$	−24.2942	+	14.0263i	−1.47577	+	0.852036i	−0.999626	−	0.0273321i	$-0.991299\pi$
$271$	−24.2942	+	14.0263i	−1.47577	+	0.852036i	−0.476143	+	0.879368i	$0.657965\pi$
$272$	3.73205			0.226289
$273$		0			0
$274$	−14.3923			−0.869471
$275$	−6.69615	+	3.86603i	−0.403793	+	0.233130i
$276$		0			0
$277$	4.66025	−	8.07180i	0.280008	−	0.484987i	−0.691379	−	0.722493i	$-0.742996\pi$
$277$	4.66025	−	8.07180i	0.280008	−	0.484987i	0.971386	+	0.237505i	$0.0763297\pi$
$278$			11.5885i			0.695029i
$279$		0			0
$280$	0.633975	+	0.366025i	0.0378872	+	0.0218742i
$281$		−	0.339746i		−	0.0202675i	−0.999949	−	0.0101338i	$-0.996774\pi$
$281$		−	0.339746i		−	0.0202675i	0.999949	−	0.0101338i	$-0.00322574\pi$
$282$		0			0
$283$	−4.92820	−	8.53590i	−0.292951	−	0.507406i	0.681555	−	0.731767i	$-0.261304\pi$
$283$	−4.92820	−	8.53590i	−0.292951	−	0.507406i	−0.974506	+	0.224360i	$0.927971\pi$
$284$	1.90192	−	1.09808i	0.112858	−	0.0651588i
$285$		0			0
$286$	−6.23205	−	0.401924i	−0.368509	−	0.0237663i
$287$	−3.00000			−0.177084
$288$		0			0
$289$	1.53590	+	2.66025i	0.0903470	+	0.156486i
$290$	−2.36603	+	4.09808i	−0.138938	+	0.240647i
$291$		0			0
$292$	4.73205	+	2.73205i	0.276922	+	0.159881i
$293$	14.7846	+	8.53590i	0.863726	+	0.498673i	0.865258	−	0.501326i	$-0.167154\pi$
$293$	14.7846	+	8.53590i	0.863726	+	0.498673i	−0.00153218	+	0.999999i	$0.500488\pi$
$294$		0			0
$295$	0.339746	−	0.588457i	0.0197808	−	0.0342613i
$296$	−3.36603	−	5.83013i	−0.195646	−	0.338869i
$297$		0			0
$298$	−13.8564			−0.802680
$299$	−6.92820	+	10.3923i	−0.400668	+	0.601003i
$300$		0			0
$301$	2.83013	−	1.63397i	0.163126	−	0.0941807i
$302$	−2.59808	−	4.50000i	−0.149502	−	0.258946i
$303$		0			0
$304$		−	1.00000i		−	0.0573539i
$305$	−3.29423	−	1.90192i	−0.188627	−	0.108904i
$306$		0			0
$307$		−	8.60770i		−	0.491267i	−0.969363	−	0.245634i	$-0.921004\pi$
$307$		−	8.60770i		−	0.491267i	0.969363	−	0.245634i	$-0.0789960\pi$
$308$	−0.866025	+	1.50000i	−0.0493464	+	0.0854704i
$309$		0			0
$310$	1.39230	−	0.803848i	0.0790776	−	0.0456555i
$311$	4.26795			0.242013			0.121007	−	0.992652i	$-0.461388\pi$
$311$	4.26795			0.242013			0.121007	+	0.992652i	$0.461388\pi$
$312$		0			0
$313$	13.5167			0.764007			0.382003	−	0.924161i	$-0.375234\pi$
$313$	13.5167			0.764007			0.382003	+	0.924161i	$0.375234\pi$
$314$	−0.464102	+	0.267949i	−0.0261908	+	0.0151212i
$315$		0			0
$316$	1.03590	−	1.79423i	0.0582738	−	0.100933i
$317$			11.8564i			0.665922i	0.942941	+	0.332961i	$0.108048\pi$
$317$			11.8564i			0.665922i	−0.942941	+	0.332961i	$0.891952\pi$
$318$		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
$323$	−3.23205	+	1.86603i	−0.179836	+	0.103828i
$324$		0			0
$325$	7.13397	+	14.4282i	0.395722	+	0.800333i
$326$	2.73205			0.151314
$327$		0			0
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−1.23205	+	2.13397i	−0.0679252	+	0.117650i
$330$		0			0
$331$	24.1244	+	13.9282i	1.32599	+	0.765563i	0.984678	−	0.174385i	$-0.0557937\pi$
$331$	24.1244	+	13.9282i	1.32599	+	0.765563i	0.341317	+	0.939948i	$0.389127\pi$
$332$	0.169873	+	0.0980762i	0.00932299	+	0.00538263i
$333$		0			0
$334$	6.92820	−	12.0000i	0.379094	−	0.656611i
$335$	3.26795	+	5.66025i	0.178547	+	0.309253i
$336$		0			0
$337$	−19.0000			−1.03500			−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000			−1.03500			−0.517498	+	0.855684i	$0.673136\pi$
$338$	−1.66987	+	12.8923i	−0.0908291	+	0.701249i
$339$		0			0
$340$	−2.36603	+	1.36603i	−0.128316	+	0.0740831i
$341$	1.90192	+	3.29423i	0.102995	+	0.178392i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−2.83013	−	1.63397i	−0.152590	−	0.0880980i
