LMFDB - Embedded newform 9.32.a.a.1.1

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			1.1
Root			$2139.16$ 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)

$f(q)$	$=$	$q-71307.9 q^{2} +2.93733e9 q^{4} +8.25073e10 q^{5} +1.14368e13 q^{7} -5.63222e13 q^{8} +O(q^{10})$	\(q-71307.9 q^{2} +2.93733e9 q^{4} +8.25073e10 q^{5} +1.14368e13 q^{7} -5.63222e13 q^{8} -5.88342e15 q^{10} +2.40262e15 q^{11} -2.01886e17 q^{13} -8.15534e17 q^{14} -2.29165e18 q^{16} -1.09264e19 q^{17} -1.42851e19 q^{19} +2.42351e20 q^{20} -1.71326e20 q^{22} +3.85062e18 q^{23} +2.15084e21 q^{25} +1.43960e22 q^{26} +3.35937e22 q^{28} -7.63087e22 q^{29} +1.86701e23 q^{31} +2.84364e23 q^{32} +7.79141e23 q^{34} +9.43620e23 q^{35} +1.23709e24 q^{37} +1.01864e24 q^{38} -4.64699e24 q^{40} -1.38199e25 q^{41} -2.67871e25 q^{43} +7.05729e24 q^{44} -2.74580e23 q^{46} -7.40922e25 q^{47} -2.69748e25 q^{49} -1.53372e26 q^{50} -5.93004e26 q^{52} -3.56092e25 q^{53} +1.98234e26 q^{55} -6.44146e26 q^{56} +5.44141e27 q^{58} +2.36122e27 q^{59} -5.44842e27 q^{61} -1.33133e28 q^{62} -1.53561e28 q^{64} -1.66570e28 q^{65} -9.41082e27 q^{67} -3.20945e28 q^{68} -6.72875e28 q^{70} +2.10678e28 q^{71} +3.92731e28 q^{73} -8.82146e28 q^{74} -4.19601e28 q^{76} +2.74783e28 q^{77} +1.79850e29 q^{79} -1.89078e29 q^{80} +9.85468e29 q^{82} +4.54329e29 q^{83} -9.01511e29 q^{85} +1.91013e30 q^{86} -1.35321e29 q^{88} -2.60812e29 q^{89} -2.30893e30 q^{91} +1.13106e28 q^{92} +5.28336e30 q^{94} -1.17863e30 q^{95} -5.38067e30 q^{97} +1.92352e30 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−71307.9	−1.53877	−0.769383	−	0.638788i	$-0.779436\pi$
$2$	−71307.9	−1.53877	−0.769383	+	0.638788i	$0.779436\pi$
$3$	0	0
$3$	0	0
$4$	2.93733e9	1.36780
$5$	8.25073e10	1.20909	0.604543	−	0.796573i	$-0.293356\pi$
$5$	8.25073e10	1.20909	0.604543	+	0.796573i	$0.293356\pi$
$6$	0	0
$7$	1.14368e13	0.910511	0.455256	−	0.890361i	$-0.349548\pi$
$7$	1.14368e13	0.910511	0.455256	+	0.890361i	$0.349548\pi$
$8$	−5.63222e13	−0.565959
$9$	0	0
$10$	−5.88342e15	−1.86050
$11$	2.40262e15	0.173420	0.0867099	−	0.996234i	$-0.472365\pi$
$11$	2.40262e15	0.173420	0.0867099	+	0.996234i	$0.472365\pi$
$12$	0	0
$13$	−2.01886e17	−1.09391	−0.546957	−	0.837161i	$-0.684214\pi$
$13$	−2.01886e17	−1.09391	−0.546957	+	0.837161i	$0.684214\pi$
$14$	−8.15534e17	−1.40106
$15$	0	0
$16$	−2.29165e18	−0.496923
$17$	−1.09264e19	−0.925807	−0.462903	−	0.886409i	$-0.653192\pi$
$17$	−1.09264e19	−0.925807	−0.462903	+	0.886409i	$0.653192\pi$
$18$	0	0
$19$	−1.42851e19	−0.215875	−0.107938	−	0.994158i	$-0.534425\pi$
$19$	−1.42851e19	−0.215875	−0.107938	+	0.994158i	$0.534425\pi$
$20$	2.42351e20	1.65379
$21$	0	0
$22$	−1.71326e20	−0.266853
$23$	3.85062e18	0.00301127	0.00150564	−	0.999999i	$-0.499521\pi$
$23$	3.85062e18	0.00301127	0.00150564	+	0.999999i	$0.499521\pi$
$24$	0	0
$25$	2.15084e21	0.461889
$26$	1.43960e22	1.68328
$27$	0	0
$28$	3.35937e22	1.24540
$29$	−7.63087e22	−1.64212	−0.821060	−	0.570842i	$-0.806617\pi$
$29$	−7.63087e22	−1.64212	−0.821060	+	0.570842i	$0.806617\pi$
$30$	0	0
$31$	1.86701e23	1.42903	0.714515	−	0.699620i	$-0.246647\pi$
$31$	1.86701e23	1.42903	0.714515	+	0.699620i	$0.246647\pi$
$32$	2.84364e23	1.33061
$33$	0	0
$34$	7.79141e23	1.42460
$35$	9.43620e23	1.10089
$36$	0	0
$37$	1.23709e24	0.609924	0.304962	−	0.952364i	$-0.401356\pi$
$37$	1.23709e24	0.609924	0.304962	+	0.952364i	$0.401356\pi$
$38$	1.01864e24	0.332182
$39$	0	0
$40$	−4.64699e24	−0.684293
$41$	−1.38199e25	−1.38789	−0.693945	−	0.720028i	$-0.744129\pi$
$41$	−1.38199e25	−1.38789	−0.693945	+	0.720028i	$0.744129\pi$
$42$	0	0
$43$	−2.67871e25	−1.28578	−0.642888	−	0.765960i	$-0.722264\pi$
$43$	−2.67871e25	−1.28578	−0.642888	+	0.765960i	$0.722264\pi$
$44$	7.05729e24	0.237204
$45$	0	0
$46$	−2.74580e23	−0.00463364
$47$	−7.40922e25	−0.895892	−0.447946	−	0.894061i	$-0.647844\pi$
$47$	−7.40922e25	−0.895892	−0.447946	+	0.894061i	$0.647844\pi$
$48$	0	0
$49$	−2.69748e25	−0.170970
$50$	−1.53372e26	−0.710739
$51$	0	0
$52$	−5.93004e26	−1.49626
$53$	−3.56092e25	−0.0668784	−0.0334392	−	0.999441i	$-0.510646\pi$
$53$	−3.56092e25	−0.0668784	−0.0334392	+	0.999441i	$0.510646\pi$
$54$	0	0
$55$	1.98234e26	0.209680
$56$	−6.44146e26	−0.515312
$57$	0	0
$58$	5.44141e27	2.52684
$59$	2.36122e27	0.841260	0.420630	−	0.907232i	$-0.361809\pi$
$59$	2.36122e27	0.841260	0.420630	+	0.907232i	$0.361809\pi$
$60$	0	0
$61$	−5.44842e27	−1.15786	−0.578932	−	0.815376i	$-0.696530\pi$
$61$	−5.44842e27	−1.15786	−0.578932	+	0.815376i	$0.696530\pi$
$62$	−1.33133e28	−2.19894
$63$	0	0
$64$	−1.53561e28	−1.55057
$65$	−1.66570e28	−1.32264
$66$	0	0
$67$	−9.41082e27	−0.467163	−0.233581	−	0.972337i	$-0.575044\pi$
$67$	−9.41082e27	−0.467163	−0.233581	+	0.972337i	$0.575044\pi$
$68$	−3.20945e28	−1.26632
$69$	0	0
$70$	−6.72875e28	−1.69401
$71$	2.10678e28	0.425712	0.212856	−	0.977084i	$-0.431724\pi$
$71$	2.10678e28	0.425712	0.212856	+	0.977084i	$0.431724\pi$
$72$	0	0
$73$	3.92731e28	0.515929	0.257965	−	0.966154i	$-0.416948\pi$
$73$	3.92731e28	0.515929	0.257965	+	0.966154i	$0.416948\pi$
$74$	−8.82146e28	−0.938531
$75$	0	0
$76$	−4.19601e28	−0.295274
$77$	2.74783e28	0.157901
$78$	0	0
$79$	1.79850e29	0.694529	0.347264	−	0.937767i	$-0.387111\pi$
