LMFDB - Embedded newform 2013.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, 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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 $ x^13 - 2x^12 - 19x^11 + 35x^10 + 136x^9 - 220x^8 - 469x^7 + 610x^6 + 841x^5 - 760x^4 - 742x^3 + 366x^2 + 236x - 47
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			1.9
Root			$1.50067$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.50067 q^{2} -1.00000 q^{3} +0.252024 q^{4} -0.569898 q^{5} -1.50067 q^{6} -3.97554 q^{7} -2.62314 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.50067 q^{2} -1.00000 q^{3} +0.252024 q^{4} -0.569898 q^{5} -1.50067 q^{6} -3.97554 q^{7} -2.62314 q^{8} +1.00000 q^{9} -0.855232 q^{10} +1.00000 q^{11} -0.252024 q^{12} -3.48724 q^{13} -5.96599 q^{14} +0.569898 q^{15} -4.44053 q^{16} +7.75664 q^{17} +1.50067 q^{18} +1.56002 q^{19} -0.143628 q^{20} +3.97554 q^{21} +1.50067 q^{22} +4.91362 q^{23} +2.62314 q^{24} -4.67522 q^{25} -5.23321 q^{26} -1.00000 q^{27} -1.00193 q^{28} +6.29679 q^{29} +0.855232 q^{30} +2.87665 q^{31} -1.41751 q^{32} -1.00000 q^{33} +11.6402 q^{34} +2.26565 q^{35} +0.252024 q^{36} -9.34414 q^{37} +2.34109 q^{38} +3.48724 q^{39} +1.49492 q^{40} +1.58419 q^{41} +5.96599 q^{42} +5.31329 q^{43} +0.252024 q^{44} -0.569898 q^{45} +7.37374 q^{46} +3.46571 q^{47} +4.44053 q^{48} +8.80489 q^{49} -7.01598 q^{50} -7.75664 q^{51} -0.878869 q^{52} +10.8254 q^{53} -1.50067 q^{54} -0.569898 q^{55} +10.4284 q^{56} -1.56002 q^{57} +9.44943 q^{58} +0.418492 q^{59} +0.143628 q^{60} -1.00000 q^{61} +4.31692 q^{62} -3.97554 q^{63} +6.75385 q^{64} +1.98737 q^{65} -1.50067 q^{66} +9.84375 q^{67} +1.95486 q^{68} -4.91362 q^{69} +3.40001 q^{70} +9.93167 q^{71} -2.62314 q^{72} +7.11859 q^{73} -14.0225 q^{74} +4.67522 q^{75} +0.393164 q^{76} -3.97554 q^{77} +5.23321 q^{78} -13.1270 q^{79} +2.53065 q^{80} +1.00000 q^{81} +2.37735 q^{82} +4.04331 q^{83} +1.00193 q^{84} -4.42050 q^{85} +7.97351 q^{86} -6.29679 q^{87} -2.62314 q^{88} -13.4410 q^{89} -0.855232 q^{90} +13.8636 q^{91} +1.23835 q^{92} -2.87665 q^{93} +5.20090 q^{94} -0.889055 q^{95} +1.41751 q^{96} -1.77923 q^{97} +13.2133 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * 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 $

$2$	1.50067	1.06114	0.530569	−	0.847642i	$-0.321978\pi$
$2$	1.50067	1.06114	0.530569	+	0.847642i	$0.321978\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.252024	0.126012
$5$	−0.569898	−0.254866	−0.127433	−	0.991847i	$-0.540674\pi$
$5$	−0.569898	−0.254866	−0.127433	+	0.991847i	$0.540674\pi$
$6$	−1.50067	−0.612648
$7$	−3.97554	−1.50261	−0.751306	−	0.659954i	$-0.770576\pi$
$7$	−3.97554	−1.50261	−0.751306	+	0.659954i	$0.770576\pi$
$8$	−2.62314	−0.927421
$9$	1.00000	0.333333
$10$	−0.855232	−0.270448
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.252024	−0.0727532
$13$	−3.48724	−0.967186	−0.483593	−	0.875293i	$-0.660669\pi$
$13$	−3.48724	−0.967186	−0.483593	+	0.875293i	$0.660669\pi$
$14$	−5.96599	−1.59448
$15$	0.569898	0.147147
$16$	−4.44053	−1.11013
$17$	7.75664	1.88126	0.940631	−	0.339430i	$-0.110234\pi$
$17$	7.75664	1.88126	0.940631	+	0.339430i	$0.110234\pi$
$18$	1.50067	0.353712
$19$	1.56002	0.357894	0.178947	−	0.983859i	$-0.442731\pi$
$19$	1.56002	0.357894	0.178947	+	0.983859i	$0.442731\pi$
$20$	−0.143628	−0.0321162
$21$	3.97554	0.867533
$22$	1.50067	0.319945
$23$	4.91362	1.02456	0.512280	−	0.858819i	$-0.328801\pi$
$23$	4.91362	1.02456	0.512280	+	0.858819i	$0.328801\pi$
$24$	2.62314	0.535447
$25$	−4.67522	−0.935043
$26$	−5.23321	−1.02632
$27$	−1.00000	−0.192450
$28$	−1.00193	−0.189347
$29$	6.29679	1.16928	0.584642	−	0.811291i	$-0.301235\pi$
$29$	6.29679	1.16928	0.584642	+	0.811291i	$0.301235\pi$
$30$	0.855232	0.156143
$31$	2.87665	0.516662	0.258331	−	0.966056i	$-0.416828\pi$
$31$	2.87665	0.516662	0.258331	+	0.966056i	$0.416828\pi$
$32$	−1.41751	−0.250583
$33$	−1.00000	−0.174078
$34$	11.6402	1.99628
$35$	2.26565	0.382965
$36$	0.252024	0.0420041
$37$	−9.34414	−1.53617	−0.768083	−	0.640350i	$-0.778789\pi$
$37$	−9.34414	−1.53617	−0.768083	+	0.640350i	$0.778789\pi$
$38$	2.34109	0.379775
$39$	3.48724	0.558405
$40$	1.49492	0.236368
$41$	1.58419	0.247409	0.123704	−	0.992319i	$-0.460523\pi$
$41$	1.58419	0.247409	0.123704	+	0.992319i	$0.460523\pi$
$42$	5.96599	0.920572
$43$	5.31329	0.810269	0.405134	−	0.914257i	$-0.367225\pi$
$43$	5.31329	0.810269	0.405134	+	0.914257i	$0.367225\pi$
$44$	0.252024	0.0379941
$45$	−0.569898	−0.0849554
$46$	7.37374	1.08720
$47$	3.46571	0.505526	0.252763	−	0.967528i	$-0.418661\pi$
$47$	3.46571	0.505526	0.252763	+	0.967528i	$0.418661\pi$
$48$	4.44053	0.640936
$49$	8.80489	1.25784
$50$	−7.01598	−0.992209
$51$	−7.75664	−1.08615
$52$	−0.878869	−0.121877
$53$	10.8254	1.48699	0.743493	−	0.668744i	$-0.233168\pi$
$53$	10.8254	1.48699	0.743493	+	0.668744i	$0.233168\pi$
$54$	−1.50067	−0.204216
$55$	−0.569898	−0.0768451
$56$	10.4284	1.39355
$57$	−1.56002	−0.206630
$58$	9.44943	1.24077
$59$	0.418492	0.0544831	0.0272415	−	0.999629i	$-0.491328\pi$
$59$	0.418492	0.0544831	0.0272415	+	0.999629i	$0.491328\pi$
$60$	0.143628	0.0185423
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	4.31692	0.548249
$63$	−3.97554	−0.500871
$64$	6.75385	0.844231
$65$	1.98737	0.246503
$66$	−1.50067	−0.184720
$67$	9.84375	1.20260	0.601302	−	0.799022i	$-0.294649\pi$
$67$	9.84375	1.20260	0.601302	+	0.799022i	$0.294649\pi$
$68$	1.95486	0.237062
$69$	−4.91362	−0.591530
$70$	3.40001	0.406378
$71$	9.93167	1.17867	0.589336	−	0.807888i	$-0.299389\pi$
$71$	9.93167	1.17867	0.589336	+	0.807888i	$0.299389\pi$
