LMFDB - Embedded newform 8003.2.a.c.1.11

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			1.11
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)

$f(q)$	$=$	$q-2.55384 q^{2} +0.729856 q^{3} +4.52207 q^{4} +2.13397 q^{5} -1.86393 q^{6} -2.81962 q^{7} -6.44096 q^{8} -2.46731 q^{9} +O(q^{10})$	\(q-2.55384 q^{2} +0.729856 q^{3} +4.52207 q^{4} +2.13397 q^{5} -1.86393 q^{6} -2.81962 q^{7} -6.44096 q^{8} -2.46731 q^{9} -5.44980 q^{10} +1.09285 q^{11} +3.30046 q^{12} -4.42859 q^{13} +7.20085 q^{14} +1.55749 q^{15} +7.40501 q^{16} -5.59961 q^{17} +6.30110 q^{18} -3.27913 q^{19} +9.64995 q^{20} -2.05792 q^{21} -2.79097 q^{22} -0.823175 q^{23} -4.70098 q^{24} -0.446190 q^{25} +11.3099 q^{26} -3.99035 q^{27} -12.7505 q^{28} -8.28436 q^{29} -3.97757 q^{30} -1.53338 q^{31} -6.02925 q^{32} +0.797626 q^{33} +14.3005 q^{34} -6.01698 q^{35} -11.1574 q^{36} -8.71974 q^{37} +8.37437 q^{38} -3.23224 q^{39} -13.7448 q^{40} +0.597035 q^{41} +5.25559 q^{42} +8.37632 q^{43} +4.94197 q^{44} -5.26515 q^{45} +2.10225 q^{46} +7.48019 q^{47} +5.40459 q^{48} +0.950276 q^{49} +1.13950 q^{50} -4.08691 q^{51} -20.0264 q^{52} -1.00000 q^{53} +10.1907 q^{54} +2.33211 q^{55} +18.1611 q^{56} -2.39330 q^{57} +21.1569 q^{58} -4.64532 q^{59} +7.04308 q^{60} -2.21778 q^{61} +3.91599 q^{62} +6.95688 q^{63} +0.587685 q^{64} -9.45046 q^{65} -2.03701 q^{66} +11.9902 q^{67} -25.3219 q^{68} -0.600800 q^{69} +15.3664 q^{70} +8.81328 q^{71} +15.8919 q^{72} +3.30737 q^{73} +22.2688 q^{74} -0.325655 q^{75} -14.8285 q^{76} -3.08144 q^{77} +8.25460 q^{78} -1.24481 q^{79} +15.8020 q^{80} +4.48955 q^{81} -1.52473 q^{82} -7.45671 q^{83} -9.30607 q^{84} -11.9494 q^{85} -21.3917 q^{86} -6.04639 q^{87} -7.03903 q^{88} -6.00577 q^{89} +13.4463 q^{90} +12.4870 q^{91} -3.72246 q^{92} -1.11914 q^{93} -19.1032 q^{94} -6.99756 q^{95} -4.40048 q^{96} -9.70815 q^{97} -2.42685 q^{98} -2.69641 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.55384	−1.80583	−0.902917	−	0.429815i	$-0.858579\pi$
$2$	−2.55384	−1.80583	−0.902917	+	0.429815i	$0.858579\pi$
$3$	0.729856	0.421383	0.210691	−	0.977553i	$-0.432428\pi$
$3$	0.729856	0.421383	0.210691	+	0.977553i	$0.432428\pi$
$4$	4.52207	2.26104
$5$	2.13397	0.954338	0.477169	−	0.878811i	$-0.341663\pi$
$5$	2.13397	0.954338	0.477169	+	0.878811i	$0.341663\pi$
$6$	−1.86393	−0.760947
$7$	−2.81962	−1.06572	−0.532859	−	0.846204i	$-0.678882\pi$
$7$	−2.81962	−1.06572	−0.532859	+	0.846204i	$0.678882\pi$
$8$	−6.44096	−2.27722
$9$	−2.46731	−0.822437
$10$	−5.44980	−1.72338
$11$	1.09285	0.329508	0.164754	−	0.986335i	$-0.447317\pi$
$11$	1.09285	0.329508	0.164754	+	0.986335i	$0.447317\pi$
$12$	3.30046	0.952762
$13$	−4.42859	−1.22827	−0.614135	−	0.789201i	$-0.710495\pi$
$13$	−4.42859	−1.22827	−0.614135	+	0.789201i	$0.710495\pi$
$14$	7.20085	1.92451
$15$	1.55749	0.402142
$16$	7.40501	1.85125
$17$	−5.59961	−1.35811	−0.679053	−	0.734090i	$-0.737609\pi$
$17$	−5.59961	−1.35811	−0.679053	+	0.734090i	$0.737609\pi$
$18$	6.30110	1.48518
$19$	−3.27913	−0.752285	−0.376143	−	0.926562i	$-0.622750\pi$
$19$	−3.27913	−0.752285	−0.376143	+	0.926562i	$0.622750\pi$
$20$	9.64995	2.15779
$21$	−2.05792	−0.449075
$22$	−2.79097	−0.595037
$23$	−0.823175	−0.171644	−0.0858220	−	0.996310i	$-0.527352\pi$
$23$	−0.823175	−0.171644	−0.0858220	+	0.996310i	$0.527352\pi$
$24$	−4.70098	−0.959583
$25$	−0.446190	−0.0892381
$26$	11.3099	2.21805
$27$	−3.99035	−0.767943
$28$	−12.7505	−2.40963
$29$	−8.28436	−1.53837	−0.769184	−	0.639028i	$-0.779337\pi$
$29$	−8.28436	−1.53837	−0.769184	+	0.639028i	$0.779337\pi$
$30$	−3.97757	−0.726201
$31$	−1.53338	−0.275402	−0.137701	−	0.990474i	$-0.543971\pi$
$31$	−1.53338	−0.275402	−0.137701	+	0.990474i	$0.543971\pi$
$32$	−6.02925	−1.06583
$33$	0.797626	0.138849
$34$	14.3005	2.45251
$35$	−6.01698	−1.01706
$36$	−11.1574	−1.85956
$37$	−8.71974	−1.43352	−0.716758	−	0.697322i	$-0.754375\pi$
$37$	−8.71974	−1.43352	−0.716758	+	0.697322i	$0.754375\pi$
$38$	8.37437	1.35850
$39$	−3.23224	−0.517572
$40$	−13.7448	−2.17324
$41$	0.597035	0.0932412	0.0466206	−	0.998913i	$-0.485155\pi$
$41$	0.597035	0.0932412	0.0466206	+	0.998913i	$0.485155\pi$
$42$	5.25559	0.810955
$43$	8.37632	1.27738	0.638688	−	0.769466i	$-0.279477\pi$
$43$	8.37632	1.27738	0.638688	+	0.769466i	$0.279477\pi$
$44$	4.94197	0.745030
$45$	−5.26515	−0.784883
$46$	2.10225	0.309960
$47$	7.48019	1.09110	0.545549	−	0.838079i	$-0.316321\pi$
$47$	7.48019	1.09110	0.545549	+	0.838079i	$0.316321\pi$
$48$	5.40459	0.780086
$49$	0.950276	0.135754
$50$	1.13950	0.161149
$51$	−4.08691	−0.572282
$52$	−20.0264	−2.77716
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	10.1907	1.38678
$55$	2.33211	0.314462
$56$	18.1611	2.42688
$57$	−2.39330	−0.317000
$58$	21.1569	2.77804
$59$	−4.64532	−0.604769	−0.302384	−	0.953186i	$-0.597783\pi$
$59$	−4.64532	−0.604769	−0.302384	+	0.953186i	$0.597783\pi$
$60$	7.04308	0.909257
$61$	−2.21778	−0.283958	−0.141979	−	0.989870i	$-0.545347\pi$
$61$	−2.21778	−0.283958	−0.141979	+	0.989870i	$0.545347\pi$
$62$	3.91599	0.497331
$63$	6.95688	0.876485
$64$	0.587685	0.0734606
$65$	−9.45046	−1.17219
$66$	−2.03701	−0.250738
$67$	11.9902	1.46483	0.732415	−	0.680858i	$-0.238393\pi$
$67$	11.9902	1.46483	0.732415	+	0.680858i	$0.238393\pi$
$68$	−25.3219	−3.07073
$69$	−0.600800	−0.0723278
$70$	15.3664	1.83663
$71$	8.81328	1.04594	0.522972	−	0.852350i	$-0.324823\pi$
$71$	8.81328	1.04594	0.522972	+	0.852350i	$0.324823\pi$
$72$	15.8919	1.87287
$73$	3.30737	0.387099	0.193549	−	0.981091i	$-0.438000\pi$
