LMFDB - Embedded newform 49.24.a.h.1.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,24,Mod(1,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.1"); S:= CuspForms(chi, 24); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 24, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	49.a (trivial)

Newform invariants

comment:select newform

sage:traces = [24,6030,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$164.249978299$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+5395.50 q^{2} -146944. q^{3} +2.07228e7 q^{4} +2.11846e8 q^{5} -7.92838e8 q^{6} +6.65494e10 q^{8} -7.25506e10 q^{9} +1.14302e12 q^{10} -2.64619e11 q^{11} -3.04510e12 q^{12} -4.96373e11 q^{13} -3.11296e13 q^{15} +1.85232e14 q^{16} -1.76570e14 q^{17} -3.91447e14 q^{18} +5.35699e14 q^{19} +4.39006e15 q^{20} -1.42775e15 q^{22} +6.88068e15 q^{23} -9.77905e15 q^{24} +3.29579e16 q^{25} -2.67818e15 q^{26} +2.44947e16 q^{27} +7.98920e16 q^{29} -1.67960e17 q^{30} -1.52936e17 q^{31} +4.41161e17 q^{32} +3.88843e16 q^{33} -9.52685e17 q^{34} -1.50345e18 q^{36} +1.47867e18 q^{37} +2.89036e18 q^{38} +7.29391e16 q^{39} +1.40982e19 q^{40} +2.17208e17 q^{41} +1.06138e18 q^{43} -5.48366e18 q^{44} -1.53696e19 q^{45} +3.71247e19 q^{46} +1.36734e19 q^{47} -2.72187e19 q^{48} +1.77825e20 q^{50} +2.59460e19 q^{51} -1.02863e19 q^{52} +2.49939e19 q^{53} +1.32161e20 q^{54} -5.60586e19 q^{55} -7.87178e19 q^{57} +4.31058e20 q^{58} -2.24890e20 q^{59} -6.45094e20 q^{60} +1.36965e20 q^{61} -8.25165e20 q^{62} +8.26451e20 q^{64} -1.05155e20 q^{65} +2.09800e20 q^{66} +4.53939e20 q^{67} -3.65904e21 q^{68} -1.01108e21 q^{69} -3.25278e21 q^{71} -4.82820e21 q^{72} -2.95436e20 q^{73} +7.97819e21 q^{74} -4.84298e21 q^{75} +1.11012e22 q^{76} +3.93543e20 q^{78} +7.94365e21 q^{79} +3.92407e22 q^{80} +3.23079e21 q^{81} +1.17194e21 q^{82} -7.92446e21 q^{83} -3.74057e22 q^{85} +5.72668e21 q^{86} -1.17397e22 q^{87} -1.76102e22 q^{88} -1.82377e22 q^{89} -8.29266e22 q^{90} +1.42587e23 q^{92} +2.24730e22 q^{93} +7.37749e22 q^{94} +1.13486e23 q^{95} -6.48261e22 q^{96} -3.45535e20 q^{97} +1.91983e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6030 q^{2} + 99000906 q^{4} + 31751706690 q^{8} + 975236583640 q^{9} + 3514223137536 q^{11} + 96662500006976 q^{15} + 850136746459362 q^{16} - 774764811988990 q^{18} + 81\!\cdots\!60 q^{22} + 34\!\cdots\!60 q^{23}+ \cdots + 70\!\cdots\!64 q^{99}+O(q^{100}) $ 24 * q + 6030 * q^2 + 99000906 * q^4 + 31751706690 * q^8 + 975236583640 * q^9 + 3514223137536 * q^11 + 96662500006976 * q^15 + 850136746459362 * q^16 - 774764811988990 * q^18 + 8148420455553060 * q^22 + 34774948016084160 * q^23 + 94149150991117272 * q^25 + 190645622093096064 * q^29 - 634449556982285592 * q^30 - 1493697165631220430 * q^32 + 6671026323612877990 * q^36 + 878462893450581120 * q^37 + 6115839814038109120 * q^39 + 20811373010373199680 * q^43 + 54730049479951369500 * q^44 + 73203364608168908808 * q^46 + 387333163519636443066 * q^50 + 270153244272168521696 * q^51 + 34330885176487486320 * q^53 + 496656755807681949600 * q^57 - 397574761992930674580 * q^58 + 292003879381856022136 * q^60 + 2439494576203335787554 * q^64 + 4869166958052334391664 * q^65 - 1121753136531158010720 * q^67 - 1755055962268130457216 * q^71 - 32377694763810926605650 * q^72 + 1005354247436267388732 * q^74 - 79646865826469682676320 * q^78 + 5008005983294871013824 * q^79 + 21826965675021517050808 * q^81 + 20177850245757616713456 * q^85 + 38898565641929075253660 * q^86 - 21751191568485361565940 * q^88 + 247141757180010545124120 * q^92 + 241670386431567345282560 * q^93 + 278606632818920869216512 * q^95 + 708951281314482353318464 * q^99

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 $

$2$	5395.50	1.86289	0.931445	−	0.363883i	$-0.118549\pi$
$2$	5395.50	1.86289	0.931445	+	0.363883i	$0.118549\pi$
$3$	−146944.	−0.478915	−0.239457	−	0.970907i	$-0.576970\pi$
$3$	−146944.	−0.478915	−0.239457	+	0.970907i	$0.576970\pi$
$4$	2.07228e7	2.47036
$5$	2.11846e8	1.94029	0.970143	−	0.242533i	$-0.0779781\pi$
$5$	2.11846e8	1.94029	0.970143	+	0.242533i	$0.0779781\pi$
$6$	−7.92838e8	−0.892165
$7$	0	0
$7$	0	0
$8$	6.65494e10	2.73911
$9$	−7.25506e10	−0.770641
$10$	1.14302e12	3.61454
$11$	−2.64619e11	−0.279644	−0.139822	−	0.990177i	$-0.544653\pi$
$11$	−2.64619e11	−0.279644	−0.139822	+	0.990177i	$0.544653\pi$
$12$	−3.04510e12	−1.18309
$13$	−4.96373e11	−0.0768173	−0.0384087	−	0.999262i	$-0.512229\pi$
$13$	−4.96373e11	−0.0768173	−0.0384087	+	0.999262i	$0.512229\pi$
$14$	0	0
$15$	−3.11296e13	−0.929232
$16$	1.85232e14	2.63230
$17$	−1.76570e14	−1.24955	−0.624776	−	0.780804i	$-0.714810\pi$
$17$	−1.76570e14	−1.24955	−0.624776	+	0.780804i	$0.714810\pi$
$18$	−3.91447e14	−1.43562
$19$	5.35699e14	1.05500	0.527502	−	0.849554i	$-0.323129\pi$
$19$	5.35699e14	1.05500	0.527502	+	0.849554i	$0.323129\pi$
$20$	4.39006e15	4.79320
$21$	0	0
$22$	−1.42775e15	−0.520946
$23$	6.88068e15	1.50578	0.752889	−	0.658147i	$-0.228660\pi$
$23$	6.88068e15	1.50578	0.752889	+	0.658147i	$0.228660\pi$
$24$	−9.77905e15	−1.31180
$25$	3.29579e16	2.76471
$26$	−2.67818e15	−0.143102
$27$	2.44947e16	0.847986
$28$	0	0
$29$	7.98920e16	1.21598	0.607990	−	0.793945i	$-0.291976\pi$
$29$	7.98920e16	1.21598	0.607990	+	0.793945i	$0.291976\pi$
$30$	−1.67960e17	−1.73106
$31$	−1.52936e17	−1.08106	−0.540529	−	0.841325i	$-0.681776\pi$
$31$	−1.52936e17	−1.08106	−0.540529	+	0.841325i	$0.681776\pi$
$32$	4.41161e17	2.16458
$33$	3.88843e16	0.133926
$34$	−9.52685e17	−2.32778
$35$	0	0
$36$	−1.50345e18	−1.90376
$37$	1.47867e18	1.36632	0.683161	−	0.730268i	$-0.260605\pi$
$37$	1.47867e18	1.36632	0.683161	+	0.730268i	$0.260605\pi$
$38$	2.89036e18	1.96536
$39$	7.29391e16	0.0367890
$40$	1.40982e19	5.31466
$41$	2.17208e17	0.0616397	0.0308199	−	0.999525i	$-0.490188\pi$
$41$	2.17208e17	0.0616397	0.0308199	+	0.999525i	$0.490188\pi$
$42$	0	0
$43$	1.06138e18	0.174174	0.0870871	−	0.996201i	$-0.472244\pi$
$43$	1.06138e18	0.174174	0.0870871	+	0.996201i	$0.472244\pi$
$44$	−5.48366e18	−0.690820
$45$	−1.53696e19	−1.49526
$46$	3.71247e19	2.80510
