LMFDB - Embedded newform 81.8.c.c.28.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,8,Mod(28,81)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("81.28"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	81.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,6,0,92] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$25.3031870642$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			28.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	81.28
Dual form			81.8.c.c.55.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.00000 + 5.19615i) q^{2} +(46.0000 - 79.6743i) q^{4} +(195.000 - 337.750i) q^{5} +(32.0000 + 55.4256i) q^{7} +1320.00 q^{8} +2340.00 q^{10} +(-474.000 - 820.992i) q^{11} +(2549.00 - 4415.00i) q^{13} +(-192.000 + 332.554i) q^{14} +(-1928.00 - 3339.39i) q^{16} -28386.0 q^{17} -8620.00 q^{19} +(-17940.0 - 31073.0i) q^{20} +(2844.00 - 4925.95i) q^{22} +(-7644.00 + 13239.8i) q^{23} +(-36987.5 - 64064.2i) q^{25} +30588.0 q^{26} +5888.00 q^{28} +(18255.0 + 31618.6i) q^{29} +(138404. - 239723. i) q^{31} +(96048.0 - 166360. i) q^{32} +(-85158.0 - 147498. i) q^{34} +24960.0 q^{35} +268526. q^{37} +(-25860.0 - 44790.8i) q^{38} +(257400. - 445830. i) q^{40} +(-314859. + 545352. i) q^{41} +(-342886. - 593896. i) q^{43} -87216.0 q^{44} -91728.0 q^{46} +(291648. + 505149. i) q^{47} +(409724. - 709662. i) q^{49} +(221925. - 384385. i) q^{50} +(-234508. - 406180. i) q^{52} +428058. q^{53} -369720. q^{55} +(42240.0 + 73161.8i) q^{56} +(-109530. + 189712. i) q^{58} +(653190. - 1.13136e6i) q^{59} +(-150331. - 260381. i) q^{61} +1.66085e6 q^{62} +659008. q^{64} +(-994110. - 1.72185e6i) q^{65} +(253622. - 439286. i) q^{67} +(-1.30576e6 + 2.26164e6i) q^{68} +(74880.0 + 129696. i) q^{70} -5.56063e6 q^{71} +1.36908e6 q^{73} +(805578. + 1.39530e6i) q^{74} +(-396520. + 686793. i) q^{76} +(30336.0 - 52543.5i) q^{77} +(3.45686e6 + 5.98746e6i) q^{79} -1.50384e6 q^{80} -3.77831e6 q^{82} +(-2.18837e6 - 3.79037e6i) q^{83} +(-5.53527e6 + 9.58737e6i) q^{85} +(2.05732e6 - 3.56338e6i) q^{86} +(-625680. - 1.08371e6i) q^{88} +8.52831e6 q^{89} +326272. q^{91} +(703248. + 1.21806e6i) q^{92} +(-1.74989e6 + 3.03089e6i) q^{94} +(-1.68090e6 + 2.91140e6i) q^{95} +(4.41341e6 + 7.64425e6i) q^{97} +4.91668e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{2} + 92 q^{4} + 390 q^{5} + 64 q^{7} + 2640 q^{8} + 4680 q^{10} - 948 q^{11} + 5098 q^{13} - 384 q^{14} - 3856 q^{16} - 56772 q^{17} - 17240 q^{19} - 35880 q^{20} + 5688 q^{22} - 15288 q^{23}+ \cdots + 9833364 q^{98}+O(q^{100}) $ 2 * q + 6 * q^2 + 92 * q^4 + 390 * q^5 + 64 * q^7 + 2640 * q^8 + 4680 * q^10 - 948 * q^11 + 5098 * q^13 - 384 * q^14 - 3856 * q^16 - 56772 * q^17 - 17240 * q^19 - 35880 * q^20 + 5688 * q^22 - 15288 * q^23 - 73975 * q^25 + 61176 * q^26 + 11776 * q^28 + 36510 * q^29 + 276808 * q^31 + 192096 * q^32 - 170316 * q^34 + 49920 * q^35 + 537052 * q^37 - 51720 * q^38 + 514800 * q^40 - 629718 * q^41 - 685772 * q^43 - 174432 * q^44 - 183456 * q^46 + 583296 * q^47 + 819447 * q^49 + 443850 * q^50 - 469016 * q^52 + 856116 * q^53 - 739440 * q^55 + 84480 * q^56 - 219060 * q^58 + 1306380 * q^59 - 300662 * q^61 + 3321696 * q^62 + 1318016 * q^64 - 1988220 * q^65 + 507244 * q^67 - 2611512 * q^68 + 149760 * q^70 - 11121264 * q^71 + 2738164 * q^73 + 1611156 * q^74 - 793040 * q^76 + 60672 * q^77 + 6913720 * q^79 - 3007680 * q^80 - 7556616 * q^82 - 4376748 * q^83 - 11070540 * q^85 + 4114632 * q^86 - 1251360 * q^88 + 17056620 * q^89 + 652544 * q^91 + 1406496 * q^92 - 3499776 * q^94 - 3361800 * q^95 + 8826814 * q^97 + 9833364 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	3.00000	+	5.19615i	0.265165	+	0.459279i	0.967607	−	0.252462i	$-0.0812402\pi$
$2$	3.00000	+	5.19615i	0.265165	+	0.459279i	−0.702442	+	0.711741i	$0.747907\pi$
$3$		0			0
$3$		0			0
$4$	46.0000	−	79.6743i	0.359375	−	0.622456i
$5$	195.000	−	337.750i	0.697653	−	1.20837i	−0.271625	−	0.962403i	$-0.587561\pi$
$5$	195.000	−	337.750i	0.697653	−	1.20837i	0.969278	−	0.245968i	$-0.0791057\pi$
$6$		0			0
$7$	32.0000	+	55.4256i	0.0352620	+	0.0610756i	0.883118	−	0.469151i	$-0.155440\pi$
$7$	32.0000	+	55.4256i	0.0352620	+	0.0610756i	−0.847856	+	0.530227i	$0.822107\pi$
$8$	1320.00			0.911505
$9$		0			0
$10$	2340.00			0.739973
$11$	−474.000	−	820.992i	−0.107375	−	0.185979i	0.807331	−	0.590099i	$-0.200911\pi$
$11$	−474.000	−	820.992i	−0.107375	−	0.185979i	−0.914706	+	0.404120i	$0.867578\pi$
$12$		0			0
$13$	2549.00	−	4415.00i	0.321787	−	0.557351i	−0.659070	−	0.752082i	$-0.729050\pi$
$13$	2549.00	−	4415.00i	0.321787	−	0.557351i	0.980857	+	0.194731i	$0.0623833\pi$
$14$	−192.000	+	332.554i	−0.0187005	+	0.0323902i
$15$		0			0
$16$	−1928.00	−	3339.39i	−0.117676	−	0.203820i
$17$	−28386.0			−1.40131			−0.700653	−	0.713502i	$-0.747108\pi$
$17$	−28386.0			−1.40131			−0.700653	+	0.713502i	$0.747108\pi$
$18$		0			0
$19$	−8620.00			−0.288317			−0.144158	−	0.989555i	$-0.546047\pi$
$19$	−8620.00			−0.288317			−0.144158	+	0.989555i	$0.546047\pi$
$20$	−17940.0	−	31073.0i	−0.501438	−	0.868517i
$21$		0			0
$22$	2844.00	−	4925.95i	0.0569443	−	0.0986304i
$23$	−7644.00	+	13239.8i	−0.131001	+	0.226900i	−0.924063	−	0.382241i	$-0.875152\pi$
$23$	−7644.00	+	13239.8i	−0.131001	+	0.226900i	0.793062	+	0.609141i	$0.208486\pi$
$24$		0			0
$25$	−36987.5	−	64064.2i	−0.473440	−	0.820022i
$26$	30588.0			0.341306
$27$		0			0
$28$	5888.00			0.0506891
$29$	18255.0	+	31618.6i	0.138992	+	0.240741i	0.927115	−	0.374776i	$-0.122281\pi$
$29$	18255.0	+	31618.6i	0.138992	+	0.240741i	−0.788124	+	0.615517i	$0.788947\pi$
$30$		0			0
$31$	138404.	−	239723.i	0.834416	−	1.44525i	−0.0600887	−	0.998193i	$-0.519138\pi$
$31$	138404.	−	239723.i	0.834416	−	1.44525i	0.894505	−	0.447058i	$-0.147528\pi$
$32$	96048.0	−	166360.i	0.518159	−	0.897478i
$33$		0			0
$34$	−85158.0	−	147498.i	−0.371577	−	0.643591i
$35$	24960.0			0.0984026
$36$		0			0
$37$	268526.			0.871526			0.435763	−	0.900061i	$-0.356479\pi$
$37$	268526.			0.871526			0.435763	+	0.900061i	$0.356479\pi$
$38$	−25860.0	−	44790.8i	−0.0764515	−	0.132418i
$39$		0			0
$40$	257400.	−	445830.i	0.635914	−	1.10144i
$41$	−314859.	+	545352.i	−0.713465	+	1.23576i	0.250084	+	0.968224i	$0.419542\pi$
$41$	−314859.	+	545352.i	−0.713465	+	1.23576i	−0.963549	+	0.267533i	$0.913791\pi$
$42$		0			0
$43$	−342886.	−	593896.i	−0.657673	−	1.13912i	−0.981216	−	0.192910i	$-0.938207\pi$
$43$	−342886.	−	593896.i	−0.657673	−	1.13912i	0.323543	−	0.946213i	$-0.395126\pi$
$44$	−87216.0			−0.154352
$45$		0			0
$46$	−91728.0			−0.138947
$47$	291648.	+	505149.i	0.409748	+	0.709704i	0.994861	−	0.101248i	$-0.0322834\pi$
$47$	291648.	+	505149.i	0.409748	+	0.709704i	−0.585114	+	0.810951i	$0.698950\pi$
$48$		0			0
$49$	409724.	−	709662.i	0.497513	−	0.861718i
$50$	221925.	−	384385.i	0.251079	−	0.434882i
$51$		0			0
$52$	−234508.	−	406180.i	−0.231284	−	0.400596i
$53$	428058.			0.394945			0.197473	−	0.980308i	$-0.436727\pi$
$53$	428058.			0.394945			0.197473	+	0.980308i	$0.436727\pi$
$54$		0			0
$55$	−369720.			−0.299643
$56$	42240.0	+	73161.8i	0.0321415	+	0.0556707i
$57$		0			0
$58$	−109530.	+	189712.i	−0.0737115	+	0.127672i
$59$	653190.	−	1.13136e6i	0.414054	−	0.717163i	−0.581274	−	0.813708i	$-0.697446\pi$
$59$	653190.	−	1.13136e6i	0.414054	−	0.717163i	0.995329	+	0.0965444i	$0.0307790\pi$
$60$		0			0
$61$	−150331.	−	260381.i	−0.0847997	−	0.146877i	0.820506	−	0.571638i	$-0.193692\pi$
$61$	−150331.	−	260381.i	−0.0847997	−	0.146877i	−0.905306	+	0.424760i	$0.860358\pi$
$62$	1.66085e6			0.885032
$63$		0			0
$64$	659008.			0.314240
$65$	−994110.	−	1.72185e6i	−0.448991	−	0.777675i
$66$		0			0
$67$	253622.	−	439286.i	0.103021	−	0.178437i	−0.809907	−	0.586558i	$-0.800482\pi$
$67$	253622.	−	439286.i	0.103021	−	0.178437i	0.912928	+	0.408121i	$0.133816\pi$
