LMFDB - Embedded newform 8041.2.a.e.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:	$0$
Dimension:	$66$
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)

$f(q)$	$=$	$q-1.35222 q^{2} +2.90367 q^{3} -0.171490 q^{4} -2.71204 q^{5} -3.92642 q^{6} -3.82442 q^{7} +2.93634 q^{8} +5.43132 q^{9} +O(q^{10})$	\(q-1.35222 q^{2} +2.90367 q^{3} -0.171490 q^{4} -2.71204 q^{5} -3.92642 q^{6} -3.82442 q^{7} +2.93634 q^{8} +5.43132 q^{9} +3.66729 q^{10} -1.00000 q^{11} -0.497952 q^{12} +6.55623 q^{13} +5.17148 q^{14} -7.87489 q^{15} -3.62761 q^{16} -1.00000 q^{17} -7.34436 q^{18} -4.53389 q^{19} +0.465090 q^{20} -11.1049 q^{21} +1.35222 q^{22} -5.04566 q^{23} +8.52618 q^{24} +2.35519 q^{25} -8.86548 q^{26} +7.05975 q^{27} +0.655852 q^{28} +1.78233 q^{29} +10.6486 q^{30} +5.17771 q^{31} -0.967341 q^{32} -2.90367 q^{33} +1.35222 q^{34} +10.3720 q^{35} -0.931419 q^{36} -2.82360 q^{37} +6.13084 q^{38} +19.0371 q^{39} -7.96349 q^{40} -1.74874 q^{41} +15.0163 q^{42} +1.00000 q^{43} +0.171490 q^{44} -14.7300 q^{45} +6.82286 q^{46} +2.93681 q^{47} -10.5334 q^{48} +7.62623 q^{49} -3.18474 q^{50} -2.90367 q^{51} -1.12433 q^{52} -7.42353 q^{53} -9.54637 q^{54} +2.71204 q^{55} -11.2298 q^{56} -13.1649 q^{57} -2.41010 q^{58} +7.83907 q^{59} +1.35047 q^{60} -4.43647 q^{61} -7.00142 q^{62} -20.7717 q^{63} +8.56328 q^{64} -17.7808 q^{65} +3.92642 q^{66} -7.03016 q^{67} +0.171490 q^{68} -14.6510 q^{69} -14.0253 q^{70} +9.18978 q^{71} +15.9482 q^{72} -11.4059 q^{73} +3.81814 q^{74} +6.83869 q^{75} +0.777519 q^{76} +3.82442 q^{77} -25.7425 q^{78} +11.9006 q^{79} +9.83824 q^{80} +4.20526 q^{81} +2.36468 q^{82} -5.82134 q^{83} +1.90438 q^{84} +2.71204 q^{85} -1.35222 q^{86} +5.17529 q^{87} -2.93634 q^{88} +16.1023 q^{89} +19.9182 q^{90} -25.0738 q^{91} +0.865282 q^{92} +15.0344 q^{93} -3.97123 q^{94} +12.2961 q^{95} -2.80884 q^{96} +15.8546 q^{97} -10.3124 q^{98} -5.43132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	−1.35222	−0.956167	−0.478083	−	0.878314i	$-0.658668\pi$
$2$	−1.35222	−0.956167	−0.478083	+	0.878314i	$0.658668\pi$
$3$	2.90367	1.67644	0.838218	−	0.545335i	$-0.183598\pi$
$3$	2.90367	1.67644	0.838218	+	0.545335i	$0.183598\pi$
$4$	−0.171490	−0.0857452
$5$	−2.71204	−1.21286	−0.606432	−	0.795136i	$-0.707400\pi$
$5$	−2.71204	−1.21286	−0.606432	+	0.795136i	$0.707400\pi$
$6$	−3.92642	−1.60295
$7$	−3.82442	−1.44550	−0.722748	−	0.691111i	$-0.757121\pi$
$7$	−3.82442	−1.44550	−0.722748	+	0.691111i	$0.757121\pi$
$8$	2.93634	1.03815
$9$	5.43132	1.81044
$10$	3.66729	1.15970
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.497952	−0.143746
$13$	6.55623	1.81837	0.909185	−	0.416393i	$-0.136706\pi$
$13$	6.55623	1.81837	0.909185	+	0.416393i	$0.136706\pi$
$14$	5.17148	1.38214
$15$	−7.87489	−2.03329
$16$	−3.62761	−0.906903
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−7.34436	−1.73108
$19$	−4.53389	−1.04015	−0.520073	−	0.854122i	$-0.674095\pi$
$19$	−4.53389	−1.04015	−0.520073	+	0.854122i	$0.674095\pi$
$20$	0.465090	0.103997
$21$	−11.1049	−2.42328
$22$	1.35222	0.288295
$23$	−5.04566	−1.05209	−0.526047	−	0.850456i	$-0.676326\pi$
$23$	−5.04566	−1.05209	−0.526047	+	0.850456i	$0.676326\pi$
$24$	8.52618	1.74040
$25$	2.35519	0.471037
$26$	−8.86548	−1.73866
$27$	7.05975	1.35865
$28$	0.655852	0.123944
$29$	1.78233	0.330970	0.165485	−	0.986212i	$-0.447081\pi$
$29$	1.78233	0.330970	0.165485	+	0.986212i	$0.447081\pi$
$30$	10.6486	1.94416
$31$	5.17771	0.929944	0.464972	−	0.885325i	$-0.346064\pi$
$31$	5.17771	0.929944	0.464972	+	0.885325i	$0.346064\pi$
$32$	−0.967341	−0.171003
$33$	−2.90367	−0.505465
$34$	1.35222	0.231904
$35$	10.3720	1.75319
$36$	−0.931419	−0.155237
$37$	−2.82360	−0.464197	−0.232098	−	0.972692i	$-0.574559\pi$
$37$	−2.82360	−0.464197	−0.232098	+	0.972692i	$0.574559\pi$
$38$	6.13084	0.994553
$39$	19.0371	3.04838
$40$	−7.96349	−1.25914
$41$	−1.74874	−0.273107	−0.136553	−	0.990633i	$-0.543603\pi$
$41$	−1.74874	−0.273107	−0.136553	+	0.990633i	$0.543603\pi$
$42$	15.0163	2.31706
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.171490	0.0258532
$45$	−14.7300	−2.19582
$46$	6.82286	1.00598
$47$	2.93681	0.428378	0.214189	−	0.976792i	$-0.431289\pi$
$47$	2.93681	0.428378	0.214189	+	0.976792i	$0.431289\pi$
$48$	−10.5334	−1.52036
$49$	7.62623	1.08946
$50$	−3.18474	−0.450390
$51$	−2.90367	−0.406596
$52$	−1.12433	−0.155916
$53$	−7.42353	−1.01970	−0.509850	−	0.860263i	$-0.670299\pi$
$53$	−7.42353	−1.01970	−0.509850	+	0.860263i	$0.670299\pi$
$54$	−9.54637	−1.29910
$55$	2.71204	0.365692
$56$	−11.2298	−1.50065
$57$	−13.1649	−1.74374
$58$	−2.41010	−0.316462
$59$	7.83907	1.02056	0.510280	−	0.860008i	$-0.329542\pi$
$59$	7.83907	1.02056	0.510280	+	0.860008i	$0.329542\pi$
$60$	1.35047	0.174345
$61$	−4.43647	−0.568032	−0.284016	−	0.958820i	$-0.591667\pi$
$61$	−4.43647	−0.568032	−0.284016	+	0.958820i	$0.591667\pi$
$62$	−7.00142	−0.889181
$63$	−20.7717	−2.61698
$64$	8.56328	1.07041
$65$	−17.7808	−2.20543
$66$	3.92642	0.483308
$67$	−7.03016	−0.858871	−0.429435	−	0.903098i	$-0.641287\pi$
$67$	−7.03016	−0.858871	−0.429435	+	0.903098i	$0.641287\pi$
$68$	0.171490	0.0207963
$69$	−14.6510	−1.76377
$70$	−14.0253	−1.67634
$71$	9.18978	1.09063	0.545313	−	0.838232i	$-0.316411\pi$
$71$	9.18978	1.09063	0.545313	+	0.838232i	$0.316411\pi$
$72$	15.9482	1.87951
$73$	−11.4059	−1.33496	−0.667482	−	0.744626i	$-0.732628\pi$
$73$	−11.4059	−1.33496	−0.667482	+	0.744626i	$0.732628\pi$
$74$	3.81814	0.443850
$75$	6.83869	0.789664
$76$	0.777519	0.0891875
$77$	3.82442	0.435834
