LMFDB - Embedded newform 9.22.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,22,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, 22, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 22 $
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:	$25.1529609858$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{649}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 162 $ x^2 - x - 162
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 7 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$13.2377$ 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)

$f(q)$	$=$	$q-1937.96 q^{2} +1.65852e6 q^{4} -2.22745e7 q^{5} +4.78205e7 q^{7} +8.50053e8 q^{8} +O(q^{10})$	\(q-1937.96 q^{2} +1.65852e6 q^{4} -2.22745e7 q^{5} +4.78205e7 q^{7} +8.50053e8 q^{8} +4.31669e10 q^{10} -1.60111e11 q^{11} -7.86968e11 q^{13} -9.26741e10 q^{14} -5.12553e12 q^{16} +2.97477e12 q^{17} -2.99456e13 q^{19} -3.69426e13 q^{20} +3.10287e14 q^{22} +1.91401e14 q^{23} +1.93148e13 q^{25} +1.52511e15 q^{26} +7.93112e13 q^{28} -9.68170e14 q^{29} +2.80459e15 q^{31} +8.15035e15 q^{32} -5.76496e15 q^{34} -1.06518e15 q^{35} +3.05038e16 q^{37} +5.80331e16 q^{38} -1.89345e16 q^{40} +2.22806e16 q^{41} +1.63711e17 q^{43} -2.65546e17 q^{44} -3.70927e17 q^{46} -4.08678e17 q^{47} -5.56259e17 q^{49} -3.74313e16 q^{50} -1.30520e18 q^{52} -4.34009e17 q^{53} +3.56638e18 q^{55} +4.06500e16 q^{56} +1.87627e18 q^{58} +5.14341e18 q^{59} +1.98980e18 q^{61} -5.43517e18 q^{62} -5.04601e18 q^{64} +1.75293e19 q^{65} -1.36361e19 q^{67} +4.93370e18 q^{68} +2.06427e18 q^{70} -7.35641e18 q^{71} +6.81650e19 q^{73} -5.91149e19 q^{74} -4.96652e19 q^{76} -7.65658e18 q^{77} -2.12282e19 q^{79} +1.14168e20 q^{80} -4.31789e19 q^{82} -1.10803e20 q^{83} -6.62613e19 q^{85} -3.17266e20 q^{86} -1.36102e20 q^{88} +7.67205e18 q^{89} -3.76333e19 q^{91} +3.17442e20 q^{92} +7.92000e20 q^{94} +6.67021e20 q^{95} +4.63755e20 q^{97} +1.07801e21 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 666 q^{2} + 1179236 q^{4} - 996876 q^{5} + 679896112 q^{7} - 2427055848 q^{8}+O(q^{10}) $ 2 * q - 666 * q^2 + 1179236 * q^4 - 996876 * q^5 + 679896112 * q^7 - 2427055848 * q^8	$ 2 q - 666 q^{2} + 1179236 q^{4} - 996876 q^{5} + 679896112 q^{7} - 2427055848 q^{8} + 70231066524 q^{10} - 219869122968 q^{11} - 48468909956 q^{13} + 711297706896 q^{14} - 8288736440560 q^{16} + 11333529041436 q^{17} + 11960585011624 q^{19} - 47140581172824 q^{20} + 234277148563128 q^{22} + 146508390063504 q^{23} - 4786354247074 q^{25} + 24\!\cdots\!16 q^{26}+ \cdots + 87\!\cdots\!14 q^{98}+O(q^{100}) $ 2 * q - 666 * q^2 + 1179236 * q^4 - 996876 * q^5 + 679896112 * q^7 - 2427055848 * q^8 + 70231066524 * q^10 - 219869122968 * q^11 - 48468909956 * q^13 + 711297706896 * q^14 - 8288736440560 * q^16 + 11333529041436 * q^17 + 11960585011624 * q^19 - 47140581172824 * q^20 + 234277148563128 * q^22 + 146508390063504 * q^23 - 4786354247074 * q^25 + 2464447363969716 * q^26 - 223631286954656 * q^28 + 1798520043674052 * q^29 + 11169107526944992 * q^31 + 10999491515934048 * q^32 + 4867007487413652 * q^34 + 12383869767948000 * q^35 + 12736264858660012 * q^37 + 111335877667820664 * q^38 - 88663459120547472 * q^40 - 122972020616468052 * q^41 + 288455418162270040 * q^43 - 236905239135592368 * q^44 - 428027981395161168 * q^46 - 837243745741596960 * q^47 - 715285396941470670 * q^49 - 68086886042031174 * q^50 - 1659150748242045896 * q^52 + 43007964012775764 * q^53 + 2294863118895313296 * q^55 - 2030730320050568640 * q^56 + 5395375030104291852 * q^58 + 3523823330903857224 * q^59 - 1779023128451013860 * q^61 + 5204128043677477536 * q^62 + 5211692013463482944 * q^64 + 33242791066177513752 * q^65 - 16454068667621610296 * q^67 + 927498335984326008 * q^68 + 19170849981674109600 * q^70 - 17379227131150420944 * q^71 + 50891146268473989076 * q^73 - 81714426393675287484 * q^74 - 69750112936092790064 * q^76 - 45428450983816025664 * q^77 - 54055785594190591040 * q^79 + 46862985896348738976 * q^80 - 227933719179803895996 * q^82 - 111108429277666677288 * q^83 + 111593012278262968152 * q^85 - 158596867265246585208 * q^86 + 59732519594715541728 * q^88 - 226920767965448065524 * q^89 + 429154174685185000352 * q^91 + 338958281810136649248 * q^92 + 246883115968835119776 * q^94 + 1558683223531725831696 * q^95 - 128331469252795746236 * q^97 + 875730737371150330614 * 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 $

$2$	−1937.96	−1.33822	−0.669112	−	0.743162i	$-0.733325\pi$
$2$	−1937.96	−1.33822	−0.669112	+	0.743162i	$0.733325\pi$
$3$	0	0
$3$	0	0
$4$	1.65852e6	0.790843
$5$	−2.22745e7	−1.02005	−0.510026	−	0.860159i	$-0.670364\pi$
$5$	−2.22745e7	−1.02005	−0.510026	+	0.860159i	$0.670364\pi$
$6$	0	0
$7$	4.78205e7	0.0639860	0.0319930	−	0.999488i	$-0.489815\pi$
$7$	4.78205e7	0.0639860	0.0319930	+	0.999488i	$0.489815\pi$
$8$	8.50053e8	0.279899
$9$	0	0
$10$	4.31669e10	1.36506
$11$	−1.60111e11	−1.86122	−0.930609	−	0.366016i	$-0.880722\pi$
$11$	−1.60111e11	−1.86122	−0.930609	+	0.366016i	$0.880722\pi$
$12$	0	0
$13$	−7.86968e11	−1.58326	−0.791630	−	0.611001i	$-0.790767\pi$
$13$	−7.86968e11	−1.58326	−0.791630	+	0.611001i	$0.790767\pi$
$14$	−9.26741e10	−0.0856276
$15$	0	0
$16$	−5.12553e12	−1.16541
$17$	2.97477e12	0.357881	0.178941	−	0.983860i	$-0.442733\pi$
$17$	2.97477e12	0.357881	0.178941	+	0.983860i	$0.442733\pi$
$18$	0	0
$19$	−2.99456e13	−1.12052	−0.560260	−	0.828317i	$-0.689299\pi$
$19$	−2.99456e13	−1.12052	−0.560260	+	0.828317i	$0.689299\pi$
$20$	−3.69426e13	−0.806701
$21$	0	0
$22$	3.10287e14	2.49073
$23$	1.91401e14	0.963390	0.481695	−	0.876339i	$-0.340021\pi$
$23$	1.91401e14	0.963390	0.481695	+	0.876339i	$0.340021\pi$
$24$	0	0
$25$	1.93148e13	0.0405061
$26$	1.52511e15	2.11876
$27$	0	0
$28$	7.93112e13	0.0506029
$29$	−9.68170e14	−0.427339	−0.213670	−	0.976906i	$-0.568542\pi$
$29$	−9.68170e14	−0.427339	−0.213670	+	0.976906i	$0.568542\pi$
