LMFDB - Embedded newform 1166.2.a.j.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1166,2,Mod(1,1166)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1166, 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("1166.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1166 = 2 \cdot 11 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1166.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,4,2,4,1,2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$9.31055687568$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.67348.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 10x^{2} + 10x + 24 $ x^4 - 2x^3 - 10x^2 + 10*x + 24
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.47808$ of defining polynomial
Character	$\chi$	$=$	1166.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -2.47808 q^{3} +1.00000 q^{4} +1.50599 q^{5} -2.47808 q^{6} +4.61899 q^{7} +1.00000 q^{8} +3.14090 q^{9} +1.50599 q^{10} -1.00000 q^{11} -2.47808 q^{12} +5.95617 q^{13} +4.61899 q^{14} -3.73198 q^{15} +1.00000 q^{16} -7.12498 q^{17} +3.14090 q^{18} -2.50599 q^{19} +1.50599 q^{20} -11.4462 q^{21} -1.00000 q^{22} +5.36509 q^{23} -2.47808 q^{24} -2.73198 q^{25} +5.95617 q^{26} -0.349170 q^{27} +4.61899 q^{28} +0.634909 q^{29} -3.73198 q^{30} +8.09707 q^{31} +1.00000 q^{32} +2.47808 q^{33} -7.12498 q^{34} +6.95617 q^{35} +3.14090 q^{36} +0.972090 q^{37} -2.50599 q^{38} -14.7599 q^{39} +1.50599 q^{40} -12.3510 q^{41} -11.4462 q^{42} -5.75989 q^{43} -1.00000 q^{44} +4.73018 q^{45} +5.36509 q^{46} +7.21007 q^{47} -2.47808 q^{48} +14.3350 q^{49} -2.73198 q^{50} +17.6563 q^{51} +5.95617 q^{52} -1.00000 q^{53} -0.349170 q^{54} -1.50599 q^{55} +4.61899 q^{56} +6.21007 q^{57} +0.634909 q^{58} +3.38101 q^{59} -3.73198 q^{60} +13.2380 q^{61} +8.09707 q^{62} +14.5078 q^{63} +1.00000 q^{64} +8.96996 q^{65} +2.47808 q^{66} +8.74397 q^{67} -7.12498 q^{68} -13.2951 q^{69} +6.95617 q^{70} -4.57909 q^{71} +3.14090 q^{72} +3.71819 q^{73} +0.972090 q^{74} +6.77008 q^{75} -2.50599 q^{76} -4.61899 q^{77} -14.7599 q^{78} +1.59501 q^{79} +1.50599 q^{80} -8.55744 q^{81} -12.3510 q^{82} +12.3452 q^{83} -11.4462 q^{84} -10.7302 q^{85} -5.75989 q^{86} -1.57336 q^{87} -1.00000 q^{88} -7.81527 q^{89} +4.73018 q^{90} +27.5115 q^{91} +5.36509 q^{92} -20.0652 q^{93} +7.21007 q^{94} -3.77401 q^{95} -2.47808 q^{96} +5.64690 q^{97} +14.3350 q^{98} -3.14090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 12 q^{9} + q^{10} - 4 q^{11} + 2 q^{12} + 6 q^{14} + 5 q^{15} + 4 q^{16} - 11 q^{17} + 12 q^{18} - 5 q^{19} + q^{20} - 4 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 12 * q^9 + q^10 - 4 * q^11 + 2 * q^12 + 6 * q^14 + 5 * q^15 + 4 * q^16 - 11 * q^17 + 12 * q^18 - 5 * q^19 + q^20 - 4 * q^22 + 17 * q^23 + 2 * q^24 + 9 * q^25 + 20 * q^27 + 6 * q^28 + 7 * q^29 + 5 * q^30 + 8 * q^31 + 4 * q^32 - 2 * q^33 - 11 * q^34 + 4 * q^35 + 12 * q^36 - 3 * q^37 - 5 * q^38 - 46 * q^39 + q^40 - 17 * q^41 - 10 * q^43 - 4 * q^44 + 10 * q^45 + 17 * q^46 - 3 * q^47 + 2 * q^48 + 8 * q^49 + 9 * q^50 - 7 * q^51 - 4 * q^53 + 20 * q^54 - q^55 + 6 * q^56 - 7 * q^57 + 7 * q^58 + 26 * q^59 + 5 * q^60 + 28 * q^61 + 8 * q^62 + 42 * q^63 + 4 * q^64 - 9 * q^65 - 2 * q^66 + 5 * q^67 - 11 * q^68 - 7 * q^69 + 4 * q^70 - 9 * q^71 + 12 * q^72 + 16 * q^73 - 3 * q^74 + 15 * q^75 - 5 * q^76 - 6 * q^77 - 46 * q^78 + 14 * q^79 + q^80 + 8 * q^81 - 17 * q^82 + q^83 - 34 * q^85 - 10 * q^86 + 19 * q^87 - 4 * q^88 - 8 * q^89 + 10 * q^90 + 6 * q^91 + 17 * q^92 - 22 * q^93 - 3 * q^94 - 30 * q^95 + 2 * q^96 + 17 * q^97 + 8 * q^98 - 12 * 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
$3$	−2.47808	−1.43072	−0.715361	−	0.698755i	$-0.753738\pi$
$3$	−2.47808	−1.43072	−0.715361	+	0.698755i	$0.753738\pi$
$4$	1.00000	0.500000
$5$	1.50599	0.673501	0.336751	−	0.941594i	$-0.390672\pi$
$5$	1.50599	0.673501	0.336751	+	0.941594i	$0.390672\pi$
$6$	−2.47808	−1.01167
$7$	4.61899	1.74581	0.872907	−	0.487887i	$-0.162232\pi$
$7$	4.61899	1.74581	0.872907	+	0.487887i	$0.162232\pi$
$8$	1.00000	0.353553
$9$	3.14090	1.04697
$10$	1.50599	0.476237
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.47808	−0.715361
$13$	5.95617	1.65194	0.825972	−	0.563711i	$-0.190627\pi$
$13$	5.95617	1.65194	0.825972	+	0.563711i	$0.190627\pi$
$14$	4.61899	1.23448
$15$	−3.73198	−0.963593
$16$	1.00000	0.250000
$17$	−7.12498	−1.72806	−0.864031	−	0.503439i	$-0.832068\pi$
$17$	−7.12498	−1.72806	−0.864031	+	0.503439i	$0.832068\pi$
$18$	3.14090	0.740318
$19$	−2.50599	−0.574915	−0.287457	−	0.957793i	$-0.592810\pi$
$19$	−2.50599	−0.574915	−0.287457	+	0.957793i	$0.592810\pi$
$20$	1.50599	0.336751
$21$	−11.4462	−2.49777
$22$	−1.00000	−0.213201
$23$	5.36509	1.11870	0.559349	−	0.828932i	$-0.311051\pi$
$23$	5.36509	1.11870	0.559349	+	0.828932i	$0.311051\pi$
$24$	−2.47808	−0.505837
$25$	−2.73198	−0.546396
$26$	5.95617	1.16810
$27$	−0.349170	−0.0671978
$28$	4.61899	0.872907
$29$	0.634909	0.117900	0.0589498	−	0.998261i	$-0.481225\pi$
$29$	0.634909	0.117900	0.0589498	+	0.998261i	$0.481225\pi$
$30$	−3.73198	−0.681363
$31$	8.09707	1.45428	0.727139	−	0.686491i	$-0.240850\pi$
$31$	8.09707	1.45428	0.727139	+	0.686491i	$0.240850\pi$
$32$	1.00000	0.176777
$33$	2.47808	0.431379
$34$	−7.12498	−1.22192
$35$	6.95617	1.17581
$36$	3.14090	0.523484
$37$	0.972090	0.159811	0.0799053	−	0.996802i	$-0.474538\pi$
$37$	0.972090	0.159811	0.0799053	+	0.996802i	$0.474538\pi$
$38$	−2.50599	−0.406526
$39$	−14.7599	−2.36347
$40$	1.50599	0.238119
$41$	−12.3510	−1.92890	−0.964449	−	0.264270i	$-0.914869\pi$
$41$	−12.3510	−1.92890	−0.964449	+	0.264270i	$0.914869\pi$
$42$	−11.4462	−1.76619
$43$	−5.75989	−0.878375	−0.439188	−	0.898395i	$-0.644734\pi$
$43$	−5.75989	−0.878375	−0.439188	+	0.898395i	$0.644734\pi$
$44$	−1.00000	−0.150756
$45$	4.73018	0.705134
$46$	5.36509	0.791040
$47$	7.21007	1.05170	0.525848	−	0.850578i	$-0.323748\pi$
