LMFDB - Embedded newform 1441.2.a.f.1.13

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:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-0.413206 q^{2} -2.92261 q^{3} -1.82926 q^{4} -1.23288 q^{5} +1.20764 q^{6} +5.16907 q^{7} +1.58227 q^{8} +5.54166 q^{9} +O(q^{10})$	\(q-0.413206 q^{2} -2.92261 q^{3} -1.82926 q^{4} -1.23288 q^{5} +1.20764 q^{6} +5.16907 q^{7} +1.58227 q^{8} +5.54166 q^{9} +0.509432 q^{10} -1.00000 q^{11} +5.34622 q^{12} -5.31732 q^{13} -2.13589 q^{14} +3.60322 q^{15} +3.00471 q^{16} +5.77862 q^{17} -2.28985 q^{18} -5.78717 q^{19} +2.25525 q^{20} -15.1072 q^{21} +0.413206 q^{22} -0.288155 q^{23} -4.62438 q^{24} -3.48002 q^{25} +2.19715 q^{26} -7.42830 q^{27} -9.45557 q^{28} -4.95167 q^{29} -1.48887 q^{30} +2.06460 q^{31} -4.40612 q^{32} +2.92261 q^{33} -2.38776 q^{34} -6.37282 q^{35} -10.1371 q^{36} +8.22558 q^{37} +2.39129 q^{38} +15.5405 q^{39} -1.95075 q^{40} -3.54569 q^{41} +6.24238 q^{42} -1.58047 q^{43} +1.82926 q^{44} -6.83219 q^{45} +0.119068 q^{46} -10.1500 q^{47} -8.78162 q^{48} +19.7193 q^{49} +1.43796 q^{50} -16.8887 q^{51} +9.72676 q^{52} +9.49951 q^{53} +3.06942 q^{54} +1.23288 q^{55} +8.17889 q^{56} +16.9136 q^{57} +2.04606 q^{58} +2.41275 q^{59} -6.59123 q^{60} -10.8321 q^{61} -0.853105 q^{62} +28.6452 q^{63} -4.18879 q^{64} +6.55559 q^{65} -1.20764 q^{66} +11.2269 q^{67} -10.5706 q^{68} +0.842166 q^{69} +2.63329 q^{70} +9.78271 q^{71} +8.76843 q^{72} -9.62082 q^{73} -3.39886 q^{74} +10.1707 q^{75} +10.5862 q^{76} -5.16907 q^{77} -6.42141 q^{78} -2.70061 q^{79} -3.70444 q^{80} +5.08504 q^{81} +1.46510 q^{82} +4.18018 q^{83} +27.6350 q^{84} -7.12432 q^{85} +0.653059 q^{86} +14.4718 q^{87} -1.58227 q^{88} +1.89575 q^{89} +2.82310 q^{90} -27.4856 q^{91} +0.527111 q^{92} -6.03402 q^{93} +4.19406 q^{94} +7.13486 q^{95} +12.8774 q^{96} +2.15336 q^{97} -8.14812 q^{98} -5.54166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.413206	−0.292181	−0.146091	−	0.989271i	$-0.546669\pi$
$2$	−0.413206	−0.292181	−0.146091	+	0.989271i	$0.546669\pi$
$3$	−2.92261	−1.68737	−0.843686	−	0.536838i	$-0.819619\pi$
$3$	−2.92261	−1.68737	−0.843686	+	0.536838i	$0.819619\pi$
$4$	−1.82926	−0.914630
$5$	−1.23288	−0.551359	−0.275680	−	0.961250i	$-0.588903\pi$
$5$	−1.23288	−0.551359	−0.275680	+	0.961250i	$0.588903\pi$
$6$	1.20764	0.493018
$7$	5.16907	1.95372	0.976862	−	0.213871i	$-0.0686073\pi$
$7$	5.16907	1.95372	0.976862	+	0.213871i	$0.0686073\pi$
$8$	1.58227	0.559419
$9$	5.54166	1.84722
$10$	0.509432	0.161097
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.34622	1.54332
$13$	−5.31732	−1.47476	−0.737379	−	0.675479i	$-0.763937\pi$
$13$	−5.31732	−1.47476	−0.737379	+	0.675479i	$0.763937\pi$
$14$	−2.13589	−0.570841
$15$	3.60322	0.930347
$16$	3.00471	0.751179
$17$	5.77862	1.40152	0.700760	−	0.713397i	$-0.252844\pi$
$17$	5.77862	1.40152	0.700760	+	0.713397i	$0.252844\pi$
$18$	−2.28985	−0.539723
$19$	−5.78717	−1.32767	−0.663834	−	0.747880i	$-0.731072\pi$
$19$	−5.78717	−1.32767	−0.663834	+	0.747880i	$0.731072\pi$
$20$	2.25525	0.504290
$21$	−15.1072	−3.29666
$22$	0.413206	0.0880959
$23$	−0.288155	−0.0600845	−0.0300423	−	0.999549i	$-0.509564\pi$
$23$	−0.288155	−0.0600845	−0.0300423	+	0.999549i	$0.509564\pi$
$24$	−4.62438	−0.943947
$25$	−3.48002	−0.696003
$26$	2.19715	0.430896
$27$	−7.42830	−1.42958
$28$	−9.45557	−1.78693
$29$	−4.95167	−0.919502	−0.459751	−	0.888048i	$-0.652061\pi$
$29$	−4.95167	−0.919502	−0.459751	+	0.888048i	$0.652061\pi$
$30$	−1.48887	−0.271830
$31$	2.06460	0.370813	0.185406	−	0.982662i	$-0.440640\pi$
$31$	2.06460	0.370813	0.185406	+	0.982662i	$0.440640\pi$
$32$	−4.40612	−0.778899
$33$	2.92261	0.508762
$34$	−2.38776	−0.409498
$35$	−6.37282	−1.07720
$36$	−10.1371	−1.68952
$37$	8.22558	1.35228	0.676138	−	0.736775i	$-0.263652\pi$
$37$	8.22558	1.35228	0.676138	+	0.736775i	$0.263652\pi$
$38$	2.39129	0.387919
$39$	15.5405	2.48846
$40$	−1.95075	−0.308441
$41$	−3.54569	−0.553744	−0.276872	−	0.960907i	$-0.589298\pi$
$41$	−3.54569	−0.553744	−0.276872	+	0.960907i	$0.589298\pi$
$42$	6.24238	0.963221
$43$	−1.58047	−0.241019	−0.120509	−	0.992712i	$-0.538453\pi$
$43$	−1.58047	−0.241019	−0.120509	+	0.992712i	$0.538453\pi$
$44$	1.82926	0.275771
$45$	−6.83219	−1.01848
$46$	0.119068	0.0175556
$47$	−10.1500	−1.48054	−0.740268	−	0.672312i	$-0.765301\pi$
$47$	−10.1500	−1.48054	−0.740268	+	0.672312i	$0.765301\pi$
$48$	−8.78162	−1.26752
$49$	19.7193	2.81704
$50$	1.43796	0.203359
$51$	−16.8887	−2.36489
$52$	9.72676	1.34886
$53$	9.49951	1.30486	0.652429	−	0.757850i	$-0.273750\pi$
$53$	9.49951	1.30486	0.652429	+	0.757850i	$0.273750\pi$
$54$	3.06942	0.417695
$55$	1.23288	0.166241
$56$	8.17889	1.09295
$57$	16.9136	2.24027
$58$	2.04606	0.268661
$59$	2.41275	0.314113	0.157057	−	0.987590i	$-0.449799\pi$
$59$	2.41275	0.314113	0.157057	+	0.987590i	$0.449799\pi$
$60$	−6.59123	−0.850924
$61$	−10.8321	−1.38690	−0.693452	−	0.720502i	$-0.743911\pi$
$61$	−10.8321	−1.38690	−0.693452	+	0.720502i	$0.743911\pi$
$62$	−0.853105	−0.108345
$63$	28.6452	3.60896
$64$	−4.18879	−0.523599
$65$	6.55559	0.813121
$66$	−1.20764	−0.148650
$67$	11.2269	1.37158	0.685790	−	0.727800i	$-0.259457\pi$
$67$	11.2269	1.37158	0.685790	+	0.727800i	$0.259457\pi$
$68$	−10.5706	−1.28187
$69$	0.842166	0.101385
$70$	2.63329	0.314738
$71$	9.78271	1.16099	0.580497	−	0.814262i	$-0.302858\pi$
$71$	9.78271	1.16099	0.580497	+	0.814262i	$0.302858\pi$
$72$	8.76843	1.03337
$73$	−9.62082	−1.12603	−0.563016	−	0.826446i	$-0.690359\pi$
$73$	−9.62082	−1.12603	−0.563016	+	0.826446i	$0.690359\pi$
