LMFDB - Embedded newform 3330.2.e.d.739.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3330,2,Mod(739,3330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3330, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("3330.739");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3330.e (of order $2$, degree $1$, 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:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 370)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			739.4
Root			$0.377861i$ of defining polynomial
Character	$\chi$	$=$	3330.739
Dual form			3330.2.e.d.739.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-1.04797 + 1.97529i) q^{5} -0.631751i q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.04797 + 1.97529i) q^{5} -0.631751i q^{7} +1.00000 q^{8} +(-1.04797 + 1.97529i) q^{10} -1.24789 q^{11} -3.34999 q^{13} -0.631751i q^{14} +1.00000 q^{16} +3.10511 q^{17} -5.97327i q^{19} +(-1.04797 + 1.97529i) q^{20} -1.24789 q^{22} -7.60706 q^{23} +(-2.80353 - 4.14008i) q^{25} -3.34999 q^{26} -0.631751i q^{28} -9.57629i q^{29} -7.26707i q^{31} +1.00000 q^{32} +3.10511 q^{34} +(1.24789 + 0.662054i) q^{35} +(4.10511 - 4.48866i) q^{37} -5.97327i q^{38} +(-1.04797 + 1.97529i) q^{40} +8.45510 q^{41} +4.86640 q^{43} -1.24789 q^{44} -7.60706 q^{46} +13.1187i q^{47} +6.60089 q^{49} +(-2.80353 - 4.14008i) q^{50} -3.34999 q^{52} -7.17340i q^{53} +(1.30775 - 2.46494i) q^{55} -0.631751i q^{56} -9.57629i q^{58} -4.36469i q^{59} +2.14666i q^{61} -7.26707i q^{62} +1.00000 q^{64} +(3.51068 - 6.61720i) q^{65} +11.3451i q^{67} +3.10511 q^{68} +(1.24789 + 0.662054i) q^{70} +12.7183 q^{71} +4.45836i q^{73} +(4.10511 - 4.48866i) q^{74} -5.97327i q^{76} +0.788355i q^{77} +8.78679i q^{79} +(-1.04797 + 1.97529i) q^{80} +8.45510 q^{82} -6.63185i q^{83} +(-3.25406 + 6.13349i) q^{85} +4.86640 q^{86} -1.24789 q^{88} -13.7784i q^{89} +2.11636i q^{91} -7.60706 q^{92} +13.1187i q^{94} +(11.7989 + 6.25979i) q^{95} -11.0583 q^{97} +6.60089 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8}+O(q^{10}) $ 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8	$ 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8} + 3 q^{10} - 2 q^{13} + 10 q^{16} - 18 q^{17} + 3 q^{20} - 10 q^{23} + 5 q^{25} - 2 q^{26} + 10 q^{32} - 18 q^{34} - 8 q^{37} + 3 q^{40} + 4 q^{41} - 10 q^{43} - 10 q^{46} - 8 q^{49} + 5 q^{50} - 2 q^{52} + 5 q^{55} + 10 q^{64} - 2 q^{65} - 18 q^{68} + 20 q^{71} - 8 q^{74} + 3 q^{80} + 4 q^{82} - 28 q^{85} - 10 q^{86} - 10 q^{92} - 2 q^{95} + 2 q^{97} - 8 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8 + 3 * q^10 - 2 * q^13 + 10 * q^16 - 18 * q^17 + 3 * q^20 - 10 * q^23 + 5 * q^25 - 2 * q^26 + 10 * q^32 - 18 * q^34 - 8 * q^37 + 3 * q^40 + 4 * q^41 - 10 * q^43 - 10 * q^46 - 8 * q^49 + 5 * q^50 - 2 * q^52 + 5 * q^55 + 10 * q^64 - 2 * q^65 - 18 * q^68 + 20 * q^71 - 8 * q^74 + 3 * q^80 + 4 * q^82 - 28 * q^85 - 10 * q^86 - 10 * q^92 - 2 * q^95 + 2 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.04797	+	1.97529i	−0.468665	+	0.883376i
$5$	−1.04797	+	1.97529i	−0.468665	+	0.883376i
$6$		0			0
$7$		−	0.631751i		−	0.238779i	−0.992847	−	0.119390i	$-0.961906\pi$
$7$		−	0.631751i		−	0.238779i	0.992847	−	0.119390i	$-0.0380938\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.04797	+	1.97529i	−0.331396	+	0.624641i
$11$	−1.24789			−0.376253			−0.188126	−	0.982145i	$-0.560241\pi$
$11$	−1.24789			−0.376253			−0.188126	+	0.982145i	$0.560241\pi$
$12$		0			0
$13$	−3.34999			−0.929120			−0.464560	−	0.885542i	$-0.653788\pi$
$13$	−3.34999			−0.929120			−0.464560	+	0.885542i	$0.653788\pi$
$14$		−	0.631751i		−	0.168843i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.10511			0.753100			0.376550	−	0.926396i	$-0.377110\pi$
$17$	3.10511			0.753100			0.376550	+	0.926396i	$0.377110\pi$
$18$		0			0
$19$		−	5.97327i		−	1.37036i	−0.728373	−	0.685181i	$-0.759723\pi$
$19$		−	5.97327i		−	1.37036i	0.728373	−	0.685181i	$-0.240277\pi$
$20$	−1.04797	+	1.97529i	−0.234333	+	0.441688i
$21$		0			0
$22$	−1.24789			−0.266051
$23$	−7.60706			−1.58618			−0.793090	−	0.609104i	$-0.791529\pi$
$23$	−7.60706			−1.58618			−0.793090	+	0.609104i	$0.791529\pi$
$24$		0			0
$25$	−2.80353	−	4.14008i	−0.560706	−	0.828015i
$26$	−3.34999			−0.656987
$27$		0			0
$28$		−	0.631751i		−	0.119390i
$29$		−	9.57629i		−	1.77827i	−0.457643	−	0.889136i	$-0.651306\pi$
$29$		−	9.57629i		−	1.77827i	0.457643	−	0.889136i	$-0.348694\pi$
$30$		0			0
$31$		−	7.26707i		−	1.30520i	−0.757701	−	0.652602i	$-0.773677\pi$
$31$		−	7.26707i		−	1.30520i	0.757701	−	0.652602i	$-0.226323\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	3.10511			0.532522
$35$	1.24789	+	0.662054i	0.210932	+	0.111908i
$36$		0			0
$37$	4.10511	−	4.48866i	0.674876	−	0.737931i
$37$	4.10511	−	4.48866i	0.674876	−	0.737931i
$38$		−	5.97327i		−	0.968992i
$39$		0			0
$40$	−1.04797	+	1.97529i	−0.165698	+	0.312321i
$41$	8.45510			1.32046			0.660232	−	0.751061i	$-0.270458\pi$
$41$	8.45510			1.32046			0.660232	+	0.751061i	$0.270458\pi$
$42$		0			0
$43$	4.86640			0.742119			0.371059	−	0.928609i	$-0.378995\pi$
$43$	4.86640			0.742119			0.371059	+	0.928609i	$0.378995\pi$
$44$	−1.24789			−0.188126
$45$		0			0
$46$	−7.60706			−1.12160
$47$			13.1187i			1.91356i	0.290815	+	0.956779i	$0.406074\pi$
$47$			13.1187i			1.91356i	−0.290815	+	0.956779i	$0.593926\pi$
$48$		0			0
$49$	6.60089			0.942984
$50$	−2.80353	−	4.14008i	−0.396479	−	0.585495i
$51$		0			0
$52$	−3.34999			−0.464560
$53$		−	7.17340i		−	0.985343i	−0.870215	−	0.492671i	$-0.836020\pi$
$53$		−	7.17340i		−	0.985343i	0.870215	−	0.492671i	$-0.163980\pi$
$54$		0			0
$55$	1.30775	−	2.46494i	0.176337	−	0.332373i
$56$		−	0.631751i		−	0.0844213i
$57$		0			0
$58$		−	9.57629i		−	1.25743i
$59$		−	4.36469i		−	0.568234i	−0.958790	−	0.284117i	$-0.908300\pi$
$59$		−	4.36469i		−	0.568234i	0.958790	−	0.284117i	$-0.0917004\pi$
$60$		0			0
$61$			2.14666i			0.274852i	0.990512	+	0.137426i	$0.0438829\pi$
$61$			2.14666i			0.274852i	−0.990512	+	0.137426i	$0.956117\pi$
$62$		−	7.26707i		−	0.922919i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.51068	−	6.61720i	0.435446	−	0.820762i
$66$		0			0
$67$			11.3451i			1.38602i	0.720926	+	0.693012i	$0.243717\pi$
