LMFDB - Embedded newform 8281.2.a.cu.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 1183)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.877203 q^{2} -0.755024 q^{3} -1.23052 q^{4} -0.265839 q^{5} -0.662309 q^{6} -2.83382 q^{8} -2.42994 q^{9} +O(q^{10})$	\(q+0.877203 q^{2} -0.755024 q^{3} -1.23052 q^{4} -0.265839 q^{5} -0.662309 q^{6} -2.83382 q^{8} -2.42994 q^{9} -0.233195 q^{10} +0.455666 q^{11} +0.929068 q^{12} +0.200715 q^{15} -0.0248023 q^{16} -3.65702 q^{17} -2.13155 q^{18} -3.55974 q^{19} +0.327119 q^{20} +0.399712 q^{22} -3.07952 q^{23} +2.13960 q^{24} -4.92933 q^{25} +4.09973 q^{27} -0.612999 q^{29} +0.176068 q^{30} -10.7090 q^{31} +5.64588 q^{32} -0.344039 q^{33} -3.20795 q^{34} +2.99008 q^{36} -2.18786 q^{37} -3.12262 q^{38} +0.753339 q^{40} +7.13669 q^{41} +6.76740 q^{43} -0.560704 q^{44} +0.645973 q^{45} -2.70137 q^{46} -7.47771 q^{47} +0.0187263 q^{48} -4.32402 q^{50} +2.76114 q^{51} -7.79148 q^{53} +3.59630 q^{54} -0.121134 q^{55} +2.68769 q^{57} -0.537725 q^{58} +11.6247 q^{59} -0.246983 q^{60} -1.59475 q^{61} -9.39396 q^{62} +5.00218 q^{64} -0.301792 q^{66} -9.39914 q^{67} +4.50002 q^{68} +2.32511 q^{69} -6.89894 q^{71} +6.88600 q^{72} +2.85100 q^{73} -1.91920 q^{74} +3.72176 q^{75} +4.38032 q^{76} +8.73448 q^{79} +0.00659341 q^{80} +4.19442 q^{81} +6.26033 q^{82} -7.51728 q^{83} +0.972179 q^{85} +5.93638 q^{86} +0.462829 q^{87} -1.29127 q^{88} +8.42769 q^{89} +0.566649 q^{90} +3.78940 q^{92} +8.08554 q^{93} -6.55947 q^{94} +0.946319 q^{95} -4.26277 q^{96} -1.61319 q^{97} -1.10724 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9}+O(q^{10}) $ 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9	$ 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9} + 5 q^{10} - q^{11} + 5 q^{12} + 5 q^{15} + 17 q^{16} - 5 q^{17} + 24 q^{19} + 34 q^{20} - 14 q^{22} + 11 q^{23} + 32 q^{24} + 33 q^{25} - 21 q^{27} + 4 q^{29} - 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} + 36 q^{34} - 15 q^{36} - 4 q^{37} - 29 q^{38} - 4 q^{40} + 49 q^{41} + 13 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 89 q^{48} - 23 q^{50} - 21 q^{51} - 18 q^{53} + 12 q^{54} - 14 q^{55} - 13 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} + 13 q^{61} + 12 q^{62} + 18 q^{64} - 38 q^{66} - 2 q^{67} - 12 q^{68} - 28 q^{69} - 19 q^{71} + 81 q^{72} + 17 q^{73} + 17 q^{74} + 24 q^{75} + 58 q^{76} - 9 q^{79} + 63 q^{80} + 16 q^{81} - 22 q^{82} + 81 q^{83} - 34 q^{85} + 22 q^{86} + 70 q^{87} - 33 q^{88} + 72 q^{89} + q^{90} - 4 q^{92} + 19 q^{93} - 30 q^{94} + 13 q^{95} + 11 q^{96} + 45 q^{97} - 39 q^{99}+O(q^{100}) $ 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9 + 5 * q^10 - q^11 + 5 * q^12 + 5 * q^15 + 17 * q^16 - 5 * q^17 + 24 * q^19 + 34 * q^20 - 14 * q^22 + 11 * q^23 + 32 * q^24 + 33 * q^25 - 21 * q^27 + 4 * q^29 - 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 + 36 * q^34 - 15 * q^36 - 4 * q^37 - 29 * q^38 - 4 * q^40 + 49 * q^41 + 13 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 89 * q^48 - 23 * q^50 - 21 * q^51 - 18 * q^53 + 12 * q^54 - 14 * q^55 - 13 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 + 13 * q^61 + 12 * q^62 + 18 * q^64 - 38 * q^66 - 2 * q^67 - 12 * q^68 - 28 * q^69 - 19 * q^71 + 81 * q^72 + 17 * q^73 + 17 * q^74 + 24 * q^75 + 58 * q^76 - 9 * q^79 + 63 * q^80 + 16 * q^81 - 22 * q^82 + 81 * q^83 - 34 * q^85 + 22 * q^86 + 70 * q^87 - 33 * q^88 + 72 * q^89 + q^90 - 4 * q^92 + 19 * q^93 - 30 * q^94 + 13 * q^95 + 11 * q^96 + 45 * q^97 - 39 * q^99

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 $

$2$	0.877203	0.620276	0.310138	−	0.950692i	$-0.399625\pi$
$2$	0.877203	0.620276	0.310138	+	0.950692i	$0.399625\pi$
$3$	−0.755024	−0.435913	−0.217957	−	0.975958i	$-0.569939\pi$
$3$	−0.755024	−0.435913	−0.217957	+	0.975958i	$0.569939\pi$
$4$	−1.23052	−0.615258
$5$	−0.265839	−0.118887	−0.0594434	−	0.998232i	$-0.518933\pi$
$5$	−0.265839	−0.118887	−0.0594434	+	0.998232i	$0.518933\pi$
$6$	−0.662309	−0.270386
$7$	0	0
$7$	0	0
$8$	−2.83382	−1.00191
$9$	−2.42994	−0.809980
$10$	−0.233195	−0.0737427
$11$	0.455666	0.137388	0.0686942	−	0.997638i	$-0.478117\pi$
$11$	0.455666	0.137388	0.0686942	+	0.997638i	$0.478117\pi$
$12$	0.929068	0.268199
$13$	0	0
$13$	0	0
$14$	0	0
$15$	0.200715	0.0518243
$16$	−0.0248023	−0.00620056
$17$	−3.65702	−0.886958	−0.443479	−	0.896285i	$-0.646256\pi$
$17$	−3.65702	−0.886958	−0.443479	+	0.896285i	$0.646256\pi$
$18$	−2.13155	−0.502411
$19$	−3.55974	−0.816661	−0.408331	−	0.912834i	$-0.633889\pi$
$19$	−3.55974	−0.816661	−0.408331	+	0.912834i	$0.633889\pi$
$20$	0.327119	0.0731460
$21$	0	0
$22$	0.399712	0.0852188
$23$	−3.07952	−0.642125	−0.321063	−	0.947058i	$-0.604040\pi$
$23$	−3.07952	−0.642125	−0.321063	+	0.947058i	$0.604040\pi$
$24$	2.13960	0.436744
$25$	−4.92933	−0.985866
$26$	0	0
$27$	4.09973	0.788994
$28$	0	0
$29$	−0.612999	−0.113831	−0.0569155	−	0.998379i	$-0.518127\pi$
$29$	−0.612999	−0.113831	−0.0569155	+	0.998379i	$0.518127\pi$
$30$	0.176068	0.0321454
$31$	−10.7090	−1.92339	−0.961696	−	0.274119i	$-0.911614\pi$
$31$	−10.7090	−1.92339	−0.961696	+	0.274119i	$0.911614\pi$
$32$	5.64588	0.998060
$33$	−0.344039	−0.0598894
$34$	−3.20795	−0.550159
$35$	0	0
$36$	2.99008	0.498346
$37$	−2.18786	−0.359682	−0.179841	−	0.983696i	$-0.557558\pi$
$37$	−2.18786	−0.359682	−0.179841	+	0.983696i	$0.557558\pi$
$38$	−3.12262	−0.506556
$39$	0	0
$40$	0.753339	0.119113
$41$	7.13669	1.11456	0.557282	−	0.830323i	$-0.311844\pi$
$41$	7.13669	1.11456	0.557282	+	0.830323i	$0.311844\pi$
$42$	0	0
$43$	6.76740	1.03202	0.516009	−	0.856583i	$-0.327417\pi$
$43$	6.76740	1.03202	0.516009	+	0.856583i	$0.327417\pi$
$44$	−0.560704	−0.0845293
$45$	0.645973	0.0962959
