LMFDB - Embedded newform 1441.2.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79989 q^{2} -0.0643329 q^{3} +1.23961 q^{4} -3.25644 q^{5} +0.115792 q^{6} +2.45508 q^{7} +1.36862 q^{8} -2.99586 q^{9} +O(q^{10})$	\(q-1.79989 q^{2} -0.0643329 q^{3} +1.23961 q^{4} -3.25644 q^{5} +0.115792 q^{6} +2.45508 q^{7} +1.36862 q^{8} -2.99586 q^{9} +5.86125 q^{10} +1.00000 q^{11} -0.0797479 q^{12} -3.20360 q^{13} -4.41889 q^{14} +0.209496 q^{15} -4.94259 q^{16} +3.74178 q^{17} +5.39223 q^{18} -6.81378 q^{19} -4.03673 q^{20} -0.157943 q^{21} -1.79989 q^{22} +7.26165 q^{23} -0.0880471 q^{24} +5.60442 q^{25} +5.76613 q^{26} +0.385731 q^{27} +3.04335 q^{28} -6.92761 q^{29} -0.377071 q^{30} -2.81610 q^{31} +6.15889 q^{32} -0.0643329 q^{33} -6.73481 q^{34} -7.99484 q^{35} -3.71371 q^{36} +1.68771 q^{37} +12.2641 q^{38} +0.206097 q^{39} -4.45682 q^{40} -3.36612 q^{41} +0.284280 q^{42} -1.13745 q^{43} +1.23961 q^{44} +9.75585 q^{45} -13.0702 q^{46} +2.03068 q^{47} +0.317971 q^{48} -0.972561 q^{49} -10.0874 q^{50} -0.240720 q^{51} -3.97122 q^{52} +0.227125 q^{53} -0.694275 q^{54} -3.25644 q^{55} +3.36007 q^{56} +0.438350 q^{57} +12.4689 q^{58} +3.11418 q^{59} +0.259694 q^{60} -2.47117 q^{61} +5.06867 q^{62} -7.35509 q^{63} -1.20017 q^{64} +10.4323 q^{65} +0.115792 q^{66} -12.0139 q^{67} +4.63836 q^{68} -0.467163 q^{69} +14.3899 q^{70} -1.91668 q^{71} -4.10018 q^{72} +14.4228 q^{73} -3.03769 q^{74} -0.360549 q^{75} -8.44644 q^{76} +2.45508 q^{77} -0.370952 q^{78} +6.50315 q^{79} +16.0952 q^{80} +8.96277 q^{81} +6.05866 q^{82} +16.1642 q^{83} -0.195788 q^{84} -12.1849 q^{85} +2.04730 q^{86} +0.445673 q^{87} +1.36862 q^{88} +12.7032 q^{89} -17.5595 q^{90} -7.86511 q^{91} +9.00163 q^{92} +0.181168 q^{93} -3.65501 q^{94} +22.1887 q^{95} -0.396219 q^{96} +2.59640 q^{97} +1.75051 q^{98} -2.99586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * 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 $

$2$	−1.79989	−1.27272	−0.636358	−	0.771394i	$-0.719560\pi$
$2$	−1.79989	−1.27272	−0.636358	+	0.771394i	$0.719560\pi$
$3$	−0.0643329	−0.0371426	−0.0185713	−	0.999828i	$-0.505912\pi$
$3$	−0.0643329	−0.0371426	−0.0185713	+	0.999828i	$0.505912\pi$
$4$	1.23961	0.619806
$5$	−3.25644	−1.45633	−0.728163	−	0.685404i	$-0.759625\pi$
$5$	−3.25644	−1.45633	−0.728163	+	0.685404i	$0.759625\pi$
$6$	0.115792	0.0472720
$7$	2.45508	0.927935	0.463967	−	0.885852i	$-0.346426\pi$
$7$	2.45508	0.927935	0.463967	+	0.885852i	$0.346426\pi$
$8$	1.36862	0.483879
$9$	−2.99586	−0.998620
$10$	5.86125	1.85349
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.0797479	−0.0230212
$13$	−3.20360	−0.888519	−0.444259	−	0.895898i	$-0.646533\pi$
$13$	−3.20360	−0.888519	−0.444259	+	0.895898i	$0.646533\pi$
$14$	−4.41889	−1.18100
$15$	0.209496	0.0540917
$16$	−4.94259	−1.23565
$17$	3.74178	0.907516	0.453758	−	0.891125i	$-0.350083\pi$
$17$	3.74178	0.907516	0.453758	+	0.891125i	$0.350083\pi$
$18$	5.39223	1.27096
$19$	−6.81378	−1.56319	−0.781594	−	0.623787i	$-0.785593\pi$
$19$	−6.81378	−1.56319	−0.781594	+	0.623787i	$0.785593\pi$
$20$	−4.03673	−0.902639
$21$	−0.157943	−0.0344659
$22$	−1.79989	−0.383738
$23$	7.26165	1.51416	0.757079	−	0.653323i	$-0.226626\pi$
$23$	7.26165	1.51416	0.757079	+	0.653323i	$0.226626\pi$
$24$	−0.0880471	−0.0179725
$25$	5.60442	1.12088
$26$	5.76613	1.13083
$27$	0.385731	0.0742340
$28$	3.04335	0.575139
$29$	−6.92761	−1.28642	−0.643212	−	0.765688i	$-0.722399\pi$
$29$	−6.92761	−1.28642	−0.643212	+	0.765688i	$0.722399\pi$
$30$	−0.377071	−0.0688434
$31$	−2.81610	−0.505786	−0.252893	−	0.967494i	$-0.581382\pi$
$31$	−2.81610	−0.505786	−0.252893	+	0.967494i	$0.581382\pi$
$32$	6.15889	1.08875
$33$	−0.0643329	−0.0111989
$34$	−6.73481	−1.15501
$35$	−7.99484	−1.35137
$36$	−3.71371	−0.618951
$37$	1.68771	0.277458	0.138729	−	0.990330i	$-0.455698\pi$
$37$	1.68771	0.277458	0.138729	+	0.990330i	$0.455698\pi$
$38$	12.2641	1.98950
$39$	0.206097	0.0330019
$40$	−4.45682	−0.704685
$41$	−3.36612	−0.525700	−0.262850	−	0.964837i	$-0.584662\pi$
$41$	−3.36612	−0.525700	−0.262850	+	0.964837i	$0.584662\pi$
$42$	0.284280	0.0438653
$43$	−1.13745	−0.173460	−0.0867301	−	0.996232i	$-0.527642\pi$
$43$	−1.13745	−0.173460	−0.0867301	+	0.996232i	$0.527642\pi$
$44$	1.23961	0.186879
$45$	9.75585	1.45432
$46$	−13.0702	−1.92709
$47$	2.03068	0.296206	0.148103	−	0.988972i	$-0.452683\pi$
$47$	2.03068	0.296206	0.148103	+	0.988972i	$0.452683\pi$
$48$	0.317971	0.0458952
$49$	−0.972561	−0.138937
$50$	−10.0874	−1.42657
$51$	−0.240720	−0.0337075
$52$	−3.97122	−0.550709
$53$	0.227125	0.0311980	0.0155990	−	0.999878i	$-0.495034\pi$
$53$	0.227125	0.0311980	0.0155990	+	0.999878i	$0.495034\pi$
$54$	−0.694275	−0.0944788
$55$	−3.25644	−0.439099
$56$	3.36007	0.449008
$57$	0.438350	0.0580609
$58$	12.4689	1.63725
$59$	3.11418	0.405431	0.202716	−	0.979238i	$-0.435023\pi$
$59$	3.11418	0.405431	0.202716	+	0.979238i	$0.435023\pi$
$60$	0.259694	0.0335264
$61$	−2.47117	−0.316401	−0.158200	−	0.987407i	$-0.550569\pi$
$61$	−2.47117	−0.316401	−0.158200	+	0.987407i	$0.550569\pi$
$62$	5.06867	0.643722
$63$	−7.35509	−0.926654
$64$	−1.20017	−0.150021
$65$	10.4323	1.29397
$66$	0.115792	0.0142530
$67$	−12.0139	−1.46773	−0.733864	−	0.679296i	$-0.762285\pi$
$67$	−12.0139	−1.46773	−0.733864	+	0.679296i	$0.762285\pi$
$68$	4.63836	0.562484
$69$	−0.467163	−0.0562398
$70$	14.3899	1.71992
$71$	−1.91668	−0.227468	−0.113734	−	0.993511i	$-0.536281\pi$
$71$	−1.91668	−0.227468	−0.113734	+	0.993511i	$0.536281\pi$
$72$	−4.10018	−0.483211
$73$	14.4228	1.68806	0.844030	−	0.536296i	$-0.180177\pi$
$73$	14.4228	1.68806	0.844030	+	0.536296i	$0.180177\pi$
$74$	−3.03769	−0.353125
$75$	−0.360549	−0.0416326
$76$	−8.44644	−0.968874
$77$	2.45508	0.279783
$78$	−0.370952	−0.0420021