$72$	−2.62314	−0.309140
$73$	7.11859	0.833168	0.416584	−	0.909097i	$-0.363227\pi$
$73$	7.11859	0.833168	0.416584	+	0.909097i	$0.363227\pi$
$74$	−14.0225	−1.63008
$75$	4.67522	0.539847
$76$	0.393164	0.0450990
$77$	−3.97554	−0.453054
$78$	5.23321	0.592545
$79$	−13.1270	−1.47690	−0.738450	−	0.674308i	$-0.764442\pi$
$79$	−13.1270	−1.47690	−0.738450	+	0.674308i	$0.764442\pi$
$80$	2.53065	0.282935
$81$	1.00000	0.111111
$82$	2.37735	0.262535
$83$	4.04331	0.443811	0.221906	−	0.975068i	$-0.428772\pi$
$83$	4.04331	0.443811	0.221906	+	0.975068i	$0.428772\pi$
$84$	1.00193	0.109320
$85$	−4.42050	−0.479470
$86$	7.97351	0.859806
$87$	−6.29679	−0.675086
$88$	−2.62314	−0.279628
$89$	−13.4410	−1.42474	−0.712371	−	0.701803i	$-0.752379\pi$
$89$	−13.4410	−1.42474	−0.712371	+	0.701803i	$0.752379\pi$
$90$	−0.855232	−0.0901493
$91$	13.8636	1.45331
$92$	1.23835	0.129107
$93$	−2.87665	−0.298295
$94$	5.20090	0.536432
$95$	−0.889055	−0.0912151
$96$	1.41751	0.144674
$97$	−1.77923	−0.180653	−0.0903267	−	0.995912i	$-0.528791\pi$
$97$	−1.77923	−0.180653	−0.0903267	+	0.995912i	$0.528791\pi$
$98$	13.2133	1.33474
$99$	1.00000	0.100504
$100$	−1.17827	−0.117827
$101$	−18.9035	−1.88096	−0.940482	−	0.339844i	$-0.889626\pi$
$101$	−18.9035	−1.88096	−0.940482	+	0.339844i	$0.889626\pi$
$102$	−11.6402	−1.15255
$103$	2.41802	0.238254	0.119127	−	0.992879i	$-0.461990\pi$
$103$	2.41802	0.238254	0.119127	+	0.992879i	$0.461990\pi$
$104$	9.14753	0.896989
$105$	−2.26565	−0.221105
$106$	16.2454	1.57790
$107$	10.7538	1.03961	0.519806	−	0.854285i	$-0.326004\pi$
$107$	10.7538	1.03961	0.519806	+	0.854285i	$0.326004\pi$
$108$	−0.252024	−0.0242511
$109$	−14.6227	−1.40060	−0.700298	−	0.713851i	$-0.746950\pi$
$109$	−14.6227	−1.40060	−0.700298	+	0.713851i	$0.746950\pi$
$110$	−0.855232	−0.0815432
$111$	9.34414	0.886906
$112$	17.6535	1.66810
$113$	−8.88757	−0.836072	−0.418036	−	0.908430i	$-0.637281\pi$
$113$	−8.88757	−0.836072	−0.418036	+	0.908430i	$0.637281\pi$
$114$	−2.34109	−0.219263
$115$	−2.80026	−0.261126
$116$	1.58694	0.147344
$117$	−3.48724	−0.322395
$118$	0.628021	0.0578140
$119$	−30.8368	−2.82681
$120$	−1.49492	−0.136467
$121$	1.00000	0.0909091
$122$	−1.50067	−0.135865
$123$	−1.58419	−0.142842
$124$	0.724986	0.0651057
$125$	5.51389	0.493177
$126$	−5.96599	−0.531492
$127$	−16.2612	−1.44295	−0.721473	−	0.692443i	$-0.756535\pi$
$127$	−16.2612	−1.44295	−0.721473	+	0.692443i	$0.756535\pi$
$128$	12.9703	1.14643
$129$	−5.31329	−0.467809
$130$	2.98240	0.261574
$131$	16.7549	1.46389	0.731943	−	0.681366i	$-0.238614\pi$
$131$	16.7549	1.46389	0.731943	+	0.681366i	$0.238614\pi$
$132$	−0.252024	−0.0219359
$133$	−6.20193	−0.537776
$134$	14.7723	1.27613
$135$	0.569898	0.0490490
$136$	−20.3468	−1.74472
$137$	21.7052	1.85440	0.927198	−	0.374571i	$-0.122210\pi$
$137$	21.7052	1.85440	0.927198	+	0.374571i	$0.122210\pi$
$138$	−7.37374	−0.627694
$139$	9.86673	0.836885	0.418442	−	0.908243i	$-0.362576\pi$
$139$	9.86673	0.836885	0.418442	+	0.908243i	$0.362576\pi$
$140$	0.570999	0.0482582
$141$	−3.46571	−0.291865
$142$	14.9042	1.25073
$143$	−3.48724	−0.291618
$144$	−4.44053	−0.370044
$145$	−3.58853	−0.298011
$146$	10.6827	0.884106
$147$	−8.80489	−0.726215
$148$	−2.35495	−0.193576
$149$	16.9431	1.38803	0.694017	−	0.719959i	$-0.255839\pi$
$149$	16.9431	1.38803	0.694017	+	0.719959i	$0.255839\pi$
$150$	7.01598	0.572852
$151$	16.5384	1.34587	0.672937	−	0.739700i	$-0.265032\pi$
$151$	16.5384	1.34587	0.672937	+	0.739700i	$0.265032\pi$
$152$	−4.09217	−0.331918
$153$	7.75664	0.627088
$154$	−5.96599	−0.480753
$155$	−1.63940	−0.131680
$156$	0.878869	0.0703659
$157$	17.8806	1.42703	0.713515	−	0.700640i	$-0.247102\pi$
$157$	17.8806	1.42703	0.713515	+	0.700640i	$0.247102\pi$
$158$	−19.6993	−1.56719
$159$	−10.8254	−0.858511
$160$	0.807836	0.0638650
$161$	−19.5343	−1.53952
$162$	1.50067	0.117904
$163$	−0.855017	−0.0669701	−0.0334851	−	0.999439i	$-0.510661\pi$
$163$	−0.855017	−0.0669701	−0.0334851	+	0.999439i	$0.510661\pi$
$164$	0.399254	0.0311765
$165$	0.569898	0.0443665
$166$	6.06770	0.470945
$167$	13.4101	1.03770	0.518852	−	0.854864i	$-0.326360\pi$
$167$	13.4101	1.03770	0.518852	+	0.854864i	$0.326360\pi$
$168$	−10.4284	−0.804568
$169$	−0.839160	−0.0645508
$170$	−6.63373	−0.508784
$171$	1.56002	0.119298
$172$	1.33908	0.102104
$173$	−9.03817	−0.687160	−0.343580	−	0.939123i	$-0.611640\pi$
$173$	−9.03817	−0.687160	−0.343580	+	0.939123i	$0.611640\pi$
$174$	−9.44943	−0.716359
$175$	18.5865	1.40501
$176$	−4.44053	−0.334718
$177$	−0.418492	−0.0314558
$178$	−20.1706	−1.51185
$179$	−26.1042	−1.95112	−0.975559	−	0.219736i	$-0.929480\pi$
$179$	−26.1042	−1.95112	−0.975559	+	0.219736i	$0.929480\pi$
$180$	−0.143628	−0.0107054
$181$	3.16435	0.235204	0.117602	−	0.993061i	$-0.462479\pi$
$181$	3.16435	0.235204	0.117602	+	0.993061i	$0.462479\pi$
$182$	20.8048	1.54216
$183$	1.00000	0.0739221
$184$	−12.8891	−0.950198
$185$	5.32521	0.391517
$186$	−4.31692	−0.316532
$187$	7.75664	0.567222
$188$	0.873443	0.0637024
$189$	3.97554	0.289178
$190$	−1.33418	−0.0967917
$191$	−0.339788	−0.0245862	−0.0122931	−	0.999924i	$-0.503913\pi$
$191$	−0.339788	−0.0245862	−0.0122931	+	0.999924i	$0.503913\pi$
$192$	−6.75385	−0.487417
$193$	−10.9988	−0.791714	−0.395857	−	0.918312i	$-0.629552\pi$
$193$	−10.9988	−0.791714	−0.395857	+	0.918312i	$0.629552\pi$
$194$	−2.67005	−0.191698
$195$	−1.98737	−0.142319
$196$	2.21905	0.158503
$197$	13.6647	0.973571	0.486786	−	0.873522i	$-0.338169\pi$
$197$	13.6647	0.973571	0.486786	+	0.873522i	$0.338169\pi$
$198$	1.50067	0.106648
$199$	−5.05352	−0.358235	−0.179117	−	0.983828i	$-0.557324\pi$
$199$	−5.05352	−0.358235	−0.179117	+	0.983828i	$0.557324\pi$