$68$	−1.30576e6	+	2.26164e6i	−0.503594	+	0.872251i
$69$		0			0
$70$	74880.0	+	129696.i	0.0260929	+	0.0451943i
$71$	−5.56063e6			−1.84383			−0.921913	−	0.387397i	$-0.873374\pi$
$71$	−5.56063e6			−1.84383			−0.921913	+	0.387397i	$0.873374\pi$
$72$		0			0
$73$	1.36908e6			0.411907			0.205954	−	0.978562i	$-0.433970\pi$
$73$	1.36908e6			0.411907			0.205954	+	0.978562i	$0.433970\pi$
$74$	805578.	+	1.39530e6i	0.231098	+	0.400274i
$75$		0			0
$76$	−396520.	+	686793.i	−0.103614	+	0.179464i
$77$	30336.0	−	52543.5i	0.00757253	−	0.0131160i
$78$		0			0
$79$	3.45686e6	+	5.98746e6i	0.788836	+	1.36630i	0.926680	+	0.375851i	$0.122649\pi$
$79$	3.45686e6	+	5.98746e6i	0.788836	+	1.36630i	−0.137844	+	0.990454i	$0.544017\pi$
$80$	−1.50384e6			−0.328388
$81$		0			0
$82$	−3.77831e6			−0.756744
$83$	−2.18837e6	−	3.79037e6i	−0.420096	−	0.727627i	0.575853	−	0.817553i	$-0.304670\pi$
$83$	−2.18837e6	−	3.79037e6i	−0.420096	−	0.727627i	−0.995948	+	0.0899264i	$0.971337\pi$
$84$		0			0
$85$	−5.53527e6	+	9.58737e6i	−0.977626	+	1.69330i
$86$	2.05732e6	−	3.56338e6i	0.348784	−	0.604111i
$87$		0			0
$88$	−625680.	−	1.08371e6i	−0.0978730	−	0.169521i
$89$	8.52831e6			1.28232			0.641162	−	0.767405i	$-0.278453\pi$
$89$	8.52831e6			1.28232			0.641162	+	0.767405i	$0.278453\pi$
$90$		0			0
$91$	326272.			0.0453874
$92$	703248.	+	1.21806e6i	0.0941567	+	0.163084i
$93$		0			0
$94$	−1.74989e6	+	3.03089e6i	−0.217302	+	0.376377i
$95$	−1.68090e6	+	2.91140e6i	−0.201145	+	0.348393i
$96$		0			0
$97$	4.41341e6	+	7.64425e6i	0.490990	+	0.850420i	0.999946	−	0.0103725i	$-0.00330171\pi$
$97$	4.41341e6	+	7.64425e6i	0.490990	+	0.850420i	−0.508956	+	0.860793i	$0.669968\pi$
$98$	4.91668e6			0.527692
$99$		0			0
$100$	−6.80570e6			−0.680570
$101$	5.99321e6	+	1.03805e7i	0.578808	+	1.00253i	0.995616	+	0.0935309i	$0.0298154\pi$
$101$	5.99321e6	+	1.03805e7i	0.578808	+	1.00253i	−0.416808	+	0.908995i	$0.636851\pi$
$102$		0			0
$103$	−3.60470e6	+	6.24352e6i	−0.325041	+	0.562988i	−0.981521	−	0.191356i	$-0.938711\pi$
$103$	−3.60470e6	+	6.24352e6i	−0.325041	+	0.562988i	0.656480	+	0.754344i	$0.272045\pi$
$104$	3.36468e6	−	5.82780e6i	0.293310	−	0.508028i
$105$		0			0
$106$	1.28417e6	+	2.22425e6i	0.104726	+	0.181390i
$107$	−1.14261e7			−0.901683			−0.450842	−	0.892604i	$-0.648876\pi$
$107$	−1.14261e7			−0.901683			−0.450842	+	0.892604i	$0.648876\pi$
$108$		0			0
$109$	4.02095e6			0.297397			0.148698	−	0.988883i	$-0.452492\pi$
$109$	4.02095e6			0.297397			0.148698	+	0.988883i	$0.452492\pi$
$110$	−1.10916e6	−	1.92112e6i	−0.0794547	−	0.137620i
$111$		0			0
$112$	123392.	−	213721.i	0.00829896	−	0.0143742i
$113$	−8.85316e6	+	1.53341e7i	−0.577197	+	0.999734i	0.418603	+	0.908169i	$0.362520\pi$
$113$	−8.85316e6	+	1.53341e7i	−0.577197	+	0.999734i	−0.995799	+	0.0915642i	$0.970813\pi$
$114$		0			0
$115$	2.98116e6	+	5.16352e6i	0.182786	+	0.316595i
$116$	3.35892e6			0.199801
$117$		0			0
$118$	7.83828e6			0.439171
$119$	−908352.	−	1.57331e6i	−0.0494128	−	0.0855855i
$120$		0			0
$121$	9.29423e6	−	1.60981e7i	0.476941	−	0.826086i
$122$	901986.	−	1.56229e6i	0.0449718	−	0.0778935i
$123$		0			0
$124$	−1.27332e7	−	2.20545e7i	−0.599737	−	1.03877i
$125$	1.61850e6			0.0741187
$126$		0			0
$127$	1.67883e7			0.727267			0.363633	−	0.931542i	$-0.381536\pi$
$127$	1.67883e7			0.727267			0.363633	+	0.931542i	$0.381536\pi$
$128$	−1.03171e7	−	1.78698e7i	−0.434834	−	0.753155i
$129$		0			0
$130$	5.96466e6	−	1.03311e7i	0.238113	−	0.412425i
$131$	8.41339e6	−	1.45724e7i	0.326980	−	0.566346i	−0.654931	−	0.755689i	$-0.727302\pi$
$131$	8.41339e6	−	1.45724e7i	0.326980	−	0.566346i	0.981911	+	0.189343i	$0.0606357\pi$
$132$		0			0
$133$	−275840.	−	477769.i	−0.0101666	−	0.0176091i
$134$	3.04346e6			0.109270
$135$		0			0
$136$	−3.74695e7			−1.27730
$137$	1.40225e7	+	2.42876e7i	0.465910	+	0.806980i	0.999242	−	0.0389262i	$-0.0123937\pi$
$137$	1.40225e7	+	2.42876e7i	0.465910	+	0.806980i	−0.533332	+	0.845906i	$0.679060\pi$
$138$		0			0
$139$	5.91365e6	−	1.02427e7i	0.186769	−	0.323493i	−0.757402	−	0.652948i	$-0.773532\pi$
$139$	5.91365e6	−	1.02427e7i	0.186769	−	0.323493i	0.944171	+	0.329456i	$0.106865\pi$
$140$	1.14816e6	−	1.98867e6i	0.0353634	−	0.0612512i
$141$		0			0
$142$	−1.66819e7	−	2.88939e7i	−0.488918	−	0.846831i
$143$	−4.83290e6			−0.138208
$144$		0			0
$145$	1.42389e7			0.387872
$146$	4.10725e6	+	7.11396e6i	0.109223	+	0.189180i
$147$		0			0
$148$	1.23522e7	−	2.13946e7i	0.313205	−	0.542486i
$149$	1.03923e7	−	1.80000e7i	0.257371	−	0.445780i	−0.708165	−	0.706046i	$-0.750477\pi$
$149$	1.03923e7	−	1.80000e7i	0.257371	−	0.445780i	0.965537	+	0.260266i	$0.0838103\pi$
$150$		0			0
$151$	−38056.0	−	65914.9i	−0.000899505	−	0.00155799i	0.865575	−	0.500779i	$-0.166953\pi$
$151$	−38056.0	−	65914.9i	−0.000899505	−	0.00155799i	−0.866475	+	0.499221i	$0.833620\pi$
$152$	−1.13784e7			−0.262802
$153$		0			0
$154$	364032.			0.00803188
$155$	−5.39776e7	−	9.34919e7i	−1.16427	−	2.01657i
$156$		0			0
$157$	1.60912e7	−	2.78708e7i	0.331849	−	0.574780i	−0.651025	−	0.759056i	$-0.725661\pi$
$157$	1.60912e7	−	2.78708e7i	0.331849	−	0.574780i	0.982874	+	0.184276i	$0.0589942\pi$
$158$	−2.07412e7	+	3.59247e7i	−0.418344	+	0.724593i
$159$		0			0
$160$	−3.74587e7	−	6.48804e7i	−0.722991	−	1.25226i
$161$	−978432.			−0.0184774
$162$		0			0
$163$	5.83435e7			1.05520			0.527601	−	0.849492i	$-0.323092\pi$
$163$	5.83435e7			1.05520			0.527601	+	0.849492i	$0.323092\pi$
$164$	2.89670e7	+	5.01724e7i	0.512803	+	0.888201i
$165$		0			0
$166$	1.31302e7	−	2.27422e7i	0.222789	−	0.385883i
$167$	−1.29183e7	+	2.23751e7i	−0.214633	+	0.371755i	−0.953159	−	0.302470i	$-0.902189\pi$
$167$	−1.29183e7	+	2.23751e7i	−0.214633	+	0.371755i	0.738526	+	0.674225i	$0.235522\pi$
$168$		0			0
$169$	1.83795e7	+	3.18342e7i	0.292907	+	0.507329i
$170$	−6.64232e7			−1.03693
$171$		0			0
$172$	−6.30910e7			−0.945405
$173$	3.17600e7	+	5.50100e7i	0.466358	+	0.807756i	0.999262	−	0.0384200i	$-0.0122325\pi$
$173$	3.17600e7	+	5.50100e7i	0.466358	+	0.807756i	−0.532904	+	0.846176i	$0.678899\pi$
$174$		0			0
$175$	2.36720e6	−	4.10011e6i	0.0333889	−	0.0578312i
$176$	−1.82774e6	+	3.16575e6i	−0.0252709	+	0.0437705i
$177$		0			0
$178$	2.55849e7	+	4.43144e7i	0.340028	+	0.588945i
$179$	8.09559e7			1.05503			0.527513	−	0.849547i	$-0.323125\pi$
$179$	8.09559e7			1.05503			0.527513	+	0.849547i	$0.323125\pi$
$180$		0			0
$181$	6.45032e7			0.808549			0.404274	−	0.914638i	$-0.367524\pi$
$181$	6.45032e7			0.808549			0.404274	+	0.914638i	$0.367524\pi$
$182$	978816.	+	1.69536e6i	0.0120351	+	0.0208455i
$183$		0			0
$184$	−1.00901e7	+	1.74765e7i	−0.119408	+	0.206820i
$185$	5.23626e7	−	9.06946e7i	0.608023	−	1.05313i
$186$		0			0
$187$	1.34550e7	+	2.33047e7i	0.150465	+	0.260614i
$188$	5.36632e7			0.589012
$189$		0			0
$190$	−2.01708e7			−0.213346
$191$	2.84137e7	+	4.92140e7i	0.295060	+	0.511060i	0.974999	−	0.222209i	$-0.0713269\pi$
$191$	2.84137e7	+	4.92140e7i	0.295060	+	0.511060i	−0.679939	+	0.733269i	$0.737994\pi$
$192$		0			0
$193$	−5.81885e7	+	1.00785e8i	−0.582621	+	1.00913i	0.412546	+	0.910937i	$0.364640\pi$
$193$	−5.81885e7	+	1.00785e8i	−0.582621	+	1.00913i	−0.995167	+	0.0981931i	$0.968694\pi$
$194$	−2.64804e7	+	4.58655e7i	−0.260387	+	0.451003i
$195$		0			0
$196$	−3.76946e7	−	6.52889e7i	−0.357588	−	0.619360i
$197$	1.18816e8			1.10724			0.553622	−	0.832768i	$-0.313245\pi$
$197$	1.18816e8			1.10724			0.553622	+	0.832768i	$0.313245\pi$
$198$		0			0
$199$	−9.50106e7			−0.854646			−0.427323	−	0.904099i	$-0.640543\pi$
$199$	−9.50106e7			−0.854646			−0.427323	+	0.904099i	$0.640543\pi$
$200$	−4.88235e7	−	8.45648e7i	−0.431543	−	0.747454i
$201$		0			0
$202$	−3.59593e7	+	6.22833e7i	−0.306959	+	0.531669i
$203$	−1.16832e6	+	2.02359e6i	−0.00980225	+	0.0169780i
$204$		0			0
