LMFDB - Embedded newform 5766.2.a.bl.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5766,2,Mod(1,5766)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5766, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5766.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5766 = 2 \cdot 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5766.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,-8,-8,8,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$46.0417418055$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{32})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 20x^{4} - 16x^{2} + 2 $ x^8 - 8x^6 + 20x^4 - 16*x^2 + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.96157$ of defining polynomial
Character	$\chi$	$=$	5766.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.452643 q^{5} +1.00000 q^{6} +1.03903 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.452643 q^{10} -6.03872 q^{11} -1.00000 q^{12} -2.71729 q^{13} -1.03903 q^{14} -0.452643 q^{15} +1.00000 q^{16} +5.60344 q^{17} -1.00000 q^{18} +1.75909 q^{19} +0.452643 q^{20} -1.03903 q^{21} +6.03872 q^{22} -1.94752 q^{23} +1.00000 q^{24} -4.79511 q^{25} +2.71729 q^{26} -1.00000 q^{27} +1.03903 q^{28} +4.61302 q^{29} +0.452643 q^{30} -1.00000 q^{32} +6.03872 q^{33} -5.60344 q^{34} +0.470308 q^{35} +1.00000 q^{36} +0.312686 q^{37} -1.75909 q^{38} +2.71729 q^{39} -0.452643 q^{40} +9.39898 q^{41} +1.03903 q^{42} +2.06748 q^{43} -6.03872 q^{44} +0.452643 q^{45} +1.94752 q^{46} +7.97717 q^{47} -1.00000 q^{48} -5.92042 q^{49} +4.79511 q^{50} -5.60344 q^{51} -2.71729 q^{52} -8.45244 q^{53} +1.00000 q^{54} -2.73339 q^{55} -1.03903 q^{56} -1.75909 q^{57} -4.61302 q^{58} +14.1890 q^{59} -0.452643 q^{60} -12.0823 q^{61} +1.03903 q^{63} +1.00000 q^{64} -1.22996 q^{65} -6.03872 q^{66} +7.69779 q^{67} +5.60344 q^{68} +1.94752 q^{69} -0.470308 q^{70} +0.831569 q^{71} -1.00000 q^{72} +3.68047 q^{73} -0.312686 q^{74} +4.79511 q^{75} +1.75909 q^{76} -6.27440 q^{77} -2.71729 q^{78} -2.36477 q^{79} +0.452643 q^{80} +1.00000 q^{81} -9.39898 q^{82} +4.74440 q^{83} -1.03903 q^{84} +2.53636 q^{85} -2.06748 q^{86} -4.61302 q^{87} +6.03872 q^{88} -3.88188 q^{89} -0.452643 q^{90} -2.82334 q^{91} -1.94752 q^{92} -7.97717 q^{94} +0.796238 q^{95} +1.00000 q^{96} -17.2595 q^{97} +5.92042 q^{98} -6.03872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{5} + 8 q^{6} - 8 q^{8} + 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 8 q^{20} + 8 q^{22} + 8 q^{24}+ \cdots - 8 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^5 + 8 * q^6 - 8 * q^8 + 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 8 * q^20 + 8 * q^22 + 8 * q^24 + 8 * q^26 - 8 * q^27 - 16 * q^29 + 8 * q^30 - 8 * q^32 + 8 * q^33 - 8 * q^34 + 16 * q^35 + 8 * q^36 + 8 * q^38 + 8 * q^39 - 8 * q^40 + 16 * q^41 - 8 * q^44 + 8 * q^45 + 24 * q^47 - 8 * q^48 - 8 * q^49 - 8 * q^51 - 8 * q^52 - 16 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 56 * q^61 + 8 * q^64 - 40 * q^65 - 8 * q^66 - 8 * q^67 + 8 * q^68 - 16 * q^70 + 8 * q^71 - 8 * q^72 - 32 * q^73 - 8 * q^76 - 16 * q^77 - 8 * q^78 + 8 * q^79 + 8 * q^80 + 8 * q^81 - 16 * q^82 + 8 * q^83 - 8 * q^85 + 16 * q^87 + 8 * q^88 - 48 * q^89 - 8 * q^90 - 32 * q^91 - 24 * q^94 - 8 * q^95 + 8 * q^96 - 8 * q^97 + 8 * q^98 - 8 * q^99

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.452643	0.202428	0.101214	−	0.994865i	$-0.467727\pi$
$5$	0.452643	0.202428	0.101214	+	0.994865i	$0.467727\pi$
$6$	1.00000	0.408248
$7$	1.03903	0.392715	0.196358	−	0.980532i	$-0.437089\pi$
$7$	1.03903	0.392715	0.196358	+	0.980532i	$0.437089\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.452643	−0.143138
$11$	−6.03872	−1.82074	−0.910372	−	0.413791i	$-0.864204\pi$
$11$	−6.03872	−1.82074	−0.910372	+	0.413791i	$0.864204\pi$
$12$	−1.00000	−0.288675
$13$	−2.71729	−0.753640	−0.376820	−	0.926287i	$-0.622982\pi$
$13$	−2.71729	−0.753640	−0.376820	+	0.926287i	$0.622982\pi$
$14$	−1.03903	−0.277692
$15$	−0.452643	−0.116872
$16$	1.00000	0.250000
$17$	5.60344	1.35903	0.679517	−	0.733659i	$-0.262189\pi$
$17$	5.60344	1.35903	0.679517	+	0.733659i	$0.262189\pi$
$18$	−1.00000	−0.235702
$19$	1.75909	0.403562	0.201781	−	0.979431i	$-0.435327\pi$
$19$	1.75909	0.403562	0.201781	+	0.979431i	$0.435327\pi$
$20$	0.452643	0.101214
$21$	−1.03903	−0.226734
$22$	6.03872	1.28746
$23$	−1.94752	−0.406085	−0.203043	−	0.979170i	$-0.565083\pi$
$23$	−1.94752	−0.406085	−0.203043	+	0.979170i	$0.565083\pi$
$24$	1.00000	0.204124
$25$	−4.79511	−0.959023
$26$	2.71729	0.532904
$27$	−1.00000	−0.192450
$28$	1.03903	0.196358
$29$	4.61302	0.856616	0.428308	−	0.903633i	$-0.359110\pi$
$29$	4.61302	0.856616	0.428308	+	0.903633i	$0.359110\pi$
$30$	0.452643	0.0826409
$31$	0	0
$31$	0	0
$32$	−1.00000	−0.176777
$33$	6.03872	1.05121
$34$	−5.60344	−0.960983
$35$	0.470308	0.0794966
$36$	1.00000	0.166667
$37$	0.312686	0.0514053	0.0257026	−	0.999670i	$-0.491818\pi$
$37$	0.312686	0.0514053	0.0257026	+	0.999670i	$0.491818\pi$
$38$	−1.75909	−0.285361
$39$	2.71729	0.435114
$40$	−0.452643	−0.0715691
$41$	9.39898	1.46787	0.733937	−	0.679217i	$-0.237681\pi$
$41$	9.39898	1.46787	0.733937	+	0.679217i	$0.237681\pi$
$42$	1.03903	0.160325
$43$	2.06748	0.315287	0.157644	−	0.987496i	$-0.449610\pi$
$43$	2.06748	0.315287	0.157644	+	0.987496i	$0.449610\pi$
$44$	−6.03872	−0.910372
$45$	0.452643	0.0674760
$46$	1.94752	0.287146
$47$	7.97717	1.16359	0.581795	−	0.813335i	$-0.302350\pi$
$47$	7.97717	1.16359	0.581795	+	0.813335i	$0.302350\pi$
$48$	−1.00000	−0.144338
$49$	−5.92042	−0.845775
$50$	4.79511	0.678132
$51$	−5.60344	−0.784639
$52$	−2.71729	−0.376820
$53$	−8.45244	−1.16103	−0.580516	−	0.814249i	$-0.697149\pi$
$53$	−8.45244	−1.16103	−0.580516	+	0.814249i	$0.697149\pi$
$54$	1.00000	0.136083
$55$	−2.73339	−0.368570