$46$	−2.70137	−0.398295
$47$	−7.47771	−1.09074	−0.545368	−	0.838197i	$-0.683610\pi$
$47$	−7.47771	−1.09074	−0.545368	+	0.838197i	$0.683610\pi$
$48$	0.0187263	0.00270291
$49$	0	0
$50$	−4.32402	−0.611509
$51$	2.76114	0.386637
$52$	0	0
$53$	−7.79148	−1.07024	−0.535121	−	0.844776i	$-0.679734\pi$
$53$	−7.79148	−1.07024	−0.535121	+	0.844776i	$0.679734\pi$
$54$	3.59630	0.489394
$55$	−0.121134	−0.0163337
$56$	0	0
$57$	2.68769	0.355993
$58$	−0.537725	−0.0706067
$59$	11.6247	1.51341	0.756703	−	0.653758i	$-0.226809\pi$
$59$	11.6247	1.51341	0.756703	+	0.653758i	$0.226809\pi$
$60$	−0.246983	−0.0318853
$61$	−1.59475	−0.204186	−0.102093	−	0.994775i	$-0.532554\pi$
$61$	−1.59475	−0.204186	−0.102093	+	0.994775i	$0.532554\pi$
$62$	−9.39396	−1.19303
$63$	0	0
$64$	5.00218	0.625273
$65$	0	0
$66$	−0.301792	−0.0371480
$67$	−9.39914	−1.14829	−0.574144	−	0.818755i	$-0.694665\pi$
$67$	−9.39914	−1.14829	−0.574144	+	0.818755i	$0.694665\pi$
$68$	4.50002	0.545708
$69$	2.32511	0.279911
$70$	0	0
$71$	−6.89894	−0.818754	−0.409377	−	0.912365i	$-0.634254\pi$
$71$	−6.89894	−0.818754	−0.409377	+	0.912365i	$0.634254\pi$
$72$	6.88600	0.811523
$73$	2.85100	0.333684	0.166842	−	0.985984i	$-0.446643\pi$
$73$	2.85100	0.333684	0.166842	+	0.985984i	$0.446643\pi$
$74$	−1.91920	−0.223102
$75$	3.72176	0.429752
$76$	4.38032	0.502457
$77$	0	0
$78$	0	0
$79$	8.73448	0.982706	0.491353	−	0.870960i	$-0.336502\pi$
$79$	8.73448	0.982706	0.491353	+	0.870960i	$0.336502\pi$
$80$	0.00659341	0.000737165 0
$81$	4.19442	0.466047
$82$	6.26033	0.691337
$83$	−7.51728	−0.825129	−0.412564	−	0.910928i	$-0.635367\pi$
$83$	−7.51728	−0.825129	−0.412564	+	0.910928i	$0.635367\pi$
$84$	0	0
$85$	0.972179	0.105448
$86$	5.93638	0.640136
$87$	0.462829	0.0496205
$88$	−1.29127	−0.137650
$89$	8.42769	0.893333	0.446666	−	0.894701i	$-0.352611\pi$
$89$	8.42769	0.893333	0.446666	+	0.894701i	$0.352611\pi$
$90$	0.566649	0.0597301
$91$	0	0
$92$	3.78940	0.395072
$93$	8.08554	0.838432
$94$	−6.55947	−0.676557
$95$	0.946319	0.0970903
$96$	−4.26277	−0.435067
$97$	−1.61319	−0.163795	−0.0818975	−	0.996641i	$-0.526098\pi$
$97$	−1.61319	−0.163795	−0.0818975	+	0.996641i	$0.526098\pi$
$98$	0	0
$99$	−1.10724	−0.111282
$100$	6.06561	0.606561
$101$	7.29769	0.726147	0.363074	−	0.931760i	$-0.381727\pi$
$101$	7.29769	0.726147	0.363074	+	0.931760i	$0.381727\pi$
$102$	2.42208	0.239822
$103$	−8.16853	−0.804869	−0.402434	−	0.915449i	$-0.631836\pi$
$103$	−8.16853	−0.804869	−0.402434	+	0.915449i	$0.631836\pi$
$104$	0	0
$105$	0	0
$106$	−6.83471	−0.663845
$107$	−16.4079	−1.58621	−0.793104	−	0.609087i	$-0.791536\pi$
$107$	−16.4079	−1.58621	−0.793104	+	0.609087i	$0.791536\pi$
$108$	−5.04478	−0.485434
$109$	−5.96790	−0.571621	−0.285811	−	0.958286i	$-0.592263\pi$
$109$	−5.96790	−0.571621	−0.285811	+	0.958286i	$0.592263\pi$
$110$	−0.106259	−0.0101314
$111$	1.65189	0.156790
$112$	0	0
$113$	−16.9748	−1.59685	−0.798426	−	0.602093i	$-0.794334\pi$
$113$	−16.9748	−1.59685	−0.798426	+	0.602093i	$0.794334\pi$
$114$	2.35765	0.220814
$115$	0.818658	0.0763402
$116$	0.754305	0.0700354
$117$	0	0
$118$	10.1972	0.938730
$119$	0	0
$120$	−0.568789	−0.0519231
$121$	−10.7924	−0.981124
$122$	−1.39892	−0.126652
$123$	−5.38837	−0.485853
$124$	13.1776	1.18338
$125$	2.63960	0.236093
$126$	0	0
$127$	13.3247	1.18238	0.591188	−	0.806534i	$-0.298659\pi$
$127$	13.3247	1.18238	0.591188	+	0.806534i	$0.298659\pi$
$128$	−6.90382	−0.610218
$129$	−5.10955	−0.449870
$130$	0	0
$131$	15.2631	1.33355	0.666773	−	0.745260i	$-0.267675\pi$
$131$	15.2631	1.33355	0.666773	+	0.745260i	$0.267675\pi$
$132$	0.423345	0.0368474
$133$	0	0
$134$	−8.24495	−0.712255
$135$	−1.08987	−0.0938010
$136$	10.3633	0.888648
$137$	−13.6118	−1.16293	−0.581466	−	0.813571i	$-0.697521\pi$
$137$	−13.6118	−1.16293	−0.581466	+	0.813571i	$0.697521\pi$
$138$	2.03960	0.173622
$139$	14.3332	1.21573	0.607863	−	0.794042i	$-0.292027\pi$
$139$	14.3332	1.21573	0.607863	+	0.794042i	$0.292027\pi$
$140$	0	0
$141$	5.64585	0.475466
$142$	−6.05177	−0.507854
$143$	0	0
$144$	0.0602680	0.00502233
$145$	0.162959	0.0135330
$146$	2.50090	0.206976
$147$	0	0
$148$	2.69220	0.221297
$149$	19.6559	1.61027	0.805136	−	0.593090i	$-0.202092\pi$
$149$	19.6559	1.61027	0.805136	+	0.593090i	$0.202092\pi$
$150$	3.26474	0.266565
$151$	1.93740	0.157664	0.0788319	−	0.996888i	$-0.474881\pi$
$151$	1.93740	0.157664	0.0788319	+	0.996888i	$0.474881\pi$
$152$	10.0877	0.818218
$153$	8.88634	0.718418
$154$	0	0
$155$	2.84687	0.228666
$156$	0	0
$157$	24.7415	1.97458	0.987291	−	0.158920i	$-0.0508013\pi$
$157$	24.7415	1.97458	0.987291	+	0.158920i	$0.0508013\pi$
$158$	7.66191	0.609549
$159$	5.88275	0.466532
$160$	−1.50089	−0.118656
$161$	0	0
$162$	3.67936	0.289078
$163$	6.74233	0.528100	0.264050	−	0.964509i	$-0.414942\pi$
$163$	6.74233	0.528100	0.264050	+	0.964509i	$0.414942\pi$
$164$	−8.78181	−0.685744
$165$	0.0914589	0.00712006
$166$	−6.59418	−0.511808
$167$	2.06354	0.159681	0.0798407	−	0.996808i	$-0.474559\pi$
$167$	2.06354	0.159681	0.0798407	+	0.996808i	$0.474559\pi$
$168$	0	0
$169$	0	0
$170$	0.852798	0.0654066
$171$	8.64996	0.661479
$172$	−8.32738	−0.634957
$173$	−13.5227	−1.02811	−0.514057	−	0.857756i	$-0.671858\pi$
$173$	−13.5227	−1.02811	−0.514057	+	0.857756i	$0.671858\pi$
$174$	0.405995	0.0307784
$175$	0	0
$176$	−0.0113015	−0.000851886 0
$177$	−8.77692	−0.659714
$178$	7.39279	0.554113
$179$	−8.62973	−0.645017	−0.322508	−	0.946567i	$-0.604526\pi$
$179$	−8.62973	−0.645017	−0.322508	+	0.946567i	$0.604526\pi$
$180$	−0.794879	−0.0592468
$181$	−23.4579	−1.74361	−0.871806	−	0.489852i	$-0.837051\pi$
$181$	−23.4579	−1.74361	−0.871806	+	0.489852i	$0.837051\pi$
$182$	0	0
$183$	1.20407	0.0890075
$184$	8.72681	0.643349