$205$	1.22795e8	+	2.12687e8i	0.995502	+	1.72426i
$206$	−4.32564e7			−0.344758
$207$		0			0
$208$	−1.96579e7			−0.151466
$209$	4.08588e6	+	7.07695e6i	0.0309581	+	0.0536209i
$210$		0			0
$211$	−8.96232e7	+	1.55232e8i	−0.656798	+	1.13761i	0.324642	+	0.945837i	$0.394756\pi$
$211$	−8.96232e7	+	1.55232e8i	−0.656798	+	1.13761i	−0.981440	+	0.191770i	$0.938577\pi$
$212$	1.96907e7	−	3.41052e7i	0.141934	−	0.245836i
$213$		0			0
$214$	−3.42782e7	−	5.93716e7i	−0.239095	−	0.414124i
$215$	−2.67451e8			−1.83531
$216$		0			0
$217$	1.77157e7			0.117693
$218$	1.20628e7	+	2.08935e7i	0.0788592	+	0.136588i
$219$		0			0
$220$	−1.70071e7	+	2.94572e7i	−0.107684	+	0.186514i
$221$	−7.23559e7	+	1.25324e8i	−0.450922	+	0.781019i
$222$		0			0
$223$	1.03268e8	+	1.78866e8i	0.623592	+	1.08009i	0.988811	+	0.149172i	$0.0476607\pi$
$223$	1.03268e8	+	1.78866e8i	0.623592	+	1.08009i	−0.365219	+	0.930922i	$0.619006\pi$
$224$	1.22941e7			0.0730853
$225$		0			0
$226$	−1.06238e8			−0.612209
$227$	2.16977e7	+	3.75815e7i	0.123118	+	0.213247i	0.920996	−	0.389572i	$-0.127377\pi$
$227$	2.16977e7	+	3.75815e7i	0.123118	+	0.213247i	−0.797877	+	0.602820i	$0.794044\pi$
$228$		0			0
$229$	1.80965e7	−	3.13441e7i	0.0995799	−	0.172477i	−0.811931	−	0.583753i	$-0.801583\pi$
$229$	1.80965e7	−	3.13441e7i	0.0995799	−	0.172477i	0.911511	+	0.411276i	$0.134917\pi$
$230$	−1.78870e7	+	3.09811e7i	−0.0969369	+	0.167900i
$231$		0			0
$232$	2.40966e7	+	4.17365e7i	0.126692	+	0.219436i
$233$	−9.22347e7			−0.477693			−0.238846	−	0.971057i	$-0.576769\pi$
$233$	−9.22347e7			−0.477693			−0.238846	+	0.971057i	$0.576769\pi$
$234$		0			0
$235$	2.27485e8			1.14345
$236$	−6.00935e7	−	1.04085e8i	−0.297602	−	0.515461i
$237$		0			0
$238$	5.45011e6	−	9.43987e6i	0.0262051	−	0.0453886i
$239$	2.49234e7	−	4.31686e7i	0.118090	−	0.204539i	−0.800920	−	0.598771i	$-0.795656\pi$
$239$	2.49234e7	−	4.31686e7i	0.118090	−	0.204539i	0.919011	+	0.394232i	$0.128989\pi$
$240$		0			0
$241$	−9.96870e7	−	1.72663e8i	−0.458753	−	0.794583i	0.540142	−	0.841574i	$-0.318370\pi$
$241$	−9.96870e7	−	1.72663e8i	−0.458753	−	0.794583i	−0.998895	+	0.0469902i	$0.985037\pi$
$242$	1.11531e8			0.505872
$243$		0			0
$244$	−2.76609e7			−0.121900
$245$	−1.59792e8	−	2.76768e8i	−0.694183	−	1.20236i
$246$		0			0
$247$	−2.19724e7	+	3.80573e7i	−0.0927765	+	0.160694i
$248$	1.82693e8	−	3.16434e8i	0.760574	−	1.31735i
$249$		0			0
$250$	4.85550e6	+	8.40997e6i	0.0196537	+	0.0340412i
$251$	3.94678e8			1.57538			0.787689	−	0.616073i	$-0.211277\pi$
$251$	3.94678e8			1.57538			0.787689	+	0.616073i	$0.211277\pi$
$252$		0			0
$253$	1.44930e7			0.0562649
$254$	5.03649e7	+	8.72345e7i	0.192846	+	0.334018i
$255$		0			0
$256$	1.04079e8	−	1.80271e8i	0.387725	−	0.671560i
$257$	−7.14427e7	+	1.23742e8i	−0.262538	+	0.454729i	−0.966916	−	0.255096i	$-0.917893\pi$
$257$	−7.14427e7	+	1.23742e8i	−0.262538	+	0.454729i	0.704378	+	0.709825i	$0.251226\pi$
$258$		0			0
$259$	8.59283e6	+	1.48832e7i	0.0307317	+	0.0532289i
$260$	−1.82916e8			−0.645425
$261$		0			0
$262$	1.00961e8			0.346815
$263$	2.20120e8	+	3.81260e8i	0.746131	+	1.29234i	0.949664	+	0.313269i	$0.101424\pi$
$263$	2.20120e8	+	3.81260e8i	0.746131	+	1.29234i	−0.203533	+	0.979068i	$0.565243\pi$
$264$		0			0
$265$	8.34713e7	−	1.44577e8i	0.275535	−	0.477241i
$266$	1.65504e6	−	2.86661e6i	0.00539166	−	0.00933863i
$267$		0			0
$268$	−2.33332e7	−	4.04143e7i	−0.0740462	−	0.128252i
$269$	−2.75405e8			−0.862657			−0.431329	−	0.902195i	$-0.641955\pi$
$269$	−2.75405e8			−0.862657			−0.431329	+	0.902195i	$0.641955\pi$
$270$		0			0
$271$	−4.24670e8			−1.29616			−0.648080	−	0.761572i	$-0.724428\pi$
$271$	−4.24670e8			−1.29616			−0.648080	+	0.761572i	$0.724428\pi$
$272$	5.47282e7	+	9.47920e7i	0.164900	+	0.285615i
$273$		0			0
$274$	−8.41347e7	+	1.45726e8i	−0.247086	+	0.427966i
$275$	−3.50642e7	+	6.07329e7i	−0.101671	+	0.176100i
$276$		0			0
$277$	−2.58079e8	−	4.47006e8i	−0.729581	−	1.26367i	−0.957060	−	0.289889i	$-0.906382\pi$
$277$	−2.58079e8	−	4.47006e8i	−0.729581	−	1.26367i	0.227479	−	0.973783i	$-0.426952\pi$
$278$	7.09638e7			0.198098
$279$		0			0
$280$	3.29472e7			0.0896944
$281$	−1.55521e8	−	2.69371e8i	−0.418137	−	0.724234i	0.577616	−	0.816309i	$-0.303983\pi$
$281$	−1.55521e8	−	2.69371e8i	−0.418137	−	0.724234i	−0.995752	+	0.0920753i	$0.970650\pi$
$282$		0			0
$283$	2.97154e8	−	5.14686e8i	0.779344	−	1.34986i	−0.152976	−	0.988230i	$-0.548886\pi$
$283$	2.97154e8	−	5.14686e8i	0.779344	−	1.34986i	0.932320	−	0.361634i	$-0.117781\pi$
$284$	−2.55789e8	+	4.43040e8i	−0.662625	+	1.14770i
$285$		0			0
$286$	−1.44987e7	−	2.51125e7i	−0.0366478	−	0.0634759i
$287$	−4.03020e7			−0.100633
$288$		0			0
$289$	3.95426e8			0.963658
$290$	4.27167e7	+	7.39875e7i	0.102850	+	0.178142i
$291$		0			0
$292$	6.29778e7	−	1.09081e8i	0.148029	−	0.256394i
$293$	5.77574e7	−	1.00039e8i	0.134144	−	0.232344i	−0.791126	−	0.611653i	$-0.790505\pi$
$293$	5.77574e7	−	1.00039e8i	0.134144	−	0.232344i	0.925270	+	0.379309i	$0.123838\pi$
$294$		0			0
$295$	−2.54744e8	−	4.41230e8i	−0.577733	−	1.00066i
$296$	3.54454e8			0.794400
$297$		0			0
$298$	1.24708e8			0.272984
$299$	3.89691e7	+	6.74965e7i	0.0843085	+	0.146027i
$300$		0			0
$301$	2.19447e7	−	3.80093e7i	0.0463817	−	0.0803355i
$302$	228336.	−	395490.i	0.000477035	−	0.000826249i
$303$		0			0
$304$	1.66194e7	+	2.87856e7i	0.0339279	+	0.0587648i
$305$	−1.17258e8			−0.236643
$306$		0			0
$307$	−2.60600e8			−0.514032			−0.257016	−	0.966407i	$-0.582739\pi$
$307$	−2.60600e8			−0.514032			−0.257016	+	0.966407i	$0.582739\pi$
$308$	−2.79091e6	−	4.83400e6i	−0.00544275	−	0.00942712i
$309$		0			0
$310$	3.23865e8	−	5.60951e8i	0.617445	−	1.06945i
$311$	2.88397e8	−	4.99519e8i	0.543663	−	0.941652i	−0.455027	−	0.890478i	$-0.650370\pi$
$311$	2.88397e8	−	4.99519e8i	0.543663	−	0.941652i	0.998690	−	0.0511744i	$-0.0162964\pi$
$312$		0			0
$313$	2.30037e8	+	3.98436e8i	0.424026	+	0.734435i	0.996329	−	0.0856073i	$-0.0272831\pi$
$313$	2.30037e8	+	3.98436e8i	0.424026	+	0.734435i	−0.572303	+	0.820043i	$0.693950\pi$
$314$	1.93095e8			0.351979
$315$		0			0
$316$	6.36062e8			1.13395
$317$	3.12781e7	+	5.41752e7i	0.0551483	+	0.0955197i	0.892282	−	0.451479i	$-0.149103\pi$
$317$	3.12781e7	+	5.41752e7i	0.0551483	+	0.0955197i	−0.837133	+	0.546999i	$0.815770\pi$
$318$		0			0
$319$	1.73057e7	−	2.99744e7i	0.0298485	−	0.0516992i
$320$	1.28507e8	−	2.22580e8i	0.219230	−	0.379718i
$321$		0			0
$322$	−2.93530e6	−	5.08408e6i	−0.00489955	−	0.00848627i
$323$	2.44687e8			0.404020
$324$		0			0
$325$	−3.77125e8			−0.609387
$326$	1.75030e8	+	3.03162e8i	0.279803	+	0.484633i
$327$		0			0
$328$	−4.15614e8	+	7.19864e8i	−0.650327	+	1.12640i
$329$	−1.86655e7	+	3.23295e7i	−0.0288970	+	0.0500511i
$330$		0			0
$331$	−3.42118e8	−	5.92566e8i	−0.518535	−	0.898128i	−0.999768	−	0.0215359i	$-0.993144\pi$
$331$	−3.42118e8	−	5.92566e8i	−0.518535	−	0.898128i	0.481233	−	0.876593i	$-0.340189\pi$
$332$	−4.02661e8			−0.603888
$333$		0			0
$334$	−1.55019e8			−0.227652
$335$	−9.89126e7	−	1.71322e8i	−0.143746	−	0.248975i
$336$		0			0
$337$	3.13156e8	−	5.42403e8i	0.445714	−	0.772000i	−0.552387	−	0.833588i	$-0.686283\pi$
$337$	3.13156e8	−	5.42403e8i	0.445714	−	0.772000i	0.998102	+	0.0615875i	$0.0196163\pi$
$338$	−1.10277e8	+	1.91005e8i	−0.155337	+	0.269052i
$339$		0			0
$340$	5.09245e8	+	8.82038e8i	0.702668	+	1.21706i
$341$	−2.62414e8			−0.358382
$342$		0			0
$343$	1.05151e8			0.140697
$344$	−4.52610e8	−	7.83943e8i	−0.599472	−	1.03832i
$345$		0			0
$346$	−1.90560e8	+	3.30060e8i	−0.247324	+	0.428377i
$347$	−6.26698e8	+	1.08547e9i	−0.805203	+	1.39465i	0.110952	+	0.993826i	$0.464610\pi$
$347$	−6.26698e8	+	1.08547e9i	−0.805203	+	1.39465i	−0.916154	+	0.400826i	$0.868723\pi$
$348$		0			0
$349$	−1.32675e8	−	2.29800e8i	−0.167071	−	0.289375i	0.770318	−	0.637660i	$-0.220098\pi$
