LMFDB - Embedded newform 9.22.a.e.1.2

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			1.2
Root			$-12.2377$ 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)

$f(q)$	$=$	$q+1271.96 q^{2} -479282. q^{4} +2.12776e7 q^{5} +6.32076e8 q^{7} -3.27711e9 q^{8} +O(q^{10})$	\(q+1271.96 q^{2} -479282. q^{4} +2.12776e7 q^{5} +6.32076e8 q^{7} -3.27711e9 q^{8} +2.70641e10 q^{10} -5.97585e10 q^{11} +7.38499e11 q^{13} +8.03972e11 q^{14} -3.16321e12 q^{16} +8.35876e12 q^{17} +4.19061e13 q^{19} -1.01980e13 q^{20} -7.60101e13 q^{22} -4.48926e13 q^{23} -2.41012e13 q^{25} +9.39338e14 q^{26} -3.02943e14 q^{28} +2.76669e15 q^{29} +8.36452e15 q^{31} +2.84914e15 q^{32} +1.06320e16 q^{34} +1.34490e16 q^{35} -1.77675e16 q^{37} +5.33027e16 q^{38} -6.97290e16 q^{40} -1.45253e17 q^{41} +1.24744e17 q^{43} +2.86412e16 q^{44} -5.71014e16 q^{46} -4.28566e17 q^{47} -1.59026e17 q^{49} -3.06556e16 q^{50} -3.53950e17 q^{52} +4.77017e17 q^{53} -1.27152e18 q^{55} -2.07138e18 q^{56} +3.51911e18 q^{58} -1.61959e18 q^{59} -3.76882e18 q^{61} +1.06393e19 q^{62} +1.02577e19 q^{64} +1.57135e19 q^{65} -2.81797e18 q^{67} -4.00621e18 q^{68} +1.71066e19 q^{70} -1.00228e19 q^{71} -1.72739e19 q^{73} -2.25995e19 q^{74} -2.00849e19 q^{76} -3.77719e19 q^{77} -3.28276e19 q^{79} -6.73054e19 q^{80} -1.84755e20 q^{82} -3.05240e17 q^{83} +1.77854e20 q^{85} +1.58669e20 q^{86} +1.95835e20 q^{88} -2.34593e20 q^{89} +4.66787e20 q^{91} +2.15162e19 q^{92} -5.45116e20 q^{94} +8.91662e20 q^{95} -5.92086e20 q^{97} -2.02274e20 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1271.96	0.878328	0.439164	−	0.898407i	$-0.355275\pi$
$2$	1271.96	0.878328	0.439164	+	0.898407i	$0.355275\pi$
$3$	0	0
$3$	0	0
$4$	−479282.	−0.228540
$5$	2.12776e7	0.974400	0.487200	−	0.873290i	$-0.338018\pi$
$5$	2.12776e7	0.974400	0.487200	+	0.873290i	$0.338018\pi$
$6$	0	0
$7$	6.32076e8	0.845745	0.422873	−	0.906189i	$-0.361022\pi$
$7$	6.32076e8	0.845745	0.422873	+	0.906189i	$0.361022\pi$
$8$	−3.27711e9	−1.07906
$9$	0	0
$10$	2.70641e10	0.855843
$11$	−5.97585e10	−0.694666	−0.347333	−	0.937742i	$-0.612913\pi$
$11$	−5.97585e10	−0.694666	−0.347333	+	0.937742i	$0.612913\pi$
$12$	0	0
$13$	7.38499e11	1.48575	0.742874	−	0.669432i	$-0.233462\pi$
$13$	7.38499e11	1.48575	0.742874	+	0.669432i	$0.233462\pi$
$14$	8.03972e11	0.742842
$15$	0	0
$16$	−3.16321e12	−0.719230
$17$	8.35876e12	1.00561	0.502804	−	0.864401i	$-0.332302\pi$
$17$	8.35876e12	1.00561	0.502804	+	0.864401i	$0.332302\pi$
$18$	0	0
$19$	4.19061e13	1.56807	0.784034	−	0.620718i	$-0.213159\pi$
$19$	4.19061e13	1.56807	0.784034	+	0.620718i	$0.213159\pi$
$20$	−1.01980e13	−0.222689
$21$	0	0
$22$	−7.60101e13	−0.610145
$23$	−4.48926e13	−0.225961	−0.112980	−	0.993597i	$-0.536040\pi$
$23$	−4.48926e13	−0.225961	−0.112980	+	0.993597i	$0.536040\pi$
$24$	0	0
$25$	−2.41012e13	−0.0505438
$26$	9.39338e14	1.30497
$27$	0	0
$28$	−3.02943e14	−0.193286
$29$	2.76669e15	1.22119	0.610593	−	0.791945i	$-0.290931\pi$
$29$	2.76669e15	1.22119	0.610593	+	0.791945i	$0.290931\pi$
$30$	0	0
$31$	8.36452e15	1.83292	0.916459	−	0.400128i	$-0.131034\pi$
$31$	8.36452e15	1.83292	0.916459	+	0.400128i	$0.131034\pi$
$32$	2.84914e15	0.447341
$33$	0	0
$34$	1.06320e16	0.883253
$35$	1.34490e16	0.824095
$36$	0	0
$37$	−1.77675e16	−0.607447	−0.303724	−	0.952760i	$-0.598230\pi$
$37$	−1.77675e16	−0.607447	−0.303724	+	0.952760i	$0.598230\pi$
$38$	5.33027e16	1.37728
$39$	0	0
$40$	−6.97290e16	−1.05144
$41$	−1.45253e17	−1.69003	−0.845013	−	0.534745i	$-0.820408\pi$
$41$	−1.45253e17	−1.69003	−0.845013	+	0.534745i	$0.820408\pi$
$42$	0	0
$43$	1.24744e17	0.880239	0.440119	−	0.897939i	$-0.354936\pi$
$43$	1.24744e17	0.880239	0.440119	+	0.897939i	$0.354936\pi$
$44$	2.86412e16	0.158759
$45$	0	0
$46$	−5.71014e16	−0.198468
$47$	−4.28566e17	−1.18847	−0.594237	−	0.804290i	$-0.702546\pi$
$47$	−4.28566e17	−1.18847	−0.594237	+	0.804290i	$0.702546\pi$
$48$	0	0
$49$	−1.59026e17	−0.284715
$50$	−3.06556e16	−0.0443941
$51$	0	0
$52$	−3.53950e17	−0.339552
$53$	4.77017e17	0.374660	0.187330	−	0.982297i	$-0.440017\pi$
$53$	4.77017e17	0.374660	0.187330	+	0.982297i	$0.440017\pi$
$54$	0	0
$55$	−1.27152e18	−0.676883
$56$	−2.07138e18	−0.912611
$57$	0	0
$58$	3.51911e18	1.07260
$59$	−1.61959e18	−0.412533	−0.206267	−	0.978496i	$-0.566131\pi$
$59$	−1.61959e18	−0.412533	−0.206267	+	0.978496i	$0.566131\pi$
$60$	0	0
$61$	−3.76882e18	−0.676461	−0.338230	−	0.941063i	$-0.609828\pi$
$61$	−3.76882e18	−0.676461	−0.338230	+	0.941063i	$0.609828\pi$
$62$	1.06393e19	1.60990
$63$	0	0
$64$	1.02577e19	1.11214
$65$	1.57135e19	1.44771
$66$	0	0
$67$	−2.81797e18	−0.188865	−0.0944324	−	0.995531i	$-0.530104\pi$
$67$	−2.81797e18	−0.188865	−0.0944324	+	0.995531i	$0.530104\pi$
$68$	−4.00621e18	−0.229821
$69$	0	0
$70$	1.71066e19	0.723826
$71$	−1.00228e19	−0.365407	−0.182704	−	0.983168i	$-0.558485\pi$
$71$	−1.00228e19	−0.365407	−0.182704	+	0.983168i	$0.558485\pi$
$72$	0	0
$73$	−1.72739e19	−0.470435	−0.235218	−	0.971943i	$-0.575580\pi$
$73$	−1.72739e19	−0.470435	−0.235218	+	0.971943i	$0.575580\pi$
$74$	−2.25995e19	−0.533538
$75$	0	0
$76$	−2.00849e19	−0.358365
$77$	−3.77719e19	−0.587511
$78$	0	0
$79$	−3.28276e19	−0.390080	−0.195040	−	0.980795i	$-0.562484\pi$
$79$	−3.28276e19	−0.390080	−0.195040	+	0.980795i	$0.562484\pi$