$30$	0	0
$31$	2.80459e15	0.614570	0.307285	−	0.951618i	$-0.400580\pi$
$31$	2.80459e15	0.614570	0.307285	+	0.951618i	$0.400580\pi$
$32$	8.15035e15	1.27968
$33$	0	0
$34$	−5.76496e15	−0.478925
$35$	−1.06518e15	−0.0652691
$36$	0	0
$37$	3.05038e16	1.04288	0.521441	−	0.853287i	$-0.325395\pi$
$37$	3.05038e16	1.04288	0.521441	+	0.853287i	$0.325395\pi$
$38$	5.80331e16	1.49951
$39$	0	0
$40$	−1.89345e16	−0.285511
$41$	2.22806e16	0.259237	0.129618	−	0.991564i	$-0.458625\pi$
$41$	2.22806e16	0.259237	0.129618	+	0.991564i	$0.458625\pi$
$42$	0	0
$43$	1.63711e17	1.15521	0.577604	−	0.816317i	$-0.303988\pi$
$43$	1.63711e17	1.15521	0.577604	+	0.816317i	$0.303988\pi$
$44$	−2.65546e17	−1.47193
$45$	0	0
$46$	−3.70927e17	−1.28923
$47$	−4.08678e17	−1.13332	−0.566662	−	0.823951i	$-0.691765\pi$
$47$	−4.08678e17	−1.13332	−0.566662	+	0.823951i	$0.691765\pi$
$48$	0	0
$49$	−5.56259e17	−0.995906
$50$	−3.74313e16	−0.0542063
$51$	0	0
$52$	−1.30520e18	−1.25211
$53$	−4.34009e17	−0.340881	−0.170440	−	0.985368i	$-0.554519\pi$
$53$	−4.34009e17	−0.340881	−0.170440	+	0.985368i	$0.554519\pi$
$54$	0	0
$55$	3.56638e18	1.89854
$56$	4.06500e16	0.0179096
$57$	0	0
$58$	1.87627e18	0.571875
$59$	5.14341e18	1.31010	0.655051	−	0.755584i	$-0.272647\pi$
$59$	5.14341e18	1.31010	0.655051	+	0.755584i	$0.272647\pi$
$60$	0	0
$61$	1.98980e18	0.357147	0.178573	−	0.983927i	$-0.442852\pi$
$61$	1.98980e18	0.357147	0.178573	+	0.983927i	$0.442852\pi$
$62$	−5.43517e18	−0.822432
$63$	0	0
$64$	−5.04601e18	−0.547089
$65$	1.75293e19	1.61501
$66$	0	0
$67$	−1.36361e19	−0.913913	−0.456956	−	0.889489i	$-0.651060\pi$
$67$	−1.36361e19	−0.913913	−0.456956	+	0.889489i	$0.651060\pi$
$68$	4.93370e18	0.283028
$69$	0	0
$70$	2.06427e18	0.0873446
$71$	−7.35641e18	−0.268196	−0.134098	−	0.990968i	$-0.542814\pi$
$71$	−7.35641e18	−0.268196	−0.134098	+	0.990968i	$0.542814\pi$
$72$	0	0
$73$	6.81650e19	1.85640	0.928200	−	0.372081i	$-0.121356\pi$
$73$	6.81650e19	1.85640	0.928200	+	0.372081i	$0.121356\pi$
$74$	−5.91149e19	−1.39561
$75$	0	0
$76$	−4.96652e19	−0.886155
$77$	−7.65658e18	−0.119092
$78$	0	0
$79$	−2.12282e19	−0.252249	−0.126124	−	0.992014i	$-0.540254\pi$
$79$	−2.12282e19	−0.252249	−0.126124	+	0.992014i	$0.540254\pi$
$80$	1.14168e20	1.18878
$81$	0	0
$82$	−4.31789e19	−0.346917
$83$	−1.10803e20	−0.783849	−0.391924	−	0.919997i	$-0.628191\pi$
$83$	−1.10803e20	−0.783849	−0.391924	+	0.919997i	$0.628191\pi$
$84$	0	0
$85$	−6.62613e19	−0.365058
$86$	−3.17266e20	−1.54593
$87$	0	0
$88$	−1.36102e20	−0.520952
$89$	7.67205e18	0.0260805	0.0130403	−	0.999915i	$-0.495849\pi$
$89$	7.67205e18	0.0260805	0.0130403	+	0.999915i	$0.495849\pi$
$90$	0	0
$91$	−3.76333e19	−0.101306
$92$	3.17442e20	0.761890
$93$	0	0
$94$	7.92000e20	1.51664
$95$	6.67021e20	1.14299
$96$	0	0
$97$	4.63755e20	0.638535	0.319268	−	0.947665i	$-0.396563\pi$
$97$	4.63755e20	0.638535	0.319268	+	0.947665i	$0.396563\pi$
$98$	1.07801e21	1.33274
$99$	0	0
$100$	3.20340e19	0.0320340
$101$	−1.75642e20	−0.158217	−0.0791086	−	0.996866i	$-0.525207\pi$
$101$	−1.75642e20	−0.158217	−0.0791086	+	0.996866i	$0.525207\pi$
$102$	0	0
$103$	−1.29018e21	−0.945933	−0.472967	−	0.881080i	$-0.656817\pi$
$103$	−1.29018e21	−0.945933	−0.472967	+	0.881080i	$0.656817\pi$
$104$	−6.68965e20	−0.443152
$105$	0	0
$106$	8.41091e20	0.456175
$107$	−5.76913e19	−0.0283518	−0.0141759	−	0.999900i	$-0.504512\pi$
$107$	−5.76913e19	−0.0283518	−0.0141759	+	0.999900i	$0.504512\pi$
$108$	0	0
$109$	−5.74941e20	−0.232619	−0.116309	−	0.993213i	$-0.537106\pi$
$109$	−5.74941e20	−0.232619	−0.116309	+	0.993213i	$0.537106\pi$
$110$	−6.91148e21	−2.54067
$111$	0	0
$112$	−2.45106e20	−0.0745700
$113$	4.56755e21	1.26578	0.632892	−	0.774240i	$-0.281868\pi$
$113$	4.56755e21	1.26578	0.632892	+	0.774240i	$0.281868\pi$
$114$	0	0
$115$	−4.26336e21	−0.982708
$116$	−1.60573e21	−0.337958
$117$	0	0
$118$	−9.96770e21	−1.75321
$119$	1.42255e20	0.0228994
$120$	0	0
$121$	1.82352e22	2.46413
$122$	−3.85615e21	−0.477942
$123$	0	0
$124$	4.65146e21	0.486028
$125$	1.01911e22	0.978734
$126$	0	0
$127$	1.84938e22	1.50344	0.751722	−	0.659480i	$-0.229224\pi$
$127$	1.84938e22	1.50344	0.751722	+	0.659480i	$0.229224\pi$
$128$	−7.31359e21	−0.547553
$129$	0	0
$130$	−3.39710e22	−2.16124
$131$	1.25296e22	0.735509	0.367754	−	0.929923i	$-0.380127\pi$
$131$	1.25296e22	0.735509	0.367754	+	0.929923i	$0.380127\pi$
$132$	0	0
$133$	−1.43201e21	−0.0716976
$134$	2.64261e22	1.22302
$135$	0	0
$136$	2.52871e21	0.100171
$137$	−3.84075e22	−1.40880	−0.704402	−	0.709801i	$-0.748785\pi$
$137$	−3.84075e22	−1.40880	−0.704402	+	0.709801i	$0.748785\pi$
$138$	0	0
$139$	−9.58856e21	−0.302063	−0.151032	−	0.988529i	$-0.548260\pi$
$139$	−9.58856e21	−0.302063	−0.151032	+	0.988529i	$0.548260\pi$
$140$	−1.76662e21	−0.0516176
$141$	0	0
$142$	1.42564e22	0.358907
$143$	1.26002e23	2.94679
$144$	0	0
$145$	2.15655e22	0.435908
$146$	−1.32101e23	−2.48428
$147$	0	0
$148$	5.05911e22	0.824757
$149$	−3.44428e22	−0.523170	−0.261585	−	0.965180i	$-0.584245\pi$
$149$	−3.44428e22	−0.523170	−0.261585	+	0.965180i	$0.584245\pi$
$150$	0	0
$151$	−3.63152e22	−0.479546	−0.239773	−	0.970829i	$-0.577073\pi$
$151$	−3.63152e22	−0.479546	−0.239773	+	0.970829i	$0.577073\pi$
$152$	−2.54553e22	−0.313632
$153$	0	0
$154$	1.48381e22	0.159372
$155$	−6.24707e22	−0.626893
$156$	0	0
$157$	−9.41986e22	−0.826225	−0.413112	−	0.910680i	$-0.635558\pi$
$157$	−9.41986e22	−0.826225	−0.413112	+	0.910680i	$0.635558\pi$
$158$	4.11393e22	0.337565
$159$	0	0
$160$	−1.81545e23	−1.30534
$161$	9.15290e21	0.0616435
$162$	0	0
$163$	−1.80771e23	−1.06945	−0.534723	−	0.845027i	$-0.679584\pi$
$163$	−1.80771e23	−1.06945	−0.534723	+	0.845027i	$0.679584\pi$
$164$	3.69528e22	0.205016
$165$	0	0
$166$	2.14732e23	1.04897
$167$	−3.71934e22	−0.170586	−0.0852929	−	0.996356i	$-0.527183\pi$
$167$	−3.71934e22	−0.170586	−0.0852929	+	0.996356i	$0.527183\pi$
$168$	0	0
$169$	3.72255e23	1.50671
