LMFDB - Embedded newform 531.8.a.d.1.1

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			1.1
Root			$24.0278$ 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)

$f(q)$	$=$	$q-22.0278 q^{2} +357.226 q^{4} +492.460 q^{5} -1209.81 q^{7} -5049.35 q^{8} +O(q^{10})$	\(q-22.0278 q^{2} +357.226 q^{4} +492.460 q^{5} -1209.81 q^{7} -5049.35 q^{8} -10847.8 q^{10} +7759.91 q^{11} +1927.14 q^{13} +26649.5 q^{14} +65501.4 q^{16} +21871.8 q^{17} -31682.0 q^{19} +175919. q^{20} -170934. q^{22} -76017.8 q^{23} +164392. q^{25} -42450.8 q^{26} -432176. q^{28} +107474. q^{29} -56872.6 q^{31} -796537. q^{32} -481789. q^{34} -595783. q^{35} -72532.0 q^{37} +697885. q^{38} -2.48660e6 q^{40} +598173. q^{41} -127161. q^{43} +2.77204e6 q^{44} +1.67451e6 q^{46} -20753.9 q^{47} +640100. q^{49} -3.62120e6 q^{50} +688425. q^{52} -1.52906e6 q^{53} +3.82145e6 q^{55} +6.10876e6 q^{56} -2.36741e6 q^{58} +205379. q^{59} +2.40366e6 q^{61} +1.25278e6 q^{62} +9.16182e6 q^{64} +949040. q^{65} -606916. q^{67} +7.81319e6 q^{68} +1.31238e7 q^{70} +3.52312e6 q^{71} +1.27495e6 q^{73} +1.59772e6 q^{74} -1.13176e7 q^{76} -9.38803e6 q^{77} +3.89830e6 q^{79} +3.22568e7 q^{80} -1.31765e7 q^{82} +4.03800e6 q^{83} +1.07710e7 q^{85} +2.80108e6 q^{86} -3.91825e7 q^{88} -5.97046e6 q^{89} -2.33148e6 q^{91} -2.71555e7 q^{92} +457163. q^{94} -1.56021e7 q^{95} -1.98127e6 q^{97} -1.41000e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−22.0278	−1.94700	−0.973502	−	0.228677i	$-0.926560\pi$
$2$	−22.0278	−1.94700	−0.973502	+	0.228677i	$0.926560\pi$
$3$	0	0
$3$	0	0
$4$	357.226	2.79083
$5$	492.460	1.76188	0.880939	−	0.473230i	$-0.156912\pi$
$5$	492.460	1.76188	0.880939	+	0.473230i	$0.156912\pi$
$6$	0	0
$7$	−1209.81	−1.33314	−0.666568	−	0.745444i	$-0.732237\pi$
$7$	−1209.81	−1.33314	−0.666568	+	0.745444i	$0.732237\pi$
$8$	−5049.35	−3.48675
$9$	0	0
$10$	−10847.8	−3.43038
$11$	7759.91	1.75785	0.878926	−	0.476958i	$-0.158261\pi$
$11$	7759.91	1.75785	0.878926	+	0.476958i	$0.158261\pi$
$12$	0	0
$13$	1927.14	0.243283	0.121642	−	0.992574i	$-0.461184\pi$
$13$	1927.14	0.243283	0.121642	+	0.992574i	$0.461184\pi$
$14$	26649.5	2.59562
$15$	0	0
$16$	65501.4	3.99789
$17$	21871.8	1.07973	0.539864	−	0.841752i	$-0.318476\pi$
$17$	21871.8	1.07973	0.539864	+	0.841752i	$0.318476\pi$
$18$	0	0
$19$	−31682.0	−1.05968	−0.529839	−	0.848098i	$-0.677748\pi$
$19$	−31682.0	−1.05968	−0.529839	+	0.848098i	$0.677748\pi$
$20$	175919.	4.91710
$21$	0	0
$22$	−170934.	−3.42255
$23$	−76017.8	−1.30277	−0.651385	−	0.758747i	$-0.725812\pi$
$23$	−76017.8	−1.30277	−0.651385	+	0.758747i	$0.725812\pi$
$24$	0	0
$25$	164392.	2.10421
$26$	−42450.8	−0.473673
$27$	0	0
$28$	−432176.	−3.72055
$29$	107474.	0.818293	0.409146	−	0.912469i	$-0.365827\pi$
$29$	107474.	0.818293	0.409146	+	0.912469i	$0.365827\pi$
$30$	0	0
$31$	−56872.6	−0.342876	−0.171438	−	0.985195i	$-0.554841\pi$
$31$	−56872.6	−0.342876	−0.171438	+	0.985195i	$0.554841\pi$
$32$	−796537.	−4.29715
$33$	0	0
$34$	−481789.	−2.10223
$35$	−595783.	−2.34882
$36$	0	0
$37$	−72532.0	−0.235409	−0.117705	−	0.993049i	$-0.537554\pi$
$37$	−72532.0	−0.235409	−0.117705	+	0.993049i	$0.537554\pi$
$38$	697885.	2.06320
$39$	0	0
$40$	−2.48660e6	−6.14322
$41$	598173.	1.35545	0.677725	−	0.735316i	$-0.262966\pi$
$41$	598173.	1.35545	0.677725	+	0.735316i	$0.262966\pi$
$42$	0	0
$43$	−127161.	−0.243902	−0.121951	−	0.992536i	$-0.538915\pi$
$43$	−127161.	−0.243902	−0.121951	+	0.992536i	$0.538915\pi$
$44$	2.77204e6	4.90586
$45$	0	0
$46$	1.67451e6	2.53650
$47$	−20753.9	−0.0291579	−0.0145790	−	0.999894i	$-0.504641\pi$
$47$	−20753.9	−0.0291579	−0.0145790	+	0.999894i	$0.504641\pi$
$48$	0	0
$49$	640100.	0.777252
$50$	−3.62120e6	−4.09691
$51$	0	0
$52$	688425.	0.678961
$53$	−1.52906e6	−1.41078	−0.705389	−	0.708821i	$-0.749228\pi$
$53$	−1.52906e6	−1.41078	−0.705389	+	0.708821i	$0.749228\pi$
$54$	0	0
$55$	3.82145e6	3.09712
$56$	6.10876e6	4.64831
$57$	0	0
$58$	−2.36741e6	−1.59322
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	2.40366e6	1.35587	0.677935	−	0.735122i	$-0.262875\pi$
$61$	2.40366e6	1.35587	0.677935	+	0.735122i	$0.262875\pi$
$62$	1.25278e6	0.667582
$63$	0	0
$64$	9.16182e6	4.36869
$65$	949040.	0.428635
$66$	0	0
$67$	−606916.	−0.246528	−0.123264	−	0.992374i	$-0.539336\pi$
$67$	−606916.	−0.246528	−0.123264	+	0.992374i	$0.539336\pi$
$68$	7.81319e6	3.01333
$69$	0	0
$70$	1.31238e7	4.57317
$71$	3.52312e6	1.16822	0.584108	−	0.811676i	$-0.301444\pi$
$71$	3.52312e6	1.16822	0.584108	+	0.811676i	$0.301444\pi$
$72$	0	0
$73$	1.27495e6	0.383585	0.191793	−	0.981435i	$-0.438570\pi$
$73$	1.27495e6	0.383585	0.191793	+	0.981435i	$0.438570\pi$
$74$	1.59772e6	0.458343
$75$	0	0
$76$	−1.13176e7	−2.95738
$77$	−9.38803e6	−2.34346
$78$	0	0
$79$	3.89830e6	0.889571	0.444786	−	0.895637i	$-0.353280\pi$
$79$	3.89830e6	0.889571	0.444786	+	0.895637i	$0.353280\pi$
$80$	3.22568e7	7.04379
$81$	0	0
$82$	−1.31765e7	−2.63907
$83$	4.03800e6	0.775164	0.387582	−	0.921835i	$-0.373310\pi$
$83$	4.03800e6	0.775164	0.387582	+	0.921835i	$0.373310\pi$
