LMFDB - Embedded newform 25.32.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,32,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 32, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 32 $
Character orbit:	$[\chi]$	$=$	25.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:	$152.192832048$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4573872 $ x^2 - x - 4573872
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2138.16$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31347.9 q^{2} +1.34921e7 q^{3} -1.16479e9 q^{4} +4.22947e11 q^{6} -1.88207e13 q^{7} -1.03833e14 q^{8} -4.35638e14 q^{9} +O(q^{10})$	\(q+31347.9 q^{2} +1.34921e7 q^{3} -1.16479e9 q^{4} +4.22947e11 q^{6} -1.88207e13 q^{7} -1.03833e14 q^{8} -4.35638e14 q^{9} -5.37973e15 q^{11} -1.57155e16 q^{12} -2.76595e17 q^{13} -5.89989e17 q^{14} -7.53562e17 q^{16} -6.29817e18 q^{17} -1.36563e19 q^{18} +1.91455e18 q^{19} -2.53930e20 q^{21} -1.68643e20 q^{22} -1.90120e21 q^{23} -1.40092e21 q^{24} -8.67065e21 q^{26} -1.42113e22 q^{27} +2.19223e22 q^{28} +5.22675e22 q^{29} -6.09679e22 q^{31} +1.99357e23 q^{32} -7.25837e22 q^{33} -1.97434e23 q^{34} +5.07428e23 q^{36} +2.07091e24 q^{37} +6.00172e22 q^{38} -3.73183e24 q^{39} -5.09498e24 q^{41} -7.96017e24 q^{42} -8.39002e24 q^{43} +6.26628e24 q^{44} -5.95984e25 q^{46} -2.13587e25 q^{47} -1.01671e25 q^{48} +1.96444e26 q^{49} -8.49753e25 q^{51} +3.22176e26 q^{52} -1.59213e26 q^{53} -4.45495e26 q^{54} +1.95421e27 q^{56} +2.58313e25 q^{57} +1.63847e27 q^{58} +2.16250e27 q^{59} -6.60780e27 q^{61} -1.91122e27 q^{62} +8.19901e27 q^{63} +7.86767e27 q^{64} -2.27534e27 q^{66} +2.77322e26 q^{67} +7.33607e27 q^{68} -2.56510e28 q^{69} +7.68524e28 q^{71} +4.52335e28 q^{72} -2.29610e28 q^{73} +6.49186e28 q^{74} -2.23006e27 q^{76} +1.01250e29 q^{77} -1.16985e29 q^{78} -2.99014e29 q^{79} +7.73416e28 q^{81} -1.59717e29 q^{82} -1.89466e29 q^{83} +2.95777e29 q^{84} -2.63009e29 q^{86} +7.05196e29 q^{87} +5.58593e29 q^{88} -2.41523e30 q^{89} +5.20571e30 q^{91} +2.21450e30 q^{92} -8.22583e29 q^{93} -6.69551e29 q^{94} +2.68973e30 q^{96} +3.68010e30 q^{97} +6.15810e30 q^{98} +2.34361e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 39960 q^{2} - 17363160 q^{3} + 1772534336 q^{4} + 2623167496224 q^{6} - 30257527577200 q^{7} - 160155058705920 q^{8} - 101266456303926 q^{9}+O(q^{10}) $ 2 * q - 39960 * q^2 - 17363160 * q^3 + 1772534336 * q^4 + 2623167496224 * q^6 - 30257527577200 * q^7 - 160155058705920 * q^8 - 101266456303926 * q^9	$ 2 q - 39960 q^{2} - 17363160 q^{3} + 1772534336 q^{4} + 2623167496224 q^{6} - 30257527577200 q^{7} - 160155058705920 q^{8} - 101266456303926 q^{9} - 77\!\cdots\!76 q^{11}+ \cdots + 15\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 39960 * q^2 - 17363160 * q^3 + 1772534336 * q^4 + 2623167496224 * q^6 - 30257527577200 * q^7 - 160155058705920 * q^8 - 101266456303926 * q^9 - 7782353745118776 * q^11 - 106347410955313920 * q^12 - 74708953050260620 * q^13 + 225544963845241152 * q^14 - 3045212913684901888 * q^16 - 17224607828987089380 * q^17 - 37499616229575978360 * q^18 - 12370563328022164040 * q^19 + 98954957416071161664 * q^21 + 2682713032996690080 * q^22 - 1897344841989911219280 * q^23 + 336914041234261985280 * q^24 - 23066680666744323279216 * q^26 - 5469986602319662295280 * q^27 - 11671395808124240043520 * q^28 + 128576144217217055807340 * q^29 + 125733527517961838793664 * q^31 + 483720527174276002775040 * q^32 + 1549761835334435045280 * q^33 + 581706909571293028834992 * q^34 + 1489586748818199413504832 * q^36 + 833815207054016911025060 * q^37 + 1078658489244045513633120 * q^38 - 9961054164411363568284912 * q^39 + 8724924335662925840671284 * q^41 - 33123669600002676603713280 * q^42 + 18397105293779438708372600 * q^43 - 791008370873332311322368 * q^44 - 59873011445275600509089856 * q^46 - 95450963964856190793148320 * q^47 + 60542278614741008947691520 * q^48 + 169469294372320202530407186 * q^49 + 252162404739970320085380144 * q^51 + 915180155081494236104643200 * q^52 - 194822508473721098983660860 * q^53 - 1068822271687374190070274240 * q^54 + 2598355397749815172431728640 * q^56 + 466601717043760934967596640 * q^57 - 3802934506602438134028187920 * q^58 - 198723263547765513990746520 * q^59 - 12056218201113004361157656276 * q^61 - 15224500099333079134598257920 * q^62 + 4374875036601718967620305360 * q^63 - 7488413368264058547677691904 * q^64 - 7561640583442461364265814912 * q^66 + 9688140802872256994032247720 * q^67 - 24758471836626330094958252160 * q^68 - 25769856286394326078494576192 * q^69 + 55784576625034657512878287344 * q^71 + 26400994734811244163462812160 * q^72 - 62234095932086098750552955380 * q^73 + 153133163632488378484794299472 * q^74 - 44190149699939358902474481920 * q^76 + 128728748793695217194494555200 * q^77 + 327207773523327347562124449600 * q^78 - 119164191093299704964212710560 * q^79 - 398906922646891269649062634158 * q^81 - 1145184549692595779551104209520 * q^82 + 264863373681569145625357596360 * q^83 + 1332316649919851794889339185152 * q^84 - 2173142482222838422832927019936 * q^86 - 1649324800814841914442821796240 * q^87 + 693913929707398651948752168960 * q^88 - 2154414614246670291602721895980 * q^89 + 2896781368068903069956049509024 * q^91 + 2225812737244025604862645470720 * q^92 - 6583298380663842229690665227520 * q^93 + 4613808251402558431525114250112 * q^94 - 6084370432669606716368714858496 * q^96 + 9060767994874032615529957205180 * q^97 + 8081619677193750912975770689320 * q^98 + 1540246307744094989457731085288 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	31347.9	0.676462	0.338231	−	0.941063i	$-0.390172\pi$
$2$	31347.9	0.676462	0.338231	+	0.941063i	$0.390172\pi$
$3$	1.34921e7	0.542874	0.271437	−	0.962456i	$-0.412501\pi$
$3$	1.34921e7	0.542874	0.271437	+	0.962456i	$0.412501\pi$
$4$	−1.16479e9	−0.542400
$5$	0	0
$5$	0	0
$6$	4.22947e11	0.367233
$7$	−1.88207e13	−1.49836	−0.749181	−	0.662366i	$-0.769553\pi$
$7$	−1.88207e13	−1.49836	−0.749181	+	0.662366i	$0.769553\pi$
$8$	−1.03833e14	−1.04337
$9$	−4.35638e14	−0.705288
$10$	0	0
$11$	−5.37973e15	−0.388306	−0.194153	−	0.980971i	$-0.562196\pi$
$11$	−5.37973e15	−0.388306	−0.194153	+	0.980971i	$0.562196\pi$
$12$	−1.57155e16	−0.294455
$13$	−2.76595e17	−1.49872	−0.749362	−	0.662161i	$-0.769640\pi$
$13$	−2.76595e17	−1.49872	−0.749362	+	0.662161i	$0.769640\pi$
$14$	−5.89989e17	−1.01358
$15$	0	0
$16$	−7.53562e17	−0.163403
$17$	−6.29817e18	−0.533649	−0.266825	−	0.963745i	$-0.585974\pi$
