LMFDB - Embedded newform 531.8.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.41303$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.413031 q^{2} -127.829 q^{4} -231.152 q^{5} +302.150 q^{7} +105.665 q^{8} +O(q^{10})$	\(q-0.413031 q^{2} -127.829 q^{4} -231.152 q^{5} +302.150 q^{7} +105.665 q^{8} +95.4729 q^{10} -1281.53 q^{11} -14851.9 q^{13} -124.797 q^{14} +16318.5 q^{16} +21166.2 q^{17} -1755.31 q^{19} +29548.0 q^{20} +529.311 q^{22} -91962.2 q^{23} -24693.8 q^{25} +6134.31 q^{26} -38623.7 q^{28} -62655.4 q^{29} -103275. q^{31} -20265.2 q^{32} -8742.32 q^{34} -69842.6 q^{35} -37921.6 q^{37} +724.998 q^{38} -24424.8 q^{40} +45664.2 q^{41} -637229. q^{43} +163817. q^{44} +37983.3 q^{46} -229428. q^{47} -732248. q^{49} +10199.3 q^{50} +1.89852e6 q^{52} +1.07832e6 q^{53} +296227. q^{55} +31926.8 q^{56} +25878.6 q^{58} +205379. q^{59} -2.75987e6 q^{61} +42655.6 q^{62} -2.08040e6 q^{64} +3.43305e6 q^{65} -3.11037e6 q^{67} -2.70567e6 q^{68} +28847.1 q^{70} -4.01814e6 q^{71} -5.86422e6 q^{73} +15662.8 q^{74} +224380. q^{76} -387214. q^{77} +4.62456e6 q^{79} -3.77206e6 q^{80} -18860.7 q^{82} -9.51599e6 q^{83} -4.89262e6 q^{85} +263195. q^{86} -135413. q^{88} +6.95658e6 q^{89} -4.48752e6 q^{91} +1.17555e7 q^{92} +94760.7 q^{94} +405743. q^{95} -9.56241e6 q^{97} +302441. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) $ 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.413031	−0.0365071	−0.0182536	−	0.999833i	$-0.505811\pi$
$2$	−0.413031	−0.0365071	−0.0182536	+	0.999833i	$0.505811\pi$
$3$	0	0
$3$	0	0
$4$	−127.829	−0.998667
$5$	−231.152	−0.826994	−0.413497	−	0.910505i	$-0.635693\pi$
$5$	−231.152	−0.826994	−0.413497	+	0.910505i	$0.635693\pi$
$6$	0	0
$7$	302.150	0.332950	0.166475	−	0.986046i	$-0.446761\pi$
$7$	302.150	0.332950	0.166475	+	0.986046i	$0.446761\pi$
$8$	105.665	0.0729656
$9$	0	0
$10$	95.4729	0.0301912
$11$	−1281.53	−0.290304	−0.145152	−	0.989409i	$-0.546367\pi$
$11$	−1281.53	−0.290304	−0.145152	+	0.989409i	$0.546367\pi$
$12$	0	0
$13$	−14851.9	−1.87491	−0.937457	−	0.348100i	$-0.886827\pi$
$13$	−14851.9	−1.87491	−0.937457	+	0.348100i	$0.886827\pi$
$14$	−124.797	−0.0121551
$15$	0	0
$16$	16318.5	0.996003
$17$	21166.2	1.04489	0.522447	−	0.852672i	$-0.325019\pi$
$17$	21166.2	1.04489	0.522447	+	0.852672i	$0.325019\pi$
$18$	0	0
$19$	−1755.31	−0.0587106	−0.0293553	−	0.999569i	$-0.509345\pi$
$19$	−1755.31	−0.0587106	−0.0293553	+	0.999569i	$0.509345\pi$
$20$	29548.0	0.825892
$21$	0	0
$22$	529.311	0.0105982
$23$	−91962.2	−1.57602	−0.788011	−	0.615662i	$-0.788889\pi$
$23$	−91962.2	−1.57602	−0.788011	+	0.615662i	$0.788889\pi$
$24$	0	0
$25$	−24693.8	−0.316081
$26$	6134.31	0.0684478
$27$	0	0
$28$	−38623.7	−0.332507
$29$	−62655.4	−0.477052	−0.238526	−	0.971136i	$-0.576664\pi$
$29$	−62655.4	−0.477052	−0.238526	+	0.971136i	$0.576664\pi$
$30$	0	0
$31$	−103275.	−0.622626	−0.311313	−	0.950307i	$-0.600769\pi$
$31$	−103275.	−0.622626	−0.311313	+	0.950307i	$0.600769\pi$
$32$	−20265.2	−0.109327
$33$	0	0
$34$	−8742.32	−0.0381461
$35$	−69842.6	−0.275348
$36$	0	0
$37$	−37921.6	−0.123078	−0.0615390	−	0.998105i	$-0.519601\pi$
$37$	−37921.6	−0.123078	−0.0615390	+	0.998105i	$0.519601\pi$
$38$	724.998	0.00214335
$39$	0	0
$40$	−24424.8	−0.0603421
$41$	45664.2	0.103474	0.0517371	−	0.998661i	$-0.483524\pi$
$41$	45664.2	0.103474	0.0517371	+	0.998661i	$0.483524\pi$
$42$	0	0
$43$	−637229.	−1.22224	−0.611119	−	0.791539i	$-0.709280\pi$
$43$	−637229.	−1.22224	−0.611119	+	0.791539i	$0.709280\pi$
$44$	163817.	0.289917
$45$	0	0
$46$	37983.3	0.0575360
$47$	−229428.	−0.322332	−0.161166	−	0.986927i	$-0.551525\pi$
$47$	−229428.	−0.322332	−0.161166	+	0.986927i	$0.551525\pi$
$48$	0	0
$49$	−732248.	−0.889144
$50$	10199.3	0.0115392
$51$	0	0
$52$	1.89852e6	1.87242
$53$	1.07832e6	0.994906	0.497453	−	0.867491i	$-0.334269\pi$
$53$	1.07832e6	0.994906	0.497453	+	0.867491i	$0.334269\pi$
$54$	0	0
$55$	296227.	0.240080
$56$	31926.8	0.0242939
$57$	0	0
$58$	25878.6	0.0174158
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−2.75987e6	−1.55680	−0.778402	−	0.627767i	$-0.783969\pi$
$61$	−2.75987e6	−1.55680	−0.778402	+	0.627767i	$0.783969\pi$
$62$	42655.6	0.0227303
$63$	0	0
$64$	−2.08040e6	−0.992012
$65$	3.43305e6	1.55054
$66$	0	0
$67$	−3.11037e6	−1.26343	−0.631715	−	0.775201i	$-0.717649\pi$
$67$	−3.11037e6	−1.26343	−0.631715	+	0.775201i	$0.717649\pi$
$68$	−2.70567e6	−1.04350
$69$	0	0
$70$	28847.1	0.0100522
$71$	−4.01814e6	−1.33236	−0.666179	−	0.745792i	$-0.732071\pi$
$71$	−4.01814e6	−1.33236	−0.666179	+	0.745792i	$0.732071\pi$
$72$	0	0
$73$	−5.86422e6	−1.76433	−0.882165	−	0.470940i	$-0.843915\pi$
$73$	−5.86422e6	−1.76433	−0.882165	+	0.470940i	$0.843915\pi$
$74$	15662.8	0.00449322
$75$	0	0
$76$	224380.	0.0586323
$77$	−387214.	−0.0966570
$78$	0	0
$79$	4.62456e6	1.05530	0.527649	−	0.849462i	$-0.323074\pi$
$79$	4.62456e6	1.05530	0.527649	+	0.849462i	$0.323074\pi$
$80$	−3.77206e6	−0.823689
$81$	0	0
$82$	−18860.7	−0.00377755
$83$	−9.51599e6	−1.82676	−0.913378	−	0.407113i	$-0.866535\pi$
$83$	−9.51599e6	−1.82676	−0.913378	+	0.407113i	$0.866535\pi$
$84$	0	0
$85$	−4.89262e6	−0.864122
$86$	263195.	0.0446204
$87$	0	0
$88$	−135413.	−0.0211822
$89$	6.95658e6	1.04600	0.522999	−	0.852333i	$-0.324813\pi$
$89$	6.95658e6	1.04600	0.522999	+	0.852333i	$0.324813\pi$
$90$	0	0
$91$	−4.48752e6	−0.624254
