LMFDB - Embedded newform 2883.2.a.s.1.11

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			1.11
Root			$2.58026$ 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)

$f(q)$	$=$	\(q+2.58026 q^{2} -1.00000 q^{3} +4.65777 q^{4} +3.86423 q^{5} -2.58026 q^{6} -3.10198 q^{7} +6.85774 q^{8} +1.00000 q^{9} +9.97074 q^{10} +1.08727 q^{11} -4.65777 q^{12} -2.38226 q^{13} -8.00392 q^{14} -3.86423 q^{15} +8.37926 q^{16} +1.64547 q^{17} +2.58026 q^{18} +0.734719 q^{19} +17.9987 q^{20} +3.10198 q^{21} +2.80545 q^{22} +0.721223 q^{23} -6.85774 q^{24} +9.93229 q^{25} -6.14685 q^{26} -1.00000 q^{27} -14.4483 q^{28} +9.74985 q^{29} -9.97074 q^{30} +7.90522 q^{32} -1.08727 q^{33} +4.24575 q^{34} -11.9868 q^{35} +4.65777 q^{36} +2.32820 q^{37} +1.89577 q^{38} +2.38226 q^{39} +26.4999 q^{40} +4.13476 q^{41} +8.00392 q^{42} +7.57178 q^{43} +5.06425 q^{44} +3.86423 q^{45} +1.86095 q^{46} +1.61129 q^{47} -8.37926 q^{48} +2.62226 q^{49} +25.6279 q^{50} -1.64547 q^{51} -11.0960 q^{52} +3.10341 q^{53} -2.58026 q^{54} +4.20147 q^{55} -21.2726 q^{56} -0.734719 q^{57} +25.1572 q^{58} -10.3370 q^{59} -17.9987 q^{60} -13.5425 q^{61} -3.10198 q^{63} +3.63904 q^{64} -9.20559 q^{65} -2.80545 q^{66} +2.64698 q^{67} +7.66421 q^{68} -0.721223 q^{69} -30.9290 q^{70} -7.51190 q^{71} +6.85774 q^{72} +1.75413 q^{73} +6.00738 q^{74} -9.93229 q^{75} +3.42215 q^{76} -3.37269 q^{77} +6.14685 q^{78} -11.0333 q^{79} +32.3794 q^{80} +1.00000 q^{81} +10.6688 q^{82} -10.9087 q^{83} +14.4483 q^{84} +6.35847 q^{85} +19.5372 q^{86} -9.74985 q^{87} +7.45622 q^{88} -6.14254 q^{89} +9.97074 q^{90} +7.38970 q^{91} +3.35929 q^{92} +4.15756 q^{94} +2.83912 q^{95} -7.90522 q^{96} +12.1208 q^{97} +6.76611 q^{98} +1.08727 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.58026	1.82452	0.912261	−	0.409609i	$-0.134335\pi$
$2$	2.58026	1.82452	0.912261	+	0.409609i	$0.134335\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.65777	2.32888
$5$	3.86423	1.72814	0.864068	−	0.503374i	$-0.167908\pi$
$5$	3.86423	1.72814	0.864068	+	0.503374i	$0.167908\pi$
$6$	−2.58026	−1.05339
$7$	−3.10198	−1.17244	−0.586218	−	0.810153i	$-0.699384\pi$
$7$	−3.10198	−1.17244	−0.586218	+	0.810153i	$0.699384\pi$
$8$	6.85774	2.42458
$9$	1.00000	0.333333
$10$	9.97074	3.15303
$11$	1.08727	0.327824	0.163912	−	0.986475i	$-0.447589\pi$
$11$	1.08727	0.327824	0.163912	+	0.986475i	$0.447589\pi$
$12$	−4.65777	−1.34458
$13$	−2.38226	−0.660719	−0.330359	−	0.943855i	$-0.607170\pi$
$13$	−2.38226	−0.660719	−0.330359	+	0.943855i	$0.607170\pi$
$14$	−8.00392	−2.13914
$15$	−3.86423	−0.997740
$16$	8.37926	2.09481
$17$	1.64547	0.399085	0.199542	−	0.979889i	$-0.436054\pi$
$17$	1.64547	0.399085	0.199542	+	0.979889i	$0.436054\pi$
$18$	2.58026	0.608174
$19$	0.734719	0.168556	0.0842780	−	0.996442i	$-0.473142\pi$
$19$	0.734719	0.168556	0.0842780	+	0.996442i	$0.473142\pi$
$20$	17.9987	4.02463
$21$	3.10198	0.676907
$22$	2.80545	0.598123
$23$	0.721223	0.150385	0.0751927	−	0.997169i	$-0.476043\pi$
$23$	0.721223	0.150385	0.0751927	+	0.997169i	$0.476043\pi$
$24$	−6.85774	−1.39983
$25$	9.93229	1.98646
$26$	−6.14685	−1.20550
$27$	−1.00000	−0.192450
$28$	−14.4483	−2.73047
$29$	9.74985	1.81050	0.905251	−	0.424878i	$-0.139683\pi$
$29$	9.74985	1.81050	0.905251	+	0.424878i	$0.139683\pi$
$30$	−9.97074	−1.82040
$31$	0	0
$31$	0	0
$32$	7.90522	1.39746
$33$	−1.08727	−0.189270
$34$	4.24575	0.728139
$35$	−11.9868	−2.02613
