LMFDB - Embedded newform 289.10.a.f.1.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,10,Mod(1,289)] 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("289.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

Newform invariants

comment:select newform

sage:traces = [24,0,0] 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:	$148.845356651$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+12.9147 q^{2} +101.422 q^{3} -345.210 q^{4} +2078.59 q^{5} +1309.84 q^{6} +2161.61 q^{7} -11070.6 q^{8} -9396.49 q^{9} +26844.4 q^{10} -13147.0 q^{11} -35012.1 q^{12} -17852.0 q^{13} +27916.6 q^{14} +210815. q^{15} +33773.6 q^{16} -121353. q^{18} -30951.0 q^{19} -717549. q^{20} +219236. q^{21} -169790. q^{22} -193663. q^{23} -1.12281e6 q^{24} +2.36740e6 q^{25} -230553. q^{26} -2.94931e6 q^{27} -746210. q^{28} +1.83211e6 q^{29} +2.72262e6 q^{30} -525734. q^{31} +6.10434e6 q^{32} -1.33340e6 q^{33} +4.49310e6 q^{35} +3.24376e6 q^{36} -1.78204e7 q^{37} -399723. q^{38} -1.81059e6 q^{39} -2.30113e7 q^{40} -1.53721e7 q^{41} +2.83137e6 q^{42} -4.23089e7 q^{43} +4.53848e6 q^{44} -1.95314e7 q^{45} -2.50111e6 q^{46} +5.91782e7 q^{47} +3.42540e6 q^{48} -3.56810e7 q^{49} +3.05743e7 q^{50} +6.16269e6 q^{52} -8.32863e7 q^{53} -3.80895e7 q^{54} -2.73272e7 q^{55} -2.39304e7 q^{56} -3.13913e6 q^{57} +2.36612e7 q^{58} +9.24034e7 q^{59} -7.27756e7 q^{60} -1.01929e8 q^{61} -6.78970e6 q^{62} -2.03115e7 q^{63} +6.15437e7 q^{64} -3.71069e7 q^{65} -1.72205e7 q^{66} +1.25363e8 q^{67} -1.96418e7 q^{69} +5.80271e7 q^{70} +2.14775e8 q^{71} +1.04025e8 q^{72} -1.02966e8 q^{73} -2.30145e8 q^{74} +2.40108e8 q^{75} +1.06846e7 q^{76} -2.84187e7 q^{77} -2.33833e7 q^{78} -9.58995e6 q^{79} +7.02013e7 q^{80} -1.14176e8 q^{81} -1.98526e8 q^{82} -6.13699e8 q^{83} -7.56824e7 q^{84} -5.46408e8 q^{86} +1.85817e8 q^{87} +1.45546e8 q^{88} +5.89040e8 q^{89} -2.52243e8 q^{90} -3.85890e7 q^{91} +6.68545e7 q^{92} -5.33212e7 q^{93} +7.64270e8 q^{94} -6.43343e7 q^{95} +6.19117e8 q^{96} +8.70682e8 q^{97} -4.60811e8 q^{98} +1.23536e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33}+ \cdots + 4413444720 q^{98}+O(q^{100}) $ 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

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 $

$2$	12.9147	0.570755	0.285378	−	0.958415i	$-0.407881\pi$
$2$	12.9147	0.570755	0.285378	+	0.958415i	$0.407881\pi$
$3$	101.422	0.722917	0.361459	−	0.932388i	$-0.382279\pi$
$3$	101.422	0.722917	0.361459	+	0.932388i	$0.382279\pi$
$4$	−345.210	−0.674238
$5$	2078.59	1.48732	0.743658	−	0.668560i	$-0.233089\pi$
$5$	2078.59	1.48732	0.743658	+	0.668560i	$0.233089\pi$
$6$	1309.84	0.412609
$7$	2161.61	0.340280	0.170140	−	0.985420i	$-0.445578\pi$
$7$	2161.61	0.340280	0.170140	+	0.985420i	$0.445578\pi$
$8$	−11070.6	−0.955580
$9$	−9396.49	−0.477391
$10$	26844.4	0.848893
$11$	−13147.0	−0.270745	−0.135372	−	0.990795i	$-0.543223\pi$
$11$	−13147.0	−0.270745	−0.135372	+	0.990795i	$0.543223\pi$
$12$	−35012.1	−0.487418
$13$	−17852.0	−0.173357	−0.0866785	−	0.996236i	$-0.527625\pi$
$13$	−17852.0	−0.173357	−0.0866785	+	0.996236i	$0.527625\pi$
$14$	27916.6	0.194217
$15$	210815.	1.07521
$16$	33773.6	0.128836
$17$	0	0
$17$	0	0
$18$	−121353.	−0.272473
$19$	−30951.0	−0.0544858	−0.0272429	−	0.999629i	$-0.508673\pi$
$19$	−30951.0	−0.0544858	−0.0272429	+	0.999629i	$0.508673\pi$
$20$	−717549.	−1.00281
$21$	219236.	0.245994
$22$	−169790.	−0.154529
$23$	−193663.	−0.144302	−0.0721510	−	0.997394i	$-0.522986\pi$
$23$	−193663.	−0.144302	−0.0721510	+	0.997394i	$0.522986\pi$
$24$	−1.12281e6	−0.690805
$25$	2.36740e6	1.21211
$26$	−230553.	−0.0989444
$27$	−2.94931e6	−1.06803
$28$	−746210.	−0.229430
$29$	1.83211e6	0.481017	0.240508	−	0.970647i	$-0.422686\pi$
$29$	1.83211e6	0.481017	0.240508	+	0.970647i	$0.422686\pi$
$30$	2.72262e6	0.613680
$31$	−525734.	−0.102244	−0.0511221	−	0.998692i	$-0.516280\pi$
$31$	−525734.	−0.102244	−0.0511221	+	0.998692i	$0.516280\pi$
$32$	6.10434e6	1.02911
$33$	−1.33340e6	−0.195726
$34$	0	0
$35$	4.49310e6	0.506104
$36$	3.24376e6	0.321875
$37$	−1.78204e7	−1.56318	−0.781591	−	0.623791i	$-0.785592\pi$
$37$	−1.78204e7	−1.56318	−0.781591	+	0.623791i	$0.785592\pi$
$38$	−399723.	−0.0310981
$39$	−1.81059e6	−0.125323
$40$	−2.30113e7	−1.42125
$41$	−1.53721e7	−0.849582	−0.424791	−	0.905291i	$-0.639652\pi$
$41$	−1.53721e7	−0.849582	−0.424791	+	0.905291i	$0.639652\pi$
$42$	2.83137e6	0.140402
$43$	−4.23089e7	−1.88723	−0.943613	−	0.331051i	$-0.892597\pi$
$43$	−4.23089e7	−1.88723	−0.943613	+	0.331051i	$0.892597\pi$
$44$	4.53848e6	0.182547
$45$	−1.95314e7	−0.710031
$46$	−2.50111e6	−0.0823611
$47$	5.91782e7	1.76897	0.884487	−	0.466565i	$-0.154509\pi$
$47$	5.91782e7	1.76897	0.884487	+	0.466565i	$0.154509\pi$
$48$	3.42540e6	0.0931377
$49$	−3.56810e7	−0.884210
$50$	3.05743e7	0.691817
$51$	0	0
$52$	6.16269e6	0.116884
$53$	−8.32863e7	−1.44988	−0.724941	−	0.688811i	$-0.758133\pi$
$53$	−8.32863e7	−1.44988	−0.724941	+	0.688811i	$0.758133\pi$
$54$	−3.80895e7	−0.609584
$55$	−2.73272e7	−0.402683
$56$	−2.39304e7	−0.325165
$57$	−3.13913e6	−0.0393887
$58$	2.36612e7	0.274543
$59$	9.24034e7	0.992782	0.496391	−	0.868099i	$-0.334658\pi$
$59$	9.24034e7	0.992782	0.496391	+	0.868099i	$0.334658\pi$
$60$	−7.27756e7	−0.724945
$61$	−1.01929e8	−0.942568	−0.471284	−	0.881981i	$-0.656209\pi$
$61$	−1.01929e8	−0.942568	−0.471284	+	0.881981i	$0.656209\pi$
$62$	−6.78970e6	−0.0583564
$63$	−2.03115e7	−0.162447
$64$	6.15437e7	0.458536
$65$	−3.71069e7	−0.257837
$66$	−1.72205e7	−0.111712
$67$	1.25363e8	0.760031	0.380015	−	0.924980i	$-0.375919\pi$
$67$	1.25363e8	0.760031	0.380015	+	0.924980i	$0.375919\pi$
$68$	0	0
$69$	−1.96418e7	−0.104318
$70$	5.80271e7	0.288861
$71$	2.14775e8	1.00305	0.501523	−	0.865144i	$-0.332773\pi$
$71$	2.14775e8	1.00305	0.501523	+	0.865144i	$0.332773\pi$
$72$	1.04025e8	0.456185
$73$	−1.02966e8	−0.424365	−0.212182	−	0.977230i	$-0.568057\pi$
$73$	−1.02966e8	−0.424365	−0.212182	+	0.977230i	$0.568057\pi$
$74$	−2.30145e8	−0.892194
$75$	2.40108e8	0.876254
$76$	1.06846e7	0.0367364
