LMFDB - Embedded newform 5577.2.a.ba.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.a (trivial)

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:	yes
Analytic conductor:	$44.5325692073$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 14 x^{10} + 13 x^{9} + 70 x^{8} - 61 x^{7} - 152 x^{6} + 127 x^{5} + 138 x^{4} + \cdots + 1 $ x^12 - x^11 - 14x^10 + 13x^9 + 70x^8 - 61x^7 - 152x^6 + 127x^5 + 138x^4 - 110x^3 - 40x^2 + 29x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.0331136$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0331136 q^{2} -1.00000 q^{3} -1.99890 q^{4} -0.127095 q^{5} -0.0331136 q^{6} -4.18754 q^{7} -0.132418 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.0331136 q^{2} -1.00000 q^{3} -1.99890 q^{4} -0.127095 q^{5} -0.0331136 q^{6} -4.18754 q^{7} -0.132418 q^{8} +1.00000 q^{9} -0.00420859 q^{10} -1.00000 q^{11} +1.99890 q^{12} -0.138664 q^{14} +0.127095 q^{15} +3.99342 q^{16} -1.22067 q^{17} +0.0331136 q^{18} +2.39853 q^{19} +0.254051 q^{20} +4.18754 q^{21} -0.0331136 q^{22} -0.152956 q^{23} +0.132418 q^{24} -4.98385 q^{25} -1.00000 q^{27} +8.37048 q^{28} +1.80039 q^{29} +0.00420859 q^{30} +0.947022 q^{31} +0.397073 q^{32} +1.00000 q^{33} -0.0404209 q^{34} +0.532217 q^{35} -1.99890 q^{36} +3.77798 q^{37} +0.0794238 q^{38} +0.0168297 q^{40} +8.57137 q^{41} +0.138664 q^{42} -5.37278 q^{43} +1.99890 q^{44} -0.127095 q^{45} -0.00506493 q^{46} +12.0422 q^{47} -3.99342 q^{48} +10.5355 q^{49} -0.165033 q^{50} +1.22067 q^{51} -0.150945 q^{53} -0.0331136 q^{54} +0.127095 q^{55} +0.554506 q^{56} -2.39853 q^{57} +0.0596174 q^{58} -6.60091 q^{59} -0.254051 q^{60} +10.0178 q^{61} +0.0313593 q^{62} -4.18754 q^{63} -7.97370 q^{64} +0.0331136 q^{66} +8.58013 q^{67} +2.44001 q^{68} +0.152956 q^{69} +0.0176236 q^{70} -13.6838 q^{71} -0.132418 q^{72} -1.11191 q^{73} +0.125102 q^{74} +4.98385 q^{75} -4.79442 q^{76} +4.18754 q^{77} -0.0174625 q^{79} -0.507546 q^{80} +1.00000 q^{81} +0.283829 q^{82} +3.69734 q^{83} -8.37048 q^{84} +0.155142 q^{85} -0.177912 q^{86} -1.80039 q^{87} +0.132418 q^{88} -8.07805 q^{89} -0.00420859 q^{90} +0.305744 q^{92} -0.947022 q^{93} +0.398760 q^{94} -0.304842 q^{95} -0.397073 q^{96} +7.47196 q^{97} +0.348867 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9	$ 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9} - 11 q^{10} - 12 q^{11} - 5 q^{12} + 9 q^{14} - 6 q^{15} - 9 q^{16} + 3 q^{17} - q^{18} - 6 q^{19} + 20 q^{20} - q^{21} + q^{22} - 22 q^{23} - 2 q^{25} - 12 q^{27} + 11 q^{28} + 13 q^{29} + 11 q^{30} - 2 q^{31} - 11 q^{32} + 12 q^{33} - 10 q^{34} - 14 q^{35} + 5 q^{36} - 3 q^{37} - 18 q^{38} - 18 q^{40} - 4 q^{41} - 9 q^{42} - 26 q^{43} - 5 q^{44} + 6 q^{45} + 18 q^{46} + 9 q^{47} + 9 q^{48} - 3 q^{49} - 29 q^{50} - 3 q^{51} - 5 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 6 q^{57} - 37 q^{58} + 22 q^{59} - 20 q^{60} - 11 q^{61} - 18 q^{62} + q^{63} - 10 q^{64} - q^{66} + 28 q^{67} + 12 q^{68} + 22 q^{69} + 29 q^{70} - 10 q^{71} + 7 q^{73} - 6 q^{74} + 2 q^{75} - 32 q^{76} - q^{77} - 40 q^{79} - 30 q^{80} + 12 q^{81} + 26 q^{82} - q^{83} - 11 q^{84} + 32 q^{85} + 9 q^{86} - 13 q^{87} - 11 q^{89} - 11 q^{90} - 38 q^{92} + 2 q^{93} - 25 q^{94} - 10 q^{95} + 11 q^{96} - 7 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9 - 11 * q^10 - 12 * q^11 - 5 * q^12 + 9 * q^14 - 6 * q^15 - 9 * q^16 + 3 * q^17 - q^18 - 6 * q^19 + 20 * q^20 - q^21 + q^22 - 22 * q^23 - 2 * q^25 - 12 * q^27 + 11 * q^28 + 13 * q^29 + 11 * q^30 - 2 * q^31 - 11 * q^32 + 12 * q^33 - 10 * q^34 - 14 * q^35 + 5 * q^36 - 3 * q^37 - 18 * q^38 - 18 * q^40 - 4 * q^41 - 9 * q^42 - 26 * q^43 - 5 * q^44 + 6 * q^45 + 18 * q^46 + 9 * q^47 + 9 * q^48 - 3 * q^49 - 29 * q^50 - 3 * q^51 - 5 * q^53 + q^54 - 6 * q^55 + 5 * q^56 + 6 * q^57 - 37 * q^58 + 22 * q^59 - 20 * q^60 - 11 * q^61 - 18 * q^62 + q^63 - 10 * q^64 - q^66 + 28 * q^67 + 12 * q^68 + 22 * q^69 + 29 * q^70 - 10 * q^71 + 7 * q^73 - 6 * q^74 + 2 * q^75 - 32 * q^76 - q^77 - 40 * q^79 - 30 * q^80 + 12 * q^81 + 26 * q^82 - q^83 - 11 * q^84 + 32 * q^85 + 9 * q^86 - 13 * q^87 - 11 * q^89 - 11 * q^90 - 38 * q^92 + 2 * q^93 - 25 * q^94 - 10 * q^95 + 11 * q^96 - 7 * q^97 - 28 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.0331136	0.0234148	0.0117074	−	0.999931i	$-0.496273\pi$
$2$	0.0331136	0.0234148	0.0117074	+	0.999931i	$0.496273\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99890	−0.999452
$5$	−0.127095	−0.0568388	−0.0284194	−	0.999596i	$-0.509047\pi$
$5$	−0.127095	−0.0568388	−0.0284194	+	0.999596i	$0.509047\pi$
$6$	−0.0331136	−0.0135186
$7$	−4.18754	−1.58274	−0.791370	−	0.611337i	$-0.790632\pi$
$7$	−4.18754	−1.58274	−0.791370	+	0.611337i	$0.790632\pi$
$8$	−0.132418	−0.0468169
$9$	1.00000	0.333333
$10$	−0.00420859	−0.00133087
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.99890	0.577034
$13$	0	0
$13$	0	0
$14$	−0.138664	−0.0370596
$15$	0.127095	0.0328159
$16$	3.99342	0.998356
$17$	−1.22067	−0.296057	−0.148028	−	0.988983i	$-0.547293\pi$
$17$	−1.22067	−0.296057	−0.148028	+	0.988983i	$0.547293\pi$
$18$	0.0331136	0.00780495
$19$	2.39853	0.550260	0.275130	−	0.961407i	$-0.411279\pi$
$19$	2.39853	0.550260	0.275130	+	0.961407i	$0.411279\pi$
$20$	0.254051	0.0568076
$21$	4.18754	0.913796
$22$	−0.0331136	−0.00705984
$23$	−0.152956	−0.0318935	−0.0159468	−	0.999873i	$-0.505076\pi$
$23$	−0.152956	−0.0318935	−0.0159468	+	0.999873i	$0.505076\pi$
$24$	0.132418	0.0270297
$25$	−4.98385	−0.996769
$26$	0	0
$27$	−1.00000	−0.192450
$28$	8.37048	1.58187
$29$	1.80039	0.334324	0.167162	−	0.985929i	$-0.446540\pi$
$29$	1.80039	0.334324	0.167162	+	0.985929i	$0.446540\pi$
$30$	0.00420859	0.000768379 0
$31$	0.947022	0.170090	0.0850451	−	0.996377i	$-0.472897\pi$
$31$	0.947022	0.170090	0.0850451	+	0.996377i	$0.472897\pi$
$32$	0.397073	0.0701932
$33$	1.00000	0.174078
$34$	−0.0404209	−0.00693213
$35$	0.532217	0.0899611
$36$	−1.99890	−0.333151
$37$	3.77798	0.621095	0.310548	−	0.950558i	$-0.399488\pi$
$37$	3.77798	0.621095	0.310548	+	0.950558i	$0.399488\pi$
$38$	0.0794238	0.0128842
$39$	0	0
$40$	0.0168297	0.00266101