$349$	−1.32675e8	−	2.29800e8i	−0.167071	−	0.289375i	−0.937389	+	0.348285i	$0.886764\pi$
$350$	2.84064e7			0.0354142
$351$		0			0
$352$	−1.82107e8			−0.222550
$353$	−2.84818e8	−	4.93319e8i	−0.344632	−	0.596920i	0.640655	−	0.767829i	$-0.278663\pi$
$353$	−2.84818e8	−	4.93319e8i	−0.344632	−	0.596920i	−0.985287	+	0.170909i	$0.945330\pi$
$354$		0			0
$355$	−1.08432e9	+	1.87810e9i	−1.28635	+	2.22803i
$356$	3.92302e8	−	6.79487e8i	0.460835	−	0.798190i
$357$		0			0
$358$	2.42868e8	+	4.20659e8i	0.279756	+	0.484551i
$359$	−9.32541e8			−1.06374			−0.531872	−	0.846825i	$-0.678511\pi$
$359$	−9.32541e8			−1.06374			−0.531872	+	0.846825i	$0.678511\pi$
$360$		0			0
$361$	−8.19567e8			−0.916874
$362$	1.93510e8	+	3.35168e8i	0.214399	+	0.371350i
$363$		0			0
$364$	1.50085e7	−	2.59955e7i	0.0163111	−	0.0282516i
$365$	2.66971e8	−	4.62407e8i	0.287368	−	0.497737i
$366$		0			0
$367$	4.26282e8	+	7.38343e8i	0.450159	+	0.779699i	0.998396	−	0.0566249i	$-0.0180339\pi$
$367$	4.26282e8	+	7.38343e8i	0.450159	+	0.779699i	−0.548236	+	0.836323i	$0.684701\pi$
$368$	5.89505e7			0.0616624
$369$		0			0
$370$	6.28351e8			0.644906
$371$	1.36979e7	+	2.37254e7i	0.0139266	+	0.0241215i
$372$		0			0
$373$	−1.90592e8	+	3.30115e8i	−0.190162	+	0.329370i	−0.945304	−	0.326192i	$-0.894235\pi$
$373$	−1.90592e8	+	3.30115e8i	−0.190162	+	0.329370i	0.755142	+	0.655561i	$0.227568\pi$
$374$	−8.07298e7	+	1.39828e8i	−0.0797964	+	0.138211i
$375$		0			0
$376$	3.84975e8	+	6.66797e8i	0.373487	+	0.646898i
$377$	1.86128e8			0.178903
$378$		0			0
$379$	−1.48353e9			−1.39978			−0.699889	−	0.714251i	$-0.746767\pi$
$379$	−1.48353e9			−1.39978			−0.699889	+	0.714251i	$0.746767\pi$
$380$	1.54643e8	+	2.67849e8i	0.144573	+	0.250408i
$381$		0			0
$382$	−1.70482e8	+	2.95284e8i	−0.156479	+	0.271030i
$383$	−3.80965e8	+	6.59851e8i	−0.346489	+	0.600136i	−0.985623	−	0.168959i	$-0.945959\pi$
$383$	−3.80965e8	+	6.59851e8i	−0.346489	+	0.600136i	0.639134	+	0.769095i	$0.279293\pi$
$384$		0			0
$385$	−1.18310e7	−	2.04920e7i	−0.0105660	−	0.0183008i
$386$	−6.98262e8			−0.617963
$387$		0			0
$388$	8.12067e8			0.705799
$389$	8.04509e8	+	1.39345e9i	0.692959	+	1.20024i	0.970864	+	0.239631i	$0.0770265\pi$
$389$	8.04509e8	+	1.39345e9i	0.692959	+	1.20024i	−0.277905	+	0.960608i	$0.589640\pi$
$390$		0			0
$391$	2.16983e8	−	3.75825e8i	0.183572	−	0.317956i
$392$	5.40835e8	−	9.36754e8i	0.453486	−	0.785460i
$393$		0			0
$394$	3.56448e8	+	6.17386e8i	0.293602	+	0.508534i
$395$	2.69635e9			2.20134
$396$		0			0
$397$	1.88016e9			1.50809			0.754046	−	0.656822i	$-0.228100\pi$
$397$	1.88016e9			1.50809			0.754046	+	0.656822i	$0.228100\pi$
$398$	−2.85032e8	−	4.93690e8i	−0.226622	−	0.392521i
$399$		0			0
$400$	−1.42624e8	+	2.47032e8i	−0.111425	+	0.192993i
$401$	1.34296e8	−	2.32608e8i	0.104006	−	0.180144i	−0.809326	−	0.587360i	$-0.800167\pi$
$401$	1.34296e8	−	2.32608e8i	0.104006	−	0.180144i	0.913332	+	0.407217i	$0.133501\pi$
$402$		0			0
$403$	−7.05584e8	−	1.22211e9i	−0.537008	−	0.930125i
$404$	1.10275e9			0.832037
$405$		0			0
$406$	−1.40198e7			−0.0103969
$407$	−1.27281e8	−	2.20458e8i	−0.0935803	−	0.162086i
$408$		0			0
$409$	−4.49739e7	+	7.78971e7i	−0.0325034	+	0.0562976i	−0.881820	−	0.471587i	$-0.843681\pi$
$409$	−4.49739e7	+	7.78971e7i	−0.0325034	+	0.0562976i	0.849316	+	0.527885i	$0.177015\pi$
$410$	−7.36770e8	+	1.27612e9i	−0.527945	+	0.914427i
$411$		0			0
$412$	3.31632e8	+	5.74404e8i	0.233623	+	0.404647i
$413$	8.36083e7			0.0584015
$414$		0			0
$415$	−1.70693e9			−1.17232
$416$	−4.89653e8	−	8.48103e8i	−0.333474	−	0.577593i
$417$		0			0
$418$	−2.45153e7	+	4.24617e7i	−0.0164180	+	0.0284368i
$419$	8.45271e8	−	1.46405e9i	0.561367	−	0.972317i	−0.436010	−	0.899942i	$-0.643609\pi$
$419$	8.45271e8	−	1.46405e9i	0.561367	−	0.972317i	0.997377	−	0.0723749i	$-0.0230578\pi$
$420$		0			0
$421$	5.66664e8	+	9.81490e8i	0.370116	+	0.641060i	0.989583	−	0.143963i	$-0.0459845\pi$
$421$	5.66664e8	+	9.81490e8i	0.370116	+	0.641060i	−0.619467	+	0.785023i	$0.712651\pi$
$422$	−1.07548e9			−0.696639
$423$		0			0
$424$	5.65037e8			0.359995
$425$	1.04993e9	+	1.81853e9i	0.663434	+	1.14910i
$426$		0			0
$427$	9.62118e6	−	1.66644e7i	0.00598041	−	0.0103584i
$428$	−5.25599e8	+	9.10365e8i	−0.324042	+	0.561258i
$429$		0			0
$430$	−8.02353e8	−	1.38972e9i	−0.486660	−	0.842921i
$431$	−2.19943e9			−1.32324			−0.661621	−	0.749839i	$-0.730131\pi$
$431$	−2.19943e9			−1.32324			−0.661621	+	0.749839i	$0.730131\pi$
$432$		0			0
$433$	−1.51738e8			−0.0898227			−0.0449114	−	0.998991i	$-0.514301\pi$
$433$	−1.51738e8			−0.0898227			−0.0449114	+	0.998991i	$0.514301\pi$
$434$	5.31471e7	+	9.20535e7i	0.0312080	+	0.0540538i
$435$		0			0
$436$	1.84964e8	−	3.20367e8i	0.106877	−	0.185116i
$437$	6.58913e7	−	1.14127e8i	0.0377696	−	0.0654189i
$438$		0			0
$439$	−4.95381e8	−	8.58026e8i	−0.279456	−	0.484032i	0.691793	−	0.722095i	$-0.256821\pi$
$439$	−4.95381e8	−	8.58026e8i	−0.279456	−	0.484032i	−0.971250	+	0.238063i	$0.923488\pi$
$440$	−4.88030e8			−0.273126
$441$		0			0
$442$	−8.68271e8			−0.478275
$443$	−8.86878e8	−	1.53612e9i	−0.484675	−	0.839482i	0.515170	−	0.857088i	$-0.327729\pi$
$443$	−8.86878e8	−	1.53612e9i	−0.484675	−	0.839482i	−0.999845	+	0.0176059i	$0.994396\pi$
$444$		0			0
$445$	1.66302e9	−	2.88044e9i	0.894618	−	1.54952i
$446$	−6.19611e8	+	1.07320e9i	−0.330710	+	0.572806i
$447$		0			0
$448$	2.10883e7	+	3.65259e7i	0.0110807	+	0.0191924i
$449$	2.77010e8			0.144422			0.0722110	−	0.997389i	$-0.476994\pi$
$449$	2.77010e8			0.144422			0.0722110	+	0.997389i	$0.476994\pi$
$450$		0			0
$451$	5.96973e8			0.306434
$452$	8.14491e8	+	1.41074e9i	0.414860	+	0.718559i
$453$		0			0
$454$	−1.30186e8	+	2.25489e8i	−0.0652934	+	0.113092i
$455$	6.36230e7	−	1.10198e8i	0.0316646	−	0.0548448i
$456$		0			0
$457$	−1.47379e9	−	2.55268e9i	−0.722320	−	1.25109i	−0.960068	−	0.279768i	$-0.909742\pi$
$457$	−1.47379e9	−	2.55268e9i	−0.722320	−	1.25109i	0.237748	−	0.971327i	$-0.423591\pi$
$458$	2.17159e8			0.105620
$459$		0			0
$460$	5.48533e8			0.262755
$461$	−1.38344e9	−	2.39618e9i	−0.657667	−	1.13911i	−0.981218	−	0.192902i	$-0.938210\pi$
$461$	−1.38344e9	−	2.39618e9i	−0.657667	−	1.13911i	0.323551	−	0.946211i	$-0.395123\pi$
$462$		0			0
$463$	−2.31776e8	+	4.01449e8i	−0.108527	+	0.187973i	−0.915174	−	0.403060i	$-0.867947\pi$
$463$	−2.31776e8	+	4.01449e8i	−0.108527	+	0.187973i	0.806647	+	0.591034i	$0.201280\pi$
$464$	7.03913e7	−	1.21921e8i	0.0327119	−	0.0566587i
$465$		0			0
$466$	−2.76704e8	−	4.79265e8i	−0.126667	−	0.219394i
$467$	4.17922e8			0.189883			0.0949415	−	0.995483i	$-0.469734\pi$
$467$	4.17922e8			0.189883			0.0949415	+	0.995483i	$0.469734\pi$
$468$		0			0
$469$	3.24636e7			0.0145309
$470$	6.82456e8	+	1.18205e9i	0.303202	+	0.525162i
$471$		0			0
$472$	8.62211e8	−	1.49339e9i	0.377413	−	0.653698i
$473$	−3.25056e8	+	5.63013e8i	−0.141236	+	0.244627i
$474$		0			0
$475$	3.18832e8	+	5.52234e8i	0.136501	+	0.236426i
$476$	−1.67137e8			−0.0710310
$477$		0			0
$478$	2.99081e8			0.125254
$479$	−7.54864e8	−	1.30746e9i	−0.313830	−	0.543570i	0.665358	−	0.746524i	$-0.268279\pi$
$479$	−7.54864e8	−	1.30746e9i	−0.313830	−	0.543570i	−0.979188	+	0.202955i	$0.934946\pi$
$480$		0			0
$481$	6.84473e8	−	1.18554e9i	0.280445	−	0.485746i
$482$	5.98122e8	−	1.03598e9i	0.243290	−	0.421392i
$483$		0			0
$484$	−8.55069e8	−	1.48102e9i	−0.342801	−	0.593750i
$485$	3.44246e9			1.37016
$486$		0			0
$487$	9.29460e8			0.364653			0.182326	−	0.983238i	$-0.441637\pi$
$487$	9.29460e8			0.364653			0.182326	+	0.983238i	$0.441637\pi$
$488$	−1.98437e8	−	3.43703e8i	−0.0772953	−	0.133879i
$489$		0			0
$490$	9.58753e8	−	1.66061e9i	0.368146	−	0.637648i
$491$	2.56401e9	−	4.44100e9i	0.977541	−	1.69315i	0.306262	−	0.951947i	$-0.400922\pi$
$491$	2.56401e9	−	4.44100e9i	0.977541	−	1.69315i	0.671280	−	0.741204i	$-0.265745\pi$