$170$	1.28412e23	0.488529
$171$	0	0
$172$	2.71518e23	0.913589
$173$	−2.58398e23	−0.818096	−0.409048	−	0.912513i	$-0.634139\pi$
$173$	−2.58398e23	−0.818096	−0.409048	+	0.912513i	$0.634139\pi$
$174$	0	0
$175$	9.23645e20	0.00259183
$176$	8.20652e23	2.16908
$177$	0	0
$178$	−1.48681e22	−0.0349016
$179$	3.35184e23	0.741868	0.370934	−	0.928659i	$-0.379038\pi$
$179$	3.35184e23	0.741868	0.370934	+	0.928659i	$0.379038\pi$
$180$	0	0
$181$	−1.92267e23	−0.378687	−0.189343	−	0.981911i	$-0.560636\pi$
$181$	−1.92267e23	−0.378687	−0.189343	+	0.981911i	$0.560636\pi$
$182$	7.29316e22	0.135571
$183$	0	0
$184$	1.62701e23	0.269652
$185$	−6.79455e23	−1.06379
$186$	0	0
$187$	−4.76292e23	−0.666095
$188$	−6.77800e23	−0.896281
$189$	0	0
$190$	−1.29266e24	−1.52957
$191$	4.60821e23	0.516038	0.258019	−	0.966140i	$-0.416930\pi$
$191$	4.60821e23	0.516038	0.258019	+	0.966140i	$0.416930\pi$
$192$	0	0
$193$	1.29600e24	1.30093	0.650465	−	0.759536i	$-0.274574\pi$
$193$	1.29600e24	1.30093	0.650465	+	0.759536i	$0.274574\pi$
$194$	−8.98736e23	−0.854503
$195$	0	0
$196$	−9.22566e23	−0.787605
$197$	−2.05711e24	−1.66480	−0.832402	−	0.554172i	$-0.813035\pi$
$197$	−2.05711e24	−1.66480	−0.832402	+	0.554172i	$0.813035\pi$
$198$	0	0
$199$	5.34557e22	0.0389078	0.0194539	−	0.999811i	$-0.493807\pi$
$199$	5.34557e22	0.0389078	0.0194539	+	0.999811i	$0.493807\pi$
$200$	1.64186e22	0.0113376
$201$	0	0
$202$	3.40386e23	0.211730
$203$	−4.62984e22	−0.0273437
$204$	0	0
$205$	−4.96289e23	−0.264435
$206$	2.50032e24	1.26587
$207$	0	0
$208$	4.03363e24	1.84515
$209$	4.79460e24	2.08553
$210$	0	0
$211$	−3.16142e24	−1.24427	−0.622137	−	0.782908i	$-0.713735\pi$
$211$	−3.16142e24	−1.24427	−0.622137	+	0.782908i	$0.713735\pi$
$212$	−7.19813e23	−0.269583
$213$	0	0
$214$	1.11803e23	0.0379410
$215$	−3.64659e24	−1.17837
$216$	0	0
$217$	1.34117e23	0.0393239
$218$	1.11421e24	0.311296
$219$	0	0
$220$	5.91491e24	1.50145
$221$	−2.34105e24	−0.566619
$222$	0	0
$223$	−3.10623e24	−0.683963	−0.341981	−	0.939707i	$-0.611098\pi$
$223$	−3.10623e24	−0.683963	−0.341981	+	0.939707i	$0.611098\pi$
$224$	3.89754e23	0.0818817
$225$	0	0
$226$	−8.85171e24	−1.69390
$227$	2.04882e24	0.374310	0.187155	−	0.982330i	$-0.440073\pi$
$227$	2.04882e24	0.374310	0.187155	+	0.982330i	$0.440073\pi$
$228$	0	0
$229$	4.12622e24	0.687512	0.343756	−	0.939059i	$-0.388301\pi$
$229$	4.12622e24	0.687512	0.343756	+	0.939059i	$0.388301\pi$
$230$	8.26219e24	1.31508
$231$	0	0
$232$	−8.22995e23	−0.119612
$233$	−3.43270e24	−0.476869	−0.238434	−	0.971159i	$-0.576634\pi$
$233$	−3.43270e24	−0.476869	−0.238434	+	0.971159i	$0.576634\pi$
$234$	0	0
$235$	9.10308e24	1.15605
$236$	8.53044e24	1.03609
$237$	0	0
$238$	−2.75684e23	−0.0306445
$239$	−8.29149e24	−0.881972	−0.440986	−	0.897514i	$-0.645371\pi$
$239$	−8.29149e24	−0.881972	−0.440986	+	0.897514i	$0.645371\pi$
$240$	0	0
$241$	−1.30526e25	−1.27209	−0.636045	−	0.771652i	$-0.719431\pi$
$241$	−1.30526e25	−1.27209	−0.636045	+	0.771652i	$0.719431\pi$
$242$	−3.53389e25	−3.29756
$243$	0	0
$244$	3.30012e24	0.282447
$245$	1.23904e25	1.01588
$246$	0	0
$247$	2.35662e25	1.77407
$248$	2.38405e24	0.172017
$249$	0	0
$250$	−1.97498e25	−1.30976
$251$	1.77630e25	1.12965	0.564823	−	0.825212i	$-0.308944\pi$
$251$	1.77630e25	1.12965	0.564823	+	0.825212i	$0.308944\pi$
$252$	0	0
$253$	−3.06453e25	−1.79308
$254$	−3.58402e25	−2.01194
$255$	0	0
$256$	2.47557e25	1.27984
$257$	5.70058e24	0.282893	0.141446	−	0.989946i	$-0.454825\pi$
$257$	5.70058e24	0.282893	0.141446	+	0.989946i	$0.454825\pi$
$258$	0	0
$259$	1.45871e24	0.0667299
$260$	2.90727e25	1.27722
$261$	0	0
$262$	−2.42818e25	−0.984275
$263$	−9.73572e23	−0.0379169	−0.0189584	−	0.999820i	$-0.506035\pi$
$263$	−9.73572e23	−0.0379169	−0.0189584	+	0.999820i	$0.506035\pi$
$264$	0	0
$265$	9.66733e24	0.347716
$266$	2.77518e24	0.0959474
$267$	0	0
$268$	−2.26157e25	−0.722761
$269$	5.78587e25	1.77816	0.889078	−	0.457756i	$-0.151347\pi$
$269$	5.78587e25	1.77816	0.889078	+	0.457756i	$0.151347\pi$
$270$	0	0
$271$	4.29033e25	1.21987	0.609934	−	0.792452i	$-0.291196\pi$
$271$	4.29033e25	1.21987	0.609934	+	0.792452i	$0.291196\pi$
$272$	−1.52473e25	−0.417079
$273$	0	0
$274$	7.44321e25	1.88530
$275$	−3.09251e24	−0.0753907
$276$	0	0
$277$	6.39000e25	1.44366	0.721828	−	0.692073i	$-0.243302\pi$
$277$	6.39000e25	1.44366	0.721828	+	0.692073i	$0.243302\pi$
$278$	1.85822e25	0.404228
$279$	0	0
$280$	−9.05457e23	−0.0182687
$281$	−3.23104e25	−0.627951	−0.313976	−	0.949431i	$-0.601661\pi$
$281$	−3.23104e25	−0.627951	−0.313976	+	0.949431i	$0.601661\pi$
$282$	0	0
$283$	−1.00627e25	−0.181534	−0.0907668	−	0.995872i	$-0.528932\pi$
$283$	−1.00627e25	−0.181534	−0.0907668	+	0.995872i	$0.528932\pi$
$284$	−1.22007e25	−0.212101
$285$	0	0
$286$	−2.44186e26	−3.94346
$287$	1.06547e24	0.0165875
$288$	0	0
$289$	−6.02427e25	−0.871921
$290$	−4.17929e25	−0.583343
$291$	0	0
$292$	1.13053e26	1.46812
$293$	−4.93011e25	−0.617656	−0.308828	−	0.951118i	$-0.599937\pi$
$293$	−4.93011e25	−0.617656	−0.308828	+	0.951118i	$0.599937\pi$
$294$	0	0
$295$	−1.14567e26	−1.33637
$296$	2.59298e25	0.291902
$297$	0	0
$298$	6.67487e25	0.700119
$299$	−1.50627e26	−1.52530
$300$	0	0
$301$	7.82877e24	0.0739172
$302$	7.03772e25	0.641740
$303$	0	0
$304$	1.53487e26	1.30587
$305$	−4.43218e25	−0.364308
$306$	0	0
$307$	−1.49828e25	−0.114985	−0.0574925	−	0.998346i	$-0.518311\pi$
$307$	−1.49828e25	−0.114985	−0.0574925	+	0.998346i	$0.518311\pi$
$308$	−1.26986e25	−0.0941830
$309$	0	0
$310$	1.21065e26	0.838924
$311$	1.48794e26	0.996786	0.498393	−	0.866951i	$-0.333924\pi$
$311$	1.48794e26	0.996786	0.498393	+	0.866951i	$0.333924\pi$
$312$	0	0
$313$	−1.10961e26	−0.694951	−0.347476	−	0.937689i	$-0.612961\pi$
$313$	−1.10961e26	−0.694951	−0.347476	+	0.937689i	$0.612961\pi$
$314$	1.82553e26	1.10567
$315$	0	0
$316$	−3.52074e25	−0.199489
$317$	−7.14805e25	−0.391801	−0.195900	−	0.980624i	$-0.562763\pi$
