LMFDB - Embedded newform 9.38.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,38,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, 38, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 38 $
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:	$78.0426343121$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 11777633936x^{2} - 35120319927360x + 11967042111800832000 $ x^4 - x^3 - 11777633936x^2 - 35120319927360x + 11967042111800832000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{10}\cdot 5\cdot 7 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-35434.6$ 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)

$f(q)$	$=$	$q-322000. q^{2} -3.37552e10 q^{4} -1.53382e13 q^{5} +2.48687e15 q^{7} +5.51245e16 q^{8} +O(q^{10})$	\(q-322000. q^{2} -3.37552e10 q^{4} -1.53382e13 q^{5} +2.48687e15 q^{7} +5.51245e16 q^{8} +4.93889e18 q^{10} +1.32093e18 q^{11} +1.53342e20 q^{13} -8.00770e20 q^{14} -1.31108e22 q^{16} -1.04822e23 q^{17} -6.96548e23 q^{19} +5.17744e23 q^{20} -4.25339e23 q^{22} -1.11946e25 q^{23} +1.62501e26 q^{25} -4.93762e25 q^{26} -8.39448e25 q^{28} -1.43220e27 q^{29} +3.90372e26 q^{31} -3.35459e27 q^{32} +3.37525e28 q^{34} -3.81440e28 q^{35} -8.53226e28 q^{37} +2.24288e29 q^{38} -8.45509e29 q^{40} -4.51987e29 q^{41} -2.04528e30 q^{43} -4.45883e28 q^{44} +3.60466e30 q^{46} +3.80345e30 q^{47} -1.23776e31 q^{49} -5.23251e31 q^{50} -5.17611e30 q^{52} -2.08682e31 q^{53} -2.02607e31 q^{55} +1.37087e32 q^{56} +4.61167e32 q^{58} +1.01104e33 q^{59} -1.04937e33 q^{61} -1.25699e32 q^{62} +2.88211e33 q^{64} -2.35199e33 q^{65} +2.33599e33 q^{67} +3.53828e33 q^{68} +1.22824e34 q^{70} -1.08272e33 q^{71} -3.23026e34 q^{73} +2.74738e34 q^{74} +2.35121e34 q^{76} +3.28498e33 q^{77} -2.35299e35 q^{79} +2.01095e35 q^{80} +1.45540e35 q^{82} +1.58763e35 q^{83} +1.60777e36 q^{85} +6.58578e35 q^{86} +7.28155e34 q^{88} +3.16700e35 q^{89} +3.81342e35 q^{91} +3.77876e35 q^{92} -1.22471e36 q^{94} +1.06838e37 q^{95} +6.89438e36 q^{97} +3.98559e36 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 437562 q^{2} + 346098955492 q^{4} + 4099829756904 q^{5} + 66\!\cdots\!84 q^{7}+ \cdots - 14\!\cdots\!76 q^{8}+O(q^{10}) $ 4 * q - 437562 * q^2 + 346098955492 * q^4 + 4099829756904 * q^5 + 6605809948153184 * q^7 - 140484113342159976 * q^8	$ 4 q - 437562 q^{2} + 346098955492 q^{4} + 4099829756904 q^{5} + 66\!\cdots\!84 q^{7}+ \cdots + 43\!\cdots\!78 q^{98}+O(q^{100}) $ 4 * q - 437562 * q^2 + 346098955492 * q^4 + 4099829756904 * q^5 + 6605809948153184 * q^7 - 140484113342159976 * q^8 - 21511023001649316 * q^10 - 20953708852195292976 * q^11 + 51830892788989874168 * q^13 + 1809002141673235613712 * q^14 + 55184727516616371757840 * q^16 - 81101770962322537501128 * q^17 - 544604242502813077907632 * q^19 + 3566083114449076353950376 * q^20 + 23909208610123411045457976 * q^22 + 6105434608113226892697888 * q^23 + 95396877753446381193398716 * q^25 - 428554172265180170762299788 * q^26 + 2469833924959492064190244448 * q^28 - 4171186009659314742454127736 * q^29 + 8995814656808409627856220864 * q^31 - 36517476440276920084276020384 * q^32 + 31219088393882932122099949524 * q^34 - 42129462142584542112964223040 * q^35 + 55519093704269258277039732824 * q^37 + 735180697664011480109320664568 * q^38 - 2663133991761021855901070923152 * q^40 + 869595339264691998704372818776 * q^41 - 509323958833633606104562745680 * q^43 - 2838804848354890092833187324336 * q^44 - 14832400342987743191058839458896 * q^46 - 4297748917019550924184843821120 * q^47 + 40223006658016971616433785618020 * q^49 - 102764730674385833857211828709414 * q^50 + 186771330756284408934646875520568 * q^52 + 125797679190958862093479980165288 * q^53 - 324441401797069196184728188134624 * q^55 - 49261177652308793436687718380480 * q^56 - 758216144723951752216603559669556 * q^58 + 1322751535061383229075407129388688 * q^59 - 1210012908287761061549313720873160 * q^61 + 3774869312329378363502064838581792 * q^62 + 8553618714336434539515354532145728 * q^64 - 1596939597234927778869711846229968 * q^65 + 16212837695473169417262127089269648 * q^67 - 6364770984875237153325176447214984 * q^68 + 8205699211322075854652286498656160 * q^70 - 10892424995451680587530033164573088 * q^71 - 19472416597596703966438677461737048 * q^73 + 89115306434605413664690690272305412 * q^74 - 95475877084130734100913860795365168 * q^76 + 256189314900709292482321902951864192 * q^77 + 42564929886993357285736803130555520 * q^79 + 955034489632094448517301530341944736 * q^80 + 335470244295388111217009211756354948 * q^82 + 462964612731837394872969166562146224 * q^83 + 1847677353245070936584728247586996912 * q^85 + 363370083621183428400243233525783304 * q^86 + 4210934419609684353108607591773010656 * q^88 + 314574774231571073544391076719446552 * q^89 + 2615056540536627234228451043107657024 * q^91 + 16598538663060910484079148451607722016 * q^92 - 573809173038711993912694394480689248 * q^94 + 8958385060094338314910240959017780256 * q^95 + 445047507548838106214452450407795848 * q^97 + 43086999614034505592591376853854433878 * 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 $

$2$	−322000.	−0.868561	−0.434281	−	0.900778i	$-0.642997\pi$
$2$	−322000.	−0.868561	−0.434281	+	0.900778i	$0.642997\pi$
$3$	0	0
$3$	0	0
$4$	−3.37552e10	−0.245602
$5$	−1.53382e13	−1.79816	−0.899081	−	0.437781i	$-0.855764\pi$
$5$	−1.53382e13	−1.79816	−0.899081	+	0.437781i	$0.855764\pi$
$6$	0	0
$7$	2.48687e15	0.577216	0.288608	−	0.957447i	$-0.406807\pi$
$7$	2.48687e15	0.577216	0.288608	+	0.957447i	$0.406807\pi$
$8$	5.51245e16	1.08188
$9$	0	0
$10$	4.93889e18	1.56181
$11$	1.32093e18	0.0716333	0.0358167	−	0.999358i	$-0.488597\pi$
$11$	1.32093e18	0.0716333	0.0358167	+	0.999358i	$0.488597\pi$
$12$	0	0
$13$	1.53342e20	0.378190	0.189095	−	0.981959i	$-0.439445\pi$
$13$	1.53342e20	0.378190	0.189095	+	0.981959i	$0.439445\pi$
$14$	−8.00770e20	−0.501348
$15$	0	0
$16$	−1.31108e22	−0.694078
$17$	−1.04822e23	−1.80778	−0.903890	−	0.427765i	$-0.859301\pi$
