LMFDB - Embedded newform 9.38.a.c.1.3

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			1.3
Root			$31743.2$ 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)

$f(q)$	$=$	$q+81067.1 q^{2} -1.30867e11 q^{4} +7.16603e12 q^{5} -5.96869e15 q^{7} -2.17508e16 q^{8} +O(q^{10})$	\(q+81067.1 q^{2} -1.30867e11 q^{4} +7.16603e12 q^{5} -5.96869e15 q^{7} -2.17508e16 q^{8} +5.80929e17 q^{10} -2.06526e19 q^{11} -4.02756e20 q^{13} -4.83865e20 q^{14} +1.62230e22 q^{16} +4.55890e22 q^{17} +1.54990e23 q^{19} -9.37797e23 q^{20} -1.67424e24 q^{22} -2.42540e25 q^{23} -2.14076e25 q^{25} -3.26502e25 q^{26} +7.81105e26 q^{28} -1.52016e27 q^{29} +6.09023e27 q^{31} +4.30456e27 q^{32} +3.69577e27 q^{34} -4.27718e28 q^{35} -6.28281e28 q^{37} +1.25646e28 q^{38} -1.55867e29 q^{40} +8.11303e29 q^{41} +4.69121e29 q^{43} +2.70274e30 q^{44} -1.96620e30 q^{46} -1.02212e31 q^{47} +1.70631e31 q^{49} -1.73545e30 q^{50} +5.27075e31 q^{52} -5.42457e31 q^{53} -1.47997e32 q^{55} +1.29824e32 q^{56} -1.23235e32 q^{58} +5.27739e32 q^{59} -6.19951e31 q^{61} +4.93717e32 q^{62} -1.88071e33 q^{64} -2.88616e33 q^{65} +9.30348e33 q^{67} -5.96611e33 q^{68} -3.46739e33 q^{70} +2.75965e34 q^{71} +2.09192e34 q^{73} -5.09329e33 q^{74} -2.02831e34 q^{76} +1.23269e35 q^{77} +1.20341e34 q^{79} +1.16254e35 q^{80} +6.57700e34 q^{82} +3.25180e34 q^{83} +3.26692e35 q^{85} +3.80303e34 q^{86} +4.49210e35 q^{88} +1.39444e36 q^{89} +2.40392e36 q^{91} +3.17405e36 q^{92} -8.28600e35 q^{94} +1.11066e36 q^{95} -6.18707e36 q^{97} +1.38326e36 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	81067.1	0.218670	0.109335	−	0.994005i	$-0.465128\pi$
$2$	81067.1	0.218670	0.109335	+	0.994005i	$0.465128\pi$
$3$	0	0
$3$	0	0
$4$	−1.30867e11	−0.952183
$5$	7.16603e12	0.840105	0.420052	−	0.907500i	$-0.362012\pi$
$5$	7.16603e12	0.840105	0.420052	+	0.907500i	$0.362012\pi$
$6$	0	0
$7$	−5.96869e15	−1.38537	−0.692684	−	0.721241i	$-0.743572\pi$
$7$	−5.96869e15	−1.38537	−0.692684	+	0.721241i	$0.743572\pi$
$8$	−2.17508e16	−0.426885
$9$	0	0
$10$	5.80929e17	0.183706
$11$	−2.06526e19	−1.11998	−0.559989	−	0.828500i	$-0.689194\pi$
$11$	−2.06526e19	−1.11998	−0.559989	+	0.828500i	$0.689194\pi$
$12$	0	0
$13$	−4.02756e20	−0.993321	−0.496661	−	0.867945i	$-0.665441\pi$
$13$	−4.02756e20	−0.993321	−0.496661	+	0.867945i	$0.665441\pi$
$14$	−4.83865e20	−0.302939
$15$	0	0
$16$	1.62230e22	0.858836
$17$	4.55890e22	0.786241	0.393120	−	0.919487i	$-0.371396\pi$
$17$	4.55890e22	0.786241	0.393120	+	0.919487i	$0.371396\pi$
$18$	0	0
$19$	1.54990e23	0.341477	0.170738	−	0.985316i	$-0.445385\pi$
$19$	1.54990e23	0.341477	0.170738	+	0.985316i	$0.445385\pi$
$20$	−9.37797e23	−0.799934
$21$	0	0
$22$	−1.67424e24	−0.244906
$23$	−2.42540e25	−1.55890	−0.779450	−	0.626464i	$-0.784501\pi$
$23$	−2.42540e25	−1.55890	−0.779450	+	0.626464i	$0.784501\pi$
$24$	0	0
$25$	−2.14076e25	−0.294224
$26$	−3.26502e25	−0.217210
$27$	0	0
$28$	7.81105e26	1.31912
$29$	−1.52016e27	−1.34130	−0.670652	−	0.741772i	$-0.733985\pi$
$29$	−1.52016e27	−1.34130	−0.670652	+	0.741772i	$0.733985\pi$
$30$	0	0
$31$	6.09023e27	1.56474	0.782370	−	0.622814i	$-0.214011\pi$
$31$	6.09023e27	1.56474	0.782370	+	0.622814i	$0.214011\pi$
$32$	4.30456e27	0.614687
$33$	0	0
$34$	3.69577e27	0.171928
$35$	−4.27718e28	−1.16385
$36$	0	0
$37$	−6.28281e28	−0.611536	−0.305768	−	0.952106i	$-0.598913\pi$
$37$	−6.28281e28	−0.611536	−0.305768	+	0.952106i	$0.598913\pi$
$38$	1.25646e28	0.0746709
$39$	0	0
$40$	−1.55867e29	−0.358628
$41$	8.11303e29	1.18217	0.591087	−	0.806608i	$-0.298699\pi$
$41$	8.11303e29	1.18217	0.591087	+	0.806608i	$0.298699\pi$
$42$	0	0
$43$	4.69121e29	0.283216	0.141608	−	0.989923i	$-0.454773\pi$
$43$	4.69121e29	0.283216	0.141608	+	0.989923i	$0.454773\pi$
$44$	2.70274e30	1.06642
$45$	0	0
$46$	−1.96620e30	−0.340885
$47$	−1.02212e31	−1.19039	−0.595196	−	0.803581i	$-0.702926\pi$
$47$	−1.02212e31	−1.19039	−0.595196	+	0.803581i	$0.702926\pi$
$48$	0	0
$49$	1.70631e31	0.919245
$50$	−1.73545e30	−0.0643380
$51$	0	0
$52$	5.27075e31	0.945824
$53$	−5.42457e31	−0.684323	−0.342162	−	0.939641i	$-0.611159\pi$
$53$	−5.42457e31	−0.684323	−0.342162	+	0.939641i	$0.611159\pi$
$54$	0	0
$55$	−1.47997e32	−0.940898
$56$	1.29824e32	0.591392
$57$	0	0
$58$	−1.23235e32	−0.293303
$59$	5.27739e32	0.915496	0.457748	−	0.889082i	$-0.348656\pi$
$59$	5.27739e32	0.915496	0.457748	+	0.889082i	$0.348656\pi$
$60$	0	0
$61$	−6.19951e31	−0.0580437	−0.0290219	−	0.999579i	$-0.509239\pi$
$61$	−6.19951e31	−0.0580437	−0.0290219	+	0.999579i	$0.509239\pi$
$62$	4.93717e32	0.342162
$63$	0	0
$64$	−1.88071e33	−0.724423
$65$	−2.88616e33	−0.834494
$66$	0	0
$67$	9.30348e33	1.53554	0.767771	−	0.640725i	$-0.221366\pi$
$67$	9.30348e33	1.53554	0.767771	+	0.640725i	$0.221366\pi$
$68$	−5.96611e33	−0.748645
$69$	0	0
$70$	−3.46739e33	−0.254500
$71$	2.75965e34	1.55802	0.779012	−	0.627010i	$-0.215721\pi$
$71$	2.75965e34	1.55802	0.779012	+	0.627010i	$0.215721\pi$
$72$	0	0
$73$	2.09192e34	0.706436	0.353218	−	0.935541i	$-0.385087\pi$
$73$	2.09192e34	0.706436	0.353218	+	0.935541i	$0.385087\pi$
$74$	−5.09329e33	−0.133725
$75$	0	0
$76$	−2.02831e34	−0.325149
$77$	1.23269e35	1.55158
$78$	0	0
$79$	1.20341e34	0.0942567	0.0471283	−	0.998889i	$-0.484993\pi$
