LMFDB - Embedded newform 9.32.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,32,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, 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("9.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 32 $
Character orbit:	$[\chi]$	$=$	9.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:	$54.7894195371$
Analytic rank:	$1$
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	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31347.9 q^{2} -1.16479e9 q^{4} -6.31161e10 q^{5} +1.88207e13 q^{7} -1.03833e14 q^{8} +O(q^{10})$	\(q+31347.9 q^{2} -1.16479e9 q^{4} -6.31161e10 q^{5} +1.88207e13 q^{7} -1.03833e14 q^{8} -1.97855e15 q^{10} +5.37973e15 q^{11} +2.76595e17 q^{13} +5.89989e17 q^{14} -7.53562e17 q^{16} -6.29817e18 q^{17} +1.91455e18 q^{19} +7.35172e19 q^{20} +1.68643e20 q^{22} -1.90120e21 q^{23} -6.72976e20 q^{25} +8.67065e21 q^{26} -2.19223e22 q^{28} -5.22675e22 q^{29} -6.09679e22 q^{31} +1.99357e23 q^{32} -1.97434e23 q^{34} -1.18789e24 q^{35} -2.07091e24 q^{37} +6.00172e22 q^{38} +6.55352e24 q^{40} +5.09498e24 q^{41} +8.39002e24 q^{43} -6.26628e24 q^{44} -5.95984e25 q^{46} -2.13587e25 q^{47} +1.96444e26 q^{49} -2.10964e25 q^{50} -3.22176e26 q^{52} -1.59213e26 q^{53} -3.39547e26 q^{55} -1.95421e27 q^{56} -1.63847e27 q^{58} -2.16250e27 q^{59} -6.60780e27 q^{61} -1.91122e27 q^{62} +7.86767e27 q^{64} -1.74576e28 q^{65} -2.77322e26 q^{67} +7.33607e27 q^{68} -3.72378e28 q^{70} -7.68524e28 q^{71} +2.29610e28 q^{73} -6.49186e28 q^{74} -2.23006e27 q^{76} +1.01250e29 q^{77} -2.99014e29 q^{79} +4.75619e28 q^{80} +1.59717e29 q^{82} -1.89466e29 q^{83} +3.97516e29 q^{85} +2.63009e29 q^{86} -5.58593e29 q^{88} +2.41523e30 q^{89} +5.20571e30 q^{91} +2.21450e30 q^{92} -6.69551e29 q^{94} -1.20839e29 q^{95} -3.68010e30 q^{97} +6.15810e30 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 39960 q^{2} + 1772534336 q^{4} + 19391218020 q^{5} + 30257527577200 q^{7} - 160155058705920 q^{8}+O(q^{10}) $ 2 * q - 39960 * q^2 + 1772534336 * q^4 + 19391218020 * q^5 + 30257527577200 * q^7 - 160155058705920 * q^8	$ 2 q - 39960 q^{2} + 1772534336 q^{4} + 19391218020 q^{5} + 30257527577200 q^{7} - 160155058705920 q^{8} - 78\!\cdots\!20 q^{10}+ \cdots + 80\!\cdots\!20 q^{98}+O(q^{100}) $ 2 * q - 39960 * q^2 + 1772534336 * q^4 + 19391218020 * q^5 + 30257527577200 * q^7 - 160155058705920 * q^8 - 7861972212281520 * q^10 + 7782353745118776 * q^11 + 74708953050260620 * q^13 - 225544963845241152 * q^14 - 3045212913684901888 * q^16 - 17224607828987089380 * q^17 - 12370563328022164040 * q^19 + 315868245501283090560 * q^20 - 2682713032996690080 * q^22 - 1897344841989911219280 * q^23 + 1477861250884539239150 * q^25 + 23066680666744323279216 * q^26 + 11671395808124240043520 * q^28 - 128576144217217055807340 * q^29 + 125733527517961838793664 * q^31 + 483720527174276002775040 * q^32 + 581706909571293028834992 * q^34 - 244269703121729304206880 * q^35 - 833815207054016911025060 * q^37 + 1078658489244045513633120 * q^38 + 1906531481497967156966400 * q^40 - 8724924335662925840671284 * q^41 - 18397105293779438708372600 * q^43 + 791008370873332311322368 * q^44 - 59873011445275600509089856 * q^46 - 95450963964856190793148320 * q^47 + 169469294372320202530407186 * q^49 - 174468018688948298981615400 * q^50 - 915180155081494236104643200 * q^52 - 194822508473721098983660860 * q^53 - 141313671368671671047892240 * q^55 - 2598355397749815172431728640 * q^56 + 3802934506602438134028187920 * q^58 + 198723263547765513990746520 * q^59 - 12056218201113004361157656276 * q^61 - 15224500099333079134598257920 * q^62 - 7488413368264058547677691904 * q^64 - 34114584794425827928886318760 * q^65 - 9688140802872256994032247720 * q^67 - 24758471836626330094958252160 * q^68 - 104525335953756946154610069120 * q^70 - 55784576625034657512878287344 * q^71 + 62234095932086098750552955380 * q^73 - 153133163632488378484794299472 * q^74 - 44190149699939358902474481920 * q^76 + 128728748793695217194494555200 * q^77 - 119164191093299704964212710560 * q^79 - 141515971255973138522638049280 * q^80 + 1145184549692595779551104209520 * q^82 + 264863373681569145625357596360 * q^83 - 503995105657776450242931421320 * q^85 + 2173142482222838422832927019936 * q^86 - 693913929707398651948752168960 * q^88 + 2154414614246670291602721895980 * q^89 + 2896781368068903069956049509024 * q^91 + 2225812737244025604862645470720 * q^92 + 4613808251402558431525114250112 * q^94 - 1299465173198290044974084355600 * q^95 - 9060767994874032615529957205180 * q^97 + 8081619677193750912975770689320 * q^98

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	$0.390172\pi$
$3$	0	0
$3$	0	0
$4$	−1.16479e9	−0.542400
$5$	−6.31161e10	−0.924921	−0.462461	−	0.886640i	$-0.653033\pi$
$5$	−6.31161e10	−0.924921	−0.462461	+	0.886640i	$0.653033\pi$
$6$	0	0
$7$	1.88207e13	1.49836	0.749181	−	0.662366i	$-0.230447\pi$
$7$	1.88207e13	1.49836	0.749181	+	0.662366i	$0.230447\pi$
$8$	−1.03833e14	−1.04337
$9$	0	0
$10$	−1.97855e15	−0.625674
$11$	5.37973e15	0.388306	0.194153	−	0.980971i	$-0.437804\pi$