$47$	7.21007	1.05170	0.525848	+	0.850578i	$0.323748\pi$
$48$	−2.47808	−0.357681
$49$	14.3350	2.04786
$50$	−2.73198	−0.386360
$51$	17.6563	2.47238
$52$	5.95617	0.825972
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−0.349170	−0.0475160
$55$	−1.50599	−0.203068
$56$	4.61899	0.617238
$57$	6.21007	0.822543
$58$	0.634909	0.0833676
$59$	3.38101	0.440170	0.220085	−	0.975481i	$-0.429366\pi$
$59$	3.38101	0.440170	0.220085	+	0.975481i	$0.429366\pi$
$60$	−3.73198	−0.481797
$61$	13.2380	1.69495	0.847475	−	0.530836i	$-0.178122\pi$
$61$	13.2380	1.69495	0.847475	+	0.530836i	$0.178122\pi$
$62$	8.09707	1.02833
$63$	14.5078	1.82781
$64$	1.00000	0.125000
$65$	8.96996	1.11259
$66$	2.47808	0.305031
$67$	8.74397	1.06825	0.534123	−	0.845407i	$-0.320642\pi$
$67$	8.74397	1.06825	0.534123	+	0.845407i	$0.320642\pi$
$68$	−7.12498	−0.864031
$69$	−13.2951	−1.60055
$70$	6.95617	0.831421
$71$	−4.57909	−0.543438	−0.271719	−	0.962377i	$-0.587592\pi$
$71$	−4.57909	−0.543438	−0.271719	+	0.962377i	$0.587592\pi$
$72$	3.14090	0.370159
$73$	3.71819	0.435182	0.217591	−	0.976040i	$-0.430180\pi$
$73$	3.71819	0.435182	0.217591	+	0.976040i	$0.430180\pi$
$74$	0.972090	0.113003
$75$	6.77008	0.781742
$76$	−2.50599	−0.287457
$77$	−4.61899	−0.526383
$78$	−14.7599	−1.67123
$79$	1.59501	0.179453	0.0897264	−	0.995966i	$-0.471401\pi$
$79$	1.59501	0.179453	0.0897264	+	0.995966i	$0.471401\pi$
$80$	1.50599	0.168375
$81$	−8.55744	−0.950826
$82$	−12.3510	−1.36394
$83$	12.3452	1.35507	0.677533	−	0.735492i	$-0.263049\pi$
$83$	12.3452	1.35507	0.677533	+	0.735492i	$0.263049\pi$
$84$	−11.4462	−1.24889
$85$	−10.7302	−1.16385
$86$	−5.75989	−0.621105
$87$	−1.57336	−0.168682
$88$	−1.00000	−0.106600
$89$	−7.81527	−0.828417	−0.414208	−	0.910182i	$-0.635941\pi$
$89$	−7.81527	−0.828417	−0.414208	+	0.910182i	$0.635941\pi$
$90$	4.73018	0.498605
$91$	27.5115	2.88399
$92$	5.36509	0.559349
$93$	−20.0652	−2.08067
$94$	7.21007	0.743662
$95$	−3.77401	−0.387206
$96$	−2.47808	−0.252918
$97$	5.64690	0.573356	0.286678	−	0.958027i	$-0.407449\pi$
$97$	5.64690	0.573356	0.286678	+	0.958027i	$0.407449\pi$
$98$	14.3350	1.44806
$99$	−3.14090	−0.315673
$100$	−2.73198	−0.273198
$101$	4.74790	0.472434	0.236217	−	0.971700i	$-0.424092\pi$
$101$	4.74790	0.472434	0.236217	+	0.971700i	$0.424092\pi$
$102$	17.6563	1.74824
$103$	−6.47415	−0.637917	−0.318959	−	0.947769i	$-0.603333\pi$
$103$	−6.47415	−0.637917	−0.318959	+	0.947769i	$0.603333\pi$
$104$	5.95617	0.584050
$105$	−17.2380	−1.68225
$106$	−1.00000	−0.0971286
$107$	4.47629	0.432739	0.216369	−	0.976312i	$-0.430578\pi$
$107$	4.47629	0.432739	0.216369	+	0.976312i	$0.430578\pi$
$108$	−0.349170	−0.0335989
$109$	−4.49007	−0.430071	−0.215036	−	0.976606i	$-0.568987\pi$
$109$	−4.49007	−0.430071	−0.215036	+	0.976606i	$0.568987\pi$
$110$	−1.50599	−0.143591
$111$	−2.40892	−0.228645
$112$	4.61899	0.436453
$113$	−17.2500	−1.62274	−0.811370	−	0.584533i	$-0.801278\pi$
$113$	−17.2500	−1.62274	−0.811370	+	0.584533i	$0.801278\pi$
$114$	6.21007	0.581626
$115$	8.07980	0.753445
$116$	0.634909	0.0589498
$117$	18.7078	1.72953
$118$	3.38101	0.311247
$119$	−32.9102	−3.01687
$120$	−3.73198	−0.340682
$121$	1.00000	0.0909091
$122$	13.2380	1.19851
$123$	30.6067	2.75972
$124$	8.09707	0.727139
$125$	−11.6443	−1.04150
$126$	14.5078	1.29246
$127$	1.11119	0.0986026	0.0493013	−	0.998784i	$-0.484301\pi$
$127$	1.11119	0.0986026	0.0493013	+	0.998784i	$0.484301\pi$
$128$	1.00000	0.0883883
$129$	14.2735	1.25671
$130$	8.96996	0.786717
$131$	−7.70014	−0.672764	−0.336382	−	0.941726i	$-0.609203\pi$
$131$	−7.70014	−0.672764	−0.336382	+	0.941726i	$0.609203\pi$
$132$	2.47808	0.215690
$133$	−11.5752	−1.00369
$134$	8.74397	0.755364
$135$	−0.525848	−0.0452578
$136$	−7.12498	−0.610962
$137$	−16.4343	−1.40407	−0.702037	−	0.712141i	$-0.747726\pi$
$137$	−16.4343	−1.40407	−0.702037	+	0.712141i	$0.747726\pi$
$138$	−13.2951	−1.13176
$139$	−22.3152	−1.89275	−0.946375	−	0.323070i	$-0.895285\pi$
$139$	−22.3152	−1.89275	−0.946375	+	0.323070i	$0.895285\pi$
$140$	6.95617	0.587904
$141$	−17.8672	−1.50469
$142$	−4.57909	−0.384269
$143$	−5.95617	−0.498080
$144$	3.14090	0.261742
$145$	0.956169	0.0794055
$146$	3.71819	0.307720
$147$	−35.5235	−2.92993
$148$	0.972090	0.0799053
$149$	−13.9003	−1.13876	−0.569381	−	0.822074i	$-0.692817\pi$
$149$	−13.9003	−1.13876	−0.569381	+	0.822074i	$0.692817\pi$
$150$	6.77008	0.552775
$151$	−3.92826	−0.319677	−0.159839	−	0.987143i	$-0.551097\pi$
$151$	−3.92826	−0.319677	−0.159839	+	0.987143i	$0.551097\pi$
$152$	−2.50599	−0.203263
$153$	−22.3789	−1.80923
$154$	−4.61899	−0.372209
$155$	12.1941	0.979457
$156$	−14.7599	−1.18174
$157$	10.4382	0.833058	0.416529	−	0.909122i	$-0.363246\pi$
$157$	10.4382	0.833058	0.416529	+	0.909122i	$0.363246\pi$
$158$	1.59501	0.126892
$159$	2.47808	0.196525
$160$	1.50599	0.119059
$161$	24.7813	1.95304
$162$	−8.55744	−0.672336
$163$	−9.09921	−0.712705	−0.356352	−	0.934352i	$-0.615980\pi$
$163$	−9.09921	−0.712705	−0.356352	+	0.934352i	$0.615980\pi$
$164$	−12.3510	−0.964449
$165$	3.73198	0.290534
$166$	12.3452	0.958176
$167$	16.6824	1.29092	0.645462	−	0.763792i	$-0.276665\pi$
$167$	16.6824	1.29092	0.645462	+	0.763792i	$0.276665\pi$
$168$	−11.4462	−0.883097
$169$	22.4760	1.72892
$170$	−10.7302	−0.822967
$171$	−7.87109	−0.601917
$172$	−5.75989	−0.439188
$173$	17.7103	1.34649	0.673246	−	0.739419i	$-0.264900\pi$
$173$	17.7103	1.34649	0.673246	+	0.739419i	$0.264900\pi$
$174$	−1.57336	−0.119276
$175$	−12.6190	−0.953906
$176$	−1.00000	−0.0753778
$177$	−8.37843	−0.629762
$178$	−7.81527	−0.585779
$179$	22.8526	1.70808	0.854041	−	0.520205i	$-0.174145\pi$
$179$	22.8526	1.70808	0.854041	+	0.520205i	$0.174145\pi$
$180$	4.73018	0.352567
$181$	−15.4875	−1.15118	−0.575588	−	0.817740i	$-0.695227\pi$
$181$	−15.4875	−1.15118	−0.575588	+	0.817740i	$0.695227\pi$
$182$	27.5115	2.03929
$183$	−32.8048	−2.42500
$184$	5.36509	0.395520
$185$	1.46396	0.107633
$186$	−20.0652	−1.47125
