LMFDB - Embedded newform 50.18.a.f.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [50,18,Mod(1,50)] 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("50.1"); S:= CuspForms(chi, 18); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(50, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 18, names="a")

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	50.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,512,1308] 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:	$91.6110436723$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{83281}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 20820 $ x^2 - x - 20820
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$144.792$ of defining polynomial
Character	$\chi$	$=$	50.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+256.000 q^{2} -8003.53 q^{3} +65536.0 q^{4} -2.04890e6 q^{6} -2.54694e7 q^{7} +1.67772e7 q^{8} -6.50836e7 q^{9} -2.81089e8 q^{11} -5.24520e8 q^{12} +1.52610e9 q^{13} -6.52016e9 q^{14} +4.29497e9 q^{16} -5.46901e10 q^{17} -1.66614e10 q^{18} +6.88947e8 q^{19} +2.03845e11 q^{21} -7.19587e10 q^{22} -3.91035e11 q^{23} -1.34277e11 q^{24} +3.90681e11 q^{26} +1.55448e12 q^{27} -1.66916e12 q^{28} +5.12259e12 q^{29} -7.31204e10 q^{31} +1.09951e12 q^{32} +2.24970e12 q^{33} -1.40007e13 q^{34} -4.26532e12 q^{36} +6.81637e12 q^{37} +1.76370e11 q^{38} -1.22142e13 q^{39} -5.76386e13 q^{41} +5.21843e13 q^{42} -7.57081e13 q^{43} -1.84214e13 q^{44} -1.00105e14 q^{46} +4.60351e13 q^{47} -3.43749e13 q^{48} +4.16059e14 q^{49} +4.37714e14 q^{51} +1.00014e14 q^{52} -6.58261e14 q^{53} +3.97946e14 q^{54} -4.27305e14 q^{56} -5.51401e12 q^{57} +1.31138e15 q^{58} -2.98287e14 q^{59} +8.50623e14 q^{61} -1.87188e13 q^{62} +1.65764e15 q^{63} +2.81475e14 q^{64} +5.75924e14 q^{66} +6.12967e15 q^{67} -3.58417e15 q^{68} +3.12966e15 q^{69} +5.41472e14 q^{71} -1.09192e15 q^{72} +7.16849e15 q^{73} +1.74499e15 q^{74} +4.51508e13 q^{76} +7.15916e15 q^{77} -3.12683e15 q^{78} +5.45373e15 q^{79} -4.03640e15 q^{81} -1.47555e16 q^{82} +3.64723e15 q^{83} +1.33592e16 q^{84} -1.93813e16 q^{86} -4.09988e16 q^{87} -4.71589e15 q^{88} +6.81792e14 q^{89} -3.88687e16 q^{91} -2.56269e16 q^{92} +5.85222e14 q^{93} +1.17850e16 q^{94} -8.79998e15 q^{96} +1.20373e17 q^{97} +1.06511e17 q^{98} +1.82943e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 512 q^{2} + 1308 q^{3} + 131072 q^{4} + 334848 q^{6} - 603844 q^{7} + 33554432 q^{8} - 107519094 q^{9} - 471481296 q^{11} + 85721088 q^{12} + 1541834228 q^{13} - 154584064 q^{14} + 8589934592 q^{16}+ \cdots + 26\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 512 * q^2 + 1308 * q^3 + 131072 * q^4 + 334848 * q^6 - 603844 * q^7 + 33554432 * q^8 - 107519094 * q^9 - 471481296 * q^11 + 85721088 * q^12 + 1541834228 * q^13 - 154584064 * q^14 + 8589934592 * q^16 - 32139900564 * q^17 - 27524888064 * q^18 + 128672529400 * q^19 + 435381246624 * q^21 - 120699211776 * q^22 - 650359859292 * q^23 + 21944598528 * q^24 + 394709562368 * q^26 - 43156034280 * q^27 - 39573520384 * q^28 + 2543054749980 * q^29 + 7839407998744 * q^31 + 2199023255552 * q^32 + 476857812816 * q^33 - 8227814544384 * q^34 - 7046371344384 * q^36 + 27805209097556 * q^37 + 32940167526400 * q^38 - 12067623537288 * q^39 - 37826364264156 * q^41 + 111457599135744 * q^42 - 29630453926852 * q^43 - 30898998214656 * q^44 - 166492123978752 * q^46 - 220791583022004 * q^47 + 5617817223168 * q^48 + 801722584677954 * q^49 + 647690491265544 * q^51 + 101045647966208 * q^52 - 1058306017600572 * q^53 - 11047944775680 * q^54 - 10130821218304 * q^56 + 1186209507102000 * q^57 + 651022015994880 * q^58 + 1527820717235160 * q^59 - 631738213122116 * q^61 + 2006888447678464 * q^62 + 602457597963468 * q^63 + 562949953421312 * q^64 + 122075600080896 * q^66 + 8843763493872596 * q^67 - 2106320523362304 * q^68 + 714953250788832 * q^69 - 3331901660912376 * q^71 - 1803871064162304 * q^72 + 10026350574292028 * q^73 + 7118133528974336 * q^74 + 8432682886758400 * q^76 + 2424946105073712 * q^77 - 3089311625545728 * q^78 + 8263606842055120 * q^79 - 13432683850659198 * q^81 - 9683549251623936 * q^82 + 10689526892336988 * q^83 + 28533145378750464 * q^84 - 7585396205274112 * q^86 - 65018171604068280 * q^87 - 7910143542951936 * q^88 + 55878412521904980 * q^89 - 38477396610603016 * q^91 - 42621983738560512 * q^92 + 74263001022197376 * q^93 - 56522645253633024 * q^94 + 1438161209131008 * q^96 + 56106580363859756 * q^97 + 205240981677556224 * q^98 + 26373671099096112 * 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 $

$2$	256.000	0.707107
$2$	256.000	0.707107
$3$	−8003.53	−0.704289	−0.352145	−	0.935946i	$-0.614548\pi$
$3$	−8003.53	−0.704289	−0.352145	+	0.935946i	$0.614548\pi$
$4$	65536.0	0.500000
$5$	0	0
$5$	0	0
$6$	−2.04890e6	−0.498008
$7$	−2.54694e7	−1.66988	−0.834939	−	0.550342i	$-0.814497\pi$
$7$	−2.54694e7	−1.66988	−0.834939	+	0.550342i	$0.814497\pi$
$8$	1.67772e7	0.353553
$9$	−6.50836e7	−0.503976
$10$	0	0
$11$	−2.81089e8	−0.395372	−0.197686	−	0.980265i	$-0.563343\pi$
$11$	−2.81089e8	−0.395372	−0.197686	+	0.980265i	$0.563343\pi$
$12$	−5.24520e8	−0.352145
$13$	1.52610e9	0.518876	0.259438	−	0.965760i	$-0.416463\pi$
$13$	1.52610e9	0.518876	0.259438	+	0.965760i	$0.416463\pi$
$14$	−6.52016e9	−1.18078
$15$	0	0
$16$	4.29497e9	0.250000
$17$	−5.46901e10	−1.90148	−0.950742	−	0.309984i	$-0.899676\pi$
$17$	−5.46901e10	−1.90148	−0.950742	+	0.309984i	$0.899676\pi$
$18$	−1.66614e10	−0.356365
$19$	6.88947e8	0.00930637	0.00465318	−	0.999989i	$-0.498519\pi$
$19$	6.88947e8	0.00930637	0.00465318	+	0.999989i	$0.498519\pi$
$20$	0	0
$21$	2.03845e11	1.17608
$22$	−7.19587e10	−0.279570
$23$	−3.91035e11	−1.04119	−0.520594	−	0.853804i	$-0.674290\pi$
$23$	−3.91035e11	−1.04119	−0.520594	+	0.853804i	$0.674290\pi$
$24$	−1.34277e11	−0.249004
$25$	0	0
$26$	3.90681e11	0.366901
$27$	1.55448e12	1.05923
$28$	−1.66916e12	−0.834939
$29$	5.12259e12	1.90154	0.950772	−	0.309892i	$-0.100293\pi$
$29$	5.12259e12	1.90154	0.950772	+	0.309892i	$0.100293\pi$
$30$	0	0
$31$	−7.31204e10	−0.0153980	−0.00769900	−	0.999970i	$-0.502451\pi$
$31$	−7.31204e10	−0.0153980	−0.00769900	+	0.999970i	$0.502451\pi$