$80$	−6.73054e19	−0.700818
$81$	0	0
$82$	−1.84755e20	−1.48440
$83$	−3.05240e17	−0.00215934	−0.00107967	−	0.999999i	$-0.500344\pi$
$83$	−3.05240e17	−0.00215934	−0.00107967	+	0.999999i	$0.500344\pi$
$84$	0	0
$85$	1.77854e20	0.979864
$86$	1.58669e20	0.773139
$87$	0	0
$88$	1.95835e20	0.749587
$89$	−2.34593e20	−0.797480	−0.398740	−	0.917064i	$-0.630552\pi$
$89$	−2.34593e20	−0.797480	−0.398740	+	0.917064i	$0.630552\pi$
$90$	0	0
$91$	4.66787e20	1.25656
$92$	2.15162e19	0.0516409
$93$	0	0
$94$	−5.45116e20	−1.04387
$95$	8.91662e20	1.52793
$96$	0	0
$97$	−5.92086e20	−0.815233	−0.407616	−	0.913153i	$-0.633640\pi$
$97$	−5.92086e20	−0.815233	−0.407616	+	0.913153i	$0.633640\pi$
$98$	−2.02274e20	−0.250073
$99$	0	0
$100$	1.15513e19	0.0115513
$101$	1.66229e21	1.49739	0.748693	−	0.662917i	$-0.230682\pi$
$101$	1.66229e21	1.49739	0.748693	+	0.662917i	$0.230682\pi$
$102$	0	0
$103$	1.17919e21	0.864552	0.432276	−	0.901741i	$-0.357711\pi$
$103$	1.17919e21	0.864552	0.432276	+	0.901741i	$0.357711\pi$
$104$	−2.42014e21	−1.60321
$105$	0	0
$106$	6.06745e20	0.329075
$107$	8.69160e20	0.427140	0.213570	−	0.976928i	$-0.431491\pi$
$107$	8.69160e20	0.427140	0.213570	+	0.976928i	$0.431491\pi$
$108$	0	0
$109$	4.12021e20	0.166702	0.0833510	−	0.996520i	$-0.473438\pi$
$109$	4.12021e20	0.166702	0.0833510	+	0.996520i	$0.473438\pi$
$110$	−1.61731e21	−0.594526
$111$	0	0
$112$	−1.99939e21	−0.608286
$113$	−2.45943e21	−0.681569	−0.340785	−	0.940141i	$-0.610693\pi$
$113$	−2.45943e21	−0.681569	−0.340785	+	0.940141i	$0.610693\pi$
$114$	0	0
$115$	−9.55207e20	−0.220176
$116$	−1.32602e21	−0.279089
$117$	0	0
$118$	−2.06005e21	−0.362340
$119$	5.28337e21	0.850487
$120$	0	0
$121$	−3.82917e21	−0.517439
$122$	−4.79378e21	−0.594155
$123$	0	0
$124$	−4.00896e21	−0.418894
$125$	−1.06588e22	−1.02365
$126$	0	0
$127$	5.53783e21	0.450195	0.225097	−	0.974336i	$-0.427730\pi$
$127$	5.53783e21	0.450195	0.225097	+	0.974336i	$0.427730\pi$
$128$	7.07226e21	0.529485
$129$	0	0
$130$	1.99869e22	1.27157
$131$	2.54630e22	1.49472	0.747362	−	0.664417i	$-0.231320\pi$
$131$	2.54630e22	1.49472	0.747362	+	0.664417i	$0.231320\pi$
$132$	0	0
$133$	2.64878e22	1.32619
$134$	−3.58433e21	−0.165885
$135$	0	0
$136$	−2.73926e22	−1.08511
$137$	4.82088e22	1.76832	0.884158	−	0.467188i	$-0.154733\pi$
$137$	4.82088e22	1.76832	0.884158	+	0.467188i	$0.154733\pi$
$138$	0	0
$139$	−2.18194e22	−0.687363	−0.343682	−	0.939086i	$-0.611674\pi$
$139$	−2.18194e22	−0.687363	−0.343682	+	0.939086i	$0.611674\pi$
$140$	−6.44589e21	−0.188338
$141$	0	0
$142$	−1.27486e22	−0.320948
$143$	−4.41316e22	−1.03210
$144$	0	0
$145$	5.88685e22	1.18992
$146$	−2.19716e22	−0.413197
$147$	0	0
$148$	8.51565e21	0.138826
$149$	−4.84140e22	−0.735386	−0.367693	−	0.929947i	$-0.619852\pi$
$149$	−4.84140e22	−0.735386	−0.367693	+	0.929947i	$0.619852\pi$
$150$	0	0
$151$	−1.22948e23	−1.62354	−0.811770	−	0.583977i	$-0.801496\pi$
$151$	−1.22948e23	−1.62354	−0.811770	+	0.583977i	$0.801496\pi$
$152$	−1.37331e23	−1.69204
$153$	0	0
$154$	−4.80441e22	−0.516027
$155$	1.77977e23	1.78600
$156$	0	0
$157$	5.89828e22	0.517344	0.258672	−	0.965965i	$-0.416715\pi$
$157$	5.89828e22	0.517344	0.258672	+	0.965965i	$0.416715\pi$
$158$	−4.17552e22	−0.342619
$159$	0	0
$160$	6.06228e22	0.435889
$161$	−2.83755e22	−0.191105
$162$	0	0
$163$	−3.18244e22	−0.188274	−0.0941369	−	0.995559i	$-0.530009\pi$
$163$	−3.18244e22	−0.188274	−0.0941369	+	0.995559i	$0.530009\pi$
$164$	6.96170e22	0.386238
$165$	0	0
$166$	−3.88252e20	−0.00189661
$167$	3.62822e22	0.166407	0.0832033	−	0.996533i	$-0.473485\pi$
$167$	3.62822e22	0.166407	0.0832033	+	0.996533i	$0.473485\pi$
$168$	0	0
$169$	2.98317e23	1.20744
$170$	2.26223e23	0.860642
$171$	0	0
$172$	−5.97875e22	−0.201169
$173$	−3.21510e23	−1.01791	−0.508956	−	0.860792i	$-0.669969\pi$
$173$	−3.21510e23	−1.01791	−0.508956	+	0.860792i	$0.669969\pi$
$174$	0	0
$175$	−1.52338e22	−0.0427472
$176$	1.89028e23	0.499625
$177$	0	0
$178$	−2.98392e23	−0.700449
$179$	1.80418e23	0.399321	0.199661	−	0.979865i	$-0.436016\pi$
$179$	1.80418e23	0.399321	0.199661	+	0.979865i	$0.436016\pi$
$180$	0	0
$181$	−6.36646e21	−0.0125393	−0.00626965	−	0.999980i	$-0.501996\pi$
$181$	−6.36646e21	−0.0125393	−0.00626965	+	0.999980i	$0.501996\pi$
$182$	5.93733e23	1.10368
$183$	0	0
$184$	1.47118e23	0.243825
$185$	−3.78050e23	−0.591897
$186$	0	0
$187$	−4.99507e23	−0.698561
$188$	2.05404e23	0.271613
$189$	0	0
$190$	1.13415e24	1.34202
$191$	−8.17882e23	−0.915883	−0.457942	−	0.888982i	$-0.651413\pi$
$191$	−8.17882e23	−0.915883	−0.457942	+	0.888982i	$0.651413\pi$
$192$	0	0
$193$	−1.80064e23	−0.180748	−0.0903742	−	0.995908i	$-0.528806\pi$
$193$	−1.80064e23	−0.180748	−0.0903742	+	0.995908i	$0.528806\pi$
$194$	−7.53107e23	−0.716042
$195$	0	0
$196$	7.62185e22	0.0650686
$197$	−1.65216e24	−1.33708	−0.668541	−	0.743675i	$-0.733081\pi$
$197$	−1.65216e24	−1.33708	−0.668541	+	0.743675i	$0.733081\pi$
$198$	0	0
$199$	−1.52537e24	−1.11024	−0.555120	−	0.831770i	$-0.687328\pi$
$199$	−1.52537e24	−1.11024	−0.555120	+	0.831770i	$0.687328\pi$
$200$	7.89822e22	0.0545399
$201$	0	0
$202$	2.11436e24	1.31520
$203$	1.74876e24	1.03281
$204$	0	0
$205$	−3.09063e24	−1.64676
$206$	1.49987e24	0.759361
$207$	0	0
$208$	−2.33603e24	−1.06859
$209$	−2.50425e24	−1.08928