$187$	7.12498	0.521030
$188$	7.21007	0.525848
$189$	−1.61281	−0.117315
$190$	−3.77401	−0.273796
$191$	6.24817	0.452101	0.226051	−	0.974116i	$-0.427419\pi$
$191$	6.24817	0.452101	0.226051	+	0.974116i	$0.427419\pi$
$192$	−2.47808	−0.178840
$193$	−19.7560	−1.42206	−0.711032	−	0.703159i	$-0.751772\pi$
$193$	−19.7560	−1.42206	−0.711032	+	0.703159i	$0.751772\pi$
$194$	5.64690	0.405424
$195$	−22.2283	−1.59180
$196$	14.3350	1.02393
$197$	5.54725	0.395225	0.197612	−	0.980280i	$-0.436681\pi$
$197$	5.54725	0.395225	0.197612	+	0.980280i	$0.436681\pi$
$198$	−3.14090	−0.223214
$199$	−20.9063	−1.48201	−0.741003	−	0.671502i	$-0.765650\pi$
$199$	−20.9063	−1.48201	−0.741003	+	0.671502i	$0.765650\pi$
$200$	−2.73198	−0.193180
$201$	−21.6683	−1.52836
$202$	4.74790	0.334061
$203$	2.93264	0.205831
$204$	17.6563	1.23619
$205$	−18.6005	−1.29911
$206$	−6.47415	−0.451076
$207$	16.8512	1.17124
$208$	5.95617	0.412986
$209$	2.50599	0.173343
$210$	−17.2380	−1.18953
$211$	−13.2899	−0.914912	−0.457456	−	0.889232i	$-0.651239\pi$
$211$	−13.2899	−0.914912	−0.457456	+	0.889232i	$0.651239\pi$
$212$	−1.00000	−0.0686803
$213$	11.3474	0.777509
$214$	4.47629	0.305993
$215$	−8.67436	−0.591587
$216$	−0.349170	−0.0237580
$217$	37.4003	2.53890
$218$	−4.49007	−0.304106
$219$	−9.21400	−0.622624
$220$	−1.50599	−0.101534
$221$	−42.4376	−2.85466
$222$	−2.40892	−0.161676
$223$	−7.07174	−0.473559	−0.236779	−	0.971563i	$-0.576092\pi$
$223$	−7.07174	−0.473559	−0.236779	+	0.971563i	$0.576092\pi$
$224$	4.61899	0.308619
$225$	−8.58089	−0.572059
$226$	−17.2500	−1.14745
$227$	−10.2460	−0.680053	−0.340026	−	0.940416i	$-0.610436\pi$
$227$	−10.2460	−0.680053	−0.340026	+	0.940416i	$0.610436\pi$
$228$	6.21007	0.411272
$229$	9.29515	0.614241	0.307120	−	0.951671i	$-0.400635\pi$
$229$	9.29515	0.614241	0.307120	+	0.951671i	$0.400635\pi$
$230$	8.07980	0.532766
$231$	11.4462	0.753107
$232$	0.634909	0.0416838
$233$	−16.1804	−1.06001	−0.530005	−	0.847994i	$-0.677810\pi$
$233$	−16.1804	−1.06001	−0.530005	+	0.847994i	$0.677810\pi$
$234$	18.7078	1.22296
$235$	10.8583	0.708319
$236$	3.38101	0.220085
$237$	−3.95257	−0.256747
$238$	−32.9102	−2.13325
$239$	8.55924	0.553651	0.276825	−	0.960920i	$-0.410718\pi$
$239$	8.55924	0.553651	0.276825	+	0.960920i	$0.410718\pi$
$240$	−3.73198	−0.240898
$241$	8.07174	0.519947	0.259973	−	0.965616i	$-0.416286\pi$
$241$	8.07174	0.519947	0.259973	+	0.965616i	$0.416286\pi$
$242$	1.00000	0.0642824
$243$	22.2536	1.42757
$244$	13.2380	0.847475
$245$	21.5885	1.37924
$246$	30.6067	1.95141
$247$	−14.9261	−0.949727
$248$	8.09707	0.514165
$249$	−30.5925	−1.93872
$250$	−11.6443	−0.736451
$251$	1.71819	0.108451	0.0542257	−	0.998529i	$-0.482731\pi$
$251$	1.71819	0.108451	0.0542257	+	0.998529i	$0.482731\pi$
$252$	14.5078	0.913905
$253$	−5.36509	−0.337300
$254$	1.11119	0.0697225
$255$	26.5903	1.66515
$256$	1.00000	0.0625000
$257$	−8.97029	−0.559551	−0.279776	−	0.960065i	$-0.590260\pi$
$257$	−8.97029	−0.559551	−0.279776	+	0.960065i	$0.590260\pi$
$258$	14.2735	0.888629
$259$	4.49007	0.279000
$260$	8.96996	0.556293
$261$	1.99419	0.123437
$262$	−7.70014	−0.475716
$263$	−8.01379	−0.494151	−0.247076	−	0.968996i	$-0.579470\pi$
$263$	−8.01379	−0.494151	−0.247076	+	0.968996i	$0.579470\pi$
$264$	2.47808	0.152516
$265$	−1.50599	−0.0925125
$266$	−11.5752	−0.709718
$267$	19.3669	1.18523
$268$	8.74397	0.534123
$269$	24.3630	1.48544	0.742718	−	0.669604i	$-0.233536\pi$
$269$	24.3630	1.48544	0.742718	+	0.669604i	$0.233536\pi$
$270$	−0.525848	−0.0320021
$271$	0.281806	0.0171185	0.00855926	−	0.999963i	$-0.497275\pi$
$271$	0.281806	0.0171185	0.00855926	+	0.999963i	$0.497275\pi$
$272$	−7.12498	−0.432015
$273$	−68.1758	−4.12618
$274$	−16.4343	−0.992830
$275$	2.73198	0.164745
$276$	−13.2951	−0.800274
$277$	11.1644	0.670806	0.335403	−	0.942075i	$-0.391128\pi$
$277$	11.1644	0.670806	0.335403	+	0.942075i	$0.391128\pi$
$278$	−22.3152	−1.33838
$279$	25.4321	1.52258
$280$	6.95617	0.415711
$281$	11.2873	0.673343	0.336671	−	0.941622i	$-0.390699\pi$
$281$	11.2873	0.673343	0.336671	+	0.941622i	$0.390699\pi$
$282$	−17.8672	−1.06397
$283$	−1.50342	−0.0893688	−0.0446844	−	0.999001i	$-0.514228\pi$
$283$	−1.50342	−0.0893688	−0.0446844	+	0.999001i	$0.514228\pi$
$284$	−4.57909	−0.271719
$285$	9.35232	0.553984
$286$	−5.95617	−0.352196
$287$	−57.0490	−3.36749
$288$	3.14090	0.185079
$289$	33.7654	1.98620
$290$	0.956169	0.0561482
$291$	−13.9935	−0.820313
$292$	3.71819	0.217591
$293$	−19.2654	−1.12550	−0.562750	−	0.826627i	$-0.690256\pi$
$293$	−19.2654	−1.12550	−0.562750	+	0.826627i	$0.690256\pi$
$294$	−35.5235	−2.07177
$295$	5.09179	0.296455
$296$	0.972090	0.0565016
$297$	0.349170	0.0202609
$298$	−13.9003	−0.805226
$299$	31.9554	1.84803
$300$	6.77008	0.390871
$301$	−26.6049	−1.53348
$302$	−3.92826	−0.226046
$303$	−11.7657	−0.675922
$304$	−2.50599	−0.143729
$305$	19.9363	1.14155
$306$	−22.3789	−1.27932
$307$	−18.4861	−1.05506	−0.527530	−	0.849536i	$-0.676882\pi$
$307$	−18.4861	−1.05506	−0.527530	+	0.849536i	$0.676882\pi$
$308$	−4.61899	−0.263191
$309$	16.0435	0.912683
$310$	12.1941	0.692581
$311$	−5.28001	−0.299402	−0.149701	−	0.988731i	$-0.547831\pi$
$311$	−5.28001	−0.299402	−0.149701	+	0.988731i	$0.547831\pi$
$312$	−14.7599	−0.835614
$313$	−15.1963	−0.858944	−0.429472	−	0.903080i	$-0.641300\pi$
$313$	−15.1963	−0.858944	−0.429472	+	0.903080i	$0.641300\pi$
$314$	10.4382	0.589061
$315$	21.8487	1.23103
$316$	1.59501	0.0897264
$317$	−21.8964	−1.22983	−0.614913	−	0.788595i	$-0.710809\pi$
$317$	−21.8964	−1.22983	−0.614913	+	0.788595i	$0.710809\pi$
$318$	2.47808	0.138964
$319$	−0.634909	−0.0355481
$320$	1.50599	0.0841876
$321$	−11.0926	−0.619129
$322$	24.7813	1.38101
$323$	17.8552	0.993488
$324$	−8.55744	−0.475413
$325$	−16.2721	−0.902616
$326$	−9.09921	−0.503958
$327$	11.1268	0.615312
$328$	−12.3510	−0.681968
$329$	33.3032	1.83607
$330$	3.73198	0.205439
$331$	26.5318	1.45832	0.729159	−	0.684344i	$-0.239911\pi$
