LMFDB - Embedded newform 8033.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61493 q^{2} -1.04206 q^{3} +4.83784 q^{4} -2.72711 q^{5} +2.72492 q^{6} +4.43987 q^{7} -7.42074 q^{8} -1.91410 q^{9} +O(q^{10})$	\(q-2.61493 q^{2} -1.04206 q^{3} +4.83784 q^{4} -2.72711 q^{5} +2.72492 q^{6} +4.43987 q^{7} -7.42074 q^{8} -1.91410 q^{9} +7.13119 q^{10} +2.33651 q^{11} -5.04134 q^{12} -1.51477 q^{13} -11.6099 q^{14} +2.84183 q^{15} +9.72900 q^{16} -5.27902 q^{17} +5.00523 q^{18} +6.08649 q^{19} -13.1933 q^{20} -4.62663 q^{21} -6.10980 q^{22} +4.29935 q^{23} +7.73289 q^{24} +2.43714 q^{25} +3.96100 q^{26} +5.12081 q^{27} +21.4794 q^{28} -1.00000 q^{29} -7.43116 q^{30} +9.77895 q^{31} -10.5991 q^{32} -2.43479 q^{33} +13.8043 q^{34} -12.1080 q^{35} -9.26011 q^{36} -1.07817 q^{37} -15.9157 q^{38} +1.57848 q^{39} +20.2372 q^{40} -9.96314 q^{41} +12.0983 q^{42} +0.190384 q^{43} +11.3037 q^{44} +5.21997 q^{45} -11.2425 q^{46} +5.67345 q^{47} -10.1382 q^{48} +12.7125 q^{49} -6.37293 q^{50} +5.50108 q^{51} -7.32819 q^{52} +4.77382 q^{53} -13.3905 q^{54} -6.37192 q^{55} -32.9471 q^{56} -6.34252 q^{57} +2.61493 q^{58} +8.46656 q^{59} +13.7483 q^{60} -11.1923 q^{61} -25.5712 q^{62} -8.49836 q^{63} +8.25799 q^{64} +4.13094 q^{65} +6.36681 q^{66} +4.13277 q^{67} -25.5391 q^{68} -4.48020 q^{69} +31.6616 q^{70} -10.5197 q^{71} +14.2040 q^{72} +9.10205 q^{73} +2.81934 q^{74} -2.53965 q^{75} +29.4455 q^{76} +10.3738 q^{77} -4.12762 q^{78} -5.14311 q^{79} -26.5321 q^{80} +0.406090 q^{81} +26.0529 q^{82} -2.33227 q^{83} -22.3829 q^{84} +14.3965 q^{85} -0.497840 q^{86} +1.04206 q^{87} -17.3386 q^{88} -11.2856 q^{89} -13.6498 q^{90} -6.72537 q^{91} +20.7996 q^{92} -10.1903 q^{93} -14.8356 q^{94} -16.5985 q^{95} +11.0450 q^{96} +6.24743 q^{97} -33.2421 q^{98} -4.47232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * 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 $

$2$	−2.61493	−1.84903	−0.924516	−	0.381143i	$-0.875530\pi$
$2$	−2.61493	−1.84903	−0.924516	+	0.381143i	$0.875530\pi$
$3$	−1.04206	−0.601636	−0.300818	−	0.953682i	$-0.597260\pi$
$3$	−1.04206	−0.601636	−0.300818	+	0.953682i	$0.597260\pi$
$4$	4.83784	2.41892
$5$	−2.72711	−1.21960	−0.609801	−	0.792555i	$-0.708750\pi$
$5$	−2.72711	−1.21960	−0.609801	+	0.792555i	$0.708750\pi$
$6$	2.72492	1.11244
$7$	4.43987	1.67811	0.839057	−	0.544044i	$-0.183108\pi$
$7$	4.43987	1.67811	0.839057	+	0.544044i	$0.183108\pi$
$8$	−7.42074	−2.62363
$9$	−1.91410	−0.638034
$10$	7.13119	2.25508
$11$	2.33651	0.704484	0.352242	−	0.935909i	$-0.385419\pi$
$11$	2.33651	0.704484	0.352242	+	0.935909i	$0.385419\pi$
$12$	−5.04134	−1.45531
$13$	−1.51477	−0.420121	−0.210060	−	0.977688i	$-0.567366\pi$
$13$	−1.51477	−0.420121	−0.210060	+	0.977688i	$0.567366\pi$
$14$	−11.6099	−3.10289
$15$	2.84183	0.733756
$16$	9.72900	2.43225
$17$	−5.27902	−1.28035	−0.640176	−	0.768229i	$-0.721138\pi$
$17$	−5.27902	−1.28035	−0.640176	+	0.768229i	$0.721138\pi$
$18$	5.00523	1.17974
$19$	6.08649	1.39634	0.698168	−	0.715934i	$-0.253999\pi$
$19$	6.08649	1.39634	0.698168	+	0.715934i	$0.253999\pi$
$20$	−13.1933	−2.95012
$21$	−4.62663	−1.00961
$22$	−6.10980	−1.30261
$23$	4.29935	0.896477	0.448239	−	0.893914i	$-0.352052\pi$
$23$	4.29935	0.896477	0.448239	+	0.893914i	$0.352052\pi$
$24$	7.73289	1.57847
$25$	2.43714	0.487427
$26$	3.96100	0.776816
$27$	5.12081	0.985500
$28$	21.4794	4.05922
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−7.43116	−1.35674
$31$	9.77895	1.75635	0.878175	−	0.478339i	$-0.158761\pi$
$31$	9.77895	1.75635	0.878175	+	0.478339i	$0.158761\pi$
$32$	−10.5991	−1.87368
$33$	−2.43479	−0.423843
$34$	13.8043	2.36741
$35$	−12.1080	−2.04663
$36$	−9.26011	−1.54335
$37$	−1.07817	−0.177251	−0.0886253	−	0.996065i	$-0.528247\pi$
$37$	−1.07817	−0.177251	−0.0886253	+	0.996065i	$0.528247\pi$
$38$	−15.9157	−2.58187
$39$	1.57848	0.252760
$40$	20.2372	3.19978
$41$	−9.96314	−1.55598	−0.777990	−	0.628276i	$-0.783761\pi$
$41$	−9.96314	−1.55598	−0.777990	+	0.628276i	$0.783761\pi$
$42$	12.0983	1.86681
$43$	0.190384	0.0290333	0.0145166	−	0.999895i	$-0.495379\pi$
$43$	0.190384	0.0290333	0.0145166	+	0.999895i	$0.495379\pi$
$44$	11.3037	1.70409
$45$	5.21997	0.778147
$46$	−11.2425	−1.65761
$47$	5.67345	0.827557	0.413779	−	0.910377i	$-0.364209\pi$
$47$	5.67345	0.827557	0.413779	+	0.910377i	$0.364209\pi$
$48$	−10.1382	−1.46333
$49$	12.7125	1.81606
$50$	−6.37293	−0.901269
$51$	5.50108	0.770306
$52$	−7.32819	−1.01624
$53$	4.77382	0.655735	0.327867	−	0.944724i	$-0.393670\pi$
$53$	4.77382	0.655735	0.327867	+	0.944724i	$0.393670\pi$
$54$	−13.3905	−1.82222
$55$	−6.37192	−0.859190
$56$	−32.9471	−4.40274
$57$	−6.34252	−0.840087
$58$	2.61493	0.343357
$59$	8.46656	1.10225	0.551126	−	0.834422i	$-0.314198\pi$
$59$	8.46656	1.10225	0.551126	+	0.834422i	$0.314198\pi$
$60$	13.7483	1.77490
$61$	−11.1923	−1.43303	−0.716513	−	0.697574i	$-0.754263\pi$
$61$	−11.1923	−1.43303	−0.716513	+	0.697574i	$0.754263\pi$
$62$	−25.5712	−3.24755
$63$	−8.49836	−1.07069
$64$	8.25799	1.03225
$65$	4.13094	0.512380
$66$	6.36681	0.783700
$67$	4.13277	0.504898	0.252449	−	0.967610i	$-0.418764\pi$
$67$	4.13277	0.504898	0.252449	+	0.967610i	$0.418764\pi$
$68$	−25.5391	−3.09707
$69$	−4.48020	−0.539353
$70$	31.6616	3.78428
$71$	−10.5197	−1.24846	−0.624232	−	0.781239i	$-0.714588\pi$
$71$	−10.5197	−1.24846	−0.624232	+	0.781239i	$0.714588\pi$
$72$	14.2040	1.67396
$73$	9.10205	1.06531	0.532657	−	0.846331i	$-0.321194\pi$
$73$	9.10205	1.06531	0.532657	+	0.846331i	$0.321194\pi$
