LMFDB - Embedded newform 50.12.a.i.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [50,12,Mod(1,50)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(50, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 12, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("50.1"); S:= CuspForms(chi, 12); N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	50.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-96,-266] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$38.4171590280$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3779x - 3381 $ x^3 - x^2 - 3779*x - 3381
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 5^{3} $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$62.4146$ 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)

$f(q)$	$=$	\(q-32.0000 q^{2} +532.146 q^{3} +1024.00 q^{4} -17028.7 q^{6} +24477.0 q^{7} -32768.0 q^{8} +106033. q^{9} -669055. q^{11} +544918. q^{12} -579245. q^{13} -783265. q^{14} +1.04858e6 q^{16} -7.85051e6 q^{17} -3.39304e6 q^{18} -1.81223e7 q^{19} +1.30254e7 q^{21} +2.14098e7 q^{22} +1.97203e7 q^{23} -1.74374e7 q^{24} +1.85358e7 q^{26} -3.78433e7 q^{27} +2.50645e7 q^{28} +2.02707e8 q^{29} +1.02789e8 q^{31} -3.35544e7 q^{32} -3.56035e8 q^{33} +2.51216e8 q^{34} +1.08577e8 q^{36} -5.02591e8 q^{37} +5.79913e8 q^{38} -3.08243e8 q^{39} +3.44964e8 q^{41} -4.16811e8 q^{42} -1.43221e9 q^{43} -6.85112e8 q^{44} -6.31051e8 q^{46} -1.38179e9 q^{47} +5.57996e8 q^{48} -1.37820e9 q^{49} -4.17762e9 q^{51} -5.93147e8 q^{52} +2.89531e8 q^{53} +1.21098e9 q^{54} -8.02063e8 q^{56} -9.64371e9 q^{57} -6.48664e9 q^{58} -2.47487e9 q^{59} +9.16284e7 q^{61} -3.28926e9 q^{62} +2.59536e9 q^{63} +1.07374e9 q^{64} +1.13931e10 q^{66} +3.09287e7 q^{67} -8.03893e9 q^{68} +1.04941e10 q^{69} +2.42503e10 q^{71} -3.47448e9 q^{72} +3.55008e9 q^{73} +1.60829e10 q^{74} -1.85572e10 q^{76} -1.63765e10 q^{77} +9.86377e9 q^{78} -1.16350e10 q^{79} -3.89215e10 q^{81} -1.10389e10 q^{82} -2.33729e10 q^{83} +1.33380e10 q^{84} +4.58307e10 q^{86} +1.07870e11 q^{87} +2.19236e10 q^{88} -1.02379e11 q^{89} -1.41782e10 q^{91} +2.01936e10 q^{92} +5.46989e10 q^{93} +4.42174e10 q^{94} -1.78559e10 q^{96} -5.87705e10 q^{97} +4.41025e10 q^{98} -7.09416e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 96 q^{2} - 266 q^{3} + 3072 q^{4} + 8512 q^{6} - 33218 q^{7} - 98304 q^{8} + 248011 q^{9} - 321364 q^{11} - 272384 q^{12} - 1394556 q^{13} + 1062976 q^{14} + 3145728 q^{16} - 3520128 q^{17} - 7936352 q^{18}+ \cdots - 260390562868 q^{99}+O(q^{100}) $ 3 * q - 96 * q^2 - 266 * q^3 + 3072 * q^4 + 8512 * q^6 - 33218 * q^7 - 98304 * q^8 + 248011 * q^9 - 321364 * q^11 - 272384 * q^12 - 1394556 * q^13 + 1062976 * q^14 + 3145728 * q^16 - 3520128 * q^17 - 7936352 * q^18 + 12054540 * q^19 + 62735596 * q^21 + 10283648 * q^22 + 46190754 * q^23 + 8716288 * q^24 + 44625792 * q^26 - 94987340 * q^27 - 34015232 * q^28 + 128204910 * q^29 + 229240896 * q^31 - 100663296 * q^32 - 226503592 * q^33 + 112644096 * q^34 + 253963264 * q^36 - 1002113948 * q^37 - 385745280 * q^38 - 659398968 * q^39 - 82384474 * q^41 - 2007539072 * q^42 - 1749934226 * q^43 - 329076736 * q^44 - 1478104128 * q^46 - 5277335658 * q^47 - 278921216 * q^48 + 337757079 * q^49 - 6530043584 * q^51 - 1428025344 * q^52 - 315194916 * q^53 + 3039594880 * q^54 + 1088487424 * q^56 - 21984280680 * q^57 - 4102557120 * q^58 - 8831981180 * q^59 - 2510396214 * q^61 - 7335708672 * q^62 - 22799454866 * q^63 + 3221225472 * q^64 + 7248114944 * q^66 - 31643371078 * q^67 - 3604611072 * q^68 - 11558506988 * q^69 + 28394209416 * q^71 - 8126824448 * q^72 + 1461795304 * q^73 + 32067646336 * q^74 + 12343848960 * q^76 + 13870520184 * q^77 + 21100766976 * q^78 - 1301275440 * q^79 - 3519953537 * q^81 + 2636303168 * q^82 + 13756798614 * q^83 + 64241250304 * q^84 + 55997895232 * q^86 + 142402696380 * q^87 + 10530455552 * q^88 - 124724206270 * q^89 - 92223383064 * q^91 + 47299332096 * q^92 + 105480959488 * q^93 + 168874741056 * q^94 + 8925478912 * q^96 + 123108208592 * q^97 - 10808226528 * q^98 - 260390562868 * 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 $

$2$	−32.0000	−0.707107
$2$	−32.0000	−0.707107
$3$	532.146	1.26434	0.632170	−	0.774830i	$-0.282164\pi$
$3$	532.146	1.26434	0.632170	+	0.774830i	$0.282164\pi$
$4$	1024.00	0.500000
$5$	0	0
$5$	0	0
$6$	−17028.7	−0.894024
$7$	24477.0	0.550452	0.275226	−	0.961380i	$-0.411247\pi$
$7$	24477.0	0.550452	0.275226	+	0.961380i	$0.411247\pi$
$8$	−32768.0	−0.353553
$9$	106033.	0.598557
$10$	0	0
$11$	−669055.	−1.25257	−0.626285	−	0.779594i	$-0.715425\pi$
$11$	−669055.	−1.25257	−0.626285	+	0.779594i	$0.715425\pi$
$12$	544918.	0.632170
$13$	−579245.	−0.432687	−0.216343	−	0.976317i	$-0.569413\pi$
$13$	−579245.	−0.432687	−0.216343	+	0.976317i	$0.569413\pi$
$14$	−783265.	−0.389228
$15$	0	0
$16$	1.04858e6	0.250000
$17$	−7.85051e6	−1.34100	−0.670500	−	0.741909i	$-0.733920\pi$
$17$	−7.85051e6	−1.34100	−0.670500	+	0.741909i	$0.733920\pi$
$18$	−3.39304e6	−0.423244
$19$	−1.81223e7	−1.67907	−0.839534	−	0.543307i	$-0.817172\pi$
$19$	−1.81223e7	−1.67907	−0.839534	+	0.543307i	$0.817172\pi$
$20$	0	0
$21$	1.30254e7	0.695959
$22$	2.14098e7	0.885701
$23$	1.97203e7	0.638868	0.319434	−	0.947609i	$-0.396507\pi$
$23$	1.97203e7	0.638868	0.319434	+	0.947609i	$0.396507\pi$
$24$	−1.74374e7	−0.447012
$25$	0	0
$26$	1.85358e7	0.305956
$27$	−3.78433e7	−0.507561
$28$	2.50645e7	0.275226
$29$	2.02707e8	1.83519	0.917594	−	0.397518i	$-0.130128\pi$
$29$	2.02707e8	1.83519	0.917594	+	0.397518i	$0.130128\pi$
$30$	0	0
$31$	1.02789e8	0.644850	0.322425	−	0.946595i	$-0.395502\pi$
$31$	1.02789e8	0.644850	0.322425	+	0.946595i	$0.395502\pi$
$32$	−3.35544e7	−0.176777
$33$	−3.56035e8	−1.58368
$34$	2.51216e8	0.948231
$35$	0	0
$36$	1.08577e8	0.299278
$37$	−5.02591e8	−1.19153	−0.595766	−	0.803158i	$-0.703151\pi$
$37$	−5.02591e8	−1.19153	−0.595766	+	0.803158i	$0.703151\pi$
$38$	5.79913e8	1.18728
$39$	−3.08243e8	−0.547063
$40$	0	0
$41$	3.44964e8	0.465011	0.232505	−	0.972595i	$-0.425308\pi$
$41$	3.44964e8	0.465011	0.232505	+	0.972595i	$0.425308\pi$
