LMFDB - Embedded newform 8003.2.a.a.1.3

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:	$1$
Dimension:	$147$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.73133 q^{2} -0.575375 q^{3} +5.46014 q^{4} -2.64139 q^{5} +1.57154 q^{6} -4.90025 q^{7} -9.45076 q^{8} -2.66894 q^{9} +O(q^{10})$	\(q-2.73133 q^{2} -0.575375 q^{3} +5.46014 q^{4} -2.64139 q^{5} +1.57154 q^{6} -4.90025 q^{7} -9.45076 q^{8} -2.66894 q^{9} +7.21448 q^{10} +2.74732 q^{11} -3.14163 q^{12} -6.16960 q^{13} +13.3842 q^{14} +1.51979 q^{15} +14.8928 q^{16} -3.28520 q^{17} +7.28975 q^{18} +2.19833 q^{19} -14.4223 q^{20} +2.81948 q^{21} -7.50382 q^{22} -2.07092 q^{23} +5.43773 q^{24} +1.97692 q^{25} +16.8512 q^{26} +3.26177 q^{27} -26.7560 q^{28} +4.07087 q^{29} -4.15104 q^{30} -1.43074 q^{31} -21.7756 q^{32} -1.58074 q^{33} +8.97296 q^{34} +12.9434 q^{35} -14.5728 q^{36} -5.05574 q^{37} -6.00434 q^{38} +3.54984 q^{39} +24.9631 q^{40} -6.11421 q^{41} -7.70092 q^{42} +6.54144 q^{43} +15.0007 q^{44} +7.04971 q^{45} +5.65635 q^{46} -9.64225 q^{47} -8.56896 q^{48} +17.0124 q^{49} -5.39961 q^{50} +1.89023 q^{51} -33.6869 q^{52} +1.00000 q^{53} -8.90895 q^{54} -7.25673 q^{55} +46.3111 q^{56} -1.26486 q^{57} -11.1189 q^{58} -1.10814 q^{59} +8.29825 q^{60} -13.3539 q^{61} +3.90781 q^{62} +13.0785 q^{63} +29.6906 q^{64} +16.2963 q^{65} +4.31751 q^{66} -13.1836 q^{67} -17.9377 q^{68} +1.19155 q^{69} -35.3528 q^{70} -2.38277 q^{71} +25.2235 q^{72} -0.628182 q^{73} +13.8089 q^{74} -1.13747 q^{75} +12.0032 q^{76} -13.4625 q^{77} -9.69575 q^{78} -4.37806 q^{79} -39.3377 q^{80} +6.13009 q^{81} +16.6999 q^{82} +17.1403 q^{83} +15.3948 q^{84} +8.67749 q^{85} -17.8668 q^{86} -2.34228 q^{87} -25.9642 q^{88} -8.42942 q^{89} -19.2550 q^{90} +30.2326 q^{91} -11.3075 q^{92} +0.823211 q^{93} +26.3361 q^{94} -5.80663 q^{95} +12.5291 q^{96} +18.3412 q^{97} -46.4665 q^{98} -7.33243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) $ 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * 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 $

$2$	−2.73133	−1.93134	−0.965669	−	0.259775i	$-0.916352\pi$
$2$	−2.73133	−1.93134	−0.965669	+	0.259775i	$0.916352\pi$
$3$	−0.575375	−0.332193	−0.166097	−	0.986109i	$-0.553116\pi$
$3$	−0.575375	−0.332193	−0.166097	+	0.986109i	$0.553116\pi$
$4$	5.46014	2.73007
$5$	−2.64139	−1.18126	−0.590632	−	0.806941i	$-0.701121\pi$
$5$	−2.64139	−1.18126	−0.590632	+	0.806941i	$0.701121\pi$
$6$	1.57154	0.641577
$7$	−4.90025	−1.85212	−0.926060	−	0.377377i	$-0.876826\pi$
$7$	−4.90025	−1.85212	−0.926060	+	0.377377i	$0.876826\pi$
$8$	−9.45076	−3.34135
$9$	−2.66894	−0.889648
$10$	7.21448	2.28142
$11$	2.74732	0.828347	0.414174	−	0.910198i	$-0.364071\pi$
$11$	2.74732	0.828347	0.414174	+	0.910198i	$0.364071\pi$
$12$	−3.14163	−0.906910
$13$	−6.16960	−1.71114	−0.855570	−	0.517688i	$-0.826793\pi$
$13$	−6.16960	−1.71114	−0.855570	+	0.517688i	$0.826793\pi$
$14$	13.3842	3.57707
$15$	1.51979	0.392408
$16$	14.8928	3.72320
$17$	−3.28520	−0.796779	−0.398390	−	0.917216i	$-0.630431\pi$
$17$	−3.28520	−0.796779	−0.398390	+	0.917216i	$0.630431\pi$
$18$	7.28975	1.71821
$19$	2.19833	0.504331	0.252165	−	0.967684i	$-0.418857\pi$
$19$	2.19833	0.504331	0.252165	+	0.967684i	$0.418857\pi$
$20$	−14.4223	−3.22493
$21$	2.81948	0.615261
$22$	−7.50382	−1.59982
$23$	−2.07092	−0.431816	−0.215908	−	0.976414i	$-0.569271\pi$
$23$	−2.07092	−0.431816	−0.215908	+	0.976414i	$0.569271\pi$
$24$	5.43773	1.10997
$25$	1.97692	0.395384
$26$	16.8512	3.30479
$27$	3.26177	0.627728
$28$	−26.7560	−5.05641
$29$	4.07087	0.755942	0.377971	−	0.925817i	$-0.376622\pi$
$29$	4.07087	0.755942	0.377971	+	0.925817i	$0.376622\pi$
$30$	−4.15104	−0.757872
$31$	−1.43074	−0.256968	−0.128484	−	0.991712i	$-0.541011\pi$
$31$	−1.43074	−0.256968	−0.128484	+	0.991712i	$0.541011\pi$
$32$	−21.7756	−3.84942
$33$	−1.58074	−0.275171
$34$	8.97296	1.53885
$35$	12.9434	2.18784
$36$	−14.5728	−2.42880
$37$	−5.05574	−0.831158	−0.415579	−	0.909557i	$-0.636421\pi$
$37$	−5.05574	−0.831158	−0.415579	+	0.909557i	$0.636421\pi$
$38$	−6.00434	−0.974033
$39$	3.54984	0.568429
$40$	24.9631	3.94701
$41$	−6.11421	−0.954879	−0.477440	−	0.878665i	$-0.658435\pi$
$41$	−6.11421	−0.954879	−0.477440	+	0.878665i	$0.658435\pi$
$42$	−7.70092	−1.18828
$43$	6.54144	0.997560	0.498780	−	0.866729i	$-0.333782\pi$
$43$	6.54144	0.997560	0.498780	+	0.866729i	$0.333782\pi$
$44$	15.0007	2.26144
$45$	7.04971	1.05091
$46$	5.65635	0.833983
$47$	−9.64225	−1.40647	−0.703233	−	0.710959i	$-0.748261\pi$
$47$	−9.64225	−1.40647	−0.703233	+	0.710959i	$0.748261\pi$
$48$	−8.56896	−1.23682
$49$	17.0124	2.43035
$50$	−5.39961	−0.763620
$51$	1.89023	0.264685
$52$	−33.6869	−4.67153
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−8.90895	−1.21236
$55$	−7.25673	−0.978497
$56$	46.3111	6.18858
$57$	−1.26486	−0.167535
$58$	−11.1189	−1.45998
$59$	−1.10814	−0.144268	−0.0721340	−	0.997395i	$-0.522981\pi$
$59$	−1.10814	−0.144268	−0.0721340	+	0.997395i	$0.522981\pi$
$60$	8.29825	1.07130
$61$	−13.3539	−1.70979	−0.854893	−	0.518804i	$-0.826377\pi$
$61$	−13.3539	−1.70979	−0.854893	+	0.518804i	$0.826377\pi$
$62$	3.90781	0.496292
$63$	13.0785	1.64773
$64$	29.6906	3.71133
$65$	16.2963	2.02131
$66$	4.31751	0.531449
$67$	−13.1836	−1.61064	−0.805319	−	0.592842i	$-0.798006\pi$
$67$	−13.1836	−1.61064	−0.805319	+	0.592842i	$0.798006\pi$
$68$	−17.9377	−2.17526
$69$	1.19155	0.143446
$70$	−35.3528	−4.22546
$71$	−2.38277	−0.282783	−0.141392	−	0.989954i	$-0.545158\pi$
$71$	−2.38277	−0.282783	−0.141392	+	0.989954i	$0.545158\pi$
