LMFDB - Embedded newform 8029.2.a.h.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.38552 q^{2} +1.91783 q^{3} -0.0803442 q^{4} -0.654097 q^{5} -2.65719 q^{6} -1.00000 q^{7} +2.88235 q^{8} +0.678074 q^{9} +O(q^{10})$	\(q-1.38552 q^{2} +1.91783 q^{3} -0.0803442 q^{4} -0.654097 q^{5} -2.65719 q^{6} -1.00000 q^{7} +2.88235 q^{8} +0.678074 q^{9} +0.906262 q^{10} +0.494961 q^{11} -0.154087 q^{12} -4.76316 q^{13} +1.38552 q^{14} -1.25445 q^{15} -3.83286 q^{16} -3.23296 q^{17} -0.939483 q^{18} -7.17527 q^{19} +0.0525529 q^{20} -1.91783 q^{21} -0.685777 q^{22} +4.32131 q^{23} +5.52786 q^{24} -4.57216 q^{25} +6.59943 q^{26} -4.45306 q^{27} +0.0803442 q^{28} -10.3672 q^{29} +1.73806 q^{30} -1.00000 q^{31} -0.454217 q^{32} +0.949252 q^{33} +4.47933 q^{34} +0.654097 q^{35} -0.0544793 q^{36} +1.00000 q^{37} +9.94146 q^{38} -9.13493 q^{39} -1.88534 q^{40} +5.12227 q^{41} +2.65719 q^{42} +8.26272 q^{43} -0.0397673 q^{44} -0.443526 q^{45} -5.98724 q^{46} -2.77054 q^{47} -7.35077 q^{48} +1.00000 q^{49} +6.33480 q^{50} -6.20028 q^{51} +0.382692 q^{52} -2.54726 q^{53} +6.16979 q^{54} -0.323753 q^{55} -2.88235 q^{56} -13.7610 q^{57} +14.3640 q^{58} +0.989415 q^{59} +0.100788 q^{60} -10.0926 q^{61} +1.38552 q^{62} -0.678074 q^{63} +8.29504 q^{64} +3.11557 q^{65} -1.31520 q^{66} +12.6403 q^{67} +0.259750 q^{68} +8.28754 q^{69} -0.906262 q^{70} -5.50355 q^{71} +1.95445 q^{72} +12.9914 q^{73} -1.38552 q^{74} -8.76862 q^{75} +0.576492 q^{76} -0.494961 q^{77} +12.6566 q^{78} +10.9908 q^{79} +2.50706 q^{80} -10.5744 q^{81} -7.09699 q^{82} -8.72673 q^{83} +0.154087 q^{84} +2.11467 q^{85} -11.4481 q^{86} -19.8826 q^{87} +1.42665 q^{88} +3.48537 q^{89} +0.614513 q^{90} +4.76316 q^{91} -0.347192 q^{92} -1.91783 q^{93} +3.83863 q^{94} +4.69332 q^{95} -0.871111 q^{96} +13.7636 q^{97} -1.38552 q^{98} +0.335621 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * 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 $

$2$	−1.38552	−0.979708	−0.489854	−	0.871804i	$-0.662950\pi$
$2$	−1.38552	−0.979708	−0.489854	+	0.871804i	$0.662950\pi$
$3$	1.91783	1.10726	0.553630	−	0.832763i	$-0.313242\pi$
$3$	1.91783	1.10726	0.553630	+	0.832763i	$0.313242\pi$
$4$	−0.0803442	−0.0401721
$5$	−0.654097	−0.292521	−0.146261	−	0.989246i	$-0.546724\pi$
$5$	−0.654097	−0.292521	−0.146261	+	0.989246i	$0.546724\pi$
$6$	−2.65719	−1.08479
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.88235	1.01907
$9$	0.678074	0.226025
$10$	0.906262	0.286585
$11$	0.494961	0.149236	0.0746182	−	0.997212i	$-0.476226\pi$
$11$	0.494961	0.149236	0.0746182	+	0.997212i	$0.476226\pi$
$12$	−0.154087	−0.0444810
$13$	−4.76316	−1.32106	−0.660531	−	0.750799i	$-0.729669\pi$
$13$	−4.76316	−1.32106	−0.660531	+	0.750799i	$0.729669\pi$
$14$	1.38552	0.370295
$15$	−1.25445	−0.323897
$16$	−3.83286	−0.958214
$17$	−3.23296	−0.784109	−0.392055	−	0.919942i	$-0.628236\pi$
$17$	−3.23296	−0.784109	−0.392055	+	0.919942i	$0.628236\pi$
$18$	−0.939483	−0.221438
$19$	−7.17527	−1.64612	−0.823060	−	0.567954i	$-0.807735\pi$
$19$	−7.17527	−1.64612	−0.823060	+	0.567954i	$0.807735\pi$
$20$	0.0525529	0.0117512
$21$	−1.91783	−0.418505
$22$	−0.685777	−0.146208
$23$	4.32131	0.901055	0.450528	−	0.892763i	$-0.351236\pi$
$23$	4.32131	0.901055	0.450528	+	0.892763i	$0.351236\pi$
$24$	5.52786	1.12837
$25$	−4.57216	−0.914431
$26$	6.59943	1.29426
$27$	−4.45306	−0.856992
$28$	0.0803442	0.0151836
$29$	−10.3672	−1.92515	−0.962574	−	0.271020i	$-0.912639\pi$
$29$	−10.3672	−1.92515	−0.962574	+	0.271020i	$0.912639\pi$
$30$	1.73806	0.317324
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−0.454217	−0.0802949
$33$	0.949252	0.165244
$34$	4.47933	0.768198
$35$	0.654097	0.110563
$36$	−0.0544793	−0.00907989
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	9.94146	1.61272
$39$	−9.13493	−1.46276
$40$	−1.88534	−0.298098
$41$	5.12227	0.799965	0.399982	−	0.916523i	$-0.369016\pi$
$41$	5.12227	0.799965	0.399982	+	0.916523i	$0.369016\pi$
$42$	2.65719	0.410013
$43$	8.26272	1.26005	0.630026	−	0.776574i	$-0.283044\pi$
$43$	8.26272	1.26005	0.630026	+	0.776574i	$0.283044\pi$
$44$	−0.0397673	−0.00599514
$45$	−0.443526	−0.0661170
$46$	−5.98724	−0.882771
$47$	−2.77054	−0.404125	−0.202063	−	0.979373i	$-0.564764\pi$
$47$	−2.77054	−0.404125	−0.202063	+	0.979373i	$0.564764\pi$
$48$	−7.35077	−1.06099
$49$	1.00000	0.142857
$50$	6.33480	0.895876
$51$	−6.20028	−0.868213
$52$	0.382692	0.0530699
$53$	−2.54726	−0.349893	−0.174946	−	0.984578i	$-0.555975\pi$
$53$	−2.54726	−0.349893	−0.174946	+	0.984578i	$0.555975\pi$
$54$	6.16979	0.839602
$55$	−0.323753	−0.0436548
$56$	−2.88235	−0.385170
$57$	−13.7610	−1.82268
$58$	14.3640	1.88608
$59$	0.989415	0.128811	0.0644054	−	0.997924i	$-0.479485\pi$
$59$	0.989415	0.128811	0.0644054	+	0.997924i	$0.479485\pi$
$60$	0.100788	0.0130116
$61$	−10.0926	−1.29223	−0.646115	−	0.763240i	$-0.723607\pi$
$61$	−10.0926	−1.29223	−0.646115	+	0.763240i	$0.723607\pi$
$62$	1.38552	0.175961
$63$	−0.678074	−0.0854293
$64$	8.29504	1.03688
$65$	3.11557	0.386439
$66$	−1.31520	−0.161890
$67$	12.6403	1.54426	0.772132	−	0.635462i	$-0.219190\pi$
$67$	12.6403	1.54426	0.772132	+	0.635462i	$0.219190\pi$
$68$	0.259750	0.0314993
$69$	8.28754	0.997702
$70$	−0.906262	−0.108319
$71$	−5.50355	−0.653151	−0.326575	−	0.945171i	$-0.605895\pi$
$71$	−5.50355	−0.653151	−0.326575	+	0.945171i	$0.605895\pi$
$72$	1.95445	0.230334
$73$	12.9914	1.52052	0.760262	−	0.649617i	$-0.225071\pi$
$73$	12.9914	1.52052	0.760262	+	0.649617i	$0.225071\pi$
$74$	−1.38552	−0.161063
$75$	−8.76862	−1.01251
$76$	0.576492	0.0661281
$77$	−0.494961	−0.0564061
$78$	12.6566	1.43308