$47$	1.36734e19	0.806773	0.403386	−	0.915030i	$-0.367833\pi$
$47$	1.36734e19	0.806773	0.403386	+	0.915030i	$0.367833\pi$
$48$	−2.72187e19	−1.26065
$49$	0	0
$50$	1.77825e20	5.15035
$51$	2.59460e19	0.598429
$52$	−1.02863e19	−0.189766
$53$	2.49939e19	0.370391	0.185196	−	0.982702i	$-0.440708\pi$
$53$	2.49939e19	0.370391	0.185196	+	0.982702i	$0.440708\pi$
$54$	1.32161e20	1.57970
$55$	−5.60586e19	−0.542589
$56$	0	0
$57$	−7.87178e19	−0.505257
$58$	4.31058e20	2.26524
$59$	−2.24890e20	−0.970895	−0.485448	−	0.874266i	$-0.661343\pi$
$59$	−2.24890e20	−0.970895	−0.485448	+	0.874266i	$0.661343\pi$
$60$	−6.45094e20	−2.29553
$61$	1.36965e20	0.403012	0.201506	−	0.979487i	$-0.435417\pi$
$61$	1.36965e20	0.403012	0.201506	+	0.979487i	$0.435417\pi$
$62$	−8.25165e20	−2.01389
$63$	0	0
$64$	8.26451e20	1.40006
$65$	−1.05155e20	−0.149048
$66$	2.09800e20	0.249488
$67$	4.53939e20	0.454085	0.227043	−	0.973885i	$-0.427094\pi$
$67$	4.53939e20	0.454085	0.227043	+	0.973885i	$0.427094\pi$
$68$	−3.65904e21	−3.08684
$69$	−1.01108e21	−0.721140
$70$	0	0
$71$	−3.25278e21	−1.67026	−0.835130	−	0.550053i	$-0.814608\pi$
$71$	−3.25278e21	−1.67026	−0.835130	+	0.550053i	$0.814608\pi$
$72$	−4.82820e21	−2.11087
$73$	−2.95436e20	−0.110218	−0.0551088	−	0.998480i	$-0.517551\pi$
$73$	−2.95436e20	−0.110218	−0.0551088	+	0.998480i	$0.517551\pi$
$74$	7.97819e21	2.54531
$75$	−4.84298e21	−1.32406
$76$	1.11012e22	2.60623
$77$	0	0
$78$	3.93543e20	0.0685337
$79$	7.94365e21	1.19484	0.597418	−	0.801930i	$-0.296193\pi$
$79$	7.94365e21	1.19484	0.597418	+	0.801930i	$0.296193\pi$
$80$	3.92407e22	5.10742
$81$	3.23079e21	0.364528
$82$	1.17194e21	0.114828
$83$	−7.92446e21	−0.675417	−0.337708	−	0.941251i	$-0.609652\pi$
$83$	−7.92446e21	−0.675417	−0.337708	+	0.941251i	$0.609652\pi$
$84$	0	0
$85$	−3.74057e22	−2.42449
$86$	5.72668e21	0.324467
$87$	−1.17397e22	−0.582351
$88$	−1.76102e22	−0.765975
$89$	−1.82377e22	−0.696603	−0.348301	−	0.937383i	$-0.613241\pi$
$89$	−1.82377e22	−0.696603	−0.348301	+	0.937383i	$0.613241\pi$
$90$	−8.29266e22	−2.78551
$91$	0	0
$92$	1.42587e23	3.71981
$93$	2.24730e22	0.517735
$94$	7.37749e22	1.50293
$95$	1.13486e23	2.04701
$96$	−6.48261e22	−1.03665
$97$	−3.45535e20	−0.00490475	−0.00245238	−	0.999997i	$-0.500781\pi$
$97$	−3.45535e20	−0.00490475	−0.00245238	+	0.999997i	$0.500781\pi$
$98$	0	0
$99$	1.91983e22	0.215505
$100$	6.82982e23	6.82982
$101$	−6.11282e22	−0.545187	−0.272594	−	0.962129i	$-0.587881\pi$
$101$	−6.11282e22	−0.545187	−0.272594	+	0.962129i	$0.587881\pi$
$102$	1.39992e23	1.11481
$103$	9.31986e22	0.663409	0.331705	−	0.943383i	$-0.392376\pi$
$103$	9.31986e22	0.663409	0.331705	+	0.943383i	$0.392376\pi$
$104$	−3.30333e22	−0.210411
$105$	0	0
$106$	1.34854e23	0.689998
$107$	6.74390e22	0.309740	0.154870	−	0.987935i	$-0.450504\pi$
$107$	6.74390e22	0.309740	0.154870	+	0.987935i	$0.450504\pi$
$108$	5.07600e23	2.09483
$109$	−3.37000e23	−1.25091	−0.625454	−	0.780261i	$-0.715086\pi$
$109$	−3.37000e23	−1.25091	−0.625454	+	0.780261i	$0.715086\pi$
$110$	−3.02464e23	−1.01078
$111$	−2.17283e23	−0.654352
$112$	0	0
$113$	1.69780e23	0.416376	0.208188	−	0.978089i	$-0.433243\pi$
$113$	1.69780e23	0.416376	0.208188	+	0.978089i	$0.433243\pi$
$114$	−4.24722e23	−0.941238
$115$	1.45765e24	2.92164
$116$	1.65559e24	3.00390
$117$	3.60121e22	0.0591986
$118$	−1.21340e24	−1.80867
$119$	0	0
$120$	−2.07166e24	−2.54527
$121$	−8.25407e23	−0.921799
$122$	7.38997e23	0.750766
$123$	−3.19174e22	−0.0295202
$124$	−3.16926e24	−2.67060
$125$	4.45661e24	3.42405
$126$	0	0
$127$	6.51558e23	0.417071	0.208536	−	0.978015i	$-0.433130\pi$
$127$	6.51558e23	0.417071	0.208536	+	0.978015i	$0.433130\pi$
$128$	7.58390e23	0.443586
$129$	−1.55964e23	−0.0834146
$130$	−5.67363e23	−0.277659
$131$	1.23011e24	0.551219	0.275609	−	0.961270i	$-0.411120\pi$
$131$	1.23011e24	0.551219	0.275609	+	0.961270i	$0.411120\pi$
$132$	8.05792e23	0.330844
$133$	0	0
$134$	2.44923e24	0.845910
$135$	5.18911e24	1.64534
$136$	−1.17506e25	−3.42266
$137$	1.77817e24	0.476087	0.238044	−	0.971254i	$-0.423494\pi$
$137$	1.77817e24	0.476087	0.238044	+	0.971254i	$0.423494\pi$
$138$	−5.45526e24	−1.34340
$139$	−7.90621e24	−1.79183	−0.895917	−	0.444221i	$-0.853481\pi$
$139$	−7.90621e24	−1.79183	−0.895917	+	0.444221i	$0.853481\pi$
$140$	0	0
$141$	−2.00923e24	−0.386375
$142$	−1.75504e25	−3.11151
$143$	1.31350e23	0.0214815
$144$	−1.34387e25	−2.02856
$145$	1.69248e25	2.35935
$146$	−1.59403e24	−0.205323
$147$	0	0
$148$	3.06423e25	3.37530
$149$	−2.75691e24	−0.281048	−0.140524	−	0.990077i	$-0.544879\pi$
$149$	−2.75691e24	−0.281048	−0.140524	+	0.990077i	$0.544879\pi$
$150$	−2.61303e25	−2.46658
$151$	−7.60291e24	−0.664883	−0.332441	−	0.943124i	$-0.607872\pi$
$151$	−7.60291e24	−0.664883	−0.332441	+	0.943124i	$0.607872\pi$
$152$	3.56504e25	2.88977
$153$	1.28103e25	0.962956
$154$	0	0
$155$	−3.23988e25	−2.09756
$156$	1.51151e24	0.0908818
$157$	−1.41120e25	−0.788392	−0.394196	−	0.919026i	$-0.628977\pi$
$157$	−1.41120e25	−0.788392	−0.394196	+	0.919026i	$0.628977\pi$
$158$	4.28600e25	2.22585
$159$	−3.67270e24	−0.177386
$160$	9.34584e25	4.19990
$161$	0	0
$162$	1.74317e25	0.679075
$163$	3.53909e25	1.28450	0.642250	−	0.766495i	$-0.278001\pi$
$163$	3.53909e25	1.28450	0.642250	+	0.766495i	$0.278001\pi$
$164$	4.50116e24	0.152272
$165$	8.23749e24	0.259854
$166$	−4.27565e25	−1.25823
$167$	3.38504e25	0.929661	0.464830	−	0.885400i	$-0.346115\pi$
$167$	3.38504e25	0.929661	0.464830	+	0.885400i	$0.346115\pi$
$168$	0	0
$169$	−4.15075e25	−0.994099
$170$	−2.01823e26	−4.51656
$171$	−3.88652e25	−0.813029
$172$	2.19948e25	0.430272
$173$	−3.37655e24	−0.0617934	−0.0308967	−	0.999523i	$-0.509836\pi$
$173$	−3.37655e24	−0.0617934	−0.0308967	+	0.999523i	$0.509836\pi$
$174$	−6.33415e25	−1.08486
$175$	0	0
$176$	−4.90158e25	−0.736107
$177$	3.30463e25	0.464976
$178$	−9.84016e25	−1.29769
$179$	−6.91526e25	−0.855064	−0.427532	−	0.904000i	$-0.640617\pi$
$179$	−6.91526e25	−0.855064	−0.427532	+	0.904000i	$0.640617\pi$
$180$	−3.18501e26	−3.69383
$181$	2.87048e25	0.312357	0.156178	−	0.987729i	$-0.450083\pi$
$181$	2.87048e25	0.312357	0.156178	+	0.987729i	$0.450083\pi$
