LMFDB - Embedded newform 1587.2.a.t.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:	$1$
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	$-0.706538\pi$
$5$	−2.70241	−1.20855	−0.604277	+	0.796775i	$0.706538\pi$
$6$	−0.568983	−0.232286
$7$	−3.38601	−1.27979	−0.639895	−	0.768462i	$-0.721022\pi$
$7$	−3.38601	−1.27979	−0.639895	+	0.768462i	$0.721022\pi$
$8$	2.09173	0.739537
$9$	1.00000	0.333333
$10$	1.53762	0.486239
$11$	4.48823	1.35325	0.676625	−	0.736327i	$-0.263442\pi$
$11$	4.48823	1.35325	0.676625	+	0.736327i	$0.263442\pi$
$12$	−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	$-0.621389\pi$
$17$	−3.06906	−0.744357	−0.372179	+	0.928161i	$0.621389\pi$
$18$	−0.568983	−0.134110
$19$	−1.04840	−0.240521	−0.120260	−	0.992742i	$-0.538373\pi$
$19$	−1.04840	−0.240521	−0.120260	+	0.992742i	$0.538373\pi$
$20$	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	$-0.507315\pi$
$37$	−0.279560	−0.0459594	−0.0229797	+	0.999736i	$0.507315\pi$
$38$	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	$-0.544796\pi$
$43$	−1.83959	−0.280534	−0.140267	+	0.990114i	$0.544796\pi$
$44$	−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	$-0.620910\pi$
$53$	−5.39864	−0.741560	−0.370780	+	0.928721i	$0.620910\pi$
$54$	−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	$-0.596951\pi$
$61$	−4.68450	−0.599789	−0.299894	+	0.953972i	$0.596951\pi$
$62$	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	$-0.496089\pi$
$67$	0.201133	0.0245724	0.0122862	+	0.999925i	$0.496089\pi$
$68$	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	$-0.643943\pi$
$79$	−7.76749	−0.873911	−0.436956	+	0.899483i	$0.643943\pi$
$80$	−5.84358	−0.653332
$81$	1.00000	0.111111
$82$	−0.807796	−0.0892061
$83$	14.7611	1.62024	0.810122	−	0.586261i	$-0.199401\pi$
$83$	14.7611	1.62024	0.810122	+	0.586261i	$0.199401\pi$
$84$	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	$-0.485256\pi$
$89$	0.873672	0.0926090	0.0463045	+	0.998927i	$0.485256\pi$
$90$	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	$-0.699888\pi$
$97$	−11.5724	−1.17500	−0.587502	+	0.809223i	$0.699888\pi$
$98$	−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	$-0.563345\pi$
$103$	−4.01274	−0.395387	−0.197693	+	0.980264i	$0.563345\pi$
$104$	13.0966	1.28423
$105$	9.15037	0.892984
$106$	3.07173	0.298353
$107$	−3.67412	−0.355190	−0.177595	−	0.984104i	$-0.556832\pi$
$107$	−3.67412	−0.355190	−0.177595	+	0.984104i	$0.556832\pi$
$108$	−1.67626	−0.161298
$109$	−13.4116	−1.28460	−0.642299	−	0.766454i	$-0.722019\pi$
$109$	−13.4116	−1.28460	−0.642299	+	0.766454i	$0.722019\pi$
$110$	6.90120	0.658003
$111$	−0.279560	−0.0265347
$112$	−7.32177	−0.691842
$113$	−0.694886	−0.0653694	−0.0326847	−	0.999466i	$-0.510406\pi$
$113$	−0.694886	−0.0653694	−0.0326847	+	0.999466i	$0.510406\pi$
$114$	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	$-0.684028\pi$
$137$	−12.7925	−1.09294	−0.546469	+	0.837479i	$0.684028\pi$
$138$	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	$-0.223919\pi$
$149$	18.6176	1.52521	0.762607	+	0.646862i	$0.223919\pi$
$150$	−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	$-0.727706\pi$
$157$	−16.4366	−1.31178	−0.655890	+	0.754856i	$0.727706\pi$
$158$	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	$-0.624544\pi$
$181$	−10.2613	−0.762719	−0.381360	+	0.924427i	$0.624544\pi$
