LMFDB - Embedded newform 8021.2.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.09018 q^{2} -2.33308 q^{3} +2.36887 q^{4} +1.26900 q^{5} +4.87656 q^{6} +3.93400 q^{7} -0.771000 q^{8} +2.44324 q^{9} +O(q^{10})$	\(q-2.09018 q^{2} -2.33308 q^{3} +2.36887 q^{4} +1.26900 q^{5} +4.87656 q^{6} +3.93400 q^{7} -0.771000 q^{8} +2.44324 q^{9} -2.65245 q^{10} +0.594536 q^{11} -5.52675 q^{12} +1.00000 q^{13} -8.22278 q^{14} -2.96068 q^{15} -3.12620 q^{16} +0.356619 q^{17} -5.10683 q^{18} +0.943128 q^{19} +3.00610 q^{20} -9.17832 q^{21} -1.24269 q^{22} +1.05114 q^{23} +1.79880 q^{24} -3.38963 q^{25} -2.09018 q^{26} +1.29896 q^{27} +9.31912 q^{28} -4.29692 q^{29} +6.18837 q^{30} +8.95361 q^{31} +8.07634 q^{32} -1.38710 q^{33} -0.745400 q^{34} +4.99227 q^{35} +5.78772 q^{36} -4.51017 q^{37} -1.97131 q^{38} -2.33308 q^{39} -0.978402 q^{40} +1.53286 q^{41} +19.1844 q^{42} -0.601067 q^{43} +1.40838 q^{44} +3.10049 q^{45} -2.19708 q^{46} +7.67167 q^{47} +7.29367 q^{48} +8.47636 q^{49} +7.08494 q^{50} -0.832020 q^{51} +2.36887 q^{52} -5.58352 q^{53} -2.71506 q^{54} +0.754468 q^{55} -3.03311 q^{56} -2.20039 q^{57} +8.98136 q^{58} -5.30846 q^{59} -7.01347 q^{60} -2.34686 q^{61} -18.7147 q^{62} +9.61172 q^{63} -10.6286 q^{64} +1.26900 q^{65} +2.89929 q^{66} -9.33733 q^{67} +0.844784 q^{68} -2.45240 q^{69} -10.4348 q^{70} +9.63204 q^{71} -1.88374 q^{72} -12.9931 q^{73} +9.42708 q^{74} +7.90826 q^{75} +2.23414 q^{76} +2.33890 q^{77} +4.87656 q^{78} -11.5251 q^{79} -3.96717 q^{80} -10.3603 q^{81} -3.20396 q^{82} -15.7864 q^{83} -21.7422 q^{84} +0.452552 q^{85} +1.25634 q^{86} +10.0250 q^{87} -0.458387 q^{88} -9.12560 q^{89} -6.48059 q^{90} +3.93400 q^{91} +2.49002 q^{92} -20.8895 q^{93} -16.0352 q^{94} +1.19683 q^{95} -18.8427 q^{96} -16.1829 q^{97} -17.7171 q^{98} +1.45259 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.09018	−1.47798	−0.738991	−	0.673715i	$-0.764698\pi$
$2$	−2.09018	−1.47798	−0.738991	+	0.673715i	$0.764698\pi$
$3$	−2.33308	−1.34700	−0.673501	−	0.739186i	$-0.735210\pi$
$3$	−2.33308	−1.34700	−0.673501	+	0.739186i	$0.735210\pi$
$4$	2.36887	1.18443
$5$	1.26900	0.567516	0.283758	−	0.958896i	$-0.408419\pi$
$5$	1.26900	0.567516	0.283758	+	0.958896i	$0.408419\pi$
$6$	4.87656	1.99085
$7$	3.93400	1.48691	0.743456	−	0.668785i	$-0.233185\pi$
$7$	3.93400	1.48691	0.743456	+	0.668785i	$0.233185\pi$
$8$	−0.771000	−0.272590
$9$	2.44324	0.814414
$10$	−2.65245	−0.838779
$11$	0.594536	0.179259	0.0896296	−	0.995975i	$-0.471432\pi$
$11$	0.594536	0.179259	0.0896296	+	0.995975i	$0.471432\pi$
$12$	−5.52675	−1.59543
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−8.22278	−2.19763
$15$	−2.96068	−0.764445
$16$	−3.12620	−0.781551
$17$	0.356619	0.0864929	0.0432465	−	0.999064i	$-0.486230\pi$
$17$	0.356619	0.0864929	0.0432465	+	0.999064i	$0.486230\pi$
$18$	−5.10683	−1.20369
$19$	0.943128	0.216368	0.108184	−	0.994131i	$-0.465496\pi$
$19$	0.943128	0.216368	0.108184	+	0.994131i	$0.465496\pi$
$20$	3.00610	0.672185
$21$	−9.17832	−2.00287
$22$	−1.24269	−0.264942
$23$	1.05114	0.219179	0.109589	−	0.993977i	$-0.465046\pi$
$23$	1.05114	0.219179	0.109589	+	0.993977i	$0.465046\pi$
$24$	1.79880	0.367179
$25$	−3.38963	−0.677925
$26$	−2.09018	−0.409919
$27$	1.29896	0.249984
$28$	9.31912	1.76115
$29$	−4.29692	−0.797918	−0.398959	−	0.916969i	$-0.630629\pi$
$29$	−4.29692	−0.797918	−0.398959	+	0.916969i	$0.630629\pi$
$30$	6.18837	1.12984
$31$	8.95361	1.60812	0.804058	−	0.594550i	$-0.202670\pi$
$31$	8.95361	1.60812	0.804058	+	0.594550i	$0.202670\pi$
$32$	8.07634	1.42771
$33$	−1.38710	−0.241462
$34$	−0.745400	−0.127835
$35$	4.99227	0.843847
$36$	5.78772	0.964620
$37$	−4.51017	−0.741467	−0.370733	−	0.928739i	$-0.620894\pi$
$37$	−4.51017	−0.741467	−0.370733	+	0.928739i	$0.620894\pi$
$38$	−1.97131	−0.319789
$39$	−2.33308	−0.373591
$40$	−0.978402	−0.154699
$41$	1.53286	0.239393	0.119696	−	0.992811i	$-0.461808\pi$
$41$	1.53286	0.239393	0.119696	+	0.992811i	$0.461808\pi$
$42$	19.1844	2.96021
$43$	−0.601067	−0.0916619	−0.0458309	−	0.998949i	$-0.514594\pi$
$43$	−0.601067	−0.0916619	−0.0458309	+	0.998949i	$0.514594\pi$
$44$	1.40838	0.212321
$45$	3.10049	0.462193
$46$	−2.19708	−0.323942
$47$	7.67167	1.11903	0.559514	−	0.828821i	$-0.310988\pi$
$47$	7.67167	1.11903	0.559514	+	0.828821i	$0.310988\pi$
$48$	7.29367	1.05275
$49$	8.47636	1.21091
$50$	7.08494	1.00196
$51$	−0.832020	−0.116506
$52$	2.36887	0.328503
$53$	−5.58352	−0.766956	−0.383478	−	0.923550i	$-0.625274\pi$
$53$	−5.58352	−0.766956	−0.383478	+	0.923550i	$0.625274\pi$
$54$	−2.71506	−0.369473
$55$	0.754468	0.101732
$56$	−3.03311	−0.405317
$57$	−2.20039	−0.291449
$58$	8.98136	1.17931
$59$	−5.30846	−0.691103	−0.345552	−	0.938400i	$-0.612308\pi$
$59$	−5.30846	−0.691103	−0.345552	+	0.938400i	$0.612308\pi$
$60$	−7.01347	−0.905435
$61$	−2.34686	−0.300484	−0.150242	−	0.988649i	$-0.548005\pi$
$61$	−2.34686	−0.300484	−0.150242	+	0.988649i	$0.548005\pi$
$62$	−18.7147	−2.37677
$63$	9.61172	1.21096
$64$	−10.6286	−1.32858
$65$	1.26900	0.157401
$66$	2.89929	0.356877
$67$	−9.33733	−1.14074	−0.570368	−	0.821389i	$-0.693200\pi$
$67$	−9.33733	−1.14074	−0.570368	+	0.821389i	$0.693200\pi$
$68$	0.844784	0.102445
$69$	−2.45240	−0.295234
$70$	−10.4348	−1.24719
$71$	9.63204	1.14311	0.571556	−	0.820563i	$-0.306340\pi$
$71$	9.63204	1.14311	0.571556	+	0.820563i	$0.306340\pi$
$72$	−1.88374	−0.222001
$73$	−12.9931	−1.52072	−0.760362	−	0.649499i	$-0.774978\pi$
$73$	−12.9931	−1.52072	−0.760362	+	0.649499i	$0.774978\pi$
$74$	9.42708	1.09588
$75$	7.90826	0.913167
