LMFDB - Embedded newform 1587.2.a.u.1.5

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			1.5
Root			$0.703704$ 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)

$f(q)$	$=$	\(q-0.703704 q^{2} +1.00000 q^{3} -1.50480 q^{4} -1.68624 q^{5} -0.703704 q^{6} +3.24908 q^{7} +2.46634 q^{8} +1.00000 q^{9} +1.18661 q^{10} +2.04318 q^{11} -1.50480 q^{12} +0.236720 q^{13} -2.28639 q^{14} -1.68624 q^{15} +1.27403 q^{16} +3.00512 q^{17} -0.703704 q^{18} -4.79422 q^{19} +2.53745 q^{20} +3.24908 q^{21} -1.43779 q^{22} +2.46634 q^{24} -2.15659 q^{25} -0.166580 q^{26} +1.00000 q^{27} -4.88921 q^{28} -7.10942 q^{29} +1.18661 q^{30} +6.70601 q^{31} -5.82922 q^{32} +2.04318 q^{33} -2.11472 q^{34} -5.47872 q^{35} -1.50480 q^{36} +11.4894 q^{37} +3.37371 q^{38} +0.236720 q^{39} -4.15885 q^{40} +8.20214 q^{41} -2.28639 q^{42} +2.88317 q^{43} -3.07458 q^{44} -1.68624 q^{45} -13.2857 q^{47} +1.27403 q^{48} +3.55650 q^{49} +1.51760 q^{50} +3.00512 q^{51} -0.356216 q^{52} +0.531658 q^{53} -0.703704 q^{54} -3.44529 q^{55} +8.01334 q^{56} -4.79422 q^{57} +5.00293 q^{58} -3.44874 q^{59} +2.53745 q^{60} +4.85262 q^{61} -4.71904 q^{62} +3.24908 q^{63} +1.55400 q^{64} -0.399166 q^{65} -1.43779 q^{66} +14.9277 q^{67} -4.52211 q^{68} +3.85540 q^{70} +13.4493 q^{71} +2.46634 q^{72} +4.44341 q^{73} -8.08512 q^{74} -2.15659 q^{75} +7.21434 q^{76} +6.63845 q^{77} -0.166580 q^{78} +2.09163 q^{79} -2.14831 q^{80} +1.00000 q^{81} -5.77188 q^{82} +6.44335 q^{83} -4.88921 q^{84} -5.06736 q^{85} -2.02890 q^{86} -7.10942 q^{87} +5.03918 q^{88} +2.50913 q^{89} +1.18661 q^{90} +0.769120 q^{91} +6.70601 q^{93} +9.34924 q^{94} +8.08420 q^{95} -5.82922 q^{96} +1.81486 q^{97} -2.50273 q^{98} +2.04318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.703704	−0.497594	−0.248797	−	0.968556i	$-0.580035\pi$
$2$	−0.703704	−0.497594	−0.248797	+	0.968556i	$0.580035\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.50480	−0.752400
$5$	−1.68624	−0.754109	−0.377055	−	0.926191i	$-0.623063\pi$
$5$	−1.68624	−0.754109	−0.377055	+	0.926191i	$0.623063\pi$
$6$	−0.703704	−0.287286
$7$	3.24908	1.22804	0.614018	−	0.789292i	$-0.289552\pi$
$7$	3.24908	1.22804	0.614018	+	0.789292i	$0.289552\pi$
$8$	2.46634	0.871984
$9$	1.00000	0.333333
$10$	1.18661	0.375240
$11$	2.04318	0.616042	0.308021	−	0.951380i	$-0.400333\pi$
$11$	2.04318	0.616042	0.308021	+	0.951380i	$0.400333\pi$
$12$	−1.50480	−0.434399
$13$	0.236720	0.0656542	0.0328271	−	0.999461i	$-0.489549\pi$
$13$	0.236720	0.0656542	0.0328271	+	0.999461i	$0.489549\pi$
$14$	−2.28639	−0.611063
$15$	−1.68624	−0.435385
$16$	1.27403	0.318506
$17$	3.00512	0.728850	0.364425	−	0.931233i	$-0.381266\pi$
$17$	3.00512	0.728850	0.364425	+	0.931233i	$0.381266\pi$
$18$	−0.703704	−0.165865
$19$	−4.79422	−1.09987	−0.549934	−	0.835208i	$-0.685347\pi$
$19$	−4.79422	−1.09987	−0.549934	+	0.835208i	$0.685347\pi$
$20$	2.53745	0.567392
$21$	3.24908	0.709007
$22$	−1.43779	−0.306539
$23$	0	0
$23$	0	0
$24$	2.46634	0.503440
$25$	−2.15659	−0.431319
$26$	−0.166580	−0.0326691
$27$	1.00000	0.192450
$28$	−4.88921	−0.923974
$29$	−7.10942	−1.32019	−0.660093	−	0.751184i	$-0.729483\pi$
$29$	−7.10942	−1.32019	−0.660093	+	0.751184i	$0.729483\pi$
$30$	1.18661	0.216645
$31$	6.70601	1.20443	0.602217	−	0.798332i	$-0.294284\pi$
$31$	6.70601	1.20443	0.602217	+	0.798332i	$0.294284\pi$
$32$	−5.82922	−1.03047
$33$	2.04318	0.355672
$34$	−2.11472	−0.362671
$35$	−5.47872	−0.926073
$36$	−1.50480	−0.250800
$37$	11.4894	1.88884	0.944421	−	0.328738i	$-0.106623\pi$
$37$	11.4894	1.88884	0.944421	+	0.328738i	$0.106623\pi$
$38$	3.37371	0.547288
$39$	0.236720	0.0379055
$40$	−4.15885	−0.657571
$41$	8.20214	1.28096	0.640480	−	0.767975i	$-0.278736\pi$
$41$	8.20214	1.28096	0.640480	+	0.767975i	$0.278736\pi$
$42$	−2.28639	−0.352797
$43$	2.88317	0.439679	0.219839	−	0.975536i	$-0.429447\pi$
$43$	2.88317	0.439679	0.219839	+	0.975536i	$0.429447\pi$
$44$	−3.07458	−0.463510
$45$	−1.68624	−0.251370
$46$	0	0
$47$	−13.2857	−1.93793	−0.968963	−	0.247206i	$-0.920487\pi$
$47$	−13.2857	−1.93793	−0.968963	+	0.247206i	$0.920487\pi$
$48$	1.27403	0.183890
$49$	3.55650	0.508072
$50$	1.51760	0.214622
$51$	3.00512	0.420802
$52$	−0.356216	−0.0493982
$53$	0.531658	0.0730288	0.0365144	−	0.999333i	$-0.488375\pi$
$53$	0.531658	0.0730288	0.0365144	+	0.999333i	$0.488375\pi$
$54$	−0.703704	−0.0957620
$55$	−3.44529	−0.464563
$56$	8.01334	1.07083
$57$	−4.79422	−0.635010
$58$	5.00293	0.656917
$59$	−3.44874	−0.448988	−0.224494	−	0.974475i	$-0.572073\pi$
$59$	−3.44874	−0.448988	−0.224494	+	0.974475i	$0.572073\pi$
$60$	2.53745	0.327584
$61$	4.85262	0.621314	0.310657	−	0.950522i	$-0.399451\pi$
$61$	4.85262	0.621314	0.310657	+	0.950522i	$0.399451\pi$
$62$	−4.71904	−0.599319
$63$	3.24908	0.409345
$64$	1.55400	0.194249
$65$	−0.399166	−0.0495104
$66$	−1.43779	−0.176980
$67$	14.9277	1.82371	0.911855	−	0.410513i	$-0.134650\pi$
$67$	14.9277	1.82371	0.911855	+	0.410513i	$0.134650\pi$
$68$	−4.52211	−0.548387
$69$	0	0
$70$	3.85540	0.460808
$71$	13.4493	1.59614	0.798068	−	0.602567i	$-0.205855\pi$
$71$	13.4493	1.59614	0.798068	+	0.602567i	$0.205855\pi$
$72$	2.46634	0.290661
$73$	4.44341	0.520061	0.260031	−	0.965600i	$-0.416267\pi$
$73$	4.44341	0.520061	0.260031	+	0.965600i	$0.416267\pi$
$74$	−8.08512	−0.939876
$75$	−2.15659	−0.249022
$76$	7.21434	0.827542
$77$	6.63845	0.756522
$78$	−0.166580	−0.0188615
$79$	2.09163	0.235327	0.117663	−	0.993054i	$-0.462460\pi$
$79$	2.09163	0.235327	0.117663	+	0.993054i	$0.462460\pi$
$80$	−2.14831	−0.240189
$81$	1.00000	0.111111