$56$	−1.03903	−0.138846
$57$	−1.75909	−0.232997
$58$	−4.61302	−0.605719
$59$	14.1890	1.84725	0.923623	−	0.383303i	$-0.125213\pi$
$59$	14.1890	1.84725	0.923623	+	0.383303i	$0.125213\pi$
$60$	−0.452643	−0.0584360
$61$	−12.0823	−1.54698	−0.773492	−	0.633806i	$-0.781492\pi$
$61$	−12.0823	−1.54698	−0.773492	+	0.633806i	$0.781492\pi$
$62$	0	0
$63$	1.03903	0.130905
$64$	1.00000	0.125000
$65$	−1.22996	−0.152558
$66$	−6.03872	−0.743315
$67$	7.69779	0.940435	0.470217	−	0.882551i	$-0.344175\pi$
$67$	7.69779	0.940435	0.470217	+	0.882551i	$0.344175\pi$
$68$	5.60344	0.679517
$69$	1.94752	0.234453
$70$	−0.470308	−0.0562126
$71$	0.831569	0.0986890	0.0493445	−	0.998782i	$-0.484287\pi$
$71$	0.831569	0.0986890	0.0493445	+	0.998782i	$0.484287\pi$
$72$	−1.00000	−0.117851
$73$	3.68047	0.430766	0.215383	−	0.976530i	$-0.430900\pi$
$73$	3.68047	0.430766	0.215383	+	0.976530i	$0.430900\pi$
$74$	−0.312686	−0.0363490
$75$	4.79511	0.553692
$76$	1.75909	0.201781
$77$	−6.27440	−0.715034
$78$	−2.71729	−0.307672
$79$	−2.36477	−0.266057	−0.133028	−	0.991112i	$-0.542470\pi$
$79$	−2.36477	−0.266057	−0.133028	+	0.991112i	$0.542470\pi$
$80$	0.452643	0.0506070
$81$	1.00000	0.111111
$82$	−9.39898	−1.03794
$83$	4.74440	0.520766	0.260383	−	0.965505i	$-0.416151\pi$
$83$	4.74440	0.520766	0.260383	+	0.965505i	$0.416151\pi$
$84$	−1.03903	−0.113367
$85$	2.53636	0.275107
$86$	−2.06748	−0.222942
$87$	−4.61302	−0.494568
$88$	6.03872	0.643730
$89$	−3.88188	−0.411478	−0.205739	−	0.978607i	$-0.565960\pi$
$89$	−3.88188	−0.411478	−0.205739	+	0.978607i	$0.565960\pi$
$90$	−0.452643	−0.0477128
$91$	−2.82334	−0.295966
$92$	−1.94752	−0.203043
$93$	0	0
$94$	−7.97717	−0.822783
$95$	0.796238	0.0816923
$96$	1.00000	0.102062
$97$	−17.2595	−1.75243	−0.876216	−	0.481918i	$-0.839940\pi$
$97$	−17.2595	−1.75243	−0.876216	+	0.481918i	$0.839940\pi$
$98$	5.92042	0.598053
$99$	−6.03872	−0.606915
$100$	−4.79511	−0.479511
$101$	−8.59736	−0.855469	−0.427735	−	0.903904i	$-0.640688\pi$
$101$	−8.59736	−0.855469	−0.427735	+	0.903904i	$0.640688\pi$
$102$	5.60344	0.554824
$103$	−5.92017	−0.583332	−0.291666	−	0.956520i	$-0.594210\pi$
$103$	−5.92017	−0.583332	−0.291666	+	0.956520i	$0.594210\pi$
$104$	2.71729	0.266452
$105$	−0.470308	−0.0458974
$106$	8.45244	0.820974
$107$	3.71557	0.359198	0.179599	−	0.983740i	$-0.442520\pi$
$107$	3.71557	0.359198	0.179599	+	0.983740i	$0.442520\pi$
$108$	−1.00000	−0.0962250
$109$	−15.9836	−1.53095	−0.765476	−	0.643464i	$-0.777496\pi$
$109$	−15.9836	−1.53095	−0.765476	+	0.643464i	$0.777496\pi$
$110$	2.73339	0.260618
$111$	−0.312686	−0.0296789
$112$	1.03903	0.0981789
$113$	−1.31804	−0.123991	−0.0619954	−	0.998076i	$-0.519746\pi$
$113$	−1.31804	−0.123991	−0.0619954	+	0.998076i	$0.519746\pi$
$114$	1.75909	0.164753
$115$	−0.881529	−0.0822030
$116$	4.61302	0.428308
$117$	−2.71729	−0.251213
$118$	−14.1890	−1.30620
$119$	5.82213	0.533714
$120$	0.452643	0.0413205
$121$	25.4662	2.31511
$122$	12.0823	1.09388
$123$	−9.39898	−0.847478
$124$	0	0
$125$	−4.43369	−0.396561
$126$	−1.03903	−0.0925639
$127$	−20.3343	−1.80438	−0.902190	−	0.431339i	$-0.858041\pi$
$127$	−20.3343	−1.80438	−0.902190	+	0.431339i	$0.858041\pi$
$128$	−1.00000	−0.0883883
$129$	−2.06748	−0.182031
$130$	1.22996	0.107875
$131$	−4.67203	−0.408197	−0.204098	−	0.978950i	$-0.565426\pi$
$131$	−4.67203	−0.408197	−0.204098	+	0.978950i	$0.565426\pi$
$132$	6.03872	0.525603
$133$	1.82774	0.158485
$134$	−7.69779	−0.664988
$135$	−0.452643	−0.0389573
$136$	−5.60344	−0.480491
$137$	−3.39948	−0.290437	−0.145218	−	0.989400i	$-0.546389\pi$
$137$	−3.39948	−0.290437	−0.145218	+	0.989400i	$0.546389\pi$
$138$	−1.94752	−0.165784
$139$	−10.5941	−0.898579	−0.449289	−	0.893386i	$-0.648323\pi$
$139$	−10.5941	−0.898579	−0.449289	+	0.893386i	$0.648323\pi$
$140$	0.470308	0.0397483
$141$	−7.97717	−0.671799
$142$	−0.831569	−0.0697837
$143$	16.4089	1.37218
$144$	1.00000	0.0833333
$145$	2.08805	0.173403
$146$	−3.68047	−0.304598
$147$	5.92042	0.488308
$148$	0.312686	0.0257026
$149$	−13.0325	−1.06766	−0.533831	−	0.845591i	$-0.679248\pi$
$149$	−13.0325	−1.06766	−0.533831	+	0.845591i	$0.679248\pi$
$150$	−4.79511	−0.391519
$151$	12.0972	0.984460	0.492230	−	0.870465i	$-0.336182\pi$
$151$	12.0972	0.984460	0.492230	+	0.870465i	$0.336182\pi$
$152$	−1.75909	−0.142681
$153$	5.60344	0.453012
$154$	6.27440	0.505605
$155$	0	0
$156$	2.71729	0.217557
$157$	−11.6754	−0.931795	−0.465898	−	0.884839i	$-0.654268\pi$
$157$	−11.6754	−0.931795	−0.465898	+	0.884839i	$0.654268\pi$
$158$	2.36477	0.188131
$159$	8.45244	0.670322
$160$	−0.452643	−0.0357846
$161$	−2.02352	−0.159476
$162$	−1.00000	−0.0785674
$163$	9.38366	0.734985	0.367492	−	0.930027i	$-0.380216\pi$
$163$	9.38366	0.734985	0.367492	+	0.930027i	$0.380216\pi$
$164$	9.39898	0.733937
$165$	2.73339	0.212794
$166$	−4.74440	−0.368237
$167$	13.0025	1.00617	0.503084	−	0.864238i	$-0.332199\pi$
$167$	13.0025	1.00617	0.503084	+	0.864238i	$0.332199\pi$
$168$	1.03903	0.0801627
$169$	−5.61635	−0.432027
$170$	−2.53636	−0.194530
$171$	1.75909	0.134521
$172$	2.06748	0.157644
$173$	−18.8230	−1.43109	−0.715543	−	0.698569i	$-0.753821\pi$
$173$	−18.8230	−1.43109	−0.715543	+	0.698569i	$0.753821\pi$
$174$	4.61302	0.349712
$175$	−4.98225	−0.376623
$176$	−6.03872	−0.455186
$177$	−14.1890	−1.06651
$178$	3.88188	0.290959
$179$	10.1841	0.761195	0.380598	−	0.924741i	$-0.375718\pi$
$179$	10.1841	0.761195	0.380598	+	0.924741i	$0.375718\pi$
$180$	0.452643	0.0337380
$181$	26.1278	1.94206	0.971032	−	0.238951i	$-0.0768035\pi$
$181$	26.1278	1.94206	0.971032	+	0.238951i	$0.0768035\pi$
$182$	2.82334	0.209280
$183$	12.0823	0.893152
$184$	1.94752	0.143573
$185$	0.141535	0.0104059
$186$	0	0
$187$	−33.8377	−2.47445
$188$	7.97717	0.581795
$189$	−1.03903	−0.0755781
$190$	−0.796238	−0.0577651
$191$	23.3508	1.68961	0.844804	−	0.535077i	$-0.179717\pi$