$72$	25.2235	2.97262
$73$	−0.628182	−0.0735232	−0.0367616	−	0.999324i	$-0.511704\pi$
$73$	−0.628182	−0.0735232	−0.0367616	+	0.999324i	$0.511704\pi$
$74$	13.8089	1.60525
$75$	−1.13747	−0.131344
$76$	12.0032	1.37686
$77$	−13.4625	−1.53420
$78$	−9.69575	−1.09783
$79$	−4.37806	−0.492570	−0.246285	−	0.969197i	$-0.579210\pi$
$79$	−4.37806	−0.492570	−0.246285	+	0.969197i	$0.579210\pi$
$80$	−39.3377	−4.39809
$81$	6.13009	0.681121
$82$	16.6999	1.84420
$83$	17.1403	1.88139	0.940695	−	0.339252i	$-0.110174\pi$
$83$	17.1403	1.88139	0.940695	+	0.339252i	$0.110174\pi$
$84$	15.3948	1.67971
$85$	8.67749	0.941206
$86$	−17.8668	−1.92663
$87$	−2.34228	−0.251119
$88$	−25.9642	−2.76780
$89$	−8.42942	−0.893516	−0.446758	−	0.894655i	$-0.647422\pi$
$89$	−8.42942	−0.893516	−0.446758	+	0.894655i	$0.647422\pi$
$90$	−19.2550	−2.02966
$91$	30.2326	3.16923
$92$	−11.3075	−1.17889
$93$	0.823211	0.0853630
$94$	26.3361	2.71636
$95$	−5.80663	−0.595748
$96$	12.5291	1.27875
$97$	18.3412	1.86226	0.931132	−	0.364684i	$-0.118823\pi$
$97$	18.3412	1.86226	0.931132	+	0.364684i	$0.118823\pi$
$98$	−46.4665	−4.69382
$99$	−7.33243	−0.736937
$100$	10.7943	1.07943
$101$	11.2876	1.12316	0.561578	−	0.827424i	$-0.310194\pi$
$101$	11.2876	1.12316	0.561578	+	0.827424i	$0.310194\pi$
$102$	−5.16282	−0.511195
$103$	−0.396992	−0.0391168	−0.0195584	−	0.999809i	$-0.506226\pi$
$103$	−0.396992	−0.0391168	−0.0195584	+	0.999809i	$0.506226\pi$
$104$	58.3074	5.71751
$105$	−7.44734	−0.726786
$106$	−2.73133	−0.265290
$107$	7.90139	0.763857	0.381928	−	0.924192i	$-0.375260\pi$
$107$	7.90139	0.763857	0.381928	+	0.924192i	$0.375260\pi$
$108$	17.8097	1.71374
$109$	17.4194	1.66847	0.834236	−	0.551408i	$-0.185909\pi$
$109$	17.4194	1.66847	0.834236	+	0.551408i	$0.185909\pi$
$110$	19.8205	1.88981
$111$	2.90895	0.276105
$112$	−72.9785	−6.89582
$113$	13.5950	1.27891	0.639456	−	0.768828i	$-0.279160\pi$
$113$	13.5950	1.27891	0.639456	+	0.768828i	$0.279160\pi$
$114$	3.45475	0.323567
$115$	5.47009	0.510089
$116$	22.2275	2.06377
$117$	16.4663	1.52231
$118$	3.02670	0.278630
$119$	16.0983	1.47573
$120$	−14.3632	−1.31117
$121$	−3.45225	−0.313841
$122$	36.4737	3.30218
$123$	3.51797	0.317204
$124$	−7.81202	−0.701540
$125$	7.98512	0.714211
$126$	−35.7216	−3.18233
$127$	3.70477	0.328745	0.164373	−	0.986398i	$-0.447440\pi$
$127$	3.70477	0.328745	0.164373	+	0.986398i	$0.447440\pi$
$128$	−37.5436	−3.31841
$129$	−3.76378	−0.331383
$130$	−44.5105	−3.90383
$131$	3.80499	0.332443	0.166222	−	0.986088i	$-0.446843\pi$
$131$	3.80499	0.332443	0.166222	+	0.986088i	$0.446843\pi$
$132$	−8.63105	−0.751236
$133$	−10.7723	−0.934081
$134$	36.0088	3.11069
$135$	−8.61559	−0.741512
$136$	31.0477	2.66232
$137$	0.853676	0.0729345	0.0364672	−	0.999335i	$-0.488390\pi$
$137$	0.853676	0.0729345	0.0364672	+	0.999335i	$0.488390\pi$
$138$	−3.25452	−0.277043
$139$	−1.85820	−0.157611	−0.0788053	−	0.996890i	$-0.525111\pi$
$139$	−1.85820	−0.157611	−0.0788053	+	0.996890i	$0.525111\pi$
$140$	70.6730	5.97296
$141$	5.54791	0.467218
$142$	6.50813	0.546150
$143$	−16.9499	−1.41742
$144$	−39.7481	−3.31234
$145$	−10.7527	−0.892967
$146$	1.71577	0.141998
$147$	−9.78853	−0.807345
$148$	−27.6050	−2.26912
$149$	19.3493	1.58515	0.792577	−	0.609772i	$-0.208739\pi$
$149$	19.3493	1.58515	0.792577	+	0.609772i	$0.208739\pi$
$150$	3.10680	0.253669
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−20.7759	−1.68514
$153$	8.76803	0.708853
$154$	36.7706	2.96306
$155$	3.77913	0.303547
$156$	19.3826	1.55185
$157$	1.22785	0.0979933	0.0489967	−	0.998799i	$-0.484398\pi$
$157$	1.22785	0.0979933	0.0489967	+	0.998799i	$0.484398\pi$
$158$	11.9579	0.951319
$159$	−0.575375	−0.0456302
$160$	57.5178	4.54718
$161$	10.1480	0.799775
$162$	−16.7433	−1.31548
$163$	13.2610	1.03868	0.519341	−	0.854567i	$-0.326177\pi$
$163$	13.2610	1.03868	0.519341	+	0.854567i	$0.326177\pi$
$164$	−33.3844	−2.60689
$165$	4.17534	0.325050
$166$	−46.8157	−3.63360
$167$	−11.4877	−0.888941	−0.444471	−	0.895793i	$-0.646608\pi$
$167$	−11.4877	−0.888941	−0.444471	+	0.895793i	$0.646608\pi$
$168$	−26.6462	−2.05580
$169$	25.0640	1.92800
$170$	−23.7011	−1.81779
$171$	−5.86721	−0.448677
$172$	35.7171	2.72341
$173$	6.92018	0.526131	0.263066	−	0.964778i	$-0.415266\pi$
$173$	6.92018	0.526131	0.263066	+	0.964778i	$0.415266\pi$
$174$	6.39753	0.484995
$175$	−9.68740	−0.732299
$176$	40.9153	3.08411
$177$	0.637598	0.0479248
$178$	23.0235	1.72568
$179$	9.09122	0.679510	0.339755	−	0.940514i	$-0.389656\pi$
$179$	9.09122	0.679510	0.339755	+	0.940514i	$0.389656\pi$
$180$	38.4924	2.86905
$181$	−21.6311	−1.60783	−0.803913	−	0.594746i	$-0.797253\pi$
$181$	−21.6311	−1.60783	−0.803913	+	0.594746i	$0.797253\pi$
$182$	−82.5750	−6.12087
$183$	7.68348	0.567979
$184$	19.5717	1.44285
$185$	13.3542	0.981817
$186$	−2.24846	−0.164865
$187$	−9.02550	−0.660010
$188$	−52.6480	−3.83975
$189$	−15.9835	−1.16263
$190$	15.8598	1.15059
$191$	24.1527	1.74762	0.873812	−	0.486263i	$-0.161640\pi$
$191$	24.1527	1.74762	0.873812	+	0.486263i	$0.161640\pi$
$192$	−17.0833	−1.23288
$193$	8.47197	0.609826	0.304913	−	0.952380i	$-0.401373\pi$
$193$	8.47197	0.609826	0.304913	+	0.952380i	$0.401373\pi$
$194$	−50.0957	−3.59666
$195$	−9.37649	−0.671464
$196$	92.8902	6.63501
$197$	19.3220	1.37664	0.688319	−	0.725408i	$-0.258349\pi$
$197$	19.3220	1.37664	0.688319	+	0.725408i	$0.258349\pi$
$198$	20.0273	1.42328
$199$	−23.5458	−1.66912	−0.834559	−	0.550918i	$-0.814278\pi$
$199$	−23.5458	−1.66912	−0.834559	+	0.550918i	$0.814278\pi$
$200$	−18.6834	−1.32112
$201$	7.58554	0.535043