$92$	1.17555e7	1.57392
$93$	0	0
$94$	94760.7	0.0117674
$95$	405743.	0.0485533
$96$	0	0
$97$	−9.56241e6	−1.06382	−0.531908	−	0.846802i	$-0.678525\pi$
$97$	−9.56241e6	−1.06382	−0.531908	+	0.846802i	$0.678525\pi$
$98$	302441.	0.0324601
$99$	0	0
$100$	3.15660e6	0.315660
$101$	9.74084e6	0.940744	0.470372	−	0.882468i	$-0.344120\pi$
$101$	9.74084e6	0.940744	0.470372	+	0.882468i	$0.344120\pi$
$102$	0	0
$103$	−1.17131e7	−1.05619	−0.528093	−	0.849186i	$-0.677093\pi$
$103$	−1.17131e7	−1.05619	−0.528093	+	0.849186i	$0.677093\pi$
$104$	−1.56934e6	−0.136804
$105$	0	0
$106$	−445380.	−0.0363212
$107$	2.32996e7	1.83867	0.919337	−	0.393471i	$-0.128726\pi$
$107$	2.32996e7	1.83867	0.919337	+	0.393471i	$0.128726\pi$
$108$	0	0
$109$	1.84368e7	1.36362	0.681808	−	0.731531i	$-0.261194\pi$
$109$	1.84368e7	1.36362	0.681808	+	0.731531i	$0.261194\pi$
$110$	−122351.	−0.00876463
$111$	0	0
$112$	4.93064e6	0.331620
$113$	1.69409e7	1.10449	0.552247	−	0.833681i	$-0.313771\pi$
$113$	1.69409e7	1.10449	0.552247	+	0.833681i	$0.313771\pi$
$114$	0	0
$115$	2.12572e7	1.30336
$116$	8.00921e6	0.476416
$117$	0	0
$118$	−84827.9	−0.00475282
$119$	6.39538e6	0.347898
$120$	0	0
$121$	−1.78449e7	−0.915723
$122$	1.13991e6	0.0568344
$123$	0	0
$124$	1.32015e7	0.621796
$125$	2.37668e7	1.08839
$126$	0	0
$127$	−1.02426e7	−0.443708	−0.221854	−	0.975080i	$-0.571211\pi$
$127$	−1.02426e7	−0.443708	−0.221854	+	0.975080i	$0.571211\pi$
$128$	3.45322e6	0.145542
$129$	0	0
$130$	−1.41796e6	−0.0566059
$131$	−2.19669e7	−0.853728	−0.426864	−	0.904316i	$-0.640382\pi$
$131$	−2.19669e7	−0.853728	−0.426864	+	0.904316i	$0.640382\pi$
$132$	0	0
$133$	−530367.	−0.0195477
$134$	1.28468e6	0.0461242
$135$	0	0
$136$	2.23654e6	0.0762414
$137$	−1.76506e6	−0.0586459	−0.0293229	−	0.999570i	$-0.509335\pi$
$137$	−1.76506e6	−0.0586459	−0.0293229	+	0.999570i	$0.509335\pi$
$138$	0	0
$139$	−2.43007e7	−0.767481	−0.383740	−	0.923441i	$-0.625364\pi$
$139$	−2.43007e7	−0.767481	−0.383740	+	0.923441i	$0.625364\pi$
$140$	8.92793e6	0.274981
$141$	0	0
$142$	1.65962e6	0.0486406
$143$	1.90332e7	0.544296
$144$	0	0
$145$	1.44829e7	0.394519
$146$	2.42210e6	0.0644107
$147$	0	0
$148$	4.84749e6	0.122914
$149$	−7.68149e7	−1.90236	−0.951181	−	0.308633i	$-0.900129\pi$
$149$	−7.68149e7	−1.90236	−0.951181	+	0.308633i	$0.900129\pi$
$150$	0	0
$151$	4.28340e7	1.01244	0.506220	−	0.862404i	$-0.331042\pi$
$151$	4.28340e7	1.01244	0.506220	+	0.862404i	$0.331042\pi$
$152$	−185476.	−0.00428385
$153$	0	0
$154$	159931.	0.00352867
$155$	2.38721e7	0.514908
$156$	0	0
$157$	5.51222e7	1.13678	0.568392	−	0.822758i	$-0.307566\pi$
$157$	5.51222e7	1.13678	0.568392	+	0.822758i	$0.307566\pi$
$158$	−1.91009e6	−0.0385259
$159$	0	0
$160$	4.68435e6	0.0904126
$161$	−2.77864e7	−0.524737
$162$	0	0
$163$	3.76340e7	0.680650	0.340325	−	0.940308i	$-0.389463\pi$
$163$	3.76340e7	0.680650	0.340325	+	0.940308i	$0.389463\pi$
$164$	−5.83723e6	−0.103336
$165$	0	0
$166$	3.93040e6	0.0666896
$167$	−9.25680e7	−1.53799	−0.768995	−	0.639255i	$-0.779243\pi$
$167$	−9.25680e7	−1.53799	−0.768995	+	0.639255i	$0.779243\pi$
$168$	0	0
$169$	1.57832e8	2.51531
$170$	2.02080e6	0.0315466
$171$	0	0
$172$	8.14566e7	1.22061
$173$	1.09599e8	1.60933	0.804665	−	0.593729i	$-0.202345\pi$
$173$	1.09599e8	1.60933	0.804665	+	0.593729i	$0.202345\pi$
$174$	0	0
$175$	−7.46124e6	−0.105239
$176$	−2.09126e7	−0.289144
$177$	0	0
$178$	−2.87328e6	−0.0381864
$179$	−4.35682e7	−0.567786	−0.283893	−	0.958856i	$-0.591626\pi$
$179$	−4.35682e7	−0.567786	−0.283893	+	0.958856i	$0.591626\pi$
$180$	0	0
$181$	−1.29762e8	−1.62656	−0.813282	−	0.581870i	$-0.802321\pi$
$181$	−1.29762e8	−1.62656	−0.813282	+	0.581870i	$0.802321\pi$
$182$	1.85348e6	0.0227897
$183$	0	0
$184$	−9.71724e6	−0.114995
$185$	8.76564e6	0.101785
$186$	0	0
$187$	−2.71251e7	−0.303337
$188$	2.93276e7	0.321902
$189$	0	0
$190$	−167585.	−0.00177254
$191$	−3.07331e7	−0.319146	−0.159573	−	0.987186i	$-0.551012\pi$
$191$	−3.07331e7	−0.319146	−0.159573	+	0.987186i	$0.551012\pi$
$192$	0	0
$193$	1.24448e8	1.24606	0.623029	−	0.782199i	$-0.285902\pi$
$193$	1.24448e8	1.24606	0.623029	+	0.782199i	$0.285902\pi$
$194$	3.94957e6	0.0388369
$195$	0	0
$196$	9.36029e7	0.887959
$197$	5.43655e7	0.506630	0.253315	−	0.967384i	$-0.418479\pi$
$197$	5.43655e7	0.506630	0.253315	+	0.967384i	$0.418479\pi$
$198$	0	0
$199$	1.40875e8	1.26721	0.633606	−	0.773656i	$-0.281574\pi$
$199$	1.40875e8	1.26721	0.633606	+	0.773656i	$0.281574\pi$
$200$	−2.60929e6	−0.0230630
$201$	0	0
$202$	−4.02327e6	−0.0343439
$203$	−1.89313e7	−0.158835
$204$	0	0
$205$	−1.05554e7	−0.0855726
$206$	4.83786e6	0.0385584
$207$	0	0
$208$	−2.42362e8	−1.86742
$209$	2.24948e6	0.0170439
$210$	0	0
$211$	2.07381e8	1.51978	0.759891	−	0.650051i	$-0.225252\pi$
$211$	2.07381e8	1.51978	0.759891	+	0.650051i	$0.225252\pi$
$212$	−1.37841e8	−0.993580
$213$	0	0
$214$	−9.62345e6	−0.0671247
$215$	1.47297e8	1.01078
$216$	0	0
$217$	−3.12044e7	−0.207304
$218$	−7.61496e6	−0.0497817
$219$	0	0
$220$	−3.78666e7	−0.239760
$221$	−3.14360e8	−1.95909
$222$	0	0
$223$	−2.57344e8	−1.55398	−0.776992	−	0.629511i	$-0.783255\pi$
$223$	−2.57344e8	−1.55398	−0.776992	+	0.629511i	$0.783255\pi$
$224$	−6.12314e6	−0.0364004
$225$	0	0
$226$	−6.99714e6	−0.0403219
$227$	1.28065e8	0.726676	0.363338	−	0.931657i	$-0.381637\pi$
$227$	1.28065e8	0.726676	0.363338	+	0.931657i	$0.381637\pi$
$228$	0	0