$492$		0			0
$493$	−5.18186e8	−	8.97525e8i	−0.194770	−	0.337351i
$494$	−2.63669e8			−0.0984043
$495$		0			0
$496$	−1.06737e9			−0.392762
$497$	−1.77940e8	−	3.08202e8i	−0.0650170	−	0.112613i
$498$		0			0
$499$	2.05325e8	−	3.55633e8i	0.0739757	−	0.128130i	−0.826665	−	0.562695i	$-0.809765\pi$
$499$	2.05325e8	−	3.55633e8i	0.0739757	−	0.128130i	0.900640	+	0.434565i	$0.143098\pi$
$500$	7.44510e7	−	1.28953e8i	0.0266364	−	0.0461356i
$501$		0			0
$502$	1.18403e9	+	2.05081e9i	0.417735	+	0.723538i
$503$	−5.02041e9			−1.75894			−0.879470	−	0.475954i	$-0.842103\pi$
$503$	−5.02041e9			−1.75894			−0.879470	+	0.475954i	$0.842103\pi$
$504$		0			0
$505$	4.67470e9			1.61523
$506$	4.34791e7	+	7.53080e7i	0.0149195	+	0.0258413i
$507$		0			0
$508$	7.72262e8	−	1.33760e9i	0.261361	−	0.452691i
$509$	−1.62463e9	+	2.81394e9i	−0.546062	+	0.945807i	0.452477	+	0.891776i	$0.350540\pi$
$509$	−1.62463e9	+	2.81394e9i	−0.546062	+	0.945807i	−0.998539	+	0.0540314i	$0.982793\pi$
$510$		0			0
$511$	4.38106e7	+	7.58822e7i	0.0145247	+	0.0251575i
$512$	−1.39223e9			−0.458423
$513$		0			0
$514$	−8.57312e8			−0.278463
$515$	1.40583e9	+	2.43497e9i	0.453532	+	0.785540i
$516$		0			0
$517$	2.76482e8	−	4.78881e8i	0.0879935	−	0.152409i
$518$	−5.15570e7	+	8.92993e7i	−0.0162980	+	0.0282289i
$519$		0			0
$520$	−1.31223e9	−	2.27284e9i	−0.409258	−	0.708855i
$521$	2.10950e9			0.653503			0.326752	−	0.945110i	$-0.394046\pi$
$521$	2.10950e9			0.653503			0.326752	+	0.945110i	$0.394046\pi$
$522$		0			0
$523$	−5.28911e9			−1.61669			−0.808345	−	0.588709i	$-0.799636\pi$
$523$	−5.28911e9			−1.61669			−0.808345	+	0.588709i	$0.799636\pi$
$524$	−7.74032e8	−	1.34066e9i	−0.235017	−	0.407061i
$525$		0			0
$526$	−1.32072e9	+	2.28756e9i	−0.395696	+	0.685365i
$527$	−3.92874e9	+	6.80477e9i	−1.16927	+	2.02524i
$528$		0			0
$529$	1.58555e9	+	2.74626e9i	0.465678	+	0.806577i
$530$	1.00166e9			0.292249
$531$		0			0
$532$	−5.07546e7			−0.0146145
$533$	1.60515e9	+	2.78020e9i	0.459167	+	0.795301i
$534$		0			0
$535$	−2.22808e9	+	3.85916e9i	−0.629062	+	1.08957i
$536$	3.34781e8	−	5.79858e8i	0.0939040	−	0.162646i
$537$		0			0
$538$	−8.26214e8	−	1.43104e9i	−0.228747	−	0.396201i
$539$	−7.76836e8			−0.213682
$540$		0			0
$541$	3.04614e9			0.827101			0.413551	−	0.910481i	$-0.364288\pi$
$541$	3.04614e9			0.827101			0.413551	+	0.910481i	$0.364288\pi$
$542$	−1.27401e9	−	2.20665e9i	−0.343696	−	0.595300i
$543$		0			0
$544$	−2.72642e9	+	4.72230e9i	−0.726100	+	1.25764i
$545$	7.84085e8	−	1.35808e9i	0.207480	−	0.359365i
$546$		0			0
$547$	2.42768e9	+	4.20487e9i	0.634215	+	1.09849i	0.986681	+	0.162668i	$0.0520100\pi$
$547$	2.42768e9	+	4.20487e9i	0.634215	+	1.09849i	−0.352466	+	0.935825i	$0.614657\pi$
$548$	2.58013e9			0.669746
$549$		0			0
$550$	−4.20770e8			−0.107839
$551$	−1.57358e8	−	2.72552e8i	−0.0400736	−	0.0694095i
$552$		0			0
$553$	−2.21239e8	+	3.83197e8i	−0.0556319	+	0.0963573i
$554$	1.54847e9	−	2.68204e9i	0.386919	−	0.670163i
$555$		0			0
$556$	−5.44056e8	−	9.42332e8i	−0.134240	−	0.232510i
$557$	−1.27762e9			−0.313263			−0.156631	−	0.987657i	$-0.550063\pi$
$557$	−1.27762e9			−0.313263			−0.156631	+	0.987657i	$0.550063\pi$
$558$		0			0
$559$	−3.49607e9			−0.846522
$560$	−4.81229e7	−	8.33513e7i	−0.0115796	−	0.0200565i
$561$		0			0
$562$	9.33129e8	−	1.61623e9i	0.221750	−	0.384083i
$563$	2.35632e9	−	4.08127e9i	0.556487	−	0.963865i	−0.441299	−	0.897360i	$-0.645482\pi$
$563$	2.35632e9	−	4.08127e9i	0.556487	−	0.963865i	0.997786	−	0.0665042i	$-0.0211846\pi$
$564$		0			0
$565$	3.45273e9	+	5.98031e9i	0.805366	+	1.39493i
$566$	3.56585e9			0.826619
$567$		0			0
$568$	−7.34003e9			−1.68066
$569$	2.28900e9	+	3.96466e9i	0.520898	+	0.902222i	0.999705	+	0.0243013i	$0.00773611\pi$
$569$	2.28900e9	+	3.96466e9i	0.520898	+	0.902222i	−0.478807	+	0.877920i	$0.658931\pi$
$570$		0			0
$571$	−2.47560e9	+	4.28786e9i	−0.556485	+	0.963860i	0.441301	+	0.897359i	$0.354517\pi$
$571$	−2.47560e9	+	4.28786e9i	−0.556485	+	0.963860i	−0.997786	+	0.0665012i	$0.978816\pi$
$572$	−2.22314e8	+	3.85058e8i	−0.0496684	+	0.0860281i
$573$		0			0
$574$	−1.20906e8	−	2.09415e8i	−0.0266843	−	0.0462186i
$575$	1.13093e9			0.248084
$576$		0			0
$577$	8.51847e9			1.84606			0.923031	−	0.384725i	$-0.125704\pi$
$577$	8.51847e9			1.84606			0.923031	+	0.384725i	$0.125704\pi$
$578$	1.18628e9	+	2.05470e9i	0.255529	+	0.442588i
$579$		0			0
$580$	6.54989e8	−	1.13447e9i	0.139392	−	0.241433i
$581$	1.40056e8	−	2.42584e8i	0.0296268	−	0.0513152i
$582$		0			0
$583$	−2.02899e8	−	3.51432e8i	−0.0424073	−	0.0734517i
$584$	1.80719e9			0.375455
$585$		0			0
$586$	6.93088e8			0.142281
$587$	−2.81124e8	−	4.86921e8i	−0.0573673	−	0.0993630i	0.835916	−	0.548858i	$-0.184937\pi$
$587$	−2.81124e8	−	4.86921e8i	−0.0573673	−	0.0993630i	−0.893283	+	0.449495i	$0.851604\pi$
$588$		0			0
$589$	−1.19304e9	+	2.06641e9i	−0.240576	+	0.416690i
$590$	1.52846e9	−	2.64738e9i	0.306389	−	0.530682i
$591$		0			0
$592$	−5.17718e8	−	8.96714e8i	−0.102557	−	0.177635i
$593$	−3.62110e9			−0.713099			−0.356549	−	0.934277i	$-0.616047\pi$
$593$	−3.62110e9			−0.713099			−0.356549	+	0.934277i	$0.616047\pi$
$594$		0			0
$595$	−7.08515e8			−0.137892
$596$	−9.56093e8	−	1.65600e9i	−0.184986	−	0.320405i
$597$		0			0
$598$	−2.33815e8	+	4.04979e8i	−0.0447113	+	0.0774423i
$599$	−3.74052e9	+	6.47877e9i	−0.711112	+	1.23168i	0.253328	+	0.967380i	$0.418475\pi$
$599$	−3.74052e9	+	6.47877e9i	−0.711112	+	1.23168i	−0.964440	+	0.264301i	$0.914859\pi$
$600$		0			0
$601$	2.90635e9	+	5.03395e9i	0.546119	+	0.945906i	0.998536	+	0.0540994i	$0.0172288\pi$
$601$	2.90635e9	+	5.03395e9i	0.546119	+	0.945906i	−0.452416	+	0.891807i	$0.649438\pi$
$602$	2.63336e8			0.0491953
$603$		0			0
$604$	−7.00230e6			−0.00129304
$605$	−3.62475e9	−	6.27825e9i	−0.665479	−	1.15264i
$606$		0			0
$607$	−1.92026e9	+	3.32598e9i	−0.348497	+	0.603614i	−0.985983	−	0.166848i	$-0.946641\pi$
$607$	−1.92026e9	+	3.32598e9i	−0.348497	+	0.603614i	0.637486	+	0.770462i	$0.279974\pi$
$608$	−8.27934e8	+	1.43402e9i	−0.149394	+	0.258758i
$609$		0			0
$610$	−3.51775e8	−	6.09291e8i	−0.0627495	−	0.108685i
$611$	2.97364e9			0.527405
$612$		0			0
$613$	1.70484e9			0.298932			0.149466	−	0.988767i	$-0.452245\pi$
$613$	1.70484e9			0.298932			0.149466	+	0.988767i	$0.452245\pi$
$614$	−7.81799e8	−	1.35412e9i	−0.136303	−	0.236084i
$615$		0			0
$616$	4.00435e7	−	6.93574e7i	0.00690239	−	0.0119553i
$617$	−1.40405e9	+	2.43188e9i	−0.240649	+	0.416816i	−0.960899	−	0.276898i	$-0.910693\pi$
$617$	−1.40405e9	+	2.43188e9i	−0.240649	+	0.416816i	0.720251	+	0.693714i	$0.244027\pi$
$618$		0			0
$619$	1.27183e9	+	2.20287e9i	0.215532	+	0.373312i	0.953437	−	0.301593i	$-0.0975182\pi$
$619$	1.27183e9	+	2.20287e9i	0.215532	+	0.373312i	−0.737905	+	0.674904i	$0.764185\pi$
$620$	−9.93187e9			−1.67363
$621$		0			0
$622$	3.46077e9			0.576642
$623$	2.72906e8	+	4.72687e8i	0.0452173	+	0.0783187i
$624$		0			0
$625$	3.20526e9	−	5.55167e9i	0.525149	−	0.909585i
$626$	−1.38022e9	+	2.39062e9i	−0.224874	+	0.389493i
$627$		0			0
$628$	−1.48039e9	−	2.56412e9i	−0.238517	−	0.413123i
$629$	−7.62238e9			−1.22127
$630$		0			0
$631$	−1.51146e8			−0.0239494			−0.0119747	−	0.999928i	$-0.503812\pi$
$631$	−1.51146e8			−0.0239494			−0.0119747	+	0.999928i	$0.503812\pi$
$632$	4.56306e9	+	7.90344e9i	0.719028	+	1.24539i
$633$		0			0
$634$	−1.87668e8	+	3.25051e8i	−0.0292468	+	0.0506570i
$635$	3.27372e9	−	5.67025e9i	0.507380	−	0.878808i
$636$		0			0
$637$	−2.08877e9	−	3.61786e9i	−0.320186	−	0.554579i
$638$	2.07669e8			0.0316591
$639$		0			0
$640$	−8.04735e9			−1.21345
$641$	−6.18126e9	−	1.07062e10i	−0.926987	−	1.60559i	−0.788334	−	0.615247i	$-0.789056\pi$
$641$	−6.18126e9	−	1.07062e10i	−0.926987	−	1.60559i	−0.138653	−	0.990341i	$-0.544277\pi$
$642$		0			0
