LMFDB - Embedded newform 8039.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$1$
Dimension:	$279$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72088 q^{2} +2.51741 q^{3} +5.40317 q^{4} -2.91261 q^{5} -6.84957 q^{6} -4.81699 q^{7} -9.25961 q^{8} +3.33737 q^{9} +O(q^{10})$	\(q-2.72088 q^{2} +2.51741 q^{3} +5.40317 q^{4} -2.91261 q^{5} -6.84957 q^{6} -4.81699 q^{7} -9.25961 q^{8} +3.33737 q^{9} +7.92486 q^{10} +0.207020 q^{11} +13.6020 q^{12} -0.00618974 q^{13} +13.1064 q^{14} -7.33225 q^{15} +14.3879 q^{16} +0.438479 q^{17} -9.08056 q^{18} -4.74599 q^{19} -15.7374 q^{20} -12.1263 q^{21} -0.563277 q^{22} +2.04782 q^{23} -23.3103 q^{24} +3.48332 q^{25} +0.0168415 q^{26} +0.849290 q^{27} -26.0270 q^{28} +3.17426 q^{29} +19.9502 q^{30} +0.681209 q^{31} -20.6285 q^{32} +0.521156 q^{33} -1.19305 q^{34} +14.0300 q^{35} +18.0324 q^{36} +2.42173 q^{37} +12.9132 q^{38} -0.0155821 q^{39} +26.9697 q^{40} +1.82167 q^{41} +32.9943 q^{42} +4.63167 q^{43} +1.11857 q^{44} -9.72046 q^{45} -5.57186 q^{46} +11.8151 q^{47} +36.2203 q^{48} +16.2034 q^{49} -9.47769 q^{50} +1.10383 q^{51} -0.0334442 q^{52} +9.97842 q^{53} -2.31081 q^{54} -0.602971 q^{55} +44.6035 q^{56} -11.9476 q^{57} -8.63676 q^{58} +1.41446 q^{59} -39.6174 q^{60} -1.61850 q^{61} -1.85349 q^{62} -16.0761 q^{63} +27.3519 q^{64} +0.0180283 q^{65} -1.41800 q^{66} +7.35788 q^{67} +2.36918 q^{68} +5.15520 q^{69} -38.1740 q^{70} -2.24598 q^{71} -30.9027 q^{72} -0.971102 q^{73} -6.58924 q^{74} +8.76896 q^{75} -25.6434 q^{76} -0.997215 q^{77} +0.0423971 q^{78} -8.12305 q^{79} -41.9065 q^{80} -7.87408 q^{81} -4.95654 q^{82} -6.30040 q^{83} -65.5208 q^{84} -1.27712 q^{85} -12.6022 q^{86} +7.99091 q^{87} -1.91693 q^{88} -1.18535 q^{89} +26.4482 q^{90} +0.0298159 q^{91} +11.0647 q^{92} +1.71488 q^{93} -32.1475 q^{94} +13.8232 q^{95} -51.9306 q^{96} -8.77799 q^{97} -44.0874 q^{98} +0.690903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) $ 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * 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 $

$2$	−2.72088	−1.92395	−0.961975	−	0.273136i	$-0.911939\pi$
$2$	−2.72088	−1.92395	−0.961975	+	0.273136i	$0.911939\pi$
$3$	2.51741	1.45343	0.726714	−	0.686940i	$-0.241046\pi$
$3$	2.51741	1.45343	0.726714	+	0.686940i	$0.241046\pi$
$4$	5.40317	2.70159
$5$	−2.91261	−1.30256	−0.651280	−	0.758837i	$-0.725768\pi$
$5$	−2.91261	−1.30256	−0.651280	+	0.758837i	$0.725768\pi$
$6$	−6.84957	−2.79633
$7$	−4.81699	−1.82065	−0.910325	−	0.413893i	$-0.864169\pi$
$7$	−4.81699	−1.82065	−0.910325	+	0.413893i	$0.864169\pi$
$8$	−9.25961	−3.27377
$9$	3.33737	1.11246
$10$	7.92486	2.50606
$11$	0.207020	0.0624190	0.0312095	−	0.999513i	$-0.490064\pi$
$11$	0.207020	0.0624190	0.0312095	+	0.999513i	$0.490064\pi$
$12$	13.6020	3.92656
$13$	−0.00618974	−0.00171673	−0.000858363	−	1.00000i	$-0.500273\pi$
$13$	−0.00618974	−0.00171673	−0.000858363		1.00000i	$0.500273\pi$
$14$	13.1064	3.50284
$15$	−7.33225	−1.89318
$16$	14.3879	3.59698
$17$	0.438479	0.106347	0.0531734	−	0.998585i	$-0.483066\pi$
$17$	0.438479	0.106347	0.0531734	+	0.998585i	$0.483066\pi$
$18$	−9.08056	−2.14031
$19$	−4.74599	−1.08880	−0.544402	−	0.838825i	$-0.683243\pi$
$19$	−4.74599	−1.08880	−0.544402	+	0.838825i	$0.683243\pi$
$20$	−15.7374	−3.51898
$21$	−12.1263	−2.64619
$22$	−0.563277	−0.120091
$23$	2.04782	0.427000	0.213500	−	0.976943i	$-0.431514\pi$
$23$	2.04782	0.427000	0.213500	+	0.976943i	$0.431514\pi$
$24$	−23.3103	−4.75819
$25$	3.48332	0.696664
$26$	0.0168415	0.00330290
$27$	0.849290	0.163446
$28$	−26.0270	−4.91864
$29$	3.17426	0.589444	0.294722	−	0.955583i	$-0.404773\pi$
$29$	3.17426	0.589444	0.294722	+	0.955583i	$0.404773\pi$
$30$	19.9502	3.64238
$31$	0.681209	0.122349	0.0611744	−	0.998127i	$-0.480515\pi$
$31$	0.681209	0.122349	0.0611744	+	0.998127i	$0.480515\pi$
$32$	−20.6285	−3.64665
$33$	0.521156	0.0907216
$34$	−1.19305	−0.204606
$35$	14.0300	2.37151
$36$	18.0324	3.00539
$37$	2.42173	0.398130	0.199065	−	0.979986i	$-0.436209\pi$
$37$	2.42173	0.398130	0.199065	+	0.979986i	$0.436209\pi$
$38$	12.9132	2.09480
$39$	−0.0155821	−0.00249514
$40$	26.9697	4.26428
$41$	1.82167	0.284497	0.142249	−	0.989831i	$-0.454567\pi$
$41$	1.82167	0.284497	0.142249	+	0.989831i	$0.454567\pi$
$42$	32.9943	5.09113
$43$	4.63167	0.706323	0.353162	−	0.935562i	$-0.385107\pi$
$43$	4.63167	0.706323	0.353162	+	0.935562i	$0.385107\pi$
$44$	1.11857	0.168630
$45$	−9.72046	−1.44904
$46$	−5.57186	−0.821526
$47$	11.8151	1.72341	0.861706	−	0.507408i	$-0.169396\pi$
$47$	11.8151	1.72341	0.861706	+	0.507408i	$0.169396\pi$
$48$	36.2203	5.22796
$49$	16.2034	2.31477
$50$	−9.47769	−1.34035
$51$	1.10383	0.154568
$52$	−0.0334442	−0.00463788
$53$	9.97842	1.37064	0.685320	−	0.728242i	$-0.259662\pi$
$53$	9.97842	1.37064	0.685320	+	0.728242i	$0.259662\pi$
$54$	−2.31081	−0.314462
$55$	−0.602971	−0.0813046
$56$	44.6035	5.96039
$57$	−11.9476	−1.58250
$58$	−8.63676	−1.13406
$59$	1.41446	0.184147	0.0920734	−	0.995752i	$-0.470651\pi$
$59$	1.41446	0.184147	0.0920734	+	0.995752i	$0.470651\pi$
$60$	−39.6174	−5.11459
$61$	−1.61850	−0.207228	−0.103614	−	0.994618i	$-0.533041\pi$
$61$	−1.61850	−0.207228	−0.103614	+	0.994618i	$0.533041\pi$
$62$	−1.85349	−0.235393
$63$	−16.0761	−2.02539
$64$	27.3519	3.41899
$65$	0.0180283	0.00223614
$66$	−1.41800	−0.174544
$67$	7.35788	0.898908	0.449454	−	0.893304i	$-0.351619\pi$
$67$	7.35788	0.898908	0.449454	+	0.893304i	$0.351619\pi$
$68$	2.36918	0.287305
$69$	5.15520	0.620614
$70$	−38.1740	−4.56266
$71$	−2.24598	−0.266549	−0.133275	−	0.991079i	$-0.542549\pi$
$71$	−2.24598	−0.266549	−0.133275	+	0.991079i	$0.542549\pi$