$11$	5.37973e15	0.388306	0.194153	+	0.980971i	$0.437804\pi$
$12$	0	0
$13$	2.76595e17	1.49872	0.749362	−	0.662161i	$-0.230360\pi$
$13$	2.76595e17	1.49872	0.749362	+	0.662161i	$0.230360\pi$
$14$	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	$0.585974\pi$
$18$	0	0
$19$	1.91455e18	0.0289326	0.0144663	−	0.999895i	$-0.495395\pi$
$19$	1.91455e18	0.0289326	0.0144663	+	0.999895i	$0.495395\pi$
$20$	7.35172e19	0.501677
$21$	0	0
$22$	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	$0.766782\pi$
$24$	0	0
$25$	−6.72976e20	−0.144521
$26$	8.67065e21	1.01383
$27$	0	0
$28$	−2.19223e22	−0.812711
$29$	−5.22675e22	−1.12477	−0.562384	−	0.826877i	$-0.690116\pi$
$29$	−5.22675e22	−1.12477	−0.562384	+	0.826877i	$0.690116\pi$
$30$	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
$33$	0	0
$34$	−1.97434e23	−0.360993
$35$	−1.18789e24	−1.38587
$36$	0	0
$37$	−2.07091e24	−1.02102	−0.510510	−	0.859872i	$-0.670543\pi$
$37$	−2.07091e24	−1.02102	−0.510510	+	0.859872i	$0.670543\pi$
$38$	6.00172e22	0.0195718
$39$	0	0
$40$	6.55352e24	0.965039
$41$	5.09498e24	0.511673	0.255837	−	0.966720i	$-0.417649\pi$
$41$	5.09498e24	0.511673	0.255837	+	0.966720i	$0.417649\pi$
$42$	0	0
$43$	8.39002e24	0.402719	0.201359	−	0.979517i	$-0.435464\pi$
$43$	8.39002e24	0.402719	0.201359	+	0.979517i	$0.435464\pi$
$44$	−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	$0.541219\pi$
$48$	0	0
$49$	1.96444e26	1.24509
$50$	−2.10964e25	−0.0977626
$51$	0	0
$52$	−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	$0.547770\pi$
$54$	0	0
$55$	−3.39547e26	−0.359152
$56$	−1.95421e27	−1.56335
$57$	0	0
$58$	−1.63847e27	−0.760862
$59$	−2.16250e27	−0.770459	−0.385229	−	0.922821i	$-0.625878\pi$
$59$	−2.16250e27	−0.770459	−0.385229	+	0.922821i	$0.625878\pi$
$60$	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
$63$	0	0
$64$	7.86767e27	0.794432
$65$	−1.74576e28	−1.38620
$66$	0	0
$67$	−2.77322e26	−0.0137665	−0.00688326	−	0.999976i	$-0.502191\pi$
$67$	−2.77322e26	−0.0137665	−0.00688326	+	0.999976i	$0.502191\pi$
$68$	7.33607e27	0.289451
$69$	0	0
$70$	−3.72378e28	−0.937485
$71$	−7.68524e28	−1.55293	−0.776467	−	0.630158i	$-0.782990\pi$
$71$	−7.68524e28	−1.55293	−0.776467	+	0.630158i	$0.782990\pi$
$72$	0	0
$73$	2.29610e28	0.301639	0.150819	−	0.988561i	$-0.451809\pi$
$73$	2.29610e28	0.301639	0.150819	+	0.988561i	$0.451809\pi$
$74$	−6.49186e28	−0.690681
$75$	0	0
$76$	−2.23006e27	−0.0156930
$77$	1.01250e29	0.581823
$78$	0	0
$79$	−2.99014e29	−1.15471	−0.577353	−	0.816494i	$-0.695914\pi$
$79$	−2.99014e29	−1.15471	−0.577353	+	0.816494i	$0.695914\pi$
$80$	4.75619e28	0.151135
$81$	0	0
$82$	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	$0.554420\pi$
$84$	0	0
$85$	3.97516e29	0.493584
$86$	2.63009e29	0.272424
$87$	0	0
$88$	−5.58593e29	−0.405148
$89$	2.41523e30	1.47032	0.735162	−	0.677892i	$-0.237106\pi$
$89$	2.41523e30	1.47032	0.735162	+	0.677892i	$0.237106\pi$
$90$	0	0
$91$	5.20571e30	2.24563
$92$	2.21450e30	0.806426
$93$	0	0
$94$	−6.69551e29	−0.174704
$95$	−1.20839e29	−0.0267603
$96$	0	0
$97$	−3.68010e30	−0.590062	−0.295031	−	0.955488i	$-0.595330\pi$
$97$	−3.68010e30	−0.590062	−0.295031	+	0.955488i	$0.595330\pi$
$98$	6.15810e30	0.842254
$99$	0	0
$100$	7.83879e29	0.0783879
$101$	4.69650e30	0.402526	0.201263	−	0.979537i	$-0.435495\pi$
$101$	4.69650e30	0.402526	0.201263	+	0.979537i	$0.435495\pi$
$102$	0	0
$103$	5.49646e30	0.347621	0.173811	−	0.984779i	$-0.444392\pi$
$103$	5.49646e30	0.347621	0.173811	+	0.984779i	$0.444392\pi$
$104$	−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	$0.529661\pi$
$108$	0	0
$109$	−5.09224e31	−1.33906	−0.669528	−	0.742787i	$-0.733503\pi$
$109$	−5.09224e31	−1.33906	−0.669528	+	0.742787i	$0.733503\pi$
$110$	−1.06441e31	−0.242953
$111$	0	0
$112$	−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	$0.642547\pi$
$114$	0	0
$115$	1.19996e32	1.37515
$116$	6.08809e31	0.610073
$117$	0	0
$118$	−6.77897e31	−0.521186
$119$	−1.18536e32	−0.799600
$120$	0	0
$121$	−1.63002e32	−0.849219
$122$	−2.07141e32	−0.949922
$123$	0	0
$124$	7.10151e31	0.253113
$125$	3.36383e32	1.05859
$126$	0	0
$127$	3.71246e32	0.913490	0.456745	−	0.889598i	$-0.349015\pi$
$127$	3.71246e32	0.913490	0.456745	+	0.889598i	$0.349015\pi$
$128$	−1.81481e32	−0.395436
$129$	0	0
$130$	−5.47257e32	−0.937712
$131$	6.43836e32	0.979648	0.489824	−	0.871821i	$-0.337061\pi$
$131$	6.43836e32	0.979648	0.489824	+	0.871821i	$0.337061\pi$
$132$	0	0
$133$	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	$0.430494\pi$
$138$	0	0
$139$	1.35322e33	0.821557	0.410779	−	0.911735i	$-0.365257\pi$
$139$	1.35322e33	0.821557	0.410779	+	0.911735i	$0.365257\pi$
$140$	1.38365e33	0.751694
$141$	0	0
$142$	−2.40916e33	−1.05050
$143$	1.48800e33	0.581963
$144$	0	0
$145$	3.29892e33	1.04032
$146$	7.19780e32	0.204047
$147$	0	0
$148$	2.41218e33	0.553801
$149$	−5.42559e33	−1.12217	−0.561086	−	0.827757i	$-0.689616\pi$
$149$	−5.42559e33	−1.12217	−0.561086	+	0.827757i	$0.689616\pi$
$150$	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
$153$	0	0
$154$	3.17399e33	0.393581
$155$	3.84806e33	0.431619
$156$	0	0
