LMFDB - Embedded newform 8049.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65333 q^{2} -1.00000 q^{3} +5.04016 q^{4} +2.95577 q^{5} +2.65333 q^{6} +2.19565 q^{7} -8.06655 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.65333 q^{2} -1.00000 q^{3} +5.04016 q^{4} +2.95577 q^{5} +2.65333 q^{6} +2.19565 q^{7} -8.06655 q^{8} +1.00000 q^{9} -7.84263 q^{10} +5.07261 q^{11} -5.04016 q^{12} +6.69874 q^{13} -5.82578 q^{14} -2.95577 q^{15} +11.3229 q^{16} -7.08134 q^{17} -2.65333 q^{18} -2.92350 q^{19} +14.8976 q^{20} -2.19565 q^{21} -13.4593 q^{22} +7.30005 q^{23} +8.06655 q^{24} +3.73657 q^{25} -17.7740 q^{26} -1.00000 q^{27} +11.0664 q^{28} +10.1255 q^{29} +7.84263 q^{30} -4.47407 q^{31} -13.9103 q^{32} -5.07261 q^{33} +18.7891 q^{34} +6.48983 q^{35} +5.04016 q^{36} -9.53194 q^{37} +7.75700 q^{38} -6.69874 q^{39} -23.8429 q^{40} +3.74556 q^{41} +5.82578 q^{42} -10.7695 q^{43} +25.5668 q^{44} +2.95577 q^{45} -19.3694 q^{46} -2.84735 q^{47} -11.3229 q^{48} -2.17913 q^{49} -9.91435 q^{50} +7.08134 q^{51} +33.7627 q^{52} +5.62744 q^{53} +2.65333 q^{54} +14.9935 q^{55} -17.7113 q^{56} +2.92350 q^{57} -26.8663 q^{58} -5.54048 q^{59} -14.8976 q^{60} -7.18958 q^{61} +11.8712 q^{62} +2.19565 q^{63} +14.2628 q^{64} +19.7999 q^{65} +13.4593 q^{66} +0.157759 q^{67} -35.6911 q^{68} -7.30005 q^{69} -17.2197 q^{70} +8.86275 q^{71} -8.06655 q^{72} +4.18889 q^{73} +25.2914 q^{74} -3.73657 q^{75} -14.7349 q^{76} +11.1377 q^{77} +17.7740 q^{78} +11.9469 q^{79} +33.4679 q^{80} +1.00000 q^{81} -9.93820 q^{82} +0.628933 q^{83} -11.0664 q^{84} -20.9308 q^{85} +28.5751 q^{86} -10.1255 q^{87} -40.9185 q^{88} -10.7086 q^{89} -7.84263 q^{90} +14.7081 q^{91} +36.7934 q^{92} +4.47407 q^{93} +7.55497 q^{94} -8.64118 q^{95} +13.9103 q^{96} -4.40771 q^{97} +5.78194 q^{98} +5.07261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * 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 $

$2$	−2.65333	−1.87619	−0.938094	−	0.346381i	$-0.887410\pi$
$2$	−2.65333	−1.87619	−0.938094	+	0.346381i	$0.887410\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.04016	2.52008
$5$	2.95577	1.32186	0.660930	−	0.750448i	$-0.270162\pi$
$5$	2.95577	1.32186	0.660930	+	0.750448i	$0.270162\pi$
$6$	2.65333	1.08322
$7$	2.19565	0.829877	0.414939	−	0.909849i	$-0.363803\pi$
$7$	2.19565	0.829877	0.414939	+	0.909849i	$0.363803\pi$
$8$	−8.06655	−2.85196
$9$	1.00000	0.333333
$10$	−7.84263	−2.48006
$11$	5.07261	1.52945	0.764725	−	0.644357i	$-0.222875\pi$
$11$	5.07261	1.52945	0.764725	+	0.644357i	$0.222875\pi$
$12$	−5.04016	−1.45497
$13$	6.69874	1.85789	0.928947	−	0.370211i	$-0.120715\pi$
$13$	6.69874	1.85789	0.928947	+	0.370211i	$0.120715\pi$
$14$	−5.82578	−1.55701
$15$	−2.95577	−0.763176
$16$	11.3229	2.83073
$17$	−7.08134	−1.71748	−0.858739	−	0.512414i	$-0.828751\pi$
$17$	−7.08134	−1.71748	−0.858739	+	0.512414i	$0.828751\pi$
$18$	−2.65333	−0.625396
$19$	−2.92350	−0.670696	−0.335348	−	0.942094i	$-0.608854\pi$
$19$	−2.92350	−0.670696	−0.335348	+	0.942094i	$0.608854\pi$
$20$	14.8976	3.33119
$21$	−2.19565	−0.479130
$22$	−13.4593	−2.86954
$23$	7.30005	1.52217	0.761083	−	0.648655i	$-0.224668\pi$
$23$	7.30005	1.52217	0.761083	+	0.648655i	$0.224668\pi$
$24$	8.06655	1.64658
$25$	3.73657	0.747314
$26$	−17.7740	−3.48576
$27$	−1.00000	−0.192450
$28$	11.0664	2.09136
$29$	10.1255	1.88026	0.940130	−	0.340817i	$-0.110704\pi$
$29$	10.1255	1.88026	0.940130	+	0.340817i	$0.110704\pi$
$30$	7.84263	1.43186
$31$	−4.47407	−0.803566	−0.401783	−	0.915735i	$-0.631609\pi$
$31$	−4.47407	−0.803566	−0.401783	+	0.915735i	$0.631609\pi$
$32$	−13.9103	−2.45902
$33$	−5.07261	−0.883029
$34$	18.7891	3.22231
$35$	6.48983	1.09698
$36$	5.04016	0.840027
$37$	−9.53194	−1.56704	−0.783521	−	0.621366i	$-0.786578\pi$
$37$	−9.53194	−1.56704	−0.783521	+	0.621366i	$0.786578\pi$
$38$	7.75700	1.25835
$39$	−6.69874	−1.07266
$40$	−23.8429	−3.76989
$41$	3.74556	0.584958	0.292479	−	0.956272i	$-0.405520\pi$
$41$	3.74556	0.584958	0.292479	+	0.956272i	$0.405520\pi$
$42$	5.82578	0.898938
$43$	−10.7695	−1.64234	−0.821168	−	0.570686i	$-0.806677\pi$
$43$	−10.7695	−1.64234	−0.821168	+	0.570686i	$0.806677\pi$
$44$	25.5668	3.85434
$45$	2.95577	0.440620
$46$	−19.3694	−2.85587
$47$	−2.84735	−0.415329	−0.207665	−	0.978200i	$-0.566586\pi$
$47$	−2.84735	−0.415329	−0.207665	+	0.978200i	$0.566586\pi$
$48$	−11.3229	−1.63432
$49$	−2.17913	−0.311304
$50$	−9.91435	−1.40210
$51$	7.08134	0.991586
$52$	33.7627	4.68205
$53$	5.62744	0.772989	0.386494	−	0.922292i	$-0.373686\pi$
$53$	5.62744	0.772989	0.386494	+	0.922292i	$0.373686\pi$
$54$	2.65333	0.361073
$55$	14.9935	2.02172
$56$	−17.7113	−2.36678
$57$	2.92350	0.387227
$58$	−26.8663	−3.52772
$59$	−5.54048	−0.721309	−0.360655	−	0.932699i	$-0.617447\pi$
$59$	−5.54048	−0.721309	−0.360655	+	0.932699i	$0.617447\pi$
$60$	−14.8976	−1.92327
$61$	−7.18958	−0.920532	−0.460266	−	0.887781i	$-0.652246\pi$
$61$	−7.18958	−0.920532	−0.460266	+	0.887781i	$0.652246\pi$
$62$	11.8712	1.50764
$63$	2.19565	0.276626
$64$	14.2628	1.78285
$65$	19.7999	2.45588
$66$	13.4593	1.65673
$67$	0.157759	0.0192733	0.00963667	−	0.999954i	$-0.496933\pi$
$67$	0.157759	0.0192733	0.00963667	+	0.999954i	$0.496933\pi$
$68$	−35.6911	−4.32818
$69$	−7.30005	−0.878822
$70$	−17.2197	−2.05814
$71$	8.86275	1.05181	0.525907	−	0.850542i	$-0.323726\pi$
$71$	8.86275	1.05181	0.525907	+	0.850542i	$0.323726\pi$
$72$	−8.06655	−0.950653
$73$	4.18889	0.490272	0.245136	−	0.969489i	$-0.421167\pi$
$73$	4.18889	0.490272	0.245136	+	0.969489i	$0.421167\pi$
