LMFDB - Embedded newform 98.10.a.i.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(1,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,48,-233] 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:	$50.4735119441$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 1115x + 2100 $ x^3 - x^2 - 1115*x + 2100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-33.8126$ of defining polynomial
Character	$\chi$	$=$	98.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+16.0000 q^{2} +23.8447 q^{3} +256.000 q^{4} -1082.37 q^{5} +381.515 q^{6} +4096.00 q^{8} -19114.4 q^{9} -17317.9 q^{10} +74908.8 q^{11} +6104.24 q^{12} +50060.6 q^{13} -25808.7 q^{15} +65536.0 q^{16} -118965. q^{17} -305831. q^{18} -804363. q^{19} -277086. q^{20} +1.19854e6 q^{22} +268788. q^{23} +97667.9 q^{24} -781606. q^{25} +800969. q^{26} -925113. q^{27} -5.29735e6 q^{29} -412940. q^{30} -5.46586e6 q^{31} +1.04858e6 q^{32} +1.78618e6 q^{33} -1.90344e6 q^{34} -4.89329e6 q^{36} +3.10892e6 q^{37} -1.28698e7 q^{38} +1.19368e6 q^{39} -4.43338e6 q^{40} -2.07841e7 q^{41} +4.76437e6 q^{43} +1.91766e7 q^{44} +2.06888e7 q^{45} +4.30061e6 q^{46} -3.01532e7 q^{47} +1.56269e6 q^{48} -1.25057e7 q^{50} -2.83669e6 q^{51} +1.28155e7 q^{52} +5.71741e7 q^{53} -1.48018e7 q^{54} -8.10788e7 q^{55} -1.91798e7 q^{57} -8.47576e7 q^{58} -1.83676e8 q^{59} -6.60703e6 q^{60} -5.30167e7 q^{61} -8.74537e7 q^{62} +1.67772e7 q^{64} -5.41839e7 q^{65} +2.85788e7 q^{66} +1.73487e8 q^{67} -3.04551e7 q^{68} +6.40918e6 q^{69} -1.68342e8 q^{71} -7.82927e7 q^{72} +4.64679e8 q^{73} +4.97427e7 q^{74} -1.86372e7 q^{75} -2.05917e8 q^{76} +1.90989e7 q^{78} -4.13728e8 q^{79} -7.09340e7 q^{80} +3.54170e8 q^{81} -3.32545e8 q^{82} -3.50584e8 q^{83} +1.28764e8 q^{85} +7.62299e7 q^{86} -1.26314e8 q^{87} +3.06826e8 q^{88} -5.17472e8 q^{89} +3.31021e8 q^{90} +6.88098e7 q^{92} -1.30332e8 q^{93} -4.82452e8 q^{94} +8.70616e8 q^{95} +2.50030e7 q^{96} -1.32529e9 q^{97} -1.43184e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 48 q^{2} - 233 q^{3} + 768 q^{4} - 733 q^{5} - 3728 q^{6} + 12288 q^{8} + 15058 q^{9} - 11728 q^{10} - 7339 q^{11} - 59648 q^{12} - 98518 q^{13} + 369119 q^{15} + 196608 q^{16} - 306665 q^{17} + 240928 q^{18}+ \cdots - 628109434 q^{99}+O(q^{100}) $ 3 * q + 48 * q^2 - 233 * q^3 + 768 * q^4 - 733 * q^5 - 3728 * q^6 + 12288 * q^8 + 15058 * q^9 - 11728 * q^10 - 7339 * q^11 - 59648 * q^12 - 98518 * q^13 + 369119 * q^15 + 196608 * q^16 - 306665 * q^17 + 240928 * q^18 - 377991 * q^19 - 187648 * q^20 - 117424 * q^22 + 2267255 * q^23 - 954368 * q^24 + 142612 * q^25 - 1576288 * q^26 - 10674179 * q^27 - 6542978 * q^29 + 5905904 * q^30 - 6654517 * q^31 + 3145728 * q^32 + 3747977 * q^33 - 4906640 * q^34 + 3854848 * q^36 + 22287969 * q^37 - 6047856 * q^38 - 3151974 * q^39 - 3002368 * q^40 - 34048098 * q^41 - 62824140 * q^43 - 1878784 * q^44 - 86300638 * q^45 + 36276080 * q^46 - 52703019 * q^47 - 15269888 * q^48 + 2281792 * q^50 - 97736333 * q^51 - 25220608 * q^52 + 12091125 * q^53 - 170786864 * q^54 - 188717699 * q^55 - 79258835 * q^57 - 104687648 * q^58 - 12949897 * q^59 + 94494464 * q^60 - 160252153 * q^61 - 106472272 * q^62 + 50331648 * q^64 - 334191270 * q^65 + 59967632 * q^66 + 480890225 * q^67 - 78506240 * q^68 - 565616581 * q^69 - 37210720 * q^71 + 61677568 * q^72 + 251382283 * q^73 + 356607504 * q^74 + 16322324 * q^75 - 96765696 * q^76 - 50431584 * q^78 - 286494785 * q^79 - 48037888 * q^80 + 2165894587 * q^81 - 544769568 * q^82 - 1147591172 * q^83 - 1194592537 * q^85 - 1005186240 * q^86 + 1412199358 * q^87 - 30060544 * q^88 - 901243845 * q^89 - 1380810208 * q^90 + 580417280 * q^92 - 710456889 * q^93 - 843248304 * q^94 + 887366177 * q^95 - 244318208 * q^96 - 314853938 * q^97 - 628109434 * 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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	23.8447	0.169960	0.0849799	−	0.996383i	$-0.472917\pi$
$3$	23.8447	0.169960	0.0849799	+	0.996383i	$0.472917\pi$
$4$	256.000	0.500000
$5$	−1082.37	−0.774479	−0.387239	−	0.921979i	$-0.626571\pi$
$5$	−1082.37	−0.774479	−0.387239	+	0.921979i	$0.626571\pi$
$6$	381.515	0.120180
$7$	0	0
$7$	0	0
$8$	4096.00	0.353553
$9$	−19114.4	−0.971114
$10$	−17317.9	−0.547639
$11$	74908.8	1.54264	0.771322	−	0.636445i	$-0.219596\pi$
$11$	74908.8	1.54264	0.771322	+	0.636445i	$0.219596\pi$
$12$	6104.24	0.0849799
$13$	50060.6	0.486128	0.243064	−	0.970010i	$-0.421847\pi$
$13$	50060.6	0.486128	0.243064	+	0.970010i	$0.421847\pi$
$14$	0	0
$15$	−25808.7	−0.131630
$16$	65536.0	0.250000
$17$	−118965.	−0.345462	−0.172731	−	0.984969i	$-0.555259\pi$
$17$	−118965.	−0.345462	−0.172731	+	0.984969i	$0.555259\pi$
$18$	−305831.	−0.686681
$19$	−804363.	−1.41599	−0.707996	−	0.706216i	$-0.750401\pi$
$19$	−804363.	−1.41599	−0.707996	+	0.706216i	$0.750401\pi$
$20$	−277086.	−0.387239
$21$	0	0
$22$	1.19854e6	1.09081
$23$	268788.	0.200279	0.100139	−	0.994973i	$-0.468071\pi$
$23$	268788.	0.200279	0.100139	+	0.994973i	$0.468071\pi$
$24$	97667.9	0.0600899
$25$	−781606.	−0.400182
$26$	800969.	0.343745
$27$	−925113.	−0.335010
$28$	0	0
$29$	−5.29735e6	−1.39081	−0.695405	−	0.718618i	$-0.744775\pi$
$29$	−5.29735e6	−1.39081	−0.695405	+	0.718618i	$0.744775\pi$
$30$	−412940.	−0.0930767
$31$	−5.46586e6	−1.06299	−0.531497	−	0.847060i	$-0.678370\pi$
$31$	−5.46586e6	−1.06299	−0.531497	+	0.847060i	$0.678370\pi$
$32$	1.04858e6	0.176777
$33$	1.78618e6	0.262187
$34$	−1.90344e6	−0.244278
$35$	0	0
$36$	−4.89329e6	−0.485557
$37$	3.10892e6	0.272710	0.136355	−	0.990660i	$-0.456461\pi$
$37$	3.10892e6	0.272710	0.136355	+	0.990660i	$0.456461\pi$
$38$	−1.28698e7	−1.00126
$39$	1.19368e6	0.0826223
$40$	−4.43338e6	−0.273820
$41$	−2.07841e7	−1.14869	−0.574345	−	0.818613i	$-0.694743\pi$
$41$	−2.07841e7	−1.14869	−0.574345	+	0.818613i	$0.694743\pi$
$42$	0	0
$43$	4.76437e6	0.212519	0.106259	−	0.994338i	$-0.466113\pi$
$43$	4.76437e6	0.212519	0.106259	+	0.994338i	$0.466113\pi$
$44$	1.91766e7	0.771322
$45$	2.06888e7	0.752107
$46$	4.30061e6	0.141619
$47$	−3.01532e7	−0.901350	−0.450675	−	0.892688i	$-0.648817\pi$
$47$	−3.01532e7	−0.901350	−0.450675	+	0.892688i	$0.648817\pi$
$48$	1.56269e6	0.0424900