$79$	1.20341e34	0.0942567	0.0471283	+	0.998889i	$0.484993\pi$
$80$	1.16254e35	0.721512
$81$	0	0
$82$	6.57700e34	0.258506
$83$	3.25180e34	0.102136	0.0510681	−	0.998695i	$-0.483737\pi$
$83$	3.25180e34	0.102136	0.0510681	+	0.998695i	$0.483737\pi$
$84$	0	0
$85$	3.26692e35	0.660525
$86$	3.80303e34	0.0619310
$87$	0	0
$88$	4.49210e35	0.478101
$89$	1.39444e36	1.20416	0.602081	−	0.798435i	$-0.294338\pi$
$89$	1.39444e36	1.20416	0.602081	+	0.798435i	$0.294338\pi$
$90$	0	0
$91$	2.40392e36	1.37612
$92$	3.17405e36	1.48436
$93$	0	0
$94$	−8.28600e35	−0.260303
$95$	1.11066e36	0.286876
$96$	0	0
$97$	−6.18707e36	−1.08695	−0.543473	−	0.839427i	$-0.682891\pi$
$97$	−6.18707e36	−1.08695	−0.543473	+	0.839427i	$0.682891\pi$
$98$	1.38326e36	0.201012
$99$	0	0
$100$	2.80155e36	0.280155
$101$	1.95203e37	1.62384	0.811918	−	0.583772i	$-0.198424\pi$
$101$	1.95203e37	1.62384	0.811918	+	0.583772i	$0.198424\pi$
$102$	0	0
$103$	3.11250e37	1.80144	0.900722	−	0.434397i	$-0.143038\pi$
$103$	3.11250e37	1.80144	0.900722	+	0.434397i	$0.143038\pi$
$104$	8.76026e36	0.424033
$105$	0	0
$106$	−4.39754e36	−0.149641
$107$	−2.91526e37	−0.833831	−0.416915	−	0.908945i	$-0.636889\pi$
$107$	−2.91526e37	−0.833831	−0.416915	+	0.908945i	$0.636889\pi$
$108$	0	0
$109$	4.34807e37	0.882890	0.441445	−	0.897288i	$-0.354466\pi$
$109$	4.34807e37	0.882890	0.441445	+	0.897288i	$0.354466\pi$
$110$	−1.19977e37	−0.205747
$111$	0	0
$112$	−9.68298e37	−1.18980
$113$	−1.30612e38	−1.36155	−0.680774	−	0.732493i	$-0.738356\pi$
$113$	−1.30612e38	−1.36155	−0.680774	+	0.732493i	$0.738356\pi$
$114$	0	0
$115$	−1.73805e38	−1.30964
$116$	1.98939e38	1.27717
$117$	0	0
$118$	4.27822e37	0.200192
$119$	−2.72107e38	−1.08923
$120$	0	0
$121$	8.64886e37	0.254349
$122$	−5.02576e36	−0.0126924
$123$	0	0
$124$	−7.97010e38	−1.48992
$125$	−6.74805e38	−1.08728
$126$	0	0
$127$	1.12113e39	1.34675	0.673373	−	0.739303i	$-0.264845\pi$
$127$	1.12113e39	1.34675	0.673373	+	0.739303i	$0.264845\pi$
$128$	−7.44077e38	−0.773096
$129$	0	0
$130$	−2.33973e38	−0.182479
$131$	−1.51287e39	−1.02396	−0.511980	−	0.858997i	$-0.671088\pi$
$131$	−1.51287e39	−1.02396	−0.511980	+	0.858997i	$0.671088\pi$
$132$	0	0
$133$	−9.25086e38	−0.473071
$134$	7.54206e38	0.335777
$135$	0	0
$136$	−9.91598e38	−0.335634
$137$	5.50009e38	0.162570	0.0812848	−	0.996691i	$-0.474098\pi$
$137$	5.50009e38	0.162570	0.0812848	+	0.996691i	$0.474098\pi$
$138$	0	0
$139$	2.01159e39	0.454743	0.227372	−	0.973808i	$-0.426987\pi$
$139$	2.01159e39	0.454743	0.227372	+	0.973808i	$0.426987\pi$
$140$	5.59742e39	1.10820
$141$	0	0
$142$	2.23717e39	0.340693
$143$	8.31793e39	1.11250
$144$	0	0
$145$	−1.08935e40	−1.12684
$146$	1.69586e39	0.154477
$147$	0	0
$148$	8.22213e39	0.582294
$149$	−1.36577e40	−0.853949	−0.426975	−	0.904264i	$-0.640421\pi$
$149$	−1.36577e40	−0.853949	−0.426975	+	0.904264i	$0.640421\pi$
$150$	0	0
$151$	3.14967e40	1.53883	0.769415	−	0.638749i	$-0.220548\pi$
$151$	3.14967e40	1.53883	0.769415	+	0.638749i	$0.220548\pi$
$152$	−3.37115e39	−0.145771
$153$	0	0
$154$	9.99304e39	0.339285
$155$	4.36428e40	1.31455
$156$	0	0
$157$	−1.57563e40	−0.374378	−0.187189	−	0.982324i	$-0.559938\pi$
$157$	−1.57563e40	−0.374378	−0.187189	+	0.982324i	$0.559938\pi$
$158$	9.75569e38	0.0206111
$159$	0	0
$160$	3.08466e40	0.516401
$161$	1.44765e41	2.15965
$162$	0	0
$163$	−9.57266e40	−1.13648	−0.568240	−	0.822863i	$-0.692376\pi$
$163$	−9.57266e40	−1.13648	−0.568240	+	0.822863i	$0.692376\pi$
$164$	−1.06173e41	−1.12565
$165$	0	0
$166$	2.63614e39	0.0223342
$167$	−1.21079e41	−0.917942	−0.458971	−	0.888451i	$-0.651782\pi$
$167$	−1.21079e41	−0.917942	−0.458971	+	0.888451i	$0.651782\pi$
$168$	0	0
$169$	−2.18871e39	−0.0133132
$170$	2.64840e40	0.144437
$171$	0	0
$172$	−6.13925e40	−0.269674
$173$	−2.37365e41	−0.936621	−0.468310	−	0.883564i	$-0.655137\pi$
$173$	−2.37365e41	−0.936621	−0.468310	+	0.883564i	$0.655137\pi$
$174$	0	0
$175$	1.27775e41	0.407608
$176$	−3.35046e41	−0.961877
$177$	0	0
$178$	1.13043e41	0.263315
$179$	−3.87672e41	−0.814110	−0.407055	−	0.913404i	$-0.633444\pi$
$179$	−3.87672e41	−0.814110	−0.407055	+	0.913404i	$0.633444\pi$
$180$	0	0
$181$	−9.37245e41	−1.60250	−0.801252	−	0.598326i	$-0.795833\pi$
$181$	−9.37245e41	−1.60250	−0.801252	+	0.598326i	$0.795833\pi$
$182$	1.94879e41	0.300916
$183$	0	0
$184$	5.27544e41	0.665470
$185$	−4.50228e41	−0.513754
$186$	0	0
$187$	−9.41530e41	−0.880572
$188$	1.33761e42	1.13347
$189$	0	0
$190$	9.00381e40	0.0627314
$191$	7.76327e41	0.490826	0.245413	−	0.969419i	$-0.421076\pi$
$191$	7.76327e41	0.490826	0.245413	+	0.969419i	$0.421076\pi$
$192$	0	0
$193$	1.83873e42	0.958758	0.479379	−	0.877608i	$-0.340862\pi$
$193$	1.83873e42	0.958758	0.479379	+	0.877608i	$0.340862\pi$
$194$	−5.01568e41	−0.237683
$195$	0	0
$196$	−2.23300e42	−0.875290
$197$	−2.38170e42	−0.849693	−0.424847	−	0.905265i	$-0.639672\pi$
$197$	−2.38170e42	−0.849693	−0.424847	+	0.905265i	$0.639672\pi$
$198$	0	0
$199$	3.72548e42	1.10256	0.551278	−	0.834322i	$-0.314141\pi$
$199$	3.72548e42	1.10256	0.551278	+	0.834322i	$0.314141\pi$
$200$	4.65633e41	0.125600
$201$	0	0
$202$	1.58246e42	0.355085
$203$	9.07338e42	1.85820
$204$	0	0
$205$	5.81382e42	0.993150