$331$	26.5318	1.45832	0.729159	+	0.684344i	$0.239911\pi$
$332$	12.3452	0.677533
$333$	3.05324	0.167317
$334$	16.6824	0.912821
$335$	13.1684	0.719465
$336$	−11.4462	−0.624444
$337$	−19.8113	−1.07919	−0.539596	−	0.841924i	$-0.681423\pi$
$337$	−19.8113	−1.07919	−0.539596	+	0.841924i	$0.681423\pi$
$338$	22.4760	1.22253
$339$	42.7469	2.32169
$340$	−10.7302	−0.581926
$341$	−8.09707	−0.438481
$342$	−7.87109	−0.425620
$343$	33.8805	1.82937
$344$	−5.75989	−0.310553
$345$	−20.0224	−1.07797
$346$	17.7103	0.952113
$347$	−16.9841	−0.911753	−0.455877	−	0.890043i	$-0.650674\pi$
$347$	−16.9841	−0.911753	−0.455877	+	0.890043i	$0.650674\pi$
$348$	−1.57336	−0.0843408
$349$	4.92859	0.263822	0.131911	−	0.991262i	$-0.457889\pi$
$349$	4.92859	0.263822	0.131911	+	0.991262i	$0.457889\pi$
$350$	−12.6190	−0.674513
$351$	−2.07972	−0.111007
$352$	−1.00000	−0.0533002
$353$	2.00787	0.106868	0.0534339	−	0.998571i	$-0.482983\pi$
$353$	2.00787	0.106868	0.0534339	+	0.998571i	$0.482983\pi$
$354$	−8.37843	−0.445309
$355$	−6.89608	−0.366006
$356$	−7.81527	−0.414208
$357$	81.5543	4.31631
$358$	22.8526	1.20780
$359$	−19.7494	−1.04234	−0.521168	−	0.853454i	$-0.674504\pi$
$359$	−19.7494	−1.04234	−0.521168	+	0.853454i	$0.674504\pi$
$360$	4.73018	0.249302
$361$	−12.7200	−0.669473
$362$	−15.4875	−0.814005
$363$	−2.47808	−0.130066
$364$	27.5115	1.44199
$365$	5.59958	0.293095
$366$	−32.8048	−1.71474
$367$	18.6882	0.975514	0.487757	−	0.872980i	$-0.337815\pi$
$367$	18.6882	0.975514	0.487757	+	0.872980i	$0.337815\pi$
$368$	5.36509	0.279675
$369$	−38.7932	−2.01949
$370$	1.46396	0.0761078
$371$	−4.61899	−0.239806
$372$	−20.0652	−1.04033
$373$	−24.4441	−1.26567	−0.632834	−	0.774288i	$-0.718108\pi$
$373$	−24.4441	−1.26567	−0.632834	+	0.774288i	$0.718108\pi$
$374$	7.12498	0.368424
$375$	28.8556	1.49010
$376$	7.21007	0.371831
$377$	3.78162	0.194764
$378$	−1.61281	−0.0829541
$379$	30.3759	1.56030	0.780151	−	0.625591i	$-0.215142\pi$
$379$	30.3759	1.56030	0.780151	+	0.625591i	$0.215142\pi$
$380$	−3.77401	−0.193603
$381$	−2.75363	−0.141073
$382$	6.24817	0.319684
$383$	−17.2155	−0.879673	−0.439837	−	0.898078i	$-0.644964\pi$
$383$	−17.2155	−0.879673	−0.439837	+	0.898078i	$0.644964\pi$
$384$	−2.47808	−0.126459
$385$	−6.95617	−0.354519
$386$	−19.7560	−1.00555
$387$	−18.0913	−0.919630
$388$	5.64690	0.286678
$389$	9.56181	0.484803	0.242402	−	0.970176i	$-0.422065\pi$
$389$	9.56181	0.484803	0.242402	+	0.970176i	$0.422065\pi$
$390$	−22.2283	−1.12557
$391$	−38.2262	−1.93318
$392$	14.3350	0.724029
$393$	19.0816	0.962539
$394$	5.54725	0.279466
$395$	2.40208	0.120862
$396$	−3.14090	−0.157836
$397$	12.0055	0.602538	0.301269	−	0.953539i	$-0.402590\pi$
$397$	12.0055	0.602538	0.301269	+	0.953539i	$0.402590\pi$
$398$	−20.9063	−1.04794
$399$	28.6842	1.43601
$400$	−2.73198	−0.136599
$401$	−2.79387	−0.139519	−0.0697595	−	0.997564i	$-0.522223\pi$
$401$	−2.79387	−0.139519	−0.0697595	+	0.997564i	$0.522223\pi$
$402$	−21.6683	−1.08072
$403$	48.2275	2.40238
$404$	4.74790	0.236217
$405$	−12.8875	−0.640383
$406$	2.93264	0.145544
$407$	−0.972090	−0.0481847
$408$	17.6563	0.874118
$409$	−21.1902	−1.04779	−0.523894	−	0.851783i	$-0.675521\pi$
$409$	−21.1902	−1.04779	−0.523894	+	0.851783i	$0.675521\pi$
$410$	−18.6005	−0.918613
$411$	40.7255	2.00884
$412$	−6.47415	−0.318959
$413$	15.6169	0.768455
$414$	16.8512	0.828193
$415$	18.5919	0.912638
$416$	5.95617	0.292025
$417$	55.2989	2.70800
$418$	2.50599	0.122572
$419$	36.3463	1.77563	0.887815	−	0.460200i	$-0.152222\pi$
$419$	36.3463	1.77563	0.887815	+	0.460200i	$0.152222\pi$
$420$	−17.2380	−0.841127
$421$	−25.2855	−1.23234	−0.616170	−	0.787614i	$-0.711316\pi$
$421$	−25.2855	−1.23234	−0.616170	+	0.787614i	$0.711316\pi$
$422$	−13.2899	−0.646940
$423$	22.6461	1.10109
$424$	−1.00000	−0.0485643
$425$	19.4653	0.944207
$426$	11.3474	0.549782
$427$	61.1460	2.95906
$428$	4.47629	0.216369
$429$	14.7599	0.712614
$430$	−8.67436	−0.418315
$431$	−22.4446	−1.08112	−0.540558	−	0.841307i	$-0.681787\pi$
$431$	−22.4446	−1.08112	−0.540558	+	0.841307i	$0.681787\pi$
$432$	−0.349170	−0.0167994
$433$	−9.08688	−0.436688	−0.218344	−	0.975872i	$-0.570065\pi$
$433$	−9.08688	−0.436688	−0.218344	+	0.975872i	$0.570065\pi$
$434$	37.4003	1.79527
$435$	−2.36947	−0.113607
$436$	−4.49007	−0.215036
$437$	−13.4449	−0.643156
$438$	−9.21400	−0.440262
$439$	25.8491	1.23371	0.616855	−	0.787077i	$-0.288406\pi$
$439$	25.8491	1.23371	0.616855	+	0.787077i	$0.288406\pi$
$440$	−1.50599	−0.0717955
$441$	45.0250	2.14405
$442$	−42.4376	−2.01855
$443$	−10.0115	−0.475663	−0.237831	−	0.971306i	$-0.576437\pi$
$443$	−10.0115	−0.475663	−0.237831	+	0.971306i	$0.576437\pi$
$444$	−2.40892	−0.114322
$445$	−11.7697	−0.557939
$446$	−7.07174	−0.334857
$447$	34.4462	1.62925
$448$	4.61899	0.218227
$449$	−26.1424	−1.23374	−0.616869	−	0.787066i	$-0.711599\pi$
$449$	−26.1424	−1.23374	−0.616869	+	0.787066i	$0.711599\pi$
$450$	−8.58089	−0.404507
$451$	12.3510	0.581584
$452$	−17.2500	−0.811370
$453$	9.73456	0.457369
$454$	−10.2460	−0.480870
$455$	41.4321	1.94237
$456$	6.21007	0.290813
$457$	18.1203	0.847631	0.423815	−	0.905749i	$-0.360691\pi$
$457$	18.1203	0.847631	0.423815	+	0.905749i	$0.360691\pi$
$458$	9.29515	0.434334
$459$	2.48783	0.116122
$460$	8.07980	0.376722
$461$	−41.4818	−1.93200	−0.965999	−	0.258545i	$-0.916757\pi$
$461$	−41.4818	−1.93200	−0.965999	+	0.258545i	$0.916757\pi$
$462$	11.4462	0.532527
$463$	−21.1485	−0.982855	−0.491427	−	0.870919i	$-0.663525\pi$
$463$	−21.1485	−0.982855	−0.491427	+	0.870919i	$0.663525\pi$
$464$	0.634909	0.0294749
$465$	−30.2181	−1.40133
$466$	−16.1804	−0.749541
$467$	−9.20613	−0.426009	−0.213005	−	0.977051i	$-0.568325\pi$
$467$	−9.20613	−0.426009	−0.213005	+	0.977051i	$0.568325\pi$
$468$	18.7078	0.864766
$469$	40.3883	1.86496
$470$	10.8583	0.500857
$471$	−25.8667	−1.19188
$472$	3.38101	0.155624
$473$	5.75989	0.264840
$474$	−3.95257	−0.181548
$475$	6.84633	0.314131