$79$	10.9908	1.23656	0.618279	−	0.785959i	$-0.287830\pi$
$79$	10.9908	1.23656	0.618279	+	0.785959i	$0.287830\pi$
$80$	2.50706	0.280298
$81$	−10.5744	−1.17494
$82$	−7.09699	−0.783732
$83$	−8.72673	−0.957883	−0.478942	−	0.877847i	$-0.658979\pi$
$83$	−8.72673	−0.957883	−0.478942	+	0.877847i	$0.658979\pi$
$84$	0.154087	0.0168122
$85$	2.11467	0.229368
$86$	−11.4481	−1.23448
$87$	−19.8826	−2.13164
$88$	1.42665	0.152082
$89$	3.48537	0.369449	0.184724	−	0.982790i	$-0.440861\pi$
$89$	3.48537	0.369449	0.184724	+	0.982790i	$0.440861\pi$
$90$	0.614513	0.0647754
$91$	4.76316	0.499315
$92$	−0.347192	−0.0361973
$93$	−1.91783	−0.198870
$94$	3.83863	0.395925
$95$	4.69332	0.481525
$96$	−0.871111	−0.0889074
$97$	13.7636	1.39748	0.698741	−	0.715375i	$-0.253744\pi$
$97$	13.7636	1.39748	0.698741	+	0.715375i	$0.253744\pi$
$98$	−1.38552	−0.139958
$99$	0.335621	0.0337311
$100$	0.367346	0.0367346
$101$	7.47524	0.743815	0.371907	−	0.928270i	$-0.378704\pi$
$101$	7.47524	0.743815	0.371907	+	0.928270i	$0.378704\pi$
$102$	8.59059	0.850595
$103$	11.4519	1.12839	0.564193	−	0.825643i	$-0.309188\pi$
$103$	11.4519	1.12839	0.564193	+	0.825643i	$0.309188\pi$
$104$	−13.7291	−1.34625
$105$	1.25445	0.122422
$106$	3.52927	0.342793
$107$	13.4579	1.30102	0.650511	−	0.759497i	$-0.274555\pi$
$107$	13.4579	1.30102	0.650511	+	0.759497i	$0.274555\pi$
$108$	0.357778	0.0344272
$109$	4.66047	0.446393	0.223196	−	0.974774i	$-0.428351\pi$
$109$	4.66047	0.446393	0.223196	+	0.974774i	$0.428351\pi$
$110$	0.448565	0.0427690
$111$	1.91783	0.182032
$112$	3.83286	0.362171
$113$	4.45458	0.419052	0.209526	−	0.977803i	$-0.432808\pi$
$113$	4.45458	0.419052	0.209526	+	0.977803i	$0.432808\pi$
$114$	19.0660	1.78570
$115$	−2.82656	−0.263578
$116$	0.832947	0.0773372
$117$	−3.22977	−0.298593
$118$	−1.37085	−0.126197
$119$	3.23296	0.296365
$120$	−3.61576	−0.330072
$121$	−10.7550	−0.977728
$122$	13.9835	1.26601
$123$	9.82365	0.885769
$124$	0.0803442	0.00721512
$125$	6.26112	0.560012
$126$	0.939483	0.0836958
$127$	−11.4569	−1.01664	−0.508318	−	0.861169i	$-0.669733\pi$
$127$	−11.4569	−1.01664	−0.508318	+	0.861169i	$0.669733\pi$
$128$	−10.5845	−0.935544
$129$	15.8465	1.39521
$130$	−4.31667	−0.378597
$131$	−0.0912483	−0.00797241	−0.00398620	−	0.999992i	$-0.501269\pi$
$131$	−0.0912483	−0.00797241	−0.00398620	+	0.999992i	$0.501269\pi$
$132$	−0.0762669	−0.00663818
$133$	7.17527	0.622175
$134$	−17.5134	−1.51293
$135$	2.91273	0.250688
$136$	−9.31854	−0.799058
$137$	−3.96368	−0.338640	−0.169320	−	0.985561i	$-0.554157\pi$
$137$	−3.96368	−0.338640	−0.169320	+	0.985561i	$0.554157\pi$
$138$	−11.4825	−0.977457
$139$	16.3010	1.38263	0.691316	−	0.722553i	$-0.257031\pi$
$139$	16.3010	1.38263	0.691316	+	0.722553i	$0.257031\pi$
$140$	−0.0525529	−0.00444153
$141$	−5.31343	−0.447472
$142$	7.62525	0.639897
$143$	−2.35758	−0.197151
$144$	−2.59896	−0.216580
$145$	6.78118	0.563146
$146$	−17.9997	−1.48967
$147$	1.91783	0.158180
$148$	−0.0803442	−0.00660425
$149$	1.22656	0.100484	0.0502419	−	0.998737i	$-0.484001\pi$
$149$	1.22656	0.100484	0.0502419	+	0.998737i	$0.484001\pi$
$150$	12.1491	0.991967
$151$	3.92882	0.319723	0.159861	−	0.987139i	$-0.448895\pi$
$151$	3.92882	0.319723	0.159861	+	0.987139i	$0.448895\pi$
$152$	−20.6817	−1.67750
$153$	−2.19219	−0.177228
$154$	0.685777	0.0552615
$155$	0.654097	0.0525383
$156$	0.733939	0.0587621
$157$	24.3546	1.94371	0.971853	−	0.235590i	$-0.0757023\pi$
$157$	24.3546	1.94371	0.971853	+	0.235590i	$0.0757023\pi$
$158$	−15.2279	−1.21147
$159$	−4.88521	−0.387422
$160$	0.297102	0.0234880
$161$	−4.32131	−0.340567
$162$	14.6511	1.15110
$163$	−24.4485	−1.91495	−0.957475	−	0.288515i	$-0.906839\pi$
$163$	−24.4485	−1.91495	−0.957475	+	0.288515i	$0.906839\pi$
$164$	−0.411545	−0.0321363
$165$	−0.620903	−0.0483372
$166$	12.0910	0.938446
$167$	−2.12194	−0.164201	−0.0821005	−	0.996624i	$-0.526163\pi$
$167$	−2.12194	−0.164201	−0.0821005	+	0.996624i	$0.526163\pi$
$168$	−5.52786	−0.426484
$169$	9.68768	0.745206
$170$	−2.92991	−0.224714
$171$	−4.86537	−0.372064
$172$	−0.663861	−0.0506190
$173$	6.64705	0.505365	0.252683	−	0.967549i	$-0.418687\pi$
$173$	6.64705	0.505365	0.252683	+	0.967549i	$0.418687\pi$
$174$	27.5477	2.08838
$175$	4.57216	0.345623
$176$	−1.89712	−0.143000
$177$	1.89753	0.142627
$178$	−4.82904	−0.361952
$179$	−6.78813	−0.507369	−0.253684	−	0.967287i	$-0.581642\pi$
$179$	−6.78813	−0.507369	−0.253684	+	0.967287i	$0.581642\pi$
$180$	0.0356348	0.00265606
$181$	−6.27520	−0.466432	−0.233216	−	0.972425i	$-0.574925\pi$
$181$	−6.27520	−0.466432	−0.233216	+	0.972425i	$0.574925\pi$
$182$	−6.59943	−0.489183
$183$	−19.3560	−1.43083
$184$	12.4555	0.918234
$185$	−0.654097	−0.0480902
$186$	2.65719	0.194834
$187$	−1.60019	−0.117018
$188$	0.222597	0.0162346
$189$	4.45306	0.323912
$190$	−6.50268	−0.471754
$191$	6.01052	0.434906	0.217453	−	0.976071i	$-0.430225\pi$
$191$	6.01052	0.434906	0.217453	+	0.976071i	$0.430225\pi$
$192$	15.9085	1.14810
$193$	15.8270	1.13925	0.569624	−	0.821905i	$-0.307089\pi$
$193$	15.8270	1.13925	0.569624	+	0.821905i	$0.307089\pi$
$194$	−19.0697	−1.36912
$195$	5.97513	0.427888
$196$	−0.0803442	−0.00573887
$197$	−10.6105	−0.755970	−0.377985	−	0.925812i	$-0.623383\pi$
$197$	−10.6105	−0.755970	−0.377985	+	0.925812i	$0.623383\pi$
$198$	−0.465008	−0.0330467
$199$	−10.2347	−0.725521	−0.362761	−	0.931882i	$-0.618166\pi$
$199$	−10.2347	−0.725521	−0.362761	+	0.931882i	$0.618166\pi$
$200$	−13.1786	−0.931865
$201$	24.2420	1.70990
$202$	−10.3571	−0.728721
$203$	10.3672	0.727637
$204$	0.498156	0.0348779
$205$	−3.35046	−0.234007
$206$	−15.8667	−1.10549