$72$	−30.9027	−3.64192
$73$	−0.971102	−0.113659	−0.0568294	−	0.998384i	$-0.518099\pi$
$73$	−0.971102	−0.113659	−0.0568294	+	0.998384i	$0.518099\pi$
$74$	−6.58924	−0.765983
$75$	8.76896	1.01255
$76$	−25.6434	−2.94150
$77$	−0.997215	−0.113643
$78$	0.0423971	0.00480052
$79$	−8.12305	−0.913915	−0.456957	−	0.889489i	$-0.651061\pi$
$79$	−8.12305	−0.913915	−0.456957	+	0.889489i	$0.651061\pi$
$80$	−41.9065	−4.68529
$81$	−7.87408	−0.874898
$82$	−4.95654	−0.547358
$83$	−6.30040	−0.691559	−0.345780	−	0.938316i	$-0.612386\pi$
$83$	−6.30040	−0.691559	−0.345780	+	0.938316i	$0.612386\pi$
$84$	−65.5208	−7.14890
$85$	−1.27712	−0.138523
$86$	−12.6022	−1.35893
$87$	7.99091	0.856716
$88$	−1.91693	−0.204345
$89$	−1.18535	−0.125647	−0.0628236	−	0.998025i	$-0.520011\pi$
$89$	−1.18535	−0.125647	−0.0628236	+	0.998025i	$0.520011\pi$
$90$	26.4482	2.78788
$91$	0.0298159	0.00312556
$92$	11.0647	1.15358
$93$	1.71488	0.177825
$94$	−32.1475	−3.31576
$95$	13.8232	1.41823
$96$	−51.9306	−5.30014
$97$	−8.77799	−0.891270	−0.445635	−	0.895215i	$-0.647022\pi$
$97$	−8.77799	−0.891270	−0.445635	+	0.895215i	$0.647022\pi$
$98$	−44.0874	−4.45350
$99$	0.690903	0.0694384
$100$	18.8210	1.88210
$101$	4.22270	0.420175	0.210087	−	0.977683i	$-0.432625\pi$
$101$	4.22270	0.420175	0.210087	+	0.977683i	$0.432625\pi$
$102$	−3.00340	−0.297380
$103$	15.4044	1.51784	0.758921	−	0.651182i	$-0.225727\pi$
$103$	15.4044	1.51784	0.758921	+	0.651182i	$0.225727\pi$
$104$	0.0573146	0.00562016
$105$	35.3194	3.44682
$106$	−27.1500	−2.63705
$107$	1.57765	0.152517	0.0762586	−	0.997088i	$-0.475703\pi$
$107$	1.57765	0.152517	0.0762586	+	0.997088i	$0.475703\pi$
$108$	4.58886	0.441563
$109$	8.62069	0.825712	0.412856	−	0.910796i	$-0.364531\pi$
$109$	8.62069	0.825712	0.412856	+	0.910796i	$0.364531\pi$
$110$	1.64061	0.156426
$111$	6.09650	0.578654
$112$	−69.3065	−6.54885
$113$	6.92491	0.651441	0.325720	−	0.945466i	$-0.394393\pi$
$113$	6.92491	0.651441	0.325720	+	0.945466i	$0.394393\pi$
$114$	32.5080	3.04465
$115$	−5.96451	−0.556193
$116$	17.1510	1.59243
$117$	−0.0206574	−0.00190978
$118$	−3.84857	−0.354289
$119$	−2.11215	−0.193621
$120$	67.8938	6.19783
$121$	−10.9571	−0.996104
$122$	4.40375	0.398696
$123$	4.58590	0.413496
$124$	3.68069	0.330536
$125$	4.41750	0.395113
$126$	43.7410	3.89676
$127$	−3.81724	−0.338725	−0.169363	−	0.985554i	$-0.554171\pi$
$127$	−3.81724	−0.338725	−0.169363	+	0.985554i	$0.554171\pi$
$128$	−33.1640	−2.93131
$129$	11.6598	1.02659
$130$	−0.0490529	−0.00430222
$131$	−17.4568	−1.52521	−0.762605	−	0.646864i	$-0.776080\pi$
$131$	−17.4568	−1.52521	−0.762605	+	0.646864i	$0.776080\pi$
$132$	2.81590	0.245092
$133$	22.8614	1.98233
$134$	−20.0199	−1.72945
$135$	−2.47366	−0.212898
$136$	−4.06015	−0.348155
$137$	−16.6195	−1.41990	−0.709948	−	0.704254i	$-0.751282\pi$
$137$	−16.6195	−1.41990	−0.709948	+	0.704254i	$0.751282\pi$
$138$	−14.0267	−1.19403
$139$	−16.0036	−1.35741	−0.678704	−	0.734412i	$-0.737458\pi$
$139$	−16.0036	−1.35741	−0.678704	+	0.734412i	$0.737458\pi$
$140$	75.8067	6.40683
$141$	29.7435	2.50486
$142$	6.11105	0.512828
$143$	−0.00128140	−0.000107156 0
$144$	48.0178	4.00148
$145$	−9.24538	−0.767787
$146$	2.64225	0.218674
$147$	40.7906	3.36435
$148$	13.0850	1.07558
$149$	14.5785	1.19431	0.597157	−	0.802124i	$-0.296297\pi$
$149$	14.5785	1.19431	0.597157	+	0.802124i	$0.296297\pi$
$150$	−23.8593	−1.94810
$151$	−17.2609	−1.40467	−0.702335	−	0.711847i	$-0.747859\pi$
$151$	−17.2609	−1.40467	−0.702335	+	0.711847i	$0.747859\pi$
$152$	43.9460	3.56449
$153$	1.46337	0.118306
$154$	2.71330	0.218644
$155$	−1.98410	−0.159367
$156$	−0.0841930	−0.00674083
$157$	−22.3201	−1.78133	−0.890667	−	0.454655i	$-0.849762\pi$
$157$	−22.3201	−1.78133	−0.890667	+	0.454655i	$0.849762\pi$
$158$	22.1018	1.75833
$159$	25.1198	1.99213
$160$	60.0830	4.74998
$161$	−9.86432	−0.777417
$162$	21.4244	1.68326
$163$	3.10207	0.242973	0.121486	−	0.992593i	$-0.461234\pi$
$163$	3.10207	0.242973	0.121486	+	0.992593i	$0.461234\pi$
$164$	9.84280	0.768594
$165$	−1.51793	−0.118170
$166$	17.1426	1.33053
$167$	0.918909	0.0711073	0.0355536	−	0.999368i	$-0.488681\pi$
$167$	0.918909	0.0711073	0.0355536	+	0.999368i	$0.488681\pi$
$168$	112.285	8.66300
$169$	−13.0000	−0.999997
$170$	3.47489	0.266512
$171$	−15.8391	−1.21125
$172$	25.0257	1.90819
$173$	6.56991	0.499501	0.249750	−	0.968310i	$-0.419651\pi$
$173$	6.56991	0.499501	0.249750	+	0.968310i	$0.419651\pi$
$174$	−21.7423	−1.64828
$175$	−16.7791	−1.26838
$176$	2.97859	0.224520
$177$	3.56078	0.267644
$178$	3.22520	0.241739
$179$	−12.2330	−0.914340	−0.457170	−	0.889379i	$-0.651137\pi$
$179$	−12.2330	−0.914340	−0.457170	+	0.889379i	$0.651137\pi$
$180$	−52.5213	−3.91471
$181$	−9.41373	−0.699717	−0.349859	−	0.936803i	$-0.613770\pi$
$181$	−9.41373	−0.699717	−0.349859	+	0.936803i	$0.613770\pi$
$182$	−0.0811255	−0.00601342
$183$	−4.07444	−0.301191
$184$	−18.9620	−1.39790
$185$	−7.05357	−0.518589
$186$	−4.66599	−0.342127
$187$	0.0907742	0.00663807
$188$	63.8391	4.65594
$189$	−4.09102	−0.297578
$190$	−37.6113	−2.72861
$191$	5.07852	0.367469	0.183734	−	0.982976i	$-0.441181\pi$
$191$	5.07852	0.367469	0.183734	+	0.982976i	$0.441181\pi$
$192$	68.8560	4.96925
$193$	−4.74101	−0.341266	−0.170633	−	0.985335i	$-0.554581\pi$
$193$	−4.74101	−0.341266	−0.170633	+	0.985335i	$0.554581\pi$
$194$	23.8838	1.71476
$195$	0.0453848	0.00325007
$196$	87.5497	6.25355
$197$	−11.4437	−0.815327	−0.407664	−	0.913132i	$-0.633656\pi$
$197$	−11.4437	−0.815327	−0.407664	+	0.913132i	$0.633656\pi$
$198$	−1.87986	−0.133596
$199$	23.1508	1.64111	0.820557	−	0.571565i	$-0.193663\pi$
$199$	23.1508	1.64111	0.820557	+	0.571565i	$0.193663\pi$
