LMFDB - Embedded newform 8047.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, 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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$1$
Dimension:	$142$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23848 q^{2} +1.32587 q^{3} +3.01078 q^{4} +3.90699 q^{5} -2.96792 q^{6} -1.03210 q^{7} -2.26261 q^{8} -1.24208 q^{9} +O(q^{10})$	\(q-2.23848 q^{2} +1.32587 q^{3} +3.01078 q^{4} +3.90699 q^{5} -2.96792 q^{6} -1.03210 q^{7} -2.26261 q^{8} -1.24208 q^{9} -8.74571 q^{10} -3.76952 q^{11} +3.99190 q^{12} +1.00000 q^{13} +2.31032 q^{14} +5.18015 q^{15} -0.956754 q^{16} -1.19568 q^{17} +2.78036 q^{18} +5.93474 q^{19} +11.7631 q^{20} -1.36842 q^{21} +8.43798 q^{22} +5.47097 q^{23} -2.99993 q^{24} +10.2646 q^{25} -2.23848 q^{26} -5.62443 q^{27} -3.10742 q^{28} -8.46985 q^{29} -11.5957 q^{30} -6.03126 q^{31} +6.66690 q^{32} -4.99788 q^{33} +2.67650 q^{34} -4.03239 q^{35} -3.73962 q^{36} +4.09348 q^{37} -13.2848 q^{38} +1.32587 q^{39} -8.84002 q^{40} -5.95287 q^{41} +3.06318 q^{42} -0.0499133 q^{43} -11.3492 q^{44} -4.85278 q^{45} -12.2466 q^{46} -11.3673 q^{47} -1.26853 q^{48} -5.93478 q^{49} -22.9771 q^{50} -1.58531 q^{51} +3.01078 q^{52} -2.35755 q^{53} +12.5902 q^{54} -14.7275 q^{55} +2.33523 q^{56} +7.86868 q^{57} +18.9596 q^{58} -2.92248 q^{59} +15.5963 q^{60} +11.4918 q^{61} +13.5008 q^{62} +1.28194 q^{63} -13.0102 q^{64} +3.90699 q^{65} +11.1876 q^{66} +2.07218 q^{67} -3.59992 q^{68} +7.25377 q^{69} +9.02642 q^{70} -15.5903 q^{71} +2.81034 q^{72} -11.0783 q^{73} -9.16317 q^{74} +13.6095 q^{75} +17.8682 q^{76} +3.89050 q^{77} -2.96792 q^{78} -11.3917 q^{79} -3.73803 q^{80} -3.73102 q^{81} +13.3254 q^{82} +14.0645 q^{83} -4.12002 q^{84} -4.67150 q^{85} +0.111730 q^{86} -11.2299 q^{87} +8.52896 q^{88} -1.14619 q^{89} +10.8628 q^{90} -1.03210 q^{91} +16.4719 q^{92} -7.99665 q^{93} +25.4453 q^{94} +23.1870 q^{95} +8.83943 q^{96} +0.332148 q^{97} +13.2849 q^{98} +4.68202 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 142 q - 13 q^{2} - 26 q^{3} + 129 q^{4} - 37 q^{5} - 15 q^{6} - 14 q^{7} - 39 q^{8} + 98 q^{9}+O(q^{10}) $ 142 * q - 13 * q^2 - 26 * q^3 + 129 * q^4 - 37 * q^5 - 15 * q^6 - 14 * q^7 - 39 * q^8 + 98 * q^9	\( 142 q - 13 q^{2} - 26 q^{3} + 129 q^{4} - 37 q^{5} - 15 q^{6} - 14 q^{7} - 39 q^{8} + 98 q^{9} - 25 q^{10} - 25 q^{11} - 62 q^{12} + 142 q^{13} - 57 q^{14} - 14 q^{15} + 111 q^{16} - 141 q^{17} - 29 q^{18} - 3 q^{19} - 87 q^{20} - 19 q^{21} - 24 q^{22} - 69 q^{23} - 40 q^{24} + 87 q^{25} - 13 q^{26} - 95 q^{27} - 34 q^{28} - 147 q^{29} - 2 q^{30} - 21 q^{31} - 66 q^{32} - 62 q^{33} - 6 q^{34} - 59 q^{35} + 74 q^{36} - 37 q^{37} - 76 q^{38} - 26 q^{39} - 61 q^{40} - 97 q^{41} - 29 q^{42} - 33 q^{43} - 57 q^{44} - 86 q^{45} - q^{46} - 102 q^{47} - 141 q^{48} + 70 q^{49} - 28 q^{50} - 13 q^{51} + 129 q^{52} - 137 q^{53} - 29 q^{54} - 24 q^{55} - 130 q^{56} - 65 q^{57} - 15 q^{58} - 56 q^{59} + 11 q^{60} - 77 q^{61} - 150 q^{62} - 32 q^{63} + 73 q^{64} - 37 q^{65} - 32 q^{66} - 9 q^{67} - 226 q^{68} - 113 q^{69} + 6 q^{70} - 18 q^{71} - 82 q^{72} - 117 q^{73} - 70 q^{74} - 83 q^{75} + 40 q^{76} - 214 q^{77} - 15 q^{78} - 52 q^{79} - 161 q^{80} - 10 q^{81} - 36 q^{82} - 74 q^{83} + 53 q^{84} + 2 q^{85} + 17 q^{86} - 49 q^{87} - 29 q^{88} - 171 q^{89} - 57 q^{90} - 14 q^{91} - 187 q^{92} - 39 q^{93} + 13 q^{94} - 150 q^{95} - 47 q^{96} - 126 q^{97} - 85 q^{98}+O(q^{100}) \) 142 * q - 13 * q^2 - 26 * q^3 + 129 * q^4 - 37 * q^5 - 15 * q^6 - 14 * q^7 - 39 * q^8 + 98 * q^9 - 25 * q^10 - 25 * q^11 - 62 * q^12 + 142 * q^13 - 57 * q^14 - 14 * q^15 + 111 * q^16 - 141 * q^17 - 29 * q^18 - 3 * q^19 - 87 * q^20 - 19 * q^21 - 24 * q^22 - 69 * q^23 - 40 * q^24 + 87 * q^25 - 13 * q^26 - 95 * q^27 - 34 * q^28 - 147 * q^29 - 2 * q^30 - 21 * q^31 - 66 * q^32 - 62 * q^33 - 6 * q^34 - 59 * q^35 + 74 * q^36 - 37 * q^37 - 76 * q^38 - 26 * q^39 - 61 * q^40 - 97 * q^41 - 29 * q^42 - 33 * q^43 - 57 * q^44 - 86 * q^45 - q^46 - 102 * q^47 - 141 * q^48 + 70 * q^49 - 28 * q^50 - 13 * q^51 + 129 * q^52 - 137 * q^53 - 29 * q^54 - 24 * q^55 - 130 * q^56 - 65 * q^57 - 15 * q^58 - 56 * q^59 + 11 * q^60 - 77 * q^61 - 150 * q^62 - 32 * q^63 + 73 * q^64 - 37 * q^65 - 32 * q^66 - 9 * q^67 - 226 * q^68 - 113 * q^69 + 6 * q^70 - 18 * q^71 - 82 * q^72 - 117 * q^73 - 70 * q^74 - 83 * q^75 + 40 * q^76 - 214 * q^77 - 15 * q^78 - 52 * q^79 - 161 * q^80 - 10 * q^81 - 36 * q^82 - 74 * q^83 + 53 * q^84 + 2 * q^85 + 17 * q^86 - 49 * q^87 - 29 * q^88 - 171 * q^89 - 57 * q^90 - 14 * q^91 - 187 * q^92 - 39 * q^93 + 13 * q^94 - 150 * q^95 - 47 * q^96 - 126 * q^97 - 85 * q^98

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 $

$2$	−2.23848	−1.58284	−0.791421	−	0.611271i	$-0.790659\pi$
$2$	−2.23848	−1.58284	−0.791421	+	0.611271i	$0.790659\pi$
$3$	1.32587	0.765490	0.382745	−	0.923854i	$-0.374979\pi$
$3$	1.32587	0.765490	0.382745	+	0.923854i	$0.374979\pi$
$4$	3.01078	1.50539
$5$	3.90699	1.74726	0.873630	−	0.486591i	$-0.161760\pi$
$5$	3.90699	1.74726	0.873630	+	0.486591i	$0.161760\pi$
$6$	−2.96792	−1.21165
$7$	−1.03210	−0.390096	−0.195048	−	0.980794i	$-0.562486\pi$
$7$	−1.03210	−0.390096	−0.195048	+	0.980794i	$0.562486\pi$
$8$	−2.26261	−0.799955
$9$	−1.24208	−0.414025
$10$	−8.74571	−2.76564
$11$	−3.76952	−1.13655	−0.568276	−	0.822838i	$-0.692389\pi$
$11$	−3.76952	−1.13655	−0.568276	+	0.822838i	$0.692389\pi$
$12$	3.99190	1.15236
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.31032	0.617460
$15$	5.18015	1.33751
$16$	−0.956754	−0.239188
$17$	−1.19568	−0.289994	−0.144997	−	0.989432i	$-0.546317\pi$
$17$	−1.19568	−0.289994	−0.144997	+	0.989432i	$0.546317\pi$
$18$	2.78036	0.655337
$19$	5.93474	1.36152	0.680761	−	0.732505i	$-0.261649\pi$
$19$	5.93474	1.36152	0.680761	+	0.732505i	$0.261649\pi$
$20$	11.7631	2.63031
$21$	−1.36842	−0.298614
$22$	8.43798	1.79898
$23$	5.47097	1.14078	0.570388	−	0.821376i	$-0.306793\pi$
$23$	5.47097	1.14078	0.570388	+	0.821376i	$0.306793\pi$
$24$	−2.99993	−0.612357
$25$	10.2646	2.05292
$26$	−2.23848	−0.439002
$27$	−5.62443	−1.08242
$28$	−3.10742	−0.587246
$29$	−8.46985	−1.57281	−0.786406	−	0.617710i	$-0.788060\pi$
