LMFDB - Embedded newform 9.38.a.c.1.4

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			1.4
Root			$105009.$ 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)

$f(q)$	$=$	$q+520663. q^{2} +1.33651e11 q^{4} +2.63441e12 q^{5} +8.34393e15 q^{7} -1.97212e15 q^{8} +O(q^{10})$	\(q+520663. q^{2} +1.33651e11 q^{4} +2.63441e12 q^{5} +8.34393e15 q^{7} -1.97212e15 q^{8} +1.37164e18 q^{10} +2.00696e19 q^{11} -1.05373e20 q^{13} +4.34438e21 q^{14} -1.93957e22 q^{16} -1.77033e22 q^{17} +4.00776e23 q^{19} +3.52092e23 q^{20} +1.04495e25 q^{22} +1.07722e25 q^{23} -6.58195e25 q^{25} -5.48640e25 q^{26} +1.11518e27 q^{28} -1.59166e27 q^{29} +4.20936e27 q^{31} -9.82758e27 q^{32} -9.21743e27 q^{34} +2.19813e28 q^{35} +1.71917e29 q^{37} +2.08669e29 q^{38} -5.19537e27 q^{40} +3.95960e29 q^{41} +3.48956e29 q^{43} +2.68233e30 q^{44} +5.60870e30 q^{46} +2.42346e30 q^{47} +5.10591e31 q^{49} -3.42698e31 q^{50} -1.40833e31 q^{52} +1.34925e32 q^{53} +5.28715e31 q^{55} -1.64552e31 q^{56} -8.28718e32 q^{58} -1.06678e33 q^{59} -7.04574e32 q^{61} +2.19166e33 q^{62} -2.45114e33 q^{64} -2.77596e32 q^{65} +7.19450e33 q^{67} -2.36606e33 q^{68} +1.14449e34 q^{70} -2.35209e34 q^{71} +2.69218e33 q^{73} +8.95108e34 q^{74} +5.35642e34 q^{76} +1.67459e35 q^{77} +2.20044e34 q^{79} -5.10962e34 q^{80} +2.06162e35 q^{82} +2.35934e35 q^{83} -4.66376e34 q^{85} +1.81689e35 q^{86} -3.95797e34 q^{88} -1.13980e35 q^{89} -8.79227e35 q^{91} +1.43972e36 q^{92} +1.26181e36 q^{94} +1.05581e36 q^{95} +8.44145e36 q^{97} +2.65846e37 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	520663.	1.40444	0.702218	−	0.711962i	$-0.252193\pi$
$2$	520663.	1.40444	0.702218	+	0.711962i	$0.252193\pi$
$3$	0	0
$3$	0	0
$4$	1.33651e11	0.972441
$5$	2.63441e12	0.308843	0.154422	−	0.988005i	$-0.450649\pi$
$5$	2.63441e12	0.308843	0.154422	+	0.988005i	$0.450649\pi$
$6$	0	0
$7$	8.34393e15	1.93668	0.968338	−	0.249642i	$-0.0803128\pi$
$7$	8.34393e15	1.93668	0.968338	+	0.249642i	$0.0803128\pi$
$8$	−1.97212e15	−0.0387051
$9$	0	0
$10$	1.37164e18	0.433750
$11$	2.00696e19	1.08836	0.544182	−	0.838967i	$-0.316840\pi$
$11$	2.00696e19	1.08836	0.544182	+	0.838967i	$0.316840\pi$
$12$	0	0
$13$	−1.05373e20	−0.259883	−0.129942	−	0.991522i	$-0.541479\pi$
$13$	−1.05373e20	−0.259883	−0.129942	+	0.991522i	$0.541479\pi$
$14$	4.34438e21	2.71994
$15$	0	0
$16$	−1.93957e22	−1.02680
$17$	−1.77033e22	−0.305315	−0.152657	−	0.988279i	$-0.548783\pi$
$17$	−1.77033e22	−0.305315	−0.152657	+	0.988279i	$0.548783\pi$
$18$	0	0
$19$	4.00776e23	0.882999	0.441499	−	0.897262i	$-0.354447\pi$
$19$	4.00776e23	0.882999	0.441499	+	0.897262i	$0.354447\pi$
$20$	3.52092e23	0.300332
$21$	0	0
$22$	1.04495e25	1.52854
$23$	1.07722e25	0.692374	0.346187	−	0.938166i	$-0.387476\pi$
$23$	1.07722e25	0.692374	0.346187	+	0.938166i	$0.387476\pi$
$24$	0	0
$25$	−6.58195e25	−0.904616
$26$	−5.48640e25	−0.364989
$27$	0	0
$28$	1.11518e27	1.88330
$29$	−1.59166e27	−1.40439	−0.702193	−	0.711986i	$-0.747796\pi$
$29$	−1.59166e27	−1.40439	−0.702193	+	0.711986i	$0.747796\pi$
$30$	0	0
$31$	4.20936e27	1.08149	0.540747	−	0.841185i	$-0.318142\pi$
$31$	4.20936e27	1.08149	0.540747	+	0.841185i	$0.318142\pi$
$32$	−9.82758e27	−1.40337
$33$	0	0
$34$	−9.21743e27	−0.428795
$35$	2.19813e28	0.598129
$36$	0	0
$37$	1.71917e29	1.67335	0.836675	−	0.547700i	$-0.184496\pi$
$37$	1.71917e29	1.67335	0.836675	+	0.547700i	$0.184496\pi$
$38$	2.08669e29	1.24012
$39$	0	0
$40$	−5.19537e27	−0.0119538
$41$	3.95960e29	0.576965	0.288483	−	0.957485i	$-0.406849\pi$
$41$	3.95960e29	0.576965	0.288483	+	0.957485i	$0.406849\pi$
$42$	0	0
$43$	3.48956e29	0.210671	0.105335	−	0.994437i	$-0.466408\pi$
$43$	3.48956e29	0.210671	0.105335	+	0.994437i	$0.466408\pi$
$44$	2.68233e30	1.05837
$45$	0	0
$46$	5.60870e30	0.972395
$47$	2.42346e30	0.282244	0.141122	−	0.989992i	$-0.454929\pi$
$47$	2.42346e30	0.282244	0.141122	+	0.989992i	$0.454929\pi$
$48$	0	0
$49$	5.10591e31	2.75072
$50$	−3.42698e31	−1.27048
$51$	0	0
$52$	−1.40833e31	−0.252721
$53$	1.34925e32	1.70212	0.851060	−	0.525068i	$-0.175960\pi$
$53$	1.34925e32	1.70212	0.851060	+	0.525068i	$0.175960\pi$
$54$	0	0
$55$	5.28715e31	0.336134
$56$	−1.64552e31	−0.0749593
$57$	0	0
$58$	−8.28718e32	−1.97237
$59$	−1.06678e33	−1.85061	−0.925304	−	0.379226i	$-0.876190\pi$
$59$	−1.06678e33	−1.85061	−0.925304	+	0.379226i	$0.876190\pi$
$60$	0	0
$61$	−7.04574e32	−0.659667	−0.329833	−	0.944039i	$-0.606993\pi$
$61$	−7.04574e32	−0.659667	−0.329833	+	0.944039i	$0.606993\pi$
$62$	2.19166e33	1.51889
$63$	0	0
$64$	−2.45114e33	−0.944143
$65$	−2.77596e32	−0.0802632
$66$	0	0
$67$	7.19450e33	1.18745	0.593727	−	0.804667i	$-0.297656\pi$
$67$	7.19450e33	1.18745	0.593727	+	0.804667i	$0.297656\pi$
$68$	−2.36606e33	−0.296901
$69$	0	0
$70$	1.14449e34	0.840034
$71$	−2.35209e34	−1.32793	−0.663964	−	0.747765i	$-0.731127\pi$
$71$	−2.35209e34	−1.32793	−0.663964	+	0.747765i	$0.731127\pi$
$72$	0	0
$73$	2.69218e33	0.0909140	0.0454570	−	0.998966i	$-0.485526\pi$
$73$	2.69218e33	0.0909140	0.0454570	+	0.998966i	$0.485526\pi$
$74$	8.95108e34	2.35011
$75$	0	0
$76$	5.35642e34	0.858664
$77$	1.67459e35	2.10781
$78$	0	0
$79$	2.20044e34	0.172349	0.0861746	−	0.996280i	$-0.472536\pi$
$79$	2.20044e34	0.172349	0.0861746	+	0.996280i	$0.472536\pi$