$76$	2.23414	0.256274
$77$	2.33890	0.266543
$78$	4.87656	0.552161
$79$	−11.5251	−1.29668	−0.648339	−	0.761352i	$-0.724536\pi$
$79$	−11.5251	−1.29668	−0.648339	+	0.761352i	$0.724536\pi$
$80$	−3.96717	−0.443543
$81$	−10.3603	−1.15114
$82$	−3.20396	−0.353818
$83$	−15.7864	−1.73278	−0.866389	−	0.499369i	$-0.833565\pi$
$83$	−15.7864	−1.73278	−0.866389	+	0.499369i	$0.833565\pi$
$84$	−21.7422	−2.37227
$85$	0.452552	0.0490861
$86$	1.25634	0.135475
$87$	10.0250	1.07480
$88$	−0.458387	−0.0488642
$89$	−9.12560	−0.967311	−0.483656	−	0.875258i	$-0.660691\pi$
$89$	−9.12560	−0.967311	−0.483656	+	0.875258i	$0.660691\pi$
$90$	−6.48059	−0.683114
$91$	3.93400	0.412395
$92$	2.49002	0.259603
$93$	−20.8895	−2.16614
$94$	−16.0352	−1.65391
$95$	1.19683	0.122793
$96$	−18.8427	−1.92313
$97$	−16.1829	−1.64312	−0.821562	−	0.570120i	$-0.806897\pi$
$97$	−16.1829	−1.64312	−0.821562	+	0.570120i	$0.806897\pi$
$98$	−17.7171	−1.78970
$99$	1.45259	0.145991
$100$	−8.02958	−0.802958
$101$	3.97644	0.395670	0.197835	−	0.980235i	$-0.436609\pi$
$101$	3.97644	0.395670	0.197835	+	0.980235i	$0.436609\pi$
$102$	1.73908	0.172194
$103$	−12.2965	−1.21161	−0.605807	−	0.795612i	$-0.707150\pi$
$103$	−12.2965	−1.21161	−0.605807	+	0.795612i	$0.707150\pi$
$104$	−0.771000	−0.0756027
$105$	−11.6473	−1.13666
$106$	11.6706	1.13355
$107$	4.98167	0.481597	0.240798	−	0.970575i	$-0.422591\pi$
$107$	4.98167	0.481597	0.240798	+	0.970575i	$0.422591\pi$
$108$	3.07706	0.296090
$109$	8.72154	0.835372	0.417686	−	0.908591i	$-0.362841\pi$
$109$	8.72154	0.835372	0.417686	+	0.908591i	$0.362841\pi$
$110$	−1.57698	−0.150359
$111$	10.5226	0.998757
$112$	−12.2985	−1.16210
$113$	11.9136	1.12073	0.560366	−	0.828245i	$-0.310660\pi$
$113$	11.9136	1.12073	0.560366	+	0.828245i	$0.310660\pi$
$114$	4.59922	0.430756
$115$	1.33391	0.124387
$116$	−10.1788	−0.945081
$117$	2.44324	0.225878
$118$	11.0957	1.02144
$119$	1.40294	0.128607
$120$	2.28269	0.208380
$121$	−10.6465	−0.967866
$122$	4.90537	0.444111
$123$	−3.57628	−0.322462
$124$	21.2099	1.90471
$125$	−10.6465	−0.952250
$126$	−20.0903	−1.78978
$127$	−6.86625	−0.609281	−0.304641	−	0.952467i	$-0.598536\pi$
$127$	−6.86625	−0.609281	−0.304641	+	0.952467i	$0.598536\pi$
$128$	6.06309	0.535907
$129$	1.40234	0.123469
$130$	−2.65245	−0.232635
$131$	−16.5224	−1.44357	−0.721786	−	0.692116i	$-0.756679\pi$
$131$	−16.5224	−1.44357	−0.721786	+	0.692116i	$0.756679\pi$
$132$	−3.28585	−0.285996
$133$	3.71027	0.321721
$134$	19.5167	1.68599
$135$	1.64838	0.141870
$136$	−0.274954	−0.0235771
$137$	−9.45389	−0.807700	−0.403850	−	0.914825i	$-0.632328\pi$
$137$	−9.45389	−0.807700	−0.403850	+	0.914825i	$0.632328\pi$
$138$	5.12596	0.436351
$139$	1.07259	0.0909763	0.0454881	−	0.998965i	$-0.485516\pi$
$139$	1.07259	0.0909763	0.0454881	+	0.998965i	$0.485516\pi$
$140$	11.8260	0.999480
$141$	−17.8986	−1.50733
$142$	−20.1327	−1.68950
$143$	0.594536	0.0497176
$144$	−7.63807	−0.636506
$145$	−5.45282	−0.452832
$146$	27.1579	2.24760
$147$	−19.7760	−1.63110
$148$	−10.6840	−0.878218
$149$	−1.92764	−0.157918	−0.0789592	−	0.996878i	$-0.525160\pi$
$149$	−1.92764	−0.157918	−0.0789592	+	0.996878i	$0.525160\pi$
$150$	−16.5297	−1.34964
$151$	5.85703	0.476638	0.238319	−	0.971187i	$-0.423404\pi$
$151$	5.85703	0.476638	0.238319	+	0.971187i	$0.423404\pi$
$152$	−0.727151	−0.0589798
$153$	0.871308	0.0704411
$154$	−4.88874	−0.393946
$155$	11.3622	0.912632
$156$	−5.52675	−0.442494
$157$	12.2998	0.981632	0.490816	−	0.871263i	$-0.336699\pi$
$157$	12.2998	0.981632	0.490816	+	0.871263i	$0.336699\pi$
$158$	24.0896	1.91647
$159$	13.0268	1.03309
$160$	10.2489	0.810248
$161$	4.13520	0.325900
$162$	21.6549	1.70137
$163$	−6.75892	−0.529399	−0.264700	−	0.964331i	$-0.585273\pi$
$163$	−6.75892	−0.529399	−0.264700	+	0.964331i	$0.585273\pi$
$164$	3.63114	0.283545
$165$	−1.76023	−0.137034
$166$	32.9964	2.56102
$167$	16.0606	1.24281	0.621405	−	0.783489i	$-0.286562\pi$
$167$	16.0606	1.24281	0.621405	+	0.783489i	$0.286562\pi$
$168$	7.07648	0.545963
$169$	1.00000	0.0769231
$170$	−0.945916	−0.0725485
$171$	2.30429	0.176214
$172$	−1.42385	−0.108567
$173$	−23.9425	−1.82031	−0.910156	−	0.414266i	$-0.864038\pi$
$173$	−23.9425	−1.82031	−0.910156	+	0.414266i	$0.864038\pi$
$174$	−20.9542	−1.58853
$175$	−13.3348	−1.00802
$176$	−1.85864	−0.140100
$177$	12.3850	0.930917
$178$	19.0742	1.42967
$179$	−1.23871	−0.0925853	−0.0462926	−	0.998928i	$-0.514741\pi$
$179$	−1.23871	−0.0925853	−0.0462926	+	0.998928i	$0.514741\pi$
$180$	7.34464	0.547437
$181$	−17.4934	−1.30028	−0.650138	−	0.759816i	$-0.725289\pi$
$181$	−17.4934	−1.30028	−0.650138	+	0.759816i	$0.725289\pi$
$182$	−8.22278	−0.609513
$183$	5.47540	0.404753
$184$	−0.810432	−0.0597458
$185$	−5.72342	−0.420794
$186$	43.6628	3.20151
$187$	0.212023	0.0155047
$188$	18.1732	1.32542
$189$	5.11010	0.371705
$190$	−2.50160	−0.181485
$191$	12.8686	0.931141	0.465571	−	0.885011i	$-0.345849\pi$
$191$	12.8686	0.931141	0.465571	+	0.885011i	$0.345849\pi$
$192$	24.7974	1.78960
$193$	0.169081	0.0121707	0.00608537	−	0.999981i	$-0.498063\pi$
$193$	0.169081	0.0121707	0.00608537	+	0.999981i	$0.498063\pi$
$194$	33.8252	2.42851
$195$	−2.96068	−0.212019
$196$	20.0794	1.43424
$197$	−18.6429	−1.32825	−0.664127	−	0.747620i	$-0.731197\pi$
$197$	−18.6429	−1.32825	−0.664127	+	0.747620i	$0.731197\pi$
$198$	−3.03619	−0.215773
$199$	−13.0939	−0.928204	−0.464102	−	0.885782i	$-0.653623\pi$
$199$	−13.0939	−0.928204	−0.464102	+	0.885782i	$0.653623\pi$
$200$	2.61340	0.184795
$201$	21.7847	1.53657
$202$	−8.31148	−0.584794
$203$	−16.9041	−1.18643
