LMFDB - Embedded newform 98.10.a.j.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [3,48,233] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$50.4735119441$
Analytic rank:	$0$
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} - 1115x + 2100 $ x^3 - x^2 - 1115*x + 2100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$32.9264$ 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)

$f(q)$	$=$	\(q+16.0000 q^{2} +270.819 q^{3} +256.000 q^{4} +1369.57 q^{5} +4333.11 q^{6} +4096.00 q^{8} +53660.1 q^{9} +21913.1 q^{10} -10924.3 q^{11} +69329.8 q^{12} -7968.27 q^{13} +370906. q^{15} +65536.0 q^{16} -324012. q^{17} +858562. q^{18} -231878. q^{19} +350610. q^{20} -174789. q^{22} +2.10662e6 q^{23} +1.10928e6 q^{24} -77402.7 q^{25} -127492. q^{26} +9.20167e6 q^{27} -5.46332e6 q^{29} +5.93450e6 q^{30} -1.97867e6 q^{31} +1.04858e6 q^{32} -2.95852e6 q^{33} -5.18419e6 q^{34} +1.37370e7 q^{36} +4.76533e6 q^{37} -3.71005e6 q^{38} -2.15796e6 q^{39} +5.60976e6 q^{40} +5.57398e6 q^{41} -3.11341e7 q^{43} -2.79663e6 q^{44} +7.34913e7 q^{45} +3.37060e7 q^{46} +4.31190e6 q^{47} +1.77484e7 q^{48} -1.23844e6 q^{50} -8.77486e7 q^{51} -2.03988e6 q^{52} -9.02903e7 q^{53} +1.47227e8 q^{54} -1.49616e7 q^{55} -6.27970e7 q^{57} -8.74131e7 q^{58} -7.29111e7 q^{59} +9.49520e7 q^{60} -7.43497e6 q^{61} -3.16588e7 q^{62} +1.67772e7 q^{64} -1.09131e7 q^{65} -4.73363e7 q^{66} +1.05787e8 q^{67} -8.29470e7 q^{68} +5.70514e8 q^{69} +1.10248e8 q^{71} +2.19792e8 q^{72} +2.04449e8 q^{73} +7.62452e7 q^{74} -2.09622e7 q^{75} -5.93607e7 q^{76} -3.45274e7 q^{78} +8.87846e7 q^{79} +8.97561e7 q^{80} +1.43580e9 q^{81} +8.91836e7 q^{82} +2.41708e8 q^{83} -4.43757e8 q^{85} -4.98146e8 q^{86} -1.47957e9 q^{87} -4.47461e7 q^{88} +5.48690e8 q^{89} +1.17586e9 q^{90} +5.39295e8 q^{92} -5.35863e8 q^{93} +6.89905e7 q^{94} -3.17573e8 q^{95} +2.83975e8 q^{96} -1.16746e9 q^{97} -5.86201e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 48 q^{2} + 233 q^{3} + 768 q^{4} + 733 q^{5} + 3728 q^{6} + 12288 q^{8} + 15058 q^{9} + 11728 q^{10} - 7339 q^{11} + 59648 q^{12} + 98518 q^{13} + 369119 q^{15} + 196608 q^{16} + 306665 q^{17} + 240928 q^{18}+ \cdots - 628109434 q^{99}+O(q^{100}) $ 3 * q + 48 * q^2 + 233 * q^3 + 768 * q^4 + 733 * q^5 + 3728 * q^6 + 12288 * q^8 + 15058 * q^9 + 11728 * q^10 - 7339 * q^11 + 59648 * q^12 + 98518 * q^13 + 369119 * q^15 + 196608 * q^16 + 306665 * q^17 + 240928 * q^18 + 377991 * q^19 + 187648 * q^20 - 117424 * q^22 + 2267255 * q^23 + 954368 * q^24 + 142612 * q^25 + 1576288 * q^26 + 10674179 * q^27 - 6542978 * q^29 + 5905904 * q^30 + 6654517 * q^31 + 3145728 * q^32 - 3747977 * q^33 + 4906640 * q^34 + 3854848 * q^36 + 22287969 * q^37 + 6047856 * q^38 - 3151974 * q^39 + 3002368 * q^40 + 34048098 * q^41 - 62824140 * q^43 - 1878784 * q^44 + 86300638 * q^45 + 36276080 * q^46 + 52703019 * q^47 + 15269888 * q^48 + 2281792 * q^50 - 97736333 * q^51 + 25220608 * q^52 + 12091125 * q^53 + 170786864 * q^54 + 188717699 * q^55 - 79258835 * q^57 - 104687648 * q^58 + 12949897 * q^59 + 94494464 * q^60 + 160252153 * q^61 + 106472272 * q^62 + 50331648 * q^64 - 334191270 * q^65 - 59967632 * q^66 + 480890225 * q^67 + 78506240 * q^68 + 565616581 * q^69 - 37210720 * q^71 + 61677568 * q^72 - 251382283 * q^73 + 356607504 * q^74 - 16322324 * q^75 + 96765696 * q^76 - 50431584 * q^78 - 286494785 * q^79 + 48037888 * q^80 + 2165894587 * q^81 + 544769568 * q^82 + 1147591172 * q^83 - 1194592537 * q^85 - 1005186240 * q^86 - 1412199358 * q^87 - 30060544 * q^88 + 901243845 * q^89 + 1380810208 * q^90 + 580417280 * q^92 - 710456889 * q^93 + 843248304 * q^94 + 887366177 * q^95 + 244318208 * q^96 + 314853938 * q^97 - 628109434 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	270.819	1.93034	0.965171	−	0.261621i	$-0.0842571\pi$
$3$	270.819	1.93034	0.965171	+	0.261621i	$0.0842571\pi$
$4$	256.000	0.500000
$5$	1369.57	0.979985	0.489992	−	0.871727i	$-0.337000\pi$
$5$	1369.57	0.979985	0.489992	+	0.871727i	$0.337000\pi$
$6$	4333.11	1.36496
$7$	0	0
$7$	0	0
$8$	4096.00	0.353553
$9$	53660.1	2.72622
$10$	21913.1	0.692954
$11$	−10924.3	−0.224972	−0.112486	−	0.993653i	$-0.535881\pi$
$11$	−10924.3	−0.224972	−0.112486	+	0.993653i	$0.535881\pi$
$12$	69329.8	0.965171
$13$	−7968.27	−0.0773783	−0.0386891	−	0.999251i	$-0.512318\pi$
$13$	−7968.27	−0.0773783	−0.0386891	+	0.999251i	$0.512318\pi$
$14$	0	0
$15$	370906.	1.89170
$16$	65536.0	0.250000
$17$	−324012.	−0.940894	−0.470447	−	0.882428i	$-0.655907\pi$
$17$	−324012.	−0.940894	−0.470447	+	0.882428i	$0.655907\pi$
$18$	858562.	1.92773
$19$	−231878.	−0.408195	−0.204098	−	0.978951i	$-0.565426\pi$
$19$	−231878.	−0.408195	−0.204098	+	0.978951i	$0.565426\pi$
$20$	350610.	0.489992
$21$	0	0
$22$	−174789.	−0.159079
$23$	2.10662e6	1.56968	0.784841	−	0.619698i	$-0.212745\pi$
$23$	2.10662e6	1.56968	0.784841	+	0.619698i	$0.212745\pi$
$24$	1.10928e6	0.682479
$25$	−77402.7	−0.0396302
$26$	−127492.	−0.0547147
$27$	9.20167e6	3.33219
$28$	0	0
$29$	−5.46332e6	−1.43438	−0.717192	−	0.696876i	$-0.754573\pi$
$29$	−5.46332e6	−1.43438	−0.717192	+	0.696876i	$0.754573\pi$
$30$	5.93450e6	1.33764
$31$	−1.97867e6	−0.384810	−0.192405	−	0.981316i	$-0.561629\pi$
$31$	−1.97867e6	−0.384810	−0.192405	+	0.981316i	$0.561629\pi$
$32$	1.04858e6	0.176777
$33$	−2.95852e6	−0.434272
$34$	−5.18419e6	−0.665312
$35$	0	0
$36$	1.37370e7	1.36311
$37$	4.76533e6	0.418008	0.209004	−	0.977915i	$-0.432978\pi$
$37$	4.76533e6	0.418008	0.209004	+	0.977915i	$0.432978\pi$
$38$	−3.71005e6	−0.288638
$39$	−2.15796e6	−0.149366
$40$	5.60976e6	0.346477
$41$	5.57398e6	0.308062	0.154031	−	0.988066i	$-0.450774\pi$
$41$	5.57398e6	0.308062	0.154031	+	0.988066i	$0.450774\pi$
$42$	0	0
$43$	−3.11341e7	−1.38876	−0.694382	−	0.719607i	$-0.744322\pi$
$43$	−3.11341e7	−1.38876	−0.694382	+	0.719607i	$0.744322\pi$
$44$	−2.79663e6	−0.112486
$45$	7.34913e7	2.67165
$46$	3.37060e7	1.10993
$47$	4.31190e6	0.128893	0.0644464	−	0.997921i	$-0.479472\pi$
$47$	4.31190e6	0.128893	0.0644464	+	0.997921i	$0.479472\pi$
$48$	1.77484e7	0.482585
$49$	0	0
$50$	−1.23844e6	−0.0280228
$51$	−8.77486e7	−1.81625
$52$	−2.03988e6	−0.0386891