$317$	−7.14805e25	−0.391801	−0.195900	+	0.980624i	$0.562763\pi$
$318$	0	0
$319$	1.55014e26	0.795371
$320$	1.12397e26	0.558060
$321$	0	0
$322$	−1.77379e25	−0.0824928
$323$	−8.90810e25	−0.401013
$324$	0	0
$325$	−1.52002e25	−0.0641317
$326$	3.50326e26	1.43116
$327$	0	0
$328$	1.89397e25	0.0725601
$329$	−1.95432e25	−0.0725168
$330$	0	0
$331$	−5.05668e26	−1.76065	−0.880323	−	0.474375i	$-0.842674\pi$
$331$	−5.05668e26	−1.76065	−0.880323	+	0.474375i	$0.842674\pi$
$332$	−1.83769e26	−0.619901
$333$	0	0
$334$	7.20791e25	0.228282
$335$	3.03737e26	0.932238
$336$	0	0
$337$	3.50546e26	1.01072	0.505360	−	0.862909i	$-0.331360\pi$
$337$	3.50546e26	1.01072	0.505360	+	0.862909i	$0.331360\pi$
$338$	−7.21413e26	−2.01632
$339$	0	0
$340$	−1.09896e26	−0.288703
$341$	−4.49044e26	−1.14385
$342$	0	0
$343$	−5.33106e25	−0.127710
$344$	1.39163e26	0.323341
$345$	0	0
$346$	5.00763e26	1.09480
$347$	3.51664e26	0.745879	0.372940	−	0.927856i	$-0.378350\pi$
$347$	3.51664e26	0.745879	0.372940	+	0.927856i	$0.378350\pi$
$348$	0	0
$349$	5.74285e26	1.14673	0.573364	−	0.819300i	$-0.305638\pi$
$349$	5.74285e26	1.14673	0.573364	+	0.819300i	$0.305638\pi$
$350$	−1.78998e24	−0.00346844
$351$	0	0
$352$	−1.30496e27	−2.38176
$353$	−1.85373e25	−0.0328406	−0.0164203	−	0.999865i	$-0.505227\pi$
$353$	−1.85373e25	−0.0328406	−0.0164203	+	0.999865i	$0.505227\pi$
$354$	0	0
$355$	1.63860e26	0.273574
$356$	1.27242e25	0.0206256
$357$	0	0
$358$	−6.49572e26	−0.992785
$359$	3.41606e26	0.507030	0.253515	−	0.967331i	$-0.418413\pi$
$359$	3.41606e26	0.507030	0.253515	+	0.967331i	$0.418413\pi$
$360$	0	0
$361$	1.82527e26	0.255565
$362$	3.72605e26	0.506768
$363$	0	0
$364$	−6.24154e25	−0.0801175
$365$	−1.51834e27	−1.89362
$366$	0	0
$367$	5.79162e26	0.682034	0.341017	−	0.940057i	$-0.389229\pi$
$367$	5.79162e26	0.682034	0.341017	+	0.940057i	$0.389229\pi$
$368$	−9.81031e26	−1.12274
$369$	0	0
$370$	1.31675e27	1.42360
$371$	−2.07546e25	−0.0218116
$372$	0	0
$373$	−1.74513e27	−1.73335	−0.866673	−	0.498877i	$-0.833746\pi$
$373$	−1.74513e27	−1.73335	−0.866673	+	0.498877i	$0.833746\pi$
$374$	9.23032e26	0.891384
$375$	0	0
$376$	−3.47398e26	−0.317216
$377$	7.61919e26	0.676588
$378$	0	0
$379$	1.08818e27	0.914093	0.457046	−	0.889443i	$-0.348907\pi$
$379$	1.08818e27	0.914093	0.457046	+	0.889443i	$0.348907\pi$
$380$	1.10627e27	0.903925
$381$	0	0
$382$	−8.93050e26	−0.690575
$383$	2.35974e27	1.77532	0.887661	−	0.460498i	$-0.152329\pi$
$383$	2.35974e27	1.77532	0.887661	+	0.460498i	$0.152329\pi$
$384$	0	0
$385$	1.70546e26	0.121480
$386$	−2.51159e27	−1.74094
$387$	0	0
$388$	7.69145e26	0.504981
$389$	2.72162e27	1.73923	0.869616	−	0.493729i	$-0.164367\pi$
$389$	2.72162e27	1.73923	0.869616	+	0.493729i	$0.164367\pi$
$390$	0	0
$391$	5.69373e26	0.344779
$392$	−4.72850e26	−0.278753
$393$	0	0
$394$	3.98660e27	2.22788
$395$	4.72847e26	0.257307
$396$	0	0
$397$	−2.20086e27	−1.13577	−0.567887	−	0.823106i	$-0.692239\pi$
$397$	−2.20086e27	−1.13577	−0.567887	+	0.823106i	$0.692239\pi$
$398$	−1.03595e26	−0.0520673
$399$	0	0
$400$	−9.89987e25	−0.0472063
$401$	−2.61699e27	−1.21559	−0.607793	−	0.794096i	$-0.707945\pi$
$401$	−2.61699e27	−1.21559	−0.607793	+	0.794096i	$0.707945\pi$
$402$	0	0
$403$	−2.20712e27	−0.973023
$404$	−2.91305e26	−0.125125
$405$	0	0
$406$	8.97242e25	0.0365920
$407$	−4.88398e27	−1.94103
$408$	0	0
$409$	−8.92474e26	−0.336900	−0.168450	−	0.985710i	$-0.553876\pi$
$409$	−8.92474e26	−0.336900	−0.168450	+	0.985710i	$0.553876\pi$
$410$	9.61786e26	0.353874
$411$	0	0
$412$	−2.13979e27	−0.748085
$413$	2.45961e26	0.0838282
$414$	0	0
$415$	2.46808e27	0.799567
$416$	−6.41407e27	−2.02607
$417$	0	0
$418$	−9.29172e27	−2.79091
$419$	2.48238e27	0.727144	0.363572	−	0.931566i	$-0.381557\pi$
$419$	2.48238e27	0.727144	0.363572	+	0.931566i	$0.381557\pi$
$420$	0	0
$421$	4.09797e27	1.14184	0.570922	−	0.821004i	$-0.306586\pi$
$421$	4.09797e27	1.14184	0.570922	+	0.821004i	$0.306586\pi$
$422$	6.12669e27	1.66512
$423$	0	0
$424$	−3.68931e26	−0.0954121
$425$	5.74571e25	0.0144964
$426$	0	0
$427$	9.51534e25	0.0228524
$428$	−9.56820e25	−0.0224218
$429$	0	0
$430$	7.06692e27	1.57693
$431$	4.89793e27	1.06660	0.533299	−	0.845927i	$-0.320952\pi$
$431$	4.89793e27	1.06660	0.533299	+	0.845927i	$0.320952\pi$
$432$	0	0
$433$	−2.06118e27	−0.427557	−0.213778	−	0.976882i	$-0.568577\pi$
$433$	−2.06118e27	−0.427557	−0.213778	+	0.976882i	$0.568577\pi$
$434$	−2.59913e26	−0.0526242
$435$	0	0
$436$	−9.53549e26	−0.183965
$437$	−5.73161e27	−1.07950
$438$	0	0
$439$	1.00358e28	1.80167	0.900835	−	0.434161i	$-0.142955\pi$
$439$	1.00358e28	1.80167	0.900835	+	0.434161i	$0.142955\pi$
$440$	3.03161e27	0.531399
$441$	0	0
$442$	4.53684e27	0.758263
$443$	−4.23345e27	−0.690964	−0.345482	−	0.938425i	$-0.612285\pi$
$443$	−4.23345e27	−0.690964	−0.345482	+	0.938425i	$0.612285\pi$
$444$	0	0
$445$	−1.70891e26	−0.0266035
$446$	6.01973e27	0.915295
$447$	0	0
$448$	−2.41303e26	−0.0350061
$449$	6.74432e27	0.955766	0.477883	−	0.878424i	$-0.341404\pi$
$449$	6.74432e27	0.955766	0.477883	+	0.878424i	$0.341404\pi$
$450$	0	0
$451$	−3.56737e27	−0.482496
$452$	7.57537e27	1.00104
$453$	0	0
$454$	−3.97052e27	−0.500911
$455$	8.38261e26	0.103338
$456$	0	0
$457$	−1.13821e28	−1.34000	−0.669998	−	0.742362i	$-0.733705\pi$
$457$	−1.13821e28	−1.34000	−0.669998	+	0.742362i	$0.733705\pi$
$458$	−7.99644e27	−0.920045
$459$	0	0
$460$	−7.07085e27	−0.777167
$461$	−6.24175e27	−0.670574	−0.335287	−	0.942116i	$-0.608833\pi$
$461$	−6.24175e27	−0.670574	−0.335287	+	0.942116i	$0.608833\pi$
$462$	0	0
$463$	−2.31855e27	−0.238021	−0.119011	−	0.992893i	$-0.537972\pi$
$463$	−2.31855e27	−0.238021	−0.119011	+	0.992893i	$0.537972\pi$
$464$	4.96238e27	0.498025
$465$	0	0
$466$	6.65242e27	0.638157
$467$	9.47846e26	0.0889018	0.0444509	−	0.999012i	$-0.485846\pi$
$467$	9.47846e26	0.0889018	0.0444509	+	0.999012i	$0.485846\pi$
$468$	0	0
$469$	−6.52086e26	−0.0584776
$470$	−1.76414e28	−1.54705
$471$	0	0
$472$	4.37217e27	0.366696