$200$	−32.2542	−2.28072
$201$	18.5228	1.30650
$202$	−11.4895	−0.808395
$203$	−15.2904	−1.07317
$204$	5.96420	0.417578
$205$	−5.30582	−0.370575
$206$	−41.9135	−2.92025
$207$	6.83432	0.475018
$208$	−0.0890575	−0.00617503
$209$	−0.982516	−0.0679621
$210$	−96.0997	−6.63151
$211$	−0.0559256	−0.00385007	−0.00192504	−	0.999998i	$-0.500613\pi$
$211$	−0.0559256	−0.00385007	−0.00192504	+	0.999998i	$0.500613\pi$
$212$	53.9151	3.70290
$213$	−5.65407	−0.387410
$214$	−4.29259	−0.293436
$215$	−13.4903	−0.920029
$216$	−7.86410	−0.535084
$217$	−3.28138	−0.222754
$218$	−23.4558	−1.58863
$219$	−2.44466	−0.165195
$220$	−3.25795	−0.219651
$221$	−0.00271407	−0.000182568 0
$222$	−16.5878	−1.11330
$223$	−4.16986	−0.279235	−0.139617	−	0.990206i	$-0.544587\pi$
$223$	−4.16986	−0.279235	−0.139617	+	0.990206i	$0.544587\pi$
$224$	99.3675	6.63927
$225$	11.6251	0.775008
$226$	−18.8418	−1.25334
$227$	−12.9360	−0.858592	−0.429296	−	0.903164i	$-0.641238\pi$
$227$	−12.9360	−0.858592	−0.429296	+	0.903164i	$0.641238\pi$
$228$	−64.5550	−4.27526
$229$	−4.46598	−0.295120	−0.147560	−	0.989053i	$-0.547142\pi$
$229$	−4.46598	−0.295120	−0.147560	+	0.989053i	$0.547142\pi$
$230$	16.2287	1.07009
$231$	−2.51040	−0.165172
$232$	−29.3924	−1.92970
$233$	22.4618	1.47152	0.735762	−	0.677240i	$-0.236824\pi$
$233$	22.4618	1.47152	0.735762	+	0.677240i	$0.236824\pi$
$234$	0.0562064	0.00367432
$235$	−34.4129	−2.24485
$236$	7.64256	0.497488
$237$	−20.4491	−1.32831
$238$	5.74690	0.372516
$239$	8.98826	0.581402	0.290701	−	0.956814i	$-0.406111\pi$
$239$	8.98826	0.581402	0.290701	+	0.956814i	$0.406111\pi$
$240$	−105.496	−6.80973
$241$	−26.3636	−1.69823	−0.849113	−	0.528212i	$-0.822863\pi$
$241$	−26.3636	−1.69823	−0.849113	+	0.528212i	$0.822863\pi$
$242$	29.8130	1.91645
$243$	−22.3702	−1.43505
$244$	−8.74505	−0.559844
$245$	−47.1942	−3.01513
$246$	−12.4777	−0.795547
$247$	0.0293764	0.00186918
$248$	−6.30773	−0.400542
$249$	−15.8607	−1.00513
$250$	−12.0195	−0.760178
$251$	18.2467	1.15172	0.575860	−	0.817548i	$-0.304667\pi$
$251$	18.2467	1.15172	0.575860	+	0.817548i	$0.304667\pi$
$252$	−86.8617	−5.47177
$253$	0.423940	0.0266529
$254$	10.3862	0.651691
$255$	−3.21504	−0.201334
$256$	35.5315	2.22072
$257$	19.0328	1.18724	0.593618	−	0.804747i	$-0.297699\pi$
$257$	19.0328	1.18724	0.593618	+	0.804747i	$0.297699\pi$
$258$	−31.7250	−1.97511
$259$	−11.6655	−0.724857
$260$	0.0974102	0.00604112
$261$	10.5937	0.655731
$262$	47.4979	2.93443
$263$	−0.526435	−0.0324614	−0.0162307	−	0.999868i	$-0.505167\pi$
$263$	−0.526435	−0.0324614	−0.0162307	+	0.999868i	$0.505167\pi$
$264$	−4.82570	−0.297001
$265$	−29.0633	−1.78534
$266$	−62.2030	−3.81391
$267$	−2.98403	−0.182619
$268$	39.7559	2.42848
$269$	−31.1138	−1.89704	−0.948520	−	0.316719i	$-0.897419\pi$
$269$	−31.1138	−1.89704	−0.948520	+	0.316719i	$0.897419\pi$
$270$	6.73051	0.409606
$271$	−8.24264	−0.500704	−0.250352	−	0.968155i	$-0.580546\pi$
$271$	−8.24264	−0.500704	−0.250352	+	0.968155i	$0.580546\pi$
$272$	6.30881	0.382528
$273$	0.0750590	0.00454278
$274$	45.2195	2.73181
$275$	0.721119	0.0434851
$276$	27.8545	1.67664
$277$	−7.66195	−0.460362	−0.230181	−	0.973148i	$-0.573932\pi$
$277$	−7.66195	−0.460362	−0.230181	+	0.973148i	$0.573932\pi$
$278$	43.5438	2.61159
$279$	2.27345	0.136108
$280$	−129.913	−7.76377
$281$	−1.35122	−0.0806068	−0.0403034	−	0.999187i	$-0.512832\pi$
$281$	−1.35122	−0.0806068	−0.0403034	+	0.999187i	$0.512832\pi$
$282$	−80.9285	−4.81922
$283$	−13.9854	−0.831345	−0.415672	−	0.909514i	$-0.636454\pi$
$283$	−13.9854	−0.831345	−0.415672	+	0.909514i	$0.636454\pi$
$284$	−12.1354	−0.720106
$285$	34.7988	2.06130
$286$	0.00348654	0.000206164 0
$287$	−8.77497	−0.517970
$288$	−68.8450	−4.05673
$289$	−16.8077	−0.988690
$290$	25.1555	1.47718
$291$	−22.0978	−1.29540
$292$	−5.24703	−0.307059
$293$	24.2556	1.41703	0.708515	−	0.705696i	$-0.249366\pi$
$293$	24.2556	1.41703	0.708515	+	0.705696i	$0.249366\pi$
$294$	−110.986	−6.47285
$295$	−4.11977	−0.239862
$296$	−22.4243	−1.30339
$297$	0.175821	0.0102021
$298$	−39.6662	−2.29780
$299$	−0.0126755	−0.000733041 0
$300$	47.3802	2.73550
$301$	−22.3107	−1.28597
$302$	46.9647	2.70252
$303$	10.6303	0.610694
$304$	−68.2849	−3.91641
$305$	4.71407	0.269927
$306$	−3.98164	−0.227615
$307$	18.5003	1.05587	0.527933	−	0.849286i	$-0.322967\pi$
$307$	18.5003	1.05587	0.527933	+	0.849286i	$0.322967\pi$
$308$	−5.38813	−0.307017
$309$	38.7793	2.20608
$310$	5.39849	0.306614
$311$	−7.96115	−0.451435	−0.225718	−	0.974193i	$-0.572473\pi$
$311$	−7.96115	−0.451435	−0.225718	+	0.974193i	$0.572473\pi$
$312$	0.144285	0.00816850
$313$	0.975886	0.0551603	0.0275802	−	0.999620i	$-0.491220\pi$
$313$	0.975886	0.0551603	0.0275802	+	0.999620i	$0.491220\pi$
$314$	60.7301	3.42720
$315$	46.8234	2.63820
$316$	−43.8902	−2.46902
$317$	10.6341	0.597273	0.298637	−	0.954367i	$-0.403468\pi$
$317$	10.6341	0.597273	0.298637	+	0.954367i	$0.403468\pi$
$318$	−68.3479	−3.83276
$319$	0.657136	0.0367925
$320$	−79.6655	−4.45344
$321$	3.97160	0.221673
$322$	26.8396	1.49571
$323$	−2.08102	−0.115791
$324$	−42.5450	−2.36361
$325$	−0.0215609	−0.00119598
$326$	−8.44035	−0.467468
$327$	21.7018	1.20011
$328$	−16.8680	−0.931378
$329$	−56.9133	−3.13773
$330$	4.13009	0.227354
$331$	−5.11180	−0.280970	−0.140485	−	0.990083i	$-0.544866\pi$
$331$	−5.11180	−0.280970	−0.140485	+	0.990083i	$0.544866\pi$
$332$	−34.0422	−1.86831
$333$	8.08221	0.442902
$334$	−2.50024	−0.136807
$335$	−21.4307	−1.17088
$336$	−174.473	−9.51828
$337$	−3.34853	−0.182406	−0.0912031	−	0.995832i	$-0.529071\pi$
$337$	−3.34853	−0.182406	−0.0912031	+	0.995832i	$0.529071\pi$