$17$	−1.04822e23	−1.80778	−0.903890	+	0.427765i	$0.859301\pi$
$18$	0	0
$19$	−6.96548e23	−1.53465	−0.767325	−	0.641258i	$-0.778413\pi$
$19$	−6.96548e23	−1.53465	−0.767325	+	0.641258i	$0.778413\pi$
$20$	5.17744e23	0.441632
$21$	0	0
$22$	−4.25339e23	−0.0622179
$23$	−1.11946e25	−0.719521	−0.359761	−	0.933045i	$-0.617142\pi$
$23$	−1.11946e25	−0.719521	−0.359761	+	0.933045i	$0.617142\pi$
$24$	0	0
$25$	1.62501e26	2.23339
$26$	−4.93762e25	−0.328481
$27$	0	0
$28$	−8.39448e25	−0.141765
$29$	−1.43220e27	−1.26369	−0.631845	−	0.775095i	$-0.717702\pi$
$29$	−1.43220e27	−1.26369	−0.631845	+	0.775095i	$0.717702\pi$
$30$	0	0
$31$	3.90372e26	0.100297	0.0501484	−	0.998742i	$-0.484031\pi$
$31$	3.90372e26	0.100297	0.0501484	+	0.998742i	$0.484031\pi$
$32$	−3.35459e27	−0.479032
$33$	0	0
$34$	3.37525e28	1.57017
$35$	−3.81440e28	−1.03793
$36$	0	0
$37$	−8.53226e28	−0.830486	−0.415243	−	0.909711i	$-0.636303\pi$
$37$	−8.53226e28	−0.830486	−0.415243	+	0.909711i	$0.636303\pi$
$38$	2.24288e29	1.33294
$39$	0	0
$40$	−8.45509e29	−1.94540
$41$	−4.51987e29	−0.658605	−0.329302	−	0.944225i	$-0.606814\pi$
$41$	−4.51987e29	−0.658605	−0.329302	+	0.944225i	$0.606814\pi$
$42$	0	0
$43$	−2.04528e30	−1.23477	−0.617384	−	0.786662i	$-0.711808\pi$
$43$	−2.04528e30	−1.23477	−0.617384	+	0.786662i	$0.711808\pi$
$44$	−4.45883e28	−0.0175933
$45$	0	0
$46$	3.60466e30	0.624948
$47$	3.80345e30	0.442963	0.221481	−	0.975165i	$-0.428911\pi$
$47$	3.80345e30	0.442963	0.221481	+	0.975165i	$0.428911\pi$
$48$	0	0
$49$	−1.23776e31	−0.666821
$50$	−5.23251e31	−1.93984
$51$	0	0
$52$	−5.17611e30	−0.0928841
$53$	−2.08682e31	−0.263257	−0.131629	−	0.991299i	$-0.542021\pi$
$53$	−2.08682e31	−0.263257	−0.131629	+	0.991299i	$0.542021\pi$
$54$	0	0
$55$	−2.02607e31	−0.128808
$56$	1.37087e32	0.624480
$57$	0	0
$58$	4.61167e32	1.09759
$59$	1.01104e33	1.75390	0.876952	−	0.480578i	$-0.159573\pi$
$59$	1.01104e33	1.75390	0.876952	+	0.480578i	$0.159573\pi$
$60$	0	0
$61$	−1.04937e33	−0.982484	−0.491242	−	0.871023i	$-0.663457\pi$
$61$	−1.04937e33	−0.982484	−0.491242	+	0.871023i	$0.663457\pi$
$62$	−1.25699e32	−0.0871138
$63$	0	0
$64$	2.88211e33	1.11015
$65$	−2.35199e33	−0.680047
$66$	0	0
$67$	2.33599e33	0.385557	0.192778	−	0.981242i	$-0.438250\pi$
$67$	2.33599e33	0.385557	0.192778	+	0.981242i	$0.438250\pi$
$68$	3.53828e33	0.443994
$69$	0	0
$70$	1.22824e34	0.901505
$71$	−1.08272e33	−0.0611275	−0.0305637	−	0.999533i	$-0.509730\pi$
$71$	−1.08272e33	−0.0611275	−0.0305637	+	0.999533i	$0.509730\pi$
$72$	0	0
$73$	−3.23026e34	−1.09085	−0.545424	−	0.838160i	$-0.683631\pi$
$73$	−3.23026e34	−1.09085	−0.545424	+	0.838160i	$0.683631\pi$
$74$	2.74738e34	0.721328
$75$	0	0
$76$	2.35121e34	0.376913
$77$	3.28498e33	0.0413479
$78$	0	0
$79$	−2.35299e35	−1.84297	−0.921486	−	0.388411i	$-0.873024\pi$
$79$	−2.35299e35	−1.84297	−0.921486	+	0.388411i	$0.873024\pi$
$80$	2.01095e35	1.24807
$81$	0	0
$82$	1.45540e35	0.572038
$83$	1.58763e35	0.498660	0.249330	−	0.968419i	$-0.419790\pi$
$83$	1.58763e35	0.498660	0.249330	+	0.968419i	$0.419790\pi$
$84$	0	0
$85$	1.60777e36	3.25068
$86$	6.58578e35	1.07247
$87$	0	0
$88$	7.28155e34	0.0774987
$89$	3.16700e35	0.273484	0.136742	−	0.990607i	$-0.456337\pi$
$89$	3.16700e35	0.273484	0.136742	+	0.990607i	$0.456337\pi$
$90$	0	0
$91$	3.81342e35	0.218298
$92$	3.77876e35	0.176716
$93$	0	0
$94$	−1.22471e36	−0.384740
$95$	1.06838e37	2.75955
$96$	0	0
$97$	6.89438e36	1.21121	0.605603	−	0.795767i	$-0.292932\pi$
$97$	6.89438e36	1.21121	0.605603	+	0.795767i	$0.292932\pi$
$98$	3.98559e36	0.579175
$99$	0	0
$100$	−5.48524e36	−0.548524
$101$	−8.14698e36	−0.677721	−0.338861	−	0.940837i	$-0.610042\pi$
$101$	−8.14698e36	−0.677721	−0.338861	+	0.940837i	$0.610042\pi$
$102$	0	0
$103$	−1.09944e37	−0.636329	−0.318165	−	0.948036i	$-0.603066\pi$
$103$	−1.09944e37	−0.636329	−0.318165	+	0.948036i	$0.603066\pi$
$104$	8.45291e36	0.409157
$105$	0	0
$106$	6.71954e36	0.228655
$107$	−2.26830e37	−0.648783	−0.324392	−	0.945923i	$-0.605160\pi$
$107$	−2.26830e37	−0.648783	−0.324392	+	0.945923i	$0.605160\pi$
$108$	0	0
$109$	3.74392e37	0.760216	0.380108	−	0.924942i	$-0.375887\pi$
$109$	3.74392e37	0.760216	0.380108	+	0.924942i	$0.375887\pi$
$110$	6.52393e36	0.111878
$111$	0	0
$112$	−3.26047e37	−0.400633
$113$	−1.81279e37	−0.188972	−0.0944858	−	0.995526i	$-0.530121\pi$
$113$	−1.81279e37	−0.188972	−0.0944858	+	0.995526i	$0.530121\pi$
$114$	0	0
$115$	1.71705e38	1.29382
$116$	4.83442e37	0.310364
$117$	0	0
$118$	−3.25554e38	−1.52337
$119$	−2.60677e38	−1.04348
$120$	0	0
$121$	−3.38295e38	−0.994869
$122$	3.37896e38	0.853348
$123$	0	0
$124$	−1.31771e37	−0.0246331
$125$	−1.37646e39	−2.21784
$126$	0	0
$127$	3.75363e38	0.450903	0.225451	−	0.974254i	$-0.427614\pi$
$127$	3.75363e38	0.450903	0.225451	+	0.974254i	$0.427614\pi$
$128$	−4.66986e38	−0.485198
$129$	0	0
$130$	7.57341e38	0.590663
$131$	−1.53812e39	−1.04105	−0.520525	−	0.853846i	$-0.674264\pi$
$131$	−1.53812e39	−1.04105	−0.520525	+	0.853846i	$0.674264\pi$
$132$	0	0
$133$	−1.73222e39	−0.885825
$134$	−7.52189e38	−0.334879
$135$	0	0
$136$	−5.77823e39	−1.95580
$137$	5.26351e39	1.55577	0.777885	−	0.628407i	$-0.216293\pi$
$137$	5.26351e39	1.55577	0.777885	+	0.628407i	$0.216293\pi$
$138$	0	0
$139$	3.79319e39	0.857494	0.428747	−	0.903425i	$-0.358955\pi$
$139$	3.79319e39	0.857494	0.428747	+	0.903425i	$0.358955\pi$
$140$	1.28756e39	0.254917
$141$	0	0
$142$	3.48635e38	0.0530930
$143$	2.02555e38	0.0270910
$144$	0	0
$145$	2.19673e40	2.27232
$146$	1.04014e40	0.947468
$147$	0	0
$148$	2.88009e39	0.203969
$149$	2.87234e40	1.79593	0.897967	−	0.440063i	$-0.145044\pi$
$149$	2.87234e40	1.79593	0.897967	+	0.440063i	$0.145044\pi$
$150$	0	0
$151$	1.01312e39	0.0494982	0.0247491	−	0.999694i	$-0.492121\pi$
$151$	1.01312e39	0.0494982	0.0247491	+	0.999694i	$0.492121\pi$
$152$	−3.83968e40	−1.66031
$153$	0	0
$154$	−1.05776e39	−0.0359132
$155$	−5.98759e39	−0.180350
$156$	0	0
$157$	−3.12964e40	−0.743620	−0.371810	−	0.928309i	$-0.621263\pi$
$157$	−3.12964e40	−0.743620	−0.371810	+	0.928309i	$0.621263\pi$
$158$	7.57662e40	1.60073
$159$	0	0