$74$	−3.39886	−0.395110
$75$	10.1707	1.17442
$76$	10.5862	1.21432
$77$	−5.16907	−0.589070
$78$	−6.42141	−0.727082
$79$	−2.70061	−0.303842	−0.151921	−	0.988393i	$-0.548546\pi$
$79$	−2.70061	−0.303842	−0.151921	+	0.988393i	$0.548546\pi$
$80$	−3.70444	−0.414169
$81$	5.08504	0.565005
$82$	1.46510	0.161794
$83$	4.18018	0.458835	0.229417	−	0.973328i	$-0.426318\pi$
$83$	4.18018	0.458835	0.229417	+	0.973328i	$0.426318\pi$
$84$	27.6350	3.01522
$85$	−7.12432	−0.772741
$86$	0.653059	0.0704211
$87$	14.4718	1.55154
$88$	−1.58227	−0.168671
$89$	1.89575	0.200949	0.100475	−	0.994940i	$-0.467964\pi$
$89$	1.89575	0.200949	0.100475	+	0.994940i	$0.467964\pi$
$90$	2.82310	0.297581
$91$	−27.4856	−2.88127
$92$	0.527111	0.0549551
$93$	−6.03402	−0.625699
$94$	4.19406	0.432585
$95$	7.13486	0.732021
$96$	12.8774	1.31429
$97$	2.15336	0.218641	0.109320	−	0.994007i	$-0.465133\pi$
$97$	2.15336	0.218641	0.109320	+	0.994007i	$0.465133\pi$
$98$	−8.14812	−0.823085
$99$	−5.54166	−0.556958
$100$	6.36586	0.636586
$101$	13.5381	1.34709	0.673547	−	0.739144i	$-0.264770\pi$
$101$	13.5381	1.34709	0.673547	+	0.739144i	$0.264770\pi$
$102$	6.97850	0.690975
$103$	3.68228	0.362826	0.181413	−	0.983407i	$-0.441933\pi$
$103$	3.68228	0.362826	0.181413	+	0.983407i	$0.441933\pi$
$104$	−8.41346	−0.825007
$105$	18.6253	1.81764
$106$	−3.92526	−0.381255
$107$	11.9137	1.15175	0.575873	−	0.817539i	$-0.304662\pi$
$107$	11.9137	1.15175	0.575873	+	0.817539i	$0.304662\pi$
$108$	13.5883	1.30753
$109$	8.85689	0.848337	0.424168	−	0.905583i	$-0.360566\pi$
$109$	8.85689	0.848337	0.424168	+	0.905583i	$0.360566\pi$
$110$	−0.509432	−0.0485725
$111$	−24.0402	−2.28179
$112$	15.5316	1.46760
$113$	18.8534	1.77358	0.886791	−	0.462170i	$-0.152929\pi$
$113$	18.8534	1.77358	0.886791	+	0.462170i	$0.152929\pi$
$114$	−6.98883	−0.654564
$115$	0.355260	0.0331281
$116$	9.05790	0.841005
$117$	−29.4668	−2.72420
$118$	−0.996964	−0.0917780
$119$	29.8701	2.73818
$120$	5.70128	0.520454
$121$	1.00000	0.0909091
$122$	4.47588	0.405227
$123$	10.3627	0.934372
$124$	−3.77669	−0.339157
$125$	10.4548	0.935107
$126$	−11.8364	−1.05447
$127$	−2.51872	−0.223500	−0.111750	−	0.993736i	$-0.535646\pi$
$127$	−2.51872	−0.223500	−0.111750	+	0.993736i	$0.535646\pi$
$128$	10.5431	0.931885
$129$	4.61909	0.406688
$130$	−2.70881	−0.237579
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−5.34622	−0.465329
$133$	−29.9143	−2.59389
$134$	−4.63901	−0.400749
$135$	9.15817	0.788210
$136$	9.14336	0.784037
$137$	−19.3835	−1.65605	−0.828024	−	0.560693i	$-0.810535\pi$
$137$	−19.3835	−1.65605	−0.828024	+	0.560693i	$0.810535\pi$
$138$	−0.347988	−0.0296227
$139$	12.1178	1.02781	0.513907	−	0.857846i	$-0.328198\pi$
$139$	12.1178	1.02781	0.513907	+	0.857846i	$0.328198\pi$
$140$	11.6575	0.985243
$141$	29.6646	2.49821
$142$	−4.04228	−0.339220
$143$	5.31732	0.444656
$144$	16.6511	1.38759
$145$	6.10480	0.506976
$146$	3.97538	0.329005
$147$	−57.6317	−4.75339
$148$	−15.0467	−1.23683
$149$	−10.8485	−0.888740	−0.444370	−	0.895843i	$-0.646572\pi$
$149$	−10.8485	−0.888740	−0.444370	+	0.895843i	$0.646572\pi$
$150$	−4.20261	−0.343142
$151$	−17.2300	−1.40215	−0.701077	−	0.713085i	$-0.747297\pi$
$151$	−17.2300	−1.40215	−0.701077	+	0.713085i	$0.747297\pi$
$152$	−9.15689	−0.742722
$153$	32.0231	2.58892
$154$	2.13589	0.172115
$155$	−2.54540	−0.204451
$156$	−28.4275	−2.27602
$157$	−10.4189	−0.831520	−0.415760	−	0.909474i	$-0.636484\pi$
$157$	−10.4189	−0.831520	−0.415760	+	0.909474i	$0.636484\pi$
$158$	1.11591	0.0887769
$159$	−27.7634	−2.20178
$160$	5.43220	0.429453
$161$	−1.48949	−0.117389
$162$	−2.10117	−0.165084
$163$	−1.13061	−0.0885564	−0.0442782	−	0.999019i	$-0.514099\pi$
$163$	−1.13061	−0.0885564	−0.0442782	+	0.999019i	$0.514099\pi$
$164$	6.48600	0.506471
$165$	−3.60322	−0.280510
$166$	−1.72728	−0.134063
$167$	11.2462	0.870258	0.435129	−	0.900368i	$-0.356703\pi$
$167$	11.2462	0.870258	0.435129	+	0.900368i	$0.356703\pi$
$168$	−23.9037	−1.84421
$169$	15.2739	1.17491
$170$	2.94381	0.225780
$171$	−32.0705	−2.45249
$172$	2.89108	0.220443
$173$	0.547138	0.0415982	0.0207991	−	0.999784i	$-0.493379\pi$
$173$	0.547138	0.0415982	0.0207991	+	0.999784i	$0.493379\pi$
$174$	−5.97985	−0.453331
$175$	−17.9884	−1.35980
$176$	−3.00471	−0.226489
$177$	−7.05153	−0.530026
$178$	−0.783337	−0.0587136
$179$	−2.24666	−0.167923	−0.0839616	−	0.996469i	$-0.526757\pi$
$179$	−2.24666	−0.167923	−0.0839616	+	0.996469i	$0.526757\pi$
$180$	12.4978	0.931535
$181$	4.28313	0.318363	0.159181	−	0.987249i	$-0.449115\pi$
$181$	4.28313	0.318363	0.159181	+	0.987249i	$0.449115\pi$
$182$	11.3572	0.841852
$183$	31.6580	2.34022
$184$	−0.455941	−0.0336124
$185$	−10.1411	−0.745590
$186$	2.49330	0.182817
$187$	−5.77862	−0.422574
$188$	18.5671	1.35414
$189$	−38.3974	−2.79300
$190$	−2.94817	−0.213883
$191$	12.0273	0.870268	0.435134	−	0.900366i	$-0.356701\pi$
$191$	12.0273	0.870268	0.435134	+	0.900366i	$0.356701\pi$
$192$	12.2422	0.883506
$193$	−21.7075	−1.56254	−0.781271	−	0.624192i	$-0.785428\pi$
$193$	−21.7075	−1.56254	−0.781271	+	0.624192i	$0.785428\pi$
$194$	−0.889782	−0.0638827
$195$	−19.1595	−1.37204
$196$	−36.0717	−2.57655
$197$	16.4544	1.17233	0.586163	−	0.810193i	$-0.300638\pi$
$197$	16.4544	1.17233	0.586163	+	0.810193i	$0.300638\pi$
$198$	2.28985	0.162733
$199$	20.2502	1.43550	0.717750	−	0.696300i	$-0.245172\pi$
$199$	20.2502	1.43550	0.717750	+	0.696300i	$0.245172\pi$
$200$	−5.50634	−0.389357
$201$	−32.8118	−2.31436
$202$	−5.59404	−0.393596
$203$	−25.5955	−1.79645
$204$	30.8938	2.16300
$205$	4.37140	0.305312