$78$	−25.7425	−2.91476
$79$	11.9006	1.33892	0.669462	−	0.742846i	$-0.266525\pi$
$79$	11.9006	1.33892	0.669462	+	0.742846i	$0.266525\pi$
$80$	9.83824	1.09995
$81$	4.20526	0.467252
$82$	2.36468	0.261136
$83$	−5.82134	−0.638975	−0.319488	−	0.947590i	$-0.603511\pi$
$83$	−5.82134	−0.638975	−0.319488	+	0.947590i	$0.603511\pi$
$84$	1.90438	0.207785
$85$	2.71204	0.294163
$86$	−1.35222	−0.145814
$87$	5.17529	0.554850
$88$	−2.93634	−0.313015
$89$	16.1023	1.70684	0.853422	−	0.521220i	$-0.174523\pi$
$89$	16.1023	1.70684	0.853422	+	0.521220i	$0.174523\pi$
$90$	19.9182	2.09957
$91$	−25.0738	−2.62845
$92$	0.865282	0.0902119
$93$	15.0344	1.55899
$94$	−3.97123	−0.409601
$95$	12.2961	1.26155
$96$	−2.80884	−0.286676
$97$	15.8546	1.60979	0.804894	−	0.593418i	$-0.202222\pi$
$97$	15.8546	1.60979	0.804894	+	0.593418i	$0.202222\pi$
$98$	−10.3124	−1.04171
$99$	−5.43132	−0.545868
$100$	−0.403892	−0.0403892
$101$	7.31163	0.727535	0.363767	−	0.931490i	$-0.381490\pi$
$101$	7.31163	0.727535	0.363767	+	0.931490i	$0.381490\pi$
$102$	3.92642	0.388773
$103$	−16.6286	−1.63847	−0.819234	−	0.573460i	$-0.805601\pi$
$103$	−16.6286	−1.63847	−0.819234	+	0.573460i	$0.805601\pi$
$104$	19.2513	1.88775
$105$	30.1169	2.93911
$106$	10.0383	0.975004
$107$	12.3905	1.19783	0.598916	−	0.800812i	$-0.295598\pi$
$107$	12.3905	1.19783	0.598916	+	0.800812i	$0.295598\pi$
$108$	−1.21068	−0.116498
$109$	3.65262	0.349857	0.174929	−	0.984581i	$-0.444031\pi$
$109$	3.65262	0.349857	0.174929	+	0.984581i	$0.444031\pi$
$110$	−3.66729	−0.349663
$111$	−8.19881	−0.778197
$112$	13.8735	1.31092
$113$	−8.03470	−0.755841	−0.377920	−	0.925838i	$-0.623361\pi$
$113$	−8.03470	−0.755841	−0.377920	+	0.925838i	$0.623361\pi$
$114$	17.8019	1.66730
$115$	13.6841	1.27604
$116$	−0.305652	−0.0283791
$117$	35.6089	3.29205
$118$	−10.6002	−0.975826
$119$	3.82442	0.350584
$120$	−23.1234	−2.11087
$121$	1.00000	0.0909091
$122$	5.99910	0.543133
$123$	−5.07776	−0.457846
$124$	−0.887927	−0.0797382
$125$	7.17286	0.641560
$126$	28.0879	2.50227
$127$	−20.9777	−1.86147	−0.930734	−	0.365697i	$-0.880831\pi$
$127$	−20.9777	−1.86147	−0.930734	+	0.365697i	$0.880831\pi$
$128$	−9.64479	−0.852487
$129$	2.90367	0.255654
$130$	24.0436	2.10876
$131$	11.9181	1.04129	0.520643	−	0.853774i	$-0.325692\pi$
$131$	11.9181	1.04129	0.520643	+	0.853774i	$0.325692\pi$
$132$	0.497952	0.0433412
$133$	17.3395	1.50353
$134$	9.50635	0.821224
$135$	−19.1464	−1.64786
$136$	−2.93634	−0.251789
$137$	−11.0622	−0.945107	−0.472554	−	0.881302i	$-0.656668\pi$
$137$	−11.0622	−0.945107	−0.472554	+	0.881302i	$0.656668\pi$
$138$	19.8114	1.68646
$139$	−7.60424	−0.644984	−0.322492	−	0.946572i	$-0.604520\pi$
$139$	−7.60424	−0.644984	−0.322492	+	0.946572i	$0.604520\pi$
$140$	−1.77870	−0.150328
$141$	8.52755	0.718149
$142$	−12.4266	−1.04282
$143$	−6.55623	−0.548259
$144$	−19.7027	−1.64189
$145$	−4.83375	−0.401421
$146$	15.4234	1.27645
$147$	22.1441	1.82641
$148$	0.484220	0.0398027
$149$	5.71999	0.468600	0.234300	−	0.972164i	$-0.424720\pi$
$149$	5.71999	0.468600	0.234300	+	0.972164i	$0.424720\pi$
$150$	−9.24744	−0.755050
$151$	3.15808	0.257001	0.128500	−	0.991709i	$-0.458984\pi$
$151$	3.15808	0.257001	0.128500	+	0.991709i	$0.458984\pi$
$152$	−13.3130	−1.07983
$153$	−5.43132	−0.439096
$154$	−5.17148	−0.416730
$155$	−14.0422	−1.12789
$156$	−3.26469	−0.261384
$157$	−10.3010	−0.822105	−0.411053	−	0.911612i	$-0.634839\pi$
$157$	−10.3010	−0.822105	−0.411053	+	0.911612i	$0.634839\pi$
$158$	−16.0923	−1.28024
$159$	−21.5555	−1.70946
$160$	2.62347	0.207404
$161$	19.2968	1.52080
$162$	−5.68646	−0.446770
$163$	−10.3686	−0.812129	−0.406064	−	0.913845i	$-0.633099\pi$
$163$	−10.3686	−0.812129	−0.406064	+	0.913845i	$0.633099\pi$
$164$	0.299892	0.0234176
$165$	7.87489	0.613059
$166$	7.87176	0.610967
$167$	14.9716	1.15854	0.579270	−	0.815136i	$-0.303338\pi$
$167$	14.9716	1.15854	0.579270	+	0.815136i	$0.303338\pi$
$168$	−32.6077	−2.51574
$169$	29.9841	2.30647
$170$	−3.66729	−0.281268
$171$	−24.6250	−1.88312
$172$	−0.171490	−0.0130760
$173$	−2.32655	−0.176884	−0.0884422	−	0.996081i	$-0.528189\pi$
$173$	−2.32655	−0.176884	−0.0884422	+	0.996081i	$0.528189\pi$
$174$	−6.99815	−0.530529
$175$	−9.00723	−0.680882
$176$	3.62761	0.273441
$177$	22.7621	1.71090
$178$	−21.7740	−1.63203
$179$	−10.4681	−0.782426	−0.391213	−	0.920300i	$-0.627944\pi$
$179$	−10.4681	−0.782426	−0.391213	+	0.920300i	$0.627944\pi$
$180$	2.52605	0.188281
$181$	0.0409755	0.00304568	0.00152284	−	0.999999i	$-0.499515\pi$
$181$	0.0409755	0.00304568	0.00152284	+	0.999999i	$0.499515\pi$
$182$	33.9054	2.51323
$183$	−12.8821	−0.952269
$184$	−14.8158	−1.09223
$185$	7.65773	0.563007
$186$	−20.3298	−1.49066
$187$	1.00000	0.0731272
$188$	−0.503635	−0.0367314
$189$	−26.9995	−1.96392
$190$	−16.6271	−1.20626
$191$	−11.8179	−0.855116	−0.427558	−	0.903988i	$-0.640626\pi$
$191$	−11.8179	−0.855116	−0.427558	+	0.903988i	$0.640626\pi$
$192$	24.8650	1.79447
$193$	−6.21284	−0.447210	−0.223605	−	0.974680i	$-0.571783\pi$
$193$	−6.21284	−0.447210	−0.223605	+	0.974680i	$0.571783\pi$
$194$	−21.4389	−1.53923
$195$	−51.6296	−3.69727
$196$	−1.30782	−0.0934160
$197$	15.7562	1.12259	0.561293	−	0.827617i	$-0.310304\pi$
$197$	15.7562	1.12259	0.561293	+	0.827617i	$0.310304\pi$
$198$	7.34436	0.521941
$199$	15.6522	1.10955	0.554776	−	0.832000i	$-0.312804\pi$
$199$	15.6522	1.10955	0.554776	+	0.832000i	$0.312804\pi$
$200$	6.91563	0.489009
$201$	−20.4133	−1.43984
$202$	−9.88697	−0.695644
$203$	−6.81637	−0.478416
$204$	0.497952	0.0348636
$205$	4.74265	0.331241
