LMFDB - Embedded newform 3024.2.q.b.2881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.b.2305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-2.50000 - 4.33013i) q^{11} +(2.50000 + 4.33013i) q^{13} +(1.50000 - 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-1.50000 + 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{29} +(-0.500000 - 2.59808i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(-2.50000 - 4.33013i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(1.00000 - 6.92820i) q^{49} +(-4.50000 + 7.79423i) q^{53} +5.00000 q^{55} -14.0000 q^{61} -5.00000 q^{65} -4.00000 q^{67} -12.0000 q^{71} +(-1.50000 + 2.59808i) q^{73} +(12.5000 + 4.33013i) q^{77} -8.00000 q^{79} +(4.50000 - 7.79423i) q^{83} +(1.50000 + 2.59808i) q^{85} +(-6.50000 - 11.2583i) q^{89} +(-12.5000 - 4.33013i) q^{91} -1.00000 q^{95} +(4.50000 - 7.79423i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{5} - 4 q^{7}+O(q^{10}) $ 2 * q - q^5 - 4 * q^7	$ 2 q - q^{5} - 4 q^{7} - 5 q^{11} + 5 q^{13} + 3 q^{17} + q^{19} - 3 q^{23} + 4 q^{25} - q^{29} - q^{35} - 3 q^{37} - 5 q^{41} - q^{43} + 2 q^{49} - 9 q^{53} + 10 q^{55} - 28 q^{61} - 10 q^{65} - 8 q^{67} - 24 q^{71} - 3 q^{73} + 25 q^{77} - 16 q^{79} + 9 q^{83} + 3 q^{85} - 13 q^{89} - 25 q^{91} - 2 q^{95} + 9 q^{97}+O(q^{100}) $ 2 * q - q^5 - 4 * q^7 - 5 * q^11 + 5 * q^13 + 3 * q^17 + q^19 - 3 * q^23 + 4 * q^25 - q^29 - q^35 - 3 * q^37 - 5 * q^41 - q^43 + 2 * q^49 - 9 * q^53 + 10 * q^55 - 28 * q^61 - 10 * q^65 - 8 * q^67 - 24 * q^71 - 3 * q^73 + 25 * q^77 - 16 * q^79 + 9 * q^83 + 3 * q^85 - 13 * q^89 - 25 * q^91 - 2 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		0			0
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		0			0
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i	−0.908708	−	0.417432i	$-0.862930\pi$
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i	0.815861	+	0.578249i	$0.196264\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.500000	−	2.59808i	−0.0845154	−	0.439155i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	0.602072	−	0.798441i	$-0.294342\pi$
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	−0.992507	+	0.122189i	$0.961009\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		0			0
$55$	5.00000			0.674200
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.00000			−0.620174
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	−0.940356	−	0.340193i	$-0.889507\pi$
$73$	−1.50000	+	2.59808i	−0.175562	+	0.304082i	0.764794	+	0.644275i	$0.222841\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	12.5000	+	4.33013i	1.42451	+	0.493464i
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.50000	−	11.2583i	−0.688999	−	1.19338i	−0.972162	−	0.234309i	$-0.924717\pi$
$89$	−6.50000	−	11.2583i	−0.688999	−	1.19338i	0.283164	−	0.959072i	$-0.408616\pi$
$90$		0			0
$91$	−12.5000	−	4.33013i	−1.31036	−	0.453921i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.00000			−0.102598
$96$		0			0
$97$	4.50000	−	7.79423i	0.456906	−	0.791384i	−0.541890	−	0.840450i	$-0.682291\pi$
$97$	4.50000	−	7.79423i	0.456906	−	0.791384i	0.998796	+	0.0490655i	$0.0156243\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.50000	−	14.7224i	−0.845782	−	1.46494i	−0.884941	−	0.465704i	$-0.845801\pi$
$101$	−8.50000	−	14.7224i	−0.845782	−	1.46494i	0.0391591	−	0.999233i	$-0.487532\pi$
$102$		0			0
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	−0.889607	−	0.456727i	$-0.849022\pi$
$103$	−0.500000	+	0.866025i	−0.0492665	+	0.0853320i	0.840341	+	0.542059i	$0.182355\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	−0.904396	−	0.426694i	$-0.859678\pi$
$107$	−8.50000	−	14.7224i	−0.821726	−	1.42327i	0.0826699	−	0.996577i	$-0.473655\pi$
$108$		0			0
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	0.841549	−	0.540181i	$-0.181644\pi$
$113$	−0.500000	−	0.866025i	−0.0470360	−	0.0814688i	−0.888585	+	0.458712i	$0.848311\pi$
$114$		0			0
$115$	−1.50000	−	2.59808i	−0.139876	−	0.242272i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.50000	+	7.79423i	0.137505	+	0.714496i
$120$		0			0
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	−0.843356	−	0.537355i	$-0.819423\pi$
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	0.887041	+	0.461690i	$0.152757\pi$
$132$		0			0
$133$	−2.50000	−	0.866025i	−0.216777	−	0.0750939i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$		0			0