$191$	23.3508	1.68961	0.844804	+	0.535077i	$0.179717\pi$
$192$	−1.00000	−0.0721688
$193$	−2.68719	−0.193428	−0.0967142	−	0.995312i	$-0.530833\pi$
$193$	−2.68719	−0.193428	−0.0967142	+	0.995312i	$0.530833\pi$
$194$	17.2595	1.23916
$195$	1.22996	0.0880793
$196$	−5.92042	−0.422887
$197$	−23.0333	−1.64106	−0.820529	−	0.571605i	$-0.806321\pi$
$197$	−23.0333	−1.64106	−0.820529	+	0.571605i	$0.806321\pi$
$198$	6.03872	0.429153
$199$	−21.1321	−1.49801	−0.749007	−	0.662562i	$-0.769469\pi$
$199$	−21.1321	−1.49801	−0.749007	+	0.662562i	$0.769469\pi$
$200$	4.79511	0.339066
$201$	−7.69779	−0.542960
$202$	8.59736	0.604908
$203$	4.79305	0.336406
$204$	−5.60344	−0.392320
$205$	4.25438	0.297139
$206$	5.92017	0.412478
$207$	−1.94752	−0.135362
$208$	−2.71729	−0.188410
$209$	−10.6226	−0.734783
$210$	0.470308	0.0324544
$211$	26.6522	1.83482	0.917408	−	0.397949i	$-0.130278\pi$
$211$	26.6522	1.83482	0.917408	+	0.397949i	$0.130278\pi$
$212$	−8.45244	−0.580516
$213$	−0.831569	−0.0569781
$214$	−3.71557	−0.253991
$215$	0.935828	0.0638230
$216$	1.00000	0.0680414
$217$	0	0
$218$	15.9836	1.08255
$219$	−3.68047	−0.248703
$220$	−2.73339	−0.184285
$221$	−15.2262	−1.02422
$222$	0.312686	0.0209861
$223$	12.0253	0.805277	0.402638	−	0.915359i	$-0.368093\pi$
$223$	12.0253	0.805277	0.402638	+	0.915359i	$0.368093\pi$
$224$	−1.03903	−0.0694229
$225$	−4.79511	−0.319674
$226$	1.31804	0.0876748
$227$	0.964464	0.0640137	0.0320069	−	0.999488i	$-0.489810\pi$
$227$	0.964464	0.0640137	0.0320069	+	0.999488i	$0.489810\pi$
$228$	−1.75909	−0.116498
$229$	2.43645	0.161005	0.0805027	−	0.996754i	$-0.474347\pi$
$229$	2.43645	0.161005	0.0805027	+	0.996754i	$0.474347\pi$
$230$	0.881529	0.0581263
$231$	6.27440	0.412825
$232$	−4.61302	−0.302860
$233$	10.9965	0.720402	0.360201	−	0.932875i	$-0.382708\pi$
$233$	10.9965	0.720402	0.360201	+	0.932875i	$0.382708\pi$
$234$	2.71729	0.177635
$235$	3.61081	0.235543
$236$	14.1890	0.923623
$237$	2.36477	0.153608
$238$	−5.82213	−0.377393
$239$	6.76301	0.437463	0.218731	−	0.975785i	$-0.429808\pi$
$239$	6.76301	0.437463	0.218731	+	0.975785i	$0.429808\pi$
$240$	−0.452643	−0.0292180
$241$	1.16965	0.0753440	0.0376720	−	0.999290i	$-0.488006\pi$
$241$	1.16965	0.0753440	0.0376720	+	0.999290i	$0.488006\pi$
$242$	−25.4662	−1.63703
$243$	−1.00000	−0.0641500
$244$	−12.0823	−0.773492
$245$	−2.67984	−0.171209
$246$	9.39898	0.599257
$247$	−4.77994	−0.304140
$248$	0	0
$249$	−4.74440	−0.300664
$250$	4.43369	0.280411
$251$	−21.7743	−1.37438	−0.687189	−	0.726478i	$-0.741156\pi$
$251$	−21.7743	−1.37438	−0.687189	+	0.726478i	$0.741156\pi$
$252$	1.03903	0.0654526
$253$	11.7605	0.739377
$254$	20.3343	1.27589
$255$	−2.53636	−0.158833
$256$	1.00000	0.0625000
$257$	−15.9408	−0.994363	−0.497181	−	0.867647i	$-0.665632\pi$
$257$	−15.9408	−0.994363	−0.497181	+	0.867647i	$0.665632\pi$
$258$	2.06748	0.128715
$259$	0.324890	0.0201877
$260$	−1.22996	−0.0762789
$261$	4.61302	0.285539
$262$	4.67203	0.288639
$263$	−14.7564	−0.909920	−0.454960	−	0.890512i	$-0.650346\pi$
$263$	−14.7564	−0.909920	−0.454960	+	0.890512i	$0.650346\pi$
$264$	−6.03872	−0.371658
$265$	−3.82594	−0.235026
$266$	−1.82774	−0.112066
$267$	3.88188	0.237567
$268$	7.69779	0.470217
$269$	−29.1813	−1.77922	−0.889608	−	0.456724i	$-0.849023\pi$
$269$	−29.1813	−1.77922	−0.889608	+	0.456724i	$0.849023\pi$
$270$	0.452643	0.0275470
$271$	−31.5650	−1.91744	−0.958718	−	0.284360i	$-0.908219\pi$
$271$	−31.5650	−1.91744	−0.958718	+	0.284360i	$0.908219\pi$
$272$	5.60344	0.339759
$273$	2.82334	0.170876
$274$	3.39948	0.205370
$275$	28.9564	1.74613
$276$	1.94752	0.117227
$277$	10.6731	0.641283	0.320641	−	0.947201i	$-0.396102\pi$
$277$	10.6731	0.641283	0.320641	+	0.947201i	$0.396102\pi$
$278$	10.5941	0.635391
$279$	0	0
$280$	−0.470308	−0.0281063
$281$	25.3949	1.51493	0.757467	−	0.652874i	$-0.226437\pi$
$281$	25.3949	1.51493	0.757467	+	0.652874i	$0.226437\pi$
$282$	7.97717	0.475034
$283$	1.64065	0.0975264	0.0487632	−	0.998810i	$-0.484472\pi$
$283$	1.64065	0.0975264	0.0487632	+	0.998810i	$0.484472\pi$
$284$	0.831569	0.0493445
$285$	−0.796238	−0.0471650
$286$	−16.4089	−0.970281
$287$	9.76580	0.576457
$288$	−1.00000	−0.0589256
$289$	14.3986	0.846976
$290$	−2.08805	−0.122615
$291$	17.2595	1.01177
$292$	3.68047	0.215383
$293$	9.53171	0.556848	0.278424	−	0.960458i	$-0.410188\pi$
$293$	9.53171	0.556848	0.278424	+	0.960458i	$0.410188\pi$
$294$	−5.92042	−0.345286
$295$	6.42253	0.373934
$296$	−0.312686	−0.0181745
$297$	6.03872	0.350402
$298$	13.0325	0.754951
$299$	5.29196	0.306042
$300$	4.79511	0.276846
$301$	2.14816	0.123818
$302$	−12.0972	−0.696118
$303$	8.59736	0.493905
$304$	1.75909	0.100890
$305$	−5.46898	−0.313153
$306$	−5.60344	−0.320328
$307$	2.88410	0.164604	0.0823020	−	0.996607i	$-0.473773\pi$
$307$	2.88410	0.164604	0.0823020	+	0.996607i	$0.473773\pi$
$308$	−6.27440	−0.357517
$309$	5.92017	0.336787
$310$	0	0
$311$	15.9285	0.903222	0.451611	−	0.892215i	$-0.350849\pi$
$311$	15.9285	0.903222	0.451611	+	0.892215i	$0.350849\pi$
$312$	−2.71729	−0.153836
$313$	−21.7160	−1.22746	−0.613731	−	0.789515i	$-0.710332\pi$
$313$	−21.7160	−1.22746	−0.613731	+	0.789515i	$0.710332\pi$
$314$	11.6754	0.658879
$315$	0.470308	0.0264989
$316$	−2.36477	−0.133028
$317$	22.2506	1.24972	0.624860	−	0.780737i	$-0.285156\pi$
$317$	22.2506	1.24972	0.624860	+	0.780737i	$0.285156\pi$
$318$	−8.45244	−0.473990
$319$	−27.8568	−1.55968
$320$	0.452643	0.0253035
$321$	−3.71557	−0.207383
$322$	2.02352	0.112766
$323$	9.85694	0.548455
$324$	1.00000	0.0555556
$325$	13.0297	0.722758
$326$	−9.38366	−0.519713
$327$	15.9836	0.883896
$328$	−9.39898	−0.518972
$329$	8.28850	0.456960
$330$	−2.73339	−0.150468
$331$	−3.01065	−0.165480	−0.0827401	−	0.996571i	$-0.526367\pi$
$331$	−3.01065	−0.165480	−0.0827401	+	0.996571i	$0.526367\pi$
$332$	4.74440	0.260383