$206$	22.4856	1.56665
$207$	−27.4046	−1.90475
$208$	−23.7834	−1.64908
$209$	4.53389	0.313616
$210$	−40.7248	−2.81028
$211$	23.2399	1.59990	0.799952	−	0.600064i	$-0.204858\pi$
$211$	23.2399	1.59990	0.799952	+	0.600064i	$0.204858\pi$
$212$	1.27306	0.0874345
$213$	26.6841	1.82837
$214$	−16.7547	−1.14533
$215$	−2.71204	−0.184960
$216$	20.7298	1.41049
$217$	−19.8018	−1.34423
$218$	−4.93916	−0.334522
$219$	−33.1191	−2.23798
$220$	−0.465090	−0.0313563
$221$	−6.55623	−0.441019
$222$	11.0866	0.744086
$223$	24.1804	1.61924	0.809621	−	0.586953i	$-0.199673\pi$
$223$	24.1804	1.61924	0.809621	+	0.586953i	$0.199673\pi$
$224$	3.69952	0.247185
$225$	12.7918	0.852784
$226$	10.8647	0.722710
$227$	4.56931	0.303276	0.151638	−	0.988436i	$-0.451545\pi$
$227$	4.56931	0.303276	0.151638	+	0.988436i	$0.451545\pi$
$228$	2.25766	0.149517
$229$	1.22928	0.0812329	0.0406164	−	0.999175i	$-0.487068\pi$
$229$	1.22928	0.0812329	0.0406164	+	0.999175i	$0.487068\pi$
$230$	−18.5039	−1.22011
$231$	11.1049	0.730647
$232$	5.23352	0.343597
$233$	−26.9387	−1.76481	−0.882407	−	0.470487i	$-0.844078\pi$
$233$	−26.9387	−1.76481	−0.882407	+	0.470487i	$0.844078\pi$
$234$	−48.1513	−3.14775
$235$	−7.96477	−0.519564
$236$	−1.34433	−0.0875082
$237$	34.5555	2.24462
$238$	−5.17148	−0.335217
$239$	9.76651	0.631743	0.315872	−	0.948802i	$-0.397703\pi$
$239$	9.76651	0.631743	0.315872	+	0.948802i	$0.397703\pi$
$240$	28.5670	1.84399
$241$	23.8483	1.53621	0.768103	−	0.640326i	$-0.221201\pi$
$241$	23.8483	1.53621	0.768103	+	0.640326i	$0.221201\pi$
$242$	−1.35222	−0.0869242
$243$	−8.96855	−0.575333
$244$	0.760812	0.0487060
$245$	−20.6827	−1.32137
$246$	6.86627	0.437777
$247$	−29.7252	−1.89137
$248$	15.2035	0.965424
$249$	−16.9033	−1.07120
$250$	−9.69931	−0.613438
$251$	3.33534	0.210525	0.105262	−	0.994444i	$-0.466432\pi$
$251$	3.33534	0.210525	0.105262	+	0.994444i	$0.466432\pi$
$252$	3.56214	0.224394
$253$	5.04566	0.317218
$254$	28.3665	1.77987
$255$	7.87489	0.493145
$256$	−4.08464	−0.255290
$257$	−26.3396	−1.64302	−0.821510	−	0.570194i	$-0.806868\pi$
$257$	−26.3396	−1.64302	−0.821510	+	0.570194i	$0.806868\pi$
$258$	−3.92642	−0.244448
$259$	10.7986	0.670995
$260$	3.04923	0.189105
$261$	9.68038	0.599201
$262$	−16.1159	−0.995644
$263$	−3.19647	−0.197103	−0.0985514	−	0.995132i	$-0.531421\pi$
$263$	−3.19647	−0.197103	−0.0985514	+	0.995132i	$0.531421\pi$
$264$	−8.52618	−0.524750
$265$	20.1330	1.23676
$266$	−23.4469	−1.43762
$267$	46.7559	2.86142
$268$	1.20561	0.0736440
$269$	8.15122	0.496989	0.248494	−	0.968633i	$-0.420064\pi$
$269$	8.15122	0.496989	0.248494	+	0.968633i	$0.420064\pi$
$270$	25.8902	1.57563
$271$	10.5868	0.643102	0.321551	−	0.946892i	$-0.395796\pi$
$271$	10.5868	0.643102	0.321551	+	0.946892i	$0.395796\pi$
$272$	3.62761	0.219956
$273$	−72.8061	−4.40643
$274$	14.9586	0.903680
$275$	−2.35519	−0.142023
$276$	2.51250	0.151235
$277$	15.0750	0.905772	0.452886	−	0.891569i	$-0.350395\pi$
$277$	15.0750	0.905772	0.452886	+	0.891569i	$0.350395\pi$
$278$	10.2826	0.616712
$279$	28.1218	1.68361
$280$	30.4558	1.82008
$281$	−15.5869	−0.929835	−0.464917	−	0.885354i	$-0.653916\pi$
$281$	−15.5869	−0.929835	−0.464917	+	0.885354i	$0.653916\pi$
$282$	−11.5312	−0.686670
$283$	13.8275	0.821962	0.410981	−	0.911644i	$-0.365186\pi$
$283$	13.8275	0.821962	0.410981	+	0.911644i	$0.365186\pi$
$284$	−1.57596	−0.0935160
$285$	35.7039	2.11492
$286$	8.86548	0.524227
$287$	6.68791	0.394775
$288$	−5.25394	−0.309591
$289$	1.00000	0.0588235
$290$	6.53631	0.383825
$291$	46.0365	2.69871
$292$	1.95601	0.114467
$293$	9.79451	0.572201	0.286101	−	0.958200i	$-0.407641\pi$
$293$	9.79451	0.572201	0.286101	+	0.958200i	$0.407641\pi$
$294$	−29.9437	−1.74635
$295$	−21.2599	−1.23780
$296$	−8.29105	−0.481908
$297$	−7.05975	−0.409648
$298$	−7.73471	−0.448059
$299$	−33.0805	−1.91309
$300$	−1.17277	−0.0677099
$301$	−3.82442	−0.220436
$302$	−4.27042	−0.245735
$303$	21.2306	1.21967
$304$	16.4472	0.943311
$305$	12.0319	0.688945
$306$	7.34436	0.419849
$307$	23.2372	1.32622	0.663109	−	0.748523i	$-0.269237\pi$
$307$	23.2372	1.32622	0.663109	+	0.748523i	$0.269237\pi$
$308$	−0.655852	−0.0373706
$309$	−48.2841	−2.74679
$310$	18.9882	1.07846
$311$	15.4005	0.873283	0.436642	−	0.899636i	$-0.356168\pi$
$311$	15.4005	0.873283	0.436642	+	0.899636i	$0.356168\pi$
$312$	55.8995	3.16469
$313$	0.459283	0.0259602	0.0129801	−	0.999916i	$-0.495868\pi$
$313$	0.459283	0.0259602	0.0129801	+	0.999916i	$0.495868\pi$
$314$	13.9292	0.786070
$315$	56.3337	3.17404
$316$	−2.04084	−0.114806
$317$	23.3642	1.31226	0.656131	−	0.754647i	$-0.272192\pi$
$317$	23.3642	1.31226	0.656131	+	0.754647i	$0.272192\pi$
$318$	29.1479	1.63453
$319$	−1.78233	−0.0997911
$320$	−23.2240	−1.29826
$321$	35.9779	2.00809
$322$	−26.0935	−1.45414
$323$	4.53389	0.252272
$324$	−0.721162	−0.0400646
$325$	15.4411	0.856519
$326$	14.0206	0.776530
$327$	10.6060	0.586514
$328$	−5.13489	−0.283527
$329$	−11.2316	−0.619219
$330$	−10.6486	−0.586187
$331$	−2.33660	−0.128431	−0.0642155	−	0.997936i	$-0.520454\pi$
$331$	−2.33660	−0.128431	−0.0642155	+	0.997936i	$0.520454\pi$
$332$	0.998305	0.0547891
$333$	−15.3359	−0.840400
$334$	−20.2450	−1.10776
$335$	19.0661	1.04169
$336$	40.2842	2.19768
$337$	13.5136	0.736132	0.368066	−	0.929800i	$-0.380020\pi$
$337$	13.5136	0.736132	0.368066	+	0.929800i	$0.380020\pi$
$338$	−40.5452	−2.20537
$339$	−23.3301	−1.26712
$340$	−0.465090	−0.0252230
$341$	−5.17771	−0.280389
$342$	33.2985	1.80058
$343$	−2.39495	−0.129315
$344$	2.93634	0.158317
$345$	39.7340	2.13921
$346$	3.14602	0.169131