$17$	−6.29817e18	−0.533649	−0.266825	+	0.963745i	$0.585974\pi$
$18$	−1.36563e19	−0.477100
$19$	1.91455e18	0.0289326	0.0144663	−	0.999895i	$-0.495395\pi$
$19$	1.91455e18	0.0289326	0.0144663	+	0.999895i	$0.495395\pi$
$20$	0	0
$21$	−2.53930e20	−0.813421
$22$	−1.68643e20	−0.262674
$23$	−1.90120e21	−1.48678	−0.743388	−	0.668861i	$-0.766782\pi$
$23$	−1.90120e21	−1.48678	−0.743388	+	0.668861i	$0.766782\pi$
$24$	−1.40092e21	−0.566420
$25$	0	0
$26$	−8.67065e21	−1.01383
$27$	−1.42113e22	−0.925756
$28$	2.19223e22	0.812711
$29$	5.22675e22	1.12477	0.562384	−	0.826877i	$-0.309884\pi$
$29$	5.22675e22	1.12477	0.562384	+	0.826877i	$0.309884\pi$
$30$	0	0
$31$	−6.09679e22	−0.466654	−0.233327	−	0.972398i	$-0.574961\pi$
$31$	−6.09679e22	−0.466654	−0.233327	+	0.972398i	$0.574961\pi$
$32$	1.99357e23	0.932838
$33$	−7.25837e22	−0.210801
$34$	−1.97434e23	−0.360993
$35$	0	0
$36$	5.07428e23	0.382548
$37$	2.07091e24	1.02102	0.510510	−	0.859872i	$-0.329457\pi$
$37$	2.07091e24	1.02102	0.510510	+	0.859872i	$0.329457\pi$
$38$	6.00172e22	0.0195718
$39$	−3.73183e24	−0.813618
$40$	0	0
$41$	−5.09498e24	−0.511673	−0.255837	−	0.966720i	$-0.582351\pi$
$41$	−5.09498e24	−0.511673	−0.255837	+	0.966720i	$0.582351\pi$
$42$	−7.96017e24	−0.550248
$43$	−8.39002e24	−0.402719	−0.201359	−	0.979517i	$-0.564536\pi$
$43$	−8.39002e24	−0.402719	−0.201359	+	0.979517i	$0.564536\pi$
$44$	6.26628e24	0.210617
$45$	0	0
$46$	−5.95984e25	−1.00575
$47$	−2.13587e25	−0.258261	−0.129130	−	0.991628i	$-0.541219\pi$
$47$	−2.13587e25	−0.258261	−0.129130	+	0.991628i	$0.541219\pi$
$48$	−1.01671e25	−0.0887071
$49$	1.96444e26	1.24509
$50$	0	0
$51$	−8.49753e25	−0.289704
$52$	3.22176e26	0.812907
$53$	−1.59213e26	−0.299022	−0.149511	−	0.988760i	$-0.547770\pi$
$53$	−1.59213e26	−0.299022	−0.149511	+	0.988760i	$0.547770\pi$
$54$	−4.45495e26	−0.626238
$55$	0	0
$56$	1.95421e27	1.56335
$57$	2.58313e25	0.0157067
$58$	1.63847e27	0.760862
$59$	2.16250e27	0.770459	0.385229	−	0.922821i	$-0.374122\pi$
$59$	2.16250e27	0.770459	0.385229	+	0.922821i	$0.374122\pi$
$60$	0	0
$61$	−6.60780e27	−1.40425	−0.702125	−	0.712053i	$-0.747765\pi$
$61$	−6.60780e27	−1.40425	−0.702125	+	0.712053i	$0.747765\pi$
$62$	−1.91122e27	−0.315674
$63$	8.19901e27	1.05678
$64$	7.86767e27	0.794432
$65$	0	0
$66$	−2.27534e27	−0.142599
$67$	2.77322e26	0.0137665	0.00688326	−	0.999976i	$-0.497809\pi$
$67$	2.77322e26	0.0137665	0.00688326	+	0.999976i	$0.497809\pi$
$68$	7.33607e27	0.289451
$69$	−2.56510e28	−0.807131
$70$	0	0
$71$	7.68524e28	1.55293	0.776467	−	0.630158i	$-0.217010\pi$
$71$	7.68524e28	1.55293	0.776467	+	0.630158i	$0.217010\pi$
$72$	4.52335e28	0.735879
$73$	−2.29610e28	−0.301639	−0.150819	−	0.988561i	$-0.548191\pi$
$73$	−2.29610e28	−0.301639	−0.150819	+	0.988561i	$0.548191\pi$
$74$	6.49186e28	0.690681
$75$	0	0
$76$	−2.23006e27	−0.0156930
$77$	1.01250e29	0.581823
$78$	−1.16985e29	−0.550381
$79$	−2.99014e29	−1.15471	−0.577353	−	0.816494i	$-0.695914\pi$
$79$	−2.99014e29	−1.15471	−0.577353	+	0.816494i	$0.695914\pi$
$80$	0	0
$81$	7.73416e28	0.202719
$82$	−1.59717e29	−0.346127
$83$	−1.89466e29	−0.340267	−0.170134	−	0.985421i	$-0.554420\pi$
$83$	−1.89466e29	−0.340267	−0.170134	+	0.985421i	$0.554420\pi$
$84$	2.95777e29	0.441199
$85$	0	0
$86$	−2.63009e29	−0.272424
$87$	7.05196e29	0.610606
$88$	5.58593e29	0.405148
$89$	−2.41523e30	−1.47032	−0.735162	−	0.677892i	$-0.762894\pi$
$89$	−2.41523e30	−1.47032	−0.735162	+	0.677892i	$0.762894\pi$
$90$	0	0
$91$	5.20571e30	2.24563
$92$	2.21450e30	0.806426
$93$	−8.22583e29	−0.253334
$94$	−6.69551e29	−0.174704
$95$	0	0
$96$	2.68973e30	0.506414
$97$	3.68010e30	0.590062	0.295031	−	0.955488i	$-0.404670\pi$
$97$	3.68010e30	0.590062	0.295031	+	0.955488i	$0.404670\pi$
$98$	6.15810e30	0.842254
$99$	2.34361e30	0.273868
$100$	0	0
$101$	−4.69650e30	−0.402526	−0.201263	−	0.979537i	$-0.564505\pi$
$101$	−4.69650e30	−0.402526	−0.201263	+	0.979537i	$0.564505\pi$
$102$	−2.66379e30	−0.195974
$103$	−5.49646e30	−0.347621	−0.173811	−	0.984779i	$-0.555608\pi$
$103$	−5.49646e30	−0.347621	−0.173811	+	0.984779i	$0.555608\pi$
$104$	2.87196e31	1.56373
$105$	0	0
$106$	−4.99100e30	−0.202277
$107$	−5.31108e30	−0.186095	−0.0930475	−	0.995662i	$-0.529661\pi$
$107$	−5.31108e30	−0.186095	−0.0930475	+	0.995662i	$0.529661\pi$
$108$	1.65533e31	0.502130
$109$	−5.09224e31	−1.33906	−0.669528	−	0.742787i	$-0.733503\pi$
$109$	−5.09224e31	−1.33906	−0.669528	+	0.742787i	$0.733503\pi$
$110$	0	0
$111$	2.79408e31	0.554285
$112$	1.41826e31	0.244836
$113$	−5.75758e31	−0.866012	−0.433006	−	0.901391i	$-0.642547\pi$
$113$	−5.75758e31	−0.866012	−0.433006	+	0.901391i	$0.642547\pi$
$114$	8.09756e29	0.0106250
$115$	0	0
$116$	−6.08809e31	−0.610073
$117$	1.20495e32	1.05703
$118$	6.77897e31	0.521186
$119$	1.18536e32	0.799600
$120$	0	0
$121$	−1.63002e32	−0.849219
$122$	−2.07141e32	−0.949922
$123$	−6.87418e31	−0.277774
$124$	7.10151e31	0.253113
$125$	0	0
$126$	2.57022e32	0.714869
$127$	−3.71246e32	−0.913490	−0.456745	−	0.889598i	$-0.650985\pi$
$127$	−3.71246e32	−0.913490	−0.456745	+	0.889598i	$0.650985\pi$
$128$	−1.81481e32	−0.395436
$129$	−1.13199e32	−0.218626
$130$	0	0
$131$	−6.43836e32	−0.979648	−0.489824	−	0.871821i	$-0.662939\pi$
$131$	−6.43836e32	−0.979648	−0.489824	+	0.871821i	$0.662939\pi$
$132$	8.45451e31	0.114338
$133$	−3.60333e31	−0.0433514
$134$	8.69344e30	0.00931252
$135$	0	0
$136$	6.53957e32	0.556796
$137$	5.70054e32	0.433259	0.216629	−	0.976254i	$-0.430494\pi$
$137$	5.70054e32	0.433259	0.216629	+	0.976254i	$0.430494\pi$
$138$	−8.04106e32	−0.545993
$139$	1.35322e33	0.821557	0.410779	−	0.911735i	$-0.365257\pi$
$139$	1.35322e33	0.821557	0.410779	+	0.911735i	$0.365257\pi$
$140$	0	0
$141$	−2.88173e32	−0.140203
$142$	2.40916e33	1.05050
$143$	1.48800e33	0.581963
$144$	3.28280e32	0.115246
$145$	0	0
$146$	−7.19780e32	−0.204047
$147$	2.65044e33	0.675925
$148$	−2.41218e33	−0.553801
$149$	5.42559e33	1.12217	0.561086	−	0.827757i	$-0.310384\pi$
$149$	5.42559e33	1.12217	0.561086	+	0.827757i	$0.310384\pi$
$150$	0	0
$151$	−2.39015e33	−0.402051	−0.201026	−	0.979586i	$-0.564427\pi$
$151$	−2.39015e33	−0.402051	−0.201026	+	0.979586i	$0.564427\pi$
$152$	−1.98794e32	−0.0301875
$153$	2.74372e33	0.376377
$154$	3.17399e33	0.393581
$155$	0	0
$156$	4.34682e33	0.441306
$157$	1.98794e34	1.82792	0.913961	−	0.405802i	$-0.133008\pi$
$157$	1.98794e34	1.82792	0.913961	+	0.405802i	$0.133008\pi$
$158$	−9.37345e33	−0.781115
$159$	−2.14812e33	−0.162331
$160$	0	0
$161$	3.57819e34	2.22773