$42$	−4.16811e8	−0.492117
$43$	−1.43221e9	−1.48570	−0.742848	−	0.669460i	$-0.766526\pi$
$43$	−1.43221e9	−1.48570	−0.742848	+	0.669460i	$0.766526\pi$
$44$	−6.85112e8	−0.626285
$45$	0	0
$46$	−6.31051e8	−0.451748
$47$	−1.38179e9	−0.878830	−0.439415	−	0.898284i	$-0.644814\pi$
$47$	−1.38179e9	−0.878830	−0.439415	+	0.898284i	$0.644814\pi$
$48$	5.57996e8	0.316085
$49$	−1.37820e9	−0.697003
$50$	0	0
$51$	−4.17762e9	−1.69548
$52$	−5.93147e8	−0.216343
$53$	2.89531e8	0.0950995	0.0475497	−	0.998869i	$-0.484859\pi$
$53$	2.89531e8	0.0950995	0.0475497	+	0.998869i	$0.484859\pi$
$54$	1.21098e9	0.358900
$55$	0	0
$56$	−8.02063e8	−0.194614
$57$	−9.64371e9	−2.12291
$58$	−6.48664e9	−1.29767
$59$	−2.47487e9	−0.450678	−0.225339	−	0.974280i	$-0.572349\pi$
$59$	−2.47487e9	−0.450678	−0.225339	+	0.974280i	$0.572349\pi$
$60$	0	0
$61$	9.16284e7	0.0138904	0.00694522	−	0.999976i	$-0.497789\pi$
$61$	9.16284e7	0.0138904	0.00694522	+	0.999976i	$0.497789\pi$
$62$	−3.28926e9	−0.455977
$63$	2.59536e9	0.329477
$64$	1.07374e9	0.125000
$65$	0	0
$66$	1.13931e10	1.11983
$67$	3.09287e7	0.00279866	0.00139933	−	0.999999i	$-0.499555\pi$
$67$	3.09287e7	0.00279866	0.00139933	+	0.999999i	$0.499555\pi$
$68$	−8.03893e9	−0.670500
$69$	1.04941e10	0.807747
$70$	0	0
$71$	2.42503e10	1.59513	0.797565	−	0.603233i	$-0.206121\pi$
$71$	2.42503e10	1.59513	0.797565	+	0.603233i	$0.206121\pi$
$72$	−3.47448e9	−0.211622
$73$	3.55008e9	0.200430	0.100215	−	0.994966i	$-0.468047\pi$
$73$	3.55008e9	0.200430	0.100215	+	0.994966i	$0.468047\pi$
$74$	1.60829e10	0.842540
$75$	0	0
$76$	−1.85572e10	−0.839534
$77$	−1.63765e10	−0.689480
$78$	9.86377e9	0.386832
$79$	−1.16350e10	−0.425419	−0.212709	−	0.977116i	$-0.568229\pi$
$79$	−1.16350e10	−0.425419	−0.212709	+	0.977116i	$0.568229\pi$
$80$	0	0
$81$	−3.89215e10	−1.24029
$82$	−1.10389e10	−0.328812
$83$	−2.33729e10	−0.651302	−0.325651	−	0.945490i	$-0.605583\pi$
$83$	−2.33729e10	−0.651302	−0.325651	+	0.945490i	$0.605583\pi$
$84$	1.33380e10	0.347979
$85$	0	0
$86$	4.58307e10	1.05055
$87$	1.07870e11	2.32030
$88$	2.19236e10	0.442851
$89$	−1.02379e11	−1.94342	−0.971710	−	0.236175i	$-0.924106\pi$
$89$	−1.02379e11	−1.94342	−0.971710	+	0.236175i	$0.924106\pi$
$90$	0	0
$91$	−1.41782e10	−0.238173
$92$	2.01936e10	0.319434
$93$	5.46989e10	0.815309
$94$	4.42174e10	0.621426
$95$	0	0
$96$	−1.78559e10	−0.223506
$97$	−5.87705e10	−0.694888	−0.347444	−	0.937701i	$-0.612950\pi$
$97$	−5.87705e10	−0.694888	−0.347444	+	0.937701i	$0.612950\pi$
$98$	4.41025e10	0.492855
$99$	−7.09416e10	−0.749735
$100$	0	0
$101$	3.48576e9	0.0330012	0.0165006	−	0.999864i	$-0.494747\pi$
$101$	3.48576e9	0.0330012	0.0165006	+	0.999864i	$0.494747\pi$
$102$	1.33684e11	1.19889
$103$	−8.04437e10	−0.683734	−0.341867	−	0.939748i	$-0.611059\pi$
$103$	−8.04437e10	−0.683734	−0.341867	+	0.939748i	$0.611059\pi$
$104$	1.89807e10	0.152978
$105$	0	0
$106$	−9.26500e9	−0.0672455
$107$	1.62166e11	1.11776	0.558880	−	0.829249i	$-0.311231\pi$
$107$	1.62166e11	1.11776	0.558880	+	0.829249i	$0.311231\pi$
$108$	−3.87515e10	−0.253780
$109$	1.55539e11	0.968266	0.484133	−	0.874994i	$-0.339135\pi$
$109$	1.55539e11	0.968266	0.484133	+	0.874994i	$0.339135\pi$
$110$	0	0
$111$	−2.67452e11	−1.50650
$112$	2.56660e10	0.137613
$113$	1.26270e11	0.644717	0.322359	−	0.946618i	$-0.395524\pi$
$113$	1.26270e11	0.644717	0.322359	+	0.946618i	$0.395524\pi$
$114$	3.08599e11	1.50113
$115$	0	0
$116$	2.07572e11	0.917594
$117$	−6.14188e10	−0.258988
$118$	7.91958e10	0.318677
$119$	−1.92157e11	−0.738157
$120$	0	0
$121$	1.62323e11	0.568933
$122$	−2.93211e9	−0.00982202
$123$	1.83572e11	0.587932
$124$	1.05256e11	0.322425
$125$	0	0
$126$	−8.30516e10	−0.232975
$127$	4.06263e11	1.09116	0.545578	−	0.838060i	$-0.316310\pi$
$127$	4.06263e11	1.09116	0.545578	+	0.838060i	$0.316310\pi$
$128$	−3.43597e10	−0.0883883
$129$	−7.62145e11	−1.87843
$130$	0	0
$131$	4.67394e11	1.05850	0.529251	−	0.848466i	$-0.322473\pi$
$131$	4.67394e11	1.05850	0.529251	+	0.848466i	$0.322473\pi$
$132$	−3.64580e11	−0.791838
$133$	−4.43580e11	−0.924247
$134$	−9.89718e8	−0.00197895
$135$	0	0
$136$	2.57246e11	0.474115
$137$	−5.88796e11	−1.04232	−0.521161	−	0.853459i	$-0.674501\pi$
$137$	−5.88796e11	−1.04232	−0.521161	+	0.853459i	$0.674501\pi$
$138$	−3.35811e11	−0.571163
$139$	−2.38206e11	−0.389378	−0.194689	−	0.980865i	$-0.562370\pi$
$139$	−2.38206e11	−0.389378	−0.194689	+	0.980865i	$0.562370\pi$
$140$	0	0
$141$	−7.35316e11	−1.11114
$142$	−7.76010e11	−1.12793
$143$	3.87547e11	0.541971
$144$	1.11183e11	0.149639
$145$	0	0
$146$	−1.13603e11	−0.141725
$147$	−7.33405e11	−0.881249
$148$	−5.14653e11	−0.595766
$149$	1.19618e12	1.33436	0.667179	−	0.744897i	$-0.267501\pi$
$149$	1.19618e12	1.33436	0.667179	+	0.744897i	$0.267501\pi$
$150$	0	0
$151$	−4.69044e10	−0.0486229	−0.0243114	−	0.999704i	$-0.507739\pi$
$151$	−4.69044e10	−0.0486229	−0.0243114	+	0.999704i	$0.507739\pi$
$152$	5.93831e11	0.593640
$153$	−8.32410e11	−0.802665
$154$	5.24047e11	0.487536
$155$	0	0
$156$	−3.15641e11	−0.273532
$157$	−1.12550e12	−0.941665	−0.470833	−	0.882223i	$-0.656046\pi$
$157$	−1.12550e12	−0.941665	−0.470833	+	0.882223i	$0.656046\pi$
$158$	3.72319e11	0.300816
$159$	1.54073e11	0.120238
$160$	0	0
$161$	4.82695e11	0.351666
$162$	1.24549e12	0.877015
$163$	1.26983e12	0.864396	0.432198	−	0.901779i	$-0.357738\pi$
$163$	1.26983e12	0.864396	0.432198	+	0.901779i	$0.357738\pi$
$164$	3.53244e11	0.232505
$165$	0	0
$166$	7.47932e11	0.460540
$167$	−6.55303e11	−0.390393	−0.195196	−	0.980764i	$-0.562534\pi$
$167$	−6.55303e11	−0.390393	−0.195196	+	0.980764i	$0.562534\pi$
$168$	−4.26815e11	−0.246059
$169$	−1.45664e12	−0.812782
$170$	0	0
$171$	−1.92155e12	−1.00502
$172$	−1.46658e12	−0.742848
$173$	−2.29440e12	−1.12568	−0.562842	−	0.826565i	$-0.690292\pi$
$173$	−2.29440e12	−1.12568	−0.562842	+	0.826565i	$0.690292\pi$
$174$	−3.45184e12	−1.64070
$175$	0	0
$176$	−7.01555e11	−0.313143
$177$	−1.31699e12	−0.569810
$178$	3.27614e12	1.37421
$179$	2.90384e12	1.18108	0.590542	−	0.807007i	$-0.298914\pi$
$179$	2.90384e12	1.18108	0.590542	+	0.807007i	$0.298914\pi$
$180$	0	0