$79$	6.50315	0.731661	0.365831	−	0.930681i	$-0.380785\pi$
$79$	6.50315	0.731661	0.365831	+	0.930681i	$0.380785\pi$
$80$	16.0952	1.79950
$81$	8.96277	0.995863
$82$	6.05866	0.669067
$83$	16.1642	1.77426	0.887128	−	0.461524i	$-0.152697\pi$
$83$	16.1642	1.77426	0.887128	+	0.461524i	$0.152697\pi$
$84$	−0.195788	−0.0213622
$85$	−12.1849	−1.32164
$86$	2.04730	0.220766
$87$	0.445673	0.0477812
$88$	1.36862	0.145895
$89$	12.7032	1.34653	0.673266	−	0.739400i	$-0.264891\pi$
$89$	12.7032	1.34653	0.673266	+	0.739400i	$0.264891\pi$
$90$	−17.5595	−1.85093
$91$	−7.86511	−0.824487
$92$	9.00163	0.938485
$93$	0.181168	0.0187862
$94$	−3.65501	−0.376986
$95$	22.1887	2.27651
$96$	−0.396219	−0.0404390
$97$	2.59640	0.263624	0.131812	−	0.991275i	$-0.457920\pi$
$97$	2.59640	0.263624	0.131812	+	0.991275i	$0.457920\pi$
$98$	1.75051	0.176828
$99$	−2.99586	−0.301095
$100$	6.94731	0.694731
$101$	3.57884	0.356107	0.178054	−	0.984021i	$-0.443020\pi$
$101$	3.57884	0.356107	0.178054	+	0.984021i	$0.443020\pi$
$102$	0.433270	0.0429001
$103$	11.7061	1.15344	0.576719	−	0.816942i	$-0.304333\pi$
$103$	11.7061	1.15344	0.576719	+	0.816942i	$0.304333\pi$
$104$	−4.38450	−0.429936
$105$	0.514331	0.0501936
$106$	−0.408801	−0.0397062
$107$	−3.39796	−0.328493	−0.164247	−	0.986419i	$-0.552519\pi$
$107$	−3.39796	−0.328493	−0.164247	+	0.986419i	$0.552519\pi$
$108$	0.478157	0.0460107
$109$	5.87341	0.562571	0.281286	−	0.959624i	$-0.409239\pi$
$109$	5.87341	0.562571	0.281286	+	0.959624i	$0.409239\pi$
$110$	5.86125	0.558848
$111$	−0.108575	−0.0103055
$112$	−12.1345	−1.14660
$113$	11.6885	1.09956	0.549779	−	0.835310i	$-0.314712\pi$
$113$	11.6885	1.09956	0.549779	+	0.835310i	$0.314712\pi$
$114$	−0.788983	−0.0738951
$115$	−23.6471	−2.20511
$116$	−8.58754	−0.797334
$117$	9.59754	0.887293
$118$	−5.60518	−0.515999
$119$	9.18640	0.842116
$120$	0.286720	0.0261739
$121$	1.00000	0.0909091
$122$	4.44784	0.402688
$123$	0.216552	0.0195259
$124$	−3.49087	−0.313489
$125$	−1.96826	−0.176046
$126$	13.2384	1.17937
$127$	−14.6927	−1.30376	−0.651882	−	0.758321i	$-0.726020\pi$
$127$	−14.6927	−1.30376	−0.651882	+	0.758321i	$0.726020\pi$
$128$	−10.1576	−0.897814
$129$	0.0731757	0.00644277
$130$	−18.7771	−1.64686
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−0.0797479	−0.00694116
$133$	−16.7284	−1.45054
$134$	21.6237	1.86800
$135$	−1.25611	−0.108109
$136$	5.12107	0.439128
$137$	−3.09832	−0.264707	−0.132354	−	0.991203i	$-0.542253\pi$
$137$	−3.09832	−0.264707	−0.132354	+	0.991203i	$0.542253\pi$
$138$	0.840843	0.0715773
$139$	−15.1228	−1.28270	−0.641348	−	0.767250i	$-0.721624\pi$
$139$	−15.1228	−1.28270	−0.641348	+	0.767250i	$0.721624\pi$
$140$	−9.91050	−0.837590
$141$	−0.130640	−0.0110019
$142$	3.44981	0.289502
$143$	−3.20360	−0.267898
$144$	14.8073	1.23394
$145$	22.5594	1.87345
$146$	−25.9595	−2.14842
$147$	0.0625677	0.00516050
$148$	2.09210	0.171970
$149$	18.9795	1.55486	0.777431	−	0.628968i	$-0.216522\pi$
$149$	18.9795	1.55486	0.777431	+	0.628968i	$0.216522\pi$
$150$	0.648949	0.0529864
$151$	3.60952	0.293738	0.146869	−	0.989156i	$-0.453080\pi$
$151$	3.60952	0.293738	0.146869	+	0.989156i	$0.453080\pi$
$152$	−9.32545	−0.756394
$153$	−11.2099	−0.906264
$154$	−4.41889	−0.356084
$155$	9.17046	0.736589
$156$	0.255480	0.0204548
$157$	7.15470	0.571007	0.285504	−	0.958378i	$-0.407839\pi$
$157$	7.15470	0.571007	0.285504	+	0.958378i	$0.407839\pi$
$158$	−11.7050	−0.931197
$159$	−0.0146116	−0.00115878
$160$	−20.0561	−1.58557
$161$	17.8280	1.40504
$162$	−16.1320	−1.26745
$163$	4.05476	0.317593	0.158797	−	0.987311i	$-0.449239\pi$
$163$	4.05476	0.317593	0.158797	+	0.987311i	$0.449239\pi$
$164$	−4.17269	−0.325832
$165$	0.209496	0.0163093
$166$	−29.0939	−2.25812
$167$	6.01566	0.465506	0.232753	−	0.972536i	$-0.425227\pi$
$167$	6.01566	0.465506	0.232753	+	0.972536i	$0.425227\pi$
$168$	−0.216163	−0.0166773
$169$	−2.73695	−0.210534
$170$	21.9315	1.68207
$171$	20.4131	1.56103
$172$	−1.41000	−0.107512
$173$	22.4387	1.70598	0.852992	−	0.521925i	$-0.174786\pi$
$173$	22.4387	1.70598	0.852992	+	0.521925i	$0.174786\pi$
$174$	−0.802164	−0.0608119
$175$	13.7593	1.04011
$176$	−4.94259	−0.372561
$177$	−0.200344	−0.0150588
$178$	−22.8643	−1.71375
$179$	12.6758	0.947435	0.473718	−	0.880677i	$-0.342912\pi$
$179$	12.6758	0.947435	0.473718	+	0.880677i	$0.342912\pi$
$180$	12.0935	0.901394
$181$	19.4592	1.44639	0.723196	−	0.690643i	$-0.242672\pi$
$181$	19.4592	1.44639	0.723196	+	0.690643i	$0.242672\pi$
$182$	14.1563	1.04934
$183$	0.158978	0.0117520
$184$	9.93841	0.732670
$185$	−5.49593	−0.404069
$186$	−0.326082	−0.0239095
$187$	3.74178	0.273626
$188$	2.51726	0.183590
$189$	0.947003	0.0688843
$190$	−39.9372	−2.89735
$191$	5.79783	0.419517	0.209758	−	0.977753i	$-0.432732\pi$
$191$	5.79783	0.419517	0.209758	+	0.977753i	$0.432732\pi$
$192$	0.0772101	0.00557216
$193$	23.4944	1.69117	0.845583	−	0.533844i	$-0.179253\pi$
$193$	23.4944	1.69117	0.845583	+	0.533844i	$0.179253\pi$
$194$	−4.67324	−0.335519
$195$	−0.671143	−0.0480615
$196$	−1.20560	−0.0861142
$197$	−13.4338	−0.957118	−0.478559	−	0.878055i	$-0.658841\pi$
$197$	−13.4338	−0.957118	−0.478559	+	0.878055i	$0.658841\pi$
$198$	5.39223	0.383209
$199$	−3.87270	−0.274529	−0.137264	−	0.990534i	$-0.543831\pi$
$199$	−3.87270	−0.274529	−0.137264	+	0.990534i	$0.543831\pi$
$200$	7.67030	0.542372
$201$	0.772887	0.0545153
$202$	−6.44152	−0.453224
$203$	−17.0079	−1.19372
$204$	−0.298399	−0.0208921
$205$	10.9616	0.765590
$206$	−21.0698	−1.46800
$207$	−21.7549	−1.51207
$208$	15.8341	1.09790
$209$	−6.81378	−0.471319
$210$	−0.925741	−0.0638822
$211$	20.1005	1.38378	0.691888	−	0.722005i	$-0.256779\pi$
$211$	20.1005	1.38378	0.691888	+	0.722005i	$0.256779\pi$
$212$	0.281547	0.0193367
$213$	0.123305	0.00844874
$214$	6.11597	0.418079