$84$	0	0
$85$	1.07710e7	1.90235
$86$	2.80108e6	0.474877
$87$	0	0
$88$	−3.91825e7	−6.12919
$89$	−5.97046e6	−0.897724	−0.448862	−	0.893601i	$-0.648170\pi$
$89$	−5.97046e6	−0.897724	−0.448862	+	0.893601i	$0.648170\pi$
$90$	0	0
$91$	−2.33148e6	−0.324330
$92$	−2.71555e7	−3.63581
$93$	0	0
$94$	457163.	0.0567706
$95$	−1.56021e7	−1.86703
$96$	0	0
$97$	−1.98127e6	−0.220415	−0.110208	−	0.993909i	$-0.535152\pi$
$97$	−1.98127e6	−0.220415	−0.110208	+	0.993909i	$0.535152\pi$
$98$	−1.41000e7	−1.51331
$99$	0	0
$100$	5.87250e7	5.87250
$101$	1.54871e7	1.49570	0.747851	−	0.663867i	$-0.231086\pi$
$101$	1.54871e7	1.49570	0.747851	+	0.663867i	$0.231086\pi$
$102$	0	0
$103$	−1.20275e7	−1.08454	−0.542269	−	0.840205i	$-0.682435\pi$
$103$	−1.20275e7	−1.08454	−0.542269	+	0.840205i	$0.682435\pi$
$104$	−9.73081e6	−0.848267
$105$	0	0
$106$	3.36819e7	2.74679
$107$	7.69022e6	0.606870	0.303435	−	0.952852i	$-0.401866\pi$
$107$	7.69022e6	0.606870	0.303435	+	0.952852i	$0.401866\pi$
$108$	0	0
$109$	−2.11383e6	−0.156342	−0.0781711	−	0.996940i	$-0.524908\pi$
$109$	−2.11383e6	−0.156342	−0.0781711	+	0.996940i	$0.524908\pi$
$110$	−8.41782e7	−6.03011
$111$	0	0
$112$	−7.92443e7	−5.32973
$113$	−2.03050e6	−0.132382	−0.0661909	−	0.997807i	$-0.521085\pi$
$113$	−2.03050e6	−0.132382	−0.0661909	+	0.997807i	$0.521085\pi$
$114$	0	0
$115$	−3.74357e7	−2.29532
$116$	3.83923e7	2.28371
$117$	0	0
$118$	−4.52406e6	−0.253478
$119$	−2.64608e7	−1.43942
$120$	0	0
$121$	4.07291e7	2.09005
$122$	−5.29474e7	−2.63989
$123$	0	0
$124$	−2.03164e7	−0.956908
$125$	4.24829e7	1.94549
$126$	0	0
$127$	1.37874e7	0.597269	0.298635	−	0.954367i	$-0.403469\pi$
$127$	1.37874e7	0.597269	0.298635	+	0.954367i	$0.403469\pi$
$128$	−9.98583e7	−4.20871
$129$	0	0
$130$	−2.09053e7	−0.834555
$131$	845013.	0.0328408	0.0164204	−	0.999865i	$-0.494773\pi$
$131$	845013.	0.0328408	0.0164204	+	0.999865i	$0.494773\pi$
$132$	0	0
$133$	3.83292e7	1.41270
$134$	1.33690e7	0.479992
$135$	0	0
$136$	−1.10439e8	−3.76474
$137$	4.84595e7	1.61012	0.805058	−	0.593196i	$-0.202134\pi$
$137$	4.84595e7	1.61012	0.805058	+	0.593196i	$0.202134\pi$
$138$	0	0
$139$	−2.05210e6	−0.0648106	−0.0324053	−	0.999475i	$-0.510317\pi$
$139$	−2.05210e6	−0.0648106	−0.0324053	+	0.999475i	$0.510317\pi$
$140$	−2.12829e8	−6.55516
$141$	0	0
$142$	−7.76067e7	−2.27452
$143$	1.49545e7	0.427656
$144$	0	0
$145$	5.29264e7	1.44173
$146$	−2.80843e7	−0.746842
$147$	0	0
$148$	−2.59103e7	−0.656987
$149$	2.53433e6	0.0627641	0.0313821	−	0.999507i	$-0.490009\pi$
$149$	2.53433e6	0.0627641	0.0313821	+	0.999507i	$0.490009\pi$
$150$	0	0
$151$	−5.49477e7	−1.29876	−0.649382	−	0.760462i	$-0.724972\pi$
$151$	−5.49477e7	−1.29876	−0.649382	+	0.760462i	$0.724972\pi$
$152$	1.59973e8	3.69483
$153$	0	0
$154$	2.06798e8	4.56272
$155$	−2.80075e7	−0.604106
$156$	0	0
$157$	7.27529e7	1.50038	0.750191	−	0.661221i	$-0.229962\pi$
$157$	7.27529e7	1.50038	0.750191	+	0.661221i	$0.229962\pi$
$158$	−8.58712e7	−1.73200
$159$	0	0
$160$	−3.92263e8	−7.57106
$161$	9.19672e7	1.73677
$162$	0	0
$163$	1.99055e6	0.0360011	0.0180006	−	0.999838i	$-0.494270\pi$
$163$	1.99055e6	0.0360011	0.0180006	+	0.999838i	$0.494270\pi$
$164$	2.13683e8	3.78283
$165$	0	0
$166$	−8.89485e7	−1.50925
$167$	3.49476e7	0.580643	0.290322	−	0.956929i	$-0.406238\pi$
$167$	3.49476e7	0.580643	0.290322	+	0.956929i	$0.406238\pi$
$168$	0	0
$169$	−5.90346e7	−0.940813
$170$	−2.37262e8	−3.70388
$171$	0	0
$172$	−4.54252e7	−0.680687
$173$	2.91994e7	0.428759	0.214380	−	0.976750i	$-0.431227\pi$
$173$	2.91994e7	0.428759	0.214380	+	0.976750i	$0.431227\pi$
$174$	0	0
$175$	−1.98883e8	−2.80520
$176$	5.08285e8	7.02769
$177$	0	0
$178$	1.31516e8	1.74787
$179$	−1.31626e8	−1.71536	−0.857680	−	0.514184i	$-0.828095\pi$
$179$	−1.31626e8	−1.71536	−0.857680	+	0.514184i	$0.828095\pi$
$180$	0	0
$181$	−1.51957e8	−1.90479	−0.952393	−	0.304872i	$-0.901386\pi$
$181$	−1.51957e8	−1.90479	−0.952393	+	0.304872i	$0.901386\pi$
$182$	5.13574e7	0.631471
$183$	0	0
$184$	3.83840e8	4.54243
$185$	−3.57191e7	−0.414763
$186$	0	0
$187$	1.69724e8	1.89800
$188$	−7.41382e6	−0.0813747
$189$	0	0
$190$	3.43680e8	3.63511
$191$	1.21713e8	1.26392	0.631962	−	0.775000i	$-0.282250\pi$
$191$	1.21713e8	1.26392	0.631962	+	0.775000i	$0.282250\pi$
$192$	0	0
$193$	1.32612e8	1.32780	0.663900	−	0.747821i	$-0.268900\pi$
$193$	1.32612e8	1.32780	0.663900	+	0.747821i	$0.268900\pi$
$194$	4.36430e7	0.429149
$195$	0	0
$196$	2.28660e8	2.16917
$197$	−1.11991e8	−1.04364	−0.521819	−	0.853056i	$-0.674746\pi$
$197$	−1.11991e8	−1.04364	−0.521819	+	0.853056i	$0.674746\pi$
$198$	0	0
$199$	−1.81688e8	−1.63433	−0.817165	−	0.576403i	$-0.804456\pi$
$199$	−1.81688e8	−1.63433	−0.817165	+	0.576403i	$0.804456\pi$
$200$	−8.30071e8	−7.33686
$201$	0	0
$202$	−3.41147e8	−2.91214
$203$	−1.30023e8	−1.09090
$204$	0	0
$205$	2.94576e8	2.38814
$206$	2.64940e8	2.11160
$207$	0	0
$208$	1.26230e8	0.972618
$209$	−2.45849e8	−1.86276
$210$	0	0
$211$	−3.34639e6	−0.0245238	−0.0122619	−	0.999925i	$-0.503903\pi$
$211$	−3.34639e6	−0.0245238	−0.0122619	+	0.999925i	$0.503903\pi$