$49$	0	0
$50$	−1.25057e7	−0.282972
$51$	−2.83669e6	−0.0587146
$52$	1.28155e7	0.243064
$53$	5.71741e7	0.995309	0.497655	−	0.867375i	$-0.334195\pi$
$53$	5.71741e7	0.995309	0.497655	+	0.867375i	$0.334195\pi$
$54$	−1.48018e7	−0.236888
$55$	−8.10788e7	−1.19475
$56$	0	0
$57$	−1.91798e7	−0.240662
$58$	−8.47576e7	−0.983451
$59$	−1.83676e8	−1.97341	−0.986706	−	0.162517i	$-0.948039\pi$
$59$	−1.83676e8	−1.97341	−0.986706	+	0.162517i	$0.948039\pi$
$60$	−6.60703e6	−0.0658152
$61$	−5.30167e7	−0.490262	−0.245131	−	0.969490i	$-0.578831\pi$
$61$	−5.30167e7	−0.490262	−0.245131	+	0.969490i	$0.578831\pi$
$62$	−8.74537e7	−0.751650
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−5.41839e7	−0.376496
$66$	2.85788e7	0.185395
$67$	1.73487e8	1.05179	0.525896	−	0.850549i	$-0.323730\pi$
$67$	1.73487e8	1.05179	0.525896	+	0.850549i	$0.323730\pi$
$68$	−3.04551e7	−0.172731
$69$	6.40918e6	0.0340394
$70$	0	0
$71$	−1.68342e8	−0.786195	−0.393097	−	0.919497i	$-0.628596\pi$
$71$	−1.68342e8	−0.786195	−0.393097	+	0.919497i	$0.628596\pi$
$72$	−7.82927e7	−0.343341
$73$	4.64679e8	1.91514	0.957570	−	0.288201i	$-0.0930573\pi$
$73$	4.64679e8	1.91514	0.957570	+	0.288201i	$0.0930573\pi$
$74$	4.97427e7	0.192835
$75$	−1.86372e7	−0.0680149
$76$	−2.05917e8	−0.707996
$77$	0	0
$78$	1.90989e7	0.0584228
$79$	−4.13728e8	−1.19507	−0.597535	−	0.801843i	$-0.703853\pi$
$79$	−4.13728e8	−1.19507	−0.597535	+	0.801843i	$0.703853\pi$
$80$	−7.09340e7	−0.193620
$81$	3.54170e8	0.914175
$82$	−3.32545e8	−0.812247
$83$	−3.50584e8	−0.810850	−0.405425	−	0.914128i	$-0.632876\pi$
$83$	−3.50584e8	−0.810850	−0.405425	+	0.914128i	$0.632876\pi$
$84$	0	0
$85$	1.28764e8	0.267553
$86$	7.62299e7	0.150274
$87$	−1.26314e8	−0.236382
$88$	3.06826e8	0.545407
$89$	−5.17472e8	−0.874243	−0.437122	−	0.899402i	$-0.644002\pi$
$89$	−5.17472e8	−0.874243	−0.437122	+	0.899402i	$0.644002\pi$
$90$	3.31021e8	0.531820
$91$	0	0
$92$	6.88098e7	0.100139
$93$	−1.30332e8	−0.180666
$94$	−4.82452e8	−0.637350
$95$	8.70616e8	1.09666
$96$	2.50030e7	0.0300449
$97$	−1.32529e9	−1.51998	−0.759990	−	0.649935i	$-0.774796\pi$
$97$	−1.32529e9	−1.51998	−0.759990	+	0.649935i	$0.774796\pi$
$98$	0	0
$99$	−1.43184e9	−1.49808
$100$	−2.00091e8	−0.200091
$101$	−6.33162e7	−0.0605437	−0.0302718	−	0.999542i	$-0.509637\pi$
$101$	−6.33162e7	−0.0605437	−0.0302718	+	0.999542i	$0.509637\pi$
$102$	−4.53871e7	−0.0415175
$103$	1.12914e9	0.988508	0.494254	−	0.869318i	$-0.335441\pi$
$103$	1.12914e9	0.988508	0.494254	+	0.869318i	$0.335441\pi$
$104$	2.05048e8	0.171872
$105$	0	0
$106$	9.14786e8	0.703790
$107$	1.84677e8	0.136202	0.0681012	−	0.997678i	$-0.478306\pi$
$107$	1.84677e8	0.136202	0.0681012	+	0.997678i	$0.478306\pi$
$108$	−2.36829e8	−0.167505
$109$	−1.20681e9	−0.818881	−0.409441	−	0.912337i	$-0.634276\pi$
$109$	−1.20681e9	−0.818881	−0.409441	+	0.912337i	$0.634276\pi$
$110$	−1.29726e9	−0.844812
$111$	7.41313e7	0.0463498
$112$	0	0
$113$	3.17054e8	0.182928	0.0914639	−	0.995808i	$-0.470845\pi$
$113$	3.17054e8	0.182928	0.0914639	+	0.995808i	$0.470845\pi$
$114$	−3.06877e8	−0.170174
$115$	−2.90928e8	−0.155112
$116$	−1.35612e9	−0.695405
$117$	−9.56879e8	−0.472086
$118$	−2.93881e9	−1.39541
$119$	0	0
$120$	−1.05713e8	−0.0465383
$121$	3.25338e9	1.37975
$122$	−8.48266e8	−0.346667
$123$	−4.95590e8	−0.195231
$124$	−1.39926e9	−0.531497
$125$	2.95998e9	1.08441
$126$	0	0
$127$	−1.91107e9	−0.651868	−0.325934	−	0.945392i	$-0.605679\pi$
$127$	−1.91107e9	−0.651868	−0.325934	+	0.945392i	$0.605679\pi$
$128$	2.68435e8	0.0883883
$129$	1.13605e8	0.0361197
$130$	−8.66943e8	−0.266223
$131$	6.05291e9	1.79574	0.897869	−	0.440262i	$-0.145114\pi$
$131$	6.05291e9	1.79574	0.897869	+	0.440262i	$0.145114\pi$
$132$	4.57261e8	0.131094
$133$	0	0
$134$	2.77579e9	0.743729
$135$	1.00131e9	0.259458
$136$	−4.87282e8	−0.122139
$137$	4.99562e9	1.21157	0.605783	−	0.795630i	$-0.292860\pi$
$137$	4.99562e9	1.21157	0.605783	+	0.795630i	$0.292860\pi$
$138$	1.02547e8	0.0240695
$139$	5.39864e9	1.22664	0.613321	−	0.789834i	$-0.289833\pi$
$139$	5.39864e9	1.22664	0.613321	+	0.789834i	$0.289833\pi$
$140$	0	0
$141$	−7.18995e8	−0.153193
$142$	−2.69347e9	−0.555924
$143$	3.74998e9	0.749923
$144$	−1.25268e9	−0.242778
$145$	5.73368e9	1.07715
$146$	7.43487e9	1.35421
$147$	0	0
$148$	7.95883e8	0.136355
$149$	6.24945e8	0.103873	0.0519366	−	0.998650i	$-0.483461\pi$
$149$	6.24945e8	0.103873	0.0519366	+	0.998650i	$0.483461\pi$
$150$	−2.98195e8	−0.0480938
$151$	−1.10168e10	−1.72448	−0.862238	−	0.506503i	$-0.830938\pi$
$151$	−1.10168e10	−1.72448	−0.862238	+	0.506503i	$0.830938\pi$
$152$	−3.29467e9	−0.500629
$153$	2.27395e9	0.335483
$154$	0	0
$155$	5.91606e9	0.823266
$156$	3.05582e8	0.0413111
$157$	6.80317e9	0.893641	0.446821	−	0.894624i	$-0.352556\pi$
$157$	6.80317e9	0.893641	0.446821	+	0.894624i	$0.352556\pi$
$158$	−6.61965e9	−0.845042
$159$	1.36330e9	0.169163
$160$	−1.13494e9	−0.136910
$161$	0	0
$162$	5.66672e9	0.646420
$163$	2.06659e9	0.229303	0.114651	−	0.993406i	$-0.463425\pi$
$163$	2.06659e9	0.229303	0.114651	+	0.993406i	$0.463425\pi$
$164$	−5.32072e9	−0.574345
$165$	−1.93330e9	−0.203059
$166$	−5.60934e9	−0.573358
$167$	6.75774e8	0.0672322	0.0336161	−	0.999435i	$-0.489298\pi$
$167$	6.75774e8	0.0672322	0.0336161	+	0.999435i	$0.489298\pi$
$168$	0	0
$169$	−8.09844e9	−0.763679
$170$	2.06023e9	0.189188
$171$	1.53749e10	1.37509
$172$	1.21968e9	0.106259
$173$	1.94416e10	1.65015	0.825076	−	0.565022i	$-0.191132\pi$
$173$	1.94416e10	1.65015	0.825076	+	0.565022i	$0.191132\pi$
$174$	−2.02102e9	−0.167147
$175$	0	0
$176$	4.90922e9	0.385661
$177$	−4.37969e9	−0.335401
$178$	−8.27956e9	−0.618183
$179$	4.09649e9	0.298245	0.149123	−	0.988819i	$-0.452355\pi$
$179$	4.09649e9	0.298245	0.149123	+	0.988819i	$0.452355\pi$
$180$	5.29634e9	0.376054
$181$	2.41926e10	1.67544	0.837720	−	0.546101i	$-0.183888\pi$
$181$	2.41926e10	1.67544	0.837720	+	0.546101i	$0.183888\pi$
$182$	0	0
$183$	−1.26417e9	−0.0833248
$184$	1.10096e9	0.0708093
$185$	−3.36499e9	−0.211209
$186$	−2.08531e9	−0.127750
$187$	−8.91154e9	−0.532924
$188$	−7.71922e9	−0.450675
$189$	0	0
$190$	1.39299e10	0.775453
$191$	5.81998e9	0.316426	0.158213	−	0.987405i	$-0.449427\pi$
$191$	5.81998e9	0.316426	0.158213	+	0.987405i	$0.449427\pi$
