LMFDB - Embedded newform 50.26.a.k.1.5

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			1.5
Root			$94661.8$ 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)

$f(q)$	$=$	\(q-4096.00 q^{2} +1.08018e6 q^{3} +1.67772e7 q^{4} -4.42443e9 q^{6} +5.43159e10 q^{7} -6.87195e10 q^{8} +3.19509e11 q^{9} -3.24375e12 q^{11} +1.81225e13 q^{12} +7.83357e13 q^{13} -2.22478e14 q^{14} +2.81475e14 q^{16} -4.33806e15 q^{17} -1.30871e15 q^{18} +8.87783e15 q^{19} +5.86711e16 q^{21} +1.32864e16 q^{22} +7.05451e16 q^{23} -7.42297e16 q^{24} -3.20863e17 q^{26} -5.70099e17 q^{27} +9.11269e17 q^{28} -1.11391e18 q^{29} +6.30227e18 q^{31} -1.15292e18 q^{32} -3.50385e18 q^{33} +1.77687e19 q^{34} +5.36047e18 q^{36} -1.55100e19 q^{37} -3.63636e19 q^{38} +8.46169e19 q^{39} -3.82653e19 q^{41} -2.40317e20 q^{42} +3.32618e20 q^{43} -5.44211e19 q^{44} -2.88953e20 q^{46} -1.01157e21 q^{47} +3.04045e20 q^{48} +1.60914e21 q^{49} -4.68591e21 q^{51} +1.31425e21 q^{52} +3.43480e21 q^{53} +2.33513e21 q^{54} -3.73256e21 q^{56} +9.58969e21 q^{57} +4.56259e21 q^{58} +4.09753e21 q^{59} +3.14378e22 q^{61} -2.58141e22 q^{62} +1.73544e22 q^{63} +4.72237e21 q^{64} +1.43518e22 q^{66} +1.01756e23 q^{67} -7.27806e22 q^{68} +7.62017e22 q^{69} +2.10284e23 q^{71} -2.19565e22 q^{72} +1.56829e23 q^{73} +6.35289e22 q^{74} +1.48945e23 q^{76} -1.76187e23 q^{77} -3.46591e23 q^{78} +6.00925e22 q^{79} -8.86528e23 q^{81} +1.56735e23 q^{82} -7.40331e23 q^{83} +9.84338e23 q^{84} -1.36240e24 q^{86} -1.20323e24 q^{87} +2.22909e23 q^{88} +3.21148e24 q^{89} +4.25487e24 q^{91} +1.18355e24 q^{92} +6.80761e24 q^{93} +4.14341e24 q^{94} -1.24537e24 q^{96} -5.32805e24 q^{97} -6.59105e24 q^{98} -1.03641e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.08018e6	1.17350	0.586749	−	0.809769i	$-0.300408\pi$
$3$	1.08018e6	1.17350	0.586749	+	0.809769i	$0.300408\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−4.42443e9	−0.829788
$7$	5.43159e10	1.48320	0.741602	−	0.670840i	$-0.234066\pi$
$7$	5.43159e10	1.48320	0.741602	+	0.670840i	$0.234066\pi$
$8$	−6.87195e10	−0.353553
$9$	3.19509e11	0.377095
$10$	0	0
$11$	−3.24375e12	−0.311630	−0.155815	−	0.987786i	$-0.549800\pi$
$11$	−3.24375e12	−0.311630	−0.155815	+	0.987786i	$0.549800\pi$
$12$	1.81225e13	0.586749
$13$	7.83357e13	0.932541	0.466270	−	0.884642i	$-0.345597\pi$
$13$	7.83357e13	0.932541	0.466270	+	0.884642i	$0.345597\pi$
$14$	−2.22478e14	−1.04878
$15$	0	0
$16$	2.81475e14	0.250000
$17$	−4.33806e15	−1.80586	−0.902931	−	0.429786i	$-0.858589\pi$
$17$	−4.33806e15	−1.80586	−0.902931	+	0.429786i	$0.858589\pi$
$18$	−1.30871e15	−0.266647
$19$	8.87783e15	0.920210	0.460105	−	0.887865i	$-0.347812\pi$
$19$	8.87783e15	0.920210	0.460105	+	0.887865i	$0.347812\pi$
$20$	0	0
$21$	5.86711e16	1.74054
$22$	1.32864e16	0.220355
$23$	7.05451e16	0.671227	0.335613	−	0.942000i	$-0.391056\pi$
$23$	7.05451e16	0.671227	0.335613	+	0.942000i	$0.391056\pi$
$24$	−7.42297e16	−0.414894
$25$	0	0
$26$	−3.20863e17	−0.659406
$27$	−5.70099e17	−0.730977
$28$	9.11269e17	0.741602
$29$	−1.11391e18	−0.584624	−0.292312	−	0.956323i	$-0.594425\pi$
$29$	−1.11391e18	−0.584624	−0.292312	+	0.956323i	$0.594425\pi$
$30$	0	0
$31$	6.30227e18	1.43706	0.718532	−	0.695494i	$-0.244815\pi$
$31$	6.30227e18	1.43706	0.718532	+	0.695494i	$0.244815\pi$
$32$	−1.15292e18	−0.176777
$33$	−3.50385e18	−0.365696
$34$	1.77687e19	1.27694
$35$	0	0
$36$	5.36047e18	0.188548
$37$	−1.55100e19	−0.387338	−0.193669	−	0.981067i	$-0.562039\pi$
$37$	−1.55100e19	−0.387338	−0.193669	+	0.981067i	$0.562039\pi$
$38$	−3.63636e19	−0.650687
$39$	8.46169e19	1.09433
$40$	0	0
$41$	−3.82653e19	−0.264854	−0.132427	−	0.991193i	$-0.542277\pi$
$41$	−3.82653e19	−0.264854	−0.132427	+	0.991193i	$0.542277\pi$
$42$	−2.40317e20	−1.23075
$43$	3.32618e20	1.26937	0.634687	−	0.772770i	$-0.281129\pi$
$43$	3.32618e20	1.26937	0.634687	+	0.772770i	$0.281129\pi$
$44$	−5.44211e19	−0.155815
$45$	0	0
$46$	−2.88953e20	−0.474629
$47$	−1.01157e21	−1.26992	−0.634958	−	0.772547i	$-0.718982\pi$
$47$	−1.01157e21	−1.26992	−0.634958	+	0.772547i	$0.718982\pi$
$48$	3.04045e20	0.293374
$49$	1.60914e21	1.19990
$50$	0	0
$51$	−4.68591e21	−2.11917
$52$	1.31425e21	0.466270
$53$	3.43480e21	0.960401	0.480201	−	0.877159i	$-0.340564\pi$
$53$	3.43480e21	0.960401	0.480201	+	0.877159i	$0.340564\pi$
$54$	2.33513e21	0.516879
$55$	0	0
$56$	−3.73256e21	−0.524392
$57$	9.58969e21	1.07986
$58$	4.56259e21	0.413392
$59$	4.09753e21	0.299828	0.149914	−	0.988699i	$-0.452100\pi$
$59$	4.09753e21	0.299828	0.149914	+	0.988699i	$0.452100\pi$
$60$	0	0
$61$	3.14378e22	1.51646	0.758228	−	0.651990i	$-0.226065\pi$
$61$	3.14378e22	1.51646	0.758228	+	0.651990i	$0.226065\pi$
$62$	−2.58141e22	−1.01616
$63$	1.73544e22	0.559310
$64$	4.72237e21	0.125000
$65$	0	0
$66$	1.43518e22	0.258586
$67$	1.01756e23	1.51923	0.759616	−	0.650372i	$-0.225387\pi$
$67$	1.01756e23	1.51923	0.759616	+	0.650372i	$0.225387\pi$
$68$	−7.27806e22	−0.902931
$69$	7.62017e22	0.787682
$70$	0	0
$71$	2.10284e23	1.52081	0.760407	−	0.649446i	$-0.224999\pi$
$71$	2.10284e23	1.52081	0.760407	+	0.649446i	$0.224999\pi$
$72$	−2.19565e22	−0.133323
$73$	1.56829e23	0.801478	0.400739	−	0.916192i	$-0.368753\pi$
$73$	1.56829e23	0.801478	0.400739	+	0.916192i	$0.368753\pi$
$74$	6.35289e22	0.273889
$75$	0	0
$76$	1.48945e23	0.460105
$77$	−1.76187e23	−0.462211
$78$	−3.46591e23	−0.773811
$79$	6.00925e22	0.114415	0.0572073	−	0.998362i	$-0.481780\pi$
$79$	6.00925e22	0.114415	0.0572073	+	0.998362i	$0.481780\pi$
$80$	0	0
$81$	−8.86528e23	−1.23489
$82$	1.56735e23	0.187280
$83$	−7.40331e23	−0.760238	−0.380119	−	0.924938i	$-0.624117\pi$