$160$	5.14533e40	0.861378
$161$	−2.78395e40	−0.415319
$162$	0	0
$163$	−6.14970e40	−0.730102	−0.365051	−	0.930988i	$-0.618948\pi$
$163$	−6.14970e40	−0.730102	−0.365051	+	0.930988i	$0.618948\pi$
$164$	1.52569e40	0.161754
$165$	0	0
$166$	−5.11216e40	−0.433117
$167$	1.95759e41	1.48411	0.742055	−	0.670339i	$-0.233851\pi$
$167$	1.95759e41	1.48411	0.742055	+	0.670339i	$0.233851\pi$
$168$	0	0
$169$	−1.40887e41	−0.856972
$170$	−5.17702e41	−2.82342
$171$	0	0
$172$	6.90388e40	0.303261
$173$	−8.49345e40	−0.335144	−0.167572	−	0.985860i	$-0.553593\pi$
$173$	−8.49345e40	−0.335144	−0.167572	+	0.985860i	$0.553593\pi$
$174$	0	0
$175$	4.04117e41	1.28915
$176$	−1.73184e40	−0.0497191
$177$	0	0
$178$	−1.01977e41	−0.237538
$179$	−5.07222e41	−1.06517	−0.532583	−	0.846378i	$-0.678778\pi$
$179$	−5.07222e41	−1.06517	−0.532583	+	0.846378i	$0.678778\pi$
$180$	0	0
$181$	2.84986e41	0.487270	0.243635	−	0.969867i	$-0.421660\pi$
$181$	2.84986e41	0.487270	0.243635	+	0.969867i	$0.421660\pi$
$182$	−1.22792e41	−0.189605
$183$	0	0
$184$	−6.17096e41	−0.778436
$185$	1.30869e42	1.49335
$186$	0	0
$187$	−1.38462e41	−0.129497
$188$	−1.28386e41	−0.108792
$189$	0	0
$190$	−3.44017e42	−2.39684
$191$	−1.34993e42	−0.853483	−0.426741	−	0.904374i	$-0.640339\pi$
$191$	−1.34993e42	−0.853483	−0.426741	+	0.904374i	$0.640339\pi$
$192$	0	0
$193$	1.53006e42	0.797806	0.398903	−	0.916993i	$-0.369391\pi$
$193$	1.53006e42	0.797806	0.398903	+	0.916993i	$0.369391\pi$
$194$	−2.21999e42	−1.05201
$195$	0	0
$196$	4.17809e41	0.163772
$197$	1.58341e42	0.564896	0.282448	−	0.959283i	$-0.408854\pi$
$197$	1.58341e42	0.564896	0.282448	+	0.959283i	$0.408854\pi$
$198$	0	0
$199$	3.81225e42	1.12823	0.564117	−	0.825695i	$-0.309217\pi$
$199$	3.81225e42	1.12823	0.564117	+	0.825695i	$0.309217\pi$
$200$	8.95775e42	2.41626
$201$	0	0
$202$	2.62332e42	0.588642
$203$	−3.56169e42	−0.729422
$204$	0	0
$205$	6.93266e42	1.18428
$206$	3.54018e42	0.552691
$207$	0	0
$208$	−2.01044e42	−0.262493
$209$	−9.20091e41	−0.109932
$210$	0	0
$211$	−1.03480e43	−1.03665	−0.518325	−	0.855184i	$-0.673444\pi$
$211$	−1.03480e43	−1.03665	−0.518325	+	0.855184i	$0.673444\pi$
$212$	7.04410e41	0.0646565
$213$	0	0
$214$	7.30390e42	0.563508
$215$	3.13708e43	2.22031
$216$	0	0
$217$	9.70802e41	0.0578929
$218$	−1.20554e43	−0.660294
$219$	0	0
$220$	6.83904e41	0.0316356
$221$	−1.60736e43	−0.683684
$222$	0	0
$223$	−2.53188e43	−0.911598	−0.455799	−	0.890083i	$-0.650646\pi$
$223$	−2.53188e43	−0.911598	−0.455799	+	0.890083i	$0.650646\pi$
$224$	−8.34241e42	−0.276505
$225$	0	0
$226$	5.83718e42	0.164133
$227$	−5.88632e43	−1.52534	−0.762668	−	0.646790i	$-0.776111\pi$
$227$	−5.88632e43	−1.52534	−0.762668	+	0.646790i	$0.776111\pi$
$228$	0	0
$229$	2.71698e43	0.598590	0.299295	−	0.954161i	$-0.403249\pi$
$229$	2.71698e43	0.598590	0.299295	+	0.954161i	$0.403249\pi$
$230$	−5.52889e43	−1.12376
$231$	0	0
$232$	−7.89492e43	−1.36716
$233$	1.14243e43	0.182703	0.0913513	−	0.995819i	$-0.470881\pi$
$233$	1.14243e43	0.182703	0.0913513	+	0.995819i	$0.470881\pi$
$234$	0	0
$235$	−5.83380e43	−0.796520
$236$	−3.41279e43	−0.430762
$237$	0	0
$238$	8.39379e43	0.906326
$239$	−1.69778e43	−0.169637	−0.0848185	−	0.996396i	$-0.527031\pi$
$239$	−1.69778e43	−0.169637	−0.0848185	+	0.996396i	$0.527031\pi$
$240$	0	0
$241$	−3.09126e43	−0.264740	−0.132370	−	0.991200i	$-0.542259\pi$
$241$	−3.09126e43	−0.264740	−0.132370	+	0.991200i	$0.542259\pi$
$242$	1.08931e44	0.864104
$243$	0	0
$244$	3.54217e43	0.241300
$245$	1.89850e44	1.19905
$246$	0	0
$247$	−1.06810e44	−0.580390
$248$	2.15190e43	0.108509
$249$	0	0
$250$	4.43221e44	1.92633
$251$	−2.54005e44	−1.02537	−0.512683	−	0.858578i	$-0.671348\pi$
$251$	−2.54005e44	−1.02537	−0.512683	+	0.858578i	$0.671348\pi$
$252$	0	0
$253$	−1.47873e43	−0.0515417
$254$	−1.20867e44	−0.391637
$255$	0	0
$256$	−2.45744e44	−0.688722
$257$	3.66815e44	0.956499	0.478249	−	0.878224i	$-0.341271\pi$
$257$	3.66815e44	0.956499	0.478249	+	0.878224i	$0.341271\pi$
$258$	0	0
$259$	−2.12186e44	−0.479370
$260$	7.93922e43	0.167021
$261$	0	0
$262$	4.95275e44	0.904216
$263$	2.74111e44	0.466385	0.233192	−	0.972431i	$-0.425083\pi$
$263$	2.74111e44	0.466385	0.233192	+	0.972431i	$0.425083\pi$
$264$	0	0
$265$	3.20080e44	0.473380
$266$	5.57775e44	0.769393
$267$	0	0
$268$	−7.88521e43	−0.0946933
$269$	−7.40366e44	−0.829906	−0.414953	−	0.909843i	$-0.636202\pi$
$269$	−7.40366e44	−0.829906	−0.414953	+	0.909843i	$0.636202\pi$
$270$	0	0
$271$	−3.47586e44	−0.339727	−0.169863	−	0.985468i	$-0.554333\pi$
$271$	−3.47586e44	−0.339727	−0.169863	+	0.985468i	$0.554333\pi$
$272$	1.37429e45	1.25474
$273$	0	0
$274$	−1.69485e45	−1.35128
$275$	2.14652e44	0.159985
$276$	0	0
$277$	1.55336e45	1.01250	0.506252	−	0.862385i	$-0.331031\pi$
$277$	1.55336e45	1.01250	0.506252	+	0.862385i	$0.331031\pi$
$278$	−1.22141e45	−0.744786
$279$	0	0
$280$	−2.10267e45	−1.12292
$281$	−5.16475e44	−0.258216	−0.129108	−	0.991631i	$-0.541211\pi$
$281$	−5.16475e44	−0.258216	−0.129108	+	0.991631i	$0.541211\pi$
$282$	0	0
$283$	2.81373e45	1.23377	0.616884	−	0.787054i	$-0.288395\pi$
$283$	2.81373e45	1.23377	0.616884	+	0.787054i	$0.288395\pi$
$284$	3.65475e43	0.0150130
$285$	0	0
$286$	−6.52225e43	−0.0235302
$287$	−1.12403e45	−0.380157
$288$	0	0
$289$	7.62546e45	2.26807
$290$	−7.07347e45	−1.97365
$291$	0	0
$292$	1.09038e45	0.267914
$293$	3.48209e45	0.803135	0.401568	−	0.915829i	$-0.368466\pi$
$293$	3.48209e45	0.803135	0.401568	+	0.915829i	$0.368466\pi$
$294$	0	0
$295$	−1.55075e46	−3.15380
$296$	−4.70336e45	−0.898487
$297$	0	0
$298$	−9.24893e45	−1.55988
$299$	−1.71661e45	−0.272116
$300$	0	0
$301$	−5.08633e45	−0.712729
$302$	−3.26226e44	−0.0429922
$303$	0	0
$304$	9.13228e45	1.06517
$305$	1.60954e46	1.76667
$306$	0	0
$307$	2.84597e45	0.276803	0.138401	−	0.990376i	$-0.455804\pi$
$307$	2.84597e45	0.276803	0.138401	+	0.990376i	$0.455804\pi$
$308$	−1.10885e44	−0.0101551
$309$	0	0
$310$	1.92800e45	0.156645
$311$	−8.10350e45	−0.620306	−0.310153	−	0.950687i	$-0.600380\pi$
$311$	−8.10350e45	−0.620306	−0.310153	+	0.950687i	$0.600380\pi$