$157$	−1.98794e34	−1.82792	−0.913961	−	0.405802i	$-0.866992\pi$
$157$	−1.98794e34	−1.82792	−0.913961	+	0.405802i	$0.866992\pi$
$158$	−9.37345e33	−0.781115
$159$	0	0
$160$	−1.25826e34	−0.862802
$161$	−3.57819e34	−2.22773
$162$	0	0
$163$	7.84574e33	0.403391	0.201696	−	0.979448i	$-0.435355\pi$
$163$	7.84574e33	0.403391	0.201696	+	0.979448i	$0.435355\pi$
$164$	−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	$0.136450\pi$
$168$	0	0
$169$	4.24446e34	1.24617
$170$	1.24613e34	0.333890
$171$	0	0
$172$	−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	$0.672456\pi$
$174$	0	0
$175$	−1.26659e34	−0.216544
$176$	−4.05396e33	−0.0634503
$177$	0	0
$178$	7.57122e34	0.994617
$179$	2.60297e34	0.313507	0.156754	−	0.987638i	$-0.449897\pi$
$179$	2.60297e34	0.313507	0.156754	+	0.987638i	$0.449897\pi$
$180$	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
$183$	0	0
$184$	1.97407e35	1.55126
$185$	1.30708e35	0.944363
$186$	0	0
$187$	−3.38825e34	−0.207219
$188$	2.48785e34	0.140081
$189$	0	0
$190$	−3.78805e33	−0.0181023
$191$	−2.27571e35	−1.00253	−0.501267	−	0.865293i	$-0.667132\pi$
$191$	−2.27571e35	−1.00253	−0.501267	+	0.865293i	$0.667132\pi$
$192$	0	0
$193$	−1.78027e35	−0.667339	−0.333670	−	0.942690i	$-0.608287\pi$
$193$	−1.78027e35	−0.667339	−0.333670	+	0.942690i	$0.608287\pi$
$194$	−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	$0.387834\pi$
$198$	0	0
$199$	4.51723e35	1.05354	0.526768	−	0.850009i	$-0.323404\pi$
$199$	4.51723e35	1.05354	0.526768	+	0.850009i	$0.323404\pi$
$200$	6.98771e34	0.150789
$201$	0	0
$202$	1.47225e35	0.272293
$203$	−9.83712e35	−1.68531
$204$	0	0
$205$	−3.21575e35	−0.473257
$206$	1.72302e35	0.235152
$207$	0	0
$208$	−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
$213$	0	0
$214$	−1.66491e35	−0.125886
$215$	−5.29545e35	−0.372483
$216$	0	0
$217$	−1.14746e36	−0.699217
$218$	−1.59631e36	−0.905819
$219$	0	0
$220$	3.95503e35	0.194804
$221$	−1.74204e36	−0.799793
$222$	0	0
$223$	1.14032e35	0.0455303	0.0227652	−	0.999741i	$-0.492753\pi$
$223$	1.14032e35	0.0455303	0.0227652	+	0.999741i	$0.492753\pi$
$224$	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	$0.508794\pi$
$228$	0	0
$229$	2.02123e36	0.534768	0.267384	−	0.963590i	$-0.413841\pi$
$229$	2.02123e36	0.534768	0.267384	+	0.963590i	$0.413841\pi$
$230$	3.76162e36	0.930236
$231$	0	0
$232$	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	$0.512655\pi$
$234$	0	0
$235$	1.34808e36	0.238871
$236$	2.51886e36	0.417897
$237$	0	0
$238$	−3.71585e36	−0.540898
$239$	1.39161e37	1.89823	0.949115	−	0.314931i	$-0.101981\pi$
$239$	1.39161e37	1.89823	0.949115	+	0.314931i	$0.101981\pi$
$240$	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
$243$	0	0
$244$	7.69673e36	0.761665
$245$	−1.23988e37	−1.15161
$246$	0	0
$247$	5.29555e35	0.0433619
$248$	6.33048e36	0.486895
$249$	0	0
$250$	1.05449e37	0.716096
$251$	−7.69469e36	−0.491189	−0.245594	−	0.969373i	$-0.578983\pi$
$251$	−7.69469e36	−0.491189	−0.245594	+	0.969373i	$0.578983\pi$
$252$	0	0
$253$	−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	$0.879438\pi$
$258$	0	0
$259$	−3.89760e37	−1.52986
$260$	2.03345e37	0.751875
$261$	0	0
$262$	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	$0.835466\pi$
$264$	0	0
$265$	1.00489e37	0.276572
$266$	1.12957e36	0.0293256
$267$	0	0
$268$	3.23023e35	0.00746696
$269$	3.06746e37	0.669296	0.334648	−	0.942343i	$-0.391383\pi$
$269$	3.06746e37	0.669296	0.334648	+	0.942343i	$0.391383\pi$
$270$	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
$273$	0	0
$274$	1.78700e37	0.293083
$275$	−3.62043e36	−0.0561182
$276$	0	0
$277$	−4.05908e37	−0.562330	−0.281165	−	0.959660i	$-0.590721\pi$
$277$	−4.05908e37	−0.562330	−0.281165	+	0.959660i	$0.590721\pi$
$278$	4.24205e37	0.555752
$279$	0	0
$280$	1.23342e38	1.44598
$281$	−7.11328e37	−0.789082	−0.394541	−	0.918878i	$-0.629096\pi$
$281$	−7.11328e37	−0.789082	−0.394541	+	0.918878i	$0.629096\pi$
$282$	0	0
$283$	−5.52066e36	−0.0548657	−0.0274329	−	0.999624i	$-0.508733\pi$
$283$	−5.52066e36	−0.0548657	−0.0274329	+	0.999624i	$0.508733\pi$
$284$	8.95173e37	0.842311
$285$	0	0
$286$	4.66458e37	0.393676
$287$	9.58912e37	0.766671
$288$	0	0
$289$	−9.96220e37	−0.715218
$290$	1.03414e38	0.703737
$291$	0	0
$292$	−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	$0.494604\pi$
$294$	0	0
$295$	1.36488e38	0.712614
$296$	2.15028e38	1.06531
$297$	0	0
$298$	−1.70081e38	−0.759107
$299$	−5.25860e38	−2.22827
$300$	0	0
$301$	1.57906e38	0.603419
$302$	−7.49260e37	−0.271972
$303$	0	0
$304$	−1.44274e36	−0.00472766
$305$	4.17058e38	1.29882
$306$	0	0
$307$	−5.70867e38	−1.60653	−0.803267	−	0.595619i	$-0.796907\pi$
$307$	−5.70867e38	−1.60653	−0.803267	+	0.595619i	$0.796907\pi$
$308$	−1.17936e38	−0.315580
$309$	0	0
$310$	1.20628e38	0.291973
$311$	2.73000e38	0.628604	0.314302	−	0.949323i	$-0.398230\pi$
$311$	2.73000e38	0.628604	0.314302	+	0.949323i	$0.398230\pi$
$312$	0	0
$313$	7.96309e38	1.66014	0.830070	−	0.557659i	$-0.188301\pi$
$313$	7.96309e38	1.66014	0.830070	+	0.557659i	$0.188301\pi$
$314$	−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	$0.592583\pi$
$318$	0	0