$207$	2.93017	0.203661
$208$	18.2565	1.26586
$209$	−3.55148	−0.245661
$210$	−1.73806	−0.119937
$211$	6.19009	0.426143	0.213072	−	0.977037i	$-0.431653\pi$
$211$	6.19009	0.426143	0.213072	+	0.977037i	$0.431653\pi$
$212$	0.204657	0.0140559
$213$	−10.5549	−0.723208
$214$	−18.6461	−1.27462
$215$	−5.40462	−0.368592
$216$	−12.8353	−0.873330
$217$	1.00000	0.0678844
$218$	−6.45716	−0.437334
$219$	24.9152	1.68362
$220$	0.0260117	0.00175371
$221$	15.3991	1.03586
$222$	−2.65719	−0.178339
$223$	7.23702	0.484626	0.242313	−	0.970198i	$-0.422094\pi$
$223$	7.23702	0.484626	0.242313	+	0.970198i	$0.422094\pi$
$224$	0.454217	0.0303486
$225$	−3.10026	−0.206684
$226$	−6.17190	−0.410549
$227$	−0.189026	−0.0125461	−0.00627305	−	0.999980i	$-0.501997\pi$
$227$	−0.189026	−0.0125461	−0.00627305	+	0.999980i	$0.501997\pi$
$228$	1.10561	0.0732210
$229$	5.24393	0.346528	0.173264	−	0.984875i	$-0.444569\pi$
$229$	5.24393	0.346528	0.173264	+	0.984875i	$0.444569\pi$
$230$	3.91624	0.258229
$231$	−0.949252	−0.0624562
$232$	−29.8820	−1.96185
$233$	24.6014	1.61169	0.805845	−	0.592127i	$-0.201712\pi$
$233$	24.6014	1.61169	0.805845	+	0.592127i	$0.201712\pi$
$234$	4.47491	0.292534
$235$	1.81220	0.118215
$236$	−0.0794938	−0.00517460
$237$	21.0784	1.36919
$238$	−4.47933	−0.290352
$239$	−7.50653	−0.485557	−0.242779	−	0.970082i	$-0.578059\pi$
$239$	−7.50653	−0.485557	−0.242779	+	0.970082i	$0.578059\pi$
$240$	4.80812	0.310363
$241$	−26.6354	−1.71574	−0.857870	−	0.513867i	$-0.828212\pi$
$241$	−26.6354	−1.71574	−0.857870	+	0.513867i	$0.828212\pi$
$242$	14.9012	0.957888
$243$	−6.92080	−0.443969
$244$	0.810885	0.0519116
$245$	−0.654097	−0.0417887
$246$	−13.6108	−0.867795
$247$	34.1770	2.17463
$248$	−2.88235	−0.183029
$249$	−16.7364	−1.06063
$250$	−8.67488	−0.548648
$251$	−26.4591	−1.67008	−0.835041	−	0.550188i	$-0.814556\pi$
$251$	−26.4591	−1.67008	−0.835041	+	0.550188i	$0.814556\pi$
$252$	0.0544793	0.00343188
$253$	2.13888	0.134470
$254$	15.8737	0.996007
$255$	4.05558	0.253971
$256$	−1.92511	−0.120319
$257$	17.6058	1.09822	0.549108	−	0.835751i	$-0.314967\pi$
$257$	17.6058	1.09822	0.549108	+	0.835751i	$0.314967\pi$
$258$	−21.9556	−1.36689
$259$	−1.00000	−0.0621370
$260$	−0.250318	−0.0155241
$261$	−7.02975	−0.435131
$262$	0.126426	0.00781063
$263$	21.5589	1.32938	0.664689	−	0.747120i	$-0.268564\pi$
$263$	21.5589	1.32938	0.664689	+	0.747120i	$0.268564\pi$
$264$	2.73608	0.168394
$265$	1.66615	0.102351
$266$	−9.94146	−0.609550
$267$	6.68436	0.409076
$268$	−1.01558	−0.0620363
$269$	−11.7840	−0.718481	−0.359240	−	0.933245i	$-0.616964\pi$
$269$	−11.7840	−0.718481	−0.359240	+	0.933245i	$0.616964\pi$
$270$	−4.03564	−0.245601
$271$	−32.5366	−1.97646	−0.988228	−	0.152989i	$-0.951110\pi$
$271$	−32.5366	−1.97646	−0.988228	+	0.152989i	$0.951110\pi$
$272$	12.3915	0.751344
$273$	9.13493	0.552871
$274$	5.49174	0.331768
$275$	−2.26304	−0.136467
$276$	−0.665856	−0.0400798
$277$	−2.92154	−0.175538	−0.0877690	−	0.996141i	$-0.527974\pi$
$277$	−2.92154	−0.175538	−0.0877690	+	0.996141i	$0.527974\pi$
$278$	−22.5853	−1.35457
$279$	−0.678074	−0.0405952
$280$	1.88534	0.112670
$281$	−28.7147	−1.71298	−0.856489	−	0.516166i	$-0.827359\pi$
$281$	−28.7147	−1.71298	−0.856489	+	0.516166i	$0.827359\pi$
$282$	7.36185	0.438392
$283$	−3.49086	−0.207510	−0.103755	−	0.994603i	$-0.533086\pi$
$283$	−3.49086	−0.207510	−0.103755	+	0.994603i	$0.533086\pi$
$284$	0.442178	0.0262384
$285$	9.00100	0.533173
$286$	3.26647	0.193150
$287$	−5.12227	−0.302358
$288$	−0.307993	−0.0181486
$289$	−6.54794	−0.385173
$290$	−9.39543	−0.551719
$291$	26.3963	1.54738
$292$	−1.04378	−0.0610826
$293$	−29.7334	−1.73704	−0.868522	−	0.495651i	$-0.834929\pi$
$293$	−29.7334	−1.73704	−0.868522	+	0.495651i	$0.834929\pi$
$294$	−2.65719	−0.154970
$295$	−0.647174	−0.0376799
$296$	2.88235	0.167533
$297$	−2.20409	−0.127894
$298$	−1.69942	−0.0984448
$299$	−20.5831	−1.19035
$300$	0.704508	0.0406748
$301$	−8.26272	−0.476255
$302$	−5.44344	−0.313235
$303$	14.3363	0.823596
$304$	27.5018	1.57734
$305$	6.60156	0.378004
$306$	3.03732	0.173632
$307$	−11.3329	−0.646805	−0.323402	−	0.946262i	$-0.604827\pi$
$307$	−11.3329	−0.646805	−0.323402	+	0.946262i	$0.604827\pi$
$308$	0.0397673	0.00226595
$309$	21.9627	1.24942
$310$	−0.906262	−0.0514722
$311$	−11.3865	−0.645672	−0.322836	−	0.946455i	$-0.604636\pi$
$311$	−11.3865	−0.645672	−0.322836	+	0.946455i	$0.604636\pi$
$312$	−26.3301	−1.49065
$313$	4.69107	0.265155	0.132577	−	0.991173i	$-0.457675\pi$
$313$	4.69107	0.265155	0.132577	+	0.991173i	$0.457675\pi$
$314$	−33.7436	−1.90426
$315$	0.443526	0.0249899
$316$	−0.883044	−0.0496751
$317$	34.2812	1.92543	0.962713	−	0.270526i	$-0.0871977\pi$
$317$	34.2812	1.92543	0.962713	+	0.270526i	$0.0871977\pi$
$318$	6.76854	0.379561
$319$	−5.13138	−0.287302
$320$	−5.42576	−0.303309
$321$	25.8099	1.44057
$322$	5.98724	0.333656
$323$	23.1974	1.29074
$324$	0.849595	0.0471997
$325$	21.7779	1.20802
$326$	33.8737	1.87609
$327$	8.93800	0.494273
$328$	14.7642	0.815216
$329$	2.77054	0.152745
$330$	0.860271	0.0473564
$331$	−9.66247	−0.531097	−0.265549	−	0.964097i	$-0.585553\pi$
$331$	−9.66247	−0.531097	−0.265549	+	0.964097i	$0.585553\pi$
$332$	0.701142	0.0384802
$333$	0.678074	0.0371582
$334$	2.93999	0.160869
$335$	−8.26801	−0.451730
$336$	7.35077	0.401017
$337$	−14.9821	−0.816125	−0.408062	−	0.912954i	$-0.633795\pi$
$337$	−14.9821	−0.816125	−0.408062	+	0.912954i	$0.633795\pi$
$338$	−13.4224	−0.730085
$339$	8.54314	0.464000
$340$	−0.169902	−0.00921421
$341$	−0.494961	−0.0268037
$342$	6.74105	0.364514
$343$	−1.00000	−0.0539949
$344$	23.8160	1.28408
$345$	−5.42085	−0.291849