$312$	0	0
$313$	1.80984e46	1.23046	0.615232	−	0.788346i	$-0.289062\pi$
$313$	1.80984e46	1.23046	0.615232	+	0.788346i	$0.289062\pi$
$314$	1.00774e46	0.645879
$315$	0	0
$316$	7.94257e45	0.452637
$317$	6.00023e45	0.322531	0.161266	−	0.986911i	$-0.448442\pi$
$317$	6.00023e45	0.322531	0.161266	+	0.986911i	$0.448442\pi$
$318$	0	0
$319$	−1.89183e45	−0.0905223
$320$	−4.42063e46	−1.99622
$321$	0	0
$322$	8.96430e45	0.360730
$323$	7.30132e46	2.77431
$324$	0	0
$325$	2.49182e46	0.844646
$326$	1.98020e46	0.634138
$327$	0	0
$328$	−2.49155e46	−0.712532
$329$	9.45867e45	0.255686
$330$	0	0
$331$	1.64524e46	0.397567	0.198784	−	0.980043i	$-0.436301\pi$
$331$	1.64524e46	0.397567	0.198784	+	0.980043i	$0.436301\pi$
$332$	−5.35908e45	−0.122472
$333$	0	0
$334$	−6.30341e46	−1.28904
$335$	−3.58299e46	−0.693293
$336$	0	0
$337$	6.90318e46	1.19645	0.598227	−	0.801327i	$-0.295872\pi$
$337$	6.90318e46	1.19645	0.598227	+	0.801327i	$0.295872\pi$
$338$	4.53655e46	0.744333
$339$	0	0
$340$	−5.42708e46	−0.798373
$341$	5.15654e44	0.00718459
$342$	0	0
$343$	−7.69430e46	−0.962117
$344$	−1.12745e47	−1.33587
$345$	0	0
$346$	2.73489e46	0.291093
$347$	−3.75519e46	−0.378911	−0.189455	−	0.981889i	$-0.560672\pi$
$347$	−3.75519e46	−0.378911	−0.189455	+	0.981889i	$0.560672\pi$
$348$	0	0
$349$	−1.14417e47	−1.03805	−0.519026	−	0.854758i	$-0.673705\pi$
$349$	−1.14417e47	−1.03805	−0.519026	+	0.854758i	$0.673705\pi$
$350$	−1.30126e47	−1.11971
$351$	0	0
$352$	−4.43118e45	−0.0343147
$353$	−9.61675e46	−0.706637	−0.353318	−	0.935503i	$-0.614947\pi$
$353$	−9.61675e46	−0.706637	−0.353318	+	0.935503i	$0.614947\pi$
$354$	0	0
$355$	1.66070e46	0.109917
$356$	−1.06903e46	−0.0671682
$357$	0	0
$358$	1.63325e47	0.925161
$359$	3.14753e45	0.0169326	0.00846629	−	0.999964i	$-0.497305\pi$
$359$	3.14753e45	0.0169326	0.00846629	+	0.999964i	$0.497305\pi$
$360$	0	0
$361$	2.79171e47	1.35515
$362$	−9.17654e46	−0.423224
$363$	0	0
$364$	−1.28723e46	−0.0536143
$365$	4.95463e47	1.96152
$366$	0	0
$367$	−6.18183e46	−0.221205	−0.110603	−	0.993865i	$-0.535278\pi$
$367$	−6.18183e46	−0.221205	−0.110603	+	0.993865i	$0.535278\pi$
$368$	1.46770e47	0.499404
$369$	0	0
$370$	−4.21399e47	−1.29706
$371$	−5.18963e46	−0.151957
$372$	0	0
$373$	−6.43130e47	−1.70485	−0.852424	−	0.522852i	$-0.824868\pi$
$373$	−6.43130e47	−1.70485	−0.852424	+	0.522852i	$0.824868\pi$
$374$	4.45847e46	0.112476
$375$	0	0
$376$	2.09663e47	0.479233
$377$	−2.19617e47	−0.477915
$378$	0	0
$379$	8.24615e47	1.62714	0.813572	−	0.581464i	$-0.197520\pi$
$379$	8.24615e47	1.62714	0.813572	+	0.581464i	$0.197520\pi$
$380$	−3.60634e47	−0.677751
$381$	0	0
$382$	4.34678e47	0.741302
$383$	1.05734e48	1.71806	0.859032	−	0.511922i	$-0.171066\pi$
$383$	1.05734e48	1.71806	0.859032	+	0.511922i	$0.171066\pi$
$384$	0	0
$385$	−5.03856e46	−0.0743503
$386$	−4.92678e47	−0.692944
$387$	0	0
$388$	−2.32721e47	−0.297474
$389$	3.81308e46	0.0464738	0.0232369	−	0.999730i	$-0.492603\pi$
$389$	3.81308e46	0.0464738	0.0232369	+	0.999730i	$0.492603\pi$
$390$	0	0
$391$	1.17343e48	1.30074
$392$	−6.82309e47	−0.721421
$393$	0	0
$394$	−5.09858e47	−0.490647
$395$	3.60906e48	3.31396
$396$	0	0
$397$	−3.87592e47	−0.324153	−0.162077	−	0.986778i	$-0.551819\pi$
$397$	−3.87592e47	−0.324153	−0.162077	+	0.986778i	$0.551819\pi$
$398$	−1.22754e48	−0.979941
$399$	0	0
$400$	−2.13051e48	−1.55015
$401$	−1.24335e48	−0.863820	−0.431910	−	0.901917i	$-0.642160\pi$
$401$	−1.24335e48	−0.863820	−0.431910	+	0.901917i	$0.642160\pi$
$402$	0	0
$403$	5.98605e46	0.0379312
$404$	2.75003e47	0.166450
$405$	0	0
$406$	1.14686e48	0.633548
$407$	−1.12705e47	−0.0594905
$408$	0	0
$409$	1.71559e48	0.827053	0.413527	−	0.910492i	$-0.364297\pi$
$409$	1.71559e48	0.827053	0.413527	+	0.910492i	$0.364297\pi$
$410$	−2.23231e48	−1.02862
$411$	0	0
$412$	3.71118e47	0.156284
$413$	2.51432e48	1.01238
$414$	0	0
$415$	−2.43514e48	−0.896672
$416$	−5.14400e47	−0.181165
$417$	0	0
$418$	2.96269e47	0.0954827
$419$	−2.35400e48	−0.725851	−0.362925	−	0.931818i	$-0.618222\pi$
$419$	−2.35400e48	−0.725851	−0.362925	+	0.931818i	$0.618222\pi$
$420$	0	0
$421$	3.28974e48	0.928844	0.464422	−	0.885614i	$-0.346262\pi$
$421$	3.28974e48	0.928844	0.464422	+	0.885614i	$0.346262\pi$
$422$	3.33206e48	0.900393
$423$	0	0
$424$	−1.15035e48	−0.284813
$425$	−1.70336e49	−4.03748
$426$	0	0
$427$	−2.60964e48	−0.567106
$428$	7.65669e47	0.159342
$429$	0	0
$430$	−1.01014e49	−1.92848
$431$	4.39374e48	0.803534	0.401767	−	0.915742i	$-0.368396\pi$
$431$	4.39374e48	0.803534	0.401767	+	0.915742i	$0.368396\pi$
$432$	0	0
$433$	1.65722e48	0.278198	0.139099	−	0.990279i	$-0.455579\pi$
$433$	1.65722e48	0.278198	0.139099	+	0.990279i	$0.455579\pi$
$434$	−3.12598e47	−0.0502835
$435$	0	0
$436$	−1.26377e48	−0.186710
$437$	7.79757e48	1.10421
$438$	0	0
$439$	4.30529e48	0.560285	0.280142	−	0.959958i	$-0.409618\pi$
$439$	4.30529e48	0.560285	0.280142	+	0.959958i	$0.409618\pi$
$440$	−1.11686e48	−0.139355
$441$	0	0
$442$	5.17569e48	0.593822
$443$	7.44863e48	0.819611	0.409805	−	0.912173i	$-0.365597\pi$
$443$	7.44863e48	0.819611	0.409805	+	0.912173i	$0.365597\pi$
$444$	0	0
$445$	−4.85760e48	−0.491769
$446$	8.15264e48	0.791778
$447$	0	0
$448$	7.16741e48	0.640795
$449$	1.42651e49	1.22382	0.611909	−	0.790928i	$-0.290402\pi$
$449$	1.42651e49	1.22382	0.611909	+	0.790928i	$0.290402\pi$
$450$	0	0
$451$	−5.97043e47	−0.0471780
$452$	6.11912e47	0.0464118
$453$	0	0
$454$	1.89539e49	1.32485
$455$	−5.84910e48	−0.392535
$456$	0	0
$457$	2.02914e49	1.25563	0.627817	−	0.778361i	$-0.283948\pi$
$457$	2.02914e49	1.25563	0.627817	+	0.778361i	$0.283948\pi$
$458$	−8.74865e48	−0.519912
$459$	0	0
$460$	−5.79594e48	−0.317763
$461$	−1.29918e49	−0.684232	−0.342116	−	0.939658i	$-0.611144\pi$
$461$	−1.29918e49	−0.684232	−0.342116	+	0.939658i	$0.611144\pi$
$462$	0	0
$463$	−1.83380e49	−0.891463	−0.445731	−	0.895167i	$-0.647056\pi$
$463$	−1.83380e49	−0.891463	−0.445731	+	0.895167i	$0.647056\pi$
$464$	1.87772e49	0.877099
$465$	0	0
$466$	−3.67861e48	−0.158688
$467$	−1.14081e49	−0.472987	−0.236494	−	0.971633i	$-0.575998\pi$