$77$	−2.84187e7	−0.0921290
$78$	−2.33833e7	−0.0715286
$79$	−9.58995e6	−0.0277009	−0.0138505	−	0.999904i	$-0.504409\pi$
$79$	−9.58995e6	−0.0277009	−0.0138505	+	0.999904i	$0.504409\pi$
$80$	7.02013e7	0.191620
$81$	−1.14176e8	−0.294707
$82$	−1.98526e8	−0.484904
$83$	−6.13699e8	−1.41940	−0.709699	−	0.704505i	$-0.751169\pi$
$83$	−6.13699e8	−1.41940	−0.709699	+	0.704505i	$0.751169\pi$
$84$	−7.56824e7	−0.165859
$85$	0	0
$86$	−5.46408e8	−1.07714
$87$	1.85817e8	0.347735
$88$	1.45546e8	0.258718
$89$	5.89040e8	0.995153	0.497576	−	0.867420i	$-0.334223\pi$
$89$	5.89040e8	0.995153	0.497576	+	0.867420i	$0.334223\pi$
$90$	−2.52243e8	−0.405254
$91$	−3.85890e7	−0.0589899
$92$	6.68545e7	0.0972939
$93$	−5.33212e7	−0.0739140
$94$	7.64270e8	1.00965
$95$	−6.43343e7	−0.0810376
$96$	6.19117e8	0.743964
$97$	8.70682e8	0.998589	0.499295	−	0.866432i	$-0.333593\pi$
$97$	8.70682e8	0.998589	0.499295	+	0.866432i	$0.333593\pi$
$98$	−4.60811e8	−0.504667
$99$	1.23536e8	0.129251
$100$	−8.17250e8	−0.817250
$101$	−1.76796e9	−1.69054	−0.845271	−	0.534338i	$-0.820561\pi$
$101$	−1.76796e9	−1.69054	−0.845271	+	0.534338i	$0.820561\pi$
$102$	0	0
$103$	8.32197e8	0.728549	0.364275	−	0.931292i	$-0.381317\pi$
$103$	8.32197e8	0.728549	0.364275	+	0.931292i	$0.381317\pi$
$104$	1.97633e8	0.165657
$105$	4.55701e8	0.365871
$106$	−1.07562e9	−0.827527
$107$	−1.49690e9	−1.10399	−0.551994	−	0.833848i	$-0.686133\pi$
$107$	−1.49690e9	−1.10399	−0.551994	+	0.833848i	$0.686133\pi$
$108$	1.01813e9	0.720108
$109$	1.25120e9	0.848998	0.424499	−	0.905428i	$-0.360450\pi$
$109$	1.25120e9	0.848998	0.424499	+	0.905428i	$0.360450\pi$
$110$	−3.52923e8	−0.229833
$111$	−1.80739e9	−1.13005
$112$	7.30053e7	0.0438403
$113$	−2.62190e9	−1.51274	−0.756369	−	0.654145i	$-0.773029\pi$
$113$	−2.62190e9	−1.51274	−0.756369	+	0.654145i	$0.773029\pi$
$114$	−4.05409e7	−0.0224813
$115$	−4.02546e8	−0.214623
$116$	−6.32462e8	−0.324320
$117$	1.67746e8	0.0827591
$118$	1.19336e9	0.566636
$119$	0	0
$120$	−2.33386e9	−1.02745
$121$	−2.18510e9	−0.926697
$122$	−1.31638e9	−0.537976
$123$	−1.55907e9	−0.614178
$124$	1.81489e8	0.0689369
$125$	8.61107e8	0.315473
$126$	−2.62318e8	−0.0927172
$127$	−3.13001e9	−1.06765	−0.533825	−	0.845595i	$-0.679246\pi$
$127$	−3.13001e9	−1.06765	−0.533825	+	0.845595i	$0.679246\pi$
$128$	−2.33060e9	−0.767402
$129$	−4.29107e9	−1.36431
$130$	−4.79225e8	−0.147162
$131$	1.31489e9	0.390094	0.195047	−	0.980794i	$-0.437514\pi$
$131$	1.31489e9	0.390094	0.195047	+	0.980794i	$0.437514\pi$
$132$	4.60304e8	0.131966
$133$	−6.69040e7	−0.0185404
$134$	1.61902e9	0.433792
$135$	−6.13040e9	−1.58850
$136$	0	0
$137$	5.14400e8	0.124755	0.0623775	−	0.998053i	$-0.480132\pi$
$137$	5.14400e8	0.124755	0.0623775	+	0.998053i	$0.480132\pi$
$138$	−2.53668e8	−0.0595402
$139$	−7.81812e9	−1.77638	−0.888189	−	0.459478i	$-0.848037\pi$
$139$	−7.81812e9	−1.77638	−0.888189	+	0.459478i	$0.848037\pi$
$140$	−1.55106e9	−0.341235
$141$	6.00200e9	1.27882
$142$	2.77376e9	0.572494
$143$	2.34700e8	0.0469355
$144$	−3.17353e8	−0.0615051
$145$	3.80820e9	0.715424
$146$	−1.32977e9	−0.242208
$147$	−3.61886e9	−0.639210
$148$	6.15178e9	1.05396
$149$	8.47199e9	1.40814	0.704072	−	0.710128i	$-0.251363\pi$
$149$	8.47199e9	1.40814	0.704072	+	0.710128i	$0.251363\pi$
$150$	3.10092e9	0.500127
$151$	−1.13940e9	−0.178353	−0.0891766	−	0.996016i	$-0.528424\pi$
$151$	−1.13940e9	−0.178353	−0.0891766	+	0.996016i	$0.528424\pi$
$152$	3.42647e8	0.0520656
$153$	0	0
$154$	−3.67020e8	−0.0525831
$155$	−1.09278e9	−0.152069
$156$	6.25035e8	0.0844974
$157$	−3.27009e9	−0.429547	−0.214774	−	0.976664i	$-0.568901\pi$
$157$	−3.27009e9	−0.429547	−0.214774	+	0.976664i	$0.568901\pi$
$158$	−1.23851e8	−0.0158105
$159$	−8.44711e9	−1.04814
$160$	1.26884e10	1.53062
$161$	−4.18625e8	−0.0491030
$162$	−1.47454e9	−0.168206
$163$	−2.09512e9	−0.232468	−0.116234	−	0.993222i	$-0.537082\pi$
$163$	−2.09512e9	−0.232468	−0.116234	+	0.993222i	$0.537082\pi$
$164$	5.30660e9	0.572821
$165$	−2.77159e9	−0.291106
$166$	−7.92575e9	−0.810129
$167$	1.40830e10	1.40110	0.700551	−	0.713603i	$-0.252938\pi$
$167$	1.40830e10	1.40110	0.700551	+	0.713603i	$0.252938\pi$
$168$	−2.42708e9	−0.235067
$169$	−1.02858e10	−0.969947
$170$	0	0
$171$	2.90831e8	0.0260110
$172$	1.46055e10	1.27244
$173$	−3.98665e9	−0.338377	−0.169188	−	0.985584i	$-0.554115\pi$
$173$	−3.98665e9	−0.338377	−0.169188	+	0.985584i	$0.554115\pi$
$174$	2.39977e9	0.198472
$175$	5.11740e9	0.412456
$176$	−4.44022e8	−0.0348817
$177$	9.37178e9	0.717699
$178$	7.60728e9	0.567989
$179$	1.82891e10	1.33154	0.665769	−	0.746158i	$-0.268104\pi$
$179$	1.82891e10	1.33154	0.665769	+	0.746158i	$0.268104\pi$
$180$	6.74244e9	0.478730
$181$	−1.12163e10	−0.776775	−0.388387	−	0.921496i	$-0.626968\pi$
$181$	−1.12163e10	−0.776775	−0.388387	+	0.921496i	$0.626968\pi$
$182$	−4.98367e8	−0.0336688
$183$	−1.03379e10	−0.681399
$184$	2.14397e9	0.137892
$185$	−3.70412e10	−2.32495
$186$	−6.88628e8	−0.0421868
$187$	0	0
$188$	−2.04289e10	−1.19271
$189$	−6.37527e9	−0.363430
$190$	−8.30860e8	−0.0462526
$191$	−6.63597e9	−0.360790	−0.180395	−	0.983594i	$-0.557738\pi$
$191$	−6.63597e9	−0.360790	−0.180395	+	0.983594i	$0.557738\pi$
$192$	6.24191e9	0.331484
$193$	1.28453e10	0.666404	0.333202	−	0.942856i	$-0.391871\pi$
$193$	1.28453e10	0.666404	0.333202	+	0.942856i	$0.391871\pi$
$194$	1.12446e10	0.569950
$195$	−3.76347e9	−0.186395
$196$	1.23175e10	0.596168
$197$	−9.15030e9	−0.432850	−0.216425	−	0.976299i	$-0.569440\pi$
$197$	−9.15030e9	−0.432850	−0.216425	+	0.976299i	$0.569440\pi$
$198$	1.59543e9	0.0737707
$199$	−4.02134e10	−1.81774	−0.908870	−	0.417079i	$-0.863054\pi$
$199$	−4.02134e10	−1.81774	−0.908870	+	0.417079i	$0.863054\pi$
$200$	−2.62086e10	−1.15827
$201$	1.27146e10	0.549439
$202$	−2.28327e10	−0.964886
$203$	3.96030e9	0.163680
$204$	0	0
$205$	−3.19522e10	−1.26360
$206$	1.07476e10	0.415823
$207$	1.81975e9	0.0688884
$208$	−6.02925e8	−0.0223346
$209$	4.06913e8	0.0147517
$210$	5.88525e9	0.208823
$211$	9.07065e9	0.315041	0.157521	−	0.987516i	$-0.449650\pi$
$211$	9.07065e9	0.315041	0.157521	+	0.987516i	$0.449650\pi$