$74$	2.81934	0.327742
$75$	−2.53965	−0.293254
$76$	29.4455	3.37763
$77$	10.3738	1.18220
$78$	−4.12762	−0.467361
$79$	−5.14311	−0.578645	−0.289323	−	0.957232i	$-0.593430\pi$
$79$	−5.14311	−0.578645	−0.289323	+	0.957232i	$0.593430\pi$
$80$	−26.5321	−2.96638
$81$	0.406090	0.0451211
$82$	26.0529	2.87706
$83$	−2.33227	−0.256000	−0.128000	−	0.991774i	$-0.540856\pi$
$83$	−2.33227	−0.256000	−0.128000	+	0.991774i	$0.540856\pi$
$84$	−22.3829	−2.44217
$85$	14.3965	1.56152
$86$	−0.497840	−0.0536835
$87$	1.04206	0.111721
$88$	−17.3386	−1.84830
$89$	−11.2856	−1.19628	−0.598138	−	0.801393i	$-0.704092\pi$
$89$	−11.2856	−1.19628	−0.598138	+	0.801393i	$0.704092\pi$
$90$	−13.6498	−1.43882
$91$	−6.72537	−0.705010
$92$	20.7996	2.16851
$93$	−10.1903	−1.05668
$94$	−14.8356	−1.53018
$95$	−16.5985	−1.70297
$96$	11.0450	1.12728
$97$	6.24743	0.634331	0.317165	−	0.948370i	$-0.397269\pi$
$97$	6.24743	0.634331	0.317165	+	0.948370i	$0.397269\pi$
$98$	−33.2421	−3.35796
$99$	−4.47232	−0.449485
$100$	11.7905	1.17905
$101$	6.30208	0.627080	0.313540	−	0.949575i	$-0.398485\pi$
$101$	6.30208	0.627080	0.313540	+	0.949575i	$0.398485\pi$
$102$	−14.3849	−1.42432
$103$	3.25619	0.320842	0.160421	−	0.987049i	$-0.448715\pi$
$103$	3.25619	0.320842	0.160421	+	0.987049i	$0.448715\pi$
$104$	11.2407	1.10224
$105$	12.6173	1.23133
$106$	−12.4832	−1.21247
$107$	15.7076	1.51851	0.759254	−	0.650794i	$-0.225564\pi$
$107$	15.7076	1.51851	0.759254	+	0.650794i	$0.225564\pi$
$108$	24.7737	2.38385
$109$	4.26146	0.408174	0.204087	−	0.978953i	$-0.434577\pi$
$109$	4.26146	0.408174	0.204087	+	0.978953i	$0.434577\pi$
$110$	16.6621	1.58867
$111$	1.12353	0.106640
$112$	43.1955	4.08159
$113$	4.54823	0.427861	0.213931	−	0.976849i	$-0.431373\pi$
$113$	4.54823	0.427861	0.213931	+	0.976849i	$0.431373\pi$
$114$	16.5852	1.55335
$115$	−11.7248	−1.09334
$116$	−4.83784	−0.449182
$117$	2.89942	0.268051
$118$	−22.1394	−2.03810
$119$	−23.4382	−2.14857
$120$	−21.0884	−1.92510
$121$	−5.54072	−0.503702
$122$	29.2670	2.64971
$123$	10.3822	0.936134
$124$	47.3090	4.24847
$125$	6.98921	0.625134
$126$	22.2226	1.97975
$127$	−10.5980	−0.940418	−0.470209	−	0.882555i	$-0.655821\pi$
$127$	−10.5980	−0.940418	−0.470209	+	0.882555i	$0.655821\pi$
$128$	−0.395723	−0.0349773
$129$	−0.198392	−0.0174675
$130$	−10.8021	−0.947406
$131$	13.5609	1.18482	0.592412	−	0.805635i	$-0.298176\pi$
$131$	13.5609	1.18482	0.592412	+	0.805635i	$0.298176\pi$
$132$	−11.7791	−1.02524
$133$	27.0232	2.34321
$134$	−10.8069	−0.933573
$135$	−13.9650	−1.20192
$136$	39.1742	3.35916
$137$	20.0969	1.71699	0.858497	−	0.512819i	$-0.171399\pi$
$137$	20.0969	1.71699	0.858497	+	0.512819i	$0.171399\pi$
$138$	11.7154	0.997281
$139$	1.36550	0.115820	0.0579099	−	0.998322i	$-0.481556\pi$
$139$	1.36550	0.115820	0.0579099	+	0.998322i	$0.481556\pi$
$140$	−58.5767	−4.95063
$141$	−5.91210	−0.497889
$142$	27.5084	2.30845
$143$	−3.53927	−0.295968
$144$	−18.6223	−1.55186
$145$	2.72711	0.226474
$146$	−23.8012	−1.96980
$147$	−13.2472	−1.09261
$148$	−5.21603	−0.428755
$149$	10.9074	0.893567	0.446784	−	0.894642i	$-0.352569\pi$
$149$	10.9074	0.893567	0.446784	+	0.894642i	$0.352569\pi$
$150$	6.64101	0.542236
$151$	9.01686	0.733781	0.366891	−	0.930264i	$-0.380422\pi$
$151$	9.01686	0.733781	0.366891	+	0.930264i	$0.380422\pi$
$152$	−45.1662	−3.66347
$153$	10.1046	0.816907
$154$	−27.1267	−2.18593
$155$	−26.6683	−2.14205
$156$	7.63645	0.611405
$157$	−8.33139	−0.664917	−0.332459	−	0.943118i	$-0.607878\pi$
$157$	−8.33139	−0.664917	−0.332459	+	0.943118i	$0.607878\pi$
$158$	13.4489	1.06993
$159$	−4.97463	−0.394514
$160$	28.9051	2.28515
$161$	19.0886	1.50439
$162$	−1.06189	−0.0834303
$163$	−10.3117	−0.807674	−0.403837	−	0.914831i	$-0.632324\pi$
$163$	−10.3117	−0.807674	−0.403837	+	0.914831i	$0.632324\pi$
$164$	−48.2000	−3.76379
$165$	6.63995	0.516920
$166$	6.09871	0.473352
$167$	9.61747	0.744223	0.372111	−	0.928188i	$-0.378634\pi$
$167$	9.61747	0.744223	0.372111	+	0.928188i	$0.378634\pi$
$168$	34.3330	2.64885
$169$	−10.7055	−0.823499
$170$	−37.6457	−2.88730
$171$	−11.6502	−0.890910
$172$	0.921047	0.0702292
$173$	−4.07180	−0.309574	−0.154787	−	0.987948i	$-0.549469\pi$
$173$	−4.07180	−0.309574	−0.154787	+	0.987948i	$0.549469\pi$
$174$	−2.72492	−0.206576
$175$	10.8206	0.817958
$176$	22.7319	1.71348
$177$	−8.82270	−0.663155
$178$	29.5111	2.21195
$179$	−23.2066	−1.73455	−0.867273	−	0.497834i	$-0.834129\pi$
$179$	−23.2066	−1.73455	−0.867273	+	0.497834i	$0.834129\pi$
$180$	25.2534	1.88227
$181$	−6.38509	−0.474600	−0.237300	−	0.971436i	$-0.576262\pi$
$181$	−6.38509	−0.474600	−0.237300	+	0.971436i	$0.576262\pi$
$182$	17.5863	1.30359
$183$	11.6631	0.862160
$184$	−31.9044	−2.35202
$185$	2.94030	0.216175
$186$	26.6469	1.95384
$187$	−12.3345	−0.901987
$188$	27.4472	2.00179
$189$	22.7357	1.65378
$190$	43.4039	3.14885
$191$	−5.73069	−0.414658	−0.207329	−	0.978271i	$-0.566477\pi$
$191$	−5.73069	−0.414658	−0.207329	+	0.978271i	$0.566477\pi$
$192$	−8.60535	−0.621038
$193$	−14.8588	−1.06956	−0.534781	−	0.844991i	$-0.679606\pi$
$193$	−14.8588	−1.06956	−0.534781	+	0.844991i	$0.679606\pi$
$194$	−16.3366	−1.17290
$195$	−4.30470	−0.308266
$196$	61.5008	4.39291
$197$	−9.09782	−0.648193	−0.324096	−	0.946024i	$-0.605060\pi$
$197$	−9.09782	−0.648193	−0.324096	+	0.946024i	$0.605060\pi$
$198$	11.6948	0.831112
$199$	10.3681	0.734976	0.367488	−	0.930028i	$-0.380218\pi$
$199$	10.3681	0.734976	0.367488	+	0.930028i	$0.380218\pi$
$200$	−18.0854	−1.27883
$201$	−4.30661	−0.303765