$473$	−2.62120e28	−2.15009
$474$	0	0
$475$	−5.78393e26	−0.0453879
$476$	2.35932e26	0.0181098
$477$	0	0
$478$	1.60685e28	1.18028
$479$	1.76996e28	1.27186	0.635932	−	0.771745i	$-0.280616\pi$
$479$	1.76996e28	1.27186	0.635932	+	0.771745i	$0.280616\pi$
$480$	0	0
$481$	−2.40055e28	−1.65115
$482$	2.52954e28	1.70234
$483$	0	0
$484$	3.02434e28	1.94874
$485$	−1.03299e28	−0.651339
$486$	0	0
$487$	1.99209e28	1.20297	0.601484	−	0.798885i	$-0.294576\pi$
$487$	1.99209e28	1.20297	0.601484	+	0.798885i	$0.294576\pi$
$488$	1.69144e27	0.0999649
$489$	0	0
$490$	−2.40120e28	−1.35947
$491$	5.71237e27	0.316563	0.158282	−	0.987394i	$-0.449405\pi$
$491$	5.71237e27	0.316563	0.158282	+	0.987394i	$0.449405\pi$
$492$	0	0
$493$	−2.88008e27	−0.152937
$494$	−4.56702e28	−2.37411
$495$	0	0
$496$	−1.43750e28	−0.716226
$497$	−3.51787e26	−0.0171608
$498$	0	0
$499$	−1.17032e28	−0.547332	−0.273666	−	0.961825i	$-0.588236\pi$
$499$	−1.17032e28	−0.547332	−0.273666	+	0.961825i	$0.588236\pi$
$500$	1.69021e28	0.774025
$501$	0	0
$502$	−3.44239e28	−1.51172
$503$	3.15184e28	1.35550	0.677750	−	0.735292i	$-0.262955\pi$
$503$	3.15184e28	1.35550	0.677750	+	0.735292i	$0.262955\pi$
$504$	0	0
$505$	3.91233e27	0.161390
$506$	5.93893e28	2.39954
$507$	0	0
$508$	3.06723e28	1.18899
$509$	−4.58029e28	−1.73923	−0.869613	−	0.493733i	$-0.835632\pi$
$509$	−4.58029e28	−1.73923	−0.869613	+	0.493733i	$0.835632\pi$
$510$	0	0
$511$	3.25969e27	0.118784
$512$	−3.26377e28	−1.16516
$513$	0	0
$514$	−1.10475e28	−0.378574
$515$	2.87382e28	0.964901
$516$	0	0
$517$	6.54337e28	2.10936
$518$	−2.82691e27	−0.0892996
$519$	0	0
$520$	1.49008e28	0.452038
$521$	5.19044e27	0.154315	0.0771575	−	0.997019i	$-0.475416\pi$
$521$	5.19044e27	0.154315	0.0771575	+	0.997019i	$0.475416\pi$
$522$	0	0
$523$	−2.08282e27	−0.0594817	−0.0297408	−	0.999558i	$-0.509468\pi$
$523$	−2.08282e27	−0.0594817	−0.0297408	+	0.999558i	$0.509468\pi$
$524$	2.07805e28	0.581672
$525$	0	0
$526$	1.88674e27	0.0507413
$527$	8.34299e27	0.219943
$528$	0	0
$529$	−2.83724e27	−0.0718805
$530$	−1.87349e28	−0.465322
$531$	0	0
$532$	−2.37502e27	−0.0567016
$533$	−1.75342e28	−0.410439
$534$	0	0
$535$	1.28504e27	0.0289203
$536$	−1.15914e28	−0.255803
$537$	0	0
$538$	−1.12128e29	−2.37957
$539$	8.90630e28	1.85360
$540$	0	0
$541$	−1.25240e28	−0.250710	−0.125355	−	0.992112i	$-0.540007\pi$
$541$	−1.25240e28	−0.250710	−0.125355	+	0.992112i	$0.540007\pi$
$542$	−8.31446e28	−1.63246
$543$	0	0
$544$	2.42454e28	0.457974
$545$	1.28065e28	0.237283
$546$	0	0
$547$	5.63104e28	1.00397	0.501987	−	0.864875i	$-0.332603\pi$
$547$	5.63104e28	1.00397	0.501987	+	0.864875i	$0.332603\pi$
$548$	−6.36996e28	−1.11414
$549$	0	0
$550$	5.99314e27	0.100890
$551$	2.89924e28	0.478842
$552$	0	0
$553$	−1.01514e27	−0.0161404
$554$	−1.23835e29	−1.93193
$555$	0	0
$556$	−1.59028e28	−0.238885
$557$	−4.80914e28	−0.708904	−0.354452	−	0.935074i	$-0.615333\pi$
$557$	−4.80914e28	−0.708904	−0.354452	+	0.935074i	$0.615333\pi$
$558$	0	0
$559$	−1.28836e29	−1.82899
$560$	5.45960e27	0.0760652
$561$	0	0
$562$	6.26161e28	0.840339
$563$	1.81812e28	0.239488	0.119744	−	0.992805i	$-0.461793\pi$
$563$	1.81812e28	0.239488	0.119744	+	0.992805i	$0.461793\pi$
$564$	0	0
$565$	−1.01740e29	−1.29117
$566$	1.95011e28	0.242933
$567$	0	0
$568$	−6.25333e27	−0.0750679
$569$	−1.75144e28	−0.206403	−0.103201	−	0.994660i	$-0.532909\pi$
$569$	−1.75144e28	−0.206403	−0.103201	+	0.994660i	$0.532909\pi$
$570$	0	0
$571$	1.67794e29	1.90589	0.952946	−	0.303140i	$-0.0980350\pi$
$571$	1.67794e29	1.90589	0.952946	+	0.303140i	$0.0980350\pi$
$572$	2.08977e29	2.33045
$573$	0	0
$574$	−2.06484e27	−0.0221978
$575$	3.69688e27	0.0390232
$576$	0	0
$577$	7.49346e28	0.762669	0.381335	−	0.924437i	$-0.375465\pi$
$577$	7.49346e28	0.762669	0.381335	+	0.924437i	$0.375465\pi$
$578$	1.16748e29	1.16683
$579$	0	0
$580$	3.57667e28	0.344735
$581$	−5.29867e27	−0.0501554
$582$	0	0
$583$	6.94895e28	0.634453
$584$	5.79439e28	0.519604
$585$	0	0
$586$	9.55433e28	0.826562
$587$	−1.69908e29	−1.44382	−0.721912	−	0.691985i	$-0.756736\pi$
$587$	−1.69908e29	−1.44382	−0.721912	+	0.691985i	$0.756736\pi$
$588$	0	0
$589$	−8.39849e28	−0.688638
$590$	2.22025e29	1.78837
$591$	0	0
$592$	−1.56348e29	−1.21539
$593$	1.26592e29	0.966787	0.483394	−	0.875403i	$-0.339404\pi$
$593$	1.26592e29	0.966787	0.483394	+	0.875403i	$0.339404\pi$
$594$	0	0
$595$	−3.16865e27	−0.0233586
$596$	−5.71241e28	−0.413746
$597$	0	0
$598$	2.91907e29	2.04119
$599$	−1.73983e29	−1.19544	−0.597718	−	0.801706i	$-0.703926\pi$
$599$	−1.73983e29	−1.19544	−0.597718	+	0.801706i	$0.703926\pi$
$600$	0	0
$601$	−2.58691e29	−1.71633	−0.858164	−	0.513376i	$-0.828395\pi$
$601$	−2.58691e29	−1.71633	−0.858164	+	0.513376i	$0.828395\pi$
$602$	−1.51718e28	−0.0989178
$603$	0	0
$604$	−6.02294e28	−0.379246
$605$	−4.06179e29	−2.51354
$606$	0	0
$607$	−1.61646e29	−0.966238	−0.483119	−	0.875555i	$-0.660496\pi$
$607$	−1.61646e29	−0.966238	−0.483119	+	0.875555i	$0.660496\pi$
$608$	−2.44067e29	−1.43391
$609$	0	0
$610$	8.58936e28	0.487526
$611$	3.21617e29	1.79434
$612$	0	0
$613$	8.86426e28	0.477868	0.238934	−	0.971036i	$-0.423202\pi$
$613$	8.86426e28	0.477868	0.238934	+	0.971036i	$0.423202\pi$
$614$	2.90361e28	0.153876
$615$	0	0
$616$	−6.50850e27	−0.0333337
$617$	7.14976e28	0.359996	0.179998	−	0.983667i	$-0.442391\pi$
$617$	7.14976e28	0.359996	0.179998	+	0.983667i	$0.442391\pi$
$618$	0	0
$619$	−3.79378e28	−0.184638	−0.0923188	−	0.995730i	$-0.529428\pi$
$619$	−3.79378e28	−0.184638	−0.0923188	+	0.995730i	$0.529428\pi$
$620$	−1.03609e29	−0.495774
$621$	0	0
$622$	−2.88356e29	−1.33392
$623$	3.66882e26	0.00166879
$624$	0	0
$625$	−2.36211e29	−1.03887
$626$	2.15037e29	0.930000
$627$	0	0
$628$	−1.56230e29	−0.653414
$629$	9.07416e28	0.373228
$630$	0	0
$631$	4.22002e29	1.67883	0.839415	−	0.543491i	$-0.182898\pi$
$631$	4.22002e29	1.67883	0.839415	+	0.543491i	$0.182898\pi$
$632$	−1.80451e28	−0.0706041