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	0.991303	−	0.131597i	$-0.0420106\pi$
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	−0.609618	+	0.792695i	$0.708677\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	12.5000	−	21.6506i	1.04530	−	1.81052i
$144$		0			0
$145$	−0.500000	−	0.866025i	−0.0415227	−	0.0719195i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	0.949637	−	0.313353i	$-0.101452\pi$
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	−0.746190	+	0.665733i	$0.768119\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.50000	−	7.79423i	−0.118217	−	0.614271i
$162$		0			0
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.50000	+	16.4545i	0.735132	+	1.27329i	0.954665	+	0.297681i	$0.0962132\pi$
$167$	9.50000	+	16.4545i	0.735132	+	1.27329i	−0.219533	+	0.975605i	$0.570453\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	14.0000			1.06440			0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000			1.06440			0.532200	+	0.846619i	$0.321365\pi$
$174$		0			0
$175$	−10.0000	−	3.46410i	−0.755929	−	0.261861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	0.254770	+	0.967002i	$0.418000\pi$
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	−0.964833	+	0.262864i	$0.915333\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.00000			0.220564
$186$		0			0
$187$	−15.0000			−1.09691
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$		0			0
$193$	−10.0000			−0.719816			−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000			−0.719816			−0.359908	+	0.932988i	$0.617192\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	−0.807950	−	0.589252i	$-0.799423\pi$
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	0.914282	+	0.405079i	$0.132756\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.500000	−	2.59808i	−0.0350931	−	0.182349i
$204$		0			0
$205$	5.00000			0.349215
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.50000	−	4.33013i	0.172929	−	0.299521i
$210$		0			0
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.500000	−	0.866025i	−0.0340997	−	0.0590624i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.0000			1.00901
$222$		0			0
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	−0.350100	−	0.936713i	$-0.613852\pi$
$223$	9.50000	−	16.4545i	0.636167	−	1.10187i	0.986267	−	0.165161i	$-0.0528144\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$		0			0
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	−0.849032	−	0.528341i	$-0.822814\pi$
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	0.882073	+	0.471113i	$0.156147\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	0.910968	−	0.412477i	$-0.135336\pi$
$233$	1.50000	+	2.59808i	0.0982683	+	0.170206i	−0.812700	+	0.582683i	$0.802003\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	0.999854	−	0.0170808i	$-0.00543724\pi$
$239$	7.50000	+	12.9904i	0.485135	+	0.840278i	−0.514719	+	0.857359i	$0.672104\pi$
$240$		0			0
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	0.632709	−	0.774389i	$-0.281943\pi$
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	−0.986996	+	0.160748i	$0.948609\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.50000	+	4.33013i	0.351382	+	0.276642i
$246$		0			0
$247$	−2.50000	+	4.33013i	−0.159071	+	0.275519i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−28.0000			−1.76734			−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000			−1.76734			−0.883672	+	0.468106i	$0.844936\pi$
$252$		0			0
$253$	15.0000			0.943042
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.5000	+	25.1147i	−0.904485	+	1.56661i	−0.0828783	+	0.996560i	$0.526411\pi$
$257$	−14.5000	+	25.1147i	−0.904485	+	1.56661i	−0.821607	+	0.570055i	$0.806922\pi$
$258$		0			0
$259$	7.50000	+	2.59808i	0.466027	+	0.161437i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.50000	−	4.33013i	−0.154157	−	0.267007i	0.778595	−	0.627527i	$-0.215933\pi$
$263$	−2.50000	−	4.33013i	−0.154157	−	0.267007i	−0.932752	+	0.360520i	$0.882599\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$		0			0
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.0000	−	17.3205i	0.603023	−	1.04447i
$276$		0			0
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	−0.996484	−	0.0837823i	$-0.973300\pi$