$32$	1.09951e12	0.176777
$33$	2.24970e12	0.278456
$34$	−1.40007e13	−1.34455
$35$	0	0
$36$	−4.26532e12	−0.251988
$37$	6.81637e12	0.319035	0.159517	−	0.987195i	$-0.449006\pi$
$37$	6.81637e12	0.319035	0.159517	+	0.987195i	$0.449006\pi$
$38$	1.76370e11	0.00658059
$39$	−1.22142e13	−0.365439
$40$	0	0
$41$	−5.76386e13	−1.12733	−0.563665	−	0.826004i	$-0.690609\pi$
$41$	−5.76386e13	−1.12733	−0.563665	+	0.826004i	$0.690609\pi$
$42$	5.21843e13	0.831613
$43$	−7.57081e13	−0.987781	−0.493890	−	0.869524i	$-0.664426\pi$
$43$	−7.57081e13	−0.987781	−0.493890	+	0.869524i	$0.664426\pi$
$44$	−1.84214e13	−0.197686
$45$	0	0
$46$	−1.00105e14	−0.736231
$47$	4.60351e13	0.282006	0.141003	−	0.990009i	$-0.454967\pi$
$47$	4.60351e13	0.282006	0.141003	+	0.990009i	$0.454967\pi$
$48$	−3.43749e13	−0.176072
$49$	4.16059e14	1.78849
$50$	0	0
$51$	4.37714e14	1.33919
$52$	1.00014e14	0.259438
$53$	−6.58261e14	−1.45229	−0.726145	−	0.687541i	$-0.758690\pi$
$53$	−6.58261e14	−1.45229	−0.726145	+	0.687541i	$0.758690\pi$
$54$	3.97946e14	0.748992
$55$	0	0
$56$	−4.27305e14	−0.590391
$57$	−5.51401e12	−0.00655437
$58$	1.31138e15	1.34459
$59$	−2.98287e14	−0.264479	−0.132240	−	0.991218i	$-0.542217\pi$
$59$	−2.98287e14	−0.264479	−0.132240	+	0.991218i	$0.542217\pi$
$60$	0	0
$61$	8.50623e14	0.568111	0.284056	−	0.958808i	$-0.408320\pi$
$61$	8.50623e14	0.568111	0.284056	+	0.958808i	$0.408320\pi$
$62$	−1.87188e13	−0.0108880
$63$	1.65764e15	0.841580
$64$	2.81475e14	0.125000
$65$	0	0
$66$	5.75924e14	0.196898
$67$	6.12967e15	1.84417	0.922085	−	0.386987i	$-0.126484\pi$
$67$	6.12967e15	1.84417	0.922085	+	0.386987i	$0.126484\pi$
$68$	−3.58417e15	−0.950742
$69$	3.12966e15	0.733298
$70$	0	0
$71$	5.41472e14	0.0995131	0.0497565	−	0.998761i	$-0.484155\pi$
$71$	5.41472e14	0.0995131	0.0497565	+	0.998761i	$0.484155\pi$
$72$	−1.09192e15	−0.178183
$73$	7.16849e15	1.04036	0.520180	−	0.854057i	$-0.325865\pi$
$73$	7.16849e15	1.04036	0.520180	+	0.854057i	$0.325865\pi$
$74$	1.74499e15	0.225592
$75$	0	0
$76$	4.51508e13	0.00465318
$77$	7.15916e15	0.660223
$78$	−3.12683e15	−0.258404
$79$	5.45373e15	0.404448	0.202224	−	0.979339i	$-0.435183\pi$
$79$	5.45373e15	0.404448	0.202224	+	0.979339i	$0.435183\pi$
$80$	0	0
$81$	−4.03640e15	−0.242031
$82$	−1.47555e16	−0.797142
$83$	3.64723e15	0.177746	0.0888728	−	0.996043i	$-0.471674\pi$
$83$	3.64723e15	0.177746	0.0888728	+	0.996043i	$0.471674\pi$
$84$	1.33592e16	0.588039
$85$	0	0
$86$	−1.93813e16	−0.698467
$87$	−4.09988e16	−1.33924
$88$	−4.71589e15	−0.139785
$89$	6.81792e14	0.0183585	0.00917925	−	0.999958i	$-0.497078\pi$
$89$	6.81792e14	0.0183585	0.00917925	+	0.999958i	$0.497078\pi$
$90$	0	0
$91$	−3.88687e16	−0.866460
$92$	−2.56269e16	−0.520594
$93$	5.85222e14	0.0108446
$94$	1.17850e16	0.199408
$95$	0	0
$96$	−8.79998e15	−0.124502
$97$	1.20373e17	1.55944	0.779720	−	0.626129i	$-0.215362\pi$
$97$	1.20373e17	1.55944	0.779720	+	0.626129i	$0.215362\pi$
$98$	1.06511e17	1.26466
$99$	1.82943e16	0.199258
$100$	0	0
$101$	7.74092e16	0.711314	0.355657	−	0.934617i	$-0.384257\pi$
$101$	7.74092e16	0.711314	0.355657	+	0.934617i	$0.384257\pi$
$102$	1.12055e17	0.946954
$103$	1.39309e17	1.08359	0.541793	−	0.840512i	$-0.317746\pi$
$103$	1.39309e17	1.08359	0.541793	+	0.840512i	$0.317746\pi$
$104$	2.56037e16	0.183450
$105$	0	0
$106$	−1.68515e17	−1.02692
$107$	−2.75662e17	−1.55101	−0.775505	−	0.631341i	$-0.782505\pi$
$107$	−2.75662e17	−1.55101	−0.775505	+	0.631341i	$0.782505\pi$
$108$	1.01874e17	0.529617
$109$	1.37550e17	0.661202	0.330601	−	0.943771i	$-0.392749\pi$
$109$	1.37550e17	0.661202	0.330601	+	0.943771i	$0.392749\pi$
$110$	0	0
$111$	−5.45550e16	−0.224693
$112$	−1.09390e17	−0.417470
$113$	3.90258e17	1.38097	0.690486	−	0.723345i	$-0.257396\pi$
$113$	3.90258e17	1.38097	0.690486	+	0.723345i	$0.257396\pi$
$114$	−1.41159e15	−0.00463464
$115$	0	0
$116$	3.35714e17	0.950772
$117$	−9.93239e16	−0.261501
$118$	−7.63614e16	−0.187015
$119$	1.39292e18	3.17525
$120$	0	0
$121$	−4.26436e17	−0.843681
$122$	2.17759e17	0.401715
$123$	4.61313e17	0.793966
$124$	−4.79202e15	−0.00769900
$125$	0	0
$126$	4.24355e17	0.595087
$127$	7.37824e17	0.967433	0.483717	−	0.875225i	$-0.339287\pi$
$127$	7.37824e17	0.967433	0.483717	+	0.875225i	$0.339287\pi$
$128$	7.20576e16	0.0883883
$129$	6.05933e17	0.695684
$130$	0	0
$131$	−1.45408e18	−1.46482	−0.732409	−	0.680865i	$-0.761604\pi$
$131$	−1.45408e18	−1.46482	−0.732409	+	0.680865i	$0.761604\pi$
$132$	1.47437e17	0.139228
$133$	−1.75470e16	−0.0155405
$134$	1.56919e18	1.30403
$135$	0	0
$136$	−9.17547e17	−0.672276
$137$	2.27534e18	1.56647	0.783236	−	0.621725i	$-0.213568\pi$
$137$	2.27534e18	1.56647	0.783236	+	0.621725i	$0.213568\pi$
$138$	8.01194e17	0.518520
$139$	1.41598e17	0.0861849	0.0430924	−	0.999071i	$-0.486279\pi$
$139$	1.41598e17	0.0861849	0.0430924	+	0.999071i	$0.486279\pi$
$140$	0	0
$141$	−3.68444e17	−0.198614
$142$	1.38617e17	0.0703664
$143$	−4.28969e17	−0.205149
$144$	−2.79532e17	−0.125994
$145$	0	0
$146$	1.83513e18	0.735646
$147$	−3.32994e18	−1.25962
$148$	4.46717e17	0.159517
$149$	−1.31089e18	−0.442063	−0.221032	−	0.975267i	$-0.570942\pi$
$149$	−1.31089e18	−0.442063	−0.221032	+	0.975267i	$0.570942\pi$
$150$	0	0
$151$	−2.76548e18	−0.832658	−0.416329	−	0.909214i	$-0.636684\pi$
$151$	−2.76548e18	−0.832658	−0.416329	+	0.909214i	$0.636684\pi$
$152$	1.15586e16	0.00329030
$153$	3.55943e18	0.958303
$154$	1.83274e18	0.466848
$155$	0	0
$156$	−8.00468e17	−0.182719
$157$	3.81235e18	0.824225	0.412112	−	0.911133i	$-0.364791\pi$
$157$	3.81235e18	0.824225	0.412112	+	0.911133i	$0.364791\pi$
$158$	1.39615e18	0.285988
$159$	5.26842e18	1.02283
$160$	0	0
$161$	9.95942e18	1.73866
$162$	−1.03332e18	−0.171142
$163$	−1.03773e19	−1.63114	−0.815570	−	0.578658i	$-0.803577\pi$
$163$	−1.03773e19	−1.63114	−0.815570	+	0.578658i	$0.803577\pi$
$164$	−3.77740e18	−0.563665
$165$	0	0
$166$	9.33690e17	0.125685
$167$	−1.21920e19	−1.55949	−0.779747	−	0.626095i	$-0.784652\pi$
$167$	−1.21920e19	−1.55949	−0.779747	+	0.626095i	$0.784652\pi$
$168$	3.41995e18	0.415806
$169$	−6.32145e18	−0.730768
$170$	0	0
$171$	−4.48391e16	−0.00469019
$172$	−4.96161e18	−0.493890
$173$	3.88210e18	0.367853	0.183927	−	0.982940i	$-0.441119\pi$