$182$	0	0
$183$	−2.01263e25	−0.193008
$184$	4.57905e26	4.12449
$185$	3.13252e26	2.65106
$186$	1.21253e26	0.964483
$187$	4.67238e25	0.349430
$188$	2.83352e26	1.99302
$189$	0	0
$190$	6.12313e26	3.81335
$191$	9.47741e25	0.555656	0.277828	−	0.960631i	$-0.410386\pi$
$191$	9.47741e25	0.555656	0.277828	+	0.960631i	$0.410386\pi$
$192$	−1.21442e26	−0.670511
$193$	−6.88246e25	−0.357960	−0.178980	−	0.983853i	$-0.557280\pi$
$193$	−6.88246e25	−0.357960	−0.178980	+	0.983853i	$0.557280\pi$
$194$	−1.86434e24	−0.00913701
$195$	1.54519e25	0.0713811
$196$	0	0
$197$	1.86705e26	0.766998	0.383499	−	0.923541i	$-0.374719\pi$
$197$	1.86705e26	0.766998	0.383499	+	0.923541i	$0.374719\pi$
$198$	1.03584e26	0.401462
$199$	−2.66630e26	−0.975212	−0.487606	−	0.873064i	$-0.662130\pi$
$199$	−2.66630e26	−0.975212	−0.487606	+	0.873064i	$0.662130\pi$
$200$	2.19333e27	7.57285
$201$	−6.67038e25	−0.217468
$202$	−3.29817e26	−1.01562
$203$	0	0
$204$	5.37674e26	1.47833
$205$	4.60146e25	0.119599
$206$	5.02854e26	1.23586
$207$	−4.99197e26	−1.16041
$208$	−9.19439e25	−0.202206
$209$	−1.41756e26	−0.295025
$210$	0	0
$211$	6.42110e26	1.19774	0.598868	−	0.800848i	$-0.295617\pi$
$211$	6.42110e26	1.19774	0.598868	+	0.800848i	$0.295617\pi$
$212$	5.17944e26	0.914998
$213$	4.77978e26	0.799912
$214$	3.63867e26	0.577012
$215$	2.24850e26	0.337948
$216$	1.63011e27	2.32273
$217$	0	0
$218$	−1.81828e27	−2.33030
$219$	4.34127e25	0.0527849
$220$	−1.16169e27	−1.34039
$221$	8.76446e25	0.0959873
$222$	−1.17235e27	−1.21898
$223$	−1.14904e27	−1.13457	−0.567283	−	0.823523i	$-0.692006\pi$
$223$	−1.14904e27	−1.13457	−0.567283	+	0.823523i	$0.692006\pi$
$224$	0	0
$225$	−2.39112e27	−2.13060
$226$	9.16051e26	0.775662
$227$	−1.07153e27	−0.862399	−0.431199	−	0.902257i	$-0.641909\pi$
$227$	−1.07153e27	−0.862399	−0.431199	+	0.902257i	$0.641909\pi$
$228$	−1.63126e27	−1.24816
$229$	−1.07256e27	−0.780396	−0.390198	−	0.920731i	$-0.627593\pi$
$229$	−1.07256e27	−0.780396	−0.390198	+	0.920731i	$0.627593\pi$
$230$	7.86473e27	5.44269
$231$	0	0
$232$	5.31677e27	3.33070
$233$	−1.90580e27	−1.13627	−0.568137	−	0.822934i	$-0.692336\pi$
$233$	−1.90580e27	−1.13627	−0.568137	+	0.822934i	$0.692336\pi$
$234$	1.94303e26	0.110280
$235$	2.89666e27	1.56537
$236$	−4.66037e27	−2.39846
$237$	−1.16727e27	−0.572225
$238$	0	0
$239$	−9.46975e25	−0.0421466	−0.0210733	−	0.999778i	$-0.506708\pi$
$239$	−9.46975e25	−0.0421466	−0.0210733	+	0.999778i	$0.506708\pi$
$240$	−5.76619e27	−2.44602
$241$	−4.69958e27	−1.90048	−0.950240	−	0.311520i	$-0.899162\pi$
$241$	−4.69958e27	−1.90048	−0.950240	+	0.311520i	$0.899162\pi$
$242$	−4.45349e27	−1.71721
$243$	−2.78075e27	−1.02256
$244$	2.83831e27	0.995582
$245$	0	0
$246$	−1.72210e26	−0.0549928
$247$	−2.65906e26	−0.0810426
$248$	−1.01778e28	−2.96114
$249$	1.16445e27	0.323467
$250$	2.40457e28	6.37862
$251$	−5.00804e27	−1.26888	−0.634440	−	0.772972i	$-0.718769\pi$
$251$	−5.00804e27	−1.26888	−0.634440	+	0.772972i	$0.718769\pi$
$252$	0	0
$253$	−1.82076e27	−0.421082
$254$	3.51548e27	0.776957
$255$	5.49656e27	1.16112
$256$	−2.84088e27	−0.573711
$257$	2.05974e27	0.397724	0.198862	−	0.980028i	$-0.436275\pi$
$257$	2.05974e27	0.397724	0.198862	+	0.980028i	$0.436275\pi$
$258$	−8.41503e26	−0.155392
$259$	0	0
$260$	−2.17910e27	−0.368201
$261$	−5.79621e27	−0.937084
$262$	6.63706e27	1.02686
$263$	−1.96389e27	−0.290821	−0.145411	−	0.989371i	$-0.546450\pi$
$263$	−1.96389e27	−0.290821	−0.145411	+	0.989371i	$0.546450\pi$
$264$	2.58772e27	0.366837
$265$	5.29486e27	0.718665
$266$	0	0
$267$	2.67993e27	0.333613
$268$	9.40691e27	1.12175
$269$	−3.50401e27	−0.400326	−0.200163	−	0.979763i	$-0.564147\pi$
$269$	−3.50401e27	−0.400326	−0.200163	+	0.979763i	$0.564147\pi$
$270$	2.79979e28	3.06508
$271$	3.15659e27	0.331186	0.165593	−	0.986194i	$-0.447046\pi$
$271$	3.15659e27	0.331186	0.165593	+	0.986194i	$0.447046\pi$
$272$	−3.27064e28	−3.28920
$273$	0	0
$274$	9.59411e27	0.886897
$275$	−8.72130e27	−0.773135
$276$	−2.09524e28	−1.78147
$277$	6.74973e26	0.0550515	0.0275257	−	0.999621i	$-0.491237\pi$
$277$	6.74973e26	0.0550515	0.0275257	+	0.999621i	$0.491237\pi$
$278$	−4.26580e28	−3.33799
$279$	1.10956e28	0.833108
$280$	0	0
$281$	1.13816e28	0.787189	0.393594	−	0.919284i	$-0.371231\pi$
$281$	1.13816e28	0.787189	0.393594	+	0.919284i	$0.371231\pi$
$282$	−1.08408e28	−0.719774
$283$	2.71342e28	1.72971	0.864855	−	0.502021i	$-0.167410\pi$
$283$	2.71342e28	1.72971	0.864855	+	0.502021i	$0.167410\pi$
$284$	−6.74069e28	−4.12613
$285$	−1.66761e28	−0.980343
$286$	7.08698e26	0.0400176
$287$	0	0
$288$	−3.20065e28	−1.66811
$289$	1.12094e28	0.561382
$290$	9.13180e28	4.39521
$291$	5.07744e25	0.00234896
$292$	−6.12228e27	−0.272277
$293$	1.63073e28	0.697277	0.348638	−	0.937257i	$-0.386644\pi$
$293$	1.63073e28	0.697277	0.348638	+	0.937257i	$0.386644\pi$
$294$	0	0
$295$	−4.76422e28	−1.88382
$296$	9.84049e28	3.74250
$297$	−6.48176e27	−0.237134
$298$	−1.48749e28	−0.523562
$299$	−3.41538e27	−0.115670
$300$	−1.00360e29	−3.27090
$301$	0	0
$302$	−4.10215e28	−1.23860
$303$	8.98244e27	0.261098
$304$	9.92284e28	2.77709
$305$	2.90156e28	0.781958
$306$	6.91178e28	1.79388
$307$	−7.01334e27	−0.175321	−0.0876604	−	0.996150i	$-0.527939\pi$
$307$	−7.01334e27	−0.175321	−0.0876604	+	0.996150i	$0.527939\pi$
$308$	0	0
$309$	−1.36950e28	−0.317717
$310$	−1.74808e29	−3.90753
$311$	−5.39255e28	−1.16158	−0.580791	−	0.814053i	$-0.697256\pi$
$311$	−5.39255e28	−1.16158	−0.580791	+	0.814053i	$0.697256\pi$
$312$	4.85405e27	0.100769
$313$	−6.12699e28	−1.22599	−0.612995	−	0.790087i	$-0.710035\pi$
$313$	−6.12699e28	−1.22599	−0.612995	+	0.790087i	$0.710035\pi$
$314$	−7.61413e28	−1.46869
$315$	0	0
$316$	1.64615e29	2.95167
$317$	1.14376e29	1.97767	0.988837	−	0.149003i	$-0.0476064\pi$
$317$	1.14376e29	1.97767	0.988837	+	0.149003i	$0.0476064\pi$
$318$	−1.98161e28	−0.330450
$319$	−2.11410e28	−0.340041
$320$	1.75081e29	2.71652
$321$	−9.90977e27	−0.148339
$322$	0	0
$323$	−9.45884e28	−1.31828
$324$	6.69511e28	0.900513
$325$	−1.63594e28	−0.212378
$326$	1.90952e29	2.39288
$327$	4.95202e28	0.599078
$328$	1.44550e28	0.168838
