LMFDB - Embedded newform 8041.2.a.g.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71913 q^{2} +3.18493 q^{3} +0.955421 q^{4} -4.00741 q^{5} -5.47533 q^{6} -0.822562 q^{7} +1.79577 q^{8} +7.14381 q^{9} +O(q^{10})$	\(q-1.71913 q^{2} +3.18493 q^{3} +0.955421 q^{4} -4.00741 q^{5} -5.47533 q^{6} -0.822562 q^{7} +1.79577 q^{8} +7.14381 q^{9} +6.88927 q^{10} -1.00000 q^{11} +3.04295 q^{12} -6.89242 q^{13} +1.41409 q^{14} -12.7633 q^{15} -4.99801 q^{16} +1.00000 q^{17} -12.2812 q^{18} +4.72993 q^{19} -3.82876 q^{20} -2.61981 q^{21} +1.71913 q^{22} -3.39021 q^{23} +5.71941 q^{24} +11.0593 q^{25} +11.8490 q^{26} +13.1978 q^{27} -0.785893 q^{28} +8.69009 q^{29} +21.9419 q^{30} -8.91260 q^{31} +5.00071 q^{32} -3.18493 q^{33} -1.71913 q^{34} +3.29634 q^{35} +6.82535 q^{36} +5.10906 q^{37} -8.13138 q^{38} -21.9519 q^{39} -7.19639 q^{40} +7.65390 q^{41} +4.50380 q^{42} +1.00000 q^{43} -0.955421 q^{44} -28.6282 q^{45} +5.82822 q^{46} +8.72236 q^{47} -15.9183 q^{48} -6.32339 q^{49} -19.0124 q^{50} +3.18493 q^{51} -6.58516 q^{52} -13.0580 q^{53} -22.6887 q^{54} +4.00741 q^{55} -1.47713 q^{56} +15.0645 q^{57} -14.9394 q^{58} +10.4689 q^{59} -12.1944 q^{60} +3.72905 q^{61} +15.3219 q^{62} -5.87623 q^{63} +1.39913 q^{64} +27.6207 q^{65} +5.47533 q^{66} +7.77990 q^{67} +0.955421 q^{68} -10.7976 q^{69} -5.66685 q^{70} -3.49805 q^{71} +12.8286 q^{72} -14.7520 q^{73} -8.78315 q^{74} +35.2232 q^{75} +4.51907 q^{76} +0.822562 q^{77} +37.7383 q^{78} +7.74481 q^{79} +20.0291 q^{80} +20.6026 q^{81} -13.1581 q^{82} -5.25584 q^{83} -2.50302 q^{84} -4.00741 q^{85} -1.71913 q^{86} +27.6774 q^{87} -1.79577 q^{88} -4.17801 q^{89} +49.2156 q^{90} +5.66944 q^{91} -3.23907 q^{92} -28.3860 q^{93} -14.9949 q^{94} -18.9547 q^{95} +15.9269 q^{96} +8.41756 q^{97} +10.8708 q^{98} -7.14381 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−1.71913	−1.21561	−0.607806	−	0.794086i	$-0.707950\pi$
$2$	−1.71913	−1.21561	−0.607806	+	0.794086i	$0.707950\pi$
$3$	3.18493	1.83882	0.919412	−	0.393297i	$-0.128666\pi$
$3$	3.18493	1.83882	0.919412	+	0.393297i	$0.128666\pi$
$4$	0.955421	0.477711
$5$	−4.00741	−1.79217	−0.896084	−	0.443885i	$-0.853600\pi$
$5$	−4.00741	−1.79217	−0.896084	+	0.443885i	$0.853600\pi$
$6$	−5.47533	−2.23529
$7$	−0.822562	−0.310899	−0.155450	−	0.987844i	$-0.549683\pi$
$7$	−0.822562	−0.310899	−0.155450	+	0.987844i	$0.549683\pi$
$8$	1.79577	0.634901
$9$	7.14381	2.38127
$10$	6.88927	2.17858
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.04295	0.878425
$13$	−6.89242	−1.91161	−0.955806	−	0.293997i	$-0.905015\pi$
$13$	−6.89242	−1.91161	−0.955806	+	0.293997i	$0.905015\pi$
$14$	1.41409	0.377933
$15$	−12.7633	−3.29548
$16$	−4.99801	−1.24950
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−12.2812	−2.89470
$19$	4.72993	1.08512	0.542560	−	0.840017i	$-0.317455\pi$
$19$	4.72993	1.08512	0.542560	+	0.840017i	$0.317455\pi$
$20$	−3.82876	−0.856137
$21$	−2.61981	−0.571689
$22$	1.71913	0.366521
$23$	−3.39021	−0.706907	−0.353453	−	0.935452i	$-0.614993\pi$
$23$	−3.39021	−0.706907	−0.353453	+	0.935452i	$0.614993\pi$
$24$	5.71941	1.16747
$25$	11.0593	2.21186
$26$	11.8490	2.32378
$27$	13.1978	2.53991
$28$	−0.785893	−0.148520
$29$	8.69009	1.61371	0.806854	−	0.590751i	$-0.201168\pi$
$29$	8.69009	1.61371	0.806854	+	0.590751i	$0.201168\pi$
$30$	21.9419	4.00602
$31$	−8.91260	−1.60075	−0.800375	−	0.599500i	$-0.795366\pi$
$31$	−8.91260	−1.60075	−0.800375	+	0.599500i	$0.795366\pi$
$32$	5.00071	0.884009
$33$	−3.18493	−0.554426
$34$	−1.71913	−0.294829
$35$	3.29634	0.557183
$36$	6.82535	1.13756
$37$	5.10906	0.839924	0.419962	−	0.907542i	$-0.362043\pi$
$37$	5.10906	0.839924	0.419962	+	0.907542i	$0.362043\pi$
$38$	−8.13138	−1.31908
$39$	−21.9519	−3.51512
$40$	−7.19639	−1.13785
$41$	7.65390	1.19534	0.597669	−	0.801743i	$-0.296094\pi$
$41$	7.65390	1.19534	0.597669	+	0.801743i	$0.296094\pi$
$42$	4.50380	0.694951
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−0.955421	−0.144035
$45$	−28.6282	−4.26763
$46$	5.82822	0.859324
$47$	8.72236	1.27229	0.636144	−	0.771571i	$-0.280529\pi$
$47$	8.72236	1.27229	0.636144	+	0.771571i	$0.280529\pi$
$48$	−15.9183	−2.29762
$49$	−6.32339	−0.903342
$50$	−19.0124	−2.68877
$51$	3.18493	0.445980
$52$	−6.58516	−0.913198
$53$	−13.0580	−1.79365	−0.896827	−	0.442381i	$-0.854134\pi$
$53$	−13.0580	−1.79365	−0.896827	+	0.442381i	$0.854134\pi$
$54$	−22.6887	−3.08754
$55$	4.00741	0.540359
$56$	−1.47713	−0.197390
$57$	15.0645	1.99534
$58$	−14.9394	−1.96164
$59$	10.4689	1.36293	0.681466	−	0.731850i	$-0.261343\pi$
$59$	10.4689	1.36293	0.681466	+	0.731850i	$0.261343\pi$
$60$	−12.1944	−1.57428
$61$	3.72905	0.477456	0.238728	−	0.971086i	$-0.423270\pi$
$61$	3.72905	0.477456	0.238728	+	0.971086i	$0.423270\pi$
$62$	15.3219	1.94589
$63$	−5.87623	−0.740335
$64$	1.39913	0.174892
$65$	27.6207	3.42593
$66$	5.47533	0.673966
$67$	7.77990	0.950466	0.475233	−	0.879860i	$-0.342364\pi$
$67$	7.77990	0.950466	0.475233	+	0.879860i	$0.342364\pi$
$68$	0.955421	0.115862
$69$	−10.7976	−1.29988
$70$	−5.66685	−0.677318
$71$	−3.49805	−0.415142	−0.207571	−	0.978220i	$-0.566556\pi$
$71$	−3.49805	−0.415142	−0.207571	+	0.978220i	$0.566556\pi$
$72$	12.8286	1.51187
$73$	−14.7520	−1.72659	−0.863294	−	0.504701i	$-0.831603\pi$
$73$	−14.7520	−1.72659	−0.863294	+	0.504701i	$0.831603\pi$
$74$	−8.78315	−1.02102
$75$	35.2232	4.06723
$76$	4.51907	0.518373
$77$	0.822562	0.0937396
$78$	37.7383	4.27302
$79$	7.74481	0.871359	0.435679	−	0.900102i	$-0.356508\pi$