$210$	0	0
$211$	1.35748e24	0.534277	0.267138	−	0.963658i	$-0.413922\pi$
$211$	1.35748e24	0.534277	0.267138	+	0.963658i	$0.413922\pi$
$212$	−2.28626e23	−0.0856247
$213$	0	0
$214$	1.10553e24	0.375169
$215$	2.65425e24	0.857705
$216$	0	0
$217$	5.28701e24	1.55018
$218$	5.24072e23	0.146419
$219$	0	0
$220$	6.09415e23	0.154695
$221$	6.17294e24	1.49408
$222$	0	0
$223$	4.73192e24	1.04192	0.520962	−	0.853580i	$-0.325573\pi$
$223$	4.73192e24	1.04192	0.520962	+	0.853580i	$0.325573\pi$
$224$	1.80087e24	0.378336
$225$	0	0
$226$	−3.12828e24	−0.598642
$227$	−8.00226e24	−1.46198	−0.730989	−	0.682389i	$-0.760941\pi$
$227$	−8.00226e24	−1.46198	−0.730989	+	0.682389i	$0.760941\pi$
$228$	0	0
$229$	2.72111e24	0.453391	0.226696	−	0.973966i	$-0.427208\pi$
$229$	2.72111e24	0.453391	0.226696	+	0.973966i	$0.427208\pi$
$230$	−1.21498e24	−0.193387
$231$	0	0
$232$	−9.06674e24	−1.31773
$233$	6.60115e24	0.917028	0.458514	−	0.888687i	$-0.348382\pi$
$233$	6.60115e24	0.917028	0.458514	+	0.888687i	$0.348382\pi$
$234$	0	0
$235$	−9.11885e24	−1.15805
$236$	7.76240e23	0.0942801
$237$	0	0
$238$	6.72021e24	0.747007
$239$	−9.92224e24	−1.05544	−0.527718	−	0.849420i	$-0.676952\pi$
$239$	−9.92224e24	−1.05544	−0.527718	+	0.849420i	$0.676952\pi$
$240$	0	0
$241$	−1.54177e25	−1.50259	−0.751295	−	0.659966i	$-0.770571\pi$
$241$	−1.54177e25	−1.50259	−0.751295	+	0.659966i	$0.770571\pi$
$242$	−4.87054e24	−0.454481
$243$	0	0
$244$	1.80633e24	0.154598
$245$	−3.38370e24	−0.277426
$246$	0	0
$247$	3.09477e25	2.32975
$248$	−2.74114e25	−1.97783
$249$	0	0
$250$	−1.35575e25	−0.899101
$251$	1.00009e25	0.636014	0.318007	−	0.948088i	$-0.396986\pi$
$251$	1.00009e25	0.636014	0.318007	+	0.948088i	$0.396986\pi$
$252$	0	0
$253$	2.68271e24	0.156967
$254$	7.04387e24	0.395419
$255$	0	0
$256$	−1.25164e25	−0.647080
$257$	3.06596e25	1.52149	0.760744	−	0.649052i	$-0.224834\pi$
$257$	3.06596e25	1.52149	0.760744	+	0.649052i	$0.224834\pi$
$258$	0	0
$259$	−1.12304e25	−0.513746
$260$	−7.53119e24	−0.330860
$261$	0	0
$262$	3.23878e25	1.31286
$263$	2.33455e25	0.909216	0.454608	−	0.890692i	$-0.349779\pi$
$263$	2.33455e25	0.909216	0.454608	+	0.890692i	$0.349779\pi$
$264$	0	0
$265$	1.01498e25	0.365069
$266$	3.36914e25	1.16483
$267$	0	0
$268$	1.35060e24	0.0431631
$269$	−2.29737e25	−0.706043	−0.353022	−	0.935615i	$-0.614846\pi$
$269$	−2.29737e25	−0.706043	−0.353022	+	0.935615i	$0.614846\pi$
$270$	0	0
$271$	−4.02085e25	−1.14325	−0.571624	−	0.820516i	$-0.693686\pi$
$271$	−4.02085e25	−1.14325	−0.571624	+	0.820516i	$0.693686\pi$
$272$	−2.64405e25	−0.723263
$273$	0	0
$274$	6.13194e25	1.55316
$275$	1.44025e24	0.0351111
$276$	0	0
$277$	−4.48722e25	−1.01377	−0.506886	−	0.862013i	$-0.669203\pi$
$277$	−4.48722e25	−1.01377	−0.506886	+	0.862013i	$0.669203\pi$
$278$	−2.77532e25	−0.603731
$279$	0	0
$280$	−4.40740e25	−0.889248
$281$	6.06489e25	1.17871	0.589355	−	0.807874i	$-0.299382\pi$
$281$	6.06489e25	1.17871	0.589355	+	0.807874i	$0.299382\pi$
$282$	0	0
$283$	1.04229e26	1.88032	0.940158	−	0.340739i	$-0.110677\pi$
$283$	1.04229e26	1.88032	0.940158	+	0.340739i	$0.110677\pi$
$284$	4.80376e24	0.0835100
$285$	0	0
$286$	−5.61334e25	−0.906521
$287$	−9.18107e25	−1.42933
$288$	0	0
$289$	7.76980e23	0.0112456
$290$	7.48781e25	1.04514
$291$	0	0
$292$	8.27907e24	0.107513
$293$	−6.24634e25	−0.782556	−0.391278	−	0.920273i	$-0.627967\pi$
$293$	−6.24634e25	−0.782556	−0.391278	+	0.920273i	$0.627967\pi$
$294$	0	0
$295$	−3.44610e25	−0.401972
$296$	5.82261e25	0.655472
$297$	0	0
$298$	−6.15805e25	−0.645911
$299$	−3.31532e25	−0.335720
$300$	0	0
$301$	7.88476e25	0.744458
$302$	−1.56384e26	−1.42600
$303$	0	0
$304$	−1.32558e26	−1.12780
$305$	−8.01915e25	−0.659144
$306$	0	0
$307$	7.14411e25	0.548271	0.274135	−	0.961691i	$-0.411608\pi$
$307$	7.14411e25	0.548271	0.274135	+	0.961691i	$0.411608\pi$
$308$	1.81034e25	0.134269
$309$	0	0
$310$	2.26379e26	1.56869
$311$	6.01915e25	0.403228	0.201614	−	0.979465i	$-0.435381\pi$
$311$	6.01915e25	0.403228	0.201614	+	0.979465i	$0.435381\pi$
$312$	0	0
$313$	−1.69049e26	−1.05876	−0.529379	−	0.848385i	$-0.677575\pi$
$313$	−1.69049e26	−1.05876	−0.529379	+	0.848385i	$0.677575\pi$
$314$	7.50235e25	0.454398
$315$	0	0
$316$	1.57337e25	0.0891488
$317$	5.71691e25	0.313357	0.156678	−	0.987650i	$-0.449921\pi$
$317$	5.71691e25	0.313357	0.156678	+	0.987650i	$0.449921\pi$
$318$	0	0
$319$	−1.65333e26	−0.848316
$320$	2.18259e26	1.08367
$321$	0	0
$322$	−3.60924e25	−0.167853
$323$	3.50283e26	1.57686
$324$	0	0
$325$	−1.77987e25	−0.0750954
$326$	−4.04792e25	−0.165366
$327$	0	0
$328$	4.76009e26	1.82364
$329$	−2.70886e26	−1.00515
$330$	0	0
$331$	6.67957e25	0.232571	0.116285	−	0.993216i	$-0.462901\pi$
$331$	6.67957e25	0.232571	0.116285	+	0.993216i	$0.462901\pi$
$332$	1.46296e23	0.000493495 0
$333$	0	0
$334$	4.61493e25	0.146160
$335$	−5.99597e25	−0.184030
$336$	0	0
$337$	3.55365e26	1.02461	0.512307	−	0.858802i	$-0.328791\pi$
$337$	3.55365e26	1.02461	0.512307	+	0.858802i	$0.328791\pi$
$338$	3.79446e26	1.06053
$339$	0	0
$340$	−8.52424e25	−0.223938
$341$	−4.99851e26	−1.27327
$342$	0	0
$343$	−4.53560e26	−1.08654
$344$	−4.08799e26	−0.949832
$345$	0	0
$346$	−4.08947e26	−0.894062
$347$	3.94238e25	0.0836179	0.0418090	−	0.999126i	$-0.486688\pi$
$347$	3.94238e25	0.0836179	0.0418090	+	0.999126i	$0.486688\pi$