$229$	9.10898e7	0.501240	0.250620	−	0.968086i	$-0.419366\pi$
$229$	9.10898e7	0.501240	0.250620	+	0.968086i	$0.419366\pi$
$230$	−8.77990e6	−0.0475819
$231$	0	0
$232$	−6.62052e6	−0.0348084
$233$	6.28725e7	0.325623	0.162812	−	0.986657i	$-0.447944\pi$
$233$	6.28725e7	0.325623	0.162812	+	0.986657i	$0.447944\pi$
$234$	0	0
$235$	5.30326e7	0.266566
$236$	−2.62535e7	−0.130015
$237$	0	0
$238$	−2.64149e6	−0.0127008
$239$	2.11572e8	1.00246	0.501229	−	0.865315i	$-0.332881\pi$
$239$	2.11572e8	1.00246	0.501229	+	0.865315i	$0.332881\pi$
$240$	0	0
$241$	1.41219e7	0.0649882	0.0324941	−	0.999472i	$-0.489655\pi$
$241$	1.41219e7	0.0649882	0.0324941	+	0.999472i	$0.489655\pi$
$242$	7.37048e6	0.0334304
$243$	0	0
$244$	3.52792e8	1.55473
$245$	1.69261e8	0.735317
$246$	0	0
$247$	2.60698e7	0.110077
$248$	−1.09126e7	−0.0454303
$249$	0	0
$250$	−9.81641e6	−0.0397340
$251$	−8.14251e7	−0.325013	−0.162506	−	0.986707i	$-0.551958\pi$
$251$	−8.14251e7	−0.325013	−0.162506	+	0.986707i	$0.551958\pi$
$252$	0	0
$253$	1.17852e8	0.457526
$254$	4.23051e6	0.0161985
$255$	0	0
$256$	2.64865e8	0.986699
$257$	−2.21346e8	−0.813402	−0.406701	−	0.913561i	$-0.633321\pi$
$257$	−2.21346e8	−0.813402	−0.406701	+	0.913561i	$0.633321\pi$
$258$	0	0
$259$	−1.14580e7	−0.0409789
$260$	−4.38845e8	−1.54848
$261$	0	0
$262$	9.07301e6	0.0311672
$263$	−4.49267e8	−1.52286	−0.761429	−	0.648249i	$-0.775502\pi$
$263$	−4.49267e8	−1.52286	−0.761429	+	0.648249i	$0.775502\pi$
$264$	0	0
$265$	−2.49256e8	−0.822781
$266$	219058.	0.000713631 0
$267$	0	0
$268$	3.97597e8	1.26175
$269$	4.00214e8	1.25360	0.626801	−	0.779180i	$-0.284364\pi$
$269$	4.00214e8	1.25360	0.626801	+	0.779180i	$0.284364\pi$
$270$	0	0
$271$	2.23102e8	0.680944	0.340472	−	0.940255i	$-0.389413\pi$
$271$	2.23102e8	0.680944	0.340472	+	0.940255i	$0.389413\pi$
$272$	3.45402e8	1.04072
$273$	0	0
$274$	729025.	0.00214099
$275$	3.16458e7	0.0917597
$276$	0	0
$277$	2.84338e8	0.803815	0.401907	−	0.915680i	$-0.368347\pi$
$277$	2.84338e8	0.803815	0.401907	+	0.915680i	$0.368347\pi$
$278$	1.00370e7	0.0280185
$279$	0	0
$280$	−7.37995e6	−0.0200909
$281$	3.25571e8	0.875332	0.437666	−	0.899138i	$-0.355805\pi$
$281$	3.25571e8	0.875332	0.437666	+	0.899138i	$0.355805\pi$
$282$	0	0
$283$	−4.66681e7	−0.122396	−0.0611980	−	0.998126i	$-0.519492\pi$
$283$	−4.66681e7	−0.122396	−0.0611980	+	0.998126i	$0.519492\pi$
$284$	5.13636e8	1.33058
$285$	0	0
$286$	−7.86129e6	−0.0198707
$287$	1.37974e7	0.0344518
$288$	0	0
$289$	3.76710e7	0.0918048
$290$	−5.98190e6	−0.0144028
$291$	0	0
$292$	7.49619e8	1.76198
$293$	7.70273e7	0.178899	0.0894495	−	0.995991i	$-0.471489\pi$
$293$	7.70273e7	0.178899	0.0894495	+	0.995991i	$0.471489\pi$
$294$	0	0
$295$	−4.74737e7	−0.107665
$296$	−4.00700e6	−0.00898046
$297$	0	0
$298$	3.17269e7	0.0694498
$299$	1.36582e9	2.95491
$300$	0	0
$301$	−1.92539e8	−0.406945
$302$	−1.76918e7	−0.0369613
$303$	0	0
$304$	−2.86441e7	−0.0584759
$305$	6.37948e8	1.28747
$306$	0	0
$307$	−1.67909e8	−0.331200	−0.165600	−	0.986193i	$-0.552956\pi$
$307$	−1.67909e8	−0.331200	−0.165600	+	0.986193i	$0.552956\pi$
$308$	4.94973e7	0.0965281
$309$	0	0
$310$	−9.85992e6	−0.0187978
$311$	2.22728e8	0.419868	0.209934	−	0.977716i	$-0.432675\pi$
$311$	2.22728e8	0.419868	0.209934	+	0.977716i	$0.432675\pi$
$312$	0	0
$313$	−2.23952e8	−0.412809	−0.206404	−	0.978467i	$-0.566176\pi$
$313$	−2.23952e8	−0.412809	−0.206404	+	0.978467i	$0.566176\pi$
$314$	−2.27672e7	−0.0415007
$315$	0	0
$316$	−5.91154e8	−1.05389
$317$	−7.57737e8	−1.33601	−0.668007	−	0.744155i	$-0.732853\pi$
$317$	−7.57737e8	−1.33601	−0.668007	+	0.744155i	$0.732853\pi$
$318$	0	0
$319$	8.02947e7	0.138490
$320$	4.80888e8	0.820388
$321$	0	0
$322$	1.14766e7	0.0191566
$323$	−3.71533e7	−0.0613464
$324$	0	0
$325$	3.66751e8	0.592625
$326$	−1.55440e7	−0.0248486
$327$	0	0
$328$	4.82513e6	0.00755006
$329$	−6.93215e7	−0.107320
$330$	0	0
$331$	2.98249e8	0.452044	0.226022	−	0.974122i	$-0.427428\pi$
$331$	2.98249e8	0.452044	0.226022	+	0.974122i	$0.427428\pi$
$332$	1.21642e9	1.82432
$333$	0	0
$334$	3.82335e7	0.0561476
$335$	7.18969e8	1.04485
$336$	0	0
$337$	−1.29895e9	−1.84879	−0.924393	−	0.381442i	$-0.875428\pi$
$337$	−1.29895e9	−1.84879	−0.924393	+	0.381442i	$0.875428\pi$
$338$	−6.51894e7	−0.0918266
$339$	0	0
$340$	6.25420e8	0.862970
$341$	1.32349e8	0.180751
$342$	0	0
$343$	−4.70083e8	−0.628991
$344$	−6.73331e7	−0.0891814
$345$	0	0
$346$	−4.52678e7	−0.0587521
$347$	−1.13535e9	−1.45874	−0.729369	−	0.684120i	$-0.760186\pi$
$347$	−1.13535e9	−1.45874	−0.729369	+	0.684120i	$0.760186\pi$
$348$	0	0
$349$	2.24671e8	0.282916	0.141458	−	0.989944i	$-0.454821\pi$
$349$	2.24671e8	0.282916	0.141458	+	0.989944i	$0.454821\pi$
$350$	3.08172e6	0.00384199
$351$	0	0
$352$	2.59705e7	0.0317381
$353$	−1.00698e9	−1.21846	−0.609228	−	0.792995i	$-0.708520\pi$
$353$	−1.00698e9	−1.21846	−0.609228	+	0.792995i	$0.708520\pi$
$354$	0	0
$355$	9.28800e8	1.10185
$356$	−8.89256e8	−1.04460
$357$	0	0
$358$	1.79950e7	0.0207282
$359$	5.34366e7	0.0609548	0.0304774	−	0.999535i	$-0.490297\pi$
$359$	5.34366e7	0.0609548	0.0304774	+	0.999535i	$0.490297\pi$
$360$	0	0
$361$	−8.90791e8	−0.996553
$362$	5.35956e7	0.0593812
$363$	0	0
$364$	5.73637e8	0.623422
$365$	1.35552e9	1.45909
$366$	0	0
$367$	1.32145e8	0.139547	0.0697733	−	0.997563i	$-0.477772\pi$
$367$	1.32145e8	0.139547	0.0697733	+	0.997563i	$0.477772\pi$