$347$	−1.24924	−0.0670630	−0.0335315	−	0.999438i	$-0.510675\pi$
$347$	−1.24924	−0.0670630	−0.0335315	+	0.999438i	$0.510675\pi$
$348$	−0.887513	−0.0475757
$349$	29.8629	1.59853	0.799263	−	0.600982i	$-0.205224\pi$
$349$	29.8629	1.59853	0.799263	+	0.600982i	$0.205224\pi$
$350$	12.1798	0.651037
$351$	46.2853	2.47053
$352$	0.967341	0.0515595
$353$	26.3886	1.40452	0.702262	−	0.711918i	$-0.252173\pi$
$353$	26.3886	1.40452	0.702262	+	0.711918i	$0.252173\pi$
$354$	−30.7795	−1.63591
$355$	−24.9231	−1.32278
$356$	−2.76140	−0.146354
$357$	11.1049	0.587733
$358$	14.1553	0.748130
$359$	32.1089	1.69464	0.847322	−	0.531079i	$-0.178213\pi$
$359$	32.1089	1.69464	0.847322	+	0.531079i	$0.178213\pi$
$360$	−43.2522	−2.27959
$361$	1.55616	0.0819032
$362$	−0.0554080	−0.00291218
$363$	2.90367	0.152403
$364$	4.29991	0.225377
$365$	30.9334	1.61913
$366$	17.4194	0.910528
$367$	−25.2704	−1.31910	−0.659551	−	0.751660i	$-0.729253\pi$
$367$	−25.2704	−1.31910	−0.659551	+	0.751660i	$0.729253\pi$
$368$	18.3037	0.954146
$369$	−9.49795	−0.494444
$370$	−10.3550	−0.538329
$371$	28.3907	1.47397
$372$	−2.57825	−0.133676
$373$	7.58114	0.392536	0.196268	−	0.980550i	$-0.437118\pi$
$373$	7.58114	0.392536	0.196268	+	0.980550i	$0.437118\pi$
$374$	−1.35222	−0.0699218
$375$	20.8276	1.07553
$376$	8.62349	0.444722
$377$	11.6853	0.601825
$378$	36.5094	1.87784
$379$	−6.41419	−0.329475	−0.164737	−	0.986337i	$-0.552678\pi$
$379$	−6.41419	−0.329475	−0.164737	+	0.986337i	$0.552678\pi$
$380$	−2.10867	−0.108172
$381$	−60.9123	−3.12063
$382$	15.9805	0.817633
$383$	2.02837	0.103645	0.0518225	−	0.998656i	$-0.483497\pi$
$383$	2.02837	0.103645	0.0518225	+	0.998656i	$0.483497\pi$
$384$	−28.0053	−1.42914
$385$	−10.3720	−0.528607
$386$	8.40115	0.427607
$387$	5.43132	0.276089
$388$	−2.71891	−0.138032
$389$	−3.17019	−0.160735	−0.0803675	−	0.996765i	$-0.525609\pi$
$389$	−3.17019	−0.160735	−0.0803675	+	0.996765i	$0.525609\pi$
$390$	69.8147	3.53521
$391$	5.04566	0.255170
$392$	22.3932	1.13103
$393$	34.6062	1.74565
$394$	−21.3060	−1.07338
$395$	−32.2750	−1.62393
$396$	0.931419	0.0468056
$397$	−23.7766	−1.19331	−0.596656	−	0.802497i	$-0.703504\pi$
$397$	−23.7766	−1.19331	−0.596656	+	0.802497i	$0.703504\pi$
$398$	−21.1652	−1.06092
$399$	50.3483	2.52057
$400$	−8.54369	−0.427185
$401$	7.66774	0.382909	0.191454	−	0.981502i	$-0.438680\pi$
$401$	7.66774	0.382909	0.191454	+	0.981502i	$0.438680\pi$
$402$	27.6033	1.37673
$403$	33.9462	1.69098
$404$	−1.25388	−0.0623826
$405$	−11.4049	−0.566712
$406$	9.21726	0.457445
$407$	2.82360	0.139961
$408$	−8.52618	−0.422109
$409$	−5.68880	−0.281293	−0.140646	−	0.990060i	$-0.544918\pi$
$409$	−5.68880	−0.281293	−0.140646	+	0.990060i	$0.544918\pi$
$410$	−6.41313	−0.316722
$411$	−32.1210	−1.58441
$412$	2.85165	0.140491
$413$	−29.9799	−1.47522
$414$	37.0571	1.82126
$415$	15.7877	0.774990
$416$	−6.34211	−0.310947
$417$	−22.0802	−1.08127
$418$	−6.13084	−0.299869
$419$	9.57191	0.467619	0.233809	−	0.972282i	$-0.424881\pi$
$419$	9.57191	0.467619	0.233809	+	0.972282i	$0.424881\pi$
$420$	−5.16476	−0.252015
$421$	−10.0032	−0.487524	−0.243762	−	0.969835i	$-0.578382\pi$
$421$	−10.0032	−0.487524	−0.243762	+	0.969835i	$0.578382\pi$
$422$	−31.4256	−1.52977
$423$	15.9508	0.775553
$424$	−21.7980	−1.05861
$425$	−2.35519	−0.114243
$426$	−36.0829	−1.74822
$427$	16.9669	0.821088
$428$	−2.12485	−0.102708
$429$	−19.0371	−0.919122
$430$	3.66729	0.176852
$431$	−9.25481	−0.445789	−0.222894	−	0.974843i	$-0.571550\pi$
$431$	−9.25481	−0.445789	−0.222894	+	0.974843i	$0.571550\pi$
$432$	−25.6100	−1.23216
$433$	31.3603	1.50708	0.753539	−	0.657403i	$-0.228345\pi$
$433$	31.3603	1.50708	0.753539	+	0.657403i	$0.228345\pi$
$434$	26.7764	1.28531
$435$	−14.0356	−0.672957
$436$	−0.626389	−0.0299986
$437$	22.8765	1.09433
$438$	44.7845	2.13988
$439$	33.2415	1.58653	0.793265	−	0.608877i	$-0.208380\pi$
$439$	33.2415	1.58653	0.793265	+	0.608877i	$0.208380\pi$
$440$	7.96349	0.379644
$441$	41.4205	1.97240
$442$	8.86548	0.421688
$443$	16.3964	0.779018	0.389509	−	0.921023i	$-0.372645\pi$
$443$	16.3964	0.779018	0.389509	+	0.921023i	$0.372645\pi$
$444$	1.40602	0.0667266
$445$	−43.6703	−2.07017
$446$	−32.6974	−1.54827
$447$	16.6090	0.785578
$448$	−32.7496	−1.54727
$449$	30.3808	1.43376	0.716880	−	0.697197i	$-0.245570\pi$
$449$	30.3808	1.43376	0.716880	+	0.697197i	$0.245570\pi$
$450$	−17.2973	−0.815404
$451$	1.74874	0.0823448
$452$	1.37787	0.0648097
$453$	9.17002	0.430845
$454$	−6.17873	−0.289982
$455$	68.0012	3.18795
$456$	−38.6567	−1.81027
$457$	3.65130	0.170801	0.0854003	−	0.996347i	$-0.472783\pi$
$457$	3.65130	0.170801	0.0854003	+	0.996347i	$0.472783\pi$
$458$	−1.66226	−0.0776722
$459$	−7.05975	−0.329521
$460$	−2.34668	−0.109415
$461$	10.9631	0.510602	0.255301	−	0.966862i	$-0.417825\pi$
$461$	10.9631	0.510602	0.255301	+	0.966862i	$0.417825\pi$
$462$	−15.0163	−0.698621
$463$	31.1279	1.44663	0.723317	−	0.690516i	$-0.242616\pi$
$463$	31.1279	1.44663	0.723317	+	0.690516i	$0.242616\pi$
$464$	−6.46558	−0.300157
$465$	−40.7739	−1.89084
$466$	36.4272	1.68746
$467$	36.0960	1.67033	0.835163	−	0.550003i	$-0.185373\pi$
$467$	36.0960	1.67033	0.835163	+	0.550003i	$0.185373\pi$
$468$	−6.10659	−0.282277
$469$	26.8863	1.24149
$470$	10.7702	0.496790
$471$	−29.9106	−1.37821
$472$	23.0182	1.05950
$473$	−1.00000	−0.0459800
$474$	−46.7268	−2.14623
$475$	−10.6782	−0.489947
$476$	−0.655852	−0.0300609
$477$	−40.3196	−1.84611
$478$	−13.2065	−0.604052
$479$	36.5287	1.66904	0.834519	−	0.550979i	$-0.185745\pi$
$479$	36.5287	1.66904	0.834519	+	0.550979i	$0.185745\pi$
