LMFDB - Embedded newform 50.26.a.k.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,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, 26, names="a")

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

chi := DirichletCharacter("50.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
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:	$197.998389976$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} - 27590779188 x^{4} + 26487255863952 x^{3} + \cdots - 30\!\cdots\!08 $ x^6 - 2x^5 - 27590779188x^4 + 26487255863952x^3 + 180405425727179733780x^2 - 1479960352440847053525960*x - 3018239644098422083113677808
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 5^{18} $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$134113.$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} +1.47469e6 q^{3} +1.67772e7 q^{4} -6.04034e9 q^{6} -3.57876e9 q^{7} -6.87195e10 q^{8} +1.32743e12 q^{9} +1.08564e12 q^{11} +2.47412e13 q^{12} -2.13293e13 q^{13} +1.46586e13 q^{14} +2.81475e14 q^{16} +3.79275e15 q^{17} -5.43715e15 q^{18} +6.90611e15 q^{19} -5.27758e15 q^{21} -4.44680e15 q^{22} +1.56245e17 q^{23} -1.01340e17 q^{24} +8.73648e16 q^{26} +7.08060e17 q^{27} -6.00417e16 q^{28} +6.08503e17 q^{29} -3.42961e18 q^{31} -1.15292e18 q^{32} +1.60099e18 q^{33} -1.55351e19 q^{34} +2.22706e19 q^{36} -7.61614e19 q^{37} -2.82874e19 q^{38} -3.14542e19 q^{39} +2.17158e20 q^{41} +2.16169e19 q^{42} -4.70339e20 q^{43} +1.82141e19 q^{44} -6.39979e20 q^{46} +6.53190e20 q^{47} +4.15089e20 q^{48} -1.32826e21 q^{49} +5.59313e21 q^{51} -3.57846e20 q^{52} +4.54358e21 q^{53} -2.90021e21 q^{54} +2.45931e20 q^{56} +1.01844e22 q^{57} -2.49243e21 q^{58} +1.39811e22 q^{59} -4.30120e21 q^{61} +1.40477e22 q^{62} -4.75056e21 q^{63} +4.72237e21 q^{64} -6.55766e21 q^{66} -3.04650e22 q^{67} +6.36317e22 q^{68} +2.30413e23 q^{69} -4.08644e22 q^{71} -9.12202e22 q^{72} +1.14063e23 q^{73} +3.11957e23 q^{74} +1.15865e23 q^{76} -3.88526e21 q^{77} +1.28836e23 q^{78} +6.98160e23 q^{79} -8.05452e22 q^{81} -8.89479e23 q^{82} -1.18110e24 q^{83} -8.85430e22 q^{84} +1.92651e24 q^{86} +8.97354e23 q^{87} -7.46049e22 q^{88} +2.79755e24 q^{89} +7.63325e22 q^{91} +2.62136e24 q^{92} -5.05762e24 q^{93} -2.67546e24 q^{94} -1.70020e24 q^{96} +1.06166e25 q^{97} +5.44056e24 q^{98} +1.44112e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24576 q^{2} + 801416 q^{3} + 100663296 q^{4} - 3282599936 q^{6} + 34007705352 q^{7} - 412316860416 q^{8} + 541468782118 q^{9} + 9861544614312 q^{11} + 13445529337856 q^{12} + 30787386783696 q^{13}+ \cdots - 20\!\cdots\!64 q^{99}+O(q^{100}) $ 6 * q - 24576 * q^2 + 801416 * q^3 + 100663296 * q^4 - 3282599936 * q^6 + 34007705352 * q^7 - 412316860416 * q^8 + 541468782118 * q^9 + 9861544614312 * q^11 + 13445529337856 * q^12 + 30787386783696 * q^13 - 139295561121792 * q^14 + 1688849860263936 * q^16 + 3432836939805312 * q^17 - 2217856131555328 * q^18 + 2007656488916520 * q^19 - 28181710291014728 * q^21 - 40392886740221952 * q^22 + 135711886432707576 * q^23 - 55072888167858176 * q^24 - 126105136266018816 * q^26 + 788054364552235760 * q^27 + 570554618354860032 * q^28 - 2926032031655504820 * q^29 + 79292935777014912 * q^31 - 6917529027641081856 * q^32 - 6844843638395003168 * q^33 - 14060900105442557952 * q^34 + 9084338714850623488 * q^36 + 3345885298190974032 * q^37 - 8223360978602065920 * q^38 + 124726636622561793456 * q^39 + 103229301719876244012 * q^41 + 115432285351996325888 * q^42 + 166390524239317503336 * q^43 + 165449264087949115392 * q^44 - 555875886828370231296 * q^46 + 405906243391034677992 * q^47 + 225578549935547088896 * q^48 + 1716280748139027694542 * q^49 - 1516225893661962013568 * q^51 + 516526638145613070336 * q^52 + 9772760301640799789616 * q^53 - 3227870677205957672960 * q^54 - 2336991716781506691072 * q^56 + 26174725126915157341920 * q^57 + 11985027201660947742720 * q^58 - 12499075130880780168840 * q^59 + 3687285610311118296612 * q^61 - 324783864942653079552 * q^62 + 93007818034972665339656 * q^63 + 28334198897217871282176 * q^64 + 28036479542865932976128 * q^66 + 16759935062266648886712 * q^67 + 57593446831892717371392 * q^68 + 185125325982378999854536 * q^69 + 74568876221253661649712 * q^71 - 37209451376028153806848 * q^72 + 381797761857106829638176 * q^73 - 13704746181390229635072 * q^74 + 33682886568354062008320 * q^76 - 80271541631956375339296 * q^77 - 510880303606013105995776 * q^78 - 400850316873811624799520 * q^79 - 1432110118616113828343714 * q^81 - 422827219844613095473152 * q^82 - 2423159733509985740001144 * q^83 - 472810640801776950837248 * q^84 - 681535587284244493664256 * q^86 - 1231328665433636473947120 * q^87 - 677680185704239576645632 * q^88 + 2982172528060341024616740 * q^89 - 7001711719121019241314768 * q^91 + 2276867632449004467388416 * q^92 - 8806417055581711481018368 * q^93 - 1662591972929678041055232 * q^94 - 923969740536000876118016 * q^96 - 4960469410756873985567808 * q^97 - 7029885944377457436844032 * q^98 - 2053720289282411723573464 * 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 $

$2$	−4096.00	−0.707107
$2$	−4096.00	−0.707107
$3$	1.47469e6	1.60209	0.801043	−	0.598607i	$-0.204279\pi$
$3$	1.47469e6	1.60209	0.801043	+	0.598607i	$0.204279\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−6.04034e9	−1.13285
$7$	−3.57876e9	−0.0977254	−0.0488627	−	0.998806i	$-0.515560\pi$
$7$	−3.57876e9	−0.0977254	−0.0488627	+	0.998806i	$0.515560\pi$
$8$	−6.87195e10	−0.353553
$9$	1.32743e12	1.56668
$10$	0	0
$11$	1.08564e12	0.104299	0.0521493	−	0.998639i	$-0.483393\pi$
$11$	1.08564e12	0.104299	0.0521493	+	0.998639i	$0.483393\pi$
$12$	2.47412e13	0.801043
$13$	−2.13293e13	−0.253913	−0.126956	−	0.991908i	$-0.540521\pi$
$13$	−2.13293e13	−0.253913	−0.126956	+	0.991908i	$0.540521\pi$
$14$	1.46586e13	0.0691023
$15$	0	0
$16$	2.81475e14	0.250000
$17$	3.79275e15	1.57886	0.789428	−	0.613844i	$-0.210377\pi$
$17$	3.79275e15	1.57886	0.789428	+	0.613844i	$0.210377\pi$
$18$	−5.43715e15	−1.10781
$19$	6.90611e15	0.715836	0.357918	−	0.933753i	$-0.383487\pi$
$19$	6.90611e15	0.715836	0.357918	+	0.933753i	$0.383487\pi$
$20$	0	0
$21$	−5.27758e15	−0.156564
$22$	−4.44680e15	−0.0737503
$23$	1.56245e17	1.48665	0.743324	−	0.668932i	$-0.233248\pi$
$23$	1.56245e17	1.48665	0.743324	+	0.668932i	$0.233248\pi$