$345$		0			0
$346$		−	9.12436i		−	0.490528i
$347$	2.69615	−	4.66987i	0.144737	−	0.250692i	−0.784538	−	0.620081i	$-0.787100\pi$
$347$	2.69615	−	4.66987i	0.144737	−	0.250692i	0.929275	+	0.369389i	$0.120433\pi$
$348$		0			0
$349$	−20.5359	+	11.8564i	−1.09926	+	0.634659i	−0.936027	−	0.351928i	$-0.885526\pi$
$349$	−20.5359	+	11.8564i	−1.09926	+	0.634659i	−0.163235	+	0.986587i	$0.552193\pi$
$350$	4.46410			0.238616
$351$		0			0
$352$	1.73205			0.0923186
$353$	8.19615	−	4.73205i	0.436237	−	0.251862i	−0.265763	−	0.964038i	$-0.585624\pi$
$353$	8.19615	−	4.73205i	0.436237	−	0.251862i	0.702000	+	0.712177i	$0.252291\pi$
$354$		0			0
$355$	−0.803848	+	1.39230i	−0.0426638	+	0.0738959i
$356$		−	10.4641i		−	0.554596i
$357$		0			0
$358$	−9.92820	−	5.73205i	−0.524722	−	0.302948i
$359$		−	3.80385i		−	0.200759i	−0.994949	−	0.100380i	$-0.967994\pi$
$359$		−	3.80385i		−	0.200759i	0.994949	−	0.100380i	$-0.0320058\pi$
$360$		0			0
$361$	−9.00000	−	15.5885i	−0.473684	−	0.820445i
$362$	2.30385	−	1.33013i	0.121088	−	0.0699099i
$363$		0			0
$364$	3.00000	+	2.00000i	0.157243	+	0.104828i
$365$	−4.00000			−0.209370
$366$		0			0
$367$	−12.6603	−	21.9282i	−0.660860	−	1.14464i	−0.980390	−	0.197067i	$-0.936858\pi$
$367$	−12.6603	−	21.9282i	−0.660860	−	1.14464i	0.319530	−	0.947576i	$-0.396475\pi$
$368$	1.73205	−	3.00000i	0.0902894	−	0.156386i
$369$		0			0
$370$	4.26795	+	2.46410i	0.221880	+	0.128103i
$371$	−6.06218	−	3.50000i	−0.314733	−	0.181711i
$372$		0			0
$373$	−4.83013	+	8.36603i	−0.250094	+	0.433176i	−0.963552	−	0.267523i	$-0.913795\pi$
$373$	−4.83013	+	8.36603i	−0.250094	+	0.433176i	0.713457	+	0.700699i	$0.247128\pi$
$374$	−3.23205	−	5.59808i	−0.167125	−	0.289470i
$375$		0			0
$376$	2.46410			0.127076
$377$	−12.9282	+	19.3923i	−0.665836	+	0.998755i
$378$		0			0
$379$	24.6340	−	14.2224i	1.26536	−	0.730557i	0.291255	−	0.956645i	$-0.405927\pi$
$379$	24.6340	−	14.2224i	1.26536	−	0.730557i	0.974107	+	0.226088i	$0.0725937\pi$
$380$	0.366025	+	0.633975i	0.0187767	+	0.0325222i
$381$		0			0
$382$		−	23.1244i		−	1.18314i
$383$	4.79423	+	2.76795i	0.244974	+	0.141436i	0.617461	−	0.786602i	$-0.288162\pi$
$383$	4.79423	+	2.76795i	0.244974	+	0.141436i	−0.372487	+	0.928037i	$0.621495\pi$
$384$		0			0
$385$		−	1.26795i		−	0.0646207i
$386$	−0.598076	+	1.03590i	−0.0304413	+	0.0527258i
$387$		0			0
$388$	13.5622	−	7.83013i	0.688515	−	0.397514i
$389$	8.39230			0.425507			0.212753	−	0.977106i	$-0.431757\pi$
$389$	8.39230			0.425507			0.212753	+	0.977106i	$0.431757\pi$
$390$		0			0
$391$	−12.9282			−0.653807
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$		0			0
$394$	−13.3301	+	23.0885i	−0.671562	+	1.16318i
$395$			1.51666i			0.0763115i
$396$		0			0
$397$	6.99038	+	4.03590i	0.350837	+	0.202556i	0.665054	−	0.746795i	$-0.268409\pi$
$397$	6.99038	+	4.03590i	0.350837	+	0.202556i	−0.314217	+	0.949351i	$0.601742\pi$
$398$			16.1962i			0.811840i
$399$		0			0
$400$	−2.23205	−	3.86603i	−0.111603	−	0.193301i
$401$	33.5885	−	19.3923i	1.67733	−	0.968405i	0.713973	−	0.700173i	$-0.246894\pi$
$401$	33.5885	−	19.3923i	1.67733	−	0.968405i	0.963354	−	0.268233i	$-0.0864396\pi$
$402$		0			0
$403$	7.09808	−	3.50962i	0.353580	−	0.174827i
$404$	−3.07180			−0.152828
$405$		0			0
$406$	3.23205	+	5.59808i	0.160404	+	0.277828i
$407$	−5.83013	+	10.0981i	−0.288989	+	0.500543i
$408$		0			0
$409$	−33.5429	−	19.3660i	−1.65859	−	0.957588i	−0.973366	−	0.229258i	$-0.926370\pi$
$409$	−33.5429	−	19.3660i	−1.65859	−	0.957588i	−0.685226	−	0.728331i	$-0.740297\pi$
$410$	−1.90192	−	1.09808i	−0.0939293	−	0.0542301i