$80$	−5.10962e34	−0.317120
$81$	0	0
$82$	2.06162e35	0.810311
$83$	2.35934e35	0.741046	0.370523	−	0.928823i	$-0.379178\pi$
$83$	2.35934e35	0.741046	0.370523	+	0.928823i	$0.379178\pi$
$84$	0	0
$85$	−4.66376e34	−0.0942944
$86$	1.81689e35	0.295874
$87$	0	0
$88$	−3.95797e34	−0.0421253
$89$	−1.13980e35	−0.0984271	−0.0492135	−	0.998788i	$-0.515671\pi$
$89$	−1.13980e35	−0.0984271	−0.0492135	+	0.998788i	$0.515671\pi$
$90$	0	0
$91$	−8.79227e35	−0.503310
$92$	1.43972e36	0.673293
$93$	0	0
$94$	1.26181e36	0.396394
$95$	1.05581e36	0.272708
$96$	0	0
$97$	8.44145e36	1.48300	0.741498	−	0.670955i	$-0.234116\pi$
$97$	8.44145e36	1.48300	0.741498	+	0.670955i	$0.234116\pi$
$98$	2.65846e37	3.86321
$99$	0	0
$100$	−8.79685e36	−0.879685
$101$	−6.86236e36	−0.570858	−0.285429	−	0.958400i	$-0.592136\pi$
$101$	−6.86236e36	−0.570858	−0.285429	+	0.958400i	$0.592136\pi$
$102$	0	0
$103$	1.30579e37	0.755760	0.377880	−	0.925855i	$-0.376653\pi$
$103$	1.30579e37	0.755760	0.377880	+	0.925855i	$0.376653\pi$
$104$	2.07809e35	0.0100588
$105$	0	0
$106$	7.02507e37	2.39052
$107$	−4.38206e37	−1.25337	−0.626683	−	0.779274i	$-0.715588\pi$
$107$	−4.38206e37	−1.25337	−0.626683	+	0.779274i	$0.715588\pi$
$108$	0	0
$109$	−1.05626e37	−0.214476	−0.107238	−	0.994233i	$-0.534201\pi$
$109$	−1.05626e37	−0.214476	−0.107238	+	0.994233i	$0.534201\pi$
$110$	2.75282e37	0.472078
$111$	0	0
$112$	−1.61836e38	−1.98858
$113$	6.38435e37	0.665527	0.332763	−	0.943010i	$-0.392019\pi$
$113$	6.38435e37	0.665527	0.332763	+	0.943010i	$0.392019\pi$
$114$	0	0
$115$	2.83784e37	0.213835
$116$	−2.12727e38	−1.36568
$117$	0	0
$118$	−5.55435e38	−2.59906
$119$	−1.47715e38	−0.591296
$120$	0	0
$121$	6.27494e37	0.184536
$122$	−3.66846e38	−0.926460
$123$	0	0
$124$	5.62586e38	1.05169
$125$	−3.65074e38	−0.588227
$126$	0	0
$127$	−2.81304e38	−0.337915	−0.168957	−	0.985623i	$-0.554040\pi$
$127$	−2.81304e38	−0.337915	−0.168957	+	0.985623i	$0.554040\pi$
$128$	7.44763e37	0.0773809
$129$	0	0
$130$	−1.44534e38	−0.112724
$131$	−1.95973e39	−1.32641	−0.663206	−	0.748437i	$-0.730805\pi$
$131$	−1.95973e39	−1.32641	−0.663206	+	0.748437i	$0.730805\pi$
$132$	0	0
$133$	3.34405e39	1.71008
$134$	3.74591e39	1.66770
$135$	0	0
$136$	3.49129e37	0.0118173
$137$	−1.41955e39	−0.419586	−0.209793	−	0.977746i	$-0.567279\pi$
$137$	−1.41955e39	−0.419586	−0.209793	+	0.977746i	$0.567279\pi$
$138$	0	0
$139$	−2.88414e39	−0.651992	−0.325996	−	0.945371i	$-0.605700\pi$
$139$	−2.88414e39	−0.651992	−0.325996	+	0.945371i	$0.605700\pi$
$140$	2.93783e39	0.581645
$141$	0	0
$142$	−1.22465e40	−1.86499
$143$	−2.11480e39	−0.282848
$144$	0	0
$145$	−4.19308e39	−0.433735
$146$	1.40172e39	0.127683
$147$	0	0
$148$	2.29769e40	1.62723
$149$	1.54836e40	0.968111	0.484055	−	0.875037i	$-0.339163\pi$
$149$	1.54836e40	0.968111	0.484055	+	0.875037i	$0.339163\pi$
$150$	0	0
$151$	−5.65320e39	−0.276198	−0.138099	−	0.990418i	$-0.544099\pi$
$151$	−5.65320e39	−0.276198	−0.138099	+	0.990418i	$0.544099\pi$
$152$	−7.90378e38	−0.0341766
$153$	0	0
$154$	8.71900e40	2.96028
$155$	1.10892e40	0.334012
$156$	0	0
$157$	−6.59332e40	−1.56661	−0.783304	−	0.621638i	$-0.786467\pi$
$157$	−6.59332e40	−1.56661	−0.783304	+	0.621638i	$0.786467\pi$
$158$	1.14569e40	0.242053
$159$	0	0
$160$	−2.58899e40	−0.433421
$161$	8.98828e40	1.34090
$162$	0	0
$163$	3.78789e40	0.449704	0.224852	−	0.974393i	$-0.427810\pi$
$163$	3.78789e40	0.449704	0.224852	+	0.974393i	$0.427810\pi$
$164$	5.29205e40	0.561065
$165$	0	0
$166$	1.22842e41	1.04075
$167$	−1.83545e41	−1.39151	−0.695757	−	0.718277i	$-0.744931\pi$
$167$	−1.83545e41	−1.39151	−0.695757	+	0.718277i	$0.744931\pi$
$168$	0	0
$169$	−1.53297e41	−0.932461
$170$	−2.42825e40	−0.132430
$171$	0	0
$172$	4.66384e40	0.204865
$173$	−1.65118e41	−0.651540	−0.325770	−	0.945449i	$-0.605624\pi$
$173$	−1.65118e41	−0.651540	−0.325770	+	0.945449i	$0.605624\pi$
$174$	0	0
$175$	−5.49193e41	−1.75195
$176$	−3.89264e41	−1.11753
$177$	0	0
$178$	−5.93454e40	−0.138235
$179$	−4.97609e41	−1.04498	−0.522489	−	0.852646i	$-0.674996\pi$
$179$	−4.97609e41	−1.04498	−0.522489	+	0.852646i	$0.674996\pi$
$180$	0	0
$181$	−7.52929e40	−0.128736	−0.0643680	−	0.997926i	$-0.520503\pi$
$181$	−7.52929e40	−0.128736	−0.0643680	+	0.997926i	$0.520503\pi$
$182$	−4.57781e41	−0.706867
$183$	0	0
$184$	−2.12441e40	−0.0267984
$185$	4.52899e41	0.516803
$186$	0	0
$187$	−3.55297e41	−0.332294
$188$	3.23898e41	0.274466
$189$	0	0
$190$	5.49720e41	0.383001
$191$	3.49406e41	0.220909	0.110454	−	0.993881i	$-0.464769\pi$
$191$	3.49406e41	0.220909	0.110454	+	0.993881i	$0.464769\pi$
$192$	0	0
$193$	−8.39189e41	−0.437572	−0.218786	−	0.975773i	$-0.570210\pi$
$193$	−8.39189e41	−0.437572	−0.218786	+	0.975773i	$0.570210\pi$
$194$	4.39515e42	2.08277
$195$	0	0
$196$	6.82411e42	2.67491
$197$	7.30118e41	0.260476	0.130238	−	0.991483i	$-0.458426\pi$
$197$	7.30118e41	0.260476	0.130238	+	0.991483i	$0.458426\pi$
$198$	0	0
$199$	5.82003e41	0.172244	0.0861218	−	0.996285i	$-0.472553\pi$
$199$	5.82003e41	0.172244	0.0861218	+	0.996285i	$0.472553\pi$
$200$	1.29804e41	0.0350133
$201$	0	0
$202$	−3.57298e42	−0.801733
$203$	−1.32807e43	−2.71984
$204$	0	0
$205$	1.04312e42	0.178192
$206$	6.79875e42	1.06142
$207$	0	0
$208$	2.04379e42	0.266848
