LMFDB - Embedded newform 1587.2.a.u.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1587,2,Mod(1,1587)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1587.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1587, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1587 = 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1587.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,-2,10,8,8,-2,19] 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:	$12.6722588008$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.10.5791333887977.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 12x^{8} + 22x^{7} + 49x^{6} - 84x^{5} - 73x^{4} + 132x^{3} + 17x^{2} - 74x + 23 $ x^10 - 2x^9 - 12x^8 + 22x^7 + 49x^6 - 84x^5 - 73x^4 + 132x^3 + 17x^2 - 74*x + 23
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.568983$ of defining polynomial
Character	$\chi$	$=$	1587.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.568983 q^{2} +1.00000 q^{3} -1.67626 q^{4} +2.70241 q^{5} -0.568983 q^{6} +3.38601 q^{7} +2.09173 q^{8} +1.00000 q^{9} -1.53762 q^{10} -4.48823 q^{11} -1.67626 q^{12} +6.26113 q^{13} -1.92658 q^{14} +2.70241 q^{15} +2.16236 q^{16} +3.06906 q^{17} -0.568983 q^{18} +1.04840 q^{19} -4.52993 q^{20} +3.38601 q^{21} +2.55372 q^{22} +2.09173 q^{24} +2.30301 q^{25} -3.56248 q^{26} +1.00000 q^{27} -5.67582 q^{28} -2.21800 q^{29} -1.53762 q^{30} -6.48711 q^{31} -5.41380 q^{32} -4.48823 q^{33} -1.74624 q^{34} +9.15037 q^{35} -1.67626 q^{36} +0.279560 q^{37} -0.596524 q^{38} +6.26113 q^{39} +5.65270 q^{40} +1.41972 q^{41} -1.92658 q^{42} +1.83959 q^{43} +7.52343 q^{44} +2.70241 q^{45} +4.74565 q^{47} +2.16236 q^{48} +4.46503 q^{49} -1.31037 q^{50} +3.06906 q^{51} -10.4953 q^{52} +5.39864 q^{53} -0.568983 q^{54} -12.1290 q^{55} +7.08260 q^{56} +1.04840 q^{57} +1.26200 q^{58} -10.8910 q^{59} -4.52993 q^{60} +4.68450 q^{61} +3.69105 q^{62} +3.38601 q^{63} -1.24436 q^{64} +16.9201 q^{65} +2.55372 q^{66} -0.201133 q^{67} -5.14454 q^{68} -5.20640 q^{70} -3.01784 q^{71} +2.09173 q^{72} -12.0906 q^{73} -0.159065 q^{74} +2.30301 q^{75} -1.75740 q^{76} -15.1972 q^{77} -3.56248 q^{78} +7.76749 q^{79} +5.84358 q^{80} +1.00000 q^{81} -0.807796 q^{82} -14.7611 q^{83} -5.67582 q^{84} +8.29386 q^{85} -1.04669 q^{86} -2.21800 q^{87} -9.38814 q^{88} -0.873672 q^{89} -1.53762 q^{90} +21.2002 q^{91} -6.48711 q^{93} -2.70019 q^{94} +2.83322 q^{95} -5.41380 q^{96} +11.5724 q^{97} -2.54053 q^{98} -4.48823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 10 q^{3} + 8 q^{4} + 8 q^{5} - 2 q^{6} + 19 q^{7} - 6 q^{8} + 10 q^{9} + 13 q^{10} + 3 q^{11} + 8 q^{12} - 4 q^{13} + 8 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} + 22 q^{19} + q^{20} + 19 q^{21}+ \cdots + 3 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + 10 * q^3 + 8 * q^4 + 8 * q^5 - 2 * q^6 + 19 * q^7 - 6 * q^8 + 10 * q^9 + 13 * q^10 + 3 * q^11 + 8 * q^12 - 4 * q^13 + 8 * q^15 - 4 * q^16 + 11 * q^17 - 2 * q^18 + 22 * q^19 + q^20 + 19 * q^21 + 13 * q^22 - 6 * q^24 - 2 * q^25 + 4 * q^26 + 10 * q^27 + 26 * q^28 - 5 * q^29 + 13 * q^30 - 7 * q^31 - 34 * q^32 + 3 * q^33 + 4 * q^34 + 9 * q^35 + 8 * q^36 + 35 * q^37 - 9 * q^38 - 4 * q^39 + 21 * q^40 + 28 * q^43 - 7 * q^44 + 8 * q^45 + 9 * q^47 - 4 * q^48 + 17 * q^49 + 11 * q^51 - 52 * q^52 + 34 * q^53 - 2 * q^54 - 14 * q^55 - 30 * q^56 + 22 * q^57 - 24 * q^58 - 2 * q^59 + q^60 + 49 * q^61 - 28 * q^62 + 19 * q^63 + 10 * q^64 + 2 * q^65 + 13 * q^66 + 26 * q^67 - 6 * q^68 + 16 * q^70 + 15 * q^71 - 6 * q^72 + 14 * q^73 - 25 * q^74 - 2 * q^75 + 19 * q^76 - 33 * q^77 + 4 * q^78 + 43 * q^79 - 49 * q^80 + 10 * q^81 + 24 * q^82 - 15 * q^83 + 26 * q^84 - 21 * q^85 - 49 * q^86 - 5 * q^87 + 15 * q^88 - 15 * q^89 + 13 * q^90 + 4 * q^91 - 7 * q^93 - 28 * q^94 + 28 * q^95 - 34 * q^96 + 22 * q^97 + 15 * q^98 + 3 * 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 $

$2$	−0.568983	−0.402331	−0.201166	−	0.979557i	$-0.564473\pi$
$2$	−0.568983	−0.402331	−0.201166	+	0.979557i	$0.564473\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.67626	−0.838129
$5$	2.70241	1.20855	0.604277	−	0.796775i	$-0.293462\pi$
$5$	2.70241	1.20855	0.604277	+	0.796775i	$0.293462\pi$
$6$	−0.568983	−0.232286
$7$	3.38601	1.27979	0.639895	−	0.768462i	$-0.278978\pi$
$7$	3.38601	1.27979	0.639895	+	0.768462i	$0.278978\pi$
$8$	2.09173	0.739537
$9$	1.00000	0.333333
$10$	−1.53762	−0.486239
$11$	−4.48823	−1.35325	−0.676625	−	0.736327i	$-0.736558\pi$
$11$	−4.48823	−1.35325	−0.676625	+	0.736327i	$0.736558\pi$
$12$	−1.67626	−0.483894
$13$	6.26113	1.73653	0.868263	−	0.496104i	$-0.165237\pi$
$13$	6.26113	1.73653	0.868263	+	0.496104i	$0.165237\pi$
$14$	−1.92658	−0.514900
$15$	2.70241	0.697759
$16$	2.16236	0.540590
$17$	3.06906	0.744357	0.372179	−	0.928161i	$-0.378611\pi$
$17$	3.06906	0.744357	0.372179	+	0.928161i	$0.378611\pi$
$18$	−0.568983	−0.134110
$19$	1.04840	0.240521	0.120260	−	0.992742i	$-0.461627\pi$
$19$	1.04840	0.240521	0.120260	+	0.992742i	$0.461627\pi$
$20$	−4.52993	−1.01292
$21$	3.38601	0.738887
$22$	2.55372	0.544455
$23$	0	0
$23$	0	0
$24$	2.09173	0.426972
$25$	2.30301	0.460601
$26$	−3.56248	−0.698659
$27$	1.00000	0.192450
$28$	−5.67582	−1.07263
$29$	−2.21800	−0.411872	−0.205936	−	0.978565i	$-0.566024\pi$
$29$	−2.21800	−0.411872	−0.205936	+	0.978565i	$0.566024\pi$
$30$	−1.53762	−0.280730
$31$	−6.48711	−1.16512	−0.582559	−	0.812788i	$-0.697949\pi$
$31$	−6.48711	−1.16512	−0.582559	+	0.812788i	$0.697949\pi$
$32$	−5.41380	−0.957034
$33$	−4.48823	−0.781300
$34$	−1.74624	−0.299478
$35$	9.15037	1.54669
$36$	−1.67626	−0.279376
$37$	0.279560	0.0459594	0.0229797	−	0.999736i	$-0.492685\pi$
$37$	0.279560	0.0459594	0.0229797	+	0.999736i	$0.492685\pi$
$38$	−0.596524	−0.0967690
$39$	6.26113	1.00258
$40$	5.65270	0.893770
$41$	1.41972	0.221723	0.110861	−	0.993836i	$-0.464639\pi$
$41$	1.41972	0.221723	0.110861	+	0.993836i	$0.464639\pi$
$42$	−1.92658	−0.297277