$206$	2.52321e42	0.393922
$207$	0	0
$208$	−6.53389e42	−0.853100
$209$	−3.20093e42	−0.382446
$210$	0	0
$211$	5.66343e42	0.567354	0.283677	−	0.958920i	$-0.408446\pi$
$211$	5.66343e42	0.567354	0.283677	+	0.958920i	$0.408446\pi$
$212$	7.09897e42	0.651601
$213$	0	0
$214$	−2.36332e42	−0.182334
$215$	3.36173e42	0.237932
$216$	0	0
$217$	−3.63507e43	−2.16774
$218$	3.52486e42	0.193062
$219$	0	0
$220$	1.93679e43	0.895907
$221$	−1.83612e43	−0.780989
$222$	0	0
$223$	3.12041e43	1.12350	0.561749	−	0.827308i	$-0.310129\pi$
$223$	3.12041e43	1.12350	0.561749	+	0.827308i	$0.310129\pi$
$224$	−2.56926e43	−0.851567
$225$	0	0
$226$	−1.05884e43	−0.297730
$227$	1.69570e43	0.439411	0.219705	−	0.975566i	$-0.429490\pi$
$227$	1.69570e43	0.439411	0.219705	+	0.975566i	$0.429490\pi$
$228$	0	0
$229$	−4.70639e42	−0.103689	−0.0518444	−	0.998655i	$-0.516510\pi$
$229$	−4.70639e42	−0.103689	−0.0518444	+	0.998655i	$0.516510\pi$
$230$	−1.40899e43	−0.286379
$231$	0	0
$232$	3.30648e43	0.572582
$233$	−8.91929e43	−1.42641	−0.713207	−	0.700953i	$-0.752758\pi$
$233$	−8.91929e43	−1.42641	−0.713207	+	0.700953i	$0.752758\pi$
$234$	0	0
$235$	−7.32451e43	−1.00005
$236$	−6.90636e43	−0.871720
$237$	0	0
$238$	−2.20589e43	−0.238183
$239$	7.05888e43	0.705301	0.352651	−	0.935755i	$-0.385280\pi$
$239$	7.05888e43	0.705301	0.352651	+	0.935755i	$0.385280\pi$
$240$	0	0
$241$	−1.03720e44	−0.888271	−0.444136	−	0.895960i	$-0.646489\pi$
$241$	−1.03720e44	−0.888271	−0.444136	+	0.895960i	$0.646489\pi$
$242$	7.01138e42	0.0556185
$243$	0	0
$244$	8.11311e42	0.0552682
$245$	1.22275e44	0.772262
$246$	0	0
$247$	−6.24230e43	−0.339196
$248$	−1.32467e44	−0.667963
$249$	0	0
$250$	−5.47045e43	−0.237757
$251$	1.06389e44	0.429470	0.214735	−	0.976672i	$-0.431111\pi$
$251$	1.06389e44	0.429470	0.214735	+	0.976672i	$0.431111\pi$
$252$	0	0
$253$	5.00907e44	1.74593
$254$	9.08865e43	0.294494
$255$	0	0
$256$	1.98162e44	0.555369
$257$	2.17429e44	0.566962	0.283481	−	0.958978i	$-0.408511\pi$
$257$	2.17429e44	0.566962	0.283481	+	0.958978i	$0.408511\pi$
$258$	0	0
$259$	3.75001e44	0.847202
$260$	3.77703e44	0.794591
$261$	0	0
$262$	−1.22644e44	−0.223910
$263$	−5.98155e44	−1.01773	−0.508865	−	0.860847i	$-0.669935\pi$
$263$	−5.98155e44	−1.01773	−0.508865	+	0.860847i	$0.669935\pi$
$264$	0	0
$265$	−3.88726e44	−0.574903
$266$	−7.49940e43	−0.103447
$267$	0	0
$268$	−1.21752e45	−1.46212
$269$	1.15434e45	1.29394	0.646972	−	0.762514i	$-0.276035\pi$
$269$	1.15434e45	1.29394	0.646972	+	0.762514i	$0.276035\pi$
$270$	0	0
$271$	1.52915e45	1.49457	0.747287	−	0.664501i	$-0.231356\pi$
$271$	1.52915e45	1.49457	0.747287	+	0.664501i	$0.231356\pi$
$272$	7.39589e44	0.675252
$273$	0	0
$274$	4.45877e43	0.0355492
$275$	4.42122e44	0.329524
$276$	0	0
$277$	−5.76088e44	−0.375503	−0.187751	−	0.982217i	$-0.560120\pi$
$277$	−5.76088e44	−0.375503	−0.187751	+	0.982217i	$0.560120\pi$
$278$	1.63074e44	0.0994388
$279$	0	0
$280$	9.30321e44	0.496832
$281$	−9.77482e44	−0.488699	−0.244350	−	0.969687i	$-0.578574\pi$
$281$	−9.77482e44	−0.488699	−0.244350	+	0.969687i	$0.578574\pi$
$282$	0	0
$283$	−2.00519e45	−0.879237	−0.439619	−	0.898185i	$-0.644886\pi$
$283$	−2.00519e45	−0.879237	−0.439619	+	0.898185i	$0.644886\pi$
$284$	−3.61147e45	−1.48352
$285$	0	0
$286$	6.74311e44	0.243270
$287$	−4.84241e45	−1.63775
$288$	0	0
$289$	−1.28373e45	−0.381826
$290$	−8.83107e44	−0.246406
$291$	0	0
$292$	−2.73764e45	−0.672656
$293$	−2.43417e45	−0.561435	−0.280717	−	0.959790i	$-0.590572\pi$
$293$	−2.43417e45	−0.561435	−0.280717	+	0.959790i	$0.590572\pi$
$294$	0	0
$295$	3.78179e45	0.769113
$296$	1.36656e45	0.261055
$297$	0	0
$298$	−1.10719e45	−0.186733
$299$	9.76843e45	1.54849
$300$	0	0
$301$	−2.80004e45	−0.392359
$302$	2.55334e45	0.336497
$303$	0	0
$304$	2.51439e45	0.293273
$305$	−4.44258e44	−0.0487628
$306$	0	0
$307$	−5.23869e45	−0.509522	−0.254761	−	0.967004i	$-0.581997\pi$
$307$	−5.23869e45	−0.509522	−0.254761	+	0.967004i	$0.581997\pi$
$308$	−1.61318e46	−1.47739
$309$	0	0
$310$	3.53799e45	0.287452
$311$	1.81624e46	1.39029	0.695146	−	0.718869i	$-0.255340\pi$
$311$	1.81624e46	1.39029	0.695146	+	0.718869i	$0.255340\pi$
$312$	0	0
$313$	−1.26517e45	−0.0860161	−0.0430081	−	0.999075i	$-0.513694\pi$
$313$	−1.26517e45	−0.0860161	−0.0430081	+	0.999075i	$0.513694\pi$
$314$	−1.27732e45	−0.0818655
$315$	0	0
$316$	−1.57487e45	−0.0897496
$317$	1.12945e46	0.607117	0.303558	−	0.952813i	$-0.401825\pi$
$317$	1.12945e46	0.607117	0.303558	+	0.952813i	$0.401825\pi$
$318$	0	0
$319$	3.13952e46	1.50223
$320$	−1.34772e46	−0.608591
$321$	0	0
$322$	1.17356e46	0.472252
$323$	7.06583e45	0.268483
$324$	0	0
$325$	8.62204e45	0.292259
$326$	−7.76028e45	−0.248515
$327$	0	0
$328$	−1.76465e46	−0.504652
$329$	6.10069e46	1.64913
$330$	0	0
$331$	−3.60502e46	−0.871145	−0.435572	−	0.900154i	$-0.643454\pi$
$331$	−3.60502e46	−0.871145	−0.435572	+	0.900154i	$0.643454\pi$
$332$	−4.25554e45	−0.0972524
$333$	0	0
$334$	−9.81555e45	−0.200727
$335$	6.66690e46	1.29002
$336$	0	0
$337$	3.50453e46	0.607403	0.303701	−	0.952767i	$-0.401777\pi$
$337$	3.50453e46	0.607403	0.303701	+	0.952767i	$0.401777\pi$
$338$	−1.77432e44	−0.00291121
$339$	0	0
$340$	−4.27533e46	−0.628940
$341$	−1.25779e47	−1.75247
$342$	0	0
$343$	8.94695e45	0.111875