$204$	−1.97095	−0.137994
$205$	1.94521	0.135859
$206$	25.7020	1.79074
$207$	2.56820	0.178502
$208$	−3.12620	−0.216763
$209$	0.560723	0.0387860
$210$	24.3451	1.67997
$211$	−9.27357	−0.638419	−0.319209	−	0.947684i	$-0.603417\pi$
$211$	−9.27357	−0.638419	−0.319209	+	0.947684i	$0.603417\pi$
$212$	−13.2266	−0.908408
$213$	−22.4723	−1.53977
$214$	−10.4126	−0.711792
$215$	−0.762757	−0.0520196
$216$	−1.00150	−0.0681431
$217$	35.2235	2.39113
$218$	−18.2296	−1.23467
$219$	30.3138	2.04842
$220$	1.78724	0.120495
$221$	0.356619	0.0239888
$222$	−21.9941	−1.47615
$223$	−21.7709	−1.45789	−0.728945	−	0.684573i	$-0.759989\pi$
$223$	−21.7709	−1.45789	−0.728945	+	0.684573i	$0.759989\pi$
$224$	31.7723	2.12288
$225$	−8.28168	−0.552112
$226$	−24.9015	−1.65642
$227$	2.61970	0.173875	0.0869376	−	0.996214i	$-0.472292\pi$
$227$	2.61970	0.173875	0.0869376	+	0.996214i	$0.472292\pi$
$228$	−5.21243	−0.345202
$229$	−14.3409	−0.947673	−0.473837	−	0.880613i	$-0.657131\pi$
$229$	−14.3409	−0.947673	−0.473837	+	0.880613i	$0.657131\pi$
$230$	−2.78811	−0.183843
$231$	−5.45684	−0.359034
$232$	3.31293	0.217504
$233$	−0.783266	−0.0513135	−0.0256567	−	0.999671i	$-0.508168\pi$
$233$	−0.783266	−0.0513135	−0.0256567	+	0.999671i	$0.508168\pi$
$234$	−5.10683	−0.333844
$235$	9.73539	0.635067
$236$	−12.5750	−0.818566
$237$	26.8890	1.74663
$238$	−2.93240	−0.190080
$239$	−21.5230	−1.39221	−0.696104	−	0.717941i	$-0.745085\pi$
$239$	−21.5230	−1.39221	−0.696104	+	0.717941i	$0.745085\pi$
$240$	9.25570	0.597453
$241$	28.9474	1.86466	0.932332	−	0.361603i	$-0.117770\pi$
$241$	28.9474	1.86466	0.932332	+	0.361603i	$0.117770\pi$
$242$	22.2532	1.43049
$243$	20.2745	1.30061
$244$	−5.55940	−0.355904
$245$	10.7565	0.687210
$246$	7.47508	0.476594
$247$	0.943128	0.0600098
$248$	−6.90323	−0.438356
$249$	36.8308	2.33406
$250$	22.2531	1.40741
$251$	14.4473	0.911908	0.455954	−	0.890003i	$-0.349298\pi$
$251$	14.4473	0.911908	0.455954	+	0.890003i	$0.349298\pi$
$252$	22.7689	1.43430
$253$	0.624943	0.0392898
$254$	14.3517	0.900508
$255$	−1.05584	−0.0661191
$256$	8.58427	0.536517
$257$	31.4180	1.95980	0.979901	−	0.199485i	$-0.0639269\pi$
$257$	31.4180	1.95980	0.979901	+	0.199485i	$0.0639269\pi$
$258$	−2.93114	−0.182485
$259$	−17.7430	−1.10250
$260$	3.00610	0.186431
$261$	−10.4984	−0.649836
$262$	34.5349	2.13358
$263$	13.5490	0.835470	0.417735	−	0.908569i	$-0.362824\pi$
$263$	13.5490	0.835470	0.417735	+	0.908569i	$0.362824\pi$
$264$	1.06945	0.0658202
$265$	−7.08551	−0.435260
$266$	−7.75514	−0.475498
$267$	21.2907	1.30297
$268$	−22.1189	−1.35113
$269$	−6.46595	−0.394236	−0.197118	−	0.980380i	$-0.563158\pi$
$269$	−6.46595	−0.394236	−0.197118	+	0.980380i	$0.563158\pi$
$270$	−3.44542	−0.209682
$271$	−21.9989	−1.33634	−0.668169	−	0.744009i	$-0.732922\pi$
$271$	−21.9989	−1.33634	−0.668169	+	0.744009i	$0.732922\pi$
$272$	−1.11486	−0.0675986
$273$	−9.17832	−0.555497
$274$	19.7604	1.19377
$275$	−2.01525	−0.121524
$276$	−5.80941	−0.349685
$277$	29.8503	1.79353	0.896766	−	0.442505i	$-0.145910\pi$
$277$	29.8503	1.79353	0.896766	+	0.442505i	$0.145910\pi$
$278$	−2.24192	−0.134461
$279$	21.8759	1.30967
$280$	−3.84904	−0.230024
$281$	−20.9747	−1.25124	−0.625622	−	0.780126i	$-0.715155\pi$
$281$	−20.9747	−1.25124	−0.625622	+	0.780126i	$0.715155\pi$
$282$	37.4114	2.22781
$283$	1.44361	0.0858135	0.0429067	−	0.999079i	$-0.486338\pi$
$283$	1.44361	0.0858135	0.0429067	+	0.999079i	$0.486338\pi$
$284$	22.8170	1.35394
$285$	−2.79230	−0.165402
$286$	−1.24269	−0.0734817
$287$	6.03027	0.355956
$288$	19.7325	1.16275
$289$	−16.8728	−0.992519
$290$	11.3974	0.669277
$291$	37.7559	2.21329
$292$	−30.7789	−1.80120
$293$	21.2415	1.24094	0.620470	−	0.784230i	$-0.286942\pi$
$293$	21.2415	1.24094	0.620470	+	0.784230i	$0.286942\pi$
$294$	41.3354	2.41073
$295$	−6.73647	−0.392212
$296$	3.47734	0.202116
$297$	0.772276	0.0448120
$298$	4.02912	0.233401
$299$	1.05114	0.0607892
$300$	18.7336	1.08159
$301$	−2.36460	−0.136293
$302$	−12.2423	−0.704463
$303$	−9.27733	−0.532969
$304$	−2.94841	−0.169103
$305$	−2.97817	−0.170530
$306$	−1.82119	−0.104111
$307$	−22.0317	−1.25741	−0.628707	−	0.777643i	$-0.716415\pi$
$307$	−22.0317	−1.25741	−0.628707	+	0.777643i	$0.716415\pi$
$308$	5.54055	0.315702
$309$	28.6887	1.63205
$310$	−23.7490	−1.34885
$311$	−1.80379	−0.102283	−0.0511417	−	0.998691i	$-0.516286\pi$
$311$	−1.80379	−0.102283	−0.0511417	+	0.998691i	$0.516286\pi$
$312$	1.79880	0.101837
$313$	−2.45010	−0.138488	−0.0692440	−	0.997600i	$-0.522059\pi$
$313$	−2.45010	−0.138488	−0.0692440	+	0.997600i	$0.522059\pi$
$314$	−25.7089	−1.45084
$315$	12.1973	0.687241
$316$	−27.3015	−1.53583
$317$	−2.03986	−0.114570	−0.0572849	−	0.998358i	$-0.518244\pi$
$317$	−2.03986	−0.114570	−0.0572849	+	0.998358i	$0.518244\pi$
$318$	−27.2284	−1.52689
$319$	−2.55467	−0.143034
$320$	−13.4878	−0.753989
$321$	−11.6226	−0.648712
$322$	−8.64333	−0.481674
$323$	0.336338	0.0187143
$324$	−24.5422	−1.36345
$325$	−3.38963	−0.188023
$326$	14.1274	0.782443
$327$	−20.3480	−1.12525
$328$	−1.18183	−0.0652559
$329$	30.1804	1.66390
$330$	3.67921	0.202534
$331$	−13.7142	−0.753798	−0.376899	−	0.926254i	$-0.623010\pi$
$331$	−13.7142	−0.753798	−0.376899	+	0.926254i	$0.623010\pi$
$332$	−37.3958	−2.05236
$333$	−11.0194	−0.603861
$334$	−33.5697	−1.83685
$335$	−11.8491	−0.647387
$336$	28.6933	1.56535
$337$	13.2739	0.723073	0.361536	−	0.932358i	$-0.382252\pi$
$337$	13.2739	0.723073	0.361536	+	0.932358i	$0.382252\pi$
$338$	−2.09018	−0.113691
$339$	−27.7952	−1.50963
$340$	1.07204	0.0581393
$341$	5.32324	0.288270