$79$	1.79850e29	0.694529	0.347264	+	0.937767i	$0.387111\pi$
$80$	−1.89078e29	−0.600822
$81$	0	0
$82$	9.85468e29	2.13564
$83$	4.54329e29	0.815944	0.407972	−	0.912995i	$-0.366236\pi$
$83$	4.54329e29	0.815944	0.407972	+	0.912995i	$0.366236\pi$
$84$	0	0
$85$	−9.01511e29	−1.11938
$86$	1.91013e30	1.97851
$87$	0	0
$88$	−1.35321e29	−0.0981485
$89$	−2.60812e29	−0.158775	−0.0793875	−	0.996844i	$-0.525296\pi$
$89$	−2.60812e29	−0.158775	−0.0793875	+	0.996844i	$0.525296\pi$
$90$	0	0
$91$	−2.30893e30	−0.996021
$92$	1.13106e28	0.00411882
$93$	0	0
$94$	5.28336e30	1.37857
$95$	−1.17863e30	−0.261012
$96$	0	0
$97$	−5.38067e30	−0.862729	−0.431365	−	0.902178i	$-0.641968\pi$
$97$	−5.38067e30	−0.862729	−0.431365	+	0.902178i	$0.641968\pi$
$98$	1.92352e30	0.263082
$99$	0	0
$100$	6.31772e30	0.631772
$101$	1.28863e31	1.10445	0.552225	−	0.833695i	$-0.313779\pi$
$101$	1.28863e31	1.10445	0.552225	+	0.833695i	$0.313779\pi$
$102$	0	0
$103$	1.91208e31	1.20928	0.604642	−	0.796497i	$-0.293316\pi$
$103$	1.91208e31	1.20928	0.604642	+	0.796497i	$0.293316\pi$
$104$	1.13706e31	0.619110
$105$	0	0
$106$	2.53922e30	0.102910
$107$	−3.15334e31	−1.10490	−0.552449	−	0.833547i	$-0.686307\pi$
$107$	−3.15334e31	−1.10490	−0.552449	+	0.833547i	$0.686307\pi$
$108$	0	0
$109$	−3.61029e31	−0.949360	−0.474680	−	0.880158i	$-0.657436\pi$
$109$	−3.61029e31	−0.949360	−0.474680	+	0.880158i	$0.657436\pi$
$110$	−1.41356e31	−0.322648
$111$	0	0
$112$	−2.62092e31	−0.452453
$113$	−1.52549e31	−0.229454	−0.114727	−	0.993397i	$-0.536599\pi$
$113$	−1.52549e31	−0.229454	−0.114727	+	0.993397i	$0.536599\pi$
$114$	0	0
$115$	3.17705e29	0.00364088
$116$	−2.24144e32	−2.24609
$117$	0	0
$118$	−1.68374e32	−1.29450
$119$	−1.24964e32	−0.842957
$120$	0	0
$121$	−1.86171e32	−0.969926
$122$	3.88515e32	1.78168
$123$	0	0
$124$	5.48404e32	1.95463
$125$	−2.06745e32	−0.650623
$126$	0	0
$127$	−5.69060e32	−1.40023	−0.700116	−	0.714029i	$-0.746869\pi$
$127$	−5.69060e32	−1.40023	−0.700116	+	0.714029i	$0.746869\pi$
$128$	4.84344e32	1.05536
$129$	0	0
$130$	1.18778e33	2.03523
$131$	−1.80373e31	−0.0274452	−0.0137226	−	0.999906i	$-0.504368\pi$
$131$	−1.80373e31	−0.0274452	−0.0137226	+	0.999906i	$0.504368\pi$
$132$	0	0
$133$	−1.63376e32	−0.196557
$134$	6.71065e32	0.718854
$135$	0	0
$136$	6.15401e32	0.523968
$137$	1.53340e32	0.116543	0.0582716	−	0.998301i	$-0.481441\pi$
$137$	1.53340e32	0.116543	0.0582716	+	0.998301i	$0.481441\pi$
$138$	0	0
$139$	1.88034e33	1.14158	0.570791	−	0.821095i	$-0.306636\pi$
$139$	1.88034e33	1.14158	0.570791	+	0.821095i	$0.306636\pi$
$140$	2.77172e33	1.50579
$141$	0	0
$142$	−1.50230e33	−0.655070
$143$	−4.85055e32	−0.189706
$144$	0	0
$145$	−6.29602e33	−1.98546
$146$	−2.80048e33	−0.793895
$147$	0	0
$148$	3.63375e33	0.834255
$149$	−6.64703e33	−1.37480	−0.687401	−	0.726278i	$-0.741249\pi$
$149$	−6.64703e33	−1.37480	−0.687401	+	0.726278i	$0.741249\pi$
$150$	0	0
$151$	−6.58887e33	−1.10833	−0.554164	−	0.832408i	$-0.686962\pi$
$151$	−6.58887e33	−1.10833	−0.554164	+	0.832408i	$0.686962\pi$
$152$	8.04569e32	0.122177
$153$	0	0
$154$	−1.95942e33	−0.242972
$155$	1.54042e34	1.72782
$156$	0	0
$157$	1.60319e34	1.47414	0.737072	−	0.675814i	$-0.236208\pi$
$157$	1.60319e34	1.47414	0.737072	+	0.675814i	$0.236208\pi$
$158$	−1.28247e34	−1.06872
$159$	0	0
$160$	2.34621e34	1.60882
$161$	4.40389e31	0.00274179
$162$	0	0
$163$	−1.63484e34	−0.840555	−0.420277	−	0.907396i	$-0.638067\pi$
$163$	−1.63484e34	−0.840555	−0.420277	+	0.907396i	$0.638067\pi$
$164$	−4.05936e34	−1.89836
$165$	0	0
$166$	−3.23972e34	−1.25555
$167$	−1.68065e34	−0.593433	−0.296717	−	0.954966i	$-0.595892\pi$
$167$	−1.68065e34	−0.593433	−0.296717	+	0.954966i	$0.595892\pi$
$168$	0	0
$169$	6.69784e33	0.196649
$170$	6.42848e34	1.72246
$171$	0	0
$172$	−7.86826e34	−1.75868
$173$	−1.67734e34	−0.342695	−0.171347	−	0.985211i	$-0.554812\pi$
$173$	−1.67734e34	−0.342695	−0.171347	+	0.985211i	$0.554812\pi$
$174$	0	0
$175$	2.45987e34	0.420555
$176$	−5.50597e33	−0.0861762
$177$	0	0
$178$	1.85979e34	0.244318
$179$	−5.67856e33	−0.0683937	−0.0341968	−	0.999415i	$-0.510887\pi$
$179$	−5.67856e33	−0.0683937	−0.0341968	+	0.999415i	$0.510887\pi$
$180$	0	0
$181$	1.47595e35	1.49642	0.748210	−	0.663462i	$-0.230914\pi$
$181$	1.47595e35	1.49642	0.748210	+	0.663462i	$0.230914\pi$
$182$	1.64645e35	1.53264
$183$	0	0
$184$	−2.16876e32	−0.00170425
$185$	1.02069e35	0.737451
$186$	0	0
$187$	−2.62521e34	−0.160553
$188$	−2.17633e35	−1.22540
$189$	0	0
$190$	8.40453e34	0.401636
$191$	4.38203e34	0.193045	0.0965224	−	0.995331i	$-0.469228\pi$
$191$	4.38203e34	0.193045	0.0965224	+	0.995331i	$0.469228\pi$
$192$	0	0
$193$	2.63656e35	0.988323	0.494161	−	0.869370i	$-0.335475\pi$
$193$	2.63656e35	0.988323	0.494161	+	0.869370i	$0.335475\pi$
$194$	3.83684e35	1.32754
$195$	0	0
$196$	−7.92339e34	−0.233852
$197$	2.72680e35	0.743749	0.371875	−	0.928283i	$-0.378715\pi$
$197$	2.72680e35	0.743749	0.371875	+	0.928283i	$0.378715\pi$
$198$	0	0
$199$	3.17714e35	0.740991	0.370496	−	0.928834i	$-0.379188\pi$
$199$	3.17714e35	0.740991	0.370496	+	0.928834i	$0.379188\pi$
$200$	−1.21140e35	−0.261410
$201$	0	0
$202$	−9.18893e35	−1.69949
$203$	−8.72728e35	−1.49517
$204$	0	0
$205$	−1.14024e36	−1.67808
$206$	−1.36346e36	−1.86081
$207$	0	0
$208$	4.62651e35	0.543591