$643$	−1.43372e9	+	2.48328e9i	−0.212680	+	0.368372i	−0.952552	−	0.304375i	$-0.901552\pi$
$643$	−1.43372e9	+	2.48328e9i	−0.212680	+	0.368372i	0.739873	+	0.672747i	$0.234886\pi$
$644$	−4.50079e7	+	7.79559e7i	−0.00664030	+	0.0115013i
$645$		0			0
$646$	7.34062e8	+	1.27143e9i	0.107132	+	0.185558i
$647$	4.10640e9			0.596068			0.298034	−	0.954555i	$-0.403669\pi$
$647$	4.10640e9			0.596068			0.298034	+	0.954555i	$0.403669\pi$
$648$		0			0
$649$	−1.23845e9			−0.177837
$650$	−1.13137e9	−	1.95960e9i	−0.161588	−	0.279879i
$651$		0			0
$652$	2.68380e9	−	4.64848e9i	0.379213	−	0.656817i
$653$	3.45550e9	−	5.98510e9i	0.485640	−	0.841153i	−0.514224	−	0.857656i	$-0.671920\pi$
$653$	3.45550e9	−	5.98510e9i	0.485640	−	0.841153i	0.999864	+	0.0165027i	$0.00525320\pi$
$654$		0			0
$655$	−3.28122e9	−	5.68324e9i	−0.456237	−	0.790226i
$656$	2.42819e9			0.335830
$657$		0			0
$658$	−2.23986e8			−0.0306499
$659$	1.71222e9	+	2.96565e9i	0.233056	+	0.403665i	0.958706	−	0.284399i	$-0.0917941\pi$
$659$	1.71222e9	+	2.96565e9i	0.233056	+	0.403665i	−0.725650	+	0.688064i	$0.758461\pi$
$660$		0			0
$661$	3.38219e9	−	5.85812e9i	0.455504	−	0.788956i	−0.543213	−	0.839595i	$-0.682792\pi$
$661$	3.38219e9	−	5.85812e9i	0.455504	−	0.788956i	0.998717	+	0.0506388i	$0.0161257\pi$
$662$	2.05271e9	−	3.55539e9i	0.274995	−	0.476305i
$663$		0			0
$664$	−2.88865e9	−	5.00329e9i	−0.382919	−	0.663236i
$665$	−2.15155e8			−0.0283711
$666$		0			0
$667$	−5.58165e8			−0.0728320
$668$	1.18848e9	+	2.05851e9i	0.154267	+	0.267199i
$669$		0			0
$670$	5.93475e8	−	1.02793e9i	0.0762326	−	0.132039i
$671$	−1.42514e8	+	2.46841e8i	−0.0182108	+	0.0315420i
$672$		0			0
$673$	8.74796e8	+	1.51519e9i	0.110625	+	0.191608i	0.916023	−	0.401127i	$-0.131381\pi$
$673$	8.74796e8	+	1.51519e9i	0.110625	+	0.191608i	−0.805397	+	0.592735i	$0.798048\pi$
$674$	3.75788e9			0.472752
$675$		0			0
$676$	3.38182e9			0.421053
$677$	4.15006e9	+	7.18811e9i	0.514036	+	0.890337i	0.999867	+	0.0162840i	$0.00518358\pi$
$677$	4.15006e9	+	7.18811e9i	0.514036	+	0.890337i	−0.485831	+	0.874053i	$0.661483\pi$
$678$		0			0
$679$	−2.82458e8	+	4.89232e8i	−0.0346266	+	0.0599750i
$680$	−7.30656e9	+	1.26553e10i	−0.891110	+	1.54345i
$681$		0			0
$682$	−7.87242e8	−	1.36354e9i	−0.0950305	−	0.164598i
$683$	1.21232e10			1.45594			0.727969	−	0.685610i	$-0.240464\pi$
$683$	1.21232e10			1.45594			0.727969	+	0.685610i	$0.240464\pi$
$684$		0			0
$685$	1.09375e10			1.30017
$686$	3.15454e8	+	5.46382e8i	0.0373080	+	0.0646193i
$687$		0			0
$688$	−1.32217e9	+	2.29006e9i	−0.154784	+	0.268094i
$689$	1.09112e9	−	1.88988e9i	0.127088	−	0.220123i
$690$		0			0
$691$	−4.10923e9	−	7.11739e9i	−0.473791	−	0.820631i	0.525758	−	0.850634i	$-0.323782\pi$
$691$	−4.10923e9	−	7.11739e9i	−0.473791	−	0.820631i	−0.999550	+	0.0300033i	$0.990448\pi$
$692$	5.84385e9			0.670390
$693$		0			0
$694$	−7.52038e9			−0.854046
$695$	−2.30632e9	−	3.99467e9i	−0.260599	−	0.451371i
$696$		0			0
$697$	8.93759e9	−	1.54804e10i	0.999783	−	1.73167i
$698$	7.96051e8	−	1.37880e9i	0.0886027	−	0.153464i
$699$		0			0
$700$	−2.17782e8	−	3.77210e8i	−0.0239983	−	0.0415662i
$701$	−4.72231e9			−0.517775			−0.258888	−	0.965907i	$-0.583356\pi$
$701$	−4.72231e9			−0.517775			−0.258888	+	0.965907i	$0.583356\pi$
$702$		0			0
$703$	−2.31469e9			−0.251275
$704$	−3.12370e8	−	5.41040e8i	−0.0337415	−	0.0584420i
$705$		0			0
$706$	1.70891e9	−	2.95991e9i	0.182769	−	0.316565i
$707$	−3.83566e8	+	6.64355e8i	−0.0408199	+	0.0707021i
$708$		0			0
$709$	−1.39487e9	−	2.41599e9i	−0.146985	−	0.254585i	0.783127	−	0.621862i	$-0.213624\pi$
$709$	−1.39487e9	−	2.41599e9i	−0.146985	−	0.254585i	−0.930112	+	0.367277i	$0.880290\pi$
$710$	−1.30119e10			−1.36438
$711$		0			0
$712$	1.12574e10			1.16885
$713$	2.11592e9	+	3.66488e9i	0.218618	+	0.378658i
$714$		0			0
$715$	−9.42416e8	+	1.63231e9i	−0.0964210	+	0.167006i
$716$	3.72397e9	−	6.45011e9i	0.379150	−	0.656707i
$717$		0			0
$718$	−2.79762e9	−	4.84562e9i	−0.282068	−	0.488556i
$719$	−1.51985e9			−0.152493			−0.0762463	−	0.997089i	$-0.524294\pi$
$719$	−1.51985e9			−0.152493			−0.0762463	+	0.997089i	$0.524294\pi$
$720$		0			0
$721$	−4.61401e8			−0.0458464
$722$	−2.45870e9	−	4.25860e9i	−0.243123	−	0.421101i
$723$		0			0
$724$	2.96715e9	−	5.13925e9i	0.290572	−	0.503286i
$725$	1.35041e9	−	2.33899e9i	0.131608	−	0.227953i
$726$		0			0
$727$	4.05880e9	+	7.03005e9i	0.391767	+	0.678560i	0.992683	−	0.120752i	$-0.0385307\pi$
$727$	4.05880e9	+	7.03005e9i	0.391767	+	0.678560i	−0.600916	+	0.799312i	$0.705197\pi$
$728$	4.30679e8			0.0413708
$729$		0			0
$730$	3.20365e9			0.304800
$731$	9.73316e9	+	1.68583e10i	0.921601	+	1.59626i
$732$		0			0
$733$	5.16203e9	−	8.94090e9i	0.484124	−	0.838528i	−0.515709	−	0.856764i	$-0.672472\pi$
$733$	5.16203e9	−	8.94090e9i	0.484124	−	0.838528i	0.999834	+	0.0182357i	$0.00580493\pi$
$734$	−2.55769e9	+	4.43006e9i	−0.238733	+	0.413498i
$735$		0			0
$736$	1.46838e9	+	2.54331e9i	0.135758	+	0.235140i
$737$	−4.80867e8			−0.0442475
$738$		0			0
$739$	−1.35365e10			−1.23382			−0.616908	−	0.787035i	$-0.711615\pi$
$739$	−1.35365e10			−1.23382			−0.616908	+	0.787035i	$0.711615\pi$
$740$	−4.81736e9	−	8.34391e9i	−0.437016	−	0.756935i
$741$		0			0
$742$	−8.21871e7	+	1.42352e8i	−0.00738567	+	0.0127924i
$743$	−8.59680e9	+	1.48901e10i	−0.768910	+	1.33179i	0.169244	+	0.985574i	$0.445868\pi$
$743$	−8.59680e9	+	1.48901e10i	−0.768910	+	1.33179i	−0.938154	+	0.346218i	$0.887466\pi$
$744$		0			0
$745$	−4.05300e9	−	7.02001e9i	−0.359112	−	0.622000i
$746$	−2.28710e9			−0.201697
$747$		0			0
$748$	2.47571e9			0.216294
$749$	−3.65634e8	−	6.33297e8i	−0.0317951	−	0.0550708i
$750$		0			0
$751$	−5.62392e9	+	9.74092e9i	−0.484506	+	0.839190i	−0.999842	−	0.0177991i	$-0.994334\pi$
$751$	−5.62392e9	+	9.74092e9i	−0.484506	+	0.839190i	0.515335	+	0.856989i	$0.327667\pi$
$752$	1.12459e9	−	1.94786e9i	0.0964348	−	0.167030i
$753$		0			0
$754$	5.58384e8	+	9.67149e8i	0.0474387	+	0.0821663i
$755$	−2.96837e7			−0.00251017
$756$		0			0
$757$	1.63068e10			1.36626			0.683131	−	0.730296i	$-0.260618\pi$
$757$	1.63068e10			1.36626			0.683131	+	0.730296i	$0.260618\pi$
$758$	−4.45059e9	−	7.70865e9i	−0.371172	−	0.642889i
$759$		0			0
$760$	−2.21879e9	+	3.84305e9i	−0.183345	+	0.317562i
$761$	3.07035e9	−	5.31800e9i	0.252546	−	0.437423i	−0.711680	−	0.702504i	$-0.752065\pi$
$761$	3.07035e9	−	5.31800e9i	0.252546	−	0.437423i	0.964226	+	0.265081i	$0.0853986\pi$
$762$		0			0
$763$	1.28670e8	+	2.22864e8i	0.0104868	+	0.0181637i
$764$	5.22812e9			0.424149
$765$		0			0
$766$	−4.57158e9			−0.367507
$767$	−3.32996e9	−	5.76766e9i	−0.266474	−	0.461547i
$768$		0			0
$769$	−1.22534e10	+	2.12236e10i	−0.971664	+	1.68297i	−0.281132	+	0.959669i	$0.590710\pi$
$769$	−1.22534e10	+	2.12236e10i	−0.971664	+	1.68297i	−0.690532	+	0.723302i	$0.742624\pi$
$770$	7.09862e7	−	1.22952e8i	0.00560346	−	0.00970549i
$771$		0			0
$772$	5.35334e9	+	9.27226e9i	0.418759	+	0.725312i
$773$	1.01722e10			0.792110			0.396055	−	0.918227i	$-0.370379\pi$
$773$	1.01722e10			0.792110			0.396055	+	0.918227i	$0.370379\pi$
$774$		0			0
$775$	−2.04769e10			−1.58018
$776$	5.82570e9	+	1.00904e10i	0.447540	+	0.775162i
$777$		0			0
$778$	−4.82705e9	+	8.36070e9i	−0.367497	+	0.636523i
$779$	2.71408e9	−	4.70093e9i	0.205704	−	0.356289i
$780$		0			0
$781$	2.63574e9	+	4.56523e9i	0.197981	+	0.342913i
$782$	2.60379e9			0.194707
$783$		0			0
$784$	−3.15979e9			−0.234181
$785$	−6.27558e9	−	1.08696e10i	−0.463031	−	0.801994i
$786$		0			0
$787$	4.89567e9	−	8.47956e9i	0.358015	−	0.620100i	−0.629614	−	0.776908i	$-0.716787\pi$
$787$	4.89567e9	−	8.47956e9i	0.358015	−	0.620100i	0.987629	+	0.156808i	$0.0501204\pi$
$788$	5.46554e9	−	9.46659e9i	0.397916	−	0.689211i
$789$		0			0
$790$	8.08905e9	+	1.40106e10i	0.583718	+	1.01103i
$791$	−1.13320e9			−0.0814124
$792$		0			0
$793$	−1.53277e9			−0.109150