$73$	3.30737	0.387099	0.193549	+	0.981091i	$0.438000\pi$
$74$	22.2688	2.58869
$75$	−0.325655	−0.0376034
$76$	−14.8285	−1.70094
$77$	−3.08144	−0.351162
$78$	8.25460	0.934649
$79$	−1.24481	−0.140052	−0.0700258	−	0.997545i	$-0.522308\pi$
$79$	−1.24481	−0.140052	−0.0700258	+	0.997545i	$0.522308\pi$
$80$	15.8020	1.76672
$81$	4.48955	0.498839
$82$	−1.52473	−0.168378
$83$	−7.45671	−0.818480	−0.409240	−	0.912427i	$-0.634206\pi$
$83$	−7.45671	−0.818480	−0.409240	+	0.912427i	$0.634206\pi$
$84$	−9.30607	−1.01538
$85$	−11.9494	−1.29609
$86$	−21.3917	−2.30673
$87$	−6.04639	−0.648241
$88$	−7.03903	−0.750363
$89$	−6.00577	−0.636610	−0.318305	−	0.947988i	$-0.603114\pi$
$89$	−6.00577	−0.636610	−0.318305	+	0.947988i	$0.603114\pi$
$90$	13.4463	1.41737
$91$	12.4870	1.30899
$92$	−3.72246	−0.388093
$93$	−1.11914	−0.116050
$94$	−19.1032	−1.97034
$95$	−6.99756	−0.717935
$96$	−4.40048	−0.449122
$97$	−9.70815	−0.985713	−0.492856	−	0.870111i	$-0.664047\pi$
$97$	−9.70815	−0.985713	−0.492856	+	0.870111i	$0.664047\pi$
$98$	−2.42685	−0.245149
$99$	−2.69641	−0.270999
$100$	−2.01771	−0.201771
$101$	−9.28873	−0.924264	−0.462132	−	0.886811i	$-0.652915\pi$
$101$	−9.28873	−0.924264	−0.462132	+	0.886811i	$0.652915\pi$
$102$	10.4373	1.03345
$103$	−2.82231	−0.278091	−0.139045	−	0.990286i	$-0.544403\pi$
$103$	−2.82231	−0.278091	−0.139045	+	0.990286i	$0.544403\pi$
$104$	28.5244	2.79705
$105$	−4.39153	−0.428569
$106$	2.55384	0.248050
$107$	17.0750	1.65070	0.825350	−	0.564621i	$-0.190978\pi$
$107$	17.0750	1.65070	0.825350	+	0.564621i	$0.190978\pi$
$108$	−18.0447	−1.73635
$109$	−19.3215	−1.85066	−0.925331	−	0.379160i	$-0.876213\pi$
$109$	−19.3215	−1.85066	−0.925331	+	0.379160i	$0.876213\pi$
$110$	−5.95583	−0.567866
$111$	−6.36416	−0.604059
$112$	−20.8793	−1.97291
$113$	19.3590	1.82114	0.910569	−	0.413357i	$-0.135644\pi$
$113$	19.3590	1.82114	0.910569	+	0.413357i	$0.135644\pi$
$114$	6.11209	0.572449
$115$	−1.75663	−0.163806
$116$	−37.4625	−3.47831
$117$	10.9267	1.01017
$118$	11.8634	1.09211
$119$	15.7888	1.44736
$120$	−10.0317	−0.915767
$121$	−9.80567	−0.891425
$122$	5.66385	0.512781
$123$	0.435750	0.0392902
$124$	−6.93404	−0.622695
$125$	−11.6220	−1.03950
$126$	−17.7667	−1.58279
$127$	12.8436	1.13969	0.569843	−	0.821754i	$-0.307004\pi$
$127$	12.8436	1.13969	0.569843	+	0.821754i	$0.307004\pi$
$128$	10.5576	0.933173
$129$	6.11351	0.538264
$130$	24.1349	2.11677
$131$	20.8926	1.82539	0.912697	−	0.408637i	$-0.133996\pi$
$131$	20.8926	1.82539	0.912697	+	0.408637i	$0.133996\pi$
$132$	3.60693	0.313943
$133$	9.24593	0.801723
$134$	−30.6209	−2.64524
$135$	−8.51527	−0.732878
$136$	36.0669	3.09271
$137$	12.4552	1.06412	0.532059	−	0.846707i	$-0.321418\pi$
$137$	12.4552	1.06412	0.532059	+	0.846707i	$0.321418\pi$
$138$	1.53434	0.130612
$139$	−8.59927	−0.729380	−0.364690	−	0.931129i	$-0.618825\pi$
$139$	−8.59927	−0.729380	−0.364690	+	0.931129i	$0.618825\pi$
$140$	−27.2092	−2.29960
$141$	5.45946	0.459770
$142$	−22.5077	−1.88880
$143$	−4.83980	−0.404725
$144$	−18.2705	−1.52254
$145$	−17.6785	−1.46812
$146$	−8.44648	−0.699036
$147$	0.693565	0.0572043
$148$	−39.4313	−3.24123
$149$	−4.75411	−0.389472	−0.194736	−	0.980856i	$-0.562385\pi$
$149$	−4.75411	−0.389472	−0.194736	+	0.980856i	$0.562385\pi$
$150$	0.831669	0.0679055
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	21.1208	1.71312
$153$	13.8160	1.11696
$154$	7.86948	0.634141
$155$	−3.27217	−0.262827
$156$	−14.6164	−1.17025
$157$	17.3100	1.38149	0.690745	−	0.723098i	$-0.257283\pi$
$157$	17.3100	1.38149	0.690745	+	0.723098i	$0.257283\pi$
$158$	3.17903	0.252910
$159$	−0.729856	−0.0578814
$160$	−12.8662	−1.01716
$161$	2.32104	0.182924
$162$	−11.4656	−0.900820
$163$	−5.71813	−0.447878	−0.223939	−	0.974603i	$-0.571892\pi$
$163$	−5.71813	−0.447878	−0.223939	+	0.974603i	$0.571892\pi$
$164$	2.69984	0.210822
$165$	1.70211	0.132509
$166$	19.0432	1.47804
$167$	−3.56364	−0.275763	−0.137881	−	0.990449i	$-0.544029\pi$
$167$	−3.56364	−0.275763	−0.137881	+	0.990449i	$0.544029\pi$
$168$	13.2550	1.02264
$169$	6.61242	0.508648
$170$	30.5167	2.34053
$171$	8.09064	0.618707
$172$	37.8783	2.88820
$173$	12.0800	0.918429	0.459215	−	0.888325i	$-0.348131\pi$
$173$	12.0800	0.918429	0.459215	+	0.888325i	$0.348131\pi$
$174$	15.4415	1.17062
$175$	1.25809	0.0951026
$176$	8.09259	0.610002
$177$	−3.39041	−0.254839
$178$	15.3377	1.14961
$179$	−15.2596	−1.14056	−0.570280	−	0.821450i	$-0.693165\pi$
$179$	−15.2596	−1.14056	−0.570280	+	0.821450i	$0.693165\pi$
$180$	−23.8094	−1.77465
$181$	2.66986	0.198449	0.0992244	−	0.995065i	$-0.468364\pi$
$181$	2.66986	0.198449	0.0992244	+	0.995065i	$0.468364\pi$
$182$	−31.8896	−2.36382
$183$	−1.61866	−0.119655
$184$	5.30204	0.390872
$185$	−18.6076	−1.36806
$186$	2.85811	0.209567
$187$	−6.11956	−0.447506
$188$	33.8260	2.46701
$189$	11.2513	0.818411
$190$	17.8706	1.29647
$191$	18.9374	1.37026	0.685131	−	0.728420i	$-0.259745\pi$
$191$	18.9374	1.37026	0.685131	+	0.728420i	$0.259745\pi$
$192$	0.428926	0.0309550
$193$	25.9853	1.87046	0.935232	−	0.354035i	$-0.115191\pi$
$193$	25.9853	1.87046	0.935232	+	0.354035i	$0.115191\pi$
$194$	24.7930	1.78003
$195$	−6.89748	−0.493939
$196$	4.29722	0.306944
$197$	−7.16000	−0.510129	−0.255064	−	0.966924i	$-0.582097\pi$
$197$	−7.16000	−0.510129	−0.255064	+	0.966924i	$0.582097\pi$
$198$	6.88619	0.489380
$199$	10.8023	0.765752	0.382876	−	0.923800i	$-0.374934\pi$
$199$	10.8023	0.765752	0.382876	+	0.923800i	$0.374934\pi$
$200$	2.87390	0.203215
$201$	8.75109	0.617254
$202$	23.7219	1.66907
$203$	23.3588	1.63946