$83$	−7.40331e23	−0.760238	−0.380119	+	0.924938i	$0.624117\pi$
$84$	9.84338e23	0.870268
$85$	0	0
$86$	−1.36240e24	−0.897583
$87$	−1.20323e24	−0.686055
$88$	2.22909e23	0.110178
$89$	3.21148e24	1.37826	0.689128	−	0.724640i	$-0.257994\pi$
$89$	3.21148e24	1.37826	0.689128	+	0.724640i	$0.257994\pi$
$90$	0	0
$91$	4.25487e24	1.38315
$92$	1.18355e24	0.335613
$93$	6.80761e24	1.68639
$94$	4.14341e24	0.897966
$95$	0	0
$96$	−1.24537e24	−0.207447
$97$	−5.32805e24	−0.779689	−0.389844	−	0.920881i	$-0.627471\pi$
$97$	−5.32805e24	−0.779689	−0.389844	+	0.920881i	$0.627471\pi$
$98$	−6.59105e24	−0.848455
$99$	−1.03641e24	−0.117514
$100$	0	0
$101$	−9.97515e24	−0.880851	−0.440425	−	0.897789i	$-0.645172\pi$
$101$	−9.97515e24	−0.880851	−0.440425	+	0.897789i	$0.645172\pi$
$102$	1.91935e25	1.49848
$103$	−6.46906e24	−0.447070	−0.223535	−	0.974696i	$-0.571760\pi$
$103$	−6.46906e24	−0.447070	−0.223535	+	0.974696i	$0.571760\pi$
$104$	−5.38319e24	−0.329703
$105$	0	0
$106$	−1.40689e25	−0.679106
$107$	−2.37528e25	−1.01957	−0.509786	−	0.860302i	$-0.670275\pi$
$107$	−2.37528e25	−1.01957	−0.509786	+	0.860302i	$0.670275\pi$
$108$	−9.56468e24	−0.365488
$109$	−4.56311e25	−1.55393	−0.776963	−	0.629547i	$-0.783241\pi$
$109$	−4.56311e25	−1.55393	−0.776963	+	0.629547i	$0.783241\pi$
$110$	0	0
$111$	−1.67536e25	−0.454540
$112$	1.52886e25	0.370801
$113$	4.40956e25	0.957005	0.478503	−	0.878086i	$-0.341180\pi$
$113$	4.40956e25	0.957005	0.478503	+	0.878086i	$0.341180\pi$
$114$	−3.92794e25	−0.763579
$115$	0	0
$116$	−1.86884e25	−0.292312
$117$	2.50289e25	0.351657
$118$	−1.67835e25	−0.212011
$119$	−2.35626e26	−2.67846
$120$	0	0
$121$	−9.78251e25	−0.902887
$122$	−1.28769e26	−1.07230
$123$	−4.13335e25	−0.310805
$124$	1.05735e26	0.718532
$125$	0	0
$126$	−7.10836e25	−0.395492
$127$	3.54526e26	1.78691	0.893453	−	0.449157i	$-0.148276\pi$
$127$	3.54526e26	1.78691	0.893453	+	0.449157i	$0.148276\pi$
$128$	−1.93428e25	−0.0883883
$129$	3.59288e26	1.48961
$130$	0	0
$131$	−3.11451e26	−1.06537	−0.532683	−	0.846315i	$-0.678816\pi$
$131$	−3.11451e26	−1.06537	−0.532683	+	0.846315i	$0.678816\pi$
$132$	−5.87848e25	−0.182848
$133$	4.82207e26	1.36486
$134$	−4.16792e26	−1.07426
$135$	0	0
$136$	2.98110e26	0.638468
$137$	−4.08877e26	−0.799072	−0.399536	−	0.916718i	$-0.630829\pi$
$137$	−4.08877e26	−0.799072	−0.399536	+	0.916718i	$0.630829\pi$
$138$	−3.12122e26	−0.556976
$139$	2.66018e26	0.433737	0.216869	−	0.976201i	$-0.430416\pi$
$139$	2.66018e26	0.433737	0.216869	+	0.976201i	$0.430416\pi$
$140$	0	0
$141$	−1.09269e27	−1.49024
$142$	−8.61322e26	−1.07538
$143$	−2.54101e26	−0.290607
$144$	8.99337e25	0.0942739
$145$	0	0
$146$	−6.42373e26	−0.566730
$147$	1.73817e27	1.40807
$148$	−2.60214e26	−0.193669
$149$	−1.37183e26	−0.0938579	−0.0469290	−	0.998898i	$-0.514943\pi$
$149$	−1.37183e26	−0.0938579	−0.0469290	+	0.998898i	$0.514943\pi$
$150$	0	0
$151$	2.28415e27	1.32286	0.661428	−	0.750009i	$-0.269951\pi$
$151$	2.28415e27	1.32286	0.661428	+	0.750009i	$0.269951\pi$
$152$	−6.10080e26	−0.325343
$153$	−1.38605e27	−0.680982
$154$	7.21662e26	0.326832
$155$	0	0
$156$	1.41964e27	0.547167
$157$	5.56736e26	0.198109	0.0990544	−	0.995082i	$-0.468418\pi$
$157$	5.56736e26	0.198109	0.0990544	+	0.995082i	$0.468418\pi$
$158$	−2.46139e26	−0.0809034
$159$	3.71021e27	1.12703
$160$	0	0
$161$	3.83172e27	0.995566
$162$	3.63122e27	0.873202
$163$	6.45827e27	1.43804	0.719020	−	0.694990i	$-0.244591\pi$
$163$	6.45827e27	1.43804	0.719020	+	0.694990i	$0.244591\pi$
$164$	−6.41985e26	−0.132427
$165$	0	0
$166$	3.03239e27	0.537569
$167$	9.17351e26	0.150862	0.0754310	−	0.997151i	$-0.475967\pi$
$167$	9.17351e26	0.150862	0.0754310	+	0.997151i	$0.475967\pi$
$168$	−4.03185e27	−0.615373
$169$	−9.19932e26	−0.130368
$170$	0	0
$171$	2.83654e27	0.347007
$172$	5.58040e27	0.634687
$173$	1.13072e28	1.19614	0.598068	−	0.801445i	$-0.295935\pi$
$173$	1.13072e28	1.19614	0.598068	+	0.801445i	$0.295935\pi$
$174$	4.92844e27	0.485114
$175$	0	0
$176$	−9.13034e26	−0.0779074
$177$	4.42609e27	0.351847
$178$	−1.31542e28	−0.974574
$179$	−3.61567e27	−0.249762	−0.124881	−	0.992172i	$-0.539855\pi$
$179$	−3.61567e27	−0.249762	−0.124881	+	0.992172i	$0.539855\pi$
$180$	0	0
$181$	−1.10646e28	−0.665201	−0.332601	−	0.943068i	$-0.607926\pi$
$181$	−1.10646e28	−0.665201	−0.332601	+	0.943068i	$0.607926\pi$
$182$	−1.74279e28	−0.978034
$183$	3.39587e28	1.77956
$184$	−4.84782e27	−0.237314
$185$	0	0
$186$	−2.78840e28	−1.19246
$187$	1.40716e28	0.562760
$188$	−1.69714e28	−0.634958
$189$	−3.09654e28	−1.08419
$190$	0	0
$191$	5.84877e27	0.179534	0.0897671	−	0.995963i	$-0.471388\pi$
$191$	5.84877e27	0.179534	0.0897671	+	0.995963i	$0.471388\pi$
$192$	5.10102e27	0.146687
$193$	−1.61649e28	−0.435620	−0.217810	−	0.975991i	$-0.569891\pi$
$193$	−1.61649e28	−0.435620	−0.217810	+	0.975991i	$0.569891\pi$
$194$	2.18237e28	0.551323
$195$	0	0
$196$	2.69969e28	0.599948
$197$	5.33679e28	1.11289	0.556445	−	0.830885i	$-0.312165\pi$
$197$	5.33679e28	1.11289	0.556445	+	0.830885i	$0.312165\pi$
$198$	4.24512e27	0.0830950
$199$	7.95288e27	0.146171	0.0730855	−	0.997326i	$-0.476715\pi$
$199$	7.95288e27	0.146171	0.0730855	+	0.997326i	$0.476715\pi$
$200$	0	0
$201$	1.09915e29	1.78281
$202$	4.08582e28	0.622855
$203$	−6.05032e28	−0.867118
$204$	−7.86165e28	−1.05959
$205$	0	0
$206$	2.64973e28	0.316127
$207$	2.25398e28	0.253116
$208$	2.20495e28	0.233135
$209$	−2.87975e28	−0.286765
$210$	0	0
$211$	−6.17913e28	−0.546257	−0.273128	−	0.961978i	$-0.588058\pi$
$211$	−6.17913e28	−0.546257	−0.273128	+	0.961978i	$0.588058\pi$