$24$	−1.01340e17	−0.566423
$25$	0	0
$26$	8.73648e16	0.179544
$27$	7.08060e17	0.907868
$28$	−6.00417e16	−0.0488627
$29$	6.08503e17	0.319365	0.159683	−	0.987168i	$-0.448953\pi$
$29$	6.08503e17	0.319365	0.159683	+	0.987168i	$0.448953\pi$
$30$	0	0
$31$	−3.42961e18	−0.782030	−0.391015	−	0.920384i	$-0.627876\pi$
$31$	−3.42961e18	−0.782030	−0.391015	+	0.920384i	$0.627876\pi$
$32$	−1.15292e18	−0.176777
$33$	1.60099e18	0.167095
$34$	−1.55351e19	−1.11642
$35$	0	0
$36$	2.22706e19	0.783339
$37$	−7.61614e19	−1.90201	−0.951006	−	0.309173i	$-0.899948\pi$
$37$	−7.61614e19	−1.90201	−0.951006	+	0.309173i	$0.899948\pi$
$38$	−2.82874e19	−0.506172
$39$	−3.14542e19	−0.406790
$40$	0	0
$41$	2.17158e20	1.50306	0.751532	−	0.659696i	$-0.229315\pi$
$41$	2.17158e20	1.50306	0.751532	+	0.659696i	$0.229315\pi$
$42$	2.16169e19	0.110708
$43$	−4.70339e20	−1.79496	−0.897481	−	0.441052i	$-0.854605\pi$
$43$	−4.70339e20	−1.79496	−0.897481	+	0.441052i	$0.854605\pi$
$44$	1.82141e19	0.0521493
$45$	0	0
$46$	−6.39979e20	−1.05122
$47$	6.53190e20	0.820004	0.410002	−	0.912085i	$-0.365528\pi$
$47$	6.53190e20	0.820004	0.410002	+	0.912085i	$0.365528\pi$
$48$	4.15089e20	0.400521
$49$	−1.32826e21	−0.990450
$50$	0	0
$51$	5.59313e21	2.52946
$52$	−3.57846e20	−0.126956
$53$	4.54358e21	1.27043	0.635214	−	0.772336i	$-0.280912\pi$
$53$	4.54358e21	1.27043	0.635214	+	0.772336i	$0.280912\pi$
$54$	−2.90021e21	−0.641960
$55$	0	0
$56$	2.45931e20	0.0345512
$57$	1.01844e22	1.14683
$58$	−2.49243e21	−0.225825
$59$	1.39811e22	1.02303	0.511517	−	0.859273i	$-0.329084\pi$
$59$	1.39811e22	1.02303	0.511517	+	0.859273i	$0.329084\pi$
$60$	0	0
$61$	−4.30120e21	−0.207475	−0.103738	−	0.994605i	$-0.533080\pi$
$61$	−4.30120e21	−0.207475	−0.103738	+	0.994605i	$0.533080\pi$
$62$	1.40477e22	0.552979
$63$	−4.75056e21	−0.153104
$64$	4.72237e21	0.125000
$65$	0	0
$66$	−6.55766e21	−0.118154
$67$	−3.04650e22	−0.454848	−0.227424	−	0.973796i	$-0.573030\pi$
$67$	−3.04650e22	−0.454848	−0.227424	+	0.973796i	$0.573030\pi$
$68$	6.36317e22	0.789428
$69$	2.30413e23	2.38174
$70$	0	0
$71$	−4.08644e22	−0.295540	−0.147770	−	0.989022i	$-0.547209\pi$
$71$	−4.08644e22	−0.295540	−0.147770	+	0.989022i	$0.547209\pi$
$72$	−9.12202e22	−0.553905
$73$	1.14063e23	0.582918	0.291459	−	0.956583i	$-0.405859\pi$
$73$	1.14063e23	0.582918	0.291459	+	0.956583i	$0.405859\pi$
$74$	3.11957e23	1.34493
$75$	0	0
$76$	1.15865e23	0.357918
$77$	−3.88526e21	−0.0101926
$78$	1.28836e23	0.287644
$79$	6.98160e23	1.32928	0.664640	−	0.747164i	$-0.268585\pi$
$79$	6.98160e23	1.32928	0.664640	+	0.747164i	$0.268585\pi$
$80$	0	0
$81$	−8.05452e22	−0.112196
$82$	−8.89479e23	−1.06283
$83$	−1.18110e24	−1.21286	−0.606428	−	0.795139i	$-0.707398\pi$
$83$	−1.18110e24	−1.21286	−0.606428	+	0.795139i	$0.707398\pi$
$84$	−8.85430e22	−0.0782822
$85$	0	0
$86$	1.92651e24	1.26923
$87$	8.97354e23	0.511650
$88$	−7.46049e22	−0.0368751
$89$	2.79755e24	1.20061	0.600307	−	0.799770i	$-0.295045\pi$
$89$	2.79755e24	1.20061	0.600307	+	0.799770i	$0.295045\pi$
$90$	0	0
$91$	7.63325e22	0.0248137
$92$	2.62136e24	0.743324
$93$	−5.05762e24	−1.25288
$94$	−2.67546e24	−0.579831
$95$	0	0
$96$	−1.70020e24	−0.283211
$97$	1.06166e25	1.55360	0.776798	−	0.629750i	$-0.216843\pi$
$97$	1.06166e25	1.55360	0.776798	+	0.629750i	$0.216843\pi$
$98$	5.44056e24	0.700354
$99$	1.44112e24	0.163403
$100$	0	0
$101$	7.61024e24	0.672019	0.336009	−	0.941859i	$-0.390923\pi$
$101$	7.61024e24	0.672019	0.336009	+	0.941859i	$0.390923\pi$
$102$	−2.29095e25	−1.78860
$103$	1.50264e25	1.03846	0.519229	−	0.854635i	$-0.326219\pi$
$103$	1.50264e25	1.03846	0.519229	+	0.854635i	$0.326219\pi$
$104$	1.46574e24	0.0897718
$105$	0	0
$106$	−1.86105e25	−0.898328
$107$	−3.03661e24	−0.130344	−0.0651721	−	0.997874i	$-0.520760\pi$
$107$	−3.03661e24	−0.130344	−0.0651721	+	0.997874i	$0.520760\pi$
$108$	1.18793e25	0.453934
$109$	−3.16922e25	−1.07925	−0.539625	−	0.841906i	$-0.681434\pi$
$109$	−3.16922e25	−1.07925	−0.539625	+	0.841906i	$0.681434\pi$
$110$	0	0
$111$	−1.12315e26	−3.04719
$112$	−1.00733e24	−0.0244314
$113$	−6.24206e25	−1.35471	−0.677357	−	0.735655i	$-0.736875\pi$
$113$	−6.24206e25	−1.35471	−0.677357	+	0.735655i	$0.736875\pi$
$114$	−4.17152e25	−0.810931
$115$	0	0
$116$	1.02090e25	0.159683
$117$	−2.83131e25	−0.397800
$118$	−5.72664e25	−0.723394
$119$	−1.35733e25	−0.154294
$120$	0	0
$121$	−1.07168e26	−0.989122
$122$	1.76177e25	0.146707
$123$	3.20241e26	2.40804
$124$	−5.75393e25	−0.391015
$125$	0	0
$126$	1.94583e25	0.108261
$127$	1.67435e26	0.843917	0.421959	−	0.906615i	$-0.361343\pi$
$127$	1.67435e26	0.843917	0.421959	+	0.906615i	$0.361343\pi$
$128$	−1.93428e25	−0.0883883
$129$	−6.93606e26	−2.87568
$130$	0	0
$131$	−1.90057e26	−0.650118	−0.325059	−	0.945694i	$-0.605384\pi$
$131$	−1.90057e26	−0.650118	−0.325059	+	0.945694i	$0.605384\pi$
$132$	2.68602e25	0.0835477
$133$	−2.47153e25	−0.0699553
$134$	1.24785e26	0.321626
$135$	0	0
$136$	−2.60636e26	−0.558210
$137$	3.51717e26	0.687364	0.343682	−	0.939086i	$-0.388326\pi$
$137$	3.51717e26	0.687364	0.343682	+	0.939086i	$0.388326\pi$
$138$	−9.43773e26	−1.68414
$139$	3.91803e26	0.638827	0.319414	−	0.947615i	$-0.396514\pi$
$139$	3.91803e26	0.638827	0.319414	+	0.947615i	$0.396514\pi$
$140$	0	0
$141$	9.63254e26	1.31372
$142$	1.67381e26	0.208978
$143$	−2.31560e25	−0.0264828
$144$	3.73638e26	0.391670
$145$	0	0
$146$	−4.67201e26	−0.412186
$147$	−1.95878e27	−1.58679
$148$	−1.27778e27	−0.951006
$149$	1.80648e27	1.23596	0.617979	−	0.786194i	$-0.287952\pi$
$149$	1.80648e27	1.23596	0.617979	+	0.786194i	$0.287952\pi$
$150$	0	0
$151$	−1.68416e26	−0.0975373	−0.0487687	−	0.998810i	$-0.515530\pi$
$151$	−1.68416e26	−0.0975373	−0.0487687	+	0.998810i	$0.515530\pi$
$152$	−4.74584e26	−0.253086
$153$	5.03460e27	2.47356
$154$	1.59140e25	0.00720728
$155$	0	0
$156$	−5.27713e26	−0.203395
$157$	1.56946e27	0.558475	0.279237	−	0.960222i	$-0.409918\pi$
$157$	1.56946e27	0.558475	0.279237	+	0.960222i	$0.409918\pi$
$158$	−2.85967e27	−0.939943
$159$	6.70039e27	2.03533
$160$	0	0
$161$	−5.59164e26	−0.145283
$162$	3.29913e26	0.0793345
$163$	5.35307e27	1.19195	0.595974	−	0.803004i	$-0.296766\pi$
$163$	5.35307e27	1.19195	0.595974	+	0.803004i	$0.296766\pi$
$164$	3.64331e27	0.751532
$165$	0	0
$166$	4.83777e27	0.857618
$167$	1.01057e28	1.66192	0.830959	−	0.556334i	$-0.187793\pi$