$43$	1.83959	0.280534	0.140267	−	0.990114i	$-0.455204\pi$
$43$	1.83959	0.280534	0.140267	+	0.990114i	$0.455204\pi$
$44$	7.52343	1.13420
$45$	2.70241	0.402851
$46$	0	0
$47$	4.74565	0.692225	0.346112	−	0.938193i	$-0.387502\pi$
$47$	4.74565	0.692225	0.346112	+	0.938193i	$0.387502\pi$
$48$	2.16236	0.312110
$49$	4.46503	0.637862
$50$	−1.31037	−0.185314
$51$	3.06906	0.429755
$52$	−10.4953	−1.45543
$53$	5.39864	0.741560	0.370780	−	0.928721i	$-0.379090\pi$
$53$	5.39864	0.741560	0.370780	+	0.928721i	$0.379090\pi$
$54$	−0.568983	−0.0774287
$55$	−12.1290	−1.63548
$56$	7.08260	0.946452
$57$	1.04840	0.138865
$58$	1.26200	0.165709
$59$	−10.8910	−1.41789	−0.708944	−	0.705265i	$-0.750828\pi$
$59$	−10.8910	−1.41789	−0.708944	+	0.705265i	$0.750828\pi$
$60$	−4.52993	−0.584812
$61$	4.68450	0.599789	0.299894	−	0.953972i	$-0.403049\pi$
$61$	4.68450	0.599789	0.299894	+	0.953972i	$0.403049\pi$
$62$	3.69105	0.468764
$63$	3.38601	0.426597
$64$	−1.24436	−0.155546
$65$	16.9201	2.09868
$66$	2.55372	0.314341
$67$	−0.201133	−0.0245724	−0.0122862	−	0.999925i	$-0.503911\pi$
$67$	−0.201133	−0.0245724	−0.0122862	+	0.999925i	$0.503911\pi$
$68$	−5.14454	−0.623868
$69$	0	0
$70$	−5.20640	−0.622284
$71$	−3.01784	−0.358151	−0.179076	−	0.983835i	$-0.557311\pi$
$71$	−3.01784	−0.358151	−0.179076	+	0.983835i	$0.557311\pi$
$72$	2.09173	0.246512
$73$	−12.0906	−1.41510	−0.707548	−	0.706666i	$-0.750198\pi$
$73$	−12.0906	−1.41510	−0.707548	+	0.706666i	$0.750198\pi$
$74$	−0.159065	−0.0184909
$75$	2.30301	0.265928
$76$	−1.75740	−0.201587
$77$	−15.1972	−1.73188
$78$	−3.56248	−0.403371
$79$	7.76749	0.873911	0.436956	−	0.899483i	$-0.356057\pi$
$79$	7.76749	0.873911	0.436956	+	0.899483i	$0.356057\pi$
$80$	5.84358	0.653332
$81$	1.00000	0.111111
$82$	−0.807796	−0.0892061
$83$	−14.7611	−1.62024	−0.810122	−	0.586261i	$-0.800599\pi$
$83$	−14.7611	−1.62024	−0.810122	+	0.586261i	$0.800599\pi$
$84$	−5.67582	−0.619283
$85$	8.29386	0.899595
$86$	−1.04669	−0.112868
$87$	−2.21800	−0.237794
$88$	−9.38814	−1.00078
$89$	−0.873672	−0.0926090	−0.0463045	−	0.998927i	$-0.514744\pi$
$89$	−0.873672	−0.0926090	−0.0463045	+	0.998927i	$0.514744\pi$
$90$	−1.53762	−0.162080
$91$	21.2002	2.22239
$92$	0	0
$93$	−6.48711	−0.672682
$94$	−2.70019	−0.278504
$95$	2.83322	0.290682
$96$	−5.41380	−0.552544
$97$	11.5724	1.17500	0.587502	−	0.809223i	$-0.300112\pi$
$97$	11.5724	1.17500	0.587502	+	0.809223i	$0.300112\pi$
$98$	−2.54053	−0.256632
$99$	−4.48823	−0.451084
$100$	−3.86044	−0.386044
$101$	9.43695	0.939011	0.469506	−	0.882929i	$-0.344432\pi$
$101$	9.43695	0.939011	0.469506	+	0.882929i	$0.344432\pi$
$102$	−1.74624	−0.172904
$103$	4.01274	0.395387	0.197693	−	0.980264i	$-0.436655\pi$
$103$	4.01274	0.395387	0.197693	+	0.980264i	$0.436655\pi$
$104$	13.0966	1.28423
$105$	9.15037	0.892984
$106$	−3.07173	−0.298353
$107$	3.67412	0.355190	0.177595	−	0.984104i	$-0.443168\pi$
$107$	3.67412	0.355190	0.177595	+	0.984104i	$0.443168\pi$
$108$	−1.67626	−0.161298
$109$	13.4116	1.28460	0.642299	−	0.766454i	$-0.277981\pi$
$109$	13.4116	1.28460	0.642299	+	0.766454i	$0.277981\pi$
$110$	6.90120	0.658003
$111$	0.279560	0.0265347
$112$	7.32177	0.691842
$113$	0.694886	0.0653694	0.0326847	−	0.999466i	$-0.489594\pi$
$113$	0.694886	0.0653694	0.0326847	+	0.999466i	$0.489594\pi$
$114$	−0.596524	−0.0558696
$115$	0	0
$116$	3.71794	0.345202
$117$	6.26113	0.578842
$118$	6.19679	0.570461
$119$	10.3919	0.952621
$120$	5.65270	0.516019
$121$	9.14417	0.831288
$122$	−2.66540	−0.241314
$123$	1.41972	0.128012
$124$	10.8741	0.976520
$125$	−7.28837	−0.651892
$126$	−1.92658	−0.171633
$127$	−10.9440	−0.971127	−0.485563	−	0.874202i	$-0.661385\pi$
$127$	−10.9440	−0.971127	−0.485563	+	0.874202i	$0.661385\pi$
$128$	11.5356	1.01961
$129$	1.83959	0.161967
$130$	−9.62726	−0.844367
$131$	−3.53749	−0.309072	−0.154536	−	0.987987i	$-0.549388\pi$
$131$	−3.53749	−0.309072	−0.154536	+	0.987987i	$0.549388\pi$
$132$	7.52343	0.654830
$133$	3.54990	0.307816
$134$	0.114441	0.00988623
$135$	2.70241	0.232586
$136$	6.41964	0.550480
$137$	12.7925	1.09294	0.546469	−	0.837479i	$-0.315972\pi$
$137$	12.7925	1.09294	0.546469	+	0.837479i	$0.315972\pi$
$138$	0	0
$139$	8.21741	0.696992	0.348496	−	0.937310i	$-0.386693\pi$
$139$	8.21741	0.696992	0.348496	+	0.937310i	$0.386693\pi$
$140$	−15.3384	−1.29633
$141$	4.74565	0.399656
$142$	1.71710	0.144095
$143$	−28.1014	−2.34996
$144$	2.16236	0.180197
$145$	−5.99393	−0.497769
$146$	6.87933	0.569337
$147$	4.46503	0.368270
$148$	−0.468615	−0.0385199
$149$	−18.6176	−1.52521	−0.762607	−	0.646862i	$-0.776081\pi$
$149$	−18.6176	−1.52521	−0.762607	+	0.646862i	$0.776081\pi$
$150$	−1.31037	−0.106991
$151$	−5.46938	−0.445092	−0.222546	−	0.974922i	$-0.571437\pi$
$151$	−5.46938	−0.445092	−0.222546	+	0.974922i	$0.571437\pi$
$152$	2.19298	0.177874
$153$	3.06906	0.248119
$154$	8.64692	0.696788
$155$	−17.5308	−1.40811
$156$	−10.4953	−0.840295
$157$	16.4366	1.31178	0.655890	−	0.754856i	$-0.272294\pi$
$157$	16.4366	1.31178	0.655890	+	0.754856i	$0.272294\pi$
$158$	−4.41957	−0.351602
$159$	5.39864	0.428140
$160$	−14.6303	−1.15663
$161$	0	0
$162$	−0.568983	−0.0447035
$163$	10.0160	0.784511	0.392256	−	0.919856i	$-0.371695\pi$
$163$	10.0160	0.784511	0.392256	+	0.919856i	$0.371695\pi$
$164$	−2.37982	−0.185833
$165$	−12.1290	−0.944243
$166$	8.39883	0.651875
$167$	−7.39906	−0.572557	−0.286278	−	0.958147i	$-0.592418\pi$
$167$	−7.39906	−0.572557	−0.286278	+	0.958147i	$0.592418\pi$
$168$	7.08260	0.546434
$169$	26.2018	2.01552
$170$	−4.71906	−0.361936
$171$	1.04840	0.0801735
$172$	−3.08362	−0.235124
$173$	5.61509	0.426908	0.213454	−	0.976953i	$-0.431529\pi$
$173$	5.61509	0.426908	0.213454	+	0.976953i	$0.431529\pi$
$174$	1.26200	0.0956721
$175$	7.79799	0.589473
$176$	−9.70517	−0.731554
$177$	−10.8910	−0.818618
$178$	0.497104	0.0372595
$179$	21.5449	1.61034	0.805169	−	0.593046i	$-0.202075\pi$
$179$	21.5449	1.61034	0.805169	+	0.593046i	$0.202075\pi$
$180$	−4.52993	−0.337641
$181$	10.2613	0.762719	0.381360	−	0.924427i	$-0.375456\pi$