$633$	0	0
$634$	1.38526e29	0.524317
$635$	−4.11940e29	−1.53359
$636$	0	0
$637$	4.37758e29	1.57678
$638$	−3.00411e29	−1.06438
$639$	0	0
$640$	1.62906e29	0.558533
$641$	2.45898e29	0.829364	0.414682	−	0.909966i	$-0.363893\pi$
$641$	2.45898e29	0.829364	0.414682	+	0.909966i	$0.363893\pi$
$642$	0	0
$643$	3.81795e29	1.24628	0.623139	−	0.782111i	$-0.285857\pi$
$643$	3.81795e29	1.24628	0.623139	+	0.782111i	$0.285857\pi$
$644$	1.51803e28	0.0487503
$645$	0	0
$646$	1.72635e29	0.536646
$647$	3.01566e29	0.922332	0.461166	−	0.887314i	$-0.347431\pi$
$647$	3.01566e29	0.922332	0.461166	+	0.887314i	$0.347431\pi$
$648$	0	0
$649$	−8.23515e29	−2.43839
$650$	2.94572e28	0.0858226
$651$	0	0
$652$	−2.99812e29	−0.845764
$653$	−2.27685e29	−0.632042	−0.316021	−	0.948752i	$-0.602347\pi$
$653$	−2.27685e29	−0.632042	−0.316021	+	0.948752i	$0.602347\pi$
$654$	0	0
$655$	−2.79090e29	−0.750257
$656$	−1.14200e29	−0.302117
$657$	0	0
$658$	3.78738e28	0.0970437
$659$	4.45804e29	1.12421	0.562104	−	0.827066i	$-0.309992\pi$
$659$	4.45804e29	1.12421	0.562104	+	0.827066i	$0.309992\pi$
$660$	0	0
$661$	4.54039e29	1.10912	0.554559	−	0.832144i	$-0.312887\pi$
$661$	4.54039e29	1.10912	0.554559	+	0.832144i	$0.312887\pi$
$662$	9.79963e29	2.35614
$663$	0	0
$664$	−9.41886e28	−0.219398
$665$	3.18973e28	0.0731353
$666$	0	0
$667$	−1.85309e29	−0.411694
$668$	−6.16859e28	−0.134907
$669$	0	0
$670$	−5.88628e29	−1.24754
$671$	−3.18588e29	−0.664727
$672$	0	0
$673$	5.05512e28	0.102229	0.0511144	−	0.998693i	$-0.483723\pi$
$673$	5.05512e28	0.102229	0.0511144	+	0.998693i	$0.483723\pi$
$674$	−6.79342e29	−1.35257
$675$	0	0
$676$	6.17391e29	1.19157
$677$	3.44673e29	0.654977	0.327489	−	0.944855i	$-0.393798\pi$
$677$	3.44673e29	0.654977	0.327489	+	0.944855i	$0.393798\pi$
$678$	0	0
$679$	2.21770e28	0.0408573
$680$	−5.63256e28	−0.102179
$681$	0	0
$682$	8.70228e29	1.53072
$683$	−3.07293e29	−0.532273	−0.266137	−	0.963935i	$-0.585747\pi$
$683$	−3.07293e29	−0.532273	−0.266137	+	0.963935i	$0.585747\pi$
$684$	0	0
$685$	8.55508e29	1.43705
$686$	1.03314e29	0.170905
$687$	0	0
$688$	−8.39108e29	−1.34629
$689$	3.41552e29	0.539703
$690$	0	0
$691$	7.85532e28	0.120405	0.0602025	−	0.998186i	$-0.480825\pi$
$691$	7.85532e28	0.120405	0.0602025	+	0.998186i	$0.480825\pi$
$692$	−4.28557e29	−0.646986
$693$	0	0
$694$	−6.81509e29	−0.998153
$695$	2.13580e29	0.308120
$696$	0	0
$697$	6.62797e28	0.0927761
$698$	−1.11294e30	−1.53458
$699$	0	0
$700$	1.53188e27	0.00204973
$701$	−7.75849e29	−1.02268	−0.511338	−	0.859380i	$-0.670850\pi$
$701$	−7.75849e29	−1.02268	−0.511338	+	0.859380i	$0.670850\pi$
$702$	0	0
$703$	−9.13453e29	−1.16857
$704$	8.07920e29	1.01825
$705$	0	0
$706$	3.59244e28	0.0439481
$707$	−8.39929e27	−0.0101237
$708$	0	0
$709$	1.53428e30	1.79523	0.897613	−	0.440785i	$-0.145300\pi$
$709$	1.53428e30	1.79523	0.897613	+	0.440785i	$0.145300\pi$
$710$	−3.17553e29	−0.366104
$711$	0	0
$712$	6.52165e27	0.00729991
$713$	5.36801e29	0.592070
$714$	0	0
$715$	−2.80663e30	−3.00588
$716$	5.55909e29	0.586701
$717$	0	0
$718$	−6.62017e29	−0.678520
$719$	−5.56901e29	−0.562503	−0.281252	−	0.959634i	$-0.590750\pi$
$719$	−5.56901e29	−0.562503	−0.281252	+	0.959634i	$0.590750\pi$
$720$	0	0
$721$	−6.16973e28	−0.0605265
$722$	−3.53729e29	−0.342003
$723$	0	0
$724$	−3.18879e29	−0.299482
$725$	−1.87000e28	−0.0173098
$726$	0	0
$727$	−1.43096e29	−0.128681	−0.0643407	−	0.997928i	$-0.520494\pi$
$727$	−1.43096e29	−0.128681	−0.0643407	+	0.997928i	$0.520494\pi$
$728$	−3.19902e28	−0.0283556
$729$	0	0
$730$	2.94247e30	2.53409
$731$	4.87003e29	0.413428
$732$	0	0
$733$	−6.81141e29	−0.561882	−0.280941	−	0.959725i	$-0.590647\pi$
$733$	−6.81141e29	−0.561882	−0.280941	+	0.959725i	$0.590647\pi$
$734$	−1.12239e30	−0.912714
$735$	0	0
$736$	1.55999e30	1.23283
$737$	2.18328e30	1.70099
$738$	0	0
$739$	2.16993e30	1.64315	0.821577	−	0.570097i	$-0.193094\pi$
$739$	2.16993e30	1.64315	0.821577	+	0.570097i	$0.193094\pi$
$740$	−1.12689e30	−0.841295
$741$	0	0
$742$	4.02214e28	0.0291888
$743$	1.40097e29	0.100241	0.0501206	−	0.998743i	$-0.484039\pi$
$743$	1.40097e29	0.100241	0.0501206	+	0.998743i	$0.484039\pi$
$744$	0	0
$745$	7.67196e29	0.533661
$746$	3.38199e30	2.31960
$747$	0	0
$748$	−7.89939e29	−0.526777
$749$	−2.75883e27	−0.00181412
$750$	0	0
$751$	8.06099e29	0.515429	0.257715	−	0.966221i	$-0.417031\pi$
$751$	8.06099e29	0.515429	0.257715	+	0.966221i	$0.417031\pi$
$752$	2.09469e30	1.32079
$753$	0	0
$754$	−1.47656e30	−0.905427
$755$	8.08901e29	0.489162
$756$	0	0
$757$	−1.54959e30	−0.911401	−0.455700	−	0.890133i	$-0.650611\pi$
$757$	−1.54959e30	−0.911401	−0.455700	+	0.890133i	$0.650611\pi$
$758$	−2.10885e30	−1.22326
$759$	0	0
$760$	5.67003e29	0.319921
$761$	−2.04061e29	−0.113559	−0.0567793	−	0.998387i	$-0.518083\pi$
$761$	−2.04061e29	−0.113559	−0.0567793	+	0.998387i	$0.518083\pi$
$762$	0	0
$763$	−2.74940e28	−0.0148843
$764$	7.64280e29	0.408105
$765$	0	0
$766$	−4.57307e30	−2.37578
$767$	−4.04770e30	−2.07423
$768$	0	0
$769$	1.27880e30	0.637641	0.318821	−	0.947815i	$-0.396713\pi$
$769$	1.27880e30	0.637641	0.318821	+	0.947815i	$0.396713\pi$
$770$	−3.30511e29	−0.162567
$771$	0	0
$772$	2.14944e30	1.02883
$773$	−3.43774e30	−1.62326	−0.811630	−	0.584172i	$-0.801419\pi$
$773$	−3.43774e30	−1.62326	−0.811630	+	0.584172i	$0.801419\pi$
$774$	0	0
$775$	5.41701e28	0.0248938
$776$	3.94216e29	0.178725
$777$	0	0
$778$	−5.27439e30	−2.32748
$779$	−6.67206e29	−0.290480
$780$	0	0
$781$	1.17784e30	0.499172
$782$	−1.10342e30	−0.461392
$783$	0	0
$784$	2.85112e30	1.16064
$785$	2.09822e30	0.842792
$786$	0	0
$787$	1.06317e30	0.415784	0.207892	−	0.978152i	$-0.433340\pi$
$787$	1.06317e30	0.415784	0.207892	+	0.978152i	$0.433340\pi$
$788$	−3.41176e30	−1.31660
$789$	0	0
$790$	−9.16357e29	−0.344334
$791$	2.18423e29	0.0809925
$792$	0	0
$793$	−1.56591e30	−0.565456
$794$	4.26517e30	1.51992
$795$	0	0
$796$	8.86572e28	0.0307699
$797$	2.59470e30	0.888742	0.444371	−	0.895843i	$-0.353427\pi$