$209$	−3.43217e34	−0.0374371
$210$	0	0
$211$	−2.10102e36	−1.97721	−0.988604	−	0.150541i	$-0.951898\pi$
$211$	−2.10102e36	−1.97721	−0.988604	+	0.150541i	$0.951898\pi$
$212$	−1.04596e35	−0.0914763
$213$	0	0
$214$	2.24858e36	1.70018
$215$	−2.21013e36	−1.55461
$216$	0	0
$217$	2.13527e36	1.30115
$218$	2.57442e36	1.46084
$219$	0	0
$220$	5.82278e35	0.286800
$221$	2.20589e36	1.01275
$222$	0	0
$223$	−2.62490e36	−1.04806	−0.524032	−	0.851699i	$-0.675573\pi$
$223$	−2.62490e36	−1.04806	−0.524032	+	0.851699i	$0.675573\pi$
$224$	3.25221e36	1.21153
$225$	0	0
$226$	1.08780e36	0.353075
$227$	−1.16088e35	−0.0351874	−0.0175937	−	0.999845i	$-0.505601\pi$
$227$	−1.16088e35	−0.0351874	−0.0175937	+	0.999845i	$0.505601\pi$
$228$	0	0
$229$	1.39980e36	0.370353	0.185177	−	0.982705i	$-0.440714\pi$
$229$	1.39980e36	0.370353	0.185177	+	0.982705i	$0.440714\pi$
$230$	−2.26548e34	−0.00560247
$231$	0	0
$232$	4.29787e36	0.929372
$233$	−7.15120e36	−1.44665	−0.723323	−	0.690510i	$-0.757386\pi$
$233$	−7.15120e36	−1.44665	−0.723323	+	0.690510i	$0.757386\pi$
$234$	0	0
$235$	−6.11315e36	−1.08321
$236$	6.93568e36	1.15068
$237$	0	0
$238$	8.91089e36	1.29711
$239$	−2.96558e36	−0.404522	−0.202261	−	0.979332i	$-0.564829\pi$
$239$	−2.96558e36	−0.404522	−0.202261	+	0.979332i	$0.564829\pi$
$240$	0	0
$241$	−7.20536e36	−0.863757	−0.431879	−	0.901932i	$-0.642149\pi$
$241$	−7.20536e36	−0.863757	−0.431879	+	0.901932i	$0.642149\pi$
$242$	1.32754e37	1.49249
$243$	0	0
$244$	−1.60038e37	−1.58373
$245$	−2.22562e36	−0.206717
$246$	0	0
$247$	2.88396e36	0.236149
$248$	−1.05154e37	−0.808772
$249$	0	0
$250$	1.47425e37	1.00116
$251$	−9.47842e36	−0.605053	−0.302526	−	0.953141i	$-0.597830\pi$
$251$	−9.47842e36	−0.605053	−0.302526	+	0.953141i	$0.597830\pi$
$252$	0	0
$253$	9.25159e33	0.000522214 0
$254$	4.05784e37	2.15463
$255$	0	0
$256$	−1.56056e36	−0.0733772
$257$	−3.15504e37	−1.39650	−0.698252	−	0.715852i	$-0.746038\pi$
$257$	−3.15504e37	−1.39650	−0.698252	+	0.715852i	$0.746038\pi$
$258$	0	0
$259$	1.41484e37	0.555343
$260$	−4.89272e37	−1.80910
$261$	0	0
$262$	1.28620e36	0.0422318
$263$	1.25731e37	0.389159	0.194580	−	0.980887i	$-0.437666\pi$
$263$	1.25731e37	0.389159	0.194580	+	0.980887i	$0.437666\pi$
$264$	0	0
$265$	−2.93802e36	−0.0808618
$266$	1.16500e37	0.302455
$267$	0	0
$268$	−2.76427e37	−0.638985
$269$	−3.34018e37	−0.728801	−0.364401	−	0.931242i	$-0.618726\pi$
$269$	−3.34018e37	−0.728801	−0.364401	+	0.931242i	$0.618726\pi$
$270$	0	0
$271$	−4.00526e36	−0.0779125	−0.0389562	−	0.999241i	$-0.512403\pi$
$271$	−4.00526e36	−0.0779125	−0.0389562	+	0.999241i	$0.512403\pi$
$272$	2.50396e37	0.460054
$273$	0	0
$274$	−1.09344e37	−0.179333
$275$	5.16765e36	0.0801007
$276$	0	0
$277$	−7.94796e37	−1.10108	−0.550541	−	0.834808i	$-0.685578\pi$
$277$	−7.94796e37	−1.10108	−0.550541	+	0.834808i	$0.685578\pi$
$278$	−1.34083e38	−1.75663
$279$	0	0
$280$	−5.31467e37	−0.623056
$281$	1.69314e38	1.87822	0.939108	−	0.343621i	$-0.111654\pi$
$281$	1.69314e38	1.87822	0.939108	+	0.343621i	$0.111654\pi$
$282$	0	0
$283$	1.18735e38	1.18002	0.590008	−	0.807397i	$-0.299125\pi$
$283$	1.18735e38	1.18002	0.590008	+	0.807397i	$0.299125\pi$
$284$	6.18832e37	0.582288
$285$	0	0
$286$	3.45882e37	0.291914
$287$	−1.58056e38	−1.26369
$288$	0	0
$289$	−1.99019e37	−0.142882
$290$	4.48956e38	3.05516
$291$	0	0
$292$	1.15358e38	0.705689
$293$	−9.32191e37	−0.540825	−0.270413	−	0.962745i	$-0.587160\pi$
$293$	−9.32191e37	−0.540825	−0.270413	+	0.962745i	$0.587160\pi$
$294$	0	0
$295$	1.94818e38	1.01716
$296$	−6.96759e37	−0.345192
$297$	0	0
$298$	4.73985e38	2.11550
$299$	−7.77386e35	−0.00329407
$300$	0	0
$301$	−3.06359e38	−1.17071
$302$	4.69838e38	1.70546
$303$	0	0
$304$	3.27365e37	0.107273
$305$	−4.49534e38	−1.39996
$306$	0	0
$307$	−2.10829e38	−0.593314	−0.296657	−	0.954984i	$-0.595872\pi$
$307$	−2.10829e38	−0.593314	−0.296657	+	0.954984i	$0.595872\pi$
$308$	8.07129e37	0.215977
$309$	0	0
$310$	−1.09844e39	−2.65871
$311$	−4.24765e38	−0.978053	−0.489027	−	0.872269i	$-0.662648\pi$
$311$	−4.24765e38	−0.978053	−0.489027	+	0.872269i	$0.662648\pi$
$312$	0	0
$313$	−3.07637e38	−0.641360	−0.320680	−	0.947188i	$-0.603911\pi$
$313$	−3.07637e38	−0.641360	−0.320680	+	0.947188i	$0.603911\pi$
$314$	−1.14320e39	−2.26836
$315$	0	0
$316$	5.28278e38	0.949976
$317$	9.76522e38	1.67210	0.836052	−	0.548650i	$-0.184858\pi$
$317$	9.76522e38	1.67210	0.836052	+	0.548650i	$0.184858\pi$
$318$	0	0
$319$	−1.83341e38	−0.284776
$320$	−1.26699e39	−1.87477
$321$	0	0
$322$	−3.14032e36	−0.00421898
$323$	1.56085e38	0.199859
$324$	0	0
$325$	−4.34223e38	−0.505267
$326$	1.16577e39	1.29342
$327$	0	0
$328$	7.78367e38	0.785489
$329$	−8.47379e38	−0.815720
$330$	0	0
$331$	8.30576e38	0.727856	0.363928	−	0.931427i	$-0.381435\pi$
$331$	8.30576e38	0.727856	0.363928	+	0.931427i	$0.381435\pi$
$332$	1.33451e39	1.11605
$333$	0	0
$334$	1.19844e39	0.913155
$335$	−7.76461e38	−0.564840
$336$	0	0
$337$	1.84495e39	1.22383	0.611916	−	0.790923i	$-0.290399\pi$
$337$	1.84495e39	1.22383	0.611916	+	0.790923i	$0.290399\pi$
$338$	−4.77609e38	−0.302596
$339$	0	0
$340$	−2.64803e39	−1.53109
$341$	4.48573e38	0.247822
$342$	0	0
$343$	−2.11295e39	−1.06618
$344$	1.50871e39	0.727696
$345$	0	0
$346$	1.19608e39	0.527327
$347$	3.59852e39	1.51711	0.758555	−	0.651609i	$-0.225906\pi$
