LMFDB - Embedded newform 8003.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74848 q^{2} +0.238468 q^{3} +5.55414 q^{4} -0.412520 q^{5} -0.655426 q^{6} -2.19155 q^{7} -9.76848 q^{8} -2.94313 q^{9} +O(q^{10})$	\(q-2.74848 q^{2} +0.238468 q^{3} +5.55414 q^{4} -0.412520 q^{5} -0.655426 q^{6} -2.19155 q^{7} -9.76848 q^{8} -2.94313 q^{9} +1.13380 q^{10} -2.64065 q^{11} +1.32449 q^{12} +3.93402 q^{13} +6.02344 q^{14} -0.0983731 q^{15} +15.7402 q^{16} -5.33110 q^{17} +8.08914 q^{18} -1.03684 q^{19} -2.29119 q^{20} -0.522616 q^{21} +7.25777 q^{22} +1.82853 q^{23} -2.32947 q^{24} -4.82983 q^{25} -10.8126 q^{26} -1.41725 q^{27} -12.1722 q^{28} +0.842287 q^{29} +0.270376 q^{30} +1.06010 q^{31} -23.7246 q^{32} -0.629712 q^{33} +14.6524 q^{34} +0.904060 q^{35} -16.3466 q^{36} +8.32535 q^{37} +2.84974 q^{38} +0.938141 q^{39} +4.02969 q^{40} -3.45194 q^{41} +1.43640 q^{42} +7.74054 q^{43} -14.6665 q^{44} +1.21410 q^{45} -5.02567 q^{46} -12.4113 q^{47} +3.75354 q^{48} -2.19710 q^{49} +13.2747 q^{50} -1.27130 q^{51} +21.8501 q^{52} -1.00000 q^{53} +3.89528 q^{54} +1.08932 q^{55} +21.4081 q^{56} -0.247255 q^{57} -2.31501 q^{58} -1.21403 q^{59} -0.546378 q^{60} -5.39749 q^{61} -2.91367 q^{62} +6.45003 q^{63} +33.7263 q^{64} -1.62286 q^{65} +1.73075 q^{66} +14.2947 q^{67} -29.6097 q^{68} +0.436046 q^{69} -2.48479 q^{70} +1.48424 q^{71} +28.7499 q^{72} -16.8540 q^{73} -22.8821 q^{74} -1.15176 q^{75} -5.75878 q^{76} +5.78712 q^{77} -2.57846 q^{78} -1.41339 q^{79} -6.49314 q^{80} +8.49143 q^{81} +9.48758 q^{82} -12.6163 q^{83} -2.90268 q^{84} +2.19919 q^{85} -21.2747 q^{86} +0.200859 q^{87} +25.7951 q^{88} -4.55754 q^{89} -3.33693 q^{90} -8.62162 q^{91} +10.1559 q^{92} +0.252801 q^{93} +34.1122 q^{94} +0.427719 q^{95} -5.65757 q^{96} -3.08528 q^{97} +6.03867 q^{98} +7.77178 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) $ 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * 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 $

$2$	−2.74848	−1.94347	−0.971734	−	0.236077i	$-0.924138\pi$
$2$	−2.74848	−1.94347	−0.971734	+	0.236077i	$0.924138\pi$
$3$	0.238468	0.137680	0.0688399	−	0.997628i	$-0.478070\pi$
$3$	0.238468	0.137680	0.0688399	+	0.997628i	$0.478070\pi$
$4$	5.55414	2.77707
$5$	−0.412520	−0.184485	−0.0922423	−	0.995737i	$-0.529403\pi$
$5$	−0.412520	−0.184485	−0.0922423	+	0.995737i	$0.529403\pi$
$6$	−0.655426	−0.267576
$7$	−2.19155	−0.828329	−0.414165	−	0.910202i	$-0.635926\pi$
$7$	−2.19155	−0.828329	−0.414165	+	0.910202i	$0.635926\pi$
$8$	−9.76848	−3.45368
$9$	−2.94313	−0.981044
$10$	1.13380	0.358540
$11$	−2.64065	−0.796186	−0.398093	−	0.917345i	$-0.630328\pi$
$11$	−2.64065	−0.796186	−0.398093	+	0.917345i	$0.630328\pi$
$12$	1.32449	0.382346
$13$	3.93402	1.09110	0.545551	−	0.838078i	$-0.316320\pi$
$13$	3.93402	1.09110	0.545551	+	0.838078i	$0.316320\pi$
$14$	6.02344	1.60983
$15$	−0.0983731	−0.0253998
$16$	15.7402	3.93505
$17$	−5.33110	−1.29298	−0.646491	−	0.762921i	$-0.723764\pi$
$17$	−5.33110	−1.29298	−0.646491	+	0.762921i	$0.723764\pi$
$18$	8.08914	1.90663
$19$	−1.03684	−0.237868	−0.118934	−	0.992902i	$-0.537948\pi$
$19$	−1.03684	−0.237868	−0.118934	+	0.992902i	$0.537948\pi$
$20$	−2.29119	−0.512327
$21$	−0.522616	−0.114044
$22$	7.25777	1.54736
$23$	1.82853	0.381274	0.190637	−	0.981661i	$-0.438945\pi$
$23$	1.82853	0.381274	0.190637	+	0.981661i	$0.438945\pi$
$24$	−2.32947	−0.475502
$25$	−4.82983	−0.965965
$26$	−10.8126	−2.12052
$27$	−1.41725	−0.272750
$28$	−12.1722	−2.30033
$29$	0.842287	0.156409	0.0782044	−	0.996937i	$-0.475081\pi$
$29$	0.842287	0.156409	0.0782044	+	0.996937i	$0.475081\pi$
$30$	0.270376	0.0493637
$31$	1.06010	0.190400	0.0952000	−	0.995458i	$-0.469651\pi$
$31$	1.06010	0.190400	0.0952000	+	0.995458i	$0.469651\pi$
$32$	−23.7246	−4.19396
$33$	−0.629712	−0.109619
$34$	14.6524	2.51287
$35$	0.904060	0.152814
$36$	−16.3466	−2.72443
$37$	8.32535	1.36868	0.684340	−	0.729164i	$-0.260091\pi$
$37$	8.32535	1.36868	0.684340	+	0.729164i	$0.260091\pi$
$38$	2.84974	0.462290
$39$	0.938141	0.150223
$40$	4.02969	0.637151
$41$	−3.45194	−0.539102	−0.269551	−	0.962986i	$-0.586875\pi$
$41$	−3.45194	−0.539102	−0.269551	+	0.962986i	$0.586875\pi$
$42$	1.43640	0.221641
$43$	7.74054	1.18042	0.590211	−	0.807249i	$-0.299045\pi$
$43$	7.74054	1.18042	0.590211	+	0.807249i	$0.299045\pi$
$44$	−14.6665	−2.21106
$45$	1.21410	0.180988
$46$	−5.02567	−0.740995
$47$	−12.4113	−1.81037	−0.905186	−	0.425015i	$-0.860269\pi$
$47$	−12.4113	−1.81037	−0.905186	+	0.425015i	$0.860269\pi$
$48$	3.75354	0.541777
$49$	−2.19710	−0.313871
$50$	13.2747	1.87732
$51$	−1.27130	−0.178018
$52$	21.8501	3.03007
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	3.89528	0.530081
$55$	1.08932	0.146884
$56$	21.4081	2.86078
$57$	−0.247255	−0.0327497
$58$	−2.31501	−0.303975
$59$	−1.21403	−0.158053	−0.0790263	−	0.996873i	$-0.525181\pi$
$59$	−1.21403	−0.158053	−0.0790263	+	0.996873i	$0.525181\pi$
$60$	−0.546378	−0.0705371
$61$	−5.39749	−0.691078	−0.345539	−	0.938404i	$-0.612304\pi$
$61$	−5.39749	−0.691078	−0.345539	+	0.938404i	$0.612304\pi$
$62$	−2.91367	−0.370037
$63$	6.45003	0.812627
$64$	33.7263	4.21578
$65$	−1.62286	−0.201292
$66$	1.73075	0.213041
$67$	14.2947	1.74638	0.873188	−	0.487383i	$-0.162049\pi$
$67$	14.2947	1.74638	0.873188	+	0.487383i	$0.162049\pi$
$68$	−29.6097	−3.59070
$69$	0.436046	0.0524938
$70$	−2.48479	−0.296989
$71$	1.48424	0.176147	0.0880734	−	0.996114i	$-0.471929\pi$
$71$	1.48424	0.176147	0.0880734	+	0.996114i	$0.471929\pi$
$72$	28.7499	3.38821
$73$	−16.8540	−1.97261	−0.986304	−	0.164938i	$-0.947257\pi$