$348$	0	0
$349$	−5.84299e26	−1.16672	−0.583362	−	0.812212i	$-0.698263\pi$
$349$	−5.84299e26	−1.16672	−0.583362	+	0.812212i	$0.698263\pi$
$350$	−1.93767e25	−0.0375461
$351$	0	0
$352$	−1.70260e26	−0.310753
$353$	−4.96062e26	−0.878823	−0.439412	−	0.898286i	$-0.644813\pi$
$353$	−4.96062e26	−0.878823	−0.439412	+	0.898286i	$0.644813\pi$
$354$	0	0
$355$	−2.13262e26	−0.356053
$356$	1.12436e26	0.182256
$357$	0	0
$358$	2.29483e26	0.350735
$359$	3.35136e26	0.497426	0.248713	−	0.968577i	$-0.419992\pi$
$359$	3.35136e26	0.497426	0.248713	+	0.968577i	$0.419992\pi$
$360$	0	0
$361$	1.04192e27	1.45884
$362$	−8.09785e24	−0.0110136
$363$	0	0
$364$	−2.23723e26	−0.287174
$365$	−3.67547e26	−0.458392
$366$	0	0
$367$	9.70198e25	0.114253	0.0571264	−	0.998367i	$-0.481806\pi$
$367$	9.70198e25	0.114253	0.0571264	+	0.998367i	$0.481806\pi$
$368$	1.42005e26	0.162518
$369$	0	0
$370$	−4.80862e26	−0.519880
$371$	3.01511e26	0.316867
$372$	0	0
$373$	1.03252e27	1.02554	0.512771	−	0.858525i	$-0.328619\pi$
$373$	1.03252e27	1.02554	0.512771	+	0.858525i	$0.328619\pi$
$374$	−6.35350e26	−0.613566
$375$	0	0
$376$	1.40446e27	1.28244
$377$	2.04320e27	1.81437
$378$	0	0
$379$	2.20881e26	0.185544	0.0927721	−	0.995687i	$-0.470427\pi$
$379$	2.20881e26	0.185544	0.0927721	+	0.995687i	$0.470427\pi$
$380$	−4.27358e26	−0.349191
$381$	0	0
$382$	−1.04031e27	−0.804446
$383$	1.59547e27	1.20033	0.600165	−	0.799876i	$-0.295101\pi$
$383$	1.59547e27	1.20033	0.600165	+	0.799876i	$0.295101\pi$
$384$	0	0
$385$	−8.03695e26	−0.572471
$386$	−2.29033e26	−0.158756
$387$	0	0
$388$	2.83776e26	0.186313
$389$	3.60474e26	0.230358	0.115179	−	0.993345i	$-0.463256\pi$
$389$	3.60474e26	0.230358	0.115179	+	0.993345i	$0.463256\pi$
$390$	0	0
$391$	−3.75247e26	−0.227228
$392$	5.21147e26	0.307225
$393$	0	0
$394$	−2.10148e27	−1.17440
$395$	−6.98492e26	−0.380095
$396$	0	0
$397$	−1.47191e27	−0.759595	−0.379798	−	0.925070i	$-0.624006\pi$
$397$	−1.47191e27	−0.759595	−0.379798	+	0.925070i	$0.624006\pi$
$398$	−1.94020e27	−0.975156
$399$	0	0
$400$	7.62370e25	0.0363527
$401$	−1.00401e27	−0.466360	−0.233180	−	0.972434i	$-0.574913\pi$
$401$	−1.00401e27	−0.466360	−0.233180	+	0.972434i	$0.574913\pi$
$402$	0	0
$403$	6.17719e27	2.72325
$404$	−7.96708e26	−0.342212
$405$	0	0
$406$	2.22434e27	0.907148
$407$	1.06176e27	0.421973
$408$	0	0
$409$	−4.41838e27	−1.66789	−0.833947	−	0.551845i	$-0.813924\pi$
$409$	−4.41838e27	−1.66789	−0.833947	+	0.551845i	$0.813924\pi$
$410$	−3.93114e27	−1.44640
$411$	0	0
$412$	−5.65163e26	−0.197584
$413$	−1.02370e27	−0.348898
$414$	0	0
$415$	−6.49477e24	−0.00210406
$416$	2.10409e27	0.664635
$417$	0	0
$418$	−3.18529e27	−0.956749
$419$	2.36639e27	0.693169	0.346584	−	0.938019i	$-0.387341\pi$
$419$	2.36639e27	0.693169	0.346584	+	0.938019i	$0.387341\pi$
$420$	0	0
$421$	2.72067e27	0.758078	0.379039	−	0.925381i	$-0.376255\pi$
$421$	2.72067e27	0.758078	0.379039	+	0.925381i	$0.376255\pi$
$422$	1.72665e27	0.469271
$423$	0	0
$424$	−1.56324e27	−0.404281
$425$	−2.01456e26	−0.0508272
$426$	0	0
$427$	−2.38218e27	−0.572114
$428$	−4.16573e26	−0.0976183
$429$	0	0
$430$	3.37609e27	0.753347
$431$	−8.87397e27	−1.93244	−0.966222	−	0.257713i	$-0.917031\pi$
$431$	−8.87397e27	−1.93244	−0.966222	+	0.257713i	$0.917031\pi$
$432$	0	0
$433$	−3.39994e27	−0.705258	−0.352629	−	0.935763i	$-0.614712\pi$
$433$	−3.39994e27	−0.705258	−0.352629	+	0.935763i	$0.614712\pi$
$434$	6.72484e27	1.36157
$435$	0	0
$436$	−1.97474e26	−0.0380980
$437$	−1.88128e27	−0.354322
$438$	0	0
$439$	2.29516e27	0.412037	0.206018	−	0.978548i	$-0.433949\pi$
$439$	2.29516e27	0.412037	0.206018	+	0.978548i	$0.433949\pi$
$440$	4.16690e27	0.730398
$441$	0	0
$442$	7.85170e27	1.31229
$443$	5.65265e27	0.922599	0.461299	−	0.887245i	$-0.347383\pi$
$443$	5.65265e27	0.922599	0.461299	+	0.887245i	$0.347383\pi$
$444$	0	0
$445$	−4.99157e27	−0.777065
$446$	6.01879e27	0.915152
$447$	0	0
$448$	6.48364e27	0.940589
$449$	−1.23324e28	−1.74768	−0.873839	−	0.486216i	$-0.838377\pi$
$449$	−1.23324e28	−1.74768	−0.873839	+	0.486216i	$0.838377\pi$
$450$	0	0
$451$	8.68008e27	1.17400
$452$	1.17876e27	0.155766
$453$	0	0
$454$	−1.01785e28	−1.28410
$455$	9.93211e27	1.22440
$456$	0	0
$457$	−7.62646e27	−0.897848	−0.448924	−	0.893570i	$-0.648193\pi$
$457$	−7.62646e27	−0.897848	−0.448924	+	0.893570i	$0.648193\pi$
$458$	3.46113e27	0.398226
$459$	0	0
$460$	4.57814e26	0.0503189
$461$	9.04851e26	0.0972114	0.0486057	−	0.998818i	$-0.484522\pi$
$461$	9.04851e26	0.0972114	0.0486057	+	0.998818i	$0.484522\pi$
$462$	0	0
$463$	−1.19705e27	−0.122889	−0.0614443	−	0.998111i	$-0.519571\pi$
$463$	−1.19705e27	−0.122889	−0.0614443	+	0.998111i	$0.519571\pi$
$464$	−8.75161e27	−0.878313
$465$	0	0
$466$	8.39637e27	0.805452
$467$	1.16951e28	1.09693	0.548464	−	0.836174i	$-0.315213\pi$
$467$	1.16951e28	1.09693	0.548464	+	0.836174i	$0.315213\pi$
$468$	0	0
$469$	−1.78117e27	−0.159732
$470$	−1.15988e28	−1.01715
$471$	0	0
$472$	5.30757e27	0.445148
$473$	−7.45451e27	−0.611472
$474$	0	0
$475$	−1.00999e27	−0.0792562
$476$	−2.53222e27	−0.194370
$477$	0	0
$478$	−1.26206e28	−0.927019
$479$	−2.04856e28	−1.47206	−0.736029	−	0.676950i	$-0.763301\pi$
$479$	−2.04856e28	−1.47206	−0.736029	+	0.676950i	$0.763301\pi$
$480$	0	0
$481$	−1.31213e28	−0.902513