$185$	0.581619	0.0427615
$186$	7.09266	0.520059
$187$	−1.66638	−0.121858
$188$	9.20143	0.671084
$189$	0	0
$190$	0.830114	0.0602228
$191$	17.1685	1.24227	0.621134	−	0.783705i	$-0.286672\pi$
$191$	17.1685	1.24227	0.621134	+	0.783705i	$0.286672\pi$
$192$	−3.77677	−0.272565
$193$	−16.1895	−1.16534	−0.582672	−	0.812707i	$-0.697993\pi$
$193$	−16.1895	−1.16534	−0.582672	+	0.812707i	$0.697993\pi$
$194$	−1.41510	−0.101598
$195$	0	0
$196$	0	0
$197$	−14.1272	−1.00652	−0.503262	−	0.864134i	$-0.667867\pi$
$197$	−14.1272	−1.00652	−0.503262	+	0.864134i	$0.667867\pi$
$198$	−0.971275	−0.0690255
$199$	13.7329	0.973499	0.486749	−	0.873542i	$-0.338183\pi$
$199$	13.7329	0.973499	0.486749	+	0.873542i	$0.338183\pi$
$200$	13.9688	0.987745
$201$	7.09657	0.500554
$202$	6.40155	0.450412
$203$	0	0
$204$	−3.39762	−0.237881
$205$	−1.89721	−0.132507
$206$	−7.16546	−0.499241
$207$	7.48306	0.520109
$208$	0	0
$209$	−1.62205	−0.112200
$210$	0	0
$211$	18.7380	1.28998	0.644988	−	0.764193i	$-0.276863\pi$
$211$	18.7380	1.28998	0.644988	+	0.764193i	$0.276863\pi$
$212$	9.58753	0.658474
$213$	5.20887	0.356906
$214$	−14.3930	−0.983886
$215$	−1.79904	−0.122693
$216$	−11.6179	−0.790497
$217$	0	0
$218$	−5.23506	−0.354563
$219$	−2.15257	−0.145457
$220$	0.149057	0.0100494
$221$	0	0
$222$	1.44904	0.0972533
$223$	−3.78482	−0.253450	−0.126725	−	0.991938i	$-0.540447\pi$
$223$	−3.78482	−0.253450	−0.126725	+	0.991938i	$0.540447\pi$
$224$	0	0
$225$	11.9780	0.798531
$226$	−14.8903	−0.990489
$227$	9.00380	0.597603	0.298802	−	0.954315i	$-0.403413\pi$
$227$	9.00380	0.597603	0.298802	+	0.954315i	$0.403413\pi$
$228$	−3.30724	−0.219028
$229$	1.08397	0.0716306	0.0358153	−	0.999358i	$-0.488597\pi$
$229$	1.08397	0.0716306	0.0358153	+	0.999358i	$0.488597\pi$
$230$	0.718129	0.0473520
$231$	0	0
$232$	1.73713	0.114048
$233$	−14.1071	−0.924186	−0.462093	−	0.886831i	$-0.652901\pi$
$233$	−14.1071	−0.924186	−0.462093	+	0.886831i	$0.652901\pi$
$234$	0	0
$235$	1.98787	0.129674
$236$	−14.3044	−0.931135
$237$	−6.59474	−0.428375
$238$	0	0
$239$	−18.9679	−1.22693	−0.613467	−	0.789721i	$-0.710225\pi$
$239$	−18.9679	−1.22693	−0.613467	+	0.789721i	$0.710225\pi$
$240$	−0.00497818	−0.000321340 0
$241$	25.1138	1.61772	0.808862	−	0.587999i	$-0.200084\pi$
$241$	25.1138	1.61772	0.808862	+	0.587999i	$0.200084\pi$
$242$	−9.46710	−0.608568
$243$	−15.4661	−0.992150
$244$	1.96236	0.125627
$245$	0	0
$246$	−4.72670	−0.301363
$247$	0	0
$248$	30.3473	1.92706
$249$	5.67572	0.359684
$250$	2.31547	0.146443
$251$	−21.2412	−1.34073	−0.670367	−	0.742030i	$-0.733863\pi$
$251$	−21.2412	−1.34073	−0.670367	+	0.742030i	$0.733863\pi$
$252$	0	0
$253$	−1.40323	−0.0882206
$254$	11.6885	0.733399
$255$	−0.734018	−0.0459660
$256$	−16.0604	−1.00378
$257$	25.3217	1.57952	0.789762	−	0.613413i	$-0.210204\pi$
$257$	25.3217	1.57952	0.789762	+	0.613413i	$0.210204\pi$
$258$	−4.48211	−0.279044
$259$	0	0
$260$	0	0
$261$	1.48955	0.0922009
$262$	13.3889	0.827167
$263$	10.4189	0.642458	0.321229	−	0.947002i	$-0.395904\pi$
$263$	10.4189	0.642458	0.321229	+	0.947002i	$0.395904\pi$
$264$	0.974943	0.0600036
$265$	2.07128	0.127238
$266$	0	0
$267$	−6.36310	−0.389416
$268$	11.5658	0.706492
$269$	29.5305	1.80051	0.900254	−	0.435365i	$-0.143381\pi$
$269$	29.5305	1.80051	0.900254	+	0.435365i	$0.143381\pi$
$270$	−0.956036	−0.0581825
$271$	25.4321	1.54489	0.772446	−	0.635081i	$-0.219033\pi$
$271$	25.4321	1.54489	0.772446	+	0.635081i	$0.219033\pi$
$272$	0.0907024	0.00549964
$273$	0	0
$274$	−11.9403	−0.721339
$275$	−2.24613	−0.135447
$276$	−2.86109	−0.172217
$277$	11.4076	0.685416	0.342708	−	0.939442i	$-0.388656\pi$
$277$	11.4076	0.685416	0.342708	+	0.939442i	$0.388656\pi$
$278$	12.5731	0.754086
$279$	26.0222	1.55791
$280$	0	0
$281$	11.9773	0.714507	0.357253	−	0.934008i	$-0.383713\pi$
$281$	11.9773	0.714507	0.357253	+	0.934008i	$0.383713\pi$
$282$	4.95255	0.294920
$283$	2.32905	0.138448	0.0692239	−	0.997601i	$-0.477948\pi$
$283$	2.32905	0.138448	0.0692239	+	0.997601i	$0.477948\pi$
$284$	8.48925	0.503745
$285$	−0.714493	−0.0423229
$286$	0	0
$287$	0	0
$288$	−13.7191	−0.808408
$289$	−3.62619	−0.213305
$290$	0.142948	0.00839421
$291$	1.21800	0.0714004
$292$	−3.50820	−0.205302
$293$	29.8421	1.74339	0.871696	−	0.490047i	$-0.163021\pi$
$293$	29.8421	1.74339	0.871696	+	0.490047i	$0.163021\pi$
$294$	0	0
$295$	−3.09030	−0.179924
$296$	6.20000	0.360368
$297$	1.86811	0.108399
$298$	17.2422	0.998813
$299$	0	0
$300$	−4.57968	−0.264408
$301$	0	0
$302$	1.69950	0.0977950
$303$	−5.50993	−0.316537
$304$	0.0882897	0.00506376
$305$	0.423946	0.0242750
$306$	7.79512	0.445618
$307$	13.3825	0.763780	0.381890	−	0.924208i	$-0.375273\pi$
$307$	13.3825	0.763780	0.381890	+	0.924208i	$0.375273\pi$
$308$	0	0
$309$	6.16743	0.350853
$310$	2.49728	0.141836
$311$	−20.2744	−1.14966	−0.574828	−	0.818275i	$-0.694931\pi$
$311$	−20.2744	−1.14966	−0.574828	+	0.818275i	$0.694931\pi$
$312$	0	0
$313$	1.18573	0.0670215	0.0335107	−	0.999438i	$-0.489331\pi$
$313$	1.18573	0.0670215	0.0335107	+	0.999438i	$0.489331\pi$
$314$	21.7033	1.22479
$315$	0	0
$316$	−10.7479	−0.604617
$317$	3.81328	0.214175	0.107087	−	0.994250i	$-0.465848\pi$
$317$	3.81328	0.214175	0.107087	+	0.994250i	$0.465848\pi$
$318$	5.16036	0.289379
$319$	−0.279323	−0.0156391
$320$	−1.32978	−0.0743367
$321$	12.3883	0.691448
$322$	0	0
$323$	13.0181	0.724344
$324$	−5.16130	−0.286739
$325$	0	0
$326$	5.91439	0.327568
$327$	4.50591	0.249177
$328$	−20.2241	−1.11669
$329$	0	0
$330$	0.0802280	0.00441641
$331$	9.78226	0.537682	0.268841	−	0.963185i	$-0.413359\pi$
$331$	9.78226	0.537682	0.268841	+	0.963185i	$0.413359\pi$
$332$	9.25013	0.507667
$333$	5.31637	0.291335
$334$	1.81014	0.0990466
$335$	2.49866	0.136516