$202$	−30.8301	−2.16919
$203$	−19.9483	−1.40010
$204$	10.3209	0.722607
$205$	16.1500	1.12796
$206$	1.08432	0.0755478
$207$	5.52716	0.384164
$208$	−91.8827	−6.37092
$209$	6.03950	0.417761
$210$	20.3411	1.40367
$211$	−3.87813	−0.266982	−0.133491	−	0.991050i	$-0.542619\pi$
$211$	−3.87813	−0.266982	−0.133491	+	0.991050i	$0.542619\pi$
$212$	5.46014	0.375004
$213$	1.37099	0.0939387
$214$	−21.5813	−1.47527
$215$	−17.2785	−1.17838
$216$	−30.8262	−2.09746
$217$	7.01097	0.475935
$218$	−47.5779	−3.22238
$219$	0.361441	0.0244239
$220$	−39.6227	−2.67136
$221$	20.2684	1.36340
$222$	−7.94528	−0.533252
$223$	−28.7057	−1.92227	−0.961137	−	0.276073i	$-0.910967\pi$
$223$	−28.7057	−1.92227	−0.961137	+	0.276073i	$0.910967\pi$
$224$	106.706	7.12959
$225$	−5.27629	−0.351753
$226$	−37.1324	−2.47001
$227$	−0.529984	−0.0351762	−0.0175881	−	0.999845i	$-0.505599\pi$
$227$	−0.529984	−0.0351762	−0.0175881	+	0.999845i	$0.505599\pi$
$228$	−6.90632	−0.457382
$229$	−13.3217	−0.880324	−0.440162	−	0.897918i	$-0.645079\pi$
$229$	−13.3217	−0.880324	−0.440162	+	0.897918i	$0.645079\pi$
$230$	−14.9406	−0.985154
$231$	7.74601	0.509650
$232$	−38.4728	−2.52587
$233$	1.85074	0.121246	0.0606229	−	0.998161i	$-0.480691\pi$
$233$	1.85074	0.121246	0.0606229	+	0.998161i	$0.480691\pi$
$234$	−44.9749	−2.94010
$235$	25.4689	1.66141
$236$	−6.05061	−0.393861
$237$	2.51903	0.163628
$238$	−43.9697	−2.85014
$239$	−20.9292	−1.35380	−0.676900	−	0.736075i	$-0.736677\pi$
$239$	−20.9292	−1.35380	−0.676900	+	0.736075i	$0.736677\pi$
$240$	22.6339	1.46101
$241$	−14.2265	−0.916410	−0.458205	−	0.888847i	$-0.651507\pi$
$241$	−14.2265	−0.916410	−0.458205	+	0.888847i	$0.651507\pi$
$242$	9.42921	0.606133
$243$	−13.3124	−0.853992
$244$	−72.9139	−4.66783
$245$	−44.9364	−2.87088
$246$	−9.60871	−0.612629
$247$	−13.5628	−0.862980
$248$	13.5215	0.858619
$249$	−9.86210	−0.624985
$250$	−21.8100	−1.37938
$251$	9.14000	0.576912	0.288456	−	0.957493i	$-0.406858\pi$
$251$	9.14000	0.576912	0.288456	+	0.957493i	$0.406858\pi$
$252$	71.4103	4.49843
$253$	−5.68947	−0.357694
$254$	−10.1189	−0.634918
$255$	−4.99282	−0.312662
$256$	43.1624	2.69765
$257$	3.44487	0.214885	0.107443	−	0.994211i	$-0.465734\pi$
$257$	3.44487	0.214885	0.107443	+	0.994211i	$0.465734\pi$
$258$	10.2801	0.640012
$259$	24.7744	1.53940
$260$	88.9800	5.51831
$261$	−10.8649	−0.672522
$262$	−10.3927	−0.642060
$263$	6.66960	0.411265	0.205632	−	0.978629i	$-0.434075\pi$
$263$	6.66960	0.411265	0.205632	+	0.978629i	$0.434075\pi$
$264$	14.9392	0.919443
$265$	−2.64139	−0.162259
$266$	29.4228	1.80403
$267$	4.85008	0.296820
$268$	−71.9845	−4.39715
$269$	25.6278	1.56255	0.781277	−	0.624185i	$-0.214569\pi$
$269$	25.6278	1.56255	0.781277	+	0.624185i	$0.214569\pi$
$270$	23.5320	1.43211
$271$	−6.73443	−0.409087	−0.204544	−	0.978857i	$-0.565571\pi$
$271$	−6.73443	−0.409087	−0.204544	+	0.978857i	$0.565571\pi$
$272$	−48.9260	−2.96657
$273$	−17.3951	−1.05280
$274$	−2.33167	−0.140861
$275$	5.43123	0.327515
$276$	6.50605	0.391618
$277$	20.9157	1.25670	0.628350	−	0.777931i	$-0.283731\pi$
$277$	20.9157	1.25670	0.628350	+	0.777931i	$0.283731\pi$
$278$	5.07536	0.304400
$279$	3.81856	0.228611
$280$	−122.325	−7.31034
$281$	−24.2535	−1.44684	−0.723422	−	0.690406i	$-0.757432\pi$
$281$	−24.2535	−1.44684	−0.723422	+	0.690406i	$0.757432\pi$
$282$	−15.1532	−0.902357
$283$	3.54041	0.210455	0.105228	−	0.994448i	$-0.466443\pi$
$283$	3.54041	0.210455	0.105228	+	0.994448i	$0.466443\pi$
$284$	−13.0103	−0.772018
$285$	3.34099	0.197903
$286$	46.2956	2.73751
$287$	29.9612	1.76855
$288$	58.1179	3.42463
$289$	−6.20743	−0.365143
$290$	29.3692	1.72462
$291$	−10.5531	−0.618631
$292$	−3.42996	−0.200723
$293$	−20.1457	−1.17692	−0.588462	−	0.808525i	$-0.700266\pi$
$293$	−20.1457	−1.17692	−0.588462	+	0.808525i	$0.700266\pi$
$294$	26.7357	1.55926
$295$	2.92703	0.170419
$296$	47.7805	2.77719
$297$	8.96112	0.519977
$298$	−52.8491	−3.06147
$299$	12.7767	0.738897
$300$	−6.21075	−0.358578
$301$	−32.0547	−1.84760
$302$	−2.73133	−0.157170
$303$	−6.49459	−0.373105
$304$	32.7393	1.87773
$305$	35.2727	2.01971
$306$	−23.9483	−1.36903
$307$	−2.42360	−0.138322	−0.0691611	−	0.997606i	$-0.522032\pi$
$307$	−2.42360	−0.138322	−0.0691611	+	0.997606i	$0.522032\pi$
$308$	−73.5073	−4.18847
$309$	0.228420	0.0129943
$310$	−10.3220	−0.586252
$311$	−0.550583	−0.0312207	−0.0156103	−	0.999878i	$-0.504969\pi$
$311$	−0.550583	−0.0312207	−0.0156103	+	0.999878i	$0.504969\pi$
$312$	−33.5486	−1.89932
$313$	8.66093	0.489545	0.244772	−	0.969581i	$-0.421287\pi$
$313$	8.66093	0.489545	0.244772	+	0.969581i	$0.421287\pi$
$314$	−3.35367	−0.189258
$315$	−34.5453	−1.94641
$316$	−23.9048	−1.34475
$317$	25.6891	1.44284	0.721421	−	0.692497i	$-0.243489\pi$
$317$	25.6891	1.44284	0.721421	+	0.692497i	$0.243489\pi$
$318$	1.57154	0.0881274
$319$	11.1840	0.626183
$320$	−78.4244	−4.38406
$321$	−4.54627	−0.253748
$322$	−27.7175	−1.54464
$323$	−7.22195	−0.401840
$324$	33.4711	1.85951
$325$	−12.1968	−0.676557
$326$	−36.2201	−2.00605
$327$	−10.0227	−0.554255
$328$	57.7839	3.19058
$329$	47.2494	2.60494
$330$	−11.4042	−0.627781
$331$	14.6489	0.805177	0.402588	−	0.915381i	$-0.368111\pi$
$331$	14.6489	0.805177	0.402588	+	0.915381i	$0.368111\pi$
$332$	93.5883	5.13633
$333$	13.4935	0.739438
$334$	31.3765	1.71685
$335$	34.8231	1.90259
$336$	41.9900	2.29074
$337$	16.9165	0.921502	0.460751	−	0.887530i	$-0.347580\pi$
$337$	16.9165	0.921502	0.460751	+	0.887530i	$0.347580\pi$
$338$	−68.4578	−3.72362
$339$	−7.82224	−0.424846
$340$	47.3803	2.56956
$341$	−3.93069	−0.212859