$209$	8.04341e42	0.961024
$210$	0	0
$211$	−1.25054e43	−1.25277	−0.626384	−	0.779515i	$-0.715466\pi$
$211$	−1.25054e43	−1.25277	−0.626384	+	0.779515i	$0.715466\pi$
$212$	1.80330e43	1.65521
$213$	0	0
$214$	−2.28158e43	−1.76027
$215$	9.19292e41	0.0650642
$216$	0	0
$217$	3.51226e43	2.09450
$218$	−5.49955e42	−0.301219
$219$	0	0
$220$	7.06634e42	0.326870
$221$	1.86545e42	0.0793462
$222$	0	0
$223$	−1.91165e43	−0.688287	−0.344143	−	0.938917i	$-0.611831\pi$
$223$	−1.91165e43	−0.688287	−0.344143	+	0.938917i	$0.611831\pi$
$224$	−8.20007e43	−2.71787
$225$	0	0
$226$	3.32410e43	0.934690
$227$	2.06794e43	0.535871	0.267936	−	0.963437i	$-0.413659\pi$
$227$	2.06794e43	0.535871	0.267936	+	0.963437i	$0.413659\pi$
$228$	0	0
$229$	6.73090e42	0.148292	0.0741458	−	0.997247i	$-0.476377\pi$
$229$	6.73090e42	0.148292	0.0741458	+	0.997247i	$0.476377\pi$
$230$	1.47756e43	0.300317
$231$	0	0
$232$	3.13894e42	0.0543570
$233$	5.29076e43	0.846123	0.423062	−	0.906101i	$-0.360955\pi$
$233$	5.29076e43	0.846123	0.423062	+	0.906101i	$0.360955\pi$
$234$	0	0
$235$	6.38437e42	0.0871692
$236$	−1.42577e44	−1.79961
$237$	0	0
$238$	−7.69096e43	−0.830438
$239$	−8.90649e43	−0.889908	−0.444954	−	0.895553i	$-0.646780\pi$
$239$	−8.90649e43	−0.889908	−0.444954	+	0.895553i	$0.646780\pi$
$240$	0	0
$241$	−1.14469e44	−0.980331	−0.490166	−	0.871629i	$-0.663064\pi$
$241$	−1.14469e44	−0.980331	−0.490166	+	0.871629i	$0.663064\pi$
$242$	3.26713e43	0.259168
$243$	0	0
$244$	−9.41672e43	−0.641487
$245$	1.34510e44	0.849540
$246$	0	0
$247$	−4.22311e43	−0.229477
$248$	−8.30135e42	−0.0418594
$249$	0	0
$250$	−1.90080e44	−0.826128
$251$	1.57202e44	0.634590	0.317295	−	0.948327i	$-0.397226\pi$
$251$	1.57202e44	0.634590	0.317295	+	0.948327i	$0.397226\pi$
$252$	0	0
$253$	2.16194e44	0.753555
$254$	−1.46465e44	−0.474579
$255$	0	0
$256$	3.75659e44	1.05282
$257$	−2.35997e44	−0.615380	−0.307690	−	0.951487i	$-0.599556\pi$
$257$	−2.35997e44	−0.615380	−0.307690	+	0.951487i	$0.599556\pi$
$258$	0	0
$259$	1.43446e45	3.24074
$260$	−3.71011e43	−0.0780512
$261$	0	0
$262$	−1.02036e45	−1.86286
$263$	1.02621e45	1.74604	0.873022	−	0.487680i	$-0.162157\pi$
$263$	1.02621e45	1.74604	0.873022	+	0.487680i	$0.162157\pi$
$264$	0	0
$265$	3.55449e44	0.525688
$266$	1.74112e45	2.40170
$267$	0	0
$268$	9.61554e44	1.15473
$269$	−2.39378e44	−0.268328	−0.134164	−	0.990959i	$-0.542835\pi$
$269$	−2.39378e44	−0.268328	−0.134164	+	0.990959i	$0.542835\pi$
$270$	0	0
$271$	−1.10518e45	−1.08019	−0.540094	−	0.841605i	$-0.681611\pi$
$271$	−1.10518e45	−1.08019	−0.540094	+	0.841605i	$0.681611\pi$
$272$	3.43367e44	0.313497
$273$	0	0
$274$	−7.39109e44	−0.589282
$275$	−1.32097e45	−0.984551
$276$	0	0
$277$	−2.08812e45	−1.36107	−0.680534	−	0.732717i	$-0.738252\pi$
$277$	−2.08812e45	−1.36107	−0.680534	+	0.732717i	$0.738252\pi$
$278$	−1.50166e45	−0.915681
$279$	0	0
$280$	−4.33498e43	−0.0231507
$281$	−2.01962e45	−1.00973	−0.504863	−	0.863200i	$-0.668457\pi$
$281$	−2.01962e45	−1.00973	−0.504863	+	0.863200i	$0.668457\pi$
$282$	0	0
$283$	2.43661e45	1.06841	0.534204	−	0.845356i	$-0.320612\pi$
$283$	2.43661e45	1.06841	0.534204	+	0.845356i	$0.320612\pi$
$284$	−3.14360e45	−1.29133
$285$	0	0
$286$	−1.10110e45	−0.397241
$287$	3.30386e45	1.11740
$288$	0	0
$289$	−3.04869e45	−0.906783
$290$	−2.18318e45	−0.609153
$291$	0	0
$292$	3.59813e44	0.0884084
$293$	−5.41508e44	−0.124898	−0.0624488	−	0.998048i	$-0.519891\pi$
$293$	−5.41508e44	−0.124898	−0.0624488	+	0.998048i	$0.519891\pi$
$294$	0	0
$295$	−2.81034e45	−0.571547
$296$	−3.39041e44	−0.0647672
$297$	0	0
$298$	8.06172e45	1.35965
$299$	−1.13511e45	−0.179936
$300$	0	0
$301$	2.91167e45	0.408001
$302$	−2.94341e45	−0.387903
$303$	0	0
$304$	−7.77333e45	−0.906663
$305$	−1.85614e45	−0.203734
$306$	0	0
$307$	3.09102e45	0.300637	0.150318	−	0.988638i	$-0.451970\pi$
$307$	3.09102e45	0.300637	0.150318	+	0.988638i	$0.451970\pi$
$308$	2.23812e46	2.04972
$309$	0	0
$310$	5.77372e45	0.469099
$311$	2.15029e46	1.64600	0.823001	−	0.568040i	$-0.192298\pi$
$311$	2.15029e46	1.64600	0.823001	+	0.568040i	$0.192298\pi$
$312$	0	0
$313$	−1.50052e42	−0.000102017 0	−5.10083e−5	−	1.00000i	$-0.500016\pi$
$313$	−1.50052e42	−0.000102017 0	−5.10083e−5		1.00000i	$0.500016\pi$
$314$	−3.43290e46	−2.20020
$315$	0	0
$316$	2.94092e45	0.167599
$317$	7.41293e45	0.398468	0.199234	−	0.979952i	$-0.436155\pi$
$317$	7.41293e45	0.398468	0.199234	+	0.979952i	$0.436155\pi$
$318$	0	0
$319$	−3.19439e46	−1.52848
$320$	−6.45729e45	−0.291592
$321$	0	0
$322$	4.67987e46	1.88321
$323$	−7.09504e45	−0.269593
$324$	0	0
$325$	6.93561e45	0.235095
$326$	1.97221e46	0.631580
$327$	0	0
$328$	−7.80880e44	−0.0223315
$329$	2.02212e46	0.546616
$330$	0	0
$331$	−2.02313e46	−0.488883	−0.244441	−	0.969664i	$-0.578605\pi$
$331$	−2.02313e46	−0.488883	−0.244441	+	0.969664i	$0.578605\pi$
$332$	3.15328e46	0.720623
$333$	0	0
$334$	−9.55651e46	−1.95429
$335$	1.89532e46	0.366737
$336$	0	0
$337$	1.40951e46	0.244295	0.122148	−	0.992512i	$-0.461022\pi$
$337$	1.40951e46	0.244295	0.122148	+	0.992512i	$0.461022\pi$
$338$	−7.98163e46	−1.30958
$339$	0	0
$340$	−6.23317e45	−0.0916957
$341$	8.44801e46	1.17706
$342$	0	0
$343$	2.71153e47	3.39057
$344$	−6.88183e44	−0.00815404
$345$	0	0
$346$	−8.59708e46	−0.915046