$202$	−16.4795	−1.15949
$203$	−4.43987	−0.311618
$204$	26.6133	1.86331
$205$	27.1706	1.89768
$206$	−8.51469	−0.593247
$207$	−8.22940	−0.571983
$208$	−14.7372	−1.02184
$209$	14.2211	0.983697
$210$	−32.9934	−2.27676
$211$	−4.14945	−0.285660	−0.142830	−	0.989747i	$-0.545620\pi$
$211$	−4.14945	−0.285660	−0.142830	+	0.989747i	$0.545620\pi$
$212$	23.0950	1.58617
$213$	10.9623	0.751121
$214$	−41.0741	−2.80777
$215$	−0.519198	−0.0354090
$216$	−38.0002	−2.58559
$217$	43.4173	2.94736
$218$	−11.1434	−0.754727
$219$	−9.48492	−0.640932
$220$	−30.8263	−2.07831
$221$	7.99648	0.537902
$222$	−2.93794	−0.197181
$223$	12.6616	0.847883	0.423941	−	0.905690i	$-0.360646\pi$
$223$	12.6616	0.847883	0.423941	+	0.905690i	$0.360646\pi$
$224$	−47.0589	−3.14425
$225$	−4.66493	−0.310995
$226$	−11.8933	−0.791129
$227$	14.1844	0.941451	0.470726	−	0.882280i	$-0.343992\pi$
$227$	14.1844	0.941451	0.470726	+	0.882280i	$0.343992\pi$
$228$	−30.6841	−2.03210
$229$	−12.4519	−0.822846	−0.411423	−	0.911444i	$-0.634968\pi$
$229$	−12.4519	−0.822846	−0.411423	+	0.911444i	$0.634968\pi$
$230$	30.6595	2.02163
$231$	−10.8102	−0.711257
$232$	7.42074	0.487195
$233$	−12.7258	−0.833696	−0.416848	−	0.908976i	$-0.636865\pi$
$233$	−12.7258	−0.833696	−0.416848	+	0.908976i	$0.636865\pi$
$234$	−7.58176	−0.495635
$235$	−15.4721	−1.00929
$236$	40.9599	2.66626
$237$	5.35946	0.348134
$238$	61.2891	3.97278
$239$	9.55410	0.618003	0.309002	−	0.951061i	$-0.400005\pi$
$239$	9.55410	0.618003	0.309002	+	0.951061i	$0.400005\pi$
$240$	27.6481	1.78468
$241$	5.70876	0.367733	0.183867	−	0.982951i	$-0.441139\pi$
$241$	5.70876	0.367733	0.183867	+	0.982951i	$0.441139\pi$
$242$	14.4886	0.931361
$243$	−15.7856	−1.01265
$244$	−54.1465	−3.46637
$245$	−34.6683	−2.21487
$246$	−27.1488	−1.73094
$247$	−9.21961	−0.586630
$248$	−72.5670	−4.60801
$249$	2.43038	0.154019
$250$	−18.2763	−1.15589
$251$	−17.4355	−1.10052	−0.550261	−	0.834993i	$-0.685472\pi$
$251$	−17.4355	−1.10052	−0.550261	+	0.834993i	$0.685472\pi$
$252$	−41.1137	−2.58992
$253$	10.0455	0.631554
$254$	27.7129	1.73886
$255$	−15.0021	−0.939466
$256$	−15.4812	−0.967574
$257$	−3.34854	−0.208876	−0.104438	−	0.994531i	$-0.533304\pi$
$257$	−3.34854	−0.208876	−0.104438	+	0.994531i	$0.533304\pi$
$258$	0.518782	0.0322979
$259$	−4.78695	−0.297447
$260$	19.9848	1.23940
$261$	1.91410	0.118480
$262$	−35.4609	−2.19078
$263$	13.1785	0.812622	0.406311	−	0.913735i	$-0.366815\pi$
$263$	13.1785	0.812622	0.406311	+	0.913735i	$0.366815\pi$
$264$	18.0680	1.11201
$265$	−13.0187	−0.799735
$266$	−70.6637	−4.33267
$267$	11.7604	0.719723
$268$	19.9937	1.22131
$269$	−18.6206	−1.13532	−0.567658	−	0.823264i	$-0.692150\pi$
$269$	−18.6206	−1.13532	−0.567658	+	0.823264i	$0.692150\pi$
$270$	36.5175	2.22238
$271$	2.53660	0.154087	0.0770436	−	0.997028i	$-0.475452\pi$
$271$	2.53660	0.154087	0.0770436	+	0.997028i	$0.475452\pi$
$272$	−51.3596	−3.11414
$273$	7.00826	0.424159
$274$	−52.5519	−3.17478
$275$	5.69439	0.343385
$276$	−21.6745	−1.30465
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−3.57067	−0.214154
$279$	−18.7179	−1.12061
$280$	89.8504	5.36959
$281$	21.3691	1.27477	0.637387	−	0.770544i	$-0.280015\pi$
$281$	21.3691	1.27477	0.637387	+	0.770544i	$0.280015\pi$
$282$	15.4597	0.920612
$283$	−13.3965	−0.796340	−0.398170	−	0.917312i	$-0.630355\pi$
$283$	−13.3965	−0.796340	−0.398170	+	0.917312i	$0.630355\pi$
$284$	−50.8928	−3.01993
$285$	17.2967	1.02457
$286$	9.25492	0.547255
$287$	−44.2350	−2.61111
$288$	20.2878	1.19547
$289$	10.8681	0.639299
$290$	−7.13119	−0.418758
$291$	−6.51023	−0.381636
$292$	44.0342	2.57691
$293$	17.3923	1.01607	0.508034	−	0.861337i	$-0.330372\pi$
$293$	17.3923	1.01607	0.508034	+	0.861337i	$0.330372\pi$
$294$	34.6404	2.02027
$295$	−23.0893	−1.34431
$296$	8.00084	0.465039
$297$	11.9648	0.694270
$298$	−28.5220	−1.65223
$299$	−6.51251	−0.376628
$300$	−12.2864	−0.709358
$301$	0.845280	0.0487212
$302$	−23.5784	−1.35679
$303$	−6.56717	−0.377274
$304$	59.2155	3.39624
$305$	30.5226	1.74772
$306$	−26.4227	−1.51049
$307$	−24.2827	−1.38589	−0.692944	−	0.720991i	$-0.743687\pi$
$307$	−24.2827	−1.38589	−0.692944	+	0.720991i	$0.743687\pi$
$308$	50.1868	2.85966
$309$	−3.39316	−0.193030
$310$	69.7356	3.96071
$311$	6.58960	0.373662	0.186831	−	0.982392i	$-0.440178\pi$
$311$	6.58960	0.373662	0.186831	+	0.982392i	$0.440178\pi$
$312$	−11.7135	−0.663147
$313$	−22.2084	−1.25529	−0.627647	−	0.778498i	$-0.715982\pi$
$313$	−22.2084	−1.25529	−0.627647	+	0.778498i	$0.715982\pi$
$314$	21.7860	1.22945
$315$	23.1760	1.30582
$316$	−24.8815	−1.39970
$317$	−4.14522	−0.232819	−0.116409	−	0.993201i	$-0.537138\pi$
$317$	−4.14522	−0.232819	−0.116409	+	0.993201i	$0.537138\pi$
$318$	13.0083	0.729469
$319$	−2.33651	−0.130819
$320$	−22.5204	−1.25893
$321$	−16.3683	−0.913590
$322$	−49.9152	−2.78167
$323$	−32.1307	−1.78780
$324$	1.96460	0.109144
$325$	−3.69169	−0.204778
$326$	26.9643	1.49342
$327$	−4.44072	−0.245572
$328$	73.9338	4.08231
$329$	25.1894	1.38874
$330$	−17.3630	−0.955801
$331$	34.9387	1.92041	0.960203	−	0.279305i	$-0.0901039\pi$
$331$	34.9387	1.92041	0.960203	+	0.279305i	$0.0901039\pi$
$332$	−11.2831	−0.619243
$333$	2.06373	0.113092
$334$	−25.1490	−1.37609
$335$	−11.2705	−0.615775
$336$	−45.0125	−2.45563
$337$	21.8371	1.18954	0.594772	−	0.803894i	$-0.297242\pi$
$337$	21.8371	1.18954	0.594772	+	0.803894i	$0.297242\pi$
$338$	27.9940	1.52268
$339$	−4.73954	−0.257417
$340$	69.6479	3.77719
$341$	22.8486	1.23732
$342$	30.4643	1.64732
$343$	25.3625	1.36945
$344$	−1.41279	−0.0761725