$212$	2.87513e10	0.977566
$213$	2.17830e10	0.725119
$214$	−1.93320e10	−0.630107
$215$	−8.79428e10	−2.80690
$216$	3.26507e10	1.02059
$217$	−1.13643e9	−0.0347916
$218$	1.61589e10	0.484570
$219$	−1.04430e10	−0.306781
$220$	9.43363e9	0.271504
$221$	0	0
$222$	−2.33419e10	−0.644982
$223$	2.83923e10	0.768827	0.384414	−	0.923161i	$-0.374404\pi$
$223$	2.83923e10	0.768827	0.384414	+	0.923161i	$0.374404\pi$
$224$	1.31952e10	0.350187
$225$	−2.22452e10	−0.578650
$226$	−3.38611e10	−0.863403
$227$	−7.74085e10	−1.93496	−0.967480	−	0.252946i	$-0.918600\pi$
$227$	−7.74085e10	−1.93496	−0.967480	+	0.252946i	$0.918600\pi$
$228$	1.08366e9	0.0265574
$229$	−1.04661e9	−0.0251492	−0.0125746	−	0.999921i	$-0.504003\pi$
$229$	−1.04661e9	−0.0251492	−0.0125746	+	0.999921i	$0.504003\pi$
$230$	−5.19877e9	−0.122497
$231$	−2.88230e9	−0.0666016
$232$	−2.02826e10	−0.459650
$233$	6.08121e10	1.35172	0.675862	−	0.737028i	$-0.263771\pi$
$233$	6.08121e10	1.35172	0.675862	+	0.737028i	$0.263771\pi$
$234$	2.16639e9	0.0472352
$235$	1.23007e11	2.63102
$236$	−3.18986e10	−0.669372
$237$	−9.72636e8	−0.0200255
$238$	0	0
$239$	−4.87053e10	−0.965574	−0.482787	−	0.875738i	$-0.660375\pi$
$239$	−4.87053e10	−0.965574	−0.482787	+	0.875738i	$0.660375\pi$
$240$	7.11999e9	0.138525
$241$	−8.61021e10	−1.64413	−0.822067	−	0.569391i	$-0.807179\pi$
$241$	−8.61021e10	−1.64413	−0.822067	+	0.569391i	$0.807179\pi$
$242$	−2.82200e10	−0.528917
$243$	4.64714e10	0.854982
$244$	3.51869e10	0.635516
$245$	−7.41662e10	−1.31510
$246$	−2.01350e10	−0.350545
$247$	5.52537e8	0.00944550
$248$	5.82020e9	0.0977025
$249$	−6.22429e10	−1.02611
$250$	1.11209e10	0.180058
$251$	1.62824e10	0.258933	0.129466	−	0.991584i	$-0.458674\pi$
$251$	1.62824e10	0.258933	0.129466	+	0.991584i	$0.458674\pi$
$252$	7.01175e9	0.109528
$253$	2.54609e9	0.0390690
$254$	−4.04232e10	−0.609366
$255$	0	0
$256$	−6.16094e10	−0.896535
$257$	−5.50549e10	−0.787221	−0.393611	−	0.919277i	$-0.628774\pi$
$257$	−5.50549e10	−0.787221	−0.393611	+	0.919277i	$0.628774\pi$
$258$	−5.54180e10	−0.778686
$259$	−3.85208e10	−0.531919
$260$	1.28097e10	0.173843
$261$	−1.72154e10	−0.229633
$262$	1.69814e10	0.222648
$263$	1.36741e10	0.176237	0.0881186	−	0.996110i	$-0.471915\pi$
$263$	1.36741e10	0.176237	0.0881186	+	0.996110i	$0.471915\pi$
$264$	1.47616e10	0.187032
$265$	−1.73118e11	−2.15643
$266$	−8.64046e8	−0.0105820
$267$	5.97419e10	0.719413
$268$	−4.32764e10	−0.512442
$269$	9.50088e10	1.10631	0.553157	−	0.833077i	$-0.313423\pi$
$269$	9.50088e10	1.10631	0.553157	+	0.833077i	$0.313423\pi$
$270$	−7.91724e10	−0.906645
$271$	7.91380e10	0.891299	0.445650	−	0.895208i	$-0.352973\pi$
$271$	7.91380e10	0.891299	0.445650	+	0.895208i	$0.352973\pi$
$272$	0	0
$273$	−3.91380e9	−0.0426448
$274$	6.64333e9	0.0712046
$275$	−3.11242e10	−0.328172
$276$	6.78055e9	0.0703354
$277$	−2.52889e10	−0.258090	−0.129045	−	0.991639i	$-0.541191\pi$
$277$	−2.52889e10	−0.258090	−0.129045	+	0.991639i	$0.541191\pi$
$278$	−1.00969e11	−1.01388
$279$	4.94005e9	0.0488104
$280$	−4.97414e10	−0.483623
$281$	9.53062e8	0.00911891	0.00455946	−	0.999990i	$-0.498549\pi$
$281$	9.53062e8	0.00911891	0.00455946	+	0.999990i	$0.498549\pi$
$282$	7.75141e10	0.729894
$283$	−3.78782e10	−0.351035	−0.175517	−	0.984476i	$-0.556160\pi$
$283$	−3.78782e10	−0.351035	−0.175517	+	0.984476i	$0.556160\pi$
$284$	−7.41425e10	−0.676292
$285$	−6.52495e9	−0.0585835
$286$	3.03109e9	0.0267887
$287$	−3.32285e10	−0.289096
$288$	−5.73593e10	−0.491290
$289$	0	0
$290$	4.91818e10	0.408332
$291$	8.83067e10	0.721897
$292$	3.55448e10	0.286123
$293$	−1.17365e11	−0.930325	−0.465163	−	0.885225i	$-0.654004\pi$
$293$	−1.17365e11	−0.930325	−0.465163	+	0.885225i	$0.654004\pi$
$294$	−4.67365e10	−0.364833
$295$	1.92069e11	1.47658
$296$	1.97283e11	1.49375
$297$	3.87747e10	0.289164
$298$	1.09413e11	0.803706
$299$	3.45727e9	0.0250157
$300$	−8.28875e10	−0.590804
$301$	−9.14554e10	−0.642185
$302$	−1.47151e10	−0.101796
$303$	−1.79311e11	−1.22212
$304$	−1.04533e9	−0.00701973
$305$	−2.11868e11	−1.40190
$306$	0	0
$307$	−8.18712e10	−0.526028	−0.263014	−	0.964792i	$-0.584717\pi$
$307$	−8.18712e10	−0.526028	−0.263014	+	0.964792i	$0.584717\pi$
$308$	9.81043e9	0.0621169
$309$	8.44035e10	0.526681
$310$	−1.41130e10	−0.0867943
$311$	1.69662e11	1.02840	0.514201	−	0.857670i	$-0.328088\pi$
$311$	1.69662e11	1.02840	0.514201	+	0.857670i	$0.328088\pi$
$312$	2.00444e10	0.119756
$313$	3.25773e11	1.91852	0.959258	−	0.282533i	$-0.0911747\pi$
$313$	3.25773e11	1.91852	0.959258	+	0.282533i	$0.0911747\pi$
$314$	−4.22323e10	−0.245166
$315$	−4.22193e10	−0.241609
$316$	3.31055e9	0.0186770
$317$	1.30550e11	0.726124	0.363062	−	0.931765i	$-0.381731\pi$
$317$	1.30550e11	0.726124	0.363062	+	0.931765i	$0.381731\pi$
$318$	−1.09092e11	−0.598234
$319$	−2.40868e10	−0.130233
$320$	1.27924e11	0.681988
$321$	−1.51819e11	−0.798092
$322$	−5.40642e9	−0.0280258
$323$	0	0
$324$	3.94145e10	0.198703
$325$	−4.22628e10	−0.210128
$326$	−2.70578e10	−0.132683
$327$	1.26900e11	0.613755
$328$	1.70179e11	0.811844
$329$	1.27920e11	0.601946
$330$	−3.57943e10	−0.166151
$331$	1.07749e11	0.493385	0.246692	−	0.969094i	$-0.420656\pi$
$331$	1.07749e11	0.493385	0.246692	+	0.969094i	$0.420656\pi$
$332$	2.11855e11	0.957013
$333$	1.67449e11	0.746249
$334$	1.81877e11	0.799686
$335$	2.60577e11	1.13041
$336$	7.40438e9	0.0316929
$337$	−2.54399e11	−1.07444	−0.537218	−	0.843444i	$-0.680525\pi$
$337$	−2.54399e11	−1.07444	−0.537218	+	0.843444i	$0.680525\pi$
$338$	−1.32838e11	−0.553603
$339$	−2.65920e11	−1.09358
$340$	0	0
$341$	6.91183e9	0.0276821
$342$	3.75599e9	0.0148459
$343$	−1.64357e11	−0.641159
$344$	4.68386e11	1.80340
$345$	−4.08272e10	−0.155154
$346$	−5.14864e10	−0.193130
$347$	4.03414e10	0.149372	0.0746859	−	0.997207i	$-0.476205\pi$
$347$	4.03414e10	0.149372	0.0746859	+	0.997207i	$0.476205\pi$
$348$	−6.41459e10	−0.234456
$349$	−2.78080e11	−1.00336	−0.501679	−	0.865054i	$-0.667284\pi$
$349$	−2.78080e11	−1.00336	−0.501679	+	0.865054i	$0.667284\pi$
$350$	6.60897e10	0.235412
$351$	5.26511e10	0.185151