$200$	12.2638	0.867179
$201$	−9.84375	−0.694324
$202$	−28.3679	−1.99596
$203$	−25.0331	−1.75698
$204$	−1.95486	−0.136868
$205$	−0.902827	−0.0630561
$206$	3.62865	0.252820
$207$	4.91362	0.341520
$208$	15.4852	1.07371
$209$	1.56002	0.107909
$210$	−3.40001	−0.234623
$211$	0.418379	0.0288024	0.0144012	−	0.999896i	$-0.495416\pi$
$211$	0.418379	0.0288024	0.0144012	+	0.999896i	$0.495416\pi$
$212$	2.72827	0.187378
$213$	−9.93167	−0.680507
$214$	16.1380	1.10317
$215$	−3.02803	−0.206510
$216$	2.62314	0.178482
$217$	−11.4362	−0.776342
$218$	−21.9438	−1.48622
$219$	−7.11859	−0.481030
$220$	−0.143628	−0.00968341
$221$	−27.0493	−1.81953
$222$	14.0225	0.941129
$223$	8.46953	0.567162	0.283581	−	0.958948i	$-0.408478\pi$
$223$	8.46953	0.567162	0.283581	+	0.958948i	$0.408478\pi$
$224$	5.63536	0.376528
$225$	−4.67522	−0.311681
$226$	−13.3373	−0.887187
$227$	−1.28958	−0.0855927	−0.0427963	−	0.999084i	$-0.513627\pi$
$227$	−1.28958	−0.0855927	−0.0427963	+	0.999084i	$0.513627\pi$
$228$	−0.393164	−0.0260379
$229$	18.0318	1.19157	0.595787	−	0.803143i	$-0.296840\pi$
$229$	18.0318	1.19157	0.595787	+	0.803143i	$0.296840\pi$
$230$	−4.20228	−0.277090
$231$	3.97554	0.261571
$232$	−16.5174	−1.08442
$233$	15.1799	0.994470	0.497235	−	0.867616i	$-0.334349\pi$
$233$	15.1799	0.994470	0.497235	+	0.867616i	$0.334349\pi$
$234$	−5.23321	−0.342106
$235$	−1.97510	−0.128841
$236$	0.105470	0.00686553
$237$	13.1270	0.852689
$238$	−46.2760	−2.99963
$239$	5.61796	0.363396	0.181698	−	0.983354i	$-0.441841\pi$
$239$	5.61796	0.363396	0.181698	+	0.983354i	$0.441841\pi$
$240$	−2.53065	−0.163353
$241$	−9.85967	−0.635117	−0.317559	−	0.948239i	$-0.602863\pi$
$241$	−9.85967	−0.635117	−0.317559	+	0.948239i	$0.602863\pi$
$242$	1.50067	0.0964670
$243$	−1.00000	−0.0641500
$244$	−0.252024	−0.0161342
$245$	−5.01789	−0.320581
$246$	−2.37735	−0.151574
$247$	−5.44018	−0.346150
$248$	−7.54587	−0.479163
$249$	−4.04331	−0.256235
$250$	8.27455	0.523329
$251$	31.0856	1.96210	0.981052	−	0.193743i	$-0.0620629\pi$
$251$	31.0856	1.96210	0.981052	+	0.193743i	$0.0620629\pi$
$252$	−1.00193	−0.0631158
$253$	4.91362	0.308916
$254$	−24.4027	−1.53116
$255$	4.42050	0.276822
$256$	5.95657	0.372286
$257$	−10.0493	−0.626855	−0.313428	−	0.949612i	$-0.601477\pi$
$257$	−10.0493	−0.626855	−0.313428	+	0.949612i	$0.601477\pi$
$258$	−7.97351	−0.496409
$259$	37.1480	2.30826
$260$	0.500866	0.0310624
$261$	6.29679	0.389761
$262$	25.1437	1.55338
$263$	19.8284	1.22267	0.611337	−	0.791370i	$-0.290632\pi$
$263$	19.8284	1.22267	0.611337	+	0.791370i	$0.290632\pi$
$264$	2.62314	0.161443
$265$	−6.16938	−0.378982
$266$	−9.30708	−0.570654
$267$	13.4410	0.822576
$268$	2.48086	0.151543
$269$	−11.7548	−0.716702	−0.358351	−	0.933587i	$-0.616661\pi$
$269$	−11.7548	−0.716702	−0.358351	+	0.933587i	$0.616661\pi$
$270$	0.855232	0.0520477
$271$	−19.0082	−1.15467	−0.577334	−	0.816508i	$-0.695907\pi$
$271$	−19.0082	−1.15467	−0.577334	+	0.816508i	$0.695907\pi$
$272$	−34.4436	−2.08845
$273$	−13.8636	−0.839066
$274$	32.5724	1.96777
$275$	−4.67522	−0.281926
$276$	−1.23835	−0.0745399
$277$	−27.7437	−1.66695	−0.833477	−	0.552553i	$-0.813654\pi$
$277$	−27.7437	−1.66695	−0.833477	+	0.552553i	$0.813654\pi$
$278$	14.8067	0.888050
$279$	2.87665	0.172221
$280$	−5.94313	−0.355170
$281$	−26.9692	−1.60885	−0.804424	−	0.594056i	$-0.797526\pi$
$281$	−26.9692	−1.60885	−0.804424	+	0.594056i	$0.797526\pi$
$282$	−5.20090	−0.309709
$283$	30.2378	1.79745	0.898725	−	0.438513i	$-0.144495\pi$
$283$	30.2378	1.79745	0.898725	+	0.438513i	$0.144495\pi$
$284$	2.50302	0.148527
$285$	0.889055	0.0526631
$286$	−5.23321	−0.309446
$287$	−6.29800	−0.371759
$288$	−1.41751	−0.0835275
$289$	43.1655	2.53915
$290$	−5.38521	−0.316230
$291$	1.77923	0.104300
$292$	1.79406	0.104989
$293$	6.99534	0.408672	0.204336	−	0.978901i	$-0.434496\pi$
$293$	6.99534	0.408672	0.204336	+	0.978901i	$0.434496\pi$
$294$	−13.2133	−0.770614
$295$	−0.238498	−0.0138859
$296$	24.5110	1.42467
$297$	−1.00000	−0.0580259
$298$	25.4261	1.47289
$299$	−17.1350	−0.990940
$300$	1.17827	0.0680273
$301$	−21.1232	−1.21752
$302$	24.8187	1.42816
$303$	18.9035	1.08597
$304$	−6.92734	−0.397310
$305$	0.569898	0.0326323
$306$	11.6402	0.665426
$307$	7.80207	0.445288	0.222644	−	0.974900i	$-0.428531\pi$
$307$	7.80207	0.445288	0.222644	+	0.974900i	$0.428531\pi$
$308$	−1.00193	−0.0570904
$309$	−2.41802	−0.137556
$310$	−2.46020	−0.139730
$311$	−1.36849	−0.0775998	−0.0387999	−	0.999247i	$-0.512353\pi$
$311$	−1.36849	−0.0775998	−0.0387999	+	0.999247i	$0.512353\pi$
$312$	−9.14753	−0.517877
$313$	−5.14485	−0.290804	−0.145402	−	0.989373i	$-0.546448\pi$
$313$	−5.14485	−0.290804	−0.145402	+	0.989373i	$0.546448\pi$
$314$	26.8330	1.51427
$315$	2.26565	0.127655
$316$	−3.30832	−0.186107
$317$	30.3916	1.70696	0.853482	−	0.521122i	$-0.174486\pi$
$317$	30.3916	1.70696	0.853482	+	0.521122i	$0.174486\pi$
$318$	−16.2454	−0.910998
$319$	6.29679	0.352552
$320$	−3.84900	−0.215166
$321$	−10.7538	−0.600220
$322$	−29.3146	−1.63364
$323$	12.1006	0.673293
$324$	0.252024	0.0140014
$325$	16.3036	0.904361
$326$	−1.28310	−0.0710645
$327$	14.6227	0.808634
$328$	−4.15555	−0.229452
$329$	−13.7781	−0.759609
$330$	0.855232	0.0470790
$331$	17.3933	0.956024	0.478012	−	0.878353i	$-0.341357\pi$
$331$	17.3933	0.956024	0.478012	+	0.878353i	$0.341357\pi$
$332$	1.01901	0.0559256
$333$	−9.34414	−0.512056
$334$	20.1242	1.10115
$335$	−5.60993	−0.306503
$336$	−17.6535	−0.963077
$337$	3.38221	0.184241	0.0921203	−	0.995748i	$-0.470636\pi$
$337$	3.38221	0.184241	0.0921203	+	0.995748i	$0.470636\pi$
$338$	−1.25931	−0.0684972
$339$	8.88757	0.482706