$181$	2.57501e12	0.985250	0.492625	−	0.870242i	$-0.336037\pi$
$181$	2.57501e12	0.985250	0.492625	+	0.870242i	$0.336037\pi$
$182$	4.53702e11	0.168414
$183$	4.87597e10	0.0175622
$184$	−6.46196e11	−0.225874
$185$	0	0
$186$	−1.75037e12	−0.576511
$187$	5.25243e12	1.67970
$188$	−1.41496e12	−0.439415
$189$	−9.26291e11	−0.279388
$190$	0	0
$191$	2.23479e11	0.0636140	0.0318070	−	0.999494i	$-0.489874\pi$
$191$	2.23479e11	0.0636140	0.0318070	+	0.999494i	$0.489874\pi$
$192$	5.71388e11	0.158043
$193$	−3.24295e12	−0.871716	−0.435858	−	0.900015i	$-0.643555\pi$
$193$	−3.24295e12	−0.871716	−0.435858	+	0.900015i	$0.643555\pi$
$194$	1.88066e12	0.491360
$195$	0	0
$196$	−1.41128e12	−0.348501
$197$	5.15178e12	1.23707	0.618534	−	0.785758i	$-0.287727\pi$
$197$	5.15178e12	1.23707	0.618534	+	0.785758i	$0.287727\pi$
$198$	2.27013e12	0.530143
$199$	−6.92866e11	−0.157383	−0.0786914	−	0.996899i	$-0.525074\pi$
$199$	−6.92866e11	−0.157383	−0.0786914	+	0.996899i	$0.525074\pi$
$200$	0	0
$201$	1.64586e10	0.00353846
$202$	−1.11544e11	−0.0233354
$203$	4.96168e12	1.01018
$204$	−4.27788e12	−0.847741
$205$	0	0
$206$	2.57420e12	0.483473
$207$	2.09100e12	0.382399
$208$	−6.07382e11	−0.108172
$209$	1.21248e13	2.10315
$210$	0	0
$211$	7.15534e12	1.17781	0.588907	−	0.808201i	$-0.299558\pi$
$211$	7.15534e12	1.17781	0.588907	+	0.808201i	$0.299558\pi$
$212$	2.96480e11	0.0475497
$213$	1.29047e13	2.01679
$214$	−5.18930e12	−0.790375
$215$	0	0
$216$	1.24005e12	0.179450
$217$	2.51598e12	0.354959
$218$	−4.97726e12	−0.684667
$219$	1.88916e12	0.253412
$220$	0	0
$221$	4.54737e12	0.580233
$222$	8.55846e12	1.06526
$223$	−7.85354e12	−0.953650	−0.476825	−	0.878998i	$-0.658212\pi$
$223$	−7.85354e12	−0.953650	−0.476825	+	0.878998i	$0.658212\pi$
$224$	−8.21313e11	−0.0973071
$225$	0	0
$226$	−4.04065e12	−0.455884
$227$	−5.24834e12	−0.577936	−0.288968	−	0.957339i	$-0.593312\pi$
$227$	−5.24834e12	−0.577936	−0.288968	+	0.957339i	$0.593312\pi$
$228$	−9.87516e12	−1.06146
$229$	2.54851e12	0.267419	0.133709	−	0.991021i	$-0.457311\pi$
$229$	2.54851e12	0.267419	0.133709	+	0.991021i	$0.457311\pi$
$230$	0	0
$231$	−8.71468e12	−0.871738
$232$	−6.64232e12	−0.648837
$233$	1.29244e13	1.23297	0.616483	−	0.787368i	$-0.288557\pi$
$233$	1.29244e13	1.23297	0.616483	+	0.787368i	$0.288557\pi$
$234$	1.96540e12	0.183132
$235$	0	0
$236$	−2.53427e12	−0.225339
$237$	−6.19151e12	−0.537874
$238$	6.14903e12	0.521955
$239$	−3.04646e12	−0.252701	−0.126350	−	0.991986i	$-0.540326\pi$
$239$	−3.04646e12	−0.252701	−0.126350	+	0.991986i	$0.540326\pi$
$240$	0	0
$241$	−1.51377e13	−1.19940	−0.599701	−	0.800224i	$-0.704714\pi$
$241$	−1.51377e13	−1.19940	−0.599701	+	0.800224i	$0.704714\pi$
$242$	−5.19434e12	−0.402296
$243$	−1.40081e13	−1.06058
$244$	9.38275e10	0.00694522
$245$	0	0
$246$	−5.87429e12	−0.415731
$247$	1.04972e13	0.726511
$248$	−3.36820e12	−0.227989
$249$	−1.24378e13	−0.823468
$250$	0	0
$251$	−5.88554e12	−0.372890	−0.186445	−	0.982465i	$-0.559697\pi$
$251$	−5.88554e12	−0.372890	−0.186445	+	0.982465i	$0.559697\pi$
$252$	2.65765e12	0.164738
$253$	−1.31940e13	−0.800227
$254$	−1.30004e13	−0.771564
$255$	0	0
$256$	1.09951e12	0.0625000
$257$	−1.26568e13	−0.704194	−0.352097	−	0.935964i	$-0.614531\pi$
$257$	−1.26568e13	−0.704194	−0.352097	+	0.935964i	$0.614531\pi$
$258$	2.43886e13	1.32825
$259$	−1.23019e13	−0.655881
$260$	0	0
$261$	2.14936e13	1.09847
$262$	−1.49566e13	−0.748473
$263$	−1.94934e13	−0.955280	−0.477640	−	0.878556i	$-0.658508\pi$
$263$	−1.94934e13	−0.955280	−0.477640	+	0.878556i	$0.658508\pi$
$264$	1.16666e13	0.559914
$265$	0	0
$266$	1.41946e13	0.653541
$267$	−5.44807e13	−2.45715
$268$	3.16710e10	0.00139933
$269$	−4.34447e12	−0.188061	−0.0940306	−	0.995569i	$-0.529975\pi$
$269$	−4.34447e12	−0.188061	−0.0940306	+	0.995569i	$0.529975\pi$
$270$	0	0
$271$	2.67882e12	0.111330	0.0556650	−	0.998449i	$-0.482272\pi$
$271$	2.67882e12	0.111330	0.0556650	+	0.998449i	$0.482272\pi$
$272$	−8.23186e12	−0.335250
$273$	−7.54487e12	−0.301132
$274$	1.88415e13	0.737032
$275$	0	0
$276$	1.07460e13	0.403873
$277$	1.30102e13	0.479343	0.239672	−	0.970854i	$-0.422960\pi$
$277$	1.30102e13	0.479343	0.239672	+	0.970854i	$0.422960\pi$
$278$	7.62260e12	0.275332
$279$	1.08990e13	0.385979
$280$	0	0
$281$	2.90772e13	0.990075	0.495037	−	0.868872i	$-0.335154\pi$
$281$	2.90772e13	0.990075	0.495037	+	0.868872i	$0.335154\pi$
$282$	2.35301e13	0.785694
$283$	8.21076e12	0.268880	0.134440	−	0.990922i	$-0.457076\pi$
$283$	8.21076e12	0.268880	0.134440	+	0.990922i	$0.457076\pi$
$284$	2.48323e13	0.797565
$285$	0	0
$286$	−1.24015e13	−0.383231
$287$	8.44371e12	0.255966
$288$	−3.55786e12	−0.105811
$289$	2.73587e13	0.798283
$290$	0	0
$291$	−3.12745e13	−0.878575
$292$	3.63529e12	0.100215
$293$	8.70497e12	0.235502	0.117751	−	0.993043i	$-0.462431\pi$
$293$	8.70497e12	0.235502	0.117751	+	0.993043i	$0.462431\pi$
$294$	2.34690e13	0.623137
$295$	0	0
$296$	1.64689e13	0.421270
$297$	2.53192e13	0.635756
$298$	−3.82778e13	−0.943534
$299$	−1.14229e13	−0.276430
$300$	0	0
$301$	−3.50562e13	−0.817805
$302$	1.50094e12	0.0343816
$303$	1.85493e12	0.0417248
$304$	−1.90026e13	−0.419767
$305$	0	0
$306$	2.66371e13	0.567570
$307$	−6.59577e13	−1.38040	−0.690199	−	0.723620i	$-0.742477\pi$
$307$	−6.59577e13	−1.38040	−0.690199	+	0.723620i	$0.742477\pi$
$308$	−1.67695e13	−0.344740
$309$	−4.28078e13	−0.864473
$310$	0	0
$311$	−2.13842e13	−0.416783	−0.208392	−	0.978045i	$-0.566823\pi$
$311$	−2.13842e13	−0.416783	−0.208392	+	0.978045i	$0.566823\pi$
$312$	1.01005e13	0.193416
$313$	2.84379e13	0.535062	0.267531	−	0.963549i	$-0.413792\pi$
$313$	2.84379e13	0.535062	0.267531	+	0.963549i	$0.413792\pi$
$314$	3.60159e13	0.665858
$315$	0	0
$316$	−1.19142e13	−0.212709
$317$	1.06352e14	1.86603	0.933017	−	0.359833i	$-0.117166\pi$
$317$	1.06352e14	1.86603	0.933017	+	0.359833i	$0.117166\pi$
$318$	−4.93033e12	−0.0850212
$319$	−1.35622e14	−2.29870
$320$	0	0
$321$	8.62959e13	1.41323
$322$	−1.54462e13	−0.248666
$323$	1.42269e14	2.25163
$324$	−3.98556e13	−0.620143
$325$	0	0
$326$	−4.06344e13	−0.611220
$327$	8.27697e13	1.22422
$328$	−1.13038e13	−0.164406
$329$	−3.38222e13	−0.483754