$167$	1.01057e28	1.66192	0.830959	+	0.556334i	$0.187793\pi$
$168$	3.62672e26	0.0553539
$169$	−6.60147e27	−0.935528
$170$	0	0
$171$	9.16737e27	1.12148
$172$	−7.89098e27	−0.897481
$173$	8.66506e26	0.0916633	0.0458316	−	0.998949i	$-0.485406\pi$
$173$	8.66506e26	0.0916633	0.0458316	+	0.998949i	$0.485406\pi$
$174$	−3.67556e27	−0.361791
$175$	0	0
$176$	3.05581e26	0.0260747
$177$	2.06178e28	1.63899
$178$	−1.14588e28	−0.848962
$179$	−2.03208e28	−1.40371	−0.701856	−	0.712319i	$-0.747645\pi$
$179$	−2.03208e28	−1.40371	−0.701856	+	0.712319i	$0.747645\pi$
$180$	0	0
$181$	−6.11555e27	−0.367666	−0.183833	−	0.982957i	$-0.558851\pi$
$181$	−6.11555e27	−0.367666	−0.183833	+	0.982957i	$0.558851\pi$
$182$	−3.12658e26	−0.0175460
$183$	−6.34295e27	−0.332393
$184$	−1.07371e28	−0.525609
$185$	0	0
$186$	2.07160e28	0.885919
$187$	4.11757e27	0.164672
$188$	1.09587e28	0.410002
$189$	−2.53398e27	−0.0887218
$190$	0	0
$191$	1.25038e28	0.383819	0.191909	−	0.981413i	$-0.438532\pi$
$191$	1.25038e28	0.383819	0.191909	+	0.981413i	$0.438532\pi$
$192$	6.96404e27	0.200261
$193$	4.00087e28	1.07817	0.539086	−	0.842251i	$-0.318770\pi$
$193$	4.00087e28	1.07817	0.539086	+	0.842251i	$0.318770\pi$
$194$	−4.34855e28	−1.09856
$195$	0	0
$196$	−2.22845e28	−0.495225
$197$	−1.19953e28	−0.250141	−0.125070	−	0.992148i	$-0.539916\pi$
$197$	−1.19953e28	−0.250141	−0.125070	+	0.992148i	$0.539916\pi$
$198$	−5.90281e27	−0.115543
$199$	3.34370e28	0.614559	0.307280	−	0.951619i	$-0.400581\pi$
$199$	3.34370e28	0.614559	0.307280	+	0.951619i	$0.400581\pi$
$200$	0	0
$201$	−4.49265e28	−0.728705
$202$	−3.11715e28	−0.475189
$203$	−2.17769e27	−0.0312101
$204$	9.38372e28	1.26473
$205$	0	0
$206$	−6.15480e28	−0.734301
$207$	2.07404e29	2.32910
$208$	−6.00366e27	−0.0634782
$209$	7.49757e27	0.0746607
$210$	0	0
$211$	6.92258e28	0.611980	0.305990	−	0.952035i	$-0.401013\pi$
$211$	6.92258e28	0.611980	0.305990	+	0.952035i	$0.401013\pi$
$212$	7.62287e28	0.635214
$213$	−6.02624e28	−0.473480
$214$	1.24379e28	0.0921672
$215$	0	0
$216$	−4.86575e28	−0.320980
$217$	1.22738e28	0.0764242
$218$	1.29811e29	0.763144
$219$	1.68207e29	0.933885
$220$	0	0
$221$	−8.08966e28	−0.400892
$222$	4.60040e29	2.15469
$223$	4.37006e29	1.93498	0.967490	−	0.252908i	$-0.0813869\pi$
$223$	4.37006e29	1.93498	0.967490	+	0.252908i	$0.0813869\pi$
$224$	4.12603e27	0.0172756
$225$	0	0
$226$	2.55675e29	0.957927
$227$	−4.51616e28	−0.160120	−0.0800600	−	0.996790i	$-0.525511\pi$
$227$	−4.51616e28	−0.160120	−0.0800600	+	0.996790i	$0.525511\pi$
$228$	1.70866e29	0.573415
$229$	−3.96675e29	−1.26035	−0.630175	−	0.776454i	$-0.717017\pi$
$229$	−3.96675e29	−1.26035	−0.630175	+	0.776454i	$0.717017\pi$
$230$	0	0
$231$	−5.72957e27	−0.0163295
$232$	−4.18160e28	−0.112913
$233$	−2.52711e29	−0.646658	−0.323329	−	0.946287i	$-0.604802\pi$
$233$	−2.52711e29	−0.646658	−0.323329	+	0.946287i	$0.604802\pi$
$234$	1.15971e29	0.281287
$235$	0	0
$236$	2.34563e29	0.511517
$237$	1.02957e30	2.12962
$238$	5.55964e28	0.109103
$239$	7.75729e29	1.44456	0.722281	−	0.691600i	$-0.243094\pi$
$239$	7.75729e29	1.44456	0.722281	+	0.691600i	$0.243094\pi$
$240$	0	0
$241$	−1.98502e28	−0.0333082	−0.0166541	−	0.999861i	$-0.505301\pi$
$241$	−1.98502e28	−0.0333082	−0.0166541	+	0.999861i	$0.505301\pi$
$242$	4.38962e29	0.699415
$243$	−7.18710e29	−1.08762
$244$	−7.21621e28	−0.103738
$245$	0	0
$246$	−1.31171e30	−1.70274
$247$	−1.47302e29	−0.181760
$248$	2.35681e29	0.276489
$249$	−1.74175e30	−1.94310
$250$	0	0
$251$	−9.10004e29	−0.918590	−0.459295	−	0.888284i	$-0.651898\pi$
$251$	−9.10004e29	−0.918590	−0.459295	+	0.888284i	$0.651898\pi$
$252$	−7.97011e28	−0.0765522
$253$	1.69626e29	0.155055
$254$	−6.85814e29	−0.596740
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	1.13259e30	0.850961	0.425480	−	0.904968i	$-0.360105\pi$
$257$	1.13259e30	0.850961	0.425480	+	0.904968i	$0.360105\pi$
$258$	2.84101e30	2.03342
$259$	2.72563e29	0.185875
$260$	0	0
$261$	8.07744e29	0.500343
$262$	7.78473e29	0.459703
$263$	7.83926e29	0.441396	0.220698	−	0.975342i	$-0.429167\pi$
$263$	7.83926e29	0.441396	0.220698	+	0.975342i	$0.429167\pi$
$264$	−1.10019e29	−0.0590771
$265$	0	0
$266$	1.01234e29	0.0494659
$267$	4.12553e30	1.92349
$268$	−5.11118e29	−0.227424
$269$	2.21562e30	0.941005	0.470502	−	0.882399i	$-0.344073\pi$
$269$	2.21562e30	0.941005	0.470502	+	0.882399i	$0.344073\pi$
$270$	0	0
$271$	−3.34900e29	−0.129658	−0.0648289	−	0.997896i	$-0.520650\pi$
$271$	−3.34900e29	−0.129658	−0.0648289	+	0.997896i	$0.520650\pi$
$272$	1.06756e30	0.394714
$273$	1.12567e29	0.0397537
$274$	−1.44063e30	−0.486040
$275$	0	0
$276$	3.86569e30	1.19087
$277$	3.78301e30	1.11388	0.556942	−	0.830552i	$-0.311975\pi$
$277$	3.78301e30	1.11388	0.556942	+	0.830552i	$0.311975\pi$
$278$	−1.60483e30	−0.451719
$279$	−4.55256e30	−1.22519
$280$	0	0
$281$	−2.06047e30	−0.507151	−0.253576	−	0.967316i	$-0.581607\pi$
$281$	−2.06047e30	−0.507151	−0.253576	+	0.967316i	$0.581607\pi$
$282$	−3.94549e30	−0.928938
$283$	1.40735e30	0.317010	0.158505	−	0.987358i	$-0.449333\pi$
$283$	1.40735e30	0.317010	0.158505	+	0.987358i	$0.449333\pi$
$284$	−6.85591e29	−0.147770
$285$	0	0
$286$	9.48471e28	0.0187261
$287$	−7.77157e29	−0.146888
$288$	−1.53042e30	−0.276952
$289$	8.61430e30	1.49278
$290$	0	0
$291$	1.56562e31	2.48899
$292$	1.91365e30	0.291459
$293$	3.14320e30	0.458698	0.229349	−	0.973344i	$-0.426340\pi$
$293$	3.14320e30	0.458698	0.229349	+	0.973344i	$0.426340\pi$
$294$	8.02315e30	1.12203
$295$	0	0
$296$	5.23377e30	0.672463
$297$	7.68701e29	0.0946894
$298$	−7.39933e30	−0.873955
$299$	−3.33260e30	−0.377479
$300$	0	0
$301$	1.68323e30	0.175413
$302$	6.89831e29	0.0689693
$303$	1.12228e31	1.07663
$304$	1.94390e30	0.178959
$305$	0	0
$306$	−2.06217e31	−1.74907
$307$	6.65869e29	0.0542200	0.0271100	−	0.999632i	$-0.491370\pi$
$307$	6.65869e29	0.0542200	0.0271100	+	0.999632i	$0.491370\pi$
$308$	−6.51839e28	−0.00509631
$309$	2.21593e31	1.66370
$310$	0	0
$311$	−1.30158e31	−0.901497	−0.450749	−	0.892651i	$-0.648843\pi$
$311$	−1.30158e31	−0.901497	−0.450749	+	0.892651i	$0.648843\pi$
$312$	2.16151e30	0.143822
$313$	1.48840e31	0.951514	0.475757	−	0.879577i	$-0.342174\pi$
$313$	1.48840e31	0.951514	0.475757	+	0.879577i	$0.342174\pi$
$314$	−6.42849e30	−0.394901
$315$	0	0
$316$	1.17132e31	0.664640