$79$	7.74481	0.871359	0.435679	+	0.900102i	$0.356508\pi$
$80$	20.0291	2.23932
$81$	20.6026	2.28918
$82$	−13.1581	−1.45307
$83$	−5.25584	−0.576904	−0.288452	−	0.957494i	$-0.593141\pi$
$83$	−5.25584	−0.576904	−0.288452	+	0.957494i	$0.593141\pi$
$84$	−2.50302	−0.273102
$85$	−4.00741	−0.434664
$86$	−1.71913	−0.185379
$87$	27.6774	2.96732
$88$	−1.79577	−0.191430
$89$	−4.17801	−0.442869	−0.221434	−	0.975175i	$-0.571074\pi$
$89$	−4.17801	−0.442869	−0.221434	+	0.975175i	$0.571074\pi$
$90$	49.2156	5.18778
$91$	5.66944	0.594319
$92$	−3.23907	−0.337697
$93$	−28.3860	−2.94350
$94$	−14.9949	−1.54661
$95$	−18.9547	−1.94472
$96$	15.9269	1.62554
$97$	8.41756	0.854674	0.427337	−	0.904093i	$-0.359452\pi$
$97$	8.41756	0.854674	0.427337	+	0.904093i	$0.359452\pi$
$98$	10.8708	1.09811
$99$	−7.14381	−0.717980
$100$	10.5663	1.05663
$101$	2.02705	0.201699	0.100849	−	0.994902i	$-0.467844\pi$
$101$	2.02705	0.201699	0.100849	+	0.994902i	$0.467844\pi$
$102$	−5.47533	−0.542138
$103$	9.74029	0.959740	0.479870	−	0.877340i	$-0.340684\pi$
$103$	9.74029	0.959740	0.479870	+	0.877340i	$0.340684\pi$
$104$	−12.3772	−1.21368
$105$	10.4986	1.02456
$106$	22.4485	2.18039
$107$	−6.14529	−0.594087	−0.297044	−	0.954864i	$-0.596001\pi$
$107$	−6.14529	−0.594087	−0.297044	+	0.954864i	$0.596001\pi$
$108$	12.6094	1.21334
$109$	−14.6358	−1.40186	−0.700928	−	0.713232i	$-0.747230\pi$
$109$	−14.6358	−1.40186	−0.700928	+	0.713232i	$0.747230\pi$
$110$	−6.88927	−0.656866
$111$	16.2720	1.54447
$112$	4.11118	0.388470
$113$	−9.45921	−0.889848	−0.444924	−	0.895568i	$-0.646769\pi$
$113$	−9.45921	−0.889848	−0.444924	+	0.895568i	$0.646769\pi$
$114$	−25.8979	−2.42556
$115$	13.5859	1.26689
$116$	8.30269	0.770886
$117$	−49.2381	−4.55207
$118$	−17.9974	−1.65680
$119$	−0.822562	−0.0754041
$120$	−22.9200	−2.09230
$121$	1.00000	0.0909091
$122$	−6.41074	−0.580401
$123$	24.3772	2.19802
$124$	−8.51528	−0.764695
$125$	−24.2822	−2.17186
$126$	10.1020	0.899960
$127$	−8.10955	−0.719607	−0.359803	−	0.933028i	$-0.617156\pi$
$127$	−8.10955	−0.719607	−0.359803	+	0.933028i	$0.617156\pi$
$128$	−12.4067	−1.09661
$129$	3.18493	0.280418
$130$	−47.4837	−4.16460
$131$	−15.6420	−1.36665	−0.683324	−	0.730115i	$-0.739466\pi$
$131$	−15.6420	−1.36665	−0.683324	+	0.730115i	$0.739466\pi$
$132$	−3.04295	−0.264855
$133$	−3.89066	−0.337363
$134$	−13.3747	−1.15540
$135$	−52.8888	−4.55195
$136$	1.79577	0.153986
$137$	−7.68724	−0.656765	−0.328383	−	0.944545i	$-0.606504\pi$
$137$	−7.68724	−0.656765	−0.328383	+	0.944545i	$0.606504\pi$
$138$	18.5625	1.58014
$139$	−8.01638	−0.679941	−0.339970	−	0.940436i	$-0.610417\pi$
$139$	−8.01638	−0.679941	−0.339970	+	0.940436i	$0.610417\pi$
$140$	3.14939	0.266172
$141$	27.7802	2.33951
$142$	6.01362	0.504651
$143$	6.89242	0.576373
$144$	−35.7049	−2.97540
$145$	−34.8247	−2.89204
$146$	25.3606	2.09886
$147$	−20.1396	−1.66109
$148$	4.88130	0.401241
$149$	−19.7477	−1.61780	−0.808899	−	0.587947i	$-0.799936\pi$
$149$	−19.7477	−1.61780	−0.808899	+	0.587947i	$0.799936\pi$
$150$	−60.5534	−4.94416
$151$	−16.9875	−1.38242	−0.691210	−	0.722654i	$-0.742922\pi$
$151$	−16.9875	−1.38242	−0.691210	+	0.722654i	$0.742922\pi$
$152$	8.49386	0.688943
$153$	7.14381	0.577543
$154$	−1.41409	−0.113951
$155$	35.7164	2.86881
$156$	−20.9733	−1.67921
$157$	20.1809	1.61061	0.805307	−	0.592858i	$-0.202001\pi$
$157$	20.1809	1.61061	0.805307	+	0.592858i	$0.202001\pi$
$158$	−13.3144	−1.05923
$159$	−41.5889	−3.29821
$160$	−20.0399	−1.58429
$161$	2.78865	0.219777
$162$	−35.4186	−2.78275
$163$	0.0456029	0.00357189	0.00178595	−	0.999998i	$-0.499432\pi$
$163$	0.0456029	0.00357189	0.00178595	+	0.999998i	$0.499432\pi$
$164$	7.31270	0.571026
$165$	12.7633	0.993624
$166$	9.03550	0.701291
$167$	−11.3955	−0.881812	−0.440906	−	0.897553i	$-0.645343\pi$
$167$	−11.3955	−0.881812	−0.440906	+	0.897553i	$0.645343\pi$
$168$	−4.70457	−0.362966
$169$	34.5054	2.65426
$170$	6.88927	0.528383
$171$	33.7897	2.58396
$172$	0.955421	0.0728502
$173$	2.42878	0.184657	0.0923285	−	0.995729i	$-0.470569\pi$
$173$	2.42878	0.184657	0.0923285	+	0.995729i	$0.470569\pi$
$174$	−47.5811	−3.60711
$175$	−9.09697	−0.687667
$176$	4.99801	0.376739
$177$	33.3427	2.50619
$178$	7.18257	0.538356
$179$	−4.95607	−0.370434	−0.185217	−	0.982698i	$-0.559299\pi$
$179$	−4.95607	−0.370434	−0.185217	+	0.982698i	$0.559299\pi$
$180$	−27.3520	−2.03869
$181$	−5.24294	−0.389704	−0.194852	−	0.980833i	$-0.562423\pi$
$181$	−5.24294	−0.389704	−0.194852	+	0.980833i	$0.562423\pi$
$182$	−9.74653	−0.722461
$183$	11.8768	0.877958
$184$	−6.08803	−0.448816
$185$	−20.4741	−1.50528
$186$	48.7994	3.57815
$187$	−1.00000	−0.0731272
$188$	8.33353	0.607785
$189$	−10.8560	−0.789656
$190$	32.5857	2.36402
$191$	−15.8324	−1.14559	−0.572797	−	0.819697i	$-0.694142\pi$
$191$	−15.8324	−1.14559	−0.572797	+	0.819697i	$0.694142\pi$
$192$	4.45615	0.321595
$193$	24.6147	1.77181	0.885904	−	0.463869i	$-0.153539\pi$
$193$	24.6147	1.77181	0.885904	+	0.463869i	$0.153539\pi$
$194$	−14.4709	−1.03895
$195$	87.9702	6.29968
$196$	−6.04150	−0.431536
$197$	−15.1604	−1.08013	−0.540066	−	0.841623i	$-0.681601\pi$
$197$	−15.1604	−1.08013	−0.540066	+	0.841623i	$0.681601\pi$
$198$	12.2812	0.872784
$199$	14.0826	0.998292	0.499146	−	0.866518i	$-0.333647\pi$
$199$	14.0826	0.998292	0.499146	+	0.866518i	$0.333647\pi$
$200$	19.8600	1.40431
$201$	24.7785	1.74774
$202$	−3.48476	−0.245187
$203$	−7.14814	−0.501701
$204$	3.04295	0.213049
$205$	−30.6723	−2.14225
$206$	−16.7449	−1.16667
$207$	−24.2190	−1.68334
$208$	34.4484	2.38857