$330$	0	0
$331$	−1.23331e14	−1.70616	−0.853079	−	0.521781i	$-0.825268\pi$
$331$	−1.23331e14	−1.70616	−0.853079	+	0.521781i	$0.825268\pi$
$332$	−2.39338e13	−0.325651
$333$	−5.32910e13	−0.713199
$334$	2.09697e13	0.276049
$335$	0	0
$336$	1.36581e13	0.173990
$337$	4.55439e13	0.570776	0.285388	−	0.958412i	$-0.407877\pi$
$337$	4.55439e13	0.570776	0.285388	+	0.958412i	$0.407877\pi$
$338$	4.66124e13	0.574724
$339$	6.71942e13	0.815142
$340$	0	0
$341$	−6.87717e13	−0.807719
$342$	6.14897e13	0.710655
$343$	−8.21334e13	−0.934119
$344$	4.69307e13	0.525273
$345$	0	0
$346$	7.34209e13	0.795978
$347$	8.36511e13	0.892605	0.446303	−	0.894882i	$-0.352741\pi$
$347$	8.36511e13	0.892605	0.446303	+	0.894882i	$0.352741\pi$
$348$	1.10459e14	1.16015
$349$	6.38318e13	0.659929	0.329965	−	0.943993i	$-0.392963\pi$
$349$	6.38318e13	0.659929	0.329965	+	0.943993i	$0.392963\pi$
$350$	0	0
$351$	2.19205e13	0.219615
$352$	2.24498e13	0.221425
$353$	−3.55388e13	−0.345097	−0.172549	−	0.985001i	$-0.555200\pi$
$353$	−3.55388e13	−0.345097	−0.172549	+	0.985001i	$0.555200\pi$
$354$	4.21437e13	0.402917
$355$	0	0
$356$	−1.04836e14	−0.971710
$357$	−1.02256e14	−0.933281
$358$	−9.29229e13	−0.835153
$359$	1.40868e14	1.24679	0.623393	−	0.781909i	$-0.285754\pi$
$359$	1.40868e14	1.24679	0.623393	+	0.781909i	$0.285754\pi$
$360$	0	0
$361$	2.11927e14	1.81927
$362$	−8.24003e13	−0.696677
$363$	8.63796e13	0.719325
$364$	−1.45185e13	−0.119087
$365$	0	0
$366$	−1.56031e12	−0.0124184
$367$	−5.21259e13	−0.408686	−0.204343	−	0.978899i	$-0.565506\pi$
$367$	−5.21259e13	−0.408686	−0.204343	+	0.978899i	$0.565506\pi$
$368$	2.06783e13	0.159717
$369$	3.65775e13	0.278336
$370$	0	0
$371$	7.08687e12	0.0523477
$372$	5.60117e13	0.407655
$373$	−1.12302e14	−0.805355	−0.402677	−	0.915342i	$-0.631920\pi$
$373$	−1.12302e14	−0.805355	−0.402677	+	0.915342i	$0.631920\pi$
$374$	−1.68078e14	−1.18773
$375$	0	0
$376$	4.52786e13	0.310713
$377$	−1.17417e14	−0.794062
$378$	2.96413e13	0.197557
$379$	−8.23254e13	−0.540777	−0.270388	−	0.962751i	$-0.587152\pi$
$379$	−8.23254e13	−0.540777	−0.270388	+	0.962751i	$0.587152\pi$
$380$	0	0
$381$	2.16191e14	1.37959
$382$	−7.15132e12	−0.0449819
$383$	−1.86623e14	−1.15710	−0.578552	−	0.815645i	$-0.696382\pi$
$383$	−1.86623e14	−1.15710	−0.578552	+	0.815645i	$0.696382\pi$
$384$	−1.82844e13	−0.111753
$385$	0	0
$386$	1.03774e14	0.616396
$387$	−1.51861e14	−0.889274
$388$	−6.01810e13	−0.347444
$389$	1.33809e14	0.761660	0.380830	−	0.924645i	$-0.375638\pi$
$389$	1.33809e14	0.761660	0.380830	+	0.924645i	$0.375638\pi$
$390$	0	0
$391$	−1.54815e14	−0.856722
$392$	4.51609e13	0.246428
$393$	2.48722e14	1.33831
$394$	−1.64857e14	−0.874739
$395$	0	0
$396$	−7.26442e13	−0.374867
$397$	−3.34373e14	−1.70170	−0.850851	−	0.525406i	$-0.823913\pi$
$397$	−3.34373e14	−1.70170	−0.850851	+	0.525406i	$0.823913\pi$
$398$	2.21717e13	0.111286
$399$	−2.36049e14	−1.16856
$400$	0	0
$401$	−1.88539e14	−0.908043	−0.454021	−	0.890991i	$-0.650011\pi$
$401$	−1.88539e14	−0.908043	−0.454021	+	0.890991i	$0.650011\pi$
$402$	−5.26675e11	−0.00250207
$403$	−5.95401e13	−0.279018
$404$	3.56942e12	0.0165006
$405$	0	0
$406$	−1.58774e14	−0.714308
$407$	3.36261e14	1.49248
$408$	1.36892e14	0.599443
$409$	3.34993e14	1.44730	0.723649	−	0.690168i	$-0.242463\pi$
$409$	3.34993e14	1.44730	0.723649	+	0.690168i	$0.242463\pi$
$410$	0	0
$411$	−3.13325e14	−1.31785
$412$	−8.23744e13	−0.341867
$413$	−6.05774e13	−0.248077
$414$	−6.69119e13	−0.270397
$415$	0	0
$416$	1.94362e13	0.0764889
$417$	−1.26761e14	−0.492307
$418$	−3.87994e14	−1.48715
$419$	−1.56423e14	−0.591729	−0.295864	−	0.955230i	$-0.595608\pi$
$419$	−1.56423e14	−0.591729	−0.295864	+	0.955230i	$0.595608\pi$
$420$	0	0
$421$	5.29550e14	1.95144	0.975721	−	0.219015i	$-0.0702845\pi$
$421$	5.29550e14	1.95144	0.975721	+	0.219015i	$0.0702845\pi$
$422$	−2.28971e14	−0.832840
$423$	−1.46515e14	−0.526030
$424$	−9.48736e12	−0.0336227
$425$	0	0
$426$	−4.12951e14	−1.42608
$427$	2.24279e12	0.00764602
$428$	1.66058e14	0.558880
$429$	2.06231e14	0.685235
$430$	0	0
$431$	8.37388e13	0.271208	0.135604	−	0.990763i	$-0.456703\pi$
$431$	8.37388e13	0.271208	0.135604	+	0.990763i	$0.456703\pi$
$432$	−3.96816e13	−0.126890
$433$	−9.93342e13	−0.313628	−0.156814	−	0.987628i	$-0.550122\pi$
$433$	−9.93342e13	−0.313628	−0.156814	+	0.987628i	$0.550122\pi$
$434$	−8.05112e13	−0.250994
$435$	0	0
$436$	1.59272e14	0.484133
$437$	−3.57378e14	−1.07270
$438$	−6.04532e13	−0.179189
$439$	5.35579e14	1.56772	0.783860	−	0.620938i	$-0.213248\pi$
$439$	5.35579e14	1.56772	0.783860	+	0.620938i	$0.213248\pi$
$440$	0	0
$441$	−1.46134e14	−0.417196
$442$	−1.45516e14	−0.410287
$443$	4.64925e14	1.29468	0.647341	−	0.762201i	$-0.275881\pi$
$443$	4.64925e14	1.29468	0.647341	+	0.762201i	$0.275881\pi$
$444$	−2.73871e14	−0.753251
$445$	0	0
$446$	2.51313e14	0.674332
$447$	6.36544e14	1.68708
$448$	2.62820e13	0.0688065
$449$	−5.07045e14	−1.31127	−0.655634	−	0.755079i	$-0.727599\pi$
$449$	−5.07045e14	−1.31127	−0.655634	+	0.755079i	$0.727599\pi$
$450$	0	0
$451$	−2.30800e14	−0.582459
$452$	1.29301e14	0.322359
$453$	−2.49600e13	−0.0614759
$454$	1.67947e14	0.408662
$455$	0	0
$456$	3.16005e14	0.750564
$457$	5.05346e14	1.18591	0.592953	−	0.805237i	$-0.297962\pi$
$457$	5.05346e14	1.18591	0.592953	+	0.805237i	$0.297962\pi$
$458$	−8.15524e13	−0.189094
$459$	2.97089e14	0.680639
$460$	0	0
$461$	7.16573e14	1.60290	0.801448	−	0.598064i	$-0.204063\pi$
$461$	7.16573e14	1.60290	0.801448	+	0.598064i	$0.204063\pi$
$462$	2.78870e14	0.616411
$463$	−1.12357e14	−0.245418	−0.122709	−	0.992443i	$-0.539158\pi$
$463$	−1.12357e14	−0.245418	−0.122709	+	0.992443i	$0.539158\pi$
$464$	2.12554e14	0.458797
$465$	0	0
$466$	−4.13579e14	−0.871839
$467$	2.21056e14	0.460532	0.230266	−	0.973128i	$-0.426040\pi$
$467$	2.21056e14	0.460532	0.230266	+	0.973128i	$0.426040\pi$
$468$	−6.28928e13	−0.129494
$469$	7.57042e11	0.00154053
$470$	0	0
$471$	−5.98929e14	−1.19059
$472$	8.10965e13	0.159339
$473$	9.58227e14	1.86094
$474$	1.98128e14	0.380334
$475$	0	0
$476$	−1.96769e14	−0.369078
$477$	3.06997e13	0.0569225
$478$	9.74866e13	0.178686