$317$	−4.63362e30	−0.252743	−0.126372	−	0.991983i	$-0.540333\pi$
$317$	−4.63362e30	−0.252743	−0.126372	+	0.991983i	$0.540333\pi$
$318$	−2.74448e31	−1.43920
$319$	6.60617e29	0.0333093
$320$	0	0
$321$	−4.47806e30	−0.208822
$322$	2.29034e30	0.102731
$323$	2.61931e31	1.13020
$324$	−1.35132e30	−0.0560980
$325$	0	0
$326$	−2.19262e31	−0.842835
$327$	−4.67363e31	−1.72905
$328$	−1.49230e31	−0.531414
$329$	−2.33761e30	−0.0801352
$330$	0	0
$331$	−1.64006e31	−0.521207	−0.260604	−	0.965446i	$-0.583922\pi$
$331$	−1.64006e31	−0.521207	−0.260604	+	0.965446i	$0.583922\pi$
$332$	−1.98155e31	−0.606428
$333$	−1.01099e32	−2.97984
$334$	−4.13928e31	−1.17515
$335$	0	0
$336$	−1.48551e30	−0.0391411
$337$	8.69817e30	0.220828	0.110414	−	0.993886i	$-0.464782\pi$
$337$	8.69817e30	0.220828	0.110414	+	0.993886i	$0.464782\pi$
$338$	2.70396e31	0.661518
$339$	−9.20512e31	−2.17037
$340$	0	0
$341$	−3.72333e30	−0.0815647
$342$	−3.75495e31	−0.793009
$343$	9.55290e30	0.194518
$344$	3.23215e31	0.634615
$345$	0	0
$346$	−3.54921e30	−0.0648157
$347$	−8.06238e31	−1.42019	−0.710093	−	0.704108i	$-0.751347\pi$
$347$	−8.06238e31	−1.42019	−0.710093	+	0.704108i	$0.751347\pi$
$348$	1.50551e31	0.255825
$349$	−9.75945e31	−1.59995	−0.799977	−	0.600031i	$-0.795155\pi$
$349$	−9.75945e31	−1.59995	−0.799977	+	0.600031i	$0.795155\pi$
$350$	0	0
$351$	−1.51024e31	−0.230519
$352$	−1.25166e30	−0.0184376
$353$	1.35792e31	0.193060	0.0965298	−	0.995330i	$-0.469226\pi$
$353$	1.35792e31	0.193060	0.0965298	+	0.995330i	$0.469226\pi$
$354$	−8.44503e31	−1.15894
$355$	0	0
$356$	4.69351e31	0.600307
$357$	−2.00165e31	−0.247193
$358$	8.32340e31	0.992574
$359$	1.23431e32	1.42148	0.710742	−	0.703453i	$-0.248359\pi$
$359$	1.23431e32	1.42148	0.710742	+	0.703453i	$0.248359\pi$
$360$	0	0
$361$	−4.53822e31	−0.487579
$362$	2.50493e31	0.259979
$363$	−1.58040e32	−1.58466
$364$	1.28065e30	0.0124069
$365$	0	0
$366$	2.59807e31	0.235038
$367$	−1.94163e31	−0.169762	−0.0848811	−	0.996391i	$-0.527051\pi$
$367$	−1.94163e31	−0.169762	−0.0848811	+	0.996391i	$0.527051\pi$
$368$	4.39791e31	0.371662
$369$	2.88262e32	2.35482
$370$	0	0
$371$	−1.62604e31	−0.124153
$372$	−8.48527e31	−0.626439
$373$	−1.75681e32	−1.25420	−0.627098	−	0.778941i	$-0.715757\pi$
$373$	−1.75681e32	−1.25420	−0.627098	+	0.778941i	$0.715757\pi$
$374$	−1.68656e31	−0.116441
$375$	0	0
$376$	−4.48869e31	−0.289915
$377$	−1.29789e31	−0.0810909
$378$	1.03792e31	0.0627358
$379$	2.09100e32	1.22283	0.611413	−	0.791312i	$-0.290601\pi$
$379$	2.09100e32	1.22283	0.611413	+	0.791312i	$0.290601\pi$
$380$	0	0
$381$	2.46915e32	1.35203
$382$	−5.12157e31	−0.271401
$383$	1.47981e32	0.758966	0.379483	−	0.925199i	$-0.376102\pi$
$383$	1.47981e32	0.758966	0.379483	+	0.925199i	$0.376102\pi$
$384$	−2.85247e31	−0.141606
$385$	0	0
$386$	−1.63876e32	−0.762383
$387$	−6.24342e32	−2.81213
$388$	1.78117e32	0.776798
$389$	2.19739e32	0.927978	0.463989	−	0.885841i	$-0.346418\pi$
$389$	2.19739e32	0.927978	0.463989	+	0.885841i	$0.346418\pi$
$390$	0	0
$391$	5.92598e32	2.34720
$392$	9.12774e31	0.350177
$393$	−2.80275e32	−1.04155
$394$	4.91329e31	0.176876
$395$	0	0
$396$	2.41779e31	0.0817013
$397$	1.95462e32	0.640003	0.320001	−	0.947417i	$-0.396317\pi$
$397$	1.95462e32	0.640003	0.320001	+	0.947417i	$0.396317\pi$
$398$	−1.36958e32	−0.434559
$399$	−3.64475e31	−0.112074
$400$	0	0
$401$	−4.71177e32	−1.36107	−0.680534	−	0.732717i	$-0.738252\pi$
$401$	−4.71177e32	−1.36107	−0.680534	+	0.732717i	$0.738252\pi$
$402$	1.84019e32	0.515273
$403$	7.31511e31	0.198567
$404$	1.27679e32	0.336009
$405$	0	0
$406$	8.91980e30	0.0220689
$407$	−8.26841e31	−0.198377
$408$	−3.84357e32	−0.894300
$409$	−4.32845e32	−0.976767	−0.488384	−	0.872629i	$-0.662413\pi$
$409$	−4.32845e32	−0.976767	−0.488384	+	0.872629i	$0.662413\pi$
$410$	0	0
$411$	5.18675e32	1.10122
$412$	2.52101e32	0.519229
$413$	−5.00349e31	−0.0999763
$414$	−8.49528e32	−1.64692
$415$	0	0
$416$	2.45910e31	0.0448859
$417$	5.77790e32	1.02346
$418$	−3.07101e31	−0.0527931
$419$	9.61858e31	0.160485	0.0802427	−	0.996775i	$-0.474430\pi$
$419$	9.61858e31	0.160485	0.0802427	+	0.996775i	$0.474430\pi$
$420$	0	0
$421$	1.59673e31	0.0251018	0.0125509	−	0.999921i	$-0.496005\pi$
$421$	1.59673e31	0.0251018	0.0125509	+	0.999921i	$0.496005\pi$
$422$	−2.83549e32	−0.432735
$423$	8.67063e32	1.28468
$424$	−3.12233e32	−0.449164
$425$	0	0
$426$	2.46835e32	0.334801
$427$	1.53930e31	0.0202756
$428$	−5.09458e31	−0.0651721
$429$	−3.41480e31	−0.0424277
$430$	0	0
$431$	−7.11839e32	−0.834479	−0.417240	−	0.908796i	$-0.637002\pi$
$431$	−7.11839e32	−0.834479	−0.417240	+	0.908796i	$0.637002\pi$
$432$	1.99301e32	0.226967
$433$	9.69753e32	1.07291	0.536454	−	0.843930i	$-0.319764\pi$
$433$	9.69753e32	1.07291	0.536454	+	0.843930i	$0.319764\pi$
$434$	−5.02733e31	−0.0540401
$435$	0	0
$436$	−5.31708e32	−0.539625
$437$	1.07904e33	1.06420
$438$	−6.88977e32	−0.660357
$439$	−6.89367e32	−0.642161	−0.321081	−	0.947052i	$-0.604046\pi$
$439$	−6.89367e32	−0.642161	−0.321081	+	0.947052i	$0.604046\pi$
$440$	0	0
$441$	−1.76317e33	−1.55172
$442$	3.31353e32	0.283473
$443$	1.47442e33	1.22624	0.613120	−	0.789990i	$-0.289914\pi$
$443$	1.47442e33	1.22624	0.613120	+	0.789990i	$0.289914\pi$
$444$	−1.88433e33	−1.52359
$445$	0	0
$446$	−1.78998e33	−1.36824
$447$	2.66400e33	1.98011
$448$	−1.69002e31	−0.0122157
$449$	2.43553e33	1.71204	0.856020	−	0.516942i	$-0.172930\pi$
$449$	2.43553e33	1.71204	0.856020	+	0.516942i	$0.172930\pi$
$450$	0	0
$451$	2.35756e32	0.156768
$452$	−1.04724e33	−0.677357
$453$	−2.48361e32	−0.156263
$454$	1.84982e32	0.113222
$455$	0	0
$456$	−6.99866e32	−0.405466
$457$	1.75801e33	0.990990	0.495495	−	0.868611i	$-0.334987\pi$
$457$	1.75801e33	0.990990	0.495495	+	0.868611i	$0.334987\pi$
$458$	1.62478e33	0.891201
$459$	2.68549e33	1.43339
$460$	0	0
$461$	2.02960e33	1.02600	0.513002	−	0.858387i	$-0.328533\pi$
$461$	2.02960e33	1.02600	0.513002	+	0.858387i	$0.328533\pi$
$462$	2.34683e31	0.0115467
$463$	−5.63047e32	−0.269639	−0.134819	−	0.990870i	$-0.543045\pi$
$463$	−5.63047e32	−0.269639	−0.134819	+	0.990870i	$0.543045\pi$
$464$	1.71278e32	0.0798413
$465$	0	0
$466$	1.03510e33	0.457256
$467$	−3.35205e33	−1.44162	−0.720808	−	0.693134i	$-0.756229\pi$
$467$	−3.35205e33	−1.44162	−0.720808	+	0.693134i	$0.756229\pi$
$468$	−4.75016e32	−0.198900
$469$	1.09027e32	0.0444502
