LMFDB - Embedded newform 2883.2.a.s.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2883,2,Mod(1,2883)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2883, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2883.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2883 = 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2883.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,5,-12,13,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$23.0208709027$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 6 x^{10} + 57 x^{9} - 9 x^{8} - 229 x^{7} + 83 x^{6} + 436 x^{5} - 111 x^{4} + \cdots + 16 $ x^12 - 5x^11 - 6x^10 + 57x^9 - 9x^8 - 229x^7 + 83x^6 + 436x^5 - 111x^4 - 390x^3 + 24x^2 + 128*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 93)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.135601$ of defining polynomial
Character	$\chi$	$=$	2883.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.135601 q^{2} -1.00000 q^{3} -1.98161 q^{4} +2.85131 q^{5} +0.135601 q^{6} -2.89040 q^{7} +0.539910 q^{8} +1.00000 q^{9} -0.386640 q^{10} -2.32104 q^{11} +1.98161 q^{12} -4.45689 q^{13} +0.391940 q^{14} -2.85131 q^{15} +3.89001 q^{16} +5.09936 q^{17} -0.135601 q^{18} -1.59754 q^{19} -5.65019 q^{20} +2.89040 q^{21} +0.314735 q^{22} -3.76563 q^{23} -0.539910 q^{24} +3.12996 q^{25} +0.604357 q^{26} -1.00000 q^{27} +5.72765 q^{28} -7.57457 q^{29} +0.386640 q^{30} -1.60731 q^{32} +2.32104 q^{33} -0.691477 q^{34} -8.24142 q^{35} -1.98161 q^{36} +9.95988 q^{37} +0.216627 q^{38} +4.45689 q^{39} +1.53945 q^{40} +7.94420 q^{41} -0.391940 q^{42} +2.12804 q^{43} +4.59940 q^{44} +2.85131 q^{45} +0.510622 q^{46} +1.31084 q^{47} -3.89001 q^{48} +1.35440 q^{49} -0.424425 q^{50} -5.09936 q^{51} +8.83182 q^{52} -7.65141 q^{53} +0.135601 q^{54} -6.61800 q^{55} -1.56055 q^{56} +1.59754 q^{57} +1.02712 q^{58} +12.7657 q^{59} +5.65019 q^{60} -2.92690 q^{61} -2.89040 q^{63} -7.56207 q^{64} -12.7080 q^{65} -0.314735 q^{66} +1.19808 q^{67} -10.1049 q^{68} +3.76563 q^{69} +1.11754 q^{70} -12.8025 q^{71} +0.539910 q^{72} +1.30056 q^{73} -1.35057 q^{74} -3.12996 q^{75} +3.16570 q^{76} +6.70873 q^{77} -0.604357 q^{78} +12.8057 q^{79} +11.0916 q^{80} +1.00000 q^{81} -1.07724 q^{82} -13.1539 q^{83} -5.72765 q^{84} +14.5398 q^{85} -0.288564 q^{86} +7.57457 q^{87} -1.25315 q^{88} -3.12383 q^{89} -0.386640 q^{90} +12.8822 q^{91} +7.46201 q^{92} -0.177752 q^{94} -4.55507 q^{95} +1.60731 q^{96} +18.2970 q^{97} -0.183658 q^{98} -2.32104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 5 q^{2} - 12 q^{3} + 13 q^{4} + 6 q^{5} - 5 q^{6} + 6 q^{7} + 24 q^{8} + 12 q^{9} + 21 q^{10} - 2 q^{11} - 13 q^{12} - 3 q^{13} + 15 q^{14} - 6 q^{15} + 19 q^{16} + 8 q^{17} + 5 q^{18} + 15 q^{19}+ \cdots - 2 q^{99}+O(q^{100}) $ 12 * q + 5 * q^2 - 12 * q^3 + 13 * q^4 + 6 * q^5 - 5 * q^6 + 6 * q^7 + 24 * q^8 + 12 * q^9 + 21 * q^10 - 2 * q^11 - 13 * q^12 - 3 * q^13 + 15 * q^14 - 6 * q^15 + 19 * q^16 + 8 * q^17 + 5 * q^18 + 15 * q^19 + 17 * q^20 - 6 * q^21 - 12 * q^22 + 12 * q^23 - 24 * q^24 + 8 * q^25 + 4 * q^26 - 12 * q^27 + 41 * q^28 + 14 * q^29 - 21 * q^30 + 18 * q^32 + 2 * q^33 + 15 * q^34 - 3 * q^35 + 13 * q^36 - 13 * q^37 + 31 * q^38 + 3 * q^39 - 23 * q^40 + 24 * q^41 - 15 * q^42 + 19 * q^43 + 27 * q^44 + 6 * q^45 - 21 * q^46 + 16 * q^47 - 19 * q^48 + 22 * q^49 + 34 * q^50 - 8 * q^51 - 36 * q^52 + 20 * q^53 - 5 * q^54 - 39 * q^55 - 28 * q^56 - 15 * q^57 + 85 * q^58 + 16 * q^59 - 17 * q^60 - 35 * q^61 + 6 * q^63 + 42 * q^64 - 21 * q^65 + 12 * q^66 - 4 * q^67 + 51 * q^68 - 12 * q^69 - 34 * q^70 - 15 * q^71 + 24 * q^72 - 27 * q^73 + 24 * q^74 - 8 * q^75 + 54 * q^76 + 10 * q^77 - 4 * q^78 - 14 * q^79 + 13 * q^80 + 12 * q^81 + 25 * q^82 + 14 * q^83 - 41 * q^84 + 32 * q^85 - 24 * q^86 - 14 * q^87 + 26 * q^88 - 4 * q^89 + 21 * q^90 - 37 * q^91 - 14 * q^92 - 40 * q^94 + 22 * q^95 - 18 * q^96 + 12 * q^97 + 14 * q^98 - 2 * 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 $

$2$	−0.135601	−0.0958843	−0.0479421	−	0.998850i	$-0.515266\pi$
$2$	−0.135601	−0.0958843	−0.0479421	+	0.998850i	$0.515266\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.98161	−0.990806
$5$	2.85131	1.27514	0.637572	−	0.770391i	$-0.279939\pi$
$5$	2.85131	1.27514	0.637572	+	0.770391i	$0.279939\pi$
$6$	0.135601	0.0553588
$7$	−2.89040	−1.09247	−0.546234	−	0.837633i	$-0.683939\pi$
$7$	−2.89040	−1.09247	−0.546234	+	0.837633i	$0.683939\pi$
$8$	0.539910	0.190887
$9$	1.00000	0.333333
$10$	−0.386640	−0.122266
$11$	−2.32104	−0.699820	−0.349910	−	0.936783i	$-0.613788\pi$
$11$	−2.32104	−0.699820	−0.349910	+	0.936783i	$0.613788\pi$
$12$	1.98161	0.572042
$13$	−4.45689	−1.23612	−0.618059	−	0.786132i	$-0.712081\pi$
$13$	−4.45689	−1.23612	−0.618059	+	0.786132i	$0.712081\pi$
$14$	0.391940	0.104750
$15$	−2.85131	−0.736205
$16$	3.89001	0.972503
$17$	5.09936	1.23678	0.618388	−	0.785873i	$-0.287786\pi$
$17$	5.09936	1.23678	0.618388	+	0.785873i	$0.287786\pi$
$18$	−0.135601	−0.0319614
$19$	−1.59754	−0.366500	−0.183250	−	0.983066i	$-0.558662\pi$
$19$	−1.59754	−0.366500	−0.183250	+	0.983066i	$0.558662\pi$
$20$	−5.65019	−1.26342
$21$	2.89040	0.630737
$22$	0.314735	0.0671017
$23$	−3.76563	−0.785187	−0.392594	−	0.919712i	$-0.628422\pi$
$23$	−3.76563	−0.785187	−0.392594	+	0.919712i	$0.628422\pi$
$24$	−0.539910	−0.110209
$25$	3.12996	0.625992
$26$	0.604357	0.118524
$27$	−1.00000	−0.192450
$28$	5.72765	1.08242
$29$	−7.57457	−1.40656	−0.703281	−	0.710912i	$-0.748282\pi$
$29$	−7.57457	−1.40656	−0.703281	+	0.710912i	$0.748282\pi$
$30$	0.386640	0.0705904
$31$	0	0
$31$	0	0
$32$	−1.60731	−0.284135
$33$	2.32104	0.404041
$34$	−0.691477	−0.118587
$35$	−8.24142	−1.39305
$36$	−1.98161	−0.330269
$37$	9.95988	1.63739	0.818697	−	0.574226i	$-0.194697\pi$
$37$	9.95988	1.63739	0.818697	+	0.574226i	$0.194697\pi$
$38$	0.216627	0.0351415
$39$	4.45689	0.713673
$40$	1.53945	0.243408
$41$	7.94420	1.24068	0.620338	−	0.784335i	$-0.286996\pi$
$41$	7.94420	1.24068	0.620338	+	0.784335i	$0.286996\pi$
$42$	−0.391940	−0.0604777