$338$	35.3713	1.92394
$339$	17.4329	0.946823
$340$	−6.90051	−0.374232
$341$	0.141024	0.00763689
$342$	43.0962	2.33038
$343$	−44.3326	−2.39374
$344$	−42.8875	−2.31234
$345$	−15.0151	−0.808387
$346$	−17.8759	−0.961015
$347$	3.21109	0.172380	0.0861902	−	0.996279i	$-0.472531\pi$
$347$	3.21109	0.172380	0.0861902	+	0.996279i	$0.472531\pi$
$348$	43.1763	2.31449
$349$	32.1191	1.71930	0.859649	−	0.510885i	$-0.170682\pi$
$349$	32.1191	1.71930	0.859649	+	0.510885i	$0.170682\pi$
$350$	45.6539	2.44030
$351$	−0.00525689	−0.000280592 0
$352$	−4.27053	−0.227620
$353$	28.5203	1.51798	0.758990	−	0.651102i	$-0.225693\pi$
$353$	28.5203	1.51798	0.758990	+	0.651102i	$0.225693\pi$
$354$	−9.68843	−0.514934
$355$	6.54168	0.347197
$356$	−6.40467	−0.339447
$357$	−5.31715	−0.281414
$358$	33.2846	1.75915
$359$	−1.64044	−0.0865793	−0.0432897	−	0.999063i	$-0.513784\pi$
$359$	−1.64044	−0.0865793	−0.0432897	+	0.999063i	$0.513784\pi$
$360$	90.0077	4.74382
$361$	3.52438	0.185494
$362$	25.6136	1.34622
$363$	−27.5836	−1.44777
$364$	0.161101	0.00844396
$365$	2.82844	0.148048
$366$	11.0860	0.579477
$367$	−16.0846	−0.839608	−0.419804	−	0.907615i	$-0.637901\pi$
$367$	−16.0846	−0.839608	−0.419804	+	0.907615i	$0.637901\pi$
$368$	29.4639	1.53591
$369$	6.07958	0.316490
$370$	19.1919	0.997740
$371$	−48.0659	−2.49546
$372$	9.26582	0.480410
$373$	−31.9943	−1.65660	−0.828300	−	0.560285i	$-0.810692\pi$
$373$	−31.9943	−1.65660	−0.828300	+	0.560285i	$0.810692\pi$
$374$	−0.246985	−0.0127713
$375$	11.1207	0.574269
$376$	−109.403	−5.64205
$377$	−0.0196478	−0.00101191
$378$	11.1312	0.572526
$379$	−21.2348	−1.09076	−0.545378	−	0.838190i	$-0.683614\pi$
$379$	−21.2348	−1.09076	−0.545378	+	0.838190i	$0.683614\pi$
$380$	74.6893	3.83148
$381$	−9.60957	−0.492313
$382$	−13.8180	−0.706992
$383$	−5.46966	−0.279487	−0.139743	−	0.990188i	$-0.544628\pi$
$383$	−5.46966	−0.279487	−0.139743	+	0.990188i	$0.544628\pi$
$384$	−83.4876	−4.26046
$385$	2.90450	0.148027
$386$	12.8997	0.656578
$387$	15.4576	0.785753
$388$	−47.4290	−2.40784
$389$	−28.1478	−1.42715	−0.713575	−	0.700579i	$-0.752925\pi$
$389$	−28.1478	−1.42715	−0.713575	+	0.700579i	$0.752925\pi$
$390$	−0.123486	−0.00625297
$391$	0.897926	0.0454101
$392$	−150.037	−7.57802
$393$	−43.9461	−2.21679
$394$	31.1368	1.56865
$395$	23.6593	1.19043
$396$	3.73307	0.187594
$397$	−3.97390	−0.199444	−0.0997222	−	0.995015i	$-0.531795\pi$
$397$	−3.97390	−0.199444	−0.0997222	+	0.995015i	$0.531795\pi$
$398$	−62.9904	−3.15742
$399$	57.5515	2.88118
$400$	50.1178	2.50589
$401$	−20.7932	−1.03836	−0.519181	−	0.854664i	$-0.673763\pi$
$401$	−20.7932	−1.03836	−0.519181	+	0.854664i	$0.673763\pi$
$402$	−50.3983	−2.51364
$403$	−0.00421651	−0.000210039 0
$404$	22.8160	1.13514
$405$	22.9342	1.13961
$406$	41.6032	2.06473
$407$	0.501348	0.0248509
$408$	−10.2211	−0.506018
$409$	30.9168	1.52874	0.764370	−	0.644778i	$-0.223050\pi$
$409$	30.9168	1.52874	0.764370	+	0.644778i	$0.223050\pi$
$410$	14.4365	0.712968
$411$	−41.8380	−2.06372
$412$	83.2327	4.10058
$413$	−6.81343	−0.335267
$414$	−18.5953	−0.913911
$415$	18.3506	0.900798
$416$	0.127685	0.00626029
$417$	−40.2877	−1.97290
$418$	2.67331	0.130756
$419$	18.9025	0.923450	0.461725	−	0.887023i	$-0.347231\pi$
$419$	18.9025	0.923450	0.461725	+	0.887023i	$0.347231\pi$
$420$	190.837	9.31188
$421$	−29.2199	−1.42409	−0.712046	−	0.702133i	$-0.752231\pi$
$421$	−29.2199	−1.42409	−0.712046	+	0.702133i	$0.752231\pi$
$422$	0.152167	0.00740735
$423$	39.4314	1.91722
$424$	−92.3963	−4.48716
$425$	1.52736	0.0740881
$426$	15.3840	0.745358
$427$	7.79631	0.377290
$428$	8.52432	0.412039
$429$	−0.00322582	−0.000155744 0
$430$	36.7054	1.77009
$431$	−6.10983	−0.294300	−0.147150	−	0.989114i	$-0.547010\pi$
$431$	−6.10983	−0.294300	−0.147150	+	0.989114i	$0.547010\pi$
$432$	12.2195	0.587912
$433$	−10.7730	−0.517716	−0.258858	−	0.965915i	$-0.583346\pi$
$433$	−10.7730	−0.517716	−0.258858	+	0.965915i	$0.583346\pi$
$434$	8.92823	0.428569
$435$	−23.2744	−1.11592
$436$	46.5790	2.23073
$437$	−9.71892	−0.464919
$438$	6.65163	0.317827
$439$	28.0848	1.34042	0.670208	−	0.742174i	$-0.266205\pi$
$439$	28.0848	1.34042	0.670208	+	0.742174i	$0.266205\pi$
$440$	5.58328	0.266172
$441$	54.0766	2.57508
$442$	0.00738466	0.000351253 0
$443$	32.7243	1.55478	0.777389	−	0.629020i	$-0.216544\pi$
$443$	32.7243	1.55478	0.777389	+	0.629020i	$0.216544\pi$
$444$	32.9404	1.56328
$445$	3.45248	0.163663
$446$	11.3457	0.537234
$447$	36.7000	1.73585
$448$	−131.754	−6.22478
$449$	11.3434	0.535328	0.267664	−	0.963512i	$-0.413748\pi$
$449$	11.3434	0.535328	0.267664	+	0.963512i	$0.413748\pi$
$450$	−31.6305	−1.49108
$451$	0.377123	0.0177580
$452$	37.4165	1.75992
$453$	−43.4527	−2.04159
$454$	35.1972	1.65189
$455$	−0.0868423	−0.00407123
$456$	110.630	5.18073
$457$	−4.77279	−0.223262	−0.111631	−	0.993750i	$-0.535607\pi$
$457$	−4.77279	−0.223262	−0.111631	+	0.993750i	$0.535607\pi$
$458$	12.1514	0.567796
$459$	0.372396	0.0173820
$460$	−32.2272	−1.50260
$461$	18.6284	0.867610	0.433805	−	0.901007i	$-0.357171\pi$
$461$	18.6284	0.867610	0.433805	+	0.901007i	$0.357171\pi$
$462$	6.83050	0.317783
$463$	38.9805	1.81158	0.905789	−	0.423728i	$-0.139279\pi$
$463$	38.9805	1.81158	0.905789	+	0.423728i	$0.139279\pi$
$464$	45.6709	2.12022
$465$	−4.99480	−0.231628
$466$	−61.1159	−2.83114
$467$	−32.0899	−1.48494	−0.742471	−	0.669878i	$-0.766346\pi$
$467$	−32.0899	−1.48494	−0.742471	+	0.669878i	$0.766346\pi$
$468$	−0.111616	−0.00515944
$469$	−35.4428	−1.63660
$470$	93.6332	4.31898
$471$	−56.1888	−2.58904
$472$	−13.0973	−0.602854
$473$	0.958851	0.0440880
$474$	55.6394	2.55560
$475$	−16.5318	−0.758531
$476$	−11.4123	−0.523083