$479$	−9.23603e14	−1.67356	−0.836778	−	0.547543i	$-0.815563\pi$
$479$	−9.23603e14	−1.67356	−0.836778	+	0.547543i	$0.815563\pi$
$480$	0	0
$481$	2.91123e14	0.515560
$482$	4.84405e14	0.848106
$483$	2.56864e14	0.444626
$484$	1.66219e14	0.284466
$485$	0	0
$486$	4.48259e14	0.749946
$487$	−4.58584e14	−0.758594	−0.379297	−	0.925275i	$-0.623834\pi$
$487$	−4.58584e14	−0.758594	−0.379297	+	0.925275i	$0.623834\pi$
$488$	−3.00248e12	−0.00491101
$489$	6.75733e14	1.09289
$490$	0	0
$491$	−2.27335e14	−0.359516	−0.179758	−	0.983711i	$-0.557531\pi$
$491$	−2.27335e14	−0.359516	−0.179758	+	0.983711i	$0.557531\pi$
$492$	1.87977e14	0.293966
$493$	−1.59136e15	−2.46099
$494$	−3.35912e14	−0.513721
$495$	0	0
$496$	1.07782e14	0.161212
$497$	5.93575e14	0.878043
$498$	3.98009e14	0.582280
$499$	−6.20100e14	−0.897240	−0.448620	−	0.893723i	$-0.648084\pi$
$499$	−6.20100e14	−0.897240	−0.448620	+	0.893723i	$0.648084\pi$
$500$	0	0
$501$	−3.48717e14	−0.493589
$502$	1.88337e14	0.263673
$503$	3.45337e14	0.478211	0.239105	−	0.970994i	$-0.423146\pi$
$503$	3.45337e14	0.478211	0.239105	+	0.970994i	$0.423146\pi$
$504$	−8.50448e13	−0.116488
$505$	0	0
$506$	4.22208e14	0.565846
$507$	−7.75143e14	−1.02763
$508$	4.16013e14	0.545578
$509$	1.29592e14	0.168125	0.0840624	−	0.996460i	$-0.473210\pi$
$509$	1.29592e14	0.168125	0.0840624	+	0.996460i	$0.473210\pi$
$510$	0	0
$511$	8.68955e13	0.110327
$512$	−3.51844e13	−0.0441942
$513$	6.85807e14	0.852229
$514$	4.05018e14	0.497940
$515$	0	0
$516$	−7.80436e14	−0.939213
$517$	9.24496e14	1.10080
$518$	3.93662e14	0.463778
$519$	−1.22096e15	−1.42325
$520$	0	0
$521$	8.63535e14	0.985536	0.492768	−	0.870161i	$-0.335985\pi$
$521$	8.63535e14	0.985536	0.492768	+	0.870161i	$0.335985\pi$
$522$	−6.87795e14	−0.776732
$523$	−1.76403e15	−1.97128	−0.985638	−	0.168870i	$-0.945988\pi$
$523$	−1.76403e15	−1.97128	−0.985638	+	0.168870i	$0.945988\pi$
$524$	4.78612e14	0.529251
$525$	0	0
$526$	6.23789e14	0.675485
$527$	−8.06948e14	−0.864744
$528$	−3.73330e14	−0.395919
$529$	−5.63918e14	−0.591848
$530$	0	0
$531$	−2.62417e14	−0.269756
$532$	−4.54226e14	−0.462123
$533$	−1.99819e14	−0.201204
$534$	1.74338e15	1.73746
$535$	0	0
$536$	−1.01347e12	−0.000989475 0
$537$	1.54527e15	1.49329
$538$	1.39023e14	0.132979
$539$	9.22093e14	0.873045
$540$	0	0
$541$	−5.96542e14	−0.553421	−0.276711	−	0.960953i	$-0.589244\pi$
$541$	−5.96542e14	−0.553421	−0.276711	+	0.960953i	$0.589244\pi$
$542$	−8.57223e13	−0.0787223
$543$	1.37028e15	1.24569
$544$	2.63419e14	0.237058
$545$	0	0
$546$	2.41436e14	0.212933
$547$	−1.72805e15	−1.50878	−0.754390	−	0.656426i	$-0.772067\pi$
$547$	−1.72805e15	−1.50878	−0.754390	+	0.656426i	$0.772067\pi$
$548$	−6.02927e14	−0.521161
$549$	9.71559e12	0.00831422
$550$	0	0
$551$	−3.67352e15	−3.08141
$552$	−3.43871e14	−0.285582
$553$	−2.84790e14	−0.234173
$554$	−4.16328e14	−0.338947
$555$	0	0
$556$	−2.43923e14	−0.194689
$557$	−1.11647e15	−0.882353	−0.441177	−	0.897420i	$-0.645439\pi$
$557$	−1.11647e15	−0.882353	−0.441177	+	0.897420i	$0.645439\pi$
$558$	−3.48768e14	−0.272928
$559$	8.29600e14	0.642841
$560$	0	0
$561$	2.79506e15	2.12371
$562$	−9.30471e14	−0.700089
$563$	−3.81802e13	−0.0284474	−0.0142237	−	0.999899i	$-0.504528\pi$
$563$	−3.81802e13	−0.0284474	−0.0142237	+	0.999899i	$0.504528\pi$
$564$	−7.52963e14	−0.555570
$565$	0	0
$566$	−2.62744e14	−0.190127
$567$	−9.52683e14	−0.682718
$568$	−7.94634e14	−0.563964
$569$	−8.00530e14	−0.562678	−0.281339	−	0.959608i	$-0.590779\pi$
$569$	−8.00530e14	−0.562678	−0.281339	+	0.959608i	$0.590779\pi$
$570$	0	0
$571$	−1.20542e12	−0.000831073 0	−0.000415536	−	1.00000i	$-0.500132\pi$
$571$	−1.20542e12	−0.000831073 0	−0.000415536		1.00000i	$0.500132\pi$
$572$	3.96848e14	0.270985
$573$	1.18923e14	0.0804297
$574$	−2.70199e14	−0.180995
$575$	0	0
$576$	1.13852e14	0.0748196
$577$	−1.11237e15	−0.724075	−0.362038	−	0.932163i	$-0.617919\pi$
$577$	−1.11237e15	−0.724075	−0.362038	+	0.932163i	$0.617919\pi$
$578$	−8.75477e14	−0.564471
$579$	−1.72572e15	−1.10215
$580$	0	0
$581$	−5.72099e14	−0.358511
$582$	1.00078e15	0.621246
$583$	−1.93712e14	−0.119119
$584$	−1.16329e14	−0.0708627
$585$	0	0
$586$	−2.78559e14	−0.166525
$587$	1.41072e15	0.835474	0.417737	−	0.908568i	$-0.362823\pi$
$587$	1.41072e15	0.835474	0.417737	+	0.908568i	$0.362823\pi$
$588$	−7.51006e14	−0.440624
$589$	−1.86278e15	−1.08275
$590$	0	0
$591$	2.74150e15	1.56407
$592$	−5.27005e14	−0.297883
$593$	2.95927e15	1.65723	0.828617	−	0.559816i	$-0.189128\pi$
$593$	2.95927e15	1.65723	0.828617	+	0.559816i	$0.189128\pi$
$594$	−8.10216e14	−0.449547
$595$	0	0
$596$	1.22489e15	0.667179
$597$	−3.68706e14	−0.198985
$598$	3.65533e14	0.195465
$599$	7.61671e14	0.403571	0.201785	−	0.979430i	$-0.435326\pi$
$599$	7.61671e14	0.403571	0.201785	+	0.979430i	$0.435326\pi$
$600$	0	0
$601$	−5.33224e14	−0.277396	−0.138698	−	0.990335i	$-0.544292\pi$
$601$	−5.33224e14	−0.277396	−0.138698	+	0.990335i	$0.544292\pi$
$602$	1.12180e15	0.578275
$603$	3.27945e12	0.00167516
$604$	−4.80301e13	−0.0243114
$605$	0	0
$606$	−5.93579e13	−0.0295039
$607$	−2.82058e15	−1.38931	−0.694657	−	0.719341i	$-0.744444\pi$
$607$	−2.82058e15	−1.38931	−0.694657	+	0.719341i	$0.744444\pi$
$608$	6.08083e14	0.296820
$609$	2.64034e15	1.27722
$610$	0	0
$611$	8.00396e14	0.380258
$612$	−8.52388e14	−0.401333
$613$	−3.94879e15	−1.84260	−0.921301	−	0.388850i	$-0.872873\pi$
$613$	−3.94879e15	−1.84260	−0.921301	+	0.388850i	$0.872873\pi$
$614$	2.11065e15	0.976089
$615$	0	0
$616$	5.36625e14	0.243768
$617$	4.71962e14	0.212490	0.106245	−	0.994340i	$-0.466117\pi$
$617$	4.71962e14	0.212490	0.106245	+	0.994340i	$0.466117\pi$
$618$	1.36985e15	0.611275
$619$	6.15999e14	0.272447	0.136223	−	0.990678i	$-0.456504\pi$
$619$	6.15999e14	0.272447	0.136223	+	0.990678i	$0.456504\pi$
$620$	0	0
$621$	−7.46282e14	−0.324264
$622$	6.84293e14	0.294710
$623$	−2.50594e15	−1.06976
$624$	−3.23216e14	−0.136766
$625$	0	0
$626$	−9.10014e14	−0.378346
$627$	6.45217e15	2.65910
$628$	−1.15251e15	−0.470833
$629$	3.94560e15	1.59784
$630$	0	0
$631$	7.19339e14	0.286267	0.143134	−	0.989703i	$-0.454282\pi$