$352$	−8.02538e10	−0.278627
$353$	2.25144e11	0.771746	0.385873	−	0.922552i	$-0.373900\pi$
$353$	2.25144e11	0.771746	0.385873	+	0.922552i	$0.373900\pi$
$354$	1.21034e11	0.409630
$355$	4.46428e11	1.49185
$356$	−2.03343e11	−0.670970
$357$	0	0
$358$	2.36198e11	0.759982
$359$	2.26898e11	0.720952	0.360476	−	0.932768i	$-0.382614\pi$
$359$	2.26898e11	0.720952	0.360476	+	0.932768i	$0.382614\pi$
$360$	2.16225e11	0.678492
$361$	−3.21730e11	−0.997031
$362$	−1.44855e11	−0.443348
$363$	−2.21619e11	−0.669925
$364$	1.33213e10	0.0397733
$365$	−2.14023e11	−0.631164
$366$	−1.33511e11	−0.388912
$367$	−3.78313e11	−1.08856	−0.544281	−	0.838903i	$-0.683198\pi$
$367$	−3.78313e11	−1.08856	−0.544281	+	0.838903i	$0.683198\pi$
$368$	−6.54070e9	−0.0185913
$369$	1.44444e11	0.405583
$370$	−4.78377e11	−1.32697
$371$	−1.80033e11	−0.493365
$372$	1.84070e10	0.0498357
$373$	6.56421e11	1.75587	0.877935	−	0.478779i	$-0.158921\pi$
$373$	6.56421e11	1.75587	0.877935	+	0.478779i	$0.158921\pi$
$374$	0	0
$375$	8.73355e10	0.228061
$376$	−6.55140e11	−1.69040
$377$	−3.27068e10	−0.0833876
$378$	−8.23348e10	−0.207429
$379$	−5.04568e11	−1.25615	−0.628077	−	0.778151i	$-0.716158\pi$
$379$	−5.04568e11	−1.25615	−0.628077	+	0.778151i	$0.716158\pi$
$380$	2.22089e10	0.0546387
$381$	−3.17453e11	−0.771822
$382$	−8.57017e10	−0.205923
$383$	−3.41936e11	−0.811990	−0.405995	−	0.913875i	$-0.633075\pi$
$383$	−3.41936e11	−0.811990	−0.405995	+	0.913875i	$0.633075\pi$
$384$	−2.36375e11	−0.554768
$385$	−5.90708e10	−0.137025
$386$	1.65894e11	0.380353
$387$	3.97555e11	0.900945
$388$	−3.00568e11	−0.673287
$389$	7.41610e11	1.64211	0.821055	−	0.570849i	$-0.193386\pi$
$389$	7.41610e11	1.64211	0.821055	+	0.570849i	$0.193386\pi$
$390$	−4.86042e10	−0.106386
$391$	0	0
$392$	3.95012e11	0.844933
$393$	1.33359e11	0.282005
$394$	−1.18174e11	−0.247051
$395$	−1.99335e10	−0.0412000
$396$	−4.26458e10	−0.0871461
$397$	2.44352e11	0.493695	0.246848	−	0.969054i	$-0.420605\pi$
$397$	2.44352e11	0.493695	0.246848	+	0.969054i	$0.420605\pi$
$398$	−5.19345e11	−1.03748
$399$	−6.78557e9	−0.0134032
$400$	7.99555e10	0.156163
$401$	4.19091e11	0.809392	0.404696	−	0.914451i	$-0.367377\pi$
$401$	4.19091e11	0.809392	0.404696	+	0.914451i	$0.367377\pi$
$402$	1.64205e11	0.313595
$403$	9.38539e9	0.0177247
$404$	6.10317e11	1.13983
$405$	−2.37324e11	−0.438322
$406$	5.11462e10	0.0934214
$407$	2.34285e11	0.423223
$408$	0	0
$409$	−5.47241e11	−0.966994	−0.483497	−	0.875346i	$-0.660634\pi$
$409$	−5.47241e11	−0.966994	−0.483497	+	0.875346i	$0.660634\pi$
$410$	−4.12654e11	−0.721205
$411$	5.21717e10	0.0901876
$412$	−2.87283e11	−0.491216
$413$	1.99740e11	0.337824
$414$	2.35016e10	0.0393184
$415$	−1.27563e12	−2.11109
$416$	−1.08975e11	−0.178404
$417$	−7.92933e11	−1.28417
$418$	5.25517e9	0.00841964
$419$	6.31112e11	1.00033	0.500165	−	0.865930i	$-0.333273\pi$
$419$	6.31112e11	1.00033	0.500165	+	0.865930i	$0.333273\pi$
$420$	−1.57313e11	−0.246684
$421$	2.59316e11	0.402309	0.201154	−	0.979560i	$-0.435531\pi$
$421$	2.59316e11	0.402309	0.201154	+	0.979560i	$0.435531\pi$
$422$	1.17145e11	0.179811
$423$	−5.56067e11	−0.844492
$424$	9.22032e11	1.38548
$425$	0	0
$426$	2.81321e11	0.413866
$427$	−2.20330e11	−0.320737
$428$	5.16744e11	0.744351
$429$	2.38039e10	0.0339305
$430$	−1.13576e12	−1.60205
$431$	−3.20451e11	−0.447315	−0.223658	−	0.974668i	$-0.571800\pi$
$431$	−3.20451e11	−0.447315	−0.223658	+	0.974668i	$0.571800\pi$
$432$	−9.96088e10	−0.137601
$433$	6.08153e11	0.831414	0.415707	−	0.909499i	$-0.363534\pi$
$433$	6.08153e11	0.831414	0.415707	+	0.909499i	$0.363534\pi$
$434$	−1.46767e10	−0.0198575
$435$	3.86237e11	0.517192
$436$	−4.31926e11	−0.572427
$437$	5.99407e9	0.00786241
$438$	−1.34869e11	−0.175097
$439$	−9.67705e11	−1.24352	−0.621760	−	0.783208i	$-0.713582\pi$
$439$	−9.67705e11	−1.24352	−0.621760	+	0.783208i	$0.713582\pi$
$440$	3.02529e11	0.384796
$441$	3.35276e11	0.422114
$442$	0	0
$443$	9.00554e11	1.11095	0.555473	−	0.831535i	$-0.312537\pi$
$443$	9.00554e11	1.11095	0.555473	+	0.831535i	$0.312537\pi$
$444$	6.23929e11	0.761924
$445$	1.22437e12	1.48011
$446$	3.66679e11	0.438812
$447$	8.59250e11	1.01797
$448$	1.33034e11	0.156031
$449$	−2.53168e11	−0.293968	−0.146984	−	0.989139i	$-0.546957\pi$
$449$	−2.53168e11	−0.293968	−0.146984	+	0.989139i	$0.546957\pi$
$450$	−2.87291e11	−0.330267
$451$	2.02097e11	0.230020
$452$	9.05108e11	1.01995
$453$	−1.15561e11	−0.128935
$454$	−9.99708e11	−1.10439
$455$	−8.02107e10	−0.0877366
$456$	3.47521e10	0.0376391
$457$	1.51148e12	1.62099	0.810495	−	0.585745i	$-0.199198\pi$
$457$	1.51148e12	1.62099	0.810495	+	0.585745i	$0.199198\pi$
$458$	−1.35166e10	−0.0143540
$459$	0	0
$460$	1.38963e11	0.144707
$461$	8.09197e11	0.834450	0.417225	−	0.908803i	$-0.363003\pi$
$461$	8.09197e11	0.834450	0.417225	+	0.908803i	$0.363003\pi$
$462$	−3.72241e10	−0.0380132
$463$	1.55999e12	1.57764	0.788819	−	0.614625i	$-0.210693\pi$
$463$	1.55999e12	1.57764	0.788819	+	0.614625i	$0.210693\pi$
$464$	6.18768e10	0.0619722
$465$	−1.10833e11	−0.109933
$466$	7.85371e11	0.771504
$467$	3.66882e11	0.356944	0.178472	−	0.983945i	$-0.442885\pi$
$467$	3.66882e11	0.356944	0.178472	+	0.983945i	$0.442885\pi$
$468$	−5.79076e10	−0.0557993
$469$	2.70985e11	0.258623
$470$	1.58860e12	1.50167
$471$	−3.31660e11	−0.310527
$472$	−1.02296e12	−0.948683
$473$	5.56236e11	0.510957
$474$	−1.25613e10	−0.0114296
$475$	−7.32734e10	−0.0660427
$476$	0	0
$477$	7.82599e11	0.692160
$478$	−6.29015e11	−0.551106
$479$	5.73621e11	0.497869	0.248935	−	0.968520i	$-0.419920\pi$
$479$	5.73621e11	0.497869	0.248935	+	0.968520i	$0.419920\pi$
$480$	1.28689e12	1.10651
$481$	3.18129e11	0.270989
$482$	−1.11198e12	−0.938398
$483$	−4.24579e10	−0.0354974
$484$	7.54320e11	0.624815
$485$	1.80979e12	1.48522
$486$	6.00164e11	0.487986
$487$	1.56412e12	1.26006	0.630028	−	0.776572i	$-0.283043\pi$
$487$	1.56412e12	1.26006	0.630028	+	0.776572i	$0.283043\pi$
$488$	1.12842e12	0.900700
$489$	−2.12492e11	−0.168055
$490$	−9.57835e11	−0.750600
$491$	−1.20510e11	−0.0935743	−0.0467872	−	0.998905i	$-0.514898\pi$