$67$			11.3451i			1.38602i	−0.720926	+	0.693012i	$0.756283\pi$
$68$	3.10511			0.376550
$69$		0			0
$70$	1.24789	+	0.662054i	0.149151	+	0.0791306i
$71$	12.7183			1.50939			0.754694	−	0.656077i	$-0.227785\pi$
$71$	12.7183			1.50939			0.754694	+	0.656077i	$0.227785\pi$
$72$		0			0
$73$			4.45836i			0.521811i	0.965364	+	0.260906i	$0.0840211\pi$
$73$			4.45836i			0.521811i	−0.965364	+	0.260906i	$0.915979\pi$
$74$	4.10511	−	4.48866i	0.477209	−	0.521796i
$75$		0			0
$76$		−	5.97327i		−	0.685181i
$77$			0.788355i			0.0898414i
$78$		0			0
$79$			8.78679i			0.988592i	0.869294	+	0.494296i	$0.164574\pi$
$79$			8.78679i			0.988592i	−0.869294	+	0.494296i	$0.835426\pi$
$80$	−1.04797	+	1.97529i	−0.117166	+	0.220844i
$81$		0			0
$82$	8.45510			0.933710
$83$		−	6.63185i		−	0.727941i	−0.931411	−	0.363970i	$-0.881421\pi$
$83$		−	6.63185i		−	0.727941i	0.931411	−	0.363970i	$-0.118579\pi$
$84$		0			0
$85$	−3.25406	+	6.13349i	−0.352952	+	0.665270i
$86$	4.86640			0.524757
$87$		0			0
$88$	−1.24789			−0.133026
$89$		−	13.7784i		−	1.46051i	−0.683175	−	0.730255i	$-0.739401\pi$
$89$		−	13.7784i		−	1.46051i	0.683175	−	0.730255i	$-0.260599\pi$
$90$		0			0
$91$			2.11636i			0.221855i
$92$	−7.60706			−0.793090
$93$		0			0
$94$			13.1187i			1.35309i
$95$	11.7989	+	6.25979i	1.21054	+	0.642241i
$96$		0			0
$97$	−11.0583			−1.12280			−0.561398	−	0.827546i	$-0.689736\pi$
$97$	−11.0583			−1.12280			−0.561398	+	0.827546i	$0.689736\pi$
$98$	6.60089			0.666791
$99$		0			0
$100$	−2.80353	−	4.14008i	−0.280353	−	0.414008i
$101$	−8.65314			−0.861019			−0.430510	−	0.902586i	$-0.641666\pi$
$101$	−8.65314			−0.861019			−0.430510	+	0.902586i	$0.641666\pi$
$102$		0			0
$103$	4.57336			0.450627			0.225313	−	0.974286i	$-0.427659\pi$
$103$	4.57336			0.450627			0.225313	+	0.974286i	$0.427659\pi$
$104$	−3.34999			−0.328494
$105$		0			0
$106$		−	7.17340i		−	0.696743i
$107$		−	11.4715i		−	1.10900i	−0.832185	−	0.554498i	$-0.812910\pi$
$107$		−	11.4715i		−	1.10900i	0.832185	−	0.554498i	$-0.187090\pi$
$108$		0			0
$109$		−	0.727748i		−	0.0697057i	−0.999392	−	0.0348528i	$-0.988904\pi$
$109$		−	0.727748i		−	0.0697057i	0.999392	−	0.0348528i	$-0.0110962\pi$
$110$	1.30775	−	2.46494i	0.124689	−	0.235023i
$111$		0			0
$112$		−	0.631751i		−	0.0596948i
$113$	−17.9970			−1.69301			−0.846506	−	0.532379i	$-0.821298\pi$
$113$	−17.9970			−1.69301			−0.846506	+	0.532379i	$0.821298\pi$
$114$		0			0
$115$	7.97195	−	15.0261i	0.743388	−	1.40119i
$116$		−	9.57629i		−	0.889136i
$117$		0			0
$118$		−	4.36469i		−	0.401802i
$119$		−	1.96166i		−	0.179825i
$120$		0			0
$121$	−9.44277			−0.858434
$122$			2.14666i			0.194350i
$123$		0			0
$124$		−	7.26707i		−	0.652602i
$125$	11.1159	−	1.19911i	0.994232	−	0.107252i
$126$		0			0
$127$		−	15.4830i		−	1.37389i	−0.726707	−	0.686947i	$-0.758950\pi$
$127$		−	15.4830i		−	1.37389i	0.726707	−	0.686947i	$-0.241050\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	3.51068	−	6.61720i	0.307907	−	0.580367i
$131$		−	6.22121i		−	0.543550i	−0.962361	−	0.271775i	$-0.912389\pi$
$131$		−	6.22121i		−	0.543550i	0.962361	−	0.271775i	$-0.0876106\pi$
$132$		0			0
$133$	−3.77362			−0.327214
$134$			11.3451i			0.980066i
$135$		0			0
$136$	3.10511			0.266261
$137$		−	14.1258i		−	1.20685i	−0.797419	−	0.603426i	$-0.793802\pi$
$137$		−	14.1258i		−	1.20685i	0.797419	−	0.603426i	$-0.206198\pi$
$138$		0			0
$139$	8.43675			0.715596			0.357798	−	0.933799i	$-0.383528\pi$
$139$	8.43675			0.715596			0.357798	+	0.933799i	$0.383528\pi$
$140$	1.24789	+	0.662054i	0.105466	+	0.0559538i
$141$		0			0
$142$	12.7183			1.06730
$143$	4.18042			0.349584
$144$		0			0
$145$	18.9159	+	10.0356i	1.57088	+	0.833414i
$146$			4.45836i			0.368976i
$147$		0			0
$148$	4.10511	−	4.48866i	0.337438	−	0.368966i
$149$	−13.6447			−1.11782			−0.558909	−	0.829229i	$-0.688780\pi$
$149$	−13.6447			−1.11782			−0.558909	+	0.829229i	$0.688780\pi$
$150$		0			0
$151$	−3.17741			−0.258574			−0.129287	−	0.991607i	$-0.541269\pi$
$151$	−3.17741			−0.258574			−0.129287	+	0.991607i	$0.541269\pi$
$152$		−	5.97327i		−	0.484496i
$153$		0			0
$154$			0.788355i			0.0635275i
$155$	14.3546	+	7.61566i	1.15299	+	0.611704i
$156$		0			0
$157$		−	0.215310i		−	0.0171836i	−0.999963	−	0.00859180i	$-0.997265\pi$
$157$		−	0.215310i		−	0.0171836i	0.999963	−	0.00859180i	$-0.00273489\pi$
$158$			8.78679i			0.699040i
$159$		0			0
$160$	−1.04797	+	1.97529i	−0.0828491	+	0.156160i
$161$			4.80576i			0.378747i
$162$		0			0
$163$	−1.66609			−0.130498			−0.0652490	−	0.997869i	$-0.520784\pi$
$163$	−1.66609			−0.130498			−0.0652490	+	0.997869i	$0.520784\pi$
$164$	8.45510			0.660232
$165$		0			0
$166$		−	6.63185i		−	0.514732i
$167$	−5.92242			−0.458290			−0.229145	−	0.973392i	$-0.573593\pi$
$167$	−5.92242			−0.458290			−0.229145	+	0.973392i	$0.573593\pi$
$168$		0			0
$169$	−1.77756			−0.136736
$170$	−3.25406	+	6.13349i	−0.249575	+	0.470417i
$171$		0			0
$172$	4.86640			0.371059
$173$		−	2.88008i		−	0.218968i	−0.993989	−	0.109484i	$-0.965080\pi$
$173$		−	2.88008i		−	0.218968i	0.993989	−	0.109484i	$-0.0349199\pi$
$174$		0			0
$175$	−2.61550	+	1.77113i	−0.197713	+	0.133885i
$176$	−1.24789			−0.0940632
$177$		0			0
$178$		−	13.7784i		−	1.03274i
$179$			4.46182i			0.333492i	0.986000	+	0.166746i	$0.0533260\pi$
$179$			4.46182i			0.333492i	−0.986000	+	0.166746i	$0.946674\pi$
$180$		0			0
$181$	3.93480			0.292472			0.146236	−	0.989250i	$-0.453284\pi$
$181$	3.93480			0.292472			0.146236	+	0.989250i	$0.453284\pi$
$182$			2.11636i			0.156875i
$183$		0			0
$184$	−7.60706			−0.560800
$185$	4.56437	+	12.8127i	0.335579	+	0.942012i
$186$		0			0
$187$	−3.87484			−0.283356
$188$			13.1187i			0.956779i
$189$		0			0
$190$	11.7989	+	6.25979i	0.855984	+	0.454133i
$191$			7.76296i			0.561708i	0.959751	+	0.280854i	$0.0906177\pi$
$191$			7.76296i			0.561708i	−0.959751	+	0.280854i	$0.909382\pi$
$192$		0			0
$193$	−3.49189			−0.251352			−0.125676	−	0.992071i	$-0.540110\pi$
$193$	−3.49189			−0.251352			−0.125676	+	0.992071i	$0.540110\pi$
$194$	−11.0583			−0.793937
$195$		0			0
$196$	6.60089			0.471492
$197$			1.07617i			0.0766736i	0.999265	+	0.0383368i	$0.0122060\pi$
$197$			1.07617i			0.0766736i	−0.999265	+	0.0383368i	$0.987794\pi$