$345$	12.2180	0.657796
$346$	10.6475	0.572411
$347$	−29.4691	−1.58199	−0.790993	−	0.611826i	$-0.790435\pi$
$347$	−29.4691	−1.58199	−0.790993	+	0.611826i	$0.790435\pi$
$348$	5.04134	0.270244
$349$	−5.94904	−0.318445	−0.159222	−	0.987243i	$-0.550899\pi$
$349$	−5.94904	−0.318445	−0.159222	+	0.987243i	$0.550899\pi$
$350$	−28.2950	−1.51243
$351$	−7.75683	−0.414029
$352$	−24.7650	−1.31998
$353$	−6.71252	−0.357271	−0.178636	−	0.983915i	$-0.557168\pi$
$353$	−6.71252	−0.357271	−0.178636	+	0.983915i	$0.557168\pi$
$354$	23.0707	1.22619
$355$	28.6885	1.52263
$356$	−54.5981	−2.89369
$357$	24.4241	1.29266
$358$	60.6836	3.20723
$359$	12.3345	0.650988	0.325494	−	0.945544i	$-0.394469\pi$
$359$	12.3345	0.650988	0.325494	+	0.945544i	$0.394469\pi$
$360$	−38.7360	−2.04157
$361$	18.0454	0.949756
$362$	16.6965	0.877551
$363$	5.77379	0.303045
$364$	−32.5362	−1.70536
$365$	−24.8223	−1.29926
$366$	−30.4981	−1.59416
$367$	−21.3652	−1.11525	−0.557627	−	0.830092i	$-0.688288\pi$
$367$	−21.3652	−1.11525	−0.557627	+	0.830092i	$0.688288\pi$
$368$	41.8284	2.18046
$369$	19.0705	0.992768
$370$	−7.68866	−0.399715
$371$	21.1952	1.10040
$372$	−49.2990	−2.55603
$373$	14.8034	0.766489	0.383245	−	0.923647i	$-0.374807\pi$
$373$	14.8034	0.766489	0.383245	+	0.923647i	$0.374807\pi$
$374$	32.2538	1.66780
$375$	−7.28321	−0.376103
$376$	−42.1012	−2.17120
$377$	1.51477	0.0780144
$378$	−59.4523	−3.05789
$379$	−3.21426	−0.165105	−0.0825527	−	0.996587i	$-0.526307\pi$
$379$	−3.21426	−0.165105	−0.0825527	+	0.996587i	$0.526307\pi$
$380$	−80.3010	−4.11936
$381$	11.0438	0.565790
$382$	14.9853	0.766716
$383$	3.34974	0.171164	0.0855818	−	0.996331i	$-0.472725\pi$
$383$	3.34974	0.171164	0.0855818	+	0.996331i	$0.472725\pi$
$384$	0.412369	0.0210436
$385$	−28.2905	−1.44182
$386$	38.8547	1.97765
$387$	−0.364414	−0.0185242
$388$	30.2241	1.53439
$389$	−11.3657	−0.576265	−0.288132	−	0.957591i	$-0.593034\pi$
$389$	−11.3657	−0.576265	−0.288132	+	0.957591i	$0.593034\pi$
$390$	11.2565	0.569994
$391$	−22.6964	−1.14781
$392$	−94.3358	−4.76468
$393$	−14.1314	−0.712834
$394$	23.7901	1.19853
$395$	14.0258	0.705717
$396$	−21.6363	−1.08727
$397$	25.6565	1.28766	0.643831	−	0.765168i	$-0.277344\pi$
$397$	25.6565	1.28766	0.643831	+	0.765168i	$0.277344\pi$
$398$	−27.1119	−1.35899
$399$	−28.1599	−1.40976
$400$	23.7109	1.18555
$401$	−9.06953	−0.452911	−0.226455	−	0.974022i	$-0.572714\pi$
$401$	−9.06953	−0.452911	−0.226455	+	0.974022i	$0.572714\pi$
$402$	11.2615	0.561671
$403$	−14.8128	−0.737879
$404$	30.4884	1.51686
$405$	−1.10745	−0.0550297
$406$	11.6099	0.576191
$407$	−2.51916	−0.124870
$408$	−40.8221	−2.02099
$409$	−28.0712	−1.38803	−0.694015	−	0.719961i	$-0.744160\pi$
$409$	−28.0712	−1.38803	−0.694015	+	0.719961i	$0.744160\pi$
$410$	−71.0491	−3.50886
$411$	−20.9423	−1.03301
$412$	15.7529	0.776090
$413$	37.5904	1.84970
$414$	21.5193	1.05761
$415$	6.36036	0.312218
$416$	16.0552	0.787173
$417$	−1.42293	−0.0696814
$418$	−37.1872	−1.81889
$419$	21.8128	1.06562	0.532812	−	0.846233i	$-0.321135\pi$
$419$	21.8128	1.06562	0.532812	+	0.846233i	$0.321135\pi$
$420$	61.0406	2.97848
$421$	−23.7581	−1.15790	−0.578948	−	0.815364i	$-0.696537\pi$
$421$	−23.7581	−1.15790	−0.578948	+	0.815364i	$0.696537\pi$
$422$	10.8505	0.528195
$423$	−10.8596	−0.528010
$424$	−35.4253	−1.72040
$425$	−12.8657	−0.624078
$426$	−28.6655	−1.38885
$427$	−49.6923	−2.40478
$428$	75.9907	3.67315
$429$	3.68814	0.178065
$430$	1.35767	0.0654724
$431$	30.1432	1.45195	0.725974	−	0.687722i	$-0.241389\pi$
$431$	30.1432	1.45195	0.725974	+	0.687722i	$0.241389\pi$
$432$	49.8204	2.39698
$433$	−4.43928	−0.213338	−0.106669	−	0.994295i	$-0.534019\pi$
$433$	−4.43928	−0.213338	−0.106669	+	0.994295i	$0.534019\pi$
$434$	−113.533	−5.44975
$435$	−2.84183	−0.136255
$436$	20.6163	0.987341
$437$	26.1680	1.25178
$438$	24.8024	1.18510
$439$	−30.1877	−1.44078	−0.720389	−	0.693570i	$-0.756037\pi$
$439$	−30.1877	−1.44078	−0.720389	+	0.693570i	$0.756037\pi$
$440$	47.2844	2.25419
$441$	−24.3329	−1.15871
$442$	−20.9102	−0.994598
$443$	14.7576	0.701155	0.350578	−	0.936534i	$-0.385985\pi$
$443$	14.7576	0.701155	0.350578	+	0.936534i	$0.385985\pi$
$444$	5.43544	0.257954
$445$	30.7772	1.45898
$446$	−33.1091	−1.56776
$447$	−11.3662	−0.537602
$448$	36.6644	1.73223
$449$	−6.61479	−0.312171	−0.156086	−	0.987744i	$-0.549888\pi$
$449$	−6.61479	−0.312171	−0.156086	+	0.987744i	$0.549888\pi$
$450$	12.1984	0.575040
$451$	−23.2790	−1.09616
$452$	22.0036	1.03496
$453$	−9.39615	−0.441469
$454$	−37.0911	−1.74077
$455$	18.3408	0.859831
$456$	47.0661	2.20407
$457$	33.9116	1.58632	0.793159	−	0.609015i	$-0.208435\pi$
$457$	33.9116	1.58632	0.793159	+	0.609015i	$0.208435\pi$
$458$	32.5609	1.52147
$459$	−27.0329	−1.26179
$460$	−56.7228	−2.64471
$461$	−30.5781	−1.42416	−0.712082	−	0.702096i	$-0.752248\pi$
$461$	−30.5781	−1.42416	−0.712082	+	0.702096i	$0.752248\pi$
$462$	28.2678	1.31514
$463$	14.2752	0.663423	0.331712	−	0.943381i	$-0.392374\pi$
$463$	14.2752	0.663423	0.331712	+	0.943381i	$0.392374\pi$
$464$	−9.72900	−0.451658
$465$	27.7901	1.28873
$466$	33.2771	1.54153
$467$	26.1481	1.20999	0.604994	−	0.796230i	$-0.293175\pi$
$467$	26.1481	1.20999	0.604994	+	0.796230i	$0.293175\pi$
$468$	14.0269	0.648394
$469$	18.3490	0.847277
$470$	40.4585	1.86621
$471$	8.68184	0.400038
$472$	−62.8281	−2.89190
$473$	0.444834	0.0204535
$474$	−14.0146	−0.643711
$475$	14.8336	0.680613
$476$	−113.390	−5.19723
$477$	−9.13758	−0.418381
$478$	−24.9833	−1.14271