$342$	16.0253	0.866546
$343$	−49.0634	−2.64917
$344$	−61.8216	−3.33319
$345$	−3.14736	−0.169448
$346$	−18.9012	−1.01614
$347$	−1.46951	−0.0788876	−0.0394438	−	0.999222i	$-0.512559\pi$
$347$	−1.46951	−0.0788876	−0.0394438	+	0.999222i	$0.512559\pi$
$348$	−12.7892	−0.685571
$349$	−21.6115	−1.15683	−0.578417	−	0.815741i	$-0.696329\pi$
$349$	−21.6115	−1.15683	−0.578417	+	0.815741i	$0.696329\pi$
$350$	26.4594	1.41432
$351$	−20.1238	−1.07413
$352$	−59.8245	−3.18866
$353$	14.5160	0.772610	0.386305	−	0.922371i	$-0.373751\pi$
$353$	14.5160	0.772610	0.386305	+	0.922371i	$0.373751\pi$
$354$	−1.74149	−0.0925590
$355$	6.29383	0.334042
$356$	−46.0258	−2.43936
$357$	−9.26257	−0.490227
$358$	−24.8311	−1.31236
$359$	29.3675	1.54996	0.774978	−	0.631988i	$-0.217761\pi$
$359$	29.3675	1.54996	0.774978	+	0.631988i	$0.217761\pi$
$360$	−66.6251	−3.51145
$361$	−14.1674	−0.745651
$362$	59.0816	3.10526
$363$	1.98634	0.104256
$364$	165.074	8.65223
$365$	1.65927	0.0868503
$366$	−20.9861	−1.09696
$367$	−11.6577	−0.608528	−0.304264	−	0.952588i	$-0.598411\pi$
$367$	−11.6577	−0.608528	−0.304264	+	0.952588i	$0.598411\pi$
$368$	−30.8418	−1.60774
$369$	16.3185	0.849506
$370$	−36.4745	−1.89622
$371$	−4.90025	−0.254408
$372$	4.49484	0.233047
$373$	23.3852	1.21084	0.605420	−	0.795906i	$-0.293005\pi$
$373$	23.3852	1.21084	0.605420	+	0.795906i	$0.293005\pi$
$374$	24.6516	1.27470
$375$	−4.59444	−0.237256
$376$	91.1266	4.69949
$377$	−25.1157	−1.29352
$378$	43.6561	2.24543
$379$	6.63621	0.340879	0.170440	−	0.985368i	$-0.445481\pi$
$379$	6.63621	0.340879	0.170440	+	0.985368i	$0.445481\pi$
$380$	−31.7050	−1.62643
$381$	−2.13163	−0.109207
$382$	−65.9687	−3.37525
$383$	6.67737	0.341198	0.170599	−	0.985341i	$-0.445430\pi$
$383$	6.67737	0.341198	0.170599	+	0.985341i	$0.445430\pi$
$384$	21.6016	1.10235
$385$	35.5598	1.81229
$386$	−23.1397	−1.17778
$387$	−17.4587	−0.887477
$388$	100.145	5.08411
$389$	7.74687	0.392782	0.196391	−	0.980526i	$-0.437078\pi$
$389$	7.74687	0.392782	0.196391	+	0.980526i	$0.437078\pi$
$390$	25.6102	1.29682
$391$	6.80339	0.344062
$392$	−160.780	−8.12064
$393$	−2.18929	−0.110435
$394$	−52.7748	−2.65875
$395$	11.5641	0.581855
$396$	−40.0361	−2.01189
$397$	−33.3661	−1.67459	−0.837297	−	0.546748i	$-0.815866\pi$
$397$	−33.3661	−1.67459	−0.837297	+	0.546748i	$0.815866\pi$
$398$	64.3113	3.22363
$399$	6.19814	0.310295
$400$	29.4419	1.47210
$401$	−17.2391	−0.860881	−0.430440	−	0.902619i	$-0.641642\pi$
$401$	−17.2391	−0.860881	−0.430440	+	0.902619i	$0.641642\pi$
$402$	−20.7186	−1.03335
$403$	8.82707	0.439708
$404$	61.6317	3.06629
$405$	−16.1919	−0.804583
$406$	54.4853	2.70406
$407$	−13.8897	−0.688487
$408$	−17.8641	−0.884403
$409$	−14.7656	−0.730113	−0.365057	−	0.930985i	$-0.618950\pi$
$409$	−14.7656	−0.730113	−0.365057	+	0.930985i	$0.618950\pi$
$410$	−44.1109	−2.17848
$411$	−0.491184	−0.0242283
$412$	−2.16763	−0.106792
$413$	5.43018	0.267202
$414$	−15.0965	−0.741951
$415$	−45.2741	−2.22242
$416$	134.347	6.58690
$417$	1.06916	0.0523572
$418$	−16.4958	−0.806838
$419$	−14.8595	−0.725933	−0.362966	−	0.931802i	$-0.618236\pi$
$419$	−14.8595	−0.725933	−0.362966	+	0.931802i	$0.618236\pi$
$420$	−40.6635	−1.98418
$421$	−4.20461	−0.204920	−0.102460	−	0.994737i	$-0.532671\pi$
$421$	−4.20461	−0.204920	−0.102460	+	0.994737i	$0.532671\pi$
$422$	10.5924	0.515632
$423$	25.7346	1.25126
$424$	−9.45076	−0.458969
$425$	−6.49459	−0.315034
$426$	−3.74462	−0.181427
$427$	65.4372	3.16673
$428$	43.1427	2.08538
$429$	9.75252	0.470856
$430$	47.1931	2.27585
$431$	7.31631	0.352414	0.176207	−	0.984353i	$-0.443617\pi$
$431$	7.31631	0.352414	0.176207	+	0.984353i	$0.443617\pi$
$432$	48.5769	2.33716
$433$	−23.9853	−1.15266	−0.576331	−	0.817217i	$-0.695516\pi$
$433$	−23.9853	−1.15266	−0.576331	+	0.817217i	$0.695516\pi$
$434$	−19.1492	−0.919192
$435$	6.18686	0.296637
$436$	95.1121	4.55504
$437$	−4.55255	−0.217778
$438$	−0.987212	−0.0471708
$439$	27.6800	1.32109	0.660547	−	0.750784i	$-0.270324\pi$
$439$	27.6800	1.32109	0.660547	+	0.750784i	$0.270324\pi$
$440$	68.5816	3.26950
$441$	−45.4052	−2.16215
$442$	−55.3596	−2.63319
$443$	−2.10595	−0.100057	−0.0500285	−	0.998748i	$-0.515931\pi$
$443$	−2.10595	−0.100057	−0.0500285	+	0.998748i	$0.515931\pi$
$444$	15.8832	0.753785
$445$	22.2653	1.05548
$446$	78.4045	3.71256
$447$	−11.1331	−0.526577
$448$	−145.492	−6.87383
$449$	−38.9864	−1.83988	−0.919942	−	0.392056i	$-0.871764\pi$
$449$	−38.9864	−1.83988	−0.919942	+	0.392056i	$0.871764\pi$
$450$	14.4113	0.679353
$451$	−16.7977	−0.790972
$452$	74.2307	3.49152
$453$	−0.575375	−0.0270335
$454$	1.44756	0.0679372
$455$	−79.8559	−3.74370
$456$	11.9539	0.559793
$457$	10.8714	0.508540	0.254270	−	0.967133i	$-0.418165\pi$
$457$	10.8714	0.508540	0.254270	+	0.967133i	$0.418165\pi$
$458$	36.3859	1.70020
$459$	−10.7156	−0.500161
$460$	29.8674	1.39258
$461$	−23.5542	−1.09703	−0.548514	−	0.836141i	$-0.684806\pi$
$461$	−23.5542	−1.09703	−0.548514	+	0.836141i	$0.684806\pi$
$462$	−21.1569	−0.984307
$463$	−13.6452	−0.634146	−0.317073	−	0.948401i	$-0.602700\pi$
$463$	−13.6452	−0.634146	−0.317073	+	0.948401i	$0.602700\pi$
$464$	60.6268	2.81453
$465$	−2.17442	−0.100836
$466$	−5.05496	−0.234167
$467$	−8.37456	−0.387528	−0.193764	−	0.981048i	$-0.562070\pi$
$467$	−8.37456	−0.387528	−0.193764	+	0.981048i	$0.562070\pi$
$468$	89.9083	4.15601
$469$	64.6031	2.98309
$470$	−69.5639	−3.20874
$471$	−0.706476	−0.0325527
$472$	10.4728	0.482049
$473$	17.9714	0.826326
$474$	−6.88028	−0.316022
$475$	4.34592	0.199404
$476$	87.8990	4.02885
$477$	−2.66894	−0.122203