$204$	−18.4813	−1.29395
$205$	1.27405	0.0889837
$206$	7.20772	0.502186
$207$	2.03103	0.141166
$208$	−32.7938	−2.27384
$209$	−3.58362	−0.247884
$210$	11.2152	0.773925
$211$	8.33284	0.573657	0.286828	−	0.957982i	$-0.407399\pi$
$211$	8.33284	0.573657	0.286828	+	0.957982i	$0.407399\pi$
$212$	−4.52207	−0.310577
$213$	6.43243	0.440743
$214$	−43.6067	−2.98089
$215$	17.8748	1.21905
$216$	25.7017	1.74878
$217$	4.32354	0.293501
$218$	49.3439	3.34199
$219$	2.41391	0.163117
$220$	10.5460	0.711010
$221$	24.7984	1.66812
$222$	16.2530	1.09083
$223$	24.0462	1.61026	0.805128	−	0.593101i	$-0.202097\pi$
$223$	24.0462	1.61026	0.805128	+	0.593101i	$0.202097\pi$
$224$	17.0002	1.13587
$225$	1.10089	0.0733927
$226$	−49.4396	−3.28867
$227$	10.8952	0.723138	0.361569	−	0.932345i	$-0.382241\pi$
$227$	10.8952	0.723138	0.361569	+	0.932345i	$0.382241\pi$
$228$	−10.8227	−0.716749
$229$	29.6467	1.95911	0.979554	−	0.201181i	$-0.0644778\pi$
$229$	29.6467	1.95911	0.979554	+	0.201181i	$0.0644778\pi$
$230$	4.48614	0.295807
$231$	−2.24901	−0.147974
$232$	53.3593	3.50321
$233$	−22.6440	−1.48345	−0.741727	−	0.670701i	$-0.765993\pi$
$233$	−22.6440	−1.48345	−0.741727	+	0.670701i	$0.765993\pi$
$234$	−27.9050	−1.82421
$235$	15.9625	1.04128
$236$	−21.0065	−1.36740
$237$	−0.908529	−0.0590153
$238$	−40.3220	−2.61369
$239$	−16.9562	−1.09681	−0.548403	−	0.836214i	$-0.684764\pi$
$239$	−16.9562	−1.09681	−0.548403	+	0.836214i	$0.684764\pi$
$240$	11.5332	0.744466
$241$	−21.1323	−1.36125	−0.680624	−	0.732633i	$-0.738291\pi$
$241$	−21.1323	−1.36125	−0.680624	+	0.732633i	$0.738291\pi$
$242$	25.0421	1.60976
$243$	15.2478	0.978145
$244$	−10.0290	−0.642040
$245$	2.02786	0.129555
$246$	−1.11283	−0.0709517
$247$	14.5219	0.924009
$248$	9.87641	0.627153
$249$	−5.44233	−0.344893
$250$	29.6806	1.87717
$251$	−20.7156	−1.30756	−0.653779	−	0.756685i	$-0.726818\pi$
$251$	−20.7156	−1.30756	−0.653779	+	0.756685i	$0.726818\pi$
$252$	31.4595	1.98177
$253$	−0.899610	−0.0565580
$254$	−32.8004	−2.05808
$255$	−8.72133	−0.546151
$256$	−28.1378	−1.75862
$257$	−23.9538	−1.49420	−0.747099	−	0.664713i	$-0.768554\pi$
$257$	−23.9538	−1.49420	−0.747099	+	0.664713i	$0.768554\pi$
$258$	−15.6129	−0.972016
$259$	24.5864	1.52772
$260$	−42.7357	−2.65036
$261$	20.4401	1.26521
$262$	−53.3562	−3.29636
$263$	26.9296	1.66055	0.830274	−	0.557356i	$-0.188184\pi$
$263$	26.9296	1.66055	0.830274	+	0.557356i	$0.188184\pi$
$264$	−5.13748	−0.316190
$265$	−2.13397	−0.131088
$266$	−23.6126	−1.44778
$267$	−4.38335	−0.268257
$268$	54.2204	3.31204
$269$	20.9728	1.27874	0.639368	−	0.768901i	$-0.279196\pi$
$269$	20.9728	1.27874	0.639368	+	0.768901i	$0.279196\pi$
$270$	21.7466	1.32346
$271$	10.9587	0.665694	0.332847	−	0.942981i	$-0.391991\pi$
$271$	10.9587	0.665694	0.332847	+	0.942981i	$0.391991\pi$
$272$	−41.4652	−2.51420
$273$	9.11369	0.551585
$274$	−31.8085	−1.92162
$275$	−0.487621	−0.0294047
$276$	−2.71686	−0.163536
$277$	1.90354	0.114373	0.0571864	−	0.998364i	$-0.481787\pi$
$277$	1.90354	0.114373	0.0571864	+	0.998364i	$0.481787\pi$
$278$	21.9611	1.31714
$279$	3.78331	0.226501
$280$	38.7551	2.31606
$281$	−20.3148	−1.21188	−0.605938	−	0.795512i	$-0.707202\pi$
$281$	−20.3148	−1.21188	−0.605938	+	0.795512i	$0.707202\pi$
$282$	−13.9426	−0.830268
$283$	−21.9415	−1.30428	−0.652142	−	0.758097i	$-0.726129\pi$
$283$	−21.9415	−1.30428	−0.652142	+	0.758097i	$0.726129\pi$
$284$	39.8543	2.36492
$285$	−5.10721	−0.302525
$286$	12.3601	0.730866
$287$	−1.68341	−0.0993688
$288$	14.8760	0.876578
$289$	14.3557	0.844450
$290$	45.1481	2.65119
$291$	−7.08555	−0.415362
$292$	14.9562	0.875245
$293$	10.4996	0.613393	0.306697	−	0.951807i	$-0.400776\pi$
$293$	10.4996	0.613393	0.306697	+	0.951807i	$0.400776\pi$
$294$	−1.77125	−0.103301
$295$	−9.91294	−0.577154
$296$	56.1635	3.26444
$297$	−4.36087	−0.253043
$298$	12.1412	0.703322
$299$	3.64551	0.210825
$300$	−1.47264	−0.0850227
$301$	−23.6181	−1.36132
$302$	−2.55384	−0.146957
$303$	−6.77944	−0.389469
$304$	−24.2820	−1.39267
$305$	−4.73267	−0.270992
$306$	−35.2837	−2.01704
$307$	−18.3866	−1.04938	−0.524690	−	0.851293i	$-0.675819\pi$
$307$	−18.3866	−1.04938	−0.524690	+	0.851293i	$0.675819\pi$
$308$	−13.9345	−0.793991
$309$	−2.05988	−0.117183
$310$	8.35659	0.474622
$311$	−18.3769	−1.04206	−0.521028	−	0.853539i	$-0.674451\pi$
$311$	−18.3769	−1.04206	−0.521028	+	0.853539i	$0.674451\pi$
$312$	20.8187	1.17863
$313$	6.66064	0.376482	0.188241	−	0.982123i	$-0.439721\pi$
$313$	6.66064	0.376482	0.188241	+	0.982123i	$0.439721\pi$
$314$	−44.2070	−2.49474
$315$	14.8458	0.836463
$316$	−5.62910	−0.316662
$317$	3.83014	0.215122	0.107561	−	0.994198i	$-0.465696\pi$
$317$	3.83014	0.215122	0.107561	+	0.994198i	$0.465696\pi$
$318$	1.86393	0.104524
$319$	−9.05360	−0.506904
$320$	1.25410	0.0701063
$321$	12.4623	0.695576
$322$	−5.92756	−0.330330
$323$	18.3619	1.02168
$324$	20.3021	1.12789
$325$	1.97600	0.109608
$326$	14.6032	0.808794
$327$	−14.1019	−0.779837
$328$	−3.84548	−0.212331
$329$	−21.0913	−1.16280
$330$	−4.34690	−0.239289
$331$	19.4957	1.07158	0.535791	−	0.844350i	$-0.320013\pi$
$331$	19.4957	1.07158	0.535791	+	0.844350i	$0.320013\pi$
$332$	−33.7198	−1.85061
$333$	21.5143	1.17898
$334$	9.10095	0.497982
$335$	25.5866	1.39794
$336$	−15.2389	−0.831351
$337$	22.3863	1.21946	0.609729	−	0.792610i	$-0.291278\pi$
$337$	22.3863	1.21946	0.609729	+	0.792610i	$0.291278\pi$
$338$	−16.8870	−0.918533
$339$	14.1293	0.767396
$340$	−54.0360	−2.93051
$341$	−1.67576	−0.0907473
$342$	−20.6622	−1.11728
$343$	17.0579	0.921042
$344$	−53.9515	−2.90887