$479$	1.34795	0.0615896	0.0307948	−	0.999526i	$-0.490196\pi$
$479$	1.34795	0.0615896	0.0307948	+	0.999526i	$0.490196\pi$
$480$	−30.1209	−1.37483
$481$	1.63318	0.0744666
$482$	−14.9280	−0.679951
$483$	−19.8915	−0.905096
$484$	−26.8051	−1.21841
$485$	−17.0374	−0.773631
$486$	41.2782	1.87242
$487$	5.84872	0.265031	0.132515	−	0.991181i	$-0.457695\pi$
$487$	5.84872	0.265031	0.132515	+	0.991181i	$0.457695\pi$
$488$	83.0550	3.75972
$489$	10.7454	0.485926
$490$	90.6550	4.09537
$491$	−23.5836	−1.06431	−0.532157	−	0.846646i	$-0.678618\pi$
$491$	−23.5836	−1.06431	−0.532157	+	0.846646i	$0.678618\pi$
$492$	50.2276	2.26443
$493$	5.27902	0.237755
$494$	24.1086	1.08470
$495$	12.1965	0.548192
$496$	95.1394	4.27189
$497$	−46.7063	−2.09506
$498$	−6.35525	−0.284786
$499$	37.1697	1.66394	0.831971	−	0.554819i	$-0.187212\pi$
$499$	37.1697	1.66394	0.831971	+	0.554819i	$0.187212\pi$
$500$	33.8127	1.51215
$501$	−10.0220	−0.447751
$502$	45.5926	2.03490
$503$	−12.7074	−0.566594	−0.283297	−	0.959032i	$-0.591428\pi$
$503$	−12.7074	−0.566594	−0.283297	+	0.959032i	$0.591428\pi$
$504$	63.0641	2.80910
$505$	−17.1865	−0.764788
$506$	−26.2682	−1.16776
$507$	11.1558	0.495447
$508$	−51.2713	−2.27480
$509$	37.8971	1.67976	0.839880	−	0.542772i	$-0.182625\pi$
$509$	37.8971	1.67976	0.839880	+	0.542772i	$0.182625\pi$
$510$	39.2293	1.73710
$511$	40.4119	1.78772
$512$	41.2736	1.82405
$513$	31.1678	1.37609
$514$	8.75619	0.386219
$515$	−8.87999	−0.391299
$516$	−0.959790	−0.0422524
$517$	13.2561	0.583001
$518$	12.5175	0.549988
$519$	4.24308	0.186251
$520$	−30.6546	−1.34429
$521$	−39.9221	−1.74902	−0.874510	−	0.485008i	$-0.838817\pi$
$521$	−39.9221	−1.74902	−0.874510	+	0.485008i	$0.838817\pi$
$522$	−5.00523	−0.219073
$523$	−26.3731	−1.15322	−0.576608	−	0.817021i	$-0.695624\pi$
$523$	−26.3731	−1.15322	−0.576608	+	0.817021i	$0.695624\pi$
$524$	65.6056	2.86600
$525$	−11.2757	−0.492113
$526$	−34.4608	−1.50256
$527$	−51.6233	−2.24875
$528$	−23.6881	−1.03089
$529$	−4.51556	−0.196329
$530$	34.0431	1.47874
$531$	−16.2059	−0.703274
$532$	130.734	5.66804
$533$	15.0918	0.653699
$534$	−30.7525	−1.33079
$535$	−42.8363	−1.85197
$536$	−30.6682	−1.32466
$537$	24.1828	1.04357
$538$	48.6914	2.09924
$539$	29.7028	1.27939
$540$	−67.5605	−2.90734
$541$	−37.7902	−1.62473	−0.812364	−	0.583151i	$-0.801819\pi$
$541$	−37.7902	−1.62473	−0.812364	+	0.583151i	$0.801819\pi$
$542$	−6.63301	−0.284912
$543$	6.65368	0.285537
$544$	55.9532	2.39897
$545$	−11.6215	−0.497810
$546$	−18.3261	−0.784284
$547$	5.45417	0.233203	0.116602	−	0.993179i	$-0.462800\pi$
$547$	5.45417	0.233203	0.116602	+	0.993179i	$0.462800\pi$
$548$	97.2255	4.15327
$549$	21.4232	0.914319
$550$	−14.8904	−0.634930
$551$	−6.08649	−0.259293
$552$	33.2464	1.41506
$553$	−22.8348	−0.971033
$554$	−2.61493	−0.111098
$555$	−3.06398	−0.130059
$556$	6.60604	0.280159
$557$	−2.16218	−0.0916145	−0.0458073	−	0.998950i	$-0.514586\pi$
$557$	−2.16218	−0.0916145	−0.0458073	+	0.998950i	$0.514586\pi$
$558$	48.9459	2.07205
$559$	−0.288387	−0.0121975
$560$	−117.799	−4.97792
$561$	12.8533	0.542668
$562$	−55.8787	−2.35710
$563$	3.32824	0.140269	0.0701343	−	0.997538i	$-0.477657\pi$
$563$	3.32824	0.140269	0.0701343	+	0.997538i	$0.477657\pi$
$564$	−28.6018	−1.20435
$565$	−12.4035	−0.521820
$566$	35.0309	1.47246
$567$	1.80299	0.0757183
$568$	78.0643	3.27550
$569$	−26.7104	−1.11976	−0.559879	−	0.828574i	$-0.689152\pi$
$569$	−26.7104	−1.11976	−0.559879	+	0.828574i	$0.689152\pi$
$570$	−45.2297	−1.89446
$571$	15.6419	0.654594	0.327297	−	0.944922i	$-0.393862\pi$
$571$	15.6419	0.654594	0.327297	+	0.944922i	$0.393862\pi$
$572$	−17.1224	−0.715923
$573$	5.97175	0.249473
$574$	115.671	4.82803
$575$	10.4781	0.436967
$576$	−15.8066	−0.658609
$577$	−1.01199	−0.0421297	−0.0210648	−	0.999778i	$-0.506706\pi$
$577$	−1.01199	−0.0421297	−0.0210648	+	0.999778i	$0.506706\pi$
$578$	−28.4192	−1.18208
$579$	15.4838	0.643487
$580$	13.1933	0.547823
$581$	−10.3550	−0.429597
$582$	17.0238	0.705658
$583$	11.1541	0.461955
$584$	−67.5439	−2.79499
$585$	−7.90703	−0.326915
$586$	−45.4796	−1.87874
$587$	−4.87834	−0.201351	−0.100675	−	0.994919i	$-0.532100\pi$
$587$	−4.87834	−0.201351	−0.100675	+	0.994919i	$0.532100\pi$
$588$	−64.0878	−2.64294
$589$	59.5195	2.45246
$590$	60.3767	2.48567
$591$	9.48051	0.389976
$592$	−10.4896	−0.431118
$593$	25.2035	1.03499	0.517493	−	0.855688i	$-0.326865\pi$
$593$	25.2035	1.03499	0.517493	+	0.855688i	$0.326865\pi$
$594$	−31.2871	−1.28373
$595$	63.9185	2.62040
$596$	52.7681	2.16147
$597$	−10.8042	−0.442188
$598$	17.0297	0.696398
$599$	−1.39083	−0.0568278	−0.0284139	−	0.999596i	$-0.509046\pi$
$599$	−1.39083	−0.0568278	−0.0284139	+	0.999596i	$0.509046\pi$
$600$	18.8461	0.769389
$601$	27.0329	1.10270	0.551348	−	0.834275i	$-0.314114\pi$
$601$	27.0329	1.10270	0.551348	+	0.834275i	$0.314114\pi$
$602$	−2.21035	−0.0900870
$603$	−7.91054	−0.322142
$604$	43.6221	1.77496
$605$	15.1102	0.614315
$606$	17.1727	0.697592
$607$	9.72749	0.394827	0.197413	−	0.980320i	$-0.436746\pi$
$607$	9.72749	0.394827	0.197413	+	0.980320i	$0.436746\pi$
$608$	−64.5116	−2.61629
$609$	4.62663	0.187481
$610$	−79.8144	−3.23159
$611$	−8.59395	−0.347674
$612$	48.8844	1.97603
$613$	17.3868	0.702248	0.351124	−	0.936329i	$-0.385800\pi$
$613$	17.3868	0.702248	0.351124	+	0.936329i	$0.385800\pi$
$614$	63.4975	2.56255
$615$	−28.3135	−1.14171
$616$	−76.9813	−3.10166
$617$	26.6713	1.07375	0.536873	−	0.843663i	$-0.319605\pi$
$617$	26.6713	1.07375	0.536873	+	0.843663i	$0.319605\pi$
$618$	8.87286	0.356919