$209$	−4.72993	−0.327176
$210$	−18.0486	−1.24547
$211$	6.60856	0.454952	0.227476	−	0.973784i	$-0.426953\pi$
$211$	6.60856	0.454952	0.227476	+	0.973784i	$0.426953\pi$
$212$	−12.4759	−0.856848
$213$	−11.1411	−0.763373
$214$	10.5646	0.722179
$215$	−4.00741	−0.273303
$216$	23.7002	1.61259
$217$	7.33116	0.497672
$218$	25.1609	1.70411
$219$	−46.9841	−3.17489
$220$	3.82876	0.258135
$221$	−6.89242	−0.463634
$222$	−27.9738	−1.87748
$223$	1.94469	0.130226	0.0651129	−	0.997878i	$-0.479259\pi$
$223$	1.94469	0.130226	0.0651129	+	0.997878i	$0.479259\pi$
$224$	−4.11339	−0.274838
$225$	79.0057	5.26704
$226$	16.2617	1.08171
$227$	−13.7058	−0.909687	−0.454843	−	0.890571i	$-0.650305\pi$
$227$	−13.7058	−0.909687	−0.454843	+	0.890571i	$0.650305\pi$
$228$	14.3930	0.953196
$229$	−0.639020	−0.0422276	−0.0211138	−	0.999777i	$-0.506721\pi$
$229$	−0.639020	−0.0422276	−0.0211138	+	0.999777i	$0.506721\pi$
$230$	−23.3560	−1.54005
$231$	2.61981	0.172371
$232$	15.6054	1.02454
$233$	4.35493	0.285301	0.142650	−	0.989773i	$-0.454438\pi$
$233$	4.35493	0.285301	0.142650	+	0.989773i	$0.454438\pi$
$234$	84.6469	5.53354
$235$	−34.9541	−2.28015
$236$	10.0022	0.651087
$237$	24.6667	1.60227
$238$	1.41409	0.0916621
$239$	−11.4300	−0.739345	−0.369673	−	0.929162i	$-0.620530\pi$
$239$	−11.4300	−0.739345	−0.369673	+	0.929162i	$0.620530\pi$
$240$	63.7913	4.11771
$241$	−12.0442	−0.775834	−0.387917	−	0.921694i	$-0.626805\pi$
$241$	−12.0442	−0.775834	−0.387917	+	0.921694i	$0.626805\pi$
$242$	−1.71913	−0.110510
$243$	26.0246	1.66948
$244$	3.56282	0.228086
$245$	25.3404	1.61894
$246$	−41.9076	−2.67193
$247$	−32.6006	−2.07433
$248$	−16.0050	−1.01632
$249$	−16.7395	−1.06082
$250$	41.7443	2.64014
$251$	−14.8383	−0.936582	−0.468291	−	0.883574i	$-0.655130\pi$
$251$	−14.8383	−0.936582	−0.468291	+	0.883574i	$0.655130\pi$
$252$	−5.61427	−0.353666
$253$	3.39021	0.213140
$254$	13.9414	0.874762
$255$	−12.7633	−0.799271
$256$	18.5305	1.15816
$257$	−7.91040	−0.493437	−0.246719	−	0.969087i	$-0.579352\pi$
$257$	−7.91040	−0.493437	−0.246719	+	0.969087i	$0.579352\pi$
$258$	−5.47533	−0.340879
$259$	−4.20252	−0.261132
$260$	26.3894	1.63660
$261$	62.0803	3.84268
$262$	26.8907	1.66131
$263$	5.76497	0.355483	0.177742	−	0.984077i	$-0.443121\pi$
$263$	5.76497	0.355483	0.177742	+	0.984077i	$0.443121\pi$
$264$	−5.71941	−0.352006
$265$	52.3287	3.21453
$266$	6.68856	0.410102
$267$	−13.3067	−0.814357
$268$	7.43308	0.454048
$269$	9.19550	0.560660	0.280330	−	0.959904i	$-0.409556\pi$
$269$	9.19550	0.560660	0.280330	+	0.959904i	$0.409556\pi$
$270$	90.9230	5.53340
$271$	−5.83545	−0.354478	−0.177239	−	0.984168i	$-0.556717\pi$
$271$	−5.83545	−0.354478	−0.177239	+	0.984168i	$0.556717\pi$
$272$	−4.99801	−0.303049
$273$	18.0568	1.09285
$274$	13.2154	0.798371
$275$	−11.0593	−0.666902
$276$	−10.3162	−0.620965
$277$	27.8947	1.67603	0.838015	−	0.545647i	$-0.183716\pi$
$277$	27.8947	1.67603	0.838015	+	0.545647i	$0.183716\pi$
$278$	13.7812	0.826543
$279$	−63.6699	−3.81182
$280$	5.91947	0.353756
$281$	−21.0646	−1.25661	−0.628304	−	0.777968i	$-0.716251\pi$
$281$	−21.0646	−1.25661	−0.628304	+	0.777968i	$0.716251\pi$
$282$	−47.7578	−2.84394
$283$	4.24418	0.252290	0.126145	−	0.992012i	$-0.459740\pi$
$283$	4.24418	0.252290	0.126145	+	0.992012i	$0.459740\pi$
$284$	−3.34211	−0.198318
$285$	−60.3696	−3.57599
$286$	−11.8490	−0.700645
$287$	−6.29581	−0.371630
$288$	35.7241	2.10506
$289$	1.00000	0.0588235
$290$	59.8684	3.51559
$291$	26.8094	1.57159
$292$	−14.0944	−0.824810
$293$	−30.0806	−1.75733	−0.878664	−	0.477441i	$-0.841564\pi$
$293$	−30.0806	−1.75733	−0.878664	+	0.477441i	$0.841564\pi$
$294$	34.6227	2.01923
$295$	−41.9531	−2.44260
$296$	9.17470	0.533268
$297$	−13.1978	−0.765812
$298$	33.9490	1.96661
$299$	23.3667	1.35133
$300$	33.6530	1.94296
$301$	−0.822562	−0.0474117
$302$	29.2037	1.68048
$303$	6.45601	0.370888
$304$	−23.6402	−1.35586
$305$	−14.9438	−0.855681
$306$	−12.2812	−0.702068
$307$	−1.44626	−0.0825425	−0.0412712	−	0.999148i	$-0.513141\pi$
$307$	−1.44626	−0.0825425	−0.0412712	+	0.999148i	$0.513141\pi$
$308$	0.785893	0.0447804
$309$	31.0222	1.76479
$310$	−61.4013	−3.48736
$311$	−12.6238	−0.715829	−0.357915	−	0.933754i	$-0.616512\pi$
$311$	−12.6238	−0.715829	−0.357915	+	0.933754i	$0.616512\pi$
$312$	−39.4206	−2.23175
$313$	1.27433	0.0720293	0.0360147	−	0.999351i	$-0.488534\pi$
$313$	1.27433	0.0720293	0.0360147	+	0.999351i	$0.488534\pi$
$314$	−34.6937	−1.95788
$315$	23.5484	1.32680
$316$	7.39955	0.416257
$317$	−14.5937	−0.819666	−0.409833	−	0.912161i	$-0.634413\pi$
$317$	−14.5937	−0.819666	−0.409833	+	0.912161i	$0.634413\pi$
$318$	71.4969	4.00934
$319$	−8.69009	−0.486551
$320$	−5.60690	−0.313435
$321$	−19.5723	−1.09242
$322$	−4.79407	−0.267163
$323$	4.72993	0.263180
$324$	19.6842	1.09356
$325$	−76.2254	−4.22823
$326$	−0.0783974	−0.00434203
$327$	−46.6141	−2.57776
$328$	13.7447	0.758921
$329$	−7.17468	−0.395553
$330$	−21.9419	−1.20786
$331$	−25.7314	−1.41433	−0.707163	−	0.707050i	$-0.750025\pi$
$331$	−25.7314	−1.41433	−0.707163	+	0.707050i	$0.750025\pi$
$332$	−5.02154	−0.275593
$333$	36.4981	2.00009
$334$	19.5904	1.07194
$335$	−31.1772	−1.70339
$336$	13.0938	0.714327
$337$	14.2213	0.774682	0.387341	−	0.921937i	$-0.373394\pi$
$337$	14.2213	0.774682	0.387341	+	0.921937i	$0.373394\pi$
$338$	−59.3194	−3.22655
$339$	−30.1270	−1.63627
$340$	−3.82876	−0.207644
$341$	8.91260	0.482644
$342$	−58.0890	−3.14109
$343$	10.9593	0.591747
$344$	1.79577	0.0968215
$345$	43.2703	2.32960
$346$	−4.17540	−0.224471