$340$	−1.11407	−0.0604191
$341$	2.87665	0.155779
$342$	2.34109	0.126592
$343$	−7.17541	−0.387436
$344$	−13.9375	−0.751460
$345$	2.80026	0.150761
$346$	−13.5634	−0.729171
$347$	22.0213	1.18217	0.591084	−	0.806610i	$-0.298700\pi$
$347$	22.0213	1.18217	0.591084	+	0.806610i	$0.298700\pi$
$348$	−1.58694	−0.0850691
$349$	−6.15318	−0.329372	−0.164686	−	0.986346i	$-0.552661\pi$
$349$	−6.15318	−0.329372	−0.164686	+	0.986346i	$0.552661\pi$
$350$	27.8923	1.49090
$351$	3.48724	0.186135
$352$	−1.41751	−0.0755535
$353$	−2.81549	−0.149853	−0.0749267	−	0.997189i	$-0.523872\pi$
$353$	−2.81549	−0.149853	−0.0749267	+	0.997189i	$0.523872\pi$
$354$	−0.628021	−0.0333789
$355$	−5.66004	−0.300404
$356$	−3.38746	−0.179535
$357$	30.8368	1.63206
$358$	−39.1739	−2.07040
$359$	−19.3450	−1.02099	−0.510494	−	0.859881i	$-0.670537\pi$
$359$	−19.3450	−1.02099	−0.510494	+	0.859881i	$0.670537\pi$
$360$	1.49492	0.0787894
$361$	−16.5663	−0.871912
$362$	4.74865	0.249584
$363$	−1.00000	−0.0524864
$364$	3.49398	0.183134
$365$	−4.05687	−0.212346
$366$	1.50067	0.0784415
$367$	9.48578	0.495154	0.247577	−	0.968868i	$-0.420366\pi$
$367$	9.48578	0.495154	0.247577	+	0.968868i	$0.420366\pi$
$368$	−21.8191	−1.13740
$369$	1.58419	0.0824696
$370$	7.99140	0.415453
$371$	−43.0368	−2.23436
$372$	−0.724986	−0.0375888
$373$	−28.1396	−1.45701	−0.728507	−	0.685038i	$-0.759785\pi$
$373$	−28.1396	−1.45701	−0.728507	+	0.685038i	$0.759785\pi$
$374$	11.6402	0.601900
$375$	−5.51389	−0.284736
$376$	−9.09105	−0.468835
$377$	−21.9584	−1.13092
$378$	5.96599	0.306857
$379$	−28.6718	−1.47277	−0.736386	−	0.676561i	$-0.763469\pi$
$379$	−28.6718	−1.47277	−0.736386	+	0.676561i	$0.763469\pi$
$380$	−0.224063	−0.0114942
$381$	16.2612	0.833085
$382$	−0.509911	−0.0260893
$383$	−35.9467	−1.83679	−0.918395	−	0.395666i	$-0.870514\pi$
$383$	−35.9467	−1.83679	−0.918395	+	0.395666i	$0.870514\pi$
$384$	−12.9703	−0.661890
$385$	2.26565	0.115468
$386$	−16.5057	−0.840118
$387$	5.31329	0.270090
$388$	−0.448409	−0.0227645
$389$	−36.5774	−1.85455	−0.927274	−	0.374383i	$-0.877855\pi$
$389$	−36.5774	−1.85455	−0.927274	+	0.374383i	$0.877855\pi$
$390$	−2.98240	−0.151020
$391$	38.1132	1.92747
$392$	−23.0965	−1.16655
$393$	−16.7549	−0.845175
$394$	20.5063	1.03309
$395$	7.48104	0.376412
$396$	0.252024	0.0126647
$397$	17.4290	0.874738	0.437369	−	0.899282i	$-0.355910\pi$
$397$	17.4290	0.874738	0.437369	+	0.899282i	$0.355910\pi$
$398$	−7.58370	−0.380136
$399$	6.20193	0.310485
$400$	20.7604	1.03802
$401$	−28.3816	−1.41731	−0.708655	−	0.705556i	$-0.750697\pi$
$401$	−28.3816	−1.41731	−0.708655	+	0.705556i	$0.750697\pi$
$402$	−14.7723	−0.736773
$403$	−10.0316	−0.499708
$404$	−4.76413	−0.237024
$405$	−0.569898	−0.0283185
$406$	−37.5665	−1.86440
$407$	−9.34414	−0.463172
$408$	20.3468	1.00732
$409$	27.6614	1.36777	0.683883	−	0.729592i	$-0.260290\pi$
$409$	27.6614	1.36777	0.683883	+	0.729592i	$0.260290\pi$
$410$	−1.35485	−0.0669112
$411$	−21.7052	−1.07064
$412$	0.609399	0.0300229
$413$	−1.66373	−0.0818669
$414$	7.37374	0.362399
$415$	−2.30428	−0.113113
$416$	4.94319	0.242360
$417$	−9.86673	−0.483176
$418$	2.34109	0.114506
$419$	−1.14196	−0.0557883	−0.0278942	−	0.999611i	$-0.508880\pi$
$419$	−1.14196	−0.0557883	−0.0278942	+	0.999611i	$0.508880\pi$
$420$	−0.570999	−0.0278619
$421$	5.24502	0.255627	0.127813	−	0.991798i	$-0.459204\pi$
$421$	5.24502	0.255627	0.127813	+	0.991798i	$0.459204\pi$
$422$	0.627850	0.0305633
$423$	3.46571	0.168509
$424$	−28.3966	−1.37906
$425$	−36.2640	−1.75906
$426$	−14.9042	−0.722111
$427$	3.97554	0.192390
$428$	2.71022	0.131004
$429$	3.48724	0.168366
$430$	−4.54409	−0.219136
$431$	39.7537	1.91487	0.957434	−	0.288651i	$-0.0932068\pi$
$431$	39.7537	1.91487	0.957434	+	0.288651i	$0.0932068\pi$
$432$	4.44053	0.213645
$433$	−22.4352	−1.07817	−0.539084	−	0.842252i	$-0.681229\pi$
$433$	−22.4352	−1.07817	−0.539084	+	0.842252i	$0.681229\pi$
$434$	−17.1621	−0.823806
$435$	3.58853	0.172057
$436$	−3.68526	−0.176492
$437$	7.66536	0.366684
$438$	−10.6827	−0.510439
$439$	−5.46960	−0.261050	−0.130525	−	0.991445i	$-0.541666\pi$
$439$	−5.46960	−0.261050	−0.130525	+	0.991445i	$0.541666\pi$
$440$	1.49492	0.0712677
$441$	8.80489	0.419280
$442$	−40.5922	−1.93077
$443$	−4.21494	−0.200258	−0.100129	−	0.994974i	$-0.531926\pi$
$443$	−4.21494	−0.200258	−0.100129	+	0.994974i	$0.531926\pi$
$444$	2.35495	0.111761
$445$	7.66000	0.363119
$446$	12.7100	0.601837
$447$	−16.9431	−0.801381
$448$	−26.8502	−1.26855
$449$	23.8577	1.12592	0.562958	−	0.826485i	$-0.309663\pi$
$449$	23.8577	1.12592	0.562958	+	0.826485i	$0.309663\pi$
$450$	−7.01598	−0.330736
$451$	1.58419	0.0745966
$452$	−2.23988	−0.105355
$453$	−16.5384	−0.777041
$454$	−1.93525	−0.0908256
$455$	−7.90087	−0.370398
$456$	4.09217	0.191633
$457$	35.7911	1.67424	0.837119	−	0.547021i	$-0.184238\pi$
$457$	35.7911	1.67424	0.837119	+	0.547021i	$0.184238\pi$
$458$	27.0598	1.26442
$459$	−7.75664	−0.362049
$460$	−0.705734	−0.0329050
$461$	33.0708	1.54026	0.770131	−	0.637886i	$-0.220191\pi$
$461$	33.0708	1.54026	0.770131	+	0.637886i	$0.220191\pi$
$462$	5.96599	0.277563
$463$	−30.1684	−1.40205	−0.701023	−	0.713139i	$-0.747273\pi$
$463$	−30.1684	−1.40205	−0.701023	+	0.713139i	$0.747273\pi$
$464$	−27.9611	−1.29806
$465$	1.63940	0.0760253
$466$	22.7801	1.05527
$467$	13.3041	0.615642	0.307821	−	0.951444i	$-0.400400\pi$
$467$	13.3041	0.615642	0.307821	+	0.951444i	$0.400400\pi$
$468$	−0.878869	−0.0406257
$469$	−39.1342	−1.80705
$470$	−2.96399	−0.136718
$471$	−17.8806	−0.823896
$472$	−1.09777	−0.0505287
$473$	5.31329	0.244305
$474$	19.6993	0.904820
$475$	−7.29345	−0.334646
$476$	−7.77163	−0.356212