$82$	−5.77188	−0.637398
$83$	6.44335	0.707250	0.353625	−	0.935387i	$-0.384949\pi$
$83$	6.44335	0.707250	0.353625	+	0.935387i	$0.384949\pi$
$84$	−4.88921	−0.533457
$85$	−5.06736	−0.549632
$86$	−2.02890	−0.218781
$87$	−7.10942	−0.762210
$88$	5.03918	0.537179
$89$	2.50913	0.265967	0.132984	−	0.991118i	$-0.457544\pi$
$89$	2.50913	0.265967	0.132984	+	0.991118i	$0.457544\pi$
$90$	1.18661	0.125080
$91$	0.769120	0.0806257
$92$	0	0
$93$	6.70601	0.695380
$94$	9.34924	0.964300
$95$	8.08420	0.829422
$96$	−5.82922	−0.594942
$97$	1.81486	0.184271	0.0921356	−	0.995746i	$-0.470631\pi$
$97$	1.81486	0.184271	0.0921356	+	0.995746i	$0.470631\pi$
$98$	−2.50273	−0.252814
$99$	2.04318	0.205347
$100$	3.24525	0.324525
$101$	−2.39938	−0.238747	−0.119373	−	0.992849i	$-0.538089\pi$
$101$	−2.39938	−0.238747	−0.119373	+	0.992849i	$0.538089\pi$
$102$	−2.11472	−0.209388
$103$	4.11009	0.404979	0.202490	−	0.979284i	$-0.435097\pi$
$103$	4.11009	0.404979	0.202490	+	0.979284i	$0.435097\pi$
$104$	0.583831	0.0572494
$105$	−5.47872	−0.534669
$106$	−0.374130	−0.0363387
$107$	13.4565	1.30089	0.650446	−	0.759552i	$-0.274582\pi$
$107$	13.4565	1.30089	0.650446	+	0.759552i	$0.274582\pi$
$108$	−1.50480	−0.144800
$109$	15.8269	1.51594	0.757972	−	0.652287i	$-0.226190\pi$
$109$	15.8269	1.51594	0.757972	+	0.652287i	$0.226190\pi$
$110$	2.42447	0.231164
$111$	11.4894	1.09052
$112$	4.13941	0.391137
$113$	−12.9344	−1.21676	−0.608382	−	0.793644i	$-0.708181\pi$
$113$	−12.9344	−1.21676	−0.608382	+	0.793644i	$0.708181\pi$
$114$	3.37371	0.315977
$115$	0	0
$116$	10.6983	0.993309
$117$	0.236720	0.0218847
$118$	2.42689	0.223414
$119$	9.76388	0.895054
$120$	−4.15885	−0.379649
$121$	−6.82542	−0.620492
$122$	−3.41481	−0.309162
$123$	8.20214	0.739562
$124$	−10.0912	−0.906217
$125$	12.0677	1.07937
$126$	−2.28639	−0.203688
$127$	5.32226	0.472274	0.236137	−	0.971720i	$-0.424119\pi$
$127$	5.32226	0.472274	0.236137	+	0.971720i	$0.424119\pi$
$128$	10.5649	0.933813
$129$	2.88317	0.253849
$130$	0.280895	0.0246361
$131$	4.54109	0.396757	0.198379	−	0.980125i	$-0.436432\pi$
$131$	4.54109	0.396757	0.198379	+	0.980125i	$0.436432\pi$
$132$	−3.07458	−0.267608
$133$	−15.5768	−1.35068
$134$	−10.5047	−0.907467
$135$	−1.68624	−0.145128
$136$	7.41167	0.635545
$137$	−16.4974	−1.40947	−0.704734	−	0.709471i	$-0.748934\pi$
$137$	−16.4974	−1.40947	−0.704734	+	0.709471i	$0.748934\pi$
$138$	0	0
$139$	3.46582	0.293967	0.146984	−	0.989139i	$-0.453044\pi$
$139$	3.46582	0.293967	0.146984	+	0.989139i	$0.453044\pi$
$140$	8.24439	0.696778
$141$	−13.2857	−1.11886
$142$	−9.46432	−0.794228
$143$	0.483661	0.0404457
$144$	1.27403	0.106169
$145$	11.9882	0.995565
$146$	−3.12684	−0.258779
$147$	3.55650	0.293335
$148$	−17.2892	−1.42117
$149$	3.06922	0.251440	0.125720	−	0.992066i	$-0.459876\pi$
$149$	3.06922	0.251440	0.125720	+	0.992066i	$0.459876\pi$
$150$	1.51760	0.123912
$151$	1.89569	0.154269	0.0771346	−	0.997021i	$-0.475423\pi$
$151$	1.89569	0.154269	0.0771346	+	0.997021i	$0.475423\pi$
$152$	−11.8242	−0.959068
$153$	3.00512	0.242950
$154$	−4.67150	−0.376441
$155$	−11.3079	−0.908275
$156$	−0.356216	−0.0285201
$157$	2.15782	0.172213	0.0861066	−	0.996286i	$-0.472557\pi$
$157$	2.15782	0.172213	0.0861066	+	0.996286i	$0.472557\pi$
$158$	−1.47189	−0.117097
$159$	0.531658	0.0421632
$160$	9.82947	0.777088
$161$	0	0
$162$	−0.703704	−0.0552882
$163$	−12.0963	−0.947457	−0.473728	−	0.880671i	$-0.657092\pi$
$163$	−12.0963	−0.947457	−0.473728	+	0.880671i	$0.657092\pi$
$164$	−12.3426	−0.963794
$165$	−3.44529	−0.268216
$166$	−4.53421	−0.351923
$167$	−13.1686	−1.01901	−0.509507	−	0.860467i	$-0.670172\pi$
$167$	−13.1686	−1.01901	−0.509507	+	0.860467i	$0.670172\pi$
$168$	8.01334	0.618242
$169$	−12.9440	−0.995690
$170$	3.56592	0.273494
$171$	−4.79422	−0.366623
$172$	−4.33859	−0.330814
$173$	−17.6417	−1.34127	−0.670636	−	0.741787i	$-0.733979\pi$
$173$	−17.6417	−1.34127	−0.670636	+	0.741787i	$0.733979\pi$
$174$	5.00293	0.379271
$175$	−7.00694	−0.529675
$176$	2.60306	0.196213
$177$	−3.44874	−0.259223
$178$	−1.76569	−0.132344
$179$	10.7685	0.804879	0.402439	−	0.915447i	$-0.368162\pi$
$179$	10.7685	0.804879	0.402439	+	0.915447i	$0.368162\pi$
$180$	2.53745	0.189131
$181$	−1.42664	−0.106041	−0.0530205	−	0.998593i	$-0.516885\pi$
$181$	−1.42664	−0.106041	−0.0530205	+	0.998593i	$0.516885\pi$
$182$	−0.541233	−0.0401189
$183$	4.85262	0.358716
$184$	0	0
$185$	−19.3738	−1.42439
$186$	−4.71904	−0.346017
$187$	6.14001	0.449002
$188$	19.9924	1.45810
$189$	3.24908	0.236336
$190$	−5.68889	−0.412715
$191$	−13.8937	−1.00531	−0.502656	−	0.864487i	$-0.667644\pi$
$191$	−13.8937	−1.00531	−0.502656	+	0.864487i	$0.667644\pi$
$192$	1.55400	0.112150
$193$	8.09563	0.582736	0.291368	−	0.956611i	$-0.405890\pi$
$193$	8.09563	0.582736	0.291368	+	0.956611i	$0.405890\pi$
$194$	−1.27712	−0.0916922
$195$	−0.399166	−0.0285849
$196$	−5.35183	−0.382273
$197$	1.77743	0.126637	0.0633183	−	0.997993i	$-0.479832\pi$
$197$	1.77743	0.126637	0.0633183	+	0.997993i	$0.479832\pi$
$198$	−1.43779	−0.102180
$199$	6.58209	0.466592	0.233296	−	0.972406i	$-0.425049\pi$
$199$	6.58209	0.466592	0.233296	+	0.972406i	$0.425049\pi$
$200$	−5.31890	−0.376103
$201$	14.9277	1.05292
$202$	1.68845	0.118799
$203$	−23.0991	−1.62124
$204$	−4.52211	−0.316611
$205$	−13.8308	−0.965984
$206$	−2.89229	−0.201515
$207$	0	0
$208$	0.301587	0.0209113
$209$	−9.79545	−0.677565
$210$	3.85540	0.266048
$211$	13.6591	0.940331	0.470166	−	0.882578i	$-0.344194\pi$
$211$	13.6591	0.940331	0.470166	+	0.882578i	$0.344194\pi$
$212$	−0.800039	−0.0549469