$619$	23.3478	0.938429	0.469214	−	0.883084i	$-0.344537\pi$
$619$	23.3478	0.938429	0.469214	+	0.883084i	$0.344537\pi$
$620$	−129.017	−5.18144
$621$	22.0162	0.883479
$622$	−17.2313	−0.690912
$623$	−50.1068	−2.00749
$624$	15.3571	0.614775
$625$	−31.2460	−1.24984
$626$	58.0734	2.32108
$627$	−14.8194	−0.591828
$628$	−40.3059	−1.60838
$629$	5.69170	0.226943
$630$	−60.6035	−2.41450
$631$	14.7756	0.588206	0.294103	−	0.955774i	$-0.404979\pi$
$631$	14.7756	0.588206	0.294103	+	0.955774i	$0.404979\pi$
$632$	38.1657	1.51815
$633$	4.32400	0.171863
$634$	10.8394	0.430490
$635$	28.9019	1.14694
$636$	−24.0665	−0.954297
$637$	−19.2564	−0.762966
$638$	6.10980	0.241889
$639$	20.1359	0.796562
$640$	1.07918	0.0426584
$641$	−40.8977	−1.61536	−0.807681	−	0.589619i	$-0.799278\pi$
$641$	−40.8977	−1.61536	−0.807681	+	0.589619i	$0.799278\pi$
$642$	42.8019	1.68926
$643$	−44.1648	−1.74169	−0.870844	−	0.491560i	$-0.836427\pi$
$643$	−44.1648	−1.74169	−0.870844	+	0.491560i	$0.836427\pi$
$644$	92.3474	3.63900
$645$	0.541038	0.0213034
$646$	84.0195	3.30570
$647$	35.7455	1.40530	0.702650	−	0.711536i	$-0.252000\pi$
$647$	35.7455	1.40530	0.702650	+	0.711536i	$0.252000\pi$
$648$	−3.01348	−0.118381
$649$	19.7822	0.776520
$650$	9.65350	0.378641
$651$	−45.2436	−1.77324
$652$	−49.8863	−1.95370
$653$	4.12670	0.161490	0.0807452	−	0.996735i	$-0.474270\pi$
$653$	4.12670	0.161490	0.0807452	+	0.996735i	$0.474270\pi$
$654$	11.6122	0.454071
$655$	−36.9822	−1.44501
$656$	−96.9314	−3.78453
$657$	−17.4222	−0.679706
$658$	−65.8684	−2.56782
$659$	0.0930759	0.00362572	0.00181286	−	0.999998i	$-0.499423\pi$
$659$	0.0930759	0.00362572	0.00181286	+	0.999998i	$0.499423\pi$
$660$	32.1230	1.25039
$661$	3.24061	0.126045	0.0630226	−	0.998012i	$-0.479926\pi$
$661$	3.24061	0.126045	0.0630226	+	0.998012i	$0.479926\pi$
$662$	−91.3621	−3.55089
$663$	−8.33285	−0.323621
$664$	17.3072	0.671648
$665$	−73.6954	−2.85778
$666$	−5.39651	−0.209111
$667$	−4.29935	−0.166472
$668$	46.5278	1.80021
$669$	−13.1942	−0.510117
$670$	29.4716	1.13859
$671$	−26.1509	−1.00954
$672$	49.0384	1.89170
$673$	44.5450	1.71708	0.858541	−	0.512745i	$-0.171371\pi$
$673$	44.5450	1.71708	0.858541	+	0.512745i	$0.171371\pi$
$674$	−57.1025	−2.19951
$675$	12.4801	0.480360
$676$	−51.7914	−1.99198
$677$	−38.2592	−1.47042	−0.735211	−	0.677838i	$-0.762917\pi$
$677$	−38.2592	−1.47042	−0.735211	+	0.677838i	$0.762917\pi$
$678$	12.3936	0.475972
$679$	27.7378	1.06448
$680$	−106.833	−4.09684
$681$	−14.7811	−0.566411
$682$	−59.7474	−2.28785
$683$	−33.0147	−1.26327	−0.631635	−	0.775266i	$-0.717616\pi$
$683$	−33.0147	−1.26327	−0.631635	+	0.775266i	$0.717616\pi$
$684$	−56.3616	−2.15504
$685$	−54.8065	−2.09405
$686$	−66.3212	−2.53215
$687$	12.9757	0.495054
$688$	1.85225	0.0706162
$689$	−7.23122	−0.275488
$690$	−31.9492	−1.21629
$691$	−20.9994	−0.798853	−0.399427	−	0.916765i	$-0.630791\pi$
$691$	−20.9994	−0.798853	−0.399427	+	0.916765i	$0.630791\pi$
$692$	−19.6987	−0.748833
$693$	−19.8565	−0.754286
$694$	77.0596	2.92514
$695$	−3.72386	−0.141254
$696$	−7.73289	−0.293114
$697$	52.5956	1.99220
$698$	15.5563	0.588815
$699$	13.2611	0.501582
$700$	52.3482	1.97857
$701$	−37.0176	−1.39814	−0.699068	−	0.715055i	$-0.746402\pi$
$701$	−37.0176	−1.39814	−0.699068	+	0.715055i	$0.746402\pi$
$702$	20.2835	0.765553
$703$	−6.56229	−0.247502
$704$	19.2949	0.727203
$705$	16.1230	0.607226
$706$	17.5527	0.660606
$707$	27.9804	1.05231
$708$	−42.6828	−1.60412
$709$	6.58216	0.247198	0.123599	−	0.992332i	$-0.460556\pi$
$709$	6.58216	0.247198	0.123599	+	0.992332i	$0.460556\pi$
$710$	−75.0184	−2.81539
$711$	9.84444	0.369195
$712$	83.7478	3.13858
$713$	42.0431	1.57453
$714$	−63.8672	−2.39017
$715$	9.65197	0.360963
$716$	−112.270	−4.19572
$717$	−9.95599	−0.371813
$718$	−32.2537	−1.20370
$719$	49.7432	1.85511	0.927554	−	0.373690i	$-0.121908\pi$
$719$	49.7432	1.85511	0.927554	+	0.373690i	$0.121908\pi$
$720$	50.7851	1.89265
$721$	14.4571	0.538409
$722$	−47.1873	−1.75613
$723$	−5.94889	−0.221242
$724$	−30.8900	−1.14802
$725$	−2.43714	−0.0905130
$726$	−15.0980	−0.560340
$727$	30.4387	1.12891	0.564454	−	0.825465i	$-0.309087\pi$
$727$	30.4387	1.12891	0.564454	+	0.825465i	$0.309087\pi$
$728$	49.9072	1.84968
$729$	15.2313	0.564124
$730$	64.9085	2.40237
$731$	−1.00504	−0.0371728
$732$	56.4241	2.08550
$733$	20.9212	0.772741	0.386371	−	0.922344i	$-0.373729\pi$
$733$	20.9212	0.772741	0.386371	+	0.922344i	$0.373729\pi$
$734$	55.8684	2.06214
$735$	36.1266	1.33255
$736$	−45.5695	−1.67971
$737$	9.65626	0.355693
$738$	−49.8678	−1.83566
$739$	49.1512	1.80806	0.904028	−	0.427473i	$-0.140596\pi$
$739$	49.1512	1.80806	0.904028	+	0.427473i	$0.140596\pi$
$740$	14.2247	0.522910
$741$	9.60743	0.352938
$742$	−55.4238	−2.03467
$743$	−3.62722	−0.133070	−0.0665349	−	0.997784i	$-0.521194\pi$
$743$	−3.62722	−0.133070	−0.0665349	+	0.997784i	$0.521194\pi$
$744$	75.6195	2.77234
$745$	−29.7456	−1.08980
$746$	−38.7097	−1.41726
$747$	4.46420	0.163337
$748$	−59.6723	−2.18183
$749$	69.7396	2.54823
$750$	19.0451	0.695427
$751$	−29.8160	−1.08800	−0.544001	−	0.839084i	$-0.683091\pi$
$751$	−29.8160	−1.08800	−0.544001	+	0.839084i	$0.683091\pi$
$752$	55.1970	2.01283
$753$	18.1690	0.662113
$754$	−3.96100	−0.144251
$755$	−24.5900	−0.894921
$756$	109.992	4.00036
$757$	−41.0093	−1.49051	−0.745253	−	0.666781i	$-0.767671\pi$
$757$	−41.0093	−1.49051	−0.745253	+	0.666781i	$0.767671\pi$
$758$	8.40505	0.305285
$759$	−10.4680	−0.379966
$760$	123.173	4.46797
$761$	30.6786	1.11210	0.556049	−	0.831150i	$-0.312317\pi$