$215$	3.70405	0.252614
$216$	0.527918	0.0359203
$217$	−6.91376	−0.469336
$218$	−10.5715	−0.715993
$219$	−0.927860	−0.0626990
$220$	−4.03673	−0.272156
$221$	−11.9872	−0.806345
$222$	0.195424	0.0131160
$223$	−0.820904	−0.0549718	−0.0274859	−	0.999622i	$-0.508750\pi$
$223$	−0.820904	−0.0549718	−0.0274859	+	0.999622i	$0.508750\pi$
$224$	15.1206	1.01029
$225$	−16.7901	−1.11934
$226$	−21.0380	−1.39943
$227$	12.5614	0.833728	0.416864	−	0.908969i	$-0.363129\pi$
$227$	12.5614	0.833728	0.416864	+	0.908969i	$0.363129\pi$
$228$	0.543384	0.0359865
$229$	−15.9020	−1.05084	−0.525418	−	0.850844i	$-0.676091\pi$
$229$	−15.9020	−1.05084	−0.525418	+	0.850844i	$0.676091\pi$
$230$	42.5623	2.80648
$231$	−0.157943	−0.0103919
$232$	−9.48124	−0.622474
$233$	14.1308	0.925740	0.462870	−	0.886426i	$-0.346820\pi$
$233$	14.1308	0.925740	0.462870	+	0.886426i	$0.346820\pi$
$234$	−17.2745	−1.12927
$235$	−6.61281	−0.431372
$236$	3.86037	0.251289
$237$	−0.418366	−0.0271758
$238$	−16.5345	−1.07177
$239$	−11.0764	−0.716471	−0.358236	−	0.933631i	$-0.616622\pi$
$239$	−11.0764	−0.716471	−0.358236	+	0.933631i	$0.616622\pi$
$240$	−1.03545	−0.0668383
$241$	18.1716	1.17054	0.585268	−	0.810840i	$-0.300989\pi$
$241$	18.1716	1.17054	0.585268	+	0.810840i	$0.300989\pi$
$242$	−1.79989	−0.115701
$243$	−1.73379	−0.111223
$244$	−3.06329	−0.196107
$245$	3.16709	0.202338
$246$	−0.389771	−0.0248509
$247$	21.8286	1.38892
$248$	−3.85416	−0.244739
$249$	−1.03989	−0.0659005
$250$	3.54265	0.224057
$251$	−11.5542	−0.729294	−0.364647	−	0.931146i	$-0.618810\pi$
$251$	−11.5542	−0.729294	−0.364647	+	0.931146i	$0.618810\pi$
$252$	−9.11746	−0.574346
$253$	7.26165	0.456536
$254$	26.4452	1.65932
$255$	0.783891	0.0490891
$256$	20.6829	1.29268
$257$	−20.4956	−1.27848	−0.639240	−	0.769008i	$-0.720751\pi$
$257$	−20.4956	−1.27848	−0.639240	+	0.769008i	$0.720751\pi$
$258$	−0.131708	−0.00819981
$259$	4.14347	0.257463
$260$	12.9321	0.802012
$261$	20.7541	1.28465
$262$	1.79989	0.111198
$263$	30.8464	1.90207	0.951036	−	0.309079i	$-0.100021\pi$
$263$	30.8464	1.90207	0.951036	+	0.309079i	$0.100021\pi$
$264$	−0.0880471	−0.00541892
$265$	−0.739620	−0.0454345
$266$	30.1093	1.84612
$267$	−0.817231	−0.0500137
$268$	−14.8925	−0.909707
$269$	−29.7328	−1.81284	−0.906420	−	0.422377i	$-0.861196\pi$
$269$	−29.7328	−1.81284	−0.906420	+	0.422377i	$0.861196\pi$
$270$	2.26087	0.137592
$271$	−20.4802	−1.24409	−0.622043	−	0.782983i	$-0.713697\pi$
$271$	−20.4802	−1.24409	−0.622043	+	0.782983i	$0.713697\pi$
$272$	−18.4941	−1.12137
$273$	0.505985	0.0306236
$274$	5.57664	0.336897
$275$	5.60442	0.337959
$276$	−0.579101	−0.0348578
$277$	2.17225	0.130518	0.0652589	−	0.997868i	$-0.479213\pi$
$277$	2.17225	0.130518	0.0652589	+	0.997868i	$0.479213\pi$
$278$	27.2193	1.63251
$279$	8.43664	0.505088
$280$	−10.9419	−0.653902
$281$	10.4658	0.624336	0.312168	−	0.950027i	$-0.398945\pi$
$281$	10.4658	0.624336	0.312168	+	0.950027i	$0.398945\pi$
$282$	0.235138	0.0140022
$283$	−21.2211	−1.26147	−0.630733	−	0.776000i	$-0.717246\pi$
$283$	−21.2211	−1.26147	−0.630733	+	0.776000i	$0.717246\pi$
$284$	−2.37593	−0.140986
$285$	−1.42746	−0.0845556
$286$	5.76613	0.340959
$287$	−8.26411	−0.487815
$288$	−18.4512	−1.08725
$289$	−2.99905	−0.176415
$290$	−40.6044	−2.38437
$291$	−0.167034	−0.00979170
$292$	17.8787	1.04627
$293$	−31.7806	−1.85664	−0.928322	−	0.371778i	$-0.878748\pi$
$293$	−31.7806	−1.85664	−0.928322	+	0.371778i	$0.878748\pi$
$294$	−0.112615	−0.00656785
$295$	−10.1411	−0.590440
$296$	2.30983	0.134256
$297$	0.385731	0.0223824
$298$	−34.1611	−1.97890
$299$	−23.2634	−1.34536
$300$	−0.446940	−0.0258041
$301$	−2.79255	−0.160960
$302$	−6.49674	−0.373845
$303$	−0.230237	−0.0132268
$304$	33.6777	1.93155
$305$	8.04722	0.460783
$306$	20.1766	1.15342
$307$	4.27905	0.244218	0.122109	−	0.992517i	$-0.461034\pi$
$307$	4.27905	0.244218	0.122109	+	0.992517i	$0.461034\pi$
$308$	3.04335	0.173411
$309$	−0.753089	−0.0428417
$310$	−16.5058	−0.937469
$311$	−29.0188	−1.64550	−0.822752	−	0.568401i	$-0.807562\pi$
$311$	−29.0188	−1.64550	−0.822752	+	0.568401i	$0.807562\pi$
$312$	0.282068	0.0159689
$313$	−19.2876	−1.09020	−0.545100	−	0.838371i	$-0.683508\pi$
$313$	−19.2876	−1.09020	−0.545100	+	0.838371i	$0.683508\pi$
$314$	−12.8777	−0.726730
$315$	23.9514	1.34951
$316$	8.06138	0.453488
$317$	23.3504	1.31149	0.655745	−	0.754983i	$-0.272355\pi$
$317$	23.3504	1.31149	0.655745	+	0.754983i	$0.272355\pi$
$318$	0.0262993	0.00147479
$319$	−6.92761	−0.387872
$320$	3.90827	0.218479
$321$	0.218601	0.0122011
$322$	−32.0884	−1.78822
$323$	−25.4957	−1.41862
$324$	11.1104	0.617242
$325$	−17.9543	−0.995926
$326$	−7.29813	−0.404206
$327$	−0.377854	−0.0208954
$328$	−4.60693	−0.254375
$329$	4.98550	0.274860
$330$	−0.377071	−0.0207571
$331$	2.92583	0.160818	0.0804090	−	0.996762i	$-0.474377\pi$
$331$	2.92583	0.160818	0.0804090	+	0.996762i	$0.474377\pi$
$332$	20.0374	1.09969
$333$	−5.05614	−0.277075
$334$	−10.8275	−0.592457
$335$	39.1225	2.13749
$336$	0.780645	0.0425877
$337$	−10.4594	−0.569758	−0.284879	−	0.958563i	$-0.591953\pi$
$337$	−10.4594	−0.569758	−0.284879	+	0.958563i	$0.591953\pi$
$338$	4.92621	0.267951
$339$	−0.751953	−0.0408405
$340$	−15.1046	−0.819160
$341$	−2.81610	−0.152500
$342$	−36.7415	−1.98675
$343$	−19.5733	−1.05686
$344$	−1.55674	−0.0839337
$345$	1.52129	0.0819035
$346$	−40.3873	−2.17123
$347$	−30.4510	−1.63469	−0.817346	−	0.576147i	$-0.804556\pi$
$347$	−30.4510	−1.63469	−0.817346	+	0.576147i	$0.804556\pi$
$348$	0.552462	0.0296151
$349$	0.801556	0.0429063	0.0214531	−	0.999770i	$-0.493171\pi$
$349$	0.801556	0.0429063	0.0214531	+	0.999770i	$0.493171\pi$
$350$	−24.7653	−1.32376
$351$	−1.23573	−0.0659583
$352$	6.15889	0.328270
$353$	−5.85878	−0.311831	−0.155916	−	0.987770i	$-0.549833\pi$