$368$	−1.50069e9	−1.56972
$369$	0	0
$370$	−3.62048e6	−0.00371587
$371$	3.25814e8	0.331254
$372$	0	0
$373$	1.16722e8	0.116458	0.0582292	−	0.998303i	$-0.481455\pi$
$373$	1.16722e8	0.116458	0.0582292	+	0.998303i	$0.481455\pi$
$374$	1.12035e7	0.0110740
$375$	0	0
$376$	−2.42426e7	−0.0235191
$377$	9.30555e8	0.894432
$378$	0	0
$379$	1.54193e9	1.45488	0.727440	−	0.686172i	$-0.240710\pi$
$379$	1.54193e9	1.45488	0.727440	+	0.686172i	$0.240710\pi$
$380$	−5.18659e7	−0.0484886
$381$	0	0
$382$	1.26937e7	0.0116511
$383$	1.11000e9	1.00955	0.504774	−	0.863252i	$-0.331576\pi$
$383$	1.11000e9	1.00955	0.504774	+	0.863252i	$0.331576\pi$
$384$	0	0
$385$	8.95052e7	0.0799347
$386$	−5.14010e7	−0.0454900
$387$	0	0
$388$	1.22236e9	1.06240
$389$	−3.52125e8	−0.303301	−0.151650	−	0.988434i	$-0.548459\pi$
$389$	−3.52125e8	−0.303301	−0.151650	+	0.988434i	$0.548459\pi$
$390$	0	0
$391$	−1.94649e9	−1.64678
$392$	−7.73734e7	−0.0648769
$393$	0	0
$394$	−2.24546e7	−0.0184956
$395$	−1.06897e9	−0.872725
$396$	0	0
$397$	1.23251e9	0.988611	0.494305	−	0.869288i	$-0.335422\pi$
$397$	1.23251e9	0.988611	0.494305	+	0.869288i	$0.335422\pi$
$398$	−5.81859e7	−0.0462623
$399$	0	0
$400$	−4.02967e8	−0.314818
$401$	1.95405e9	1.51332	0.756661	−	0.653808i	$-0.226829\pi$
$401$	1.95405e9	1.51332	0.756661	+	0.653808i	$0.226829\pi$
$402$	0	0
$403$	1.53383e9	1.16737
$404$	−1.24517e9	−0.939491
$405$	0	0
$406$	7.81924e6	0.00579860
$407$	4.85975e7	0.0357301
$408$	0	0
$409$	−8.06706e8	−0.583020	−0.291510	−	0.956568i	$-0.594158\pi$
$409$	−8.06706e8	−0.583020	−0.291510	+	0.956568i	$0.594158\pi$
$410$	4.35969e6	0.00312401
$411$	0	0
$412$	1.49728e9	1.05478
$413$	6.20553e7	0.0433465
$414$	0	0
$415$	2.19964e9	1.51072
$416$	3.00978e8	0.204979
$417$	0	0
$418$	−929105.	−0.000622225 0
$419$	1.37468e9	0.912960	0.456480	−	0.889734i	$-0.349110\pi$
$419$	1.37468e9	0.912960	0.456480	+	0.889734i	$0.349110\pi$
$420$	0	0
$421$	−8.51303e8	−0.556028	−0.278014	−	0.960577i	$-0.589676\pi$
$421$	−8.51303e8	−0.556028	−0.278014	+	0.960577i	$0.589676\pi$
$422$	−8.56549e7	−0.0554829
$423$	0	0
$424$	1.13941e8	0.0725939
$425$	−5.22675e8	−0.330271
$426$	0	0
$427$	−8.33894e8	−0.518338
$428$	−2.97837e9	−1.83622
$429$	0	0
$430$	−6.08381e7	−0.0369008
$431$	−3.76775e8	−0.226679	−0.113339	−	0.993556i	$-0.536155\pi$
$431$	−3.76775e8	−0.226679	−0.113339	+	0.993556i	$0.536155\pi$
$432$	0	0
$433$	1.14074e9	0.675270	0.337635	−	0.941277i	$-0.390373\pi$
$433$	1.14074e9	0.675270	0.337635	+	0.941277i	$0.390373\pi$
$434$	1.28884e7	0.00756806
$435$	0	0
$436$	−2.35676e9	−1.36180
$437$	1.61422e8	0.0925291
$438$	0	0
$439$	1.15020e9	0.648854	0.324427	−	0.945911i	$-0.394829\pi$
$439$	1.15020e9	0.648854	0.324427	+	0.945911i	$0.394829\pi$
$440$	3.13010e7	0.0175176
$441$	0	0
$442$	1.29840e8	0.0715207
$443$	−4.99658e8	−0.273061	−0.136531	−	0.990636i	$-0.543595\pi$
$443$	−4.99658e8	−0.273061	−0.136531	+	0.990636i	$0.543595\pi$
$444$	0	0
$445$	−1.60803e9	−0.865034
$446$	1.06291e8	0.0567315
$447$	0	0
$448$	−6.28593e8	−0.330291
$449$	−1.70526e9	−0.889054	−0.444527	−	0.895766i	$-0.646628\pi$
$449$	−1.70526e9	−0.889054	−0.444527	+	0.895766i	$0.646628\pi$
$450$	0	0
$451$	−5.85199e7	−0.0300390
$452$	−2.16555e9	−1.10302
$453$	0	0
$454$	−5.28949e7	−0.0265289
$455$	1.03730e9	0.516254
$456$	0	0
$457$	−6.10097e8	−0.299015	−0.149507	−	0.988761i	$-0.547769\pi$
$457$	−6.10097e8	−0.299015	−0.149507	+	0.988761i	$0.547769\pi$
$458$	−3.76229e7	−0.0182988
$459$	0	0
$460$	−2.71730e9	−1.30162
$461$	−2.09113e9	−0.994093	−0.497046	−	0.867724i	$-0.665582\pi$
$461$	−2.09113e9	−0.994093	−0.497046	+	0.867724i	$0.665582\pi$
$462$	0	0
$463$	−3.87258e8	−0.181329	−0.0906643	−	0.995882i	$-0.528899\pi$
$463$	−3.87258e8	−0.181329	−0.0906643	+	0.995882i	$0.528899\pi$
$464$	−1.02244e9	−0.475146
$465$	0	0
$466$	−2.59683e7	−0.0118876
$467$	−2.46901e8	−0.112180	−0.0560898	−	0.998426i	$-0.517863\pi$
$467$	−2.46901e8	−0.112180	−0.0560898	+	0.998426i	$0.517863\pi$
$468$	0	0
$469$	−9.39800e8	−0.420659
$470$	−2.19041e7	−0.00973157
$471$	0	0
$472$	2.17015e7	0.00949931
$473$	8.16627e8	0.354821
$474$	0	0
$475$	4.33453e7	0.0185573
$476$	−8.17518e8	−0.347434
$477$	0	0
$478$	−8.73860e7	−0.0365969
$479$	3.29359e9	1.36929	0.684645	−	0.728877i	$-0.259957\pi$
$479$	3.29359e9	1.36929	0.684645	+	0.728877i	$0.259957\pi$
$480$	0	0
$481$	5.63209e8	0.230761
$482$	−5.83280e6	−0.00237253
$483$	0	0
$484$	2.28110e9	0.914503
$485$	2.21037e9	0.879769
$486$	0	0
$487$	1.64421e9	0.645070	0.322535	−	0.946558i	$-0.395465\pi$
$487$	1.64421e9	0.645070	0.322535	+	0.946558i	$0.395465\pi$
$488$	−2.91623e8	−0.113593
$489$	0	0
$490$	−6.99099e7	−0.0268443
$491$	−2.85157e9	−1.08717	−0.543587	−	0.839353i	$-0.682934\pi$
$491$	−2.85157e9	−1.08717	−0.543587	+	0.839353i	$0.682934\pi$
$492$	0	0
$493$	−1.32618e9	−0.498469
$494$	−1.07676e7	−0.00401861
$495$	0	0
$496$	−1.68529e9	−0.620138
$497$	−1.21408e9	−0.443609
$498$	0	0
$499$	3.73412e9	1.34535	0.672676	−	0.739937i	$-0.265145\pi$
$499$	3.73412e9	1.34535	0.672676	+	0.739937i	$0.265145\pi$
$500$	−3.03809e9	−1.08694
$501$	0	0
$502$	3.36311e7	0.0118653
$503$	4.65904e9	1.63233	0.816166	−	0.577817i	$-0.196095\pi$
$503$	4.65904e9	1.63233	0.816166	+	0.577817i	$0.196095\pi$
$504$	0	0
$505$	−2.25161e9	−0.777990
$506$	−4.86766e7	−0.0167030
$507$	0	0
$508$	1.30931e9	0.443117
$509$	−4.17061e9	−1.40180	−0.700902	−	0.713258i	$-0.747219\pi$