$477$	10.8254	0.495662
$478$	8.43073	0.385613
$479$	36.2381	1.65576	0.827881	−	0.560904i	$-0.189546\pi$
$479$	36.2381	1.65576	0.827881	+	0.560904i	$0.189546\pi$
$480$	−0.807836	−0.0368725
$481$	32.5852	1.48576
$482$	−14.7962	−0.673947
$483$	19.5343	0.888839
$484$	0.252024	0.0114557
$485$	1.01398	0.0460425
$486$	−1.50067	−0.0680720
$487$	4.94148	0.223920	0.111960	−	0.993713i	$-0.464287\pi$
$487$	4.94148	0.223920	0.111960	+	0.993713i	$0.464287\pi$
$488$	2.62314	0.118744
$489$	0.855017	0.0386652
$490$	−7.53022	−0.340181
$491$	−14.0150	−0.632489	−0.316245	−	0.948678i	$-0.602422\pi$
$491$	−14.0150	−0.632489	−0.316245	+	0.948678i	$0.602422\pi$
$492$	−0.399254	−0.0179998
$493$	48.8419	2.19973
$494$	−8.16394	−0.367313
$495$	−0.569898	−0.0256150
$496$	−12.7739	−0.573563
$497$	−39.4837	−1.77109
$498$	−6.06770	−0.271900
$499$	15.0317	0.672913	0.336456	−	0.941699i	$-0.390772\pi$
$499$	15.0317	0.672913	0.336456	+	0.941699i	$0.390772\pi$
$500$	1.38963	0.0621463
$501$	−13.4101	−0.599118
$502$	46.6493	2.08206
$503$	−4.69369	−0.209281	−0.104641	−	0.994510i	$-0.533369\pi$
$503$	−4.69369	−0.209281	−0.104641	+	0.994510i	$0.533369\pi$
$504$	10.4284	0.464518
$505$	10.7730	0.479394
$506$	7.37374	0.327803
$507$	0.839160	0.0372684
$508$	−4.09821	−0.181829
$509$	2.29316	0.101643	0.0508214	−	0.998708i	$-0.483816\pi$
$509$	2.29316	0.101643	0.0508214	+	0.998708i	$0.483816\pi$
$510$	6.63373	0.293746
$511$	−28.3002	−1.25193
$512$	−17.0018	−0.751381
$513$	−1.56002	−0.0688767
$514$	−15.0807	−0.665179
$515$	−1.37802	−0.0607229
$516$	−1.33908	−0.0589496
$517$	3.46571	0.152422
$518$	55.7470	2.44938
$519$	9.03817	0.396732
$520$	−5.21316	−0.228612
$521$	6.53621	0.286356	0.143178	−	0.989697i	$-0.454268\pi$
$521$	6.53621	0.286356	0.143178	+	0.989697i	$0.454268\pi$
$522$	9.44943	0.413590
$523$	28.4759	1.24516	0.622582	−	0.782554i	$-0.286084\pi$
$523$	28.4759	1.24516	0.622582	+	0.782554i	$0.286084\pi$
$524$	4.22265	0.184467
$525$	−18.5865	−0.811181
$526$	29.7560	1.29742
$527$	22.3132	0.971977
$528$	4.44053	0.193249
$529$	1.14362	0.0497224
$530$	−9.25824	−0.402152
$531$	0.418492	0.0181610
$532$	−1.56304	−0.0677663
$533$	−5.52445	−0.239290
$534$	20.1706	0.872866
$535$	−6.12858	−0.264962
$536$	−25.8215	−1.11532
$537$	26.1042	1.12648
$538$	−17.6401	−0.760519
$539$	8.80489	0.379253
$540$	0.143628	0.00618077
$541$	−22.4670	−0.965931	−0.482965	−	0.875640i	$-0.660440\pi$
$541$	−22.4670	−0.965931	−0.482965	+	0.875640i	$0.660440\pi$
$542$	−28.5252	−1.22526
$543$	−3.16435	−0.135795
$544$	−10.9951	−0.471412
$545$	8.33342	0.356965
$546$	−20.8048	−0.890364
$547$	−21.9796	−0.939779	−0.469889	−	0.882725i	$-0.655706\pi$
$547$	−21.9796	−0.939779	−0.469889	+	0.882725i	$0.655706\pi$
$548$	5.47023	0.233677
$549$	−1.00000	−0.0426790
$550$	−7.01598	−0.299162
$551$	9.82314	0.418480
$552$	12.8891	0.548597
$553$	52.1868	2.21921
$554$	−41.6342	−1.76887
$555$	−5.32521	−0.226042
$556$	2.48665	0.105458
$557$	−0.280608	−0.0118897	−0.00594487	−	0.999982i	$-0.501892\pi$
$557$	−0.280608	−0.0118897	−0.00594487	+	0.999982i	$0.501892\pi$
$558$	4.31692	0.182750
$559$	−18.5287	−0.783681
$560$	−10.0607	−0.425142
$561$	−7.75664	−0.327486
$562$	−40.4720	−1.70721
$563$	5.01496	0.211355	0.105678	−	0.994400i	$-0.466299\pi$
$563$	5.01496	0.211355	0.105678	+	0.994400i	$0.466299\pi$
$564$	−0.873443	−0.0367786
$565$	5.06501	0.213087
$566$	45.3771	1.90734
$567$	−3.97554	−0.166957
$568$	−26.0522	−1.09313
$569$	−0.592920	−0.0248565	−0.0124282	−	0.999923i	$-0.503956\pi$
$569$	−0.592920	−0.0248565	−0.0124282	+	0.999923i	$0.503956\pi$
$570$	1.33418	0.0558827
$571$	0.318940	0.0133472	0.00667360	−	0.999978i	$-0.497876\pi$
$571$	0.318940	0.0133472	0.00667360	+	0.999978i	$0.497876\pi$
$572$	−0.878869	−0.0367474
$573$	0.339788	0.0141948
$574$	−9.45125	−0.394488
$575$	−22.9722	−0.958008
$576$	6.75385	0.281410
$577$	36.7863	1.53143	0.765716	−	0.643179i	$-0.222385\pi$
$577$	36.7863	1.53143	0.765716	+	0.643179i	$0.222385\pi$
$578$	64.7774	2.69439
$579$	10.9988	0.457097
$580$	−0.904396	−0.0375530
$581$	−16.0743	−0.666876
$582$	2.67005	0.110677
$583$	10.8254	0.448343
$584$	−18.6731	−0.772698
$585$	1.98737	0.0821677
$586$	10.4977	0.433657
$587$	35.9317	1.48306	0.741530	−	0.670920i	$-0.234101\pi$
$587$	35.9317	1.48306	0.741530	+	0.670920i	$0.234101\pi$
$588$	−2.21905	−0.0915119
$589$	4.48765	0.184910
$590$	−0.357908	−0.0147348
$591$	−13.6647	−0.562092
$592$	41.4929	1.70535
$593$	5.63179	0.231270	0.115635	−	0.993292i	$-0.463110\pi$
$593$	5.63179	0.231270	0.115635	+	0.993292i	$0.463110\pi$
$594$	−1.50067	−0.0615734
$595$	17.5739	0.720458
$596$	4.27008	0.174909
$597$	5.05352	0.206827
$598$	−25.7140	−1.05152
$599$	−25.5479	−1.04386	−0.521929	−	0.852989i	$-0.674787\pi$
$599$	−25.5479	−1.04386	−0.521929	+	0.852989i	$0.674787\pi$
$600$	−12.2638	−0.500666
$601$	39.1627	1.59748	0.798741	−	0.601675i	$-0.205500\pi$
$601$	39.1627	1.59748	0.798741	+	0.601675i	$0.205500\pi$
$602$	−31.6990	−1.29195
$603$	9.84375	0.400868
$604$	4.16807	0.169597
$605$	−0.569898	−0.0231697
$606$	28.3679	1.15237
$607$	8.19398	0.332583	0.166292	−	0.986077i	$-0.446821\pi$
$607$	8.19398	0.332583	0.166292	+	0.986077i	$0.446821\pi$
$608$	−2.21135	−0.0896820
$609$	25.0331	1.01439
$610$	0.855232	0.0346273
$611$	−12.0858	−0.488938
$612$	1.95486	0.0790207
$613$	29.6138	1.19609	0.598046	−	0.801462i	$-0.295944\pi$
$613$	29.6138	1.19609	0.598046	+	0.801462i	$0.295944\pi$
$614$	11.7084	0.472511
$615$	0.902827	0.0364055
$616$	10.4284	0.420172
$617$	24.1413	0.971894	0.485947	−	0.873988i	$-0.338475\pi$
$617$	24.1413	0.971894	0.485947	+	0.873988i	$0.338475\pi$
$618$	−3.62865	−0.145966