$333$	0.312686	0.0171351
$334$	−13.0025	−0.711468
$335$	3.48435	0.190370
$336$	−1.03903	−0.0566836
$337$	29.5566	1.61005	0.805026	−	0.593239i	$-0.202151\pi$
$337$	29.5566	1.61005	0.805026	+	0.593239i	$0.202151\pi$
$338$	5.61635	0.305489
$339$	1.31804	0.0715862
$340$	2.53636	0.137553
$341$	0	0
$342$	−1.75909	−0.0951204
$343$	−13.4247	−0.724864
$344$	−2.06748	−0.111471
$345$	0.881529	0.0474599
$346$	18.8230	1.01193
$347$	−9.66889	−0.519053	−0.259527	−	0.965736i	$-0.583567\pi$
$347$	−9.66889	−0.519053	−0.259527	+	0.965736i	$0.583567\pi$
$348$	−4.61302	−0.247284
$349$	−27.2280	−1.45748	−0.728742	−	0.684789i	$-0.759894\pi$
$349$	−27.2280	−1.45748	−0.728742	+	0.684789i	$0.759894\pi$
$350$	4.98225	0.266313
$351$	2.71729	0.145038
$352$	6.03872	0.321865
$353$	12.7070	0.676328	0.338164	−	0.941087i	$-0.390194\pi$
$353$	12.7070	0.676328	0.338164	+	0.941087i	$0.390194\pi$
$354$	14.1890	0.754135
$355$	0.376404	0.0199774
$356$	−3.88188	−0.205739
$357$	−5.82213	−0.308140
$358$	−10.1841	−0.538246
$359$	−30.7945	−1.62527	−0.812637	−	0.582771i	$-0.801969\pi$
$359$	−30.7945	−1.62527	−0.812637	+	0.582771i	$0.801969\pi$
$360$	−0.452643	−0.0238564
$361$	−15.9056	−0.837138
$362$	−26.1278	−1.37325
$363$	−25.4662	−1.33663
$364$	−2.82334	−0.147983
$365$	1.66594	0.0871991
$366$	−12.0823	−0.631554
$367$	5.45656	0.284830	0.142415	−	0.989807i	$-0.454513\pi$
$367$	5.45656	0.284830	0.142415	+	0.989807i	$0.454513\pi$
$368$	−1.94752	−0.101521
$369$	9.39898	0.489292
$370$	−0.141535	−0.00735807
$371$	−8.78232	−0.455955
$372$	0	0
$373$	−36.4919	−1.88948	−0.944739	−	0.327825i	$-0.893684\pi$
$373$	−36.4919	−1.88948	−0.944739	+	0.327825i	$0.893684\pi$
$374$	33.8377	1.74970
$375$	4.43369	0.228955
$376$	−7.97717	−0.411391
$377$	−12.5349	−0.645580
$378$	1.03903	0.0534418
$379$	−34.3740	−1.76567	−0.882837	−	0.469679i	$-0.844370\pi$
$379$	−34.3740	−1.76567	−0.882837	+	0.469679i	$0.844370\pi$
$380$	0.796238	0.0408461
$381$	20.3343	1.04176
$382$	−23.3508	−1.19473
$383$	−32.8342	−1.67775	−0.838874	−	0.544326i	$-0.816785\pi$
$383$	−32.8342	−1.67775	−0.838874	+	0.544326i	$0.816785\pi$
$384$	1.00000	0.0510310
$385$	−2.84006	−0.144743
$386$	2.68719	0.136775
$387$	2.06748	0.105096
$388$	−17.2595	−0.876216
$389$	−20.1379	−1.02103	−0.510515	−	0.859869i	$-0.670545\pi$
$389$	−20.1379	−1.02103	−0.510515	+	0.859869i	$0.670545\pi$
$390$	−1.22996	−0.0622815
$391$	−10.9128	−0.551884
$392$	5.92042	0.299026
$393$	4.67203	0.235673
$394$	23.0333	1.16040
$395$	−1.07039	−0.0538574
$396$	−6.03872	−0.303457
$397$	−16.7439	−0.840351	−0.420175	−	0.907443i	$-0.638031\pi$
$397$	−16.7439	−0.840351	−0.420175	+	0.907443i	$0.638031\pi$
$398$	21.1321	1.05926
$399$	−1.82774	−0.0915013
$400$	−4.79511	−0.239756
$401$	−8.96258	−0.447570	−0.223785	−	0.974639i	$-0.571841\pi$
$401$	−8.96258	−0.447570	−0.223785	+	0.974639i	$0.571841\pi$
$402$	7.69779	0.383931
$403$	0	0
$404$	−8.59736	−0.427735
$405$	0.452643	0.0224920
$406$	−4.79305	−0.237875
$407$	−1.88823	−0.0935959
$408$	5.60344	0.277412
$409$	−11.0924	−0.548485	−0.274243	−	0.961661i	$-0.588427\pi$
$409$	−11.0924	−0.548485	−0.274243	+	0.961661i	$0.588427\pi$
$410$	−4.25438	−0.210109
$411$	3.39948	0.167684
$412$	−5.92017	−0.291666
$413$	14.7427	0.725442
$414$	1.94752	0.0957152
$415$	2.14752	0.105418
$416$	2.71729	0.133226
$417$	10.5941	0.518795
$418$	10.6226	0.519570
$419$	−30.1990	−1.47532	−0.737660	−	0.675173i	$-0.764069\pi$
$419$	−30.1990	−1.47532	−0.737660	+	0.675173i	$0.764069\pi$
$420$	−0.470308	−0.0229487
$421$	24.9352	1.21527	0.607634	−	0.794217i	$-0.292119\pi$
$421$	24.9352	1.21527	0.607634	+	0.794217i	$0.292119\pi$
$422$	−26.6522	−1.29741
$423$	7.97717	0.387864
$424$	8.45244	0.410487
$425$	−26.8692	−1.30335
$426$	0.831569	0.0402896
$427$	−12.5539	−0.607525
$428$	3.71557	0.179599
$429$	−16.4089	−0.792231
$430$	−0.935828	−0.0451296
$431$	−16.1355	−0.777221	−0.388611	−	0.921402i	$-0.627045\pi$
$431$	−16.1355	−0.777221	−0.388611	+	0.921402i	$0.627045\pi$
$432$	−1.00000	−0.0481125
$433$	−1.99194	−0.0957264	−0.0478632	−	0.998854i	$-0.515241\pi$
$433$	−1.99194	−0.0957264	−0.0478632	+	0.998854i	$0.515241\pi$
$434$	0	0
$435$	−2.08805	−0.100114
$436$	−15.9836	−0.765476
$437$	−3.42585	−0.163880
$438$	3.68047	0.175859
$439$	−10.4789	−0.500130	−0.250065	−	0.968229i	$-0.580452\pi$
$439$	−10.4789	−0.500130	−0.250065	+	0.968229i	$0.580452\pi$
$440$	2.73339	0.130309
$441$	−5.92042	−0.281925
$442$	15.2262	0.724235
$443$	9.00174	0.427686	0.213843	−	0.976868i	$-0.431402\pi$
$443$	9.00174	0.427686	0.213843	+	0.976868i	$0.431402\pi$
$444$	−0.312686	−0.0148394
$445$	−1.75710	−0.0832947
$446$	−12.0253	−0.569417
$447$	13.0325	0.616415
$448$	1.03903	0.0490894
$449$	−27.8763	−1.31556	−0.657781	−	0.753209i	$-0.728505\pi$
$449$	−27.8763	−1.31556	−0.657781	+	0.753209i	$0.728505\pi$
$450$	4.79511	0.226044
$451$	−56.7579	−2.67262
$452$	−1.31804	−0.0619954
$453$	−12.0972	−0.568378
$454$	−0.964464	−0.0452646
$455$	−1.27796	−0.0599118
$456$	1.75909	0.0823767
$457$	7.57262	0.354232	0.177116	−	0.984190i	$-0.443323\pi$
$457$	7.57262	0.354232	0.177116	+	0.984190i	$0.443323\pi$
$458$	−2.43645	−0.113848
$459$	−5.60344	−0.261546
$460$	−0.881529	−0.0411015
$461$	−10.0697	−0.468991	−0.234496	−	0.972117i	$-0.575344\pi$
$461$	−10.0697	−0.468991	−0.234496	+	0.972117i	$0.575344\pi$
$462$	−6.27440	−0.291911
$463$	31.0939	1.44506	0.722529	−	0.691340i	$-0.242980\pi$
$463$	31.0939	1.44506	0.722529	+	0.691340i	$0.242980\pi$
$464$	4.61302	0.214154
$465$	0	0
$466$	−10.9965	−0.509401
$467$	−19.2620	−0.891341	−0.445670	−	0.895197i	$-0.647035\pi$
$467$	−19.2620	−0.891341	−0.445670	+	0.895197i	$0.647035\pi$
$468$	−2.71729	−0.125607
$469$	7.99822	0.369323
$470$	−3.61081	−0.166554
$471$	11.6754	0.537972
$472$	−14.1890	−0.653100
$473$	−12.4849	−0.574057
$474$	−2.36477	−0.108617