$491$	−1.20510e11	−0.0935743	−0.0467872	+	0.998905i	$0.514898\pi$
$492$	5.38208e11	0.414102
$493$	0	0
$494$	7.13585e9	0.00539107
$495$	2.56780e11	0.192237
$496$	−1.77559e10	−0.0131727
$497$	4.64260e11	0.341316
$498$	−8.03849e11	−0.585656
$499$	4.96049e11	0.358156	0.179078	−	0.983835i	$-0.442689\pi$
$499$	4.96049e11	0.358156	0.179078	+	0.983835i	$0.442689\pi$
$500$	−2.97263e11	−0.212704
$501$	1.42833e12	1.01288
$502$	2.10283e11	0.147787
$503$	−1.48407e11	−0.103371	−0.0516853	−	0.998663i	$-0.516459\pi$
$503$	−1.48407e11	−0.103371	−0.0516853	+	0.998663i	$0.516459\pi$
$504$	2.24861e11	0.155231
$505$	−3.67486e12	−2.51437
$506$	3.28821e10	0.0222988
$507$	−1.04321e12	−0.701191
$508$	1.08051e12	0.719850
$509$	8.49687e11	0.561085	0.280543	−	0.959842i	$-0.409486\pi$
$509$	8.49687e11	0.561085	0.280543	+	0.959842i	$0.409486\pi$
$510$	0	0
$511$	−2.22572e11	−0.144403
$512$	3.97599e11	0.255700
$513$	9.12842e10	0.0581925
$514$	−7.11018e11	−0.449311
$515$	1.72979e12	1.08358
$516$	1.48132e12	0.919869
$517$	−7.78017e11	−0.478941
$518$	−4.97485e11	−0.303596
$519$	−4.04336e11	−0.244618
$520$	4.10797e11	0.246384
$521$	4.63859e11	0.275814	0.137907	−	0.990445i	$-0.455962\pi$
$521$	4.63859e11	0.275814	0.137907	+	0.990445i	$0.455962\pi$
$522$	−2.22332e11	−0.131064
$523$	−3.01502e11	−0.176211	−0.0881054	−	0.996111i	$-0.528081\pi$
$523$	−3.01502e11	−0.176211	−0.0881054	+	0.996111i	$0.528081\pi$
$524$	−4.53913e11	−0.263016
$525$	5.19019e11	0.298172
$526$	1.76597e11	0.100588
$527$	0	0
$528$	−4.50338e10	−0.0252165
$529$	−1.76365e12	−0.979177
$530$	−2.23577e12	−1.23079
$531$	−8.68267e11	−0.473945
$532$	2.30959e10	0.0125007
$533$	2.74422e11	0.147281
$534$	7.71550e11	0.410609
$535$	−3.11143e12	−1.64198
$536$	−1.38784e12	−0.726271
$537$	1.85492e12	0.962591
$538$	1.22701e12	0.631435
$539$	4.69099e11	0.239395
$540$	2.11628e12	1.07103
$541$	2.05647e12	1.03213	0.516066	−	0.856549i	$-0.327396\pi$
$541$	2.05647e12	1.03213	0.516066	+	0.856549i	$0.327396\pi$
$542$	1.02205e12	0.508714
$543$	−1.13758e12	−0.561544
$544$	0	0
$545$	2.60072e12	1.26273
$546$	−5.05456e10	−0.0243398
$547$	3.11555e12	1.48796	0.743981	−	0.668201i	$-0.232935\pi$
$547$	3.11555e12	1.48796	0.743981	+	0.668201i	$0.232935\pi$
$548$	−1.77576e11	−0.0841147
$549$	9.57773e11	0.449973
$550$	−4.01961e11	−0.187306
$551$	−5.67056e10	−0.0262086
$552$	2.17447e11	0.0996845
$553$	−2.07297e10	−0.00942607
$554$	−3.26599e11	−0.147306
$555$	−3.75681e12	−1.68074
$556$	2.69889e12	1.19770
$557$	2.06457e12	0.908828	0.454414	−	0.890791i	$-0.349849\pi$
$557$	2.06457e12	0.908828	0.454414	+	0.890791i	$0.349849\pi$
$558$	6.37993e10	0.0278588
$559$	7.55298e11	0.327164
$560$	1.51748e11	0.0652043
$561$	0	0
$562$	1.23085e10	0.00520467
$563$	3.11121e12	1.30509	0.652547	−	0.757748i	$-0.273700\pi$
$563$	3.11121e12	1.30509	0.652547	+	0.757748i	$0.273700\pi$
$564$	−2.07195e12	−0.862231
$565$	−5.44986e12	−2.24992
$566$	−4.89186e11	−0.200355
$567$	−2.46803e11	−0.100283
$568$	−2.37769e12	−0.958491
$569$	4.33084e11	0.173207	0.0866037	−	0.996243i	$-0.472399\pi$
$569$	4.33084e11	0.173207	0.0866037	+	0.996243i	$0.472399\pi$
$570$	−8.42678e10	−0.0334368
$571$	−4.07139e12	−1.60280	−0.801402	−	0.598126i	$-0.795912\pi$
$571$	−4.07139e12	−1.60280	−0.801402	+	0.598126i	$0.795912\pi$
$572$	−8.10209e10	−0.0316457
$573$	−6.73037e11	−0.260821
$574$	−4.29136e11	−0.165003
$575$	−4.58478e11	−0.174910
$576$	−5.78295e11	−0.218901
$577$	−2.10704e12	−0.791375	−0.395687	−	0.918385i	$-0.629494\pi$
$577$	−2.10704e12	−0.791375	−0.395687	+	0.918385i	$0.629494\pi$
$578$	0	0
$579$	1.30280e12	0.481754
$580$	−1.31463e12	−0.482366
$581$	−1.32658e12	−0.482993
$582$	1.14046e12	0.412027
$583$	1.09497e12	0.392548
$584$	1.13989e12	0.405515
$585$	3.48675e11	0.123089
$586$	−1.51574e12	−0.530988
$587$	−1.65360e12	−0.574857	−0.287428	−	0.957802i	$-0.592800\pi$
$587$	−1.65360e12	−0.574857	−0.287428	+	0.957802i	$0.592800\pi$
$588$	1.24927e12	0.430980
$589$	1.62720e10	0.00557085
$590$	2.48051e12	0.842766
$591$	−9.28046e11	−0.312915
$592$	−6.01858e11	−0.201394
$593$	−1.28308e12	−0.426096	−0.213048	−	0.977042i	$-0.568339\pi$
$593$	−1.28308e12	−0.426096	−0.213048	+	0.977042i	$0.568339\pi$
$594$	5.00764e11	0.165042
$595$	0	0
$596$	−2.92462e12	−0.949425
$597$	−4.07854e12	−1.31408
$598$	4.46497e10	0.0142779
$599$	2.16567e12	0.687341	0.343671	−	0.939090i	$-0.388330\pi$
$599$	2.16567e12	0.687341	0.343671	+	0.939090i	$0.388330\pi$
$600$	−2.65814e12	−0.837331
$601$	7.68293e11	0.240210	0.120105	−	0.992761i	$-0.461677\pi$
$601$	7.68293e11	0.240210	0.120105	+	0.992761i	$0.461677\pi$
$602$	−1.18112e12	−0.366531
$603$	−1.17797e12	−0.362832
$604$	3.93333e11	0.120253
$605$	−4.54193e12	−1.37829
$606$	−2.31575e12	−0.697532
$607$	2.89113e12	0.864406	0.432203	−	0.901776i	$-0.357736\pi$
$607$	2.89113e12	0.864406	0.432203	+	0.901776i	$0.357736\pi$
$608$	−1.88935e11	−0.0560721
$609$	4.01664e11	0.118327
$610$	−2.73621e12	−0.800140
$611$	−1.05645e12	−0.306664
$612$	0	0
$613$	−5.08236e12	−1.45376	−0.726881	−	0.686763i	$-0.759031\pi$
$613$	−5.08236e12	−1.45376	−0.726881	+	0.686763i	$0.759031\pi$
$614$	−1.05734e12	−0.300233
$615$	−3.24067e12	−0.913476
$616$	3.14613e11	0.0880367
$617$	−2.83974e12	−0.788852	−0.394426	−	0.918928i	$-0.629056\pi$
$617$	−2.83974e12	−0.788852	−0.394426	+	0.918928i	$0.629056\pi$
$618$	1.09005e12	0.300606
$619$	2.75485e12	0.754206	0.377103	−	0.926171i	$-0.376920\pi$
$619$	2.75485e12	0.754206	0.377103	+	0.926171i	$0.376920\pi$
$620$	3.77240e11	0.102531
$621$	5.71174e11	0.154119
$622$	2.19114e12	0.586966
$623$	1.27328e12	0.338630
$624$	−6.11502e10	−0.0161461
$625$	−2.83394e12	−0.742901
$626$	4.20726e12	1.09500
$627$	4.12701e10	0.0106643
$628$	1.12887e12	0.289617
$629$	0	0
$630$	−5.45250e11	−0.137900
$631$	4.35581e12	1.09380	0.546899	−	0.837199i	$-0.315808\pi$
$631$	4.35581e12	1.09380	0.546899	+	0.837199i	$0.315808\pi$
$632$	1.06167e11	0.0264705
$633$	9.19968e11	0.227749
$634$	1.68602e12	0.414439
$635$	−6.50599e12	−1.58793
$636$	2.91603e12	0.706699
$637$	6.36978e11	0.153284
$638$	−3.11074e11	−0.0743310
