LMFDB - Embedded newform 25.14.a.b.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,14,Mod(1,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25.1"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	25.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-142] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$26.8077322380$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4466x - 18720 $ x^3 - x^2 - 4466*x - 18720
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 5 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4.21238$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-56.4248 q^{2} -2114.98 q^{3} -5008.25 q^{4} +119337. q^{6} -325303. q^{7} +744821. q^{8} +2.87881e6 q^{9} -1.61316e6 q^{11} +1.05923e7 q^{12} +3.19654e7 q^{13} +1.83551e7 q^{14} -998777. q^{16} -3.82330e6 q^{17} -1.62436e8 q^{18} -1.98761e8 q^{19} +6.88008e8 q^{21} +9.10219e7 q^{22} +1.86577e8 q^{23} -1.57528e9 q^{24} -1.80364e9 q^{26} -2.71667e9 q^{27} +1.62920e9 q^{28} +2.45694e9 q^{29} -9.66435e8 q^{31} -6.04522e9 q^{32} +3.41179e9 q^{33} +2.15729e8 q^{34} -1.44178e10 q^{36} -2.20805e10 q^{37} +1.12151e10 q^{38} -6.76061e10 q^{39} +4.05651e10 q^{41} -3.88207e10 q^{42} -2.28510e10 q^{43} +8.07908e9 q^{44} -1.05275e10 q^{46} +7.97391e10 q^{47} +2.11239e9 q^{48} +8.93279e9 q^{49} +8.08620e9 q^{51} -1.60091e11 q^{52} +2.25113e11 q^{53} +1.53287e11 q^{54} -2.42292e11 q^{56} +4.20376e11 q^{57} -1.38632e11 q^{58} +7.96680e10 q^{59} +4.91133e11 q^{61} +5.45308e10 q^{62} -9.36485e11 q^{63} +3.49282e11 q^{64} -1.92509e11 q^{66} -2.25405e11 q^{67} +1.91480e10 q^{68} -3.94606e11 q^{69} -6.50849e11 q^{71} +2.14420e12 q^{72} +1.03710e11 q^{73} +1.24588e12 q^{74} +9.95446e11 q^{76} +5.24764e11 q^{77} +3.81466e12 q^{78} +2.08051e12 q^{79} +1.15594e12 q^{81} -2.28888e12 q^{82} -3.39017e12 q^{83} -3.44571e12 q^{84} +1.28936e12 q^{86} -5.19638e12 q^{87} -1.20151e12 q^{88} -7.20835e12 q^{89} -1.03984e13 q^{91} -9.34422e11 q^{92} +2.04399e12 q^{93} -4.49926e12 q^{94} +1.27855e13 q^{96} -7.00185e12 q^{97} -5.04030e11 q^{98} -4.64397e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 142 q^{2} - 416 q^{3} + 17876 q^{4} + 120376 q^{6} - 448292 q^{7} - 2580360 q^{8} + 1286119 q^{9} - 6604004 q^{11} + 23722448 q^{12} + 33501974 q^{13} - 46562928 q^{14} + 199912208 q^{16} - 83129542 q^{17}+ \cdots + 126787366508 q^{99}+O(q^{100}) $ 3 * q - 142 * q^2 - 416 * q^3 + 17876 * q^4 + 120376 * q^6 - 448292 * q^7 - 2580360 * q^8 + 1286119 * q^9 - 6604004 * q^11 + 23722448 * q^12 + 33501974 * q^13 - 46562928 * q^14 + 199912208 * q^16 - 83129542 * q^17 + 30983914 * q^18 + 97491100 * q^19 + 438200736 * q^21 + 530907256 * q^22 - 316255836 * q^23 - 3890359200 * q^24 - 3746814044 * q^26 - 6518951360 * q^27 + 6227646976 * q^28 + 2236171850 * q^29 + 7482994376 * q^31 - 32169857312 * q^32 - 359182912 * q^33 - 30236073988 * q^34 - 43361833852 * q^36 - 31447174242 * q^37 + 42518132360 * q^38 - 70188571072 * q^39 - 10752884434 * q^41 - 92283853824 * q^42 - 16930554856 * q^43 - 68395825168 * q^44 + 246828204336 * q^46 - 31934201692 * q^47 + 80078828864 * q^48 - 38956926629 * q^49 - 129369882944 * q^51 + 18152597928 * q^52 + 221149123934 * q^53 + 246121937200 * q^54 - 522876451200 * q^56 + 763110695680 * q^57 - 854269976260 * q^58 - 55436423900 * q^59 + 496161392746 * q^61 + 598069940736 * q^62 - 1085454385236 * q^63 + 3297565494336 * q^64 - 22883875168 * q^66 - 459297824792 * q^67 + 2008021178776 * q^68 - 333379292832 * q^69 + 521997878336 * q^71 + 5658040941720 * q^72 - 2505025571086 * q^73 - 2418323586508 * q^74 + 621688050000 * q^76 + 385562457456 * q^77 + 2386950332528 * q^78 + 2990636883200 * q^79 + 320549052763 * q^81 - 5784848206924 * q^82 - 5137135467696 * q^83 - 814234130688 * q^84 + 2343313645096 * q^86 - 6885420178880 * q^87 + 8660607864480 * q^88 - 19423025958450 * q^89 - 6792522370184 * q^91 - 26870022340992 * q^92 + 11095902136128 * q^93 - 7003557875968 * q^94 - 2208331214464 * q^96 + 11088325396458 * q^97 + 10176508990306 * q^98 + 126787366508 * 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 $

$2$	−56.4248	−0.623411	−0.311706	−	0.950179i	$-0.600900\pi$
$2$	−56.4248	−0.623411	−0.311706	+	0.950179i	$0.600900\pi$
$3$	−2114.98	−1.67501	−0.837506	−	0.546428i	$-0.815987\pi$
$3$	−2114.98	−1.67501	−0.837506	+	0.546428i	$0.815987\pi$
$4$	−5008.25	−0.611358
$5$	0	0
$5$	0	0
$6$	119337.	1.04422
$7$	−325303.	−1.04508	−0.522541	−	0.852614i	$-0.675016\pi$
$7$	−325303.	−1.04508	−0.522541	+	0.852614i	$0.675016\pi$
$8$	744821.	1.00454
$9$	2.87881e6	1.80566
$10$	0	0
$11$	−1.61316e6	−0.274551	−0.137276	−	0.990533i	$-0.543835\pi$
$11$	−1.61316e6	−0.274551	−0.137276	+	0.990533i	$0.543835\pi$
$12$	1.05923e7	1.02403
$13$	3.19654e7	1.83674	0.918371	−	0.395720i	$-0.129505\pi$
$13$	3.19654e7	1.83674	0.918371	+	0.395720i	$0.129505\pi$
$14$	1.83551e7	0.651516
$15$	0	0
$16$	−998777.	−0.0148829
$17$	−3.82330e6	−0.0384167	−0.0192084	−	0.999816i	$-0.506115\pi$
$17$	−3.82330e6	−0.0384167	−0.0192084	+	0.999816i	$0.506115\pi$
$18$	−1.62436e8	−1.12567
$19$	−1.98761e8	−0.969245	−0.484622	−	0.874723i	$-0.661043\pi$
$19$	−1.98761e8	−0.969245	−0.484622	+	0.874723i	$0.661043\pi$
$20$	0	0
$21$	6.88008e8	1.75052
$22$	9.10219e7	0.171159
$23$	1.86577e8	0.262801	0.131400	−	0.991329i	$-0.458053\pi$
$23$	1.86577e8	0.262801	0.131400	+	0.991329i	$0.458053\pi$
$24$	−1.57528e9	−1.68261
$25$	0	0
$26$	−1.80364e9	−1.14505
$27$	−2.71667e9	−1.34950
$28$	1.62920e9	0.638919
$29$	2.45694e9	0.767022	0.383511	−	0.923536i	$-0.374715\pi$
$29$	2.45694e9	0.767022	0.383511	+	0.923536i	$0.374715\pi$
$30$	0	0
$31$	−9.66435e8	−0.195579	−0.0977893	−	0.995207i	$-0.531177\pi$
$31$	−9.66435e8	−0.195579	−0.0977893	+	0.995207i	$0.531177\pi$
$32$	−6.04522e9	−0.995261
$33$	3.41179e9	0.459877
$34$	2.15729e8	0.0239494
$35$	0	0
$36$	−1.44178e10	−1.10391
$37$	−2.20805e10	−1.41481	−0.707403	−	0.706810i	$-0.750133\pi$
$37$	−2.20805e10	−1.41481	−0.707403	+	0.706810i	$0.750133\pi$
$38$	1.12151e10	0.604238
$39$	−6.76061e10	−3.07656
$40$	0	0
$41$	4.05651e10	1.33370	0.666850	−	0.745192i	$-0.267642\pi$
