LMFDB - Embedded newform 9.7.b.a.8.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,7,Mod(8,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.8"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	9.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07048675258$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-2}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 2 $ x^2 + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			8.1
Root			$-1.41421i$ of defining polynomial
Character	$\chi$	$=$	9.8
Dual form			9.7.b.a.8.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-12.7279i q^{2} -98.0000 q^{4} -63.6396i q^{5} +524.000 q^{7} +432.749i q^{8} -810.000 q^{10} +865.499i q^{11} +344.000 q^{13} -6669.43i q^{14} -764.000 q^{16} +7140.36i q^{17} -2320.00 q^{19} +6236.68i q^{20} +11016.0 q^{22} -5753.02i q^{23} +11575.0 q^{25} -4378.41i q^{26} -51352.0 q^{28} -23152.1i q^{29} -10564.0 q^{31} +37420.1i q^{32} +90882.0 q^{34} -33347.2i q^{35} -24082.0 q^{37} +29528.8i q^{38} +27540.0 q^{40} +108836. i q^{41} -90952.0 q^{43} -84818.9i q^{44} -73224.0 q^{46} -128959. i q^{47} +156927. q^{49} -147326. i q^{50} -33712.0 q^{52} +196685. i q^{53} +55080.0 q^{55} +226761. i q^{56} -294678. q^{58} -39812.9i q^{59} +251138. q^{61} +134458. i q^{62} +427384. q^{64} -21892.0i q^{65} -216088. q^{67} -699756. i q^{68} -424440. q^{70} -53915.5i q^{71} -308176. q^{73} +306514. i q^{74} +227360. q^{76} +453521. i q^{77} -540124. q^{79} +48620.7i q^{80} +1.38526e6 q^{82} -932346. i q^{83} +454410. q^{85} +1.15763e6i q^{86} -374544. q^{88} -223413. i q^{89} +180256. q^{91} +563796. i q^{92} -1.64138e6 q^{94} +147644. i q^{95} -37168.0 q^{97} -1.99735e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 196 q^{4} + 1048 q^{7} - 1620 q^{10} + 688 q^{13} - 1528 q^{16} - 4640 q^{19} + 22032 q^{22} + 23150 q^{25} - 102704 q^{28} - 21128 q^{31} + 181764 q^{34} - 48164 q^{37} + 55080 q^{40} - 181904 q^{43}+ \cdots - 74336 q^{97}+O(q^{100}) $ 2 * q - 196 * q^4 + 1048 * q^7 - 1620 * q^10 + 688 * q^13 - 1528 * q^16 - 4640 * q^19 + 22032 * q^22 + 23150 * q^25 - 102704 * q^28 - 21128 * q^31 + 181764 * q^34 - 48164 * q^37 + 55080 * q^40 - 181904 * q^43 - 146448 * q^46 + 313854 * q^49 - 67424 * q^52 + 110160 * q^55 - 589356 * q^58 + 502276 * q^61 + 854768 * q^64 - 432176 * q^67 - 848880 * q^70 - 616352 * q^73 + 454720 * q^76 - 1080248 * q^79 + 2770524 * q^82 + 908820 * q^85 - 749088 * q^88 + 360512 * q^91 - 3282768 * q^94 - 74336 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 12.7279i	− 1.59099i	−0.605960	−	0.795495i	$-0.707211\pi$
$2$	− 12.7279i	− 1.59099i	0.605960	−	0.795495i	$-0.292789\pi$
$3$	0	0
$3$	0	0
$4$	−98.0000	−1.53125
$5$	− 63.6396i	− 0.509117i	−0.967057	−	0.254558i	$-0.918070\pi$
$5$	− 63.6396i	− 0.509117i	0.967057	−	0.254558i	$-0.0819301\pi$
$6$	0	0
$7$	524.000	1.52770	0.763848	−	0.645396i	$-0.223308\pi$
$7$	524.000	1.52770	0.763848	+	0.645396i	$0.223308\pi$
$8$	432.749i	0.845214i
$9$	0	0
$10$	−810.000	−0.810000
$11$	865.499i	0.650262i	0.945669	+	0.325131i	$0.105408\pi$
$11$	865.499i	0.650262i	−0.945669	+	0.325131i	$0.894592\pi$
$12$	0	0
$13$	344.000	0.156577	0.0782886	−	0.996931i	$-0.475054\pi$
$13$	344.000	0.156577	0.0782886	+	0.996931i	$0.475054\pi$
$14$	− 6669.43i	− 2.43055i
$15$	0	0
$16$	−764.000	−0.186523
$17$	7140.36i	1.45336i	0.686975	+	0.726681i	$0.258938\pi$
$17$	7140.36i	1.45336i	−0.686975	+	0.726681i	$0.741062\pi$
$18$	0	0
$19$	−2320.00	−0.338242	−0.169121	−	0.985595i	$-0.554093\pi$
$19$	−2320.00	−0.338242	−0.169121	+	0.985595i	$0.554093\pi$
$20$	6236.68i	0.779585i
$21$	0	0
$22$	11016.0	1.03456
$23$	− 5753.02i	− 0.472838i	−0.971651	−	0.236419i	$-0.924026\pi$
$23$	− 5753.02i	− 0.472838i	0.971651	−	0.236419i	$-0.0759738\pi$
$24$	0	0
$25$	11575.0	0.740800
$26$	− 4378.41i	− 0.249113i
$27$	0	0
$28$	−51352.0	−2.33929
$29$	− 23152.1i	− 0.949284i	−0.880179	−	0.474642i	$-0.842578\pi$
$29$	− 23152.1i	− 0.949284i	0.880179	−	0.474642i	$-0.157422\pi$
$30$	0	0
$31$	−10564.0	−0.354604	−0.177302	−	0.984157i	$-0.556737\pi$
$31$	−10564.0	−0.354604	−0.177302	+	0.984157i	$0.556737\pi$
$32$	37420.1i	1.14197i
$33$	0	0
$34$	90882.0	2.31228
$35$	− 33347.2i	− 0.777776i
$36$	0	0
$37$	−24082.0	−0.475431	−0.237715	−	0.971335i	$-0.576399\pi$
$37$	−24082.0	−0.475431	−0.237715	+	0.971335i	$0.576399\pi$
$38$	29528.8i	0.538139i
$39$	0	0
$40$	27540.0	0.430312
$41$	108836.i	1.57915i	0.613655	+	0.789574i	$0.289698\pi$
$41$	108836.i	1.57915i	−0.613655	+	0.789574i	$0.710302\pi$
$42$	0	0
$43$	−90952.0	−1.14395	−0.571975	−	0.820271i	$-0.693822\pi$
$43$	−90952.0	−1.14395	−0.571975	+	0.820271i	$0.693822\pi$
$44$	− 84818.9i	− 0.995714i
$45$	0	0
$46$	−73224.0	−0.752281
$47$	− 128959.i	− 1.24211i	−0.783768	−	0.621054i	$-0.786705\pi$
$47$	− 128959.i	− 1.24211i	0.783768	−	0.621054i	$-0.213295\pi$
$48$	0	0
$49$	156927.	1.33386
$50$	− 147326.i	− 1.17861i
$51$	0	0
$52$	−33712.0	−0.239759
$53$	196685.i	1.32112i	0.750773	+	0.660561i	$0.229681\pi$
$53$	196685.i	1.32112i	−0.750773	+	0.660561i	$0.770319\pi$
$54$	0	0
$55$	55080.0	0.331059
$56$	226761.i	1.29123i
$57$	0	0
$58$	−294678.	−1.51030
$59$	− 39812.9i	− 0.193851i	−0.995292	−	0.0969255i	$-0.969099\pi$
$59$	− 39812.9i	− 0.193851i	0.995292	−	0.0969255i	$-0.0309009\pi$
$60$	0	0
$61$	251138.	1.10643	0.553214	−	0.833039i	$-0.313401\pi$
$61$	251138.	1.10643	0.553214	+	0.833039i	$0.313401\pi$
$62$	134458.i	0.564171i
$63$	0	0
$64$	427384.	1.63034
$65$	− 21892.0i	− 0.0797161i
$66$	0	0
$67$	−216088.	−0.718466	−0.359233	−	0.933248i	$-0.616962\pi$