$206$	−1.52154	−0.106011
$207$	−1.59686	−0.110989
$208$	−15.9770	−1.10781
$209$	5.78717	0.400307
$210$	−7.69609	−0.531080
$211$	13.7289	0.945135	0.472568	−	0.881294i	$-0.343327\pi$
$211$	13.7289	0.945135	0.472568	+	0.881294i	$0.343327\pi$
$212$	−17.3771	−1.19346
$213$	−28.5911	−1.95903
$214$	−4.92284	−0.336518
$215$	1.94852	0.132888
$216$	−11.7536	−0.799732
$217$	10.6721	0.724466
$218$	−3.65973	−0.247868
$219$	28.1179	1.90003
$220$	−2.25525	−0.152049
$221$	−30.7267	−2.06690
$222$	9.93355	0.666696
$223$	5.27344	0.353136	0.176568	−	0.984288i	$-0.443500\pi$
$223$	5.27344	0.353136	0.176568	+	0.984288i	$0.443500\pi$
$224$	−22.7755	−1.52175
$225$	−19.2851	−1.28567
$226$	−7.79036	−0.518207
$227$	9.21023	0.611304	0.305652	−	0.952143i	$-0.401126\pi$
$227$	9.21023	0.611304	0.305652	+	0.952143i	$0.401126\pi$
$228$	−30.9395	−2.04902
$229$	−6.78252	−0.448202	−0.224101	−	0.974566i	$-0.571944\pi$
$229$	−6.78252	−0.448202	−0.224101	+	0.974566i	$0.571944\pi$
$230$	−0.146796	−0.00967941
$231$	15.1072	0.993979
$232$	−7.83491	−0.514387
$233$	8.27756	0.542281	0.271141	−	0.962540i	$-0.412599\pi$
$233$	8.27756	0.542281	0.271141	+	0.962540i	$0.412599\pi$
$234$	12.1759	0.795961
$235$	12.5137	0.816307
$236$	−4.41355	−0.287298
$237$	7.89283	0.512694
$238$	−12.3425	−0.800045
$239$	24.0135	1.55330	0.776652	−	0.629930i	$-0.216916\pi$
$239$	24.0135	1.55330	0.776652	+	0.629930i	$0.216916\pi$
$240$	10.8266	0.698857
$241$	−12.3120	−0.793087	−0.396544	−	0.918016i	$-0.629790\pi$
$241$	−12.3120	−0.793087	−0.396544	+	0.918016i	$0.629790\pi$
$242$	−0.413206	−0.0265619
$243$	7.42328	0.476204
$244$	19.8147	1.26851
$245$	−24.3114	−1.55320
$246$	−4.28193	−0.273006
$247$	30.7722	1.95799
$248$	3.26676	0.207440
$249$	−12.2171	−0.774224
$250$	−4.31999	−0.273220
$251$	7.96312	0.502628	0.251314	−	0.967906i	$-0.419137\pi$
$251$	7.96312	0.502628	0.251314	+	0.967906i	$0.419137\pi$
$252$	−52.3996	−3.30086
$253$	0.288155	0.0181162
$254$	1.04075	0.0653025
$255$	20.8216	1.30390
$256$	4.02112	0.251320
$257$	6.88733	0.429620	0.214810	−	0.976656i	$-0.431087\pi$
$257$	6.88733	0.429620	0.214810	+	0.976656i	$0.431087\pi$
$258$	−1.90864	−0.118827
$259$	42.5186	2.64197
$260$	−11.9919	−0.743705
$261$	−27.4405	−1.69852
$262$	−0.413206	−0.0255280
$263$	2.61692	0.161367	0.0806833	−	0.996740i	$-0.474290\pi$
$263$	2.61692	0.161367	0.0806833	+	0.996740i	$0.474290\pi$
$264$	4.62438	0.284611
$265$	−11.7117	−0.719445
$266$	12.3608	0.757887
$267$	−5.54055	−0.339076
$268$	−20.5368	−1.25449
$269$	18.5464	1.13079	0.565397	−	0.824819i	$-0.308723\pi$
$269$	18.5464	1.13079	0.565397	+	0.824819i	$0.308723\pi$
$270$	−3.78422	−0.230300
$271$	10.0160	0.608428	0.304214	−	0.952604i	$-0.401606\pi$
$271$	10.0160	0.608428	0.304214	+	0.952604i	$0.401606\pi$
$272$	17.3631	1.05279
$273$	80.3297	4.86177
$274$	8.00940	0.483866
$275$	3.48002	0.209853
$276$	−1.54054	−0.0927297
$277$	1.66317	0.0999305	0.0499652	−	0.998751i	$-0.484089\pi$
$277$	1.66317	0.0999305	0.0499652	+	0.998751i	$0.484089\pi$
$278$	−5.00713	−0.300308
$279$	11.4413	0.684973
$280$	−10.0836	−0.602608
$281$	23.8478	1.42264	0.711320	−	0.702869i	$-0.248098\pi$
$281$	23.8478	1.42264	0.711320	+	0.702869i	$0.248098\pi$
$282$	−12.2576	−0.729931
$283$	−5.75559	−0.342135	−0.171067	−	0.985259i	$-0.554722\pi$
$283$	−5.75559	−0.342135	−0.171067	+	0.985259i	$0.554722\pi$
$284$	−17.8951	−1.06188
$285$	−20.8524	−1.23519
$286$	−2.19715	−0.129920
$287$	−18.3279	−1.08186
$288$	−24.4172	−1.43880
$289$	16.3924	0.964260
$290$	−2.52254	−0.148129
$291$	−6.29344	−0.368928
$292$	17.5990	1.02990
$293$	3.71446	0.217001	0.108501	−	0.994096i	$-0.465395\pi$
$293$	3.71446	0.217001	0.108501	+	0.994096i	$0.465395\pi$
$294$	23.8138	1.38885
$295$	−2.97462	−0.173189
$296$	13.0151	0.756489
$297$	7.42830	0.431034
$298$	4.48265	0.259673
$299$	1.53221	0.0886101
$300$	−18.6049	−1.07416
$301$	−8.16953	−0.470884
$302$	7.11953	0.409683
$303$	−39.5667	−2.27305
$304$	−17.3888	−0.997315
$305$	13.3546	0.764683
$306$	−13.2322	−0.756433
$307$	23.8411	1.36068	0.680341	−	0.732896i	$-0.261832\pi$
$307$	23.8411	1.36068	0.680341	+	0.732896i	$0.261832\pi$
$308$	9.45557	0.538781
$309$	−10.7619	−0.612223
$310$	1.05177	0.0597367
$311$	−11.3458	−0.643360	−0.321680	−	0.946849i	$-0.604247\pi$
$311$	−11.3458	−0.643360	−0.321680	+	0.946849i	$0.604247\pi$
$312$	24.5893	1.39209
$313$	15.8227	0.894353	0.447176	−	0.894446i	$-0.352430\pi$
$313$	15.8227	0.894353	0.447176	+	0.894446i	$0.352430\pi$
$314$	4.30516	0.242954
$315$	−35.3160	−1.98983
$316$	4.94011	0.277903
$317$	7.51810	0.422259	0.211129	−	0.977458i	$-0.432286\pi$
$317$	7.51810	0.422259	0.211129	+	0.977458i	$0.432286\pi$
$318$	11.4720	0.643318
$319$	4.95167	0.277240
$320$	5.16427	0.288691
$321$	−34.8193	−1.94342
$322$	0.615468	0.0342987
$323$	−33.4418	−1.86075
$324$	−9.30187	−0.516770
$325$	18.5043	1.02644
$326$	0.467176	0.0258745
$327$	−25.8853	−1.43146
$328$	−5.61026	−0.309775
$329$	−52.4663	−2.89256
$330$	1.48887	0.0819598
$331$	31.6086	1.73737	0.868683	−	0.495368i	$-0.164967\pi$
$331$	31.6086	1.73737	0.868683	+	0.495368i	$0.164967\pi$
$332$	−7.64664	−0.419664
$333$	45.5834	2.49795
$334$	−4.64701	−0.254273
$335$	−13.8413	−0.756233
$336$	−45.3928	−2.47638
$337$	−30.2795	−1.64943	−0.824714	−	0.565550i	$-0.808664\pi$
$337$	−30.2795	−1.64943	−0.824714	+	0.565550i	$0.808664\pi$
$338$	−6.31125	−0.343287
$339$	−55.1013	−2.99269
$340$	13.0322	0.706772
$341$	−2.06460	−0.111804
$342$	13.2517	0.716572
$343$	65.7467	3.54999
$344$	−2.50073	−0.134830
$345$	−1.03829	−0.0558995