$329$	0	0
$330$	4.44454e28	0.484079
$331$	4.26019e27	0.0448133	0.0224066	−	0.999749i	$-0.492867\pi$
$331$	4.26019e27	0.0448133	0.0224066	+	0.999749i	$0.492867\pi$
$332$	−1.64217e29	−1.66852
$333$	−1.07279e29	−1.05294
$334$	1.82640e29	1.73185
$335$	9.61653e28	0.881056
$336$	0	0
$337$	−9.42207e28	−0.806125	−0.403063	−	0.915172i	$-0.632054\pi$
$337$	−9.42207e28	−0.806125	−0.403063	+	0.915172i	$0.632054\pi$
$338$	−2.23954e29	−1.85190
$339$	−2.49483e28	−0.199408
$340$	−7.75153e29	−5.98935
$341$	4.04697e28	0.302311
$342$	−2.09697e29	−1.51458
$343$	0	0
$344$	7.06343e28	0.477082
$345$	−2.14193e29	−1.39922
$346$	−1.82182e28	−0.115114
$347$	1.30731e28	0.0799079	0.0399540	−	0.999202i	$-0.487279\pi$
$347$	1.30731e28	0.0799079	0.0399540	+	0.999202i	$0.487279\pi$
$348$	−2.43280e29	−1.43861
$349$	3.15582e29	1.80559	0.902795	−	0.430071i	$-0.141511\pi$
$349$	3.15582e29	1.80559	0.902795	+	0.430071i	$0.141511\pi$
$350$	0	0
$351$	−1.21585e28	−0.0651400
$352$	−1.16740e29	−0.605310
$353$	2.27397e29	1.14124	0.570618	−	0.821216i	$-0.306704\pi$
$353$	2.27397e29	1.14124	0.570618	+	0.821216i	$0.306704\pi$
$354$	1.78302e29	0.866199
$355$	−6.89090e29	−3.24078
$356$	−3.77937e29	−1.72086
$357$	0	0
$358$	−3.73113e29	−1.59289
$359$	−1.99310e29	−0.824029	−0.412014	−	0.911177i	$-0.635175\pi$
$359$	−1.99310e29	−0.824029	−0.412014	+	0.911177i	$0.635175\pi$
$360$	−1.02284e30	−4.09569
$361$	2.91434e28	0.113033
$362$	1.54877e29	0.581886
$363$	1.21289e29	0.441463
$364$	0	0
$365$	−6.25871e28	−0.213854
$366$	−1.08591e29	−0.359553
$367$	4.03566e29	1.29495	0.647477	−	0.762085i	$-0.275824\pi$
$367$	4.03566e29	1.29495	0.647477	+	0.762085i	$0.275824\pi$
$368$	1.27452e30	3.96366
$369$	−1.57585e28	−0.0475021
$370$	1.69015e30	4.93862
$371$	0	0
$372$	4.65705e29	1.27899
$373$	−7.16275e29	−1.90734	−0.953670	−	0.300853i	$-0.902729\pi$
$373$	−7.16275e29	−1.90734	−0.953670	+	0.300853i	$0.902729\pi$
$374$	2.52099e29	0.650949
$375$	−6.54874e29	−1.63983
$376$	9.09957e29	2.20984
$377$	−3.96562e28	−0.0934084
$378$	0	0
$379$	−1.68238e29	−0.372883	−0.186442	−	0.982466i	$-0.559696\pi$
$379$	−1.68238e29	−0.372883	−0.186442	+	0.982466i	$0.559696\pi$
$380$	2.35175e30	5.05684
$381$	−9.57427e28	−0.199742
$382$	5.11354e29	1.03513
$383$	−3.80955e28	−0.0748321	−0.0374160	−	0.999300i	$-0.511913\pi$
$383$	−3.80955e28	−0.0748321	−0.0374160	+	0.999300i	$0.511913\pi$
$384$	−1.11441e29	−0.212440
$385$	0	0
$386$	−3.71343e29	−0.666840
$387$	−7.70038e28	−0.134226
$388$	−7.16047e27	−0.0121165
$389$	8.00421e29	1.31492	0.657458	−	0.753491i	$-0.271632\pi$
$389$	8.00421e29	1.31492	0.657458	+	0.753491i	$0.271632\pi$
$390$	8.33707e28	0.132975
$391$	−1.21492e30	−1.88155
$392$	0	0
$393$	−1.80758e29	−0.263987
$394$	1.00737e30	1.42883
$395$	1.68283e30	2.31832
$396$	3.97843e29	0.532374
$397$	−7.06194e29	−0.917980	−0.458990	−	0.888441i	$-0.651789\pi$
$397$	−7.06194e29	−0.917980	−0.458990	+	0.888441i	$0.651789\pi$
$398$	−1.43860e30	−1.81671
$399$	0	0
$400$	6.10485e30	7.27755
$401$	−5.71555e28	−0.0662061	−0.0331030	−	0.999452i	$-0.510539\pi$
$401$	−5.71555e28	−0.0662061	−0.0331030	+	0.999452i	$0.510539\pi$
$402$	−3.59900e29	−0.405119
$403$	7.59130e28	0.0830440
$404$	−1.26675e30	−1.34681
$405$	6.84430e29	0.707288
$406$	0	0
$407$	−3.91286e29	−0.382083
$408$	1.72669e30	1.63916
$409$	−1.18982e30	−1.09815	−0.549077	−	0.835772i	$-0.685021\pi$
$409$	−1.18982e30	−1.09815	−0.549077	+	0.835772i	$0.685021\pi$
$410$	2.48272e29	0.222799
$411$	−2.61292e29	−0.228005
$412$	1.93134e30	1.63886
$413$	0	0
$414$	−2.69342e30	−2.16172
$415$	−1.67877e30	−1.31050
$416$	−2.18980e29	−0.166277
$417$	1.16177e30	0.858136
$418$	−7.64845e29	−0.549600
$419$	1.90556e30	1.33217	0.666087	−	0.745874i	$-0.267968\pi$
$419$	1.90556e30	1.33217	0.666087	+	0.745874i	$0.267968\pi$
$420$	0	0
$421$	−2.33460e30	−1.54514	−0.772571	−	0.634928i	$-0.781030\pi$
$421$	−2.33460e30	−1.54514	−0.772571	+	0.634928i	$0.781030\pi$
$422$	3.46450e30	2.23125
$423$	−9.92013e29	−0.621732
$424$	1.66333e30	1.01454
$425$	−5.81939e30	−3.45465
$426$	2.57893e30	1.49015
$427$	0	0
$428$	1.39753e30	0.765168
$429$	−1.93011e28	−0.0102878
$430$	1.21318e30	0.629560
$431$	−9.97451e29	−0.503968	−0.251984	−	0.967731i	$-0.581083\pi$
$431$	−9.97451e29	−0.503968	−0.251984	+	0.967731i	$0.581083\pi$
$432$	4.53719e30	2.23215
$433$	−3.45904e29	−0.165708	−0.0828542	−	0.996562i	$-0.526404\pi$
$433$	−3.45904e29	−0.165708	−0.0828542	+	0.996562i	$0.526404\pi$
$434$	0	0
$435$	−2.48701e30	−1.12993
$436$	−6.98360e30	−3.09019
$437$	3.68597e30	1.58860
$438$	2.34233e29	0.0983323
$439$	2.61648e30	1.06998	0.534990	−	0.844858i	$-0.320315\pi$
$439$	2.61648e30	1.06998	0.534990	+	0.844858i	$0.320315\pi$
$440$	−3.73067e30	−1.48621
$441$	0	0
$442$	4.72887e29	0.178814
$443$	−2.44169e30	−0.899595	−0.449797	−	0.893131i	$-0.648504\pi$
$443$	−2.44169e30	−0.899595	−0.449797	+	0.893131i	$0.648504\pi$
$444$	−4.50272e30	−1.61648
$445$	−3.86359e30	−1.35161
$446$	−6.19966e30	−2.11357
$447$	4.05113e29	0.134598
$448$	0	0
$449$	−2.67412e30	−0.844012	−0.422006	−	0.906593i	$-0.638674\pi$
$449$	−2.67412e30	−0.844012	−0.422006	+	0.906593i	$0.638674\pi$
$450$	−1.29013e31	−3.96907
$451$	−5.74773e28	−0.0172372
$452$	3.51833e30	1.02860
$453$	1.11720e30	0.318422
$454$	−5.78146e30	−1.60655
$455$	0	0
$456$	−5.23863e30	−1.38395
$457$	2.43338e30	0.626864	0.313432	−	0.949611i	$-0.398521\pi$
$457$	2.43338e30	0.626864	0.313432	+	0.949611i	$0.398521\pi$
$458$	−5.78702e30	−1.45379
$459$	−4.32503e30	−1.05960
$460$	3.02066e31	7.21749
$461$	4.95318e30	1.15431	0.577156	−	0.816634i	$-0.304162\pi$
$461$	4.95318e30	1.15431	0.577156	+	0.816634i	$0.304162\pi$
$462$	0	0
$463$	6.94348e30	1.53956	0.769778	−	0.638311i	$-0.220367\pi$
$463$	6.94348e30	1.53956	0.769778	+	0.638311i	$0.220367\pi$
$464$	1.47985e31	3.20083
$465$	4.76083e30	1.00455
$466$	−1.02827e31	−2.11675
$467$	−8.52378e30	−1.71194	−0.855969	−	0.517028i	$-0.827038\pi$
$467$	−8.52378e30	−1.71194	−0.855969	+	0.517028i	$0.827038\pi$
$468$	7.46273e29	0.146241
$469$	0	0
$470$	1.56289e31	2.91611
$471$	2.07368e30	0.377573
$472$	−1.49663e31	−2.65939