$67$	−216088.	−0.718466	−0.359233	+	0.933248i	$0.616962\pi$
$68$	− 699756.i	− 2.22546i
$69$	0	0
$70$	−424440.	−1.23743
$71$	− 53915.5i	− 0.150639i	−0.997159	−	0.0753197i	$-0.976002\pi$
$71$	− 53915.5i	− 0.150639i	0.997159	−	0.0753197i	$-0.0239977\pi$
$72$	0	0
$73$	−308176.	−0.792192	−0.396096	−	0.918209i	$-0.629635\pi$
$73$	−308176.	−0.792192	−0.396096	+	0.918209i	$0.629635\pi$
$74$	306514.i	0.756406i
$75$	0	0
$76$	227360.	0.517933
$77$	453521.i	0.993403i
$78$	0	0
$79$	−540124.	−1.09550	−0.547750	−	0.836642i	$-0.684515\pi$
$79$	−540124.	−1.09550	−0.547750	+	0.836642i	$0.684515\pi$
$80$	48620.7i	0.0949622i
$81$	0	0
$82$	1.38526e6	2.51241
$83$	− 932346.i	− 1.63058i	−0.579051	−	0.815291i	$-0.696577\pi$
$83$	− 932346.i	− 1.63058i	0.579051	−	0.815291i	$-0.303423\pi$
$84$	0	0
$85$	454410.	0.739931
$86$	1.15763e6i	1.82001i
$87$	0	0
$88$	−374544.	−0.549610
$89$	− 223413.i	− 0.316912i	−0.987366	−	0.158456i	$-0.949348\pi$
$89$	− 223413.i	− 0.316912i	0.987366	−	0.158456i	$-0.0506516\pi$
$90$	0	0
$91$	180256.	0.239202
$92$	563796.i	0.724033i
$93$	0	0
$94$	−1.64138e6	−1.97618
$95$	147644.i	0.172205i
$96$	0	0
$97$	−37168.0	−0.0407243	−0.0203622	−	0.999793i	$-0.506482\pi$
$97$	−37168.0	−0.0407243	−0.0203622	+	0.999793i	$0.506482\pi$
$98$	− 1.99735e6i	− 2.12215i
$99$	0	0
$100$	−1.13435e6	−1.13435
$101$	− 559787.i	− 0.543323i	−0.962393	−	0.271662i	$-0.912427\pi$
$101$	− 559787.i	− 0.543323i	0.962393	−	0.271662i	$-0.0875732\pi$
$102$	0	0
$103$	1.46018e6	1.33627	0.668136	−	0.744039i	$-0.267093\pi$
$103$	1.46018e6	1.33627	0.668136	+	0.744039i	$0.267093\pi$
$104$	148866.i	0.132341i
$105$	0	0
$106$	2.50339e6	2.10189
$107$	1.29031e6i	1.05327i	0.850090	+	0.526637i	$0.176547\pi$
$107$	1.29031e6i	1.05327i	−0.850090	+	0.526637i	$0.823453\pi$
$108$	0	0
$109$	−1.43548e6	−1.10845	−0.554227	−	0.832366i	$-0.686986\pi$
$109$	−1.43548e6	−1.10845	−0.554227	+	0.832366i	$0.686986\pi$
$110$	− 701054.i	− 0.526712i
$111$	0	0
$112$	−400336.	−0.284951
$113$	186426.i	0.129202i	0.997911	+	0.0646012i	$0.0205775\pi$
$113$	186426.i	0.129202i	−0.997911	+	0.0646012i	$0.979422\pi$
$114$	0	0
$115$	−366120.	−0.240730
$116$	2.26890e6i	1.45359i
$117$	0	0
$118$	−506736.	−0.308415
$119$	3.74155e6i	2.22030i
$120$	0	0
$121$	1.02247e6	0.577159
$122$	− 3.19646e6i	− 1.76032i
$123$	0	0
$124$	1.03527e6	0.542987
$125$	− 1.73100e6i	− 0.886271i
$126$	0	0
$127$	−127060.	−0.0620294	−0.0310147	−	0.999519i	$-0.509874\pi$
$127$	−127060.	−0.0620294	−0.0310147	+	0.999519i	$0.509874\pi$
$128$	− 3.04482e6i	− 1.45189i
$129$	0	0
$130$	−278640.	−0.126827
$131$	− 2.62348e6i	− 1.16698i	−0.812120	−	0.583490i	$-0.801687\pi$
$131$	− 2.62348e6i	− 1.16698i	0.812120	−	0.583490i	$-0.198313\pi$
$132$	0	0
$133$	−1.21568e6	−0.516731
$134$	2.75035e6i	1.14307i
$135$	0	0
$136$	−3.08999e6	−1.22840
$137$	− 202310.i	− 0.0786785i	−0.999226	−	0.0393393i	$-0.987475\pi$
$137$	− 202310.i	− 0.0786785i	0.999226	−	0.0393393i	$-0.0125253\pi$
$138$	0	0
$139$	2.02642e6	0.754546	0.377273	−	0.926102i	$-0.376862\pi$
$139$	2.02642e6	0.754546	0.377273	+	0.926102i	$0.376862\pi$
$140$	3.26802e6i	1.19097i
$141$	0	0
$142$	−686232.	−0.239666
$143$	297732.i	0.101816i
$144$	0	0
$145$	−1.47339e6	−0.483297
$146$	3.92244e6i	1.26037i
$147$	0	0
$148$	2.36004e6	0.728004
$149$	− 4.25534e6i	− 1.28640i	−0.765699	−	0.643199i	$-0.777607\pi$
$149$	− 4.25534e6i	− 1.28640i	0.765699	−	0.643199i	$-0.222393\pi$
$150$	0	0
$151$	3.74035e6	1.08638	0.543189	−	0.839610i	$-0.317217\pi$
$151$	3.74035e6	1.08638	0.543189	+	0.839610i	$0.317217\pi$
$152$	− 1.00398e6i	− 0.285886i
$153$	0	0
$154$	5.77238e6	1.58049
$155$	672289.i	0.180535i
$156$	0	0
$157$	−2.38813e6	−0.617105	−0.308552	−	0.951207i	$-0.599845\pi$
$157$	−2.38813e6	−0.617105	−0.308552	+	0.951207i	$0.599845\pi$
$158$	6.87466e6i	1.74293i
$159$	0	0
$160$	2.38140e6	0.581396
$161$	− 3.01458e6i	− 0.722353i
$162$	0	0
$163$	−6.74519e6	−1.55751	−0.778756	−	0.627327i	$-0.784149\pi$
$163$	−6.74519e6	−1.55751	−0.778756	+	0.627327i	$0.784149\pi$
$164$	− 1.06660e7i	− 2.41807i
$165$	0	0
$166$	−1.18668e7	−2.59424
$167$	6.61699e6i	1.42073i	0.703834	+	0.710364i	$0.251470\pi$
$167$	6.61699e6i	1.42073i	−0.703834	+	0.710364i	$0.748530\pi$
$168$	0	0
$169$	−4.70847e6	−0.975484
$170$	− 5.78370e6i	− 1.17722i
$171$	0	0
$172$	8.91330e6	1.75167
$173$	5.58077e6i	1.07784i	0.842356	+	0.538922i	$0.181168\pi$
$173$	5.58077e6i	1.07784i	−0.842356	+	0.538922i	$0.818832\pi$
$174$	0	0
$175$	6.06530e6	1.13172
$176$	− 661241.i	− 0.121289i
$177$	0	0
$178$	−2.84359e6	−0.504204
$179$	− 4.87103e6i	− 0.849301i	−0.905357	−	0.424650i	$-0.860397\pi$
$179$	− 4.87103e6i	− 0.849301i	0.905357	−	0.424650i	$-0.139603\pi$
$180$	0	0
$181$	8.47546e6	1.42931	0.714657	−	0.699475i	$-0.246583\pi$
$181$	8.47546e6	1.42931	0.714657	+	0.699475i	$0.246583\pi$
$182$	− 2.29428e6i	− 0.380569i
$183$	0	0
$184$	2.48962e6	0.399649
$185$	1.53257e6i	0.242050i
$186$	0	0
$187$	−6.17998e6	−0.945066
$188$	1.26380e7i	1.90198i
$189$	0	0
$190$	1.87920e6	0.273976
$191$	− 97037.7i	− 0.0139264i	−0.999976	−	0.00696322i	$-0.997784\pi$
$191$	− 97037.7i	− 0.0139264i	0.999976	−	0.00696322i	$-0.00221648\pi$
$192$	0	0
$193$	7.49473e6	1.04252	0.521260	−	0.853398i	$-0.325462\pi$
$193$	7.49473e6	1.04252	0.521260	+	0.853398i	$0.325462\pi$
$194$	473071.i	0.0647920i
$195$	0	0
$196$	−1.53788e7	−2.04247
$197$	9.84656e6i	1.28791i	0.765063	+	0.643956i	$0.222708\pi$
$197$	9.84656e6i	1.28791i	−0.765063	+	0.643956i	$0.777292\pi$
$198$	0	0
$199$	3.54170e6	0.449420	0.224710	−	0.974426i	$-0.427856\pi$
$199$	3.54170e6	0.449420	0.224710	+	0.974426i	$0.427856\pi$