$213$	13.4493	0.921530
$214$	−9.46942	−0.647316
$215$	−4.86171	−0.331566
$216$	2.46634	0.167813
$217$	21.7883	1.47909
$218$	−11.1375	−0.754325
$219$	4.44341	0.300258
$220$	5.18448	0.349537
$221$	0.711372	0.0478520
$222$	−8.08512	−0.542638
$223$	11.4010	0.763468	0.381734	−	0.924272i	$-0.375327\pi$
$223$	11.4010	0.763468	0.381734	+	0.924272i	$0.375327\pi$
$224$	−18.9396	−1.26545
$225$	−2.15659	−0.143773
$226$	9.10198	0.605454
$227$	−1.58935	−0.105489	−0.0527443	−	0.998608i	$-0.516797\pi$
$227$	−1.58935	−0.105489	−0.0527443	+	0.998608i	$0.516797\pi$
$228$	7.21434	0.477781
$229$	26.2296	1.73330	0.866650	−	0.498916i	$-0.166268\pi$
$229$	26.2296	1.73330	0.866650	+	0.498916i	$0.166268\pi$
$230$	0	0
$231$	6.63845	0.436778
$232$	−17.5343	−1.15118
$233$	−9.94908	−0.651786	−0.325893	−	0.945407i	$-0.605665\pi$
$233$	−9.94908	−0.651786	−0.325893	+	0.945407i	$0.605665\pi$
$234$	−0.166580	−0.0108897
$235$	22.4030	1.46141
$236$	5.18967	0.337819
$237$	2.09163	0.135866
$238$	−6.87088	−0.445373
$239$	11.5465	0.746881	0.373441	−	0.927654i	$-0.378178\pi$
$239$	11.5465	0.746881	0.373441	+	0.927654i	$0.378178\pi$
$240$	−2.14831	−0.138673
$241$	−5.49731	−0.354113	−0.177057	−	0.984201i	$-0.556658\pi$
$241$	−5.49731	−0.354113	−0.177057	+	0.984201i	$0.556658\pi$
$242$	4.80307	0.308753
$243$	1.00000	0.0641500
$244$	−7.30222	−0.467477
$245$	−5.99712	−0.383142
$246$	−5.77188	−0.368002
$247$	−1.13488	−0.0722110
$248$	16.5393	1.05025
$249$	6.44335	0.408331
$250$	−8.49212	−0.537089
$251$	−20.5259	−1.29558	−0.647790	−	0.761819i	$-0.724307\pi$
$251$	−20.5259	−1.29558	−0.647790	+	0.761819i	$0.724307\pi$
$252$	−4.88921	−0.307991
$253$	0	0
$254$	−3.74529	−0.235001
$255$	−5.06736	−0.317330
$256$	−10.5425	−0.658909
$257$	−17.4240	−1.08688	−0.543438	−	0.839449i	$-0.682878\pi$
$257$	−17.4240	−1.08688	−0.543438	+	0.839449i	$0.682878\pi$
$258$	−2.02890	−0.126314
$259$	37.3299	2.31957
$260$	0.600665	0.0372517
$261$	−7.10942	−0.440062
$262$	−3.19559	−0.197424
$263$	−19.2301	−1.18578	−0.592888	−	0.805285i	$-0.702012\pi$
$263$	−19.2301	−1.18578	−0.592888	+	0.805285i	$0.702012\pi$
$264$	5.03918	0.310140
$265$	−0.896502	−0.0550717
$266$	10.9614	0.672089
$267$	2.50913	0.153556
$268$	−22.4632	−1.37216
$269$	23.9928	1.46287	0.731434	−	0.681912i	$-0.238851\pi$
$269$	23.9928	1.46287	0.731434	+	0.681912i	$0.238851\pi$
$270$	1.18661	0.0722150
$271$	−22.5924	−1.37239	−0.686196	−	0.727417i	$-0.740721\pi$
$271$	−22.5924	−1.37239	−0.686196	+	0.727417i	$0.740721\pi$
$272$	3.82861	0.232143
$273$	0.769120	0.0465493
$274$	11.6093	0.701343
$275$	−4.40631	−0.265711
$276$	0	0
$277$	2.08852	0.125487	0.0627435	−	0.998030i	$-0.480015\pi$
$277$	2.08852	0.125487	0.0627435	+	0.998030i	$0.480015\pi$
$278$	−2.43891	−0.146276
$279$	6.70601	0.401478
$280$	−13.5124	−0.807521
$281$	19.6055	1.16956	0.584782	−	0.811190i	$-0.301180\pi$
$281$	19.6055	1.16956	0.584782	+	0.811190i	$0.301180\pi$
$282$	9.34924	0.556739
$283$	5.02461	0.298682	0.149341	−	0.988786i	$-0.452285\pi$
$283$	5.02461	0.298682	0.149341	+	0.988786i	$0.452285\pi$
$284$	−20.2385	−1.20093
$285$	8.08420	0.478867
$286$	−0.340354	−0.0201255
$287$	26.6494	1.57306
$288$	−5.82922	−0.343490
$289$	−7.96923	−0.468778
$290$	−8.43614	−0.495387
$291$	1.81486	0.106389
$292$	−6.68644	−0.391294
$293$	2.95809	0.172814	0.0864068	−	0.996260i	$-0.472462\pi$
$293$	2.95809	0.172814	0.0864068	+	0.996260i	$0.472462\pi$
$294$	−2.50273	−0.145962
$295$	5.81541	0.338586
$296$	28.3367	1.64704
$297$	2.04318	0.118557
$298$	−2.15982	−0.125115
$299$	0	0
$300$	3.24525	0.187364
$301$	9.36763	0.539941
$302$	−1.33401	−0.0767634
$303$	−2.39938	−0.137841
$304$	−6.10796	−0.350315
$305$	−8.18268	−0.468539
$306$	−2.11472	−0.120890
$307$	23.6903	1.35208	0.676039	−	0.736866i	$-0.263695\pi$
$307$	23.6903	1.35208	0.676039	+	0.736866i	$0.263695\pi$
$308$	−9.98954	−0.569207
$309$	4.11009	0.233815
$310$	7.95744	0.451952
$311$	26.2136	1.48644	0.743218	−	0.669049i	$-0.233299\pi$
$311$	26.2136	1.48644	0.743218	+	0.669049i	$0.233299\pi$
$312$	0.583831	0.0330529
$313$	−6.62548	−0.374494	−0.187247	−	0.982313i	$-0.559956\pi$
$313$	−6.62548	−0.374494	−0.187247	+	0.982313i	$0.559956\pi$
$314$	−1.51847	−0.0856922
$315$	−5.47872	−0.308691
$316$	−3.14749	−0.177060
$317$	11.1028	0.623593	0.311796	−	0.950149i	$-0.399069\pi$
$317$	11.1028	0.623593	0.311796	+	0.950149i	$0.399069\pi$
$318$	−0.374130	−0.0209801
$319$	−14.5258	−0.813290
$320$	−2.62041	−0.146485
$321$	13.4565	0.751070
$322$	0	0
$323$	−14.4072	−0.801639
$324$	−1.50480	−0.0836000
$325$	−0.510508	−0.0283179
$326$	8.51223	0.471449
$327$	15.8269	0.875231
$328$	20.2293	1.11698
$329$	−43.1664	−2.37984
$330$	2.42447	0.133462
$331$	22.4571	1.23435	0.617177	−	0.786825i	$-0.288276\pi$
$331$	22.4571	1.23435	0.617177	+	0.786825i	$0.288276\pi$
$332$	−9.69596	−0.532135
$333$	11.4894	0.629614
$334$	9.26677	0.507055
$335$	−25.1717	−1.37528
$336$	4.13941	0.225823
$337$	−34.9270	−1.90259	−0.951297	−	0.308276i	$-0.900248\pi$
$337$	−34.9270	−1.90259	−0.951297	+	0.308276i	$0.900248\pi$
$338$	9.10872	0.495449
$339$	−12.9344	−0.702499
$340$	7.62537	0.413544
$341$	13.7016	0.741982
$342$	3.37371	0.182429
$343$	−11.1882	−0.604105
$344$	7.11087	0.383393
$345$	0	0
$346$	12.4145	0.667409
$347$	−10.2694	−0.551289	−0.275645	−	0.961260i	$-0.588891\pi$
$347$	−10.2694	−0.551289	−0.275645	+	0.961260i	$0.588891\pi$
$348$	10.6983	0.573487
$349$	−30.2360	−1.61850	−0.809248	−	0.587467i	$-0.800125\pi$
$349$	−30.2360	−1.61850	−0.809248	+	0.587467i	$0.800125\pi$
$350$	4.93081	0.263563
$351$	0.236720	0.0126352