$41$	4.05651e10	1.33370	0.666850	+	0.745192i	$0.267642\pi$
$42$	−3.88207e10	−1.09130
$43$	−2.28510e10	−0.551264	−0.275632	−	0.961263i	$-0.588887\pi$
$43$	−2.28510e10	−0.551264	−0.275632	+	0.961263i	$0.588887\pi$
$44$	8.07908e9	0.167849
$45$	0	0
$46$	−1.05275e10	−0.163833
$47$	7.97391e10	1.07903	0.539517	−	0.841975i	$-0.318607\pi$
$47$	7.97391e10	1.07903	0.539517	+	0.841975i	$0.318607\pi$
$48$	2.11239e9	0.0249291
$49$	8.93279e9	0.0921961
$50$	0	0
$51$	8.08620e9	0.0643485
$52$	−1.60091e11	−1.12291
$53$	2.25113e11	1.39511	0.697553	−	0.716534i	$-0.254272\pi$
$53$	2.25113e11	1.39511	0.697553	+	0.716534i	$0.254272\pi$
$54$	1.53287e11	0.841292
$55$	0	0
$56$	−2.42292e11	−1.04983
$57$	4.20376e11	1.62350
$58$	−1.38632e11	−0.478170
$59$	7.96680e10	0.245893	0.122946	−	0.992413i	$-0.460766\pi$
$59$	7.96680e10	0.245893	0.122946	+	0.992413i	$0.460766\pi$
$60$	0	0
$61$	4.91133e11	1.22055	0.610275	−	0.792190i	$-0.291059\pi$
$61$	4.91133e11	1.22055	0.610275	+	0.792190i	$0.291059\pi$
$62$	5.45308e10	0.121926
$63$	−9.36485e11	−1.88707
$64$	3.49282e11	0.635340
$65$	0	0
$66$	−1.92509e11	−0.286693
$67$	−2.25405e11	−0.304423	−0.152212	−	0.988348i	$-0.548640\pi$
$67$	−2.25405e11	−0.304423	−0.152212	+	0.988348i	$0.548640\pi$
$68$	1.91480e10	0.0234864
$69$	−3.94606e11	−0.440194
$70$	0	0
$71$	−6.50849e11	−0.602978	−0.301489	−	0.953470i	$-0.597484\pi$
$71$	−6.50849e11	−0.602978	−0.301489	+	0.953470i	$0.597484\pi$
$72$	2.14420e12	1.81386
$73$	1.03710e11	0.0802087	0.0401043	−	0.999195i	$-0.487231\pi$
$73$	1.03710e11	0.0802087	0.0401043	+	0.999195i	$0.487231\pi$
$74$	1.24588e12	0.882006
$75$	0	0
$76$	9.95446e11	0.592556
$77$	5.24764e11	0.286929
$78$	3.81466e12	1.91797
$79$	2.08051e12	0.962927	0.481464	−	0.876466i	$-0.340105\pi$
$79$	2.08051e12	0.962927	0.481464	+	0.876466i	$0.340105\pi$
$80$	0	0
$81$	1.15594e12	0.454760
$82$	−2.28888e12	−0.831443
$83$	−3.39017e12	−1.13819	−0.569094	−	0.822272i	$-0.692706\pi$
$83$	−3.39017e12	−1.13819	−0.569094	+	0.822272i	$0.692706\pi$
$84$	−3.44571e12	−1.07020
$85$	0	0
$86$	1.28936e12	0.343664
$87$	−5.19638e12	−1.28477
$88$	−1.20151e12	−0.275798
$89$	−7.20835e12	−1.53745	−0.768724	−	0.639580i	$-0.779108\pi$
$89$	−7.20835e12	−1.53745	−0.768724	+	0.639580i	$0.779108\pi$
$90$	0	0
$91$	−1.03984e13	−1.91955
$92$	−9.34422e11	−0.160665
$93$	2.04399e12	0.327597
$94$	−4.49926e12	−0.672682
$95$	0	0
$96$	1.27855e13	1.66707
$97$	−7.00185e12	−0.853486	−0.426743	−	0.904373i	$-0.640339\pi$
$97$	−7.00185e12	−0.853486	−0.426743	+	0.904373i	$0.640339\pi$
$98$	−5.04030e11	−0.0574761
$99$	−4.64397e12	−0.495748
$100$	0	0
$101$	−1.36319e13	−1.27781	−0.638907	−	0.769284i	$-0.720613\pi$
$101$	−1.36319e13	−1.27781	−0.638907	+	0.769284i	$0.720613\pi$
$102$	−4.56262e11	−0.0401156
$103$	6.72899e12	0.555275	0.277637	−	0.960686i	$-0.410449\pi$
$103$	6.72899e12	0.555275	0.277637	+	0.960686i	$0.410449\pi$
$104$	2.38085e13	1.84508
$105$	0	0
$106$	−1.27019e13	−0.869724
$107$	−5.49424e12	−0.353927	−0.176963	−	0.984217i	$-0.556627\pi$
$107$	−5.49424e12	−0.353927	−0.176963	+	0.984217i	$0.556627\pi$
$108$	1.36057e13	0.825026
$109$	1.05471e13	0.602369	0.301184	−	0.953566i	$-0.402618\pi$
$109$	1.05471e13	0.602369	0.301184	+	0.953566i	$0.402618\pi$
$110$	0	0
$111$	4.66997e13	2.36982
$112$	3.24905e11	0.0155539
$113$	−1.30490e13	−0.589612	−0.294806	−	0.955557i	$-0.595255\pi$
$113$	−1.30490e13	−0.589612	−0.294806	+	0.955557i	$0.595255\pi$
$114$	−2.37196e13	−1.01211
$115$	0	0
$116$	−1.23050e13	−0.468925
$117$	9.20224e13	3.31654
$118$	−4.49525e12	−0.153292
$119$	1.24373e12	0.0401486
$120$	0	0
$121$	−3.19204e13	−0.924622
$122$	−2.77121e13	−0.760905
$123$	−8.57944e13	−2.23396
$124$	4.84014e12	0.119569
$125$	0	0
$126$	5.28410e13	1.17642
$127$	1.04514e13	0.221030	0.110515	−	0.993874i	$-0.464750\pi$
$127$	1.04514e13	0.221030	0.110515	+	0.993874i	$0.464750\pi$
$128$	2.98143e13	0.599183
$129$	4.83293e13	0.923374
$130$	0	0
$131$	8.39814e12	0.145184	0.0725922	−	0.997362i	$-0.476873\pi$
$131$	8.39814e12	0.145184	0.0725922	+	0.997362i	$0.476873\pi$
$132$	−1.70871e13	−0.281150
$133$	6.46576e13	1.01294
$134$	1.27184e13	0.189781
$135$	0	0
$136$	−2.84767e12	−0.0385911
$137$	−2.62849e13	−0.339643	−0.169822	−	0.985475i	$-0.554319\pi$
$137$	−2.62849e13	−0.339643	−0.169822	+	0.985475i	$0.554319\pi$
$138$	2.22655e13	0.274422
$139$	6.83006e13	0.803209	0.401604	−	0.915813i	$-0.368453\pi$
$139$	6.83006e13	0.803209	0.401604	+	0.915813i	$0.368453\pi$
$140$	0	0
$141$	−1.68646e14	−1.80739
$142$	3.67240e13	0.375903
$143$	−5.15651e13	−0.504280
$144$	−2.87529e12	−0.0268736
$145$	0	0
$146$	−5.85180e12	−0.0500030
$147$	−1.88927e13	−0.154430
$148$	1.10584e14	0.864953
$149$	−1.70193e14	−1.27418	−0.637089	−	0.770790i	$-0.719862\pi$
$149$	−1.70193e14	−1.27418	−0.637089	+	0.770790i	$0.719862\pi$
$150$	0	0
$151$	1.84944e13	0.126967	0.0634835	−	0.997983i	$-0.479779\pi$
$151$	1.84944e13	0.126967	0.0634835	+	0.997983i	$0.479779\pi$
$152$	−1.48042e14	−0.973644
$153$	−1.10066e13	−0.0693677
$154$	−2.96097e13	−0.178875
$155$	0	0
$156$	3.38588e14	1.88088
$157$	−1.72832e14	−0.921035	−0.460517	−	0.887651i	$-0.652336\pi$
$157$	−1.72832e14	−0.921035	−0.460517	+	0.887651i	$0.652336\pi$
$158$	−1.17392e14	−0.600300
$159$	−4.76109e14	−2.33682
$160$	0	0
$161$	−6.06939e13	−0.274648
$162$	−6.52235e13	−0.283502
$163$	−2.52994e14	−1.05655	−0.528275	−	0.849073i	$-0.677161\pi$
$163$	−2.52994e14	−1.05655	−0.528275	+	0.849073i	$0.677161\pi$
$164$	−2.03160e14	−0.815368
$165$	0	0
$166$	1.91290e14	0.709559
$167$	1.37321e14	0.489870	0.244935	−	0.969539i	$-0.421233\pi$
$167$	1.37321e14	0.489870	0.244935	+	0.969539i	$0.421233\pi$
$168$	5.12443e14	1.75847
$169$	7.18911e14	2.37362
$170$	0	0
$171$	−5.72197e14	−1.75013
$172$	1.14443e14	0.337020
$173$	1.57684e14	0.447186	0.223593	−	0.974683i	$-0.428221\pi$
$173$	1.57684e14	0.447186	0.223593	+	0.974683i	$0.428221\pi$
$174$	2.93204e14	0.800941
$175$	0	0
$176$	1.61118e12	0.00408613
$177$	−1.68496e14	−0.411873
$178$	4.06729e14	0.958463
$179$	−2.76902e14	−0.629189	−0.314595	−	0.949226i	$-0.601869\pi$
