LMFDB - Embedded newform 50.28.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,28,Mod(1,50)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 28, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("50.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	50.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$230.927787419$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{12929}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3232 $ x^2 - x - 3232
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3}\cdot 5\cdot 7 $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$57.3529$ 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)

$f(q)$	$=$	\(q+8192.00 q^{2} -1.45602e6 q^{3} +6.71089e7 q^{4} -1.19278e10 q^{6} +3.42070e11 q^{7} +5.49756e11 q^{8} -5.50559e12 q^{9} +1.20755e13 q^{11} -9.77122e13 q^{12} +1.02154e14 q^{13} +2.80224e15 q^{14} +4.50360e15 q^{16} -1.63337e16 q^{17} -4.51018e16 q^{18} -2.21733e15 q^{19} -4.98063e17 q^{21} +9.89228e16 q^{22} +1.90828e17 q^{23} -8.00458e17 q^{24} +8.36847e17 q^{26} +1.91193e19 q^{27} +2.29560e19 q^{28} -6.52176e19 q^{29} +4.50679e19 q^{31} +3.68935e19 q^{32} -1.75823e19 q^{33} -1.33806e20 q^{34} -3.69474e20 q^{36} -2.51294e21 q^{37} -1.81644e19 q^{38} -1.48739e20 q^{39} +6.73990e20 q^{41} -4.08013e21 q^{42} +1.21806e21 q^{43} +8.10376e20 q^{44} +1.56326e21 q^{46} -4.88526e22 q^{47} -6.55735e21 q^{48} +5.12997e22 q^{49} +2.37823e22 q^{51} +6.85545e21 q^{52} -9.75271e21 q^{53} +1.56626e23 q^{54} +1.88055e23 q^{56} +3.22849e21 q^{57} -5.34263e23 q^{58} +1.09826e24 q^{59} +9.88829e23 q^{61} +3.69197e23 q^{62} -1.88330e24 q^{63} +3.02231e23 q^{64} -1.44034e23 q^{66} -8.13848e24 q^{67} -1.09614e24 q^{68} -2.77850e23 q^{69} -1.38068e25 q^{71} -3.02673e24 q^{72} +2.27541e25 q^{73} -2.05860e25 q^{74} -1.48803e23 q^{76} +4.13068e24 q^{77} -1.21847e24 q^{78} +2.55487e24 q^{79} +1.41452e25 q^{81} +5.52132e24 q^{82} +9.67997e25 q^{83} -3.34244e25 q^{84} +9.97833e24 q^{86} +9.49584e25 q^{87} +6.63860e24 q^{88} +3.24368e26 q^{89} +3.49439e25 q^{91} +1.28062e25 q^{92} -6.56200e25 q^{93} -4.00200e26 q^{94} -5.37178e25 q^{96} -4.91800e26 q^{97} +4.20247e26 q^{98} -6.64830e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16384 q^{2} + 2245644 q^{3} + 134217728 q^{4} + 18396315648 q^{6} + 120196732292 q^{7} + 1099511627776 q^{8} + 571163616594 q^{9} + 7112122732704 q^{11} + 150702617788416 q^{12} + 323114990355404 q^{13}+ \cdots - 96\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 16384 * q^2 + 2245644 * q^3 + 134217728 * q^4 + 18396315648 * q^6 + 120196732292 * q^7 + 1099511627776 * q^8 + 571163616594 * q^9 + 7112122732704 * q^11 + 150702617788416 * q^12 + 323114990355404 * q^13 + 984651630936064 * q^14 + 9007199254740992 * q^16 + 11949781720794252 * q^17 + 4678972347138048 * q^18 - 310800626187534200 * q^19 - 1319365315134326376 * q^21 + 58262509426311168 * q^22 + 1207992822578557644 * q^23 + 1234555844922703872 * q^24 + 2646958000991469568 * q^26 + 13386024338103046440 * q^27 + 8066266160628236288 * q^28 - 85089627076663724580 * q^29 - 169891626304914480056 * q^31 + 73786976294838206464 * q^32 - 35955214564003682112 * q^33 + 97892611856746512384 * q^34 + 38330141467754889216 * q^36 - 1001687425876018532308 * q^37 - 2546078729728280166400 * q^38 + 669184707607358092488 * q^39 + 6829708525832119000044 * q^41 - 10808240661580401672192 * q^42 - 15331910221739375128036 * q^43 + 477286477220341088256 * q^44 + 9895877202563544219648 * q^46 - 44654607958183509227628 * q^47 + 10113481481606790119424 * q^48 + 34815266426190611168346 * q^49 + 128478598882379942153544 * q^51 + 21683879944122118701056 * q^52 - 259350970067880627435396 * q^53 + 109658311377740156436480 * q^54 + 66078852387866511671296 * q^56 - 1139044611805451608251600 * q^57 - 697054225012029231759360 * q^58 + 2082093442621301023169640 * q^59 + 677925769536334246319284 * q^61 - 1391752202689859420618752 * q^62 - 3231569874371732206566876 * q^63 + 604462909807314587353088 * q^64 - 294545117708318163861504 * q^66 - 2453617552336948143390028 * q^67 + 801936276330467429449728 * q^68 + 3487358239126020846890568 * q^69 - 23890193584108132090228776 * q^71 + 314000518903848052457472 * q^72 + 13919420706136886544146204 * q^73 - 8205823392776343816667136 * q^74 - 20857476953934071123148800 * q^76 + 5231935501660614540408384 * q^77 + 5481961124719477493661696 * q^78 - 53659327270981104663051920 * q^79 - 53416489016311609709962998 * q^81 + 55948972243616718848360448 * q^82 - 5756571261014435461903716 * q^83 - 88541107499666650498596864 * q^84 - 125599008536488961048870912 * q^86 + 21398789661957929503788840 * q^87 + 3909930821389034194993152 * q^88 + 174438127411287409220344020 * q^89 - 14081455302088161819283816 * q^91 + 81067026043400554247356416 * q^92 - 861329117078544091150519632 * q^93 - 365810548393439307592728576 * q^94 + 82849640297322824658321408 * q^96 + 21732067184289340167295292 * q^97 + 285206662563353486691090432 * q^98 - 96644441211111069636758112 * 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 $

$2$	8192.00	0.707107
$2$	8192.00	0.707107
$3$	−1.45602e6	−0.527268	−0.263634	−	0.964623i	$-0.584921\pi$
$3$	−1.45602e6	−0.527268	−0.263634	+	0.964623i	$0.584921\pi$
$4$	6.71089e7	0.500000
$5$	0	0
$5$	0	0
$6$	−1.19278e10	−0.372835
$7$	3.42070e11	1.33442	0.667209	−	0.744871i	$-0.267489\pi$
$7$	3.42070e11	1.33442	0.667209	+	0.744871i	$0.267489\pi$
$8$	5.49756e11	0.353553
$9$	−5.50559e12	−0.721988
$10$	0	0
$11$	1.20755e13	0.105464	0.0527321	−	0.998609i	$-0.483207\pi$
$11$	1.20755e13	0.105464	0.0527321	+	0.998609i	$0.483207\pi$
$12$	−9.77122e13	−0.263634
$13$	1.02154e14	0.0935451	0.0467725	−	0.998906i	$-0.485106\pi$
$13$	1.02154e14	0.0935451	0.0467725	+	0.998906i	$0.485106\pi$
$14$	2.80224e15	0.943576
$15$	0	0
$16$	4.50360e15	0.250000
$17$	−1.63337e16	−0.399968	−0.199984	−	0.979799i	$-0.564089\pi$
$17$	−1.63337e16	−0.399968	−0.199984	+	0.979799i	$0.564089\pi$
$18$	−4.51018e16	−0.510523
$19$	−2.21733e15	−0.0120964	−0.00604822	−	0.999982i	$-0.501925\pi$
$19$	−2.21733e15	−0.0120964	−0.00604822	+	0.999982i	$0.501925\pi$
$20$	0	0
$21$	−4.98063e17	−0.703596
$22$	9.89228e16	0.0745745
$23$	1.90828e17	0.0789434	0.0394717	−	0.999221i	$-0.487433\pi$
$23$	1.90828e17	0.0789434	0.0394717	+	0.999221i	$0.487433\pi$