$347$	3.59852e39	1.51711	0.758555	+	0.651609i	$0.225906\pi$
$348$	0	0
$349$	4.09325e38	0.157861	0.0789303	−	0.996880i	$-0.474850\pi$
$349$	4.09325e38	0.157861	0.0789303	+	0.996880i	$0.474850\pi$
$350$	−1.75408e39	−0.647136
$351$	0	0
$352$	6.83218e38	0.230754
$353$	5.32510e39	1.72116	0.860578	−	0.509319i	$-0.170103\pi$
$353$	5.32510e39	1.72116	0.860578	+	0.509319i	$0.170103\pi$
$354$	0	0
$355$	1.73825e39	0.514722
$356$	−7.66090e38	−0.217173
$357$	0	0
$358$	4.04926e38	0.105242
$359$	−4.10824e39	−1.02257	−0.511283	−	0.859412i	$-0.670830\pi$
$359$	−4.10824e39	−1.02257	−0.511283	+	0.859412i	$0.670830\pi$
$360$	0	0
$361$	−4.17480e39	−0.953398
$362$	−1.05247e40	−2.30264
$363$	0	0
$364$	−6.78208e39	−1.36236
$365$	3.24031e39	0.623803
$366$	0	0
$367$	9.50139e39	1.68060	0.840298	−	0.542125i	$-0.182380\pi$
$367$	9.50139e39	1.68060	0.840298	+	0.542125i	$0.182380\pi$
$368$	−8.82429e36	−0.00149637
$369$	0	0
$370$	−7.27834e39	−1.13476
$371$	−4.07255e38	−0.0608935
$372$	0	0
$373$	5.31105e39	0.730624	0.365312	−	0.930885i	$-0.380962\pi$
$373$	5.31105e39	0.730624	0.365312	+	0.930885i	$0.380962\pi$
$374$	1.87198e39	0.247054
$375$	0	0
$376$	4.17304e39	0.507038
$377$	1.54056e40	1.79634
$378$	0	0
$379$	6.56433e39	0.705152	0.352576	−	0.935783i	$-0.385306\pi$
$379$	6.56433e39	0.705152	0.352576	+	0.935783i	$0.385306\pi$
$380$	−3.46201e39	−0.357012
$381$	0	0
$382$	−3.12473e39	−0.297051
$383$	−4.90622e39	−0.447884	−0.223942	−	0.974602i	$-0.571893\pi$
$383$	−4.90622e39	−0.447884	−0.223942	+	0.974602i	$0.571893\pi$
$384$	0	0
$385$	2.26716e39	0.190916
$386$	−1.88007e40	−1.52080
$387$	0	0
$388$	−1.58048e40	−1.18004
$389$	−1.47786e40	−1.06026	−0.530132	−	0.847915i	$-0.677858\pi$
$389$	−1.47786e40	−1.06026	−0.530132	+	0.847915i	$0.677858\pi$
$390$	0	0
$391$	−4.20736e37	−0.00278785
$392$	1.51928e39	0.0967617
$393$	0	0
$394$	−1.94442e40	−1.14446
$395$	1.48389e40	0.839745
$396$	0	0
$397$	9.79733e39	0.512690	0.256345	−	0.966585i	$-0.417482\pi$
$397$	9.79733e39	0.512690	0.256345	+	0.966585i	$0.417482\pi$
$398$	−2.26555e40	−1.14021
$399$	0	0
$400$	−4.92897e39	−0.229523
$401$	−1.11974e40	−0.501624	−0.250812	−	0.968036i	$-0.580698\pi$
$401$	−1.11974e40	−0.501624	−0.250812	+	0.968036i	$0.580698\pi$
$402$	0	0
$403$	−3.76923e40	−1.56324
$404$	3.78513e40	1.51067
$405$	0	0
$406$	6.22323e40	2.30071
$407$	2.97227e39	0.105773
$408$	0	0
$409$	−2.34914e40	−0.774815	−0.387408	−	0.921909i	$-0.626629\pi$
$409$	−2.34914e40	−0.774815	−0.387408	+	0.921909i	$0.626629\pi$
$410$	8.13083e40	2.58217
$411$	0	0
$412$	5.61640e40	1.65406
$413$	2.70048e40	0.765977
$414$	0	0
$415$	3.74855e40	0.986546
$416$	−5.74089e40	−1.45557
$417$	0	0
$418$	2.44741e39	0.0576069
$419$	−4.42578e40	−1.00386	−0.501929	−	0.864909i	$-0.667376\pi$
$419$	−4.42578e40	−1.00386	−0.501929	+	0.864909i	$0.667376\pi$
$420$	0	0
$421$	−4.58467e40	−0.965907	−0.482954	−	0.875646i	$-0.660436\pi$
$421$	−4.58467e40	−0.965907	−0.482954	+	0.875646i	$0.660436\pi$
$422$	1.49819e41	3.04246
$423$	0	0
$424$	2.00559e39	0.0378504
$425$	−2.35010e40	−0.427620
$426$	0	0
$427$	−6.23125e40	−1.05425
$428$	−9.26239e40	−1.51128
$429$	0	0
$430$	1.57600e41	2.39219
$431$	1.63894e40	0.239975	0.119987	−	0.992775i	$-0.461715\pi$
$431$	1.63894e40	0.239975	0.119987	+	0.992775i	$0.461715\pi$
$432$	0	0
$433$	7.21840e39	0.0983737	0.0491868	−	0.998790i	$-0.484337\pi$
$433$	7.21840e39	0.0983737	0.0491868	+	0.998790i	$0.484337\pi$
$434$	−1.52261e41	−2.00216
$435$	0	0
$436$	−1.06046e41	−1.29854
$437$	−5.50066e37	−0.000650059 0
$438$	0	0
$439$	1.72040e40	0.189422	0.0947109	−	0.995505i	$-0.469807\pi$
$439$	1.72040e40	0.189422	0.0947109	+	0.995505i	$0.469807\pi$
$440$	−1.11650e40	−0.118670
$441$	0	0
$442$	−1.57297e41	−1.55839
$443$	9.22567e39	0.0882552	0.0441276	−	0.999026i	$-0.485949\pi$
$443$	9.22567e39	0.0882552	0.0441276	+	0.999026i	$0.485949\pi$
$444$	0	0
$445$	−2.15189e40	−0.191973
$446$	1.87176e41	1.61272
$447$	0	0
$448$	−1.75625e41	−1.41181
$449$	−1.80147e41	−1.39897	−0.699484	−	0.714648i	$-0.746587\pi$
$449$	−1.80147e41	−1.39897	−0.699484	+	0.714648i	$0.746587\pi$
$450$	0	0
$451$	−3.32040e40	−0.240688
$452$	−4.48088e40	−0.313847
$453$	0	0
$454$	8.27801e39	0.0541452
$455$	−1.90503e41	−1.20428
$456$	0	0
$457$	7.03528e40	0.415509	0.207754	−	0.978181i	$-0.433385\pi$
$457$	7.03528e40	0.415509	0.207754	+	0.978181i	$0.433385\pi$
$458$	−9.98168e40	−0.569887
$459$	0	0
$460$	9.33203e38	0.00498000
$461$	2.15013e40	0.110943	0.0554717	−	0.998460i	$-0.482334\pi$
$461$	2.15013e40	0.110943	0.0554717	+	0.998460i	$0.482334\pi$
$462$	0	0
$463$	3.68798e41	1.77944	0.889720	−	0.456506i	$-0.150899\pi$
$463$	3.68798e41	1.77944	0.889720	+	0.456506i	$0.150899\pi$
$464$	1.74873e41	0.816006
$465$	0	0
$466$	5.09937e41	2.22605
$467$	3.35225e41	1.41555	0.707775	−	0.706438i	$-0.249699\pi$
$467$	3.35225e41	1.41555	0.707775	+	0.706438i	$0.249699\pi$
$468$	0	0
$469$	−1.07630e41	−0.425357
$470$	4.35916e41	1.66681
$471$	0	0
$472$	−1.32989e41	−0.476118
$473$	−6.43593e40	−0.222979
$474$	0	0
$475$	−3.07250e40	−0.0997104
$476$	−3.67059e41	−1.15300
$477$	0	0
$478$	2.11469e41	0.622464
$479$	1.78256e41	0.507976	0.253988	−	0.967207i	$-0.418258\pi$
$479$	1.78256e41	0.507976	0.253988	+	0.967207i	$0.418258\pi$