$73$	−16.8540	−1.97261	−0.986304	+	0.164938i	$0.947257\pi$
$74$	−22.8821	−2.65998
$75$	−1.15176	−0.132994
$76$	−5.75878	−0.660577
$77$	5.78712	0.659504
$78$	−2.57846	−0.291953
$79$	−1.41339	−0.159019	−0.0795093	−	0.996834i	$-0.525335\pi$
$79$	−1.41339	−0.159019	−0.0795093	+	0.996834i	$0.525335\pi$
$80$	−6.49314	−0.725956
$81$	8.49143	0.943492
$82$	9.48758	1.04773
$83$	−12.6163	−1.38482	−0.692410	−	0.721504i	$-0.743451\pi$
$83$	−12.6163	−1.38482	−0.692410	+	0.721504i	$0.743451\pi$
$84$	−2.90268	−0.316709
$85$	2.19919	0.238535
$86$	−21.2747	−2.29411
$87$	0.200859	0.0215343
$88$	25.7951	2.74977
$89$	−4.55754	−0.483099	−0.241549	−	0.970389i	$-0.577656\pi$
$89$	−4.55754	−0.483099	−0.241549	+	0.970389i	$0.577656\pi$
$90$	−3.33693	−0.351744
$91$	−8.62162	−0.903791
$92$	10.1559	1.05883
$93$	0.252801	0.0262143
$94$	34.1122	3.51840
$95$	0.427719	0.0438831
$96$	−5.65757	−0.577424
$97$	−3.08528	−0.313263	−0.156631	−	0.987657i	$-0.550063\pi$
$97$	−3.08528	−0.313263	−0.156631	+	0.987657i	$0.550063\pi$
$98$	6.03867	0.609998
$99$	7.77178	0.781094
$100$	−26.8255	−2.68255
$101$	5.33388	0.530741	0.265371	−	0.964146i	$-0.414506\pi$
$101$	5.33388	0.530741	0.265371	+	0.964146i	$0.414506\pi$
$102$	3.49414	0.345972
$103$	−17.0550	−1.68048	−0.840240	−	0.542214i	$-0.817586\pi$
$103$	−17.0550	−1.68048	−0.840240	+	0.542214i	$0.817586\pi$
$104$	−38.4294	−3.76832
$105$	0.215590	0.0210394
$106$	2.74848	0.266956
$107$	−3.80411	−0.367757	−0.183879	−	0.982949i	$-0.558865\pi$
$107$	−3.80411	−0.367757	−0.183879	+	0.982949i	$0.558865\pi$
$108$	−7.87160	−0.757445
$109$	−10.4944	−1.00518	−0.502592	−	0.864523i	$-0.667620\pi$
$109$	−10.4944	−1.00518	−0.502592	+	0.864523i	$0.667620\pi$
$110$	−2.99398	−0.285465
$111$	1.98533	0.188440
$112$	−34.4954	−3.25951
$113$	−8.16366	−0.767973	−0.383986	−	0.923339i	$-0.625449\pi$
$113$	−8.16366	−0.767973	−0.383986	+	0.923339i	$0.625449\pi$
$114$	0.679574	0.0636480
$115$	−0.754305	−0.0703393
$116$	4.67818	0.434358
$117$	−11.5784	−1.07042
$118$	3.33672	0.307170
$119$	11.6834	1.07101
$120$	0.960955	0.0877228
$121$	−4.02697	−0.366088
$122$	14.8349	1.34309
$123$	−0.823178	−0.0742235
$124$	5.88796	0.528754
$125$	4.05500	0.362690
$126$	−17.7278	−1.57932
$127$	−20.4811	−1.81741	−0.908703	−	0.417443i	$-0.862926\pi$
$127$	−20.4811	−1.81741	−0.908703	+	0.417443i	$0.862926\pi$
$128$	−45.2467	−3.99928
$129$	1.84587	0.162520
$130$	4.46041	0.391204
$131$	−9.85467	−0.861007	−0.430503	−	0.902589i	$-0.641664\pi$
$131$	−9.85467	−0.861007	−0.430503	+	0.902589i	$0.641664\pi$
$132$	−3.49751	−0.304419
$133$	2.27230	0.197033
$134$	−39.2887	−3.39403
$135$	0.584644	0.0503182
$136$	52.0768	4.46555
$137$	14.5623	1.24414	0.622069	−	0.782962i	$-0.286292\pi$
$137$	14.5623	1.24414	0.622069	+	0.782962i	$0.286292\pi$
$138$	−1.19846	−0.102020
$139$	−12.1199	−1.02800	−0.513999	−	0.857791i	$-0.671837\pi$
$139$	−12.1199	−1.02800	−0.513999	+	0.857791i	$0.671837\pi$
$140$	5.02127	0.424375
$141$	−2.95970	−0.249252
$142$	−4.07940	−0.342336
$143$	−10.3884	−0.868720
$144$	−46.3255	−3.86045
$145$	−0.347460	−0.0288550
$146$	46.3228	3.83370
$147$	−0.523938	−0.0432137
$148$	46.2402	3.80092
$149$	−20.8172	−1.70541	−0.852707	−	0.522389i	$-0.825041\pi$
$149$	−20.8172	−1.70541	−0.852707	+	0.522389i	$0.825041\pi$
$150$	3.16559	0.258470
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	10.1284	0.821521
$153$	15.6901	1.26847
$154$	−15.9058	−1.28173
$155$	−0.437314	−0.0351259
$156$	5.21056	0.417179
$157$	−0.0650482	−0.00519141	−0.00259571	−	0.999997i	$-0.500826\pi$
$157$	−0.0650482	−0.00519141	−0.00259571	+	0.999997i	$0.500826\pi$
$158$	3.88467	0.309047
$159$	−0.238468	−0.0189118
$160$	9.78688	0.773721
$161$	−4.00732	−0.315821
$162$	−23.3385	−1.83365
$163$	21.2262	1.66257	0.831283	−	0.555850i	$-0.187607\pi$
$163$	21.2262	1.66257	0.831283	+	0.555850i	$0.187607\pi$
$164$	−19.1725	−1.49712
$165$	0.259769	0.0202230
$166$	34.6757	2.69135
$167$	21.9854	1.70128	0.850639	−	0.525750i	$-0.176215\pi$
$167$	21.9854	1.70128	0.850639	+	0.525750i	$0.176215\pi$
$168$	5.10517	0.393872
$169$	2.47654	0.190503
$170$	−6.04442	−0.463586
$171$	3.05157	0.233359
$172$	42.9920	3.27811
$173$	−2.58642	−0.196642	−0.0983208	−	0.995155i	$-0.531347\pi$
$173$	−2.58642	−0.196642	−0.0983208	+	0.995155i	$0.531347\pi$
$174$	−0.552056	−0.0418513
$175$	10.5848	0.800137
$176$	−41.5643	−3.13303
$177$	−0.289507	−0.0217607
$178$	12.5263	0.938887
$179$	5.69131	0.425388	0.212694	−	0.977119i	$-0.431776\pi$
$179$	5.69131	0.425388	0.212694	+	0.977119i	$0.431776\pi$
$180$	6.74329	0.502615
$181$	−1.47326	−0.109507	−0.0547534	−	0.998500i	$-0.517437\pi$
$181$	−1.47326	−0.109507	−0.0547534	+	0.998500i	$0.517437\pi$
$182$	23.6963	1.75649
$183$	−1.28713	−0.0951475
$184$	−17.8619	−1.31680
$185$	−3.43437	−0.252500
$186$	−0.694819	−0.0509466
$187$	14.0776	1.02945
$188$	−68.9340	−5.02753
$189$	3.10598	0.225927
$190$	−1.17558	−0.0852853
$191$	−12.8033	−0.926414	−0.463207	−	0.886250i	$-0.653301\pi$
$191$	−12.8033	−0.926414	−0.463207	+	0.886250i	$0.653301\pi$
$192$	8.04265	0.580428
$193$	−21.2051	−1.52637	−0.763187	−	0.646177i	$-0.776367\pi$
$193$	−21.2051	−1.52637	−0.763187	+	0.646177i	$0.776367\pi$
$194$	8.47982	0.608816
$195$	−0.387002	−0.0277138
$196$	−12.2030	−0.871641
$197$	25.0498	1.78473	0.892363	−	0.451317i	$-0.149046\pi$
$197$	25.0498	1.78473	0.892363	+	0.451317i	$0.149046\pi$
$198$	−21.3606	−1.51803
$199$	−5.99756	−0.425156	−0.212578	−	0.977144i	$-0.568186\pi$
$199$	−5.99756	−0.425156	−0.212578	+	0.977144i	$0.568186\pi$
$200$	47.1801	3.33613