$411$		0			0
$412$	−7.36603	+	12.7583i	−0.362898	+	0.628558i
$413$	−0.464102	−	0.803848i	−0.0228369	−	0.0395548i
$414$		0			0
$415$	−0.143594			−0.00704873
$416$	0.232051	−	3.59808i	0.0113772	−	0.176410i
$417$		0			0
$418$	−1.50000	+	0.866025i	−0.0733674	+	0.0423587i
$419$	0.366025	+	0.633975i	0.0178815	+	0.0309717i	0.874828	−	0.484434i	$-0.160975\pi$
$419$	0.366025	+	0.633975i	0.0178815	+	0.0309717i	−0.856946	+	0.515406i	$0.827641\pi$
$420$		0			0
$421$		−	22.3923i		−	1.09133i	−0.838002	−	0.545667i	$-0.816276\pi$
$421$		−	22.3923i		−	1.09133i	0.838002	−	0.545667i	$-0.183724\pi$
$422$	−22.5167	−	13.0000i	−1.09609	−	0.632830i
$423$		0			0
$424$			7.00000i			0.339950i
$425$	−8.33013	+	14.4282i	−0.404071	+	0.699871i
$426$		0			0
$427$	−4.50000	+	2.59808i	−0.217770	+	0.125730i
$428$	10.8564			0.524764
$429$		0			0
$430$	2.39230			0.115367
$431$	12.2942	−	7.09808i	0.592192	−	0.341902i	−0.173772	−	0.984786i	$-0.555595\pi$
$431$	12.2942	−	7.09808i	0.592192	−	0.341902i	0.765964	+	0.642884i	$0.222262\pi$
$432$		0			0
$433$	−13.5359	+	23.4449i	−0.650494	+	1.12669i	0.332509	+	0.943100i	$0.392105\pi$
$433$	−13.5359	+	23.4449i	−0.650494	+	1.12669i	−0.983003	+	0.183588i	$0.941229\pi$
$434$		−	2.19615i		−	0.105419i
$435$		0			0
$436$	−4.09808	−	2.36603i	−0.196262	−	0.113312i
$437$			3.46410i			0.165710i
$438$		0			0
$439$	−12.5885	−	21.8038i	−0.600814	−	1.04064i	−0.992698	−	0.120626i	$-0.961510\pi$
$439$	−12.5885	−	21.8038i	−0.600814	−	1.04064i	0.391884	−	0.920015i	$-0.371824\pi$
$440$	−1.09808	+	0.633975i	−0.0523487	+	0.0302236i
$441$		0			0
$442$	−12.0622	+	5.96410i	−0.573739	+	0.283683i
$443$	33.6410			1.59833			0.799166	−	0.601110i	$-0.205275\pi$
$443$	33.6410			1.59833			0.799166	+	0.601110i	$0.205275\pi$
$444$		0			0
$445$	3.83013	+	6.63397i	0.181565	+	0.314481i
$446$	12.1962	−	21.1244i	0.577505	−	1.00027i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	−17.8301	−	10.2942i	−0.841456	−	0.485815i	0.0163031	−	0.999867i	$-0.494810\pi$
$449$	−17.8301	−	10.2942i	−0.841456	−	0.485815i	−0.857759	+	0.514052i	$0.828144\pi$
$450$		0			0
$451$	2.59808	−	4.50000i	0.122339	−	0.211897i
$452$	−7.63397	−	13.2224i	−0.359072	−	0.621931i
$453$		0			0
$454$	−18.3923			−0.863194
$455$	−2.63397	−	0.169873i	−0.123483	−	0.00796377i
$456$		0			0
$457$	10.2679	−	5.92820i	0.480314	−	0.277310i	−0.240233	−	0.970715i	$-0.577224\pi$
$457$	10.2679	−	5.92820i	0.480314	−	0.277310i	0.720548	+	0.693406i	$0.243891\pi$
$458$	9.96410	+	17.2583i	0.465592	+	0.806429i
$459$		0			0
$460$			2.53590i			0.118237i
$461$	23.3205	+	13.4641i	1.08614	+	0.627086i	0.932547	−	0.361048i	$-0.117581\pi$
$461$	23.3205	+	13.4641i	1.08614	+	0.627086i	0.153597	+	0.988134i	$0.450914\pi$
$462$		0			0
$463$			6.26795i			0.291296i	0.989336	+	0.145648i	$0.0465267\pi$
$463$			6.26795i			0.291296i	−0.989336	+	0.145648i	$0.953473\pi$
$464$	3.23205	−	5.59808i	0.150044	−	0.259884i
$465$		0			0
$466$	−7.90192	+	4.56218i	−0.366050	+	0.211339i
$467$	−13.8564			−0.641198			−0.320599	−	0.947215i	$-0.603884\pi$
$467$	−13.8564			−0.641198			−0.320599	+	0.947215i	$0.603884\pi$
$468$		0			0
$469$	8.92820			0.412266
$470$	−1.56218	+	0.901924i	−0.0720579	+	0.0416026i
$471$		0			0
$472$	−0.464102	+	0.803848i	−0.0213620	+	0.0370001i
$473$			5.66025i			0.260259i
$474$		0			0
$475$	3.86603	+	2.23205i	0.177385	+	0.102414i
$476$			3.73205i			0.171058i
$477$		0			0
$478$	0.366025	+	0.633975i	0.0167416	+	0.0289973i
$479$	28.1147	−	16.2321i	1.28460	−	0.741661i	0.306910	−	0.951738i	$-0.400705\pi$
$479$	28.1147	−	16.2321i	1.28460	−	0.741661i	0.977685	+	0.210077i	$0.0673715\pi$