$346$	−9.20959	−0.495111
$347$	18.0458	0.968749	0.484375	−	0.874861i	$-0.339047\pi$
$347$	18.0458	0.968749	0.484375	+	0.874861i	$0.339047\pi$
$348$	1.59745	0.0856324
$349$	25.6319	1.37205	0.686023	−	0.727580i	$-0.259355\pi$
$349$	25.6319	1.37205	0.686023	+	0.727580i	$0.259355\pi$
$350$	−6.33480	−0.338609
$351$	21.2106	1.13214
$352$	−0.224820	−0.0119829
$353$	−1.05167	−0.0559747	−0.0279873	−	0.999608i	$-0.508910\pi$
$353$	−1.05167	−0.0559747	−0.0279873	+	0.999608i	$0.508910\pi$
$354$	−2.62906	−0.139733
$355$	3.59985	0.191060
$356$	−0.280030	−0.0148415
$357$	6.20028	0.328154
$358$	9.40507	0.497073
$359$	32.5303	1.71689	0.858443	−	0.512910i	$-0.171432\pi$
$359$	32.5303	1.71689	0.858443	+	0.512910i	$0.171432\pi$
$360$	−1.27840	−0.0673775
$361$	32.4845	1.70971
$362$	8.69439	0.456967
$363$	−20.6263	−1.08260
$364$	−0.382692	−0.0200585
$365$	−8.49761	−0.444785
$366$	26.8180	1.40180
$367$	−9.40838	−0.491113	−0.245557	−	0.969382i	$-0.578971\pi$
$367$	−9.40838	−0.491113	−0.245557	+	0.969382i	$0.578971\pi$
$368$	−16.5630	−0.863404
$369$	3.47328	0.180812
$370$	0.906262	0.0471143
$371$	2.54726	0.132247
$372$	0.154087	0.00798902
$373$	−6.45738	−0.334350	−0.167175	−	0.985927i	$-0.553465\pi$
$373$	−6.45738	−0.334350	−0.167175	+	0.985927i	$0.553465\pi$
$374$	2.21709	0.114643
$375$	12.0078	0.620078
$376$	−7.98568	−0.411830
$377$	49.3808	2.54324
$378$	−6.16979	−0.317340
$379$	28.0756	1.44215	0.721074	−	0.692859i	$-0.243649\pi$
$379$	28.0756	1.44215	0.721074	+	0.692859i	$0.243649\pi$
$380$	−0.377081	−0.0193439
$381$	−21.9724	−1.12568
$382$	−8.32767	−0.426081
$383$	0.153828	0.00786023	0.00393012	−	0.999992i	$-0.498749\pi$
$383$	0.153828	0.00786023	0.00393012	+	0.999992i	$0.498749\pi$
$384$	−20.2992	−1.03589
$385$	0.323753	0.0165000
$386$	−21.9285	−1.11613
$387$	5.60273	0.284803
$388$	−1.10583	−0.0561398
$389$	11.3857	0.577277	0.288639	−	0.957438i	$-0.406797\pi$
$389$	11.3857	0.577277	0.288639	+	0.957438i	$0.406797\pi$
$390$	−8.27864	−0.419205
$391$	−13.9706	−0.706526
$392$	2.88235	0.145581
$393$	−0.174999	−0.00882753
$394$	14.7011	0.740630
$395$	−7.18903	−0.361719
$396$	−0.0269652	−0.00135505
$397$	10.1042	0.507116	0.253558	−	0.967320i	$-0.418399\pi$
$397$	10.1042	0.507116	0.253558	+	0.967320i	$0.418399\pi$
$398$	14.1804	0.710799
$399$	13.7610	0.688910
$400$	17.5244	0.876221
$401$	18.0916	0.903452	0.451726	−	0.892157i	$-0.350809\pi$
$401$	18.0916	0.903452	0.451726	+	0.892157i	$0.350809\pi$
$402$	−33.5878	−1.67520
$403$	4.76316	0.237270
$404$	−0.600593	−0.0298806
$405$	6.91671	0.343694
$406$	−14.3640	−0.712872
$407$	0.494961	0.0245343
$408$	−17.8714	−0.884765
$409$	−4.83636	−0.239143	−0.119571	−	0.992826i	$-0.538152\pi$
$409$	−4.83636	−0.239143	−0.119571	+	0.992826i	$0.538152\pi$
$410$	4.64212	0.229258
$411$	−7.60166	−0.374962
$412$	−0.920091	−0.0453296
$413$	−0.989415	−0.0486859
$414$	−4.05980	−0.199528
$415$	5.70813	0.280201
$416$	2.16351	0.106075
$417$	31.2625	1.53093
$418$	4.92064	0.240676
$419$	−14.8168	−0.723847	−0.361924	−	0.932208i	$-0.617880\pi$
$419$	−14.8168	−0.723847	−0.361924	+	0.932208i	$0.617880\pi$
$420$	−0.100788	−0.00491793
$421$	−11.5090	−0.560914	−0.280457	−	0.959867i	$-0.590486\pi$
$421$	−11.5090	−0.560914	−0.280457	+	0.959867i	$0.590486\pi$
$422$	−8.57647	−0.417496
$423$	−1.87863	−0.0913423
$424$	−7.34209	−0.356564
$425$	14.7816	0.717014
$426$	14.6239	0.708533
$427$	10.0926	0.488417
$428$	−1.08126	−0.0522648
$429$	−4.52144	−0.218297
$430$	7.48819	0.361112
$431$	−3.01630	−0.145290	−0.0726451	−	0.997358i	$-0.523144\pi$
$431$	−3.01630	−0.145290	−0.0726451	+	0.997358i	$0.523144\pi$
$432$	17.0679	0.821182
$433$	−4.17470	−0.200623	−0.100312	−	0.994956i	$-0.531984\pi$
$433$	−4.17470	−0.200623	−0.100312	+	0.994956i	$0.531984\pi$
$434$	−1.38552	−0.0665069
$435$	13.0052	0.623549
$436$	−0.374442	−0.0179325
$437$	−31.0066	−1.48325
$438$	−34.5205	−1.64945
$439$	−12.9443	−0.617798	−0.308899	−	0.951095i	$-0.599961\pi$
$439$	−12.9443	−0.617798	−0.308899	+	0.951095i	$0.599961\pi$
$440$	−0.933169	−0.0444871
$441$	0.678074	0.0322892
$442$	−21.3357	−1.01484
$443$	19.4247	0.922894	0.461447	−	0.887168i	$-0.347330\pi$
$443$	19.4247	0.922894	0.461447	+	0.887168i	$0.347330\pi$
$444$	−0.154087	−0.00731263
$445$	−2.27977	−0.108072
$446$	−10.0270	−0.474792
$447$	2.35234	0.111262
$448$	−8.29504	−0.391904
$449$	16.7467	0.790328	0.395164	−	0.918611i	$-0.370688\pi$
$449$	16.7467	0.790328	0.395164	+	0.918611i	$0.370688\pi$
$450$	4.29546	0.202490
$451$	2.53533	0.119384
$452$	−0.357900	−0.0168342
$453$	7.53481	0.354016
$454$	0.261899	0.0122915
$455$	−3.11557	−0.146060
$456$	−39.6639	−1.85743
$457$	−18.3414	−0.857974	−0.428987	−	0.903311i	$-0.641129\pi$
$457$	−18.3414	−0.857974	−0.428987	+	0.903311i	$0.641129\pi$
$458$	−7.26555	−0.339497
$459$	14.3966	0.671975
$460$	0.227097	0.0105885
$461$	31.2805	1.45688	0.728439	−	0.685110i	$-0.240246\pi$
$461$	31.2805	1.45688	0.728439	+	0.685110i	$0.240246\pi$
$462$	1.31520	0.0611888
$463$	−15.5635	−0.723296	−0.361648	−	0.932315i	$-0.617786\pi$
$463$	−15.5635	−0.723296	−0.361648	+	0.932315i	$0.617786\pi$
$464$	39.7361	1.84470
$465$	1.25445	0.0581736
$466$	−34.0856	−1.57899
$467$	−10.6210	−0.491480	−0.245740	−	0.969336i	$-0.579031\pi$
$467$	−10.6210	−0.491480	−0.245740	+	0.969336i	$0.579031\pi$
$468$	0.259494	0.0119951
$469$	−12.6403	−0.583677
$470$	−2.51084	−0.115816
$471$	46.7079	2.15219
$472$	2.85184	0.131267
$473$	4.08973	0.188046
$474$	−29.2045	−1.34141
$475$	32.8065	1.50526
$476$	−0.259750	−0.0119056
$477$	−1.72723	−0.0790844
$478$	10.4004	0.475704
$479$	−8.38532	−0.383135	−0.191568	−	0.981479i	$-0.561357\pi$