$74$	25.2914	2.94006
$75$	−3.73657	−0.431462
$76$	−14.7349	−1.69021
$77$	11.1377	1.26926
$78$	17.7740	2.01250
$79$	11.9469	1.34413	0.672066	−	0.740491i	$-0.265407\pi$
$79$	11.9469	1.34413	0.672066	+	0.740491i	$0.265407\pi$
$80$	33.4679	3.74183
$81$	1.00000	0.111111
$82$	−9.93820	−1.09749
$83$	0.628933	0.0690344	0.0345172	−	0.999404i	$-0.489011\pi$
$83$	0.628933	0.0690344	0.0345172	+	0.999404i	$0.489011\pi$
$84$	−11.0664	−1.20745
$85$	−20.9308	−2.27026
$86$	28.5751	3.08133
$87$	−10.1255	−1.08557
$88$	−40.9185	−4.36193
$89$	−10.7086	−1.13511	−0.567554	−	0.823336i	$-0.692110\pi$
$89$	−10.7086	−1.13511	−0.567554	+	0.823336i	$0.692110\pi$
$90$	−7.84263	−0.826686
$91$	14.7081	1.54182
$92$	36.7934	3.83598
$93$	4.47407	0.463939
$94$	7.55497	0.779236
$95$	−8.64118	−0.886567
$96$	13.9103	1.41972
$97$	−4.40771	−0.447536	−0.223768	−	0.974642i	$-0.571836\pi$
$97$	−4.40771	−0.447536	−0.223768	+	0.974642i	$0.571836\pi$
$98$	5.78194	0.584064
$99$	5.07261	0.509817
$100$	18.8329	1.88329
$101$	−3.12654	−0.311102	−0.155551	−	0.987828i	$-0.549715\pi$
$101$	−3.12654	−0.311102	−0.155551	+	0.987828i	$0.549715\pi$
$102$	−18.7891	−1.86040
$103$	10.2674	1.01168	0.505839	−	0.862628i	$-0.331183\pi$
$103$	10.2674	1.01168	0.505839	+	0.862628i	$0.331183\pi$
$104$	−54.0357	−5.29864
$105$	−6.48983	−0.633343
$106$	−14.9315	−1.45027
$107$	−9.08282	−0.878070	−0.439035	−	0.898470i	$-0.644680\pi$
$107$	−9.08282	−0.878070	−0.439035	+	0.898470i	$0.644680\pi$
$108$	−5.04016	−0.484990
$109$	3.82055	0.365943	0.182971	−	0.983118i	$-0.441428\pi$
$109$	3.82055	0.365943	0.182971	+	0.983118i	$0.441428\pi$
$110$	−39.7826	−3.79313
$111$	9.53194	0.904732
$112$	24.8611	2.34916
$113$	−6.33851	−0.596276	−0.298138	−	0.954523i	$-0.596366\pi$
$113$	−6.33851	−0.596276	−0.298138	+	0.954523i	$0.596366\pi$
$114$	−7.75700	−0.726510
$115$	21.5773	2.01209
$116$	51.0342	4.73841
$117$	6.69874	0.619298
$118$	14.7007	1.35331
$119$	−15.5481	−1.42530
$120$	23.8429	2.17655
$121$	14.7314	1.33922
$122$	19.0763	1.72709
$123$	−3.74556	−0.337726
$124$	−22.5500	−2.02505
$125$	−3.73441	−0.334016
$126$	−5.82578	−0.519002
$127$	4.36562	0.387386	0.193693	−	0.981062i	$-0.437953\pi$
$127$	4.36562	0.387386	0.193693	+	0.981062i	$0.437953\pi$
$128$	−10.0234	−0.885951
$129$	10.7695	0.948203
$130$	−52.5357	−4.60769
$131$	17.8322	1.55801	0.779005	−	0.627017i	$-0.215724\pi$
$131$	17.8322	1.55801	0.779005	+	0.627017i	$0.215724\pi$
$132$	−25.5668	−2.22530
$133$	−6.41897	−0.556596
$134$	−0.418587	−0.0361604
$135$	−2.95577	−0.254392
$136$	57.1220	4.89817
$137$	19.7949	1.69119	0.845595	−	0.533825i	$-0.179246\pi$
$137$	19.7949	1.69119	0.845595	+	0.533825i	$0.179246\pi$
$138$	19.3694	1.64884
$139$	−17.4514	−1.48021	−0.740104	−	0.672492i	$-0.765224\pi$
$139$	−17.4514	−1.48021	−0.740104	+	0.672492i	$0.765224\pi$
$140$	32.7098	2.76448
$141$	2.84735	0.239791
$142$	−23.5158	−1.97340
$143$	33.9801	2.84156
$144$	11.3229	0.943576
$145$	29.9287	2.48544
$146$	−11.1145	−0.919842
$147$	2.17913	0.179731
$148$	−48.0425	−3.94907
$149$	20.4140	1.67238	0.836189	−	0.548441i	$-0.184778\pi$
$149$	20.4140	1.67238	0.836189	+	0.548441i	$0.184778\pi$
$150$	9.91435	0.809503
$151$	−1.51306	−0.123131	−0.0615656	−	0.998103i	$-0.519609\pi$
$151$	−1.51306	−0.123131	−0.0615656	+	0.998103i	$0.519609\pi$
$152$	23.5826	1.91280
$153$	−7.08134	−0.572492
$154$	−29.5519	−2.38136
$155$	−13.2243	−1.06220
$156$	−33.7627	−2.70318
$157$	6.44900	0.514686	0.257343	−	0.966320i	$-0.417153\pi$
$157$	6.44900	0.514686	0.257343	+	0.966320i	$0.417153\pi$
$158$	−31.6991	−2.52184
$159$	−5.62744	−0.446285
$160$	−41.1157	−3.25048
$161$	16.0283	1.26321
$162$	−2.65333	−0.208465
$163$	22.3197	1.74822	0.874108	−	0.485732i	$-0.161447\pi$
$163$	22.3197	1.74822	0.874108	+	0.485732i	$0.161447\pi$
$164$	18.8782	1.47414
$165$	−14.9935	−1.16724
$166$	−1.66877	−0.129521
$167$	12.2180	0.945456	0.472728	−	0.881208i	$-0.343269\pi$
$167$	12.2180	0.945456	0.472728	+	0.881208i	$0.343269\pi$
$168$	17.7113	1.36646
$169$	31.8731	2.45177
$170$	55.5363	4.25944
$171$	−2.92350	−0.223565
$172$	−54.2801	−4.13882
$173$	4.14860	0.315412	0.157706	−	0.987486i	$-0.449590\pi$
$173$	4.14860	0.315412	0.157706	+	0.987486i	$0.449590\pi$
$174$	26.8663	2.03673
$175$	8.20419	0.620179
$176$	57.4367	4.32946
$177$	5.54048	0.416448
$178$	28.4134	2.12968
$179$	14.7356	1.10139	0.550695	−	0.834707i	$-0.314363\pi$
$179$	14.7356	1.10139	0.550695	+	0.834707i	$0.314363\pi$
$180$	14.8976	1.11040
$181$	−0.00445939	−0.000331464 0	−0.000165732	−	1.00000i	$-0.500053\pi$
$181$	−0.00445939	−0.000331464 0	−0.000165732		1.00000i	$0.500053\pi$
$182$	−39.0254	−2.89275
$183$	7.18958	0.531469
$184$	−58.8862	−4.34115
$185$	−28.1742	−2.07141
$186$	−11.8712	−0.870437
$187$	−35.9209	−2.62680
$188$	−14.3511	−1.04666
$189$	−2.19565	−0.159710
$190$	22.9279	1.66337
$191$	20.5684	1.48828	0.744138	−	0.668026i	$-0.232861\pi$
$191$	20.5684	1.48828	0.744138	+	0.668026i	$0.232861\pi$
$192$	−14.2628	−1.02933
$193$	−0.809249	−0.0582510	−0.0291255	−	0.999576i	$-0.509272\pi$
$193$	−0.809249	−0.0582510	−0.0291255	+	0.999576i	$0.509272\pi$
$194$	11.6951	0.839661
$195$	−19.7999	−1.41790
$196$	−10.9831	−0.784510
$197$	−0.212268	−0.0151235	−0.00756175	−	0.999971i	$-0.502407\pi$
$197$	−0.212268	−0.0151235	−0.00756175	+	0.999971i	$0.502407\pi$
$198$	−13.4593	−0.956512
$199$	21.3431	1.51297	0.756485	−	0.654011i	$-0.226915\pi$
$199$	21.3431	1.51297	0.756485	+	0.654011i	$0.226915\pi$
$200$	−30.1412	−2.13131
$201$	−0.157759	−0.0111275
$202$	8.29573	0.583686
