LMFDB - Embedded newform 98.10.a.h.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)

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,-48,71] 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:	$3$
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} - 4037x + 70980 $ x^3 - x^2 - 4037*x + 70980
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 7 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$52.2593$ 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)

$f(q)$	$=$	\(q-16.0000 q^{2} +76.8690 q^{3} +256.000 q^{4} +1092.26 q^{5} -1229.90 q^{6} -4096.00 q^{8} -13774.2 q^{9} -17476.2 q^{10} +54060.9 q^{11} +19678.5 q^{12} -37802.6 q^{13} +83960.9 q^{15} +65536.0 q^{16} +353470. q^{17} +220387. q^{18} -50210.7 q^{19} +279618. q^{20} -864974. q^{22} +2.45852e6 q^{23} -314855. q^{24} -760094. q^{25} +604841. q^{26} -2.57182e6 q^{27} +1.40865e6 q^{29} -1.34337e6 q^{30} -5.78323e6 q^{31} -1.04858e6 q^{32} +4.15560e6 q^{33} -5.65552e6 q^{34} -3.52619e6 q^{36} +5.45877e6 q^{37} +803370. q^{38} -2.90584e6 q^{39} -4.47390e6 q^{40} +1.73066e7 q^{41} +1.43644e6 q^{43} +1.38396e7 q^{44} -1.50450e7 q^{45} -3.93364e7 q^{46} -3.04387e7 q^{47} +5.03768e6 q^{48} +1.21615e7 q^{50} +2.71709e7 q^{51} -9.67746e6 q^{52} -4.30796e6 q^{53} +4.11491e7 q^{54} +5.90485e7 q^{55} -3.85964e6 q^{57} -2.25385e7 q^{58} +6.61456e7 q^{59} +2.14940e7 q^{60} +2.00925e8 q^{61} +9.25317e7 q^{62} +1.67772e7 q^{64} -4.12902e7 q^{65} -6.64896e7 q^{66} -2.72602e8 q^{67} +9.04883e7 q^{68} +1.88984e8 q^{69} +1.43433e8 q^{71} +5.64190e7 q^{72} +3.68032e8 q^{73} -8.73403e7 q^{74} -5.84276e7 q^{75} -1.28539e7 q^{76} +4.64935e7 q^{78} +4.63995e8 q^{79} +7.15823e7 q^{80} +7.34239e7 q^{81} -2.76906e8 q^{82} +7.47626e8 q^{83} +3.86081e8 q^{85} -2.29830e7 q^{86} +1.08282e8 q^{87} -2.21433e8 q^{88} +1.12789e9 q^{89} +2.40719e8 q^{90} +6.29382e8 q^{92} -4.44551e8 q^{93} +4.87019e8 q^{94} -5.48431e7 q^{95} -8.06029e7 q^{96} +1.27313e8 q^{97} -7.44643e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 48 q^{2} + 71 q^{3} + 768 q^{4} - 1085 q^{5} - 1136 q^{6} - 12288 q^{8} + 9106 q^{9} + 17360 q^{10} - 2555 q^{11} + 18176 q^{12} - 18070 q^{13} - 353073 q^{15} + 196608 q^{16} + 20759 q^{17} - 145696 q^{18}+ \cdots - 1303712634 q^{99}+O(q^{100}) $ 3 * q - 48 * q^2 + 71 * q^3 + 768 * q^4 - 1085 * q^5 - 1136 * q^6 - 12288 * q^8 + 9106 * q^9 + 17360 * q^10 - 2555 * q^11 + 18176 * q^12 - 18070 * q^13 - 353073 * q^15 + 196608 * q^16 + 20759 * q^17 - 145696 * q^18 + 1220649 * q^19 - 277760 * q^20 + 40880 * q^22 + 1960903 * q^23 - 290816 * q^24 + 863572 * q^25 + 289120 * q^26 - 2888659 * q^27 - 2606146 * q^29 + 5649168 * q^30 - 9377989 * q^31 - 3145728 * q^32 - 10778103 * q^33 - 332144 * q^34 + 2331136 * q^36 + 25814913 * q^37 - 19530384 * q^38 - 37990822 * q^39 + 4444160 * q^40 - 209250 * q^41 + 2944308 * q^43 - 654080 * q^44 - 37350558 * q^45 - 31374448 * q^46 + 48391269 * q^47 + 4653056 * q^48 - 13817152 * q^50 + 75441987 * q^51 - 4625920 * q^52 - 102186411 * q^53 + 46218544 * q^54 + 228278701 * q^55 + 43084589 * q^57 + 41698336 * q^58 + 144220135 * q^59 - 90386688 * q^60 + 280936871 * q^61 + 150047824 * q^62 + 50331648 * q^64 + 186819738 * q^65 + 172449648 * q^66 - 170710399 * q^67 + 5314304 * q^68 + 903654171 * q^69 + 469758688 * q^71 - 37298176 * q^72 + 613838539 * q^73 - 413038608 * q^74 + 902254676 * q^75 + 312486144 * q^76 + 607853152 * q^78 - 197445809 * q^79 - 71106560 * q^80 - 887872901 * q^81 + 3348000 * q^82 + 1074181436 * q^83 + 411272519 * q^85 - 47108928 * q^86 + 753428670 * q^87 + 10465280 * q^88 + 805730427 * q^89 + 597608928 * q^90 + 501991168 * q^92 + 1721516327 * q^93 - 774260304 * q^94 - 1799421743 * q^95 - 74448896 * q^96 + 2262918094 * q^97 - 1303712634 * 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
$3$	76.8690	0.547905	0.273953	−	0.961743i	$-0.411669\pi$
$3$	76.8690	0.547905	0.273953	+	0.961743i	$0.411669\pi$
$4$	256.000	0.500000
$5$	1092.26	0.781557	0.390779	−	0.920485i	$-0.372206\pi$
$5$	1092.26	0.781557	0.390779	+	0.920485i	$0.372206\pi$
$6$	−1229.90	−0.387427
$7$	0	0
$7$	0	0
$8$	−4096.00	−0.353553
$9$	−13774.2	−0.699800
$10$	−17476.2	−0.552644
$11$	54060.9	1.11331	0.556655	−	0.830744i	$-0.312085\pi$
$11$	54060.9	1.11331	0.556655	+	0.830744i	$0.312085\pi$
$12$	19678.5	0.273953
$13$	−37802.6	−0.367093	−0.183547	−	0.983011i	$-0.558758\pi$
$13$	−37802.6	−0.367093	−0.183547	+	0.983011i	$0.558758\pi$
$14$	0	0
$15$	83960.9	0.428219
$16$	65536.0	0.250000
$17$	353470.	1.02644	0.513218	−	0.858258i	$-0.328453\pi$
$17$	353470.	1.02644	0.513218	+	0.858258i	$0.328453\pi$
$18$	220387.	0.494833
$19$	−50210.7	−0.0883903	−0.0441952	−	0.999023i	$-0.514072\pi$
$19$	−50210.7	−0.0883903	−0.0441952	+	0.999023i	$0.514072\pi$
$20$	279618.	0.390779
$21$	0	0
$22$	−864974.	−0.787228
$23$	2.45852e6	1.83189	0.915944	−	0.401305i	$-0.131443\pi$
$23$	2.45852e6	1.83189	0.915944	+	0.401305i	$0.131443\pi$
$24$	−314855.	−0.193714
$25$	−760094.	−0.389168
$26$	604841.	0.259574
$27$	−2.57182e6	−0.931329
$28$	0	0
$29$	1.40865e6	0.369840	0.184920	−	0.982754i	$-0.440797\pi$
$29$	1.40865e6	0.369840	0.184920	+	0.982754i	$0.440797\pi$
$30$	−1.34337e6	−0.302797
$31$	−5.78323e6	−1.12472	−0.562358	−	0.826894i	$-0.690106\pi$
$31$	−5.78323e6	−1.12472	−0.562358	+	0.826894i	$0.690106\pi$
$32$	−1.04858e6	−0.176777
$33$	4.15560e6	0.609988
$34$	−5.65552e6	−0.725800
$35$	0	0
$36$	−3.52619e6	−0.349900
$37$	5.45877e6	0.478836	0.239418	−	0.970917i	$-0.423043\pi$
$37$	5.45877e6	0.478836	0.239418	+	0.970917i	$0.423043\pi$
$38$	803370.	0.0625014
$39$	−2.90584e6	−0.201132
$40$	−4.47390e6	−0.276322
$41$	1.73066e7	0.956501	0.478251	−	0.878223i	$-0.341271\pi$
$41$	1.73066e7	0.956501	0.478251	+	0.878223i	$0.341271\pi$
$42$	0	0
$43$	1.43644e6	0.0640735	0.0320367	−	0.999487i	$-0.489801\pi$
$43$	1.43644e6	0.0640735	0.0320367	+	0.999487i	$0.489801\pi$
$44$	1.38396e7	0.556655
$45$	−1.50450e7	−0.546934
$46$	−3.93364e7	−1.29534
$47$	−3.04387e7	−0.909883	−0.454942	−	0.890521i	$-0.650340\pi$
$47$	−3.04387e7	−0.909883	−0.454942	+	0.890521i	$0.650340\pi$
$48$	5.03768e6	0.136976
$49$	0	0
$50$	1.21615e7	0.275183