$476$	−32.9102	−1.50844
$477$	−3.14090	−0.143812
$478$	8.55924	0.391490
$479$	23.0648	1.05386	0.526928	−	0.849910i	$-0.323344\pi$
$479$	23.0648	1.05386	0.526928	+	0.849910i	$0.323344\pi$
$480$	−3.73198	−0.170341
$481$	5.78993	0.263998
$482$	8.07174	0.367658
$483$	−61.4101	−2.79426
$484$	1.00000	0.0454545
$485$	8.50420	0.386156
$486$	22.2536	1.00944
$487$	−14.0786	−0.637961	−0.318981	−	0.947761i	$-0.603340\pi$
$487$	−14.0786	−0.637961	−0.318981	+	0.947761i	$0.603340\pi$
$488$	13.2380	0.599255
$489$	22.5486	1.01968
$490$	21.5885	0.975269
$491$	−11.0754	−0.499827	−0.249913	−	0.968268i	$-0.580402\pi$
$491$	−11.0754	−0.499827	−0.249913	+	0.968268i	$0.580402\pi$
$492$	30.6067	1.37986
$493$	−4.52371	−0.203738
$494$	−14.9261	−0.671558
$495$	−4.73018	−0.212606
$496$	8.09707	0.363569
$497$	−21.1508	−0.948741
$498$	−30.5925	−1.37088
$499$	−41.7805	−1.87035	−0.935176	−	0.354183i	$-0.884759\pi$
$499$	−41.7805	−1.87035	−0.935176	+	0.354183i	$0.884759\pi$
$500$	−11.6443	−0.520750
$501$	−41.3404	−1.84695
$502$	1.71819	0.0766867
$503$	−8.86851	−0.395427	−0.197714	−	0.980260i	$-0.563352\pi$
$503$	−8.86851	−0.395427	−0.197714	+	0.980260i	$0.563352\pi$
$504$	14.5078	0.646228
$505$	7.15031	0.318185
$506$	−5.36509	−0.238507
$507$	−55.6973	−2.47360
$508$	1.11119	0.0493013
$509$	24.5211	1.08688	0.543440	−	0.839448i	$-0.317121\pi$
$509$	24.5211	1.08688	0.543440	+	0.839448i	$0.317121\pi$
$510$	26.5903	1.17744
$511$	17.1743	0.759746
$512$	1.00000	0.0441942
$513$	0.875018	0.0386330
$514$	−8.97029	−0.395663
$515$	−9.75004	−0.429638
$516$	14.2735	0.628356
$517$	−7.21007	−0.317098
$518$	4.49007	0.197282
$519$	−43.8877	−1.92646
$520$	8.96996	0.393359
$521$	31.0051	1.35836	0.679180	−	0.733972i	$-0.262336\pi$
$521$	31.0051	1.35836	0.679180	+	0.733972i	$0.262336\pi$
$522$	1.99419	0.0872832
$523$	16.6116	0.726373	0.363187	−	0.931716i	$-0.381689\pi$
$523$	16.6116	0.726373	0.363187	+	0.931716i	$0.381689\pi$
$524$	−7.70014	−0.336382
$525$	31.2709	1.36477
$526$	−8.01379	−0.349418
$527$	−57.6915	−2.51308
$528$	2.47808	0.107845
$529$	5.78420	0.251487
$530$	−1.50599	−0.0654162
$531$	10.6194	0.460844
$532$	−11.5752	−0.501847
$533$	−73.5645	−3.18643
$534$	19.3669	0.838087
$535$	6.74126	0.291450
$536$	8.74397	0.377682
$537$	−56.6306	−2.44379
$538$	24.3630	1.05036
$539$	−14.3350	−0.617454
$540$	−0.525848	−0.0226289
$541$	−0.830853	−0.0357211	−0.0178606	−	0.999840i	$-0.505685\pi$
$541$	−0.830853	−0.0357211	−0.0178606	+	0.999840i	$0.505685\pi$
$542$	0.281806	0.0121046
$543$	38.3793	1.64701
$544$	−7.12498	−0.305481
$545$	−6.76202	−0.289653
$546$	−68.1758	−2.91765
$547$	−32.1203	−1.37336	−0.686682	−	0.726958i	$-0.740933\pi$
$547$	−32.1203	−1.37336	−0.686682	+	0.726958i	$0.740933\pi$
$548$	−16.4343	−0.702037
$549$	41.5792	1.77456
$550$	2.73198	0.116492
$551$	−1.59108	−0.0677822
$552$	−13.2951	−0.565879
$553$	7.36733	0.313291
$554$	11.1644	0.474331
$555$	−3.62782	−0.153992
$556$	−22.3152	−0.946375
$557$	27.8247	1.17897	0.589485	−	0.807780i	$-0.299331\pi$
$557$	27.8247	1.17897	0.589485	+	0.807780i	$0.299331\pi$
$558$	25.4321	1.07663
$559$	−34.3069	−1.45103
$560$	6.95617	0.293952
$561$	−17.6563	−0.745450
$562$	11.2873	0.476125
$563$	16.2278	0.683920	0.341960	−	0.939715i	$-0.388909\pi$
$563$	16.2278	0.683920	0.341960	+	0.939715i	$0.388909\pi$
$564$	−17.8672	−0.752343
$565$	−25.9783	−1.09292
$566$	−1.50342	−0.0631933
$567$	−39.5267	−1.65997
$568$	−4.57909	−0.192134
$569$	23.4141	0.981569	0.490784	−	0.871281i	$-0.336710\pi$
$569$	23.4141	0.981569	0.490784	+	0.871281i	$0.336710\pi$
$570$	9.35232	0.391726
$571$	29.1330	1.21918	0.609590	−	0.792717i	$-0.291334\pi$
$571$	29.1330	1.21918	0.609590	+	0.792717i	$0.291334\pi$
$572$	−5.95617	−0.249040
$573$	−15.4835	−0.646832
$574$	−57.0490	−2.38118
$575$	−14.6573	−0.611253
$576$	3.14090	0.130871
$577$	−45.9355	−1.91232	−0.956161	−	0.292842i	$-0.905399\pi$
$577$	−45.9355	−1.91232	−0.956161	+	0.292842i	$0.905399\pi$
$578$	33.7654	1.40445
$579$	48.9569	2.03458
$580$	0.956169	0.0397028
$581$	57.0225	2.36569
$582$	−13.9935	−0.580049
$583$	1.00000	0.0414158
$584$	3.71819	0.153860
$585$	28.1738	1.16484
$586$	−19.2654	−0.795848
$587$	−20.6697	−0.853128	−0.426564	−	0.904457i	$-0.640276\pi$
$587$	−20.6697	−0.853128	−0.426564	+	0.904457i	$0.640276\pi$
$588$	−35.5235	−1.46496
$589$	−20.2912	−0.836085
$590$	5.09179	0.209625
$591$	−13.7465	−0.565457
$592$	0.972090	0.0399527
$593$	−17.5530	−0.720814	−0.360407	−	0.932795i	$-0.617362\pi$
$593$	−17.5530	−0.720814	−0.360407	+	0.932795i	$0.617362\pi$
$594$	0.349170	0.0143266
$595$	−49.5626	−2.03187
$596$	−13.9003	−0.569381
$597$	51.8075	2.12034
$598$	31.9554	1.30675
$599$	11.5697	0.472724	0.236362	−	0.971665i	$-0.424045\pi$
$599$	11.5697	0.472724	0.236362	+	0.971665i	$0.424045\pi$
$600$	6.77008	0.276387
$601$	40.9759	1.67144	0.835720	−	0.549155i	$-0.185050\pi$
$601$	40.9759	1.67144	0.835720	+	0.549155i	$0.185050\pi$
$602$	−26.6049	−1.08433
$603$	27.4640	1.11842
$604$	−3.92826	−0.159839
$605$	1.50599	0.0612274
$606$	−11.7657	−0.477949
$607$	33.9630	1.37852	0.689258	−	0.724516i	$-0.257937\pi$
$607$	33.9630	1.37852	0.689258	+	0.724516i	$0.257937\pi$
$608$	−2.50599	−0.101631
$609$	−7.26732	−0.294487
$610$	19.9363	0.807198
$611$	42.9444	1.73734
$612$	−22.3789	−0.904613
$613$	−14.3748	−0.580594	−0.290297	−	0.956937i	$-0.593754\pi$
$613$	−14.3748	−0.580594	−0.290297	+	0.956937i	$0.593754\pi$
$614$	−18.4861	−0.746040
$615$	46.0936	1.85867
$616$	−4.61899	−0.186104
$617$	10.0789	0.405762	0.202881	−	0.979203i	$-0.434970\pi$
$617$	10.0789	0.405762	0.202881	+	0.979203i	$0.434970\pi$
$618$	16.0435	0.645364
$619$	−6.83711	−0.274807	−0.137403	−	0.990515i	$-0.543876\pi$
$619$	−6.83711	−0.274807	−0.137403	+	0.990515i	$0.543876\pi$
$620$	12.1941	0.489729
$621$	−1.87333	−0.0751741
$622$	−5.28001	−0.211709
$623$	−36.0986	−1.44626
$624$	−14.7599	−0.590869
$625$	−3.87637	−0.155055
$626$	−15.1963	−0.607365