$639$	−2.01813e12	−0.478845
$640$	−4.84436e12	−1.14137
$641$	9.78124e11	0.228840	0.114420	−	0.993432i	$-0.463499\pi$
$641$	9.78124e11	0.228840	0.114420	+	0.993432i	$0.463499\pi$
$642$	−1.96070e12	−0.455515
$643$	−6.72829e11	−0.155223	−0.0776114	−	0.996984i	$-0.524729\pi$
$643$	−6.72829e11	−0.155223	−0.0776114	+	0.996984i	$0.524729\pi$
$644$	1.44513e11	0.0331072
$645$	−8.91937e12	−2.02916
$646$	0	0
$647$	−6.23882e12	−1.39969	−0.699847	−	0.714293i	$-0.746748\pi$
$647$	−6.23882e12	−1.39969	−0.699847	+	0.714293i	$0.746748\pi$
$648$	1.26399e12	0.281616
$649$	−1.21483e12	−0.268791
$650$	−5.45812e11	−0.119931
$651$	−1.15260e11	−0.0251515
$652$	7.23255e11	0.156739
$653$	9.10099e12	1.95875	0.979375	−	0.202049i	$-0.0647601\pi$
$653$	9.10099e12	1.95875	0.979375	+	0.202049i	$0.0647601\pi$
$654$	1.63887e12	0.350304
$655$	2.73311e12	0.580192
$656$	−5.19170e11	−0.109457
$657$	9.67515e11	0.202588
$658$	1.65205e12	0.343564
$659$	−5.03909e12	−1.04080	−0.520400	−	0.853922i	$-0.674217\pi$
$659$	−5.03909e12	−1.04080	−0.520400	+	0.853922i	$0.674217\pi$
$660$	9.56782e11	0.196275
$661$	−8.54137e12	−1.74029	−0.870144	−	0.492798i	$-0.835974\pi$
$661$	−8.54137e12	−1.74029	−0.870144	+	0.492798i	$0.835974\pi$
$662$	1.39154e12	0.281602
$663$	0	0
$664$	6.79404e12	1.35635
$665$	−1.39066e11	−0.0275755
$666$	2.16256e12	0.425925
$667$	−3.54812e11	−0.0694116
$668$	−4.86158e12	−0.944676
$669$	2.87962e12	0.555798
$670$	3.36528e12	0.645185
$671$	1.34006e12	0.255195
$672$	1.33829e12	0.253156
$673$	−1.57979e12	−0.296846	−0.148423	−	0.988924i	$-0.547420\pi$
$673$	−1.57979e12	−0.296846	−0.148423	+	0.988924i	$0.547420\pi$
$674$	−3.28549e12	−0.613240
$675$	−6.98220e12	−1.29457
$676$	3.55076e12	0.653976
$677$	1.28465e12	0.235037	0.117519	−	0.993071i	$-0.462506\pi$
$677$	1.28465e12	0.235037	0.117519	+	0.993071i	$0.462506\pi$
$678$	−3.43428e12	−0.624169
$679$	1.88208e12	0.339800
$680$	0	0
$681$	−7.85096e12	−1.39882
$682$	8.92643e10	0.0157997
$683$	7.81658e12	1.37443	0.687217	−	0.726453i	$-0.258832\pi$
$683$	7.81658e12	1.37443	0.687217	+	0.726453i	$0.258832\pi$
$684$	−1.00398e11	−0.0175376
$685$	1.06922e12	0.185550
$686$	−2.12263e12	−0.365945
$687$	−1.06149e11	−0.0181808
$688$	−1.42892e12	−0.243143
$689$	1.48683e12	0.251347
$690$	−5.27272e11	−0.0885551
$691$	−5.29472e12	−0.883470	−0.441735	−	0.897146i	$-0.645637\pi$
$691$	−5.29472e12	−0.883470	−0.441735	+	0.897146i	$0.645637\pi$
$692$	1.37623e12	0.228147
$693$	2.67036e11	0.0439816
$694$	5.20998e11	0.0852547
$695$	−1.62506e13	−2.64204
$696$	−2.05711e12	−0.332289
$697$	0	0
$698$	−3.59133e12	−0.572672
$699$	6.16771e12	0.977185
$700$	−1.76658e12	−0.278094
$701$	−4.08705e12	−0.639262	−0.319631	−	0.947542i	$-0.603559\pi$
$701$	−4.08705e12	−0.639262	−0.319631	+	0.947542i	$0.603559\pi$
$702$	6.79974e11	0.105676
$703$	5.51559e11	0.0851712
$704$	−8.09116e11	−0.124146
$705$	1.24757e13	1.90201
$706$	2.90767e12	0.440478
$707$	−3.82164e12	−0.575257
$708$	−3.23523e12	−0.483900
$709$	7.02438e12	1.04400	0.522000	−	0.852946i	$-0.325186\pi$
$709$	7.02438e12	1.04400	0.522000	+	0.852946i	$0.325186\pi$
$710$	5.76550e12	0.851479
$711$	9.01118e10	0.0132242
$712$	−6.52104e12	−0.950948
$713$	1.01815e11	0.0147540
$714$	0	0
$715$	4.87845e11	0.0698079
$716$	−6.31358e12	−0.897773
$717$	−4.93981e12	−0.698030
$718$	2.93033e12	0.411487
$719$	1.05283e13	1.46919	0.734594	−	0.678507i	$-0.237373\pi$
$719$	1.05283e13	1.46919	0.734594	+	0.678507i	$0.237373\pi$
$720$	−6.59646e11	−0.0914775
$721$	1.79889e12	0.247911
$722$	−4.15505e12	−0.569061
$723$	−8.73269e12	−1.18857
$724$	3.87197e12	0.523731
$725$	4.33733e12	0.583044
$726$	−2.86214e12	−0.382363
$727$	−9.94519e11	−0.132041	−0.0660204	−	0.997818i	$-0.521030\pi$
$727$	−9.94519e11	−0.132041	−0.0660204	+	0.997818i	$0.521030\pi$
$728$	4.27205e11	0.0563696
$729$	6.96056e12	0.912788
$730$	−2.76405e12	−0.360240
$731$	0	0
$732$	3.56874e12	0.459425
$733$	3.00202e12	0.384101	0.192051	−	0.981385i	$-0.438486\pi$
$733$	3.00202e12	0.384101	0.192051	+	0.981385i	$0.438486\pi$
$734$	−4.88580e12	−0.621303
$735$	−7.52211e12	−0.950708
$736$	−1.18219e12	−0.148503
$737$	−1.64814e12	−0.205774
$738$	1.86545e12	0.231489
$739$	−1.31885e13	−1.62665	−0.813325	−	0.581810i	$-0.802345\pi$
$739$	−1.31885e13	−1.62665	−0.813325	+	0.581810i	$0.802345\pi$
$740$	1.27870e13	1.56757
$741$	5.60396e10	0.00682831
$742$	−2.32507e12	−0.281591
$743$	−4.22387e12	−0.508464	−0.254232	−	0.967143i	$-0.581823\pi$
$743$	−4.22387e12	−0.508464	−0.254232	+	0.967143i	$0.581823\pi$
$744$	5.90299e11	0.0706308
$745$	1.76098e13	2.09436
$746$	8.47749e12	1.00217
$747$	5.76662e12	0.677608
$748$	0	0
$749$	−3.23571e12	−0.375665
$750$	1.12791e12	0.130167
$751$	−8.30449e12	−0.952649	−0.476325	−	0.879270i	$-0.658031\pi$
$751$	−8.30449e12	−0.952649	−0.476325	+	0.879270i	$0.658031\pi$
$752$	1.99866e12	0.227907
$753$	1.65140e12	0.187187
$754$	−4.22399e11	−0.0475939
$755$	−2.36835e12	−0.265268
$756$	2.20081e12	0.245038
$757$	−9.58086e12	−1.06041	−0.530204	−	0.847870i	$-0.677885\pi$
$757$	−9.58086e12	−1.06041	−0.530204	+	0.847870i	$0.677885\pi$
$758$	−6.51635e12	−0.716957
$759$	2.58231e11	0.0282436
$760$	7.12221e11	0.0774379
$761$	−3.82260e12	−0.413169	−0.206585	−	0.978429i	$-0.566235\pi$
$761$	−3.82260e12	−0.413169	−0.206585	+	0.978429i	$0.566235\pi$
$762$	−4.09982e12	−0.440521
$763$	2.70460e12	0.288897
$764$	2.29081e12	0.243259
$765$	0	0
$766$	−4.41601e12	−0.463448
$767$	−1.64958e12	−0.172106
$768$	−6.24858e12	−0.648121
$769$	−1.25991e13	−1.29919	−0.649595	−	0.760281i	$-0.725061\pi$
$769$	−1.25991e13	−1.29919	−0.649595	+	0.760281i	$0.725061\pi$
$770$	−7.62883e11	−0.0782077
$771$	−5.58380e12	−0.569096
$772$	−4.43434e12	−0.449315
$773$	3.83859e12	0.386691	0.193345	−	0.981131i	$-0.438066\pi$
$773$	3.83859e12	0.386691	0.193345	+	0.981131i	$0.438066\pi$
$774$	5.13431e12	0.514219
$775$	−1.24462e12	−0.123931
$776$	−9.63900e12	−0.954232
$777$	−3.90687e12	−0.384534
$778$	9.57768e12	0.937243
$779$	4.75781e11	0.0462902
$780$	1.29919e12	0.125674
$781$	−2.82365e12	−0.271570