$41$	8.57137	1.33862	0.669311	−	0.742982i	$-0.266589\pi$
$41$	8.57137	1.33862	0.669311	+	0.742982i	$0.266589\pi$
$42$	0.138664	0.0213964
$43$	−5.37278	−0.819341	−0.409671	−	0.912233i	$-0.634356\pi$
$43$	−5.37278	−0.819341	−0.409671	+	0.912233i	$0.634356\pi$
$44$	1.99890	0.301346
$45$	−0.127095	−0.0189463
$46$	−0.00506493	−0.000746782 0
$47$	12.0422	1.75653	0.878267	−	0.478171i	$-0.158700\pi$
$47$	12.0422	1.75653	0.878267	+	0.478171i	$0.158700\pi$
$48$	−3.99342	−0.576401
$49$	10.5355	1.50507
$50$	−0.165033	−0.0233392
$51$	1.22067	0.170928
$52$	0	0
$53$	−0.150945	−0.0207338	−0.0103669	−	0.999946i	$-0.503300\pi$
$53$	−0.150945	−0.0207338	−0.0103669	+	0.999946i	$0.503300\pi$
$54$	−0.0331136	−0.00450619
$55$	0.127095	0.0171375
$56$	0.554506	0.0740989
$57$	−2.39853	−0.317692
$58$	0.0596174	0.00782815
$59$	−6.60091	−0.859365	−0.429683	−	0.902980i	$-0.641375\pi$
$59$	−6.60091	−0.859365	−0.429683	+	0.902980i	$0.641375\pi$
$60$	−0.254051	−0.0327979
$61$	10.0178	1.28265	0.641325	−	0.767269i	$-0.278385\pi$
$61$	10.0178	1.28265	0.641325	+	0.767269i	$0.278385\pi$
$62$	0.0313593	0.00398263
$63$	−4.18754	−0.527580
$64$	−7.97370	−0.996712
$65$	0	0
$66$	0.0331136	0.00407600
$67$	8.58013	1.04823	0.524115	−	0.851648i	$-0.324396\pi$
$67$	8.58013	1.04823	0.524115	+	0.851648i	$0.324396\pi$
$68$	2.44001	0.295895
$69$	0.152956	0.0184137
$70$	0.0176236	0.00210642
$71$	−13.6838	−1.62397	−0.811985	−	0.583678i	$-0.801613\pi$
$71$	−13.6838	−1.62397	−0.811985	+	0.583678i	$0.801613\pi$
$72$	−0.132418	−0.0156056
$73$	−1.11191	−0.130139	−0.0650695	−	0.997881i	$-0.520727\pi$
$73$	−1.11191	−0.130139	−0.0650695	+	0.997881i	$0.520727\pi$
$74$	0.125102	0.0145429
$75$	4.98385	0.575485
$76$	−4.79442	−0.549958
$77$	4.18754	0.477214
$78$	0	0
$79$	−0.0174625	−0.00196469	−0.000982345	−	1.00000i	$-0.500313\pi$
$79$	−0.0174625	−0.00196469	−0.000982345		1.00000i	$0.500313\pi$
$80$	−0.507546	−0.0567453
$81$	1.00000	0.111111
$82$	0.283829	0.0313436
$83$	3.69734	0.405836	0.202918	−	0.979196i	$-0.434958\pi$
$83$	3.69734	0.405836	0.202918	+	0.979196i	$0.434958\pi$
$84$	−8.37048	−0.913295
$85$	0.155142	0.0168275
$86$	−0.177912	−0.0191848
$87$	−1.80039	−0.193022
$88$	0.132418	0.0141158
$89$	−8.07805	−0.856272	−0.428136	−	0.903714i	$-0.640830\pi$
$89$	−8.07805	−0.856272	−0.428136	+	0.903714i	$0.640830\pi$
$90$	−0.00420859	−0.000443624 0
$91$	0	0
$92$	0.305744	0.0318761
$93$	−0.947022	−0.0982016
$94$	0.398760	0.0411290
$95$	−0.304842	−0.0312761
$96$	−0.397073	−0.0405261
$97$	7.47196	0.758663	0.379331	−	0.925261i	$-0.376154\pi$
$97$	7.47196	0.758663	0.379331	+	0.925261i	$0.376154\pi$
$98$	0.348867	0.0352409
$99$	−1.00000	−0.100504
$100$	9.96223	0.996223
$101$	11.1449	1.10896	0.554479	−	0.832198i	$-0.312918\pi$
$101$	11.1449	1.10896	0.554479	+	0.832198i	$0.312918\pi$
$102$	0.0404209	0.00400226
$103$	−8.11515	−0.799610	−0.399805	−	0.916600i	$-0.630922\pi$
$103$	−8.11515	−0.799610	−0.399805	+	0.916600i	$0.630922\pi$
$104$	0	0
$105$	−0.532217	−0.0519390
$106$	−0.00499832	−0.000485479 0
$107$	−2.82228	−0.272840	−0.136420	−	0.990651i	$-0.543560\pi$
$107$	−2.82228	−0.272840	−0.136420	+	0.990651i	$0.543560\pi$
$108$	1.99890	0.192345
$109$	16.7063	1.60017	0.800086	−	0.599885i	$-0.204787\pi$
$109$	16.7063	1.60017	0.800086	+	0.599885i	$0.204787\pi$
$110$	0.00420859	0.000401273 0
$111$	−3.77798	−0.358590
$112$	−16.7226	−1.58014
$113$	2.62553	0.246989	0.123494	−	0.992345i	$-0.460590\pi$
$113$	2.62553	0.246989	0.123494	+	0.992345i	$0.460590\pi$
$114$	−0.0794238	−0.00743872
$115$	0.0194400	0.00181279
$116$	−3.59881	−0.334141
$117$	0	0
$118$	−0.218580	−0.0201219
$119$	5.11162	0.468581
$120$	−0.0168297	−0.00153634
$121$	1.00000	0.0909091
$122$	0.331726	0.0300331
$123$	−8.57137	−0.772854
$124$	−1.89300	−0.169997
$125$	1.26890	0.113494
$126$	−0.138664	−0.0123532
$127$	10.0605	0.892725	0.446363	−	0.894852i	$-0.352719\pi$
$127$	10.0605	0.892725	0.446363	+	0.894852i	$0.352719\pi$
$128$	−1.05818	−0.0935311
$129$	5.37278	0.473047
$130$	0	0
$131$	−11.5683	−1.01073	−0.505364	−	0.862906i	$-0.668642\pi$
$131$	−11.5683	−1.01073	−0.505364	+	0.862906i	$0.668642\pi$
$132$	−1.99890	−0.173982
$133$	−10.0439	−0.870918
$134$	0.284119	0.0245441
$135$	0.127095	0.0109386
$136$	0.161639	0.0138605
$137$	12.9712	1.10821	0.554104	−	0.832448i	$-0.313061\pi$
$137$	12.9712	1.10821	0.554104	+	0.832448i	$0.313061\pi$
$138$	0.00506493	0.000431155 0
$139$	−6.33975	−0.537731	−0.268865	−	0.963178i	$-0.586649\pi$
$139$	−6.33975	−0.537731	−0.268865	+	0.963178i	$0.586649\pi$
$140$	−1.06385	−0.0899117
$141$	−12.0422	−1.01414
$142$	−0.453120	−0.0380250
$143$	0	0
$144$	3.99342	0.332785
$145$	−0.228821	−0.0190026
$146$	−0.0368193	−0.00304719
$147$	−10.5355	−0.868951
$148$	−7.55181	−0.620755
$149$	−2.87224	−0.235303	−0.117651	−	0.993055i	$-0.537537\pi$
$149$	−2.87224	−0.235303	−0.117651	+	0.993055i	$0.537537\pi$
$150$	0.165033	0.0134749
$151$	−4.06288	−0.330632	−0.165316	−	0.986241i	$-0.552864\pi$
$151$	−4.06288	−0.330632	−0.165316	+	0.986241i	$0.552864\pi$
$152$	−0.317608	−0.0257614
$153$	−1.22067	−0.0986856
$154$	0.138664	0.0111739
$155$	−0.120362	−0.00966772
$156$	0	0
$157$	−17.3704	−1.38631	−0.693155	−	0.720789i	$-0.743780\pi$
$157$	−17.3704	−1.38631	−0.693155	+	0.720789i	$0.743780\pi$
$158$	−0.000578248 0	−4.60029e−5 0
$159$	0.150945	0.0119707
$160$	−0.0504661	−0.00398970
$161$	0.640509	0.0504792
$162$	0.0331136	0.00260165
$163$	−2.02485	−0.158598	−0.0792991	−	0.996851i	$-0.525268\pi$
$163$	−2.02485	−0.158598	−0.0792991	+	0.996851i	$0.525268\pi$
$164$	−17.1333	−1.33789
$165$	−0.127095	−0.00989436
$166$	0.122432	0.00950259
$167$	−22.4232	−1.73516	−0.867581	−	0.497296i	$-0.834326\pi$
$167$	−22.4232	−1.73516	−0.867581	+	0.497296i	$0.834326\pi$
$168$	−0.554506	−0.0427810
$169$	0	0
$170$	0.00513731	0.000394014 0
$171$	2.39853	0.183420
$172$	10.7397	0.818892
$173$	−20.0904	−1.52745	−0.763724	−	0.645543i	$-0.776631\pi$
$173$	−20.0904	−1.52745	−0.763724	+	0.645543i	$0.776631\pi$
$174$	−0.0596174	−0.00451959
$175$	20.8700	1.57763
$176$	−3.99342	−0.301016
$177$	6.60091	0.496155
$178$	−0.267493	−0.0200495
$179$	20.3510	1.52110	0.760552	−	0.649277i	$-0.224928\pi$