$319$	−2.81185e38	−0.436754
$320$	−4.96577e38	−0.734787
$321$	0	0
$322$	−1.12169e39	−1.50697
$323$	−1.20582e37	−0.0154398
$324$	0	0
$325$	−1.86142e38	−0.216596
$326$	2.45947e38	0.272879
$327$	0	0
$328$	−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
$333$	0	0
$334$	1.61494e39	1.23051
$335$	1.75034e37	0.0127330
$336$	0	0
$337$	1.14148e39	0.757187	0.378594	−	0.925563i	$-0.376408\pi$
$337$	1.14148e39	0.757187	0.378594	+	0.925563i	$0.376408\pi$
$338$	1.33055e39	0.842988
$339$	0	0
$340$	−4.63024e38	−0.267720
$341$	−3.27991e38	−0.181205
$342$	0	0
$343$	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	$0.209887\pi$
$348$	0	0
$349$	7.67977e38	0.296179	0.148089	−	0.988974i	$-0.452688\pi$
$349$	7.67977e38	0.296179	0.148089	+	0.988974i	$0.452688\pi$
$350$	−3.97049e38	−0.146484
$351$	0	0
$352$	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	$0.368581\pi$
$354$	0	0
$355$	4.85062e39	1.43634
$356$	−2.81324e39	−0.797503
$357$	0	0
$358$	8.15976e38	0.212076
$359$	6.14909e39	1.53055	0.765274	−	0.643704i	$-0.222603\pi$
$359$	6.14909e39	1.53055	0.765274	+	0.643704i	$0.222603\pi$
$360$	0	0
$361$	−4.37520e39	−0.999163
$362$	−3.78571e39	−0.828256
$363$	0	0
$364$	−6.06358e39	−1.21803
$365$	−1.44921e39	−0.278992
$366$	0	0
$367$	5.66753e39	1.00247	0.501233	−	0.865312i	$-0.332880\pi$
$367$	5.66753e39	1.00247	0.501233	+	0.865312i	$0.332880\pi$
$368$	1.43267e39	0.242943
$369$	0	0
$370$	4.09741e39	0.638826
$371$	−2.99651e39	−0.448043
$372$	0	0
$373$	−8.05893e39	−1.10864	−0.554320	−	0.832303i	$-0.687022\pi$
$373$	−8.05893e39	−1.10864	−0.554320	+	0.832303i	$0.687022\pi$
$374$	−1.06214e39	−0.140176
$375$	0	0
$376$	2.21774e39	0.269463
$377$	−1.44569e40	−1.68572
$378$	0	0
$379$	−9.24240e39	−0.992835	−0.496417	−	0.868084i	$-0.665351\pi$
$379$	−9.24240e39	−0.992835	−0.496417	+	0.868084i	$0.665351\pi$
$380$	1.40753e38	0.0145148
$381$	0	0
$382$	−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	$0.637128\pi$
$384$	0	0
$385$	−6.39053e39	−0.538140
$386$	−5.58076e39	−0.451429
$387$	0	0
$388$	4.28656e39	0.320049
$389$	2.19075e40	1.57172	0.785858	−	0.618407i	$-0.212222\pi$
$389$	2.19075e40	1.57172	0.785858	+	0.618407i	$0.212222\pi$
$390$	0	0
$391$	1.19741e40	0.793417
$392$	−2.03974e40	−1.29909
$393$	0	0
$394$	7.93323e39	0.466937
$395$	1.88726e40	1.06801
$396$	0	0
$397$	2.07807e40	1.08744	0.543722	−	0.839265i	$-0.317015\pi$
$397$	2.07807e40	1.08744	0.543722	+	0.839265i	$0.317015\pi$
$398$	1.41605e40	0.712676
$399$	0	0
$400$	5.07130e38	0.0236151
$401$	2.58688e40	1.15888	0.579441	−	0.815014i	$-0.303271\pi$
$401$	2.58688e40	1.15888	0.579441	+	0.815014i	$0.303271\pi$
$402$	0	0
$403$	−1.68634e40	−0.699386
$404$	−5.47046e39	−0.218330
$405$	0	0
$406$	−3.08373e40	−1.14005
$407$	−1.11409e40	−0.396468
$408$	0	0
$409$	4.06410e40	1.34046	0.670229	−	0.742155i	$-0.266196\pi$
$409$	4.06410e40	1.34046	0.670229	+	0.742155i	$0.266196\pi$
$410$	−1.00807e40	−0.320140
$411$	0	0
$412$	−6.40225e39	−0.188550
$413$	−4.06997e40	−1.15443
$414$	0	0
$415$	1.19583e40	0.314721
$416$	5.51410e40	1.39807
$417$	0	0
$418$	3.22876e38	0.00759983
$419$	6.77858e40	1.53752	0.768761	−	0.639536i	$-0.220874\pi$
$419$	6.77858e40	1.53752	0.768761	+	0.639536i	$0.220874\pi$
$420$	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
$423$	0	0
$424$	1.65316e40	0.311992
$425$	4.23852e39	0.0771233
$426$	0	0
$427$	−1.24364e41	−2.10407
$428$	6.18632e39	0.100938
$429$	0	0
$430$	−1.66001e40	−0.251971
$431$	−1.21642e41	−1.78109	−0.890547	−	0.454890i	$-0.849678\pi$
$431$	−1.21642e41	−1.78109	−0.890547	+	0.454890i	$0.849678\pi$
$432$	0	0
$433$	3.18876e39	0.0434570	0.0217285	−	0.999764i	$-0.493083\pi$
$433$	3.18876e39	0.0434570	0.0217285	+	0.999764i	$0.493083\pi$
$434$	−3.59704e40	−0.472993
$435$	0	0
$436$	5.93142e40	0.726303
$437$	−3.63994e39	−0.0430162
$438$	0	0
$439$	7.39242e40	0.813929	0.406965	−	0.913444i	$-0.366587\pi$
$439$	7.39242e40	0.813929	0.406965	+	0.913444i	$0.366587\pi$
$440$	3.52562e40	0.374730
$441$	0	0
$442$	−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	$0.534793\pi$
$444$	0	0
$445$	−1.52440e41	−1.35993
$446$	3.57466e39	0.0307995
$447$	0	0
$448$	1.48075e41	1.19035
$449$	−6.27451e40	−0.487261	−0.243630	−	0.969868i	$-0.578338\pi$
$449$	−6.27451e40	−0.487261	−0.243630	+	0.969868i	$0.578338\pi$
$450$	0	0
$451$	2.74096e40	0.198686
$452$	6.70639e40	0.469725
$453$	0	0
$454$	−5.71397e39	−0.0373742
$455$	−3.28564e41	−2.07703
$456$	0	0
$457$	−2.37596e39	−0.0140326	−0.00701629	−	0.999975i	$-0.502233\pi$
$457$	−2.37596e39	−0.0140326	−0.00701629	+	0.999975i	$0.502233\pi$
$458$	6.33612e40	0.361750
$459$	0	0
$460$	−1.39771e41	−0.745881
$461$	6.79165e40	0.350438	0.175219	−	0.984529i	$-0.443937\pi$
$461$	6.79165e40	0.350438	0.175219	+	0.984529i	$0.443937\pi$
$462$	0	0
$463$	−1.40330e41	−0.677090	−0.338545	−	0.940950i	$-0.609935\pi$
$463$	−1.40330e41	−0.677090	−0.338545	+	0.940950i	$0.609935\pi$
$464$	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	$0.285516\pi$
$468$	0	0
$469$	−5.21939e39	−0.0206272
$470$	4.22594e40	0.161587
$471$	0	0
$472$	2.24538e41	0.803877
$473$	4.51361e40	0.156378