$344$	−1.02038e46	−0.120901
$345$	0	0
$346$	−1.92425e46	−0.204811
$347$	−1.32955e47	−1.34156	−0.670781	−	0.741655i	$-0.734041\pi$
$347$	−1.32955e47	−1.34156	−0.670781	+	0.741655i	$0.734041\pi$
$348$	0	0
$349$	5.30968e46	0.481724	0.240862	−	0.970559i	$-0.422570\pi$
$349$	5.30968e46	0.481724	0.240862	+	0.970559i	$0.422570\pi$
$350$	1.03584e46	0.0891319
$351$	0	0
$352$	−8.89001e46	−0.688435
$353$	−9.80590e46	−0.720535	−0.360268	−	0.932849i	$-0.617315\pi$
$353$	−9.80590e46	−0.720535	−0.360268	+	0.932849i	$0.617315\pi$
$354$	0	0
$355$	1.97757e47	1.30890
$356$	−1.82487e47	−1.14658
$357$	0	0
$358$	−3.14274e46	−0.178022
$359$	3.23469e47	1.74015	0.870073	−	0.492924i	$-0.164072\pi$
$359$	3.23469e47	1.74015	0.870073	+	0.492924i	$0.164072\pi$
$360$	0	0
$361$	−1.81986e47	−0.883394
$362$	−7.59797e46	−0.350420
$363$	0	0
$364$	−3.14594e47	−1.31031
$365$	1.49908e47	0.593480
$366$	0	0
$367$	5.30423e46	0.189802	0.0949009	−	0.995487i	$-0.469747\pi$
$367$	5.30423e46	0.189802	0.0949009	+	0.995487i	$0.469747\pi$
$368$	−3.93472e47	−1.33884
$369$	0	0
$370$	−3.64987e46	−0.112343
$371$	3.23775e47	0.948040
$372$	0	0
$373$	1.73609e47	0.460212	0.230106	−	0.973166i	$-0.426093\pi$
$373$	1.73609e47	0.460212	0.230106	+	0.973166i	$0.426093\pi$
$374$	−7.63272e46	−0.192555
$375$	0	0
$376$	2.22318e47	0.508160
$377$	6.12254e47	1.33235
$378$	0	0
$379$	−7.77135e45	−0.0153345	−0.00766727	−	0.999971i	$-0.502441\pi$
$379$	−7.77135e45	−0.0153345	−0.00766727	+	0.999971i	$0.502441\pi$
$380$	−1.45349e47	−0.273159
$381$	0	0
$382$	6.29346e46	0.107329
$383$	1.37051e47	0.222692	0.111346	−	0.993782i	$-0.464484\pi$
$383$	1.37051e47	0.222692	0.111346	+	0.993782i	$0.464484\pi$
$384$	0	0
$385$	8.83347e47	1.30349
$386$	1.49061e47	0.209652
$387$	0	0
$388$	8.09683e47	1.03497
$389$	5.22275e47	0.636549	0.318274	−	0.947999i	$-0.396897\pi$
$389$	5.22275e47	0.636549	0.318274	+	0.947999i	$0.396897\pi$
$390$	0	0
$391$	−1.10572e48	−1.22567
$392$	−3.71137e47	−0.392412
$393$	0	0
$394$	−1.93078e47	−0.185803
$395$	8.62367e46	0.0791855
$396$	0	0
$397$	1.08193e48	0.904844	0.452422	−	0.891804i	$-0.350560\pi$
$397$	1.08193e48	0.904844	0.452422	+	0.891804i	$0.350560\pi$
$398$	3.02014e47	0.241096
$399$	0	0
$400$	−3.47295e47	−0.252690
$401$	1.57080e48	1.09132	0.545659	−	0.838007i	$-0.316279\pi$
$401$	1.57080e48	1.09132	0.545659	+	0.838007i	$0.316279\pi$
$402$	0	0
$403$	−2.45287e48	−1.55429
$404$	−2.55457e48	−1.54619
$405$	0	0
$406$	7.35553e47	0.406333
$407$	1.29756e48	0.684906
$408$	0	0
$409$	7.85596e47	0.378720	0.189360	−	0.981908i	$-0.439359\pi$
$409$	7.85596e47	0.378720	0.189360	+	0.981908i	$0.439359\pi$
$410$	4.71309e47	0.217172
$411$	0	0
$412$	−4.07324e48	−1.71530
$413$	−3.14991e48	−1.26830
$414$	0	0
$415$	2.33025e47	0.0858051
$416$	−1.73368e48	−0.610581
$417$	0	0
$418$	−2.59491e47	−0.0836297
$419$	−4.22926e48	−1.30408	−0.652040	−	0.758184i	$-0.726087\pi$
$419$	−4.22926e48	−1.30408	−0.652040	+	0.758184i	$0.726087\pi$
$420$	0	0
$421$	4.83549e48	1.36528	0.682640	−	0.730755i	$-0.260832\pi$
$421$	4.83549e48	1.36528	0.682640	+	0.730755i	$0.260832\pi$
$422$	4.59118e47	0.124063
$423$	0	0
$424$	1.17989e48	0.292127
$425$	−9.75953e47	−0.231331
$426$	0	0
$427$	3.70029e47	0.0804119
$428$	3.81512e48	0.793960
$429$	0	0
$430$	2.72526e47	0.0520286
$431$	1.35672e48	0.248119	0.124060	−	0.992275i	$-0.460409\pi$
$431$	1.35672e48	0.248119	0.124060	+	0.992275i	$0.460409\pi$
$432$	0	0
$433$	−3.36809e48	−0.565403	−0.282701	−	0.959208i	$-0.591231\pi$
$433$	−3.36809e48	−0.565403	−0.282701	+	0.959208i	$0.591231\pi$
$434$	−2.94685e48	−0.474021
$435$	0	0
$436$	−5.69019e48	−0.840673
$437$	−3.75912e48	−0.532328
$438$	0	0
$439$	−3.07628e48	−0.400343	−0.200172	−	0.979761i	$-0.564150\pi$
$439$	−3.07628e48	−0.400343	−0.200172	+	0.979761i	$0.564150\pi$
$440$	3.21905e48	0.401655
$441$	0	0
$442$	−1.48849e48	−0.170779
$443$	1.21772e49	1.33992	0.669961	−	0.742396i	$-0.266311\pi$
$443$	1.21772e49	1.33992	0.669961	+	0.742396i	$0.266311\pi$
$444$	0	0
$445$	9.99261e48	1.01162
$446$	2.52963e48	0.245675
$447$	0	0
$448$	1.12254e49	1.00359
$449$	−6.54698e48	−0.561674	−0.280837	−	0.959756i	$-0.590612\pi$
$449$	−6.54698e48	−0.561674	−0.280837	+	0.959756i	$0.590612\pi$
$450$	0	0
$451$	−1.67555e49	−1.32401
$452$	1.70929e49	1.29644
$453$	0	0
$454$	1.37466e48	0.0960861
$455$	1.72266e49	1.15608
$456$	0	0
$457$	1.51332e49	0.936444	0.468222	−	0.883611i	$-0.344895\pi$
$457$	1.51332e49	0.936444	0.468222	+	0.883611i	$0.344895\pi$
$458$	−3.81534e47	−0.0226737
$459$	0	0
$460$	2.27453e49	1.24702
$461$	−2.09024e49	−1.10085	−0.550426	−	0.834884i	$-0.685535\pi$
$461$	−2.09024e49	−1.10085	−0.550426	+	0.834884i	$0.685535\pi$
$462$	0	0
$463$	1.99414e49	0.969412	0.484706	−	0.874677i	$-0.338927\pi$
$463$	1.99414e49	0.969412	0.484706	+	0.874677i	$0.338927\pi$
$464$	−2.46615e49	−1.15196
$465$	0	0
$466$	−7.23061e48	−0.311915
$467$	1.49903e49	0.621508	0.310754	−	0.950490i	$-0.399418\pi$
$467$	1.49903e49	0.621508	0.310754	+	0.950490i	$0.399418\pi$
$468$	0	0
$469$	−5.55296e49	−2.12729
$470$	−5.93777e48	−0.218682
$471$	0	0
$472$	−1.14787e49	−0.390811
$473$	−9.68855e48	−0.317196
$474$	0	0
$475$	−3.31796e48	−0.100471
$476$	3.56098e49	1.03715