$345$	−1.28209	−0.0690252
$346$	−30.8505	−1.65853
$347$	7.23197	0.388233	0.194116	−	0.980979i	$-0.437816\pi$
$347$	7.23197	0.388233	0.194116	+	0.980979i	$0.437816\pi$
$348$	−27.3422	−1.46570
$349$	29.8632	1.59854	0.799271	−	0.600971i	$-0.205219\pi$
$349$	29.8632	1.59854	0.799271	+	0.600971i	$0.205219\pi$
$350$	−3.21295	−0.171740
$351$	17.6716	0.943242
$352$	−6.58909	−0.351199
$353$	−10.7817	−0.573850	−0.286925	−	0.957953i	$-0.592633\pi$
$353$	−10.7817	−0.573850	−0.286925	+	0.957953i	$0.592633\pi$
$354$	8.65856	0.460197
$355$	18.8072	0.998185
$356$	−27.1585	−1.43940
$357$	11.5236	0.609891
$358$	38.9706	2.05966
$359$	−35.7863	−1.88873	−0.944365	−	0.328900i	$-0.893322\pi$
$359$	−35.7863	−1.88873	−0.944365	+	0.328900i	$0.893322\pi$
$360$	33.9127	1.78735
$361$	−8.24727	−0.434067
$362$	−6.81837	−0.358366
$363$	−7.15673	−0.375631
$364$	56.4670	2.95967
$365$	7.05782	0.369423
$366$	4.13380	0.216077
$367$	0.419435	0.0218943	0.0109472	−	0.999940i	$-0.496515\pi$
$367$	0.419435	0.0218943	0.0109472	+	0.999940i	$0.496515\pi$
$368$	−6.09562	−0.317756
$369$	−1.47307	−0.0766850
$370$	47.5208	2.47049
$371$	2.81962	0.146388
$372$	−5.06085	−0.262393
$373$	−17.7337	−0.918214	−0.459107	−	0.888381i	$-0.651830\pi$
$373$	−17.7337	−0.918214	−0.459107	+	0.888381i	$0.651830\pi$
$374$	15.6283	0.808122
$375$	−8.48238	−0.438028
$376$	−48.1796	−2.48467
$377$	36.6880	1.88953
$378$	−28.7339	−1.47791
$379$	−23.7837	−1.22169	−0.610843	−	0.791752i	$-0.709169\pi$
$379$	−23.7837	−1.22169	−0.610843	+	0.791752i	$0.709169\pi$
$380$	−31.6435	−1.62328
$381$	9.37398	0.480244
$382$	−48.3630	−2.47446
$383$	−18.4771	−0.944136	−0.472068	−	0.881562i	$-0.656492\pi$
$383$	−18.4771	−0.944136	−0.472068	+	0.881562i	$0.656492\pi$
$384$	7.70556	0.393223
$385$	−6.57568	−0.335128
$386$	−66.3622	−3.37775
$387$	−20.6670	−1.05056
$388$	−43.9010	−2.22873
$389$	−1.01483	−0.0514537	−0.0257268	−	0.999669i	$-0.508190\pi$
$389$	−1.01483	−0.0514537	−0.0257268	+	0.999669i	$0.508190\pi$
$390$	17.6150	0.891971
$391$	4.60946	0.233111
$392$	−6.12069	−0.309142
$393$	15.2486	0.769190
$394$	18.2855	0.921208
$395$	−2.65637	−0.133657
$396$	−12.1934	−0.612740
$397$	35.1697	1.76512	0.882560	−	0.470201i	$-0.155818\pi$
$397$	35.1697	1.76512	0.882560	+	0.470201i	$0.155818\pi$
$398$	−27.5872	−1.38282
$399$	6.74820	0.337832
$400$	−3.30404	−0.165202
$401$	−1.01543	−0.0507083	−0.0253541	−	0.999679i	$-0.508071\pi$
$401$	−1.01543	−0.0507083	−0.0253541	+	0.999679i	$0.508071\pi$
$402$	−22.3488	−1.11466
$403$	6.79069	0.338269
$404$	−42.0043	−2.08979
$405$	9.58054	0.476061
$406$	−59.6545	−2.96060
$407$	−9.52940	−0.472355
$408$	26.3236	1.30321
$409$	−13.2334	−0.654348	−0.327174	−	0.944964i	$-0.606096\pi$
$409$	−13.2334	−0.654348	−0.327174	+	0.944964i	$0.606096\pi$
$410$	−3.25372	−0.160690
$411$	9.09050	0.448401
$412$	−12.7627	−0.628773
$413$	13.0980	0.644512
$414$	−5.18691	−0.254923
$415$	−15.9124	−0.781107
$416$	26.7011	1.30913
$417$	−6.27623	−0.307348
$418$	9.15196	0.447637
$419$	20.3812	0.995684	0.497842	−	0.867268i	$-0.334126\pi$
$419$	20.3812	0.995684	0.497842	+	0.867268i	$0.334126\pi$
$420$	−19.8588	−0.969012
$421$	27.7561	1.35275	0.676374	−	0.736558i	$-0.263550\pi$
$421$	27.7561	1.35275	0.676374	+	0.736558i	$0.263550\pi$
$422$	−21.2807	−1.03593
$423$	−18.4559	−0.897359
$424$	6.44096	0.312801
$425$	2.49849	0.121195
$426$	−16.4274	−0.795909
$427$	6.25331	0.302619
$428$	77.2143	3.73229
$429$	−3.53236	−0.170544
$430$	−45.6492	−2.20140
$431$	−23.8871	−1.15060	−0.575300	−	0.817943i	$-0.695115\pi$
$431$	−23.8871	−1.15060	−0.575300	+	0.817943i	$0.695115\pi$
$432$	−29.5486	−1.42166
$433$	2.60680	0.125275	0.0626375	−	0.998036i	$-0.480049\pi$
$433$	2.60680	0.125275	0.0626375	+	0.998036i	$0.480049\pi$
$434$	−11.0416	−0.530014
$435$	−12.9028	−0.618642
$436$	−87.3732	−4.18442
$437$	2.69930	0.129125
$438$	−6.16472	−0.294562
$439$	−5.80839	−0.277219	−0.138610	−	0.990347i	$-0.544263\pi$
$439$	−5.80839	−0.277219	−0.138610	+	0.990347i	$0.544263\pi$
$440$	−15.0211	−0.716101
$441$	−2.34463	−0.111649
$442$	−63.3310	−3.01235
$443$	−20.4494	−0.971580	−0.485790	−	0.874076i	$-0.661468\pi$
$443$	−20.4494	−0.971580	−0.485790	+	0.874076i	$0.661468\pi$
$444$	−28.7792	−1.36580
$445$	−12.8161	−0.607542
$446$	−61.4102	−2.90785
$447$	−3.46982	−0.164117
$448$	−1.65705	−0.0782883
$449$	12.6569	0.597316	0.298658	−	0.954360i	$-0.403461\pi$
$449$	12.6569	0.597316	0.298658	+	0.954360i	$0.403461\pi$
$450$	−2.81149	−0.132535
$451$	0.652472	0.0307237
$452$	87.5427	4.11766
$453$	0.729856	0.0342916
$454$	−27.8245	−1.30587
$455$	26.6467	1.24922
$456$	15.4151	0.721880
$457$	−8.77412	−0.410436	−0.205218	−	0.978716i	$-0.565790\pi$
$457$	−8.77412	−0.410436	−0.205218	+	0.978716i	$0.565790\pi$
$458$	−75.7128	−3.53782
$459$	22.3444	1.04295
$460$	−7.94360	−0.370372
$461$	1.06999	0.0498345	0.0249172	−	0.999690i	$-0.492068\pi$
$461$	1.06999	0.0498345	0.0249172	+	0.999690i	$0.492068\pi$
$462$	5.74359	0.267216
$463$	−31.2019	−1.45007	−0.725037	−	0.688710i	$-0.758177\pi$
$463$	−31.2019	−1.45007	−0.725037	+	0.688710i	$0.758177\pi$
$464$	−61.3458	−2.84791
$465$	−2.38821	−0.110751
$466$	57.8289	2.67887
$467$	6.90823	0.319675	0.159837	−	0.987143i	$-0.448903\pi$
$467$	6.90823	0.319675	0.159837	+	0.987143i	$0.448903\pi$
$468$	49.4114	2.28404
$469$	−33.8077	−1.56110
$470$	−40.7655	−1.88037
$471$	12.6338	0.582136
$472$	29.9203	1.37719
$473$	9.15409	0.420906
$474$	2.32023	0.106572
$475$	1.46312	0.0671325
$476$	71.3981	3.27253
$477$	2.46731	0.112970
$478$	43.3033	1.98065