$467$	−1.14081e49	−0.472987	−0.236494	+	0.971633i	$0.575998\pi$
$468$	0	0
$469$	5.80931e48	0.222550
$470$	1.87848e49	0.691826
$471$	0	0
$472$	5.57330e49	1.89752
$473$	−2.70167e48	−0.0884506
$474$	0	0
$475$	−1.13189e50	−3.42747
$476$	8.79922e48	0.256281
$477$	0	0
$478$	5.46685e48	0.147340
$479$	2.24706e48	0.0582649	0.0291324	−	0.999576i	$-0.490726\pi$
$479$	2.24706e48	0.0582649	0.0291324	+	0.999576i	$0.490726\pi$
$480$	0	0
$481$	−1.30836e49	−0.314082
$482$	9.95383e48	0.229943
$483$	0	0
$484$	1.14192e49	0.244341
$485$	−1.05747e50	−2.17794
$486$	0	0
$487$	−6.62105e49	−1.26369	−0.631846	−	0.775094i	$-0.717702\pi$
$487$	−6.62105e49	−1.26369	−0.631846	+	0.775094i	$0.717702\pi$
$488$	−5.78458e49	−1.06293
$489$	0	0
$490$	−6.11317e49	−1.04145
$491$	−1.27151e49	−0.208599	−0.104300	−	0.994546i	$-0.533260\pi$
$491$	−1.27151e49	−0.208599	−0.104300	+	0.994546i	$0.533260\pi$
$492$	0	0
$493$	1.50125e50	2.28447
$494$	3.43929e49	0.504104
$495$	0	0
$496$	−5.11807e48	−0.0696138
$497$	−2.69258e48	−0.0352838
$498$	0	0
$499$	−1.07378e49	−0.130633	−0.0653166	−	0.997865i	$-0.520806\pi$
$499$	−1.07378e49	−0.130633	−0.0653166	+	0.997865i	$0.520806\pi$
$500$	4.64629e49	0.544704
$501$	0	0
$502$	8.17896e49	0.890593
$503$	−8.93827e48	−0.0938093	−0.0469046	−	0.998899i	$-0.514936\pi$
$503$	−8.93827e48	−0.0938093	−0.0469046	+	0.998899i	$0.514936\pi$
$504$	0	0
$505$	1.24960e50	1.21865
$506$	4.76150e48	0.0447671
$507$	0	0
$508$	−1.26705e49	−0.110743
$509$	−1.92539e50	−1.62270	−0.811352	−	0.584558i	$-0.801268\pi$
$509$	−1.92539e50	−1.62270	−0.811352	+	0.584558i	$0.801268\pi$
$510$	0	0
$511$	−8.03322e49	−0.629655
$512$	1.43312e50	1.08340
$513$	0	0
$514$	−1.18114e50	−0.830778
$515$	1.68634e50	1.14422
$516$	0	0
$517$	5.02409e48	0.0317309
$518$	6.83238e49	0.416362
$519$	0	0
$520$	−1.29652e50	−0.735731
$521$	1.93636e50	1.06045	0.530223	−	0.847858i	$-0.322108\pi$
$521$	1.93636e50	1.06045	0.530223	+	0.847858i	$0.322108\pi$
$522$	0	0
$523$	1.09154e50	0.556875	0.278438	−	0.960454i	$-0.410183\pi$
$523$	1.09154e50	0.556875	0.278438	+	0.960454i	$0.410183\pi$
$524$	5.19197e49	0.255684
$525$	0	0
$526$	−8.82635e49	−0.405084
$527$	−4.09194e49	−0.181314
$528$	0	0
$529$	−1.16745e50	−0.482289
$530$	−1.03066e50	−0.411159
$531$	0	0
$532$	5.84716e49	0.217560
$533$	−6.93088e49	−0.249078
$534$	0	0
$535$	3.47915e50	1.16662
$536$	1.28770e50	0.417126
$537$	0	0
$538$	2.38397e50	0.720824
$539$	−1.63500e49	−0.0477666
$540$	0	0
$541$	2.05140e50	0.559630	0.279815	−	0.960054i	$-0.409727\pi$
$541$	2.05140e50	0.559630	0.279815	+	0.960054i	$0.409727\pi$
$542$	1.11922e50	0.295073
$543$	0	0
$544$	3.51633e50	0.865984
$545$	−5.74250e50	−1.36699
$546$	0	0
$547$	−5.42161e50	−1.20604	−0.603021	−	0.797725i	$-0.706036\pi$
$547$	−5.42161e50	−1.20604	−0.603021	+	0.797725i	$0.706036\pi$
$548$	−1.77671e50	−0.382100
$549$	0	0
$550$	−6.91178e49	−0.138957
$551$	9.97595e50	1.93932
$552$	0	0
$553$	−5.85157e50	−1.06379
$554$	−5.00182e50	−0.879422
$555$	0	0
$556$	−1.28040e50	−0.210602
$557$	−7.40435e50	−1.17806	−0.589028	−	0.808113i	$-0.700489\pi$
$557$	−7.40435e50	−1.17806	−0.589028	+	0.808113i	$0.700489\pi$
$558$	0	0
$559$	−3.13628e50	−0.466977
$560$	5.00097e50	0.720404
$561$	0	0
$562$	1.66305e50	0.224276
$563$	5.85968e50	0.764660	0.382330	−	0.924026i	$-0.375122\pi$
$563$	5.85968e50	0.764660	0.382330	+	0.924026i	$0.375122\pi$
$564$	0	0
$565$	2.78049e50	0.339802
$566$	−9.06020e50	−1.07160
$567$	0	0
$568$	−5.96843e49	−0.0661327
$569$	6.38178e50	0.684486	0.342243	−	0.939611i	$-0.388813\pi$
$569$	6.38178e50	0.684486	0.342243	+	0.939611i	$0.388813\pi$
$570$	0	0
$571$	3.57695e50	0.359538	0.179769	−	0.983709i	$-0.442465\pi$
$571$	3.57695e50	0.359538	0.179769	+	0.983709i	$0.442465\pi$
$572$	−6.83728e48	−0.00665360
$573$	0	0
$574$	3.61938e50	0.330190
$575$	−1.81913e51	−1.60697
$576$	0	0
$577$	−1.18260e51	−0.979680	−0.489840	−	0.871812i	$-0.662945\pi$
$577$	−1.18260e51	−0.979680	−0.489840	+	0.871812i	$0.662945\pi$
$578$	−2.45540e51	−1.96996
$579$	0	0
$580$	−7.41513e50	−0.558086
$581$	3.94822e50	0.287835
$582$	0	0
$583$	−2.75654e49	−0.0188580
$584$	−1.78066e51	−1.18017
$585$	0	0
$586$	−1.12123e51	−0.697572
$587$	2.16256e51	1.30366	0.651828	−	0.758367i	$-0.274002\pi$
$587$	2.16256e51	1.30366	0.651828	+	0.758367i	$0.274002\pi$
$588$	0	0
$589$	−2.71913e50	−0.153920
$590$	4.99341e51	2.73927
$591$	0	0
$592$	1.11864e51	0.576422
$593$	1.31685e51	0.657695	0.328847	−	0.944383i	$-0.393340\pi$
$593$	1.31685e51	0.657695	0.328847	+	0.944383i	$0.393340\pi$
$594$	0	0
$595$	3.99832e51	1.87635
$596$	−9.69566e50	−0.441084
$597$	0	0
$598$	5.52746e50	0.236349
$599$	−2.09368e51	−0.867990	−0.433995	−	0.900915i	$-0.642896\pi$
$599$	−2.09368e51	−0.867990	−0.433995	+	0.900915i	$0.642896\pi$
$600$	0	0
$601$	4.42052e50	0.172304	0.0861521	−	0.996282i	$-0.472543\pi$
$601$	4.42052e50	0.172304	0.0861521	+	0.996282i	$0.472543\pi$
$602$	1.63780e51	0.619048
$603$	0	0
$604$	−3.41983e49	−0.0121568
$605$	5.18883e51	1.78894
$606$	0	0
$607$	4.41338e51	1.43146	0.715732	−	0.698375i	$-0.246093\pi$
$607$	4.41338e51	1.43146	0.715732	+	0.698375i	$0.246093\pi$
$608$	2.33663e51	0.735147
$609$	0	0
$610$	−5.18271e51	−1.53446
$611$	5.83230e50	0.167524
$612$	0	0
$613$	−3.52904e51	−0.954198	−0.477099	−	0.878850i	$-0.658312\pi$
$613$	−3.52904e51	−0.954198	−0.477099	+	0.878850i	$0.658312\pi$
$614$	−9.16402e50	−0.240420
$615$	0	0
$616$	1.81083e50	0.0447336
$617$	−6.46795e51	−1.55057	−0.775284	−	0.631613i	$-0.782393\pi$
$617$	−6.46795e51	−1.55057	−0.775284	+	0.631613i	$0.782393\pi$
$618$	0	0
$619$	−1.51171e51	−0.341344	−0.170672	−	0.985328i	$-0.554594\pi$
$619$	−1.51171e51	−0.341344	−0.170672	+	0.985328i	$0.554594\pi$
$620$	2.02113e50	0.0442942
$621$	0	0
$622$	2.60932e51	0.538773
$623$	7.87590e50	0.157860
$624$	0	0
$625$	9.28899e51	1.75464
$626$	−5.82766e51	−1.06873
$627$	0	0
$628$	1.05642e51	0.182634
$629$	8.94365e51	1.50134
$630$	0	0
$631$	−7.44924e51	−1.17915	−0.589575	−	0.807714i	$-0.700705\pi$
$631$	−7.44924e51	−1.17915	−0.589575	+	0.807714i	$0.700705\pi$