$477$	0	0
$478$	5.72243e48	0.154229
$479$	1.97535e49	0.512198	0.256099	−	0.966651i	$-0.417563\pi$
$479$	1.97535e49	0.512198	0.256099	+	0.966651i	$0.417563\pi$
$480$	0	0
$481$	2.53044e49	0.607451
$482$	−8.40825e48	−0.194239
$483$	0	0
$484$	−1.13185e49	−0.242187
$485$	−4.43367e49	−0.913148
$486$	0	0
$487$	−2.15937e49	−0.412136	−0.206068	−	0.978538i	$-0.566067\pi$
$487$	−2.15937e49	−0.412136	−0.206068	+	0.978538i	$0.566067\pi$
$488$	1.34844e48	0.0247780
$489$	0	0
$490$	9.91248e48	0.168871
$491$	−4.27399e49	−0.701174	−0.350587	−	0.936530i	$-0.614018\pi$
$491$	−4.27399e49	−0.701174	−0.350587	+	0.936530i	$0.614018\pi$
$492$	0	0
$493$	−6.93028e49	−1.05459
$494$	−5.06045e48	−0.0741722
$495$	0	0
$496$	9.88015e49	1.34386
$497$	−1.64715e50	−2.15844
$498$	0	0
$499$	−6.52314e49	−0.793591	−0.396796	−	0.917907i	$-0.629878\pi$
$499$	−6.52314e49	−0.793591	−0.396796	+	0.917907i	$0.629878\pi$
$500$	8.83097e49	1.03529
$501$	0	0
$502$	8.62466e48	0.0939124
$503$	−8.97219e49	−0.941653	−0.470826	−	0.882226i	$-0.656044\pi$
$503$	−8.97219e49	−0.941653	−0.470826	+	0.882226i	$0.656044\pi$
$504$	0	0
$505$	1.39883e50	1.36419
$506$	4.06071e49	0.381784
$507$	0	0
$508$	−1.46719e50	−1.28235
$509$	−4.50563e49	−0.379731	−0.189866	−	0.981810i	$-0.560805\pi$
$509$	−4.50563e49	−0.379731	−0.189866	+	0.981810i	$0.560805\pi$
$510$	0	0
$511$	−1.24860e50	−0.978674
$512$	1.18330e50	0.894539
$513$	0	0
$514$	1.76263e49	0.123978
$515$	2.23043e50	1.51340
$516$	0	0
$517$	2.11093e50	1.33321
$518$	3.04003e49	0.185258
$519$	0	0
$520$	6.27763e49	0.356233
$521$	5.45339e49	0.298654	0.149327	−	0.988788i	$-0.452289\pi$
$521$	5.45339e49	0.298654	0.149327	+	0.988788i	$0.452289\pi$
$522$	0	0
$523$	−1.36223e50	−0.694975	−0.347488	−	0.937685i	$-0.612965\pi$
$523$	−1.36223e50	−0.694975	−0.347488	+	0.937685i	$0.612965\pi$
$524$	1.97985e50	0.974998
$525$	0	0
$526$	−4.84907e49	−0.222547
$527$	2.77648e50	1.23026
$528$	0	0
$529$	3.46192e50	1.43017
$530$	−3.15129e49	−0.125714
$531$	0	0
$532$	1.21063e50	0.450451
$533$	−3.26757e50	−1.17428
$534$	0	0
$535$	−2.08909e50	−0.700505
$536$	−2.02358e50	−0.655499
$537$	0	0
$538$	9.35787e49	0.282947
$539$	−3.52397e50	−1.02953
$540$	0	0
$541$	−1.89994e50	−0.518310	−0.259155	−	0.965836i	$-0.583444\pi$
$541$	−1.89994e50	−0.518310	−0.259155	+	0.965836i	$0.583444\pi$
$542$	1.23964e50	0.326819
$543$	0	0
$544$	1.96241e50	0.483292
$545$	3.11584e50	0.741720
$546$	0	0
$547$	−1.73538e49	−0.0386037	−0.0193019	−	0.999814i	$-0.506144\pi$
$547$	−1.73538e49	−0.0386037	−0.0193019	+	0.999814i	$0.506144\pi$
$548$	−7.19781e49	−0.154796
$549$	0	0
$550$	3.58416e49	0.0720571
$551$	−2.35610e50	−0.458024
$552$	0	0
$553$	−7.18278e49	−0.130580
$554$	−4.67018e49	−0.0821114
$555$	0	0
$556$	−2.63251e50	−0.432999
$557$	9.83753e50	1.56518	0.782591	−	0.622536i	$-0.213898\pi$
$557$	9.83753e50	1.56518	0.782591	+	0.622536i	$0.213898\pi$
$558$	0	0
$559$	−1.88941e50	−0.281325
$560$	−6.93885e50	−0.999560
$561$	0	0
$562$	−7.92416e49	−0.106864
$563$	−2.99781e50	−0.391200	−0.195600	−	0.980684i	$-0.562665\pi$
$563$	−2.99781e50	−0.391200	−0.195600	+	0.980684i	$0.562665\pi$
$564$	0	0
$565$	−9.35972e50	−1.14384
$566$	−1.62555e50	−0.192263
$567$	0	0
$568$	−6.00245e50	−0.665096
$569$	−1.02631e51	−1.10078	−0.550392	−	0.834906i	$-0.685522\pi$
$569$	−1.02631e51	−1.10078	−0.550392	+	0.834906i	$0.685522\pi$
$570$	0	0
$571$	−8.60079e47	−0.000864511 0	−0.000432255	−	1.00000i	$-0.500138\pi$
$571$	−8.60079e47	−0.000864511 0	−0.000432255		1.00000i	$0.500138\pi$
$572$	−1.08854e51	−1.05930
$573$	0	0
$574$	−3.92560e50	−0.358127
$575$	5.19220e50	0.458666
$576$	0	0
$577$	1.49637e51	1.23961	0.619806	−	0.784755i	$-0.287211\pi$
$577$	1.49637e51	1.23961	0.619806	+	0.784755i	$0.287211\pi$
$578$	−1.04069e50	−0.0834940
$579$	0	0
$580$	1.42560e51	1.07295
$581$	−1.94090e50	−0.141496
$582$	0	0
$583$	1.12031e51	0.766427
$584$	−4.55010e50	−0.301567
$585$	0	0
$586$	−1.97331e50	−0.122769
$587$	2.21173e51	1.33330	0.666650	−	0.745371i	$-0.267728\pi$
$587$	2.21173e51	1.33330	0.666650	+	0.745371i	$0.267728\pi$
$588$	0	0
$589$	9.43923e50	0.534323
$590$	3.06579e50	0.168182
$591$	0	0
$592$	−1.01926e51	−0.525209
$593$	9.58294e50	0.478616	0.239308	−	0.970944i	$-0.423079\pi$
$593$	9.58294e50	0.478616	0.239308	+	0.970944i	$0.423079\pi$
$594$	0	0
$595$	−1.94993e51	−0.915070
$596$	1.78734e51	0.813116
$597$	0	0
$598$	7.91899e50	0.338608
$599$	−1.22432e49	−0.00507572	−0.00253786	−	0.999997i	$-0.500808\pi$
$599$	−1.22432e49	−0.00507572	−0.00253786	+	0.999997i	$0.500808\pi$
$600$	0	0
$601$	−1.08866e51	−0.424339	−0.212169	−	0.977233i	$-0.568053\pi$
$601$	−1.08866e51	−0.424339	−0.212169	+	0.977233i	$0.568053\pi$
$602$	−2.26991e50	−0.0857973
$603$	0	0
$604$	−4.12188e51	−1.46525
$605$	6.19780e50	0.213680
$606$	0	0
$607$	4.94921e51	1.60526	0.802629	−	0.596479i	$-0.203434\pi$
$607$	4.94921e51	1.60526	0.802629	+	0.596479i	$0.203434\pi$
$608$	6.67162e50	0.209901
$609$	0	0
$610$	−3.60148e49	−0.0106630
$611$	4.11663e51	1.18244
$612$	0	0
$613$	3.53515e51	0.955848	0.477924	−	0.878401i	$-0.341390\pi$
$613$	3.53515e51	0.955848	0.477924	+	0.878401i	$0.341390\pi$
$614$	−4.24685e50	−0.111417
$615$	0	0
$616$	−2.68119e51	−0.662346