$179$	−2.76902e14	−0.629189	−0.314595	+	0.949226i	$0.601869\pi$
$180$	0	0
$181$	−1.39415e14	−0.294712	−0.147356	−	0.989084i	$-0.547076\pi$
$181$	−1.39415e14	−0.294712	−0.147356	+	0.989084i	$0.547076\pi$
$182$	5.86729e14	1.19667
$183$	−1.03874e15	−2.04444
$184$	1.38966e14	0.263994
$185$	0	0
$186$	−1.15332e14	−0.204227
$187$	6.16758e12	0.0105474
$188$	−3.99353e14	−0.659676
$189$	8.83739e14	1.41034
$190$	0	0
$191$	6.42718e14	0.957864	0.478932	−	0.877852i	$-0.341024\pi$
$191$	6.42718e14	0.957864	0.478932	+	0.877852i	$0.341024\pi$
$192$	−7.38724e14	−1.06420
$193$	1.22414e14	0.170494	0.0852470	−	0.996360i	$-0.472832\pi$
$193$	1.22414e14	0.170494	0.0852470	+	0.996360i	$0.472832\pi$
$194$	3.95078e14	0.532073
$195$	0	0
$196$	−4.47376e13	−0.0563648
$197$	1.36916e15	1.66887	0.834435	−	0.551106i	$-0.185794\pi$
$197$	1.36916e15	1.66887	0.834435	+	0.551106i	$0.185794\pi$
$198$	2.62035e14	0.309055
$199$	−1.51380e15	−1.72792	−0.863961	−	0.503558i	$-0.832024\pi$
$199$	−1.51380e15	−1.72792	−0.863961	+	0.503558i	$0.832024\pi$
$200$	0	0
$201$	4.76727e14	0.509912
$202$	7.69177e14	0.796604
$203$	−7.99250e14	−0.801601
$204$	−4.04977e13	−0.0393400
$205$	0	0
$206$	−3.79681e14	−0.346164
$207$	5.37119e14	0.474530
$208$	−3.19263e13	−0.0273361
$209$	3.20633e14	0.266108
$210$	0	0
$211$	1.41808e15	1.10628	0.553141	−	0.833088i	$-0.313429\pi$
$211$	1.41808e15	1.10628	0.553141	+	0.833088i	$0.313429\pi$
$212$	−1.12742e15	−0.852909
$213$	1.37653e15	1.00999
$214$	3.10011e14	0.220642
$215$	0	0
$216$	−2.02343e15	−1.35562
$217$	3.14384e14	0.204396
$218$	−5.95120e14	−0.375523
$219$	−2.19344e14	−0.134350
$220$	0	0
$221$	−1.22213e14	−0.0705616
$222$	−2.63502e15	−1.47737
$223$	3.48697e15	1.89874	0.949371	−	0.314157i	$-0.101722\pi$
$223$	3.48697e15	1.89874	0.949371	+	0.314157i	$0.101722\pi$
$224$	1.96652e15	1.04013
$225$	0	0
$226$	7.36285e14	0.367571
$227$	−1.43848e15	−0.697808	−0.348904	−	0.937158i	$-0.613446\pi$
$227$	−1.43848e15	−0.697808	−0.348904	+	0.937158i	$0.613446\pi$
$228$	−2.10535e15	−0.992538
$229$	1.00326e14	0.0459709	0.0229855	−	0.999736i	$-0.492683\pi$
$229$	1.00326e14	0.0459709	0.0229855	+	0.999736i	$0.492683\pi$
$230$	0	0
$231$	−1.10986e15	−0.480609
$232$	1.82998e15	0.770504
$233$	−1.04926e15	−0.429607	−0.214803	−	0.976657i	$-0.568911\pi$
$233$	−1.04926e15	−0.429607	−0.214803	+	0.976657i	$0.568911\pi$
$234$	−5.19234e15	−2.06757
$235$	0	0
$236$	−3.98997e14	−0.150329
$237$	−4.40023e15	−1.61291
$238$	−7.01771e13	−0.0250291
$239$	−4.68165e15	−1.62485	−0.812424	−	0.583067i	$-0.801853\pi$
$239$	−4.68165e15	−1.62485	−0.812424	+	0.583067i	$0.801853\pi$
$240$	0	0
$241$	−1.22689e15	−0.403361	−0.201680	−	0.979451i	$-0.564640\pi$
$241$	−1.22689e15	−0.403361	−0.201680	+	0.979451i	$0.564640\pi$
$242$	1.80110e15	0.576420
$243$	1.88646e15	0.587770
$244$	−2.45972e15	−0.746193
$245$	0	0
$246$	4.84093e15	1.39268
$247$	−6.35348e15	−1.78025
$248$	−7.19821e14	−0.196466
$249$	7.17014e15	1.90648
$250$	0	0
$251$	−2.74250e15	−0.692258	−0.346129	−	0.938187i	$-0.612504\pi$
$251$	−2.74250e15	−0.692258	−0.346129	+	0.938187i	$0.612504\pi$
$252$	4.69015e15	1.15367
$253$	−3.00977e14	−0.0721523
$254$	−5.89720e14	−0.137793
$255$	0	0
$256$	−4.54358e15	−1.00888
$257$	3.96785e15	0.858994	0.429497	−	0.903068i	$-0.358691\pi$
$257$	3.96785e15	0.858994	0.429497	+	0.903068i	$0.358691\pi$
$258$	−2.72697e15	−0.575642
$259$	7.18283e15	1.47859
$260$	0	0
$261$	7.07307e15	1.38498
$262$	−4.73863e14	−0.0905096
$263$	−4.19100e15	−0.780917	−0.390459	−	0.920621i	$-0.627684\pi$
$263$	−4.19100e15	−0.780917	−0.390459	+	0.920621i	$0.627684\pi$
$264$	2.54117e15	0.461964
$265$	0	0
$266$	−3.64829e15	−0.631478
$267$	1.52455e16	2.57524
$268$	1.12888e15	0.186112
$269$	1.20414e15	0.193771	0.0968854	−	0.995296i	$-0.469112\pi$
$269$	1.20414e15	0.193771	0.0968854	+	0.995296i	$0.469112\pi$
$270$	0	0
$271$	8.17556e15	1.25377	0.626884	−	0.779113i	$-0.284330\pi$
$271$	8.17556e15	1.25377	0.626884	+	0.779113i	$0.284330\pi$
$272$	3.81862e12	0.000571753 0
$273$	2.19924e16	3.21526
$274$	1.48312e15	0.211738
$275$	0	0
$276$	1.97628e15	0.269116
$277$	−5.65506e15	−0.752175	−0.376088	−	0.926584i	$-0.622731\pi$
$277$	−5.65506e15	−0.752175	−0.376088	+	0.926584i	$0.622731\pi$
$278$	−3.85385e15	−0.500730
$279$	−2.78218e15	−0.353149
$280$	0	0
$281$	−1.38960e16	−1.68383	−0.841917	−	0.539607i	$-0.818573\pi$
$281$	−1.38960e16	−1.68383	−0.841917	+	0.539607i	$0.818573\pi$
$282$	9.51584e15	1.12675
$283$	−1.68555e16	−1.95042	−0.975212	−	0.221271i	$-0.928979\pi$
$283$	−1.68555e16	−1.95042	−0.975212	+	0.221271i	$0.928979\pi$
$284$	3.25961e15	0.368635
$285$	0	0
$286$	2.90955e15	0.314374
$287$	−1.31959e16	−1.39383
$288$	−1.74030e16	−1.79711
$289$	−9.88996e15	−0.998524
$290$	0	0
$291$	1.48088e16	1.42960
$292$	−5.19404e14	−0.0490362
$293$	−8.49847e15	−0.784696	−0.392348	−	0.919817i	$-0.628337\pi$
$293$	−8.49847e15	−0.784696	−0.392348	+	0.919817i	$0.628337\pi$
$294$	1.06601e15	0.0962731
$295$	0	0
$296$	−1.64460e16	−1.42123
$297$	4.38241e15	0.370506
$298$	9.60308e15	0.794337
$299$	5.96400e15	0.482697
$300$	0	0
$301$	7.43348e15	0.576116
$302$	−1.04354e15	−0.0791527
$303$	2.88312e16	2.14035
$304$	1.98518e14	0.0144252
$305$	0	0
$306$	6.21043e14	0.0432446
$307$	2.68116e14	0.0182778	0.00913890	−	0.999958i	$-0.497091\pi$
$307$	2.68116e14	0.0182778	0.00913890	+	0.999958i	$0.497091\pi$
$308$	−2.62815e15	−0.175416
$309$	−1.42317e16	−0.930091
$310$	0	0
$311$	−2.25419e16	−1.41270	−0.706348	−	0.707865i	$-0.749659\pi$
$311$	−2.25419e16	−1.41270	−0.706348	+	0.707865i	$0.749659\pi$
$312$	−5.03544e16	−3.09053
$313$	−2.91559e15	−0.175262	−0.0876312	−	0.996153i	$-0.527930\pi$
$313$	−2.91559e15	−0.175262	−0.0876312	+	0.996153i	$0.527930\pi$
$314$	9.75200e15	0.574184
$315$	0	0
$316$	−1.04197e16	−0.588693
$317$	2.90121e16	1.60581	0.802903	−	0.596109i	$-0.203287\pi$
$317$	2.90121e16	1.60581	0.802903	+	0.596109i	$0.203287\pi$
$318$	2.68643e16	1.45680
$319$	−3.96343e15	−0.210587
$320$	0	0
$321$	1.16202e16	0.592831
$322$	3.42464e15	0.171219
$323$	7.59924e14	0.0372352
$324$	−5.78922e15	−0.278021
$325$	0	0