$200$	5.00907e6i	0.626134i
$201$	0	0
$202$	−7.12492e6	−0.864422
$203$	− 1.21317e7i	− 1.45022i
$204$	0	0
$205$	6.92631e6	0.803971
$206$	− 1.85851e7i	− 2.12600i
$207$	0	0
$208$	−262816.	−0.0292053
$209$	− 2.00796e6i	− 0.219946i
$210$	0	0
$211$	−6.77298e6	−0.720996	−0.360498	−	0.932760i	$-0.617393\pi$
$211$	−6.77298e6	−0.720996	−0.360498	+	0.932760i	$0.617393\pi$
$212$	− 1.92751e7i	− 2.02297i
$213$	0	0
$214$	1.64229e7	1.67575
$215$	5.78815e6i	0.582404i
$216$	0	0
$217$	−5.53554e6	−0.541727
$218$	1.82707e7i	1.76354i
$219$	0	0
$220$	−5.39784e6	−0.506935
$221$	2.45629e6i	0.227563i
$222$	0	0
$223$	−3.34186e6	−0.301352	−0.150676	−	0.988583i	$-0.548145\pi$
$223$	−3.34186e6	−0.301352	−0.150676	+	0.988583i	$0.548145\pi$
$224$	1.96081e7i	1.74458i
$225$	0	0
$226$	2.37281e6	0.205560
$227$	− 1.62013e7i	− 1.38507i	−0.721385	−	0.692535i	$-0.756494\pi$
$227$	− 1.62013e7i	− 1.38507i	0.721385	−	0.692535i	$-0.243506\pi$
$228$	0	0
$229$	−1.66351e7	−1.38522	−0.692611	−	0.721311i	$-0.743540\pi$
$229$	−1.66351e7	−1.38522	−0.692611	+	0.721311i	$0.743540\pi$
$230$	4.65995e6i	0.382999i
$231$	0	0
$232$	1.00191e7	0.802348
$233$	8.85600e6i	0.700116i	0.936728	+	0.350058i	$0.113838\pi$
$233$	8.85600e6i	0.700116i	−0.936728	+	0.350058i	$0.886162\pi$
$234$	0	0
$235$	−8.20692e6	−0.632378
$236$	3.90167e6i	0.296834i
$237$	0	0
$238$	4.76222e7	3.53247
$239$	1.12995e7i	0.827689i	0.910348	+	0.413845i	$0.135814\pi$
$239$	1.12995e7i	0.827689i	−0.910348	+	0.413845i	$0.864186\pi$
$240$	0	0
$241$	1.50090e7	1.07226	0.536129	−	0.844136i	$-0.319886\pi$
$241$	1.50090e7	1.07226	0.536129	+	0.844136i	$0.319886\pi$
$242$	− 1.30140e7i	− 0.918255i
$243$	0	0
$244$	−2.46115e7	−1.69422
$245$	− 9.98677e6i	− 0.679089i
$246$	0	0
$247$	−798080.	−0.0529609
$248$	− 4.57156e6i	− 0.299716i
$249$	0	0
$250$	−2.20320e7	−1.41005
$251$	− 3.04076e7i	− 1.92292i	−0.274950	−	0.961458i	$-0.588661\pi$
$251$	− 3.04076e7i	− 1.92292i	0.274950	−	0.961458i	$-0.411339\pi$
$252$	0	0
$253$	4.97923e6	0.307469
$254$	1.61721e6i	0.0986882i
$255$	0	0
$256$	−1.14017e7	−0.679595
$257$	1.97422e7i	1.16305i	0.813530	+	0.581523i	$0.197543\pi$
$257$	1.97422e7i	1.16305i	−0.813530	+	0.581523i	$0.802457\pi$
$258$	0	0
$259$	−1.26190e7	−0.726314
$260$	2.14542e6i	0.122065i
$261$	0	0
$262$	−3.33914e7	−1.85666
$263$	− 3.48531e6i	− 0.191591i	−0.995401	−	0.0957954i	$-0.969461\pi$
$263$	− 3.48531e6i	− 0.191591i	0.995401	−	0.0957954i	$-0.0305394\pi$
$264$	0	0
$265$	1.25169e7	0.672605
$266$	1.54731e7i	0.822114i
$267$	0	0
$268$	2.11766e7	1.10015
$269$	− 5.65391e6i	− 0.290464i	−0.989398	−	0.145232i	$-0.953607\pi$
$269$	− 5.65391e6i	− 0.290464i	0.989398	−	0.145232i	$-0.0463928\pi$
$270$	0	0
$271$	2.91893e7	1.46662	0.733308	−	0.679897i	$-0.237976\pi$
$271$	2.91893e7	1.46662	0.733308	+	0.679897i	$0.237976\pi$
$272$	− 5.45524e6i	− 0.271086i
$273$	0	0
$274$	−2.57499e6	−0.125177
$275$	1.00181e7i	0.481714i
$276$	0	0
$277$	2.29938e7	1.08186	0.540931	−	0.841067i	$-0.318072\pi$
$277$	2.29938e7	1.08186	0.540931	+	0.841067i	$0.318072\pi$
$278$	− 2.57922e7i	− 1.20048i
$279$	0	0
$280$	1.44310e7	0.657387
$281$	1.25303e6i	0.0564730i	0.999601	+	0.0282365i	$0.00898916\pi$
$281$	1.25303e6i	0.0564730i	−0.999601	+	0.0282365i	$0.991011\pi$
$282$	0	0
$283$	−1.45129e7	−0.640317	−0.320159	−	0.947364i	$-0.603736\pi$
$283$	−1.45129e7	−0.640317	−0.320159	+	0.947364i	$0.603736\pi$
$284$	5.28372e6i	0.230666i
$285$	0	0
$286$	3.78950e6	0.161989
$287$	5.70303e7i	2.41246i
$288$	0	0
$289$	−2.68472e7	−1.11226
$290$	1.87532e7i	0.768920i
$291$	0	0
$292$	3.02012e7	1.21304
$293$	− 1.12729e7i	− 0.448160i	−0.974571	−	0.224080i	$-0.928062\pi$
$293$	− 1.12729e7i	− 0.448160i	0.974571	−	0.224080i	$-0.0719377\pi$
$294$	0	0
$295$	−2.53368e6	−0.0986929
$296$	− 1.04215e7i	− 0.401841i
$297$	0	0
$298$	−5.41616e7	−2.04665
$299$	− 1.97904e6i	− 0.0740356i
$300$	0	0
$301$	−4.76588e7	−1.74761
$302$	− 4.76069e7i	− 1.72842i
$303$	0	0
$304$	1.77248e6	0.0630900
$305$	− 1.59823e7i	− 0.563301i
$306$	0	0
$307$	4.51916e7	1.56186	0.780930	−	0.624618i	$-0.214745\pi$
$307$	4.51916e7	1.56186	0.780930	+	0.624618i	$0.214745\pi$
$308$	− 4.44451e7i	− 1.52115i
$309$	0	0
$310$	8.55684e6	0.287229
$311$	9.74134e6i	0.323845i	0.986803	+	0.161923i	$0.0517695\pi$
$311$	9.74134e6i	0.323845i	−0.986803	+	0.161923i	$0.948230\pi$
$312$	0	0
$313$	−5.30265e6	−0.172926	−0.0864630	−	0.996255i	$-0.527556\pi$
$313$	−5.30265e6	−0.172926	−0.0864630	+	0.996255i	$0.527556\pi$
$314$	3.03959e7i	0.981808i
$315$	0	0
$316$	5.29322e7	1.67748
$317$	1.05462e7i	0.331068i	0.986204	+	0.165534i	$0.0529348\pi$
$317$	1.05462e7i	0.331068i	−0.986204	+	0.165534i	$0.947065\pi$
$318$	0	0
$319$	2.00381e7	0.617283
$320$	− 2.71986e7i	− 0.830034i
$321$	0	0
$322$	−3.83694e7	−1.14926
$323$	− 1.65656e7i	− 0.491587i
$324$	0	0
$325$	3.98180e6	0.115992
$326$	8.58523e7i	2.47799i
$327$	0	0
$328$	−4.70989e7	−1.33472
$329$	− 6.75747e7i	− 1.89756i
$330$	0	0
$331$	−3.81242e7	−1.05128	−0.525638	−	0.850708i	$-0.676174\pi$
$331$	−3.81242e7	−1.05128	−0.525638	+	0.850708i	$0.676174\pi$
$332$	9.13699e7i	2.49683i
$333$	0	0
$334$	8.42206e7	2.26037
$335$	1.37518e7i	0.365783i
$336$	0	0
$337$	−1.22682e7	−0.320548	−0.160274	−	0.987073i	$-0.551238\pi$
$337$	−1.22682e7	−0.320548	−0.160274	+	0.987073i	$0.551238\pi$
$338$	5.99291e7i	1.55198i
$339$	0	0
$340$	−4.45322e7	−1.13302
$341$	− 9.14313e6i	− 0.230585i
$342$	0	0
$343$	2.05817e7	0.510033
$344$	− 3.93594e7i	− 0.966882i
$345$	0	0
$346$	7.10317e7	1.71484
$347$	− 1.65809e7i	− 0.396843i	−0.980117	−	0.198422i	$-0.936418\pi$