$782$	0	0
$783$	−5.40346e12	−0.513741
$784$	−1.20508e12	−0.113918
$785$	−6.79716e12	−0.638873
$786$	1.72230e12	0.160956
$787$	2.26189e12	0.210177	0.105089	−	0.994463i	$-0.466487\pi$
$787$	2.26189e12	0.210177	0.105089	+	0.994463i	$0.466487\pi$
$788$	3.15878e12	0.291844
$789$	1.38686e12	0.127405
$790$	−2.57436e11	−0.0235151
$791$	−5.66754e12	−0.514754
$792$	−1.36762e12	−0.123510
$793$	1.81963e12	0.163401
$794$	3.15574e12	0.281779
$795$	−1.75580e13	−1.55892
$796$	1.38821e13	1.22559
$797$	1.88804e13	1.65748	0.828741	−	0.559632i	$-0.189058\pi$
$797$	1.88804e13	1.65748	0.828741	+	0.559632i	$0.189058\pi$
$798$	−8.76337e10	−0.00764994
$799$	0	0
$800$	1.44514e13	1.24740
$801$	−5.53491e12	−0.475077
$802$	5.41245e12	0.461965
$803$	1.35369e12	0.114895
$804$	−4.38920e12	−0.370453
$805$	−8.70148e11	−0.0730317
$806$	1.21210e11	0.0101165
$807$	9.63602e12	0.799773
$808$	1.95724e13	1.61545
$809$	3.59571e11	0.0295132	0.0147566	−	0.999891i	$-0.495303\pi$
$809$	3.59571e11	0.0295132	0.0147566	+	0.999891i	$0.495303\pi$
$810$	−3.06497e12	−0.250175
$811$	1.94199e13	1.57635	0.788174	−	0.615452i	$-0.211027\pi$
$811$	1.94199e13	1.57635	0.788174	+	0.615452i	$0.211027\pi$
$812$	−1.36714e12	−0.110360
$813$	8.02637e12	0.644335
$814$	3.02572e12	0.241557
$815$	−4.35488e12	−0.345754
$816$	0	0
$817$	1.30950e12	0.102827
$818$	−7.06746e12	−0.551917
$819$	3.62601e11	0.0281612
$820$	1.10302e13	0.851966
$821$	1.20567e13	0.926153	0.463077	−	0.886318i	$-0.346745\pi$
$821$	1.20567e13	0.926153	0.463077	+	0.886318i	$0.346745\pi$
$822$	6.73783e11	0.0514750
$823$	−1.80283e13	−1.36979	−0.684897	−	0.728640i	$-0.740153\pi$
$823$	−1.80283e13	−1.36979	−0.684897	+	0.728640i	$0.740153\pi$
$824$	−9.21295e12	−0.696187
$825$	−3.15670e12	−0.237241
$826$	2.57959e12	0.192815
$827$	1.53472e13	1.14092	0.570458	−	0.821326i	$-0.306766\pi$
$827$	1.53472e13	1.14092	0.570458	+	0.821326i	$0.306766\pi$
$828$	−6.28198e11	−0.0464472
$829$	1.06941e13	0.786412	0.393206	−	0.919450i	$-0.371366\pi$
$829$	1.06941e13	0.786412	0.393206	+	0.919450i	$0.371366\pi$
$830$	−1.64744e13	−1.20492
$831$	−2.56487e12	−0.186578
$832$	−1.09868e12	−0.0794905
$833$	0	0
$834$	−1.02405e13	−0.732949
$835$	2.92726e13	2.08388
$836$	−1.40471e11	−0.00994620
$837$	1.55055e12	0.109200
$838$	8.15064e12	0.570944
$839$	1.24511e13	0.867518	0.433759	−	0.901029i	$-0.357187\pi$
$839$	1.24511e13	0.867518	0.433759	+	0.901029i	$0.357187\pi$
$840$	−5.04489e12	−0.349619
$841$	−1.11505e13	−0.768623
$842$	3.34899e12	0.229620
$843$	9.66619e10	0.00659222
$844$	−3.13128e12	−0.212413
$845$	−2.13799e13	−1.44262
$846$	−7.18145e12	−0.481998
$847$	−4.72334e12	−0.315336
$848$	−2.81288e12	−0.186797
$849$	−3.84170e12	−0.253769
$850$	0	0
$851$	3.45116e12	0.225570
$852$	−7.51971e12	−0.488903
$853$	1.72550e13	1.11595	0.557974	−	0.829858i	$-0.311579\pi$
$853$	1.72550e13	1.11595	0.557974	+	0.829858i	$0.311579\pi$
$854$	−2.84551e12	−0.183062
$855$	6.04517e11	0.0386866
$856$	1.65716e13	1.05495
$857$	5.66030e12	0.358447	0.179224	−	0.983808i	$-0.442641\pi$
$857$	5.66030e12	0.358447	0.179224	+	0.983808i	$0.442641\pi$
$858$	3.07420e11	0.0193660
$859$	−6.43103e12	−0.403006	−0.201503	−	0.979488i	$-0.564583\pi$
$859$	−6.43103e12	−0.403006	−0.201503	+	0.979488i	$0.564583\pi$
$860$	3.03587e13	1.89252
$861$	−3.37011e12	−0.208992
$862$	−4.13853e12	−0.255307
$863$	−1.51972e13	−0.932645	−0.466322	−	0.884615i	$-0.654421\pi$
$863$	−1.51972e13	−0.932645	−0.466322	+	0.884615i	$0.654421\pi$
$864$	−1.80036e13	−1.09913
$865$	−8.28660e12	−0.503273
$866$	7.85412e12	0.474534
$867$	0	0
$868$	3.92308e11	0.0234578
$869$	1.26079e11	0.00749988
$870$	4.98814e12	0.295190
$871$	−2.23797e12	−0.131757
$872$	−1.38515e13	−0.811286
$873$	−8.18135e12	−0.476718
$874$	7.74117e10	0.00448751
$875$	1.86138e12	0.107349
$876$	3.60504e12	0.206843
$877$	1.55933e13	0.890104	0.445052	−	0.895505i	$-0.353185\pi$
$877$	1.55933e13	0.890104	0.445052	+	0.895505i	$0.353185\pi$
$878$	−1.24976e13	−0.709745
$879$	−1.19035e13	−0.672548
$880$	−9.22938e11	−0.0518800
$881$	6.53525e12	0.365486	0.182743	−	0.983161i	$-0.441502\pi$
$881$	6.53525e12	0.365486	0.182743	+	0.983161i	$0.441502\pi$
$882$	4.33000e12	0.240924
$883$	7.83304e12	0.433618	0.216809	−	0.976214i	$-0.430435\pi$
$883$	7.83304e12	0.433618	0.216809	+	0.976214i	$0.430435\pi$
$884$	0	0
$885$	1.94801e13	1.06745
$886$	1.16304e13	0.634078
$887$	1.69970e13	0.921967	0.460983	−	0.887409i	$-0.347497\pi$
$887$	1.69970e13	0.921967	0.460983	+	0.887409i	$0.347497\pi$
$888$	2.00089e13	1.07985
$889$	−6.76586e12	−0.363300
$890$	1.58124e13	0.844779
$891$	1.50107e12	0.0797904
$892$	−9.80131e12	−0.518373
$893$	−1.83162e12	−0.0963840
$894$	1.10970e13	0.581013
$895$	3.80154e13	1.98042
$896$	−5.03785e12	−0.261132
$897$	3.50645e11	0.0180843
$898$	−3.26959e12	−0.167784
$899$	−9.63201e11	−0.0491811
$900$	7.67928e12	0.390148
$901$	0	0
$902$	2.61003e12	0.131285
$903$	−9.27563e12	−0.464247
$904$	2.90261e13	1.44554
$905$	−2.33140e13	−1.15531
$906$	−1.49244e12	−0.0735901
$907$	−2.70047e13	−1.32497	−0.662486	−	0.749075i	$-0.730498\pi$
$907$	−2.70047e13	−1.32497	−0.662486	+	0.749075i	$0.730498\pi$
$908$	2.67222e13	1.30462
$909$	1.66126e13	0.807049
$910$	−1.03590e12	−0.0500761
$911$	−4.11523e13	−1.97953	−0.989763	−	0.142722i	$-0.954415\pi$
$911$	−4.11523e13	−1.97953	−0.989763	+	0.142722i	$0.954415\pi$
$912$	−1.06019e11	−0.00507468
$913$	8.06832e12	0.384295
$914$	1.95204e13	0.925189
$915$	−2.14882e13	−1.01345
$916$	3.61299e11	0.0169566
$917$	2.84228e12	0.132741
$918$	0	0
$919$	−3.01787e12	−0.139566	−0.0697832	−	0.997562i	$-0.522231\pi$
$919$	−3.01787e12	−0.139566	−0.0697832	+	0.997562i	$0.522231\pi$
$920$	4.45644e12	0.205089
$921$	−8.30358e12	−0.380274
$922$	1.04506e13	0.476267
$923$	−3.83416e12	−0.173885
$924$	9.94998e11	0.0449054
$925$	−4.21880e13	−1.89475
$926$	2.01468e13	0.900445
$927$	−7.81973e12	−0.347803
$928$	1.11838e13	0.495021
$929$	2.85800e13	1.25890	0.629449	−	0.777041i	$-0.283280\pi$
$929$	2.85800e13	1.25890	0.629449	+	0.777041i	$0.283280\pi$
$930$	−1.43137e12	−0.0627451