$192$	4.00048e8	0.0212450
$193$	2.38583e10	1.23775	0.618874	−	0.785490i	$-0.287589\pi$
$193$	2.38583e10	1.23775	0.618874	+	0.785490i	$0.287589\pi$
$194$	−2.12046e10	−1.07479
$195$	−1.29200e9	−0.0639892
$196$	0	0
$197$	−1.13267e10	−0.535802	−0.267901	−	0.963446i	$-0.586330\pi$
$197$	−1.13267e10	−0.535802	−0.267901	+	0.963446i	$0.586330\pi$
$198$	−2.29094e10	−1.05930
$199$	−1.75287e10	−0.792337	−0.396168	−	0.918178i	$-0.629660\pi$
$199$	−1.75287e10	−0.792337	−0.396168	+	0.918178i	$0.629660\pi$
$200$	−3.20146e9	−0.141486
$201$	4.13674e9	0.178762
$202$	−1.01306e9	−0.0428108
$203$	0	0
$204$	−7.26193e8	−0.0293573
$205$	2.24960e10	0.889636
$206$	1.80662e10	0.698980
$207$	−5.13773e9	−0.194494
$208$	3.28077e9	0.121532
$209$	−6.02538e10	−2.18437
$210$	0	0
$211$	−3.12620e10	−1.08579	−0.542895	−	0.839801i	$-0.682672\pi$
$211$	−3.12620e10	−1.08579	−0.542895	+	0.839801i	$0.682672\pi$
$212$	1.46366e10	0.497655
$213$	−4.01407e9	−0.133622
$214$	2.95483e9	0.0963097
$215$	−5.15680e9	−0.164591
$216$	−3.78926e9	−0.118444
$217$	0	0
$218$	−1.93090e10	−0.579037
$219$	1.10801e10	0.325497
$220$	−2.07562e10	−0.597373
$221$	−5.95547e9	−0.167939
$222$	1.18610e9	0.0327743
$223$	−2.74321e10	−0.742825	−0.371413	−	0.928468i	$-0.621127\pi$
$223$	−2.74321e10	−0.742825	−0.371413	+	0.928468i	$0.621127\pi$
$224$	0	0
$225$	1.49400e10	0.388622
$226$	5.07286e9	0.129350
$227$	−1.15661e10	−0.289115	−0.144557	−	0.989496i	$-0.546176\pi$
$227$	−1.15661e10	−0.289115	−0.144557	+	0.989496i	$0.546176\pi$
$228$	−4.91003e9	−0.120331
$229$	−4.23783e10	−1.01832	−0.509159	−	0.860672i	$-0.670044\pi$
$229$	−4.23783e10	−1.01832	−0.509159	+	0.860672i	$0.670044\pi$
$230$	−4.65484e9	−0.109681
$231$	0	0
$232$	−2.16980e10	−0.491726
$233$	−8.52369e10	−1.89464	−0.947318	−	0.320294i	$-0.896218\pi$
$233$	−8.52369e10	−1.89464	−0.947318	+	0.320294i	$0.896218\pi$
$234$	−1.53101e10	−0.333815
$235$	3.26369e10	0.698076
$236$	−4.70210e10	−0.986706
$237$	−9.86522e9	−0.203114
$238$	0	0
$239$	1.81331e10	0.359486	0.179743	−	0.983714i	$-0.442473\pi$
$239$	1.81331e10	0.359486	0.179743	+	0.983714i	$0.442473\pi$
$240$	−1.69140e9	−0.0329076
$241$	−2.49196e10	−0.475843	−0.237921	−	0.971284i	$-0.576466\pi$
$241$	−2.49196e10	−0.475843	−0.237921	+	0.971284i	$0.576466\pi$
$242$	5.20540e10	0.975630
$243$	2.66541e10	0.490383
$244$	−1.35723e10	−0.245131
$245$	0	0
$246$	−7.92943e9	−0.138049
$247$	−4.02669e10	−0.688354
$248$	−2.23882e10	−0.375825
$249$	−8.35957e9	−0.137812
$250$	4.73597e10	0.766795
$251$	3.47730e9	0.0552981	0.0276491	−	0.999618i	$-0.491198\pi$
$251$	3.47730e9	0.0552981	0.0276491	+	0.999618i	$0.491198\pi$
$252$	0	0
$253$	2.01346e10	0.308959
$254$	−3.05771e10	−0.460940
$255$	3.07034e9	0.0454732
$256$	4.29497e9	0.0625000
$257$	−7.54137e10	−1.07833	−0.539164	−	0.842201i	$-0.681260\pi$
$257$	−7.54137e10	−1.07833	−0.539164	+	0.842201i	$0.681260\pi$
$258$	1.81768e9	0.0255405
$259$	0	0
$260$	−1.38711e10	−0.188248
$261$	1.01256e11	1.35063
$262$	9.68465e10	1.26978
$263$	1.17605e11	1.51574	0.757870	−	0.652405i	$-0.226240\pi$
$263$	1.17605e11	1.51574	0.757870	+	0.652405i	$0.226240\pi$
$264$	7.31618e9	0.0926973
$265$	−6.18834e10	−0.770846
$266$	0	0
$267$	−1.23390e10	−0.148586
$268$	4.44126e10	0.525896
$269$	7.42567e10	0.864670	0.432335	−	0.901713i	$-0.357690\pi$
$269$	7.42567e10	0.864670	0.432335	+	0.901713i	$0.357690\pi$
$270$	1.60210e10	0.183465
$271$	−8.03991e10	−0.905502	−0.452751	−	0.891637i	$-0.649557\pi$
$271$	−8.03991e10	−0.905502	−0.452751	+	0.891637i	$0.649557\pi$
$272$	−7.79651e9	−0.0863654
$273$	0	0
$274$	7.99300e10	0.856707
$275$	−5.85492e10	−0.617339
$276$	1.64075e9	0.0170197
$277$	−1.30578e11	−1.33263	−0.666316	−	0.745670i	$-0.732130\pi$
$277$	−1.30578e11	−1.33263	−0.666316	+	0.745670i	$0.732130\pi$
$278$	8.63782e10	0.867367
$279$	1.04477e11	1.03229
$280$	0	0
$281$	−6.23328e10	−0.596401	−0.298200	−	0.954503i	$-0.596386\pi$
$281$	−6.23328e10	−0.596401	−0.298200	+	0.954503i	$0.596386\pi$
$282$	−1.15039e10	−0.108324
$283$	−6.78313e8	−0.00628625	−0.00314312	−	0.999995i	$-0.501000\pi$
$283$	−6.78313e8	−0.00628625	−0.00314312	+	0.999995i	$0.501000\pi$
$284$	−4.30956e10	−0.393097
$285$	2.07596e10	0.186388
$286$	5.99996e10	0.530275
$287$	0	0
$288$	−2.00429e10	−0.171670
$289$	−1.04435e11	−0.880656
$290$	9.17389e10	0.761662
$291$	−3.16011e10	−0.258335
$292$	1.18958e11	0.957570
$293$	−5.67165e9	−0.0449578	−0.0224789	−	0.999747i	$-0.507156\pi$
$293$	−5.67165e9	−0.0449578	−0.0224789	+	0.999747i	$0.507156\pi$
$294$	0	0
$295$	1.98805e11	1.52837
$296$	1.27341e10	0.0964177
$297$	−6.92991e10	−0.516801
$298$	9.99912e9	0.0734494
$299$	1.34557e10	0.0973612
$300$	−4.77111e9	−0.0340075
$301$	0	0
$302$	−1.76268e11	−1.21939
$303$	−1.50976e9	−0.0102900
$304$	−5.27147e10	−0.353998
$305$	5.73835e10	0.379697
$306$	3.63832e10	0.237222
$307$	1.81171e11	1.16403	0.582017	−	0.813176i	$-0.302264\pi$
$307$	1.81171e11	1.16403	0.582017	+	0.813176i	$0.302264\pi$
$308$	0	0
$309$	2.69240e10	0.168007
$310$	9.46570e10	0.582137
$311$	−1.03806e11	−0.629220	−0.314610	−	0.949221i	$-0.601874\pi$
$311$	−1.03806e11	−0.629220	−0.314610	+	0.949221i	$0.601874\pi$
$312$	4.88931e9	0.0292114
$313$	1.48864e11	0.876678	0.438339	−	0.898810i	$-0.355567\pi$
$313$	1.48864e11	0.876678	0.438339	+	0.898810i	$0.355567\pi$
$314$	1.08851e11	0.631900
$315$	0	0
$316$	−1.05914e11	−0.597535
$317$	1.97699e11	1.09961	0.549803	−	0.835294i	$-0.314703\pi$
$317$	1.97699e11	1.09961	0.549803	+	0.835294i	$0.314703\pi$
$318$	2.18128e10	0.119616
$319$	−3.96818e11	−2.14552
$320$	−1.81591e10	−0.0968099
$321$	4.40356e9	0.0231489
$322$	0	0
$323$	9.56912e10	0.489171
$324$	9.06676e10	0.457088
$325$	−3.91277e10	−0.194540
$326$	3.30654e10	0.162141
$327$	−2.87761e10	−0.139177
$328$	−8.51315e10	−0.406123
$329$	0	0
$330$	−3.09328e10	−0.143584
$331$	5.57880e10	0.255455	0.127728	−	0.991809i	$-0.459232\pi$
$331$	5.57880e10	0.255455	0.127728	+	0.991809i	$0.459232\pi$
$332$	−8.97495e10	−0.405425
$333$	−5.94252e10	−0.264833
$334$	1.08124e10	0.0475404
$335$	−1.87776e11	−0.814590
$336$	0	0
$337$	4.01748e11	1.69676	0.848378	−	0.529391i	$-0.177580\pi$
$337$	4.01748e11	1.69676	0.848378	+	0.529391i	$0.177580\pi$