$632$	−1.29707e52	−1.99388
$633$	0	0
$634$	−1.93207e51	−0.280138
$635$	−5.75739e51	−0.810797
$636$	0	0
$637$	−1.89801e51	−0.252185
$638$	6.09170e50	0.0786241
$639$	0	0
$640$	7.16271e51	0.872465
$641$	2.96058e51	0.350351	0.175176	−	0.984537i	$-0.443951\pi$
$641$	2.96058e51	0.350351	0.175176	+	0.984537i	$0.443951\pi$
$642$	0	0
$643$	−1.66529e52	−1.86032	−0.930159	−	0.367157i	$-0.880331\pi$
$643$	−1.66529e52	−1.86032	−0.930159	+	0.367157i	$0.880331\pi$
$644$	9.39728e50	0.102003
$645$	0	0
$646$	−2.35102e52	−2.40966
$647$	3.47499e51	0.346118	0.173059	−	0.984911i	$-0.444635\pi$
$647$	3.47499e51	0.346118	0.173059	+	0.984911i	$0.444635\pi$
$648$	0	0
$649$	1.33551e51	0.125638
$650$	−8.02365e51	−0.733627
$651$	0	0
$652$	2.07585e51	0.179314
$653$	−1.71299e51	−0.143834	−0.0719169	−	0.997411i	$-0.522912\pi$
$653$	−1.71299e51	−0.143834	−0.0719169	+	0.997411i	$0.522912\pi$
$654$	0	0
$655$	2.35920e52	1.87198
$656$	5.92590e51	0.457123
$657$	0	0
$658$	−3.04569e51	−0.222078
$659$	−7.36499e51	−0.522146	−0.261073	−	0.965319i	$-0.584076\pi$
$659$	−7.36499e51	−0.522146	−0.261073	+	0.965319i	$0.584076\pi$
$660$	0	0
$661$	1.02642e52	0.688017	0.344009	−	0.938967i	$-0.388215\pi$
$661$	1.02642e52	0.688017	0.344009	+	0.938967i	$0.388215\pi$
$662$	−5.29765e51	−0.345311
$663$	0	0
$664$	8.75173e51	0.539491
$665$	2.65691e52	1.59286
$666$	0	0
$667$	1.60329e52	0.909251
$668$	−6.60788e51	−0.364500
$669$	0	0
$670$	1.15372e52	0.602168
$671$	−1.38614e51	−0.0703786
$672$	0	0
$673$	−1.32994e52	−0.639077	−0.319539	−	0.947573i	$-0.603528\pi$
$673$	−1.32994e52	−0.639077	−0.319539	+	0.947573i	$0.603528\pi$
$674$	−2.22282e52	−1.03919
$675$	0	0
$676$	4.75567e51	0.210474
$677$	−8.79193e51	−0.378611	−0.189306	−	0.981918i	$-0.560624\pi$
$677$	−8.79193e51	−0.378611	−0.189306	+	0.981918i	$0.560624\pi$
$678$	0	0
$679$	1.71454e52	0.699128
$680$	8.86276e52	3.51685
$681$	0	0
$682$	−1.66040e50	−0.00624025
$683$	−2.88301e52	−1.05454	−0.527269	−	0.849698i	$-0.676784\pi$
$683$	−2.88301e52	−1.05454	−0.527269	+	0.849698i	$0.676784\pi$
$684$	0	0
$685$	−8.07328e52	−2.79753
$686$	2.47756e52	0.835657
$687$	0	0
$688$	2.68151e52	0.857026
$689$	−3.19997e51	−0.0995614
$690$	0	0
$691$	−6.30524e52	−1.85933	−0.929667	−	0.368401i	$-0.879905\pi$
$691$	−6.30524e52	−1.85933	−0.929667	+	0.368401i	$0.879905\pi$
$692$	2.86698e51	0.0823119
$693$	0	0
$694$	1.20917e52	0.329107
$695$	−5.81807e52	−1.54191
$696$	0	0
$697$	4.73780e52	1.19061
$698$	3.68422e52	0.901612
$699$	0	0
$700$	−1.36411e52	−0.316617
$701$	4.33208e52	0.979294	0.489647	−	0.871921i	$-0.337126\pi$
$701$	4.33208e52	0.979294	0.489647	+	0.871921i	$0.337126\pi$
$702$	0	0
$703$	5.94313e52	1.27451
$704$	3.80706e51	0.0795235
$705$	0	0
$706$	3.09659e52	0.613757
$707$	−2.02605e52	−0.391192
$708$	0	0
$709$	−2.56002e52	−0.469124	−0.234562	−	0.972101i	$-0.575366\pi$
$709$	−2.56002e52	−0.469124	−0.234562	+	0.972101i	$0.575366\pi$
$710$	−5.34743e51	−0.0954698
$711$	0	0
$712$	1.74579e52	0.295877
$713$	−4.37005e51	−0.0721656
$714$	0	0
$715$	−3.10682e51	−0.0487141
$716$	1.71214e52	0.261606
$717$	0	0
$718$	−1.01350e51	−0.0147070
$719$	−6.18204e52	−0.874274	−0.437137	−	0.899395i	$-0.644008\pi$
$719$	−6.18204e52	−0.874274	−0.437137	+	0.899395i	$0.644008\pi$
$720$	0	0
$721$	−2.73415e52	−0.367300
$722$	−8.98931e52	−1.17703
$723$	0	0
$724$	−9.61978e51	−0.119674
$725$	−2.32733e53	−2.82231
$726$	0	0
$727$	−3.15811e52	−0.363949	−0.181975	−	0.983303i	$-0.558249\pi$
$727$	−3.15811e52	−0.363949	−0.181975	+	0.983303i	$0.558249\pi$
$728$	2.10213e52	0.236172
$729$	0	0
$730$	−1.59539e53	−1.70370
$731$	2.14389e53	2.23219
$732$	0	0
$733$	1.64324e53	1.62659	0.813296	−	0.581850i	$-0.197671\pi$
$733$	1.64324e53	1.62659	0.813296	+	0.581850i	$0.197671\pi$
$734$	1.99055e52	0.192130
$735$	0	0
$736$	3.75533e52	0.344674
$737$	3.08569e51	0.0276187
$738$	0	0
$739$	9.02443e52	0.768241	0.384120	−	0.923283i	$-0.374505\pi$
$739$	9.02443e52	0.768241	0.384120	+	0.923283i	$0.374505\pi$
$740$	−4.41753e52	−0.366769
$741$	0	0
$742$	1.67106e52	0.131984
$743$	−5.81589e51	−0.0448047	−0.0224023	−	0.999749i	$-0.507131\pi$
$743$	−5.81589e51	−0.0448047	−0.0224023	+	0.999749i	$0.507131\pi$
$744$	0	0
$745$	−4.40565e53	−3.22938
$746$	2.07088e53	1.48076
$747$	0	0
$748$	4.67382e51	0.0318048
$749$	−5.64095e52	−0.374488
$750$	0	0
$751$	−2.03346e53	−1.28498	−0.642491	−	0.766293i	$-0.722099\pi$
$751$	−2.03346e53	−1.28498	−0.642491	+	0.766293i	$0.722099\pi$
$752$	−4.98661e52	−0.307451
$753$	0	0
$754$	7.07165e52	0.415098
$755$	−1.55395e52	−0.0890058
$756$	0	0
$757$	8.46759e52	0.461834	0.230917	−	0.972973i	$-0.425827\pi$
$757$	8.46759e52	0.461834	0.230917	+	0.972973i	$0.425827\pi$
$758$	−2.65526e53	−1.41327
$759$	0	0
$760$	5.88938e53	2.98551
$761$	6.60711e52	0.326885	0.163443	−	0.986553i	$-0.447740\pi$
$761$	6.60711e52	0.326885	0.163443	+	0.986553i	$0.447740\pi$
$762$	0	0
$763$	9.31064e52	0.438809
$764$	4.55673e52	0.209617
$765$	0	0
$766$	−3.40465e53	−1.49224
$767$	1.55035e53	0.663309
$768$	0	0
$769$	4.12388e53	1.68139	0.840696	−	0.541507i	$-0.182146\pi$
$769$	4.12388e53	1.68139	0.840696	+	0.541507i	$0.182146\pi$
$770$	1.62241e52	0.0645778
$771$	0	0
$772$	−5.16475e52	−0.195943
$773$	1.80579e53	0.668879	0.334439	−	0.942417i	$-0.391453\pi$
$773$	1.80579e53	0.668879	0.334439	+	0.942417i	$0.391453\pi$
$774$	0	0
$775$	6.34356e52	0.224002
$776$	3.80049e53	1.31038
$777$	0	0
$778$	−1.22781e52	−0.0403653
$779$	3.14831e53	1.01073
$780$	0	0
$781$	−1.43020e51	−0.00437877
$782$	−3.77846e53	−1.12977
$783$	0	0
$784$	1.62280e53	0.462826
$785$	4.80030e53	1.33715
$786$	0	0
$787$	6.04656e53	1.60685	0.803425	−	0.595405i	$-0.203009\pi$
$787$	6.04656e53	1.60685	0.803425	+	0.595405i	$0.203009\pi$
$788$	−5.34484e52	−0.138739
$789$	0	0
$790$	−1.16212e54	−2.87838
$791$	−4.50817e52	−0.109078
$792$	0	0
$793$	−1.60913e53	−0.371566
$794$	1.24804e53	0.281547
$795$	0	0
$796$	−1.28683e53	−0.277096
$797$	−6.79705e53	−1.43002	−0.715009	−	0.699116i	$-0.753577\pi$
$797$	−6.79705e53	−1.43002	−0.715009	+	0.699116i	$0.753577\pi$