$212$	−5.46219e8	−3.93724
$213$	0	0
$214$	−1.69399e8	−1.18158
$215$	−6.26217e7	−0.429725
$216$	0	0
$217$	6.88051e7	0.457101
$218$	4.65630e7	0.304399
$219$	0	0
$220$	1.36512e9	8.64353
$221$	4.21501e7	0.262679
$222$	0	0
$223$	3.23603e7	0.195410	0.0977048	−	0.995215i	$-0.468850\pi$
$223$	3.23603e7	0.195410	0.0977048	+	0.995215i	$0.468850\pi$
$224$	9.63659e8	5.72869
$225$	0	0
$226$	4.47275e7	0.257748
$227$	−1.60575e8	−0.911145	−0.455573	−	0.890199i	$-0.650565\pi$
$227$	−1.60575e8	−0.911145	−0.455573	+	0.890199i	$0.650565\pi$
$228$	0	0
$229$	4.34106e7	0.238876	0.119438	−	0.992842i	$-0.461891\pi$
$229$	4.34106e7	0.238876	0.119438	+	0.992842i	$0.461891\pi$
$230$	8.24628e8	4.46900
$231$	0	0
$232$	−5.42672e8	−2.85318
$233$	2.86270e7	0.148262	0.0741310	−	0.997249i	$-0.476382\pi$
$233$	2.86270e7	0.148262	0.0741310	+	0.997249i	$0.476382\pi$
$234$	0	0
$235$	−1.02204e7	−0.0513727
$236$	7.33667e7	0.363335
$237$	0	0
$238$	5.82874e8	2.80256
$239$	6.06584e7	0.287408	0.143704	−	0.989621i	$-0.454099\pi$
$239$	6.06584e7	0.287408	0.143704	+	0.989621i	$0.454099\pi$
$240$	0	0
$241$	5.03046e7	0.231498	0.115749	−	0.993278i	$-0.463073\pi$
$241$	5.03046e7	0.231498	0.115749	+	0.993278i	$0.463073\pi$
$242$	−8.97173e8	−4.06933
$243$	0	0
$244$	8.58648e8	3.78400
$245$	3.15224e8	1.36942
$246$	0	0
$247$	−6.10556e7	−0.257802
$248$	2.87170e8	1.19552
$249$	0	0
$250$	−9.35807e8	−3.78788
$251$	−1.79753e8	−0.717494	−0.358747	−	0.933435i	$-0.616796\pi$
$251$	−1.79753e8	−0.717494	−0.358747	+	0.933435i	$0.616796\pi$
$252$	0	0
$253$	−5.89891e8	−2.29008
$254$	−3.03707e8	−1.16289
$255$	0	0
$256$	1.02695e9	3.82569
$257$	−8.52960e7	−0.313446	−0.156723	−	0.987643i	$-0.550093\pi$
$257$	−8.52960e7	−0.313446	−0.156723	+	0.987643i	$0.550093\pi$
$258$	0	0
$259$	8.77500e7	0.313833
$260$	3.39022e8	1.19625
$261$	0	0
$262$	−1.86138e7	−0.0639412
$263$	−4.14430e8	−1.40477	−0.702386	−	0.711796i	$-0.747882\pi$
$263$	−4.14430e8	−1.40477	−0.702386	+	0.711796i	$0.747882\pi$
$264$	0	0
$265$	−7.53000e8	−2.48562
$266$	−8.44309e8	−2.75053
$267$	0	0
$268$	−2.16806e8	−0.688018
$269$	3.07821e8	0.964196	0.482098	−	0.876117i	$-0.339875\pi$
$269$	3.07821e8	0.964196	0.482098	+	0.876117i	$0.339875\pi$
$270$	0	0
$271$	−2.35783e8	−0.719646	−0.359823	−	0.933021i	$-0.617163\pi$
$271$	−2.35783e8	−0.719646	−0.359823	+	0.933021i	$0.617163\pi$
$272$	1.43264e9	4.31663
$273$	0	0
$274$	−1.06746e9	−3.13490
$275$	1.27567e9	3.69890
$276$	0	0
$277$	−2.15483e8	−0.609165	−0.304582	−	0.952486i	$-0.598517\pi$
$277$	−2.15483e8	−0.609165	−0.304582	+	0.952486i	$0.598517\pi$
$278$	4.52032e7	0.126186
$279$	0	0
$280$	3.00832e9	8.18975
$281$	2.06356e8	0.554810	0.277405	−	0.960753i	$-0.410526\pi$
$281$	2.06356e8	0.554810	0.277405	+	0.960753i	$0.410526\pi$
$282$	0	0
$283$	6.73678e8	1.76685	0.883426	−	0.468571i	$-0.155231\pi$
$283$	6.73678e8	1.76685	0.883426	+	0.468571i	$0.155231\pi$
$284$	1.25855e9	3.26029
$285$	0	0
$286$	−3.29414e8	−0.832648
$287$	−7.23677e8	−1.80700
$288$	0	0
$289$	6.80388e7	0.165811
$290$	−1.16586e9	−2.80706
$291$	0	0
$292$	4.55444e8	1.07052
$293$	2.68265e8	0.623056	0.311528	−	0.950237i	$-0.399159\pi$
$293$	2.68265e8	0.623056	0.311528	+	0.950237i	$0.399159\pi$
$294$	0	0
$295$	1.01141e8	0.229377
$296$	3.66239e8	0.820813
$297$	0	0
$298$	−5.58259e7	−0.122202
$299$	−1.46497e8	−0.316942
$300$	0	0
$301$	1.53841e8	0.325154
$302$	1.21038e9	2.52870
$303$	0	0
$304$	−2.07521e9	−4.23648
$305$	1.18370e9	2.38888
$306$	0	0
$307$	6.59253e8	1.30037	0.650186	−	0.759775i	$-0.274691\pi$
$307$	6.59253e8	1.30037	0.650186	+	0.759775i	$0.274691\pi$
$308$	−3.35365e9	−6.54018
$309$	0	0
$310$	6.16945e8	1.17620
$311$	8.73613e8	1.64686	0.823432	−	0.567415i	$-0.192056\pi$
$311$	8.73613e8	1.64686	0.823432	+	0.567415i	$0.192056\pi$
$312$	0	0
$313$	2.84022e8	0.523537	0.261768	−	0.965131i	$-0.415694\pi$
$313$	2.84022e8	0.523537	0.261768	+	0.965131i	$0.415694\pi$
$314$	−1.60259e9	−2.92125
$315$	0	0
$316$	1.39257e9	2.48264
$317$	2.16935e8	0.382491	0.191246	−	0.981542i	$-0.438747\pi$
$317$	2.16935e8	0.382491	0.191246	+	0.981542i	$0.438747\pi$
$318$	0	0
$319$	8.33986e8	1.43844
$320$	4.51183e9	7.69711
$321$	0	0
$322$	−2.02584e9	−3.38150
$323$	−6.92943e8	−1.14416
$324$	0	0
$325$	3.16806e8	0.511920
$326$	−4.38475e7	−0.0700943
$327$	0	0
$328$	−3.02039e9	−4.72611
$329$	2.51083e7	0.0388715
$330$	0	0
$331$	−9.98498e8	−1.51338	−0.756692	−	0.653772i	$-0.773186\pi$
$331$	−9.98498e8	−1.51338	−0.756692	+	0.653772i	$0.773186\pi$
$332$	1.44248e9	2.16335
$333$	0	0
$334$	−7.69820e8	−1.13052
$335$	−2.98882e8	−0.434353
$336$	0	0
$337$	−1.17882e9	−1.67780	−0.838902	−	0.544282i	$-0.816802\pi$
$337$	−1.17882e9	−1.67780	−0.838902	+	0.544282i	$0.816802\pi$
$338$	1.30041e9	1.83177
$339$	0	0
$340$	3.84768e9	5.30912
$341$	−4.41327e8	−0.602726
$342$	0	0
$343$	2.21931e8	0.296954
$344$	6.42081e8	0.850423
$345$	0	0
$346$	−6.43201e8	−0.834796
$347$	8.46545e8	1.08767	0.543835	−	0.839192i	$-0.316972\pi$
$347$	8.46545e8	1.08767	0.543835	+	0.839192i	$0.316972\pi$
$348$	0	0