$338$	−1.29575e11	−0.540003
$339$	7.56005e9	0.0310904
$340$	3.29636e10	0.133776
$341$	−4.09441e11	−1.63982
$342$	2.45999e11	0.972335
$343$	0	0
$344$	1.95149e10	0.0751368
$345$	−6.93708e9	−0.0263628
$346$	3.11065e11	1.16683
$347$	−3.37872e11	−1.25104	−0.625518	−	0.780210i	$-0.715112\pi$
$347$	−3.37872e11	−1.25104	−0.625518	+	0.780210i	$0.715112\pi$
$348$	−3.23363e10	−0.118191
$349$	3.59959e11	1.29879	0.649395	−	0.760451i	$-0.275022\pi$
$349$	3.59959e11	1.29879	0.649395	+	0.760451i	$0.275022\pi$
$350$	0	0
$351$	−4.63117e10	−0.162858
$352$	7.85475e10	0.272703
$353$	−1.90346e11	−0.652467	−0.326233	−	0.945289i	$-0.605780\pi$
$353$	−1.90346e11	−0.652467	−0.326233	+	0.945289i	$0.605780\pi$
$354$	−7.00751e10	−0.237164
$355$	1.82208e11	0.608891
$356$	−1.32473e11	−0.437122
$357$	0	0
$358$	6.55439e10	0.210891
$359$	3.92698e11	1.24777	0.623884	−	0.781517i	$-0.285554\pi$
$359$	3.92698e11	1.24777	0.623884	+	0.781517i	$0.285554\pi$
$360$	8.47415e10	0.265910
$361$	3.24312e11	1.00503
$362$	3.87081e11	1.18471
$363$	7.75758e10	0.234502
$364$	0	0
$365$	−5.02954e11	−1.48324
$366$	−2.02267e10	−0.0589195
$367$	3.24474e10	0.0933646	0.0466823	−	0.998910i	$-0.485135\pi$
$367$	3.24474e10	0.0933646	0.0466823	+	0.998910i	$0.485135\pi$
$368$	1.76153e10	0.0500697
$369$	3.97275e11	1.11551
$370$	−5.38399e10	−0.149347
$371$	0	0
$372$	−3.33649e10	−0.0903331
$373$	−4.38999e11	−1.17429	−0.587143	−	0.809483i	$-0.699748\pi$
$373$	−4.38999e11	−1.17429	−0.587143	+	0.809483i	$0.699748\pi$
$374$	−1.42585e11	−0.376834
$375$	7.05799e10	0.184306
$376$	−1.23508e11	−0.318675
$377$	−2.65189e11	−0.676112
$378$	0	0
$379$	−3.56933e11	−0.888607	−0.444304	−	0.895876i	$-0.646549\pi$
$379$	−3.56933e11	−0.888607	−0.444304	+	0.895876i	$0.646549\pi$
$380$	2.22878e11	0.548328
$381$	−4.55689e10	−0.110791
$382$	9.31197e10	0.223747
$383$	1.52473e11	0.362074	0.181037	−	0.983476i	$-0.442055\pi$
$383$	1.52473e11	0.362074	0.181037	+	0.983476i	$0.442055\pi$
$384$	6.40076e9	0.0150225
$385$	0	0
$386$	3.81733e11	0.875220
$387$	−9.10682e10	−0.206380
$388$	−3.39274e11	−0.759990
$389$	5.57118e11	1.23360	0.616800	−	0.787120i	$-0.288429\pi$
$389$	5.57118e11	1.23360	0.616800	+	0.787120i	$0.288429\pi$
$390$	−2.06720e10	−0.0452472
$391$	−3.19765e10	−0.0691887
$392$	0	0
$393$	1.44330e11	0.305203
$394$	−1.81227e11	−0.378869
$395$	4.47806e11	0.925556
$396$	−3.66551e11	−0.749041
$397$	−8.65912e11	−1.74951	−0.874755	−	0.484566i	$-0.838978\pi$
$397$	−8.65912e11	−1.74951	−0.874755	+	0.484566i	$0.838978\pi$
$398$	−2.80458e11	−0.560267
$399$	0	0
$400$	−5.12233e10	−0.100046
$401$	−6.76491e11	−1.30651	−0.653254	−	0.757138i	$-0.726597\pi$
$401$	−6.76491e11	−1.30651	−0.653254	+	0.757138i	$0.726597\pi$
$402$	6.61878e10	0.126404
$403$	−2.73624e11	−0.516751
$404$	−1.62090e10	−0.0302718
$405$	−3.83342e11	−0.708010
$406$	0	0
$407$	2.32885e11	0.420695
$408$	−1.16191e10	−0.0207588
$409$	2.79042e11	0.493078	0.246539	−	0.969133i	$-0.420707\pi$
$409$	2.79042e11	0.493078	0.246539	+	0.969133i	$0.420707\pi$
$410$	3.59936e11	0.629068
$411$	1.19119e11	0.205918
$412$	2.89060e11	0.494254
$413$	0	0
$414$	−8.22038e10	−0.137528
$415$	3.79461e11	0.627986
$416$	5.24923e10	0.0859361
$417$	1.28729e11	0.208480
$418$	−9.64061e11	−1.54458
$419$	9.62344e10	0.152534	0.0762671	−	0.997087i	$-0.475700\pi$
$419$	9.62344e10	0.152534	0.0762671	+	0.997087i	$0.475700\pi$
$420$	0	0
$421$	4.35437e10	0.0675547	0.0337774	−	0.999429i	$-0.489246\pi$
$421$	4.35437e10	0.0675547	0.0337774	+	0.999429i	$0.489246\pi$
$422$	−5.00192e11	−0.767769
$423$	5.76362e11	0.875313
$424$	2.34185e11	0.351895
$425$	9.29839e10	0.138248
$426$	−6.42251e10	−0.0944847
$427$	0	0
$428$	4.72772e10	0.0681012
$429$	8.94171e10	0.127457
$430$	−8.25088e10	−0.116384
$431$	7.76147e11	1.08342	0.541709	−	0.840566i	$-0.317777\pi$
$431$	7.76147e11	1.08342	0.541709	+	0.840566i	$0.317777\pi$
$432$	−6.06282e10	−0.0837525
$433$	−5.97634e11	−0.817033	−0.408517	−	0.912751i	$-0.633954\pi$
$433$	−5.97634e11	−0.817033	−0.408517	+	0.912751i	$0.633954\pi$
$434$	0	0
$435$	1.36718e11	0.183073
$436$	−3.08944e11	−0.409441
$437$	−2.16203e11	−0.283593
$438$	1.77282e11	0.230161
$439$	3.19834e11	0.410992	0.205496	−	0.978658i	$-0.434119\pi$
$439$	3.19834e11	0.410992	0.205496	+	0.978658i	$0.434119\pi$
$440$	−3.32099e11	−0.422406
$441$	0	0
$442$	−9.52875e10	−0.118751
$443$	−4.42099e11	−0.545384	−0.272692	−	0.962101i	$-0.587914\pi$
$443$	−4.42099e11	−0.545384	−0.272692	+	0.962101i	$0.587914\pi$
$444$	1.89776e10	0.0231749
$445$	5.60095e11	0.677083
$446$	−4.38913e11	−0.525257
$447$	1.49016e10	0.0176543
$448$	0	0
$449$	−7.93959e11	−0.921913	−0.460956	−	0.887423i	$-0.652494\pi$
$449$	−7.93959e11	−0.921913	−0.460956	+	0.887423i	$0.652494\pi$
$450$	2.39039e11	0.274798
$451$	−1.55691e12	−1.77202
$452$	8.11658e10	0.0914639
$453$	−2.62691e11	−0.293092
$454$	−1.85058e11	−0.204435
$455$	0	0
$456$	−7.85604e10	−0.0850868
$457$	9.71595e10	0.104199	0.0520993	−	0.998642i	$-0.483409\pi$
$457$	9.71595e10	0.104199	0.0520993	+	0.998642i	$0.483409\pi$
$458$	−6.78052e11	−0.720060
$459$	1.10056e11	0.115733
$460$	−7.44775e10	−0.0775559
$461$	−8.96191e11	−0.924158	−0.462079	−	0.886839i	$-0.652896\pi$
$461$	−8.96191e11	−0.924158	−0.462079	+	0.886839i	$0.652896\pi$
$462$	0	0
$463$	−6.89366e11	−0.697164	−0.348582	−	0.937278i	$-0.613337\pi$
$463$	−6.89366e11	−0.697164	−0.348582	+	0.937278i	$0.613337\pi$
$464$	−3.47167e11	−0.347703
$465$	1.41067e11	0.139922
$466$	−1.36379e12	−1.33971
$467$	3.75580e11	0.365407	0.182703	−	0.983168i	$-0.441515\pi$
$467$	3.75580e11	0.365407	0.182703	+	0.983168i	$0.441515\pi$
$468$	−2.44961e11	−0.236043
$469$	0	0
$470$	5.22190e11	0.493615
$471$	1.62220e11	0.151883
$472$	−7.52336e11	−0.697706
$473$	3.56893e11	0.327841
$474$	−1.57844e11	−0.143623
$475$	6.28695e11	0.566655
$476$	0	0
$477$	−1.09285e12	−0.966558
$478$	2.90130e11	0.254195
$479$	1.18198e12	1.02589	0.512946	−	0.858421i	$-0.328554\pi$
$479$	1.18198e12	1.02589	0.512946	+	0.858421i	$0.328554\pi$
$480$	−2.70624e10	−0.0232692
$481$	1.55634e11	0.132572
$482$	−3.98713e11	−0.336472
$483$	0	0
$484$	8.32865e11	0.689875
$485$	1.43445e12	1.17719
$486$	4.26465e11	0.346753