$201$	3.40884	0.240441
$202$	−14.6601	−1.03148
$203$	−1.84592	−0.129558
$204$	−7.06098	−0.494367
$205$	1.42399	0.0994560
$206$	46.8754	3.26596
$207$	−5.38160	−0.374047
$208$	61.9223	4.29354
$209$	2.73794	0.189387
$210$	−0.592544	−0.0408894
$211$	−0.935467	−0.0644002	−0.0322001	−	0.999481i	$-0.510251\pi$
$211$	−0.935467	−0.0644002	−0.0322001	+	0.999481i	$0.510251\pi$
$212$	−5.55414	−0.381460
$213$	0.353944	0.0242519
$214$	10.4555	0.714724
$215$	−3.19313	−0.217770
$216$	13.8444	0.941990
$217$	−2.32327	−0.157714
$218$	28.8437	1.95355
$219$	−4.01914	−0.271588
$220$	6.05024	0.407907
$221$	−20.9727	−1.41078
$222$	−5.45665	−0.366226
$223$	28.1042	1.88200	0.940999	−	0.338409i	$-0.109889\pi$
$223$	28.1042	1.88200	0.940999	+	0.338409i	$0.109889\pi$
$224$	51.9938	3.47398
$225$	14.2148	0.947655
$226$	22.4377	1.49253
$227$	−11.0889	−0.735994	−0.367997	−	0.929827i	$-0.619956\pi$
$227$	−11.0889	−0.735994	−0.367997	+	0.929827i	$0.619956\pi$
$228$	−1.37329	−0.0909481
$229$	−5.30945	−0.350858	−0.175429	−	0.984492i	$-0.556131\pi$
$229$	−5.30945	−0.350858	−0.175429	+	0.984492i	$0.556131\pi$
$230$	2.07319	0.136702
$231$	1.38005	0.0908004
$232$	−8.22786	−0.540186
$233$	15.8837	1.04057	0.520287	−	0.853992i	$-0.325825\pi$
$233$	15.8837	1.04057	0.520287	+	0.853992i	$0.325825\pi$
$234$	31.8229	2.08033
$235$	5.11991	0.333986
$236$	−6.74287	−0.438923
$237$	−0.337048	−0.0218936
$238$	−32.1116	−2.08148
$239$	20.7308	1.34096	0.670481	−	0.741926i	$-0.266088\pi$
$239$	20.7308	1.34096	0.670481	+	0.741926i	$0.266088\pi$
$240$	−1.54841	−0.0999494
$241$	24.9321	1.60602	0.803009	−	0.595967i	$-0.203231\pi$
$241$	24.9321	1.60602	0.803009	+	0.595967i	$0.203231\pi$
$242$	11.0680	0.711480
$243$	6.27669	0.402650
$244$	−29.9784	−1.91917
$245$	0.906347	0.0579044
$246$	2.26249	0.144251
$247$	−4.07897	−0.259539
$248$	−10.3556	−0.657581
$249$	−3.00859	−0.190662
$250$	−11.1451	−0.704877
$251$	−7.61604	−0.480720	−0.240360	−	0.970684i	$-0.577266\pi$
$251$	−7.61604	−0.480720	−0.240360	+	0.970684i	$0.577266\pi$
$252$	35.8244	2.25672
$253$	−4.82850	−0.303565
$254$	56.2920	3.53207
$255$	0.524437	0.0328415
$256$	56.9071	3.55669
$257$	23.2174	1.44826	0.724132	−	0.689661i	$-0.242241\pi$
$257$	23.2174	1.44826	0.724132	+	0.689661i	$0.242241\pi$
$258$	−5.07335	−0.315853
$259$	−18.2454	−1.13372
$260$	−9.01361	−0.559001
$261$	−2.47896	−0.153444
$262$	27.0854	1.67334
$263$	−8.81371	−0.543477	−0.271738	−	0.962371i	$-0.587599\pi$
$263$	−8.81371	−0.543477	−0.271738	+	0.962371i	$0.587599\pi$
$264$	6.15133	0.378588
$265$	0.412520	0.0253409
$266$	−6.24537	−0.382928
$267$	−1.08683	−0.0665130
$268$	79.3948	4.84981
$269$	−2.88827	−0.176101	−0.0880505	−	0.996116i	$-0.528064\pi$
$269$	−2.88827	−0.176101	−0.0880505	+	0.996116i	$0.528064\pi$
$270$	−1.60688	−0.0977918
$271$	29.3948	1.78561	0.892804	−	0.450445i	$-0.148735\pi$
$271$	29.3948	1.78561	0.892804	+	0.450445i	$0.148735\pi$
$272$	−83.9126	−5.08795
$273$	−2.05598	−0.124434
$274$	−40.0241	−2.41794
$275$	12.7539	0.769088
$276$	2.42186	0.145779
$277$	27.5132	1.65311	0.826555	−	0.562855i	$-0.190297\pi$
$277$	27.5132	1.65311	0.826555	+	0.562855i	$0.190297\pi$
$278$	33.3114	1.99788
$279$	−3.12002	−0.186791
$280$	−8.83129	−0.527770
$281$	15.4491	0.921619	0.460809	−	0.887499i	$-0.347559\pi$
$281$	15.4491	0.921619	0.460809	+	0.887499i	$0.347559\pi$
$282$	8.13468	0.484413
$283$	27.9123	1.65921	0.829606	−	0.558349i	$-0.188565\pi$
$283$	27.9123	1.65921	0.829606	+	0.558349i	$0.188565\pi$
$284$	8.24367	0.489172
$285$	0.101998	0.00604181
$286$	28.5523	1.68833
$287$	7.56510	0.446554
$288$	69.8247	4.11446
$289$	11.4207	0.671804
$290$	0.954988	0.0560788
$291$	−0.735742	−0.0431299
$292$	−93.6093	−5.47807
$293$	−30.2037	−1.76452	−0.882261	−	0.470761i	$-0.843979\pi$
$293$	−30.2037	−1.76452	−0.882261	+	0.470761i	$0.843979\pi$
$294$	1.44003	0.0839845
$295$	0.500810	0.0291583
$296$	−81.3260	−4.72698
$297$	3.74246	0.217160
$298$	57.2158	3.31442
$299$	7.19347	0.416009
$300$	−6.39704	−0.369333
$301$	−16.9638	−0.977777
$302$	−2.74848	−0.158157
$303$	1.27196	0.0730724
$304$	−16.3201	−0.936023
$305$	2.22657	0.127493
$306$	−43.1240	−2.46524
$307$	−20.6567	−1.17894	−0.589471	−	0.807790i	$-0.700664\pi$
$307$	−20.6567	−1.17894	−0.589471	+	0.807790i	$0.700664\pi$
$308$	32.1425	1.83149
$309$	−4.06708	−0.231368
$310$	1.20195	0.0682661
$311$	22.7889	1.29224	0.646121	−	0.763235i	$-0.276390\pi$
$311$	22.7889	1.29224	0.646121	+	0.763235i	$0.276390\pi$
$312$	−9.16421	−0.518821
$313$	16.7220	0.945185	0.472593	−	0.881281i	$-0.343318\pi$
$313$	16.7220	0.945185	0.472593	+	0.881281i	$0.343318\pi$
$314$	0.178784	0.0100894
$315$	−2.66077	−0.149917
$316$	−7.85015	−0.441605
$317$	−1.93173	−0.108497	−0.0542484	−	0.998527i	$-0.517276\pi$
$317$	−1.93173	−0.108497	−0.0542484	+	0.998527i	$0.517276\pi$
$318$	0.655426	0.0367544
$319$	−2.22419	−0.124530
$320$	−13.9128	−0.777747
$321$	−0.907160	−0.0506327
$322$	11.0140	0.613788
$323$	5.52752	0.307560
$324$	47.1626	2.62014
$325$	−19.0007	−1.05397
$326$	−58.3398	−3.23114
$327$	−2.50259	−0.138394
$328$	33.7202	1.86188
$329$	27.2000	1.49958
$330$	−0.713969	−0.0393027
$331$	−15.4924	−0.851541	−0.425770	−	0.904831i	$-0.639997\pi$
$331$	−15.4924	−0.851541	−0.425770	+	0.904831i	$0.639997\pi$
$332$	−70.0727	−3.84574
$333$	−24.5026	−1.34273
$334$	−60.4263	−3.30638
$335$	−5.89685	−0.322180
$336$	−8.22608	−0.448769
$337$	26.2758	1.43133	0.715666	−	0.698442i	$-0.246123\pi$
$337$	26.2758	1.43133	0.715666	+	0.698442i	$0.246123\pi$
$338$	−6.80673	−0.370237
$339$	−1.94678	−0.105734
$340$	12.2146	0.662429