$470$	0	0
$471$	2.31447e33	0.894725
$472$	−9.60771e32	−0.361697
$473$	−5.10621e32	−0.187212
$474$	−4.21713e33	−1.50587
$475$	0	0
$476$	−2.27723e32	−0.0771471
$477$	6.03128e33	1.99035
$478$	−3.17739e33	−1.02146
$479$	3.28090e33	1.02754	0.513770	−	0.857928i	$-0.328248\pi$
$479$	3.28090e33	1.02754	0.513770	+	0.857928i	$0.328248\pi$
$480$	0	0
$481$	1.62447e33	0.482945
$482$	8.13063e31	0.0235525
$483$	−8.24595e32	−0.232756
$484$	−1.79799e33	−0.494561
$485$	0	0
$486$	2.94384e33	0.769061
$487$	2.83575e33	0.722032	0.361016	−	0.932560i	$-0.382430\pi$
$487$	2.83575e33	0.722032	0.361016	+	0.932560i	$0.382430\pi$
$488$	2.95576e32	0.0733536
$489$	7.89413e33	1.90960
$490$	0	0
$491$	−6.18264e33	−1.42120	−0.710600	−	0.703596i	$-0.751576\pi$
$491$	−6.18264e33	−1.42120	−0.710600	+	0.703596i	$0.751576\pi$
$492$	5.37276e33	1.20402
$493$	2.30790e33	0.504231
$494$	6.03351e32	0.128524
$495$	0	0
$496$	−9.65349e32	−0.195507
$497$	1.46244e32	0.0288817
$498$	7.13422e33	1.37398
$499$	−2.73531e33	−0.513748	−0.256874	−	0.966445i	$-0.582693\pi$
$499$	−2.73531e33	−0.513748	−0.256874	+	0.966445i	$0.582693\pi$
$500$	0	0
$501$	1.49028e34	2.66253
$502$	3.72738e33	0.649542
$503$	−1.17377e33	−0.199519	−0.0997597	−	0.995012i	$-0.531807\pi$
$503$	−1.17377e33	−0.199519	−0.0997597	+	0.995012i	$0.531807\pi$
$504$	3.26456e32	0.0541306
$505$	0	0
$506$	−6.94790e32	−0.109641
$507$	−9.73514e33	−1.49880
$508$	2.80909e33	0.421959
$509$	−4.20998e33	−0.617031	−0.308516	−	0.951219i	$-0.599832\pi$
$509$	−4.20998e33	−0.617031	−0.308516	+	0.951219i	$0.599832\pi$
$510$	0	0
$511$	−4.08203e32	−0.0569659
$512$	−3.24519e32	−0.0441942
$513$	4.88994e33	0.649885
$514$	−4.63910e33	−0.601720
$515$	0	0
$516$	−1.16368e34	−1.43784
$517$	7.09131e32	0.0855253
$518$	−1.11642e33	−0.131433
$519$	1.27783e33	0.146852
$520$	0	0
$521$	−1.42619e34	−1.56208	−0.781042	−	0.624478i	$-0.785312\pi$
$521$	−1.42619e34	−1.56208	−0.781042	+	0.624478i	$0.785312\pi$
$522$	−3.30852e33	−0.353796
$523$	−1.07993e34	−1.12752	−0.563760	−	0.825939i	$-0.690646\pi$
$523$	−1.07993e34	−1.12752	−0.563760	+	0.825939i	$0.690646\pi$
$524$	−3.18863e33	−0.325059
$525$	0	0
$526$	−3.21096e33	−0.312114
$527$	−1.30076e34	−1.23471
$528$	4.50639e32	0.0417738
$529$	1.33667e34	1.21012
$530$	0	0
$531$	1.85589e34	1.60276
$532$	−4.14654e32	−0.0349777
$533$	−4.63183e33	−0.381647
$534$	−1.68982e34	−1.36011
$535$	0	0
$536$	2.09354e33	0.160813
$537$	−2.99669e34	−2.24887
$538$	−9.07518e33	−0.665391
$539$	−1.44202e33	−0.103303
$540$	0	0
$541$	−9.36097e32	−0.0640258	−0.0320129	−	0.999487i	$-0.510192\pi$
$541$	−9.36097e32	−0.0640258	−0.0320129	+	0.999487i	$0.510192\pi$
$542$	1.37175e33	0.0916819
$543$	−9.01856e33	−0.589033
$544$	−4.37274e33	−0.279105
$545$	0	0
$546$	−4.61074e32	−0.0281101
$547$	1.05246e34	0.627137	0.313568	−	0.949566i	$-0.398475\pi$
$547$	1.05246e34	0.627137	0.313568	+	0.949566i	$0.398475\pi$
$548$	5.90084e33	0.343682
$549$	−5.70954e33	−0.325047
$550$	0	0
$551$	4.20238e33	0.228613
$552$	−1.58339e34	−0.842071
$553$	−2.49855e33	−0.129904
$554$	−1.54952e34	−0.787635
$555$	0	0
$556$	6.57337e33	0.319414
$557$	9.65307e33	0.458644	0.229322	−	0.973351i	$-0.426349\pi$
$557$	9.65307e33	0.458644	0.229322	+	0.973351i	$0.426349\pi$
$558$	1.86473e34	0.866340
$559$	1.00320e34	0.455764
$560$	0	0
$561$	6.07215e33	0.263819
$562$	8.43969e33	0.358610
$563$	−4.08658e34	−1.69826	−0.849132	−	0.528180i	$-0.822875\pi$
$563$	−4.08658e34	−1.69826	−0.849132	+	0.528180i	$0.822875\pi$
$564$	1.61607e34	0.656859
$565$	0	0
$566$	−5.76452e33	−0.224160
$567$	2.88252e32	0.0109644
$568$	2.80818e33	0.104489
$569$	8.49519e33	0.309221	0.154611	−	0.987975i	$-0.450588\pi$
$569$	8.49519e33	0.309221	0.154611	+	0.987975i	$0.450588\pi$
$570$	0	0
$571$	−2.91693e34	−1.01619	−0.508095	−	0.861301i	$-0.669650\pi$
$571$	−2.91693e34	−1.01619	−0.508095	+	0.861301i	$0.669650\pi$
$572$	−3.88494e32	−0.0132414
$573$	1.84393e34	0.614910
$574$	3.18324e33	0.103865
$575$	0	0
$576$	6.26861e33	0.195835
$577$	−5.12659e33	−0.156722	−0.0783611	−	0.996925i	$-0.524969\pi$
$577$	−5.12659e33	−0.156722	−0.0783611	+	0.996925i	$0.524969\pi$
$578$	−3.52842e34	−1.05556
$579$	5.90005e34	1.72732
$580$	0	0
$581$	4.22686e33	0.118527
$582$	−6.41278e34	−1.75998
$583$	4.93271e33	0.132504
$584$	−7.83833e33	−0.206093
$585$	0	0
$586$	−1.28746e34	−0.324349
$587$	−6.37641e34	−1.57253	−0.786266	−	0.617888i	$-0.787989\pi$
$587$	−6.37641e34	−1.57253	−0.786266	+	0.617888i	$0.787989\pi$
$588$	−3.28628e34	−0.793393
$589$	−2.36852e34	−0.559805
$590$	0	0
$591$	−1.76894e34	−0.400747
$592$	−2.14375e34	−0.475503
$593$	7.56532e34	1.64302	0.821511	−	0.570192i	$-0.193131\pi$
$593$	7.56532e34	1.64302	0.821511	+	0.570192i	$0.193131\pi$
$594$	−3.14860e33	−0.0669556
$595$	0	0
$596$	3.03076e34	0.617979
$597$	4.93093e34	0.984577
$598$	1.36503e34	0.266918
$599$	6.58590e34	1.26119	0.630594	−	0.776113i	$-0.282811\pi$
$599$	6.58590e34	1.26119	0.630594	+	0.776113i	$0.282811\pi$
$600$	0	0
$601$	−3.63692e34	−0.668041	−0.334020	−	0.942566i	$-0.608405\pi$
$601$	−3.63692e34	−0.668041	−0.334020	+	0.942566i	$0.608405\pi$
$602$	−6.89452e33	−0.124036
$603$	−4.04401e34	−0.712601
$604$	−2.82555e33	−0.0487687
$605$	0	0
$606$	−4.59684e34	−0.761293
$607$	−1.13535e35	−1.84193	−0.920963	−	0.389650i	$-0.872596\pi$
$607$	−1.13535e35	−1.84193	−0.920963	+	0.389650i	$0.872596\pi$
$608$	−7.96220e33	−0.126543
$609$	−3.21142e33	−0.0500012
$610$	0	0
$611$	−1.39321e34	−0.208210
$612$	8.44666e34	1.23678
$613$	8.49768e34	1.21911	0.609557	−	0.792742i	$-0.291347\pi$
$613$	8.49768e34	1.21911	0.609557	+	0.792742i	$0.291347\pi$
$614$	−2.72740e33	−0.0383393
$615$	0	0
$616$	2.66993e32	0.00360364
$617$	1.49456e35	1.97674	0.988368	−	0.152079i	$-0.0485967\pi$
$617$	1.49456e35	1.97674	0.988368	+	0.152079i	$0.0485967\pi$
$618$	−9.07644e34	−1.17641
$619$	−5.75885e34	−0.731481	−0.365740	−	0.930717i	$-0.619184\pi$
$619$	−5.75885e34	−0.731481	−0.365740	+	0.930717i	$0.619184\pi$
$620$	0	0
$621$	1.10631e35	1.34968
$622$	5.33125e34	0.637455
$623$	−1.00118e34	−0.117330
$624$	−8.85356e33	−0.101698
$625$	0	0
$626$	−6.09648e34	−0.672822
$627$	1.10566e34	0.119613
$628$	2.63311e34	0.279237
$629$	−2.88861e35	−3.00300
$630$	0	0
$631$	3.54832e34	0.354532	0.177266	−	0.984163i	$-0.443275\pi$