$162$	2.42449e33	0.137132
$163$	−7.84574e33	−0.403391	−0.201696	−	0.979448i	$-0.564645\pi$
$163$	−7.84574e33	−0.403391	−0.201696	+	0.979448i	$0.564645\pi$
$164$	5.93460e33	0.277531
$165$	0	0
$166$	−5.93935e33	−0.230178
$167$	5.15166e34	1.81904	0.909519	−	0.415662i	$-0.136450\pi$
$167$	5.15166e34	1.81904	0.909519	+	0.415662i	$0.136450\pi$
$168$	2.63663e34	0.848703
$169$	4.24446e34	1.24617
$170$	0	0
$171$	−8.34052e32	−0.0204058
$172$	9.77265e33	0.218435
$173$	−5.04795e34	−1.03134	−0.515668	−	0.856788i	$-0.672456\pi$
$173$	−5.04795e34	−1.03134	−0.515668	+	0.856788i	$0.672456\pi$
$174$	2.21064e34	0.413052
$175$	0	0
$176$	4.05396e33	0.0634503
$177$	2.91765e34	0.418262
$178$	−7.57122e34	−0.994617
$179$	−2.60297e34	−0.313507	−0.156754	−	0.987638i	$-0.550103\pi$
$179$	−2.60297e34	−0.313507	−0.156754	+	0.987638i	$0.550103\pi$
$180$	0	0
$181$	−1.20765e35	−1.22440	−0.612198	−	0.790705i	$-0.709714\pi$
$181$	−1.20765e35	−1.22440	−0.612198	+	0.790705i	$0.709714\pi$
$182$	1.63188e35	1.51908
$183$	−8.91529e34	−0.762331
$184$	1.97407e35	1.55126
$185$	0	0
$186$	−2.57862e34	−0.171371
$187$	3.38825e34	0.207219
$188$	2.48785e34	0.140081
$189$	2.67468e35	1.38712
$190$	0	0
$191$	2.27571e35	1.00253	0.501267	−	0.865293i	$-0.332868\pi$
$191$	2.27571e35	1.00253	0.501267	+	0.865293i	$0.332868\pi$
$192$	1.06151e35	0.431276
$193$	1.78027e35	0.667339	0.333670	−	0.942690i	$-0.391713\pi$
$193$	1.78027e35	0.667339	0.333670	+	0.942690i	$0.391713\pi$
$194$	1.15363e35	0.399154
$195$	0	0
$196$	−2.28817e35	−0.675335
$197$	2.53071e35	0.690264	0.345132	−	0.938554i	$-0.387834\pi$
$197$	2.53071e35	0.690264	0.345132	+	0.938554i	$0.387834\pi$
$198$	7.34673e34	0.185261
$199$	4.51723e35	1.05354	0.526768	−	0.850009i	$-0.323404\pi$
$199$	4.51723e35	1.05354	0.526768	+	0.850009i	$0.323404\pi$
$200$	0	0
$201$	3.74164e33	0.00747348
$202$	−1.47225e35	−0.272293
$203$	−9.83712e35	−1.68531
$204$	9.89787e34	0.157136
$205$	0	0
$206$	−1.72302e35	−0.235152
$207$	8.28232e35	1.04860
$208$	2.08431e35	0.244896
$209$	−1.02998e34	−0.0112347
$210$	0	0
$211$	6.25554e34	0.0588690	0.0294345	−	0.999567i	$-0.490629\pi$
$211$	6.25554e34	0.0588690	0.0294345	+	0.999567i	$0.490629\pi$
$212$	1.85451e35	0.162190
$213$	1.03690e36	0.843047
$214$	−1.66491e35	−0.125886
$215$	0	0
$216$	1.47560e36	0.965910
$217$	1.14746e36	0.699217
$218$	−1.59631e36	−0.905819
$219$	−3.09792e35	−0.163752
$220$	0	0
$221$	1.74204e36	0.799793
$222$	8.75886e35	0.374953
$223$	−1.14032e35	−0.0455303	−0.0227652	−	0.999741i	$-0.507247\pi$
$223$	−1.14032e35	−0.0455303	−0.0227652	+	0.999741i	$0.507247\pi$
$224$	−3.75204e36	−1.39773
$225$	0	0
$226$	−1.80488e36	−0.585824
$227$	−1.82276e35	−0.0552496	−0.0276248	−	0.999618i	$-0.508794\pi$
$227$	−1.82276e35	−0.0552496	−0.0276248	+	0.999618i	$0.508794\pi$
$228$	−3.00881e34	−0.00851932
$229$	2.02123e36	0.534768	0.267384	−	0.963590i	$-0.413841\pi$
$229$	2.02123e36	0.534768	0.267384	+	0.963590i	$0.413841\pi$
$230$	0	0
$231$	1.36608e36	0.315856
$232$	−5.42708e36	−1.17355
$233$	−3.92949e35	−0.0794912	−0.0397456	−	0.999210i	$-0.512655\pi$
$233$	−3.92949e35	−0.0794912	−0.0397456	+	0.999210i	$0.512655\pi$
$234$	3.77726e36	0.715042
$235$	0	0
$236$	−2.51886e36	−0.417897
$237$	−4.03432e36	−0.626860
$238$	3.71585e36	0.540898
$239$	−1.39161e37	−1.89823	−0.949115	−	0.314931i	$-0.898019\pi$
$239$	−1.39161e37	−1.89823	−0.949115	+	0.314931i	$0.898019\pi$
$240$	0	0
$241$	−1.56350e36	−0.187428	−0.0937140	−	0.995599i	$-0.529874\pi$
$241$	−1.56350e36	−0.187428	−0.0937140	+	0.995599i	$0.529874\pi$
$242$	−5.10976e36	−0.574464
$243$	9.82146e36	1.03581
$244$	7.69673e36	0.761665
$245$	0	0
$246$	−2.15491e36	−0.187903
$247$	−5.29555e35	−0.0433619
$248$	6.33048e36	0.486895
$249$	−2.55628e36	−0.184722
$250$	0	0
$251$	7.69469e36	0.491189	0.245594	−	0.969373i	$-0.421017\pi$
$251$	7.69469e36	0.491189	0.245594	+	0.969373i	$0.421017\pi$
$252$	−9.55017e36	−0.573195
$253$	1.02279e37	0.577324
$254$	−1.16378e37	−0.617941
$255$	0	0
$256$	−2.25847e37	−1.06193
$257$	−4.19824e37	−1.85825	−0.929125	−	0.369765i	$-0.879438\pi$
$257$	−4.19824e37	−1.85825	−0.929125	+	0.369765i	$0.879438\pi$
$258$	−3.54854e36	−0.147892
$259$	−3.89760e37	−1.52986
$260$	0	0
$261$	−2.27697e37	−0.793285
$262$	−2.01829e37	−0.662694
$263$	−5.61748e37	−1.73871	−0.869356	−	0.494186i	$-0.835466\pi$
$263$	−5.61748e37	−1.73871	−0.869356	+	0.494186i	$0.835466\pi$
$264$	7.53657e36	0.219944
$265$	0	0
$266$	−1.12957e36	−0.0293256
$267$	−3.25864e37	−0.798200
$268$	−3.23023e35	−0.00746696
$269$	−3.06746e37	−0.669296	−0.334648	−	0.942343i	$-0.608617\pi$
$269$	−3.06746e37	−0.669296	−0.334648	+	0.942343i	$0.608617\pi$
$270$	0	0
$271$	−6.26560e35	−0.0121882	−0.00609409	−	0.999981i	$-0.501940\pi$
$271$	−6.26560e35	−0.0121882	−0.00609409	+	0.999981i	$0.501940\pi$
$272$	4.74606e36	0.0871998
$273$	7.02357e37	1.21909
$274$	1.78700e37	0.293083
$275$	0	0
$276$	2.98782e37	0.437788
$277$	4.05908e37	0.562330	0.281165	−	0.959660i	$-0.409279\pi$
$277$	4.05908e37	0.562330	0.281165	+	0.959660i	$0.409279\pi$
$278$	4.24205e37	0.555752
$279$	2.65599e37	0.329126
$280$	0	0
$281$	7.11328e37	0.789082	0.394541	−	0.918878i	$-0.370904\pi$
$281$	7.11328e37	0.789082	0.394541	+	0.918878i	$0.370904\pi$
$282$	−9.03362e36	−0.0948420
$283$	5.52066e36	0.0548657	0.0274329	−	0.999624i	$-0.491267\pi$
$283$	5.52066e36	0.0548657	0.0274329	+	0.999624i	$0.491267\pi$
$284$	−8.95173e37	−0.842311
$285$	0	0
$286$	4.66458e37	0.393676
$287$	9.58912e37	0.766671
$288$	−8.68473e37	−0.657920
$289$	−9.96220e37	−0.715218
$290$	0	0
$291$	4.96521e37	0.320329
$292$	2.67449e37	0.163609
$293$	5.84412e36	0.0339056	0.0169528	−	0.999856i	$-0.494604\pi$
$293$	5.84412e36	0.0339056	0.0169528	+	0.999856i	$0.494604\pi$
$294$	8.30855e37	0.457237
$295$	0	0
$296$	−2.15028e38	−1.06531
$297$	7.64532e37	0.359477
$298$	1.70081e38	0.759107
$299$	5.25860e38	2.22827
$300$	0	0
$301$	1.57906e38	0.603419
$302$	−7.49260e37	−0.271972
$303$	−6.33655e37	−0.218521
$304$	−1.44274e36	−0.00472766
$305$	0	0
$306$	8.60098e37	0.254604
$307$	5.70867e38	1.60653	0.803267	−	0.595619i	$-0.203093\pi$
$307$	5.70867e38	1.60653	0.803267	+	0.595619i	$0.203093\pi$
$308$	−1.17936e38	−0.315580
$309$	−7.41586e37	−0.188714
$310$	0	0
$311$	−2.73000e38	−0.628604	−0.314302	−	0.949323i	$-0.601770\pi$
$311$	−2.73000e38	−0.628604	−0.314302	+	0.949323i	$0.601770\pi$
$312$	3.87487e38	0.848908
$313$	−7.96309e38	−1.66014	−0.830070	−	0.557659i	$-0.811699\pi$
$313$	−7.96309e38	−1.66014	−0.830070	+	0.557659i	$0.811699\pi$