$487$	−2.78467e11	−0.224333	−0.112167	−	0.993689i	$-0.535779\pi$
$487$	−2.78467e11	−0.224333	−0.112167	+	0.993689i	$0.535779\pi$
$488$	−2.17156e11	−0.173334
$489$	4.92771e10	0.0389722
$490$	0	0
$491$	7.96998e10	0.0618857	0.0309429	−	0.999521i	$-0.490149\pi$
$491$	7.96998e10	0.0618857	0.0309429	+	0.999521i	$0.490149\pi$
$492$	−1.26871e11	−0.0976156
$493$	6.30201e11	0.480472
$494$	−6.44270e11	−0.486740
$495$	1.54978e12	1.16023
$496$	−3.58210e11	−0.265748
$497$	0	0
$498$	−1.33753e11	−0.0974478
$499$	3.19872e11	0.230953	0.115477	−	0.993310i	$-0.463160\pi$
$499$	3.19872e11	0.230953	0.115477	+	0.993310i	$0.463160\pi$
$500$	7.57756e11	0.542206
$501$	1.61136e10	0.0114268
$502$	5.56368e10	0.0391017
$503$	1.67487e12	1.16661	0.583306	−	0.812253i	$-0.301759\pi$
$503$	1.67487e12	1.16661	0.583306	+	0.812253i	$0.301759\pi$
$504$	0	0
$505$	6.85314e10	0.0468898
$506$	3.22154e11	0.218467
$507$	−1.93105e11	−0.129795
$508$	−4.89234e11	−0.325934
$509$	6.24609e11	0.412457	0.206228	−	0.978504i	$-0.433881\pi$
$509$	6.24609e11	0.412457	0.206228	+	0.978504i	$0.433881\pi$
$510$	4.91255e10	0.0321544
$511$	0	0
$512$	6.87195e10	0.0441942
$513$	7.44127e11	0.474372
$514$	−1.20662e12	−0.762494
$515$	−1.22214e12	−0.765578
$516$	2.90829e10	0.0180598
$517$	−2.25874e12	−1.39046
$518$	0	0
$519$	4.63579e11	0.280460
$520$	−2.21937e11	−0.133111
$521$	−6.42947e11	−0.382301	−0.191150	−	0.981561i	$-0.561222\pi$
$521$	−6.42947e11	−0.382301	−0.191150	+	0.981561i	$0.561222\pi$
$522$	1.62009e12	0.955043
$523$	−1.61733e12	−0.945239	−0.472619	−	0.881267i	$-0.656691\pi$
$523$	−1.61733e12	−0.945239	−0.472619	+	0.881267i	$0.656691\pi$
$524$	1.54954e12	0.897869
$525$	0	0
$526$	1.88168e12	1.07179
$527$	6.50247e11	0.367224
$528$	1.17059e11	0.0655469
$529$	−1.72891e12	−0.959888
$530$	−9.90134e11	−0.545070
$531$	3.51086e12	1.91641
$532$	0	0
$533$	−1.04046e12	−0.558411
$534$	−1.97424e11	−0.105066
$535$	−1.99888e11	−0.105486
$536$	7.10601e11	0.371864
$537$	9.76796e10	0.0506897
$538$	1.18811e12	0.611414
$539$	0	0
$540$	2.56336e11	0.129729
$541$	−2.43457e12	−1.22190	−0.610948	−	0.791670i	$-0.709212\pi$
$541$	−2.43457e12	−1.22190	−0.610948	+	0.791670i	$0.709212\pi$
$542$	−1.28639e12	−0.640287
$543$	5.76865e11	0.284757
$544$	−1.24744e11	−0.0610696
$545$	1.30622e12	0.634206
$546$	0	0
$547$	3.63462e12	1.73587	0.867934	−	0.496680i	$-0.165448\pi$
$547$	3.63462e12	1.73587	0.867934	+	0.496680i	$0.165448\pi$
$548$	1.27888e12	0.605783
$549$	1.01338e12	0.476100
$550$	−9.36786e11	−0.436524
$551$	4.26099e12	1.96938
$552$	2.62520e10	0.0120347
$553$	0	0
$554$	−2.08924e12	−0.942313
$555$	−8.02373e10	−0.0358970
$556$	1.38205e12	0.613321
$557$	−4.44468e10	−0.0195656	−0.00978278	−	0.999952i	$-0.503114\pi$
$557$	−4.44468e10	−0.0195656	−0.00978278	+	0.999952i	$0.503114\pi$
$558$	1.67163e12	0.729938
$559$	2.38507e11	0.103311
$560$	0	0
$561$	−2.12493e11	−0.0905757
$562$	−9.97324e11	−0.421719
$563$	3.86358e12	1.62070	0.810349	−	0.585947i	$-0.199277\pi$
$563$	3.86358e12	1.62070	0.810349	+	0.585947i	$0.199277\pi$
$564$	−1.84063e11	−0.0765966
$565$	−3.43169e11	−0.141674
$566$	−1.08530e10	−0.00444505
$567$	0	0
$568$	−6.89529e11	−0.277962
$569$	−2.06493e12	−0.825849	−0.412925	−	0.910765i	$-0.635493\pi$
$569$	−2.06493e12	−0.825849	−0.412925	+	0.910765i	$0.635493\pi$
$570$	3.32153e11	0.131796
$571$	−3.10168e12	−1.22105	−0.610527	−	0.791996i	$-0.709042\pi$
$571$	−3.10168e12	−1.22105	−0.610527	+	0.791996i	$0.709042\pi$
$572$	9.59994e11	0.374961
$573$	1.38776e11	0.0537796
$574$	0	0
$575$	−2.10087e11	−0.0801480
$576$	−3.20687e11	−0.121389
$577$	−2.08223e11	−0.0782055	−0.0391027	−	0.999235i	$-0.512450\pi$
$577$	−2.08223e11	−0.0782055	−0.0391027	+	0.999235i	$0.512450\pi$
$578$	−1.67096e12	−0.622718
$579$	5.68895e11	0.210367
$580$	1.46782e12	0.538577
$581$	0	0
$582$	−5.05618e11	−0.182671
$583$	4.28284e12	1.53541
$584$	1.90333e12	0.677104
$585$	1.03570e12	0.365620
$586$	−9.07464e10	−0.0317900
$587$	2.56958e12	0.893286	0.446643	−	0.894712i	$-0.352619\pi$
$587$	2.56958e12	0.893286	0.446643	+	0.894712i	$0.352619\pi$
$588$	0	0
$589$	4.39653e12	1.50519
$590$	3.18087e12	1.08072
$591$	−2.70081e11	−0.0910648
$592$	2.03746e11	0.0681776
$593$	−2.03548e12	−0.675960	−0.337980	−	0.941153i	$-0.609744\pi$
$593$	−2.03548e12	−0.675960	−0.337980	+	0.941153i	$0.609744\pi$
$594$	−1.10879e12	−0.365434
$595$	0	0
$596$	1.59986e11	0.0519366
$597$	−4.17966e11	−0.134665
$598$	2.15291e11	0.0688448
$599$	−2.81749e12	−0.894213	−0.447107	−	0.894481i	$-0.647546\pi$
$599$	−2.81749e12	−0.894213	−0.447107	+	0.894481i	$0.647546\pi$
$600$	−7.63378e10	−0.0240469
$601$	−2.84630e12	−0.889908	−0.444954	−	0.895553i	$-0.646780\pi$
$601$	−2.84630e12	−0.889908	−0.444954	+	0.895553i	$0.646780\pi$
$602$	0	0
$603$	−3.31610e12	−1.02141
$604$	−2.82029e12	−0.862238
$605$	−3.52135e12	−1.06859
$606$	−2.41561e10	−0.00727612
$607$	−3.03944e12	−0.908749	−0.454375	−	0.890811i	$-0.650137\pi$
$607$	−3.03944e12	−0.908749	−0.454375	+	0.890811i	$0.650137\pi$
$608$	−8.43436e11	−0.250314
$609$	0	0
$610$	9.18136e11	0.268487
$611$	−1.50949e12	−0.438171
$612$	5.82132e11	0.167741
$613$	5.70963e12	1.63319	0.816594	−	0.577213i	$-0.195860\pi$
$613$	5.70963e12	1.63319	0.816594	+	0.577213i	$0.195860\pi$
$614$	2.89874e12	0.823097
$615$	5.36410e11	0.151202
$616$	0	0
$617$	−2.92315e12	−0.812023	−0.406011	−	0.913868i	$-0.633081\pi$
$617$	−2.92315e12	−0.812023	−0.406011	+	0.913868i	$0.633081\pi$
$618$	4.30784e11	0.118799
$619$	−5.77560e12	−1.58121	−0.790604	−	0.612328i	$-0.790233\pi$
$619$	−5.77560e12	−1.58121	−0.790604	+	0.612328i	$0.790233\pi$
$620$	1.51451e12	0.411633
$621$	−2.48660e11	−0.0670954
$622$	−1.66090e12	−0.444925
$623$	0	0
$624$	7.82290e10	0.0206556
$625$	−1.67721e12	−0.439672
$626$	2.38182e12	0.619905
$627$	−1.43674e12	−0.371255
$628$	1.74161e12	0.446821
$629$	−3.69853e11	−0.0942110
$630$	0	0
$631$	2.44150e12	0.613090	0.306545	−	0.951856i	$-0.400827\pi$
$631$	2.44150e12	0.613090	0.306545	+	0.951856i	$0.400827\pi$
$632$	−1.69463e12	−0.422521
$633$	−7.45433e11	−0.184541
$634$	3.16318e12	0.777539
$635$	2.06848e12	0.504858
$636$	3.49005e11	0.0845813
$637$	0	0
$638$	−6.34909e12	−1.51711
$639$	3.21776e12	0.763484