$212$	5.76263e28	0.480201
$213$	2.27145e29	1.78467
$214$	9.72914e28	0.720946
$215$	0	0
$216$	3.91769e28	0.258439
$217$	3.42313e29	2.13146
$218$	1.86905e29	1.09879
$219$	1.69404e29	0.940532
$220$	0	0
$221$	−3.39825e29	−1.68404
$222$	6.86229e28	0.321408
$223$	−3.94158e29	−1.74526	−0.872630	−	0.488382i	$-0.837587\pi$
$223$	−3.94158e29	−1.74526	−0.872630	+	0.488382i	$0.837587\pi$
$224$	−6.26219e28	−0.262196
$225$	0	0
$226$	−1.80615e29	−0.676705
$227$	1.43566e29	0.509012	0.254506	−	0.967071i	$-0.418087\pi$
$227$	1.43566e29	0.509012	0.254506	+	0.967071i	$0.418087\pi$
$228$	1.60888e29	0.539932
$229$	3.75130e29	1.19189	0.595947	−	0.803023i	$-0.296777\pi$
$229$	3.75130e29	1.19189	0.595947	+	0.803023i	$0.296777\pi$
$230$	0	0
$231$	−1.90314e29	−0.542403
$232$	7.65476e28	0.206696
$233$	4.51422e29	1.15514	0.577569	−	0.816342i	$-0.304001\pi$
$233$	4.51422e29	1.15514	0.577569	+	0.816342i	$0.304001\pi$
$234$	−1.02518e29	−0.248659
$235$	0	0
$236$	6.87452e28	0.149914
$237$	6.49109e28	0.134265
$238$	9.65123e29	1.89396
$239$	−1.77838e29	−0.331169	−0.165585	−	0.986196i	$-0.552951\pi$
$239$	−1.77838e29	−0.331169	−0.165585	+	0.986196i	$0.552951\pi$
$240$	0	0
$241$	−5.18328e28	−0.0869745	−0.0434872	−	0.999054i	$-0.513847\pi$
$241$	−5.18328e28	−0.0869745	−0.0434872	+	0.999054i	$0.513847\pi$
$242$	4.00692e29	0.638438
$243$	−4.74575e29	−0.718168
$244$	5.27439e29	0.758228
$245$	0	0
$246$	1.69302e29	0.219773
$247$	6.95451e29	0.858133
$248$	−4.33089e29	−0.508079
$249$	−7.99693e29	−0.892137
$250$	0	0
$251$	9.22037e29	0.930737	0.465368	−	0.885117i	$-0.345922\pi$
$251$	9.22037e29	0.930737	0.465368	+	0.885117i	$0.345922\pi$
$252$	2.91158e29	0.279655
$253$	−2.28831e29	−0.209174
$254$	−1.45214e30	−1.26353
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	2.62664e30	1.97350	0.986749	−	0.162254i	$-0.0518765\pi$
$257$	2.62664e30	1.97350	0.986749	+	0.162254i	$0.0518765\pi$
$258$	−1.47164e30	−1.05331
$259$	−8.42438e29	−0.574501
$260$	0	0
$261$	−3.55905e29	−0.220459
$262$	1.27570e30	0.753328
$263$	1.28488e30	0.723465	0.361732	−	0.932282i	$-0.382185\pi$
$263$	1.28488e30	0.723465	0.361732	+	0.932282i	$0.382185\pi$
$264$	2.40782e29	0.129293
$265$	0	0
$266$	−1.97512e30	−0.965102
$267$	3.46899e30	1.61738
$268$	1.70718e30	0.759616
$269$	−2.87870e30	−1.22262	−0.611312	−	0.791390i	$-0.709358\pi$
$269$	−2.87870e30	−1.22262	−0.611312	+	0.791390i	$0.709358\pi$
$270$	0	0
$271$	6.47478e29	0.250674	0.125337	−	0.992114i	$-0.459999\pi$
$271$	6.47478e29	0.250674	0.125337	+	0.992114i	$0.459999\pi$
$272$	−1.22106e30	−0.451465
$273$	4.59604e30	1.62312
$274$	1.67476e30	0.565029
$275$	0	0
$276$	1.27845e30	0.393841
$277$	−3.36035e30	−0.989436	−0.494718	−	0.869054i	$-0.664729\pi$
$277$	−3.36035e30	−0.989436	−0.494718	+	0.869054i	$0.664729\pi$
$278$	−1.08961e30	−0.306699
$279$	2.01363e30	0.541910
$280$	0	0
$281$	3.79608e30	0.934343	0.467172	−	0.884167i	$-0.345273\pi$
$281$	3.79608e30	0.934343	0.467172	+	0.884167i	$0.345273\pi$
$282$	4.47564e30	1.05376
$283$	−2.26117e30	−0.509334	−0.254667	−	0.967029i	$-0.581966\pi$
$283$	−2.26117e30	−0.509334	−0.254667	+	0.967029i	$0.581966\pi$
$284$	3.52798e30	0.760407
$285$	0	0
$286$	1.04080e30	0.205490
$287$	−2.07841e30	−0.392833
$288$	−3.68368e29	−0.0666617
$289$	1.30482e31	2.26114
$290$	0	0
$291$	−5.75527e30	−0.914962
$292$	2.63116e30	0.400739
$293$	8.20237e30	1.19700	0.598500	−	0.801123i	$-0.295764\pi$
$293$	8.20237e30	1.19700	0.598500	+	0.801123i	$0.295764\pi$
$294$	−7.11955e30	−0.995659
$295$	0	0
$296$	1.06584e30	0.136945
$297$	1.84926e30	0.227794
$298$	5.61900e29	0.0663676
$299$	5.52620e30	0.625946
$300$	0	0
$301$	1.80664e31	1.88274
$302$	−9.35588e30	−0.935401
$303$	−1.07750e31	−1.03368
$304$	2.49889e30	0.230052
$305$	0	0
$306$	5.67726e30	0.481527
$307$	1.16923e31	0.952072	0.476036	−	0.879426i	$-0.342073\pi$
$307$	1.16923e31	0.952072	0.476036	+	0.879426i	$0.342073\pi$
$308$	−2.95593e30	−0.231105
$309$	−6.98778e30	−0.524636
$310$	0	0
$311$	−9.75410e30	−0.675588	−0.337794	−	0.941220i	$-0.609681\pi$
$311$	−9.75410e30	−0.675588	−0.337794	+	0.941220i	$0.609681\pi$
$312$	−5.81483e30	−0.386905
$313$	2.13999e31	1.36807	0.684035	−	0.729449i	$-0.260224\pi$
$313$	2.13999e31	1.36807	0.684035	+	0.729449i	$0.260224\pi$
$314$	−2.28039e30	−0.140084
$315$	0	0
$316$	1.00818e30	0.0572073
$317$	2.87837e31	1.57002	0.785011	−	0.619482i	$-0.212657\pi$
$317$	2.87837e31	1.57002	0.785011	+	0.619482i	$0.212657\pi$
$318$	−1.51970e31	−0.796929
$319$	3.61326e30	0.182186
$320$	0	0
$321$	−2.56574e31	−1.19646
$322$	−1.56947e31	−0.703972
$323$	−3.85126e31	−1.66177
$324$	−1.48735e31	−0.617447
$325$	0	0
$326$	−2.64531e31	−1.01685
$327$	−4.92900e31	−1.82353
$328$	2.62957e30	0.0936400
$329$	−5.49445e31	−1.88354
$330$	0	0
$331$	7.95904e30	0.252936	0.126468	−	0.991971i	$-0.459636\pi$
$331$	7.95904e30	0.252936	0.126468	+	0.991971i	$0.459636\pi$
$332$	−1.24207e31	−0.380119
$333$	−4.95557e30	−0.146063
$334$	−3.75747e30	−0.106675
$335$	0	0
$336$	1.65144e31	0.435134
$337$	−5.91626e31	−1.50201	−0.751006	−	0.660295i	$-0.770431\pi$
$337$	−5.91626e31	−1.50201	−0.751006	+	0.660295i	$0.770431\pi$
$338$	3.76804e30	0.0921842
$339$	4.76313e31	1.12304
$340$	0	0
$341$	−2.04430e31	−0.447832
$342$	−1.16185e31	−0.245371
$343$	1.45607e31	0.296487
$344$	−2.28573e31	−0.448791
$345$	0	0
$346$	−4.63145e31	−0.845796
$347$	2.62292e31	0.462026	0.231013	−	0.972951i	$-0.425796\pi$
$347$	2.62292e31	0.462026	0.231013	+	0.972951i	$0.425796\pi$
$348$	−2.01869e31	−0.343028
$349$	6.42126e31	1.05269	0.526347	−	0.850270i	$-0.323561\pi$