$480$	7.61771	0.347699
$481$	−18.5122	−0.844082
$482$	−32.2483	−1.46887
$483$	56.0315	2.54952
$484$	−0.171490	−0.00779502
$485$	−42.9983	−1.95245
$486$	12.1275	0.550114
$487$	23.1007	1.04679	0.523397	−	0.852089i	$-0.324664\pi$
$487$	23.1007	1.04679	0.523397	+	0.852089i	$0.324664\pi$
$488$	−13.0270	−0.589704
$489$	−30.1069	−1.36148
$490$	27.9676	1.26345
$491$	−15.8353	−0.714639	−0.357319	−	0.933982i	$-0.616309\pi$
$491$	−15.8353	−0.714639	−0.357319	+	0.933982i	$0.616309\pi$
$492$	0.870788	0.0392581
$493$	−1.78233	−0.0802719
$494$	40.1951	1.80846
$495$	14.7300	0.662063
$496$	−18.7827	−0.843368
$497$	−35.1456	−1.57650
$498$	22.8570	1.02425
$499$	−3.86130	−0.172855	−0.0864277	−	0.996258i	$-0.527545\pi$
$499$	−3.86130	−0.172855	−0.0864277	+	0.996258i	$0.527545\pi$
$500$	−1.23008	−0.0550107
$501$	43.4727	1.94222
$502$	−4.51013	−0.201297
$503$	35.3284	1.57521	0.787607	−	0.616177i	$-0.211320\pi$
$503$	35.3284	1.57521	0.787607	+	0.616177i	$0.211320\pi$
$504$	−60.9927	−2.71683
$505$	−19.8295	−0.882400
$506$	−6.82286	−0.303313
$507$	87.0640	3.86665
$508$	3.59747	0.159612
$509$	−37.6483	−1.66873	−0.834365	−	0.551212i	$-0.814166\pi$
$509$	−37.6483	−1.66873	−0.834365	+	0.551212i	$0.814166\pi$
$510$	−10.6486	−0.471529
$511$	43.6211	1.92969
$512$	24.8129	1.09659
$513$	−32.0082	−1.41319
$514$	35.6171	1.57100
$515$	45.0976	1.98724
$516$	−0.497952	−0.0219211
$517$	−2.93681	−0.129161
$518$	−14.6022	−0.641583
$519$	−6.75555	−0.296536
$520$	−52.2104	−2.28958
$521$	27.0494	1.18506	0.592528	−	0.805550i	$-0.298130\pi$
$521$	27.0494	1.18506	0.592528	+	0.805550i	$0.298130\pi$
$522$	−13.0900	−0.572936
$523$	13.2877	0.581030	0.290515	−	0.956870i	$-0.406173\pi$
$523$	13.2877	0.581030	0.290515	+	0.956870i	$0.406173\pi$
$524$	−2.04384	−0.0892854
$525$	−26.1540	−1.14146
$526$	4.32235	0.188463
$527$	−5.17771	−0.225544
$528$	10.5334	0.458407
$529$	2.45870	0.106900
$530$	−27.2243	−1.18255
$531$	42.5765	1.84766
$532$	−2.97356	−0.128920
$533$	−11.4651	−0.496609
$534$	−63.2245	−2.73599
$535$	−33.6035	−1.45281
$536$	−20.6429	−0.891640
$537$	−30.3961	−1.31169
$538$	−11.0223	−0.475204
$539$	−7.62623	−0.328485
$540$	3.28342	0.141296
$541$	34.3858	1.47836	0.739180	−	0.673508i	$-0.235213\pi$
$541$	34.3858	1.47836	0.739180	+	0.673508i	$0.235213\pi$
$542$	−14.3157	−0.614913
$543$	0.118979	0.00510589
$544$	0.967341	0.0414744
$545$	−9.90606	−0.424329
$546$	98.4501	4.21328
$547$	−11.3789	−0.486529	−0.243264	−	0.969960i	$-0.578218\pi$
$547$	−11.3789	−0.486529	−0.243264	+	0.969960i	$0.578218\pi$
$548$	1.89706	0.0810384
$549$	−24.0959	−1.02839
$550$	3.18474	0.135798
$551$	−8.08087	−0.344257
$552$	−43.0202	−1.83106
$553$	−45.5130	−1.93541
$554$	−20.3848	−0.866069
$555$	22.2355	0.943846
$556$	1.30406	0.0553043
$557$	15.0746	0.638729	0.319365	−	0.947632i	$-0.396531\pi$
$557$	15.0746	0.638729	0.319365	+	0.947632i	$0.396531\pi$
$558$	−38.0269	−1.60981
$559$	6.55623	0.277299
$560$	−37.6256	−1.58997
$561$	2.90367	0.122593
$562$	21.0769	0.889077
$563$	0.978991	0.0412595	0.0206298	−	0.999787i	$-0.493433\pi$
$563$	0.978991	0.0412595	0.0206298	+	0.999787i	$0.493433\pi$
$564$	−1.46239	−0.0615778
$565$	21.7905	0.916731
$566$	−18.6979	−0.785933
$567$	−16.0827	−0.675411
$568$	26.9843	1.13224
$569$	20.9669	0.878977	0.439489	−	0.898248i	$-0.355160\pi$
$569$	20.9669	0.878977	0.439489	+	0.898248i	$0.355160\pi$
$570$	−48.2797	−2.02221
$571$	6.84194	0.286326	0.143163	−	0.989699i	$-0.454273\pi$
$571$	6.84194	0.286326	0.143163	+	0.989699i	$0.454273\pi$
$572$	1.12433	0.0470106
$573$	−34.3154	−1.43355
$574$	−9.04356	−0.377471
$575$	−11.8835	−0.495575
$576$	46.5099	1.93791
$577$	22.2671	0.926990	0.463495	−	0.886099i	$-0.346595\pi$
$577$	22.2671	0.926990	0.463495	+	0.886099i	$0.346595\pi$
$578$	−1.35222	−0.0562451
$579$	−18.0401	−0.749719
$580$	0.828941	0.0344199
$581$	22.2633	0.923637
$582$	−62.2517	−2.58042
$583$	7.42353	0.307451
$584$	−33.4917	−1.38590
$585$	−96.5730	−3.99280
$586$	−13.2444	−0.547120
$587$	−32.1014	−1.32497	−0.662483	−	0.749077i	$-0.730497\pi$
$587$	−32.1014	−1.32497	−0.662483	+	0.749077i	$0.730497\pi$
$588$	−3.79749	−0.156606
$589$	−23.4752	−0.967277
$590$	28.7482	1.18354
$591$	45.7510	1.88194
$592$	10.2429	0.420981
$593$	3.78570	0.155460	0.0777300	−	0.996974i	$-0.475233\pi$
$593$	3.78570	0.155460	0.0777300	+	0.996974i	$0.475233\pi$
$594$	9.54637	0.391692
$595$	−10.3720	−0.425211
$596$	−0.980923	−0.0401802
$597$	45.4487	1.86009
$598$	44.7322	1.82924
$599$	13.6792	0.558918	0.279459	−	0.960158i	$-0.409845\pi$
$599$	13.6792	0.558918	0.279459	+	0.960158i	$0.409845\pi$
$600$	20.0807	0.819792
$601$	−39.8451	−1.62531	−0.812657	−	0.582742i	$-0.801980\pi$
$601$	−39.8451	−1.62531	−0.812657	+	0.582742i	$0.801980\pi$
$602$	5.17148	0.210774
$603$	−38.1830	−1.55493
$604$	−0.541580	−0.0220366
$605$	−2.71204	−0.110260
$606$	−28.7085	−1.16620
$607$	37.1126	1.50636	0.753178	−	0.657817i	$-0.228520\pi$
$607$	37.1126	1.50636	0.753178	+	0.657817i	$0.228520\pi$
$608$	4.38582	0.177868
$609$	−19.7925	−0.802033
$610$	−16.2698	−0.658746
$611$	19.2544	0.778950
$612$	0.931419	0.0376504
$613$	−0.0657236	−0.00265455	−0.00132728	−	0.999999i	$-0.500422\pi$
$613$	−0.0657236	−0.00265455	−0.00132728	+	0.999999i	$0.500422\pi$
$614$	−31.4219	−1.26808
$615$	13.7711	0.555305
$616$	11.2298	0.452462
$617$	−29.9394	−1.20531	−0.602657	−	0.798000i	$-0.705891\pi$
$617$	−29.9394	−1.20531	−0.602657	+	0.798000i	$0.705891\pi$
$618$	65.2909	2.62639
$619$	−44.6983	−1.79658	−0.898288	−	0.439407i	$-0.855188\pi$