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	0.425684	−	0.904872i	$-0.360033\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.5000	+	25.1147i	−0.864997	+	1.49822i	0.00205220	+	0.999998i	$0.499347\pi$
$281$	−14.5000	+	25.1147i	−0.864997	+	1.49822i	−0.867050	+	0.498222i	$0.833987\pi$
$282$		0			0
$283$	−28.0000			−1.66443			−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000			−1.66443			−0.832214	+	0.554455i	$0.812927\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	12.5000	+	4.33013i	0.737852	+	0.255599i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.50000	−	4.33013i	−0.146052	−	0.252969i	0.783713	−	0.621123i	$-0.213323\pi$
$293$	−2.50000	−	4.33013i	−0.146052	−	0.252969i	−0.929765	+	0.368154i	$0.879990\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−15.0000			−0.867472
$300$		0			0
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.00000	−	12.1244i	0.400819	−	0.694239i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$		0			0
$319$	5.00000			0.279946
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.00000			0.166924
$324$		0			0
$325$	−10.0000	+	17.3205i	−0.554700	+	0.960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.00000	−	3.46410i	0.109272	−	0.189264i
$336$		0			0
$337$	14.5000	+	25.1147i	0.789865	+	1.36809i	0.926049	+	0.377403i	$0.123183\pi$
$337$	14.5000	+	25.1147i	0.789865	+	1.36809i	−0.136184	+	0.990684i	$0.543484\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.00000			0.214731			0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000			0.214731			0.107366	+	0.994220i	$0.465758\pi$
$348$		0			0
$349$	−9.50000	+	16.4545i	−0.508523	+	0.880788i	0.491428	+	0.870918i	$0.336475\pi$
$349$	−9.50000	+	16.4545i	−0.508523	+	0.880788i	−0.999951	+	0.00987003i	$0.996858\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.50000	+	9.52628i	0.292735	+	0.507033i	0.974456	−	0.224580i	$-0.0721011\pi$
$353$	5.50000	+	9.52628i	0.292735	+	0.507033i	−0.681720	+	0.731613i	$0.738768\pi$
$354$		0			0
$355$	6.00000	−	10.3923i	0.318447	−	0.551566i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.50000	+	9.52628i	0.290279	+	0.502778i	0.973876	−	0.227082i	$-0.0729186\pi$
$359$	5.50000	+	9.52628i	0.290279	+	0.502778i	−0.683597	+	0.729860i	$0.739585\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.50000	−	2.59808i	−0.0785136	−	0.135990i
$366$		0			0
$367$	−1.50000	−	2.59808i	−0.0782994	−	0.135618i	0.824217	−	0.566274i	$-0.191616\pi$
$367$	−1.50000	−	2.59808i	−0.0782994	−	0.135618i	−0.902516	+	0.430656i	$0.858282\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.50000	−	23.3827i	−0.233628	−	1.21397i
$372$		0			0
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.00000			−0.257513
$378$		0			0
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	0.282079	+	0.959391i	$0.408976\pi$
$383$	−13.5000	+	23.3827i	−0.689818	+	1.19480i	−0.971897	+	0.235408i	$0.924357\pi$
$384$		0			0
$385$	−10.0000	+	8.66025i	−0.509647	+	0.441367i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	0.729103	−	0.684403i	$-0.239937\pi$
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	−0.957263	+	0.289220i	$0.906604\pi$
$390$		0			0
$391$	4.50000	+	7.79423i	0.227575	+	0.394171i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$		0			0
$397$	−7.50000	−	12.9904i	−0.376414	−	0.651969i	0.614123	−	0.789210i	$-0.289510\pi$
$397$	−7.50000	−	12.9904i	−0.376414	−	0.651969i	−0.990538	+	0.137241i	$0.956176\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.50000	+	12.9904i	−0.371761	+	0.643909i
$408$		0			0
$409$	14.0000			0.692255			0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000			0.692255			0.346128	+	0.938187i	$0.387496\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	4.50000	+	7.79423i	0.220896	+	0.382604i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$		0			0
$421$	0.500000	−	0.866025i	0.0243685	−	0.0422075i	−0.853584	−	0.520955i	$-0.825576\pi$
$421$	0.500000	−	0.866025i	0.0243685	−	0.0422075i	0.877952	+	0.478748i	$0.158909\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.0000			0.582086
$426$		0			0
$427$	28.0000	−	24.2487i	1.35501	−	1.17348i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	−0.737057	−	0.675830i	$-0.763785\pi$
$431$	4.50000	−	7.79423i	0.216757	−	0.375435i	0.953815	+	0.300395i	$0.0971186\pi$
$432$		0			0
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.00000			−0.143509