$198$		0			0
$199$			5.71343i			0.405014i	0.979281	+	0.202507i	$0.0649090\pi$
$199$			5.71343i			0.405014i	−0.979281	+	0.202507i	$0.935091\pi$
$200$	−2.80353	−	4.14008i	−0.198239	−	0.292748i
$201$		0			0
$202$	−8.65314			−0.608833
$203$	−6.04983			−0.424615
$204$		0			0
$205$	−8.86067	+	16.7013i	−0.618856	+	1.16647i
$206$	4.57336			0.318641
$207$		0			0
$208$	−3.34999			−0.232280
$209$			7.45398i			0.515603i
$210$		0			0
$211$	22.8397			1.57235			0.786176	−	0.618003i	$-0.212058\pi$
$211$	22.8397			1.57235			0.786176	+	0.618003i	$0.212058\pi$
$212$		−	7.17340i		−	0.492671i
$213$		0			0
$214$		−	11.4715i		−	0.784178i
$215$	−5.09983	+	9.61254i	−0.347805	+	0.655570i
$216$		0			0
$217$	−4.59098			−0.311656
$218$		−	0.727748i		−	0.0492893i
$219$		0			0
$220$	1.30775	−	2.46494i	0.0881684	−	0.166186i
$221$	−10.4021			−0.699720
$222$		0			0
$223$			3.32116i			0.222401i	0.993798	+	0.111201i	$0.0354696\pi$
$223$			3.32116i			0.222401i	−0.993798	+	0.111201i	$0.964530\pi$
$224$		−	0.631751i		−	0.0422106i
$225$		0			0
$226$	−17.9970			−1.19714
$227$	−5.62938			−0.373635			−0.186818	−	0.982395i	$-0.559817\pi$
$227$	−5.62938			−0.373635			−0.186818	+	0.982395i	$0.559817\pi$
$228$		0			0
$229$	−0.973208			−0.0643114			−0.0321557	−	0.999483i	$-0.510237\pi$
$229$	−0.973208			−0.0643114			−0.0321557	+	0.999483i	$0.510237\pi$
$230$	7.97195	−	15.0261i	0.525655	−	0.990794i
$231$		0			0
$232$		−	9.57629i		−	0.628714i
$233$		−	14.4150i		−	0.944357i	−0.881503	−	0.472178i	$-0.843468\pi$
$233$		−	14.4150i		−	0.944357i	0.881503	−	0.472178i	$-0.156532\pi$
$234$		0			0
$235$	−25.9132	−	13.7480i	−1.69039	−	0.896819i
$236$		−	4.36469i		−	0.284117i
$237$		0			0
$238$		−	1.96166i		−	0.127155i
$239$			8.43344i			0.545514i	0.962083	+	0.272757i	$0.0879355\pi$
$239$			8.43344i			0.545514i	−0.962083	+	0.272757i	$0.912065\pi$
$240$		0			0
$241$		−	18.6567i		−	1.20178i	−0.799331	−	0.600891i	$-0.794812\pi$
$241$		−	18.6567i		−	1.20178i	0.799331	−	0.600891i	$-0.205188\pi$
$242$	−9.44277			−0.607004
$243$		0			0
$244$			2.14666i			0.137426i
$245$	−6.91752	+	13.0387i	−0.441944	+	0.833010i
$246$		0			0
$247$			20.0104i			1.27323i
$248$		−	7.26707i		−	0.461460i
$249$		0			0
$250$	11.1159	−	1.19911i	0.703028	−	0.0758385i
$251$		−	25.1189i		−	1.58549i	−0.609553	−	0.792746i	$-0.708651\pi$
$251$		−	25.1189i		−	1.58549i	0.609553	−	0.792746i	$-0.291349\pi$
$252$		0			0
$253$	9.49277			0.596805
$254$		−	15.4830i		−	0.971490i
$255$		0			0
$256$	1.00000			0.0625000
$257$	20.3552			1.26973			0.634863	−	0.772625i	$-0.281057\pi$
$257$	20.3552			1.26973			0.634863	+	0.772625i	$0.281057\pi$
$258$		0			0
$259$	−2.83571	−	2.59341i	−0.176203	−	0.161146i
$260$	3.51068	−	6.61720i	0.217723	−	0.410381i
$261$		0			0
$262$		−	6.22121i		−	0.384348i
$263$			22.2211i			1.37021i	0.728443	+	0.685107i	$0.240244\pi$
$263$			22.2211i			1.37021i	−0.728443	+	0.685107i	$0.759756\pi$
$264$		0			0
$265$	14.1695	+	7.51750i	0.870428	+	0.461796i
$266$	−3.77362			−0.231375
$267$		0			0
$268$			11.3451i			0.693012i
$269$	15.8411			0.965850			0.482925	−	0.875662i	$-0.339574\pi$
$269$	15.8411			0.965850			0.482925	+	0.875662i	$0.339574\pi$
$270$		0			0
$271$	−2.00602			−0.121857			−0.0609285	−	0.998142i	$-0.519406\pi$
$271$	−2.00602			−0.121857			−0.0609285	+	0.998142i	$0.519406\pi$
$272$	3.10511			0.188275
$273$		0			0
$274$		−	14.1258i		−	0.853373i
$275$	3.49849	+	5.16636i	0.210967	+	0.311543i
$276$		0			0
$277$	−11.5671			−0.695000			−0.347500	−	0.937680i	$-0.612969\pi$
$277$	−11.5671			−0.695000			−0.347500	+	0.937680i	$0.612969\pi$
$278$	8.43675			0.506003
$279$		0			0
$280$	1.24789	+	0.662054i	0.0745757	+	0.0395653i
$281$		−	14.2909i		−	0.852521i	−0.904600	−	0.426261i	$-0.859831\pi$
$281$		−	14.2909i		−	0.852521i	0.904600	−	0.426261i	$-0.140169\pi$
$282$		0			0
$283$	−12.3837			−0.736137			−0.368068	−	0.929799i	$-0.619981\pi$
$283$	−12.3837			−0.736137			−0.368068	+	0.929799i	$0.619981\pi$
$284$	12.7183			0.754694
$285$		0			0
$286$	4.18042			0.247193
$287$		−	5.34152i		−	0.315300i
$288$		0			0
$289$	−7.35829			−0.432840
$290$	18.9159	+	10.0356i	1.11078	+	0.589313i
$291$		0			0
$292$			4.45836i			0.260906i
$293$		−	27.8374i		−	1.62628i	−0.582068	−	0.813140i	$-0.697756\pi$
$293$		−	27.8374i		−	1.62628i	0.582068	−	0.813140i	$-0.302244\pi$
$294$		0			0
$295$	8.62152	+	4.57405i	0.501964	+	0.266312i
$296$	4.10511	−	4.48866i	0.238605	−	0.260898i
$297$		0			0
$298$	−13.6447			−0.790416
$299$	25.4836			1.47375
$300$		0			0
$301$		−	3.07435i		−	0.177203i
$302$	−3.17741			−0.182839
$303$		0			0
$304$		−	5.97327i		−	0.342590i
$305$	−4.24028	−	2.24963i	−0.242798	−	0.128814i
$306$		0			0
$307$			19.9411i			1.13810i	0.822304	+	0.569049i	$0.192688\pi$
$307$			19.9411i			1.13810i	−0.822304	+	0.569049i	$0.807312\pi$
$308$			0.788355i			0.0449207i
$309$		0			0
$310$	14.3546	+	7.61566i	0.815284	+	0.432540i
$311$		−	4.96832i		−	0.281727i	−0.990029	−	0.140864i	$-0.955012\pi$
$311$		−	4.96832i		−	0.281727i	0.990029	−	0.140864i	$-0.0449879\pi$
$312$		0			0
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$		−	0.215310i		−	0.0121506i
$315$		0			0
$316$			8.78679i			0.494296i
$317$			22.9198i			1.28730i	0.765319	+	0.643651i	$0.222581\pi$
$317$			22.9198i			1.28730i	−0.765319	+	0.643651i	$0.777419\pi$
$318$		0			0
$319$			11.9502i			0.669080i
$320$	−1.04797	+	1.97529i	−0.0585832	+	0.110422i
$321$		0			0
$322$			4.80576i			0.267815i
$323$		−	18.5477i		−	1.03202i
$324$		0			0
$325$	9.39179	+	13.8692i	0.520963	+	0.769326i
$326$	−1.66609			−0.0922760
$327$		0			0
$328$	8.45510			0.466855
$329$	8.28775			0.456918
$330$		0			0
$331$		−	5.54265i		−	0.304651i	−0.988330	−	0.152326i	$-0.951324\pi$
$331$		−	5.54265i		−	0.304651i	0.988330	−	0.152326i	$-0.0486763\pi$
$332$		−	6.63185i		−	0.363970i
$333$		0			0
$334$	−5.92242			−0.324060
$335$	−22.4098	−	11.8893i	−1.22438	−	0.649581i
$336$		0			0
$337$		−	25.6348i		−	1.39642i	−0.715894	−	0.698209i	$-0.753981\pi$
$337$		−	25.6348i		−	1.39642i	0.715894	−	0.698209i	$-0.246019\pi$
$338$	−1.77756			−0.0966867
$339$		0			0
$340$	−3.25406	+	6.13349i	−0.176476	+	0.332635i
$341$			9.06851i			0.491087i
$342$		0			0
$343$		−	8.59237i		−	0.463945i
