LMFDB - Embedded newform 98.10.a.d.1.2

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)

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);

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")

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

Newform invariants

comment:select newform

sage:traces = [2,-32,0] 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:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{43}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 43 $ x^2 - 43
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$6.55744$ 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)

$f(q)$	$=$	\(q-16.0000 q^{2} +52.4595 q^{3} +256.000 q^{4} +1836.08 q^{5} -839.352 q^{6} -4096.00 q^{8} -16931.0 q^{9} -29377.3 q^{10} +9380.00 q^{11} +13429.6 q^{12} +179044. q^{13} +96320.0 q^{15} +65536.0 q^{16} +97889.4 q^{17} +270896. q^{18} +562733. q^{19} +470037. q^{20} -150080. q^{22} -978936. q^{23} -214874. q^{24} +1.41808e6 q^{25} -2.86471e6 q^{26} -1.92075e6 q^{27} -4.31721e6 q^{29} -1.54112e6 q^{30} +7.97458e6 q^{31} -1.04858e6 q^{32} +492070. q^{33} -1.56623e6 q^{34} -4.33434e6 q^{36} +2.71439e6 q^{37} -9.00373e6 q^{38} +9.39258e6 q^{39} -7.52060e6 q^{40} +9.00237e6 q^{41} -3.47557e7 q^{43} +2.40128e6 q^{44} -3.10867e7 q^{45} +1.56630e7 q^{46} +4.21775e7 q^{47} +3.43799e6 q^{48} -2.26892e7 q^{50} +5.13523e6 q^{51} +4.58353e7 q^{52} +6.80679e7 q^{53} +3.07320e7 q^{54} +1.72225e7 q^{55} +2.95207e7 q^{57} +6.90754e7 q^{58} -3.42318e7 q^{59} +2.46579e7 q^{60} -1.65833e8 q^{61} -1.27593e8 q^{62} +1.67772e7 q^{64} +3.28740e8 q^{65} -7.87312e6 q^{66} +2.42944e8 q^{67} +2.50597e7 q^{68} -5.13545e7 q^{69} -9.42925e7 q^{71} +6.93494e7 q^{72} +1.33334e8 q^{73} -4.34303e7 q^{74} +7.43915e7 q^{75} +1.44060e8 q^{76} -1.50281e8 q^{78} +6.77625e8 q^{79} +1.20330e8 q^{80} +2.32491e8 q^{81} -1.44038e8 q^{82} +4.41313e8 q^{83} +1.79733e8 q^{85} +5.56091e8 q^{86} -2.26479e8 q^{87} -3.84205e7 q^{88} +5.55278e8 q^{89} +4.97387e8 q^{90} -2.50608e8 q^{92} +4.18343e8 q^{93} -6.74841e8 q^{94} +1.03322e9 q^{95} -5.50078e7 q^{96} -1.26895e9 q^{97} -1.58813e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} + 512 q^{4} - 8192 q^{8} - 33862 q^{9} + 18760 q^{11} + 192640 q^{15} + 131072 q^{16} + 541792 q^{18} - 300160 q^{22} - 1957872 q^{23} + 2836150 q^{25} - 8634428 q^{29} - 3082240 q^{30} - 2097152 q^{32}+ \cdots - 317625560 q^{99}+O(q^{100}) $ 2 * q - 32 * q^2 + 512 * q^4 - 8192 * q^8 - 33862 * q^9 + 18760 * q^11 + 192640 * q^15 + 131072 * q^16 + 541792 * q^18 - 300160 * q^22 - 1957872 * q^23 + 2836150 * q^25 - 8634428 * q^29 - 3082240 * q^30 - 2097152 * q^32 - 8668672 * q^36 + 5428788 * q^37 + 18785152 * q^39 - 69511384 * q^43 + 4802560 * q^44 + 31325952 * q^46 - 45378400 * q^50 + 10270464 * q^51 + 136135852 * q^53 + 59041408 * q^57 + 138150848 * q^58 + 49315840 * q^60 + 33554432 * q^64 + 657480320 * q^65 + 485888840 * q^67 - 188584928 * q^71 + 138698752 * q^72 - 86860608 * q^74 - 300562432 * q^78 + 1355250320 * q^79 + 464982290 * q^81 + 359466240 * q^85 + 1112182144 * q^86 - 76840960 * q^88 - 501215232 * q^92 + 836685056 * q^93 + 2066449280 * q^95 - 317625560 * 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
$3$	52.4595	0.373920	0.186960	−	0.982368i	$-0.440137\pi$
$3$	52.4595	0.373920	0.186960	+	0.982368i	$0.440137\pi$
$4$	256.000	0.500000
$5$	1836.08	1.31379	0.656897	−	0.753980i	$-0.271869\pi$
$5$	1836.08	1.31379	0.656897	+	0.753980i	$0.271869\pi$
$6$	−839.352	−0.264401
$7$	0	0
$7$	0	0
$8$	−4096.00	−0.353553
$9$	−16931.0	−0.860184
$10$	−29377.3	−0.928993
$11$	9380.00	0.193168	0.0965841	−	0.995325i	$-0.469208\pi$
$11$	9380.00	0.193168	0.0965841	+	0.995325i	$0.469208\pi$
$12$	13429.6	0.186960
$13$	179044.	1.73866	0.869332	−	0.494229i	$-0.164550\pi$
$13$	179044.	1.73866	0.869332	+	0.494229i	$0.164550\pi$
$14$	0	0
$15$	96320.0	0.491254
$16$	65536.0	0.250000
$17$	97889.4	0.284260	0.142130	−	0.989848i	$-0.454605\pi$
$17$	97889.4	0.284260	0.142130	+	0.989848i	$0.454605\pi$
$18$	270896.	0.608242
$19$	562733.	0.990630	0.495315	−	0.868714i	$-0.335053\pi$
$19$	562733.	0.990630	0.495315	+	0.868714i	$0.335053\pi$
$20$	470037.	0.656897
$21$	0	0
$22$	−150080.	−0.136591
$23$	−978936.	−0.729422	−0.364711	−	0.931121i	$-0.618832\pi$
$23$	−978936.	−0.729422	−0.364711	+	0.931121i	$0.618832\pi$
$24$	−214874.	−0.132201
$25$	1.41808e6	0.726054
$26$	−2.86471e6	−1.22942
$27$	−1.92075e6	−0.695560
$28$	0	0
$29$	−4.31721e6	−1.13348	−0.566738	−	0.823898i	$-0.691795\pi$
$29$	−4.31721e6	−1.13348	−0.566738	+	0.823898i	$0.691795\pi$
$30$	−1.54112e6	−0.347369
$31$	7.97458e6	1.55089	0.775444	−	0.631417i	$-0.217526\pi$
$31$	7.97458e6	1.55089	0.775444	+	0.631417i	$0.217526\pi$
$32$	−1.04858e6	−0.176777
$33$	492070.	0.0722295
$34$	−1.56623e6	−0.201002
$35$	0	0
$36$	−4.33434e6	−0.430092
$37$	2.71439e6	0.238103	0.119052	−	0.992888i	$-0.462015\pi$
$37$	2.71439e6	0.238103	0.119052	+	0.992888i	$0.462015\pi$
$38$	−9.00373e6	−0.700481
$39$	9.39258e6	0.650121
$40$	−7.52060e6	−0.464496
$41$	9.00237e6	0.497542	0.248771	−	0.968562i	$-0.419973\pi$
$41$	9.00237e6	0.497542	0.248771	+	0.968562i	$0.419973\pi$
$42$	0	0
$43$	−3.47557e7	−1.55031	−0.775154	−	0.631773i	$-0.782328\pi$
$43$	−3.47557e7	−1.55031	−0.775154	+	0.631773i	$0.782328\pi$
$44$	2.40128e6	0.0965841
$45$	−3.10867e7	−1.13010
$46$	1.56630e7	0.515779
$47$	4.21775e7	1.26078	0.630392	−	0.776277i	$-0.282894\pi$
$47$	4.21775e7	1.26078	0.630392	+	0.776277i	$0.282894\pi$
$48$	3.43799e6	0.0934800
$49$	0	0
$50$	−2.26892e7	−0.513398
$51$	5.13523e6	0.106290
$52$	4.58353e7	0.869332
$53$	6.80679e7	1.18495	0.592476	−	0.805588i	$-0.298150\pi$
$53$	6.80679e7	1.18495	0.592476	+	0.805588i	$0.298150\pi$
$54$	3.07320e7	0.491835
$55$	1.72225e7	0.253783
$56$	0	0
$57$	2.95207e7	0.370416
$58$	6.90754e7	0.801489
$59$	−3.42318e7	−0.367786	−0.183893	−	0.982946i	$-0.558870\pi$
$59$	−3.42318e7	−0.367786	−0.183893	+	0.982946i	$0.558870\pi$