$179$	20.3510	1.52110	0.760552	+	0.649277i	$0.224928\pi$
$180$	0.254051	0.0189359
$181$	−18.2363	−1.35550	−0.677749	−	0.735294i	$-0.737044\pi$
$181$	−18.2363	−1.35550	−0.677749	+	0.735294i	$0.737044\pi$
$182$	0	0
$183$	−10.0178	−0.740538
$184$	0.0202541	0.00149316
$185$	−0.480163	−0.0353023
$186$	−0.0313593	−0.00229937
$187$	1.22067	0.0892645
$188$	−24.0712	−1.75557
$189$	4.18754	0.304599
$190$	−0.0100944	−0.000732325 0
$191$	−26.5067	−1.91796	−0.958978	−	0.283479i	$-0.908511\pi$
$191$	−26.5067	−1.91796	−0.958978	+	0.283479i	$0.908511\pi$
$192$	7.97370	0.575452
$193$	19.7859	1.42422	0.712109	−	0.702069i	$-0.247740\pi$
$193$	19.7859	1.42422	0.712109	+	0.702069i	$0.247740\pi$
$194$	0.247424	0.0177640
$195$	0	0
$196$	−21.0594	−1.50424
$197$	−25.9338	−1.84771	−0.923855	−	0.382743i	$-0.874979\pi$
$197$	−25.9338	−1.84771	−0.923855	+	0.382743i	$0.874979\pi$
$198$	−0.0331136	−0.00235328
$199$	14.9274	1.05818	0.529089	−	0.848566i	$-0.322534\pi$
$199$	14.9274	1.05818	0.529089	+	0.848566i	$0.322534\pi$
$200$	0.659951	0.0466656
$201$	−8.58013	−0.605195
$202$	0.369047	0.0259661
$203$	−7.53921	−0.529149
$204$	−2.44001	−0.170835
$205$	−1.08938	−0.0760857
$206$	−0.268722	−0.0187227
$207$	−0.152956	−0.0106312
$208$	0	0
$209$	−2.39853	−0.165909
$210$	−0.0176236	−0.00121614
$211$	−5.89562	−0.405871	−0.202936	−	0.979192i	$-0.565048\pi$
$211$	−5.89562	−0.405871	−0.202936	+	0.979192i	$0.565048\pi$
$212$	0.301724	0.0207225
$213$	13.6838	0.937600
$214$	−0.0934560	−0.00638852
$215$	0.682856	0.0465704
$216$	0.132418	0.00900991
$217$	−3.96569	−0.269209
$218$	0.553205	0.0374678
$219$	1.11191	0.0751358
$220$	−0.254051	−0.0171281
$221$	0	0
$222$	−0.125102	−0.00839632
$223$	9.65551	0.646581	0.323290	−	0.946300i	$-0.395211\pi$
$223$	9.65551	0.646581	0.323290	+	0.946300i	$0.395211\pi$
$224$	−1.66276	−0.111098
$225$	−4.98385	−0.332256
$226$	0.0869406	0.00578321
$227$	−6.44679	−0.427889	−0.213944	−	0.976846i	$-0.568631\pi$
$227$	−6.44679	−0.427889	−0.213944	+	0.976846i	$0.568631\pi$
$228$	4.79442	0.317518
$229$	−9.53606	−0.630161	−0.315080	−	0.949065i	$-0.602031\pi$
$229$	−9.53606	−0.630161	−0.315080	+	0.949065i	$0.602031\pi$
$230$	0.000643729 0	4.24462e−5 0
$231$	−4.18754	−0.275520
$232$	−0.238404	−0.0156520
$233$	−27.0134	−1.76971	−0.884855	−	0.465867i	$-0.845743\pi$
$233$	−27.0134	−1.76971	−0.884855	+	0.465867i	$0.845743\pi$
$234$	0	0
$235$	−1.53051	−0.0998392
$236$	13.1946	0.858894
$237$	0.0174625	0.00113431
$238$	0.169264	0.0109718
$239$	25.5242	1.65103	0.825513	−	0.564383i	$-0.190886\pi$
$239$	25.5242	1.65103	0.825513	+	0.564383i	$0.190886\pi$
$240$	0.507546	0.0327619
$241$	−10.8030	−0.695884	−0.347942	−	0.937516i	$-0.613119\pi$
$241$	−10.8030	−0.695884	−0.347942	+	0.937516i	$0.613119\pi$
$242$	0.0331136	0.00212862
$243$	−1.00000	−0.0641500
$244$	−20.0247	−1.28195
$245$	−1.33901	−0.0855462
$246$	−0.283829	−0.0180963
$247$	0	0
$248$	−0.125403	−0.00796308
$249$	−3.69734	−0.234310
$250$	0.0420179	0.00265744
$251$	−3.43833	−0.217025	−0.108513	−	0.994095i	$-0.534609\pi$
$251$	−3.43833	−0.217025	−0.108513	+	0.994095i	$0.534609\pi$
$252$	8.37048	0.527291
$253$	0.152956	0.00961626
$254$	0.333139	0.0209030
$255$	−0.155142	−0.00971537
$256$	15.9124	0.994522
$257$	−22.7966	−1.42201	−0.711007	−	0.703185i	$-0.751761\pi$
$257$	−22.7966	−1.42201	−0.711007	+	0.703185i	$0.751761\pi$
$258$	0.177912	0.0110763
$259$	−15.8204	−0.983033
$260$	0	0
$261$	1.80039	0.111441
$262$	−0.383068	−0.0236660
$263$	−6.13478	−0.378286	−0.189143	−	0.981950i	$-0.560571\pi$
$263$	−6.13478	−0.378286	−0.189143	+	0.981950i	$0.560571\pi$
$264$	−0.132418	−0.00814977
$265$	0.0191844	0.00117849
$266$	−0.332590	−0.0203924
$267$	8.07805	0.494369
$268$	−17.1508	−1.04765
$269$	17.5115	1.06769	0.533847	−	0.845581i	$-0.320746\pi$
$269$	17.5115	1.06769	0.533847	+	0.845581i	$0.320746\pi$
$270$	0.00420859	0.000256126 0
$271$	−19.4939	−1.18417	−0.592086	−	0.805875i	$-0.701695\pi$
$271$	−19.4939	−1.18417	−0.592086	+	0.805875i	$0.701695\pi$
$272$	−4.87467	−0.295570
$273$	0	0
$274$	0.429524	0.0259485
$275$	4.98385	0.300537
$276$	−0.305744	−0.0184036
$277$	1.06561	0.0640266	0.0320133	−	0.999487i	$-0.489808\pi$
$277$	1.06561	0.0640266	0.0320133	+	0.999487i	$0.489808\pi$
$278$	−0.209932	−0.0125909
$279$	0.947022	0.0566967
$280$	−0.0704751	−0.00421169
$281$	10.7973	0.644115	0.322058	−	0.946720i	$-0.395625\pi$
$281$	10.7973	0.644115	0.322058	+	0.946720i	$0.395625\pi$
$282$	−0.398760	−0.0237458
$283$	−5.42195	−0.322302	−0.161151	−	0.986930i	$-0.551521\pi$
$283$	−5.42195	−0.322302	−0.161151	+	0.986930i	$0.551521\pi$
$284$	27.3526	1.62308
$285$	0.304842	0.0180573
$286$	0	0
$287$	−35.8929	−2.11869
$288$	0.397073	0.0233977
$289$	−15.5100	−0.912350
$290$	−0.00757710	−0.000444943 0
$291$	−7.47196	−0.438014
$292$	2.22260	0.130068
$293$	17.4565	1.01982	0.509910	−	0.860228i	$-0.329679\pi$
$293$	17.4565	1.01982	0.509910	+	0.860228i	$0.329679\pi$
$294$	−0.348867	−0.0203464
$295$	0.838945	0.0488453
$296$	−0.500272	−0.0290777
$297$	1.00000	0.0580259
$298$	−0.0951101	−0.00550958
$299$	0	0
$300$	−9.96223	−0.575170
$301$	22.4987	1.29680
$302$	−0.134536	−0.00774170
$303$	−11.1449	−0.640257
$304$	9.57833	0.549355
$305$	−1.27322	−0.0729043
$306$	−0.0404209	−0.00231071
$307$	−7.78956	−0.444574	−0.222287	−	0.974981i	$-0.571352\pi$
$307$	−7.78956	−0.444574	−0.222287	+	0.974981i	$0.571352\pi$
$308$	−8.37048	−0.476953
$309$	8.11515	0.461655
$310$	−0.00398562	−0.000226368 0
$311$	22.5426	1.27827	0.639136	−	0.769094i	$-0.279292\pi$
$311$	22.5426	1.27827	0.639136	+	0.769094i	$0.279292\pi$
$312$	0	0
$313$	10.4445	0.590356	0.295178	−	0.955442i	$-0.404621\pi$
$313$	10.4445	0.590356	0.295178	+	0.955442i	$0.404621\pi$
$314$	−0.575197	−0.0324602
$315$	0.532217	0.0299870
$316$	0.0349059	0.00196361
$317$	−6.43727	−0.361553	−0.180776	−	0.983524i	$-0.557861\pi$
$317$	−6.43727	−0.361553	−0.180776	+	0.983524i	$0.557861\pi$
$318$	0.00499832	0.000280292 0
$319$	−1.80039	−0.100803
$320$	1.01342	0.0566519
$321$	2.82228	0.157524
$322$	0.0212096	0.00118196
$323$	−2.92782	−0.162908
$324$	−1.99890	−0.111050
$325$	0	0
$326$	−0.0670499	−0.00371355