$203$	22.2321	1.56038
$204$	35.6911	2.49888
$205$	11.0710	0.773232
$206$	−27.2428	−1.89810
$207$	7.30005	0.507388
$208$	75.8492	5.25919
$209$	−14.8298	−1.02580
$210$	17.2197	1.18827
$211$	1.16288	0.0800563	0.0400281	−	0.999199i	$-0.487255\pi$
$211$	1.16288	0.0800563	0.0400281	+	0.999199i	$0.487255\pi$
$212$	28.3632	1.94799
$213$	−8.86275	−0.607265
$214$	24.0997	1.64742
$215$	−31.8322	−2.17094
$216$	8.06655	0.548860
$217$	−9.82348	−0.666861
$218$	−10.1372	−0.686577
$219$	−4.18889	−0.283059
$220$	75.5695	5.09490
$221$	−47.4360	−3.19089
$222$	−25.2914	−1.69745
$223$	−13.4137	−0.898250	−0.449125	−	0.893469i	$-0.648264\pi$
$223$	−13.4137	−0.898250	−0.449125	+	0.893469i	$0.648264\pi$
$224$	−30.5422	−2.04068
$225$	3.73657	0.249105
$226$	16.8181	1.11873
$227$	−26.2705	−1.74363	−0.871817	−	0.489832i	$-0.837058\pi$
$227$	−26.2705	−1.74363	−0.871817	+	0.489832i	$0.837058\pi$
$228$	14.7349	0.975843
$229$	28.5019	1.88346	0.941728	−	0.336375i	$-0.109201\pi$
$229$	28.5019	1.88346	0.941728	+	0.336375i	$0.109201\pi$
$230$	−57.2516	−3.77506
$231$	−11.1377	−0.732805
$232$	−81.6780	−5.36242
$233$	11.7737	0.771318	0.385659	−	0.922641i	$-0.373974\pi$
$233$	11.7737	0.771318	0.385659	+	0.922641i	$0.373974\pi$
$234$	−17.7740	−1.16192
$235$	−8.41612	−0.549007
$236$	−27.9249	−1.81776
$237$	−11.9469	−0.776035
$238$	41.2543	2.67412
$239$	27.8128	1.79906	0.899531	−	0.436857i	$-0.143909\pi$
$239$	27.8128	1.79906	0.899531	+	0.436857i	$0.143909\pi$
$240$	−33.4679	−2.16034
$241$	−10.1424	−0.653331	−0.326666	−	0.945140i	$-0.605925\pi$
$241$	−10.1424	−0.653331	−0.326666	+	0.945140i	$0.605925\pi$
$242$	−39.0873	−2.51263
$243$	−1.00000	−0.0641500
$244$	−36.2367	−2.31981
$245$	−6.44099	−0.411500
$246$	9.93820	0.633637
$247$	−19.5837	−1.24608
$248$	36.0903	2.29174
$249$	−0.628933	−0.0398570
$250$	9.90863	0.626677
$251$	3.13090	0.197621	0.0988105	−	0.995106i	$-0.468496\pi$
$251$	3.13090	0.197621	0.0988105	+	0.995106i	$0.468496\pi$
$252$	11.0664	0.697119
$253$	37.0303	2.32808
$254$	−11.5834	−0.726809
$255$	20.9308	1.31074
$256$	−1.93030	−0.120644
$257$	−13.2762	−0.828144	−0.414072	−	0.910244i	$-0.635894\pi$
$257$	−13.2762	−0.828144	−0.414072	+	0.910244i	$0.635894\pi$
$258$	−28.5751	−1.77901
$259$	−20.9288	−1.30045
$260$	99.7948	6.18901
$261$	10.1255	0.626753
$262$	−47.3148	−2.92312
$263$	−3.75546	−0.231572	−0.115786	−	0.993274i	$-0.536939\pi$
$263$	−3.75546	−0.231572	−0.115786	+	0.993274i	$0.536939\pi$
$264$	40.9185	2.51836
$265$	16.6334	1.02178
$266$	17.0317	1.04428
$267$	10.7086	0.655355
$268$	0.795131	0.0485704
$269$	5.40995	0.329850	0.164925	−	0.986306i	$-0.447262\pi$
$269$	5.40995	0.329850	0.164925	+	0.986306i	$0.447262\pi$
$270$	7.84263	0.477287
$271$	28.1770	1.71163	0.855814	−	0.517284i	$-0.173057\pi$
$271$	28.1770	1.71163	0.855814	+	0.517284i	$0.173057\pi$
$272$	−80.1814	−4.86171
$273$	−14.7081	−0.890173
$274$	−52.5223	−3.17299
$275$	18.9542	1.14298
$276$	−36.7934	−2.21470
$277$	−23.2959	−1.39972	−0.699858	−	0.714282i	$-0.746753\pi$
$277$	−23.2959	−1.39972	−0.699858	+	0.714282i	$0.746753\pi$
$278$	46.3043	2.77715
$279$	−4.47407	−0.267855
$280$	−52.3506	−3.12855
$281$	−9.45018	−0.563750	−0.281875	−	0.959451i	$-0.590956\pi$
$281$	−9.45018	−0.563750	−0.281875	+	0.959451i	$0.590956\pi$
$282$	−7.55497	−0.449892
$283$	15.1708	0.901810	0.450905	−	0.892572i	$-0.351101\pi$
$283$	15.1708	0.901810	0.450905	+	0.892572i	$0.351101\pi$
$284$	44.6697	2.65066
$285$	8.64118	0.511859
$286$	−90.1604	−5.33130
$287$	8.22393	0.485443
$288$	−13.9103	−0.819673
$289$	33.1454	1.94973
$290$	−79.4106	−4.66315
$291$	4.40771	0.258385
$292$	21.1127	1.23553
$293$	11.3679	0.664117	0.332059	−	0.943259i	$-0.392257\pi$
$293$	11.3679	0.664117	0.332059	+	0.943259i	$0.392257\pi$
$294$	−5.78194	−0.337210
$295$	−16.3764	−0.953470
$296$	76.8899	4.46914
$297$	−5.07261	−0.294343
$298$	−54.1650	−3.13770
$299$	48.9011	2.82802
$300$	−18.8329	−1.08732
$301$	−23.6461	−1.36294
$302$	4.01465	0.231017
$303$	3.12654	0.179615
$304$	−33.1025	−1.89856
$305$	−21.2507	−1.21681
$306$	18.7891	1.07410
$307$	9.43381	0.538416	0.269208	−	0.963082i	$-0.413238\pi$
$307$	9.43381	0.538416	0.269208	+	0.963082i	$0.413238\pi$
$308$	56.1357	3.19863
$309$	−10.2674	−0.584092
$310$	35.0884	1.99289
$311$	−8.25927	−0.468340	−0.234170	−	0.972196i	$-0.575237\pi$
$311$	−8.25927	−0.468340	−0.234170	+	0.972196i	$0.575237\pi$
$312$	54.0357	3.05917
$313$	1.56342	0.0883698	0.0441849	−	0.999023i	$-0.485931\pi$
$313$	1.56342	0.0883698	0.0441849	+	0.999023i	$0.485931\pi$
$314$	−17.1113	−0.965648
$315$	6.48983	0.365661
$316$	60.2144	3.38732
$317$	9.97320	0.560151	0.280075	−	0.959978i	$-0.409641\pi$
$317$	9.97320	0.560151	0.280075	+	0.959978i	$0.409641\pi$
$318$	14.9315	0.837315
$319$	51.3628	2.87576
$320$	42.1576	2.35668
$321$	9.08282	0.506954
$322$	−42.5285	−2.37002
$323$	20.7023	1.15191
$324$	5.04016	0.280009
$325$	25.0303	1.38843
$326$	−59.2216	−3.27998
$327$	−3.82055	−0.211277
$328$	−30.2138	−1.66828
$329$	−6.25179	−0.344672
$330$	39.7826	2.18996
$331$	9.59505	0.527392	0.263696	−	0.964606i	$-0.415058\pi$
$331$	9.59505	0.527392	0.263696	+	0.964606i	$0.415058\pi$
$332$	3.16993	0.173972
$333$	−9.53194	−0.522347
$334$	−32.4184	−1.77385
$335$	0.466299	0.0254766
$336$	−24.8611	−1.35629
$337$	−13.5973	−0.740691	−0.370346	−	0.928894i	$-0.620761\pi$
$337$	−13.5973	−0.740691	−0.370346	+	0.928894i	$0.620761\pi$
$338$	−84.5698	−4.59999
$339$	6.33851	0.344260
$340$	−105.495	−5.72125
$341$	−22.6952	−1.22901
$342$	7.75700	0.419451
$343$	−20.1541	−1.08822