$627$	−6.21007	−0.248006
$628$	10.4382	0.416529
$629$	−6.92613	−0.276163
$630$	21.8487	0.870471
$631$	−12.1720	−0.484558	−0.242279	−	0.970207i	$-0.577895\pi$
$631$	−12.1720	−0.484558	−0.242279	+	0.970207i	$0.577895\pi$
$632$	1.59501	0.0634461
$633$	32.9334	1.30899
$634$	−21.8964	−0.869618
$635$	1.67345	0.0664089
$636$	2.47808	0.0982624
$637$	85.3820	3.38296
$638$	−0.634909	−0.0251363
$639$	−14.3825	−0.568962
$640$	1.50599	0.0595297
$641$	−36.7916	−1.45318	−0.726590	−	0.687071i	$-0.758896\pi$
$641$	−36.7916	−1.45318	−0.726590	+	0.687071i	$0.758896\pi$
$642$	−11.0926	−0.437791
$643$	0.536038	0.0211393	0.0105696	−	0.999944i	$-0.496636\pi$
$643$	0.536038	0.0211393	0.0105696	+	0.999944i	$0.496636\pi$
$644$	24.7813	0.976520
$645$	21.4958	0.846396
$646$	17.8552	0.702502
$647$	−46.1383	−1.81388	−0.906942	−	0.421255i	$-0.861590\pi$
$647$	−46.1383	−1.81388	−0.906942	+	0.421255i	$0.861590\pi$
$648$	−8.55744	−0.336168
$649$	−3.38101	−0.132716
$650$	−16.2721	−0.638246
$651$	−92.6811	−3.63246
$652$	−9.09921	−0.356352
$653$	−25.1503	−0.984208	−0.492104	−	0.870536i	$-0.663772\pi$
$653$	−25.1503	−0.984208	−0.492104	+	0.870536i	$0.663772\pi$
$654$	11.1268	0.435092
$655$	−11.5964	−0.453107
$656$	−12.3510	−0.482224
$657$	11.6785	0.455621
$658$	33.3032	1.29829
$659$	−48.0610	−1.87219	−0.936095	−	0.351748i	$-0.885587\pi$
$659$	−48.0610	−1.87219	−0.936095	+	0.351748i	$0.885587\pi$
$660$	3.73198	0.145267
$661$	21.4763	0.835331	0.417665	−	0.908601i	$-0.362848\pi$
$661$	21.4763	0.835331	0.417665	+	0.908601i	$0.362848\pi$
$662$	26.5318	1.03119
$663$	105.164	4.08423
$664$	12.3452	0.479088
$665$	−17.4321	−0.675989
$666$	3.05324	0.118311
$667$	3.40634	0.131894
$668$	16.6824	0.645462
$669$	17.5244	0.677531
$670$	13.1684	0.508738
$671$	−13.2380	−0.511046
$672$	−11.4462	−0.441548
$673$	−49.6321	−1.91318	−0.956588	−	0.291444i	$-0.905864\pi$
$673$	−49.6321	−1.91318	−0.956588	+	0.291444i	$0.905864\pi$
$674$	−19.8113	−0.763104
$675$	0.953926	0.0367166
$676$	22.4760	0.864460
$677$	29.2620	1.12463	0.562314	−	0.826924i	$-0.309911\pi$
$677$	29.2620	1.12463	0.562314	+	0.826924i	$0.309911\pi$
$678$	42.7469	1.64168
$679$	26.0830	1.00097
$680$	−10.7302	−0.411484
$681$	25.3905	0.972967
$682$	−8.09707	−0.310053
$683$	−8.42484	−0.322368	−0.161184	−	0.986924i	$-0.551531\pi$
$683$	−8.42484	−0.322368	−0.161184	+	0.986924i	$0.551531\pi$
$684$	−7.87109	−0.300958
$685$	−24.7499	−0.945645
$686$	33.8805	1.29356
$687$	−23.0342	−0.878808
$688$	−5.75989	−0.219594
$689$	−5.95617	−0.226912
$690$	−20.0224	−0.762240
$691$	37.6009	1.43041	0.715203	−	0.698916i	$-0.246334\pi$
$691$	37.6009	1.43041	0.715203	+	0.698916i	$0.246334\pi$
$692$	17.7103	0.673246
$693$	−14.5078	−0.551105
$694$	−16.9841	−0.644707
$695$	−33.6066	−1.27477
$696$	−1.57336	−0.0596380
$697$	88.0004	3.33325
$698$	4.92859	0.186550
$699$	40.0963	1.51658
$700$	−12.6190	−0.476953
$701$	19.9540	0.753654	0.376827	−	0.926284i	$-0.377015\pi$
$701$	19.9540	0.753654	0.376827	+	0.926284i	$0.377015\pi$
$702$	−2.07972	−0.0784938
$703$	−2.43605	−0.0918775
$704$	−1.00000	−0.0376889
$705$	−26.9078	−1.01341
$706$	2.00787	0.0755670
$707$	21.9305	0.824781
$708$	−8.37843	−0.314881
$709$	48.5447	1.82313	0.911567	−	0.411152i	$-0.134874\pi$
$709$	48.5447	1.82313	0.911567	+	0.411152i	$0.134874\pi$
$710$	−6.89608	−0.258805
$711$	5.00977	0.187881
$712$	−7.81527	−0.292889
$713$	43.4415	1.62690
$714$	81.5543	3.05209
$715$	−8.96996	−0.335457
$716$	22.8526	0.854041
$717$	−21.2105	−0.792121
$718$	−19.7494	−0.737043
$719$	−23.4561	−0.874765	−0.437382	−	0.899276i	$-0.644094\pi$
$719$	−23.4561	−0.874765	−0.437382	+	0.899276i	$0.644094\pi$
$720$	4.73018	0.176283
$721$	−29.9040	−1.11368
$722$	−12.7200	−0.473389
$723$	−20.0025	−0.743899
$724$	−15.4875	−0.575588
$725$	−1.73456	−0.0644199
$726$	−2.47808	−0.0919703
$727$	7.85381	0.291282	0.145641	−	0.989338i	$-0.453476\pi$
$727$	7.85381	0.291282	0.145641	+	0.989338i	$0.453476\pi$
$728$	27.5115	1.01964
$729$	−29.4739	−1.09163
$730$	5.59958	0.207250
$731$	41.0391	1.51789
$732$	−32.8048	−1.21250
$733$	−22.9665	−0.848286	−0.424143	−	0.905595i	$-0.639425\pi$
$733$	−22.9665	−0.848286	−0.424143	+	0.905595i	$0.639425\pi$
$734$	18.6882	0.689792
$735$	−53.4981	−1.97331
$736$	5.36509	0.197760
$737$	−8.74397	−0.322088
$738$	−38.7932	−1.42800
$739$	9.97937	0.367097	0.183548	−	0.983011i	$-0.441242\pi$
$739$	9.97937	0.367097	0.183548	+	0.983011i	$0.441242\pi$
$740$	1.46396	0.0538163
$741$	36.9882	1.35880
$742$	−4.61899	−0.169568
$743$	−26.0157	−0.954422	−0.477211	−	0.878789i	$-0.658352\pi$
$743$	−26.0157	−0.954422	−0.477211	+	0.878789i	$0.658352\pi$
$744$	−20.0652	−0.735627
$745$	−20.9338	−0.766957
$746$	−24.4441	−0.894962
$747$	38.7752	1.41871
$748$	7.12498	0.260515
$749$	20.6759	0.755481
$750$	28.8556	1.05366
$751$	−17.5806	−0.641526	−0.320763	−	0.947159i	$-0.603939\pi$
$751$	−17.5806	−0.641526	−0.320763	+	0.947159i	$0.603939\pi$
$752$	7.21007	0.262924
$753$	−4.25783	−0.155164
$754$	3.78162	0.137719
$755$	−5.91594	−0.215303
$756$	−1.61281	−0.0586574
$757$	21.8029	0.792441	0.396221	−	0.918155i	$-0.370322\pi$
$757$	21.8029	0.792441	0.396221	+	0.918155i	$0.370322\pi$
$758$	30.3759	1.10330
$759$	13.2951	0.482583
$760$	−3.77401	−0.136898
$761$	20.5054	0.743320	0.371660	−	0.928369i	$-0.378789\pi$
$761$	20.5054	0.743320	0.371660	+	0.928369i	$0.378789\pi$
$762$	−2.75363	−0.0997536
$763$	−20.7396	−0.750824
$764$	6.24817	0.226051
$765$	−33.7025	−1.21852
$766$	−17.2155	−0.622023
$767$	20.1379	0.727137
$768$	−2.47808	−0.0894202
$769$	16.5069	0.595254	0.297627	−	0.954682i	$-0.403805\pi$
$769$	16.5069	0.595254	0.297627	+	0.954682i	$0.403805\pi$
$770$	−6.95617	−0.250683
$771$	22.2291	0.800563
$772$	−19.7560	−0.711032
$773$	−21.7273	−0.781476	−0.390738	−	0.920502i	$-0.627780\pi$
$773$	−21.7273	−0.781476	−0.390738	+	0.920502i	$0.627780\pi$
$774$	−18.0913	−0.650277
$775$	−22.1210	−0.794612