$29$	−8.46985	−1.57281	−0.786406	+	0.617710i	$0.788060\pi$
$30$	−11.5957	−2.11707
$31$	−6.03126	−1.08325	−0.541623	−	0.840621i	$-0.682190\pi$
$31$	−6.03126	−1.08325	−0.541623	+	0.840621i	$0.682190\pi$
$32$	6.66690	1.17855
$33$	−4.99788	−0.870019
$34$	2.67650	0.459015
$35$	−4.03239	−0.681598
$36$	−3.73962	−0.623270
$37$	4.09348	0.672964	0.336482	−	0.941690i	$-0.390763\pi$
$37$	4.09348	0.672964	0.336482	+	0.941690i	$0.390763\pi$
$38$	−13.2848	−2.15508
$39$	1.32587	0.212309
$40$	−8.84002	−1.39773
$41$	−5.95287	−0.929682	−0.464841	−	0.885394i	$-0.653889\pi$
$41$	−5.95287	−0.929682	−0.464841	+	0.885394i	$0.653889\pi$
$42$	3.06318	0.472659
$43$	−0.0499133	−0.00761171	−0.00380586	−	0.999993i	$-0.501211\pi$
$43$	−0.0499133	−0.00761171	−0.00380586	+	0.999993i	$0.501211\pi$
$44$	−11.3492	−1.71095
$45$	−4.85278	−0.723410
$46$	−12.2466	−1.80567
$47$	−11.3673	−1.65808	−0.829042	−	0.559186i	$-0.811114\pi$
$47$	−11.3673	−1.65808	−0.829042	+	0.559186i	$0.811114\pi$
$48$	−1.26853	−0.183096
$49$	−5.93478	−0.847825
$50$	−22.9771	−3.24945
$51$	−1.58531	−0.221988
$52$	3.01078	0.417520
$53$	−2.35755	−0.323835	−0.161917	−	0.986804i	$-0.551768\pi$
$53$	−2.35755	−0.323835	−0.161917	+	0.986804i	$0.551768\pi$
$54$	12.5902	1.71330
$55$	−14.7275	−1.98585
$56$	2.33523	0.312059
$57$	7.86868	1.04223
$58$	18.9596	2.48951
$59$	−2.92248	−0.380474	−0.190237	−	0.981738i	$-0.560926\pi$
$59$	−2.92248	−0.380474	−0.190237	+	0.981738i	$0.560926\pi$
$60$	15.5963	2.01348
$61$	11.4918	1.47137	0.735685	−	0.677324i	$-0.236860\pi$
$61$	11.4918	1.47137	0.735685	+	0.677324i	$0.236860\pi$
$62$	13.5008	1.71461
$63$	1.28194	0.161509
$64$	−13.0102	−1.62627
$65$	3.90699	0.484603
$66$	11.1876	1.37710
$67$	2.07218	0.253157	0.126579	−	0.991957i	$-0.459600\pi$
$67$	2.07218	0.253157	0.126579	+	0.991957i	$0.459600\pi$
$68$	−3.59992	−0.436555
$69$	7.25377	0.873252
$70$	9.02642	1.07886
$71$	−15.5903	−1.85023	−0.925113	−	0.379692i	$-0.876030\pi$
$71$	−15.5903	−1.85023	−0.925113	+	0.379692i	$0.876030\pi$
$72$	2.81034	0.331201
$73$	−11.0783	−1.29662	−0.648308	−	0.761378i	$-0.724523\pi$
$73$	−11.0783	−1.29662	−0.648308	+	0.761378i	$0.724523\pi$
$74$	−9.16317	−1.06520
$75$	13.6095	1.57149
$76$	17.8682	2.04962
$77$	3.89050	0.443364
$78$	−2.96792	−0.336051
$79$	−11.3917	−1.28167	−0.640833	−	0.767680i	$-0.721411\pi$
$79$	−11.3917	−1.28167	−0.640833	+	0.767680i	$0.721411\pi$
$80$	−3.73803	−0.417924
$81$	−3.73102	−0.414558
$82$	13.3254	1.47154
$83$	14.0645	1.54378	0.771889	−	0.635757i	$-0.219312\pi$
$83$	14.0645	1.54378	0.771889	+	0.635757i	$0.219312\pi$
$84$	−4.12002	−0.449531
$85$	−4.67150	−0.506695
$86$	0.111730	0.0120481
$87$	−11.2299	−1.20397
$88$	8.52896	0.909190
$89$	−1.14619	−0.121496	−0.0607480	−	0.998153i	$-0.519349\pi$
$89$	−1.14619	−0.121496	−0.0607480	+	0.998153i	$0.519349\pi$
$90$	10.8628	1.14504
$91$	−1.03210	−0.108193
$92$	16.4719	1.71731
$93$	−7.99665	−0.829214
$94$	25.4453	2.62449
$95$	23.1870	2.37893
$96$	8.83943	0.902170
$97$	0.332148	0.0337246	0.0168623	−	0.999858i	$-0.494632\pi$
$97$	0.332148	0.0337246	0.0168623	+	0.999858i	$0.494632\pi$
$98$	13.2849	1.34197
$99$	4.68202	0.470561
$100$	30.9044	3.09044
$101$	3.65611	0.363796	0.181898	−	0.983317i	$-0.441776\pi$
$101$	3.65611	0.363796	0.181898	+	0.983317i	$0.441776\pi$
$102$	3.54868	0.351372
$103$	12.6244	1.24392	0.621959	−	0.783049i	$-0.286337\pi$
$103$	12.6244	1.24392	0.621959	+	0.783049i	$0.286337\pi$
$104$	−2.26261	−0.221868
$105$	−5.34641	−0.521757
$106$	5.27732	0.512579
$107$	6.73786	0.651373	0.325687	−	0.945478i	$-0.394405\pi$
$107$	6.73786	0.651373	0.325687	+	0.945478i	$0.394405\pi$
$108$	−16.9339	−1.62947
$109$	−13.6342	−1.30592	−0.652958	−	0.757394i	$-0.726472\pi$
$109$	−13.6342	−1.30592	−0.652958	+	0.757394i	$0.726472\pi$
$110$	32.9671	3.14329
$111$	5.42741	0.515147
$112$	0.987462	0.0933064
$113$	−11.5464	−1.08619	−0.543096	−	0.839671i	$-0.682748\pi$
$113$	−11.5464	−1.08619	−0.543096	+	0.839671i	$0.682748\pi$
$114$	−17.6139	−1.64969
$115$	21.3750	1.99323
$116$	−25.5009	−2.36770
$117$	−1.24208	−0.114830
$118$	6.54190	0.602231
$119$	1.23405	0.113125
$120$	−11.7207	−1.06995
$121$	3.20925	0.291750
$122$	−25.7241	−2.32895
$123$	−7.89272	−0.711662
$124$	−18.1588	−1.63071
$125$	20.5687	1.83972
$126$	−2.86960	−0.255644
$127$	12.9198	1.14644	0.573222	−	0.819400i	$-0.305693\pi$
$127$	12.9198	1.14644	0.573222	+	0.819400i	$0.305693\pi$
$128$	15.7892	1.39559
$129$	−0.0661785	−0.00582669
$130$	−8.74571	−0.767050
$131$	−13.2359	−1.15643	−0.578214	−	0.815885i	$-0.696250\pi$
$131$	−13.2359	−1.15643	−0.578214	+	0.815885i	$0.696250\pi$
$132$	−15.0475	−1.30972
$133$	−6.12522	−0.531124
$134$	−4.63853	−0.400708
$135$	−21.9746	−1.89127
$136$	2.70536	0.231982
$137$	10.3092	0.880777	0.440389	−	0.897807i	$-0.354841\pi$
$137$	10.3092	0.880777	0.440389	+	0.897807i	$0.354841\pi$
$138$	−16.2374	−1.38222
$139$	−9.66127	−0.819458	−0.409729	−	0.912207i	$-0.634377\pi$
$139$	−9.66127	−0.819458	−0.409729	+	0.912207i	$0.634377\pi$
$140$	−12.1406	−1.02607
$141$	−15.0715	−1.26925
$142$	34.8985	2.92862
$143$	−3.76952	−0.315223
$144$	1.18836	0.0990301
$145$	−33.0916	−2.74811
$146$	24.7985	2.05234
$147$	−7.86873	−0.649002
$148$	12.3246	1.01307
$149$	16.5334	1.35447	0.677235	−	0.735767i	$-0.263178\pi$
$149$	16.5334	1.35447	0.677235	+	0.735767i	$0.263178\pi$
$150$	−30.4645	−2.48742
$151$	−22.1723	−1.80436	−0.902180	−	0.431360i	$-0.858034\pi$
$151$	−22.1723	−1.80436	−0.902180	+	0.431360i	$0.858034\pi$
$152$	−13.4280	−1.08916
$153$	1.48512	0.120065
$154$	−8.70880	−0.701775
$155$	−23.5641	−1.89271
$156$	3.99190	0.319608
$157$	−18.3149	−1.46169	−0.730845	−	0.682543i	$-0.760874\pi$
$157$	−18.3149	−1.46169	−0.730845	+	0.682543i	$0.760874\pi$
$158$	25.5001	2.02868
$159$	−3.12580	−0.247892
$160$	26.0475	2.05924
$161$	−5.64656	−0.445011
$162$	8.35181	0.656180
$163$	7.27759	0.570025	0.285012	−	0.958524i	$-0.408002\pi$
$163$	7.27759	0.570025	0.285012	+	0.958524i	$0.408002\pi$
$164$	−17.9228	−1.39954
$165$	−19.5267	−1.52015
$166$	−31.4830	−2.44356
$167$	3.84224	0.297321	0.148661	−	0.988888i	$-0.452504\pi$
$167$	3.84224	0.297321	0.148661	+	0.988888i	$0.452504\pi$
$168$	3.09621	0.238878
$169$	1.00000	0.0769231
$170$	10.4571	0.802019