$349$	6.62378e8	0.834098	0.417049	−	0.908884i	$-0.363064\pi$
$349$	6.62378e8	0.834098	0.417049	+	0.908884i	$0.363064\pi$
$350$	4.38096e9	5.46174
$351$	0	0
$352$	−6.18106e9	−7.55376
$353$	−8.83004e8	−1.06844	−0.534221	−	0.845345i	$-0.679395\pi$
$353$	−8.83004e8	−1.06844	−0.534221	+	0.845345i	$0.679395\pi$
$354$	0	0
$355$	1.73500e9	2.05825
$356$	−2.13280e9	−2.50539
$357$	0	0
$358$	2.89943e9	3.33981
$359$	−7.02849e7	−0.0801736	−0.0400868	−	0.999196i	$-0.512763\pi$
$359$	−7.02849e7	−0.0801736	−0.0400868	+	0.999196i	$0.512763\pi$
$360$	0	0
$361$	1.09874e8	0.122919
$362$	3.34729e9	3.70863
$363$	0	0
$364$	−8.32864e8	−0.905147
$365$	6.27860e8	0.675830
$366$	0	0
$367$	−1.46843e9	−1.55068	−0.775340	−	0.631544i	$-0.782421\pi$
$367$	−1.46843e9	−1.55068	−0.775340	+	0.631544i	$0.782421\pi$
$368$	−4.97927e9	−5.20833
$369$	0	0
$370$	7.86815e8	0.807544
$371$	1.84987e9	1.88076
$372$	0	0
$373$	1.19545e9	1.19275	0.596376	−	0.802705i	$-0.296607\pi$
$373$	1.19545e9	1.19275	0.596376	+	0.802705i	$0.296607\pi$
$374$	−3.73864e9	−3.69542
$375$	0	0
$376$	1.04794e8	0.101666
$377$	2.07117e8	0.199077
$378$	0	0
$379$	1.21004e9	1.14173	0.570863	−	0.821045i	$-0.306609\pi$
$379$	1.21004e9	1.14173	0.570863	+	0.821045i	$0.306609\pi$
$380$	−5.57347e9	−5.21054
$381$	0	0
$382$	−2.68108e9	−2.46086
$383$	1.02900e9	0.935876	0.467938	−	0.883761i	$-0.344997\pi$
$383$	1.02900e9	0.935876	0.467938	+	0.883761i	$0.344997\pi$
$384$	0	0
$385$	−4.62323e9	−4.12888
$386$	−2.92116e9	−2.58523
$387$	0	0
$388$	−7.07759e8	−0.615141
$389$	2.22572e9	1.91711	0.958556	−	0.284904i	$-0.0919616\pi$
$389$	2.22572e9	1.91711	0.958556	+	0.284904i	$0.0919616\pi$
$390$	0	0
$391$	−1.66265e9	−1.40664
$392$	−3.23209e9	−2.71008
$393$	0	0
$394$	2.46691e9	2.03197
$395$	1.91976e9	1.56732
$396$	0	0
$397$	9.68593e8	0.776917	0.388458	−	0.921466i	$-0.373008\pi$
$397$	9.68593e8	0.776917	0.388458	+	0.921466i	$0.373008\pi$
$398$	4.00219e9	3.18205
$399$	0	0
$400$	1.07679e10	8.41241
$401$	−9.25332e6	−0.00716626	−0.00358313	−	0.999994i	$-0.501141\pi$
$401$	−9.25332e6	−0.00716626	−0.00358313	+	0.999994i	$0.501141\pi$
$402$	0	0
$403$	−1.09602e8	−0.0834160
$404$	5.53239e9	4.17425
$405$	0	0
$406$	2.86412e9	2.12398
$407$	−5.62842e8	−0.413815
$408$	0	0
$409$	4.22397e8	0.305274	0.152637	−	0.988282i	$-0.451224\pi$
$409$	4.22397e8	0.305274	0.152637	+	0.988282i	$0.451224\pi$
$410$	−6.48888e9	−4.64971
$411$	0	0
$412$	−4.29653e9	−3.02676
$413$	−2.48470e8	−0.173560
$414$	0	0
$415$	1.98856e9	1.36574
$416$	−1.53504e9	−1.04543
$417$	0	0
$418$	5.41553e9	3.62680
$419$	1.30988e9	0.869925	0.434962	−	0.900449i	$-0.356762\pi$
$419$	1.30988e9	0.869925	0.434962	+	0.900449i	$0.356762\pi$
$420$	0	0
$421$	2.15584e9	1.40809	0.704043	−	0.710158i	$-0.251376\pi$
$421$	2.15584e9	1.40809	0.704043	+	0.710158i	$0.251376\pi$
$422$	7.37137e7	0.0477479
$423$	0	0
$424$	7.72075e9	4.91902
$425$	3.59555e9	2.27198
$426$	0	0
$427$	−2.90797e9	−1.80756
$428$	2.74715e9	1.69367
$429$	0	0
$430$	1.37942e9	0.836676
$431$	−8.50792e8	−0.511862	−0.255931	−	0.966695i	$-0.582382\pi$
$431$	−8.50792e8	−0.511862	−0.255931	+	0.966695i	$0.582382\pi$
$432$	0	0
$433$	−1.01714e9	−0.602109	−0.301054	−	0.953607i	$-0.597339\pi$
$433$	−1.01714e9	−0.602109	−0.301054	+	0.953607i	$0.597339\pi$
$434$	−1.51563e9	−0.889977
$435$	0	0
$436$	−7.55113e8	−0.436324
$437$	2.40839e9	1.38052
$438$	0	0
$439$	−1.42920e9	−0.806245	−0.403123	−	0.915146i	$-0.632075\pi$
$439$	−1.42920e9	−0.806245	−0.403123	+	0.915146i	$0.632075\pi$
$440$	−1.92958e10	−10.7989
$441$	0	0
$442$	−9.28477e8	−0.511438
$443$	−2.71763e8	−0.148517	−0.0742586	−	0.997239i	$-0.523659\pi$
$443$	−2.71763e8	−0.148517	−0.0742586	+	0.997239i	$0.523659\pi$
$444$	0	0
$445$	−2.94021e9	−1.58168
$446$	−7.12828e8	−0.380463
$447$	0	0
$448$	−1.10841e10	−5.82406
$449$	1.24125e9	0.647138	0.323569	−	0.946205i	$-0.395117\pi$
$449$	1.24125e9	0.647138	0.323569	+	0.946205i	$0.395117\pi$
$450$	0	0
$451$	4.64177e9	2.38268
$452$	−7.25346e8	−0.369454
$453$	0	0
$454$	3.53712e9	1.77400
$455$	−1.14816e9	−0.571429
$456$	0	0
$457$	−3.37198e9	−1.65264	−0.826320	−	0.563201i	$-0.809570\pi$
$457$	−3.37198e9	−1.65264	−0.826320	+	0.563201i	$0.809570\pi$
$458$	−9.56242e8	−0.465092
$459$	0	0
$460$	−1.33730e10	−6.40585
$461$	2.86356e9	1.36130	0.680650	−	0.732609i	$-0.261698\pi$
$461$	2.86356e9	1.36130	0.680650	+	0.732609i	$0.261698\pi$
$462$	0	0
$463$	4.00910e8	0.187721	0.0938607	−	0.995585i	$-0.470079\pi$
$463$	4.00910e8	0.187721	0.0938607	+	0.995585i	$0.470079\pi$
$464$	7.03967e9	3.27144
$465$	0	0
$466$	−6.30591e8	−0.288667
$467$	8.05487e8	0.365973	0.182987	−	0.983115i	$-0.441423\pi$
$467$	8.05487e8	0.365973	0.182987	+	0.983115i	$0.441423\pi$
$468$	0	0
$469$	7.34254e8	0.328656
$470$	2.25134e8	0.100023
$471$	0	0
$472$	−1.03703e9	−0.453936
$473$	−9.86759e8	−0.428743
$474$	0	0
$475$	−5.20825e9	−2.22979
$476$	−9.45248e9	−4.01718
$477$	0	0
$478$	−1.33617e9	−0.559584
$479$	1.45641e9	0.605495	0.302747	−	0.953071i	$-0.402096\pi$
$479$	1.45641e9	0.605495	0.302747	+	0.953071i	$0.402096\pi$
$480$	0	0
$481$	−1.39779e8	−0.0572711