$346$	−0.226081	−0.0121542
$347$	−3.81947	−0.205040	−0.102520	−	0.994731i	$-0.532691\pi$
$347$	−3.81947	−0.205040	−0.102520	+	0.994731i	$0.532691\pi$
$348$	−26.4727	−1.41909
$349$	−24.2262	−1.29680	−0.648398	−	0.761301i	$-0.724561\pi$
$349$	−24.2262	−1.29680	−0.648398	+	0.761301i	$0.724561\pi$
$350$	7.43294	0.397307
$351$	39.4986	2.10828
$352$	4.40612	0.234847
$353$	−3.27107	−0.174102	−0.0870509	−	0.996204i	$-0.527744\pi$
$353$	−3.27107	−0.174102	−0.0870509	+	0.996204i	$0.527744\pi$
$354$	2.91374	0.154863
$355$	−12.0609	−0.640125
$356$	−3.46782	−0.183794
$357$	−87.2986	−4.62033
$358$	0.928333	0.0490639
$359$	23.7118	1.25146	0.625730	−	0.780039i	$-0.284801\pi$
$359$	23.7118	1.25146	0.625730	+	0.780039i	$0.284801\pi$
$360$	−10.8104	−0.569758
$361$	14.4913	0.762700
$362$	−1.76982	−0.0930195
$363$	−2.92261	−0.153397
$364$	50.2783	2.63530
$365$	11.8613	0.620848
$366$	−13.0813	−0.683769
$367$	31.2443	1.63094	0.815470	−	0.578800i	$-0.196479\pi$
$367$	31.2443	1.63094	0.815470	+	0.578800i	$0.196479\pi$
$368$	−0.865824	−0.0451342
$369$	−19.6490	−1.02289
$370$	4.19037	0.217847
$371$	49.1036	2.54933
$372$	11.0378	0.572283
$373$	−36.9781	−1.91465	−0.957326	−	0.289009i	$-0.906674\pi$
$373$	−36.9781	−1.91465	−0.957326	+	0.289009i	$0.906674\pi$
$374$	2.38776	0.123468
$375$	−30.5554	−1.57787
$376$	−16.0602	−0.828239
$377$	26.3296	1.35604
$378$	15.8660	0.816061
$379$	9.00065	0.462332	0.231166	−	0.972914i	$-0.425746\pi$
$379$	9.00065	0.462332	0.231166	+	0.972914i	$0.425746\pi$
$380$	−13.0515	−0.669529
$381$	7.36124	0.377128
$382$	−4.96977	−0.254276
$383$	0.387343	0.0197923	0.00989616	−	0.999951i	$-0.496850\pi$
$383$	0.387343	0.0197923	0.00989616	+	0.999951i	$0.496850\pi$
$384$	−30.8133	−1.57244
$385$	6.37282	0.324789
$386$	8.96968	0.456545
$387$	−8.75841	−0.445215
$388$	−3.93906	−0.199975
$389$	−7.88312	−0.399690	−0.199845	−	0.979828i	$-0.564044\pi$
$389$	−7.88312	−0.399690	−0.199845	+	0.979828i	$0.564044\pi$
$390$	7.91681	0.400883
$391$	−1.66514	−0.0842097
$392$	31.2013	1.57590
$393$	−2.92261	−0.147426
$394$	−6.79906	−0.342532
$395$	3.32951	0.167526
$396$	10.1371	0.509411
$397$	4.69461	0.235616	0.117808	−	0.993036i	$-0.462413\pi$
$397$	4.69461	0.235616	0.117808	+	0.993036i	$0.462413\pi$
$398$	−8.36752	−0.419426
$399$	87.4278	4.37686
$400$	−10.4565	−0.522823
$401$	19.1759	0.957597	0.478799	−	0.877925i	$-0.341072\pi$
$401$	19.1759	0.957597	0.478799	+	0.877925i	$0.341072\pi$
$402$	13.5580	0.676213
$403$	−10.9781	−0.546859
$404$	−24.7648	−1.23209
$405$	−6.26923	−0.311521
$406$	10.5762	0.524890
$407$	−8.22558	−0.407727
$408$	−26.7225	−1.32296
$409$	−16.0424	−0.793243	−0.396622	−	0.917982i	$-0.629818\pi$
$409$	−16.0424	−0.793243	−0.396622	+	0.917982i	$0.629818\pi$
$410$	−1.80629	−0.0892064
$411$	56.6506	2.79437
$412$	−6.73586	−0.331852
$413$	12.4717	0.613691
$414$	0.659832	0.0324290
$415$	−5.15365	−0.252983
$416$	23.4287	1.14869
$417$	−35.4155	−1.73430
$418$	−2.39129	−0.116962
$419$	25.3206	1.23699	0.618496	−	0.785788i	$-0.287742\pi$
$419$	25.3206	1.23699	0.618496	+	0.785788i	$0.287742\pi$
$420$	−34.0705	−1.66247
$421$	23.0899	1.12533	0.562666	−	0.826684i	$-0.309776\pi$
$421$	23.0899	1.12533	0.562666	+	0.826684i	$0.309776\pi$
$422$	−5.67286	−0.276151
$423$	−56.2481	−2.73488
$424$	15.0308	0.729962
$425$	−20.1097	−0.975463
$426$	11.8140	0.572391
$427$	−55.9917	−2.70963
$428$	−21.7934	−1.05342
$429$	−15.5405	−0.750300
$430$	−0.805140	−0.0388273
$431$	−4.51076	−0.217276	−0.108638	−	0.994081i	$-0.534649\pi$
$431$	−4.51076	−0.217276	−0.108638	+	0.994081i	$0.534649\pi$
$432$	−22.3199	−1.07387
$433$	−18.5129	−0.889671	−0.444836	−	0.895612i	$-0.646738\pi$
$433$	−18.5129	−0.889671	−0.444836	+	0.895612i	$0.646738\pi$
$434$	−4.40976	−0.211675
$435$	−17.8420	−0.855457
$436$	−16.2016	−0.775914
$437$	1.66760	0.0797722
$438$	−11.6185	−0.555153
$439$	−22.6333	−1.08023	−0.540115	−	0.841591i	$-0.681619\pi$
$439$	−22.6333	−1.08023	−0.540115	+	0.841591i	$0.681619\pi$
$440$	1.95075	0.0929983
$441$	109.277	5.20369
$442$	12.6965	0.603910
$443$	2.58929	0.123021	0.0615105	−	0.998106i	$-0.480408\pi$
$443$	2.58929	0.123021	0.0615105	+	0.998106i	$0.480408\pi$
$444$	43.9757	2.08700
$445$	−2.33723	−0.110795
$446$	−2.17902	−0.103180
$447$	31.7058	1.49963
$448$	−21.6522	−1.02297
$449$	34.5277	1.62946	0.814731	−	0.579839i	$-0.196885\pi$
$449$	34.5277	1.62946	0.814731	+	0.579839i	$0.196885\pi$
$450$	7.96872	0.375649
$451$	3.54569	0.166960
$452$	−34.4879	−1.62217
$453$	50.3565	2.36596
$454$	−3.80572	−0.178611
$455$	33.8863	1.58861
$456$	26.7620	1.25325
$457$	−14.0413	−0.656827	−0.328413	−	0.944534i	$-0.606514\pi$
$457$	−14.0413	−0.656827	−0.328413	+	0.944534i	$0.606514\pi$
$458$	2.80258	0.130956
$459$	−42.9253	−2.00358
$460$	−0.649863	−0.0303000
$461$	10.1607	0.473233	0.236616	−	0.971603i	$-0.423962\pi$
$461$	10.1607	0.473233	0.236616	+	0.971603i	$0.423962\pi$
$462$	−6.24238	−0.290422
$463$	17.0414	0.791980	0.395990	−	0.918255i	$-0.370402\pi$
$463$	17.0414	0.791980	0.395990	+	0.918255i	$0.370402\pi$
$464$	−14.8784	−0.690711
$465$	7.43920	0.344985
$466$	−3.42034	−0.158444
$467$	−4.21409	−0.195005	−0.0975024	−	0.995235i	$-0.531085\pi$
$467$	−4.21409	−0.195005	−0.0975024	+	0.995235i	$0.531085\pi$
$468$	53.9024	2.49164
$469$	58.0324	2.67969
$470$	−5.17076	−0.238509
$471$	30.4504	1.40308
$472$	3.81763	0.175721
$473$	1.58047	0.0726699
$474$	−3.26137	−0.149800
$475$	20.1394	0.924060
$476$	−54.6401	−2.50443
$477$	52.6431	2.41036
$478$	−9.92253	−0.453846
$479$	30.3387	1.38621	0.693106	−	0.720836i	$-0.256242\pi$