$53$	−9.02903e7	−1.57181	−0.785905	−	0.618348i	$-0.787802\pi$
$53$	−9.02903e7	−1.57181	−0.785905	+	0.618348i	$0.787802\pi$
$54$	1.47227e8	2.35621
$55$	−1.49616e7	−0.220469
$56$	0	0
$57$	−6.27970e7	−0.787957
$58$	−8.74131e7	−1.01426
$59$	−7.29111e7	−0.783357	−0.391678	−	0.920102i	$-0.628105\pi$
$59$	−7.29111e7	−0.783357	−0.391678	+	0.920102i	$0.628105\pi$
$60$	9.49520e7	0.945852
$61$	−7.43497e6	−0.0687535	−0.0343768	−	0.999409i	$-0.510945\pi$
$61$	−7.43497e6	−0.0687535	−0.0343768	+	0.999409i	$0.510945\pi$
$62$	−3.16588e7	−0.272102
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−1.09131e7	−0.0758295
$66$	−4.73363e7	−0.307077
$67$	1.05787e8	0.641352	0.320676	−	0.947189i	$-0.396090\pi$
$67$	1.05787e8	0.641352	0.320676	+	0.947189i	$0.396090\pi$
$68$	−8.29470e7	−0.470447
$69$	5.70514e8	3.03002
$70$	0	0
$71$	1.10248e8	0.514884	0.257442	−	0.966294i	$-0.417120\pi$
$71$	1.10248e8	0.514884	0.257442	+	0.966294i	$0.417120\pi$
$72$	2.19792e8	0.963863
$73$	2.04449e8	0.842621	0.421311	−	0.906916i	$-0.361570\pi$
$73$	2.04449e8	0.842621	0.421311	+	0.906916i	$0.361570\pi$
$74$	7.62452e7	0.295576
$75$	−2.09622e7	−0.0764998
$76$	−5.93607e7	−0.204098
$77$	0	0
$78$	−3.45274e7	−0.105618
$79$	8.87846e7	0.256458	0.128229	−	0.991745i	$-0.459071\pi$
$79$	8.87846e7	0.256458	0.128229	+	0.991745i	$0.459071\pi$
$80$	8.97561e7	0.244996
$81$	1.43580e9	3.70604
$82$	8.91836e7	0.217833
$83$	2.41708e8	0.559035	0.279517	−	0.960141i	$-0.409826\pi$
$83$	2.41708e8	0.559035	0.279517	+	0.960141i	$0.409826\pi$
$84$	0	0
$85$	−4.43757e8	−0.922061
$86$	−4.98146e8	−0.982004
$87$	−1.47957e9	−2.76885
$88$	−4.47461e7	−0.0795395
$89$	5.48690e8	0.926984	0.463492	−	0.886101i	$-0.346596\pi$
$89$	5.48690e8	0.926984	0.463492	+	0.886101i	$0.346596\pi$
$90$	1.17586e9	1.88914
$91$	0	0
$92$	5.39295e8	0.784841
$93$	−5.35863e8	−0.742814
$94$	6.89905e7	0.0911410
$95$	−3.17573e8	−0.400025
$96$	2.83975e8	0.341239
$97$	−1.16746e9	−1.33897	−0.669483	−	0.742828i	$-0.733484\pi$
$97$	−1.16746e9	−1.33897	−0.669483	+	0.742828i	$0.733484\pi$
$98$	0	0
$99$	−5.86201e8	−0.613322
$100$	−1.98151e7	−0.0198151
$101$	1.38986e9	1.32900	0.664498	−	0.747290i	$-0.268646\pi$
$101$	1.38986e9	1.32900	0.664498	+	0.747290i	$0.268646\pi$
$102$	−1.40398e9	−1.28428
$103$	9.38808e8	0.821881	0.410941	−	0.911662i	$-0.365200\pi$
$103$	9.38808e8	0.821881	0.410941	+	0.911662i	$0.365200\pi$
$104$	−3.26380e7	−0.0273573
$105$	0	0
$106$	−1.44465e9	−1.11144
$107$	2.59288e8	0.191230	0.0956149	−	0.995418i	$-0.469518\pi$
$107$	2.59288e8	0.191230	0.0956149	+	0.995418i	$0.469518\pi$
$108$	2.35563e9	1.66609
$109$	−8.25786e7	−0.0560336	−0.0280168	−	0.999607i	$-0.508919\pi$
$109$	−8.25786e7	−0.0560336	−0.0280168	+	0.999607i	$0.508919\pi$
$110$	−2.39386e8	−0.155895
$111$	1.29054e9	0.806899
$112$	0	0
$113$	1.17279e9	0.676654	0.338327	−	0.941029i	$-0.390139\pi$
$113$	1.17279e9	0.676654	0.338327	+	0.941029i	$0.390139\pi$
$114$	−1.00475e9	−0.557169
$115$	2.88517e9	1.53826
$116$	−1.39861e9	−0.717192
$117$	−4.27578e8	−0.210950
$118$	−1.16658e9	−0.553917
$119$	0	0
$120$	1.51923e9	0.668819
$121$	−2.23861e9	−0.949388
$122$	−1.18960e8	−0.0486161
$123$	1.50954e9	0.594664
$124$	−5.06540e8	−0.192405
$125$	−2.78095e9	−1.01882
$126$	0	0
$127$	−2.85883e9	−0.975150	−0.487575	−	0.873081i	$-0.662118\pi$
$127$	−2.85883e9	−0.975150	−0.487575	+	0.873081i	$0.662118\pi$
$128$	2.68435e8	0.0883883
$129$	−8.43172e9	−2.68079
$130$	−1.74610e8	−0.0536196
$131$	−5.17100e9	−1.53410	−0.767050	−	0.641587i	$-0.778276\pi$
$131$	−5.17100e9	−1.53410	−0.767050	+	0.641587i	$0.778276\pi$
$132$	−7.57382e8	−0.217136
$133$	0	0
$134$	1.69260e9	0.453505
$135$	1.26023e10	3.26549
$136$	−1.32715e9	−0.332656
$137$	−1.69648e9	−0.411440	−0.205720	−	0.978611i	$-0.565954\pi$
$137$	−1.69648e9	−0.411440	−0.205720	+	0.978611i	$0.565954\pi$
$138$	9.12823e9	2.14255
$139$	5.00914e9	1.13814	0.569071	−	0.822288i	$-0.307303\pi$
$139$	5.00914e9	1.13814	0.569071	+	0.822288i	$0.307303\pi$
$140$	0	0
$141$	1.16775e9	0.248807
$142$	1.76397e9	0.364078
$143$	8.70480e7	0.0174079
$144$	3.51667e9	0.681554
$145$	−7.48240e9	−1.40567
$146$	3.27119e9	0.595823
$147$	0	0
$148$	1.21992e9	0.209004
$149$	1.67994e9	0.279226	0.139613	−	0.990206i	$-0.455414\pi$
$149$	1.67994e9	0.279226	0.139613	+	0.990206i	$0.455414\pi$
$150$	−3.35395e8	−0.0540935
$151$	−6.81460e9	−1.06671	−0.533353	−	0.845893i	$-0.679068\pi$
$151$	−6.81460e9	−1.06671	−0.533353	+	0.845893i	$0.679068\pi$
$152$	−9.49772e8	−0.144319
$153$	−1.73865e10	−2.56508
$154$	0	0
$155$	−2.70993e9	−0.377108
$156$	−5.52438e8	−0.0746832
$157$	9.56661e8	0.125664	0.0628318	−	0.998024i	$-0.479987\pi$
$157$	9.56661e8	0.125664	0.0628318	+	0.998024i	$0.479987\pi$
$158$	1.42055e9	0.181343
$159$	−2.44524e10	−3.03413
$160$	1.43610e9	0.173238
$161$	0	0
$162$	2.29728e10	2.62057
$163$	−6.21953e9	−0.690102	−0.345051	−	0.938584i	$-0.612138\pi$
$163$	−6.21953e9	−0.690102	−0.345051	+	0.938584i	$0.612138\pi$
$164$	1.42694e9	0.154031
$165$	−4.05190e9	−0.425580
$166$	3.86732e9	0.395297
$167$	−3.33475e9	−0.331771	−0.165886	−	0.986145i	$-0.553048\pi$
$167$	−3.33475e9	−0.331771	−0.165886	+	0.986145i	$0.553048\pi$
$168$	0	0
$169$	−1.05410e10	−0.994013
$170$	−7.10011e9	−0.651996
$171$	−1.24426e10	−1.11283
$172$	−7.97033e9	−0.694382
$173$	1.13002e10	0.959131	0.479566	−	0.877506i	$-0.340794\pi$
$173$	1.13002e10	0.959131	0.479566	+	0.877506i	$0.340794\pi$
$174$	−2.36732e10	−1.95787
$175$	0	0
$176$	−7.15937e8	−0.0562429
$177$	−1.97457e10	−1.51215
$178$	8.77904e9	0.655477
$179$	1.85514e9	0.135063	0.0675316	−	0.997717i	$-0.478488\pi$
$179$	1.85514e9	0.135063	0.0675316	+	0.997717i	$0.478488\pi$
$180$	1.88138e10	1.33583
$181$	1.64314e9	0.113794	0.0568972	−	0.998380i	$-0.481879\pi$
$181$	1.64314e9	0.113794	0.0568972	+	0.998380i	$0.481879\pi$
$182$	0	0
$183$	−2.01353e9	−0.132718
$184$	8.62873e9	0.554966
$185$	6.52645e9	0.409642
$186$	−8.57380e9	−0.525249
$187$	3.53961e9	0.211674
$188$	1.10385e9	0.0644464
$189$	0	0
$190$	−5.08117e9	−0.282861
$191$	1.13687e10	0.618103	0.309052	−	0.951045i	$-0.399988\pi$
$191$	1.13687e10	0.618103	0.309052	+	0.951045i	$0.399988\pi$
$192$	4.54360e9	0.241293