$619$	−15.2803	−0.614168	−0.307084	−	0.951682i	$-0.599353\pi$
$619$	−15.2803	−0.614168	−0.307084	+	0.951682i	$0.599353\pi$
$620$	−0.413168	−0.0165932
$621$	−4.91362	−0.197177
$622$	−2.05365	−0.0823440
$623$	53.4352	2.14084
$624$	−15.4852	−0.619904
$625$	20.2337	0.809349
$626$	−7.72075	−0.308583
$627$	−1.56002	−0.0623014
$628$	4.50635	0.179823
$629$	−72.4791	−2.88993
$630$	3.40001	0.135459
$631$	−25.2273	−1.00428	−0.502142	−	0.864785i	$-0.667454\pi$
$631$	−25.2273	−1.00428	−0.502142	+	0.864785i	$0.667454\pi$
$632$	34.4339	1.36971
$633$	−0.418379	−0.0166291
$634$	45.6080	1.81132
$635$	9.26722	0.367758
$636$	−2.72827	−0.108183
$637$	−30.7048	−1.21657
$638$	9.44943	0.374106
$639$	9.93167	0.392891
$640$	−7.39177	−0.292186
$641$	−11.1758	−0.441417	−0.220709	−	0.975340i	$-0.570837\pi$
$641$	−11.1758	−0.441417	−0.220709	+	0.975340i	$0.570837\pi$
$642$	−16.1380	−0.636916
$643$	33.0083	1.30172	0.650861	−	0.759197i	$-0.274408\pi$
$643$	33.0083	1.30172	0.650861	+	0.759197i	$0.274408\pi$
$644$	−4.92311	−0.193998
$645$	3.02803	0.119229
$646$	18.1590	0.714456
$647$	−10.2919	−0.404616	−0.202308	−	0.979322i	$-0.564844\pi$
$647$	−10.2919	−0.404616	−0.202308	+	0.979322i	$0.564844\pi$
$648$	−2.62314	−0.103047
$649$	0.418492	0.0164273
$650$	24.4664	0.959651
$651$	11.4362	0.448221
$652$	−0.215485	−0.00843905
$653$	−8.56890	−0.335327	−0.167664	−	0.985844i	$-0.553622\pi$
$653$	−8.56890	−0.335327	−0.167664	+	0.985844i	$0.553622\pi$
$654$	21.9438	0.858072
$655$	−9.54861	−0.373095
$656$	−7.03464	−0.274657
$657$	7.11859	0.277723
$658$	−20.6764	−0.806049
$659$	0.185337	0.00721972	0.00360986	−	0.999993i	$-0.498851\pi$
$659$	0.185337	0.00721972	0.00360986	+	0.999993i	$0.498851\pi$
$660$	0.143628	0.00559072
$661$	6.58896	0.256281	0.128141	−	0.991756i	$-0.459099\pi$
$661$	6.58896	0.256281	0.128141	+	0.991756i	$0.459099\pi$
$662$	26.1017	1.01447
$663$	27.0493	1.05051
$664$	−10.6062	−0.411600
$665$	3.53447	0.137061
$666$	−14.0225	−0.543361
$667$	30.9400	1.19800
$668$	3.37967	0.130763
$669$	−8.46953	−0.327451
$670$	−8.41868	−0.325242
$671$	−1.00000	−0.0386046
$672$	−5.63536	−0.217389
$673$	32.8732	1.26717	0.633584	−	0.773674i	$-0.281583\pi$
$673$	32.8732	1.26717	0.633584	+	0.773674i	$0.281583\pi$
$674$	5.07559	0.195505
$675$	4.67522	0.179949
$676$	−0.211489	−0.00813418
$677$	−49.0282	−1.88431	−0.942154	−	0.335181i	$-0.891203\pi$
$677$	−49.0282	−1.88431	−0.942154	+	0.335181i	$0.891203\pi$
$678$	13.3373	0.512218
$679$	7.07339	0.271452
$680$	11.5956	0.444671
$681$	1.28958	0.0494170
$682$	4.31692	0.165303
$683$	−24.9821	−0.955912	−0.477956	−	0.878384i	$-0.658622\pi$
$683$	−24.9821	−0.955912	−0.477956	+	0.878384i	$0.658622\pi$
$684$	0.393164	0.0150330
$685$	−12.3697	−0.472623
$686$	−10.7680	−0.411122
$687$	−18.0318	−0.687955
$688$	−23.5938	−0.899506
$689$	−37.7508	−1.43819
$690$	4.20228	0.159978
$691$	8.91705	0.339221	0.169610	−	0.985511i	$-0.445749\pi$
$691$	8.91705	0.339221	0.169610	+	0.985511i	$0.445749\pi$
$692$	−2.27784	−0.0865905
$693$	−3.97554	−0.151018
$694$	33.0469	1.25444
$695$	−5.62303	−0.213294
$696$	16.5174	0.626089
$697$	12.2880	0.465441
$698$	−9.23392	−0.349509
$699$	−15.1799	−0.574158
$700$	4.68425	0.177048
$701$	−19.3770	−0.731861	−0.365930	−	0.930642i	$-0.619249\pi$
$701$	−19.3770	−0.731861	−0.365930	+	0.930642i	$0.619249\pi$
$702$	5.23321	0.197515
$703$	−14.5771	−0.549785
$704$	6.75385	0.254545
$705$	1.97510	0.0743866
$706$	−4.22513	−0.159015
$707$	75.1514	2.82636
$708$	−0.105470	−0.00396382
$709$	−31.7098	−1.19089	−0.595444	−	0.803397i	$-0.703024\pi$
$709$	−31.7098	−1.19089	−0.595444	+	0.803397i	$0.703024\pi$
$710$	−8.49388	−0.318770
$711$	−13.1270	−0.492300
$712$	35.2577	1.32134
$713$	14.1348	0.529351
$714$	46.2760	1.73184
$715$	1.98737	0.0743235
$716$	−6.57889	−0.245865
$717$	−5.61796	−0.209807
$718$	−29.0305	−1.08341
$719$	−29.9033	−1.11521	−0.557603	−	0.830108i	$-0.688279\pi$
$719$	−29.9033	−1.11521	−0.557603	+	0.830108i	$0.688279\pi$
$720$	2.53065	0.0943118
$721$	−9.61291	−0.358003
$722$	−24.8607	−0.925218
$723$	9.85967	0.366685
$724$	0.797492	0.0296386
$725$	−29.4388	−1.09333
$726$	−1.50067	−0.0556953
$727$	−11.3206	−0.419859	−0.209930	−	0.977717i	$-0.567323\pi$
$727$	−11.3206	−0.419859	−0.209930	+	0.977717i	$0.567323\pi$
$728$	−36.3663	−1.34783
$729$	1.00000	0.0370370
$730$	−6.08805	−0.225329
$731$	41.2133	1.52433
$732$	0.252024	0.00931509
$733$	46.5548	1.71954	0.859771	−	0.510680i	$-0.170606\pi$
$733$	46.5548	1.71954	0.859771	+	0.510680i	$0.170606\pi$
$734$	14.2351	0.525426
$735$	5.01789	0.185088
$736$	−6.96509	−0.256737
$737$	9.84375	0.362599
$738$	2.37735	0.0875116
$739$	3.40428	0.125229	0.0626143	−	0.998038i	$-0.480056\pi$
$739$	3.40428	0.125229	0.0626143	+	0.998038i	$0.480056\pi$
$740$	1.34208	0.0493359
$741$	5.44018	0.199850
$742$	−64.5843	−2.37096
$743$	3.46368	0.127070	0.0635350	−	0.997980i	$-0.479763\pi$
$743$	3.46368	0.127070	0.0635350	+	0.997980i	$0.479763\pi$
$744$	7.54587	0.276645
$745$	−9.65585	−0.353763
$746$	−42.2284	−1.54609
$747$	4.04331	0.147937
$748$	1.95486	0.0714769
$749$	−42.7522	−1.56213
$750$	−8.27455	−0.302144
$751$	−1.89930	−0.0693065	−0.0346532	−	0.999399i	$-0.511033\pi$
$751$	−1.89930	−0.0693065	−0.0346532	+	0.999399i	$0.511033\pi$
$752$	−15.3896	−0.561201
$753$	−31.0856	−1.13282
$754$	−32.9524	−1.20006
$755$	−9.42519	−0.343018
$756$	1.00193	0.0364399
$757$	8.67210	0.315193	0.157596	−	0.987504i	$-0.449626\pi$
$757$	8.67210	0.315193	0.157596	+	0.987504i	$0.449626\pi$
$758$	−43.0271	−1.56281
$759$	−4.91362	−0.178353
$760$	2.33212	0.0845948
$761$	37.5110	1.35977	0.679887	−	0.733317i	$-0.262029\pi$