$314$	6.23176e38	1.23652
$315$	0	0
$316$	3.48290e38	0.626313
$317$	−3.34956e38	−0.573548	−0.286774	−	0.957998i	$-0.592583\pi$
$317$	−3.34956e38	−0.573548	−0.286774	+	0.957998i	$0.592583\pi$
$318$	−6.73389e37	−0.109811
$319$	−2.81185e38	−0.436754
$320$	0	0
$321$	−7.16575e37	−0.101026
$322$	1.12169e39	1.50697
$323$	−1.20582e37	−0.0154398
$324$	−9.00871e37	−0.109955
$325$	0	0
$326$	−2.45947e38	−0.272879
$327$	−6.87049e38	−0.726938
$328$	5.29026e38	0.533866
$329$	4.01987e38	0.386968
$330$	0	0
$331$	−8.30533e38	−0.727818	−0.363909	−	0.931435i	$-0.618558\pi$
$331$	−8.30533e38	−0.727818	−0.363909	+	0.931435i	$0.618558\pi$
$332$	2.20689e38	0.184561
$333$	−9.02166e38	−0.720113
$334$	1.61494e39	1.23051
$335$	0	0
$336$	1.91352e38	0.132915
$337$	−1.14148e39	−0.757187	−0.378594	−	0.925563i	$-0.623592\pi$
$337$	−1.14148e39	−0.757187	−0.378594	+	0.925563i	$0.623592\pi$
$338$	1.33055e39	0.842988
$339$	−7.76816e38	−0.470135
$340$	0	0
$341$	3.27991e38	0.181205
$342$	−2.61457e37	−0.0138037
$343$	−7.27773e38	−0.367229
$344$	8.71160e38	0.420187
$345$	0	0
$346$	−1.58242e39	−0.697660
$347$	3.74946e39	1.58075	0.790373	−	0.612626i	$-0.209887\pi$
$347$	3.74946e39	1.58075	0.790373	+	0.612626i	$0.209887\pi$
$348$	−8.21408e38	−0.331193
$349$	7.67977e38	0.296179	0.148089	−	0.988974i	$-0.452688\pi$
$349$	7.67977e38	0.296179	0.148089	+	0.988974i	$0.452688\pi$
$350$	0	0
$351$	3.93078e39	1.38745
$352$	−1.07249e39	−0.362227
$353$	2.48278e39	0.802472	0.401236	−	0.915975i	$-0.368581\pi$
$353$	2.48278e39	0.802472	0.401236	+	0.915975i	$0.368581\pi$
$354$	9.14622e38	0.282938
$355$	0	0
$356$	2.81324e39	0.797503
$357$	1.59930e39	0.434082
$358$	−8.15976e38	−0.212076
$359$	−6.14909e39	−1.53055	−0.765274	−	0.643704i	$-0.777397\pi$
$359$	−6.14909e39	−1.53055	−0.765274	+	0.643704i	$0.777397\pi$
$360$	0	0
$361$	−4.37520e39	−0.999163
$362$	−3.78571e39	−0.828256
$363$	−2.19923e39	−0.461018
$364$	−6.06358e39	−1.21803
$365$	0	0
$366$	−2.79475e39	−0.515687
$367$	−5.66753e39	−1.00247	−0.501233	−	0.865312i	$-0.667120\pi$
$367$	−5.66753e39	−1.00247	−0.501233	+	0.865312i	$0.667120\pi$
$368$	1.43267e39	0.242943
$369$	2.21956e39	0.360877
$370$	0	0
$371$	2.99651e39	0.448043
$372$	9.58140e38	0.137409
$373$	8.05893e39	1.10864	0.554320	−	0.832303i	$-0.312978\pi$
$373$	8.05893e39	1.10864	0.554320	+	0.832303i	$0.312978\pi$
$374$	1.06214e39	0.140176
$375$	0	0
$376$	2.21774e39	0.269463
$377$	−1.44569e40	−1.68572
$378$	8.38454e39	0.938332
$379$	−9.24240e39	−0.992835	−0.496417	−	0.868084i	$-0.665351\pi$
$379$	−9.24240e39	−0.992835	−0.496417	+	0.868084i	$0.665351\pi$
$380$	0	0
$381$	−5.00887e39	−0.495910
$382$	7.13385e39	0.678175
$383$	−9.14893e39	−0.835198	−0.417599	−	0.908631i	$-0.637128\pi$
$383$	−9.14893e39	−0.835198	−0.417599	+	0.908631i	$0.637128\pi$
$384$	−2.44855e39	−0.214672
$385$	0	0
$386$	5.58076e39	0.451429
$387$	3.65501e39	0.284033
$388$	−4.28656e39	−0.320049
$389$	−2.19075e40	−1.57172	−0.785858	−	0.618407i	$-0.787778\pi$
$389$	−2.19075e40	−1.57172	−0.785858	+	0.618407i	$0.787778\pi$
$390$	0	0
$391$	1.19741e40	0.793417
$392$	−2.03974e40	−1.29909
$393$	−8.68667e39	−0.531825
$394$	7.93323e39	0.466937
$395$	0	0
$396$	−2.72983e39	−0.148546
$397$	−2.07807e40	−1.08744	−0.543722	−	0.839265i	$-0.682985\pi$
$397$	−2.07807e40	−1.08744	−0.543722	+	0.839265i	$0.682985\pi$
$398$	1.41605e40	0.712676
$399$	−4.86163e38	−0.0235343
$400$	0	0
$401$	−2.58688e40	−1.15888	−0.579441	−	0.815014i	$-0.696729\pi$
$401$	−2.58688e40	−1.15888	−0.579441	+	0.815014i	$0.696729\pi$
$402$	1.17292e38	0.00505552
$403$	1.68634e40	0.699386
$404$	5.47046e39	0.218330
$405$	0	0
$406$	−3.08373e40	−1.14005
$407$	−1.11409e40	−0.396468
$408$	8.82323e39	0.302270
$409$	4.06410e40	1.34046	0.670229	−	0.742155i	$-0.266196\pi$
$409$	4.06410e40	1.34046	0.670229	+	0.742155i	$0.266196\pi$
$410$	0	0
$411$	7.69121e39	0.235205
$412$	6.40225e39	0.188550
$413$	−4.06997e40	−1.15443
$414$	2.59633e40	0.709341
$415$	0	0
$416$	−5.51410e40	−1.39807
$417$	1.82577e40	0.446002
$418$	−3.22876e38	−0.00759983
$419$	−6.77858e40	−1.53752	−0.768761	−	0.639536i	$-0.779126\pi$
$419$	−6.77858e40	−1.53752	−0.768761	+	0.639536i	$0.779126\pi$
$420$	0	0
$421$	3.82000e40	0.804805	0.402403	−	0.915463i	$-0.368175\pi$
$421$	3.82000e40	0.804805	0.402403	+	0.915463i	$0.368175\pi$
$422$	1.96098e39	0.0398226
$423$	9.30467e39	0.182148
$424$	1.65316e40	0.311992
$425$	0	0
$426$	3.25045e40	0.570289
$427$	1.24364e41	2.10407
$428$	6.18632e39	0.100938
$429$	2.00762e40	0.315933
$430$	0	0
$431$	1.21642e41	1.78109	0.890547	−	0.454890i	$-0.150322\pi$
$431$	1.21642e41	1.78109	0.890547	+	0.454890i	$0.150322\pi$
$432$	1.07091e40	0.151271
$433$	−3.18876e39	−0.0434570	−0.0217285	−	0.999764i	$-0.506917\pi$
$433$	−3.18876e39	−0.0434570	−0.0217285	+	0.999764i	$0.506917\pi$
$434$	3.59704e40	0.472993
$435$	0	0
$436$	5.93142e40	0.726303
$437$	−3.63994e39	−0.0430162
$438$	−9.71131e39	−0.110772
$439$	7.39242e40	0.813929	0.406965	−	0.913444i	$-0.366587\pi$
$439$	7.39242e40	0.813929	0.406965	+	0.913444i	$0.366587\pi$
$440$	0	0
$441$	−8.55785e40	−0.878145
$442$	5.46092e40	0.541029
$443$	−2.28069e40	−0.218177	−0.109088	−	0.994032i	$-0.534793\pi$
$443$	−2.28069e40	−0.218177	−0.109088	+	0.994032i	$0.534793\pi$
$444$	−3.25453e40	−0.300644
$445$	0	0
$446$	−3.57466e39	−0.0307995
$447$	7.32024e40	0.609198
$448$	−1.48075e41	−1.19035
$449$	6.27451e40	0.487261	0.243630	−	0.969868i	$-0.421662\pi$
$449$	6.27451e40	0.487261	0.243630	+	0.969868i	$0.421662\pi$
$450$	0	0
$451$	2.74096e40	0.198686
$452$	6.70639e40	0.469725
$453$	−3.22480e40	−0.218263
$454$	−5.71397e39	−0.0373742
$455$	0	0
$456$	−2.68214e39	−0.0163880
$457$	2.37596e39	0.0140326	0.00701629	−	0.999975i	$-0.497767\pi$
$457$	2.37596e39	0.0140326	0.00701629	+	0.999975i	$0.497767\pi$
$458$	6.33612e40	0.361750
$459$	8.95054e40	0.494029
$460$	0	0
$461$	−6.79165e40	−0.350438	−0.175219	−	0.984529i	$-0.556063\pi$
$461$	−6.79165e40	−0.350438	−0.175219	+	0.984529i	$0.556063\pi$
$462$	4.28236e40	0.213665
$463$	1.40330e41	0.677090	0.338545	−	0.940950i	$-0.390065\pi$
$463$	1.40330e41	0.677090	0.338545	+	0.940950i	$0.390065\pi$
$464$	−3.93868e40	−0.183790
$465$	0	0
$466$	−1.23181e40	−0.0537727
$467$	2.95535e41	1.24795	0.623976	−	0.781444i	$-0.285516\pi$
$467$	2.95535e41	1.24795	0.623976	+	0.781444i	$0.285516\pi$
$468$	−1.40352e41	−0.573334
$469$	−5.21939e39	−0.0206272
$470$	0	0
$471$	2.68214e41	0.992331
$472$	−2.24538e41	−0.803877
$473$	4.51361e40	0.156378
$474$	−1.26467e41	−0.424047