$344$	86.8729	4.68387
$345$	−21.5773	−1.16168
$346$	−11.0076	−0.591772
$347$	−21.4317	−1.15052	−0.575258	−	0.817972i	$-0.695098\pi$
$347$	−21.4317	−1.15052	−0.575258	+	0.817972i	$0.695098\pi$
$348$	−51.0342	−2.73572
$349$	−6.91959	−0.370397	−0.185199	−	0.982701i	$-0.559293\pi$
$349$	−6.91959	−0.370397	−0.185199	+	0.982701i	$0.559293\pi$
$350$	−21.7684	−1.16357
$351$	−6.69874	−0.357552
$352$	−70.5616	−3.76095
$353$	−8.99358	−0.478680	−0.239340	−	0.970936i	$-0.576931\pi$
$353$	−8.99358	−0.478680	−0.239340	+	0.970936i	$0.576931\pi$
$354$	−14.7007	−0.781335
$355$	26.1962	1.39035
$356$	−53.9730	−2.86056
$357$	15.5481	0.822895
$358$	−39.0984	−2.06641
$359$	−9.46333	−0.499455	−0.249728	−	0.968316i	$-0.580341\pi$
$359$	−9.46333	−0.499455	−0.249728	+	0.968316i	$0.580341\pi$
$360$	−23.8429	−1.25663
$361$	−10.4532	−0.550166
$362$	0.0118322	0.000621889 0
$363$	−14.7314	−0.773198
$364$	74.1311	3.88552
$365$	12.3814	0.648071
$366$	−19.0763	−0.997136
$367$	−25.1418	−1.31239	−0.656194	−	0.754592i	$-0.727835\pi$
$367$	−25.1418	−1.31239	−0.656194	+	0.754592i	$0.727835\pi$
$368$	82.6578	4.30884
$369$	3.74556	0.194986
$370$	74.7555	3.88635
$371$	12.3559	0.641486
$372$	22.5500	1.16916
$373$	−36.1962	−1.87417	−0.937083	−	0.349106i	$-0.886485\pi$
$373$	−36.1962	−1.87417	−0.937083	+	0.349106i	$0.886485\pi$
$374$	95.3100	4.92836
$375$	3.73441	0.192844
$376$	22.9683	1.18450
$377$	67.8281	3.49332
$378$	5.82578	0.299646
$379$	−17.7259	−0.910516	−0.455258	−	0.890360i	$-0.650453\pi$
$379$	−17.7259	−0.910516	−0.455258	+	0.890360i	$0.650453\pi$
$380$	−43.5530	−2.23422
$381$	−4.36562	−0.223657
$382$	−54.5747	−2.79228
$383$	−20.0977	−1.02694	−0.513471	−	0.858107i	$-0.671641\pi$
$383$	−20.0977	−1.02694	−0.513471	+	0.858107i	$0.671641\pi$
$384$	10.0234	0.511504
$385$	32.9204	1.67778
$386$	2.14721	0.109290
$387$	−10.7695	−0.547446
$388$	−22.2156	−1.12783
$389$	30.5342	1.54815	0.774073	−	0.633096i	$-0.218216\pi$
$389$	30.5342	1.54815	0.774073	+	0.633096i	$0.218216\pi$
$390$	52.5357	2.66025
$391$	−51.6941	−2.61428
$392$	17.5780	0.887825
$393$	−17.8322	−0.899518
$394$	0.563218	0.0283745
$395$	35.3123	1.77675
$396$	25.5668	1.28478
$397$	−0.339071	−0.0170175	−0.00850876	−	0.999964i	$-0.502708\pi$
$397$	−0.339071	−0.0170175	−0.00850876	+	0.999964i	$0.502708\pi$
$398$	−56.6302	−2.83862
$399$	6.41897	0.321351
$400$	42.3088	2.11544
$401$	−1.00665	−0.0502696	−0.0251348	−	0.999684i	$-0.508001\pi$
$401$	−1.00665	−0.0502696	−0.0251348	+	0.999684i	$0.508001\pi$
$402$	0.418587	0.0208772
$403$	−29.9706	−1.49294
$404$	−15.7582	−0.784002
$405$	2.95577	0.146873
$406$	−58.9890	−2.92758
$407$	−48.3519	−2.39671
$408$	−57.1220	−2.82796
$409$	−10.6435	−0.526289	−0.263144	−	0.964756i	$-0.584760\pi$
$409$	−10.6435	−0.526289	−0.263144	+	0.964756i	$0.584760\pi$
$410$	−29.3750	−1.45073
$411$	−19.7949	−0.976409
$412$	51.7494	2.54951
$413$	−12.1650	−0.598598
$414$	−19.3694	−0.951956
$415$	1.85898	0.0912538
$416$	−93.1815	−4.56860
$417$	17.4514	0.854599
$418$	39.3483	1.92459
$419$	−19.9134	−0.972834	−0.486417	−	0.873727i	$-0.661696\pi$
$419$	−19.9134	−0.972834	−0.486417	+	0.873727i	$0.661696\pi$
$420$	−32.7098	−1.59607
$421$	20.4077	0.994612	0.497306	−	0.867575i	$-0.334323\pi$
$421$	20.4077	0.994612	0.497306	+	0.867575i	$0.334323\pi$
$422$	−3.08552	−0.150201
$423$	−2.84735	−0.138443
$424$	−45.3941	−2.20453
$425$	−26.4599	−1.28349
$426$	23.5158	1.13934
$427$	−15.7858	−0.763928
$428$	−45.7789	−2.21281
$429$	−33.9801	−1.64057
$430$	84.4614	4.07309
$431$	−0.790059	−0.0380558	−0.0190279	−	0.999819i	$-0.506057\pi$
$431$	−0.790059	−0.0380558	−0.0190279	+	0.999819i	$0.506057\pi$
$432$	−11.3229	−0.544774
$433$	−12.9283	−0.621293	−0.310646	−	0.950526i	$-0.600545\pi$
$433$	−12.9283	−0.621293	−0.310646	+	0.950526i	$0.600545\pi$
$434$	26.0649	1.25116
$435$	−29.9287	−1.43497
$436$	19.2562	0.922205
$437$	−21.3417	−1.02091
$438$	11.1145	0.531071
$439$	20.2351	0.965771	0.482885	−	0.875684i	$-0.339589\pi$
$439$	20.2351	0.965771	0.482885	+	0.875684i	$0.339589\pi$
$440$	−120.946	−5.76586
$441$	−2.17913	−0.103768
$442$	125.863	5.98671
$443$	26.2459	1.24698	0.623491	−	0.781831i	$-0.285714\pi$
$443$	26.2459	1.24698	0.623491	+	0.781831i	$0.285714\pi$
$444$	48.0425	2.28000
$445$	−31.6521	−1.50045
$446$	35.5911	1.68529
$447$	−20.4140	−0.965548
$448$	31.3162	1.47955
$449$	−30.9630	−1.46123	−0.730617	−	0.682787i	$-0.760768\pi$
$449$	−30.9630	−1.46123	−0.730617	+	0.682787i	$0.760768\pi$
$450$	−9.91435	−0.467367
$451$	18.9998	0.894664
$452$	−31.9471	−1.50267
$453$	1.51306	0.0710898
$454$	69.7043	3.27138
$455$	43.4737	2.03808
$456$	−23.5826	−1.10435
$457$	−1.90204	−0.0889738	−0.0444869	−	0.999010i	$-0.514165\pi$
$457$	−1.90204	−0.0889738	−0.0444869	+	0.999010i	$0.514165\pi$
$458$	−75.6249	−3.53372
$459$	7.08134	0.330529
$460$	108.753	5.07063
$461$	18.5401	0.863499	0.431749	−	0.901994i	$-0.357896\pi$
$461$	18.5401	0.863499	0.431749	+	0.901994i	$0.357896\pi$
$462$	29.5519	1.37488
$463$	37.3867	1.73751	0.868754	−	0.495243i	$-0.164921\pi$
$463$	37.3867	1.73751	0.868754	+	0.495243i	$0.164921\pi$
$464$	114.650	5.32250
$465$	13.2243	0.613262
$466$	−31.2394	−1.44714
$467$	−5.37640	−0.248790	−0.124395	−	0.992233i	$-0.539699\pi$
$467$	−5.37640	−0.248790	−0.124395	+	0.992233i	$0.539699\pi$
$468$	33.7627	1.56068
$469$	0.346383	0.0159945
$470$	22.3308	1.03004
$471$	−6.44900	−0.297154
$472$	44.6926	2.05714
$473$	−54.6296	−2.51187
$474$	31.6991	1.45599
$475$	−10.9238	−0.501220
$476$	−78.3651	−3.59186
$477$	5.62744	0.257663