$478$	57.1646	2.61465
$479$	−23.1887	−1.05952	−0.529760	−	0.848147i	$-0.677718\pi$
$479$	−23.1887	−1.05952	−0.529760	+	0.848147i	$0.677718\pi$
$480$	−33.0943	−1.51054
$481$	31.1919	1.42223
$482$	38.8572	1.76990
$483$	−5.83891	−0.265680
$484$	−18.8497	−0.856806
$485$	−48.4461	−2.19982
$486$	36.3605	1.64935
$487$	−18.0318	−0.817101	−0.408550	−	0.912736i	$-0.633966\pi$
$487$	−18.0318	−0.817101	−0.408550	+	0.912736i	$0.633966\pi$
$488$	126.204	5.71299
$489$	−7.63005	−0.345043
$490$	122.736	5.54464
$491$	34.8994	1.57499	0.787494	−	0.616322i	$-0.211378\pi$
$491$	34.8994	1.57499	0.787494	+	0.616322i	$0.211378\pi$
$492$	19.2086	0.865990
$493$	−13.3737	−0.602319
$494$	37.0444	1.66671
$495$	19.3678	0.870517
$496$	−21.3077	−0.956744
$497$	11.6762	0.523749
$498$	26.9366	1.20706
$499$	−16.1475	−0.722859	−0.361430	−	0.932399i	$-0.617711\pi$
$499$	−16.1475	−0.722859	−0.361430	+	0.932399i	$0.617711\pi$
$500$	43.5998	1.94984
$501$	6.60971	0.295300
$502$	−24.9643	−1.11421
$503$	−17.5941	−0.784481	−0.392240	−	0.919863i	$-0.628300\pi$
$503$	−17.5941	−0.784481	−0.392240	+	0.919863i	$0.628300\pi$
$504$	−123.602	−5.50565
$505$	−29.8149	−1.32674
$506$	15.5398	0.690828
$507$	−14.4212	−0.640467
$508$	20.2285	0.897497
$509$	27.9151	1.23731	0.618657	−	0.785662i	$-0.287677\pi$
$509$	27.9151	1.23731	0.618657	+	0.785662i	$0.287677\pi$
$510$	13.6370	0.603857
$511$	3.07825	0.136174
$512$	−42.8034	−1.89166
$513$	7.17043	0.316582
$514$	−9.40906	−0.415016
$515$	1.04861	0.0462073
$516$	−20.5508	−0.904697
$517$	−26.4903	−1.16504
$518$	−67.6668	−2.97311
$519$	−3.98170	−0.174777
$520$	−154.012	−6.75389
$521$	−7.07207	−0.309833	−0.154916	−	0.987928i	$-0.549511\pi$
$521$	−7.07207	−0.309833	−0.154916	+	0.987928i	$0.549511\pi$
$522$	29.6757	1.29887
$523$	24.1616	1.05651	0.528257	−	0.849084i	$-0.322846\pi$
$523$	24.1616	1.05651	0.528257	+	0.849084i	$0.322846\pi$
$524$	20.7757	0.907592
$525$	5.57389	0.243265
$526$	−18.2168	−0.794292
$527$	4.70026	0.204747
$528$	−23.5417	−1.02452
$529$	−18.7113	−0.813535
$530$	7.21448	0.313377
$531$	2.95757	0.128348
$532$	−58.8185	−2.55010
$533$	37.7222	1.63393
$534$	−13.2471	−0.573260
$535$	−20.8706	−0.902316
$536$	124.595	5.38170
$537$	−5.23086	−0.225728
$538$	−69.9978	−3.01782
$539$	46.7386	2.01317
$540$	−47.0423	−2.02438
$541$	−18.5530	−0.797657	−0.398829	−	0.917025i	$-0.630583\pi$
$541$	−18.5530	−0.797657	−0.398829	+	0.917025i	$0.630583\pi$
$542$	18.3939	0.790086
$543$	12.4460	0.534109
$544$	71.5374	3.06714
$545$	−46.0112	−1.97091
$546$	47.5116	2.03331
$547$	−15.0943	−0.645385	−0.322692	−	0.946504i	$-0.604588\pi$
$547$	−15.0943	−0.645385	−0.322692	+	0.946504i	$0.604588\pi$
$548$	4.66119	0.199116
$549$	35.6407	1.52111
$550$	−14.8344	−0.632543
$551$	8.94911	0.381245
$552$	−11.2611	−0.479304
$553$	21.4536	0.912298
$554$	−57.1275	−2.42711
$555$	−7.68365	−0.326153
$556$	−10.1460	−0.430288
$557$	31.1494	1.31984	0.659921	−	0.751335i	$-0.270590\pi$
$557$	31.1494	1.31984	0.659921	+	0.751335i	$0.270590\pi$
$558$	−10.4297	−0.441525
$559$	−40.3581	−1.70696
$560$	192.764	8.14578
$561$	5.19305	0.219251
$562$	66.2443	2.79435
$563$	−12.1573	−0.512367	−0.256184	−	0.966628i	$-0.582465\pi$
$563$	−12.1573	−0.512367	−0.256184	+	0.966628i	$0.582465\pi$
$564$	30.2924	1.27554
$565$	−35.9097	−1.51073
$566$	−9.67000	−0.406460
$567$	−30.0390	−1.26152
$568$	22.5190	0.944877
$569$	−4.48897	−0.188187	−0.0940937	−	0.995563i	$-0.529995\pi$
$569$	−4.48897	−0.188187	−0.0940937	+	0.995563i	$0.529995\pi$
$570$	−9.12533	−0.382218
$571$	−24.4695	−1.02402	−0.512009	−	0.858980i	$-0.671099\pi$
$571$	−24.4695	−1.02402	−0.512009	+	0.858980i	$0.671099\pi$
$572$	−92.5485	−3.86965
$573$	−13.8968	−0.580549
$574$	−81.8337	−3.41567
$575$	−4.09404	−0.170733
$576$	−79.2426	−3.30178
$577$	36.4216	1.51625	0.758126	−	0.652108i	$-0.226115\pi$
$577$	36.4216	1.51625	0.758126	+	0.652108i	$0.226115\pi$
$578$	16.9545	0.705214
$579$	−4.87456	−0.202580
$580$	−58.7115	−2.43786
$581$	−83.9917	−3.48456
$582$	28.8238	1.19479
$583$	2.74732	0.113782
$584$	5.93680	0.245667
$585$	−43.4939	−1.79825
$586$	55.0244	2.27304
$587$	−3.84720	−0.158791	−0.0793955	−	0.996843i	$-0.525299\pi$
$587$	−3.84720	−0.158791	−0.0793955	+	0.996843i	$0.525299\pi$
$588$	−53.4467	−2.20411
$589$	−3.14523	−0.129597
$590$	−7.99468	−0.329136
$591$	−11.1174	−0.457310
$592$	−75.2942	−3.09457
$593$	4.26454	0.175124	0.0875619	−	0.996159i	$-0.472092\pi$
$593$	4.26454	0.175124	0.0875619	+	0.996159i	$0.472092\pi$
$594$	−24.4757	−1.00425
$595$	−42.5219	−1.74323
$596$	105.650	4.32758
$597$	13.5477	0.554470
$598$	−34.8974	−1.42706
$599$	−13.2976	−0.543327	−0.271664	−	0.962392i	$-0.587574\pi$
$599$	−13.2976	−0.543327	−0.271664	+	0.962392i	$0.587574\pi$
$600$	10.7500	0.438865
$601$	29.8511	1.21765	0.608825	−	0.793305i	$-0.291641\pi$
$601$	29.8511	1.21765	0.608825	+	0.793305i	$0.291641\pi$
$602$	87.5517	3.56834
$603$	35.1864	1.43290
$604$	5.46014	0.222170
$605$	9.11872	0.370729
$606$	17.7388	0.720592
$607$	−40.9061	−1.66033	−0.830164	−	0.557519i	$-0.811753\pi$
$607$	−40.9061	−1.66033	−0.830164	+	0.557519i	$0.811753\pi$
$608$	−47.8699	−1.94138
$609$	11.4778	0.465102
$610$	−96.3412	−3.90074
$611$	59.4888	2.40666
$612$	47.8746	1.93522
$613$	−15.8282	−0.639294	−0.319647	−	0.947537i	$-0.603564\pi$
$613$	−15.8282	−0.639294	−0.319647	+	0.947537i	$0.603564\pi$
$614$	6.61964	0.267147
$615$	−9.29231	−0.374702
$616$	127.231	5.12629
$617$	−14.4552	−0.581944	−0.290972	−	0.956732i	$-0.593979\pi$
$617$	−14.4552	−0.581944	−0.290972	+	0.956732i	$0.593979\pi$
$618$	−0.623888	−0.0250965