$509$	−4.17061e9	−1.40180	−0.700902	+	0.713258i	$0.747219\pi$
$510$	0	0
$511$	−1.77187e9	−0.587435
$512$	−5.51410e8	−0.181564
$513$	0	0
$514$	9.14226e7	0.0296950
$515$	2.70750e9	0.873460
$516$	0	0
$517$	2.94018e8	0.0935743
$518$	4.73251e6	0.00149602
$519$	0	0
$520$	3.62755e8	0.113136
$521$	1.08528e9	0.336209	0.168104	−	0.985769i	$-0.446235\pi$
$521$	1.08528e9	0.336209	0.168104	+	0.985769i	$0.446235\pi$
$522$	0	0
$523$	−4.07601e9	−1.24589	−0.622945	−	0.782266i	$-0.714064\pi$
$523$	−4.07601e9	−1.24589	−0.622945	+	0.782266i	$0.714064\pi$
$524$	2.80802e9	0.852590
$525$	0	0
$526$	1.85561e8	0.0555952
$527$	−2.18593e9	−0.650579
$528$	0	0
$529$	5.05223e9	1.48384
$530$	1.02950e8	0.0300374
$531$	0	0
$532$	6.77965e7	0.0195217
$533$	−6.78202e8	−0.194005
$534$	0	0
$535$	−5.38574e9	−1.52057
$536$	−3.28659e8	−0.0921869
$537$	0	0
$538$	−1.65301e8	−0.0457654
$539$	9.38396e8	0.258122
$540$	0	0
$541$	−4.61079e9	−1.25194	−0.625972	−	0.779846i	$-0.715297\pi$
$541$	−4.61079e9	−1.25194	−0.625972	+	0.779846i	$0.715297\pi$
$542$	−9.21481e7	−0.0248593
$543$	0	0
$544$	−4.28939e8	−0.114235
$545$	−4.26169e9	−1.12770
$546$	0	0
$547$	−3.70849e9	−0.968817	−0.484409	−	0.874842i	$-0.660965\pi$
$547$	−3.70849e9	−0.968817	−0.484409	+	0.874842i	$0.660965\pi$
$548$	2.25627e8	0.0585677
$549$	0	0
$550$	−1.30707e7	−0.00334988
$551$	1.09980e8	0.0280080
$552$	0	0
$553$	1.39731e9	0.351362
$554$	−1.17441e8	−0.0293450
$555$	0	0
$556$	3.10635e9	0.766458
$557$	4.17975e9	1.02484	0.512421	−	0.858734i	$-0.328749\pi$
$557$	4.17975e9	1.02484	0.512421	+	0.858734i	$0.328749\pi$
$558$	0	0
$559$	9.46409e9	2.29159
$560$	−1.13973e9	−0.274248
$561$	0	0
$562$	−1.34471e8	−0.0319559
$563$	−5.00396e9	−1.18178	−0.590888	−	0.806754i	$-0.701222\pi$
$563$	−5.00396e9	−1.18178	−0.590888	+	0.806754i	$0.701222\pi$
$564$	0	0
$565$	−3.91593e9	−0.913410
$566$	1.92754e7	0.00446833
$567$	0	0
$568$	−4.24579e8	−0.0972163
$569$	−5.07854e8	−0.115570	−0.0577851	−	0.998329i	$-0.518404\pi$
$569$	−5.07854e8	−0.115570	−0.0577851	+	0.998329i	$0.518404\pi$
$570$	0	0
$571$	−5.27683e9	−1.18617	−0.593085	−	0.805140i	$-0.702090\pi$
$571$	−5.27683e9	−1.18617	−0.593085	+	0.805140i	$0.702090\pi$
$572$	−2.43300e9	−0.543571
$573$	0	0
$574$	−5.69877e6	−0.00125774
$575$	2.27090e9	0.498150
$576$	0	0
$577$	−1.54218e9	−0.334209	−0.167105	−	0.985939i	$-0.553442\pi$
$577$	−1.54218e9	−0.334209	−0.167105	+	0.985939i	$0.553442\pi$
$578$	−1.55593e7	−0.00335153
$579$	0	0
$580$	−1.85134e9	−0.393993
$581$	−2.87526e9	−0.608219
$582$	0	0
$583$	−1.38190e9	−0.288826
$584$	−6.19645e8	−0.128735
$585$	0	0
$586$	−3.18147e7	−0.00653109
$587$	−9.40246e8	−0.191870	−0.0959352	−	0.995388i	$-0.530584\pi$
$587$	−9.40246e8	−0.191870	−0.0959352	+	0.995388i	$0.530584\pi$
$588$	0	0
$589$	1.81279e8	0.0365547
$590$	1.96081e7	0.00393056
$591$	0	0
$592$	−6.18824e8	−0.122586
$593$	−3.28316e9	−0.646547	−0.323274	−	0.946306i	$-0.604783\pi$
$593$	−3.28316e9	−0.646547	−0.323274	+	0.946306i	$0.604783\pi$
$594$	0	0
$595$	−1.47830e9	−0.287710
$596$	9.81920e9	1.89983
$597$	0	0
$598$	−5.64125e8	−0.107875
$599$	−7.40433e8	−0.140764	−0.0703820	−	0.997520i	$-0.522422\pi$
$599$	−7.40433e8	−0.140764	−0.0703820	+	0.997520i	$0.522422\pi$
$600$	0	0
$601$	−2.01096e9	−0.377870	−0.188935	−	0.981990i	$-0.560504\pi$
$601$	−2.01096e9	−0.377870	−0.188935	+	0.981990i	$0.560504\pi$
$602$	7.95245e7	0.0148564
$603$	0	0
$604$	−5.47545e9	−1.01109
$605$	4.12487e9	0.757298
$606$	0	0
$607$	−4.88190e9	−0.885990	−0.442995	−	0.896524i	$-0.646084\pi$
$607$	−4.88190e9	−0.885990	−0.442995	+	0.896524i	$0.646084\pi$
$608$	3.55718e7	0.00641864
$609$	0	0
$610$	−2.63493e8	−0.0470017
$611$	3.40744e9	0.604344
$612$	0	0
$613$	−6.53926e9	−1.14661	−0.573306	−	0.819341i	$-0.694339\pi$
$613$	−6.53926e9	−1.14661	−0.573306	+	0.819341i	$0.694339\pi$
$614$	6.93517e7	0.0120912
$615$	0	0
$616$	−4.09151e7	−0.00705264
$617$	−1.08583e9	−0.186108	−0.0930541	−	0.995661i	$-0.529663\pi$
$617$	−1.08583e9	−0.186108	−0.0930541	+	0.995661i	$0.529663\pi$
$618$	0	0
$619$	−1.46677e9	−0.248568	−0.124284	−	0.992247i	$-0.539663\pi$
$619$	−1.46677e9	−0.248568	−0.124284	+	0.992247i	$0.539663\pi$
$620$	−3.05156e9	−0.514222
$621$	0	0
$622$	−9.19935e7	−0.0153282
$623$	2.10193e9	0.348266
$624$	0	0
$625$	−3.56453e9	−0.584012
$626$	9.24990e7	0.0150705
$627$	0	0
$628$	−7.04624e9	−1.13527
$629$	−8.02657e8	−0.128603
$630$	0	0
$631$	5.56162e9	0.881248	0.440624	−	0.897692i	$-0.354757\pi$
$631$	5.56162e9	0.881248	0.440624	+	0.897692i	$0.354757\pi$
$632$	4.88656e8	0.0770005
$633$	0	0
$634$	3.12969e8	0.0487741
$635$	2.36760e9	0.366944
$636$	0	0
$637$	1.08753e10	1.66707
$638$	−3.31642e7	−0.00505588
$639$	0	0
$640$	−7.98218e8	−0.120363
$641$	8.98365e8	0.134726	0.0673628	−	0.997729i	$-0.478542\pi$
$641$	8.98365e8	0.134726	0.0673628	+	0.997729i	$0.478542\pi$
$642$	0	0
$643$	6.66060e9	0.988042	0.494021	−	0.869450i	$-0.335527\pi$
$643$	6.66060e9	0.988042	0.494021	+	0.869450i	$0.335527\pi$
$644$	3.55192e9	0.524038
$645$	0	0
$646$	1.53455e7	0.00223958
$647$	−2.89308e9	−0.419948	−0.209974	−	0.977707i	$-0.567338\pi$
$647$	−2.89308e9	−0.419948	−0.209974	+	0.977707i	$0.567338\pi$
$648$	0	0
$649$	−2.63199e8	−0.0377944
$650$	−1.51480e8	−0.0216350
$651$	0	0
$652$	−4.81074e9	−0.679743
$653$	−5.97319e9	−0.839480	−0.419740	−	0.907644i	$-0.637879\pi$