$761$	30.6786	1.11210	0.556049	+	0.831150i	$0.312317\pi$
$762$	−28.8786	−1.04616
$763$	18.9204	0.684963
$764$	−27.7242	−1.00302
$765$	−27.5563	−0.996301
$766$	−8.75932	−0.316487
$767$	−12.8249	−0.463079
$768$	16.1324	0.582128
$769$	41.3530	1.49123	0.745615	−	0.666377i	$-0.232156\pi$
$769$	41.3530	1.49123	0.745615	+	0.666377i	$0.232156\pi$
$770$	73.9776	2.66597
$771$	3.48940	0.125668
$772$	−71.8846	−2.58718
$773$	16.0165	0.576074	0.288037	−	0.957619i	$-0.406997\pi$
$773$	16.0165	0.576074	0.288037	+	0.957619i	$0.406997\pi$
$774$	0.952917	0.0342519
$775$	23.8326	0.856093
$776$	−46.3606	−1.66425
$777$	4.98831	0.178955
$778$	29.7205	1.06553
$779$	−60.6405	−2.17267
$780$	−20.8255	−0.745671
$781$	−24.5795	−0.879523
$782$	59.3494	2.12233
$783$	−5.12081	−0.183003
$784$	123.679	4.41712
$785$	22.7206	0.810934
$786$	36.9525	1.31805
$787$	41.1610	1.46723	0.733615	−	0.679565i	$-0.237831\pi$
$787$	41.1610	1.46723	0.733615	+	0.679565i	$0.237831\pi$
$788$	−44.0138	−1.56793
$789$	−13.7329	−0.488903
$790$	−36.6765	−1.30489
$791$	20.1935	0.717999
$792$	33.1879	1.17928
$793$	16.9537	0.602043
$794$	−67.0898	−2.38093
$795$	13.5664	0.481150
$796$	50.1593	1.77785
$797$	−17.9363	−0.635335	−0.317668	−	0.948202i	$-0.602900\pi$
$797$	−17.9363	−0.635335	−0.317668	+	0.948202i	$0.602900\pi$
$798$	73.6362	2.60669
$799$	−29.9503	−1.05956
$800$	−25.8316	−0.913284
$801$	21.6019	0.763264
$802$	23.7161	0.837446
$803$	21.2670	0.750497
$804$	−20.8347	−0.734783
$805$	−52.0567	−1.83476
$806$	38.7344	1.36436
$807$	19.4038	0.683048
$808$	−46.7661	−1.64522
$809$	47.0974	1.65585	0.827927	−	0.560835i	$-0.189520\pi$
$809$	47.0974	1.65585	0.827927	+	0.560835i	$0.189520\pi$
$810$	2.89590	0.101752
$811$	46.2111	1.62269	0.811345	−	0.584568i	$-0.198736\pi$
$811$	46.2111	1.62269	0.811345	+	0.584568i	$0.198736\pi$
$812$	−21.4794	−0.753778
$813$	−2.64330	−0.0927044
$814$	6.58742	0.230889
$815$	28.1211	0.985040
$816$	53.5200	1.87358
$817$	1.15877	0.0405402
$818$	73.4040	2.56651
$819$	12.8730	0.449820
$820$	131.447	4.59032
$821$	−3.74232	−0.130608	−0.0653039	−	0.997865i	$-0.520802\pi$
$821$	−3.74232	−0.130608	−0.0653039	+	0.997865i	$0.520802\pi$
$822$	54.7625	1.91006
$823$	37.9368	1.32240	0.661198	−	0.750212i	$-0.270048\pi$
$823$	37.9368	1.32240	0.661198	+	0.750212i	$0.270048\pi$
$824$	−24.1633	−0.841769
$825$	−5.93393	−0.206593
$826$	−98.2962	−3.42016
$827$	18.5244	0.644155	0.322078	−	0.946713i	$-0.395619\pi$
$827$	18.5244	0.644155	0.322078	+	0.946713i	$0.395619\pi$
$828$	−39.8125	−1.38358
$829$	25.4963	0.885523	0.442761	−	0.896640i	$-0.353999\pi$
$829$	25.4963	0.885523	0.442761	+	0.896640i	$0.353999\pi$
$830$	−16.6319	−0.577301
$831$	−1.04206	−0.0361488
$832$	−12.5089	−0.433669
$833$	−67.1093	−2.32520
$834$	3.72087	0.128843
$835$	−26.2279	−0.907655
$836$	68.7996	2.37948
$837$	50.0761	1.73088
$838$	−57.0388	−1.97037
$839$	−45.4070	−1.56762	−0.783812	−	0.620998i	$-0.786728\pi$
$839$	−45.4070	−1.56762	−0.783812	+	0.620998i	$0.786728\pi$
$840$	−93.6300	−3.23054
$841$	1.00000	0.0344828
$842$	62.1255	2.14099
$843$	−22.2680	−0.766951
$844$	−20.0744	−0.690989
$845$	29.1950	1.00434
$846$	28.3969	0.976307
$847$	−24.6001	−0.845269
$848$	46.4445	1.59491
$849$	13.9600	0.479107
$850$	33.6429	1.15394
$851$	−4.63545	−0.158901
$852$	53.0336	1.81690
$853$	29.1717	0.998819	0.499409	−	0.866366i	$-0.333550\pi$
$853$	29.1717	0.998819	0.499409	+	0.866366i	$0.333550\pi$
$854$	129.942	4.44651
$855$	31.7713	1.08656
$856$	−116.562	−3.98400
$857$	22.4634	0.767334	0.383667	−	0.923471i	$-0.374661\pi$
$857$	22.4634	0.767334	0.383667	+	0.923471i	$0.374661\pi$
$858$	−9.64422	−0.329248
$859$	−35.2199	−1.20169	−0.600844	−	0.799366i	$-0.705169\pi$
$859$	−35.2199	−1.20169	−0.600844	+	0.799366i	$0.705169\pi$
$860$	−2.51180	−0.0856516
$861$	46.0958	1.57094
$862$	−78.8224	−2.68470
$863$	13.6074	0.463201	0.231601	−	0.972811i	$-0.425604\pi$
$863$	13.6074	0.463201	0.231601	+	0.972811i	$0.425604\pi$
$864$	−54.2762	−1.84652
$865$	11.1043	0.377556
$866$	11.6084	0.394469
$867$	−11.3252	−0.384625
$868$	210.046	7.12941
$869$	−12.0169	−0.407647
$870$	7.43116	0.251940
$871$	−6.26018	−0.212118
$872$	−31.6232	−1.07090
$873$	−11.9582	−0.404724
$874$	−68.4273	−2.31459
$875$	31.0312	1.04905
$876$	−45.8865	−1.55036
$877$	46.8417	1.58173	0.790867	−	0.611989i	$-0.209630\pi$
$877$	46.8417	1.58173	0.790867	+	0.611989i	$0.209630\pi$
$878$	78.9385	2.66405
$879$	−18.1239	−0.611304
$880$	−61.9925	−2.08977
$881$	14.0802	0.474376	0.237188	−	0.971464i	$-0.423774\pi$
$881$	14.0802	0.474376	0.237188	+	0.971464i	$0.423774\pi$
$882$	63.6288	2.14249
$883$	50.0348	1.68381	0.841903	−	0.539628i	$-0.181435\pi$
$883$	50.0348	1.68381	0.841903	+	0.539628i	$0.181435\pi$
$884$	38.6857	1.30114
$885$	24.0605	0.808785
$886$	−38.5901	−1.29646
$887$	6.49840	0.218195	0.109098	−	0.994031i	$-0.465204\pi$
$887$	6.49840	0.218195	0.109098	+	0.994031i	$0.465204\pi$
$888$	−8.33739	−0.279785
$889$	−47.0536	−1.57813
$890$	−80.4801	−2.69770
$891$	0.948832	0.0317871
$892$	61.2547	2.05096
$893$	34.5314	1.15555
$894$	29.7217	0.994044
$895$	63.2871	2.11545
$896$	−1.75696	−0.0586959
$897$	6.78646	0.226593
$898$	17.2972	0.577214
$899$	−9.77895	−0.326146
$900$	−22.5682	−0.752272
$901$	−25.2011	−0.839571
$902$	60.8728	2.02684
$903$	−0.880837	−0.0293124
$904$	−33.7512	−1.12255
$905$	17.4129	0.578823
$906$	24.5702	0.816291
$907$	2.96851	0.0985678	0.0492839	−	0.998785i	$-0.484306\pi$
$907$	2.96851	0.0985678	0.0492839	+	0.998785i	$0.484306\pi$