$794$	5.64047e9	+	9.76959e9i	0.399893	+	0.692635i
$795$		0			0
$796$	−4.37049e9	+	7.56991e9i	−0.307139	+	0.531980i
$797$	−4.87891e9	+	8.45052e9i	−0.341365	+	0.591261i	−0.984686	−	0.174335i	$-0.944222\pi$
$797$	−4.87891e9	+	8.45052e9i	−0.341365	+	0.591261i	0.643322	+	0.765596i	$0.277556\pi$
$798$		0			0
$799$	−8.27872e9	−	1.43392e10i	−0.574182	−	0.994512i
$800$	−1.42103e10			−0.981270
$801$		0			0
$802$	1.61155e9			0.110315
$803$	−6.48945e8	−	1.12401e9i	−0.0442286	−	0.0766062i
$804$		0			0
$805$	−1.90794e8	+	3.30465e8i	−0.0128908	+	0.0223275i
$806$	4.23350e9	−	7.33264e9i	0.284792	−	0.493273i
$807$		0			0
$808$	7.91104e9	+	1.37023e10i	0.527587	+	0.913807i
$809$	2.78706e9			0.185066			0.0925330	−	0.995710i	$-0.470504\pi$
$809$	2.78706e9			0.185066			0.0925330	+	0.995710i	$0.470504\pi$
$810$		0			0
$811$	−7.99983e9			−0.526633			−0.263316	−	0.964710i	$-0.584816\pi$
$811$	−7.99983e9			−0.526633			−0.263316	+	0.964710i	$0.584816\pi$
$812$	1.07485e8	+	1.86170e8i	0.00704537	+	0.0122029i
$813$		0			0
$814$	7.63688e8	−	1.32275e9i	0.0496284	−	0.0859590i
$815$	1.13770e10	−	1.97055e10i	0.736165	−	1.27508i
$816$		0			0
$817$	2.95568e9	+	5.11938e9i	0.189618	+	0.328428i
$818$	−5.39687e8			−0.0344751
$819$		0			0
$820$	2.25943e10			1.43103
$821$	−5.12009e9	−	8.86826e9i	−0.322906	−	0.559290i	0.658180	−	0.752861i	$-0.271327\pi$
$821$	−5.12009e9	−	8.86826e9i	−0.322906	−	0.559290i	−0.981086	+	0.193570i	$0.937993\pi$
$822$		0			0
$823$	−1.39341e10	+	2.41346e10i	−0.871324	+	1.50918i	−0.0106973	+	0.999943i	$0.503405\pi$
$823$	−1.39341e10	+	2.41346e10i	−0.871324	+	1.50918i	−0.860627	+	0.509236i	$0.829928\pi$
$824$	−4.75820e9	+	8.24144e9i	−0.296277	+	0.513166i
$825$		0			0
$826$	2.50825e8	+	4.34442e8i	0.0154860	+	0.0268226i
$827$	−2.35125e10			−1.44554			−0.722769	−	0.691090i	$-0.757131\pi$
$827$	−2.35125e10			−1.44554			−0.722769	+	0.691090i	$0.757131\pi$
$828$		0			0
$829$	−1.28598e10			−0.783960			−0.391980	−	0.919974i	$-0.628210\pi$
$829$	−1.28598e10			−0.783960			−0.391980	+	0.919974i	$0.628210\pi$
$830$	−5.12080e9	−	8.86948e9i	−0.310859	−	0.538424i
$831$		0			0
$832$	1.67981e9	−	2.90952e9i	0.101118	−	0.175142i
$833$	−1.16304e10	+	2.01445e10i	−0.697168	+	1.20753i
$834$		0			0
$835$	5.03812e9	+	8.72628e9i	0.299479	+	0.518712i
$836$	7.51802e8			0.0445022
$837$		0			0
$838$	1.01433e10			0.595420
$839$	−3.99916e9	−	6.92675e9i	−0.233777	−	0.404914i	0.725139	−	0.688602i	$-0.241775\pi$
$839$	−3.99916e9	−	6.92675e9i	−0.233777	−	0.404914i	−0.958917	+	0.283688i	$0.908442\pi$
$840$		0			0
$841$	7.95845e9	−	1.37844e10i	0.461363	−	0.799103i
$842$	−3.39998e9	+	5.88894e9i	−0.196284	+	0.339973i
$843$		0			0
$844$	8.24533e9	+	1.42813e10i	0.472074	+	0.817655i
$845$	1.43360e10			0.817389
$846$		0			0
$847$	1.18966e9			0.0672716
$848$	−8.25296e8	−	1.42945e9i	−0.0464755	−	0.0804979i
$849$		0			0
$850$	−6.29956e9	+	1.09112e10i	−0.351839	+	0.609403i
$851$	−2.05261e9	+	3.55523e9i	−0.114170	+	0.197749i
$852$		0			0
$853$	−2.10414e9	−	3.64447e9i	−0.116079	−	0.201054i	0.802132	−	0.597147i	$-0.203699\pi$
$853$	−2.10414e9	−	3.64447e9i	−0.116079	−	0.201054i	−0.918210	+	0.396093i	$0.870366\pi$
$854$	1.15454e8			0.00634318
$855$		0			0
$856$	−1.50824e10			−0.821888
$857$	1.59653e10	+	2.76528e10i	0.866453	+	1.50074i	0.865597	+	0.500741i	$0.166939\pi$
$857$	1.59653e10	+	2.76528e10i	0.866453	+	1.50074i	0.000855933		1.00000i	$0.499728\pi$
$858$		0			0
$859$	−1.09001e10	+	1.88795e10i	−0.586752	+	1.01628i	0.407903	+	0.913025i	$0.366260\pi$
$859$	−1.09001e10	+	1.88795e10i	−0.586752	+	1.01628i	−0.994655	+	0.103259i	$0.967073\pi$
$860$	−1.23027e10	+	2.13090e10i	−0.659565	+	1.14240i
$861$		0			0
$862$	−6.59828e9	−	1.14286e10i	−0.350877	−	0.607737i
$863$	−1.04728e10			−0.554657			−0.277329	−	0.960775i	$-0.589449\pi$
$863$	−1.04728e10			−0.554657			−0.277329	+	0.960775i	$0.589449\pi$
$864$		0			0
$865$	2.47728e10			1.30142
$866$	−4.55214e8	−	7.88453e8i	−0.0238178	−	0.0412537i
$867$		0			0
$868$	8.14923e8	−	1.41149e9i	0.0422958	−	0.0732585i
$869$	3.27710e9	−	5.67611e9i	0.169403	−	0.293414i
$870$		0			0
$871$	−1.29296e9	−	2.23948e9i	−0.0663015	−	0.114838i
$872$	5.30765e9			0.271078
$873$		0			0
$874$	7.90695e8			0.0400608
$875$	5.17920e7	+	8.97064e7i	0.00261357	+	0.00452684i
$876$		0			0
$877$	8.88935e9	−	1.53968e10i	0.445012	−	0.770783i	−0.553041	−	0.833154i	$-0.686533\pi$
$877$	8.88935e9	−	1.53968e10i	0.445012	−	0.770783i	0.998053	+	0.0623707i	$0.0198661\pi$
$878$	2.97229e9	−	5.14815e9i	0.148204	−	0.256697i
$879$		0			0
$880$	7.12820e8	+	1.23464e9i	0.0352607	+	0.0610733i
$881$	7.64253e9			0.376549			0.188274	−	0.982116i	$-0.439711\pi$
$881$	7.64253e9			0.376549			0.188274	+	0.982116i	$0.439711\pi$
$882$		0			0
$883$	−2.76375e10			−1.35094			−0.675472	−	0.737386i	$-0.736060\pi$
$883$	−2.76375e10			−1.35094			−0.675472	+	0.737386i	$0.736060\pi$
$884$	6.65674e9	+	1.15298e10i	0.324100	+	0.561358i
$885$		0			0
$886$	5.32127e9	−	9.21671e9i	0.257038	−	0.445203i
$887$	1.61544e10	−	2.79802e10i	0.777243	−	1.34622i	−0.156282	−	0.987713i	$-0.549951\pi$
$887$	1.61544e10	−	2.79802e10i	0.777243	−	1.34622i	0.933525	−	0.358512i	$-0.116716\pi$
$888$		0			0
$889$	5.37225e8	+	9.30502e8i	0.0256449	+	0.0444182i
$890$	1.99562e10			0.948886
$891$		0			0
$892$	1.90014e10			0.896414
$893$	−2.51401e9	−	4.35439e9i	−0.118137	−	0.204619i
$894$		0			0
$895$	1.57864e10	−	2.73428e10i	0.736042	−	1.27486i
$896$	6.60296e8	−	1.14367e9i	0.0306662	−	0.0531155i
$897$		0			0
$898$	8.31031e8	+	1.43939e9i	0.0382957	+	0.0663301i
$899$	1.01063e10			0.463908
$900$		0			0
$901$	−1.21509e10			−0.553439
$902$	1.79092e9	+	3.10196e9i	0.0812555	+	0.140739i
$903$		0			0
$904$	−1.16862e10	+	2.02410e10i	−0.526117	+	0.911262i
$905$	1.25781e10	−	2.17859e10i	0.564087	−	0.977027i
$906$		0			0
$907$	−1.13571e10	−	1.96711e10i	−0.505409	−	0.875394i	−0.999980	−	0.00625673i	$-0.998008\pi$
$907$	−1.13571e10	−	1.96711e10i	−0.505409	−	0.875394i	0.494572	−	0.869137i	$-0.335325\pi$
$908$	3.99238e9			0.176983
$909$		0			0
$910$	7.63476e8			0.0335854
$911$	3.75463e9	+	6.50320e9i	0.164533	+	0.284979i	0.936489	−	0.350696i	$-0.114055\pi$
$911$	3.75463e9	+	6.50320e9i	0.164533	+	0.284979i	−0.771957	+	0.635675i	$0.780722\pi$
$912$		0			0
$913$	−2.07458e9	+	3.59328e9i	−0.0902157	+	0.156258i
$914$	8.84275e9	−	1.53161e10i	0.383068	−	0.663493i
$915$		0			0
$916$	−1.66488e9	−	2.88366e9i	−0.0715730	−	0.123968i
$917$	1.07691e9			0.0461199
$918$		0			0
$919$	−2.49374e10			−1.05986			−0.529928	−	0.848043i	$-0.677781\pi$
$919$	−2.49374e10			−1.05986			−0.529928	+	0.848043i	$0.677781\pi$
$920$	3.93513e9	+	6.81585e9i	0.166610	+	0.288577i
$921$		0			0
$922$	8.30062e9	−	1.43771e10i	0.348781	−	0.604106i
$923$	−1.41741e10	+	2.45502e10i	−0.593319	+	1.02766i
$924$		0			0
$925$	−9.93211e9	−	1.72029e10i	−0.412615	−	0.714671i
$926$	−2.78132e9			−0.115110
$927$		0			0
$928$	7.01342e9			0.288079
$929$	−4.33103e9	−	7.50156e9i	−0.177229	−	0.306970i	0.763701	−	0.645570i	$-0.223380\pi$
$929$	−4.33103e9	−	7.50156e9i	−0.177229	−	0.306970i	−0.940931	+	0.338600i	$0.890047\pi$
$930$		0			0
$931$	−3.53182e9	+	6.11729e9i	−0.143441	+	0.248448i
$932$	−4.24280e9	+	7.34874e9i	−0.171671	+	0.297343i
$933$		0			0
$934$	1.25377e9	+	2.17159e9i	0.0503503	+	0.0872093i
$935$	1.04949e10			0.419891
$936$		0			0
$937$	2.82655e10			1.12245			0.561226	−	0.827663i	$-0.310330\pi$
$937$	2.82655e10			1.12245			0.561226	+	0.827663i	$0.310330\pi$
$938$	9.73908e7	+	1.68686e8i	0.00385308	+	0.00667373i
$939$		0			0
$940$	1.04643e10	−	1.81248e10i	0.410926	−	0.711745i
$941$	−2.33541e10	+	4.04505e10i	−0.913691	+	1.58256i	−0.104884	+	0.994484i	$0.533447\pi$
$941$	−2.33541e10	+	4.04505e10i	−0.913691	+	1.58256i	−0.808807	+	0.588074i	$0.799886\pi$
$942$		0			0
$943$	−4.81356e9	−	8.33734e9i	−0.186929	−	0.323770i