$349$	6.42126e31	1.05269	0.526347	+	0.850270i	$0.323561\pi$
$350$	0	0
$351$	−4.46591e31	−0.681665
$352$	3.73979e30	0.0550889
$353$	3.67958e31	0.523136	0.261568	−	0.965185i	$-0.415760\pi$
$353$	3.67958e31	0.523136	0.261568	+	0.965185i	$0.415760\pi$
$354$	−1.81293e31	−0.248794
$355$	0	0
$356$	5.38797e31	0.689128
$357$	−2.54519e32	−3.14317
$358$	1.48098e31	0.176608
$359$	−1.54521e32	−1.77953	−0.889766	−	0.456418i	$-0.849132\pi$
$359$	−1.54521e32	−1.77953	−0.889766	+	0.456418i	$0.849132\pi$
$360$	0	0
$361$	−1.42606e31	−0.153214
$362$	4.53205e31	0.470368
$363$	−1.05669e32	−1.05954
$364$	7.13849e31	0.691574
$365$	0	0
$366$	−1.39095e32	−1.25834
$367$	−3.45113e31	−0.301742	−0.150871	−	0.988553i	$-0.548208\pi$
$367$	−3.45113e31	−0.301742	−0.150871	+	0.988553i	$0.548208\pi$
$368$	1.98567e31	0.167807
$369$	−1.22261e31	−0.0998752
$370$	0	0
$371$	1.86564e32	1.42447
$372$	1.14213e32	0.843195
$373$	−5.25010e31	−0.374807	−0.187403	−	0.982283i	$-0.560007\pi$
$373$	−5.25010e31	−0.374807	−0.187403	+	0.982283i	$0.560007\pi$
$374$	−5.76372e31	−0.397931
$375$	0	0
$376$	6.95149e31	0.448983
$377$	−8.72593e31	−0.545186
$378$	1.26834e32	0.766637
$379$	3.14351e32	1.83834	0.919169	−	0.393864i	$-0.128862\pi$
$379$	3.14351e32	1.83834	0.919169	+	0.393864i	$0.128862\pi$
$380$	0	0
$381$	3.82953e32	2.09693
$382$	−2.39566e31	−0.126950
$383$	−2.45971e32	−1.26154	−0.630768	−	0.775972i	$-0.717260\pi$
$383$	−2.45971e32	−1.26154	−0.630768	+	0.775972i	$0.717260\pi$
$384$	−2.08938e31	−0.103723
$385$	0	0
$386$	6.62116e31	0.308030
$387$	1.06274e32	0.478675
$388$	−8.93898e31	−0.389844
$389$	2.32919e32	0.983638	0.491819	−	0.870698i	$-0.336332\pi$
$389$	2.32919e32	0.983638	0.491819	+	0.870698i	$0.336332\pi$
$390$	0	0
$391$	−3.06029e32	−1.21214
$392$	−1.10579e32	−0.424227
$393$	−3.36425e32	−1.25020
$394$	−2.18595e32	−0.786932
$395$	0	0
$396$	−1.73880e31	−0.0587571
$397$	−2.38017e32	−0.779338	−0.389669	−	0.920955i	$-0.627411\pi$
$397$	−2.38017e32	−0.779338	−0.389669	+	0.920955i	$0.627411\pi$
$398$	−3.25750e31	−0.103358
$399$	5.20872e32	1.60166
$400$	0	0
$401$	5.61815e32	1.62289	0.811444	−	0.584430i	$-0.198682\pi$
$401$	5.61815e32	1.62289	0.811444	+	0.584430i	$0.198682\pi$
$402$	−4.50212e32	−1.26064
$403$	4.93693e32	1.34012
$404$	−1.67355e32	−0.440425
$405$	0	0
$406$	2.47821e32	0.613145
$407$	5.03105e31	0.120706
$408$	3.22013e32	0.749241
$409$	−3.90144e32	−0.880408	−0.440204	−	0.897898i	$-0.645094\pi$
$409$	−3.90144e32	−0.880408	−0.440204	+	0.897898i	$0.645094\pi$
$410$	0	0
$411$	−4.41662e32	−0.937708
$412$	−1.08533e32	−0.223535
$413$	2.22561e32	0.444707
$414$	−9.23229e31	−0.178980
$415$	0	0
$416$	−9.03149e31	−0.164851
$417$	2.87349e32	0.508989
$418$	1.17954e32	0.202773
$419$	5.77394e32	0.963378	0.481689	−	0.876342i	$-0.340023\pi$
$419$	5.77394e32	0.963378	0.481689	+	0.876342i	$0.340023\pi$
$420$	0	0
$421$	−9.43709e32	−1.48358	−0.741792	−	0.670630i	$-0.766024\pi$
$421$	−9.43709e32	−1.48358	−0.741792	+	0.670630i	$0.766024\pi$
$422$	2.53097e32	0.386262
$423$	−3.23207e32	−0.478879
$424$	−2.36037e32	−0.339553
$425$	0	0
$426$	−9.30386e32	−1.26195
$427$	1.70757e33	2.24921
$428$	−3.98506e32	−0.509786
$429$	−2.74476e32	−0.341027
$430$	0	0
$431$	3.90741e32	0.458061	0.229030	−	0.973419i	$-0.426444\pi$
$431$	3.90741e32	0.458061	0.229030	+	0.973419i	$0.426444\pi$
$432$	−1.60469e32	−0.182744
$433$	7.17692e32	0.794034	0.397017	−	0.917811i	$-0.370045\pi$
$433$	7.17692e32	0.794034	0.397017	+	0.917811i	$0.370045\pi$
$434$	−1.40211e33	−1.50717
$435$	0	0
$436$	−7.65564e32	−0.776963
$437$	6.26288e32	0.617669
$438$	−6.93881e32	−0.665056
$439$	−4.73065e32	−0.440671	−0.220336	−	0.975424i	$-0.570715\pi$
$439$	−4.73065e32	−0.440671	−0.220336	+	0.975424i	$0.570715\pi$
$440$	0	0
$441$	5.14135e32	0.452475
$442$	1.39192e33	1.19080
$443$	1.16496e33	0.968871	0.484436	−	0.874827i	$-0.339025\pi$
$443$	1.16496e33	0.968871	0.484436	+	0.874827i	$0.339025\pi$
$444$	−2.81079e32	−0.227270
$445$	0	0
$446$	1.61447e33	1.23408
$447$	−1.48183e32	−0.110142
$448$	2.56499e32	0.185401
$449$	−1.31459e33	−0.924082	−0.462041	−	0.886859i	$-0.652883\pi$
$449$	−1.31459e33	−0.924082	−0.462041	+	0.886859i	$0.652883\pi$
$450$	0	0
$451$	1.24123e32	0.0825363
$452$	7.39801e32	0.478503
$453$	2.46730e33	1.55237
$454$	−5.88046e32	−0.359926
$455$	0	0
$456$	−6.58999e32	−0.381789
$457$	−4.66527e32	−0.262981	−0.131490	−	0.991317i	$-0.541976\pi$
$457$	−4.66527e32	−0.262981	−0.131490	+	0.991317i	$0.541976\pi$
$458$	−1.53653e33	−0.842797
$459$	2.47313e33	1.32004
$460$	0	0
$461$	1.54013e33	0.778566	0.389283	−	0.921118i	$-0.372723\pi$
$461$	1.54013e33	0.778566	0.389283	+	0.921118i	$0.372723\pi$
$462$	7.79528e32	0.383537
$463$	−2.04979e33	−0.981628	−0.490814	−	0.871264i	$-0.663301\pi$
$463$	−2.04979e33	−0.981628	−0.490814	+	0.871264i	$0.663301\pi$
$464$	−3.13539e32	−0.146156
$465$	0	0
$466$	−1.84903e33	−0.816806
$467$	1.89201e33	0.813699	0.406849	−	0.913495i	$-0.366627\pi$
$467$	1.89201e33	0.813699	0.406849	+	0.913495i	$0.366627\pi$
$468$	4.19916e32	0.175828
$469$	5.52695e33	2.25333
$470$	0	0
$471$	6.01378e32	0.232480
$472$	−2.81580e32	−0.106005
$473$	−1.07893e33	−0.395574
$474$	−2.65875e32	−0.0949399
$475$	0	0
$476$	−3.95314e33	−1.33923
$477$	1.09745e33	0.362163
$478$	7.28423e32	0.234172
$479$	9.31244e32	0.291655	0.145828	−	0.989310i	$-0.453416\pi$
$479$	9.31244e32	0.291655	0.145828	+	0.989310i	$0.453416\pi$
$480$	0	0
$481$	−1.21499e33	−0.361208
$482$	2.12307e32	0.0615003
$483$	4.13896e33	1.16829
$484$	−1.64123e33	−0.451443
$485$	0	0
$486$	1.94386e33	0.507822
$487$	−1.90079e33	−0.483973	−0.241987	−	0.970280i	$-0.577799\pi$