$479$	30.3387	1.38621	0.693106	+	0.720836i	$0.256242\pi$
$480$	−15.8762	−0.724646
$481$	−43.7380	−1.99428
$482$	5.08741	0.231725
$483$	4.35321	0.198078
$484$	−1.82926	−0.0831482
$485$	−2.65483	−0.120550
$486$	−3.06735	−0.139138
$487$	−14.1318	−0.640372	−0.320186	−	0.947355i	$-0.603745\pi$
$487$	−14.1318	−0.640372	−0.320186	+	0.947355i	$0.603745\pi$
$488$	−17.1393	−0.775860
$489$	3.30434	0.149427
$490$	10.0456	0.453815
$491$	−39.7622	−1.79444	−0.897222	−	0.441580i	$-0.854418\pi$
$491$	−39.7622	−1.79444	−0.897222	+	0.441580i	$0.854418\pi$
$492$	−18.9561	−0.854605
$493$	−28.6138	−1.28870
$494$	−12.7153	−0.572087
$495$	6.83219	0.307084
$496$	6.20353	0.278547
$497$	50.5675	2.26826
$498$	5.04817	0.226214
$499$	11.6415	0.521147	0.260573	−	0.965454i	$-0.416088\pi$
$499$	11.6415	0.521147	0.260573	+	0.965454i	$0.416088\pi$
$500$	−19.1246	−0.855277
$501$	−32.8683	−1.46845
$502$	−3.29041	−0.146858
$503$	−7.28907	−0.325004	−0.162502	−	0.986708i	$-0.551956\pi$
$503$	−7.28907	−0.325004	−0.162502	+	0.986708i	$0.551956\pi$
$504$	45.3246	2.01892
$505$	−16.6908	−0.742733
$506$	−0.119068	−0.00529320
$507$	−44.6395	−1.98251
$508$	4.60739	0.204420
$509$	−4.12687	−0.182921	−0.0914603	−	0.995809i	$-0.529153\pi$
$509$	−4.12687	−0.182921	−0.0914603	+	0.995809i	$0.529153\pi$
$510$	−8.60363	−0.380975
$511$	−49.7306	−2.19995
$512$	−22.7477	−1.00532
$513$	42.9888	1.89800
$514$	−2.84589	−0.125527
$515$	−4.53980	−0.200048
$516$	−8.44952	−0.371969
$517$	10.1500	0.446398
$518$	−17.5689	−0.771935
$519$	−1.59907	−0.0701915
$520$	10.3728	0.454875
$521$	−9.26075	−0.405721	−0.202860	−	0.979208i	$-0.565024\pi$
$521$	−9.26075	−0.405721	−0.202860	+	0.979208i	$0.565024\pi$
$522$	11.3386	0.496277
$523$	−42.7762	−1.87047	−0.935236	−	0.354025i	$-0.884813\pi$
$523$	−42.7762	−1.87047	−0.935236	+	0.354025i	$0.884813\pi$
$524$	−1.82926	−0.0799116
$525$	52.5732	2.29448
$526$	−1.08133	−0.0471482
$527$	11.9305	0.519702
$528$	8.78162	0.382171
$529$	−22.9170	−0.996390
$530$	4.83936	0.210208
$531$	13.3707	0.580237
$532$	54.7210	2.37245
$533$	18.8536	0.816639
$534$	2.28939	0.0990716
$535$	−14.6882	−0.635025
$536$	17.7640	0.767287
$537$	6.56611	0.283349
$538$	−7.66348	−0.330396
$539$	−19.7193	−0.849368
$540$	−16.7527	−0.720921
$541$	−8.92233	−0.383601	−0.191801	−	0.981434i	$-0.561433\pi$
$541$	−8.92233	−0.383601	−0.191801	+	0.981434i	$0.561433\pi$
$542$	−4.13867	−0.177771
$543$	−12.5179	−0.537196
$544$	−25.4613	−1.09164
$545$	−10.9195	−0.467738
$546$	−33.1927	−1.42052
$547$	13.3512	0.570856	0.285428	−	0.958400i	$-0.407864\pi$
$547$	13.3512	0.570856	0.285428	+	0.958400i	$0.407864\pi$
$548$	35.4575	1.51467
$549$	−60.0277	−2.56192
$550$	−1.43796	−0.0613150
$551$	28.6561	1.22079
$552$	1.33254	0.0567166
$553$	−13.9596	−0.593623
$554$	−0.687234	−0.0291978
$555$	29.6386	1.25809
$556$	−22.1665	−0.940070
$557$	28.9568	1.22694	0.613469	−	0.789719i	$-0.289774\pi$
$557$	28.9568	1.22694	0.613469	+	0.789719i	$0.289774\pi$
$558$	−4.72762	−0.200136
$559$	8.40384	0.355444
$560$	−19.1485	−0.809172
$561$	16.8887	0.713040
$562$	−9.85406	−0.415668
$563$	−25.7456	−1.08505	−0.542524	−	0.840040i	$-0.682531\pi$
$563$	−25.7456	−1.08505	−0.542524	+	0.840040i	$0.682531\pi$
$564$	−54.2644	−2.28494
$565$	−23.2440	−0.977881
$566$	2.37825	0.0999652
$567$	26.2849	1.10386
$568$	15.4789	0.649482
$569$	−19.8407	−0.831766	−0.415883	−	0.909418i	$-0.636527\pi$
$569$	−19.8407	−0.831766	−0.415883	+	0.909418i	$0.636527\pi$
$570$	8.61636	0.360900
$571$	21.0323	0.880173	0.440087	−	0.897955i	$-0.354948\pi$
$571$	21.0323	0.880173	0.440087	+	0.897955i	$0.354948\pi$
$572$	−9.72676	−0.406696
$573$	−35.1513	−1.46846
$574$	7.57322	0.316100
$575$	1.00278	0.0418190
$576$	−23.2129	−0.967204
$577$	−22.5349	−0.938142	−0.469071	−	0.883161i	$-0.655411\pi$
$577$	−22.5349	−0.938142	−0.469071	+	0.883161i	$0.655411\pi$
$578$	−6.77345	−0.281738
$579$	63.4427	2.63659
$580$	−11.1673	−0.463696
$581$	21.6077	0.896436
$582$	2.60049	0.107794
$583$	−9.49951	−0.393429
$584$	−15.2228	−0.629923
$585$	36.3289	1.50201
$586$	−1.53484	−0.0634036
$587$	−29.2813	−1.20857	−0.604284	−	0.796769i	$-0.706541\pi$
$587$	−29.2813	−1.20857	−0.604284	+	0.796769i	$0.706541\pi$
$588$	105.423	4.34759
$589$	−11.9482	−0.492316
$590$	1.22913	0.0506026
$591$	−48.0898	−1.97815
$592$	24.7155	1.01580
$593$	−41.3526	−1.69815	−0.849074	−	0.528274i	$-0.822839\pi$
$593$	−41.3526	−1.69815	−0.849074	+	0.528274i	$0.822839\pi$
$594$	−3.06942	−0.125940
$595$	−36.8261	−1.50972
$596$	19.8446	0.812868
$597$	−59.1836	−2.42222
$598$	−0.633120	−0.0258902
$599$	43.3336	1.77056	0.885282	−	0.465054i	$-0.153965\pi$
$599$	43.3336	1.77056	0.885282	+	0.465054i	$0.153965\pi$
$600$	16.0929	0.656990
$601$	9.39567	0.383257	0.191629	−	0.981467i	$-0.438623\pi$
$601$	9.39567	0.383257	0.191629	+	0.981467i	$0.438623\pi$
$602$	3.37570	0.137583
$603$	62.2155	2.53361
$604$	31.5181	1.28245
$605$	−1.23288	−0.0501236
$606$	16.3492	0.664142
$607$	5.48240	0.222524	0.111262	−	0.993791i	$-0.464511\pi$
$607$	5.48240	0.222524	0.111262	+	0.993791i	$0.464511\pi$
$608$	25.4989	1.03412
$609$	74.8058	3.03128
$610$	−5.51821	−0.223426
$611$	53.9710	2.18343
$612$	−58.5787	−2.36790
$613$	16.0284	0.647379	0.323690	−	0.946163i	$-0.395077\pi$
$613$	16.0284	0.647379	0.323690	+	0.946163i	$0.395077\pi$
$614$	−9.85128	−0.397565
$615$	−12.7759	−0.515175
$616$	−8.17889	−0.329537
$617$	−3.54404	−0.142678	−0.0713389	−	0.997452i	$-0.522727\pi$
$617$	−3.54404	−0.142678	−0.0713389	+	0.997452i	$0.522727\pi$
$618$	4.44688	0.178880