$475$	0	0
$476$	−1.38070e41	−0.433703
$477$	6.93593e40	0.210897
$478$	−4.36239e41	−1.28408
$479$	3.59879e41	1.02555	0.512774	−	0.858524i	$-0.328618\pi$
$479$	3.59879e41	1.02555	0.512774	+	0.858524i	$0.328618\pi$
$480$	0	0
$481$	−5.72802e41	−1.53023
$482$	−4.90125e40	−0.126788
$483$	4.82771e41	1.20937
$484$	1.89864e41	0.460616
$485$	0	0
$486$	3.07882e41	0.700684
$487$	−8.64633e41	−1.90604	−0.953022	−	0.302901i	$-0.902045\pi$
$487$	−8.64633e41	−1.90604	−0.953022	+	0.302901i	$0.902045\pi$
$488$	6.86107e41	1.46516
$489$	−1.05855e41	−0.218990
$490$	0	0
$491$	−8.25010e41	−1.60212	−0.801062	−	0.598582i	$-0.795731\pi$
$491$	−8.25010e41	−1.60212	−0.801062	+	0.598582i	$0.795731\pi$
$492$	8.00700e40	0.150664
$493$	−3.29189e41	−0.600231
$494$	−1.66004e40	−0.0293327
$495$	0	0
$496$	4.59431e40	0.0762526
$497$	−1.44642e42	−2.32686
$498$	−8.01340e40	−0.124957
$499$	−4.70553e41	−0.711295	−0.355647	−	0.934620i	$-0.615740\pi$
$499$	−4.70553e41	−0.711295	−0.355647	+	0.934620i	$0.615740\pi$
$500$	0	0
$501$	6.95065e41	0.987508
$502$	2.41212e41	0.332270
$503$	−1.02731e41	−0.137214	−0.0686068	−	0.997644i	$-0.521855\pi$
$503$	−1.02731e41	−0.137214	−0.0686068	+	0.997644i	$0.521855\pi$
$504$	−8.51327e41	−1.10261
$505$	0	0
$506$	3.20624e41	0.390537
$507$	5.72665e41	0.676515
$508$	4.32425e41	0.495477
$509$	−6.79468e41	−0.755168	−0.377584	−	0.925975i	$-0.623245\pi$
$509$	−6.79468e41	−0.755168	−0.377584	+	0.925975i	$0.623245\pi$
$510$	0	0
$511$	4.32143e41	0.451964
$512$	−3.18257e41	−0.322919
$513$	−2.72084e40	−0.0267845
$514$	−1.31606e42	−1.25704
$515$	0	0
$516$	1.31853e41	0.118582
$517$	1.14904e41	0.100284
$518$	−1.22181e42	−1.03489
$519$	−6.81073e41	−0.559886
$520$	0	0
$521$	4.70689e41	0.364543	0.182272	−	0.983248i	$-0.441655\pi$
$521$	4.70689e41	0.364543	0.182272	+	0.983248i	$0.441655\pi$
$522$	−7.13781e41	−0.536627
$523$	1.48934e42	1.08697	0.543485	−	0.839419i	$-0.317105\pi$
$523$	1.48934e42	1.08697	0.543485	+	0.839419i	$0.317105\pi$
$524$	7.49937e41	0.531361
$525$	0	0
$526$	−1.76096e42	−1.17617
$527$	3.83986e41	0.249030
$528$	5.46963e40	0.0344455
$529$	1.97937e42	1.21050
$530$	0	0
$531$	−9.42065e41	−0.543395
$532$	4.19714e40	0.0235138
$533$	1.40924e42	0.766857
$534$	−1.02151e42	−0.539951
$535$	0	0
$536$	−2.87951e40	−0.0143636
$537$	−3.51194e41	−0.170195
$538$	−9.61583e41	−0.452753
$539$	−1.05682e42	−0.483475
$540$	0	0
$541$	2.37435e42	1.02562	0.512811	−	0.858502i	$-0.328604\pi$
$541$	2.37435e42	1.02562	0.512811	+	0.858502i	$0.328604\pi$
$542$	−1.96413e40	−0.00824484
$543$	−1.62936e42	−0.664692
$544$	−1.25558e42	−0.497809
$545$	0	0
$546$	2.20174e42	0.824670
$547$	−3.75591e42	−1.36745	−0.683725	−	0.729740i	$-0.739641\pi$
$547$	−3.75591e42	−1.36745	−0.683725	+	0.729740i	$0.739641\pi$
$548$	−6.63996e41	−0.235000
$549$	2.87861e42	0.990401
$550$	0	0
$551$	1.00069e41	0.0325424
$552$	2.66342e42	0.842140
$553$	5.62766e42	1.73017
$554$	1.27243e42	0.380394
$555$	0	0
$556$	−1.57622e42	−0.445613
$557$	5.38624e42	1.48092	0.740458	−	0.672103i	$-0.234609\pi$
$557$	5.38624e42	1.48092	0.740458	+	0.672103i	$0.234609\pi$
$558$	8.32597e41	0.222641
$559$	2.32063e42	0.603565
$560$	0	0
$561$	4.57144e41	0.112494
$562$	2.22986e42	0.533784
$563$	−2.93646e42	−0.683823	−0.341912	−	0.939732i	$-0.611074\pi$
$563$	−2.93646e42	−0.683823	−0.341912	+	0.939732i	$0.611074\pi$
$564$	3.35663e41	0.0760461
$565$	0	0
$566$	1.73061e41	0.0371145
$567$	−1.45562e42	−0.303747
$568$	−7.97981e42	−1.62029
$569$	1.22480e42	0.242005	0.121002	−	0.992652i	$-0.461389\pi$
$569$	1.22480e42	0.242005	0.121002	+	0.992652i	$0.461389\pi$
$570$	0	0
$571$	−8.00625e42	−1.49820	−0.749099	−	0.662458i	$-0.769513\pi$
$571$	−8.00625e42	−1.49820	−0.749099	+	0.662458i	$0.769513\pi$
$572$	−1.73322e42	−0.315657
$573$	3.07040e42	0.544249
$574$	3.00598e42	0.518624
$575$	0	0
$576$	−3.42746e42	−0.560304
$577$	5.67748e42	0.903505	0.451753	−	0.892143i	$-0.350799\pi$
$577$	5.67748e42	0.903505	0.451753	+	0.892143i	$0.350799\pi$
$578$	−3.12294e42	−0.483818
$579$	2.40195e42	0.362281
$580$	0	0
$581$	3.56588e42	0.509843
$582$	1.55649e42	0.216690
$583$	8.56525e41	0.116112
$584$	2.38411e42	0.314722
$585$	0	0
$586$	1.83201e41	0.0229358
$587$	−3.58214e41	−0.0436770	−0.0218385	−	0.999762i	$-0.506952\pi$
$587$	−3.58214e41	−0.0436770	−0.0218385	+	0.999762i	$0.506952\pi$
$588$	−3.08721e42	−0.366622
$589$	−1.16726e41	−0.0135015
$590$	0	0
$591$	3.41445e42	0.374726
$592$	−1.56056e42	−0.166838
$593$	−1.84785e43	−1.92450	−0.962251	−	0.272164i	$-0.912261\pi$
$593$	−1.84785e43	−1.92450	−0.962251	+	0.272164i	$0.912261\pi$
$594$	2.39664e42	0.243172
$595$	0	0
$596$	−6.31970e42	−0.608666
$597$	6.09467e42	0.571937
$598$	1.64846e43	1.50734
$599$	−3.08643e42	−0.275005	−0.137503	−	0.990501i	$-0.543908\pi$
$599$	−3.08643e42	−0.275005	−0.137503	+	0.990501i	$0.543908\pi$
$600$	0	0
$601$	2.05195e43	1.73625	0.868125	−	0.496346i	$-0.165325\pi$
$601$	2.05195e43	1.73625	0.868125	+	0.496346i	$0.165325\pi$
$602$	4.95003e42	0.408189
$603$	−1.20812e41	−0.00970937
$604$	2.78403e42	0.218073
$605$	0	0
$606$	−1.98637e42	−0.147821
$607$	2.07151e43	1.50267	0.751333	−	0.659923i	$-0.229411\pi$
$607$	2.07151e43	1.50267	0.751333	+	0.659923i	$0.229411\pi$
$608$	3.81679e41	0.0269894
$609$	−1.32723e43	−0.914909
$610$	0	0
$611$	5.90771e42	0.387062
$612$	−3.19587e42	−0.204147
$613$	6.35024e42	0.395506	0.197753	−	0.980252i	$-0.436636\pi$
$613$	6.35024e42	0.395506	0.197753	+	0.980252i	$0.436636\pi$
$614$	1.78955e43	1.08676
$615$	0	0
$616$	−1.05131e43	−0.607059
$617$	−1.92676e43	−1.08495	−0.542473	−	0.840073i	$-0.682512\pi$
$617$	−1.92676e43	−1.08495	−0.542473	+	0.840073i	$0.682512\pi$
$618$	−2.32471e42	−0.127658
$619$	7.41921e42	0.397331	0.198666	−	0.980067i	$-0.436339\pi$
$619$	7.41921e42	0.397331	0.198666	+	0.980067i	$0.436339\pi$
$620$	0	0
$621$	2.70185e43	1.37639
$622$	−8.55798e42	−0.425226
$623$	4.54563e43	2.20308
$624$	2.81217e42	0.132947
$625$	0	0
$626$	−2.49626e43	−1.12302
$627$	−1.38965e41	−0.00609901
$628$	−2.31554e43	−0.991465
$629$	−1.30429e43	−0.544867
$630$	0	0
$631$	−1.64967e43	−0.656058	−0.328029	−	0.944668i	$-0.606384\pi$
$631$	−1.64967e43	−0.656058	−0.328029	+	0.944668i	$0.606384\pi$
$632$	3.10475e43	1.20479
$633$	8.44001e41	0.0319584
$634$	−1.05002e43	−0.387983
$635$	0	0
$636$	2.50211e42	0.0880485
$637$	−5.43354e43	−1.86604
$638$	−8.81455e42	−0.295447
$639$	−3.34798e43	−1.09527
$640$	0	0
$641$	1.02463e43	0.319349	0.159675	−	0.987170i	$-0.448955\pi$
$641$	1.02463e43	0.319349	0.159675	+	0.987170i	$0.448955\pi$