$479$	−22.3765	−1.02241	−0.511204	−	0.859460i	$-0.670800\pi$
$479$	−22.3765	−1.02241	−0.511204	+	0.859460i	$0.670800\pi$
$480$	−9.39048	−0.428615
$481$	38.6162	1.76075
$482$	53.9683	2.45819
$483$	1.69403	0.0770810
$484$	−44.3420	−2.01554
$485$	−20.7169	−0.940704
$486$	−38.9403	−1.76637
$487$	9.68816	0.439012	0.219506	−	0.975611i	$-0.429555\pi$
$487$	9.68816	0.439012	0.219506	+	0.975611i	$0.429555\pi$
$488$	14.2847	0.646636
$489$	−4.17341	−0.188728
$490$	−5.17881	−0.233955
$491$	−43.0213	−1.94152	−0.970762	−	0.240043i	$-0.922838\pi$
$491$	−43.0213	−1.94152	−0.970762	+	0.240043i	$0.922838\pi$
$492$	1.97049	0.0888367
$493$	46.3892	2.08926
$494$	−37.0867	−1.66861
$495$	−5.75405	−0.258625
$496$	−11.3547	−0.509839
$497$	−24.8501	−1.11468
$498$	13.8988	0.622820
$499$	13.4548	0.602319	0.301160	−	0.953574i	$-0.402626\pi$
$499$	13.4548	0.602319	0.301160	+	0.953574i	$0.402626\pi$
$500$	−52.5555	−2.35035
$501$	−2.60095	−0.116202
$502$	52.9043	2.36123
$503$	−29.8700	−1.33184	−0.665918	−	0.746025i	$-0.731960\pi$
$503$	−29.8700	−1.33184	−0.665918	+	0.746025i	$0.731960\pi$
$504$	−44.8090	−1.99595
$505$	−19.8218	−0.882060
$506$	2.29746	0.102134
$507$	4.82612	0.214335
$508$	58.0797	2.57687
$509$	−29.4385	−1.30484	−0.652419	−	0.757859i	$-0.726246\pi$
$509$	−29.4385	−1.30484	−0.652419	+	0.757859i	$0.726246\pi$
$510$	22.2728	0.986258
$511$	−9.32555	−0.412538
$512$	50.7441	2.24260
$513$	13.0849	0.577712
$514$	61.1741	2.69827
$515$	−6.02272	−0.265393
$516$	27.6457	1.21704
$517$	8.17476	0.359525
$518$	−62.7896	−2.75882
$519$	8.81670	0.387010
$520$	60.8701	2.66933
$521$	−5.49431	−0.240710	−0.120355	−	0.992731i	$-0.538403\pi$
$521$	−5.49431	−0.240710	−0.120355	+	0.992731i	$0.538403\pi$
$522$	−52.2006	−2.28476
$523$	9.05912	0.396127	0.198064	−	0.980189i	$-0.436535\pi$
$523$	9.05912	0.396127	0.198064	+	0.980189i	$0.436535\pi$
$524$	94.4779	4.12728
$525$	0.918224	0.0400746
$526$	−68.7737	−2.99867
$527$	8.58631	0.374025
$528$	5.90643	0.257044
$529$	−22.3224	−0.970538
$530$	5.44980	0.236724
$531$	11.4614	0.497384
$532$	41.8108	1.81273
$533$	−2.64402	−0.114525
$534$	11.1943	0.484427
$535$	36.4374	1.57533
$536$	−77.2281	−3.33575
$537$	−11.1373	−0.480612
$538$	−53.5611	−2.30918
$539$	1.03851	0.0447319
$540$	−38.5067	−1.65706
$541$	7.67049	0.329780	0.164890	−	0.986312i	$-0.447273\pi$
$541$	7.67049	0.329780	0.164890	+	0.986312i	$0.447273\pi$
$542$	−27.9867	−1.20213
$543$	1.94861	0.0836229
$544$	33.7614	1.44751
$545$	−41.2314	−1.76616
$546$	−23.2749	−0.996072
$547$	−31.9952	−1.36802	−0.684008	−	0.729475i	$-0.739764\pi$
$547$	−31.9952	−1.36802	−0.684008	+	0.729475i	$0.739764\pi$
$548$	56.3233	2.40601
$549$	5.47196	0.233538
$550$	1.24530	0.0530999
$551$	27.1655	1.15729
$552$	3.86973	0.164707
$553$	3.50988	0.149255
$554$	−4.86134	−0.206538
$555$	−13.5809	−0.576477
$556$	−38.8865	−1.64916
$557$	−26.5681	−1.12573	−0.562863	−	0.826550i	$-0.690300\pi$
$557$	−26.5681	−1.12573	−0.562863	+	0.826550i	$0.690300\pi$
$558$	−9.66196	−0.409023
$559$	−37.0953	−1.56896
$560$	−44.5558	−1.88283
$561$	−4.46640	−0.188571
$562$	51.8805	2.18845
$563$	−23.1168	−0.974256	−0.487128	−	0.873331i	$-0.661955\pi$
$563$	−23.1168	−0.974256	−0.487128	+	0.873331i	$0.661955\pi$
$564$	24.6881	1.03956
$565$	41.3114	1.73798
$566$	56.0349	2.35532
$567$	−12.6588	−0.531621
$568$	−56.7660	−2.38185
$569$	−1.69936	−0.0712409	−0.0356204	−	0.999365i	$-0.511341\pi$
$569$	−1.69936	−0.0712409	−0.0356204	+	0.999365i	$0.511341\pi$
$570$	13.0430	0.546310
$571$	−15.2525	−0.638296	−0.319148	−	0.947705i	$-0.603397\pi$
$571$	−15.2525	−0.638296	−0.319148	+	0.947705i	$0.603397\pi$
$572$	−21.8860	−0.915098
$573$	13.8216	0.577404
$574$	4.29916	0.179444
$575$	0.367293	0.0153172
$576$	−1.45000	−0.0604167
$577$	−9.06043	−0.377191	−0.188595	−	0.982055i	$-0.560393\pi$
$577$	−9.06043	−0.377191	−0.188595	+	0.982055i	$0.560393\pi$
$578$	−36.6620	−1.52494
$579$	18.9656	0.788181
$580$	−79.9437	−3.31948
$581$	21.0251	0.872269
$582$	18.0953	0.750076
$583$	−1.09285	−0.0452614
$584$	−21.3027	−0.881511
$585$	23.3172	0.964048
$586$	−26.8143	−1.10769
$587$	−21.7927	−0.899482	−0.449741	−	0.893159i	$-0.648484\pi$
$587$	−21.7927	−0.899482	−0.449741	+	0.893159i	$0.648484\pi$
$588$	3.13635	0.129341
$589$	5.02815	0.207181
$590$	25.3160	1.04224
$591$	−5.22577	−0.214959
$592$	−64.5698	−2.65380
$593$	−44.8556	−1.84200	−0.921000	−	0.389562i	$-0.872626\pi$
$593$	−44.8556	−1.84200	−0.921000	+	0.389562i	$0.872626\pi$
$594$	11.1369	0.456954
$595$	33.6927	1.38127
$596$	−21.4984	−0.880610
$597$	7.88410	0.322675
$598$	−9.31002	−0.380715
$599$	−7.71732	−0.315321	−0.157660	−	0.987493i	$-0.550395\pi$
$599$	−7.71732	−0.315321	−0.157660	+	0.987493i	$0.550395\pi$
$600$	2.09753	0.0856313
$601$	44.4377	1.81265	0.906325	−	0.422581i	$-0.138876\pi$
$601$	44.4377	1.81265	0.906325	+	0.422581i	$0.138876\pi$
$602$	60.3166	2.45832
$603$	−29.5834	−1.20473
$604$	4.52207	0.184001
$605$	−20.9250	−0.850721
$606$	17.3136	0.703316
$607$	22.9546	0.931699	0.465849	−	0.884864i	$-0.345749\pi$
$607$	22.9546	0.931699	0.465849	+	0.884864i	$0.345749\pi$
$608$	19.7707	0.801808
$609$	17.0486	0.690842
$610$	12.0865	0.489367
$611$	−33.1267	−1.34016
$612$	62.4769	2.52548
$613$	33.0754	1.33590	0.667951	−	0.744205i	$-0.267171\pi$
$613$	33.0754	1.33590	0.667951	+	0.744205i	$0.267171\pi$
$614$	46.9564	1.89501
$615$	0.929875	0.0374962
$616$	19.8474	0.799675
$617$	1.87003	0.0752847	0.0376423	−	0.999291i	$-0.488015\pi$
$617$	1.87003	0.0752847	0.0376423	+	0.999291i	$0.488015\pi$