$617$	3.24058e51	0.776868	0.388434	−	0.921477i	$-0.373016\pi$
$617$	3.24058e51	0.776868	0.388434	+	0.921477i	$0.373016\pi$
$618$	0	0
$619$	2.49425e51	0.563201	0.281600	−	0.959532i	$-0.409135\pi$
$619$	2.49425e51	0.563201	0.281600	+	0.959532i	$0.409135\pi$
$620$	−5.71140e51	−1.25169
$621$	0	0
$622$	1.47237e51	0.304016
$623$	−8.32299e51	−1.66821
$624$	0	0
$625$	−3.27806e51	−0.619208
$626$	−1.02564e50	−0.0188092
$627$	0	0
$628$	2.06198e51	0.356477
$629$	−2.86427e51	−0.480814
$630$	0	0
$631$	3.22282e51	0.510145	0.255072	−	0.966922i	$-0.417901\pi$
$631$	3.22282e51	0.510145	0.255072	+	0.966922i	$0.417901\pi$
$632$	−2.61751e50	−0.0402367
$633$	0	0
$634$	9.15616e50	0.132758
$635$	8.03403e51	1.13141
$636$	0	0
$637$	−6.87227e51	−0.913106
$638$	2.54512e51	0.328493
$639$	0	0
$640$	−5.33208e51	−0.649482
$641$	8.20930e51	0.971477	0.485739	−	0.874104i	$-0.338551\pi$
$641$	8.20930e51	0.971477	0.485739	+	0.874104i	$0.338551\pi$
$642$	0	0
$643$	−4.47682e51	−0.500112	−0.250056	−	0.968231i	$-0.580449\pi$
$643$	−4.47682e51	−0.500112	−0.250056	+	0.968231i	$0.580449\pi$
$644$	−1.89449e52	−2.05638
$645$	0	0
$646$	5.72807e50	0.0587093
$647$	−1.90676e52	−1.89919	−0.949594	−	0.313483i	$-0.898504\pi$
$647$	−1.90676e52	−1.89919	−0.949594	+	0.313483i	$0.898504\pi$
$648$	0	0
$649$	−1.08991e52	−1.02533
$650$	6.98964e50	0.0639083
$651$	0	0
$652$	1.25275e52	1.08214
$653$	9.48302e51	0.796256	0.398128	−	0.917330i	$-0.369660\pi$
$653$	9.48302e51	0.796256	0.398128	+	0.917330i	$0.369660\pi$
$654$	0	0
$655$	−1.08413e52	−0.860234
$656$	1.31617e52	1.01529
$657$	0	0
$658$	4.94566e51	0.360616
$659$	−1.04759e52	−0.742693	−0.371347	−	0.928494i	$-0.621104\pi$
$659$	−1.04759e52	−0.742693	−0.371347	+	0.928494i	$0.621104\pi$
$660$	0	0
$661$	−8.65976e51	−0.580469	−0.290234	−	0.956956i	$-0.593733\pi$
$661$	−8.65976e51	−0.580469	−0.290234	+	0.956956i	$0.593733\pi$
$662$	−2.92249e51	−0.190494
$663$	0	0
$664$	−7.07293e50	−0.0436004
$665$	−6.62919e51	−0.397429
$666$	0	0
$667$	3.68700e52	2.09096
$668$	1.58453e52	0.874049
$669$	0	0
$670$	5.40467e51	0.282088
$671$	1.28036e51	0.0650076
$672$	0	0
$673$	−2.18723e52	−1.05103	−0.525515	−	0.850784i	$-0.676127\pi$
$673$	−2.18723e52	−1.05103	−0.525515	+	0.850784i	$0.676127\pi$
$674$	2.84102e51	0.132821
$675$	0	0
$676$	2.86430e50	0.0126766
$677$	1.59031e52	0.684845	0.342422	−	0.939546i	$-0.388753\pi$
$677$	1.59031e52	0.684845	0.342422	+	0.939546i	$0.388753\pi$
$678$	0	0
$679$	3.69287e52	1.50582
$680$	−7.10582e51	−0.281968
$681$	0	0
$682$	−1.01965e52	−0.383214
$683$	3.09230e51	0.113109	0.0565547	−	0.998400i	$-0.481988\pi$
$683$	3.09230e51	0.113109	0.0565547	+	0.998400i	$0.481988\pi$
$684$	0	0
$685$	3.94138e51	0.136576
$686$	7.25303e50	0.0244638
$687$	0	0
$688$	7.61053e51	0.243237
$689$	2.18477e52	0.679753
$690$	0	0
$691$	−4.14754e52	−1.22306	−0.611528	−	0.791222i	$-0.709445\pi$
$691$	−4.14754e52	−1.22306	−0.611528	+	0.791222i	$0.709445\pi$
$692$	3.10633e52	0.891835
$693$	0	0
$694$	−1.07783e52	−0.293360
$695$	1.44151e52	0.382032
$696$	0	0
$697$	3.69865e52	0.929473
$698$	4.30440e51	0.105339
$699$	0	0
$700$	−1.67216e52	−0.388118
$701$	2.82631e52	0.638904	0.319452	−	0.947602i	$-0.396501\pi$
$701$	2.82631e52	0.638904	0.319452	+	0.947602i	$0.396501\pi$
$702$	0	0
$703$	−9.73771e51	−0.208825
$704$	3.88414e52	0.811337
$705$	0	0
$706$	−7.94936e51	−0.157560
$707$	−1.16511e53	−2.24961
$708$	0	0
$709$	4.89940e52	0.897817	0.448909	−	0.893578i	$-0.351813\pi$
$709$	4.89940e52	0.897817	0.448909	+	0.893578i	$0.351813\pi$
$710$	1.60316e52	0.286218
$711$	0	0
$712$	−3.03302e52	−0.514039
$713$	−1.47712e53	−2.43927
$714$	0	0
$715$	5.96066e52	0.934614
$716$	5.07334e52	0.775182
$717$	0	0
$718$	2.62227e52	0.380518
$719$	−4.55246e52	−0.643816	−0.321908	−	0.946771i	$-0.604324\pi$
$719$	−4.55246e52	−0.643816	−0.321908	+	0.946771i	$0.604324\pi$
$720$	0	0
$721$	−1.85775e53	−2.49566
$722$	−1.47531e52	−0.193172
$723$	0	0
$724$	1.22654e53	1.52588
$725$	3.25430e52	0.394644
$726$	0	0
$727$	−6.55544e52	−0.755467	−0.377733	−	0.925914i	$-0.623296\pi$
$727$	−6.55544e52	−0.755467	−0.377733	+	0.925914i	$0.623296\pi$
$728$	−5.22873e52	−0.587442
$729$	0	0
$730$	1.21526e52	0.129777
$731$	2.13868e52	0.222676
$732$	0	0
$733$	5.46489e52	0.540951	0.270476	−	0.962727i	$-0.412819\pi$
$733$	5.46489e52	0.540951	0.270476	+	0.962727i	$0.412819\pi$
$734$	4.29999e51	0.0415040
$735$	0	0
$736$	−1.04403e53	−0.958235
$737$	−1.92141e53	−1.71977
$738$	0	0
$739$	−1.98761e53	−1.69203	−0.846017	−	0.533156i	$-0.821006\pi$
$739$	−1.98761e53	−1.69203	−0.846017	+	0.533156i	$0.821006\pi$
$740$	5.89200e52	0.489188
$741$	0	0
$742$	2.62476e52	0.207308
$743$	1.44490e53	1.11313	0.556564	−	0.830805i	$-0.312120\pi$
$743$	1.44490e53	1.11313	0.556564	+	0.830805i	$0.312120\pi$
$744$	0	0
$745$	−9.78716e52	−0.717407
$746$	1.40740e52	0.100635
$747$	0	0
$748$	1.23215e53	0.838465
$749$	1.74003e53	1.15516
$750$	0	0
$751$	1.98670e53	1.25544	0.627718	−	0.778441i	$-0.283989\pi$
$751$	1.98670e53	1.25544	0.627718	+	0.778441i	$0.283989\pi$
$752$	−1.65817e53	−1.02235
$753$	0	0
$754$	4.96337e52	0.291344
$755$	2.25706e53	1.29278
$756$	0	0
$757$	3.23306e53	1.76336	0.881679	−	0.471850i	$-0.156414\pi$