$347$	− 1.65809e7i	− 0.396843i	0.980117	−	0.198422i	$-0.0635815\pi$
$348$	0	0
$349$	4.81038e7	1.13163	0.565813	−	0.824534i	$-0.308562\pi$
$349$	4.81038e7	1.13163	0.565813	+	0.824534i	$0.308562\pi$
$350$	− 7.71987e7i	− 1.80055i
$351$	0	0
$352$	−3.23870e7	−0.742580
$353$	− 1.47570e7i	− 0.335485i	−0.985831	−	0.167742i	$-0.946352\pi$
$353$	− 1.47570e7i	− 0.335485i	0.985831	−	0.167742i	$-0.0536477\pi$
$354$	0	0
$355$	−3.43116e6	−0.0766930
$356$	2.18945e7i	0.485272i
$357$	0	0
$358$	−6.19980e7	−1.35123
$359$	− 1.78509e7i	− 0.385813i	−0.981217	−	0.192907i	$-0.938209\pi$
$359$	− 1.78509e7i	− 0.385813i	0.981217	−	0.192907i	$-0.0617914\pi$
$360$	0	0
$361$	−4.16635e7	−0.885593
$362$	− 1.07875e8i	− 2.27403i
$363$	0	0
$364$	−1.76651e7	−0.366279
$365$	1.96122e7i	0.403318i
$366$	0	0
$367$	8.67940e6	0.175587	0.0877934	−	0.996139i	$-0.472018\pi$
$367$	8.67940e6	0.175587	0.0877934	+	0.996139i	$0.472018\pi$
$368$	4.39531e6i	0.0881954i
$369$	0	0
$370$	1.95064e7	0.385099
$371$	1.03063e8i	2.01827i
$372$	0	0
$373$	−7.94052e7	−1.53011	−0.765055	−	0.643965i	$-0.777288\pi$
$373$	−7.94052e7	−1.53011	−0.765055	+	0.643965i	$0.777288\pi$
$374$	7.86583e7i	1.50359i
$375$	0	0
$376$	5.58071e7	1.04985
$377$	− 7.96432e6i	− 0.148636i
$378$	0	0
$379$	−1.46346e7	−0.268821	−0.134410	−	0.990926i	$-0.542914\pi$
$379$	−1.46346e7	−0.268821	−0.134410	+	0.990926i	$0.542914\pi$
$380$	− 1.44691e7i	− 0.263688i
$381$	0	0
$382$	−1.23509e6	−0.0221568
$383$	9.16736e6i	0.163173i	0.996666	+	0.0815865i	$0.0259987\pi$
$383$	9.16736e6i	0.163173i	−0.996666	+	0.0815865i	$0.974001\pi$
$384$	0	0
$385$	2.88619e7	0.505758
$386$	− 9.53924e7i	− 1.65864i
$387$	0	0
$388$	3.64246e6	0.0623591
$389$	− 9.26668e6i	− 0.157426i	−0.996897	−	0.0787128i	$-0.974919\pi$
$389$	− 9.26668e6i	− 0.157426i	0.996897	−	0.0787128i	$-0.0250810\pi$
$390$	0	0
$391$	4.10787e7	0.687205
$392$	6.79101e7i	1.12739i
$393$	0	0
$394$	1.25326e8	2.04905
$395$	3.43733e7i	0.557737i
$396$	0	0
$397$	7.25544e7	1.15956	0.579779	−	0.814774i	$-0.303139\pi$
$397$	7.25544e7	1.15956	0.579779	+	0.814774i	$0.303139\pi$
$398$	− 4.50785e7i	− 0.715023i
$399$	0	0
$400$	−8.84330e6	−0.138177
$401$	7.37246e7i	1.14335i	0.820480	+	0.571675i	$0.193706\pi$
$401$	7.37246e7i	1.14335i	−0.820480	+	0.571675i	$0.806294\pi$
$402$	0	0
$403$	−3.63402e6	−0.0555228
$404$	5.48591e7i	0.831964i
$405$	0	0
$406$	−1.54411e8	−2.30728
$407$	− 2.08429e7i	− 0.309155i
$408$	0	0
$409$	3.43558e7	0.502146	0.251073	−	0.967968i	$-0.419217\pi$
$409$	3.43558e7	0.502146	0.251073	+	0.967968i	$0.419217\pi$
$410$	− 8.81575e7i	− 1.27911i
$411$	0	0
$412$	−1.43098e8	−2.04617
$413$	− 2.08620e7i	− 0.296146i
$414$	0	0
$415$	−5.93341e7	−0.830157
$416$	1.28725e7i	0.178806i
$417$	0	0
$418$	−2.55571e7	−0.349932
$419$	− 1.31347e8i	− 1.78557i	−0.450479	−	0.892787i	$-0.648747\pi$
$419$	− 1.31347e8i	− 1.78557i	0.450479	−	0.892787i	$-0.351253\pi$
$420$	0	0
$421$	2.36756e6	0.0317289	0.0158644	−	0.999874i	$-0.494950\pi$
$421$	2.36756e6	0.0317289	0.0158644	+	0.999874i	$0.494950\pi$
$422$	8.62060e7i	1.14710i
$423$	0	0
$424$	−8.51151e7	−1.11663
$425$	8.26497e7i	1.07665i
$426$	0	0
$427$	1.31596e8	1.69029
$428$	− 1.26450e8i	− 1.61283i
$429$	0	0
$430$	7.36711e7	0.926599
$431$	− 1.13049e8i	− 1.41200i	−0.708212	−	0.705999i	$-0.750498\pi$
$431$	− 1.13049e8i	− 1.41200i	0.708212	−	0.705999i	$-0.249502\pi$
$432$	0	0
$433$	4.50927e7	0.555447	0.277723	−	0.960661i	$-0.410420\pi$
$433$	4.50927e7	0.555447	0.277723	+	0.960661i	$0.410420\pi$
$434$	7.04559e7i	0.861882i
$435$	0	0
$436$	1.40677e8	1.69732
$437$	1.33470e7i	0.159934i
$438$	0	0
$439$	−1.61605e8	−1.91013	−0.955064	−	0.296399i	$-0.904214\pi$
$439$	−1.61605e8	−1.91013	−0.955064	+	0.296399i	$0.904214\pi$
$440$	2.38358e7i	0.279816i
$441$	0	0
$442$	3.12634e7	0.362051
$443$	− 2.54011e7i	− 0.292174i	−0.989272	−	0.146087i	$-0.953332\pi$
$443$	− 2.54011e7i	− 0.292174i	0.989272	−	0.146087i	$-0.0466679\pi$
$444$	0	0
$445$	−1.42179e7	−0.161345
$446$	4.25349e7i	0.479448i
$447$	0	0
$448$	2.23949e8	2.49067
$449$	9.43898e7i	1.04276i	0.853323	+	0.521382i	$0.174583\pi$
$449$	9.43898e7i	1.04276i	−0.853323	+	0.521382i	$0.825417\pi$
$450$	0	0
$451$	−9.41978e7	−1.02686
$452$	− 1.82697e7i	− 0.197841i
$453$	0	0
$454$	−2.06209e8	−2.20363
$455$	− 1.14714e7i	− 0.121782i
$456$	0	0
$457$	4.68452e7	0.490813	0.245407	−	0.969420i	$-0.421078\pi$
$457$	4.68452e7	0.490813	0.245407	+	0.969420i	$0.421078\pi$
$458$	2.11730e8i	2.20387i
$459$	0	0
$460$	3.58798e7	0.368618
$461$	− 2.33797e7i	− 0.238636i	−0.992856	−	0.119318i	$-0.961929\pi$
$461$	− 2.33797e7i	− 0.238636i	0.992856	−	0.119318i	$-0.0380708\pi$
$462$	0	0
$463$	−4.98269e7	−0.502019	−0.251010	−	0.967985i	$-0.580763\pi$
$463$	−4.98269e7	−0.502019	−0.251010	+	0.967985i	$0.580763\pi$
$464$	1.76882e7i	0.177064i
$465$	0	0
$466$	1.12718e8	1.11388
$467$	9.52369e7i	0.935092i	0.883969	+	0.467546i	$0.154862\pi$
$467$	9.52369e7i	0.935092i	−0.883969	+	0.467546i	$0.845138\pi$
$468$	0	0
$469$	−1.13230e8	−1.09760
$470$	1.04457e8i	1.00611i
$471$	0	0
$472$	1.72290e7	0.163846
$473$	− 7.87188e7i	− 0.743867i
$474$	0	0
$475$	−2.68540e7	−0.250569
$476$	− 3.66672e8i	− 3.39983i
$477$	0	0
$478$	1.43820e8	1.31685
$479$	− 1.97141e8i	− 1.79378i	−0.442251	−	0.896891i	$-0.645820\pi$
$479$	− 1.97141e8i	− 1.79378i	0.442251	−	0.896891i	$-0.354180\pi$
$480$	0	0
$481$	−8.28421e6	−0.0744416
$482$	− 1.91033e8i	− 1.70595i
$483$	0	0
$484$	−1.00202e8	−0.883775
$485$	2.36536e6i	0.0207334i
$486$	0	0
$487$	1.92602e6	0.0166753	0.00833765	−	0.999965i	$-0.497346\pi$
$487$	1.92602e6	0.0166753	0.00833765	+	0.999965i	$0.497346\pi$