$344$	4.86640			0.262379
$345$		0			0
$346$		−	2.88008i		−	0.154834i
$347$	−19.6225			−1.05339			−0.526696	−	0.850054i	$-0.676569\pi$
$347$	−19.6225			−1.05339			−0.526696	+	0.850054i	$0.676569\pi$
$348$		0			0
$349$	−15.6263			−0.836459			−0.418230	−	0.908341i	$-0.637349\pi$
$349$	−15.6263			−0.836459			−0.418230	+	0.908341i	$0.637349\pi$
$350$	−2.61550	+	1.77113i	−0.139804	+	0.0946709i
$351$		0			0
$352$	−1.24789			−0.0665128
$353$	−23.5724			−1.25463			−0.627316	−	0.778765i	$-0.715847\pi$
$353$	−23.5724			−1.25463			−0.627316	+	0.778765i	$0.715847\pi$
$354$		0			0
$355$	−13.3284	+	25.1224i	−0.707398	+	1.33336i
$356$		−	13.7784i		−	0.730255i
$357$		0			0
$358$			4.46182i			0.235815i
$359$	9.34905			0.493424			0.246712	−	0.969089i	$-0.420650\pi$
$359$	9.34905			0.493424			0.246712	+	0.969089i	$0.420650\pi$
$360$		0			0
$361$	−16.6799			−0.877891
$362$	3.93480			0.206809
$363$		0			0
$364$			2.11636i			0.110927i
$365$	−8.80654	−	4.67221i	−0.460955	−	0.244555i
$366$		0			0
$367$			12.2379i			0.638811i	0.947618	+	0.319406i	$0.103483\pi$
$367$			12.2379i			0.638811i	−0.947618	+	0.319406i	$0.896517\pi$
$368$	−7.60706			−0.396545
$369$		0			0
$370$	4.56437	+	12.8127i	0.237291	+	0.666103i
$371$	−4.53180			−0.235280
$372$		0			0
$373$		−	10.1918i		−	0.527712i	−0.964562	−	0.263856i	$-0.915006\pi$
$373$		−	10.1918i		−	0.527712i	0.964562	−	0.263856i	$-0.0849943\pi$
$374$	−3.87484			−0.200363
$375$		0			0
$376$			13.1187i			0.676545i
$377$			32.0805i			1.65223i
$378$		0			0
$379$	20.7538			1.06605			0.533025	−	0.846099i	$-0.321055\pi$
$379$	20.7538			1.06605			0.533025	+	0.846099i	$0.321055\pi$
$380$	11.7989	+	6.25979i	0.605272	+	0.321120i
$381$		0			0
$382$			7.76296i			0.397188i
$383$	−17.7328			−0.906103			−0.453052	−	0.891484i	$-0.649665\pi$
$383$	−17.7328			−0.906103			−0.453052	+	0.891484i	$0.649665\pi$
$384$		0			0
$385$	−1.55723	−	0.826171i	−0.0793638	−	0.0421056i
$386$	−3.49189			−0.177732
$387$		0			0
$388$	−11.0583			−0.561398
$389$			10.9054i			0.552923i	0.961025	+	0.276462i	$0.0891619\pi$
$389$			10.9054i			0.552923i	−0.961025	+	0.276462i	$0.910838\pi$
$390$		0			0
$391$	−23.6208			−1.19455
$392$	6.60089			0.333395
$393$		0			0
$394$			1.07617i			0.0542164i
$395$	−17.3565	−	9.20827i	−0.873298	−	0.463319i
$396$		0			0
$397$			23.0106i			1.15487i	0.816437	+	0.577435i	$0.195946\pi$
$397$			23.0106i			1.15487i	−0.816437	+	0.577435i	$0.804054\pi$
$398$			5.71343i			0.286388i
$399$		0			0
$400$	−2.80353	−	4.14008i	−0.140176	−	0.207004i
$401$		−	16.5769i		−	0.827809i	−0.910320	−	0.413904i	$-0.864165\pi$
$401$		−	16.5769i		−	0.827809i	0.910320	−	0.413904i	$-0.135835\pi$
$402$		0			0
$403$			24.3446i			1.21269i
$404$	−8.65314			−0.430510
$405$		0			0
$406$	−6.04983			−0.300248
$407$	−5.12273	+	5.60135i	−0.253924	+	0.277649i
$408$		0			0
$409$		−	5.05401i		−	0.249905i	−0.992163	−	0.124952i	$-0.960122\pi$
$409$		−	5.05401i		−	0.249905i	0.992163	−	0.124952i	$-0.0398778\pi$
$410$	−8.86067	+	16.7013i	−0.437597	+	0.824817i
$411$		0			0
$412$	4.57336			0.225313
$413$	−2.75740			−0.135683
$414$		0			0
$415$	13.0998	+	6.94997i	0.643045	+	0.341161i
$416$	−3.34999			−0.164247
$417$		0			0
$418$			7.45398i			0.364586i
$419$	24.2194			1.18319			0.591597	−	0.806234i	$-0.298498\pi$
$419$	24.2194			1.18319			0.591597	+	0.806234i	$0.298498\pi$
$420$		0			0
$421$		−	20.8487i		−	1.01611i	−0.861326	−	0.508053i	$-0.830365\pi$
$421$		−	20.8487i		−	1.01611i	0.861326	−	0.508053i	$-0.169635\pi$
$422$	22.8397			1.11182
$423$		0			0
$424$		−	7.17340i		−	0.348371i
$425$	−8.70527	−	12.8554i	−0.422267	−	0.623578i
$426$		0			0
$427$	1.35616			0.0656290
$428$		−	11.4715i		−	0.554498i
$429$		0			0
$430$	−5.09983	+	9.61254i	−0.245935	+	0.463558i
$431$			28.2298i			1.35978i	0.733314	+	0.679890i	$0.237973\pi$
$431$			28.2298i			1.35978i	−0.733314	+	0.679890i	$0.762027\pi$
$432$		0			0
$433$			30.3997i			1.46091i	0.682958	+	0.730457i	$0.260693\pi$
$433$			30.3997i			1.46091i	−0.682958	+	0.730457i	$0.739307\pi$
$434$	−4.59098			−0.220374
$435$		0			0
$436$		−	0.727748i		−	0.0348528i
$437$			45.4390i			2.17364i
$438$		0			0
$439$		−	33.7591i		−	1.61123i	−0.592438	−	0.805616i	$-0.701834\pi$
$439$		−	33.7591i		−	1.61123i	0.592438	−	0.805616i	$-0.298166\pi$
$440$	1.30775	−	2.46494i	0.0623444	−	0.117512i
$441$		0			0
$442$	−10.4021			−0.494777
$443$			15.5413i			0.738388i	0.929352	+	0.369194i	$0.120366\pi$
$443$			15.5413i			0.738388i	−0.929352	+	0.369194i	$0.879634\pi$
$444$		0			0
$445$	27.2164	+	14.4393i	1.29018	+	0.684490i
$446$			3.32116i			0.157261i
$447$		0			0
$448$		−	0.631751i		−	0.0298474i
$449$			14.2184i			0.671006i	0.942039	+	0.335503i	$0.108906\pi$
$449$			14.2184i			0.671006i	−0.942039	+	0.335503i	$0.891094\pi$
$450$		0			0
$451$	−10.5510			−0.496829
$452$	−17.9970			−0.846506
$453$		0			0
$454$	−5.62938			−0.264200
$455$	−4.18042	−	2.21788i	−0.195981	−	0.103976i
$456$		0			0
$457$	9.17031			0.428969			0.214484	−	0.976727i	$-0.431193\pi$
$457$	9.17031			0.428969			0.214484	+	0.976727i	$0.431193\pi$
$458$	−0.973208			−0.0454750
$459$		0			0
$460$	7.97195	−	15.0261i	0.371694	−	0.700597i
$461$			10.3300i			0.481114i	0.970635	+	0.240557i	$0.0773301\pi$
$461$			10.3300i			0.481114i	−0.970635	+	0.240557i	$0.922670\pi$
$462$		0			0
$463$	−25.8049			−1.19926			−0.599629	−	0.800278i	$-0.704685\pi$
$463$	−25.8049			−1.19926			−0.599629	+	0.800278i	$0.704685\pi$
$464$		−	9.57629i		−	0.444568i
$465$		0			0
$466$		−	14.4150i		−	0.667761i
$467$	34.4582			1.59454			0.797268	−	0.603625i	$-0.206278\pi$
$467$	34.4582			1.59454			0.797268	+	0.603625i	$0.206278\pi$
$468$		0			0
$469$	7.16727			0.330954
$470$	−25.9132	−	13.7480i	−1.19529	−	0.634147i
$471$		0			0
$472$		−	4.36469i		−	0.200901i
$473$	−6.07273			−0.279224
$474$		0			0
$475$	−24.7298	+	16.7462i	−1.13468	+	0.768369i
$476$		−	1.96166i		−	0.0899124i
$477$		0			0
$478$			8.43344i			0.385737i
$479$			29.6039i			1.35264i	0.736610	+	0.676318i	$0.236426\pi$
$479$			29.6039i			1.35264i	−0.736610	+	0.676318i	$0.763574\pi$
$480$		0			0
$481$	−13.7521	+	15.0370i	−0.627041	+	0.685627i
$482$		−	18.6567i		−	0.849789i
$483$		0			0
$484$	−9.44277			−0.429217