$336$	0	0
$337$	−7.21841	−0.393212	−0.196606	−	0.980483i	$-0.562992\pi$
$337$	−7.21841	−0.393212	−0.196606	+	0.980483i	$0.562992\pi$
$338$	0	0
$339$	12.8164	0.696089
$340$	−1.19628	−0.0648775
$341$	−4.87972	−0.264252
$342$	7.58777	0.410300
$343$	0	0
$344$	−19.1776	−1.03399
$345$	−0.618106	−0.0332777
$346$	−11.8622	−0.637714
$347$	14.8788	0.798736	0.399368	−	0.916791i	$-0.369230\pi$
$347$	14.8788	0.798736	0.399368	+	0.916791i	$0.369230\pi$
$348$	−0.569518	−0.0305294
$349$	6.61098	0.353878	0.176939	−	0.984222i	$-0.443380\pi$
$349$	6.61098	0.353878	0.176939	+	0.984222i	$0.443380\pi$
$350$	0	0
$351$	0	0
$352$	2.57263	0.137122
$353$	35.3388	1.88089	0.940447	−	0.339939i	$-0.110407\pi$
$353$	35.3388	1.88089	0.940447	+	0.339939i	$0.110407\pi$
$354$	−7.69914	−0.409205
$355$	1.83401	0.0973391
$356$	−10.3704	−0.549630
$357$	0	0
$358$	−7.57003	−0.400088
$359$	−14.0258	−0.740252	−0.370126	−	0.928981i	$-0.620686\pi$
$359$	−14.0258	−0.740252	−0.370126	+	0.928981i	$0.620686\pi$
$360$	−1.83057	−0.0964794
$361$	−6.32822	−0.333064
$362$	−20.5773	−1.08152
$363$	8.14849	0.427685
$364$	0	0
$365$	−0.757907	−0.0396707
$366$	1.05621	0.0552092
$367$	−25.3700	−1.32430	−0.662152	−	0.749369i	$-0.730357\pi$
$367$	−25.3700	−1.32430	−0.662152	+	0.749369i	$0.730357\pi$
$368$	0.0763792	0.00398154
$369$	−17.3417	−0.902774
$370$	0.510198	0.0265239
$371$	0	0
$372$	−9.94938	−0.515851
$373$	18.2160	0.943188	0.471594	−	0.881816i	$-0.343679\pi$
$373$	18.2160	0.943188	0.471594	+	0.881816i	$0.343679\pi$
$374$	−1.46175	−0.0755855
$375$	−1.99296	−0.102916
$376$	21.1905	1.09281
$377$	0	0
$378$	0	0
$379$	7.24143	0.371968	0.185984	−	0.982553i	$-0.440453\pi$
$379$	7.24143	0.371968	0.185984	+	0.982553i	$0.440453\pi$
$380$	−1.16446	−0.0597355
$381$	−10.0605	−0.515413
$382$	15.0602	0.770549
$383$	−0.367176	−0.0187618	−0.00938091	−	0.999956i	$-0.502986\pi$
$383$	−0.367176	−0.0187618	−0.00938091	+	0.999956i	$0.502986\pi$
$384$	5.21255	0.266002
$385$	0	0
$386$	−14.2015	−0.722835
$387$	−16.4444	−0.835914
$388$	1.98506	0.100776
$389$	11.1560	0.565631	0.282815	−	0.959174i	$-0.408732\pi$
$389$	11.1560	0.565631	0.282815	+	0.959174i	$0.408732\pi$
$390$	0	0
$391$	11.2619	0.569538
$392$	0	0
$393$	−11.5240	−0.581311
$394$	−12.3924	−0.624322
$395$	−2.32197	−0.116831
$396$	1.36248	0.0684670
$397$	3.17876	0.159537	0.0797686	−	0.996813i	$-0.474582\pi$
$397$	3.17876	0.159537	0.0797686	+	0.996813i	$0.474582\pi$
$398$	12.0465	0.603838
$399$	0	0
$400$	0.122258	0.00611292
$401$	8.09236	0.404113	0.202057	−	0.979374i	$-0.435237\pi$
$401$	8.09236	0.404113	0.202057	+	0.979374i	$0.435237\pi$
$402$	6.22513	0.310481
$403$	0	0
$404$	−8.97992	−0.446767
$405$	−1.11504	−0.0554068
$406$	0	0
$407$	−0.996934	−0.0494162
$408$	−7.82456	−0.387374
$409$	3.13028	0.154783	0.0773913	−	0.997001i	$-0.475341\pi$
$409$	3.13028	0.154783	0.0773913	+	0.997001i	$0.475341\pi$
$410$	−1.66424	−0.0821909
$411$	10.2772	0.506937
$412$	10.0515	0.495202
$413$	0	0
$414$	6.56416	0.322611
$415$	1.99839	0.0980969
$416$	0	0
$417$	−10.8219	−0.529951
$418$	−1.42287	−0.0695949
$419$	11.4655	0.560128	0.280064	−	0.959981i	$-0.409644\pi$
$419$	11.4655	0.560128	0.280064	+	0.959981i	$0.409644\pi$
$420$	0	0
$421$	22.1642	1.08022	0.540108	−	0.841596i	$-0.318383\pi$
$421$	22.1642	1.08022	0.540108	+	0.841596i	$0.318383\pi$
$422$	16.4370	0.800141
$423$	18.1704	0.883474
$424$	22.0796	1.07228
$425$	18.0267	0.874422
$426$	4.56923	0.221380
$427$	0	0
$428$	20.1901	0.975926
$429$	0	0
$430$	−1.57812	−0.0761038
$431$	−21.3135	−1.02664	−0.513319	−	0.858198i	$-0.671584\pi$
$431$	−21.3135	−1.02664	−0.513319	+	0.858198i	$0.671584\pi$
$432$	−0.101683	−0.00489221
$433$	0.0447167	0.00214895	0.00107447	−	0.999999i	$-0.499658\pi$
$433$	0.0447167	0.00214895	0.00107447	+	0.999999i	$0.499658\pi$
$434$	0	0
$435$	−0.123038	−0.00589922
$436$	7.34359	0.351694
$437$	10.9623	0.524399
$438$	−1.88824	−0.0902237
$439$	−3.32925	−0.158896	−0.0794481	−	0.996839i	$-0.525316\pi$
$439$	−3.32925	−0.158896	−0.0794481	+	0.996839i	$0.525316\pi$
$440$	0.343271	0.0163648
$441$	0	0
$442$	0	0
$443$	30.4552	1.44697	0.723485	−	0.690340i	$-0.242539\pi$
$443$	30.4552	1.44697	0.723485	+	0.690340i	$0.242539\pi$
$444$	−2.03267	−0.0964664
$445$	−2.24041	−0.106206
$446$	−3.32006	−0.157209
$447$	−14.8407	−0.701939
$448$	0	0
$449$	−6.77363	−0.319667	−0.159834	−	0.987144i	$-0.551096\pi$
$449$	−6.77363	−0.319667	−0.159834	+	0.987144i	$0.551096\pi$
$450$	10.5071	0.495310
$451$	3.25195	0.153128
$452$	20.8877	0.982475
$453$	−1.46279	−0.0687277
$454$	7.89816	0.370679
$455$	0	0
$456$	−7.61643	−0.356672
$457$	32.1702	1.50486	0.752430	−	0.658672i	$-0.228882\pi$
$457$	32.1702	1.50486	0.752430	+	0.658672i	$0.228882\pi$
$458$	0.950859	0.0444307
$459$	−14.9928	−0.699805
$460$	−1.00737	−0.0469689
$461$	−24.4018	−1.13651	−0.568253	−	0.822854i	$-0.692380\pi$
$461$	−24.4018	−1.13651	−0.568253	+	0.822854i	$0.692380\pi$
$462$	0	0
$463$	−23.4370	−1.08921	−0.544604	−	0.838693i	$-0.683320\pi$
$463$	−23.4370	−1.08921	−0.544604	+	0.838693i	$0.683320\pi$
$464$	0.0152038	0.000705817 0
$465$	−2.14945	−0.0996785
$466$	−12.3748	−0.573251
$467$	−27.8751	−1.28990	−0.644952	−	0.764223i	$-0.723123\pi$
$467$	−27.8751	−1.28990	−0.644952	+	0.764223i	$0.723123\pi$
$468$	0	0
$469$	0	0
$470$	1.74376	0.0804338
$471$	−18.6804	−0.860747
$472$	−32.9423	−1.51629
$473$	3.08367	0.141787
$474$	−5.78493	−0.265710
$475$	17.5472	0.805119
$476$	0	0
$477$	18.9328	0.866874
$478$	−16.6387	−0.761037
$479$	2.07202	0.0946729	0.0473365	−	0.998879i	$-0.484927\pi$
$479$	2.07202	0.0946729	0.0473365	+	0.998879i	$0.484927\pi$
$480$	1.13321	0.0517238
$481$	0	0
$482$	22.0299	1.00343
$483$	0	0
$484$	13.2802	0.603644