$24$	−8.00458e17	−0.186418
$25$	0	0
$26$	8.36847e17	0.0661463
$27$	1.91193e19	0.907950
$28$	2.29560e19	0.667209
$29$	−6.52176e19	−1.18030	−0.590149	−	0.807294i	$-0.700931\pi$
$29$	−6.52176e19	−1.18030	−0.590149	+	0.807294i	$0.700931\pi$
$30$	0	0
$31$	4.50679e19	0.331501	0.165750	−	0.986168i	$-0.446995\pi$
$31$	4.50679e19	0.331501	0.165750	+	0.986168i	$0.446995\pi$
$32$	3.68935e19	0.176777
$33$	−1.75823e19	−0.0556080
$34$	−1.33806e20	−0.282820
$35$	0	0
$36$	−3.69474e20	−0.360994
$37$	−2.51294e21	−1.69613	−0.848063	−	0.529895i	$-0.822231\pi$
$37$	−2.51294e21	−1.69613	−0.848063	+	0.529895i	$0.822231\pi$
$38$	−1.81644e19	−0.00855347
$39$	−1.48739e20	−0.0493234
$40$	0	0
$41$	6.73990e20	0.113781	0.0568907	−	0.998380i	$-0.481881\pi$
$41$	6.73990e20	0.113781	0.0568907	+	0.998380i	$0.481881\pi$
$42$	−4.08013e21	−0.497518
$43$	1.21806e21	0.108104	0.0540522	−	0.998538i	$-0.482786\pi$
$43$	1.21806e21	0.108104	0.0540522	+	0.998538i	$0.482786\pi$
$44$	8.10376e20	0.0527321
$45$	0	0
$46$	1.56326e21	0.0558214
$47$	−4.88526e22	−1.30487	−0.652434	−	0.757846i	$-0.726252\pi$
$47$	−4.88526e22	−1.30487	−0.652434	+	0.757846i	$0.726252\pi$
$48$	−6.55735e21	−0.131817
$49$	5.12997e22	0.780671
$50$	0	0
$51$	2.37823e22	0.210891
$52$	6.85545e21	0.0467725
$53$	−9.75271e21	−0.0514519	−0.0257259	−	0.999669i	$-0.508190\pi$
$53$	−9.75271e21	−0.0514519	−0.0257259	+	0.999669i	$0.508190\pi$
$54$	1.56626e23	0.642018
$55$	0	0
$56$	1.88055e23	0.471788
$57$	3.22849e21	0.00637807
$58$	−5.34263e23	−0.834597
$59$	1.09826e24	1.36208	0.681042	−	0.732245i	$-0.261527\pi$
$59$	1.09826e24	1.36208	0.681042	+	0.732245i	$0.261527\pi$
$60$	0	0
$61$	9.88829e23	0.781931	0.390966	−	0.920405i	$-0.372141\pi$
$61$	9.88829e23	0.781931	0.390966	+	0.920405i	$0.372141\pi$
$62$	3.69197e23	0.234407
$63$	−1.88330e24	−0.963434
$64$	3.02231e23	0.125000
$65$	0	0
$66$	−1.44034e23	−0.0393208
$67$	−8.13848e24	−1.81357	−0.906784	−	0.421597i	$-0.861470\pi$
$67$	−8.13848e24	−1.81357	−0.906784	+	0.421597i	$0.861470\pi$
$68$	−1.09614e24	−0.199984
$69$	−2.77850e23	−0.0416244
$70$	0	0
$71$	−1.38068e25	−1.40638	−0.703192	−	0.711000i	$-0.748243\pi$
$71$	−1.38068e25	−1.40638	−0.703192	+	0.711000i	$0.748243\pi$
$72$	−3.02673e24	−0.255261
$73$	2.27541e25	1.59294	0.796471	−	0.604676i	$-0.206698\pi$
$73$	2.27541e25	1.59294	0.796471	+	0.604676i	$0.206698\pi$
$74$	−2.05860e25	−1.19934
$75$	0	0
$76$	−1.48803e23	−0.00604822
$77$	4.13068e24	0.140733
$78$	−1.21847e24	−0.0348769
$79$	2.55487e24	0.0615748	0.0307874	−	0.999526i	$-0.490199\pi$
$79$	2.55487e24	0.0615748	0.0307874	+	0.999526i	$0.490199\pi$
$80$	0	0
$81$	1.41452e25	0.243255
$82$	5.52132e24	0.0804556
$83$	9.67997e25	1.19762	0.598811	−	0.800891i	$-0.295640\pi$
$83$	9.67997e25	1.19762	0.598811	+	0.800891i	$0.295640\pi$
$84$	−3.34244e25	−0.351798
$85$	0	0
$86$	9.97833e24	0.0764414
$87$	9.49584e25	0.622334
$88$	6.63860e24	0.0372872
$89$	3.24368e26	1.56413	0.782064	−	0.623198i	$-0.214167\pi$
$89$	3.24368e26	1.56413	0.782064	+	0.623198i	$0.214167\pi$
$90$	0	0
$91$	3.49439e25	0.124828
$92$	1.28062e25	0.0394717
$93$	−6.56200e25	−0.174790
$94$	−4.00200e26	−0.922681
$95$	0	0
$96$	−5.37178e25	−0.0932088
$97$	−4.91800e26	−0.741943	−0.370971	−	0.928644i	$-0.620975\pi$
$97$	−4.91800e26	−0.741943	−0.370971	+	0.928644i	$0.620975\pi$
$98$	4.20247e26	0.552018
$99$	−6.64830e25	−0.0761439
$100$	0	0
$101$	2.12114e27	1.85452	0.927259	−	0.374421i	$-0.122159\pi$
$101$	2.12114e27	1.85452	0.927259	+	0.374421i	$0.122159\pi$
$102$	1.94825e26	0.149122
$103$	−3.47783e25	−0.0233349	−0.0116675	−	0.999932i	$-0.503714\pi$
$103$	−3.47783e25	−0.0233349	−0.0116675	+	0.999932i	$0.503714\pi$
$104$	5.61599e25	0.0330732
$105$	0	0
$106$	−7.98942e25	−0.0363820
$107$	−4.84969e27	−1.94551	−0.972754	−	0.231841i	$-0.925525\pi$
$107$	−4.84969e27	−1.94551	−0.972754	+	0.231841i	$0.925525\pi$
$108$	1.28308e27	0.453975
$109$	−1.76094e27	−0.550158	−0.275079	−	0.961422i	$-0.588704\pi$
$109$	−1.76094e27	−0.550158	−0.275079	+	0.961422i	$0.588704\pi$
$110$	0	0
$111$	3.65890e27	0.894314
$112$	1.54055e27	0.333604
$113$	−3.51618e27	−0.675324	−0.337662	−	0.941268i	$-0.609636\pi$
$113$	−3.51618e27	−0.675324	−0.337662	+	0.941268i	$0.609636\pi$
$114$	2.64478e25	0.00450997
$115$	0	0
$116$	−4.37668e27	−0.590149
$117$	−5.62419e26	−0.0675384
$118$	8.99696e27	0.963138
$119$	−5.58729e27	−0.533725
$120$	0	0
$121$	−1.29642e28	−0.988877
$122$	8.10049e27	0.552909
$123$	−9.81346e26	−0.0599933
$124$	3.02446e27	0.165750
$125$	0	0
$126$	−1.54280e28	−0.681250
$127$	−8.77438e27	−0.348230	−0.174115	−	0.984725i	$-0.555706\pi$
$127$	−8.77438e27	−0.348230	−0.174115	+	0.984725i	$0.555706\pi$
$128$	2.47588e27	0.0883883
$129$	−1.77352e27	−0.0570001
$130$	0	0
$131$	−3.38485e28	−0.883846	−0.441923	−	0.897053i	$-0.645703\pi$
$131$	−3.38485e28	−0.883846	−0.441923	+	0.897053i	$0.645703\pi$
$132$	−1.17993e27	−0.0278040
$133$	−7.58484e26	−0.0161417
$134$	−6.66705e28	−1.28239
$135$	0	0
$136$	−8.97957e27	−0.141410
$137$	−1.01883e29	−1.45337	−0.726683	−	0.686973i	$-0.758939\pi$
$137$	−1.01883e29	−1.45337	−0.726683	+	0.686973i	$0.758939\pi$
$138$	−2.27615e27	−0.0294329
$139$	−4.45983e28	−0.523141	−0.261571	−	0.965184i	$-0.584240\pi$
$139$	−4.45983e28	−0.523141	−0.261571	+	0.965184i	$0.584240\pi$
$140$	0	0
$141$	7.11306e28	0.688015
$142$	−1.13105e29	−0.994463
$143$	1.23357e27	0.00986566
$144$	−2.47950e28	−0.180497
$145$	0	0
$146$	1.86401e29	1.12638
$147$	−7.46937e28	−0.411623
$148$	−1.68640e29	−0.848063
$149$	−5.58786e28	−0.256585	−0.128292	−	0.991736i	$-0.540950\pi$
$149$	−5.58786e28	−0.256585	−0.128292	+	0.991736i	$0.540950\pi$
$150$	0	0
$151$	−2.68196e29	−1.02864	−0.514320	−	0.857598i	$-0.671956\pi$
$151$	−2.68196e29	−1.02864	−0.514320	+	0.857598i	$0.671956\pi$
$152$	−1.21899e27	−0.00427673
$153$	8.99269e28	0.288772
$154$	3.38386e28	0.0995135
$155$	0	0
$156$	−9.98171e27	−0.0246617
$157$	3.96402e28	0.0898443	0.0449222	−	0.998990i	$-0.485696\pi$
$157$	3.96402e28	0.0898443	0.0449222	+	0.998990i	$0.485696\pi$
$158$	2.09295e28	0.0435400
$159$	1.42002e28	0.0271289
$160$	0	0
$161$	6.52765e28	0.105343
$162$	1.15877e29	0.172007
$163$	7.23256e29	0.988005	0.494003	−	0.869460i	$-0.335533\pi$
$163$	7.23256e29	0.988005	0.494003	+	0.869460i	$0.335533\pi$
$164$	4.52307e28	0.0568907
$165$	0	0
$166$	7.92983e29	0.846846
$167$	9.65355e28	0.0950637	0.0475318	−	0.998870i	$-0.484864\pi$