$475$	−8.43501	−0.387025
$476$	5.82213	0.266857
$477$	−8.45244	−0.387011
$478$	−6.76301	−0.309333
$479$	3.98157	0.181923	0.0909613	−	0.995854i	$-0.471006\pi$
$479$	3.98157	0.181923	0.0909613	+	0.995854i	$0.471006\pi$
$480$	0.452643	0.0206602
$481$	−0.849658	−0.0387411
$482$	−1.16965	−0.0532762
$483$	2.02352	0.0920734
$484$	25.4662	1.15755
$485$	−7.81237	−0.354742
$486$	1.00000	0.0453609
$487$	−17.4003	−0.788481	−0.394241	−	0.919007i	$-0.628992\pi$
$487$	−17.4003	−0.788481	−0.394241	+	0.919007i	$0.628992\pi$
$488$	12.0823	0.546942
$489$	−9.38366	−0.424344
$490$	2.67984	0.121063
$491$	−27.6396	−1.24736	−0.623678	−	0.781681i	$-0.714363\pi$
$491$	−27.6396	−1.24736	−0.623678	+	0.781681i	$0.714363\pi$
$492$	−9.39898	−0.423739
$493$	25.8488	1.16417
$494$	4.77994	0.215060
$495$	−2.73339	−0.122857
$496$	0	0
$497$	0.864022	0.0387567
$498$	4.74440	0.212602
$499$	−9.21673	−0.412597	−0.206299	−	0.978489i	$-0.566142\pi$
$499$	−9.21673	−0.412597	−0.206299	+	0.978489i	$0.566142\pi$
$500$	−4.43369	−0.198281
$501$	−13.0025	−0.580911
$502$	21.7743	0.971832
$503$	31.6456	1.41101	0.705503	−	0.708707i	$-0.250721\pi$
$503$	31.6456	1.41101	0.705503	+	0.708707i	$0.250721\pi$
$504$	−1.03903	−0.0462820
$505$	−3.89153	−0.173171
$506$	−11.7605	−0.522818
$507$	5.61635	0.249431
$508$	−20.3343	−0.902190
$509$	−9.65782	−0.428075	−0.214038	−	0.976825i	$-0.568662\pi$
$509$	−9.65782	−0.428075	−0.214038	+	0.976825i	$0.568662\pi$
$510$	2.53636	0.112312
$511$	3.82410	0.169168
$512$	−1.00000	−0.0441942
$513$	−1.75909	−0.0776655
$514$	15.9408	0.703121
$515$	−2.67972	−0.118083
$516$	−2.06748	−0.0910155
$517$	−48.1720	−2.11860
$518$	−0.324890	−0.0142748
$519$	18.8230	0.826238
$520$	1.22996	0.0539373
$521$	15.2543	0.668304	0.334152	−	0.942519i	$-0.391550\pi$
$521$	15.2543	0.668304	0.334152	+	0.942519i	$0.391550\pi$
$522$	−4.61302	−0.201906
$523$	−40.4061	−1.76683	−0.883417	−	0.468587i	$-0.844763\pi$
$523$	−40.4061	−1.76683	−0.883417	+	0.468587i	$0.844763\pi$
$524$	−4.67203	−0.204098
$525$	4.98225	0.217443
$526$	14.7564	0.643411
$527$	0	0
$528$	6.03872	0.262802
$529$	−19.2072	−0.835095
$530$	3.82594	0.166188
$531$	14.1890	0.615748
$532$	1.82774	0.0792425
$533$	−25.5397	−1.10625
$534$	−3.88188	−0.167985
$535$	1.68183	0.0727117
$536$	−7.69779	−0.332494
$537$	−10.1841	−0.439476
$538$	29.1813	1.25810
$539$	35.7518	1.53994
$540$	−0.452643	−0.0194787
$541$	−23.7449	−1.02087	−0.510437	−	0.859915i	$-0.670516\pi$
$541$	−23.7449	−1.02087	−0.510437	+	0.859915i	$0.670516\pi$
$542$	31.5650	1.35583
$543$	−26.1278	−1.12125
$544$	−5.60344	−0.240246
$545$	−7.23487	−0.309908
$546$	−2.82334	−0.120828
$547$	−27.3114	−1.16775	−0.583876	−	0.811843i	$-0.698464\pi$
$547$	−27.3114	−1.16775	−0.583876	+	0.811843i	$0.698464\pi$
$548$	−3.39948	−0.145218
$549$	−12.0823	−0.515661
$550$	−28.9564	−1.23470
$551$	8.11470	0.345698
$552$	−1.94752	−0.0828918
$553$	−2.45706	−0.104485
$554$	−10.6731	−0.453456
$555$	−0.141535	−0.00600784
$556$	−10.5941	−0.449289
$557$	22.8327	0.967451	0.483725	−	0.875220i	$-0.339283\pi$
$557$	22.8327	0.967451	0.483725	+	0.875220i	$0.339283\pi$
$558$	0	0
$559$	−5.61792	−0.237613
$560$	0.470308	0.0198742
$561$	33.8377	1.42863
$562$	−25.3949	−1.07122
$563$	−27.9550	−1.17816	−0.589081	−	0.808074i	$-0.700510\pi$
$563$	−27.9550	−1.17816	−0.589081	+	0.808074i	$0.700510\pi$
$564$	−7.97717	−0.335900
$565$	−0.596602	−0.0250992
$566$	−1.64065	−0.0689616
$567$	1.03903	0.0436350
$568$	−0.831569	−0.0348918
$569$	−26.7165	−1.12001	−0.560006	−	0.828488i	$-0.689201\pi$
$569$	−26.7165	−1.12001	−0.560006	+	0.828488i	$0.689201\pi$
$570$	0.796238	0.0333507
$571$	24.1160	1.00922	0.504612	−	0.863346i	$-0.331636\pi$
$571$	24.1160	1.00922	0.504612	+	0.863346i	$0.331636\pi$
$572$	16.4089	0.686092
$573$	−23.3508	−0.975495
$574$	−9.76580	−0.407617
$575$	9.33856	0.389445
$576$	1.00000	0.0416667
$577$	−4.18019	−0.174023	−0.0870117	−	0.996207i	$-0.527732\pi$
$577$	−4.18019	−0.174023	−0.0870117	+	0.996207i	$0.527732\pi$
$578$	−14.3986	−0.598903
$579$	2.68719	0.111676
$580$	2.08805	0.0867016
$581$	4.92956	0.204513
$582$	−17.2595	−0.715428
$583$	51.0420	2.11394
$584$	−3.68047	−0.152299
$585$	−1.22996	−0.0508526
$586$	−9.53171	−0.393751
$587$	34.9184	1.44124	0.720619	−	0.693331i	$-0.243858\pi$
$587$	34.9184	1.44124	0.720619	+	0.693331i	$0.243858\pi$
$588$	5.92042	0.244154
$589$	0	0
$590$	−6.42253	−0.264412
$591$	23.0333	0.947465
$592$	0.312686	0.0128513
$593$	3.22818	0.132566	0.0662828	−	0.997801i	$-0.478886\pi$
$593$	3.22818	0.132566	0.0662828	+	0.997801i	$0.478886\pi$
$594$	−6.03872	−0.247772
$595$	2.63535	0.108039
$596$	−13.0325	−0.533831
$597$	21.1321	0.864878
$598$	−5.29196	−0.216404
$599$	29.8275	1.21872	0.609359	−	0.792894i	$-0.291427\pi$
$599$	29.8275	1.21872	0.609359	+	0.792894i	$0.291427\pi$
$600$	−4.79511	−0.195760
$601$	0.0511050	0.00208462	0.00104231	−	0.999999i	$-0.499668\pi$
$601$	0.0511050	0.00208462	0.00104231	+	0.999999i	$0.499668\pi$
$602$	−2.14816	−0.0875526
$603$	7.69779	0.313478
$604$	12.0972	0.492230
$605$	11.5271	0.468643
$606$	−8.59736	−0.349244
$607$	13.6006	0.552029	0.276015	−	0.961153i	$-0.410986\pi$
$607$	13.6006	0.552029	0.276015	+	0.961153i	$0.410986\pi$
$608$	−1.75909	−0.0713403
$609$	−4.79305	−0.194224
$610$	5.46898	0.221433
$611$	−21.6763	−0.876928
$612$	5.60344	0.226506
$613$	18.4853	0.746616	0.373308	−	0.927708i	$-0.378224\pi$
$613$	18.4853	0.746616	0.373308	+	0.927708i	$0.378224\pi$
$614$	−2.88410	−0.116393
$615$	−4.25438	−0.171553
$616$	6.27440	0.252803
$617$	4.86131	0.195709	0.0978545	−	0.995201i	$-0.468802\pi$
$617$	4.86131	0.195709	0.0978545	+	0.995201i	$0.468802\pi$
$618$	−5.92017	−0.238144
$619$	−5.09128	−0.204636	−0.102318	−	0.994752i	$-0.532626\pi$
$619$	−5.09128	−0.204636	−0.102318	+	0.994752i	$0.532626\pi$
$620$	0	0
$621$	1.94752	0.0781511