$631$	7.19339e14	0.286267	0.143134	+	0.989703i	$0.454282\pi$
$632$	3.81255e14	0.150408
$633$	3.80769e15	1.48916
$634$	−3.40326e15	−1.31949
$635$	0	0
$636$	1.57771e14	0.0601191
$637$	7.98316e14	0.301584
$638$	4.33992e15	1.62543
$639$	2.57132e15	0.954777
$640$	0	0
$641$	−2.58937e15	−0.945094	−0.472547	−	0.881306i	$-0.656665\pi$
$641$	−2.58937e15	−0.945094	−0.472547	+	0.881306i	$0.656665\pi$
$642$	−2.76147e15	−0.999303
$643$	−9.64667e14	−0.346112	−0.173056	−	0.984912i	$-0.555364\pi$
$643$	−9.64667e14	−0.346112	−0.173056	+	0.984912i	$0.555364\pi$
$644$	4.94280e14	0.175833
$645$	0	0
$646$	−4.55262e15	−1.59214
$647$	1.46486e15	0.507951	0.253976	−	0.967211i	$-0.418262\pi$
$647$	1.46486e15	0.507951	0.253976	+	0.967211i	$0.418262\pi$
$648$	1.27538e15	0.438508
$649$	1.65582e15	0.564506
$650$	0	0
$651$	1.33887e15	0.448789
$652$	1.30030e15	0.432198
$653$	−6.05527e14	−0.199577	−0.0997886	−	0.995009i	$-0.531817\pi$
$653$	−6.05527e14	−0.199577	−0.0997886	+	0.995009i	$0.531817\pi$
$654$	−2.64863e15	−0.865653
$655$	0	0
$656$	3.61721e14	0.116253
$657$	3.76424e14	0.119969
$658$	1.08231e15	0.342065
$659$	−3.25431e15	−1.01998	−0.509988	−	0.860182i	$-0.670350\pi$
$659$	−3.25431e15	−1.01998	−0.509988	+	0.860182i	$0.670350\pi$
$660$	0	0
$661$	3.71162e15	1.14408	0.572038	−	0.820227i	$-0.306153\pi$
$661$	3.71162e15	1.14408	0.572038	+	0.820227i	$0.306153\pi$
$662$	3.94660e15	1.20644
$663$	2.41986e15	0.733612
$664$	7.65882e14	0.230270
$665$	0	0
$666$	1.70531e15	0.504308
$667$	3.99746e15	1.17244
$668$	−6.71031e14	−0.195196
$669$	−4.17923e15	−1.20574
$670$	0	0
$671$	−6.13044e13	−0.0173987
$672$	−4.37059e14	−0.123029
$673$	−9.34378e14	−0.260879	−0.130440	−	0.991456i	$-0.541639\pi$
$673$	−9.34378e14	−0.260879	−0.130440	+	0.991456i	$0.541639\pi$
$674$	−1.45741e15	−0.403600
$675$	0	0
$676$	−1.49160e15	−0.406391
$677$	−4.76512e15	−1.28776	−0.643882	−	0.765125i	$-0.722677\pi$
$677$	−4.76512e15	−1.28776	−0.643882	+	0.765125i	$0.722677\pi$
$678$	−2.15021e15	−0.576393
$679$	−1.43853e15	−0.382503
$680$	0	0
$681$	−2.79288e15	−0.730708
$682$	2.20069e15	0.571144
$683$	−2.09026e14	−0.0538130	−0.0269065	−	0.999638i	$-0.508566\pi$
$683$	−2.09026e14	−0.0538130	−0.0269065	+	0.999638i	$0.508566\pi$
$684$	−1.96767e15	−0.502509
$685$	0	0
$686$	2.62827e15	0.660522
$687$	1.35618e15	0.338108
$688$	−1.50178e15	−0.371424
$689$	−1.67709e14	−0.0411483
$690$	0	0
$691$	−3.22483e15	−0.778712	−0.389356	−	0.921087i	$-0.627302\pi$
$691$	−3.22483e15	−0.778712	−0.389356	+	0.921087i	$0.627302\pi$
$692$	−2.34947e15	−0.562842
$693$	−1.73644e15	−0.412693
$694$	−2.67683e15	−0.631167
$695$	0	0
$696$	−3.53468e15	−0.820351
$697$	−2.70815e15	−0.623580
$698$	−2.04262e15	−0.466641
$699$	6.87764e15	1.55889
$700$	0	0
$701$	−1.50206e13	−0.00335149	−0.00167575	−	0.999999i	$-0.500533\pi$
$701$	−1.50206e13	−0.00335149	−0.00167575	+	0.999999i	$0.500533\pi$
$702$	−7.01457e14	−0.155291
$703$	9.10811e15	2.00066
$704$	−7.18393e14	−0.156571
$705$	0	0
$706$	1.13724e15	0.244021
$707$	8.53211e13	0.0181656
$708$	−1.34860e15	−0.284905
$709$	2.05916e14	0.0431654	0.0215827	−	0.999767i	$-0.493129\pi$
$709$	2.05916e14	0.0431654	0.0215827	+	0.999767i	$0.493129\pi$
$710$	0	0
$711$	−1.23369e15	−0.254637
$712$	3.35476e15	0.687103
$713$	2.02704e15	0.411974
$714$	3.27218e15	0.659929
$715$	0	0
$716$	2.97353e15	0.590542
$717$	−1.62116e15	−0.319500
$718$	−4.50776e15	−0.881611
$719$	1.06708e15	0.207104	0.103552	−	0.994624i	$-0.466979\pi$
$719$	1.06708e15	0.207104	0.103552	+	0.994624i	$0.466979\pi$
$720$	0	0
$721$	−1.96902e15	−0.376363
$722$	−6.78168e15	−1.28642
$723$	−8.05545e15	−1.51645
$724$	2.63681e15	0.492625
$725$	0	0
$726$	−2.76415e15	−0.508639
$727$	−3.85905e15	−0.704759	−0.352380	−	0.935857i	$-0.614627\pi$
$727$	−3.85905e15	−0.704759	−0.352380	+	0.935857i	$0.614627\pi$
$728$	4.64591e14	0.0842070
$729$	−5.59533e14	−0.100652
$730$	0	0
$731$	1.12436e16	1.99232
$732$	4.99299e13	0.00878112
$733$	1.09224e15	0.190653	0.0953267	−	0.995446i	$-0.469610\pi$
$733$	1.09224e15	0.190653	0.0953267	+	0.995446i	$0.469610\pi$
$734$	1.66803e15	0.288985
$735$	0	0
$736$	−6.61704e14	−0.112937
$737$	−2.06930e13	−0.00350552
$738$	−1.17048e15	−0.196813
$739$	4.82140e15	0.804691	0.402345	−	0.915488i	$-0.368195\pi$
$739$	4.82140e15	0.804691	0.402345	+	0.915488i	$0.368195\pi$
$740$	0	0
$741$	5.58607e15	0.918557
$742$	−2.26780e14	−0.0370154
$743$	2.51982e15	0.408255	0.204128	−	0.978944i	$-0.434564\pi$
$743$	2.51982e15	0.408255	0.204128	+	0.978944i	$0.434564\pi$
$744$	−1.79237e15	−0.288255
$745$	0	0
$746$	3.59365e15	0.569472
$747$	−2.47829e15	−0.389841
$748$	5.37848e15	0.839849
$749$	3.96934e15	0.615273
$750$	0	0
$751$	7.47268e15	1.14145	0.570725	−	0.821142i	$-0.306662\pi$
$751$	7.47268e15	1.14145	0.570725	+	0.821142i	$0.306662\pi$
$752$	−1.44891e15	−0.219707
$753$	−3.13197e15	−0.471460
$754$	3.75735e15	0.561487
$755$	0	0
$756$	−9.48522e14	−0.139694
$757$	3.09514e15	0.452535	0.226268	−	0.974065i	$-0.427348\pi$
$757$	3.09514e15	0.452535	0.226268	+	0.974065i	$0.427348\pi$
$758$	2.63441e15	0.382387
$759$	−7.02113e15	−1.01176
$760$	0	0
$761$	−6.77183e15	−0.961812	−0.480906	−	0.876772i	$-0.659692\pi$
$761$	−6.77183e15	−0.961812	−0.480906	+	0.876772i	$0.659692\pi$
$762$	−6.91812e15	−0.975520
$763$	3.80714e15	0.532984
$764$	2.28842e14	0.0318070
$765$	0	0
$766$	5.97194e15	0.818196
$767$	1.43355e15	0.195002
$768$	5.85101e14	0.0790213
$769$	−1.04403e16	−1.39997	−0.699984	−	0.714159i	$-0.746810\pi$
$769$	−1.04403e16	−1.39997	−0.699984	+	0.714159i	$0.746810\pi$
$770$	0	0
$771$	−6.73528e15	−0.890341
$772$	−3.32078e15	−0.435858
$773$	−1.34162e16	−1.74841	−0.874204	−	0.485558i	$-0.838616\pi$
$773$	−1.34162e16	−1.74841	−0.874204	+	0.485558i	$0.838616\pi$
$774$	4.85955e15	0.628812
$775$	0	0
$776$	1.92579e15	0.245680
$777$	−6.54643e15	−0.829257
$778$	−4.28187e15	−0.538575
$779$	−6.25155e15	−0.780785
$780$	0	0
$781$	−1.62248e16	−1.99801
$782$	4.95407e15	0.605794
$783$	−7.67112e15	−0.931470
$784$	−1.44515e15	−0.174251
$785$	0	0
$786$	−7.95911e15	−0.946325
$787$	−1.58544e16	−1.87193	−0.935964	−	0.352097i	$-0.885469\pi$