$631$	3.54832e34	0.354532	0.177266	+	0.984163i	$0.443275\pi$
$632$	−4.79772e34	−0.469972
$633$	1.02087e35	0.980445
$634$	1.89793e34	0.178716
$635$	0	0
$636$	1.12414e35	1.01767
$637$	2.83309e34	0.251488
$638$	−2.70589e33	−0.0235533
$639$	−5.42446e34	−0.463016
$640$	0	0
$641$	1.20958e35	0.992909	0.496454	−	0.868063i	$-0.334635\pi$
$641$	1.20958e35	0.992909	0.496454	+	0.868063i	$0.334635\pi$
$642$	1.83421e34	0.147660
$643$	4.32278e34	0.341292	0.170646	−	0.985332i	$-0.445415\pi$
$643$	4.32278e34	0.341292	0.170646	+	0.985332i	$0.445415\pi$
$644$	−9.38121e33	−0.0726416
$645$	0	0
$646$	−1.07287e35	−0.799173
$647$	4.93254e34	0.360385	0.180193	−	0.983631i	$-0.442328\pi$
$647$	4.93254e34	0.360385	0.180193	+	0.983631i	$0.442328\pi$
$648$	5.53503e33	0.0396673
$649$	1.51784e34	0.106701
$650$	0	0
$651$	1.81000e34	0.122438
$652$	8.98095e34	0.595974
$653$	−2.81796e35	−1.83451	−0.917255	−	0.398301i	$-0.869600\pi$
$653$	−2.81796e35	−1.83451	−0.917255	+	0.398301i	$0.869600\pi$
$654$	1.91432e35	1.22262
$655$	0	0
$656$	6.11245e34	0.375766
$657$	1.51410e35	0.913246
$658$	9.57486e33	0.0566642
$659$	−1.27642e35	−0.741185	−0.370592	−	0.928796i	$-0.620845\pi$
$659$	−1.27642e35	−0.741185	−0.370592	+	0.928796i	$0.620845\pi$
$660$	0	0
$661$	−3.04753e35	−1.70384	−0.851921	−	0.523671i	$-0.824562\pi$
$661$	−3.04753e35	−1.70384	−0.851921	+	0.523671i	$0.824562\pi$
$662$	6.71770e34	0.368549
$663$	−1.19298e35	−0.642263
$664$	8.11643e34	0.428809
$665$	0	0
$666$	4.14101e35	2.10707
$667$	9.50755e34	0.474783
$668$	1.69545e35	0.830959
$669$	6.44450e35	3.10001
$670$	0	0
$671$	−4.66957e33	−0.0216394
$672$	6.08463e33	0.0276770
$673$	2.27652e35	1.01644	0.508221	−	0.861227i	$-0.330303\pi$
$673$	2.27652e35	1.01644	0.508221	+	0.861227i	$0.330303\pi$
$674$	−3.56277e34	−0.156149
$675$	0	0
$676$	−1.10754e35	−0.467764
$677$	1.12736e35	0.467416	0.233708	−	0.972307i	$-0.424914\pi$
$677$	1.12736e35	0.467416	0.233708	+	0.972307i	$0.424914\pi$
$678$	3.77042e35	1.53468
$679$	−3.79942e34	−0.151826
$680$	0	0
$681$	−6.65994e34	−0.256526
$682$	1.52508e34	0.0576749
$683$	1.62407e35	0.603039	0.301520	−	0.953460i	$-0.402506\pi$
$683$	1.62407e35	0.603039	0.301520	+	0.953460i	$0.402506\pi$
$684$	1.53803e35	0.560742
$685$	0	0
$686$	−3.91287e34	−0.137545
$687$	−5.84973e35	−2.01919
$688$	−1.32389e35	−0.448741
$689$	−9.69114e34	−0.322578
$690$	0	0
$691$	−2.17749e35	−0.699006	−0.349503	−	0.936935i	$-0.613649\pi$
$691$	−2.17749e35	−0.699006	−0.349503	+	0.936935i	$0.613649\pi$
$692$	1.45376e34	0.0458316
$693$	−5.15741e33	−0.0159686
$694$	3.30235e35	1.00422
$695$	0	0
$696$	−6.16657e34	−0.180896
$697$	8.23625e35	2.37312
$698$	3.99747e35	1.13134
$699$	−3.72671e35	−1.03600
$700$	0	0
$701$	−1.31197e35	−0.351923	−0.175961	−	0.984397i	$-0.556303\pi$
$701$	−1.31197e35	−0.351923	−0.175961	+	0.984397i	$0.556303\pi$
$702$	6.18595e34	0.163002
$703$	−5.25979e35	−1.36153
$704$	5.12681e33	0.0130373
$705$	0	0
$706$	−5.56205e34	−0.136514
$707$	−2.72353e34	−0.0656733
$708$	3.45908e35	0.819493
$709$	1.07011e35	0.249088	0.124544	−	0.992214i	$-0.460253\pi$
$709$	1.07011e35	0.249088	0.124544	+	0.992214i	$0.460253\pi$
$710$	0	0
$711$	9.26759e35	2.08256
$712$	−1.92246e35	−0.424481
$713$	−5.35859e35	−1.16260
$714$	8.19876e34	0.174792
$715$	0	0
$716$	−3.40927e35	−0.701856
$717$	1.14396e36	2.31431
$718$	−5.05572e35	−1.00514
$719$	−7.33489e35	−1.43312	−0.716560	−	0.697526i	$-0.754284\pi$
$719$	−7.33489e35	−1.43312	−0.716560	+	0.697526i	$0.754284\pi$
$720$	0	0
$721$	−5.37759e34	−0.101484
$722$	1.85885e35	0.344771
$723$	−2.92729e34	−0.0533626
$724$	−1.02602e35	−0.183833
$725$	0	0
$726$	6.47334e35	1.12052
$727$	−1.00868e36	−1.71622	−0.858111	−	0.513465i	$-0.828362\pi$
$727$	−1.00868e36	−1.71622	−0.858111	+	0.513465i	$0.828362\pi$
$728$	−5.24553e33	−0.00877298
$729$	−9.91632e35	−1.63026
$730$	0	0
$731$	−1.78388e36	−2.83399
$732$	−1.06417e35	−0.166197
$733$	1.19811e36	1.83948	0.919741	−	0.392525i	$-0.128398\pi$
$733$	1.19811e36	1.83948	0.919741	+	0.392525i	$0.128398\pi$
$734$	7.95292e34	0.120040
$735$	0	0
$736$	−1.80138e35	−0.262805
$737$	−3.30741e34	−0.0474400
$738$	−1.18072e36	−1.66511
$739$	−7.47298e35	−1.03619	−0.518094	−	0.855324i	$-0.673358\pi$
$739$	−7.47298e35	−1.03619	−0.518094	+	0.855324i	$0.673358\pi$
$740$	0	0
$741$	−2.17226e35	−0.291195
$742$	6.66026e34	0.0877895
$743$	1.09617e36	1.42075	0.710376	−	0.703822i	$-0.248525\pi$
$743$	1.09617e36	1.42075	0.710376	+	0.703822i	$0.248525\pi$
$744$	3.47557e35	0.442960
$745$	0	0
$746$	7.19590e35	0.886850
$747$	−1.56782e36	−1.90015
$748$	6.90814e34	0.0823362
$749$	1.08673e34	0.0127379
$750$	0	0
$751$	−4.75595e34	−0.0539186	−0.0269593	−	0.999637i	$-0.508582\pi$
$751$	−4.75595e34	−0.0539186	−0.0269593	+	0.999637i	$0.508582\pi$
$752$	1.83857e35	0.205001
$753$	−1.34198e36	−1.47166
$754$	5.31617e34	0.0573399
$755$	0	0
$756$	−4.25131e34	−0.0443609
$757$	−1.35534e36	−1.39107	−0.695537	−	0.718490i	$-0.744834\pi$
$757$	−1.35534e36	−1.39107	−0.695537	+	0.718490i	$0.744834\pi$
$758$	−8.56475e35	−0.864669
$759$	2.50147e35	0.248412
$760$	0	0
$761$	−4.04146e35	−0.388356	−0.194178	−	0.980966i	$-0.562204\pi$
$761$	−4.04146e35	−0.388356	−0.194178	+	0.980966i	$0.562204\pi$
$762$	−1.01136e36	−0.956028
$763$	1.13419e35	0.105470
$764$	2.09779e35	0.191909
$765$	0	0
$766$	−6.06132e35	−0.536670
$767$	−2.98206e35	−0.259761
$768$	1.16837e35	0.100130
$769$	−1.59517e36	−1.34502	−0.672509	−	0.740089i	$-0.734783\pi$
$769$	−1.59517e36	−1.34502	−0.672509	+	0.740089i	$0.734783\pi$
$770$	0	0
$771$	1.67023e36	1.36331
$772$	6.71234e35	0.539086
$773$	5.09562e35	0.402674	0.201337	−	0.979522i	$-0.435471\pi$
$773$	5.09562e35	0.402674	0.201337	+	0.979522i	$0.435471\pi$
$774$	2.55730e36	1.98848
$775$	0	0
$776$	−7.29566e35	−0.549279
$777$	4.01947e35	0.297787
$778$	−9.00052e35	−0.656180
$779$	1.49972e36	1.07595
$780$	0	0
$781$	−4.43642e34	−0.0308244
$782$	−2.42728e36	−1.65972
$783$	4.30856e35	0.289941
$784$	−3.73872e35	−0.247612
$785$	0	0
$786$	1.14801e36	0.736484
$787$	−1.58597e36	−1.00141	−0.500703	−	0.865619i	$-0.666925\pi$
$787$	−1.58597e36	−1.00141	−0.500703	+	0.865619i	$0.666925\pi$
$788$	−2.01248e35	−0.125070
$789$	1.15605e36	0.707154
$790$	0	0
$791$	2.23389e35	0.132390
$792$	−9.90327e34	−0.0577715
$793$	9.17416e34	0.0526807
$794$	−8.00614e35	−0.452550
$795$	0	0