$171$	−7.37140	−0.563705
$172$	−0.150278	−0.0114586
$173$	5.35078	0.406812	0.203406	−	0.979094i	$-0.434799\pi$
$173$	5.35078	0.406812	0.203406	+	0.979094i	$0.434799\pi$
$174$	25.1379	1.90570
$175$	−10.5940	−0.800834
$176$	3.60650	0.271850
$177$	−3.87482	−0.291249
$178$	2.56572	0.192309
$179$	−20.2863	−1.51627	−0.758136	−	0.652097i	$-0.773890\pi$
$179$	−20.2863	−1.51627	−0.758136	+	0.652097i	$0.773890\pi$
$180$	−14.6107	−1.08901
$181$	7.59052	0.564199	0.282100	−	0.959385i	$-0.408969\pi$
$181$	7.59052	0.564199	0.282100	+	0.959385i	$0.408969\pi$
$182$	2.31032	0.171253
$183$	15.2366	1.12632
$184$	−12.3787	−0.912569
$185$	15.9932	1.17584
$186$	17.9003	1.31252
$187$	4.50712	0.329593
$188$	−34.2243	−2.49607
$189$	5.80495	0.422248
$190$	−51.9035	−3.76548
$191$	14.5409	1.05214	0.526071	−	0.850441i	$-0.323665\pi$
$191$	14.5409	1.05214	0.526071	+	0.850441i	$0.323665\pi$
$192$	−17.2498	−1.24490
$193$	−20.2721	−1.45922	−0.729608	−	0.683866i	$-0.760297\pi$
$193$	−20.2721	−1.45922	−0.729608	+	0.683866i	$0.760297\pi$
$194$	−0.743507	−0.0533807
$195$	5.18015	0.370959
$196$	−17.8683	−1.27631
$197$	−19.6310	−1.39865	−0.699326	−	0.714803i	$-0.746516\pi$
$197$	−19.6310	−1.39865	−0.699326	+	0.714803i	$0.746516\pi$
$198$	−10.4806	−0.744824
$199$	13.5115	0.957806	0.478903	−	0.877868i	$-0.341035\pi$
$199$	13.5115	0.957806	0.478903	+	0.877868i	$0.341035\pi$
$200$	−23.2248	−1.64224
$201$	2.74744	0.193789
$202$	−8.18412	−0.575832
$203$	8.74169	0.613547
$204$	−4.77302	−0.334178
$205$	−23.2578	−1.62440
$206$	−28.2594	−1.96893
$207$	−6.79535	−0.472310
$208$	−0.956754	−0.0663389
$209$	−22.3711	−1.54744
$210$	11.9678	0.825859
$211$	9.47000	0.651942	0.325971	−	0.945380i	$-0.394309\pi$
$211$	9.47000	0.651942	0.325971	+	0.945380i	$0.394309\pi$
$212$	−7.09807	−0.487498
$213$	−20.6706	−1.41633
$214$	−15.0825	−1.03102
$215$	−0.195011	−0.0132996
$216$	12.7259	0.865889
$217$	6.22484	0.422570
$218$	30.5198	2.06706
$219$	−14.6883	−0.992546
$220$	−44.3412	−2.98948
$221$	−1.19568	−0.0804299
$222$	−12.1491	−0.815397
$223$	21.4757	1.43812	0.719059	−	0.694949i	$-0.244573\pi$
$223$	21.4757	1.43812	0.719059	+	0.694949i	$0.244573\pi$
$224$	−6.88088	−0.459748
$225$	−12.7494	−0.849960
$226$	25.8463	1.71927
$227$	18.2247	1.20962	0.604808	−	0.796371i	$-0.293250\pi$
$227$	18.2247	1.20962	0.604808	+	0.796371i	$0.293250\pi$
$228$	23.6909	1.56897
$229$	−18.8810	−1.24769	−0.623847	−	0.781546i	$-0.714431\pi$
$229$	−18.8810	−1.24769	−0.623847	+	0.781546i	$0.714431\pi$
$230$	−47.8475	−3.15497
$231$	5.15829	0.339390
$232$	19.1640	1.25818
$233$	−13.0345	−0.853920	−0.426960	−	0.904271i	$-0.640415\pi$
$233$	−13.0345	−0.853920	−0.426960	+	0.904271i	$0.640415\pi$
$234$	2.78036	0.181758
$235$	−44.4118	−2.89710
$236$	−8.79895	−0.572763
$237$	−15.1039	−0.981103
$238$	−2.76240	−0.179060
$239$	−26.4703	−1.71222	−0.856110	−	0.516794i	$-0.827125\pi$
$239$	−26.4703	−1.71222	−0.856110	+	0.516794i	$0.827125\pi$
$240$	−4.95613	−0.319917
$241$	20.8309	1.34184	0.670918	−	0.741531i	$-0.265900\pi$
$241$	20.8309	1.34184	0.670918	+	0.741531i	$0.265900\pi$
$242$	−7.18383	−0.461794
$243$	11.9264	0.765082
$244$	34.5992	2.21499
$245$	−23.1871	−1.48137
$246$	17.6677	1.12645
$247$	5.93474	0.377618
$248$	13.6464	0.866548
$249$	18.6476	1.18175
$250$	−46.0426	−2.91199
$251$	3.58261	0.226132	0.113066	−	0.993587i	$-0.463933\pi$
$251$	3.58261	0.226132	0.113066	+	0.993587i	$0.463933\pi$
$252$	3.85965	0.243135
$253$	−20.6229	−1.29655
$254$	−28.9206	−1.81464
$255$	−6.19379	−0.387870
$256$	−9.32347	−0.582717
$257$	−18.8765	−1.17749	−0.588743	−	0.808320i	$-0.700377\pi$
$257$	−18.8765	−1.17749	−0.588743	+	0.808320i	$0.700377\pi$
$258$	0.148139	0.00922273
$259$	−4.22487	−0.262520
$260$	11.7631	0.729517
$261$	10.5202	0.651184
$262$	29.6283	1.83044
$263$	−8.91152	−0.549508	−0.274754	−	0.961515i	$-0.588596\pi$
$263$	−8.91152	−0.549508	−0.274754	+	0.961515i	$0.588596\pi$
$264$	11.3083	0.695976
$265$	−9.21093	−0.565823
$266$	13.7112	0.840686
$267$	−1.51970	−0.0930040
$268$	6.23888	0.381101
$269$	−9.72144	−0.592727	−0.296363	−	0.955075i	$-0.595774\pi$
$269$	−9.72144	−0.592727	−0.296363	+	0.955075i	$0.595774\pi$
$270$	49.1897	2.99359
$271$	24.2752	1.47462	0.737308	−	0.675557i	$-0.236097\pi$
$271$	24.2752	1.47462	0.737308	+	0.675557i	$0.236097\pi$
$272$	1.14397	0.0693633
$273$	−1.36842	−0.0828207
$274$	−23.0770	−1.39413
$275$	−38.6925	−2.33325
$276$	21.8395	1.31459
$277$	−14.4959	−0.870972	−0.435486	−	0.900196i	$-0.643423\pi$
$277$	−14.4959	−0.870972	−0.435486	+	0.900196i	$0.643423\pi$
$278$	21.6265	1.29707
$279$	7.49128	0.448491
$280$	9.12374	0.545248
$281$	12.1992	0.727743	0.363871	−	0.931449i	$-0.381455\pi$
$281$	12.1992	0.727743	0.363871	+	0.931449i	$0.381455\pi$
$282$	33.7372	2.00902
$283$	−23.3560	−1.38837	−0.694186	−	0.719796i	$-0.744235\pi$
$283$	−23.3560	−1.38837	−0.694186	+	0.719796i	$0.744235\pi$
$284$	−46.9390	−2.78531
$285$	30.7429	1.82105
$286$	8.43798	0.498948
$287$	6.14393	0.362665
$288$	−8.28079	−0.487950
$289$	−15.5704	−0.915903
$290$	74.0749	4.34983
$291$	0.440385	0.0258158
$292$	−33.3543	−1.95191
$293$	−1.33650	−0.0780791	−0.0390395	−	0.999238i	$-0.512430\pi$
$293$	−1.33650	−0.0780791	−0.0390395	+	0.999238i	$0.512430\pi$
$294$	17.6140	1.02727
$295$	−11.4181	−0.664788
$296$	−9.26197	−0.538341
$297$	21.2014	1.23023
$298$	−37.0097	−2.14391
$299$	5.47097	0.316394
$300$	40.9752	2.36570
$301$	0.0515153	0.00296929
$302$	49.6323	2.85602
$303$	4.84752	0.278482
$304$	−5.67809	−0.325661
$305$	44.8982	2.57087
$306$	−3.32441	−0.190044
$307$	29.8792	1.70530	0.852648	−	0.522485i	$-0.174995\pi$
$307$	29.8792	1.70530	0.852648	+	0.522485i	$0.174995\pi$
$308$	11.7135	0.667436
$309$	16.7383	0.952207
$310$	52.7477	2.99587
$311$	16.7174	0.947958	0.473979	−	0.880536i	$-0.342817\pi$
$311$	16.7174	0.947958	0.473979	+	0.880536i	$0.342817\pi$
$312$	−2.99993	−0.169837
$313$	−28.2330	−1.59583	−0.797913	−	0.602773i	$-0.794063\pi$
$313$	−28.2330	−1.59583	−0.797913	+	0.602773i	$0.794063\pi$
$314$	40.9976	2.31363
$315$	5.00853	0.282199
$316$	−34.2979	−1.92941
$317$	33.5934	1.88680	0.943398	−	0.331663i	$-0.107610\pi$
$317$	33.5934	1.88680	0.943398	+	0.331663i	$0.107610\pi$
$318$	6.99703	0.392374