$342$	−4.81639	−0.260441
$343$	5.80800	0.313602
$344$	0.463423	0.0249861
$345$	−3.11211	−0.167550
$346$	50.0441	2.69039
$347$	3.36141	0.180450	0.0902249	−	0.995921i	$-0.471241\pi$
$347$	3.36141	0.180450	0.0902249	+	0.995921i	$0.471241\pi$
$348$	23.7480	1.27303
$349$	20.9003	1.11877	0.559383	−	0.828909i	$-0.311038\pi$
$349$	20.9003	1.11877	0.559383	+	0.828909i	$0.311038\pi$
$350$	27.8722	1.48983
$351$	1.29896	0.0693332
$352$	4.80167	0.255930
$353$	11.3589	0.604573	0.302286	−	0.953217i	$-0.402250\pi$
$353$	11.3589	0.604573	0.302286	+	0.953217i	$0.402250\pi$
$354$	−25.8870	−1.37588
$355$	12.2231	0.648735
$356$	−21.6173	−1.14572
$357$	−3.27317	−0.173234
$358$	2.58912	0.136839
$359$	10.0049	0.528038	0.264019	−	0.964517i	$-0.414952\pi$
$359$	10.0049	0.528038	0.264019	+	0.964517i	$0.414952\pi$
$360$	−2.39047	−0.125989
$361$	−18.1105	−0.953185
$362$	36.5645	1.92179
$363$	24.8392	1.30372
$364$	9.31912	0.488455
$365$	−16.4883	−0.863036
$366$	−11.4446	−0.598218
$367$	−8.72258	−0.455315	−0.227657	−	0.973741i	$-0.573107\pi$
$367$	−8.72258	−0.455315	−0.227657	+	0.973741i	$0.573107\pi$
$368$	−3.28609	−0.171299
$369$	3.74515	0.194965
$370$	11.9630	0.621927
$371$	−21.9656	−1.14040
$372$	−49.4844	−2.56564
$373$	36.4617	1.88792	0.943959	−	0.330064i	$-0.107070\pi$
$373$	36.4617	1.88792	0.943959	+	0.330064i	$0.107070\pi$
$374$	−0.443167	−0.0229156
$375$	24.8390	1.28268
$376$	−5.91486	−0.305036
$377$	−4.29692	−0.221303
$378$	−10.6810	−0.549373
$379$	19.6000	1.00678	0.503392	−	0.864058i	$-0.332085\pi$
$379$	19.6000	1.00678	0.503392	+	0.864058i	$0.332085\pi$
$380$	2.83514	0.145440
$381$	16.0195	0.820703
$382$	−26.8978	−1.37621
$383$	27.3446	1.39724	0.698621	−	0.715492i	$-0.253797\pi$
$383$	27.3446	1.39724	0.698621	+	0.715492i	$0.253797\pi$
$384$	−14.1457	−0.721868
$385$	2.96808	0.151267
$386$	−0.353411	−0.0179882
$387$	−1.46855	−0.0746508
$388$	−38.3351	−1.94617
$389$	−12.4435	−0.630910	−0.315455	−	0.948940i	$-0.602157\pi$
$389$	−12.4435	−0.630910	−0.315455	+	0.948940i	$0.602157\pi$
$390$	6.18837	0.313360
$391$	0.374859	0.0189574
$392$	−6.53527	−0.330081
$393$	38.5481	1.94449
$394$	38.9672	1.96314
$395$	−14.6254	−0.735886
$396$	3.44100	0.172917
$397$	−36.5064	−1.83220	−0.916102	−	0.400945i	$-0.868682\pi$
$397$	−36.5064	−1.83220	−0.916102	+	0.400945i	$0.868682\pi$
$398$	27.3687	1.37187
$399$	−8.65633	−0.433359
$400$	10.5967	0.529833
$401$	3.79485	0.189506	0.0947529	−	0.995501i	$-0.469794\pi$
$401$	3.79485	0.189506	0.0947529	+	0.995501i	$0.469794\pi$
$402$	−45.5340	−2.27103
$403$	8.95361	0.446011
$404$	9.41965	0.468645
$405$	−13.1473	−0.653293
$406$	35.3327	1.75353
$407$	−2.68145	−0.132915
$408$	0.641487	0.0317584
$409$	1.79064	0.0885413	0.0442706	−	0.999020i	$-0.485904\pi$
$409$	1.79064	0.0885413	0.0442706	+	0.999020i	$0.485904\pi$
$410$	−4.06584	−0.200797
$411$	22.0566	1.08797
$412$	−29.1288	−1.43508
$413$	−20.8835	−1.02761
$414$	−5.36801	−0.263823
$415$	−20.0330	−0.983380
$416$	8.07634	0.395975
$417$	−2.50244	−0.122545
$418$	−1.17201	−0.0573251
$419$	−33.3636	−1.62992	−0.814960	−	0.579518i	$-0.803241\pi$
$419$	−33.3636	−1.62992	−0.814960	+	0.579518i	$0.803241\pi$
$420$	−27.5910	−1.34630
$421$	−32.7426	−1.59578	−0.797888	−	0.602806i	$-0.794049\pi$
$421$	−32.7426	−1.59578	−0.797888	+	0.602806i	$0.794049\pi$
$422$	19.3835	0.943572
$423$	18.7438	0.911353
$424$	4.30489	0.209064
$425$	−1.20881	−0.0586357
$426$	46.9712	2.27576
$427$	−9.23254	−0.446794
$428$	11.8009	0.570419
$429$	−1.38710	−0.0669696
$430$	1.59430	0.0768841
$431$	−0.419800	−0.0202210	−0.0101105	−	0.999949i	$-0.503218\pi$
$431$	−0.419800	−0.0202210	−0.0101105	+	0.999949i	$0.503218\pi$
$432$	−4.06080	−0.195375
$433$	20.5649	0.988284	0.494142	−	0.869381i	$-0.335482\pi$
$433$	20.5649	0.988284	0.494142	+	0.869381i	$0.335482\pi$
$434$	−73.6236	−3.53405
$435$	12.7218	0.609965
$436$	20.6602	0.989443
$437$	0.991364	0.0474234
$438$	−63.3615	−3.02753
$439$	9.91692	0.473309	0.236654	−	0.971594i	$-0.423949\pi$
$439$	9.91692	0.473309	0.236654	+	0.971594i	$0.423949\pi$
$440$	−0.581695	−0.0277312
$441$	20.7098	0.986181
$442$	−0.745400	−0.0354551
$443$	36.7168	1.74447	0.872235	−	0.489087i	$-0.162670\pi$
$443$	36.7168	1.74447	0.872235	+	0.489087i	$0.162670\pi$
$444$	24.9266	1.18296
$445$	−11.5804	−0.548965
$446$	45.5052	2.15474
$447$	4.49733	0.212716
$448$	−41.8130	−1.97548
$449$	−14.6997	−0.693723	−0.346861	−	0.937916i	$-0.612753\pi$
$449$	−14.6997	−0.693723	−0.346861	+	0.937916i	$0.612753\pi$
$450$	17.3102	0.816012
$451$	0.911340	0.0429133
$452$	28.2216	1.32743
$453$	−13.6649	−0.642033
$454$	−5.47564	−0.256985
$455$	4.99227	0.234041
$456$	1.69650	0.0794459
$457$	36.3611	1.70090	0.850450	−	0.526056i	$-0.176330\pi$
$457$	36.3611	1.70090	0.850450	+	0.526056i	$0.176330\pi$
$458$	29.9751	1.40065
$459$	0.463233	0.0216219
$460$	3.15985	0.147329
$461$	24.9163	1.16047	0.580233	−	0.814451i	$-0.302961\pi$
$461$	24.9163	1.16047	0.580233	+	0.814451i	$0.302961\pi$
$462$	11.4058	0.530645
$463$	20.6262	0.958580	0.479290	−	0.877657i	$-0.340894\pi$
$463$	20.6262	0.958580	0.479290	+	0.877657i	$0.340894\pi$
$464$	13.4331	0.623614
$465$	−26.5088	−1.22932
$466$	1.63717	0.0758404
$467$	−0.512602	−0.0237204	−0.0118602	−	0.999930i	$-0.503775\pi$
$467$	−0.512602	−0.0237204	−0.0118602	+	0.999930i	$0.503775\pi$
$468$	5.78772	0.267537
$469$	−36.7331	−1.69618
$470$	−20.3488	−0.938618
$471$	−28.6964	−1.32226
$472$	4.09282	0.188387
$473$	−0.357356	−0.0164312
$474$	−56.2030	−2.58149
$475$	−3.19685	−0.146682
$476$	3.32338	0.152327
$477$	−13.6419	−0.624620