$487$	−1.90079e33	−0.483973	−0.241987	+	0.970280i	$0.577799\pi$
$488$	−2.16039e33	−0.536148
$489$	6.97611e33	1.68754
$490$	0	0
$491$	−1.53089e32	−0.0351905	−0.0175953	−	0.999845i	$-0.505601\pi$
$491$	−1.53089e32	−0.0351905	−0.0175953	+	0.999845i	$0.505601\pi$
$492$	−6.93461e32	−0.155403
$493$	4.83223e33	1.05575
$494$	−2.84857e33	−0.606792
$495$	0	0
$496$	1.77393e33	0.359266
$497$	1.14217e34	2.25568
$498$	3.27554e33	0.630836
$499$	−3.99567e33	−0.750469	−0.375234	−	0.926930i	$-0.622438\pi$
$499$	−3.99567e33	−0.750469	−0.375234	+	0.926930i	$0.622438\pi$
$500$	0	0
$501$	9.90908e32	0.177036
$502$	−3.77666e33	−0.658130
$503$	−7.03745e33	−1.19623	−0.598116	−	0.801410i	$-0.704084\pi$
$503$	−7.03745e33	−1.19623	−0.598116	+	0.801410i	$0.704084\pi$
$504$	−1.19258e33	−0.197746
$505$	0	0
$506$	9.37291e32	0.147908
$507$	−9.93695e32	−0.152987
$508$	5.94796e33	0.893453
$509$	5.62123e32	0.0823870	0.0411935	−	0.999151i	$-0.486884\pi$
$509$	5.62123e32	0.0823870	0.0411935	+	0.999151i	$0.486884\pi$
$510$	0	0
$511$	8.51832e33	1.18876
$512$	−3.24519e32	−0.0441942
$513$	−5.06125e33	−0.672652
$514$	−1.07587e34	−1.39547
$515$	0	0
$516$	6.02785e33	0.744803
$517$	3.28129e33	0.395743
$518$	3.45063e33	0.406234
$519$	1.22139e34	1.40366
$520$	0	0
$521$	1.15250e34	1.26232	0.631162	−	0.775651i	$-0.282578\pi$
$521$	1.15250e34	1.26232	0.631162	+	0.775651i	$0.282578\pi$
$522$	1.45779e33	0.155888
$523$	−1.37858e34	−1.43933	−0.719663	−	0.694323i	$-0.755704\pi$
$523$	−1.37858e34	−1.43933	−0.719663	+	0.694323i	$0.755704\pi$
$524$	−5.22529e33	−0.532683
$525$	0	0
$526$	−5.26289e33	−0.511567
$527$	−2.73397e34	−2.59514
$528$	−9.86245e32	−0.0914241
$529$	−6.06915e33	−0.549455
$530$	0	0
$531$	1.30920e33	0.113064
$532$	8.09009e33	0.682430
$533$	−2.99754e33	−0.246987
$534$	−1.42090e34	−1.14366
$535$	0	0
$536$	−6.99260e33	−0.537129
$537$	−3.90559e33	−0.293095
$538$	1.17911e34	0.864525
$539$	−5.21966e33	−0.373923
$540$	0	0
$541$	−2.20638e34	−1.50909	−0.754543	−	0.656251i	$-0.772141\pi$
$541$	−2.20638e34	−1.50909	−0.754543	+	0.656251i	$0.772141\pi$
$542$	−2.65207e33	−0.177253
$543$	−1.19518e34	−0.780612
$544$	5.00145e33	0.319234
$545$	0	0
$546$	−1.88254e34	−1.14772
$547$	−1.59179e34	−0.948514	−0.474257	−	0.880387i	$-0.657283\pi$
$547$	−1.59179e34	−0.948514	−0.474257	+	0.880387i	$0.657283\pi$
$548$	−6.85982e33	−0.399536
$549$	1.00447e34	0.571849
$550$	0	0
$551$	−9.88915e33	−0.537977
$552$	−5.23654e33	−0.278488
$553$	3.26398e33	0.169700
$554$	1.37640e34	0.699637
$555$	0	0
$556$	4.46305e33	0.216869
$557$	−1.37117e34	−0.651479	−0.325739	−	0.945460i	$-0.605613\pi$
$557$	−1.37117e34	−0.651479	−0.325739	+	0.945460i	$0.605613\pi$
$558$	−8.24783e33	−0.383188
$559$	2.60558e34	1.18374
$560$	0	0
$561$	1.51999e34	0.660397
$562$	−1.55488e34	−0.660681
$563$	3.01185e34	1.25164	0.625818	−	0.779969i	$-0.284765\pi$
$563$	3.01185e34	1.25164	0.625818	+	0.779969i	$0.284765\pi$
$564$	−1.83322e34	−0.745121
$565$	0	0
$566$	9.26175e33	0.360153
$567$	−4.81525e34	−1.83160
$568$	−1.44506e34	−0.537689
$569$	1.37959e34	0.502166	0.251083	−	0.967966i	$-0.419213\pi$
$569$	1.37959e34	0.502166	0.251083	+	0.967966i	$0.419213\pi$
$570$	0	0
$571$	1.46730e34	0.511173	0.255587	−	0.966786i	$-0.417731\pi$
$571$	1.46730e34	0.511173	0.255587	+	0.966786i	$0.417731\pi$
$572$	−4.26311e33	−0.145304
$573$	6.31775e33	0.210683
$574$	8.51317e33	0.277775
$575$	0	0
$576$	1.50884e33	0.0471369
$577$	5.61780e34	1.71739	0.858694	−	0.512488i	$-0.171276\pi$
$577$	5.61780e34	1.71739	0.858694	+	0.512488i	$0.171276\pi$
$578$	−5.34453e34	−1.59886
$579$	−1.74611e34	−0.511199
$580$	0	0
$581$	−4.02117e34	−1.12759
$582$	2.35736e34	0.646976
$583$	−1.11416e34	−0.299290
$584$	−1.07772e34	−0.283365
$585$	0	0
$586$	−3.35969e34	−0.846407
$587$	−3.79085e34	−0.934889	−0.467444	−	0.884022i	$-0.654825\pi$
$587$	−3.79085e34	−0.934889	−0.467444	+	0.884022i	$0.654825\pi$
$588$	2.91617e34	0.704037
$589$	5.59505e34	1.32240
$590$	0	0
$591$	5.76471e34	1.30597
$592$	−4.36567e33	−0.0968344
$593$	−1.87221e34	−0.406604	−0.203302	−	0.979116i	$-0.565167\pi$
$593$	−1.87221e34	−0.406604	−0.203302	+	0.979116i	$0.565167\pi$
$594$	−7.57457e33	−0.161075
$595$	0	0
$596$	−2.30154e33	−0.0469290
$597$	8.59057e33	0.171531
$598$	−2.26353e34	−0.442611
$599$	−5.76089e34	−1.10320	−0.551601	−	0.834108i	$-0.685983\pi$
$599$	−5.76089e34	−1.10320	−0.551601	+	0.834108i	$0.685983\pi$
$600$	0	0
$601$	4.67680e34	0.859049	0.429525	−	0.903055i	$-0.358681\pi$
$601$	4.67680e34	0.859049	0.429525	+	0.903055i	$0.358681\pi$
$602$	−7.40000e34	−1.33130
$603$	3.25118e34	0.572895
$604$	3.83217e34	0.661428
$605$	0	0
$606$	4.41344e34	0.730919
$607$	−3.27875e33	−0.0531924	−0.0265962	−	0.999646i	$-0.508467\pi$
$607$	−3.27875e33	−0.0531924	−0.0265962	+	0.999646i	$0.508467\pi$
$608$	−1.02354e34	−0.162672
$609$	−6.53546e34	−1.01756
$610$	0	0
$611$	−7.92424e34	−1.18425
$612$	−2.32540e34	−0.340491
$613$	−3.82074e34	−0.548140	−0.274070	−	0.961710i	$-0.588370\pi$
$613$	−3.82074e34	−0.548140	−0.274070	+	0.961710i	$0.588370\pi$
$614$	−4.78916e34	−0.673216
$615$	0	0
$616$	1.21075e34	0.163416
$617$	8.69280e34	1.14973	0.574864	−	0.818249i	$-0.305055\pi$
$617$	8.69280e34	1.14973	0.574864	+	0.818249i	$0.305055\pi$
$618$	2.86219e34	0.370974
$619$	−3.61889e34	−0.459666	−0.229833	−	0.973230i	$-0.573818\pi$
$619$	−3.61889e34	−0.459666	−0.229833	+	0.973230i	$0.573818\pi$
$620$	0	0
$621$	−4.02177e34	−0.490651
$622$	3.99528e34	0.477713
$623$	1.74434e35	2.04424
$624$	2.38176e34	0.273583
$625$	0	0
$626$	−8.76542e34	−0.967372
$627$	−3.11066e34	−0.336517