$173$	3.88210e18	0.367853	0.183927	+	0.982940i	$0.441119\pi$
$174$	−1.04957e19	−0.946983
$175$	0	0
$176$	−1.20727e18	−0.0988430
$177$	2.38735e18	0.186270
$178$	1.74539e17	0.0129814
$179$	−1.62354e19	−1.15136	−0.575680	−	0.817675i	$-0.695263\pi$
$179$	−1.62354e19	−1.15136	−0.575680	+	0.817675i	$0.695263\pi$
$180$	0	0
$181$	−2.32195e19	−1.49825	−0.749127	−	0.662427i	$-0.769527\pi$
$181$	−2.32195e19	−1.49825	−0.749127	+	0.662427i	$0.769527\pi$
$182$	−9.95039e18	−0.612680
$183$	−6.80799e18	−0.400115
$184$	−6.56048e18	−0.368116
$185$	0	0
$186$	1.49817e17	0.00766832
$187$	1.53728e19	0.751793
$188$	3.01696e18	0.141003
$189$	−3.95915e19	−1.76879
$190$	0	0
$191$	4.47928e19	1.82989	0.914944	−	0.403580i	$-0.132234\pi$
$191$	4.47928e19	1.82989	0.914944	+	0.403580i	$0.132234\pi$
$192$	−2.25279e18	−0.0880362
$193$	−3.61154e19	−1.35038	−0.675189	−	0.737645i	$-0.735938\pi$
$193$	−3.61154e19	−1.35038	−0.675189	+	0.737645i	$0.735938\pi$
$194$	3.08154e19	1.10269
$195$	0	0
$196$	2.72668e19	0.894247
$197$	1.80503e19	0.566920	0.283460	−	0.958984i	$-0.408518\pi$
$197$	1.80503e19	0.566920	0.283460	+	0.958984i	$0.408518\pi$
$198$	4.68333e18	0.140897
$199$	−6.39636e18	−0.184366	−0.0921832	−	0.995742i	$-0.529385\pi$
$199$	−6.39636e18	−0.184366	−0.0921832	+	0.995742i	$0.529385\pi$
$200$	0	0
$201$	−4.90590e19	−1.29883
$202$	1.98168e19	0.502975
$203$	−1.30469e20	−3.17535
$204$	2.86860e19	0.669597
$205$	0	0
$206$	3.56631e19	0.766211
$207$	2.54500e19	0.524734
$208$	6.55453e18	0.129719
$209$	−1.93655e17	−0.00367948
$210$	0	0
$211$	7.72101e18	0.135292	0.0676462	−	0.997709i	$-0.478451\pi$
$211$	7.72101e18	0.135292	0.0676462	+	0.997709i	$0.478451\pi$
$212$	−4.31398e19	−0.726145
$213$	−4.33369e18	−0.0700860
$214$	−7.05695e19	−1.09673
$215$	0	0
$216$	2.60798e19	0.374496
$217$	1.86233e18	0.0257128
$218$	3.52127e19	0.467541
$219$	−5.73733e19	−0.732715
$220$	0	0
$221$	−8.34623e19	−0.986634
$222$	−1.39661e19	−0.158882
$223$	1.08588e20	1.18902	0.594510	−	0.804088i	$-0.297346\pi$
$223$	1.08588e20	1.18902	0.594510	+	0.804088i	$0.297346\pi$
$224$	−2.80039e19	−0.295196
$225$	0	0
$226$	9.99061e19	0.976495
$227$	−1.95539e19	−0.184083	−0.0920415	−	0.995755i	$-0.529339\pi$
$227$	−1.95539e19	−0.184083	−0.0920415	+	0.995755i	$0.529339\pi$
$228$	−3.61366e17	−0.00327719
$229$	1.20601e20	1.05378	0.526890	−	0.849933i	$-0.323358\pi$
$229$	1.20601e20	1.05378	0.526890	+	0.849933i	$0.323358\pi$
$230$	0	0
$231$	−5.72986e19	−0.464988
$232$	8.59427e19	0.672297
$233$	−7.20388e19	−0.543302	−0.271651	−	0.962396i	$-0.587570\pi$
$233$	−7.20388e19	−0.543302	−0.271651	+	0.962396i	$0.587570\pi$
$234$	−2.54269e19	−0.184909
$235$	0	0
$236$	−1.95485e19	−0.132240
$237$	−4.36491e19	−0.284849
$238$	3.56588e20	2.24524
$239$	1.70425e20	1.03550	0.517750	−	0.855532i	$-0.326770\pi$
$239$	1.70425e20	1.03550	0.517750	+	0.855532i	$0.326770\pi$
$240$	0	0
$241$	−1.71129e20	−0.968679	−0.484340	−	0.874880i	$-0.660940\pi$
$241$	−1.71129e20	−0.968679	−0.484340	+	0.874880i	$0.660940\pi$
$242$	−1.09168e20	−0.596573
$243$	−1.68440e20	−0.888775
$244$	5.57464e19	0.284056
$245$	0	0
$246$	1.18096e20	0.561419
$247$	1.05140e18	0.00482885
$248$	−1.22676e18	−0.00544401
$249$	−2.91907e19	−0.125184
$250$	0	0
$251$	1.85831e20	0.744546	0.372273	−	0.928123i	$-0.378578\pi$
$251$	1.85831e20	0.744546	0.372273	+	0.928123i	$0.378578\pi$
$252$	1.08635e20	0.420790
$253$	1.09916e20	0.411657
$254$	1.88883e20	0.684078
$255$	0	0
$256$	1.84467e19	0.0625000
$257$	−1.68273e19	−0.0551547	−0.0275773	−	0.999620i	$-0.508779\pi$
$257$	−1.68273e19	−0.0551547	−0.0275773	+	0.999620i	$0.508779\pi$
$258$	1.55119e20	0.491923
$259$	−1.73609e20	−0.532750
$260$	0	0
$261$	−3.33396e20	−0.958333
$262$	−3.72245e20	−1.03578
$263$	−2.77268e20	−0.746924	−0.373462	−	0.927645i	$-0.621829\pi$
$263$	−2.77268e20	−0.746924	−0.373462	+	0.927645i	$0.621829\pi$
$264$	3.77438e19	0.0984491
$265$	0	0
$266$	−4.49204e18	−0.0109888
$267$	−5.45675e18	−0.0129297
$268$	4.01714e20	0.922085
$269$	9.40799e19	0.209220	0.104610	−	0.994513i	$-0.466641\pi$
$269$	9.40799e19	0.209220	0.104610	+	0.994513i	$0.466641\pi$
$270$	0	0
$271$	−6.17628e20	−1.28970	−0.644849	−	0.764310i	$-0.723080\pi$
$271$	−6.17628e20	−1.28970	−0.644849	+	0.764310i	$0.723080\pi$
$272$	−2.34892e20	−0.475371
$273$	3.11087e20	0.610238
$274$	5.82488e20	1.10766
$275$	0	0
$276$	2.05106e20	0.366649
$277$	6.67865e20	1.15774	0.578869	−	0.815420i	$-0.303494\pi$
$277$	6.67865e20	1.15774	0.578869	+	0.815420i	$0.303494\pi$
$278$	3.62491e19	0.0609419
$279$	4.75894e18	0.00776023
$280$	0	0
$281$	−1.13640e20	−0.174393	−0.0871963	−	0.996191i	$-0.527791\pi$
$281$	−1.13640e20	−0.174393	−0.0871963	+	0.996191i	$0.527791\pi$
$282$	−9.43216e19	−0.140441
$283$	3.76957e20	0.544637	0.272318	−	0.962207i	$-0.412210\pi$
$283$	3.76957e20	0.544637	0.272318	+	0.962207i	$0.412210\pi$
$284$	3.54859e19	0.0497565
$285$	0	0
$286$	−1.09816e20	−0.145062
$287$	1.46802e21	1.88250
$288$	−7.15602e19	−0.0890913
$289$	2.16376e21	2.61564
$290$	0	0
$291$	−9.63408e20	−1.09830
$292$	4.69794e20	0.520180
$293$	3.57350e20	0.384344	0.192172	−	0.981361i	$-0.438447\pi$
$293$	3.57350e20	0.384344	0.192172	+	0.981361i	$0.438447\pi$
$294$	−8.52464e20	−0.890684
$295$	0	0
$296$	1.14360e20	0.112796
$297$	−4.36946e20	−0.418792
$298$	−3.35589e20	−0.312586
$299$	−5.96757e20	−0.540247
$300$	0	0
$301$	1.92824e21	1.64947
$302$	−7.07963e20	−0.588778
$303$	−6.19547e20	−0.500971
$304$	2.95900e18	0.00232659
$305$	0	0
$306$	9.11213e20	0.677623
$307$	−2.25658e21	−1.63220	−0.816102	−	0.577908i	$-0.803869\pi$
$307$	−2.25658e21	−1.63220	−0.816102	+	0.577908i	$0.803869\pi$
$308$	4.69182e20	0.330112
$309$	−1.11497e21	−0.763158
$310$	0	0
$311$	5.76844e20	0.373762	0.186881	−	0.982383i	$-0.440162\pi$
$311$	5.76844e20	0.373762	0.186881	+	0.982383i	$0.440162\pi$
$312$	−2.04920e20	−0.129202
$313$	−2.63218e21	−1.61506	−0.807530	−	0.589827i	$-0.799196\pi$
$313$	−2.63218e21	−1.61506	−0.807530	+	0.589827i	$0.799196\pi$
$314$	9.75961e20	0.582815
$315$	0	0
$316$	3.57415e20	0.202224
$317$	9.95998e20	0.548599	0.274299	−	0.961644i	$-0.411554\pi$
$317$	9.95998e20	0.548599	0.274299	+	0.961644i	$0.411554\pi$
$318$	1.34871e21	0.723252
$319$	−1.43990e21	−0.751817