$485$	0.428850	0.0194731
$486$	−13.5669	−0.615407
$487$	6.01962	0.272775	0.136388	−	0.990656i	$-0.456451\pi$
$487$	6.01962	0.272775	0.136388	+	0.990656i	$0.456451\pi$
$488$	4.51922	0.204575
$489$	−5.09062	−0.230206
$490$	0	0
$491$	2.01551	0.0909588	0.0454794	−	0.998965i	$-0.485518\pi$
$491$	2.01551	0.0909588	0.0454794	+	0.998965i	$0.485518\pi$
$492$	6.63047	0.298925
$493$	2.24175	0.100963
$494$	0	0
$495$	0.294348	0.0132299
$496$	0.265607	0.0119261
$497$	0	0
$498$	4.97876	0.223104
$499$	−7.51174	−0.336272	−0.168136	−	0.985764i	$-0.553775\pi$
$499$	−7.51174	−0.336272	−0.168136	+	0.985764i	$0.553775\pi$
$500$	−3.24807	−0.145258
$501$	−1.55802	−0.0696072
$502$	−18.6329	−0.831625
$503$	−15.1154	−0.673962	−0.336981	−	0.941511i	$-0.609406\pi$
$503$	−15.1154	−0.673962	−0.336981	+	0.941511i	$0.609406\pi$
$504$	0	0
$505$	−1.94001	−0.0863293
$506$	−1.23092	−0.0547211
$507$	0	0
$508$	−16.3962	−0.727466
$509$	36.6699	1.62537	0.812683	−	0.582706i	$-0.198006\pi$
$509$	36.6699	1.62537	0.812683	+	0.582706i	$0.198006\pi$
$510$	−0.643883	−0.0285116
$511$	0	0
$512$	−0.280601	−0.0124009
$513$	−14.5940	−0.644341
$514$	22.2123	0.979742
$515$	2.17151	0.0956883
$516$	6.28737	0.276786
$517$	−3.40734	−0.149855
$518$	0	0
$519$	10.2100	0.448168
$520$	0	0
$521$	−31.8083	−1.39355	−0.696774	−	0.717291i	$-0.745382\pi$
$521$	−31.8083	−1.39355	−0.696774	+	0.717291i	$0.745382\pi$
$522$	1.30664	0.0571900
$523$	−39.5596	−1.72982	−0.864909	−	0.501928i	$-0.832624\pi$
$523$	−39.5596	−1.72982	−0.864909	+	0.501928i	$0.832624\pi$
$524$	−18.7815	−0.820475
$525$	0	0
$526$	9.13951	0.398501
$527$	39.1630	1.70597
$528$	0.00853293	0.000371348 0
$529$	−13.5165	−0.587675
$530$	1.81693	0.0789224
$531$	−28.2473	−1.22583
$532$	0	0
$533$	0	0
$534$	−5.58173	−0.241545
$535$	4.36185	0.188579
$536$	26.6354	1.15048
$537$	6.51565	0.281171
$538$	25.9043	1.11681
$539$	0	0
$540$	1.34110	0.0577118
$541$	22.2284	0.955673	0.477836	−	0.878449i	$-0.341421\pi$
$541$	22.2284	0.955673	0.477836	+	0.878449i	$0.341421\pi$
$542$	22.3091	0.958259
$543$	17.7113	0.760063
$544$	−20.6471	−0.885237
$545$	1.58650	0.0679582
$546$	0	0
$547$	−14.1989	−0.607100	−0.303550	−	0.952816i	$-0.598172\pi$
$547$	−14.1989	−0.607100	−0.303550	+	0.952816i	$0.598172\pi$
$548$	16.7495	0.715503
$549$	3.87513	0.165387
$550$	−1.97031	−0.0840143
$551$	2.18212	0.0929615
$552$	−6.58895	−0.280444
$553$	0	0
$554$	10.0068	0.425147
$555$	−0.439136	−0.0186403
$556$	−17.6372	−0.747985
$557$	26.6179	1.12784	0.563918	−	0.825831i	$-0.309293\pi$
$557$	26.6179	1.12784	0.563918	+	0.825831i	$0.309293\pi$
$558$	22.8267	0.966333
$559$	0	0
$560$	0	0
$561$	1.25816	0.0531194
$562$	10.5065	0.443191
$563$	−20.9514	−0.882996	−0.441498	−	0.897262i	$-0.645553\pi$
$563$	−20.9514	−0.882996	−0.441498	+	0.897262i	$0.645553\pi$
$564$	−6.94730	−0.292534
$565$	4.51256	0.189845
$566$	2.04305	0.0858759
$567$	0	0
$568$	19.5503	0.820314
$569$	−1.12515	−0.0471686	−0.0235843	−	0.999722i	$-0.507508\pi$
$569$	−1.12515	−0.0471686	−0.0235843	+	0.999722i	$0.507508\pi$
$570$	−0.626755	−0.0262519
$571$	−41.6288	−1.74211	−0.871055	−	0.491185i	$-0.836564\pi$
$571$	−41.6288	−1.74211	−0.871055	+	0.491185i	$0.836564\pi$
$572$	0	0
$573$	−12.9626	−0.541521
$574$	0	0
$575$	15.1800	0.633049
$576$	−12.1550	−0.506459
$577$	−29.4246	−1.22496	−0.612481	−	0.790485i	$-0.709829\pi$
$577$	−29.4246	−1.22496	−0.612481	+	0.790485i	$0.709829\pi$
$578$	−3.18090	−0.132308
$579$	12.2234	0.507989
$580$	−0.200524	−0.00832629
$581$	0	0
$582$	1.06843	0.0442879
$583$	−3.55031	−0.147039
$584$	−8.07921	−0.334320
$585$	0	0
$586$	26.1775	1.08138
$587$	36.0961	1.48985	0.744923	−	0.667150i	$-0.232486\pi$
$587$	36.0961	1.48985	0.744923	+	0.667150i	$0.232486\pi$
$588$	0	0
$589$	38.1213	1.57076
$590$	−2.71082	−0.111603
$591$	10.6664	0.438757
$592$	0.0542639	0.00223023
$593$	4.07766	0.167449	0.0837246	−	0.996489i	$-0.473318\pi$
$593$	4.07766	0.167449	0.0837246	+	0.996489i	$0.473318\pi$
$594$	1.63871	0.0672371
$595$	0	0
$596$	−24.1869	−0.990732
$597$	−10.3687	−0.424361
$598$	0	0
$599$	−25.3993	−1.03779	−0.518894	−	0.854839i	$-0.673656\pi$
$599$	−25.3993	−1.03779	−0.518894	+	0.854839i	$0.673656\pi$
$600$	−10.5468	−0.430571
$601$	−43.4761	−1.77343	−0.886713	−	0.462321i	$-0.847017\pi$
$601$	−43.4761	−1.77343	−0.886713	+	0.462321i	$0.847017\pi$
$602$	0	0
$603$	22.8393	0.930089
$604$	−2.38401	−0.0970038
$605$	2.86903	0.116643
$606$	−4.83332	−0.196340
$607$	−18.2340	−0.740094	−0.370047	−	0.929013i	$-0.620658\pi$
$607$	−18.2340	−0.740094	−0.370047	+	0.929013i	$0.620658\pi$
$608$	−20.0979	−0.815077
$609$	0	0
$610$	0.371886	0.0150572
$611$	0	0
$612$	−10.9348	−0.442012
$613$	−32.2272	−1.30165	−0.650823	−	0.759230i	$-0.725576\pi$
$613$	−32.2272	−1.30165	−0.650823	+	0.759230i	$0.725576\pi$
$614$	11.7392	0.473755
$615$	1.43244	0.0577615
$616$	0	0
$617$	−37.0753	−1.49260	−0.746298	−	0.665612i	$-0.768170\pi$
$617$	−37.0753	−1.49260	−0.746298	+	0.665612i	$0.768170\pi$
$618$	5.41009	0.217626
$619$	33.8527	1.36066	0.680328	−	0.732908i	$-0.261837\pi$
$619$	33.8527	1.36066	0.680328	+	0.732908i	$0.261837\pi$
$620$	−3.50311	−0.140688
$621$	−12.6252	−0.506633
$622$	−17.7848	−0.713104
$623$	0	0
$624$	0	0
$625$	23.9449	0.957798
$626$	1.04013	0.0415718
$627$	1.22469	0.0489094
$628$	−30.4447	−1.21488
$629$	8.00106	0.319023
$630$	0	0
$631$	−33.2239	−1.32262	−0.661311	−	0.750111i	$-0.730000\pi$
$631$	−33.2239	−1.32262	−0.661311	+	0.750111i	$0.730000\pi$
$632$	−24.7519	−0.984579
$633$	−14.1476	−0.562317
$634$	3.34502	0.132848
$635$	−3.54222	−0.140569
$636$	−7.23881	−0.287038
$637$	0	0
$638$	−0.245023	−0.00970055
$639$	16.7640	0.663174
$640$	1.83531	0.0725468
$641$	−11.8377	−0.467561	−0.233780	−	0.972289i	$-0.575110\pi$