$761$	37.5110	1.35977	0.679887	+	0.733317i	$0.262029\pi$
$762$	24.4027	0.884018
$763$	58.1329	2.10455
$764$	−0.0856348	−0.00309816
$765$	−4.42050	−0.159823
$766$	−53.9443	−1.94909
$767$	−1.45938	−0.0526953
$768$	−5.95657	−0.214939
$769$	−30.1552	−1.08743	−0.543713	−	0.839271i	$-0.682982\pi$
$769$	−30.1552	−1.08743	−0.543713	+	0.839271i	$0.682982\pi$
$770$	3.40001	0.122528
$771$	10.0493	0.361915
$772$	−2.77198	−0.0997656
$773$	−23.2997	−0.838031	−0.419015	−	0.907979i	$-0.637625\pi$
$773$	−23.2997	−0.838031	−0.419015	+	0.907979i	$0.637625\pi$
$774$	7.97351	0.286602
$775$	−13.4490	−0.483101
$776$	4.66717	0.167542
$777$	−37.1480	−1.33268
$778$	−54.8908	−1.96793
$779$	2.47137	0.0885461
$780$	−0.500866	−0.0179339
$781$	9.93167	0.355383
$782$	57.1955	2.04531
$783$	−6.29679	−0.225029
$784$	−39.0984	−1.39637
$785$	−10.1901	−0.363702
$786$	−25.1437	−0.896847
$787$	51.3754	1.83134	0.915668	−	0.401936i	$-0.131663\pi$
$787$	51.3754	1.83134	0.915668	+	0.401936i	$0.131663\pi$
$788$	3.44384	0.122682
$789$	−19.8284	−0.705911
$790$	11.2266	0.399425
$791$	35.3329	1.25629
$792$	−2.62314	−0.0932093
$793$	3.48724	0.123836
$794$	26.1553	0.928217
$795$	6.16938	0.218806
$796$	−1.27361	−0.0451419
$797$	17.7177	0.627593	0.313796	−	0.949490i	$-0.398399\pi$
$797$	17.7177	0.627593	0.313796	+	0.949490i	$0.398399\pi$
$798$	9.30708	0.329467
$799$	26.8823	0.951027
$800$	6.62716	0.234305
$801$	−13.4410	−0.474914
$802$	−42.5915	−1.50396
$803$	7.11859	0.251210
$804$	−2.48086	−0.0874933
$805$	11.1325	0.392370
$806$	−15.0541	−0.530259
$807$	11.7548	0.413788
$808$	49.5864	1.74445
$809$	16.0592	0.564612	0.282306	−	0.959324i	$-0.408901\pi$
$809$	16.0592	0.564612	0.282306	+	0.959324i	$0.408901\pi$
$810$	−0.855232	−0.0300498
$811$	−12.0185	−0.422028	−0.211014	−	0.977483i	$-0.567677\pi$
$811$	−12.0185	−0.422028	−0.211014	+	0.977483i	$0.567677\pi$
$812$	−6.30895	−0.221401
$813$	19.0082	0.666648
$814$	−14.0225	−0.491489
$815$	0.487273	0.0170684
$816$	34.4436	1.20577
$817$	8.28885	0.289990
$818$	41.5107	1.45139
$819$	13.8636	0.484435
$820$	−0.227534	−0.00794584
$821$	−12.6542	−0.441636	−0.220818	−	0.975315i	$-0.570873\pi$
$821$	−12.6542	−0.441636	−0.220818	+	0.975315i	$0.570873\pi$
$822$	−32.5724	−1.13609
$823$	−0.0537888	−0.00187496	−0.000937480	−	1.00000i	$-0.500298\pi$
$823$	−0.0537888	−0.00187496	−0.000937480		1.00000i	$0.500298\pi$
$824$	−6.34280	−0.220962
$825$	4.67522	0.162770
$826$	−2.49672	−0.0868720
$827$	−31.9496	−1.11100	−0.555498	−	0.831518i	$-0.687472\pi$
$827$	−31.9496	−1.11100	−0.555498	+	0.831518i	$0.687472\pi$
$828$	1.23835	0.0430357
$829$	35.7815	1.24274	0.621372	−	0.783516i	$-0.286576\pi$
$829$	35.7815	1.24274	0.621372	+	0.783516i	$0.286576\pi$
$830$	−3.45797	−0.120028
$831$	27.7437	0.962417
$832$	−23.5523	−0.816528
$833$	68.2964	2.36633
$834$	−14.8067	−0.512716
$835$	−7.64238	−0.264476
$836$	0.393164	0.0135979
$837$	−2.87665	−0.0994316
$838$	−1.71371	−0.0591990
$839$	6.85181	0.236551	0.118275	−	0.992981i	$-0.462263\pi$
$839$	6.85181	0.236551	0.118275	+	0.992981i	$0.462263\pi$
$840$	5.94313	0.205057
$841$	10.6495	0.367224
$842$	7.87107	0.271255
$843$	26.9692	0.928869
$844$	0.105442	0.00362945
$845$	0.478236	0.0164518
$846$	5.20090	0.178811
$847$	−3.97554	−0.136601
$848$	−48.0706	−1.65075
$849$	−30.2378	−1.03776
$850$	−54.4204	−1.86661
$851$	−45.9135	−1.57389
$852$	−2.50302	−0.0857521
$853$	−42.9971	−1.47219	−0.736096	−	0.676877i	$-0.763333\pi$
$853$	−42.9971	−1.47219	−0.736096	+	0.676877i	$0.763333\pi$
$854$	5.96599	0.204152
$855$	−0.889055	−0.0304050
$856$	−28.2088	−0.964157
$857$	−3.32058	−0.113429	−0.0567145	−	0.998390i	$-0.518062\pi$
$857$	−3.32058	−0.113429	−0.0567145	+	0.998390i	$0.518062\pi$
$858$	5.23321	0.178659
$859$	46.4438	1.58464	0.792321	−	0.610105i	$-0.208873\pi$
$859$	46.4438	1.58464	0.792321	+	0.610105i	$0.208873\pi$
$860$	−0.763138	−0.0260228
$861$	6.29800	0.214635
$862$	59.6574	2.03194
$863$	11.1536	0.379672	0.189836	−	0.981816i	$-0.439204\pi$
$863$	11.1536	0.379672	0.189836	+	0.981816i	$0.439204\pi$
$864$	1.41751	0.0482246
$865$	5.15084	0.175134
$866$	−33.6679	−1.14408
$867$	−43.1655	−1.46598
$868$	−2.88221	−0.0978286
$869$	−13.1270	−0.445302
$870$	5.38521	0.182576
$871$	−34.3275	−1.16314
$872$	38.3573	1.29894
$873$	−1.77923	−0.0602178
$874$	11.5032	0.389102
$875$	−21.9207	−0.741054
$876$	−1.79406	−0.0606156
$877$	−29.0494	−0.980929	−0.490464	−	0.871461i	$-0.663173\pi$
$877$	−29.0494	−0.980929	−0.490464	+	0.871461i	$0.663173\pi$
$878$	−8.20810	−0.277010
$879$	−6.99534	−0.235947
$880$	2.53065	0.0853082
$881$	−21.4381	−0.722269	−0.361134	−	0.932514i	$-0.617610\pi$
$881$	−21.4381	−0.722269	−0.361134	+	0.932514i	$0.617610\pi$
$882$	13.2133	0.444914
$883$	−35.2149	−1.18508	−0.592538	−	0.805542i	$-0.701874\pi$
$883$	−35.2149	−1.18508	−0.592538	+	0.805542i	$0.701874\pi$
$884$	−6.81708	−0.229283
$885$	0.238498	0.00801703
$886$	−6.32525	−0.212501
$887$	41.4951	1.39327	0.696635	−	0.717426i	$-0.254680\pi$
$887$	41.4951	1.39327	0.696635	+	0.717426i	$0.254680\pi$
$888$	−24.5110	−0.822535
$889$	64.6469	2.16819
$890$	11.4952	0.385319
$891$	1.00000	0.0335013
$892$	2.13453	0.0714693
$893$	5.40659	0.180925
$894$	−25.4261	−0.850376
$895$	14.8767	0.497274
$896$	−51.5641	−1.72263
$897$	17.1350	0.572119
$898$	35.8027	1.19475
$899$	18.1137	0.604124
$900$	−1.17827	−0.0392756
$901$	83.9689	2.79741
$902$	2.37735	0.0791572
$903$	21.1232	0.702935
$904$	23.3134	0.775391
$905$	−1.80336	−0.0599456
$906$	−24.8187	−0.824547
$907$	−21.7745	−0.723009	−0.361505	−	0.932370i	$-0.617737\pi$
$907$	−21.7745	−0.723009	−0.361505	+	0.932370i	$0.617737\pi$