$320$	0	0
$321$	2.20627e21	1.09236
$322$	2.54961e21	1.22942
$323$	−3.76786e19	−0.0176959
$324$	−2.64529e20	−0.121016
$325$	0	0
$326$	−2.65660e21	−1.15339
$327$	−1.10088e21	−0.465678
$328$	−9.67016e20	−0.398571
$329$	−1.17249e21	−0.470915
$330$	0	0
$331$	−3.56520e21	−1.36002	−0.680011	−	0.733202i	$-0.738025\pi$
$331$	−3.56520e21	−1.36002	−0.680011	+	0.733202i	$0.738025\pi$
$332$	2.39025e20	0.0888728
$333$	−4.43634e20	−0.160786
$334$	−3.12114e21	−1.10273
$335$	0	0
$336$	8.75508e20	0.294019
$337$	−3.65283e20	−0.119612	−0.0598060	−	0.998210i	$-0.519048\pi$
$337$	−3.65283e20	−0.119612	−0.0598060	+	0.998210i	$0.519048\pi$
$338$	−1.61829e21	−0.516731
$339$	−3.12344e21	−0.972605
$340$	0	0
$341$	2.05533e19	0.00608793
$342$	−1.14788e19	−0.00331646
$343$	−4.67180e21	−1.31669
$344$	−1.27017e21	−0.349233
$345$	0	0
$346$	9.93818e20	0.260112
$347$	2.06934e21	0.528483	0.264242	−	0.964457i	$-0.414878\pi$
$347$	2.06934e21	0.528483	0.264242	+	0.964457i	$0.414878\pi$
$348$	−2.68690e21	−0.669618
$349$	3.13803e20	0.0763204	0.0381602	−	0.999272i	$-0.487850\pi$
$349$	3.13803e20	0.0763204	0.0381602	+	0.999272i	$0.487850\pi$
$350$	0	0
$351$	2.37228e21	0.549611
$352$	−3.09060e20	−0.0698925
$353$	6.87901e21	1.51859	0.759296	−	0.650746i	$-0.225544\pi$
$353$	6.87901e21	1.51859	0.759296	+	0.650746i	$0.225544\pi$
$354$	6.11161e20	0.131713
$355$	0	0
$356$	4.46820e19	0.00917925
$357$	−1.11483e22	−2.23629
$358$	−4.15625e21	−0.814134
$359$	−9.50907e21	−1.81901	−0.909505	−	0.415693i	$-0.863539\pi$
$359$	−9.50907e21	−1.81901	−0.909505	+	0.415693i	$0.863539\pi$
$360$	0	0
$361$	−5.47991e21	−0.999913
$362$	−5.94420e21	−1.05943
$363$	3.41300e21	0.594196
$364$	−2.54730e21	−0.433230
$365$	0	0
$366$	−1.74285e21	−0.282924
$367$	−1.88008e20	−0.0298205	−0.0149103	−	0.999889i	$-0.504746\pi$
$367$	−1.88008e20	−0.0298205	−0.0149103	+	0.999889i	$0.504746\pi$
$368$	−1.67948e21	−0.260297
$369$	3.75133e21	0.568147
$370$	0	0
$371$	1.67655e22	2.42515
$372$	3.83531e19	0.00542232
$373$	−9.66745e20	−0.133594	−0.0667970	−	0.997767i	$-0.521278\pi$
$373$	−9.66745e20	−0.133594	−0.0667970	+	0.997767i	$0.521278\pi$
$374$	3.93543e21	0.531598
$375$	0	0
$376$	7.72342e20	0.0997040
$377$	7.81756e21	0.986665
$378$	−1.01354e22	−1.25073
$379$	1.09478e22	1.32097	0.660484	−	0.750840i	$-0.270351\pi$
$379$	1.09478e22	1.32097	0.660484	+	0.750840i	$0.270351\pi$
$380$	0	0
$381$	−5.90520e21	−0.681353
$382$	1.14670e22	1.29393
$383$	9.48135e21	1.04636	0.523179	−	0.852223i	$-0.324746\pi$
$383$	9.48135e21	1.04636	0.523179	+	0.852223i	$0.324746\pi$
$384$	−5.76715e20	−0.0622510
$385$	0	0
$386$	−9.24554e21	−0.954861
$387$	4.92736e21	0.497818
$388$	7.88875e21	0.779720
$389$	8.68048e21	0.839406	0.419703	−	0.907661i	$-0.362134\pi$
$389$	8.68048e21	0.839406	0.419703	+	0.907661i	$0.362134\pi$
$390$	0	0
$391$	2.13857e22	1.97980
$392$	6.98030e21	0.632328
$393$	1.16378e22	1.03166
$394$	4.62088e21	0.400873
$395$	0	0
$396$	1.19893e21	0.0996291
$397$	5.61938e21	0.457055	0.228528	−	0.973537i	$-0.426609\pi$
$397$	5.61938e21	0.457055	0.228528	+	0.973537i	$0.426609\pi$
$398$	−1.63747e21	−0.130367
$399$	1.40438e20	0.0109450
$400$	0	0
$401$	−4.97857e21	−0.371858	−0.185929	−	0.982563i	$-0.559530\pi$
$401$	−4.97857e21	−0.371858	−0.185929	+	0.982563i	$0.559530\pi$
$402$	−1.25591e22	−0.918411
$403$	−1.11589e20	−0.00798965
$404$	5.07309e21	0.355657
$405$	0	0
$406$	−3.34001e22	−2.24531
$407$	−1.91600e21	−0.126137
$408$	7.34362e21	0.473477
$409$	2.65693e20	0.0167777	0.00838883	−	0.999965i	$-0.497330\pi$
$409$	2.65693e20	0.0167777	0.00838883	+	0.999965i	$0.497330\pi$
$410$	0	0
$411$	−1.82108e22	−1.10325
$412$	9.12977e21	0.541793
$413$	7.59717e21	0.441648
$414$	6.51519e21	0.371043
$415$	0	0
$416$	1.67796e21	0.0917252
$417$	−1.13328e21	−0.0606991
$418$	−4.95757e19	−0.00260178
$419$	1.71242e22	0.880626	0.440313	−	0.897844i	$-0.354867\pi$
$419$	1.71242e22	0.880626	0.440313	+	0.897844i	$0.354867\pi$
$420$	0	0
$421$	2.71839e22	1.34250	0.671249	−	0.741231i	$-0.265758\pi$
$421$	2.71839e22	1.34250	0.671249	+	0.741231i	$0.265758\pi$
$422$	1.97658e21	0.0956662
$423$	−2.99613e21	−0.142124
$424$	−1.10438e22	−0.513462
$425$	0	0
$426$	−1.10942e21	−0.0495583
$427$	−2.16648e22	−0.948677
$428$	−1.80658e22	−0.775505
$429$	3.43327e21	0.144484
$430$	0	0
$431$	−2.34759e22	−0.949656	−0.474828	−	0.880079i	$-0.657490\pi$
$431$	−2.34759e22	−0.949656	−0.474828	+	0.880079i	$0.657490\pi$
$432$	6.67643e21	0.264809
$433$	1.88732e22	0.734003	0.367002	−	0.930220i	$-0.380384\pi$
$433$	1.88732e22	0.734003	0.367002	+	0.930220i	$0.380384\pi$
$434$	4.76757e20	0.0181817
$435$	0	0
$436$	9.01446e21	0.330601
$437$	−2.69402e20	−0.00968968
$438$	−1.46876e22	−0.518107
$439$	5.51895e22	1.90945	0.954724	−	0.297494i	$-0.0961509\pi$
$439$	5.51895e22	1.90945	0.954724	+	0.297494i	$0.0961509\pi$
$440$	0	0
$441$	−2.70786e22	−0.901359
$442$	−2.13664e22	−0.697656
$443$	1.20735e22	0.386723	0.193362	−	0.981128i	$-0.438061\pi$
$443$	1.20735e22	0.386723	0.193362	+	0.981128i	$0.438061\pi$
$444$	−3.57532e21	−0.112346
$445$	0	0
$446$	2.77984e22	0.840764
$447$	1.04918e22	0.311341
$448$	−7.16899e21	−0.208735
$449$	2.57466e22	0.735573	0.367787	−	0.929910i	$-0.380116\pi$
$449$	2.57466e22	0.735573	0.367787	+	0.929910i	$0.380116\pi$
$450$	0	0
$451$	1.62016e22	0.445714
$452$	2.55760e22	0.690486
$453$	2.21336e22	0.586432
$454$	−5.00580e21	−0.130166
$455$	0	0
$456$	−9.25097e19	−0.00231732
$457$	1.01069e22	0.248503	0.124252	−	0.992251i	$-0.460347\pi$
$457$	1.01069e22	0.248503	0.124252	+	0.992251i	$0.460347\pi$
$458$	3.08739e22	0.745136
$459$	−8.50144e22	−2.01412
$460$	0	0
$461$	1.68599e21	0.0384942	0.0192471	−	0.999815i	$-0.493873\pi$
$461$	1.68599e21	0.0384942	0.0192471	+	0.999815i	$0.493873\pi$
$462$	−1.46684e22	−0.328796
$463$	2.77945e22	0.611674	0.305837	−	0.952084i	$-0.401064\pi$
$463$	2.77945e22	0.611674	0.305837	+	0.952084i	$0.401064\pi$
$464$	2.20013e22	0.475386
$465$	0	0
$466$	−1.84419e22	−0.384172
$467$	−8.26643e22	−1.69093	−0.845463	−	0.534034i	$-0.820676\pi$
$467$	−8.26643e22	−1.69093	−0.845463	+	0.534034i	$0.820676\pi$
$468$	−6.50929e21	−0.130751
$469$	−1.56119e23	−3.07954
$470$	0	0
$471$	−3.05123e22	−0.580493