$480$		0			0
$481$	20.1962	+	13.4641i	0.920865	+	0.613910i
$482$	−8.00000			−0.364390
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	−5.73205	+	9.92820i	−0.260279	+	0.450816i
$486$		0			0
$487$	−14.4282	−	8.33013i	−0.653804	−	0.377474i	0.136108	−	0.990694i	$-0.456541\pi$
$487$	−14.4282	−	8.33013i	−0.653804	−	0.377474i	−0.789912	+	0.613220i	$0.789874\pi$
$488$	4.50000	+	2.59808i	0.203705	+	0.117609i
$489$		0			0
$490$	−0.366025	+	0.633975i	−0.0165353	+	0.0286401i
$491$	−17.7321	−	30.7128i	−0.800236	−	1.38605i	−0.919460	−	0.393182i	$-0.871374\pi$
$491$	−17.7321	−	30.7128i	−0.800236	−	1.38605i	0.119224	−	0.992867i	$-0.461959\pi$
$492$		0			0
$493$	−24.1244			−1.08651
$494$	1.59808	+	3.23205i	0.0719008	+	0.145417i
$495$		0			0
$496$	−1.90192	+	1.09808i	−0.0853989	+	0.0493051i
$497$	1.09808	+	1.90192i	0.0492554	+	0.0853129i
$498$		0			0
$499$			11.5167i			0.515557i	0.966204	+	0.257778i	$0.0829904\pi$
$499$			11.5167i			0.515557i	−0.966204	+	0.257778i	$0.917010\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$		0			0
$502$			13.1244i			0.585769i
$503$	3.46410	−	6.00000i	0.154457	−	0.267527i	−0.778404	−	0.627763i	$-0.783971\pi$
$503$	3.46410	−	6.00000i	0.154457	−	0.267527i	0.932861	+	0.360236i	$0.117304\pi$
$504$		0			0
$505$	1.94744	−	1.12436i	0.0866600	−	0.0500332i
$506$	−6.00000			−0.266733
$507$		0			0
$508$	−15.4641			−0.686109
$509$	19.3468	−	11.1699i	0.857531	−	0.495096i	−0.00565352	−	0.999984i	$-0.501800\pi$
$509$	19.3468	−	11.1699i	0.857531	−	0.495096i	0.863185	+	0.504888i	$0.168466\pi$
$510$		0			0
$511$	−2.73205	+	4.73205i	−0.120859	+	0.209334i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−17.8923	−	10.3301i	−0.789196	−	0.455642i
$515$		−	10.7846i		−	0.475227i
$516$		0			0
$517$	−2.13397	−	3.69615i	−0.0938521	−	0.162557i
$518$	5.83013	−	3.36603i	0.256161	−	0.147895i
$519$		0			0
$520$	1.16987	+	2.36603i	0.0513023	+	0.103757i
$521$	−7.05256			−0.308978			−0.154489	−	0.987994i	$-0.549373\pi$
$521$	−7.05256			−0.308978			−0.154489	+	0.987994i	$0.549373\pi$
$522$		0			0
$523$	6.93782	+	12.0167i	0.303370	+	0.525452i	0.976897	−	0.213711i	$-0.0685549\pi$
$523$	6.93782	+	12.0167i	0.303370	+	0.525452i	−0.673527	+	0.739162i	$0.735222\pi$
$524$	6.92820	−	12.0000i	0.302660	−	0.524222i
$525$		0			0
$526$	−13.0981	−	7.56218i	−0.571103	−	0.329727i
$527$	7.09808	+	4.09808i	0.309197	+	0.178515i
$528$		0			0
$529$	5.50000	−	9.52628i	0.239130	−	0.414186i
$530$	−2.56218	−	4.43782i	−0.111294	−	0.192767i
$531$		0			0
$532$	1.00000			0.0433555
$533$	−9.00000	−	6.00000i	−0.389833	−	0.259889i
$534$		0			0
$535$	−6.88269	+	3.97372i	−0.297564	+	0.171799i
$536$	−4.46410	−	7.73205i	−0.192820	−	0.333974i
$537$		0			0
$538$			9.85641i			0.424940i
$539$	−1.50000	−	0.866025i	−0.0646096	−	0.0373024i
$540$		0			0
$541$			24.3397i			1.04645i	0.852195	+	0.523224i	$0.175271\pi$
$541$			24.3397i			1.04645i	−0.852195	+	0.523224i	$0.824729\pi$
$542$	−14.0263	+	24.2942i	−0.602480	+	1.04353i
$543$		0			0
$544$	3.23205	−	1.86603i	0.138573	−	0.0800052i
$545$	3.46410			0.148386
$546$		0			0
$547$	−1.26795			−0.0542136			−0.0271068	−	0.999633i	$-0.508629\pi$
$547$	−1.26795			−0.0542136			−0.0271068	+	0.999633i	$0.508629\pi$
$548$	−12.4641	+	7.19615i	−0.532440	+	0.307404i
$549$		0			0
$550$	−3.86603	+	6.69615i	−0.164848	+	0.285525i
$551$			6.46410i			0.275380i
$552$		0			0
$553$	1.79423	+	1.03590i	0.0762984	+	0.0440509i
$554$		−	9.32051i		−	0.395990i
$555$		0			0
$556$	5.79423	+	10.0359i	0.245730	+	0.425617i