$181$	10.2613	0.762719	0.381360	+	0.924427i	$0.375456\pi$
$182$	−12.0626	−0.894137
$183$	4.68450	0.346288
$184$	0	0
$185$	0.755486	0.0555444
$186$	3.69105	0.270641
$187$	−13.7746	−1.00730
$188$	−7.95494	−0.580174
$189$	3.38601	0.246296
$190$	−1.61205	−0.116950
$191$	8.45001	0.611421	0.305710	−	0.952125i	$-0.401106\pi$
$191$	8.45001	0.611421	0.305710	+	0.952125i	$0.401106\pi$
$192$	−1.24436	−0.0898043
$193$	0.392108	0.0282246	0.0141123	−	0.999900i	$-0.495508\pi$
$193$	0.392108	0.0282246	0.0141123	+	0.999900i	$0.495508\pi$
$194$	−6.58452	−0.472741
$195$	16.9201	1.21168
$196$	−7.48455	−0.534611
$197$	−22.5670	−1.60783	−0.803915	−	0.594744i	$-0.797253\pi$
$197$	−22.5670	−1.60783	−0.803915	+	0.594744i	$0.797253\pi$
$198$	2.55372	0.181485
$199$	13.3644	0.947375	0.473687	−	0.880693i	$-0.342923\pi$
$199$	13.3644	0.947375	0.473687	+	0.880693i	$0.342923\pi$
$200$	4.81726	0.340632
$201$	−0.201133	−0.0141869
$202$	−5.36946	−0.377794
$203$	−7.51015	−0.527109
$204$	−5.14454	−0.360190
$205$	3.83666	0.267964
$206$	−2.28318	−0.159076
$207$	0	0
$208$	13.5388	0.938749
$209$	−4.70548	−0.325485
$210$	−5.20640	−0.359276
$211$	−0.559001	−0.0384832	−0.0192416	−	0.999815i	$-0.506125\pi$
$211$	−0.559001	−0.0384832	−0.0192416	+	0.999815i	$0.506125\pi$
$212$	−9.04951	−0.621523
$213$	−3.01784	−0.206779
$214$	−2.09051	−0.142904
$215$	4.97131	0.339041
$216$	2.09173	0.142324
$217$	−21.9654	−1.49111
$218$	−7.63097	−0.516834
$219$	−12.0906	−0.817006
$220$	20.3314	1.37074
$221$	19.2158	1.29260
$222$	−0.159065	−0.0106757
$223$	−29.6961	−1.98860	−0.994299	−	0.106631i	$-0.965994\pi$
$223$	−29.6961	−1.98860	−0.994299	+	0.106631i	$0.965994\pi$
$224$	−18.3312	−1.22480
$225$	2.30301	0.153534
$226$	−0.395378	−0.0263002
$227$	−24.6703	−1.63743	−0.818713	−	0.574203i	$-0.805312\pi$
$227$	−24.6703	−1.63743	−0.818713	+	0.574203i	$0.805312\pi$
$228$	−1.75740	−0.116387
$229$	−28.4810	−1.88207	−0.941037	−	0.338302i	$-0.890147\pi$
$229$	−28.4810	−1.88207	−0.941037	+	0.338302i	$0.890147\pi$
$230$	0	0
$231$	−15.1972	−0.999899
$232$	−4.63945	−0.304595
$233$	−15.0630	−0.986812	−0.493406	−	0.869799i	$-0.664248\pi$
$233$	−15.0630	−0.986812	−0.493406	+	0.869799i	$0.664248\pi$
$234$	−3.56248	−0.232886
$235$	12.8247	0.836591
$236$	18.2561	1.18837
$237$	7.76749	0.504553
$238$	−5.91279	−0.383269
$239$	−26.9624	−1.74405	−0.872027	−	0.489457i	$-0.837195\pi$
$239$	−26.9624	−1.74405	−0.872027	+	0.489457i	$0.837195\pi$
$240$	5.84358	0.377202
$241$	21.1091	1.35976	0.679879	−	0.733324i	$-0.262032\pi$
$241$	21.1091	1.35976	0.679879	+	0.733324i	$0.262032\pi$
$242$	−5.20287	−0.334453
$243$	1.00000	0.0641500
$244$	−7.85243	−0.502701
$245$	12.0663	0.770890
$246$	−0.807796	−0.0515032
$247$	6.56420	0.417670
$248$	−13.5693	−0.861649
$249$	−14.7611	−0.935449
$250$	4.14696	0.262277
$251$	−2.32705	−0.146882	−0.0734411	−	0.997300i	$-0.523398\pi$
$251$	−2.32705	−0.146882	−0.0734411	+	0.997300i	$0.523398\pi$
$252$	−5.67582	−0.357543
$253$	0	0
$254$	6.22697	0.390715
$255$	8.29386	0.519382
$256$	−4.07484	−0.254677
$257$	26.6953	1.66520	0.832602	−	0.553871i	$-0.186850\pi$
$257$	26.6953	1.66520	0.832602	+	0.553871i	$0.186850\pi$
$258$	−1.04669	−0.0651642
$259$	0.946593	0.0588184
$260$	−28.3625	−1.75897
$261$	−2.21800	−0.137291
$262$	2.01277	0.124349
$263$	10.0028	0.616801	0.308401	−	0.951257i	$-0.400206\pi$
$263$	10.0028	0.616801	0.308401	+	0.951257i	$0.400206\pi$
$264$	−9.38814	−0.577800
$265$	14.5893	0.896215
$266$	−2.01983	−0.123844
$267$	−0.873672	−0.0534678
$268$	0.337152	0.0205948
$269$	−17.5445	−1.06971	−0.534853	−	0.844945i	$-0.679633\pi$
$269$	−17.5445	−1.06971	−0.534853	+	0.844945i	$0.679633\pi$
$270$	−1.53762	−0.0935767
$271$	1.13946	0.0692174	0.0346087	−	0.999401i	$-0.488982\pi$
$271$	1.13946	0.0692174	0.0346087	+	0.999401i	$0.488982\pi$
$272$	6.63642	0.402392
$273$	21.2002	1.28310
$274$	−7.27872	−0.439724
$275$	−10.3364	−0.623309
$276$	0	0
$277$	−21.3674	−1.28384	−0.641920	−	0.766772i	$-0.721862\pi$
$277$	−21.3674	−1.28384	−0.641920	+	0.766772i	$0.721862\pi$
$278$	−4.67556	−0.280422
$279$	−6.48711	−0.388373
$280$	19.1401	1.14384
$281$	−12.3835	−0.738737	−0.369369	−	0.929283i	$-0.620426\pi$
$281$	−12.3835	−0.738737	−0.369369	+	0.929283i	$0.620426\pi$
$282$	−2.70019	−0.160794
$283$	−7.11666	−0.423041	−0.211521	−	0.977374i	$-0.567842\pi$
$283$	−7.11666	−0.423041	−0.211521	+	0.977374i	$0.567842\pi$
$284$	5.05867	0.300177
$285$	2.83322	0.167825
$286$	15.9892	0.945461
$287$	4.80718	0.283759
$288$	−5.41380	−0.319011
$289$	−7.58085	−0.445932
$290$	3.41044	0.200268
$291$	11.5724	0.678389
$292$	20.2669	1.18603
$293$	−17.9845	−1.05066	−0.525332	−	0.850898i	$-0.676059\pi$
$293$	−17.9845	−1.05066	−0.525332	+	0.850898i	$0.676059\pi$
$294$	−2.54053	−0.148166
$295$	−29.4319	−1.71359
$296$	0.584764	0.0339887
$297$	−4.48823	−0.260433
$298$	10.5931	0.613641
$299$	0	0
$300$	−3.86044	−0.222882
$301$	6.22885	0.359025
$302$	3.11198	0.179074
$303$	9.43695	0.542138
$304$	2.26703	0.130023
$305$	12.6594	0.724877
$306$	−1.74624	−0.0998261
$307$	1.83085	0.104492	0.0522460	−	0.998634i	$-0.483362\pi$
$307$	1.83085	0.104492	0.0522460	+	0.998634i	$0.483362\pi$
$308$	25.4744	1.45154
$309$	4.01274	0.228277
$310$	9.97472	0.566526
$311$	−9.26634	−0.525446	−0.262723	−	0.964871i	$-0.584621\pi$
$311$	−9.26634	−0.525446	−0.262723	+	0.964871i	$0.584621\pi$
$312$	13.0966	0.741448
$313$	13.9170	0.786634	0.393317	−	0.919403i	$-0.371327\pi$
$313$	13.9170	0.786634	0.393317	+	0.919403i	$0.371327\pi$
$314$	−9.35211	−0.527770
$315$	9.15037	0.515565
$316$	−13.0203	−0.732451
$317$	−27.0529	−1.51944	−0.759722	−	0.650248i	$-0.774665\pi$
$317$	−27.0529	−1.51944	−0.759722	+	0.650248i	$0.774665\pi$
$318$	−3.07173	−0.172254
$319$	9.95488	0.557366
$320$	−3.36278	−0.187985
$321$	3.67412	0.205069
$322$	0	0
$323$	3.21762	0.179033
$324$	−1.67626	−0.0931255
$325$	14.4194	0.799846
$326$	−5.69891	−0.315633
$327$	13.4116	0.741663
$328$	2.96967	0.163972