$628$	9.34049e33	0.0990544
$629$	6.72833e34	0.699478
$630$	0	0
$631$	−6.79781e34	−0.679207	−0.339604	−	0.940569i	$-0.610293\pi$
$631$	−6.79781e34	−0.679207	−0.339604	+	0.940569i	$0.610293\pi$
$632$	−4.12953e33	−0.0404517
$633$	−6.67460e34	−0.641030
$634$	−1.17898e35	−1.11017
$635$	0	0
$636$	6.22470e34	0.563514
$637$	1.26053e35	1.11895
$638$	−1.47999e34	−0.128825
$639$	6.71875e34	0.573492
$640$	0	0
$641$	−8.90435e34	−0.730932	−0.365466	−	0.930825i	$-0.619090\pi$
$641$	−8.90435e34	−0.730932	−0.365466	+	0.930825i	$0.619090\pi$
$642$	1.05093e35	0.846028
$643$	−1.28997e35	−1.01846	−0.509230	−	0.860630i	$-0.670070\pi$
$643$	−1.28997e35	−1.01846	−0.509230	+	0.860630i	$0.670070\pi$
$644$	6.42856e34	0.497783
$645$	0	0
$646$	1.57748e35	1.17505
$647$	−1.39383e34	−0.101837	−0.0509186	−	0.998703i	$-0.516215\pi$
$647$	−1.39383e34	−0.101837	−0.0509186	+	0.998703i	$0.516215\pi$
$648$	6.09218e34	0.436601
$649$	−1.32914e34	−0.0934353
$650$	0	0
$651$	3.69761e35	2.50126
$652$	1.08352e35	0.719020
$653$	1.27030e35	0.826970	0.413485	−	0.910511i	$-0.364311\pi$
$653$	1.27030e35	0.826970	0.413485	+	0.910511i	$0.364311\pi$
$654$	2.01892e35	1.28943
$655$	0	0
$656$	−1.07707e34	−0.0662135
$657$	5.01083e34	0.302234
$658$	2.25053e35	1.33187
$659$	4.18479e34	0.243000	0.121500	−	0.992591i	$-0.461230\pi$
$659$	4.18479e34	0.243000	0.121500	+	0.992591i	$0.461230\pi$
$660$	0	0
$661$	−2.05843e34	−0.115085	−0.0575424	−	0.998343i	$-0.518326\pi$
$661$	−2.05843e34	−0.115085	−0.0575424	+	0.998343i	$0.518326\pi$
$662$	−3.26002e34	−0.178853
$663$	−3.67074e35	−1.97621
$664$	5.08751e34	0.268785
$665$	0	0
$666$	2.02980e34	0.103282
$667$	−7.85813e34	−0.392415
$668$	1.53906e34	0.0754310
$669$	−4.25764e35	−2.04806
$670$	0	0
$671$	−1.01976e35	−0.472573
$672$	−6.76432e34	−0.307686
$673$	1.99051e35	0.888741	0.444370	−	0.895843i	$-0.353427\pi$
$673$	1.99051e35	0.888741	0.444370	+	0.895843i	$0.353427\pi$
$674$	2.42330e35	1.06208
$675$	0	0
$676$	−1.54339e34	−0.0651841
$677$	3.44905e35	1.43002	0.715008	−	0.699116i	$-0.246423\pi$
$677$	3.44905e35	1.43002	0.715008	+	0.699116i	$0.246423\pi$
$678$	−1.95098e35	−0.794111
$679$	−2.89397e35	−1.15644
$680$	0	0
$681$	1.55078e35	0.597324
$682$	8.37345e34	0.316665
$683$	3.76388e35	1.39758	0.698791	−	0.715326i	$-0.253722\pi$
$683$	3.76388e35	1.39758	0.698791	+	0.715326i	$0.253722\pi$
$684$	4.75893e34	0.173503
$685$	0	0
$686$	−5.96407e34	−0.209648
$687$	4.05209e35	1.39869
$688$	9.36235e34	0.317343
$689$	2.69067e35	0.895613
$690$	0	0
$691$	−5.21059e35	−1.67268	−0.836338	−	0.548215i	$-0.815308\pi$
$691$	−5.21059e35	−1.67268	−0.836338	+	0.548215i	$0.815308\pi$
$692$	1.89704e35	0.598068
$693$	−5.62933e34	−0.174297
$694$	−1.07435e35	−0.326702
$695$	0	0
$696$	8.26855e34	0.242557
$697$	1.65997e35	0.478290
$698$	−2.63015e35	−0.744368
$699$	4.87619e35	1.35555
$700$	0	0
$701$	2.95057e35	0.791462	0.395731	−	0.918366i	$-0.370491\pi$
$701$	2.95057e35	0.791462	0.395731	+	0.918366i	$0.370491\pi$
$702$	1.82924e35	0.482010
$703$	−1.37695e35	−0.356432
$704$	−1.53182e34	−0.0389537
$705$	0	0
$706$	−1.50716e35	−0.369913
$707$	−5.41809e35	−1.30648
$708$	7.42575e34	0.175924
$709$	−6.60823e35	−1.53818	−0.769090	−	0.639141i	$-0.779290\pi$
$709$	−6.60823e35	−1.53818	−0.769090	+	0.639141i	$0.779290\pi$
$710$	0	0
$711$	1.92001e34	0.0431452
$712$	−2.20691e35	−0.487287
$713$	4.44595e35	0.964595
$714$	1.04251e36	2.22256
$715$	0	0
$716$	−6.06609e34	−0.124881
$717$	−1.92097e35	−0.388626
$718$	6.32916e35	1.25832
$719$	−5.66102e35	−1.10607	−0.553036	−	0.833157i	$-0.686531\pi$
$719$	−5.66102e35	−1.10607	−0.553036	+	0.833157i	$0.686531\pi$
$720$	0	0
$721$	−3.51373e35	−0.663097
$722$	5.84114e34	0.108339
$723$	−5.59890e34	−0.102064
$724$	−1.85633e35	−0.332601
$725$	0	0
$726$	4.32821e35	0.749205
$727$	−1.18938e35	−0.202368	−0.101184	−	0.994868i	$-0.532263\pi$
$727$	−1.18938e35	−0.202368	−0.101184	+	0.994868i	$0.532263\pi$
$728$	−2.92392e35	−0.489017
$729$	2.38517e35	0.392126
$730$	0	0
$731$	−1.44292e36	−2.29231
$732$	5.69732e35	0.889778
$733$	−2.75860e35	−0.423534	−0.211767	−	0.977320i	$-0.567922\pi$
$733$	−2.75860e35	−0.423534	−0.211767	+	0.977320i	$0.567922\pi$
$734$	1.41358e35	0.213364
$735$	0	0
$736$	−8.13330e34	−0.118657
$737$	−3.30070e35	−0.473438
$738$	5.00780e34	0.0706224
$739$	−7.44302e35	−1.03203	−0.516017	−	0.856579i	$-0.672586\pi$
$739$	−7.44302e35	−1.03203	−0.516017	+	0.856579i	$0.672586\pi$
$740$	0	0
$741$	7.51215e35	1.00702
$742$	−7.64166e35	−1.00725
$743$	−9.71605e35	−1.25930	−0.629651	−	0.776878i	$-0.716802\pi$
$743$	−9.71605e35	−1.25930	−0.629651	+	0.776878i	$0.716802\pi$
$744$	−4.67816e35	−0.596229
$745$	0	0
$746$	2.15044e35	0.265028
$747$	−2.36542e35	−0.286682
$748$	2.36082e35	0.281380
$749$	−1.29015e36	−1.51223
$750$	0	0
$751$	−3.81212e35	−0.432183	−0.216091	−	0.976373i	$-0.569331\pi$
$751$	−3.81212e35	−0.432183	−0.216091	+	0.976373i	$0.569331\pi$
$752$	−2.84733e35	−0.317479
$753$	9.95969e35	1.09222
$754$	3.57414e35	0.385505
$755$	0	0
$756$	−5.19514e35	−0.542094
$757$	−1.20614e35	−0.123794	−0.0618968	−	0.998083i	$-0.519715\pi$
$757$	−1.20614e35	−0.123794	−0.0618968	+	0.998083i	$0.519715\pi$
$758$	−1.28758e36	−1.29990
$759$	−2.47179e35	−0.245465
$760$	0	0
$761$	−1.39110e36	−1.33675	−0.668374	−	0.743825i	$-0.733010\pi$
$761$	−1.39110e36	−1.33675	−0.668374	+	0.743825i	$0.733010\pi$
$762$	−1.56858e36	−1.48275
$763$	−2.47849e36	−2.30479
$764$	9.81260e34	0.0897671
$765$	0	0
$766$	1.00750e36	0.892040
$767$	3.20983e35	0.279602
$768$	8.55810e34	0.0733436
$769$	5.62814e35	0.474554	0.237277	−	0.971442i	$-0.423745\pi$