$326$	1.42751e16	0.658665
$327$	−2.23070e16	−1.00897
$328$	3.02138e16	1.33975
$329$	−2.59393e16	−1.12768
$330$	0	0
$331$	3.67428e16	1.53564	0.767821	−	0.640665i	$-0.221341\pi$
$331$	3.67428e16	1.53564	0.767821	+	0.640665i	$0.221341\pi$
$332$	1.69788e16	0.695841
$333$	−6.35655e16	−2.55466
$334$	−7.74833e15	−0.305391
$335$	0	0
$336$	−6.87166e14	−0.0260529
$337$	−2.62017e16	−0.974395	−0.487197	−	0.873292i	$-0.661981\pi$
$337$	−2.62017e16	−0.974395	−0.487197	+	0.873292i	$0.661981\pi$
$338$	−4.05644e16	−1.47974
$339$	2.75983e16	0.987608
$340$	0	0
$341$	1.55901e15	0.0536964
$342$	3.22861e16	1.09105
$343$	2.86124e16	0.948729
$344$	−1.70199e16	−0.553767
$345$	0	0
$346$	−8.89729e15	−0.278781
$347$	−4.16211e15	−0.127989	−0.0639944	−	0.997950i	$-0.520384\pi$
$347$	−4.16211e15	−0.127989	−0.0639944	+	0.997950i	$0.520384\pi$
$348$	2.60248e16	0.785455
$349$	−3.79966e16	−1.12559	−0.562794	−	0.826597i	$-0.690274\pi$
$349$	−3.79966e16	−1.12559	−0.562794	+	0.826597i	$0.690274\pi$
$350$	0	0
$351$	−8.68393e16	−2.47868
$352$	9.75187e15	0.273250
$353$	−6.24372e16	−1.71754	−0.858772	−	0.512358i	$-0.828772\pi$
$353$	−6.24372e16	−1.71754	−0.858772	+	0.512358i	$0.828772\pi$
$354$	9.50735e15	0.256767
$355$	0	0
$356$	3.61012e16	0.939932
$357$	−2.63046e15	−0.0672494
$358$	1.56241e16	0.392244
$359$	4.66231e16	1.14944	0.574721	−	0.818349i	$-0.305110\pi$
$359$	4.66231e16	1.14944	0.574721	+	0.818349i	$0.305110\pi$
$360$	0	0
$361$	−2.54692e15	−0.0605646
$362$	7.86645e15	0.183727
$363$	6.75111e16	1.54875
$364$	5.20779e16	1.17353
$365$	0	0
$366$	5.86105e16	1.27452
$367$	5.72445e16	1.22294	0.611469	−	0.791269i	$-0.290579\pi$
$367$	5.72445e16	1.22294	0.611469	+	0.791269i	$0.290579\pi$
$368$	−1.86348e14	−0.00391124
$369$	1.16779e17	2.40821
$370$	0	0
$371$	−7.32298e16	−1.45800
$372$	−1.02368e16	−0.200279
$373$	2.68476e16	0.516176	0.258088	−	0.966121i	$-0.416908\pi$
$373$	2.68476e16	0.516176	0.258088	+	0.966121i	$0.416908\pi$
$374$	−3.48004e14	−0.00657535
$375$	0	0
$376$	5.93913e16	1.08393
$377$	7.85371e16	1.40882
$378$	−4.98648e16	−0.879219
$379$	3.18194e16	0.551489	0.275744	−	0.961231i	$-0.411076\pi$
$379$	3.18194e16	0.551489	0.275744	+	0.961231i	$0.411076\pi$
$380$	0	0
$381$	−2.21046e16	−0.370228
$382$	−3.62652e16	−0.597143
$383$	−1.08164e17	−1.75101	−0.875505	−	0.483208i	$-0.839471\pi$
$383$	−1.08164e17	−1.75101	−0.875505	+	0.483208i	$0.839471\pi$
$384$	−6.30565e16	−1.00364
$385$	0	0
$386$	−6.90719e15	−0.106288
$387$	−6.57837e16	−0.995398
$388$	3.50670e16	0.521786
$389$	−9.51462e16	−1.39226	−0.696128	−	0.717918i	$-0.745095\pi$
$389$	−9.51462e16	−1.39226	−0.696128	+	0.717918i	$0.745095\pi$
$390$	0	0
$391$	−7.13339e14	−0.0100959
$392$	6.65333e15	0.0926146
$393$	−1.77619e16	−0.243185
$394$	−7.72543e16	−1.04039
$395$	0	0
$396$	2.32582e16	0.303079
$397$	4.83241e16	0.619477	0.309739	−	0.950822i	$-0.399758\pi$
$397$	4.83241e16	0.619477	0.309739	+	0.950822i	$0.399758\pi$
$398$	8.54160e16	1.07721
$399$	−1.36749e17	−1.69669
$400$	0	0
$401$	4.29285e16	0.515593	0.257797	−	0.966199i	$-0.417004\pi$
$401$	4.29285e16	0.515593	0.257797	+	0.966199i	$0.417004\pi$
$402$	−2.68992e16	−0.317885
$403$	−3.08925e16	−0.359228
$404$	6.82719e16	0.781202
$405$	0	0
$406$	4.50975e16	0.499727
$407$	3.56192e16	0.388437
$408$	6.02277e15	0.0646405
$409$	8.36651e16	0.883777	0.441889	−	0.897070i	$-0.354309\pi$
$409$	8.36651e16	0.883777	0.441889	+	0.897070i	$0.354309\pi$
$410$	0	0
$411$	5.55921e16	0.568907
$412$	−3.37004e16	−0.339472
$413$	−2.59162e16	−0.256978
$414$	−3.03068e16	−0.295827
$415$	0	0
$416$	−1.93238e17	−1.82804
$417$	−1.44454e17	−1.34538
$418$	−1.80916e16	−0.165894
$419$	−1.35543e17	−1.22373	−0.611865	−	0.790962i	$-0.709580\pi$
$419$	−1.35543e17	−1.22373	−0.611865	+	0.790962i	$0.709580\pi$
$420$	0	0
$421$	5.25025e16	0.459565	0.229782	−	0.973242i	$-0.426199\pi$
$421$	5.25025e16	0.459565	0.229782	+	0.973242i	$0.426199\pi$
$422$	−8.00150e16	−0.689669
$423$	2.29554e17	1.94837
$424$	1.67669e17	1.40144
$425$	0	0
$426$	−7.76705e16	−0.629642
$427$	−1.59767e17	−1.27557
$428$	2.75165e16	0.216376
$429$	1.09059e17	0.844675
$430$	0	0
$431$	2.51192e15	0.0188757	0.00943785	−	0.999955i	$-0.496996\pi$
$431$	2.51192e15	0.0188757	0.00943785	+	0.999955i	$0.496996\pi$
$432$	2.71334e15	0.0200845
$433$	7.31447e16	0.533349	0.266675	−	0.963787i	$-0.414075\pi$
$433$	7.31447e16	0.533349	0.266675	+	0.963787i	$0.414075\pi$
$434$	−1.77390e16	−0.127423
$435$	0	0
$436$	−5.28227e16	−0.368263
$437$	−3.70842e16	−0.254718
$438$	1.23764e16	0.0837556
$439$	−7.23430e16	−0.482367	−0.241183	−	0.970480i	$-0.577536\pi$
$439$	−7.23430e16	−0.482367	−0.241183	+	0.970480i	$0.577536\pi$
$440$	0	0
$441$	2.57158e16	0.166475
$442$	6.89585e15	0.0439889
$443$	−2.25527e17	−1.41767	−0.708833	−	0.705377i	$-0.750778\pi$
$443$	−2.25527e17	−1.41767	−0.708833	+	0.705377i	$0.750778\pi$
$444$	−2.33884e17	−1.44881
$445$	0	0
$446$	−1.96751e17	−1.18370
$447$	3.59954e17	2.13426
$448$	−1.13622e17	−0.663982
$449$	5.33358e16	0.307197	0.153599	−	0.988133i	$-0.450914\pi$
$449$	5.33358e16	0.307197	0.153599	+	0.988133i	$0.450914\pi$
$450$	0	0
$451$	−6.54379e16	−0.366169
$452$	6.53525e16	0.360464
$453$	−3.91153e16	−0.212671
$454$	8.11659e16	0.435022
$455$	0	0
$456$	3.13105e17	1.63087
$457$	9.83492e16	0.505028	0.252514	−	0.967593i	$-0.418743\pi$
$457$	9.83492e16	0.505028	0.252514	+	0.967593i	$0.418743\pi$
$458$	−5.66087e15	−0.0286588
$459$	1.03866e16	0.0518433
$460$	0	0
$461$	2.01882e17	0.979583	0.489791	−	0.871840i	$-0.337073\pi$
$461$	2.01882e17	0.979583	0.489791	+	0.871840i	$0.337073\pi$
$462$	6.26238e16	0.299617
$463$	1.21471e17	0.573057	0.286528	−	0.958072i	$-0.407499\pi$
$463$	1.21471e17	0.573057	0.286528	+	0.958072i	$0.407499\pi$
$464$	−2.45394e15	−0.0114155
$465$	0	0
$466$	5.92045e16	0.267822
$467$	−4.32550e17	−1.92964	−0.964820	−	0.262910i	$-0.915318\pi$
$467$	−4.32550e17	−1.92964	−0.964820	+	0.262910i	$0.915318\pi$
$468$	−4.60871e17	−2.02759
$469$	7.33249e16	0.318147
$470$	0	0
$471$	3.65536e17	1.54274
$472$	5.93384e16	0.247009
$473$	3.68622e16	0.151350
$474$	2.48282e17	1.00551
$475$	0	0