$329$	16.0688	0.885902
$330$	6.90120	0.379898
$331$	16.4225	0.902661	0.451331	−	0.892357i	$-0.350949\pi$
$331$	16.4225	0.902661	0.451331	+	0.892357i	$0.350949\pi$
$332$	24.7435	1.35797
$333$	0.279560	0.0153198
$334$	4.20994	0.230358
$335$	−0.543544	−0.0296970
$336$	7.32177	0.399435
$337$	−16.5746	−0.902878	−0.451439	−	0.892302i	$-0.649089\pi$
$337$	−16.5746	−0.902878	−0.451439	+	0.892302i	$0.649089\pi$
$338$	−14.9084	−0.810908
$339$	0.694886	0.0377411
$340$	−13.9027	−0.753977
$341$	29.1156	1.57670
$342$	−0.596524	−0.0322563
$343$	−8.58341	−0.463461
$344$	3.84791	0.207466
$345$	0	0
$346$	−3.19489	−0.171758
$347$	−0.186730	−0.0100242	−0.00501208	−	0.999987i	$-0.501595\pi$
$347$	−0.186730	−0.0100242	−0.00501208	+	0.999987i	$0.501595\pi$
$348$	3.71794	0.199302
$349$	10.5157	0.562892	0.281446	−	0.959577i	$-0.409186\pi$
$349$	10.5157	0.562892	0.281446	+	0.959577i	$0.409186\pi$
$350$	−4.43692	−0.237163
$351$	6.26113	0.334195
$352$	24.2984	1.29511
$353$	−20.6655	−1.09991	−0.549956	−	0.835194i	$-0.685355\pi$
$353$	−20.6655	−1.09991	−0.549956	+	0.835194i	$0.685355\pi$
$354$	6.19679	0.329356
$355$	−8.15542	−0.432845
$356$	1.46450	0.0776183
$357$	10.3919	0.549996
$358$	−12.2586	−0.647889
$359$	15.6775	0.827425	0.413712	−	0.910408i	$-0.364232\pi$
$359$	15.6775	0.827425	0.413712	+	0.910408i	$0.364232\pi$
$360$	5.65270	0.297923
$361$	−17.9008	−0.942150
$362$	−5.83852	−0.306866
$363$	9.14417	0.479944
$364$	−35.5371	−1.86265
$365$	−32.6737	−1.71022
$366$	−2.66540	−0.139323
$367$	5.44563	0.284259	0.142130	−	0.989848i	$-0.454605\pi$
$367$	5.44563	0.284259	0.142130	+	0.989848i	$0.454605\pi$
$368$	0	0
$369$	1.41972	0.0739076
$370$	−0.429858	−0.0223473
$371$	18.2798	0.949041
$372$	10.8741	0.563794
$373$	−4.02738	−0.208530	−0.104265	−	0.994550i	$-0.533249\pi$
$373$	−4.02738	−0.208530	−0.104265	+	0.994550i	$0.533249\pi$
$374$	7.83753	0.405269
$375$	−7.28837	−0.376370
$376$	9.92661	0.511926
$377$	−13.8872	−0.715226
$378$	−1.92658	−0.0990925
$379$	−11.1490	−0.572684	−0.286342	−	0.958127i	$-0.592439\pi$
$379$	−11.1490	−0.572684	−0.286342	+	0.958127i	$0.592439\pi$
$380$	−4.74921	−0.243629
$381$	−10.9440	−0.560680
$382$	−4.80791	−0.245994
$383$	−15.0122	−0.767090	−0.383545	−	0.923522i	$-0.625297\pi$
$383$	−15.0122	−0.767090	−0.383545	+	0.923522i	$0.625297\pi$
$384$	11.5356	0.588675
$385$	−41.0689	−2.09307
$386$	−0.223103	−0.0113556
$387$	1.83959	0.0935114
$388$	−19.3984	−0.984805
$389$	−33.1611	−1.68134	−0.840668	−	0.541551i	$-0.817837\pi$
$389$	−33.1611	−1.68134	−0.840668	+	0.541551i	$0.817837\pi$
$390$	−9.62726	−0.487495
$391$	0	0
$392$	9.33963	0.471723
$393$	−3.53749	−0.178443
$394$	12.8402	0.646881
$395$	20.9909	1.05617
$396$	7.52343	0.378066
$397$	−6.67063	−0.334789	−0.167395	−	0.985890i	$-0.553535\pi$
$397$	−6.67063	−0.334789	−0.167395	+	0.985890i	$0.553535\pi$
$398$	−7.60409	−0.381159
$399$	3.54990	0.177718
$400$	4.97993	0.248997
$401$	−6.22639	−0.310931	−0.155466	−	0.987841i	$-0.549688\pi$
$401$	−6.22639	−0.310931	−0.155466	+	0.987841i	$0.549688\pi$
$402$	0.114441	0.00570782
$403$	−40.6166	−2.02326
$404$	−15.8188	−0.787013
$405$	2.70241	0.134284
$406$	4.27315	0.212073
$407$	−1.25473	−0.0621946
$408$	6.41964	0.317820
$409$	−1.95994	−0.0969128	−0.0484564	−	0.998825i	$-0.515430\pi$
$409$	−1.95994	−0.0969128	−0.0484564	+	0.998825i	$0.515430\pi$
$410$	−2.18299	−0.107810
$411$	12.7925	0.631008
$412$	−6.72638	−0.331385
$413$	−36.8770	−1.81460
$414$	0	0
$415$	−39.8906	−1.95815
$416$	−33.8965	−1.66191
$417$	8.21741	0.402408
$418$	2.67733	0.130953
$419$	8.26445	0.403745	0.201872	−	0.979412i	$-0.435297\pi$
$419$	8.26445	0.403745	0.201872	+	0.979412i	$0.435297\pi$
$420$	−15.3384	−0.748436
$421$	−1.77108	−0.0863170	−0.0431585	−	0.999068i	$-0.513742\pi$
$421$	−1.77108	−0.0863170	−0.0431585	+	0.999068i	$0.513742\pi$
$422$	0.318062	0.0154830
$423$	4.74565	0.230742
$424$	11.2925	0.548411
$425$	7.06807	0.342852
$426$	1.71710	0.0831936
$427$	15.8617	0.767604
$428$	−6.15877	−0.297695
$429$	−28.1014	−1.35675
$430$	−2.82859	−0.136407
$431$	26.7569	1.28884	0.644418	−	0.764674i	$-0.277100\pi$
$431$	26.7569	1.28884	0.644418	+	0.764674i	$0.277100\pi$
$432$	2.16236	0.104037
$433$	24.5762	1.18106	0.590529	−	0.807017i	$-0.298919\pi$
$433$	24.5762	1.18106	0.590529	+	0.807017i	$0.298919\pi$
$434$	12.4979	0.599919
$435$	−5.99393	−0.287387
$436$	−22.4813	−1.07666
$437$	0	0
$438$	6.87933	0.328707
$439$	5.59553	0.267060	0.133530	−	0.991045i	$-0.457369\pi$
$439$	5.59553	0.267060	0.133530	+	0.991045i	$0.457369\pi$
$440$	−25.3706	−1.20950
$441$	4.46503	0.212621
$442$	−10.9335	−0.520052
$443$	12.5170	0.594701	0.297351	−	0.954768i	$-0.403897\pi$
$443$	12.5170	0.594701	0.297351	+	0.954768i	$0.403897\pi$
$444$	−0.468615	−0.0222395
$445$	−2.36102	−0.111923
$446$	16.8966	0.800075
$447$	−18.6176	−0.880583
$448$	−4.21343	−0.199066
$449$	−8.14963	−0.384605	−0.192302	−	0.981336i	$-0.561595\pi$
$449$	−8.14963	−0.384605	−0.192302	+	0.981336i	$0.561595\pi$
$450$	−1.31037	−0.0617715
$451$	−6.37202	−0.300047
$452$	−1.16481	−0.0547880
$453$	−5.46938	−0.256974
$454$	14.0370	0.658788
$455$	57.2917	2.68587
$456$	2.19298	0.102696
$457$	−18.1009	−0.846723	−0.423361	−	0.905961i	$-0.639150\pi$
$457$	−18.1009	−0.846723	−0.423361	+	0.905961i	$0.639150\pi$
$458$	16.2052	0.757218
$459$	3.06906	0.143252
$460$	0	0
$461$	13.1011	0.610180	0.305090	−	0.952324i	$-0.401313\pi$
$461$	13.1011	0.610180	0.305090	+	0.952324i	$0.401313\pi$
$462$	8.64692	0.402291
$463$	−19.4661	−0.904668	−0.452334	−	0.891849i	$-0.649409\pi$
$463$	−19.4661	−0.904668	−0.452334	+	0.891849i	$0.649409\pi$
$464$	−4.79611	−0.222654
$465$	−17.5308	−0.812972
$466$	8.57060	0.397025
$467$	−1.19583	−0.0553365	−0.0276682	−	0.999617i	$-0.508808\pi$
$467$	−1.19583	−0.0553365	−0.0276682	+	0.999617i	$0.508808\pi$
$468$	−10.4953	−0.485144
$469$	−0.681039	−0.0314474
$470$	−7.29702	−0.336587
$471$	16.4366	0.757357
$472$	−22.7810	−1.04858