$193$	−3.81022e10	−1.97671	−0.988354	−	0.152175i	$-0.951372\pi$
$193$	−3.81022e10	−1.97671	−0.988354	+	0.152175i	$0.951372\pi$
$194$	−1.86794e10	−0.946792
$195$	−2.95548e9	−0.146377
$196$	0	0
$197$	−1.71349e10	−0.810558	−0.405279	−	0.914193i	$-0.632826\pi$
$197$	−1.71349e10	−0.810558	−0.405279	+	0.914193i	$0.632826\pi$
$198$	−9.37922e9	−0.433684
$199$	−2.30179e10	−1.04046	−0.520232	−	0.854025i	$-0.674155\pi$
$199$	−2.30179e10	−1.04046	−0.520232	+	0.854025i	$0.674155\pi$
$200$	−3.17042e8	−0.0140114
$201$	2.86492e10	1.23803
$202$	2.22377e10	0.939741
$203$	0	0
$204$	−2.24637e10	−0.908123
$205$	7.63395e9	0.301896
$206$	1.50209e10	0.581158
$207$	1.13042e11	4.27929
$208$	−5.22209e8	−0.0193446
$209$	2.53311e9	0.0918324
$210$	0	0
$211$	4.95907e10	1.72238	0.861190	−	0.508283i	$-0.169720\pi$
$211$	4.95907e10	1.72238	0.861190	+	0.508283i	$0.169720\pi$
$212$	−2.31143e10	−0.785905
$213$	2.98574e10	0.993901
$214$	4.14861e9	0.135220
$215$	−4.26403e10	−1.36097
$216$	3.76900e10	1.17811
$217$	0	0
$218$	−1.32126e9	−0.0396217
$219$	5.53688e10	1.62655
$220$	−3.83018e9	−0.110234
$221$	2.58181e9	0.0728047
$222$	2.06487e10	0.570563
$223$	5.54434e10	1.50134	0.750669	−	0.660679i	$-0.229731\pi$
$223$	5.54434e10	1.50134	0.750669	+	0.660679i	$0.229731\pi$
$224$	0	0
$225$	−4.15344e9	−0.108041
$226$	1.87646e10	0.478466
$227$	−3.53834e9	−0.0884471	−0.0442236	−	0.999022i	$-0.514081\pi$
$227$	−3.53834e9	−0.0884471	−0.0442236	+	0.999022i	$0.514081\pi$
$228$	−1.60760e10	−0.393978
$229$	−3.04328e10	−0.731278	−0.365639	−	0.930757i	$-0.619150\pi$
$229$	−3.04328e10	−0.731278	−0.365639	+	0.930757i	$0.619150\pi$
$230$	4.61627e10	1.08772
$231$	0	0
$232$	−2.23777e10	−0.507131
$233$	6.16096e9	0.136945	0.0684725	−	0.997653i	$-0.478187\pi$
$233$	6.16096e9	0.136945	0.0684725	+	0.997653i	$0.478187\pi$
$234$	−6.84126e9	−0.149164
$235$	5.90545e9	0.126313
$236$	−1.86652e10	−0.391678
$237$	2.40446e10	0.495051
$238$	0	0
$239$	−6.33526e10	−1.25595	−0.627977	−	0.778232i	$-0.716117\pi$
$239$	−6.33526e10	−1.25595	−0.627977	+	0.778232i	$0.716117\pi$
$240$	2.43077e10	0.472926
$241$	7.51528e10	1.43506	0.717528	−	0.696530i	$-0.245274\pi$
$241$	7.51528e10	1.43506	0.717528	+	0.696530i	$0.245274\pi$
$242$	−3.58177e10	−0.671319
$243$	2.07725e11	3.82174
$244$	−1.90335e9	−0.0343768
$245$	0	0
$246$	2.41527e10	0.420491
$247$	1.84767e9	0.0315855
$248$	−8.10464e9	−0.136051
$249$	6.54591e10	1.07913
$250$	−4.44952e10	−0.720416
$251$	1.01701e11	1.61731	0.808653	−	0.588286i	$-0.200197\pi$
$251$	1.01701e11	1.61731	0.808653	+	0.588286i	$0.200197\pi$
$252$	0	0
$253$	−2.30135e10	−0.353134
$254$	−4.57413e10	−0.689535
$255$	−1.20178e11	−1.77989
$256$	4.29497e9	0.0625000
$257$	5.51693e10	0.788857	0.394429	−	0.918927i	$-0.370943\pi$
$257$	5.51693e10	0.788857	0.394429	+	0.918927i	$0.370943\pi$
$258$	−1.34908e11	−1.89560
$259$	0	0
$260$	−2.79375e9	−0.0379147
$261$	−2.93162e11	−3.91044
$262$	−8.27360e10	−1.08477
$263$	−2.24461e10	−0.289294	−0.144647	−	0.989483i	$-0.546205\pi$
$263$	−2.24461e10	−0.289294	−0.144647	+	0.989483i	$0.546205\pi$
$264$	−1.21181e10	−0.153538
$265$	−1.23659e11	−1.54035
$266$	0	0
$267$	1.48596e11	1.78940
$268$	2.70815e10	0.320676
$269$	2.35215e9	0.0273892	0.0136946	−	0.999906i	$-0.495641\pi$
$269$	2.35215e9	0.0273892	0.0136946	+	0.999906i	$0.495641\pi$
$270$	2.01637e11	2.30905
$271$	−1.49406e11	−1.68269	−0.841346	−	0.540496i	$-0.818236\pi$
$271$	−1.49406e11	−1.68269	−0.841346	+	0.540496i	$0.818236\pi$
$272$	−2.12344e10	−0.235223
$273$	0	0
$274$	−2.71437e10	−0.290932
$275$	8.45573e8	0.00891567
$276$	1.46052e11	1.51501
$277$	−1.44399e11	−1.47368	−0.736842	−	0.676065i	$-0.763684\pi$
$277$	−1.44399e11	−1.47368	−0.736842	+	0.676065i	$0.763684\pi$
$278$	8.01463e10	0.804788
$279$	−1.06176e11	−1.04908
$280$	0	0
$281$	−7.04301e10	−0.673876	−0.336938	−	0.941527i	$-0.609391\pi$
$281$	−7.04301e10	−0.673876	−0.336938	+	0.941527i	$0.609391\pi$
$282$	1.86840e10	0.175933
$283$	2.04558e11	1.89574	0.947868	−	0.318665i	$-0.103234\pi$
$283$	2.04558e11	1.89574	0.947868	+	0.318665i	$0.103234\pi$
$284$	2.82235e10	0.257442
$285$	−8.60049e10	−0.772185
$286$	1.39277e9	0.0123093
$287$	0	0
$288$	5.62667e10	0.481932
$289$	−1.36043e10	−0.114719
$290$	−1.19718e11	−0.993962
$291$	−3.16171e11	−2.58466
$292$	5.23390e10	0.421311
$293$	1.08283e11	0.858335	0.429168	−	0.903225i	$-0.358807\pi$
$293$	1.08283e11	0.858335	0.429168	+	0.903225i	$0.358807\pi$
$294$	0	0
$295$	−9.98569e10	−0.767677
$296$	1.95188e10	0.147788
$297$	−1.00522e11	−0.749648
$298$	2.68790e10	0.197443
$299$	−1.67861e10	−0.121459
$300$	−5.36631e9	−0.0382499
$301$	0	0
$302$	−1.09034e11	−0.754274
$303$	3.76400e11	2.56541
$304$	−1.51964e10	−0.102049
$305$	−1.01827e10	−0.0673774
$306$	−2.78184e11	−1.81379
$307$	−1.17650e11	−0.755912	−0.377956	−	0.925824i	$-0.623373\pi$
$307$	−1.17650e11	−0.755912	−0.377956	+	0.925824i	$0.623373\pi$
$308$	0	0
$309$	2.54247e11	1.58651
$310$	−4.33589e10	−0.266655
$311$	−1.77275e10	−0.107455	−0.0537273	−	0.998556i	$-0.517110\pi$
$311$	−1.77275e10	−0.107455	−0.0537273	+	0.998556i	$0.517110\pi$
$312$	−8.83901e9	−0.0528090
$313$	1.06637e11	0.627996	0.313998	−	0.949424i	$-0.398331\pi$
$313$	1.06637e11	0.627996	0.313998	+	0.949424i	$0.398331\pi$
$314$	1.53066e10	0.0888576
$315$	0	0
$316$	2.27288e10	0.128229
$317$	−3.31101e10	−0.184159	−0.0920797	−	0.995752i	$-0.529351\pi$
$317$	−3.31101e10	−0.184159	−0.0920797	+	0.995752i	$0.529351\pi$
$318$	−3.91238e11	−2.14545
$319$	5.96831e10	0.322696
$320$	2.29776e10	0.122498
$321$	7.02203e10	0.369139
$322$	0	0
$323$	7.51311e10	0.384068
$324$	3.67564e11	1.85302
$325$	6.16766e8	0.00306652
$326$	−9.95125e10	−0.487976
$327$	−2.23639e10	−0.108164
$328$	2.28310e10	0.108916
$329$	0	0
$330$	−6.48304e10	−0.300931
$331$	−2.20016e11	−1.00746	−0.503730	−	0.863861i	$-0.668039\pi$
$331$	−2.20016e11	−1.00746	−0.503730	+	0.863861i	$0.668039\pi$
$332$	6.18771e10	0.279517
$333$	2.55708e11	1.13958
$334$	−5.33560e10	−0.234598
$335$	1.44883e11	0.628515
$336$	0	0
$337$	1.58927e11	0.671217	0.335609	−	0.942001i	$-0.391058\pi$
$337$	1.58927e11	0.671217	0.335609	+	0.942001i	$0.391058\pi$
$338$	−1.68656e11	−0.702873