$60$	2.46579e7	0.245627
$61$	−1.65833e8	−1.53351	−0.766753	−	0.641942i	$-0.778129\pi$
$61$	−1.65833e8	−1.53351	−0.766753	+	0.641942i	$0.778129\pi$
$62$	−1.27593e8	−1.09664
$63$	0	0
$64$	1.67772e7	0.125000
$65$	3.28740e8	2.28424
$66$	−7.87312e6	−0.0510739
$67$	2.42944e8	1.47289	0.736445	−	0.676497i	$-0.236503\pi$
$67$	2.42944e8	1.47289	0.736445	+	0.676497i	$0.236503\pi$
$68$	2.50597e7	0.142130
$69$	−5.13545e7	−0.272746
$70$	0	0
$71$	−9.42925e7	−0.440367	−0.220183	−	0.975459i	$-0.570666\pi$
$71$	−9.42925e7	−0.440367	−0.220183	+	0.975459i	$0.570666\pi$
$72$	6.93494e7	0.304121
$73$	1.33334e8	0.549528	0.274764	−	0.961512i	$-0.411400\pi$
$73$	1.33334e8	0.549528	0.274764	+	0.961512i	$0.411400\pi$
$74$	−4.34303e7	−0.168364
$75$	7.43915e7	0.271486
$76$	1.44060e8	0.495315
$77$	0	0
$78$	−1.50281e8	−0.459705
$79$	6.77625e8	1.95735	0.978673	−	0.205424i	$-0.0658574\pi$
$79$	6.77625e8	1.95735	0.978673	+	0.205424i	$0.0658574\pi$
$80$	1.20330e8	0.328448
$81$	2.32491e8	0.600100
$82$	−1.44038e8	−0.351815
$83$	4.41313e8	1.02069	0.510347	−	0.859968i	$-0.329517\pi$
$83$	4.41313e8	1.02069	0.510347	+	0.859968i	$0.329517\pi$
$84$	0	0
$85$	1.79733e8	0.373459
$86$	5.56091e8	1.09623
$87$	−2.26479e8	−0.423829
$88$	−3.84205e7	−0.0682953
$89$	5.55278e8	0.938113	0.469056	−	0.883168i	$-0.344594\pi$
$89$	5.55278e8	0.938113	0.469056	+	0.883168i	$0.344594\pi$
$90$	4.97387e8	0.799104
$91$	0	0
$92$	−2.50608e8	−0.364711
$93$	4.18343e8	0.579908
$94$	−6.74841e8	−0.891510
$95$	1.03322e9	1.30148
$96$	−5.50078e7	−0.0661003
$97$	−1.26895e9	−1.45536	−0.727680	−	0.685917i	$-0.759401\pi$
$97$	−1.26895e9	−1.45536	−0.727680	+	0.685917i	$0.759401\pi$
$98$	0	0
$99$	−1.58813e8	−0.166160
$100$	3.63027e8	0.363027
$101$	1.36830e9	1.30838	0.654191	−	0.756329i	$-0.273009\pi$
$101$	1.36830e9	1.30838	0.654191	+	0.756329i	$0.273009\pi$
$102$	−8.21637e7	−0.0751587
$103$	−1.92152e8	−0.168219	−0.0841097	−	0.996456i	$-0.526805\pi$
$103$	−1.92152e8	−0.168219	−0.0841097	+	0.996456i	$0.526805\pi$
$104$	−7.33365e8	−0.614710
$105$	0	0
$106$	−1.08909e9	−0.837888
$107$	−1.04855e9	−0.773325	−0.386663	−	0.922221i	$-0.626372\pi$
$107$	−1.04855e9	−0.773325	−0.386663	+	0.922221i	$0.626372\pi$
$108$	−4.91713e8	−0.347780
$109$	2.03758e9	1.38259	0.691297	−	0.722571i	$-0.257040\pi$
$109$	2.03758e9	1.38259	0.691297	+	0.722571i	$0.257040\pi$
$110$	−2.75559e8	−0.179452
$111$	1.42396e8	0.0890315
$112$	0	0
$113$	−4.70999e8	−0.271748	−0.135874	−	0.990726i	$-0.543384\pi$
$113$	−4.70999e8	−0.271748	−0.135874	+	0.990726i	$0.543384\pi$
$114$	−4.72331e8	−0.261924
$115$	−1.79741e9	−0.958311
$116$	−1.10521e9	−0.566738
$117$	−3.03140e9	−1.49557
$118$	5.47708e8	0.260064
$119$	0	0
$120$	−3.94527e8	−0.173684
$121$	−2.26996e9	−0.962686
$122$	2.65332e9	1.08435
$123$	4.72260e8	0.186041
$124$	2.04149e9	0.775444
$125$	−9.82396e8	−0.359908
$126$	0	0
$127$	2.87598e9	0.981001	0.490500	−	0.871441i	$-0.336814\pi$
$127$	2.87598e9	0.981001	0.490500	+	0.871441i	$0.336814\pi$
$128$	−2.68435e8	−0.0883883
$129$	−1.82327e9	−0.579691
$130$	−5.25984e9	−1.61521
$131$	5.97107e9	1.77146	0.885729	−	0.464202i	$-0.153659\pi$
$131$	5.97107e9	1.77146	0.885729	+	0.464202i	$0.153659\pi$
$132$	1.25970e8	0.0361147
$133$	0	0
$134$	−3.88711e9	−1.04149
$135$	−3.52666e9	−0.913822
$136$	−4.00955e8	−0.100501
$137$	−1.39710e9	−0.338832	−0.169416	−	0.985545i	$-0.554188\pi$
$137$	−1.39710e9	−0.338832	−0.169416	+	0.985545i	$0.554188\pi$
$138$	8.21672e8	0.192860
$139$	7.96582e9	1.80994	0.904969	−	0.425477i	$-0.139894\pi$
$139$	7.96582e9	1.80994	0.904969	+	0.425477i	$0.139894\pi$
$140$	0	0
$141$	2.21261e9	0.471433
$142$	1.50868e9	0.311386
$143$	1.67944e9	0.335855
$144$	−1.10959e9	−0.215046
$145$	−7.92676e9	−1.48915
$146$	−2.13335e9	−0.388575
$147$	0	0
$148$	6.94885e8	0.119052
$149$	−1.10260e10	−1.83266	−0.916329	−	0.400425i	$-0.868862\pi$
$149$	−1.10260e10	−1.83266	−0.916329	+	0.400425i	$0.868862\pi$
$150$	−1.19026e9	−0.191970
$151$	−3.94474e9	−0.617479	−0.308739	−	0.951147i	$-0.599907\pi$
$151$	−3.94474e9	−0.617479	−0.308739	+	0.951147i	$0.599907\pi$
$152$	−2.30495e9	−0.350240
$153$	−1.65737e9	−0.244516
$154$	0	0
$155$	1.46420e10	2.03755
$156$	2.40450e9	0.325060
$157$	6.76342e9	0.888419	0.444209	−	0.895923i	$-0.353485\pi$
$157$	6.76342e9	0.888419	0.444209	+	0.895923i	$0.353485\pi$
$158$	−1.08420e10	−1.38405
$159$	3.57081e9	0.443077
$160$	−1.92527e9	−0.232248
$161$	0	0
$162$	−3.71986e9	−0.424335
$163$	−2.94473e9	−0.326740	−0.163370	−	0.986565i	$-0.552236\pi$
$163$	−2.94473e9	−0.326740	−0.163370	+	0.986565i	$0.552236\pi$
$164$	2.30461e9	0.248771
$165$	9.03482e8	0.0948946
$166$	−7.06102e9	−0.721740
$167$	−1.59064e10	−1.58251	−0.791256	−	0.611485i	$-0.790573\pi$
$167$	−1.59064e10	−1.58251	−0.791256	+	0.611485i	$0.790573\pi$
$168$	0	0
$169$	2.14524e10	2.02295
$170$	−2.87573e9	−0.264075
$171$	−9.52763e9	−0.852124
$172$	−8.89746e9	−0.775154
$173$	1.03299e10	0.876773	0.438386	−	0.898787i	$-0.355550\pi$
$173$	1.03299e10	0.876773	0.438386	+	0.898787i	$0.355550\pi$
$174$	3.62366e9	0.299693
$175$	0	0
$176$	6.14728e8	0.0482921
$177$	−1.79578e9	−0.137523
$178$	−8.88444e9	−0.663346
$179$	1.08025e10	0.786479	0.393239	−	0.919436i	$-0.371354\pi$
$179$	1.08025e10	0.786479	0.393239	+	0.919436i	$0.371354\pi$
$180$	−7.95820e9	−0.565052
$181$	6.13942e9	0.425181	0.212591	−	0.977141i	$-0.431810\pi$
$181$	6.13942e9	0.425181	0.212591	+	0.977141i	$0.431810\pi$
$182$	0	0
$183$	−8.69949e9	−0.573408
$184$	4.00972e9	0.257890
$185$	4.98385e9	0.312818
$186$	−6.69348e9	−0.410057
$187$	9.18203e8	0.0549100
$188$	1.07975e10	0.630392
$189$	0	0
$190$	−1.65316e10	−0.920288
$191$	−9.38711e9	−0.510366	−0.255183	−	0.966893i	$-0.582136\pi$
$191$	−9.38711e9	−0.510366	−0.255183	+	0.966893i	$0.582136\pi$
$192$	8.80125e8	0.0467400
$193$	9.06409e9	0.470236	0.235118	−	0.971967i	$-0.424452\pi$
$193$	9.06409e9	0.470236	0.235118	+	0.971967i	$0.424452\pi$
$194$	2.03031e10	1.02909
$195$	1.72455e10	0.854125
$196$	0	0