$480$	0	0
$481$	−2.49751e41	−0.667205
$482$	5.13799e41	1.32912
$483$	0	0
$484$	−5.46845e41	−1.32666
$485$	−4.43944e41	−1.04311
$486$	0	0
$487$	−2.96115e41	−0.652772	−0.326386	−	0.945237i	$-0.605831\pi$
$487$	−2.96115e41	−0.652772	−0.326386	+	0.945237i	$0.605831\pi$
$488$	3.06867e41	0.655304
$489$	0	0
$490$	1.58704e41	0.318089
$491$	−2.87172e41	−0.557671	−0.278836	−	0.960339i	$-0.589948\pi$
$491$	−2.87172e41	−0.557671	−0.278836	+	0.960339i	$0.589948\pi$
$492$	0	0
$493$	8.33782e41	1.52029
$494$	−2.05649e41	−0.363378
$495$	0	0
$496$	−4.27855e41	−0.710117
$497$	2.40949e41	0.387615
$498$	0	0
$499$	−1.19160e42	−1.80125	−0.900623	−	0.434601i	$-0.856889\pi$
$499$	−1.19160e42	−1.80125	−0.900623	+	0.434601i	$0.856889\pi$
$500$	−6.07277e41	−0.889922
$501$	0	0
$502$	6.75886e41	0.931035
$503$	−1.92359e41	−0.256926	−0.128463	−	0.991714i	$-0.541004\pi$
$503$	−1.92359e41	−0.256926	−0.128463	+	0.991714i	$0.541004\pi$
$504$	0	0
$505$	1.06321e42	1.33538
$506$	−6.59712e38	−0.000803565 0
$507$	0	0
$508$	−1.67152e42	−1.91524
$509$	4.08219e41	0.453699	0.226849	−	0.973930i	$-0.427157\pi$
$509$	4.08219e41	0.453699	0.226849	+	0.973930i	$0.427157\pi$
$510$	0	0
$511$	4.49158e41	0.469759
$512$	−9.28840e41	−0.942446
$513$	0	0
$514$	2.24980e42	2.14889
$515$	1.57760e42	1.46213
$516$	0	0
$517$	−1.78016e41	−0.155366
$518$	−1.00889e42	−0.854543
$519$	0	0
$520$	9.38160e41	0.748558
$521$	−8.76030e41	−0.678476	−0.339238	−	0.940701i	$-0.610169\pi$
$521$	−8.76030e41	−0.678476	−0.339238	+	0.940701i	$0.610169\pi$
$522$	0	0
$523$	−1.52051e42	−1.10972	−0.554859	−	0.831944i	$-0.687228\pi$
$523$	−1.52051e42	−1.10972	−0.554859	+	0.831944i	$0.687228\pi$
$524$	−5.29815e40	−0.0375396
$525$	0	0
$526$	−8.96559e41	−0.598825
$527$	−2.03998e42	−1.32301
$528$	0	0
$529$	−1.63516e42	−0.999991
$530$	2.09504e41	0.124427
$531$	0	0
$532$	−4.79889e41	−0.268851
$533$	2.79004e42	1.51823
$534$	0	0
$535$	−2.60173e42	−1.33592
$536$	5.30038e41	0.264395
$537$	0	0
$538$	2.38181e42	1.12145
$539$	−6.48102e40	−0.0296495
$540$	0	0
$541$	2.17683e42	0.940301	0.470150	−	0.882586i	$-0.344200\pi$
$541$	2.17683e42	0.940301	0.470150	+	0.882586i	$0.344200\pi$
$542$	2.85607e41	0.119889
$543$	0	0
$544$	−3.10708e42	−1.23188
$545$	−2.97875e42	−1.14786
$546$	0	0
$547$	2.57006e42	0.935707	0.467854	−	0.883806i	$-0.345027\pi$
$547$	2.57006e42	0.935707	0.467854	+	0.883806i	$0.345027\pi$
$548$	4.50410e41	0.159408
$549$	0	0
$550$	−3.68494e41	−0.123256
$551$	1.09008e42	0.354493
$552$	0	0
$553$	2.05691e42	0.632376
$554$	5.66752e42	1.69431
$555$	0	0
$556$	5.52318e42	1.56146
$557$	2.88974e42	0.794517	0.397258	−	0.917707i	$-0.369962\pi$
$557$	2.88974e42	0.794517	0.397258	+	0.917707i	$0.369962\pi$
$558$	0	0
$559$	5.40793e42	1.40653
$560$	−2.16245e42	−0.547055
$561$	0	0
$562$	−1.20734e43	−2.89014
$563$	5.57652e42	1.29862	0.649312	−	0.760522i	$-0.275057\pi$
$563$	5.57652e42	1.29862	0.649312	+	0.760522i	$0.275057\pi$
$564$	0	0
$565$	−1.25864e42	−0.277429
$566$	−8.46672e42	−1.81577
$567$	0	0
$568$	−1.18659e42	−0.240935
$569$	3.00301e42	0.593357	0.296679	−	0.954977i	$-0.404121\pi$
$569$	3.00301e42	0.593357	0.296679	+	0.954977i	$0.404121\pi$
$570$	0	0
$571$	1.00812e43	1.88649	0.943245	−	0.332099i	$-0.107757\pi$
$571$	1.00812e43	1.88649	0.943245	+	0.332099i	$0.107757\pi$
$572$	−1.42477e42	−0.259481
$573$	0	0
$574$	1.12706e43	1.94452
$575$	8.28207e39	0.00139087
$576$	0	0
$577$	−7.02075e42	−1.11727	−0.558635	−	0.829413i	$-0.688675\pi$
$577$	−7.02075e42	−1.11727	−0.558635	+	0.829413i	$0.688675\pi$
$578$	1.41916e42	0.219862
$579$	0	0
$580$	−1.84935e43	−2.71572
$581$	5.19607e42	0.742926
$582$	0	0
$583$	−8.55554e40	−0.0115980
$584$	−2.21194e42	−0.291995
$585$	0	0
$586$	6.64726e42	0.832203
$587$	−1.56627e43	−1.90974	−0.954872	−	0.297018i	$-0.904008\pi$
$587$	−1.56627e43	−1.90974	−0.954872	+	0.297018i	$0.904008\pi$
$588$	0	0
$589$	−2.66705e42	−0.308492
$590$	−1.38920e43	−1.56516
$591$	0	0
$592$	−2.83499e42	−0.303085
$593$	1.51645e42	0.157936	0.0789678	−	0.996877i	$-0.474838\pi$
$593$	1.51645e42	0.157936	0.0789678	+	0.996877i	$0.474838\pi$
$594$	0	0
$595$	−1.03104e43	−1.01921
$596$	−1.95245e43	−1.88046
$597$	0	0
$598$	5.54337e40	0.00506880
$599$	8.56958e42	0.763561	0.381781	−	0.924253i	$-0.375311\pi$
$599$	8.56958e42	0.763561	0.381781	+	0.924253i	$0.375311\pi$
$600$	0	0
$601$	−2.71633e42	−0.229841	−0.114921	−	0.993375i	$-0.536661\pi$
$601$	−2.71633e42	−0.229841	−0.114921	+	0.993375i	$0.536661\pi$
$602$	2.18458e43	1.80145
$603$	0	0
$604$	−1.93537e43	−1.51597
$605$	−1.53604e43	−1.17272
$606$	0	0
$607$	5.39744e42	0.391528	0.195764	−	0.980651i	$-0.437281\pi$
$607$	5.39744e42	0.391528	0.195764	+	0.980651i	$0.437281\pi$
$608$	−4.06217e42	−0.287245
$609$	0	0
$610$	3.20553e43	2.15421
$611$	1.49582e43	0.980030
$612$	0	0
$613$	6.77481e42	0.421949	0.210975	−	0.977492i	$-0.432336\pi$
$613$	6.77481e42	0.421949	0.210975	+	0.977492i	$0.432336\pi$
$614$	1.50337e43	0.912972
$615$	0	0
$616$	−1.54764e42	−0.0893653
$617$	8.39156e41	0.0472523	0.0236261	−	0.999721i	$-0.492479\pi$
$617$	8.39156e41	0.0472523	0.0236261	+	0.999721i	$0.492479\pi$
$618$	0	0
$619$	1.34876e43	0.722318	0.361159	−	0.932504i	$-0.382381\pi$
$619$	1.34876e43	0.722318	0.361159	+	0.932504i	$0.382381\pi$