$485$	11.5887	−	21.8433i	0.526216	−	0.991852i
$486$		0			0
$487$	−27.0961			−1.22784			−0.613920	−	0.789369i	$-0.710408\pi$
$487$	−27.0961			−1.22784			−0.613920	+	0.789369i	$0.710408\pi$
$488$			2.14666i			0.0971749i
$489$		0			0
$490$	−6.91752	+	13.0387i	−0.312502	+	0.589027i
$491$	−2.46033			−0.111033			−0.0555166	−	0.998458i	$-0.517681\pi$
$491$	−2.46033			−0.111033			−0.0555166	+	0.998458i	$0.517681\pi$
$492$		0			0
$493$		−	29.7354i		−	1.33922i
$494$			20.0104i			0.900310i
$495$		0			0
$496$		−	7.26707i		−	0.326301i
$497$		−	8.03482i		−	0.360411i
$498$		0			0
$499$			31.4091i			1.40606i	0.711158	+	0.703032i	$0.248171\pi$
$499$			31.4091i			1.40606i	−0.711158	+	0.703032i	$0.751829\pi$
$500$	11.1159	−	1.19911i	0.497116	−	0.0536259i
$501$		0			0
$502$		−	25.1189i		−	1.12111i
$503$	−1.78145			−0.0794311			−0.0397156	−	0.999211i	$-0.512645\pi$
$503$	−1.78145			−0.0794311			−0.0397156	+	0.999211i	$0.512645\pi$
$504$		0			0
$505$	9.06821	−	17.0924i	0.403530	−	0.760604i
$506$	9.49277			0.422005
$507$		0			0
$508$		−	15.4830i		−	0.686947i
$509$	−21.2370			−0.941314			−0.470657	−	0.882316i	$-0.655983\pi$
$509$	−21.2370			−0.941314			−0.470657	+	0.882316i	$0.655983\pi$
$510$		0			0
$511$	2.81657			0.124598
$512$	1.00000			0.0441942
$513$		0			0
$514$	20.3552			0.897831
$515$	−4.79274	+	9.03371i	−0.211193	+	0.398073i
$516$		0			0
$517$		−	16.3707i		−	0.719982i
$518$	−2.83571	−	2.59341i	−0.124594	−	0.113948i
$519$		0			0
$520$	3.51068	−	6.61720i	0.153954	−	0.290183i
$521$	−2.52950			−0.110819			−0.0554097	−	0.998464i	$-0.517646\pi$
$521$	−2.52950			−0.110819			−0.0554097	+	0.998464i	$0.517646\pi$
$522$		0			0
$523$	−1.60848			−0.0703338			−0.0351669	−	0.999381i	$-0.511196\pi$
$523$	−1.60848			−0.0703338			−0.0351669	+	0.999381i	$0.511196\pi$
$524$		−	6.22121i		−	0.271775i
$525$		0			0
$526$			22.2211i			0.968887i
$527$		−	22.5651i		−	0.982950i
$528$		0			0
$529$	34.8673			1.51597
$530$	14.1695	+	7.51750i	0.615486	+	0.326539i
$531$		0			0
$532$	−3.77362			−0.163607
$533$	−28.3245			−1.22687
$534$		0			0
$535$	22.6596	+	12.0218i	0.979660	+	0.519748i
$536$			11.3451i			0.490033i
$537$		0			0
$538$	15.8411			0.682959
$539$	−8.23719			−0.354801
$540$		0			0
$541$			3.12463i			0.134338i	0.997742	+	0.0671692i	$0.0213967\pi$
$541$			3.12463i			0.134338i	−0.997742	+	0.0671692i	$0.978603\pi$
$542$	−2.00602			−0.0861660
$543$		0			0
$544$	3.10511			0.133131
$545$	1.43751	+	0.762657i	0.0615763	+	0.0326686i
$546$		0			0
$547$	5.44201			0.232683			0.116342	−	0.993209i	$-0.462883\pi$
$547$	5.44201			0.232683			0.116342	+	0.993209i	$0.462883\pi$
$548$		−	14.1258i		−	0.603426i
$549$		0			0
$550$	3.49849	+	5.16636i	0.149176	+	0.220294i
$551$	−57.2017			−2.43688
$552$		0			0
$553$	5.55106			0.236055
$554$	−11.5671			−0.491440
$555$		0			0
$556$	8.43675			0.357798
$557$	36.3451			1.53999			0.769995	−	0.638050i	$-0.220259\pi$
$557$	36.3451			1.53999			0.769995	+	0.638050i	$0.220259\pi$
$558$		0			0
$559$	−16.3024			−0.689517
$560$	1.24789	+	0.662054i	0.0527330	+	0.0279769i
$561$		0			0
$562$		−	14.2909i		−	0.602824i
$563$	38.4949			1.62237			0.811184	−	0.584791i	$-0.198823\pi$
$563$	38.4949			1.62237			0.811184	+	0.584791i	$0.198823\pi$
$564$		0			0
$565$	18.8602	−	35.5492i	0.793456	−	1.49557i
$566$	−12.3837			−0.520527
$567$		0			0
$568$	12.7183			0.533649
$569$			41.2793i			1.73052i	0.501324	+	0.865260i	$0.332846\pi$
$569$			41.2793i			1.73052i	−0.501324	+	0.865260i	$0.667154\pi$
$570$		0			0
$571$	−26.0635			−1.09072			−0.545362	−	0.838200i	$-0.683608\pi$
$571$	−26.0635			−1.09072			−0.545362	+	0.838200i	$0.683608\pi$
$572$	4.18042			0.174792
$573$		0			0
$574$		−	5.34152i		−	0.222951i
$575$	21.3266	+	31.4938i	0.889381	+	1.31338i
$576$		0			0
$577$	11.8411			0.492952			0.246476	−	0.969149i	$-0.420727\pi$
$577$	11.8411			0.492952			0.246476	+	0.969149i	$0.420727\pi$
$578$	−7.35829			−0.306064
$579$		0			0
$580$	18.9159	+	10.0356i	0.785441	+	0.416707i
$581$	−4.18968			−0.173817
$582$		0			0
$583$			8.95162i			0.370738i
$584$			4.45836i			0.184488i
$585$		0			0
$586$		−	27.8374i		−	1.14995i
$587$	26.7315			1.10333			0.551663	−	0.834067i	$-0.313994\pi$
$587$	26.7315			1.10333			0.551663	+	0.834067i	$0.313994\pi$
$588$		0			0
$589$	−43.4082			−1.78860
$590$	8.62152	+	4.57405i	0.354942	+	0.188311i
$591$		0			0
$592$	4.10511	−	4.48866i	0.168719	−	0.184483i
$593$		−	22.6119i		−	0.928560i	−0.885688	−	0.464280i	$-0.846313\pi$
$593$		−	22.6119i		−	0.928560i	0.885688	−	0.464280i	$-0.153687\pi$
$594$		0			0
$595$	3.87484	+	2.05575i	0.158853	+	0.0842776i
$596$	−13.6447			−0.558909
$597$		0			0
$598$	25.4836			1.04210
$599$	−14.3406			−0.585942			−0.292971	−	0.956121i	$-0.594644\pi$
$599$	−14.3406			−0.585942			−0.292971	+	0.956121i	$0.594644\pi$
$600$		0			0
$601$	15.0845			0.615308			0.307654	−	0.951498i	$-0.400456\pi$
$601$	15.0845			0.615308			0.307654	+	0.951498i	$0.400456\pi$
$602$		−	3.07435i		−	0.125301i
$603$		0			0
$604$	−3.17741			−0.129287
$605$	9.89572	−	18.6522i	0.402318	−	0.758320i
$606$		0			0
$607$	41.5964			1.68835			0.844174	−	0.536070i	$-0.180092\pi$
$607$	41.5964			1.68835			0.844174	+	0.536070i	$0.180092\pi$
$608$		−	5.97327i		−	0.242248i
$609$		0			0
$610$	−4.24028	−	2.24963i	−0.171684	−	0.0910850i
$611$		−	43.9475i		−	1.77793i
$612$		0			0
$613$		−	30.4369i		−	1.22934i	−0.788786	−	0.614668i	$-0.789290\pi$
$613$		−	30.4369i		−	1.22934i	0.788786	−	0.614668i	$-0.210710\pi$
$614$			19.9411i			0.804756i
$615$		0			0
$616$			0.788355i			0.0317637i
$617$			39.8195i			1.60307i	0.597946	+	0.801536i	$0.295984\pi$
$617$			39.8195i			1.60307i	−0.597946	+	0.801536i	$0.704016\pi$
$618$		0			0
$619$	39.4011			1.58367			0.791833	−	0.610738i	$-0.209127\pi$
$619$	39.4011			1.58367			0.791833	+	0.610738i	$0.209127\pi$
$620$	14.3546	+	7.61566i	0.576493	+	0.305852i
$621$		0			0
$622$		−	4.96832i		−	0.199211i
$623$	−8.70453			−0.348740
$624$		0			0
$625$	−9.28046	+	23.2136i	−0.371218	+	0.928546i
$626$	−10.0000			−0.399680
$627$		0			0
$628$		−	0.215310i		−	0.00859180i
$629$	12.7468	−	13.9378i	0.508249	−	0.555736i
$630$		0			0
$631$			0.114985i			0.00457750i	0.999997	+	0.00228875i	$0.000728532\pi$