$619$	38.6790	1.55464	0.777321	−	0.629104i	$-0.216578\pi$
$619$	38.6790	1.55464	0.777321	+	0.629104i	$0.216578\pi$
$620$	20.6346	0.828704
$621$	−6.75486	−0.271063
$622$	1.50382	0.0602977
$623$	41.3062	1.65490
$624$	52.8671	2.11638
$625$	−30.9764	−1.23906
$626$	−23.6558	−0.945477
$627$	−3.47498	−0.138777
$628$	6.70424	0.267528
$629$	16.6091	0.662249
$630$	94.3545	3.75917
$631$	−32.4603	−1.29222	−0.646112	−	0.763243i	$-0.723606\pi$
$631$	−32.4603	−1.29222	−0.646112	+	0.763243i	$0.723606\pi$
$632$	41.3760	1.64585
$633$	2.23138	0.0886894
$634$	−70.1652	−2.78662
$635$	−9.78572	−0.388335
$636$	−3.14163	−0.124574
$637$	−104.960	−4.15866
$638$	−30.5471	−1.20937
$639$	6.35949	0.251578
$640$	99.1671	3.91992
$641$	28.4310	1.12296	0.561478	−	0.827492i	$-0.310233\pi$
$641$	28.4310	1.12296	0.561478	+	0.827492i	$0.310233\pi$
$642$	12.4173	0.490073
$643$	39.3640	1.55237	0.776183	−	0.630508i	$-0.217153\pi$
$643$	39.3640	1.55237	0.776183	+	0.630508i	$0.217153\pi$
$644$	55.4095	2.18344
$645$	9.94160	0.391450
$646$	19.7255	0.776089
$647$	18.5602	0.729679	0.364839	−	0.931070i	$-0.381124\pi$
$647$	18.5602	0.729679	0.364839	+	0.931070i	$0.381124\pi$
$648$	−57.9340	−2.27586
$649$	−3.04442	−0.119504
$650$	33.3134	1.30666
$651$	−4.03394	−0.158102
$652$	72.4069	2.83567
$653$	36.0884	1.41225	0.706124	−	0.708088i	$-0.250442\pi$
$653$	36.0884	1.41225	0.706124	+	0.708088i	$0.250442\pi$
$654$	27.3752	1.07045
$655$	−10.0504	−0.392703
$656$	−91.0578	−3.55521
$657$	1.67658	0.0654098
$658$	−129.054	−5.03103
$659$	−43.8411	−1.70781	−0.853904	−	0.520430i	$-0.825772\pi$
$659$	−43.8411	−1.70781	−0.853904	+	0.520430i	$0.825772\pi$
$660$	22.7979	0.887408
$661$	19.5309	0.759664	0.379832	−	0.925056i	$-0.375982\pi$
$661$	19.5309	0.759664	0.379832	+	0.925056i	$0.375982\pi$
$662$	−40.0109	−1.55507
$663$	−11.6619	−0.452912
$664$	−161.989	−6.28638
$665$	28.4539	1.10340
$666$	−36.8551	−1.42810
$667$	−8.43044	−0.326428
$668$	−62.7242	−2.42687
$669$	16.5165	0.638566
$670$	−95.1131	−3.67454
$671$	−36.6873	−1.41630
$672$	−61.3959	−2.36840
$673$	28.5897	1.10205	0.551025	−	0.834488i	$-0.314237\pi$
$673$	28.5897	1.10205	0.551025	+	0.834488i	$0.314237\pi$
$674$	−46.2045	−1.77973
$675$	6.44826	0.248194
$676$	136.853	5.26357
$677$	−8.85121	−0.340180	−0.170090	−	0.985429i	$-0.554406\pi$
$677$	−8.85121	−0.340180	−0.170090	+	0.985429i	$0.554406\pi$
$678$	21.3651	0.820521
$679$	−89.8763	−3.44913
$680$	−82.0089	−3.14490
$681$	0.304939	0.0116853
$682$	10.7360	0.411102
$683$	−37.7590	−1.44481	−0.722404	−	0.691471i	$-0.756963\pi$
$683$	−37.7590	−1.44481	−0.722404	+	0.691471i	$0.756963\pi$
$684$	−32.0358	−1.22492
$685$	−2.25489	−0.0861549
$686$	134.008	5.11645
$687$	7.66499	0.292437
$688$	97.4205	3.71412
$689$	−6.16960	−0.235043
$690$	8.59645	0.327261
$691$	26.1824	0.996027	0.498013	−	0.867169i	$-0.334063\pi$
$691$	26.1824	0.996027	0.498013	+	0.867169i	$0.334063\pi$
$692$	37.7851	1.43637
$693$	35.9307	1.36490
$694$	4.01372	0.152359
$695$	4.90823	0.186180
$696$	22.1363	0.839075
$697$	20.0864	0.760828
$698$	59.0279	2.23424
$699$	−1.06487	−0.0402770
$700$	−52.8945	−1.99923
$701$	−2.39126	−0.0903168	−0.0451584	−	0.998980i	$-0.514379\pi$
$701$	−2.39126	−0.0903168	−0.0451584	+	0.998980i	$0.514379\pi$
$702$	54.9647	2.07451
$703$	−11.1142	−0.419178
$704$	81.5696	3.07427
$705$	−14.6542	−0.551908
$706$	−39.6480	−1.49217
$707$	−55.3119	−2.08022
$708$	3.48137	0.130838
$709$	20.7695	0.780016	0.390008	−	0.920812i	$-0.372472\pi$
$709$	20.7695	0.780016	0.390008	+	0.920812i	$0.372472\pi$
$710$	−17.1905	−0.645148
$711$	11.6848	0.438214
$712$	79.6644	2.98555
$713$	2.96294	0.110963
$714$	25.2991	0.946795
$715$	44.7711	1.67434
$716$	49.6393	1.85511
$717$	12.0422	0.449723
$718$	−80.2121	−2.99349
$719$	49.1076	1.83140	0.915702	−	0.401859i	$-0.131636\pi$
$719$	49.1076	1.83140	0.915702	+	0.401859i	$0.131636\pi$
$720$	104.990	3.91275
$721$	1.94536	0.0724490
$722$	38.6957	1.44010
$723$	8.18558	0.304425
$724$	−118.109	−4.38948
$725$	8.04779	0.298887
$726$	−5.42533	−0.201353
$727$	10.0583	0.373043	0.186522	−	0.982451i	$-0.440279\pi$
$727$	10.0583	0.373043	0.186522	+	0.982451i	$0.440279\pi$
$728$	−285.721	−10.5895
$729$	−10.7306	−0.397431
$730$	−4.53201	−0.167737
$731$	−21.4900	−0.794835
$732$	41.9529	1.55062
$733$	42.8635	1.58320	0.791599	−	0.611040i	$-0.209249\pi$
$733$	42.8635	1.58320	0.791599	+	0.611040i	$0.209249\pi$
$734$	31.8410	1.17527
$735$	25.8553	0.953687
$736$	45.0955	1.66224
$737$	−36.2196	−1.33417
$738$	−44.5711	−1.64068
$739$	26.8053	0.986049	0.493025	−	0.870015i	$-0.335891\pi$
$739$	26.8053	0.986049	0.493025	+	0.870015i	$0.335891\pi$
$740$	72.9155	2.68043
$741$	7.80370	0.286676
$742$	13.3842	0.491348
$743$	−6.29381	−0.230898	−0.115449	−	0.993313i	$-0.536831\pi$
$743$	−6.29381	−0.230898	−0.115449	+	0.993313i	$0.536831\pi$
$744$	−7.77996	−0.285227
$745$	−51.1089	−1.87249
$746$	−63.8726	−2.33854
$747$	−45.7465	−1.67378
$748$	−49.2805	−1.80187
$749$	−38.7188	−1.41475
$750$	12.5489	0.458221
$751$	−23.7239	−0.865696	−0.432848	−	0.901467i	$-0.642491\pi$
$751$	−23.7239	−0.865696	−0.432848	+	0.901467i	$0.642491\pi$
$752$	−143.600	−5.23656
$753$	−5.25893	−0.191646
$754$	68.5990	2.49823
$755$	−2.64139	−0.0961299
$756$	−87.2720	−3.17405
$757$	−18.0022	−0.654302	−0.327151	−	0.944972i	$-0.606089\pi$
$757$	−18.0022	−0.654302	−0.327151	+	0.944972i	$0.606089\pi$
$758$	−18.1256	−0.658353
$759$	3.27358	0.118823
$760$	54.8770	1.99060
$761$	31.4649	1.14060	0.570301	−	0.821436i	$-0.306827\pi$
$761$	31.4649	1.14060	0.570301	+	0.821436i	$0.306827\pi$