$51$	2.71709e7	0.562390
$52$	−9.67746e6	−0.183547
$53$	−4.30796e6	−0.0749947	−0.0374973	−	0.999297i	$-0.511939\pi$
$53$	−4.30796e6	−0.0749947	−0.0374973	+	0.999297i	$0.511939\pi$
$54$	4.11491e7	0.658549
$55$	5.90485e7	0.870115
$56$	0	0
$57$	−3.85964e6	−0.0484295
$58$	−2.25385e7	−0.261516
$59$	6.61456e7	0.710668	0.355334	−	0.934739i	$-0.384367\pi$
$59$	6.61456e7	0.710668	0.355334	+	0.934739i	$0.384367\pi$
$60$	2.14940e7	0.214110
$61$	2.00925e8	1.85802	0.929008	−	0.370061i	$-0.120663\pi$
$61$	2.00925e8	1.85802	0.929008	+	0.370061i	$0.120663\pi$
$62$	9.25317e7	0.795295
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−4.12902e7	−0.286904
$66$	−6.64896e7	−0.431327
$67$	−2.72602e8	−1.65269	−0.826347	−	0.563161i	$-0.809585\pi$
$67$	−2.72602e8	−1.65269	−0.826347	+	0.563161i	$0.809585\pi$
$68$	9.04883e7	0.513218
$69$	1.88984e8	1.00370
$70$	0	0
$71$	1.43433e8	0.669866	0.334933	−	0.942242i	$-0.391286\pi$
$71$	1.43433e8	0.669866	0.334933	+	0.942242i	$0.391286\pi$
$72$	5.64190e7	0.247417
$73$	3.68032e8	1.51681	0.758407	−	0.651781i	$-0.225978\pi$
$73$	3.68032e8	1.51681	0.758407	+	0.651781i	$0.225978\pi$
$74$	−8.73403e7	−0.338588
$75$	−5.84276e7	−0.213227
$76$	−1.28539e7	−0.0441952
$77$	0	0
$78$	4.64935e7	0.142222
$79$	4.63995e8	1.34027	0.670134	−	0.742240i	$-0.266236\pi$
$79$	4.63995e8	1.34027	0.670134	+	0.742240i	$0.266236\pi$
$80$	7.15823e7	0.195389
$81$	7.34239e7	0.189520
$82$	−2.76906e8	−0.676349
$83$	7.47626e8	1.72915	0.864576	−	0.502503i	$-0.167587\pi$
$83$	7.47626e8	1.72915	0.864576	+	0.502503i	$0.167587\pi$
$84$	0	0
$85$	3.86081e8	0.802219
$86$	−2.29830e7	−0.0453068
$87$	1.08282e8	0.202637
$88$	−2.21433e8	−0.393614
$89$	1.12789e9	1.90551	0.952753	−	0.303746i	$-0.0982374\pi$
$89$	1.12789e9	1.90551	0.952753	+	0.303746i	$0.0982374\pi$
$90$	2.40719e8	0.386741
$91$	0	0
$92$	6.29382e8	0.915944
$93$	−4.44551e8	−0.616238
$94$	4.87019e8	0.643385
$95$	−5.48431e7	−0.0690821
$96$	−8.06029e7	−0.0968569
$97$	1.27313e8	0.146016	0.0730079	−	0.997331i	$-0.476740\pi$
$97$	1.27313e8	0.146016	0.0730079	+	0.997331i	$0.476740\pi$
$98$	0	0
$99$	−7.44643e8	−0.779094
$100$	−1.94584e8	−0.194584
$101$	−1.50545e9	−1.43953	−0.719764	−	0.694219i	$-0.755750\pi$
$101$	−1.50545e9	−1.43953	−0.719764	+	0.694219i	$0.755750\pi$
$102$	−4.34734e8	−0.397670
$103$	5.94955e8	0.520855	0.260428	−	0.965493i	$-0.416136\pi$
$103$	5.94955e8	0.520855	0.260428	+	0.965493i	$0.416136\pi$
$104$	1.54839e8	0.129787
$105$	0	0
$106$	6.89274e7	0.0530292
$107$	1.35491e9	0.999274	0.499637	−	0.866235i	$-0.333467\pi$
$107$	1.35491e9	0.999274	0.499637	+	0.866235i	$0.333467\pi$
$108$	−6.58385e8	−0.465665
$109$	−1.93784e9	−1.31492	−0.657459	−	0.753490i	$-0.728369\pi$
$109$	−1.93784e9	−1.31492	−0.657459	+	0.753490i	$0.728369\pi$
$110$	−9.44776e8	−0.615264
$111$	4.19610e8	0.262357
$112$	0	0
$113$	−1.98306e9	−1.14415	−0.572074	−	0.820202i	$-0.693861\pi$
$113$	−1.98306e9	−1.14415	−0.572074	+	0.820202i	$0.693861\pi$
$114$	6.17543e7	0.0342448
$115$	2.68535e9	1.43173
$116$	3.60616e8	0.184920
$117$	5.20699e8	0.256892
$118$	−1.05833e9	−0.502518
$119$	0	0
$120$	−3.43904e8	−0.151398
$121$	5.64628e8	0.239457
$122$	−3.21480e9	−1.31382
$123$	1.33034e9	0.524072
$124$	−1.48051e9	−0.562358
$125$	−2.96354e9	−1.08571
$126$	0	0
$127$	3.90286e7	0.0133127	0.00665635	−	0.999978i	$-0.497881\pi$
$127$	3.90286e7	0.0133127	0.00665635	+	0.999978i	$0.497881\pi$
$128$	−2.68435e8	−0.0883883
$129$	1.10417e8	0.0351062
$130$	6.60643e8	0.202872
$131$	−1.59378e9	−0.472832	−0.236416	−	0.971652i	$-0.575973\pi$
$131$	−1.59378e9	−0.472832	−0.236416	+	0.971652i	$0.575973\pi$
$132$	1.06383e9	0.304994
$133$	0	0
$134$	4.36163e9	1.16863
$135$	−2.80909e9	−0.727887
$136$	−1.44781e9	−0.362900
$137$	5.63635e9	1.36696	0.683479	−	0.729970i	$-0.260466\pi$
$137$	5.63635e9	1.36696	0.683479	+	0.729970i	$0.260466\pi$
$138$	−3.02375e9	−0.709724
$139$	−2.40520e9	−0.546493	−0.273246	−	0.961944i	$-0.588097\pi$
$139$	−2.40520e9	−0.546493	−0.273246	+	0.961944i	$0.588097\pi$
$140$	0	0
$141$	−2.33979e9	−0.498530
$142$	−2.29494e9	−0.473667
$143$	−2.04364e9	−0.408688
$144$	−9.02704e8	−0.174950
$145$	1.53862e9	0.289051
$146$	−5.88851e9	−1.07255
$147$	0	0
$148$	1.39744e9	0.239418
$149$	4.82927e9	0.802682	0.401341	−	0.915929i	$-0.368544\pi$
$149$	4.82927e9	0.802682	0.401341	+	0.915929i	$0.368544\pi$
$150$	9.34842e8	0.150774
$151$	1.06662e10	1.66960	0.834802	−	0.550550i	$-0.185582\pi$
$151$	1.06662e10	1.66960	0.834802	+	0.550550i	$0.185582\pi$
$152$	2.05663e8	0.0312507
$153$	−4.86875e9	−0.718300
$154$	0	0
$155$	−6.31679e9	−0.879030
$156$	−7.43896e8	−0.100566
$157$	9.90602e9	1.30122	0.650610	−	0.759412i	$-0.274513\pi$
$157$	9.90602e9	1.30122	0.650610	+	0.759412i	$0.274513\pi$
$158$	−7.42393e9	−0.947713
$159$	−3.31149e8	−0.0410900
$160$	−1.14532e9	−0.138161
$161$	0	0
$162$	−1.17478e9	−0.134011
$163$	−1.24288e10	−1.37907	−0.689533	−	0.724255i	$-0.742184\pi$
$163$	−1.24288e10	−1.37907	−0.689533	+	0.724255i	$0.742184\pi$
$164$	4.43050e9	0.478251
$165$	4.53900e9	0.476740
$166$	−1.19620e10	−1.22269
$167$	5.48234e9	0.545434	0.272717	−	0.962094i	$-0.412078\pi$
$167$	5.48234e9	0.545434	0.272717	+	0.962094i	$0.412078\pi$
$168$	0	0
$169$	−9.17547e9	−0.865243
$170$	−6.17729e9	−0.567255
$171$	6.91610e8	0.0618555
$172$	3.67728e8	0.0320367
$173$	4.59767e9	0.390238	0.195119	−	0.980780i	$-0.437491\pi$
$173$	4.59767e9	0.390238	0.195119	+	0.980780i	$0.437491\pi$
$174$	−1.73251e9	−0.143286
$175$	0	0
$176$	3.54293e9	0.278327
$177$	5.08454e9	0.389379
$178$	−1.80462e10	−1.34740
$179$	2.56403e9	0.186674	0.0933370	−	0.995635i	$-0.470247\pi$
$179$	2.56403e9	0.186674	0.0933370	+	0.995635i	$0.470247\pi$
$180$	−3.85151e9	−0.273467
$181$	3.58323e9	0.248154	0.124077	−	0.992273i	$-0.460403\pi$
$181$	3.58323e9	0.248154	0.124077	+	0.992273i	$0.460403\pi$
$182$	0	0
$183$	1.54449e10	1.01802
$184$	−1.00701e10	−0.647671
$185$	5.96239e9	0.374238
$186$	7.11282e9	0.435746
$187$	1.91089e10	1.14274
$188$	−7.79231e9	−0.454942
$189$	0	0
$190$	8.77489e8	0.0488484
$191$	−6.97388e8	−0.0379162	−0.0189581	−	0.999820i	$-0.506035\pi$
$191$	−6.97388e8	−0.0379162	−0.0189581	+	0.999820i	$0.506035\pi$
$192$	1.28965e9	0.0684881