$557$	−11.3038	+	6.52628i	−0.478959	+	0.276527i	−0.719983	−	0.693992i	$-0.755850\pi$
$557$	−11.3038	+	6.52628i	−0.478959	+	0.276527i	0.241023	+	0.970519i	$0.422517\pi$
$558$		0			0
$559$	11.7583	+	0.758330i	0.497324	+	0.0320740i
$560$	0.732051			0.0309348
$561$		0			0
$562$	−0.169873	−	0.294229i	−0.00716566	−	0.0124113i
$563$	18.0981	−	31.3468i	0.762743	−	1.32111i	−0.178689	−	0.983906i	$-0.557185\pi$
$563$	18.0981	−	31.3468i	0.762743	−	1.32111i	0.941432	−	0.337204i	$-0.109481\pi$
$564$		0			0
$565$	9.67949	+	5.58846i	0.407219	+	0.235108i
$566$	−8.53590	−	4.92820i	−0.358791	−	0.207148i
$567$		0			0
$568$	1.09808	−	1.90192i	0.0460743	−	0.0798029i
$569$	19.2224	+	33.2942i	0.805846	+	1.39577i	0.915718	+	0.401821i	$0.131623\pi$
$569$	19.2224	+	33.2942i	0.805846	+	1.39577i	−0.109872	+	0.993946i	$0.535044\pi$
$570$		0			0
$571$	−16.9808			−0.710623			−0.355311	−	0.934748i	$-0.615625\pi$
$571$	−16.9808			−0.710623			−0.355311	+	0.934748i	$0.615625\pi$
$572$	−5.59808	+	2.76795i	−0.234067	+	0.115734i
$573$		0			0
$574$	−2.59808	+	1.50000i	−0.108442	+	0.0626088i
$575$	7.73205	+	13.3923i	0.322449	+	0.558498i
$576$		0			0
$577$			10.3397i			0.430449i	0.976565	+	0.215225i	$0.0690484\pi$
$577$			10.3397i			0.430449i	−0.976565	+	0.215225i	$0.930952\pi$
$578$	2.66025	+	1.53590i	0.110652	+	0.0638850i
$579$		0			0
$580$			4.73205i			0.196488i
$581$	−0.0980762	+	0.169873i	−0.00406889	+	0.00704752i
$582$		0			0
$583$	10.5000	−	6.06218i	0.434866	−	0.251070i
$584$	5.46410			0.226106
$585$		0			0
$586$	17.0718			0.705229
$587$	−10.6865	+	6.16987i	−0.441080	+	0.254658i	−0.704056	−	0.710145i	$-0.748630\pi$
$587$	−10.6865	+	6.16987i	−0.441080	+	0.254658i	0.262975	+	0.964803i	$0.415296\pi$
$588$		0			0
$589$	1.09808	−	1.90192i	0.0452454	−	0.0783674i
$590$		−	0.679492i		−	0.0279742i
$591$		0			0
$592$	−5.83013	−	3.36603i	−0.239617	−	0.138343i
$593$			0.464102i			0.0190584i	0.999955	+	0.00952918i	$0.00303328\pi$
$593$			0.464102i			0.0190584i	−0.999955	+	0.00952918i	$0.996967\pi$
$594$		0			0
$595$	−1.36603	−	2.36603i	−0.0560016	−	0.0969976i
$596$	−12.0000	+	6.92820i	−0.491539	+	0.283790i
$597$		0			0
$598$	−0.803848	+	12.4641i	−0.0328718	+	0.509695i
$599$	28.6410			1.17024			0.585120	−	0.810947i	$-0.301047\pi$
$599$	28.6410			1.17024			0.585120	+	0.810947i	$0.301047\pi$
$600$		0			0
$601$	11.3660	+	19.6865i	0.463630	+	0.803030i	0.999139	−	0.0414993i	$-0.0132134\pi$
$601$	11.3660	+	19.6865i	0.463630	+	0.803030i	−0.535509	+	0.844530i	$0.679880\pi$
$602$	1.63397	−	2.83013i	0.0665958	−	0.115347i
$603$		0			0
$604$	−4.50000	−	2.59808i	−0.183102	−	0.105714i
$605$	−5.07180	−	2.92820i	−0.206198	−	0.119048i
$606$		0			0
$607$	15.7583	−	27.2942i	0.639611	−	1.10784i	−0.345907	−	0.938269i	$-0.612429\pi$
$607$	15.7583	−	27.2942i	0.639611	−	1.10784i	0.985518	−	0.169570i	$-0.0542378\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$		0			0
$610$	−3.80385			−0.154013
$611$	−7.96410	+	3.93782i	−0.322193	+	0.159307i
$612$		0			0
$613$	3.46410	−	2.00000i	0.139914	−	0.0807792i	−0.428409	−	0.903585i	$-0.640926\pi$
$613$	3.46410	−	2.00000i	0.139914	−	0.0807792i	0.568323	+	0.822806i	$0.307592\pi$
$614$	−4.30385	−	7.45448i	−0.173689	−	0.300838i
$615$		0			0
$616$			1.73205i			0.0697863i
$617$	−1.90192	−	1.09808i	−0.0765686	−	0.0442069i	0.461227	−	0.887282i	$-0.347409\pi$
$617$	−1.90192	−	1.09808i	−0.0765686	−	0.0442069i	−0.537795	+	0.843075i	$0.680743\pi$
$618$		0			0
$619$		−	22.0718i		−	0.887140i	−0.896240	−	0.443570i	$-0.853712\pi$
$619$		−	22.0718i		−	0.887140i	0.896240	−	0.443570i	$-0.146288\pi$
$620$	0.803848	−	1.39230i	0.0322833	−	0.0559163i