$476$	−6.22890e15	−0.0245452
$477$	6.48057e17	2.51909
$478$	2.64161e17	1.01295
$479$	−1.80742e17	−0.683719	−0.341860	−	0.939751i	$-0.611057\pi$
$479$	−1.80742e17	−0.683719	−0.341860	+	0.939751i	$0.611057\pi$
$480$	0	0
$481$	−7.05810e17	−2.59863
$482$	6.92268e16	0.251460
$483$	1.28366e17	0.460039
$484$	1.59865e17	0.565275
$485$	0	0
$486$	−1.06443e17	−0.366422
$487$	−1.79248e17	−0.608858	−0.304429	−	0.952535i	$-0.598466\pi$
$487$	−1.79248e17	−0.608858	−0.304429	+	0.952535i	$0.598466\pi$
$488$	3.65806e17	1.22609
$489$	5.35076e17	1.76973
$490$	0	0
$491$	3.27397e17	1.05450	0.527248	−	0.849712i	$-0.323224\pi$
$491$	3.27397e17	1.05450	0.527248	+	0.849712i	$0.323224\pi$
$492$	4.29680e17	1.36575
$493$	−9.39362e15	−0.0294665
$494$	3.58494e17	1.10983
$495$	0	0
$496$	9.65252e14	0.00291078
$497$	2.11723e17	0.630161
$498$	−4.04573e17	−1.18852
$499$	−4.14032e17	−1.20055	−0.600275	−	0.799794i	$-0.704942\pi$
$499$	−4.14032e17	−1.20055	−0.600275	+	0.799794i	$0.704942\pi$
$500$	0	0
$501$	−2.90432e17	−0.820539
$502$	1.54745e17	0.431562
$503$	−1.04795e17	−0.288503	−0.144251	−	0.989541i	$-0.546077\pi$
$503$	−1.04795e17	−0.288503	−0.144251	+	0.989541i	$0.546077\pi$
$504$	−6.97514e17	−1.89563
$505$	0	0
$506$	1.69826e16	0.0449806
$507$	−1.52048e18	−3.97584
$508$	−5.23434e16	−0.135129
$509$	4.12726e17	1.05195	0.525976	−	0.850499i	$-0.323700\pi$
$509$	4.12726e17	1.05195	0.525976	+	0.850499i	$0.323700\pi$
$510$	0	0
$511$	−3.37371e16	−0.0838246
$512$	1.21319e16	0.0297629
$513$	5.39968e17	1.30799
$514$	−2.23885e17	−0.535507
$515$	0	0
$516$	−2.42045e17	−0.564512
$517$	−1.28632e17	−0.296250
$518$	−4.05290e17	−0.921769
$519$	−3.33499e17	−0.749042
$520$	0	0
$521$	2.21835e17	0.485942	0.242971	−	0.970034i	$-0.421878\pi$
$521$	2.21835e17	0.485942	0.242971	+	0.970034i	$0.421878\pi$
$522$	−3.99097e17	−0.863415
$523$	−7.40537e17	−1.58229	−0.791145	−	0.611629i	$-0.790514\pi$
$523$	−7.40537e17	−1.58229	−0.791145	+	0.611629i	$0.790514\pi$
$524$	−4.20600e16	−0.0887596
$525$	0	0
$526$	2.36476e17	0.486833
$527$	3.69497e15	0.00751349
$528$	−3.40762e15	−0.00684432
$529$	−4.69225e17	−0.930936
$530$	0	0
$531$	2.29349e17	0.444000
$532$	−3.23821e17	−0.619269
$533$	1.29668e18	2.44966
$534$	−8.60224e17	−1.60544
$535$	0	0
$536$	−1.67886e17	−0.305805
$537$	5.85642e17	1.05390
$538$	−6.79435e16	−0.120799
$539$	−1.44100e16	−0.0253126
$540$	0	0
$541$	1.10461e18	1.89420	0.947101	−	0.320936i	$-0.103997\pi$
$541$	1.10461e18	1.89420	0.947101	+	0.320936i	$0.103997\pi$
$542$	−4.61304e17	−0.781613
$543$	2.94859e17	0.493646
$544$	2.31127e16	0.0382347
$545$	0	0
$546$	−1.24092e18	−2.00443
$547$	6.13521e17	0.979292	0.489646	−	0.871921i	$-0.337126\pi$
$547$	6.13521e17	0.979292	0.489646	+	0.871921i	$0.337126\pi$
$548$	1.31641e17	0.207644
$549$	1.41388e18	2.20390
$550$	0	0
$551$	−4.88345e17	−0.743432
$552$	−2.93911e17	−0.442192
$553$	−6.76795e17	−1.00634
$554$	3.19086e17	0.468915
$555$	0	0
$556$	−3.42066e17	−0.491048
$557$	2.17270e17	0.308276	0.154138	−	0.988049i	$-0.450740\pi$
$557$	2.17270e17	0.308276	0.154138	+	0.988049i	$0.450740\pi$
$558$	1.56984e17	0.220157
$559$	−7.30440e17	−1.01253
$560$	0	0
$561$	−1.30443e16	−0.0176670
$562$	7.84080e17	1.04972
$563$	1.16883e18	1.54684	0.773422	−	0.633892i	$-0.218543\pi$
$563$	1.16883e18	1.54684	0.773422	+	0.633892i	$0.218543\pi$
$564$	8.44623e17	1.10497
$565$	0	0
$566$	9.51066e17	1.21592
$567$	−3.76030e17	−0.475261
$568$	−4.84766e17	−0.605715
$569$	−4.86769e17	−0.601302	−0.300651	−	0.953734i	$-0.597204\pi$
$569$	−4.86769e17	−0.601302	−0.300651	+	0.953734i	$0.597204\pi$
$570$	0	0
$571$	−3.75968e17	−0.453958	−0.226979	−	0.973900i	$-0.572885\pi$
$571$	−3.75968e17	−0.453958	−0.226979	+	0.973900i	$0.572885\pi$
$572$	2.58251e17	0.308296
$573$	−1.35934e18	−1.60443
$574$	7.44578e17	0.868926
$575$	0	0
$576$	1.00552e18	1.14721
$577$	−2.49769e17	−0.281771	−0.140885	−	0.990026i	$-0.544995\pi$
$577$	−2.49769e17	−0.281771	−0.140885	+	0.990026i	$0.544995\pi$
$578$	5.58039e17	0.622491
$579$	−2.58903e17	−0.285579
$580$	0	0
$581$	1.10283e18	1.18950
$582$	−8.35581e17	−0.891228
$583$	−3.63142e17	−0.383028
$584$	7.72452e16	0.0805728
$585$	0	0
$586$	4.79524e17	0.489188
$587$	1.02718e18	1.03633	0.518165	−	0.855281i	$-0.326615\pi$
$587$	1.02718e18	1.03633	0.518165	+	0.855281i	$0.326615\pi$
$588$	9.46191e16	0.0944118
$589$	1.92090e17	0.189564
$590$	0	0
$591$	−2.89574e18	−2.79538
$592$	2.20534e16	0.0210565
$593$	−1.25381e18	−1.18406	−0.592032	−	0.805914i	$-0.701674\pi$
$593$	−1.25381e18	−1.18406	−0.592032	+	0.805914i	$0.701674\pi$
$594$	−2.47276e17	−0.230978
$595$	0	0
$596$	8.52367e17	0.778979
$597$	3.20166e18	2.89429
$598$	−3.36517e17	−0.300919
$599$	−5.76424e17	−0.509879	−0.254940	−	0.966957i	$-0.582056\pi$
$599$	−5.76424e17	−0.509879	−0.254940	+	0.966957i	$0.582056\pi$
$600$	0	0
$601$	−1.23224e18	−1.06663	−0.533313	−	0.845918i	$-0.679053\pi$
$601$	−1.23224e18	−1.06663	−0.533313	+	0.845918i	$0.679053\pi$
$602$	−4.19433e17	−0.359158
$603$	−6.48899e17	−0.549686
$604$	−9.26247e16	−0.0776223
$605$	0	0
$606$	−1.62679e18	−1.33432
$607$	−1.17936e18	−0.957019	−0.478510	−	0.878082i	$-0.658823\pi$
$607$	−1.17936e18	−0.957019	−0.478510	+	0.878082i	$0.658823\pi$
$608$	1.20156e18	0.964651
$609$	1.69040e18	1.34269
$610$	0	0
$611$	2.54889e18	1.98191
$612$	5.51236e16	0.0424085
$613$	−7.39177e17	−0.562672	−0.281336	−	0.959609i	$-0.590778\pi$
$613$	−7.39177e17	−0.562672	−0.281336	+	0.959609i	$0.590778\pi$
$614$	−1.51284e16	−0.0113946
$615$	0	0
$616$	3.90855e17	0.288231
$617$	−2.13054e18	−1.55467	−0.777333	−	0.629090i	$-0.783428\pi$
$617$	−2.13054e18	−1.55467	−0.777333	+	0.629090i	$0.783428\pi$
$618$	8.03018e17	0.579830
$619$	1.66755e18	1.19149	0.595744	−	0.803175i	$-0.296857\pi$
$619$	1.66755e18	1.19149	0.595744	+	0.803175i	$0.296857\pi$
$620$	0	0
$621$	−5.06867e17	−0.354649
$622$	1.27192e18	0.880691
$623$	2.34489e18	1.60676
$624$	6.75234e16	0.0457883
$625$	0	0
$626$	1.64512e17	0.109261
$627$	−6.78132e17	−0.445733
$628$	8.65584e17	0.563082
$629$	8.44202e16	0.0543522
$630$	0	0
$631$	−7.05851e16	−0.0445166	−0.0222583	−	0.999752i	$-0.507086\pi$