$482$	−1.10810e9	−0.450728
$483$	0	0
$484$	1.45495e10	5.83295
$485$	−9.75694e8	−0.388345
$486$	0	0
$487$	1.91160e9	0.749973	0.374986	−	0.927030i	$-0.377647\pi$
$487$	1.91160e9	0.749973	0.374986	+	0.927030i	$0.377647\pi$
$488$	−1.21369e10	−4.72758
$489$	0	0
$490$	−6.94370e9	−2.66627
$491$	−3.11951e8	−0.118933	−0.0594663	−	0.998230i	$-0.518940\pi$
$491$	−3.11951e8	−0.118933	−0.0594663	+	0.998230i	$0.518940\pi$
$492$	0	0
$493$	2.35065e9	0.883533
$494$	1.34492e9	0.501942
$495$	0	0
$496$	−3.72524e9	−1.37078
$497$	−4.26231e9	−1.55739
$498$	0	0
$499$	−1.10424e9	−0.397844	−0.198922	−	0.980015i	$-0.563744\pi$
$499$	−1.10424e9	−0.397844	−0.198922	+	0.980015i	$0.563744\pi$
$500$	1.51760e10	5.42953
$501$	0	0
$502$	3.95957e9	1.39696
$503$	3.17067e9	1.11087	0.555434	−	0.831560i	$-0.312552\pi$
$503$	3.17067e9	1.11087	0.555434	+	0.831560i	$0.312552\pi$
$504$	0	0
$505$	7.62677e9	2.63524
$506$	1.29940e10	4.45879
$507$	0	0
$508$	4.92523e9	1.66688
$509$	−1.80020e9	−0.605074	−0.302537	−	0.953138i	$-0.597834\pi$
$509$	−1.80020e9	−0.605074	−0.302537	+	0.953138i	$0.597834\pi$
$510$	0	0
$511$	−1.54244e9	−0.511371
$512$	−9.83963e9	−3.23992
$513$	0	0
$514$	1.87889e9	0.610281
$515$	−5.92306e9	−1.91082
$516$	0	0
$517$	−1.61048e8	−0.0512553
$518$	−1.93294e9	−0.611034
$519$	0	0
$520$	−4.79204e9	−1.49454
$521$	1.90764e9	0.590968	0.295484	−	0.955348i	$-0.404519\pi$
$521$	1.90764e9	0.590968	0.295484	+	0.955348i	$0.404519\pi$
$522$	0	0
$523$	1.01205e9	0.309347	0.154673	−	0.987966i	$-0.450567\pi$
$523$	1.01205e9	0.309347	0.154673	+	0.987966i	$0.450567\pi$
$524$	3.01860e8	0.0916530
$525$	0	0
$526$	9.12900e9	2.73510
$527$	−1.24391e9	−0.370213
$528$	0	0
$529$	2.37388e9	0.697211
$530$	1.65870e10	4.83951
$531$	0	0
$532$	1.36922e10	3.94259
$533$	1.15276e9	0.329758
$534$	0	0
$535$	3.78713e9	1.06923
$536$	3.06453e9	0.859582
$537$	0	0
$538$	−6.78063e9	−1.87729
$539$	4.96712e9	1.36629
$540$	0	0
$541$	−5.50100e9	−1.49366	−0.746829	−	0.665016i	$-0.768425\pi$
$541$	−5.50100e9	−1.49366	−0.746829	+	0.665016i	$0.768425\pi$
$542$	5.19378e9	1.40115
$543$	0	0
$544$	−1.74217e10	−4.63976
$545$	−1.04097e9	−0.275456
$546$	0	0
$547$	4.40039e9	1.14957	0.574786	−	0.818304i	$-0.305085\pi$
$547$	4.40039e9	1.14957	0.574786	+	0.818304i	$0.305085\pi$
$548$	1.73110e10	4.49355
$549$	0	0
$550$	−2.81002e10	−7.20177
$551$	−3.40497e9	−0.867128
$552$	0	0
$553$	−4.71621e9	−1.18592
$554$	4.74664e9	1.18605
$555$	0	0
$556$	−7.33062e8	−0.180875
$557$	−5.20574e9	−1.27641	−0.638203	−	0.769868i	$-0.720322\pi$
$557$	−5.20574e9	−1.27641	−0.638203	+	0.769868i	$0.720322\pi$
$558$	0	0
$559$	−2.45057e8	−0.0593371
$560$	−3.90246e10	−9.39033
$561$	0	0
$562$	−4.54557e9	−1.08022
$563$	−6.20253e9	−1.46484	−0.732419	−	0.680854i	$-0.761609\pi$
$563$	−6.20253e9	−1.46484	−0.732419	+	0.680854i	$0.761609\pi$
$564$	0	0
$565$	−9.99939e8	−0.233240
$566$	−1.48397e10	−3.44007
$567$	0	0
$568$	−1.77895e10	−4.07328
$569$	−6.72094e9	−1.52946	−0.764728	−	0.644353i	$-0.777127\pi$
$569$	−6.72094e9	−1.52946	−0.764728	+	0.644353i	$0.777127\pi$
$570$	0	0
$571$	3.74441e8	0.0841700	0.0420850	−	0.999114i	$-0.486600\pi$
$571$	3.74441e8	0.0841700	0.0420850	+	0.999114i	$0.486600\pi$
$572$	5.34212e9	1.19351
$573$	0	0
$574$	1.59410e10	3.51824
$575$	−1.24967e10	−2.74131
$576$	0	0
$577$	1.91890e9	0.415851	0.207925	−	0.978145i	$-0.433329\pi$
$577$	1.91890e9	0.415851	0.207925	+	0.978145i	$0.433329\pi$
$578$	−1.49875e9	−0.322835
$579$	0	0
$580$	1.89067e10	4.02362
$581$	−4.88522e9	−1.03340
$582$	0	0
$583$	−1.18654e10	−2.47994
$584$	−6.43765e9	−1.33746
$585$	0	0
$586$	−5.90929e9	−1.21309
$587$	9.08556e9	1.85404	0.927018	−	0.375016i	$-0.122363\pi$
$587$	9.08556e9	1.85404	0.927018	+	0.375016i	$0.122363\pi$
$588$	0	0
$589$	1.80184e9	0.363339
$590$	−2.22792e9	−0.446598
$591$	0	0
$592$	−4.75095e9	−0.941140
$593$	1.90930e9	0.375997	0.187998	−	0.982169i	$-0.439800\pi$
$593$	1.90930e9	0.375997	0.187998	+	0.982169i	$0.439800\pi$
$594$	0	0
$595$	−1.30309e10	−2.53609
$596$	9.05329e8	0.175164
$597$	0	0
$598$	3.22701e9	0.617088
$599$	5.47139e9	1.04017	0.520084	−	0.854115i	$-0.325901\pi$
$599$	5.47139e9	1.04017	0.520084	+	0.854115i	$0.325901\pi$
$600$	0	0
$601$	3.55169e9	0.667381	0.333691	−	0.942683i	$-0.391706\pi$
$601$	3.55169e9	0.667381	0.333691	+	0.942683i	$0.391706\pi$
$602$	−3.38878e9	−0.633076
$603$	0	0
$604$	−1.96287e10	−3.62463
$605$	2.00574e10	3.68240
$606$	0	0
$607$	5.38370e9	0.977057	0.488529	−	0.872548i	$-0.337534\pi$
$607$	5.38370e9	0.977057	0.488529	+	0.872548i	$0.337534\pi$
$608$	2.52358e10	4.55360
$609$	0	0
$610$	−2.60745e10	−4.65116
$611$	−3.99956e7	−0.00709363
$612$	0	0
$613$	5.24608e9	0.919863	0.459932	−	0.887954i	$-0.347874\pi$
$613$	5.24608e9	0.919863	0.459932	+	0.887954i	$0.347874\pi$
$614$	−1.45219e10	−2.53183
$615$	0	0
$616$	4.74034e10	8.17104
$617$	−6.88172e9	−1.17950	−0.589751	−	0.807585i	$-0.700774\pi$
$617$	−6.88172e9	−1.17950	−0.589751	+	0.807585i	$0.700774\pi$
$618$	0	0
$619$	5.67281e9	0.961350	0.480675	−	0.876899i	$-0.340392\pi$