$482$	−1.96106e28	−1.31977
$483$	0	0
$484$	1.83525e27	0.118255
$485$	−1.25982e28	−0.794363
$486$	0	0
$487$	−3.75693e27	−0.226871	−0.113436	−	0.993545i	$-0.536186\pi$
$487$	−3.75693e27	−0.226871	−0.113436	+	0.993545i	$0.536186\pi$
$488$	1.23508e28	0.729942
$489$	0	0
$490$	−4.30391e27	−0.243671
$491$	1.53173e28	0.848841	0.424420	−	0.905465i	$-0.360478\pi$
$491$	1.53173e28	0.848841	0.424420	+	0.905465i	$0.360478\pi$
$492$	0	0
$493$	2.31261e28	1.22803
$494$	3.93640e28	2.04629
$495$	0	0
$496$	−2.64587e28	−1.31829
$497$	−6.33518e27	−0.309042
$498$	0	0
$499$	3.84836e27	0.179978	0.0899890	−	0.995943i	$-0.471317\pi$
$499$	3.84836e27	0.179978	0.0899890	+	0.995943i	$0.471317\pi$
$500$	5.10855e27	0.233945
$501$	0	0
$502$	1.27208e28	0.558629
$503$	2.25177e28	0.968411	0.484205	−	0.874954i	$-0.339109\pi$
$503$	2.25177e28	0.968411	0.484205	+	0.874954i	$0.339109\pi$
$504$	0	0
$505$	3.53696e28	1.45905
$506$	3.41229e27	0.137869
$507$	0	0
$508$	−2.65418e27	−0.102887
$509$	−2.09122e27	−0.0794078	−0.0397039	−	0.999211i	$-0.512641\pi$
$509$	−2.09122e27	−0.0794078	−0.0397039	+	0.999211i	$0.512641\pi$
$510$	0	0
$511$	−1.09184e28	−0.397869
$512$	−3.07519e28	−1.09783
$513$	0	0
$514$	3.89976e28	1.33637
$515$	2.50902e28	0.842420
$516$	0	0
$517$	2.56104e28	0.825594
$518$	−1.42846e28	−0.451237
$519$	0	0
$520$	−5.14948e28	−1.56217
$521$	3.76486e27	0.111932	0.0559659	−	0.998433i	$-0.482176\pi$
$521$	3.76486e27	0.111932	0.0559659	+	0.998433i	$0.482176\pi$
$522$	0	0
$523$	−1.74944e28	−0.499611	−0.249806	−	0.968296i	$-0.580367\pi$
$523$	−1.74944e28	−0.499611	−0.249806	+	0.968296i	$0.580367\pi$
$524$	−1.22040e28	−0.341604
$525$	0	0
$526$	2.96944e28	0.798590
$527$	6.99170e28	1.84320
$528$	0	0
$529$	−3.74562e28	−0.948942
$530$	1.29101e28	0.320650
$531$	0	0
$532$	−1.26952e28	−0.303086
$533$	−1.07269e29	−2.51095
$534$	0	0
$535$	1.84936e28	0.416205
$536$	9.23480e27	0.203797
$537$	0	0
$538$	−2.92215e28	−0.620138
$539$	9.50317e27	0.197782
$540$	0	0
$541$	−6.99960e28	−1.40121	−0.700603	−	0.713552i	$-0.747085\pi$
$541$	−6.99960e28	−1.40121	−0.700603	+	0.713552i	$0.747085\pi$
$542$	−5.11434e28	−1.00415
$543$	0	0
$544$	2.38153e28	0.449849
$545$	8.76680e27	0.162434
$546$	0	0
$547$	3.00896e28	0.536476	0.268238	−	0.963353i	$-0.413559\pi$
$547$	3.00896e28	0.536476	0.268238	+	0.963353i	$0.413559\pi$
$548$	−2.31056e28	−0.404130
$549$	0	0
$550$	1.83193e27	0.0308391
$551$	1.15941e29	1.91490
$552$	0	0
$553$	−2.07495e28	−0.329909
$554$	−5.70754e28	−0.890424
$555$	0	0
$556$	1.04576e28	0.157090
$557$	−1.17263e29	−1.72855	−0.864277	−	0.503017i	$-0.832223\pi$
$557$	−1.17263e29	−1.72855	−0.864277	+	0.503017i	$0.832223\pi$
$558$	0	0
$559$	9.21233e28	1.30781
$560$	−4.25421e28	−0.592714
$561$	0	0
$562$	7.71427e28	1.03529
$563$	−6.46986e28	−0.852230	−0.426115	−	0.904669i	$-0.640118\pi$
$563$	−6.46986e28	−0.852230	−0.426115	+	0.904669i	$0.640118\pi$
$564$	0	0
$565$	−5.23307e28	−0.664121
$566$	1.32575e29	1.65153
$567$	0	0
$568$	3.28459e28	0.394297
$569$	1.35009e29	1.59105	0.795527	−	0.605918i	$-0.207194\pi$
$569$	1.35009e29	1.59105	0.795527	+	0.605918i	$0.207194\pi$
$570$	0	0
$571$	2.55750e28	0.290494	0.145247	−	0.989395i	$-0.453602\pi$
$571$	2.55750e28	0.290494	0.145247	+	0.989395i	$0.453602\pi$
$572$	2.11515e28	0.235875
$573$	0	0
$574$	−1.16779e29	−1.25542
$575$	1.08197e27	0.0114209
$576$	0	0
$577$	−1.52580e29	−1.55293	−0.776465	−	0.630160i	$-0.782989\pi$
$577$	−1.52580e29	−1.55293	−0.776465	+	0.630160i	$0.782989\pi$
$578$	9.88284e26	0.00987733
$579$	0	0
$580$	−2.82146e28	−0.271944
$581$	−1.92935e26	−0.00182625
$582$	0	0
$583$	−2.85058e28	−0.260264
$584$	5.66084e28	0.507629
$585$	0	0
$586$	−7.94506e28	−0.687341
$587$	1.08485e29	0.921868	0.460934	−	0.887434i	$-0.347514\pi$
$587$	1.08485e29	0.921868	0.460934	+	0.887434i	$0.347514\pi$
$588$	0	0
$589$	3.50525e29	2.87414
$590$	−4.38328e28	−0.353064
$591$	0	0
$592$	5.62023e28	0.436894
$593$	−8.82363e28	−0.673865	−0.336933	−	0.941529i	$-0.609389\pi$
$593$	−8.82363e28	−0.673865	−0.336933	+	0.941529i	$0.609389\pi$
$594$	0	0
$595$	1.12417e29	0.828715
$596$	2.32040e28	0.168065
$597$	0	0
$598$	−4.21694e28	−0.294873
$599$	−9.23342e28	−0.634426	−0.317213	−	0.948354i	$-0.602747\pi$
$599$	−9.23342e28	−0.634426	−0.317213	+	0.948354i	$0.602747\pi$
$600$	0	0
$601$	−7.30699e28	−0.484793	−0.242397	−	0.970177i	$-0.577934\pi$
$601$	−7.30699e28	−0.484793	−0.242397	+	0.970177i	$0.577934\pi$
$602$	1.00291e29	0.653878
$603$	0	0
$604$	5.89267e28	0.371043
$605$	−8.14756e28	−0.504192
$606$	0	0
$607$	8.07544e28	0.482709	0.241354	−	0.970437i	$-0.422408\pi$
$607$	8.07544e28	0.482709	0.241354	+	0.970437i	$0.422408\pi$
$608$	1.19396e29	0.701461
$609$	0	0
$610$	−1.02000e29	−0.578945
$611$	−3.16496e29	−1.76577
$612$	0	0
$613$	−2.21326e29	−1.19316	−0.596578	−	0.802555i	$-0.703473\pi$
$613$	−2.21326e29	−1.19316	−0.596578	+	0.802555i	$0.703473\pi$
$614$	9.08699e28	0.481562
$615$	0	0
$616$	1.23783e29	0.633960
$617$	2.16026e29	1.08771	0.543854	−	0.839180i	$-0.316965\pi$
$617$	2.16026e29	1.08771	0.543854	+	0.839180i	$0.316965\pi$
$618$	0	0
$619$	−2.09908e29	−1.02159	−0.510795	−	0.859702i	$-0.670649\pi$
$619$	−2.09908e29	−1.02159	−0.510795	+	0.859702i	$0.670649\pi$
$620$	−8.53011e28	−0.408171
$621$	0	0