$352$	−11.9101	−0.634813
$353$	−3.15640	−0.167998	−0.0839990	−	0.996466i	$-0.526769\pi$
$353$	−3.15640	−0.167998	−0.0839990	+	0.996466i	$0.526769\pi$
$354$	2.42689	0.128988
$355$	−22.6787	−1.20366
$356$	−3.77574	−0.200114
$357$	9.76388	0.516759
$358$	−7.57787	−0.400503
$359$	−21.8676	−1.15413	−0.577063	−	0.816699i	$-0.695801\pi$
$359$	−21.8676	−1.15413	−0.577063	+	0.816699i	$0.695801\pi$
$360$	−4.15885	−0.219190
$361$	3.98452	0.209712
$362$	1.00393	0.0527654
$363$	−6.82542	−0.358241
$364$	−1.15737	−0.0606628
$365$	−7.49265	−0.392183
$366$	−3.41481	−0.178495
$367$	−8.13884	−0.424844	−0.212422	−	0.977178i	$-0.568135\pi$
$367$	−8.13884	−0.424844	−0.212422	+	0.977178i	$0.568135\pi$
$368$	0	0
$369$	8.20214	0.426987
$370$	13.6335	0.708770
$371$	1.72740	0.0896820
$372$	−10.0912	−0.523204
$373$	4.42191	0.228958	0.114479	−	0.993426i	$-0.463480\pi$
$373$	4.42191	0.228958	0.114479	+	0.993426i	$0.463480\pi$
$374$	−4.32075	−0.223421
$375$	12.0677	0.623175
$376$	−32.7672	−1.68984
$377$	−1.68294	−0.0866758
$378$	−2.28639	−0.117599
$379$	10.5488	0.541854	0.270927	−	0.962600i	$-0.412670\pi$
$379$	10.5488	0.541854	0.270927	+	0.962600i	$0.412670\pi$
$380$	−12.1651	−0.624057
$381$	5.32226	0.272667
$382$	9.77704	0.500237
$383$	−5.40203	−0.276031	−0.138016	−	0.990430i	$-0.544072\pi$
$383$	−5.40203	−0.276031	−0.138016	+	0.990430i	$0.544072\pi$
$384$	10.5649	0.539137
$385$	−11.1940	−0.570500
$386$	−5.69693	−0.289966
$387$	2.88317	0.146560
$388$	−2.73100	−0.138646
$389$	1.60249	0.0812494	0.0406247	−	0.999174i	$-0.487065\pi$
$389$	1.60249	0.0812494	0.0406247	+	0.999174i	$0.487065\pi$
$390$	0.280895	0.0142237
$391$	0	0
$392$	8.77156	0.443030
$393$	4.54109	0.229068
$394$	−1.25078	−0.0630136
$395$	−3.52699	−0.177462
$396$	−3.07458	−0.154503
$397$	−6.97432	−0.350031	−0.175015	−	0.984566i	$-0.555998\pi$
$397$	−6.97432	−0.350031	−0.175015	+	0.984566i	$0.555998\pi$
$398$	−4.63184	−0.232173
$399$	−15.5768	−0.779815
$400$	−2.74756	−0.137378
$401$	−0.955119	−0.0476964	−0.0238482	−	0.999716i	$-0.507592\pi$
$401$	−0.955119	−0.0476964	−0.0238482	+	0.999716i	$0.507592\pi$
$402$	−10.5047	−0.523926
$403$	1.58744	0.0790761
$404$	3.61058	0.179633
$405$	−1.68624	−0.0837899
$406$	16.2549	0.806717
$407$	23.4749	1.16361
$408$	7.41167	0.366932
$409$	15.5761	0.770190	0.385095	−	0.922877i	$-0.374169\pi$
$409$	15.5761	0.770190	0.385095	+	0.922877i	$0.374169\pi$
$410$	9.73278	0.480668
$411$	−16.4974	−0.813757
$412$	−6.18487	−0.304707
$413$	−11.2052	−0.551373
$414$	0	0
$415$	−10.8650	−0.533344
$416$	−1.37989	−0.0676547
$417$	3.46582	0.169722
$418$	6.89310	0.337152
$419$	−30.4472	−1.48744	−0.743721	−	0.668491i	$-0.766941\pi$
$419$	−30.4472	−1.48744	−0.743721	+	0.668491i	$0.766941\pi$
$420$	8.24439	0.402285
$421$	−24.2516	−1.18195	−0.590974	−	0.806690i	$-0.701257\pi$
$421$	−24.2516	−1.18195	−0.590974	+	0.806690i	$0.701257\pi$
$422$	−9.61197	−0.467903
$423$	−13.2857	−0.645975
$424$	1.31125	0.0636799
$425$	−6.48084	−0.314367
$426$	−9.46432	−0.458548
$427$	15.7665	0.762996
$428$	−20.2494	−0.978792
$429$	0.483661	0.0233514
$430$	3.42120	0.164985
$431$	9.74016	0.469167	0.234583	−	0.972096i	$-0.424627\pi$
$431$	9.74016	0.469167	0.234583	+	0.972096i	$0.424627\pi$
$432$	1.27403	0.0612966
$433$	−6.24267	−0.300004	−0.150002	−	0.988686i	$-0.547928\pi$
$433$	−6.24267	−0.300004	−0.150002	+	0.988686i	$0.547928\pi$
$434$	−15.3325	−0.735985
$435$	11.9882	0.574790
$436$	−23.8164	−1.14060
$437$	0	0
$438$	−3.12684	−0.149406
$439$	−16.7224	−0.798116	−0.399058	−	0.916926i	$-0.630663\pi$
$439$	−16.7224	−0.798116	−0.399058	+	0.916926i	$0.630663\pi$
$440$	−8.49727	−0.405091
$441$	3.55650	0.169357
$442$	−0.500595	−0.0238109
$443$	30.3921	1.44397	0.721985	−	0.691909i	$-0.243230\pi$
$443$	30.3921	1.44397	0.721985	+	0.691909i	$0.243230\pi$
$444$	−17.2892	−0.820510
$445$	−4.23100	−0.200569
$446$	−8.02294	−0.379897
$447$	3.06922	0.145169
$448$	5.04905	0.238545
$449$	17.2191	0.812620	0.406310	−	0.913735i	$-0.366815\pi$
$449$	17.2191	0.812620	0.406310	+	0.913735i	$0.366815\pi$
$450$	1.51760	0.0715406
$451$	16.7585	0.789125
$452$	19.4637	0.915494
$453$	1.89569	0.0890674
$454$	1.11843	0.0524905
$455$	−1.29692	−0.0608006
$456$	−11.8242	−0.553718
$457$	−11.5413	−0.539880	−0.269940	−	0.962877i	$-0.587004\pi$
$457$	−11.5413	−0.539880	−0.269940	+	0.962877i	$0.587004\pi$
$458$	−18.4579	−0.862480
$459$	3.00512	0.140267
$460$	0	0
$461$	−36.3205	−1.69162	−0.845808	−	0.533488i	$-0.820881\pi$
$461$	−36.3205	−1.69162	−0.845808	+	0.533488i	$0.820881\pi$
$462$	−4.67150	−0.217338
$463$	−14.7451	−0.685261	−0.342631	−	0.939470i	$-0.611318\pi$
$463$	−14.7451	−0.685261	−0.342631	+	0.939470i	$0.611318\pi$
$464$	−9.05759	−0.420488
$465$	−11.3079	−0.524393
$466$	7.00121	0.324325
$467$	−8.10976	−0.375275	−0.187637	−	0.982238i	$-0.560083\pi$
$467$	−8.10976	−0.375275	−0.187637	+	0.982238i	$0.560083\pi$
$468$	−0.356216	−0.0164661
$469$	48.5013	2.23958
$470$	−15.7651	−0.727188
$471$	2.15782	0.0994273
$472$	−8.50578	−0.391510
$473$	5.89083	0.270860
$474$	−1.47189	−0.0676061
$475$	10.3392	0.474394
$476$	−14.6927	−0.673439
$477$	0.531658	0.0243429
$478$	−8.12532	−0.371644
$479$	−30.9352	−1.41347	−0.706733	−	0.707480i	$-0.749832\pi$
$479$	−30.9352	−1.41347	−0.706733	+	0.707480i	$0.749832\pi$
$480$	9.82947	0.448652
$481$	2.71976	0.124010
$482$	3.86848	0.176205
$483$	0	0
$484$	10.2709	0.466859
$485$	−3.06029	−0.138961
$486$	−0.703704	−0.0319207
$487$	15.8463	0.718066	0.359033	−	0.933325i	$-0.383107\pi$
$487$	15.8463	0.718066	0.359033	+	0.933325i	$0.383107\pi$