$478$	−73.7966	−3.37538
$479$	9.99499	0.456683	0.228341	−	0.973581i	$-0.426670\pi$
$479$	9.99499	0.456683	0.228341	+	0.973581i	$0.426670\pi$
$480$	41.1157	1.87667
$481$	−63.8520	−2.91140
$482$	26.9112	1.22577
$483$	−16.0283	−0.729315
$484$	74.2487	3.37494
$485$	−13.0282	−0.591579
$486$	2.65333	0.120358
$487$	13.9246	0.630982	0.315491	−	0.948929i	$-0.397831\pi$
$487$	13.9246	0.630982	0.315491	+	0.948929i	$0.397831\pi$
$488$	57.9952	2.62532
$489$	−22.3197	−1.00933
$490$	17.0901	0.772051
$491$	4.04000	0.182323	0.0911614	−	0.995836i	$-0.470942\pi$
$491$	4.04000	0.182323	0.0911614	+	0.995836i	$0.470942\pi$
$492$	−18.8782	−0.851096
$493$	−71.7022	−3.22930
$494$	51.9621	2.33789
$495$	14.9935	0.673906
$496$	−50.6594	−2.27468
$497$	19.4595	0.872877
$498$	1.66877	0.0747793
$499$	−15.3674	−0.687938	−0.343969	−	0.938981i	$-0.611772\pi$
$499$	−15.3674	−0.687938	−0.343969	+	0.938981i	$0.611772\pi$
$500$	−18.8220	−0.841748
$501$	−12.2180	−0.545859
$502$	−8.30732	−0.370774
$503$	−10.9715	−0.489196	−0.244598	−	0.969625i	$-0.578656\pi$
$503$	−10.9715	−0.489196	−0.244598	+	0.969625i	$0.578656\pi$
$504$	−17.7113	−0.788925
$505$	−9.24132	−0.411233
$506$	−98.2537	−4.36791
$507$	−31.8731	−1.41553
$508$	22.0034	0.976244
$509$	−7.31636	−0.324292	−0.162146	−	0.986767i	$-0.551842\pi$
$509$	−7.31636	−0.324292	−0.162146	+	0.986767i	$0.551842\pi$
$510$	−55.5363	−2.45919
$511$	9.19732	0.406866
$512$	25.1685	1.11230
$513$	2.92350	0.129076
$514$	35.2260	1.55375
$515$	30.3481	1.33730
$516$	54.2801	2.38955
$517$	−14.4435	−0.635226
$518$	55.5310	2.43989
$519$	−4.14860	−0.182103
$520$	−159.717	−7.00406
$521$	−25.6652	−1.12441	−0.562206	−	0.826997i	$-0.690047\pi$
$521$	−25.6652	−1.12441	−0.562206	+	0.826997i	$0.690047\pi$
$522$	−26.8663	−1.17591
$523$	34.2524	1.49775	0.748877	−	0.662709i	$-0.230594\pi$
$523$	34.2524	1.49775	0.748877	+	0.662709i	$0.230594\pi$
$524$	89.8774	3.92631
$525$	−8.20419	−0.358060
$526$	9.96448	0.434472
$527$	31.6824	1.38011
$528$	−57.4367	−2.49961
$529$	30.2907	1.31699
$530$	−44.1340	−1.91706
$531$	−5.54048	−0.240436
$532$	−32.3527	−1.40267
$533$	25.0905	1.08679
$534$	−28.4134	−1.22957
$535$	−26.8467	−1.16069
$536$	−1.27257	−0.0549667
$537$	−14.7356	−0.635887
$538$	−14.3544	−0.618861
$539$	−11.0539	−0.476123
$540$	−14.8976	−0.641089
$541$	−1.94949	−0.0838150	−0.0419075	−	0.999121i	$-0.513343\pi$
$541$	−1.94949	−0.0838150	−0.0419075	+	0.999121i	$0.513343\pi$
$542$	−74.7628	−3.21134
$543$	0.00445939	0.000191371 0
$544$	98.5037	4.22331
$545$	11.2927	0.483725
$546$	39.0254	1.67013
$547$	−26.6832	−1.14089	−0.570445	−	0.821336i	$-0.693229\pi$
$547$	−26.6832	−1.14089	−0.570445	+	0.821336i	$0.693229\pi$
$548$	99.7694	4.26194
$549$	−7.18958	−0.306844
$550$	−50.2917	−2.14444
$551$	−29.6019	−1.26108
$552$	58.8862	2.50636
$553$	26.2312	1.11546
$554$	61.8117	2.62613
$555$	28.1742	1.19593
$556$	−87.9579	−3.73025
$557$	−20.9020	−0.885648	−0.442824	−	0.896609i	$-0.646023\pi$
$557$	−20.9020	−0.885648	−0.442824	+	0.896609i	$0.646023\pi$
$558$	11.8712	0.502547
$559$	−72.1422	−3.05129
$560$	73.4838	3.10526
$561$	35.9209	1.51658
$562$	25.0744	1.05770
$563$	39.8544	1.67966	0.839832	−	0.542846i	$-0.182653\pi$
$563$	39.8544	1.67966	0.839832	+	0.542846i	$0.182653\pi$
$564$	14.3511	0.604292
$565$	−18.7352	−0.788194
$566$	−40.2531	−1.69196
$567$	2.19565	0.0922086
$568$	−71.4918	−2.99973
$569$	−14.6082	−0.612409	−0.306205	−	0.951966i	$-0.599059\pi$
$569$	−14.6082	−0.612409	−0.306205	+	0.951966i	$0.599059\pi$
$570$	−22.9279	−0.960344
$571$	17.2057	0.720037	0.360018	−	0.932945i	$-0.382770\pi$
$571$	17.2057	0.720037	0.360018	+	0.932945i	$0.382770\pi$
$572$	171.265	7.16096
$573$	−20.5684	−0.859256
$574$	−21.8208	−0.910783
$575$	27.2771	1.13753
$576$	14.2628	0.594285
$577$	−2.18138	−0.0908122	−0.0454061	−	0.998969i	$-0.514458\pi$
$577$	−2.18138	−0.0908122	−0.0454061	+	0.998969i	$0.514458\pi$
$578$	−87.9456	−3.65805
$579$	0.809249	0.0336312
$580$	150.845	6.26351
$581$	1.38092	0.0572901
$582$	−11.6951	−0.484778
$583$	28.5458	1.18225
$584$	−33.7899	−1.39823
$585$	19.7999	0.818626
$586$	−30.1627	−1.24601
$587$	−38.6159	−1.59385	−0.796923	−	0.604080i	$-0.793541\pi$
$587$	−38.6159	−1.59385	−0.796923	+	0.604080i	$0.793541\pi$
$588$	10.9831	0.452937
$589$	13.0799	0.538949
$590$	43.4519	1.78889
$591$	0.212268	0.00873156
$592$	−107.929	−4.43587
$593$	38.2630	1.57127	0.785636	−	0.618690i	$-0.212336\pi$
$593$	38.2630	1.57127	0.785636	+	0.618690i	$0.212336\pi$
$594$	13.4593	0.552243
$595$	−45.9567	−1.88404
$596$	102.890	4.21453
$597$	−21.3431	−0.873514
$598$	−129.751	−5.30590
$599$	34.1933	1.39710	0.698550	−	0.715561i	$-0.253829\pi$
$599$	34.1933	1.39710	0.698550	+	0.715561i	$0.253829\pi$
$600$	30.1412	1.23051
$601$	−32.3453	−1.31939	−0.659696	−	0.751533i	$-0.729315\pi$
$601$	−32.3453	−1.31939	−0.659696	+	0.751533i	$0.729315\pi$
$602$	62.7409	2.55713
$603$	0.157759	0.00642444
$604$	−7.62608	−0.310301
$605$	43.5426	1.77026
$606$	−8.29573	−0.336991
$607$	−29.8881	−1.21312	−0.606559	−	0.795038i	$-0.707451\pi$
$607$	−29.8881	−1.21312	−0.606559	+	0.795038i	$0.707451\pi$
$608$	40.6668	1.64926
$609$	−22.2321	−0.900889
$610$	56.3852	2.28297
$611$	−19.0737	−0.771638
$612$	−35.6911	−1.44273
$613$	4.09390	0.165351	0.0826754	−	0.996577i	$-0.473654\pi$
$613$	4.09390	0.165351	0.0826754	+	0.996577i	$0.473654\pi$
$614$	−25.0310	−1.01017
$615$	−11.0710	−0.446426
$616$	−89.8427	−3.61987
$617$	29.4096	1.18398	0.591992	−	0.805944i	$-0.298342\pi$
$617$	29.4096	1.18398	0.591992	+	0.805944i	$0.298342\pi$