$197$	−7.31102e9	−0.345844	−0.172922	−	0.984936i	$-0.555321\pi$
$197$	−7.31102e9	−0.345844	−0.172922	+	0.984936i	$0.555321\pi$
$198$	2.54100e9	0.117493
$199$	−1.51050e9	−0.0682782	−0.0341391	−	0.999417i	$-0.510869\pi$
$199$	−1.51050e9	−0.0682782	−0.0341391	+	0.999417i	$0.510869\pi$
$200$	−5.80844e9	−0.256699
$201$	1.27447e10	0.550743
$202$	−2.18928e10	−0.925166
$203$	0	0
$204$	1.31462e9	0.0531452
$205$	1.65291e10	0.653667
$206$	3.07442e9	0.118949
$207$	1.65744e10	0.627437
$208$	1.17338e10	0.434666
$209$	5.27844e9	0.191358
$210$	0	0
$211$	−1.89147e10	−0.656945	−0.328472	−	0.944514i	$-0.606534\pi$
$211$	−1.89147e10	−0.656945	−0.328472	+	0.944514i	$0.606534\pi$
$212$	1.74254e10	0.592476
$213$	−4.94654e9	−0.164662
$214$	1.67768e10	0.546823
$215$	−6.38143e10	−2.03678
$216$	7.86740e9	0.245918
$217$	0	0
$218$	−3.26012e10	−0.977641
$219$	6.99466e9	0.205479
$220$	4.40895e9	0.126892
$221$	1.75265e10	0.494232
$222$	−2.27833e9	−0.0629548
$223$	−5.37387e10	−1.45518	−0.727588	−	0.686015i	$-0.759359\pi$
$223$	−5.37387e10	−1.45518	−0.727588	+	0.686015i	$0.759359\pi$
$224$	0	0
$225$	−2.40094e10	−0.624540
$226$	7.53598e9	0.192155
$227$	−6.51335e9	−0.162813	−0.0814063	−	0.996681i	$-0.525941\pi$
$227$	−6.51335e9	−0.162813	−0.0814063	+	0.996681i	$0.525941\pi$
$228$	7.55730e9	0.185208
$229$	−2.08552e10	−0.501134	−0.250567	−	0.968099i	$-0.580617\pi$
$229$	−2.08552e10	−0.501134	−0.250567	+	0.968099i	$0.580617\pi$
$230$	2.87585e10	0.677628
$231$	0	0
$232$	1.76833e10	0.400745
$233$	1.91559e10	0.425794	0.212897	−	0.977075i	$-0.431710\pi$
$233$	1.91559e10	0.425794	0.212897	+	0.977075i	$0.431710\pi$
$234$	4.85024e10	1.05753
$235$	7.74415e10	1.65641
$236$	−8.76333e9	−0.183893
$237$	3.55479e10	0.731891
$238$	0	0
$239$	−2.58648e10	−0.512764	−0.256382	−	0.966575i	$-0.582531\pi$
$239$	−2.58648e10	−0.512764	−0.256382	+	0.966575i	$0.582531\pi$
$240$	6.31243e9	0.122813
$241$	3.21806e10	0.614493	0.307246	−	0.951630i	$-0.400592\pi$
$241$	3.21806e10	0.614493	0.307246	+	0.951630i	$0.400592\pi$
$242$	3.63194e10	0.680722
$243$	5.00025e10	0.919949
$244$	−4.24531e10	−0.766753
$245$	0	0
$246$	−7.55616e9	−0.131551
$247$	1.00754e11	1.72237
$248$	−3.26639e10	−0.548321
$249$	2.31511e10	0.381658
$250$	1.57183e10	0.254493
$251$	−2.42280e10	−0.385288	−0.192644	−	0.981269i	$-0.561706\pi$
$251$	−2.42280e10	−0.385288	−0.192644	+	0.981269i	$0.561706\pi$
$252$	0	0
$253$	−9.18242e9	−0.140901
$254$	−4.60157e10	−0.693672
$255$	9.42871e9	0.139644
$256$	4.29497e9	0.0625000
$257$	3.56541e10	0.509812	0.254906	−	0.966966i	$-0.417955\pi$
$257$	3.56541e10	0.509812	0.254906	+	0.966966i	$0.417955\pi$
$258$	2.91723e10	0.409903
$259$	0	0
$260$	8.41575e10	1.14212
$261$	7.30948e10	0.974998
$262$	−9.55371e10	−1.25261
$263$	−1.19369e11	−1.53848	−0.769238	−	0.638963i	$-0.779364\pi$
$263$	−1.19369e11	−1.53848	−0.769238	+	0.638963i	$0.779364\pi$
$264$	−2.01552e9	−0.0255370
$265$	1.24978e11	1.55678
$266$	0	0
$267$	2.91296e10	0.350779
$268$	6.21938e10	0.736445
$269$	−1.05580e11	−1.22941	−0.614706	−	0.788756i	$-0.710725\pi$
$269$	−1.05580e11	−1.22941	−0.614706	+	0.788756i	$0.710725\pi$
$270$	5.64266e10	0.646170
$271$	6.30528e10	0.710138	0.355069	−	0.934840i	$-0.384457\pi$
$271$	6.30528e10	0.710138	0.355069	+	0.934840i	$0.384457\pi$
$272$	6.41528e9	0.0710650
$273$	0	0
$274$	2.23536e10	0.239591
$275$	1.33015e10	0.140251
$276$	−1.31468e10	−0.136373
$277$	−8.82953e10	−0.901111	−0.450556	−	0.892748i	$-0.648774\pi$
$277$	−8.82953e10	−0.901111	−0.450556	+	0.892748i	$0.648774\pi$
$278$	−1.27453e11	−1.27982
$279$	−1.35018e11	−1.33405
$280$	0	0
$281$	−1.42216e10	−0.136072	−0.0680361	−	0.997683i	$-0.521673\pi$
$281$	−1.42216e10	−0.136072	−0.0680361	+	0.997683i	$0.521673\pi$
$282$	−3.54018e10	−0.333353
$283$	1.44191e11	1.33629	0.668144	−	0.744032i	$-0.267089\pi$
$283$	1.44191e11	1.33629	0.668144	+	0.744032i	$0.267089\pi$
$284$	−2.41389e10	−0.220183
$285$	5.42025e10	0.486650
$286$	−2.68710e10	−0.237485
$287$	0	0
$288$	1.77534e10	0.152060
$289$	−1.09006e11	−0.919196
$290$	1.26828e11	1.05299
$291$	−6.65683e10	−0.544188
$292$	3.41336e10	0.274764
$293$	−7.39164e10	−0.585918	−0.292959	−	0.956125i	$-0.594640\pi$
$293$	−7.39164e10	−0.585918	−0.292959	+	0.956125i	$0.594640\pi$
$294$	0	0
$295$	−6.28524e10	−0.483195
$296$	−1.11182e10	−0.0841822
$297$	−1.80167e10	−0.134360
$298$	1.76417e11	1.29589
$299$	−1.75273e11	−1.26822
$300$	1.90442e10	0.135743
$301$	0	0
$302$	6.31158e10	0.436623
$303$	7.17803e10	0.489230
$304$	3.68793e10	0.247657
$305$	−3.04482e11	−2.01471
$306$	2.65179e10	0.172899
$307$	1.11736e11	0.717908	0.358954	−	0.933355i	$-0.383134\pi$
$307$	1.11736e11	0.717908	0.358954	+	0.933355i	$0.383134\pi$
$308$	0	0
$309$	−1.00802e10	−0.0629006
$310$	−2.34272e11	−1.44076
$311$	−2.21039e11	−1.33982	−0.669912	−	0.742441i	$-0.733668\pi$
$311$	−2.21039e11	−1.33982	−0.669912	+	0.742441i	$0.733668\pi$
$312$	−3.84720e10	−0.229852
$313$	−1.07627e11	−0.633826	−0.316913	−	0.948455i	$-0.602646\pi$
$313$	−1.07627e11	−0.633826	−0.316913	+	0.948455i	$0.602646\pi$
$314$	−1.08215e11	−0.628207
$315$	0	0
$316$	1.73472e11	0.978673
$317$	−3.25634e11	−1.81119	−0.905594	−	0.424145i	$-0.860575\pi$
$317$	−3.25634e11	−1.81119	−0.905594	+	0.424145i	$0.860575\pi$
$318$	−5.71330e10	−0.313303
$319$	−4.04955e10	−0.218952
$320$	3.08044e10	0.164224
$321$	−5.50064e10	−0.289162
$322$	0	0
$323$	5.50856e10	0.281596
$324$	5.95177e10	0.300050
$325$	2.53898e11	1.26236
$326$	4.71157e10	0.231040
$327$	1.06890e11	0.516979
$328$	−3.68737e10	−0.175907
$329$	0	0
$330$	−1.44557e10	−0.0671006
$331$	−1.69545e11	−0.776350	−0.388175	−	0.921586i	$-0.626894\pi$
$331$	−1.69545e11	−0.776350	−0.388175	+	0.921586i	$0.626894\pi$
$332$	1.12976e11	0.510347
$333$	−4.59574e10	−0.204812
$334$	2.54502e11	1.11901
$335$	4.46066e11	1.93507
$336$	0	0
$337$	−1.26756e11	−0.535347	−0.267673	−	0.963510i	$-0.586255\pi$
$337$	−1.26756e11	−0.535347	−0.267673	+	0.963510i	$0.586255\pi$
$338$	−3.43238e11	−1.43044