$797$	2.59470e30	0.888742	0.444371	+	0.895843i	$0.353427\pi$
$798$	0	0
$799$	−1.21572e30	−0.405595
$800$	1.57423e29	0.0518349
$801$	0	0
$802$	5.07160e30	1.62672
$803$	−1.09139e31	−3.45516
$804$	0	0
$805$	−2.03876e29	−0.0628795
$806$	4.27730e30	1.30212
$807$	0	0
$808$	−1.49305e29	−0.0442848
$809$	4.54632e30	1.33107	0.665534	−	0.746367i	$-0.268204\pi$
$809$	4.54632e30	1.33107	0.665534	+	0.746367i	$0.268204\pi$
$810$	0	0
$811$	−5.33885e30	−1.52310	−0.761550	−	0.648106i	$-0.775561\pi$
$811$	−5.33885e30	−1.52310	−0.761550	+	0.648106i	$0.775561\pi$
$812$	−7.67867e28	−0.0216246
$813$	0	0
$814$	9.46493e30	2.59753
$815$	4.02658e30	1.09089
$816$	0	0
$817$	−4.90243e30	−1.29443
$818$	1.72957e30	0.450847
$819$	0	0
$820$	−8.23105e29	−0.209127
$821$	6.77652e30	1.69982	0.849911	−	0.526926i	$-0.176656\pi$
$821$	6.77652e30	1.69982	0.849911	+	0.526926i	$0.176656\pi$
$822$	0	0
$823$	2.32096e30	0.567506	0.283753	−	0.958897i	$-0.408420\pi$
$823$	2.32096e30	0.567506	0.283753	+	0.958897i	$0.408420\pi$
$824$	−1.09672e30	−0.264766
$825$	0	0
$826$	−4.76661e29	−0.112181
$827$	−3.93890e30	−0.915307	−0.457654	−	0.889131i	$-0.651310\pi$
$827$	−3.93890e30	−0.915307	−0.457654	+	0.889131i	$0.651310\pi$
$828$	0	0
$829$	3.15777e30	0.715415	0.357708	−	0.933834i	$-0.383558\pi$
$829$	3.15777e30	0.715415	0.357708	+	0.933834i	$0.383558\pi$
$830$	−4.78303e30	−1.07000
$831$	0	0
$832$	3.97105e30	0.866184
$833$	−1.65474e30	−0.356416
$834$	0	0
$835$	8.28463e29	0.174006
$836$	7.95194e30	1.64933
$837$	0	0
$838$	−4.81074e30	−0.973082
$839$	1.71221e28	0.00342024	0.00171012	−	0.999999i	$-0.499456\pi$
$839$	1.71221e28	0.00342024	0.00171012	+	0.999999i	$0.499456\pi$
$840$	0	0
$841$	−4.19549e30	−0.817381
$842$	−7.94168e30	−1.52804
$843$	0	0
$844$	−5.24327e30	−0.984026
$845$	−8.29177e30	−1.53692
$846$	0	0
$847$	8.72016e29	0.157670
$848$	2.22453e30	0.397266
$849$	0	0
$850$	−1.11349e29	−0.0193994
$851$	5.83845e30	1.00470
$852$	0	0
$853$	2.27930e30	0.382680	0.191340	−	0.981524i	$-0.438717\pi$
$853$	2.27930e30	0.382680	0.191340	+	0.981524i	$0.438717\pi$
$854$	−1.84403e29	−0.0305816
$855$	0	0
$856$	−4.90406e28	−0.00793563
$857$	1.06629e31	1.70441	0.852207	−	0.523204i	$-0.175263\pi$
$857$	1.06629e31	1.70441	0.852207	+	0.523204i	$0.175263\pi$
$858$	0	0
$859$	−8.93547e29	−0.139376	−0.0696882	−	0.997569i	$-0.522200\pi$
$859$	−8.93547e29	−0.139376	−0.0696882	+	0.997569i	$0.522200\pi$
$860$	−6.04793e30	−0.931908
$861$	0	0
$862$	−9.49196e30	−1.42735
$863$	−2.82417e30	−0.419543	−0.209772	−	0.977750i	$-0.567272\pi$
$863$	−2.82417e30	−0.419543	−0.209772	+	0.977750i	$0.567272\pi$
$864$	0	0
$865$	5.75567e30	0.834501
$866$	3.99448e30	0.572167
$867$	0	0
$868$	2.22435e29	0.0310990
$869$	3.39886e30	0.469490
$870$	0	0
$871$	1.07312e31	1.44696
$872$	−4.88730e29	−0.0651097
$873$	0	0
$874$	1.11076e31	1.44461
$875$	4.87342e29	0.0626253
$876$	0	0
$877$	9.06575e30	1.13739	0.568693	−	0.822550i	$-0.307449\pi$
$877$	9.06575e30	1.13739	0.568693	+	0.822550i	$0.307449\pi$
$878$	−1.94490e31	−2.41104
$879$	0	0
$880$	−1.82796e31	−2.21258
$881$	−1.51630e31	−1.81359	−0.906794	−	0.421574i	$-0.861478\pi$
$881$	−1.51630e31	−1.81359	−0.906794	+	0.421574i	$0.861478\pi$
$882$	0	0
$883$	−1.16543e31	−1.36113	−0.680565	−	0.732688i	$-0.738265\pi$
$883$	−1.16543e31	−1.36113	−0.680565	+	0.732688i	$0.738265\pi$
$884$	−3.88267e30	−0.448107
$885$	0	0
$886$	8.20424e30	0.924664
$887$	7.76908e30	0.865309	0.432655	−	0.901560i	$-0.357577\pi$
$887$	7.76908e30	0.865309	0.432655	+	0.901560i	$0.357577\pi$
$888$	0	0
$889$	8.84384e29	0.0961994
$890$	3.31179e29	0.0356014
$891$	0	0
$892$	−5.15174e30	−0.540907
$893$	1.22381e31	1.26991
$894$	0	0
$895$	−7.46605e30	−0.756744
$896$	−3.49740e29	−0.0350357
$897$	0	0
$898$	−1.30702e31	−1.27903
$899$	−2.71532e30	−0.262630
$900$	0	0
$901$	−1.29108e30	−0.121995
$902$	6.91340e30	0.645688
$903$	0	0
$904$	3.88266e30	0.354292
$905$	4.28265e30	0.386280
$906$	0	0
$907$	5.71533e30	0.503692	0.251846	−	0.967767i	$-0.418962\pi$
$907$	5.71533e30	0.503692	0.251846	+	0.967767i	$0.418962\pi$
$908$	3.39800e30	0.296021
$909$	0	0
$910$	−1.62451e30	−0.138289
$911$	−2.22259e30	−0.187032	−0.0935160	−	0.995618i	$-0.529811\pi$
$911$	−2.22259e30	−0.187032	−0.0935160	+	0.995618i	$0.529811\pi$
$912$	0	0
$913$	1.77408e31	1.45891
$914$	2.20581e31	1.79322
$915$	0	0
$916$	6.84342e30	0.543714
$917$	5.99171e29	0.0470623
$918$	0	0
$919$	−9.94638e30	−0.763576	−0.381788	−	0.924250i	$-0.624692\pi$
$919$	−9.94638e30	−0.763576	−0.381788	+	0.924250i	$0.624692\pi$
$920$	−3.62408e30	−0.275059
$921$	0	0
$922$	1.20962e31	0.897378
$923$	5.78926e30	0.424624
$924$	0	0
$925$	5.89175e29	0.0422431
$926$	4.49324e30	0.318526
$927$	0	0
$928$	−7.89093e30	−0.546858
$929$	−6.57341e30	−0.450429	−0.225214	−	0.974309i	$-0.572308\pi$
$929$	−6.57341e30	−0.450429	−0.225214	+	0.974309i	$0.572308\pi$
$930$	0	0
$931$	1.66575e31	1.11593
$932$	−5.69320e30	−0.377128
$933$	0	0
$934$	−1.83688e30	−0.118970
$935$	1.06091e31	0.679452
$936$	0	0
$937$	−9.88672e30	−0.619137	−0.309568	−	0.950877i	$-0.600185\pi$
$937$	−9.88672e30	−0.619137	−0.309568	+	0.950877i	$0.600185\pi$
$938$	1.26371e30	0.0782561
$939$	0	0
$940$	1.50976e31	0.914253
$941$	−1.35253e31	−0.809947	−0.404973	−	0.914328i	$-0.632719\pi$
$941$	−1.35253e31	−0.809947	−0.404973	+	0.914328i	$0.632719\pi$
$942$	0	0
$943$	4.26454e30	0.249746
$944$	−2.63627e31	−1.52681
$945$	0	0
$946$	5.07976e31	2.87731
$947$	2.26830e31	1.27065	0.635325	−	0.772245i	$-0.280866\pi$
$947$	2.26830e31	1.27065	0.635325	+	0.772245i	$0.280866\pi$
$948$	0	0
$949$	−5.36437e31	−2.93916
$950$	1.12090e30	0.0607392
$951$	0	0
$952$	1.20924e29	0.00640952
$953$	−3.45875e31	−1.81319	−0.906595	−	0.422002i	$-0.861327\pi$
$953$	−3.45875e31	−1.81319	−0.906595	+	0.422002i	$0.861327\pi$
$954$	0	0
$955$	−1.02645e31	−0.526386
$956$	−1.37516e31	−0.697501
$957$	0	0
$958$	−3.43011e31	−1.70204