$339$	3.17614e11	1.30617
$340$	−1.13602e11	−0.461031
$341$	2.16157e10	0.0865713
$342$	−1.99082e11	−0.786889
$343$	0	0
$344$	−1.27525e11	−0.491002
$345$	7.81359e11	2.96937
$346$	1.80803e11	0.678208
$347$	9.05893e10	0.335424	0.167712	−	0.985836i	$-0.446362\pi$
$347$	9.05893e10	0.335424	0.167712	+	0.985836i	$0.446362\pi$
$348$	−3.78771e11	−1.38443
$349$	−1.82702e11	−0.659219	−0.329609	−	0.944117i	$-0.606917\pi$
$349$	−1.82702e11	−0.659219	−0.329609	+	0.944117i	$0.606917\pi$
$350$	0	0
$351$	−7.33214e10	−0.257839
$352$	−1.14550e10	−0.0397698
$353$	2.89147e11	0.991136	0.495568	−	0.868569i	$-0.334960\pi$
$353$	2.89147e11	0.991136	0.495568	+	0.868569i	$0.334960\pi$
$354$	−3.15932e11	−1.06925
$355$	1.50993e11	0.504578
$356$	1.40465e11	0.463492
$357$	0	0
$358$	2.96822e10	0.0955041
$359$	−3.29047e11	−1.04552	−0.522761	−	0.852479i	$-0.675098\pi$
$359$	−3.29047e11	−1.04552	−0.522761	+	0.852479i	$0.675098\pi$
$360$	3.01020e11	0.944571
$361$	−2.68920e11	−0.833376
$362$	2.62902e10	0.0804647
$363$	−6.06258e11	−1.83264
$364$	0	0
$365$	2.80007e11	0.825756
$366$	−3.22165e10	−0.0938456
$367$	−4.16454e11	−1.19831	−0.599156	−	0.800632i	$-0.704497\pi$
$367$	−4.16454e11	−1.19831	−0.599156	+	0.800632i	$0.704497\pi$
$368$	1.38060e11	0.392420
$369$	2.99100e11	0.839843
$370$	1.04423e11	0.289660
$371$	0	0
$372$	−1.37181e11	−0.371407
$373$	1.07630e11	0.287900	0.143950	−	0.989585i	$-0.454020\pi$
$373$	1.07630e11	0.287900	0.143950	+	0.989585i	$0.454020\pi$
$374$	5.66338e10	0.149676
$375$	−7.53135e11	−1.96667
$376$	1.76616e10	0.0455705
$377$	4.35332e10	0.110990
$378$	0	0
$379$	5.34243e11	1.33003	0.665016	−	0.746829i	$-0.268425\pi$
$379$	5.34243e11	1.33003	0.665016	+	0.746829i	$0.268425\pi$
$380$	−8.12987e10	−0.200013
$381$	−7.74226e11	−1.88237
$382$	1.81899e11	0.437065
$383$	−3.07903e11	−0.731173	−0.365586	−	0.930777i	$-0.619132\pi$
$383$	−3.07903e11	−0.731173	−0.365586	+	0.930777i	$0.619132\pi$
$384$	7.26975e10	0.170620
$385$	0	0
$386$	−6.09635e11	−1.39774
$387$	−1.67066e12	−3.78607
$388$	−2.98870e11	−0.669483
$389$	5.87210e11	1.30023	0.650115	−	0.759836i	$-0.274721\pi$
$389$	5.87210e11	1.30023	0.650115	+	0.759836i	$0.274721\pi$
$390$	−4.72877e10	−0.103504
$391$	−6.82570e11	−1.47690
$392$	0	0
$393$	−1.40041e12	−2.96134
$394$	−2.74159e11	−0.573151
$395$	1.21597e11	0.251324
$396$	−1.50068e11	−0.306661
$397$	5.93603e11	1.19933	0.599665	−	0.800251i	$-0.295301\pi$
$397$	5.93603e11	1.19933	0.599665	+	0.800251i	$0.295301\pi$
$398$	−3.68287e11	−0.735720
$399$	0	0
$400$	−5.07267e9	−0.00990755
$401$	4.50186e11	0.869446	0.434723	−	0.900564i	$-0.356846\pi$
$401$	4.50186e11	0.869446	0.434723	+	0.900564i	$0.356846\pi$
$402$	4.58388e11	0.875419
$403$	1.57666e10	0.0297759
$404$	3.55803e11	0.664498
$405$	1.96643e12	3.63187
$406$	0	0
$407$	−5.20580e10	−0.0940400
$408$	−3.59418e11	−0.642140
$409$	4.34640e11	0.768023	0.384012	−	0.923328i	$-0.374542\pi$
$409$	4.34640e11	0.768023	0.384012	+	0.923328i	$0.374542\pi$
$410$	1.22143e11	0.213473
$411$	−4.59440e11	−0.794219
$412$	2.40335e11	0.410941
$413$	0	0
$414$	1.80867e12	3.02592
$415$	3.31036e11	0.547846
$416$	−8.35534e9	−0.0136787
$417$	1.35657e12	2.19700
$418$	4.05298e10	0.0649353
$419$	−4.94533e11	−0.783848	−0.391924	−	0.919998i	$-0.628190\pi$
$419$	−4.94533e11	−0.783848	−0.391924	+	0.919998i	$0.628190\pi$
$420$	0	0
$421$	6.78076e11	1.05198	0.525992	−	0.850490i	$-0.323694\pi$
$421$	6.78076e11	1.05198	0.525992	+	0.850490i	$0.323694\pi$
$422$	7.93451e11	1.21791
$423$	2.31377e11	0.351390
$424$	−3.69829e11	−0.555718
$425$	2.50794e10	0.0372878
$426$	4.77718e11	0.702794
$427$	0	0
$428$	6.63778e10	0.0956149
$429$	2.35743e10	0.0336032
$430$	−6.82245e11	−0.962349
$431$	1.14262e12	1.59497	0.797485	−	0.603339i	$-0.206163\pi$
$431$	1.14262e12	1.59497	0.797485	+	0.603339i	$0.206163\pi$
$432$	6.03040e11	0.833047
$433$	9.94314e11	1.35934	0.679670	−	0.733518i	$-0.262123\pi$
$433$	9.94314e11	1.35934	0.679670	+	0.733518i	$0.262123\pi$
$434$	0	0
$435$	−2.02638e12	−2.71343
$436$	−2.11401e10	−0.0280168
$437$	−4.88479e11	−0.640737
$438$	8.85901e11	1.15014
$439$	2.16942e11	0.278775	0.139387	−	0.990238i	$-0.455487\pi$
$439$	2.16942e11	0.278775	0.139387	+	0.990238i	$0.455487\pi$
$440$	−6.12829e10	−0.0779475
$441$	0	0
$442$	4.13090e10	0.0514807
$443$	1.06952e12	1.31939	0.659693	−	0.751535i	$-0.270686\pi$
$443$	1.06952e12	1.31939	0.659693	+	0.751535i	$0.270686\pi$
$444$	3.30379e11	0.403449
$445$	7.51470e11	0.908430
$446$	8.87095e11	1.06161
$447$	4.54960e11	0.539001
$448$	0	0
$449$	1.65225e12	1.91853	0.959264	−	0.282510i	$-0.0911669\pi$
$449$	1.65225e12	1.91853	0.959264	+	0.282510i	$0.0911669\pi$
$450$	−6.64551e10	−0.0763962
$451$	−6.08920e10	−0.0693052
$452$	3.00234e11	0.338327
$453$	−1.84553e12	−2.05910
$454$	−5.66135e10	−0.0625416
$455$	0	0
$456$	−2.57217e11	−0.278585
$457$	−7.46509e10	−0.0800594	−0.0400297	−	0.999198i	$-0.512745\pi$
$457$	−7.46509e10	−0.0800594	−0.0400297	+	0.999198i	$0.512745\pi$
$458$	−4.86925e11	−0.517092
$459$	−2.98145e12	−3.13524
$460$	7.38603e11	0.769132
$461$	5.63966e11	0.581565	0.290783	−	0.956789i	$-0.406084\pi$
$461$	5.63966e11	0.581565	0.290783	+	0.956789i	$0.406084\pi$
$462$	0	0
$463$	9.11377e11	0.921687	0.460844	−	0.887481i	$-0.347547\pi$
$463$	9.11377e11	0.921687	0.460844	+	0.887481i	$0.347547\pi$
$464$	−3.58044e11	−0.358596
$465$	−7.33902e11	−0.727947
$466$	9.85753e10	0.0968348
$467$	−1.91784e11	−0.186589	−0.0932946	−	0.995639i	$-0.529740\pi$
$467$	−1.91784e11	−0.186589	−0.0932946	+	0.995639i	$0.529740\pi$
$468$	−1.09460e11	−0.105475
$469$	0	0
$470$	9.44873e10	0.0893168
$471$	2.59082e11	0.242574
$472$	−2.98644e11	−0.276958
$473$	3.40119e11	0.312433
$474$	3.84713e11	0.350054
$475$	1.79480e10	0.0161769
$476$	0	0
$477$	−4.84499e12	−4.28509
$478$	−1.01364e12	−0.888093
$479$	1.49058e12	1.29373	0.646866	−	0.762604i	$-0.276079\pi$
$479$	1.49058e12	1.29373	0.646866	+	0.762604i	$0.276079\pi$
$480$	3.88923e11	0.334409
$481$	−3.79714e10	−0.0323447
$482$	1.20245e12	1.01474
$483$	0	0
$484$	−5.73083e11	−0.474694
$485$	−1.59892e12	−1.31217
$486$	3.32361e12	2.70238
$487$	−1.26948e12	−1.02269	−0.511345	−	0.859376i	$-0.670853\pi$