$478$	44.9871	2.05766
$479$	−36.3578	−1.66123	−0.830615	−	0.556847i	$-0.812011\pi$
$479$	−36.3578	−1.66123	−0.830615	+	0.556847i	$0.812011\pi$
$480$	−23.9115	−1.09141
$481$	−4.51017	−0.205646
$482$	−60.5053	−2.75594
$483$	−9.64774	−0.438987
$484$	−25.2202	−1.14637
$485$	−20.5362	−0.932499
$486$	−42.3774	−1.92228
$487$	−23.8286	−1.07978	−0.539889	−	0.841736i	$-0.681534\pi$
$487$	−23.8286	−1.07978	−0.539889	+	0.841736i	$0.681534\pi$
$488$	1.80943	0.0819089
$489$	15.7691	0.713102
$490$	−22.4831	−1.01568
$491$	−14.5725	−0.657648	−0.328824	−	0.944391i	$-0.606652\pi$
$491$	−14.5725	−0.657648	−0.328824	+	0.944391i	$0.606652\pi$
$492$	−8.47173	−0.381935
$493$	−1.53237	−0.0690143
$494$	−1.97131	−0.0886935
$495$	1.84335	0.0828524
$496$	−27.9908	−1.25682
$497$	37.8924	1.69971
$498$	−76.9831	−3.44969
$499$	−8.33960	−0.373332	−0.186666	−	0.982423i	$-0.559768\pi$
$499$	−8.33960	−0.373332	−0.186666	+	0.982423i	$0.559768\pi$
$500$	−25.2201	−1.12788
$501$	−37.4707	−1.67407
$502$	−30.1976	−1.34778
$503$	1.20170	0.0535812	0.0267906	−	0.999641i	$-0.491471\pi$
$503$	1.20170	0.0535812	0.0267906	+	0.999641i	$0.491471\pi$
$504$	−7.41063	−0.330096
$505$	5.04612	0.224549
$506$	−1.30624	−0.0580697
$507$	−2.33308	−0.103616
$508$	−16.2652	−0.721653
$509$	4.83702	0.214397	0.107199	−	0.994238i	$-0.465812\pi$
$509$	4.83702	0.214397	0.107199	+	0.994238i	$0.465812\pi$
$510$	2.20689	0.0977229
$511$	−51.1148	−2.26118
$512$	−30.0689	−1.32887
$513$	1.22508	0.0540887
$514$	−65.6694	−2.89655
$515$	−15.6044	−0.687610
$516$	3.32195	0.146241
$517$	4.56108	0.200596
$518$	37.0861	1.62947
$519$	55.8596	2.45196
$520$	−0.978402	−0.0429058
$521$	32.4755	1.42278	0.711388	−	0.702799i	$-0.248067\pi$
$521$	32.4755	1.42278	0.711388	+	0.702799i	$0.248067\pi$
$522$	21.9436	0.960447
$523$	21.3802	0.934893	0.467446	−	0.884021i	$-0.345174\pi$
$523$	21.3802	0.934893	0.467446	+	0.884021i	$0.345174\pi$
$524$	−39.1395	−1.70982
$525$	31.1111	1.35780
$526$	−28.3200	−1.23481
$527$	3.19303	0.139091
$528$	4.33635	0.188715
$529$	−21.8951	−0.951961
$530$	14.8100	0.643306
$531$	−12.9699	−0.562844
$532$	8.78913	0.381057
$533$	1.53286	0.0663955
$534$	−44.5015	−1.92577
$535$	6.32177	0.273314
$536$	7.19908	0.310953
$537$	2.89000	0.124713
$538$	13.5150	0.582674
$539$	5.03950	0.217066
$540$	3.90480	0.168036
$541$	5.85414	0.251689	0.125844	−	0.992050i	$-0.459836\pi$
$541$	5.85414	0.251689	0.125844	+	0.992050i	$0.459836\pi$
$542$	45.9817	1.97509
$543$	40.8135	1.75147
$544$	2.88018	0.123487
$545$	11.0677	0.474087
$546$	19.1844	0.821015
$547$	−37.0025	−1.58211	−0.791055	−	0.611745i	$-0.790468\pi$
$547$	−37.0025	−1.58211	−0.791055	+	0.611745i	$0.790468\pi$
$548$	−22.3950	−0.956667
$549$	−5.73395	−0.244719
$550$	4.21225	0.179611
$551$	−4.05255	−0.172644
$552$	1.89080	0.0804778
$553$	−45.3399	−1.92805
$554$	−62.3927	−2.65081
$555$	13.3532	0.566811
$556$	2.54083	0.107755
$557$	7.66363	0.324718	0.162359	−	0.986732i	$-0.448090\pi$
$557$	7.66363	0.324718	0.162359	+	0.986732i	$0.448090\pi$
$558$	−45.7245	−1.93567
$559$	−0.601067	−0.0254224
$560$	−15.6068	−0.659509
$561$	−0.494666	−0.0208848
$562$	43.8409	1.84932
$563$	−16.2677	−0.685604	−0.342802	−	0.939408i	$-0.611376\pi$
$563$	−16.2677	−0.685604	−0.342802	+	0.939408i	$0.611376\pi$
$564$	−42.3994	−1.78534
$565$	15.1184	0.636034
$566$	−3.01740	−0.126831
$567$	−40.7574	−1.71165
$568$	−7.42630	−0.311601
$569$	−2.22546	−0.0932960	−0.0466480	−	0.998911i	$-0.514854\pi$
$569$	−2.22546	−0.0932960	−0.0466480	+	0.998911i	$0.514854\pi$
$570$	5.83643	0.244461
$571$	−4.02640	−0.168500	−0.0842498	−	0.996445i	$-0.526849\pi$
$571$	−4.02640	−0.168500	−0.0842498	+	0.996445i	$0.526849\pi$
$572$	1.40838	0.0588871
$573$	−30.0235	−1.25425
$574$	−12.6044	−0.526096
$575$	−3.56299	−0.148587
$576$	−25.9683	−1.08201
$577$	−2.73297	−0.113775	−0.0568876	−	0.998381i	$-0.518118\pi$
$577$	−2.73297	−0.113775	−0.0568876	+	0.998381i	$0.518118\pi$
$578$	35.2673	1.46693
$579$	−0.394480	−0.0163940
$580$	−12.9170	−0.536349
$581$	−62.1036	−2.57649
$582$	−78.9168	−3.27120
$583$	−3.31960	−0.137484
$584$	10.0177	0.414534
$585$	3.10049	0.128189
$586$	−44.3986	−1.83409
$587$	4.70475	0.194186	0.0970929	−	0.995275i	$-0.469046\pi$
$587$	4.70475	0.194186	0.0970929	+	0.995275i	$0.469046\pi$
$588$	−46.8467	−1.93192
$589$	8.44440	0.347946
$590$	14.0804	0.579683
$591$	43.4954	1.78916
$592$	14.0997	0.579494
$593$	−7.51256	−0.308504	−0.154252	−	0.988032i	$-0.549297\pi$
$593$	−7.51256	−0.308504	−0.154252	+	0.988032i	$0.549297\pi$
$594$	−1.61420	−0.0662313
$595$	1.78034	0.0729868
$596$	−4.56632	−0.187044
$597$	30.5491	1.25029
$598$	−2.19708	−0.0898455
$599$	11.6528	0.476121	0.238061	−	0.971250i	$-0.423488\pi$
$599$	11.6528	0.476121	0.238061	+	0.971250i	$0.423488\pi$
$600$	−6.09726	−0.248920
$601$	18.4273	0.751663	0.375832	−	0.926688i	$-0.377357\pi$
$601$	18.4273	0.751663	0.375832	+	0.926688i	$0.377357\pi$
$602$	4.94245	0.201439
$603$	−22.8134	−0.929032
$604$	13.8745	0.564546
$605$	−13.5105	−0.549280
$606$	19.3913	0.787719
$607$	16.1309	0.654735	0.327367	−	0.944897i	$-0.393839\pi$
$607$	16.1309	0.654735	0.327367	+	0.944897i	$0.393839\pi$
$608$	7.61702	0.308911
$609$	39.4385	1.59813
$610$	6.22493	0.252040
$611$	7.67167	0.310363
$612$	2.06401	0.0834328
$613$	14.6581	0.592035	0.296018	−	0.955183i	$-0.404341\pi$
$613$	14.6581	0.592035	0.296018	+	0.955183i	$0.404341\pi$
$614$	46.0502	1.85844
$615$	−4.53832	−0.183003
$616$	−1.80329	−0.0726568
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−59.9647	−2.41214