$474$	0	0
$475$	−1.28845e39	−0.00418135
$476$	1.38070e41	0.433703
$477$	0	0
$478$	4.36239e41	1.28408
$479$	−3.59879e41	−1.02555	−0.512774	−	0.858524i	$-0.671382\pi$
$479$	−3.59879e41	−1.02555	−0.512774	+	0.858524i	$0.671382\pi$
$480$	0	0
$481$	−5.72802e41	−1.53023
$482$	−4.90125e40	−0.126788
$483$	0	0
$484$	1.89864e41	0.460616
$485$	2.32273e41	0.545761
$486$	0	0
$487$	8.64633e41	1.90604	0.953022	−	0.302901i	$-0.0979550\pi$
$487$	8.64633e41	1.90604	0.953022	+	0.302901i	$0.0979550\pi$
$488$	6.86107e41	1.46516
$489$	0	0
$490$	−3.88675e41	−0.779018
$491$	8.25010e41	1.60212	0.801062	−	0.598582i	$-0.204269\pi$
$491$	8.25010e41	1.60212	0.801062	+	0.598582i	$0.204269\pi$
$492$	0	0
$493$	3.29189e41	0.600231
$494$	1.66004e40	0.0293327
$495$	0	0
$496$	4.59431e40	0.0762526
$497$	−1.44642e42	−2.32686
$498$	0	0
$499$	−4.70553e41	−0.711295	−0.355647	−	0.934620i	$-0.615740\pi$
$499$	−4.70553e41	−0.711295	−0.355647	+	0.934620i	$0.615740\pi$
$500$	−3.91817e41	−0.574180
$501$	0	0
$502$	−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	$0.521855\pi$
$504$	0	0
$505$	−2.96425e41	−0.372304
$506$	−3.20624e41	−0.390537
$507$	0	0
$508$	−4.32425e41	−0.495477
$509$	6.79468e41	0.755168	0.377584	−	0.925975i	$-0.376755\pi$
$509$	6.79468e41	0.755168	0.377584	+	0.925975i	$0.376755\pi$
$510$	0	0
$511$	4.32143e41	0.451964
$512$	−3.18257e41	−0.322919
$513$	0	0
$514$	−1.31606e42	−1.25704
$515$	−3.46915e41	−0.321522
$516$	0	0
$517$	−1.14904e41	−0.100284
$518$	−1.22181e42	−1.03489
$519$	0	0
$520$	1.81267e42	1.44633
$521$	−4.70689e41	−0.364543	−0.182272	−	0.983248i	$-0.558345\pi$
$521$	−4.70689e41	−0.364543	−0.182272	+	0.983248i	$0.558345\pi$
$522$	0	0
$523$	−1.48934e42	−1.08697	−0.543485	−	0.839419i	$-0.682895\pi$
$523$	−1.48934e42	−1.08697	−0.543485	+	0.839419i	$0.682895\pi$
$524$	−7.49937e41	−0.531361
$525$	0	0
$526$	−1.76096e42	−1.17617
$527$	3.83986e41	0.249030
$528$	0	0
$529$	1.97937e42	1.21050
$530$	3.15012e41	0.187090
$531$	0	0
$532$	−4.19714e40	−0.0235138
$533$	1.40924e42	0.766857
$534$	0	0
$535$	3.35215e41	0.172123
$536$	2.87951e40	0.0143636
$537$	0	0
$538$	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
$543$	0	0
$544$	−1.25558e42	−0.497809
$545$	3.21402e42	1.23852
$546$	0	0
$547$	3.75591e42	1.36745	0.683725	−	0.729740i	$-0.260359\pi$
$547$	3.75591e42	1.36745	0.683725	+	0.729740i	$0.260359\pi$
$548$	−6.63996e41	−0.235000
$549$	0	0
$550$	−1.13493e41	−0.0379618
$551$	−1.00069e41	−0.0325424
$552$	0	0
$553$	−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	$0.234609\pi$
$558$	0	0
$559$	2.32063e42	0.603565
$560$	8.95149e41	0.226454
$561$	0	0
$562$	−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	$0.611074\pi$
$564$	0	0
$565$	3.63395e42	0.800993
$566$	−1.73061e41	−0.0371145
$567$	0	0
$568$	7.97981e42	1.62029
$569$	−1.22480e42	−0.242005	−0.121002	−	0.992652i	$-0.538611\pi$
$569$	−1.22480e42	−0.242005	−0.121002	+	0.992652i	$0.538611\pi$
$570$	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
$573$	0	0
$574$	3.00598e42	0.518624
$575$	1.27946e42	0.214870
$576$	0	0
$577$	−5.67748e42	−0.903505	−0.451753	−	0.892143i	$-0.649201\pi$
$577$	−5.67748e42	−0.903505	−0.451753	+	0.892143i	$0.649201\pi$
$578$	−3.12294e42	−0.483818
$579$	0	0
$580$	−3.84256e42	−0.564270
$581$	−3.56588e42	−0.509843
$582$	0	0
$583$	−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	$0.506952\pi$
$588$	0	0
$589$	−1.16726e41	−0.0135015
$590$	4.27862e42	0.482056
$591$	0	0
$592$	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	$0.912261\pi$
$594$	0	0
$595$	7.48153e42	0.739567
$596$	6.31970e42	0.608666
$597$	0	0
$598$	−1.64846e43	−1.50734
$599$	3.08643e42	0.275005	0.137503	−	0.990501i	$-0.456092\pi$
$599$	3.08643e42	0.275005	0.137503	+	0.990501i	$0.456092\pi$
$600$	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
$603$	0	0
$604$	2.78403e42	0.218073
$605$	1.02880e43	0.785460
$606$	0	0
$607$	−2.07151e43	−1.50267	−0.751333	−	0.659923i	$-0.770589\pi$
$607$	−2.07151e43	−1.50267	−0.751333	+	0.659923i	$0.770589\pi$
$608$	3.81679e41	0.0269894
$609$	0	0
$610$	1.30739e43	0.878603
$611$	−5.90771e42	−0.387062
$612$	0	0
$613$	−6.35024e42	−0.395506	−0.197753	−	0.980252i	$-0.563364\pi$
$613$	−6.35024e42	−0.395506	−0.197753	+	0.980252i	$0.563364\pi$
$614$	−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	$0.682512\pi$
$618$	0	0
$619$	7.41921e42	0.397331	0.198666	−	0.980067i	$-0.436339\pi$
$619$	7.41921e42	0.397331	0.198666	+	0.980067i	$0.436339\pi$
$620$	−4.48220e42	−0.234110
$621$	0	0
$622$	8.55798e42	0.425226
$623$	4.54563e43	2.20308
$624$	0	0
$625$	−1.80974e43	−0.834593
$626$	2.49626e43	1.12302
$627$	0	0
$628$	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
$633$	0	0
$634$	−1.05002e43	−0.387983
$635$	−2.34316e43	−0.844906
$636$	0	0
$637$	5.43354e43	1.86604
$638$	−8.81455e42	−0.295447
$639$	0	0
$640$	1.14543e43	0.365747
$641$	−1.02463e43	−0.319349	−0.159675	−	0.987170i	$-0.551045\pi$
$641$	−1.02463e43	−0.319349	−0.159675	+	0.987170i	$0.551045\pi$
$642$	0	0
$643$	1.32606e43	0.393817	0.196908	−	0.980422i	$-0.436910\pi$
$643$	1.32606e43	0.393817	0.196908	+	0.980422i	$0.436910\pi$