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	36.0000			1.71041			0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000			1.71041			0.855206	+	0.518289i	$0.173431\pi$
$444$		0			0
$445$	13.0000			0.616259
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−12.5000	+	21.6506i	−0.588602	+	1.01949i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.0000	−	8.66025i	0.468807	−	0.405999i
$456$		0			0
$457$	22.0000			1.02912			0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000			1.02912			0.514558	+	0.857455i	$0.327956\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.50000	−	16.4545i	0.442459	−	0.766362i	−0.555412	−	0.831575i	$-0.687440\pi$
$461$	9.50000	−	16.4545i	0.442459	−	0.766362i	0.997871	+	0.0652135i	$0.0207728\pi$
$462$		0			0
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	0.976607	−	0.215032i	$-0.0689855\pi$
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	−0.674526	+	0.738251i	$0.735652\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.5000	+	23.3827i	0.624705	+	1.08202i	0.988598	+	0.150581i	$0.0481143\pi$
$467$	13.5000	+	23.3827i	0.624705	+	1.08202i	−0.363892	+	0.931441i	$0.618552\pi$
$468$		0			0
$469$	8.00000	−	6.92820i	0.369406	−	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.00000			0.229900
$474$		0			0
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.5000	−	21.6506i	−0.571140	−	0.989243i	−0.996449	−	0.0841949i	$-0.973168\pi$
$479$	−12.5000	−	21.6506i	−0.571140	−	0.989243i	0.425310	−	0.905048i	$-0.360165\pi$
$480$		0			0
$481$	7.50000	−	12.9904i	0.341971	−	0.592310i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.50000	+	7.79423i	0.204334	+	0.353918i
$486$		0			0
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	0.996915	+	0.0784867i	$0.0250088\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.50000	−	11.2583i	−0.293341	−	0.508081i	0.681257	−	0.732045i	$-0.261434\pi$
$491$	−6.50000	−	11.2583i	−0.293341	−	0.508081i	−0.974598	+	0.223963i	$0.928100\pi$
$492$		0			0
$493$	1.50000	+	2.59808i	0.0675566	+	0.117011i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.0000	−	20.7846i	1.07655	−	0.932317i
$498$		0			0
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	17.0000			0.756490
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	0.342126	+	0.939654i	$0.388853\pi$
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	−0.984827	+	0.173537i	$0.944480\pi$
$510$		0			0
$511$	−1.50000	−	7.79423i	−0.0663561	−	0.344796i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.500000	−	0.866025i	−0.0220326	−	0.0381616i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	−0.831295	−	0.555831i	$-0.812400\pi$
$521$	1.50000	−	2.59808i	0.0657162	−	0.113824i	0.897011	+	0.442007i	$0.145733\pi$
$522$		0			0
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.5000	−	21.6506i	0.541435	−	0.937793i
$534$		0			0
$535$	17.0000			0.734974
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−32.5000	+	12.9904i	−1.39987	+	0.559535i
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.50000	+	7.79423i	0.192759	+	0.333868i
$546$		0			0
$547$	−14.5000	+	25.1147i	−0.619975	+	1.07383i	0.369514	+	0.929225i	$0.379524\pi$
$547$	−14.5000	+	25.1147i	−0.619975	+	1.07383i	−0.989490	+	0.144604i	$0.953809\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.00000			−0.0426014
$552$		0			0
$553$	16.0000	−	13.8564i	0.680389	−	0.589234i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.5000	+	32.0429i	−0.783870	+	1.35770i	0.145802	+	0.989314i	$0.453424\pi$
$557$	−18.5000	+	32.0429i	−0.783870	+	1.35770i	−0.929672	+	0.368389i	$0.879909\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−28.0000			−1.18006			−0.590030	−	0.807382i	$-0.700884\pi$
$563$	−28.0000			−1.18006			−0.590030	+	0.807382i	$0.700884\pi$
$564$		0			0
$565$	1.00000			0.0420703
$566$		0			0
$567$		0			0
$568$		0			0
$569$	34.0000			1.42535			0.712677	−	0.701492i	$-0.247483\pi$
$569$	34.0000			1.42535			0.712677	+	0.701492i	$0.247483\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	0.338965	+	0.940799i	$0.389923\pi$
$577$	−15.5000	+	26.8468i	−0.645273	+	1.11765i	−0.984238	+	0.176847i	$0.943410\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.50000	+	23.3827i	0.186691	+	0.970077i
$582$		0			0
$583$	45.0000			1.86371
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.5000	−	32.0429i	0.763577	−	1.32255i	−0.177419	−	0.984135i	$-0.556775\pi$