$619$	−30.9896	−1.24558	−0.622789	−	0.782390i	$-0.714001\pi$
$619$	−30.9896	−1.24558	−0.622789	+	0.782390i	$0.714001\pi$
$620$	26.9155	1.08095
$621$	1.36539	0.0547912
$622$	3.77024	0.151173
$623$	−35.9001	−1.43831
$624$	7.29367	0.291980
$625$	3.43771	0.137508
$626$	5.12117	0.204683
$627$	−1.30821	−0.0522449
$628$	29.1366	1.16268
$629$	−1.60841	−0.0641316
$630$	−25.4946	−1.01573
$631$	24.2934	0.967105	0.483553	−	0.875315i	$-0.339346\pi$
$631$	24.2934	0.967105	0.483553	+	0.875315i	$0.339346\pi$
$632$	8.88587	0.353461
$633$	21.6359	0.859951
$634$	4.26368	0.169332
$635$	−8.71331	−0.345777
$636$	30.8587	1.22363
$637$	8.47636	0.335846
$638$	5.33974	0.211402
$639$	23.5334	0.930967
$640$	7.69409	0.304136
$641$	45.4853	1.79656	0.898280	−	0.439423i	$-0.144817\pi$
$641$	45.4853	1.79656	0.898280	+	0.439423i	$0.144817\pi$
$642$	24.2934	0.958785
$643$	17.5784	0.693223	0.346612	−	0.938009i	$-0.387332\pi$
$643$	17.5784	0.693223	0.346612	+	0.938009i	$0.387332\pi$
$644$	9.79574	0.386006
$645$	1.77957	0.0700705
$646$	−0.703008	−0.0276595
$647$	45.3923	1.78456	0.892278	−	0.451487i	$-0.149106\pi$
$647$	45.3923	1.78456	0.892278	+	0.451487i	$0.149106\pi$
$648$	7.98778	0.313790
$649$	−3.15607	−0.123887
$650$	7.08494	0.277894
$651$	−82.1791	−3.22085
$652$	−16.0110	−0.627038
$653$	−25.9357	−1.01494	−0.507471	−	0.861669i	$-0.669420\pi$
$653$	−25.9357	−1.01494	−0.507471	+	0.861669i	$0.669420\pi$
$654$	42.5311	1.66310
$655$	−20.9671	−0.819251
$656$	−4.79203	−0.187097
$657$	−31.7452	−1.23850
$658$	−63.0825	−2.45921
$659$	−15.8752	−0.618411	−0.309205	−	0.950995i	$-0.600063\pi$
$659$	−15.8752	−0.618411	−0.309205	+	0.950995i	$0.600063\pi$
$660$	−4.16976	−0.162308
$661$	6.26682	0.243751	0.121875	−	0.992545i	$-0.461109\pi$
$661$	6.26682	0.243751	0.121875	+	0.992545i	$0.461109\pi$
$662$	28.6651	1.11410
$663$	−0.832020	−0.0323130
$664$	12.1713	0.472337
$665$	4.70835	0.182582
$666$	23.0326	0.892497
$667$	−4.51669	−0.174887
$668$	38.0455	1.47203
$669$	50.7932	1.96378
$670$	24.7668	0.956826
$671$	−1.39529	−0.0538646
$672$	−74.1272	−2.85952
$673$	−1.88677	−0.0727295	−0.0363648	−	0.999339i	$-0.511578\pi$
$673$	−1.88677	−0.0727295	−0.0363648	+	0.999339i	$0.511578\pi$
$674$	−27.7448	−1.06869
$675$	−4.40298	−0.169471
$676$	2.36887	0.0911103
$677$	22.5363	0.866139	0.433069	−	0.901361i	$-0.357431\pi$
$677$	22.5363	0.866139	0.433069	+	0.901361i	$0.357431\pi$
$678$	58.0971	2.23121
$679$	−63.6635	−2.44318
$680$	−0.348917	−0.0133804
$681$	−6.11195	−0.234210
$682$	−11.1266	−0.426058
$683$	−8.43173	−0.322631	−0.161316	−	0.986903i	$-0.551574\pi$
$683$	−8.43173	−0.322631	−0.161316	+	0.986903i	$0.551574\pi$
$684$	5.45856	0.208713
$685$	−11.9970	−0.458383
$686$	−12.1398	−0.463499
$687$	33.4584	1.27652
$688$	1.87906	0.0716384
$689$	−5.58352	−0.212715
$690$	6.50487	0.247636
$691$	−32.8082	−1.24808	−0.624042	−	0.781391i	$-0.714511\pi$
$691$	−32.8082	−1.24808	−0.624042	+	0.781391i	$0.714511\pi$
$692$	−56.7165	−2.15604
$693$	5.71451	0.217076
$694$	−7.02596	−0.266702
$695$	1.36113	0.0516305
$696$	−7.72931	−0.292979
$697$	0.546648	0.0207058
$698$	−43.6854	−1.65352
$699$	1.82742	0.0691194
$700$	−31.5884	−1.19393
$701$	−44.5816	−1.68382	−0.841911	−	0.539616i	$-0.818569\pi$
$701$	−44.5816	−1.68382	−0.841911	+	0.539616i	$0.818569\pi$
$702$	−2.71506	−0.102473
$703$	−4.25367	−0.160430
$704$	−6.31909	−0.238160
$705$	−22.7134	−0.855436
$706$	−23.7422	−0.893548
$707$	15.6433	0.588327
$708$	29.3385	1.10261
$709$	−37.1682	−1.39588	−0.697940	−	0.716157i	$-0.745900\pi$
$709$	−37.1682	−1.39588	−0.697940	+	0.716157i	$0.745900\pi$
$710$	−25.5485	−0.958819
$711$	−28.1587	−1.05603
$712$	7.03583	0.263679
$713$	9.41154	0.352465
$714$	6.84152	0.256038
$715$	0.754468	0.0282155
$716$	−2.93433	−0.109661
$717$	50.2149	1.87531
$718$	−20.9121	−0.780431
$719$	−29.8968	−1.11496	−0.557482	−	0.830189i	$-0.688232\pi$
$719$	−29.8968	−1.11496	−0.557482	+	0.830189i	$0.688232\pi$
$720$	−9.69275	−0.361228
$721$	−48.3746	−1.80156
$722$	37.8543	1.40879
$723$	−67.5364	−2.51171
$724$	−41.4396	−1.54009
$725$	14.5650	0.540929
$726$	−51.9184	−1.92687
$727$	16.3942	0.608028	0.304014	−	0.952668i	$-0.401673\pi$
$727$	16.3942	0.608028	0.304014	+	0.952668i	$0.401673\pi$
$728$	−3.03311	−0.112415
$729$	−16.2210	−0.600779
$730$	34.4635	1.27555
$731$	−0.214352	−0.00792811
$732$	12.9705	0.479403
$733$	−17.7639	−0.656126	−0.328063	−	0.944656i	$-0.606396\pi$
$733$	−17.7639	−0.656126	−0.328063	+	0.944656i	$0.606396\pi$
$734$	18.2318	0.672948
$735$	−25.0958	−0.925673
$736$	8.48940	0.312923
$737$	−5.55138	−0.204488
$738$	−7.82805	−0.288155
$739$	53.4089	1.96468	0.982339	−	0.187110i	$-0.0599120\pi$
$739$	53.4089	1.96468	0.982339	+	0.187110i	$0.0599120\pi$
$740$	−13.5580	−0.498403
$741$	−2.20039	−0.0808333
$742$	45.9121	1.68549
$743$	−31.4914	−1.15531	−0.577653	−	0.816282i	$-0.696031\pi$
$743$	−31.4914	−1.15531	−0.577653	+	0.816282i	$0.696031\pi$
$744$	16.1058	0.590466
$745$	−2.44618	−0.0896212
$746$	−76.2117	−2.79031
$747$	−38.5699	−1.41120
$748$	0.502254	0.0183642
$749$	19.5979	0.716092
$750$	−51.9181	−1.89578
$751$	50.6213	1.84720	0.923599	−	0.383360i	$-0.125233\pi$
$751$	50.6213	1.84720	0.923599	+	0.383360i	$0.125233\pi$
$752$	−23.9832	−0.874578
$753$	−33.7067	−1.22834
$754$	8.98136	0.327082
$755$	7.43260	0.270500
$756$	12.1051	0.440260
$757$	32.5132	1.18171	0.590857	−	0.806776i	$-0.298790\pi$
$757$	32.5132	1.18171	0.590857	+	0.806776i	$0.298790\pi$
$758$	−40.9676	−1.48801
$759$	−1.45804	−0.0529234
$760$	−0.922759	−0.0334720
$761$	−51.9771	−1.88417	−0.942085	−	0.335374i	$-0.891137\pi$