$43$	2.12804	0.324523	0.162262	−	0.986748i	$-0.448121\pi$
$43$	2.12804	0.324523	0.162262	+	0.986748i	$0.448121\pi$
$44$	4.59940	0.693386
$45$	2.85131	0.425048
$46$	0.510622	0.0752871
$47$	1.31084	0.191206	0.0956032	−	0.995420i	$-0.469522\pi$
$47$	1.31084	0.191206	0.0956032	+	0.995420i	$0.469522\pi$
$48$	−3.89001	−0.561475
$49$	1.35440	0.193486
$50$	−0.424425	−0.0600228
$51$	−5.09936	−0.714053
$52$	8.83182	1.22475
$53$	−7.65141	−1.05100	−0.525501	−	0.850793i	$-0.676122\pi$
$53$	−7.65141	−1.05100	−0.525501	+	0.850793i	$0.676122\pi$
$54$	0.135601	0.0184529
$55$	−6.61800	−0.892371
$56$	−1.56055	−0.208538
$57$	1.59754	0.211599
$58$	1.02712	0.134867
$59$	12.7657	1.66196	0.830978	−	0.556306i	$-0.187782\pi$
$59$	12.7657	1.66196	0.830978	+	0.556306i	$0.187782\pi$
$60$	5.65019	0.729436
$61$	−2.92690	−0.374751	−0.187375	−	0.982288i	$-0.559998\pi$
$61$	−2.92690	−0.374751	−0.187375	+	0.982288i	$0.559998\pi$
$62$	0	0
$63$	−2.89040	−0.364156
$64$	−7.56207	−0.945259
$65$	−12.7080	−1.57623
$66$	−0.314735	−0.0387412
$67$	1.19808	0.146369	0.0731847	−	0.997318i	$-0.476684\pi$
$67$	1.19808	0.146369	0.0731847	+	0.997318i	$0.476684\pi$
$68$	−10.1049	−1.22541
$69$	3.76563	0.453328
$70$	1.11754	0.133572
$71$	−12.8025	−1.51938	−0.759689	−	0.650287i	$-0.774649\pi$
$71$	−12.8025	−1.51938	−0.759689	+	0.650287i	$0.774649\pi$
$72$	0.539910	0.0636290
$73$	1.30056	0.152219	0.0761095	−	0.997099i	$-0.475750\pi$
$73$	1.30056	0.152219	0.0761095	+	0.997099i	$0.475750\pi$
$74$	−1.35057	−0.157000
$75$	−3.12996	−0.361417
$76$	3.16570	0.363130
$77$	6.70873	0.764531
$78$	−0.604357	−0.0684300
$79$	12.8057	1.44075	0.720377	−	0.693582i	$-0.243969\pi$
$79$	12.8057	1.44075	0.720377	+	0.693582i	$0.243969\pi$
$80$	11.0916	1.24008
$81$	1.00000	0.111111
$82$	−1.07724	−0.118961
$83$	−13.1539	−1.44382	−0.721912	−	0.691985i	$-0.756736\pi$
$83$	−13.1539	−1.44382	−0.721912	+	0.691985i	$0.756736\pi$
$84$	−5.72765	−0.624938
$85$	14.5398	1.57707
$86$	−0.288564	−0.0311167
$87$	7.57457	0.812079
$88$	−1.25315	−0.133587
$89$	−3.12383	−0.331125	−0.165563	−	0.986199i	$-0.552944\pi$
$89$	−3.12383	−0.331125	−0.165563	+	0.986199i	$0.552944\pi$
$90$	−0.386640	−0.0407554
$91$	12.8822	1.35042
$92$	7.46201	0.777969
$93$	0	0
$94$	−0.177752	−0.0183337
$95$	−4.55507	−0.467340
$96$	1.60731	0.164045
$97$	18.2970	1.85778	0.928889	−	0.370359i	$-0.120765\pi$
$97$	18.2970	1.85778	0.928889	+	0.370359i	$0.120765\pi$
$98$	−0.183658	−0.0185522
$99$	−2.32104	−0.233273
$100$	−6.20237	−0.620237
$101$	14.8706	1.47968	0.739838	−	0.672785i	$-0.234902\pi$
$101$	14.8706	1.47968	0.739838	+	0.672785i	$0.234902\pi$
$102$	0.691477	0.0684664
$103$	15.0259	1.48055	0.740274	−	0.672305i	$-0.234696\pi$
$103$	15.0259	1.48055	0.740274	+	0.672305i	$0.234696\pi$
$104$	−2.40632	−0.235959
$105$	8.24142	0.804280
$106$	1.03754	0.100775
$107$	1.12235	0.108501	0.0542506	−	0.998527i	$-0.482723\pi$
$107$	1.12235	0.108501	0.0542506	+	0.998527i	$0.482723\pi$
$108$	1.98161	0.190681
$109$	3.02972	0.290195	0.145097	−	0.989417i	$-0.453650\pi$
$109$	3.02972	0.290195	0.145097	+	0.989417i	$0.453650\pi$
$110$	0.897407	0.0855644
$111$	−9.95988	−0.945350
$112$	−11.2437	−1.06243
$113$	4.84082	0.455386	0.227693	−	0.973733i	$-0.426882\pi$
$113$	4.84082	0.455386	0.227693	+	0.973733i	$0.426882\pi$
$114$	−0.216627	−0.0202890
$115$	−10.7370	−1.00123
$116$	15.0099	1.39363
$117$	−4.45689	−0.412039
$118$	−1.73104	−0.159355
$119$	−14.7392	−1.35114
$120$	−1.53945	−0.140532
$121$	−5.61277	−0.510252
$122$	0.396890	0.0359327
$123$	−7.94420	−0.716304
$124$	0	0
$125$	−5.33206	−0.476914
$126$	0.391940	0.0349168
$127$	−12.2294	−1.08518	−0.542591	−	0.839997i	$-0.682556\pi$
$127$	−12.2294	−1.08518	−0.542591	+	0.839997i	$0.682556\pi$
$128$	4.24004	0.374770
$129$	−2.12804	−0.187364
$130$	1.72321	0.151135
$131$	5.05331	0.441510	0.220755	−	0.975329i	$-0.429148\pi$
$131$	5.05331	0.441510	0.220755	+	0.975329i	$0.429148\pi$
$132$	−4.59940	−0.400327
$133$	4.61751	0.400389
$134$	−0.162461	−0.0140345
$135$	−2.85131	−0.245402
$136$	2.75319	0.236084
$137$	9.05240	0.773399	0.386699	−	0.922206i	$-0.373615\pi$
$137$	9.05240	0.773399	0.386699	+	0.922206i	$0.373615\pi$
$138$	−0.510622	−0.0434670
$139$	6.36354	0.539749	0.269874	−	0.962896i	$-0.413018\pi$
$139$	6.36354	0.539749	0.269874	+	0.962896i	$0.413018\pi$
$140$	16.3313	1.38025
$141$	−1.31084	−0.110393
$142$	1.73603	0.145684
$143$	10.3446	0.865060
$144$	3.89001	0.324168
$145$	−21.5974	−1.79357
$146$	−0.176357	−0.0145954
$147$	−1.35440	−0.111709
$148$	−19.7366	−1.62234
$149$	17.0881	1.39991	0.699956	−	0.714185i	$-0.253203\pi$
$149$	17.0881	1.39991	0.699956	+	0.714185i	$0.253203\pi$
$150$	0.424425	0.0346542
$151$	6.65343	0.541448	0.270724	−	0.962657i	$-0.412737\pi$
$151$	6.65343	0.541448	0.270724	+	0.962657i	$0.412737\pi$
$152$	−0.862525	−0.0699600
$153$	5.09936	0.412259
$154$	−0.909709	−0.0733065
$155$	0	0
$156$	−8.83182	−0.707111
$157$	12.7706	1.01920	0.509601	−	0.860411i	$-0.329793\pi$
$157$	12.7706	1.01920	0.509601	+	0.860411i	$0.329793\pi$
$158$	−1.73646	−0.138146
$159$	7.65141	0.606797
$160$	−4.58293	−0.362313
$161$	10.8842	0.857792
$162$	−0.135601	−0.0106538
$163$	−10.0001	−0.783271	−0.391635	−	0.920121i	$-0.628091\pi$
$163$	−10.0001	−0.783271	−0.391635	+	0.920121i	$0.628091\pi$
$164$	−15.7423	−1.22927
$165$	6.61800	0.515211
$166$	1.78367	0.138440
$167$	7.50364	0.580649	0.290325	−	0.956928i	$-0.406237\pi$
$167$	7.50364	0.580649	0.290325	+	0.956928i	$0.406237\pi$
$168$	1.56055	0.120399
$169$	6.86383	0.527987
$170$	−1.97161	−0.151216
$171$	−1.59754	−0.122167
$172$	−4.21695	−0.321540
$173$	21.9320	1.66746	0.833731	−	0.552171i	$-0.186200\pi$
$173$	21.9320	1.66746	0.833731	+	0.552171i	$0.186200\pi$
$174$	−1.02712	−0.0778656
$175$	−9.04683	−0.683876
$176$	−9.02888	−0.680577
$177$	−12.7657	−0.959530
$178$	0.423594	0.0317497
$179$	3.39484	0.253742	0.126871	−	0.991919i	$-0.459507\pi$
$179$	3.39484	0.253742	0.126871	+	0.991919i	$0.459507\pi$
$180$	−5.65019	−0.421140