$644$	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	$0.712297\pi$
$648$	0	0
$649$	−1.16337e43	−0.299174
$650$	−5.83514e42	−0.146519
$651$	0	0
$652$	−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	$0.426190\pi$
$654$	0	0
$655$	−4.06364e43	−0.906097
$656$	−3.83938e42	−0.0836088
$657$	0	0
$658$	−1.26014e43	−0.261769
$659$	−4.60611e43	−0.934568	−0.467284	−	0.884107i	$-0.654767\pi$
$659$	−4.60611e43	−0.934568	−0.467284	+	0.884107i	$0.654767\pi$
$660$	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
$663$	0	0
$664$	1.96728e43	0.355026
$665$	−2.27428e42	−0.0400967
$666$	0	0
$667$	9.93707e43	1.67228
$668$	−6.00063e43	−0.986646
$669$	0	0
$670$	5.48696e41	0.00861335
$671$	−3.55482e43	−0.545279
$672$	0	0
$673$	−5.70208e43	−0.835218	−0.417609	−	0.908627i	$-0.637132\pi$
$673$	−5.70208e43	−0.835218	−0.417609	+	0.908627i	$0.637132\pi$
$674$	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	$0.465830\pi$
$678$	0	0
$679$	−6.92621e43	−0.884126
$680$	−4.12752e43	−0.514992
$681$	0	0
$682$	−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	$0.384605\pi$
$684$	0	0
$685$	−3.59796e43	−0.400730
$686$	2.28141e43	0.248416
$687$	0	0
$688$	−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
$693$	0	0
$694$	1.17538e44	1.06931
$695$	−8.54097e43	−0.759876
$696$	0	0
$697$	−3.20890e43	−0.273054
$698$	2.40744e43	0.200354
$699$	0	0
$700$	1.47532e43	0.117453
$701$	5.20421e43	0.405252	0.202626	−	0.979256i	$-0.435052\pi$
$701$	5.20421e43	0.405252	0.202626	+	0.979256i	$0.435052\pi$
$702$	0	0
$703$	−3.96487e42	−0.0295407
$704$	4.23260e43	0.308483
$705$	0	0
$706$	7.78298e43	0.542842
$707$	8.83916e43	0.603129
$708$	0	0
$709$	2.25028e44	1.46967	0.734836	−	0.678245i	$-0.237259\pi$
$709$	2.25028e44	1.46967	0.734836	+	0.678245i	$0.237259\pi$
$710$	1.52057e44	0.971630
$711$	0	0
$712$	−2.50780e44	−1.53410
$713$	1.15912e44	0.693810
$714$	0	0
$715$	−9.39170e43	−0.538270
$716$	−3.03193e43	−0.170046
$717$	0	0
$718$	1.92761e44	1.03536
$719$	2.22431e44	1.16922	0.584611	−	0.811314i	$-0.301247\pi$
$719$	2.22431e44	1.16922	0.584611	+	0.811314i	$0.301247\pi$
$720$	0	0
$721$	1.03447e44	0.520862
$722$	−1.37153e44	−0.675895
$723$	0	0
$724$	1.40666e44	0.664112
$725$	3.51748e43	0.162552
$726$	0	0
$727$	−4.26635e44	−1.88918	−0.944591	−	0.328251i	$-0.893541\pi$
$727$	−4.26635e44	−1.88918	−0.944591	+	0.328251i	$0.893541\pi$
$728$	−5.40524e44	−2.34303
$729$	0	0
$730$	−4.54297e43	−0.188727
$731$	−5.28418e43	−0.214911
$732$	0	0
$733$	−2.38496e44	−0.929758	−0.464879	−	0.885374i	$-0.653902\pi$
$733$	−2.38496e44	−0.929758	−0.464879	+	0.885374i	$0.653902\pi$
$734$	1.77665e44	0.678130
$735$	0	0
$736$	−3.79016e44	−1.38692
$737$	−1.49192e42	−0.00534562
$738$	0	0
$739$	3.50761e44	1.20510	0.602549	−	0.798082i	$-0.294152\pi$
$739$	3.50761e44	1.20510	0.602549	+	0.798082i	$0.294152\pi$
$740$	−1.52248e44	−0.512223
$741$	0	0
$742$	−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	$0.461996\pi$
$744$	0	0
$745$	3.42442e44	1.03792
$746$	−2.52630e44	−0.749953
$747$	0	0
$748$	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
$753$	0	0
$754$	−4.53193e44	−1.14032
$755$	1.50857e44	0.371866
$756$	0	0
$757$	−2.09917e43	−0.0496663	−0.0248332	−	0.999692i	$-0.507905\pi$
$757$	−2.09917e43	−0.0496663	−0.0248332	+	0.999692i	$0.507905\pi$
$758$	−2.89730e44	−0.671615
$759$	0	0
$760$	1.25471e43	0.0279210
$761$	3.45290e43	0.0752873	0.0376436	−	0.999291i	$-0.488015\pi$
$761$	3.45290e43	0.0752873	0.0376436	+	0.999291i	$0.488015\pi$
$762$	0	0
$763$	−9.58397e44	−2.00639
$764$	2.65073e44	0.543774
$765$	0	0
$766$	−2.86800e44	−0.564979
$767$	−5.98135e44	−1.15470
$768$	0	0
$769$	7.01102e44	1.29994	0.649970	−	0.759960i	$-0.274782\pi$
$769$	7.01102e44	1.29994	0.649970	+	0.759960i	$0.274782\pi$
$770$	−2.00329e44	−0.364031
$771$	0	0
$772$	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	$0.430348\pi$
$774$	0	0
$775$	4.10300e43	0.0674411
$776$	3.82115e44	0.615655
$777$	0	0
$778$	6.86753e44	1.06321
$779$	9.75461e42	0.0148040
$780$	0	0
$781$	−4.13445e44	−0.603014
$782$	3.75361e44	0.536716
$783$	0	0
$784$	−1.48033e44	−0.203451
$785$	1.25471e45	1.69068
$786$	0	0
$787$	5.16912e44	0.669589	0.334795	−	0.942291i	$-0.391333\pi$
$787$	5.16912e44	0.669589	0.334795	+	0.942291i	$0.391333\pi$
$788$	−2.94775e44	−0.374399
$789$	0	0
$790$	5.91615e44	0.722470
$791$	−1.08362e45	−1.29760
$792$	0	0
$793$	−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	$0.461781\pi$
$798$	0	0
$799$	1.34521e44	0.137821
$800$	−1.34162e44	−0.134814
$801$	0	0
$802$	8.10933e44	0.783939
$803$	1.23524e44	0.117128
$804$	0	0
$805$	2.25841e45	2.06047
$806$	−5.28632e44	−0.473108
$807$	0	0
$808$	−4.87652e44	−0.419985
$809$	1.09436e45	0.924612	0.462306	−	0.886720i	$-0.347022\pi$
$809$	1.09436e45	0.924612	0.462306	+	0.886720i	$0.347022\pi$
$810$	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
$813$	0	0
$814$	−3.49245e44	−0.268196
$815$	−4.95192e44	−0.373105
$816$	0	0
$817$	1.60632e43	0.0116517
$818$	1.27401e45	0.906768
$819$	0	0
$820$	3.74569e44	0.256695
$821$	−1.30182e45	−0.875454	−0.437727	−	0.899108i	$-0.644216\pi$