$353$	−5.85878	−0.311831	−0.155916	+	0.987770i	$0.549833\pi$
$354$	0.360598	0.0191655
$355$	6.24154	0.331267
$356$	15.7470	0.834589
$357$	−0.590988	−0.0312784
$358$	−22.8151	−1.20582
$359$	23.8327	1.25784	0.628922	−	0.777469i	$-0.283497\pi$
$359$	23.8327	1.25784	0.628922	+	0.777469i	$0.283497\pi$
$360$	13.3520	0.703713
$361$	27.4276	1.44356
$362$	−35.0245	−1.84085
$363$	−0.0643329	−0.00337660
$364$	−9.74968	−0.511022
$365$	−46.9670	−2.45836
$366$	−0.286142	−0.0149569
$367$	14.1756	0.739959	0.369980	−	0.929040i	$-0.379365\pi$
$367$	14.1756	0.739959	0.369980	+	0.929040i	$0.379365\pi$
$368$	−35.8913	−1.87096
$369$	10.0844	0.524975
$370$	9.89208	0.514265
$371$	0.557611	0.0289497
$372$	0.224578	0.0116438
$373$	13.8923	0.719316	0.359658	−	0.933084i	$-0.382893\pi$
$373$	13.8923	0.719316	0.359658	+	0.933084i	$0.382893\pi$
$374$	−6.73481	−0.348249
$375$	0.126624	0.00653882
$376$	2.77923	0.143328
$377$	22.1933	1.14301
$378$	−1.70450	−0.0876702
$379$	3.31402	0.170230	0.0851149	−	0.996371i	$-0.472874\pi$
$379$	3.31402	0.170230	0.0851149	+	0.996371i	$0.472874\pi$
$380$	27.5054	1.41100
$381$	0.945222	0.0484252
$382$	−10.4355	−0.533925
$383$	−17.9038	−0.914843	−0.457422	−	0.889250i	$-0.651227\pi$
$383$	−17.9038	−0.914843	−0.457422	+	0.889250i	$0.651227\pi$
$384$	0.653469	0.0333472
$385$	−7.99484	−0.407455
$386$	−42.2874	−2.15237
$387$	3.40766	0.173221
$388$	3.21853	0.163396
$389$	0.657540	0.0333386	0.0166693	−	0.999861i	$-0.494694\pi$
$389$	0.657540	0.0333386	0.0166693	+	0.999861i	$0.494694\pi$
$390$	1.20798	0.0611687
$391$	27.1715	1.37412
$392$	−1.33106	−0.0672288
$393$	0.0643329	0.00324517
$394$	24.1794	1.21814
$395$	−21.1771	−1.06554
$396$	−3.71371	−0.186621
$397$	29.3794	1.47451	0.737255	−	0.675615i	$-0.236122\pi$
$397$	29.3794	1.47451	0.737255	+	0.675615i	$0.236122\pi$
$398$	6.97045	0.349397
$399$	1.07619	0.0538767
$400$	−27.7003	−1.38502
$401$	4.20432	0.209954	0.104977	−	0.994475i	$-0.466523\pi$
$401$	4.20432	0.209954	0.104977	+	0.994475i	$0.466523\pi$
$402$	−1.39111	−0.0693825
$403$	9.02165	0.449400
$404$	4.43637	0.220718
$405$	−29.1867	−1.45030
$406$	30.6123	1.51926
$407$	1.68771	0.0836566
$408$	−0.329453	−0.0163104
$409$	−30.8354	−1.52471	−0.762356	−	0.647158i	$-0.775958\pi$
$409$	−30.8354	−1.52471	−0.762356	+	0.647158i	$0.775958\pi$
$410$	−19.7297	−0.974379
$411$	0.199324	0.00983191
$412$	14.5111	0.714908
$413$	7.64556	0.376214
$414$	39.1565	1.92444
$415$	−52.6379	−2.58389
$416$	−19.7306	−0.967373
$417$	0.972891	0.0476427
$418$	12.2641	0.599855
$419$	6.62390	0.323598	0.161799	−	0.986824i	$-0.448270\pi$
$419$	6.62390	0.323598	0.161799	+	0.986824i	$0.448270\pi$
$420$	0.637571	0.0311103
$421$	40.4506	1.97144	0.985721	−	0.168389i	$-0.0538564\pi$
$421$	40.4506	1.97144	0.985721	+	0.168389i	$0.0538564\pi$
$422$	−36.1787	−1.76115
$423$	−6.08365	−0.295797
$424$	0.310847	0.0150961
$425$	20.9705	1.01722
$426$	−0.221936	−0.0107528
$427$	−6.06693	−0.293599
$428$	−4.21216	−0.203602
$429$	0.206097	0.00995045
$430$	−6.66690	−0.321506
$431$	37.9173	1.82641	0.913207	−	0.407497i	$-0.133598\pi$
$431$	37.9173	1.82641	0.913207	+	0.407497i	$0.133598\pi$
$432$	−1.90651	−0.0917270
$433$	−11.1703	−0.536811	−0.268405	−	0.963306i	$-0.586497\pi$
$433$	−11.1703	−0.536811	−0.268405	+	0.963306i	$0.586497\pi$
$434$	12.4440	0.597332
$435$	−1.45131	−0.0695849
$436$	7.28075	0.348685
$437$	−49.4793	−2.36692
$438$	1.67005	0.0797980
$439$	34.4055	1.64208	0.821041	−	0.570869i	$-0.193393\pi$
$439$	34.4055	1.64208	0.821041	+	0.570869i	$0.193393\pi$
$440$	−4.45682	−0.212471
$441$	2.91366	0.138746
$442$	21.5756	1.02625
$443$	−8.99994	−0.427600	−0.213800	−	0.976877i	$-0.568584\pi$
$443$	−8.99994	−0.427600	−0.213800	+	0.976877i	$0.568584\pi$
$444$	−0.134591	−0.00638741
$445$	−41.3671	−1.96099
$446$	1.47754	0.0699635
$447$	−1.22101	−0.0577517
$448$	−2.94651	−0.139209
$449$	−22.7091	−1.07171	−0.535853	−	0.844311i	$-0.680010\pi$
$449$	−22.7091	−1.07171	−0.535853	+	0.844311i	$0.680010\pi$
$450$	30.2203	1.42460
$451$	−3.36612	−0.158504
$452$	14.4892	0.681513
$453$	−0.232211	−0.0109102
$454$	−22.6091	−1.06110
$455$	25.6123	1.20072
$456$	0.599933	0.0280945
$457$	9.09866	0.425617	0.212809	−	0.977094i	$-0.431739\pi$
$457$	9.09866	0.425617	0.212809	+	0.977094i	$0.431739\pi$
$458$	28.6220	1.33742
$459$	1.44332	0.0673685
$460$	−29.3133	−1.36674
$461$	−3.32606	−0.154910	−0.0774549	−	0.996996i	$-0.524679\pi$
$461$	−3.32606	−0.154910	−0.0774549	+	0.996996i	$0.524679\pi$
$462$	0.284280	0.0132259
$463$	−27.2810	−1.26786	−0.633929	−	0.773391i	$-0.718559\pi$
$463$	−27.2810	−1.26786	−0.633929	+	0.773391i	$0.718559\pi$
$464$	34.2403	1.58957
$465$	−0.589962	−0.0273589
$466$	−25.4339	−1.17820
$467$	10.3041	0.476819	0.238409	−	0.971165i	$-0.423374\pi$
$467$	10.3041	0.476819	0.238409	+	0.971165i	$0.423374\pi$
$468$	11.8972	0.549950
$469$	−29.4951	−1.36196
$470$	11.9023	0.549014
$471$	−0.460283	−0.0212087
$472$	4.26211	0.196180
$473$	−1.13745	−0.0523002
$474$	0.753014	0.0345871
$475$	−38.1873	−1.75215
$476$	11.3876	0.521948
$477$	−0.680435	−0.0311550
$478$	19.9363	0.911864
$479$	−10.0501	−0.459201	−0.229601	−	0.973285i	$-0.573742\pi$
$479$	−10.0501	−0.459201	−0.229601	+	0.973285i	$0.573742\pi$
$480$	1.29027	0.0588923
$481$	−5.40674	−0.246526
$482$	−32.7070	−1.48976
$483$	−1.14692	−0.0521869
$484$	1.23961	0.0563460
$485$	−8.45502	−0.383923
$486$	3.12064	0.141555
$487$	38.8796	1.76180	0.880902	−	0.473299i	$-0.156937\pi$
$487$	38.8796	1.76180	0.880902	+	0.473299i	$0.156937\pi$
$488$	−3.38208	−0.153100
$489$	−0.260854	−0.0117962
$490$	−5.70042	−0.257519
$491$	31.2750	1.41142	0.705710	−	0.708501i	$-0.250628\pi$
$491$	31.2750	1.41142	0.705710	+	0.708501i	$0.250628\pi$
$492$	0.268441	0.0121023
$493$	−25.9216	−1.16745