$487$	−1.26948e12	−1.02269	−0.511345	+	0.859376i	$0.670853\pi$
$488$	−3.04536e10	−0.0243080
$489$	−1.68437e12	−1.33213
$490$	0	0
$491$	−7.11119e11	−0.552173	−0.276087	−	0.961133i	$-0.589038\pi$
$491$	−7.11119e11	−0.552173	−0.276087	+	0.961133i	$0.589038\pi$
$492$	3.86442e11	0.297332
$493$	1.77018e12	1.34960
$494$	2.95626e10	0.0223343
$495$	−8.02844e11	−0.601046
$496$	−1.29674e11	−0.0962025
$497$	0	0
$498$	1.04735e12	0.763059
$499$	1.60263e12	1.15712	0.578562	−	0.815639i	$-0.303614\pi$
$499$	1.60263e12	1.15712	0.578562	+	0.815639i	$0.303614\pi$
$500$	−7.11923e11	−0.509411
$501$	−9.03114e11	−0.640432
$502$	1.62721e12	1.14361
$503$	−6.48944e11	−0.452013	−0.226007	−	0.974126i	$-0.572567\pi$
$503$	−6.48944e11	−0.452013	−0.226007	+	0.974126i	$0.572567\pi$
$504$	0	0
$505$	1.90350e12	1.30239
$506$	−3.68215e11	−0.249703
$507$	−2.85471e12	−1.91878
$508$	−7.31860e11	−0.487575
$509$	−3.81925e10	−0.0252202	−0.0126101	−	0.999920i	$-0.504014\pi$
$509$	−3.81925e10	−0.0252202	−0.0126101	+	0.999920i	$0.504014\pi$
$510$	−1.92285e12	−1.25857
$511$	0	0
$512$	6.87195e10	0.0441942
$513$	−2.13366e12	−1.36018
$514$	8.82709e11	0.557806
$515$	1.28576e12	0.805431
$516$	−2.15852e12	−1.34039
$517$	−4.71047e10	−0.0289972
$518$	0	0
$519$	3.06031e12	1.85145
$520$	−4.47001e10	−0.0268098
$521$	−1.16818e12	−0.694606	−0.347303	−	0.937753i	$-0.612902\pi$
$521$	−1.16818e12	−0.694606	−0.347303	+	0.937753i	$0.612902\pi$
$522$	−4.69060e12	−2.76510
$523$	1.51866e12	0.887572	0.443786	−	0.896133i	$-0.353635\pi$
$523$	1.51866e12	0.887572	0.443786	+	0.896133i	$0.353635\pi$
$524$	−1.32378e12	−0.767050
$525$	0	0
$526$	−3.59137e11	−0.204562
$527$	6.41113e11	0.362065
$528$	−1.93890e11	−0.108568
$529$	2.63671e12	1.46390
$530$	−1.97854e12	−1.08919
$531$	−3.91242e12	−2.13560
$532$	0	0
$533$	−4.44149e10	−0.0238373
$534$	2.37754e12	1.26529
$535$	3.55113e11	0.187402
$536$	4.33304e11	0.226752
$537$	5.02407e11	0.260718
$538$	3.76344e10	0.0193671
$539$	0	0
$540$	3.22620e12	1.63275
$541$	1.19442e12	0.599473	0.299736	−	0.954022i	$-0.403101\pi$
$541$	1.19442e12	0.599473	0.299736	+	0.954022i	$0.403101\pi$
$542$	−2.39049e12	−1.18984
$543$	4.44994e11	0.219662
$544$	−3.39751e11	−0.166328
$545$	−1.13097e11	−0.0549120
$546$	0	0
$547$	−3.52503e11	−0.168353	−0.0841764	−	0.996451i	$-0.526826\pi$
$547$	−3.52503e11	−0.168353	−0.0841764	+	0.996451i	$0.526826\pi$
$548$	−4.34299e11	−0.205720
$549$	−3.98962e11	−0.187437
$550$	1.35292e10	0.00630433
$551$	1.26682e12	0.585509
$552$	2.33683e12	1.07127
$553$	0	0
$554$	−2.31038e12	−1.04205
$555$	1.76749e12	0.790748
$556$	1.28234e12	0.569071
$557$	−1.81198e12	−0.797638	−0.398819	−	0.917030i	$-0.630580\pi$
$557$	−1.81198e12	−0.797638	−0.398819	+	0.917030i	$0.630580\pi$
$558$	−1.69881e12	−0.741808
$559$	2.48085e11	0.107460
$560$	0	0
$561$	9.58595e11	0.408604
$562$	−1.12688e12	−0.476502
$563$	−2.83080e12	−1.18747	−0.593733	−	0.804662i	$-0.702346\pi$
$563$	−2.83080e12	−1.18747	−0.593733	+	0.804662i	$0.702346\pi$
$564$	2.98943e11	0.124404
$565$	1.60621e12	0.663110
$566$	3.27293e12	1.34049
$567$	0	0
$568$	4.51577e11	0.182039
$569$	3.53471e12	1.41367	0.706837	−	0.707377i	$-0.250122\pi$
$569$	3.53471e12	1.41367	0.706837	+	0.707377i	$0.250122\pi$
$570$	−1.37608e12	−0.546017
$571$	1.06393e12	0.418842	0.209421	−	0.977826i	$-0.432842\pi$
$571$	1.06393e12	0.418842	0.209421	+	0.977826i	$0.432842\pi$
$572$	2.22843e10	0.00870396
$573$	3.07887e12	1.19315
$574$	0	0
$575$	−1.63058e11	−0.0622068
$576$	9.00268e11	0.340777
$577$	3.55526e12	1.33530	0.667652	−	0.744474i	$-0.267300\pi$
$577$	3.55526e12	1.33530	0.667652	+	0.744474i	$0.267300\pi$
$578$	−2.17669e11	−0.0811188
$579$	−1.03188e13	−3.81572
$580$	−1.91549e12	−0.702837
$581$	0	0
$582$	−5.05873e12	−1.82763
$583$	9.86362e11	0.353613
$584$	8.37424e11	0.297912
$585$	−5.85599e11	−0.206728
$586$	1.73253e12	0.606935
$587$	−5.01945e12	−1.74496	−0.872478	−	0.488653i	$-0.837488\pi$
$587$	−5.01945e12	−1.74496	−0.872478	+	0.488653i	$0.837488\pi$
$588$	0	0
$589$	4.58810e11	0.157078
$590$	−1.59771e12	−0.542830
$591$	−4.64047e12	−1.56465
$592$	3.12300e11	0.104502
$593$	−3.61438e12	−1.20029	−0.600146	−	0.799890i	$-0.704891\pi$
$593$	−3.61438e12	−1.20029	−0.600146	+	0.799890i	$0.704891\pi$
$594$	−1.60835e12	−0.530081
$595$	0	0
$596$	4.30065e11	0.139613
$597$	−6.23370e12	−2.00845
$598$	−2.68578e11	−0.0858846
$599$	−8.96553e11	−0.284548	−0.142274	−	0.989827i	$-0.545441\pi$
$599$	−8.96553e11	−0.284548	−0.142274	+	0.989827i	$0.545441\pi$
$600$	−8.58610e10	−0.0270468
$601$	2.12154e11	0.0663310	0.0331655	−	0.999450i	$-0.489441\pi$
$601$	2.12154e11	0.0663310	0.0331655	+	0.999450i	$0.489441\pi$
$602$	0	0
$603$	5.67656e12	1.74847
$604$	−1.74454e12	−0.533353
$605$	−3.06593e12	−0.930385
$606$	6.02240e12	1.81402
$607$	1.97565e12	0.590692	0.295346	−	0.955390i	$-0.404565\pi$
$607$	1.97565e12	0.590692	0.295346	+	0.955390i	$0.404565\pi$
$608$	−2.43142e11	−0.0721594
$609$	0	0
$610$	−1.62923e11	−0.0476430
$611$	−3.43584e10	−0.00997350
$612$	−4.45095e12	−1.28254
$613$	−3.85941e12	−1.10395	−0.551974	−	0.833861i	$-0.686125\pi$
$613$	−3.85941e12	−1.10395	−0.551974	+	0.833861i	$0.686125\pi$
$614$	−1.88241e12	−0.534510
$615$	2.06742e12	0.582762
$616$	0	0
$617$	−3.19932e12	−0.888738	−0.444369	−	0.895844i	$-0.646572\pi$
$617$	−3.19932e12	−0.888738	−0.444369	+	0.895844i	$0.646572\pi$
$618$	4.06796e12	1.12183
$619$	5.73209e12	1.56930	0.784649	−	0.619940i	$-0.212843\pi$
$619$	5.73209e12	1.56930	0.784649	+	0.619940i	$0.212843\pi$
$620$	−6.93742e11	−0.188554
$621$	1.93844e13	5.23048
$622$	−2.83639e11	−0.0759819
$623$	0	0
$624$	−1.41424e11	−0.0373416
$625$	−3.65753e12	−0.958799
$626$	1.70619e12	0.444060
$627$	6.86016e11	0.177268
$628$	2.44905e11	0.0628318
$629$	−1.54402e12	−0.393301
$630$	0	0
$631$	6.65474e12	1.67109	0.835543	−	0.549425i	$-0.185153\pi$
$631$	6.65474e12	1.67109	0.835543	+	0.549425i	$0.185153\pi$
$632$	3.63662e11	0.0906714
$633$	1.34301e13	3.32478
$634$	−5.29762e11	−0.130220
$635$	−3.91537e12	−0.955632
$636$	−6.25981e12	−1.51706
$637$	0	0
$638$	9.54930e11	0.228180
$639$	5.91594e12	1.40368
$640$	3.67641e11	0.0866192
$641$	−4.60320e12	−1.07696	−0.538479	−	0.842639i	$-0.681001\pi$