$944$	−5.03740e9			−0.194897
$945$		0			0
$946$	−3.90067e9			−0.149803
$947$	−2.33696e10	−	4.04774e10i	−0.894184	−	1.54877i	−0.834812	−	0.550535i	$-0.814424\pi$
$947$	−2.33696e10	−	4.04774e10i	−0.894184	−	1.54877i	−0.0593718	−	0.998236i	$-0.518910\pi$
$948$		0			0
$949$	3.48979e9	−	6.04449e9i	0.132546	−	0.229577i
$950$	−1.91299e9	+	3.31340e9i	−0.0723904	+	0.125384i
$951$		0			0
$952$	−1.19902e9	−	2.07677e9i	−0.0450400	−	0.0780116i
$953$	−3.82420e10			−1.43125			−0.715625	−	0.698484i	$-0.753858\pi$
$953$	−3.82420e10			−1.43125			−0.715625	+	0.698484i	$0.753858\pi$
$954$		0			0
$955$	2.21627e10			0.823399
$956$	−2.29295e9	−	3.97151e9i	−0.0848775	−	0.147012i
$957$		0			0
$958$	4.52919e9	−	7.84478e9i	0.166434	−	0.288271i
$959$	−8.97437e8	+	1.55441e9i	−0.0328578	+	0.0569114i
$960$		0			0
$961$	−2.45550e10	−	4.25306e10i	−0.892501	−	1.54586i
$962$	8.21367e9			0.297457
$963$		0			0
$964$	−1.83424e10			−0.659457
$965$	2.26935e10	+	3.93063e10i	0.812935	+	1.40805i
$966$		0			0
$967$	2.45006e10	−	4.24363e10i	0.871333	−	1.50919i	0.0107146	−	0.999943i	$-0.496589\pi$
$967$	2.45006e10	−	4.24363e10i	0.871333	−	1.50919i	0.860618	−	0.509250i	$-0.170077\pi$
$968$	1.22684e10	−	2.12495e10i	0.434734	−	0.752982i
$969$		0			0
$970$	1.03274e10	+	1.78875e10i	0.363320	+	0.629288i
$971$	−2.72929e10			−0.956713			−0.478357	−	0.878166i	$-0.658767\pi$
$971$	−2.72929e10			−0.956713			−0.478357	+	0.878166i	$0.658767\pi$
$972$		0			0
$973$	7.56947e8			0.0263433
$974$	2.78838e9	+	4.82962e9i	0.0966931	+	0.167477i
$975$		0			0
$976$	−5.79676e8	+	1.00403e9i	−0.0199577	+	0.0345678i
$977$	1.97241e9	−	3.41631e9i	0.0676653	−	0.117200i	−0.830208	−	0.557454i	$-0.811778\pi$
$977$	1.97241e9	−	3.41631e9i	0.0676653	−	0.117200i	0.897873	+	0.440254i	$0.145112\pi$
$978$		0			0
$979$	−4.04242e9	−	7.00167e9i	−0.137690	−	0.238486i
$980$	−2.94018e10			−0.997889
$981$		0			0
$982$	3.07682e10			1.03684
$983$	2.37160e8	+	4.10774e8i	0.00796351	+	0.0137932i	0.869980	−	0.493088i	$-0.164132\pi$
$983$	2.37160e8	+	4.10774e8i	0.00796351	+	0.0137932i	−0.862016	+	0.506881i	$0.830798\pi$
$984$		0			0
$985$	2.31691e10	−	4.01301e10i	0.772472	−	1.33796i
$986$	3.10912e9	−	5.38515e9i	0.103292	−	0.178908i
$987$		0			0
$988$	2.02146e9	+	3.50127e9i	0.0666831	+	0.115498i
$989$	1.04841e10			0.344622
$990$		0			0
$991$	1.22197e10			0.398843			0.199421	−	0.979914i	$-0.436094\pi$
$991$	1.22197e10			0.398843			0.199421	+	0.979914i	$0.436094\pi$
$992$	−2.65869e10	−	4.60498e10i	−0.864721	−	1.49774i
$993$		0			0
$994$	1.06764e9	−	1.84921e9i	0.0344805	−	0.0597219i
$995$	−1.85271e10	+	3.20898e10i	−0.596247	+	1.03273i
$996$		0			0
$997$	1.80345e10	+	3.12367e10i	0.576330	+	0.998233i	0.995896	+	0.0905079i	$0.0288490\pi$
$997$	1.80345e10	+	3.12367e10i	0.576330	+	0.998233i	−0.419566	+	0.907725i	$0.637818\pi$
$998$	2.46390e9			0.0784631
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.8.c.c.28.1		2
3.2	odd	2		81.8.c.a.28.1		2
9.2	odd	6		81.8.c.a.55.1		2
9.4	even	3		9.8.a.a.1.1		1
9.5	odd	6		3.8.a.a.1.1	✓	1
9.7	even	3	inner	81.8.c.c.55.1		2
36.23	even	6		48.8.a.g.1.1		1
36.31	odd	6		144.8.a.b.1.1		1
45.4	even	6		225.8.a.i.1.1		1
45.13	odd	12		225.8.b.f.199.2		2
45.14	odd	6		75.8.a.a.1.1		1
45.22	odd	12		225.8.b.f.199.1		2
45.23	even	12		75.8.b.c.49.1		2
45.32	even	12		75.8.b.c.49.2		2
63.5	even	6		147.8.e.a.67.1		2
63.13	odd	6		441.8.a.a.1.1		1
63.23	odd	6		147.8.e.b.67.1		2
63.32	odd	6		147.8.e.b.79.1		2
63.41	even	6		147.8.a.b.1.1		1
63.59	even	6		147.8.e.a.79.1		2
72.5	odd	6		192.8.a.i.1.1		1
72.13	even	6		576.8.a.w.1.1		1
72.59	even	6		192.8.a.a.1.1		1
72.67	odd	6		576.8.a.x.1.1		1
99.32	even	6		363.8.a.b.1.1		1
117.77	odd	6		507.8.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.8.a.a.1.1	✓	1	9.5	odd	6
9.8.a.a.1.1		1	9.4	even	3
48.8.a.g.1.1		1	36.23	even	6
75.8.a.a.1.1		1	45.14	odd	6
75.8.b.c.49.1		2	45.23	even	12
75.8.b.c.49.2		2	45.32	even	12
81.8.c.a.28.1		2	3.2	odd	2
81.8.c.a.55.1		2	9.2	odd	6
81.8.c.c.28.1		2	1.1	even	1	trivial
81.8.c.c.55.1		2	9.7	even	3	inner
144.8.a.b.1.1		1	36.31	odd	6
147.8.a.b.1.1		1	63.41	even	6
147.8.e.a.67.1		2	63.5	even	6
147.8.e.a.79.1		2	63.59	even	6
147.8.e.b.67.1		2	63.23	odd	6
147.8.e.b.79.1		2	63.32	odd	6
192.8.a.a.1.1		1	72.59	even	6
192.8.a.i.1.1		1	72.5	odd	6
225.8.a.i.1.1		1	45.4	even	6
225.8.b.f.199.1		2	45.22	odd	12
225.8.b.f.199.2		2	45.13	odd	12
363.8.a.b.1.1		1	99.32	even	6
441.8.a.a.1.1		1	63.13	odd	6
507.8.a.a.1.1		1	117.77	odd	6
576.8.a.w.1.1		1	72.13	even	6
576.8.a.x.1.1		1	72.67	odd	6

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	81.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.00000 + 5.19615i) q^{2} +(46.0000 - 79.6743i) q^{4} +(195.000 - 337.750i) q^{5} +(32.0000 + 55.4256i) q^{7} +1320.00 q^{8} +2340.00 q^{10} +(-474.000 - 820.992i) q^{11} +(2549.00 - 4415.00i) q^{13} +(-192.000 + 332.554i) q^{14} +(-1928.00 - 3339.39i) q^{16} -28386.0 q^{17} -8620.00 q^{19} +(-17940.0 - 31073.0i) q^{20} +(2844.00 - 4925.95i) q^{22} +(-7644.00 + 13239.8i) q^{23} +(-36987.5 - 64064.2i) q^{25} +30588.0 q^{26} +5888.00 q^{28} +(18255.0 + 31618.6i) q^{29} +(138404. - 239723. i) q^{31} +(96048.0 - 166360. i) q^{32} +(-85158.0 - 147498. i) q^{34} +24960.0 q^{35} +268526. q^{37} +(-25860.0 - 44790.8i) q^{38} +(257400. - 445830. i) q^{40} +(-314859. + 545352. i) q^{41} +(-342886. - 593896. i) q^{43} -87216.0 q^{44} -91728.0 q^{46} +(291648. + 505149. i) q^{47} +(409724. - 709662. i) q^{49} +(221925. - 384385. i) q^{50} +(-234508. - 406180. i) q^{52} +428058. q^{53} -369720. q^{55} +(42240.0 + 73161.8i) q^{56} +(-109530. + 189712. i) q^{58} +(653190. - 1.13136e6i) q^{59} +(-150331. - 260381. i) q^{61} +1.66085e6 q^{62} +659008. q^{64} +(-994110. - 1.72185e6i) q^{65} +(253622. - 439286. i) q^{67} +(-1.30576e6 + 2.26164e6i) q^{68} +(74880.0 + 129696. i) q^{70} -5.56063e6 q^{71} +1.36908e6 q^{73} +(805578. + 1.39530e6i) q^{74} +(-396520. + 686793. i) q^{76} +(30336.0 - 52543.5i) q^{77} +(3.45686e6 + 5.98746e6i) q^{79} -1.50384e6 q^{80} -3.77831e6 q^{82} +(-2.18837e6 - 3.79037e6i) q^{83} +(-5.53527e6 + 9.58737e6i) q^{85} +(2.05732e6 - 3.56338e6i) q^{86} +(-625680. - 1.08371e6i) q^{88} +8.52831e6 q^{89} +326272. q^{91} +(703248. + 1.21806e6i) q^{92} +(-1.74989e6 + 3.03089e6i) q^{94} +(-1.68090e6 + 2.91140e6i) q^{95} +(4.41341e6 + 7.64425e6i) q^{97} +4.91668e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{2} + 92 q^{4} + 390 q^{5} + 64 q^{7} + 2640 q^{8} + 4680 q^{10} - 948 q^{11} + 5098 q^{13} - 384 q^{14} - 3856 q^{16} - 56772 q^{17} - 17240 q^{19} - 35880 q^{20} + 5688 q^{22} - 15288 q^{23}+ \cdots + 9833364 q^{98}+O(q^{100}) \) 2 * q + 6 * q^2 + 92 * q^4 + 390 * q^5 + 64 * q^7 + 2640 * q^8 + 4680 * q^10 - 948 * q^11 + 5098 * q^13 - 384 * q^14 - 3856 * q^16 - 56772 * q^17 - 17240 * q^19 - 35880 * q^20 + 5688 * q^22 - 15288 * q^23 - 73975 * q^25 + 61176 * q^26 + 11776 * q^28 + 36510 * q^29 + 276808 * q^31 + 192096 * q^32 - 170316 * q^34 + 49920 * q^35 + 537052 * q^37 - 51720 * q^38 + 514800 * q^40 - 629718 * q^41 - 685772 * q^43 - 174432 * q^44 - 183456 * q^46 + 583296 * q^47 + 819447 * q^49 + 443850 * q^50 - 469016 * q^52 + 856116 * q^53 - 739440 * q^55 + 84480 * q^56 - 219060 * q^58 + 1306380 * q^59 - 300662 * q^61 + 3321696 * q^62 + 1318016 * q^64 - 1988220 * q^65 + 507244 * q^67 - 2611512 * q^68 + 149760 * q^70 - 11121264 * q^71 + 2738164 * q^73 + 1611156 * q^74 - 793040 * q^76 + 60672 * q^77 + 6913720 * q^79 - 3007680 * q^80 - 7556616 * q^82 - 4376748 * q^83 - 11070540 * q^85 + 4114632 * q^86 - 1251360 * q^88 + 17056620 * q^89 + 652544 * q^91 + 1406496 * q^92 - 3499776 * q^94 - 3361800 * q^95 + 8826814 * q^97 + 9833364 * q^98

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