$931$	1.10436e12	0.0481769
$932$	−2.09929e13	−0.911385
$933$	1.72075e13	0.743450
$934$	4.73818e12	0.203728
$935$	0	0
$936$	−1.85705e12	−0.0790829
$937$	−3.78192e13	−1.60282	−0.801409	−	0.598117i	$-0.795916\pi$
$937$	−3.78192e13	−1.60282	−0.801409	+	0.598117i	$0.795916\pi$
$938$	3.49969e12	0.147611
$939$	3.30407e13	1.38693
$940$	−4.24633e13	−1.77394
$941$	−2.17056e13	−0.902441	−0.451220	−	0.892413i	$-0.649011\pi$
$941$	−2.17056e13	−0.902441	−0.451220	+	0.892413i	$0.649011\pi$
$942$	−4.28330e12	−0.177235
$943$	2.97701e12	0.122596
$944$	3.12079e12	0.127906
$945$	−1.32515e13	−0.540535
$946$	7.18363e12	0.291631
$947$	−1.29191e13	−0.521986	−0.260993	−	0.965341i	$-0.584050\pi$
$947$	−1.29191e13	−0.521986	−0.260993	+	0.965341i	$0.584050\pi$
$948$	3.35764e11	0.0135019
$949$	1.83814e12	0.0735666
$950$	−9.46305e11	−0.0376942
$951$	1.32407e13	0.524927
$952$	0	0
$953$	2.66939e13	1.04832	0.524159	−	0.851620i	$-0.324380\pi$
$953$	2.66939e13	1.04832	0.524159	+	0.851620i	$0.324380\pi$
$954$	1.01070e13	0.395054
$955$	−1.37935e13	−0.536609
$956$	1.68135e13	0.651027
$957$	−2.44294e12	−0.0941475
$958$	7.40815e12	0.284162
$959$	1.11193e12	0.0424517
$960$	1.29744e13	0.493021
$961$	−2.61632e13	−0.989546
$962$	4.10855e12	0.154668
$963$	1.40656e13	0.527034
$964$	2.97233e13	1.10854
$965$	2.67001e13	0.991153
$966$	−5.48332e11	−0.0202603
$967$	2.52091e13	0.927124	0.463562	−	0.886064i	$-0.346571\pi$
$967$	2.52091e13	0.927124	0.463562	+	0.886064i	$0.346571\pi$
$968$	2.41905e13	0.885534
$969$	0	0
$970$	2.33729e13	0.847696
$971$	−3.23630e13	−1.16832	−0.584161	−	0.811638i	$-0.698576\pi$
$971$	−3.23630e13	−1.16832	−0.584161	+	0.811638i	$0.698576\pi$
$972$	−1.60424e13	−0.576462
$973$	−1.68997e13	−0.604466
$974$	2.02002e13	0.719184
$975$	−4.28640e12	−0.151905
$976$	−3.44250e12	−0.121437
$977$	−3.01878e13	−1.06000	−0.530001	−	0.847997i	$-0.677808\pi$
$977$	−3.01878e13	−1.06000	−0.530001	+	0.847997i	$0.677808\pi$
$978$	−2.74427e12	−0.0959184
$979$	−7.74412e12	−0.269432
$980$	2.56029e13	0.886690
$981$	−1.17569e13	−0.405304
$982$	−1.55635e12	−0.0534080
$983$	−4.00385e13	−1.36769	−0.683843	−	0.729629i	$-0.739693\pi$
$983$	−4.00385e13	−1.36769	−0.683843	+	0.729629i	$0.739693\pi$
$984$	1.72599e13	0.586896
$985$	−1.90197e13	−0.643785
$986$	0	0
$987$	1.29740e13	0.435157
$988$	−1.90741e11	−0.00636852
$989$	8.19369e12	0.272330
$990$	3.31624e12	0.109720
$991$	1.77191e13	0.583593	0.291796	−	0.956480i	$-0.405747\pi$
$991$	1.77191e13	0.583593	0.291796	+	0.956480i	$0.405747\pi$
$992$	−3.20926e12	−0.105221
$993$	1.09281e13	0.356676
$994$	5.99578e12	0.194808
$995$	−8.35870e13	−2.70355
$996$	2.14869e13	0.691841
$997$	−1.52000e13	−0.487210	−0.243605	−	0.969875i	$-0.578330\pi$
$997$	−1.52000e13	−0.487210	−0.243605	+	0.969875i	$0.578330\pi$
$998$	6.40633e12	0.204419
$999$	5.25579e13	1.66953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.f.1.16		24
17.8	even	8		17.10.c.a.13.5	yes	24
17.15	even	8		17.10.c.a.4.8	✓	24
17.16	even	2	inner	289.10.a.f.1.15		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.c.a.4.8	✓	24	17.15	even	8
17.10.c.a.13.5	yes	24	17.8	even	8
289.10.a.f.1.15		24	17.16	even	2	inner
289.10.a.f.1.16		24	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+12.9147 q^{2} +101.422 q^{3} -345.210 q^{4} +2078.59 q^{5} +1309.84 q^{6} +2161.61 q^{7} -11070.6 q^{8} -9396.49 q^{9} +26844.4 q^{10} -13147.0 q^{11} -35012.1 q^{12} -17852.0 q^{13} +27916.6 q^{14} +210815. q^{15} +33773.6 q^{16} -121353. q^{18} -30951.0 q^{19} -717549. q^{20} +219236. q^{21} -169790. q^{22} -193663. q^{23} -1.12281e6 q^{24} +2.36740e6 q^{25} -230553. q^{26} -2.94931e6 q^{27} -746210. q^{28} +1.83211e6 q^{29} +2.72262e6 q^{30} -525734. q^{31} +6.10434e6 q^{32} -1.33340e6 q^{33} +4.49310e6 q^{35} +3.24376e6 q^{36} -1.78204e7 q^{37} -399723. q^{38} -1.81059e6 q^{39} -2.30113e7 q^{40} -1.53721e7 q^{41} +2.83137e6 q^{42} -4.23089e7 q^{43} +4.53848e6 q^{44} -1.95314e7 q^{45} -2.50111e6 q^{46} +5.91782e7 q^{47} +3.42540e6 q^{48} -3.56810e7 q^{49} +3.05743e7 q^{50} +6.16269e6 q^{52} -8.32863e7 q^{53} -3.80895e7 q^{54} -2.73272e7 q^{55} -2.39304e7 q^{56} -3.13913e6 q^{57} +2.36612e7 q^{58} +9.24034e7 q^{59} -7.27756e7 q^{60} -1.01929e8 q^{61} -6.78970e6 q^{62} -2.03115e7 q^{63} +6.15437e7 q^{64} -3.71069e7 q^{65} -1.72205e7 q^{66} +1.25363e8 q^{67} -1.96418e7 q^{69} +5.80271e7 q^{70} +2.14775e8 q^{71} +1.04025e8 q^{72} -1.02966e8 q^{73} -2.30145e8 q^{74} +2.40108e8 q^{75} +1.06846e7 q^{76} -2.84187e7 q^{77} -2.33833e7 q^{78} -9.58995e6 q^{79} +7.02013e7 q^{80} -1.14176e8 q^{81} -1.98526e8 q^{82} -6.13699e8 q^{83} -7.56824e7 q^{84} -5.46408e8 q^{86} +1.85817e8 q^{87} +1.45546e8 q^{88} +5.89040e8 q^{89} -2.52243e8 q^{90} -3.85890e7 q^{91} +6.68545e7 q^{92} -5.33212e7 q^{93} +7.64270e8 q^{94} -6.43343e7 q^{95} +6.19117e8 q^{96} +8.70682e8 q^{97} -4.60811e8 q^{98} +1.23536e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5124 q^{4} + 108368 q^{9} - 244832 q^{13} - 127332 q^{15} - 279932 q^{16} + 888764 q^{18} - 2280212 q^{19} + 775748 q^{21} - 2762628 q^{25} - 3334452 q^{26} - 39084792 q^{30} + 2010240 q^{32} - 30349992 q^{33}+ \cdots + 4413444720 q^{98}+O(q^{100}) \) 24 * q + 5124 * q^4 + 108368 * q^9 - 244832 * q^13 - 127332 * q^15 - 279932 * q^16 + 888764 * q^18 - 2280212 * q^19 + 775748 * q^21 - 2762628 * q^25 - 3334452 * q^26 - 39084792 * q^30 + 2010240 * q^32 - 30349992 * q^33 - 25532364 * q^35 + 31177320 * q^36 - 13171392 * q^38 - 86527192 * q^42 + 61046960 * q^43 - 153365328 * q^47 + 169445876 * q^49 - 236105676 * q^50 - 209898380 * q^52 + 85777812 * q^53 - 255767540 * q^55 - 767709024 * q^59 + 429639656 * q^60 - 1006108924 * q^64 + 346830788 * q^66 - 26076868 * q^67 - 751973532 * q^69 - 319504544 * q^70 - 1171736028 * q^72 - 1640047616 * q^76 - 174401076 * q^77 - 347156560 * q^81 - 1649346672 * q^83 - 935672904 * q^84 + 690159588 * q^86 - 257027500 * q^87 + 191594460 * q^89 + 1842509012 * q^93 + 2877218432 * q^94 + 4413444720 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more