$641$	−4.60320e12	−1.07696	−0.538479	+	0.842639i	$0.681001\pi$
$642$	1.12352e12	0.261021
$643$	6.55681e12	1.51267	0.756333	−	0.654186i	$-0.226989\pi$
$643$	6.55681e12	1.51267	0.756333	+	0.654186i	$0.226989\pi$
$644$	0	0
$645$	−1.15478e13	−2.62713
$646$	1.20210e12	0.271577
$647$	1.79575e12	0.402880	0.201440	−	0.979501i	$-0.435438\pi$
$647$	1.79575e12	0.402880	0.201440	+	0.979501i	$0.435438\pi$
$648$	5.88103e12	1.31028
$649$	7.96505e11	0.176233
$650$	9.86825e9	0.00216835
$651$	0	0
$652$	−1.59220e12	−0.345051
$653$	−6.30641e12	−1.35729	−0.678645	−	0.734466i	$-0.737433\pi$
$653$	−6.30641e12	−1.35729	−0.678645	+	0.734466i	$0.737433\pi$
$654$	−3.57822e11	−0.0764834
$655$	−7.08205e12	−1.50339
$656$	3.65296e11	0.0770154
$657$	1.09708e13	2.29717
$658$	0	0
$659$	−6.63478e12	−1.37038	−0.685191	−	0.728363i	$-0.740281\pi$
$659$	−6.63478e12	−1.37038	−0.685191	+	0.728363i	$0.740281\pi$
$660$	−1.03729e12	−0.212790
$661$	−2.38444e11	−0.0485825	−0.0242913	−	0.999705i	$-0.507733\pi$
$661$	−2.38444e11	−0.0485825	−0.0242913	+	0.999705i	$0.507733\pi$
$662$	−3.52025e12	−0.712382
$663$	6.99205e11	0.140538
$664$	9.90034e11	0.197649
$665$	0	0
$666$	4.09133e12	0.805806
$667$	−1.15091e13	−2.25153
$668$	−8.53695e11	−0.165886
$669$	1.50152e13	2.89809
$670$	2.31813e12	0.444427
$671$	8.12221e10	0.0154676
$672$	0	0
$673$	7.84956e12	1.47495	0.737475	−	0.675374i	$-0.236018\pi$
$673$	7.84956e12	1.47495	0.737475	+	0.675374i	$0.236018\pi$
$674$	2.54283e12	0.474622
$675$	−7.12234e11	−0.132055
$676$	−2.69850e12	−0.497006
$677$	−7.27382e11	−0.133080	−0.0665401	−	0.997784i	$-0.521196\pi$
$677$	−7.27382e11	−0.133080	−0.0665401	+	0.997784i	$0.521196\pi$
$678$	5.08182e12	0.923603
$679$	0	0
$680$	−1.81763e12	−0.325998
$681$	−9.58252e11	−0.170733
$682$	3.45851e11	0.0612152
$683$	−2.03252e11	−0.0357390	−0.0178695	−	0.999840i	$-0.505688\pi$
$683$	−2.03252e11	−0.0357390	−0.0178695	+	0.999840i	$0.505688\pi$
$684$	−3.18531e12	−0.556415
$685$	−2.32345e12	−0.403205
$686$	0	0
$687$	−8.24180e12	−1.41162
$688$	−2.04040e12	−0.347191
$689$	7.19458e11	0.121624
$690$	1.25017e13	2.09966
$691$	4.66699e12	0.778728	0.389364	−	0.921084i	$-0.372695\pi$
$691$	4.66699e12	0.778728	0.389364	+	0.921084i	$0.372695\pi$
$692$	2.89285e12	0.479566
$693$	0	0
$694$	1.44943e12	0.237181
$695$	6.86037e12	1.11536
$696$	−6.06033e12	−0.978937
$697$	−1.80603e12	−0.289853
$698$	−2.92324e12	−0.466138
$699$	1.66851e12	0.264351
$700$	0	0
$701$	−1.00377e12	−0.157001	−0.0785003	−	0.996914i	$-0.525013\pi$
$701$	−1.00377e12	−0.157001	−0.0785003	+	0.996914i	$0.525013\pi$
$702$	−1.17314e12	−0.182320
$703$	−1.10497e12	−0.170629
$704$	−1.83280e11	−0.0281215
$705$	1.59931e12	0.243827
$706$	4.62636e12	0.700839
$707$	0	0
$708$	−5.05491e12	−0.756073
$709$	3.02087e12	0.448977	0.224488	−	0.974477i	$-0.427929\pi$
$709$	3.02087e12	0.448977	0.224488	+	0.974477i	$0.427929\pi$
$710$	2.41588e12	0.356791
$711$	4.76419e12	0.699159
$712$	2.24744e12	0.327738
$713$	−4.16832e12	−0.604029
$714$	0	0
$715$	1.19218e11	0.0170595
$716$	4.74915e11	0.0675316
$717$	−1.71571e13	−2.42442
$718$	−5.26476e12	−0.739296
$719$	−1.09553e13	−1.52877	−0.764386	−	0.644758i	$-0.776958\pi$
$719$	−1.09553e13	−1.52877	−0.764386	+	0.644758i	$0.776958\pi$
$720$	4.81633e12	0.667913
$721$	0	0
$722$	−4.30273e12	−0.589286
$723$	2.03528e13	2.77015
$724$	4.20643e11	0.0568972
$725$	4.22876e11	0.0568449
$726$	−9.70013e12	−1.29587
$727$	1.28144e13	1.70135	0.850674	−	0.525694i	$-0.176194\pi$
$727$	1.28144e13	1.70135	0.850674	+	0.525694i	$0.176194\pi$
$728$	0	0
$729$	2.79953e13	3.67122
$730$	4.48012e12	0.583898
$731$	1.00878e13	1.30668
$732$	−5.15465e11	−0.0663589
$733$	7.12017e12	0.911009	0.455505	−	0.890233i	$-0.349459\pi$
$733$	7.12017e12	0.911009	0.455505	+	0.890233i	$0.349459\pi$
$734$	−6.66326e12	−0.847334
$735$	0	0
$736$	2.20895e12	0.277483
$737$	−1.15566e12	−0.144286
$738$	4.78560e12	0.593859
$739$	−5.53361e12	−0.682509	−0.341254	−	0.939971i	$-0.610852\pi$
$739$	−5.53361e12	−0.682509	−0.341254	+	0.939971i	$0.610852\pi$
$740$	1.67077e12	0.204821
$741$	5.00384e11	0.0609707
$742$	0	0
$743$	2.58825e12	0.311571	0.155785	−	0.987791i	$-0.450209\pi$
$743$	2.58825e12	0.311571	0.155785	+	0.987791i	$0.450209\pi$
$744$	−2.19489e12	−0.262625
$745$	2.30080e12	0.273637
$746$	1.72207e12	0.203576
$747$	1.29701e13	1.52405
$748$	9.06141e11	0.105837
$749$	0	0
$750$	−1.20502e13	−1.39065
$751$	−5.64331e12	−0.647373	−0.323686	−	0.946164i	$-0.604922\pi$
$751$	−5.64331e12	−0.647373	−0.323686	+	0.946164i	$0.604922\pi$
$752$	2.82585e11	0.0322232
$753$	2.75425e13	3.12195
$754$	6.96531e11	0.0784819
$755$	−9.33308e12	−1.04535
$756$	0	0
$757$	−1.51570e13	−1.67757	−0.838786	−	0.544462i	$-0.816734\pi$
$757$	−1.51570e13	−1.67757	−0.838786	+	0.544462i	$0.816734\pi$
$758$	8.54789e12	0.940475
$759$	−6.23249e12	−0.681669
$760$	−1.30078e12	−0.141430
$761$	−8.05711e12	−0.870860	−0.435430	−	0.900222i	$-0.643404\pi$
$761$	−8.05711e12	−0.870860	−0.435430	+	0.900222i	$0.643404\pi$
$762$	−1.23876e13	−1.33104
$763$	0	0
$764$	2.91039e12	0.309052
$765$	−2.38120e13	−2.51374
$766$	−4.92646e12	−0.517017
$767$	5.80975e11	0.0606148
$768$	1.16316e12	0.120646
$769$	−2.31836e12	−0.239063	−0.119531	−	0.992830i	$-0.538139\pi$
$769$	−2.31836e12	−0.239063	−0.119531	+	0.992830i	$0.538139\pi$
$770$	0	0
$771$	1.49409e13	1.52276
$772$	−9.75417e12	−0.988354
$773$	−1.70922e13	−1.72183	−0.860916	−	0.508747i	$-0.830109\pi$
$773$	−1.70922e13	−1.72183	−0.860916	+	0.508747i	$0.830109\pi$
$774$	−2.67306e13	−2.67716
$775$	1.53155e11	0.0152501
$776$	−4.78192e12	−0.473396
$777$	0	0
$778$	9.39536e12	0.919402
$779$	−1.29248e12	−0.125749
$780$	−7.56603e11	−0.0731884
$781$	−1.20439e12	−0.115834
$782$	−1.09211e13	−1.04433
$783$	−5.02716e13	−4.77964
$784$	0	0
$785$	1.31021e12	0.123148
$786$	−2.24065e13	−2.09398
$787$	−4.18824e12	−0.389176	−0.194588	−	0.980885i	$-0.562337\pi$
$787$	−4.18824e12	−0.389176	−0.194588	+	0.980885i	$0.562337\pi$
$788$	−4.38654e12	−0.405279
$789$	−6.07883e12	−0.558436
$790$	1.94555e12	0.177713
$791$	0	0
$792$	−2.40108e12	−0.216842
$793$	5.92438e10	0.00532003
$794$	9.49764e12	0.848054