$488$	1.08680e8i	0.935167i
$489$	0	0
$490$	−1.27111e8	−1.08042
$491$	1.79722e8i	1.51830i	0.650916	+	0.759150i	$0.274385\pi$
$491$	1.79722e8i	1.51830i	−0.650916	+	0.759150i	$0.725615\pi$
$492$	0	0
$493$	1.65314e8	1.37965
$494$	1.01579e7i	0.0842603i
$495$	0	0
$496$	8.07090e6	0.0661419
$497$	− 2.82517e7i	− 0.230131i
$498$	0	0
$499$	1.54018e8	1.23956	0.619782	−	0.784774i	$-0.287221\pi$
$499$	1.54018e8	1.23956	0.619782	+	0.784774i	$0.287221\pi$
$500$	1.69638e8i	1.35710i
$501$	0	0
$502$	−3.87025e8	−3.05934
$503$	− 2.25142e7i	− 0.176910i	−0.996080	−	0.0884551i	$-0.971807\pi$
$503$	− 2.25142e7i	− 0.176910i	0.996080	−	0.0884551i	$-0.0281930\pi$
$504$	0	0
$505$	−3.56246e7	−0.276615
$506$	− 6.33753e7i	− 0.489180i
$507$	0	0
$508$	1.24519e7	0.0949825
$509$	2.16126e8i	1.63891i	0.573147	+	0.819453i	$0.305722\pi$
$509$	2.16126e8i	1.63891i	−0.573147	+	0.819453i	$0.694278\pi$
$510$	0	0
$511$	−1.61484e8	−1.21023
$512$	− 4.97487e7i	− 0.370656i
$513$	0	0
$514$	2.51278e8	1.85040
$515$	− 9.29253e7i	− 0.680318i
$516$	0	0
$517$	1.11614e8	0.807695
$518$	1.60613e8i	1.15556i
$519$	0	0
$520$	9.47376e6	0.0673771
$521$	− 8.35166e7i	− 0.590554i	−0.955412	−	0.295277i	$-0.904588\pi$
$521$	− 8.35166e7i	− 0.590554i	0.955412	−	0.295277i	$-0.0954120\pi$
$522$	0	0
$523$	2.08856e8	1.45997	0.729983	−	0.683466i	$-0.239528\pi$
$523$	2.08856e8	1.45997	0.729983	+	0.683466i	$0.239528\pi$
$524$	2.57101e8i	1.78694i
$525$	0	0
$526$	−4.43608e7	−0.304819
$527$	− 7.54308e7i	− 0.515367i
$528$	0	0
$529$	1.14939e8	0.776424
$530$	− 1.59315e8i	− 1.07011i
$531$	0	0
$532$	1.19137e8	0.791244
$533$	3.74397e7i	0.247258i
$534$	0	0
$535$	8.21146e7	0.536240
$536$	− 9.35119e7i	− 0.607257i
$537$	0	0
$538$	−7.19625e7	−0.462125
$539$	1.35820e8i	0.867357i
$540$	0	0
$541$	−1.21245e8	−0.765727	−0.382863	−	0.923805i	$-0.625062\pi$
$541$	−1.21245e8	−0.765727	−0.382863	+	0.923805i	$0.625062\pi$
$542$	− 3.71519e8i	− 2.33337i
$543$	0	0
$544$	−2.67193e8	−1.65970
$545$	9.13534e7i	0.564333i
$546$	0	0
$547$	−1.33857e8	−0.817861	−0.408931	−	0.912565i	$-0.634098\pi$
$547$	−1.33857e8	−0.817861	−0.408931	+	0.912565i	$0.634098\pi$
$548$	1.98264e7i	0.120477i
$549$	0	0
$550$	1.27510e8	0.766402
$551$	5.37128e7i	0.321087i
$552$	0	0
$553$	−2.83025e8	−1.67359
$554$	− 2.92664e8i	− 1.72123i
$555$	0	0
$556$	−1.98590e8	−1.15540
$557$	8.20694e7i	0.474915i	0.971398	+	0.237457i	$0.0763140\pi$
$557$	8.20694e7i	0.474915i	−0.971398	+	0.237457i	$0.923686\pi$
$558$	0	0
$559$	−3.12875e7	−0.179116
$560$	2.54772e7i	0.145073i
$561$	0	0
$562$	1.59484e7	0.0898480
$563$	2.21977e8i	1.24389i	0.783059	+	0.621947i	$0.213658\pi$
$563$	2.21977e8i	1.24389i	−0.783059	+	0.621947i	$0.786342\pi$
$564$	0	0
$565$	1.18641e7	0.0657792
$566$	1.84719e8i	1.01874i
$567$	0	0
$568$	2.33319e7	0.127322
$569$	− 2.88087e8i	− 1.56382i	−0.623391	−	0.781911i	$-0.714245\pi$
$569$	− 2.88087e8i	− 1.56382i	0.623391	−	0.781911i	$-0.285755\pi$
$570$	0	0
$571$	1.83227e8	0.984197	0.492098	−	0.870540i	$-0.336230\pi$
$571$	1.83227e8	0.984197	0.492098	+	0.870540i	$0.336230\pi$
$572$	− 2.91777e7i	− 0.155906i
$573$	0	0
$574$	7.25877e8	3.83820
$575$	− 6.65912e7i	− 0.350278i
$576$	0	0
$577$	−2.07783e8	−1.08164	−0.540820	−	0.841139i	$-0.681886\pi$
$577$	−2.07783e8	−1.08164	−0.540820	+	0.841139i	$0.681886\pi$
$578$	3.41709e8i	1.76959i
$579$	0	0
$580$	1.44392e8	0.740048
$581$	− 4.88549e8i	− 2.49104i
$582$	0	0
$583$	−1.70230e8	−0.859075
$584$	− 1.33363e8i	− 0.669571i
$585$	0	0
$586$	−1.43481e8	−0.713018
$587$	3.28908e8i	1.62615i	0.582161	+	0.813073i	$0.302207\pi$
$587$	3.28908e8i	1.62615i	−0.582161	+	0.813073i	$0.697793\pi$
$588$	0	0
$589$	2.45085e7	0.119942
$590$	3.22485e7i	0.157019i
$591$	0	0
$592$	1.83986e7	0.0886790
$593$	1.97249e7i	0.0945914i	0.998881	+	0.0472957i	$0.0150603\pi$
$593$	1.97249e7i	0.0945914i	−0.998881	+	0.0472957i	$0.984940\pi$
$594$	0	0
$595$	2.38111e8	1.13039
$596$	4.17023e8i	1.96980i
$597$	0	0
$598$	−2.51891e7	−0.117790
$599$	− 9.38486e7i	− 0.436664i	−0.975875	−	0.218332i	$-0.929938\pi$
$599$	− 9.38486e7i	− 0.436664i	0.975875	−	0.218332i	$-0.0700616\pi$
$600$	0	0
$601$	1.53106e8	0.705293	0.352646	−	0.935757i	$-0.385282\pi$
$601$	1.53106e8	0.705293	0.352646	+	0.935757i	$0.385282\pi$
$602$	6.06598e8i	2.78043i
$603$	0	0
$604$	−3.66554e8	−1.66352
$605$	− 6.50698e7i	− 0.293842i
$606$	0	0
$607$	1.08279e8	0.484147	0.242074	−	0.970258i	$-0.422172\pi$
$607$	1.08279e8	0.484147	0.242074	+	0.970258i	$0.422172\pi$
$608$	− 8.68146e7i	− 0.386262i
$609$	0	0
$610$	−2.03422e8	−0.896206
$611$	− 4.43620e7i	− 0.194486i
$612$	0	0
$613$	−2.60288e8	−1.12999	−0.564993	−	0.825096i	$-0.691121\pi$
$613$	−2.60288e8	−1.12999	−0.564993	+	0.825096i	$0.691121\pi$
$614$	− 5.75195e8i	− 2.48491i
$615$	0	0
$616$	−1.96261e8	−0.839638
$617$	− 1.65376e8i	− 0.704073i	−0.935986	−	0.352036i	$-0.885489\pi$
$617$	− 1.65376e8i	− 0.704073i	0.935986	−	0.352036i	$-0.114511\pi$
$618$	0	0
$619$	−1.36836e8	−0.576935	−0.288468	−	0.957490i	$-0.593146\pi$
$619$	−1.36836e8	−0.576935	−0.288468	+	0.957490i	$0.593146\pi$
$620$	− 6.58843e7i	− 0.276444i
$621$	0	0
$622$	1.23987e8	0.515235
$623$	− 1.17069e8i	− 0.484146i
$624$	0	0
$625$	7.06994e7	0.289585
$626$	6.74918e7i	0.275124i
$627$	0	0
$628$	2.34037e8	0.944942
$629$	− 1.71954e8i	− 0.690973i
$630$	0	0
$631$	2.66941e8	1.06249	0.531247	−	0.847217i	$-0.321723\pi$
$631$	2.66941e8	1.06249	0.531247	+	0.847217i	$0.321723\pi$
$632$	− 2.33738e8i	− 0.925931i
$633$	0	0
$634$	1.34231e8	0.526727
$635$	8.08605e6i	0.0315802i
$636$	0	0
$637$	5.39829e7	0.208852
$638$	− 2.55043e8i	− 0.982092i
$639$	0	0