$327$	−16.7063	−0.923860
$328$	−1.13500	−0.0626701
$329$	−50.4271	−2.78014
$330$	−0.00420859	−0.000231675 0
$331$	−21.8573	−1.20139	−0.600693	−	0.799480i	$-0.705109\pi$
$331$	−21.8573	−1.20139	−0.600693	+	0.799480i	$0.705109\pi$
$332$	−7.39063	−0.405614
$333$	3.77798	0.207032
$334$	−0.742514	−0.0406286
$335$	−1.09049	−0.0595801
$336$	16.7226	0.912293
$337$	−1.04293	−0.0568118	−0.0284059	−	0.999596i	$-0.509043\pi$
$337$	−1.04293	−0.0568118	−0.0284059	+	0.999596i	$0.509043\pi$
$338$	0	0
$339$	−2.62553	−0.142599
$340$	−0.310114	−0.0168183
$341$	−0.947022	−0.0512841
$342$	0.0794238	0.00429475
$343$	−14.8049	−0.799391
$344$	0.711453	0.0383590
$345$	−0.0194400	−0.00104661
$346$	−0.665267	−0.0357650
$347$	19.2225	1.03192	0.515960	−	0.856613i	$-0.327435\pi$
$347$	19.2225	1.03192	0.515960	+	0.856613i	$0.327435\pi$
$348$	3.59881	0.192916
$349$	5.18731	0.277670	0.138835	−	0.990316i	$-0.455664\pi$
$349$	5.18731	0.277670	0.138835	+	0.990316i	$0.455664\pi$
$350$	0.691082	0.0369399
$351$	0	0
$352$	−0.397073	−0.0211640
$353$	17.3689	0.924452	0.462226	−	0.886762i	$-0.347051\pi$
$353$	17.3689	0.924452	0.462226	+	0.886762i	$0.347051\pi$
$354$	0.218580	0.0116174
$355$	1.73915	0.0923045
$356$	16.1473	0.855803
$357$	−5.11162	−0.270535
$358$	0.673895	0.0356164
$359$	−5.00146	−0.263967	−0.131984	−	0.991252i	$-0.542135\pi$
$359$	−5.00146	−0.263967	−0.131984	+	0.991252i	$0.542135\pi$
$360$	0.0168297	0.000887005 0
$361$	−13.2471	−0.697214
$362$	−0.603871	−0.0317388
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	0.141318	0.00739695
$366$	−0.331726	−0.0173396
$367$	−9.82535	−0.512879	−0.256440	−	0.966560i	$-0.582549\pi$
$367$	−9.82535	−0.512879	−0.256440	+	0.966560i	$0.582549\pi$
$368$	−0.610818	−0.0318411
$369$	8.57137	0.446208
$370$	−0.0158999	−0.000826598 0
$371$	0.632086	0.0328163
$372$	1.89300	0.0981477
$373$	−24.0530	−1.24541	−0.622707	−	0.782455i	$-0.713967\pi$
$373$	−24.0530	−1.24541	−0.622707	+	0.782455i	$0.713967\pi$
$374$	0.0404209	0.00209011
$375$	−1.26890	−0.0655258
$376$	−1.59460	−0.0822354
$377$	0	0
$378$	0.138664	0.00713213
$379$	32.8065	1.68516	0.842578	−	0.538574i	$-0.181037\pi$
$379$	32.8065	1.68516	0.842578	+	0.538574i	$0.181037\pi$
$380$	0.609349	0.0312589
$381$	−10.0605	−0.515415
$382$	−0.877732	−0.0449087
$383$	−1.09635	−0.0560211	−0.0280105	−	0.999608i	$-0.508917\pi$
$383$	−1.09635	−0.0560211	−0.0280105	+	0.999608i	$0.508917\pi$
$384$	1.05818	0.0540002
$385$	−0.532217	−0.0271243
$386$	0.655181	0.0333478
$387$	−5.37278	−0.273114
$388$	−14.9357	−0.758247
$389$	28.2431	1.43198	0.715991	−	0.698109i	$-0.245975\pi$
$389$	28.2431	1.43198	0.715991	+	0.698109i	$0.245975\pi$
$390$	0	0
$391$	0.186709	0.00944230
$392$	−1.39509	−0.0704625
$393$	11.5683	0.583544
$394$	−0.858763	−0.0432638
$395$	0.00221941	0.000111671 0
$396$	1.99890	0.100449
$397$	−20.2935	−1.01850	−0.509250	−	0.860618i	$-0.670077\pi$
$397$	−20.2935	−1.01850	−0.509250	+	0.860618i	$0.670077\pi$
$398$	0.494301	0.0247771
$399$	10.0439	0.502825
$400$	−19.9026	−0.995130
$401$	23.3589	1.16649	0.583244	−	0.812297i	$-0.301783\pi$
$401$	23.3589	1.16649	0.583244	+	0.812297i	$0.301783\pi$
$402$	−0.284119	−0.0141706
$403$	0	0
$404$	−22.2775	−1.10835
$405$	−0.127095	−0.00631542
$406$	−0.249650	−0.0123899
$407$	−3.77798	−0.187267
$408$	−0.161639	−0.00800234
$409$	−8.79642	−0.434955	−0.217477	−	0.976065i	$-0.569783\pi$
$409$	−8.79642	−0.434955	−0.217477	+	0.976065i	$0.569783\pi$
$410$	−0.0360733	−0.00178153
$411$	−12.9712	−0.639824
$412$	16.2214	0.799171
$413$	27.6416	1.36015
$414$	−0.00506493	−0.000248927 0
$415$	−0.469915	−0.0230672
$416$	0	0
$417$	6.33975	0.310459
$418$	−0.0794238	−0.00388475
$419$	−2.67285	−0.130577	−0.0652886	−	0.997866i	$-0.520797\pi$
$419$	−2.67285	−0.130577	−0.0652886	+	0.997866i	$0.520797\pi$
$420$	1.06385	0.0519106
$421$	1.84010	0.0896810	0.0448405	−	0.998994i	$-0.485722\pi$
$421$	1.84010	0.0896810	0.0448405	+	0.998994i	$0.485722\pi$
$422$	−0.195225	−0.00950341
$423$	12.0422	0.585511
$424$	0.0199878	0.000970693 0
$425$	6.08365	0.295100
$426$	0.453120	0.0219538
$427$	−41.9500	−2.03010
$428$	5.64147	0.272691
$429$	0	0
$430$	0.0226118	0.00109044
$431$	1.43082	0.0689203	0.0344602	−	0.999406i	$-0.489029\pi$
$431$	1.43082	0.0689203	0.0344602	+	0.999406i	$0.489029\pi$
$432$	−3.99342	−0.192134
$433$	−17.0462	−0.819190	−0.409595	−	0.912267i	$-0.634330\pi$
$433$	−17.0462	−0.819190	−0.409595	+	0.912267i	$0.634330\pi$
$434$	−0.131318	−0.00630348
$435$	0.228821	0.0109712
$436$	−33.3943	−1.59930
$437$	−0.366869	−0.0175497
$438$	0.0368193	0.00175929
$439$	−33.2743	−1.58809	−0.794047	−	0.607856i	$-0.792030\pi$
$439$	−33.2743	−1.58809	−0.794047	+	0.607856i	$0.792030\pi$
$440$	−0.0168297	−0.000802326 0
$441$	10.5355	0.501689
$442$	0	0
$443$	4.56112	0.216705	0.108353	−	0.994113i	$-0.465442\pi$
$443$	4.56112	0.216705	0.108353	+	0.994113i	$0.465442\pi$
$444$	7.55181	0.358393
$445$	1.02668	0.0486695
$446$	0.319729	0.0151396
$447$	2.87224	0.135852
$448$	33.3902	1.57754
$449$	9.08697	0.428841	0.214420	−	0.976741i	$-0.431214\pi$
$449$	9.08697	0.428841	0.214420	+	0.976741i	$0.431214\pi$
$450$	−0.165033	−0.00777973
$451$	−8.57137	−0.403610
$452$	−5.24818	−0.246853
$453$	4.06288	0.190891
$454$	−0.213476	−0.0100189
$455$	0	0
$456$	0.317608	0.0148734
$457$	18.9061	0.884388	0.442194	−	0.896919i	$-0.354200\pi$
$457$	18.9061	0.884388	0.442194	+	0.896919i	$0.354200\pi$
$458$	−0.315773	−0.0147551
$459$	1.22067	0.0569762
$460$	−0.0388587	−0.00181180
$461$	29.1063	1.35562	0.677808	−	0.735239i	$-0.262930\pi$
$461$	29.1063	1.35562	0.677808	+	0.735239i	$0.262930\pi$
$462$	−0.138664	−0.00645125
$463$	30.6124	1.42268	0.711340	−	0.702848i	$-0.248089\pi$
$463$	30.6124	1.42268	0.711340	+	0.702848i	$0.248089\pi$
$464$	7.18972	0.333775
$465$	0.120362	0.00558166
$466$	−0.894512	−0.0414375
$467$	−21.0631	−0.974684	−0.487342	−	0.873211i	$-0.662033\pi$
$467$	−21.0631	−0.974684	−0.487342	+	0.873211i	$0.662033\pi$
$468$	0	0
$469$	−35.9296	−1.65907
$470$	−0.0506806	−0.00233772
$471$	17.3704	0.800386
$472$	0.874080	0.0402328
$473$	5.37278	0.247041
$474$	0.000578248 0	2.65598e−5 0
$475$	−11.9539	−0.548482