$193$	−5.70859e8	−0.0296156	−0.0148078	−	0.999890i	$-0.504714\pi$
$193$	−5.70859e8	−0.0296156	−0.0148078	+	0.999890i	$0.504714\pi$
$194$	−2.03701e9	−0.103249
$195$	−3.17394e9	−0.157196
$196$	0	0
$197$	−4.88945e9	−0.231293	−0.115646	−	0.993290i	$-0.536894\pi$
$197$	−4.88945e9	−0.231293	−0.115646	+	0.993290i	$0.536894\pi$
$198$	1.19143e10	0.550902
$199$	−1.01824e10	−0.460269	−0.230134	−	0.973159i	$-0.573917\pi$
$199$	−1.01824e10	−0.460269	−0.230134	+	0.973159i	$0.573917\pi$
$200$	3.11335e9	0.137592
$201$	−2.09546e10	−0.905519
$202$	2.40872e10	1.01790
$203$	0	0
$204$	6.95574e9	0.281195
$205$	1.89033e10	0.747561
$206$	−9.51929e9	−0.368300
$207$	−3.38641e10	−1.28196
$208$	−2.47743e9	−0.0917733
$209$	−2.71443e9	−0.0984058
$210$	0	0
$211$	−2.89906e10	−1.00690	−0.503450	−	0.864025i	$-0.667936\pi$
$211$	−2.89906e10	−1.00690	−0.503450	+	0.864025i	$0.667936\pi$
$212$	−1.10284e9	−0.0374973
$213$	1.10256e10	0.367023
$214$	−2.16786e10	−0.706594
$215$	1.56896e9	0.0500771
$216$	1.05342e10	0.329275
$217$	0	0
$218$	3.10054e10	0.929788
$219$	2.82902e10	0.831070
$220$	1.51164e10	0.435057
$221$	−1.33621e10	−0.376798
$222$	−6.71376e9	−0.185514
$223$	9.01973e9	0.244243	0.122121	−	0.992515i	$-0.461030\pi$
$223$	9.01973e9	0.244243	0.122121	+	0.992515i	$0.461030\pi$
$224$	0	0
$225$	1.04697e10	0.272340
$226$	3.17289e10	0.809035
$227$	−1.32631e10	−0.331533	−0.165767	−	0.986165i	$-0.553010\pi$
$227$	−1.32631e10	−0.331533	−0.165767	+	0.986165i	$0.553010\pi$
$228$	−9.88068e8	−0.0242148
$229$	7.67667e10	1.84465	0.922323	−	0.386420i	$-0.126288\pi$
$229$	7.67667e10	1.84465	0.922323	+	0.386420i	$0.126288\pi$
$230$	−4.29655e10	−1.01238
$231$	0	0
$232$	−5.76985e9	−0.130758
$233$	−2.29389e9	−0.0509883	−0.0254942	−	0.999675i	$-0.508116\pi$
$233$	−2.29389e9	−0.0509883	−0.0254942	+	0.999675i	$0.508116\pi$
$234$	−8.33118e9	−0.181650
$235$	−3.32470e10	−0.711126
$236$	1.69333e10	0.355334
$237$	3.56669e10	0.734340
$238$	0	0
$239$	−4.06748e10	−0.806372	−0.403186	−	0.915118i	$-0.632097\pi$
$239$	−4.06748e10	−0.806372	−0.403186	+	0.915118i	$0.632097\pi$
$240$	5.50246e9	0.107055
$241$	−9.43703e9	−0.180202	−0.0901008	−	0.995933i	$-0.528719\pi$
$241$	−9.43703e9	−0.180202	−0.0901008	+	0.995933i	$0.528719\pi$
$242$	−9.03405e9	−0.169322
$243$	5.62651e10	1.03517
$244$	5.14367e10	0.929008
$245$	0	0
$246$	−2.12855e10	−0.370575
$247$	1.89809e9	0.0324475
$248$	2.36881e10	0.397647
$249$	5.74692e10	0.947411
$250$	4.74166e10	0.767716
$251$	7.60552e10	1.20948	0.604738	−	0.796425i	$-0.293278\pi$
$251$	7.60552e10	1.20948	0.604738	+	0.796425i	$0.293278\pi$
$252$	0	0
$253$	1.32910e11	2.03946
$254$	−6.24457e8	−0.00941350
$255$	2.96776e10	0.439540
$256$	4.29497e9	0.0625000
$257$	−9.02211e10	−1.29006	−0.645028	−	0.764159i	$-0.723154\pi$
$257$	−9.02211e10	−1.29006	−0.645028	+	0.764159i	$0.723154\pi$
$258$	−1.76668e9	−0.0248238
$259$	0	0
$260$	−1.05703e10	−0.143452
$261$	−1.94030e10	−0.258814
$262$	2.55005e10	0.334343
$263$	−9.35682e10	−1.20594	−0.602972	−	0.797762i	$-0.706017\pi$
$263$	−9.35682e10	−1.20594	−0.602972	+	0.797762i	$0.706017\pi$
$264$	−1.70213e10	−0.215663
$265$	−4.70541e9	−0.0586126
$266$	0	0
$267$	8.66995e10	1.04404
$268$	−6.97861e10	−0.826347
$269$	−1.48563e10	−0.172992	−0.0864960	−	0.996252i	$-0.527567\pi$
$269$	−1.48563e10	−0.172992	−0.0864960	+	0.996252i	$0.527567\pi$
$270$	4.49455e10	0.514694
$271$	−1.17185e11	−1.31980	−0.659902	−	0.751352i	$-0.729402\pi$
$271$	−1.17185e11	−1.31980	−0.659902	+	0.751352i	$0.729402\pi$
$272$	2.31650e10	0.256609
$273$	0	0
$274$	−9.01815e10	−0.966585
$275$	−4.10913e10	−0.433264
$276$	4.83799e10	0.501851
$277$	−2.87224e10	−0.293131	−0.146565	−	0.989201i	$-0.546822\pi$
$277$	−2.87224e10	−0.293131	−0.146565	+	0.989201i	$0.546822\pi$
$278$	3.84832e10	0.386429
$279$	7.96592e10	0.787076
$280$	0	0
$281$	−7.39690e10	−0.707736	−0.353868	−	0.935295i	$-0.615134\pi$
$281$	−7.39690e10	−0.707736	−0.353868	+	0.935295i	$0.615134\pi$
$282$	3.74367e10	0.352514
$283$	7.27488e10	0.674197	0.337098	−	0.941469i	$-0.390554\pi$
$283$	7.27488e10	0.674197	0.337098	+	0.941469i	$0.390554\pi$
$284$	3.67190e10	0.334933
$285$	−4.21573e9	−0.0378504
$286$	3.26982e10	0.288986
$287$	0	0
$288$	1.44433e10	0.123708
$289$	6.35304e9	0.0535724
$290$	−2.46179e10	−0.204390
$291$	9.78642e9	0.0800028
$292$	9.42161e10	0.758407
$293$	−2.43926e11	−1.93354	−0.966771	−	0.255644i	$-0.917712\pi$
$293$	−2.43926e11	−1.93354	−0.966771	+	0.255644i	$0.917712\pi$
$294$	0	0
$295$	7.22481e10	0.555428
$296$	−2.23591e10	−0.169294
$297$	−1.39035e11	−1.03686
$298$	−7.72683e10	−0.567582
$299$	−9.29385e10	−0.672474
$300$	−1.49575e10	−0.106614
$301$	0	0
$302$	−1.70659e11	−1.18059
$303$	−1.15722e11	−0.788725
$304$	−3.29061e9	−0.0220976
$305$	2.19462e11	1.45215
$306$	7.79000e10	0.507915
$307$	−1.41661e11	−0.910182	−0.455091	−	0.890445i	$-0.650393\pi$
$307$	−1.41661e11	−0.910182	−0.455091	+	0.890445i	$0.650393\pi$
$308$	0	0
$309$	4.57336e10	0.285379
$310$	1.01069e11	0.621568
$311$	−1.29174e11	−0.782986	−0.391493	−	0.920181i	$-0.628041\pi$
$311$	−1.29174e11	−0.782986	−0.391493	+	0.920181i	$0.628041\pi$
$312$	1.19023e10	0.0711110
$313$	−4.44649e10	−0.261859	−0.130930	−	0.991392i	$-0.541796\pi$
$313$	−4.44649e10	−0.261859	−0.130930	+	0.991392i	$0.541796\pi$
$314$	−1.58496e11	−0.920101
$315$	0	0
$316$	1.18783e11	0.670134
$317$	−2.48426e11	−1.38175	−0.690877	−	0.722973i	$-0.742775\pi$
$317$	−2.48426e11	−1.38175	−0.690877	+	0.722973i	$0.742775\pi$
$318$	5.29838e9	0.0290550
$319$	7.61531e10	0.411746
$320$	1.83251e10	0.0976947
$321$	1.04151e11	0.547508
$322$	0	0
$323$	−1.77480e10	−0.0907271
$324$	1.87965e10	0.0947600
$325$	2.87335e10	0.142861
$326$	1.98861e11	0.975146
$327$	−1.48960e11	−0.720451
$328$	−7.08880e10	−0.338174
$329$	0	0
$330$	−7.26239e10	−0.337106
$331$	3.62219e11	1.65861	0.829307	−	0.558793i	$-0.188735\pi$
$331$	3.62219e11	1.65861	0.829307	+	0.558793i	$0.188735\pi$
$332$	1.91392e11	0.864576
$333$	−7.51900e10	−0.335089
$334$	−8.77175e10	−0.385680
$335$	−2.97752e11	−1.29167
$336$	0	0
$337$	−4.33951e11	−1.83276	−0.916380	−	0.400309i	$-0.868903\pi$
$337$	−4.33951e11	−1.83276	−0.916380	+	0.400309i	$0.868903\pi$