$640$	−1.93771e8	−0.739179
$641$	3.69866e8i	1.40433i	0.712013	+	0.702167i	$0.247784\pi$
$641$	3.69866e8i	1.40433i	−0.712013	+	0.702167i	$0.752216\pi$
$642$	0	0
$643$	−9.29168e7	−0.349511	−0.174756	−	0.984612i	$-0.555914\pi$
$643$	−9.29168e7	−0.349511	−0.174756	+	0.984612i	$0.555914\pi$
$644$	2.95429e8i	1.10610i
$645$	0	0
$646$	−2.10846e8	−0.782111
$647$	− 9.21336e7i	− 0.340177i	−0.985429	−	0.170089i	$-0.945595\pi$
$647$	− 9.21336e7i	− 0.340177i	0.985429	−	0.170089i	$-0.0544054\pi$
$648$	0	0
$649$	3.44580e7	0.126054
$650$	− 5.06800e7i	− 0.184543i
$651$	0	0
$652$	6.61029e8	2.38494
$653$	2.20689e8i	0.792576i	0.918126	+	0.396288i	$0.129702\pi$
$653$	2.20689e8i	0.792576i	−0.918126	+	0.396288i	$0.870298\pi$
$654$	0	0
$655$	−1.66957e8	−0.594130
$656$	− 8.31511e7i	− 0.294548i
$657$	0	0
$658$	−8.60085e8	−3.01900
$659$	5.01619e8i	1.75274i	0.481639	+	0.876370i	$0.340042\pi$
$659$	5.01619e8i	1.75274i	−0.481639	+	0.876370i	$0.659958\pi$
$660$	0	0
$661$	−2.78166e8	−0.963163	−0.481582	−	0.876401i	$-0.659937\pi$
$661$	−2.78166e8	−0.963163	−0.481582	+	0.876401i	$0.659937\pi$
$662$	4.85242e8i	1.67257i
$663$	0	0
$664$	4.03472e8	1.37819
$665$	7.73654e7i	0.263076i
$666$	0	0
$667$	−1.33194e8	−0.448858
$668$	− 6.48465e8i	− 2.17549i
$669$	0	0
$670$	1.75031e8	0.581957
$671$	2.17360e8i	0.719468i
$672$	0	0
$673$	5.34850e8	1.75464	0.877318	−	0.479910i	$-0.159331\pi$
$673$	5.34850e8	1.75464	0.877318	+	0.479910i	$0.159331\pi$
$674$	1.56149e8i	0.509988i
$675$	0	0
$676$	4.61430e8	1.49371
$677$	− 1.41358e6i	− 0.00455568i	−0.999997	−	0.00227784i	$-0.999275\pi$
$677$	− 1.41358e6i	− 0.00455568i	0.999997	−	0.00227784i	$-0.000725059\pi$
$678$	0	0
$679$	−1.94760e7	−0.0622144
$680$	1.96646e8i	0.625400i
$681$	0	0
$682$	−1.16373e8	−0.366859
$683$	− 2.41616e8i	− 0.758340i	−0.925327	−	0.379170i	$-0.876209\pi$
$683$	− 2.41616e8i	− 0.758340i	0.925327	−	0.379170i	$-0.123791\pi$
$684$	0	0
$685$	−1.28750e7	−0.0400566
$686$	− 2.61962e8i	− 0.811458i
$687$	0	0
$688$	6.94873e7	0.213373
$689$	6.76595e7i	0.206857i
$690$	0	0
$691$	5.30543e8	1.60800	0.804001	−	0.594628i	$-0.202701\pi$
$691$	5.30543e8	1.60800	0.804001	+	0.594628i	$0.202701\pi$
$692$	− 5.46916e8i	− 1.65045i
$693$	0	0
$694$	−2.11040e8	−0.631374
$695$	− 1.28961e8i	− 0.384152i
$696$	0	0
$697$	−7.77132e8	−2.29507
$698$	− 6.12261e8i	− 1.80041i
$699$	0	0
$700$	−5.94399e8	−1.73294
$701$	5.49256e7i	0.159449i	0.996817	+	0.0797244i	$0.0254040\pi$
$701$	5.49256e7i	0.159449i	−0.996817	+	0.0797244i	$0.974596\pi$
$702$	0	0
$703$	5.58702e7	0.160811
$704$	3.69900e8i	1.06015i
$705$	0	0
$706$	−1.87826e8	−0.533753
$707$	− 2.93328e8i	− 0.830034i
$708$	0	0
$709$	3.16706e7	0.0888622	0.0444311	−	0.999012i	$-0.485852\pi$
$709$	3.16706e7	0.0888622	0.0444311	+	0.999012i	$0.485852\pi$
$710$	4.36715e7i	0.122018i
$711$	0	0
$712$	9.66819e7	0.267858
$713$	6.07749e7i	0.167670i
$714$	0	0
$715$	1.89475e7	0.0518363
$716$	4.77361e8i	1.30049i
$717$	0	0
$718$	−2.27205e8	−0.613825
$719$	4.37723e8i	1.17764i	0.808264	+	0.588820i	$0.200407\pi$
$719$	4.37723e8i	1.17764i	−0.808264	+	0.588820i	$0.799593\pi$
$720$	0	0
$721$	7.65134e8	2.04142
$722$	5.30290e8i	1.40897i
$723$	0	0
$724$	−8.30595e8	−2.18864
$725$	− 2.67985e8i	− 0.703230i
$726$	0	0
$727$	−4.64180e8	−1.20805	−0.604023	−	0.796967i	$-0.706436\pi$
$727$	−4.64180e8	−1.20805	−0.604023	+	0.796967i	$0.706436\pi$
$728$	7.80057e7i	0.202177i
$729$	0	0
$730$	2.49623e8	0.641675
$731$	− 6.49430e8i	− 1.66257i
$732$	0	0
$733$	7.04886e8	1.78981	0.894905	−	0.446256i	$-0.147243\pi$
$733$	7.04886e8	1.78981	0.894905	+	0.446256i	$0.147243\pi$
$734$	− 1.10471e8i	− 0.279357i
$735$	0	0
$736$	2.15279e8	0.539967
$737$	− 1.87024e8i	− 0.467191i
$738$	0	0
$739$	−2.83900e8	−0.703448	−0.351724	−	0.936104i	$-0.614404\pi$
$739$	−2.83900e8	−0.703448	−0.351724	+	0.936104i	$0.614404\pi$
$740$	− 1.50192e8i	− 0.370639i
$741$	0	0
$742$	1.31177e9	3.21105
$743$	− 5.01018e8i	− 1.22148i	−0.791830	−	0.610741i	$-0.790872\pi$
$743$	− 5.01018e8i	− 1.22148i	0.791830	−	0.610741i	$-0.209128\pi$
$744$	0	0
$745$	−2.70808e8	−0.654927
$746$	1.01066e9i	2.43439i
$747$	0	0
$748$	6.05638e8	1.44713
$749$	6.76120e8i	1.60908i
$750$	0	0
$751$	−1.48249e8	−0.350004	−0.175002	−	0.984568i	$-0.555993\pi$
$751$	−1.48249e8	−0.350004	−0.175002	+	0.984568i	$0.555993\pi$
$752$	9.85249e7i	0.231682i
$753$	0	0
$754$	−1.01369e8	−0.236479
$755$	− 2.38034e8i	− 0.553094i
$756$	0	0
$757$	2.14422e8	0.494291	0.247145	−	0.968978i	$-0.420507\pi$
$757$	2.14422e8	0.494291	0.247145	+	0.968978i	$0.420507\pi$
$758$	1.86268e8i	0.427691i
$759$	0	0
$760$	−6.38928e7	−0.145550
$761$	− 2.69760e7i	− 0.0612101i	−0.999532	−	0.0306051i	$-0.990257\pi$
$761$	− 2.69760e7i	− 0.0612101i	0.999532	−	0.0306051i	$-0.00974341\pi$
$762$	0	0
$763$	−7.52192e8	−1.69338
$764$	9.50969e6i	0.0213249i
$765$	0	0
$766$	1.16681e8	0.259607
$767$	− 1.36957e7i	− 0.0303526i
$768$	0	0
$769$	−4.90064e8	−1.07764	−0.538821	−	0.842421i	$-0.681130\pi$
$769$	−4.90064e8	−1.07764	−0.538821	+	0.842421i	$0.681130\pi$
$770$	− 3.67352e8i	− 0.804657i
$771$	0	0
$772$	−7.34484e8	−1.59636
$773$	4.17032e8i	0.902882i	0.892301	+	0.451441i	$0.149090\pi$
$773$	4.17032e8i	0.902882i	−0.892301	+	0.451441i	$0.850910\pi$
$774$	0	0
$775$	−1.22278e8	−0.262690
$776$	− 1.60844e7i	− 0.0344208i
$777$	0	0
$778$	−1.17946e8	−0.250463
$779$	− 2.52501e8i	− 0.534134i
$780$	0	0
$781$	4.66638e7	0.0979550
$782$	− 5.22846e8i	− 1.09334i
$783$	0	0
$784$	−1.19892e8	−0.248796
$785$	1.51980e8i	0.314179i
$786$	0	0
$787$	−3.46111e8	−0.710054	−0.355027	−	0.934856i	$-0.615528\pi$