$479$	−8.38532	−0.383135	−0.191568	+	0.981479i	$0.561357\pi$
$480$	0.569791	0.0260073
$481$	−4.76316	−0.217181
$482$	36.9038	1.68092
$483$	−8.28754	−0.377096
$484$	0.864103	0.0392774
$485$	−9.00273	−0.408793
$486$	9.58888	0.434960
$487$	−17.0500	−0.772607	−0.386304	−	0.922372i	$-0.626248\pi$
$487$	−17.0500	−0.772607	−0.386304	+	0.922372i	$0.626248\pi$
$488$	−29.0905	−1.31687
$489$	−46.8880	−2.12035
$490$	0.906262	0.0409408
$491$	−0.367699	−0.0165940	−0.00829702	−	0.999966i	$-0.502641\pi$
$491$	−0.367699	−0.0165940	−0.00829702	+	0.999966i	$0.502641\pi$
$492$	−0.789274	−0.0355832
$493$	33.5169	1.50953
$494$	−47.3527	−2.13050
$495$	−0.219528	−0.00986707
$496$	3.83286	0.172100
$497$	5.50355	0.246868
$498$	23.1886	1.03910
$499$	10.9653	0.490876	0.245438	−	0.969412i	$-0.421068\pi$
$499$	10.9653	0.490876	0.245438	+	0.969412i	$0.421068\pi$
$500$	−0.503045	−0.0224968
$501$	−4.06953	−0.181813
$502$	36.6595	1.63619
$503$	−10.8421	−0.483426	−0.241713	−	0.970348i	$-0.577709\pi$
$503$	−10.8421	−0.483426	−0.241713	+	0.970348i	$0.577709\pi$
$504$	−1.95445	−0.0870580
$505$	−4.88953	−0.217581
$506$	−2.96345	−0.131742
$507$	18.5793	0.825137
$508$	0.920497	0.0408404
$509$	−10.4989	−0.465357	−0.232678	−	0.972554i	$-0.574749\pi$
$509$	−10.4989	−0.465357	−0.232678	+	0.972554i	$0.574749\pi$
$510$	−5.61908	−0.248817
$511$	−12.9914	−0.574704
$512$	23.8362	1.05342
$513$	31.9519	1.41071
$514$	−24.3931	−1.07593
$515$	−7.49063	−0.330076
$516$	−1.27317	−0.0560483
$517$	−1.37131	−0.0603102
$518$	1.38552	0.0608761
$519$	12.7479	0.559571
$520$	8.98016	0.393806
$521$	25.6077	1.12189	0.560947	−	0.827851i	$-0.310437\pi$
$521$	25.6077	1.12189	0.560947	+	0.827851i	$0.310437\pi$
$522$	9.73984	0.426301
$523$	21.8690	0.956267	0.478133	−	0.878287i	$-0.341314\pi$
$523$	21.8690	0.956267	0.478133	+	0.878287i	$0.341314\pi$
$524$	0.00733128	0.000320268 0
$525$	8.76862	0.382694
$526$	−29.8702	−1.30240
$527$	3.23296	0.140830
$528$	−3.63835	−0.158339
$529$	−4.32629	−0.188100
$530$	−2.30848	−0.100274
$531$	0.670897	0.0291144
$532$	−0.576492	−0.0249941
$533$	−24.3982	−1.05680
$534$	−9.26129	−0.400775
$535$	−8.80275	−0.380576
$536$	36.4339	1.57371
$537$	−13.0185	−0.561789
$538$	16.3269	0.703902
$539$	0.494961	0.0213195
$540$	−0.234021	−0.0100707
$541$	34.9308	1.50179	0.750897	−	0.660420i	$-0.229622\pi$
$541$	34.9308	1.50179	0.750897	+	0.660420i	$0.229622\pi$
$542$	45.0800	1.93635
$543$	−12.0348	−0.516461
$544$	1.46847	0.0629600
$545$	−3.04840	−0.130579
$546$	−12.6566	−0.541652
$547$	17.6169	0.753244	0.376622	−	0.926367i	$-0.377086\pi$
$547$	17.6169	0.753244	0.376622	+	0.926367i	$0.377086\pi$
$548$	0.318458	0.0136039
$549$	−6.84355	−0.292076
$550$	3.13548	0.133697
$551$	74.3877	3.16902
$552$	23.8876	1.01672
$553$	−10.9908	−0.467375
$554$	4.04784	0.171976
$555$	−1.25445	−0.0532483
$556$	−1.30969	−0.0555432
$557$	−40.8567	−1.73116	−0.865578	−	0.500774i	$-0.833049\pi$
$557$	−40.8567	−1.73116	−0.865578	+	0.500774i	$0.833049\pi$
$558$	0.939483	0.0397715
$559$	−39.3566	−1.66461
$560$	−2.50706	−0.105943
$561$	−3.06890	−0.129569
$562$	39.7847	1.67822
$563$	10.1710	0.428655	0.214328	−	0.976762i	$-0.431244\pi$
$563$	10.1710	0.428655	0.214328	+	0.976762i	$0.431244\pi$
$564$	0.426903	0.0179759
$565$	−2.91373	−0.122582
$566$	4.83665	0.203300
$567$	10.5744	0.444085
$568$	−15.8632	−0.665603
$569$	37.0492	1.55318	0.776592	−	0.630004i	$-0.216947\pi$
$569$	37.0492	1.55318	0.776592	+	0.630004i	$0.216947\pi$
$570$	−12.4710	−0.522354
$571$	−32.6982	−1.36838	−0.684189	−	0.729304i	$-0.739844\pi$
$571$	−32.6982	−1.36838	−0.684189	+	0.729304i	$0.739844\pi$
$572$	0.189418	0.00791996
$573$	11.5272	0.481554
$574$	7.09699	0.296223
$575$	−19.7577	−0.823953
$576$	5.62465	0.234360
$577$	−16.2424	−0.676178	−0.338089	−	0.941114i	$-0.609781\pi$
$577$	−16.2424	−0.676178	−0.338089	+	0.941114i	$0.609781\pi$
$578$	9.07228	0.377357
$579$	30.3534	1.26144
$580$	−0.544828	−0.0226228
$581$	8.72673	0.362046
$582$	−36.5725	−1.51598
$583$	−1.26079	−0.0522168
$584$	37.4457	1.54951
$585$	2.11259	0.0873447
$586$	41.1961	1.70180
$587$	22.4059	0.924789	0.462395	−	0.886674i	$-0.346990\pi$
$587$	22.4059	0.924789	0.462395	+	0.886674i	$0.346990\pi$
$588$	−0.154087	−0.00635442
$589$	7.17527	0.295652
$590$	0.896670	0.0369153
$591$	−20.3492	−0.837056
$592$	−3.83286	−0.157529
$593$	−23.2204	−0.953549	−0.476774	−	0.879026i	$-0.658194\pi$
$593$	−23.2204	−0.953549	−0.476774	+	0.879026i	$0.658194\pi$
$594$	3.05381	0.125299
$595$	−2.11467	−0.0866931
$596$	−0.0985471	−0.00403665
$597$	−19.6285	−0.803341
$598$	28.5182	1.16620
$599$	0.0939350	0.00383808	0.00191904	−	0.999998i	$-0.499389\pi$
$599$	0.0939350	0.00383808	0.00191904	+	0.999998i	$0.499389\pi$
$600$	−25.2742	−1.03182
$601$	−8.16125	−0.332904	−0.166452	−	0.986050i	$-0.553231\pi$
$601$	−8.16125	−0.332904	−0.166452	+	0.986050i	$0.553231\pi$
$602$	11.4481	0.466591
$603$	8.57109	0.349042
$604$	−0.315658	−0.0128439
$605$	7.03482	0.286006
$606$	−19.8631	−0.806884
$607$	−27.6120	−1.12074	−0.560369	−	0.828243i	$-0.689341\pi$
$607$	−27.6120	−1.12074	−0.560369	+	0.828243i	$0.689341\pi$
$608$	3.25913	0.132175
$609$	19.8826	0.805684
$610$	−9.14657	−0.370334
$611$	13.1965	0.533875
$612$	0.176130	0.00711962
$613$	10.7423	0.433877	0.216939	−	0.976185i	$-0.430393\pi$
$613$	10.7423	0.433877	0.216939	+	0.976185i	$0.430393\pi$
$614$	15.7020	0.633680
$615$	−6.42562	−0.259106
$616$	−1.42665	−0.0574815
$617$	25.7465	1.03652	0.518258	−	0.855225i	$-0.326581\pi$
$617$	25.7465	1.03652	0.518258	+	0.855225i	$0.326581\pi$
$618$	−30.4297	−1.22406