$338$	1.46807e11	0.611819
$339$	−1.52435e11	−0.626884
$340$	9.88367e10	0.401110
$341$	−3.12646e11	−1.25216
$342$	−1.10658e10	−0.0437385
$343$	0	0
$344$	−5.88364e9	−0.0226534
$345$	2.06420e11	0.784450
$346$	−7.35626e10	−0.275940
$347$	1.92978e11	0.714537	0.357268	−	0.934002i	$-0.383708\pi$
$347$	1.92978e11	0.714537	0.357268	+	0.934002i	$0.383708\pi$
$348$	2.77201e10	0.101319
$349$	−2.85795e11	−1.03119	−0.515596	−	0.856832i	$-0.672430\pi$
$349$	−2.85795e11	−1.03119	−0.515596	+	0.856832i	$0.672430\pi$
$350$	0	0
$351$	9.72213e10	0.341884
$352$	−5.66869e10	−0.196807
$353$	−4.16138e10	−0.142643	−0.0713217	−	0.997453i	$-0.522722\pi$
$353$	−4.16138e10	−0.142643	−0.0713217	+	0.997453i	$0.522722\pi$
$354$	−8.13526e10	−0.275332
$355$	1.56667e11	0.523539
$356$	2.88739e11	0.952753
$357$	0	0
$358$	−4.10244e10	−0.131998
$359$	−4.10775e11	−1.30521	−0.652604	−	0.757699i	$-0.726323\pi$
$359$	−4.10775e11	−1.30521	−0.652604	+	0.757699i	$0.726323\pi$
$360$	6.16242e10	0.193370
$361$	−3.20167e11	−0.992187
$362$	−5.73316e10	−0.175471
$363$	4.34024e10	0.131200
$364$	0	0
$365$	4.01986e11	1.18548
$366$	−2.47118e11	−0.719846
$367$	−1.83042e11	−0.526688	−0.263344	−	0.964702i	$-0.584825\pi$
$367$	−1.83042e11	−0.526688	−0.263344	+	0.964702i	$0.584825\pi$
$368$	1.61122e11	0.457972
$369$	−2.38385e11	−0.669360
$370$	−9.53983e10	−0.264626
$371$	0	0
$372$	−1.13805e11	−0.308119
$373$	−2.85765e11	−0.764396	−0.382198	−	0.924080i	$-0.624833\pi$
$373$	−2.85765e11	−0.764396	−0.382198	+	0.924080i	$0.624833\pi$
$374$	−3.05742e11	−0.808040
$375$	−2.27804e11	−0.594869
$376$	1.24677e11	0.321692
$377$	−5.32508e10	−0.135766
$378$	0	0
$379$	4.76362e10	0.118593	0.0592967	−	0.998240i	$-0.481114\pi$
$379$	4.76362e10	0.118593	0.0592967	+	0.998240i	$0.481114\pi$
$380$	−1.40398e10	−0.0345410
$381$	3.00009e9	0.00729409
$382$	1.11582e10	0.0268108
$383$	4.08991e11	0.971223	0.485611	−	0.874175i	$-0.338597\pi$
$383$	4.08991e11	0.971223	0.485611	+	0.874175i	$0.338597\pi$
$384$	−2.06344e10	−0.0484284
$385$	0	0
$386$	9.13374e9	0.0209414
$387$	−1.97857e10	−0.0448386
$388$	3.25921e10	0.0730079
$389$	−1.12325e11	−0.248716	−0.124358	−	0.992237i	$-0.539687\pi$
$389$	−1.12325e11	−0.248716	−0.124358	+	0.992237i	$0.539687\pi$
$390$	5.07830e10	0.111155
$391$	8.69014e11	1.88032
$392$	0	0
$393$	−1.22512e11	−0.259067
$394$	7.82311e10	0.163549
$395$	5.06804e11	1.04750
$396$	−1.90629e11	−0.389547
$397$	3.85685e11	0.779248	0.389624	−	0.920974i	$-0.372605\pi$
$397$	3.85685e11	0.779248	0.389624	+	0.920974i	$0.372605\pi$
$398$	1.62918e11	0.325459
$399$	0	0
$400$	−4.98135e10	−0.0972920
$401$	1.80685e11	0.348958	0.174479	−	0.984661i	$-0.444176\pi$
$401$	1.80685e11	0.348958	0.174479	+	0.984661i	$0.444176\pi$
$402$	3.35274e11	0.640299
$403$	2.18621e11	0.412876
$404$	−3.85395e11	−0.719764
$405$	8.01980e10	0.148121
$406$	0	0
$407$	2.95106e11	0.533093
$408$	−1.11292e11	−0.198835
$409$	2.48017e11	0.438255	0.219127	−	0.975696i	$-0.429679\pi$
$409$	2.48017e11	0.438255	0.219127	+	0.975696i	$0.429679\pi$
$410$	−3.02454e11	−0.528605
$411$	4.33260e11	0.748963
$412$	1.52309e11	0.260428
$413$	0	0
$414$	5.41826e11	0.906480
$415$	8.16602e11	1.35143
$416$	3.96389e10	0.0648935
$417$	−1.84885e11	−0.299426
$418$	4.34309e10	0.0695834
$419$	2.26007e11	0.358227	0.179113	−	0.983828i	$-0.442677\pi$
$419$	2.26007e11	0.358227	0.179113	+	0.983828i	$0.442677\pi$
$420$	0	0
$421$	−3.76981e11	−0.584858	−0.292429	−	0.956287i	$-0.594464\pi$
$421$	−3.76981e11	−0.584858	−0.292429	+	0.956287i	$0.594464\pi$
$422$	4.63849e11	0.711985
$423$	4.19268e11	0.636736
$424$	1.76454e10	0.0265146
$425$	−2.68670e11	−0.399456
$426$	−1.76409e11	−0.259525
$427$	0	0
$428$	3.46858e11	0.499637
$429$	−1.57092e11	−0.223922
$430$	−2.51034e10	−0.0354099
$431$	−1.43102e11	−0.199756	−0.0998779	−	0.995000i	$-0.531845\pi$
$431$	−1.43102e11	−0.199756	−0.0998779	+	0.995000i	$0.531845\pi$
$432$	−1.68547e11	−0.232832
$433$	1.36985e12	1.87275	0.936373	−	0.351007i	$-0.114161\pi$
$433$	1.36985e12	1.87275	0.936373	+	0.351007i	$0.114161\pi$
$434$	0	0
$435$	1.18272e11	0.158373
$436$	−4.96087e11	−0.657459
$437$	−1.23444e11	−0.161921
$438$	−4.52643e11	−0.587655
$439$	1.05555e12	1.35641	0.678203	−	0.734875i	$-0.262759\pi$
$439$	1.05555e12	1.35641	0.678203	+	0.734875i	$0.262759\pi$
$440$	−2.41863e11	−0.307632
$441$	0	0
$442$	2.13793e11	0.266436
$443$	7.36777e11	0.908906	0.454453	−	0.890771i	$-0.349835\pi$
$443$	7.36777e11	0.908906	0.454453	+	0.890771i	$0.349835\pi$
$444$	1.07420e11	0.131178
$445$	1.23194e12	1.48926
$446$	−1.44316e11	−0.172706
$447$	3.71221e11	0.439793
$448$	0	0
$449$	−1.37800e11	−0.160007	−0.0800036	−	0.996795i	$-0.525493\pi$
$449$	−1.37800e11	−0.160007	−0.0800036	+	0.996795i	$0.525493\pi$
$450$	−1.67515e11	−0.192573
$451$	9.35612e11	1.06488
$452$	−5.07662e11	−0.572074
$453$	8.19900e11	0.914785
$454$	2.12209e11	0.234429
$455$	0	0
$456$	1.58091e10	0.0171224
$457$	−8.17482e11	−0.876708	−0.438354	−	0.898802i	$-0.644438\pi$
$457$	−8.17482e11	−0.876708	−0.438354	+	0.898802i	$0.644438\pi$
$458$	−1.22827e12	−1.30436
$459$	−9.09060e11	−0.955950
$460$	6.87449e11	0.715863
$461$	−1.54090e12	−1.58899	−0.794495	−	0.607270i	$-0.792265\pi$
$461$	−1.54090e12	−1.58899	−0.794495	+	0.607270i	$0.792265\pi$
$462$	0	0
$463$	−7.47957e11	−0.756419	−0.378209	−	0.925720i	$-0.623460\pi$
$463$	−7.47957e11	−0.756419	−0.378209	+	0.925720i	$0.623460\pi$
$464$	9.23176e10	0.0924599
$465$	−4.85565e11	−0.481625
$466$	3.67022e10	0.0360542
$467$	−2.41074e11	−0.234544	−0.117272	−	0.993100i	$-0.537415\pi$
$467$	−2.41074e11	−0.234544	−0.117272	+	0.993100i	$0.537415\pi$
$468$	1.33299e11	0.128446
$469$	0	0
$470$	5.31951e11	0.502842
$471$	7.61465e11	0.712945
$472$	−2.70932e11	−0.251259
$473$	7.76550e10	0.0713336
$474$	−5.70670e11	−0.519257
$475$	3.81648e10	0.0343987
$476$	0	0
$477$	5.93386e10	0.0524813
$478$	6.50797e11	0.570191
$479$	−4.18088e11	−0.362876	−0.181438	−	0.983402i	$-0.558075\pi$
$479$	−4.18088e11	−0.362876	−0.181438	+	0.983402i	$0.558075\pi$
$480$	−8.80393e10	−0.0756992
$481$	−2.06355e11	−0.175777
$482$	1.50992e11	0.127422
$483$	0	0
$484$	1.44545e11	0.119729
$485$	1.39059e11	0.114120
$486$	−9.00242e11	−0.731974