$641$	−11.8377	−0.467561	−0.233780	+	0.972289i	$0.575110\pi$
$642$	10.8671	0.428889
$643$	40.1562	1.58360	0.791802	−	0.610778i	$-0.209143\pi$
$643$	40.1562	1.58360	0.791802	+	0.610778i	$0.209143\pi$
$644$	0	0
$645$	1.35832	0.0534837
$646$	11.4195	0.449294
$647$	3.17699	0.124900	0.0624501	−	0.998048i	$-0.480109\pi$
$647$	3.17699	0.124900	0.0624501	+	0.998048i	$0.480109\pi$
$648$	−11.8862	−0.466935
$649$	5.29698	0.207925
$650$	0	0
$651$	0	0
$652$	−8.29654	−0.324918
$653$	30.6776	1.20051	0.600253	−	0.799810i	$-0.295067\pi$
$653$	30.6776	1.20051	0.600253	+	0.799810i	$0.295067\pi$
$654$	3.95259	0.154559
$655$	−4.05754	−0.158541
$656$	−0.177006	−0.00691093
$657$	−6.92775	−0.270277
$658$	0	0
$659$	−8.19638	−0.319286	−0.159643	−	0.987175i	$-0.551034\pi$
$659$	−8.19638	−0.319286	−0.159643	+	0.987175i	$0.551034\pi$
$660$	−0.112542	−0.00438067
$661$	30.8005	1.19800	0.599000	−	0.800749i	$-0.295565\pi$
$661$	30.8005	1.19800	0.599000	+	0.800749i	$0.295565\pi$
$662$	8.58102	0.333511
$663$	0	0
$664$	21.3026	0.826701
$665$	0	0
$666$	4.66354	0.180708
$667$	1.88775	0.0730938
$668$	−2.53922	−0.0982452
$669$	2.85763	0.110482
$670$	2.19183	0.0846778
$671$	−0.726671	−0.0280528
$672$	0	0
$673$	−29.7292	−1.14598	−0.572988	−	0.819564i	$-0.694216\pi$
$673$	−29.7292	−1.14598	−0.572988	+	0.819564i	$0.694216\pi$
$674$	−6.33201	−0.243900
$675$	−20.2089	−0.777842
$676$	0	0
$677$	−27.8067	−1.06870	−0.534349	−	0.845264i	$-0.679443\pi$
$677$	−27.8067	−1.06870	−0.534349	+	0.845264i	$0.679443\pi$
$678$	11.2425	0.431767
$679$	0	0
$680$	−2.75498	−0.105649
$681$	−6.79808	−0.260503
$682$	−4.28051	−0.163909
$683$	13.8232	0.528929	0.264465	−	0.964395i	$-0.414805\pi$
$683$	13.8232	0.528929	0.264465	+	0.964395i	$0.414805\pi$
$684$	−10.6439	−0.406980
$685$	3.61854	0.138257
$686$	0	0
$687$	−0.818421	−0.0312247
$688$	−0.167847	−0.00639910
$689$	0	0
$690$	−0.542204	−0.0206414
$691$	−2.04187	−0.0776762	−0.0388381	−	0.999246i	$-0.512366\pi$
$691$	−2.04187	−0.0776762	−0.0388381	+	0.999246i	$0.512366\pi$
$692$	16.6399	0.632555
$693$	0	0
$694$	13.0517	0.495437
$695$	−3.81032	−0.144534
$696$	−1.31157	−0.0497150
$697$	−26.0990	−0.988572
$698$	5.79917	0.219502
$699$	10.6512	0.402865
$700$	0	0
$701$	−27.0161	−1.02039	−0.510193	−	0.860060i	$-0.670426\pi$
$701$	−27.0161	−1.02039	−0.510193	+	0.860060i	$0.670426\pi$
$702$	0	0
$703$	7.78823	0.293739
$704$	2.27933	0.0859053
$705$	−1.50089	−0.0565267
$706$	30.9993	1.16667
$707$	0	0
$708$	10.8001	0.405894
$709$	−2.83830	−0.106595	−0.0532973	−	0.998579i	$-0.516973\pi$
$709$	−2.83830	−0.106595	−0.0532973	+	0.998579i	$0.516973\pi$
$710$	1.60880	0.0603771
$711$	−21.2243	−0.795972
$712$	−23.8825	−0.895035
$713$	32.9786	1.23506
$714$	0	0
$715$	0	0
$716$	10.6190	0.396851
$717$	14.3212	0.534836
$718$	−12.3035	−0.459161
$719$	39.2389	1.46336	0.731682	−	0.681646i	$-0.238736\pi$
$719$	39.2389	1.46336	0.731682	+	0.681646i	$0.238736\pi$
$720$	−0.0160216	−0.000597089 0
$721$	0	0
$722$	−5.55113	−0.206592
$723$	−18.9615	−0.705187
$724$	28.8653	1.07277
$725$	3.02168	0.112222
$726$	7.14788	0.265283
$727$	12.9172	0.479074	0.239537	−	0.970887i	$-0.423004\pi$
$727$	12.9172	0.479074	0.239537	+	0.970887i	$0.423004\pi$
$728$	0	0
$729$	−0.906005	−0.0335558
$730$	−0.664838	−0.0246068
$731$	−24.7485	−0.915357
$732$	−1.48163	−0.0547625
$733$	−7.21963	−0.266663	−0.133332	−	0.991071i	$-0.542568\pi$
$733$	−7.21963	−0.266663	−0.133332	+	0.991071i	$0.542568\pi$
$734$	−22.2547	−0.821434
$735$	0	0
$736$	−17.3866	−0.640879
$737$	−4.28287	−0.157761
$738$	−15.2122	−0.559969
$739$	24.4029	0.897677	0.448838	−	0.893613i	$-0.351838\pi$
$739$	24.4029	0.897677	0.448838	+	0.893613i	$0.351838\pi$
$740$	−0.715691	−0.0263093
$741$	0	0
$742$	0	0
$743$	43.6054	1.59973	0.799864	−	0.600182i	$-0.204905\pi$
$743$	43.6054	1.59973	0.799864	+	0.600182i	$0.204905\pi$
$744$	−22.9129	−0.840029
$745$	−5.22530	−0.191440
$746$	15.9791	0.585037
$747$	18.2665	0.668338
$748$	2.05051	0.0749739
$749$	0	0
$750$	−1.74823	−0.0638364
$751$	0.527048	0.0192322	0.00961612	−	0.999954i	$-0.496939\pi$
$751$	0.527048	0.0192322	0.00961612	+	0.999954i	$0.496939\pi$
$752$	0.185464	0.00676318
$753$	16.0376	0.584444
$754$	0	0
$755$	−0.515038	−0.0187441
$756$	0	0
$757$	−17.4591	−0.634563	−0.317282	−	0.948331i	$-0.602770\pi$
$757$	−17.4591	−0.634563	−0.317282	+	0.948331i	$0.602770\pi$
$758$	6.35221	0.230723
$759$	1.05948	0.0384565
$760$	−2.68169	−0.0972753
$761$	−36.3311	−1.31700	−0.658501	−	0.752580i	$-0.728809\pi$
$761$	−36.3311	−1.31700	−0.658501	+	0.752580i	$0.728809\pi$
$762$	−8.82507	−0.319698
$763$	0	0
$764$	−21.1261	−0.764314
$765$	−2.36234	−0.0854104
$766$	−0.322088	−0.0116375
$767$	0	0
$768$	12.1260	0.437559
$769$	−30.7750	−1.10977	−0.554887	−	0.831926i	$-0.687239\pi$
$769$	−30.7750	−1.10977	−0.554887	+	0.831926i	$0.687239\pi$
$770$	0	0
$771$	−19.1185	−0.688536
$772$	19.9214	0.716987
$773$	29.6721	1.06723	0.533616	−	0.845727i	$-0.320833\pi$
$773$	29.6721	1.06723	0.533616	+	0.845727i	$0.320833\pi$
$774$	−14.4250	−0.518497
$775$	52.7881	1.89621
$776$	4.57149	0.164107
$777$	0	0
$778$	9.78606	0.350847
$779$	−25.4048	−0.910221
$780$	0	0
$781$	−3.14361	−0.112487
$782$	9.87896	0.353271
$783$	−2.51313	−0.0898120
$784$	0	0
$785$	−6.57724	−0.234752
$786$	−10.1089	−0.360573
$787$	−27.5755	−0.982959	−0.491479	−	0.870889i	$-0.663544\pi$
$787$	−27.5755	−0.982959	−0.491479	+	0.870889i	$0.663544\pi$
$788$	17.3838	0.619271
$789$	−7.86653	−0.280056
$790$	−2.03684	−0.0724674
$791$	0	0
$792$	3.13772	0.111494
$793$	0	0
$794$	2.78842	0.0989572
$795$	−1.56386	−0.0554645
$796$	−16.8985	−0.598952
$797$	−15.4319	−0.546627	−0.273314	−	0.961925i	$-0.588120\pi$