$181$	6.16367	0.458142	0.229071	−	0.973410i	$-0.426431\pi$
$181$	6.16367	0.458142	0.229071	+	0.973410i	$0.426431\pi$
$182$	−1.74683	−0.129484
$183$	2.92690	0.216362
$184$	−2.03310	−0.149882
$185$	28.3987	2.08791
$186$	0	0
$187$	−11.8358	−0.865520
$188$	−2.59759	−0.189448
$189$	2.89040	0.210246
$190$	0.617671	0.0448105
$191$	−8.30833	−0.601170	−0.300585	−	0.953755i	$-0.597182\pi$
$191$	−8.30833	−0.601170	−0.300585	+	0.953755i	$0.597182\pi$
$192$	7.56207	0.545746
$193$	−0.0301820	−0.00217255	−0.00108628	−	0.999999i	$-0.500346\pi$
$193$	−0.0301820	−0.00217255	−0.00108628	+	0.999999i	$0.500346\pi$
$194$	−2.48109	−0.178132
$195$	12.7080	0.910036
$196$	−2.68390	−0.191707
$197$	3.91077	0.278631	0.139315	−	0.990248i	$-0.455510\pi$
$197$	3.91077	0.278631	0.139315	+	0.990248i	$0.455510\pi$
$198$	0.314735	0.0223672
$199$	−8.40479	−0.595800	−0.297900	−	0.954597i	$-0.596286\pi$
$199$	−8.40479	−0.595800	−0.297900	+	0.954597i	$0.596286\pi$
$200$	1.68990	0.119494
$201$	−1.19808	−0.0845064
$202$	−2.01646	−0.141878
$203$	21.8935	1.53662
$204$	10.1049	0.707488
$205$	22.6514	1.58204
$206$	−2.03753	−0.141961
$207$	−3.76563	−0.261729
$208$	−17.3373	−1.20213
$209$	3.70794	0.256484
$210$	−1.11754	−0.0771178
$211$	9.75000	0.671218	0.335609	−	0.942001i	$-0.391058\pi$
$211$	9.75000	0.671218	0.335609	+	0.942001i	$0.391058\pi$
$212$	15.1621	1.04134
$213$	12.8025	0.877213
$214$	−0.152191	−0.0104036
$215$	6.06770	0.413814
$216$	−0.539910	−0.0367362
$217$	0	0
$218$	−0.410833	−0.0278251
$219$	−1.30056	−0.0878837
$220$	13.1143	0.884167
$221$	−22.7272	−1.52880
$222$	1.35057	0.0906442
$223$	4.32182	0.289410	0.144705	−	0.989475i	$-0.453777\pi$
$223$	4.32182	0.289410	0.144705	+	0.989475i	$0.453777\pi$
$224$	4.64576	0.310408
$225$	3.12996	0.208664
$226$	−0.656419	−0.0436644
$227$	6.33675	0.420585	0.210292	−	0.977639i	$-0.432558\pi$
$227$	6.33675	0.420585	0.210292	+	0.977639i	$0.432558\pi$
$228$	−3.16570	−0.209653
$229$	12.7159	0.840289	0.420145	−	0.907457i	$-0.361979\pi$
$229$	12.7159	0.840289	0.420145	+	0.907457i	$0.361979\pi$
$230$	1.45594	0.0960019
$231$	−6.70873	−0.441402
$232$	−4.08958	−0.268494
$233$	−8.19366	−0.536785	−0.268392	−	0.963310i	$-0.586492\pi$
$233$	−8.19366	−0.536785	−0.268392	+	0.963310i	$0.586492\pi$
$234$	0.604357	0.0395081
$235$	3.73762	0.243816
$236$	−25.2967	−1.64668
$237$	−12.8057	−0.831820
$238$	1.99864	0.129553
$239$	22.0641	1.42721	0.713603	−	0.700550i	$-0.247062\pi$
$239$	22.0641	1.42721	0.713603	+	0.700550i	$0.247062\pi$
$240$	−11.0916	−0.715961
$241$	14.8684	0.957761	0.478880	−	0.877880i	$-0.341043\pi$
$241$	14.8684	0.957761	0.478880	+	0.877880i	$0.341043\pi$
$242$	0.761096	0.0489251
$243$	−1.00000	−0.0641500
$244$	5.79997	0.371305
$245$	3.86181	0.246722
$246$	1.07724	0.0686823
$247$	7.12003	0.453037
$248$	0	0
$249$	13.1539	0.833592
$250$	0.723031	0.0457285
$251$	−20.1278	−1.27046	−0.635229	−	0.772324i	$-0.719094\pi$
$251$	−20.1278	−1.27046	−0.635229	+	0.772324i	$0.719094\pi$
$252$	5.72765	0.360808
$253$	8.74017	0.549490
$254$	1.65831	0.104052
$255$	−14.5398	−0.910520
$256$	14.5492	0.909325
$257$	2.63430	0.164323	0.0821616	−	0.996619i	$-0.473818\pi$
$257$	2.63430	0.164323	0.0821616	+	0.996619i	$0.473818\pi$
$258$	0.288564	0.0179652
$259$	−28.7880	−1.78880
$260$	25.1822	1.56174
$261$	−7.57457	−0.468854
$262$	−0.685233	−0.0423338
$263$	13.5125	0.833215	0.416608	−	0.909086i	$-0.363219\pi$
$263$	13.5125	0.833215	0.416608	+	0.909086i	$0.363219\pi$
$264$	1.25315	0.0771262
$265$	−21.8165	−1.34018
$266$	−0.626138	−0.0383910
$267$	3.12383	0.191175
$268$	−2.37414	−0.145024
$269$	19.7335	1.20317	0.601587	−	0.798807i	$-0.294535\pi$
$269$	19.7335	1.20317	0.601587	+	0.798807i	$0.294535\pi$
$270$	0.386640	0.0235301
$271$	−18.5574	−1.12728	−0.563640	−	0.826020i	$-0.690600\pi$
$271$	−18.5574	−1.12728	−0.563640	+	0.826020i	$0.690600\pi$
$272$	19.8366	1.20277
$273$	−12.8822	−0.779665
$274$	−1.22751	−0.0741568
$275$	−7.26477	−0.438082
$276$	−7.46201	−0.449160
$277$	1.27067	0.0763470	0.0381735	−	0.999271i	$-0.487846\pi$
$277$	1.27067	0.0763470	0.0381735	+	0.999271i	$0.487846\pi$
$278$	−0.862902	−0.0517534
$279$	0	0
$280$	−4.44962	−0.265916
$281$	−4.32347	−0.257917	−0.128958	−	0.991650i	$-0.541163\pi$
$281$	−4.32347	−0.257917	−0.128958	+	0.991650i	$0.541163\pi$
$282$	0.177752	0.0105850
$283$	−6.10839	−0.363106	−0.181553	−	0.983381i	$-0.558112\pi$
$283$	−6.10839	−0.363106	−0.181553	+	0.983381i	$0.558112\pi$
$284$	25.3696	1.50541
$285$	4.55507	0.269819
$286$	−1.40274	−0.0829456
$287$	−22.9619	−1.35540
$288$	−1.60731	−0.0947116
$289$	9.00344	0.529614
$290$	2.92863	0.171975
$291$	−18.2970	−1.07259
$292$	−2.57720	−0.150819
$293$	30.9979	1.81091	0.905457	−	0.424438i	$-0.139528\pi$
$293$	30.9979	1.81091	0.905457	+	0.424438i	$0.139528\pi$
$294$	0.183658	0.0107111
$295$	36.3990	2.11923
$296$	5.37744	0.312557
$297$	2.32104	0.134680
$298$	−2.31716	−0.134230
$299$	16.7830	0.970584
$300$	6.20237	0.358094
$301$	−6.15089	−0.354531
$302$	−0.902210	−0.0519164
$303$	−14.8706	−0.854291
$304$	−6.21443	−0.356422
$305$	−8.34549	−0.477861
$306$	−0.691477	−0.0395291
$307$	11.1527	0.636519	0.318260	−	0.948004i	$-0.396902\pi$
$307$	11.1527	0.636519	0.318260	+	0.948004i	$0.396902\pi$
$308$	−13.2941	−0.757502
$309$	−15.0259	−0.854795
$310$	0	0
$311$	−4.21465	−0.238991	−0.119495	−	0.992835i	$-0.538128\pi$
$311$	−4.21465	−0.238991	−0.119495	+	0.992835i	$0.538128\pi$
$312$	2.40632	0.136231
$313$	3.09257	0.174802	0.0874011	−	0.996173i	$-0.472144\pi$
$313$	3.09257	0.174802	0.0874011	+	0.996173i	$0.472144\pi$
$314$	−1.73170	−0.0977255
$315$	−8.24142	−0.464351
$316$	−25.3759	−1.42751
$317$	12.8095	0.719451	0.359726	−	0.933058i	$-0.382870\pi$
$317$	12.8095	0.719451	0.359726	+	0.933058i	$0.382870\pi$
$318$	−1.03754	−0.0581822
$319$	17.5809	0.984340
$320$	−21.5618	−1.20534
$321$	−1.12235	−0.0626432
$322$	−1.47590	−0.0822487
$323$	−8.14640	−0.453278
$324$	−1.98161	−0.110090
$325$	−13.9499	−0.773800
$326$	1.35603	0.0751033
$327$	−3.02972	−0.167544
$328$	4.28915	0.236829
$329$	−3.78886	−0.208887