$473$	−2.80862e29	−0.0487068
$474$	−6.29803e30	−1.06599
$475$	1.76555e31	2.91678
$476$	0	0
$477$	−1.81332e30	−0.285439
$478$	−5.10940e29	−0.0785144
$479$	6.00461e30	0.900796	0.450398	−	0.892828i	$-0.351282\pi$
$479$	6.00461e30	0.900796	0.450398	+	0.892828i	$0.351282\pi$
$480$	−1.37332e31	−2.01139
$481$	−7.33974e29	−0.104957
$482$	−2.53566e31	−3.54038
$483$	0	0
$484$	−1.71048e31	−2.27717
$485$	−7.32003e28	−0.00951663
$486$	−1.50036e31	−1.90492
$487$	4.85072e30	0.601483	0.300741	−	0.953706i	$-0.402766\pi$
$487$	4.85072e30	0.601483	0.300741	+	0.953706i	$0.402766\pi$
$488$	9.11496e30	1.10389
$489$	−5.20049e30	−0.615166
$490$	0	0
$491$	−9.14997e30	−1.03272	−0.516360	−	0.856372i	$-0.672713\pi$
$491$	−9.14997e30	−1.03272	−0.516360	+	0.856372i	$0.672713\pi$
$492$	−6.61420e29	−0.0729253
$493$	−1.41065e31	−1.51943
$494$	−1.43470e30	−0.150973
$495$	4.06708e30	0.418141
$496$	−2.83285e31	−2.84567
$497$	0	0
$498$	6.28282e30	0.602583
$499$	−6.01229e30	−0.563487	−0.281743	−	0.959490i	$-0.590913\pi$
$499$	−6.01229e30	−0.563487	−0.281743	+	0.959490i	$0.590913\pi$
$500$	9.23537e31	8.45861
$501$	−4.97412e30	−0.445228
$502$	−2.70209e31	−2.36378
$503$	−1.86292e31	−1.59281	−0.796403	−	0.604766i	$-0.793267\pi$
$503$	−1.86292e31	−1.59281	−0.796403	+	0.604766i	$0.793267\pi$
$504$	0	0
$505$	−1.29498e31	−1.05782
$506$	−9.82391e30	−0.784429
$507$	6.09929e30	0.476089
$508$	1.35021e31	1.03031
$509$	3.82237e30	0.285153	0.142577	−	0.989784i	$-0.454461\pi$
$509$	3.82237e30	0.285153	0.142577	+	0.989784i	$0.454461\pi$
$510$	2.96567e31	2.16305
$511$	0	0
$512$	−2.16898e31	−1.51235
$513$	1.31218e31	0.894629
$514$	1.11133e31	0.740915
$515$	1.97438e31	1.28720
$516$	−3.23201e30	−0.206064
$517$	−3.61824e30	−0.225609
$518$	0	0
$519$	4.96164e29	0.0295938
$520$	−6.99798e30	−0.408258
$521$	−1.98996e31	−1.13556	−0.567781	−	0.823180i	$-0.692198\pi$
$521$	−1.98996e31	−1.13556	−0.567781	+	0.823180i	$0.692198\pi$
$522$	−3.12735e31	−1.74568
$523$	−3.07108e31	−1.67696	−0.838479	−	0.544933i	$-0.816555\pi$
$523$	−3.07108e31	−1.67696	−0.838479	+	0.544933i	$0.816555\pi$
$524$	2.54914e31	1.36171
$525$	0	0
$526$	−1.05962e31	−0.541768
$527$	2.70039e31	1.35084
$528$	7.20260e30	0.352532
$529$	2.64633e31	1.26737
$530$	2.85684e31	1.33879
$531$	1.63159e31	0.748212
$532$	0	0
$533$	−1.07816e29	−0.00473500
$534$	1.44596e31	0.621485
$535$	1.42867e31	0.600985
$536$	3.02094e31	1.24379
$537$	1.01616e31	0.409503
$538$	−1.89059e31	−0.745764
$539$	0	0
$540$	1.07533e32	4.06456
$541$	−1.86142e31	−0.688771	−0.344385	−	0.938828i	$-0.611913\pi$
$541$	−1.86142e31	−0.688771	−0.344385	+	0.938828i	$0.611913\pi$
$542$	1.70314e31	0.616962
$543$	−4.21800e30	−0.149592
$544$	−7.78959e31	−2.70475
$545$	−7.13922e31	−2.42712
$546$	0	0
$547$	2.51242e31	0.818914	0.409457	−	0.912329i	$-0.365718\pi$
$547$	2.51242e31	0.818914	0.409457	+	0.912329i	$0.365718\pi$
$548$	3.68487e31	1.17610
$549$	−9.93691e30	−0.310577
$550$	−4.70558e31	−1.44026
$551$	4.27981e31	1.28286
$552$	−6.72865e31	−1.97528
$553$	0	0
$554$	3.64182e30	0.102555
$555$	−4.60306e31	−1.26963
$556$	−1.63839e32	−4.42647
$557$	4.65884e31	1.23294	0.616471	−	0.787377i	$-0.288562\pi$
$557$	4.65884e31	1.23294	0.616471	+	0.787377i	$0.288562\pi$
$558$	5.98661e31	1.55199
$559$	−5.26840e29	−0.0133796
$560$	0	0
$561$	−6.86580e30	−0.167347
$562$	6.14092e31	1.46645
$563$	2.57936e31	0.603483	0.301742	−	0.953390i	$-0.402432\pi$
$563$	2.57936e31	0.603483	0.301742	+	0.953390i	$0.402432\pi$
$564$	−4.16369e31	−0.954485
$565$	3.59673e31	0.807888
$566$	1.46403e32	3.22226
$567$	0	0
$568$	−2.16471e32	−4.57502
$569$	2.34945e31	0.486603	0.243301	−	0.969951i	$-0.421770\pi$
$569$	2.34945e31	0.486603	0.243301	+	0.969951i	$0.421770\pi$
$570$	−8.99759e31	−1.82627
$571$	−9.43382e31	−1.87660	−0.938301	−	0.345819i	$-0.887601\pi$
$571$	−9.43382e31	−1.87660	−0.938301	+	0.345819i	$0.887601\pi$
$572$	2.72194e30	0.0530669
$573$	−1.39265e31	−0.266112
$574$	0	0
$575$	2.26773e32	4.16304
$576$	−5.99595e31	−1.07895
$577$	3.20905e31	0.566050	0.283025	−	0.959113i	$-0.408662\pi$
$577$	3.20905e31	0.566050	0.283025	+	0.959113i	$0.408662\pi$
$578$	6.04806e31	1.04579
$579$	1.01134e31	0.171432
$580$	3.50731e32	5.82843
$581$	0	0
$582$	2.73953e29	0.00437585
$583$	−6.61385e30	−0.103578
$584$	−1.96611e31	−0.301898
$585$	7.62903e30	0.114862
$586$	8.79863e31	1.29895
$587$	1.19872e31	0.173531	0.0867657	−	0.996229i	$-0.472347\pi$
$587$	1.19872e31	0.173531	0.0867657	+	0.996229i	$0.472347\pi$
$588$	0	0
$589$	−8.19274e31	−1.14052
$590$	−2.57053e32	−3.50934
$591$	−2.74352e31	−0.367327
$592$	2.73897e32	3.59657
$593$	−1.02221e32	−1.31647	−0.658236	−	0.752812i	$-0.728697\pi$
$593$	−1.02221e32	−1.31647	−0.658236	+	0.752812i	$0.728697\pi$
$594$	−3.49724e31	−0.441754
$595$	0	0
$596$	−5.71311e31	−0.694289
$597$	3.91798e31	0.467044
$598$	−1.84277e31	−0.215480
$599$	−1.71851e31	−0.197126	−0.0985631	−	0.995131i	$-0.531425\pi$
$599$	−1.71851e31	−0.197126	−0.0985631	+	0.995131i	$0.531425\pi$
$600$	−3.22297e32	−3.62675
$601$	−6.06884e31	−0.669961	−0.334980	−	0.942225i	$-0.608730\pi$
$601$	−6.06884e31	−0.669961	−0.334980	+	0.942225i	$0.608730\pi$
$602$	0	0
$603$	−3.29335e31	−0.349937
$604$	−1.57554e32	−1.64250
$605$	−1.74859e32	−1.78855
$606$	4.84648e31	0.486397
$607$	1.25731e32	1.23814	0.619072	−	0.785334i	$-0.287509\pi$
$607$	1.25731e32	1.23814	0.619072	+	0.785334i	$0.287509\pi$
$608$	2.36330e32	2.28364
$609$	0	0
$610$	1.56554e32	1.45670
$611$	−6.78710e30	−0.0619741
$612$	2.65465e32	2.37884
$613$	8.10348e31	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$613$	8.10348e31	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$614$	−3.78405e31	−0.326603
$615$	−6.76159e30	−0.0572776
$616$	0	0
$617$	−7.03288e31	−0.573923	−0.286962	−	0.957942i	$-0.592645\pi$
$617$	−7.03288e31	−0.573923	−0.286962	+	0.957942i	$0.592645\pi$
$618$	−7.38915e31	−0.591871
$619$	1.91808e32	1.50808	0.754039	−	0.656830i	$-0.228103\pi$
$619$	1.91808e32	1.50808	0.754039	+	0.656830i	$0.228103\pi$
$620$	−6.71396e32	−5.18173
$621$	1.68540e32	1.27688
$622$	−2.90955e32	−2.16390
$623$	0	0