$798$	0	0
$799$	−3.98684e53	−0.800779
$800$	−5.45122e53	−1.06987
$801$	0	0
$802$	4.00359e53	0.750280
$803$	−4.26694e52	−0.0781411
$804$	0	0
$805$	4.27007e53	0.746812
$806$	−1.92751e52	−0.0329456
$807$	0	0
$808$	−4.49098e53	−0.733214
$809$	−1.11799e54	−1.78397	−0.891987	−	0.452061i	$-0.850689\pi$
$809$	−1.11799e54	−1.78397	−0.891987	+	0.452061i	$0.850689\pi$
$810$	0	0
$811$	−9.12670e53	−1.39132	−0.695662	−	0.718369i	$-0.744889\pi$
$811$	−9.12670e53	−1.39132	−0.695662	+	0.718369i	$0.744889\pi$
$812$	1.20226e53	0.179147
$813$	0	0
$814$	3.62910e52	0.0516711
$815$	9.43253e53	1.31284
$816$	0	0
$817$	1.42463e54	1.89494
$818$	−5.52421e53	−0.718346
$819$	0	0
$820$	−2.34014e53	−0.290861
$821$	−4.11474e53	−0.500027	−0.250014	−	0.968242i	$-0.580435\pi$
$821$	−4.11474e53	−0.500027	−0.250014	+	0.968242i	$0.580435\pi$
$822$	0	0
$823$	2.41018e53	0.279996	0.139998	−	0.990152i	$-0.455290\pi$
$823$	2.41018e53	0.279996	0.139998	+	0.990152i	$0.455290\pi$
$824$	−6.06059e53	−0.688432
$825$	0	0
$826$	−8.09610e53	−0.879316
$827$	−1.22285e54	−1.29873	−0.649367	−	0.760475i	$-0.724966\pi$
$827$	−1.22285e54	−1.29873	−0.649367	+	0.760475i	$0.724966\pi$
$828$	0	0
$829$	5.14834e53	0.522888	0.261444	−	0.965219i	$-0.415801\pi$
$829$	5.14834e53	0.522888	0.261444	+	0.965219i	$0.415801\pi$
$830$	7.84113e53	0.778815
$831$	0	0
$832$	4.41949e53	0.419846
$833$	1.29744e54	1.20547
$834$	0	0
$835$	−3.00258e54	−2.66867
$836$	3.10579e52	0.0269995
$837$	0	0
$838$	7.57988e53	0.630446
$839$	1.47001e54	1.19598	0.597990	−	0.801504i	$-0.295966\pi$
$839$	1.47001e54	1.19598	0.597990	+	0.801504i	$0.295966\pi$
$840$	0	0
$841$	7.66718e53	0.596911
$842$	−1.05929e54	−0.806757
$843$	0	0
$844$	3.49300e53	0.254603
$845$	2.16095e54	1.54098
$846$	0	0
$847$	−8.41294e53	−0.574255
$848$	2.73598e53	0.182721
$849$	0	0
$850$	5.48480e54	3.50680
$851$	9.55152e53	0.597552
$852$	0	0
$853$	−2.39398e54	−1.43405	−0.717024	−	0.697048i	$-0.754496\pi$
$853$	−2.39398e54	−1.43405	−0.717024	+	0.697048i	$0.754496\pi$
$854$	8.40302e53	0.492566
$855$	0	0
$856$	−1.25039e54	−0.701907
$857$	−1.12045e54	−0.615526	−0.307763	−	0.951463i	$-0.599580\pi$
$857$	−1.12045e54	−0.615526	−0.307763	+	0.951463i	$0.599580\pi$
$858$	0	0
$859$	2.95876e54	1.55681	0.778405	−	0.627762i	$-0.216029\pi$
$859$	2.95876e54	1.55681	0.778405	+	0.627762i	$0.216029\pi$
$860$	−1.05893e54	−0.545313
$861$	0	0
$862$	−1.41478e54	−0.697919
$863$	2.90233e52	0.0140135	0.00700675	−	0.999975i	$-0.497770\pi$
$863$	2.90233e52	0.0140135	0.00700675	+	0.999975i	$0.497770\pi$
$864$	0	0
$865$	1.30274e54	0.602643
$866$	−5.33623e53	−0.241632
$867$	0	0
$868$	−3.27697e52	−0.0142186
$869$	−3.10813e53	−0.132018
$870$	0	0
$871$	3.58207e53	0.145814
$872$	2.06382e54	0.822463
$873$	0	0
$874$	−2.51082e54	−0.959077
$875$	−3.42308e54	−1.28017
$876$	0	0
$877$	−9.87214e53	−0.353931	−0.176966	−	0.984217i	$-0.556628\pi$
$877$	−9.87214e53	−0.353931	−0.176966	+	0.984217i	$0.556628\pi$
$878$	−1.38630e54	−0.486642
$879$	0	0
$880$	2.65633e53	0.0894031
$881$	3.43429e54	1.13183	0.565916	−	0.824463i	$-0.308523\pi$
$881$	3.43429e54	1.13183	0.565916	+	0.824463i	$0.308523\pi$
$882$	0	0
$883$	−3.21368e54	−1.01561	−0.507807	−	0.861471i	$-0.669544\pi$
$883$	−3.21368e54	−1.01561	−0.507807	+	0.861471i	$0.669544\pi$
$884$	5.42568e53	0.167914
$885$	0	0
$886$	−2.39846e54	−0.711882
$887$	3.18523e54	0.925879	0.462940	−	0.886390i	$-0.346795\pi$
$887$	3.18523e54	0.925879	0.462940	+	0.886390i	$0.346795\pi$
$888$	0	0
$889$	9.33479e53	0.260269
$890$	1.56414e54	0.427132
$891$	0	0
$892$	8.54643e53	0.223890
$893$	−2.64929e54	−0.679793
$894$	0	0
$895$	7.77987e54	1.91534
$896$	−1.16133e54	−0.280064
$897$	0	0
$898$	−4.59335e54	−1.06296
$899$	−5.59090e53	−0.126744
$900$	0	0
$901$	2.18743e54	0.475911
$902$	1.92248e53	0.0409770
$903$	0	0
$904$	−9.99291e53	−0.204445
$905$	−4.37117e54	−0.876192
$906$	0	0
$907$	−1.66261e54	−0.319931	−0.159966	−	0.987123i	$-0.551138\pi$
$907$	−1.66261e54	−0.319931	−0.159966	+	0.987123i	$0.551138\pi$
$908$	1.98694e54	0.374625
$909$	0	0
$910$	1.88341e54	0.340940
$911$	−1.12509e55	−1.99570	−0.997851	−	0.0655227i	$-0.979129\pi$
$911$	−1.12509e55	−1.99570	−0.997851	+	0.0655227i	$0.979129\pi$
$912$	0	0
$913$	2.09715e53	0.0357207
$914$	−6.53384e54	−1.09060
$915$	0	0
$916$	−9.17122e53	−0.147015
$917$	−3.82510e54	−0.600912
$918$	0	0
$919$	−1.81936e54	−0.274525	−0.137263	−	0.990535i	$-0.543830\pi$
$919$	−1.81936e54	−0.274525	−0.137263	+	0.990535i	$0.543830\pi$
$920$	9.46514e54	1.39976
$921$	0	0
$922$	4.18336e54	0.594297
$923$	−1.66027e53	−0.0231178
$924$	0	0
$925$	−1.38650e55	−1.85480
$926$	5.90482e54	0.774290
$927$	0	0
$928$	4.80444e54	0.605348
$929$	−6.12532e52	−0.00756550	−0.00378275	−	0.999993i	$-0.501204\pi$
$929$	−6.12532e52	−0.00756550	−0.00378275	+	0.999993i	$0.501204\pi$
$930$	0	0
$931$	8.62160e54	1.02334
$932$	−3.85630e53	−0.0448721
$933$	0	0
$934$	3.67339e54	0.410818
$935$	2.12376e54	0.232857
$936$	0	0
$937$	−1.54519e55	−1.62855	−0.814274	−	0.580481i	$-0.802865\pi$
$937$	−1.54519e55	−1.62855	−0.814274	+	0.580481i	$0.802865\pi$
$938$	−1.87059e54	−0.193298
$939$	0	0
$940$	1.96922e54	0.195627
$941$	1.06842e55	1.04072	0.520361	−	0.853946i	$-0.325797\pi$
$941$	1.06842e55	1.04072	0.520361	+	0.853946i	$0.325797\pi$
$942$	0	0
$943$	5.05981e54	0.473880
$944$	−1.32555e55	−1.21735
$945$	0	0
$946$	8.69935e53	0.0768247
$947$	−3.77859e54	−0.327232	−0.163616	−	0.986524i	$-0.552316\pi$
$947$	−3.77859e54	−0.327232	−0.163616	+	0.986524i	$0.552316\pi$
$948$	0	0
$949$	−4.95335e54	−0.412548
$950$	3.64469e55	2.97697
$951$	0	0
$952$	−1.43697e55	−1.12892
$953$	−5.53742e53	−0.0426667	−0.0213333	−	0.999772i	$-0.506791\pi$
$953$	−5.53742e53	−0.0426667	−0.0213333	+	0.999772i	$0.506791\pi$
$954$	0	0
$955$	2.07055e55	1.53470
$956$	5.73090e53	0.0416631
$957$	0	0
$958$	−7.23551e53	−0.0506066
$959$	1.30897e55	0.898016
$960$	0	0
$961$	−1.49966e55	−0.989941
$962$	4.21290e54	0.272799
$963$	0	0
$964$	1.04346e54	0.0650206
$965$	−2.34683e55	−1.43459
$966$	0	0
$967$	1.91207e55	1.12490	0.562449	−	0.826832i	$-0.309859\pi$