$908$	68.6218	2.27729
$909$	−12.0628	−0.400099
$910$	−47.9599	−1.58985
$911$	−53.3391	−1.76720	−0.883602	−	0.468239i	$-0.844889\pi$
$911$	−53.3391	−1.76720	−0.883602	+	0.468239i	$0.844889\pi$
$912$	−61.7064	−2.04330
$913$	−5.44937	−0.180348
$914$	−88.6763	−2.93315
$915$	−31.8065	−1.05149
$916$	−60.2404	−1.99040
$917$	60.2088	1.98827
$918$	70.6890	2.33308
$919$	−0.681166	−0.0224696	−0.0112348	−	0.999937i	$-0.503576\pi$
$919$	−0.681166	−0.0224696	−0.0112348	+	0.999937i	$0.503576\pi$
$920$	87.0068	2.86853
$921$	25.3042	0.833801
$922$	79.9595	2.63332
$923$	15.9350	0.524505
$924$	−52.2979	−1.72047
$925$	−2.62766	−0.0863968
$926$	−37.3285	−1.22669
$927$	−6.23267	−0.204708
$928$	10.5991	0.347934
$929$	21.4155	0.702618	0.351309	−	0.936259i	$-0.385737\pi$
$929$	21.4155	0.702618	0.351309	+	0.936259i	$0.385737\pi$
$930$	−72.6690	−2.38291
$931$	77.3742	2.53584
$932$	−61.5655	−2.01664
$933$	−6.86678	−0.224808
$934$	−68.3753	−2.23731
$935$	33.6375	1.10006
$936$	−21.5158	−0.703266
$937$	28.0312	0.915738	0.457869	−	0.889020i	$-0.348613\pi$
$937$	28.0312	0.915738	0.457869	+	0.889020i	$0.348613\pi$
$938$	−47.9812	−1.56664
$939$	23.1426	0.755230
$940$	−74.8516	−2.44139
$941$	23.6144	0.769806	0.384903	−	0.922957i	$-0.374235\pi$
$941$	23.6144	0.769806	0.384903	+	0.922957i	$0.374235\pi$
$942$	−22.7024	−0.739683
$943$	−42.8350	−1.39490
$944$	82.3712	2.68095
$945$	−62.0029	−2.01695
$946$	−1.16321	−0.0378192
$947$	34.8816	1.13350	0.566749	−	0.823890i	$-0.308201\pi$
$947$	34.8816	1.13350	0.566749	+	0.823890i	$0.308201\pi$
$948$	25.9282	0.842108
$949$	−13.7875	−0.447560
$950$	−38.7888	−1.25847
$951$	4.31959	0.140072
$952$	173.929	5.63706
$953$	4.47300	0.144895	0.0724473	−	0.997372i	$-0.476919\pi$
$953$	4.47300	0.144895	0.0724473	+	0.997372i	$0.476919\pi$
$954$	23.8941	0.773600
$955$	15.6282	0.505718
$956$	46.2212	1.49490
$957$	2.43479	0.0787057
$958$	−3.52480	−0.113881
$959$	89.2276	2.88131
$960$	23.4678	0.757419
$961$	64.6278	2.08477
$962$	−4.27065	−0.137691
$963$	−30.0659	−0.968860
$964$	27.6180	0.889517
$965$	40.5217	1.30444
$966$	52.0149	1.67355
$967$	−4.94573	−0.159044	−0.0795220	−	0.996833i	$-0.525339\pi$
$967$	−4.94573	−0.159044	−0.0795220	+	0.996833i	$0.525339\pi$
$968$	41.1162	1.32153
$969$	33.4823	1.07561
$970$	44.5517	1.43047
$971$	19.9874	0.641425	0.320713	−	0.947177i	$-0.396078\pi$
$971$	19.9874	0.641425	0.320713	+	0.947177i	$0.396078\pi$
$972$	−76.3682	−2.44951
$973$	6.06262	0.194359
$974$	−15.2940	−0.490050
$975$	3.84698	0.123202
$976$	−108.890	−3.48548
$977$	−6.65199	−0.212816	−0.106408	−	0.994323i	$-0.533935\pi$
$977$	−6.65199	−0.212816	−0.106408	+	0.994323i	$0.533935\pi$
$978$	−28.0986	−0.898493
$979$	−26.3690	−0.842757
$980$	−167.719	−5.35760
$981$	−8.15688	−0.260429
$982$	61.6694	1.96795
$983$	57.4759	1.83320	0.916598	−	0.399810i	$-0.130924\pi$
$983$	57.4759	1.83320	0.916598	+	0.399810i	$0.130924\pi$
$984$	−77.0438	−2.45607
$985$	24.8108	0.790536
$986$	−13.8043	−0.439617
$987$	−26.2490	−0.835513
$988$	−44.6030	−1.41901
$989$	0.818528	0.0260277
$990$	−31.8930	−1.01363
$991$	44.4219	1.41111	0.705554	−	0.708657i	$-0.250698\pi$
$991$	44.4219	1.41111	0.705554	+	0.708657i	$0.250698\pi$
$992$	−103.649	−3.29084
$993$	−36.4084	−1.15539
$994$	122.134	3.87384
$995$	−28.2750	−0.896378
$996$	11.7578	0.372559
$997$	−2.27515	−0.0720548	−0.0360274	−	0.999351i	$-0.511470\pi$
$997$	−2.27515	−0.0720548	−0.0360274	+	0.999351i	$0.511470\pi$
$998$	−97.1959	−3.07668
$999$	−5.52112	−0.174681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.10	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.10	✓	169	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61493 q^{2} -1.04206 q^{3} +4.83784 q^{4} -2.72711 q^{5} +2.72492 q^{6} +4.43987 q^{7} -7.42074 q^{8} -1.91410 q^{9} +O(q^{10})\)	\(q-2.61493 q^{2} -1.04206 q^{3} +4.83784 q^{4} -2.72711 q^{5} +2.72492 q^{6} +4.43987 q^{7} -7.42074 q^{8} -1.91410 q^{9} +7.13119 q^{10} +2.33651 q^{11} -5.04134 q^{12} -1.51477 q^{13} -11.6099 q^{14} +2.84183 q^{15} +9.72900 q^{16} -5.27902 q^{17} +5.00523 q^{18} +6.08649 q^{19} -13.1933 q^{20} -4.62663 q^{21} -6.10980 q^{22} +4.29935 q^{23} +7.73289 q^{24} +2.43714 q^{25} +3.96100 q^{26} +5.12081 q^{27} +21.4794 q^{28} -1.00000 q^{29} -7.43116 q^{30} +9.77895 q^{31} -10.5991 q^{32} -2.43479 q^{33} +13.8043 q^{34} -12.1080 q^{35} -9.26011 q^{36} -1.07817 q^{37} -15.9157 q^{38} +1.57848 q^{39} +20.2372 q^{40} -9.96314 q^{41} +12.0983 q^{42} +0.190384 q^{43} +11.3037 q^{44} +5.21997 q^{45} -11.2425 q^{46} +5.67345 q^{47} -10.1382 q^{48} +12.7125 q^{49} -6.37293 q^{50} +5.50108 q^{51} -7.32819 q^{52} +4.77382 q^{53} -13.3905 q^{54} -6.37192 q^{55} -32.9471 q^{56} -6.34252 q^{57} +2.61493 q^{58} +8.46656 q^{59} +13.7483 q^{60} -11.1923 q^{61} -25.5712 q^{62} -8.49836 q^{63} +8.25799 q^{64} +4.13094 q^{65} +6.36681 q^{66} +4.13277 q^{67} -25.5391 q^{68} -4.48020 q^{69} +31.6616 q^{70} -10.5197 q^{71} +14.2040 q^{72} +9.10205 q^{73} +2.81934 q^{74} -2.53965 q^{75} +29.4455 q^{76} +10.3738 q^{77} -4.12762 q^{78} -5.14311 q^{79} -26.5321 q^{80} +0.406090 q^{81} +26.0529 q^{82} -2.33227 q^{83} -22.3829 q^{84} +14.3965 q^{85} -0.497840 q^{86} +1.04206 q^{87} -17.3386 q^{88} -11.2856 q^{89} -13.6498 q^{90} -6.72537 q^{91} +20.7996 q^{92} -10.1903 q^{93} -14.8356 q^{94} -16.5985 q^{95} +11.0450 q^{96} +6.24743 q^{97} -33.2421 q^{98} -4.47232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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