$330$	−0.897407	−0.0494006
$331$	19.7594	1.08607	0.543036	−	0.839709i	$-0.317275\pi$
$331$	19.7594	1.08607	0.543036	+	0.839709i	$0.317275\pi$
$332$	26.0659	1.43055
$333$	9.95988	0.545798
$334$	−1.01750	−0.0556751
$335$	3.41611	0.186642
$336$	11.2437	0.613393
$337$	−26.0944	−1.42145	−0.710727	−	0.703468i	$-0.751634\pi$
$337$	−26.0944	−1.42145	−0.710727	+	0.703468i	$0.751634\pi$
$338$	−0.930741	−0.0506256
$339$	−4.84082	−0.262917
$340$	−28.8123	−1.56257
$341$	0	0
$342$	0.216627	0.0117138
$343$	16.3180	0.881091
$344$	1.14895	0.0619473
$345$	10.7370	0.578059
$346$	−2.97400	−0.159883
$347$	21.4411	1.15102	0.575508	−	0.817796i	$-0.304804\pi$
$347$	21.4411	1.15102	0.575508	+	0.817796i	$0.304804\pi$
$348$	−15.0099	−0.804613
$349$	18.3252	0.980926	0.490463	−	0.871462i	$-0.336828\pi$
$349$	18.3252	0.980926	0.490463	+	0.871462i	$0.336828\pi$
$350$	1.22676	0.0655730
$351$	4.45689	0.237891
$352$	3.73063	0.198843
$353$	−29.8671	−1.58967	−0.794834	−	0.606827i	$-0.792442\pi$
$353$	−29.8671	−1.58967	−0.794834	+	0.606827i	$0.792442\pi$
$354$	1.73104	0.0920038
$355$	−36.5039	−1.93743
$356$	6.19022	0.328081
$357$	14.7392	0.780080
$358$	−0.460343	−0.0243299
$359$	−21.6724	−1.14382	−0.571912	−	0.820315i	$-0.693798\pi$
$359$	−21.6724	−1.14382	−0.571912	+	0.820315i	$0.693798\pi$
$360$	1.53945	0.0811361
$361$	−16.4479	−0.865678
$362$	−0.835798	−0.0439286
$363$	5.61277	0.294594
$364$	−25.5275	−1.33800
$365$	3.70830	0.194101
$366$	−0.396890	−0.0207457
$367$	−0.231759	−0.0120977	−0.00604885	−	0.999982i	$-0.501925\pi$
$367$	−0.231759	−0.0120977	−0.00604885	+	0.999982i	$0.501925\pi$
$368$	−14.6483	−0.763597
$369$	7.94420	0.413558
$370$	−3.85089	−0.200198
$371$	22.1156	1.14819
$372$	0	0
$373$	23.9527	1.24023	0.620113	−	0.784512i	$-0.287087\pi$
$373$	23.9527	1.24023	0.620113	+	0.784512i	$0.287087\pi$
$374$	1.60495	0.0829898
$375$	5.33206	0.275346
$376$	0.707738	0.0364988
$377$	33.7590	1.73868
$378$	−0.391940	−0.0201592
$379$	−0.715025	−0.0367283	−0.0183642	−	0.999831i	$-0.505846\pi$
$379$	−0.715025	−0.0367283	−0.0183642	+	0.999831i	$0.505846\pi$
$380$	9.02637	0.463043
$381$	12.2294	0.626530
$382$	1.12662	0.0576427
$383$	24.0287	1.22781	0.613904	−	0.789381i	$-0.289598\pi$
$383$	24.0287	1.22781	0.613904	+	0.789381i	$0.289598\pi$
$384$	−4.24004	−0.216374
$385$	19.1287	0.974887
$386$	0.00409271	0.000208313 0
$387$	2.12804	0.108174
$388$	−36.2575	−1.84070
$389$	13.5918	0.689129	0.344565	−	0.938763i	$-0.388027\pi$
$389$	13.5918	0.689129	0.344565	+	0.938763i	$0.388027\pi$
$390$	−1.72321	−0.0872581
$391$	−19.2023	−0.971101
$392$	0.731254	0.0369339
$393$	−5.05331	−0.254906
$394$	−0.530304	−0.0267163
$395$	36.5130	1.83717
$396$	4.59940	0.231129
$397$	−24.5001	−1.22962	−0.614811	−	0.788674i	$-0.710768\pi$
$397$	−24.5001	−1.22962	−0.614811	+	0.788674i	$0.710768\pi$
$398$	1.13970	0.0571278
$399$	−4.61751	−0.231165
$400$	12.1756	0.608779
$401$	−18.5690	−0.927293	−0.463646	−	0.886020i	$-0.653459\pi$
$401$	−18.5690	−0.927293	−0.463646	+	0.886020i	$0.653459\pi$
$402$	0.162461	0.00810283
$403$	0	0
$404$	−29.4677	−1.46607
$405$	2.85131	0.141683
$406$	−2.96878	−0.147338
$407$	−23.1173	−1.14588
$408$	−2.75319	−0.136303
$409$	3.76712	0.186272	0.0931360	−	0.995653i	$-0.470311\pi$
$409$	3.76712	0.186272	0.0931360	+	0.995653i	$0.470311\pi$
$410$	−3.07154	−0.151693
$411$	−9.05240	−0.446522
$412$	−29.7756	−1.46694
$413$	−36.8980	−1.81563
$414$	0.510622	0.0250957
$415$	−37.5057	−1.84108
$416$	7.16359	0.351224
$417$	−6.36354	−0.311624
$418$	−0.502800	−0.0245928
$419$	−17.8145	−0.870296	−0.435148	−	0.900359i	$-0.643304\pi$
$419$	−17.8145	−0.870296	−0.435148	+	0.900359i	$0.643304\pi$
$420$	−16.3313	−0.796886
$421$	−39.2291	−1.91191	−0.955955	−	0.293513i	$-0.905176\pi$
$421$	−39.2291	−1.91191	−0.955955	+	0.293513i	$0.905176\pi$
$422$	−1.32211	−0.0643592
$423$	1.31084	0.0637355
$424$	−4.13107	−0.200623
$425$	15.9608	0.774212
$426$	−1.73603	−0.0841109
$427$	8.45990	0.409403
$428$	−2.22405	−0.107504
$429$	−10.3446	−0.499443
$430$	−0.822786	−0.0396782
$431$	3.76486	0.181347	0.0906733	−	0.995881i	$-0.471098\pi$
$431$	3.76486	0.181347	0.0906733	+	0.995881i	$0.471098\pi$
$432$	−3.89001	−0.187158
$433$	5.67881	0.272906	0.136453	−	0.990647i	$-0.456430\pi$
$433$	5.67881	0.272906	0.136453	+	0.990647i	$0.456430\pi$
$434$	0	0
$435$	21.5974	1.03552
$436$	−6.00374	−0.287527
$437$	6.01572	0.287771
$438$	0.176357	0.00842666
$439$	−30.7261	−1.46648	−0.733238	−	0.679972i	$-0.761992\pi$
$439$	−30.7261	−1.46648	−0.733238	+	0.679972i	$0.761992\pi$
$440$	−3.57313	−0.170342
$441$	1.35440	0.0644952
$442$	3.08183	0.146588
$443$	−34.7126	−1.64925	−0.824623	−	0.565682i	$-0.808613\pi$
$443$	−34.7126	−1.64925	−0.824623	+	0.565682i	$0.808613\pi$
$444$	19.7366	0.936658
$445$	−8.90700	−0.422232
$446$	−0.586042	−0.0277499
$447$	−17.0881	−0.808240
$448$	21.8574	1.03267
$449$	−27.7826	−1.31114	−0.655570	−	0.755134i	$-0.727572\pi$
$449$	−27.7826	−1.31114	−0.655570	+	0.755134i	$0.727572\pi$
$450$	−0.424425	−0.0200076
$451$	−18.4388	−0.868250
$452$	−9.59263	−0.451199
$453$	−6.65343	−0.312605
$454$	−0.859268	−0.0403275
$455$	36.7310	1.72198
$456$	0.862525	0.0403914
$457$	−22.0585	−1.03185	−0.515926	−	0.856633i	$-0.672552\pi$
$457$	−22.0585	−1.03185	−0.515926	+	0.856633i	$0.672552\pi$
$458$	−1.72428	−0.0805705
$459$	−5.09936	−0.238018
$460$	21.2765	0.992022
$461$	24.2126	1.12769	0.563847	−	0.825879i	$-0.309321\pi$
$461$	24.2126	1.12769	0.563847	+	0.825879i	$0.309321\pi$
$462$	0.909709	0.0423235
$463$	25.5775	1.18869	0.594344	−	0.804211i	$-0.297412\pi$
$463$	25.5775	1.18869	0.594344	+	0.804211i	$0.297412\pi$
$464$	−29.4652	−1.36789
$465$	0	0
$466$	1.11107	0.0514692
$467$	−14.7000	−0.680233	−0.340116	−	0.940383i	$-0.610466\pi$
$467$	−14.7000	−0.680233	−0.340116	+	0.940383i	$0.610466\pi$
$468$	8.83182	0.408251
$469$	−3.46294	−0.159904
$470$	−0.506825	−0.0233781
$471$	−12.7706	−0.588437
$472$	6.89234	0.317246
$473$	−4.93927	−0.227108
$474$	1.73646	0.0797584
$475$	−5.00022	−0.229426