$620$	4.52473e43	2.36331
$621$	0	0
$622$	3.02891e43	1.50499
$623$	−2.98286e42	−0.144566
$624$	0	0
$625$	−2.70736e43	−1.24855
$626$	2.19370e43	0.986902
$627$	0	0
$628$	4.70909e43	2.01634
$629$	−1.35170e43	−0.564672
$630$	0	0
$631$	−4.65263e42	−0.185031	−0.0925153	−	0.995711i	$-0.529491\pi$
$631$	−4.65263e42	−0.185031	−0.0925153	+	0.995711i	$0.529491\pi$
$632$	−1.01295e43	−0.393074
$633$	0	0
$634$	−6.96337e43	−2.57298
$635$	−4.69516e43	−1.69300
$636$	0	0
$637$	5.44582e42	0.187026
$638$	1.30736e43	0.438204
$639$	0	0
$640$	3.99619e43	1.27602
$641$	−4.24972e43	−1.32453	−0.662263	−	0.749271i	$-0.730404\pi$
$641$	−4.24972e43	−1.32453	−0.662263	+	0.749271i	$0.730404\pi$
$642$	0	0
$643$	−5.33186e43	−1.58347	−0.791733	−	0.610868i	$-0.790821\pi$
$643$	−5.33186e43	−1.58347	−0.791733	+	0.610868i	$0.790821\pi$
$644$	1.29357e41	0.00375023
$645$	0	0
$646$	−1.11301e43	−0.307536
$647$	1.00492e43	0.271092	0.135546	−	0.990771i	$-0.456721\pi$
$647$	1.00492e43	0.271092	0.135546	+	0.990771i	$0.456721\pi$
$648$	0	0
$649$	5.67312e42	0.145891
$650$	3.09635e43	0.777487
$651$	0	0
$652$	−4.80205e43	−1.14971
$653$	7.98263e43	1.86634	0.933172	−	0.359430i	$-0.117029\pi$
$653$	7.98263e43	1.86634	0.933172	+	0.359430i	$0.117029\pi$
$654$	0	0
$655$	−1.48821e42	−0.0331836
$656$	3.16704e43	0.689674
$657$	0	0
$658$	6.04248e43	1.25520
$659$	−7.54017e43	−1.52988	−0.764940	−	0.644102i	$-0.777231\pi$
$659$	−7.54017e43	−1.52988	−0.764940	+	0.644102i	$0.777231\pi$
$660$	0	0
$661$	−3.00409e42	−0.0581555	−0.0290777	−	0.999577i	$-0.509257\pi$
$661$	−3.00409e42	−0.0581555	−0.0290777	+	0.999577i	$0.509257\pi$
$662$	−5.92266e43	−1.12000
$663$	0	0
$664$	−2.55888e43	−0.461790
$665$	−1.34797e43	−0.237654
$666$	0	0
$667$	−2.93836e41	−0.00494487
$668$	−4.93662e43	−0.811698
$669$	0	0
$670$	5.53678e43	0.869156
$671$	−1.30905e43	−0.200797
$672$	0	0
$673$	2.05730e43	0.301346	0.150673	−	0.988584i	$-0.451856\pi$
$673$	2.05730e43	0.301346	0.150673	+	0.988584i	$0.451856\pi$
$674$	−1.31560e44	−1.88319
$675$	0	0
$676$	1.96738e43	0.268976
$677$	1.03692e44	1.38554	0.692772	−	0.721157i	$-0.256389\pi$
$677$	1.03692e44	1.38554	0.692772	+	0.721157i	$0.256389\pi$
$678$	0	0
$679$	−6.15377e43	−0.785524
$680$	5.07751e43	0.633523
$681$	0	0
$682$	−3.19868e43	−0.381340
$683$	−1.01818e44	−1.18660	−0.593302	−	0.804980i	$-0.702176\pi$
$683$	−1.01818e44	−1.18660	−0.593302	+	0.804980i	$0.702176\pi$
$684$	0	0
$685$	1.26517e43	0.140911
$686$	1.50670e44	1.64060
$687$	0	0
$688$	6.13867e43	0.638931
$689$	7.18898e42	0.0731593
$690$	0	0
$691$	1.12626e44	1.09579	0.547895	−	0.836547i	$-0.315429\pi$
$691$	1.12626e44	1.09579	0.547895	+	0.836547i	$0.315429\pi$
$692$	−4.92691e43	−0.468738
$693$	0	0
$694$	−2.56603e44	−2.33448
$695$	1.55142e44	1.38027
$696$	0	0
$697$	1.51002e44	1.28492
$698$	−2.91881e43	−0.242911
$699$	0	0
$700$	7.22545e43	0.575235
$701$	−3.06210e43	−0.238446	−0.119223	−	0.992867i	$-0.538040\pi$
$701$	−3.06210e43	−0.238446	−0.119223	+	0.992867i	$0.538040\pi$
$702$	0	0
$703$	−1.76720e43	−0.131668
$704$	−3.68949e43	−0.268899
$705$	0	0
$706$	−3.79722e44	−2.64846
$707$	1.47378e44	1.00561
$708$	0	0
$709$	−9.24433e43	−0.603752	−0.301876	−	0.953347i	$-0.597613\pi$
$709$	−9.24433e43	−0.603752	−0.301876	+	0.953347i	$0.597613\pi$
$710$	−1.23951e44	−0.792036
$711$	0	0
$712$	1.46895e43	0.0898601
$713$	7.18917e41	0.00430320
$714$	0	0
$715$	−4.00205e43	−0.229371
$716$	−1.66798e43	−0.0935489
$717$	0	0
$718$	2.92950e44	1.57349
$719$	9.29670e43	0.488687	0.244344	−	0.969689i	$-0.421428\pi$
$719$	9.29670e43	0.488687	0.244344	+	0.969689i	$0.421428\pi$
$720$	0	0
$721$	2.18681e44	1.10107
$722$	2.97696e44	1.46706
$723$	0	0
$724$	4.33535e44	2.04680
$725$	−1.64128e44	−0.758477
$726$	0	0
$727$	1.34756e44	0.596710	0.298355	−	0.954455i	$-0.403562\pi$
$727$	1.34756e44	0.596710	0.298355	+	0.954455i	$0.403562\pi$
$728$	1.30044e44	0.563707
$729$	0	0
$730$	−2.31060e44	−0.959887
$731$	2.92688e44	1.19038
$732$	0	0
$733$	1.96770e44	0.767093	0.383546	−	0.923522i	$-0.374703\pi$
$733$	1.96770e44	0.767093	0.383546	+	0.923522i	$0.374703\pi$
$734$	−6.77524e44	−2.58604
$735$	0	0
$736$	1.09498e42	0.00400681
$737$	−2.26106e43	−0.0810153
$738$	0	0
$739$	−3.41064e44	−1.17178	−0.585891	−	0.810390i	$-0.699255\pi$
$739$	−3.41064e44	−1.17178	−0.585891	+	0.810390i	$0.699255\pi$
$740$	2.99811e44	1.00869
$741$	0	0
$742$	2.90405e43	0.0937009
$743$	2.64820e44	0.836805	0.418403	−	0.908262i	$-0.362590\pi$
$743$	2.64820e44	0.836805	0.418403	+	0.908262i	$0.362590\pi$
$744$	0	0
$745$	−5.48428e44	−1.66225
$746$	−3.78720e44	−1.12426
$747$	0	0
$748$	−7.71111e43	−0.219605
$749$	−3.60641e44	−1.00602
$750$	0	0
$751$	3.88190e44	1.03902	0.519511	−	0.854464i	$-0.326114\pi$
$751$	3.88190e44	1.03902	0.519511	+	0.854464i	$0.326114\pi$
$752$	1.69794e44	0.445189
$753$	0	0
$754$	−1.09854e45	−2.76414
$755$	−5.43630e44	−1.34006
$756$	0	0
$757$	2.10907e44	0.499004	0.249502	−	0.968374i	$-0.419733\pi$
$757$	2.10907e44	0.499004	0.249502	+	0.968374i	$0.419733\pi$
$758$	−4.68088e44	−1.08506
$759$	0	0
$760$	6.63828e43	0.147722
$761$	−3.24151e43	−0.0706782	−0.0353391	−	0.999375i	$-0.511251\pi$
$761$	−3.24151e43	−0.0706782	−0.0353391	+	0.999375i	$0.511251\pi$
$762$	0	0
$763$	−4.12902e44	−0.864403
$764$	1.28715e44	0.264047