$619$	−2.16176	−0.0868884	−0.0434442	−	0.999056i	$-0.513833\pi$
$619$	−2.16176	−0.0868884	−0.0434442	+	0.999056i	$0.513833\pi$
$620$	4.65619	0.186997
$621$	2.14050	0.0858954
$622$	4.68815	0.187977
$623$	9.79927	0.392599
$624$	46.6946	1.86928
$625$	4.51059	0.180424
$626$	−6.53805	−0.261313
$627$	−16.9136	−0.675466
$628$	19.0589	0.760533
$629$	47.5325	1.89524
$630$	14.5928	0.581391
$631$	9.83671	0.391593	0.195797	−	0.980645i	$-0.437271\pi$
$631$	9.83671	0.391593	0.195797	+	0.980645i	$0.437271\pi$
$632$	−4.27310	−0.169975
$633$	−40.1242	−1.59479
$634$	−3.10653	−0.123376
$635$	3.10527	0.123229
$636$	50.7865	2.01381
$637$	−104.854	−4.15445
$638$	−2.04606	−0.0810044
$639$	54.2125	2.14461
$640$	−12.9983	−0.513803
$641$	33.2479	1.31321	0.656606	−	0.754234i	$-0.271992\pi$
$641$	33.2479	1.31321	0.656606	+	0.754234i	$0.271992\pi$
$642$	14.3875	0.567831
$643$	−7.92020	−0.312342	−0.156171	−	0.987730i	$-0.549915\pi$
$643$	−7.92020	−0.312342	−0.156171	+	0.987730i	$0.549915\pi$
$644$	2.72467	0.107367
$645$	−5.69477	−0.224231
$646$	13.8184	0.543677
$647$	5.07965	0.199702	0.0998509	−	0.995002i	$-0.468163\pi$
$647$	5.07965	0.199702	0.0998509	+	0.995002i	$0.468163\pi$
$648$	8.04594	0.316074
$649$	−2.41275	−0.0947087
$650$	−7.64611	−0.299905
$651$	−31.1903	−1.22244
$652$	2.06818	0.0809963
$653$	−28.0318	−1.09697	−0.548484	−	0.836161i	$-0.684795\pi$
$653$	−28.0318	−1.09697	−0.548484	+	0.836161i	$0.684795\pi$
$654$	10.6960	0.418245
$655$	−1.23288	−0.0481725
$656$	−10.6538	−0.415961
$657$	−53.3153	−2.08003
$658$	21.6794	0.845151
$659$	−3.65649	−0.142436	−0.0712182	−	0.997461i	$-0.522689\pi$
$659$	−3.65649	−0.142436	−0.0712182	+	0.997461i	$0.522689\pi$
$660$	6.59123	0.256563
$661$	41.4435	1.61196	0.805982	−	0.591939i	$-0.201638\pi$
$661$	41.4435	1.61196	0.805982	+	0.591939i	$0.201638\pi$
$662$	−13.0609	−0.507625
$663$	89.8023	3.48763
$664$	6.61420	0.256681
$665$	36.8806	1.43017
$666$	−18.8353	−0.729855
$667$	1.42685	0.0552478
$668$	−20.5723	−0.795964
$669$	−15.4122	−0.595871
$670$	5.71933	0.220957
$671$	10.8321	0.418168
$672$	66.5640	2.56776
$673$	17.5618	0.676957	0.338479	−	0.940974i	$-0.390088\pi$
$673$	17.5618	0.676957	0.338479	+	0.940974i	$0.390088\pi$
$674$	12.5117	0.481931
$675$	25.8506	0.994990
$676$	−27.9399	−1.07461
$677$	−35.6002	−1.36822	−0.684112	−	0.729377i	$-0.739810\pi$
$677$	−35.6002	−1.36822	−0.684112	+	0.729377i	$0.739810\pi$
$678$	22.7682	0.874408
$679$	11.1309	0.427163
$680$	−11.2726	−0.432286
$681$	−26.9179	−1.03150
$682$	0.853105	0.0326671
$683$	4.66626	0.178550	0.0892748	−	0.996007i	$-0.471545\pi$
$683$	4.66626	0.178550	0.0892748	+	0.996007i	$0.471545\pi$
$684$	58.6654	2.24313
$685$	23.8975	0.913077
$686$	−27.1670	−1.03724
$687$	19.8227	0.756282
$688$	−4.74885	−0.181048
$689$	−50.5119	−1.92435
$690$	0.429027	0.0163328
$691$	−18.9621	−0.721351	−0.360675	−	0.932691i	$-0.617454\pi$
$691$	−18.9621	−0.721351	−0.360675	+	0.932691i	$0.617454\pi$
$692$	−1.00086	−0.0380469
$693$	−28.6452	−1.08814
$694$	1.57823	0.0599087
$695$	−14.9397	−0.566695
$696$	22.8984	0.867961
$697$	−20.4892	−0.776084
$698$	10.0104	0.378899
$699$	−24.1921	−0.915030
$700$	32.9055	1.24371
$701$	23.9745	0.905505	0.452752	−	0.891636i	$-0.350442\pi$
$701$	23.9745	0.905505	0.452752	+	0.891636i	$0.350442\pi$
$702$	−16.3211	−0.615999
$703$	−47.6028	−1.79537
$704$	4.18879	0.157871
$705$	−36.5728	−1.37741
$706$	1.35163	0.0508692
$707$	69.9795	2.63185
$708$	12.8991	0.484778
$709$	−50.9290	−1.91268	−0.956339	−	0.292261i	$-0.905593\pi$
$709$	−50.9290	−1.91268	−0.956339	+	0.292261i	$0.905593\pi$
$710$	4.98363	0.187032
$711$	−14.9659	−0.561263
$712$	2.99960	0.112415
$713$	−0.594925	−0.0222801
$714$	36.0723	1.34997
$715$	−6.55559	−0.245165
$716$	4.10972	0.153588
$717$	−70.1822	−2.62100
$718$	−9.79786	−0.365653
$719$	−44.1434	−1.64627	−0.823136	−	0.567845i	$-0.807777\pi$
$719$	−44.1434	−1.64627	−0.823136	+	0.567845i	$0.807777\pi$
$720$	−20.5288	−0.765062
$721$	19.0340	0.708862
$722$	−5.98790	−0.222846
$723$	35.9833	1.33823
$724$	−7.83496	−0.291184
$725$	17.2319	0.639977
$726$	1.20764	0.0448198
$727$	−43.1461	−1.60020	−0.800101	−	0.599866i	$-0.795221\pi$
$727$	−43.1461	−1.60020	−0.800101	+	0.599866i	$0.795221\pi$
$728$	−43.4897	−1.61184
$729$	−36.9505	−1.36854
$730$	−4.90115	−0.181400
$731$	−9.13291	−0.337793
$732$	−57.9106	−2.14044
$733$	31.2934	1.15585	0.577925	−	0.816090i	$-0.303863\pi$
$733$	31.2934	1.15585	0.577925	+	0.816090i	$0.303863\pi$
$734$	−12.9103	−0.476529
$735$	71.0528	2.62082
$736$	1.26965	0.0467998
$737$	−11.2269	−0.413547
$738$	8.11911	0.298869
$739$	−7.98578	−0.293762	−0.146881	−	0.989154i	$-0.546923\pi$
$739$	−7.98578	−0.293762	−0.146881	+	0.989154i	$0.546923\pi$
$740$	18.5507	0.681939
$741$	−89.9352	−3.30385
$742$	−20.2899	−0.744866
$743$	−4.75855	−0.174574	−0.0872871	−	0.996183i	$-0.527820\pi$
$743$	−4.75855	−0.174574	−0.0872871	+	0.996183i	$0.527820\pi$
$744$	−9.54748	−0.350028
$745$	13.3748	0.490015
$746$	15.2796	0.559425
$747$	23.1652	0.847569
$748$	10.5706	0.386499
$749$	61.5830	2.25019
$750$	12.6257	0.461024
$751$	−21.1353	−0.771238	−0.385619	−	0.922658i	$-0.626012\pi$
$751$	−21.1353	−0.771238	−0.385619	+	0.922658i	$0.626012\pi$
$752$	−30.4980	−1.11215
$753$	−23.2731	−0.848119
$754$	−10.8796	−0.396210
$755$	21.2424	0.773091
$756$	70.2388	2.55456
$757$	−54.1140	−1.96681	−0.983403	−	0.181433i	$-0.941927\pi$
$757$	−54.1140	−1.96681	−0.983403	+	0.181433i	$0.941927\pi$
$758$	−3.71913	−0.135085
$759$	−0.842166	−0.0305687
$760$	11.2893	0.409506
$761$	20.7890	0.753600	0.376800	−	0.926295i	$-0.377024\pi$