$622$	7.65609e28	0.354167
$623$	−1.48280e29	−0.674465
$624$	0	0
$625$	−2.15300e29	−0.946901
$626$	−2.15023e29	−0.929938
$627$	0	0
$628$	−2.82694e28	−0.118234
$629$	−1.48514e29	−0.610853
$630$	0	0
$631$	4.81094e28	0.191391	0.0956955	−	0.995411i	$-0.469492\pi$
$631$	4.81094e28	0.191391	0.0956955	+	0.995411i	$0.469492\pi$
$632$	1.07580e29	0.420921
$633$	0	0
$634$	7.27166e28	0.275230
$635$	1.17832e29	0.438670
$636$	0	0
$637$	−1.17441e29	−0.423014
$638$	−2.10296e29	−0.745100
$639$	0	0
$640$	1.50481e29	0.515930
$641$	5.04867e28	0.170282	0.0851408	−	0.996369i	$-0.472866\pi$
$641$	5.04867e28	0.170282	0.0851408	+	0.996369i	$0.472866\pi$
$642$	0	0
$643$	−3.93930e29	−1.28589	−0.642945	−	0.765912i	$-0.722288\pi$
$643$	−3.93930e29	−1.28589	−0.642945	+	0.765912i	$0.722288\pi$
$644$	1.35999e28	0.0436751
$645$	0	0
$646$	4.45545e29	1.38500
$647$	1.38475e29	0.423523	0.211762	−	0.977321i	$-0.432080\pi$
$647$	1.38475e29	0.423523	0.211762	+	0.977321i	$0.432080\pi$
$648$	0	0
$649$	9.67842e28	0.286573
$650$	−2.26392e28	−0.0659584
$651$	0	0
$652$	1.52528e28	0.0430280
$653$	−1.16655e29	−0.323830	−0.161915	−	0.986805i	$-0.551767\pi$
$653$	−1.16655e29	−0.323830	−0.161915	+	0.986805i	$0.551767\pi$
$654$	0	0
$655$	5.41792e29	1.45646
$656$	4.59464e29	1.21552
$657$	0	0
$658$	−3.44555e29	−0.882849
$659$	3.36819e29	0.849377	0.424688	−	0.905340i	$-0.360384\pi$
$659$	3.36819e29	0.849377	0.424688	+	0.905340i	$0.360384\pi$
$660$	0	0
$661$	4.31449e29	1.05394	0.526968	−	0.849885i	$-0.323329\pi$
$661$	4.31449e29	1.05394	0.526968	+	0.849885i	$0.323329\pi$
$662$	8.49612e28	0.204273
$663$	0	0
$664$	1.00030e27	0.00233006
$665$	5.63598e29	1.29224
$666$	0	0
$667$	−1.24204e29	−0.275940
$668$	−1.73894e28	−0.0380305
$669$	0	0
$670$	−7.62660e28	−0.161639
$671$	2.25219e29	0.469915
$672$	0	0
$673$	−1.19710e29	−0.242088	−0.121044	−	0.992647i	$-0.538624\pi$
$673$	−1.19710e29	−0.242088	−0.121044	+	0.992647i	$0.538624\pi$
$674$	4.52008e29	0.899948
$675$	0	0
$676$	−1.42978e29	−0.275949
$677$	−7.71503e29	−1.46608	−0.733038	−	0.680188i	$-0.761898\pi$
$677$	−7.71503e29	−1.46608	−0.733038	+	0.680188i	$0.761898\pi$
$678$	0	0
$679$	−3.74243e29	−0.689479
$680$	−5.82848e29	−1.05733
$681$	0	0
$682$	−6.35788e29	−1.11835
$683$	−6.40488e29	−1.10941	−0.554707	−	0.832046i	$-0.687170\pi$
$683$	−6.40488e29	−1.10941	−0.554707	+	0.832046i	$0.687170\pi$
$684$	0	0
$685$	1.02577e30	1.72305
$686$	−5.76908e29	−0.954340
$687$	0	0
$688$	−3.94591e29	−0.633094
$689$	3.52277e29	0.556650
$690$	0	0
$691$	1.07309e30	1.64482	0.822408	−	0.568898i	$-0.192630\pi$
$691$	1.07309e30	1.64482	0.822408	+	0.568898i	$0.192630\pi$
$692$	1.54094e29	0.232633
$693$	0	0
$694$	5.01454e28	0.0734440
$695$	−4.64263e29	−0.669767
$696$	0	0
$697$	−1.21413e30	−1.69950
$698$	−7.43202e29	−1.02477
$699$	0	0
$700$	7.30127e27	0.00976943
$701$	7.18115e29	0.946574	0.473287	−	0.880908i	$-0.343067\pi$
$701$	7.18115e29	0.946574	0.473287	+	0.880908i	$0.343067\pi$
$702$	0	0
$703$	−7.44568e29	−0.952518
$704$	−6.12985e29	−0.772568
$705$	0	0
$706$	−6.30969e29	−0.771895
$707$	1.05070e30	1.26641
$708$	0	0
$709$	4.24360e29	0.496534	0.248267	−	0.968692i	$-0.420139\pi$
$709$	4.24360e29	0.496534	0.248267	+	0.968692i	$0.420139\pi$
$710$	−2.71259e29	−0.312732
$711$	0	0
$712$	7.68786e29	0.860529
$713$	−3.75505e29	−0.414167
$714$	0	0
$715$	−9.39014e29	−1.00568
$716$	−8.64710e28	−0.0912607
$717$	0	0
$718$	4.26277e29	0.436904
$719$	5.73272e29	0.579038	0.289519	−	0.957172i	$-0.406505\pi$
$719$	5.73272e29	0.579038	0.289519	+	0.957172i	$0.406505\pi$
$720$	0	0
$721$	7.45334e29	0.731191
$722$	1.32527e30	1.28134
$723$	0	0
$724$	3.05133e27	0.00286572
$725$	−6.66805e28	−0.0617234
$726$	0	0
$727$	1.42987e30	1.28583	0.642916	−	0.765937i	$-0.277725\pi$
$727$	1.42987e30	1.28583	0.642916	+	0.765937i	$0.277725\pi$
$728$	−1.52971e30	−1.35591
$729$	0	0
$730$	−4.67503e29	−0.402619
$731$	1.04270e30	0.885175
$732$	0	0
$733$	1.99143e30	1.64276	0.821380	−	0.570381i	$-0.193205\pi$
$733$	1.99143e30	1.64276	0.821380	+	0.570381i	$0.193205\pi$
$734$	1.23405e29	0.100351
$735$	0	0
$736$	−1.27905e29	−0.101081
$737$	1.68398e29	0.131198
$738$	0	0
$739$	−2.11124e30	−1.59872	−0.799359	−	0.600854i	$-0.794827\pi$
$739$	−2.11124e30	−1.59872	−0.799359	+	0.600854i	$0.794827\pi$
$740$	1.81193e29	0.135272
$741$	0	0
$742$	3.83509e29	0.278313
$743$	−1.11538e30	−0.798067	−0.399033	−	0.916936i	$-0.630654\pi$
$743$	−1.11538e30	−0.798067	−0.399033	+	0.916936i	$0.630654\pi$
$744$	0	0
$745$	−1.03013e30	−0.716561
$746$	1.31331e30	0.900763
$747$	0	0
$748$	2.39405e29	0.159649
$749$	5.49375e29	0.361251
$750$	0	0
$751$	−2.28371e30	−1.46023	−0.730116	−	0.683323i	$-0.760534\pi$
$751$	−2.28371e30	−1.46023	−0.730116	+	0.683323i	$0.760534\pi$
$752$	1.35564e30	0.854787
$753$	0	0
$754$	2.59886e30	1.59361
$755$	−2.61603e30	−1.58198
$756$	0	0
$757$	9.73411e29	0.572519	0.286259	−	0.958152i	$-0.407588\pi$
$757$	9.73411e29	0.572519	0.286259	+	0.958152i	$0.407588\pi$
$758$	2.80951e29	0.162969
$759$	0	0
$760$	−2.92207e30	−1.64873
$761$	3.06985e30	1.70836	0.854179	−	0.519979i	$-0.174060\pi$
$761$	3.06985e30	1.70836	0.854179	+	0.519979i	$0.174060\pi$
$762$	0	0
$763$	2.60428e29	0.140987
$764$	3.91996e29	0.209316
$765$	0	0
$766$	2.02936e30	1.05428
$767$	−1.19607e30	−0.612920