$640$	−2.90546e11	−0.0684549
$641$	7.90697e12	1.84990	0.924952	−	0.380085i	$-0.124105\pi$
$641$	7.90697e12	1.84990	0.924952	+	0.380085i	$0.124105\pi$
$642$	7.04569e10	0.0163688
$643$	−1.32729e12	−0.306208	−0.153104	−	0.988210i	$-0.548927\pi$
$643$	−1.32729e12	−0.306208	−0.153104	+	0.988210i	$0.548927\pi$
$644$	0	0
$645$	−1.22962e11	−0.0279739
$646$	1.53106e12	0.345896
$647$	3.23220e12	0.725152	0.362576	−	0.931954i	$-0.381897\pi$
$647$	3.23220e12	0.725152	0.362576	+	0.931954i	$0.381897\pi$
$648$	1.45068e12	0.323210
$649$	−1.37589e13	−3.04427
$650$	−6.26042e11	−0.137560
$651$	0	0
$652$	5.29046e11	0.114651
$653$	−1.83929e12	−0.395859	−0.197929	−	0.980216i	$-0.563422\pi$
$653$	−1.83929e12	−0.395859	−0.197929	+	0.980216i	$0.563422\pi$
$654$	−4.60418e11	−0.0984130
$655$	−6.55147e12	−1.39076
$656$	−1.36210e12	−0.287173
$657$	−8.88208e12	−1.85982
$658$	0	0
$659$	5.84606e12	1.20748	0.603738	−	0.797182i	$-0.293677\pi$
$659$	5.84606e12	1.20748	0.603738	+	0.797182i	$0.293677\pi$
$660$	−4.94925e11	−0.101529
$661$	−5.65188e12	−1.15156	−0.575780	−	0.817605i	$-0.695302\pi$
$661$	−5.65188e12	−1.15156	−0.575780	+	0.817605i	$0.695302\pi$
$662$	8.92609e11	0.180634
$663$	−1.42006e11	−0.0285428
$664$	−1.43599e12	−0.286679
$665$	0	0
$666$	−9.50804e11	−0.187265
$667$	−1.42387e12	−0.278550
$668$	1.72998e11	0.0336161
$669$	−6.54110e11	−0.126250
$670$	−3.00442e12	−0.576002
$671$	−3.97141e12	−0.756299
$672$	0	0
$673$	−1.86409e12	−0.350267	−0.175133	−	0.984545i	$-0.556036\pi$
$673$	−1.86409e12	−0.350267	−0.175133	+	0.984545i	$0.556036\pi$
$674$	6.42797e12	1.19979
$675$	7.23074e11	0.134065
$676$	−2.07320e12	−0.381840
$677$	2.29426e12	0.419753	0.209877	−	0.977728i	$-0.432694\pi$
$677$	2.29426e12	0.419753	0.209877	+	0.977728i	$0.432694\pi$
$678$	1.20961e11	0.0219842
$679$	0	0
$680$	5.27418e11	0.0945942
$681$	−2.75790e11	−0.0491379
$682$	−6.55105e12	−1.15953
$683$	−4.93542e12	−0.867822	−0.433911	−	0.900956i	$-0.642867\pi$
$683$	−4.93542e12	−0.867822	−0.433911	+	0.900956i	$0.642867\pi$
$684$	3.93598e12	0.687545
$685$	−5.40710e12	−0.938332
$686$	0	0
$687$	−1.01050e12	−0.173073
$688$	3.12238e11	0.0531297
$689$	2.86217e12	0.483848
$690$	−1.10993e11	−0.0186413
$691$	−7.91985e12	−1.32149	−0.660747	−	0.750608i	$-0.729761\pi$
$691$	−7.91985e12	−1.32149	−0.660747	+	0.750608i	$0.729761\pi$
$692$	4.97704e12	0.825076
$693$	0	0
$694$	−5.40595e12	−0.884616
$695$	−5.84331e12	−0.950008
$696$	−5.17381e11	−0.0835736
$697$	2.47258e12	0.396828
$698$	5.75935e12	0.918384
$699$	−2.03245e12	−0.322012
$700$	0	0
$701$	−1.24405e12	−0.194584	−0.0972919	−	0.995256i	$-0.531018\pi$
$701$	−1.24405e12	−0.194584	−0.0972919	+	0.995256i	$0.531018\pi$
$702$	−7.40987e11	−0.115158
$703$	−2.50070e12	−0.386156
$704$	1.25676e12	0.192830
$705$	7.78216e11	0.118645
$706$	−3.04554e12	−0.461364
$707$	0	0
$708$	−1.12120e12	−0.167700
$709$	−7.28329e12	−1.08248	−0.541239	−	0.840869i	$-0.682045\pi$
$709$	−7.28329e12	−1.08248	−0.541239	+	0.840869i	$0.682045\pi$
$710$	2.91533e12	0.430551
$711$	7.90818e12	1.16055
$712$	−2.11957e12	−0.309092
$713$	−1.46916e12	−0.212895
$714$	0	0
$715$	−4.05885e12	−0.580799
$716$	1.04870e12	0.149123
$717$	4.32379e11	0.0610982
$718$	6.28317e12	0.882305
$719$	3.94689e12	0.550776	0.275388	−	0.961333i	$-0.411194\pi$
$719$	3.94689e12	0.550776	0.275388	+	0.961333i	$0.411194\pi$
$720$	1.35586e12	0.188027
$721$	0	0
$722$	5.18899e12	0.710666
$723$	−5.94199e11	−0.0808742
$724$	6.19330e12	0.837720
$725$	4.14044e12	0.556578
$726$	1.24121e12	0.165818
$727$	1.29298e13	1.71667	0.858335	−	0.513089i	$-0.171499\pi$
$727$	1.29298e13	1.71667	0.858335	+	0.513089i	$0.171499\pi$
$728$	0	0
$729$	−6.33557e12	−0.830830
$730$	−8.04726e12	−1.04881
$731$	−5.66794e11	−0.0734171
$732$	−3.23627e11	−0.0416624
$733$	7.05388e11	0.0902527	0.0451263	−	0.998981i	$-0.485631\pi$
$733$	7.05388e11	0.0902527	0.0451263	+	0.998981i	$0.485631\pi$
$734$	5.19158e11	0.0660187
$735$	0	0
$736$	2.81845e11	0.0354046
$737$	1.29957e13	1.62254
$738$	6.35641e12	0.788784
$739$	2.48471e12	0.306461	0.153231	−	0.988190i	$-0.451032\pi$
$739$	2.48471e12	0.306461	0.153231	+	0.988190i	$0.451032\pi$
$740$	−8.61438e11	−0.105604
$741$	−9.60152e11	−0.116992
$742$	0	0
$743$	7.27764e12	0.876074	0.438037	−	0.898957i	$-0.355674\pi$
$743$	7.27764e12	0.876074	0.438037	+	0.898957i	$0.355674\pi$
$744$	−5.33839e11	−0.0638752
$745$	−6.76420e11	−0.0804476
$746$	−7.02399e12	−0.830346
$747$	6.70121e12	0.787428
$748$	−2.28135e12	−0.266462
$749$	0	0
$750$	1.12928e12	0.130324
$751$	−5.50393e12	−0.631383	−0.315691	−	0.948862i	$-0.602236\pi$
$751$	−5.50393e12	−0.631383	−0.315691	+	0.948862i	$0.602236\pi$
$752$	−1.97612e12	−0.225337
$753$	8.29152e10	0.00939846
$754$	−4.24302e12	−0.478083
$755$	1.19242e13	1.33557
$756$	0	0
$757$	1.41842e13	1.56991	0.784955	−	0.619553i	$-0.212686\pi$
$757$	1.41842e13	1.56991	0.784955	+	0.619553i	$0.212686\pi$
$758$	−5.71092e12	−0.628340
$759$	4.80104e11	0.0525106
$760$	3.56604e12	0.387727
$761$	−1.00139e13	−1.08236	−0.541180	−	0.840907i	$-0.682022\pi$
$761$	−1.00139e13	−1.08236	−0.541180	+	0.840907i	$0.682022\pi$
$762$	−7.29102e11	−0.0783414
$763$	0	0
$764$	1.48992e12	0.158213
$765$	−2.46125e12	−0.259824
$766$	2.43956e12	0.256025
$767$	−9.19491e12	−0.959331
$768$	1.02412e11	0.0106225
$769$	−1.39641e12	−0.143994	−0.0719968	−	0.997405i	$-0.522937\pi$
$769$	−1.39641e12	−0.143994	−0.0719968	+	0.997405i	$0.522937\pi$
$770$	0	0
$771$	−1.79822e12	−0.183273
$772$	6.10773e12	0.618874
$773$	7.42756e12	0.748236	0.374118	−	0.927381i	$-0.377945\pi$
$773$	7.42756e12	0.748236	0.374118	+	0.927381i	$0.377945\pi$
$774$	−1.45709e12	−0.145933
$775$	4.27215e12	0.425391
$776$	−5.42838e12	−0.537394
$777$	0	0
$778$	8.91389e12	0.872286
$779$	1.67179e13	1.62654
$780$	−3.30752e11	−0.0319946
$781$	−1.26103e13	−1.21282
$782$	−5.11623e11	−0.0489238
$783$	4.90065e12	0.465935
$784$	0	0
$785$	−7.36353e12	−0.692106
$786$	2.30928e12	0.215811
$787$	4.31315e12	0.400782	0.200391	−	0.979716i	$-0.435779\pi$
$787$	4.31315e12	0.400782	0.200391	+	0.979716i	$0.435779\pi$
$788$	−2.89963e12	−0.267901
$789$	2.80426e12	0.257615
$790$	7.16489e12	0.654467
$791$	0	0
$792$	−5.86481e12	−0.529652