$476$	−10.2176	−0.468324
$477$	−0.150945	−0.00691128
$478$	0.845200	0.0386585
$479$	10.3083	0.471000	0.235500	−	0.971874i	$-0.424327\pi$
$479$	10.3083	0.471000	0.235500	+	0.971874i	$0.424327\pi$
$480$	0.0504661	0.00230345
$481$	0	0
$482$	−0.357727	−0.0162940
$483$	−0.640509	−0.0291442
$484$	−1.99890	−0.0908592
$485$	−0.949652	−0.0431215
$486$	−0.0331136	−0.00150206
$487$	−18.4782	−0.837327	−0.418664	−	0.908141i	$-0.637501\pi$
$487$	−18.4782	−0.837327	−0.418664	+	0.908141i	$0.637501\pi$
$488$	−1.32654	−0.0600497
$489$	2.02485	0.0915667
$490$	−0.0443394	−0.00200305
$491$	−29.2252	−1.31891	−0.659457	−	0.751742i	$-0.729214\pi$
$491$	−29.2252	−1.31891	−0.659457	+	0.751742i	$0.729214\pi$
$492$	17.1333	0.772430
$493$	−2.19769	−0.0989790
$494$	0	0
$495$	0.127095	0.00571251
$496$	3.78186	0.169810
$497$	57.3015	2.57032
$498$	−0.122432	−0.00548632
$499$	37.4073	1.67458	0.837291	−	0.546758i	$-0.184138\pi$
$499$	37.4073	1.67458	0.837291	+	0.546758i	$0.184138\pi$
$500$	−2.53641	−0.113432
$501$	22.4232	1.00180
$502$	−0.113855	−0.00508162
$503$	−26.5335	−1.18307	−0.591535	−	0.806280i	$-0.701478\pi$
$503$	−26.5335	−1.18307	−0.591535	+	0.806280i	$0.701478\pi$
$504$	0.554506	0.0246996
$505$	−1.41646	−0.0630318
$506$	0.00506493	0.000225163 0
$507$	0	0
$508$	−20.1100	−0.892236
$509$	−4.95089	−0.219444	−0.109722	−	0.993962i	$-0.534996\pi$
$509$	−4.95089	−0.219444	−0.109722	+	0.993962i	$0.534996\pi$
$510$	−0.00513731	−0.000227484 0
$511$	4.65616	0.205976
$512$	2.64328	0.116818
$513$	−2.39853	−0.105897
$514$	−0.754878	−0.0332963
$515$	1.03140	0.0454489
$516$	−10.7397	−0.472788
$517$	−12.0422	−0.529615
$518$	−0.523871	−0.0230176
$519$	20.0904	0.881872
$520$	0	0
$521$	40.5197	1.77520	0.887601	−	0.460613i	$-0.152370\pi$
$521$	40.5197	1.77520	0.887601	+	0.460613i	$0.152370\pi$
$522$	0.0596174	0.00260938
$523$	−40.3978	−1.76647	−0.883237	−	0.468927i	$-0.844641\pi$
$523$	−40.3978	−1.76647	−0.883237	+	0.468927i	$0.844641\pi$
$524$	23.1239	1.01017
$525$	−20.8700	−0.910844
$526$	−0.203144	−0.00885752
$527$	−1.15600	−0.0503563
$528$	3.99342	0.173791
$529$	−22.9766	−0.998983
$530$	0.000635263 0	2.75941e−5 0
$531$	−6.60091	−0.286455
$532$	20.0768	0.870441
$533$	0	0
$534$	0.267493	0.0115756
$535$	0.358699	0.0155079
$536$	−1.13616	−0.0490748
$537$	−20.3510	−0.878210
$538$	0.579869	0.0249999
$539$	−10.5355	−0.453795
$540$	−0.254051	−0.0109326
$541$	14.3530	0.617082	0.308541	−	0.951211i	$-0.400159\pi$
$541$	14.3530	0.617082	0.308541	+	0.951211i	$0.400159\pi$
$542$	−0.645514	−0.0277272
$543$	18.2363	0.782597
$544$	−0.484696	−0.0207812
$545$	−2.12329	−0.0909519
$546$	0	0
$547$	−11.0000	−0.470325	−0.235162	−	0.971956i	$-0.575562\pi$
$547$	−11.0000	−0.470325	−0.235162	+	0.971956i	$0.575562\pi$
$548$	−25.9283	−1.10760
$549$	10.0178	0.427550
$550$	0.165033	0.00703703
$551$	4.31829	0.183965
$552$	−0.0202541	−0.000862074 0
$553$	0.0731251	0.00310959
$554$	0.0352863	0.00149917
$555$	0.480163	0.0203818
$556$	12.6726	0.537436
$557$	−32.8158	−1.39045	−0.695225	−	0.718793i	$-0.744695\pi$
$557$	−32.8158	−1.39045	−0.695225	+	0.718793i	$0.744695\pi$
$558$	0.0313593	0.00132754
$559$	0	0
$560$	2.12537	0.0898131
$561$	−1.22067	−0.0515369
$562$	0.357539	0.0150819
$563$	−43.5674	−1.83615	−0.918074	−	0.396409i	$-0.870256\pi$
$563$	−43.5674	−1.83615	−0.918074	+	0.396409i	$0.870256\pi$
$564$	24.0712	1.01358
$565$	−0.333692	−0.0140385
$566$	−0.179540	−0.00754664
$567$	−4.18754	−0.175860
$568$	1.81198	0.0760292
$569$	32.7311	1.37216	0.686080	−	0.727526i	$-0.259330\pi$
$569$	32.7311	1.37216	0.686080	+	0.727526i	$0.259330\pi$
$570$	0.0100944	0.000422808 0
$571$	−31.1412	−1.30322	−0.651610	−	0.758554i	$-0.725906\pi$
$571$	−31.1412	−1.30322	−0.651610	+	0.758554i	$0.725906\pi$
$572$	0	0
$573$	26.5067	1.10733
$574$	−1.18854	−0.0496089
$575$	0.762310	0.0317905
$576$	−7.97370	−0.332237
$577$	−25.7812	−1.07329	−0.536643	−	0.843809i	$-0.680308\pi$
$577$	−25.7812	−1.07329	−0.536643	+	0.843809i	$0.680308\pi$
$578$	−0.513590	−0.0213625
$579$	−19.7859	−0.822273
$580$	0.457392	0.0189922
$581$	−15.4828	−0.642333
$582$	−0.247424	−0.0102560
$583$	0.150945	0.00625148
$584$	0.147237	0.00609270
$585$	0	0
$586$	0.578048	0.0238789
$587$	−23.3845	−0.965183	−0.482592	−	0.875846i	$-0.660304\pi$
$587$	−23.3845	−0.965183	−0.482592	+	0.875846i	$0.660304\pi$
$588$	21.0594	0.868475
$589$	2.27146	0.0935937
$590$	0.0277805	0.00114370
$591$	25.9338	1.06678
$592$	15.0871	0.620074
$593$	−15.3335	−0.629671	−0.314836	−	0.949146i	$-0.601949\pi$
$593$	−15.3335	−0.629671	−0.314836	+	0.949146i	$0.601949\pi$
$594$	0.0331136	0.00135867
$595$	−0.649663	−0.0266336
$596$	5.74132	0.235174
$597$	−14.9274	−0.610940
$598$	0	0
$599$	18.3246	0.748724	0.374362	−	0.927283i	$-0.377862\pi$
$599$	18.3246	0.748724	0.374362	+	0.927283i	$0.377862\pi$
$600$	−0.659951	−0.0269424
$601$	−46.9476	−1.91503	−0.957517	−	0.288378i	$-0.906884\pi$
$601$	−46.9476	−1.91503	−0.957517	+	0.288378i	$0.906884\pi$
$602$	0.745014	0.0303645
$603$	8.58013	0.349410
$604$	8.12130	0.330451
$605$	−0.127095	−0.00516716
$606$	−0.369047	−0.0149915
$607$	3.92921	0.159482	0.0797409	−	0.996816i	$-0.474591\pi$
$607$	3.92921	0.159482	0.0797409	+	0.996816i	$0.474591\pi$
$608$	0.952389	0.0386245
$609$	7.53921	0.305504
$610$	−0.0421608	−0.00170704
$611$	0	0
$612$	2.44001	0.0986315
$613$	−12.6524	−0.511027	−0.255514	−	0.966805i	$-0.582245\pi$
$613$	−12.6524	−0.511027	−0.255514	+	0.966805i	$0.582245\pi$
$614$	−0.257940	−0.0104096
$615$	1.08938	0.0439281
$616$	−0.554506	−0.0223417
$617$	−28.1177	−1.13198	−0.565989	−	0.824413i	$-0.691505\pi$
$617$	−28.1177	−1.13198	−0.565989	+	0.824413i	$0.691505\pi$
$618$	0.268722	0.0108096
$619$	13.8836	0.558030	0.279015	−	0.960287i	$-0.409992\pi$
$619$	13.8836	0.558030	0.279015	+	0.960287i	$0.409992\pi$
$620$	0.240592	0.00966242
$621$	0.152956	0.00613792
$622$	0.746466	0.0299306
$623$	33.8272	1.35526
$624$	0	0
$625$	24.7580	0.990318
$626$	0.345854	0.0138231
$627$	2.39853	0.0957879
$628$	34.7218	1.38555
$629$	−4.61168	−0.183880
$630$	0.0176236	0.000702141 0
$631$	−33.5264	−1.33467	−0.667333	−	0.744759i	$-0.732564\pi$