$167$	9.65355e28	0.0950637	0.0475318	+	0.998870i	$0.484864\pi$
$168$	−2.73813e29	−0.248759
$169$	−1.18210e30	−0.991249
$170$	0	0
$171$	1.22077e28	0.00873348
$172$	8.17424e28	0.0540522
$173$	6.03771e29	0.369190	0.184595	−	0.982815i	$-0.440903\pi$
$173$	6.03771e29	0.369190	0.184595	+	0.982815i	$0.440903\pi$
$174$	7.77900e29	0.440057
$175$	0	0
$176$	5.43834e28	0.0263661
$177$	−1.59910e30	−0.718184
$178$	2.65722e30	1.10601
$179$	−3.15544e30	−1.21771	−0.608854	−	0.793282i	$-0.708371\pi$
$179$	−3.15544e30	−1.21771	−0.608854	+	0.793282i	$0.708371\pi$
$180$	0	0
$181$	−2.41563e30	−0.802362	−0.401181	−	0.915999i	$-0.631400\pi$
$181$	−2.41563e30	−0.802362	−0.401181	+	0.915999i	$0.631400\pi$
$182$	2.86261e29	0.0882669
$183$	−1.43976e30	−0.412288
$184$	1.04909e29	0.0279107
$185$	0	0
$186$	−5.37559e29	−0.123595
$187$	−1.97239e29	−0.0421824
$188$	−3.27844e30	−0.652434
$189$	6.54016e30	1.21158
$190$	0	0
$191$	1.23727e30	0.198845	0.0994227	−	0.995045i	$-0.468300\pi$
$191$	1.23727e30	0.198845	0.0994227	+	0.995045i	$0.468300\pi$
$192$	−4.40056e29	−0.0659086
$193$	−9.55053e30	−1.33353	−0.666766	−	0.745267i	$-0.732322\pi$
$193$	−9.55053e30	−1.33353	−0.666766	+	0.745267i	$0.732322\pi$
$194$	−4.02883e30	−0.524633
$195$	0	0
$196$	3.44267e30	0.390336
$197$	5.01468e30	0.530822	0.265411	−	0.964135i	$-0.414492\pi$
$197$	5.01468e30	0.530822	0.265411	+	0.964135i	$0.414492\pi$
$198$	−5.44629e29	−0.0538419
$199$	1.64461e31	1.51896	0.759481	−	0.650530i	$-0.225453\pi$
$199$	1.64461e31	1.51896	0.759481	+	0.650530i	$0.225453\pi$
$200$	0	0
$201$	1.18498e31	0.956237
$202$	1.73764e31	1.31134
$203$	−2.23090e31	−1.57501
$204$	1.59601e30	0.105445
$205$	0	0
$206$	−2.84904e29	−0.0165003
$207$	−1.05062e30	−0.0569962
$208$	4.60062e29	0.0233863
$209$	−2.67755e28	−0.00127574
$210$	0	0
$211$	−1.40300e31	−0.587820	−0.293910	−	0.955833i	$-0.594957\pi$
$211$	−1.40300e31	−0.587820	−0.293910	+	0.955833i	$0.594957\pi$
$212$	−6.54493e29	−0.0257259
$213$	2.01030e31	0.741542
$214$	−3.97286e31	−1.37568
$215$	0	0
$216$	1.05110e31	0.321009
$217$	1.54164e31	0.442361
$218$	−1.44256e31	−0.389021
$219$	−3.31305e31	−0.839908
$220$	0	0
$221$	−1.66856e30	−0.0374150
$222$	2.99737e31	0.632376
$223$	−1.89499e31	−0.376264	−0.188132	−	0.982144i	$-0.560243\pi$
$223$	−1.89499e31	−0.376264	−0.188132	+	0.982144i	$0.560243\pi$
$224$	1.26202e31	0.235894
$225$	0	0
$226$	−2.88045e31	−0.477526
$227$	−2.62637e31	−0.410211	−0.205106	−	0.978740i	$-0.565754\pi$
$227$	−2.62637e31	−0.410211	−0.205106	+	0.978740i	$0.565754\pi$
$228$	2.16660e29	0.00318903
$229$	−1.17074e32	−1.62436	−0.812182	−	0.583405i	$-0.801720\pi$
$229$	−1.17074e32	−1.62436	−0.812182	+	0.583405i	$0.801720\pi$
$230$	0	0
$231$	−6.01438e30	−0.0742043
$232$	−3.58538e31	−0.417299
$233$	−4.74248e31	−0.520835	−0.260418	−	0.965496i	$-0.583860\pi$
$233$	−4.74248e31	−0.520835	−0.260418	+	0.965496i	$0.583860\pi$
$234$	−4.60734e30	−0.0477569
$235$	0	0
$236$	7.37031e31	0.681042
$237$	−3.71995e30	−0.0324664
$238$	−4.57711e31	−0.377400
$239$	−4.45355e31	−0.347004	−0.173502	−	0.984834i	$-0.555508\pi$
$239$	−4.45355e31	−0.347004	−0.173502	+	0.984834i	$0.555508\pi$
$240$	0	0
$241$	1.62097e32	1.12861	0.564307	−	0.825565i	$-0.309144\pi$
$241$	1.62097e32	1.12861	0.564307	+	0.825565i	$0.309144\pi$
$242$	−1.06203e32	−0.699242
$243$	−1.66392e32	−1.03621
$244$	6.63592e31	0.390966
$245$	0	0
$246$	−8.03918e30	−0.0424217
$247$	−2.26510e29	−0.00113156
$248$	2.47764e31	0.117203
$249$	−1.40943e32	−0.631468
$250$	0	0
$251$	6.55019e31	0.263426	0.131713	−	0.991288i	$-0.457952\pi$
$251$	6.55019e31	0.263426	0.131713	+	0.991288i	$0.457952\pi$
$252$	−1.26386e32	−0.481717
$253$	2.30435e30	0.00832571
$254$	−7.18797e31	−0.246236
$255$	0	0
$256$	2.02824e31	0.0625000
$257$	−3.76002e32	−1.09924	−0.549621	−	0.835414i	$-0.685228\pi$
$257$	−3.76002e32	−1.09924	−0.549621	+	0.835414i	$0.685228\pi$
$258$	−1.45287e31	−0.0403051
$259$	−8.59601e32	−2.26334
$260$	0	0
$261$	3.59061e32	0.852161
$262$	−2.77287e32	−0.624973
$263$	−1.47130e32	−0.314992	−0.157496	−	0.987520i	$-0.550342\pi$
$263$	−1.47130e32	−0.314992	−0.157496	+	0.987520i	$0.550342\pi$
$264$	−9.66596e30	−0.0196604
$265$	0	0
$266$	−6.21350e30	−0.0114139
$267$	−4.72287e32	−0.824715
$268$	−5.46164e32	−0.906784
$269$	−1.09666e33	−1.73148	−0.865738	−	0.500498i	$-0.833150\pi$
$269$	−1.09666e33	−1.73148	−0.865738	+	0.500498i	$0.833150\pi$
$270$	0	0
$271$	−7.97318e32	−1.13906	−0.569530	−	0.821971i	$-0.692875\pi$
$271$	−7.97318e32	−1.13906	−0.569530	+	0.821971i	$0.692875\pi$
$272$	−7.35607e31	−0.0999920
$273$	−5.08792e31	−0.0658180
$274$	−8.34627e32	−1.02768
$275$	0	0
$276$	−1.86462e31	−0.0208122
$277$	1.37742e33	1.46416	0.732081	−	0.681218i	$-0.238549\pi$
$277$	1.37742e33	1.46416	0.732081	+	0.681218i	$0.238549\pi$
$278$	−3.65350e32	−0.369917
$279$	−2.48126e32	−0.239340
$280$	0	0
$281$	1.94855e33	1.70677	0.853387	−	0.521277i	$-0.174544\pi$
$281$	1.94855e33	1.70677	0.853387	+	0.521277i	$0.174544\pi$
$282$	5.82702e32	0.486500
$283$	−2.07385e33	−1.65067	−0.825336	−	0.564642i	$-0.809014\pi$
$283$	−2.07385e33	−1.65067	−0.825336	+	0.564642i	$0.809014\pi$
$284$	−9.26555e32	−0.703192
$285$	0	0
$286$	1.01054e31	0.00697608
$287$	2.30552e32	0.151832
$288$	−2.03120e32	−0.127631
$289$	−1.40092e33	−0.840025
$290$	0	0
$291$	7.16073e32	0.391203
$292$	1.52700e33	0.796471
$293$	−1.62146e33	−0.807596	−0.403798	−	0.914848i	$-0.632310\pi$
$293$	−1.62146e33	−0.807596	−0.403798	+	0.914848i	$0.632310\pi$
$294$	−6.11891e32	−0.291062
$295$	0	0
$296$	−1.38150e33	−0.599671
$297$	2.30876e32	0.0957563
$298$	−4.57758e32	−0.181433
$299$	1.94939e31	0.00738476
$300$	0	0
$301$	4.16661e32	0.144257
$302$	−2.19706e33	−0.727358
$303$	−3.08843e33	−0.977828
$304$	−9.98598e30	−0.00302411
$305$	0	0
$306$	7.36681e32	0.204193
$307$	−4.28458e33	−1.13642	−0.568212	−	0.822882i	$-0.692365\pi$
$307$	−4.28458e33	−1.13642	−0.568212	+	0.822882i	$0.692365\pi$
$308$	2.77206e32	0.0703667
$309$	5.06381e31	0.0123038
$310$	0	0
$311$	1.87537e33	0.417658	0.208829	−	0.977952i	$-0.433035\pi$
$311$	1.87537e33	0.417658	0.208829	+	0.977952i	$0.433035\pi$
$312$	−8.17701e31	−0.0174384
$313$	−7.71677e33	−1.57611	−0.788056	−	0.615604i	$-0.788912\pi$
$313$	−7.71677e33	−1.57611	−0.788056	+	0.615604i	$0.788912\pi$
$314$	3.24733e32	0.0635295
$315$	0	0
$316$	1.71454e32	0.0307874