$182$	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	$-0.598894\pi$
$191$	−8.45001	−0.611421	−0.305710	+	0.952125i	$0.598894\pi$
$192$	−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	$-0.657077\pi$
$199$	−13.3644	−0.947375	−0.473687	+	0.880693i	$0.657077\pi$
$200$	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	$-0.194688\pi$
$227$	24.6703	1.63743	0.818713	+	0.574203i	$0.194688\pi$
$228$	1.75740	0.116387
$229$	28.4810	1.88207	0.941037	−	0.338302i	$-0.109853\pi$
$229$	28.4810	1.88207	0.941037	+	0.338302i	$0.109853\pi$
$230$	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	$-0.737968\pi$
$241$	−21.1091	−1.35976	−0.679879	+	0.733324i	$0.737968\pi$
$242$	−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	$-0.476602\pi$
$251$	2.32705	0.146882	0.0734411	+	0.997300i	$0.476602\pi$
$252$	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	$-0.599794\pi$
$263$	−10.0028	−0.616801	−0.308401	+	0.951257i	$0.599794\pi$
$264$	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	$-0.379574\pi$
$281$	12.3835	0.738737	0.369369	+	0.929283i	$0.379574\pi$
$282$	−2.70019	−0.160794
$283$	7.11666	0.423041	0.211521	−	0.977374i	$-0.432158\pi$
$283$	7.11666	0.423041	0.211521	+	0.977374i	$0.432158\pi$
$284$	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	$-0.323941\pi$
$293$	17.9845	1.05066	0.525332	+	0.850898i	$0.323941\pi$
$294$	−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	$-0.628673\pi$
$313$	−13.9170	−0.786634	−0.393317	+	0.919403i	$0.628673\pi$
$314$	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	$-0.350911\pi$
$337$	16.5746	0.902878	0.451439	+	0.892302i	$0.350911\pi$
$338$	−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	$-0.635768\pi$
$359$	−15.6775	−0.827425	−0.413712	+	0.910408i	$0.635768\pi$
$360$	−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	$-0.545395\pi$
$367$	−5.44563	−0.284259	−0.142130	+	0.989848i	$0.545395\pi$
$368$	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	$-0.466751\pi$
$373$	4.02738	0.208530	0.104265	+	0.994550i	$0.466751\pi$
$374$	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	$-0.407561\pi$
$379$	11.1490	0.572684	0.286342	+	0.958127i	$0.407561\pi$
$380$	−4.74921	−0.243629
$381$	−10.9440	−0.560680
$382$	4.80791	0.245994
$383$	15.0122	0.767090	0.383545	−	0.923522i	$-0.374703\pi$
$383$	15.0122	0.767090	0.383545	+	0.923522i	$0.374703\pi$
$384$	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	$-0.182163\pi$
$389$	33.1611	1.68134	0.840668	+	0.541551i	$0.182163\pi$
$390$	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	$-0.450312\pi$
$401$	6.22639	0.310931	0.155466	+	0.987841i	$0.450312\pi$
$402$	−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	$-0.564703\pi$
$419$	−8.26445	−0.403745	−0.201872	+	0.979412i	$0.564703\pi$
$420$	−15.3384	−0.748436
$421$	1.77108	0.0863170	0.0431585	−	0.999068i	$-0.486258\pi$
$421$	1.77108	0.0863170	0.0431585	+	0.999068i	$0.486258\pi$
$422$	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	$-0.722900\pi$
$431$	−26.7569	−1.28884	−0.644418	+	0.764674i	$0.722900\pi$
$432$	2.16236	0.104037
$433$	−24.5762	−1.18106	−0.590529	−	0.807017i	$-0.701081\pi$
$433$	−24.5762	−1.18106	−0.590529	+	0.807017i	$0.701081\pi$
$434$	−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	$-0.360850\pi$
$457$	18.1009	0.846723	0.423361	+	0.905961i	$0.360850\pi$
$458$	−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	$-0.491192\pi$