$487$	−1.71573e12	−1.38219	−0.691095	−	0.722764i	$-0.742871\pi$
$487$	−1.71573e12	−1.38219	−0.691095	+	0.722764i	$0.742871\pi$
$488$	−8.22988e11	−0.656908
$489$	−9.55388e11	−0.755597
$490$	0	0
$491$	3.34731e11	0.259914	0.129957	−	0.991520i	$-0.458516\pi$
$491$	3.34731e11	0.259914	0.129957	+	0.991520i	$0.458516\pi$
$492$	3.40568e11	0.262036
$493$	4.97917e11	0.379617
$494$	−3.03695e10	−0.0229438
$495$	−8.13343e11	−0.608906
$496$	−3.79010e11	−0.281179
$497$	0	0
$498$	−9.19508e11	−0.669921
$499$	7.10044e11	0.512664	0.256332	−	0.966589i	$-0.417486\pi$
$499$	7.10044e11	0.512664	0.256332	+	0.966589i	$0.417486\pi$
$500$	−7.58666e11	−0.542857
$501$	4.21422e11	0.298846
$502$	−1.21688e12	−0.855228
$503$	2.16835e12	1.51033	0.755167	−	0.655532i	$-0.227556\pi$
$503$	2.16835e12	1.51033	0.755167	+	0.655532i	$0.227556\pi$
$504$	0	0
$505$	−1.64434e12	−1.12507
$506$	−2.12656e12	−1.44212
$507$	−7.05308e11	−0.474071
$508$	9.99132e9	0.00665635
$509$	−7.69897e11	−0.508396	−0.254198	−	0.967152i	$-0.581812\pi$
$509$	−7.69897e11	−0.508396	−0.254198	+	0.967152i	$0.581812\pi$
$510$	−4.74842e11	−0.310802
$511$	0	0
$512$	−6.87195e10	−0.0441942
$513$	1.29133e11	0.0823205
$514$	1.44354e12	0.912208
$515$	6.49846e11	0.407078
$516$	2.82668e10	0.0175531
$517$	−1.64554e12	−1.01298
$518$	0	0
$519$	3.53418e11	0.213814
$520$	1.69125e11	0.101436
$521$	−2.32093e11	−0.138004	−0.0690021	−	0.997617i	$-0.521982\pi$
$521$	−2.32093e11	−0.138004	−0.0690021	+	0.997617i	$0.521982\pi$
$522$	3.10449e11	0.183009
$523$	2.08260e12	1.21716	0.608580	−	0.793493i	$-0.291740\pi$
$523$	2.08260e12	1.21716	0.608580	+	0.793493i	$0.291740\pi$
$524$	−4.08007e11	−0.236416
$525$	0	0
$526$	1.49709e12	0.852731
$527$	−2.04420e12	−1.15445
$528$	2.72341e11	0.152497
$529$	4.24319e12	2.35582
$530$	7.52866e10	0.0414454
$531$	−9.11100e11	−0.497325
$532$	0	0
$533$	−6.54236e11	−0.351125
$534$	−1.38719e12	−0.738245
$535$	1.47992e12	0.780990
$536$	1.11658e12	0.584316
$537$	1.97094e11	0.102280
$538$	2.37701e11	0.122324
$539$	0	0
$540$	−7.19128e11	−0.363944
$541$	−8.39742e11	−0.421462	−0.210731	−	0.977544i	$-0.567584\pi$
$541$	−8.39742e11	−0.421462	−0.210731	+	0.977544i	$0.567584\pi$
$542$	1.87496e12	0.933242
$543$	2.75439e11	0.135965
$544$	−3.70640e11	−0.181450
$545$	−2.11662e12	−1.02768
$546$	0	0
$547$	−7.58235e11	−0.362127	−0.181064	−	0.983471i	$-0.557954\pi$
$547$	−7.58235e11	−0.362127	−0.181064	+	0.983471i	$0.557954\pi$
$548$	1.44290e12	0.683479
$549$	−2.76757e12	−1.30024
$550$	6.57461e11	0.306364
$551$	−7.07295e10	−0.0326903
$552$	−7.74079e11	−0.354862
$553$	0	0
$554$	4.59558e11	0.207275
$555$	4.58323e11	0.205047
$556$	−6.15731e11	−0.273246
$557$	1.59724e12	0.703110	0.351555	−	0.936167i	$-0.385653\pi$
$557$	1.59724e12	0.703110	0.351555	+	0.936167i	$0.385653\pi$
$558$	−1.27455e12	−0.556547
$559$	−5.43010e10	−0.0235209
$560$	0	0
$561$	1.46888e12	0.626114
$562$	1.18350e12	0.500445
$563$	−2.60961e11	−0.109468	−0.0547340	−	0.998501i	$-0.517431\pi$
$563$	−2.60961e11	−0.109468	−0.0547340	+	0.998501i	$0.517431\pi$
$564$	−5.98987e11	−0.249265
$565$	−2.16601e12	−0.894217
$566$	−1.16398e12	−0.476729
$567$	0	0
$568$	−5.87504e11	−0.236833
$569$	−1.53339e12	−0.613264	−0.306632	−	0.951828i	$-0.599202\pi$
$569$	−1.53339e12	−0.613264	−0.306632	+	0.951828i	$0.599202\pi$
$570$	6.74517e10	0.0267643
$571$	−2.76112e12	−1.08698	−0.543492	−	0.839415i	$-0.682898\pi$
$571$	−2.76112e12	−1.08698	−0.543492	+	0.839415i	$0.682898\pi$
$572$	−5.23172e11	−0.204344
$573$	−5.36075e10	−0.0207745
$574$	0	0
$575$	−1.86871e12	−0.712913
$576$	−2.31092e11	−0.0874750
$577$	4.00470e12	1.50411	0.752054	−	0.659101i	$-0.229063\pi$
$577$	4.00470e12	1.50411	0.752054	+	0.659101i	$0.229063\pi$
$578$	−1.01649e11	−0.0378814
$579$	−4.38813e10	−0.0162265
$580$	3.93886e11	0.144525
$581$	0	0
$582$	−1.56583e11	−0.0565705
$583$	−2.32892e11	−0.0834923
$584$	−1.50746e12	−0.536275
$585$	5.68738e11	0.200776
$586$	3.90281e12	1.36722
$587$	1.31451e12	0.456976	0.228488	−	0.973547i	$-0.426622\pi$
$587$	1.31451e12	0.456976	0.228488	+	0.973547i	$0.426622\pi$
$588$	0	0
$589$	2.90380e11	0.0994140
$590$	−1.15597e12	−0.392747
$591$	−3.75847e11	−0.126726
$592$	3.57746e11	0.119709
$593$	−4.18573e12	−1.39003	−0.695016	−	0.718994i	$-0.744603\pi$
$593$	−4.18573e12	−1.39003	−0.695016	+	0.718994i	$0.744603\pi$
$594$	2.22455e12	0.733169
$595$	0	0
$596$	1.23629e12	0.401341
$597$	−7.82710e11	−0.252183
$598$	1.48702e12	0.475511
$599$	−1.94567e12	−0.617517	−0.308758	−	0.951140i	$-0.599913\pi$
$599$	−1.94567e12	−0.617517	−0.308758	+	0.951140i	$0.599913\pi$
$600$	2.39320e11	0.0753872
$601$	−4.58168e12	−1.43248	−0.716242	−	0.697852i	$-0.754139\pi$
$601$	−4.58168e12	−1.43248	−0.716242	+	0.697852i	$0.754139\pi$
$602$	0	0
$603$	3.75486e12	1.15656
$604$	2.73055e12	0.834802
$605$	6.16720e11	0.187150
$606$	1.85156e12	0.557713
$607$	3.73888e12	1.11787	0.558936	−	0.829211i	$-0.311210\pi$
$607$	3.73888e12	1.11787	0.558936	+	0.829211i	$0.311210\pi$
$608$	5.26497e10	0.0156253
$609$	0	0
$610$	−3.51139e12	−1.02682
$611$	1.15066e12	0.334012
$612$	−1.24640e12	−0.359150
$613$	1.12397e12	0.321501	0.160751	−	0.986995i	$-0.448608\pi$
$613$	1.12397e12	0.321501	0.160751	+	0.986995i	$0.448608\pi$
$614$	2.26658e12	0.643596
$615$	1.45308e12	0.409592
$616$	0	0
$617$	8.34463e11	0.231805	0.115903	−	0.993261i	$-0.463024\pi$
$617$	8.34463e11	0.231805	0.115903	+	0.993261i	$0.463024\pi$
$618$	−7.31738e11	−0.201794
$619$	−2.47746e12	−0.678264	−0.339132	−	0.940739i	$-0.610133\pi$
$619$	−2.47746e12	−0.678264	−0.339132	+	0.940739i	$0.610133\pi$
$620$	−1.61710e12	−0.439515
$621$	−6.32287e12	−1.70609
$622$	2.06679e12	0.553655
$623$	0	0
$624$	−1.90437e11	−0.0502830
$625$	−1.75240e12	−0.459380
$626$	7.11439e11	0.185163
$627$	−2.08655e11	−0.0539170
$628$	2.53594e12	0.650610
$629$	1.92951e12	0.491495
$630$	0	0
$631$	1.00841e12	0.253223	0.126612	−	0.991952i	$-0.459590\pi$
$631$	1.00841e12	0.253223	0.126612	+	0.991952i	$0.459590\pi$
$632$	−1.90053e12	−0.473857
$633$	−2.22848e12	−0.551685
$634$	3.97482e12	0.977047
$635$	4.26293e10	0.0104046
$636$	−8.47740e10	−0.0205450
$637$	0	0
$638$	−1.21845e12	−0.291148
$639$	−1.97568e12	−0.468772