$347$	−2.77170	−0.148793	−0.0743964	−	0.997229i	$-0.523703\pi$
$347$	−2.77170	−0.148793	−0.0743964	+	0.997229i	$0.523703\pi$
$348$	26.4435	1.41752
$349$	−28.3921	−1.51980	−0.759898	−	0.650042i	$-0.774751\pi$
$349$	−28.3921	−1.51980	−0.759898	+	0.650042i	$0.774751\pi$
$350$	15.6389	0.835935
$351$	−90.9645	−4.85533
$352$	−5.00071	−0.266539
$353$	−17.0272	−0.906268	−0.453134	−	0.891442i	$-0.649694\pi$
$353$	−17.0272	−0.906268	−0.453134	+	0.891442i	$0.649694\pi$
$354$	−57.3206	−3.04655
$355$	14.0181	0.744004
$356$	−3.99176	−0.211563
$357$	−2.61981	−0.138655
$358$	8.52015	0.450304
$359$	21.5498	1.13735	0.568677	−	0.822561i	$-0.307455\pi$
$359$	21.5498	1.13735	0.568677	+	0.822561i	$0.307455\pi$
$360$	−51.4096	−2.70952
$361$	3.37221	0.177485
$362$	9.01331	0.473729
$363$	3.18493	0.167166
$364$	5.41670	0.283912
$365$	59.1172	3.09434
$366$	−20.4178	−1.06726
$367$	34.0951	1.77975	0.889875	−	0.456205i	$-0.150791\pi$
$367$	34.0951	1.77975	0.889875	+	0.456205i	$0.150791\pi$
$368$	16.9443	0.883282
$369$	54.6780	2.84642
$370$	35.1977	1.82984
$371$	10.7410	0.557646
$372$	−27.1206	−1.40614
$373$	−16.1783	−0.837679	−0.418840	−	0.908060i	$-0.637563\pi$
$373$	−16.1783	−0.837679	−0.418840	+	0.908060i	$0.637563\pi$
$374$	1.71913	0.0888943
$375$	−77.3371	−3.99367
$376$	15.6634	0.807776
$377$	−59.8957	−3.08479
$378$	18.6629	0.959915
$379$	−12.5070	−0.642442	−0.321221	−	0.947004i	$-0.604093\pi$
$379$	−12.5070	−0.642442	−0.321221	+	0.947004i	$0.604093\pi$
$380$	−18.1098	−0.929011
$381$	−25.8284	−1.32323
$382$	27.2180	1.39260
$383$	5.89385	0.301162	0.150581	−	0.988598i	$-0.451886\pi$
$383$	5.89385	0.301162	0.150581	+	0.988598i	$0.451886\pi$
$384$	−39.5146	−2.01647
$385$	−3.29634	−0.167997
$386$	−42.3160	−2.15383
$387$	7.14381	0.363140
$388$	8.04231	0.408287
$389$	27.8834	1.41375	0.706873	−	0.707341i	$-0.250105\pi$
$389$	27.8834	1.41375	0.706873	+	0.707341i	$0.250105\pi$
$390$	−151.233	−7.65796
$391$	−3.39021	−0.171450
$392$	−11.3554	−0.573532
$393$	−49.8188	−2.51302
$394$	26.0627	1.31302
$395$	−31.0366	−1.56162
$396$	−6.82535	−0.342987
$397$	24.7785	1.24360	0.621798	−	0.783178i	$-0.286403\pi$
$397$	24.7785	1.24360	0.621798	+	0.783178i	$0.286403\pi$
$398$	−24.2099	−1.21353
$399$	−12.3915	−0.620351
$400$	−55.2746	−2.76373
$401$	12.0064	0.599571	0.299785	−	0.954007i	$-0.403085\pi$
$401$	12.0064	0.599571	0.299785	+	0.954007i	$0.403085\pi$
$402$	−42.5975	−2.12457
$403$	61.4293	3.06001
$404$	1.93668	0.0963535
$405$	−82.5630	−4.10259
$406$	12.2886	0.609873
$407$	−5.10906	−0.253247
$408$	5.71941	0.283153
$409$	8.41052	0.415874	0.207937	−	0.978142i	$-0.433325\pi$
$409$	8.41052	0.415874	0.207937	+	0.978142i	$0.433325\pi$
$410$	52.7298	2.60414
$411$	−24.4834	−1.20768
$412$	9.30608	0.458478
$413$	−8.61131	−0.423735
$414$	41.6357	2.04628
$415$	21.0623	1.03391
$416$	−34.4670	−1.68988
$417$	−25.5317	−1.25029
$418$	8.13138	0.397719
$419$	0.618466	0.0302140	0.0151070	−	0.999886i	$-0.495191\pi$
$419$	0.618466	0.0302140	0.0151070	+	0.999886i	$0.495191\pi$
$420$	10.0306	0.489444
$421$	4.69991	0.229060	0.114530	−	0.993420i	$-0.463464\pi$
$421$	4.69991	0.229060	0.114530	+	0.993420i	$0.463464\pi$
$422$	−11.3610	−0.553045
$423$	62.3109	3.02966
$424$	−23.4492	−1.13879
$425$	11.0593	0.536456
$426$	19.1530	0.927965
$427$	−3.06738	−0.148441
$428$	−5.87134	−0.283802
$429$	21.9519	1.05985
$430$	6.88927	0.332230
$431$	7.18414	0.346048	0.173024	−	0.984918i	$-0.444646\pi$
$431$	7.18414	0.346048	0.173024	+	0.984918i	$0.444646\pi$
$432$	−65.9626	−3.17363
$433$	−10.1282	−0.486733	−0.243366	−	0.969934i	$-0.578252\pi$
$433$	−10.1282	−0.486733	−0.243366	+	0.969934i	$0.578252\pi$
$434$	−12.6033	−0.604975
$435$	−110.914	−5.31794
$436$	−13.9834	−0.669681
$437$	−16.0354	−0.767078
$438$	80.7719	3.85943
$439$	−7.68547	−0.366807	−0.183404	−	0.983038i	$-0.558712\pi$
$439$	−7.68547	−0.366807	−0.183404	+	0.983038i	$0.558712\pi$
$440$	7.19639	0.343074
$441$	−45.1731	−2.15110
$442$	11.8490	0.563599
$443$	−27.7559	−1.31872	−0.659361	−	0.751827i	$-0.729173\pi$
$443$	−27.7559	−1.31872	−0.659361	+	0.751827i	$0.729173\pi$
$444$	15.5466	0.737810
$445$	16.7430	0.793695
$446$	−3.34318	−0.158304
$447$	−62.8953	−2.97485
$448$	−1.15087	−0.0543737
$449$	−1.09419	−0.0516378	−0.0258189	−	0.999667i	$-0.508219\pi$
$449$	−1.09419	−0.0516378	−0.0258189	+	0.999667i	$0.508219\pi$
$450$	−135.821	−6.40268
$451$	−7.65390	−0.360408
$452$	−9.03753	−0.425090
$453$	−54.1039	−2.54203
$454$	23.5621	1.10583
$455$	−22.7198	−1.06512
$456$	27.0524	1.26685
$457$	−28.4495	−1.33081	−0.665407	−	0.746481i	$-0.731742\pi$
$457$	−28.4495	−1.33081	−0.665407	+	0.746481i	$0.731742\pi$
$458$	1.09856	0.0513324
$459$	13.1978	0.616019
$460$	12.9803	0.605209
$461$	15.3779	0.716219	0.358110	−	0.933680i	$-0.383421\pi$
$461$	15.3779	0.716219	0.358110	+	0.933680i	$0.383421\pi$
$462$	−4.50380	−0.209536
$463$	−7.20865	−0.335014	−0.167507	−	0.985871i	$-0.553572\pi$
$463$	−7.20865	−0.335014	−0.167507	+	0.985871i	$0.553572\pi$
$464$	−43.4332	−2.01633
$465$	113.754	5.27524
$466$	−7.48671	−0.346815
$467$	40.6280	1.88004	0.940021	−	0.341118i	$-0.110806\pi$
$467$	40.6280	1.88004	0.940021	+	0.341118i	$0.110806\pi$
$468$	−47.0431	−2.17457
$469$	−6.39945	−0.295499
$470$	60.0907	2.77178
$471$	64.2750	2.96163
$472$	18.7997	0.865327
$473$	−1.00000	−0.0459800
$474$	−42.4054	−1.94774
$475$	52.3098	2.40014
$476$	−0.785893	−0.0360214
$477$	−93.2839	−4.27118
$478$	19.6497	0.898757
$479$	−40.5934	−1.85476	−0.927380	−	0.374120i	$-0.877945\pi$