$631$			0.114985i			0.00457750i	−0.999997	+	0.00228875i	$0.999271\pi$
$632$			8.78679i			0.349520i
$633$		0			0
$634$			22.9198i			0.910260i
$635$	30.5834	+	16.2257i	1.21366	+	0.643897i
$636$		0			0
$637$	−22.1129			−0.876146
$638$			11.9502i			0.473111i
$639$		0			0
$640$	−1.04797	+	1.97529i	−0.0414246	+	0.0780801i
$641$	−34.9774			−1.38153			−0.690763	−	0.723081i	$-0.742725\pi$
$641$	−34.9774			−1.38153			−0.690763	+	0.723081i	$0.742725\pi$
$642$		0			0
$643$	−25.2868			−0.997216			−0.498608	−	0.866828i	$-0.666155\pi$
$643$	−25.2868			−0.997216			−0.498608	+	0.866828i	$0.666155\pi$
$644$			4.80576i			0.189374i
$645$		0			0
$646$		−	18.5477i		−	0.729748i
$647$	−23.5824			−0.927120			−0.463560	−	0.886066i	$-0.653428\pi$
$647$	−23.5824			−0.927120			−0.463560	+	0.886066i	$0.653428\pi$
$648$		0			0
$649$			5.44665i			0.213800i
$650$	9.39179	+	13.8692i	0.368376	+	0.543995i
$651$		0			0
$652$	−1.66609			−0.0652490
$653$	9.89261			0.387128			0.193564	−	0.981088i	$-0.437995\pi$
$653$	9.89261			0.387128			0.193564	+	0.981088i	$0.437995\pi$
$654$		0			0
$655$	12.2887	+	6.51963i	0.480159	+	0.254743i
$656$	8.45510			0.330116
$657$		0			0
$658$	8.28775			0.323090
$659$	25.4137			0.989976			0.494988	−	0.868900i	$-0.335173\pi$
$659$	25.4137			0.989976			0.494988	+	0.868900i	$0.335173\pi$
$660$		0			0
$661$		−	28.4574i		−	1.10687i	−0.832894	−	0.553433i	$-0.813318\pi$
$661$		−	28.4574i		−	1.10687i	0.832894	−	0.553433i	$-0.186682\pi$
$662$		−	5.54265i		−	0.215421i
$663$		0			0
$664$		−	6.63185i		−	0.257366i
$665$	3.95463	−	7.45398i	0.153354	−	0.289053i
$666$		0			0
$667$			72.8474i			2.82066i
$668$	−5.92242			−0.229145
$669$		0			0
$670$	−22.4098	−	11.8893i	−0.865767	−	0.459323i
$671$		−	2.67880i		−	0.103414i
$672$		0			0
$673$		−	20.4187i		−	0.787082i	−0.919307	−	0.393541i	$-0.871250\pi$
$673$		−	20.4187i		−	0.787082i	0.919307	−	0.393541i	$-0.128750\pi$
$674$		−	25.6348i		−	0.987416i
$675$		0			0
$676$	−1.77756			−0.0683678
$677$		−	18.5163i		−	0.711641i	−0.934554	−	0.355821i	$-0.884201\pi$
$677$		−	18.5163i		−	0.711641i	0.934554	−	0.355821i	$-0.115799\pi$
$678$		0			0
$679$			6.98607i			0.268101i
$680$	−3.25406	+	6.13349i	−0.124787	+	0.235209i
$681$		0			0
$682$			9.06851i			0.347251i
$683$	32.0667			1.22700			0.613499	−	0.789695i	$-0.289761\pi$
$683$	32.0667			1.22700			0.613499	+	0.789695i	$0.289761\pi$
$684$		0			0
$685$	27.9026	+	14.8034i	1.06610	+	0.565609i
$686$		−	8.59237i		−	0.328058i
$687$		0			0
$688$	4.86640			0.185530
$689$			24.0308i			0.915502i
$690$		0			0
$691$	−6.57629			−0.250174			−0.125087	−	0.992146i	$-0.539921\pi$
$691$	−6.57629			−0.250174			−0.125087	+	0.992146i	$0.539921\pi$
$692$		−	2.88008i		−	0.109484i
$693$		0			0
$694$	−19.6225			−0.744860
$695$	−8.84144	+	16.6650i	−0.335375	+	0.632140i
$696$		0			0
$697$	26.2540			0.994442
$698$	−15.6263			−0.591466
$699$		0			0
$700$	−2.61550	+	1.77113i	−0.0988565	+	0.0669425i
$701$		−	9.62168i		−	0.363406i	−0.983353	−	0.181703i	$-0.941839\pi$
$701$		−	9.62168i		−	0.363406i	0.983353	−	0.181703i	$-0.0581609\pi$
$702$		0			0
$703$	−26.8120	−	24.5209i	−1.01123	−	0.924824i
$704$	−1.24789			−0.0470316
$705$		0			0
$706$	−23.5724			−0.887159
$707$			5.46663i			0.205594i
$708$		0			0
$709$			8.65759i			0.325142i	0.986697	+	0.162571i	$0.0519787\pi$
$709$			8.65759i			0.325142i	−0.986697	+	0.162571i	$0.948021\pi$
$710$	−13.3284	+	25.1224i	−0.500206	+	0.942826i
$711$		0			0
$712$		−	13.7784i		−	0.516368i
$713$			55.2810i			2.07029i
$714$		0			0
$715$	−4.38094	+	8.25753i	−0.163838	+	0.308814i
$716$			4.46182i			0.166746i
$717$		0			0
$718$	9.34905			0.348904
$719$	−51.5303			−1.92176			−0.960878	−	0.276972i	$-0.910669\pi$
$719$	−51.5303			−1.92176			−0.960878	+	0.276972i	$0.910669\pi$
$720$		0			0
$721$		−	2.88923i		−	0.107600i
$722$	−16.6799			−0.620763
$723$		0			0
$724$	3.93480			0.146236
$725$	−39.6466	+	26.8474i	−1.47244	+	0.997087i
$726$		0			0
$727$	11.3224			0.419924			0.209962	−	0.977710i	$-0.432666\pi$
$727$	11.3224			0.419924			0.209962	+	0.977710i	$0.432666\pi$
$728$			2.11636i			0.0784375i
$729$		0			0
$730$	−8.80654	−	4.67221i	−0.325945	−	0.172926i
$731$	15.1107			0.558890
$732$		0			0
$733$			2.74231i			0.101290i	0.998717	+	0.0506448i	$0.0161276\pi$
$733$			2.74231i			0.101290i	−0.998717	+	0.0506448i	$0.983872\pi$
$734$			12.2379i			0.451708i
$735$		0			0
$736$	−7.60706			−0.280400
$737$		−	14.1574i		−	0.521495i
$738$		0			0
$739$	8.18878			0.301229			0.150614	−	0.988593i	$-0.451875\pi$
$739$	8.18878			0.301229			0.150614	+	0.988593i	$0.451875\pi$
$740$	4.56437	+	12.8127i	0.167790	+	0.471006i
$741$		0			0
$742$	−4.53180			−0.166368
$743$			22.1217i			0.811567i	0.913969	+	0.405784i	$0.133001\pi$
$743$			22.1217i			0.811567i	−0.913969	+	0.405784i	$0.866999\pi$
$744$		0			0
$745$	14.2992	−	26.9522i	0.523882	−	0.987453i
$746$		−	10.1918i		−	0.373149i
$747$		0			0
$748$	−3.87484			−0.141678
$749$	−7.24715			−0.264805
$750$		0			0
$751$	−19.0818			−0.696306			−0.348153	−	0.937438i	$-0.613191\pi$
$751$	−19.0818			−0.696306			−0.348153	+	0.937438i	$0.613191\pi$
$752$			13.1187i			0.478390i
$753$		0			0
$754$			32.0805i			1.16830i
$755$	3.32982	−	6.27630i	0.121185	−	0.228418i
$756$		0			0
$757$	31.2209			1.13474			0.567372	−	0.823462i	$-0.307960\pi$
$757$	31.2209			1.13474			0.567372	+	0.823462i	$0.307960\pi$
$758$	20.7538			0.753811
$759$		0			0
$760$	11.7989	+	6.25979i	0.427992	+	0.227066i
$761$	29.3163			1.06271			0.531357	−	0.847148i	$-0.321682\pi$
$761$	29.3163			1.06271			0.531357	+	0.847148i	$0.321682\pi$
$762$		0			0
$763$	−0.459756			−0.0166443
$764$			7.76296i			0.280854i
$765$		0			0
$766$	−17.7328			−0.640712
$767$			14.6217i			0.527958i
$768$		0			0
$769$			29.0289i			1.04681i	0.852084	+	0.523404i	$0.175338\pi$
$769$			29.0289i			1.04681i	−0.852084	+	0.523404i	$0.824662\pi$
$770$	−1.55723	−	0.826171i	−0.0561187	−	0.0297731i
$771$		0			0
$772$	−3.49189			−0.125676
$773$		−	43.4153i		−	1.56154i	−0.624819	−	0.780769i	$-0.714827\pi$
$773$		−	43.4153i		−	1.56154i	0.624819	−	0.780769i	$-0.285173\pi$
$774$		0			0
$775$	−30.0862	+	20.3734i	−1.08073	+	0.731836i
$776$	−11.0583			−0.396969
$777$		0			0
$778$			10.9054i			0.390976i