$795$	−3.34892e13	−2.97340
$796$	−5.89259e12	−0.520232
$797$	1.78707e13	1.56884	0.784421	−	0.620229i	$-0.212960\pi$
$797$	1.78707e13	1.56884	0.784421	+	0.620229i	$0.212960\pi$
$798$	0	0
$799$	−1.39711e12	−0.121274
$800$	−8.11626e10	−0.00700570
$801$	2.94428e13	2.52716
$802$	7.20298e12	0.614791
$803$	−2.23347e12	−0.189566
$804$	7.33420e12	0.619014
$805$	0	0
$806$	2.52265e11	0.0210547
$807$	6.37007e11	0.0528705
$808$	5.69285e12	0.469871
$809$	−3.19043e12	−0.261867	−0.130934	−	0.991391i	$-0.541797\pi$
$809$	−3.19043e12	−0.261867	−0.130934	+	0.991391i	$0.541797\pi$
$810$	3.14628e13	2.56812
$811$	−1.37637e12	−0.111722	−0.0558612	−	0.998439i	$-0.517790\pi$
$811$	−1.37637e12	−0.111722	−0.0558612	+	0.998439i	$0.517790\pi$
$812$	0	0
$813$	−4.04619e13	−3.24817
$814$	−8.32928e11	−0.0664963
$815$	−8.51808e12	−0.676290
$816$	−5.75069e12	−0.454061
$817$	7.21931e12	0.566887
$818$	6.95423e12	0.543075
$819$	0	0
$820$	1.95429e12	0.150948
$821$	2.10169e13	1.61445	0.807223	−	0.590247i	$-0.200970\pi$
$821$	2.10169e13	1.61445	0.807223	+	0.590247i	$0.200970\pi$
$822$	−7.35104e12	−0.561598
$823$	−1.36094e13	−1.03405	−0.517024	−	0.855971i	$-0.672960\pi$
$823$	−1.36094e13	−1.03405	−0.517024	+	0.855971i	$0.672960\pi$
$824$	3.84536e12	0.290579
$825$	2.28998e11	0.0172103
$826$	0	0
$827$	1.02944e13	0.765288	0.382644	−	0.923896i	$-0.375014\pi$
$827$	1.02944e13	0.765288	0.382644	+	0.923896i	$0.375014\pi$
$828$	2.89387e13	2.13965
$829$	2.59127e13	1.90554	0.952769	−	0.303695i	$-0.0982204\pi$
$829$	2.59127e13	1.90554	0.952769	+	0.303695i	$0.0982204\pi$
$830$	5.29657e12	0.387385
$831$	−3.91059e13	−2.84471
$832$	−1.33685e11	−0.00967228
$833$	0	0
$834$	2.17052e13	1.55352
$835$	−4.56717e12	−0.325131
$836$	6.48477e11	0.0459162
$837$	−1.82071e13	−1.28226
$838$	−7.91252e12	−0.554264
$839$	−5.20978e12	−0.362986	−0.181493	−	0.983392i	$-0.558093\pi$
$839$	−5.20978e12	−0.362986	−0.181493	+	0.983392i	$0.558093\pi$
$840$	0	0
$841$	1.53407e13	1.05746
$842$	1.08492e13	0.743864
$843$	−1.90738e13	−1.30081
$844$	1.26952e13	0.861190
$845$	−1.44366e13	−0.974117
$846$	3.70204e12	0.248470
$847$	0	0
$848$	−5.91727e12	−0.392952
$849$	5.53983e13	3.65942
$850$	4.01270e11	0.0263665
$851$	1.00387e13	0.656140
$852$	7.64348e12	0.496951
$853$	−2.58714e12	−0.167321	−0.0836604	−	0.996494i	$-0.526661\pi$
$853$	−2.58714e12	−0.167321	−0.0836604	+	0.996494i	$0.526661\pi$
$854$	0	0
$855$	−1.70410e13	−1.09056
$856$	1.06204e12	0.0676100
$857$	−1.91338e13	−1.21168	−0.605838	−	0.795588i	$-0.707162\pi$
$857$	−1.91338e13	−1.21168	−0.605838	+	0.795588i	$0.707162\pi$
$858$	3.77189e11	0.0237611
$859$	2.66475e13	1.66989	0.834945	−	0.550334i	$-0.185499\pi$
$859$	2.66475e13	1.66989	0.834945	+	0.550334i	$0.185499\pi$
$860$	−1.09159e13	−0.680483
$861$	0	0
$862$	1.82819e13	1.12781
$863$	−2.48333e13	−1.52401	−0.762003	−	0.647574i	$-0.775784\pi$
$863$	−2.48333e13	−1.52401	−0.762003	+	0.647574i	$0.775784\pi$
$864$	9.64865e12	0.589053
$865$	1.54764e13	0.939934
$866$	1.59090e13	0.961198
$867$	−3.68431e12	−0.221447
$868$	0	0
$869$	−9.69912e11	−0.0576957
$870$	−3.24220e13	−1.91869
$871$	−8.42941e11	−0.0496267
$872$	−3.38242e11	−0.0198109
$873$	−6.26461e13	−3.65031
$874$	−7.81567e12	−0.453069
$875$	0	0
$876$	1.41744e13	0.813273
$877$	1.18382e13	0.675753	0.337876	−	0.941190i	$-0.390291\pi$
$877$	1.18382e13	0.675753	0.337876	+	0.941190i	$0.390291\pi$
$878$	3.47107e12	0.197124
$879$	2.93252e13	1.65688
$880$	−9.80526e11	−0.0551172
$881$	2.57086e13	1.43776	0.718882	−	0.695133i	$-0.244654\pi$
$881$	2.57086e13	1.43776	0.718882	+	0.695133i	$0.244654\pi$
$882$	0	0
$883$	−1.32530e13	−0.733656	−0.366828	−	0.930289i	$-0.619556\pi$
$883$	−1.32530e13	−0.733656	−0.366828	+	0.930289i	$0.619556\pi$
$884$	6.60944e11	0.0364024
$885$	−2.70432e13	−1.48188
$886$	1.71123e13	0.932947
$887$	−3.14489e11	−0.0170588	−0.00852941	−	0.999964i	$-0.502715\pi$
$887$	−3.14489e11	−0.0170588	−0.00852941	+	0.999964i	$0.502715\pi$
$888$	5.28606e12	0.285282
$889$	0	0
$890$	1.20235e13	0.642357
$891$	−1.56851e13	−0.833755
$892$	1.41935e13	0.750669
$893$	−9.99835e11	−0.0526135
$894$	7.27937e12	0.381131
$895$	2.54074e12	0.132360
$896$	0	0
$897$	−4.54601e12	−0.234458
$898$	2.64361e13	1.35660
$899$	1.08101e13	0.551965
$900$	−1.06328e12	−0.0540203
$901$	2.92551e13	1.47891
$902$	−9.74272e11	−0.0490062
$903$	0	0
$904$	4.80374e12	0.239233
$905$	2.25039e12	0.111517
$906$	−2.95284e13	−1.45601
$907$	3.68141e12	0.180627	0.0903133	−	0.995913i	$-0.471213\pi$
$907$	3.68141e12	0.180627	0.0903133	+	0.995913i	$0.471213\pi$
$908$	−9.05816e11	−0.0442236
$909$	7.45798e13	3.62313
$910$	0	0
$911$	−2.58776e13	−1.24478	−0.622388	−	0.782709i	$-0.713837\pi$
$911$	−2.58776e13	−1.24478	−0.622388	+	0.782709i	$0.713837\pi$
$912$	−4.11547e12	−0.196989
$913$	−2.64049e12	−0.125767
$914$	−1.19441e12	−0.0566105
$915$	−2.75768e12	−0.130061
$916$	−7.79080e12	−0.365639
$917$	0	0
$918$	−4.77032e13	−2.21695
$919$	−1.22244e13	−0.565340	−0.282670	−	0.959217i	$-0.591220\pi$
$919$	−1.22244e13	−0.565340	−0.282670	+	0.959217i	$0.591220\pi$
$920$	1.18176e13	0.543858
$921$	−3.18620e13	−1.45917
$922$	9.02345e12	0.411229
$923$	−8.78488e11	−0.0398408
$924$	0	0
$925$	−3.68849e11	−0.0165657
$926$	1.45820e13	0.651731
$927$	5.03765e13	2.24063
$928$	−5.72870e12	−0.253566
$929$	2.78231e13	1.22556	0.612780	−	0.790254i	$-0.290051\pi$
$929$	2.78231e13	1.22556	0.612780	+	0.790254i	$0.290051\pi$
$930$	−1.17424e13	−0.514736
$931$	0	0
$932$	1.57720e12	0.0684725
$933$	−4.80094e12	−0.207424
$934$	−3.06855e12	−0.131939
$935$	4.84775e12	0.207438
$936$	−1.75136e12	−0.0745821
$937$	−3.45042e13	−1.46232	−0.731162	−	0.682204i	$-0.761022\pi$
$937$	−3.45042e13	−1.46232	−0.731162	+	0.682204i	$0.761022\pi$
$938$	0	0
$939$	2.88793e13	1.21225
$940$	1.51180e12	0.0631565
$941$	−4.18564e13	−1.74024	−0.870119	−	0.492842i	$-0.835958\pi$
$941$	−4.18564e13	−1.74024	−0.870119	+	0.492842i	$0.835958\pi$
$942$	4.14532e12	0.171526
$943$	1.17423e13	0.483559
$944$	−4.77830e12	−0.195839
$945$	0	0
$946$	5.44191e12	0.220923
$947$	−1.65956e13	−0.670529	−0.335265	−	0.942124i	$-0.608826\pi$
$947$	−1.65956e13	−0.670529	−0.335265	+	0.942124i	$0.608826\pi$