$640$	−2.93201e11	−0.0690806
$641$	−6.98225e12	−1.63356	−0.816778	−	0.576952i	$-0.804242\pi$
$641$	−6.98225e12	−1.63356	−0.816778	+	0.576952i	$0.804242\pi$
$642$	−1.66641e12	−0.387146
$643$	5.09779e12	1.17607	0.588034	−	0.808836i	$-0.299902\pi$
$643$	5.09779e12	1.17607	0.588034	+	0.808836i	$0.299902\pi$
$644$	0	0
$645$	1.20604e11	0.0274375
$646$	2.83967e11	0.0641537
$647$	−2.20736e12	−0.495226	−0.247613	−	0.968859i	$-0.579646\pi$
$647$	−2.20736e12	−0.495226	−0.247613	+	0.968859i	$0.579646\pi$
$648$	−3.00744e11	−0.0670054
$649$	3.57589e12	0.791193
$650$	−4.59736e11	−0.101018
$651$	0	0
$652$	−3.18177e12	−0.689533
$653$	8.20909e12	1.76679	0.883397	−	0.468626i	$-0.155251\pi$
$653$	8.20909e12	1.76679	0.883397	+	0.468626i	$0.155251\pi$
$654$	2.38336e12	0.509435
$655$	−1.74082e12	−0.369546
$656$	1.13421e12	0.239125
$657$	−5.06933e12	−1.06147
$658$	0	0
$659$	5.75171e12	1.18799	0.593994	−	0.804469i	$-0.297550\pi$
$659$	5.75171e12	1.18799	0.593994	+	0.804469i	$0.297550\pi$
$660$	1.16198e12	0.238370
$661$	−3.40404e12	−0.693566	−0.346783	−	0.937945i	$-0.612726\pi$
$661$	−3.40404e12	−0.693566	−0.346783	+	0.937945i	$0.612726\pi$
$662$	−5.79551e12	−1.17282
$663$	−1.02713e12	−0.206449
$664$	−3.06228e12	−0.611347
$665$	0	0
$666$	1.20304e12	0.236944
$667$	3.46321e12	0.677505
$668$	1.40348e12	0.272717
$669$	6.93337e11	0.133822
$670$	4.76403e12	0.913352
$671$	1.08622e13	2.06855
$672$	0	0
$673$	−7.13050e12	−1.33984	−0.669918	−	0.742435i	$-0.733671\pi$
$673$	−7.13050e12	−1.33984	−0.669918	+	0.742435i	$0.733671\pi$
$674$	6.94321e12	1.29596
$675$	1.95482e12	0.362444
$676$	−2.34892e12	−0.432621
$677$	1.30195e12	0.238202	0.119101	−	0.992882i	$-0.461999\pi$
$677$	1.30195e12	0.238202	0.119101	+	0.992882i	$0.461999\pi$
$678$	2.43897e12	0.443274
$679$	0	0
$680$	−1.58139e12	−0.283627
$681$	−1.01952e12	−0.181649
$682$	5.00234e12	0.885409
$683$	−4.62558e12	−0.813341	−0.406671	−	0.913575i	$-0.633310\pi$
$683$	−4.62558e12	−0.813341	−0.406671	+	0.913575i	$0.633310\pi$
$684$	1.77052e11	0.0309278
$685$	6.15635e12	1.06836
$686$	0	0
$687$	5.90097e12	1.01069
$688$	9.41383e10	0.0160184
$689$	1.62852e11	0.0275300
$690$	−3.30272e12	−0.554690
$691$	2.92633e12	0.488284	0.244142	−	0.969740i	$-0.421494\pi$
$691$	2.92633e12	0.488284	0.244142	+	0.969740i	$0.421494\pi$
$692$	1.17700e12	0.195119
$693$	0	0
$694$	−3.08764e12	−0.505254
$695$	−2.62710e12	−0.427116
$696$	−4.43522e11	−0.0716430
$697$	6.11738e12	0.981788
$698$	4.57272e12	0.729163
$699$	−1.76329e11	−0.0279368
$700$	0	0
$701$	5.32710e12	0.833220	0.416610	−	0.909085i	$-0.363218\pi$
$701$	5.32710e12	0.833220	0.416610	+	0.909085i	$0.363218\pi$
$702$	−1.55554e12	−0.241749
$703$	−2.74088e11	−0.0423245
$704$	9.06991e11	0.139164
$705$	−2.55566e12	−0.389630
$706$	6.65821e11	0.100864
$707$	0	0
$708$	1.30164e12	0.194689
$709$	3.14221e12	0.467012	0.233506	−	0.972355i	$-0.424980\pi$
$709$	3.14221e12	0.467012	0.233506	+	0.972355i	$0.424980\pi$
$710$	−2.50667e12	−0.370198
$711$	−6.39115e12	−0.937920
$712$	−4.61982e12	−0.673698
$713$	−1.42182e13	−2.06036
$714$	0	0
$715$	−2.23218e12	−0.319413
$716$	6.56391e11	0.0933370
$717$	−3.12663e12	−0.441815
$718$	6.57241e12	0.922921
$719$	−1.59235e12	−0.222207	−0.111104	−	0.993809i	$-0.535439\pi$
$719$	−1.59235e12	−0.222207	−0.111104	+	0.993809i	$0.535439\pi$
$720$	−9.85987e11	−0.136733
$721$	0	0
$722$	5.12267e12	0.701582
$723$	−7.25415e11	−0.0987334
$724$	9.17306e11	0.124077
$725$	−1.07071e12	−0.143930
$726$	−6.94438e11	−0.0927724
$727$	−6.30493e11	−0.0837096	−0.0418548	−	0.999124i	$-0.513327\pi$
$727$	−6.30493e11	−0.0837096	−0.0418548	+	0.999124i	$0.513327\pi$
$728$	0	0
$729$	2.87984e12	0.377654
$730$	−6.43178e12	−0.838259
$731$	5.07737e11	0.0657674
$732$	3.95389e12	0.509008
$733$	1.19410e13	1.52782	0.763910	−	0.645323i	$-0.223277\pi$
$733$	1.19410e13	1.52782	0.763910	+	0.645323i	$0.223277\pi$
$734$	2.92867e12	0.372424
$735$	0	0
$736$	−2.57795e12	−0.323835
$737$	−1.47371e13	−1.83996
$738$	3.81415e12	0.473309
$739$	−5.36462e11	−0.0661667	−0.0330833	−	0.999453i	$-0.510533\pi$
$739$	−5.36462e11	−0.0661667	−0.0330833	+	0.999453i	$0.510533\pi$
$740$	1.52637e12	0.187119
$741$	1.45904e11	0.0177781
$742$	0	0
$743$	7.16300e12	0.862274	0.431137	−	0.902286i	$-0.358112\pi$
$743$	7.16300e12	0.862274	0.431137	+	0.902286i	$0.358112\pi$
$744$	1.82088e12	0.217873
$745$	5.27482e12	0.627342
$746$	4.57223e12	0.540510
$747$	−1.02979e13	−1.21006
$748$	4.89187e12	0.571371
$749$	0	0
$750$	3.64487e12	0.420636
$751$	1.28950e13	1.47925	0.739623	−	0.673022i	$-0.235004\pi$
$751$	1.28950e13	1.47925	0.739623	+	0.673022i	$0.235004\pi$
$752$	−1.99483e12	−0.227471
$753$	5.84628e12	0.662678
$754$	8.52012e11	0.0960008
$755$	1.16503e13	1.30489
$756$	0	0
$757$	−1.53380e13	−1.69761	−0.848804	−	0.528708i	$-0.822677\pi$
$757$	−1.53380e13	−1.69761	−0.848804	+	0.528708i	$0.822677\pi$
$758$	−7.62179e11	−0.0838582
$759$	1.02166e13	1.11743
$760$	2.24637e11	0.0244242
$761$	−8.55348e12	−0.924511	−0.462256	−	0.886747i	$-0.652960\pi$
$761$	−8.55348e12	−0.924511	−0.462256	+	0.886747i	$0.652960\pi$
$762$	−4.80014e10	−0.00515770
$763$	0	0
$764$	−1.78531e11	−0.0189581
$765$	−5.31794e12	−0.561393
$766$	−6.54385e12	−0.686758
$767$	−2.50047e12	−0.260881
$768$	3.30150e11	0.0342441
$769$	−5.63703e12	−0.581275	−0.290638	−	0.956833i	$-0.593867\pi$
$769$	−5.63703e12	−0.581275	−0.290638	+	0.956833i	$0.593867\pi$
$770$	0	0
$771$	−6.93520e12	−0.706829
$772$	−1.46140e11	−0.0148078
$773$	2.48942e12	0.250779	0.125390	−	0.992108i	$-0.459982\pi$
$773$	2.48942e12	0.250779	0.125390	+	0.992108i	$0.459982\pi$
$774$	3.16571e11	0.0317057
$775$	4.39580e12	0.437704
$776$	−5.21474e11	−0.0516244
$777$	0	0
$778$	1.79720e12	0.175869
$779$	−8.68978e11	−0.0845454
$780$	−8.12528e11	−0.0785982
$781$	7.75414e12	0.745768
$782$	−1.39042e13	−1.32959
$783$	−3.62280e12	−0.344443
$784$	0	0
$785$	1.08199e13	1.01698
$786$	1.96019e12	0.183188
$787$	1.37507e13	1.27773	0.638866	−	0.769318i	$-0.279404\pi$
$787$	1.37507e13	1.27773	0.638866	+	0.769318i	$0.279404\pi$
$788$	−1.25170e12	−0.115646
$789$	−7.19249e12	−0.660743
$790$	−8.10886e12	−0.740692
$791$	0	0
$792$	3.05006e12	0.275451
$793$	−7.59547e12	−0.682065