$488$	11.9682	0.541776
$489$	−12.0963	−0.547014
$490$	4.22020	0.190649
$491$	0.751664	0.0339221	0.0169611	−	0.999856i	$-0.494601\pi$
$491$	0.751664	0.0339221	0.0169611	+	0.999856i	$0.494601\pi$
$492$	−12.3426	−0.556447
$493$	−21.3647	−0.962218
$494$	0.798623	0.0359318
$495$	−3.44529	−0.154854
$496$	8.54362	0.383620
$497$	43.6978	1.96011
$498$	−4.53421	−0.203183
$499$	−30.9290	−1.38457	−0.692285	−	0.721624i	$-0.743396\pi$
$499$	−30.9290	−1.38457	−0.692285	+	0.721624i	$0.743396\pi$
$500$	−18.1595	−0.812119
$501$	−13.1686	−0.588328
$502$	14.4441	0.644673
$503$	−28.0316	−1.24987	−0.624933	−	0.780678i	$-0.714874\pi$
$503$	−28.0316	−1.24987	−0.624933	+	0.780678i	$0.714874\pi$
$504$	8.01334	0.356942
$505$	4.04593	0.180041
$506$	0	0
$507$	−12.9440	−0.574862
$508$	−8.00893	−0.355339
$509$	22.2602	0.986668	0.493334	−	0.869840i	$-0.335778\pi$
$509$	22.2602	0.986668	0.493334	+	0.869840i	$0.335778\pi$
$510$	3.56592	0.157902
$511$	14.4370	0.638654
$512$	−13.7109	−0.605944
$513$	−4.79422	−0.211670
$514$	12.2613	0.540823
$515$	−6.93060	−0.305399
$516$	−4.33859	−0.190996
$517$	−27.1452	−1.19384
$518$	−26.2692	−1.15420
$519$	−17.6417	−0.774383
$520$	−0.984480	−0.0431723
$521$	−12.1481	−0.532218	−0.266109	−	0.963943i	$-0.585738\pi$
$521$	−12.1481	−0.532218	−0.266109	+	0.963943i	$0.585738\pi$
$522$	5.00293	0.218972
$523$	20.1975	0.883173	0.441586	−	0.897219i	$-0.354416\pi$
$523$	20.1975	0.883173	0.441586	+	0.897219i	$0.354416\pi$
$524$	−6.83344	−0.298520
$525$	−7.00694	−0.305808
$526$	13.5323	0.590035
$527$	20.1524	0.877851
$528$	2.60306	0.113284
$529$	0	0
$530$	0.630872	0.0274033
$531$	−3.44874	−0.149663
$532$	23.4400	1.01625
$533$	1.94161	0.0841004
$534$	−1.76569	−0.0764087
$535$	−22.6909	−0.981015
$536$	36.8168	1.59025
$537$	10.7685	0.464697
$538$	−16.8839	−0.727914
$539$	7.26658	0.312994
$540$	2.53745	0.109195
$541$	−19.0260	−0.817991	−0.408996	−	0.912536i	$-0.634121\pi$
$541$	−19.0260	−0.817991	−0.408996	+	0.912536i	$0.634121\pi$
$542$	15.8984	0.682893
$543$	−1.42664	−0.0612228
$544$	−17.5175	−0.751058
$545$	−26.6880	−1.14319
$546$	−0.541233	−0.0231626
$547$	−0.354761	−0.0151685	−0.00758424	−	0.999971i	$-0.502414\pi$
$547$	−0.354761	−0.0151685	−0.00758424	+	0.999971i	$0.502414\pi$
$548$	24.8253	1.06048
$549$	4.85262	0.207105
$550$	3.10074	0.132216
$551$	34.0841	1.45203
$552$	0	0
$553$	6.79587	0.288990
$554$	−1.46970	−0.0624416
$555$	−19.3738	−0.822374
$556$	−5.21537	−0.221181
$557$	−10.3542	−0.438720	−0.219360	−	0.975644i	$-0.570397\pi$
$557$	−10.3542	−0.438720	−0.219360	+	0.975644i	$0.570397\pi$
$558$	−4.71904	−0.199773
$559$	0.682502	0.0288667
$560$	−6.98004	−0.294960
$561$	6.14001	0.259231
$562$	−13.7964	−0.581968
$563$	14.4045	0.607078	0.303539	−	0.952819i	$-0.401832\pi$
$563$	14.4045	0.607078	0.303539	+	0.952819i	$0.401832\pi$
$564$	19.9924	0.841832
$565$	21.8105	0.917573
$566$	−3.53584	−0.148622
$567$	3.24908	0.136448
$568$	33.1706	1.39181
$569$	18.9591	0.794806	0.397403	−	0.917644i	$-0.369912\pi$
$569$	18.9591	0.794806	0.397403	+	0.917644i	$0.369912\pi$
$570$	−5.68889	−0.238281
$571$	6.71213	0.280894	0.140447	−	0.990088i	$-0.455146\pi$
$571$	6.71213	0.280894	0.140447	+	0.990088i	$0.455146\pi$
$572$	−0.727813	−0.0304314
$573$	−13.8937	−0.580417
$574$	−18.7533	−0.782747
$575$	0	0
$576$	1.55400	0.0647498
$577$	12.5286	0.521573	0.260786	−	0.965397i	$-0.416018\pi$
$577$	12.5286	0.521573	0.260786	+	0.965397i	$0.416018\pi$
$578$	5.60798	0.233261
$579$	8.09563	0.336443
$580$	−18.0398	−0.749063
$581$	20.9349	0.868528
$582$	−1.27712	−0.0529385
$583$	1.08627	0.0449888
$584$	10.9590	0.453485
$585$	−0.399166	−0.0165035
$586$	−2.08162	−0.0859910
$587$	−6.88857	−0.284322	−0.142161	−	0.989844i	$-0.545405\pi$
$587$	−6.88857	−0.284322	−0.142161	+	0.989844i	$0.545405\pi$
$588$	−5.35183	−0.220706
$589$	−32.1501	−1.32472
$590$	−4.09233	−0.168478
$591$	1.77743	0.0731137
$592$	14.6378	0.601608
$593$	−32.7138	−1.34340	−0.671698	−	0.740825i	$-0.734435\pi$
$593$	−32.7138	−1.34340	−0.671698	+	0.740825i	$0.734435\pi$
$594$	−1.43779	−0.0589934
$595$	−16.4642	−0.674968
$596$	−4.61856	−0.189183
$597$	6.58209	0.269387
$598$	0	0
$599$	26.8624	1.09757	0.548784	−	0.835964i	$-0.315091\pi$
$599$	26.8624	1.09757	0.548784	+	0.835964i	$0.315091\pi$
$600$	−5.31890	−0.217143
$601$	−30.8383	−1.25792	−0.628960	−	0.777438i	$-0.716519\pi$
$601$	−30.8383	−1.25792	−0.628960	+	0.777438i	$0.716519\pi$
$602$	−6.59204	−0.268671
$603$	14.9277	0.607903
$604$	−2.85264	−0.116072
$605$	11.5093	0.467919
$606$	1.68845	0.0685886
$607$	−35.9785	−1.46032	−0.730161	−	0.683275i	$-0.760555\pi$
$607$	−35.9785	−1.46032	−0.730161	+	0.683275i	$0.760555\pi$
$608$	27.9466	1.13338
$609$	−23.0991	−0.936021
$610$	5.75818	0.233142
$611$	−3.14500	−0.127233
$612$	−4.52211	−0.182796
$613$	20.8131	0.840634	0.420317	−	0.907377i	$-0.361919\pi$
$613$	20.8131	0.840634	0.420317	+	0.907377i	$0.361919\pi$
$614$	−16.6710	−0.672786
$615$	−13.8308	−0.557711
$616$	16.3727	0.659675
$617$	−18.2187	−0.733455	−0.366728	−	0.930328i	$-0.619522\pi$
$617$	−18.2187	−0.733455	−0.366728	+	0.930328i	$0.619522\pi$
$618$	−2.89229	−0.116345
$619$	−21.0975	−0.847981	−0.423991	−	0.905667i	$-0.639371\pi$
$619$	−21.0975	−0.847981	−0.423991	+	0.905667i	$0.639371\pi$
$620$	17.0162	0.683386
$621$	0	0
$622$	−18.4466	−0.739642
$623$	8.15236	0.326618
$624$	0.301587	0.0120731
$625$	−9.56612	−0.382645
$626$	4.66238	0.186346
$627$	−9.79545	−0.391193
$628$	−3.24710	−0.129573
$629$	34.5270	1.37668
$630$	3.85540	0.153603
$631$	29.4538	1.17254	0.586268	−	0.810117i	$-0.300596\pi$