$796$	5.60980e35	0.307280
$797$	1.54676e36	0.834053	0.417027	−	0.908894i	$-0.363072\pi$
$797$	1.54676e36	0.834053	0.417027	+	0.908894i	$0.363072\pi$
$798$	1.49289e35	0.0792486
$799$	2.47738e36	1.29467
$800$	0	0
$801$	3.71355e36	1.88098
$802$	1.92994e36	0.962420
$803$	1.23831e35	0.0607976
$804$	−7.53742e35	−0.364353
$805$	0	0
$806$	−2.99627e35	−0.140408
$807$	3.26736e36	1.50757
$808$	−5.22972e35	−0.237594
$809$	6.21020e35	0.277811	0.138905	−	0.990306i	$-0.455642\pi$
$809$	6.21020e35	0.277811	0.138905	+	0.990306i	$0.455642\pi$
$810$	0	0
$811$	4.69897e35	0.203818	0.101909	−	0.994794i	$-0.467505\pi$
$811$	4.69897e35	0.203818	0.101909	+	0.994794i	$0.467505\pi$
$812$	−3.65355e34	−0.0156050
$813$	−4.93874e35	−0.207723
$814$	3.38674e35	0.140274
$815$	0	0
$816$	1.57433e36	0.632365
$817$	−3.24821e36	−1.28490
$818$	1.77293e36	0.690679
$819$	1.01326e35	0.0388752
$820$	0	0
$821$	−3.77384e36	−1.40441	−0.702205	−	0.711975i	$-0.747801\pi$
$821$	−3.77384e36	−1.40441	−0.702205	+	0.711975i	$0.747801\pi$
$822$	−2.12449e36	−0.778677
$823$	−1.31964e36	−0.476385	−0.238192	−	0.971218i	$-0.576555\pi$
$823$	−1.31964e36	−0.476385	−0.238192	+	0.971218i	$0.576555\pi$
$824$	−1.03260e36	−0.367150
$825$	0	0
$826$	2.04943e35	0.0706939
$827$	−2.35273e36	−0.799380	−0.399690	−	0.916650i	$-0.630882\pi$
$827$	−2.35273e36	−0.799380	−0.399690	+	0.916650i	$0.630882\pi$
$828$	3.47966e36	1.16455
$829$	−1.44960e36	−0.477878	−0.238939	−	0.971035i	$-0.576800\pi$
$829$	−1.44960e36	−0.477878	−0.238939	+	0.971035i	$0.576800\pi$
$830$	0	0
$831$	5.57877e36	1.78454
$832$	−1.00725e35	−0.0317391
$833$	−5.03776e36	−1.56378
$834$	−2.36663e36	−0.723692
$835$	0	0
$836$	1.25788e35	0.0373304
$837$	−2.42837e36	−0.709980
$838$	−3.93977e35	−0.113480
$839$	−6.60849e35	−0.187533	−0.0937665	−	0.995594i	$-0.529891\pi$
$839$	−6.60849e35	−0.187533	−0.0937665	+	0.995594i	$0.529891\pi$
$840$	0	0
$841$	−3.26009e36	−0.898006
$842$	−6.54019e34	−0.0177496
$843$	−3.03856e36	−0.812500
$844$	1.16142e36	0.305990
$845$	0	0
$846$	−3.55149e36	−0.908408
$847$	3.83530e35	0.0966623
$848$	1.27890e36	0.317607
$849$	2.07541e36	0.507877
$850$	0	0
$851$	−1.18998e37	−2.82762
$852$	−1.01104e36	−0.236740
$853$	−5.07169e35	−0.117028	−0.0585140	−	0.998287i	$-0.518636\pi$
$853$	−5.07169e35	−0.117028	−0.0585140	+	0.998287i	$0.518636\pi$
$854$	−6.30496e34	−0.0143370
$855$	0	0
$856$	2.08674e35	0.0460836
$857$	2.45792e36	0.534943	0.267471	−	0.963566i	$-0.413812\pi$
$857$	2.45792e36	0.534943	0.267471	+	0.963566i	$0.413812\pi$
$858$	1.39870e35	0.0300009
$859$	−7.15238e36	−1.51194	−0.755972	−	0.654603i	$-0.772836\pi$
$859$	−7.15238e36	−1.51194	−0.755972	+	0.654603i	$0.772836\pi$
$860$	0	0
$861$	−1.14607e36	−0.235327
$862$	2.91569e36	0.590066
$863$	−2.16205e36	−0.431252	−0.215626	−	0.976476i	$-0.569179\pi$
$863$	−2.16205e36	−0.431252	−0.215626	+	0.976476i	$0.569179\pi$
$864$	−8.16337e35	−0.160490
$865$	0	0
$866$	−3.97211e36	−0.758660
$867$	1.27034e37	2.39157
$868$	2.05919e35	0.0382121
$869$	7.57953e35	0.138642
$870$	0	0
$871$	6.49797e35	0.115492
$872$	2.17787e36	0.381572
$873$	1.40928e37	2.43399
$874$	−4.41977e36	−0.752500
$875$	0	0
$876$	2.82205e36	0.466943
$877$	−6.84625e36	−1.11676	−0.558378	−	0.829587i	$-0.688576\pi$
$877$	−6.84625e36	−1.11676	−0.558378	+	0.829587i	$0.688576\pi$
$878$	2.82365e36	0.454077
$879$	4.63526e36	0.734874
$880$	0	0
$881$	2.59663e36	0.400139	0.200069	−	0.979782i	$-0.435883\pi$
$881$	2.59663e36	0.400139	0.200069	+	0.979782i	$0.435883\pi$
$882$	7.22196e36	1.09723
$883$	−1.13962e36	−0.170707	−0.0853533	−	0.996351i	$-0.527202\pi$
$883$	−1.13962e36	−0.170707	−0.0853533	+	0.996351i	$0.527202\pi$
$884$	−1.35722e36	−0.200446
$885$	0	0
$886$	−6.03924e36	−0.867083
$887$	2.38557e36	0.337713	0.168856	−	0.985641i	$-0.445993\pi$
$887$	2.38557e36	0.337713	0.168856	+	0.985641i	$0.445993\pi$
$888$	7.71820e36	1.07734
$889$	−5.99211e35	−0.0824722
$890$	0	0
$891$	−8.74434e34	−0.0117019
$892$	7.33175e36	0.967490
$893$	4.51100e36	0.586988
$894$	−1.09117e37	−1.40015
$895$	0	0
$896$	6.92234e34	0.00863779
$897$	−4.91456e36	−0.604754
$898$	−9.97593e36	−1.21060
$899$	−2.08693e36	−0.249753
$900$	0	0
$901$	1.72327e37	2.00582
$902$	−9.65657e35	−0.110851
$903$	2.48225e36	0.281027
$904$	4.28951e36	0.478964
$905$	0	0
$906$	1.01729e36	0.110495
$907$	1.67063e37	1.78974	0.894870	−	0.446326i	$-0.147268\pi$
$907$	1.67063e37	1.78974	0.894870	+	0.446326i	$0.147268\pi$
$908$	−7.57685e35	−0.0800600
$909$	1.01021e37	1.05284
$910$	0	0
$911$	1.13215e37	1.14795	0.573976	−	0.818872i	$-0.305400\pi$
$911$	1.13215e37	1.14795	0.573976	+	0.818872i	$0.305400\pi$
$912$	2.86665e36	0.286708
$913$	−1.28225e36	−0.126499
$914$	−7.20082e36	−0.700736
$915$	0	0
$916$	−6.65510e36	−0.630175
$917$	6.80169e35	0.0635331
$918$	−1.09998e37	−1.01356
$919$	1.76508e37	1.60443	0.802215	−	0.597035i	$-0.203655\pi$
$919$	1.76508e37	1.60443	0.802215	+	0.597035i	$0.203655\pi$
$920$	0	0
$921$	9.81953e35	0.0868651
$922$	−8.31325e36	−0.725495
$923$	8.71609e35	0.0750413
$924$	−9.61262e34	−0.00816473
$925$	0	0
$926$	2.30624e36	0.190663
$927$	1.99465e37	1.62693
$928$	−7.01556e35	−0.0564563
$929$	2.88984e36	0.229445	0.114722	−	0.993398i	$-0.463402\pi$
$929$	2.88984e36	0.229445	0.114722	+	0.993398i	$0.463402\pi$
$930$	0	0
$931$	−9.17311e36	−0.708999
$932$	−4.23978e36	−0.323329
$933$	−1.91942e37	−1.44428
$934$	1.37300e37	1.01938
$935$	0	0
$936$	1.94566e36	0.140644
$937$	−1.29200e37	−0.921545	−0.460772	−	0.887518i	$-0.652428\pi$
$937$	−1.29200e37	−0.921545	−0.460772	+	0.887518i	$0.652428\pi$
$938$	−4.46575e35	−0.0314310
$939$	2.19493e37	1.52441
$940$	0	0
$941$	2.06414e37	1.39595	0.697973	−	0.716124i	$-0.254086\pi$
$941$	2.06414e37	1.39595	0.697973	+	0.716124i	$0.254086\pi$
$942$	−9.48005e36	−0.632666
$943$	3.39299e37	2.23453
$944$	3.93532e36	0.255758
$945$	0	0
$946$	2.09150e36	0.132379
$947$	−2.09426e36	−0.130815	−0.0654073	−	0.997859i	$-0.520835\pi$
$947$	−2.09426e36	−0.130815	−0.0654073	+	0.997859i	$0.520835\pi$
$948$	1.72734e37	1.06481
$949$	−2.43288e36	−0.148010
$950$	0	0
$951$	−6.83316e36	−0.404916
$952$	9.32753e35	0.0545513
$953$	1.70726e37	0.985461	0.492731	−	0.870182i	$-0.335999\pi$
$953$	1.70726e37	0.985461	0.492731	+	0.870182i	$0.335999\pi$
$954$	−2.47041e37	−1.40739
$955$	0	0
$956$	1.30146e37	0.722281
$957$	9.74207e35	0.0533644