$618$	5.26060	0.211612
$619$	15.7357	0.632472	0.316236	−	0.948680i	$-0.397581\pi$
$619$	15.7357	0.632472	0.316236	+	0.948680i	$0.397581\pi$
$620$	−14.7970	−0.594262
$621$	3.28476	0.131813
$622$	46.9315	1.88178
$623$	16.9340	0.678447
$624$	−23.9347	−0.958156
$625$	−22.5700	−0.902798
$626$	−17.0102	−0.679863
$627$	−2.61552	−0.104454
$628$	78.2772	3.12360
$629$	48.8272	1.94687
$630$	−37.9136	−1.51051
$631$	31.3859	1.24945	0.624727	−	0.780844i	$-0.285210\pi$
$631$	31.3859	1.24945	0.624727	+	0.780844i	$0.285210\pi$
$632$	8.01775	0.318929
$633$	6.08178	0.241729
$634$	−9.78154	−0.388475
$635$	27.4078	1.08765
$636$	−3.30046	−0.130872
$637$	−4.20838	−0.166742
$638$	23.1214	0.915385
$639$	−21.7451	−0.860223
$640$	22.5296	0.890562
$641$	−1.10668	−0.0437113	−0.0218556	−	0.999761i	$-0.506957\pi$
$641$	−1.10668	−0.0437113	−0.0218556	+	0.999761i	$0.506957\pi$
$642$	−31.8266	−1.25610
$643$	13.4690	0.531166	0.265583	−	0.964088i	$-0.414436\pi$
$643$	13.4690	0.531166	0.265583	+	0.964088i	$0.414436\pi$
$644$	10.4959	0.413598
$645$	13.0460	0.513686
$646$	−46.8932	−1.84499
$647$	−9.06661	−0.356445	−0.178223	−	0.983990i	$-0.557035\pi$
$647$	−9.06661	−0.356445	−0.178223	+	0.983990i	$0.557035\pi$
$648$	−28.9170	−1.13597
$649$	−5.07665	−0.199276
$650$	−5.04637	−0.197935
$651$	3.15556	0.123676
$652$	−25.8578	−1.01267
$653$	−29.7557	−1.16443	−0.582216	−	0.813034i	$-0.697814\pi$
$653$	−29.7557	−1.16443	−0.582216	+	0.813034i	$0.697814\pi$
$654$	36.0139	1.40826
$655$	44.5841	1.74204
$656$	4.42105	0.172613
$657$	−8.16031	−0.318364
$658$	53.8637	2.09983
$659$	2.36426	0.0920983	0.0460492	−	0.998939i	$-0.485337\pi$
$659$	2.36426	0.0920983	0.0460492	+	0.998939i	$0.485337\pi$
$660$	7.69706	0.299608
$661$	−32.7273	−1.27294	−0.636472	−	0.771300i	$-0.719607\pi$
$661$	−32.7273	−1.27294	−0.636472	+	0.771300i	$0.719607\pi$
$662$	−49.7889	−1.93510
$663$	18.0993	0.702917
$664$	48.0284	1.86386
$665$	19.7305	0.765115
$666$	−54.9440	−2.12904
$667$	6.81948	0.264051
$668$	−16.1150	−0.623510
$669$	17.5503	0.678534
$670$	−65.3439	−2.52446
$671$	−2.42371	−0.0935664
$672$	12.4077	0.478638
$673$	−17.5284	−0.675671	−0.337835	−	0.941205i	$-0.609695\pi$
$673$	−17.5284	−0.675671	−0.337835	+	0.941205i	$0.609695\pi$
$674$	−57.1708	−2.20214
$675$	1.78046	0.0685298
$676$	29.9019	1.15007
$677$	−21.9636	−0.844130	−0.422065	−	0.906566i	$-0.638695\pi$
$677$	−21.9636	−0.844130	−0.422065	+	0.906566i	$0.638695\pi$
$678$	−36.0838	−1.38579
$679$	27.3733	1.05049
$680$	76.9655	2.95149
$681$	7.95191	0.304718
$682$	4.27960	0.163875
$683$	16.0766	0.615154	0.307577	−	0.951523i	$-0.400482\pi$
$683$	16.0766	0.615154	0.307577	+	0.951523i	$0.400482\pi$
$684$	36.5865	1.39892
$685$	26.5789	1.01553
$686$	−43.5632	−1.66325
$687$	21.6378	0.825534
$688$	62.0267	2.36475
$689$	4.42859	0.168716
$690$	3.27424	0.124648
$691$	46.0777	1.75288	0.876439	−	0.481513i	$-0.159913\pi$
$691$	46.0777	1.75288	0.876439	+	0.481513i	$0.159913\pi$
$692$	54.6269	2.07660
$693$	7.60286	0.288809
$694$	−18.4693	−0.701084
$695$	−18.3505	−0.696076
$696$	38.9446	1.47619
$697$	−3.34317	−0.126631
$698$	−76.2657	−2.88670
$699$	−16.5268	−0.625102
$700$	5.68917	0.215031
$701$	9.81293	0.370629	0.185315	−	0.982679i	$-0.440670\pi$
$701$	9.81293	0.370629	0.185315	+	0.982679i	$0.440670\pi$
$702$	−45.1304	−1.70334
$703$	28.5932	1.07841
$704$	0.642254	0.0242059
$705$	11.6503	0.438776
$706$	27.5346	1.03628
$707$	26.1907	0.985004
$708$	−15.3317	−0.576200
$709$	−2.26986	−0.0852465	−0.0426232	−	0.999091i	$-0.513572\pi$
$709$	−2.26986	−0.0852465	−0.0426232	+	0.999091i	$0.513572\pi$
$710$	−48.0306	−1.80256
$711$	3.07132	0.115184
$712$	38.6829	1.44970
$713$	1.26224	0.0472711
$714$	−29.4293	−1.10136
$715$	−10.3280	−0.386244
$716$	−69.0053	−2.57885
$717$	−12.3756	−0.462175
$718$	91.3923	3.41073
$719$	−1.74326	−0.0650128	−0.0325064	−	0.999472i	$-0.510349\pi$
$719$	−1.74326	−0.0650128	−0.0325064	+	0.999472i	$0.510349\pi$
$720$	−38.9885	−1.45302
$721$	7.95786	0.296366
$722$	21.0622	0.783853
$723$	−15.4235	−0.573606
$724$	12.0733	0.448700
$725$	3.69640	0.137281
$726$	18.2771	0.678327
$727$	43.4349	1.61091	0.805456	−	0.592655i	$-0.201920\pi$
$727$	43.4349	1.61091	0.805456	+	0.592655i	$0.201920\pi$
$728$	−80.4280	−2.98086
$729$	−2.33996	−0.0866651
$730$	−18.0245	−0.667117
$731$	−46.9041	−1.73481
$732$	−7.31972	−0.270544
$733$	−32.8810	−1.21449	−0.607244	−	0.794515i	$-0.707725\pi$
$733$	−32.8810	−1.21449	−0.607244	+	0.794515i	$0.707725\pi$
$734$	−1.07117	−0.0395375
$735$	1.48004	0.0545922
$736$	4.96313	0.182943
$737$	13.1035	0.482673
$738$	3.76198	0.138480
$739$	−48.7941	−1.79492	−0.897460	−	0.441095i	$-0.854590\pi$
$739$	−48.7941	−1.79492	−0.897460	+	0.441095i	$0.854590\pi$
$740$	−84.1451	−3.09323
$741$	10.5989	0.389362
$742$	−7.20085	−0.264352
$743$	21.7432	0.797679	0.398840	−	0.917021i	$-0.369413\pi$
$743$	21.7432	0.797679	0.398840	+	0.917021i	$0.369413\pi$
$744$	7.20836	0.264271
$745$	−10.1451	−0.371688
$746$	45.2888	1.65814
$747$	18.3980	0.673148
$748$	−27.6731	−1.01183
$749$	−48.1450	−1.75918
$750$	21.6626	0.791006
$751$	42.1164	1.53685	0.768425	−	0.639940i	$-0.221041\pi$
$751$	42.1164	1.53685	0.768425	+	0.639940i	$0.221041\pi$
$752$	55.3909	2.01990
$753$	−15.1194	−0.550983
$754$	−93.6952	−3.41218
$755$	2.13397	0.0776630
$756$	50.8791	1.85046
$757$	−10.7465	−0.390588	−0.195294	−	0.980745i	$-0.562566\pi$
$757$	−10.7465	−0.390588	−0.195294	+	0.980745i	$0.562566\pi$
$758$	60.7396	2.20616
$759$	−0.656586	−0.0238326
$760$	45.0710	1.63490
$761$	36.2695	1.31477	0.657384	−	0.753556i	$-0.271663\pi$