$631$	29.4538	1.17254	0.586268	+	0.810117i	$0.300596\pi$
$632$	5.15868	0.205201
$633$	13.6591	0.542901
$634$	−7.81305	−0.310296
$635$	−8.97460	−0.356146
$636$	−0.800039	−0.0317236
$637$	0.841894	0.0333570
$638$	10.2219	0.404688
$639$	13.4493	0.532046
$640$	−17.8149	−0.704197
$641$	39.7856	1.57144	0.785719	−	0.618583i	$-0.212293\pi$
$641$	39.7856	1.57144	0.785719	+	0.618583i	$0.212293\pi$
$642$	−9.46942	−0.373728
$643$	−33.1070	−1.30561	−0.652806	−	0.757525i	$-0.726408\pi$
$643$	−33.1070	−1.30561	−0.652806	+	0.757525i	$0.726408\pi$
$644$	0	0
$645$	−4.86171	−0.191430
$646$	10.1384	0.398891
$647$	31.5757	1.24137	0.620684	−	0.784061i	$-0.286855\pi$
$647$	31.5757	1.24137	0.620684	+	0.784061i	$0.286855\pi$
$648$	2.46634	0.0968871
$649$	−7.04640	−0.276595
$650$	0.359247	0.0140908
$651$	21.7883	0.853952
$652$	18.2025	0.712867
$653$	14.1445	0.553516	0.276758	−	0.960940i	$-0.410740\pi$
$653$	14.1445	0.553516	0.276758	+	0.960940i	$0.410740\pi$
$654$	−11.1375	−0.435510
$655$	−7.65737	−0.299198
$656$	10.4497	0.407994
$657$	4.44341	0.173354
$658$	30.3764	1.18420
$659$	−5.20591	−0.202794	−0.101397	−	0.994846i	$-0.532331\pi$
$659$	−5.20591	−0.202794	−0.101397	+	0.994846i	$0.532331\pi$
$660$	5.18448	0.201805
$661$	−10.5082	−0.408723	−0.204361	−	0.978895i	$-0.565512\pi$
$661$	−10.5082	−0.408723	−0.204361	+	0.978895i	$0.565512\pi$
$662$	−15.8031	−0.614207
$663$	0.711372	0.0276274
$664$	15.8915	0.616710
$665$	26.2662	1.01856
$666$	−8.08512	−0.313292
$667$	0	0
$668$	19.8161	0.766706
$669$	11.4010	0.440789
$670$	17.7134	0.684329
$671$	9.91477	0.382755
$672$	−18.9396	−0.730611
$673$	−27.7214	−1.06858	−0.534291	−	0.845300i	$-0.679422\pi$
$673$	−27.7214	−1.06858	−0.534291	+	0.845300i	$0.679422\pi$
$674$	24.5783	0.946719
$675$	−2.15659	−0.0830074
$676$	19.4781	0.749157
$677$	27.7836	1.06781	0.533905	−	0.845544i	$-0.320724\pi$
$677$	27.7836	1.06781	0.533905	+	0.845544i	$0.320724\pi$
$678$	9.10198	0.349559
$679$	5.89662	0.226292
$680$	−12.4978	−0.479271
$681$	−1.58935	−0.0609039
$682$	−9.64185	−0.369206
$683$	−10.8112	−0.413677	−0.206839	−	0.978375i	$-0.566318\pi$
$683$	−10.8112	−0.413677	−0.206839	+	0.978375i	$0.566318\pi$
$684$	7.21434	0.275847
$685$	27.8186	1.06289
$686$	7.87317	0.300599
$687$	26.2296	1.00072
$688$	3.67323	0.140040
$689$	0.125854	0.00479464
$690$	0	0
$691$	6.10633	0.232296	0.116148	−	0.993232i	$-0.462945\pi$
$691$	6.10633	0.232296	0.116148	+	0.993232i	$0.462945\pi$
$692$	26.5472	1.00917
$693$	6.63845	0.252174
$694$	7.22660	0.274318
$695$	−5.84421	−0.221684
$696$	−17.5343	−0.664635
$697$	24.6485	0.933627
$698$	21.2772	0.805354
$699$	−9.94908	−0.376309
$700$	10.5441	0.398528
$701$	−18.7929	−0.709799	−0.354899	−	0.934905i	$-0.615485\pi$
$701$	−18.7929	−0.709799	−0.354899	+	0.934905i	$0.615485\pi$
$702$	−0.166580	−0.00628718
$703$	−55.0826	−2.07748
$704$	3.17509	0.119666
$705$	22.4030	0.843744
$706$	2.22117	0.0835948
$707$	−7.79576	−0.293190
$708$	5.18967	0.195040
$709$	14.9303	0.560718	0.280359	−	0.959895i	$-0.409546\pi$
$709$	14.9303	0.560718	0.280359	+	0.959895i	$0.409546\pi$
$710$	15.9591	0.598935
$711$	2.09163	0.0784422
$712$	6.18838	0.231919
$713$	0	0
$714$	−6.87088	−0.257136
$715$	−0.815568	−0.0305005
$716$	−16.2045	−0.605591
$717$	11.5465	0.431212
$718$	15.3883	0.574286
$719$	15.2490	0.568692	0.284346	−	0.958722i	$-0.408224\pi$
$719$	15.2490	0.568692	0.284346	+	0.958722i	$0.408224\pi$
$720$	−2.14831	−0.0800629
$721$	13.3540	0.497329
$722$	−2.80393	−0.104351
$723$	−5.49731	−0.204447
$724$	2.14680	0.0797853
$725$	15.3321	0.569421
$726$	4.80307	0.178259
$727$	−23.3673	−0.866647	−0.433323	−	0.901239i	$-0.642659\pi$
$727$	−23.3673	−0.866647	−0.433323	+	0.901239i	$0.642659\pi$
$728$	1.89691	0.0703043
$729$	1.00000	0.0370370
$730$	5.27261	0.195148
$731$	8.66427	0.320460
$732$	−7.30222	−0.269898
$733$	53.6845	1.98288	0.991441	−	0.130557i	$-0.0416765\pi$
$733$	53.6845	1.98288	0.991441	+	0.130557i	$0.0416765\pi$
$734$	5.72733	0.211400
$735$	−5.99712	−0.221207
$736$	0	0
$737$	30.5000	1.12348
$738$	−5.77188	−0.212466
$739$	−8.44575	−0.310682	−0.155341	−	0.987861i	$-0.549648\pi$
$739$	−8.44575	−0.310682	−0.155341	+	0.987861i	$0.549648\pi$
$740$	29.1538	1.07171
$741$	−1.13488	−0.0416910
$742$	−1.21558	−0.0446252
$743$	10.8228	0.397051	0.198526	−	0.980096i	$-0.436385\pi$
$743$	10.8228	0.397051	0.198526	+	0.980096i	$0.436385\pi$
$744$	16.5393	0.606360
$745$	−5.17543	−0.189613
$746$	−3.11171	−0.113928
$747$	6.44335	0.235750
$748$	−9.23949	−0.337829
$749$	43.7213	1.59754
$750$	−8.49212	−0.310088
$751$	15.0445	0.548980	0.274490	−	0.961590i	$-0.411491\pi$
$751$	15.0445	0.548980	0.274490	+	0.961590i	$0.411491\pi$
$752$	−16.9264	−0.617242
$753$	−20.5259	−0.748004
$754$	1.18429	0.0431293
$755$	−3.19659	−0.116336
$756$	−4.88921	−0.177819
$757$	3.62405	0.131718	0.0658592	−	0.997829i	$-0.479021\pi$
$757$	3.62405	0.131718	0.0658592	+	0.997829i	$0.479021\pi$
$758$	−7.42321	−0.269623
$759$	0	0
$760$	19.9384	0.723242
$761$	−0.846775	−0.0306956	−0.0153478	−	0.999882i	$-0.504886\pi$
$761$	−0.846775	−0.0306956	−0.0153478	+	0.999882i	$0.504886\pi$
$762$	−3.74529	−0.135678
$763$	51.4229	1.86163
$764$	20.9072	0.756397
$765$	−5.06736	−0.183211
$766$	3.80143	0.137351
$767$	−0.816385	−0.0294779
$768$	−10.5425	−0.380421
$769$	40.0399	1.44388	0.721938	−	0.691957i	$-0.243251\pi$
$769$	40.0399	1.44388	0.721938	+	0.691957i	$0.243251\pi$
$770$	7.87728	0.283877
$771$	−17.4240	−0.627508
$772$	−12.1823	−0.438451
$773$	39.0132	1.40321	0.701603	−	0.712568i	$-0.252468\pi$