$757$	3.23306e53	1.76336	0.881679	+	0.471850i	$0.156414\pi$
$758$	−6.30001e50	−0.00335321
$759$	0	0
$760$	−2.41578e52	−0.122463
$761$	4.26585e52	0.211052	0.105526	−	0.994417i	$-0.466347\pi$
$761$	4.26585e52	0.211052	0.105526	+	0.994417i	$0.466347\pi$
$762$	0	0
$763$	−2.59523e53	−1.22313
$764$	−1.01596e53	−0.467356
$765$	0	0
$766$	1.11103e52	0.0486962
$767$	−2.12550e53	−0.909382
$768$	0	0
$769$	4.26123e53	1.73739	0.868695	−	0.495347i	$-0.164959\pi$
$769$	4.26123e53	1.73739	0.868695	+	0.495347i	$0.164959\pi$
$770$	7.16104e52	0.285035
$771$	0	0
$772$	−2.40630e53	−0.912913
$773$	9.95037e52	0.368569	0.184284	−	0.982873i	$-0.441003\pi$
$773$	9.95037e52	0.368569	0.184284	+	0.982873i	$0.441003\pi$
$774$	0	0
$775$	−1.30377e53	−0.460384
$776$	1.34574e53	0.464000
$777$	0	0
$778$	4.23394e52	0.139194
$779$	1.25744e53	0.403685
$780$	0	0
$781$	−5.69937e53	−1.74495
$782$	−8.96373e52	−0.268018
$783$	0	0
$784$	2.76815e53	0.789481
$785$	−1.12910e53	−0.314517
$786$	0	0
$787$	4.51390e53	1.19955	0.599777	−	0.800167i	$-0.295256\pi$
$787$	4.51390e53	1.19955	0.599777	+	0.800167i	$0.295256\pi$
$788$	3.11686e53	0.809064
$789$	0	0
$790$	6.99096e51	0.0173155
$791$	7.79585e53	1.88625
$792$	0	0
$793$	2.49689e52	0.0576560
$794$	8.77088e52	0.197863
$795$	0	0
$796$	−4.87543e53	−1.04983
$797$	−3.86364e53	−0.812864	−0.406432	−	0.913681i	$-0.633227\pi$
$797$	−3.86364e53	−0.812864	−0.406432	+	0.913681i	$0.633227\pi$
$798$	0	0
$799$	−4.65973e53	−0.935934
$800$	−9.21502e52	−0.180856
$801$	0	0
$802$	1.27341e53	0.238639
$803$	−4.32036e53	−0.791192
$804$	0	0
$805$	1.03739e54	1.81433
$806$	−1.98847e53	−0.339877
$807$	0	0
$808$	−4.24583e53	−0.693190
$809$	−8.90010e53	−1.42019	−0.710097	−	0.704104i	$-0.751349\pi$
$809$	−8.90010e53	−1.42019	−0.710097	+	0.704104i	$0.751349\pi$
$810$	0	0
$811$	−3.07699e53	−0.469072	−0.234536	−	0.972107i	$-0.575357\pi$
$811$	−3.07699e53	−0.469072	−0.234536	+	0.972107i	$0.575357\pi$
$812$	−1.18741e54	−1.76935
$813$	0	0
$814$	1.05189e53	0.149769
$815$	−6.85980e53	−0.954763
$816$	0	0
$817$	7.27090e52	0.0967119
$818$	6.36860e52	0.0828148
$819$	0	0
$820$	−7.60837e53	−0.945661
$821$	1.44038e54	1.75037	0.875185	−	0.483789i	$-0.160740\pi$
$821$	1.44038e54	1.75037	0.875185	+	0.483789i	$0.160740\pi$
$822$	0	0
$823$	7.25265e53	0.842558	0.421279	−	0.906931i	$-0.361581\pi$
$823$	7.25265e53	0.842558	0.421279	+	0.906931i	$0.361581\pi$
$824$	−6.76993e53	−0.769008
$825$	0	0
$826$	−2.55354e53	−0.277339
$827$	4.48759e53	0.476608	0.238304	−	0.971191i	$-0.423408\pi$
$827$	4.48759e53	0.476608	0.238304	+	0.971191i	$0.423408\pi$
$828$	0	0
$829$	−4.38009e53	−0.444861	−0.222430	−	0.974949i	$-0.571399\pi$
$829$	−4.38009e53	−0.444861	−0.222430	+	0.974949i	$0.571399\pi$
$830$	1.88907e52	0.0187630
$831$	0	0
$832$	7.57466e53	0.719584
$833$	7.77892e53	0.722748
$834$	0	0
$835$	−8.67658e53	−0.771167
$836$	4.18897e53	0.364159
$837$	0	0
$838$	−3.42854e53	−0.285164
$839$	3.60758e53	0.293508	0.146754	−	0.989173i	$-0.453117\pi$
$839$	3.60758e53	0.293508	0.146754	+	0.989173i	$0.453117\pi$
$840$	0	0
$841$	1.02642e54	0.799095
$842$	3.91999e53	0.298546
$843$	0	0
$844$	−7.41156e53	−0.540225
$845$	−1.56843e52	−0.0111845
$846$	0	0
$847$	−5.16224e53	−0.352367
$848$	−8.80025e53	−0.587722
$849$	0	0
$850$	−7.91177e52	−0.0505852
$851$	1.52383e54	0.953323
$852$	0	0
$853$	−3.15083e53	−0.188742	−0.0943708	−	0.995537i	$-0.530084\pi$
$853$	−3.15083e53	−0.188742	−0.0943708	+	0.995537i	$0.530084\pi$
$854$	2.99972e52	0.0175837
$855$	0	0
$856$	6.34093e53	0.355949
$857$	−9.67011e53	−0.531234	−0.265617	−	0.964079i	$-0.585576\pi$
$857$	−9.67011e53	−0.531234	−0.265617	+	0.964079i	$0.585576\pi$
$858$	0	0
$859$	3.56564e54	1.87614	0.938068	−	0.346452i	$-0.112614\pi$
$859$	3.56564e54	1.87614	0.938068	+	0.346452i	$0.112614\pi$
$860$	−4.39940e53	−0.226554
$861$	0	0
$862$	1.09985e53	0.0542564
$863$	2.25029e54	1.08652	0.543262	−	0.839564i	$-0.317189\pi$
$863$	2.25029e54	1.08652	0.543262	+	0.839564i	$0.317189\pi$
$864$	0	0
$865$	−1.70096e54	−0.786860
$866$	−2.73042e53	−0.123637
$867$	0	0
$868$	4.75711e54	2.06409
$869$	−2.48535e53	−0.105565
$870$	0	0
$871$	−3.74703e54	−1.52529
$872$	−9.45740e53	−0.376892
$873$	0	0
$874$	−3.04741e53	−0.116404
$875$	4.02770e54	1.50629
$876$	0	0
$877$	4.14049e54	1.48443	0.742214	−	0.670163i	$-0.233776\pi$
$877$	4.14049e54	1.48443	0.742214	+	0.670163i	$0.233776\pi$
$878$	−2.49385e53	−0.0875432
$879$	0	0
$880$	−2.40095e54	−0.808077
$881$	−3.03676e54	−1.00082	−0.500410	−	0.865789i	$-0.666817\pi$
$881$	−3.03676e54	−1.00082	−0.500410	+	0.865789i	$0.666817\pi$
$882$	0	0
$883$	2.77430e54	0.876760	0.438380	−	0.898790i	$-0.355552\pi$
$883$	2.77430e54	0.876760	0.438380	+	0.898790i	$0.355552\pi$
$884$	2.40288e54	0.743645
$885$	0	0
$886$	9.87173e53	0.293001
$887$	9.39883e53	0.273204	0.136602	−	0.990626i	$-0.456382\pi$
$887$	9.39883e53	0.273204	0.136602	+	0.990626i	$0.456382\pi$
$888$	0	0
$889$	−6.69166e54	−1.86574
$890$	8.10072e53	0.221212
$891$	0	0
$892$	−4.08359e54	−1.06978
$893$	−1.58418e54	−0.406491
$894$	0	0
$895$	−2.77807e54	−0.683937
$896$	4.44117e54	1.07102
$897$	0	0
$898$	−5.30745e53	−0.122821
$899$	−9.25814e54	−2.09879
$900$	0	0
$901$	−2.47301e54	−0.538043
$902$	−1.35832e54	−0.289521