$762$	5.82218	0.210915
$763$	−85.3592	−3.09021
$764$	131.877	4.77113
$765$	−23.1597	−0.837342
$766$	−18.2381	−0.658968
$767$	6.83680	0.246863
$768$	−24.8346	−0.896141
$769$	13.8206	0.498385	0.249193	−	0.968454i	$-0.419835\pi$
$769$	13.8206	0.498385	0.249193	+	0.968454i	$0.419835\pi$
$770$	−97.1253	−3.50015
$771$	−1.98209	−0.0713833
$772$	46.2581	1.66487
$773$	−12.2649	−0.441138	−0.220569	−	0.975371i	$-0.570791\pi$
$773$	−12.2649	−0.441138	−0.220569	+	0.975371i	$0.570791\pi$
$774$	47.6855	1.71402
$775$	−2.82845	−0.101601
$776$	−173.338	−6.22247
$777$	−14.2546	−0.511379
$778$	−21.1592	−0.758595
$779$	−13.4410	−0.481575
$780$	−51.1969	−1.83314
$781$	−6.54624	−0.234243
$782$	−18.5823	−0.664500
$783$	13.2783	0.474526
$784$	253.363	9.04868
$785$	−3.24323	−0.115756
$786$	5.97967	0.213288
$787$	32.0594	1.14280	0.571398	−	0.820673i	$-0.306401\pi$
$787$	32.0594	1.14280	0.571398	+	0.820673i	$0.306401\pi$
$788$	105.501	3.75832
$789$	−3.83752	−0.136619
$790$	−31.5854	−1.12376
$791$	−66.6190	−2.36870
$792$	69.2971	2.46236
$793$	82.3880	2.92568
$794$	91.1335	3.23421
$795$	1.51979	0.0539013
$796$	−128.563	−4.55681
$797$	31.2883	1.10829	0.554144	−	0.832421i	$-0.313046\pi$
$797$	31.2883	1.10829	0.554144	+	0.832421i	$0.313046\pi$
$798$	−16.9291	−0.599285
$799$	31.6768	1.12064
$800$	−43.0487	−1.52200
$801$	22.4976	0.794915
$802$	47.0856	1.66265
$803$	−1.72582	−0.0609027
$804$	41.4181	1.46070
$805$	−26.8048	−0.944745
$806$	−24.1096	−0.849225
$807$	−14.7456	−0.519070
$808$	−106.676	−3.75286
$809$	5.41718	0.190458	0.0952290	−	0.995455i	$-0.469642\pi$
$809$	5.41718	0.190458	0.0952290	+	0.995455i	$0.469642\pi$
$810$	44.2254	1.55392
$811$	10.1906	0.357839	0.178919	−	0.983864i	$-0.442740\pi$
$811$	10.1906	0.357839	0.178919	+	0.983864i	$0.442740\pi$
$812$	−108.920	−3.82236
$813$	3.87482	0.135896
$814$	37.9373	1.32970
$815$	−35.0274	−1.22696
$816$	28.1508	0.985475
$817$	14.3802	0.503100
$818$	40.3297	1.41010
$819$	−80.6890	−2.81950
$820$	88.1812	3.07942
$821$	−51.7441	−1.80588	−0.902941	−	0.429765i	$-0.858596\pi$
$821$	−51.7441	−1.80588	−0.902941	+	0.429765i	$0.858596\pi$
$822$	1.34158	0.0467931
$823$	−2.69848	−0.0940629	−0.0470315	−	0.998893i	$-0.514976\pi$
$823$	−2.69848	−0.0940629	−0.0470315	+	0.998893i	$0.514976\pi$
$824$	3.75188	0.130703
$825$	−3.12499	−0.108798
$826$	−14.8316	−0.516057
$827$	10.7667	0.374394	0.187197	−	0.982322i	$-0.440060\pi$
$827$	10.7667	0.374394	0.187197	+	0.982322i	$0.440060\pi$
$828$	30.1791	1.04879
$829$	−7.38433	−0.256468	−0.128234	−	0.991744i	$-0.540931\pi$
$829$	−7.38433	−0.256468	−0.128234	+	0.991744i	$0.540931\pi$
$830$	123.658	4.29224
$831$	−12.0344	−0.417467
$832$	−183.179	−6.35060
$833$	−55.8893	−1.93645
$834$	−2.92023	−0.101119
$835$	30.3433	1.05007
$836$	32.9765	1.14052
$837$	−4.66673	−0.161306
$838$	40.5861	1.40202
$839$	−54.0406	−1.86569	−0.932845	−	0.360279i	$-0.882682\pi$
$839$	−54.0406	−1.86569	−0.932845	+	0.360279i	$0.882682\pi$
$840$	70.3830	2.42844
$841$	−12.4280	−0.428552
$842$	11.4842	0.395771
$843$	13.9549	0.480632
$844$	−21.1751	−0.728878
$845$	−66.2036	−2.27747
$846$	−70.2896	−2.41661
$847$	16.9169	0.581270
$848$	14.8928	0.511422
$849$	−2.03706	−0.0699118
$850$	17.7388	0.608437
$851$	10.4700	0.358907
$852$	7.48579	0.256459
$853$	−19.2839	−0.660269	−0.330135	−	0.943934i	$-0.607094\pi$
$853$	−19.2839	−0.660269	−0.330135	+	0.943934i	$0.607094\pi$
$854$	−178.730	−6.11603
$855$	15.4976	0.530005
$856$	−74.6742	−2.55231
$857$	25.6579	0.876458	0.438229	−	0.898863i	$-0.355606\pi$
$857$	25.6579	0.876458	0.438229	+	0.898863i	$0.355606\pi$
$858$	−26.6373	−0.909383
$859$	18.2205	0.621677	0.310838	−	0.950463i	$-0.399390\pi$
$859$	18.2205	0.621677	0.310838	+	0.950463i	$0.399390\pi$
$860$	−94.3428	−3.21706
$861$	−17.2389	−0.587500
$862$	−19.9832	−0.680631
$863$	−3.84426	−0.130860	−0.0654301	−	0.997857i	$-0.520842\pi$
$863$	−3.84426	−0.130860	−0.0654301	+	0.997857i	$0.520842\pi$
$864$	−71.0270	−2.41639
$865$	−18.2789	−0.621500
$866$	65.5117	2.22618
$867$	3.57160	0.121298
$868$	38.2808	1.29934
$869$	−12.0279	−0.408019
$870$	−16.8983	−0.572907
$871$	81.3378	2.75603
$872$	−164.626	−5.57494
$873$	−48.9515	−1.65676
$874$	12.4345	0.420603
$875$	−39.1291	−1.32280
$876$	1.97352	0.0666789
$877$	−22.4495	−0.758067	−0.379033	−	0.925383i	$-0.623743\pi$
$877$	−22.4495	−0.758067	−0.379033	+	0.925383i	$0.623743\pi$
$878$	−75.6031	−2.55148
$879$	11.5913	0.390966
$880$	−108.073	−3.64314
$881$	−47.1947	−1.59003	−0.795015	−	0.606589i	$-0.792537\pi$
$881$	−47.1947	−1.59003	−0.795015	+	0.606589i	$0.792537\pi$
$882$	124.016	4.17585
$883$	−31.3745	−1.05584	−0.527918	−	0.849296i	$-0.677027\pi$
$883$	−31.3745	−1.05584	−0.527918	+	0.849296i	$0.677027\pi$
$884$	110.668	3.72218
$885$	−1.68414	−0.0566118
$886$	5.75205	0.193244
$887$	−39.4489	−1.32456	−0.662282	−	0.749255i	$-0.730412\pi$
$887$	−39.4489	−1.32456	−0.662282	+	0.749255i	$0.730412\pi$
$888$	−27.4917	−0.922562
$889$	−18.1543	−0.608875
$890$	−60.8139	−2.03849
$891$	16.8413	0.564205
$892$	−156.737	−5.24794
$893$	−21.1968	−0.709324
$894$	30.4081	1.01700
$895$	−24.0134	−0.802680
$896$	183.973	6.14610
$897$	−7.35142	−0.245457
$898$	106.485	3.55344
$899$	−5.82435	−0.194253
$900$	−28.8093	−0.960309
$901$	−3.28520	−0.109446
$902$	45.8799	1.52763
$903$	18.4435	0.613760
$904$	−128.483	−4.27329
$905$	57.1361	1.89927
$906$	1.57154	0.0522108
$907$	13.3248	0.442444	0.221222	−	0.975224i	$-0.428996\pi$
$907$	13.3248	0.442444	0.221222	+	0.975224i	$0.428996\pi$
$908$	−2.89378	−0.0960336