$773$	39.0132	1.40321	0.701603	+	0.712568i	$0.252468\pi$
$774$	−2.02890	−0.0729271
$775$	−14.4621	−0.519495
$776$	4.47607	0.160681
$777$	37.3299	1.33920
$778$	−1.12768	−0.0404292
$779$	−39.3229	−1.40889
$780$	0.600665	0.0215073
$781$	27.4793	0.983287
$782$	0	0
$783$	−7.10942	−0.254070
$784$	4.53108	0.161824
$785$	−3.63861	−0.129868
$786$	−3.19559	−0.113983
$787$	−38.9477	−1.38834	−0.694168	−	0.719813i	$-0.744227\pi$
$787$	−38.9477	−1.38834	−0.694168	+	0.719813i	$0.744227\pi$
$788$	−2.67468	−0.0952814
$789$	−19.2301	−0.684608
$790$	2.48196	0.0883041
$791$	−42.0248	−1.49423
$792$	5.03918	0.179060
$793$	1.14871	0.0407919
$794$	4.90786	0.174173
$795$	−0.896502	−0.0317957
$796$	−9.90473	−0.351064
$797$	22.2433	0.787900	0.393950	−	0.919132i	$-0.371108\pi$
$797$	22.2433	0.787900	0.393950	+	0.919132i	$0.371108\pi$
$798$	10.9614	0.388031
$799$	−39.9253	−1.41246
$800$	12.5713	0.444462
$801$	2.50913	0.0886558
$802$	0.672121	0.0237334
$803$	9.07868	0.320380
$804$	−22.4632	−0.792217
$805$	0	0
$806$	−1.11709	−0.0393478
$807$	23.9928	0.844588
$808$	−5.91769	−0.208183
$809$	−53.9409	−1.89646	−0.948231	−	0.317581i	$-0.897129\pi$
$809$	−53.9409	−1.89646	−0.948231	+	0.317581i	$0.897129\pi$
$810$	1.18661	0.0416934
$811$	−49.4006	−1.73469	−0.867345	−	0.497708i	$-0.834175\pi$
$811$	−49.4006	−1.73469	−0.867345	+	0.497708i	$0.834175\pi$
$812$	34.7595	1.21982
$813$	−22.5924	−0.792350
$814$	−16.5194	−0.579003
$815$	20.3973	0.714486
$816$	3.82861	0.134028
$817$	−13.8225	−0.483589
$818$	−10.9610	−0.383242
$819$	0.769120	0.0268752
$820$	20.8126	0.726806
$821$	17.5113	0.611147	0.305574	−	0.952168i	$-0.401152\pi$
$821$	17.5113	0.611147	0.305574	+	0.952168i	$0.401152\pi$
$822$	11.6093	0.404921
$823$	−13.6118	−0.474476	−0.237238	−	0.971452i	$-0.576242\pi$
$823$	−13.6118	−0.474476	−0.237238	+	0.971452i	$0.576242\pi$
$824$	10.1369	0.353135
$825$	−4.40631	−0.153408
$826$	7.88517	0.274360
$827$	−22.5564	−0.784365	−0.392182	−	0.919888i	$-0.628280\pi$
$827$	−22.5564	−0.784365	−0.392182	+	0.919888i	$0.628280\pi$
$828$	0	0
$829$	−49.2936	−1.71204	−0.856019	−	0.516944i	$-0.827070\pi$
$829$	−49.2936	−1.71204	−0.856019	+	0.516944i	$0.827070\pi$
$830$	7.64577	0.265389
$831$	2.08852	0.0724500
$832$	0.367861	0.0127533
$833$	10.6877	0.370308
$834$	−2.43891	−0.0844527
$835$	22.2054	0.768448
$836$	14.7402	0.509800
$837$	6.70601	0.231793
$838$	21.4258	0.740142
$839$	−5.69638	−0.196661	−0.0983304	−	0.995154i	$-0.531350\pi$
$839$	−5.69638	−0.196661	−0.0983304	+	0.995154i	$0.531350\pi$
$840$	−13.5124	−0.466222
$841$	21.5439	0.742892
$842$	17.0659	0.588131
$843$	19.6055	0.675248
$844$	−20.5542	−0.707506
$845$	21.8266	0.750859
$846$	9.34924	0.321433
$847$	−22.1763	−0.761987
$848$	0.677345	0.0232601
$849$	5.02461	0.172444
$850$	4.56059	0.156427
$851$	0	0
$852$	−20.2385	−0.693360
$853$	35.5577	1.21747	0.608737	−	0.793372i	$-0.291677\pi$
$853$	35.5577	1.21747	0.608737	+	0.793372i	$0.291677\pi$
$854$	−11.0950	−0.379662
$855$	8.08420	0.276474
$856$	33.1884	1.13436
$857$	−25.5075	−0.871320	−0.435660	−	0.900111i	$-0.643485\pi$
$857$	−25.5075	−0.871320	−0.435660	+	0.900111i	$0.643485\pi$
$858$	−0.340354	−0.0116195
$859$	−34.2195	−1.16755	−0.583777	−	0.811914i	$-0.698426\pi$
$859$	−34.2195	−1.16755	−0.583777	+	0.811914i	$0.698426\pi$
$860$	7.31590	0.249470
$861$	26.6494	0.908209
$862$	−6.85419	−0.233455
$863$	−28.1505	−0.958253	−0.479126	−	0.877746i	$-0.659046\pi$
$863$	−28.1505	−0.958253	−0.479126	+	0.877746i	$0.659046\pi$
$864$	−5.82922	−0.198314
$865$	29.7481	1.01147
$866$	4.39299	0.149280
$867$	−7.96923	−0.270649
$868$	−32.7871	−1.11287
$869$	4.27358	0.144971
$870$	−8.43614	−0.286012
$871$	3.53368	0.119734
$872$	39.0346	1.32188
$873$	1.81486	0.0614237
$874$	0	0
$875$	39.2090	1.32551
$876$	−6.68644	−0.225914
$877$	−14.8860	−0.502665	−0.251333	−	0.967901i	$-0.580869\pi$
$877$	−14.8860	−0.502665	−0.251333	+	0.967901i	$0.580869\pi$
$878$	11.7676	0.397138
$879$	2.95809	0.0997740
$880$	−4.38939	−0.147966
$881$	26.1139	0.879801	0.439901	−	0.898046i	$-0.355014\pi$
$881$	26.1139	0.879801	0.439901	+	0.898046i	$0.355014\pi$
$882$	−2.50273	−0.0842712
$883$	−34.6376	−1.16565	−0.582824	−	0.812599i	$-0.698052\pi$
$883$	−34.6376	−1.16565	−0.582824	+	0.812599i	$0.698052\pi$
$884$	−1.07047	−0.0360039
$885$	5.81541	0.195483
$886$	−21.3870	−0.718511
$887$	−54.7575	−1.83858	−0.919288	−	0.393586i	$-0.871234\pi$
$887$	−54.7575	−1.83858	−0.919288	+	0.393586i	$0.871234\pi$
$888$	28.3367	0.950919
$889$	17.2924	0.579969
$890$	2.97737	0.0998017
$891$	2.04318	0.0684491
$892$	−17.1562	−0.574434
$893$	63.6948	2.13146
$894$	−2.15982	−0.0722352
$895$	−18.1583	−0.606967
$896$	34.3261	1.14676
$897$	0	0
$898$	−12.1172	−0.404355
$899$	−47.6758	−1.59008
$900$	3.24525	0.108175
$901$	1.59770	0.0532270
$902$	−11.7930	−0.392664
$903$	9.36763	0.311735
$904$	−31.9006	−1.06100
$905$	2.40565	0.0799666
$906$	−1.33401	−0.0443194
$907$	−10.1709	−0.337718	−0.168859	−	0.985640i	$-0.554008\pi$
$907$	−10.1709	−0.337718	−0.168859	+	0.985640i	$0.554008\pi$
$908$	2.39165	0.0793697
$909$	−2.39938	−0.0795823
$910$	0.912649	0.0302540
$911$	30.8989	1.02372	0.511862	−	0.859068i	$-0.328956\pi$
$911$	30.8989	1.02372	0.511862	+	0.859068i	$0.328956\pi$
$912$	−6.10796	−0.202255
$913$	13.1649	0.435695
$914$	8.12167	0.268641
$915$	−8.18268	−0.270511
$916$	−39.4703	−1.30414
$917$	14.7544	0.487232
$918$	−2.11472	−0.0697961
$919$	1.12747	0.0371917	0.0185959	−	0.999827i	$-0.494080\pi$
$919$	1.12747	0.0371917	0.0185959	+	0.999827i	$0.494080\pi$
$920$	0	0
$921$	23.6903	0.780622