$619$	−44.6983	−1.79658	−0.898288	+	0.439407i	$0.855188\pi$
$620$	2.40810	0.0967115
$621$	−35.6211	−1.42943
$622$	−20.8249	−0.835004
$623$	−61.5822	−2.46724
$624$	−69.0593	−2.76458
$625$	−31.2290	−1.24916
$626$	−0.621053	−0.0248223
$627$	13.1649	0.525757
$628$	1.76651	0.0704916
$629$	2.82360	0.112584
$630$	−76.1758	−3.03492
$631$	−12.6505	−0.503610	−0.251805	−	0.967778i	$-0.581024\pi$
$631$	−12.6505	−0.503610	−0.251805	+	0.967778i	$0.581024\pi$
$632$	34.9443	1.39001
$633$	67.4812	2.68214
$634$	−31.5936	−1.25474
$635$	56.8924	2.25771
$636$	3.69656	0.146578
$637$	49.9993	1.98104
$638$	2.41010	0.0954169
$639$	49.9126	1.97451
$640$	26.1571	1.03395
$641$	−23.7748	−0.939047	−0.469524	−	0.882920i	$-0.655574\pi$
$641$	−23.7748	−0.939047	−0.469524	+	0.882920i	$0.655574\pi$
$642$	−48.6502	−1.92007
$643$	−30.5374	−1.20428	−0.602138	−	0.798392i	$-0.705684\pi$
$643$	−30.5374	−1.20428	−0.602138	+	0.798392i	$0.705684\pi$
$644$	−3.30921	−0.130401
$645$	−7.87489	−0.310074
$646$	−6.13084	−0.241214
$647$	8.56003	0.336529	0.168265	−	0.985742i	$-0.446184\pi$
$647$	8.56003	0.336529	0.168265	+	0.985742i	$0.446184\pi$
$648$	12.3481	0.485079
$649$	−7.83907	−0.307711
$650$	−20.8799	−0.818975
$651$	−57.4978	−2.25352
$652$	1.77811	0.0696361
$653$	4.82113	0.188666	0.0943328	−	0.995541i	$-0.469928\pi$
$653$	4.82113	0.188666	0.0943328	+	0.995541i	$0.469928\pi$
$654$	−14.3417	−0.560805
$655$	−32.3223	−1.26294
$656$	6.34374	0.247681
$657$	−61.9493	−2.41687
$658$	15.1877	0.592077
$659$	28.9821	1.12898	0.564490	−	0.825440i	$-0.309073\pi$
$659$	28.9821	1.12898	0.564490	+	0.825440i	$0.309073\pi$
$660$	−1.35047	−0.0525669
$661$	−38.1439	−1.48362	−0.741812	−	0.670608i	$-0.766033\pi$
$661$	−38.1439	−1.48362	−0.741812	+	0.670608i	$0.766033\pi$
$662$	3.15960	0.122801
$663$	−19.0371	−0.739341
$664$	−17.0935	−0.663355
$665$	−47.0256	−1.82357
$666$	20.7375	0.803563
$667$	−8.99301	−0.348211
$668$	−2.56749	−0.0993392
$669$	70.2121	2.71456
$670$	−25.7816	−0.996032
$671$	4.43647	0.171268
$672$	10.7422	0.414390
$673$	−39.5529	−1.52465	−0.762326	−	0.647194i	$-0.775943\pi$
$673$	−39.5529	−1.52465	−0.762326	+	0.647194i	$0.775943\pi$
$674$	−18.2734	−0.703865
$675$	16.6270	0.639975
$676$	−5.14198	−0.197769
$677$	23.1792	0.890849	0.445425	−	0.895319i	$-0.353053\pi$
$677$	23.1792	0.890849	0.445425	+	0.895319i	$0.353053\pi$
$678$	31.5476	1.21158
$679$	−60.6347	−2.32694
$680$	7.96349	0.305386
$681$	13.2678	0.508422
$682$	7.00142	0.268098
$683$	45.3107	1.73377	0.866883	−	0.498511i	$-0.166120\pi$
$683$	45.3107	1.73377	0.866883	+	0.498511i	$0.166120\pi$
$684$	4.22295	0.161469
$685$	30.0012	1.14629
$686$	3.23851	0.123647
$687$	3.56942	0.136182
$688$	−3.62761	−0.138301
$689$	−48.6704	−1.85419
$690$	−53.7293	−2.04544
$691$	−20.6230	−0.784535	−0.392267	−	0.919851i	$-0.628309\pi$
$691$	−20.6230	−0.784535	−0.392267	+	0.919851i	$0.628309\pi$
$692$	0.398981	0.0151670
$693$	20.7717	0.789050
$694$	1.68926	0.0641234
$695$	20.6230	0.782277
$696$	15.1964	0.576019
$697$	1.74874	0.0662382
$698$	−40.3813	−1.52846
$699$	−78.2212	−2.95860
$700$	1.54465	0.0583824
$701$	31.7742	1.20010	0.600048	−	0.799964i	$-0.295148\pi$
$701$	31.7742	1.20010	0.600048	+	0.799964i	$0.295148\pi$
$702$	−62.5881	−2.36224
$703$	12.8019	0.482832
$704$	−8.56328	−0.322741
$705$	−23.1271	−0.871016
$706$	−35.6833	−1.34296
$707$	−27.9628	−1.05165
$708$	−3.90348	−0.146702
$709$	−44.7416	−1.68030	−0.840152	−	0.542351i	$-0.817534\pi$
$709$	−44.7416	−1.68030	−0.840152	+	0.542351i	$0.817534\pi$
$710$	33.7016	1.26480
$711$	64.6361	2.42404
$712$	47.2820	1.77197
$713$	−26.1250	−0.978387
$714$	−15.0163	−0.561970
$715$	17.7808	0.664963
$716$	1.79519	0.0670893
$717$	28.3588	1.05908
$718$	−43.4185	−1.62036
$719$	36.9506	1.37803	0.689013	−	0.724749i	$-0.258044\pi$
$719$	36.9506	1.37803	0.689013	+	0.724749i	$0.258044\pi$
$720$	53.4346	1.99139
$721$	63.5949	2.36840
$722$	−2.10428	−0.0783131
$723$	69.2478	2.57535
$724$	−0.00702690	−0.000261153 0
$725$	4.19771	0.155899
$726$	−3.92642	−0.145723
$727$	−20.3689	−0.755440	−0.377720	−	0.925920i	$-0.623292\pi$
$727$	−20.3689	−0.755440	−0.377720	+	0.925920i	$0.623292\pi$
$728$	−73.6252	−2.72873
$729$	−38.6575	−1.43176
$730$	−41.8289	−1.54816
$731$	−1.00000	−0.0369863
$732$	2.20915	0.0816525
$733$	−17.1672	−0.634085	−0.317042	−	0.948411i	$-0.602690\pi$
$733$	−17.1672	−0.634085	−0.317042	+	0.948411i	$0.602690\pi$
$734$	34.1712	1.26128
$735$	−60.0557	−2.21519
$736$	4.88088	0.179911
$737$	7.03016	0.258959
$738$	12.8434	0.472770
$739$	−35.9594	−1.32279	−0.661394	−	0.750039i	$-0.730035\pi$
$739$	−35.9594	−1.32279	−0.661394	+	0.750039i	$0.730035\pi$
$740$	−1.31323	−0.0482752
$741$	−86.3123	−3.17076
$742$	−38.3907	−1.40937
$743$	−19.3251	−0.708968	−0.354484	−	0.935062i	$-0.615343\pi$
$743$	−19.3251	−0.708968	−0.354484	+	0.935062i	$0.615343\pi$
$744$	44.1460	1.61847
$745$	−15.5129	−0.568347
$746$	−10.2514	−0.375330
$747$	−31.6176	−1.15683
$748$	−0.171490	−0.00627031
$749$	−47.3864	−1.73146
$750$	−28.1636	−1.02839
$751$	−46.7552	−1.70612	−0.853060	−	0.521813i	$-0.825256\pi$
$751$	−46.7552	−1.70612	−0.853060	+	0.521813i	$0.825256\pi$
$752$	−10.6536	−0.388497
$753$	9.68474	0.352932
$754$	−15.8012	−0.575445
$755$	−8.56484	−0.311706
$756$	4.63016	0.168397
$757$	−45.1596	−1.64135	−0.820676	−	0.571393i	$-0.806403\pi$
$757$	−45.1596	−1.64135	−0.820676	+	0.571393i	$0.806403\pi$
$758$	8.67342	0.315033
$759$	14.6510	0.531796
$760$	36.1056	1.30969
$761$	−6.60063	−0.239273	−0.119636	−	0.992818i	$-0.538173\pi$