$621$		0			0
$622$	3.69615	−	2.13397i	0.148202	−	0.0855646i
$623$	10.4641			0.419235
$624$		0			0
$625$	17.2487			0.689948
$626$	11.7058	−	6.75833i	0.467857	−	0.270117i
$627$		0			0
$628$	−0.267949	+	0.464102i	−0.0106923	+	0.0185197i
$629$			25.1244i			1.00177i
$630$		0			0
$631$	14.5526	+	8.40192i	0.579328	+	0.334475i	0.760866	−	0.648909i	$-0.224774\pi$
$631$	14.5526	+	8.40192i	0.579328	+	0.334475i	−0.181538	+	0.983384i	$0.558108\pi$
$632$		−	2.07180i		−	0.0824117i
$633$		0			0
$634$	5.92820	+	10.2679i	0.235439	+	0.407792i
$635$	9.80385	−	5.66025i	0.389054	−	0.224620i
$636$		0			0
$637$	−2.00000	+	3.00000i	−0.0792429	+	0.118864i
$638$	−11.1962			−0.443260
$639$		0			0
$640$	−0.366025	−	0.633975i	−0.0144684	−	0.0250600i
$641$	−15.5885	+	27.0000i	−0.615707	+	1.06644i	0.374553	+	0.927206i	$0.377796\pi$
$641$	−15.5885	+	27.0000i	−0.615707	+	1.06644i	−0.990260	+	0.139230i	$0.955537\pi$
$642$		0			0
$643$	28.4545	+	16.4282i	1.12214	+	0.647865i	0.941945	−	0.335767i	$-0.108995\pi$
$643$	28.4545	+	16.4282i	1.12214	+	0.647865i	0.180190	+	0.983632i	$0.442329\pi$
$644$	3.00000	+	1.73205i	0.118217	+	0.0682524i
$645$		0			0
$646$	−1.86603	+	3.23205i	−0.0734178	+	0.127163i
$647$	−17.9186	−	31.0359i	−0.704452	−	1.22015i	−0.966889	−	0.255198i	$-0.917859\pi$
$647$	−17.9186	−	31.0359i	−0.704452	−	1.22015i	0.262437	−	0.964949i	$-0.415474\pi$
$648$		0			0
$649$	1.60770			0.0631076
$650$	13.3923	+	8.92820i	0.525289	+	0.350193i
$651$		0			0
$652$	2.36603	−	1.36603i	0.0926607	−	0.0534977i
$653$	23.3564	+	40.4545i	0.914007	+	1.58311i	0.808349	+	0.588704i	$0.200362\pi$
$653$	23.3564	+	40.4545i	0.914007	+	1.58311i	0.105658	+	0.994403i	$0.466305\pi$
$654$		0			0
$655$			10.1436i			0.396343i
$656$	2.59808	+	1.50000i	0.101438	+	0.0585652i
$657$		0			0
$658$			2.46410i			0.0960607i
$659$	9.30385	−	16.1147i	0.362426	−	0.627741i	−0.625933	−	0.779877i	$-0.715282\pi$
$659$	9.30385	−	16.1147i	0.362426	−	0.627741i	0.988360	+	0.152136i	$0.0486151\pi$
$660$		0			0
$661$	10.7321	−	6.19615i	0.417428	−	0.241002i	−0.276548	−	0.961000i	$-0.589190\pi$
$661$	10.7321	−	6.19615i	0.417428	−	0.241002i	0.693976	+	0.719998i	$0.255857\pi$
$662$	27.8564			1.08267
$663$		0			0
$664$	0.196152			0.00761219
$665$	−0.633975	+	0.366025i	−0.0245845	+	0.0141939i
$666$		0			0
$667$	−11.1962	+	19.3923i	−0.433517	+	0.750873i
$668$		−	13.8564i		−	0.536120i
$669$		0			0
$670$	5.66025	+	3.26795i	0.218675	+	0.126252i
$671$		−	9.00000i		−	0.347441i
$672$		0			0
$673$	−16.3564	−	28.3301i	−0.630493	−	1.09205i	−0.987451	−	0.157926i	$-0.949519\pi$
$673$	−16.3564	−	28.3301i	−0.630493	−	1.09205i	0.356958	−	0.934120i	$-0.383814\pi$
$674$	−16.4545	+	9.50000i	−0.633803	+	0.365926i
$675$		0			0
$676$	5.00000	+	12.0000i	0.192308	+	0.461538i
$677$	−36.7321			−1.41173			−0.705864	−	0.708348i	$-0.749441\pi$
$677$	−36.7321			−1.41173			−0.705864	+	0.708348i	$0.749441\pi$
$678$		0			0
$679$	7.83013	+	13.5622i	0.300493	+	0.520469i
$680$	−1.36603	+	2.36603i	−0.0523847	+	0.0907329i
$681$		0			0
$682$	3.29423	+	1.90192i	0.126143	+	0.0728284i
$683$	−25.6410	−	14.8038i	−0.981126	−	0.566453i	−0.0785163	−	0.996913i	$-0.525018\pi$
$683$	−25.6410	−	14.8038i	−0.981126	−	0.566453i	−0.902610	+	0.430459i	$0.858352\pi$
$684$		0			0
$685$	5.26795	−	9.12436i	0.201278	−	0.348624i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−3.26795			−0.124589
$689$	−11.1865	−	22.6244i	−0.426173	−	0.861919i
$690$		0			0
$691$	37.8564	−	21.8564i	1.44013	−	0.831457i	0.442268	−	0.896883i	$-0.354174\pi$
$691$	37.8564	−	21.8564i	1.44013	−	0.831457i	0.997857	+	0.0654260i	$0.0208406\pi$