$619$	5.67281e9	0.961350	0.480675	+	0.876899i	$0.340392\pi$
$620$	−1.00050e10	−1.68596
$621$	0	0
$622$	−1.92438e10	−3.20645
$623$	7.22313e9	1.19679
$624$	0	0
$625$	8.07802e9	1.32350
$626$	−6.25640e9	−1.01933
$627$	0	0
$628$	2.59892e10	4.18730
$629$	−1.58641e9	−0.254178
$630$	0	0
$631$	1.88338e9	0.298425	0.149212	−	0.988805i	$-0.452326\pi$
$631$	1.88338e9	0.298425	0.149212	+	0.988805i	$0.452326\pi$
$632$	−1.96839e10	−3.10171
$633$	0	0
$634$	−4.77860e9	−0.744713
$635$	6.78976e9	1.05232
$636$	0	0
$637$	1.23356e9	0.189092
$638$	−1.83709e10	−2.80065
$639$	0	0
$640$	−4.91762e10	−7.41524
$641$	−5.23503e9	−0.785084	−0.392542	−	0.919734i	$-0.628404\pi$
$641$	−5.23503e9	−0.785084	−0.392542	+	0.919734i	$0.628404\pi$
$642$	0	0
$643$	−7.39762e8	−0.109737	−0.0548686	−	0.998494i	$-0.517474\pi$
$643$	−7.39762e8	−0.109737	−0.0548686	+	0.998494i	$0.517474\pi$
$644$	3.28530e10	4.84702
$645$	0	0
$646$	1.52640e10	2.22769
$647$	7.49507e9	1.08796	0.543978	−	0.839100i	$-0.316918\pi$
$647$	7.49507e9	1.08796	0.543978	+	0.839100i	$0.316918\pi$
$648$	0	0
$649$	1.59372e9	0.228853
$650$	−6.97856e9	−0.996710
$651$	0	0
$652$	7.11075e8	0.100473
$653$	−9.12022e9	−1.28177	−0.640884	−	0.767638i	$-0.721432\pi$
$653$	−9.12022e9	−1.28177	−0.640884	+	0.767638i	$0.721432\pi$
$654$	0	0
$655$	4.16135e8	0.0578615
$656$	3.91812e10	5.41893
$657$	0	0
$658$	−5.53081e8	−0.0756829
$659$	−8.11531e9	−1.10460	−0.552301	−	0.833645i	$-0.686250\pi$
$659$	−8.11531e9	−1.10460	−0.552301	+	0.833645i	$0.686250\pi$
$660$	0	0
$661$	6.72245e9	0.905362	0.452681	−	0.891672i	$-0.350468\pi$
$661$	6.72245e9	0.905362	0.452681	+	0.891672i	$0.350468\pi$
$662$	2.19947e10	2.94656
$663$	0	0
$664$	−2.03893e10	−2.70280
$665$	1.88756e10	2.48900
$666$	0	0
$667$	−8.16991e9	−1.06605
$668$	1.24842e10	1.62047
$669$	0	0
$670$	6.58372e9	0.845687
$671$	1.86522e10	2.38342
$672$	0	0
$673$	1.14461e10	1.44745	0.723725	−	0.690089i	$-0.242429\pi$
$673$	1.14461e10	1.44745	0.723725	+	0.690089i	$0.242429\pi$
$674$	2.59668e10	3.26669
$675$	0	0
$676$	−2.10887e10	−2.62565
$677$	4.26750e9	0.528583	0.264292	−	0.964443i	$-0.414862\pi$
$677$	4.26750e9	0.528583	0.264292	+	0.964443i	$0.414862\pi$
$678$	0	0
$679$	2.39696e9	0.293843
$680$	−5.43866e10	−6.63301
$681$	0	0
$682$	9.72147e9	1.17351
$683$	−6.74829e9	−0.810441	−0.405220	−	0.914219i	$-0.632805\pi$
$683$	−6.74829e9	−0.810441	−0.405220	+	0.914219i	$0.632805\pi$
$684$	0	0
$685$	2.38644e10	2.83683
$686$	−4.88867e9	−0.578171
$687$	0	0
$688$	−8.32922e9	−0.975091
$689$	−2.94671e9	−0.343218
$690$	0	0
$691$	−6.41648e9	−0.739816	−0.369908	−	0.929068i	$-0.620611\pi$
$691$	−6.41648e9	−0.739816	−0.369908	+	0.929068i	$0.620611\pi$
$692$	1.04308e10	1.19659
$693$	0	0
$694$	−1.86476e10	−2.11770
$695$	−1.01057e9	−0.114188
$696$	0	0
$697$	1.30832e10	1.46352
$698$	−1.45908e10	−1.62399
$699$	0	0
$700$	−7.10461e10	−7.82884
$701$	1.49165e10	1.63552	0.817758	−	0.575562i	$-0.195216\pi$
$701$	1.49165e10	1.63552	0.817758	+	0.575562i	$0.195216\pi$
$702$	0	0
$703$	2.29796e9	0.249458
$704$	7.10949e10	7.67952
$705$	0	0
$706$	1.94507e10	2.08026
$707$	−1.87365e10	−1.99397
$708$	0	0
$709$	5.36963e9	0.565826	0.282913	−	0.959146i	$-0.408699\pi$
$709$	5.36963e9	0.565826	0.282913	+	0.959146i	$0.408699\pi$
$710$	−3.82182e10	−4.00743
$711$	0	0
$712$	3.01469e10	3.13014
$713$	4.32333e9	0.446689
$714$	0	0
$715$	7.36447e9	0.753477
$716$	−4.70201e10	−4.78727
$717$	0	0
$718$	1.54822e9	0.156098
$719$	2.42754e9	0.243565	0.121783	−	0.992557i	$-0.461139\pi$
$719$	2.42754e9	0.243565	0.121783	+	0.992557i	$0.461139\pi$
$720$	0	0
$721$	1.45510e10	1.44584
$722$	−2.42029e9	−0.239325
$723$	0	0
$724$	−5.42830e10	−5.31593
$725$	1.76678e10	1.72186
$726$	0	0
$727$	1.20971e10	1.16764	0.583822	−	0.811882i	$-0.301557\pi$
$727$	1.20971e10	1.16764	0.583822	+	0.811882i	$0.301557\pi$
$728$	1.17724e10	1.13086
$729$	0	0
$730$	−1.38304e10	−1.31584
$731$	−2.78125e9	−0.263347
$732$	0	0
$733$	3.52480e7	0.00330575	0.00165288	−	0.999999i	$-0.499474\pi$
$733$	3.52480e7	0.00330575	0.00165288	+	0.999999i	$0.499474\pi$
$734$	3.23463e10	3.01918
$735$	0	0
$736$	6.05510e10	5.59821
$737$	−4.70962e9	−0.433360
$738$	0	0
$739$	9.27198e9	0.845118	0.422559	−	0.906336i	$-0.361132\pi$
$739$	9.27198e9	0.845118	0.422559	+	0.906336i	$0.361132\pi$
$740$	−1.27598e10	−1.15753
$741$	0	0
$742$	−4.07487e10	−3.66184
$743$	1.63793e10	1.46499	0.732494	−	0.680773i	$-0.238356\pi$
$743$	1.63793e10	1.46499	0.732494	+	0.680773i	$0.238356\pi$
$744$	0	0
$745$	1.24806e9	0.110583
$746$	−2.63331e10	−2.32229
$747$	0	0
$748$	6.06296e10	5.29699
$749$	−9.30372e9	−0.809040
$750$	0	0
$751$	2.46248e9	0.212145	0.106073	−	0.994358i	$-0.466172\pi$
$751$	2.46248e9	0.212145	0.106073	+	0.994358i	$0.466172\pi$
$752$	−1.35941e9	−0.116570
$753$	0	0
$754$	−4.56234e9	−0.387604
$755$	−2.70596e10	−2.28826
$756$	0	0
$757$	7.88850e9	0.660935	0.330468	−	0.943817i	$-0.392794\pi$
$757$	7.88850e9	0.660935	0.330468	+	0.943817i	$0.392794\pi$
$758$	−2.66545e10	−2.22295
$759$	0	0
$760$	7.87804e10	6.50984
$761$	2.28543e10	1.87984	0.939922	−	0.341390i	$-0.110898\pi$