$631$	−7.05851e16	−0.0445166	−0.0222583	+	0.999752i	$0.507086\pi$
$632$	1.54961e18	0.967298
$633$	−2.99922e18	−1.85304
$634$	−1.63700e18	−1.00108
$635$	0	0
$636$	2.38447e18	1.42863
$637$	2.85540e17	0.169340
$638$	2.23636e17	0.131282
$639$	−1.87367e18	−1.08878
$640$	0	0
$641$	−2.27477e18	−1.29527	−0.647635	−	0.761951i	$-0.724242\pi$
$641$	−2.27477e18	−1.29527	−0.647635	+	0.761951i	$0.724242\pi$
$642$	−6.55667e17	−0.369578
$643$	1.40077e18	0.781621	0.390810	−	0.920471i	$-0.372195\pi$
$643$	1.40077e18	0.781621	0.390810	+	0.920471i	$0.372195\pi$
$644$	3.03970e17	0.167908
$645$	0	0
$646$	−4.28785e16	−0.0232129
$647$	−3.49376e18	−1.87247	−0.936237	−	0.351369i	$-0.885716\pi$
$647$	−3.49376e18	−1.87247	−0.936237	+	0.351369i	$0.885716\pi$
$648$	8.60967e17	0.456824
$649$	−1.28517e17	−0.0675102
$650$	0	0
$651$	−6.64915e17	−0.342365
$652$	1.26705e18	0.645930
$653$	−4.17303e17	−0.210628	−0.105314	−	0.994439i	$-0.533585\pi$
$653$	−4.17303e17	−0.210628	−0.105314	+	0.994439i	$0.533585\pi$
$654$	1.25867e18	0.629006
$655$	0	0
$656$	−4.05155e16	−0.0198494
$657$	2.98561e17	0.144830
$658$	1.46362e18	0.703008
$659$	−2.83630e18	−1.34895	−0.674477	−	0.738296i	$-0.735631\pi$
$659$	−2.83630e18	−1.34895	−0.674477	+	0.738296i	$0.735631\pi$
$660$	0	0
$661$	8.05065e17	0.375423	0.187712	−	0.982224i	$-0.439893\pi$
$661$	8.05065e17	0.375423	0.187712	+	0.982224i	$0.439893\pi$
$662$	−2.07320e18	−0.957336
$663$	2.58478e17	0.118192
$664$	−2.52507e18	−1.14335
$665$	0	0
$666$	3.58667e18	1.59261
$667$	4.58408e17	0.201574
$668$	−6.87740e17	−0.299486
$669$	−7.37486e18	−3.18042
$670$	0	0
$671$	−7.92274e17	−0.335104
$672$	−4.15916e18	−1.74223
$673$	−3.03151e18	−1.25765	−0.628827	−	0.777546i	$-0.716465\pi$
$673$	−3.03151e18	−1.25765	−0.628827	+	0.777546i	$0.716465\pi$
$674$	1.47842e18	0.607449
$675$	0	0
$676$	−3.60048e18	−1.45113
$677$	1.58711e18	0.633551	0.316775	−	0.948501i	$-0.397400\pi$
$677$	1.58711e18	0.633551	0.316775	+	0.948501i	$0.397400\pi$
$678$	−1.55723e18	−0.615686
$679$	2.27772e18	0.891963
$680$	0	0
$681$	3.04236e18	1.16884
$682$	−8.79667e16	−0.0334749
$683$	−9.37243e17	−0.353279	−0.176640	−	0.984276i	$-0.556523\pi$
$683$	−9.37243e17	−0.353279	−0.176640	+	0.984276i	$0.556523\pi$
$684$	2.86570e18	1.06996
$685$	0	0
$686$	−1.61445e18	−0.591449
$687$	−2.12187e17	−0.0770018
$688$	2.28230e16	0.00820443
$689$	7.19582e18	2.56245
$690$	0	0
$691$	−4.89005e18	−1.70886	−0.854428	−	0.519569i	$-0.826093\pi$
$691$	−4.89005e18	−1.70886	−0.854428	+	0.519569i	$0.826093\pi$
$692$	−7.89721e17	−0.273391
$693$	1.51070e18	0.518097
$694$	2.34846e17	0.0797897
$695$	0	0
$696$	−3.87037e18	−1.29060
$697$	−1.55093e17	−0.0512364
$698$	2.14395e18	0.701704
$699$	2.21917e18	0.719597
$700$	0	0
$701$	1.21554e18	0.386902	0.193451	−	0.981110i	$-0.438032\pi$
$701$	1.21554e18	0.386902	0.193451	+	0.981110i	$0.438032\pi$
$702$	4.89989e18	1.54524
$703$	4.38874e18	1.37129
$704$	−5.63446e17	−0.174433
$705$	0	0
$706$	3.52300e18	1.07074
$707$	4.43449e18	1.33542
$708$	8.43870e17	0.251802
$709$	2.62006e18	0.774658	0.387329	−	0.921942i	$-0.373398\pi$
$709$	2.62006e18	0.774658	0.387329	+	0.921942i	$0.373398\pi$
$710$	0	0
$711$	5.98939e18	1.73872
$712$	−5.36893e18	−1.54443
$713$	−1.80314e17	−0.0513982
$714$	1.48423e17	0.0419240
$715$	0	0
$716$	1.38679e18	0.384660
$717$	9.90160e18	2.72164
$718$	−2.63070e18	−0.716576
$719$	−2.75759e18	−0.744375	−0.372187	−	0.928158i	$-0.621392\pi$
$719$	−2.75759e18	−0.744375	−0.372187	+	0.928158i	$0.621392\pi$
$720$	0	0
$721$	−2.18896e18	−0.580307
$722$	1.43710e17	0.0377567
$723$	2.59484e18	0.675634
$724$	6.98224e17	0.180175
$725$	0	0
$726$	−3.80930e18	−0.965510
$727$	−5.02204e18	−1.26156	−0.630778	−	0.775963i	$-0.717264\pi$
$727$	−5.02204e18	−1.26156	−0.630778	+	0.775963i	$0.717264\pi$
$728$	−7.74496e18	−1.92826
$729$	−5.83276e18	−1.43928
$730$	0	0
$731$	8.73661e16	0.0211778
$732$	5.20225e18	1.24988
$733$	4.44902e17	0.105947	0.0529734	−	0.998596i	$-0.483130\pi$
$733$	4.44902e17	0.105947	0.0529734	+	0.998596i	$0.483130\pi$
$734$	−3.23001e18	−0.762393
$735$	0	0
$736$	−1.12790e18	−0.261555
$737$	3.63614e17	0.0835798
$738$	−6.58925e18	−1.50131
$739$	7.66043e18	1.73007	0.865037	−	0.501709i	$-0.167295\pi$
$739$	7.66043e18	1.73007	0.865037	+	0.501709i	$0.167295\pi$
$740$	0	0
$741$	1.34375e19	2.98194
$742$	4.13197e18	0.908933
$743$	−2.91989e18	−0.636706	−0.318353	−	0.947972i	$-0.603130\pi$
$743$	−2.91989e18	−0.636706	−0.318353	+	0.947972i	$0.603130\pi$
$744$	1.52241e18	0.329084
$745$	0	0
$746$	−1.51487e18	−0.321790
$747$	−9.75967e18	−2.05519
$748$	−3.08887e16	−0.00644822
$749$	1.78729e18	0.369882
$750$	0	0
$751$	1.98445e18	0.403628	0.201814	−	0.979424i	$-0.435316\pi$
$751$	1.98445e18	0.403628	0.201814	+	0.979424i	$0.435316\pi$
$752$	−7.96415e16	−0.0160592
$753$	5.80034e18	1.15954
$754$	−4.43144e18	−0.878276
$755$	0	0
$756$	−4.42598e18	−0.862220
$757$	4.46722e18	0.862807	0.431404	−	0.902159i	$-0.358018\pi$
$757$	4.46722e18	0.862807	0.431404	+	0.902159i	$0.358018\pi$
$758$	−1.79540e18	−0.343805
$759$	6.36560e17	0.120856
$760$	0	0
$761$	−7.81343e18	−1.45828	−0.729141	−	0.684363i	$-0.760080\pi$
$761$	−7.81343e18	−1.45828	−0.729141	+	0.684363i	$0.760080\pi$
$762$	1.24724e18	0.230805
$763$	−3.43101e18	−0.629525
$764$	−3.21889e18	−0.585598
$765$	0	0
$766$	6.10310e18	1.09160
$767$	2.54662e18	0.451642
$768$	9.60957e18	1.68988
$769$	2.15334e17	0.0375483	0.0187742	−	0.999824i	$-0.494024\pi$
$769$	2.15334e17	0.0375483	0.0187742	+	0.999824i	$0.494024\pi$
$770$	0	0
$771$	−8.39193e18	−1.43883
$772$	−6.13080e17	−0.104233
$773$	7.73551e18	1.30413	0.652067	−	0.758162i	$-0.273902\pi$
$773$	7.73551e18	1.30413	0.652067	+	0.758162i	$0.273902\pi$
$774$	3.71183e18	0.620543
$775$	0	0
$776$	−5.21512e18	−0.857360
$777$	−1.51915e19	−2.47665
$778$	5.36860e18	0.867948
$779$	−8.06278e18	−1.29268
$780$	0	0
$781$	1.04992e18	0.165548
$782$	4.02500e16	0.00629392
$783$	−6.67469e18	−1.03509
$784$	−8.92186e15	−0.00137215
$785$	0	0
$786$	1.00221e18	0.151605
$787$	−7.07633e18	−1.06163	−0.530814	−	0.847488i	$-0.678114\pi$
$787$	−7.07633e18	−1.06163	−0.530814	+	0.847488i	$0.678114\pi$