$769$	5.62814e35	0.474554	0.237277	+	0.971442i	$0.423745\pi$
$770$	0	0
$771$	2.83726e36	2.31589
$772$	−2.71203e35	−0.217810
$773$	1.08729e36	0.859211	0.429605	−	0.903017i	$-0.358653\pi$
$773$	1.08729e36	0.859211	0.429605	+	0.903017i	$0.358653\pi$
$774$	−4.35299e35	−0.338474
$775$	0	0
$776$	3.66141e35	0.275662
$777$	−9.09988e35	−0.674175
$778$	−9.54037e35	−0.695537
$779$	−3.39713e35	−0.243721
$780$	0	0
$781$	−6.82108e35	−0.473931
$782$	1.25350e36	0.857114
$783$	6.35042e35	0.427347
$784$	4.52934e35	0.299974
$785$	0	0
$786$	1.37800e36	0.884028
$787$	−5.64847e35	−0.356654	−0.178327	−	0.983971i	$-0.557068\pi$
$787$	−5.64847e35	−0.356654	−0.178327	+	0.983971i	$0.557068\pi$
$788$	8.95364e35	0.556445
$789$	1.38791e36	0.848984
$790$	0	0
$791$	2.39509e36	1.41943
$792$	7.12213e34	0.0415475
$793$	2.46270e36	1.41416
$794$	9.74916e35	0.551075
$795$	0	0
$796$	1.33427e35	0.0730855
$797$	−2.16083e34	−0.0116517	−0.00582587	−	0.999983i	$-0.501854\pi$
$797$	−2.16083e34	−0.0116517	−0.00582587	+	0.999983i	$0.501854\pi$
$798$	−2.13349e36	−1.13254
$799$	4.38828e36	2.29329
$800$	0	0
$801$	1.02610e36	0.519734
$802$	−2.30119e36	−1.14756
$803$	−5.08715e35	−0.249764
$804$	1.84407e36	0.891407
$805$	0	0
$806$	−2.02217e36	−0.947608
$807$	−3.10952e36	−1.43474
$808$	6.85487e35	0.311428
$809$	−3.34498e36	−1.49637	−0.748183	−	0.663493i	$-0.769073\pi$
$809$	−3.34498e36	−1.49637	−0.748183	+	0.663493i	$0.769073\pi$
$810$	0	0
$811$	−3.06093e36	−1.32768	−0.663838	−	0.747876i	$-0.731074\pi$
$811$	−3.06093e36	−1.32768	−0.663838	+	0.747876i	$0.731074\pi$
$812$	−1.01508e36	−0.433559
$813$	6.99395e35	0.294165
$814$	−2.06072e35	−0.0853520
$815$	0	0
$816$	−1.31897e36	−0.529793
$817$	2.95292e36	1.16809
$818$	1.59803e36	0.622542
$819$	1.35947e36	0.521579
$820$	0	0
$821$	4.35079e36	1.61912	0.809559	−	0.587039i	$-0.199706\pi$
$821$	4.35079e36	1.61912	0.809559	+	0.587039i	$0.199706\pi$
$822$	1.80905e36	0.663060
$823$	−2.15419e35	−0.0777655	−0.0388827	−	0.999244i	$-0.512380\pi$
$823$	−2.15419e35	−0.0777655	−0.0388827	+	0.999244i	$0.512380\pi$
$824$	4.44550e35	0.158063
$825$	0	0
$826$	−9.11610e35	−0.314455
$827$	−1.29774e36	−0.440929	−0.220465	−	0.975395i	$-0.570757\pi$
$827$	−1.29774e36	−0.440929	−0.220465	+	0.975395i	$0.570757\pi$
$828$	3.78155e35	0.126558
$829$	2.45539e36	0.809447	0.404723	−	0.914439i	$-0.367368\pi$
$829$	2.45539e36	0.809447	0.404723	+	0.914439i	$0.367368\pi$
$830$	0	0
$831$	−3.62980e36	−1.16110
$832$	3.69930e35	0.116568
$833$	−6.98057e36	−2.16685
$834$	−1.17698e36	−0.359910
$835$	0	0
$836$	−4.83141e35	−0.143382
$837$	−3.59292e36	−1.05046
$838$	−2.36500e36	−0.681211
$839$	−4.28477e36	−1.21591	−0.607957	−	0.793970i	$-0.708011\pi$
$839$	−4.28477e36	−1.21591	−0.607957	+	0.793970i	$0.708011\pi$
$840$	0	0
$841$	−2.38956e36	−0.658214
$842$	3.86543e36	1.04905
$843$	4.10047e36	1.09645
$844$	−1.03669e36	−0.273128
$845$	0	0
$846$	1.32386e36	0.338619
$847$	−5.31346e36	−1.33917
$848$	9.66810e35	0.240100
$849$	−2.44248e36	−0.597702
$850$	0	0
$851$	−1.09415e36	−0.259991
$852$	3.81086e36	0.892336
$853$	−5.04634e36	−1.16443	−0.582215	−	0.813035i	$-0.697814\pi$
$853$	−5.04634e36	−1.16443	−0.582215	+	0.813035i	$0.697814\pi$
$854$	−6.99422e36	−1.59043
$855$	0	0
$856$	1.63228e36	0.360473
$857$	−1.55987e35	−0.0339491	−0.0169745	−	0.999856i	$-0.505403\pi$
$857$	−1.55987e35	−0.0339491	−0.0169745	+	0.999856i	$0.505403\pi$
$858$	1.12425e36	0.241142
$859$	−6.31632e36	−1.33521	−0.667605	−	0.744516i	$-0.732680\pi$
$859$	−6.31632e36	−1.33521	−0.667605	+	0.744516i	$0.732680\pi$
$860$	0	0
$861$	−2.24507e36	−0.460988
$862$	−1.60048e36	−0.323898
$863$	3.19641e36	0.637569	0.318785	−	0.947827i	$-0.396725\pi$
$863$	3.19641e36	0.637569	0.318785	+	0.947827i	$0.396725\pi$
$864$	6.57280e35	0.129220
$865$	0	0
$866$	−2.93967e36	−0.561467
$867$	1.40944e37	2.65344
$868$	5.74306e36	1.06573
$869$	−1.94925e35	−0.0356550
$870$	0	0
$871$	7.97111e36	1.41674
$872$	3.13575e36	0.549396
$873$	−1.70236e36	−0.294017
$874$	−2.56527e36	−0.436758
$875$	0	0
$876$	2.84214e36	0.470266
$877$	1.75514e36	0.286297	0.143148	−	0.989701i	$-0.454277\pi$
$877$	1.75514e36	0.286297	0.143148	+	0.989701i	$0.454277\pi$
$878$	1.93768e36	0.311602
$879$	8.86007e36	1.40468
$880$	0	0
$881$	−1.15533e36	−0.178035	−0.0890177	−	0.996030i	$-0.528373\pi$
$881$	−1.15533e36	−0.178035	−0.0890177	+	0.996030i	$0.528373\pi$
$882$	−2.10590e36	−0.319948
$883$	−2.62306e35	−0.0392916	−0.0196458	−	0.999807i	$-0.506254\pi$
$883$	−2.62306e35	−0.0392916	−0.0196458	+	0.999807i	$0.506254\pi$
$884$	−5.70132e36	−0.842020
$885$	0	0
$886$	−4.77170e36	−0.685096
$887$	1.26656e37	1.79299	0.896497	−	0.443049i	$-0.146103\pi$
$887$	1.26656e37	1.79299	0.896497	+	0.443049i	$0.146103\pi$
$888$	1.15130e36	0.160704
$889$	1.92564e37	2.65035
$890$	0	0
$891$	2.87568e36	0.384830
$892$	−6.61288e36	−0.872630
$893$	−8.98059e36	−1.16859
$894$	6.06956e35	0.0778822
$895$	0	0
$896$	−1.05062e36	−0.131098
$897$	5.96931e36	0.734546
$898$	5.38455e36	0.653424
$899$	−7.02019e36	−0.840142
$900$	0	0
$901$	−1.49004e37	−1.73435
$902$	−5.08408e35	−0.0583620
$903$	1.95150e37	2.20939
$904$	−3.03022e36	−0.338352
$905$	0	0
$906$	−1.01061e37	−1.09769
$907$	1.10945e37	1.18855	0.594275	−	0.804262i	$-0.297439\pi$
$907$	1.10945e37	1.18855	0.594275	+	0.804262i	$0.297439\pi$
$908$	2.40864e36	0.254506
$909$	−3.18715e36	−0.332165
$910$	0	0
$911$	−6.00569e36	−0.608952	−0.304476	−	0.952520i	$-0.598481\pi$
$911$	−6.00569e36	−0.608952	−0.304476	+	0.952520i	$0.598481\pi$
$912$	2.69926e36	0.269966
$913$	2.40145e36	0.236913
$914$	1.91089e36	0.185956