$761$	2.28543e10	1.87984	0.939922	+	0.341390i	$0.110898\pi$
$762$	0	0
$763$	2.55733e9	0.208426
$764$	4.34791e10	3.52739
$765$	0	0
$766$	−2.26666e10	−1.82216
$767$	3.95795e8	0.0316728
$768$	0	0
$769$	3.75836e9	0.298028	0.149014	−	0.988835i	$-0.452390\pi$
$769$	3.75836e9	0.298028	0.149014	+	0.988835i	$0.452390\pi$
$770$	1.01840e11	8.03896
$771$	0	0
$772$	4.73725e10	3.70566
$773$	2.31574e10	1.80327	0.901637	−	0.432494i	$-0.142366\pi$
$773$	2.31574e10	1.80327	0.901637	+	0.432494i	$0.142366\pi$
$774$	0	0
$775$	−9.34939e9	−0.721485
$776$	1.00041e10	0.768532
$777$	0	0
$778$	−4.90279e10	−3.73263
$779$	−1.89513e10	−1.43634
$780$	0	0
$781$	2.73391e10	2.05355
$782$	3.66246e10	2.73873
$783$	0	0
$784$	4.19274e10	3.10736
$785$	3.58279e10	2.64349
$786$	0	0
$787$	7.24985e8	0.0530173	0.0265087	−	0.999649i	$-0.491561\pi$
$787$	7.24985e8	0.0530173	0.0265087	+	0.999649i	$0.491561\pi$
$788$	−4.00059e10	−2.91261
$789$	0	0
$790$	−4.22881e10	−3.05157
$791$	2.45652e9	0.176483
$792$	0	0
$793$	4.63219e9	0.329860
$794$	−2.13360e10	−1.51266
$795$	0	0
$796$	−6.49036e10	−4.56113
$797$	−1.66646e10	−1.16598	−0.582989	−	0.812480i	$-0.698117\pi$
$797$	−1.66646e10	−1.16598	−0.582989	+	0.812480i	$0.698117\pi$
$798$	0	0
$799$	−4.53925e8	−0.0314826
$800$	−1.30944e11	−9.04213
$801$	0	0
$802$	2.03831e8	0.0139527
$803$	9.89347e9	0.674286
$804$	0	0
$805$	4.52901e10	3.05998
$806$	2.41429e9	0.162411
$807$	0	0
$808$	−7.81997e10	−5.21514
$809$	1.50299e10	0.998010	0.499005	−	0.866599i	$-0.333699\pi$
$809$	1.50299e10	0.998010	0.499005	+	0.866599i	$0.333699\pi$
$810$	0	0
$811$	−1.62482e10	−1.06963	−0.534813	−	0.844971i	$-0.679618\pi$
$811$	−1.62482e10	−1.06963	−0.534813	+	0.844971i	$0.679618\pi$
$812$	−4.64475e10	−3.04450
$813$	0	0
$814$	1.23982e10	0.805699
$815$	9.80265e8	0.0634296
$816$	0	0
$817$	4.02871e9	0.258457
$818$	−9.30449e9	−0.594369
$819$	0	0
$820$	1.05230e11	6.66488
$821$	2.31309e10	1.45879	0.729393	−	0.684095i	$-0.239803\pi$
$821$	2.31309e10	1.45879	0.729393	+	0.684095i	$0.239803\pi$
$822$	0	0
$823$	−2.00237e10	−1.25211	−0.626057	−	0.779777i	$-0.715332\pi$
$823$	−2.00237e10	−1.25211	−0.626057	+	0.779777i	$0.715332\pi$
$824$	6.07310e10	3.78151
$825$	0	0
$826$	5.47325e9	0.337921
$827$	1.75153e10	1.07683	0.538417	−	0.842679i	$-0.319023\pi$
$827$	1.75153e10	1.07683	0.538417	+	0.842679i	$0.319023\pi$
$828$	0	0
$829$	1.27473e10	0.777099	0.388550	−	0.921428i	$-0.372976\pi$
$829$	1.27473e10	0.777099	0.388550	+	0.921428i	$0.372976\pi$
$830$	−4.38036e10	−2.65911
$831$	0	0
$832$	1.76561e10	1.06283
$833$	1.40002e10	0.839220
$834$	0	0
$835$	1.72103e10	1.02302
$836$	−8.78237e10	−5.19864
$837$	0	0
$838$	−2.88538e10	−1.69375
$839$	−1.43905e10	−0.841217	−0.420609	−	0.907242i	$-0.638183\pi$
$839$	−1.43905e10	−0.841217	−0.420609	+	0.907242i	$0.638183\pi$
$840$	0	0
$841$	−5.69930e9	−0.330397
$842$	−4.74885e10	−2.74155
$843$	0	0
$844$	−1.19542e9	−0.0684416
$845$	−2.90722e10	−1.65760
$846$	0	0
$847$	−4.92745e10	−2.78631
$848$	−1.00155e11	−5.64013
$849$	0	0
$850$	−7.92022e10	−4.42355
$851$	5.51372e9	0.306684
$852$	0	0
$853$	−2.47811e10	−1.36710	−0.683549	−	0.729905i	$-0.739564\pi$
$853$	−2.47811e10	−1.36710	−0.683549	+	0.729905i	$0.739564\pi$
$854$	6.40563e10	3.51933
$855$	0	0
$856$	−3.88306e10	−2.11600
$857$	−1.34333e10	−0.729036	−0.364518	−	0.931196i	$-0.618766\pi$
$857$	−1.34333e10	−0.729036	−0.364518	+	0.931196i	$0.618766\pi$
$858$	0	0
$859$	1.54319e10	0.830701	0.415350	−	0.909662i	$-0.363659\pi$
$859$	1.54319e10	0.830701	0.415350	+	0.909662i	$0.363659\pi$
$860$	−2.23701e10	−1.19929
$861$	0	0
$862$	1.87411e10	0.996598
$863$	1.32034e10	0.699273	0.349636	−	0.936885i	$-0.386305\pi$
$863$	1.32034e10	0.699273	0.349636	+	0.936885i	$0.386305\pi$
$864$	0	0
$865$	1.43796e10	0.755421
$866$	2.24055e10	1.17231
$867$	0	0
$868$	2.45790e10	1.27569
$869$	3.02505e10	1.56373
$870$	0	0
$871$	−1.16961e9	−0.0599762
$872$	1.06734e10	0.545126
$873$	0	0
$874$	−5.30517e10	−2.68788
$875$	−5.13963e10	−2.59360
$876$	0	0
$877$	−1.39419e10	−0.697949	−0.348975	−	0.937132i	$-0.613470\pi$
$877$	−1.39419e10	−0.697949	−0.348975	+	0.937132i	$0.613470\pi$
$878$	3.14822e10	1.56976
$879$	0	0
$880$	2.50310e11	12.3819
$881$	−1.37479e10	−0.677360	−0.338680	−	0.940902i	$-0.609980\pi$
$881$	−1.37479e10	−0.677360	−0.338680	+	0.940902i	$0.609980\pi$
$882$	0	0
$883$	8.50641e9	0.415799	0.207900	−	0.978150i	$-0.433337\pi$
$883$	8.50641e9	0.415799	0.207900	+	0.978150i	$0.433337\pi$
$884$	1.50571e10	0.733093
$885$	0	0
$886$	5.98635e9	0.289164
$887$	1.27701e10	0.614417	0.307208	−	0.951642i	$-0.400605\pi$
$887$	1.27701e10	0.614417	0.307208	+	0.951642i	$0.400605\pi$
$888$	0	0
$889$	−1.66802e10	−0.796241
$890$	6.47665e10	3.07954
$891$	0	0
$892$	1.15599e10	0.545354
$893$	6.57523e8	0.0308980
$894$	0	0
$895$	−6.48204e10	−3.02225
$896$	1.20810e11	5.61079
$897$	0	0
$898$	−2.73420e10	−1.25998
$899$	−6.11231e9	−0.280573
$900$	0	0
$901$	−3.34433e10	−1.52326
$902$	−1.02248e11	−4.63909
$903$	0	0
$904$	1.02527e10	0.461582
$905$	−7.48328e10	−3.35600