$776$	5.64690	0.202712
$777$	−11.1268	−0.399171
$778$	9.56181	0.342808
$779$	30.9515	1.10895
$780$	−22.2283	−0.795901
$781$	4.57909	0.163853
$782$	−38.2262	−1.36697
$783$	−0.221691	−0.00792259
$784$	14.3350	0.511966
$785$	15.7198	0.561065
$786$	19.0816	0.680618
$787$	4.20085	0.149744	0.0748720	−	0.997193i	$-0.476145\pi$
$787$	4.20085	0.149744	0.0748720	+	0.997193i	$0.476145\pi$
$788$	5.54725	0.197612
$789$	19.8588	0.706994
$790$	2.40208	0.0854621
$791$	−79.6774	−2.83300
$792$	−3.14090	−0.111607
$793$	78.8476	2.79996
$794$	12.0055	0.426058
$795$	3.73198	0.132360
$796$	−20.9063	−0.741003
$797$	31.5614	1.11796	0.558981	−	0.829181i	$-0.311193\pi$
$797$	31.5614	1.11796	0.558981	+	0.829181i	$0.311193\pi$
$798$	28.6842	1.01541
$799$	−51.3716	−1.81740
$800$	−2.73198	−0.0965901
$801$	−24.5470	−0.867325
$802$	−2.79387	−0.0986549
$803$	−3.71819	−0.131212
$804$	−21.6683	−0.764182
$805$	37.3205	1.31537
$806$	48.2275	1.69874
$807$	−60.3735	−2.12525
$808$	4.74790	0.167031
$809$	−5.16604	−0.181628	−0.0908142	−	0.995868i	$-0.528947\pi$
$809$	−5.16604	−0.181628	−0.0908142	+	0.995868i	$0.528947\pi$
$810$	−12.8875	−0.452819
$811$	−23.8436	−0.837263	−0.418631	−	0.908156i	$-0.637490\pi$
$811$	−23.8436	−0.837263	−0.418631	+	0.908156i	$0.637490\pi$
$812$	2.93264	0.102915
$813$	−0.698340	−0.0244919
$814$	−0.972090	−0.0340717
$815$	−13.7034	−0.480007
$816$	17.6563	0.618094
$817$	14.4343	0.504991
$818$	−21.1902	−0.740898
$819$	86.4109	3.01944
$820$	−18.6005	−0.649557
$821$	1.12363	0.0392149	0.0196074	−	0.999808i	$-0.493758\pi$
$821$	1.12363	0.0392149	0.0196074	+	0.999808i	$0.493758\pi$
$822$	40.7255	1.42046
$823$	34.1301	1.18970	0.594851	−	0.803836i	$-0.297211\pi$
$823$	34.1301	1.18970	0.594851	+	0.803836i	$0.297211\pi$
$824$	−6.47415	−0.225538
$825$	−6.77008	−0.235704
$826$	15.6169	0.543380
$827$	57.2747	1.99164	0.995818	−	0.0913553i	$-0.0291199\pi$
$827$	57.2747	1.99164	0.995818	+	0.0913553i	$0.0291199\pi$
$828$	16.8512	0.585621
$829$	−0.817175	−0.0283817	−0.0141908	−	0.999899i	$-0.504517\pi$
$829$	−0.817175	−0.0283817	−0.0141908	+	0.999899i	$0.504517\pi$
$830$	18.5919	0.645333
$831$	−27.6664	−0.959737
$832$	5.95617	0.206493
$833$	−102.137	−3.53884
$834$	55.2989	1.91485
$835$	25.1236	0.869439
$836$	2.50599	0.0866716
$837$	−2.82725	−0.0977242
$838$	36.3463	1.25556
$839$	52.6583	1.81797	0.908983	−	0.416833i	$-0.136860\pi$
$839$	52.6583	1.81797	0.908983	+	0.416833i	$0.136860\pi$
$840$	−17.2380	−0.594767
$841$	−28.5969	−0.986100
$842$	−25.2855	−0.871395
$843$	−27.9708	−0.963367
$844$	−13.2899	−0.457456
$845$	33.8487	1.16443
$846$	22.6461	0.778590
$847$	4.61899	0.158710
$848$	−1.00000	−0.0343401
$849$	3.72559	0.127862
$850$	19.4653	0.667655
$851$	5.21535	0.178780
$852$	11.3474	0.388755
$853$	−9.20254	−0.315089	−0.157544	−	0.987512i	$-0.550358\pi$
$853$	−9.20254	−0.315089	−0.157544	+	0.987512i	$0.550358\pi$
$854$	61.1460	2.09237
$855$	−11.8538	−0.405392
$856$	4.47629	0.152996
$857$	−18.7853	−0.641695	−0.320847	−	0.947131i	$-0.603968\pi$
$857$	−18.7853	−0.641695	−0.320847	+	0.947131i	$0.603968\pi$
$858$	14.7599	0.503894
$859$	29.0913	0.992584	0.496292	−	0.868156i	$-0.334695\pi$
$859$	29.0913	0.992584	0.496292	+	0.868156i	$0.334695\pi$
$860$	−8.67436	−0.295793
$861$	141.372	4.81795
$862$	−22.4446	−0.764465
$863$	3.58579	0.122062	0.0610309	−	0.998136i	$-0.480561\pi$
$863$	3.58579	0.122062	0.0610309	+	0.998136i	$0.480561\pi$
$864$	−0.349170	−0.0118790
$865$	26.6717	0.906863
$866$	−9.08688	−0.308785
$867$	−83.6734	−2.84170
$868$	37.4003	1.26945
$869$	−1.59501	−0.0541070
$870$	−2.36947	−0.0803325
$871$	52.0806	1.76468
$872$	−4.49007	−0.152053
$873$	17.7364	0.600285
$874$	−13.4449	−0.454780
$875$	−53.7850	−1.81826
$876$	−9.21400	−0.311312
$877$	39.9449	1.34885	0.674423	−	0.738346i	$-0.264393\pi$
$877$	39.9449	1.34885	0.674423	+	0.738346i	$0.264393\pi$
$878$	25.8491	0.872365
$879$	47.7414	1.61028
$880$	−1.50599	−0.0507671
$881$	−7.72445	−0.260243	−0.130122	−	0.991498i	$-0.541537\pi$
$881$	−7.72445	−0.260243	−0.130122	+	0.991498i	$0.541537\pi$
$882$	45.0250	1.51607
$883$	−8.37450	−0.281824	−0.140912	−	0.990022i	$-0.545004\pi$
$883$	−8.37450	−0.281824	−0.140912	+	0.990022i	$0.545004\pi$
$884$	−42.4376	−1.42733
$885$	−12.6179	−0.424145
$886$	−10.0115	−0.336344
$887$	0.0673636	0.00226185	0.00113092	−	0.999999i	$-0.499640\pi$
$887$	0.0673636	0.00226185	0.00113092	+	0.999999i	$0.499640\pi$
$888$	−2.40892	−0.0808381
$889$	5.13259	0.172142
$890$	−11.7697	−0.394523
$891$	8.55744	0.286685
$892$	−7.07174	−0.236779
$893$	−18.0684	−0.604635
$894$	34.4462	1.15205
$895$	34.4159	1.15040
$896$	4.61899	0.154310
$897$	−79.1882	−2.64402
$898$	−26.1424	−0.872385
$899$	5.14090	0.171459
$900$	−8.58089	−0.286030
$901$	7.12498	0.237368
$902$	12.3510	0.411242
$903$	65.9291	2.19398
$904$	−17.2500	−0.573725
$905$	−23.3241	−0.775319
$906$	9.73456	0.323409
$907$	33.9356	1.12681	0.563407	−	0.826179i	$-0.309490\pi$
$907$	33.9356	1.12681	0.563407	+	0.826179i	$0.309490\pi$
$908$	−10.2460	−0.340026
$909$	14.9127	0.494623
$910$	41.4321	1.37346
$911$	29.0764	0.963345	0.481673	−	0.876351i	$-0.340029\pi$
$911$	29.0764	0.963345	0.481673	+	0.876351i	$0.340029\pi$
$912$	6.21007	0.205636
$913$	−12.3452	−0.408568
$914$	18.1203	0.599365
$915$	−49.4039	−1.63324
$916$	9.29515	0.307120
$917$	−35.5668	−1.17452
$918$	2.48783	0.0821106
$919$	−50.5913	−1.66885	−0.834426	−	0.551120i	$-0.814201\pi$
$919$	−50.5913	−1.66885	−0.834426	+	0.551120i	$0.814201\pi$
$920$	8.07980	0.266383
$921$	45.8102	1.50950
$922$	−41.4818	−1.36613
$923$	−27.2738	−0.897729
$924$	11.4462	0.376554
$925$	−2.65573	−0.0873199
$926$	−21.1485	−0.694983
$927$	−20.3347	−0.667879
$928$	0.634909	0.0208419
$929$	−17.4365	−0.572073	−0.286036	−	0.958219i	$-0.592338\pi$
$929$	−17.4365	−0.572073	−0.286036	+	0.958219i	$0.592338\pi$
$930$	−30.2181	−0.990891
$931$	−35.9235	−1.17735
$932$	−16.1804	−0.530005
$933$	13.0843	0.428361