$347$	−1.91978e46	−0.193711	−0.0968557	−	0.995298i	$-0.530879\pi$
$347$	−1.91978e46	−0.193711	−0.0968557	+	0.995298i	$0.530879\pi$
$348$	0	0
$349$	1.61862e47	1.46851	0.734253	−	0.678876i	$-0.237533\pi$
$349$	1.61862e47	1.46851	0.734253	+	0.678876i	$0.237533\pi$
$350$	−2.85945e47	−2.46050
$351$	0	0
$352$	−1.97236e47	−1.52738
$353$	9.35860e46	0.687668	0.343834	−	0.939030i	$-0.388274\pi$
$353$	9.35860e46	0.687668	0.343834	+	0.939030i	$0.388274\pi$
$354$	0	0
$355$	−6.19636e46	−0.410121
$356$	−1.52336e46	−0.0957145
$357$	0	0
$358$	−2.59086e47	−1.46760
$359$	−3.05449e47	−1.64321	−0.821603	−	0.570060i	$-0.806920\pi$
$359$	−3.05449e47	−1.64321	−0.821603	+	0.570060i	$0.806920\pi$
$360$	0	0
$361$	−4.53862e46	−0.220313
$362$	−3.92022e46	−0.180802
$363$	0	0
$364$	−1.17510e47	−0.489439
$365$	7.09229e45	0.0280781
$366$	0	0
$367$	−3.45206e47	−1.23526	−0.617628	−	0.786471i	$-0.711906\pi$
$367$	−3.45206e47	−1.23526	−0.617628	+	0.786471i	$0.711906\pi$
$368$	−2.08935e47	−0.710929
$369$	0	0
$370$	2.35808e47	0.725816
$371$	1.12581e48	3.29646
$372$	0	0
$373$	5.25222e47	1.39229	0.696145	−	0.717901i	$-0.254897\pi$
$373$	5.25222e47	1.39229	0.696145	+	0.717901i	$0.254897\pi$
$374$	−1.84990e47	−0.466685
$375$	0	0
$376$	−4.77935e45	−0.0109243
$377$	1.67718e47	0.364977
$378$	0	0
$379$	1.07624e47	0.212365	0.106183	−	0.994347i	$-0.466137\pi$
$379$	1.07624e47	0.212365	0.106183	+	0.994347i	$0.466137\pi$
$380$	1.41110e47	0.265192
$381$	0	0
$382$	1.81923e47	0.310252
$383$	−3.92097e44	−0.000637112 0	−0.000318556	−	1.00000i	$-0.500101\pi$
$383$	−3.92097e44	−0.000637112 0	−0.000318556		1.00000i	$0.500101\pi$
$384$	0	0
$385$	4.41156e47	0.650982
$386$	−4.36935e47	−0.614542
$387$	0	0
$388$	1.12821e48	1.44213
$389$	1.07652e48	1.31206	0.656029	−	0.754736i	$-0.272235\pi$
$389$	1.07652e48	1.31206	0.656029	+	0.754736i	$0.272235\pi$
$390$	0	0
$391$	−1.90704e47	−0.211392
$392$	−1.00695e47	−0.106467
$393$	0	0
$394$	3.80145e47	0.365822
$395$	5.79687e46	0.0532288
$396$	0	0
$397$	−9.91329e47	−0.829074	−0.414537	−	0.910032i	$-0.636056\pi$
$397$	−9.91329e47	−0.829074	−0.414537	+	0.910032i	$0.636056\pi$
$398$	3.03027e47	0.241905
$399$	0	0
$400$	1.27661e48	0.928859
$401$	−5.74839e47	−0.399370	−0.199685	−	0.979860i	$-0.563992\pi$
$401$	−5.74839e47	−0.399370	−0.199685	+	0.979860i	$0.563992\pi$
$402$	0	0
$403$	−4.43553e47	−0.281062
$404$	−9.17163e47	−0.555125
$405$	0	0
$406$	−6.91477e48	−3.81985
$407$	3.45030e48	1.82121
$408$	0	0
$409$	−1.42222e48	−0.685623	−0.342812	−	0.939404i	$-0.611379\pi$
$409$	−1.42222e48	−0.685623	−0.342812	+	0.939404i	$0.611379\pi$
$410$	5.43114e47	0.250259
$411$	0	0
$412$	1.74520e48	0.734932
$413$	−8.90118e48	−3.58403
$414$	0	0
$415$	6.21545e47	0.228867
$416$	1.03556e48	0.364712
$417$	0	0
$418$	4.18791e48	1.34970
$419$	2.58159e47	0.0796026	0.0398013	−	0.999208i	$-0.487328\pi$
$419$	2.58159e47	0.0796026	0.0398013	+	0.999208i	$0.487328\pi$
$420$	0	0
$421$	2.31697e48	0.654186	0.327093	−	0.944992i	$-0.393931\pi$
$421$	2.31697e48	0.654186	0.327093	+	0.944992i	$0.393931\pi$
$422$	−6.51108e48	−1.75943
$423$	0	0
$424$	−2.66089e47	−0.0658808
$425$	1.16522e48	0.276193
$426$	0	0
$427$	−5.87892e48	−1.27756
$428$	−5.85668e48	−1.21883
$429$	0	0
$430$	4.78642e47	0.0913785
$431$	3.89804e48	0.712881	0.356441	−	0.934318i	$-0.383990\pi$
$431$	3.89804e48	0.712881	0.356441	+	0.934318i	$0.383990\pi$
$432$	0	0
$433$	9.77220e48	1.64046	0.820231	−	0.572032i	$-0.193845\pi$
$433$	9.77220e48	1.64046	0.820231	+	0.572032i	$0.193845\pi$
$434$	1.82870e49	2.94160
$435$	0	0
$436$	−1.41170e48	−0.208566
$437$	4.31725e48	0.611365
$438$	0	0
$439$	−1.19379e48	−0.155359	−0.0776793	−	0.996978i	$-0.524751\pi$
$439$	−1.19379e48	−0.155359	−0.0776793	+	0.996978i	$0.524751\pi$
$440$	−1.04269e47	−0.0130101
$441$	0	0
$442$	9.71271e47	0.111437
$443$	1.49848e48	0.164886	0.0824429	−	0.996596i	$-0.473728\pi$
$443$	1.49848e48	0.164886	0.0824429	+	0.996596i	$0.473728\pi$
$444$	0	0
$445$	−3.00271e47	−0.0303985
$446$	−9.95328e48	−0.966655
$447$	0	0
$448$	−2.04521e49	−1.82850
$449$	−9.14003e48	−0.784134	−0.392067	−	0.919937i	$-0.628240\pi$
$449$	−9.14003e48	−0.784134	−0.392067	+	0.919937i	$0.628240\pi$
$450$	0	0
$451$	7.94675e48	0.627948
$452$	8.53277e48	0.647185
$453$	0	0
$454$	1.07670e49	0.752597
$455$	−2.31624e48	−0.155444
$456$	0	0
$457$	−7.21363e48	−0.446379	−0.223190	−	0.974775i	$-0.571647\pi$
$457$	−7.21363e48	−0.446379	−0.223190	+	0.974775i	$0.571647\pi$
$458$	3.50453e48	0.208266
$459$	0	0
$460$	3.79281e48	0.207942
$461$	3.62582e48	0.190959	0.0954793	−	0.995431i	$-0.469562\pi$
$461$	3.62582e48	0.190959	0.0954793	+	0.995431i	$0.469562\pi$
$462$	0	0
$463$	−2.42342e49	−1.17810	−0.589048	−	0.808098i	$-0.700497\pi$
$463$	−2.42342e49	−1.17810	−0.589048	+	0.808098i	$0.700497\pi$
$464$	3.08713e49	1.44202
$465$	0	0
$466$	2.75471e49	1.18833
$467$	−2.11890e49	−0.878514	−0.439257	−	0.898362i	$-0.644758\pi$
$467$	−2.11890e49	−0.878514	−0.439257	+	0.898362i	$0.644758\pi$
$468$	0	0
$469$	6.00304e49	2.29971
$470$	3.32411e48	0.122424
$471$	0	0
$472$	2.10383e48	0.0716280
$473$	7.00341e48	0.229286
$474$	0	0
$475$	−2.63789e49	−0.798775
$476$	−1.97423e49	−0.575001
$477$	0	0
$478$	−4.63728e49	−1.24982
$479$	3.96549e49	1.02823	0.514115	−	0.857721i	$-0.328121\pi$