$779$		−	50.5046i		−	1.80951i
$780$		0			0
$781$	−15.8711			−0.567912
$782$	−23.6208			−0.844676
$783$		0			0
$784$	6.60089			0.235746
$785$	0.425299	+	0.225638i	0.0151796	+	0.00805336i
$786$		0			0
$787$			18.9119i			0.674136i	0.941480	+	0.337068i	$0.109435\pi$
$787$			18.9119i			0.674136i	−0.941480	+	0.337068i	$0.890565\pi$
$788$			1.07617i			0.0383368i
$789$		0			0
$790$	−17.3565	−	9.20827i	−0.617515	−	0.327616i
$791$			11.3696i			0.404256i
$792$		0			0
$793$		−	7.19130i		−	0.255371i
$794$			23.0106i			0.816616i
$795$		0			0
$796$			5.71343i			0.202507i
$797$	−6.65779			−0.235831			−0.117916	−	0.993024i	$-0.537621\pi$
$797$	−6.65779			−0.235831			−0.117916	+	0.993024i	$0.537621\pi$
$798$		0			0
$799$			40.7350i			1.44110i
$800$	−2.80353	−	4.14008i	−0.0991197	−	0.146374i
$801$		0			0
$802$		−	16.5769i		−	0.585349i
$803$		−	5.56354i		−	0.196333i
$804$		0			0
$805$	−9.49277	−	5.03628i	−0.334576	−	0.177506i
$806$			24.3446i			0.857503i
$807$		0			0
$808$	−8.65314			−0.304416
$809$		−	35.3855i		−	1.24409i	−0.782982	−	0.622044i	$-0.786302\pi$
$809$		−	35.3855i		−	1.24409i	0.782982	−	0.622044i	$-0.213698\pi$
$810$		0			0
$811$	34.1205			1.19813			0.599067	−	0.800699i	$-0.295538\pi$
$811$	34.1205			1.19813			0.599067	+	0.800699i	$0.295538\pi$
$812$	−6.04983			−0.212307
$813$		0			0
$814$	−5.12273	+	5.60135i	−0.179551	+	0.196327i
$815$	1.74600	−	3.29100i	0.0611599	−	0.115279i
$816$		0			0
$817$		−	29.0683i		−	1.01697i
$818$		−	5.05401i		−	0.176709i
$819$		0			0
$820$	−8.86067	+	16.7013i	−0.309428	+	0.583233i
$821$	50.1981			1.75193			0.875963	−	0.482378i	$-0.160227\pi$
$821$	50.1981			1.75193			0.875963	+	0.482378i	$0.160227\pi$
$822$		0			0
$823$			47.6713i			1.66172i	0.556483	+	0.830859i	$0.312150\pi$
$823$			47.6713i			1.66172i	−0.556483	+	0.830859i	$0.687850\pi$
$824$	4.57336			0.159321
$825$		0			0
$826$	−2.75740			−0.0959420
$827$	3.77813			0.131378			0.0656892	−	0.997840i	$-0.479075\pi$
$827$	3.77813			0.131378			0.0656892	+	0.997840i	$0.479075\pi$
$828$		0			0
$829$			11.9862i			0.416297i	0.978097	+	0.208149i	$0.0667438\pi$
$829$			11.9862i			0.416297i	−0.978097	+	0.208149i	$0.933256\pi$
$830$	13.0998	+	6.94997i	0.454702	+	0.241237i
$831$		0			0
$832$	−3.34999			−0.116140
$833$	20.4965			0.710162
$834$		0			0
$835$	6.20650	−	11.6985i	0.214785	−	0.404843i
$836$			7.45398i			0.257801i
$837$		0			0
$838$	24.2194			0.836644
$839$	54.1303			1.86879			0.934393	−	0.356243i	$-0.115942\pi$
$839$	54.1303			1.86879			0.934393	+	0.356243i	$0.115942\pi$
$840$		0			0
$841$	−62.7053			−2.16225
$842$		−	20.8487i		−	0.718495i
$843$		0			0
$844$	22.8397			0.786176
$845$	1.86283	−	3.51120i	0.0640833	−	0.120789i
$846$		0			0
$847$			5.96548i			0.204976i
$848$		−	7.17340i		−	0.246336i
$849$		0			0
$850$	−8.70527	−	12.8554i	−0.298588	−	0.440936i
$851$	−31.2278	+	34.1455i	−1.07048	+	1.17049i
$852$		0			0
$853$	54.7590			1.87491			0.937457	−	0.348101i	$-0.113173\pi$
$853$	54.7590			1.87491			0.937457	+	0.348101i	$0.113173\pi$
$854$	1.35616			0.0464067
$855$		0			0
$856$		−	11.4715i		−	0.392089i
$857$	13.8273			0.472331			0.236165	−	0.971713i	$-0.424109\pi$
$857$	13.8273			0.472331			0.236165	+	0.971713i	$0.424109\pi$
$858$		0			0
$859$		−	27.9420i		−	0.953368i	−0.879075	−	0.476684i	$-0.841839\pi$
$859$		−	27.9420i		−	0.953368i	0.879075	−	0.476684i	$-0.158161\pi$
$860$	−5.09983	+	9.61254i	−0.173903	+	0.327785i
$861$		0			0
$862$			28.2298i			0.961510i
$863$			0.665448i			0.0226521i	0.999936	+	0.0113261i	$0.00360527\pi$
$863$			0.665448i			0.0226521i	−0.999936	+	0.0113261i	$0.996395\pi$
$864$		0			0
$865$	5.68899	+	3.01823i	0.193431	+	0.102623i
$866$			30.3997i			1.03302i
$867$		0			0
$868$	−4.59098			−0.155828
$869$		−	10.9650i		−	0.371961i
$870$		0			0
$871$		−	38.0059i		−	1.28778i
$872$		−	0.727748i		−	0.0246447i
$873$		0			0
$874$			45.4390i			1.53700i
$875$	−0.757540	−	7.02245i	−0.0256095	−	0.237402i
$876$		0			0
$877$			2.04026i			0.0688948i	0.999407	+	0.0344474i	$0.0109671\pi$
$877$			2.04026i			0.0688948i	−0.999407	+	0.0344474i	$0.989033\pi$
$878$		−	33.7591i		−	1.13931i
$879$		0			0
$880$	1.30775	−	2.46494i	0.0440842	−	0.0830932i
$881$	−19.5251			−0.657816			−0.328908	−	0.944362i	$-0.606681\pi$
$881$	−19.5251			−0.657816			−0.328908	+	0.944362i	$0.606681\pi$
$882$		0			0
$883$	21.6799			0.729586			0.364793	−	0.931089i	$-0.381140\pi$
$883$	21.6799			0.729586			0.364793	+	0.931089i	$0.381140\pi$
$884$	−10.4021			−0.349860
$885$		0			0
$886$			15.5413i			0.522119i
$887$		−	35.0252i		−	1.17603i	−0.808850	−	0.588015i	$-0.799910\pi$
$887$		−	35.0252i		−	1.17603i	0.808850	−	0.588015i	$-0.200090\pi$
$888$		0			0
$889$	−9.78140			−0.328058
$890$	27.2164	+	14.4393i	0.912294	+	0.484008i
$891$		0			0
$892$			3.32116i			0.111201i
$893$	78.3615			2.62227
$894$		0			0
$895$	−8.81339	−	4.67585i	−0.294599	−	0.156296i
$896$		−	0.631751i		−	0.0211053i
$897$		0			0
$898$			14.2184i			0.474473i
$899$	−69.5916			−2.32101
$900$		0			0
$901$		−	22.2742i		−	0.742062i
$902$	−10.5510			−0.351311
$903$		0			0
$904$	−17.9970			−0.598570
$905$	−4.12355	+	7.77237i	−0.137071	+	0.258362i
$906$		0			0
$907$	19.4042			0.644307			0.322153	−	0.946688i	$-0.395593\pi$
$907$	19.4042			0.644307			0.322153	+	0.946688i	$0.395593\pi$
$908$	−5.62938			−0.186818
$909$		0			0
$910$	−4.18042	−	2.21788i	−0.138580	−	0.0735219i
$911$		−	7.46474i		−	0.247318i	−0.992325	−	0.123659i	$-0.960537\pi$
$911$		−	7.46474i		−	0.247318i	0.992325	−	0.123659i	$-0.0394629\pi$
$912$		0			0
$913$			8.27583i			0.273890i
$914$	9.17031			0.303327
$915$		0			0
$916$	−0.973208			−0.0321557
$917$	−3.93025			−0.129788
$918$		0			0
$919$			27.8014i			0.917083i	0.888673	+	0.458541i	$0.151628\pi$
$919$			27.8014i			0.917083i	−0.888673	+	0.458541i	$0.848372\pi$
$920$	7.97195	−	15.0261i	0.262827	−	0.495397i
$921$		0			0
$922$			10.3300i			0.340199i
$923$	−42.6063			−1.40240
$924$		0			0
$925$	−30.0922	−	4.41139i	−0.989425	−	0.145046i
$926$	−25.8049			−0.848003
$927$		0			0
$928$		−	9.57629i		−	0.314357i
$929$	−19.4503			−0.638145			−0.319072	−	0.947730i	$-0.603371\pi$
$929$	−19.4503			−0.638145			−0.319072	+	0.947730i	$0.603371\pi$
$930$		0			0
$931$		−	39.4289i		−	1.29223i