$587$	18.5000	−	32.0429i	0.763577	−	1.32255i	0.940996	−	0.338418i	$-0.109892\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.50000	+	12.9904i	0.307988	+	0.533451i	0.977922	−	0.208970i	$-0.0670110\pi$
$593$	7.50000	+	12.9904i	0.307988	+	0.533451i	−0.669934	+	0.742421i	$0.733678\pi$
$594$		0			0
$595$	−7.50000	−	2.59808i	−0.307470	−	0.106511i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	4.50000	−	7.79423i	0.183559	−	0.317933i	−0.759531	−	0.650471i	$-0.774572\pi$
$601$	4.50000	−	7.79423i	0.183559	−	0.317933i	0.943090	+	0.332538i	$0.107905\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	−0.991588	−	0.129433i	$-0.958684\pi$
$613$	−9.50000	+	16.4545i	−0.383701	+	0.664590i	0.607887	+	0.794024i	$0.292017\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	0.998700	+	0.0509678i	$0.0162306\pi$
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	−0.455211	+	0.890384i	$0.650436\pi$
$618$		0			0
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	0.999996	+	0.00279365i	$0.000889247\pi$
$619$	12.5000	+	21.6506i	0.502417	+	0.870212i	−0.497579	+	0.867419i	$0.665777\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	32.5000	+	11.2583i	1.30209	+	0.451055i
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.00000			−0.358854
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.00000	+	10.3923i	−0.238103	+	0.412406i
$636$		0			0
$637$	32.5000	−	12.9904i	1.28770	−	0.514698i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	0.763367	−	0.645966i	$-0.223545\pi$
$641$	−4.50000	−	7.79423i	−0.177739	−	0.307854i	−0.941106	+	0.338112i	$0.890212\pi$
$642$		0			0
$643$	−9.50000	−	16.4545i	−0.374643	−	0.648901i	0.615630	−	0.788035i	$-0.288902\pi$
$643$	−9.50000	−	16.4545i	−0.374643	−	0.648901i	−0.990274	+	0.139134i	$0.955568\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.5000	+	26.8468i	−0.609368	+	1.05546i	0.381977	+	0.924172i	$0.375243\pi$
$647$	−15.5000	+	26.8468i	−0.609368	+	1.05546i	−0.991345	+	0.131284i	$0.958090\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	−0.835182	−	0.549973i	$-0.814638\pi$
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	0.893882	+	0.448303i	$0.147971\pi$
$654$		0			0
$655$	0.500000	+	0.866025i	0.0195366	+	0.0338384i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.5000	+	23.3827i	−0.525885	+	0.910860i	0.473660	+	0.880708i	$0.342933\pi$
$659$	−13.5000	+	23.3827i	−0.525885	+	0.910860i	−0.999545	+	0.0301523i	$0.990401\pi$
$660$		0			0
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.00000	−	1.73205i	0.0775567	−	0.0671660i
$666$		0			0
$667$	−1.50000	−	2.59808i	−0.0580802	−	0.100598i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	35.0000	+	60.6218i	1.35116	+	2.34028i
$672$		0			0
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−42.0000			−1.61419			−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000			−1.61419			−0.807096	+	0.590421i	$0.798962\pi$
$678$		0			0
$679$	4.50000	+	23.3827i	0.172694	+	0.897345i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$		0			0
$685$	9.00000			0.343872
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−45.0000			−1.71436
$690$		0			0
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.00000			−0.341389
$696$		0			0
$697$	−15.0000			−0.568166
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	1.50000	−	2.59808i	0.0565736	−	0.0979883i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	42.5000	+	14.7224i	1.59838	+	0.553694i
$708$		0			0
$709$	−6.00000			−0.225335			−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000			−0.225335			−0.112667	+	0.993633i	$0.535939\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$	12.5000	+	21.6506i	0.467473	+	0.809688i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	0.999992	+	0.00400572i	$0.00127506\pi$
$719$	13.5000	+	23.3827i	0.503465	+	0.872027i	−0.496527	+	0.868021i	$0.665392\pi$
$720$		0			0
$721$	−0.500000	−	2.59808i	−0.0186210	−	0.0967574i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.00000			−0.148556
$726$		0			0
$727$	23.5000	−	40.7032i	0.871567	−	1.50960i	0.0111912	−	0.999937i	$-0.496438\pi$
$727$	23.5000	−	40.7032i	0.871567	−	1.50960i	0.860376	−	0.509661i	$-0.170229\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$		0			0
$733$	−13.5000	+	23.3827i	−0.498634	+	0.863659i	−0.999999	−	0.00157675i	$-0.999498\pi$