$761$	36.2695	1.31477	0.657384	+	0.753556i	$0.271663\pi$
$762$	−23.9396	−0.867240
$763$	54.4793	1.97228
$764$	85.6363	3.09821
$765$	29.4828	1.06595
$766$	47.1875	1.70495
$767$	20.5722	0.742819
$768$	−20.5366	−0.741050
$769$	−22.1488	−0.798705	−0.399353	−	0.916797i	$-0.630765\pi$
$769$	−22.1488	−0.798705	−0.399353	+	0.916797i	$0.630765\pi$
$770$	16.7932	0.605185
$771$	−17.4828	−0.629629
$772$	117.508	4.22919
$773$	−14.5901	−0.524769	−0.262384	−	0.964963i	$-0.584509\pi$
$773$	−14.5901	−0.524769	−0.262384	+	0.964963i	$0.584509\pi$
$774$	52.7800	1.89714
$775$	0.684178	0.0245764
$776$	62.5298	2.24469
$777$	17.9445	0.643756
$778$	2.59170	0.0929168
$779$	−1.95776	−0.0701440
$780$	−31.1909	−1.11681
$781$	9.63163	0.344647
$782$	−11.7718	−0.420959
$783$	33.0575	1.18138
$784$	7.03680	0.251314
$785$	36.9390	1.31841
$786$	−38.9424	−1.38903
$787$	39.3555	1.40287	0.701437	−	0.712732i	$-0.252542\pi$
$787$	39.3555	1.40287	0.701437	+	0.712732i	$0.252542\pi$
$788$	−32.3781	−1.15342
$789$	19.6547	0.699726
$790$	6.78394	0.241362
$791$	−54.5850	−1.94082
$792$	17.3675	0.617126
$793$	9.82166	0.348777
$794$	−89.8177	−3.18751
$795$	−1.55749	−0.0552384
$796$	48.8486	1.73139
$797$	−33.9897	−1.20398	−0.601988	−	0.798505i	$-0.705624\pi$
$797$	−33.9897	−1.20398	−0.601988	+	0.798505i	$0.705624\pi$
$798$	−17.2338	−0.610069
$799$	−41.8862	−1.48183
$800$	2.69019	0.0951127
$801$	14.8181	0.523572
$802$	2.59325	0.0915707
$803$	3.61448	0.127552
$804$	39.5731	1.39563
$805$	4.95303	0.174571
$806$	−17.3423	−0.610857
$807$	15.3071	0.538837
$808$	59.8284	2.10476
$809$	−20.1773	−0.709396	−0.354698	−	0.934981i	$-0.615416\pi$
$809$	−20.1773	−0.709396	−0.354698	+	0.934981i	$0.615416\pi$
$810$	−24.4671	−0.859687
$811$	9.21731	0.323663	0.161832	−	0.986818i	$-0.448260\pi$
$811$	9.21731	0.323663	0.161832	+	0.986818i	$0.448260\pi$
$812$	105.630	3.70689
$813$	7.99828	0.280512
$814$	24.3365	0.852995
$815$	−12.2023	−0.427427
$816$	−30.2636	−1.05944
$817$	−27.4671	−0.960951
$818$	33.7958	1.18164
$819$	−30.8092	−1.07656
$820$	5.76136	0.201195
$821$	5.70135	0.198978	0.0994892	−	0.995039i	$-0.468279\pi$
$821$	5.70135	0.198978	0.0994892	+	0.995039i	$0.468279\pi$
$822$	−23.2156	−0.809738
$823$	24.6078	0.857774	0.428887	−	0.903358i	$-0.358906\pi$
$823$	24.6078	0.857774	0.428887	+	0.903358i	$0.358906\pi$
$824$	18.1784	0.633275
$825$	−0.355893	−0.0123906
$826$	−33.4502	−1.16388
$827$	8.66963	0.301472	0.150736	−	0.988574i	$-0.451836\pi$
$827$	8.66963	0.301472	0.150736	+	0.988574i	$0.451836\pi$
$828$	9.18446	0.319182
$829$	25.7103	0.892956	0.446478	−	0.894795i	$-0.352678\pi$
$829$	25.7103	0.892956	0.446478	+	0.894795i	$0.352678\pi$
$830$	40.6375	1.41055
$831$	1.38931	0.0481948
$832$	−2.60262	−0.0902295
$833$	−5.32118	−0.184368
$834$	16.0285	0.555020
$835$	−7.60469	−0.263171
$836$	−16.2054	−0.560475
$837$	6.11871	0.211493
$838$	−52.0501	−1.79804
$839$	7.72525	0.266705	0.133353	−	0.991069i	$-0.457426\pi$
$839$	7.72525	0.266705	0.133353	+	0.991069i	$0.457426\pi$
$840$	28.2857	0.975949
$841$	39.6306	1.36657
$842$	−70.8844	−2.44284
$843$	−14.8269	−0.510664
$844$	37.6817	1.29706
$845$	14.1107	0.485422
$846$	47.1334	1.62048
$847$	27.6483	0.950007
$848$	−7.40501	−0.254289
$849$	−16.0141	−0.549603
$850$	−6.38074	−0.218858
$851$	7.17787	0.246054
$852$	29.0879	0.996536
$853$	−44.5631	−1.52581	−0.762906	−	0.646509i	$-0.776228\pi$
$853$	−44.5631	−1.52581	−0.762906	+	0.646509i	$0.776228\pi$
$854$	−15.9699	−0.546480
$855$	17.2652	0.590456
$856$	−109.979	−3.75901
$857$	41.5158	1.41815	0.709077	−	0.705131i	$-0.249112\pi$
$857$	41.5158	1.41815	0.709077	+	0.705131i	$0.249112\pi$
$858$	9.02107	0.307974
$859$	19.1047	0.651845	0.325923	−	0.945396i	$-0.394325\pi$
$859$	19.1047	0.651845	0.325923	+	0.945396i	$0.394325\pi$
$860$	80.8310	2.75632
$861$	−1.22865	−0.0418723
$862$	61.0036	2.07779
$863$	39.1858	1.33390	0.666950	−	0.745102i	$-0.267599\pi$
$863$	39.1858	1.33390	0.666950	+	0.745102i	$0.267599\pi$
$864$	24.0588	0.818497
$865$	25.7784	0.876492
$866$	−6.65734	−0.226226
$867$	10.4776	0.355837
$868$	19.5514	0.663617
$869$	−1.36039	−0.0461481
$870$	32.9516	1.11716
$871$	−53.0995	−1.79921
$872$	124.449	4.21437
$873$	23.9530	0.810686
$874$	−6.89357	−0.233179
$875$	32.7696	1.10782
$876$	10.9159	0.368813
$877$	−39.9717	−1.34975	−0.674875	−	0.737932i	$-0.735802\pi$
$877$	−39.9717	−1.34975	−0.674875	+	0.737932i	$0.735802\pi$
$878$	14.8337	0.500612
$879$	7.66320	0.258473
$880$	17.2693	0.582149
$881$	29.7652	1.00281	0.501407	−	0.865211i	$-0.332816\pi$
$881$	29.7652	1.00281	0.501407	+	0.865211i	$0.332816\pi$
$882$	5.98779	0.201619
$883$	−4.26862	−0.143650	−0.0718252	−	0.997417i	$-0.522882\pi$
$883$	−4.26862	−0.143650	−0.0718252	+	0.997417i	$0.522882\pi$
$884$	112.140	3.77168
$885$	−7.23502	−0.243203
$886$	52.2244	1.75451
$887$	−10.1905	−0.342162	−0.171081	−	0.985257i	$-0.554726\pi$
$887$	−10.1905	−0.342162	−0.171081	+	0.985257i	$0.554726\pi$
$888$	40.9913	1.37558
$889$	−36.2141	−1.21458
$890$	32.7302	1.09712
$891$	4.90642	0.164371
$892$	108.739	3.64085
$893$	−24.5286	−0.820817
$894$	8.86134	0.296368
$895$	−32.5636	−1.08848
$896$	−29.7686	−0.994498
$897$	2.66070	0.0888381
$898$	−32.3237	−1.07865
$899$	12.7030	0.423670
$900$	4.97831	0.165944
$901$	5.59961	0.186550
$902$	−1.66631	−0.0554820
$903$	−17.2378	−0.573638
$904$	−124.690	−4.14714
$905$	5.69738	0.189387
$906$	−1.86393	−0.0619250
$907$	−2.14239	−0.0711368	−0.0355684	−	0.999367i	$-0.511324\pi$
$907$	−2.14239	−0.0711368	−0.0355684	+	0.999367i	$0.511324\pi$