$494$	−39.2892	−1.76770
$495$	9.75585	0.438493
$496$	13.9188	0.624973
$497$	−4.70560	−0.211075
$498$	1.87169	0.0838726
$499$	−31.4616	−1.40841	−0.704206	−	0.709995i	$-0.748697\pi$
$499$	−31.4616	−1.40841	−0.704206	+	0.709995i	$0.748697\pi$
$500$	−2.43987	−0.109114
$501$	−0.387005	−0.0172901
$502$	20.7963	0.928185
$503$	−0.303544	−0.0135344	−0.00676718	−	0.999977i	$-0.502154\pi$
$503$	−0.303544	−0.0135344	−0.00676718	+	0.999977i	$0.502154\pi$
$504$	−10.0663	−0.448389
$505$	−11.6543	−0.518608
$506$	−13.0702	−0.581041
$507$	0.176076	0.00781980
$508$	−18.2132	−0.808081
$509$	−35.2525	−1.56254	−0.781270	−	0.624193i	$-0.785428\pi$
$509$	−35.2525	−1.56254	−0.781270	+	0.624193i	$0.785428\pi$
$510$	−1.41092	−0.0624765
$511$	35.4092	1.56641
$512$	−16.9118	−0.747405
$513$	−2.62829	−0.116042
$514$	36.8898	1.62714
$515$	−38.1203	−1.67978
$516$	0.0907095	0.00399326
$517$	2.03068	0.0893094
$518$	−7.45780	−0.327677
$519$	−1.44355	−0.0633647
$520$	14.2779	0.626126
$521$	−5.39310	−0.236276	−0.118138	−	0.992997i	$-0.537693\pi$
$521$	−5.39310	−0.236276	−0.118138	+	0.992997i	$0.537693\pi$
$522$	−37.3552	−1.63499
$523$	5.25856	0.229941	0.114970	−	0.993369i	$-0.463323\pi$
$523$	5.25856	0.229941	0.114970	+	0.993369i	$0.463323\pi$
$524$	−1.23961	−0.0541527
$525$	−0.885177	−0.0386323
$526$	−55.5203	−2.42080
$527$	−10.5372	−0.459009
$528$	0.317971	0.0138379
$529$	29.7316	1.29268
$530$	1.33124	0.0578252
$531$	−9.32964	−0.404872
$532$	−20.7367	−0.899051
$533$	10.7837	0.467094
$534$	1.47093	0.0636533
$535$	11.0653	0.478393
$536$	−16.4424	−0.710203
$537$	−0.815472	−0.0351902
$538$	53.5158	2.30723
$539$	−0.972561	−0.0418912
$540$	−1.55709	−0.0670065
$541$	−9.14990	−0.393385	−0.196692	−	0.980465i	$-0.563020\pi$
$541$	−9.14990	−0.393385	−0.196692	+	0.980465i	$0.563020\pi$
$542$	36.8622	1.58337
$543$	−1.25187	−0.0537228
$544$	23.0452	0.988056
$545$	−19.1264	−0.819287
$546$	−0.910719	−0.0389752
$547$	33.2667	1.42238	0.711190	−	0.703000i	$-0.248156\pi$
$547$	33.2667	1.42238	0.711190	+	0.703000i	$0.248156\pi$
$548$	−3.84071	−0.164067
$549$	7.40328	0.315964
$550$	−10.0874	−0.430126
$551$	47.2032	2.01092
$552$	−0.639367	−0.0272133
$553$	15.9658	0.678934
$554$	−3.90981	−0.166112
$555$	0.353569	0.0150082
$556$	−18.7464	−0.795023
$557$	−30.2751	−1.28280	−0.641398	−	0.767208i	$-0.721645\pi$
$557$	−30.2751	−1.28280	−0.641398	+	0.767208i	$0.721645\pi$
$558$	−15.1850	−0.642834
$559$	3.64395	0.154123
$560$	39.5152	1.66982
$561$	−0.240720	−0.0101632
$562$	−18.8373	−0.794602
$563$	9.75079	0.410947	0.205473	−	0.978663i	$-0.434127\pi$
$563$	9.75079	0.410947	0.205473	+	0.978663i	$0.434127\pi$
$564$	−0.161943	−0.00681902
$565$	−38.0628	−1.60132
$566$	38.1958	1.60549
$567$	22.0044	0.924096
$568$	−2.62319	−0.110067
$569$	2.03238	0.0852020	0.0426010	−	0.999092i	$-0.486436\pi$
$569$	2.03238	0.0852020	0.0426010	+	0.999092i	$0.486436\pi$
$570$	2.56928	0.107615
$571$	14.9943	0.627492	0.313746	−	0.949507i	$-0.398416\pi$
$571$	14.9943	0.627492	0.313746	+	0.949507i	$0.398416\pi$
$572$	−3.97122	−0.166045
$573$	−0.372992	−0.0155819
$574$	14.8745	0.620850
$575$	40.6973	1.69720
$576$	3.59553	0.149814
$577$	−13.6092	−0.566559	−0.283279	−	0.959037i	$-0.591422\pi$
$577$	−13.6092	−0.566559	−0.283279	+	0.959037i	$0.591422\pi$
$578$	5.39797	0.224526
$579$	−1.51146	−0.0628143
$580$	27.9648	1.16118
$581$	39.6846	1.64639
$582$	0.300643	0.0124621
$583$	0.227125	0.00940656
$584$	19.7393	0.816817
$585$	−31.2538	−1.29219
$586$	57.2017	2.36298
$587$	12.9708	0.535362	0.267681	−	0.963508i	$-0.413743\pi$
$587$	12.9708	0.535362	0.267681	+	0.963508i	$0.413743\pi$
$588$	0.0775597	0.00319851
$589$	19.1883	0.790639
$590$	18.2530	0.751462
$591$	0.864235	0.0355499
$592$	−8.34165	−0.342840
$593$	21.3527	0.876852	0.438426	−	0.898767i	$-0.355536\pi$
$593$	21.3527	0.876852	0.438426	+	0.898767i	$0.355536\pi$
$594$	−0.694275	−0.0284864
$595$	−29.9150	−1.22639
$596$	23.5272	0.963713
$597$	0.249142	0.0101967
$598$	41.8717	1.71226
$599$	23.3568	0.954334	0.477167	−	0.878813i	$-0.341664\pi$
$599$	23.3568	0.954334	0.477167	+	0.878813i	$0.341664\pi$
$600$	−0.493453	−0.0201451
$601$	−43.5011	−1.77445	−0.887224	−	0.461339i	$-0.847369\pi$
$601$	−43.5011	−1.77445	−0.887224	+	0.461339i	$0.847369\pi$
$602$	5.02628	0.204856
$603$	35.9919	1.46570
$604$	4.47440	0.182061
$605$	−3.25644	−0.132393
$606$	0.414402	0.0168339
$607$	43.2585	1.75581	0.877904	−	0.478837i	$-0.158942\pi$
$607$	43.2585	1.75581	0.877904	+	0.478837i	$0.158942\pi$
$608$	−41.9653	−1.70192
$609$	1.09417	0.0443378
$610$	−14.4841	−0.586445
$611$	−6.50550	−0.263184
$612$	−13.8959	−0.561708
$613$	8.01972	0.323913	0.161957	−	0.986798i	$-0.448220\pi$
$613$	8.01972	0.323913	0.161957	+	0.986798i	$0.448220\pi$
$614$	−7.70183	−0.310821
$615$	−0.705191	−0.0284360
$616$	3.36007	0.135381
$617$	19.0372	0.766409	0.383205	−	0.923664i	$-0.374820\pi$
$617$	19.0372	0.766409	0.383205	+	0.923664i	$0.374820\pi$
$618$	1.35548	0.0545254
$619$	−1.78447	−0.0717238	−0.0358619	−	0.999357i	$-0.511418\pi$
$619$	−1.78447	−0.0717238	−0.0358619	+	0.999357i	$0.511418\pi$
$620$	11.3678	0.456542
$621$	2.80105	0.112402
$622$	52.2307	2.09426
$623$	31.1873	1.24949
$624$	−1.01865	−0.0407787
$625$	−21.6126	−0.864503
$626$	34.7156	1.38751
$627$	0.438350	0.0175060
$628$	8.86905	0.353914
$629$	6.31504	0.251797
$630$	−43.1100	−1.71754
$631$	−25.4490	−1.01311	−0.506554	−	0.862208i	$-0.669081\pi$
$631$	−25.4490	−1.01311	−0.506554	+	0.862208i	$0.669081\pi$
$632$	8.90031	0.354035
$633$	−1.29312	−0.0513971
$634$	−42.0282	−1.66915
$635$	47.8458	1.89870
$636$	−0.0181127	−0.000718217 0
$637$	3.11570	0.123448
$638$	12.4689	0.493650
$639$	5.74209	0.227154
$640$	33.0777	1.30751
$641$	0.0335428	0.00132486	0.000662431	−	1.00000i	$-0.499789\pi$