$467$	1.19583	0.0553365	0.0276682	+	0.999617i	$0.491192\pi$
$468$	−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	$-0.369195\pi$
$479$	17.4856	0.798937	0.399468	+	0.916747i	$0.369195\pi$
$480$	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	$-0.494783\pi$
$503$	0.735172	0.0327797	0.0163898	+	0.999866i	$0.494783\pi$
$504$	−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	$-0.383127\pi$
$521$	16.3874	0.717944	0.358972	+	0.933348i	$0.383127\pi$
$522$	1.26200	0.0552363
$523$	−24.8590	−1.08701	−0.543504	−	0.839406i	$-0.682903\pi$
$523$	−24.8590	−1.08701	−0.543504	+	0.839406i	$0.682903\pi$
$524$	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	$-0.660223\pi$
$557$	−22.7686	−0.964736	−0.482368	+	0.875969i	$0.660223\pi$
$558$	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	$-0.374673\pi$
$563$	18.2054	0.767264	0.383632	+	0.923486i	$0.374673\pi$
$564$	−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	$-0.270363\pi$
$569$	31.5087	1.32091	0.660456	+	0.750865i	$0.270363\pi$
$570$	−1.61205	−0.0675214
$571$	−4.84071	−0.202577	−0.101289	−	0.994857i	$-0.532297\pi$
$571$	−4.84071	−0.202577	−0.101289	+	0.994857i	$0.532297\pi$
$572$	−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	$-0.830827\pi$
$613$	−42.6873	−1.72412	−0.862062	+	0.506802i	$0.830827\pi$
$614$	−1.04172	−0.0420404
$615$	−3.83666	−0.154709
$616$	−31.7883	−1.28079
$617$	−0.397854	−0.0160170	−0.00800849	−	0.999968i	$-0.502549\pi$
$617$	−0.397854	−0.0160170	−0.00800849	+	0.999968i	$0.502549\pi$
$618$	2.28318	0.0918428
$619$	30.0498	1.20780	0.603902	−	0.797058i	$-0.293612\pi$
$619$	30.0498	1.20780	0.603902	+	0.797058i	$0.293612\pi$
$620$	−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	$-0.340473\pi$
$631$	24.1375	0.960900	0.480450	+	0.877022i	$0.340473\pi$
$632$	−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	$-0.725646\pi$
$641$	−32.9635	−1.30198	−0.650990	+	0.759086i	$0.725646\pi$
$642$	2.09051	0.0825058
$643$	−7.50786	−0.296081	−0.148040	−	0.988981i	$-0.547297\pi$
$643$	−7.50786	−0.296081	−0.148040	+	0.988981i	$0.547297\pi$
$644$	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	$-0.631721\pi$
$659$	−20.6448	−0.804207	−0.402104	+	0.915594i	$0.631721\pi$
$660$	20.3314	0.791397
$661$	45.8471	1.78325	0.891624	−	0.452777i	$-0.149567\pi$
$661$	45.8471	1.78325	0.891624	+	0.452777i	$0.149567\pi$
$662$	−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	$-0.704876\pi$
$677$	−31.2288	−1.20022	−0.600109	+	0.799918i	$0.704876\pi$
$678$	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	$-0.660416\pi$
$701$	−25.5709	−0.965799	−0.482900	+	0.875676i	$0.660416\pi$
$702$	−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	$-0.368995\pi$
$709$	21.3040	0.800089	0.400045	+	0.916496i	$0.368995\pi$
$710$	−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	$-0.165471\pi$
$727$	46.8022	1.73580	0.867898	+	0.496742i	$0.165471\pi$
$728$	−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	$-0.492830\pi$
$733$	1.21960	0.0450470	0.0225235	+	0.999746i	$0.492830\pi$
$734$	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	$-0.337156\pi$
$743$	26.6891	0.979128	0.489564	+	0.871967i	$0.337156\pi$
$744$	−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	$-0.507930\pi$
$751$	−1.36537	−0.0498232	−0.0249116	+	0.999690i	$0.507930\pi$