$339$	−2.47084e10	−0.101612
$340$	4.60117e10	0.186730
$341$	7.48016e10	0.299582
$342$	1.52442e11	0.602542
$343$	0	0
$344$	1.42359e11	0.548117
$345$	−9.42911e10	−0.358331
$346$	−1.65278e11	−0.619972
$347$	−1.79108e11	−0.663180	−0.331590	−	0.943424i	$-0.607585\pi$
$347$	−1.79108e11	−0.663180	−0.331590	+	0.943424i	$0.607585\pi$
$348$	−5.79786e10	−0.211915
$349$	−1.73876e11	−0.627372	−0.313686	−	0.949527i	$-0.601564\pi$
$349$	−1.73876e11	−0.627372	−0.313686	+	0.949527i	$0.601564\pi$
$350$	0	0
$351$	−3.43900e11	−1.20934
$352$	−9.83564e9	−0.0341476
$353$	−9.03498e10	−0.309700	−0.154850	−	0.987938i	$-0.549489\pi$
$353$	−9.03498e10	−0.309700	−0.154850	+	0.987938i	$0.549489\pi$
$354$	2.87325e10	0.0972431
$355$	−1.73129e11	−0.578551
$356$	1.42151e11	0.469056
$357$	0	0
$358$	−1.72841e11	−0.556124
$359$	−1.83950e11	−0.584486	−0.292243	−	0.956344i	$-0.594402\pi$
$359$	−1.83950e11	−0.584486	−0.292243	+	0.956344i	$0.594402\pi$
$360$	1.27331e11	0.399552
$361$	−6.01911e9	−0.0186530
$362$	−9.82308e10	−0.300648
$363$	−1.19081e11	−0.359967
$364$	0	0
$365$	2.44813e11	0.721966
$366$	1.39192e11	0.405461
$367$	−3.61312e11	−1.03965	−0.519823	−	0.854274i	$-0.674002\pi$
$367$	−3.61312e11	−1.03965	−0.519823	+	0.854274i	$0.674002\pi$
$368$	−6.41555e10	−0.182356
$369$	−1.52419e11	−0.427977
$370$	−7.97416e10	−0.221196
$371$	0	0
$372$	1.07096e11	0.289954
$373$	1.62421e11	0.434461	0.217231	−	0.976120i	$-0.430298\pi$
$373$	1.62421e11	0.434461	0.217231	+	0.976120i	$0.430298\pi$
$374$	−1.46912e10	−0.0388272
$375$	−5.15360e10	−0.134577
$376$	−1.72759e11	−0.445755
$377$	−7.72973e11	−1.97073
$378$	0	0
$379$	−1.07832e10	−0.0268455	−0.0134227	−	0.999910i	$-0.504273\pi$
$379$	−1.07832e10	−0.0268455	−0.0134227	+	0.999910i	$0.504273\pi$
$380$	2.64506e11	0.650742
$381$	1.50873e11	0.366816
$382$	1.50194e11	0.360883
$383$	6.97857e11	1.65719	0.828594	−	0.559850i	$-0.189141\pi$
$383$	6.97857e11	1.65719	0.828594	+	0.559850i	$0.189141\pi$
$384$	−1.40820e10	−0.0330502
$385$	0	0
$386$	−1.45025e11	−0.332507
$387$	5.88449e11	1.33355
$388$	−3.24850e11	−0.727680
$389$	−5.98959e11	−1.32625	−0.663123	−	0.748510i	$-0.730769\pi$
$389$	−5.98959e11	−1.32625	−0.663123	+	0.748510i	$0.730769\pi$
$390$	−2.75929e11	−0.603957
$391$	−9.58275e10	−0.207346
$392$	0	0
$393$	3.13239e11	0.662384
$394$	1.16976e11	0.244549
$395$	1.24418e12	2.57155
$396$	−4.06561e10	−0.0830801
$397$	−3.68159e11	−0.743838	−0.371919	−	0.928265i	$-0.621300\pi$
$397$	−3.68159e11	−0.743838	−0.371919	+	0.928265i	$0.621300\pi$
$398$	2.41680e10	0.0482800
$399$	0	0
$400$	9.29350e10	0.181514
$401$	1.11219e11	0.214798	0.107399	−	0.994216i	$-0.465748\pi$
$401$	1.11219e11	0.214798	0.107399	+	0.994216i	$0.465748\pi$
$402$	−2.03916e11	−0.389434
$403$	1.42780e12	2.69647
$404$	3.50285e11	0.654191
$405$	4.26873e11	0.788408
$406$	0	0
$407$	2.54610e10	0.0459940
$408$	−2.10339e10	−0.0375794
$409$	−4.42431e11	−0.781791	−0.390896	−	0.920435i	$-0.627835\pi$
$409$	−4.42431e11	−0.781791	−0.390896	+	0.920435i	$0.627835\pi$
$410$	−2.64465e11	−0.462212
$411$	−7.32911e10	−0.126696
$412$	−4.91908e10	−0.0841097
$413$	0	0
$414$	−2.65190e11	−0.443665
$415$	8.10288e11	1.34098
$416$	−1.87742e11	−0.307355
$417$	4.17883e11	0.676772
$418$	−8.44550e10	−0.135311
$419$	7.54997e11	1.19669	0.598346	−	0.801238i	$-0.295825\pi$
$419$	7.54997e11	1.19669	0.598346	+	0.801238i	$0.295825\pi$
$420$	0	0
$421$	4.31285e11	0.669106	0.334553	−	0.942377i	$-0.391415\pi$
$421$	4.31285e11	0.669106	0.334553	+	0.942377i	$0.391415\pi$
$422$	3.02636e11	0.464530
$423$	−7.14108e11	−1.08451
$424$	−2.78806e11	−0.418944
$425$	1.38815e11	0.206388
$426$	7.91446e10	0.116434
$427$	0	0
$428$	−2.68429e11	−0.386663
$429$	8.81024e10	0.125583
$430$	1.02103e12	1.44022
$431$	1.01375e12	1.41509	0.707545	−	0.706669i	$-0.249803\pi$
$431$	1.01375e12	1.41509	0.707545	+	0.706669i	$0.249803\pi$
$432$	−1.25878e11	−0.173890
$433$	6.02971e11	0.824329	0.412165	−	0.911109i	$-0.364773\pi$
$433$	6.02971e11	0.824329	0.412165	+	0.911109i	$0.364773\pi$
$434$	0	0
$435$	−4.15834e11	−0.556825
$436$	5.21620e11	0.691297
$437$	−5.50880e11	−0.722587
$438$	−1.11915e11	−0.145296
$439$	4.54285e11	0.583765	0.291883	−	0.956454i	$-0.405718\pi$
$439$	4.54285e11	0.583765	0.291883	+	0.956454i	$0.405718\pi$
$440$	−7.05432e10	−0.0897259
$441$	0	0
$442$	−2.80425e11	−0.349475
$443$	1.00889e12	1.24459	0.622294	−	0.782783i	$-0.286201\pi$
$443$	1.00889e12	1.24459	0.622294	+	0.782783i	$0.286201\pi$
$444$	3.64533e10	0.0445158
$445$	1.01954e12	1.23249
$446$	8.59819e11	1.02896
$447$	−5.78421e11	−0.685268
$448$	0	0
$449$	1.51070e10	0.0175416	0.00877082	−	0.999962i	$-0.497208\pi$
$449$	1.51070e10	0.0175416	0.00877082	+	0.999962i	$0.497208\pi$
$450$	3.84151e11	0.441617
$451$	8.44422e10	0.0961092
$452$	−1.20576e11	−0.135874
$453$	−2.06939e11	−0.230888
$454$	1.04214e11	0.115126
$455$	0	0
$456$	−1.20917e11	−0.130962
$457$	−1.03380e12	−1.10870	−0.554348	−	0.832285i	$-0.687032\pi$
$457$	−1.03380e12	−1.10870	−0.554348	+	0.832285i	$0.687032\pi$
$458$	3.33683e11	0.354356
$459$	−1.88021e11	−0.197720
$460$	−4.60136e11	−0.479155
$461$	−6.16178e11	−0.635407	−0.317704	−	0.948190i	$-0.602912\pi$
$461$	−6.16178e11	−0.635407	−0.317704	+	0.948190i	$0.602912\pi$
$462$	0	0
$463$	8.87425e11	0.897464	0.448732	−	0.893666i	$-0.351876\pi$
$463$	8.87425e11	0.897464	0.448732	+	0.893666i	$0.351876\pi$
$464$	−2.82933e11	−0.283369
$465$	7.68112e11	0.761879
$466$	−3.06494e11	−0.301082
$467$	−1.76248e12	−1.71474	−0.857371	−	0.514699i	$-0.827904\pi$
$467$	−1.76248e12	−1.71474	−0.857371	+	0.514699i	$0.827904\pi$
$468$	−7.76038e11	−0.747785
$469$	0	0
$470$	−1.23906e12	−1.17126
$471$	3.54806e11	0.332198
$472$	1.40213e11	0.130032
$473$	−3.26008e11	−0.299470
$474$	−5.68766e11	−0.517525
$475$	7.97998e11	0.719251
$476$	0	0
$477$	−1.15246e12	−1.01928
$478$	4.13836e11	0.362579
$479$	−1.25213e11	−0.108678	−0.0543388	−	0.998523i	$-0.517305\pi$
$479$	−1.25213e11	−0.108678	−0.0543388	+	0.998523i	$0.517305\pi$