$641$	0.0335428	0.00132486	0.000662431		1.00000i	$0.499789\pi$
$642$	−0.393458	−0.0155285
$643$	43.8386	1.72883	0.864413	−	0.502783i	$-0.167690\pi$
$643$	43.8386	1.72883	0.864413	+	0.502783i	$0.167690\pi$
$644$	22.0998	0.870852
$645$	−0.238293	−0.00938276
$646$	45.8895	1.80550
$647$	−2.05765	−0.0808947	−0.0404474	−	0.999182i	$-0.512878\pi$
$647$	−2.05765	−0.0808947	−0.0404474	+	0.999182i	$0.512878\pi$
$648$	12.2666	0.481877
$649$	3.11418	0.122242
$650$	32.3158	1.26753
$651$	0.444782	0.0174324
$652$	5.02633	0.196846
$653$	43.8589	1.71633	0.858165	−	0.513373i	$-0.171604\pi$
$653$	43.8589	1.71633	0.858165	+	0.513373i	$0.171604\pi$
$654$	0.680096	0.0265939
$655$	3.25644	0.127240
$656$	16.6373	0.649579
$657$	−43.2087	−1.68573
$658$	−8.97337	−0.349818
$659$	7.51497	0.292742	0.146371	−	0.989230i	$-0.453241\pi$
$659$	7.51497	0.292742	0.146371	+	0.989230i	$0.453241\pi$
$660$	0.259694	0.0101086
$661$	39.8339	1.54936	0.774679	−	0.632355i	$-0.217912\pi$
$661$	39.8339	1.54936	0.774679	+	0.632355i	$0.217912\pi$
$662$	−5.26617	−0.204676
$663$	0.771170	0.0299498
$664$	22.1226	0.858525
$665$	54.4751	2.11245
$666$	9.10051	0.352638
$667$	−50.3059	−1.94785
$668$	7.45709	0.288523
$669$	0.0528112	0.00204180
$670$	−70.4163	−2.72042
$671$	−2.47117	−0.0953984
$672$	−0.972752	−0.0375247
$673$	−14.4400	−0.556620	−0.278310	−	0.960491i	$-0.589774\pi$
$673$	−14.4400	−0.556620	−0.278310	+	0.960491i	$0.589774\pi$
$674$	18.8257	0.725140
$675$	2.16180	0.0832077
$676$	−3.39275	−0.130491
$677$	−9.06911	−0.348554	−0.174277	−	0.984697i	$-0.555759\pi$
$677$	−9.06911	−0.348554	−0.174277	+	0.984697i	$0.555759\pi$
$678$	1.35343	0.0519784
$679$	6.37438	0.244626
$680$	−16.6765	−0.639513
$681$	−0.808110	−0.0309669
$682$	5.06867	0.194090
$683$	36.4455	1.39455	0.697274	−	0.716805i	$-0.254396\pi$
$683$	36.4455	1.39455	0.697274	+	0.716805i	$0.254396\pi$
$684$	25.3044	0.967537
$685$	10.0895	0.385500
$686$	35.2298	1.34508
$687$	1.02302	0.0390308
$688$	5.62197	0.214335
$689$	−0.727618	−0.0277200
$690$	−2.73816	−0.104240
$691$	−27.7404	−1.05529	−0.527647	−	0.849464i	$-0.676926\pi$
$691$	−27.7404	−1.05529	−0.527647	+	0.849464i	$0.676926\pi$
$692$	27.8153	1.05738
$693$	−7.35509	−0.279397
$694$	54.8084	2.08050
$695$	49.2464	1.86802
$696$	0.609956	0.0231203
$697$	−12.5953	−0.477081
$698$	−1.44271	−0.0546075
$699$	−0.909076	−0.0343844
$700$	17.0562	0.644665
$701$	27.8780	1.05294	0.526469	−	0.850194i	$-0.323516\pi$
$701$	27.8780	1.05294	0.526469	+	0.850194i	$0.323516\pi$
$702$	2.22418	0.0839462
$703$	−11.4997	−0.433719
$704$	−1.20017	−0.0452329
$705$	0.425421	0.0160223
$706$	10.5452	0.396873
$707$	8.78634	0.330444
$708$	−0.248349	−0.00933352
$709$	9.39974	0.353015	0.176507	−	0.984299i	$-0.443520\pi$
$709$	9.39974	0.353015	0.176507	+	0.984299i	$0.443520\pi$
$710$	−11.2341	−0.421609
$711$	−19.4825	−0.730652
$712$	17.3857	0.651558
$713$	−20.4495	−0.765840
$714$	1.06371	0.0398085
$715$	10.4323	0.390147
$716$	15.7131	0.587226
$717$	0.712576	0.0266116
$718$	−42.8963	−1.60088
$719$	−22.2829	−0.831011	−0.415505	−	0.909591i	$-0.636395\pi$
$719$	−22.2829	−0.831011	−0.415505	+	0.909591i	$0.636395\pi$
$720$	−48.2191	−1.79702
$721$	28.7395	1.07032
$722$	−49.3667	−1.83724
$723$	−1.16903	−0.0434768
$724$	24.1219	0.896482
$725$	−38.8252	−1.44193
$726$	0.115792	0.00429746
$727$	−35.5643	−1.31901	−0.659503	−	0.751702i	$-0.729233\pi$
$727$	−35.5643	−1.31901	−0.659503	+	0.751702i	$0.729233\pi$
$728$	−10.7643	−0.398952
$729$	−26.7768	−0.991732
$730$	84.5355	3.12880
$731$	−4.25611	−0.157418
$732$	0.197070	0.00728393
$733$	−36.6731	−1.35455	−0.677275	−	0.735730i	$-0.736839\pi$
$733$	−36.6731	−1.35455	−0.677275	+	0.735730i	$0.736839\pi$
$734$	−25.5145	−0.941758
$735$	−0.203748	−0.00751536
$736$	44.7237	1.64854
$737$	−12.0139	−0.442537
$738$	−18.1509	−0.668144
$739$	−33.7859	−1.24284	−0.621418	−	0.783480i	$-0.713443\pi$
$739$	−33.7859	−1.24284	−0.621418	+	0.783480i	$0.713443\pi$
$740$	−6.81282	−0.250444
$741$	−1.40430	−0.0515882
$742$	−1.00364	−0.0368448
$743$	9.50100	0.348558	0.174279	−	0.984696i	$-0.444241\pi$
$743$	9.50100	0.348558	0.174279	+	0.984696i	$0.444241\pi$
$744$	0.247949	0.00909026
$745$	−61.8057	−2.26439
$746$	−25.0046	−0.915485
$747$	−48.4258	−1.77181
$748$	4.63836	0.169595
$749$	−8.34229	−0.304820
$750$	−0.227909	−0.00832206
$751$	−24.8795	−0.907864	−0.453932	−	0.891036i	$-0.649979\pi$
$751$	−24.8795	−0.907864	−0.453932	+	0.891036i	$0.649979\pi$
$752$	−10.0368	−0.366006
$753$	0.743315	0.0270879
$754$	−39.9455	−1.45473
$755$	−11.7542	−0.427778
$756$	1.17392	0.0426949
$757$	5.46785	0.198732	0.0993662	−	0.995051i	$-0.468318\pi$
$757$	5.46785	0.198732	0.0993662	+	0.995051i	$0.468318\pi$
$758$	−5.96488	−0.216654
$759$	−0.467163	−0.0169569
$760$	30.3678	1.10156
$761$	−30.6616	−1.11148	−0.555741	−	0.831355i	$-0.687565\pi$
$761$	−30.6616	−1.11148	−0.555741	+	0.831355i	$0.687565\pi$
$762$	−1.70130	−0.0616315
$763$	14.4197	0.522029
$764$	7.18707	0.260019
$765$	36.5043	1.31982
$766$	32.2250	1.16434
$767$	−9.97657	−0.360233
$768$	−1.33059	−0.0480137
$769$	−25.3589	−0.914464	−0.457232	−	0.889347i	$-0.651159\pi$
$769$	−25.3589	−0.914464	−0.457232	+	0.889347i	$0.651159\pi$
$770$	14.3899	0.518574
$771$	1.31854	0.0474861
$772$	29.1240	1.04819
$773$	14.7257	0.529646	0.264823	−	0.964297i	$-0.414686\pi$
$773$	14.7257	0.529646	0.264823	+	0.964297i	$0.414686\pi$
$774$	−6.13341	−0.220461
$775$	−15.7826	−0.566927
$776$	3.55347	0.127562
$777$	−0.266561	−0.00956284
$778$	−1.18350	−0.0424306
$779$	22.9360	0.821768
$780$	−0.831957	−0.0297888
$781$	−1.91668	−0.0685840
$782$	−48.9058	−1.74887
$783$	−2.67219	−0.0954964
$784$	4.80697	0.171677
$785$	−23.2989	−0.831572
$786$	−0.115792	−0.00413017
$787$	28.3441	1.01036	0.505179	−	0.863015i	$-0.331427\pi$