$761$	−51.9771	−1.88417	−0.942085	+	0.335374i	$0.891137\pi$
$762$	−33.4837	−1.21299
$763$	34.3106	1.24213
$764$	30.4841	1.10287
$765$	1.10569	0.0399765
$766$	−57.1552	−2.06510
$767$	−5.30846	−0.191678
$768$	−20.0277	−0.722689
$769$	−48.9162	−1.76396	−0.881982	−	0.471284i	$-0.843791\pi$
$769$	−48.9162	−1.76396	−0.881982	+	0.471284i	$0.843791\pi$
$770$	−6.20383	−0.223570
$771$	−73.3006	−2.63986
$772$	0.400531	0.0144154
$773$	25.9124	0.932005	0.466002	−	0.884784i	$-0.345694\pi$
$773$	25.9124	0.932005	0.466002	+	0.884784i	$0.345694\pi$
$774$	3.06955	0.110333
$775$	−30.3494	−1.09018
$776$	12.4770	0.447898
$777$	41.3958	1.48506
$778$	26.0092	0.932475
$779$	1.44568	0.0517970
$780$	−7.01347	−0.251122
$781$	5.72659	0.204913
$782$	−0.783523	−0.0280187
$783$	−5.58152	−0.199467
$784$	−26.4988	−0.946386
$785$	15.6085	0.557092
$786$	−80.5726	−2.87393
$787$	−25.6651	−0.914862	−0.457431	−	0.889245i	$-0.651230\pi$
$787$	−25.6651	−0.914862	−0.457431	+	0.889245i	$0.651230\pi$
$788$	−44.1626	−1.57323
$789$	−31.6110	−1.12538
$790$	30.5699	1.08763
$791$	46.8679	1.66643
$792$	−1.11995	−0.0397957
$793$	−2.34686	−0.0833394
$794$	76.3051	2.70797
$795$	16.5310	0.586296
$796$	−31.0178	−1.09940
$797$	30.1552	1.06815	0.534076	−	0.845436i	$-0.320660\pi$
$797$	30.1552	1.06815	0.534076	+	0.845436i	$0.320660\pi$
$798$	18.0933	0.640497
$799$	2.73587	0.0967881
$800$	−27.3758	−0.967880
$801$	−22.2961	−0.787792
$802$	−7.93194	−0.280086
$803$	−7.72484	−0.272604
$804$	51.6051	1.81997
$805$	5.24759	0.184953
$806$	−18.7147	−0.659197
$807$	15.0855	0.531036
$808$	−3.06583	−0.107856
$809$	−11.1658	−0.392569	−0.196285	−	0.980547i	$-0.562888\pi$
$809$	−11.1658	−0.392569	−0.196285	+	0.980547i	$0.562888\pi$
$810$	27.4802	0.965555
$811$	−42.8489	−1.50463	−0.752315	−	0.658804i	$-0.771063\pi$
$811$	−42.8489	−1.50463	−0.752315	+	0.658804i	$0.771063\pi$
$812$	−40.0436	−1.40525
$813$	51.3251	1.80005
$814$	5.60473	0.196446
$815$	−8.57710	−0.300443
$816$	2.60106	0.0910555
$817$	−0.566883	−0.0198327
$818$	−3.74276	−0.130863
$819$	9.61172	0.335861
$820$	4.60794	0.160916
$821$	16.3169	0.569465	0.284732	−	0.958607i	$-0.408095\pi$
$821$	16.3169	0.569465	0.284732	+	0.958607i	$0.408095\pi$
$822$	−46.1024	−1.60801
$823$	−32.6925	−1.13959	−0.569794	−	0.821788i	$-0.692977\pi$
$823$	−32.6925	−1.13959	−0.569794	+	0.821788i	$0.692977\pi$
$824$	9.48062	0.330273
$825$	4.70174	0.163694
$826$	43.6503	1.51879
$827$	42.4194	1.47507	0.737534	−	0.675310i	$-0.235990\pi$
$827$	42.4194	1.47507	0.737534	+	0.675310i	$0.235990\pi$
$828$	6.08373	0.211424
$829$	−29.6322	−1.02917	−0.514585	−	0.857439i	$-0.672054\pi$
$829$	−29.6322	−1.02917	−0.514585	+	0.857439i	$0.672054\pi$
$830$	41.8726	1.45342
$831$	−69.6431	−2.41589
$832$	−10.6286	−0.368481
$833$	3.02283	0.104735
$834$	5.23057	0.181120
$835$	20.3810	0.705315
$836$	1.32828	0.0459395
$837$	11.6304	0.402004
$838$	69.7361	2.40899
$839$	32.0792	1.10750	0.553748	−	0.832684i	$-0.313197\pi$
$839$	32.0792	1.10750	0.553748	+	0.832684i	$0.313197\pi$
$840$	8.98009	0.309843
$841$	−10.5365	−0.363326
$842$	68.4380	2.35853
$843$	48.9355	1.68543
$844$	−21.9678	−0.756164
$845$	1.26900	0.0436551
$846$	−39.1779	−1.34696
$847$	−41.8834	−1.43913
$848$	17.4552	0.599415
$849$	−3.36804	−0.115591
$850$	2.52663	0.0866626
$851$	−4.74084	−0.162514
$852$	−53.2338	−1.82376
$853$	10.0400	0.343763	0.171882	−	0.985118i	$-0.445015\pi$
$853$	10.0400	0.343763	0.171882	+	0.985118i	$0.445015\pi$
$854$	19.2977	0.660354
$855$	2.92416	0.100004
$856$	−3.84087	−0.131278
$857$	43.4488	1.48418	0.742091	−	0.670300i	$-0.233834\pi$
$857$	43.4488	1.48418	0.742091	+	0.670300i	$0.233834\pi$
$858$	2.89929	0.0989800
$859$	−43.5521	−1.48598	−0.742988	−	0.669304i	$-0.766592\pi$
$859$	−43.5521	−1.48598	−0.742988	+	0.669304i	$0.766592\pi$
$860$	−1.80687	−0.0616138
$861$	−14.0691	−0.479473
$862$	0.877459	0.0298864
$863$	29.5209	1.00490	0.502451	−	0.864606i	$-0.332432\pi$
$863$	29.5209	1.00490	0.502451	+	0.864606i	$0.332432\pi$
$864$	10.4908	0.356905
$865$	−30.3831	−1.03306
$866$	−42.9843	−1.46067
$867$	39.3656	1.33693
$868$	83.4398	2.83213
$869$	−6.85210	−0.232442
$870$	−26.5910	−0.901518
$871$	−9.33733	−0.316383
$872$	−6.72431	−0.227714
$873$	−39.5387	−1.33818
$874$	−2.07213	−0.0700909
$875$	−41.8832	−1.41591
$876$	71.8094	2.42622
$877$	−27.8800	−0.941439	−0.470720	−	0.882283i	$-0.656006\pi$
$877$	−27.8800	−0.941439	−0.470720	+	0.882283i	$0.656006\pi$
$878$	−20.7282	−0.699542
$879$	−49.5580	−1.67155
$880$	−2.35862	−0.0795091
$881$	44.4122	1.49629	0.748143	−	0.663537i	$-0.230946\pi$
$881$	44.4122	1.49629	0.748143	+	0.663537i	$0.230946\pi$
$882$	−43.2873	−1.45756
$883$	−10.0140	−0.336997	−0.168498	−	0.985702i	$-0.553892\pi$
$883$	−10.0140	−0.336997	−0.168498	+	0.985702i	$0.553892\pi$
$884$	0.844784	0.0284132
$885$	15.7167	0.528311
$886$	−76.7449	−2.57830
$887$	−34.8779	−1.17108	−0.585542	−	0.810642i	$-0.699118\pi$
$887$	−34.8779	−1.17108	−0.585542	+	0.810642i	$0.699118\pi$
$888$	−8.11289	−0.272251
$889$	−27.0118	−0.905948
$890$	24.2052	0.811361
$891$	−6.15956	−0.206353
$892$	−51.5724	−1.72677
$893$	7.23537	0.242122
$894$	−9.40024	−0.314391
$895$	−1.57192	−0.0525436
$896$	23.8522	0.796846
$897$	−2.45240	−0.0818832
$898$	30.7251	1.02531
$899$	−38.4730	−1.28315
$900$	−19.6182	−0.653940
$901$	−1.99119	−0.0663362
$902$	−1.90487	−0.0634251
$903$	5.51679	0.183587
$904$	−9.18535	−0.305500
$905$	−22.1992	−0.737928
$906$	28.5621	0.948913
$907$	−46.1010	−1.53076	−0.765380	−	0.643579i	$-0.777449\pi$