$631$	−33.5264	−1.33467	−0.667333	+	0.744759i	$0.732564\pi$
$632$	0.00231236	9.19806e−5 0
$633$	5.89562	0.234330
$634$	−0.213161	−0.00846571
$635$	−1.27864	−0.0507414
$636$	−0.301724	−0.0119641
$637$	0	0
$638$	−0.0596174	−0.00236028
$639$	−13.6838	−0.541324
$640$	0.134490	0.00531619
$641$	27.9062	1.10223	0.551114	−	0.834430i	$-0.314203\pi$
$641$	27.9062	1.10223	0.551114	+	0.834430i	$0.314203\pi$
$642$	0.0934560	0.00368841
$643$	−11.6371	−0.458921	−0.229461	−	0.973318i	$-0.573696\pi$
$643$	−11.6371	−0.458921	−0.229461	+	0.973318i	$0.573696\pi$
$644$	−1.28032	−0.0504515
$645$	−0.682856	−0.0268874
$646$	−0.0969506	−0.00381447
$647$	19.9793	0.785467	0.392733	−	0.919652i	$-0.371530\pi$
$647$	19.9793	0.785467	0.392733	+	0.919652i	$0.371530\pi$
$648$	−0.132418	−0.00520187
$649$	6.60091	0.259108
$650$	0	0
$651$	3.96569	0.155428
$652$	4.04747	0.158511
$653$	13.3379	0.521954	0.260977	−	0.965345i	$-0.415955\pi$
$653$	13.3379	0.521954	0.260977	+	0.965345i	$0.415955\pi$
$654$	−0.553205	−0.0216320
$655$	1.47028	0.0574485
$656$	34.2291	1.33642
$657$	−1.11191	−0.0433797
$658$	−1.66982	−0.0650965
$659$	18.3212	0.713691	0.356845	−	0.934163i	$-0.383852\pi$
$659$	18.3212	0.713691	0.356845	+	0.934163i	$0.383852\pi$
$660$	0.254051	0.00988894
$661$	−7.02777	−0.273349	−0.136674	−	0.990616i	$-0.543641\pi$
$661$	−7.02777	−0.273349	−0.136674	+	0.990616i	$0.543641\pi$
$662$	−0.723774	−0.0281303
$663$	0	0
$664$	−0.489595	−0.0190000
$665$	1.27654	0.0495019
$666$	0.125102	0.00484762
$667$	−0.275381	−0.0106628
$668$	44.8219	1.73421
$669$	−9.65551	−0.373304
$670$	−0.0361102	−0.00139506
$671$	−10.0178	−0.386734
$672$	1.66276	0.0641422
$673$	20.9922	0.809191	0.404595	−	0.914496i	$-0.367412\pi$
$673$	20.9922	0.809191	0.404595	+	0.914496i	$0.367412\pi$
$674$	−0.0345350	−0.00133024
$675$	4.98385	0.191828
$676$	0	0
$677$	41.5986	1.59877	0.799383	−	0.600822i	$-0.205160\pi$
$677$	41.5986	1.59877	0.799383	+	0.600822i	$0.205160\pi$
$678$	−0.0869406	−0.00333894
$679$	−31.2891	−1.20077
$680$	−0.0205436	−0.000787811 0
$681$	6.44679	0.247042
$682$	−0.0313593	−0.00120081
$683$	−1.28137	−0.0490304	−0.0245152	−	0.999699i	$-0.507804\pi$
$683$	−1.28137	−0.0490304	−0.0245152	+	0.999699i	$0.507804\pi$
$684$	−4.79442	−0.183319
$685$	−1.64858	−0.0629892
$686$	−0.490245	−0.0187176
$687$	9.53606	0.363823
$688$	−21.4558	−0.817994
$689$	0	0
$690$	−0.000643729 0	−2.45063e−5 0
$691$	24.8967	0.947114	0.473557	−	0.880763i	$-0.342970\pi$
$691$	24.8967	0.947114	0.473557	+	0.880763i	$0.342970\pi$
$692$	40.1588	1.52661
$693$	4.18754	0.159071
$694$	0.636527	0.0241623
$695$	0.805754	0.0305640
$696$	0.238404	0.00903670
$697$	−10.4628	−0.396308
$698$	0.171770	0.00650161
$699$	27.0134	1.02174
$700$	−41.7172	−1.57676
$701$	−45.7991	−1.72981	−0.864905	−	0.501936i	$-0.832621\pi$
$701$	−45.7991	−1.72981	−0.864905	+	0.501936i	$0.832621\pi$
$702$	0	0
$703$	9.06157	0.341764
$704$	7.97370	0.300520
$705$	1.53051	0.0576422
$706$	0.575146	0.0216459
$707$	−46.6696	−1.75519
$708$	−13.1946	−0.495883
$709$	14.0687	0.528361	0.264180	−	0.964473i	$-0.414899\pi$
$709$	14.0687	0.528361	0.264180	+	0.964473i	$0.414899\pi$
$710$	0.0575895	0.00216130
$711$	−0.0174625	−0.000654896 0
$712$	1.06968	0.0400880
$713$	−0.144853	−0.00542478
$714$	−0.169264	−0.00633455
$715$	0	0
$716$	−40.6797	−1.52027
$717$	−25.5242	−0.953220
$718$	−0.165616	−0.00618075
$719$	45.5180	1.69753	0.848767	−	0.528767i	$-0.177346\pi$
$719$	45.5180	1.69753	0.848767	+	0.528767i	$0.177346\pi$
$720$	−0.507546	−0.0189151
$721$	33.9825	1.26557
$722$	−0.438658	−0.0163252
$723$	10.8030	0.401769
$724$	36.4527	1.35475
$725$	−8.97288	−0.333244
$726$	−0.0331136	−0.00122896
$727$	−2.47173	−0.0916714	−0.0458357	−	0.998949i	$-0.514595\pi$
$727$	−2.47173	−0.0916714	−0.0458357	+	0.998949i	$0.514595\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0.00467956	0.000173198 0
$731$	6.55841	0.242572
$732$	20.0247	0.740132
$733$	−40.0089	−1.47776	−0.738881	−	0.673836i	$-0.764645\pi$
$733$	−40.0089	−1.47776	−0.738881	+	0.673836i	$0.764645\pi$
$734$	−0.325353	−0.0120090
$735$	1.33901	0.0493901
$736$	−0.0607347	−0.00223871
$737$	−8.58013	−0.316053
$738$	0.283829	0.0104479
$739$	−25.8009	−0.949100	−0.474550	−	0.880229i	$-0.657389\pi$
$739$	−25.8009	−0.949100	−0.474550	+	0.880229i	$0.657389\pi$
$740$	0.959800	0.0352830
$741$	0	0
$742$	0.0209306	0.000768388 0
$743$	6.56605	0.240885	0.120442	−	0.992720i	$-0.461569\pi$
$743$	6.56605	0.240885	0.120442	+	0.992720i	$0.461569\pi$
$744$	0.125403	0.00459749
$745$	0.365048	0.0133743
$746$	−0.796480	−0.0291612
$747$	3.69734	0.135279
$748$	−2.44001	−0.0892156
$749$	11.8184	0.431836
$750$	−0.0420179	−0.00153428
$751$	−17.0757	−0.623101	−0.311551	−	0.950230i	$-0.600848\pi$
$751$	−17.0757	−0.623101	−0.311551	+	0.950230i	$0.600848\pi$
$752$	48.0895	1.75365
$753$	3.43833	0.125300
$754$	0	0
$755$	0.516373	0.0187927
$756$	−8.37048	−0.304432
$757$	22.7782	0.827887	0.413943	−	0.910303i	$-0.364151\pi$
$757$	22.7782	0.827887	0.413943	+	0.910303i	$0.364151\pi$
$758$	1.08634	0.0394577
$759$	−0.152956	−0.00555195
$760$	0.0403665	0.00146425
$761$	26.5658	0.963008	0.481504	−	0.876444i	$-0.340091\pi$
$761$	26.5658	0.963008	0.481504	+	0.876444i	$0.340091\pi$
$762$	−0.333139	−0.0120684
$763$	−69.9582	−2.53266
$764$	52.9843	1.91691
$765$	0.155142	0.00560917
$766$	−0.0363042	−0.00131173
$767$	0	0
$768$	−15.9124	−0.574188
$769$	−5.74864	−0.207301	−0.103651	−	0.994614i	$-0.533052\pi$
$769$	−5.74864	−0.207301	−0.103651	+	0.994614i	$0.533052\pi$
$770$	−0.0176236	−0.000635111 0
$771$	22.7966	0.821000
$772$	−39.5500	−1.42344
$773$	−7.94739	−0.285848	−0.142924	−	0.989734i	$-0.545650\pi$
$773$	−7.94739	−0.285848	−0.142924	+	0.989734i	$0.545650\pi$
$774$	−0.177912	−0.00639492
$775$	−4.71981	−0.169541
$776$	−0.989423	−0.0355182
$777$	15.8204	0.567554
$778$	0.935231	0.0335296
$779$	20.5586	0.736590
$780$	0	0
$781$	13.6838	0.489646
$782$	0.00618262	0.000221090 0
$783$	−1.80039	−0.0643408
$784$	42.0726	1.50259
$785$	2.20770	0.0787961
$786$	0.383068	0.0136636
$787$	34.7859	1.23998	0.619992	−	0.784608i	$-0.287136\pi$
$787$	34.7859	1.23998	0.619992	+	0.784608i	$0.287136\pi$