$948$	6.15541e12	0.247525
$949$	−1.62911e12	−0.0652006
$950$	2.87168e11	0.0114388
$951$	−8.96686e12	−0.355491
$952$	0	0
$953$	1.49663e13	0.587756	0.293878	−	0.955843i	$-0.405054\pi$
$953$	1.49663e13	0.587756	0.293878	+	0.955843i	$0.405054\pi$
$954$	−7.75199e13	−3.03002
$955$	1.55702e13	0.605732
$956$	−1.62183e13	−0.627977
$957$	1.61633e13	0.622913
$958$	2.38492e13	0.914806
$959$	0	0
$960$	6.22277e12	0.236463
$961$	−2.25245e13	−0.851921
$962$	−6.07542e11	−0.0228712
$963$	1.39134e13	0.521334
$964$	1.92391e13	0.717528
$965$	−5.21837e13	−1.93714
$966$	0	0
$967$	2.21214e13	0.813568	0.406784	−	0.913524i	$-0.366650\pi$
$967$	2.21214e13	0.813568	0.406784	+	0.913524i	$0.366650\pi$
$968$	−9.16933e12	−0.335659
$969$	2.03470e13	0.741383
$970$	−2.55827e13	−0.927841
$971$	−1.17366e13	−0.423696	−0.211848	−	0.977303i	$-0.567948\pi$
$971$	−1.17366e13	−0.423696	−0.211848	+	0.977303i	$0.567948\pi$
$972$	5.31777e13	1.91087
$973$	0	0
$974$	−2.03116e13	−0.723151
$975$	1.67032e11	0.00591942
$976$	−4.87258e11	−0.0171884
$977$	5.58753e13	1.96198	0.980989	−	0.194065i	$-0.0621674\pi$
$977$	5.58753e13	1.96198	0.980989	+	0.194065i	$0.0621674\pi$
$978$	−2.69499e13	−0.941960
$979$	−5.99408e12	−0.208545
$980$	0	0
$981$	−4.43118e12	−0.152760
$982$	−1.13779e13	−0.390445
$983$	−3.86757e13	−1.32113	−0.660567	−	0.750767i	$-0.729684\pi$
$983$	−3.86757e13	−1.32113	−0.660567	+	0.750767i	$0.729684\pi$
$984$	6.18308e12	0.210246
$985$	−2.34675e13	−0.794334
$986$	2.83229e13	0.954313
$987$	0	0
$988$	4.73002e11	0.0157927
$989$	−6.55878e13	−2.17992
$990$	−1.28455e13	−0.425004
$991$	−2.49912e13	−0.823106	−0.411553	−	0.911386i	$-0.635014\pi$
$991$	−2.49912e13	−0.823106	−0.411553	+	0.911386i	$0.635014\pi$
$992$	−2.07479e12	−0.0680254
$993$	−5.95845e13	−1.94474
$994$	0	0
$995$	−3.15247e13	−1.01964
$996$	1.67575e13	0.539564
$997$	1.35204e13	0.433373	0.216687	−	0.976241i	$-0.430475\pi$
$997$	1.35204e13	0.433373	0.216687	+	0.976241i	$0.430475\pi$
$998$	2.56420e13	0.818210
$999$	4.38489e13	1.39288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.j.1.3		3
7.2	even	3		14.10.c.a.11.1	yes	6
7.3	odd	6		98.10.c.k.79.3		6
7.4	even	3		14.10.c.a.9.1	✓	6
7.5	odd	6		98.10.c.k.67.3		6
7.6	odd	2		98.10.a.i.1.1		3
21.2	odd	6		126.10.g.f.109.3		6
21.11	odd	6		126.10.g.f.37.3		6
28.11	odd	6		112.10.i.b.65.3		6
28.23	odd	6		112.10.i.b.81.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.a.9.1	✓	6	7.4	even	3
14.10.c.a.11.1	yes	6	7.2	even	3
98.10.a.i.1.1		3	7.6	odd	2
98.10.a.j.1.3		3	1.1	even	1	trivial
98.10.c.k.67.3		6	7.5	odd	6
98.10.c.k.79.3		6	7.3	odd	6
112.10.i.b.65.3		6	28.11	odd	6
112.10.i.b.81.3		6	28.23	odd	6
126.10.g.f.37.3		6	21.11	odd	6
126.10.g.f.109.3		6	21.2	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)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +270.819 q^{3} +256.000 q^{4} +1369.57 q^{5} +4333.11 q^{6} +4096.00 q^{8} +53660.1 q^{9} +21913.1 q^{10} -10924.3 q^{11} +69329.8 q^{12} -7968.27 q^{13} +370906. q^{15} +65536.0 q^{16} -324012. q^{17} +858562. q^{18} -231878. q^{19} +350610. q^{20} -174789. q^{22} +2.10662e6 q^{23} +1.10928e6 q^{24} -77402.7 q^{25} -127492. q^{26} +9.20167e6 q^{27} -5.46332e6 q^{29} +5.93450e6 q^{30} -1.97867e6 q^{31} +1.04858e6 q^{32} -2.95852e6 q^{33} -5.18419e6 q^{34} +1.37370e7 q^{36} +4.76533e6 q^{37} -3.71005e6 q^{38} -2.15796e6 q^{39} +5.60976e6 q^{40} +5.57398e6 q^{41} -3.11341e7 q^{43} -2.79663e6 q^{44} +7.34913e7 q^{45} +3.37060e7 q^{46} +4.31190e6 q^{47} +1.77484e7 q^{48} -1.23844e6 q^{50} -8.77486e7 q^{51} -2.03988e6 q^{52} -9.02903e7 q^{53} +1.47227e8 q^{54} -1.49616e7 q^{55} -6.27970e7 q^{57} -8.74131e7 q^{58} -7.29111e7 q^{59} +9.49520e7 q^{60} -7.43497e6 q^{61} -3.16588e7 q^{62} +1.67772e7 q^{64} -1.09131e7 q^{65} -4.73363e7 q^{66} +1.05787e8 q^{67} -8.29470e7 q^{68} +5.70514e8 q^{69} +1.10248e8 q^{71} +2.19792e8 q^{72} +2.04449e8 q^{73} +7.62452e7 q^{74} -2.09622e7 q^{75} -5.93607e7 q^{76} -3.45274e7 q^{78} +8.87846e7 q^{79} +8.97561e7 q^{80} +1.43580e9 q^{81} +8.91836e7 q^{82} +2.41708e8 q^{83} -4.43757e8 q^{85} -4.98146e8 q^{86} -1.47957e9 q^{87} -4.47461e7 q^{88} +5.48690e8 q^{89} +1.17586e9 q^{90} +5.39295e8 q^{92} -5.35863e8 q^{93} +6.89905e7 q^{94} -3.17573e8 q^{95} +2.83975e8 q^{96} -1.16746e9 q^{97} -5.86201e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 48 q^{2} + 233 q^{3} + 768 q^{4} + 733 q^{5} + 3728 q^{6} + 12288 q^{8} + 15058 q^{9} + 11728 q^{10} - 7339 q^{11} + 59648 q^{12} + 98518 q^{13} + 369119 q^{15} + 196608 q^{16} + 306665 q^{17} + 240928 q^{18}+ \cdots - 628109434 q^{99}+O(q^{100}) \) 3 * q + 48 * q^2 + 233 * q^3 + 768 * q^4 + 733 * q^5 + 3728 * q^6 + 12288 * q^8 + 15058 * q^9 + 11728 * q^10 - 7339 * q^11 + 59648 * q^12 + 98518 * q^13 + 369119 * q^15 + 196608 * q^16 + 306665 * q^17 + 240928 * q^18 + 377991 * q^19 + 187648 * q^20 - 117424 * q^22 + 2267255 * q^23 + 954368 * q^24 + 142612 * q^25 + 1576288 * q^26 + 10674179 * q^27 - 6542978 * q^29 + 5905904 * q^30 + 6654517 * q^31 + 3145728 * q^32 - 3747977 * q^33 + 4906640 * q^34 + 3854848 * q^36 + 22287969 * q^37 + 6047856 * q^38 - 3151974 * q^39 + 3002368 * q^40 + 34048098 * q^41 - 62824140 * q^43 - 1878784 * q^44 + 86300638 * q^45 + 36276080 * q^46 + 52703019 * q^47 + 15269888 * q^48 + 2281792 * q^50 - 97736333 * q^51 + 25220608 * q^52 + 12091125 * q^53 + 170786864 * q^54 + 188717699 * q^55 - 79258835 * q^57 - 104687648 * q^58 + 12949897 * q^59 + 94494464 * q^60 + 160252153 * q^61 + 106472272 * q^62 + 50331648 * q^64 - 334191270 * q^65 - 59967632 * q^66 + 480890225 * q^67 + 78506240 * q^68 + 565616581 * q^69 - 37210720 * q^71 + 61677568 * q^72 - 251382283 * q^73 + 356607504 * q^74 - 16322324 * q^75 + 96765696 * q^76 - 50431584 * q^78 - 286494785 * q^79 + 48037888 * q^80 + 2165894587 * q^81 + 544769568 * q^82 + 1147591172 * q^83 - 1194592537 * q^85 - 1005186240 * q^86 - 1412199358 * q^87 - 30060544 * q^88 + 901243845 * q^89 + 1380810208 * q^90 + 580417280 * q^92 - 710456889 * q^93 + 843248304 * q^94 + 887366177 * q^95 + 244318208 * q^96 + 314853938 * q^97 - 628109434 * q^99

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