$479$	−40.5934	−1.85476	−0.927380	+	0.374120i	$0.877945\pi$
$480$	−63.8257	−2.91323
$481$	−35.2138	−1.60561
$482$	20.7056	0.943113
$483$	8.88168	0.404130
$484$	0.955421	0.0434282
$485$	−33.7326	−1.53172
$486$	−44.7398	−2.02944
$487$	1.20329	0.0545264	0.0272632	−	0.999628i	$-0.491321\pi$
$487$	1.20329	0.0545264	0.0272632	+	0.999628i	$0.491321\pi$
$488$	6.69652	0.303137
$489$	0.145242	0.00656808
$490$	−43.5636	−1.96800
$491$	20.8972	0.943079	0.471539	−	0.881845i	$-0.343698\pi$
$491$	20.8972	0.943079	0.471539	+	0.881845i	$0.343698\pi$
$492$	23.2905	1.05002
$493$	8.69009	0.391382
$494$	56.0449	2.52158
$495$	28.6282	1.28674
$496$	44.5453	2.00014
$497$	2.87736	0.129067
$498$	28.7775	1.28955
$499$	−37.7858	−1.69152	−0.845762	−	0.533561i	$-0.820854\pi$
$499$	−37.7858	−1.69152	−0.845762	+	0.533561i	$0.820854\pi$
$500$	−23.1997	−1.03752
$501$	−36.2940	−1.62150
$502$	25.5089	1.13852
$503$	−13.6211	−0.607336	−0.303668	−	0.952778i	$-0.598211\pi$
$503$	−13.6211	−0.607336	−0.303668	+	0.952778i	$0.598211\pi$
$504$	−10.5524	−0.470039
$505$	−8.12320	−0.361478
$506$	−5.82822	−0.259096
$507$	109.898	4.88072
$508$	−7.74804	−0.343764
$509$	−0.510111	−0.0226103	−0.0113051	−	0.999936i	$-0.503599\pi$
$509$	−0.510111	−0.0226103	−0.0113051	+	0.999936i	$0.503599\pi$
$510$	21.9419	0.971603
$511$	12.1344	0.536795
$512$	−7.04305	−0.311262
$513$	62.4245	2.75611
$514$	13.5990	0.599828
$515$	−39.0333	−1.72001
$516$	3.04295	0.133959
$517$	−8.72236	−0.383609
$518$	7.22469	0.317435
$519$	7.73552	0.339551
$520$	49.6005	2.17513
$521$	−15.6940	−0.687565	−0.343783	−	0.939049i	$-0.611708\pi$
$521$	−15.6940	−0.687565	−0.343783	+	0.939049i	$0.611708\pi$
$522$	−106.724	−4.67120
$523$	−1.90606	−0.0833462	−0.0416731	−	0.999131i	$-0.513269\pi$
$523$	−1.90606	−0.0833462	−0.0416731	+	0.999131i	$0.513269\pi$
$524$	−14.9447	−0.652862
$525$	−28.9733	−1.26450
$526$	−9.91076	−0.432130
$527$	−8.91260	−0.388239
$528$	15.9183	0.692757
$529$	−11.5065	−0.500283
$530$	−89.9601	−3.90762
$531$	74.7877	3.24551
$532$	−3.71722	−0.161162
$533$	−52.7539	−2.28502
$534$	22.8760	0.989942
$535$	24.6267	1.06470
$536$	13.9709	0.603452
$537$	−15.7848	−0.681163
$538$	−15.8083	−0.681544
$539$	6.32339	0.272368
$540$	−50.5311	−2.17451
$541$	−21.0959	−0.906984	−0.453492	−	0.891260i	$-0.649822\pi$
$541$	−21.0959	−0.906984	−0.453492	+	0.891260i	$0.649822\pi$
$542$	10.0319	0.430908
$543$	−16.6984	−0.716597
$544$	5.00071	0.214404
$545$	58.6516	2.51236
$546$	−31.0421	−1.32848
$547$	24.6020	1.05190	0.525952	−	0.850514i	$-0.323709\pi$
$547$	24.6020	1.05190	0.525952	+	0.850514i	$0.323709\pi$
$548$	−7.34455	−0.313744
$549$	26.6396	1.13695
$550$	19.0124	0.810693
$551$	41.1035	1.75107
$552$	−19.3900	−0.825293
$553$	−6.37058	−0.270905
$554$	−47.9547	−2.03740
$555$	−65.2086	−2.76795
$556$	−7.65902	−0.324815
$557$	41.3337	1.75137	0.875683	−	0.482886i	$-0.160411\pi$
$557$	41.3337	1.75137	0.875683	+	0.482886i	$0.160411\pi$
$558$	109.457	4.63369
$559$	−6.89242	−0.291518
$560$	−16.4752	−0.696202
$561$	−3.18493	−0.134468
$562$	36.2129	1.52755
$563$	1.51411	0.0638122	0.0319061	−	0.999491i	$-0.489842\pi$
$563$	1.51411	0.0638122	0.0319061	+	0.999491i	$0.489842\pi$
$564$	26.5418	1.11761
$565$	37.9069	1.59476
$566$	−7.29631	−0.306687
$567$	−16.9469	−0.711703
$568$	−6.28170	−0.263574
$569$	−37.9906	−1.59265	−0.796324	−	0.604871i	$-0.793225\pi$
$569$	−37.9906	−1.59265	−0.796324	+	0.604871i	$0.793225\pi$
$570$	103.783	4.34701
$571$	−28.3497	−1.18640	−0.593199	−	0.805056i	$-0.702135\pi$
$571$	−28.3497	−1.18640	−0.593199	+	0.805056i	$0.702135\pi$
$572$	6.58516	0.275339
$573$	−50.4252	−2.10654
$574$	10.8233	0.451757
$575$	−37.4934	−1.56358
$576$	9.99515	0.416464
$577$	9.59058	0.399261	0.199631	−	0.979871i	$-0.436026\pi$
$577$	9.59058	0.399261	0.199631	+	0.979871i	$0.436026\pi$
$578$	−1.71913	−0.0715065
$579$	78.3963	3.25804
$580$	−33.2723	−1.38156
$581$	4.32326	0.179359
$582$	−46.0889	−1.91045
$583$	13.0580	0.540807
$584$	−26.4912	−1.09621
$585$	197.317	8.15806
$586$	51.7126	2.13623
$587$	10.5657	0.436094	0.218047	−	0.975938i	$-0.430031\pi$
$587$	10.5657	0.436094	0.218047	+	0.975938i	$0.430031\pi$
$588$	−19.2418	−0.793518
$589$	−42.1559	−1.73700
$590$	72.1230	2.96926
$591$	−48.2848	−1.98617
$592$	−25.5351	−1.04949
$593$	−26.1162	−1.07247	−0.536233	−	0.844070i	$-0.680153\pi$
$593$	−26.1162	−1.07247	−0.536233	+	0.844070i	$0.680153\pi$
$594$	22.6887	0.930930
$595$	3.29634	0.135137
$596$	−18.8674	−0.772839
$597$	44.8523	1.83568
$598$	−40.1705	−1.64269
$599$	−48.0725	−1.96419	−0.982094	−	0.188394i	$-0.939672\pi$
$599$	−48.0725	−1.96419	−0.982094	+	0.188394i	$0.939672\pi$
$600$	63.2528	2.58229
$601$	−44.8799	−1.83069	−0.915344	−	0.402672i	$-0.868082\pi$
$601$	−44.8799	−1.83069	−0.915344	+	0.402672i	$0.868082\pi$
$602$	1.41409	0.0576342
$603$	55.5782	2.26332
$604$	−16.2302	−0.660396
$605$	−4.00741	−0.162924
$606$	−11.0987	−0.450856
$607$	−21.6854	−0.880184	−0.440092	−	0.897953i	$-0.645054\pi$
$607$	−21.6854	−0.880184	−0.440092	+	0.897953i	$0.645054\pi$
$608$	23.6530	0.959256
$609$	−22.7663	−0.922539
$610$	25.6905	1.04018
$611$	−60.1182	−2.43212
$612$	6.82535	0.275898
$613$	7.97223	0.321995	0.160998	−	0.986955i	$-0.448529\pi$
$613$	7.97223	0.321995	0.160998	+	0.986955i	$0.448529\pi$
$614$	2.48632	0.100340
$615$	−97.6893	−3.93921
$616$	1.47713	0.0595154
$617$	9.21159	0.370845	0.185422	−	0.982659i	$-0.440635\pi$
$617$	9.21159	0.370845	0.185422	+	0.982659i	$0.440635\pi$
$618$	−53.3313	−2.14530
$619$	−12.7248	−0.511451	−0.255726	−	0.966749i	$-0.582314\pi$