$472$	−5.00442e21	−0.0935075
$473$	2.12807e22	0.390541
$474$	−1.11742e22	−0.201418
$475$	0	0
$476$	9.12865e22	1.58762
$477$	4.28420e22	0.731920
$478$	4.36287e22	0.732209
$479$	2.59191e22	0.427335	0.213667	−	0.976906i	$-0.431459\pi$
$479$	2.59191e22	0.427335	0.213667	+	0.976906i	$0.431459\pi$
$480$	0	0
$481$	1.04024e22	0.165540
$482$	−4.38091e22	−0.684960
$483$	−7.97106e22	−1.22452
$484$	−2.79469e22	−0.421841
$485$	0	0
$486$	−4.31206e22	−0.628459
$487$	4.14828e22	0.594116	0.297058	−	0.954859i	$-0.403994\pi$
$487$	4.14828e22	0.594116	0.297058	+	0.954859i	$0.403994\pi$
$488$	1.42711e22	0.200858
$489$	8.30554e22	1.14879
$490$	0	0
$491$	3.08644e22	0.412349	0.206174	−	0.978515i	$-0.433899\pi$
$491$	3.08644e22	0.412349	0.206174	+	0.978515i	$0.433899\pi$
$492$	3.02326e22	0.396983
$493$	−2.80155e23	−3.61575
$494$	2.69158e20	0.00341451
$495$	0	0
$496$	−3.14050e20	−0.00384950
$497$	−1.37910e22	−0.166175
$498$	−7.47282e21	−0.0885187
$499$	3.24182e22	0.377516	0.188758	−	0.982024i	$-0.439554\pi$
$499$	3.24182e22	0.377516	0.188758	+	0.982024i	$0.439554\pi$
$500$	0	0
$501$	9.75788e22	1.09833
$502$	4.75728e22	0.526474
$503$	−6.39324e22	−0.695654	−0.347827	−	0.937559i	$-0.613080\pi$
$503$	−6.39324e22	−0.695654	−0.347827	+	0.937559i	$0.613080\pi$
$504$	2.78106e22	0.297543
$505$	0	0
$506$	2.81384e22	0.291085
$507$	5.05939e22	0.514672
$508$	4.83540e22	0.483717
$509$	−9.33355e22	−0.918218	−0.459109	−	0.888380i	$-0.651831\pi$
$509$	−9.33355e22	−0.918218	−0.459109	+	0.888380i	$0.651831\pi$
$510$	0	0
$511$	−1.82577e23	−1.73728
$512$	4.72237e21	0.0441942
$513$	1.07095e21	0.00985763
$514$	−4.30778e21	−0.0390003
$515$	0	0
$516$	3.97104e22	0.347842
$517$	−1.29400e22	−0.111497
$518$	−4.44438e22	−0.376711
$519$	−3.10705e22	−0.259075
$520$	0	0
$521$	3.30201e22	0.266476	0.133238	−	0.991084i	$-0.457463\pi$
$521$	3.30201e22	0.266476	0.133238	+	0.991084i	$0.457463\pi$
$522$	−8.53495e22	−0.677644
$523$	−4.06002e22	−0.317149	−0.158575	−	0.987347i	$-0.550690\pi$
$523$	−4.06002e22	−0.317149	−0.158575	+	0.987347i	$0.550690\pi$
$524$	−9.52948e22	−0.732409
$525$	0	0
$526$	−7.09807e22	−0.528155
$527$	3.99896e21	0.0292790
$528$	9.66240e21	0.0696140
$529$	1.18585e22	0.0840729
$530$	0	0
$531$	1.94136e22	0.133291
$532$	−1.14996e21	−0.00777025
$533$	−8.79621e22	−0.584944
$534$	−1.39693e21	−0.00914268
$535$	0	0
$536$	1.02839e23	0.652013
$537$	1.29940e23	0.810890
$538$	2.40844e22	0.147941
$539$	−1.16949e23	−0.707121
$540$	0	0
$541$	−4.20460e22	−0.246347	−0.123174	−	0.992385i	$-0.539307\pi$
$541$	−4.20460e22	−0.246347	−0.123174	+	0.992385i	$0.539307\pi$
$542$	−1.58113e23	−0.911954
$543$	1.85838e23	1.05520
$544$	−6.01324e22	−0.336138
$545$	0	0
$546$	7.96383e22	0.431504
$547$	2.01110e23	1.07285	0.536427	−	0.843947i	$-0.319774\pi$
$547$	2.01110e23	1.07285	0.536427	+	0.843947i	$0.319774\pi$
$548$	1.49117e23	0.783236
$549$	−5.53616e22	−0.286315
$550$	0	0
$551$	3.52919e21	0.0176965
$552$	5.25070e22	0.259260
$553$	−1.38903e23	−0.675380
$554$	1.70973e23	0.818645
$555$	0	0
$556$	9.27976e21	0.0430924
$557$	−1.46727e23	−0.671030	−0.335515	−	0.942035i	$-0.608910\pi$
$557$	−1.46727e23	−0.671030	−0.335515	+	0.942035i	$0.608910\pi$
$558$	1.21829e21	0.00548731
$559$	−1.15538e23	−0.512536
$560$	0	0
$561$	−1.23036e23	−0.529480
$562$	−2.90919e22	−0.123314
$563$	3.39706e23	1.41834	0.709172	−	0.705036i	$-0.249069\pi$
$563$	3.39706e23	1.41834	0.709172	+	0.705036i	$0.249069\pi$
$564$	−2.41463e22	−0.0993068
$565$	0	0
$566$	9.65010e22	0.385116
$567$	1.02805e23	0.404163
$568$	9.08439e21	0.0351832
$569$	2.72602e23	1.04010	0.520050	−	0.854136i	$-0.325913\pi$
$569$	2.72602e23	1.04010	0.520050	+	0.854136i	$0.325913\pi$
$570$	0	0
$571$	−2.79882e22	−0.103650	−0.0518249	−	0.998656i	$-0.516504\pi$
$571$	−2.79882e22	−0.103650	−0.0518249	+	0.998656i	$0.516504\pi$
$572$	−2.81129e22	−0.102574
$573$	−3.58501e23	−1.28877
$574$	3.75813e23	1.33113
$575$	0	0
$576$	−1.83194e22	−0.0629971
$577$	−3.86678e23	−1.31025	−0.655127	−	0.755519i	$-0.727385\pi$
$577$	−3.86678e23	−1.31025	−0.655127	+	0.755519i	$0.727385\pi$
$578$	5.53923e23	1.84954
$579$	2.89051e23	0.951056
$580$	0	0
$581$	−9.28926e22	−0.296814
$582$	−2.46632e23	−0.776613
$583$	1.85030e23	0.574195
$584$	1.20267e23	0.367823
$585$	0	0
$586$	9.14817e22	0.271772
$587$	−3.64152e23	−1.06625	−0.533125	−	0.846036i	$-0.678983\pi$
$587$	−3.64152e23	−1.06625	−0.533125	+	0.846036i	$0.678983\pi$
$588$	−2.18231e23	−0.629809
$589$	−5.03761e19	−0.000143299 0
$590$	0	0
$591$	−1.44466e23	−0.399276
$592$	2.92761e22	0.0797587
$593$	6.86689e23	1.84415	0.922073	−	0.387017i	$-0.126494\pi$
$593$	6.86689e23	1.84415	0.922073	+	0.387017i	$0.126494\pi$
$594$	−1.11858e23	−0.296130
$595$	0	0
$596$	−8.59108e22	−0.221032
$597$	5.11935e22	0.129847
$598$	−1.52770e23	−0.382013
$599$	−3.82850e23	−0.943846	−0.471923	−	0.881640i	$-0.656440\pi$
$599$	−3.82850e23	−0.943846	−0.471923	+	0.881640i	$0.656440\pi$
$600$	0	0
$601$	−2.66402e23	−0.638417	−0.319209	−	0.947684i	$-0.603417\pi$
$601$	−2.66402e23	−0.638417	−0.319209	+	0.947684i	$0.603417\pi$
$602$	4.93629e23	1.16635
$603$	−3.98941e23	−0.929418
$604$	−1.81239e23	−0.416329
$605$	0	0
$606$	−1.58604e23	−0.354240
$607$	1.11277e23	0.245076	0.122538	−	0.992464i	$-0.460897\pi$
$607$	1.11277e23	0.245076	0.122538	+	0.992464i	$0.460897\pi$
$608$	7.57505e20	0.00164515
$609$	1.04421e24	2.23636
$610$	0	0
$611$	7.02541e22	0.146326
$612$	2.33271e23	0.479152
$613$	3.91229e23	0.792532	0.396266	−	0.918136i	$-0.370306\pi$
$613$	3.91229e23	0.792532	0.396266	+	0.918136i	$0.370306\pi$
$614$	−5.77684e23	−1.15414
$615$	0	0
$616$	1.20111e23	0.233424
$617$	5.72626e23	1.09761	0.548804	−	0.835951i	$-0.315083\pi$
$617$	5.72626e23	1.09761	0.548804	+	0.835951i	$0.315083\pi$
$618$	−2.85431e23	−0.539634
$619$	7.86155e23	1.46601	0.733007	−	0.680222i	$-0.238116\pi$
$619$	7.86155e23	1.46601	0.733007	+	0.680222i	$0.238116\pi$
$620$	0	0
$621$	−6.07855e23	−1.10286
$622$	1.47672e23	0.264290
$623$	−1.73648e22	−0.0306565
$624$	−5.24594e22	−0.0913597
$625$	0	0
$626$	−6.73838e23	−1.14202
$627$	1.54993e21	0.00259142
$628$	2.49846e23	0.412112
$629$	−3.72788e23	−0.606640
$630$	0	0
$631$	6.52712e23	1.03389	0.516943	−	0.856020i	$-0.327070\pi$