$642$	−2.24631e42	−0.0683403
$643$	−1.32606e43	−0.393817	−0.196908	−	0.980422i	$-0.563090\pi$
$643$	−1.32606e43	−0.393817	−0.196908	+	0.980422i	$0.563090\pi$
$644$	−4.16785e43	−1.20832
$645$	0	0
$646$	−3.77998e41	−0.0104445
$647$	−4.58618e43	−1.23718	−0.618592	−	0.785712i	$-0.712297\pi$
$647$	−4.58618e43	−1.23718	−0.618592	+	0.785712i	$0.712297\pi$
$648$	−8.03060e42	−0.211512
$649$	−1.16337e43	−0.299174
$650$	0	0
$651$	1.54816e43	0.379586
$652$	9.13868e42	0.218799
$653$	1.96584e43	0.459614	0.229807	−	0.973236i	$-0.426190\pi$
$653$	1.96584e43	0.459614	0.229807	+	0.973236i	$0.426190\pi$
$654$	−2.15375e43	−0.491746
$655$	0	0
$656$	3.83938e42	0.0836088
$657$	1.00027e43	0.212742
$658$	1.26014e43	0.261769
$659$	4.60611e43	0.934568	0.467284	−	0.884107i	$-0.345233\pi$
$659$	4.60611e43	0.934568	0.467284	+	0.884107i	$0.345233\pi$
$660$	0	0
$661$	−6.03515e43	−1.16833	−0.584165	−	0.811635i	$-0.698578\pi$
$661$	−6.03515e43	−1.16833	−0.584165	+	0.811635i	$0.698578\pi$
$662$	−2.60354e43	−0.492341
$663$	2.35037e43	0.434187
$664$	1.96728e43	0.355026
$665$	0	0
$666$	−2.82810e43	−0.487129
$667$	−9.93707e43	−1.67228
$668$	−6.00063e43	−0.986646
$669$	−1.53853e42	−0.0247172
$670$	0	0
$671$	3.55482e43	0.545279
$672$	−5.06227e43	−0.758790
$673$	5.70208e43	0.835218	0.417609	−	0.908627i	$-0.362868\pi$
$673$	5.70208e43	0.835218	0.417609	+	0.908627i	$0.362868\pi$
$674$	−3.57829e43	−0.512208
$675$	0	0
$676$	−4.94392e43	−0.675924
$677$	1.60365e43	0.214282	0.107141	−	0.994244i	$-0.465830\pi$
$677$	1.60365e43	0.214282	0.107141	+	0.994244i	$0.465830\pi$
$678$	−2.43515e43	−0.318028
$679$	−6.92621e43	−0.884126
$680$	0	0
$681$	−2.45928e42	−0.0299935
$682$	1.02818e43	0.122578
$683$	6.08600e43	0.709269	0.354634	−	0.935005i	$-0.384605\pi$
$683$	6.08600e43	0.709269	0.354634	+	0.935005i	$0.384605\pi$
$684$	9.71499e41	0.0110681
$685$	0	0
$686$	−2.28141e43	−0.248416
$687$	2.72705e43	0.290311
$688$	6.32240e42	0.0658054
$689$	4.40375e43	0.448152
$690$	0	0
$691$	1.43014e44	1.39146	0.695729	−	0.718304i	$-0.255082\pi$
$691$	1.43014e44	1.39146	0.695729	+	0.718304i	$0.255082\pi$
$692$	5.87983e43	0.559397
$693$	−4.41085e43	−0.410353
$694$	1.17538e44	1.06931
$695$	0	0
$696$	−7.32225e43	−0.637091
$697$	3.20890e43	0.273054
$698$	2.40744e43	0.200354
$699$	−5.30169e42	−0.0431537
$700$	0	0
$701$	−5.20421e43	−0.405252	−0.202626	−	0.979256i	$-0.564948\pi$
$701$	−5.20421e43	−0.405252	−0.202626	+	0.979256i	$0.564948\pi$
$702$	1.23222e44	0.938559
$703$	3.96487e42	0.0295407
$704$	−4.23260e43	−0.308483
$705$	0	0
$706$	7.78298e43	0.542842
$707$	8.83916e43	0.603129
$708$	−3.39847e43	−0.226865
$709$	2.25028e44	1.46967	0.734836	−	0.678245i	$-0.237259\pi$
$709$	2.25028e44	1.46967	0.734836	+	0.678245i	$0.237259\pi$
$710$	0	0
$711$	1.30262e44	0.814401
$712$	2.50780e44	1.53410
$713$	1.15912e44	0.693810
$714$	5.01345e43	0.293640
$715$	0	0
$716$	3.03193e43	0.170046
$717$	−1.87756e44	−1.03050
$718$	−1.92761e44	−1.03536
$719$	−2.22431e44	−1.16922	−0.584611	−	0.811314i	$-0.698753\pi$
$719$	−2.22431e44	−1.16922	−0.584611	+	0.811314i	$0.698753\pi$
$720$	0	0
$721$	1.03447e44	0.520862
$722$	−1.37153e44	−0.675895
$723$	−2.10949e43	−0.101750
$724$	1.40666e44	0.664112
$725$	0	0
$726$	−6.89412e43	−0.311861
$727$	4.26635e44	1.88918	0.944591	−	0.328251i	$-0.106459\pi$
$727$	4.26635e44	1.88918	0.944591	+	0.328251i	$0.106459\pi$
$728$	−5.40524e44	−2.34303
$729$	8.47399e43	0.359593
$730$	0	0
$731$	5.28418e43	0.214911
$732$	1.03845e44	0.413488
$733$	2.38496e44	0.929758	0.464879	−	0.885374i	$-0.346098\pi$
$733$	2.38496e44	0.929758	0.464879	+	0.885374i	$0.346098\pi$
$734$	−1.77665e44	−0.678130
$735$	0	0
$736$	−3.79016e44	−1.38692
$737$	−1.49192e42	−0.00534562
$738$	6.95786e43	0.244119
$739$	3.50761e44	1.20510	0.602549	−	0.798082i	$-0.294152\pi$
$739$	3.50761e44	1.20510	0.602549	+	0.798082i	$0.294152\pi$
$740$	0	0
$741$	−7.14479e42	−0.0235400
$742$	9.39342e43	0.303084
$743$	7.53875e43	0.238217	0.119108	−	0.992881i	$-0.461996\pi$
$743$	7.53875e43	0.238217	0.119108	+	0.992881i	$0.461996\pi$
$744$	8.54112e43	0.264323
$745$	0	0
$746$	2.52630e44	0.749953
$747$	8.25384e43	0.239986
$748$	−3.94661e43	−0.112396
$749$	9.99584e43	0.278838
$750$	0	0
$751$	6.25728e44	1.67481	0.837407	−	0.546580i	$-0.184071\pi$
$751$	6.25728e44	1.67481	0.837407	+	0.546580i	$0.184071\pi$
$752$	1.60951e43	0.0422006
$753$	1.03817e44	0.266654
$754$	−4.53193e44	−1.14032
$755$	0	0
$756$	−3.11545e44	−0.752372
$757$	2.09917e43	0.0496663	0.0248332	−	0.999692i	$-0.492095\pi$
$757$	2.09917e43	0.0496663	0.0248332	+	0.999692i	$0.492095\pi$
$758$	−2.89730e44	−0.671615
$759$	1.37996e44	0.313414
$760$	0	0
$761$	−3.45290e43	−0.0752873	−0.0376436	−	0.999291i	$-0.511985\pi$
$761$	−3.45290e43	−0.0752873	−0.0376436	+	0.999291i	$0.511985\pi$
$762$	−1.57017e44	−0.335464
$763$	9.58397e44	2.00639
$764$	−2.65073e44	−0.543774
$765$	0	0
$766$	−2.86800e44	−0.564979
$767$	−5.98135e44	−1.15470
$768$	−3.04715e44	−0.576493
$769$	7.01102e44	1.29994	0.649970	−	0.759960i	$-0.274782\pi$
$769$	7.01102e44	1.29994	0.649970	+	0.759960i	$0.274782\pi$
$770$	0	0
$771$	−5.66430e44	−1.00880
$772$	−2.07364e44	−0.361965
$773$	2.53762e44	0.434154	0.217077	−	0.976154i	$-0.430348\pi$
$773$	2.53762e44	0.434154	0.217077	+	0.976154i	$0.430348\pi$
$774$	1.14577e44	0.192137
$775$	0	0
$776$	−3.82115e44	−0.615655
$777$	−5.25867e44	−0.830519
$778$	−6.86753e44	−1.06321
$779$	−9.75461e42	−0.0148040
$780$	0	0
$781$	−4.13445e44	−0.603014
$782$	3.75361e44	0.536716
$783$	−7.42791e44	−1.04126
$784$	−1.48033e44	−0.203451
$785$	0	0
$786$	−2.72309e44	−0.359759
$787$	−5.16912e44	−0.669589	−0.334795	−	0.942291i	$-0.608667\pi$
$787$	−5.16912e44	−0.669589	−0.334795	+	0.942291i	$0.608667\pi$
$788$	−2.94775e44	−0.374399
$789$	−7.57914e44	−0.943901
$790$	0	0
$791$	1.08362e45	1.29760
$792$	−2.43344e44	−0.285746
$793$	1.82768e45	2.10458
$794$	−6.51430e44	−0.735614
$795$	0	0
$796$	−5.26164e44	−0.571437
$797$	2.24914e44	0.239559	0.119780	−	0.992800i	$-0.461781\pi$
$797$	2.24914e44	0.239559	0.119780	+	0.992800i	$0.461781\pi$
$798$	−1.52402e43	−0.0159201
$799$	1.34521e44	0.137821
$800$	0	0
$801$	1.05216e45	1.03700
$802$	−8.10933e44	−0.783939
$803$	1.23524e44	0.117128
$804$	−4.35824e42	−0.00405362
$805$	0	0
$806$	5.28632e44	0.473108
$807$	−4.13863e44	−0.363343
$808$	4.87652e44	0.419985
$809$	−1.09436e45	−0.924612	−0.462306	−	0.886720i	$-0.652978\pi$
$809$	−1.09436e45	−0.924612	−0.462306	+	0.886720i	$0.652978\pi$
$810$	0	0