$692$	−4.56218	−	7.90192i	−0.173428	−	0.300386i
$693$		0			0
$694$		−	5.39230i		−	0.204689i
$695$	−7.34679	−	4.24167i	−0.278680	−	0.160896i
$696$		0			0
$697$		−	11.1962i		−	0.424085i
$698$	−11.8564	+	20.5359i	−0.448772	+	0.777295i
$699$		0			0
$700$	3.86603	−	2.23205i	0.146122	−	0.0843636i
$701$	1.14359			0.0431929			0.0215965	−	0.999767i	$-0.493125\pi$
$701$	1.14359			0.0431929			0.0215965	+	0.999767i	$0.493125\pi$
$702$		0			0
$703$	6.73205			0.253904
$704$	1.50000	−	0.866025i	0.0565334	−	0.0326396i
$705$		0			0
$706$	4.73205	−	8.19615i	0.178093	−	0.308466i
$707$		−	3.07180i		−	0.115527i
$708$		0			0
$709$	−27.7583	−	16.0263i	−1.04249	−	0.601880i	−0.121950	−	0.992536i	$-0.538915\pi$
$709$	−27.7583	−	16.0263i	−1.04249	−	0.601880i	−0.920536	+	0.390657i	$0.872248\pi$
$710$			1.60770i			0.0603357i
$711$		0			0
$712$	−5.23205	−	9.06218i	−0.196079	−	0.339619i
$713$	6.58846	−	3.80385i	0.246740	−	0.142455i
$714$		0			0
$715$	2.53590	−	3.80385i	0.0948372	−	0.142256i
$716$	−11.4641			−0.428434
$717$		0			0
$718$	−1.90192	−	3.29423i	−0.0709792	−	0.122940i
$719$	−13.2583	+	22.9641i	−0.494452	+	0.856416i	−0.999980	−	0.00639415i	$-0.997965\pi$
$719$	−13.2583	+	22.9641i	−0.494452	+	0.856416i	0.505527	+	0.862811i	$0.331298\pi$
$720$		0			0
$721$	−12.7583	−	7.36603i	−0.475145	−	0.274325i
$722$	−15.5885	−	9.00000i	−0.580142	−	0.334945i
$723$		0			0
$724$	1.33013	−	2.30385i	0.0494338	−	0.0856218i
$725$	14.4282	+	24.9904i	0.535850	+	0.928119i
$726$		0			0
$727$	19.3205			0.716558			0.358279	−	0.933615i	$-0.383364\pi$
$727$	19.3205			0.716558			0.358279	+	0.933615i	$0.383364\pi$
$728$	3.59808	+	0.232051i	0.133354	+	0.00860038i
$729$		0			0
$730$	−3.46410	+	2.00000i	−0.128212	+	0.0740233i
$731$	6.09808	+	10.5622i	0.225545	+	0.390656i
$732$		0			0
$733$			48.1769i			1.77945i	0.456492	+	0.889727i	$0.349106\pi$
$733$			48.1769i			1.77945i	−0.456492	+	0.889727i	$0.650894\pi$
$734$	−21.9282	−	12.6603i	−0.809385	−	0.467299i
$735$		0			0
$736$		−	3.46410i		−	0.127688i
$737$	−7.73205	+	13.3923i	−0.284814	+	0.493312i
$738$		0			0
$739$	13.1436	−	7.58846i	0.483495	−	0.279146i	−0.238377	−	0.971173i	$-0.576615\pi$
$739$	13.1436	−	7.58846i	0.483495	−	0.279146i	0.721872	+	0.692027i	$0.243282\pi$
$740$	4.92820			0.181164
$741$		0			0
$742$	−7.00000			−0.256978
$743$	12.1699	−	7.02628i	0.446469	−	0.257769i	−0.259869	−	0.965644i	$-0.583679\pi$
$743$	12.1699	−	7.02628i	0.446469	−	0.257769i	0.706338	+	0.707875i	$0.250346\pi$
$744$		0			0
$745$	5.07180	−	8.78461i	0.185816	−	0.321843i
$746$			9.66025i			0.353687i
$747$		0			0
$748$	−5.59808	−	3.23205i	−0.204686	−	0.118175i
$749$			10.8564i			0.396684i
$750$		0			0
$751$	−9.57180	−	16.5788i	−0.349280	−	0.604970i	0.636842	−	0.770994i	$-0.280240\pi$
$751$	−9.57180	−	16.5788i	−0.349280	−	0.604970i	−0.986122	+	0.166024i	$0.946907\pi$
$752$	2.13397	−	1.23205i	0.0778180	−	0.0449283i
$753$		0			0
$754$	−1.50000	+	23.2583i	−0.0546268	+	0.847018i
$755$	3.80385			0.138436
$756$		0			0
$757$	0.294229	+	0.509619i	0.0106939	+	0.0185224i	0.871323	−	0.490710i	$-0.163263\pi$
$757$	0.294229	+	0.509619i	0.0106939	+	0.0185224i	−0.860629	+	0.509233i	$0.829929\pi$
$758$	14.2224	−	24.6340i	0.516582	−	0.894746i
$759$		0			0
$760$	0.633975	+	0.366025i	0.0229967	+	0.0132771i
$761$	−13.2679	−	7.66025i	−0.480963	−	0.277684i	0.239855	−	0.970809i	$-0.422900\pi$
$761$	−13.2679	−	7.66025i	−0.480963	−	0.277684i	−0.720818	+	0.693125i	$0.756233\pi$
$762$		0			0
$763$	2.36603	−	4.09808i	0.0856559	−	0.148360i
$764$	−11.5622	−	20.0263i	−0.418305	−	0.724525i