$479$	3.96549e49	1.02823	0.514115	+	0.857721i	$0.328121\pi$
$480$	0	0
$481$	−1.81154e49	−0.434876
$482$	−5.95998e49	−1.37681
$483$	0	0
$484$	8.38653e48	0.179450
$485$	2.22382e49	0.458013
$486$	0	0
$487$	−3.49809e49	−0.667644	−0.333822	−	0.942636i	$-0.608338\pi$
$487$	−3.49809e49	−0.667644	−0.333822	+	0.942636i	$0.608338\pi$
$488$	1.38950e48	0.0255325
$489$	0	0
$490$	7.00347e49	1.19312
$491$	−1.54468e49	−0.253414	−0.126707	−	0.991940i	$-0.540441\pi$
$491$	−1.54468e49	−0.253414	−0.126707	+	0.991940i	$0.540441\pi$
$492$	0	0
$493$	2.81775e49	0.428780
$494$	−2.19882e49	−0.322285
$495$	0	0
$496$	−8.16434e49	−1.11048
$497$	−1.96257e50	−2.57177
$498$	0	0
$499$	−8.88148e49	−1.08050	−0.540250	−	0.841504i	$-0.681670\pi$
$499$	−8.88148e49	−1.08050	−0.540250	+	0.841504i	$0.681670\pi$
$500$	−4.87926e49	−0.572016
$501$	0	0
$502$	8.18491e49	0.891240
$503$	4.16645e49	0.437279	0.218639	−	0.975806i	$-0.429838\pi$
$503$	4.16645e49	0.437279	0.218639	+	0.975806i	$0.429838\pi$
$504$	0	0
$505$	−1.80782e49	−0.176305
$506$	1.12564e50	1.05832
$507$	0	0
$508$	−3.75966e49	−0.328602
$509$	−1.88211e50	−1.58623	−0.793114	−	0.609074i	$-0.791541\pi$
$509$	−1.88211e50	−1.58623	−0.793114	+	0.609074i	$0.791541\pi$
$510$	0	0
$511$	2.24633e49	0.176071
$512$	1.85356e50	1.40124
$513$	0	0
$514$	−1.22875e50	−0.864262
$515$	3.43998e49	0.233411
$516$	0	0
$517$	4.86378e49	0.307184
$518$	7.46872e50	4.55141
$519$	0	0
$520$	5.47453e47	0.00310660
$521$	−2.50866e50	−1.37386	−0.686931	−	0.726723i	$-0.741043\pi$
$521$	−2.50866e50	−1.37386	−0.686931	+	0.726723i	$0.741043\pi$
$522$	0	0
$523$	1.68115e49	0.0857682	0.0428841	−	0.999080i	$-0.486345\pi$
$523$	1.68115e49	0.0857682	0.0428841	+	0.999080i	$0.486345\pi$
$524$	−2.61921e50	−1.28986
$525$	0	0
$526$	5.34310e50	2.45221
$527$	−7.45193e49	−0.330196
$528$	0	0
$529$	−1.26023e50	−0.520618
$530$	1.85069e50	0.738295
$531$	0	0
$532$	4.46936e50	1.66295
$533$	−4.17236e49	−0.149944
$534$	0	0
$535$	−1.15441e50	−0.387094
$536$	−1.41884e49	−0.0459606
$537$	0	0
$538$	−1.24635e50	−0.376850
$539$	1.02474e51	2.99378
$540$	0	0
$541$	9.81522e49	0.267763	0.133882	−	0.990997i	$-0.457256\pi$
$541$	9.81522e49	0.267763	0.133882	+	0.990997i	$0.457256\pi$
$542$	−5.75425e50	−1.51706
$543$	0	0
$544$	1.73980e50	0.428470
$545$	−2.78261e49	−0.0662396
$546$	0	0
$547$	−6.05828e50	−1.34767	−0.673836	−	0.738881i	$-0.735354\pi$
$547$	−6.05828e50	−1.34767	−0.673836	+	0.738881i	$0.735354\pi$
$548$	−1.89725e50	−0.408023
$549$	0	0
$550$	−6.87781e50	−1.38274
$551$	−6.37898e50	−1.24007
$552$	0	0
$553$	1.83604e50	0.333785
$554$	−1.08721e51	−1.91153
$555$	0	0
$556$	−3.85469e50	−0.634023
$557$	−1.04564e50	−0.166365	−0.0831826	−	0.996534i	$-0.526508\pi$
$557$	−1.04564e50	−0.166365	−0.0831826	+	0.996534i	$0.526508\pi$
$558$	0	0
$559$	−3.67706e49	−0.0547498
$560$	−4.26343e50	−0.614159
$561$	0	0
$562$	−1.05154e51	−1.41809
$563$	6.57533e50	0.858050	0.429025	−	0.903293i	$-0.358857\pi$
$563$	6.57533e50	0.858050	0.429025	+	0.903293i	$0.358857\pi$
$564$	0	0
$565$	1.68190e50	0.205543
$566$	1.26865e51	1.50051
$567$	0	0
$568$	4.63860e49	0.0513976
$569$	2.74695e50	0.294628	0.147314	−	0.989090i	$-0.452937\pi$
$569$	2.74695e50	0.294628	0.147314	+	0.989090i	$0.452937\pi$
$570$	0	0
$571$	−2.57528e50	−0.258855	−0.129428	−	0.991589i	$-0.541314\pi$
$571$	−2.57528e50	−0.258855	−0.129428	+	0.991589i	$0.541314\pi$
$572$	−2.82646e50	−0.275053
$573$	0	0
$574$	1.72020e51	1.56931
$575$	−7.09023e50	−0.626332
$576$	0	0
$577$	1.01888e51	0.844058	0.422029	−	0.906582i	$-0.361318\pi$
$577$	1.01888e51	0.844058	0.422029	+	0.906582i	$0.361318\pi$
$578$	−1.58734e51	−1.27352
$579$	0	0
$580$	−5.60410e50	−0.421782
$581$	1.96861e51	1.43517
$582$	0	0
$583$	2.70790e51	1.85253
$584$	−5.30929e48	−0.00351884
$585$	0	0
$586$	−2.81943e50	−0.175411
$587$	−2.83210e51	−1.70728	−0.853638	−	0.520867i	$-0.825609\pi$
$587$	−2.83210e51	−1.70728	−0.853638	+	0.520867i	$0.825609\pi$
$588$	0	0
$589$	1.68701e51	0.954958
$590$	−1.46324e51	−0.802702
$591$	0	0
$592$	−3.33445e51	−1.71820
$593$	3.45126e51	1.72372	0.861858	−	0.507150i	$-0.169301\pi$
$593$	3.45126e51	1.72372	0.861858	+	0.507150i	$0.169301\pi$
$594$	0	0
$595$	−3.89141e50	−0.182618
$596$	2.06940e51	0.941430
$597$	0	0
$598$	−5.91007e50	−0.252709
$599$	4.18318e51	1.73425	0.867123	−	0.498094i	$-0.165966\pi$
$599$	4.18318e51	1.73425	0.867123	+	0.498094i	$0.165966\pi$
$600$	0	0
$601$	−2.49077e51	−0.970860	−0.485430	−	0.874276i	$-0.661337\pi$
$601$	−2.49077e51	−0.970860	−0.485430	+	0.874276i	$0.661337\pi$
$602$	1.51600e51	0.573011
$603$	0	0
$604$	−7.55557e50	−0.268586
$605$	1.65307e50	0.0569925
$606$	0	0
$607$	1.98679e50	0.0644409	0.0322204	−	0.999481i	$-0.489742\pi$
$607$	1.98679e50	0.0644409	0.0322204	+	0.999481i	$0.489742\pi$
$608$	−3.93866e51	−1.23917
$609$	0	0
$610$	−9.66421e50	−0.286131
$611$	−2.55368e50	−0.0733505
$612$	0	0
$613$	3.22821e50	0.0872856	0.0436428	−	0.999047i	$-0.486104\pi$
$613$	3.22821e50	0.0872856	0.0436428	+	0.999047i	$0.486104\pi$
$614$	1.60938e51	0.422225
$615$	0	0
$616$	−3.30250e50	−0.0815830
$617$	−2.17195e51	−0.520683	−0.260342	−	0.965517i	$-0.583835\pi$
$617$	−2.17195e51	−0.520683	−0.260342	+	0.965517i	$0.583835\pi$
$618$	0	0