$934$	−9.20613	−0.301234
$935$	10.7302	0.350914
$936$	18.7078	0.611482
$937$	−36.6042	−1.19581	−0.597903	−	0.801568i	$-0.703999\pi$
$937$	−36.6042	−1.19581	−0.597903	+	0.801568i	$0.703999\pi$
$938$	40.3883	1.31872
$939$	37.6577	1.22891
$940$	10.8583	0.354159
$941$	17.0033	0.554293	0.277147	−	0.960828i	$-0.410611\pi$
$941$	17.0033	0.554293	0.277147	+	0.960828i	$0.410611\pi$
$942$	−25.8667	−0.842783
$943$	−66.2641	−2.15786
$944$	3.38101	0.110043
$945$	−2.42889	−0.0790116
$946$	5.75989	0.187270
$947$	−1.51934	−0.0493718	−0.0246859	−	0.999695i	$-0.507859\pi$
$947$	−1.51934	−0.0493718	−0.0246859	+	0.999695i	$0.507859\pi$
$948$	−3.95257	−0.128374
$949$	22.1462	0.718896
$950$	6.84633	0.222124
$951$	54.2612	1.75954
$952$	−32.9102	−1.06663
$953$	10.6194	0.343997	0.171999	−	0.985097i	$-0.444978\pi$
$953$	10.6194	0.343997	0.171999	+	0.985097i	$0.444978\pi$
$954$	−3.14090	−0.101690
$955$	9.40970	0.304491
$956$	8.55924	0.276825
$957$	1.57336	0.0508594
$958$	23.0648	0.745189
$959$	−75.9096	−2.45125
$960$	−3.73198	−0.120449
$961$	34.5626	1.11492
$962$	5.78993	0.186675
$963$	14.0596	0.453064
$964$	8.07174	0.259973
$965$	−29.7524	−0.957762
$966$	−61.4101	−1.97584
$967$	8.90079	0.286230	0.143115	−	0.989706i	$-0.454288\pi$
$967$	8.90079	0.286230	0.143115	+	0.989706i	$0.454288\pi$
$968$	1.00000	0.0321412
$969$	−44.2466	−1.42141
$970$	8.50420	0.273053
$971$	7.99169	0.256466	0.128233	−	0.991744i	$-0.459070\pi$
$971$	7.99169	0.256466	0.128233	+	0.991744i	$0.459070\pi$
$972$	22.2536	0.713783
$973$	−103.074	−3.30439
$974$	−14.0786	−0.451107
$975$	40.3237	1.29139
$976$	13.2380	0.423737
$977$	39.3402	1.25860	0.629302	−	0.777161i	$-0.283341\pi$
$977$	39.3402	1.25860	0.629302	+	0.777161i	$0.283341\pi$
$978$	22.5486	0.721025
$979$	7.81527	0.249777
$980$	21.5885	0.689619
$981$	−14.1029	−0.450270
$982$	−11.0754	−0.353431
$983$	23.6506	0.754336	0.377168	−	0.926145i	$-0.376898\pi$
$983$	23.6506	0.754336	0.377168	+	0.926145i	$0.376898\pi$
$984$	30.6067	0.975707
$985$	8.35412	0.266184
$986$	−4.52371	−0.144064
$987$	−82.5282	−2.62690
$988$	−14.9261	−0.474863
$989$	−30.9023	−0.982637
$990$	−4.73018	−0.150335
$991$	53.1586	1.68864	0.844319	−	0.535841i	$-0.180006\pi$
$991$	53.1586	1.68864	0.844319	+	0.535841i	$0.180006\pi$
$992$	8.09707	0.257082
$993$	−65.7480	−2.08645
$994$	−21.1508	−0.670861
$995$	−31.4847	−0.998133
$996$	−30.5925	−0.969362
$997$	−23.6527	−0.749089	−0.374544	−	0.927209i	$-0.622201\pi$
$997$	−23.6527	−0.749089	−0.374544	+	0.927209i	$0.622201\pi$
$998$	−41.7805	−1.32254
$999$	−0.339425	−0.0107389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1166.2.a.j.1.1	✓	4
4.3	odd	2		9328.2.a.y.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1166.2.a.j.1.1	✓	4	1.1	even	1	trivial
9328.2.a.y.1.4		4	4.3	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:	\( N \)	\(=\)	\( 1166 = 2 \cdot 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1166.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.47808 q^{3} +1.00000 q^{4} +1.50599 q^{5} -2.47808 q^{6} +4.61899 q^{7} +1.00000 q^{8} +3.14090 q^{9} +1.50599 q^{10} -1.00000 q^{11} -2.47808 q^{12} +5.95617 q^{13} +4.61899 q^{14} -3.73198 q^{15} +1.00000 q^{16} -7.12498 q^{17} +3.14090 q^{18} -2.50599 q^{19} +1.50599 q^{20} -11.4462 q^{21} -1.00000 q^{22} +5.36509 q^{23} -2.47808 q^{24} -2.73198 q^{25} +5.95617 q^{26} -0.349170 q^{27} +4.61899 q^{28} +0.634909 q^{29} -3.73198 q^{30} +8.09707 q^{31} +1.00000 q^{32} +2.47808 q^{33} -7.12498 q^{34} +6.95617 q^{35} +3.14090 q^{36} +0.972090 q^{37} -2.50599 q^{38} -14.7599 q^{39} +1.50599 q^{40} -12.3510 q^{41} -11.4462 q^{42} -5.75989 q^{43} -1.00000 q^{44} +4.73018 q^{45} +5.36509 q^{46} +7.21007 q^{47} -2.47808 q^{48} +14.3350 q^{49} -2.73198 q^{50} +17.6563 q^{51} +5.95617 q^{52} -1.00000 q^{53} -0.349170 q^{54} -1.50599 q^{55} +4.61899 q^{56} +6.21007 q^{57} +0.634909 q^{58} +3.38101 q^{59} -3.73198 q^{60} +13.2380 q^{61} +8.09707 q^{62} +14.5078 q^{63} +1.00000 q^{64} +8.96996 q^{65} +2.47808 q^{66} +8.74397 q^{67} -7.12498 q^{68} -13.2951 q^{69} +6.95617 q^{70} -4.57909 q^{71} +3.14090 q^{72} +3.71819 q^{73} +0.972090 q^{74} +6.77008 q^{75} -2.50599 q^{76} -4.61899 q^{77} -14.7599 q^{78} +1.59501 q^{79} +1.50599 q^{80} -8.55744 q^{81} -12.3510 q^{82} +12.3452 q^{83} -11.4462 q^{84} -10.7302 q^{85} -5.75989 q^{86} -1.57336 q^{87} -1.00000 q^{88} -7.81527 q^{89} +4.73018 q^{90} +27.5115 q^{91} +5.36509 q^{92} -20.0652 q^{93} +7.21007 q^{94} -3.77401 q^{95} -2.47808 q^{96} +5.64690 q^{97} +14.3350 q^{98} -3.14090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + q^{5} + 2 q^{6} + 6 q^{7} + 4 q^{8} + 12 q^{9} + q^{10} - 4 q^{11} + 2 q^{12} + 6 q^{14} + 5 q^{15} + 4 q^{16} - 11 q^{17} + 12 q^{18} - 5 q^{19} + q^{20} - 4 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + q^5 + 2 * q^6 + 6 * q^7 + 4 * q^8 + 12 * q^9 + q^10 - 4 * q^11 + 2 * q^12 + 6 * q^14 + 5 * q^15 + 4 * q^16 - 11 * q^17 + 12 * q^18 - 5 * q^19 + q^20 - 4 * q^22 + 17 * q^23 + 2 * q^24 + 9 * q^25 + 20 * q^27 + 6 * q^28 + 7 * q^29 + 5 * q^30 + 8 * q^31 + 4 * q^32 - 2 * q^33 - 11 * q^34 + 4 * q^35 + 12 * q^36 - 3 * q^37 - 5 * q^38 - 46 * q^39 + q^40 - 17 * q^41 - 10 * q^43 - 4 * q^44 + 10 * q^45 + 17 * q^46 - 3 * q^47 + 2 * q^48 + 8 * q^49 + 9 * q^50 - 7 * q^51 - 4 * q^53 + 20 * q^54 - q^55 + 6 * q^56 - 7 * q^57 + 7 * q^58 + 26 * q^59 + 5 * q^60 + 28 * q^61 + 8 * q^62 + 42 * q^63 + 4 * q^64 - 9 * q^65 - 2 * q^66 + 5 * q^67 - 11 * q^68 - 7 * q^69 + 4 * q^70 - 9 * q^71 + 12 * q^72 + 16 * q^73 - 3 * q^74 + 15 * q^75 - 5 * q^76 - 6 * q^77 - 46 * q^78 + 14 * q^79 + q^80 + 8 * q^81 - 17 * q^82 + q^83 - 34 * q^85 - 10 * q^86 + 19 * q^87 - 4 * q^88 - 8 * q^89 + 10 * q^90 + 6 * q^91 + 17 * q^92 - 22 * q^93 - 3 * q^94 - 30 * q^95 + 2 * q^96 + 17 * q^97 + 8 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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