$622$	−15.9285	−0.638674
$623$	−4.03338	−0.161594
$624$	2.71729	0.108779
$625$	21.9687	0.878748
$626$	21.7160	0.867946
$627$	10.6226	0.424227
$628$	−11.6754	−0.465898
$629$	1.75212	0.0698616
$630$	−0.470308	−0.0187375
$631$	−28.7446	−1.14430	−0.572152	−	0.820148i	$-0.693891\pi$
$631$	−28.7446	−1.14430	−0.572152	+	0.820148i	$0.693891\pi$
$632$	2.36477	0.0940653
$633$	−26.6522	−1.05933
$634$	−22.2506	−0.883685
$635$	−9.20419	−0.365257
$636$	8.45244	0.335161
$637$	16.0875	0.637409
$638$	27.8568	1.10286
$639$	0.831569	0.0328963
$640$	−0.452643	−0.0178923
$641$	25.3997	1.00323	0.501613	−	0.865092i	$-0.332740\pi$
$641$	25.3997	1.00323	0.501613	+	0.865092i	$0.332740\pi$
$642$	3.71557	0.146642
$643$	10.9276	0.430944	0.215472	−	0.976510i	$-0.430871\pi$
$643$	10.9276	0.430944	0.215472	+	0.976510i	$0.430871\pi$
$644$	−2.02352	−0.0797379
$645$	−0.935828	−0.0368482
$646$	−9.85694	−0.387816
$647$	24.7688	0.973761	0.486881	−	0.873469i	$-0.338135\pi$
$647$	24.7688	0.973761	0.486881	+	0.873469i	$0.338135\pi$
$648$	−1.00000	−0.0392837
$649$	−85.6832	−3.36336
$650$	−13.0297	−0.511067
$651$	0	0
$652$	9.38366	0.367492
$653$	−33.1745	−1.29822	−0.649110	−	0.760695i	$-0.724859\pi$
$653$	−33.1745	−1.29822	−0.649110	+	0.760695i	$0.724859\pi$
$654$	−15.9836	−0.625009
$655$	−2.11476	−0.0826305
$656$	9.39898	0.366969
$657$	3.68047	0.143589
$658$	−8.28850	−0.323119
$659$	−40.2751	−1.56889	−0.784447	−	0.620196i	$-0.787053\pi$
$659$	−40.2751	−1.56889	−0.784447	+	0.620196i	$0.787053\pi$
$660$	2.73339	0.106397
$661$	−10.3006	−0.400649	−0.200324	−	0.979730i	$-0.564200\pi$
$661$	−10.3006	−0.400649	−0.200324	+	0.979730i	$0.564200\pi$
$662$	3.01065	0.117012
$663$	15.2262	0.591335
$664$	−4.74440	−0.184119
$665$	0.827313	0.0320818
$666$	−0.312686	−0.0121163
$667$	−8.98393	−0.347859
$668$	13.0025	0.503084
$669$	−12.0253	−0.464927
$670$	−3.48435	−0.134612
$671$	72.9619	2.81666
$672$	1.03903	0.0400813
$673$	41.6602	1.60588	0.802941	−	0.596058i	$-0.203267\pi$
$673$	41.6602	1.60588	0.802941	+	0.596058i	$0.203267\pi$
$674$	−29.5566	−1.13848
$675$	4.79511	0.184564
$676$	−5.61635	−0.216014
$677$	−38.9841	−1.49828	−0.749140	−	0.662412i	$-0.769533\pi$
$677$	−38.9841	−1.49828	−0.749140	+	0.662412i	$0.769533\pi$
$678$	−1.31804	−0.0506191
$679$	−17.9330	−0.688207
$680$	−2.53636	−0.0972650
$681$	−0.964464	−0.0369584
$682$	0	0
$683$	17.6986	0.677220	0.338610	−	0.940927i	$-0.390043\pi$
$683$	17.6986	0.677220	0.338610	+	0.940927i	$0.390043\pi$
$684$	1.75909	0.0672603
$685$	−1.53875	−0.0587926
$686$	13.4247	0.512556
$687$	−2.43645	−0.0929565
$688$	2.06748	0.0788218
$689$	22.9677	0.875000
$690$	−0.881529	−0.0335592
$691$	−19.9387	−0.758506	−0.379253	−	0.925293i	$-0.623819\pi$
$691$	−19.9387	−0.758506	−0.379253	+	0.925293i	$0.623819\pi$
$692$	−18.8230	−0.715543
$693$	−6.27440	−0.238345
$694$	9.66889	0.367026
$695$	−4.79534	−0.181898
$696$	4.61302	0.174856
$697$	52.6667	1.99489
$698$	27.2280	1.03060
$699$	−10.9965	−0.415924
$700$	−4.98225	−0.188312
$701$	27.1258	1.02453	0.512263	−	0.858829i	$-0.328807\pi$
$701$	27.1258	1.02453	0.512263	+	0.858829i	$0.328807\pi$
$702$	−2.71729	−0.102557
$703$	0.550042	0.0207452
$704$	−6.03872	−0.227593
$705$	−3.61081	−0.135991
$706$	−12.7070	−0.478236
$707$	−8.93289	−0.335956
$708$	−14.1890	−0.533254
$709$	−6.69909	−0.251590	−0.125795	−	0.992056i	$-0.540148\pi$
$709$	−6.69909	−0.251590	−0.125795	+	0.992056i	$0.540148\pi$
$710$	−0.376404	−0.0141262
$711$	−2.36477	−0.0886856
$712$	3.88188	0.145480
$713$	0	0
$714$	5.82213	0.217888
$715$	7.42739	0.277769
$716$	10.1841	0.380598
$717$	−6.76301	−0.252569
$718$	30.7945	1.14924
$719$	18.4695	0.688796	0.344398	−	0.938824i	$-0.388083\pi$
$719$	18.4695	0.688796	0.344398	+	0.938824i	$0.388083\pi$
$720$	0.452643	0.0168690
$721$	−6.15122	−0.229083
$722$	15.9056	0.591946
$723$	−1.16965	−0.0434999
$724$	26.1278	0.971032
$725$	−22.1200	−0.821515
$726$	25.4662	0.945139
$727$	4.00269	0.148452	0.0742258	−	0.997241i	$-0.476351\pi$
$727$	4.00269	0.148452	0.0742258	+	0.997241i	$0.476351\pi$
$728$	2.82334	0.104640
$729$	1.00000	0.0370370
$730$	−1.66594	−0.0616591
$731$	11.5850	0.428486
$732$	12.0823	0.446576
$733$	4.51552	0.166784	0.0833922	−	0.996517i	$-0.473425\pi$
$733$	4.51552	0.166784	0.0833922	+	0.996517i	$0.473425\pi$
$734$	−5.45656	−0.201405
$735$	2.67984	0.0988473
$736$	1.94752	0.0717864
$737$	−46.4848	−1.71229
$738$	−9.39898	−0.345981
$739$	31.9421	1.17501	0.587504	−	0.809221i	$-0.300111\pi$
$739$	31.9421	1.17501	0.587504	+	0.809221i	$0.300111\pi$
$740$	0.141535	0.00520294
$741$	4.77994	0.175595
$742$	8.78232	0.322409
$743$	10.4260	0.382493	0.191247	−	0.981542i	$-0.438747\pi$
$743$	10.4260	0.382493	0.191247	+	0.981542i	$0.438747\pi$
$744$	0	0
$745$	−5.89906	−0.216125
$746$	36.4919	1.33606
$747$	4.74440	0.173589
$748$	−33.8377	−1.23723
$749$	3.86058	0.141062
$750$	−4.43369	−0.161895
$751$	32.7809	1.19619	0.598096	−	0.801425i	$-0.295924\pi$
$751$	32.7809	1.19619	0.598096	+	0.801425i	$0.295924\pi$
$752$	7.97717	0.290898
$753$	21.7743	0.793498
$754$	12.5349	0.456494
$755$	5.47573	0.199282
$756$	−1.03903	−0.0377891
$757$	−49.1534	−1.78651	−0.893256	−	0.449548i	$-0.851585\pi$
$757$	−49.1534	−1.78651	−0.893256	+	0.449548i	$0.851585\pi$
$758$	34.3740	1.24852
$759$	−11.7605	−0.426879
$760$	−0.796238	−0.0288826
$761$	28.6442	1.03835	0.519175	−	0.854668i	$-0.326239\pi$
$761$	28.6442	1.03835	0.519175	+	0.854668i	$0.326239\pi$
$762$	−20.3343	−0.736635
$763$	−16.6074	−0.601229
$764$	23.3508	0.844804
$765$	2.53636	0.0917023
$766$	32.8342	1.18635
$767$	−38.5555	−1.39216
$768$	−1.00000	−0.0360844
$769$	33.9265	1.22342	0.611710	−	0.791082i	$-0.290482\pi$
$769$	33.9265	1.22342	0.611710	+	0.791082i	$0.290482\pi$
$770$	2.84006	0.102349
$771$	15.9408	0.574095
$772$	−2.68719	−0.0967142
$773$	0.419818	0.0150998	0.00754990	−	0.999971i	$-0.497597\pi$