$765$	0	0
$766$	3.49852e44	0.689189
$767$	−4.76696e44	−0.920266
$768$	0	0
$769$	−6.38736e44	−1.18430	−0.592152	−	0.805827i	$-0.701721\pi$
$769$	−6.38736e44	−1.18430	−0.592152	+	0.805827i	$0.701721\pi$
$770$	−1.61666e44	−0.293774
$771$	0	0
$772$	7.74443e44	1.35183
$773$	8.28645e44	1.41771	0.708853	−	0.705356i	$-0.249213\pi$
$773$	8.28645e44	1.41771	0.708853	+	0.705356i	$0.249213\pi$
$774$	0	0
$775$	4.01565e44	0.660053
$776$	3.03051e44	0.488269
$777$	0	0
$778$	1.05383e45	1.63150
$779$	1.97419e44	0.299611
$780$	0	0
$781$	5.06180e43	0.0738268
$782$	3.00018e42	0.00428985
$783$	0	0
$784$	6.18168e43	0.0849587
$785$	1.32275e45	1.78237
$786$	0	0
$787$	−8.07362e44	−1.04583	−0.522913	−	0.852386i	$-0.675155\pi$
$787$	−8.07362e44	−1.04583	−0.522913	+	0.852386i	$0.675155\pi$
$788$	8.00950e44	1.01730
$789$	0	0
$790$	−1.05813e45	−1.29217
$791$	−1.74468e44	−0.208920
$792$	0	0
$793$	1.09996e45	1.26660
$794$	−6.98627e44	−0.788910
$795$	0	0
$796$	9.33229e44	1.01353
$797$	−8.20375e44	−0.873792	−0.436896	−	0.899512i	$-0.643922\pi$
$797$	−8.20375e44	−0.873792	−0.436896	+	0.899512i	$0.643922\pi$
$798$	0	0
$799$	8.09564e44	0.829423
$800$	6.11620e44	0.614592
$801$	0	0
$802$	7.98461e44	0.771882
$803$	9.43583e43	0.0894724
$804$	0	0
$805$	3.63353e42	0.00331507
$806$	2.68776e45	2.40546
$807$	0	0
$808$	−7.25784e44	−0.625073
$809$	2.25872e44	0.190836	0.0954182	−	0.995437i	$-0.469581\pi$
$809$	2.25872e44	0.190836	0.0954182	+	0.995437i	$0.469581\pi$
$810$	0	0
$811$	−1.42546e45	−1.15913	−0.579565	−	0.814926i	$-0.696778\pi$
$811$	−1.42546e45	−1.15913	−0.579565	+	0.814926i	$0.696778\pi$
$812$	−2.56349e45	−2.04509
$813$	0	0
$814$	−2.11946e44	−0.162760
$815$	−1.34886e45	−1.01630
$816$	0	0
$817$	3.82657e44	0.277567
$818$	1.67512e45	1.19226
$819$	0	0
$820$	−3.34927e45	−2.29528
$821$	2.34861e44	0.157940	0.0789699	−	0.996877i	$-0.474837\pi$
$821$	2.34861e44	0.157940	0.0789699	+	0.996877i	$0.474837\pi$
$822$	0	0
$823$	2.26372e45	1.46597	0.732984	−	0.680246i	$-0.238127\pi$
$823$	2.26372e45	1.46597	0.732984	+	0.680246i	$0.238127\pi$
$824$	−1.07692e45	−0.684405
$825$	0	0
$826$	−1.92566e45	−1.17866
$827$	−1.11856e45	−0.671929	−0.335965	−	0.941875i	$-0.609062\pi$
$827$	−1.11856e45	−0.671929	−0.335965	+	0.941875i	$0.609062\pi$
$828$	0	0
$829$	−2.19670e45	−1.27109	−0.635544	−	0.772064i	$-0.719224\pi$
$829$	−2.19670e45	−1.27109	−0.635544	+	0.772064i	$0.719224\pi$
$830$	−2.67301e45	−1.51806
$831$	0	0
$832$	3.10017e45	1.69619
$833$	2.94738e44	0.158285
$834$	0	0
$835$	−1.38666e45	−0.717512
$836$	−1.00814e44	−0.0512064
$837$	0	0
$838$	3.15593e45	1.54470
$839$	−3.71878e45	−1.78686	−0.893429	−	0.449204i	$-0.851707\pi$
$839$	−3.71878e45	−1.78686	−0.893429	+	0.449204i	$0.851707\pi$
$840$	0	0
$841$	3.66359e45	1.69656
$842$	3.26923e45	1.48631
$843$	0	0
$844$	−6.17139e45	−2.70442
$845$	5.52621e44	0.237765
$846$	0	0
$847$	−2.12920e45	−0.883128
$848$	8.16038e43	0.0332334
$849$	0	0
$850$	1.67581e45	0.658007
$851$	4.76359e42	0.00183665
$852$	0	0
$853$	2.48938e45	0.925509	0.462754	−	0.886487i	$-0.346861\pi$
$853$	2.48938e45	0.925509	0.462754	+	0.886487i	$0.346861\pi$
$854$	4.44337e45	1.62224
$855$	0	0
$856$	1.77603e45	0.625326
$857$	8.68133e44	0.300181	0.150091	−	0.988672i	$-0.452043\pi$
$857$	8.68133e44	0.300181	0.150091	+	0.988672i	$0.452043\pi$
$858$	0	0
$859$	−1.43587e45	−0.478875	−0.239437	−	0.970912i	$-0.576963\pi$
$859$	−1.43587e45	−0.478875	−0.239437	+	0.970912i	$0.576963\pi$
$860$	−6.49189e45	−2.12640
$861$	0	0
$862$	−1.16869e45	−0.369265
$863$	3.91776e45	1.21582	0.607911	−	0.794005i	$-0.292008\pi$
$863$	3.91776e45	1.21582	0.607911	+	0.794005i	$0.292008\pi$
$864$	0	0
$865$	−1.38393e45	−0.414347
$866$	−5.14729e44	−0.151374
$867$	0	0
$868$	6.27199e45	1.77971
$869$	4.32111e44	0.120445
$870$	0	0
$871$	1.89991e45	0.511036
$872$	2.03339e45	0.537299
$873$	0	0
$874$	3.92241e42	0.00100029
$875$	−2.36450e45	−0.592399
$876$	0	0
$877$	−2.59910e45	−0.628535	−0.314267	−	0.949335i	$-0.601759\pi$
$877$	−2.59910e45	−0.628535	−0.314267	+	0.949335i	$0.601759\pi$
$878$	−1.22678e45	−0.291476
$879$	0	0
$880$	−4.54283e44	−0.104194
$881$	−1.04135e45	−0.234676	−0.117338	−	0.993092i	$-0.537436\pi$
$881$	−1.04135e45	−0.234676	−0.117338	+	0.993092i	$0.537436\pi$
$882$	0	0
$883$	−9.31982e44	−0.202776	−0.101388	−	0.994847i	$-0.532328\pi$
$883$	−9.31982e44	−0.202776	−0.101388	+	0.994847i	$0.532328\pi$
$884$	6.47943e45	1.38524
$885$	0	0
$886$	−6.57863e44	−0.135804
$887$	−1.93996e45	−0.393529	−0.196764	−	0.980451i	$-0.563043\pi$
$887$	−1.93996e45	−0.393529	−0.196764	+	0.980451i	$0.563043\pi$
$888$	0	0
$889$	−6.50823e45	−1.27493
$890$	1.53447e45	0.295401
$891$	0	0
$892$	−7.71020e45	−1.43354
$893$	1.05842e45	0.193401
$894$	0	0
$895$	−4.68522e44	−0.0826939
$896$	5.53934e45	0.960913
$897$	0	0
$898$	1.28459e46	2.15269
$899$	−1.42469e46	−2.34664
$900$	0	0
$901$	3.89082e44	0.0619165
$902$	2.36771e45	0.370362
$903$	0	0
$904$	8.59192e44	0.129861
$905$	1.21777e46	1.80930
$906$	0	0
$907$	−8.10222e45	−1.16330	−0.581649	−	0.813440i	$-0.697592\pi$
$907$	−8.10222e45	−1.16330	−0.581649	+	0.813440i	$0.697592\pi$
$908$	−3.40990e44	−0.0481294
$909$	0	0
$910$	1.35844e46	1.85310
$911$	1.13425e46	1.52115	0.760575	−	0.649250i	$-0.224917\pi$