$619$	−12.7248	−0.511451	−0.255726	+	0.966749i	$0.582314\pi$
$620$	34.1242	1.37046
$621$	−44.7431	−1.79548
$622$	21.7020	0.870170
$623$	3.43668	0.137688
$624$	109.716	4.39215
$625$	42.0119	1.68048
$626$	−2.19074	−0.0875596
$627$	−15.0645	−0.601619
$628$	19.2813	0.769407
$629$	5.10906	0.203711
$630$	−40.4829	−1.61288
$631$	3.09587	0.123245	0.0616223	−	0.998100i	$-0.480373\pi$
$631$	3.09587	0.123245	0.0616223	+	0.998100i	$0.480373\pi$
$632$	13.9079	0.553227
$633$	21.0478	0.836577
$634$	25.0886	0.996395
$635$	32.4983	1.28966
$636$	−39.7349	−1.57559
$637$	43.5835	1.72684
$638$	14.9394	0.591457
$639$	−24.9894	−0.988565
$640$	49.7188	1.96531
$641$	5.51031	0.217644	0.108822	−	0.994061i	$-0.465292\pi$
$641$	5.51031	0.217644	0.108822	+	0.994061i	$0.465292\pi$
$642$	33.6475	1.32796
$643$	−27.0367	−1.06622	−0.533112	−	0.846044i	$-0.678978\pi$
$643$	−27.0367	−1.06622	−0.533112	+	0.846044i	$0.678978\pi$
$644$	2.66434	0.104990
$645$	−12.7633	−0.502556
$646$	−8.13138	−0.319925
$647$	46.5177	1.82880	0.914400	−	0.404811i	$-0.132663\pi$
$647$	46.5177	1.82880	0.914400	+	0.404811i	$0.132663\pi$
$648$	36.9975	1.45340
$649$	−10.4689	−0.410940
$650$	131.042	5.13988
$651$	23.3493	0.915130
$652$	0.0435699	0.00170633
$653$	32.1229	1.25707	0.628533	−	0.777783i	$-0.283656\pi$
$653$	32.1229	1.25707	0.628533	+	0.777783i	$0.283656\pi$
$654$	80.1358	3.13356
$655$	62.6839	2.44926
$656$	−38.2543	−1.49358
$657$	−105.385	−4.11147
$658$	12.3342	0.480839
$659$	12.8047	0.498801	0.249400	−	0.968400i	$-0.419766\pi$
$659$	12.8047	0.498801	0.249400	+	0.968400i	$0.419766\pi$
$660$	12.1944	0.474665
$661$	36.9761	1.43820	0.719101	−	0.694905i	$-0.244554\pi$
$661$	36.9761	1.43820	0.719101	+	0.694905i	$0.244554\pi$
$662$	44.2358	1.71927
$663$	−21.9519	−0.852541
$664$	−9.43829	−0.366277
$665$	15.5915	0.604611
$666$	−62.7452	−2.43133
$667$	−29.4612	−1.14074
$668$	−10.8875	−0.421251
$669$	6.19370	0.239462
$670$	53.5979	2.07067
$671$	−3.72905	−0.143958
$672$	−13.1009	−0.505378
$673$	34.5176	1.33055	0.665277	−	0.746596i	$-0.268313\pi$
$673$	34.5176	1.33055	0.665277	+	0.746596i	$0.268313\pi$
$674$	−24.4483	−0.941712
$675$	145.958	5.61794
$676$	32.9672	1.26797
$677$	18.5221	0.711863	0.355932	−	0.934512i	$-0.384164\pi$
$677$	18.5221	0.711863	0.355932	+	0.934512i	$0.384164\pi$
$678$	51.7923	1.98907
$679$	−6.92396	−0.265717
$680$	−7.19639	−0.275969
$681$	−43.6521	−1.67275
$682$	−15.3219	−0.586708
$683$	−26.6500	−1.01974	−0.509868	−	0.860253i	$-0.670306\pi$
$683$	−26.6500	−1.01974	−0.509868	+	0.860253i	$0.670306\pi$
$684$	32.2834	1.23439
$685$	30.8059	1.17703
$686$	−18.8405	−0.719335
$687$	−2.03524	−0.0776491
$688$	−4.99801	−0.190547
$689$	90.0012	3.42877
$690$	−74.3875	−2.83188
$691$	−38.0756	−1.44846	−0.724232	−	0.689557i	$-0.757805\pi$
$691$	−38.0756	−1.44846	−0.724232	+	0.689557i	$0.757805\pi$
$692$	2.32051	0.0882126
$693$	5.87623	0.223219
$694$	4.76493	0.180874
$695$	32.1249	1.21857
$696$	49.7022	1.88396
$697$	7.65390	0.289912
$698$	48.8099	1.84748
$699$	13.8702	0.524618
$700$	−8.69144	−0.328506
$701$	−18.2094	−0.687761	−0.343880	−	0.939013i	$-0.611742\pi$
$701$	−18.2094	−0.687761	−0.343880	+	0.939013i	$0.611742\pi$
$702$	156.380	5.90219
$703$	24.1655	0.911418
$704$	−1.39913	−0.0527318
$705$	−111.326	−4.19280
$706$	29.2721	1.10167
$707$	−1.66737	−0.0627079
$708$	31.8563	1.19723
$709$	7.95631	0.298806	0.149403	−	0.988776i	$-0.452265\pi$
$709$	7.95631	0.298806	0.149403	+	0.988776i	$0.452265\pi$
$710$	−24.0990	−0.904420
$711$	55.3274	2.07494
$712$	−7.50276	−0.281178
$713$	30.2155	1.13158
$714$	4.50380	0.168550
$715$	−27.6207	−1.03296
$716$	−4.73513	−0.176960
$717$	−36.4038	−1.35953
$718$	−37.0470	−1.38258
$719$	30.9824	1.15545	0.577723	−	0.816233i	$-0.303941\pi$
$719$	30.9824	1.15545	0.577723	+	0.816233i	$0.303941\pi$
$720$	143.084	5.33242
$721$	−8.01199	−0.298382
$722$	−5.79728	−0.215752
$723$	−38.3599	−1.42662
$724$	−5.00921	−0.186166
$725$	96.1064	3.56930
$726$	−5.47533	−0.203209
$727$	13.0988	0.485809	0.242905	−	0.970050i	$-0.421900\pi$
$727$	13.0988	0.485809	0.242905	+	0.970050i	$0.421900\pi$
$728$	10.1810	0.377334
$729$	21.0790	0.780702
$730$	−101.630	−3.76151
$731$	1.00000	0.0369863
$732$	11.3473	0.419410
$733$	−26.8523	−0.991814	−0.495907	−	0.868376i	$-0.665164\pi$
$733$	−26.8523	−0.991814	−0.495907	+	0.868376i	$0.665164\pi$
$734$	−58.6140	−2.16348
$735$	80.7076	2.97694
$736$	−16.9534	−0.624912
$737$	−7.77990	−0.286576
$738$	−93.9988	−3.46014
$739$	−35.4966	−1.30576	−0.652882	−	0.757460i	$-0.726440\pi$
$739$	−35.4966	−1.30576	−0.652882	+	0.757460i	$0.726440\pi$
$740$	−19.5614	−0.719090
$741$	−103.831	−3.81432
$742$	−18.4652	−0.677880
$743$	−28.8571	−1.05866	−0.529332	−	0.848415i	$-0.677557\pi$
$743$	−28.8571	−1.05866	−0.529332	+	0.848415i	$0.677557\pi$
$744$	−50.9748	−1.86883
$745$	79.1373	2.89937
$746$	27.8126	1.01829
$747$	−37.5468	−1.37376
$748$	−0.955421	−0.0349337
$749$	5.05488	0.184701
$750$	132.953	4.85475
$751$	−10.9151	−0.398299	−0.199149	−	0.979969i	$-0.563818\pi$
$751$	−10.9151	−0.398299	−0.199149	+	0.979969i	$0.563818\pi$
$752$	−43.5945	−1.58973
$753$	−47.2589	−1.72221
$754$	102.969	3.74990
$755$	68.0757	2.47753
$756$	−10.3720	−0.377227
$757$	4.74972	0.172632	0.0863158	−	0.996268i	$-0.472491\pi$
$757$	4.74972	0.172632	0.0863158	+	0.996268i	$0.472491\pi$
$758$	21.5012	0.780960
$759$	10.7976	0.391927
$760$	−34.0384	−1.23470
$761$	14.5171	0.526246	0.263123	−	0.964762i	$-0.415248\pi$
$761$	14.5171	0.526246	0.263123	+	0.964762i	$0.415248\pi$