$787$	−1.58544e16	−1.87193	−0.935964	+	0.352097i	$0.885469\pi$
$788$	5.27543e15	0.618534
$789$	−1.03733e16	−1.20780
$790$	0	0
$791$	3.09072e15	0.354886
$792$	2.32462e15	0.265071
$793$	−5.30752e13	−0.00601021
$794$	1.06999e16	1.20329
$795$	0	0
$796$	−7.09495e14	−0.0786914
$797$	2.54021e14	0.0279800	0.0139900	−	0.999902i	$-0.495547\pi$
$797$	2.54021e14	0.0279800	0.0139900	+	0.999902i	$0.495547\pi$
$798$	7.55358e15	0.826299
$799$	1.08478e16	1.17851
$800$	0	0
$801$	−1.08555e16	−1.16325
$802$	6.03324e15	0.642083
$803$	−2.37520e15	−0.251053
$804$	1.68536e13	0.00176923
$805$	0	0
$806$	1.90528e15	0.197295
$807$	−2.31189e15	−0.237773
$808$	−1.14221e14	−0.0116677
$809$	−1.13120e16	−1.14768	−0.573842	−	0.818966i	$-0.694548\pi$
$809$	−1.13120e16	−1.14768	−0.573842	+	0.818966i	$0.694548\pi$
$810$	0	0
$811$	1.05859e16	1.05953	0.529767	−	0.848143i	$-0.322279\pi$
$811$	1.05859e16	1.05953	0.529767	+	0.848143i	$0.322279\pi$
$812$	5.08076e15	0.505092
$813$	1.42552e15	0.140759
$814$	−1.07604e16	−1.05534
$815$	0	0
$816$	−4.38055e15	−0.423870
$817$	2.59549e16	2.49459
$818$	−1.07198e16	−1.02339
$819$	−1.50335e15	−0.142560
$820$	0	0
$821$	−2.04679e16	−1.91508	−0.957539	−	0.288303i	$-0.906909\pi$
$821$	−2.04679e16	−1.91508	−0.957539	+	0.288303i	$0.906909\pi$
$822$	1.00264e16	0.931860
$823$	1.10300e16	1.01830	0.509151	−	0.860677i	$-0.329959\pi$
$823$	1.10300e16	1.01830	0.509151	+	0.860677i	$0.329959\pi$
$824$	2.63598e15	0.241737
$825$	0	0
$826$	1.93848e15	0.175417
$827$	8.21173e15	0.738167	0.369083	−	0.929396i	$-0.379672\pi$
$827$	8.21173e15	0.738167	0.369083	+	0.929396i	$0.379672\pi$
$828$	2.14118e15	0.191199
$829$	3.82596e15	0.339383	0.169691	−	0.985497i	$-0.445723\pi$
$829$	3.82596e15	0.339383	0.169691	+	0.985497i	$0.445723\pi$
$830$	0	0
$831$	6.92335e15	0.606053
$832$	−6.21959e14	−0.0540858
$833$	1.08196e16	0.934681
$834$	4.05634e15	0.348113
$835$	0	0
$836$	1.24158e16	1.05158
$837$	−3.88988e15	−0.327300
$838$	5.00553e15	0.418415
$839$	−2.86284e15	−0.237742	−0.118871	−	0.992910i	$-0.537928\pi$
$839$	−2.86284e15	−0.237742	−0.118871	+	0.992910i	$0.537928\pi$
$840$	0	0
$841$	2.88898e16	2.36792
$842$	−1.69456e16	−1.37988
$843$	1.54733e16	1.25179
$844$	7.32707e15	0.588907
$845$	0	0
$846$	4.68848e15	0.371959
$847$	3.97319e15	0.313170
$848$	3.03596e14	0.0237749
$849$	4.36933e15	0.339956
$850$	0	0
$851$	−9.91126e15	−0.761231
$852$	1.32144e16	1.00839
$853$	8.25498e15	0.625888	0.312944	−	0.949772i	$-0.398685\pi$
$853$	8.25498e15	0.625888	0.312944	+	0.949772i	$0.398685\pi$
$854$	−7.17693e13	−0.00540655
$855$	0	0
$856$	−5.31385e15	−0.395188
$857$	−7.60811e15	−0.562189	−0.281094	−	0.959680i	$-0.590697\pi$
$857$	−7.60811e15	−0.562189	−0.281094	+	0.959680i	$0.590697\pi$
$858$	−6.59941e15	−0.484535
$859$	−4.89672e15	−0.357226	−0.178613	−	0.983919i	$-0.557161\pi$
$859$	−4.89672e15	−0.357226	−0.178613	+	0.983919i	$0.557161\pi$
$860$	0	0
$861$	4.49329e15	0.323628
$862$	−2.67964e15	−0.191773
$863$	−2.33733e16	−1.66212	−0.831058	−	0.556186i	$-0.812264\pi$
$863$	−2.33733e16	−1.66212	−0.831058	+	0.556186i	$0.812264\pi$
$864$	1.26981e15	0.0897249
$865$	0	0
$866$	3.17869e15	0.221769
$867$	1.45588e16	1.00930
$868$	2.57636e15	0.177479
$869$	7.78444e15	0.532867
$870$	0	0
$871$	−1.79153e13	−0.00121094
$872$	−5.09671e15	−0.342334
$873$	−6.23159e15	−0.415930
$874$	1.14361e16	0.758516
$875$	0	0
$876$	1.93450e15	0.126706
$877$	2.29255e16	1.49218	0.746089	−	0.665846i	$-0.231929\pi$
$877$	2.29255e16	1.49218	0.746089	+	0.665846i	$0.231929\pi$
$878$	−1.71385e16	−1.10855
$879$	4.63232e15	0.297755
$880$	0	0
$881$	−4.14708e15	−0.263254	−0.131627	−	0.991299i	$-0.542020\pi$
$881$	−4.14708e15	−0.263254	−0.131627	+	0.991299i	$0.542020\pi$
$882$	4.67630e15	0.295002
$883$	1.24171e15	0.0778461	0.0389231	−	0.999242i	$-0.487607\pi$
$883$	1.24171e15	0.0778461	0.0389231	+	0.999242i	$0.487607\pi$
$884$	4.65650e15	0.290117
$885$	0	0
$886$	−1.48776e16	−0.915478
$887$	7.53940e15	0.461060	0.230530	−	0.973065i	$-0.425954\pi$
$887$	7.53940e15	0.461060	0.230530	+	0.973065i	$0.425954\pi$
$888$	8.76387e15	0.532629
$889$	9.94412e15	0.600629
$890$	0	0
$891$	2.60406e16	1.55355
$892$	−8.04203e15	−0.476825
$893$	2.50413e16	1.47562
$894$	−2.03694e16	−1.19295
$895$	0	0
$896$	−8.41024e14	−0.0486535
$897$	−6.07865e15	−0.349501
$898$	1.62254e16	0.927207
$899$	2.08362e16	1.18342
$900$	0	0
$901$	−2.27297e15	−0.127528
$902$	7.38561e15	0.411861
$903$	−1.86550e16	−1.03398
$904$	−4.13762e15	−0.227942
$905$	0	0
$906$	7.98721e14	0.0434700
$907$	−1.84213e16	−0.996505	−0.498253	−	0.867032i	$-0.666025\pi$
$907$	−1.84213e16	−0.996505	−0.498253	+	0.867032i	$0.666025\pi$
$908$	−5.37430e15	−0.288968
$909$	3.69604e14	0.0197531
$910$	0	0
$911$	−1.91486e16	−1.01108	−0.505539	−	0.862804i	$-0.668706\pi$
$911$	−1.91486e16	−1.01108	−0.505539	+	0.862804i	$0.668706\pi$
$912$	−1.01122e16	−0.530729
$913$	1.56377e16	0.815802
$914$	−1.61711e16	−0.838562
$915$	0	0
$916$	2.60968e15	0.133709
$917$	1.14404e16	0.582654
$918$	−9.50685e15	−0.481285
$919$	−2.24328e16	−1.12888	−0.564440	−	0.825474i	$-0.690908\pi$
$919$	−2.24328e16	−1.12888	−0.564440	+	0.825474i	$0.690908\pi$
$920$	0	0
$921$	−3.50991e16	−1.74529
$922$	−2.29303e16	−1.13342
$923$	−1.40469e16	−0.690192
$924$	−8.92384e15	−0.435869
$925$	0	0
$926$	3.59543e15	0.173536
$927$	−8.52965e15	−0.409254
$928$	−6.80173e15	−0.324419
$929$	−3.69311e16	−1.75108	−0.875540	−	0.483145i	$-0.839494\pi$
$929$	−3.69311e16	−1.75108	−0.875540	+	0.483145i	$0.839494\pi$
$930$	0	0
$931$	2.49762e16	1.17031
$932$	1.32345e16	0.616483
$933$	−1.13795e16	−0.526956
$934$	−7.07380e15	−0.325646
$935$	0	0
$936$	2.01257e15	0.0915660
$937$	−2.97721e15	−0.134661	−0.0673306	−	0.997731i	$-0.521448\pi$
$937$	−2.97721e15	−0.134661	−0.0673306	+	0.997731i	$0.521448\pi$
$938$	−2.42254e13	−0.00108932
$939$	1.51331e16	0.676501
$940$	0	0
$941$	−1.24483e16	−0.550004	−0.275002	−	0.961444i	$-0.588679\pi$
$941$	−1.24483e16	−0.550004	−0.275002	+	0.961444i	$0.588679\pi$
$942$	1.91657e16	0.841871
$943$	6.80281e15	0.297081
$944$	−2.59509e15	−0.112669
$945$	0	0
$946$	−3.06633e16	−1.31588