$341$	−2.79936	−0.151594
$342$	−8.38718	−0.453527
$343$	20.1559	1.08832
$344$	−75.6133	−4.07680
$345$	−0.179878	−0.00968430
$346$	7.10872	0.382167
$347$	−34.6702	−1.86120	−0.930598	−	0.366042i	$-0.880713\pi$
$347$	−34.6702	−1.86120	−0.930598	+	0.366042i	$0.880713\pi$
$348$	1.11560	0.0598023
$349$	10.6823	0.571808	0.285904	−	0.958258i	$-0.407706\pi$
$349$	10.6823	0.571808	0.285904	+	0.958258i	$0.407706\pi$
$350$	−29.0922	−1.55504
$351$	−5.57549	−0.297598
$352$	62.6484	3.33917
$353$	19.5956	1.04297	0.521485	−	0.853260i	$-0.325378\pi$
$353$	19.5956	1.04297	0.521485	+	0.853260i	$0.325378\pi$
$354$	0.795704	0.0422912
$355$	−0.612279	−0.0324964
$356$	−25.3132	−1.34160
$357$	2.78612	0.147457
$358$	−15.6424	−0.826729
$359$	3.78090	0.199548	0.0997740	−	0.995010i	$-0.468188\pi$
$359$	3.78090	0.199548	0.0997740	+	0.995010i	$0.468188\pi$
$360$	−11.8599	−0.625073
$361$	−17.9250	−0.943419
$362$	4.04923	0.212823
$363$	−0.960304	−0.0504029
$364$	−47.8857	−2.50989
$365$	6.95260	0.363916
$366$	3.53766	0.184916
$367$	−19.5281	−1.01936	−0.509678	−	0.860365i	$-0.670235\pi$
$367$	−19.5281	−1.01936	−0.509678	+	0.860365i	$0.670235\pi$
$368$	28.7814	1.50033
$369$	10.1595	0.528883
$370$	9.43931	0.490726
$371$	2.19155	0.113780
$372$	1.40409	0.0727988
$373$	−26.7208	−1.38355	−0.691774	−	0.722114i	$-0.743171\pi$
$373$	−26.7208	−1.38355	−0.691774	+	0.722114i	$0.743171\pi$
$374$	−38.6919	−2.00071
$375$	0.966990	0.0499352
$376$	121.239	6.25245
$377$	3.31358	0.170658
$378$	−8.53672	−0.439081
$379$	14.0660	0.722519	0.361260	−	0.932465i	$-0.382347\pi$
$379$	14.0660	0.722519	0.361260	+	0.932465i	$0.382347\pi$
$380$	2.37561	0.121866
$381$	−4.88410	−0.250220
$382$	35.1896	1.80046
$383$	24.7595	1.26515	0.632575	−	0.774499i	$-0.281998\pi$
$383$	24.7595	1.26515	0.632575	+	0.774499i	$0.281998\pi$
$384$	−10.7899	−0.550620
$385$	−2.38731	−0.121668
$386$	58.2817	2.96646
$387$	−22.7814	−1.15805
$388$	−17.1361	−0.869952
$389$	−22.3343	−1.13240	−0.566198	−	0.824269i	$-0.691586\pi$
$389$	−22.3343	−1.13240	−0.566198	+	0.824269i	$0.691586\pi$
$390$	1.06367	0.0538609
$391$	−9.74807	−0.492981
$392$	21.4623	1.08401
$393$	−2.35003	−0.118543
$394$	−68.8490	−3.46856
$395$	0.583051	0.0293365
$396$	43.1656	2.16915
$397$	−5.95504	−0.298875	−0.149437	−	0.988771i	$-0.547746\pi$
$397$	−5.95504	−0.298875	−0.149437	+	0.988771i	$0.547746\pi$
$398$	16.4842	0.826277
$399$	0.541872	0.0271275
$400$	−76.0224	−3.80112
$401$	−12.1710	−0.607790	−0.303895	−	0.952706i	$-0.598287\pi$
$401$	−12.1710	−0.607790	−0.303895	+	0.952706i	$0.598287\pi$
$402$	−9.36912	−0.467289
$403$	4.17047	0.207746
$404$	29.6251	1.47391
$405$	−3.50289	−0.174060
$406$	5.07346	0.251792
$407$	−21.9843	−1.08972
$408$	12.4187	0.614816
$409$	28.6059	1.41447	0.707236	−	0.706977i	$-0.249942\pi$
$409$	28.6059	1.41447	0.707236	+	0.706977i	$0.249942\pi$
$410$	−3.91382	−0.193290
$411$	3.47264	0.171293
$412$	−94.7260	−4.66681
$413$	2.66060	0.130920
$414$	14.7912	0.726949
$415$	5.20448	0.255478
$416$	−93.3332	−4.57604
$417$	−2.89022	−0.141535
$418$	−7.52518	−0.368069
$419$	−2.31252	−0.112974	−0.0564870	−	0.998403i	$-0.517990\pi$
$419$	−2.31252	−0.112974	−0.0564870	+	0.998403i	$0.517990\pi$
$420$	1.19742	0.0584279
$421$	−25.7766	−1.25628	−0.628138	−	0.778102i	$-0.716183\pi$
$421$	−25.7766	−1.25628	−0.628138	+	0.778102i	$0.716183\pi$
$422$	2.57111	0.125160
$423$	36.5281	1.77606
$424$	9.76848	0.474399
$425$	25.7483	1.24898
$426$	−0.972809	−0.0471327
$427$	11.8289	0.572440
$428$	−21.1286	−1.02129
$429$	−2.47730	−0.119605
$430$	8.77625	0.423228
$431$	−22.2185	−1.07023	−0.535114	−	0.844780i	$-0.679731\pi$
$431$	−22.2185	−1.07023	−0.535114	+	0.844780i	$0.679731\pi$
$432$	−22.3078	−1.07328
$433$	−2.97650	−0.143042	−0.0715208	−	0.997439i	$-0.522785\pi$
$433$	−2.97650	−0.143042	−0.0715208	+	0.997439i	$0.522785\pi$
$434$	6.38546	0.306512
$435$	−0.0828583	−0.00397275
$436$	−58.2876	−2.79147
$437$	−1.89590	−0.0906931
$438$	11.0465	0.527823
$439$	−11.1916	−0.534147	−0.267073	−	0.963676i	$-0.586057\pi$
$439$	−11.1916	−0.534147	−0.267073	+	0.963676i	$0.586057\pi$
$440$	−10.6410	−0.507291
$441$	6.46635	0.307921
$442$	57.6430	2.74180
$443$	3.31945	0.157712	0.0788560	−	0.996886i	$-0.474873\pi$
$443$	3.31945	0.157712	0.0788560	+	0.996886i	$0.474873\pi$
$444$	11.0268	0.523310
$445$	1.88008	0.0891243
$446$	−77.2439	−3.65760
$447$	−4.96426	−0.234801
$448$	−73.9129	−3.49205
$449$	7.92122	0.373825	0.186913	−	0.982377i	$-0.440152\pi$
$449$	7.92122	0.373825	0.186913	+	0.982377i	$0.440152\pi$
$450$	−39.0691	−1.84174
$451$	9.11536	0.429225
$452$	−45.3421	−2.13271
$453$	0.238468	0.0112042
$454$	30.4775	1.43038
$455$	3.55659	0.166736
$456$	2.41530	0.113107
$457$	18.1734	0.850115	0.425058	−	0.905166i	$-0.360254\pi$
$457$	18.1734	0.850115	0.425058	+	0.905166i	$0.360254\pi$
$458$	14.5929	0.681882
$459$	7.55551	0.352661
$460$	−4.18951	−0.195337
$461$	36.1755	1.68486	0.842431	−	0.538805i	$-0.181124\pi$
$461$	36.1755	1.68486	0.842431	+	0.538805i	$0.181124\pi$
$462$	−3.79303	−0.176468
$463$	1.34779	0.0626372	0.0313186	−	0.999509i	$-0.490029\pi$
$463$	1.34779	0.0626372	0.0313186	+	0.999509i	$0.490029\pi$
$464$	13.2578	0.615476
$465$	−0.104286	−0.00483613
$466$	−43.6559	−2.02232
$467$	−19.3246	−0.894238	−0.447119	−	0.894474i	$-0.647550\pi$
$467$	−19.3246	−0.894238	−0.447119	+	0.894474i	$0.647550\pi$
$468$	−64.3078	−2.97263
$469$	−31.3276	−1.44657
$470$	−14.0720	−0.649091
$471$	−0.0155120	−0.000714753 0
$472$	11.8592	0.545863
$473$	−20.4401	−0.939835
$474$	0.926370	0.0425496
$475$	5.00778	0.229773
$476$	64.8912	2.97428