$797$	−15.4319	−0.546627	−0.273314	+	0.961925i	$0.588120\pi$
$798$	0	0
$799$	27.3461	0.967437
$800$	−27.8304	−0.983953
$801$	−20.4788	−0.723582
$802$	7.09864	0.250662
$803$	1.29910	0.0458444
$804$	−8.73244	−0.307969
$805$	0	0
$806$	0	0
$807$	−22.2962	−0.784865
$808$	−20.6803	−0.727531
$809$	6.45513	0.226950	0.113475	−	0.993541i	$-0.463802\pi$
$809$	6.45513	0.226950	0.113475	+	0.993541i	$0.463802\pi$
$810$	−0.978117	−0.0343675
$811$	−21.6726	−0.761027	−0.380513	−	0.924775i	$-0.624253\pi$
$811$	−21.6726	−0.761027	−0.380513	+	0.924775i	$0.624253\pi$
$812$	0	0
$813$	−19.2019	−0.673438
$814$	−0.874514	−0.0306517
$815$	−1.79238	−0.0627842
$816$	−0.0684825	−0.00239737
$817$	−24.0902	−0.842810
$818$	2.74589	0.0960079
$819$	0	0
$820$	2.33455	0.0815259
$821$	−24.7869	−0.865068	−0.432534	−	0.901618i	$-0.642380\pi$
$821$	−24.7869	−0.865068	−0.432534	+	0.901618i	$0.642380\pi$
$822$	9.01520	0.314441
$823$	−12.1129	−0.422230	−0.211115	−	0.977461i	$-0.567709\pi$
$823$	−12.1129	−0.422230	−0.211115	+	0.977461i	$0.567709\pi$
$824$	23.1481	0.806403
$825$	1.69588	0.0590430
$826$	0	0
$827$	44.8946	1.56114	0.780569	−	0.625069i	$-0.214929\pi$
$827$	44.8946	1.56114	0.780569	+	0.625069i	$0.214929\pi$
$828$	−9.20802	−0.320001
$829$	−1.74161	−0.0604885	−0.0302443	−	0.999543i	$-0.509629\pi$
$829$	−1.74161	−0.0604885	−0.0302443	+	0.999543i	$0.509629\pi$
$830$	1.75299	0.0608472
$831$	−8.61300	−0.298782
$832$	0	0
$833$	0	0
$834$	−9.49301	−0.328716
$835$	−0.548569	−0.0189840
$836$	1.99596	0.0690318
$837$	−43.9040	−1.51754
$838$	10.0576	0.347434
$839$	−6.96538	−0.240472	−0.120236	−	0.992745i	$-0.538365\pi$
$839$	−6.96538	−0.240472	−0.120236	+	0.992745i	$0.538365\pi$
$840$	0	0
$841$	−28.6242	−0.987042
$842$	19.4425	0.670033
$843$	−9.04316	−0.311463
$844$	−23.0574	−0.793667
$845$	0	0
$846$	15.9391	0.547998
$847$	0	0
$848$	0.193246	0.00663610
$849$	−1.75849	−0.0603512
$850$	15.8130	0.542383
$851$	6.73758	0.230961
$852$	−6.40959	−0.219589
$853$	10.5953	0.362774	0.181387	−	0.983412i	$-0.441941\pi$
$853$	10.5953	0.362774	0.181387	+	0.983412i	$0.441941\pi$
$854$	0	0
$855$	−2.29950	−0.0786412
$856$	46.4969	1.58923
$857$	−18.4590	−0.630548	−0.315274	−	0.949001i	$-0.602096\pi$
$857$	−18.4590	−0.630548	−0.315274	+	0.949001i	$0.602096\pi$
$858$	0	0
$859$	−38.9766	−1.32986	−0.664932	−	0.746904i	$-0.731540\pi$
$859$	−38.9766	−1.32986	−0.664932	+	0.746904i	$0.731540\pi$
$860$	2.21374	0.0754880
$861$	0	0
$862$	−18.6963	−0.636799
$863$	4.16284	0.141705	0.0708524	−	0.997487i	$-0.477428\pi$
$863$	4.16284	0.141705	0.0708524	+	0.997487i	$0.477428\pi$
$864$	23.1466	0.787463
$865$	3.59487	0.122229
$866$	0.0392256	0.00133294
$867$	2.73786	0.0929825
$868$	0	0
$869$	3.98001	0.135012
$870$	−0.107929	−0.00365914
$871$	0	0
$872$	16.9119	0.572711
$873$	3.91996	0.132671
$874$	9.61618	0.325272
$875$	0	0
$876$	2.64877	0.0894937
$877$	3.57332	0.120662	0.0603312	−	0.998178i	$-0.480784\pi$
$877$	3.57332	0.120662	0.0603312	+	0.998178i	$0.480784\pi$
$878$	−2.92042	−0.0985595
$879$	−22.5315	−0.759967
$880$	0.00300439	0.000101278 0
$881$	−21.4938	−0.724144	−0.362072	−	0.932150i	$-0.617931\pi$
$881$	−21.4938	−0.724144	−0.362072	+	0.932150i	$0.617931\pi$
$882$	0	0
$883$	7.48321	0.251830	0.125915	−	0.992041i	$-0.459813\pi$
$883$	7.48321	0.251830	0.125915	+	0.992041i	$0.459813\pi$
$884$	0	0
$885$	2.33325	0.0784313
$886$	26.7154	0.897521
$887$	29.4870	0.990076	0.495038	−	0.868871i	$-0.335154\pi$
$887$	29.4870	0.990076	0.495038	+	0.868871i	$0.335154\pi$
$888$	−4.68115	−0.157089
$889$	0	0
$890$	−1.96529	−0.0658767
$891$	1.91126	0.0640295
$892$	4.65728	0.155937
$893$	26.6187	0.890762
$894$	−13.0183	−0.435396
$895$	2.29412	0.0766840
$896$	0	0
$897$	0	0
$898$	−5.94185	−0.198282
$899$	6.56460	0.218942
$900$	−14.7391	−0.491303
$901$	28.4936	0.949259
$902$	2.85262	0.0949818
$903$	0	0
$904$	48.1034	1.59990
$905$	6.23602	0.207292
$906$	−1.28316	−0.0426301
$907$	−24.7641	−0.822280	−0.411140	−	0.911572i	$-0.634869\pi$
$907$	−24.7641	−0.822280	−0.411140	+	0.911572i	$0.634869\pi$
$908$	−11.0793	−0.367680
$909$	−17.7329	−0.588164
$910$	0	0
$911$	−5.42252	−0.179656	−0.0898281	−	0.995957i	$-0.528632\pi$
$911$	−5.42252	−0.179656	−0.0898281	+	0.995957i	$0.528632\pi$
$912$	−0.0666608	−0.00220736
$913$	−3.42537	−0.113363
$914$	28.2198	0.933429
$915$	−0.320089	−0.0105818
$916$	−1.33384	−0.0440713
$917$	0	0
$918$	−13.1517	−0.434072
$919$	13.8605	0.457215	0.228607	−	0.973519i	$-0.426583\pi$
$919$	13.8605	0.457215	0.228607	+	0.973519i	$0.426583\pi$
$920$	−2.31993	−0.0764857
$921$	−10.1041	−0.332942
$922$	−21.4053	−0.704947
$923$	0	0
$924$	0	0
$925$	10.7847	0.354599
$926$	−20.5590	−0.675610
$927$	19.8490	0.651927
$928$	−3.46092	−0.113610
$929$	13.5503	0.444572	0.222286	−	0.974982i	$-0.428648\pi$
$929$	13.5503	0.444572	0.222286	+	0.974982i	$0.428648\pi$
$930$	−1.88551	−0.0618282
$931$	0	0
$932$	17.3590	0.568613
$933$	15.3076	0.501150
$934$	−24.4521	−0.800097
$935$	0.442989	0.0144873
$936$	0	0
$937$	−9.85431	−0.321926	−0.160963	−	0.986960i	$-0.551460\pi$
$937$	−9.85431	−0.321926	−0.160963	+	0.986960i	$0.551460\pi$
$938$	0	0
$939$	−0.895255	−0.0292155
$940$	−2.44610	−0.0797830
$941$	38.6166	1.25887	0.629433	−	0.777055i	$-0.283287\pi$
$941$	38.6166	1.25887	0.629433	+	0.777055i	$0.283287\pi$
$942$	−16.3865	−0.533901
$943$	−21.9776	−0.715690
$944$	−0.288319	−0.00938398
$945$	0	0
$946$	2.70501	0.0879473
$947$	−34.7023	−1.12767	−0.563837	−	0.825886i	$-0.690675\pi$
$947$	−34.7023	−1.12767	−0.563837	+	0.825886i	$0.690675\pi$
$948$	8.11493	0.263561
$949$	0	0
$950$	15.3924	0.499396
$951$	−2.87911	−0.0933617
$952$	0	0
$953$	−8.61339	−0.279015	−0.139508	−	0.990221i	$-0.544552\pi$
$953$	−8.61339	−0.279015	−0.139508	+	0.990221i	$0.544552\pi$