$821$	−1.30182e45	−0.875454	−0.437727	+	0.899108i	$0.644216\pi$
$822$	0	0
$823$	−8.40972e43	−0.0544608	−0.0272304	−	0.999629i	$-0.508669\pi$
$823$	−8.40972e43	−0.0544608	−0.0272304	+	0.999629i	$0.508669\pi$
$824$	−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	$0.722392\pi$
$828$	0	0
$829$	−8.75462e44	−0.506573	−0.253286	−	0.967391i	$-0.581512\pi$
$829$	−8.75462e44	−0.506573	−0.253286	+	0.967391i	$0.581512\pi$
$830$	3.74868e44	0.212896
$831$	0	0
$832$	2.17616e45	1.19063
$833$	−1.23724e45	−0.664440
$834$	0	0
$835$	−3.25152e45	−1.68247
$836$	−1.19971e43	−0.00609369
$837$	0	0
$838$	2.12494e45	1.04007
$839$	−8.96946e44	−0.430979	−0.215489	−	0.976506i	$-0.569135\pi$
$839$	−8.96946e44	−0.430979	−0.215489	+	0.976506i	$0.569135\pi$
$840$	0	0
$841$	5.72465e44	0.265101
$842$	1.19749e45	0.544420
$843$	0	0
$844$	−7.28641e43	−0.0319305
$845$	−2.67894e45	−1.15261
$846$	0	0
$847$	−3.06781e45	−1.27244
$848$	1.19977e44	0.0488611
$849$	0	0
$850$	1.32869e44	0.0521710
$851$	3.93720e45	1.51803
$852$	0	0
$853$	−3.47906e45	−1.29346	−0.646728	−	0.762721i	$-0.723863\pi$
$853$	−3.47906e45	−1.29346	−0.646728	+	0.762721i	$0.723863\pi$
$854$	−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	$0.540057\pi$
$858$	0	0
$859$	4.44826e45	1.48353	0.741765	−	0.670660i	$-0.233989\pi$
$859$	4.44826e45	1.48353	0.741765	+	0.670660i	$0.233989\pi$
$860$	6.16811e44	0.202035
$861$	0	0
$862$	−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	$0.637149\pi$
$864$	0	0
$865$	3.18607e45	0.953905
$866$	9.99609e43	0.0293970
$867$	0	0
$868$	1.33656e45	0.379255
$869$	−1.60862e45	−0.448379
$870$	0	0
$871$	−7.67056e43	−0.0206322
$872$	5.28742e45	1.39714
$873$	0	0
$874$	−1.14104e44	−0.0290988
$875$	6.33096e45	1.58615
$876$	0	0
$877$	−5.87091e44	−0.141975	−0.0709875	−	0.997477i	$-0.522615\pi$
$877$	−5.87091e44	−0.141975	−0.0709875	+	0.997477i	$0.522615\pi$
$878$	2.31737e45	0.550592
$879$	0	0
$880$	2.55870e44	0.0586865
$881$	5.61916e45	1.26632	0.633162	−	0.774020i	$-0.281757\pi$
$881$	5.61916e45	1.26632	0.633162	+	0.774020i	$0.281757\pi$
$882$	0	0
$883$	3.14941e45	0.685232	0.342616	−	0.939476i	$-0.388687\pi$
$883$	3.14941e45	0.685232	0.342616	+	0.939476i	$0.388687\pi$
$884$	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	$0.600269\pi$
$888$	0	0
$889$	6.98711e45	1.36874
$890$	−4.77866e45	−0.919942
$891$	0	0
$892$	−1.32824e44	−0.0246956
$893$	−4.08924e43	−0.00747215
$894$	0	0
$895$	−1.64289e45	−0.289969
$896$	−3.41560e45	−0.592506
$897$	0	0
$898$	−1.96692e45	−0.329613
$899$	3.18664e45	0.524877
$900$	0	0
$901$	1.00275e45	0.159573
$902$	8.59233e44	0.134403
$903$	0	0
$904$	5.97826e45	0.903574
$905$	7.62218e45	1.13247
$906$	0	0
$907$	1.69836e44	0.0243847	0.0121924	−	0.999926i	$-0.496119\pi$
$907$	1.69836e44	0.0243847	0.0121924	+	0.999926i	$0.496119\pi$
$908$	2.12314e44	0.0299673
$909$	0	0
$910$	−1.02998e46	−1.40503
$911$	−1.24574e46	−1.67067	−0.835336	−	0.549739i	$-0.814727\pi$
$911$	−1.24574e46	−1.67067	−0.835336	+	0.549739i	$0.814727\pi$
$912$	0	0
$913$	−1.01927e45	−0.132128
$914$	−7.44812e43	−0.00949250
$915$	0	0
$916$	−2.35432e45	−0.290058
$917$	1.21175e46	1.46787
$918$	0	0
$919$	−1.08191e46	−1.26707	−0.633535	−	0.773714i	$-0.718397\pi$
$919$	−1.08191e46	−1.26707	−0.633535	+	0.773714i	$0.718397\pi$
$920$	−1.24595e46	−1.43480
$921$	0	0
$922$	2.12904e45	0.237058
$923$	−2.12570e46	−2.32742
$924$	0	0
$925$	1.39367e45	0.147558
$926$	−4.39906e45	−0.458025
$927$	0	0
$928$	−1.04199e46	−1.04923
$929$	9.79872e45	0.970344	0.485172	−	0.874419i	$-0.338757\pi$
$929$	9.79872e45	0.970344	0.485172	+	0.874419i	$0.338757\pi$
$930$	0	0
$931$	3.76103e44	0.0360235
$932$	4.57704e44	0.0431160
$933$	0	0
$934$	9.26440e45	0.844191
$935$	2.13853e45	0.191661
$936$	0	0
$937$	1.01455e46	0.879650	0.439825	−	0.898083i	$-0.355040\pi$
$937$	1.01455e46	0.879650	0.439825	+	0.898083i	$0.355040\pi$
$938$	−1.63617e44	−0.0139535
$939$	0	0
$940$	−1.57024e45	−0.129564
$941$	1.48680e46	1.20674	0.603370	−	0.797461i	$-0.293824\pi$
$941$	1.48680e46	1.20674	0.603370	+	0.797461i	$0.293824\pi$
$942$	0	0
$943$	−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	$0.814969\pi$
$948$	0	0
$949$	6.35090e45	0.452073
$950$	−4.03901e43	−0.00282852
$951$	0	0
$952$	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	$0.418591\pi$
$954$	0	0
$955$	1.43634e46	0.927265
$956$	−1.62093e46	−1.02960
$957$	0	0
$958$	−1.12814e46	−0.693744
$959$	1.07288e46	0.649178
$960$	0	0
$961$	−1.33521e46	−0.782234
$962$	−1.79561e46	−1.03514
$963$	0	0
$964$	1.82116e45	0.101661
$965$	1.12363e46	0.617236
$966$	0	0
$967$	−3.35350e46	−1.78397	−0.891986	−	0.452064i	$-0.850688\pi$
$967$	−3.35350e46	−1.78397	−0.891986	+	0.452064i	$0.850688\pi$
$968$	1.69250e46	0.886053
$969$	0	0
$970$	7.28127e45	0.369186
$971$	2.14498e46	1.07035	0.535175	−	0.844741i	$-0.320246\pi$
$971$	2.14498e46	1.07035	0.535175	+	0.844741i	$0.320246\pi$
$972$	0	0
$973$	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	$0.648614\pi$
$978$	0	0
$979$	1.29933e46	0.570935
$980$	1.44420e46	0.624632
$981$	0	0
$982$	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	$0.397474\pi$