$477$	2.94313	0.134757
$478$	−56.9781	−2.60612
$479$	−38.9174	−1.77818	−0.889090	−	0.457733i	$-0.848661\pi$
$479$	−38.9174	−1.77818	−0.889090	+	0.457733i	$0.848661\pi$
$480$	2.33386	0.106526
$481$	32.7521	1.49337
$482$	−68.5254	−3.12125
$483$	−0.955618	−0.0434821
$484$	−22.3663	−1.01665
$485$	1.27274	0.0577921
$486$	−17.2513	−0.782537
$487$	−7.78220	−0.352645	−0.176323	−	0.984332i	$-0.556420\pi$
$487$	−7.78220	−0.352645	−0.176323	+	0.984332i	$0.556420\pi$
$488$	52.7253	2.38676
$489$	5.06178	0.228902
$490$	−2.49108	−0.112535
$491$	3.54822	0.160129	0.0800644	−	0.996790i	$-0.474487\pi$
$491$	3.54822	0.160129	0.0800644	+	0.996790i	$0.474487\pi$
$492$	−4.57204	−0.206124
$493$	−4.49032	−0.202234
$494$	11.2110	0.504405
$495$	−3.20602	−0.144100
$496$	16.6862	0.749233
$497$	−3.25279	−0.145908
$498$	8.26905	0.370545
$499$	−22.4647	−1.00566	−0.502828	−	0.864386i	$-0.667707\pi$
$499$	−22.4647	−1.00566	−0.502828	+	0.864386i	$0.667707\pi$
$500$	22.5220	1.00722
$501$	5.24281	0.234232
$502$	20.9325	0.934264
$503$	9.72259	0.433509	0.216754	−	0.976226i	$-0.430453\pi$
$503$	9.72259	0.433509	0.216754	+	0.976226i	$0.430453\pi$
$504$	−63.0070	−2.80655
$505$	−2.20033	−0.0979136
$506$	13.2710	0.589970
$507$	0.590577	0.0262285
$508$	−113.755	−5.04706
$509$	−18.8731	−0.836534	−0.418267	−	0.908324i	$-0.637362\pi$
$509$	−18.8731	−0.836534	−0.418267	+	0.908324i	$0.637362\pi$
$510$	−1.44140	−0.0638265
$511$	36.9364	1.63397
$512$	−65.9146	−2.91304
$513$	1.46947	0.0648786
$514$	−63.8127	−2.81466
$515$	7.03554	0.310023
$516$	10.2522	0.451330
$517$	32.7739	1.44139
$518$	50.1472	2.20334
$519$	−0.616779	−0.0270736
$520$	15.8529	0.695196
$521$	21.6984	0.950624	0.475312	−	0.879817i	$-0.342335\pi$
$521$	21.6984	0.950624	0.475312	+	0.879817i	$0.342335\pi$
$522$	6.81338	0.298213
$523$	28.0161	1.22506	0.612530	−	0.790447i	$-0.290152\pi$
$523$	28.0161	1.22506	0.612530	+	0.790447i	$0.290152\pi$
$524$	−54.7342	−2.39108
$525$	2.52415	0.110163
$526$	24.2243	1.05623
$527$	−5.65152	−0.246184
$528$	−9.91178	−0.431355
$529$	−19.6565	−0.854630
$530$	−1.13380	−0.0492493
$531$	3.57304	0.155057
$532$	12.6207	0.547175
$533$	−13.5800	−0.588215
$534$	2.98713	0.129266
$535$	1.56927	0.0678455
$536$	−139.638	−6.03142
$537$	1.35720	0.0585674
$538$	7.93835	0.342247
$539$	5.80176	0.249900
$540$	3.24720	0.139737
$541$	11.9549	0.513980	0.256990	−	0.966414i	$-0.417269\pi$
$541$	11.9549	0.513980	0.256990	+	0.966414i	$0.417269\pi$
$542$	−80.7911	−3.47027
$543$	−0.351327	−0.0150769
$544$	126.478	5.42272
$545$	4.32917	0.185441
$546$	5.65083	0.241833
$547$	34.0535	1.45602	0.728010	−	0.685566i	$-0.240445\pi$
$547$	34.0535	1.45602	0.728010	+	0.685566i	$0.240445\pi$
$548$	80.8809	3.45506
$549$	15.8855	0.677978
$550$	−35.0538	−1.49470
$551$	−0.873320	−0.0372047
$552$	−4.25951	−0.181297
$553$	3.09751	0.131720
$554$	−75.6196	−3.21277
$555$	−0.818990	−0.0347642
$556$	−67.3157	−2.85482
$557$	15.8329	0.670863	0.335432	−	0.942065i	$-0.391118\pi$
$557$	15.8329	0.670863	0.335432	+	0.942065i	$0.391118\pi$
$558$	8.57532	0.363022
$559$	30.4515	1.28796
$560$	14.2301	0.601330
$561$	3.35706	0.141735
$562$	−42.4617	−1.79114
$563$	15.2080	0.640940	0.320470	−	0.947259i	$-0.396159\pi$
$563$	15.2080	0.640940	0.320470	+	0.947259i	$0.396159\pi$
$564$	−16.4386	−0.692190
$565$	3.36767	0.141679
$566$	−76.7163	−3.22463
$567$	−18.6094	−0.781522
$568$	−14.4988	−0.608355
$569$	−36.4444	−1.52783	−0.763914	−	0.645318i	$-0.776725\pi$
$569$	−36.4444	−1.52783	−0.763914	+	0.645318i	$0.776725\pi$
$570$	−0.280338	−0.0117421
$571$	−36.2681	−1.51777	−0.758887	−	0.651223i	$-0.774256\pi$
$571$	−36.2681	−1.51777	−0.758887	+	0.651223i	$0.774256\pi$
$572$	−57.6985	−2.41250
$573$	−3.05318	−0.127549
$574$	−20.7925	−0.867863
$575$	−8.83147	−0.368298
$576$	−99.2609	−4.13587
$577$	−17.9724	−0.748201	−0.374100	−	0.927388i	$-0.622048\pi$
$577$	−17.9724	−0.748201	−0.374100	+	0.927388i	$0.622048\pi$
$578$	−31.3895	−1.30563
$579$	−5.05674	−0.210151
$580$	−1.92984	−0.0801324
$581$	27.6493	1.14709
$582$	2.02217	0.0838217
$583$	2.64065	0.109365
$584$	164.638	6.81275
$585$	4.77631	0.197476
$586$	83.0144	3.42929
$587$	35.3145	1.45758	0.728792	−	0.684735i	$-0.240082\pi$
$587$	35.3145	1.45758	0.728792	+	0.684735i	$0.240082\pi$
$588$	−2.91003	−0.120007
$589$	−1.09916	−0.0452902
$590$	−1.37647	−0.0566682
$591$	5.97360	0.245721
$592$	131.043	5.38582
$593$	27.2470	1.11890	0.559450	−	0.828864i	$-0.311012\pi$
$593$	27.2470	1.11890	0.559450	+	0.828864i	$0.311012\pi$
$594$	−10.2861	−0.422043
$595$	−4.81964	−0.197586
$596$	−115.622	−4.73606
$597$	−1.43023	−0.0585354
$598$	−19.7711	−0.808501
$599$	−14.4232	−0.589314	−0.294657	−	0.955603i	$-0.595205\pi$
$599$	−14.4232	−0.589314	−0.294657	+	0.955603i	$0.595205\pi$
$600$	11.2510	0.459318
$601$	42.7442	1.74357	0.871786	−	0.489886i	$-0.162962\pi$
$601$	42.7442	1.74357	0.871786	+	0.489886i	$0.162962\pi$
$602$	46.6247	1.90028
$603$	−42.0712	−1.71327
$604$	5.55414	0.225995
$605$	1.66120	0.0675376
$606$	−3.49596	−0.142014
$607$	5.15322	0.209163	0.104581	−	0.994516i	$-0.466650\pi$
$607$	5.15322	0.209163	0.104581	+	0.994516i	$0.466650\pi$
$608$	24.5987	0.997610
$609$	−0.440193	−0.0178375
$610$	−6.11970	−0.247779
$611$	−48.8263	−1.97530
$612$	87.1453	3.52264
$613$	23.8602	0.963703	0.481852	−	0.876253i	$-0.339964\pi$
$613$	23.8602	0.963703	0.481852	+	0.876253i	$0.339964\pi$
$614$	56.7746	2.29124
$615$	0.339578	0.0136931
$616$	−56.5314	−2.27772
$617$	17.6555	0.710785	0.355393	−	0.934717i	$-0.384347\pi$
$617$	17.6555	0.710785	0.355393	+	0.934717i	$0.384347\pi$
$618$	11.1783	0.449657