$752$	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	$-0.897074\pi$
$757$	−52.1755	−1.89635	−0.948176	+	0.317746i	$0.897074\pi$
$758$	−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	$-0.737524\pi$
$769$	−37.6505	−1.35771	−0.678856	+	0.734271i	$0.737524\pi$
$770$	−23.3675	−0.842106
$771$	26.6953	0.961407
$772$	−0.657275	−0.0236559
$773$	−1.82449	−0.0656225	−0.0328112	−	0.999462i	$-0.510446\pi$
$773$	−1.82449	−0.0656225	−0.0328112	+	0.999462i	$0.510446\pi$
$774$	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	$-0.328286\pi$
$787$	28.8204	1.02734	0.513668	+	0.857989i	$0.328286\pi$
$788$	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	$-0.494939\pi$
$797$	0.897615	0.0317952	0.0158976	+	0.999874i	$0.494939\pi$
$798$	−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	$-0.455096\pi$
$827$	8.08676	0.281204	0.140602	+	0.990066i	$0.455096\pi$
$828$	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	$-0.295190\pi$
$839$	34.7553	1.19989	0.599943	+	0.800043i	$0.295190\pi$
$840$	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	$-0.706677\pi$
$881$	−35.8925	−1.20925	−0.604624	+	0.796511i	$0.706677\pi$
$882$	−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	$-0.372626\pi$
$907$	23.4646	0.779128	0.389564	+	0.920999i	$0.372626\pi$
$908$	−41.3538	−1.37238
$909$	9.43695	0.313004
$910$	−32.5980	−1.08061
$911$	−27.8151	−0.921557	−0.460778	−	0.887515i	$-0.652430\pi$
$911$	−27.8151	−0.921557	−0.460778	+	0.887515i	$0.652430\pi$
$912$	−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	$-0.720950\pi$
$919$	−38.7863	−1.27944	−0.639720	+	0.768608i	$0.720950\pi$
$920$	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	$-0.492562\pi$
$937$	1.43049	0.0467320	0.0233660	+	0.999727i	$0.492562\pi$
$938$	0.387499	0.0126523
$939$	−13.9170	−0.454164
$940$	21.4975	0.701171
$941$	0.634645	0.0206889	0.0103444	−	0.999946i	$-0.496707\pi$
$941$	0.634645	0.0206889	0.0103444	+	0.999946i	$0.496707\pi$
$942$	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	$-0.275748\pi$
$953$	39.9874	1.29532	0.647660	+	0.761930i	$0.275748\pi$
$954$	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	$-0.741782\pi$
$971$	−42.9158	−1.37723	−0.688617	+	0.725125i	$0.741782\pi$
$972$	−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	$-0.554051\pi$
$977$	−10.5644	−0.337985	−0.168992	+	0.985617i	$0.554051\pi$
$978$	−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	$-0.772448\pi$
$983$	−47.3537	−1.51035	−0.755175	+	0.655524i	$0.772448\pi$
$984$	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.t.1.6		10
3.2	odd	2		4761.2.a.bu.1.5		10
23.11	odd	22		69.2.e.c.52.2	yes	20
23.21	odd	22		69.2.e.c.4.2	✓	20
23.22	odd	2		1587.2.a.u.1.6		10
69.11	even	22		207.2.i.d.190.1		20
69.44	even	22		207.2.i.d.73.1		20
69.68	even	2		4761.2.a.bt.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.4.2	✓	20	23.21	odd	22
69.2.e.c.52.2	yes	20	23.11	odd	22
207.2.i.d.73.1		20	69.44	even	22
207.2.i.d.190.1		20	69.11	even	22
1587.2.a.t.1.6		10	1.1	even	1	trivial
1587.2.a.u.1.6		10	23.22	odd	2
4761.2.a.bt.1.5		10	69.68	even	2
4761.2.a.bu.1.5		10	3.2	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:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
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

Fields

Representations

Groups

Database

Properties

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