$793$	−2.65404e12	−0.238330
$794$	−1.38546e13	−1.23709
$795$	−1.47559e12	−0.131013
$796$	−4.48734e12	−0.396168
$797$	6.97760e12	0.612553	0.306276	−	0.951943i	$-0.400917\pi$
$797$	6.97760e12	0.612553	0.306276	+	0.951943i	$0.400917\pi$
$798$	0	0
$799$	3.58718e12	0.311382
$800$	−8.19573e11	−0.0707429
$801$	9.89119e12	0.848989
$802$	−1.08239e13	−0.923841
$803$	3.48086e13	2.95438
$804$	1.05900e12	0.0893811
$805$	0	0
$806$	−4.37798e12	−0.365398
$807$	1.77063e12	0.146959
$808$	−2.59343e11	−0.0214054
$809$	2.28389e11	0.0187459	0.00937296	−	0.999956i	$-0.497016\pi$
$809$	2.28389e11	0.0187459	0.00937296	+	0.999956i	$0.497016\pi$
$810$	−6.13348e12	−0.500638
$811$	1.24712e12	0.101231	0.0506156	−	0.998718i	$-0.483882\pi$
$811$	1.24712e12	0.101231	0.0506156	+	0.998718i	$0.483882\pi$
$812$	0	0
$813$	−1.91709e12	−0.153899
$814$	3.72617e12	0.297476
$815$	−2.23680e12	−0.177590
$816$	−1.85905e11	−0.0146787
$817$	−3.83228e12	−0.300925
$818$	4.46468e12	0.348658
$819$	0	0
$820$	5.75897e12	0.444818
$821$	−4.26405e11	−0.0327550	−0.0163775	−	0.999866i	$-0.505213\pi$
$821$	−4.26405e11	−0.0327550	−0.0163775	+	0.999866i	$0.505213\pi$
$822$	1.90591e12	0.145606
$823$	−1.02124e12	−0.0775939	−0.0387970	−	0.999247i	$-0.512353\pi$
$823$	−1.02124e12	−0.0775939	−0.0387970	+	0.999247i	$0.512353\pi$
$824$	4.62495e12	0.349490
$825$	−1.39609e12	−0.104923
$826$	0	0
$827$	−5.09034e12	−0.378418	−0.189209	−	0.981937i	$-0.560592\pi$
$827$	−5.09034e12	−0.378418	−0.189209	+	0.981937i	$0.560592\pi$
$828$	−1.31526e12	−0.0972468
$829$	−1.29008e13	−0.948681	−0.474340	−	0.880342i	$-0.657313\pi$
$829$	−1.29008e13	−0.948681	−0.474340	+	0.880342i	$0.657313\pi$
$830$	6.07137e12	0.444053
$831$	−3.11359e12	−0.226494
$832$	8.39877e11	0.0607660
$833$	0	0
$834$	2.05966e12	0.147418
$835$	−7.31436e11	−0.0520699
$836$	−1.54250e13	−1.09219
$837$	5.05654e12	0.356114
$838$	1.53975e12	0.107858
$839$	6.08459e12	0.423938	0.211969	−	0.977276i	$-0.432012\pi$
$839$	6.08459e12	0.423938	0.211969	+	0.977276i	$0.432012\pi$
$840$	0	0
$841$	1.35548e13	0.934353
$842$	6.96699e11	0.0477684
$843$	−1.48631e12	−0.101364
$844$	−8.00307e12	−0.542895
$845$	8.76548e12	0.591454
$846$	9.22179e12	0.618940
$847$	0	0
$848$	3.74696e12	0.248827
$849$	−1.61742e10	−0.00106841
$850$	1.48774e12	0.0977559
$851$	8.35641e11	0.0546181
$852$	−1.02760e12	−0.0668108
$853$	−1.69683e13	−1.09741	−0.548703	−	0.836017i	$-0.684878\pi$
$853$	−1.69683e13	−1.09741	−0.548703	+	0.836017i	$0.684878\pi$
$854$	0	0
$855$	−1.66413e13	−1.06498
$856$	7.56435e11	0.0481548
$857$	4.71057e12	0.298305	0.149152	−	0.988814i	$-0.452346\pi$
$857$	4.71057e12	0.298305	0.149152	+	0.988814i	$0.452346\pi$
$858$	1.43067e12	0.0901255
$859$	−8.04517e12	−0.504157	−0.252079	−	0.967707i	$-0.581114\pi$
$859$	−8.04517e12	−0.504157	−0.252079	+	0.967707i	$0.581114\pi$
$860$	−1.32014e12	−0.0822957
$861$	0	0
$862$	1.24184e13	0.766093
$863$	1.75627e13	1.07781	0.538907	−	0.842365i	$-0.318837\pi$
$863$	1.75627e13	1.07781	0.538907	+	0.842365i	$0.318837\pi$
$864$	−9.70052e11	−0.0592220
$865$	−2.10429e13	−1.27801
$866$	−9.56214e12	−0.577730
$867$	−2.49023e12	−0.149676
$868$	0	0
$869$	−3.09919e13	−1.84357
$870$	2.18749e12	0.129452
$871$	8.68484e12	0.511305
$872$	−4.94311e12	−0.289518
$873$	2.53321e13	1.47607
$874$	−3.45925e12	−0.200531
$875$	0	0
$876$	2.83652e12	0.162748
$877$	8.42019e12	0.480644	0.240322	−	0.970693i	$-0.422747\pi$
$877$	8.42019e12	0.480644	0.240322	+	0.970693i	$0.422747\pi$
$878$	5.11734e12	0.290615
$879$	−1.35239e11	−0.00764102
$880$	−5.31358e12	−0.298686
$881$	3.03091e13	1.69504	0.847522	−	0.530760i	$-0.178093\pi$
$881$	3.03091e13	1.69504	0.847522	+	0.530760i	$0.178093\pi$
$882$	0	0
$883$	−2.44649e12	−0.135432	−0.0677159	−	0.997705i	$-0.521571\pi$
$883$	−2.44649e12	−0.135432	−0.0677159	+	0.997705i	$0.521571\pi$
$884$	−1.52460e12	−0.0839693
$885$	4.74044e12	0.259761
$886$	−7.07358e12	−0.385645
$887$	−2.05372e13	−1.11400	−0.557001	−	0.830512i	$-0.688048\pi$
$887$	−2.05372e13	−1.11400	−0.557001	+	0.830512i	$0.688048\pi$
$888$	3.03642e11	0.0163871
$889$	0	0
$890$	8.96152e12	0.478770
$891$	2.65305e13	1.41025
$892$	−7.02261e12	−0.371413
$893$	2.42541e13	1.27630
$894$	2.38426e11	0.0124835
$895$	−4.43391e12	−0.230985
$896$	0	0
$897$	3.20847e11	0.0165475
$898$	−1.27033e13	−0.651891
$899$	2.89546e13	1.47842
$900$	3.82463e12	0.194311
$901$	−6.80173e12	−0.343841
$902$	−2.49105e13	−1.25301
$903$	0	0
$904$	1.29865e12	0.0646748
$905$	−2.61853e13	−1.29759
$906$	−4.20306e12	−0.207247
$907$	1.35046e13	0.662598	0.331299	−	0.943526i	$-0.392513\pi$
$907$	1.35046e13	0.662598	0.331299	+	0.943526i	$0.392513\pi$
$908$	−2.96092e12	−0.144557
$909$	1.21025e12	0.0587948
$910$	0	0
$911$	2.83771e13	1.36501	0.682504	−	0.730882i	$-0.260891\pi$
$911$	2.83771e13	1.36501	0.682504	+	0.730882i	$0.260891\pi$
$912$	−1.25697e12	−0.0601654
$913$	−2.62618e13	−1.25085
$914$	1.55455e12	0.0736796
$915$	1.36829e12	0.0645333
$916$	−1.08488e13	−0.509159
$917$	0	0
$918$	1.76090e12	0.0818357
$919$	−2.60212e13	−1.20339	−0.601696	−	0.798725i	$-0.705508\pi$
$919$	−2.60212e13	−1.20339	−0.601696	+	0.798725i	$0.705508\pi$
$920$	−1.19164e12	−0.0548403
$921$	4.31997e12	0.197839
$922$	−1.43391e13	−0.653478
$923$	−8.42730e12	−0.382191
$924$	0	0
$925$	−2.42995e12	−0.109134
$926$	−1.10299e13	−0.492970
$927$	−2.15829e13	−0.959953
$928$	−5.55468e12	−0.245863
$929$	1.70441e13	0.750764	0.375382	−	0.926870i	$-0.377512\pi$
$929$	1.70441e13	0.750764	0.375382	+	0.926870i	$0.377512\pi$
$930$	2.25707e12	0.0989399
$931$	0	0
$932$	−2.18206e13	−0.947318
$933$	−2.47523e12	−0.106942
$934$	6.00928e12	0.258382
$935$	9.64556e12	0.412739
$936$	−3.91938e12	−0.166908
$937$	−1.17078e13	−0.496188	−0.248094	−	0.968736i	$-0.579804\pi$
$937$	−1.17078e13	−0.496188	−0.248094	+	0.968736i	$0.579804\pi$
$938$	0	0
$939$	3.54962e12	0.149000
$940$	8.35504e12	0.349038
$941$	1.59944e13	0.664990	0.332495	−	0.943105i	$-0.392110\pi$
$941$	1.59944e13	0.664990	0.332495	+	0.943105i	$0.392110\pi$
$942$	2.59551e12	0.107398
$943$	−5.58651e12	−0.230058
$944$	−1.20374e13	−0.493353
$945$	0	0
$946$	5.71029e12	0.231819
$947$	−2.70384e13	−1.09246	−0.546231	−	0.837635i	$-0.683938\pi$