$619$	3.90977e51	0.882824	0.441412	−	0.897305i	$-0.354478\pi$
$619$	3.90977e51	0.882824	0.441412	+	0.897305i	$0.354478\pi$
$620$	1.48208e51	0.324807
$621$	0	0
$622$	1.11958e52	2.31171
$623$	−9.51044e50	−0.190621
$624$	0	0
$625$	3.82724e51	0.722946
$626$	−7.81264e47	−0.000143276 0
$627$	0	0
$628$	−8.81205e51	−1.52343
$629$	−3.04349e51	−0.510899
$630$	0	0
$631$	−7.04074e51	−1.11449	−0.557244	−	0.830349i	$-0.688141\pi$
$631$	−7.04074e51	−1.11449	−0.557244	+	0.830349i	$0.688141\pi$
$632$	−4.33954e49	−0.00667080
$633$	0	0
$634$	3.85964e51	0.559623
$635$	−7.41069e50	−0.104363
$636$	0	0
$637$	−5.38026e51	−0.714865
$638$	−1.66320e52	−2.14666
$639$	0	0
$640$	1.96201e50	0.0238985
$641$	1.31488e52	1.55601	0.778003	−	0.628260i	$-0.216233\pi$
$641$	1.31488e52	1.55601	0.778003	+	0.628260i	$0.216233\pi$
$642$	0	0
$643$	1.39124e52	1.55417	0.777084	−	0.629397i	$-0.216698\pi$
$643$	1.39124e52	1.55417	0.777084	+	0.629397i	$0.216698\pi$
$644$	1.20129e52	1.30395
$645$	0	0
$646$	−3.69413e51	−0.378626
$647$	−1.43133e52	−1.42564	−0.712821	−	0.701346i	$-0.752583\pi$
$647$	−1.43133e52	−1.42564	−0.712821	+	0.701346i	$0.752583\pi$
$648$	0	0
$649$	−2.14099e52	−2.01413
$650$	3.61112e51	0.330175
$651$	0	0
$652$	5.06256e51	0.437310
$653$	−5.93896e51	−0.498674	−0.249337	−	0.968417i	$-0.580213\pi$
$653$	−5.93896e51	−0.498674	−0.249337	+	0.968417i	$0.580213\pi$
$654$	0	0
$655$	−5.16274e51	−0.409653
$656$	−7.67992e51	−0.592428
$657$	0	0
$658$	1.05284e52	0.767687
$659$	1.23688e52	0.876898	0.438449	−	0.898756i	$-0.355528\pi$
$659$	1.23688e52	0.876898	0.438449	+	0.898756i	$0.355528\pi$
$660$	0	0
$661$	−2.33294e52	−1.56378	−0.781891	−	0.623415i	$-0.785745\pi$
$661$	−2.33294e52	−1.56378	−0.781891	+	0.623415i	$0.785745\pi$
$662$	−1.05337e52	−0.686605
$663$	0	0
$664$	−4.65289e50	−0.0286823
$665$	8.80959e51	0.528147
$666$	0	0
$667$	−1.71457e52	−0.972361
$668$	−2.45310e52	−1.35316
$669$	0	0
$670$	9.86826e51	0.515058
$671$	−1.41405e52	−0.717958
$672$	0	0
$673$	1.92388e52	0.924484	0.462242	−	0.886754i	$-0.347045\pi$
$673$	1.92388e52	0.924484	0.462242	+	0.886754i	$0.347045\pi$
$674$	7.33880e51	0.343097
$675$	0	0
$676$	−2.04884e52	−0.906763
$677$	6.78443e51	0.292162	0.146081	−	0.989273i	$-0.453334\pi$
$677$	6.78443e51	0.292162	0.146081	+	0.989273i	$0.453334\pi$
$678$	0	0
$679$	7.04349e52	2.87208
$680$	9.19749e49	0.00364968
$681$	0	0
$682$	4.39857e52	1.65310
$683$	1.97532e52	0.722528	0.361264	−	0.932464i	$-0.382345\pi$
$683$	1.97532e52	0.722528	0.361264	+	0.932464i	$0.382345\pi$
$684$	0	0
$685$	−3.73968e51	−0.129586
$686$	1.41179e53	4.76184
$687$	0	0
$688$	−6.76824e51	−0.216317
$689$	−1.42175e52	−0.442353
$690$	0	0
$691$	−2.82676e52	−0.833575	−0.416788	−	0.909004i	$-0.636844\pi$
$691$	−2.82676e52	−0.833575	−0.416788	+	0.909004i	$0.636844\pi$
$692$	−2.20682e52	−0.633584
$693$	0	0
$694$	−9.99557e51	−0.272055
$695$	−7.59799e51	−0.201363
$696$	0	0
$697$	−7.00977e51	−0.176156
$698$	8.42758e52	2.06242
$699$	0	0
$700$	−7.34004e52	−1.70367
$701$	−6.97961e52	−1.57778	−0.788892	−	0.614532i	$-0.789345\pi$
$701$	−6.97961e52	−1.57778	−0.788892	+	0.614532i	$0.789345\pi$
$702$	0	0
$703$	6.89002e52	1.47757
$704$	−4.91933e52	−1.02757
$705$	0	0
$706$	4.87268e52	0.965785
$707$	−5.72591e52	−1.10557
$708$	0	0
$709$	−2.71632e52	−0.497766	−0.248883	−	0.968534i	$-0.580063\pi$
$709$	−2.71632e52	−0.497766	−0.248883	+	0.968534i	$0.580063\pi$
$710$	−3.22622e52	−0.575989
$711$	0	0
$712$	2.24783e50	0.00380963
$713$	4.53441e52	0.748798
$714$	0	0
$715$	−5.57124e51	−0.0873555
$716$	−6.65060e52	−1.01618
$717$	0	0
$718$	−1.59036e53	−2.30778
$719$	−1.18694e53	−1.67860	−0.839298	−	0.543672i	$-0.817033\pi$
$719$	−1.18694e53	−1.67860	−0.839298	+	0.543672i	$0.817033\pi$
$720$	0	0
$721$	1.08954e53	1.46366
$722$	−2.36309e52	−0.309416
$723$	0	0
$724$	−1.00630e52	−0.125188
$725$	1.04762e53	1.27043
$726$	0	0
$727$	−5.48820e52	−0.632475	−0.316237	−	0.948680i	$-0.602420\pi$
$727$	−5.48820e52	−0.632475	−0.316237	+	0.948680i	$0.602420\pi$
$728$	1.73394e51	0.0194807
$729$	0	0
$730$	3.69269e51	0.0394340
$731$	−6.17765e51	−0.0643209
$732$	0	0
$733$	−1.43675e53	−1.42219	−0.711097	−	0.703094i	$-0.751801\pi$
$733$	−1.43675e53	−1.42219	−0.711097	+	0.703094i	$0.751801\pi$
$734$	−1.79736e53	−1.73484
$735$	0	0
$736$	−1.05865e53	−0.971656
$737$	1.44391e53	1.29238
$738$	0	0
$739$	−1.14941e53	−0.978484	−0.489242	−	0.872148i	$-0.662727\pi$
$739$	−1.14941e53	−0.978484	−0.489242	+	0.872148i	$0.662727\pi$
$740$	6.05306e52	0.502560
$741$	0	0
$742$	5.86167e53	4.62966
$743$	7.23269e52	0.557195	0.278597	−	0.960408i	$-0.410130\pi$
$743$	7.23269e52	0.557195	0.278597	+	0.960408i	$0.410130\pi$
$744$	0	0
$745$	4.07900e52	0.298994
$746$	2.73464e53	1.95538
$747$	0	0
$748$	−4.74859e52	−0.323136
$749$	−3.65636e53	−2.42737
$750$	0	0
$751$	−1.89145e53	−1.19524	−0.597621	−	0.801779i	$-0.703887\pi$
$751$	−1.89145e53	−1.19524	−0.597621	+	0.801779i	$0.703887\pi$
$752$	−4.70046e52	−0.289808
$753$	0	0
$754$	8.73247e52	0.512586
$755$	−1.48928e52	−0.0853018
$756$	0	0
$757$	1.52507e53	0.831796	0.415898	−	0.909411i	$-0.363467\pi$
$757$	1.52507e53	0.831796	0.415898	+	0.909411i	$0.363467\pi$
$758$	5.60358e52	0.298253
$759$	0	0
$760$	−2.08218e51	−0.0105552