$476$	29.2073	1.33872
$477$	−7.65141	−0.350334
$478$	−2.99191	−0.136847
$479$	−18.4132	−0.841320	−0.420660	−	0.907218i	$-0.638201\pi$
$479$	−18.4132	−0.841320	−0.420660	+	0.907218i	$0.638201\pi$
$480$	4.58293	0.209181
$481$	−44.3900	−2.02401
$482$	−2.01617	−0.0918342
$483$	−10.8842	−0.495246
$484$	11.1223	0.505561
$485$	52.1704	2.36893
$486$	0.135601	0.00615098
$487$	−15.2201	−0.689686	−0.344843	−	0.938660i	$-0.612068\pi$
$487$	−15.2201	−0.689686	−0.344843	+	0.938660i	$0.612068\pi$
$488$	−1.58026	−0.0715350
$489$	10.0001	0.452222
$490$	−0.523665	−0.0236568
$491$	−4.69213	−0.211753	−0.105877	−	0.994379i	$-0.533765\pi$
$491$	−4.69213	−0.211753	−0.105877	+	0.994379i	$0.533765\pi$
$492$	15.7423	0.709719
$493$	−38.6254	−1.73960
$494$	−0.965482	−0.0434391
$495$	−6.61800	−0.297457
$496$	0	0
$497$	37.0043	1.65987
$498$	−1.78367	−0.0799284
$499$	3.67921	0.164704	0.0823521	−	0.996603i	$-0.473757\pi$
$499$	3.67921	0.164704	0.0823521	+	0.996603i	$0.473757\pi$
$500$	10.5661	0.472529
$501$	−7.50364	−0.335238
$502$	2.72935	0.121817
$503$	24.8069	1.10609	0.553044	−	0.833152i	$-0.313466\pi$
$503$	24.8069	1.10609	0.553044	+	0.833152i	$0.313466\pi$
$504$	−1.56055	−0.0695126
$505$	42.4005	1.88680
$506$	−1.18517	−0.0526874
$507$	−6.86383	−0.304833
$508$	24.2339	1.07520
$509$	17.7641	0.787378	0.393689	−	0.919244i	$-0.371199\pi$
$509$	17.7641	0.787378	0.393689	+	0.919244i	$0.371199\pi$
$510$	1.97161	0.0873045
$511$	−3.75913	−0.166294
$512$	−10.4530	−0.461960
$513$	1.59754	0.0705329
$514$	−0.357213	−0.0157560
$515$	42.8436	1.88791
$516$	4.21695	0.185641
$517$	−3.04252	−0.133810
$518$	3.90368	0.171518
$519$	−21.9320	−0.962709
$520$	−6.86115	−0.300881
$521$	18.0438	0.790515	0.395257	−	0.918570i	$-0.370655\pi$
$521$	18.0438	0.790515	0.395257	+	0.918570i	$0.370655\pi$
$522$	1.02712	0.0449557
$523$	18.6624	0.816049	0.408025	−	0.912971i	$-0.366218\pi$
$523$	18.6624	0.816049	0.408025	+	0.912971i	$0.366218\pi$
$524$	−10.0137	−0.437450
$525$	9.04683	0.394836
$526$	−1.83230	−0.0798922
$527$	0	0
$528$	9.02888	0.392931
$529$	−8.82005	−0.383481
$530$	2.95834	0.128502
$531$	12.7657	0.553985
$532$	−9.15012	−0.396708
$533$	−35.4064	−1.53362
$534$	−0.423594	−0.0183307
$535$	3.20015	0.138355
$536$	0.646858	0.0279400
$537$	−3.39484	−0.146498
$538$	−2.67588	−0.115365
$539$	−3.14362	−0.135405
$540$	5.65019	0.243145
$541$	−18.5739	−0.798555	−0.399278	−	0.916830i	$-0.630739\pi$
$541$	−18.5739	−0.798555	−0.399278	+	0.916830i	$0.630739\pi$
$542$	2.51640	0.108088
$543$	−6.16367	−0.264508
$544$	−8.19624	−0.351411
$545$	8.63868	0.370040
$546$	1.74683	0.0747576
$547$	−1.58403	−0.0677281	−0.0338640	−	0.999426i	$-0.510781\pi$
$547$	−1.58403	−0.0677281	−0.0338640	+	0.999426i	$0.510781\pi$
$548$	−17.9384	−0.766289
$549$	−2.92690	−0.124917
$550$	0.985108	0.0420052
$551$	12.1006	0.515505
$552$	2.03310	0.0865345
$553$	−37.0136	−1.57398
$554$	−0.172304	−0.00732048
$555$	−28.3987	−1.20546
$556$	−12.6101	−0.534786
$557$	16.2178	0.687168	0.343584	−	0.939122i	$-0.388359\pi$
$557$	16.2178	0.687168	0.343584	+	0.939122i	$0.388359\pi$
$558$	0	0
$559$	−9.48444	−0.401149
$560$	−32.0592	−1.35475
$561$	11.8358	0.499708
$562$	0.586267	0.0247302
$563$	−14.9949	−0.631961	−0.315981	−	0.948766i	$-0.602333\pi$
$563$	−14.9949	−0.631961	−0.315981	+	0.948766i	$0.602333\pi$
$564$	2.59759	0.109378
$565$	13.8027	0.580683
$566$	0.828302	0.0348161
$567$	−2.89040	−0.121385
$568$	−6.91220	−0.290029
$569$	−1.51909	−0.0636837	−0.0318418	−	0.999493i	$-0.510137\pi$
$569$	−1.51909	−0.0636837	−0.0318418	+	0.999493i	$0.510137\pi$
$570$	−0.617671	−0.0258714
$571$	−0.758974	−0.0317621	−0.0158810	−	0.999874i	$-0.505055\pi$
$571$	−0.758974	−0.0317621	−0.0158810	+	0.999874i	$0.505055\pi$
$572$	−20.4990	−0.857107
$573$	8.30833	0.347086
$574$	3.11365	0.129961
$575$	−11.7863	−0.491521
$576$	−7.56207	−0.315086
$577$	9.37218	0.390169	0.195085	−	0.980786i	$-0.437502\pi$
$577$	9.37218	0.390169	0.195085	+	0.980786i	$0.437502\pi$
$578$	−1.22087	−0.0507817
$579$	0.0301820	0.00125432
$580$	42.7977	1.77708
$581$	38.0199	1.57733
$582$	2.48109	0.102844
$583$	17.7592	0.735513
$584$	0.702185	0.0290566
$585$	−12.7080	−0.525409
$586$	−4.20333	−0.173638
$587$	−24.9622	−1.03030	−0.515151	−	0.857099i	$-0.672264\pi$
$587$	−24.9622	−1.03030	−0.515151	+	0.857099i	$0.672264\pi$
$588$	2.68390	0.110682
$589$	0	0
$590$	−4.93573	−0.203201
$591$	−3.91077	−0.160868
$592$	38.7441	1.59237
$593$	−28.2065	−1.15830	−0.579151	−	0.815220i	$-0.696616\pi$
$593$	−28.2065	−1.15830	−0.579151	+	0.815220i	$0.696616\pi$
$594$	−0.314735	−0.0129137
$595$	−42.0259	−1.72289
$596$	−33.8620	−1.38704
$597$	8.40479	0.343985
$598$	−2.27578	−0.0930637
$599$	−35.0087	−1.43042	−0.715209	−	0.698910i	$-0.753669\pi$
$599$	−35.0087	−1.43042	−0.715209	+	0.698910i	$0.753669\pi$
$600$	−1.68990	−0.0689898
$601$	−24.9349	−1.01712	−0.508558	−	0.861028i	$-0.669821\pi$
$601$	−24.9349	−1.01712	−0.508558	+	0.861028i	$0.669821\pi$
$602$	0.834065	0.0339940
$603$	1.19808	0.0487898
$604$	−13.1845	−0.536470
$605$	−16.0037	−0.650645
$606$	2.01646	0.0819131
$607$	−23.5335	−0.955194	−0.477597	−	0.878579i	$-0.658492\pi$
$607$	−23.5335	−0.955194	−0.477597	+	0.878579i	$0.658492\pi$
$608$	2.56773	0.104135
$609$	−21.8935	−0.887170
$610$	1.13165	0.0458194
$611$	−5.84229	−0.236354
$612$	−10.1049	−0.408468
$613$	10.6445	0.429928	0.214964	−	0.976622i	$-0.431037\pi$
$613$	10.6445	0.429928	0.214964	+	0.976622i	$0.431037\pi$
$614$	−1.51232	−0.0610322
$615$	−22.6514	−0.913391
$616$	3.62211	0.145939
$617$	−4.11284	−0.165577	−0.0827884	−	0.996567i	$-0.526383\pi$
$617$	−4.11284	−0.165577	−0.0827884	+	0.996567i	$0.526383\pi$
$618$	2.03753	0.0819614
$619$	−27.4112	−1.10175	−0.550875	−	0.834588i	$-0.685706\pi$
$619$	−27.4112	−1.10175	−0.550875	+	0.834588i	$0.685706\pi$
$620$	0	0
$621$	3.76563	0.151109
$622$	0.571510	0.0229154
$623$	9.02911	0.361744
$624$	17.3373	0.694049
$625$	−30.8531	−1.23413
$626$	−0.419355	−0.0167608
$627$	−3.70794	−0.148081
$628$	−25.3063	−1.00983
$629$	50.7890	2.02509