$773$	0.419818	0.0150998	0.00754990	+	0.999971i	$0.497597\pi$
$774$	−2.06748	−0.0743139
$775$	0	0
$776$	17.2595	0.619578
$777$	−0.324890	−0.0116553
$778$	20.1379	0.721978
$779$	16.5336	0.592378
$780$	1.22996	0.0440397
$781$	−5.02161	−0.179687
$782$	10.9128	0.390241
$783$	−4.61302	−0.164856
$784$	−5.92042	−0.211444
$785$	−5.28477	−0.188622
$786$	−4.67203	−0.166646
$787$	−51.4576	−1.83427	−0.917133	−	0.398581i	$-0.869503\pi$
$787$	−51.4576	−1.83427	−0.917133	+	0.398581i	$0.869503\pi$
$788$	−23.0333	−0.820529
$789$	14.7564	0.525342
$790$	1.07039	0.0380829
$791$	−1.36948	−0.0486931
$792$	6.03872	0.214577
$793$	32.8312	1.16587
$794$	16.7439	0.594218
$795$	3.82594	0.135692
$796$	−21.1321	−0.749007
$797$	18.8390	0.667311	0.333656	−	0.942695i	$-0.391718\pi$
$797$	18.8390	0.667311	0.333656	+	0.942695i	$0.391718\pi$
$798$	1.82774	0.0647012
$799$	44.6997	1.58136
$800$	4.79511	0.169533
$801$	−3.88188	−0.137159
$802$	8.96258	0.316480
$803$	−22.2253	−0.784314
$804$	−7.69779	−0.271480
$805$	−0.915933	−0.0322824
$806$	0	0
$807$	29.1813	1.02723
$808$	8.59736	0.302454
$809$	53.0523	1.86522	0.932610	−	0.360885i	$-0.117525\pi$
$809$	53.0523	1.86522	0.932610	+	0.360885i	$0.117525\pi$
$810$	−0.452643	−0.0159043
$811$	−28.9397	−1.01621	−0.508106	−	0.861295i	$-0.669654\pi$
$811$	−28.9397	−1.01621	−0.508106	+	0.861295i	$0.669654\pi$
$812$	4.79305	0.168203
$813$	31.5650	1.10703
$814$	1.88823	0.0661823
$815$	4.24745	0.148782
$816$	−5.60344	−0.196160
$817$	3.63687	0.127238
$818$	11.0924	0.387838
$819$	−2.82334	−0.0986553
$820$	4.25438	0.148570
$821$	−17.5436	−0.612275	−0.306138	−	0.951987i	$-0.599037\pi$
$821$	−17.5436	−0.612275	−0.306138	+	0.951987i	$0.599037\pi$
$822$	−3.39948	−0.118570
$823$	1.19433	0.0416318	0.0208159	−	0.999783i	$-0.493374\pi$
$823$	1.19433	0.0416318	0.0208159	+	0.999783i	$0.493374\pi$
$824$	5.92017	0.206239
$825$	−28.9564	−1.00813
$826$	−14.7427	−0.512965
$827$	43.1763	1.50139	0.750693	−	0.660651i	$-0.229720\pi$
$827$	43.1763	1.50139	0.750693	+	0.660651i	$0.229720\pi$
$828$	−1.94752	−0.0676808
$829$	−11.7627	−0.408535	−0.204267	−	0.978915i	$-0.565481\pi$
$829$	−11.7627	−0.408535	−0.204267	+	0.978915i	$0.565481\pi$
$830$	−2.14752	−0.0745415
$831$	−10.6731	−0.370245
$832$	−2.71729	−0.0942050
$833$	−33.1748	−1.14944
$834$	−10.5941	−0.366843
$835$	5.88551	0.203676
$836$	−10.6226	−0.367391
$837$	0	0
$838$	30.1990	1.04321
$839$	−6.43921	−0.222306	−0.111153	−	0.993803i	$-0.535454\pi$
$839$	−6.43921	−0.222306	−0.111153	+	0.993803i	$0.535454\pi$
$840$	0.470308	0.0162272
$841$	−7.72004	−0.266208
$842$	−24.9352	−0.859324
$843$	−25.3949	−0.874647
$844$	26.6522	0.917408
$845$	−2.54220	−0.0874544
$846$	−7.97717	−0.274261
$847$	26.4601	0.909178
$848$	−8.45244	−0.290258
$849$	−1.64065	−0.0563069
$850$	26.8692	0.921605
$851$	−0.608961	−0.0208749
$852$	−0.831569	−0.0284891
$853$	17.4546	0.597633	0.298817	−	0.954311i	$-0.403408\pi$
$853$	17.4546	0.597633	0.298817	+	0.954311i	$0.403408\pi$
$854$	12.5539	0.429585
$855$	0.796238	0.0272308
$856$	−3.71557	−0.126996
$857$	−15.1812	−0.518580	−0.259290	−	0.965799i	$-0.583489\pi$
$857$	−15.1812	−0.518580	−0.259290	+	0.965799i	$0.583489\pi$
$858$	16.4089	0.560192
$859$	17.6302	0.601533	0.300767	−	0.953698i	$-0.402758\pi$
$859$	17.6302	0.601533	0.300767	+	0.953698i	$0.402758\pi$
$860$	0.935828	0.0319115
$861$	−9.76580	−0.332818
$862$	16.1355	0.549578
$863$	33.5411	1.14175	0.570876	−	0.821037i	$-0.306604\pi$
$863$	33.5411	1.14175	0.570876	+	0.821037i	$0.306604\pi$
$864$	1.00000	0.0340207
$865$	−8.52010	−0.289692
$866$	1.99194	0.0676888
$867$	−14.3986	−0.489002
$868$	0	0
$869$	14.2802	0.484421
$870$	2.08805	0.0707916
$871$	−20.9171	−0.708749
$872$	15.9836	0.541273
$873$	−17.2595	−0.584144
$874$	3.42585	0.115881
$875$	−4.60673	−0.155736
$876$	−3.68047	−0.124351
$877$	−34.6928	−1.17149	−0.585746	−	0.810494i	$-0.699199\pi$
$877$	−34.6928	−1.17149	−0.585746	+	0.810494i	$0.699199\pi$
$878$	10.4789	0.353646
$879$	−9.53171	−0.321497
$880$	−2.73339	−0.0921424
$881$	−12.8319	−0.432318	−0.216159	−	0.976358i	$-0.569353\pi$
$881$	−12.8319	−0.432318	−0.216159	+	0.976358i	$0.569353\pi$
$882$	5.92042	0.199351
$883$	19.0016	0.639456	0.319728	−	0.947509i	$-0.396408\pi$
$883$	19.0016	0.639456	0.319728	+	0.947509i	$0.396408\pi$
$884$	−15.2262	−0.512111
$885$	−6.42253	−0.215891
$886$	−9.00174	−0.302419
$887$	−32.9743	−1.10717	−0.553585	−	0.832793i	$-0.686741\pi$
$887$	−32.9743	−1.10717	−0.553585	+	0.832793i	$0.686741\pi$
$888$	0.312686	0.0104931
$889$	−21.1279	−0.708608
$890$	1.75710	0.0588983
$891$	−6.03872	−0.202305
$892$	12.0253	0.402638
$893$	14.0325	0.469581
$894$	−13.0325	−0.435871
$895$	4.60976	0.154087
$896$	−1.03903	−0.0347115
$897$	−5.29196	−0.176693
$898$	27.8763	0.930243
$899$	0	0
$900$	−4.79511	−0.159837
$901$	−47.3628	−1.57788
$902$	56.7579	1.88983
$903$	−2.14816	−0.0714864
$904$	1.31804	0.0438374
$905$	11.8266	0.393128
$906$	12.0972	0.401904
$907$	32.8258	1.08996	0.544981	−	0.838449i	$-0.316537\pi$
$907$	32.8258	1.08996	0.544981	+	0.838449i	$0.316537\pi$
$908$	0.964464	0.0320069
$909$	−8.59736	−0.285156
$910$	1.27796	0.0423641
$911$	−38.5568	−1.27744	−0.638721	−	0.769438i	$-0.720536\pi$
$911$	−38.5568	−1.27744	−0.638721	+	0.769438i	$0.720536\pi$
$912$	−1.75909	−0.0582491
$913$	−28.6501	−0.948181
$914$	−7.57262	−0.250480
$915$	5.46898	0.180799
$916$	2.43645	0.0805027
$917$	−4.85436	−0.160305
$918$	5.60344	0.184941
$919$	−25.8811	−0.853738	−0.426869	−	0.904313i	$-0.640383\pi$
$919$	−25.8811	−0.853738	−0.426869	+	0.904313i	$0.640383\pi$
$920$	0.881529	0.0290632
$921$	−2.88410	−0.0950342
$922$	10.0697	0.331627
$923$	−2.25961	−0.0743760
$924$	6.27440	0.206413
$925$	−1.49937	−0.0492989
$926$	−31.0939	−1.02181
$927$	−5.92017	−0.194444
$928$	−4.61302	−0.151430