$761$	20.7890	0.753600	0.376800	+	0.926295i	$0.377024\pi$
$762$	−3.04171	−0.110190
$763$	45.7819	1.65742
$764$	−22.0011	−0.795973
$765$	−39.4806	−1.42742
$766$	−0.160053	−0.00578294
$767$	−12.8294	−0.463241
$768$	−11.7522	−0.424071
$769$	10.1360	0.365515	0.182757	−	0.983158i	$-0.441498\pi$
$769$	10.1360	0.365515	0.182757	+	0.983158i	$0.441498\pi$
$770$	−2.63329	−0.0948972
$771$	−20.1290	−0.724928
$772$	39.7087	1.42915
$773$	−53.9503	−1.94046	−0.970229	−	0.242191i	$-0.922134\pi$
$773$	−53.9503	−1.94046	−0.970229	+	0.242191i	$0.922134\pi$
$774$	3.61903	0.130083
$775$	−7.18484	−0.258087
$776$	3.40721	0.122312
$777$	−124.265	−4.45799
$778$	3.25736	0.116782
$779$	20.5195	0.735188
$780$	35.0476	1.25491
$781$	−9.78271	−0.350053
$782$	0.688046	0.0246045
$783$	36.7825	1.31450
$784$	59.2507	2.11610
$785$	12.8452	0.458466
$786$	1.20764	0.0430752
$787$	51.7600	1.84505	0.922523	−	0.385943i	$-0.126124\pi$
$787$	51.7600	1.84505	0.922523	+	0.385943i	$0.126124\pi$
$788$	−30.0994	−1.07225
$789$	−7.64826	−0.272285
$790$	−1.37578	−0.0489479
$791$	97.4547	3.46509
$792$	−8.76843	−0.311573
$793$	57.5976	2.04535
$794$	−1.93984	−0.0688425
$795$	34.2288	1.21397
$796$	−37.0429	−1.31295
$797$	−34.1062	−1.20810	−0.604052	−	0.796945i	$-0.706448\pi$
$797$	−34.1062	−1.20810	−0.604052	+	0.796945i	$0.706448\pi$
$798$	−36.1257	−1.27884
$799$	−58.6532	−2.07500
$800$	15.3334	0.542116
$801$	10.5056	0.371198
$802$	−7.92359	−0.279792
$803$	9.62082	0.339511
$804$	60.0213	2.11679
$805$	1.83636	0.0647232
$806$	4.53623	0.159782
$807$	−54.2039	−1.90807
$808$	21.4211	0.753590
$809$	31.5714	1.10999	0.554996	−	0.831853i	$-0.312720\pi$
$809$	31.5714	1.10999	0.554996	+	0.831853i	$0.312720\pi$
$810$	2.59049	0.0910204
$811$	30.7791	1.08080	0.540401	−	0.841408i	$-0.318273\pi$
$811$	30.7791	1.08080	0.540401	+	0.841408i	$0.318273\pi$
$812$	46.8209	1.64309
$813$	−29.2729	−1.02664
$814$	3.39886	0.119130
$815$	1.39390	0.0488264
$816$	−50.7456	−1.77645
$817$	9.14642	0.319993
$818$	6.62880	0.231771
$819$	−152.316	−5.32234
$820$	−7.99644	−0.279248
$821$	−29.7529	−1.03838	−0.519191	−	0.854658i	$-0.673767\pi$
$821$	−29.7529	−1.03838	−0.519191	+	0.854658i	$0.673767\pi$
$822$	−23.4084	−0.816461
$823$	16.4987	0.575109	0.287555	−	0.957764i	$-0.407158\pi$
$823$	16.4987	0.575109	0.287555	+	0.957764i	$0.407158\pi$
$824$	5.82639	0.202972
$825$	−10.1707	−0.354100
$826$	−5.15337	−0.179309
$827$	20.5615	0.714993	0.357496	−	0.933915i	$-0.383630\pi$
$827$	20.5615	0.714993	0.357496	+	0.933915i	$0.383630\pi$
$828$	2.92107	0.101514
$829$	13.4786	0.468130	0.234065	−	0.972221i	$-0.424797\pi$
$829$	13.4786	0.468130	0.234065	+	0.972221i	$0.424797\pi$
$830$	2.12952	0.0739167
$831$	−4.86082	−0.168620
$832$	22.2731	0.772182
$833$	113.950	3.94813
$834$	14.6339	0.506731
$835$	−13.8652	−0.479825
$836$	−10.5862	−0.366133
$837$	−15.3365	−0.530105
$838$	−10.4626	−0.361426
$839$	−13.4820	−0.465449	−0.232725	−	0.972543i	$-0.574764\pi$
$839$	−13.4820	−0.465449	−0.232725	+	0.972543i	$0.574764\pi$
$840$	29.4703	1.01682
$841$	−4.48095	−0.154515
$842$	−9.54089	−0.328801
$843$	−69.6978	−2.40052
$844$	−25.1137	−0.864449
$845$	−18.8308	−0.647798
$846$	23.2421	0.799079
$847$	5.16907	0.177611
$848$	28.5433	0.980181
$849$	16.8214	0.577308
$850$	8.30945	0.285012
$851$	−2.37024	−0.0812509
$852$	52.3005	1.79179
$853$	7.16287	0.245252	0.122626	−	0.992453i	$-0.460868\pi$
$853$	7.16287	0.245252	0.122626	+	0.992453i	$0.460868\pi$
$854$	23.1361	0.791702
$855$	39.5390	1.35221
$856$	18.8508	0.644308
$857$	48.0656	1.64189	0.820944	−	0.571009i	$-0.193448\pi$
$857$	48.0656	1.64189	0.820944	+	0.571009i	$0.193448\pi$
$858$	6.42141	0.219223
$859$	−14.6237	−0.498955	−0.249478	−	0.968381i	$-0.580259\pi$
$859$	−14.6237	−0.498955	−0.249478	+	0.968381i	$0.580259\pi$
$860$	−3.56435	−0.121543
$861$	53.5654	1.82551
$862$	1.86388	0.0634838
$863$	28.1400	0.957897	0.478948	−	0.877843i	$-0.341018\pi$
$863$	28.1400	0.957897	0.478948	+	0.877843i	$0.341018\pi$
$864$	32.7299	1.11350
$865$	−0.674554	−0.0229355
$866$	7.64963	0.259945
$867$	−47.9087	−1.62706
$868$	−19.5220	−0.662619
$869$	2.70061	0.0916118
$870$	7.37241	0.249948
$871$	−59.6968	−2.02275
$872$	14.0140	0.474575
$873$	11.9332	0.403878
$874$	−0.689064	−0.0233079
$875$	54.0416	1.82694
$876$	−51.4350	−1.73783
$877$	−49.1008	−1.65802	−0.829008	−	0.559237i	$-0.811094\pi$
$877$	−49.1008	−1.65802	−0.829008	+	0.559237i	$0.811094\pi$
$878$	9.35223	0.315623
$879$	−10.8559	−0.366162
$880$	3.70444	0.124877
$881$	−21.7041	−0.731231	−0.365615	−	0.930766i	$-0.619141\pi$
$881$	−21.7041	−0.731231	−0.365615	+	0.930766i	$0.619141\pi$
$882$	−45.1542	−1.52042
$883$	15.3118	0.515282	0.257641	−	0.966241i	$-0.417055\pi$
$883$	15.3118	0.515282	0.257641	+	0.966241i	$0.417055\pi$
$884$	56.2072	1.89045
$885$	8.69367	0.292235
$886$	−1.06991	−0.0359444
$887$	−39.7234	−1.33378	−0.666891	−	0.745155i	$-0.732375\pi$
$887$	−39.7234	−1.33378	−0.666891	+	0.745155i	$0.732375\pi$
$888$	−38.0382	−1.27648
$889$	−13.0194	−0.436658
$890$	0.965757	0.0323723
$891$	−5.08504	−0.170355
$892$	−9.64650	−0.322989
$893$	58.7400	1.96566
$894$	−13.1010	−0.438164
$895$	2.76985	0.0925859
$896$	54.4978	1.82065
$897$	−4.47806	−0.149518
$898$	−14.2671	−0.476098
$899$	−10.2232	−0.340963
$900$	35.2774	1.17591
$901$	54.8940	1.82878
$902$	−1.46510	−0.0487826
$903$	23.8764	0.794556
$904$	29.8313	0.992175
$905$	−5.28057	−0.175532
$906$	−20.8076	−0.691287
$907$	41.1447	1.36619	0.683093	−	0.730331i	$-0.260634\pi$
$907$	41.1447	1.36619	0.683093	+	0.730331i	$0.260634\pi$