$908$	−0.325007	−0.0107857
$909$	−18.9035	−0.626988
$910$	−11.8566	−0.393044
$911$	26.9675	0.893472	0.446736	−	0.894666i	$-0.352586\pi$
$911$	26.9675	0.893472	0.446736	+	0.894666i	$0.352586\pi$
$912$	6.92734	0.229387
$913$	4.04331	0.133814
$914$	53.7108	1.77660
$915$	−0.569898	−0.0188403
$916$	4.54445	0.150153
$917$	−66.6099	−2.19965
$918$	−11.6402	−0.384184
$919$	25.4015	0.837917	0.418958	−	0.908005i	$-0.362395\pi$
$919$	25.4015	0.837917	0.418958	+	0.908005i	$0.362395\pi$
$920$	7.34548	0.242173
$921$	−7.80207	−0.257087
$922$	49.6285	1.63443
$923$	−34.6341	−1.14000
$924$	1.00193	0.0329611
$925$	43.6859	1.43638
$926$	−45.2730	−1.48776
$927$	2.41802	0.0794181
$928$	−8.92575	−0.293002
$929$	−29.0759	−0.953949	−0.476975	−	0.878917i	$-0.658267\pi$
$929$	−29.0759	−0.953949	−0.476975	+	0.878917i	$0.658267\pi$
$930$	2.46020	0.0806733
$931$	13.7358	0.450174
$932$	3.82571	0.125315
$933$	1.36849	0.0448022
$934$	19.9652	0.653280
$935$	−4.42050	−0.144566
$936$	9.14753	0.298996
$937$	−21.2285	−0.693506	−0.346753	−	0.937957i	$-0.612716\pi$
$937$	−21.2285	−0.693506	−0.346753	+	0.937957i	$0.612716\pi$
$938$	−58.7277	−1.91753
$939$	5.14485	0.167896
$940$	−0.497774	−0.0162356
$941$	53.6582	1.74921	0.874604	−	0.484839i	$-0.161122\pi$
$941$	53.6582	1.74921	0.874604	+	0.484839i	$0.161122\pi$
$942$	−26.8330	−0.874266
$943$	7.78410	0.253485
$944$	−1.85833	−0.0604835
$945$	−2.26565	−0.0737016
$946$	7.97351	0.259241
$947$	42.9691	1.39631	0.698154	−	0.715947i	$-0.254005\pi$
$947$	42.9691	1.39631	0.698154	+	0.715947i	$0.254005\pi$
$948$	3.30832	0.107449
$949$	−24.8242	−0.805829
$950$	−10.9451	−0.355106
$951$	−30.3916	−0.985516
$952$	80.8894	2.62164
$953$	20.7043	0.670678	0.335339	−	0.942098i	$-0.391149\pi$
$953$	20.7043	0.670678	0.335339	+	0.942098i	$0.391149\pi$
$954$	16.2454	0.525965
$955$	0.193644	0.00626619
$956$	1.41586	0.0457923
$957$	−6.29679	−0.203546
$958$	54.3816	1.75699
$959$	−86.2896	−2.78644
$960$	3.84900	0.124226
$961$	−22.7249	−0.733060
$962$	48.8998	1.57659
$963$	10.7538	0.346537
$964$	−2.48488	−0.0800325
$965$	6.26822	0.201781
$966$	29.3146	0.943181
$967$	−28.9634	−0.931401	−0.465701	−	0.884942i	$-0.654198\pi$
$967$	−28.9634	−0.931401	−0.465701	+	0.884942i	$0.654198\pi$
$968$	−2.62314	−0.0843110
$969$	−12.1006	−0.388726
$970$	1.52165	0.0488574
$971$	41.1027	1.31905	0.659524	−	0.751684i	$-0.270758\pi$
$971$	41.1027	1.31905	0.659524	+	0.751684i	$0.270758\pi$
$972$	−0.252024	−0.00808368
$973$	−39.2255	−1.25751
$974$	7.41556	0.237610
$975$	−16.3036	−0.522133
$976$	4.44053	0.142138
$977$	0.544347	0.0174152	0.00870761	−	0.999962i	$-0.497228\pi$
$977$	0.544347	0.0174152	0.00870761	+	0.999962i	$0.497228\pi$
$978$	1.28310	0.0410291
$979$	−13.4410	−0.429576
$980$	−1.26463	−0.0403971
$981$	−14.6227	−0.466865
$982$	−21.0320	−0.671158
$983$	19.5398	0.623224	0.311612	−	0.950209i	$-0.399131\pi$
$983$	19.5398	0.623224	0.311612	+	0.950209i	$0.399131\pi$
$984$	4.15555	0.132474
$985$	−7.78750	−0.248130
$986$	73.2958	2.33422
$987$	13.7781	0.438560
$988$	−1.37106	−0.0436191
$989$	26.1074	0.830169
$990$	−0.855232	−0.0271811
$991$	−45.5206	−1.44601	−0.723004	−	0.690843i	$-0.757239\pi$
$991$	−45.5206	−1.44601	−0.723004	+	0.690843i	$0.757239\pi$
$992$	−4.07768	−0.129466
$993$	−17.3933	−0.551961
$994$	−59.2522	−1.87937
$995$	2.87999	0.0913020
$996$	−1.01901	−0.0322887
$997$	8.42755	0.266903	0.133452	−	0.991055i	$-0.457394\pi$
$997$	8.42755	0.266903	0.133452	+	0.991055i	$0.457394\pi$
$998$	22.5577	0.714052
$999$	9.34414	0.295635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.e.1.9	✓	13
3.2	odd	2		6039.2.a.i.1.5		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.e.1.9	✓	13	1.1	even	1	trivial
6039.2.a.i.1.5		13	3.2	odd	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+1.50067 q^{2} -1.00000 q^{3} +0.252024 q^{4} -0.569898 q^{5} -1.50067 q^{6} -3.97554 q^{7} -2.62314 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.50067 q^{2} -1.00000 q^{3} +0.252024 q^{4} -0.569898 q^{5} -1.50067 q^{6} -3.97554 q^{7} -2.62314 q^{8} +1.00000 q^{9} -0.855232 q^{10} +1.00000 q^{11} -0.252024 q^{12} -3.48724 q^{13} -5.96599 q^{14} +0.569898 q^{15} -4.44053 q^{16} +7.75664 q^{17} +1.50067 q^{18} +1.56002 q^{19} -0.143628 q^{20} +3.97554 q^{21} +1.50067 q^{22} +4.91362 q^{23} +2.62314 q^{24} -4.67522 q^{25} -5.23321 q^{26} -1.00000 q^{27} -1.00193 q^{28} +6.29679 q^{29} +0.855232 q^{30} +2.87665 q^{31} -1.41751 q^{32} -1.00000 q^{33} +11.6402 q^{34} +2.26565 q^{35} +0.252024 q^{36} -9.34414 q^{37} +2.34109 q^{38} +3.48724 q^{39} +1.49492 q^{40} +1.58419 q^{41} +5.96599 q^{42} +5.31329 q^{43} +0.252024 q^{44} -0.569898 q^{45} +7.37374 q^{46} +3.46571 q^{47} +4.44053 q^{48} +8.80489 q^{49} -7.01598 q^{50} -7.75664 q^{51} -0.878869 q^{52} +10.8254 q^{53} -1.50067 q^{54} -0.569898 q^{55} +10.4284 q^{56} -1.56002 q^{57} +9.44943 q^{58} +0.418492 q^{59} +0.143628 q^{60} -1.00000 q^{61} +4.31692 q^{62} -3.97554 q^{63} +6.75385 q^{64} +1.98737 q^{65} -1.50067 q^{66} +9.84375 q^{67} +1.95486 q^{68} -4.91362 q^{69} +3.40001 q^{70} +9.93167 q^{71} -2.62314 q^{72} +7.11859 q^{73} -14.0225 q^{74} +4.67522 q^{75} +0.393164 q^{76} -3.97554 q^{77} +5.23321 q^{78} -13.1270 q^{79} +2.53065 q^{80} +1.00000 q^{81} +2.37735 q^{82} +4.04331 q^{83} +1.00193 q^{84} -4.42050 q^{85} +7.97351 q^{86} -6.29679 q^{87} -2.62314 q^{88} -13.4410 q^{89} -0.855232 q^{90} +13.8636 q^{91} +1.23835 q^{92} -2.87665 q^{93} +5.20090 q^{94} -0.889055 q^{95} +1.41751 q^{96} -1.77923 q^{97} +13.2133 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * q^99

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