$319$	31.9272	1.78758
$320$	−50.8307	−2.84153
$321$	8.93350	0.498620
$322$	12.6397	0.704383
$323$	−7.09603	−0.394834
$324$	−11.2333	−0.624072
$325$	10.2646	0.569377
$326$	−16.2907	−0.902260
$327$	−18.0771	−0.999666
$328$	13.4690	0.743704
$329$	11.7321	0.646811
$330$	43.7100	2.40616
$331$	14.4142	0.792274	0.396137	−	0.918191i	$-0.370351\pi$
$331$	14.4142	0.792274	0.396137	+	0.918191i	$0.370351\pi$
$332$	42.3451	2.32399
$333$	−5.08441	−0.278624
$334$	−8.60076	−0.470613
$335$	8.09599	0.442331
$336$	1.30924	0.0714251
$337$	15.5676	0.848022	0.424011	−	0.905657i	$-0.360622\pi$
$337$	15.5676	0.848022	0.424011	+	0.905657i	$0.360622\pi$
$338$	−2.23848	−0.121757
$339$	−15.3090	−0.831468
$340$	−14.0649	−0.762775
$341$	22.7349	1.23117
$342$	16.5007	0.892256
$343$	13.3499	0.720828
$344$	0.112935	0.00608903
$345$	28.3404	1.52580
$346$	−11.9776	−0.643920
$347$	−29.3825	−1.57733	−0.788666	−	0.614821i	$-0.789228\pi$
$347$	−29.3825	−1.57733	−0.788666	+	0.614821i	$0.789228\pi$
$348$	−33.8108	−1.81245
$349$	−4.65305	−0.249072	−0.124536	−	0.992215i	$-0.539744\pi$
$349$	−4.65305	−0.249072	−0.124536	+	0.992215i	$0.539744\pi$
$350$	23.7145	1.26759
$351$	−5.62443	−0.300210
$352$	−25.1310	−1.33949
$353$	−11.1882	−0.595487	−0.297744	−	0.954646i	$-0.596234\pi$
$353$	−11.1882	−0.595487	−0.297744	+	0.954646i	$0.596234\pi$
$354$	8.67370	0.461002
$355$	−60.9111	−3.23283
$356$	−3.45093	−0.182899
$357$	1.63619	0.0865964
$358$	45.4105	2.40002
$359$	−1.40414	−0.0741078	−0.0370539	−	0.999313i	$-0.511797\pi$
$359$	−1.40414	−0.0741078	−0.0370539	+	0.999313i	$0.511797\pi$
$360$	10.9800	0.578695
$361$	16.2211	0.853744
$362$	−16.9912	−0.893039
$363$	4.25504	0.223331
$364$	−3.10742	−0.162873
$365$	−43.2828	−2.26552
$366$	−34.1067	−1.78279
$367$	12.8753	0.672087	0.336043	−	0.941847i	$-0.390911\pi$
$367$	12.8753	0.672087	0.336043	+	0.941847i	$0.390911\pi$
$368$	−5.23437	−0.272860
$369$	7.39391	0.384912
$370$	−35.8004	−1.86118
$371$	2.43322	0.126326
$372$	−24.0762	−1.24829
$373$	0.326143	0.0168871	0.00844353	−	0.999964i	$-0.497312\pi$
$373$	0.326143	0.0168871	0.00844353	+	0.999964i	$0.497312\pi$
$374$	−10.0891	−0.521695
$375$	27.2714	1.40829
$376$	25.7197	1.32639
$377$	−8.46985	−0.436219
$378$	−12.9943	−0.668352
$379$	−36.6353	−1.88183	−0.940915	−	0.338643i	$-0.890032\pi$
$379$	−36.6353	−1.88183	−0.940915	+	0.338643i	$0.890032\pi$
$380$	69.8110	3.58123
$381$	17.1299	0.877592
$382$	−32.5494	−1.66537
$383$	15.3572	0.784717	0.392358	−	0.919812i	$-0.371659\pi$
$383$	15.3572	0.784717	0.392358	+	0.919812i	$0.371659\pi$
$384$	20.9344	1.06831
$385$	15.2002	0.774672
$386$	45.3786	2.30971
$387$	0.0619961	0.00315144
$388$	1.00003	0.0507687
$389$	−12.3326	−0.625289	−0.312645	−	0.949870i	$-0.601215\pi$
$389$	−12.3326	−0.625289	−0.312645	+	0.949870i	$0.601215\pi$
$390$	−11.5957	−0.587169
$391$	−6.54151	−0.330818
$392$	13.4281	0.678222
$393$	−17.5491	−0.885234
$394$	43.9436	2.21385
$395$	−44.5073	−2.23940
$396$	14.0966	0.708378
$397$	13.4070	0.672878	0.336439	−	0.941705i	$-0.390777\pi$
$397$	13.4070	0.672878	0.336439	+	0.941705i	$0.390777\pi$
$398$	−30.2452	−1.51606
$399$	−8.12123	−0.406570
$400$	−9.82068	−0.491034
$401$	5.26038	0.262691	0.131345	−	0.991337i	$-0.458070\pi$
$401$	5.26038	0.262691	0.131345	+	0.991337i	$0.458070\pi$
$402$	−6.15008	−0.306738
$403$	−6.03126	−0.300439
$404$	11.0077	0.547656
$405$	−14.5771	−0.724340
$406$	−19.5681	−0.971148
$407$	−15.4304	−0.764859
$408$	3.58694	0.177580
$409$	−10.7035	−0.529253	−0.264627	−	0.964351i	$-0.585249\pi$
$409$	−10.7035	−0.529253	−0.264627	+	0.964351i	$0.585249\pi$
$410$	52.0621	2.57116
$411$	13.6687	0.674226
$412$	38.0093	1.87258
$413$	3.01628	0.148421
$414$	15.2112	0.747592
$415$	54.9498	2.69738
$416$	6.66690	0.326872
$417$	−12.8096	−0.627287
$418$	50.0772	2.44936
$419$	4.24356	0.207311	0.103656	−	0.994613i	$-0.466946\pi$
$419$	4.24356	0.207311	0.103656	+	0.994613i	$0.466946\pi$
$420$	−16.0969	−0.785448
$421$	17.0084	0.828937	0.414469	−	0.910064i	$-0.363967\pi$
$421$	17.0084	0.828937	0.414469	+	0.910064i	$0.363967\pi$
$422$	−21.1984	−1.03192
$423$	14.1190	0.686489
$424$	5.33423	0.259053
$425$	−12.2731	−0.595334
$426$	46.2708	2.24183
$427$	−11.8606	−0.573975
$428$	20.2862	0.980571
$429$	−4.99788	−0.241300
$430$	0.436528	0.0210512
$431$	−27.9992	−1.34867	−0.674336	−	0.738425i	$-0.735570\pi$
$431$	−27.9992	−1.34867	−0.674336	+	0.738425i	$0.735570\pi$
$432$	5.38120	0.258903
$433$	−22.4619	−1.07945	−0.539726	−	0.841841i	$-0.681472\pi$
$433$	−22.4619	−1.07945	−0.539726	+	0.841841i	$0.681472\pi$
$434$	−13.9342	−0.668861
$435$	−43.8751	−2.10365
$436$	−41.0495	−1.96592
$437$	32.4688	1.55319
$438$	32.8795	1.57104
$439$	−34.0975	−1.62738	−0.813692	−	0.581296i	$-0.802546\pi$
$439$	−34.0975	−1.62738	−0.813692	+	0.581296i	$0.802546\pi$
$440$	33.3226	1.58859
$441$	7.37144	0.351021
$442$	2.67650	0.127308
$443$	−25.9131	−1.23117	−0.615584	−	0.788071i	$-0.711080\pi$
$443$	−25.9131	−1.23117	−0.615584	+	0.788071i	$0.711080\pi$
$444$	16.3408	0.775498
$445$	−4.47816	−0.212285
$446$	−48.0728	−2.27632
$447$	21.9211	1.03683
$448$	13.4278	0.634403
$449$	11.2111	0.529087	0.264543	−	0.964374i	$-0.414779\pi$
$449$	11.2111	0.529087	0.264543	+	0.964374i	$0.414779\pi$
$450$	28.5392	1.34535
$451$	22.4394	1.05663
$452$	−34.7636	−1.63514
$453$	−29.3976	−1.38122
$454$	−40.7956	−1.91463
$455$	−4.03239	−0.189041
$456$	−17.8038	−0.833738
$457$	24.0944	1.12709	0.563545	−	0.826086i	$-0.309437\pi$
$457$	24.0944	1.12709	0.563545	+	0.826086i	$0.309437\pi$
$458$	42.2648	1.97490
$459$	6.72500	0.313896
$460$	64.3555	3.00059
$461$	−26.7250	−1.24471	−0.622353	−	0.782737i	$-0.713823\pi$
$461$	−26.7250	−1.24471	−0.622353	+	0.782737i	$0.713823\pi$
$462$	−11.5467	−0.537202
$463$	−17.9898	−0.836059	−0.418029	−	0.908434i	$-0.637279\pi$
$463$	−17.9898	−0.836059	−0.418029	+	0.908434i	$0.637279\pi$
$464$	8.10356	0.376198
$465$	−31.2429	−1.44885
$466$	29.1775	1.35162
$467$	−11.3932	−0.527214	−0.263607	−	0.964630i	$-0.584912\pi$
$467$	−11.3932	−0.527214	−0.263607	+	0.964630i	$0.584912\pi$
$468$	−3.73962	−0.172864
$469$	−2.13869	−0.0987555
$470$	99.4148	4.58566
$471$	−24.2832	−1.11891
$472$	6.61244	0.304362
$473$	0.188149	0.00865110