$653$	−5.97319e9	−0.839480	−0.419740	+	0.907644i	$0.637879\pi$
$654$	0	0
$655$	5.07769e9	0.706028
$656$	7.45172e8	0.103061
$657$	0	0
$658$	2.86320e7	0.00391796
$659$	−8.14255e9	−1.10831	−0.554155	−	0.832414i	$-0.686959\pi$
$659$	−8.14255e9	−1.10831	−0.554155	+	0.832414i	$0.686959\pi$
$660$	0	0
$661$	3.91035e9	0.526635	0.263318	−	0.964709i	$-0.415183\pi$
$661$	3.91035e9	0.526635	0.263318	+	0.964709i	$0.415183\pi$
$662$	−1.23186e8	−0.0165028
$663$	0	0
$664$	−1.00551e9	−0.133290
$665$	1.22595e8	0.0161658
$666$	0	0
$667$	5.76193e9	0.751844
$668$	1.18329e10	1.53594
$669$	0	0
$670$	−2.96956e8	−0.0381444
$671$	3.53685e9	0.451947
$672$	0	0
$673$	−8.56370e9	−1.08295	−0.541475	−	0.840717i	$-0.682134\pi$
$673$	−8.56370e9	−1.08295	−0.541475	+	0.840717i	$0.682134\pi$
$674$	5.36505e8	0.0674939
$675$	0	0
$676$	−2.01755e10	−2.51195
$677$	1.32503e10	1.64122	0.820608	−	0.571492i	$-0.193635\pi$
$677$	1.32503e10	1.64122	0.820608	+	0.571492i	$0.193635\pi$
$678$	0	0
$679$	−2.88928e9	−0.354198
$680$	−5.16981e8	−0.0630512
$681$	0	0
$682$	−5.46643e7	−0.00659870
$683$	−1.52557e10	−1.83214	−0.916070	−	0.401018i	$-0.868656\pi$
$683$	−1.52557e10	−1.83214	−0.916070	+	0.401018i	$0.868656\pi$
$684$	0	0
$685$	4.07997e8	0.0484998
$686$	1.94159e8	0.0229627
$687$	0	0
$688$	−1.03986e10	−1.21735
$689$	−1.60151e10	−1.86536
$690$	0	0
$691$	2.37047e9	0.273314	0.136657	−	0.990618i	$-0.456364\pi$
$691$	2.37047e9	0.273314	0.136657	+	0.990618i	$0.456364\pi$
$692$	−1.40100e10	−1.60719
$693$	0	0
$694$	4.68936e8	0.0532544
$695$	5.61716e9	0.634702
$696$	0	0
$697$	9.66540e8	0.108120
$698$	−9.27960e7	−0.0103285
$699$	0	0
$700$	9.53766e8	0.105099
$701$	8.71012e9	0.955017	0.477508	−	0.878627i	$-0.341540\pi$
$701$	8.71012e9	0.955017	0.477508	+	0.878627i	$0.341540\pi$
$702$	0	0
$703$	6.65641e7	0.00722598
$704$	2.66609e9	0.287985
$705$	0	0
$706$	4.15914e8	0.0444823
$707$	2.94320e9	0.313221
$708$	0	0
$709$	−8.22562e9	−0.866775	−0.433388	−	0.901208i	$-0.642682\pi$
$709$	−8.22562e9	−0.866775	−0.433388	+	0.901208i	$0.642682\pi$
$710$	−3.83623e8	−0.0402254
$711$	0	0
$712$	7.35071e8	0.0763219
$713$	9.49736e9	0.981272
$714$	0	0
$715$	−4.39955e9	−0.450130
$716$	5.56930e9	0.567029
$717$	0	0
$718$	−2.20710e7	−0.00222529
$719$	5.78538e9	0.580471	0.290236	−	0.956955i	$-0.406266\pi$
$719$	5.78538e9	0.580471	0.290236	+	0.956955i	$0.406266\pi$
$720$	0	0
$721$	−3.53911e9	−0.351658
$722$	3.67924e8	0.0363813
$723$	0	0
$724$	1.65873e10	1.62440
$725$	1.54720e9	0.150787
$726$	0	0
$727$	−1.00474e10	−0.969798	−0.484899	−	0.874570i	$-0.661144\pi$
$727$	−1.00474e10	−0.969798	−0.484899	+	0.874570i	$0.661144\pi$
$728$	−4.74176e8	−0.0455491
$729$	0	0
$730$	−5.59874e8	−0.0532672
$731$	−1.34877e10	−1.27711
$732$	0	0
$733$	7.89455e9	0.740395	0.370198	−	0.928953i	$-0.379290\pi$
$733$	7.89455e9	0.740395	0.370198	+	0.928953i	$0.379290\pi$
$734$	−5.45800e7	−0.00509445
$735$	0	0
$736$	1.86364e9	0.172301
$737$	3.98603e9	0.366779
$738$	0	0
$739$	8.45416e9	0.770575	0.385288	−	0.922797i	$-0.374102\pi$
$739$	8.45416e9	0.770575	0.385288	+	0.922797i	$0.374102\pi$
$740$	−1.12051e9	−0.101649
$741$	0	0
$742$	−1.34571e8	−0.0120931
$743$	−5.05511e9	−0.452137	−0.226068	−	0.974111i	$-0.572587\pi$
$743$	−5.05511e9	−0.452137	−0.226068	+	0.974111i	$0.572587\pi$
$744$	0	0
$745$	1.77559e10	1.57324
$746$	−4.82097e7	−0.00425156
$747$	0	0
$748$	3.46739e9	0.302933
$749$	7.03997e9	0.612187
$750$	0	0
$751$	−1.42778e10	−1.23005	−0.615023	−	0.788509i	$-0.710853\pi$
$751$	−1.42778e10	−1.23005	−0.615023	+	0.788509i	$0.710853\pi$
$752$	−3.74392e9	−0.321043
$753$	0	0
$754$	−3.84348e8	−0.0326532
$755$	−9.90116e9	−0.837282
$756$	0	0
$757$	1.01019e10	0.846388	0.423194	−	0.906039i	$-0.360909\pi$
$757$	1.01019e10	0.846388	0.423194	+	0.906039i	$0.360909\pi$
$758$	−6.36864e8	−0.0531135
$759$	0	0
$760$	4.28731e7	0.00354272
$761$	3.03041e9	0.249261	0.124631	−	0.992203i	$-0.460225\pi$
$761$	3.03041e9	0.249261	0.124631	+	0.992203i	$0.460225\pi$
$762$	0	0
$763$	5.57067e9	0.454016
$764$	3.92859e9	0.318720
$765$	0	0
$766$	−4.58464e8	−0.0368557
$767$	−3.05028e9	−0.244093
$768$	0	0
$769$	−1.80433e10	−1.43078	−0.715392	−	0.698723i	$-0.753752\pi$
$769$	−1.80433e10	−1.43078	−0.715392	+	0.698723i	$0.753752\pi$
$770$	−3.69684e7	−0.00291819
$771$	0	0
$772$	−1.59081e10	−1.24440
$773$	1.03732e10	0.807766	0.403883	−	0.914811i	$-0.367660\pi$
$773$	1.03732e10	0.807766	0.403883	+	0.914811i	$0.367660\pi$
$774$	0	0
$775$	2.55024e9	0.196800
$776$	−1.01042e9	−0.0776220
$777$	0	0
$778$	1.45439e8	0.0110726
$779$	−8.01549e7	−0.00607503
$780$	0	0
$781$	5.14936e9	0.386789
$782$	8.03963e8	0.0601191
$783$	0	0
$784$	−1.19492e10	−0.885590
$785$	−1.27416e10	−0.940113
$786$	0	0
$787$	−1.10014e10	−0.804518	−0.402259	−	0.915526i	$-0.631775\pi$
$787$	−1.10014e10	−0.804518	−0.402259	+	0.915526i	$0.631775\pi$
$788$	−6.94950e9	−0.505955
$789$	0	0
$790$	4.41520e8	0.0318607
$791$	5.11871e9	0.367742
$792$	0	0
$793$	4.09894e10	2.91887
$794$	−5.09067e8	−0.0360913
$795$	0	0
$796$	−1.80080e10	−1.26552
$797$	−1.83467e10	−1.28367	−0.641834	−	0.766843i	$-0.721826\pi$
$797$	−1.83467e10	−1.28367	−0.641834	+	0.766843i	$0.721826\pi$
$798$	0	0
$799$	−4.85612e9	−0.336803
$800$	5.00426e8	0.0345561
$801$	0	0
$802$	−8.07085e8	−0.0552470
$803$	7.51515e9	0.512193
$804$	0	0
$805$	6.42288e9	0.433954
$806$	−6.33518e8	−0.0426174
$807$	0	0