$787$	28.3441	1.01036	0.505179	+	0.863015i	$0.331427\pi$
$788$	−16.6527	−0.593228
$789$	−1.98444	−0.0706480
$790$	38.1165	1.35613
$791$	28.6962	1.02032
$792$	−4.10018	−0.145694
$793$	7.91664	0.281128
$794$	−52.8797	−1.87663
$795$	0.0475819	0.00168756
$796$	−4.80065	−0.170155
$797$	23.6196	0.836649	0.418325	−	0.908298i	$-0.362617\pi$
$797$	23.6196	0.836649	0.418325	+	0.908298i	$0.362617\pi$
$798$	−1.93702	−0.0685698
$799$	7.59838	0.268811
$800$	34.5170	1.22036
$801$	−38.0569	−1.34467
$802$	−7.56732	−0.267211
$803$	14.4228	0.508969
$804$	0.958081	0.0337889
$805$	−58.0557	−2.04620
$806$	−16.2380	−0.571959
$807$	1.91280	0.0673336
$808$	4.89805	0.172313
$809$	11.5150	0.404845	0.202423	−	0.979298i	$-0.435119\pi$
$809$	11.5150	0.404845	0.202423	+	0.979298i	$0.435119\pi$
$810$	52.5330	1.84582
$811$	47.1127	1.65435	0.827175	−	0.561944i	$-0.189946\pi$
$811$	47.1127	1.65435	0.827175	+	0.561944i	$0.189946\pi$
$812$	−21.0831	−0.739873
$813$	1.31755	0.0462086
$814$	−3.03769	−0.106471
$815$	−13.2041	−0.462519
$816$	1.18978	0.0416506
$817$	7.75036	0.271151
$818$	55.5004	1.94053
$819$	23.5628	0.823350
$820$	13.5881	0.474517
$821$	−2.47067	−0.0862271	−0.0431135	−	0.999070i	$-0.513728\pi$
$821$	−2.47067	−0.0862271	−0.0431135	+	0.999070i	$0.513728\pi$
$822$	−0.358761	−0.0125132
$823$	15.0509	0.524641	0.262320	−	0.964981i	$-0.415512\pi$
$823$	15.0509	0.524641	0.262320	+	0.964981i	$0.415512\pi$
$824$	16.0212	0.558125
$825$	−0.360549	−0.0125527
$826$	−13.7612	−0.478813
$827$	−33.6750	−1.17100	−0.585498	−	0.810674i	$-0.699101\pi$
$827$	−33.6750	−1.17100	−0.585498	+	0.810674i	$0.699101\pi$
$828$	−26.9676	−0.937190
$829$	−49.6045	−1.72284	−0.861418	−	0.507896i	$-0.830423\pi$
$829$	−49.6045	−1.72284	−0.861418	+	0.507896i	$0.830423\pi$
$830$	94.7426	3.28856
$831$	−0.139747	−0.00484777
$832$	3.84485	0.133296
$833$	−3.63911	−0.126088
$834$	−1.75110	−0.0606356
$835$	−19.5897	−0.677928
$836$	−8.44644	−0.292126
$837$	−1.08626	−0.0375465
$838$	−11.9223	−0.411849
$839$	11.6059	0.400680	0.200340	−	0.979726i	$-0.435795\pi$
$839$	11.6059	0.400680	0.200340	+	0.979726i	$0.435795\pi$
$840$	0.703922	0.0242876
$841$	18.9917	0.654887
$842$	−72.8067	−2.50908
$843$	−0.673294	−0.0231895
$844$	24.9168	0.857672
$845$	8.91271	0.306607
$846$	10.9499	0.376466
$847$	2.45508	0.0843577
$848$	−1.12259	−0.0385497
$849$	1.36522	0.0468541
$850$	−37.7447	−1.29463
$851$	12.2556	0.420115
$852$	0.152851	0.00523658
$853$	13.4357	0.460030	0.230015	−	0.973187i	$-0.426122\pi$
$853$	13.4357	0.460030	0.230015	+	0.973187i	$0.426122\pi$
$854$	10.9198	0.373668
$855$	−66.4742	−2.27337
$856$	−4.65051	−0.158951
$857$	−20.2461	−0.691592	−0.345796	−	0.938310i	$-0.612391\pi$
$857$	−20.2461	−0.691592	−0.345796	+	0.938310i	$0.612391\pi$
$858$	−0.370952	−0.0126641
$859$	−14.4837	−0.494179	−0.247089	−	0.968993i	$-0.579474\pi$
$859$	−14.4837	−0.494179	−0.247089	+	0.968993i	$0.579474\pi$
$860$	4.59159	0.156572
$861$	0.531654	0.0181187
$862$	−68.2471	−2.32451
$863$	−15.0567	−0.512535	−0.256267	−	0.966606i	$-0.582493\pi$
$863$	−15.0567	−0.512535	−0.256267	+	0.966606i	$0.582493\pi$
$864$	2.37568	0.0808221
$865$	−73.0704	−2.48447
$866$	20.1054	0.683208
$867$	0.192938	0.00655250
$868$	−8.57038	−0.290898
$869$	6.50315	0.220604
$870$	2.61220	0.0885619
$871$	38.4876	1.30410
$872$	8.03845	0.272216
$873$	−7.77845	−0.263261
$874$	89.0574	3.01241
$875$	−4.83223	−0.163359
$876$	−1.15019	−0.0388612
$877$	29.9062	1.00986	0.504931	−	0.863160i	$-0.331518\pi$
$877$	29.9062	1.00986	0.504931	+	0.863160i	$0.331518\pi$
$878$	−61.9261	−2.08990
$879$	2.04454	0.0689606
$880$	16.0952	0.542571
$881$	15.9274	0.536607	0.268304	−	0.963334i	$-0.413537\pi$
$881$	15.9274	0.536607	0.268304	+	0.963334i	$0.413537\pi$
$882$	−5.24427	−0.176584
$883$	−11.9251	−0.401310	−0.200655	−	0.979662i	$-0.564307\pi$
$883$	−11.9251	−0.401310	−0.200655	+	0.979662i	$0.564307\pi$
$884$	−14.8595	−0.499777
$885$	0.652409	0.0219305
$886$	16.1989	0.544213
$887$	33.2052	1.11492	0.557461	−	0.830203i	$-0.311776\pi$
$887$	33.2052	1.11492	0.557461	+	0.830203i	$0.311776\pi$
$888$	−0.148598	−0.00498662
$889$	−36.0717	−1.20981
$890$	74.4563	2.49578
$891$	8.96277	0.300264
$892$	−1.01760	−0.0340719
$893$	−13.8366	−0.463025
$894$	2.19768	0.0735015
$895$	−41.2781	−1.37977
$896$	−24.9378	−0.833113
$897$	1.49660	0.0499701
$898$	40.8739	1.36398
$899$	19.5088	0.650656
$900$	−20.8132	−0.693772
$901$	0.849853	0.0283127
$902$	6.05866	0.201731
$903$	0.179653	0.00597847
$904$	15.9970	0.532053
$905$	−63.3678	−2.10642
$906$	0.417954	0.0138856
$907$	−21.4111	−0.710943	−0.355471	−	0.934687i	$-0.615680\pi$
$907$	−21.4111	−0.710943	−0.355471	+	0.934687i	$0.615680\pi$
$908$	15.5712	0.516750
$909$	−10.7217	−0.355616
$910$	−46.0993	−1.52818
$911$	36.6152	1.21312	0.606558	−	0.795040i	$-0.292550\pi$
$911$	36.6152	1.21312	0.606558	+	0.795040i	$0.292550\pi$
$912$	−2.16658	−0.0717428
$913$	16.1642	0.534958
$914$	−16.3766	−0.541690
$915$	−0.517701	−0.0171147
$916$	−19.7124	−0.651315
$917$	−2.45508	−0.0810740
$918$	−2.59783	−0.0857410
$919$	35.4357	1.16892	0.584458	−	0.811424i	$-0.301307\pi$
$919$	35.4357	1.16892	0.584458	+	0.811424i	$0.301307\pi$
$920$	−32.3639	−1.06701
$921$	−0.275284	−0.00907091
$922$	5.98654	0.197156
$923$	6.14026	0.202109
$924$	−0.195788	−0.00644094
$925$	9.45863	0.310998
$926$	49.1029	1.61362
$927$	−35.0699	−1.15185
$928$	−42.6664	−1.40059
$929$	41.0030	1.34526	0.672632	−	0.739977i	$-0.265164\pi$
$929$	41.0030	1.34526	0.672632	+	0.739977i	$0.265164\pi$
$930$	1.06187	0.0348201
$931$	6.62682	0.217185
$932$	17.5167	0.573779
$933$	1.86686	0.0611183
$934$	−18.5463	−0.606855
$935$	−12.1849	−0.398489
$936$	13.1354	0.429342
$937$	−46.2391	−1.51057	−0.755283	−	0.655398i	$-0.772501\pi$