$788$	51.8392	1.84670
$789$	6.13478	0.218404
$790$	7.34926e−5 0	2.61475e−6 0
$791$	−10.9945	−0.390919
$792$	0.132418	0.00470527
$793$	0	0
$794$	−0.671990	−0.0238480
$795$	−0.0191844	−0.000680399 0
$796$	−29.8385	−1.05760
$797$	−5.33207	−0.188872	−0.0944358	−	0.995531i	$-0.530105\pi$
$797$	−5.33207	−0.188872	−0.0944358	+	0.995531i	$0.530105\pi$
$798$	0.332590	0.0117736
$799$	−14.6996	−0.520034
$800$	−1.97895	−0.0699664
$801$	−8.07805	−0.285424
$802$	0.773497	0.0273131
$803$	1.11191	0.0392384
$804$	17.1508	0.604864
$805$	−0.0814058	−0.00286918
$806$	0	0
$807$	−17.5115	−0.616434
$808$	−1.47578	−0.0519179
$809$	−27.9403	−0.982328	−0.491164	−	0.871067i	$-0.663428\pi$
$809$	−27.9403	−0.982328	−0.491164	+	0.871067i	$0.663428\pi$
$810$	−0.00420859	−0.000147875 0
$811$	−30.6104	−1.07488	−0.537438	−	0.843303i	$-0.680608\pi$
$811$	−30.6104	−1.07488	−0.537438	+	0.843303i	$0.680608\pi$
$812$	15.0702	0.528859
$813$	19.4939	0.683682
$814$	−0.125102	−0.00438484
$815$	0.257349	0.00901453
$816$	4.87467	0.170647
$817$	−12.8868	−0.450850
$818$	−0.291281	−0.0101844
$819$	0	0
$820$	2.17757	0.0760440
$821$	−38.7339	−1.35182	−0.675910	−	0.736984i	$-0.736249\pi$
$821$	−38.7339	−1.35182	−0.675910	+	0.736984i	$0.736249\pi$
$822$	−0.429524	−0.0149814
$823$	−19.6863	−0.686222	−0.343111	−	0.939295i	$-0.611481\pi$
$823$	−19.6863	−0.686222	−0.343111	+	0.939295i	$0.611481\pi$
$824$	1.07459	0.0374352
$825$	−4.98385	−0.173515
$826$	0.915311	0.0318478
$827$	−9.61602	−0.334382	−0.167191	−	0.985925i	$-0.553470\pi$
$827$	−9.61602	−0.334382	−0.167191	+	0.985925i	$0.553470\pi$
$828$	0.305744	0.0106254
$829$	36.6764	1.27382	0.636912	−	0.770936i	$-0.280211\pi$
$829$	36.6764	1.27382	0.636912	+	0.770936i	$0.280211\pi$
$830$	−0.0155606	−0.000540116 0
$831$	−1.06561	−0.0369657
$832$	0	0
$833$	−12.8604	−0.445586
$834$	0.209932	0.00726935
$835$	2.84989	0.0986245
$836$	4.79442	0.165819
$837$	−0.947022	−0.0327339
$838$	−0.0885077	−0.00305745
$839$	−30.1320	−1.04027	−0.520136	−	0.854083i	$-0.674119\pi$
$839$	−30.1320	−1.04027	−0.520136	+	0.854083i	$0.674119\pi$
$840$	0.0704751	0.00243162
$841$	−25.7586	−0.888227
$842$	0.0609323	0.00209987
$843$	−10.7973	−0.371880
$844$	11.7848	0.405649
$845$	0	0
$846$	0.398760	0.0137097
$847$	−4.18754	−0.143886
$848$	−0.602785	−0.0206997
$849$	5.42195	0.186081
$850$	0.201452	0.00690973
$851$	−0.577864	−0.0198089
$852$	−27.3526	−0.937086
$853$	−2.26710	−0.0776240	−0.0388120	−	0.999247i	$-0.512357\pi$
$853$	−2.26710	−0.0776240	−0.0388120	+	0.999247i	$0.512357\pi$
$854$	−1.38912	−0.0475345
$855$	−0.304842	−0.0104254
$856$	0.373721	0.0127735
$857$	1.61909	0.0553072	0.0276536	−	0.999618i	$-0.491196\pi$
$857$	1.61909	0.0553072	0.0276536	+	0.999618i	$0.491196\pi$
$858$	0	0
$859$	53.0711	1.81076	0.905381	−	0.424601i	$-0.139586\pi$
$859$	53.0711	1.81076	0.905381	+	0.424601i	$0.139586\pi$
$860$	−1.36496	−0.0465448
$861$	35.8929	1.22323
$862$	0.0473797	0.00161376
$863$	−7.43020	−0.252927	−0.126463	−	0.991971i	$-0.540363\pi$
$863$	−7.43020	−0.252927	−0.126463	+	0.991971i	$0.540363\pi$
$864$	−0.397073	−0.0135087
$865$	2.55340	0.0868183
$866$	−0.564462	−0.0191812
$867$	15.5100	0.526746
$868$	7.92703	0.269061
$869$	0.0174625	0.000592376 0
$870$	0.00757710	0.000256888 0
$871$	0	0
$872$	−2.21222	−0.0749151
$873$	7.47196	0.252888
$874$	−0.0121484	−0.000410924 0
$875$	−5.31357	−0.179631
$876$	−2.22260	−0.0750946
$877$	43.9322	1.48349	0.741743	−	0.670684i	$-0.233999\pi$
$877$	43.9322	1.48349	0.741743	+	0.670684i	$0.233999\pi$
$878$	−1.10183	−0.0371850
$879$	−17.4565	−0.588793
$880$	0.507546	0.0171094
$881$	39.1892	1.32032	0.660158	−	0.751126i	$-0.270489\pi$
$881$	39.1892	1.32032	0.660158	+	0.751126i	$0.270489\pi$
$882$	0.348867	0.0117470
$883$	−28.2949	−0.952199	−0.476099	−	0.879391i	$-0.657950\pi$
$883$	−28.2949	−0.952199	−0.476099	+	0.879391i	$0.657950\pi$
$884$	0	0
$885$	−0.838945	−0.0282008
$886$	0.151035	0.00507412
$887$	12.0234	0.403706	0.201853	−	0.979416i	$-0.435304\pi$
$887$	12.0234	0.403706	0.201853	+	0.979416i	$0.435304\pi$
$888$	0.500272	0.0167880
$889$	−42.1287	−1.41295
$890$	0.0339972	0.00113959
$891$	−1.00000	−0.0335013
$892$	−19.3004	−0.646226
$893$	28.8835	0.966549
$894$	0.0951101	0.00318096
$895$	−2.58652	−0.0864577
$896$	4.43118	0.148035
$897$	0	0
$898$	0.300902	0.0100412
$899$	1.70501	0.0568653
$900$	9.96223	0.332074
$901$	0.184254	0.00613839
$902$	−0.283829	−0.00945046
$903$	−22.4987	−0.748711
$904$	−0.347667	−0.0115632
$905$	2.31776	0.0770448
$906$	0.134536	0.00446967
$907$	−36.7736	−1.22105	−0.610524	−	0.791998i	$-0.709041\pi$
$907$	−36.7736	−1.22105	−0.610524	+	0.791998i	$0.709041\pi$
$908$	12.8865	0.427654
$909$	11.1449	0.369652
$910$	0	0
$911$	25.4312	0.842574	0.421287	−	0.906927i	$-0.361579\pi$
$911$	25.4312	0.842574	0.421287	+	0.906927i	$0.361579\pi$
$912$	−9.57833	−0.317170
$913$	−3.69734	−0.122364
$914$	0.626047	0.0207078
$915$	1.27322	0.0420913
$916$	19.0617	0.629815
$917$	48.4427	1.59972
$918$	0.0404209	0.00133409
$919$	−40.0270	−1.32037	−0.660184	−	0.751104i	$-0.729522\pi$
$919$	−40.0270	−1.32037	−0.660184	+	0.751104i	$0.729522\pi$
$920$	−0.00257421	−8.48691e−5 0
$921$	7.78956	0.256675
$922$	0.963814	0.0317415
$923$	0	0
$924$	8.37048	0.275369
$925$	−18.8289	−0.619089
$926$	1.01369	0.0333118
$927$	−8.11515	−0.266537
$928$	0.714886	0.0234673
$929$	−11.1834	−0.366917	−0.183458	−	0.983027i	$-0.558729\pi$
$929$	−11.1834	−0.366917	−0.183458	+	0.983027i	$0.558729\pi$
$930$	0.00398562	0.000130694 0
$931$	25.2696	0.828178
$932$	53.9973	1.76874
$933$	−22.5426	−0.738011
$934$	−0.697475	−0.0228221
$935$	−0.155142	−0.00507369
$936$	0	0
$937$	47.4809	1.55113	0.775566	−	0.631267i	$-0.217465\pi$
$937$	47.4809	1.55113	0.775566	+	0.631267i	$0.217465\pi$
$938$	−1.18976	−0.0388470
$939$	−10.4445	−0.340842
$940$	3.05934	0.0997845
$941$	11.7744	0.383836	0.191918	−	0.981411i	$-0.438529\pi$
$941$	11.7744	0.383836	0.191918	+	0.981411i	$0.438529\pi$
$942$	0.575197	0.0187409
$943$	−1.31104	−0.0426934
$944$	−26.3602	−0.857952
$945$	−0.532217	−0.0173130
$946$	0.177912	0.00578442
$947$	−19.1556	−0.622474	−0.311237	−	0.950332i	$-0.600743\pi$