$624$	1.35106e31	0.0968396
$625$	5.51228e32	3.87892
$626$	−3.30582e32	−2.28388
$627$	2.08302e31	0.141292
$628$	−2.92441e32	−1.94761
$629$	−2.61090e32	−1.70729
$630$	0	0
$631$	2.17908e32	1.37384	0.686918	−	0.726735i	$-0.258963\pi$
$631$	2.17908e32	1.37384	0.686918	+	0.726735i	$0.258963\pi$
$632$	5.28645e32	3.27279
$633$	−9.43543e31	−0.573613
$634$	6.17118e32	3.68419
$635$	1.38030e32	0.809238
$636$	−7.61089e31	−0.438206
$637$	0	0
$638$	−1.14066e32	−0.633459
$639$	2.35991e32	1.28717
$640$	1.60662e32	0.860684
$641$	−6.95564e31	−0.365990	−0.182995	−	0.983114i	$-0.558579\pi$
$641$	−6.95564e31	−0.365990	−0.182995	+	0.983114i	$0.558579\pi$
$642$	−5.34682e31	−0.276339
$643$	1.25648e32	0.637866	0.318933	−	0.947777i	$-0.396676\pi$
$643$	1.25648e32	0.637866	0.318933	+	0.947777i	$0.396676\pi$
$644$	0	0
$645$	−3.30404e31	−0.161848
$646$	−5.10352e32	−2.45582
$647$	1.15116e32	0.544171	0.272086	−	0.962273i	$-0.412287\pi$
$647$	1.15116e32	0.544171	0.272086	+	0.962273i	$0.412287\pi$
$648$	2.15007e32	0.998481
$649$	5.95103e31	0.271505
$650$	−8.82673e31	−0.395636
$651$	0	0
$652$	7.33400e32	3.17317
$653$	−2.81877e32	−1.19828	−0.599139	−	0.800645i	$-0.704490\pi$
$653$	−2.81877e32	−1.19828	−0.599139	+	0.800645i	$0.704490\pi$
$654$	2.67186e32	1.11602
$655$	2.60594e32	1.06952
$656$	4.02337e31	0.162254
$657$	2.14341e31	0.0849382
$658$	0	0
$659$	4.43093e32	1.69556	0.847779	−	0.530350i	$-0.177939\pi$
$659$	4.43093e32	1.69556	0.847779	+	0.530350i	$0.177939\pi$
$660$	1.70704e32	0.641932
$661$	−2.32877e32	−0.860616	−0.430308	−	0.902682i	$-0.641595\pi$
$661$	−2.32877e32	−0.860616	−0.430308	+	0.902682i	$0.641595\pi$
$662$	2.29859e31	0.0834822
$663$	−1.28789e31	−0.0459697
$664$	−5.27368e32	−1.85004
$665$	0	0
$666$	−5.78822e32	−1.96152
$667$	5.49711e32	1.83100
$668$	7.01477e32	2.29659
$669$	1.68845e32	0.543361
$670$	5.18860e32	1.64131
$671$	−3.62436e31	−0.112700
$672$	0	0
$673$	−4.99094e30	−0.0149972	−0.00749858	−	0.999972i	$-0.502387\pi$
$673$	−4.99094e30	−0.0149972	−0.00749858	+	0.999972i	$0.502387\pi$
$674$	−5.08368e32	−1.50172
$675$	8.07294e32	2.34444
$676$	−8.60154e32	−2.45578
$677$	−2.66559e32	−0.748209	−0.374105	−	0.927386i	$-0.622050\pi$
$677$	−2.66559e32	−0.748209	−0.374105	+	0.927386i	$0.622050\pi$
$678$	−1.34608e32	−0.371476
$679$	0	0
$680$	−2.48933e33	−6.64094
$681$	1.57456e32	0.413015
$682$	2.18354e32	0.563173
$683$	−2.25043e32	−0.570726	−0.285363	−	0.958419i	$-0.592114\pi$
$683$	−2.25043e32	−0.570726	−0.285363	+	0.958419i	$0.592114\pi$
$684$	−8.05398e32	−2.00847
$685$	3.76698e32	0.923745
$686$	0	0
$687$	1.57607e32	0.373743
$688$	1.96601e32	0.458479
$689$	−1.24063e31	−0.0284525
$690$	−1.15568e33	−2.60659
$691$	4.47511e32	0.992674	0.496337	−	0.868130i	$-0.334678\pi$
$691$	4.47511e32	0.992674	0.496337	+	0.868130i	$0.334678\pi$
$692$	−6.99716e31	−0.152652
$693$	0	0
$694$	7.05360e31	0.148860
$695$	−1.67490e33	−3.47667
$696$	−7.81269e32	−1.59512
$697$	−3.83524e31	−0.0770221
$698$	1.70272e33	3.36361
$699$	2.80046e32	0.544179
$700$	0	0
$701$	−2.46741e32	−0.463963	−0.231982	−	0.972720i	$-0.574521\pi$
$701$	−2.46741e32	−0.463963	−0.231982	+	0.972720i	$0.574521\pi$
$702$	−6.56012e31	−0.121349
$703$	7.92124e32	1.44147
$704$	−2.18695e32	−0.391519
$705$	−4.25648e32	−0.749679
$706$	1.22692e33	2.12600
$707$	0	0
$708$	6.84814e32	1.14866
$709$	6.21669e32	1.02595	0.512977	−	0.858403i	$-0.328543\pi$
$709$	6.21669e32	1.02595	0.512977	+	0.858403i	$0.328543\pi$
$710$	−3.71799e33	−6.03722
$711$	−5.76316e32	−0.920789
$712$	−1.21371e33	−1.90807
$713$	−1.05230e33	−1.62783
$714$	0	0
$715$	2.78259e31	0.0416803
$716$	−1.43304e33	−2.11231
$717$	1.39152e31	0.0201846
$718$	−1.07538e33	−1.53507
$719$	−9.12211e32	−1.28148	−0.640742	−	0.767756i	$-0.721373\pi$
$719$	−9.12211e32	−1.28148	−0.640742	+	0.767756i	$0.721373\pi$
$720$	−2.84693e33	−3.93598
$721$	0	0
$722$	1.57243e32	0.210569
$723$	6.90576e32	0.910168
$724$	5.94845e32	0.771632
$725$	2.63308e33	3.36184
$726$	6.54414e32	0.822397
$727$	−6.08188e30	−0.00752302	−0.00376151	−	0.999993i	$-0.501197\pi$
$727$	−6.08188e30	−0.00752302	−0.00376151	+	0.999993i	$0.501197\pi$
$728$	0	0
$729$	1.04459e32	0.125193
$730$	−3.37689e32	−0.398386
$731$	−1.87408e32	−0.217640
$732$	−4.17074e32	−0.476799
$733$	−6.96832e32	−0.784210	−0.392105	−	0.919921i	$-0.628253\pi$
$733$	−6.96832e32	−0.784210	−0.392105	+	0.919921i	$0.628253\pi$
$734$	2.17744e33	2.41236
$735$	0	0
$736$	3.03549e33	3.25937
$737$	−1.20121e32	−0.126982
$738$	−8.50252e31	−0.0884911
$739$	−8.27264e32	−0.847682	−0.423841	−	0.905737i	$-0.639319\pi$
$739$	−8.27264e32	−0.847682	−0.423841	+	0.905737i	$0.639319\pi$
$740$	6.49147e33	6.54905
$741$	3.90734e31	0.0388125
$742$	0	0
$743$	5.85434e32	0.563776	0.281888	−	0.959447i	$-0.409039\pi$
$743$	5.85434e32	0.563776	0.281888	+	0.959447i	$0.409039\pi$
$744$	1.49557e33	1.41813
$745$	−5.84042e32	−0.545314
$746$	−3.86466e33	−3.55316
$747$	5.74924e32	0.520504
$748$	9.68251e32	0.863216
$749$	0	0
$750$	−3.53337e33	−3.05481
$751$	−1.11186e33	−0.946655	−0.473327	−	0.880887i	$-0.656947\pi$
$751$	−1.11186e33	−0.946655	−0.473327	+	0.880887i	$0.656947\pi$
$752$	2.53275e33	2.12367
$753$	7.35903e32	0.607685
$754$	−2.13965e32	−0.174009
$755$	−1.61065e33	−1.29006
$756$	0	0
$757$	−1.91038e33	−1.48428	−0.742142	−	0.670242i	$-0.766190\pi$
$757$	−1.91038e33	−1.48428	−0.742142	+	0.670242i	$0.766190\pi$
$758$	−9.07728e32	−0.694640
$759$	2.67550e32	0.201662
$760$	7.55241e33	5.60698
$761$	−2.05494e33	−1.50271	−0.751355	−	0.659899i	$-0.770599\pi$
$761$	−2.05494e33	−1.50271	−0.751355	+	0.659899i	$0.770599\pi$
$762$	−5.16580e32	−0.372096
$763$	0	0
$764$	1.96399e33	1.37267
$765$	2.71381e33	1.86841
$766$	−2.05544e32	−0.139404
$767$	1.11629e32	0.0745816
$768$	4.17451e32	0.274759
$769$	−7.25356e32	−0.470325	−0.235162	−	0.971956i	$-0.575562\pi$
$769$	−7.25356e32	−0.470325	−0.235162	+	0.971956i	$0.575562\pi$
$770$	0	0
$771$	−3.02667e32	−0.190476
$772$	−1.42624e33	−0.884288
$773$	9.82682e32	0.600273	0.300136	−	0.953896i	$-0.402968\pi$
$773$	9.82682e32	0.600273	0.300136	+	0.953896i	$0.402968\pi$
$774$	−4.15474e32	−0.250048