$911$	1.13425e46	1.52115	0.760575	+	0.649250i	$0.224917\pi$
$912$	0	0
$913$	1.09158e45	0.141501
$914$	−5.01671e45	−0.639370
$915$	0	0
$916$	4.11167e45	0.506569
$917$	−2.06289e44	−0.0249892
$918$	0	0
$919$	1.39631e46	1.63527	0.817637	−	0.575734i	$-0.195283\pi$
$919$	1.39631e46	1.63527	0.817637	+	0.575734i	$0.195283\pi$
$920$	−1.78938e43	−0.00206059
$921$	0	0
$922$	−1.53322e45	−0.170716
$923$	−4.25329e45	−0.465692
$924$	0	0
$925$	2.66079e45	0.281717
$926$	−2.62982e46	−2.73814
$927$	0	0
$928$	−2.16994e46	−2.18501
$929$	3.21761e45	0.318632	0.159316	−	0.987228i	$-0.449071\pi$
$929$	3.21761e45	0.318632	0.159316	+	0.987228i	$0.449071\pi$
$930$	0	0
$931$	3.85338e44	0.0369081
$932$	−2.10054e46	−1.97872
$933$	0	0
$934$	−2.39042e46	−2.17820
$935$	−2.16599e45	−0.194123
$936$	0	0
$937$	1.44001e46	1.24853	0.624267	−	0.781211i	$-0.285398\pi$
$937$	1.44001e46	1.24853	0.624267	+	0.781211i	$0.285398\pi$
$938$	7.67485e45	0.654524
$939$	0	0
$940$	−1.79563e46	−1.48162
$941$	1.38781e46	1.12640	0.563198	−	0.826322i	$-0.309571\pi$
$941$	1.38781e46	1.12640	0.563198	+	0.826322i	$0.309571\pi$
$942$	0	0
$943$	−5.32153e43	−0.00417931
$944$	−5.41109e45	−0.418041
$945$	0	0
$946$	4.58933e45	0.343112
$947$	3.58686e45	0.263809	0.131905	−	0.991262i	$-0.457891\pi$
$947$	3.58686e45	0.263809	0.131905	+	0.991262i	$0.457891\pi$
$948$	0	0
$949$	−7.92866e45	−0.564383
$950$	2.19093e45	0.153431
$951$	0	0
$952$	7.03822e45	0.477079
$953$	−8.63539e45	−0.575893	−0.287947	−	0.957646i	$-0.592973\pi$
$953$	−8.63539e45	−0.575893	−0.287947	+	0.957646i	$0.592973\pi$
$954$	0	0
$955$	3.61549e45	0.233408
$956$	−8.71088e45	−0.553305
$957$	0	0
$958$	−1.27110e46	−0.781656
$959$	1.75372e45	0.106114
$960$	0	0
$961$	1.77883e46	1.04213
$962$	1.78092e46	1.02667
$963$	0	0
$964$	−2.11645e46	−1.18145
$965$	2.17535e46	1.19497
$966$	0	0
$967$	−1.07239e46	−0.570481	−0.285241	−	0.958456i	$-0.592073\pi$
$967$	−1.07239e46	−0.570481	−0.285241	+	0.958456i	$0.592073\pi$
$968$	1.04855e46	0.548938
$969$	0	0
$970$	3.16567e46	1.60511
$971$	−1.69197e46	−0.844295	−0.422148	−	0.906527i	$-0.638724\pi$
$971$	−1.69197e46	−0.844295	−0.422148	+	0.906527i	$0.638724\pi$
$972$	0	0
$973$	2.15051e46	1.03942
$974$	2.11153e46	1.00446
$975$	0	0
$976$	1.24859e46	0.575369
$977$	1.63831e46	0.743069	0.371534	−	0.928419i	$-0.378832\pi$
$977$	1.63831e46	0.743069	0.371534	+	0.928419i	$0.378832\pi$
$978$	0	0
$979$	−6.26632e44	−0.0275347
$980$	−6.53737e45	−0.282748
$981$	0	0
$982$	2.04776e46	0.858126
$983$	−1.26750e46	−0.522839	−0.261419	−	0.965225i	$-0.584191\pi$
$983$	−1.26750e46	−0.522839	−0.261419	+	0.965225i	$0.584191\pi$
$984$	0	0
$985$	2.24981e46	0.899257
$986$	−5.94552e46	−2.33936
$987$	0	0
$988$	8.47114e45	0.323005
$989$	−1.03147e44	−0.00387182
$990$	0	0
$991$	−3.41939e46	−1.24396	−0.621980	−	0.783033i	$-0.713672\pi$
$991$	−3.41939e46	−1.24396	−0.621980	+	0.783033i	$0.713672\pi$
$992$	5.30911e46	1.90148
$993$	0	0
$994$	−1.71815e46	−0.596449
$995$	2.62137e46	0.895922
$996$	0	0
$997$	3.16608e46	1.04893	0.524466	−	0.851432i	$-0.324265\pi$
$997$	3.16608e46	1.04893	0.524466	+	0.851432i	$0.324265\pi$
$998$	8.49707e46	2.77170
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.32.a.a.1.1		2
3.2	odd	2		1.32.a.a.1.2	✓	2
12.11	even	2		16.32.a.b.1.1		2
15.2	even	4		25.32.b.a.24.4		4
15.8	even	4		25.32.b.a.24.1		4
15.14	odd	2		25.32.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.32.a.a.1.2	✓	2	3.2	odd	2
9.32.a.a.1.1		2	1.1	even	1	trivial
16.32.a.b.1.1		2	12.11	even	2
25.32.a.a.1.1		2	15.14	odd	2
25.32.b.a.24.1		4	15.8	even	4
25.32.b.a.24.4		4	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-71307.9 q^{2} +2.93733e9 q^{4} +8.25073e10 q^{5} +1.14368e13 q^{7} -5.63222e13 q^{8} +O(q^{10})\)	\(q-71307.9 q^{2} +2.93733e9 q^{4} +8.25073e10 q^{5} +1.14368e13 q^{7} -5.63222e13 q^{8} -5.88342e15 q^{10} +2.40262e15 q^{11} -2.01886e17 q^{13} -8.15534e17 q^{14} -2.29165e18 q^{16} -1.09264e19 q^{17} -1.42851e19 q^{19} +2.42351e20 q^{20} -1.71326e20 q^{22} +3.85062e18 q^{23} +2.15084e21 q^{25} +1.43960e22 q^{26} +3.35937e22 q^{28} -7.63087e22 q^{29} +1.86701e23 q^{31} +2.84364e23 q^{32} +7.79141e23 q^{34} +9.43620e23 q^{35} +1.23709e24 q^{37} +1.01864e24 q^{38} -4.64699e24 q^{40} -1.38199e25 q^{41} -2.67871e25 q^{43} +7.05729e24 q^{44} -2.74580e23 q^{46} -7.40922e25 q^{47} -2.69748e25 q^{49} -1.53372e26 q^{50} -5.93004e26 q^{52} -3.56092e25 q^{53} +1.98234e26 q^{55} -6.44146e26 q^{56} +5.44141e27 q^{58} +2.36122e27 q^{59} -5.44842e27 q^{61} -1.33133e28 q^{62} -1.53561e28 q^{64} -1.66570e28 q^{65} -9.41082e27 q^{67} -3.20945e28 q^{68} -6.72875e28 q^{70} +2.10678e28 q^{71} +3.92731e28 q^{73} -8.82146e28 q^{74} -4.19601e28 q^{76} +2.74783e28 q^{77} +1.79850e29 q^{79} -1.89078e29 q^{80} +9.85468e29 q^{82} +4.54329e29 q^{83} -9.01511e29 q^{85} +1.91013e30 q^{86} -1.35321e29 q^{88} -2.60812e29 q^{89} -2.30893e30 q^{91} +1.13106e28 q^{92} +5.28336e30 q^{94} -1.17863e30 q^{95} -5.38067e30 q^{97} +1.92352e30 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 39960 q^{2} + 1772534336 q^{4} + 19391218020 q^{5} + 30257527577200 q^{7} - 160155058705920 q^{8}+O(q^{10}) \) 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

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