$762$	44.4025	1.60853
$763$	12.0389	0.435836
$764$	−15.1266	−0.547262
$765$	−28.6282	−1.03505
$766$	−10.1323	−0.366096
$767$	−72.1559	−2.60540
$768$	59.0186	2.12965
$769$	−50.7644	−1.83061	−0.915306	−	0.402760i	$-0.868051\pi$
$769$	−50.7644	−1.83061	−0.915306	+	0.402760i	$0.868051\pi$
$770$	5.66685	0.204219
$771$	−25.1941	−0.907344
$772$	23.5174	0.846411
$773$	−5.74692	−0.206702	−0.103351	−	0.994645i	$-0.532957\pi$
$773$	−5.74692	−0.206702	−0.103351	+	0.994645i	$0.532957\pi$
$774$	−12.2812	−0.441437
$775$	−98.5672	−3.54064
$776$	15.1160	0.542633
$777$	−13.3847	−0.480175
$778$	−47.9353	−1.71857
$779$	36.2024	1.29709
$780$	84.0486	3.00942
$781$	3.49805	0.125170
$782$	5.82822	0.208417
$783$	114.690	4.09868
$784$	31.6044	1.12873
$785$	−80.8732	−2.88649
$786$	85.6451	3.05486
$787$	−15.8025	−0.563298	−0.281649	−	0.959517i	$-0.590881\pi$
$787$	−15.8025	−0.563298	−0.281649	+	0.959517i	$0.590881\pi$
$788$	−14.4845	−0.515990
$789$	18.3611	0.653671
$790$	53.3561	1.89832
$791$	7.78079	0.276653
$792$	−12.8286	−0.455846
$793$	−25.7022	−0.912711
$794$	−42.5975	−1.51173
$795$	166.664	5.91095
$796$	13.4548	0.476894
$797$	13.6540	0.483649	0.241825	−	0.970320i	$-0.422254\pi$
$797$	13.6540	0.483649	0.241825	+	0.970320i	$0.422254\pi$
$798$	21.3026	0.754105
$799$	8.72236	0.308575
$800$	55.3044	1.95531
$801$	−29.8469	−1.05459
$802$	−20.6406	−0.728845
$803$	14.7520	0.520586
$804$	23.6739	0.834914
$805$	−11.1753	−0.393877
$806$	−105.605	−3.71979
$807$	29.2871	1.03095
$808$	3.64011	0.128059
$809$	−12.6313	−0.444093	−0.222046	−	0.975036i	$-0.571274\pi$
$809$	−12.6313	−0.444093	−0.222046	+	0.975036i	$0.571274\pi$
$810$	141.937	4.98715
$811$	−31.7960	−1.11651	−0.558253	−	0.829670i	$-0.688528\pi$
$811$	−31.7960	−1.11651	−0.558253	+	0.829670i	$0.688528\pi$
$812$	−6.82948	−0.239668
$813$	−18.5855	−0.651823
$814$	8.78315	0.307849
$815$	−0.182749	−0.00640143
$816$	−15.9183	−0.557254
$817$	4.72993	0.165479
$818$	−14.4588	−0.505541
$819$	40.5014	1.41523
$820$	−29.3050	−1.02337
$821$	−19.5069	−0.680797	−0.340398	−	0.940281i	$-0.610562\pi$
$821$	−19.5069	−0.680797	−0.340398	+	0.940281i	$0.610562\pi$
$822$	42.0902	1.46806
$823$	26.4286	0.921244	0.460622	−	0.887596i	$-0.347626\pi$
$823$	26.4286	0.921244	0.460622	+	0.887596i	$0.347626\pi$
$824$	17.4913	0.609339
$825$	−35.2232	−1.22631
$826$	14.8040	0.515097
$827$	26.1691	0.909990	0.454995	−	0.890494i	$-0.349641\pi$
$827$	26.1691	0.909990	0.454995	+	0.890494i	$0.349641\pi$
$828$	−23.1393	−0.804147
$829$	25.8391	0.897430	0.448715	−	0.893675i	$-0.351882\pi$
$829$	25.8391	0.897430	0.448715	+	0.893675i	$0.351882\pi$
$830$	−36.2089	−1.25683
$831$	88.8428	3.08192
$832$	−9.64342	−0.334325
$833$	−6.32339	−0.219093
$834$	43.8923	1.51987
$835$	45.6665	1.58036
$836$	−4.51907	−0.156295
$837$	−117.626	−4.06576
$838$	−1.06323	−0.0367285
$839$	8.37733	0.289218	0.144609	−	0.989489i	$-0.453808\pi$
$839$	8.37733	0.289218	0.144609	+	0.989489i	$0.453808\pi$
$840$	18.8531	0.650495
$841$	46.5176	1.60406
$842$	−8.07978	−0.278448
$843$	−67.0894	−2.31068
$844$	6.31396	0.217336
$845$	−138.277	−4.75688
$846$	−107.121	−3.68289
$847$	−0.822562	−0.0282636
$848$	65.2641	2.24118
$849$	13.5174	0.463917
$850$	−19.0124	−0.652122
$851$	−17.3208	−0.593748
$852$	−10.6444	−0.364671
$853$	19.3539	0.662666	0.331333	−	0.943514i	$-0.392502\pi$
$853$	19.3539	0.662666	0.331333	+	0.943514i	$0.392502\pi$
$854$	5.27323	0.180446
$855$	−135.409	−4.63089
$856$	−11.0355	−0.377186
$857$	−9.21330	−0.314720	−0.157360	−	0.987541i	$-0.550298\pi$
$857$	−9.21330	−0.314720	−0.157360	+	0.987541i	$0.550298\pi$
$858$	−37.7383	−1.28836
$859$	−34.4835	−1.17656	−0.588281	−	0.808656i	$-0.700195\pi$
$859$	−34.4835	−1.17656	−0.588281	+	0.808656i	$0.700195\pi$
$860$	−3.82876	−0.130560
$861$	−20.0517	−0.683361
$862$	−12.3505	−0.420660
$863$	−41.1491	−1.40073	−0.700365	−	0.713784i	$-0.746980\pi$
$863$	−41.1491	−1.40073	−0.700365	+	0.713784i	$0.746980\pi$
$864$	65.9982	2.24530
$865$	−9.73312	−0.330936
$866$	17.4118	0.591678
$867$	3.18493	0.108166
$868$	7.00435	0.237743
$869$	−7.74481	−0.262725
$870$	190.677	6.46455
$871$	−53.6223	−1.81692
$872$	−26.2825	−0.890039
$873$	60.1334	2.03521
$874$	27.5670	0.932469
$875$	19.9736	0.675230
$876$	−44.8896	−1.51668
$877$	10.9195	0.368726	0.184363	−	0.982858i	$-0.440978\pi$
$877$	10.9195	0.368726	0.184363	+	0.982858i	$0.440978\pi$
$878$	13.2123	0.445895
$879$	−95.8048	−3.23141
$880$	−20.0291	−0.675180
$881$	−29.1905	−0.983452	−0.491726	−	0.870750i	$-0.663634\pi$
$881$	−29.1905	−0.983452	−0.491726	+	0.870750i	$0.663634\pi$
$882$	77.6586	2.61490
$883$	12.1443	0.408688	0.204344	−	0.978899i	$-0.434494\pi$
$883$	12.1443	0.408688	0.204344	+	0.978899i	$0.434494\pi$
$884$	−6.58516	−0.221483
$885$	−133.618	−4.49151
$886$	47.7161	1.60305
$887$	27.7654	0.932272	0.466136	−	0.884713i	$-0.345646\pi$
$887$	27.7654	0.932272	0.466136	+	0.884713i	$0.345646\pi$
$888$	29.2208	0.980586
$889$	6.67061	0.223725
$890$	−28.7835	−0.964824
$891$	−20.6026	−0.690213
$892$	1.85800	0.0622103
$893$	41.2561	1.38058
$894$	108.125	3.61626
$895$	19.8610	0.663880
$896$	10.2053	0.340935
$897$	74.4215	2.48486
$898$	1.88105	0.0627715
$899$	−77.4512	−2.58314
$900$	75.4837	2.51612
$901$	−13.0580	−0.435025
$902$	13.1581	0.438116
$903$	−2.61981	−0.0871817
$904$	−16.9866	−0.564965
$905$	21.0106	0.698416
$906$	93.0119	3.09011
$907$	49.3816	1.63969	0.819844	−	0.572587i	$-0.194060\pi$
$907$	49.3816	1.63969	0.819844	+	0.572587i	$0.194060\pi$