$954$	16.6079	0.537701
$955$	−4.56405	−0.147689
$956$	23.3403	0.754880
$957$	0.210895	0.00681728
$958$	1.81758	0.0587234
$959$	0	0
$960$	1.00401	0.0324044
$961$	83.6825	2.69943
$962$	0	0
$963$	39.8701	1.28480
$964$	−30.9029	−0.995316
$965$	4.30379	0.138544
$966$	0	0
$967$	−12.9432	−0.416225	−0.208113	−	0.978105i	$-0.566732\pi$
$967$	−12.9432	−0.416225	−0.208113	+	0.978105i	$0.566732\pi$
$968$	30.5836	0.982994
$969$	−9.82895	−0.315751
$970$	0.376188	0.0120787
$971$	31.7833	1.01997	0.509987	−	0.860182i	$-0.329650\pi$
$971$	31.7833	1.01997	0.509987	+	0.860182i	$0.329650\pi$
$972$	19.0313	0.610428
$973$	0	0
$974$	5.28043	0.169196
$975$	0	0
$976$	0.0395533	0.00126607
$977$	18.7110	0.598618	0.299309	−	0.954156i	$-0.403244\pi$
$977$	18.7110	0.598618	0.299309	+	0.954156i	$0.403244\pi$
$978$	−4.46551	−0.142791
$979$	3.84021	0.122734
$980$	0	0
$981$	14.5016	0.463002
$982$	1.76801	0.0564196
$983$	6.32468	0.201726	0.100863	−	0.994900i	$-0.467840\pi$
$983$	6.32468	0.201726	0.100863	+	0.994900i	$0.467840\pi$
$984$	15.2697	0.486779
$985$	3.75557	0.119662
$986$	1.96647	0.0626252
$987$	0	0
$988$	0	0
$989$	−20.8404	−0.662685
$990$	0.258203	0.00820622
$991$	15.5948	0.495387	0.247693	−	0.968838i	$-0.420327\pi$
$991$	15.5948	0.495387	0.247693	+	0.968838i	$0.420327\pi$
$992$	−60.4617	−1.91966
$993$	−7.38584	−0.234382
$994$	0	0
$995$	−3.65074	−0.115736
$996$	−6.98407	−0.221299
$997$	31.1034	0.985056	0.492528	−	0.870297i	$-0.336073\pi$
$997$	31.1034	0.985056	0.492528	+	0.870297i	$0.336073\pi$
$998$	−6.58932	−0.208581
$999$	−8.96965	−0.283787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.cu.1.15		24
7.2	even	3		1183.2.e.l.508.10	yes	48
7.4	even	3		1183.2.e.l.170.10	yes	48
7.6	odd	2		8281.2.a.ct.1.15		24
13.12	even	2		8281.2.a.cv.1.10		24
91.25	even	6		1183.2.e.k.170.15	✓	48
91.51	even	6		1183.2.e.k.508.15	yes	48
91.90	odd	2		8281.2.a.cw.1.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.15	✓	48	91.25	even	6
1183.2.e.k.508.15	yes	48	91.51	even	6
1183.2.e.l.170.10	yes	48	7.4	even	3
1183.2.e.l.508.10	yes	48	7.2	even	3
8281.2.a.ct.1.15		24	7.6	odd	2
8281.2.a.cu.1.15		24	1.1	even	1	trivial
8281.2.a.cv.1.10		24	13.12	even	2
8281.2.a.cw.1.10		24	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q+0.877203 q^{2} -0.755024 q^{3} -1.23052 q^{4} -0.265839 q^{5} -0.662309 q^{6} -2.83382 q^{8} -2.42994 q^{9} +O(q^{10})\)	\(q+0.877203 q^{2} -0.755024 q^{3} -1.23052 q^{4} -0.265839 q^{5} -0.662309 q^{6} -2.83382 q^{8} -2.42994 q^{9} -0.233195 q^{10} +0.455666 q^{11} +0.929068 q^{12} +0.200715 q^{15} -0.0248023 q^{16} -3.65702 q^{17} -2.13155 q^{18} -3.55974 q^{19} +0.327119 q^{20} +0.399712 q^{22} -3.07952 q^{23} +2.13960 q^{24} -4.92933 q^{25} +4.09973 q^{27} -0.612999 q^{29} +0.176068 q^{30} -10.7090 q^{31} +5.64588 q^{32} -0.344039 q^{33} -3.20795 q^{34} +2.99008 q^{36} -2.18786 q^{37} -3.12262 q^{38} +0.753339 q^{40} +7.13669 q^{41} +6.76740 q^{43} -0.560704 q^{44} +0.645973 q^{45} -2.70137 q^{46} -7.47771 q^{47} +0.0187263 q^{48} -4.32402 q^{50} +2.76114 q^{51} -7.79148 q^{53} +3.59630 q^{54} -0.121134 q^{55} +2.68769 q^{57} -0.537725 q^{58} +11.6247 q^{59} -0.246983 q^{60} -1.59475 q^{61} -9.39396 q^{62} +5.00218 q^{64} -0.301792 q^{66} -9.39914 q^{67} +4.50002 q^{68} +2.32511 q^{69} -6.89894 q^{71} +6.88600 q^{72} +2.85100 q^{73} -1.91920 q^{74} +3.72176 q^{75} +4.38032 q^{76} +8.73448 q^{79} +0.00659341 q^{80} +4.19442 q^{81} +6.26033 q^{82} -7.51728 q^{83} +0.972179 q^{85} +5.93638 q^{86} +0.462829 q^{87} -1.29127 q^{88} +8.42769 q^{89} +0.566649 q^{90} +3.78940 q^{92} +8.08554 q^{93} -6.55947 q^{94} +0.946319 q^{95} -4.26277 q^{96} -1.61319 q^{97} -1.10724 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9}+O(q^{10}) \) 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9	\( 24 q - q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9} + 5 q^{10} - q^{11} + 5 q^{12} + 5 q^{15} + 17 q^{16} - 5 q^{17} + 24 q^{19} + 34 q^{20} - 14 q^{22} + 11 q^{23} + 32 q^{24} + 33 q^{25} - 21 q^{27} + 4 q^{29} - 22 q^{30} + 40 q^{31} - 6 q^{32} + 24 q^{33} + 36 q^{34} - 15 q^{36} - 4 q^{37} - 29 q^{38} - 4 q^{40} + 49 q^{41} + 13 q^{43} + 10 q^{44} + 58 q^{45} - 10 q^{46} + 62 q^{47} + 89 q^{48} - 23 q^{50} - 21 q^{51} - 18 q^{53} + 12 q^{54} - 14 q^{55} - 13 q^{57} + 56 q^{58} + 79 q^{59} + 22 q^{60} + 13 q^{61} + 12 q^{62} + 18 q^{64} - 38 q^{66} - 2 q^{67} - 12 q^{68} - 28 q^{69} - 19 q^{71} + 81 q^{72} + 17 q^{73} + 17 q^{74} + 24 q^{75} + 58 q^{76} - 9 q^{79} + 63 q^{80} + 16 q^{81} - 22 q^{82} + 81 q^{83} - 34 q^{85} + 22 q^{86} + 70 q^{87} - 33 q^{88} + 72 q^{89} + q^{90} - 4 q^{92} + 19 q^{93} - 30 q^{94} + 13 q^{95} + 11 q^{96} + 45 q^{97} - 39 q^{99}+O(q^{100}) \) 24 * q - q^2 + 23 * q^4 + 13 * q^5 + 14 * q^6 + 26 * q^9 + 5 * q^10 - q^11 + 5 * q^12 + 5 * q^15 + 17 * q^16 - 5 * q^17 + 24 * q^19 + 34 * q^20 - 14 * q^22 + 11 * q^23 + 32 * q^24 + 33 * q^25 - 21 * q^27 + 4 * q^29 - 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 + 36 * q^34 - 15 * q^36 - 4 * q^37 - 29 * q^38 - 4 * q^40 + 49 * q^41 + 13 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 89 * q^48 - 23 * q^50 - 21 * q^51 - 18 * q^53 + 12 * q^54 - 14 * q^55 - 13 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 + 13 * q^61 + 12 * q^62 + 18 * q^64 - 38 * q^66 - 2 * q^67 - 12 * q^68 - 28 * q^69 - 19 * q^71 + 81 * q^72 + 17 * q^73 + 17 * q^74 + 24 * q^75 + 58 * q^76 - 9 * q^79 + 63 * q^80 + 16 * q^81 - 22 * q^82 + 81 * q^83 - 34 * q^85 + 22 * q^86 + 70 * q^87 - 33 * q^88 + 72 * q^89 + q^90 - 4 * q^92 + 19 * q^93 - 30 * q^94 + 13 * q^95 + 11 * q^96 + 45 * q^97 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more