$317$	3.06539e32	0.0527455	0.0263728	−	0.999652i	$-0.491604\pi$
$317$	3.06539e32	0.0527455	0.0263728	+	0.999652i	$0.491604\pi$
$318$	1.16328e32	0.0191831
$319$	−7.87538e32	−0.124479
$320$	0	0
$321$	7.06127e33	1.02580
$322$	5.34745e32	0.0744891
$323$	3.62174e31	0.00483819
$324$	9.49268e32	0.121627
$325$	0	0
$326$	5.92491e33	0.698625
$327$	2.56398e33	0.290081
$328$	3.70530e32	0.0402278
$329$	−1.67110e34	−1.74124
$330$	0	0
$331$	−1.08931e34	−1.04586	−0.522930	−	0.852375i	$-0.675161\pi$
$331$	−1.08931e34	−1.04586	−0.522930	+	0.852375i	$0.675161\pi$
$332$	6.49612e33	0.598811
$333$	1.38352e34	1.22458
$334$	7.90819e32	0.0672202
$335$	0	0
$336$	−2.24308e33	−0.175899
$337$	2.14689e34	1.61736	0.808680	−	0.588249i	$-0.200183\pi$
$337$	2.14689e34	1.61736	0.808680	+	0.588249i	$0.200183\pi$
$338$	−9.68375e33	−0.700919
$339$	5.11964e33	0.356077
$340$	0	0
$341$	5.44220e32	0.0349615
$342$	1.00006e32	0.00617550
$343$	−4.93013e33	−0.292676
$344$	6.69634e32	0.0382207
$345$	0	0
$346$	4.94609e33	0.261057
$347$	−2.88990e34	−1.46702	−0.733509	−	0.679680i	$-0.762119\pi$
$347$	−2.88990e34	−1.46702	−0.733509	+	0.679680i	$0.762119\pi$
$348$	6.37255e33	0.311167
$349$	−4.64738e33	−0.218306	−0.109153	−	0.994025i	$-0.534814\pi$
$349$	−4.64738e33	−0.218306	−0.109153	+	0.994025i	$0.534814\pi$
$350$	0	0
$351$	1.95312e33	0.0849342
$352$	4.45509e32	0.0186436
$353$	2.34595e34	0.944845	0.472422	−	0.881372i	$-0.343380\pi$
$353$	2.34595e34	0.944845	0.472422	+	0.881372i	$0.343380\pi$
$354$	−1.30998e34	−0.507832
$355$	0	0
$356$	2.17679e34	0.782064
$357$	8.13523e33	0.281416
$358$	−2.58493e34	−0.861050
$359$	2.11955e34	0.679937	0.339968	−	0.940437i	$-0.389584\pi$
$359$	2.11955e34	0.679937	0.339968	+	0.940437i	$0.389584\pi$
$360$	0	0
$361$	−3.35957e34	−0.999854
$362$	−1.97889e34	−0.567356
$363$	1.88762e34	0.521404
$364$	2.34505e33	0.0624141
$365$	0	0
$366$	−1.17945e34	−0.291531
$367$	−5.17652e34	−1.23323	−0.616617	−	0.787263i	$-0.711497\pi$
$367$	−5.17652e34	−1.23323	−0.616617	+	0.787263i	$0.711497\pi$
$368$	8.59412e32	0.0197358
$369$	−3.71071e33	−0.0821488
$370$	0	0
$371$	−3.33611e33	−0.0686583
$372$	−4.40369e33	−0.0873950
$373$	−2.59719e34	−0.497089	−0.248545	−	0.968620i	$-0.579952\pi$
$373$	−2.59719e34	−0.497089	−0.248545	+	0.968620i	$0.579952\pi$
$374$	−1.61578e33	−0.0298274
$375$	0	0
$376$	−2.68570e34	−0.461340
$377$	−6.66225e33	−0.110411
$378$	5.35770e34	0.856720
$379$	6.29669e34	0.971590	0.485795	−	0.874073i	$-0.338530\pi$
$379$	6.29669e34	0.971590	0.485795	+	0.874073i	$0.338530\pi$
$380$	0	0
$381$	1.27757e34	0.183611
$382$	1.01358e34	0.140605
$383$	5.45282e34	0.730193	0.365097	−	0.930970i	$-0.381036\pi$
$383$	5.45282e34	0.730193	0.365097	+	0.930970i	$0.381036\pi$
$384$	−3.60494e33	−0.0466044
$385$	0	0
$386$	−7.82379e34	−0.942950
$387$	−6.70612e33	−0.0780501
$388$	−3.30042e34	−0.370971
$389$	1.15416e35	1.25299	0.626495	−	0.779425i	$-0.284489\pi$
$389$	1.15416e35	1.25299	0.626495	+	0.779425i	$0.284489\pi$
$390$	0	0
$391$	−3.11693e33	−0.0315748
$392$	2.82023e34	0.276009
$393$	4.92842e34	0.466024
$394$	4.10802e34	0.375348
$395$	0	0
$396$	−4.46160e33	−0.0380720
$397$	5.65268e34	0.466211	0.233106	−	0.972451i	$-0.425111\pi$
$397$	5.65268e34	0.466211	0.233106	+	0.972451i	$0.425111\pi$
$398$	1.34727e35	1.07407
$399$	1.10437e33	0.00851101
$400$	0	0
$401$	−3.91339e33	−0.0281906	−0.0140953	−	0.999901i	$-0.504487\pi$
$401$	−3.91339e33	−0.0281906	−0.0140953	+	0.999901i	$0.504487\pi$
$402$	9.70738e34	0.676161
$403$	4.60388e33	0.0310103
$404$	1.42347e35	0.927259
$405$	0	0
$406$	−1.82755e35	−1.11370
$407$	−3.03451e34	−0.178881
$408$	1.30745e34	0.0745611
$409$	−2.50975e34	−0.138473	−0.0692366	−	0.997600i	$-0.522056\pi$
$409$	−2.50975e34	−0.138473	−0.0692366	+	0.997600i	$0.522056\pi$
$410$	0	0
$411$	1.48344e35	0.766314
$412$	−2.33393e33	−0.0116675
$413$	3.75683e35	1.81759
$414$	−8.60667e33	−0.0403024
$415$	0	0
$416$	3.76882e33	0.0165366
$417$	6.49363e34	0.275836
$418$	−2.19345e32	−0.000902085 0
$419$	4.06859e35	1.62015	0.810073	−	0.586329i	$-0.199427\pi$
$419$	4.06859e35	1.62015	0.810073	+	0.586329i	$0.199427\pi$
$420$	0	0
$421$	−2.35168e35	−0.878153	−0.439076	−	0.898450i	$-0.644694\pi$
$421$	−2.35168e35	−0.878153	−0.439076	+	0.898450i	$0.644694\pi$
$422$	−1.14934e35	−0.415652
$423$	2.68962e35	0.942099
$424$	−5.36161e33	−0.0181910
$425$	0	0
$426$	1.64684e35	0.524349
$427$	3.38249e35	1.04342
$428$	−3.25457e35	−0.972754
$429$	−1.79610e33	−0.00520185
$430$	0	0
$431$	5.93896e35	1.61535	0.807676	−	0.589626i	$-0.200725\pi$
$431$	5.93896e35	1.61535	0.807676	+	0.589626i	$0.200725\pi$
$432$	8.61058e34	0.226987
$433$	5.11209e35	1.30621	0.653104	−	0.757269i	$-0.273467\pi$
$433$	5.11209e35	1.30621	0.653104	+	0.757269i	$0.273467\pi$
$434$	1.26291e35	0.312796
$435$	0	0
$436$	−1.18175e35	−0.275079
$437$	−4.23129e32	−0.000954933 0
$438$	−2.71405e35	−0.593905
$439$	6.22583e35	1.32107	0.660536	−	0.750794i	$-0.270329\pi$
$439$	6.22583e35	1.32107	0.660536	+	0.750794i	$0.270329\pi$
$440$	0	0
$441$	−2.82435e35	−0.563635
$442$	−1.36688e34	−0.0264564
$443$	−7.89880e35	−1.48290	−0.741448	−	0.671010i	$-0.765861\pi$
$443$	−7.89880e35	−1.48290	−0.741448	+	0.671010i	$0.765861\pi$
$444$	2.45545e35	0.447157
$445$	0	0
$446$	−1.55238e35	−0.266059
$447$	8.13607e34	0.135289
$448$	1.03384e35	0.166802
$449$	8.32672e35	1.30361	0.651806	−	0.758385i	$-0.274011\pi$
$449$	8.32672e35	1.30361	0.651806	+	0.758385i	$0.274011\pi$
$450$	0	0
$451$	8.13879e33	0.0119999
$452$	−2.35967e35	−0.337662
$453$	3.90500e35	0.542369
$454$	−2.15152e35	−0.290063
$455$	0	0
$456$	1.77488e33	0.00225499
$457$	3.61787e35	0.446257	0.223128	−	0.974789i	$-0.428373\pi$
$457$	3.61787e35	0.446257	0.223128	+	0.974789i	$0.428373\pi$
$458$	−9.59074e35	−1.14860
$459$	−3.12290e35	−0.363151
$460$	0	0
$461$	−4.32462e35	−0.474226	−0.237113	−	0.971482i	$-0.576201\pi$
$461$	−4.32462e35	−0.474226	−0.237113	+	0.971482i	$0.576201\pi$
$462$	−4.92698e34	−0.0524704
$463$	5.74369e35	0.594084	0.297042	−	0.954864i	$-0.404000\pi$
$463$	5.74369e35	0.594084	0.297042	+	0.954864i	$0.404000\pi$
$464$	−2.93714e35	−0.295075
$465$	0	0
$466$	−3.88504e35	−0.368286
$467$	−8.79293e35	−0.809759	−0.404879	−	0.914370i	$-0.632686\pi$
$467$	−8.79293e35	−0.809759	−0.404879	+	0.914370i	$0.632686\pi$
$468$	−3.77433e34	−0.0337692
$469$	−2.78393e36	−2.42006
$470$	0	0
$471$	−5.77171e34	−0.0473721