$903$	0	0
$904$	2.84092e54	0.581224
$905$	−6.71632e54	−1.34627
$906$	0	0
$907$	2.17105e54	0.417767	0.208884	−	0.977941i	$-0.433017\pi$
$907$	2.17105e54	0.417767	0.208884	+	0.977941i	$0.433017\pi$
$908$	−2.21911e54	−0.418400
$909$	0	0
$910$	1.39651e54	0.252801
$911$	−7.42098e54	−1.31635	−0.658175	−	0.752865i	$-0.728671\pi$
$911$	−7.42098e54	−1.31635	−0.658175	+	0.752865i	$0.728671\pi$
$912$	0	0
$913$	−6.71581e53	−0.114390
$914$	1.22681e54	0.204772
$915$	0	0
$916$	6.15912e53	0.0987307
$917$	9.02986e54	1.41856
$918$	0	0
$919$	6.80622e54	1.02700	0.513498	−	0.858091i	$-0.328349\pi$
$919$	6.80622e54	1.02700	0.513498	+	0.858091i	$0.328349\pi$
$920$	3.78039e54	0.559065
$921$	0	0
$922$	−1.69450e54	−0.240724
$923$	−1.11146e55	−1.54762
$924$	0	0
$925$	1.34500e54	0.179928
$926$	1.61660e54	0.211982
$927$	0	0
$928$	−6.54362e54	−0.824481
$929$	6.45233e54	0.796940	0.398470	−	0.917181i	$-0.369541\pi$
$929$	6.45233e54	0.796940	0.398470	+	0.917181i	$0.369541\pi$
$930$	0	0
$931$	2.64461e54	0.313901
$932$	1.16724e55	1.35821
$933$	0	0
$934$	1.21522e54	0.135905
$935$	−6.74703e54	−0.739772
$936$	0	0
$937$	7.02165e53	0.0740042	0.0370021	−	0.999315i	$-0.488219\pi$
$937$	7.02165e53	0.0740042	0.0370021	+	0.999315i	$0.488219\pi$
$938$	−4.50162e54	−0.465175
$939$	0	0
$940$	9.58538e54	0.952234
$941$	8.40171e53	0.0818388	0.0409194	−	0.999162i	$-0.486971\pi$
$941$	8.40171e53	0.0818388	0.0409194	+	0.999162i	$0.486971\pi$
$942$	0	0
$943$	−1.96773e55	−1.84289
$944$	8.56148e54	0.786261
$945$	0	0
$946$	−7.85423e53	−0.0693613
$947$	7.39324e54	0.640266	0.320133	−	0.947373i	$-0.396272\pi$
$947$	7.39324e54	0.640266	0.320133	+	0.947373i	$0.396272\pi$
$948$	0	0
$949$	−8.42534e54	−0.701718
$950$	−2.68977e53	−0.0219700
$951$	0	0
$952$	5.91854e54	0.464977
$953$	2.15051e55	1.65700	0.828499	−	0.559990i	$-0.189195\pi$
$953$	2.15051e55	1.65700	0.828499	+	0.559990i	$0.189195\pi$
$954$	0	0
$955$	5.56319e54	0.412345
$956$	−9.23775e54	−0.671576
$957$	0	0
$958$	1.60136e54	0.112002
$959$	−3.28283e54	−0.225219
$960$	0	0
$961$	2.19419e55	1.44841
$962$	2.05135e54	0.132832
$963$	0	0
$964$	1.35735e55	0.845797
$965$	1.31764e55	0.805457
$966$	0	0
$967$	1.31747e55	0.775085	0.387543	−	0.921852i	$-0.373324\pi$
$967$	1.31747e55	0.775085	0.387543	+	0.921852i	$0.373324\pi$
$968$	−1.88120e54	−0.108578
$969$	0	0
$970$	−3.59425e54	−0.199678
$971$	−8.47915e54	−0.462164	−0.231082	−	0.972934i	$-0.574227\pi$
$971$	−8.47915e54	−0.462164	−0.231082	+	0.972934i	$0.574227\pi$
$972$	0	0
$973$	−1.20066e55	−0.629987
$974$	−1.75054e54	−0.0901220
$975$	0	0
$976$	−1.00574e54	−0.0498500
$977$	−1.06113e55	−0.516080	−0.258040	−	0.966134i	$-0.583077\pi$
$977$	−1.06113e55	−0.516080	−0.258040	+	0.966134i	$0.583077\pi$
$978$	0	0
$979$	−2.87988e55	−1.34863
$980$	−1.60018e55	−0.735335
$981$	0	0
$982$	−3.46480e54	−0.153326
$983$	−1.52477e54	−0.0662161	−0.0331081	−	0.999452i	$-0.510541\pi$
$983$	−1.52477e54	−0.0662161	−0.0331081	+	0.999452i	$0.510541\pi$
$984$	0	0
$985$	−1.70673e55	−0.713831
$986$	−5.61818e54	−0.230607
$987$	0	0
$988$	8.16912e54	0.322977
$989$	−1.13781e55	−0.441506
$990$	0	0
$991$	2.88078e55	1.07683	0.538416	−	0.842679i	$-0.319023\pi$
$991$	2.88078e55	1.07683	0.538416	+	0.842679i	$0.319023\pi$
$992$	2.62157e55	0.961825
$993$	0	0
$994$	−1.33529e55	−0.471986
$995$	2.66969e55	0.926262
$996$	0	0
$997$	−2.89753e55	−0.968651	−0.484326	−	0.874888i	$-0.660935\pi$
$997$	−2.89753e55	−0.968651	−0.484326	+	0.874888i	$0.660935\pi$
$998$	−5.28813e54	−0.173535
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+81067.1 q^{2} -1.30867e11 q^{4} +7.16603e12 q^{5} -5.96869e15 q^{7} -2.17508e16 q^{8} +O(q^{10})\)	\(q+81067.1 q^{2} -1.30867e11 q^{4} +7.16603e12 q^{5} -5.96869e15 q^{7} -2.17508e16 q^{8} +5.80929e17 q^{10} -2.06526e19 q^{11} -4.02756e20 q^{13} -4.83865e20 q^{14} +1.62230e22 q^{16} +4.55890e22 q^{17} +1.54990e23 q^{19} -9.37797e23 q^{20} -1.67424e24 q^{22} -2.42540e25 q^{23} -2.14076e25 q^{25} -3.26502e25 q^{26} +7.81105e26 q^{28} -1.52016e27 q^{29} +6.09023e27 q^{31} +4.30456e27 q^{32} +3.69577e27 q^{34} -4.27718e28 q^{35} -6.28281e28 q^{37} +1.25646e28 q^{38} -1.55867e29 q^{40} +8.11303e29 q^{41} +4.69121e29 q^{43} +2.70274e30 q^{44} -1.96620e30 q^{46} -1.02212e31 q^{47} +1.70631e31 q^{49} -1.73545e30 q^{50} +5.27075e31 q^{52} -5.42457e31 q^{53} -1.47997e32 q^{55} +1.29824e32 q^{56} -1.23235e32 q^{58} +5.27739e32 q^{59} -6.19951e31 q^{61} +4.93717e32 q^{62} -1.88071e33 q^{64} -2.88616e33 q^{65} +9.30348e33 q^{67} -5.96611e33 q^{68} -3.46739e33 q^{70} +2.75965e34 q^{71} +2.09192e34 q^{73} -5.09329e33 q^{74} -2.02831e34 q^{76} +1.23269e35 q^{77} +1.20341e34 q^{79} +1.16254e35 q^{80} +6.57700e34 q^{82} +3.25180e34 q^{83} +3.26692e35 q^{85} +3.80303e34 q^{86} +4.49210e35 q^{88} +1.39444e36 q^{89} +2.40392e36 q^{91} +3.17405e36 q^{92} -8.28600e35 q^{94} +1.11066e36 q^{95} -6.18707e36 q^{97} +1.38326e36 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 437562 q^{2} + 346098955492 q^{4} + 4099829756904 q^{5} + 66\!\cdots\!84 q^{7}+ \cdots - 14\!\cdots\!76 q^{8}+O(q^{10}) \) 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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