$477$	33.3016	1.52478
$478$	−24.4560	−1.11859
$479$	12.5053	0.571383	0.285692	−	0.958322i	$-0.407777\pi$
$479$	12.5053	0.571383	0.285692	+	0.958322i	$0.407777\pi$
$480$	151.254	6.90375
$481$	−0.0149899	−0.000683481 0
$482$	71.7320	3.26730
$483$	−24.8326	−1.12992
$484$	−59.2033	−2.69106
$485$	25.5669	1.16093
$486$	60.8665	2.76096
$487$	−19.4247	−0.880219	−0.440110	−	0.897944i	$-0.645060\pi$
$487$	−19.4247	−0.880219	−0.440110	+	0.897944i	$0.645060\pi$
$488$	14.9867	0.678416
$489$	7.80919	0.353144
$490$	128.410	5.80096
$491$	−13.2382	−0.597433	−0.298717	−	0.954342i	$-0.596559\pi$
$491$	−13.2382	−0.597433	−0.298717	+	0.954342i	$0.596559\pi$
$492$	24.7784	1.11710
$493$	1.39185	0.0626856
$494$	−0.0799297	−0.00359621
$495$	−2.01233	−0.0904477
$496$	9.80119	0.440086
$497$	10.8189	0.485293
$498$	43.1551	1.93382
$499$	20.2462	0.906346	0.453173	−	0.891423i	$-0.350292\pi$
$499$	20.2462	0.906346	0.453173	+	0.891423i	$0.350292\pi$
$500$	23.8685	1.06743
$501$	2.31327	0.103349
$502$	−49.6470	−2.21585
$503$	28.1785	1.25642	0.628209	−	0.778044i	$-0.283788\pi$
$503$	28.1785	1.25642	0.628209	+	0.778044i	$0.283788\pi$
$504$	148.858	6.63067
$505$	−12.2991	−0.547303
$506$	−1.15349	−0.0512789
$507$	−32.7263	−1.45342
$508$	−20.6252	−0.915095
$509$	−16.8411	−0.746468	−0.373234	−	0.927737i	$-0.621751\pi$
$509$	−16.8411	−0.746468	−0.373234	+	0.927737i	$0.621751\pi$
$510$	8.74773	0.387356
$511$	4.67779	0.206933
$512$	−30.3487	−1.34124
$513$	−4.03072	−0.177961
$514$	−51.7860	−2.28418
$515$	−44.8671	−1.97708
$516$	63.0001	2.77342
$517$	2.44597	0.107574
$518$	31.7403	1.39459
$519$	16.5392	0.725989
$520$	−0.166935	−0.00732060
$521$	3.81091	0.166959	0.0834794	−	0.996510i	$-0.473397\pi$
$521$	3.81091	0.166959	0.0834794	+	0.996510i	$0.473397\pi$
$522$	−28.8240	−1.26159
$523$	−25.0381	−1.09484	−0.547419	−	0.836859i	$-0.684390\pi$
$523$	−25.0381	−1.09484	−0.547419	+	0.836859i	$0.684390\pi$
$524$	−94.3223	−4.12049
$525$	−42.2400	−1.84350
$526$	1.43237	0.0624541
$527$	0.298696	0.0130114
$528$	7.49835	0.326324
$529$	−18.8064	−0.817671
$530$	79.0776	3.43491
$531$	4.72057	0.204855
$532$	123.524	5.35544
$533$	−0.0112757	−0.000488404 0
$534$	8.11917	0.351351
$535$	−4.59509	−0.198663
$536$	−68.1311	−2.94281
$537$	−30.7956	−1.32893
$538$	84.6567	3.64981
$539$	3.35443	0.144486
$540$	−13.3656	−0.575163
$541$	−45.3673	−1.95049	−0.975245	−	0.221126i	$-0.929027\pi$
$541$	−45.3673	−1.95049	−0.975245	+	0.221126i	$0.929027\pi$
$542$	22.4272	0.963331
$543$	−23.6982	−1.01699
$544$	−9.04519	−0.387809
$545$	−25.1087	−1.07554
$546$	−0.204226	−0.00874008
$547$	27.2502	1.16514	0.582568	−	0.812782i	$-0.302048\pi$
$547$	27.2502	1.16514	0.582568	+	0.812782i	$0.302048\pi$
$548$	−89.7978	−3.83597
$549$	−5.40154	−0.230532
$550$	−1.96208	−0.0836632
$551$	−15.0650	−0.641789
$552$	−47.7352	−2.03174
$553$	39.1287	1.66392
$554$	20.8472	0.885714
$555$	−17.7568	−0.753732
$556$	−86.4702	−3.66716
$557$	−34.0933	−1.44458	−0.722289	−	0.691591i	$-0.756910\pi$
$557$	−34.0933	−1.44458	−0.722289	+	0.691591i	$0.756910\pi$
$558$	−6.18576	−0.261864
$559$	−0.0286689	−0.00121256
$560$	201.863	8.53027
$561$	0.228516	0.00964796
$562$	3.67649	0.155083
$563$	−32.3289	−1.36250	−0.681250	−	0.732051i	$-0.738563\pi$
$563$	−32.3289	−1.36250	−0.681250	+	0.732051i	$0.738563\pi$
$564$	160.709	6.76708
$565$	−20.1696	−0.848541
$566$	38.0525	1.59947
$567$	37.9294	1.59288
$568$	20.7969	0.872620
$569$	−5.03326	−0.211005	−0.105503	−	0.994419i	$-0.533645\pi$
$569$	−5.03326	−0.211005	−0.105503	+	0.994419i	$0.533645\pi$
$570$	−94.6831	−3.96584
$571$	26.8372	1.12310	0.561550	−	0.827443i	$-0.310205\pi$
$571$	26.8372	1.12310	0.561550	+	0.827443i	$0.310205\pi$
$572$	−0.00692364	−0.000289492 0
$573$	12.7847	0.534090
$574$	23.8756	0.996549
$575$	7.13321	0.297475
$576$	91.2833	3.80347
$577$	28.6840	1.19413	0.597066	−	0.802192i	$-0.296333\pi$
$577$	28.6840	1.19413	0.597066	+	0.802192i	$0.296333\pi$
$578$	45.7318	1.90219
$579$	−11.9351	−0.496005
$580$	−49.9544	−2.07424
$581$	30.3490	1.25909
$582$	60.1255	2.49228
$583$	2.06574	0.0855541
$584$	8.99202	0.372093
$585$	0.0601671	0.00248761
$586$	−65.9966	−2.72630
$587$	5.15813	0.212899	0.106449	−	0.994318i	$-0.466052\pi$
$587$	5.15813	0.212899	0.106449	+	0.994318i	$0.466052\pi$
$588$	220.399	9.08909
$589$	−3.23301	−0.133214
$590$	11.2094	0.461483
$591$	−28.8084	−1.18502
$592$	34.8437	1.43207
$593$	−18.0525	−0.741325	−0.370663	−	0.928768i	$-0.620869\pi$
$593$	−18.0525	−0.741325	−0.370663	+	0.928768i	$0.620869\pi$
$594$	−0.478386	−0.0196284
$595$	6.15188	0.252202
$596$	78.7699	3.22654
$597$	58.2800	2.38524
$598$	0.0344884	0.00141034
$599$	41.1748	1.68236	0.841179	−	0.540757i	$-0.181862\pi$
$599$	41.1748	1.68236	0.841179	+	0.540757i	$0.181862\pi$
$600$	−81.1971	−3.31486
$601$	−43.9948	−1.79458	−0.897292	−	0.441437i	$-0.854469\pi$
$601$	−43.9948	−1.79458	−0.897292	+	0.441437i	$0.854469\pi$
$602$	60.7047	2.47414
$603$	24.5559	0.999995
$604$	−93.2635	−3.79484
$605$	31.9139	1.29749
$606$	−28.9237	−1.17495
$607$	24.4290	0.991541	0.495770	−	0.868454i	$-0.334886\pi$
$607$	24.4290	0.991541	0.495770	+	0.868454i	$0.334886\pi$
$608$	97.9028	3.97048
$609$	−38.4921	−1.55978
$610$	−12.8264	−0.519326
$611$	−0.0731325	−0.00295862
$612$	7.90682	0.319614
$613$	44.4286	1.79445	0.897227	−	0.441569i	$-0.145578\pi$
$613$	44.4286	1.79445	0.897227	+	0.441569i	$0.145578\pi$
$614$	−50.3369	−2.03143
$615$	−13.3569	−0.538604
$616$	9.23383	0.372042
$617$	−35.8041	−1.44142	−0.720710	−	0.693237i	$-0.756184\pi$
$617$	−35.8041	−1.44142	−0.720710	+	0.693237i	$0.756184\pi$
$618$	−105.514	−4.24438