$618$	27.2428	1.09587
$619$	−11.7339	−0.471625	−0.235813	−	0.971799i	$-0.575775\pi$
$619$	−11.7339	−0.471625	−0.235813	+	0.971799i	$0.575775\pi$
$620$	−66.6526	−2.67683
$621$	−7.30005	−0.292941
$622$	21.9146	0.878694
$623$	−23.5123	−0.942000
$624$	−75.8492	−3.03640
$625$	−29.7209	−1.18884
$626$	−4.14827	−0.165798
$627$	14.8298	0.592244
$628$	32.5040	1.29705
$629$	67.4989	2.69136
$630$	−17.2197	−0.686048
$631$	−30.0782	−1.19739	−0.598697	−	0.800976i	$-0.704315\pi$
$631$	−30.0782	−1.19739	−0.598697	+	0.800976i	$0.704315\pi$
$632$	−96.3704	−3.83341
$633$	−1.16288	−0.0462205
$634$	−26.4622	−1.05095
$635$	12.9038	0.512070
$636$	−28.3632	−1.12468
$637$	−14.5974	−0.578369
$638$	−136.282	−5.39547
$639$	8.86275	0.350605
$640$	−29.6268	−1.17110
$641$	11.7844	0.465456	0.232728	−	0.972542i	$-0.425235\pi$
$641$	11.7844	0.465456	0.232728	+	0.972542i	$0.425235\pi$
$642$	−24.0997	−0.951141
$643$	−12.3974	−0.488904	−0.244452	−	0.969661i	$-0.578608\pi$
$643$	−12.3974	−0.488904	−0.244452	+	0.969661i	$0.578608\pi$
$644$	80.7854	3.18339
$645$	31.8322	1.25339
$646$	−54.9300	−2.16119
$647$	37.0849	1.45796	0.728979	−	0.684536i	$-0.239995\pi$
$647$	37.0849	1.45796	0.728979	+	0.684536i	$0.239995\pi$
$648$	−8.06655	−0.316884
$649$	−28.1047	−1.10321
$650$	−66.4136	−2.60496
$651$	9.82348	0.385012
$652$	112.495	4.40564
$653$	37.0812	1.45110	0.725550	−	0.688170i	$-0.241586\pi$
$653$	37.0812	1.45110	0.725550	+	0.688170i	$0.241586\pi$
$654$	10.1372	0.396396
$655$	52.7080	2.05947
$656$	42.4106	1.65586
$657$	4.18889	0.163424
$658$	16.5881	0.646670
$659$	−30.3828	−1.18355	−0.591773	−	0.806104i	$-0.701572\pi$
$659$	−30.3828	−1.18355	−0.591773	+	0.806104i	$0.701572\pi$
$660$	−75.5695	−2.94154
$661$	11.9367	0.464282	0.232141	−	0.972682i	$-0.425427\pi$
$661$	11.9367	0.464282	0.232141	+	0.972682i	$0.425427\pi$
$662$	−25.4588	−0.989486
$663$	47.4360	1.84226
$664$	−5.07332	−0.196883
$665$	−18.9730	−0.735741
$666$	25.2914	0.980022
$667$	73.9167	2.86207
$668$	61.5806	2.38263
$669$	13.4137	0.518605
$670$	−1.23725	−0.0477990
$671$	−36.4700	−1.40791
$672$	30.5422	1.17819
$673$	9.24881	0.356515	0.178258	−	0.983984i	$-0.442954\pi$
$673$	9.24881	0.356515	0.178258	+	0.983984i	$0.442954\pi$
$674$	36.0781	1.38968
$675$	−3.73657	−0.143821
$676$	160.645	6.17867
$677$	−23.0582	−0.886200	−0.443100	−	0.896472i	$-0.646121\pi$
$677$	−23.0582	−0.886200	−0.443100	+	0.896472i	$0.646121\pi$
$678$	−16.8181	−0.645897
$679$	−9.67779	−0.371400
$680$	168.839	6.47470
$681$	26.2705	1.00669
$682$	60.2179	2.30586
$683$	0.409164	0.0156562	0.00782811	−	0.999969i	$-0.497508\pi$
$683$	0.409164	0.0156562	0.00782811	+	0.999969i	$0.497508\pi$
$684$	−14.7349	−0.563403
$685$	58.5091	2.23552
$686$	53.4756	2.04171
$687$	−28.5019	−1.08741
$688$	−121.942	−4.64901
$689$	37.6968	1.43613
$690$	57.2516	2.17953
$691$	−15.2738	−0.581042	−0.290521	−	0.956869i	$-0.593829\pi$
$691$	−15.2738	−0.581042	−0.290521	+	0.956869i	$0.593829\pi$
$692$	20.9096	0.794864
$693$	11.1377	0.423085
$694$	56.8655	2.15858
$695$	−51.5823	−1.95663
$696$	81.6780	3.09600
$697$	−26.5236	−1.00465
$698$	18.3600	0.694935
$699$	−11.7737	−0.445321
$700$	41.3505	1.56290
$701$	−10.3681	−0.391596	−0.195798	−	0.980644i	$-0.562730\pi$
$701$	−10.3681	−0.391596	−0.195798	+	0.980644i	$0.562730\pi$
$702$	17.7740	0.670835
$703$	27.8666	1.05101
$704$	72.3499	2.72679
$705$	8.41612	0.316970
$706$	23.8629	0.898094
$707$	−6.86477	−0.258176
$708$	27.9249	1.04948
$709$	51.2156	1.92344	0.961722	−	0.274028i	$-0.0883561\pi$
$709$	51.2156	1.92344	0.961722	+	0.274028i	$0.0883561\pi$
$710$	−69.5073	−2.60856
$711$	11.9469	0.448044
$712$	86.3814	3.23728
$713$	−32.6609	−1.22316
$714$	−41.2543	−1.54390
$715$	100.437	3.75614
$716$	74.2697	2.77559
$717$	−27.8128	−1.03869
$718$	25.1093	0.937072
$719$	−42.3871	−1.58077	−0.790386	−	0.612609i	$-0.790120\pi$
$719$	−42.3871	−1.58077	−0.790386	+	0.612609i	$0.790120\pi$
$720$	33.4679	1.24728
$721$	22.5436	0.839568
$722$	27.7357	1.03222
$723$	10.1424	0.377201
$724$	−0.0224761	−0.000835316 0
$725$	37.8346	1.40514
$726$	39.0873	1.45067
$727$	15.8873	0.589227	0.294613	−	0.955617i	$-0.404809\pi$
$727$	15.8873	0.589227	0.294613	+	0.955617i	$0.404809\pi$
$728$	−118.643	−4.39722
$729$	1.00000	0.0370370
$730$	−32.8519	−1.21590
$731$	76.2626	2.82068
$732$	36.2367	1.33935
$733$	−19.6262	−0.724910	−0.362455	−	0.932001i	$-0.618061\pi$
$733$	−19.6262	−0.724910	−0.362455	+	0.932001i	$0.618061\pi$
$734$	66.7094	2.46229
$735$	6.44099	0.237580
$736$	−101.546	−3.74303
$737$	0.800251	0.0294776
$738$	−9.93820	−0.365830
$739$	6.19175	0.227767	0.113884	−	0.993494i	$-0.463671\pi$
$739$	6.19175	0.227767	0.113884	+	0.993494i	$0.463671\pi$
$740$	−142.003	−5.22012
$741$	19.5837	0.719427
$742$	−32.7843	−1.20355
$743$	−40.3594	−1.48064	−0.740321	−	0.672254i	$-0.765326\pi$
$743$	−40.3594	−1.48064	−0.740321	+	0.672254i	$0.765326\pi$
$744$	−36.0903	−1.32313
$745$	60.3390	2.21065
$746$	96.0404	3.51629
$747$	0.628933	0.0230115
$748$	−181.047	−6.61974
$749$	−19.9427	−0.728690
$750$	−9.90863	−0.361812
$751$	−33.7494	−1.23153	−0.615766	−	0.787929i	$-0.711153\pi$
$751$	−33.7494	−1.23153	−0.615766	+	0.787929i	$0.711153\pi$
$752$	−32.2403	−1.17568
$753$	−3.13090	−0.114096
$754$	−179.970	−6.55413
$755$	−4.47226	−0.162762
$756$	−11.0664	−0.402482
$757$	0.665094	0.0241733	0.0120866	−	0.999927i	$-0.496153\pi$
$757$	0.665094	0.0241733	0.0120866	+	0.999927i	$0.496153\pi$
$758$	47.0325	1.70830
$759$	−37.0303	−1.34412
$760$	69.7046	2.52845