$619$	15.1771	0.610018	0.305009	−	0.952349i	$-0.401341\pi$
$619$	15.1771	0.610018	0.305009	+	0.952349i	$0.401341\pi$
$620$	−0.0525529	−0.00211058
$621$	−19.2430	−0.772197
$622$	15.7763	0.632570
$623$	−3.48537	−0.139639
$624$	35.0129	1.40164
$625$	18.7654	0.750616
$626$	−6.49955	−0.259774
$627$	−6.81114	−0.272011
$628$	−1.95675	−0.0780827
$629$	−3.23296	−0.128907
$630$	−0.614513	−0.0244828
$631$	−14.3149	−0.569866	−0.284933	−	0.958547i	$-0.591971\pi$
$631$	−14.3149	−0.569866	−0.284933	+	0.958547i	$0.591971\pi$
$632$	31.6792	1.26013
$633$	11.8715	0.471851
$634$	−47.4972	−1.88635
$635$	7.49393	0.297388
$636$	0.392498	0.0155636
$637$	−4.76316	−0.188723
$638$	7.10961	0.281472
$639$	−3.73181	−0.147628
$640$	6.92328	0.273666
$641$	21.4237	0.846186	0.423093	−	0.906086i	$-0.360944\pi$
$641$	21.4237	0.846186	0.423093	+	0.906086i	$0.360944\pi$
$642$	−35.7601	−1.41134
$643$	−24.7765	−0.977091	−0.488545	−	0.872538i	$-0.662472\pi$
$643$	−24.7765	−0.977091	−0.488545	+	0.872538i	$0.662472\pi$
$644$	0.347192	0.0136813
$645$	−10.3651	−0.408127
$646$	−32.1404	−1.26455
$647$	0.516564	0.0203082	0.0101541	−	0.999948i	$-0.496768\pi$
$647$	0.516564	0.0203082	0.0101541	+	0.999948i	$0.496768\pi$
$648$	−30.4792	−1.19734
$649$	0.489722	0.0192233
$650$	−30.1737	−1.18351
$651$	1.91783	0.0751657
$652$	1.96429	0.0769276
$653$	31.1456	1.21882	0.609410	−	0.792855i	$-0.291406\pi$
$653$	31.1456	1.21882	0.609410	+	0.792855i	$0.291406\pi$
$654$	−12.3837	−0.484243
$655$	0.0596853	0.00233210
$656$	−19.6329	−0.766537
$657$	8.80911	0.343676
$658$	−3.83863	−0.149645
$659$	−25.4776	−0.992467	−0.496233	−	0.868189i	$-0.665284\pi$
$659$	−25.4776	−0.992467	−0.496233	+	0.868189i	$0.665284\pi$
$660$	0.0498860	0.00194181
$661$	−9.94334	−0.386751	−0.193376	−	0.981125i	$-0.561944\pi$
$661$	−9.94334	−0.386751	−0.193376	+	0.981125i	$0.561944\pi$
$662$	13.3875	0.520320
$663$	29.5329	1.14696
$664$	−25.1535	−0.976145
$665$	−4.69332	−0.181999
$666$	−0.939483	−0.0364042
$667$	−44.8000	−1.73466
$668$	0.170486	0.00659630
$669$	13.8794	0.536607
$670$	11.4555	0.442563
$671$	−4.99546	−0.192848
$672$	0.871111	0.0336038
$673$	−36.9807	−1.42550	−0.712750	−	0.701418i	$-0.752551\pi$
$673$	−36.9807	−1.42550	−0.712750	+	0.701418i	$0.752551\pi$
$674$	20.7579	0.799564
$675$	20.3601	0.783660
$676$	−0.778349	−0.0299365
$677$	−6.60358	−0.253796	−0.126898	−	0.991916i	$-0.540502\pi$
$677$	−6.60358	−0.253796	−0.126898	+	0.991916i	$0.540502\pi$
$678$	−11.8367	−0.454584
$679$	−13.7636	−0.528199
$680$	6.09523	0.233741
$681$	−0.362520	−0.0138918
$682$	0.685777	0.0262598
$683$	27.9861	1.07086	0.535429	−	0.844580i	$-0.320150\pi$
$683$	27.9861	1.07086	0.535429	+	0.844580i	$0.320150\pi$
$684$	0.390904	0.0149466
$685$	2.59263	0.0990593
$686$	1.38552	0.0528993
$687$	10.0570	0.383697
$688$	−31.6698	−1.20740
$689$	12.1330	0.462230
$690$	7.51068	0.285927
$691$	21.4828	0.817243	0.408621	−	0.912704i	$-0.366010\pi$
$691$	21.4828	0.817243	0.408621	+	0.912704i	$0.366010\pi$
$692$	−0.534052	−0.0203016
$693$	−0.335621	−0.0127492
$694$	−25.0028	−0.949091
$695$	−10.6624	−0.404449
$696$	−57.3086	−2.17228
$697$	−16.5601	−0.627260
$698$	−35.5135	−1.34420
$699$	47.1813	1.78456
$700$	−0.367346	−0.0138844
$701$	22.3284	0.843334	0.421667	−	0.906751i	$-0.361445\pi$
$701$	22.3284	0.843334	0.421667	+	0.906751i	$0.361445\pi$
$702$	−29.3877	−1.10917
$703$	−7.17527	−0.270621
$704$	4.10572	0.154740
$705$	3.47550	0.130895
$706$	1.45710	0.0548388
$707$	−7.47524	−0.281135
$708$	−0.152456	−0.00572963
$709$	−13.6265	−0.511752	−0.255876	−	0.966710i	$-0.582364\pi$
$709$	−13.6265	−0.511752	−0.255876	+	0.966710i	$0.582364\pi$
$710$	−4.98766	−0.187183
$711$	7.45255	0.279493
$712$	10.0461	0.376492
$713$	−4.32131	−0.161834
$714$	−8.59059	−0.321495
$715$	1.54209	0.0576707
$716$	0.545387	0.0203821
$717$	−14.3963	−0.537638
$718$	−45.0713	−1.68205
$719$	−10.2328	−0.381620	−0.190810	−	0.981627i	$-0.561111\pi$
$719$	−10.2328	−0.381620	−0.190810	+	0.981627i	$0.561111\pi$
$720$	1.69997	0.0633542
$721$	−11.4519	−0.426490
$722$	−45.0079	−1.67502
$723$	−51.0823	−1.89977
$724$	0.504176	0.0187375
$725$	47.4006	1.76042
$726$	28.5781	1.06063
$727$	−50.9552	−1.88982	−0.944912	−	0.327326i	$-0.893853\pi$
$727$	−50.9552	−1.88982	−0.944912	+	0.327326i	$0.893853\pi$
$728$	13.7291	0.508834
$729$	18.4504	0.683348
$730$	11.7736	0.435760
$731$	−26.7131	−0.988019
$732$	1.55514	0.0574796
$733$	−21.1686	−0.781879	−0.390940	−	0.920416i	$-0.627850\pi$
$733$	−21.1686	−0.781879	−0.390940	+	0.920416i	$0.627850\pi$
$734$	13.0355	0.481148
$735$	−1.25445	−0.0462710
$736$	−1.96281	−0.0723501
$737$	6.25648	0.230461
$738$	−4.81229	−0.177143
$739$	−15.5669	−0.572638	−0.286319	−	0.958134i	$-0.592432\pi$
$739$	−15.5669	−0.572638	−0.286319	+	0.958134i	$0.592432\pi$
$740$	0.0525529	0.00193188
$741$	65.5456	2.40788
$742$	−3.52927	−0.129564
$743$	−38.6395	−1.41755	−0.708773	−	0.705437i	$-0.750751\pi$
$743$	−38.6395	−1.41755	−0.708773	+	0.705437i	$0.750751\pi$
$744$	−5.52786	−0.202661
$745$	−0.802290	−0.0293936
$746$	8.94680	0.327566
$747$	−5.91737	−0.216505
$748$	0.128566	0.00470085
$749$	−13.4579	−0.491740
$750$	−16.6370	−0.607496
$751$	20.4325	0.745592	0.372796	−	0.927913i	$-0.378399\pi$
$751$	20.4325	0.745592	0.372796	+	0.927913i	$0.378399\pi$
$752$	10.6191	0.387238
$753$	−50.7440	−1.84921
$754$	−68.4179	−2.49163
$755$	−2.56983	−0.0935256
$756$	−0.357778	−0.0130122
$757$	12.8443	0.466834	0.233417	−	0.972377i	$-0.425009\pi$
$757$	12.8443	0.466834	0.233417	+	0.972377i	$0.425009\pi$
$758$	−38.8992	−1.41288
$759$	4.10201	0.148894
$760$	13.5278	0.490705
$761$	−42.2716	−1.53234	−0.766172	−	0.642636i	$-0.777841\pi$