$619$	−0.865881	−0.0348027	−0.0174014	−	0.999849i	$-0.505539\pi$
$619$	−0.865881	−0.0348027	−0.0174014	+	0.999849i	$0.505539\pi$
$620$	−10.7204	−0.430543
$621$	1.73919	0.0697914
$622$	21.6613	0.868539
$623$	5.70984	0.228760
$624$	−0.224195	−0.00897497
$625$	−30.2831	−1.21132
$626$	−2.65527	−0.106126
$627$	−2.47340	−0.0987780
$628$	−120.599	−4.81243
$629$	1.06188	0.0423399
$630$	−127.401	−5.07576
$631$	−15.3866	−0.612531	−0.306265	−	0.951946i	$-0.599079\pi$
$631$	−15.3866	−0.612531	−0.306265	+	0.951946i	$0.599079\pi$
$632$	75.2163	2.99194
$633$	−0.140788	−0.00559581
$634$	−28.9342	−1.14912
$635$	11.1181	0.441210
$636$	135.727	5.38191
$637$	−0.100295	−0.00397382
$638$	−1.78799	−0.0707870
$639$	−7.49567	−0.296524
$640$	96.5940	3.81821
$641$	−1.49491	−0.0590453	−0.0295227	−	0.999564i	$-0.509399\pi$
$641$	−1.49491	−0.0590453	−0.0295227	+	0.999564i	$0.509399\pi$
$642$	−10.8062	−0.426488
$643$	−3.91482	−0.154386	−0.0771928	−	0.997016i	$-0.524596\pi$
$643$	−3.91482	−0.154386	−0.0771928	+	0.997016i	$0.524596\pi$
$644$	−53.2986	−2.10026
$645$	−33.9606	−1.33720
$646$	5.66219	0.222776
$647$	−46.7454	−1.83775	−0.918875	−	0.394549i	$-0.870901\pi$
$647$	−46.7454	−1.83775	−0.918875	+	0.394549i	$0.870901\pi$
$648$	72.9110	2.86421
$649$	0.292822	0.0114943
$650$	0.0586645	0.00230101
$651$	−8.26058	−0.323758
$652$	16.7610	0.656412
$653$	46.1157	1.80465	0.902323	−	0.431061i	$-0.141861\pi$
$653$	46.1157	1.80465	0.902323	+	0.431061i	$0.141861\pi$
$654$	−59.0480	−2.30896
$655$	50.8450	1.98668
$656$	26.2101	1.02333
$657$	−3.24092	−0.126440
$658$	154.854	6.03684
$659$	33.9190	1.32130	0.660648	−	0.750696i	$-0.270282\pi$
$659$	33.9190	1.32130	0.660648	+	0.750696i	$0.270282\pi$
$660$	−8.20162	−0.319247
$661$	17.6354	0.685936	0.342968	−	0.939347i	$-0.388568\pi$
$661$	17.6354	0.685936	0.342968	+	0.939347i	$0.388568\pi$
$662$	13.9086	0.540573
$663$	−0.00683245	−0.000265350 0
$664$	58.3393	2.26400
$665$	−66.5863	−2.58211
$666$	−21.9907	−0.852122
$667$	6.50030	0.251693
$668$	4.96502	0.192102
$669$	−10.4973	−0.405848
$670$	58.3102	2.25272
$671$	−0.335063	−0.0129350
$672$	250.149	9.64971
$673$	−15.8171	−0.609706	−0.304853	−	0.952399i	$-0.598607\pi$
$673$	−15.8171	−0.609706	−0.304853	+	0.952399i	$0.598607\pi$
$674$	9.11094	0.350940
$675$	2.95835	0.113867
$676$	−70.2410	−2.70158
$677$	−4.50072	−0.172977	−0.0864884	−	0.996253i	$-0.527565\pi$
$677$	−4.50072	−0.172977	−0.0864884	+	0.996253i	$0.527565\pi$
$678$	−47.4327	−1.82164
$679$	42.2835	1.62269
$680$	11.8256	0.453493
$681$	−32.5652	−1.24790
$682$	−0.383710	−0.0146930
$683$	−3.01116	−0.115219	−0.0576095	−	0.998339i	$-0.518348\pi$
$683$	−3.01116	−0.115219	−0.0576095	+	0.998339i	$0.518348\pi$
$684$	−85.5813	−3.27228
$685$	48.4061	1.84950
$686$	120.624	4.60543
$687$	−11.2427	−0.428936
$688$	66.6401	2.54063
$689$	−0.0617638	−0.00235301
$690$	40.8543	1.55530
$691$	6.91606	0.263099	0.131550	−	0.991310i	$-0.458005\pi$
$691$	6.91606	0.263099	0.131550	+	0.991310i	$0.458005\pi$
$692$	35.4983	1.34944
$693$	−3.32807	−0.126423
$694$	−8.73698	−0.331651
$695$	46.6123	1.76811
$696$	−73.9927	−2.80469
$697$	0.798765	0.0302554
$698$	−87.3922	−3.30784
$699$	56.5457	2.13876
$700$	−90.6605	−3.42664
$701$	−24.8307	−0.937842	−0.468921	−	0.883240i	$-0.655357\pi$
$701$	−24.8307	−0.937842	−0.468921	+	0.883240i	$0.655357\pi$
$702$	0.0143033	0.000539845 0
$703$	−11.4935	−0.433486
$704$	5.66240	0.213410
$705$	−86.6314	−3.26273
$706$	−77.6001	−2.92052
$707$	−20.3407	−0.764991
$708$	19.2395	0.723064
$709$	47.4829	1.78326	0.891630	−	0.452765i	$-0.149562\pi$
$709$	47.4829	1.78326	0.891630	+	0.452765i	$0.149562\pi$
$710$	−17.7991	−0.667989
$711$	−27.1096	−1.01669
$712$	10.9759	0.411340
$713$	1.39499	0.0522429
$714$	14.4673	0.541426
$715$	0.00373223	0.000139578 0
$716$	−66.0972	−2.47017
$717$	22.6272	0.845027
$718$	4.46345	0.166574
$719$	−10.0948	−0.376474	−0.188237	−	0.982124i	$-0.560277\pi$
$719$	−10.0948	−0.376474	−0.188237	+	0.982124i	$0.560277\pi$
$720$	−139.857	−5.21217
$721$	−74.2029	−2.76346
$722$	−9.58940	−0.356880
$723$	−66.3679	−2.46825
$724$	−50.8640	−1.89035
$725$	11.0570	0.410645
$726$	75.0517	2.78543
$727$	14.7180	0.545859	0.272929	−	0.962034i	$-0.412007\pi$
$727$	14.7180	0.545859	0.272929	+	0.962034i	$0.412007\pi$
$728$	−0.276084	−0.0102324
$729$	−32.6927	−1.21084
$730$	−7.69585	−0.284836
$731$	2.03089	0.0751153
$732$	−22.0149	−0.813694
$733$	−25.7110	−0.949657	−0.474828	−	0.880078i	$-0.657490\pi$
$733$	−25.7110	−0.949657	−0.474828	+	0.880078i	$0.657490\pi$
$734$	43.7642	1.61537
$735$	−118.807	−4.38227
$736$	−42.2435	−1.55712
$737$	1.52323	0.0561089
$738$	−16.5418	−0.608912
$739$	−15.2668	−0.561598	−0.280799	−	0.959767i	$-0.590599\pi$
$739$	−15.2668	−0.561598	−0.280799	+	0.959767i	$0.590599\pi$
$740$	−38.1117	−1.40101
$741$	0.0739526	0.00271672
$742$	130.781	4.80114
$743$	−2.45676	−0.0901298	−0.0450649	−	0.998984i	$-0.514349\pi$
$743$	−2.45676	−0.0901298	−0.0450649	+	0.998984i	$0.514349\pi$
$744$	−15.8792	−0.582159
$745$	−42.4614	−1.55567
$746$	87.0525	3.18722
$747$	−21.0268	−0.769329
$748$	0.490469	0.0179333
$749$	−7.59953	−0.277681
$750$	−30.2580	−1.10487
$751$	−5.03293	−0.183654	−0.0918271	−	0.995775i	$-0.529271\pi$
$751$	−5.03293	−0.183654	−0.0918271	+	0.995775i	$0.529271\pi$
$752$	169.995	6.19908
$753$	45.9344	1.67394
$754$	0.0534593	0.00194687
$755$	50.2743	1.82967
$756$	−22.1045	−0.803933
$757$	−19.7942	−0.719433	−0.359716	−	0.933062i	$-0.617127\pi$
$757$	−19.7942	−0.719433	−0.359716	+	0.933062i	$0.617127\pi$
$758$	57.7772	2.09856
$759$	1.06723	0.0387381
$760$	−127.998	−4.64296
$761$	−13.7965	−0.500123	−0.250061	−	0.968230i	$-0.580451\pi$