$811$	−1.65483e44	−0.134564	−0.0672821	−	0.997734i	$-0.521433\pi$
$811$	−1.65483e44	−0.134564	−0.0672821	+	0.997734i	$0.521433\pi$
$812$	1.14582e45	0.914110
$813$	−8.45359e42	−0.00661664
$814$	−3.49245e44	−0.268196
$815$	0	0
$816$	6.40342e43	0.0473385
$817$	−1.60632e43	−0.0116517
$818$	1.27401e45	0.906768
$819$	−2.26780e45	−1.58382
$820$	0	0
$821$	1.30182e45	0.875454	0.437727	−	0.899108i	$-0.355784\pi$
$821$	1.30182e45	0.875454	0.437727	+	0.899108i	$0.355784\pi$
$822$	2.41103e44	0.159107
$823$	8.40972e43	0.0544608	0.0272304	−	0.999629i	$-0.491331\pi$
$823$	8.40972e43	0.0544608	0.0272304	+	0.999629i	$0.491331\pi$
$824$	5.70713e44	0.362699
$825$	0	0
$826$	−1.27585e45	−0.780924
$827$	−2.14145e45	−1.28639	−0.643196	−	0.765702i	$-0.722392\pi$
$827$	−2.14145e45	−1.28639	−0.643196	+	0.765702i	$0.722392\pi$
$828$	−9.64721e44	−0.568763
$829$	−8.75462e44	−0.506573	−0.253286	−	0.967391i	$-0.581512\pi$
$829$	−8.75462e44	−0.506573	−0.253286	+	0.967391i	$0.581512\pi$
$830$	0	0
$831$	5.47653e44	0.305274
$832$	−2.17616e45	−1.19063
$833$	−1.23724e45	−0.664440
$834$	5.72339e44	0.301703
$835$	0	0
$836$	1.19971e43	0.00609369
$837$	8.66436e44	0.432008
$838$	−2.12494e45	−1.04007
$839$	8.96946e44	0.430979	0.215489	−	0.976506i	$-0.430865\pi$
$839$	8.96946e44	0.430979	0.215489	+	0.976506i	$0.430865\pi$
$840$	0	0
$841$	5.72465e44	0.265101
$842$	1.19749e45	0.544420
$843$	9.59728e44	0.428372
$844$	−7.28641e43	−0.0319305
$845$	0	0
$846$	2.91682e44	0.123216
$847$	3.06781e45	1.27244
$848$	1.19977e44	0.0488611
$849$	7.44850e43	0.0297851
$850$	0	0
$851$	−3.93720e45	−1.51803
$852$	−1.20777e45	−0.457269
$853$	3.47906e45	1.29346	0.646728	−	0.762721i	$-0.276137\pi$
$853$	3.47906e45	1.29346	0.646728	+	0.762721i	$0.276137\pi$
$854$	3.89853e45	1.42333
$855$	0	0
$856$	5.51465e44	0.194167
$857$	−7.25970e44	−0.251024	−0.125512	−	0.992092i	$-0.540057\pi$
$857$	−7.25970e44	−0.251024	−0.125512	+	0.992092i	$0.540057\pi$
$858$	6.29348e44	0.213716
$859$	4.44826e45	1.48353	0.741765	−	0.670660i	$-0.233989\pi$
$859$	4.44826e45	1.48353	0.741765	+	0.670660i	$0.233989\pi$
$860$	0	0
$861$	1.29377e45	0.416206
$862$	3.81323e45	1.20484
$863$	−2.69165e45	−0.835318	−0.417659	−	0.908604i	$-0.637149\pi$
$863$	−2.69165e45	−0.835318	−0.417659	+	0.908604i	$0.637149\pi$
$864$	−2.83313e45	−0.863581
$865$	0	0
$866$	−9.99609e43	−0.0293970
$867$	−1.34411e45	−0.388273
$868$	−1.33656e45	−0.379255
$869$	1.60862e45	0.448379
$870$	0	0
$871$	−7.67056e43	−0.0206322
$872$	5.28742e45	1.39714
$873$	−1.60319e45	−0.416164
$874$	−1.14104e44	−0.0290988
$875$	0	0
$876$	3.60844e44	0.0888189
$877$	5.87091e44	0.141975	0.0709875	−	0.997477i	$-0.477385\pi$
$877$	5.87091e44	0.141975	0.0709875	+	0.997477i	$0.477385\pi$
$878$	2.31737e45	0.550592
$879$	7.88492e43	0.0184064
$880$	0	0
$881$	−5.61916e45	−1.26632	−0.633162	−	0.774020i	$-0.718243\pi$
$881$	−5.61916e45	−1.26632	−0.633162	+	0.774020i	$0.718243\pi$
$882$	−2.68270e45	−0.594031
$883$	−3.14941e45	−0.685232	−0.342616	−	0.939476i	$-0.611313\pi$
$883$	−3.14941e45	−0.685232	−0.342616	+	0.939476i	$0.611313\pi$
$884$	−2.02912e45	−0.433808
$885$	0	0
$886$	−7.14947e44	−0.147588
$887$	−3.05461e45	−0.619641	−0.309821	−	0.950795i	$-0.600269\pi$
$887$	−3.05461e45	−0.619641	−0.309821	+	0.950795i	$0.600269\pi$
$888$	−2.90118e45	−0.578327
$889$	6.98711e45	1.36874
$890$	0	0
$891$	−4.16077e44	−0.0787171
$892$	1.32824e44	0.0246956
$893$	−4.08924e43	−0.00747215
$894$	2.29474e45	0.412099
$895$	0	0
$896$	3.41560e45	0.592506
$897$	7.09494e45	1.20967
$898$	1.96692e45	0.329613
$899$	−3.18664e45	−0.524877
$900$	0	0
$901$	1.00275e45	0.159573
$902$	8.59233e44	0.134403
$903$	2.13048e45	0.327580
$904$	5.97826e45	0.903574
$905$	0	0
$906$	−1.01091e45	−0.147647
$907$	−1.69836e44	−0.0243847	−0.0121924	−	0.999926i	$-0.503881\pi$
$907$	−1.69836e44	−0.0243847	−0.0121924	+	0.999926i	$0.503881\pi$
$908$	2.12314e44	0.0299673
$909$	2.04597e45	0.283896
$910$	0	0
$911$	1.24574e46	1.67067	0.835336	−	0.549739i	$-0.185273\pi$
$911$	1.24574e46	1.67067	0.835336	+	0.549739i	$0.185273\pi$
$912$	−1.94655e43	−0.00256652
$913$	1.01927e45	0.132128
$914$	7.44812e43	0.00949250
$915$	0	0
$916$	−2.35432e45	−0.290058
$917$	1.21175e46	1.46787
$918$	2.80580e45	0.334192
$919$	−1.08191e46	−1.26707	−0.633535	−	0.773714i	$-0.718397\pi$
$919$	−1.08191e46	−1.26707	−0.633535	+	0.773714i	$0.718397\pi$
$920$	0	0
$921$	7.70217e45	0.872145
$922$	−2.12904e45	−0.237058
$923$	−2.12570e46	−2.32742
$924$	−1.59120e45	−0.171320
$925$	0	0
$926$	4.39906e45	0.458025
$927$	2.39447e45	0.245173
$928$	1.04199e46	1.04923
$929$	−9.79872e45	−0.970344	−0.485172	−	0.874419i	$-0.661243\pi$
$929$	−9.79872e45	−0.970344	−0.485172	+	0.874419i	$0.661243\pi$
$930$	0	0
$931$	3.76103e44	0.0360235
$932$	4.57704e44	0.0431160
$933$	−3.68334e45	−0.341253
$934$	9.26440e45	0.844191
$935$	0	0
$936$	−1.25113e46	−1.10288
$937$	−1.01455e46	−0.879650	−0.439825	−	0.898083i	$-0.644960\pi$
$937$	−1.01455e46	−0.879650	−0.439825	+	0.898083i	$0.644960\pi$
$938$	−1.63617e44	−0.0139535
$939$	−1.07439e46	−0.901246
$940$	0	0
$941$	−1.48680e46	−1.20674	−0.603370	−	0.797461i	$-0.706176\pi$
$941$	−1.48680e46	−1.20674	−0.603370	+	0.797461i	$0.706176\pi$
$942$	8.40792e45	0.671274
$943$	9.68655e45	0.760743
$944$	−1.62958e45	−0.125895
$945$	0	0
$946$	1.41492e45	0.105784
$947$	−2.27265e46	−1.67151	−0.835754	−	0.549104i	$-0.814969\pi$
$947$	−2.27265e46	−1.67151	−0.835754	+	0.549104i	$0.814969\pi$
$948$	4.69915e45	0.340009
$949$	6.35090e45	0.452073
$950$	0	0
$951$	−4.51925e45	−0.311364
$952$	−1.23079e46	−0.834282
$953$	7.58661e45	0.505950	0.252975	−	0.967473i	$-0.418591\pi$
$953$	7.58661e45	0.505950	0.252975	+	0.967473i	$0.418591\pi$
$954$	2.17427e45	0.142664
$955$	0	0
$956$	1.62093e46	1.02960
$957$	−3.79377e45	−0.237102
$958$	1.12814e46	0.693744
$959$	−1.07288e46	−0.649178
$960$	0	0
$961$	−1.33521e46	−0.782234
$962$	−1.79561e46	−1.03514
$963$	2.31371e45	0.131251
$964$	1.82116e45	0.101661
$965$	0	0
$966$	1.51338e46	0.818095
$967$	3.35350e46	1.78397	0.891986	−	0.452064i	$-0.149312\pi$
$967$	3.35350e46	1.78397	0.891986	+	0.452064i	$0.149312\pi$
$968$	1.69250e46	0.886053
$969$	−1.62690e44	−0.00838188
$970$	0	0
$971$	−2.14498e46	−1.07035	−0.535175	−	0.844741i	$-0.679754\pi$
$971$	−2.14498e46	−1.07035	−0.535175	+	0.844741i	$0.679754\pi$
$972$	−1.14400e46	−0.561822
$973$	−2.54685e46	−1.23099
$974$	−2.71044e46	−1.28937
$975$	0	0
$976$	4.97939e45	0.229458
$977$	−1.98478e46	−0.900215	−0.450107	−	0.892974i	$-0.648614\pi$