$472$	6.03776e35	0.481569
$473$	1.47087e34	0.0114012
$474$	−3.04739e34	−0.0229572
$475$	0	0
$476$	−3.74957e35	−0.266862
$477$	5.36944e34	0.0371476
$478$	−3.64835e35	−0.245369
$479$	−1.32449e36	−0.866001	−0.433000	−	0.901394i	$-0.642545\pi$
$479$	−1.32449e36	−0.866001	−0.433000	+	0.901394i	$0.642545\pi$
$480$	0	0
$481$	−2.56707e35	−0.158664
$482$	1.32790e36	0.798050
$483$	−9.50442e34	−0.0555443
$484$	−8.70011e35	−0.494439
$485$	0	0
$486$	−1.36308e36	−0.732711
$487$	−2.77661e36	−1.45169	−0.725844	−	0.687859i	$-0.758551\pi$
$487$	−2.77661e36	−1.45169	−0.725844	+	0.687859i	$0.758551\pi$
$488$	5.43615e35	0.276454
$489$	−1.05308e36	−0.520944
$490$	0	0
$491$	3.83404e36	1.79497	0.897485	−	0.441046i	$-0.145392\pi$
$491$	3.83404e36	1.79497	0.897485	+	0.441046i	$0.145392\pi$
$492$	−6.58570e34	−0.0299967
$493$	1.06525e36	0.472082
$494$	−1.85557e33	−0.000800135 0
$495$	0	0
$496$	2.02968e35	0.0828752
$497$	−4.72288e36	−1.87670
$498$	−1.15460e36	−0.446515
$499$	−1.37412e35	−0.0517210	−0.0258605	−	0.999666i	$-0.508233\pi$
$499$	−1.37412e35	−0.0517210	−0.0258605	+	0.999666i	$0.508233\pi$
$500$	0	0
$501$	−1.40558e35	−0.0501241
$502$	5.36591e35	0.186270
$503$	−4.60357e36	−1.55570	−0.777852	−	0.628447i	$-0.783691\pi$
$503$	−4.60357e36	−1.55570	−0.777852	+	0.628447i	$0.783691\pi$
$504$	−1.03535e36	−0.340625
$505$	0	0
$506$	1.88772e34	0.00588716
$507$	1.72116e36	0.522654
$508$	−5.88839e35	−0.174115
$509$	1.03517e36	0.298071	0.149035	−	0.988832i	$-0.452383\pi$
$509$	1.03517e36	0.298071	0.149035	+	0.988832i	$0.452383\pi$
$510$	0	0
$511$	7.78349e36	2.12565
$512$	1.66153e35	0.0441942
$513$	−4.23939e34	−0.0109830
$514$	−3.08021e36	−0.777281
$515$	0	0
$516$	−1.19019e35	−0.0285000
$517$	−5.89921e35	−0.137617
$518$	−7.04185e36	−1.60042
$519$	−8.79106e35	−0.194662
$520$	0	0
$521$	5.78940e36	1.21709	0.608547	−	0.793518i	$-0.291753\pi$
$521$	5.78940e36	1.21709	0.608547	+	0.793518i	$0.291753\pi$
$522$	2.94143e36	0.602569
$523$	5.79695e36	1.15725	0.578625	−	0.815594i	$-0.303590\pi$
$523$	5.79695e36	1.15725	0.578625	+	0.815594i	$0.303590\pi$
$524$	−2.27153e36	−0.441923
$525$	0	0
$526$	−1.20529e36	−0.222733
$527$	−7.36128e35	−0.132590
$528$	−7.91836e34	−0.0139020
$529$	−5.80680e36	−0.993768
$530$	0	0
$531$	−6.04658e36	−0.983408
$532$	−5.09010e34	−0.00807085
$533$	6.88509e34	0.0106437
$534$	−3.86898e36	−0.583162
$535$	0	0
$536$	−4.47418e36	−0.641193
$537$	4.59439e36	0.642059
$538$	−8.98384e36	−1.22434
$539$	6.19472e35	0.0823329
$540$	0	0
$541$	4.55675e35	0.0576093	0.0288046	−	0.999585i	$-0.490830\pi$
$541$	4.55675e35	0.0576093	0.0288046	+	0.999585i	$0.490830\pi$
$542$	−6.53163e36	−0.805436
$543$	3.51722e36	0.423060
$544$	−6.02609e35	−0.0707051
$545$	0	0
$546$	−4.16802e35	−0.0465403
$547$	−7.34964e36	−0.800640	−0.400320	−	0.916375i	$-0.631101\pi$
$547$	−7.34964e36	−0.800640	−0.400320	+	0.916375i	$0.631101\pi$
$548$	−6.83726e36	−0.726683
$549$	−5.44409e36	−0.564545
$550$	0	0
$551$	1.44609e35	0.0142774
$552$	−1.52750e35	−0.0147164
$553$	8.73945e35	0.0821665
$554$	1.12838e37	1.03532
$555$	0	0
$556$	−2.99294e36	−0.261571
$557$	1.11649e37	0.952381	0.476191	−	0.879342i	$-0.342017\pi$
$557$	1.11649e37	0.952381	0.476191	+	0.879342i	$0.342017\pi$
$558$	−2.03264e36	−0.169239
$559$	1.24430e35	0.0101126
$560$	0	0
$561$	2.87185e35	0.0222414
$562$	1.59625e37	1.20687
$563$	1.14995e37	0.848820	0.424410	−	0.905470i	$-0.360482\pi$
$563$	1.14995e37	0.848820	0.424410	+	0.905470i	$0.360482\pi$
$564$	4.77349e36	0.344008
$565$	0	0
$566$	−1.69890e37	−1.16720
$567$	4.83865e36	0.324603
$568$	−7.59034e36	−0.497232
$569$	4.14930e36	0.265436	0.132718	−	0.991154i	$-0.457630\pi$
$569$	4.14930e36	0.265436	0.132718	+	0.991154i	$0.457630\pi$
$570$	0	0
$571$	1.01000e37	0.616220	0.308110	−	0.951351i	$-0.400304\pi$
$571$	1.01000e37	0.616220	0.308110	+	0.951351i	$0.400304\pi$
$572$	8.27833e34	0.00493283
$573$	−1.80150e36	−0.104845
$574$	1.88868e36	0.107361
$575$	0	0
$576$	−1.66396e36	−0.0902485
$577$	1.31282e37	0.695557	0.347779	−	0.937577i	$-0.386936\pi$
$577$	1.31282e37	0.695557	0.347779	+	0.937577i	$0.386936\pi$
$578$	−1.14763e37	−0.593988
$579$	1.39058e37	0.703130
$580$	0	0
$581$	3.31123e37	1.59813
$582$	5.86607e36	0.276622
$583$	−1.17769e35	−0.00542633
$584$	1.25092e37	0.563190
$585$	0	0
$586$	−1.32830e37	−0.571056
$587$	−9.82196e36	−0.412652	−0.206326	−	0.978483i	$-0.566151\pi$
$587$	−9.82196e36	−0.412652	−0.206326	+	0.978483i	$0.566151\pi$
$588$	−5.01261e36	−0.205812
$589$	−9.99306e34	−0.00400998
$590$	0	0
$591$	−7.30149e36	−0.279886
$592$	−1.13173e37	−0.424032
$593$	1.06673e37	0.390676	0.195338	−	0.980736i	$-0.437420\pi$
$593$	1.06673e37	0.390676	0.195338	+	0.980736i	$0.437420\pi$
$594$	1.89134e36	0.0677099
$595$	0	0
$596$	−3.74995e36	−0.128292
$597$	−2.39459e37	−0.800900
$598$	1.59694e35	0.00522182
$599$	1.34901e37	0.431274	0.215637	−	0.976474i	$-0.430817\pi$
$599$	1.34901e37	0.431274	0.215637	+	0.976474i	$0.430817\pi$
$600$	0	0
$601$	3.52554e37	1.07751	0.538754	−	0.842463i	$-0.318895\pi$
$601$	3.52554e37	1.07751	0.538754	+	0.842463i	$0.318895\pi$
$602$	3.41329e36	0.102005
$603$	4.48071e37	1.30937
$604$	−1.79983e37	−0.514320
$605$	0	0
$606$	−2.53004e37	−0.691429
$607$	−2.43922e37	−0.651934	−0.325967	−	0.945381i	$-0.605690\pi$
$607$	−2.43922e37	−0.651934	−0.325967	+	0.945381i	$0.605690\pi$
$608$	−8.18051e34	−0.00213837
$609$	3.24825e37	0.830454
$610$	0	0
$611$	−4.99050e36	−0.122064
$612$	6.03489e36	0.144386
$613$	5.62323e37	1.31604	0.658020	−	0.753000i	$-0.271394\pi$
$613$	5.62323e37	1.31604	0.658020	+	0.753000i	$0.271394\pi$
$614$	−3.50993e37	−0.803573
$615$	0	0
$616$	2.27087e36	0.0497568
$617$	−4.80049e37	−1.02905	−0.514525	−	0.857476i	$-0.672032\pi$
$617$	−4.80049e37	−1.02905	−0.514525	+	0.857476i	$0.672032\pi$
$618$	4.14827e35	0.00870007
$619$	2.24910e37	0.461513	0.230757	−	0.973011i	$-0.425880\pi$
$619$	2.24910e37	0.461513	0.230757	+	0.973011i	$0.425880\pi$
$620$	0	0
$621$	3.64850e36	0.0716766
$622$	1.53630e37	0.295329
$623$	1.10956e38	2.08720
$624$	−6.69861e35	−0.0123308
$625$	0	0
$626$	−6.32158e37	−1.11448
$627$	3.89858e34	0.000672658 0
$628$	2.66021e36	0.0449222
$629$	4.10457e37	0.678397
$630$	0	0
$631$	−1.02822e38	−1.62814	−0.814068	−	0.580770i	$-0.802751\pi$
$631$	−1.02822e38	−1.62814	−0.814068	+	0.580770i	$0.802751\pi$
$632$	1.40455e36	0.0217700