$947$	−3.25711e16	−1.38966	−0.694829	−	0.719175i	$-0.744520\pi$
$947$	−3.25711e16	−1.38966	−0.694829	+	0.719175i	$0.744520\pi$
$948$	−6.34010e15	−0.268937
$949$	−2.05637e15	−0.0867234
$950$	0	0
$951$	5.65948e16	2.35930
$952$	6.29661e15	0.260978
$953$	−8.18081e15	−0.337121	−0.168560	−	0.985691i	$-0.553912\pi$
$953$	−8.18081e15	−0.337121	−0.168560	+	0.985691i	$0.553912\pi$
$954$	−9.82392e14	−0.0402503
$955$	0	0
$956$	−3.11957e15	−0.126350
$957$	−7.21710e16	−2.90634
$958$	2.95553e16	1.18338
$959$	−1.44120e16	−0.573748
$960$	0	0
$961$	−1.48428e16	−0.584169
$962$	−9.31594e15	−0.364556
$963$	1.71948e16	0.669043
$964$	−1.55010e16	−0.599701
$965$	0	0
$966$	−8.21966e15	−0.314398
$967$	2.01660e16	0.766961	0.383480	−	0.923549i	$-0.374725\pi$
$967$	2.01660e16	0.766961	0.383480	+	0.923549i	$0.374725\pi$
$968$	−5.31900e15	−0.201148
$969$	7.57081e16	2.84683
$970$	0	0
$971$	−2.84728e16	−1.05858	−0.529291	−	0.848440i	$-0.677542\pi$
$971$	−2.84728e16	−1.05858	−0.529291	+	0.848440i	$0.677542\pi$
$972$	−1.43443e16	−0.530292
$973$	−5.83058e15	−0.214334
$974$	1.46747e16	0.536407
$975$	0	0
$976$	9.60793e13	0.00347261
$977$	−1.91832e15	−0.0689448	−0.0344724	−	0.999406i	$-0.510975\pi$
$977$	−1.91832e15	−0.0689448	−0.0344724	+	0.999406i	$0.510975\pi$
$978$	−2.16235e16	−0.772790
$979$	6.84974e16	2.43427
$980$	0	0
$981$	1.64922e16	0.579562
$982$	7.27472e15	0.254216
$983$	−2.65744e16	−0.923463	−0.461732	−	0.887020i	$-0.652772\pi$
$983$	−2.65744e16	−0.923463	−0.461732	+	0.887020i	$0.652772\pi$
$984$	−6.01527e15	−0.207865
$985$	0	0
$986$	5.09234e16	1.74018
$987$	−1.79983e16	−0.611629
$988$	1.07492e16	0.363255
$989$	−2.82436e16	−0.949164
$990$	0	0
$991$	−4.40916e16	−1.46538	−0.732690	−	0.680562i	$-0.761736\pi$
$991$	−4.40916e16	−1.46538	−0.732690	+	0.680562i	$0.761736\pi$
$992$	−3.44903e15	−0.113994
$993$	−6.56303e16	−2.15717
$994$	−1.89944e16	−0.620870
$995$	0	0
$996$	−1.27363e16	−0.411734
$997$	3.52203e16	1.13232	0.566161	−	0.824295i	$-0.308428\pi$
$997$	3.52203e16	1.13232	0.566161	+	0.824295i	$0.308428\pi$
$998$	1.98432e16	0.634444
$999$	1.90197e16	0.604774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.12.a.i.1.3		3
5.2	odd	4		10.12.b.a.9.1	✓	6
5.3	odd	4		10.12.b.a.9.6	yes	6
5.4	even	2		50.12.a.j.1.1		3
15.2	even	4		90.12.c.b.19.5		6
15.8	even	4		90.12.c.b.19.2		6
20.3	even	4		80.12.c.c.49.2		6
20.7	even	4		80.12.c.c.49.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.b.a.9.1	✓	6	5.2	odd	4
10.12.b.a.9.6	yes	6	5.3	odd	4
50.12.a.i.1.3		3	1.1	even	1	trivial
50.12.a.j.1.1		3	5.4	even	2
80.12.c.c.49.2		6	20.3	even	4
80.12.c.c.49.5		6	20.7	even	4
90.12.c.b.19.2		6	15.8	even	4
90.12.c.b.19.5		6	15.2	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q-32.0000 q^{2} +532.146 q^{3} +1024.00 q^{4} -17028.7 q^{6} +24477.0 q^{7} -32768.0 q^{8} +106033. q^{9} -669055. q^{11} +544918. q^{12} -579245. q^{13} -783265. q^{14} +1.04858e6 q^{16} -7.85051e6 q^{17} -3.39304e6 q^{18} -1.81223e7 q^{19} +1.30254e7 q^{21} +2.14098e7 q^{22} +1.97203e7 q^{23} -1.74374e7 q^{24} +1.85358e7 q^{26} -3.78433e7 q^{27} +2.50645e7 q^{28} +2.02707e8 q^{29} +1.02789e8 q^{31} -3.35544e7 q^{32} -3.56035e8 q^{33} +2.51216e8 q^{34} +1.08577e8 q^{36} -5.02591e8 q^{37} +5.79913e8 q^{38} -3.08243e8 q^{39} +3.44964e8 q^{41} -4.16811e8 q^{42} -1.43221e9 q^{43} -6.85112e8 q^{44} -6.31051e8 q^{46} -1.38179e9 q^{47} +5.57996e8 q^{48} -1.37820e9 q^{49} -4.17762e9 q^{51} -5.93147e8 q^{52} +2.89531e8 q^{53} +1.21098e9 q^{54} -8.02063e8 q^{56} -9.64371e9 q^{57} -6.48664e9 q^{58} -2.47487e9 q^{59} +9.16284e7 q^{61} -3.28926e9 q^{62} +2.59536e9 q^{63} +1.07374e9 q^{64} +1.13931e10 q^{66} +3.09287e7 q^{67} -8.03893e9 q^{68} +1.04941e10 q^{69} +2.42503e10 q^{71} -3.47448e9 q^{72} +3.55008e9 q^{73} +1.60829e10 q^{74} -1.85572e10 q^{76} -1.63765e10 q^{77} +9.86377e9 q^{78} -1.16350e10 q^{79} -3.89215e10 q^{81} -1.10389e10 q^{82} -2.33729e10 q^{83} +1.33380e10 q^{84} +4.58307e10 q^{86} +1.07870e11 q^{87} +2.19236e10 q^{88} -1.02379e11 q^{89} -1.41782e10 q^{91} +2.01936e10 q^{92} +5.46989e10 q^{93} +4.42174e10 q^{94} -1.78559e10 q^{96} -5.87705e10 q^{97} +4.41025e10 q^{98} -7.09416e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 96 q^{2} - 266 q^{3} + 3072 q^{4} + 8512 q^{6} - 33218 q^{7} - 98304 q^{8} + 248011 q^{9} - 321364 q^{11} - 272384 q^{12} - 1394556 q^{13} + 1062976 q^{14} + 3145728 q^{16} - 3520128 q^{17} - 7936352 q^{18}+ \cdots - 260390562868 q^{99}+O(q^{100}) \) 3 * q - 96 * q^2 - 266 * q^3 + 3072 * q^4 + 8512 * q^6 - 33218 * q^7 - 98304 * q^8 + 248011 * q^9 - 321364 * q^11 - 272384 * q^12 - 1394556 * q^13 + 1062976 * q^14 + 3145728 * q^16 - 3520128 * q^17 - 7936352 * q^18 + 12054540 * q^19 + 62735596 * q^21 + 10283648 * q^22 + 46190754 * q^23 + 8716288 * q^24 + 44625792 * q^26 - 94987340 * q^27 - 34015232 * q^28 + 128204910 * q^29 + 229240896 * q^31 - 100663296 * q^32 - 226503592 * q^33 + 112644096 * q^34 + 253963264 * q^36 - 1002113948 * q^37 - 385745280 * q^38 - 659398968 * q^39 - 82384474 * q^41 - 2007539072 * q^42 - 1749934226 * q^43 - 329076736 * q^44 - 1478104128 * q^46 - 5277335658 * q^47 - 278921216 * q^48 + 337757079 * q^49 - 6530043584 * q^51 - 1428025344 * q^52 - 315194916 * q^53 + 3039594880 * q^54 + 1088487424 * q^56 - 21984280680 * q^57 - 4102557120 * q^58 - 8831981180 * q^59 - 2510396214 * q^61 - 7335708672 * q^62 - 22799454866 * q^63 + 3221225472 * q^64 + 7248114944 * q^66 - 31643371078 * q^67 - 3604611072 * q^68 - 11558506988 * q^69 + 28394209416 * q^71 - 8126824448 * q^72 + 1461795304 * q^73 + 32067646336 * q^74 + 12343848960 * q^76 + 13870520184 * q^77 + 21100766976 * q^78 - 1301275440 * q^79 - 3519953537 * q^81 + 2636303168 * q^82 + 13756798614 * q^83 + 64241250304 * q^84 + 55997895232 * q^86 + 142402696380 * q^87 + 10530455552 * q^88 - 124724206270 * q^89 - 92223383064 * q^91 + 47299332096 * q^92 + 105480959488 * q^93 + 168874741056 * q^94 + 8925478912 * q^96 + 123108208592 * q^97 - 10808226528 * q^98 - 260390562868 * q^99

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