$761$	1.93715e53	0.958399	0.479199	−	0.877706i	$-0.340927\pi$
$761$	1.93715e53	0.958399	0.479199	+	0.877706i	$0.340927\pi$
$762$	0	0
$763$	−8.81334e52	−0.415372
$764$	4.66986e52	0.214821
$765$	0	0
$766$	−2.04150e50	−0.000894783 0
$767$	1.12411e53	0.480942
$768$	0	0
$769$	3.76633e53	1.53561	0.767805	−	0.640683i	$-0.221349\pi$
$769$	3.76633e53	1.53561	0.767805	+	0.640683i	$0.221349\pi$
$770$	2.29694e53	0.914263
$771$	0	0
$772$	−1.12159e53	−0.425513
$773$	−2.46250e53	−0.912127	−0.456064	−	0.889947i	$-0.650741\pi$
$773$	−2.46250e53	−0.912127	−0.456064	+	0.889947i	$0.650741\pi$
$774$	0	0
$775$	−2.77058e53	−0.978337
$776$	−1.66475e52	−0.0573995
$777$	0	0
$778$	5.60503e53	1.84270
$779$	1.58691e53	0.509460
$780$	0	0
$781$	−4.72055e53	−1.44527
$782$	−9.92923e52	−0.296887
$783$	0	0
$784$	−9.90327e53	−2.82443
$785$	−1.73695e53	−0.483836
$786$	0	0
$787$	3.69252e53	0.981275	0.490638	−	0.871364i	$-0.336764\pi$
$787$	3.69252e53	0.981275	0.490638	+	0.871364i	$0.336764\pi$
$788$	9.75812e52	0.253298
$789$	0	0
$790$	3.01822e52	0.0747565
$791$	5.32706e53	1.28891
$792$	0	0
$793$	7.42433e52	0.171436
$794$	−5.16148e53	−1.16438
$795$	0	0
$796$	7.77854e52	0.167497
$797$	−5.45878e53	−1.14846	−0.574231	−	0.818694i	$-0.694699\pi$
$797$	−5.45878e53	−1.14846	−0.574231	+	0.818694i	$0.694699\pi$
$798$	0	0
$799$	−4.29031e52	−0.0861733
$800$	6.46846e53	1.26951
$801$	0	0
$802$	−2.99297e53	−0.560889
$803$	5.40309e52	0.0989475
$804$	0	0
$805$	2.36788e53	0.414129
$806$	−2.30942e53	−0.394734
$807$	0	0
$808$	1.35334e52	0.0220951
$809$	1.10283e54	1.75979	0.879893	−	0.475171i	$-0.157614\pi$
$809$	1.10283e54	1.75979	0.879893	+	0.475171i	$0.157614\pi$
$810$	0	0
$811$	7.85452e53	1.19739	0.598693	−	0.800979i	$-0.295687\pi$
$811$	7.85452e53	1.19739	0.598693	+	0.800979i	$0.295687\pi$
$812$	−1.77498e54	−2.64489
$813$	0	0
$814$	1.79645e54	2.55778
$815$	9.97884e52	0.138888
$816$	0	0
$817$	1.39853e53	0.186022
$818$	−7.40497e53	−0.962914
$819$	0	0
$820$	1.39414e53	0.173281
$821$	−1.01998e54	−1.23949	−0.619744	−	0.784804i	$-0.712764\pi$
$821$	−1.01998e54	−1.23949	−0.619744	+	0.784804i	$0.712764\pi$
$822$	0	0
$823$	−1.92578e52	−0.0223722	−0.0111861	−	0.999937i	$-0.503561\pi$
$823$	−1.92578e52	−0.0223722	−0.0111861	+	0.999937i	$0.503561\pi$
$824$	−2.57517e52	−0.0292518
$825$	0	0
$826$	−4.63452e54	−5.03354
$827$	5.47526e53	0.581504	0.290752	−	0.956798i	$-0.406095\pi$
$827$	5.47526e53	0.581504	0.290752	+	0.956798i	$0.406095\pi$
$828$	0	0
$829$	−1.39168e53	−0.141346	−0.0706728	−	0.997500i	$-0.522515\pi$
$829$	−1.39168e53	−0.141346	−0.0706728	+	0.997500i	$0.522515\pi$
$830$	3.23616e53	0.321429
$831$	0	0
$832$	2.58284e53	0.245367
$833$	−9.03912e53	−0.839835
$834$	0	0
$835$	−4.83532e53	−0.429759
$836$	1.07501e54	0.934539
$837$	0	0
$838$	1.34414e53	0.111797
$839$	1.43760e54	1.16961	0.584804	−	0.811174i	$-0.301171\pi$
$839$	1.43760e54	1.16961	0.584804	+	0.811174i	$0.301171\pi$
$840$	0	0
$841$	1.24890e54	0.972302
$842$	1.20636e54	0.918762
$843$	0	0
$844$	−1.67136e54	−1.21824
$845$	−4.03848e53	−0.287984
$846$	0	0
$847$	5.23577e53	0.357386
$848$	−2.61697e54	−1.74774
$849$	0	0
$850$	6.06687e53	0.387895
$851$	1.85193e54	1.15858
$852$	0	0
$853$	1.36560e54	0.818024	0.409012	−	0.912529i	$-0.365873\pi$
$853$	1.36560e54	0.818024	0.409012	+	0.912529i	$0.365873\pi$
$854$	−3.06094e54	−1.79425
$855$	0	0
$856$	8.64194e52	0.0485117
$857$	3.06618e54	1.68443	0.842213	−	0.539145i	$-0.181253\pi$
$857$	3.06618e54	1.68443	0.842213	+	0.539145i	$0.181253\pi$
$858$	0	0
$859$	−2.99741e53	−0.157715	−0.0788575	−	0.996886i	$-0.525127\pi$
$859$	−2.99741e53	−0.157715	−0.0788575	+	0.996886i	$0.525127\pi$
$860$	1.22865e53	0.0632711
$861$	0	0
$862$	2.02957e54	1.00120
$863$	4.97031e53	0.239985	0.119992	−	0.992775i	$-0.461713\pi$
$863$	4.97031e53	0.239985	0.119992	+	0.992775i	$0.461713\pi$
$864$	0	0
$865$	−4.34988e53	−0.201224
$866$	5.08802e54	2.30392
$867$	0	0
$868$	4.69418e54	2.03678
$869$	4.41620e53	0.187579
$870$	0	0
$871$	−7.58108e53	−0.308599
$872$	2.08307e52	0.00830134
$873$	0	0
$874$	2.24783e54	0.858624
$875$	−3.04615e54	−1.13921
$876$	0	0
$877$	5.81431e53	0.208452	0.104226	−	0.994554i	$-0.466764\pi$
$877$	5.81431e53	0.208452	0.104226	+	0.994554i	$0.466764\pi$
$878$	−6.21564e53	−0.218191
$879$	0	0
$880$	−1.02548e54	−0.345142
$881$	2.08913e54	0.688510	0.344255	−	0.938876i	$-0.388131\pi$
$881$	2.08913e54	0.688510	0.344255	+	0.938876i	$0.388131\pi$
$882$	0	0
$883$	−3.47147e54	−1.09709	−0.548543	−	0.836122i	$-0.684817\pi$
$883$	−3.47147e54	−1.09709	−0.548543	+	0.836122i	$0.684817\pi$
$884$	2.49320e53	0.0771595
$885$	0	0
$886$	7.80205e53	0.231572
$887$	−5.12164e54	−1.48875	−0.744376	−	0.667761i	$-0.767253\pi$
$887$	−5.12164e54	−1.48875	−0.744376	+	0.667761i	$0.767253\pi$
$888$	0	0
$889$	−2.34718e54	−0.654431
$890$	−1.56340e53	−0.0426928
$891$	0	0
$892$	−2.55495e54	−0.669318
$893$	9.71264e53	0.249221
$894$	0	0
$895$	−1.31090e54	−0.322734
$896$	6.21425e53	0.149862
$897$	0	0
$898$	−4.75888e54	−1.10127
$899$	−6.69985e54	−1.51884
$900$	0	0
$901$	−2.38862e54	−0.519683
$902$	4.13758e54	0.881913
$903$	0	0
$904$	−1.25907e53	−0.0257593
$905$	−1.98352e53	−0.0397592
$906$	0	0
$907$	−6.23293e53	−0.119938	−0.0599691	−	0.998200i	$-0.519100\pi$