$619$	−29.4338	−1.18304	−0.591521	−	0.806289i	$-0.701472\pi$
$619$	−29.4338	−1.18304	−0.591521	+	0.806289i	$0.701472\pi$
$620$	−2.42890	−0.0975471
$621$	−2.59148	−0.103993
$622$	−62.6349	−2.51143
$623$	9.98810	0.400165
$624$	14.7665	0.591133
$625$	22.4764	0.899055
$626$	−45.9602	−1.83694
$627$	0.652913	0.0260748
$628$	−0.361287	−0.0144169
$629$	−44.3833	−1.76968
$630$	7.31307	0.291360
$631$	29.2421	1.16411	0.582055	−	0.813149i	$-0.302249\pi$
$631$	29.2421	1.16411	0.582055	+	0.813149i	$0.302249\pi$
$632$	13.8066	0.549199
$633$	−0.223079	−0.00886661
$634$	5.30933	0.210860
$635$	8.44888	0.335284
$636$	−1.32449	−0.0525193
$637$	−8.64343	−0.342465
$638$	6.11313	0.242021
$639$	−4.36831	−0.172808
$640$	18.6652	0.737806
$641$	34.1225	1.34776	0.673878	−	0.738843i	$-0.264627\pi$
$641$	34.1225	1.34776	0.673878	+	0.738843i	$0.264627\pi$
$642$	2.49331	0.0984031
$643$	20.0041	0.788884	0.394442	−	0.918921i	$-0.370938\pi$
$643$	20.0041	0.788884	0.394442	+	0.918921i	$0.370938\pi$
$644$	−22.2572	−0.877056
$645$	−0.761461	−0.0299825
$646$	−15.1923	−0.597732
$647$	26.0194	1.02293	0.511464	−	0.859305i	$-0.329104\pi$
$647$	26.0194	1.02293	0.511464	+	0.859305i	$0.329104\pi$
$648$	−82.9483	−3.25852
$649$	3.20582	0.125839
$650$	52.2229	2.04835
$651$	−0.554027	−0.0217140
$652$	117.893	4.61706
$653$	−12.3743	−0.484244	−0.242122	−	0.970246i	$-0.577843\pi$
$653$	−12.3743	−0.484244	−0.242122	+	0.970246i	$0.577843\pi$
$654$	6.87832	0.268964
$655$	4.06525	0.158843
$656$	−54.3341	−2.12139
$657$	49.6035	1.93522
$658$	−74.7586	−2.91439
$659$	−8.72013	−0.339688	−0.169844	−	0.985471i	$-0.554326\pi$
$659$	−8.72013	−0.339688	−0.169844	+	0.985471i	$0.554326\pi$
$660$	1.44279	0.0561606
$661$	47.1666	1.83457	0.917284	−	0.398234i	$-0.130377\pi$
$661$	47.1666	1.83457	0.917284	+	0.398234i	$0.130377\pi$
$662$	42.5806	1.65494
$663$	−5.00132	−0.194235
$664$	123.242	4.78272
$665$	−0.937369	−0.0363496
$666$	67.3449	2.60956
$667$	1.54014	0.0596346
$668$	122.110	4.72457
$669$	6.70197	0.259113
$670$	16.2074	0.626146
$671$	14.2529	0.550227
$672$	12.3989	0.478297
$673$	21.6516	0.834607	0.417303	−	0.908767i	$-0.362975\pi$
$673$	21.6516	0.834607	0.417303	+	0.908767i	$0.362975\pi$
$674$	−72.2184	−2.78175
$675$	6.84507	0.263467
$676$	13.7551	0.529041
$677$	37.5664	1.44379	0.721897	−	0.692001i	$-0.243270\pi$
$677$	37.5664	1.44379	0.721897	+	0.692001i	$0.243270\pi$
$678$	5.35067	0.205491
$679$	6.76155	0.259484
$680$	−21.4827	−0.823825
$681$	−2.64434	−0.101332
$682$	7.69399	0.294618
$683$	45.4196	1.73793	0.868967	−	0.494870i	$-0.164785\pi$
$683$	45.4196	1.73793	0.868967	+	0.494870i	$0.164785\pi$
$684$	16.9488	0.648055
$685$	−6.00723	−0.229525
$686$	−55.3981	−2.11511
$687$	−1.26614	−0.0483061
$688$	121.838	4.64501
$689$	−3.93402	−0.149874
$690$	0.494391	0.0188211
$691$	47.9918	1.82570	0.912848	−	0.408301i	$-0.133878\pi$
$691$	47.9918	1.82570	0.912848	+	0.408301i	$0.133878\pi$
$692$	−14.3653	−0.546088
$693$	−17.0323	−0.647003
$694$	95.2905	3.61718
$695$	4.99971	0.189650
$696$	−1.96209	−0.0743727
$697$	18.4026	0.697049
$698$	−29.3600	−1.11129
$699$	3.78775	0.143266
$700$	58.7896	2.22204
$701$	−38.7490	−1.46353	−0.731765	−	0.681558i	$-0.761303\pi$
$701$	−38.7490	−1.46353	−0.731765	+	0.681558i	$0.761303\pi$
$702$	15.3241	0.578372
$703$	−8.63209	−0.325565
$704$	−89.0593	−3.35655
$705$	1.22094	0.0459831
$706$	−53.8582	−2.02698
$707$	−11.6895	−0.439628
$708$	−1.60796	−0.0604309
$709$	34.2842	1.28757	0.643785	−	0.765207i	$-0.277363\pi$
$709$	34.2842	1.28757	0.643785	+	0.765207i	$0.277363\pi$
$710$	1.68284	0.0631557
$711$	4.15979	0.156004
$712$	44.5203	1.66847
$713$	1.93843	0.0725947
$714$	−7.65760	−0.286578
$715$	4.28542	0.160266
$716$	31.6103	1.18133
$717$	4.94364	0.184623
$718$	−10.3917	−0.387815
$719$	−5.36942	−0.200246	−0.100123	−	0.994975i	$-0.531924\pi$
$719$	−5.36942	−0.200246	−0.100123	+	0.994975i	$0.531924\pi$
$720$	19.1102	0.712195
$721$	37.3770	1.39199
$722$	49.2664	1.83350
$723$	5.94552	0.221116
$724$	−8.18271	−0.304108
$725$	−4.06810	−0.151085
$726$	2.63938	0.0979565
$727$	27.8642	1.03343	0.516713	−	0.856159i	$-0.327156\pi$
$727$	27.8642	1.03343	0.516713	+	0.856159i	$0.327156\pi$
$728$	84.2201	3.12141
$729$	−23.9775	−0.888055
$730$	−19.1091	−0.707259
$731$	−41.2656	−1.52626
$732$	−7.14891	−0.264231
$733$	−11.7695	−0.434718	−0.217359	−	0.976092i	$-0.569744\pi$
$733$	−11.7695	−0.434718	−0.217359	+	0.976092i	$0.569744\pi$
$734$	53.6725	1.98109
$735$	0.216135	0.00797226
$736$	−43.3811	−1.59905
$737$	−37.7473	−1.39044
$738$	−27.9232	−1.02787
$739$	−23.0687	−0.848598	−0.424299	−	0.905522i	$-0.639479\pi$
$739$	−23.0687	−0.848598	−0.424299	+	0.905522i	$0.639479\pi$
$740$	−19.0750	−0.701211
$741$	−0.972706	−0.0357332
$742$	−6.02344	−0.221127
$743$	−46.5146	−1.70646	−0.853228	−	0.521539i	$-0.825358\pi$
$743$	−46.5146	−1.70646	−0.853228	+	0.521539i	$0.825358\pi$
$744$	−2.46948	−0.0905356
$745$	8.58753	0.314623
$746$	73.4415	2.68888
$747$	37.1315	1.35857
$748$	78.1888	2.85887
$749$	8.33690	0.304624
$750$	−2.65775	−0.0970474
$751$	−33.1354	−1.20913	−0.604564	−	0.796556i	$-0.706653\pi$
$751$	−33.1354	−1.20913	−0.604564	+	0.796556i	$0.706653\pi$
$752$	−195.356	−7.12390
$753$	−1.81619	−0.0661855
$754$	−9.10730	−0.331668
$755$	−0.412520	−0.0150131
$756$	17.2510	0.627414
$757$	53.5118	1.94492	0.972459	−	0.233074i	$-0.0748784\pi$
$757$	53.5118	1.94492	0.972459	+	0.233074i	$0.0748784\pi$
$758$	−38.6600	−1.40419
$759$	−1.15145	−0.0417948
$760$	−4.17817	−0.151558
$761$	−36.0192	−1.30570	−0.652848	−	0.757489i	$-0.726426\pi$