$473$	−8.25648	−0.379633
$474$	−4.41957	−0.202998
$475$	2.41448	0.110784
$476$	−17.4195	−0.798419
$477$	5.39864	0.247187
$478$	15.3412	0.701688
$479$	−17.4856	−0.798937	−0.399468	−	0.916747i	$-0.630805\pi$
$479$	−17.4856	−0.798937	−0.399468	+	0.916747i	$0.630805\pi$
$480$	−14.6303	−0.667779
$481$	1.75036	0.0798097
$482$	−12.0107	−0.547073
$483$	0	0
$484$	−15.3280	−0.696727
$485$	31.2735	1.42005
$486$	−0.568983	−0.0258096
$487$	−22.5133	−1.02018	−0.510088	−	0.860122i	$-0.670387\pi$
$487$	−22.5133	−1.02018	−0.510088	+	0.860122i	$0.670387\pi$
$488$	9.79870	0.443566
$489$	10.0160	0.452938
$490$	−6.86554	−0.310153
$491$	29.4342	1.32835	0.664174	−	0.747578i	$-0.268783\pi$
$491$	29.4342	1.32835	0.664174	+	0.747578i	$0.268783\pi$
$492$	−2.37982	−0.107290
$493$	−6.80718	−0.306580
$494$	−3.73492	−0.168042
$495$	−12.1290	−0.545159
$496$	−14.0275	−0.629852
$497$	−10.2184	−0.458358
$498$	8.39883	0.376360
$499$	−12.9838	−0.581233	−0.290616	−	0.956840i	$-0.593860\pi$
$499$	−12.9838	−0.581233	−0.290616	+	0.956840i	$0.593860\pi$
$500$	12.2172	0.546370
$501$	−7.39906	−0.330566
$502$	1.32405	0.0590953
$503$	−0.735172	−0.0327797	−0.0163898	−	0.999866i	$-0.505217\pi$
$503$	−0.735172	−0.0327797	−0.0163898	+	0.999866i	$0.505217\pi$
$504$	7.08260	0.315484
$505$	25.5025	1.13485
$506$	0	0
$507$	26.2018	1.16366
$508$	18.3450	0.813930
$509$	2.76431	0.122526	0.0612629	−	0.998122i	$-0.480487\pi$
$509$	2.76431	0.122526	0.0612629	+	0.998122i	$0.480487\pi$
$510$	−4.71906	−0.208964
$511$	−40.9388	−1.81102
$512$	−20.7527	−0.917150
$513$	1.04840	0.0462882
$514$	−15.1891	−0.669964
$515$	10.8440	0.477846
$516$	−3.08362	−0.135749
$517$	−21.2996	−0.936754
$518$	−0.538595	−0.0236645
$519$	5.61509	0.246475
$520$	35.3923	1.55206
$521$	−16.3874	−0.717944	−0.358972	−	0.933348i	$-0.616873\pi$
$521$	−16.3874	−0.717944	−0.358972	+	0.933348i	$0.616873\pi$
$522$	1.26200	0.0552363
$523$	24.8590	1.08701	0.543504	−	0.839406i	$-0.317097\pi$
$523$	24.8590	1.08701	0.543504	+	0.839406i	$0.317097\pi$
$524$	5.92975	0.259042
$525$	7.79799	0.340332
$526$	−5.69144	−0.248159
$527$	−19.9093	−0.867265
$528$	−9.70517	−0.422363
$529$	0	0
$530$	−8.30107	−0.360575
$531$	−10.8910	−0.472629
$532$	−5.95056	−0.257989
$533$	8.88905	0.385028
$534$	0.497104	0.0215118
$535$	9.92896	0.429267
$536$	−0.420716	−0.0181722
$537$	21.5449	0.929729
$538$	9.98250	0.430376
$539$	−20.0401	−0.863187
$540$	−4.52993	−0.194937
$541$	38.3120	1.64716	0.823581	−	0.567199i	$-0.191973\pi$
$541$	38.3120	1.64716	0.823581	+	0.567199i	$0.191973\pi$
$542$	−0.648334	−0.0278483
$543$	10.2613	0.440356
$544$	−16.6153	−0.712375
$545$	36.2436	1.55251
$546$	−12.0626	−0.516230
$547$	−18.8583	−0.806324	−0.403162	−	0.915129i	$-0.632089\pi$
$547$	−18.8583	−0.806324	−0.403162	+	0.915129i	$0.632089\pi$
$548$	−21.4436	−0.916024
$549$	4.68450	0.199930
$550$	5.88124	0.250777
$551$	−2.32536	−0.0990637
$552$	0	0
$553$	26.3008	1.11842
$554$	12.1577	0.516529
$555$	0.755486	0.0320686
$556$	−13.7745	−0.584169
$557$	22.7686	0.964736	0.482368	−	0.875969i	$-0.339777\pi$
$557$	22.7686	0.964736	0.482368	+	0.875969i	$0.339777\pi$
$558$	3.69105	0.156255
$559$	11.5179	0.487155
$560$	19.7864	0.836128
$561$	−13.7746	−0.581566
$562$	7.04599	0.297217
$563$	−18.2054	−0.767264	−0.383632	−	0.923486i	$-0.625327\pi$
$563$	−18.2054	−0.767264	−0.383632	+	0.923486i	$0.625327\pi$
$564$	−7.95494	−0.334964
$565$	1.87787	0.0790024
$566$	4.04925	0.170203
$567$	3.38601	0.142199
$568$	−6.31249	−0.264866
$569$	−31.5087	−1.32091	−0.660456	−	0.750865i	$-0.729637\pi$
$569$	−31.5087	−1.32091	−0.660456	+	0.750865i	$0.729637\pi$
$570$	−1.61205	−0.0675214
$571$	4.84071	0.202577	0.101289	−	0.994857i	$-0.467703\pi$
$571$	4.84071	0.202577	0.101289	+	0.994857i	$0.467703\pi$
$572$	47.1052	1.96957
$573$	8.45001	0.353004
$574$	−2.73520	−0.114165
$575$	0	0
$576$	−1.24436	−0.0518485
$577$	25.1384	1.04653	0.523263	−	0.852171i	$-0.324715\pi$
$577$	25.1384	1.04653	0.523263	+	0.852171i	$0.324715\pi$
$578$	4.31337	0.179413
$579$	0.392108	0.0162955
$580$	10.0474	0.417195
$581$	−49.9813	−2.07357
$582$	−6.58452	−0.272937
$583$	−24.2303	−1.00352
$584$	−25.2902	−1.04652
$585$	16.9201	0.699561
$586$	10.2328	0.422715
$587$	31.1328	1.28499	0.642495	−	0.766290i	$-0.277899\pi$
$587$	31.1328	1.28499	0.642495	+	0.766290i	$0.277899\pi$
$588$	−7.48455	−0.308658
$589$	−6.80111	−0.280235
$590$	16.7462	0.689432
$591$	−22.5670	−0.928281
$592$	0.604510	0.0248452
$593$	−25.8767	−1.06263	−0.531315	−	0.847174i	$-0.678302\pi$
$593$	−25.8767	−1.06263	−0.531315	+	0.847174i	$0.678302\pi$
$594$	2.55372	0.104780
$595$	28.0831	1.15129
$596$	31.2079	1.27833
$597$	13.3644	0.546967
$598$	0	0
$599$	−43.7707	−1.78842	−0.894210	−	0.447647i	$-0.852262\pi$
$599$	−43.7707	−1.78842	−0.894210	+	0.447647i	$0.852262\pi$
$600$	4.81726	0.196664
$601$	13.0905	0.533972	0.266986	−	0.963700i	$-0.413972\pi$
$601$	13.0905	0.533972	0.266986	+	0.963700i	$0.413972\pi$
$602$	−3.54411	−0.144447
$603$	−0.201133	−0.00819079
$604$	9.16810	0.373045
$605$	24.7113	1.00466
$606$	−5.36946	−0.218119
$607$	12.1643	0.493732	0.246866	−	0.969050i	$-0.420599\pi$
$607$	12.1643	0.493732	0.246866	+	0.969050i	$0.420599\pi$
$608$	−5.67585	−0.230186
$609$	−7.51015	−0.304327
$610$	−7.20299	−0.291641
$611$	29.7132	1.20207
$612$	−5.14454	−0.207956
$613$	42.6873	1.72412	0.862062	−	0.506802i	$-0.169173\pi$
$613$	42.6873	1.72412	0.862062	+	0.506802i	$0.169173\pi$
$614$	−1.04172	−0.0420404
$615$	3.83666	0.154709
$616$	−31.7883	−1.28079
$617$	0.397854	0.0160170	0.00800849	−	0.999968i	$-0.497451\pi$
$617$	0.397854	0.0160170	0.00800849	+	0.999968i	$0.497451\pi$
$618$	−2.28318	−0.0918428
$619$	−30.0498	−1.20780	−0.603902	−	0.797058i	$-0.706388\pi$
$619$	−30.0498	−1.20780	−0.603902	+	0.797058i	$0.706388\pi$
$620$	29.3862	1.18018
$621$	0	0
$622$	5.27239	0.211403
$623$	−2.95826	−0.118520
$624$	13.5388	0.541987
$625$	−31.2112	−1.24845
$626$	−7.91852	−0.316488
$627$	−4.70548	−0.187919
$628$	−27.5519	−1.09944