$761$	−42.2716	−1.53234	−0.766172	+	0.642636i	$0.777841\pi$
$762$	30.4431	1.10284
$763$	−4.66047	−0.168721
$764$	−0.482910	−0.0174711
$765$	1.43390	0.0518429
$766$	−0.213131	−0.00770073
$767$	−4.71274	−0.170167
$768$	−3.69203	−0.133225
$769$	−35.6878	−1.28693	−0.643467	−	0.765474i	$-0.722505\pi$
$769$	−35.6878	−1.28693	−0.643467	+	0.765474i	$0.722505\pi$
$770$	−0.448565	−0.0161652
$771$	33.7648	1.21601
$772$	−1.27160	−0.0457660
$773$	31.4671	1.13179	0.565896	−	0.824476i	$-0.308530\pi$
$773$	31.4671	1.13179	0.565896	+	0.824476i	$0.308530\pi$
$774$	−7.76268	−0.279024
$775$	4.57216	0.164237
$776$	39.6715	1.42413
$777$	−1.91783	−0.0688018
$778$	−15.7751	−0.565563
$779$	−36.7537	−1.31684
$780$	−0.480067	−0.0171892
$781$	−2.72404	−0.0974739
$782$	19.3565	0.692189
$783$	46.1659	1.64984
$784$	−3.83286	−0.136888
$785$	−15.9302	−0.568575
$786$	0.242464	0.00864840
$787$	41.0770	1.46424	0.732118	−	0.681177i	$-0.238532\pi$
$787$	41.0770	1.46424	0.732118	+	0.681177i	$0.238532\pi$
$788$	0.852496	0.0303689
$789$	41.3463	1.47197
$790$	9.96051	0.354379
$791$	−4.45458	−0.158387
$792$	0.967376	0.0343742
$793$	48.0728	1.70712
$794$	−13.9996	−0.496826
$795$	3.19540	0.113329
$796$	0.822302	0.0291457
$797$	−31.2556	−1.10713	−0.553564	−	0.832806i	$-0.686733\pi$
$797$	−31.2556	−1.10713	−0.553564	+	0.832806i	$0.686733\pi$
$798$	−19.0660	−0.674930
$799$	8.95707	0.316878
$800$	2.07675	0.0734242
$801$	2.36334	0.0835046
$802$	−25.0662	−0.885119
$803$	6.43022	0.226918
$804$	−1.94771	−0.0686904
$805$	2.82656	0.0996230
$806$	−6.59943	−0.232455
$807$	−22.5996	−0.795545
$808$	21.5463	0.757995
$809$	−6.70858	−0.235861	−0.117930	−	0.993022i	$-0.537626\pi$
$809$	−6.70858	−0.235861	−0.117930	+	0.993022i	$0.537626\pi$
$810$	−9.58321	−0.336720
$811$	−9.88229	−0.347014	−0.173507	−	0.984833i	$-0.555510\pi$
$811$	−9.88229	−0.347014	−0.173507	+	0.984833i	$0.555510\pi$
$812$	−0.832947	−0.0292307
$813$	−62.3996	−2.18845
$814$	−0.685777	−0.0240365
$815$	15.9917	0.560163
$816$	23.7648	0.831934
$817$	−59.2872	−2.07420
$818$	6.70086	0.234290
$819$	3.22977	0.112857
$820$	0.269190	0.00940053
$821$	15.9859	0.557912	0.278956	−	0.960304i	$-0.410012\pi$
$821$	15.9859	0.557912	0.278956	+	0.960304i	$0.410012\pi$
$822$	10.5322	0.367354
$823$	−36.6094	−1.27612	−0.638062	−	0.769985i	$-0.720264\pi$
$823$	−36.6094	−1.27612	−0.638062	+	0.769985i	$0.720264\pi$
$824$	33.0083	1.14990
$825$	−4.34013	−0.151104
$826$	1.37085	0.0476980
$827$	−43.0813	−1.49809	−0.749043	−	0.662522i	$-0.769486\pi$
$827$	−43.0813	−1.49809	−0.749043	+	0.662522i	$0.769486\pi$
$828$	−0.235422	−0.00818148
$829$	39.0892	1.35762	0.678812	−	0.734312i	$-0.262495\pi$
$829$	39.0892	1.35762	0.678812	+	0.734312i	$0.262495\pi$
$830$	−7.90871	−0.274515
$831$	−5.60301	−0.194366
$832$	−39.5106	−1.36978
$833$	−3.23296	−0.112016
$834$	−43.3147	−1.49987
$835$	1.38796	0.0480322
$836$	0.285341	0.00986873
$837$	4.45306	0.153920
$838$	20.5289	0.709159
$839$	2.25316	0.0777877	0.0388938	−	0.999243i	$-0.487617\pi$
$839$	2.25316	0.0777877	0.0388938	+	0.999243i	$0.487617\pi$
$840$	3.61576	0.124755
$841$	78.4796	2.70619
$842$	15.9459	0.549532
$843$	−55.0700	−1.89671
$844$	−0.497338	−0.0171191
$845$	−6.33668	−0.217989
$846$	2.60288	0.0894888
$847$	10.7550	0.369547
$848$	9.76328	0.335272
$849$	−6.69489	−0.229768
$850$	−20.4802	−0.702464
$851$	4.32131	0.148133
$852$	0.848023	0.0290528
$853$	48.9262	1.67520	0.837600	−	0.546284i	$-0.183958\pi$
$853$	48.9262	1.67520	0.837600	+	0.546284i	$0.183958\pi$
$854$	−13.9835	−0.478506
$855$	3.18242	0.108837
$856$	38.7903	1.32583
$857$	−9.03895	−0.308765	−0.154382	−	0.988011i	$-0.549339\pi$
$857$	−9.03895	−0.308765	−0.154382	+	0.988011i	$0.549339\pi$
$858$	6.26453	0.213867
$859$	44.0640	1.50345	0.751723	−	0.659479i	$-0.229223\pi$
$859$	44.0640	1.50345	0.751723	+	0.659479i	$0.229223\pi$
$860$	0.434230	0.0148071
$861$	−9.82365	−0.334789
$862$	4.17914	0.142342
$863$	31.9183	1.08651	0.543256	−	0.839567i	$-0.317191\pi$
$863$	31.9183	1.08651	0.543256	+	0.839567i	$0.317191\pi$
$864$	2.02265	0.0688121
$865$	−4.34781	−0.147830
$866$	5.78411	0.196552
$867$	−12.5578	−0.426487
$868$	−0.0803442	−0.00272706
$869$	5.44000	0.184539
$870$	−18.0188	−0.610896
$871$	−60.2080	−2.04007
$872$	13.4331	0.454903
$873$	9.33274	0.315866
$874$	42.9601	1.45315
$875$	−6.26112	−0.211664
$876$	−2.00179	−0.0676344
$877$	−36.1719	−1.22144	−0.610720	−	0.791847i	$-0.709120\pi$
$877$	−36.1719	−1.22144	−0.610720	+	0.791847i	$0.709120\pi$
$878$	17.9345	0.605262
$879$	−57.0236	−1.92336
$880$	1.24090	0.0418307
$881$	6.79708	0.228999	0.114500	−	0.993423i	$-0.463474\pi$
$881$	6.79708	0.228999	0.114500	+	0.993423i	$0.463474\pi$
$882$	−0.939483	−0.0316340
$883$	49.4603	1.66447	0.832236	−	0.554422i	$-0.187061\pi$
$883$	49.4603	1.66447	0.832236	+	0.554422i	$0.187061\pi$
$884$	−1.23723	−0.0416126
$885$	−1.24117	−0.0417214
$886$	−26.9132	−0.904167
$887$	−7.88562	−0.264773	−0.132387	−	0.991198i	$-0.542264\pi$
$887$	−7.88562	−0.264773	−0.132387	+	0.991198i	$0.542264\pi$
$888$	5.52786	0.185503
$889$	11.4569	0.384253
$890$	3.15866	0.105879
$891$	−5.23394	−0.175344
$892$	−0.581452	−0.0194685
$893$	19.8794	0.665239
$894$	−3.25920	−0.109004
$895$	4.44010	0.148416
$896$	10.5845	0.353603
$897$	−39.4749	−1.31803
$898$	−23.2029	−0.774290
$899$	10.3672	0.345767
$900$	0.249088	0.00830294
$901$	8.23520	0.274354
$902$	−3.51274	−0.116961
$903$	−15.8465	−0.527338
$904$	12.8397	0.427041
$905$	4.10459	0.136441
$906$	−10.4396	−0.346832
$907$	55.4766	1.84207	0.921035	−	0.389479i	$-0.127345\pi$