$937$	−46.2391	−1.51057	−0.755283	+	0.655398i	$0.772501\pi$
$938$	53.0879	1.73338
$939$	1.24083	0.0404929
$940$	−8.19732	−0.267367
$941$	34.2488	1.11648	0.558239	−	0.829680i	$-0.311477\pi$
$941$	34.2488	1.11648	0.558239	+	0.829680i	$0.311477\pi$
$942$	0.828459	0.0269927
$943$	−24.4436	−0.795993
$944$	−15.3921	−0.500970
$945$	−3.08386	−0.100318
$946$	2.04730	0.0665633
$947$	−19.0131	−0.617844	−0.308922	−	0.951087i	$-0.599968\pi$
$947$	−19.0131	−0.617844	−0.308922	+	0.951087i	$0.599968\pi$
$948$	−0.518612	−0.0168437
$949$	−46.2049	−1.49987
$950$	68.7330	2.22999
$951$	−1.50220	−0.0487122
$952$	12.5727	0.407482
$953$	−15.8364	−0.512991	−0.256496	−	0.966545i	$-0.582568\pi$
$953$	−15.8364	−0.512991	−0.256496	+	0.966545i	$0.582568\pi$
$954$	1.22471	0.0396515
$955$	−18.8803	−0.610953
$956$	−13.7304	−0.444073
$957$	0.445673	0.0144066
$958$	18.0891	0.584433
$959$	−7.60663	−0.245631
$960$	−0.251430	−0.00811488
$961$	−23.0696	−0.744180
$962$	9.73156	0.313758
$963$	10.1798	0.328040
$964$	22.5258	0.725506
$965$	−76.5082	−2.46289
$966$	2.06434	0.0664191
$967$	20.1609	0.648332	0.324166	−	0.946000i	$-0.394916\pi$
$967$	20.1609	0.648332	0.324166	+	0.946000i	$0.394916\pi$
$968$	1.36862	0.0439890
$969$	1.64021	0.0526912
$970$	15.2181	0.488625
$971$	−5.76929	−0.185145	−0.0925727	−	0.995706i	$-0.529509\pi$
$971$	−5.76929	−0.185145	−0.0925727	+	0.995706i	$0.529509\pi$
$972$	−2.14923	−0.0689367
$973$	−37.1276	−1.19026
$974$	−69.9791	−2.24228
$975$	1.15505	0.0369913
$976$	12.2140	0.390960
$977$	8.56944	0.274161	0.137080	−	0.990560i	$-0.456228\pi$
$977$	8.56944	0.274161	0.137080	+	0.990560i	$0.456228\pi$
$978$	0.469510	0.0150133
$979$	12.7032	0.405995
$980$	3.92596	0.125410
$981$	−17.5959	−0.561795
$982$	−56.2916	−1.79634
$983$	−1.15044	−0.0366934	−0.0183467	−	0.999832i	$-0.505840\pi$
$983$	−1.15044	−0.0366934	−0.0183467	+	0.999832i	$0.505840\pi$
$984$	0.296377	0.00944816
$985$	43.7464	1.39388
$986$	46.6561	1.48583
$987$	−0.320732	−0.0102090
$988$	27.0590	0.860862
$989$	−8.25979	−0.262646
$990$	−17.5595	−0.558077
$991$	−19.0654	−0.605632	−0.302816	−	0.953049i	$-0.597927\pi$
$991$	−19.0654	−0.605632	−0.302816	+	0.953049i	$0.597927\pi$
$992$	−17.3440	−0.550674
$993$	−0.188227	−0.00597320
$994$	8.46957	0.268639
$995$	12.6112	0.399803
$996$	−1.28906	−0.0408455
$997$	25.6608	0.812687	0.406343	−	0.913720i	$-0.366804\pi$
$997$	25.6608	0.812687	0.406343	+	0.913720i	$0.366804\pi$
$998$	56.6274	1.79251
$999$	0.651002	0.0205968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.e.1.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.e.1.5	✓	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-1.79989 q^{2} -0.0643329 q^{3} +1.23961 q^{4} -3.25644 q^{5} +0.115792 q^{6} +2.45508 q^{7} +1.36862 q^{8} -2.99586 q^{9} +O(q^{10})\)	\(q-1.79989 q^{2} -0.0643329 q^{3} +1.23961 q^{4} -3.25644 q^{5} +0.115792 q^{6} +2.45508 q^{7} +1.36862 q^{8} -2.99586 q^{9} +5.86125 q^{10} +1.00000 q^{11} -0.0797479 q^{12} -3.20360 q^{13} -4.41889 q^{14} +0.209496 q^{15} -4.94259 q^{16} +3.74178 q^{17} +5.39223 q^{18} -6.81378 q^{19} -4.03673 q^{20} -0.157943 q^{21} -1.79989 q^{22} +7.26165 q^{23} -0.0880471 q^{24} +5.60442 q^{25} +5.76613 q^{26} +0.385731 q^{27} +3.04335 q^{28} -6.92761 q^{29} -0.377071 q^{30} -2.81610 q^{31} +6.15889 q^{32} -0.0643329 q^{33} -6.73481 q^{34} -7.99484 q^{35} -3.71371 q^{36} +1.68771 q^{37} +12.2641 q^{38} +0.206097 q^{39} -4.45682 q^{40} -3.36612 q^{41} +0.284280 q^{42} -1.13745 q^{43} +1.23961 q^{44} +9.75585 q^{45} -13.0702 q^{46} +2.03068 q^{47} +0.317971 q^{48} -0.972561 q^{49} -10.0874 q^{50} -0.240720 q^{51} -3.97122 q^{52} +0.227125 q^{53} -0.694275 q^{54} -3.25644 q^{55} +3.36007 q^{56} +0.438350 q^{57} +12.4689 q^{58} +3.11418 q^{59} +0.259694 q^{60} -2.47117 q^{61} +5.06867 q^{62} -7.35509 q^{63} -1.20017 q^{64} +10.4323 q^{65} +0.115792 q^{66} -12.0139 q^{67} +4.63836 q^{68} -0.467163 q^{69} +14.3899 q^{70} -1.91668 q^{71} -4.10018 q^{72} +14.4228 q^{73} -3.03769 q^{74} -0.360549 q^{75} -8.44644 q^{76} +2.45508 q^{77} -0.370952 q^{78} +6.50315 q^{79} +16.0952 q^{80} +8.96277 q^{81} +6.05866 q^{82} +16.1642 q^{83} -0.195788 q^{84} -12.1849 q^{85} +2.04730 q^{86} +0.445673 q^{87} +1.36862 q^{88} +12.7032 q^{89} -17.5595 q^{90} -7.86511 q^{91} +9.00163 q^{92} +0.181168 q^{93} -3.65501 q^{94} +22.1887 q^{95} -0.396219 q^{96} +2.59640 q^{97} +1.75051 q^{98} -2.99586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9	\( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99}+O(q^{100}) \) 28 * q + 7 * q^2 - 2 * q^3 + 27 * q^4 + 3 * q^5 - q^6 + 7 * q^7 + 21 * q^8 + 28 * q^9 + 14 * q^10 + 28 * q^11 - 6 * q^12 + 3 * q^13 - q^14 + 19 * q^15 + 29 * q^16 + 9 * q^17 - 2 * q^18 + 20 * q^19 + 6 * q^20 + 6 * q^21 + 7 * q^22 + 24 * q^23 + 20 * q^24 + 23 * q^25 + 10 * q^26 - 20 * q^27 - 3 * q^28 + 43 * q^29 + 11 * q^30 + 3 * q^31 + 44 * q^32 - 2 * q^33 - 28 * q^34 + 32 * q^35 + 24 * q^36 - 4 * q^37 + 24 * q^38 + 37 * q^39 + 22 * q^40 + 32 * q^41 - 27 * q^42 + 25 * q^43 + 27 * q^44 - 36 * q^45 + 10 * q^46 + 19 * q^47 + 42 * q^48 + 17 * q^49 + q^50 + 39 * q^51 - 19 * q^52 + 5 * q^53 + 6 * q^54 + 3 * q^55 + 8 * q^56 + 2 * q^57 + 21 * q^58 + 44 * q^59 + 65 * q^60 + 28 * q^61 + 60 * q^62 - 8 * q^63 + 5 * q^64 + 33 * q^65 - q^66 + 7 * q^67 + 13 * q^68 - 22 * q^69 + 9 * q^70 + 117 * q^71 - 17 * q^72 + 7 * q^73 + 41 * q^74 - 40 * q^75 + 34 * q^76 + 7 * q^77 - 97 * q^78 + 48 * q^79 + 41 * q^80 + 40 * q^81 + 2 * q^82 + 22 * q^83 + 27 * q^84 + 30 * q^85 + 24 * q^86 + 37 * q^87 + 21 * q^88 - 6 * q^89 + 4 * q^90 - 33 * q^91 + 18 * q^92 + 5 * q^93 - 43 * q^94 + 64 * q^95 + 55 * q^96 - 50 * q^97 + 97 * q^98 + 28 * q^99

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