$633$	2.04280e37	0.309939
$634$	2.51117e36	0.0372967
$635$	0	0
$636$	9.52958e35	0.0135645
$637$	5.24048e36	0.0730279
$638$	−6.45151e36	−0.0880202
$639$	7.60143e37	1.01539
$640$	0	0
$641$	6.67226e37	0.854456	0.427228	−	0.904144i	$-0.359490\pi$
$641$	6.67226e37	0.854456	0.427228	+	0.904144i	$0.359490\pi$
$642$	5.78459e37	0.725353
$643$	2.92763e37	0.359474	0.179737	−	0.983715i	$-0.442475\pi$
$643$	2.92763e37	0.359474	0.179737	+	0.983715i	$0.442475\pi$
$644$	4.38063e36	0.0526717
$645$	0	0
$646$	2.96693e35	0.00342112
$647$	6.89266e37	0.778357	0.389179	−	0.921162i	$-0.372759\pi$
$647$	6.89266e37	0.778357	0.389179	+	0.921162i	$0.372759\pi$
$648$	7.77640e36	0.0860035
$649$	1.32621e37	0.143651
$650$	0	0
$651$	−2.24467e37	−0.233243
$652$	4.85369e37	0.494003
$653$	6.00351e37	0.598518	0.299259	−	0.954172i	$-0.403260\pi$
$653$	6.00351e37	0.598518	0.299259	+	0.954172i	$0.403260\pi$
$654$	2.10041e37	0.205118
$655$	0	0
$656$	3.03538e36	0.0284454
$657$	−1.25274e38	−1.15009
$658$	−1.36897e38	−1.23124
$659$	−3.15651e37	−0.278134	−0.139067	−	0.990283i	$-0.544410\pi$
$659$	−3.15651e37	−0.278134	−0.139067	+	0.990283i	$0.544410\pi$
$660$	0	0
$661$	−5.72052e37	−0.483855	−0.241928	−	0.970294i	$-0.577780\pi$
$661$	−5.72052e37	−0.483855	−0.241928	+	0.970294i	$0.577780\pi$
$662$	−8.92363e37	−0.739535
$663$	2.42947e36	0.0197278
$664$	5.32162e37	0.423423
$665$	0	0
$666$	1.13338e38	0.865911
$667$	−1.24453e37	−0.0931768
$668$	6.47839e36	0.0475318
$669$	2.75916e37	0.198392
$670$	0	0
$671$	1.19407e37	0.0824658
$672$	−1.83753e37	−0.124379
$673$	−2.84152e38	−1.88516	−0.942578	−	0.333987i	$-0.891606\pi$
$673$	−2.84152e38	−1.88516	−0.942578	+	0.333987i	$0.891606\pi$
$674$	1.75873e38	1.14365
$675$	0	0
$676$	−7.93292e37	−0.495625
$677$	−1.71997e37	−0.105336	−0.0526678	−	0.998612i	$-0.516772\pi$
$677$	−1.71997e37	−0.105336	−0.0526678	+	0.998612i	$0.516772\pi$
$678$	4.19401e37	0.251784
$679$	−1.68230e38	−0.990062
$680$	0	0
$681$	3.82406e37	0.216291
$682$	4.45825e36	0.0247215
$683$	7.22090e37	0.392565	0.196283	−	0.980547i	$-0.437113\pi$
$683$	7.22090e37	0.392565	0.196283	+	0.980547i	$0.437113\pi$
$684$	8.19247e35	0.00436674
$685$	0	0
$686$	−4.03876e37	−0.206953
$687$	1.70463e38	0.856475
$688$	5.48564e36	0.0270261
$689$	−9.96280e35	−0.00481307
$690$	0	0
$691$	8.09519e37	0.376074	0.188037	−	0.982162i	$-0.439787\pi$
$691$	8.09519e37	0.376074	0.188037	+	0.982162i	$0.439787\pi$
$692$	4.05184e37	0.184595
$693$	−2.27419e37	−0.101608
$694$	−2.36741e38	−1.03734
$695$	0	0
$696$	5.22040e37	0.220028
$697$	−1.10088e37	−0.0455089
$698$	−3.80714e37	−0.154366
$699$	6.90517e37	0.274620
$700$	0	0
$701$	5.38842e37	0.206190	0.103095	−	0.994671i	$-0.467125\pi$
$701$	5.38842e37	0.206190	0.103095	+	0.994671i	$0.467125\pi$
$702$	1.60000e37	0.0600576
$703$	5.57202e36	0.0205171
$704$	3.64961e36	0.0131830
$705$	0	0
$706$	1.92180e38	0.668106
$707$	7.25579e38	2.47470
$708$	−1.07314e38	−0.359092
$709$	−6.64239e37	−0.218072	−0.109036	−	0.994038i	$-0.534776\pi$
$709$	−6.64239e37	−0.218072	−0.109036	+	0.994038i	$0.534776\pi$
$710$	0	0
$711$	−1.40661e37	−0.0444563
$712$	1.78323e38	0.553003
$713$	8.60021e36	0.0261698
$714$	6.66438e37	0.198991
$715$	0	0
$716$	−2.11758e38	−0.608854
$717$	6.48448e37	0.182964
$718$	1.73633e38	0.480788
$719$	−2.15626e38	−0.585950	−0.292975	−	0.956120i	$-0.594645\pi$
$719$	−2.15626e38	−0.585950	−0.292975	+	0.956120i	$0.594645\pi$
$720$	0	0
$721$	−1.18966e37	−0.0311385
$722$	−2.75216e38	−0.707003
$723$	−2.36017e38	−0.595082
$724$	−1.62111e38	−0.401181
$725$	0	0
$726$	1.54633e38	0.368688
$727$	−7.29285e38	−1.70680	−0.853401	−	0.521255i	$-0.825464\pi$
$727$	−7.29285e38	−1.70680	−0.853401	+	0.521255i	$0.825464\pi$
$728$	1.92106e37	0.0441334
$729$	1.34405e38	0.303106
$730$	0	0
$731$	−1.98954e37	−0.0432383
$732$	−9.66207e37	−0.206144
$733$	−8.53218e38	−1.78713	−0.893566	−	0.448932i	$-0.851805\pi$
$733$	−8.53218e38	−1.78713	−0.893566	+	0.448932i	$0.851805\pi$
$734$	−4.24060e38	−0.872029
$735$	0	0
$736$	7.04030e36	0.0139553
$737$	−9.82766e37	−0.191267
$738$	−3.03981e37	−0.0580880
$739$	6.54496e37	0.122802	0.0614012	−	0.998113i	$-0.480443\pi$
$739$	6.54496e37	0.122802	0.0614012	+	0.998113i	$0.480443\pi$
$740$	0	0
$741$	3.29804e35	0.000596637 0
$742$	−2.73294e37	−0.0485487
$743$	1.95541e38	0.341105	0.170553	−	0.985349i	$-0.445445\pi$
$743$	1.95541e38	0.341105	0.170553	+	0.985349i	$0.445445\pi$
$744$	−3.60750e37	−0.0617976
$745$	0	0
$746$	−2.12762e38	−0.351495
$747$	−5.32939e38	−0.864668
$748$	−1.32365e37	−0.0210912
$749$	−1.65893e39	−2.59612
$750$	0	0
$751$	9.02110e38	1.36182	0.680911	−	0.732366i	$-0.261584\pi$
$751$	9.02110e38	1.36182	0.680911	+	0.732366i	$0.261584\pi$
$752$	−2.20012e38	−0.326217
$753$	−9.53724e37	−0.138896
$754$	−5.45772e37	−0.0780724
$755$	0	0
$756$	4.38902e38	0.605792
$757$	−7.72330e38	−1.04715	−0.523575	−	0.851980i	$-0.675402\pi$
$757$	−7.72330e38	−1.04715	−0.523575	+	0.851980i	$0.675402\pi$
$758$	5.15825e38	0.687018
$759$	−3.35519e36	−0.00438988
$760$	0	0
$761$	−6.10975e38	−0.771490	−0.385745	−	0.922605i	$-0.626056\pi$
$761$	−6.10975e38	−0.771490	−0.385745	+	0.922605i	$0.626056\pi$
$762$	1.04659e38	0.129832
$763$	−6.02366e38	−0.734141
$764$	8.30321e37	0.0994227
$765$	0	0
$766$	4.46695e38	0.516325
$767$	1.12192e38	0.127416
$768$	−2.95317e37	−0.0329543
$769$	−7.47622e38	−0.819741	−0.409870	−	0.912144i	$-0.634426\pi$
$769$	−7.47622e38	−0.819741	−0.409870	+	0.912144i	$0.634426\pi$
$770$	0	0
$771$	5.47468e38	0.579595
$772$	−6.40925e38	−0.666766
$773$	−1.33482e39	−1.36458	−0.682288	−	0.731083i	$-0.739015\pi$
$773$	−1.33482e39	−1.36458	−0.682288	+	0.731083i	$0.739015\pi$
$774$	−5.49366e37	−0.0551898
$775$	0	0
$776$	−2.70370e38	−0.262316
$777$	1.25160e39	1.19339
$778$	9.45491e38	0.885998
$779$	−1.49446e36	−0.00137635
$780$	0	0
$781$	−1.66724e38	−0.148323
$782$	−2.55339e37	−0.0223268
$783$	−1.24692e39	−1.07165
$784$	2.31033e38	0.195168
$785$	0	0
$786$	4.03736e38	0.329529
$787$	1.55203e38	0.124521	0.0622603	−	0.998060i	$-0.480169\pi$
$787$	1.55203e38	0.124521	0.0622603	+	0.998060i	$0.480169\pi$
$788$	3.36529e38	0.265411
$789$	2.14225e38	0.166085
$790$	0	0
$791$	−1.20278e39	−0.901164
$792$	−3.65494e37	−0.0269209
$793$	1.01013e38	0.0731458
$794$	4.63068e38	0.329661
$795$	0	0
$796$	1.10368e39	0.759481
$797$	1.19576e39	0.809019	0.404509	−	0.914534i	$-0.367442\pi$