$733$	−13.5000	+	23.3827i	−0.498634	+	0.863659i	0.501365	+	0.865236i	$0.332831\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	10.0000	+	17.3205i	0.368355	+	0.638009i
$738$		0			0
$739$	−4.50000	+	7.79423i	−0.165535	+	0.286715i	−0.936845	−	0.349744i	$-0.886268\pi$
$739$	−4.50000	+	7.79423i	−0.165535	+	0.286715i	0.771310	+	0.636460i	$0.219602\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.50000	+	12.9904i	0.275148	+	0.476571i	0.970173	−	0.242415i	$-0.0779397\pi$
$743$	7.50000	+	12.9904i	0.275148	+	0.476571i	−0.695024	+	0.718986i	$0.744606\pi$
$744$		0			0
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	42.5000	+	14.7224i	1.55292	+	0.537946i
$750$		0			0
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.00000			−0.181969
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	−0.510551	−	0.859848i	$-0.670558\pi$
$761$	13.5000	−	23.3827i	0.489375	−	0.847622i	0.999925	+	0.0122260i	$0.00389175\pi$
$762$		0			0
$763$	4.50000	+	23.3827i	0.162911	+	0.846510i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.5000	−	26.8468i	0.557496	−	0.965612i	−0.440208	−	0.897896i	$-0.645095\pi$
$773$	15.5000	−	26.8468i	0.557496	−	0.965612i	0.997705	−	0.0677162i	$-0.0215712\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.50000	−	4.33013i	0.0895718	−	0.155143i
$780$		0			0
$781$	30.0000	+	51.9615i	1.07348	+	1.85933i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.00000	−	12.1244i	0.249841	−	0.432737i
$786$		0			0
$787$	−28.0000			−0.998092			−0.499046	−	0.866575i	$-0.666316\pi$
$787$	−28.0000			−0.998092			−0.499046	+	0.866575i	$0.666316\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.50000	+	0.866025i	0.0888898	+	0.0307923i
$792$		0			0
$793$	−35.0000	−	60.6218i	−1.24289	−	2.15274i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.5000	+	19.9186i	0.407351	+	0.705552i	0.994592	−	0.103860i	$-0.0331193\pi$
$797$	11.5000	+	19.9186i	0.407351	+	0.705552i	−0.587241	+	0.809412i	$0.699786\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15.0000			0.529339
$804$		0			0
$805$	7.50000	+	2.59808i	0.264340	+	0.0915702i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	−0.934224	−	0.356687i	$-0.883906\pi$
$809$	−4.50000	+	7.79423i	−0.158212	+	0.274030i	0.776012	+	0.630718i	$0.217239\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.0000			0.385313
$816$		0			0
$817$	−1.00000			−0.0349856
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−22.0000			−0.767805			−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000			−0.767805			−0.383903	+	0.923374i	$0.625420\pi$
$822$		0			0
$823$	24.0000			0.836587			0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000			0.836587			0.418294	+	0.908312i	$0.362628\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	−0.563082	−	0.826401i	$-0.690385\pi$
$829$	12.5000	−	21.6506i	0.434143	−	0.751958i	0.997225	+	0.0744432i	$0.0237179\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−16.5000	−	12.9904i	−0.571691	−	0.450090i
$834$		0			0
$835$	−19.0000			−0.657522
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.5000	−	32.0429i	0.638691	−	1.10625i	−0.347029	−	0.937854i	$-0.612810\pi$
$839$	18.5000	−	32.0429i	0.638691	−	1.10625i	0.985720	−	0.168391i	$-0.0538571\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	−7.00000	−	36.3731i	−0.240523	−	1.24979i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.00000			0.308516
$852$		0			0
$853$	18.5000	−	32.0429i	0.633428	−	1.09713i	−0.353418	−	0.935466i	$-0.614981\pi$
$853$	18.5000	−	32.0429i	0.633428	−	1.09713i	0.986846	−	0.161664i	$-0.0516860\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.50000	+	9.52628i	0.187876	+	0.325412i	0.944542	−	0.328391i	$-0.106506\pi$
$857$	5.50000	+	9.52628i	0.187876	+	0.325412i	−0.756666	+	0.653802i	$0.773173\pi$
$858$		0			0
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	−0.874429	−	0.485153i	$-0.838764\pi$
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	0.857369	+	0.514701i	$0.172097\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	0.979612	+	0.200897i	$0.0643855\pi$
$863$	19.5000	+	33.7750i	0.663788	+	1.14971i	−0.315825	+	0.948818i	$0.602281\pi$
$864$		0			0
$865$	−7.00000	+	12.1244i	−0.238007	+	0.412240i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	20.0000	+	34.6410i	0.678454	+	1.17512i
$870$		0			0