$915$	0	0
$916$	6.29363e36	0.595947
$917$	−1.69167e37	−1.58016
$918$	−1.01299e37	−0.933411
$919$	8.07538e36	0.734039	0.367020	−	0.930213i	$-0.380378\pi$
$919$	8.07538e36	0.734039	0.367020	+	0.930213i	$0.380378\pi$
$920$	0	0
$921$	1.26298e37	1.11725
$922$	−6.30837e36	−0.550529
$923$	1.64727e37	1.41822
$924$	−3.19295e36	−0.271201
$925$	0	0
$926$	8.39594e36	0.694116
$927$	−2.06692e36	−0.168588
$928$	1.28426e36	0.103348
$929$	1.77412e37	1.40860	0.704299	−	0.709903i	$-0.251261\pi$
$929$	1.77412e37	1.40860	0.704299	+	0.709903i	$0.251261\pi$
$930$	0	0
$931$	1.42857e37	1.10416
$932$	7.57361e36	0.577569
$933$	−1.05362e37	−0.792801
$934$	−7.74969e36	−0.575372
$935$	0	0
$936$	−1.71997e36	−0.124329
$937$	1.54851e37	1.10451	0.552254	−	0.833676i	$-0.313768\pi$
$937$	1.54851e37	1.10451	0.552254	+	0.833676i	$0.313768\pi$
$938$	−2.26384e37	−1.59335
$939$	2.31159e37	1.60543
$940$	0	0
$941$	6.87286e36	0.464801	0.232400	−	0.972620i	$-0.425342\pi$
$941$	6.87286e36	0.464801	0.232400	+	0.972620i	$0.425342\pi$
$942$	−2.46324e36	−0.164388
$943$	−2.69943e36	−0.177777
$944$	1.15335e36	0.0749570
$945$	0	0
$946$	4.41929e36	0.279713
$947$	−6.52055e36	−0.407295	−0.203648	−	0.979044i	$-0.565280\pi$
$947$	−6.52055e36	−0.407295	−0.203648	+	0.979044i	$0.565280\pi$
$948$	1.08903e36	0.0671326
$949$	1.22853e37	0.747410
$950$	0	0
$951$	3.10917e37	1.84242
$952$	1.61921e37	0.946979
$953$	8.60992e36	0.496979	0.248489	−	0.968635i	$-0.420066\pi$
$953$	8.60992e36	0.496979	0.248489	+	0.968635i	$0.420066\pi$
$954$	−4.49515e36	−0.256088
$955$	0	0
$956$	−2.98362e36	−0.165585
$957$	3.90299e36	0.213795
$958$	−3.81438e36	−0.206231
$959$	−2.22085e37	−1.18519
$960$	0	0
$961$	2.04858e37	1.06515
$962$	4.97658e36	0.255413
$963$	−7.58922e36	−0.384476
$964$	−8.69611e35	−0.0434872
$965$	0	0
$966$	−1.69532e37	−0.826109
$967$	1.52261e37	0.732415	0.366208	−	0.930533i	$-0.380656\pi$
$967$	1.52261e37	0.732415	0.366208	+	0.930533i	$0.380656\pi$
$968$	6.72249e36	0.319219
$969$	−4.16007e37	−1.95008
$970$	0	0
$971$	−1.36186e37	−0.622145	−0.311072	−	0.950386i	$-0.600688\pi$
$971$	−1.36186e37	−0.622145	−0.311072	+	0.950386i	$0.600688\pi$
$972$	−7.96204e36	−0.359084
$973$	1.44490e37	0.643321
$974$	7.78562e36	0.342221
$975$	0	0
$976$	8.84897e36	0.379114
$977$	−1.77242e37	−0.749696	−0.374848	−	0.927086i	$-0.622305\pi$
$977$	−1.77242e37	−0.749696	−0.374848	+	0.927086i	$0.622305\pi$
$978$	−2.85742e37	−1.19327
$979$	−1.04172e37	−0.429505
$980$	0	0
$981$	−1.45795e37	−0.585978
$982$	6.27053e35	0.0248835
$983$	−1.62613e37	−0.637140	−0.318570	−	0.947899i	$-0.603203\pi$
$983$	−1.62613e37	−0.637140	−0.318570	+	0.947899i	$0.603203\pi$
$984$	2.84042e36	0.109886
$985$	0	0
$986$	−1.97928e37	−0.746528
$987$	−5.93502e37	−2.21033
$988$	1.16677e37	0.429066
$989$	2.34645e37	0.852037
$990$	0	0
$991$	−2.62346e37	−0.928869	−0.464434	−	0.885608i	$-0.653742\pi$
$991$	−2.62346e37	−0.928869	−0.464434	+	0.885608i	$0.653742\pi$
$992$	−7.26602e36	−0.254039
$993$	8.59723e36	0.296820
$994$	−4.67835e37	−1.59501
$995$	0	0
$996$	−1.34166e37	−0.446069
$997$	−4.75249e37	−1.56038	−0.780192	−	0.625540i	$-0.784879\pi$
$997$	−4.75249e37	−1.56038	−0.780192	+	0.625540i	$0.784879\pi$
$998$	1.63663e37	0.530662
$999$	8.84223e36	0.283135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.k.1.5		6
5.2	odd	4		10.26.b.a.9.2	✓	12
5.3	odd	4		10.26.b.a.9.11	yes	12
5.4	even	2		50.26.a.l.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.2	✓	12	5.2	odd	4
10.26.b.a.9.11	yes	12	5.3	odd	4
50.26.a.k.1.5		6	1.1	even	1	trivial
50.26.a.l.1.2		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)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} +1.08018e6 q^{3} +1.67772e7 q^{4} -4.42443e9 q^{6} +5.43159e10 q^{7} -6.87195e10 q^{8} +3.19509e11 q^{9} -3.24375e12 q^{11} +1.81225e13 q^{12} +7.83357e13 q^{13} -2.22478e14 q^{14} +2.81475e14 q^{16} -4.33806e15 q^{17} -1.30871e15 q^{18} +8.87783e15 q^{19} +5.86711e16 q^{21} +1.32864e16 q^{22} +7.05451e16 q^{23} -7.42297e16 q^{24} -3.20863e17 q^{26} -5.70099e17 q^{27} +9.11269e17 q^{28} -1.11391e18 q^{29} +6.30227e18 q^{31} -1.15292e18 q^{32} -3.50385e18 q^{33} +1.77687e19 q^{34} +5.36047e18 q^{36} -1.55100e19 q^{37} -3.63636e19 q^{38} +8.46169e19 q^{39} -3.82653e19 q^{41} -2.40317e20 q^{42} +3.32618e20 q^{43} -5.44211e19 q^{44} -2.88953e20 q^{46} -1.01157e21 q^{47} +3.04045e20 q^{48} +1.60914e21 q^{49} -4.68591e21 q^{51} +1.31425e21 q^{52} +3.43480e21 q^{53} +2.33513e21 q^{54} -3.73256e21 q^{56} +9.58969e21 q^{57} +4.56259e21 q^{58} +4.09753e21 q^{59} +3.14378e22 q^{61} -2.58141e22 q^{62} +1.73544e22 q^{63} +4.72237e21 q^{64} +1.43518e22 q^{66} +1.01756e23 q^{67} -7.27806e22 q^{68} +7.62017e22 q^{69} +2.10284e23 q^{71} -2.19565e22 q^{72} +1.56829e23 q^{73} +6.35289e22 q^{74} +1.48945e23 q^{76} -1.76187e23 q^{77} -3.46591e23 q^{78} +6.00925e22 q^{79} -8.86528e23 q^{81} +1.56735e23 q^{82} -7.40331e23 q^{83} +9.84338e23 q^{84} -1.36240e24 q^{86} -1.20323e24 q^{87} +2.22909e23 q^{88} +3.21148e24 q^{89} +4.25487e24 q^{91} +1.18355e24 q^{92} +6.80761e24 q^{93} +4.14341e24 q^{94} -1.24537e24 q^{96} -5.32805e24 q^{97} -6.59105e24 q^{98} -1.03641e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24576 q^{2} + 801416 q^{3} + 100663296 q^{4} - 3282599936 q^{6} + 34007705352 q^{7} - 412316860416 q^{8} + 541468782118 q^{9} + 9861544614312 q^{11} + 13445529337856 q^{12} + 30787386783696 q^{13}+ \cdots - 20\!\cdots\!64 q^{99}+O(q^{100}) \) 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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