$947$	−2.70384e13	−1.09246	−0.546231	+	0.837635i	$0.683938\pi$
$948$	−2.52550e12	−0.101557
$949$	2.32621e13	0.931003
$950$	1.00591e13	0.400686
$951$	4.71407e12	0.186889
$952$	0	0
$953$	−3.10710e13	−1.22022	−0.610108	−	0.792318i	$-0.708874\pi$
$953$	−3.10710e13	−1.22022	−0.610108	+	0.792318i	$0.708874\pi$
$954$	−1.74856e13	−0.683460
$955$	−6.29936e12	−0.245065
$956$	4.64208e12	0.179743
$957$	−9.46201e12	−0.364653
$958$	1.89117e13	0.725415
$959$	0	0
$960$	−4.32999e11	−0.0164538
$961$	3.43597e12	0.129955
$962$	2.49015e12	0.0937427
$963$	−3.52999e12	−0.132268
$964$	−6.37941e12	−0.237921
$965$	−2.58235e13	−0.958610
$966$	0	0
$967$	−1.42603e13	−0.524457	−0.262228	−	0.965006i	$-0.584457\pi$
$967$	−1.42603e13	−0.524457	−0.262228	+	0.965006i	$0.584457\pi$
$968$	1.33258e13	0.487815
$969$	2.28173e12	0.0831394
$970$	2.29512e13	0.832401
$971$	−2.58561e13	−0.933418	−0.466709	−	0.884411i	$-0.654561\pi$
$971$	−2.58561e13	−0.933418	−0.466709	+	0.884411i	$0.654561\pi$
$972$	6.82345e12	0.245192
$973$	0	0
$974$	−4.45548e12	−0.158628
$975$	−9.32987e11	−0.0330640
$976$	−3.47450e12	−0.122565
$977$	1.08261e13	0.380141	0.190071	−	0.981770i	$-0.439128\pi$
$977$	1.08261e13	0.380141	0.190071	+	0.981770i	$0.439128\pi$
$978$	7.88434e11	0.0275575
$979$	−3.87632e13	−1.34865
$980$	0	0
$981$	2.30676e13	0.795227
$982$	1.27520e12	0.0437598
$983$	2.76603e13	0.944855	0.472428	−	0.881369i	$-0.343378\pi$
$983$	2.76603e13	0.944855	0.472428	+	0.881369i	$0.343378\pi$
$984$	−2.02994e12	−0.0690246
$985$	1.22596e13	0.414967
$986$	1.00832e13	0.339745
$987$	0	0
$988$	−1.03083e13	−0.344177
$989$	1.28061e12	0.0425630
$990$	2.47964e13	0.820409
$991$	−2.70965e13	−0.892446	−0.446223	−	0.894922i	$-0.647231\pi$
$991$	−2.70965e13	−0.892446	−0.446223	+	0.894922i	$0.647231\pi$
$992$	−5.73137e12	−0.187912
$993$	1.33025e12	0.0434172
$994$	0	0
$995$	1.89724e13	0.613648
$996$	−2.14005e12	−0.0689060
$997$	−3.13132e13	−1.00369	−0.501845	−	0.864958i	$-0.667345\pi$
$997$	−3.13132e13	−1.00369	−0.501845	+	0.864958i	$0.667345\pi$
$998$	5.11795e12	0.163309
$999$	−2.87610e12	−0.0913608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.i.1.3		3
7.2	even	3		98.10.c.k.67.1		6
7.3	odd	6		14.10.c.a.9.3	✓	6
7.4	even	3		98.10.c.k.79.1		6
7.5	odd	6		14.10.c.a.11.3	yes	6
7.6	odd	2		98.10.a.j.1.1		3
21.5	even	6		126.10.g.f.109.2		6
21.17	even	6		126.10.g.f.37.2		6
28.3	even	6		112.10.i.b.65.1		6
28.19	even	6		112.10.i.b.81.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.a.9.3	✓	6	7.3	odd	6
14.10.c.a.11.3	yes	6	7.5	odd	6
98.10.a.i.1.3		3	1.1	even	1	trivial
98.10.a.j.1.1		3	7.6	odd	2
98.10.c.k.67.1		6	7.2	even	3
98.10.c.k.79.1		6	7.4	even	3
112.10.i.b.65.1		6	28.3	even	6
112.10.i.b.81.1		6	28.19	even	6
126.10.g.f.37.2		6	21.17	even	6
126.10.g.f.109.2		6	21.5	even	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +23.8447 q^{3} +256.000 q^{4} -1082.37 q^{5} +381.515 q^{6} +4096.00 q^{8} -19114.4 q^{9} -17317.9 q^{10} +74908.8 q^{11} +6104.24 q^{12} +50060.6 q^{13} -25808.7 q^{15} +65536.0 q^{16} -118965. q^{17} -305831. q^{18} -804363. q^{19} -277086. q^{20} +1.19854e6 q^{22} +268788. q^{23} +97667.9 q^{24} -781606. q^{25} +800969. q^{26} -925113. q^{27} -5.29735e6 q^{29} -412940. q^{30} -5.46586e6 q^{31} +1.04858e6 q^{32} +1.78618e6 q^{33} -1.90344e6 q^{34} -4.89329e6 q^{36} +3.10892e6 q^{37} -1.28698e7 q^{38} +1.19368e6 q^{39} -4.43338e6 q^{40} -2.07841e7 q^{41} +4.76437e6 q^{43} +1.91766e7 q^{44} +2.06888e7 q^{45} +4.30061e6 q^{46} -3.01532e7 q^{47} +1.56269e6 q^{48} -1.25057e7 q^{50} -2.83669e6 q^{51} +1.28155e7 q^{52} +5.71741e7 q^{53} -1.48018e7 q^{54} -8.10788e7 q^{55} -1.91798e7 q^{57} -8.47576e7 q^{58} -1.83676e8 q^{59} -6.60703e6 q^{60} -5.30167e7 q^{61} -8.74537e7 q^{62} +1.67772e7 q^{64} -5.41839e7 q^{65} +2.85788e7 q^{66} +1.73487e8 q^{67} -3.04551e7 q^{68} +6.40918e6 q^{69} -1.68342e8 q^{71} -7.82927e7 q^{72} +4.64679e8 q^{73} +4.97427e7 q^{74} -1.86372e7 q^{75} -2.05917e8 q^{76} +1.90989e7 q^{78} -4.13728e8 q^{79} -7.09340e7 q^{80} +3.54170e8 q^{81} -3.32545e8 q^{82} -3.50584e8 q^{83} +1.28764e8 q^{85} +7.62299e7 q^{86} -1.26314e8 q^{87} +3.06826e8 q^{88} -5.17472e8 q^{89} +3.31021e8 q^{90} +6.88098e7 q^{92} -1.30332e8 q^{93} -4.82452e8 q^{94} +8.70616e8 q^{95} +2.50030e7 q^{96} -1.32529e9 q^{97} -1.43184e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 48 q^{2} - 233 q^{3} + 768 q^{4} - 733 q^{5} - 3728 q^{6} + 12288 q^{8} + 15058 q^{9} - 11728 q^{10} - 7339 q^{11} - 59648 q^{12} - 98518 q^{13} + 369119 q^{15} + 196608 q^{16} - 306665 q^{17} + 240928 q^{18}+ \cdots - 628109434 q^{99}+O(q^{100}) \) 3 * q + 48 * q^2 - 233 * q^3 + 768 * q^4 - 733 * q^5 - 3728 * q^6 + 12288 * q^8 + 15058 * q^9 - 11728 * q^10 - 7339 * q^11 - 59648 * q^12 - 98518 * q^13 + 369119 * q^15 + 196608 * q^16 - 306665 * q^17 + 240928 * q^18 - 377991 * q^19 - 187648 * q^20 - 117424 * q^22 + 2267255 * q^23 - 954368 * q^24 + 142612 * q^25 - 1576288 * q^26 - 10674179 * q^27 - 6542978 * q^29 + 5905904 * q^30 - 6654517 * q^31 + 3145728 * q^32 + 3747977 * q^33 - 4906640 * q^34 + 3854848 * q^36 + 22287969 * q^37 - 6047856 * q^38 - 3151974 * q^39 - 3002368 * q^40 - 34048098 * q^41 - 62824140 * q^43 - 1878784 * q^44 - 86300638 * q^45 + 36276080 * q^46 - 52703019 * q^47 - 15269888 * q^48 + 2281792 * q^50 - 97736333 * q^51 - 25220608 * q^52 + 12091125 * q^53 - 170786864 * q^54 - 188717699 * q^55 - 79258835 * q^57 - 104687648 * q^58 - 12949897 * q^59 + 94494464 * q^60 - 160252153 * q^61 - 106472272 * q^62 + 50331648 * q^64 - 334191270 * q^65 + 59967632 * q^66 + 480890225 * q^67 - 78506240 * q^68 - 565616581 * q^69 - 37210720 * q^71 + 61677568 * q^72 + 251382283 * q^73 + 356607504 * q^74 + 16322324 * q^75 - 96765696 * q^76 - 50431584 * q^78 - 286494785 * q^79 - 48037888 * q^80 + 2165894587 * q^81 - 544769568 * q^82 - 1147591172 * q^83 - 1194592537 * q^85 - 1005186240 * q^86 + 1412199358 * q^87 - 30060544 * q^88 - 901243845 * q^89 - 1380810208 * q^90 + 580417280 * q^92 - 710456889 * q^93 - 843248304 * q^94 + 887366177 * q^95 - 244318208 * q^96 - 314853938 * q^97 - 628109434 * q^99

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