$959$	−1.83667e30	−0.0901438
$960$	0	0
$961$	−1.29598e31	−0.622304
$962$	4.65216e31	2.20961
$963$	0	0
$964$	−2.16480e31	−1.00602
$965$	−2.88678e31	−1.32702
$966$	0	0
$967$	−1.92820e31	−0.867311	−0.433655	−	0.901079i	$-0.642776\pi$
$967$	−1.92820e31	−0.867311	−0.433655	+	0.901079i	$0.642776\pi$
$968$	1.55009e31	0.689707
$969$	0	0
$970$	2.00189e31	0.871638
$971$	2.95793e31	1.27405	0.637024	−	0.770844i	$-0.280165\pi$
$971$	2.95793e31	1.27405	0.637024	+	0.770844i	$0.280165\pi$
$972$	0	0
$973$	−4.58530e29	−0.0193278
$974$	−3.86058e31	−1.60984
$975$	0	0
$976$	−1.01988e31	−0.416222
$977$	−4.86581e31	−1.96455	−0.982274	−	0.187453i	$-0.939977\pi$
$977$	−4.86581e31	−1.96455	−0.982274	+	0.187453i	$0.939977\pi$
$978$	0	0
$979$	−1.22838e30	−0.0485415
$980$	2.05497e31	0.803398
$981$	0	0
$982$	−1.10703e31	−0.423633
$983$	−4.31738e31	−1.63459	−0.817294	−	0.576220i	$-0.804527\pi$
$983$	−4.31738e31	−1.63459	−0.817294	+	0.576220i	$0.804527\pi$
$984$	0	0
$985$	4.58211e31	1.69819
$986$	5.58146e30	0.204664
$987$	0	0
$988$	3.90850e31	1.40301
$989$	3.13345e31	1.11292
$990$	0	0
$991$	3.44591e31	1.19820	0.599101	−	0.800673i	$-0.295525\pi$
$991$	3.44591e31	1.19820	0.599101	+	0.800673i	$0.295525\pi$
$992$	2.28584e31	0.786453
$993$	0	0
$994$	6.81748e29	0.0229650
$995$	−1.19070e30	−0.0396880
$996$	0	0
$997$	3.62353e31	1.18259	0.591293	−	0.806457i	$-0.298618\pi$
$997$	3.62353e31	1.18259	0.591293	+	0.806457i	$0.298618\pi$
$998$	2.26804e31	0.732452
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.22.a.e.1.1		2
3.2	odd	2		3.22.a.c.1.2	✓	2
12.11	even	2		48.22.a.g.1.2		2
15.2	even	4		75.22.b.d.49.4		4
15.8	even	4		75.22.b.d.49.1		4
15.14	odd	2		75.22.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.c.1.2	✓	2	3.2	odd	2
9.22.a.e.1.1		2	1.1	even	1	trivial
48.22.a.g.1.2		2	12.11	even	2
75.22.a.d.1.1		2	15.14	odd	2
75.22.b.d.49.1		4	15.8	even	4
75.22.b.d.49.4		4	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-1937.96 q^{2} +1.65852e6 q^{4} -2.22745e7 q^{5} +4.78205e7 q^{7} +8.50053e8 q^{8} +O(q^{10})\)	\(q-1937.96 q^{2} +1.65852e6 q^{4} -2.22745e7 q^{5} +4.78205e7 q^{7} +8.50053e8 q^{8} +4.31669e10 q^{10} -1.60111e11 q^{11} -7.86968e11 q^{13} -9.26741e10 q^{14} -5.12553e12 q^{16} +2.97477e12 q^{17} -2.99456e13 q^{19} -3.69426e13 q^{20} +3.10287e14 q^{22} +1.91401e14 q^{23} +1.93148e13 q^{25} +1.52511e15 q^{26} +7.93112e13 q^{28} -9.68170e14 q^{29} +2.80459e15 q^{31} +8.15035e15 q^{32} -5.76496e15 q^{34} -1.06518e15 q^{35} +3.05038e16 q^{37} +5.80331e16 q^{38} -1.89345e16 q^{40} +2.22806e16 q^{41} +1.63711e17 q^{43} -2.65546e17 q^{44} -3.70927e17 q^{46} -4.08678e17 q^{47} -5.56259e17 q^{49} -3.74313e16 q^{50} -1.30520e18 q^{52} -4.34009e17 q^{53} +3.56638e18 q^{55} +4.06500e16 q^{56} +1.87627e18 q^{58} +5.14341e18 q^{59} +1.98980e18 q^{61} -5.43517e18 q^{62} -5.04601e18 q^{64} +1.75293e19 q^{65} -1.36361e19 q^{67} +4.93370e18 q^{68} +2.06427e18 q^{70} -7.35641e18 q^{71} +6.81650e19 q^{73} -5.91149e19 q^{74} -4.96652e19 q^{76} -7.65658e18 q^{77} -2.12282e19 q^{79} +1.14168e20 q^{80} -4.31789e19 q^{82} -1.10803e20 q^{83} -6.62613e19 q^{85} -3.17266e20 q^{86} -1.36102e20 q^{88} +7.67205e18 q^{89} -3.76333e19 q^{91} +3.17442e20 q^{92} +7.92000e20 q^{94} +6.67021e20 q^{95} +4.63755e20 q^{97} +1.07801e21 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 666 q^{2} + 1179236 q^{4} - 996876 q^{5} + 679896112 q^{7} - 2427055848 q^{8}+O(q^{10}) \) 2 * q - 666 * q^2 + 1179236 * q^4 - 996876 * q^5 + 679896112 * q^7 - 2427055848 * q^8	\( 2 q - 666 q^{2} + 1179236 q^{4} - 996876 q^{5} + 679896112 q^{7} - 2427055848 q^{8} + 70231066524 q^{10} - 219869122968 q^{11} - 48468909956 q^{13} + 711297706896 q^{14} - 8288736440560 q^{16} + 11333529041436 q^{17} + 11960585011624 q^{19} - 47140581172824 q^{20} + 234277148563128 q^{22} + 146508390063504 q^{23} - 4786354247074 q^{25} + 24\!\cdots\!16 q^{26}+ \cdots + 87\!\cdots\!14 q^{98}+O(q^{100}) \) 2 * q - 666 * q^2 + 1179236 * q^4 - 996876 * q^5 + 679896112 * q^7 - 2427055848 * q^8 + 70231066524 * q^10 - 219869122968 * q^11 - 48468909956 * q^13 + 711297706896 * q^14 - 8288736440560 * q^16 + 11333529041436 * q^17 + 11960585011624 * q^19 - 47140581172824 * q^20 + 234277148563128 * q^22 + 146508390063504 * q^23 - 4786354247074 * q^25 + 2464447363969716 * q^26 - 223631286954656 * q^28 + 1798520043674052 * q^29 + 11169107526944992 * q^31 + 10999491515934048 * q^32 + 4867007487413652 * q^34 + 12383869767948000 * q^35 + 12736264858660012 * q^37 + 111335877667820664 * q^38 - 88663459120547472 * q^40 - 122972020616468052 * q^41 + 288455418162270040 * q^43 - 236905239135592368 * q^44 - 428027981395161168 * q^46 - 837243745741596960 * q^47 - 715285396941470670 * q^49 - 68086886042031174 * q^50 - 1659150748242045896 * q^52 + 43007964012775764 * q^53 + 2294863118895313296 * q^55 - 2030730320050568640 * q^56 + 5395375030104291852 * q^58 + 3523823330903857224 * q^59 - 1779023128451013860 * q^61 + 5204128043677477536 * q^62 + 5211692013463482944 * q^64 + 33242791066177513752 * q^65 - 16454068667621610296 * q^67 + 927498335984326008 * q^68 + 19170849981674109600 * q^70 - 17379227131150420944 * q^71 + 50891146268473989076 * q^73 - 81714426393675287484 * q^74 - 69750112936092790064 * q^76 - 45428450983816025664 * q^77 - 54055785594190591040 * q^79 + 46862985896348738976 * q^80 - 227933719179803895996 * q^82 - 111108429277666677288 * q^83 + 111593012278262968152 * q^85 - 158596867265246585208 * q^86 + 59732519594715541728 * q^88 - 226920767965448065524 * q^89 + 429154174685185000352 * q^91 + 338958281810136649248 * q^92 + 246883115968835119776 * q^94 + 1558683223531725831696 * q^95 - 128331469252795746236 * q^97 + 875730737371150330614 * q^98

Introduction

L-functions

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Groups

Database

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