$907$	−46.1010	−1.53076	−0.765380	+	0.643579i	$0.777449\pi$
$908$	6.20571	0.205944
$909$	9.71540	0.322240
$910$	−10.4348	−0.345909
$911$	0.856350	0.0283721	0.0141861	−	0.999899i	$-0.495484\pi$
$911$	0.856350	0.0283721	0.0141861	+	0.999899i	$0.495484\pi$
$912$	6.87886	0.227782
$913$	−9.38555	−0.310616
$914$	−76.0013	−2.51390
$915$	6.94831	0.229704
$916$	−33.9717	−1.12246
$917$	−64.9993	−2.14647
$918$	−0.968242	−0.0319568
$919$	3.77782	0.124619	0.0623095	−	0.998057i	$-0.480153\pi$
$919$	3.77782	0.124619	0.0623095	+	0.998057i	$0.480153\pi$
$920$	−1.02844	−0.0339067
$921$	51.4015	1.69374
$922$	−52.0796	−1.71515
$923$	9.63204	0.317042
$924$	−12.9265	−0.425251
$925$	15.2878	0.502659
$926$	−43.1125	−1.41676
$927$	−30.0434	−0.986755
$928$	−34.7034	−1.13919
$929$	14.3255	0.470004	0.235002	−	0.971995i	$-0.424490\pi$
$929$	14.3255	0.470004	0.235002	+	0.971995i	$0.424490\pi$
$930$	55.4083	1.81691
$931$	7.99429	0.262002
$932$	−1.85545	−0.0607774
$933$	4.20837	0.137776
$934$	1.07143	0.0350583
$935$	0.269058	0.00879914
$936$	−1.88374	−0.0615720
$937$	−1.69404	−0.0553419	−0.0276709	−	0.999617i	$-0.508809\pi$
$937$	−1.69404	−0.0553419	−0.0276709	+	0.999617i	$0.508809\pi$
$938$	76.7789	2.50692
$939$	5.71628	0.186544
$940$	23.0618	0.752195
$941$	57.7807	1.88360	0.941799	−	0.336178i	$-0.109134\pi$
$941$	57.7807	1.88360	0.941799	+	0.336178i	$0.109134\pi$
$942$	59.9807	1.95428
$943$	1.61126	0.0524698
$944$	16.5953	0.540132
$945$	6.48474	0.210948
$946$	0.746939	0.0242851
$947$	47.4372	1.54150	0.770751	−	0.637137i	$-0.219881\pi$
$947$	47.4372	1.54150	0.770751	+	0.637137i	$0.219881\pi$
$948$	63.6965	2.06877
$949$	−12.9931	−0.421773
$950$	6.68201	0.216793
$951$	4.75914	0.154326
$952$	−1.08167	−0.0350570
$953$	−44.0583	−1.42719	−0.713594	−	0.700559i	$-0.752934\pi$
$953$	−44.0583	−1.42719	−0.713594	+	0.700559i	$0.752934\pi$
$954$	28.5141	0.923177
$955$	16.3303	0.528438
$956$	−50.9852	−1.64898
$957$	5.96025	0.192667
$958$	75.9945	2.45527
$959$	−37.1916	−1.20098
$960$	31.4680	1.01563
$961$	49.1672	1.58604
$962$	9.42708	0.303941
$963$	12.1714	0.392219
$964$	68.5725	2.20857
$965$	0.214565	0.00690709
$966$	20.1655	0.648816
$967$	20.4034	0.656128	0.328064	−	0.944656i	$-0.393604\pi$
$967$	20.4034	0.656128	0.328064	+	0.944656i	$0.393604\pi$
$968$	8.20847	0.263830
$969$	−0.784702	−0.0252082
$970$	42.9243	1.37822
$971$	−17.9394	−0.575704	−0.287852	−	0.957675i	$-0.592941\pi$
$971$	−17.9394	−0.575704	−0.287852	+	0.957675i	$0.592941\pi$
$972$	48.0275	1.54048
$973$	4.21959	0.135274
$974$	49.8062	1.59589
$975$	7.90826	0.253267
$976$	7.33676	0.234844
$977$	−22.8010	−0.729470	−0.364735	−	0.931111i	$-0.618840\pi$
$977$	−22.8010	−0.729470	−0.364735	+	0.931111i	$0.618840\pi$
$978$	−32.9602	−1.05395
$979$	−5.42549	−0.173399
$980$	25.4808	0.813955
$981$	21.3088	0.680339
$982$	30.4592	0.971992
$983$	31.5278	1.00558	0.502791	−	0.864408i	$-0.332306\pi$
$983$	31.5278	1.00558	0.502791	+	0.864408i	$0.332306\pi$
$984$	2.75731	0.0878998
$985$	−23.6580	−0.753806
$986$	3.20293	0.102002
$987$	−70.4131	−2.24127
$988$	2.23414	0.0710776
$989$	−0.631808	−0.0200903
$990$	−3.85294	−0.122454
$991$	6.06283	0.192592	0.0962961	−	0.995353i	$-0.469300\pi$
$991$	6.06283	0.192592	0.0962961	+	0.995353i	$0.469300\pi$
$992$	72.3124	2.29592
$993$	31.9962	1.01537
$994$	−79.2022	−2.51214
$995$	−16.6163	−0.526771
$996$	87.2472	2.76453
$997$	−3.19880	−0.101307	−0.0506535	−	0.998716i	$-0.516130\pi$
$997$	−3.19880	−0.101307	−0.0506535	+	0.998716i	$0.516130\pi$
$998$	17.4313	0.551778
$999$	−5.85851	−0.185355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.20	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.20	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.09018 q^{2} -2.33308 q^{3} +2.36887 q^{4} +1.26900 q^{5} +4.87656 q^{6} +3.93400 q^{7} -0.771000 q^{8} +2.44324 q^{9} +O(q^{10})\)	\(q-2.09018 q^{2} -2.33308 q^{3} +2.36887 q^{4} +1.26900 q^{5} +4.87656 q^{6} +3.93400 q^{7} -0.771000 q^{8} +2.44324 q^{9} -2.65245 q^{10} +0.594536 q^{11} -5.52675 q^{12} +1.00000 q^{13} -8.22278 q^{14} -2.96068 q^{15} -3.12620 q^{16} +0.356619 q^{17} -5.10683 q^{18} +0.943128 q^{19} +3.00610 q^{20} -9.17832 q^{21} -1.24269 q^{22} +1.05114 q^{23} +1.79880 q^{24} -3.38963 q^{25} -2.09018 q^{26} +1.29896 q^{27} +9.31912 q^{28} -4.29692 q^{29} +6.18837 q^{30} +8.95361 q^{31} +8.07634 q^{32} -1.38710 q^{33} -0.745400 q^{34} +4.99227 q^{35} +5.78772 q^{36} -4.51017 q^{37} -1.97131 q^{38} -2.33308 q^{39} -0.978402 q^{40} +1.53286 q^{41} +19.1844 q^{42} -0.601067 q^{43} +1.40838 q^{44} +3.10049 q^{45} -2.19708 q^{46} +7.67167 q^{47} +7.29367 q^{48} +8.47636 q^{49} +7.08494 q^{50} -0.832020 q^{51} +2.36887 q^{52} -5.58352 q^{53} -2.71506 q^{54} +0.754468 q^{55} -3.03311 q^{56} -2.20039 q^{57} +8.98136 q^{58} -5.30846 q^{59} -7.01347 q^{60} -2.34686 q^{61} -18.7147 q^{62} +9.61172 q^{63} -10.6286 q^{64} +1.26900 q^{65} +2.89929 q^{66} -9.33733 q^{67} +0.844784 q^{68} -2.45240 q^{69} -10.4348 q^{70} +9.63204 q^{71} -1.88374 q^{72} -12.9931 q^{73} +9.42708 q^{74} +7.90826 q^{75} +2.23414 q^{76} +2.33890 q^{77} +4.87656 q^{78} -11.5251 q^{79} -3.96717 q^{80} -10.3603 q^{81} -3.20396 q^{82} -15.7864 q^{83} -21.7422 q^{84} +0.452552 q^{85} +1.25634 q^{86} +10.0250 q^{87} -0.458387 q^{88} -9.12560 q^{89} -6.48059 q^{90} +3.93400 q^{91} +2.49002 q^{92} -20.8895 q^{93} -16.0352 q^{94} +1.19683 q^{95} -18.8427 q^{96} -16.1829 q^{97} -17.7171 q^{98} +1.45259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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