$906$	0	0
$907$	3.70884e10	1.65049	0.825244	−	0.564776i	$-0.191037\pi$
$907$	3.70884e10	1.65049	0.825244	+	0.564776i	$0.191037\pi$
$908$	−5.73616e10	−2.54285
$909$	0	0
$910$	2.52915e10	1.11257
$911$	−1.58470e10	−0.694436	−0.347218	−	0.937784i	$-0.612874\pi$
$911$	−1.58470e10	−0.694436	−0.347218	+	0.937784i	$0.612874\pi$
$912$	0	0
$913$	3.13346e10	1.36262
$914$	7.42774e10	3.21770
$915$	0	0
$916$	1.55074e10	0.666660
$917$	−1.02231e9	−0.0437813
$918$	0	0
$919$	1.09730e10	0.466359	0.233180	−	0.972434i	$-0.425087\pi$
$919$	1.09730e10	0.466359	0.233180	+	0.972434i	$0.425087\pi$
$920$	1.89026e11	8.00321
$921$	0	0
$922$	−6.30781e10	−2.65046
$923$	6.78955e9	0.284207
$924$	0	0
$925$	−1.19237e10	−0.495352
$926$	−8.83119e9	−0.365494
$927$	0	0
$928$	−8.56067e10	−3.51633
$929$	−3.30298e10	−1.35161	−0.675804	−	0.737081i	$-0.736203\pi$
$929$	−3.30298e10	−1.35161	−0.675804	+	0.737081i	$0.736203\pi$
$930$	0	0
$931$	−2.02796e10	−0.823637
$932$	1.02263e10	0.413774
$933$	0	0
$934$	−1.77431e10	−0.712552
$935$	8.35821e10	3.34405
$936$	0	0
$937$	−1.81069e10	−0.719045	−0.359522	−	0.933136i	$-0.617060\pi$
$937$	−1.81069e10	−0.719045	−0.359522	+	0.933136i	$0.617060\pi$
$938$	−1.61740e10	−0.639894
$939$	0	0
$940$	−3.65101e9	−0.143372
$941$	−2.38460e10	−0.932938	−0.466469	−	0.884538i	$-0.654474\pi$
$941$	−2.38460e10	−0.932938	−0.466469	+	0.884538i	$0.654474\pi$
$942$	0	0
$943$	−4.54718e10	−1.76584
$944$	1.34526e10	0.520480
$945$	0	0
$946$	2.17362e10	0.834764
$947$	−2.50480e10	−0.958404	−0.479202	−	0.877705i	$-0.659074\pi$
$947$	−2.50480e10	−0.958404	−0.479202	+	0.877705i	$0.659074\pi$
$948$	0	0
$949$	2.45700e9	0.0933198
$950$	1.14727e11	4.34141
$951$	0	0
$952$	1.33610e11	5.01891
$953$	2.27700e10	0.852194	0.426097	−	0.904677i	$-0.359888\pi$
$953$	2.27700e10	0.852194	0.426097	+	0.904677i	$0.359888\pi$
$954$	0	0
$955$	5.99389e10	2.22688
$956$	2.16688e10	0.802105
$957$	0	0
$958$	−3.20816e10	−1.17890
$959$	−5.86269e10	−2.14650
$960$	0	0
$961$	−2.42781e10	−0.882436
$962$	3.07904e9	0.111507
$963$	0	0
$964$	1.79701e10	0.646072
$965$	6.53062e10	2.33942
$966$	0	0
$967$	1.53182e10	0.544772	0.272386	−	0.962188i	$-0.412187\pi$
$967$	1.53182e10	0.544772	0.272386	+	0.962188i	$0.412187\pi$
$968$	−2.05655e11	−7.28746
$969$	0	0
$970$	2.14924e10	0.756109
$971$	−1.35596e10	−0.475314	−0.237657	−	0.971349i	$-0.576379\pi$
$971$	−1.35596e10	−0.475314	−0.237657	+	0.971349i	$0.576379\pi$
$972$	0	0
$973$	2.48265e9	0.0864013
$974$	−4.21084e10	−1.46020
$975$	0	0
$976$	1.57443e11	5.42061
$977$	−5.16415e10	−1.77161	−0.885804	−	0.464060i	$-0.846392\pi$
$977$	−5.16415e10	−1.77161	−0.885804	+	0.464060i	$0.846392\pi$
$978$	0	0
$979$	−4.63302e10	−1.57807
$980$	1.12606e11	3.82182
$981$	0	0
$982$	6.87160e9	0.231562
$983$	−2.68451e10	−0.901421	−0.450711	−	0.892670i	$-0.648829\pi$
$983$	−2.68451e10	−0.901421	−0.450711	+	0.892670i	$0.648829\pi$
$984$	0	0
$985$	−5.51509e10	−1.83876
$986$	−5.17796e10	−1.72024
$987$	0	0
$988$	−2.18106e10	−0.719481
$989$	9.66650e9	0.317748
$990$	0	0
$991$	3.98369e10	1.30025	0.650126	−	0.759826i	$-0.274716\pi$
$991$	3.98369e10	1.30025	0.650126	+	0.759826i	$0.274716\pi$
$992$	4.53012e10	1.47339
$993$	0	0
$994$	9.38895e10	3.03225
$995$	−8.94740e10	−2.87949
$996$	0	0
$997$	−5.65997e9	−0.180876	−0.0904380	−	0.995902i	$-0.528827\pi$
$997$	−5.65997e9	−0.180876	−0.0904380	+	0.995902i	$0.528827\pi$
$998$	2.43241e10	0.774605
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.d.1.1		17
3.2	odd	2		177.8.a.b.1.17	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.17	✓	17	3.2	odd	2
531.8.a.d.1.1		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)

\(f(q)\)	\(=\)	\(q-22.0278 q^{2} +357.226 q^{4} +492.460 q^{5} -1209.81 q^{7} -5049.35 q^{8} +O(q^{10})\)	\(q-22.0278 q^{2} +357.226 q^{4} +492.460 q^{5} -1209.81 q^{7} -5049.35 q^{8} -10847.8 q^{10} +7759.91 q^{11} +1927.14 q^{13} +26649.5 q^{14} +65501.4 q^{16} +21871.8 q^{17} -31682.0 q^{19} +175919. q^{20} -170934. q^{22} -76017.8 q^{23} +164392. q^{25} -42450.8 q^{26} -432176. q^{28} +107474. q^{29} -56872.6 q^{31} -796537. q^{32} -481789. q^{34} -595783. q^{35} -72532.0 q^{37} +697885. q^{38} -2.48660e6 q^{40} +598173. q^{41} -127161. q^{43} +2.77204e6 q^{44} +1.67451e6 q^{46} -20753.9 q^{47} +640100. q^{49} -3.62120e6 q^{50} +688425. q^{52} -1.52906e6 q^{53} +3.82145e6 q^{55} +6.10876e6 q^{56} -2.36741e6 q^{58} +205379. q^{59} +2.40366e6 q^{61} +1.25278e6 q^{62} +9.16182e6 q^{64} +949040. q^{65} -606916. q^{67} +7.81319e6 q^{68} +1.31238e7 q^{70} +3.52312e6 q^{71} +1.27495e6 q^{73} +1.59772e6 q^{74} -1.13176e7 q^{76} -9.38803e6 q^{77} +3.89830e6 q^{79} +3.22568e7 q^{80} -1.31765e7 q^{82} +4.03800e6 q^{83} +1.07710e7 q^{85} +2.80108e6 q^{86} -3.91825e7 q^{88} -5.97046e6 q^{89} -2.33148e6 q^{91} -2.71555e7 q^{92} +457163. q^{94} -1.56021e7 q^{95} -1.98127e6 q^{97} -1.41000e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 32 q^{2} + 1166 q^{4} + 1072 q^{5} - 2407 q^{7} + 6645 q^{8}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more