$630$	1.11754	0.0445240
$631$	40.5448	1.61406	0.807031	−	0.590510i	$-0.201073\pi$
$631$	40.5448	1.61406	0.807031	+	0.590510i	$0.201073\pi$
$632$	6.91393	0.275021
$633$	−9.75000	−0.387528
$634$	−1.73697	−0.0689841
$635$	−34.8697	−1.38376
$636$	−15.1621	−0.601218
$637$	−6.03640	−0.239171
$638$	−2.38398	−0.0943827
$639$	−12.8025	−0.506459
$640$	12.0897	0.477886
$641$	−37.2864	−1.47273	−0.736363	−	0.676587i	$-0.763458\pi$
$641$	−37.2864	−1.47273	−0.736363	+	0.676587i	$0.763458\pi$
$642$	0.152191	0.00600650
$643$	1.38973	0.0548057	0.0274028	−	0.999624i	$-0.491276\pi$
$643$	1.38973	0.0548057	0.0274028	+	0.999624i	$0.491276\pi$
$644$	−21.5682	−0.849906
$645$	−6.06770	−0.238916
$646$	1.10466	0.0434622
$647$	23.0086	0.904560	0.452280	−	0.891876i	$-0.350611\pi$
$647$	23.0086	0.904560	0.452280	+	0.891876i	$0.350611\pi$
$648$	0.539910	0.0212097
$649$	−29.6298	−1.16307
$650$	1.89161	0.0741952
$651$	0	0
$652$	19.8164	0.776069
$653$	20.2893	0.793981	0.396991	−	0.917823i	$-0.370055\pi$
$653$	20.2893	0.793981	0.396991	+	0.917823i	$0.370055\pi$
$654$	0.410833	0.0160648
$655$	14.4085	0.562988
$656$	30.9030	1.20656
$657$	1.30056	0.0507396
$658$	0.513773	0.0200290
$659$	−44.6702	−1.74010	−0.870052	−	0.492961i	$-0.835915\pi$
$659$	−44.6702	−1.74010	−0.870052	+	0.492961i	$0.835915\pi$
$660$	−13.1143	−0.510474
$661$	−17.1746	−0.668016	−0.334008	−	0.942570i	$-0.608401\pi$
$661$	−17.1746	−0.668016	−0.334008	+	0.942570i	$0.608401\pi$
$662$	−2.67938	−0.104137
$663$	22.7272	0.882653
$664$	−7.10190	−0.275607
$665$	13.1660	0.510554
$666$	−1.35057	−0.0523334
$667$	28.5230	1.10441
$668$	−14.8693	−0.575311
$669$	−4.32182	−0.167091
$670$	−0.463227	−0.0178960
$671$	6.79345	0.262258
$672$	−4.64576	−0.179214
$673$	11.0367	0.425434	0.212717	−	0.977114i	$-0.431769\pi$
$673$	11.0367	0.425434	0.212717	+	0.977114i	$0.431769\pi$
$674$	3.53843	0.136295
$675$	−3.12996	−0.120472
$676$	−13.6014	−0.523132
$677$	4.13682	0.158991	0.0794955	−	0.996835i	$-0.474669\pi$
$677$	4.13682	0.158991	0.0794955	+	0.996835i	$0.474669\pi$
$678$	0.656419	0.0252096
$679$	−52.8856	−2.02956
$680$	7.85020	0.301042
$681$	−6.33675	−0.242825
$682$	0	0
$683$	−17.8255	−0.682076	−0.341038	−	0.940050i	$-0.610778\pi$
$683$	−17.8255	−0.682076	−0.341038	+	0.940050i	$0.610778\pi$
$684$	3.16570	0.121043
$685$	25.8112	0.986195
$686$	−2.21274	−0.0844827
$687$	−12.7159	−0.485141
$688$	8.27811	0.315600
$689$	34.1015	1.29916
$690$	−1.45594	−0.0554267
$691$	−23.9337	−0.910479	−0.455240	−	0.890369i	$-0.650446\pi$
$691$	−23.9337	−0.910479	−0.455240	+	0.890369i	$0.650446\pi$
$692$	−43.4608	−1.65213
$693$	6.70873	0.254844
$694$	−2.90743	−0.110364
$695$	18.1444	0.688257
$696$	4.08958	0.155015
$697$	40.5103	1.53444
$698$	−2.48491	−0.0940554
$699$	8.19366	0.309913
$700$	17.9273	0.677589
$701$	2.07407	0.0783365	0.0391683	−	0.999233i	$-0.487529\pi$
$701$	2.07407	0.0783365	0.0391683	+	0.999233i	$0.487529\pi$
$702$	−0.604357	−0.0228100
$703$	−15.9113	−0.600104
$704$	17.5519	0.661511
$705$	−3.73762	−0.140767
$706$	4.05001	0.152424
$707$	−42.9818	−1.61650
$708$	25.2967	0.950708
$709$	5.34612	0.200778	0.100389	−	0.994948i	$-0.467991\pi$
$709$	5.34612	0.200778	0.100389	+	0.994948i	$0.467991\pi$
$710$	4.94996	0.185769
$711$	12.8057	0.480252
$712$	−1.68659	−0.0632075
$713$	0	0
$714$	−1.99864	−0.0747974
$715$	29.4957	1.10308
$716$	−6.72726	−0.251410
$717$	−22.0641	−0.823998
$718$	2.93879	0.109675
$719$	5.26476	0.196342	0.0981712	−	0.995170i	$-0.468701\pi$
$719$	5.26476	0.196342	0.0981712	+	0.995170i	$0.468701\pi$
$720$	11.0916	0.413361
$721$	−43.4309	−1.61745
$722$	2.23035	0.0830049
$723$	−14.8684	−0.552963
$724$	−12.2140	−0.453930
$725$	−23.7081	−0.880497
$726$	−0.761096	−0.0282469
$727$	34.5926	1.28297	0.641484	−	0.767136i	$-0.278319\pi$
$727$	34.5926	1.28297	0.641484	+	0.767136i	$0.278319\pi$
$728$	6.95521	0.257777
$729$	1.00000	0.0370370
$730$	−0.502848	−0.0186112
$731$	10.8516	0.401363
$732$	−5.79997	−0.214373
$733$	19.7731	0.730336	0.365168	−	0.930942i	$-0.381012\pi$
$733$	19.7731	0.730336	0.365168	+	0.930942i	$0.381012\pi$
$734$	0.0314267	0.00115998
$735$	−3.86181	−0.142445
$736$	6.05252	0.223099
$737$	−2.78080	−0.102432
$738$	−1.07724	−0.0396537
$739$	−12.6319	−0.464672	−0.232336	−	0.972636i	$-0.574637\pi$
$739$	−12.6319	−0.464672	−0.232336	+	0.972636i	$0.574637\pi$
$740$	−56.2752	−2.06872
$741$	−7.12003	−0.261561
$742$	−2.99890	−0.110093
$743$	11.5104	0.422274	0.211137	−	0.977456i	$-0.432283\pi$
$743$	11.5104	0.422274	0.211137	+	0.977456i	$0.432283\pi$
$744$	0	0
$745$	48.7235	1.78509
$746$	−3.24801	−0.118918
$747$	−13.1539	−0.481275
$748$	23.4540	0.857563
$749$	−3.24403	−0.118534
$750$	−0.723031	−0.0264014
$751$	−18.9676	−0.692139	−0.346070	−	0.938209i	$-0.612484\pi$
$751$	−18.9676	−0.692139	−0.346070	+	0.938209i	$0.612484\pi$
$752$	5.09920	0.185949
$753$	20.1278	0.733499
$754$	−4.57775	−0.166712
$755$	18.9710	0.690425
$756$	−5.72765	−0.208313
$757$	−36.5777	−1.32944	−0.664720	−	0.747092i	$-0.731449\pi$
$757$	−36.5777	−1.32944	−0.664720	+	0.747092i	$0.731449\pi$
$758$	0.0969579	0.00352167
$759$	−8.74017	−0.317248
$760$	−2.45932	−0.0892091
$761$	11.7188	0.424806	0.212403	−	0.977182i	$-0.431871\pi$
$761$	11.7188	0.424806	0.212403	+	0.977182i	$0.431871\pi$
$762$	−1.65831	−0.0600743
$763$	−8.75711	−0.317029
$764$	16.4639	0.595643
$765$	14.5398	0.525689
$766$	−3.25831	−0.117727
$767$	−56.8953	−2.05437
$768$	−14.5492	−0.524999
$769$	−20.1073	−0.725088	−0.362544	−	0.931967i	$-0.618092\pi$
$769$	−20.1073	−0.725088	−0.362544	+	0.931967i	$0.618092\pi$
$770$	−2.59386	−0.0934763
$771$	−2.63430	−0.0948720
$772$	0.0598091	0.00215258
$773$	19.6800	0.707842	0.353921	−	0.935275i	$-0.384848\pi$
$773$	19.6800	0.707842	0.353921	+	0.935275i	$0.384848\pi$
$774$	−0.288564	−0.0103722
$775$	0	0
$776$	9.87873	0.354626
$777$	28.7880	1.03276
$778$	−1.84305	−0.0660766
$779$	−12.6911	−0.454707
$780$	−25.1822	−0.901669
$781$	29.7151	1.06329
$782$	2.60384	0.0931133
$783$	7.57457	0.270693
$784$	5.26863	0.188165
$785$	36.4129	1.29963