$907$	−6.23293e53	−0.119938	−0.0599691	+	0.998200i	$0.519100\pi$
$908$	2.76383e54	0.521103
$909$	0	0
$910$	−1.20598e54	−0.218311
$911$	−2.11014e54	−0.374302	−0.187151	−	0.982331i	$-0.559925\pi$
$911$	−2.11014e54	−0.374302	−0.187151	+	0.982331i	$0.559925\pi$
$912$	0	0
$913$	4.73509e54	0.806527
$914$	−3.75587e54	−0.626911
$915$	0	0
$916$	8.99593e53	0.144205
$917$	−1.63519e55	−2.56883
$918$	0	0
$919$	1.59651e52	0.00240899	0.00120450	−	0.999999i	$-0.499617\pi$
$919$	1.59651e52	0.00240899	0.00120450	+	0.999999i	$0.499617\pi$
$920$	−5.59657e52	−0.00827651
$921$	0	0
$922$	1.88783e54	0.268189
$923$	2.47847e54	0.345106
$924$	0	0
$925$	−1.13155e55	−1.51374
$926$	−1.26179e55	−1.65456
$927$	0	0
$928$	1.56421e55	1.97087
$929$	4.23691e54	0.523309	0.261654	−	0.965162i	$-0.415732\pi$
$929$	4.23691e54	0.523309	0.261654	+	0.965162i	$0.415732\pi$
$930$	0	0
$931$	2.04633e55	2.42888
$932$	7.07117e54	0.822805
$933$	0	0
$934$	−1.10323e55	−1.23382
$935$	−9.35998e53	−0.102627
$936$	0	0
$937$	−1.28910e55	−1.35863	−0.679317	−	0.733845i	$-0.737724\pi$
$937$	−1.28910e55	−1.35863	−0.679317	+	0.733845i	$0.737724\pi$
$938$	3.12556e55	3.22980
$939$	0	0
$940$	8.53279e53	0.0847668
$941$	4.90525e54	0.477807	0.238904	−	0.971043i	$-0.423212\pi$
$941$	4.90525e54	0.477807	0.238904	+	0.971043i	$0.423212\pi$
$942$	0	0
$943$	4.26537e54	0.399476
$944$	2.06910e55	1.90020
$945$	0	0
$946$	3.64642e54	0.322018
$947$	7.97016e54	0.690228	0.345114	−	0.938561i	$-0.387840\pi$
$947$	7.97016e54	0.690228	0.345114	+	0.938561i	$0.387840\pi$
$948$	0	0
$949$	−2.83683e53	−0.0236270
$950$	−1.37345e55	−1.12183
$951$	0	0
$952$	2.91311e53	0.0228862
$953$	1.23666e55	0.952864	0.476432	−	0.879211i	$-0.341930\pi$
$953$	1.23666e55	0.952864	0.476432	+	0.879211i	$0.341930\pi$
$954$	0	0
$955$	9.20478e53	0.0682262
$956$	−1.19036e55	−0.865383
$957$	0	0
$958$	2.06469e55	1.44408
$959$	−1.18447e55	−0.812603
$960$	0	0
$961$	2.56972e54	0.169630
$962$	−9.43205e54	−0.610755
$963$	0	0
$964$	−1.52989e55	−0.953314
$965$	−2.21077e54	−0.135141
$966$	0	0
$967$	−1.79944e55	−1.05864	−0.529318	−	0.848424i	$-0.677552\pi$
$967$	−1.79944e55	−1.05864	−0.529318	+	0.848424i	$0.677552\pi$
$968$	−1.23749e53	−0.00714247
$969$	0	0
$970$	1.15786e55	0.643250
$971$	−1.81554e55	−0.989577	−0.494789	−	0.869013i	$-0.664755\pi$
$971$	−1.81554e55	−0.989577	−0.494789	+	0.869013i	$0.664755\pi$
$972$	0	0
$973$	−2.40651e55	−1.26270
$974$	−1.82133e55	−0.937664
$975$	0	0
$976$	1.36657e55	0.677346
$977$	1.52699e54	0.0742656	0.0371328	−	0.999310i	$-0.488178\pi$
$977$	1.52699e54	0.0742656	0.0371328	+	0.999310i	$0.488178\pi$
$978$	0	0
$979$	−2.28754e54	−0.107124
$980$	1.79775e55	0.826127
$981$	0	0
$982$	−8.04259e54	−0.355904
$983$	3.38697e55	1.47086	0.735431	−	0.677600i	$-0.236980\pi$
$983$	3.38697e55	1.47086	0.735431	+	0.677600i	$0.236980\pi$
$984$	0	0
$985$	1.92343e54	0.0804462
$986$	1.46710e55	0.602194
$987$	0	0
$988$	−5.64424e54	−0.223152
$989$	3.75903e54	0.145863
$990$	0	0
$991$	4.67890e55	1.74897	0.874483	−	0.485057i	$-0.161201\pi$
$991$	4.67890e55	1.74897	0.874483	+	0.485057i	$0.161201\pi$
$992$	−4.13678e55	−1.51774
$993$	0	0
$994$	−1.02184e56	−3.61188
$995$	1.53323e54	0.0531962
$996$	0	0
$997$	4.89388e55	1.63603	0.818017	−	0.575193i	$-0.195073\pi$
$997$	4.89388e55	1.63603	0.818017	+	0.575193i	$0.195073\pi$
$998$	−4.62426e55	−1.51749
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.38.a.c.1.4		4
3.2	odd	2		3.38.a.b.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.38.a.b.1.1	✓	4	3.2	odd	2
9.38.a.c.1.4		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)

\(f(q)\)	\(=\)	\(q+520663. q^{2} +1.33651e11 q^{4} +2.63441e12 q^{5} +8.34393e15 q^{7} -1.97212e15 q^{8} +O(q^{10})\)	\(q+520663. q^{2} +1.33651e11 q^{4} +2.63441e12 q^{5} +8.34393e15 q^{7} -1.97212e15 q^{8} +1.37164e18 q^{10} +2.00696e19 q^{11} -1.05373e20 q^{13} +4.34438e21 q^{14} -1.93957e22 q^{16} -1.77033e22 q^{17} +4.00776e23 q^{19} +3.52092e23 q^{20} +1.04495e25 q^{22} +1.07722e25 q^{23} -6.58195e25 q^{25} -5.48640e25 q^{26} +1.11518e27 q^{28} -1.59166e27 q^{29} +4.20936e27 q^{31} -9.82758e27 q^{32} -9.21743e27 q^{34} +2.19813e28 q^{35} +1.71917e29 q^{37} +2.08669e29 q^{38} -5.19537e27 q^{40} +3.95960e29 q^{41} +3.48956e29 q^{43} +2.68233e30 q^{44} +5.60870e30 q^{46} +2.42346e30 q^{47} +5.10591e31 q^{49} -3.42698e31 q^{50} -1.40833e31 q^{52} +1.34925e32 q^{53} +5.28715e31 q^{55} -1.64552e31 q^{56} -8.28718e32 q^{58} -1.06678e33 q^{59} -7.04574e32 q^{61} +2.19166e33 q^{62} -2.45114e33 q^{64} -2.77596e32 q^{65} +7.19450e33 q^{67} -2.36606e33 q^{68} +1.14449e34 q^{70} -2.35209e34 q^{71} +2.69218e33 q^{73} +8.95108e34 q^{74} +5.35642e34 q^{76} +1.67459e35 q^{77} +2.20044e34 q^{79} -5.10962e34 q^{80} +2.06162e35 q^{82} +2.35934e35 q^{83} -4.66376e34 q^{85} +1.81689e35 q^{86} -3.95797e34 q^{88} -1.13980e35 q^{89} -8.79227e35 q^{91} +1.43972e36 q^{92} +1.26181e36 q^{94} +1.05581e36 q^{95} +8.44145e36 q^{97} +2.65846e37 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 437562 q^{2} + 346098955492 q^{4} + 4099829756904 q^{5} + 66\!\cdots\!84 q^{7}+ \cdots - 14\!\cdots\!76 q^{8}+O(q^{10}) \) 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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