$631$	6.52712e23	1.03389	0.516943	+	0.856020i	$0.327070\pi$
$632$	9.14983e22	0.142994
$633$	−6.17954e22	−0.0952850
$634$	2.54975e23	0.387918
$635$	0	0
$636$	3.45271e23	0.511416
$637$	6.34945e23	0.928007
$638$	−3.68615e23	−0.531615
$639$	−3.52410e22	−0.0501522
$640$	0	0
$641$	7.10734e23	0.984950	0.492475	−	0.870327i	$-0.336092\pi$
$641$	7.10734e23	0.984950	0.492475	+	0.870327i	$0.336092\pi$
$642$	5.64805e23	0.772415
$643$	−2.34278e23	−0.316183	−0.158092	−	0.987424i	$-0.550534\pi$
$643$	−2.34278e23	−0.316183	−0.158092	+	0.987424i	$0.550534\pi$
$644$	6.52701e23	0.869329
$645$	0	0
$646$	−9.64571e21	−0.0125129
$647$	−1.50806e23	−0.193078	−0.0965391	−	0.995329i	$-0.530777\pi$
$647$	−1.50806e23	−0.193078	−0.0965391	+	0.995329i	$0.530777\pi$
$648$	−6.77195e22	−0.0855710
$649$	8.38450e22	0.104568
$650$	0	0
$651$	−1.49052e22	−0.0181092
$652$	−6.80089e23	−0.815570
$653$	−6.74375e22	−0.0798251	−0.0399126	−	0.999203i	$-0.512708\pi$
$653$	−6.74375e22	−0.0798251	−0.0399126	+	0.999203i	$0.512708\pi$
$654$	−2.81826e23	−0.329284
$655$	0	0
$656$	−2.47556e23	−0.281832
$657$	−4.66551e23	−0.524317
$658$	−3.00157e23	−0.332987
$659$	7.11301e22	0.0778981	0.0389491	−	0.999241i	$-0.487599\pi$
$659$	7.11301e22	0.0778981	0.0389491	+	0.999241i	$0.487599\pi$
$660$	0	0
$661$	1.69805e24	1.81233	0.906164	−	0.422926i	$-0.138997\pi$
$661$	1.69805e24	1.81233	0.906164	+	0.422926i	$0.138997\pi$
$662$	−9.12691e23	−0.961680
$663$	6.67994e23	0.694876
$664$	6.11903e22	0.0628426
$665$	0	0
$666$	−1.13570e23	−0.113693
$667$	−2.00311e24	−1.97986
$668$	−7.99012e23	−0.779747
$669$	−8.69085e23	−0.837414
$670$	0	0
$671$	−2.39101e23	−0.224615
$672$	2.24130e23	0.207903
$673$	1.39848e24	1.28094	0.640469	−	0.767984i	$-0.278740\pi$
$673$	1.39848e24	1.28094	0.640469	+	0.767984i	$0.278740\pi$
$674$	−9.35124e22	−0.0845785
$675$	0	0
$676$	−4.14282e23	−0.365384
$677$	9.38639e23	0.817514	0.408757	−	0.912643i	$-0.365962\pi$
$677$	9.38639e23	0.817514	0.408757	+	0.912643i	$0.365962\pi$
$678$	−7.99602e23	−0.687735
$679$	−3.06582e24	−2.60408
$680$	0	0
$681$	1.56500e23	0.129648
$682$	5.26165e21	0.00430482
$683$	−1.23254e24	−0.995922	−0.497961	−	0.867199i	$-0.665918\pi$
$683$	−1.23254e24	−0.995922	−0.497961	+	0.867199i	$0.665918\pi$
$684$	−2.93858e21	−0.00234509
$685$	0	0
$686$	−1.19598e24	−0.931041
$687$	−9.65236e23	−0.742167
$688$	−3.25164e23	−0.246945
$689$	−1.00457e24	−0.753559
$690$	0	0
$691$	3.83055e23	0.280348	0.140174	−	0.990127i	$-0.455234\pi$
$691$	3.83055e23	0.280348	0.140174	+	0.990127i	$0.455234\pi$
$692$	2.54417e23	0.183927
$693$	−4.65944e23	−0.332737
$694$	5.29751e23	0.373694
$695$	0	0
$696$	−6.87845e23	−0.473492
$697$	3.15226e24	2.14360
$698$	8.03335e22	0.0539667
$699$	5.76565e23	0.382642
$700$	0	0
$701$	1.63235e24	1.05733	0.528665	−	0.848831i	$-0.322693\pi$
$701$	1.63235e24	1.05733	0.528665	+	0.848831i	$0.322693\pi$
$702$	6.07304e23	0.388634
$703$	4.69611e21	0.00296906
$704$	−7.91195e22	−0.0494215
$705$	0	0
$706$	1.76103e24	1.07381
$707$	−1.97156e24	−1.18781
$708$	1.56457e23	0.0931350
$709$	−6.09431e23	−0.358453	−0.179226	−	0.983808i	$-0.557359\pi$
$709$	−6.09431e23	−0.358453	−0.179226	+	0.983808i	$0.557359\pi$
$710$	0	0
$711$	−3.54948e23	−0.203832
$712$	1.14386e22	0.00649071
$713$	2.85926e22	0.0160322
$714$	−2.85396e24	−1.58130
$715$	0	0
$716$	−1.06400e24	−0.575680
$717$	−1.36400e24	−0.729292
$718$	−2.43432e24	−1.28623
$719$	−4.49148e23	−0.234527	−0.117264	−	0.993101i	$-0.537412\pi$
$719$	−4.49148e23	−0.234527	−0.117264	+	0.993101i	$0.537412\pi$
$720$	0	0
$721$	−3.54812e24	−1.80946
$722$	−1.40286e24	−0.707046
$723$	1.36964e24	0.682230
$724$	−1.52171e24	−0.749127
$725$	0	0
$726$	8.73727e23	0.420160
$727$	5.00713e23	0.237983	0.118992	−	0.992895i	$-0.462034\pi$
$727$	5.00713e23	0.237983	0.118992	+	0.992895i	$0.462034\pi$
$728$	−6.52109e23	−0.306340
$729$	1.86938e24	0.867986
$730$	0	0
$731$	4.14048e24	1.87825
$732$	−4.46168e23	−0.200057
$733$	−1.20329e24	−0.533320	−0.266660	−	0.963791i	$-0.585920\pi$
$733$	−1.20329e24	−0.533320	−0.266660	+	0.963791i	$0.585920\pi$
$734$	−4.81301e22	−0.0210863
$735$	0	0
$736$	−4.29948e23	−0.184058
$737$	−1.72298e24	−0.729133
$738$	9.60340e23	0.401741
$739$	−2.19426e24	−0.907426	−0.453713	−	0.891148i	$-0.649901\pi$
$739$	−2.19426e24	−0.907426	−0.453713	+	0.891148i	$0.649901\pi$
$740$	0	0
$741$	−8.41491e21	−0.00340091
$742$	4.29197e24	1.71484
$743$	9.89633e22	0.0390903	0.0195452	−	0.999809i	$-0.493778\pi$
$743$	9.89633e22	0.0390903	0.0195452	+	0.999809i	$0.493778\pi$
$744$	9.81839e21	0.00383416
$745$	0	0
$746$	−2.47487e23	−0.0944652
$747$	−2.37375e23	−0.0895796
$748$	1.00747e24	0.375897
$749$	7.02094e24	2.59000
$750$	0	0
$751$	−1.01856e24	−0.367322	−0.183661	−	0.982990i	$-0.558795\pi$
$751$	−1.01856e24	−0.367322	−0.183661	+	0.982990i	$0.558795\pi$
$752$	1.97719e23	0.0705014
$753$	−1.48731e24	−0.524376
$754$	2.00130e24	0.697677
$755$	0	0
$756$	−2.59467e24	−0.884397
$757$	1.43989e24	0.485305	0.242653	−	0.970113i	$-0.421982\pi$
$757$	1.43989e24	0.485305	0.242653	+	0.970113i	$0.421982\pi$
$758$	2.80263e24	0.934066
$759$	−8.79713e23	−0.289925
$760$	0	0
$761$	−7.15424e23	−0.230565	−0.115283	−	0.993333i	$-0.536777\pi$
$761$	−7.15424e23	−0.230565	−0.115283	+	0.993333i	$0.536777\pi$
$762$	−1.51173e24	−0.481789
$763$	−3.50330e24	−1.10413
$764$	2.93554e24	0.914944
$765$	0	0
$766$	2.42722e24	0.739887
$767$	−4.55214e23	−0.137232
$768$	−1.47639e23	−0.0440181
$769$	1.87177e24	0.551922	0.275961	−	0.961169i	$-0.411004\pi$
$769$	1.87177e24	0.551922	0.275961	+	0.961169i	$0.411004\pi$
$770$	0	0
$771$	1.34678e23	0.0388449
$772$	−2.36686e24	−0.675189
$773$	1.86999e24	0.527611	0.263805	−	0.964576i	$-0.415022\pi$
$773$	1.86999e24	0.527611	0.263805	+	0.964576i	$0.415022\pi$
$774$	1.26140e24	0.352011
$775$	0	0
$776$	2.01952e24	0.551345
$777$	1.38948e24	0.375210
$778$	2.22220e24	0.593550
$779$	−3.97099e22	−0.0104913
$780$	0	0
$781$	−1.52202e23	−0.0393447
$782$	5.47475e24	1.39993
$783$	7.96294e24	2.01418
$784$	1.78696e24	0.447124
$785$	0	0
$786$	2.97928e24	0.729490
$787$	3.29304e24	0.797648	0.398824	−	0.917027i	$-0.369418\pi$
$787$	3.29304e24	0.797648	0.398824	+	0.917027i	$0.369418\pi$
$788$	1.18295e24	0.283460