$761$	−13.7965	−0.500123	−0.250061	+	0.968230i	$0.580451\pi$
$762$	26.1464	0.947186
$763$	−41.5258	−1.50333
$764$	27.4401	0.992748
$765$	−4.26222	−0.154101
$766$	14.8823	0.537719
$767$	−0.00875513	−0.000316130 0
$768$	89.4474	3.22766
$769$	19.4408	0.701054	0.350527	−	0.936553i	$-0.386002\pi$
$769$	19.4408	0.701054	0.350527	+	0.936553i	$0.386002\pi$
$770$	−7.90280	−0.284797
$771$	47.9135	1.72556
$772$	−25.6165	−0.921959
$773$	−14.2648	−0.513071	−0.256535	−	0.966535i	$-0.582581\pi$
$773$	−14.2648	−0.513071	−0.256535	+	0.966535i	$0.582581\pi$
$774$	−42.0582	−1.51175
$775$	2.37287	0.0852360
$776$	81.2808	2.91781
$777$	−29.3668	−1.05353
$778$	76.5866	2.74576
$779$	−8.64562	−0.309762
$780$	0.245222	0.00878034
$781$	−0.464965	−0.0166377
$782$	−2.44315	−0.0873668
$783$	2.69586	0.0963424
$784$	233.133	8.32618
$785$	65.0097	2.32030
$786$	119.572	4.26499
$787$	22.6157	0.806163	0.403082	−	0.915164i	$-0.367939\pi$
$787$	22.6157	0.806163	0.403082	+	0.915164i	$0.367939\pi$
$788$	−61.8321	−2.20268
$789$	−1.32525	−0.0471803
$790$	−64.3741	−2.29033
$791$	−33.3572	−1.18605
$792$	−6.39750	−0.227325
$793$	0.0100181	0.000355754 0
$794$	10.8125	0.383721
$795$	−73.1643	−2.59487
$796$	125.088	4.43361
$797$	−1.63312	−0.0578481	−0.0289241	−	0.999582i	$-0.509208\pi$
$797$	−1.63312	−0.0578481	−0.0289241	+	0.999582i	$0.509208\pi$
$798$	−156.591	−5.54324
$799$	5.18068	0.183279
$800$	−71.8558	−2.54049
$801$	−3.95596	−0.139777
$802$	56.5757	1.99776
$803$	−0.201038	−0.00709447
$804$	100.082	3.52962
$805$	28.7310	1.01263
$806$	0.0114726	0.000404105 0
$807$	−78.3262	−2.75721
$808$	−39.1006	−1.37555
$809$	−20.8689	−0.733713	−0.366857	−	0.930278i	$-0.619566\pi$
$809$	−20.8689	−0.733713	−0.366857	+	0.930278i	$0.619566\pi$
$810$	−62.4011	−2.19255
$811$	36.9201	1.29644	0.648220	−	0.761453i	$-0.275514\pi$
$811$	36.9201	1.29644	0.648220	+	0.761453i	$0.275514\pi$
$812$	−82.6164	−2.89927
$813$	−20.7501	−0.727738
$814$	−1.36411	−0.0478119
$815$	−9.03513	−0.316487
$816$	15.8819	0.555977
$817$	−21.9818	−0.769047
$818$	−84.1209	−2.94122
$819$	0.0995067	0.00347704
$820$	−28.6683	−1.00114
$821$	−6.91140	−0.241209	−0.120605	−	0.992701i	$-0.538483\pi$
$821$	−6.91140	−0.241209	−0.120605	+	0.992701i	$0.538483\pi$
$822$	113.836	3.97049
$823$	18.4419	0.642843	0.321421	−	0.946936i	$-0.395839\pi$
$823$	18.4419	0.642843	0.321421	+	0.946936i	$0.395839\pi$
$824$	−142.639	−4.96906
$825$	1.81535	0.0632025
$826$	18.5385	0.645037
$827$	25.6250	0.891067	0.445534	−	0.895265i	$-0.353014\pi$
$827$	25.6250	0.891067	0.445534	+	0.895265i	$0.353014\pi$
$828$	36.9270	1.28330
$829$	−35.2365	−1.22381	−0.611907	−	0.790930i	$-0.709597\pi$
$829$	−35.2365	−1.22381	−0.611907	+	0.790930i	$0.709597\pi$
$830$	−49.9298	−1.73309
$831$	−19.2883	−0.669104
$832$	−0.169301	−0.00586946
$833$	7.10485	0.246169
$834$	109.618	3.79576
$835$	−2.67643	−0.0926216
$836$	−5.30870	−0.183605
$837$	0.578545	0.0199974
$838$	−51.4315	−1.77667
$839$	−3.78076	−0.130526	−0.0652631	−	0.997868i	$-0.520789\pi$
$839$	−3.78076	−0.130526	−0.0652631	+	0.997868i	$0.520789\pi$
$840$	−327.044	−11.2841
$841$	−18.9241	−0.652555
$842$	79.5038	2.73988
$843$	−3.40157	−0.117156
$844$	−0.302175	−0.0104013
$845$	37.8639	1.30256
$846$	−107.288	−3.68863
$847$	52.7804	1.81356
$848$	143.569	4.93017
$849$	−35.2070	−1.20830
$850$	−4.15577	−0.142542
$851$	4.95927	0.170002
$852$	−30.5499	−1.04662
$853$	29.9964	1.02706	0.513528	−	0.858073i	$-0.328338\pi$
$853$	29.9964	1.02706	0.513528	+	0.858073i	$0.328338\pi$
$854$	−21.2128	−0.725887
$855$	46.1332	1.57772
$856$	−14.6084	−0.499306
$857$	−6.77323	−0.231369	−0.115685	−	0.993286i	$-0.536906\pi$
$857$	−6.77323	−0.231369	−0.115685	+	0.993286i	$0.536906\pi$
$858$	0.00877706	0.000299644 0
$859$	−20.5556	−0.701348	−0.350674	−	0.936498i	$-0.614047\pi$
$859$	−20.5556	−0.701348	−0.350674	+	0.936498i	$0.614047\pi$
$860$	−72.8903	−2.48554
$861$	−22.0902	−0.752833
$862$	16.6241	0.566219
$863$	−13.7292	−0.467347	−0.233674	−	0.972315i	$-0.575075\pi$
$863$	−13.7292	−0.467347	−0.233674	+	0.972315i	$0.575075\pi$
$864$	−17.5196	−0.596030
$865$	−19.1356	−0.650630
$866$	29.3119	0.996060
$867$	−42.3120	−1.43699
$868$	−17.7298	−0.601790
$869$	−1.68164	−0.0570457
$870$	63.3269	2.14698
$871$	−0.0455434	−0.00154318
$872$	−79.8242	−2.70319
$873$	−29.2954	−0.991498
$874$	26.4440	0.894481
$875$	−21.2791	−0.719363
$876$	−13.2089	−0.446289
$877$	−7.26524	−0.245330	−0.122665	−	0.992448i	$-0.539144\pi$
$877$	−7.26524	−0.245330	−0.122665	+	0.992448i	$0.539144\pi$
$878$	−76.4154	−2.57889
$879$	61.0615	2.05955
$880$	−8.67550	−0.292451
$881$	−18.0691	−0.608763	−0.304382	−	0.952550i	$-0.598450\pi$
$881$	−18.0691	−0.608763	−0.304382	+	0.952550i	$0.598450\pi$
$882$	−147.136	−4.95432
$883$	−33.0745	−1.11305	−0.556523	−	0.830832i	$-0.687865\pi$
$883$	−33.0745	−1.11305	−0.556523	+	0.830832i	$0.687865\pi$
$884$	−0.0146646	−0.000493224 0
$885$	−10.3712	−0.348623
$886$	−89.0388	−2.99132
$887$	−12.5999	−0.423062	−0.211531	−	0.977371i	$-0.567845\pi$
$887$	−12.5999	−0.423062	−0.211531	+	0.977371i	$0.567845\pi$
$888$	−56.4512	−1.89438
$889$	18.3876	0.616700
$890$	−9.39377	−0.314880
$891$	−1.63010	−0.0546103
$892$	−22.5305	−0.754377
$893$	−56.0744	−1.87646
$894$	−99.8562	−3.33969
$895$	35.6301	1.19098
$896$	159.751	5.33690
$897$	−0.0319094	−0.00106542
$898$	−30.8640	−1.02994
$899$	2.16233	0.0721178
$900$	62.8125	2.09375
$901$	4.37533	0.145763
$902$	−1.02611	−0.0341656
$903$	−56.1653	−1.86906
$904$	−64.1220	−2.13267
$905$	27.4186	0.911424
$906$	118.230	3.92791
$907$	−25.8661	−0.858871	−0.429436	−	0.903098i	$-0.641287\pi$