$908$	49.2688	1.63504
$909$	22.9182	0.760148
$910$	−68.0514	−2.25588
$911$	−12.5564	−0.416012	−0.208006	−	0.978128i	$-0.566697\pi$
$911$	−12.5564	−0.416012	−0.208006	+	0.978128i	$0.566697\pi$
$912$	−17.7224	−0.586847
$913$	−8.14909	−0.269696
$914$	22.4076	0.741179
$915$	−3.45417	−0.114191
$916$	134.065	4.42962
$917$	−58.9092	−1.94535
$918$	−57.0639	−1.88339
$919$	2.62984	0.0867504	0.0433752	−	0.999059i	$-0.486189\pi$
$919$	2.62984	0.0867504	0.0433752	+	0.999059i	$0.486189\pi$
$920$	11.3144	0.373024
$921$	−13.4196	−0.442191
$922$	−2.73258	−0.0899928
$923$	−39.0304	−1.28470
$924$	−10.1702	−0.334574
$925$	3.89066	0.127924
$926$	79.6844	2.61859
$927$	6.96352	0.228712
$928$	49.9485	1.63964
$929$	−41.7999	−1.37141	−0.685705	−	0.727880i	$-0.740506\pi$
$929$	−41.7999	−1.37141	−0.685705	+	0.727880i	$0.740506\pi$
$930$	6.09911	0.199998
$931$	−3.11608	−0.102125
$932$	−102.398	−3.35415
$933$	−13.4125	−0.439105
$934$	−17.6425	−0.577280
$935$	−13.0589	−0.427073
$936$	−70.3785	−2.30039
$937$	10.2185	0.333823	0.166911	−	0.985972i	$-0.446621\pi$
$937$	10.2185	0.333823	0.166911	+	0.985972i	$0.446621\pi$
$938$	86.3394	2.81908
$939$	4.86131	0.158643
$940$	72.1835	2.35437
$941$	24.0777	0.784912	0.392456	−	0.919771i	$-0.371626\pi$
$941$	24.0777	0.784912	0.392456	+	0.919771i	$0.371626\pi$
$942$	−32.2647	−1.05124
$943$	−0.491465	−0.0160043
$944$	−34.3986	−1.11958
$945$	24.0099	0.781041
$946$	−23.3780	−0.760086
$947$	16.1112	0.523543	0.261771	−	0.965130i	$-0.415693\pi$
$947$	16.1112	0.523543	0.261771	+	0.965130i	$0.415693\pi$
$948$	−4.10844	−0.133436
$949$	−14.6470	−0.475462
$950$	−3.73656	−0.121230
$951$	2.79545	0.0906487
$952$	−101.695	−3.29596
$953$	51.8519	1.67965	0.839824	−	0.542858i	$-0.182658\pi$
$953$	51.8519	1.67965	0.839824	+	0.542858i	$0.182658\pi$
$954$	−6.30110	−0.204006
$955$	40.4117	1.30769
$956$	−76.6772	−2.47992
$957$	−6.60783	−0.213601
$958$	57.1458	1.84630
$959$	−35.1189	−1.13405
$960$	0.915313	0.0295416
$961$	−28.6488	−0.924154
$962$	−98.6193	−3.17961
$963$	−42.1292	−1.35760
$964$	−95.5616	−3.07783
$965$	55.4518	1.78506
$966$	−4.32627	−0.139195
$967$	−59.9603	−1.92819	−0.964096	−	0.265553i	$-0.914446\pi$
$967$	−59.9603	−1.92819	−0.964096	+	0.265553i	$0.914446\pi$
$968$	63.1580	2.02997
$969$	13.4015	0.430519
$970$	52.9074	1.69876
$971$	41.8943	1.34445	0.672227	−	0.740345i	$-0.265338\pi$
$971$	41.8943	1.34445	0.672227	+	0.740345i	$0.265338\pi$
$972$	68.9516	2.21162
$973$	24.2467	0.777313
$974$	−24.7420	−0.792783
$975$	1.44219	0.0461871
$976$	−16.4227	−0.525678
$977$	−42.7352	−1.36722	−0.683609	−	0.729848i	$-0.739591\pi$
$977$	−42.7352	−1.36722	−0.683609	+	0.729848i	$0.739591\pi$
$978$	10.6582	0.340812
$979$	−6.56343	−0.209768
$980$	9.17012	0.292929
$981$	47.6721	1.52205
$982$	109.869	3.50607
$983$	−24.5491	−0.782993	−0.391497	−	0.920179i	$-0.628043\pi$
$983$	−24.5491	−0.782993	−0.391497	+	0.920179i	$0.628043\pi$
$984$	−2.80665	−0.0894727
$985$	−15.2792	−0.486836
$986$	−118.470	−3.77287
$987$	−15.3936	−0.489985
$988$	65.6693	2.08922
$989$	−6.89518	−0.219254
$990$	14.6949	0.467034
$991$	−27.0581	−0.859529	−0.429765	−	0.902941i	$-0.641403\pi$
$991$	−27.0581	−0.859529	−0.429765	+	0.902941i	$0.641403\pi$
$992$	9.24510	0.293532
$993$	14.2291	0.451547
$994$	63.4632	2.01293
$995$	23.0517	0.730787
$996$	−24.6106	−0.779817
$997$	0.763959	0.0241948	0.0120974	−	0.999927i	$-0.496149\pi$
$997$	0.763959	0.0241948	0.0120974	+	0.999927i	$0.496149\pi$
$998$	−34.3613	−1.08769
$999$	34.7948	1.10086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.11	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-2.55384 q^{2} +0.729856 q^{3} +4.52207 q^{4} +2.13397 q^{5} -1.86393 q^{6} -2.81962 q^{7} -6.44096 q^{8} -2.46731 q^{9} +O(q^{10})\)	\(q-2.55384 q^{2} +0.729856 q^{3} +4.52207 q^{4} +2.13397 q^{5} -1.86393 q^{6} -2.81962 q^{7} -6.44096 q^{8} -2.46731 q^{9} -5.44980 q^{10} +1.09285 q^{11} +3.30046 q^{12} -4.42859 q^{13} +7.20085 q^{14} +1.55749 q^{15} +7.40501 q^{16} -5.59961 q^{17} +6.30110 q^{18} -3.27913 q^{19} +9.64995 q^{20} -2.05792 q^{21} -2.79097 q^{22} -0.823175 q^{23} -4.70098 q^{24} -0.446190 q^{25} +11.3099 q^{26} -3.99035 q^{27} -12.7505 q^{28} -8.28436 q^{29} -3.97757 q^{30} -1.53338 q^{31} -6.02925 q^{32} +0.797626 q^{33} +14.3005 q^{34} -6.01698 q^{35} -11.1574 q^{36} -8.71974 q^{37} +8.37437 q^{38} -3.23224 q^{39} -13.7448 q^{40} +0.597035 q^{41} +5.25559 q^{42} +8.37632 q^{43} +4.94197 q^{44} -5.26515 q^{45} +2.10225 q^{46} +7.48019 q^{47} +5.40459 q^{48} +0.950276 q^{49} +1.13950 q^{50} -4.08691 q^{51} -20.0264 q^{52} -1.00000 q^{53} +10.1907 q^{54} +2.33211 q^{55} +18.1611 q^{56} -2.39330 q^{57} +21.1569 q^{58} -4.64532 q^{59} +7.04308 q^{60} -2.21778 q^{61} +3.91599 q^{62} +6.95688 q^{63} +0.587685 q^{64} -9.45046 q^{65} -2.03701 q^{66} +11.9902 q^{67} -25.3219 q^{68} -0.600800 q^{69} +15.3664 q^{70} +8.81328 q^{71} +15.8919 q^{72} +3.30737 q^{73} +22.2688 q^{74} -0.325655 q^{75} -14.8285 q^{76} -3.08144 q^{77} +8.25460 q^{78} -1.24481 q^{79} +15.8020 q^{80} +4.48955 q^{81} -1.52473 q^{82} -7.45671 q^{83} -9.30607 q^{84} -11.9494 q^{85} -21.3917 q^{86} -6.04639 q^{87} -7.03903 q^{88} -6.00577 q^{89} +13.4463 q^{90} +12.4870 q^{91} -3.72246 q^{92} -1.11914 q^{93} -19.1032 q^{94} -6.99756 q^{95} -4.40048 q^{96} -9.70815 q^{97} -2.42685 q^{98} -2.69641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 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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