$480$	−1.00999e11	−0.0868422
$481$	4.85997e11	0.413981
$482$	−5.14889e11	−0.434512
$483$	0	0
$484$	−5.81111e11	−0.481343
$485$	−2.32989e12	−1.91204
$486$	−8.00041e11	−0.650502
$487$	1.91907e12	1.54600	0.773001	−	0.634404i	$-0.218755\pi$
$487$	1.91907e12	1.54600	0.773001	+	0.634404i	$0.218755\pi$
$488$	6.79250e11	0.542176
$489$	−1.54479e11	−0.122174
$490$	0	0
$491$	−1.29801e12	−1.00789	−0.503944	−	0.863736i	$-0.668118\pi$
$491$	−1.29801e12	−1.00789	−0.503944	+	0.863736i	$0.668118\pi$
$492$	1.20898e11	0.0930203
$493$	−4.22610e11	−0.322202
$494$	−1.61207e12	−1.21790
$495$	−2.91593e11	−0.218300
$496$	5.22622e11	0.387722
$497$	0	0
$498$	−3.70417e11	−0.269873
$499$	−4.26076e11	−0.307634	−0.153817	−	0.988099i	$-0.549157\pi$
$499$	−4.26076e11	−0.307634	−0.153817	+	0.988099i	$0.549157\pi$
$500$	−2.51493e11	−0.179954
$501$	−8.34441e11	−0.591733
$502$	3.87648e11	0.272440
$503$	−1.75682e12	−1.22369	−0.611844	−	0.790978i	$-0.709572\pi$
$503$	−1.75682e12	−1.22369	−0.611844	+	0.790978i	$0.709572\pi$
$504$	0	0
$505$	2.51231e12	1.71895
$506$	1.46919e11	0.0996322
$507$	1.12538e12	0.756421
$508$	7.36251e11	0.490500
$509$	2.59034e12	1.71052	0.855258	−	0.518203i	$-0.173399\pi$
$509$	2.59034e12	1.71052	0.855258	+	0.518203i	$0.173399\pi$
$510$	−1.50859e11	−0.0987430
$511$	0	0
$512$	−6.87195e10	−0.0441942
$513$	−1.08087e12	−0.689042
$514$	−5.70465e11	−0.360491
$515$	−3.52806e11	−0.221006
$516$	−4.66756e11	−0.289845
$517$	3.95625e11	0.243544
$518$	0	0
$519$	5.41899e11	0.327843
$520$	−1.34652e12	−0.807603
$521$	−9.63629e11	−0.572981	−0.286490	−	0.958083i	$-0.592489\pi$
$521$	−9.63629e11	−0.572981	−0.286490	+	0.958083i	$0.592489\pi$
$522$	−1.16952e12	−0.689428
$523$	6.27990e11	0.367024	0.183512	−	0.983017i	$-0.441253\pi$
$523$	6.27990e11	0.367024	0.183512	+	0.983017i	$0.441253\pi$
$524$	1.52859e12	0.885729
$525$	0	0
$526$	1.90990e12	1.08787
$527$	7.80627e11	0.440855
$528$	3.22483e10	0.0180574
$529$	−8.42837e11	−0.467943
$530$	−1.99965e12	−1.10081
$531$	5.79578e11	0.316364
$532$	0	0
$533$	1.61182e12	0.865057
$534$	−4.66073e11	−0.248038
$535$	−1.92522e12	−1.01599
$536$	−9.95100e11	−0.520745
$537$	5.66696e11	0.294080
$538$	1.68928e12	0.869325
$539$	0	0
$540$	−9.02825e11	−0.456911
$541$	−3.11573e12	−1.56377	−0.781884	−	0.623424i	$-0.785741\pi$
$541$	−3.11573e12	−1.56377	−0.781884	+	0.623424i	$0.785741\pi$
$542$	−1.00884e12	−0.502143
$543$	3.22071e11	0.158984
$544$	−1.02645e11	−0.0502505
$545$	3.74116e12	1.81644
$546$	0	0
$547$	1.73766e12	0.829890	0.414945	−	0.909846i	$-0.363801\pi$
$547$	1.73766e12	0.829890	0.414945	+	0.909846i	$0.363801\pi$
$548$	−3.57657e11	−0.169416
$549$	2.80771e12	1.31910
$550$	−2.12825e11	−0.0991722
$551$	−2.42944e12	−1.12286
$552$	2.10348e11	0.0964301
$553$	0	0
$554$	1.41272e12	0.637182
$555$	2.61450e11	0.116969
$556$	2.03925e12	0.904969
$557$	−4.38426e12	−1.92996	−0.964980	−	0.262323i	$-0.915512\pi$
$557$	−4.38426e12	−1.92996	−0.964980	+	0.262323i	$0.915512\pi$
$558$	2.16028e12	0.943314
$559$	−6.22281e12	−2.69546
$560$	0	0
$561$	4.81685e10	0.0205319
$562$	2.27545e11	0.0962176
$563$	2.60529e12	1.09287	0.546434	−	0.837502i	$-0.315985\pi$
$563$	2.60529e12	1.09287	0.546434	+	0.837502i	$0.315985\pi$
$564$	5.66429e11	0.235716
$565$	−8.64793e11	−0.357021
$566$	−2.30706e12	−0.944898
$567$	0	0
$568$	3.86222e11	0.155693
$569$	−1.02052e12	−0.408145	−0.204073	−	0.978956i	$-0.565418\pi$
$569$	−1.02052e12	−0.408145	−0.204073	+	0.978956i	$0.565418\pi$
$570$	−8.67239e11	−0.344114
$571$	3.02032e11	0.118902	0.0594512	−	0.998231i	$-0.481065\pi$
$571$	3.02032e11	0.118902	0.0594512	+	0.998231i	$0.481065\pi$
$572$	4.29936e11	0.167927
$573$	−4.92443e11	−0.190836
$574$	0	0
$575$	−1.38820e12	−0.529600
$576$	−2.84055e11	−0.107523
$577$	−7.23583e11	−0.271767	−0.135884	−	0.990725i	$-0.543387\pi$
$577$	−7.23583e11	−0.271767	−0.135884	+	0.990725i	$0.543387\pi$
$578$	1.74409e12	0.649970
$579$	4.75498e11	0.175831
$580$	−2.02925e12	−0.744577
$581$	0	0
$582$	1.06509e12	0.384799
$583$	6.38477e11	0.228895
$584$	−5.46138e11	−0.194287
$585$	−5.56590e12	−1.96487
$586$	1.18266e12	0.414306
$587$	4.21402e12	1.46496	0.732479	−	0.680789i	$-0.238363\pi$
$587$	4.21402e12	1.46496	0.732479	+	0.680789i	$0.238363\pi$
$588$	0	0
$589$	4.48756e12	1.53635
$590$	1.00564e12	0.341671
$591$	−3.83533e11	−0.129318
$592$	1.77891e11	0.0595258
$593$	−5.62279e12	−1.86727	−0.933633	−	0.358232i	$-0.883380\pi$
$593$	−5.62279e12	−1.86727	−0.933633	+	0.358232i	$0.883380\pi$
$594$	2.88267e11	0.0950069
$595$	0	0
$596$	−2.82267e12	−0.916329
$597$	−7.92401e10	−0.0255306
$598$	2.80437e12	0.896767
$599$	7.65734e11	0.243028	0.121514	−	0.992590i	$-0.461225\pi$
$599$	7.65734e11	0.243028	0.121514	+	0.992590i	$0.461225\pi$
$600$	−3.04708e11	−0.0959849
$601$	−9.63630e11	−0.301283	−0.150642	−	0.988588i	$-0.548134\pi$
$601$	−9.63630e11	−0.301283	−0.150642	+	0.988588i	$0.548134\pi$
$602$	0	0
$603$	−4.11329e12	−1.26696
$604$	−1.00985e12	−0.308739
$605$	−4.16784e12	−1.26477
$606$	−1.14848e12	−0.345938
$607$	2.28495e12	0.683167	0.341583	−	0.939851i	$-0.389037\pi$
$607$	2.28495e12	0.683167	0.341583	+	0.939851i	$0.389037\pi$
$608$	−5.90068e11	−0.175120
$609$	0	0
$610$	4.87172e12	1.42462
$611$	7.55165e12	2.19208
$612$	−4.24286e11	−0.122258
$613$	1.19459e12	0.341703	0.170851	−	0.985297i	$-0.445348\pi$
$613$	1.19459e12	0.341703	0.170851	+	0.985297i	$0.445348\pi$
$614$	−1.78777e12	−0.507637
$615$	8.67108e11	0.244419
$616$	0	0
$617$	−3.40574e12	−0.946082	−0.473041	−	0.881040i	$-0.656844\pi$
$617$	−3.40574e12	−0.946082	−0.473041	+	0.881040i	$0.656844\pi$
$618$	1.61283e11	0.0444775
$619$	−1.61630e10	−0.00442501	−0.00221250	−	0.999998i	$-0.500704\pi$
$619$	−1.61630e10	−0.00442501	−0.00221250	+	0.999998i	$0.500704\pi$
$620$	3.74835e12	1.01877
$621$	1.88029e12	0.507357
$622$	3.53663e12	0.947398
$623$	0	0
$624$	6.15552e11	0.162530
$625$	−4.57344e12	−1.19890
$626$	1.72203e12	0.448183
$627$	2.76904e11	0.0715526