$768$	0	0
$769$	−7.51816e29	−0.374874	−0.187437	−	0.982277i	$-0.560018\pi$
$769$	−7.51816e29	−0.374874	−0.187437	+	0.982277i	$0.560018\pi$
$770$	−1.02226e30	−0.502817
$771$	0	0
$772$	8.63013e28	0.0413081
$773$	−1.23771e30	−0.584434	−0.292217	−	0.956352i	$-0.594393\pi$
$773$	−1.23771e30	−0.584434	−0.292217	+	0.956352i	$0.594393\pi$
$774$	0	0
$775$	−2.01595e29	−0.0926427
$776$	1.94033e30	0.879686
$777$	0	0
$778$	4.58507e29	0.202330
$779$	−6.08698e30	−2.65008
$780$	0	0
$781$	5.98949e29	0.253836
$782$	−4.77297e29	−0.199580
$783$	0	0
$784$	5.03033e29	0.204776
$785$	1.25501e30	0.504100
$786$	0	0
$787$	2.14352e30	0.838288	0.419144	−	0.907920i	$-0.362330\pi$
$787$	2.14352e30	0.838288	0.419144	+	0.907920i	$0.362330\pi$
$788$	7.91853e29	0.305576
$789$	0	0
$790$	−8.88450e29	−0.333848
$791$	−1.55454e30	−0.576434
$792$	0	0
$793$	−2.78327e30	−1.00505
$794$	−1.87221e30	−0.667174
$795$	0	0
$796$	7.31081e29	0.253734
$797$	−3.01280e30	−1.03195	−0.515974	−	0.856605i	$-0.672570\pi$
$797$	−3.01280e30	−1.03195	−0.515974	+	0.856605i	$0.672570\pi$
$798$	0	0
$799$	−3.58228e30	−1.19514
$800$	−6.86676e28	−0.0226103
$801$	0	0
$802$	−1.27705e30	−0.409617
$803$	1.03226e30	0.326796
$804$	0	0
$805$	−6.03763e29	−0.186213
$806$	7.85711e30	2.39191
$807$	0	0
$808$	−5.44752e30	−1.61577
$809$	5.76883e30	1.68900	0.844498	−	0.535559i	$-0.179899\pi$
$809$	5.76883e30	1.68900	0.844498	+	0.535559i	$0.179899\pi$
$810$	0	0
$811$	3.98728e30	1.13752	0.568759	−	0.822504i	$-0.307424\pi$
$811$	3.98728e30	1.13752	0.568759	+	0.822504i	$0.307424\pi$
$812$	−8.38148e29	−0.236038
$813$	0	0
$814$	1.35051e30	0.370631
$815$	−6.77146e29	−0.183454
$816$	0	0
$817$	5.22754e30	1.38027
$818$	−5.61998e30	−1.46496
$819$	0	0
$820$	1.48128e30	0.376350
$821$	4.09615e30	1.02748	0.513739	−	0.857946i	$-0.328260\pi$
$821$	4.09615e30	1.02748	0.513739	+	0.857946i	$0.328260\pi$
$822$	0	0
$823$	1.43384e30	0.350592	0.175296	−	0.984516i	$-0.443912\pi$
$823$	1.43384e30	0.350592	0.175296	+	0.984516i	$0.443912\pi$
$824$	−3.86432e30	−0.932905
$825$	0	0
$826$	−1.30210e30	−0.306447
$827$	3.13142e30	0.727668	0.363834	−	0.931464i	$-0.381468\pi$
$827$	3.13142e30	0.727668	0.363834	+	0.931464i	$0.381468\pi$
$828$	0	0
$829$	−4.44329e30	−1.00666	−0.503329	−	0.864095i	$-0.667892\pi$
$829$	−4.44329e30	−1.00666	−0.503329	+	0.864095i	$0.667892\pi$
$830$	−8.26106e27	−0.00184806
$831$	0	0
$832$	7.57531e30	1.65236
$833$	−1.32926e30	−0.286311
$834$	0	0
$835$	7.71998e29	0.162147
$836$	1.20024e30	0.248944
$837$	0	0
$838$	3.00994e30	0.608829
$839$	9.30057e29	0.185784	0.0928922	−	0.995676i	$-0.470389\pi$
$839$	9.30057e29	0.185784	0.0928922	+	0.995676i	$0.470389\pi$
$840$	0	0
$841$	2.52173e30	0.491293
$842$	3.46057e30	0.665842
$843$	0	0
$844$	−6.50614e29	−0.122103
$845$	6.34746e30	1.17653
$846$	0	0
$847$	−2.42033e30	−0.437621
$848$	−1.50891e30	−0.269467
$849$	0	0
$850$	−2.56243e29	−0.0446430
$851$	7.97630e29	0.137259
$852$	0	0
$853$	−2.27471e30	−0.381911	−0.190955	−	0.981599i	$-0.561159\pi$
$853$	−2.27471e30	−0.381911	−0.190955	+	0.981599i	$0.561159\pi$
$854$	−3.03003e30	−0.502503
$855$	0	0
$856$	−2.84833e30	−0.460910
$857$	−3.05003e30	−0.487534	−0.243767	−	0.969834i	$-0.578383\pi$
$857$	−3.05003e30	−0.487534	−0.243767	+	0.969834i	$0.578383\pi$
$858$	0	0
$859$	1.34073e30	0.209128	0.104564	−	0.994518i	$-0.466655\pi$
$859$	1.34073e30	0.209128	0.104564	+	0.994518i	$0.466655\pi$
$860$	−1.27213e30	−0.196020
$861$	0	0
$862$	−1.12873e31	−1.69732
$863$	−1.14916e31	−1.70713	−0.853566	−	0.520985i	$-0.825565\pi$
$863$	−1.14916e31	−1.70713	−0.853566	+	0.520985i	$0.825565\pi$
$864$	0	0
$865$	−6.84096e30	−0.991855
$866$	−4.32457e30	−0.619448
$867$	0	0
$868$	−2.53397e30	−0.354278
$869$	1.96173e30	0.270976
$870$	0	0
$871$	−2.08107e30	−0.280606
$872$	−1.35024e30	−0.179882
$873$	0	0
$874$	−2.39290e30	−0.311211
$875$	−6.73714e30	−0.865747
$876$	0	0
$877$	9.06320e30	1.13707	0.568533	−	0.822660i	$-0.307511\pi$
$877$	9.06320e30	1.13707	0.568533	+	0.822660i	$0.307511\pi$
$878$	2.91934e30	0.361904
$879$	0	0
$880$	4.02207e30	0.486835
$881$	6.50767e30	0.778356	0.389178	−	0.921163i	$-0.372759\pi$
$881$	6.50767e30	0.778356	0.389178	+	0.921163i	$0.372759\pi$
$882$	0	0
$883$	5.90742e30	0.689939	0.344969	−	0.938614i	$-0.387889\pi$
$883$	5.90742e30	0.689939	0.344969	+	0.938614i	$0.387889\pi$
$884$	−2.95858e30	−0.341456
$885$	0	0
$886$	7.18992e30	0.810344
$887$	3.42312e30	0.381263	0.190632	−	0.981662i	$-0.438946\pi$
$887$	3.42312e30	0.381263	0.190632	+	0.981662i	$0.438946\pi$
$888$	0	0
$889$	3.50032e30	0.380750
$890$	−6.34905e30	−0.682518
$891$	0	0
$892$	−2.26792e30	−0.238121
$893$	−1.79595e31	−1.86361
$894$	0	0
$895$	3.83886e30	0.389099
$896$	4.47020e30	0.447810
$897$	0	0
$898$	−1.56863e31	−1.53503
$899$	2.31420e31	2.23833
$900$	0	0
$901$	3.98728e30	0.376761
$902$	1.10407e31	1.03116
$903$	0	0
$904$	8.05980e30	0.735455
$905$	−1.35463e29	−0.0122183
$906$	0	0
$907$	−1.16251e31	−1.02452	−0.512262	−	0.858829i	$-0.671192\pi$
$907$	−1.16251e31	−1.02452	−0.512262	+	0.858829i	$0.671192\pi$
$908$	3.83534e30	0.334120
$909$	0	0
$910$	1.26332e31	1.07542
$911$	1.34510e31	1.13191	0.565957	−	0.824435i	$-0.308507\pi$
$911$	1.34510e31	1.13191	0.565957	+	0.824435i	$0.308507\pi$
$912$	0	0
$913$	1.82407e28	0.00150002