$929$	29.8957	0.980845	0.490422	−	0.871485i	$-0.336843\pi$
$929$	29.8957	0.980845	0.490422	+	0.871485i	$0.336843\pi$
$930$	0	0
$931$	−10.4145	−0.341322
$932$	10.9965	0.360201
$933$	−15.9285	−0.521475
$934$	19.2620	0.630273
$935$	−15.3164	−0.500899
$936$	2.71729	0.0888173
$937$	36.7548	1.20073	0.600364	−	0.799727i	$-0.295023\pi$
$937$	36.7548	1.20073	0.600364	+	0.799727i	$0.295023\pi$
$938$	−7.99822	−0.261151
$939$	21.7160	0.708675
$940$	3.61081	0.117772
$941$	−4.16587	−0.135804	−0.0679018	−	0.997692i	$-0.521630\pi$
$941$	−4.16587	−0.135804	−0.0679018	+	0.997692i	$0.521630\pi$
$942$	−11.6754	−0.380404
$943$	−18.3047	−0.596082
$944$	14.1890	0.461811
$945$	−0.470308	−0.0152991
$946$	12.4849	0.405920
$947$	14.4092	0.468237	0.234119	−	0.972208i	$-0.424780\pi$
$947$	14.4092	0.468237	0.234119	+	0.972208i	$0.424780\pi$
$948$	2.36477	0.0768040
$949$	−10.0009	−0.324642
$950$	8.43501	0.273668
$951$	−22.2506	−0.721526
$952$	−5.82213	−0.188696
$953$	24.7635	0.802168	0.401084	−	0.916041i	$-0.368634\pi$
$953$	24.7635	0.802168	0.401084	+	0.916041i	$0.368634\pi$
$954$	8.45244	0.273658
$955$	10.5696	0.342024
$956$	6.76301	0.218731
$957$	27.8568	0.900481
$958$	−3.98157	−0.128639
$959$	−3.53215	−0.114059
$960$	−0.452643	−0.0146090
$961$	0	0
$962$	0.849658	0.0273941
$963$	3.71557	0.119733
$964$	1.16965	0.0376720
$965$	−1.21634	−0.0391554
$966$	−2.02352	−0.0651058
$967$	−36.8404	−1.18471	−0.592353	−	0.805678i	$-0.701801\pi$
$967$	−36.8404	−1.18471	−0.592353	+	0.805678i	$0.701801\pi$
$968$	−25.4662	−0.818514
$969$	−9.85694	−0.316650
$970$	7.81237	0.250840
$971$	−11.8854	−0.381421	−0.190711	−	0.981646i	$-0.561079\pi$
$971$	−11.8854	−0.381421	−0.190711	+	0.981646i	$0.561079\pi$
$972$	−1.00000	−0.0320750
$973$	−11.0075	−0.352886
$974$	17.4003	0.557541
$975$	−13.0297	−0.417284
$976$	−12.0823	−0.386746
$977$	31.1938	0.997978	0.498989	−	0.866608i	$-0.333705\pi$
$977$	31.1938	0.997978	0.498989	+	0.866608i	$0.333705\pi$
$978$	9.38366	0.300056
$979$	23.4416	0.749196
$980$	−2.67984	−0.0856043
$981$	−15.9836	−0.510317
$982$	27.6396	0.882014
$983$	30.8821	0.984985	0.492492	−	0.870317i	$-0.336086\pi$
$983$	30.8821	0.984985	0.492492	+	0.870317i	$0.336086\pi$
$984$	9.39898	0.299629
$985$	−10.4259	−0.332196
$986$	−25.8488	−0.823194
$987$	−8.28850	−0.263826
$988$	−4.77994	−0.152070
$989$	−4.02644	−0.128033
$990$	2.73339	0.0868727
$991$	−44.9287	−1.42721	−0.713604	−	0.700550i	$-0.752938\pi$
$991$	−44.9287	−1.42721	−0.713604	+	0.700550i	$0.752938\pi$
$992$	0	0
$993$	3.01065	0.0955400
$994$	−0.864022	−0.0274051
$995$	−9.56529	−0.303240
$996$	−4.74440	−0.150332
$997$	4.51937	0.143130	0.0715649	−	0.997436i	$-0.477201\pi$
$997$	4.51937	0.143130	0.0715649	+	0.997436i	$0.477201\pi$
$998$	9.21673	0.291750
$999$	−0.312686	−0.00989295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5766.2.a.bl.1.3	✓	8
31.30	odd	2		5766.2.a.bn.1.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5766.2.a.bl.1.3	✓	8	1.1	even	1	trivial
5766.2.a.bn.1.3	yes	8	31.30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5766 = 2 \cdot 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5766.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.452643 q^{5} +1.00000 q^{6} +1.03903 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.452643 q^{10} -6.03872 q^{11} -1.00000 q^{12} -2.71729 q^{13} -1.03903 q^{14} -0.452643 q^{15} +1.00000 q^{16} +5.60344 q^{17} -1.00000 q^{18} +1.75909 q^{19} +0.452643 q^{20} -1.03903 q^{21} +6.03872 q^{22} -1.94752 q^{23} +1.00000 q^{24} -4.79511 q^{25} +2.71729 q^{26} -1.00000 q^{27} +1.03903 q^{28} +4.61302 q^{29} +0.452643 q^{30} -1.00000 q^{32} +6.03872 q^{33} -5.60344 q^{34} +0.470308 q^{35} +1.00000 q^{36} +0.312686 q^{37} -1.75909 q^{38} +2.71729 q^{39} -0.452643 q^{40} +9.39898 q^{41} +1.03903 q^{42} +2.06748 q^{43} -6.03872 q^{44} +0.452643 q^{45} +1.94752 q^{46} +7.97717 q^{47} -1.00000 q^{48} -5.92042 q^{49} +4.79511 q^{50} -5.60344 q^{51} -2.71729 q^{52} -8.45244 q^{53} +1.00000 q^{54} -2.73339 q^{55} -1.03903 q^{56} -1.75909 q^{57} -4.61302 q^{58} +14.1890 q^{59} -0.452643 q^{60} -12.0823 q^{61} +1.03903 q^{63} +1.00000 q^{64} -1.22996 q^{65} -6.03872 q^{66} +7.69779 q^{67} +5.60344 q^{68} +1.94752 q^{69} -0.470308 q^{70} +0.831569 q^{71} -1.00000 q^{72} +3.68047 q^{73} -0.312686 q^{74} +4.79511 q^{75} +1.75909 q^{76} -6.27440 q^{77} -2.71729 q^{78} -2.36477 q^{79} +0.452643 q^{80} +1.00000 q^{81} -9.39898 q^{82} +4.74440 q^{83} -1.03903 q^{84} +2.53636 q^{85} -2.06748 q^{86} -4.61302 q^{87} +6.03872 q^{88} -3.88188 q^{89} -0.452643 q^{90} -2.82334 q^{91} -1.94752 q^{92} -7.97717 q^{94} +0.796238 q^{95} +1.00000 q^{96} -17.2595 q^{97} +5.92042 q^{98} -6.03872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 8 q^{5} + 8 q^{6} - 8 q^{8} + 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 8 q^{20} + 8 q^{22} + 8 q^{24}+ \cdots - 8 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 8 * q^5 + 8 * q^6 - 8 * q^8 + 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 8 * q^20 + 8 * q^22 + 8 * q^24 + 8 * q^26 - 8 * q^27 - 16 * q^29 + 8 * q^30 - 8 * q^32 + 8 * q^33 - 8 * q^34 + 16 * q^35 + 8 * q^36 + 8 * q^38 + 8 * q^39 - 8 * q^40 + 16 * q^41 - 8 * q^44 + 8 * q^45 + 24 * q^47 - 8 * q^48 - 8 * q^49 - 8 * q^51 - 8 * q^52 - 16 * q^53 + 8 * q^54 - 8 * q^55 + 8 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 56 * q^61 + 8 * q^64 - 40 * q^65 - 8 * q^66 - 8 * q^67 + 8 * q^68 - 16 * q^70 + 8 * q^71 - 8 * q^72 - 32 * q^73 - 8 * q^76 - 16 * q^77 - 8 * q^78 + 8 * q^79 + 8 * q^80 + 8 * q^81 - 16 * q^82 + 8 * q^83 - 8 * q^85 + 16 * q^87 + 8 * q^88 - 48 * q^89 - 8 * q^90 - 32 * q^91 - 24 * q^94 - 8 * q^95 + 8 * q^96 - 8 * q^97 + 8 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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