$787$	−3.46111e8	−0.710054	−0.355027	+	0.934856i	$0.615528\pi$
$788$	− 9.64963e8i	− 1.97211i
$789$	0	0
$790$	4.37500e8	0.887355
$791$	9.76872e7i	0.197382i
$792$	0	0
$793$	8.63915e7	0.173241
$794$	− 9.23467e8i	− 1.84484i
$795$	0	0
$796$	−3.47087e8	−0.688175
$797$	7.25306e8i	1.43267i	0.697756	+	0.716335i	$0.254182\pi$
$797$	7.25306e8i	1.43267i	−0.697756	+	0.716335i	$0.745818\pi$
$798$	0	0
$799$	9.20816e8	1.80523
$800$	4.33138e8i	0.845972i
$801$	0	0
$802$	9.38361e8	1.81906
$803$	− 2.66726e8i	− 0.515132i
$804$	0	0
$805$	−1.91847e8	−0.367762
$806$	4.62535e7i	0.0883363i
$807$	0	0
$808$	2.42247e8	0.459224
$809$	− 4.93161e8i	− 0.931415i	−0.884939	−	0.465707i	$-0.845800\pi$
$809$	− 4.93161e8i	− 0.931415i	0.884939	−	0.465707i	$-0.154200\pi$
$810$	0	0
$811$	−5.34731e7	−0.100247	−0.0501237	−	0.998743i	$-0.515962\pi$
$811$	−5.34731e7	−0.100247	−0.0501237	+	0.998743i	$0.515962\pi$
$812$	1.18891e9i	2.22065i
$813$	0	0
$814$	−2.65287e8	−0.491862
$815$	4.29261e8i	0.792956i
$816$	0	0
$817$	2.11009e8	0.386931
$818$	− 4.37278e8i	− 0.798909i
$819$	0	0
$820$	−6.78778e8	−1.23108
$821$	− 1.07674e9i	− 1.94573i	−0.231377	−	0.972864i	$-0.574323\pi$
$821$	− 1.07674e9i	− 1.94573i	0.231377	−	0.972864i	$-0.425677\pi$
$822$	0	0
$823$	8.88441e7	0.159378	0.0796891	−	0.996820i	$-0.474607\pi$
$823$	8.88441e7	0.159378	0.0796891	+	0.996820i	$0.474607\pi$
$824$	6.31892e8i	1.12943i
$825$	0	0
$826$	−2.65530e8	−0.471165
$827$	− 9.82047e7i	− 0.173626i	−0.996225	−	0.0868132i	$-0.972332\pi$
$827$	− 9.82047e7i	− 0.173626i	0.996225	−	0.0868132i	$-0.0276683\pi$
$828$	0	0
$829$	2.25045e8	0.395008	0.197504	−	0.980302i	$-0.436717\pi$
$829$	2.25045e8	0.395008	0.197504	+	0.980302i	$0.436717\pi$
$830$	7.55200e8i	1.32077i
$831$	0	0
$832$	1.47020e8	0.255274
$833$	1.12052e9i	1.93858i
$834$	0	0
$835$	4.21103e8	0.723317
$836$	1.96780e8i	0.336792i
$837$	0	0
$838$	−1.67177e9	−2.84083
$839$	7.84433e8i	1.32822i	0.747635	+	0.664110i	$0.231189\pi$
$839$	7.84433e8i	1.32822i	−0.747635	+	0.664110i	$0.768811\pi$
$840$	0	0
$841$	5.88040e7	0.0988597
$842$	− 3.01341e7i	− 0.0504803i
$843$	0	0
$844$	6.63752e8	1.10402
$845$	2.99645e8i	0.496635i
$846$	0	0
$847$	5.35776e8	0.881724
$848$	− 1.50267e8i	− 0.246420i
$849$	0	0
$850$	1.05196e9	1.71294
$851$	1.38544e8i	0.224802i
$852$	0	0
$853$	−7.97906e7	−0.128560	−0.0642798	−	0.997932i	$-0.520475\pi$
$853$	−7.97906e7	−0.128560	−0.0642798	+	0.997932i	$0.520475\pi$
$854$	− 1.67495e9i	− 2.68923i
$855$	0	0
$856$	−5.58379e8	−0.890241
$857$	− 1.06107e9i	− 1.68579i	−0.538080	−	0.842894i	$-0.680850\pi$
$857$	− 1.06107e9i	− 1.68579i	0.538080	−	0.842894i	$-0.319150\pi$
$858$	0	0
$859$	3.34286e8	0.527399	0.263699	−	0.964605i	$-0.415057\pi$
$859$	3.34286e8	0.527399	0.263699	+	0.964605i	$0.415057\pi$
$860$	− 5.67239e8i	− 0.891806i
$861$	0	0
$862$	−1.43888e9	−2.24648
$863$	2.65292e7i	0.0412754i	0.999787	+	0.0206377i	$0.00656965\pi$
$863$	2.65292e7i	0.0412754i	−0.999787	+	0.0206377i	$0.993430\pi$
$864$	0	0
$865$	3.55158e8	0.548749
$866$	− 5.73936e8i	− 0.883711i
$867$	0	0
$868$	5.42483e8	0.829519
$869$	− 4.67477e8i	− 0.712362i
$870$	0	0
$871$	−7.43343e7	−0.112495
$872$	− 6.21203e8i	− 0.936880i
$873$	0	0
$874$	1.69880e8	0.254453
$875$	− 9.07043e8i	− 1.35395i
$876$	0	0
$877$	−1.30791e8	−0.193901	−0.0969504	−	0.995289i	$-0.530909\pi$
$877$	−1.30791e8	−0.193901	−0.0969504	+	0.995289i	$0.530909\pi$
$878$	2.05690e9i	3.03900i
$879$	0	0
$880$	−4.20811e7	−0.0617503
$881$	9.18953e8i	1.34390i	0.740598	+	0.671948i	$0.234542\pi$
$881$	9.18953e8i	1.34390i	−0.740598	+	0.671948i	$0.765458\pi$
$882$	0	0
$883$	−1.09112e9	−1.58486	−0.792432	−	0.609961i	$-0.791185\pi$
$883$	−1.09112e9	−1.58486	−0.792432	+	0.609961i	$0.791185\pi$
$884$	− 2.40716e8i	− 0.348456i
$885$	0	0
$886$	−3.23303e8	−0.464846
$887$	5.36427e8i	0.768670i	0.923194	+	0.384335i	$0.125569\pi$
$887$	5.36427e8i	0.768670i	−0.923194	+	0.384335i	$0.874431\pi$
$888$	0	0
$889$	−6.65794e7	−0.0947621
$890$	1.80965e8i	0.256699i
$891$	0	0
$892$	3.27502e8	0.461445
$893$	2.99186e8i	0.420133i
$894$	0	0
$895$	−3.09990e8	−0.432393
$896$	− 1.59549e9i	− 2.21804i
$897$	0	0
$898$	1.20139e9	1.65903
$899$	2.44579e8i	0.336620i
$900$	0	0
$901$	−1.40440e9	−1.92007
$902$	1.19894e9i	1.63372i
$903$	0	0
$904$	−8.06757e7	−0.109204
$905$	− 5.39375e8i	− 0.727688i
$906$	0	0
$907$	−4.60985e8	−0.617824	−0.308912	−	0.951091i	$-0.599965\pi$
$907$	−4.60985e8	−0.617824	−0.308912	+	0.951091i	$0.599965\pi$
$908$	1.58772e9i	2.12089i
$909$	0	0
$910$	−1.46007e8	−0.193754
$911$	8.68400e8i	1.14859i	0.818649	+	0.574295i	$0.194724\pi$
$911$	8.68400e8i	1.14859i	−0.818649	+	0.574295i	$0.805276\pi$
$912$	0	0
$913$	8.06944e8	1.06031
$914$	− 5.96242e8i	− 0.780879i
$915$	0	0
$916$	1.63024e9	2.12112
$917$	− 1.37470e9i	− 1.78279i
$918$	0	0
$919$	1.28061e9	1.64995	0.824976	−	0.565168i	$-0.191189\pi$
$919$	1.28061e9	1.64995	0.824976	+	0.565168i	$0.191189\pi$
$920$	− 1.58438e8i	− 0.203468i
$921$	0	0
$922$	−2.97575e8	−0.379668
$923$	− 1.85469e7i	− 0.0235867i
$924$	0	0
$925$	−2.78749e8	−0.352199
$926$	6.34192e8i	0.798708i
$927$	0	0
$928$	8.66353e8	1.08405
$929$	3.23960e8i	0.404058i	0.979380	+	0.202029i	$0.0647536\pi$
$929$	3.23960e8i	0.404058i	−0.979380	+	0.202029i	$0.935246\pi$
$930$	0	0
$931$	−3.64071e8	−0.451166
$932$	− 8.67888e8i	− 1.07205i
$933$	0	0
$934$	1.21217e9	1.48772
$935$	3.93291e8i	0.481149i
$936$	0	0
$937$	−1.33188e9	−1.61900	−0.809498	−	0.587123i	$-0.800261\pi$
$937$	−1.33188e9	−1.61900	−0.809498	+	0.587123i	$0.800261\pi$
$938$	1.44118e9i	1.74627i
$939$	0	0
$940$	8.04278e8	0.968329
$941$	− 8.24869e8i	− 0.989957i	−0.868905	−	0.494978i	$-0.835176\pi$