$909$	−30.1259	−0.999213
$910$	218.112	7.23036
$911$	0.934055	0.0309466	0.0154733	−	0.999880i	$-0.495074\pi$
$911$	0.934055	0.0309466	0.0154733	+	0.999880i	$0.495074\pi$
$912$	−18.8374	−0.623768
$913$	47.0898	1.55845
$914$	−29.6932	−0.982164
$915$	−20.2950	−0.670933
$916$	−72.7384	−2.40334
$917$	−18.6454	−0.615724
$918$	29.2677	0.965979
$919$	42.4609	1.40065	0.700327	−	0.713822i	$-0.253037\pi$
$919$	42.4609	1.40065	0.700327	+	0.713822i	$0.253037\pi$
$920$	−51.6965	−1.70438
$921$	1.39448	0.0459497
$922$	64.3341	2.11873
$923$	14.7008	0.483882
$924$	42.2943	1.39138
$925$	−9.99479	−0.328627
$926$	37.2695	1.22475
$927$	1.05955	0.0348002
$928$	−88.6458	−2.90994
$929$	−5.17476	−0.169779	−0.0848893	−	0.996390i	$-0.527054\pi$
$929$	−5.17476	−0.169779	−0.0848893	+	0.996390i	$0.527054\pi$
$930$	5.93904	0.194749
$931$	37.3989	1.22570
$932$	10.1053	0.331009
$933$	0.316792	0.0103713
$934$	22.8736	0.748449
$935$	23.8398	0.779646
$936$	−155.619	−5.08657
$937$	−29.1477	−0.952214	−0.476107	−	0.879387i	$-0.657953\pi$
$937$	−29.1477	−0.952214	−0.476107	+	0.879387i	$0.657953\pi$
$938$	−176.452	−5.76136
$939$	−4.98329	−0.162623
$940$	139.064	4.53576
$941$	47.3813	1.54459	0.772293	−	0.635266i	$-0.219110\pi$
$941$	47.3813	1.54459	0.772293	+	0.635266i	$0.219110\pi$
$942$	1.92962	0.0628703
$943$	12.6620	0.412332
$944$	−16.5034	−0.537139
$945$	42.2185	1.37337
$946$	−49.0858	−1.59592
$947$	−15.4857	−0.503218	−0.251609	−	0.967829i	$-0.580960\pi$
$947$	−15.4857	−0.503218	−0.251609	+	0.967829i	$0.580960\pi$
$948$	13.7542	0.446716
$949$	3.87563	0.125808
$950$	−11.8701	−0.385117
$951$	−14.7809	−0.479302
$952$	−152.141	−4.93093
$953$	−3.79731	−0.123007	−0.0615035	−	0.998107i	$-0.519590\pi$
$953$	−3.79731	−0.123007	−0.0615035	+	0.998107i	$0.519590\pi$
$954$	7.28975	0.236014
$955$	−63.7965	−2.06441
$956$	−114.277	−3.69597
$957$	−6.43499	−0.208014
$958$	63.3360	2.04629
$959$	−4.18323	−0.135083
$960$	45.1235	1.45635
$961$	−28.9530	−0.933967
$962$	−85.1951	−2.74680
$963$	−21.0884	−0.679563
$964$	−77.6787	−2.50186
$965$	−22.3778	−0.720365
$966$	15.9480	0.513118
$967$	−7.55009	−0.242795	−0.121397	−	0.992604i	$-0.538738\pi$
$967$	−7.55009	−0.242795	−0.121397	+	0.992604i	$0.538738\pi$
$968$	32.6264	1.04865
$969$	4.15533	0.133489
$970$	132.322	4.24860
$971$	−44.7035	−1.43460	−0.717302	−	0.696762i	$-0.754623\pi$
$971$	−44.7035	−1.43460	−0.717302	+	0.696762i	$0.754623\pi$
$972$	−72.6876	−2.33146
$973$	9.10565	0.291914
$974$	49.2508	1.57810
$975$	7.01774	0.224748
$976$	−198.877	−6.36589
$977$	−30.5984	−0.978929	−0.489465	−	0.872023i	$-0.662808\pi$
$977$	−30.5984	−0.978929	−0.489465	+	0.872023i	$0.662808\pi$
$978$	20.8402	0.666395
$979$	−23.1583	−0.740142
$980$	−245.359	−7.83770
$981$	−46.4913	−1.48435
$982$	−95.3216	−3.04183
$983$	−12.3787	−0.394820	−0.197410	−	0.980321i	$-0.563253\pi$
$983$	−12.3787	−0.394820	−0.197410	+	0.980321i	$0.563253\pi$
$984$	−33.2474	−1.05989
$985$	−51.0370	−1.62617
$986$	36.5278	1.16328
$987$	−27.1861	−0.865345
$988$	−74.0547	−2.35599
$989$	−13.5468	−0.430762
$990$	−52.8997	−1.68126
$991$	−35.8896	−1.14007	−0.570035	−	0.821620i	$-0.693070\pi$
$991$	−35.8896	−1.14007	−0.570035	+	0.821620i	$0.693070\pi$
$992$	31.1552	0.989178
$993$	−8.42862	−0.267474
$994$	−31.8915	−1.01154
$995$	62.1936	1.97167
$996$	−53.8484	−1.70625
$997$	−3.12251	−0.0988908	−0.0494454	−	0.998777i	$-0.515745\pi$
$997$	−3.12251	−0.0988908	−0.0494454	+	0.998777i	$0.515745\pi$
$998$	44.1039	1.39609
$999$	−16.4906	−0.521741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.a.1.3	✓	147

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.a.1.3	✓	147	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)

\(f(q)\)	\(=\)	\(q-2.73133 q^{2} -0.575375 q^{3} +5.46014 q^{4} -2.64139 q^{5} +1.57154 q^{6} -4.90025 q^{7} -9.45076 q^{8} -2.66894 q^{9} +O(q^{10})\)	\(q-2.73133 q^{2} -0.575375 q^{3} +5.46014 q^{4} -2.64139 q^{5} +1.57154 q^{6} -4.90025 q^{7} -9.45076 q^{8} -2.66894 q^{9} +7.21448 q^{10} +2.74732 q^{11} -3.14163 q^{12} -6.16960 q^{13} +13.3842 q^{14} +1.51979 q^{15} +14.8928 q^{16} -3.28520 q^{17} +7.28975 q^{18} +2.19833 q^{19} -14.4223 q^{20} +2.81948 q^{21} -7.50382 q^{22} -2.07092 q^{23} +5.43773 q^{24} +1.97692 q^{25} +16.8512 q^{26} +3.26177 q^{27} -26.7560 q^{28} +4.07087 q^{29} -4.15104 q^{30} -1.43074 q^{31} -21.7756 q^{32} -1.58074 q^{33} +8.97296 q^{34} +12.9434 q^{35} -14.5728 q^{36} -5.05574 q^{37} -6.00434 q^{38} +3.54984 q^{39} +24.9631 q^{40} -6.11421 q^{41} -7.70092 q^{42} +6.54144 q^{43} +15.0007 q^{44} +7.04971 q^{45} +5.65635 q^{46} -9.64225 q^{47} -8.56896 q^{48} +17.0124 q^{49} -5.39961 q^{50} +1.89023 q^{51} -33.6869 q^{52} +1.00000 q^{53} -8.90895 q^{54} -7.25673 q^{55} +46.3111 q^{56} -1.26486 q^{57} -11.1189 q^{58} -1.10814 q^{59} +8.29825 q^{60} -13.3539 q^{61} +3.90781 q^{62} +13.0785 q^{63} +29.6906 q^{64} +16.2963 q^{65} +4.31751 q^{66} -13.1836 q^{67} -17.9377 q^{68} +1.19155 q^{69} -35.3528 q^{70} -2.38277 q^{71} +25.2235 q^{72} -0.628182 q^{73} +13.8089 q^{74} -1.13747 q^{75} +12.0032 q^{76} -13.4625 q^{77} -9.69575 q^{78} -4.37806 q^{79} -39.3377 q^{80} +6.13009 q^{81} +16.6999 q^{82} +17.1403 q^{83} +15.3948 q^{84} +8.67749 q^{85} -17.8668 q^{86} -2.34228 q^{87} -25.9642 q^{88} -8.42942 q^{89} -19.2550 q^{90} +30.2326 q^{91} -11.3075 q^{92} +0.823211 q^{93} +26.3361 q^{94} -5.80663 q^{95} +12.5291 q^{96} +18.3412 q^{97} -46.4665 q^{98} -7.33243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * q^99

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