$932$		−	14.4150i		−	0.472178i
$933$		0			0
$934$	34.4582			1.12751
$935$	4.06070	−	7.65392i	0.132799	−	0.250310i
$936$		0			0
$937$		−	14.2786i		−	0.466463i	−0.972421	−	0.233231i	$-0.925070\pi$
$937$		−	14.2786i		−	0.466463i	0.972421	−	0.233231i	$-0.0749299\pi$
$938$	7.16727			0.234020
$939$		0			0
$940$	−25.9132	−	13.7480i	−0.845196	−	0.448409i
$941$	18.0266			0.587649			0.293825	−	0.955859i	$-0.405072\pi$
$941$	18.0266			0.587649			0.293825	+	0.955859i	$0.405072\pi$
$942$		0			0
$943$	−64.3184			−2.09450
$944$		−	4.36469i		−	0.142058i
$945$		0			0
$946$	−6.07273			−0.197441
$947$	20.7621			0.674679			0.337339	−	0.941383i	$-0.390473\pi$
$947$	20.7621			0.674679			0.337339	+	0.941383i	$0.390473\pi$
$948$		0			0
$949$		−	14.9354i		−	0.484825i
$950$	−24.7298	+	16.7462i	−0.802340	+	0.543319i
$951$		0			0
$952$		−	1.96166i		−	0.0635776i
$953$			40.9858i			1.32766i	0.747883	+	0.663831i	$0.231071\pi$
$953$			40.9858i			1.32766i	−0.747883	+	0.663831i	$0.768929\pi$
$954$		0			0
$955$	−15.3341	−	8.13533i	−0.496199	−	0.263253i
$956$			8.43344i			0.272757i
$957$		0			0
$958$			29.6039i			0.956458i
$959$	−8.92401			−0.288171
$960$		0			0
$961$	−21.8103			−0.703560
$962$	−13.7521	+	15.0370i	−0.443385	+	0.484811i
$963$		0			0
$964$		−	18.6567i		−	0.600891i
$965$	3.65939	−	6.89749i	0.117800	−	0.222038i
$966$		0			0
$967$	25.1227			0.807892			0.403946	−	0.914783i	$-0.367638\pi$
$967$	25.1227			0.807892			0.403946	+	0.914783i	$0.367638\pi$
$968$	−9.44277			−0.303502
$969$		0			0
$970$	11.5887	−	21.8433i	0.372091	−	0.701345i
$971$	10.0012			0.320953			0.160476	−	0.987040i	$-0.448697\pi$
$971$	10.0012			0.320953			0.160476	+	0.987040i	$0.448697\pi$
$972$		0			0
$973$		−	5.32992i		−	0.170869i
$974$	−27.0961			−0.868214
$975$		0			0
$976$			2.14666i			0.0687130i
$977$	49.4636			1.58248			0.791240	−	0.611505i	$-0.209436\pi$
$977$	49.4636			1.58248			0.791240	+	0.611505i	$0.209436\pi$
$978$		0			0
$979$			17.1940i			0.549521i
$980$	−6.91752	+	13.0387i	−0.220972	+	0.416505i
$981$		0			0
$982$	−2.46033			−0.0785123
$983$			36.4329i			1.16203i	0.813894	+	0.581014i	$0.197344\pi$
$983$			36.4329i			1.16203i	−0.813894	+	0.581014i	$0.802656\pi$
$984$		0			0
$985$	−2.12574	−	1.12779i	−0.0677316	−	0.0359343i
$986$		−	29.7354i		−	0.946969i
$987$		0			0
$988$			20.0104i			0.636615i
$989$	−37.0190			−1.17713
$990$		0			0
$991$			49.5991i			1.57557i	0.615953	+	0.787783i	$0.288771\pi$
$991$			49.5991i			1.57557i	−0.615953	+	0.787783i	$0.711229\pi$
$992$		−	7.26707i		−	0.230730i
$993$		0			0
$994$		−	8.03482i		−	0.254849i
$995$	−11.2857	−	5.98749i	−0.357780	−	0.189816i
$996$		0			0
$997$	3.21866			0.101936			0.0509680	−	0.998700i	$-0.483769\pi$
$997$	3.21866			0.101936			0.0509680	+	0.998700i	$0.483769\pi$
$998$			31.4091i			0.994238i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.e.d.739.4		10
3.2	odd	2		370.2.c.a.369.5	✓	10
5.4	even	2		3330.2.e.c.739.8		10
15.2	even	4		1850.2.d.i.1701.5		20
15.8	even	4		1850.2.d.i.1701.16		20
15.14	odd	2		370.2.c.b.369.6	yes	10
37.36	even	2		3330.2.e.c.739.7		10
111.110	odd	2		370.2.c.b.369.5	yes	10
185.184	even	2	inner	3330.2.e.d.739.3		10
555.332	even	4		1850.2.d.i.1701.15		20
555.443	even	4		1850.2.d.i.1701.6		20
555.554	odd	2		370.2.c.a.369.6	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.5	✓	10	3.2	odd	2
370.2.c.a.369.6	yes	10	555.554	odd	2
370.2.c.b.369.5	yes	10	111.110	odd	2
370.2.c.b.369.6	yes	10	15.14	odd	2
1850.2.d.i.1701.5		20	15.2	even	4
1850.2.d.i.1701.6		20	555.443	even	4
1850.2.d.i.1701.15		20	555.332	even	4
1850.2.d.i.1701.16		20	15.8	even	4
3330.2.e.c.739.7		10	37.36	even	2
3330.2.e.c.739.8		10	5.4	even	2
3330.2.e.d.739.3		10	185.184	even	2	inner
3330.2.e.d.739.4		10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.04797 + 1.97529i) q^{5} -0.631751i q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.04797 + 1.97529i) q^{5} -0.631751i q^{7} +1.00000 q^{8} +(-1.04797 + 1.97529i) q^{10} -1.24789 q^{11} -3.34999 q^{13} -0.631751i q^{14} +1.00000 q^{16} +3.10511 q^{17} -5.97327i q^{19} +(-1.04797 + 1.97529i) q^{20} -1.24789 q^{22} -7.60706 q^{23} +(-2.80353 - 4.14008i) q^{25} -3.34999 q^{26} -0.631751i q^{28} -9.57629i q^{29} -7.26707i q^{31} +1.00000 q^{32} +3.10511 q^{34} +(1.24789 + 0.662054i) q^{35} +(4.10511 - 4.48866i) q^{37} -5.97327i q^{38} +(-1.04797 + 1.97529i) q^{40} +8.45510 q^{41} +4.86640 q^{43} -1.24789 q^{44} -7.60706 q^{46} +13.1187i q^{47} +6.60089 q^{49} +(-2.80353 - 4.14008i) q^{50} -3.34999 q^{52} -7.17340i q^{53} +(1.30775 - 2.46494i) q^{55} -0.631751i q^{56} -9.57629i q^{58} -4.36469i q^{59} +2.14666i q^{61} -7.26707i q^{62} +1.00000 q^{64} +(3.51068 - 6.61720i) q^{65} +11.3451i q^{67} +3.10511 q^{68} +(1.24789 + 0.662054i) q^{70} +12.7183 q^{71} +4.45836i q^{73} +(4.10511 - 4.48866i) q^{74} -5.97327i q^{76} +0.788355i q^{77} +8.78679i q^{79} +(-1.04797 + 1.97529i) q^{80} +8.45510 q^{82} -6.63185i q^{83} +(-3.25406 + 6.13349i) q^{85} +4.86640 q^{86} -1.24789 q^{88} -13.7784i q^{89} +2.11636i q^{91} -7.60706 q^{92} +13.1187i q^{94} +(11.7989 + 6.25979i) q^{95} -11.0583 q^{97} +6.60089 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8}+O(q^{10}) \) 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8	\( 10 q + 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{8} + 3 q^{10} - 2 q^{13} + 10 q^{16} - 18 q^{17} + 3 q^{20} - 10 q^{23} + 5 q^{25} - 2 q^{26} + 10 q^{32} - 18 q^{34} - 8 q^{37} + 3 q^{40} + 4 q^{41} - 10 q^{43} - 10 q^{46} - 8 q^{49} + 5 q^{50} - 2 q^{52} + 5 q^{55} + 10 q^{64} - 2 q^{65} - 18 q^{68} + 20 q^{71} - 8 q^{74} + 3 q^{80} + 4 q^{82} - 28 q^{85} - 10 q^{86} - 10 q^{92} - 2 q^{95} + 2 q^{97} - 8 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 10 * q^4 + 3 * q^5 + 10 * q^8 + 3 * q^10 - 2 * q^13 + 10 * q^16 - 18 * q^17 + 3 * q^20 - 10 * q^23 + 5 * q^25 - 2 * q^26 + 10 * q^32 - 18 * q^34 - 8 * q^37 + 3 * q^40 + 4 * q^41 - 10 * q^43 - 10 * q^46 - 8 * q^49 + 5 * q^50 - 2 * q^52 + 5 * q^55 + 10 * q^64 - 2 * q^65 - 18 * q^68 + 20 * q^71 - 8 * q^74 + 3 * q^80 + 4 * q^82 - 28 * q^85 - 10 * q^86 - 10 * q^92 - 2 * q^95 + 2 * q^97 - 8 * q^98

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