$629$	0.857988	0.0342102
$630$	−5.20640	−0.207428
$631$	−24.1375	−0.960900	−0.480450	−	0.877022i	$-0.659527\pi$
$631$	−24.1375	−0.960900	−0.480450	+	0.877022i	$0.659527\pi$
$632$	16.2475	0.646290
$633$	−0.559001	−0.0222183
$634$	15.3926	0.611320
$635$	−29.5753	−1.17366
$636$	−9.04951	−0.358836
$637$	27.9562	1.10766
$638$	−5.66415	−0.224246
$639$	−3.01784	−0.119384
$640$	31.1740	1.23226
$641$	32.9635	1.30198	0.650990	−	0.759086i	$-0.274354\pi$
$641$	32.9635	1.30198	0.650990	+	0.759086i	$0.274354\pi$
$642$	−2.09051	−0.0825058
$643$	7.50786	0.296081	0.148040	−	0.988981i	$-0.452703\pi$
$643$	7.50786	0.296081	0.148040	+	0.988981i	$0.452703\pi$
$644$	0	0
$645$	4.97131	0.195745
$646$	−1.83077	−0.0720307
$647$	13.8074	0.542824	0.271412	−	0.962463i	$-0.412509\pi$
$647$	13.8074	0.542824	0.271412	+	0.962463i	$0.412509\pi$
$648$	2.09173	0.0821708
$649$	48.8813	1.91876
$650$	−8.20441	−0.321803
$651$	−21.9654	−0.860891
$652$	−16.7894	−0.657522
$653$	23.8790	0.934458	0.467229	−	0.884136i	$-0.345252\pi$
$653$	23.8790	0.934458	0.467229	+	0.884136i	$0.345252\pi$
$654$	−7.63097	−0.298394
$655$	−9.55974	−0.373530
$656$	3.06995	0.119861
$657$	−12.0906	−0.471698
$658$	−9.14287	−0.356426
$659$	20.6448	0.804207	0.402104	−	0.915594i	$-0.368279\pi$
$659$	20.6448	0.804207	0.402104	+	0.915594i	$0.368279\pi$
$660$	20.3314	0.791397
$661$	−45.8471	−1.78325	−0.891624	−	0.452777i	$-0.850433\pi$
$661$	−45.8471	−1.78325	−0.891624	+	0.452777i	$0.850433\pi$
$662$	−9.34411	−0.363169
$663$	19.2158	0.746280
$664$	−30.8763	−1.19823
$665$	9.59329	0.372012
$666$	−0.159065	−0.00616364
$667$	0	0
$668$	12.4027	0.479877
$669$	−29.6961	−1.14812
$670$	0.309267	0.0119480
$671$	−21.0251	−0.811665
$672$	−18.3312	−0.707140
$673$	34.7483	1.33945	0.669725	−	0.742609i	$-0.266412\pi$
$673$	34.7483	1.33945	0.669725	+	0.742609i	$0.266412\pi$
$674$	9.43068	0.363256
$675$	2.30301	0.0886428
$676$	−43.9210	−1.68927
$677$	31.2288	1.20022	0.600109	−	0.799918i	$-0.295124\pi$
$677$	31.2288	1.20022	0.600109	+	0.799918i	$0.295124\pi$
$678$	−0.395378	−0.0151844
$679$	39.1844	1.50376
$680$	17.3485	0.665284
$681$	−24.6703	−0.945368
$682$	−16.5663	−0.634355
$683$	25.0559	0.958738	0.479369	−	0.877613i	$-0.340866\pi$
$683$	25.0559	0.958738	0.479369	+	0.877613i	$0.340866\pi$
$684$	−1.75740	−0.0671958
$685$	34.5706	1.32087
$686$	4.88381	0.186465
$687$	−28.4810	−1.08662
$688$	3.97785	0.151654
$689$	33.8016	1.28774
$690$	0	0
$691$	47.0943	1.79155	0.895775	−	0.444507i	$-0.146621\pi$
$691$	47.0943	1.79155	0.895775	+	0.444507i	$0.146621\pi$
$692$	−9.41235	−0.357804
$693$	−15.1972	−0.577292
$694$	0.106246	0.00403304
$695$	22.2068	0.842351
$696$	−4.63945	−0.175858
$697$	4.35721	0.165041
$698$	−5.98325	−0.226469
$699$	−15.0630	−0.569736
$700$	−13.0715	−0.494055
$701$	25.5709	0.965799	0.482900	−	0.875676i	$-0.339584\pi$
$701$	25.5709	0.965799	0.482900	+	0.875676i	$0.339584\pi$
$702$	−3.56248	−0.134457
$703$	0.293092	0.0110542
$704$	5.58499	0.210492
$705$	12.8247	0.483006
$706$	11.7583	0.442529
$707$	31.9536	1.20174
$708$	18.2561	0.686108
$709$	−21.3040	−0.800089	−0.400045	−	0.916496i	$-0.631005\pi$
$709$	−21.3040	−0.800089	−0.400045	+	0.916496i	$0.631005\pi$
$710$	4.64029	0.174147
$711$	7.76749	0.291304
$712$	−1.82748	−0.0684878
$713$	0	0
$714$	−5.91279	−0.221281
$715$	−75.9414	−2.84005
$716$	−36.1147	−1.34967
$717$	−26.9624	−1.00693
$718$	−8.92020	−0.332899
$719$	−16.8868	−0.629771	−0.314885	−	0.949130i	$-0.601966\pi$
$719$	−16.8868	−0.629771	−0.314885	+	0.949130i	$0.601966\pi$
$720$	5.84358	0.217777
$721$	13.5871	0.506012
$722$	10.1853	0.379057
$723$	21.1091	0.785056
$724$	−17.2007	−0.639257
$725$	−5.10807	−0.189709
$726$	−5.20287	−0.193097
$727$	−46.8022	−1.73580	−0.867898	−	0.496742i	$-0.834529\pi$
$727$	−46.8022	−1.73580	−0.867898	+	0.496742i	$0.834529\pi$
$728$	44.3451	1.64354
$729$	1.00000	0.0370370
$730$	18.5907	0.688074
$731$	5.64581	0.208818
$732$	−7.85243	−0.290234
$733$	−1.21960	−0.0450470	−0.0225235	−	0.999746i	$-0.507170\pi$
$733$	−1.21960	−0.0450470	−0.0225235	+	0.999746i	$0.507170\pi$
$734$	−3.09847	−0.114367
$735$	12.0663	0.445074
$736$	0	0
$737$	0.902732	0.0332526
$738$	−0.807796	−0.0297354
$739$	−29.0460	−1.06848	−0.534238	−	0.845334i	$-0.679401\pi$
$739$	−29.0460	−1.06848	−0.534238	+	0.845334i	$0.679401\pi$
$740$	−1.26639	−0.0465534
$741$	6.56420	0.241142
$742$	−10.4009	−0.381829
$743$	−26.6891	−0.979128	−0.489564	−	0.871967i	$-0.662844\pi$
$743$	−26.6891	−0.979128	−0.489564	+	0.871967i	$0.662844\pi$
$744$	−13.5693	−0.497473
$745$	−50.3124	−1.84330
$746$	2.29151	0.0838982
$747$	−14.7611	−0.540082
$748$	23.0899	0.844249
$749$	12.4406	0.454569
$750$	4.14696	0.151425
$751$	1.36537	0.0498232	0.0249116	−	0.999690i	$-0.492070\pi$
$751$	1.36537	0.0498232	0.0249116	+	0.999690i	$0.492070\pi$
$752$	10.2618	0.374210
$753$	−2.32705	−0.0848024
$754$	7.90156	0.287758
$755$	−14.7805	−0.537917
$756$	−5.67582	−0.206428
$757$	52.1755	1.89635	0.948176	−	0.317746i	$-0.102926\pi$
$757$	52.1755	1.89635	0.948176	+	0.317746i	$0.102926\pi$
$758$	6.34357	0.230409
$759$	0	0
$760$	5.92632	0.214970
$761$	21.7889	0.789847	0.394923	−	0.918714i	$-0.370771\pi$
$761$	21.7889	0.789847	0.394923	+	0.918714i	$0.370771\pi$
$762$	6.22697	0.225579
$763$	45.4118	1.64402
$764$	−14.1644	−0.512450
$765$	8.29386	0.299865
$766$	8.54170	0.308624
$767$	−68.1900	−2.46220
$768$	−4.07484	−0.147038
$769$	37.6505	1.35771	0.678856	−	0.734271i	$-0.262476\pi$
$769$	37.6505	1.35771	0.678856	+	0.734271i	$0.262476\pi$
$770$	23.3675	0.842106
$771$	26.6953	0.961407
$772$	−0.657275	−0.0236559
$773$	1.82449	0.0656225	0.0328112	−	0.999462i	$-0.489554\pi$
$773$	1.82449	0.0656225	0.0328112	+	0.999462i	$0.489554\pi$
$774$	−1.04669	−0.0376226
$775$	−14.9399	−0.536655
$776$	24.2064	0.868959
$777$	0.946593	0.0339588
$778$	18.8681	0.676454
$779$	1.48844	0.0533289
$780$	−28.3625	−1.01554
$781$	13.5447	0.484668
$782$	0	0
$783$	−2.21800	−0.0792648