$474$	33.8097	1.55293
$475$	60.9177	2.79509
$476$	3.71547	0.170298
$477$	2.92826	0.134076
$478$	59.2531	2.71017
$479$	2.37177	0.108369	0.0541844	−	0.998531i	$-0.482744\pi$
$479$	2.37177	0.108369	0.0541844	+	0.998531i	$0.482744\pi$
$480$	34.5356	1.57633
$481$	4.09348	0.186647
$482$	−46.6295	−2.12392
$483$	−7.48659	−0.340652
$484$	9.66234	0.439197
$485$	1.29770	0.0589256
$486$	−26.6971	−1.21100
$487$	3.72897	0.168976	0.0844879	−	0.996425i	$-0.473075\pi$
$487$	3.72897	0.168976	0.0844879	+	0.996425i	$0.473075\pi$
$488$	−26.0014	−1.17703
$489$	9.64912	0.436348
$490$	51.9039	2.34478
$491$	−15.0464	−0.679032	−0.339516	−	0.940600i	$-0.610263\pi$
$491$	−15.0464	−0.679032	−0.339516	+	0.940600i	$0.610263\pi$
$492$	−23.7632	−1.07133
$493$	10.1272	0.456106
$494$	−13.2848	−0.597711
$495$	18.2926	0.822192
$496$	5.77043	0.259100
$497$	16.0907	0.721765
$498$	−41.7423	−1.87052
$499$	−4.53998	−0.203237	−0.101619	−	0.994823i	$-0.532402\pi$
$499$	−4.53998	−0.203237	−0.101619	+	0.994823i	$0.532402\pi$
$500$	61.9279	2.76950
$501$	5.09430	0.227596
$502$	−8.01958	−0.357932
$503$	3.13257	0.139675	0.0698373	−	0.997558i	$-0.477752\pi$
$503$	3.13257	0.139675	0.0698373	+	0.997558i	$0.477752\pi$
$504$	−2.90054	−0.129200
$505$	14.2844	0.635647
$506$	46.1639	2.05223
$507$	1.32587	0.0588838
$508$	38.8986	1.72585
$509$	4.02397	0.178359	0.0891796	−	0.996016i	$-0.471575\pi$
$509$	4.02397	0.178359	0.0891796	+	0.996016i	$0.471575\pi$
$510$	13.8647	0.613938
$511$	11.4339	0.505804
$512$	−10.7081	−0.473236
$513$	−33.3795	−1.47374
$514$	42.2547	1.86377
$515$	49.3234	2.17345
$516$	−0.199249	−0.00877145
$517$	42.8490	1.88450
$518$	9.45727	0.415528
$519$	7.09442	0.311411
$520$	−8.84002	−0.387660
$521$	−28.8083	−1.26212	−0.631058	−	0.775736i	$-0.717379\pi$
$521$	−28.8083	−1.26212	−0.631058	+	0.775736i	$0.717379\pi$
$522$	−23.5492	−1.03072
$523$	28.2127	1.23366	0.616828	−	0.787098i	$-0.288417\pi$
$523$	28.2127	1.23366	0.616828	+	0.787098i	$0.288417\pi$
$524$	−39.8505	−1.74088
$525$	−14.0463	−0.613030
$526$	19.9482	0.869784
$527$	7.21144	0.314135
$528$	4.78174	0.208098
$529$	6.93146	0.301368
$530$	20.6185	0.895609
$531$	3.62994	0.157526
$532$	−18.4417	−0.799549
$533$	−5.95287	−0.257847
$534$	3.40181	0.147211
$535$	26.3247	1.13812
$536$	−4.68854	−0.202514
$537$	−26.8970	−1.16069
$538$	21.7612	0.938193
$539$	22.3712	0.963597
$540$	−66.1607	−2.84711
$541$	10.6367	0.457306	0.228653	−	0.973508i	$-0.426568\pi$
$541$	10.6367	0.457306	0.228653	+	0.973508i	$0.426568\pi$
$542$	−54.3396	−2.33408
$543$	10.0640	0.431889
$544$	−7.97146	−0.341774
$545$	−53.2686	−2.28178
$546$	3.06318	0.131092
$547$	1.20662	0.0515912	0.0257956	−	0.999667i	$-0.491788\pi$
$547$	1.20662	0.0515912	0.0257956	+	0.999667i	$0.491788\pi$
$548$	31.0389	1.32591
$549$	−14.2736	−0.609184
$550$	86.6123	3.69316
$551$	−50.2663	−2.14142
$552$	−16.4125	−0.698562
$553$	11.7573	0.499972
$554$	32.4487	1.37861
$555$	21.2049	0.900096
$556$	−29.0880	−1.23360
$557$	−10.0578	−0.426161	−0.213080	−	0.977035i	$-0.568350\pi$
$557$	−10.0578	−0.426161	−0.213080	+	0.977035i	$0.568350\pi$
$558$	−16.7691	−0.709891
$559$	−0.0499133	−0.00211111
$560$	3.85800	0.163030
$561$	5.97585	0.252300
$562$	−27.3076	−1.15190
$563$	29.9102	1.26056	0.630282	−	0.776366i	$-0.282939\pi$
$563$	29.9102	1.26056	0.630282	+	0.776366i	$0.282939\pi$
$564$	−45.3769	−1.91071
$565$	−45.1116	−1.89786
$566$	52.2819	2.19757
$567$	3.85077	0.161717
$568$	35.2748	1.48010
$569$	26.7110	1.11978	0.559892	−	0.828566i	$-0.310843\pi$
$569$	26.7110	1.11978	0.559892	+	0.828566i	$0.310843\pi$
$570$	−68.8172	−2.88244
$571$	2.79583	0.117002	0.0585009	−	0.998287i	$-0.481368\pi$
$571$	2.79583	0.117002	0.0585009	+	0.998287i	$0.481368\pi$
$572$	−11.3492	−0.474534
$573$	19.2793	0.805403
$574$	−13.7531	−0.574041
$575$	56.1572	2.34192
$576$	16.1597	0.673319
$577$	−18.2546	−0.759948	−0.379974	−	0.924997i	$-0.624067\pi$
$577$	−18.2546	−0.759948	−0.379974	+	0.924997i	$0.624067\pi$
$578$	34.8539	1.44973
$579$	−26.8781	−1.11701
$580$	−99.6317	−4.13698
$581$	−14.5159	−0.602221
$582$	−0.985791	−0.0408624
$583$	8.88682	0.368055
$584$	25.0659	1.03723
$585$	−4.85278	−0.200638
$586$	2.99172	0.123587
$587$	7.62208	0.314597	0.157298	−	0.987551i	$-0.449722\pi$
$587$	7.62208	0.314597	0.157298	+	0.987551i	$0.449722\pi$
$588$	−23.6910	−0.977002
$589$	−35.7940	−1.47486
$590$	25.5592	1.05225
$591$	−26.0281	−1.07065
$592$	−3.91645	−0.160965
$593$	14.7775	0.606841	0.303421	−	0.952857i	$-0.401871\pi$
$593$	14.7775	0.606841	0.303421	+	0.952857i	$0.401871\pi$
$594$	−47.4588	−1.94726
$595$	4.82144	0.197660
$596$	49.7785	2.03901
$597$	17.9145	0.733191
$598$	−12.2466	−0.500802
$599$	−7.58443	−0.309891	−0.154946	−	0.987923i	$-0.549520\pi$
$599$	−7.58443	−0.309891	−0.154946	+	0.987923i	$0.549520\pi$
$600$	−30.7930	−1.25712
$601$	9.09656	0.371056	0.185528	−	0.982639i	$-0.440600\pi$
$601$	9.09656	0.371056	0.185528	+	0.982639i	$0.440600\pi$
$602$	−0.115316	−0.00469993
$603$	−2.57380	−0.104813
$604$	−66.7561	−2.71627
$605$	12.5385	0.509763
$606$	−10.8511	−0.440794
$607$	29.2873	1.18873	0.594367	−	0.804194i	$-0.297403\pi$
$607$	29.2873	1.18873	0.594367	+	0.804194i	$0.297403\pi$
$608$	39.5663	1.60463
$609$	11.5903	0.469664
$610$	−100.504	−4.06928
$611$	−11.3673	−0.459870
$612$	4.47138	0.180745
$613$	8.42301	0.340202	0.170101	−	0.985427i	$-0.445591\pi$
$613$	8.42301	0.340202	0.170101	+	0.985427i	$0.445591\pi$
$614$	−66.8840	−2.69922
$615$	−30.8368	−1.24346
$616$	−8.80270	−0.354671
$617$	−6.87233	−0.276670	−0.138335	−	0.990386i	$-0.544175\pi$
$617$	−6.87233	−0.276670	−0.138335	+	0.990386i	$0.544175\pi$
$618$	−37.4683	−1.50719
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	−70.9464	−2.84927
$621$	−30.7711	−1.23480
$622$	−37.4216	−1.50047
$623$	1.18298	0.0473951
$624$	−1.26853	−0.0507818
$625$	29.0388	1.16155
$626$	63.1990	2.52594
$627$	−29.6611	−1.18455
$628$	−55.1423	−2.20042
$629$	−4.89448	−0.195156
$630$	−11.2115	−0.446676
$631$	−49.0171	−1.95134	−0.975671	−	0.219241i	$-0.929642\pi$
$631$	−49.0171	−1.95134	−0.975671	+	0.219241i	$0.929642\pi$
$632$	25.7750	1.02528
$633$	12.5560	0.499055
$634$	−75.1982	−2.98650
$635$	50.4775	2.00314
$636$	−9.41110	−0.373175
$637$	−5.93478	−0.235144