$628$	1.73144e12	0.444209
$629$	2.65711e11	0.0676832
$630$	0	0
$631$	−4.72735e12	−1.18710	−0.593548	−	0.804799i	$-0.702273\pi$
$631$	−4.72735e12	−1.18710	−0.593548	+	0.804799i	$0.702273\pi$
$632$	−2.77555e12	−0.692026
$633$	−9.92257e11	−0.245645
$634$	5.21015e12	1.28070
$635$	5.28054e12	1.28883
$636$	9.14127e11	0.221539
$637$	0	0
$638$	6.47927e11	0.154822
$639$	1.59647e12	0.378796
$640$	−4.92870e11	−0.116124
$641$	−1.83470e12	−0.429243	−0.214621	−	0.976697i	$-0.568852\pi$
$641$	−1.83470e12	−0.429243	−0.214621	+	0.976697i	$0.568852\pi$
$642$	8.80103e11	0.204468
$643$	3.00823e12	0.694003	0.347001	−	0.937865i	$-0.387200\pi$
$643$	3.00823e12	0.694003	0.347001	+	0.937865i	$0.387200\pi$
$644$	0	0
$645$	−3.34767e12	−0.761594
$646$	−8.81370e11	−0.199119
$647$	−5.10356e12	−1.14500	−0.572499	−	0.819906i	$-0.694026\pi$
$647$	−5.10356e12	−1.14500	−0.572499	+	0.819906i	$0.694026\pi$
$648$	−9.52284e11	−0.212167
$649$	−3.21094e11	−0.0710446
$650$	−4.06237e12	−0.892626
$651$	0	0
$652$	−7.53852e11	−0.163370
$653$	4.12342e12	0.887458	0.443729	−	0.896161i	$-0.353655\pi$
$653$	4.12342e12	0.887458	0.443729	+	0.896161i	$0.353655\pi$
$654$	−1.71024e12	−0.365560
$655$	1.09634e13	2.32733
$656$	5.89979e11	0.124385
$657$	−2.25749e12	−0.472695
$658$	0	0
$659$	−7.14612e12	−1.47600	−0.737999	−	0.674802i	$-0.764229\pi$
$659$	−7.14612e12	−1.47600	−0.737999	+	0.674802i	$0.764229\pi$
$660$	2.31291e11	0.0474473
$661$	7.53617e12	1.53548	0.767740	−	0.640761i	$-0.221381\pi$
$661$	7.53617e12	1.53548	0.767740	+	0.640761i	$0.221381\pi$
$662$	2.71271e12	0.548963
$663$	9.19434e11	0.184803
$664$	−1.80762e12	−0.360870
$665$	0	0
$666$	7.35318e11	0.144824
$667$	4.22628e12	0.826783
$668$	−4.07203e12	−0.791256
$669$	−2.81911e12	−0.544119
$670$	−7.13706e12	−1.36830
$671$	−1.55551e12	−0.296225
$672$	0	0
$673$	2.71281e12	0.509743	0.254872	−	0.966975i	$-0.417967\pi$
$673$	2.71281e12	0.509743	0.254872	+	0.966975i	$0.417967\pi$
$674$	2.02810e12	0.378547
$675$	−2.72377e12	−0.505014
$676$	5.49180e12	1.01147
$677$	−1.68158e12	−0.307658	−0.153829	−	0.988097i	$-0.549160\pi$
$677$	−1.68158e12	−0.307658	−0.153829	+	0.988097i	$0.549160\pi$
$678$	3.95334e11	0.0718506
$679$	0	0
$680$	−7.36187e11	−0.132038
$681$	−3.41687e11	−0.0608789
$682$	−1.19682e12	−0.211837
$683$	3.57937e12	0.629380	0.314690	−	0.949194i	$-0.398099\pi$
$683$	3.57937e12	0.629380	0.314690	+	0.949194i	$0.398099\pi$
$684$	−2.43907e12	−0.426062
$685$	−2.56519e12	−0.445156
$686$	0	0
$687$	−1.09405e12	−0.187384
$688$	−2.27775e12	−0.387577
$689$	1.21872e13	2.06023
$690$	1.50866e12	0.253379
$691$	−4.21356e12	−0.703069	−0.351535	−	0.936175i	$-0.614340\pi$
$691$	−4.21356e12	−0.703069	−0.351535	+	0.936175i	$0.614340\pi$
$692$	2.64444e12	0.438386
$693$	0	0
$694$	2.86572e12	0.468939
$695$	1.46259e13	2.37789
$696$	9.27658e11	0.149846
$697$	8.81237e11	0.141431
$698$	2.78202e12	0.443619
$699$	1.00491e12	0.159213
$700$	0	0
$701$	−6.32382e12	−0.989119	−0.494560	−	0.869144i	$-0.664671\pi$
$701$	−6.32382e12	−0.989119	−0.494560	+	0.869144i	$0.664671\pi$
$702$	5.50240e12	0.855135
$703$	1.52748e12	0.235872
$704$	1.57370e11	0.0241460
$705$	4.06254e12	0.619365
$706$	1.44560e12	0.218991
$707$	0	0
$708$	−4.59720e11	−0.0687613
$709$	−8.01320e12	−1.19096	−0.595481	−	0.803369i	$-0.703039\pi$
$709$	−8.01320e12	−1.19096	−0.595481	+	0.803369i	$0.703039\pi$
$710$	2.77006e12	0.409097
$711$	−1.14729e13	−1.68368
$712$	−2.27442e12	−0.331673
$713$	−7.80660e12	−1.13125
$714$	0	0
$715$	3.08358e12	0.441244
$716$	2.76545e12	0.393239
$717$	−1.35685e12	−0.191733
$718$	2.94319e12	0.413294
$719$	1.84798e12	0.257879	0.128940	−	0.991652i	$-0.458843\pi$
$719$	1.84798e12	0.257879	0.128940	+	0.991652i	$0.458843\pi$
$720$	−2.03730e12	−0.282526
$721$	0	0
$722$	9.63057e10	0.0131897
$723$	1.68818e12	0.229771
$724$	1.57169e12	0.212591
$725$	−6.12213e12	−0.822966
$726$	1.90530e12	0.254535
$727$	9.54988e12	1.26792	0.633962	−	0.773365i	$-0.281428\pi$
$727$	9.54988e12	1.26792	0.633962	+	0.773365i	$0.281428\pi$
$728$	0	0
$729$	−1.95301e12	−0.256113
$730$	−3.91701e12	−0.510507
$731$	−3.40222e12	−0.440690
$732$	−2.22707e12	−0.286704
$733$	−2.45279e12	−0.313828	−0.156914	−	0.987612i	$-0.550155\pi$
$733$	−2.45279e12	−0.313828	−0.156914	+	0.987612i	$0.550155\pi$
$734$	5.78100e12	0.735141
$735$	0	0
$736$	1.02649e12	0.128945
$737$	2.27882e12	0.284516
$738$	2.43871e12	0.302626
$739$	1.03314e13	1.27426	0.637131	−	0.770755i	$-0.280121\pi$
$739$	1.03314e13	1.27426	0.637131	+	0.770755i	$0.280121\pi$
$740$	1.27587e12	0.156409
$741$	5.28551e12	0.644029
$742$	0	0
$743$	2.90098e12	0.349216	0.174608	−	0.984638i	$-0.444134\pi$
$743$	2.90098e12	0.349216	0.174608	+	0.984638i	$0.444134\pi$
$744$	−1.71353e12	−0.205028
$745$	−2.02447e13	−2.40774
$746$	−2.59873e12	−0.307211
$747$	−7.47188e12	−0.877985
$748$	2.35060e11	0.0274550
$749$	0	0
$750$	8.24576e11	0.0951602
$751$	1.75532e12	0.201362	0.100681	−	0.994919i	$-0.467898\pi$
$751$	1.75532e12	0.201362	0.100681	+	0.994919i	$0.467898\pi$
$752$	2.76415e12	0.315196
$753$	−1.27099e12	−0.144067
$754$	1.23676e13	1.39352
$755$	−7.24286e12	−0.811240
$756$	0	0
$757$	1.28835e13	1.42594	0.712972	−	0.701193i	$-0.247349\pi$
$757$	1.28835e13	1.42594	0.712972	+	0.701193i	$0.247349\pi$
$758$	1.72531e11	0.0189826
$759$	−4.81705e11	−0.0526858
$760$	−4.23209e12	−0.460144
$761$	−1.97149e12	−0.213090	−0.106545	−	0.994308i	$-0.533979\pi$
$761$	−1.97149e12	−0.213090	−0.106545	+	0.994308i	$0.533979\pi$
$762$	−2.41396e12	−0.259378
$763$	0	0
$764$	−2.40310e12	−0.255183
$765$	−3.04306e12	−0.321243
$766$	−1.11657e13	−1.17181
$767$	−6.12900e12	−0.639456
$768$	2.25312e11	0.0233700
$769$	8.44373e12	0.870694	0.435347	−	0.900263i	$-0.356626\pi$
$769$	8.44373e12	0.870694	0.435347	+	0.900263i	$0.356626\pi$
$770$	0	0
$771$	1.87039e12	0.190629
$772$	2.32041e12	0.235118
$773$	1.27925e13	1.28869	0.644344	−	0.764736i	$-0.277131\pi$
$773$	1.27925e13	1.28869	0.644344	+	0.764736i	$0.277131\pi$