$788$	−6.85707e18	−1.02028
$789$	8.86387e18	1.30805
$790$	0	0
$791$	4.24487e18	0.616193
$792$	−3.45893e18	−0.497998
$793$	1.56993e19	2.24184
$794$	−2.72668e18	−0.386189
$795$	0	0
$796$	7.58150e18	1.05638
$797$	−8.43425e17	−0.116565	−0.0582824	−	0.998300i	$-0.518562\pi$
$797$	−8.43425e17	−0.116565	−0.0582824	+	0.998300i	$0.518562\pi$
$798$	7.71605e18	1.05773
$799$	−3.04866e17	−0.0414529
$800$	0	0
$801$	−2.07515e19	−2.77612
$802$	−2.42223e18	−0.321427
$803$	−1.67300e17	−0.0220214
$804$	−2.38757e18	−0.311739
$805$	0	0
$806$	1.74310e18	0.223947
$807$	−2.54674e18	−0.324568
$808$	−1.01533e19	−1.28361
$809$	5.80962e18	0.728588	0.364294	−	0.931284i	$-0.381310\pi$
$809$	5.80962e18	0.728588	0.364294	+	0.931284i	$0.381310\pi$
$810$	0	0
$811$	1.15747e19	1.42848	0.714240	−	0.699901i	$-0.246773\pi$
$811$	1.15747e19	1.42848	0.714240	+	0.699901i	$0.246773\pi$
$812$	4.00284e18	0.490065
$813$	−1.72911e19	−2.10008
$814$	−2.00981e18	−0.242156
$815$	0	0
$816$	−8.07630e15	−0.000957694 0
$817$	4.54189e18	0.534310
$818$	−4.72078e18	−0.550957
$819$	−2.99351e19	−3.46606
$820$	0	0
$821$	4.73256e18	0.539343	0.269672	−	0.962952i	$-0.413085\pi$
$821$	4.73256e18	0.539343	0.269672	+	0.962952i	$0.413085\pi$
$822$	−3.13677e18	−0.354663
$823$	−5.39004e18	−0.604634	−0.302317	−	0.953207i	$-0.597760\pi$
$823$	−5.39004e18	−0.604634	−0.302317	+	0.953207i	$0.597760\pi$
$824$	5.01189e18	0.557795
$825$	0	0
$826$	1.46232e18	0.160203
$827$	4.87314e18	0.529692	0.264846	−	0.964291i	$-0.414679\pi$
$827$	4.87314e18	0.529692	0.264846	+	0.964291i	$0.414679\pi$
$828$	−2.69003e18	−0.290108
$829$	−1.10498e19	−1.18236	−0.591182	−	0.806538i	$-0.701339\pi$
$829$	−1.10498e19	−1.18236	−0.591182	+	0.806538i	$0.701339\pi$
$830$	0	0
$831$	1.19603e19	1.25990
$832$	1.11649e19	1.16696
$833$	−3.41527e16	−0.00354187
$834$	8.15080e18	0.838728
$835$	0	0
$836$	−1.60581e18	−0.162687
$837$	2.62548e18	0.263933
$838$	7.64797e18	0.762887
$839$	8.80967e17	0.0871981	0.0435990	−	0.999049i	$-0.486118\pi$
$839$	8.80967e17	0.0871981	0.0435990	+	0.999049i	$0.486118\pi$
$840$	0	0
$841$	−4.22407e18	−0.411677
$842$	−2.96244e18	−0.286498
$843$	2.93898e19	2.82044
$844$	−7.10211e18	−0.676335
$845$	0	0
$846$	−1.29525e19	−1.21464
$847$	1.03838e19	0.966305
$848$	−2.24837e17	−0.0207633
$849$	3.56490e19	3.26698
$850$	0	0
$851$	−4.11970e18	−0.371812
$852$	−6.89401e18	−0.617469
$853$	5.43444e18	0.483043	0.241522	−	0.970395i	$-0.422354\pi$
$853$	5.43444e18	0.483043	0.241522	+	0.970395i	$0.422354\pi$
$854$	9.01481e18	0.795208
$855$	0	0
$856$	−4.09223e18	−0.355533
$857$	−3.79499e18	−0.327217	−0.163608	−	0.986525i	$-0.552313\pi$
$857$	−3.79499e18	−0.327217	−0.163608	+	0.986525i	$0.552313\pi$
$858$	−6.15364e18	−0.526580
$859$	−1.65792e17	−0.0140802	−0.00704010	−	0.999975i	$-0.502241\pi$
$859$	−1.65792e17	−0.0140802	−0.00704010	+	0.999975i	$0.502241\pi$
$860$	0	0
$861$	2.79091e19	2.33467
$862$	−1.41734e17	−0.0117673
$863$	−1.66111e19	−1.36877	−0.684383	−	0.729123i	$-0.739928\pi$
$863$	−1.66111e19	−1.36877	−0.684383	+	0.729123i	$0.739928\pi$
$864$	1.64228e19	1.34310
$865$	0	0
$866$	−4.12717e18	−0.332496
$867$	2.09171e19	1.67254
$868$	−1.57451e18	−0.124959
$869$	−3.35618e18	−0.264373
$870$	0	0
$871$	−7.20517e18	−0.559147
$872$	7.85573e18	0.605103
$873$	−2.01570e19	−1.54111
$874$	2.09247e18	0.158794
$875$	0	0
$876$	1.09853e18	0.0821363
$877$	2.03717e18	0.151192	0.0755960	−	0.997139i	$-0.475914\pi$
$877$	2.03717e18	0.151192	0.0755960	+	0.997139i	$0.475914\pi$
$878$	4.08194e18	0.300713
$879$	1.79741e19	1.31437
$880$	0	0
$881$	−1.97226e19	−1.42109	−0.710545	−	0.703652i	$-0.751551\pi$
$881$	−1.97226e19	−1.42109	−0.710545	+	0.703652i	$0.751551\pi$
$882$	−1.45101e18	−0.103783
$883$	−4.19713e18	−0.297994	−0.148997	−	0.988838i	$-0.547604\pi$
$883$	−4.19713e18	−0.297994	−0.148997	+	0.988838i	$0.547604\pi$
$884$	6.12074e17	0.0431384
$885$	0	0
$886$	1.27253e19	0.883789
$887$	6.63464e18	0.457418	0.228709	−	0.973495i	$-0.426550\pi$
$887$	6.63464e18	0.457418	0.228709	+	0.973495i	$0.426550\pi$
$888$	3.47829e19	2.38057
$889$	−3.39988e18	−0.230995
$890$	0	0
$891$	−1.86471e18	−0.124855
$892$	−1.74636e19	−1.16081
$893$	−1.58490e19	−1.04585
$894$	−2.03103e19	−1.33052
$895$	0	0
$896$	−9.69866e18	−0.626195
$897$	−1.26137e19	−0.808523
$898$	−3.00946e18	−0.191510
$899$	−2.37447e18	−0.150013
$900$	0	0
$901$	−8.60673e17	−0.0535954
$902$	3.69232e18	0.228274
$903$	−1.57217e19	−0.965002
$904$	−9.71915e18	−0.592289
$905$	0	0
$906$	2.20707e18	0.132582
$907$	−5.59272e18	−0.333561	−0.166781	−	0.985994i	$-0.553337\pi$
$907$	−5.59272e18	−0.333561	−0.166781	+	0.985994i	$0.553337\pi$
$908$	7.20427e18	0.426611
$909$	−3.92437e19	−2.30730
$910$	0	0
$911$	4.19586e18	0.243193	0.121597	−	0.992580i	$-0.461199\pi$
$911$	4.19586e18	0.243193	0.121597	+	0.992580i	$0.461199\pi$
$912$	−4.19862e17	−0.0241624
$913$	5.46887e18	0.312491
$914$	−5.54933e18	−0.314840
$915$	0	0
$916$	−5.02458e17	−0.0281047
$917$	−2.73194e18	−0.151730
$918$	−5.86063e17	−0.0323197
$919$	6.83436e18	0.374237	0.187119	−	0.982337i	$-0.440085\pi$
$919$	6.83436e18	0.374237	0.187119	+	0.982337i	$0.440085\pi$
$920$	0	0
$921$	−5.67061e17	−0.0306155
$922$	−1.13911e19	−0.610683
$923$	−2.08047e19	−1.10751
$924$	5.55847e18	0.293824
$925$	0	0
$926$	−6.85399e18	−0.357250
$927$	1.93715e19	1.00264
$928$	−1.48527e19	−0.763387
$929$	−7.68529e18	−0.392246	−0.196123	−	0.980579i	$-0.562835\pi$
$929$	−7.68529e18	−0.392246	−0.196123	+	0.980579i	$0.562835\pi$
$930$	0	0
$931$	−1.77549e18	−0.0893606
$932$	5.25497e18	0.262644
$933$	4.76757e19	2.36628
$934$	2.44065e19	1.20296
$935$	0	0
$936$	6.85402e19	3.33159
$937$	−1.82302e19	−0.880004	−0.440002	−	0.897997i	$-0.645022\pi$
$937$	−1.82302e19	−0.880004	−0.440002	+	0.897997i	$0.645022\pi$
$938$	−4.13734e18	−0.198337
$939$	6.16641e18	0.293566
$940$	0	0
$941$	4.01498e18	0.188517	0.0942586	−	0.995548i	$-0.469952\pi$
$941$	4.01498e18	0.188517	0.0942586	+	0.995548i	$0.469952\pi$
$942$	−2.06253e19	−0.961764
$943$	7.56851e18	0.350497
$944$	−7.95705e16	−0.00365961
$945$	0	0
$946$	−2.07994e18	−0.0943536