$761$	−36.0192	−1.30570	−0.652848	+	0.757489i	$0.726426\pi$
$762$	13.4239	0.486295
$763$	22.9991	0.832624
$764$	−71.1113	−2.57272
$765$	−6.47250	−0.234014
$766$	−68.0509	−2.45878
$767$	−4.77601	−0.172452
$768$	13.5705	0.489685
$769$	33.3401	1.20227	0.601136	−	0.799146i	$-0.294715\pi$
$769$	33.3401	1.20227	0.601136	+	0.799146i	$0.294715\pi$
$770$	6.56146	0.236459
$771$	5.53663	0.199397
$772$	−117.776	−4.23885
$773$	−24.5740	−0.883864	−0.441932	−	0.897049i	$-0.645707\pi$
$773$	−24.5740	−0.883864	−0.441932	+	0.897049i	$0.645707\pi$
$774$	62.6143	2.25063
$775$	−5.12011	−0.183920
$776$	30.1385	1.08191
$777$	−4.35096	−0.156090
$778$	61.3855	2.20078
$779$	3.57912	0.128235
$780$	−2.14946	−0.0769631
$781$	−3.91936	−0.140246
$782$	26.7924	0.958093
$783$	−1.19373	−0.0426605
$784$	−34.5827	−1.23510
$785$	0.0268337	0.000957736 0
$786$	6.45901	0.230385
$787$	−40.7178	−1.45143	−0.725716	−	0.687995i	$-0.758491\pi$
$787$	−40.7178	−1.45143	−0.725716	+	0.687995i	$0.758491\pi$
$788$	139.130	4.95631
$789$	−2.10179	−0.0748258
$790$	−1.60250	−0.0570145
$791$	17.8911	0.636134
$792$	−75.9185	−2.69765
$793$	−21.2339	−0.754037
$794$	16.3673	0.580854
$795$	0.0983731	0.00348893
$796$	−33.3113	−1.18069
$797$	32.0546	1.13543	0.567716	−	0.823224i	$-0.307827\pi$
$797$	32.0546	1.13543	0.567716	+	0.823224i	$0.307827\pi$
$798$	−1.48932	−0.0527215
$799$	66.1659	2.34078
$800$	114.586	4.05122
$801$	13.4135	0.473941
$802$	33.4517	1.18122
$803$	44.5054	1.57056
$804$	18.9332	0.667721
$805$	1.65310	0.0582641
$806$	−11.4625	−0.403748
$807$	−0.688761	−0.0242455
$808$	−52.1039	−1.83301
$809$	6.27117	0.220482	0.110241	−	0.993905i	$-0.464838\pi$
$809$	6.27117	0.220482	0.110241	+	0.993905i	$0.464838\pi$
$810$	9.62761	0.338280
$811$	−40.1550	−1.41003	−0.705016	−	0.709191i	$-0.749060\pi$
$811$	−40.1550	−1.41003	−0.705016	+	0.709191i	$0.749060\pi$
$812$	−10.2525	−0.359791
$813$	7.00974	0.245842
$814$	60.4235	2.11784
$815$	−8.75624	−0.306718
$816$	−20.0105	−0.700508
$817$	−8.02573	−0.280785
$818$	−78.6228	−2.74898
$819$	25.3746	0.886659
$820$	7.90906	0.276196
$821$	6.98921	0.243925	0.121963	−	0.992535i	$-0.461081\pi$
$821$	6.98921	0.243925	0.121963	+	0.992535i	$0.461081\pi$
$822$	−9.54449	−0.332902
$823$	−24.3141	−0.847537	−0.423769	−	0.905771i	$-0.639293\pi$
$823$	−24.3141	−0.847537	−0.423769	+	0.905771i	$0.639293\pi$
$824$	166.602	5.80384
$825$	3.04140	0.105888
$826$	−7.31261	−0.254438
$827$	25.7913	0.896850	0.448425	−	0.893821i	$-0.351985\pi$
$827$	25.7913	0.896850	0.448425	+	0.893821i	$0.351985\pi$
$828$	−29.8902	−1.03875
$829$	−16.2924	−0.565859	−0.282929	−	0.959141i	$-0.591306\pi$
$829$	−16.2924	−0.565859	−0.282929	+	0.959141i	$0.591306\pi$
$830$	−14.3044	−0.496513
$831$	6.56104	0.227600
$832$	132.680	4.59985
$833$	11.7129	0.405830
$834$	7.94371	0.275068
$835$	−9.06940	−0.313860
$836$	15.2069	0.525942
$837$	−1.50243	−0.0519316
$838$	6.35592	0.219562
$839$	−5.07065	−0.175058	−0.0875291	−	0.996162i	$-0.527897\pi$
$839$	−5.07065	−0.175058	−0.0875291	+	0.996162i	$0.527897\pi$
$840$	−2.10598	−0.0726633
$841$	−28.2906	−0.975536
$842$	70.8466	2.44153
$843$	3.68413	0.126888
$844$	−5.19571	−0.178844
$845$	−1.02162	−0.0351449
$846$	−100.397	−3.45171
$847$	8.82531	0.303241
$848$	−15.7402	−0.540520
$849$	6.65619	0.228440
$850$	−70.7687	−2.42735
$851$	15.2231	0.521842
$852$	1.96586	0.0673491
$853$	−19.6202	−0.671782	−0.335891	−	0.941901i	$-0.609037\pi$
$853$	−19.6202	−0.671782	−0.335891	+	0.941901i	$0.609037\pi$
$854$	−32.5115	−1.11252
$855$	−1.25883	−0.0430512
$856$	37.1604	1.27011
$857$	−35.1597	−1.20103	−0.600516	−	0.799613i	$-0.705038\pi$
$857$	−35.1597	−1.20103	−0.600516	+	0.799613i	$0.705038\pi$
$858$	6.80881	0.232449
$859$	−25.0893	−0.856037	−0.428019	−	0.903770i	$-0.640788\pi$
$859$	−25.0893	−0.856037	−0.428019	+	0.903770i	$0.640788\pi$
$860$	−17.7351	−0.604761
$861$	1.80404	0.0614814
$862$	61.0671	2.07995
$863$	9.16258	0.311898	0.155949	−	0.987765i	$-0.450156\pi$
$863$	9.16258	0.311898	0.155949	+	0.987765i	$0.450156\pi$
$864$	33.6237	1.14390
$865$	1.06695	0.0362774
$866$	8.18086	0.277997
$867$	2.72347	0.0924938
$868$	−12.9038	−0.437983
$869$	3.73226	0.126608
$870$	0.227734	0.00772092
$871$	56.2357	1.90547
$872$	102.515	3.47159
$873$	9.08038	0.307324
$874$	5.21084	0.176259
$875$	−8.88675	−0.300427
$876$	−22.3229	−0.754220
$877$	−21.1278	−0.713436	−0.356718	−	0.934212i	$-0.616104\pi$
$877$	−21.1278	−0.713436	−0.356718	+	0.934212i	$0.616104\pi$
$878$	30.7599	1.03810
$879$	−7.20264	−0.242939
$880$	17.1461	0.577996
$881$	53.2948	1.79555	0.897775	−	0.440455i	$-0.145183\pi$
$881$	53.2948	1.79555	0.897775	+	0.440455i	$0.145183\pi$
$882$	−17.7726	−0.598435
$883$	−6.76432	−0.227638	−0.113819	−	0.993502i	$-0.536308\pi$
$883$	−6.76432	−0.227638	−0.113819	+	0.993502i	$0.536308\pi$
$884$	−116.485	−3.91782
$885$	0.119427	0.00401451
$886$	−9.12344	−0.306508
$887$	−37.7121	−1.26625	−0.633124	−	0.774050i	$-0.718228\pi$
$887$	−37.7121	−1.26625	−0.633124	+	0.774050i	$0.718228\pi$
$888$	−19.3937	−0.650810
$889$	44.8855	1.50541
$890$	−5.16736	−0.173210
$891$	−22.4229	−0.751195
$892$	156.095	5.22644
$893$	12.8686	0.430630
$894$	13.6442	0.456329
$895$	−2.34778	−0.0784776
$896$	99.1605	3.31272
$897$	1.71542	0.0572761
$898$	−21.7713	−0.726518
$899$	0.892911	0.0297802
$900$	78.9511	2.63170
$901$	5.33110	0.177605
$902$	−25.0534	−0.834186
$903$	−4.04533	−0.134620
$904$	79.7465	2.65233
$905$	0.607751	0.0202023
$906$	−0.655426	−0.0217751
$907$	−30.5305	−1.01375	−0.506875	−	0.862020i	$-0.669199\pi$
$907$	−30.5305	−1.01375	−0.506875	+	0.862020i	$0.669199\pi$