$638$	−71.4684	−2.82946
$639$	19.3643	0.766040
$640$	61.6884	2.43845
$641$	6.97605	0.275537	0.137769	−	0.990464i	$-0.456007\pi$
$641$	6.97605	0.275537	0.137769	+	0.990464i	$0.456007\pi$
$642$	−19.9974	−0.789236
$643$	12.3210	0.485893	0.242947	−	0.970040i	$-0.421886\pi$
$643$	12.3210	0.485893	0.242947	+	0.970040i	$0.421886\pi$
$644$	−17.0006	−0.669916
$645$	−0.258559	−0.0101807
$646$	15.8843	0.624960
$647$	−4.35098	−0.171055	−0.0855273	−	0.996336i	$-0.527257\pi$
$647$	−4.35098	−0.171055	−0.0855273	+	0.996336i	$0.527257\pi$
$648$	8.44186	0.331628
$649$	11.0163	0.432429
$650$	−22.9771	−0.901234
$651$	8.25331	0.323473
$652$	21.9112	0.858111
$653$	−48.6301	−1.90304	−0.951521	−	0.307583i	$-0.900480\pi$
$653$	−48.6301	−1.90304	−0.951521	+	0.307583i	$0.900480\pi$
$654$	40.4652	1.58231
$655$	−51.7127	−2.02058
$656$	5.69543	0.222369
$657$	13.7601	0.536832
$658$	−26.2620	−1.02380
$659$	−31.2362	−1.21679	−0.608394	−	0.793635i	$-0.708186\pi$
$659$	−31.2362	−1.21679	−0.608394	+	0.793635i	$0.708186\pi$
$660$	−58.7906	−2.28842
$661$	−26.7161	−1.03914	−0.519568	−	0.854429i	$-0.673907\pi$
$661$	−26.7161	−1.03914	−0.519568	+	0.854429i	$0.673907\pi$
$662$	−32.2658	−1.25405
$663$	−1.58531	−0.0615683
$664$	−31.8225	−1.23495
$665$	−23.9312	−0.928012
$666$	11.3813	0.441018
$667$	−46.3382	−1.79422
$668$	11.5681	0.447585
$669$	28.4739	1.10087
$670$	−18.1227	−0.700141
$671$	−43.3184	−1.67229
$672$	−9.12313	−0.351933
$673$	39.8203	1.53496	0.767480	−	0.641073i	$-0.221510\pi$
$673$	39.8203	1.53496	0.767480	+	0.641073i	$0.221510\pi$
$674$	−34.8478	−1.34229
$675$	−57.7325	−2.22212
$676$	3.01078	0.115799
$677$	32.4723	1.24801	0.624006	−	0.781420i	$-0.285504\pi$
$677$	32.4723	1.24801	0.624006	+	0.781420i	$0.285504\pi$
$678$	34.2688	1.31608
$679$	−0.342809	−0.0131558
$680$	10.5698	0.405333
$681$	24.1635	0.925949
$682$	−50.8916	−1.94874
$683$	−41.2303	−1.57764	−0.788818	−	0.614627i	$-0.789306\pi$
$683$	−41.2303	−1.57764	−0.788818	+	0.614627i	$0.789306\pi$
$684$	−22.1937	−0.848596
$685$	40.2781	1.53895
$686$	−29.8835	−1.14096
$687$	−25.0338	−0.955098
$688$	0.0477548	0.00182063
$689$	−2.35755	−0.0898155
$690$	−63.4394	−2.41510
$691$	43.8536	1.66827	0.834135	−	0.551560i	$-0.185967\pi$
$691$	43.8536	1.66827	0.834135	+	0.551560i	$0.185967\pi$
$692$	16.1100	0.612411
$693$	−4.83230	−0.183564
$694$	65.7720	2.49667
$695$	−37.7465	−1.43181
$696$	25.4089	0.963123
$697$	7.11771	0.269602
$698$	10.4157	0.394242
$699$	−17.2820	−0.653667
$700$	−31.8963	−1.20557
$701$	−0.400398	−0.0151228	−0.00756141	−	0.999971i	$-0.502407\pi$
$701$	−0.400398	−0.0151228	−0.00756141	+	0.999971i	$0.502407\pi$
$702$	12.5902	0.475185
$703$	24.2938	0.916256
$704$	49.0421	1.84835
$705$	−58.8841	−2.21770
$706$	25.0445	0.942563
$707$	−3.77345	−0.141915
$708$	−11.6662	−0.438444
$709$	23.4093	0.879154	0.439577	−	0.898205i	$-0.355128\pi$
$709$	23.4093	0.879154	0.439577	+	0.898205i	$0.355128\pi$
$710$	136.348	5.11706
$711$	14.1494	0.530642
$712$	2.59339	0.0971914
$713$	−32.9968	−1.23574
$714$	−3.66258	−0.137068
$715$	−14.7275	−0.550776
$716$	−61.0777	−2.28258
$717$	−35.0961	−1.31069
$718$	3.14314	0.117301
$719$	7.12733	0.265805	0.132902	−	0.991129i	$-0.457570\pi$
$719$	7.12733	0.265805	0.132902	+	0.991129i	$0.457570\pi$
$720$	4.64292	0.173031
$721$	−13.0296	−0.485247
$722$	−36.3107	−1.35134
$723$	27.6190	1.02716
$724$	22.8534	0.849340
$725$	−86.9395	−3.22885
$726$	−9.52480	−0.353499
$727$	38.7900	1.43864	0.719321	−	0.694677i	$-0.244453\pi$
$727$	38.7900	1.43864	0.719321	+	0.694677i	$0.244453\pi$
$728$	2.33523	0.0865495
$729$	27.0060	1.00022
$730$	96.8875	3.58597
$731$	0.0596802	0.00220735
$732$	45.8740	1.69555
$733$	33.5070	1.23761	0.618805	−	0.785544i	$-0.287617\pi$
$733$	33.5070	1.23761	0.618805	+	0.785544i	$0.287617\pi$
$734$	−28.8211	−1.06381
$735$	−30.7431	−1.13397
$736$	36.4744	1.34446
$737$	−7.81112	−0.287726
$738$	−16.5511	−0.609255
$739$	21.6782	0.797444	0.398722	−	0.917072i	$-0.369454\pi$
$739$	21.6782	0.797444	0.398722	+	0.917072i	$0.369454\pi$
$740$	48.1521	1.77010
$741$	7.86868	0.289063
$742$	−5.44670	−0.199955
$743$	52.1191	1.91206	0.956032	−	0.293263i	$-0.0947411\pi$
$743$	52.1191	1.91206	0.956032	+	0.293263i	$0.0947411\pi$
$744$	18.0933	0.663334
$745$	64.5959	2.36661
$746$	−0.730065	−0.0267296
$747$	−17.4692	−0.639163
$748$	13.5700	0.496167
$749$	−6.95411	−0.254098
$750$	−61.0464	−2.22910
$751$	−51.4811	−1.87857	−0.939285	−	0.343137i	$-0.888510\pi$
$751$	−51.4811	−1.87857	−0.939285	+	0.343137i	$0.888510\pi$
$752$	10.8757	0.396595
$753$	4.75006	0.173102
$754$	18.9596	0.690467
$755$	−86.6272	−3.15269
$756$	17.4774	0.635648
$757$	−36.3738	−1.32203	−0.661014	−	0.750374i	$-0.729874\pi$
$757$	−36.3738	−1.32203	−0.661014	+	0.750374i	$0.729874\pi$
$758$	82.0073	2.97864
$759$	−27.3432	−0.992496
$760$	−52.4632	−1.90304
$761$	50.0496	1.81430	0.907149	−	0.420810i	$-0.138254\pi$
$761$	50.0496	1.81430	0.907149	+	0.420810i	$0.138254\pi$
$762$	−38.3449	−1.38909
$763$	14.0718	0.509432
$764$	43.7794	1.58388
$765$	5.80236	0.209785
$766$	−34.3768	−1.24208
$767$	−2.92248	−0.105525
$768$	−12.3617	−0.446064
$769$	7.18707	0.259172	0.129586	−	0.991568i	$-0.458635\pi$
$769$	7.18707	0.259172	0.129586	+	0.991568i	$0.458635\pi$
$770$	−34.0252	−1.22618
$771$	−25.0278	−0.901353
$772$	−61.0348	−2.19669
$773$	−40.9826	−1.47404	−0.737021	−	0.675869i	$-0.763768\pi$
$773$	−40.9826	−1.47404	−0.737021	+	0.675869i	$0.763768\pi$
$774$	−0.138777	−0.00498824
$775$	−61.9084	−2.22382
$776$	−0.751524	−0.0269781
$777$	−5.60161	−0.200957
$778$	27.6063	0.989734
$779$	−35.3287	−1.26578
$780$	15.5963	0.558438
$781$	58.7678	2.10288
$782$	14.6430	0.523633
$783$	47.6381	1.70245
$784$	5.67812	0.202790
$785$	−71.5563	−2.55395
$786$	39.2832	1.40119
$787$	17.1646	0.611850	0.305925	−	0.952056i	$-0.401034\pi$
$787$	17.1646	0.611850	0.305925	+	0.952056i	$0.401034\pi$
$788$	−59.1047	−2.10552
$789$	−11.8155	−0.420643
$790$	99.6286	3.54463
$791$	11.9170	0.423718
$792$	−10.5936	−0.376428
$793$	11.4918	0.408085
$794$	−30.0113	−1.06506
$795$	−12.2125	−0.433132
$796$	40.6802	1.44187
$797$	5.73226	0.203047	0.101524	−	0.994833i	$-0.467628\pi$
$797$	5.73226	0.203047	0.101524	+	0.994833i	$0.467628\pi$