$775$	−5.04044e33	−2.98882
$776$	−2.29952e31	−0.0134347
$777$	0	0
$778$	4.31868e33	2.44954
$779$	1.16358e32	0.0650301
$780$	3.20207e32	0.176337
$781$	8.60748e32	0.467078
$782$	−6.55512e33	−3.50512
$783$	1.95693e33	1.03113
$784$	0	0
$785$	−2.98957e33	−1.52971
$786$	−9.75278e32	−0.491778
$787$	2.95753e33	1.46967	0.734834	−	0.678247i	$-0.237260\pi$
$787$	2.95753e33	1.46967	0.734834	+	0.678247i	$0.237260\pi$
$788$	3.86906e33	1.89476
$789$	2.88583e32	0.139279
$790$	9.07972e33	4.31878
$791$	0	0
$792$	1.27763e33	0.590292
$793$	−6.79858e31	−0.0309583
$794$	−3.81027e33	−1.71009
$795$	−7.78049e32	−0.344179
$796$	−5.52534e33	−2.40912
$797$	−2.29301e33	−0.985451	−0.492725	−	0.870185i	$-0.663999\pi$
$797$	−2.29301e33	−0.985451	−0.492725	+	0.870185i	$0.663999\pi$
$798$	0	0
$799$	−2.41431e33	−1.00811
$800$	1.45398e34	5.98443
$801$	1.32316e33	0.536830
$802$	−3.08383e32	−0.123335
$803$	7.81781e31	0.0308217
$804$	−1.38229e33	−0.537224
$805$	0	0
$806$	4.09589e32	0.154702
$807$	5.14894e32	0.191722
$808$	−4.06805e33	−1.49333
$809$	−5.46911e33	−1.97929	−0.989643	−	0.143553i	$-0.954147\pi$
$809$	−5.46911e33	−1.97929	−0.989643	+	0.143553i	$0.954147\pi$
$810$	3.69284e33	1.31760
$811$	4.78306e33	1.68254	0.841271	−	0.540614i	$-0.181808\pi$
$811$	4.78306e33	1.68254	0.841271	+	0.540614i	$0.181808\pi$
$812$	0	0
$813$	−4.63843e32	−0.158610
$814$	−2.11118e33	−0.711779
$815$	7.49743e33	2.49230
$816$	4.80602e33	1.57525
$817$	5.68580e32	0.183755
$818$	−6.41968e33	−2.04574
$819$	0	0
$820$	9.53554e32	0.295451
$821$	−9.18752e31	−0.0280706	−0.0140353	−	0.999902i	$-0.504468\pi$
$821$	−9.18752e31	−0.0280706	−0.0140353	+	0.999902i	$0.504468\pi$
$822$	−1.40980e33	−0.424748
$823$	4.65953e33	1.38434	0.692172	−	0.721733i	$-0.256654\pi$
$823$	4.65953e33	1.38434	0.692172	+	0.721733i	$0.256654\pi$
$824$	6.20231e33	1.81715
$825$	1.28154e33	0.370266
$826$	0	0
$827$	5.39653e33	1.51636	0.758179	−	0.652047i	$-0.226089\pi$
$827$	5.39653e33	1.51636	0.758179	+	0.652047i	$0.226089\pi$
$828$	−1.03448e34	−2.86664
$829$	2.13449e33	0.583334	0.291667	−	0.956520i	$-0.405790\pi$
$829$	2.13449e33	0.583334	0.291667	+	0.956520i	$0.405790\pi$
$830$	−9.05780e33	−2.44132
$831$	−9.91834e31	−0.0263650
$832$	−4.10228e32	−0.107549
$833$	0	0
$834$	6.26834e33	1.59861
$835$	7.17108e33	1.80381
$836$	−2.93759e33	−0.728818
$837$	−3.74611e33	−0.916722
$838$	1.02814e34	2.48169
$839$	−2.21991e33	−0.528535	−0.264267	−	0.964449i	$-0.585130\pi$
$839$	−2.21991e33	−0.528535	−0.264267	+	0.964449i	$0.585130\pi$
$840$	0	0
$841$	2.06602e33	0.478608
$842$	−1.25963e34	−2.87843
$843$	−1.67245e33	−0.376996
$844$	1.33063e34	2.95883
$845$	−8.79322e33	−1.92884
$846$	−5.35241e33	−1.15822
$847$	0	0
$848$	4.62965e33	0.974981
$849$	−3.98722e33	−0.828384
$850$	−3.13985e34	−6.43564
$851$	1.01743e34	2.05738
$852$	9.90506e33	1.97607
$853$	8.35177e33	1.64386	0.821930	−	0.569589i	$-0.192898\pi$
$853$	8.35177e33	1.64386	0.821930	+	0.569589i	$0.192898\pi$
$854$	0	0
$855$	−8.23346e33	−1.57751
$856$	4.48802e33	0.848412
$857$	3.22920e33	0.602304	0.301152	−	0.953576i	$-0.402629\pi$
$857$	3.22920e33	0.602304	0.301152	+	0.953576i	$0.402629\pi$
$858$	−1.04139e32	−0.0191650
$859$	3.66819e33	0.666086	0.333043	−	0.942912i	$-0.391925\pi$
$859$	3.66819e33	0.666086	0.333043	+	0.942912i	$0.391925\pi$
$860$	4.65952e33	0.834852
$861$	0	0
$862$	−5.38175e33	−0.938836
$863$	3.05514e33	0.525904	0.262952	−	0.964809i	$-0.415304\pi$
$863$	3.05514e33	0.525904	0.262952	+	0.964809i	$0.415304\pi$
$864$	1.08061e34	1.83553
$865$	−7.15309e32	−0.119897
$866$	−1.86633e33	−0.308697
$867$	−1.64716e33	−0.268854
$868$	0	0
$869$	−2.10204e33	−0.334129
$870$	−1.34187e34	−2.10493
$871$	−2.25323e32	−0.0348816
$872$	−2.24271e34	−3.42637
$873$	2.50688e31	0.00377980
$874$	1.98877e34	2.95939
$875$	0	0
$876$	8.99635e32	0.130397
$877$	2.88335e33	0.412479	0.206240	−	0.978502i	$-0.433877\pi$
$877$	2.88335e33	0.412479	0.206240	+	0.978502i	$0.433877\pi$
$878$	1.41172e34	1.99325
$879$	−2.39627e33	−0.333936
$880$	−1.03838e34	−1.42826
$881$	−9.12355e33	−1.23863	−0.619314	−	0.785143i	$-0.712589\pi$
$881$	−9.12355e33	−1.23863	−0.619314	+	0.785143i	$0.712589\pi$
$882$	0	0
$883$	−1.31742e34	−1.74251	−0.871255	−	0.490831i	$-0.836693\pi$
$883$	−1.31742e34	−1.74251	−0.871255	+	0.490831i	$0.836693\pi$
$884$	1.81624e33	0.237123
$885$	7.00074e33	0.902187
$886$	−1.31741e34	−1.67584
$887$	6.86712e32	0.0862289	0.0431145	−	0.999070i	$-0.486272\pi$
$887$	6.86712e32	0.0862289	0.0431145	+	0.999070i	$0.486272\pi$
$888$	−1.44600e34	−1.79234
$889$	0	0
$890$	−2.08460e34	−2.51790
$891$	−8.54928e32	−0.101938
$892$	−2.38114e34	−2.80278
$893$	7.32482e33	0.851148
$894$	2.18579e33	0.250742
$895$	−1.46497e34	−1.65907
$896$	0	0
$897$	5.01871e32	0.0553960
$898$	−1.44282e34	−1.57230
$899$	−1.22183e34	−1.31455
$900$	−4.95507e34	−5.26334
$901$	−4.41317e33	−0.462823
$902$	−3.10119e32	−0.0321109
$903$	0	0
$904$	1.12988e34	1.14050
$905$	6.08100e33	0.606061
$906$	6.02788e33	0.593185
$907$	8.45343e33	0.821389	0.410695	−	0.911773i	$-0.365286\pi$
$907$	8.45343e33	0.821389	0.410695	+	0.911773i	$0.365286\pi$
$908$	−2.22052e34	−2.13043
$909$	4.43489e33	0.420144
$910$	0	0
$911$	1.30548e34	1.20590	0.602948	−	0.797780i	$-0.293992\pi$
$911$	1.30548e34	1.20590	0.602948	+	0.797780i	$0.293992\pi$
$912$	−1.45810e34	−1.32999
$913$	2.09696e33	0.188876
$914$	1.31293e34	1.16778
$915$	−4.26368e33	−0.374491
$916$	−2.22266e34	−1.92786
$917$	0	0
$918$	−2.33357e34	−1.97392
$919$	−3.41817e33	−0.285539	−0.142769	−	0.989756i	$-0.545601\pi$
$919$	−3.41817e33	−0.285539	−0.142769	+	0.989756i	$0.545601\pi$
$920$	9.70055e34	8.00270
$921$	1.03057e33	0.0839637
$922$	2.67249e34	2.15036
$923$	1.61459e33	0.128305
$924$	0	0
$925$	4.87341e34	3.77749
$926$	3.74636e34	2.86802
$927$	−6.76161e33	−0.511250
$928$	3.52453e34	2.63208
$929$	5.50940e33	0.406372	0.203186	−	0.979140i	$-0.434870\pi$
$929$	5.50940e33	0.406372	0.203186	+	0.979140i	$0.434870\pi$
$930$	2.56870e34	1.87137
$931$	0	0
$932$	−3.94935e34	−2.80700
$933$	7.92404e33	0.556298
$934$	−4.59901e34	−3.18915
$935$	9.89827e33	0.677994