$808$	1.02927e9	0.0686420
$809$	−1.83197e10	−1.21646	−0.608231	−	0.793760i	$-0.708121\pi$
$809$	−1.83197e10	−1.21646	−0.608231	+	0.793760i	$0.708121\pi$
$810$	0	0
$811$	−8.15379e9	−0.536768	−0.268384	−	0.963312i	$-0.586490\pi$
$811$	−8.15379e9	−0.536768	−0.268384	+	0.963312i	$0.586490\pi$
$812$	2.41998e9	0.158623
$813$	0	0
$814$	−2.00723e7	−0.00130440
$815$	−8.69918e9	−0.562894
$816$	0	0
$817$	1.11853e9	0.0717583
$818$	3.33195e8	0.0212844
$819$	0	0
$820$	1.34929e9	0.0854586
$821$	1.71557e10	1.08195	0.540977	−	0.841038i	$-0.318055\pi$
$821$	1.71557e10	1.08195	0.540977	+	0.841038i	$0.318055\pi$
$822$	0	0
$823$	3.13687e10	1.96154	0.980771	−	0.195160i	$-0.0625227\pi$
$823$	3.13687e10	1.96154	0.980771	+	0.195160i	$0.0625227\pi$
$824$	−1.23767e9	−0.0770653
$825$	0	0
$826$	−2.56308e7	−0.00158246
$827$	3.08831e10	1.89868	0.949338	−	0.314256i	$-0.101755\pi$
$827$	3.08831e10	1.89868	0.949338	+	0.314256i	$0.101755\pi$
$828$	0	0
$829$	2.08621e10	1.27180	0.635899	−	0.771773i	$-0.280630\pi$
$829$	2.08621e10	1.27180	0.635899	+	0.771773i	$0.280630\pi$
$830$	−9.08519e8	−0.0551519
$831$	0	0
$832$	3.08980e10	1.85994
$833$	−1.54989e10	−0.929062
$834$	0	0
$835$	2.13973e10	1.27191
$836$	−2.87550e8	−0.0170212
$837$	0	0
$838$	−5.67784e8	−0.0333295
$839$	−3.33343e10	−1.94861	−0.974303	−	0.225241i	$-0.927683\pi$
$839$	−3.33343e10	−1.94861	−0.974303	+	0.225241i	$0.927683\pi$
$840$	0	0
$841$	−1.33242e10	−0.772421
$842$	3.51615e8	0.0202990
$843$	0	0
$844$	−2.65094e10	−1.51776
$845$	−3.64831e10	−2.08014
$846$	0	0
$847$	−5.39183e9	−0.304891
$848$	1.75966e10	0.990930
$849$	0	0
$850$	2.15881e8	0.0120573
$851$	3.48735e9	0.193973
$852$	0	0
$853$	−5.30610e9	−0.292721	−0.146360	−	0.989231i	$-0.546756\pi$
$853$	−5.30610e9	−0.292721	−0.146360	+	0.989231i	$0.546756\pi$
$854$	3.44424e8	0.0189231
$855$	0	0
$856$	2.46196e9	0.134160
$857$	3.22916e9	0.175250	0.0876248	−	0.996154i	$-0.472072\pi$
$857$	3.22916e9	0.175250	0.0876248	+	0.996154i	$0.472072\pi$
$858$	0	0
$859$	−1.09723e10	−0.590637	−0.295318	−	0.955399i	$-0.595426\pi$
$859$	−1.09723e10	−0.590637	−0.295318	+	0.955399i	$0.595426\pi$
$860$	−1.88288e10	−1.00944
$861$	0	0
$862$	1.55620e8	0.00827540
$863$	−1.83908e10	−0.974009	−0.487005	−	0.873399i	$-0.661910\pi$
$863$	−1.83908e10	−0.974009	−0.487005	+	0.873399i	$0.661910\pi$
$864$	0	0
$865$	−2.53340e10	−1.33091
$866$	−4.71159e8	−0.0246522
$867$	0	0
$868$	3.98884e9	0.207027
$869$	−5.92650e9	−0.306358
$870$	0	0
$871$	4.61951e10	2.36882
$872$	1.94813e9	0.0994970
$873$	0	0
$874$	−6.66724e7	−0.00337797
$875$	7.18113e9	0.362380
$876$	0	0
$877$	2.93823e10	1.47091	0.735456	−	0.677572i	$-0.236968\pi$
$877$	2.93823e10	1.47091	0.735456	+	0.677572i	$0.236968\pi$
$878$	−4.75068e8	−0.0236878
$879$	0	0
$880$	4.83399e9	0.239120
$881$	−7.96639e9	−0.392506	−0.196253	−	0.980553i	$-0.562877\pi$
$881$	−7.96639e9	−0.392506	−0.196253	+	0.980553i	$0.562877\pi$
$882$	0	0
$883$	−2.11047e10	−1.03161	−0.515806	−	0.856706i	$-0.672507\pi$
$883$	−2.11047e10	−1.03161	−0.515806	+	0.856706i	$0.672507\pi$
$884$	4.01844e10	1.95648
$885$	0	0
$886$	2.06374e8	0.00996868
$887$	3.91929e10	1.88571	0.942854	−	0.333206i	$-0.108130\pi$
$887$	3.91929e10	1.88571	0.942854	+	0.333206i	$0.108130\pi$
$888$	0	0
$889$	−3.09480e9	−0.147733
$890$	6.64165e8	0.0315799
$891$	0	0
$892$	3.28961e10	1.55191
$893$	4.02717e8	0.0189243
$894$	0	0
$895$	1.00709e10	0.469555
$896$	1.04339e9	0.0484584
$897$	0	0
$898$	7.04325e8	0.0324568
$899$	6.47071e9	0.297025
$900$	0	0
$901$	2.28240e10	1.03957
$902$	2.41706e7	0.00109664
$903$	0	0
$904$	1.79007e9	0.0805901
$905$	2.99946e10	1.34516
$906$	0	0
$907$	7.45412e9	0.331719	0.165860	−	0.986149i	$-0.446960\pi$
$907$	7.45412e9	0.331719	0.165860	+	0.986149i	$0.446960\pi$
$908$	−1.63705e10	−0.725707
$909$	0	0
$910$	−4.28436e8	−0.0188470
$911$	−3.46618e9	−0.151893	−0.0759463	−	0.997112i	$-0.524198\pi$
$911$	−3.46618e9	−0.151893	−0.0759463	+	0.997112i	$0.524198\pi$
$912$	0	0
$913$	1.21950e10	0.530315
$914$	2.51989e8	0.0109162
$915$	0	0
$916$	−1.16440e10	−0.500572
$917$	−6.63730e9	−0.284249
$918$	0	0
$919$	−1.94364e9	−0.0826060	−0.0413030	−	0.999147i	$-0.513151\pi$
$919$	−1.94364e9	−0.0826060	−0.0413030	+	0.999147i	$0.513151\pi$
$920$	2.24616e9	0.0951005
$921$	0	0
$922$	8.63700e8	0.0362915
$923$	5.96772e10	2.49806
$924$	0	0
$925$	9.36428e8	0.0389026
$926$	1.59949e8	0.00661979
$927$	0	0
$928$	1.26973e9	0.0521546
$929$	−3.65536e10	−1.49581	−0.747904	−	0.663807i	$-0.768939\pi$
$929$	−3.65536e10	−1.49581	−0.747904	+	0.663807i	$0.768939\pi$
$930$	0	0
$931$	1.28532e9	0.0522022
$932$	−8.03696e9	−0.325189
$933$	0	0
$934$	1.01978e8	0.00409536
$935$	6.27002e9	0.250858
$936$	0	0
$937$	−2.70613e10	−1.07463	−0.537317	−	0.843380i	$-0.680562\pi$
$937$	−2.70613e10	−1.07463	−0.537317	+	0.843380i	$0.680562\pi$
$938$	3.88167e8	0.0153571
$939$	0	0
$940$	−6.77912e9	−0.266211
$941$	3.52735e10	1.38002	0.690010	−	0.723800i	$-0.257606\pi$
$941$	3.52735e10	1.38002	0.690010	+	0.723800i	$0.257606\pi$
$942$	0	0
$943$	−4.19938e9	−0.163078
$944$	3.35148e9	0.129669
$945$	0	0
$946$	−3.37292e8	−0.0129535
$947$	1.60900e10	0.615648	0.307824	−	0.951443i	$-0.400399\pi$
$947$	1.60900e10	0.615648	0.307824	+	0.951443i	$0.400399\pi$
$948$	0	0
$949$	8.70950e10	3.30797
$950$	−1.79030e7	−0.000677474 0
$951$	0	0
$952$	6.75771e8	0.0253846
$953$	−2.34617e10	−0.878081	−0.439040	−	0.898467i	$-0.644681\pi$