$797$	1.19576e39	0.809019	0.404509	+	0.914534i	$0.367442\pi$
$798$	9.04701e36	0.00601819
$799$	7.97946e38	0.521905
$800$	0	0
$801$	−1.78583e39	−1.12928
$802$	−3.20585e37	−0.0199337
$803$	2.74767e38	0.167999
$804$	7.95229e38	0.478118
$805$	0	0
$806$	3.77150e37	0.0219276
$807$	1.59676e39	0.912952
$808$	1.16611e39	0.655671
$809$	−2.75200e39	−1.52175	−0.760874	−	0.648899i	$-0.775230\pi$
$809$	−2.75200e39	−1.52175	−0.760874	+	0.648899i	$0.775230\pi$
$810$	0	0
$811$	−2.91604e39	−1.55960	−0.779798	−	0.626032i	$-0.784678\pi$
$811$	−2.91604e39	−1.55960	−0.779798	+	0.626032i	$0.784678\pi$
$812$	−1.49713e39	−0.787506
$813$	1.16092e39	0.600590
$814$	−2.48587e38	−0.126488
$815$	0	0
$816$	1.07106e38	0.0527226
$817$	−2.70084e36	−0.00130768
$818$	−2.05599e38	−0.0979154
$819$	−1.92387e38	−0.0901245
$820$	0	0
$821$	2.55103e38	0.115633	0.0578165	−	0.998327i	$-0.481586\pi$
$821$	2.55103e38	0.115633	0.0578165	+	0.998327i	$0.481586\pi$
$822$	1.21524e39	0.541866
$823$	2.16576e39	0.949977	0.474989	−	0.879992i	$-0.342452\pi$
$823$	2.16576e39	0.949977	0.474989	+	0.879992i	$0.342452\pi$
$824$	−1.91196e37	−0.00825014
$825$	0	0
$826$	3.07759e39	1.28523
$827$	−1.43961e39	−0.591453	−0.295727	−	0.955273i	$-0.595562\pi$
$827$	−1.43961e39	−0.591453	−0.295727	+	0.955273i	$0.595562\pi$
$828$	−7.05059e37	−0.0284981
$829$	3.12334e39	1.24203	0.621016	−	0.783798i	$-0.286720\pi$
$829$	3.12334e39	1.24203	0.621016	+	0.783798i	$0.286720\pi$
$830$	0	0
$831$	−2.00555e39	−0.772006
$832$	3.08742e37	0.0116931
$833$	−8.37917e38	−0.312244
$834$	5.31958e38	0.195045
$835$	0	0
$836$	−1.79687e36	−0.000637871 0
$837$	8.61669e38	0.300986
$838$	3.33299e39	1.14562
$839$	5.81719e39	1.96755	0.983777	−	0.179397i	$-0.0574145\pi$
$839$	5.81719e39	1.96755	0.983777	+	0.179397i	$0.0574145\pi$
$840$	0	0
$841$	1.20020e39	0.393105
$842$	−1.92650e39	−0.620948
$843$	−2.83714e39	−0.899928
$844$	−9.41537e38	−0.293910
$845$	0	0
$846$	2.20334e39	0.666164
$847$	−4.43466e39	−1.31958
$848$	−4.39223e37	−0.0128630
$849$	3.01958e39	0.870347
$850$	0	0
$851$	−4.79538e38	−0.133898
$852$	1.34909e39	0.370771
$853$	1.88847e39	0.510854	0.255427	−	0.966828i	$-0.417784\pi$
$853$	1.88847e39	0.510854	0.255427	+	0.966828i	$0.417784\pi$
$854$	2.77094e39	0.737812
$855$	0	0
$856$	−2.66614e39	−0.687841
$857$	4.20096e39	1.06686	0.533429	−	0.845845i	$-0.320903\pi$
$857$	4.20096e39	1.06686	0.533429	+	0.845845i	$0.320903\pi$
$858$	−1.47137e37	−0.00367826
$859$	7.26089e39	1.78683	0.893413	−	0.449236i	$-0.148304\pi$
$859$	7.26089e39	1.78683	0.893413	+	0.449236i	$0.148304\pi$
$860$	0	0
$861$	−3.35689e38	−0.0800562
$862$	4.86520e39	1.14223
$863$	−9.99655e38	−0.231049	−0.115525	−	0.993305i	$-0.536855\pi$
$863$	−9.99655e38	−0.231049	−0.115525	+	0.993305i	$0.536855\pi$
$864$	7.05379e38	0.160504
$865$	0	0
$866$	4.18783e39	0.923628
$867$	2.03977e39	0.442919
$868$	1.03458e39	0.221180
$869$	3.08514e37	0.00649394
$870$	0	0
$871$	−8.31380e38	−0.169650
$872$	−9.68089e38	−0.194510
$873$	2.70765e39	0.535674
$874$	−3.46627e36	−0.000675240 0
$875$	0	0
$876$	−2.22335e39	−0.419954
$877$	4.39906e39	0.818211	0.409105	−	0.912487i	$-0.365841\pi$
$877$	4.39906e39	0.818211	0.409105	+	0.912487i	$0.365841\pi$
$878$	5.10020e39	0.934139
$879$	2.36089e39	0.425820
$880$	0	0
$881$	−2.21444e39	−0.387338	−0.193669	−	0.981067i	$-0.562039\pi$
$881$	−2.21444e39	−0.387338	−0.193669	+	0.981067i	$0.562039\pi$
$882$	−2.31371e39	−0.398550
$883$	−3.04198e38	−0.0516044	−0.0258022	−	0.999667i	$-0.508214\pi$
$883$	−3.04198e38	−0.0516044	−0.0258022	+	0.999667i	$0.508214\pi$
$884$	−1.11975e38	−0.0187075
$885$	0	0
$886$	−6.47069e39	−1.04857
$887$	−3.06989e39	−0.489953	−0.244977	−	0.969529i	$-0.578780\pi$
$887$	−3.06989e39	−0.489953	−0.244977	+	0.969529i	$0.578780\pi$
$888$	2.01150e39	0.316188
$889$	−3.00145e39	−0.464684
$890$	0	0
$891$	1.70811e38	0.0256547
$892$	−1.27171e39	−0.188132
$893$	1.08322e38	0.0157842
$894$	6.66506e38	0.0956639
$895$	0	0
$896$	8.46925e38	0.117947
$897$	−2.83835e37	−0.00389375
$898$	6.82125e39	0.921793
$899$	−2.93922e39	−0.391270
$900$	0	0
$901$	1.59298e38	0.0205791
$902$	6.66730e37	0.00848519
$903$	−6.06669e38	−0.0760619
$904$	−1.93304e39	−0.238763
$905$	0	0
$906$	3.19898e39	0.383513
$907$	6.69307e39	0.790546	0.395273	−	0.918564i	$-0.370650\pi$
$907$	6.69307e39	0.790546	0.395273	+	0.918564i	$0.370650\pi$
$908$	−1.76253e39	−0.205106
$909$	−1.16781e40	−1.33894
$910$	0	0
$911$	−2.24684e39	−0.250077	−0.125039	−	0.992152i	$-0.539905\pi$
$911$	−2.24684e39	−0.250077	−0.125039	+	0.992152i	$0.539905\pi$
$912$	1.45398e37	0.00159452
$913$	1.16891e39	0.126306
$914$	2.96376e39	0.315551
$915$	0	0
$916$	−7.85673e39	−0.812182
$917$	−1.15786e40	−1.17942
$918$	−2.55828e39	−0.256787
$919$	−1.71198e40	−1.69332	−0.846662	−	0.532131i	$-0.821391\pi$
$919$	−1.71198e40	−1.69332	−0.846662	+	0.532131i	$0.821391\pi$
$920$	0	0
$921$	6.23845e39	0.599200
$922$	−3.54273e39	−0.335328
$923$	−1.41042e39	−0.131560
$924$	−4.03618e38	−0.0371021
$925$	0	0
$926$	4.70523e39	0.420081
$927$	1.91475e38	0.0168475
$928$	−2.40610e39	−0.208649
$929$	1.02221e40	0.873632	0.436816	−	0.899551i	$-0.356106\pi$
$929$	1.02221e40	0.873632	0.436816	+	0.899551i	$0.356106\pi$
$930$	0	0
$931$	−1.13749e38	−0.00944333
$932$	−3.18262e39	−0.260418
$933$	−2.73058e39	−0.220218
$934$	−7.20317e39	−0.572586
$935$	0	0
$936$	−3.09193e38	−0.0238784
$937$	−9.74565e39	−0.741868	−0.370934	−	0.928659i	$-0.620962\pi$
$937$	−9.74565e39	−0.741868	−0.370934	+	0.928659i	$0.620962\pi$
$938$	−2.28060e40	−1.71124
$939$	1.12358e40	0.831034
$940$	0	0
$941$	2.57094e39	0.184771	0.0923853	−	0.995723i	$-0.470551\pi$
$941$	2.57094e39	0.184771	0.0923853	+	0.995723i	$0.470551\pi$
$942$	−4.72819e38	−0.0334971
$943$	1.28616e38	0.00898229
$944$	4.94613e39	0.340521
$945$	0	0
$946$	1.20494e38	0.00806183
$947$	1.22271e39	0.0806490	0.0403245	−	0.999187i	$-0.487161\pi$
$947$	1.22271e39	0.0806490	0.0403245	+	0.999187i	$0.487161\pi$
$948$	−2.49642e38	−0.0162332
$949$	2.32442e39	0.149012
$950$	0	0
$951$	−4.46328e38	−0.0278111
$952$	−3.07165e39	−0.188700
$953$	−7.65794e39	−0.463829	−0.231914	−	0.972736i	$-0.574499\pi$
$953$	−7.65794e39	−0.463829	−0.231914	+	0.972736i	$0.574499\pi$
$954$	4.39865e38	0.0262673
$955$	0	0
$956$	−2.98873e39	−0.173502
$957$	1.14667e39	0.0656340
$958$	−1.08502e40	−0.612355
$959$	−3.48512e40	−1.93940
$960$	0	0