$794$	−6.17096e12	−0.551011
$795$	−3.61700e11	−0.0321142
$796$	−2.60669e12	−0.230134
$797$	−1.44214e12	−0.126603	−0.0633016	−	0.997994i	$-0.520163\pi$
$797$	−1.44214e12	−0.126603	−0.0633016	+	0.997994i	$0.520163\pi$
$798$	0	0
$799$	−1.07592e13	−0.933938
$800$	7.97016e11	0.0687959
$801$	−1.55357e13	−1.33347
$802$	−2.89096e12	−0.246751
$803$	1.98961e13	1.68868
$804$	−5.36439e12	−0.452760
$805$	0	0
$806$	−3.49794e12	−0.291947
$807$	−1.14199e12	−0.0947832
$808$	6.16632e12	0.508950
$809$	2.70988e11	0.0222424	0.0111212	−	0.999938i	$-0.496460\pi$
$809$	2.70988e11	0.0222424	0.0111212	+	0.999938i	$0.496460\pi$
$810$	−1.28317e12	−0.104737
$811$	−1.23287e13	−1.00075	−0.500373	−	0.865810i	$-0.666804\pi$
$811$	−1.23287e13	−1.00075	−0.500373	+	0.865810i	$0.666804\pi$
$812$	0	0
$813$	−9.00787e12	−0.723127
$814$	−4.72169e12	−0.376953
$815$	−1.35755e13	−1.07782
$816$	1.78067e12	0.140597
$817$	−7.21244e10	−0.00566348
$818$	−3.96827e12	−0.309893
$819$	0	0
$820$	4.83926e12	0.373780
$821$	−8.75616e12	−0.672620	−0.336310	−	0.941751i	$-0.609179\pi$
$821$	−8.75616e12	−0.672620	−0.336310	+	0.941751i	$0.609179\pi$
$822$	−6.93216e12	−0.529597
$823$	1.32813e13	1.00911	0.504557	−	0.863379i	$-0.331656\pi$
$823$	1.32813e13	1.00911	0.504557	+	0.863379i	$0.331656\pi$
$824$	−2.43694e12	−0.184150
$825$	−3.15865e12	−0.237388
$826$	0	0
$827$	−1.28106e13	−0.952345	−0.476173	−	0.879352i	$-0.657976\pi$
$827$	−1.28106e13	−0.952345	−0.476173	+	0.879352i	$0.657976\pi$
$828$	−8.66921e12	−0.640978
$829$	−1.42592e13	−1.04858	−0.524289	−	0.851540i	$-0.675669\pi$
$829$	−1.42592e13	−1.04858	−0.524289	+	0.851540i	$0.675669\pi$
$830$	−1.30656e13	−0.955606
$831$	−2.20786e12	−0.160608
$832$	−6.34222e11	−0.0458866
$833$	0	0
$834$	2.95816e12	0.211726
$835$	5.98814e12	0.426288
$836$	−6.94894e11	−0.0492029
$837$	1.48734e13	1.04748
$838$	−3.61611e12	−0.253305
$839$	−5.62810e12	−0.392133	−0.196066	−	0.980591i	$-0.562817\pi$
$839$	−5.62810e12	−0.392133	−0.196066	+	0.980591i	$0.562817\pi$
$840$	0	0
$841$	−1.25228e13	−0.863219
$842$	6.03170e12	0.413557
$843$	−5.68592e12	−0.387772
$844$	−7.42159e12	−0.503450
$845$	−1.00220e13	−0.676237
$846$	−6.70828e12	−0.450241
$847$	0	0
$848$	−2.82327e11	−0.0187487
$849$	5.59212e12	0.369396
$850$	4.29872e12	0.282458
$851$	1.34205e13	0.877174
$852$	2.82255e12	0.183512
$853$	−1.54422e13	−0.998709	−0.499354	−	0.866398i	$-0.666429\pi$
$853$	−1.54422e13	−0.998709	−0.499354	+	0.866398i	$0.666429\pi$
$854$	0	0
$855$	7.55417e11	0.0483437
$856$	−5.54973e12	−0.353297
$857$	1.60833e13	1.01850	0.509251	−	0.860618i	$-0.329923\pi$
$857$	1.60833e13	1.01850	0.509251	+	0.860618i	$0.329923\pi$
$858$	2.51348e12	0.158337
$859$	3.02922e12	0.189828	0.0949141	−	0.995485i	$-0.469742\pi$
$859$	3.02922e12	0.189828	0.0949141	+	0.995485i	$0.469742\pi$
$860$	4.01654e11	0.0250386
$861$	0	0
$862$	2.28964e12	0.141249
$863$	1.35636e13	0.832391	0.416195	−	0.909275i	$-0.363363\pi$
$863$	1.35636e13	0.832391	0.416195	+	0.909275i	$0.363363\pi$
$864$	2.69675e12	0.164637
$865$	5.02184e12	0.304994
$866$	−2.19177e13	−1.32423
$867$	4.88351e11	0.0293526
$868$	0	0
$869$	2.50840e13	1.49213
$870$	−1.89235e12	−0.111986
$871$	1.03051e13	0.606692
$872$	7.93740e12	0.464894
$873$	−1.75363e12	−0.102182
$874$	1.97511e12	0.114496
$875$	0	0
$876$	7.24229e12	0.415535
$877$	2.08383e13	1.18950	0.594751	−	0.803910i	$-0.297251\pi$
$877$	2.08383e13	1.18950	0.594751	+	0.803910i	$0.297251\pi$
$878$	−1.68888e13	−0.959124
$879$	−1.87503e13	−1.05940
$880$	3.86980e12	0.217529
$881$	1.45413e13	0.813225	0.406612	−	0.913601i	$-0.366710\pi$
$881$	1.45413e13	0.813225	0.406612	+	0.913601i	$0.366710\pi$
$882$	0	0
$883$	6.56890e12	0.363638	0.181819	−	0.983332i	$-0.441802\pi$
$883$	6.56890e12	0.363638	0.181819	+	0.983332i	$0.441802\pi$
$884$	−3.42069e12	−0.188399
$885$	5.55364e12	0.304322
$886$	−1.17884e13	−0.642694
$887$	−1.22620e12	−0.0665130	−0.0332565	−	0.999447i	$-0.510588\pi$
$887$	−1.22620e12	−0.0665130	−0.0332565	+	0.999447i	$0.510588\pi$
$888$	−1.71872e12	−0.0927571
$889$	0	0
$890$	−1.97111e13	−1.05307
$891$	3.96936e12	0.210994
$892$	2.30905e12	0.122121
$893$	1.52835e12	0.0804249
$894$	−5.93954e12	−0.310981
$895$	2.80058e12	0.145896
$896$	0	0
$897$	−7.14409e12	−0.368452
$898$	2.20479e12	0.113142
$899$	−8.14658e12	−0.415965
$900$	2.68023e12	0.136170
$901$	−1.52273e12	−0.0769773
$902$	−1.49698e13	−0.752985
$903$	0	0
$904$	8.12260e12	0.404517
$905$	3.91381e12	0.193946
$906$	−1.31184e13	−0.646851
$907$	−1.39154e13	−0.682752	−0.341376	−	0.939927i	$-0.610893\pi$
$907$	−1.39154e13	−0.682752	−0.341376	+	0.939927i	$0.610893\pi$
$908$	−3.39534e12	−0.165767
$909$	2.07363e13	1.00738
$910$	0	0
$911$	5.99228e11	0.0288243	0.0144122	−	0.999896i	$-0.495412\pi$
$911$	5.99228e11	0.0288243	0.0144122	+	0.999896i	$0.495412\pi$
$912$	−2.52945e11	−0.0121074
$913$	4.04173e13	1.92508
$914$	1.30797e13	0.619926
$915$	1.68698e13	0.795638
$916$	1.96523e13	0.922323
$917$	0	0
$918$	1.45450e13	0.675959
$919$	−5.20770e12	−0.240839	−0.120419	−	0.992723i	$-0.538424\pi$
$919$	−5.20770e12	−0.240839	−0.120419	+	0.992723i	$0.538424\pi$
$920$	−1.09992e13	−0.506192
$921$	−1.08893e13	−0.498693
$922$	2.46545e13	1.12359
$923$	−5.42215e12	−0.245903
$924$	0	0
$925$	−4.14918e12	−0.186348
$926$	1.19673e13	0.534869
$927$	−8.19501e12	−0.364494
$928$	−1.47708e12	−0.0653790
$929$	2.02860e13	0.893565	0.446783	−	0.894643i	$-0.352570\pi$
$929$	2.02860e13	0.893565	0.446783	+	0.894643i	$0.352570\pi$
$930$	7.76904e12	0.340560
$931$	0	0
$932$	−5.87236e11	−0.0254942
$933$	−9.92949e12	−0.429002
$934$	3.85718e12	0.165848
$935$	2.08719e13	0.893118
$936$	−2.13278e12	−0.0908249
$937$	3.47244e13	1.47166	0.735828	−	0.677169i	$-0.236793\pi$
$937$	3.47244e13	1.47166	0.735828	+	0.677169i	$0.236793\pi$
$938$	0	0
$939$	−3.41797e12	−0.143474
$940$	−8.51122e12	−0.355563
$941$	4.65584e12	0.193573	0.0967866	−	0.995305i	$-0.469144\pi$
$941$	4.65584e12	0.193573	0.0967866	+	0.995305i	$0.469144\pi$
$942$	−1.21834e13	−0.504128
$943$	4.25488e13	1.75220
$944$	4.33492e12	0.177667
$945$	0	0
$946$	−1.24248e12	−0.0504405
$947$	−3.96340e13	−1.60137	−0.800687	−	0.599083i	$-0.795532\pi$
$947$	−3.96340e13	−1.60137	−0.800687	+	0.599083i	$0.795532\pi$