$953$	−2.34617e10	−0.878081	−0.439040	+	0.898467i	$0.644681\pi$
$954$	0	0
$955$	7.10400e9	0.263932
$956$	−2.70452e10	−1.00112
$957$	0	0
$958$	−1.36035e9	−0.0499888
$959$	−5.33313e8	−0.0195262
$960$	0	0
$961$	−1.68470e10	−0.612337
$962$	−2.32623e8	−0.00842441
$963$	0	0
$964$	−1.80520e9	−0.0649016
$965$	−2.87664e10	−1.03048
$966$	0	0
$967$	2.75570e10	0.980029	0.490014	−	0.871714i	$-0.336992\pi$
$967$	2.75570e10	0.980029	0.490014	+	0.871714i	$0.336992\pi$
$968$	−1.88559e9	−0.0668163
$969$	0	0
$970$	−9.12951e8	−0.0321179
$971$	3.36601e10	1.17991	0.589954	−	0.807437i	$-0.299146\pi$
$971$	3.36601e10	1.17991	0.589954	+	0.807437i	$0.299146\pi$
$972$	0	0
$973$	−7.34247e9	−0.255533
$974$	−6.79111e8	−0.0235496
$975$	0	0
$976$	−4.50370e10	−1.55058
$977$	3.08878e9	0.105963	0.0529817	−	0.998595i	$-0.483128\pi$
$977$	3.08878e9	0.105963	0.0529817	+	0.998595i	$0.483128\pi$
$978$	0	0
$979$	−8.91505e9	−0.303658
$980$	−2.16365e10	−0.734337
$981$	0	0
$982$	1.17779e9	0.0396896
$983$	4.00750e10	1.34566	0.672832	−	0.739796i	$-0.265078\pi$
$983$	4.00750e10	1.34566	0.672832	+	0.739796i	$0.265078\pi$
$984$	0	0
$985$	−1.25667e10	−0.418980
$986$	5.47754e8	0.0181977
$987$	0	0
$988$	−3.33248e9	−0.109931
$989$	5.86010e10	1.92627
$990$	0	0
$991$	−3.18674e9	−0.104013	−0.0520066	−	0.998647i	$-0.516562\pi$
$991$	−3.18674e9	−0.104013	−0.0520066	+	0.998647i	$0.516562\pi$
$992$	2.09288e9	0.0680697
$993$	0	0
$994$	5.01453e8	0.0161949
$995$	−3.25636e10	−1.04798
$996$	0	0
$997$	−4.16475e8	−0.0133093	−0.00665465	−	0.999978i	$-0.502118\pi$
$997$	−4.16475e8	−0.0133093	−0.00665465	+	0.999978i	$0.502118\pi$
$998$	−1.54231e9	−0.0491150
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.8		17
3.2	odd	2		177.8.a.b.1.10	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.10	✓	17	3.2	odd	2
531.8.a.d.1.8		17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q-0.413031 q^{2} -127.829 q^{4} -231.152 q^{5} +302.150 q^{7} +105.665 q^{8} +O(q^{10})\)	\(q-0.413031 q^{2} -127.829 q^{4} -231.152 q^{5} +302.150 q^{7} +105.665 q^{8} +95.4729 q^{10} -1281.53 q^{11} -14851.9 q^{13} -124.797 q^{14} +16318.5 q^{16} +21166.2 q^{17} -1755.31 q^{19} +29548.0 q^{20} +529.311 q^{22} -91962.2 q^{23} -24693.8 q^{25} +6134.31 q^{26} -38623.7 q^{28} -62655.4 q^{29} -103275. q^{31} -20265.2 q^{32} -8742.32 q^{34} -69842.6 q^{35} -37921.6 q^{37} +724.998 q^{38} -24424.8 q^{40} +45664.2 q^{41} -637229. q^{43} +163817. q^{44} +37983.3 q^{46} -229428. q^{47} -732248. q^{49} +10199.3 q^{50} +1.89852e6 q^{52} +1.07832e6 q^{53} +296227. q^{55} +31926.8 q^{56} +25878.6 q^{58} +205379. q^{59} -2.75987e6 q^{61} +42655.6 q^{62} -2.08040e6 q^{64} +3.43305e6 q^{65} -3.11037e6 q^{67} -2.70567e6 q^{68} +28847.1 q^{70} -4.01814e6 q^{71} -5.86422e6 q^{73} +15662.8 q^{74} +224380. q^{76} -387214. q^{77} +4.62456e6 q^{79} -3.77206e6 q^{80} -18860.7 q^{82} -9.51599e6 q^{83} -4.89262e6 q^{85} +263195. q^{86} -135413. q^{88} +6.95658e6 q^{89} -4.48752e6 q^{91} +1.17555e7 q^{92} +94760.7 q^{94} +405743. q^{95} -9.56241e6 q^{97} +302441. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8} - 6391 q^{10} + 8888 q^{11} - 12702 q^{13} + 17555 q^{14} + 139226 q^{16} + 36167 q^{17} - 71037 q^{19} + 274883 q^{20} - 325182 q^{22} + 269995 q^{23} + 97329 q^{25} + 336906 q^{26} - 901362 q^{28} + 543825 q^{29} - 633109 q^{31} + 837062 q^{32} - 529288 q^{34} + 287621 q^{35} - 867607 q^{37} + 1727169 q^{38} - 815662 q^{40} + 1428939 q^{41} - 477060 q^{43} + 1667926 q^{44} + 5305549 q^{46} + 1217849 q^{47} + 4350738 q^{49} - 4561369 q^{50} + 4175994 q^{52} + 3487068 q^{53} - 960484 q^{55} + 5363196 q^{56} - 3082906 q^{58} + 3491443 q^{59} + 998917 q^{61} + 5742614 q^{62} + 17531621 q^{64} + 6075816 q^{65} - 356026 q^{67} + 16149231 q^{68} - 548798 q^{70} + 12879428 q^{71} - 6176157 q^{73} + 5971906 q^{74} - 17624580 q^{76} - 239687 q^{77} - 18886490 q^{79} + 70463349 q^{80} - 19351611 q^{82} + 22824893 q^{83} - 7973079 q^{85} + 27502196 q^{86} - 62527651 q^{88} + 30609647 q^{89} - 36301521 q^{91} + 41388548 q^{92} + 1010176 q^{94} + 29303629 q^{95} - 26249806 q^{97} + 93110852 q^{98}+O(q^{100}) \) 17 * q + 32 * q^2 + 1166 * q^4 + 1072 * q^5 - 2407 * q^7 + 6645 * q^8 - 6391 * q^10 + 8888 * q^11 - 12702 * q^13 + 17555 * q^14 + 139226 * q^16 + 36167 * q^17 - 71037 * q^19 + 274883 * q^20 - 325182 * q^22 + 269995 * q^23 + 97329 * q^25 + 336906 * q^26 - 901362 * q^28 + 543825 * q^29 - 633109 * q^31 + 837062 * q^32 - 529288 * q^34 + 287621 * q^35 - 867607 * q^37 + 1727169 * q^38 - 815662 * q^40 + 1428939 * q^41 - 477060 * q^43 + 1667926 * q^44 + 5305549 * q^46 + 1217849 * q^47 + 4350738 * q^49 - 4561369 * q^50 + 4175994 * q^52 + 3487068 * q^53 - 960484 * q^55 + 5363196 * q^56 - 3082906 * q^58 + 3491443 * q^59 + 998917 * q^61 + 5742614 * q^62 + 17531621 * q^64 + 6075816 * q^65 - 356026 * q^67 + 16149231 * q^68 - 548798 * q^70 + 12879428 * q^71 - 6176157 * q^73 + 5971906 * q^74 - 17624580 * q^76 - 239687 * q^77 - 18886490 * q^79 + 70463349 * q^80 - 19351611 * q^82 + 22824893 * q^83 - 7973079 * q^85 + 27502196 * q^86 - 62527651 * q^88 + 30609647 * q^89 - 36301521 * q^91 + 41388548 * q^92 + 1010176 * q^94 + 29303629 * q^95 - 26249806 * q^97 + 93110852 * q^98

Introduction

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