$984$	0	0
$985$	−1.59728e46	−0.638440
$986$	1.03194e46	0.406033
$987$	0	0
$988$	−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
$993$	0	0
$994$	−4.53421e46	−1.57403
$995$	−2.85109e46	−0.974437
$996$	0	0
$997$	3.45614e46	1.14503	0.572514	−	0.819895i	$-0.305968\pi$
$997$	3.45614e46	1.14503	0.572514	+	0.819895i	$0.305968\pi$
$998$	−1.47508e46	−0.481164
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.32.a.a.1.2		2
3.2	odd	2		1.32.a.a.1.1	✓	2
12.11	even	2		16.32.a.b.1.2		2
15.2	even	4		25.32.b.a.24.2		4
15.8	even	4		25.32.b.a.24.3		4
15.14	odd	2		25.32.a.a.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.32.a.a.1.1	✓	2	3.2	odd	2
9.32.a.a.1.2		2	1.1	even	1	trivial
16.32.a.b.1.2		2	12.11	even	2
25.32.a.a.1.2		2	15.14	odd	2
25.32.b.a.24.2		4	15.2	even	4
25.32.b.a.24.3		4	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+31347.9 q^{2} -1.16479e9 q^{4} -6.31161e10 q^{5} +1.88207e13 q^{7} -1.03833e14 q^{8} +O(q^{10})\)	\(q+31347.9 q^{2} -1.16479e9 q^{4} -6.31161e10 q^{5} +1.88207e13 q^{7} -1.03833e14 q^{8} -1.97855e15 q^{10} +5.37973e15 q^{11} +2.76595e17 q^{13} +5.89989e17 q^{14} -7.53562e17 q^{16} -6.29817e18 q^{17} +1.91455e18 q^{19} +7.35172e19 q^{20} +1.68643e20 q^{22} -1.90120e21 q^{23} -6.72976e20 q^{25} +8.67065e21 q^{26} -2.19223e22 q^{28} -5.22675e22 q^{29} -6.09679e22 q^{31} +1.99357e23 q^{32} -1.97434e23 q^{34} -1.18789e24 q^{35} -2.07091e24 q^{37} +6.00172e22 q^{38} +6.55352e24 q^{40} +5.09498e24 q^{41} +8.39002e24 q^{43} -6.26628e24 q^{44} -5.95984e25 q^{46} -2.13587e25 q^{47} +1.96444e26 q^{49} -2.10964e25 q^{50} -3.22176e26 q^{52} -1.59213e26 q^{53} -3.39547e26 q^{55} -1.95421e27 q^{56} -1.63847e27 q^{58} -2.16250e27 q^{59} -6.60780e27 q^{61} -1.91122e27 q^{62} +7.86767e27 q^{64} -1.74576e28 q^{65} -2.77322e26 q^{67} +7.33607e27 q^{68} -3.72378e28 q^{70} -7.68524e28 q^{71} +2.29610e28 q^{73} -6.49186e28 q^{74} -2.23006e27 q^{76} +1.01250e29 q^{77} -2.99014e29 q^{79} +4.75619e28 q^{80} +1.59717e29 q^{82} -1.89466e29 q^{83} +3.97516e29 q^{85} +2.63009e29 q^{86} -5.58593e29 q^{88} +2.41523e30 q^{89} +5.20571e30 q^{91} +2.21450e30 q^{92} -6.69551e29 q^{94} -1.20839e29 q^{95} -3.68010e30 q^{97} +6.15810e30 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 39960 q^{2} + 1772534336 q^{4} + 19391218020 q^{5} + 30257527577200 q^{7} - 160155058705920 q^{8}+O(q^{10}) \) 2 * q - 39960 * q^2 + 1772534336 * q^4 + 19391218020 * q^5 + 30257527577200 * q^7 - 160155058705920 * q^8	\( 2 q - 39960 q^{2} + 1772534336 q^{4} + 19391218020 q^{5} + 30257527577200 q^{7} - 160155058705920 q^{8} - 78\!\cdots\!20 q^{10}+ \cdots + 80\!\cdots\!20 q^{98}+O(q^{100}) \) 2 * q - 39960 * q^2 + 1772534336 * q^4 + 19391218020 * q^5 + 30257527577200 * q^7 - 160155058705920 * q^8 - 7861972212281520 * q^10 + 7782353745118776 * q^11 + 74708953050260620 * q^13 - 225544963845241152 * q^14 - 3045212913684901888 * q^16 - 17224607828987089380 * q^17 - 12370563328022164040 * q^19 + 315868245501283090560 * q^20 - 2682713032996690080 * q^22 - 1897344841989911219280 * q^23 + 1477861250884539239150 * q^25 + 23066680666744323279216 * q^26 + 11671395808124240043520 * q^28 - 128576144217217055807340 * q^29 + 125733527517961838793664 * q^31 + 483720527174276002775040 * q^32 + 581706909571293028834992 * q^34 - 244269703121729304206880 * q^35 - 833815207054016911025060 * q^37 + 1078658489244045513633120 * q^38 + 1906531481497967156966400 * q^40 - 8724924335662925840671284 * q^41 - 18397105293779438708372600 * q^43 + 791008370873332311322368 * q^44 - 59873011445275600509089856 * q^46 - 95450963964856190793148320 * q^47 + 169469294372320202530407186 * q^49 - 174468018688948298981615400 * q^50 - 915180155081494236104643200 * q^52 - 194822508473721098983660860 * q^53 - 141313671368671671047892240 * q^55 - 2598355397749815172431728640 * q^56 + 3802934506602438134028187920 * q^58 + 198723263547765513990746520 * q^59 - 12056218201113004361157656276 * q^61 - 15224500099333079134598257920 * q^62 - 7488413368264058547677691904 * q^64 - 34114584794425827928886318760 * q^65 - 9688140802872256994032247720 * q^67 - 24758471836626330094958252160 * q^68 - 104525335953756946154610069120 * q^70 - 55784576625034657512878287344 * q^71 + 62234095932086098750552955380 * q^73 - 153133163632488378484794299472 * q^74 - 44190149699939358902474481920 * q^76 + 128728748793695217194494555200 * q^77 - 119164191093299704964212710560 * q^79 - 141515971255973138522638049280 * q^80 + 1145184549692595779551104209520 * q^82 + 264863373681569145625357596360 * q^83 - 503995105657776450242931421320 * q^85 + 2173142482222838422832927019936 * q^86 - 693913929707398651948752168960 * q^88 + 2154414614246670291602721895980 * q^89 + 2896781368068903069956049509024 * q^91 + 2225812737244025604862645470720 * q^92 + 4613808251402558431525114250112 * q^94 - 1299465173198290044974084355600 * q^95 - 9060767994874032615529957205180 * q^97 + 8081619677193750912975770689320 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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