$789$	2.21913e24	0.526051
$790$	0	0
$791$	−9.93963e24	−2.30606
$792$	3.06927e23	0.0704484
$793$	1.29813e24	0.294779
$794$	1.43856e24	0.323187
$795$	0	0
$796$	−4.19192e23	−0.0921832
$797$	3.80089e24	0.826969	0.413485	−	0.910511i	$-0.364312\pi$
$797$	3.80089e24	0.826969	0.413485	+	0.910511i	$0.364312\pi$
$798$	3.59522e22	0.00773929
$799$	−2.51767e24	−0.536229
$800$	0	0
$801$	−4.43735e22	−0.00925225
$802$	−1.27451e24	−0.262944
$803$	−2.01498e24	−0.411329
$804$	−3.21513e24	−0.649415
$805$	0	0
$806$	−2.85667e22	−0.00564953
$807$	−7.52972e23	−0.147351
$808$	1.29871e24	0.251487
$809$	1.38713e24	0.265799	0.132900	−	0.991129i	$-0.457571\pi$
$809$	1.38713e24	0.265799	0.132900	+	0.991129i	$0.457571\pi$
$810$	0	0
$811$	2.43418e24	0.456747	0.228374	−	0.973574i	$-0.426659\pi$
$811$	2.43418e24	0.456747	0.228374	+	0.973574i	$0.426659\pi$
$812$	−8.55042e24	−1.58767
$813$	4.94321e24	0.908321
$814$	−4.90497e23	−0.0891926
$815$	0	0
$816$	1.87997e24	0.334799
$817$	−5.21589e22	−0.00919265
$818$	6.80174e22	0.0118636
$819$	2.52972e24	0.436675
$820$	0	0
$821$	−7.07675e24	−1.19651	−0.598256	−	0.801305i	$-0.704140\pi$
$821$	−7.07675e24	−1.19651	−0.598256	+	0.801305i	$0.704140\pi$
$822$	−4.66196e24	−0.780115
$823$	5.31425e24	0.880124	0.440062	−	0.897968i	$-0.354957\pi$
$823$	5.31425e24	0.880124	0.440062	+	0.897968i	$0.354957\pi$
$824$	2.33722e24	0.383105
$825$	0	0
$826$	1.94488e24	0.312292
$827$	−5.13487e24	−0.816080	−0.408040	−	0.912964i	$-0.633788\pi$
$827$	−5.13487e24	−0.816080	−0.408040	+	0.912964i	$0.633788\pi$
$828$	1.66789e24	0.262367
$829$	1.06738e25	1.66191	0.830954	−	0.556341i	$-0.187795\pi$
$829$	1.06738e25	1.66191	0.830954	+	0.556341i	$0.187795\pi$
$830$	0	0
$831$	−5.34528e24	−0.815383
$832$	4.29558e23	0.0648595
$833$	−2.27543e25	−3.40079
$834$	−2.90121e23	−0.0429208
$835$	0	0
$836$	−1.26914e22	−0.00183974
$837$	−1.13664e23	−0.0163101
$838$	4.38380e24	0.622697
$839$	−6.47302e24	−0.910186	−0.455093	−	0.890444i	$-0.650394\pi$
$839$	−6.47302e24	−0.910186	−0.455093	+	0.890444i	$0.650394\pi$
$840$	0	0
$841$	1.89837e25	2.61587
$842$	6.95908e24	0.949290
$843$	9.09523e23	0.122823
$844$	5.06004e23	0.0676462
$845$	0	0
$846$	−7.67010e23	−0.100497
$847$	1.08611e25	1.40885
$848$	−2.82721e24	−0.363073
$849$	−3.01699e24	−0.383582
$850$	0	0
$851$	−2.66544e24	−0.332175
$852$	−2.84013e23	−0.0350430
$853$	−2.69306e24	−0.328988	−0.164494	−	0.986378i	$-0.552599\pi$
$853$	−2.69306e24	−0.328988	−0.164494	+	0.986378i	$0.552599\pi$
$854$	−5.54620e24	−0.670816
$855$	0	0
$856$	−4.62484e24	−0.548365
$857$	1.86785e24	0.219283	0.109641	−	0.993971i	$-0.465030\pi$
$857$	1.86785e24	0.219283	0.109641	+	0.993971i	$0.465030\pi$
$858$	8.78916e23	0.102166
$859$	−1.13124e25	−1.30200	−0.651000	−	0.759077i	$-0.725650\pi$
$859$	−1.13124e25	−1.30200	−0.651000	+	0.759077i	$0.725650\pi$
$860$	0	0
$861$	−1.17493e25	−1.32583
$862$	−6.00984e24	−0.671508
$863$	2.37061e24	0.262282	0.131141	−	0.991364i	$-0.458136\pi$
$863$	2.37061e24	0.262282	0.131141	+	0.991364i	$0.458136\pi$
$864$	1.70917e24	0.187248
$865$	0	0
$866$	4.83153e24	0.519019
$867$	−1.73178e25	−1.84217
$868$	1.22050e23	0.0128564
$869$	−1.53298e24	−0.159907
$870$	0	0
$871$	9.35446e24	0.956895
$872$	2.30770e24	0.233770
$873$	−7.83429e24	−0.785921
$874$	−6.89670e22	−0.00685164
$875$	0	0
$876$	−3.76002e24	−0.366357
$877$	6.79534e24	0.655714	0.327857	−	0.944727i	$-0.393674\pi$
$877$	6.79534e24	0.655714	0.327857	+	0.944727i	$0.393674\pi$
$878$	1.41285e25	1.35018
$879$	−2.86007e24	−0.270689
$880$	0	0
$881$	−1.88402e25	−1.74900	−0.874501	−	0.485024i	$-0.838811\pi$
$881$	−1.88402e25	−1.74900	−0.874501	+	0.485024i	$0.838811\pi$
$882$	−6.93212e24	−0.637357
$883$	−3.85491e24	−0.351033	−0.175517	−	0.984476i	$-0.556160\pi$
$883$	−3.85491e24	−0.351033	−0.175517	+	0.984476i	$0.556160\pi$
$884$	−5.46979e24	−0.493317
$885$	0	0
$886$	3.09081e24	0.273455
$887$	−8.32727e24	−0.729712	−0.364856	−	0.931064i	$-0.618882\pi$
$887$	−8.32727e24	−0.729712	−0.364856	+	0.931064i	$0.618882\pi$
$888$	−9.15281e23	−0.0794410
$889$	−1.87919e25	−1.61550
$890$	0	0
$891$	1.13459e24	0.0956924
$892$	7.11640e24	0.594510
$893$	3.17158e22	0.00262445
$894$	2.68590e24	0.220151
$895$	0	0
$896$	−1.83526e24	−0.147598
$897$	4.77617e24	0.380491
$898$	6.59113e24	0.520129
$899$	−3.74565e23	−0.0292799
$900$	0	0
$901$	3.60004e25	2.76151
$902$	4.14760e24	0.315168
$903$	−1.54327e25	−1.16171
$904$	6.54744e24	0.488248
$905$	0	0
$906$	5.66621e24	0.414670
$907$	−1.92435e25	−1.39515	−0.697576	−	0.716511i	$-0.745738\pi$
$907$	−1.92435e25	−1.39515	−0.697576	+	0.716511i	$0.745738\pi$
$908$	−1.28148e24	−0.0920415
$909$	−5.03807e24	−0.358485
$910$	0	0
$911$	−1.57682e25	−1.10123	−0.550613	−	0.834761i	$-0.685606\pi$
$911$	−1.57682e25	−1.10123	−0.550613	+	0.834761i	$0.685606\pi$
$912$	−2.36825e22	−0.00163859
$913$	−1.02519e24	−0.0702756
$914$	2.58738e24	0.175718
$915$	0	0
$916$	7.90373e24	0.526890
$917$	3.70346e25	2.44607
$918$	−2.17637e25	−1.42420
$919$	1.03058e25	0.668189	0.334094	−	0.942540i	$-0.391570\pi$
$919$	1.03058e25	0.668189	0.334094	+	0.942540i	$0.391570\pi$
$920$	0	0
$921$	1.80606e25	1.14954
$922$	4.31612e23	0.0272195
$923$	8.26339e23	0.0516349
$924$	−3.75512e24	−0.232494
$925$	0	0
$926$	7.11539e24	0.432519
$927$	−9.06674e24	−0.546102
$928$	5.63234e24	0.336149
$929$	9.73688e24	0.575819	0.287910	−	0.957658i	$-0.407040\pi$
$929$	9.73688e24	0.575819	0.287910	+	0.957658i	$0.407040\pi$
$930$	0	0
$931$	2.86642e23	0.0166444
$932$	−4.72113e24	−0.271651
$933$	−4.61679e24	−0.263236
$934$	−2.11621e25	−1.19567
$935$	0	0
$936$	−1.66638e24	−0.0924547
$937$	3.22145e25	1.77119	0.885594	−	0.464459i	$-0.153751\pi$
$937$	3.22145e25	1.77119	0.885594	+	0.464459i	$0.153751\pi$
$938$	−3.99664e25	−2.17756
$939$	2.10667e25	1.13747
$940$	0	0
$941$	−7.90374e24	−0.419103	−0.209552	−	0.977798i	$-0.567200\pi$
$941$	−7.90374e24	−0.419103	−0.209552	+	0.977798i	$0.567200\pi$
$942$	−7.81114e24	−0.410470
$943$	2.25387e25	1.17376
$944$	−1.28113e24	−0.0661198
$945$	0	0
$946$	5.44786e24	0.276154
$947$	−2.36682e25	−1.18902	−0.594512	−	0.804086i	$-0.702655\pi$
$947$	−2.36682e25	−1.18902	−0.594512	+	0.804086i	$0.702655\pi$
$948$	−2.86059e24	−0.142424