$977$	−1.98478e46	−0.900215	−0.450107	+	0.892974i	$0.648614\pi$
$978$	−3.31834e45	−0.148139
$979$	1.29933e46	0.570935
$980$	0	0
$981$	2.21837e46	0.944420
$982$	−2.58623e46	−1.08377
$983$	1.53482e46	0.633107	0.316554	−	0.948575i	$-0.397474\pi$
$983$	1.53482e46	0.633107	0.316554	+	0.948575i	$0.397474\pi$
$984$	7.13765e45	0.289822
$985$	0	0
$986$	−1.03194e46	−0.406033
$987$	5.42363e45	0.210075
$988$	6.16823e44	0.0235195
$989$	1.59511e46	0.598753
$990$	0	0
$991$	−8.58630e45	−0.312367	−0.156183	−	0.987728i	$-0.549919\pi$
$991$	−8.58630e45	−0.312367	−0.156183	+	0.987728i	$0.549919\pi$
$992$	−1.21544e46	−0.435313
$993$	−1.12056e46	−0.395113
$994$	−4.53421e46	−1.57403
$995$	0	0
$996$	2.97754e45	0.100193
$997$	−3.45614e46	−1.14503	−0.572514	−	0.819895i	$-0.694032\pi$
$997$	−3.45614e46	−1.14503	−0.572514	+	0.819895i	$0.694032\pi$
$998$	−1.47508e46	−0.481164
$999$	−2.94304e46	−0.945216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.32.a.a.1.2		2
5.2	odd	4		25.32.b.a.24.3		4
5.3	odd	4		25.32.b.a.24.2		4
5.4	even	2		1.32.a.a.1.1	✓	2
15.14	odd	2		9.32.a.a.1.2		2
20.19	odd	2		16.32.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.32.a.a.1.1	✓	2	5.4	even	2
9.32.a.a.1.2		2	15.14	odd	2
16.32.a.b.1.2		2	20.19	odd	2
25.32.a.a.1.2		2	1.1	even	1	trivial
25.32.b.a.24.2		4	5.3	odd	4
25.32.b.a.24.3		4	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+31347.9 q^{2} +1.34921e7 q^{3} -1.16479e9 q^{4} +4.22947e11 q^{6} -1.88207e13 q^{7} -1.03833e14 q^{8} -4.35638e14 q^{9} +O(q^{10})\)	\(q+31347.9 q^{2} +1.34921e7 q^{3} -1.16479e9 q^{4} +4.22947e11 q^{6} -1.88207e13 q^{7} -1.03833e14 q^{8} -4.35638e14 q^{9} -5.37973e15 q^{11} -1.57155e16 q^{12} -2.76595e17 q^{13} -5.89989e17 q^{14} -7.53562e17 q^{16} -6.29817e18 q^{17} -1.36563e19 q^{18} +1.91455e18 q^{19} -2.53930e20 q^{21} -1.68643e20 q^{22} -1.90120e21 q^{23} -1.40092e21 q^{24} -8.67065e21 q^{26} -1.42113e22 q^{27} +2.19223e22 q^{28} +5.22675e22 q^{29} -6.09679e22 q^{31} +1.99357e23 q^{32} -7.25837e22 q^{33} -1.97434e23 q^{34} +5.07428e23 q^{36} +2.07091e24 q^{37} +6.00172e22 q^{38} -3.73183e24 q^{39} -5.09498e24 q^{41} -7.96017e24 q^{42} -8.39002e24 q^{43} +6.26628e24 q^{44} -5.95984e25 q^{46} -2.13587e25 q^{47} -1.01671e25 q^{48} +1.96444e26 q^{49} -8.49753e25 q^{51} +3.22176e26 q^{52} -1.59213e26 q^{53} -4.45495e26 q^{54} +1.95421e27 q^{56} +2.58313e25 q^{57} +1.63847e27 q^{58} +2.16250e27 q^{59} -6.60780e27 q^{61} -1.91122e27 q^{62} +8.19901e27 q^{63} +7.86767e27 q^{64} -2.27534e27 q^{66} +2.77322e26 q^{67} +7.33607e27 q^{68} -2.56510e28 q^{69} +7.68524e28 q^{71} +4.52335e28 q^{72} -2.29610e28 q^{73} +6.49186e28 q^{74} -2.23006e27 q^{76} +1.01250e29 q^{77} -1.16985e29 q^{78} -2.99014e29 q^{79} +7.73416e28 q^{81} -1.59717e29 q^{82} -1.89466e29 q^{83} +2.95777e29 q^{84} -2.63009e29 q^{86} +7.05196e29 q^{87} +5.58593e29 q^{88} -2.41523e30 q^{89} +5.20571e30 q^{91} +2.21450e30 q^{92} -8.22583e29 q^{93} -6.69551e29 q^{94} +2.68973e30 q^{96} +3.68010e30 q^{97} +6.15810e30 q^{98} +2.34361e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 39960 q^{2} - 17363160 q^{3} + 1772534336 q^{4} + 2623167496224 q^{6} - 30257527577200 q^{7} - 160155058705920 q^{8} - 101266456303926 q^{9}+O(q^{10}) \) 2 * q - 39960 * q^2 - 17363160 * q^3 + 1772534336 * q^4 + 2623167496224 * q^6 - 30257527577200 * q^7 - 160155058705920 * q^8 - 101266456303926 * q^9	\( 2 q - 39960 q^{2} - 17363160 q^{3} + 1772534336 q^{4} + 2623167496224 q^{6} - 30257527577200 q^{7} - 160155058705920 q^{8} - 101266456303926 q^{9} - 77\!\cdots\!76 q^{11}+ \cdots + 15\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 39960 * q^2 - 17363160 * q^3 + 1772534336 * q^4 + 2623167496224 * q^6 - 30257527577200 * q^7 - 160155058705920 * q^8 - 101266456303926 * q^9 - 7782353745118776 * q^11 - 106347410955313920 * q^12 - 74708953050260620 * q^13 + 225544963845241152 * q^14 - 3045212913684901888 * q^16 - 17224607828987089380 * q^17 - 37499616229575978360 * q^18 - 12370563328022164040 * q^19 + 98954957416071161664 * q^21 + 2682713032996690080 * q^22 - 1897344841989911219280 * q^23 + 336914041234261985280 * q^24 - 23066680666744323279216 * q^26 - 5469986602319662295280 * q^27 - 11671395808124240043520 * q^28 + 128576144217217055807340 * q^29 + 125733527517961838793664 * q^31 + 483720527174276002775040 * q^32 + 1549761835334435045280 * q^33 + 581706909571293028834992 * q^34 + 1489586748818199413504832 * q^36 + 833815207054016911025060 * q^37 + 1078658489244045513633120 * q^38 - 9961054164411363568284912 * q^39 + 8724924335662925840671284 * q^41 - 33123669600002676603713280 * q^42 + 18397105293779438708372600 * q^43 - 791008370873332311322368 * q^44 - 59873011445275600509089856 * q^46 - 95450963964856190793148320 * q^47 + 60542278614741008947691520 * q^48 + 169469294372320202530407186 * q^49 + 252162404739970320085380144 * q^51 + 915180155081494236104643200 * q^52 - 194822508473721098983660860 * q^53 - 1068822271687374190070274240 * q^54 + 2598355397749815172431728640 * q^56 + 466601717043760934967596640 * q^57 - 3802934506602438134028187920 * q^58 - 198723263547765513990746520 * q^59 - 12056218201113004361157656276 * q^61 - 15224500099333079134598257920 * q^62 + 4374875036601718967620305360 * q^63 - 7488413368264058547677691904 * q^64 - 7561640583442461364265814912 * q^66 + 9688140802872256994032247720 * q^67 - 24758471836626330094958252160 * q^68 - 25769856286394326078494576192 * q^69 + 55784576625034657512878287344 * q^71 + 26400994734811244163462812160 * q^72 - 62234095932086098750552955380 * q^73 + 153133163632488378484794299472 * q^74 - 44190149699939358902474481920 * q^76 + 128728748793695217194494555200 * q^77 + 327207773523327347562124449600 * q^78 - 119164191093299704964212710560 * q^79 - 398906922646891269649062634158 * q^81 - 1145184549692595779551104209520 * q^82 + 264863373681569145625357596360 * q^83 + 1332316649919851794889339185152 * q^84 - 2173142482222838422832927019936 * q^86 - 1649324800814841914442821796240 * q^87 + 693913929707398651948752168960 * q^88 - 2154414614246670291602721895980 * q^89 + 2896781368068903069956049509024 * q^91 + 2225812737244025604862645470720 * q^92 - 6583298380663842229690665227520 * q^93 + 4613808251402558431525114250112 * q^94 - 6084370432669606716368714858496 * q^96 + 9060767994874032615529957205180 * q^97 + 8081619677193750912975770689320 * q^98 + 1540246307744094989457731085288 * q^99

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