$784$	9.65501	0.344822
$785$	44.4183	1.58536
$786$	2.01277	0.0717931
$787$	−28.8204	−1.02734	−0.513668	−	0.857989i	$-0.671714\pi$
$787$	−28.8204	−1.02734	−0.513668	+	0.857989i	$0.671714\pi$
$788$	37.8281	1.34757
$789$	10.0028	0.356110
$790$	−11.9435	−0.424930
$791$	2.35289	0.0836591
$792$	−9.38814	−0.333593
$793$	29.3303	1.04155
$794$	3.79547	0.134696
$795$	14.5893	0.517430
$796$	−22.4021	−0.794023
$797$	−0.897615	−0.0317952	−0.0158976	−	0.999874i	$-0.505061\pi$
$797$	−0.897615	−0.0317952	−0.0158976	+	0.999874i	$0.505061\pi$
$798$	−2.01983	−0.0715013
$799$	14.5647	0.515262
$800$	−12.4680	−0.440811
$801$	−0.873672	−0.0308697
$802$	3.54271	0.125097
$803$	54.2652	1.91498
$804$	0.337152	0.0118904
$805$	0	0
$806$	23.1102	0.814021
$807$	−17.5445	−0.617595
$808$	19.7395	0.694434
$809$	−37.6547	−1.32387	−0.661934	−	0.749562i	$-0.730264\pi$
$809$	−37.6547	−1.32387	−0.661934	+	0.749562i	$0.730264\pi$
$810$	−1.53762	−0.0540266
$811$	−20.4727	−0.718893	−0.359446	−	0.933166i	$-0.617034\pi$
$811$	−20.4727	−0.718893	−0.359446	+	0.933166i	$0.617034\pi$
$812$	12.5890	0.441786
$813$	1.13946	0.0399627
$814$	0.713919	0.0250229
$815$	27.0672	0.948124
$816$	6.63642	0.232321
$817$	1.92863	0.0674743
$818$	1.11517	0.0389911
$819$	21.2002	0.740796
$820$	−6.43124	−0.224589
$821$	−16.1822	−0.564761	−0.282381	−	0.959302i	$-0.591124\pi$
$821$	−16.1822	−0.564761	−0.282381	+	0.959302i	$0.591124\pi$
$822$	−7.27872	−0.253875
$823$	−17.8806	−0.623279	−0.311640	−	0.950200i	$-0.600878\pi$
$823$	−17.8806	−0.623279	−0.311640	+	0.950200i	$0.600878\pi$
$824$	8.39355	0.292403
$825$	−10.3364	−0.359868
$826$	20.9824	0.730070
$827$	−8.08676	−0.281204	−0.140602	−	0.990066i	$-0.544904\pi$
$827$	−8.08676	−0.281204	−0.140602	+	0.990066i	$0.544904\pi$
$828$	0	0
$829$	−37.2365	−1.29328	−0.646639	−	0.762796i	$-0.723826\pi$
$829$	−37.2365	−1.29328	−0.646639	+	0.762796i	$0.723826\pi$
$830$	22.6971	0.787826
$831$	−21.3674	−0.741225
$832$	−7.79113	−0.270109
$833$	13.7035	0.474797
$834$	−4.67556	−0.161901
$835$	−19.9953	−0.691965
$836$	7.88760	0.272798
$837$	−6.48711	−0.224227
$838$	−4.70233	−0.162439
$839$	−34.7553	−1.19989	−0.599943	−	0.800043i	$-0.704810\pi$
$839$	−34.7553	−1.19989	−0.599943	+	0.800043i	$0.704810\pi$
$840$	19.1401	0.660395
$841$	−24.0805	−0.830362
$842$	1.00771	0.0347281
$843$	−12.3835	−0.426510
$844$	0.937030	0.0322539
$845$	70.8079	2.43587
$846$	−2.70019	−0.0928346
$847$	30.9622	1.06387
$848$	11.6738	0.400880
$849$	−7.11666	−0.244243
$850$	−4.02161	−0.137940
$851$	0	0
$852$	5.05867	0.173307
$853$	−28.2381	−0.966855	−0.483428	−	0.875384i	$-0.660608\pi$
$853$	−28.2381	−0.966855	−0.483428	+	0.875384i	$0.660608\pi$
$854$	−9.02505	−0.308831
$855$	2.83322	0.0968940
$856$	7.68525	0.262677
$857$	−7.43551	−0.253992	−0.126996	−	0.991903i	$-0.540534\pi$
$857$	−7.43551	−0.253992	−0.126996	+	0.991903i	$0.540534\pi$
$858$	15.9892	0.545862
$859$	40.8947	1.39531	0.697654	−	0.716435i	$-0.254227\pi$
$859$	40.8947	1.39531	0.697654	+	0.716435i	$0.254227\pi$
$860$	−8.33320	−0.284160
$861$	4.80718	0.163828
$862$	−15.2242	−0.518539
$863$	−21.2318	−0.722738	−0.361369	−	0.932423i	$-0.617691\pi$
$863$	−21.2318	−0.722738	−0.361369	+	0.932423i	$0.617691\pi$
$864$	−5.41380	−0.184181
$865$	15.1743	0.515941
$866$	−13.9834	−0.475176
$867$	−7.58085	−0.257459
$868$	36.8197	1.24974
$869$	−34.8623	−1.18262
$870$	3.41044	0.115625
$871$	−1.25932	−0.0426705
$872$	28.0534	0.950008
$873$	11.5724	0.391668
$874$	0	0
$875$	−24.6785	−0.834285
$876$	20.2669	0.684756
$877$	18.7101	0.631795	0.315897	−	0.948793i	$-0.397694\pi$
$877$	18.7101	0.631795	0.315897	+	0.948793i	$0.397694\pi$
$878$	−3.18376	−0.107447
$879$	−17.9845	−0.606601
$880$	−26.2273	−0.884123
$881$	35.8925	1.20925	0.604624	−	0.796511i	$-0.293323\pi$
$881$	35.8925	1.20925	0.604624	+	0.796511i	$0.293323\pi$
$882$	−2.54053	−0.0855439
$883$	6.34991	0.213691	0.106846	−	0.994276i	$-0.465925\pi$
$883$	6.34991	0.213691	0.106846	+	0.994276i	$0.465925\pi$
$884$	−32.2107	−1.08336
$885$	−29.4319	−0.989343
$886$	−7.12196	−0.239267
$887$	15.9876	0.536810	0.268405	−	0.963306i	$-0.413503\pi$
$887$	15.9876	0.536810	0.268405	+	0.963306i	$0.413503\pi$
$888$	0.584764	0.0196234
$889$	−37.0566	−1.24284
$890$	1.34338	0.0450301
$891$	−4.48823	−0.150361
$892$	49.7783	1.66670
$893$	4.97537	0.166494
$894$	10.5931	0.354286
$895$	58.2230	1.94618
$896$	39.0597	1.30489
$897$	0	0
$898$	4.63700	0.154739
$899$	14.3884	0.479880
$900$	−3.86044	−0.128681
$901$	16.5688	0.551985
$902$	3.62557	0.120718
$903$	6.22885	0.207283
$904$	1.45351	0.0483431
$905$	27.7303	0.921787
$906$	3.11198	0.103389
$907$	−23.4646	−0.779128	−0.389564	−	0.920999i	$-0.627374\pi$
$907$	−23.4646	−0.779128	−0.389564	+	0.920999i	$0.627374\pi$
$908$	41.3538	1.37238
$909$	9.43695	0.313004
$910$	−32.5980	−1.08061
$911$	27.8151	0.921557	0.460778	−	0.887515i	$-0.347570\pi$
$911$	27.8151	0.921557	0.460778	+	0.887515i	$0.347570\pi$
$912$	2.26703	0.0750689
$913$	66.2513	2.19260
$914$	10.2991	0.340663
$915$	12.6594	0.418508
$916$	47.7415	1.57742
$917$	−11.9780	−0.395547
$918$	−1.74624	−0.0576346
$919$	38.7863	1.27944	0.639720	−	0.768608i	$-0.279050\pi$
$919$	38.7863	1.27944	0.639720	+	0.768608i	$0.279050\pi$
$920$	0	0
$921$	1.83085	0.0603285
$922$	−7.45431	−0.245495
$923$	−18.8951	−0.621939
$924$	25.4744	0.838045
$925$	0.643829	0.0211690
$926$	11.0759	0.363977
$927$	4.01274	0.131796
$928$	12.0078	0.394175
$929$	−32.3914	−1.06273	−0.531364	−	0.847144i	$-0.678320\pi$
$929$	−32.3914	−1.06273	−0.531364	+	0.847144i	$0.678320\pi$
$930$	9.97472	0.327084
$931$	4.68116	0.153419
$932$	25.2495	0.827076
$933$	−9.26634	−0.303366
$934$	0.680407	0.0222636
$935$	−37.2247	−1.21738
$936$	13.0966	0.428075
$937$	−1.43049	−0.0467320	−0.0233660	−	0.999727i	$-0.507438\pi$
$937$	−1.43049	−0.0467320	−0.0233660	+	0.999727i	$0.507438\pi$
$938$	0.387499	0.0126523
$939$	13.9170	0.454164
$940$	−21.4975	−0.701171
$941$	−0.634645	−0.0206889	−0.0103444	−	0.999946i	$-0.503293\pi$