$786$	0.685233	0.0244414
$787$	24.1448	0.860670	0.430335	−	0.902669i	$-0.358395\pi$
$787$	24.1448	0.860670	0.430335	+	0.902669i	$0.358395\pi$
$788$	−7.74963	−0.276069
$789$	−13.5125	−0.481057
$790$	−4.95120	−0.176156
$791$	−13.9919	−0.497495
$792$	−1.25315	−0.0445288
$793$	13.0448	0.463236
$794$	3.32223	0.117901
$795$	21.8165	0.773753
$796$	16.6550	0.590322
$797$	12.5882	0.445898	0.222949	−	0.974830i	$-0.428432\pi$
$797$	12.5882	0.445898	0.222949	+	0.974830i	$0.428432\pi$
$798$	0.626138	0.0221651
$799$	6.68447	0.236479
$800$	−5.03081	−0.177866
$801$	−3.12383	−0.110375
$802$	2.51797	0.0889128
$803$	−3.01865	−0.106526
$804$	2.37414	0.0837294
$805$	31.0341	1.09381
$806$	0	0
$807$	−19.7335	−0.694653
$808$	8.02876	0.282451
$809$	45.5787	1.60246	0.801231	−	0.598355i	$-0.204179\pi$
$809$	45.5787	1.60246	0.801231	+	0.598355i	$0.204179\pi$
$810$	−0.386640	−0.0135851
$811$	41.3002	1.45025	0.725123	−	0.688620i	$-0.241783\pi$
$811$	41.3002	1.45025	0.725123	+	0.688620i	$0.241783\pi$
$812$	−43.3845	−1.52250
$813$	18.5574	0.650836
$814$	3.13472	0.109872
$815$	−28.5135	−0.998783
$816$	−19.8366	−0.694419
$817$	−3.39962	−0.118938
$818$	−0.510824	−0.0178606
$819$	12.8822	0.450140
$820$	−44.8862	−1.56749
$821$	28.6694	1.00057	0.500284	−	0.865862i	$-0.333229\pi$
$821$	28.6694	1.00057	0.500284	+	0.865862i	$0.333229\pi$
$822$	1.22751	0.0428144
$823$	19.9295	0.694698	0.347349	−	0.937736i	$-0.387082\pi$
$823$	19.9295	0.694698	0.347349	+	0.937736i	$0.387082\pi$
$824$	8.11265	0.282618
$825$	7.26477	0.252927
$826$	5.00340	0.174091
$827$	44.3154	1.54100	0.770499	−	0.637441i	$-0.220007\pi$
$827$	44.3154	1.54100	0.770499	+	0.637441i	$0.220007\pi$
$828$	7.46201	0.259323
$829$	−4.10806	−0.142679	−0.0713394	−	0.997452i	$-0.522727\pi$
$829$	−4.10806	−0.142679	−0.0713394	+	0.997452i	$0.522727\pi$
$830$	5.08581	0.176531
$831$	−1.27067	−0.0440790
$832$	33.7033	1.16845
$833$	6.90657	0.239298
$834$	0.862902	0.0298798
$835$	21.3952	0.740412
$836$	−7.34771	−0.254126
$837$	0	0
$838$	2.41566	0.0834477
$839$	29.9761	1.03489	0.517445	−	0.855716i	$-0.326883\pi$
$839$	29.9761	1.03489	0.517445	+	0.855716i	$0.326883\pi$
$840$	4.44962	0.153527
$841$	28.3741	0.978417
$842$	5.31950	0.183322
$843$	4.32347	0.148908
$844$	−19.3207	−0.665047
$845$	19.5709	0.673259
$846$	−0.177752	−0.00611123
$847$	16.2231	0.557434
$848$	−29.7641	−1.02210
$849$	6.10839	0.209639
$850$	−2.16430	−0.0742347
$851$	−37.5052	−1.28566
$852$	−25.3696	−0.869148
$853$	−13.1100	−0.448877	−0.224438	−	0.974488i	$-0.572055\pi$
$853$	−13.1100	−0.448877	−0.224438	+	0.974488i	$0.572055\pi$
$854$	−1.14717	−0.0392553
$855$	−4.55507	−0.155780
$856$	0.605966	0.0207115
$857$	−9.29585	−0.317540	−0.158770	−	0.987316i	$-0.550753\pi$
$857$	−9.29585	−0.317540	−0.158770	+	0.987316i	$0.550753\pi$
$858$	1.40274	0.0478887
$859$	46.2394	1.57767	0.788834	−	0.614606i	$-0.210685\pi$
$859$	46.2394	1.57767	0.788834	+	0.614606i	$0.210685\pi$
$860$	−12.0238	−0.410009
$861$	22.9619	0.782539
$862$	−0.510517	−0.0173883
$863$	46.3548	1.57794	0.788968	−	0.614434i	$-0.210615\pi$
$863$	46.3548	1.57794	0.788968	+	0.614434i	$0.210615\pi$
$864$	1.60731	0.0546818
$865$	62.5350	2.12625
$866$	−0.770051	−0.0261674
$867$	−9.00344	−0.305773
$868$	0	0
$869$	−29.7226	−1.00827
$870$	−2.92863	−0.0992898
$871$	−5.33973	−0.180930
$872$	1.63578	0.0553944
$873$	18.2970	0.619259
$874$	−0.815737	−0.0275927
$875$	15.4118	0.521013
$876$	2.57720	0.0870757
$877$	30.4791	1.02921	0.514603	−	0.857429i	$-0.327939\pi$
$877$	30.4791	1.02921	0.514603	+	0.857429i	$0.327939\pi$
$878$	4.16648	0.140612
$879$	−30.9979	−1.04553
$880$	−25.7441	−0.867834
$881$	26.7393	0.900869	0.450435	−	0.892809i	$-0.351269\pi$
$881$	26.7393	0.900869	0.450435	+	0.892809i	$0.351269\pi$
$882$	−0.183658	−0.00618408
$883$	−15.1276	−0.509085	−0.254542	−	0.967062i	$-0.581925\pi$
$883$	−15.1276	−0.509085	−0.254542	+	0.967062i	$0.581925\pi$
$884$	45.0366	1.51474
$885$	−36.3990	−1.22354
$886$	4.70706	0.158137
$887$	4.81887	0.161802	0.0809010	−	0.996722i	$-0.474220\pi$
$887$	4.81887	0.161802	0.0809010	+	0.996722i	$0.474220\pi$
$888$	−5.37744	−0.180455
$889$	35.3477	1.18553
$890$	1.20780	0.0404854
$891$	−2.32104	−0.0777578
$892$	−8.56417	−0.286750
$893$	−2.09412	−0.0700771
$894$	2.31716	0.0774975
$895$	9.67974	0.323558
$896$	−12.2554	−0.409424
$897$	−16.7830	−0.560367
$898$	3.76734	0.125718
$899$	0	0
$900$	−6.20237	−0.206746
$901$	−39.0173	−1.29985
$902$	2.50032	0.0832515
$903$	6.15089	0.204689
$904$	2.61361	0.0869273
$905$	17.5745	0.584197
$906$	0.902210	0.0299739
$907$	−9.14390	−0.303618	−0.151809	−	0.988410i	$-0.548510\pi$
$907$	−9.14390	−0.303618	−0.151809	+	0.988410i	$0.548510\pi$
$908$	−12.5570	−0.416718
$909$	14.8706	0.493225
$910$	−4.98076	−0.165111
$911$	−24.2794	−0.804411	−0.402205	−	0.915549i	$-0.631756\pi$
$911$	−24.2794	−0.804411	−0.402205	+	0.915549i	$0.631756\pi$
$912$	6.21443	0.205780
$913$	30.5306	1.01042
$914$	2.99115	0.0989384
$915$	8.34549	0.275893
$916$	−25.1980	−0.832564
$917$	−14.6061	−0.482335
$918$	0.691477	0.0228221
$919$	49.5447	1.63433	0.817164	−	0.576405i	$-0.195545\pi$
$919$	49.5447	1.63433	0.817164	+	0.576405i	$0.195545\pi$
$920$	−5.79699	−0.191121
$921$	−11.1527	−0.367494
$922$	−3.28325	−0.108128
$923$	57.0593	1.87813
$924$	13.2941	0.437344
$925$	31.1740	1.02500
$926$	−3.46833	−0.113976
$927$	15.0259	0.493516
$928$	12.1747	0.399653
$929$	−10.1197	−0.332016	−0.166008	−	0.986124i	$-0.553088\pi$
$929$	−10.1197	−0.332016	−0.166008	+	0.986124i	$0.553088\pi$
$930$	0	0
$931$	−2.16370	−0.0709124
$932$	16.2367	0.531850
$933$	4.21465	0.137981
$934$	1.99333	0.0652236
$935$	−33.7476	−1.10366
$936$	−2.40632	−0.0786529
$937$	−2.52636	−0.0825326	−0.0412663	−	0.999148i	$-0.513139\pi$
$937$	−2.52636	−0.0825326	−0.0412663	+	0.999148i	$0.513139\pi$
$938$	0.469578	0.0153323
$939$	−3.09257	−0.100922
$940$	−7.40652	−0.241574
$941$	−27.9395	−0.910801	−0.455400	−	0.890287i	$-0.650504\pi$
$941$	−27.9395	−0.910801	−0.455400	+	0.890287i	$0.650504\pi$
$942$	1.73170	0.0564219