$948$	9.13071e12	0.367170
$949$	−1.39125e13	−0.556812
$950$	−6.10637e11	−0.0243236
$951$	−1.90963e13	−0.757070
$952$	0	0
$953$	−3.33592e13	−1.31008	−0.655040	−	0.755594i	$-0.727348\pi$
$953$	−3.33592e13	−1.31008	−0.655040	+	0.755594i	$0.727348\pi$
$954$	−9.49417e11	−0.0371099
$955$	−7.61729e11	−0.0296337
$956$	−1.04128e13	−0.403186
$957$	5.85381e12	0.225598
$958$	6.68941e12	0.256592
$959$	0	0
$960$	1.40863e12	0.0535274
$961$	7.00615e12	0.264987
$962$	3.30169e12	0.124293
$963$	−1.86628e13	−0.699292
$964$	−2.41588e12	−0.0901008
$965$	−6.23526e11	−0.0231463
$966$	0	0
$967$	3.72454e13	1.36979	0.684893	−	0.728643i	$-0.259849\pi$
$967$	3.72454e13	1.36979	0.684893	+	0.728643i	$0.259849\pi$
$968$	−2.31272e12	−0.0846610
$969$	−1.36427e12	−0.0497098
$970$	−2.22494e12	−0.0806948
$971$	−2.47356e13	−0.892969	−0.446485	−	0.894791i	$-0.647324\pi$
$971$	−2.47356e13	−0.892969	−0.446485	+	0.894791i	$0.647324\pi$
$972$	1.44039e13	0.517584
$973$	0	0
$974$	2.74516e13	0.977356
$975$	2.20871e12	0.0782742
$976$	1.31678e13	0.464504
$977$	−3.93652e13	−1.38225	−0.691125	−	0.722736i	$-0.742884\pi$
$977$	−3.93652e13	−1.38225	−0.691125	+	0.722736i	$0.742884\pi$
$978$	1.52862e13	0.534288
$979$	6.09745e13	2.12142
$980$	0	0
$981$	2.66921e13	0.920180
$982$	−5.35570e12	−0.183787
$983$	3.70349e13	1.26509	0.632544	−	0.774524i	$-0.282011\pi$
$983$	3.70349e13	1.26509	0.632544	+	0.774524i	$0.282011\pi$
$984$	−5.44909e12	−0.185287
$985$	−5.34054e12	−0.180768
$986$	−7.96667e12	−0.268430
$987$	0	0
$988$	4.85911e11	0.0162237
$989$	3.53151e12	0.117376
$990$	1.30135e13	0.430562
$991$	2.82296e13	0.929766	0.464883	−	0.885372i	$-0.346096\pi$
$991$	2.82296e13	0.929766	0.464883	+	0.885372i	$0.346096\pi$
$992$	6.06416e12	0.198824
$993$	2.78434e13	0.908763
$994$	0	0
$995$	−1.11218e13	−0.359726
$996$	1.47121e13	0.473705
$997$	−3.44510e13	−1.10426	−0.552132	−	0.833757i	$-0.686186\pi$
$997$	−3.44510e13	−1.10426	−0.552132	+	0.833757i	$0.686186\pi$
$998$	−1.13607e13	−0.362508
$999$	−1.40390e13	−0.445954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.h.1.2		3
7.2	even	3		98.10.c.l.67.2		6
7.3	odd	6		14.10.c.b.9.2	✓	6
7.4	even	3		98.10.c.l.79.2		6
7.5	odd	6		14.10.c.b.11.2	yes	6
7.6	odd	2		98.10.a.g.1.2		3
21.5	even	6		126.10.g.e.109.1		6
21.17	even	6		126.10.g.e.37.1		6
28.3	even	6		112.10.i.a.65.2		6
28.19	even	6		112.10.i.a.81.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.b.9.2	✓	6	7.3	odd	6
14.10.c.b.11.2	yes	6	7.5	odd	6
98.10.a.g.1.2		3	7.6	odd	2
98.10.a.h.1.2		3	1.1	even	1	trivial
98.10.c.l.67.2		6	7.2	even	3
98.10.c.l.79.2		6	7.4	even	3
112.10.i.a.65.2		6	28.3	even	6
112.10.i.a.81.2		6	28.19	even	6
126.10.g.e.37.1		6	21.17	even	6
126.10.g.e.109.1		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)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +76.8690 q^{3} +256.000 q^{4} +1092.26 q^{5} -1229.90 q^{6} -4096.00 q^{8} -13774.2 q^{9} -17476.2 q^{10} +54060.9 q^{11} +19678.5 q^{12} -37802.6 q^{13} +83960.9 q^{15} +65536.0 q^{16} +353470. q^{17} +220387. q^{18} -50210.7 q^{19} +279618. q^{20} -864974. q^{22} +2.45852e6 q^{23} -314855. q^{24} -760094. q^{25} +604841. q^{26} -2.57182e6 q^{27} +1.40865e6 q^{29} -1.34337e6 q^{30} -5.78323e6 q^{31} -1.04858e6 q^{32} +4.15560e6 q^{33} -5.65552e6 q^{34} -3.52619e6 q^{36} +5.45877e6 q^{37} +803370. q^{38} -2.90584e6 q^{39} -4.47390e6 q^{40} +1.73066e7 q^{41} +1.43644e6 q^{43} +1.38396e7 q^{44} -1.50450e7 q^{45} -3.93364e7 q^{46} -3.04387e7 q^{47} +5.03768e6 q^{48} +1.21615e7 q^{50} +2.71709e7 q^{51} -9.67746e6 q^{52} -4.30796e6 q^{53} +4.11491e7 q^{54} +5.90485e7 q^{55} -3.85964e6 q^{57} -2.25385e7 q^{58} +6.61456e7 q^{59} +2.14940e7 q^{60} +2.00925e8 q^{61} +9.25317e7 q^{62} +1.67772e7 q^{64} -4.12902e7 q^{65} -6.64896e7 q^{66} -2.72602e8 q^{67} +9.04883e7 q^{68} +1.88984e8 q^{69} +1.43433e8 q^{71} +5.64190e7 q^{72} +3.68032e8 q^{73} -8.73403e7 q^{74} -5.84276e7 q^{75} -1.28539e7 q^{76} +4.64935e7 q^{78} +4.63995e8 q^{79} +7.15823e7 q^{80} +7.34239e7 q^{81} -2.76906e8 q^{82} +7.47626e8 q^{83} +3.86081e8 q^{85} -2.29830e7 q^{86} +1.08282e8 q^{87} -2.21433e8 q^{88} +1.12789e9 q^{89} +2.40719e8 q^{90} +6.29382e8 q^{92} -4.44551e8 q^{93} +4.87019e8 q^{94} -5.48431e7 q^{95} -8.06029e7 q^{96} +1.27313e8 q^{97} -7.44643e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 48 q^{2} + 71 q^{3} + 768 q^{4} - 1085 q^{5} - 1136 q^{6} - 12288 q^{8} + 9106 q^{9} + 17360 q^{10} - 2555 q^{11} + 18176 q^{12} - 18070 q^{13} - 353073 q^{15} + 196608 q^{16} + 20759 q^{17} - 145696 q^{18}+ \cdots - 1303712634 q^{99}+O(q^{100}) \) 3 * q - 48 * q^2 + 71 * q^3 + 768 * q^4 - 1085 * q^5 - 1136 * q^6 - 12288 * q^8 + 9106 * q^9 + 17360 * q^10 - 2555 * q^11 + 18176 * q^12 - 18070 * q^13 - 353073 * q^15 + 196608 * q^16 + 20759 * q^17 - 145696 * q^18 + 1220649 * q^19 - 277760 * q^20 + 40880 * q^22 + 1960903 * q^23 - 290816 * q^24 + 863572 * q^25 + 289120 * q^26 - 2888659 * q^27 - 2606146 * q^29 + 5649168 * q^30 - 9377989 * q^31 - 3145728 * q^32 - 10778103 * q^33 - 332144 * q^34 + 2331136 * q^36 + 25814913 * q^37 - 19530384 * q^38 - 37990822 * q^39 + 4444160 * q^40 - 209250 * q^41 + 2944308 * q^43 - 654080 * q^44 - 37350558 * q^45 - 31374448 * q^46 + 48391269 * q^47 + 4653056 * q^48 - 13817152 * q^50 + 75441987 * q^51 - 4625920 * q^52 - 102186411 * q^53 + 46218544 * q^54 + 228278701 * q^55 + 43084589 * q^57 + 41698336 * q^58 + 144220135 * q^59 - 90386688 * q^60 + 280936871 * q^61 + 150047824 * q^62 + 50331648 * q^64 + 186819738 * q^65 + 172449648 * q^66 - 170710399 * q^67 + 5314304 * q^68 + 903654171 * q^69 + 469758688 * q^71 - 37298176 * q^72 + 613838539 * q^73 - 413038608 * q^74 + 902254676 * q^75 + 312486144 * q^76 + 607853152 * q^78 - 197445809 * q^79 - 71106560 * q^80 - 887872901 * q^81 + 3348000 * q^82 + 1074181436 * q^83 + 411272519 * q^85 - 47108928 * q^86 + 753428670 * q^87 + 10465280 * q^88 + 805730427 * q^89 + 597608928 * q^90 + 501991168 * q^92 + 1721516327 * q^93 - 774260304 * q^94 - 1799421743 * q^95 - 74448896 * q^96 + 2262918094 * q^97 - 1303712634 * q^99

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