$961$	−1.64516e40	−0.890107
$962$	−2.10294e39	−0.112193
$963$	2.67004e40	1.40463
$964$	1.08781e40	0.564307
$965$	0	0
$966$	−7.78602e38	−0.0392757
$967$	2.57889e37	0.00128285	0.000641425	−	1.00000i	$-0.499796\pi$
$967$	2.57889e37	0.00128285	0.000641425		1.00000i	$0.499796\pi$
$968$	−7.12713e39	−0.349621
$969$	−5.27334e37	−0.00255102
$970$	0	0
$971$	3.64031e40	1.71269	0.856345	−	0.516404i	$-0.172730\pi$
$971$	3.64031e40	1.71269	0.856345	+	0.516404i	$0.172730\pi$
$972$	−1.11664e40	−0.518105
$973$	−1.52558e40	−0.698089
$974$	−2.27460e40	−1.02650
$975$	0	0
$976$	4.45329e39	0.195483
$977$	−9.13450e39	−0.395465	−0.197733	−	0.980256i	$-0.563358\pi$
$977$	−9.13450e39	−0.395465	−0.197733	+	0.980256i	$0.563358\pi$
$978$	−8.62682e39	−0.368363
$979$	3.91691e39	0.164960
$980$	0	0
$981$	9.69503e39	0.397208
$982$	3.14085e40	1.26923
$983$	1.10897e40	0.442025	0.221012	−	0.975271i	$-0.429064\pi$
$983$	1.10897e40	0.442025	0.221012	+	0.975271i	$0.429064\pi$
$984$	−5.39501e38	−0.0212108
$985$	0	0
$986$	8.72651e39	0.333812
$987$	2.43317e40	0.918100
$988$	−1.52008e37	−0.000565781 0
$989$	2.32439e38	0.00853413
$990$	0	0
$991$	4.45006e40	1.58991	0.794954	−	0.606670i	$-0.207495\pi$
$991$	4.45006e40	1.58991	0.794954	+	0.606670i	$0.207495\pi$
$992$	1.66271e39	0.0586017
$993$	1.58606e40	0.551449
$994$	−3.86898e40	−1.32703
$995$	0	0
$996$	−9.45850e39	−0.315734
$997$	−2.41234e40	−0.794427	−0.397213	−	0.917726i	$-0.630023\pi$
$997$	−2.41234e40	−0.794427	−0.397213	+	0.917726i	$0.630023\pi$
$998$	−1.12568e39	−0.0365723
$999$	−4.80457e40	−1.54000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.28.a.d.1.1		2
5.2	odd	4		50.28.b.d.49.4		4
5.3	odd	4		50.28.b.d.49.1		4
5.4	even	2		10.28.a.b.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.a.b.1.2	✓	2	5.4	even	2
50.28.a.d.1.1		2	1.1	even	1	trivial
50.28.b.d.49.1		4	5.3	odd	4
50.28.b.d.49.4		4	5.2	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q+8192.00 q^{2} -1.45602e6 q^{3} +6.71089e7 q^{4} -1.19278e10 q^{6} +3.42070e11 q^{7} +5.49756e11 q^{8} -5.50559e12 q^{9} +1.20755e13 q^{11} -9.77122e13 q^{12} +1.02154e14 q^{13} +2.80224e15 q^{14} +4.50360e15 q^{16} -1.63337e16 q^{17} -4.51018e16 q^{18} -2.21733e15 q^{19} -4.98063e17 q^{21} +9.89228e16 q^{22} +1.90828e17 q^{23} -8.00458e17 q^{24} +8.36847e17 q^{26} +1.91193e19 q^{27} +2.29560e19 q^{28} -6.52176e19 q^{29} +4.50679e19 q^{31} +3.68935e19 q^{32} -1.75823e19 q^{33} -1.33806e20 q^{34} -3.69474e20 q^{36} -2.51294e21 q^{37} -1.81644e19 q^{38} -1.48739e20 q^{39} +6.73990e20 q^{41} -4.08013e21 q^{42} +1.21806e21 q^{43} +8.10376e20 q^{44} +1.56326e21 q^{46} -4.88526e22 q^{47} -6.55735e21 q^{48} +5.12997e22 q^{49} +2.37823e22 q^{51} +6.85545e21 q^{52} -9.75271e21 q^{53} +1.56626e23 q^{54} +1.88055e23 q^{56} +3.22849e21 q^{57} -5.34263e23 q^{58} +1.09826e24 q^{59} +9.88829e23 q^{61} +3.69197e23 q^{62} -1.88330e24 q^{63} +3.02231e23 q^{64} -1.44034e23 q^{66} -8.13848e24 q^{67} -1.09614e24 q^{68} -2.77850e23 q^{69} -1.38068e25 q^{71} -3.02673e24 q^{72} +2.27541e25 q^{73} -2.05860e25 q^{74} -1.48803e23 q^{76} +4.13068e24 q^{77} -1.21847e24 q^{78} +2.55487e24 q^{79} +1.41452e25 q^{81} +5.52132e24 q^{82} +9.67997e25 q^{83} -3.34244e25 q^{84} +9.97833e24 q^{86} +9.49584e25 q^{87} +6.63860e24 q^{88} +3.24368e26 q^{89} +3.49439e25 q^{91} +1.28062e25 q^{92} -6.56200e25 q^{93} -4.00200e26 q^{94} -5.37178e25 q^{96} -4.91800e26 q^{97} +4.20247e26 q^{98} -6.64830e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16384 q^{2} + 2245644 q^{3} + 134217728 q^{4} + 18396315648 q^{6} + 120196732292 q^{7} + 1099511627776 q^{8} + 571163616594 q^{9} + 7112122732704 q^{11} + 150702617788416 q^{12} + 323114990355404 q^{13}+ \cdots - 96\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 16384 * q^2 + 2245644 * q^3 + 134217728 * q^4 + 18396315648 * q^6 + 120196732292 * q^7 + 1099511627776 * q^8 + 571163616594 * q^9 + 7112122732704 * q^11 + 150702617788416 * q^12 + 323114990355404 * q^13 + 984651630936064 * q^14 + 9007199254740992 * q^16 + 11949781720794252 * q^17 + 4678972347138048 * q^18 - 310800626187534200 * q^19 - 1319365315134326376 * q^21 + 58262509426311168 * q^22 + 1207992822578557644 * q^23 + 1234555844922703872 * q^24 + 2646958000991469568 * q^26 + 13386024338103046440 * q^27 + 8066266160628236288 * q^28 - 85089627076663724580 * q^29 - 169891626304914480056 * q^31 + 73786976294838206464 * q^32 - 35955214564003682112 * q^33 + 97892611856746512384 * q^34 + 38330141467754889216 * q^36 - 1001687425876018532308 * q^37 - 2546078729728280166400 * q^38 + 669184707607358092488 * q^39 + 6829708525832119000044 * q^41 - 10808240661580401672192 * q^42 - 15331910221739375128036 * q^43 + 477286477220341088256 * q^44 + 9895877202563544219648 * q^46 - 44654607958183509227628 * q^47 + 10113481481606790119424 * q^48 + 34815266426190611168346 * q^49 + 128478598882379942153544 * q^51 + 21683879944122118701056 * q^52 - 259350970067880627435396 * q^53 + 109658311377740156436480 * q^54 + 66078852387866511671296 * q^56 - 1139044611805451608251600 * q^57 - 697054225012029231759360 * q^58 + 2082093442621301023169640 * q^59 + 677925769536334246319284 * q^61 - 1391752202689859420618752 * q^62 - 3231569874371732206566876 * q^63 + 604462909807314587353088 * q^64 - 294545117708318163861504 * q^66 - 2453617552336948143390028 * q^67 + 801936276330467429449728 * q^68 + 3487358239126020846890568 * q^69 - 23890193584108132090228776 * q^71 + 314000518903848052457472 * q^72 + 13919420706136886544146204 * q^73 - 8205823392776343816667136 * q^74 - 20857476953934071123148800 * q^76 + 5231935501660614540408384 * q^77 + 5481961124719477493661696 * q^78 - 53659327270981104663051920 * q^79 - 53416489016311609709962998 * q^81 + 55948972243616718848360448 * q^82 - 5756571261014435461903716 * q^83 - 88541107499666650498596864 * q^84 - 125599008536488961048870912 * q^86 + 21398789661957929503788840 * q^87 + 3909930821389034194993152 * q^88 + 174438127411287409220344020 * q^89 - 14081455302088161819283816 * q^91 + 81067026043400554247356416 * q^92 - 861329117078544091150519632 * q^93 - 365810548393439307592728576 * q^94 + 82849640297322824658321408 * q^96 + 21732067184289340167295292 * q^97 + 285206662563353486691090432 * q^98 - 96644441211111069636758112 * q^99

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