$907$	−25.8661	−0.858871	−0.429436	+	0.903098i	$0.641287\pi$
$908$	−69.8954	−2.31956
$909$	14.0927	0.467426
$910$	0.236287	0.00783284
$911$	−54.1621	−1.79447	−0.897236	−	0.441551i	$-0.854428\pi$
$911$	−54.1621	−1.79447	−0.897236	+	0.441551i	$0.854428\pi$
$912$	−171.901	−5.69222
$913$	−1.30431	−0.0431664
$914$	12.9862	0.429545
$915$	11.8673	0.392320
$916$	−24.1304	−0.797292
$917$	84.0894	2.77688
$918$	−1.01324	−0.0334421
$919$	−44.5293	−1.46889	−0.734444	−	0.678670i	$-0.762557\pi$
$919$	−44.5293	−1.46889	−0.734444	+	0.678670i	$0.762557\pi$
$920$	55.2290	1.82085
$921$	46.5728	1.53463
$922$	−50.6855	−1.66924
$923$	0.0139021	0.000457592 0
$924$	−13.5641	−0.446227
$925$	8.43567	0.277363
$926$	−106.061	−3.48539
$927$	51.4102	1.68853
$928$	−65.4803	−2.14950
$929$	−34.1876	−1.12166	−0.560829	−	0.827931i	$-0.689518\pi$
$929$	−34.1876	−1.12166	−0.560829	+	0.827931i	$0.689518\pi$
$930$	13.5902	0.445641
$931$	−76.9010	−2.52033
$932$	121.365	3.97545
$933$	−20.0415	−0.656129
$934$	87.3126	2.85696
$935$	−0.264390	−0.00864649
$936$	0.191280	0.00625218
$937$	21.5639	0.704463	0.352232	−	0.935913i	$-0.385423\pi$
$937$	21.5639	0.704463	0.352232	+	0.935913i	$0.385423\pi$
$938$	96.4355	3.14873
$939$	2.45671	0.0801716
$940$	−185.939	−6.06465
$941$	−9.25653	−0.301754	−0.150877	−	0.988553i	$-0.548210\pi$
$941$	−9.25653	−0.301754	−0.150877	+	0.988553i	$0.548210\pi$
$942$	152.883	4.98119
$943$	3.73045	0.121480
$944$	20.3511	0.662373
$945$	11.9156	0.387614
$946$	−2.60892	−0.0848232
$947$	−24.5549	−0.797928	−0.398964	−	0.916967i	$-0.630630\pi$
$947$	−24.5549	−0.797928	−0.398964	+	0.916967i	$0.630630\pi$
$948$	−110.490	−3.58854
$949$	0.00601087	0.000195121 0
$950$	44.9810	1.45938
$951$	26.7705	0.868094
$952$	19.5577	0.633869
$953$	−2.27710	−0.0737626	−0.0368813	−	0.999320i	$-0.511742\pi$
$953$	−2.27710	−0.0737626	−0.0368813	+	0.999320i	$0.511742\pi$
$954$	−90.6096	−2.93360
$955$	−14.7918	−0.478650
$956$	48.5651	1.57071
$957$	1.65428	0.0534753
$958$	−34.0255	−1.09931
$959$	80.0558	2.58514
$960$	−200.551	−6.47275
$961$	−30.5360	−0.985031
$962$	0.0407857	0.00131498
$963$	5.26520	0.169669
$964$	−142.447	−4.58790
$965$	13.8087	0.444519
$966$	67.5664	2.17391
$967$	34.7180	1.11646	0.558228	−	0.829687i	$-0.311481\pi$
$967$	34.7180	1.11646	0.558228	+	0.829687i	$0.311481\pi$
$968$	101.459	3.26101
$969$	−5.23878	−0.168294
$970$	−69.5644	−2.23358
$971$	−10.2997	−0.330533	−0.165266	−	0.986249i	$-0.552848\pi$
$971$	−10.2997	−0.330533	−0.165266	+	0.986249i	$0.552848\pi$
$972$	−120.870	−3.87691
$973$	77.0892	2.47137
$974$	52.8523	1.69350
$975$	−0.0542776	−0.00173827
$976$	−23.2869	−0.745395
$977$	35.1193	1.12357	0.561783	−	0.827285i	$-0.310116\pi$
$977$	35.1193	1.12357	0.561783	+	0.827285i	$0.310116\pi$
$978$	−21.2478	−0.679431
$979$	−0.245393	−0.00784278
$980$	−254.998	−8.14563
$981$	28.7704	0.918568
$982$	36.0196	1.14943
$983$	−11.8839	−0.379038	−0.189519	−	0.981877i	$-0.560693\pi$
$983$	−11.8839	−0.379038	−0.189519	+	0.981877i	$0.560693\pi$
$984$	−42.4636	−1.35369
$985$	33.3310	1.06201
$986$	−3.78704	−0.120604
$987$	−143.274	−4.56047
$988$	0.158726	0.00504974
$989$	9.48482	0.301600
$990$	5.47531	0.174017
$991$	46.7047	1.48362	0.741812	−	0.670608i	$-0.233967\pi$
$991$	46.7047	1.48362	0.741812	+	0.670608i	$0.233967\pi$
$992$	−14.0524	−0.446163
$993$	−12.8685	−0.408370
$994$	−29.4368	−0.933680
$995$	−67.4292	−2.13765
$996$	−85.6982	−2.71545
$997$	−5.31484	−0.168323	−0.0841614	−	0.996452i	$-0.526821\pi$
$997$	−5.31484	−0.168323	−0.0841614	+	0.996452i	$0.526821\pi$
$998$	−55.0875	−1.74376
$999$	2.05675	0.0650728

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.a.1.3	✓	279

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.a.1.3	✓	279	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72088 q^{2} +2.51741 q^{3} +5.40317 q^{4} -2.91261 q^{5} -6.84957 q^{6} -4.81699 q^{7} -9.25961 q^{8} +3.33737 q^{9} +O(q^{10})\)	\(q-2.72088 q^{2} +2.51741 q^{3} +5.40317 q^{4} -2.91261 q^{5} -6.84957 q^{6} -4.81699 q^{7} -9.25961 q^{8} +3.33737 q^{9} +7.92486 q^{10} +0.207020 q^{11} +13.6020 q^{12} -0.00618974 q^{13} +13.1064 q^{14} -7.33225 q^{15} +14.3879 q^{16} +0.438479 q^{17} -9.08056 q^{18} -4.74599 q^{19} -15.7374 q^{20} -12.1263 q^{21} -0.563277 q^{22} +2.04782 q^{23} -23.3103 q^{24} +3.48332 q^{25} +0.0168415 q^{26} +0.849290 q^{27} -26.0270 q^{28} +3.17426 q^{29} +19.9502 q^{30} +0.681209 q^{31} -20.6285 q^{32} +0.521156 q^{33} -1.19305 q^{34} +14.0300 q^{35} +18.0324 q^{36} +2.42173 q^{37} +12.9132 q^{38} -0.0155821 q^{39} +26.9697 q^{40} +1.82167 q^{41} +32.9943 q^{42} +4.63167 q^{43} +1.11857 q^{44} -9.72046 q^{45} -5.57186 q^{46} +11.8151 q^{47} +36.2203 q^{48} +16.2034 q^{49} -9.47769 q^{50} +1.10383 q^{51} -0.0334442 q^{52} +9.97842 q^{53} -2.31081 q^{54} -0.602971 q^{55} +44.6035 q^{56} -11.9476 q^{57} -8.63676 q^{58} +1.41446 q^{59} -39.6174 q^{60} -1.61850 q^{61} -1.85349 q^{62} -16.0761 q^{63} +27.3519 q^{64} +0.0180283 q^{65} -1.41800 q^{66} +7.35788 q^{67} +2.36918 q^{68} +5.15520 q^{69} -38.1740 q^{70} -2.24598 q^{71} -30.9027 q^{72} -0.971102 q^{73} -6.58924 q^{74} +8.76896 q^{75} -25.6434 q^{76} -0.997215 q^{77} +0.0423971 q^{78} -8.12305 q^{79} -41.9065 q^{80} -7.87408 q^{81} -4.95654 q^{82} -6.30040 q^{83} -65.5208 q^{84} -1.27712 q^{85} -12.6022 q^{86} +7.99091 q^{87} -1.91693 q^{88} -1.18535 q^{89} +26.4482 q^{90} +0.0298159 q^{91} +11.0647 q^{92} +1.71488 q^{93} -32.1475 q^{94} +13.8232 q^{95} -51.9306 q^{96} -8.77799 q^{97} -44.0874 q^{98} +0.690903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * q^99

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