$914$	−9.70051e30	−0.788605
$915$	0	0
$916$	−1.30418e30	−0.103618
$917$	1.60945e31	1.26416
$918$	0	0
$919$	−8.55562e30	−0.656808	−0.328404	−	0.944537i	$-0.606511\pi$
$919$	−8.55562e30	−0.656808	−0.328404	+	0.944537i	$0.606511\pi$
$920$	3.13032e30	0.237583
$921$	0	0
$922$	1.15093e30	0.0853835
$923$	−7.40185e30	−0.542903
$924$	0	0
$925$	4.28218e29	0.0307027
$926$	−1.52259e30	−0.107937
$927$	0	0
$928$	7.88268e30	0.546286
$929$	−9.93712e30	−0.680919	−0.340460	−	0.940259i	$-0.610583\pi$
$929$	−9.93712e30	−0.680919	−0.340460	+	0.940259i	$0.610583\pi$
$930$	0	0
$931$	−6.66418e30	−0.446452
$932$	−3.16381e30	−0.209577
$933$	0	0
$934$	1.48757e31	0.963462
$935$	−1.06283e31	−0.680679
$936$	0	0
$937$	−2.14272e30	−0.134183	−0.0670917	−	0.997747i	$-0.521372\pi$
$937$	−2.14272e30	−0.134183	−0.0670917	+	0.997747i	$0.521372\pi$
$938$	−2.26557e30	−0.140297
$939$	0	0
$940$	4.37050e30	0.264660
$941$	−1.69148e31	−1.01292	−0.506459	−	0.862264i	$-0.669046\pi$
$941$	−1.69148e31	−1.01292	−0.506459	+	0.862264i	$0.669046\pi$
$942$	0	0
$943$	6.52077e30	0.381879
$944$	5.12310e30	0.296706
$945$	0	0
$946$	−9.48180e30	−0.537074
$947$	1.96530e31	1.10092	0.550459	−	0.834862i	$-0.314453\pi$
$947$	1.96530e31	1.10092	0.550459	+	0.834862i	$0.314453\pi$
$948$	0	0
$949$	−1.27568e31	−0.698948
$950$	−1.28466e30	−0.0696129
$951$	0	0
$952$	−1.73142e31	−0.917728
$953$	−2.39001e31	−1.25292	−0.626462	−	0.779452i	$-0.715498\pi$
$953$	−2.39001e31	−1.25292	−0.626462	+	0.779452i	$0.715498\pi$
$954$	0	0
$955$	−1.74026e31	−0.892437
$956$	4.75555e30	0.241209
$957$	0	0
$958$	−2.60567e31	−1.29295
$959$	3.04716e31	1.49555
$960$	0	0
$961$	4.91397e31	2.35959
$962$	−1.66897e31	−0.792703
$963$	0	0
$964$	7.38943e30	0.343401
$965$	−3.83132e30	−0.176121
$966$	0	0
$967$	1.63072e31	0.733504	0.366752	−	0.930319i	$-0.380470\pi$
$967$	1.63072e31	0.733504	0.366752	+	0.930319i	$0.380470\pi$
$968$	1.25486e31	0.558348
$969$	0	0
$970$	−1.60243e31	−0.697712
$971$	−3.09343e31	−1.33241	−0.666207	−	0.745767i	$-0.732083\pi$
$971$	−3.09343e31	−1.33241	−0.666207	+	0.745767i	$0.732083\pi$
$972$	0	0
$973$	−1.37915e31	−0.581334
$974$	−4.77865e30	−0.199267
$975$	0	0
$976$	1.19216e31	0.486531
$977$	−1.98044e31	−0.799592	−0.399796	−	0.916604i	$-0.630919\pi$
$977$	−1.98044e31	−0.799592	−0.399796	+	0.916604i	$0.630919\pi$
$978$	0	0
$979$	1.40189e31	0.553982
$980$	1.62175e30	0.0634029
$981$	0	0
$982$	1.94829e31	0.745561
$983$	4.34284e30	0.164423	0.0822114	−	0.996615i	$-0.473802\pi$
$983$	4.34284e30	0.164423	0.0822114	+	0.996615i	$0.473802\pi$
$984$	0	0
$985$	−3.51541e31	−1.30285
$986$	2.94154e31	1.07862
$987$	0	0
$988$	−1.48327e31	−0.532441
$989$	−5.60008e30	−0.198899
$990$	0	0
$991$	4.70795e30	0.163704	0.0818518	−	0.996645i	$-0.473917\pi$
$991$	4.70795e30	0.163704	0.0818518	+	0.996645i	$0.473917\pi$
$992$	2.38317e31	0.819939
$993$	0	0
$994$	−8.05807e30	−0.271440
$995$	−3.24561e31	−1.08182
$996$	0	0
$997$	−1.58934e31	−0.518700	−0.259350	−	0.965783i	$-0.583508\pi$
$997$	−1.58934e31	−0.518700	−0.259350	+	0.965783i	$0.583508\pi$
$998$	4.89494e30	0.158080
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.22.a.e.1.2		2
3.2	odd	2		3.22.a.c.1.1	✓	2
12.11	even	2		48.22.a.g.1.1		2
15.2	even	4		75.22.b.d.49.2		4
15.8	even	4		75.22.b.d.49.3		4
15.14	odd	2		75.22.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.c.1.1	✓	2	3.2	odd	2
9.22.a.e.1.2		2	1.1	even	1	trivial
48.22.a.g.1.1		2	12.11	even	2
75.22.a.d.1.2		2	15.14	odd	2
75.22.b.d.49.2		4	15.2	even	4
75.22.b.d.49.3		4	15.8	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)

\(f(q)\)	\(=\)	\(q+1271.96 q^{2} -479282. q^{4} +2.12776e7 q^{5} +6.32076e8 q^{7} -3.27711e9 q^{8} +O(q^{10})\)	\(q+1271.96 q^{2} -479282. q^{4} +2.12776e7 q^{5} +6.32076e8 q^{7} -3.27711e9 q^{8} +2.70641e10 q^{10} -5.97585e10 q^{11} +7.38499e11 q^{13} +8.03972e11 q^{14} -3.16321e12 q^{16} +8.35876e12 q^{17} +4.19061e13 q^{19} -1.01980e13 q^{20} -7.60101e13 q^{22} -4.48926e13 q^{23} -2.41012e13 q^{25} +9.39338e14 q^{26} -3.02943e14 q^{28} +2.76669e15 q^{29} +8.36452e15 q^{31} +2.84914e15 q^{32} +1.06320e16 q^{34} +1.34490e16 q^{35} -1.77675e16 q^{37} +5.33027e16 q^{38} -6.97290e16 q^{40} -1.45253e17 q^{41} +1.24744e17 q^{43} +2.86412e16 q^{44} -5.71014e16 q^{46} -4.28566e17 q^{47} -1.59026e17 q^{49} -3.06556e16 q^{50} -3.53950e17 q^{52} +4.77017e17 q^{53} -1.27152e18 q^{55} -2.07138e18 q^{56} +3.51911e18 q^{58} -1.61959e18 q^{59} -3.76882e18 q^{61} +1.06393e19 q^{62} +1.02577e19 q^{64} +1.57135e19 q^{65} -2.81797e18 q^{67} -4.00621e18 q^{68} +1.71066e19 q^{70} -1.00228e19 q^{71} -1.72739e19 q^{73} -2.25995e19 q^{74} -2.00849e19 q^{76} -3.77719e19 q^{77} -3.28276e19 q^{79} -6.73054e19 q^{80} -1.84755e20 q^{82} -3.05240e17 q^{83} +1.77854e20 q^{85} +1.58669e20 q^{86} +1.95835e20 q^{88} -2.34593e20 q^{89} +4.66787e20 q^{91} +2.15162e19 q^{92} -5.45116e20 q^{94} +8.91662e20 q^{95} -5.92086e20 q^{97} -2.02274e20 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 666 q^{2} + 1179236 q^{4} - 996876 q^{5} + 679896112 q^{7} - 2427055848 q^{8}+O(q^{10}) \) 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

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Database

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