$761$	−6.60063	−0.239273	−0.119636	+	0.992818i	$0.538173\pi$
$762$	82.3671	2.98384
$763$	−13.9692	−0.505718
$764$	2.02666	0.0733221
$765$	14.7300	0.532563
$766$	−2.74281	−0.0991019
$767$	51.3947	1.85576
$768$	−11.8605	−0.427978
$769$	39.1599	1.41214	0.706071	−	0.708141i	$-0.250466\pi$
$769$	39.1599	1.41214	0.706071	+	0.708141i	$0.250466\pi$
$770$	14.0253	0.505436
$771$	−76.4817	−2.75442
$772$	1.06544	0.0383461
$773$	−32.7745	−1.17882	−0.589409	−	0.807835i	$-0.700639\pi$
$773$	−32.7745	−1.17882	−0.589409	+	0.807835i	$0.700639\pi$
$774$	−7.34436	−0.263988
$775$	12.1945	0.438038
$776$	46.5545	1.67121
$777$	31.3557	1.12488
$778$	4.28681	0.153689
$779$	7.92858	0.284071
$780$	8.85397	0.317023
$781$	−9.18978	−0.328836
$782$	−6.82286	−0.243985
$783$	12.5828	0.449672
$784$	−27.6650	−0.988035
$785$	27.9366	0.997101
$786$	−46.7953	−1.66913
$787$	−16.9436	−0.603973	−0.301986	−	0.953312i	$-0.597650\pi$
$787$	−16.9436	−0.603973	−0.301986	+	0.953312i	$0.597650\pi$
$788$	−2.70205	−0.0962564
$789$	−9.28151	−0.330430
$790$	43.6431	1.55275
$791$	30.7281	1.09257
$792$	−15.9482	−0.566695
$793$	−29.0865	−1.03289
$794$	32.1512	1.14100
$795$	58.4595	2.07335
$796$	−2.68419	−0.0951387
$797$	50.6406	1.79378	0.896891	−	0.442252i	$-0.145820\pi$
$797$	50.6406	1.79378	0.896891	+	0.442252i	$0.145820\pi$
$798$	−68.0822	−2.41008
$799$	−2.93681	−0.103897
$800$	−2.27827	−0.0805489
$801$	87.4569	3.09014
$802$	−10.3685	−0.366125
$803$	11.4059	0.402507
$804$	3.50068	0.123460
$805$	−52.3336	−1.84452
$806$	−45.9029	−1.61686
$807$	23.6685	0.833170
$808$	21.4695	0.755293
$809$	17.9321	0.630457	0.315229	−	0.949016i	$-0.397919\pi$
$809$	17.9321	0.630457	0.315229	+	0.949016i	$0.397919\pi$
$810$	15.4219	0.541871
$811$	33.7816	1.18623	0.593117	−	0.805117i	$-0.297897\pi$
$811$	33.7816	1.18623	0.593117	+	0.805117i	$0.297897\pi$
$812$	1.16894	0.0410218
$813$	30.7406	1.07812
$814$	−3.81814	−0.133826
$815$	28.1200	0.985001
$816$	10.5334	0.368743
$817$	−4.53389	−0.158621
$818$	7.69253	0.268963
$819$	−136.184	−4.75865
$820$	−0.813320	−0.0284024
$821$	−3.46824	−0.121042	−0.0605211	−	0.998167i	$-0.519276\pi$
$821$	−3.46824	−0.121042	−0.0605211	+	0.998167i	$0.519276\pi$
$822$	43.4348	1.51496
$823$	−30.3712	−1.05867	−0.529336	−	0.848412i	$-0.677559\pi$
$823$	−30.3712	−1.05867	−0.529336	+	0.848412i	$0.677559\pi$
$824$	−48.8273	−1.70098
$825$	−6.83869	−0.238093
$826$	40.5396	1.41055
$827$	−34.9041	−1.21374	−0.606868	−	0.794803i	$-0.707574\pi$
$827$	−34.9041	−1.21374	−0.606868	+	0.794803i	$0.707574\pi$
$828$	4.69962	0.163323
$829$	12.3081	0.427479	0.213739	−	0.976891i	$-0.431436\pi$
$829$	12.3081	0.427479	0.213739	+	0.976891i	$0.431436\pi$
$830$	−21.3486	−0.741019
$831$	43.7730	1.51847
$832$	56.1428	1.94640
$833$	−7.62623	−0.264233
$834$	29.8574	1.03388
$835$	−40.6037	−1.40515
$836$	−0.777519	−0.0268910
$837$	36.5533	1.26347
$838$	−12.9434	−0.447121
$839$	15.3505	0.529958	0.264979	−	0.964254i	$-0.414635\pi$
$839$	15.3505	0.529958	0.264979	+	0.964254i	$0.414635\pi$
$840$	88.4336	3.05125
$841$	−25.8233	−0.890459
$842$	13.5265	0.466155
$843$	−45.2592	−1.55881
$844$	−3.98543	−0.137184
$845$	−81.3182	−2.79743
$846$	−21.5690	−0.741558
$847$	−3.82442	−0.131409
$848$	26.9297	0.924769
$849$	40.1507	1.37797
$850$	3.18474	0.109236
$851$	14.2469	0.488378
$852$	−4.57607	−0.156774
$853$	3.13432	0.107317	0.0536585	−	0.998559i	$-0.482912\pi$
$853$	3.13432	0.107317	0.0536585	+	0.998559i	$0.482912\pi$
$854$	−22.9431	−0.785097
$855$	66.7841	2.28397
$856$	36.3827	1.24353
$857$	−36.4168	−1.24397	−0.621987	−	0.783027i	$-0.713674\pi$
$857$	−36.4168	−1.24397	−0.621987	+	0.783027i	$0.713674\pi$
$858$	25.7425	0.878833
$859$	−48.5351	−1.65599	−0.827997	−	0.560732i	$-0.810520\pi$
$859$	−48.5351	−1.65599	−0.827997	+	0.560732i	$0.810520\pi$
$860$	0.465090	0.0158594
$861$	19.4195	0.661815
$862$	12.5146	0.426248
$863$	25.9828	0.884463	0.442232	−	0.896901i	$-0.354187\pi$
$863$	25.9828	0.884463	0.442232	+	0.896901i	$0.354187\pi$
$864$	−6.82919	−0.232334
$865$	6.30971	0.214537
$866$	−42.4061	−1.44102
$867$	2.90367	0.0986139
$868$	3.39581	0.115261
$869$	−11.9006	−0.403701
$870$	18.9793	0.643459
$871$	−46.0913	−1.56174
$872$	10.7253	0.363206
$873$	86.1113	2.91443
$874$	−30.9341	−1.04636
$875$	−27.4320	−0.927372
$876$	5.67961	0.191896
$877$	−9.31643	−0.314594	−0.157297	−	0.987551i	$-0.550278\pi$
$877$	−9.31643	−0.314594	−0.157297	+	0.987551i	$0.550278\pi$
$878$	−44.9499	−1.51699
$879$	28.4400	0.959259
$880$	−9.83824	−0.331647
$881$	4.88254	0.164497	0.0822485	−	0.996612i	$-0.473790\pi$
$881$	4.88254	0.164497	0.0822485	+	0.996612i	$0.473790\pi$
$882$	−56.0097	−1.88595
$883$	−25.2231	−0.848824	−0.424412	−	0.905469i	$-0.639519\pi$
$883$	−25.2231	−0.848824	−0.424412	+	0.905469i	$0.639519\pi$
$884$	1.12433	0.0378153
$885$	−61.7318	−2.07509
$886$	−22.1716	−0.744871
$887$	58.7875	1.97389	0.986946	−	0.161054i	$-0.0514895\pi$
$887$	58.7875	1.97389	0.986946	+	0.161054i	$0.0514895\pi$
$888$	−24.0745	−0.807887
$889$	80.2275	2.69075
$890$	59.0520	1.97943
$891$	−4.20526	−0.140882
$892$	−4.14671	−0.138842
$893$	−13.3152	−0.445576
$894$	−22.4591	−0.751143
$895$	28.3901	0.948975
$896$	36.8858	1.23227
$897$	−96.0549	−3.20718
$898$	−41.0817	−1.37091
$899$	9.22836	0.307783
$900$	−2.19366	−0.0731221
$901$	7.42353	0.247314
$902$	−2.36468	−0.0787354
$903$	−11.1049	−0.369547
$904$	−23.5926	−0.784679
$905$	−0.111127	−0.00369399
$906$	−12.3999	−0.411960
$907$	−9.26028	−0.307483	−0.153741	−	0.988111i	$-0.549132\pi$
$907$	−9.26028	−0.307483	−0.153741	+	0.988111i	$0.549132\pi$