$765$		0			0
$766$	5.53590			0.200020
$767$	0.215390	−	3.33975i	0.00777729	−	0.120591i
$768$		0			0
$769$	36.6340	−	21.1506i	1.32105	−	0.762711i	0.337158	−	0.941448i	$-0.390534\pi$
$769$	36.6340	−	21.1506i	1.32105	−	0.762711i	0.983897	+	0.178737i	$0.0572010\pi$
$770$	−0.633975	−	1.09808i	−0.0228469	−	0.0395719i
$771$		0			0
$772$			1.19615i			0.0430505i
$773$	40.8564	+	23.5885i	1.46950	+	0.848418i	0.999415	−	0.0342018i	$-0.0108889\pi$
$773$	40.8564	+	23.5885i	1.46950	+	0.848418i	0.470088	+	0.882620i	$0.344222\pi$
$774$		0			0
$775$		−	9.80385i		−	0.352165i
$776$	7.83013	−	13.5622i	0.281085	−	0.486854i
$777$		0			0
$778$	7.26795	−	4.19615i	0.260569	−	0.150439i
$779$	−3.00000			−0.107486
$780$		0			0
$781$	−3.80385			−0.136112
$782$	−11.1962	+	6.46410i	−0.400374	+	0.231156i
$783$		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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.366025 + 0.633975i) q^{10} +(-1.50000 + 0.866025i) q^{11} +(1.59808 + 3.23205i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.86603 + 3.23205i) q^{17} +(0.866025 + 0.500000i) q^{19} +(0.633975 + 0.366025i) q^{20} +(-0.866025 + 1.50000i) q^{22} +(1.73205 + 3.00000i) q^{23} +4.46410 q^{25} +(3.00000 + 2.00000i) q^{26} +(0.866025 - 0.500000i) q^{28} +(3.23205 + 5.59808i) q^{29} -2.19615i q^{31} +(-0.866025 - 0.500000i) q^{32} +3.73205i q^{34} +(-0.366025 + 0.633975i) q^{35} +(5.83013 - 3.36603i) q^{37} +1.00000 q^{38} +0.732051 q^{40} +(-2.59808 + 1.50000i) q^{41} +(1.63397 - 2.83013i) q^{43} +1.73205i q^{44} +(3.00000 + 1.73205i) q^{46} +2.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(3.86603 - 2.23205i) q^{50} +(3.59808 + 0.232051i) q^{52} -7.00000 q^{53} +(-0.633975 - 1.09808i) q^{55} +(0.500000 - 0.866025i) q^{56} +(5.59808 + 3.23205i) q^{58} +(-0.803848 - 0.464102i) q^{59} +(-2.59808 + 4.50000i) q^{61} +(-1.09808 - 1.90192i) q^{62} -1.00000 q^{64} +(-2.36603 + 1.16987i) q^{65} +(7.73205 - 4.46410i) q^{67} +(1.86603 + 3.23205i) q^{68} +0.732051i q^{70} +(1.90192 + 1.09808i) q^{71} +5.46410i q^{73} +(3.36603 - 5.83013i) q^{74} +(0.866025 - 0.500000i) q^{76} -1.73205 q^{77} +2.07180 q^{79} +(0.633975 - 0.366025i) q^{80} +(-1.50000 + 2.59808i) q^{82} +0.196152i q^{83} +(-2.36603 - 1.36603i) q^{85} -3.26795i q^{86} +(0.866025 + 1.50000i) q^{88} +(9.06218 - 5.23205i) q^{89} +(-0.232051 + 3.59808i) q^{91} +3.46410 q^{92} +(1.23205 + 2.13397i) q^{94} +(-0.366025 + 0.633975i) q^{95} +(13.5622 + 7.83013i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} - 2 q^{10} - 6 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} - 4 q^{17} + 6 q^{20} + 4 q^{25} + 12 q^{26} + 6 q^{29} + 2 q^{35} + 6 q^{37} + 4 q^{38} - 4 q^{40} + 10 q^{43} + 12 q^{46} + 2 q^{49} + 12 q^{50} + 4 q^{52} - 28 q^{53} - 6 q^{55} + 2 q^{56} + 12 q^{58} - 24 q^{59} + 6 q^{62} - 4 q^{64} - 6 q^{65} + 24 q^{67} + 4 q^{68} + 18 q^{71} + 10 q^{74} + 36 q^{79} + 6 q^{80} - 6 q^{82} - 6 q^{85} + 12 q^{89} + 6 q^{91} - 2 q^{94} + 2 q^{95} + 30 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 - 2 * q^10 - 6 * q^11 - 4 * q^13 + 4 * q^14 - 2 * q^16 - 4 * q^17 + 6 * q^20 + 4 * q^25 + 12 * q^26 + 6 * q^29 + 2 * q^35 + 6 * q^37 + 4 * q^38 - 4 * q^40 + 10 * q^43 + 12 * q^46 + 2 * q^49 + 12 * q^50 + 4 * q^52 - 28 * q^53 - 6 * q^55 + 2 * q^56 + 12 * q^58 - 24 * q^59 + 6 * q^62 - 4 * q^64 - 6 * q^65 + 24 * q^67 + 4 * q^68 + 18 * q^71 + 10 * q^74 + 36 * q^79 + 6 * q^80 - 6 * q^82 - 6 * q^85 + 12 * q^89 + 6 * q^91 - 2 * q^94 + 2 * q^95 + 30 * q^97

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