$761$	−44.6184	−1.61742	−0.808708	−	0.588210i	$-0.799833\pi$
$761$	−44.6184	−1.61742	−0.808708	+	0.588210i	$0.799833\pi$
$762$	11.5834	0.419623
$763$	8.38859	0.303687
$764$	103.668	3.75057
$765$	−20.9308	−0.756755
$766$	53.3258	1.92674
$767$	−37.1142	−1.34012
$768$	1.93030	0.0696538
$769$	4.33485	0.156319	0.0781594	−	0.996941i	$-0.475096\pi$
$769$	4.33485	0.156319	0.0781594	+	0.996941i	$0.475096\pi$
$770$	−87.3487	−3.14783
$771$	13.2762	0.478129
$772$	−4.07875	−0.146797
$773$	38.8666	1.39794	0.698968	−	0.715153i	$-0.253643\pi$
$773$	38.8666	1.39794	0.698968	+	0.715153i	$0.253643\pi$
$774$	28.5751	1.02711
$775$	−16.7176	−0.600516
$776$	35.5551	1.27635
$777$	20.9288	0.750817
$778$	−81.0174	−2.90461
$779$	−10.9501	−0.392329
$780$	−99.7948	−3.57323
$781$	44.9573	1.60870
$782$	137.162	4.90489
$783$	−10.1255	−0.361856
$784$	−24.6740	−0.881216
$785$	19.0618	0.680343
$786$	47.3148	1.68766
$787$	20.4746	0.729839	0.364920	−	0.931039i	$-0.381096\pi$
$787$	20.4746	0.729839	0.364920	+	0.931039i	$0.381096\pi$
$788$	−1.06987	−0.0381125
$789$	3.75546	0.133698
$790$	−93.6952	−3.33353
$791$	−13.9171	−0.494836
$792$	−40.9185	−1.45398
$793$	−48.1611	−1.71025
$794$	0.899669	0.0319280
$795$	−16.6334	−0.589927
$796$	107.573	3.81281
$797$	5.91607	0.209558	0.104779	−	0.994496i	$-0.466587\pi$
$797$	5.91607	0.209558	0.104779	+	0.994496i	$0.466587\pi$
$798$	−17.0317	−0.602914
$799$	20.1631	0.713319
$800$	−51.9768	−1.83766
$801$	−10.7086	−0.378369
$802$	2.67097	0.0943152
$803$	21.2486	0.749847
$804$	−0.795131	−0.0280421
$805$	47.3761	1.66979
$806$	79.5219	2.80104
$807$	−5.40995	−0.190439
$808$	25.2204	0.887250
$809$	17.7592	0.624379	0.312190	−	0.950020i	$-0.398938\pi$
$809$	17.7592	0.624379	0.312190	+	0.950020i	$0.398938\pi$
$810$	−7.84263	−0.275562
$811$	34.9742	1.22811	0.614054	−	0.789264i	$-0.289538\pi$
$811$	34.9742	1.22811	0.614054	+	0.789264i	$0.289538\pi$
$812$	112.053	3.93230
$813$	−28.1770	−0.988209
$814$	128.293	4.49668
$815$	65.9719	2.31090
$816$	80.1814	2.80691
$817$	31.4847	1.10151
$818$	28.2408	0.987416
$819$	14.7081	0.513942
$820$	55.7997	1.94861
$821$	36.6679	1.27972	0.639860	−	0.768491i	$-0.278992\pi$
$821$	36.6679	1.27972	0.639860	+	0.768491i	$0.278992\pi$
$822$	52.5223	1.83193
$823$	20.6549	0.719984	0.359992	−	0.932955i	$-0.382780\pi$
$823$	20.6549	0.719984	0.359992	+	0.932955i	$0.382780\pi$
$824$	−82.8226	−2.88526
$825$	−18.9542	−0.659899
$826$	32.2776	1.12308
$827$	−13.0282	−0.453034	−0.226517	−	0.974007i	$-0.572734\pi$
$827$	−13.0282	−0.453034	−0.226517	+	0.974007i	$0.572734\pi$
$828$	36.7934	1.27866
$829$	−26.2450	−0.911526	−0.455763	−	0.890101i	$-0.650633\pi$
$829$	−26.2450	−0.911526	−0.455763	+	0.890101i	$0.650633\pi$
$830$	−4.93249	−0.171209
$831$	23.2959	0.808126
$832$	95.5430	3.31236
$833$	15.4311	0.534657
$834$	−46.3043	−1.60339
$835$	36.1135	1.24976
$836$	−74.7445	−2.58509
$837$	4.47407	0.154646
$838$	52.8369	1.82522
$839$	−42.0857	−1.45296	−0.726480	−	0.687187i	$-0.758845\pi$
$839$	−42.0857	−1.45296	−0.726480	+	0.687187i	$0.758845\pi$
$840$	52.3506	1.80627
$841$	73.5259	2.53538
$842$	−54.1485	−1.86608
$843$	9.45018	0.325481
$844$	5.86113	0.201748
$845$	94.2094	3.24090
$846$	7.55497	0.259745
$847$	32.3450	1.11139
$848$	63.7190	2.18812
$849$	−15.1708	−0.520660
$850$	70.2069	2.40808
$851$	−69.5836	−2.38530
$852$	−44.6697	−1.53036
$853$	−49.9446	−1.71007	−0.855035	−	0.518570i	$-0.826465\pi$
$853$	−49.9446	−1.71007	−0.855035	+	0.518570i	$0.826465\pi$
$854$	41.8849	1.43327
$855$	−8.64118	−0.295522
$856$	73.2671	2.50422
$857$	47.2592	1.61434	0.807172	−	0.590317i	$-0.200997\pi$
$857$	47.2592	1.61434	0.807172	+	0.590317i	$0.200997\pi$
$858$	90.1604	3.07803
$859$	45.2524	1.54399	0.771996	−	0.635627i	$-0.219259\pi$
$859$	45.2524	1.54399	0.771996	+	0.635627i	$0.219259\pi$
$860$	−160.440	−5.47094
$861$	−8.22393	−0.280271
$862$	2.09629	0.0713998
$863$	48.8160	1.66172	0.830858	−	0.556485i	$-0.187850\pi$
$863$	48.8160	1.66172	0.830858	+	0.556485i	$0.187850\pi$
$864$	13.9103	0.473239
$865$	12.2623	0.416931
$866$	34.3030	1.16566
$867$	−33.1454	−1.12568
$868$	−49.5119	−1.68054
$869$	60.6020	2.05578
$870$	79.4106	2.69227
$871$	1.05679	0.0358078
$872$	−30.8187	−1.04365
$873$	−4.40771	−0.149179
$874$	56.6265	1.91542
$875$	−8.19946	−0.277192
$876$	−21.1127	−0.713331
$877$	−49.7198	−1.67892	−0.839460	−	0.543422i	$-0.817128\pi$
$877$	−49.7198	−1.67892	−0.839460	+	0.543422i	$0.817128\pi$
$878$	−53.6905	−1.81197
$879$	−11.3679	−0.383428
$880$	169.770	5.72294
$881$	7.69596	0.259283	0.129642	−	0.991561i	$-0.458617\pi$
$881$	7.69596	0.259283	0.129642	+	0.991561i	$0.458617\pi$
$882$	5.78194	0.194688
$883$	41.9626	1.41215	0.706077	−	0.708135i	$-0.250463\pi$
$883$	41.9626	1.41215	0.706077	+	0.708135i	$0.250463\pi$
$884$	−239.085	−8.04131
$885$	16.3764	0.550486
$886$	−69.6391	−2.33957
$887$	−13.0924	−0.439599	−0.219799	−	0.975545i	$-0.570540\pi$
$887$	−13.0924	−0.439599	−0.219799	+	0.975545i	$0.570540\pi$
$888$	−76.8899	−2.58026
$889$	9.58536	0.321483
$890$	83.9835	2.81513
$891$	5.07261	0.169939
$892$	−67.6074	−2.26366
$893$	8.32423	0.278560
$894$	54.1650	1.81155
$895$	43.5550	1.45588
$896$	−22.0079	−0.735231
$897$	−48.9011	−1.63276
$898$	82.1551	2.74155
$899$	−45.3022	−1.51091
$900$	18.8329	0.627764
$901$	−39.8498	−1.32759
$902$	−50.4127	−1.67856
$903$	23.6461	0.786893
$904$	51.1299	1.70056
$905$	−0.0131809	−0.000438149 0
$906$	−4.01465	−0.133378
$907$	−37.0287	−1.22952	−0.614759	−	0.788715i	$-0.710747\pi$
$907$	−37.0287	−1.22952	−0.614759	+	0.788715i	$0.710747\pi$