$798$	18.1792	0.643536
$799$	13.5916	0.480835
$800$	68.4330	2.41947
$801$	1.42366	0.0503024
$802$	−11.7752	−0.415798
$803$	41.7598	1.47367
$804$	8.27193	0.291729
$805$	−22.0611	−0.777550
$806$	13.5008	0.475547
$807$	−12.8893	−0.453726
$808$	−8.27236	−0.291021
$809$	11.0768	0.389438	0.194719	−	0.980859i	$-0.437621\pi$
$809$	11.0768	0.389438	0.194719	+	0.980859i	$0.437621\pi$
$810$	32.6304	1.14652
$811$	38.1818	1.34074	0.670372	−	0.742025i	$-0.266135\pi$
$811$	38.1818	1.34074	0.670372	+	0.742025i	$0.266135\pi$
$812$	26.3193	0.923628
$813$	32.1857	1.12880
$814$	34.5407	1.21065
$815$	28.4335	0.995982
$816$	1.51675	0.0530969
$817$	−0.296223	−0.0103635
$818$	23.9595	0.837725
$819$	1.28194	0.0447946
$820$	−70.0242	−2.44535
$821$	22.3533	0.780136	0.390068	−	0.920786i	$-0.372451\pi$
$821$	22.3533	0.780136	0.390068	+	0.920786i	$0.372451\pi$
$822$	−30.5970	−1.06719
$823$	−29.5354	−1.02954	−0.514770	−	0.857328i	$-0.672123\pi$
$823$	−29.5354	−1.02954	−0.514770	+	0.857328i	$0.672123\pi$
$824$	−28.5641	−0.995079
$825$	−51.3012	−1.78608
$826$	−6.75187	−0.234928
$827$	−42.0989	−1.46392	−0.731961	−	0.681347i	$-0.761395\pi$
$827$	−42.0989	−1.46392	−0.731961	+	0.681347i	$0.761395\pi$
$828$	−20.4593	−0.711011
$829$	−49.5363	−1.72047	−0.860234	−	0.509899i	$-0.829683\pi$
$829$	−49.5363	−1.72047	−0.860234	+	0.509899i	$0.829683\pi$
$830$	−123.004	−4.26953
$831$	−19.2196	−0.666720
$832$	−13.0102	−0.451048
$833$	7.09608	0.245865
$834$	28.6739	0.992896
$835$	15.0116	0.519498
$836$	−67.3545	−2.32950
$837$	33.9224	1.17253
$838$	−9.49910	−0.328141
$839$	−21.5369	−0.743538	−0.371769	−	0.928325i	$-0.621249\pi$
$839$	−21.5369	−0.743538	−0.371769	+	0.928325i	$0.621249\pi$
$840$	12.0969	0.417382
$841$	42.7383	1.47374
$842$	−38.0729	−1.31208
$843$	16.1745	0.557080
$844$	28.5121	0.981427
$845$	3.90699	0.134405
$846$	−31.6050	−1.08660
$847$	−3.31225	−0.113810
$848$	2.25560	0.0774575
$849$	−30.9670	−1.06278
$850$	27.4731	0.942321
$851$	22.3953	0.767701
$852$	−62.2348	−2.13213
$853$	−45.9227	−1.57236	−0.786182	−	0.617995i	$-0.787945\pi$
$853$	−45.9227	−1.57236	−0.786182	+	0.617995i	$0.787945\pi$
$854$	26.5497	0.908512
$855$	−28.8000	−0.984939
$856$	−15.2452	−0.521069
$857$	−43.5480	−1.48757	−0.743786	−	0.668417i	$-0.766972\pi$
$857$	−43.5480	−1.48757	−0.743786	+	0.668417i	$0.766972\pi$
$858$	11.1876	0.381940
$859$	−37.8011	−1.28976	−0.644878	−	0.764286i	$-0.723092\pi$
$859$	−37.8011	−1.28976	−0.644878	+	0.764286i	$0.723092\pi$
$860$	−0.587136	−0.0200212
$861$	8.14604	0.277616
$862$	62.6755	2.13474
$863$	−2.80812	−0.0955896	−0.0477948	−	0.998857i	$-0.515219\pi$
$863$	−2.80812	−0.0955896	−0.0477948	+	0.998857i	$0.515219\pi$
$864$	−37.4975	−1.27569
$865$	20.9054	0.710806
$866$	50.2805	1.70860
$867$	−20.6442	−0.701115
$868$	18.7416	0.636133
$869$	42.9412	1.45668
$870$	98.2135	3.32975
$871$	2.07218	0.0702132
$872$	30.8489	1.04467
$873$	−0.412553	−0.0139628
$874$	−72.6806	−2.45846
$875$	−21.2289	−0.717667
$876$	−44.2234	−1.49417
$877$	−0.199904	−0.00675028	−0.00337514	−	0.999994i	$-0.501074\pi$
$877$	−0.199904	−0.00675028	−0.00337514	+	0.999994i	$0.501074\pi$
$878$	76.3265	2.57589
$879$	−1.77202	−0.0597687
$880$	14.0906	0.474993
$881$	−31.5566	−1.06317	−0.531584	−	0.847006i	$-0.678403\pi$
$881$	−31.5566	−1.06317	−0.531584	+	0.847006i	$0.678403\pi$
$882$	−16.5008	−0.555611
$883$	44.5139	1.49801	0.749005	−	0.662564i	$-0.230532\pi$
$883$	44.5139	1.49801	0.749005	+	0.662564i	$0.230532\pi$
$884$	−3.59992	−0.121079
$885$	−15.1389	−0.508888
$886$	58.0059	1.94875
$887$	18.6140	0.624998	0.312499	−	0.949918i	$-0.398834\pi$
$887$	18.6140	0.624998	0.312499	+	0.949918i	$0.398834\pi$
$888$	−12.2801	−0.412095
$889$	−13.3344	−0.447223
$890$	10.0243	0.336014
$891$	14.0641	0.471166
$892$	64.6586	2.16493
$893$	−67.4617	−2.25752
$894$	−49.0699	−1.64114
$895$	−79.2585	−2.64932
$896$	−16.2960	−0.544411
$897$	7.25377	0.242196
$898$	−25.0959	−0.837461
$899$	51.0839	1.70374
$900$	−38.3857	−1.27952
$901$	2.81887	0.0939102
$902$	−50.2302	−1.67248
$903$	0.0683025	0.00227297
$904$	26.1250	0.868904
$905$	29.6561	0.985803
$906$	65.8058	2.18625
$907$	38.1532	1.26686	0.633428	−	0.773801i	$-0.281647\pi$
$907$	38.1532	1.26686	0.633428	+	0.773801i	$0.281647\pi$
$908$	54.8706	1.82094
$909$	−4.54116	−0.150621
$910$	9.02642	0.299223
$911$	−13.3450	−0.442139	−0.221069	−	0.975258i	$-0.570955\pi$
$911$	−13.3450	−0.442139	−0.221069	+	0.975258i	$0.570955\pi$
$912$	−7.52839	−0.249290
$913$	−53.0163	−1.75458
$914$	−53.9348	−1.78401
$915$	59.5291	1.96797
$916$	−56.8467	−1.87827
$917$	13.6607	0.451117
$918$	−15.0538	−0.496848
$919$	−0.672650	−0.0221887	−0.0110943	−	0.999938i	$-0.503532\pi$
$919$	−0.672650	−0.0221887	−0.0110943	+	0.999938i	$0.503532\pi$
$920$	−48.3634	−1.59449
$921$	39.6159	1.30539
$922$	59.8233	1.97017
$923$	−15.5903	−0.513160
$924$	15.5305	0.510915
$925$	42.0179	1.38154
$926$	40.2698	1.32335
$927$	−15.6805	−0.515014
$928$	−56.4676	−1.85364
$929$	−39.7353	−1.30367	−0.651837	−	0.758359i	$-0.726001\pi$
$929$	−39.7353	−1.30367	−0.651837	+	0.758359i	$0.726001\pi$
$930$	69.9365	2.29331
$931$	−35.2214	−1.15433
$932$	−39.2441	−1.28548
$933$	22.1651	0.725653
$934$	25.5034	0.834497
$935$	17.6093	0.575886
$936$	2.81034	0.0918588
$937$	−7.21086	−0.235569	−0.117784	−	0.993039i	$-0.537579\pi$
$937$	−7.21086	−0.235569	−0.117784	+	0.993039i	$0.537579\pi$
$938$	4.78741	0.156314
$939$	−37.4333	−1.22159
$940$	−133.714	−4.36128
$941$	−1.52336	−0.0496600	−0.0248300	−	0.999692i	$-0.507904\pi$
$941$	−1.52336	−0.0496600	−0.0248300	+	0.999692i	$0.507904\pi$
$942$	54.3573	1.77106
$943$	−32.5679	−1.06056
$944$	2.79609	0.0910051
$945$	22.6799	0.737777
$946$	−0.421168	−0.0136933
$947$	−4.31072	−0.140080	−0.0700398	−	0.997544i	$-0.522313\pi$
$947$	−4.31072	−0.140080	−0.0700398	+	0.997544i	$0.522313\pi$
$948$	−45.4745	−1.47694
$949$	−11.0783	−0.359616
$950$	−136.363	−4.42419
$951$	44.5404	1.44432
$952$	−2.79219	−0.0904953
$953$	−4.38181	−0.141941	−0.0709704	−	0.997478i	$-0.522610\pi$
$953$	−4.38181	−0.141941	−0.0709704	+	0.997478i	$0.522610\pi$
$954$	−6.55484	−0.212221
$955$	56.8111	1.83836
$956$	−79.6962	−2.57756
$957$	42.3313	1.36838
$958$	−5.30915	−0.171531
$959$	−10.6401	−0.343587