$922$	25.5589	0.841738
$923$	3.18371	0.104793
$924$	−9.98954	−0.328632
$925$	−24.7779	−0.814693
$926$	10.3762	0.340982
$927$	4.11009	0.134993
$928$	41.4424	1.36041
$929$	11.0988	0.364139	0.182069	−	0.983286i	$-0.441720\pi$
$929$	11.0988	0.364139	0.182069	+	0.983286i	$0.441720\pi$
$930$	7.95744	0.260935
$931$	−17.0507	−0.558813
$932$	14.9714	0.490404
$933$	26.2136	0.858194
$934$	5.70687	0.186735
$935$	−10.3535	−0.338597
$936$	0.583831	0.0190831
$937$	35.5204	1.16040	0.580200	−	0.814474i	$-0.302974\pi$
$937$	35.5204	1.16040	0.580200	+	0.814474i	$0.302974\pi$
$938$	−34.1305	−1.11440
$939$	−6.62548	−0.216214
$940$	−33.7120	−1.09956
$941$	57.2758	1.86714	0.933569	−	0.358398i	$-0.116677\pi$
$941$	57.2758	1.86714	0.933569	+	0.358398i	$0.116677\pi$
$942$	−1.51847	−0.0494744
$943$	0	0
$944$	−4.39379	−0.143006
$945$	−5.47872	−0.178223
$946$	−4.14540	−0.134779
$947$	−24.3344	−0.790761	−0.395381	−	0.918517i	$-0.629387\pi$
$947$	−24.3344	−0.790761	−0.395381	+	0.918517i	$0.629387\pi$
$948$	−3.14749	−0.102226
$949$	1.05184	0.0341442
$950$	−7.27573	−0.236056
$951$	11.1028	0.360031
$952$	24.0811	0.780472
$953$	−49.7366	−1.61113	−0.805563	−	0.592511i	$-0.798137\pi$
$953$	−49.7366	−1.61113	−0.805563	+	0.592511i	$0.798137\pi$
$954$	−0.374130	−0.0121129
$955$	23.4281	0.758115
$956$	−17.3752	−0.561954
$957$	−14.5258	−0.469553
$958$	21.7692	0.703332
$959$	−53.6014	−1.73088
$960$	−2.62041	−0.0845733
$961$	13.9705	0.450662
$962$	−1.91391	−0.0617068
$963$	13.4565	0.433631
$964$	8.27236	0.266435
$965$	−13.6512	−0.439447
$966$	0	0
$967$	46.0629	1.48128	0.740641	−	0.671901i	$-0.234522\pi$
$967$	46.0629	1.48128	0.740641	+	0.671901i	$0.234522\pi$
$968$	−16.8338	−0.541059
$969$	−14.4072	−0.462827
$970$	2.15354	0.0691460
$971$	−24.9783	−0.801591	−0.400796	−	0.916167i	$-0.631266\pi$
$971$	−24.9783	−0.801591	−0.400796	+	0.916167i	$0.631266\pi$
$972$	−1.50480	−0.0482665
$973$	11.2607	0.361002
$974$	−11.1511	−0.357305
$975$	−0.510508	−0.0163493
$976$	6.18236	0.197893
$977$	−23.9932	−0.767610	−0.383805	−	0.923414i	$-0.625387\pi$
$977$	−23.9932	−0.767610	−0.383805	+	0.923414i	$0.625387\pi$
$978$	8.51223	0.272191
$979$	5.12661	0.163847
$980$	9.02447	0.288276
$981$	15.8269	0.505315
$982$	−0.528949	−0.0168794
$983$	6.10549	0.194735	0.0973674	−	0.995249i	$-0.468958\pi$
$983$	6.10549	0.194735	0.0973674	+	0.995249i	$0.468958\pi$
$984$	20.2293	0.644886
$985$	−2.99717	−0.0954979
$986$	15.0344	0.478794
$987$	−43.1664	−1.37400
$988$	1.70778	0.0543316
$989$	0	0
$990$	2.42447	0.0770546
$991$	−16.0959	−0.511304	−0.255652	−	0.966769i	$-0.582290\pi$
$991$	−16.0959	−0.511304	−0.255652	+	0.966769i	$0.582290\pi$
$992$	−39.0908	−1.24113
$993$	22.4571	0.712654
$994$	−30.7503	−0.975341
$995$	−11.0990	−0.351861
$996$	−9.69596	−0.307228
$997$	16.9296	0.536164	0.268082	−	0.963396i	$-0.413610\pi$
$997$	16.9296	0.536164	0.268082	+	0.963396i	$0.413610\pi$
$998$	21.7648	0.688954
$999$	11.4894	0.363508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1587.2.a.u.1.5		10
3.2	odd	2		4761.2.a.bt.1.6		10
23.4	even	11		69.2.e.c.16.2	yes	20
23.6	even	11		69.2.e.c.13.2	✓	20
23.22	odd	2		1587.2.a.t.1.5		10
69.29	odd	22		207.2.i.d.82.1		20
69.50	odd	22		207.2.i.d.154.1		20
69.68	even	2		4761.2.a.bu.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.13.2	✓	20	23.6	even	11
69.2.e.c.16.2	yes	20	23.4	even	11
207.2.i.d.82.1		20	69.29	odd	22
207.2.i.d.154.1		20	69.50	odd	22
1587.2.a.t.1.5		10	23.22	odd	2
1587.2.a.u.1.5		10	1.1	even	1	trivial
4761.2.a.bt.1.6		10	3.2	odd	2
4761.2.a.bu.1.6		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)

\(f(q)\)	\(=\)	\(q-0.703704 q^{2} +1.00000 q^{3} -1.50480 q^{4} -1.68624 q^{5} -0.703704 q^{6} +3.24908 q^{7} +2.46634 q^{8} +1.00000 q^{9} +1.18661 q^{10} +2.04318 q^{11} -1.50480 q^{12} +0.236720 q^{13} -2.28639 q^{14} -1.68624 q^{15} +1.27403 q^{16} +3.00512 q^{17} -0.703704 q^{18} -4.79422 q^{19} +2.53745 q^{20} +3.24908 q^{21} -1.43779 q^{22} +2.46634 q^{24} -2.15659 q^{25} -0.166580 q^{26} +1.00000 q^{27} -4.88921 q^{28} -7.10942 q^{29} +1.18661 q^{30} +6.70601 q^{31} -5.82922 q^{32} +2.04318 q^{33} -2.11472 q^{34} -5.47872 q^{35} -1.50480 q^{36} +11.4894 q^{37} +3.37371 q^{38} +0.236720 q^{39} -4.15885 q^{40} +8.20214 q^{41} -2.28639 q^{42} +2.88317 q^{43} -3.07458 q^{44} -1.68624 q^{45} -13.2857 q^{47} +1.27403 q^{48} +3.55650 q^{49} +1.51760 q^{50} +3.00512 q^{51} -0.356216 q^{52} +0.531658 q^{53} -0.703704 q^{54} -3.44529 q^{55} +8.01334 q^{56} -4.79422 q^{57} +5.00293 q^{58} -3.44874 q^{59} +2.53745 q^{60} +4.85262 q^{61} -4.71904 q^{62} +3.24908 q^{63} +1.55400 q^{64} -0.399166 q^{65} -1.43779 q^{66} +14.9277 q^{67} -4.52211 q^{68} +3.85540 q^{70} +13.4493 q^{71} +2.46634 q^{72} +4.44341 q^{73} -8.08512 q^{74} -2.15659 q^{75} +7.21434 q^{76} +6.63845 q^{77} -0.166580 q^{78} +2.09163 q^{79} -2.14831 q^{80} +1.00000 q^{81} -5.77188 q^{82} +6.44335 q^{83} -4.88921 q^{84} -5.06736 q^{85} -2.02890 q^{86} -7.10942 q^{87} +5.03918 q^{88} +2.50913 q^{89} +1.18661 q^{90} +0.769120 q^{91} +6.70601 q^{93} +9.34924 q^{94} +8.08420 q^{95} -5.82922 q^{96} +1.81486 q^{97} -2.50273 q^{98} +2.04318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 10 q^{3} + 8 q^{4} + 8 q^{5} - 2 q^{6} + 19 q^{7} - 6 q^{8} + 10 q^{9} + 13 q^{10} + 3 q^{11} + 8 q^{12} - 4 q^{13} + 8 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} + 22 q^{19} + q^{20} + 19 q^{21}+ \cdots + 3 q^{99}+O(q^{100}) \) 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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