$908$	−132.407	−4.39410
$909$	−3.12654	−0.103701
$910$	−115.350	−3.82381
$911$	2.78950	0.0924204	0.0462102	−	0.998932i	$-0.485286\pi$
$911$	2.78950	0.0924204	0.0462102	+	0.998932i	$0.485286\pi$
$912$	33.1025	1.09613
$913$	3.19033	0.105585
$914$	5.04675	0.166932
$915$	21.2507	0.702528
$916$	143.654	4.74646
$917$	39.1534	1.29296
$918$	−18.7891	−0.620134
$919$	16.7999	0.554176	0.277088	−	0.960844i	$-0.410631\pi$
$919$	16.7999	0.554176	0.277088	+	0.960844i	$0.410631\pi$
$920$	−174.054	−5.73839
$921$	−9.43381	−0.310855
$922$	−49.1930	−1.62009
$923$	59.3692	1.95416
$924$	−56.1357	−1.84673
$925$	−35.6167	−1.17107
$926$	−99.1994	−3.25989
$927$	10.2674	0.337226
$928$	−140.849	−4.62359
$929$	14.8232	0.486333	0.243166	−	0.969985i	$-0.421814\pi$
$929$	14.8232	0.486333	0.243166	+	0.969985i	$0.421814\pi$
$930$	−35.0884	−1.15060
$931$	6.37067	0.208790
$932$	59.3411	1.94378
$933$	8.25927	0.270396
$934$	14.2654	0.466777
$935$	−106.174	−3.47226
$936$	−54.0357	−1.76621
$937$	−15.1830	−0.496007	−0.248004	−	0.968759i	$-0.579775\pi$
$937$	−15.1830	−0.496007	−0.248004	+	0.968759i	$0.579775\pi$
$938$	−0.919070	−0.0300087
$939$	−1.56342	−0.0510203
$940$	−42.4186	−1.38354
$941$	24.7180	0.805782	0.402891	−	0.915248i	$-0.368005\pi$
$941$	24.7180	0.805782	0.402891	+	0.915248i	$0.368005\pi$
$942$	17.1113	0.557517
$943$	27.3428	0.890403
$944$	−62.7344	−2.04183
$945$	−6.48983	−0.211114
$946$	144.950	4.71274
$947$	−12.9585	−0.421093	−0.210547	−	0.977584i	$-0.567524\pi$
$947$	−12.9585	−0.421093	−0.210547	+	0.977584i	$0.567524\pi$
$948$	−60.2144	−1.95567
$949$	28.0602	0.910874
$950$	28.9846	0.940384
$951$	−9.97320	−0.323403
$952$	125.420	4.06488
$953$	−6.02229	−0.195081	−0.0975405	−	0.995232i	$-0.531098\pi$
$953$	−6.02229	−0.195081	−0.0975405	+	0.995232i	$0.531098\pi$
$954$	−14.9315	−0.483424
$955$	60.7953	1.96729
$956$	140.181	4.53378
$957$	−51.3628	−1.66032
$958$	−26.5200	−0.856823
$959$	43.4626	1.40348
$960$	−42.1576	−1.36063
$961$	−10.9827	−0.354282
$962$	169.420	5.46233
$963$	−9.08282	−0.292690
$964$	−51.1195	−1.64645
$965$	−2.39195	−0.0769997
$966$	42.5285	1.36833
$967$	27.7903	0.893677	0.446839	−	0.894615i	$-0.352550\pi$
$967$	27.7903	0.893677	0.446839	+	0.894615i	$0.352550\pi$
$968$	−118.832	−3.81939
$969$	−20.7023	−0.665053
$970$	34.5681	1.10991
$971$	56.0877	1.79994	0.899970	−	0.435952i	$-0.143588\pi$
$971$	56.0877	1.79994	0.899970	+	0.435952i	$0.143588\pi$
$972$	−5.04016	−0.161663
$973$	−38.3172	−1.22839
$974$	−36.9465	−1.18384
$975$	−25.0303	−0.801611
$976$	−81.4070	−2.60577
$977$	−12.2814	−0.392918	−0.196459	−	0.980512i	$-0.562944\pi$
$977$	−12.2814	−0.392918	−0.196459	+	0.980512i	$0.562944\pi$
$978$	59.2216	1.89370
$979$	−54.3205	−1.73609
$980$	−32.4636	−1.03701
$981$	3.82055	0.121981
$982$	−10.7195	−0.342072
$983$	−39.3671	−1.25561	−0.627807	−	0.778369i	$-0.716047\pi$
$983$	−39.3671	−1.25561	−0.627807	+	0.778369i	$0.716047\pi$
$984$	30.2138	0.963179
$985$	−0.627417	−0.0199912
$986$	190.250	6.05878
$987$	6.25179	0.198997
$988$	−98.7052	−3.14023
$989$	−78.6180	−2.49991
$990$	−39.7826	−1.26438
$991$	−11.3532	−0.360645	−0.180323	−	0.983608i	$-0.557714\pi$
$991$	−11.3532	−0.360645	−0.180323	+	0.983608i	$0.557714\pi$
$992$	62.2357	1.97598
$993$	−9.59505	−0.304490
$994$	−51.6324	−1.63768
$995$	63.0852	1.99994
$996$	−3.16993	−0.100443
$997$	−29.9521	−0.948592	−0.474296	−	0.880365i	$-0.657297\pi$
$997$	−29.9521	−0.948592	−0.474296	+	0.880365i	$0.657297\pi$
$998$	40.7747	1.29070
$999$	9.53194	0.301577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.5	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.5	✓	119	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65333 q^{2} -1.00000 q^{3} +5.04016 q^{4} +2.95577 q^{5} +2.65333 q^{6} +2.19565 q^{7} -8.06655 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.65333 q^{2} -1.00000 q^{3} +5.04016 q^{4} +2.95577 q^{5} +2.65333 q^{6} +2.19565 q^{7} -8.06655 q^{8} +1.00000 q^{9} -7.84263 q^{10} +5.07261 q^{11} -5.04016 q^{12} +6.69874 q^{13} -5.82578 q^{14} -2.95577 q^{15} +11.3229 q^{16} -7.08134 q^{17} -2.65333 q^{18} -2.92350 q^{19} +14.8976 q^{20} -2.19565 q^{21} -13.4593 q^{22} +7.30005 q^{23} +8.06655 q^{24} +3.73657 q^{25} -17.7740 q^{26} -1.00000 q^{27} +11.0664 q^{28} +10.1255 q^{29} +7.84263 q^{30} -4.47407 q^{31} -13.9103 q^{32} -5.07261 q^{33} +18.7891 q^{34} +6.48983 q^{35} +5.04016 q^{36} -9.53194 q^{37} +7.75700 q^{38} -6.69874 q^{39} -23.8429 q^{40} +3.74556 q^{41} +5.82578 q^{42} -10.7695 q^{43} +25.5668 q^{44} +2.95577 q^{45} -19.3694 q^{46} -2.84735 q^{47} -11.3229 q^{48} -2.17913 q^{49} -9.91435 q^{50} +7.08134 q^{51} +33.7627 q^{52} +5.62744 q^{53} +2.65333 q^{54} +14.9935 q^{55} -17.7113 q^{56} +2.92350 q^{57} -26.8663 q^{58} -5.54048 q^{59} -14.8976 q^{60} -7.18958 q^{61} +11.8712 q^{62} +2.19565 q^{63} +14.2628 q^{64} +19.7999 q^{65} +13.4593 q^{66} +0.157759 q^{67} -35.6911 q^{68} -7.30005 q^{69} -17.2197 q^{70} +8.86275 q^{71} -8.06655 q^{72} +4.18889 q^{73} +25.2914 q^{74} -3.73657 q^{75} -14.7349 q^{76} +11.1377 q^{77} +17.7740 q^{78} +11.9469 q^{79} +33.4679 q^{80} +1.00000 q^{81} -9.93820 q^{82} +0.628933 q^{83} -11.0664 q^{84} -20.9308 q^{85} +28.5751 q^{86} -10.1255 q^{87} -40.9185 q^{88} -10.7086 q^{89} -7.84263 q^{90} +14.7081 q^{91} +36.7934 q^{92} +4.47407 q^{93} +7.55497 q^{94} -8.64118 q^{95} +13.9103 q^{96} -4.40771 q^{97} +5.78194 q^{98} +5.07261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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