$967$	1.91207e55	1.12490	0.562449	+	0.826832i	$0.309859\pi$
$968$	−1.86483e55	−1.07633
$969$	0	0
$970$	3.40506e55	1.89168
$971$	−8.30735e54	−0.452800	−0.226400	−	0.974034i	$-0.572696\pi$
$971$	−8.30735e54	−0.452800	−0.226400	+	0.974034i	$0.572696\pi$
$972$	0	0
$973$	9.43317e54	0.494960
$974$	2.13197e55	1.09759
$975$	0	0
$976$	1.37580e55	0.681921
$977$	3.32881e55	1.61897	0.809486	−	0.587140i	$-0.199746\pi$
$977$	3.32881e55	1.61897	0.809486	+	0.587140i	$0.199746\pi$
$978$	0	0
$979$	4.18338e53	0.0195906
$980$	−6.40844e54	−0.294490
$981$	0	0
$982$	4.09426e54	0.181181
$983$	5.66371e54	0.245958	0.122979	−	0.992409i	$-0.460755\pi$
$983$	5.66371e54	0.245958	0.122979	+	0.992409i	$0.460755\pi$
$984$	0	0
$985$	−2.42867e55	−1.01578
$986$	−4.83403e55	−1.98420
$987$	0	0
$988$	3.60541e54	0.142545
$989$	2.28960e55	0.888442
$990$	0	0
$991$	−3.93647e55	−1.47145	−0.735723	−	0.677283i	$-0.763157\pi$
$991$	−3.93647e55	−1.47145	−0.735723	+	0.677283i	$0.763157\pi$
$992$	−1.30954e54	−0.0480453
$993$	0	0
$994$	8.67009e53	0.0306461
$995$	−5.84730e55	−2.02875
$996$	0	0
$997$	1.67431e53	0.00559727	0.00279863	−	0.999996i	$-0.499109\pi$
$997$	1.67431e53	0.00559727	0.00279863	+	0.999996i	$0.499109\pi$
$998$	3.45755e54	0.113463
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.38.a.c.1.2		4
3.2	odd	2		3.38.a.b.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.38.a.b.1.3	✓	4	3.2	odd	2
9.38.a.c.1.2		4	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-322000. q^{2} -3.37552e10 q^{4} -1.53382e13 q^{5} +2.48687e15 q^{7} +5.51245e16 q^{8} +O(q^{10})\)	\(q-322000. q^{2} -3.37552e10 q^{4} -1.53382e13 q^{5} +2.48687e15 q^{7} +5.51245e16 q^{8} +4.93889e18 q^{10} +1.32093e18 q^{11} +1.53342e20 q^{13} -8.00770e20 q^{14} -1.31108e22 q^{16} -1.04822e23 q^{17} -6.96548e23 q^{19} +5.17744e23 q^{20} -4.25339e23 q^{22} -1.11946e25 q^{23} +1.62501e26 q^{25} -4.93762e25 q^{26} -8.39448e25 q^{28} -1.43220e27 q^{29} +3.90372e26 q^{31} -3.35459e27 q^{32} +3.37525e28 q^{34} -3.81440e28 q^{35} -8.53226e28 q^{37} +2.24288e29 q^{38} -8.45509e29 q^{40} -4.51987e29 q^{41} -2.04528e30 q^{43} -4.45883e28 q^{44} +3.60466e30 q^{46} +3.80345e30 q^{47} -1.23776e31 q^{49} -5.23251e31 q^{50} -5.17611e30 q^{52} -2.08682e31 q^{53} -2.02607e31 q^{55} +1.37087e32 q^{56} +4.61167e32 q^{58} +1.01104e33 q^{59} -1.04937e33 q^{61} -1.25699e32 q^{62} +2.88211e33 q^{64} -2.35199e33 q^{65} +2.33599e33 q^{67} +3.53828e33 q^{68} +1.22824e34 q^{70} -1.08272e33 q^{71} -3.23026e34 q^{73} +2.74738e34 q^{74} +2.35121e34 q^{76} +3.28498e33 q^{77} -2.35299e35 q^{79} +2.01095e35 q^{80} +1.45540e35 q^{82} +1.58763e35 q^{83} +1.60777e36 q^{85} +6.58578e35 q^{86} +7.28155e34 q^{88} +3.16700e35 q^{89} +3.81342e35 q^{91} +3.77876e35 q^{92} -1.22471e36 q^{94} +1.06838e37 q^{95} +6.89438e36 q^{97} +3.98559e36 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 437562 q^{2} + 346098955492 q^{4} + 4099829756904 q^{5} + 66\!\cdots\!84 q^{7}+ \cdots - 14\!\cdots\!76 q^{8}+O(q^{10}) \) 4 * q - 437562 * q^2 + 346098955492 * q^4 + 4099829756904 * q^5 + 6605809948153184 * q^7 - 140484113342159976 * q^8	\( 4 q - 437562 q^{2} + 346098955492 q^{4} + 4099829756904 q^{5} + 66\!\cdots\!84 q^{7}+ \cdots + 43\!\cdots\!78 q^{98}+O(q^{100}) \) 4 * q - 437562 * q^2 + 346098955492 * q^4 + 4099829756904 * q^5 + 6605809948153184 * q^7 - 140484113342159976 * q^8 - 21511023001649316 * q^10 - 20953708852195292976 * q^11 + 51830892788989874168 * q^13 + 1809002141673235613712 * q^14 + 55184727516616371757840 * q^16 - 81101770962322537501128 * q^17 - 544604242502813077907632 * q^19 + 3566083114449076353950376 * q^20 + 23909208610123411045457976 * q^22 + 6105434608113226892697888 * q^23 + 95396877753446381193398716 * q^25 - 428554172265180170762299788 * q^26 + 2469833924959492064190244448 * q^28 - 4171186009659314742454127736 * q^29 + 8995814656808409627856220864 * q^31 - 36517476440276920084276020384 * q^32 + 31219088393882932122099949524 * q^34 - 42129462142584542112964223040 * q^35 + 55519093704269258277039732824 * q^37 + 735180697664011480109320664568 * q^38 - 2663133991761021855901070923152 * q^40 + 869595339264691998704372818776 * q^41 - 509323958833633606104562745680 * q^43 - 2838804848354890092833187324336 * q^44 - 14832400342987743191058839458896 * q^46 - 4297748917019550924184843821120 * q^47 + 40223006658016971616433785618020 * q^49 - 102764730674385833857211828709414 * q^50 + 186771330756284408934646875520568 * q^52 + 125797679190958862093479980165288 * q^53 - 324441401797069196184728188134624 * q^55 - 49261177652308793436687718380480 * q^56 - 758216144723951752216603559669556 * q^58 + 1322751535061383229075407129388688 * q^59 - 1210012908287761061549313720873160 * q^61 + 3774869312329378363502064838581792 * q^62 + 8553618714336434539515354532145728 * q^64 - 1596939597234927778869711846229968 * q^65 + 16212837695473169417262127089269648 * q^67 - 6364770984875237153325176447214984 * q^68 + 8205699211322075854652286498656160 * q^70 - 10892424995451680587530033164573088 * q^71 - 19472416597596703966438677461737048 * q^73 + 89115306434605413664690690272305412 * q^74 - 95475877084130734100913860795365168 * q^76 + 256189314900709292482321902951864192 * q^77 + 42564929886993357285736803130555520 * q^79 + 955034489632094448517301530341944736 * q^80 + 335470244295388111217009211756354948 * q^82 + 462964612731837394872969166562146224 * q^83 + 1847677353245070936584728247586996912 * q^85 + 363370083621183428400243233525783304 * q^86 + 4210934419609684353108607591773010656 * q^88 + 314574774231571073544391076719446552 * q^89 + 2615056540536627234228451043107657024 * q^91 + 16598538663060910484079148451607722016 * q^92 - 573809173038711993912694394480689248 * q^94 + 8958385060094338314910240959017780256 * q^95 + 445047507548838106214452450407795848 * q^97 + 43086999614034505592591376853854433878 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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