$941$	−0.634645	−0.0206889	−0.0103444	+	0.999946i	$0.503293\pi$
$942$	−9.35211	−0.304708
$943$	0	0
$944$	−23.5503	−0.766496
$945$	9.15037	0.297661
$946$	4.69779	0.152738
$947$	−33.2751	−1.08130	−0.540648	−	0.841249i	$-0.681821\pi$
$947$	−33.2751	−1.08130	−0.540648	+	0.841249i	$0.681821\pi$
$948$	−13.0203	−0.422881
$949$	−75.7007	−2.45735
$950$	−1.37380	−0.0445719
$951$	−27.0529	−0.877251
$952$	21.7369	0.704498
$953$	−39.9874	−1.29532	−0.647660	−	0.761930i	$-0.724252\pi$
$953$	−39.9874	−1.29532	−0.647660	+	0.761930i	$0.724252\pi$
$954$	−3.07173	−0.0994509
$955$	22.8354	0.738935
$956$	45.1960	1.46174
$957$	9.95488	0.321795
$958$	9.94899	0.321437
$959$	43.3155	1.39873
$960$	−3.36278	−0.108533
$961$	11.0826	0.357502
$962$	−0.995927	−0.0321100
$963$	3.67412	0.118397
$964$	−35.3843	−1.13965
$965$	1.05964	0.0341109
$966$	0	0
$967$	50.8204	1.63427	0.817136	−	0.576444i	$-0.195560\pi$
$967$	50.8204	1.63427	0.817136	+	0.576444i	$0.195560\pi$
$968$	19.1271	0.614769
$969$	3.21762	0.103365
$970$	−17.7941	−0.571333
$971$	42.9158	1.37723	0.688617	−	0.725125i	$-0.258218\pi$
$971$	42.9158	1.37723	0.688617	+	0.725125i	$0.258218\pi$
$972$	−1.67626	−0.0537660
$973$	27.8242	0.892003
$974$	12.8097	0.410449
$975$	14.4194	0.461791
$976$	10.1296	0.324240
$977$	10.5644	0.337985	0.168992	−	0.985617i	$-0.445949\pi$
$977$	10.5644	0.337985	0.168992	+	0.985617i	$0.445949\pi$
$978$	−5.69891	−0.182231
$979$	3.92124	0.125323
$980$	−20.2263	−0.646106
$981$	13.4116	0.428199
$982$	−16.7476	−0.534436
$983$	47.3537	1.51035	0.755175	−	0.655524i	$-0.227552\pi$
$983$	47.3537	1.51035	0.755175	+	0.655524i	$0.227552\pi$
$984$	2.96967	0.0946695
$985$	−60.9852	−1.94315
$986$	3.87316	0.123347
$987$	16.0688	0.511476
$988$	−11.0033	−0.350062
$989$	0	0
$990$	6.90120	0.219334
$991$	24.1058	0.765745	0.382872	−	0.923801i	$-0.374935\pi$
$991$	24.1058	0.765745	0.382872	+	0.923801i	$0.374935\pi$
$992$	35.1199	1.11506
$993$	16.4225	0.521152
$994$	5.81410	0.184412
$995$	36.1160	1.14495
$996$	24.7435	0.784027
$997$	28.2519	0.894747	0.447374	−	0.894347i	$-0.352359\pi$
$997$	28.2519	0.894747	0.447374	+	0.894347i	$0.352359\pi$
$998$	7.38753	0.233848
$999$	0.279560	0.00884490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1587.2.a.u.1.6		10
3.2	odd	2		4761.2.a.bt.1.5		10
23.2	even	11		69.2.e.c.4.2	✓	20
23.12	even	11		69.2.e.c.52.2	yes	20
23.22	odd	2		1587.2.a.t.1.6		10
69.2	odd	22		207.2.i.d.73.1		20
69.35	odd	22		207.2.i.d.190.1		20
69.68	even	2		4761.2.a.bu.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.4.2	✓	20	23.2	even	11
69.2.e.c.52.2	yes	20	23.12	even	11
207.2.i.d.73.1		20	69.2	odd	22
207.2.i.d.190.1		20	69.35	odd	22
1587.2.a.t.1.6		10	23.22	odd	2
1587.2.a.u.1.6		10	1.1	even	1	trivial
4761.2.a.bt.1.5		10	3.2	odd	2
4761.2.a.bu.1.5		10	69.68	even	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:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1587.a (trivial)

\(f(q)\)	\(=\)	\(q-0.568983 q^{2} +1.00000 q^{3} -1.67626 q^{4} +2.70241 q^{5} -0.568983 q^{6} +3.38601 q^{7} +2.09173 q^{8} +1.00000 q^{9} -1.53762 q^{10} -4.48823 q^{11} -1.67626 q^{12} +6.26113 q^{13} -1.92658 q^{14} +2.70241 q^{15} +2.16236 q^{16} +3.06906 q^{17} -0.568983 q^{18} +1.04840 q^{19} -4.52993 q^{20} +3.38601 q^{21} +2.55372 q^{22} +2.09173 q^{24} +2.30301 q^{25} -3.56248 q^{26} +1.00000 q^{27} -5.67582 q^{28} -2.21800 q^{29} -1.53762 q^{30} -6.48711 q^{31} -5.41380 q^{32} -4.48823 q^{33} -1.74624 q^{34} +9.15037 q^{35} -1.67626 q^{36} +0.279560 q^{37} -0.596524 q^{38} +6.26113 q^{39} +5.65270 q^{40} +1.41972 q^{41} -1.92658 q^{42} +1.83959 q^{43} +7.52343 q^{44} +2.70241 q^{45} +4.74565 q^{47} +2.16236 q^{48} +4.46503 q^{49} -1.31037 q^{50} +3.06906 q^{51} -10.4953 q^{52} +5.39864 q^{53} -0.568983 q^{54} -12.1290 q^{55} +7.08260 q^{56} +1.04840 q^{57} +1.26200 q^{58} -10.8910 q^{59} -4.52993 q^{60} +4.68450 q^{61} +3.69105 q^{62} +3.38601 q^{63} -1.24436 q^{64} +16.9201 q^{65} +2.55372 q^{66} -0.201133 q^{67} -5.14454 q^{68} -5.20640 q^{70} -3.01784 q^{71} +2.09173 q^{72} -12.0906 q^{73} -0.159065 q^{74} +2.30301 q^{75} -1.75740 q^{76} -15.1972 q^{77} -3.56248 q^{78} +7.76749 q^{79} +5.84358 q^{80} +1.00000 q^{81} -0.807796 q^{82} -14.7611 q^{83} -5.67582 q^{84} +8.29386 q^{85} -1.04669 q^{86} -2.21800 q^{87} -9.38814 q^{88} -0.873672 q^{89} -1.53762 q^{90} +21.2002 q^{91} -6.48711 q^{93} -2.70019 q^{94} +2.83322 q^{95} -5.41380 q^{96} +11.5724 q^{97} -2.54053 q^{98} -4.48823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 10 q^{3} + 8 q^{4} + 8 q^{5} - 2 q^{6} + 19 q^{7} - 6 q^{8} + 10 q^{9} + 13 q^{10} + 3 q^{11} + 8 q^{12} - 4 q^{13} + 8 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} + 22 q^{19} + q^{20} + 19 q^{21}+ \cdots + 3 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 10 * q^3 + 8 * q^4 + 8 * q^5 - 2 * q^6 + 19 * q^7 - 6 * q^8 + 10 * q^9 + 13 * q^10 + 3 * q^11 + 8 * q^12 - 4 * q^13 + 8 * q^15 - 4 * q^16 + 11 * q^17 - 2 * q^18 + 22 * q^19 + q^20 + 19 * q^21 + 13 * q^22 - 6 * q^24 - 2 * q^25 + 4 * q^26 + 10 * q^27 + 26 * q^28 - 5 * q^29 + 13 * q^30 - 7 * q^31 - 34 * q^32 + 3 * q^33 + 4 * q^34 + 9 * q^35 + 8 * q^36 + 35 * q^37 - 9 * q^38 - 4 * q^39 + 21 * q^40 + 28 * q^43 - 7 * q^44 + 8 * q^45 + 9 * q^47 - 4 * q^48 + 17 * q^49 + 11 * q^51 - 52 * q^52 + 34 * q^53 - 2 * q^54 - 14 * q^55 - 30 * q^56 + 22 * q^57 - 24 * q^58 - 2 * q^59 + q^60 + 49 * q^61 - 28 * q^62 + 19 * q^63 + 10 * q^64 + 2 * q^65 + 13 * q^66 + 26 * q^67 - 6 * q^68 + 16 * q^70 + 15 * q^71 - 6 * q^72 + 14 * q^73 - 25 * q^74 - 2 * q^75 + 19 * q^76 - 33 * q^77 + 4 * q^78 + 43 * q^79 - 49 * q^80 + 10 * q^81 + 24 * q^82 - 15 * q^83 + 26 * q^84 - 21 * q^85 - 49 * q^86 - 5 * q^87 + 15 * q^88 - 15 * q^89 + 13 * q^90 + 4 * q^91 - 7 * q^93 - 28 * q^94 + 28 * q^95 - 34 * q^96 + 22 * q^97 + 15 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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