$958$	−1.34386e37	−0.726581
$959$	−1.25871e36	−0.0671729
$960$	0	0
$961$	−7.47058e36	−0.388429
$962$	−6.65382e36	−0.341494
$963$	−4.03088e36	−0.204207
$964$	−3.33031e35	−0.0166541
$965$	0	0
$966$	3.37754e36	0.164584
$967$	1.41585e37	0.681063	0.340532	−	0.940233i	$-0.389393\pi$
$967$	1.41585e37	0.681063	0.340532	+	0.940233i	$0.389393\pi$
$968$	7.36456e36	0.349707
$969$	3.86268e37	1.81068
$970$	0	0
$971$	−1.45645e37	−0.665357	−0.332678	−	0.943040i	$-0.607952\pi$
$971$	−1.45645e37	−0.665357	−0.332678	+	0.943040i	$0.607952\pi$
$972$	−1.20580e37	−0.543808
$973$	−1.40217e36	−0.0624296
$974$	−1.16153e37	−0.510554
$975$	0	0
$976$	−1.21068e36	−0.0518688
$977$	−2.61043e36	−0.110415	−0.0552077	−	0.998475i	$-0.517582\pi$
$977$	−2.61043e36	−0.110415	−0.0552077	+	0.998475i	$0.517582\pi$
$978$	−3.23343e37	−1.35029
$979$	3.03714e36	0.125222
$980$	0	0
$981$	−4.20692e37	−1.69084
$982$	2.53241e37	1.00494
$983$	−4.36771e37	−1.71133	−0.855667	−	0.517527i	$-0.826853\pi$
$983$	−4.36771e37	−1.71133	−0.855667	+	0.517527i	$0.826853\pi$
$984$	−2.20068e37	−0.851370
$985$	0	0
$986$	−9.45314e36	−0.356545
$987$	−3.44726e36	−0.128384
$988$	−2.47133e36	−0.0908800
$989$	−7.34881e37	−2.66848
$990$	0	0
$991$	5.30135e37	1.87701	0.938503	−	0.345271i	$-0.112213\pi$
$991$	5.30135e37	1.87701	0.938503	+	0.345271i	$0.112213\pi$
$992$	3.95407e36	0.138245
$993$	−2.41859e37	−0.835019
$994$	−5.99015e35	−0.0204225
$995$	0	0
$996$	−2.92218e37	−0.971549
$997$	−4.76523e37	−1.56457	−0.782284	−	0.622921i	$-0.785946\pi$
$997$	−4.76523e37	−1.56457	−0.782284	+	0.622921i	$0.785946\pi$
$998$	1.12038e37	0.363275
$999$	−5.39268e37	−1.72678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.k.1.6		6
5.2	odd	4		10.26.b.a.9.1	✓	12
5.3	odd	4		10.26.b.a.9.12	yes	12
5.4	even	2		50.26.a.l.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.1	✓	12	5.2	odd	4
10.26.b.a.9.12	yes	12	5.3	odd	4
50.26.a.k.1.6		6	1.1	even	1	trivial
50.26.a.l.1.1		6	5.4	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} +1.47469e6 q^{3} +1.67772e7 q^{4} -6.04034e9 q^{6} -3.57876e9 q^{7} -6.87195e10 q^{8} +1.32743e12 q^{9} +1.08564e12 q^{11} +2.47412e13 q^{12} -2.13293e13 q^{13} +1.46586e13 q^{14} +2.81475e14 q^{16} +3.79275e15 q^{17} -5.43715e15 q^{18} +6.90611e15 q^{19} -5.27758e15 q^{21} -4.44680e15 q^{22} +1.56245e17 q^{23} -1.01340e17 q^{24} +8.73648e16 q^{26} +7.08060e17 q^{27} -6.00417e16 q^{28} +6.08503e17 q^{29} -3.42961e18 q^{31} -1.15292e18 q^{32} +1.60099e18 q^{33} -1.55351e19 q^{34} +2.22706e19 q^{36} -7.61614e19 q^{37} -2.82874e19 q^{38} -3.14542e19 q^{39} +2.17158e20 q^{41} +2.16169e19 q^{42} -4.70339e20 q^{43} +1.82141e19 q^{44} -6.39979e20 q^{46} +6.53190e20 q^{47} +4.15089e20 q^{48} -1.32826e21 q^{49} +5.59313e21 q^{51} -3.57846e20 q^{52} +4.54358e21 q^{53} -2.90021e21 q^{54} +2.45931e20 q^{56} +1.01844e22 q^{57} -2.49243e21 q^{58} +1.39811e22 q^{59} -4.30120e21 q^{61} +1.40477e22 q^{62} -4.75056e21 q^{63} +4.72237e21 q^{64} -6.55766e21 q^{66} -3.04650e22 q^{67} +6.36317e22 q^{68} +2.30413e23 q^{69} -4.08644e22 q^{71} -9.12202e22 q^{72} +1.14063e23 q^{73} +3.11957e23 q^{74} +1.15865e23 q^{76} -3.88526e21 q^{77} +1.28836e23 q^{78} +6.98160e23 q^{79} -8.05452e22 q^{81} -8.89479e23 q^{82} -1.18110e24 q^{83} -8.85430e22 q^{84} +1.92651e24 q^{86} +8.97354e23 q^{87} -7.46049e22 q^{88} +2.79755e24 q^{89} +7.63325e22 q^{91} +2.62136e24 q^{92} -5.05762e24 q^{93} -2.67546e24 q^{94} -1.70020e24 q^{96} +1.06166e25 q^{97} +5.44056e24 q^{98} +1.44112e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24576 q^{2} + 801416 q^{3} + 100663296 q^{4} - 3282599936 q^{6} + 34007705352 q^{7} - 412316860416 q^{8} + 541468782118 q^{9} + 9861544614312 q^{11} + 13445529337856 q^{12} + 30787386783696 q^{13}+ \cdots - 20\!\cdots\!64 q^{99}+O(q^{100}) \) 6 * q - 24576 * q^2 + 801416 * q^3 + 100663296 * q^4 - 3282599936 * q^6 + 34007705352 * q^7 - 412316860416 * q^8 + 541468782118 * q^9 + 9861544614312 * q^11 + 13445529337856 * q^12 + 30787386783696 * q^13 - 139295561121792 * q^14 + 1688849860263936 * q^16 + 3432836939805312 * q^17 - 2217856131555328 * q^18 + 2007656488916520 * q^19 - 28181710291014728 * q^21 - 40392886740221952 * q^22 + 135711886432707576 * q^23 - 55072888167858176 * q^24 - 126105136266018816 * q^26 + 788054364552235760 * q^27 + 570554618354860032 * q^28 - 2926032031655504820 * q^29 + 79292935777014912 * q^31 - 6917529027641081856 * q^32 - 6844843638395003168 * q^33 - 14060900105442557952 * q^34 + 9084338714850623488 * q^36 + 3345885298190974032 * q^37 - 8223360978602065920 * q^38 + 124726636622561793456 * q^39 + 103229301719876244012 * q^41 + 115432285351996325888 * q^42 + 166390524239317503336 * q^43 + 165449264087949115392 * q^44 - 555875886828370231296 * q^46 + 405906243391034677992 * q^47 + 225578549935547088896 * q^48 + 1716280748139027694542 * q^49 - 1516225893661962013568 * q^51 + 516526638145613070336 * q^52 + 9772760301640799789616 * q^53 - 3227870677205957672960 * q^54 - 2336991716781506691072 * q^56 + 26174725126915157341920 * q^57 + 11985027201660947742720 * q^58 - 12499075130880780168840 * q^59 + 3687285610311118296612 * q^61 - 324783864942653079552 * q^62 + 93007818034972665339656 * q^63 + 28334198897217871282176 * q^64 + 28036479542865932976128 * q^66 + 16759935062266648886712 * q^67 + 57593446831892717371392 * q^68 + 185125325982378999854536 * q^69 + 74568876221253661649712 * q^71 - 37209451376028153806848 * q^72 + 381797761857106829638176 * q^73 - 13704746181390229635072 * q^74 + 33682886568354062008320 * q^76 - 80271541631956375339296 * q^77 - 510880303606013105995776 * q^78 - 400850316873811624799520 * q^79 - 1432110118616113828343714 * q^81 - 422827219844613095473152 * q^82 - 2423159733509985740001144 * q^83 - 472810640801776950837248 * q^84 - 681535587284244493664256 * q^86 - 1231328665433636473947120 * q^87 - 677680185704239576645632 * q^88 + 2982172528060341024616740 * q^89 - 7001711719121019241314768 * q^91 + 2276867632449004467388416 * q^92 - 8806417055581711481018368 * q^93 - 1662591972929678041055232 * q^94 - 923969740536000876118016 * q^96 - 4960469410756873985567808 * q^97 - 7029885944377457436844032 * q^98 - 2053720289282411723573464 * q^99

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