$949$	1.09398e25	0.539818
$950$	0	0
$951$	−7.97150e24	−0.386372
$952$	2.33693e25	1.12262
$953$	−9.09477e24	−0.433014	−0.216507	−	0.976281i	$-0.569466\pi$
$953$	−9.09477e24	−0.433014	−0.216507	+	0.976281i	$0.569466\pi$
$954$	1.09676e25	0.517546
$955$	0	0
$956$	1.11690e25	0.517750
$957$	1.15243e25	0.529496
$958$	6.63529e24	0.302171
$959$	−5.79516e25	−2.61582
$960$	0	0
$961$	−2.25448e25	−0.999763
$962$	2.66302e24	0.117054
$963$	1.79411e25	0.781673
$964$	−1.12151e25	−0.484340
$965$	0	0
$966$	−2.04059e25	−0.865865
$967$	−3.62970e25	−1.52667	−0.763337	−	0.646001i	$-0.776440\pi$
$967$	−3.62970e25	−1.52667	−0.763337	+	0.646001i	$0.776440\pi$
$968$	−7.15441e24	−0.298286
$969$	3.01562e23	0.0124630
$970$	0	0
$971$	−9.70396e24	−0.394081	−0.197040	−	0.980395i	$-0.563133\pi$
$971$	−9.70396e24	−0.394081	−0.197040	+	0.980395i	$0.563133\pi$
$972$	−1.10389e25	−0.444387
$973$	−3.60641e24	−0.143918
$974$	1.06196e25	0.420104
$975$	0	0
$976$	3.65340e24	0.142028
$977$	−3.70141e25	−1.42647	−0.713236	−	0.700924i	$-0.752771\pi$
$977$	−3.70141e25	−1.42647	−0.713236	+	0.700924i	$0.752771\pi$
$978$	2.12622e25	0.812321
$979$	−1.91644e23	−0.00725843
$980$	0	0
$981$	−8.95223e24	−0.333230
$982$	7.90127e24	0.291574
$983$	6.43184e24	0.235305	0.117652	−	0.993055i	$-0.462463\pi$
$983$	6.43184e24	0.235305	0.117652	+	0.993055i	$0.462463\pi$
$984$	7.73954e24	0.280709
$985$	0	0
$986$	−7.17196e25	−2.55672
$987$	9.38403e24	0.331661
$988$	6.89045e22	0.00241442
$989$	2.96045e25	1.02847
$990$	0	0
$991$	5.17070e25	1.76573	0.882863	−	0.469631i	$-0.155613\pi$
$991$	5.17070e25	1.76573	0.882863	+	0.469631i	$0.155613\pi$
$992$	−8.03967e22	−0.00272201
$993$	2.85342e25	0.957848
$994$	−3.53048e24	−0.117503
$995$	0	0
$996$	−1.91304e24	−0.0625922
$997$	2.77457e25	0.900093	0.450047	−	0.893005i	$-0.351407\pi$
$997$	2.77457e25	0.900093	0.450047	+	0.893005i	$0.351407\pi$
$998$	8.29907e24	0.266944
$999$	1.05959e25	0.337933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.18.a.f.1.1		2
5.2	odd	4		50.18.b.d.49.4		4
5.3	odd	4		50.18.b.d.49.1		4
5.4	even	2		10.18.a.c.1.2	✓	2
15.14	odd	2		90.18.a.k.1.2		2
20.19	odd	2		80.18.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.c.1.2	✓	2	5.4	even	2
50.18.a.f.1.1		2	1.1	even	1	trivial
50.18.b.d.49.1		4	5.3	odd	4
50.18.b.d.49.4		4	5.2	odd	4
80.18.a.d.1.1		2	20.19	odd	2
90.18.a.k.1.2		2	15.14	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q+256.000 q^{2} -8003.53 q^{3} +65536.0 q^{4} -2.04890e6 q^{6} -2.54694e7 q^{7} +1.67772e7 q^{8} -6.50836e7 q^{9} -2.81089e8 q^{11} -5.24520e8 q^{12} +1.52610e9 q^{13} -6.52016e9 q^{14} +4.29497e9 q^{16} -5.46901e10 q^{17} -1.66614e10 q^{18} +6.88947e8 q^{19} +2.03845e11 q^{21} -7.19587e10 q^{22} -3.91035e11 q^{23} -1.34277e11 q^{24} +3.90681e11 q^{26} +1.55448e12 q^{27} -1.66916e12 q^{28} +5.12259e12 q^{29} -7.31204e10 q^{31} +1.09951e12 q^{32} +2.24970e12 q^{33} -1.40007e13 q^{34} -4.26532e12 q^{36} +6.81637e12 q^{37} +1.76370e11 q^{38} -1.22142e13 q^{39} -5.76386e13 q^{41} +5.21843e13 q^{42} -7.57081e13 q^{43} -1.84214e13 q^{44} -1.00105e14 q^{46} +4.60351e13 q^{47} -3.43749e13 q^{48} +4.16059e14 q^{49} +4.37714e14 q^{51} +1.00014e14 q^{52} -6.58261e14 q^{53} +3.97946e14 q^{54} -4.27305e14 q^{56} -5.51401e12 q^{57} +1.31138e15 q^{58} -2.98287e14 q^{59} +8.50623e14 q^{61} -1.87188e13 q^{62} +1.65764e15 q^{63} +2.81475e14 q^{64} +5.75924e14 q^{66} +6.12967e15 q^{67} -3.58417e15 q^{68} +3.12966e15 q^{69} +5.41472e14 q^{71} -1.09192e15 q^{72} +7.16849e15 q^{73} +1.74499e15 q^{74} +4.51508e13 q^{76} +7.15916e15 q^{77} -3.12683e15 q^{78} +5.45373e15 q^{79} -4.03640e15 q^{81} -1.47555e16 q^{82} +3.64723e15 q^{83} +1.33592e16 q^{84} -1.93813e16 q^{86} -4.09988e16 q^{87} -4.71589e15 q^{88} +6.81792e14 q^{89} -3.88687e16 q^{91} -2.56269e16 q^{92} +5.85222e14 q^{93} +1.17850e16 q^{94} -8.79998e15 q^{96} +1.20373e17 q^{97} +1.06511e17 q^{98} +1.82943e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 512 q^{2} + 1308 q^{3} + 131072 q^{4} + 334848 q^{6} - 603844 q^{7} + 33554432 q^{8} - 107519094 q^{9} - 471481296 q^{11} + 85721088 q^{12} + 1541834228 q^{13} - 154584064 q^{14} + 8589934592 q^{16}+ \cdots + 26\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 512 * q^2 + 1308 * q^3 + 131072 * q^4 + 334848 * q^6 - 603844 * q^7 + 33554432 * q^8 - 107519094 * q^9 - 471481296 * q^11 + 85721088 * q^12 + 1541834228 * q^13 - 154584064 * q^14 + 8589934592 * q^16 - 32139900564 * q^17 - 27524888064 * q^18 + 128672529400 * q^19 + 435381246624 * q^21 - 120699211776 * q^22 - 650359859292 * q^23 + 21944598528 * q^24 + 394709562368 * q^26 - 43156034280 * q^27 - 39573520384 * q^28 + 2543054749980 * q^29 + 7839407998744 * q^31 + 2199023255552 * q^32 + 476857812816 * q^33 - 8227814544384 * q^34 - 7046371344384 * q^36 + 27805209097556 * q^37 + 32940167526400 * q^38 - 12067623537288 * q^39 - 37826364264156 * q^41 + 111457599135744 * q^42 - 29630453926852 * q^43 - 30898998214656 * q^44 - 166492123978752 * q^46 - 220791583022004 * q^47 + 5617817223168 * q^48 + 801722584677954 * q^49 + 647690491265544 * q^51 + 101045647966208 * q^52 - 1058306017600572 * q^53 - 11047944775680 * q^54 - 10130821218304 * q^56 + 1186209507102000 * q^57 + 651022015994880 * q^58 + 1527820717235160 * q^59 - 631738213122116 * q^61 + 2006888447678464 * q^62 + 602457597963468 * q^63 + 562949953421312 * q^64 + 122075600080896 * q^66 + 8843763493872596 * q^67 - 2106320523362304 * q^68 + 714953250788832 * q^69 - 3331901660912376 * q^71 - 1803871064162304 * q^72 + 10026350574292028 * q^73 + 7118133528974336 * q^74 + 8432682886758400 * q^76 + 2424946105073712 * q^77 - 3089311625545728 * q^78 + 8263606842055120 * q^79 - 13432683850659198 * q^81 - 9683549251623936 * q^82 + 10689526892336988 * q^83 + 28533145378750464 * q^84 - 7585396205274112 * q^86 - 65018171604068280 * q^87 - 7910143542951936 * q^88 + 55878412521904980 * q^89 - 38477396610603016 * q^91 - 42621983738560512 * q^92 + 74263001022197376 * q^93 - 56522645253633024 * q^94 + 1438161209131008 * q^96 + 56106580363859756 * q^97 + 205240981677556224 * q^98 + 26373671099096112 * q^99

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