$774$	−9.41518e12	−0.942962
$775$	1.13086e13	1.12603
$776$	5.19760e12	0.514547
$777$	0	0
$778$	9.58335e12	0.937798
$779$	5.06593e12	0.492879
$780$	4.41486e12	0.427062
$781$	−8.84463e11	−0.0850649
$782$	1.53324e12	0.146615
$783$	8.29230e12	0.788401
$784$	0	0
$785$	1.24182e13	1.16720
$786$	−5.01183e12	−0.468376
$787$	1.46833e13	1.36439	0.682194	−	0.731171i	$-0.261026\pi$
$787$	1.46833e13	1.36439	0.682194	+	0.731171i	$0.261026\pi$
$788$	−1.87162e12	−0.172922
$789$	−6.26204e12	−0.575267
$790$	−1.99068e13	−1.81836
$791$	0	0
$792$	6.50497e11	0.0587465
$793$	−2.96914e13	−2.66625
$794$	5.89055e12	0.525973
$795$	6.55630e12	0.582112
$796$	−3.86688e11	−0.0341391
$797$	−1.35485e13	−1.18940	−0.594699	−	0.803948i	$-0.702729\pi$
$797$	−1.35485e13	−1.18940	−0.594699	+	0.803948i	$0.702729\pi$
$798$	0	0
$799$	4.12874e12	0.358391
$800$	−1.48696e12	−0.128349
$801$	−9.40141e12	−0.806950
$802$	−1.77951e12	−0.151885
$803$	1.25068e12	0.106151
$804$	3.26265e12	0.275371
$805$	0	0
$806$	−2.28448e13	−1.90669
$807$	−5.53869e12	−0.459702
$808$	−5.60455e12	−0.462583
$809$	−1.43230e13	−1.17562	−0.587810	−	0.808999i	$-0.700010\pi$
$809$	−1.43230e13	−1.17562	−0.587810	+	0.808999i	$0.700010\pi$
$810$	−6.82997e12	−0.557489
$811$	−2.09686e13	−1.70206	−0.851030	−	0.525117i	$-0.824021\pi$
$811$	−2.09686e13	−1.70206	−0.851030	+	0.525117i	$0.824021\pi$
$812$	0	0
$813$	3.30772e12	0.265535
$814$	−4.07376e11	−0.0325226
$815$	−5.40678e12	−0.429269
$816$	3.36543e11	0.0265726
$817$	−1.95582e13	−1.53578
$818$	7.07890e12	0.552810
$819$	0	0
$820$	4.23145e12	0.326834
$821$	−1.45338e13	−1.11644	−0.558219	−	0.829694i	$-0.688515\pi$
$821$	−1.45338e13	−1.11644	−0.558219	+	0.829694i	$0.688515\pi$
$822$	1.17266e12	0.0895877
$823$	1.83532e13	1.39448	0.697240	−	0.716837i	$-0.254411\pi$
$823$	1.83532e13	1.39448	0.697240	+	0.716837i	$0.254411\pi$
$824$	7.87053e11	0.0594746
$825$	6.97792e11	0.0524425
$826$	0	0
$827$	−7.78350e11	−0.0578629	−0.0289315	−	0.999581i	$-0.509210\pi$
$827$	−7.78350e11	−0.0578629	−0.0289315	+	0.999581i	$0.509210\pi$
$828$	4.24304e12	0.313719
$829$	−9.79518e12	−0.720306	−0.360153	−	0.932893i	$-0.617276\pi$
$829$	−9.79518e12	−0.720306	−0.360153	+	0.932893i	$0.617276\pi$
$830$	−1.29646e13	−0.948218
$831$	−4.63193e12	−0.336943
$832$	3.00386e12	0.217333
$833$	0	0
$834$	−6.68613e12	−0.478550
$835$	−2.92054e13	−2.07910
$836$	1.35128e12	0.0956791
$837$	−1.53172e13	−1.07873
$838$	−1.20800e13	−0.846189
$839$	2.38998e12	0.166520	0.0832598	−	0.996528i	$-0.473467\pi$
$839$	2.38998e12	0.166520	0.0832598	+	0.996528i	$0.473467\pi$
$840$	0	0
$841$	4.13119e12	0.284769
$842$	−6.90056e12	−0.473130
$843$	−7.46057e11	−0.0508801
$844$	−4.84217e12	−0.328472
$845$	3.93883e13	2.65774
$846$	1.14257e13	0.766862
$847$	0	0
$848$	4.46090e12	0.296238
$849$	7.56420e12	0.499664
$850$	−2.22103e12	−0.145938
$851$	−2.65722e12	−0.173678
$852$	−1.26631e12	−0.0823309
$853$	1.36355e13	0.881860	0.440930	−	0.897541i	$-0.354649\pi$
$853$	1.36355e13	0.881860	0.440930	+	0.897541i	$0.354649\pi$
$854$	0	0
$855$	−1.74935e13	−1.11951
$856$	4.29486e12	0.273412
$857$	3.26982e12	0.207067	0.103533	−	0.994626i	$-0.466985\pi$
$857$	3.26982e12	0.207067	0.103533	+	0.994626i	$0.466985\pi$
$858$	−1.40964e12	−0.0888004
$859$	1.96336e11	0.0123035	0.00615177	−	0.999981i	$-0.498042\pi$
$859$	1.96336e11	0.0123035	0.00615177	+	0.999981i	$0.498042\pi$
$860$	−1.63365e13	−1.01839
$861$	0	0
$862$	−1.62200e13	−1.00062
$863$	−9.03351e12	−0.554381	−0.277190	−	0.960815i	$-0.589403\pi$
$863$	−9.03351e12	−0.554381	−0.277190	+	0.960815i	$0.589403\pi$
$864$	2.01405e12	0.122959
$865$	1.89665e13	1.15190
$866$	−9.64753e12	−0.582889
$867$	−5.71838e12	−0.343706
$868$	0	0
$869$	6.35612e12	0.378097
$870$	6.65334e12	0.393734
$871$	4.34978e13	2.56086
$872$	−8.34591e12	−0.488821
$873$	2.14845e13	1.25188
$874$	8.81408e12	0.510946
$875$	0	0
$876$	1.79063e12	0.102740
$877$	7.05313e12	0.402609	0.201305	−	0.979529i	$-0.435482\pi$
$877$	7.05313e12	0.402609	0.201305	+	0.979529i	$0.435482\pi$
$878$	−7.26856e12	−0.412784
$879$	−3.87762e12	−0.219086
$880$	1.12869e12	0.0634458
$881$	3.36898e13	1.88411	0.942056	−	0.335456i	$-0.108890\pi$
$881$	3.36898e13	1.88411	0.942056	+	0.335456i	$0.108890\pi$
$882$	0	0
$883$	2.36891e13	1.31137	0.655686	−	0.755034i	$-0.272379\pi$
$883$	2.36891e13	1.31137	0.655686	+	0.755034i	$0.272379\pi$
$884$	4.48680e12	0.247116
$885$	−3.29720e12	−0.180676
$886$	−1.61422e13	−0.880057
$887$	−2.18995e13	−1.18790	−0.593948	−	0.804503i	$-0.702432\pi$
$887$	−2.18995e13	−1.18790	−0.593948	+	0.804503i	$0.702432\pi$
$888$	−5.83253e11	−0.0314774
$889$	0	0
$890$	−1.63126e13	−0.871500
$891$	2.18077e12	0.115920
$892$	−1.37571e13	−0.727588
$893$	2.37347e13	1.24897
$894$	9.25474e12	0.484557
$895$	1.98343e13	1.03327
$896$	0	0
$897$	−9.19473e12	−0.474213
$898$	−2.41712e11	−0.0124038
$899$	−3.44280e13	−1.75789
$900$	−6.14641e12	−0.312270
$901$	6.66313e12	0.336835
$902$	−1.35108e12	−0.0679595
$903$	0	0
$904$	1.92921e12	0.0960775
$905$	1.12725e13	0.558600
$906$	3.31102e12	0.163262
$907$	1.41797e13	0.695720	0.347860	−	0.937546i	$-0.386908\pi$
$907$	1.41797e13	0.695720	0.347860	+	0.937546i	$0.386908\pi$
$908$	−1.66742e12	−0.0814063
$909$	−2.31667e13	−1.12545
$910$	0	0
$911$	−5.44567e12	−0.261950	−0.130975	−	0.991386i	$-0.541811\pi$
$911$	−5.44567e12	−0.261950	−0.130975	+	0.991386i	$0.541811\pi$
$912$	1.93467e12	0.0926040
$913$	4.13952e12	0.197166
$914$	1.65408e13	0.783966
$915$	−1.59730e13	−0.753340
$916$	−5.33893e12	−0.250567
$917$	0	0
$918$	3.00834e12	0.139809
$919$	2.75583e13	1.27448	0.637240	−	0.770665i	$-0.280076\pi$
$919$	2.75583e13	1.27448	0.637240	+	0.770665i	$0.280076\pi$
$920$	7.36218e12	0.338814
$921$	5.86159e12	0.268440
$922$	9.85885e12	0.449301
$923$	−1.68825e13	−0.765649
$924$	0	0
$925$	3.84921e12	0.172876
$926$	−1.41988e13	−0.634603
$927$	3.25332e12	0.144700
$928$	4.52693e12	0.200372
$929$	−1.01769e13	−0.448276	−0.224138	−	0.974557i	$-0.571957\pi$