$947$	−19.1556	−0.622474	−0.311237	+	0.950332i	$0.600743\pi$
$948$	−0.0349059	−0.00113369
$949$	0	0
$950$	−0.395836	−0.0128426
$951$	6.43727	0.208743
$952$	−0.676871	−0.0219375
$953$	47.9923	1.55462	0.777311	−	0.629117i	$-0.216583\pi$
$953$	47.9923	1.55462	0.777311	+	0.629117i	$0.216583\pi$
$954$	−0.00499832	−0.000161826 0
$955$	3.36888	0.109014
$956$	−51.0205	−1.65012
$957$	1.80039	0.0581984
$958$	0.341346	0.0110284
$959$	−54.3175	−1.75401
$960$	−1.01342	−0.0327080
$961$	−30.1031	−0.971069
$962$	0	0
$963$	−2.82228	−0.0909468
$964$	21.5942	0.695503
$965$	−2.51469	−0.0809508
$966$	−0.0212096	−0.000682407 0
$967$	−46.4422	−1.49348	−0.746741	−	0.665115i	$-0.768382\pi$
$967$	−46.4422	−1.49348	−0.746741	+	0.665115i	$0.768382\pi$
$968$	−0.132418	−0.00425608
$969$	2.92782	0.0940550
$970$	−0.0314464	−0.00100968
$971$	−12.1185	−0.388902	−0.194451	−	0.980912i	$-0.562293\pi$
$971$	−12.1185	−0.388902	−0.194451	+	0.980912i	$0.562293\pi$
$972$	1.99890	0.0641149
$973$	26.5480	0.851089
$974$	−0.611880	−0.0196059
$975$	0	0
$976$	40.0054	1.28054
$977$	−38.3291	−1.22626	−0.613128	−	0.789984i	$-0.710089\pi$
$977$	−38.3291	−1.22626	−0.613128	+	0.789984i	$0.710089\pi$
$978$	0.0670499	0.00214402
$979$	8.07805	0.258176
$980$	2.67655	0.0854993
$981$	16.7063	0.533391
$982$	−0.967752	−0.0308822
$983$	50.9329	1.62451	0.812254	−	0.583304i	$-0.198240\pi$
$983$	50.9329	1.62451	0.812254	+	0.583304i	$0.198240\pi$
$984$	1.13500	0.0361826
$985$	3.29607	0.105022
$986$	−0.0727734	−0.00231758
$987$	50.4271	1.60511
$988$	0	0
$989$	0.821799	0.0261317
$990$	0.00420859	0.000133758 0
$991$	−50.8521	−1.61537	−0.807686	−	0.589613i	$-0.799280\pi$
$991$	−50.8521	−1.61537	−0.807686	+	0.589613i	$0.799280\pi$
$992$	0.376036	0.0119392
$993$	21.8573	0.693621
$994$	1.89746	0.0601837
$995$	−1.89721	−0.0601456
$996$	7.39063	0.234181
$997$	41.5771	1.31676	0.658380	−	0.752686i	$-0.271242\pi$
$997$	41.5771	1.31676	0.658380	+	0.752686i	$0.271242\pi$
$998$	1.23869	0.0392101
$999$	−3.77798	−0.119530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.ba.1.7	✓	12
13.12	even	2		5577.2.a.bc.1.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5577.2.a.ba.1.7	✓	12	1.1	even	1	trivial
5577.2.a.bc.1.6	yes	12	13.12	even	2

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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0331136 q^{2} -1.00000 q^{3} -1.99890 q^{4} -0.127095 q^{5} -0.0331136 q^{6} -4.18754 q^{7} -0.132418 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.0331136 q^{2} -1.00000 q^{3} -1.99890 q^{4} -0.127095 q^{5} -0.0331136 q^{6} -4.18754 q^{7} -0.132418 q^{8} +1.00000 q^{9} -0.00420859 q^{10} -1.00000 q^{11} +1.99890 q^{12} -0.138664 q^{14} +0.127095 q^{15} +3.99342 q^{16} -1.22067 q^{17} +0.0331136 q^{18} +2.39853 q^{19} +0.254051 q^{20} +4.18754 q^{21} -0.0331136 q^{22} -0.152956 q^{23} +0.132418 q^{24} -4.98385 q^{25} -1.00000 q^{27} +8.37048 q^{28} +1.80039 q^{29} +0.00420859 q^{30} +0.947022 q^{31} +0.397073 q^{32} +1.00000 q^{33} -0.0404209 q^{34} +0.532217 q^{35} -1.99890 q^{36} +3.77798 q^{37} +0.0794238 q^{38} +0.0168297 q^{40} +8.57137 q^{41} +0.138664 q^{42} -5.37278 q^{43} +1.99890 q^{44} -0.127095 q^{45} -0.00506493 q^{46} +12.0422 q^{47} -3.99342 q^{48} +10.5355 q^{49} -0.165033 q^{50} +1.22067 q^{51} -0.150945 q^{53} -0.0331136 q^{54} +0.127095 q^{55} +0.554506 q^{56} -2.39853 q^{57} +0.0596174 q^{58} -6.60091 q^{59} -0.254051 q^{60} +10.0178 q^{61} +0.0313593 q^{62} -4.18754 q^{63} -7.97370 q^{64} +0.0331136 q^{66} +8.58013 q^{67} +2.44001 q^{68} +0.152956 q^{69} +0.0176236 q^{70} -13.6838 q^{71} -0.132418 q^{72} -1.11191 q^{73} +0.125102 q^{74} +4.98385 q^{75} -4.79442 q^{76} +4.18754 q^{77} -0.0174625 q^{79} -0.507546 q^{80} +1.00000 q^{81} +0.283829 q^{82} +3.69734 q^{83} -8.37048 q^{84} +0.155142 q^{85} -0.177912 q^{86} -1.80039 q^{87} +0.132418 q^{88} -8.07805 q^{89} -0.00420859 q^{90} +0.305744 q^{92} -0.947022 q^{93} +0.398760 q^{94} -0.304842 q^{95} -0.397073 q^{96} +7.47196 q^{97} +0.348867 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9	\( 12 q - q^{2} - 12 q^{3} + 5 q^{4} + 6 q^{5} + q^{6} + q^{7} + 12 q^{9} - 11 q^{10} - 12 q^{11} - 5 q^{12} + 9 q^{14} - 6 q^{15} - 9 q^{16} + 3 q^{17} - q^{18} - 6 q^{19} + 20 q^{20} - q^{21} + q^{22} - 22 q^{23} - 2 q^{25} - 12 q^{27} + 11 q^{28} + 13 q^{29} + 11 q^{30} - 2 q^{31} - 11 q^{32} + 12 q^{33} - 10 q^{34} - 14 q^{35} + 5 q^{36} - 3 q^{37} - 18 q^{38} - 18 q^{40} - 4 q^{41} - 9 q^{42} - 26 q^{43} - 5 q^{44} + 6 q^{45} + 18 q^{46} + 9 q^{47} + 9 q^{48} - 3 q^{49} - 29 q^{50} - 3 q^{51} - 5 q^{53} + q^{54} - 6 q^{55} + 5 q^{56} + 6 q^{57} - 37 q^{58} + 22 q^{59} - 20 q^{60} - 11 q^{61} - 18 q^{62} + q^{63} - 10 q^{64} - q^{66} + 28 q^{67} + 12 q^{68} + 22 q^{69} + 29 q^{70} - 10 q^{71} + 7 q^{73} - 6 q^{74} + 2 q^{75} - 32 q^{76} - q^{77} - 40 q^{79} - 30 q^{80} + 12 q^{81} + 26 q^{82} - q^{83} - 11 q^{84} + 32 q^{85} + 9 q^{86} - 13 q^{87} - 11 q^{89} - 11 q^{90} - 38 q^{92} + 2 q^{93} - 25 q^{94} - 10 q^{95} + 11 q^{96} - 7 q^{97} - 28 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - q^2 - 12 * q^3 + 5 * q^4 + 6 * q^5 + q^6 + q^7 + 12 * q^9 - 11 * q^10 - 12 * q^11 - 5 * q^12 + 9 * q^14 - 6 * q^15 - 9 * q^16 + 3 * q^17 - q^18 - 6 * q^19 + 20 * q^20 - q^21 + q^22 - 22 * q^23 - 2 * q^25 - 12 * q^27 + 11 * q^28 + 13 * q^29 + 11 * q^30 - 2 * q^31 - 11 * q^32 + 12 * q^33 - 10 * q^34 - 14 * q^35 + 5 * q^36 - 3 * q^37 - 18 * q^38 - 18 * q^40 - 4 * q^41 - 9 * q^42 - 26 * q^43 - 5 * q^44 + 6 * q^45 + 18 * q^46 + 9 * q^47 + 9 * q^48 - 3 * q^49 - 29 * q^50 - 3 * q^51 - 5 * q^53 + q^54 - 6 * q^55 + 5 * q^56 + 6 * q^57 - 37 * q^58 + 22 * q^59 - 20 * q^60 - 11 * q^61 - 18 * q^62 + q^63 - 10 * q^64 - q^66 + 28 * q^67 + 12 * q^68 + 22 * q^69 + 29 * q^70 - 10 * q^71 + 7 * q^73 - 6 * q^74 + 2 * q^75 - 32 * q^76 - q^77 - 40 * q^79 - 30 * q^80 + 12 * q^81 + 26 * q^82 - q^83 - 11 * q^84 + 32 * q^85 + 9 * q^86 - 13 * q^87 - 11 * q^89 - 11 * q^90 - 38 * q^92 + 2 * q^93 - 25 * q^94 - 10 * q^95 + 11 * q^96 - 7 * q^97 - 28 * q^98 - 12 * q^99

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