$908$	−13.0948	−0.434567
$909$	14.4808	0.480299
$910$	39.0583	1.29477
$911$	−5.46742	−0.181144	−0.0905719	−	0.995890i	$-0.528870\pi$
$911$	−5.46742	−0.181144	−0.0905719	+	0.995890i	$0.528870\pi$
$912$	−75.2926	−2.49319
$913$	5.25584	0.173943
$914$	48.9086	1.61775
$915$	−47.5951	−1.57345
$916$	−0.610533	−0.0201726
$917$	12.8665	0.424890
$918$	−22.6887	−0.748840
$919$	19.9275	0.657348	0.328674	−	0.944443i	$-0.393398\pi$
$919$	19.9275	0.657348	0.328674	+	0.944443i	$0.393398\pi$
$920$	24.3972	0.804353
$921$	−4.60625	−0.151781
$922$	−26.4366	−0.870644
$923$	24.1100	0.793591
$924$	2.50302	0.0823433
$925$	56.5027	1.85780
$926$	12.3926	0.407247
$927$	69.5828	2.28540
$928$	43.4566	1.42653
$929$	−22.3310	−0.732655	−0.366327	−	0.930486i	$-0.619385\pi$
$929$	−22.3310	−0.732655	−0.366327	+	0.930486i	$0.619385\pi$
$930$	−195.559	−6.41264
$931$	−29.9092	−0.980234
$932$	4.16079	0.136291
$933$	−40.2059	−1.31628
$934$	−69.8450	−2.28540
$935$	4.00741	0.131056
$936$	−88.4204	−2.89011
$937$	−14.1693	−0.462890	−0.231445	−	0.972848i	$-0.574345\pi$
$937$	−14.1693	−0.462890	−0.231445	+	0.972848i	$0.574345\pi$
$938$	11.0015	0.359212
$939$	4.05865	0.132449
$940$	−33.3959	−1.08925
$941$	−20.1180	−0.655829	−0.327915	−	0.944707i	$-0.606346\pi$
$941$	−20.1180	−0.655829	−0.327915	+	0.944707i	$0.606346\pi$
$942$	−110.497	−3.60020
$943$	−25.9483	−0.844993
$944$	−52.3236	−1.70299
$945$	43.5043	1.41520
$946$	1.71913	0.0558939
$947$	24.0244	0.780688	0.390344	−	0.920669i	$-0.372356\pi$
$947$	24.0244	0.780688	0.390344	+	0.920669i	$0.372356\pi$
$948$	23.5671	0.765424
$949$	101.677	3.30057
$950$	−89.9275	−2.91763
$951$	−46.4801	−1.50722
$952$	−1.47713	−0.0478742
$953$	−59.0554	−1.91299	−0.956496	−	0.291746i	$-0.905764\pi$
$953$	−59.0554	−1.91299	−0.956496	+	0.291746i	$0.905764\pi$
$954$	160.367	5.19209
$955$	63.4470	2.05310
$956$	−10.9205	−0.353193
$957$	−27.6774	−0.894682
$958$	69.7855	2.25467
$959$	6.32323	0.204188
$960$	−17.8576	−0.576352
$961$	48.4344	1.56240
$962$	60.5372	1.95180
$963$	−43.9008	−1.41468
$964$	−11.5073	−0.370624
$965$	−98.6413	−3.17538
$966$	−15.2688	−0.491266
$967$	34.9430	1.12369	0.561846	−	0.827242i	$-0.310091\pi$
$967$	34.9430	1.12369	0.561846	+	0.827242i	$0.310091\pi$
$968$	1.79577	0.0577183
$969$	15.0645	0.483942
$970$	57.9908	1.86197
$971$	−53.7492	−1.72489	−0.862447	−	0.506148i	$-0.831069\pi$
$971$	−53.7492	−1.72489	−0.862447	+	0.506148i	$0.831069\pi$
$972$	24.8645	0.797529
$973$	6.59397	0.211393
$974$	−2.06862	−0.0662829
$975$	−242.773	−7.77496
$976$	−18.6379	−0.596583
$977$	−17.9431	−0.574052	−0.287026	−	0.957923i	$-0.592667\pi$
$977$	−17.9431	−0.574052	−0.287026	+	0.957923i	$0.592667\pi$
$978$	−0.249691	−0.00798423
$979$	4.17801	0.133530
$980$	24.2108	0.773384
$981$	−104.555	−3.33820
$982$	−35.9251	−1.14642
$983$	4.70761	0.150150	0.0750748	−	0.997178i	$-0.476080\pi$
$983$	4.70761	0.150150	0.0750748	+	0.997178i	$0.476080\pi$
$984$	43.7758	1.39552
$985$	60.7538	1.93578
$986$	−14.9394	−0.475768
$987$	−22.8509	−0.727352
$988$	−31.1473	−0.990929
$989$	−3.39021	−0.107802
$990$	−49.2156	−1.56418
$991$	19.5584	0.621292	0.310646	−	0.950526i	$-0.399455\pi$
$991$	19.5584	0.621292	0.310646	+	0.950526i	$0.399455\pi$
$992$	−44.5693	−1.41508
$993$	−81.9529	−2.60070
$994$	−4.94657	−0.156896
$995$	−56.4349	−1.78911
$996$	−15.9933	−0.506767
$997$	13.8085	0.437320	0.218660	−	0.975801i	$-0.429831\pi$
$997$	13.8085	0.437320	0.218660	+	0.975801i	$0.429831\pi$
$998$	64.9588	2.05623
$999$	67.4282	2.13333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.17	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.17	✓	69	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71913 q^{2} +3.18493 q^{3} +0.955421 q^{4} -4.00741 q^{5} -5.47533 q^{6} -0.822562 q^{7} +1.79577 q^{8} +7.14381 q^{9} +O(q^{10})\)	\(q-1.71913 q^{2} +3.18493 q^{3} +0.955421 q^{4} -4.00741 q^{5} -5.47533 q^{6} -0.822562 q^{7} +1.79577 q^{8} +7.14381 q^{9} +6.88927 q^{10} -1.00000 q^{11} +3.04295 q^{12} -6.89242 q^{13} +1.41409 q^{14} -12.7633 q^{15} -4.99801 q^{16} +1.00000 q^{17} -12.2812 q^{18} +4.72993 q^{19} -3.82876 q^{20} -2.61981 q^{21} +1.71913 q^{22} -3.39021 q^{23} +5.71941 q^{24} +11.0593 q^{25} +11.8490 q^{26} +13.1978 q^{27} -0.785893 q^{28} +8.69009 q^{29} +21.9419 q^{30} -8.91260 q^{31} +5.00071 q^{32} -3.18493 q^{33} -1.71913 q^{34} +3.29634 q^{35} +6.82535 q^{36} +5.10906 q^{37} -8.13138 q^{38} -21.9519 q^{39} -7.19639 q^{40} +7.65390 q^{41} +4.50380 q^{42} +1.00000 q^{43} -0.955421 q^{44} -28.6282 q^{45} +5.82822 q^{46} +8.72236 q^{47} -15.9183 q^{48} -6.32339 q^{49} -19.0124 q^{50} +3.18493 q^{51} -6.58516 q^{52} -13.0580 q^{53} -22.6887 q^{54} +4.00741 q^{55} -1.47713 q^{56} +15.0645 q^{57} -14.9394 q^{58} +10.4689 q^{59} -12.1944 q^{60} +3.72905 q^{61} +15.3219 q^{62} -5.87623 q^{63} +1.39913 q^{64} +27.6207 q^{65} +5.47533 q^{66} +7.77990 q^{67} +0.955421 q^{68} -10.7976 q^{69} -5.66685 q^{70} -3.49805 q^{71} +12.8286 q^{72} -14.7520 q^{73} -8.78315 q^{74} +35.2232 q^{75} +4.51907 q^{76} +0.822562 q^{77} +37.7383 q^{78} +7.74481 q^{79} +20.0291 q^{80} +20.6026 q^{81} -13.1581 q^{82} -5.25584 q^{83} -2.50302 q^{84} -4.00741 q^{85} -1.71913 q^{86} +27.6774 q^{87} -1.79577 q^{88} -4.17801 q^{89} +49.2156 q^{90} +5.66944 q^{91} -3.23907 q^{92} -28.3860 q^{93} -14.9949 q^{94} -18.9547 q^{95} +15.9269 q^{96} +8.41756 q^{97} +10.8708 q^{98} -7.14381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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