$929$	−1.01769e13	−0.448276	−0.224138	+	0.974557i	$0.571957\pi$
$930$	−1.22898e13	−0.538730
$931$	0	0
$932$	4.90390e12	0.212897
$933$	−1.15956e13	−0.500987
$934$	2.81997e13	1.21251
$935$	1.68590e12	0.0721404
$936$	1.24166e13	0.528764
$937$	−1.96831e13	−0.834192	−0.417096	−	0.908863i	$-0.636952\pi$
$937$	−1.96831e13	−0.834192	−0.417096	+	0.908863i	$0.636952\pi$
$938$	0	0
$939$	−5.64604e12	−0.237000
$940$	1.98250e13	0.828206
$941$	−7.56033e12	−0.314331	−0.157166	−	0.987572i	$-0.550236\pi$
$941$	−7.56033e12	−0.314331	−0.157166	+	0.987572i	$0.550236\pi$
$942$	−5.67689e12	−0.234899
$943$	−8.81274e12	−0.362918
$944$	−2.24341e12	−0.0919465
$945$	0	0
$946$	5.21613e12	0.211757
$947$	2.42370e13	0.979274	0.489637	−	0.871926i	$-0.337129\pi$
$947$	2.42370e13	0.979274	0.489637	+	0.871926i	$0.337129\pi$
$948$	9.10026e12	0.365945
$949$	2.38728e13	0.955443
$950$	−1.27680e13	−0.508587
$951$	−1.70826e13	−0.677239
$952$	0	0
$953$	2.69411e13	1.05803	0.529015	−	0.848613i	$-0.322562\pi$
$953$	2.69411e13	1.05803	0.529015	+	0.848613i	$0.322562\pi$
$954$	1.84393e13	0.720738
$955$	−1.72355e13	−0.670516
$956$	−6.62138e12	−0.256382
$957$	−2.12437e12	−0.0818704
$958$	2.00341e12	0.0768467
$959$	0	0
$960$	1.61598e12	0.0614067
$961$	3.71543e13	1.40525
$962$	−7.77595e12	−0.292729
$963$	1.77530e13	0.665202
$964$	8.23822e12	0.307246
$965$	1.66424e13	0.617794
$966$	0	0
$967$	2.13513e13	0.785245	0.392623	−	0.919700i	$-0.371568\pi$
$967$	2.13513e13	0.785245	0.392623	+	0.919700i	$0.371568\pi$
$968$	9.29777e12	0.340361
$969$	2.88977e12	0.105294
$970$	3.72782e13	1.35202
$971$	6.21151e11	0.0224239	0.0112119	−	0.999937i	$-0.496431\pi$
$971$	6.21151e11	0.0224239	0.0112119	+	0.999937i	$0.496431\pi$
$972$	1.28007e13	0.459975
$973$	0	0
$974$	−3.07051e13	−1.09319
$975$	1.33194e13	0.472023
$976$	−1.08680e13	−0.383376
$977$	−2.12880e13	−0.747496	−0.373748	−	0.927530i	$-0.621927\pi$
$977$	−2.12880e13	−0.747496	−0.373748	+	0.927530i	$0.621927\pi$
$978$	2.47167e12	0.0863904
$979$	5.20850e12	0.181214
$980$	0	0
$981$	−3.44982e13	−1.18928
$982$	2.07682e13	0.712685
$983$	5.65684e12	0.193234	0.0966169	−	0.995322i	$-0.469198\pi$
$983$	5.65684e12	0.193234	0.0966169	+	0.995322i	$0.469198\pi$
$984$	−1.93438e12	−0.0657753
$985$	−1.34236e13	−0.454368
$986$	6.76175e12	0.227831
$987$	0	0
$988$	2.57931e13	0.861186
$989$	3.40236e13	1.13083
$990$	4.66549e12	0.154362
$991$	−1.82458e13	−0.600939	−0.300469	−	0.953791i	$-0.597143\pi$
$991$	−1.82458e13	−0.600939	−0.300469	+	0.953791i	$0.597143\pi$
$992$	−8.36195e12	−0.274161
$993$	−8.89422e12	−0.290293
$994$	0	0
$995$	−2.77340e12	−0.0897035
$996$	5.92668e12	0.190829
$997$	−9.67315e12	−0.310056	−0.155028	−	0.987910i	$-0.549547\pi$
$997$	−9.67315e12	−0.310056	−0.155028	+	0.987910i	$0.549547\pi$
$998$	6.81721e12	0.217530
$999$	−5.21368e12	−0.165615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.d.1.2	yes	2
7.2	even	3		98.10.c.i.67.1		4
7.3	odd	6		98.10.c.i.79.2		4
7.4	even	3		98.10.c.i.79.1		4
7.5	odd	6		98.10.c.i.67.2		4
7.6	odd	2	inner	98.10.a.d.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.d.1.1	✓	2	7.6	odd	2	inner
98.10.a.d.1.2	yes	2	1.1	even	1	trivial
98.10.c.i.67.1		4	7.2	even	3
98.10.c.i.67.2		4	7.5	odd	6
98.10.c.i.79.1		4	7.4	even	3
98.10.c.i.79.2		4	7.3	odd	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)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +52.4595 q^{3} +256.000 q^{4} +1836.08 q^{5} -839.352 q^{6} -4096.00 q^{8} -16931.0 q^{9} -29377.3 q^{10} +9380.00 q^{11} +13429.6 q^{12} +179044. q^{13} +96320.0 q^{15} +65536.0 q^{16} +97889.4 q^{17} +270896. q^{18} +562733. q^{19} +470037. q^{20} -150080. q^{22} -978936. q^{23} -214874. q^{24} +1.41808e6 q^{25} -2.86471e6 q^{26} -1.92075e6 q^{27} -4.31721e6 q^{29} -1.54112e6 q^{30} +7.97458e6 q^{31} -1.04858e6 q^{32} +492070. q^{33} -1.56623e6 q^{34} -4.33434e6 q^{36} +2.71439e6 q^{37} -9.00373e6 q^{38} +9.39258e6 q^{39} -7.52060e6 q^{40} +9.00237e6 q^{41} -3.47557e7 q^{43} +2.40128e6 q^{44} -3.10867e7 q^{45} +1.56630e7 q^{46} +4.21775e7 q^{47} +3.43799e6 q^{48} -2.26892e7 q^{50} +5.13523e6 q^{51} +4.58353e7 q^{52} +6.80679e7 q^{53} +3.07320e7 q^{54} +1.72225e7 q^{55} +2.95207e7 q^{57} +6.90754e7 q^{58} -3.42318e7 q^{59} +2.46579e7 q^{60} -1.65833e8 q^{61} -1.27593e8 q^{62} +1.67772e7 q^{64} +3.28740e8 q^{65} -7.87312e6 q^{66} +2.42944e8 q^{67} +2.50597e7 q^{68} -5.13545e7 q^{69} -9.42925e7 q^{71} +6.93494e7 q^{72} +1.33334e8 q^{73} -4.34303e7 q^{74} +7.43915e7 q^{75} +1.44060e8 q^{76} -1.50281e8 q^{78} +6.77625e8 q^{79} +1.20330e8 q^{80} +2.32491e8 q^{81} -1.44038e8 q^{82} +4.41313e8 q^{83} +1.79733e8 q^{85} +5.56091e8 q^{86} -2.26479e8 q^{87} -3.84205e7 q^{88} +5.55278e8 q^{89} +4.97387e8 q^{90} -2.50608e8 q^{92} +4.18343e8 q^{93} -6.74841e8 q^{94} +1.03322e9 q^{95} -5.50078e7 q^{96} -1.26895e9 q^{97} -1.58813e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} + 512 q^{4} - 8192 q^{8} - 33862 q^{9} + 18760 q^{11} + 192640 q^{15} + 131072 q^{16} + 541792 q^{18} - 300160 q^{22} - 1957872 q^{23} + 2836150 q^{25} - 8634428 q^{29} - 3082240 q^{30} - 2097152 q^{32}+ \cdots - 317625560 q^{99}+O(q^{100}) \) 2 * q - 32 * q^2 + 512 * q^4 - 8192 * q^8 - 33862 * q^9 + 18760 * q^11 + 192640 * q^15 + 131072 * q^16 + 541792 * q^18 - 300160 * q^22 - 1957872 * q^23 + 2836150 * q^25 - 8634428 * q^29 - 3082240 * q^30 - 2097152 * q^32 - 8668672 * q^36 + 5428788 * q^37 + 18785152 * q^39 - 69511384 * q^43 + 4802560 * q^44 + 31325952 * q^46 - 45378400 * q^50 + 10270464 * q^51 + 136135852 * q^53 + 59041408 * q^57 + 138150848 * q^58 + 49315840 * q^60 + 33554432 * q^64 + 657480320 * q^65 + 485888840 * q^67 - 188584928 * q^71 + 138698752 * q^72 - 86860608 * q^74 - 300562432 * q^78 + 1355250320 * q^79 + 464982290 * q^81 + 359466240 * q^85 + 1112182144 * q^86 - 76840960 * q^88 - 501215232 * q^92 + 836685056 * q^93 + 2066449280 * q^95 - 317625560 * q^99

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