$941$	− 8.24869e8i	− 0.989957i	0.868905	−	0.494978i	$-0.164824\pi$
$942$	0	0
$943$	6.26138e8	0.746681
$944$	3.04171e7i	0.0361578i
$945$	0	0
$946$	−1.00193e9	−1.18349
$947$	− 7.33660e8i	− 0.863863i	−0.901906	−	0.431931i	$-0.857832\pi$
$947$	− 7.33660e8i	− 0.863863i	0.901906	−	0.431931i	$-0.142168\pi$
$948$	0	0
$949$	−1.06013e8	−0.124039
$950$	3.41796e8i	0.398654i
$951$	0	0
$952$	−1.61915e9	−1.87662
$953$	− 6.87744e8i	− 0.794600i	−0.917689	−	0.397300i	$-0.869947\pi$
$953$	− 6.87744e8i	− 0.794600i	0.917689	−	0.397300i	$-0.130053\pi$
$954$	0	0
$955$	−6.17544e6	−0.00709019
$956$	− 1.10736e9i	− 1.26740i
$957$	0	0
$958$	−2.50919e9	−2.85389
$959$	− 1.06011e8i	− 0.120197i
$960$	0	0
$961$	−7.75906e8	−0.874256
$962$	1.05441e8i	0.118436i
$963$	0	0
$964$	−1.47088e9	−1.64190
$965$	− 4.76962e8i	− 0.530764i
$966$	0	0
$967$	1.43001e9	1.58147	0.790733	−	0.612162i	$-0.209700\pi$
$967$	1.43001e9	1.58147	0.790733	+	0.612162i	$0.209700\pi$
$968$	4.42475e8i	0.487823i
$969$	0	0
$970$	3.01061e7	0.0329867
$971$	1.05628e9i	1.15377i	0.816824	+	0.576887i	$0.195733\pi$
$971$	1.05628e9i	1.15377i	−0.816824	+	0.576887i	$0.804267\pi$
$972$	0	0
$973$	1.06185e9	1.15272
$974$	− 2.45142e7i	− 0.0265303i
$975$	0	0
$976$	−1.91869e8	−0.206375
$977$	− 8.72371e8i	− 0.935443i	−0.883876	−	0.467722i	$-0.845075\pi$
$977$	− 8.72371e8i	− 0.935443i	0.883876	−	0.467722i	$-0.154925\pi$
$978$	0	0
$979$	1.93364e8	0.206076
$980$	9.78704e8i	1.03986i
$981$	0	0
$982$	2.28749e9	2.41560
$983$	7.90860e8i	0.832605i	0.909226	+	0.416302i	$0.136674\pi$
$983$	7.90860e8i	0.832605i	−0.909226	+	0.416302i	$0.863326\pi$
$984$	0	0
$985$	6.26631e8	0.655697
$986$	− 2.10411e9i	− 2.19501i
$987$	0	0
$988$	7.82118e7	0.0810964
$989$	5.23249e8i	0.540903i
$990$	0	0
$991$	1.38796e8	0.142612	0.0713062	−	0.997454i	$-0.477283\pi$
$991$	1.38796e8	0.142612	0.0713062	+	0.997454i	$0.477283\pi$
$992$	− 3.95306e8i	− 0.404947i
$993$	0	0
$994$	−3.59586e8	−0.366137
$995$	− 2.25392e8i	− 0.228807i
$996$	0	0
$997$	−3.29036e8	−0.332015	−0.166008	−	0.986124i	$-0.553088\pi$
$997$	−3.29036e8	−0.332015	−0.166008	+	0.986124i	$0.553088\pi$
$998$	− 1.96032e9i	− 1.97213i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.7.b.a.8.1	✓	2
3.2	odd	2	inner	9.7.b.a.8.2	yes	2
4.3	odd	2		144.7.e.a.17.1		2
5.2	odd	4		225.7.d.a.224.4		4
5.3	odd	4		225.7.d.a.224.1		4
5.4	even	2		225.7.c.a.26.2		2
7.6	odd	2		441.7.b.a.197.1		2
8.3	odd	2		576.7.e.a.449.2		2
8.5	even	2		576.7.e.l.449.2		2
9.2	odd	6		81.7.d.d.53.2		4
9.4	even	3		81.7.d.d.26.2		4
9.5	odd	6		81.7.d.d.26.1		4
9.7	even	3		81.7.d.d.53.1		4
12.11	even	2		144.7.e.a.17.2		2
15.2	even	4		225.7.d.a.224.2		4
15.8	even	4		225.7.d.a.224.3		4
15.14	odd	2		225.7.c.a.26.1		2
21.20	even	2		441.7.b.a.197.2		2
24.5	odd	2		576.7.e.l.449.1		2
24.11	even	2		576.7.e.a.449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.7.b.a.8.1	✓	2	1.1	even	1	trivial
9.7.b.a.8.2	yes	2	3.2	odd	2	inner
81.7.d.d.26.1		4	9.5	odd	6
81.7.d.d.26.2		4	9.4	even	3
81.7.d.d.53.1		4	9.7	even	3
81.7.d.d.53.2		4	9.2	odd	6
144.7.e.a.17.1		2	4.3	odd	2
144.7.e.a.17.2		2	12.11	even	2
225.7.c.a.26.1		2	15.14	odd	2
225.7.c.a.26.2		2	5.4	even	2
225.7.d.a.224.1		4	5.3	odd	4
225.7.d.a.224.2		4	15.2	even	4
225.7.d.a.224.3		4	15.8	even	4
225.7.d.a.224.4		4	5.2	odd	4
441.7.b.a.197.1		2	7.6	odd	2
441.7.b.a.197.2		2	21.20	even	2
576.7.e.a.449.1		2	24.11	even	2
576.7.e.a.449.2		2	8.3	odd	2
576.7.e.l.449.1		2	24.5	odd	2
576.7.e.l.449.2		2	8.5	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	9.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-12.7279i q^{2} -98.0000 q^{4} -63.6396i q^{5} +524.000 q^{7} +432.749i q^{8} -810.000 q^{10} +865.499i q^{11} +344.000 q^{13} -6669.43i q^{14} -764.000 q^{16} +7140.36i q^{17} -2320.00 q^{19} +6236.68i q^{20} +11016.0 q^{22} -5753.02i q^{23} +11575.0 q^{25} -4378.41i q^{26} -51352.0 q^{28} -23152.1i q^{29} -10564.0 q^{31} +37420.1i q^{32} +90882.0 q^{34} -33347.2i q^{35} -24082.0 q^{37} +29528.8i q^{38} +27540.0 q^{40} +108836. i q^{41} -90952.0 q^{43} -84818.9i q^{44} -73224.0 q^{46} -128959. i q^{47} +156927. q^{49} -147326. i q^{50} -33712.0 q^{52} +196685. i q^{53} +55080.0 q^{55} +226761. i q^{56} -294678. q^{58} -39812.9i q^{59} +251138. q^{61} +134458. i q^{62} +427384. q^{64} -21892.0i q^{65} -216088. q^{67} -699756. i q^{68} -424440. q^{70} -53915.5i q^{71} -308176. q^{73} +306514. i q^{74} +227360. q^{76} +453521. i q^{77} -540124. q^{79} +48620.7i q^{80} +1.38526e6 q^{82} -932346. i q^{83} +454410. q^{85} +1.15763e6i q^{86} -374544. q^{88} -223413. i q^{89} +180256. q^{91} +563796. i q^{92} -1.64138e6 q^{94} +147644. i q^{95} -37168.0 q^{97} -1.99735e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 196 q^{4} + 1048 q^{7} - 1620 q^{10} + 688 q^{13} - 1528 q^{16} - 4640 q^{19} + 22032 q^{22} + 23150 q^{25} - 102704 q^{28} - 21128 q^{31} + 181764 q^{34} - 48164 q^{37} + 55080 q^{40} - 181904 q^{43}+ \cdots - 74336 q^{97}+O(q^{100}) \) 2 * q - 196 * q^4 + 1048 * q^7 - 1620 * q^10 + 688 * q^13 - 1528 * q^16 - 4640 * q^19 + 22032 * q^22 + 23150 * q^25 - 102704 * q^28 - 21128 * q^31 + 181764 * q^34 - 48164 * q^37 + 55080 * q^40 - 181904 * q^43 - 146448 * q^46 + 313854 * q^49 - 67424 * q^52 + 110160 * q^55 - 589356 * q^58 + 502276 * q^61 + 854768 * q^64 - 432176 * q^67 - 848880 * q^70 - 616352 * q^73 + 454720 * q^76 - 1080248 * q^79 + 2770524 * q^82 + 908820 * q^85 - 749088 * q^88 + 360512 * q^91 - 3282768 * q^94 - 74336 * q^97

Introduction

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