$908$	−61.5891	−2.04391
$909$	−15.6983	−0.520681
$910$	−9.77522	−0.324045
$911$	−40.7746	−1.35092	−0.675462	−	0.737395i	$-0.736056\pi$
$911$	−40.7746	−1.35092	−0.675462	+	0.737395i	$0.736056\pi$
$912$	−3.89183	−0.128872
$913$	33.3153	1.10257
$914$	−49.9492	−1.65217
$915$	0.530968	0.0175533
$916$	−29.4894	−0.974358
$917$	21.5970	0.713197
$918$	−20.7662	−0.685385
$919$	−19.6351	−0.647701	−0.323850	−	0.946108i	$-0.604977\pi$
$919$	−19.6351	−0.647701	−0.323850	+	0.946108i	$0.604977\pi$
$920$	7.36841	0.242929
$921$	−4.92598	−0.162316
$922$	−99.4276	−3.27447
$923$	5.83903	0.192194
$924$	7.66497	0.252159
$925$	−40.2100	−1.32210
$926$	−3.70438	−0.121733
$927$	50.1952	1.64863
$928$	−19.9829	−0.655972
$929$	−12.8998	−0.423229	−0.211614	−	0.977353i	$-0.567872\pi$
$929$	−12.8998	−0.423229	−0.211614	+	0.977353i	$0.567872\pi$
$930$	0.286627	0.00939886
$931$	2.27805	0.0746600
$932$	88.2201	2.88975
$933$	5.43444	0.177916
$934$	53.1134	1.73792
$935$	−5.80729	−0.189919
$936$	113.103	3.69688
$937$	−1.81698	−0.0593583	−0.0296791	−	0.999559i	$-0.509449\pi$
$937$	−1.81698	−0.0593583	−0.0296791	+	0.999559i	$0.509449\pi$
$938$	86.1033	2.81137
$939$	3.98768	0.130133
$940$	28.4367	0.927502
$941$	9.20764	0.300160	0.150080	−	0.988674i	$-0.452047\pi$
$941$	9.20764	0.300160	0.150080	+	0.988674i	$0.452047\pi$
$942$	0.0426343	0.00138910
$943$	−6.31196	−0.205546
$944$	−19.1090	−0.621945
$945$	−1.28128	−0.0416800
$946$	56.1791	1.82654
$947$	53.8833	1.75097	0.875485	−	0.483245i	$-0.160542\pi$
$947$	53.8833	1.75097	0.875485	+	0.483245i	$0.160542\pi$
$948$	−1.87201	−0.0608002
$949$	−66.3039	−2.15232
$950$	−13.7638	−0.446556
$951$	−0.460657	−0.0149378
$952$	−114.129	−3.69894
$953$	−4.40191	−0.142592	−0.0712960	−	0.997455i	$-0.522713\pi$
$953$	−4.40191	−0.142592	−0.0712960	+	0.997455i	$0.522713\pi$
$954$	−8.08914	−0.261896
$955$	5.28162	0.170909
$956$	115.142	3.72395
$957$	−0.530398	−0.0171453
$958$	106.964	3.45584
$959$	−31.9140	−1.03056
$960$	−3.31776	−0.107080
$961$	−29.8762	−0.963748
$962$	−90.0185	−2.90231
$963$	11.1960	0.360786
$964$	138.476	4.46002
$965$	8.74752	0.281593
$966$	2.62650	0.0845062
$967$	−19.8485	−0.638286	−0.319143	−	0.947707i	$-0.603395\pi$
$967$	−19.8485	−0.638286	−0.319143	+	0.947707i	$0.603395\pi$
$968$	39.3373	1.26435
$969$	1.31814	0.0423448
$970$	−3.49810	−0.112317
$971$	44.4251	1.42567	0.712835	−	0.701331i	$-0.247411\pi$
$971$	44.4251	1.42567	0.712835	+	0.701331i	$0.247411\pi$
$972$	34.8616	1.11819
$973$	26.5614	0.851521
$974$	21.3892	0.685355
$975$	−4.53106	−0.145110
$976$	−84.9575	−2.71942
$977$	−28.6370	−0.916179	−0.458089	−	0.888906i	$-0.651466\pi$
$977$	−28.6370	−0.916179	−0.458089	+	0.888906i	$0.651466\pi$
$978$	−13.9122	−0.444863
$979$	12.0349	0.384636
$980$	5.03398	0.160804
$981$	30.8865	0.986131
$982$	−9.75220	−0.311205
$983$	13.7442	0.438373	0.219187	−	0.975683i	$-0.429660\pi$
$983$	13.7442	0.438373	0.219187	+	0.975683i	$0.429660\pi$
$984$	8.04120	0.256344
$985$	−10.3336	−0.329255
$986$	12.3415	0.393035
$987$	6.48634	0.206463
$988$	−22.6552	−0.720757
$989$	14.1538	0.450065
$990$	8.81168	0.280053
$991$	−14.6537	−0.465489	−0.232745	−	0.972538i	$-0.574771\pi$
$991$	−14.6537	−0.465489	−0.232745	+	0.972538i	$0.574771\pi$
$992$	−25.1505	−0.798530
$993$	−3.69446	−0.117240
$994$	8.94022	0.283567
$995$	2.47411	0.0784347
$996$	−16.7101	−0.529481
$997$	−27.0195	−0.855718	−0.427859	−	0.903846i	$-0.640732\pi$
$997$	−27.0195	−0.855718	−0.427859	+	0.903846i	$0.640732\pi$
$998$	61.7436	1.95446
$999$	−11.7991	−0.373307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.4	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.4	✓	172	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74848 q^{2} +0.238468 q^{3} +5.55414 q^{4} -0.412520 q^{5} -0.655426 q^{6} -2.19155 q^{7} -9.76848 q^{8} -2.94313 q^{9} +O(q^{10})\)	\(q-2.74848 q^{2} +0.238468 q^{3} +5.55414 q^{4} -0.412520 q^{5} -0.655426 q^{6} -2.19155 q^{7} -9.76848 q^{8} -2.94313 q^{9} +1.13380 q^{10} -2.64065 q^{11} +1.32449 q^{12} +3.93402 q^{13} +6.02344 q^{14} -0.0983731 q^{15} +15.7402 q^{16} -5.33110 q^{17} +8.08914 q^{18} -1.03684 q^{19} -2.29119 q^{20} -0.522616 q^{21} +7.25777 q^{22} +1.82853 q^{23} -2.32947 q^{24} -4.82983 q^{25} -10.8126 q^{26} -1.41725 q^{27} -12.1722 q^{28} +0.842287 q^{29} +0.270376 q^{30} +1.06010 q^{31} -23.7246 q^{32} -0.629712 q^{33} +14.6524 q^{34} +0.904060 q^{35} -16.3466 q^{36} +8.32535 q^{37} +2.84974 q^{38} +0.938141 q^{39} +4.02969 q^{40} -3.45194 q^{41} +1.43640 q^{42} +7.74054 q^{43} -14.6665 q^{44} +1.21410 q^{45} -5.02567 q^{46} -12.4113 q^{47} +3.75354 q^{48} -2.19710 q^{49} +13.2747 q^{50} -1.27130 q^{51} +21.8501 q^{52} -1.00000 q^{53} +3.89528 q^{54} +1.08932 q^{55} +21.4081 q^{56} -0.247255 q^{57} -2.31501 q^{58} -1.21403 q^{59} -0.546378 q^{60} -5.39749 q^{61} -2.91367 q^{62} +6.45003 q^{63} +33.7263 q^{64} -1.62286 q^{65} +1.73075 q^{66} +14.2947 q^{67} -29.6097 q^{68} +0.436046 q^{69} -2.48479 q^{70} +1.48424 q^{71} +28.7499 q^{72} -16.8540 q^{73} -22.8821 q^{74} -1.15176 q^{75} -5.75878 q^{76} +5.78712 q^{77} -2.57846 q^{78} -1.41339 q^{79} -6.49314 q^{80} +8.49143 q^{81} +9.48758 q^{82} -12.6163 q^{83} -2.90268 q^{84} +2.19919 q^{85} -21.2747 q^{86} +0.200859 q^{87} +25.7951 q^{88} -4.55754 q^{89} -3.33693 q^{90} -8.62162 q^{91} +10.1559 q^{92} +0.252801 q^{93} +34.1122 q^{94} +0.427719 q^{95} -5.65757 q^{96} -3.08528 q^{97} +6.03867 q^{98} +7.77178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

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