$960$	−67.3948	−2.17516
$961$	5.37612	0.173423
$962$	−9.16317	−0.295432
$963$	−8.36893	−0.269685
$964$	62.7173	2.01999
$965$	−79.2028	−2.54963
$966$	16.7586	0.539198
$967$	19.2219	0.618134	0.309067	−	0.951040i	$-0.399983\pi$
$967$	19.2219	0.618134	0.309067	+	0.951040i	$0.399983\pi$
$968$	−7.26129	−0.233387
$969$	−9.40840	−0.302241
$970$	−2.90488	−0.0932699
$971$	−7.62570	−0.244720	−0.122360	−	0.992486i	$-0.539046\pi$
$971$	−7.62570	−0.244720	−0.122360	+	0.992486i	$0.539046\pi$
$972$	35.9079	1.15175
$973$	9.97135	0.319667
$974$	−8.34722	−0.267462
$975$	13.6095	0.435852
$976$	−10.9948	−0.351935
$977$	13.5509	0.433533	0.216766	−	0.976223i	$-0.430449\pi$
$977$	13.5509	0.433533	0.216766	+	0.976223i	$0.430449\pi$
$978$	−21.5993	−0.690671
$979$	4.32059	0.138087
$980$	−69.8114	−2.23004
$981$	16.9347	0.540683
$982$	33.6809	1.07480
$983$	−62.3913	−1.98997	−0.994986	−	0.100013i	$-0.968112\pi$
$983$	−62.3913	−1.98997	−0.994986	+	0.100013i	$0.968112\pi$
$984$	17.8582	0.569298
$985$	−76.6982	−2.44381
$986$	−22.6695	−0.721945
$987$	15.5552	0.495128
$988$	17.8682	0.568464
$989$	−0.273074	−0.00868325
$990$	−40.9476	−1.30140
$991$	−1.75024	−0.0555983	−0.0277991	−	0.999614i	$-0.508850\pi$
$991$	−1.75024	−0.0555983	−0.0277991	+	0.999614i	$0.508850\pi$
$992$	−40.2098	−1.27666
$993$	19.1113	0.606478
$994$	−36.0186	−1.14244
$995$	52.7894	1.67354
$996$	56.1440	1.77899
$997$	38.5253	1.22011	0.610054	−	0.792359i	$-0.291148\pi$
$997$	38.5253	1.22011	0.610054	+	0.792359i	$0.291148\pi$
$998$	10.1626	0.321693
$999$	−23.0235	−0.728431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.b.1.18	✓	142

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.b.1.18	✓	142	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23848 q^{2} +1.32587 q^{3} +3.01078 q^{4} +3.90699 q^{5} -2.96792 q^{6} -1.03210 q^{7} -2.26261 q^{8} -1.24208 q^{9} +O(q^{10})\)	\(q-2.23848 q^{2} +1.32587 q^{3} +3.01078 q^{4} +3.90699 q^{5} -2.96792 q^{6} -1.03210 q^{7} -2.26261 q^{8} -1.24208 q^{9} -8.74571 q^{10} -3.76952 q^{11} +3.99190 q^{12} +1.00000 q^{13} +2.31032 q^{14} +5.18015 q^{15} -0.956754 q^{16} -1.19568 q^{17} +2.78036 q^{18} +5.93474 q^{19} +11.7631 q^{20} -1.36842 q^{21} +8.43798 q^{22} +5.47097 q^{23} -2.99993 q^{24} +10.2646 q^{25} -2.23848 q^{26} -5.62443 q^{27} -3.10742 q^{28} -8.46985 q^{29} -11.5957 q^{30} -6.03126 q^{31} +6.66690 q^{32} -4.99788 q^{33} +2.67650 q^{34} -4.03239 q^{35} -3.73962 q^{36} +4.09348 q^{37} -13.2848 q^{38} +1.32587 q^{39} -8.84002 q^{40} -5.95287 q^{41} +3.06318 q^{42} -0.0499133 q^{43} -11.3492 q^{44} -4.85278 q^{45} -12.2466 q^{46} -11.3673 q^{47} -1.26853 q^{48} -5.93478 q^{49} -22.9771 q^{50} -1.58531 q^{51} +3.01078 q^{52} -2.35755 q^{53} +12.5902 q^{54} -14.7275 q^{55} +2.33523 q^{56} +7.86868 q^{57} +18.9596 q^{58} -2.92248 q^{59} +15.5963 q^{60} +11.4918 q^{61} +13.5008 q^{62} +1.28194 q^{63} -13.0102 q^{64} +3.90699 q^{65} +11.1876 q^{66} +2.07218 q^{67} -3.59992 q^{68} +7.25377 q^{69} +9.02642 q^{70} -15.5903 q^{71} +2.81034 q^{72} -11.0783 q^{73} -9.16317 q^{74} +13.6095 q^{75} +17.8682 q^{76} +3.89050 q^{77} -2.96792 q^{78} -11.3917 q^{79} -3.73803 q^{80} -3.73102 q^{81} +13.3254 q^{82} +14.0645 q^{83} -4.12002 q^{84} -4.67150 q^{85} +0.111730 q^{86} -11.2299 q^{87} +8.52896 q^{88} -1.14619 q^{89} +10.8628 q^{90} -1.03210 q^{91} +16.4719 q^{92} -7.99665 q^{93} +25.4453 q^{94} +23.1870 q^{95} +8.83943 q^{96} +0.332148 q^{97} +13.2849 q^{98} +4.68202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 142 q - 13 q^{2} - 26 q^{3} + 129 q^{4} - 37 q^{5} - 15 q^{6} - 14 q^{7} - 39 q^{8} + 98 q^{9}+O(q^{10}) \) 142 * q - 13 * q^2 - 26 * q^3 + 129 * q^4 - 37 * q^5 - 15 * q^6 - 14 * q^7 - 39 * q^8 + 98 * q^9	\( 142 q - 13 q^{2} - 26 q^{3} + 129 q^{4} - 37 q^{5} - 15 q^{6} - 14 q^{7} - 39 q^{8} + 98 q^{9} - 25 q^{10} - 25 q^{11} - 62 q^{12} + 142 q^{13} - 57 q^{14} - 14 q^{15} + 111 q^{16} - 141 q^{17} - 29 q^{18} - 3 q^{19} - 87 q^{20} - 19 q^{21} - 24 q^{22} - 69 q^{23} - 40 q^{24} + 87 q^{25} - 13 q^{26} - 95 q^{27} - 34 q^{28} - 147 q^{29} - 2 q^{30} - 21 q^{31} - 66 q^{32} - 62 q^{33} - 6 q^{34} - 59 q^{35} + 74 q^{36} - 37 q^{37} - 76 q^{38} - 26 q^{39} - 61 q^{40} - 97 q^{41} - 29 q^{42} - 33 q^{43} - 57 q^{44} - 86 q^{45} - q^{46} - 102 q^{47} - 141 q^{48} + 70 q^{49} - 28 q^{50} - 13 q^{51} + 129 q^{52} - 137 q^{53} - 29 q^{54} - 24 q^{55} - 130 q^{56} - 65 q^{57} - 15 q^{58} - 56 q^{59} + 11 q^{60} - 77 q^{61} - 150 q^{62} - 32 q^{63} + 73 q^{64} - 37 q^{65} - 32 q^{66} - 9 q^{67} - 226 q^{68} - 113 q^{69} + 6 q^{70} - 18 q^{71} - 82 q^{72} - 117 q^{73} - 70 q^{74} - 83 q^{75} + 40 q^{76} - 214 q^{77} - 15 q^{78} - 52 q^{79} - 161 q^{80} - 10 q^{81} - 36 q^{82} - 74 q^{83} + 53 q^{84} + 2 q^{85} + 17 q^{86} - 49 q^{87} - 29 q^{88} - 171 q^{89} - 57 q^{90} - 14 q^{91} - 187 q^{92} - 39 q^{93} + 13 q^{94} - 150 q^{95} - 47 q^{96} - 126 q^{97} - 85 q^{98}+O(q^{100}) \) 142 * q - 13 * q^2 - 26 * q^3 + 129 * q^4 - 37 * q^5 - 15 * q^6 - 14 * q^7 - 39 * q^8 + 98 * q^9 - 25 * q^10 - 25 * q^11 - 62 * q^12 + 142 * q^13 - 57 * q^14 - 14 * q^15 + 111 * q^16 - 141 * q^17 - 29 * q^18 - 3 * q^19 - 87 * q^20 - 19 * q^21 - 24 * q^22 - 69 * q^23 - 40 * q^24 + 87 * q^25 - 13 * q^26 - 95 * q^27 - 34 * q^28 - 147 * q^29 - 2 * q^30 - 21 * q^31 - 66 * q^32 - 62 * q^33 - 6 * q^34 - 59 * q^35 + 74 * q^36 - 37 * q^37 - 76 * q^38 - 26 * q^39 - 61 * q^40 - 97 * q^41 - 29 * q^42 - 33 * q^43 - 57 * q^44 - 86 * q^45 - q^46 - 102 * q^47 - 141 * q^48 + 70 * q^49 - 28 * q^50 - 13 * q^51 + 129 * q^52 - 137 * q^53 - 29 * q^54 - 24 * q^55 - 130 * q^56 - 65 * q^57 - 15 * q^58 - 56 * q^59 + 11 * q^60 - 77 * q^61 - 150 * q^62 - 32 * q^63 + 73 * q^64 - 37 * q^65 - 32 * q^66 - 9 * q^67 - 226 * q^68 - 113 * q^69 + 6 * q^70 - 18 * q^71 - 82 * q^72 - 117 * q^73 - 70 * q^74 - 83 * q^75 + 40 * q^76 - 214 * q^77 - 15 * q^78 - 52 * q^79 - 161 * q^80 - 10 * q^81 - 36 * q^82 - 74 * q^83 + 53 * q^84 + 2 * q^85 + 17 * q^86 - 49 * q^87 - 29 * q^88 - 171 * q^89 - 57 * q^90 - 14 * q^91 - 187 * q^92 - 39 * q^93 + 13 * q^94 - 150 * q^95 - 47 * q^96 - 126 * q^97 - 85 * q^98

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