$908$	−0.783592	−0.0260044
$909$	39.7118	1.31716
$910$	−91.9529	−3.04821
$911$	9.85948	0.326659	0.163329	−	0.986572i	$-0.447777\pi$
$911$	9.85948	0.326659	0.163329	+	0.986572i	$0.447777\pi$
$912$	47.7573	1.58140
$913$	5.82134	0.192658
$914$	−4.93737	−0.163314
$915$	34.9367	1.15497
$916$	−0.210809	−0.00696533
$917$	−45.5798	−1.50518
$918$	9.54637	0.315077
$919$	−11.4635	−0.378147	−0.189073	−	0.981963i	$-0.560548\pi$
$919$	−11.4635	−0.378147	−0.189073	+	0.981963i	$0.560548\pi$
$920$	40.1811	1.32473
$921$	67.4732	2.22332
$922$	−14.8245	−0.488220
$923$	60.2503	1.98316
$924$	−1.90438	−0.0626495
$925$	−6.65010	−0.218654
$926$	−42.0918	−1.38322
$927$	−90.3154	−2.96635
$928$	−1.72412	−0.0565969
$929$	−9.94867	−0.326405	−0.163203	−	0.986593i	$-0.552182\pi$
$929$	−9.94867	−0.326405	−0.163203	+	0.986593i	$0.552182\pi$
$930$	55.1354	1.80796
$931$	−34.5765	−1.13320
$932$	4.61973	0.151324
$933$	44.7181	1.46400
$934$	−48.8099	−1.59711
$935$	−2.71204	−0.0886933
$936$	104.560	3.41765
$937$	−12.6998	−0.414884	−0.207442	−	0.978247i	$-0.566514\pi$
$937$	−12.6998	−0.414884	−0.207442	+	0.978247i	$0.566514\pi$
$938$	−36.3563	−1.18708
$939$	1.33361	0.0435206
$940$	1.36588	0.0445501
$941$	−16.0382	−0.522829	−0.261415	−	0.965227i	$-0.584189\pi$
$941$	−16.0382	−0.522829	−0.261415	+	0.965227i	$0.584189\pi$
$942$	40.4458	1.31780
$943$	8.82354	0.287334
$944$	−28.4371	−0.925549
$945$	73.2238	2.38197
$946$	1.35222	0.0439646
$947$	8.65237	0.281164	0.140582	−	0.990069i	$-0.455103\pi$
$947$	8.65237	0.281164	0.140582	+	0.990069i	$0.455103\pi$
$948$	−5.92594	−0.192466
$949$	−74.7799	−2.42746
$950$	14.4393	0.468471
$951$	67.8419	2.19992
$952$	11.2298	0.363960
$953$	−23.0662	−0.747188	−0.373594	−	0.927592i	$-0.621875\pi$
$953$	−23.0662	−0.747188	−0.373594	+	0.927592i	$0.621875\pi$
$954$	54.5211	1.76519
$955$	32.0508	1.03714
$956$	−1.67486	−0.0541690
$957$	−5.17529	−0.167293
$958$	−49.3950	−1.59588
$959$	42.3065	1.36615
$960$	−67.4349	−2.17645
$961$	−4.19135	−0.135205
$962$	25.0326	0.807083
$963$	67.2966	2.16860
$964$	−4.08976	−0.131722
$965$	16.8495	0.542405
$966$	−75.7671	−2.43777
$967$	−8.01458	−0.257732	−0.128866	−	0.991662i	$-0.541134\pi$
$967$	−8.01458	−0.257732	−0.128866	+	0.991662i	$0.541134\pi$
$968$	2.93634	0.0943776
$969$	13.1649	0.422919
$970$	58.1434	1.86687
$971$	12.8506	0.412396	0.206198	−	0.978510i	$-0.433891\pi$
$971$	12.8506	0.412396	0.206198	+	0.978510i	$0.433891\pi$
$972$	1.53802	0.0493320
$973$	29.0819	0.932322
$974$	−31.2374	−1.00091
$975$	44.8360	1.43590
$976$	16.0938	0.515149
$977$	41.3415	1.32263	0.661316	−	0.750108i	$-0.269998\pi$
$977$	41.3415	1.32263	0.661316	+	0.750108i	$0.269998\pi$
$978$	40.7113	1.30180
$979$	−16.1023	−0.514633
$980$	3.54688	0.113301
$981$	19.8385	0.633396
$982$	21.4129	0.683314
$983$	4.55883	0.145404	0.0727021	−	0.997354i	$-0.476838\pi$
$983$	4.55883	0.145404	0.0727021	+	0.997354i	$0.476838\pi$
$984$	−14.9100	−0.475315
$985$	−42.7316	−1.36154
$986$	2.41010	0.0767533
$987$	−32.6130	−1.03808
$988$	5.09759	0.162176
$989$	−5.04566	−0.160443
$990$	−19.9182	−0.633043
$991$	43.3979	1.37858	0.689290	−	0.724486i	$-0.257923\pi$
$991$	43.3979	1.37858	0.689290	+	0.724486i	$0.257923\pi$
$992$	−5.00861	−0.159024
$993$	−6.78471	−0.215306
$994$	47.5248	1.50739
$995$	−42.4493	−1.34573
$996$	2.89875	0.0918504
$997$	20.2454	0.641178	0.320589	−	0.947218i	$-0.396119\pi$
$997$	20.2454	0.641178	0.320589	+	0.947218i	$0.396119\pi$
$998$	5.22134	0.165279
$999$	−19.9339	−0.630681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.17	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.17	✓	66	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)

\(f(q)\)	\(=\)	\(q-1.35222 q^{2} +2.90367 q^{3} -0.171490 q^{4} -2.71204 q^{5} -3.92642 q^{6} -3.82442 q^{7} +2.93634 q^{8} +5.43132 q^{9} +O(q^{10})\)	\(q-1.35222 q^{2} +2.90367 q^{3} -0.171490 q^{4} -2.71204 q^{5} -3.92642 q^{6} -3.82442 q^{7} +2.93634 q^{8} +5.43132 q^{9} +3.66729 q^{10} -1.00000 q^{11} -0.497952 q^{12} +6.55623 q^{13} +5.17148 q^{14} -7.87489 q^{15} -3.62761 q^{16} -1.00000 q^{17} -7.34436 q^{18} -4.53389 q^{19} +0.465090 q^{20} -11.1049 q^{21} +1.35222 q^{22} -5.04566 q^{23} +8.52618 q^{24} +2.35519 q^{25} -8.86548 q^{26} +7.05975 q^{27} +0.655852 q^{28} +1.78233 q^{29} +10.6486 q^{30} +5.17771 q^{31} -0.967341 q^{32} -2.90367 q^{33} +1.35222 q^{34} +10.3720 q^{35} -0.931419 q^{36} -2.82360 q^{37} +6.13084 q^{38} +19.0371 q^{39} -7.96349 q^{40} -1.74874 q^{41} +15.0163 q^{42} +1.00000 q^{43} +0.171490 q^{44} -14.7300 q^{45} +6.82286 q^{46} +2.93681 q^{47} -10.5334 q^{48} +7.62623 q^{49} -3.18474 q^{50} -2.90367 q^{51} -1.12433 q^{52} -7.42353 q^{53} -9.54637 q^{54} +2.71204 q^{55} -11.2298 q^{56} -13.1649 q^{57} -2.41010 q^{58} +7.83907 q^{59} +1.35047 q^{60} -4.43647 q^{61} -7.00142 q^{62} -20.7717 q^{63} +8.56328 q^{64} -17.7808 q^{65} +3.92642 q^{66} -7.03016 q^{67} +0.171490 q^{68} -14.6510 q^{69} -14.0253 q^{70} +9.18978 q^{71} +15.9482 q^{72} -11.4059 q^{73} +3.81814 q^{74} +6.83869 q^{75} +0.777519 q^{76} +3.82442 q^{77} -25.7425 q^{78} +11.9006 q^{79} +9.83824 q^{80} +4.20526 q^{81} +2.36468 q^{82} -5.82134 q^{83} +1.90438 q^{84} +2.71204 q^{85} -1.35222 q^{86} +5.17529 q^{87} -2.93634 q^{88} +16.1023 q^{89} +19.9182 q^{90} -25.0738 q^{91} +0.865282 q^{92} +15.0344 q^{93} -3.97123 q^{94} +12.2961 q^{95} -2.80884 q^{96} +15.8546 q^{97} -10.3124 q^{98} -5.43132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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