$947$	−2.28347e19	−1.02877	−0.514387	−	0.857558i	$-0.671980\pi$
$947$	−2.28347e19	−1.02877	−0.514387	+	0.857558i	$0.671980\pi$
$948$	2.20374e19	0.986068
$949$	3.31513e18	0.147323
$950$	0	0
$951$	−6.13599e19	−2.68975
$952$	9.26355e17	0.0403309
$953$	3.72340e19	1.61004	0.805018	−	0.593250i	$-0.202155\pi$
$953$	3.72340e19	1.61004	0.805018	+	0.593250i	$0.202155\pi$
$954$	−3.65665e19	−1.57043
$955$	0	0
$956$	2.34469e19	0.993364
$957$	8.38257e18	0.352736
$958$	1.01983e19	0.426238
$959$	8.55056e18	0.354955
$960$	0	0
$961$	−2.34836e19	−0.961749
$962$	3.98252e19	1.62002
$963$	−1.58169e19	−0.639073
$964$	6.14455e18	0.246598
$965$	0	0
$966$	−7.24304e18	−0.286794
$967$	−1.86235e19	−0.732471	−0.366235	−	0.930522i	$-0.619353\pi$
$967$	−1.86235e19	−0.732471	−0.366235	+	0.930522i	$0.619353\pi$
$968$	−2.37750e19	−0.928818
$969$	−1.60722e18	−0.0623694
$970$	0	0
$971$	−4.46491e19	−1.70957	−0.854787	−	0.518980i	$-0.826312\pi$
$971$	−4.46491e19	−1.70957	−0.854787	+	0.518980i	$0.826312\pi$
$972$	−9.44786e18	−0.359338
$973$	−2.22184e19	−0.839419
$974$	1.01140e19	0.379569
$975$	0	0
$976$	−4.90533e17	−0.0181654
$977$	−3.67191e19	−1.35076	−0.675378	−	0.737471i	$-0.736020\pi$
$977$	−3.67191e19	−1.35076	−0.675378	+	0.737471i	$0.736020\pi$
$978$	−3.01915e19	−1.10327
$979$	1.16282e19	0.422109
$980$	0	0
$981$	3.03632e19	1.08768
$982$	−1.84733e19	−0.657384
$983$	1.84031e19	0.650570	0.325285	−	0.945616i	$-0.394540\pi$
$983$	1.84031e19	0.650570	0.325285	+	0.945616i	$0.394540\pi$
$984$	−6.39015e19	−2.24410
$985$	0	0
$986$	5.30033e17	0.0183697
$987$	5.48611e19	1.88888
$988$	3.18198e19	1.08837
$989$	−4.26346e18	−0.144873
$990$	0	0
$991$	5.17113e19	1.73423	0.867115	−	0.498108i	$-0.165972\pi$
$991$	5.17113e19	1.73423	0.867115	+	0.498108i	$0.165972\pi$
$992$	5.84231e18	0.194652
$993$	−7.77102e19	−2.57222
$994$	−1.19464e19	−0.392850
$995$	0	0
$996$	−3.59098e19	−1.16554
$997$	4.39824e19	1.41827	0.709137	−	0.705071i	$-0.249085\pi$
$997$	4.39824e19	1.41827	0.709137	+	0.705071i	$0.249085\pi$
$998$	2.33617e19	0.748437
$999$	5.99853e19	1.90928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.14.a.b.1.2		3
5.2	odd	4		25.14.b.b.24.3		6
5.3	odd	4		25.14.b.b.24.4		6
5.4	even	2		5.14.a.b.1.2	✓	3
15.14	odd	2		45.14.a.e.1.2		3
20.19	odd	2		80.14.a.g.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.14.a.b.1.2	✓	3	5.4	even	2
25.14.a.b.1.2		3	1.1	even	1	trivial
25.14.b.b.24.3		6	5.2	odd	4
25.14.b.b.24.4		6	5.3	odd	4
45.14.a.e.1.2		3	15.14	odd	2
80.14.a.g.1.1		3	20.19	odd	2

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-56.4248 q^{2} -2114.98 q^{3} -5008.25 q^{4} +119337. q^{6} -325303. q^{7} +744821. q^{8} +2.87881e6 q^{9} -1.61316e6 q^{11} +1.05923e7 q^{12} +3.19654e7 q^{13} +1.83551e7 q^{14} -998777. q^{16} -3.82330e6 q^{17} -1.62436e8 q^{18} -1.98761e8 q^{19} +6.88008e8 q^{21} +9.10219e7 q^{22} +1.86577e8 q^{23} -1.57528e9 q^{24} -1.80364e9 q^{26} -2.71667e9 q^{27} +1.62920e9 q^{28} +2.45694e9 q^{29} -9.66435e8 q^{31} -6.04522e9 q^{32} +3.41179e9 q^{33} +2.15729e8 q^{34} -1.44178e10 q^{36} -2.20805e10 q^{37} +1.12151e10 q^{38} -6.76061e10 q^{39} +4.05651e10 q^{41} -3.88207e10 q^{42} -2.28510e10 q^{43} +8.07908e9 q^{44} -1.05275e10 q^{46} +7.97391e10 q^{47} +2.11239e9 q^{48} +8.93279e9 q^{49} +8.08620e9 q^{51} -1.60091e11 q^{52} +2.25113e11 q^{53} +1.53287e11 q^{54} -2.42292e11 q^{56} +4.20376e11 q^{57} -1.38632e11 q^{58} +7.96680e10 q^{59} +4.91133e11 q^{61} +5.45308e10 q^{62} -9.36485e11 q^{63} +3.49282e11 q^{64} -1.92509e11 q^{66} -2.25405e11 q^{67} +1.91480e10 q^{68} -3.94606e11 q^{69} -6.50849e11 q^{71} +2.14420e12 q^{72} +1.03710e11 q^{73} +1.24588e12 q^{74} +9.95446e11 q^{76} +5.24764e11 q^{77} +3.81466e12 q^{78} +2.08051e12 q^{79} +1.15594e12 q^{81} -2.28888e12 q^{82} -3.39017e12 q^{83} -3.44571e12 q^{84} +1.28936e12 q^{86} -5.19638e12 q^{87} -1.20151e12 q^{88} -7.20835e12 q^{89} -1.03984e13 q^{91} -9.34422e11 q^{92} +2.04399e12 q^{93} -4.49926e12 q^{94} +1.27855e13 q^{96} -7.00185e12 q^{97} -5.04030e11 q^{98} -4.64397e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 142 q^{2} - 416 q^{3} + 17876 q^{4} + 120376 q^{6} - 448292 q^{7} - 2580360 q^{8} + 1286119 q^{9} - 6604004 q^{11} + 23722448 q^{12} + 33501974 q^{13} - 46562928 q^{14} + 199912208 q^{16} - 83129542 q^{17}+ \cdots + 126787366508 q^{99}+O(q^{100}) \) 3 * q - 142 * q^2 - 416 * q^3 + 17876 * q^4 + 120376 * q^6 - 448292 * q^7 - 2580360 * q^8 + 1286119 * q^9 - 6604004 * q^11 + 23722448 * q^12 + 33501974 * q^13 - 46562928 * q^14 + 199912208 * q^16 - 83129542 * q^17 + 30983914 * q^18 + 97491100 * q^19 + 438200736 * q^21 + 530907256 * q^22 - 316255836 * q^23 - 3890359200 * q^24 - 3746814044 * q^26 - 6518951360 * q^27 + 6227646976 * q^28 + 2236171850 * q^29 + 7482994376 * q^31 - 32169857312 * q^32 - 359182912 * q^33 - 30236073988 * q^34 - 43361833852 * q^36 - 31447174242 * q^37 + 42518132360 * q^38 - 70188571072 * q^39 - 10752884434 * q^41 - 92283853824 * q^42 - 16930554856 * q^43 - 68395825168 * q^44 + 246828204336 * q^46 - 31934201692 * q^47 + 80078828864 * q^48 - 38956926629 * q^49 - 129369882944 * q^51 + 18152597928 * q^52 + 221149123934 * q^53 + 246121937200 * q^54 - 522876451200 * q^56 + 763110695680 * q^57 - 854269976260 * q^58 - 55436423900 * q^59 + 496161392746 * q^61 + 598069940736 * q^62 - 1085454385236 * q^63 + 3297565494336 * q^64 - 22883875168 * q^66 - 459297824792 * q^67 + 2008021178776 * q^68 - 333379292832 * q^69 + 521997878336 * q^71 + 5658040941720 * q^72 - 2505025571086 * q^73 - 2418323586508 * q^74 + 621688050000 * q^76 + 385562457456 * q^77 + 2386950332528 * q^78 + 2990636883200 * q^79 + 320549052763 * q^81 - 5784848206924 * q^82 - 5137135467696 * q^83 - 814234130688 * q^84 + 2343313645096 * q^86 - 6885420178880 * q^87 + 8660607864480 * q^88 - 19423025958450 * q^89 - 6792522370184 * q^91 - 26870022340992 * q^92 + 11095902136128 * q^93 - 7003557875968 * q^94 - 2208331214464 * q^96 + 11088325396458 * q^97 + 10176508990306 * q^98 + 126787366508 * q^99

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