$871$	−10.0000	−	17.3205i	−0.338837	−	0.586883i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	18.0000	−	15.5885i	0.608511	−	0.526986i
$876$		0			0
$877$	26.5000	−	45.8993i	0.894841	−	1.54991i	0.0608407	−	0.998147i	$-0.480622\pi$
$877$	26.5000	−	45.8993i	0.894841	−	1.54991i	0.834001	−	0.551763i	$-0.186045\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.5000	−	25.1147i	0.486862	−	0.843270i	−0.513024	−	0.858375i	$-0.671475\pi$
$887$	14.5000	−	25.1147i	0.486862	−	0.843270i	0.999886	+	0.0151042i	$0.00480800\pi$
$888$		0			0
$889$	−24.0000	+	20.7846i	−0.804934	+	0.697093i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−9.50000	−	16.4545i	−0.317550	−	0.550013i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	13.5000	+	23.3827i	0.449750	+	0.778990i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.00000	−	12.1244i	0.232688	−	0.403027i
$906$		0			0
$907$	2.50000	+	4.33013i	0.0830111	+	0.143780i	0.904542	−	0.426385i	$-0.140213\pi$
$907$	2.50000	+	4.33013i	0.0830111	+	0.143780i	−0.821531	+	0.570164i	$0.806880\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−13.5000	+	23.3827i	−0.447275	+	0.774703i	−0.998208	−	0.0598468i	$-0.980939\pi$
$911$	−13.5000	+	23.3827i	−0.447275	+	0.774703i	0.550933	+	0.834550i	$0.314272\pi$
$912$		0			0
$913$	−45.0000			−1.48928
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.500000	+	2.59808i	0.0165115	+	0.0857960i
$918$		0			0
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	0.971481	−	0.237119i	$-0.0762032\pi$
$919$	8.50000	+	14.7224i	0.280389	+	0.485648i	−0.691091	+	0.722767i	$0.742870\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−30.0000	−	51.9615i	−0.987462	−	1.71033i
$924$		0			0
$925$	6.00000	−	10.3923i	0.197279	−	0.341697i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	14.0000			0.459325			0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000			0.459325			0.229663	+	0.973270i	$0.426238\pi$
$930$		0			0
$931$	6.50000	−	2.59808i	0.213029	−	0.0851485i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.50000	−	12.9904i	0.245276	−	0.424831i
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.0000			0.456387			0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000			0.456387			0.228193	+	0.973616i	$0.426718\pi$
$942$		0			0
$943$	15.0000			0.488467
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.0000			−0.649913			−0.324956	−	0.945729i	$-0.605350\pi$
$947$	−20.0000			−0.649913			−0.324956	+	0.945729i	$0.605350\pi$
$948$		0			0
$949$	−15.0000			−0.486921
$950$		0			0
$951$		0			0
$952$		0			0
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$		0			0
$955$	−4.00000	+	6.92820i	−0.129437	+	0.224191i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	22.5000	+	7.79423i	0.726563	+	0.251689i
$960$		0			0
$961$	−31.0000			−1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	5.00000	−	8.66025i	0.160956	−	0.278783i
$966$		0			0
$967$	6.50000	+	11.2583i	0.209026	+	0.362043i	0.951408	−	0.307933i	$-0.0996374\pi$
$967$	6.50000	+	11.2583i	0.209026	+	0.362043i	−0.742382	+	0.669977i	$0.766304\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.5000	−	49.3634i	−0.914609	−	1.58415i	−0.807473	−	0.589904i	$-0.799166\pi$
$971$	−28.5000	−	49.3634i	−0.914609	−	1.58415i	−0.107135	−	0.994244i	$-0.534168\pi$
$972$		0			0
$973$	−22.5000	−	7.79423i	−0.721317	−	0.249871i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.0000			−0.575871			−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000			−0.575871			−0.287936	+	0.957650i	$0.592969\pi$
$978$		0			0
$979$	−32.5000	+	56.2917i	−1.03870	+	1.79909i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	0.888955	−	0.457995i	$-0.151432\pi$
$983$	1.50000	+	2.59808i	0.0478426	+	0.0828658i	−0.841112	+	0.540860i	$0.818099\pi$
$984$		0			0
$985$	1.00000	−	1.73205i	0.0318626	−	0.0551877i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.50000	−	2.59808i	−0.0476972	−	0.0826140i
$990$		0			0
$991$	−18.5000	+	32.0429i	−0.587672	+	1.01788i	0.406865	+	0.913488i	$0.366622\pi$
$991$	−18.5000	+	32.0429i	−0.587672	+	1.01788i	−0.994537	+	0.104389i	$0.966711\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.50000	+	2.59808i	0.0475532	+	0.0823646i
$996$		0			0
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	0.968655	−	0.248410i	$-0.0799082\pi$
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	−0.699457	+	0.714675i	$0.746575\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.b.2881.1		2