$908$	−16.8479	−0.559117
$909$	75.0238	2.48838
$910$	−14.0020	−0.464163
$911$	7.56885	0.250767	0.125384	−	0.992108i	$-0.459984\pi$
$911$	7.56885	0.250767	0.125384	+	0.992108i	$0.459984\pi$
$912$	50.8207	1.68284
$913$	−4.18018	−0.138344
$914$	5.80197	0.191912
$915$	−39.0303	−1.29030
$916$	12.4070	0.409939
$917$	5.16907	0.170698
$918$	17.7370	0.585408
$919$	20.7480	0.684412	0.342206	−	0.939625i	$-0.388826\pi$
$919$	20.7480	0.684412	0.342206	+	0.939625i	$0.388826\pi$
$920$	0.562119	0.0185325
$921$	−69.6782	−2.29597
$922$	−4.19848	−0.138270
$923$	−52.0178	−1.71219
$924$	−27.6350	−0.909124
$925$	−28.6251	−0.941189
$926$	−7.04160	−0.231401
$927$	20.4060	0.670220
$928$	21.8176	0.716199
$929$	−6.51581	−0.213777	−0.106888	−	0.994271i	$-0.534089\pi$
$929$	−6.51581	−0.213777	−0.106888	+	0.994271i	$0.534089\pi$
$930$	−3.07393	−0.100798
$931$	−114.119	−3.74009
$932$	−15.1418	−0.495987
$933$	33.1593	1.08559
$934$	1.74129	0.0569767
$935$	7.12432	0.232990
$936$	−46.6245	−1.52397
$937$	−39.0399	−1.27538	−0.637688	−	0.770295i	$-0.720109\pi$
$937$	−39.0399	−1.27538	−0.637688	+	0.770295i	$0.720109\pi$
$938$	−23.9794	−0.782954
$939$	−46.2437	−1.50911
$940$	−22.8909	−0.746619
$941$	−50.7122	−1.65317	−0.826586	−	0.562810i	$-0.809720\pi$
$941$	−50.7122	−1.65317	−0.826586	+	0.562810i	$0.809720\pi$
$942$	−12.5823	−0.409954
$943$	1.02171	0.0332715
$944$	7.24963	0.235955
$945$	47.3392	1.53994
$946$	−0.653059	−0.0212328
$947$	−30.2937	−0.984412	−0.492206	−	0.870479i	$-0.663809\pi$
$947$	−30.2937	−0.984412	−0.492206	+	0.870479i	$0.663809\pi$
$948$	−14.4380	−0.468926
$949$	51.1569	1.66062
$950$	−8.32174	−0.269993
$951$	−21.9725	−0.712507
$952$	47.2626	1.53179
$953$	43.1913	1.39910	0.699551	−	0.714582i	$-0.253383\pi$
$953$	43.1913	1.39910	0.699551	+	0.714582i	$0.253383\pi$
$954$	−21.7525	−0.704262
$955$	−14.8282	−0.479830
$956$	−43.9270	−1.42070
$957$	−14.4718	−0.467807
$958$	−12.5362	−0.405025
$959$	−100.195	−3.23546
$960$	−15.0931	−0.487129
$961$	−26.7374	−0.862498
$962$	18.0728	0.582691
$963$	66.0220	2.12753
$964$	22.5219	0.725382
$965$	26.7627	0.861521
$966$	−1.79878	−0.0578746
$967$	42.6100	1.37025	0.685123	−	0.728427i	$-0.259748\pi$
$967$	42.6100	1.37025	0.685123	+	0.728427i	$0.259748\pi$
$968$	1.58227	0.0508562
$969$	97.7375	3.13978
$970$	1.09699	0.0352223
$971$	46.4314	1.49006	0.745028	−	0.667033i	$-0.232436\pi$
$971$	46.4314	1.49006	0.745028	+	0.667033i	$0.232436\pi$
$972$	−13.5791	−0.435550
$973$	62.6375	2.00807
$974$	5.83934	0.187105
$975$	−54.0810	−1.73198
$976$	−32.5473	−1.04181
$977$	28.8141	0.921846	0.460923	−	0.887440i	$-0.347518\pi$
$977$	28.8141	0.921846	0.460923	+	0.887440i	$0.347518\pi$
$978$	−1.36537	−0.0436599
$979$	−1.89575	−0.0605885
$980$	44.4719	1.42060
$981$	49.0819	1.56707
$982$	16.4300	0.524302
$983$	13.4085	0.427663	0.213832	−	0.976871i	$-0.431406\pi$
$983$	13.4085	0.427663	0.213832	+	0.976871i	$0.431406\pi$
$984$	16.3966	0.522705
$985$	−20.2862	−0.646373
$986$	11.8234	0.376534
$987$	153.339	4.88082
$988$	−56.2904	−1.79083
$989$	0.455419	0.0144815
$990$	−2.82310	−0.0897241
$991$	8.36250	0.265643	0.132822	−	0.991140i	$-0.457596\pi$
$991$	8.36250	0.265643	0.132822	+	0.991140i	$0.457596\pi$
$992$	−9.09686	−0.288826
$993$	−92.3797	−2.93158
$994$	−20.8948	−0.662743
$995$	−24.9660	−0.791476
$996$	22.3482	0.708129
$997$	36.7654	1.16437	0.582186	−	0.813056i	$-0.302198\pi$
$997$	36.7654	1.16437	0.582186	+	0.813056i	$0.302198\pi$
$998$	−4.81036	−0.152269
$999$	−61.1020	−1.93318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.13	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.13	✓	31	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)

\(f(q)\)	\(=\)	\(q-0.413206 q^{2} -2.92261 q^{3} -1.82926 q^{4} -1.23288 q^{5} +1.20764 q^{6} +5.16907 q^{7} +1.58227 q^{8} +5.54166 q^{9} +O(q^{10})\)	\(q-0.413206 q^{2} -2.92261 q^{3} -1.82926 q^{4} -1.23288 q^{5} +1.20764 q^{6} +5.16907 q^{7} +1.58227 q^{8} +5.54166 q^{9} +0.509432 q^{10} -1.00000 q^{11} +5.34622 q^{12} -5.31732 q^{13} -2.13589 q^{14} +3.60322 q^{15} +3.00471 q^{16} +5.77862 q^{17} -2.28985 q^{18} -5.78717 q^{19} +2.25525 q^{20} -15.1072 q^{21} +0.413206 q^{22} -0.288155 q^{23} -4.62438 q^{24} -3.48002 q^{25} +2.19715 q^{26} -7.42830 q^{27} -9.45557 q^{28} -4.95167 q^{29} -1.48887 q^{30} +2.06460 q^{31} -4.40612 q^{32} +2.92261 q^{33} -2.38776 q^{34} -6.37282 q^{35} -10.1371 q^{36} +8.22558 q^{37} +2.39129 q^{38} +15.5405 q^{39} -1.95075 q^{40} -3.54569 q^{41} +6.24238 q^{42} -1.58047 q^{43} +1.82926 q^{44} -6.83219 q^{45} +0.119068 q^{46} -10.1500 q^{47} -8.78162 q^{48} +19.7193 q^{49} +1.43796 q^{50} -16.8887 q^{51} +9.72676 q^{52} +9.49951 q^{53} +3.06942 q^{54} +1.23288 q^{55} +8.17889 q^{56} +16.9136 q^{57} +2.04606 q^{58} +2.41275 q^{59} -6.59123 q^{60} -10.8321 q^{61} -0.853105 q^{62} +28.6452 q^{63} -4.18879 q^{64} +6.55559 q^{65} -1.20764 q^{66} +11.2269 q^{67} -10.5706 q^{68} +0.842166 q^{69} +2.63329 q^{70} +9.78271 q^{71} +8.76843 q^{72} -9.62082 q^{73} -3.39886 q^{74} +10.1707 q^{75} +10.5862 q^{76} -5.16907 q^{77} -6.42141 q^{78} -2.70061 q^{79} -3.70444 q^{80} +5.08504 q^{81} +1.46510 q^{82} +4.18018 q^{83} +27.6350 q^{84} -7.12432 q^{85} +0.653059 q^{86} +14.4718 q^{87} -1.58227 q^{88} +1.89575 q^{89} +2.82310 q^{90} -27.4856 q^{91} +0.527111 q^{92} -6.03402 q^{93} +4.19406 q^{94} +7.13486 q^{95} +12.8774 q^{96} +2.15336 q^{97} -8.14812 q^{98} -5.54166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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