$943$	−29.9149	−0.974163
$944$	49.6588	1.61626
$945$	8.24142	0.268093
$946$	0.669769	0.0217761
$947$	41.6169	1.35237	0.676183	−	0.736734i	$-0.263633\pi$
$947$	41.6169	1.35237	0.676183	+	0.736734i	$0.263633\pi$
$948$	25.3759	0.824172
$949$	−5.79644	−0.188161
$950$	0.678034	0.0219983
$951$	−12.8095	−0.415375
$952$	−7.95782	−0.257915
$953$	−50.6784	−1.64163	−0.820817	−	0.571191i	$-0.806482\pi$
$953$	−50.6784	−1.64163	−0.820817	+	0.571191i	$0.806482\pi$
$954$	1.03754	0.0335915
$955$	−23.6896	−0.766578
$956$	−43.7224	−1.41409
$957$	−17.5809	−0.568309
$958$	2.49684	0.0806693
$959$	−26.1650	−0.844913
$960$	21.5618	0.695904
$961$	0	0
$962$	6.01933	0.194071
$963$	1.12235	0.0361671
$964$	−29.4635	−0.948955
$965$	−0.0860583	−0.00277032
$966$	1.47590	0.0474863
$967$	8.66079	0.278512	0.139256	−	0.990256i	$-0.455529\pi$
$967$	8.66079	0.278512	0.139256	+	0.990256i	$0.455529\pi$
$968$	−3.03039	−0.0974004
$969$	8.14640	0.261700
$970$	−7.07434	−0.227143
$971$	46.6438	1.49687	0.748435	−	0.663208i	$-0.230806\pi$
$971$	46.6438	1.49687	0.748435	+	0.663208i	$0.230806\pi$
$972$	1.98161	0.0635602
$973$	−18.3932	−0.589658
$974$	2.06385	0.0661301
$975$	13.9499	0.446754
$976$	−11.3857	−0.364446
$977$	−17.8313	−0.570474	−0.285237	−	0.958457i	$-0.592072\pi$
$977$	−17.8313	−0.570474	−0.285237	+	0.958457i	$0.592072\pi$
$978$	−1.35603	−0.0433609
$979$	7.25054	0.231728
$980$	−7.65261	−0.244454
$981$	3.02972	0.0967316
$982$	0.636257	0.0203038
$983$	8.08619	0.257909	0.128955	−	0.991650i	$-0.458838\pi$
$983$	8.08619	0.257909	0.128955	+	0.991650i	$0.458838\pi$
$984$	−4.28915	−0.136733
$985$	11.1508	0.355295
$986$	5.23764	0.166800
$987$	3.78886	0.120601
$988$	−14.1091	−0.448872
$989$	−8.01341	−0.254812
$990$	0.897407	0.0285215
$991$	−54.7383	−1.73882	−0.869409	−	0.494093i	$-0.835500\pi$
$991$	−54.7383	−1.73882	−0.869409	+	0.494093i	$0.835500\pi$
$992$	0	0
$993$	−19.7594	−0.627044
$994$	−5.01782	−0.159155
$995$	−23.9646	−0.759730
$996$	−26.0659	−0.825928
$997$	42.7521	1.35397	0.676986	−	0.735996i	$-0.263286\pi$
$997$	42.7521	1.35397	0.676986	+	0.735996i	$0.263286\pi$
$998$	−0.498904	−0.0157925
$999$	−9.95988	−0.315117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2883.2.a.s.1.6		12
3.2	odd	2		8649.2.a.bl.1.7		12
31.12	odd	30		93.2.m.b.82.2	yes	24
31.13	odd	30		93.2.m.b.76.2	✓	24
31.30	odd	2		2883.2.a.t.1.6		12
93.44	even	30		279.2.y.d.262.2		24
93.74	even	30		279.2.y.d.82.2		24
93.92	even	2		8649.2.a.bk.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.76.2	✓	24	31.13	odd	30
93.2.m.b.82.2	yes	24	31.12	odd	30
279.2.y.d.82.2		24	93.74	even	30
279.2.y.d.262.2		24	93.44	even	30
2883.2.a.s.1.6		12	1.1	even	1	trivial
2883.2.a.t.1.6		12	31.30	odd	2
8649.2.a.bk.1.7		12	93.92	even	2
8649.2.a.bl.1.7		12	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:	\( N \)	\(=\)	\( 2883 = 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2883.a (trivial)

\(f(q)\)	\(=\)	\(q-0.135601 q^{2} -1.00000 q^{3} -1.98161 q^{4} +2.85131 q^{5} +0.135601 q^{6} -2.89040 q^{7} +0.539910 q^{8} +1.00000 q^{9} -0.386640 q^{10} -2.32104 q^{11} +1.98161 q^{12} -4.45689 q^{13} +0.391940 q^{14} -2.85131 q^{15} +3.89001 q^{16} +5.09936 q^{17} -0.135601 q^{18} -1.59754 q^{19} -5.65019 q^{20} +2.89040 q^{21} +0.314735 q^{22} -3.76563 q^{23} -0.539910 q^{24} +3.12996 q^{25} +0.604357 q^{26} -1.00000 q^{27} +5.72765 q^{28} -7.57457 q^{29} +0.386640 q^{30} -1.60731 q^{32} +2.32104 q^{33} -0.691477 q^{34} -8.24142 q^{35} -1.98161 q^{36} +9.95988 q^{37} +0.216627 q^{38} +4.45689 q^{39} +1.53945 q^{40} +7.94420 q^{41} -0.391940 q^{42} +2.12804 q^{43} +4.59940 q^{44} +2.85131 q^{45} +0.510622 q^{46} +1.31084 q^{47} -3.89001 q^{48} +1.35440 q^{49} -0.424425 q^{50} -5.09936 q^{51} +8.83182 q^{52} -7.65141 q^{53} +0.135601 q^{54} -6.61800 q^{55} -1.56055 q^{56} +1.59754 q^{57} +1.02712 q^{58} +12.7657 q^{59} +5.65019 q^{60} -2.92690 q^{61} -2.89040 q^{63} -7.56207 q^{64} -12.7080 q^{65} -0.314735 q^{66} +1.19808 q^{67} -10.1049 q^{68} +3.76563 q^{69} +1.11754 q^{70} -12.8025 q^{71} +0.539910 q^{72} +1.30056 q^{73} -1.35057 q^{74} -3.12996 q^{75} +3.16570 q^{76} +6.70873 q^{77} -0.604357 q^{78} +12.8057 q^{79} +11.0916 q^{80} +1.00000 q^{81} -1.07724 q^{82} -13.1539 q^{83} -5.72765 q^{84} +14.5398 q^{85} -0.288564 q^{86} +7.57457 q^{87} -1.25315 q^{88} -3.12383 q^{89} -0.386640 q^{90} +12.8822 q^{91} +7.46201 q^{92} -0.177752 q^{94} -4.55507 q^{95} +1.60731 q^{96} +18.2970 q^{97} -0.183658 q^{98} -2.32104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 5 q^{2} - 12 q^{3} + 13 q^{4} + 6 q^{5} - 5 q^{6} + 6 q^{7} + 24 q^{8} + 12 q^{9} + 21 q^{10} - 2 q^{11} - 13 q^{12} - 3 q^{13} + 15 q^{14} - 6 q^{15} + 19 q^{16} + 8 q^{17} + 5 q^{18} + 15 q^{19}+ \cdots - 2 q^{99}+O(q^{100}) \) 12 * q + 5 * q^2 - 12 * q^3 + 13 * q^4 + 6 * q^5 - 5 * q^6 + 6 * q^7 + 24 * q^8 + 12 * q^9 + 21 * q^10 - 2 * q^11 - 13 * q^12 - 3 * q^13 + 15 * q^14 - 6 * q^15 + 19 * q^16 + 8 * q^17 + 5 * q^18 + 15 * q^19 + 17 * q^20 - 6 * q^21 - 12 * q^22 + 12 * q^23 - 24 * q^24 + 8 * q^25 + 4 * q^26 - 12 * q^27 + 41 * q^28 + 14 * q^29 - 21 * q^30 + 18 * q^32 + 2 * q^33 + 15 * q^34 - 3 * q^35 + 13 * q^36 - 13 * q^37 + 31 * q^38 + 3 * q^39 - 23 * q^40 + 24 * q^41 - 15 * q^42 + 19 * q^43 + 27 * q^44 + 6 * q^45 - 21 * q^46 + 16 * q^47 - 19 * q^48 + 22 * q^49 + 34 * q^50 - 8 * q^51 - 36 * q^52 + 20 * q^53 - 5 * q^54 - 39 * q^55 - 28 * q^56 - 15 * q^57 + 85 * q^58 + 16 * q^59 - 17 * q^60 - 35 * q^61 + 6 * q^63 + 42 * q^64 - 21 * q^65 + 12 * q^66 - 4 * q^67 + 51 * q^68 - 12 * q^69 - 34 * q^70 - 15 * q^71 + 24 * q^72 - 27 * q^73 + 24 * q^74 - 8 * q^75 + 54 * q^76 + 10 * q^77 - 4 * q^78 - 14 * q^79 + 13 * q^80 + 12 * q^81 + 25 * q^82 + 14 * q^83 - 41 * q^84 + 32 * q^85 - 24 * q^86 - 14 * q^87 + 26 * q^88 - 4 * q^89 + 21 * q^90 - 37 * q^91 - 14 * q^92 - 40 * q^94 + 22 * q^95 - 18 * q^96 + 12 * q^97 + 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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