3.2	odd	2		1008.2.q.c.529.1		2
4.3	odd	2		189.2.h.a.46.1		2
7.2	even	3		3024.2.t.d.289.1		2
9.4	even	3		3024.2.t.d.1873.1		2
9.5	odd	6		1008.2.t.d.193.1		2
12.11	even	2		63.2.h.a.25.1	yes	2
21.2	odd	6		1008.2.t.d.961.1		2
28.3	even	6		1323.2.f.b.883.1		2
28.11	odd	6		1323.2.f.a.883.1		2
28.19	even	6		1323.2.g.a.667.1		2
28.23	odd	6		189.2.g.a.100.1		2
28.27	even	2		1323.2.h.a.802.1		2
36.7	odd	6		567.2.e.b.487.1		2
36.11	even	6		567.2.e.a.487.1		2
36.23	even	6		63.2.g.a.4.1	✓	2
36.31	odd	6		189.2.g.a.172.1		2
63.23	odd	6		1008.2.q.c.625.1		2
63.58	even	3	inner	3024.2.q.b.2305.1		2
84.11	even	6		441.2.f.b.295.1		2
84.23	even	6		63.2.g.a.16.1	yes	2
84.47	odd	6		441.2.g.a.79.1		2
84.59	odd	6		441.2.f.a.295.1		2
84.83	odd	2		441.2.h.a.214.1		2
252.11	even	6		3969.2.a.d.1.1		1
252.23	even	6		63.2.h.a.58.1	yes	2
252.31	even	6		1323.2.f.b.442.1		2
252.59	odd	6		441.2.f.a.148.1		2
252.67	odd	6		1323.2.f.a.442.1		2
252.79	odd	6		567.2.e.b.163.1		2
252.95	even	6		441.2.f.b.148.1		2
252.103	even	6		1323.2.h.a.226.1		2
252.115	even	6		3969.2.a.a.1.1		1
252.131	odd	6		441.2.h.a.373.1		2
252.139	even	6		1323.2.g.a.361.1		2
252.151	odd	6		3969.2.a.c.1.1		1
252.167	odd	6		441.2.g.a.67.1		2
252.191	even	6		567.2.e.a.163.1		2
252.227	odd	6		3969.2.a.f.1.1		1
252.247	odd	6		189.2.h.a.37.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.a.4.1	✓	2	36.23	even	6
63.2.g.a.16.1	yes	2	84.23	even	6
63.2.h.a.25.1	yes	2	12.11	even	2
63.2.h.a.58.1	yes	2	252.23	even	6
189.2.g.a.100.1		2	28.23	odd	6
189.2.g.a.172.1		2	36.31	odd	6
189.2.h.a.37.1		2	252.247	odd	6
189.2.h.a.46.1		2	4.3	odd	2
441.2.f.a.148.1		2	252.59	odd	6
441.2.f.a.295.1		2	84.59	odd	6
441.2.f.b.148.1		2	252.95	even	6
441.2.f.b.295.1		2	84.11	even	6
441.2.g.a.67.1		2	252.167	odd	6
441.2.g.a.79.1		2	84.47	odd	6
441.2.h.a.214.1		2	84.83	odd	2
441.2.h.a.373.1		2	252.131	odd	6
567.2.e.a.163.1		2	252.191	even	6
567.2.e.a.487.1		2	36.11	even	6
567.2.e.b.163.1		2	252.79	odd	6
567.2.e.b.487.1		2	36.7	odd	6
1008.2.q.c.529.1		2	3.2	odd	2
1008.2.q.c.625.1		2	63.23	odd	6
1008.2.t.d.193.1		2	9.5	odd	6
1008.2.t.d.961.1		2	21.2	odd	6
1323.2.f.a.442.1		2	252.67	odd	6
1323.2.f.a.883.1		2	28.11	odd	6
1323.2.f.b.442.1		2	252.31	even	6
1323.2.f.b.883.1		2	28.3	even	6
1323.2.g.a.361.1		2	252.139	even	6
1323.2.g.a.667.1		2	28.19	even	6
1323.2.h.a.226.1		2	252.103	even	6
1323.2.h.a.802.1		2	28.27	even	2
3024.2.q.b.2305.1		2	63.58	even	3	inner
3024.2.q.b.2881.1		2	1.1	even	1	trivial
3024.2.t.d.289.1		2	7.2	even	3
3024.2.t.d.1873.1		2	9.4	even	3
3969.2.a.a.1.1		1	252.115	even	6
3969.2.a.c.1.1		1	252.151	odd	6
3969.2.a.d.1.1		1	252.11	even	6
3969.2.a.f.1.1		1	252.227	odd	6

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(-2.50000 - 4.33013i) q^{11} +(2.50000 + 4.33013i) q^{13} +(1.50000 - 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-1.50000 + 2.59808i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-0.500000 + 0.866025i) q^{29} +(-0.500000 - 2.59808i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(-2.50000 - 4.33013i) q^{41} +(-0.500000 + 0.866025i) q^{43} +(1.00000 - 6.92820i) q^{49} +(-4.50000 + 7.79423i) q^{53} +5.00000 q^{55} -14.0000 q^{61} -5.00000 q^{65} -4.00000 q^{67} -12.0000 q^{71} +(-1.50000 + 2.59808i) q^{73} +(12.5000 + 4.33013i) q^{77} -8.00000 q^{79} +(4.50000 - 7.79423i) q^{83} +(1.50000 + 2.59808i) q^{85} +(-6.50000 - 11.2583i) q^{89} +(-12.5000 - 4.33013i) q^{91} -1.00000 q^{95} +(4.50000 - 7.79423i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} - 4 q^{7}+O(q^{10}) \) 2 * q - q^5 - 4 * q^7	\( 2 q - q^{5} - 4 q^{7} - 5 q^{11} + 5 q^{13} + 3 q^{17} + q^{19} - 3 q^{23} + 4 q^{25} - q^{29} - q^{35} - 3 q^{37} - 5 q^{41} - q^{43} + 2 q^{49} - 9 q^{53} + 10 q^{55} - 28 q^{61} - 10 q^{65} - 8 q^{67} - 24 q^{71} - 3 q^{73} + 25 q^{77} - 16 q^{79} + 9 q^{83} + 3 q^{85} - 13 q^{89} - 25 q^{91} - 2 q^{95} + 9 q^{97}+O(q^{100}) \) 2 * q - q^5 - 4 * q^7 - 5 * q^11 + 5 * q^13 + 3 * q^17 + q^19 - 3 * q^23 + 4 * q^25 - q^29 - q^35 - 3 * q^37 - 5 * q^41 - q^43 + 2 * q^49 - 9 * q^53 + 10 * q^55 - 28 * q^61 - 10 * q^65 - 8 * q^67 - 24 * q^71 - 3 * q^73 + 25 * q^77 - 16 * q^79 + 9 * q^83 + 3 * q^85 - 13 * q^89 - 25 * q^91 - 2 * q^95 + 9 * q^97

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