$907$	55.4766	1.84207	0.921035	+	0.389479i	$0.127345\pi$
$908$	0.0151872	0.000504004 0
$909$	5.06877	0.168120
$910$	4.31667	0.143096
$911$	−42.9962	−1.42453	−0.712264	−	0.701912i	$-0.752330\pi$
$911$	−42.9962	−1.42453	−0.712264	+	0.701912i	$0.752330\pi$
$912$	52.7438	1.74652
$913$	−4.31940	−0.142951
$914$	25.4123	0.840564
$915$	12.6607	0.418549
$916$	−0.421319	−0.0139208
$917$	0.0912483	0.00301329
$918$	−19.9467	−0.658339
$919$	21.5778	0.711785	0.355892	−	0.934527i	$-0.384177\pi$
$919$	21.5778	0.711785	0.355892	+	0.934527i	$0.384177\pi$
$920$	−8.14712	−0.268603
$921$	−21.7346	−0.716181
$922$	−43.3397	−1.42732
$923$	26.2143	0.862853
$924$	0.0762669	0.00250900
$925$	−4.57216	−0.150332
$926$	21.5635	0.708619
$927$	7.76521	0.255043
$928$	4.70897	0.154580
$929$	12.6529	0.415127	0.207563	−	0.978222i	$-0.433447\pi$
$929$	12.6529	0.415127	0.207563	+	0.978222i	$0.433447\pi$
$930$	−1.73806	−0.0569931
$931$	−7.17527	−0.235160
$932$	−1.97658	−0.0647450
$933$	−21.8375	−0.714927
$934$	14.7155	0.481507
$935$	1.04668	0.0342301
$936$	−9.30935	−0.304285
$937$	19.8453	0.648318	0.324159	−	0.946003i	$-0.394919\pi$
$937$	19.8453	0.648318	0.324159	+	0.946003i	$0.394919\pi$
$938$	17.5134	0.571833
$939$	8.99668	0.293595
$940$	−0.145600	−0.00474895
$941$	−25.5772	−0.833792	−0.416896	−	0.908954i	$-0.636882\pi$
$941$	−25.5772	−0.833792	−0.416896	+	0.908954i	$0.636882\pi$
$942$	−64.7146	−2.10851
$943$	22.1349	0.720812
$944$	−3.79229	−0.123428
$945$	−2.91273	−0.0947512
$946$	−5.66638	−0.184230
$947$	15.7204	0.510845	0.255423	−	0.966829i	$-0.417785\pi$
$947$	15.7204	0.510845	0.255423	+	0.966829i	$0.417785\pi$
$948$	−1.69353	−0.0550033
$949$	−61.8799	−2.00871
$950$	−45.4539	−1.47472
$951$	65.7456	2.13195
$952$	9.31854	0.302016
$953$	−52.7300	−1.70809	−0.854045	−	0.520198i	$-0.825858\pi$
$953$	−52.7300	−1.70809	−0.854045	+	0.520198i	$0.825858\pi$
$954$	2.39311	0.0774797
$955$	−3.93146	−0.127219
$956$	0.603106	0.0195058
$957$	−9.84112	−0.318118
$958$	11.6180	0.375361
$959$	3.96368	0.127994
$960$	−10.4057	−0.335842
$961$	1.00000	0.0322581
$962$	6.59943	0.212774
$963$	9.12543	0.294063
$964$	2.14000	0.0689249
$965$	−10.3524	−0.333254
$966$	11.4825	0.369444
$967$	34.9157	1.12281	0.561407	−	0.827540i	$-0.310260\pi$
$967$	34.9157	1.12281	0.561407	+	0.827540i	$0.310260\pi$
$968$	−30.9997	−0.996369
$969$	44.4887	1.42918
$970$	12.4734	0.400498
$971$	−7.33256	−0.235313	−0.117657	−	0.993054i	$-0.537538\pi$
$971$	−7.33256	−0.235313	−0.117657	+	0.993054i	$0.537538\pi$
$972$	0.556046	0.0178352
$973$	−16.3010	−0.522585
$974$	23.6230	0.756930
$975$	41.7663	1.33759
$976$	38.6836	1.23823
$977$	−30.2181	−0.966763	−0.483382	−	0.875410i	$-0.660592\pi$
$977$	−30.2181	−0.966763	−0.483382	+	0.875410i	$0.660592\pi$
$978$	64.9641	2.07732
$979$	1.72513	0.0551353
$980$	0.0525529	0.00167874
$981$	3.16015	0.100896
$982$	0.509454	0.0162573
$983$	47.3426	1.51000	0.754998	−	0.655727i	$-0.227638\pi$
$983$	47.3426	1.51000	0.754998	+	0.655727i	$0.227638\pi$
$984$	28.3152	0.902656
$985$	6.94033	0.221137
$986$	−46.4382	−1.47889
$987$	5.31343	0.169128
$988$	−2.74592	−0.0873594
$989$	35.7057	1.13538
$990$	0.304160	0.00966685
$991$	−28.1909	−0.895514	−0.447757	−	0.894155i	$-0.647777\pi$
$991$	−28.1909	−0.895514	−0.447757	+	0.894155i	$0.647777\pi$
$992$	0.454217	0.0144214
$993$	−18.5310	−0.588063
$994$	−7.62525	−0.241858
$995$	6.69451	0.212230
$996$	1.34467	0.0426076
$997$	19.9217	0.630926	0.315463	−	0.948938i	$-0.397840\pi$
$997$	19.9217	0.630926	0.315463	+	0.948938i	$0.397840\pi$
$998$	−15.1927	−0.480915
$999$	−4.45306	−0.140889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.20	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.20	✓	71	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.38552 q^{2} +1.91783 q^{3} -0.0803442 q^{4} -0.654097 q^{5} -2.65719 q^{6} -1.00000 q^{7} +2.88235 q^{8} +0.678074 q^{9} +O(q^{10})\)	\(q-1.38552 q^{2} +1.91783 q^{3} -0.0803442 q^{4} -0.654097 q^{5} -2.65719 q^{6} -1.00000 q^{7} +2.88235 q^{8} +0.678074 q^{9} +0.906262 q^{10} +0.494961 q^{11} -0.154087 q^{12} -4.76316 q^{13} +1.38552 q^{14} -1.25445 q^{15} -3.83286 q^{16} -3.23296 q^{17} -0.939483 q^{18} -7.17527 q^{19} +0.0525529 q^{20} -1.91783 q^{21} -0.685777 q^{22} +4.32131 q^{23} +5.52786 q^{24} -4.57216 q^{25} +6.59943 q^{26} -4.45306 q^{27} +0.0803442 q^{28} -10.3672 q^{29} +1.73806 q^{30} -1.00000 q^{31} -0.454217 q^{32} +0.949252 q^{33} +4.47933 q^{34} +0.654097 q^{35} -0.0544793 q^{36} +1.00000 q^{37} +9.94146 q^{38} -9.13493 q^{39} -1.88534 q^{40} +5.12227 q^{41} +2.65719 q^{42} +8.26272 q^{43} -0.0397673 q^{44} -0.443526 q^{45} -5.98724 q^{46} -2.77054 q^{47} -7.35077 q^{48} +1.00000 q^{49} +6.33480 q^{50} -6.20028 q^{51} +0.382692 q^{52} -2.54726 q^{53} +6.16979 q^{54} -0.323753 q^{55} -2.88235 q^{56} -13.7610 q^{57} +14.3640 q^{58} +0.989415 q^{59} +0.100788 q^{60} -10.0926 q^{61} +1.38552 q^{62} -0.678074 q^{63} +8.29504 q^{64} +3.11557 q^{65} -1.31520 q^{66} +12.6403 q^{67} +0.259750 q^{68} +8.28754 q^{69} -0.906262 q^{70} -5.50355 q^{71} +1.95445 q^{72} +12.9914 q^{73} -1.38552 q^{74} -8.76862 q^{75} +0.576492 q^{76} -0.494961 q^{77} +12.6566 q^{78} +10.9908 q^{79} +2.50706 q^{80} -10.5744 q^{81} -7.09699 q^{82} -8.72673 q^{83} +0.154087 q^{84} +2.11467 q^{85} -11.4481 q^{86} -19.8826 q^{87} +1.42665 q^{88} +3.48537 q^{89} +0.614513 q^{90} +4.76316 q^{91} -0.347192 q^{92} -1.91783 q^{93} +3.83863 q^{94} +4.69332 q^{95} -0.871111 q^{96} +13.7636 q^{97} -1.38552 q^{98} +0.335621 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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