$936$	2.39658e33	0.162151
$937$	−7.13928e33	−0.477144	−0.238572	−	0.971125i	$-0.576679\pi$
$937$	−7.13928e33	−0.477144	−0.238572	+	0.971125i	$0.576679\pi$
$938$	0	0
$939$	9.00325e33	0.587145
$940$	6.00270e34	3.86702
$941$	2.95867e34	1.88285	0.941425	−	0.337222i	$-0.109487\pi$
$941$	2.95867e34	1.88285	0.941425	+	0.337222i	$0.109487\pi$
$942$	1.11885e34	0.703376
$943$	1.49454e33	0.0928158
$944$	−4.16568e34	−2.55569
$945$	0	0
$946$	−1.51539e33	−0.0907353
$947$	7.46702e33	0.441695	0.220847	−	0.975308i	$-0.429118\pi$
$947$	7.46702e33	0.441695	0.220847	+	0.975308i	$0.429118\pi$
$948$	−2.41892e34	−1.41360
$949$	1.46647e32	0.00846663
$950$	9.52604e34	5.43364
$951$	−1.68069e34	−0.947137
$952$	0	0
$953$	1.52946e34	0.841335	0.420668	−	0.907215i	$-0.361796\pi$
$953$	1.52946e34	0.841335	0.420668	+	0.907215i	$0.361796\pi$
$954$	−9.78376e33	−0.531740
$955$	2.00775e34	1.07813
$956$	−1.96240e33	−0.104117
$957$	3.10654e33	0.162851
$958$	3.23979e34	1.67808
$959$	0	0
$960$	−2.57271e34	−1.30098
$961$	3.37599e33	0.168687
$962$	−3.96016e33	−0.195524
$963$	−4.89273e33	−0.238698
$964$	−9.73887e34	−4.69486
$965$	−1.45802e34	−0.694545
$966$	0	0
$967$	7.77078e33	0.361460	0.180730	−	0.983533i	$-0.442154\pi$
$967$	7.77078e33	0.361460	0.180730	+	0.983533i	$0.442154\pi$
$968$	−5.49303e34	−2.52491
$969$	1.38992e34	0.631345
$970$	−3.94953e32	−0.0177284
$971$	−1.84473e34	−0.818297	−0.409149	−	0.912468i	$-0.634174\pi$
$971$	−1.84473e34	−0.818297	−0.409149	+	0.912468i	$0.634174\pi$
$972$	−5.76251e34	−2.52610
$973$	0	0
$974$	2.61721e34	1.12050
$975$	2.40392e33	0.101711
$976$	2.53703e34	1.06085
$977$	−4.44473e34	−1.83678	−0.918391	−	0.395673i	$-0.870511\pi$
$977$	−4.44473e34	−1.83678	−0.918391	+	0.395673i	$0.870511\pi$
$978$	−2.80592e34	−1.14599
$979$	4.82605e33	0.194801
$980$	0	0
$981$	2.44495e34	0.964000
$982$	−4.93687e34	−1.92384
$983$	−3.08066e34	−1.18653	−0.593264	−	0.805008i	$-0.702161\pi$
$983$	−3.08066e34	−1.18653	−0.593264	+	0.805008i	$0.702161\pi$
$984$	−2.12408e33	−0.0808590
$985$	3.95528e34	1.48820
$986$	−7.61119e34	−2.83053
$987$	0	0
$988$	−5.51033e33	−0.200204
$989$	7.30302e33	0.262268
$990$	2.19440e34	0.778951
$991$	4.32291e34	1.51680	0.758401	−	0.651788i	$-0.225981\pi$
$991$	4.32291e34	1.51680	0.758401	+	0.651788i	$0.225981\pi$
$992$	−6.74693e34	−2.34003
$993$	−6.26010e32	−0.0214617
$994$	0	0
$995$	−5.64847e34	−1.89219
$996$	2.41308e34	0.799079
$997$	−5.18143e34	−1.69611	−0.848057	−	0.529904i	$-0.822228\pi$
$997$	−5.18143e34	−1.69611	−0.848057	+	0.529904i	$0.822228\pi$
$998$	−3.24393e34	−1.04971
$999$	3.62197e34	1.15862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.24.a.h.1.23	✓	24
7.6	odd	2	inner	49.24.a.h.1.24	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.24.a.h.1.23	✓	24	1.1	even	1	trivial
49.24.a.h.1.24	yes	24	7.6	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+5395.50 q^{2} -146944. q^{3} +2.07228e7 q^{4} +2.11846e8 q^{5} -7.92838e8 q^{6} +6.65494e10 q^{8} -7.25506e10 q^{9} +1.14302e12 q^{10} -2.64619e11 q^{11} -3.04510e12 q^{12} -4.96373e11 q^{13} -3.11296e13 q^{15} +1.85232e14 q^{16} -1.76570e14 q^{17} -3.91447e14 q^{18} +5.35699e14 q^{19} +4.39006e15 q^{20} -1.42775e15 q^{22} +6.88068e15 q^{23} -9.77905e15 q^{24} +3.29579e16 q^{25} -2.67818e15 q^{26} +2.44947e16 q^{27} +7.98920e16 q^{29} -1.67960e17 q^{30} -1.52936e17 q^{31} +4.41161e17 q^{32} +3.88843e16 q^{33} -9.52685e17 q^{34} -1.50345e18 q^{36} +1.47867e18 q^{37} +2.89036e18 q^{38} +7.29391e16 q^{39} +1.40982e19 q^{40} +2.17208e17 q^{41} +1.06138e18 q^{43} -5.48366e18 q^{44} -1.53696e19 q^{45} +3.71247e19 q^{46} +1.36734e19 q^{47} -2.72187e19 q^{48} +1.77825e20 q^{50} +2.59460e19 q^{51} -1.02863e19 q^{52} +2.49939e19 q^{53} +1.32161e20 q^{54} -5.60586e19 q^{55} -7.87178e19 q^{57} +4.31058e20 q^{58} -2.24890e20 q^{59} -6.45094e20 q^{60} +1.36965e20 q^{61} -8.25165e20 q^{62} +8.26451e20 q^{64} -1.05155e20 q^{65} +2.09800e20 q^{66} +4.53939e20 q^{67} -3.65904e21 q^{68} -1.01108e21 q^{69} -3.25278e21 q^{71} -4.82820e21 q^{72} -2.95436e20 q^{73} +7.97819e21 q^{74} -4.84298e21 q^{75} +1.11012e22 q^{76} +3.93543e20 q^{78} +7.94365e21 q^{79} +3.92407e22 q^{80} +3.23079e21 q^{81} +1.17194e21 q^{82} -7.92446e21 q^{83} -3.74057e22 q^{85} +5.72668e21 q^{86} -1.17397e22 q^{87} -1.76102e22 q^{88} -1.82377e22 q^{89} -8.29266e22 q^{90} +1.42587e23 q^{92} +2.24730e22 q^{93} +7.37749e22 q^{94} +1.13486e23 q^{95} -6.48261e22 q^{96} -3.45535e20 q^{97} +1.91983e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6030 q^{2} + 99000906 q^{4} + 31751706690 q^{8} + 975236583640 q^{9} + 3514223137536 q^{11} + 96662500006976 q^{15} + 850136746459362 q^{16} - 774764811988990 q^{18} + 81\!\cdots\!60 q^{22} + 34\!\cdots\!60 q^{23}+ \cdots + 70\!\cdots\!64 q^{99}+O(q^{100}) \) 24 * q + 6030 * q^2 + 99000906 * q^4 + 31751706690 * q^8 + 975236583640 * q^9 + 3514223137536 * q^11 + 96662500006976 * q^15 + 850136746459362 * q^16 - 774764811988990 * q^18 + 8148420455553060 * q^22 + 34774948016084160 * q^23 + 94149150991117272 * q^25 + 190645622093096064 * q^29 - 634449556982285592 * q^30 - 1493697165631220430 * q^32 + 6671026323612877990 * q^36 + 878462893450581120 * q^37 + 6115839814038109120 * q^39 + 20811373010373199680 * q^43 + 54730049479951369500 * q^44 + 73203364608168908808 * q^46 + 387333163519636443066 * q^50 + 270153244272168521696 * q^51 + 34330885176487486320 * q^53 + 496656755807681949600 * q^57 - 397574761992930674580 * q^58 + 292003879381856022136 * q^60 + 2439494576203335787554 * q^64 + 4869166958052334391664 * q^65 - 1121753136531158010720 * q^67 - 1755055962268130457216 * q^71 - 32377694763810926605650 * q^72 + 1005354247436267388732 * q^74 - 79646865826469682676320 * q^78 + 5008005983294871013824 * q^79 + 21826965675021517050808 * q^81 + 20177850245757616713456 * q^85 + 38898565641929075253660 * q^86 - 21751191568485361565940 * q^88 + 247141757180010545124120 * q^92 + 241670386431567345282560 * q^93 + 278606632818920869216512 * q^95 + 708951281314482353318464 * q^99

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