$36$	4.65777	0.776294
$37$	2.32820	0.382754	0.191377	−	0.981517i	$-0.438705\pi$
$37$	2.32820	0.382754	0.191377	+	0.981517i	$0.438705\pi$
$38$	1.89577	0.307534
$39$	2.38226	0.381466
$40$	26.4999	4.19000
$41$	4.13476	0.645741	0.322870	−	0.946443i	$-0.395352\pi$
$41$	4.13476	0.645741	0.322870	+	0.946443i	$0.395352\pi$
$42$	8.00392	1.23503
$43$	7.57178	1.15469	0.577343	−	0.816502i	$-0.304090\pi$
$43$	7.57178	1.15469	0.577343	+	0.816502i	$0.304090\pi$
$44$	5.06425	0.763465
$45$	3.86423	0.576046
$46$	1.86095	0.274382
$47$	1.61129	0.235031	0.117516	−	0.993071i	$-0.462507\pi$
$47$	1.61129	0.235031	0.117516	+	0.993071i	$0.462507\pi$
$48$	−8.37926	−1.20944
$49$	2.62226	0.374608
$50$	25.6279	3.62434
$51$	−1.64547	−0.230412
$52$	−11.0960	−1.53874
$53$	3.10341	0.426287	0.213143	−	0.977021i	$-0.431630\pi$
$53$	3.10341	0.426287	0.213143	+	0.977021i	$0.431630\pi$
$54$	−2.58026	−0.351130
$55$	4.20147	0.566525
$56$	−21.2726	−2.84266
$57$	−0.734719	−0.0973159
$58$	25.1572	3.30330
$59$	−10.3370	−1.34576	−0.672881	−	0.739750i	$-0.734944\pi$
$59$	−10.3370	−1.34576	−0.672881	+	0.739750i	$0.734944\pi$
$60$	−17.9987	−2.32362
$61$	−13.5425	−1.73395	−0.866973	−	0.498355i	$-0.833937\pi$
$61$	−13.5425	−1.73395	−0.866973	+	0.498355i	$0.833937\pi$
$62$	0	0
$63$	−3.10198	−0.390812
$64$	3.63904	0.454880
$65$	−9.20559	−1.14181
$66$	−2.80545	−0.345327
$67$	2.64698	0.323380	0.161690	−	0.986842i	$-0.448306\pi$
$67$	2.64698	0.323380	0.161690	+	0.986842i	$0.448306\pi$
$68$	7.66421	0.929422
$69$	−0.721223	−0.0868251
$70$	−30.9290	−3.69672
$71$	−7.51190	−0.891499	−0.445749	−	0.895158i	$-0.647063\pi$
$71$	−7.51190	−0.891499	−0.445749	+	0.895158i	$0.647063\pi$
$72$	6.85774	0.808193
$73$	1.75413	0.205306	0.102653	−	0.994717i	$-0.467267\pi$
$73$	1.75413	0.205306	0.102653	+	0.994717i	$0.467267\pi$
$74$	6.00738	0.698343
$75$	−9.93229	−1.14688
$76$	3.42215	0.392547
$77$	−3.37269	−0.384353
$78$	6.14685	0.695994
$79$	−11.0333	−1.24134	−0.620670	−	0.784072i	$-0.713139\pi$
$79$	−11.0333	−1.24134	−0.620670	+	0.784072i	$0.713139\pi$
$80$	32.3794	3.62013
$81$	1.00000	0.111111
$82$	10.6688	1.17817
$83$	−10.9087	−1.19738	−0.598692	−	0.800979i	$-0.704313\pi$
$83$	−10.9087	−1.19738	−0.598692	+	0.800979i	$0.704313\pi$
$84$	14.4483	1.57644
$85$	6.35847	0.689673
$86$	19.5372	2.10675
$87$	−9.74985	−1.04529
$88$	7.45622	0.794836
$89$	−6.14254	−0.651108	−0.325554	−	0.945523i	$-0.605551\pi$
$89$	−6.14254	−0.651108	−0.325554	+	0.945523i	$0.605551\pi$
$90$	9.97074	1.05101
$91$	7.38970	0.774651
$92$	3.35929	0.350230
$93$	0	0
$94$	4.15756	0.428820
$95$	2.83912	0.291288
$96$	−7.90522	−0.806823
$97$	12.1208	1.23068	0.615339	−	0.788263i	$-0.289019\pi$
$97$	12.1208	1.23068	0.615339	+	0.788263i	$0.289019\pi$
$98$	6.76611	0.683481
$99$	1.08727	0.109275
$100$	46.2623	4.62623
$101$	9.66716	0.961918	0.480959	−	0.876743i	$-0.340289\pi$
$101$	9.66716	0.961918	0.480959	+	0.876743i	$0.340289\pi$
$102$	−4.24575	−0.420391
$103$	−5.58949	−0.550749	−0.275374	−	0.961337i	$-0.588802\pi$
$103$	−5.58949	−0.550749	−0.275374	+	0.961337i	$0.588802\pi$
$104$	−16.3369	−1.60196
$105$	11.9868	1.16979
$106$	8.00763	0.777770
$107$	−4.18641	−0.404715	−0.202358	−	0.979312i	$-0.564860\pi$
$107$	−4.18641	−0.404715	−0.202358	+	0.979312i	$0.564860\pi$
$108$	−4.65777	−0.448194
$109$	−5.46382	−0.523339	−0.261670	−	0.965158i	$-0.584273\pi$
$109$	−5.46382	−0.523339	−0.261670	+	0.965158i	$0.584273\pi$
$110$	10.8409	1.03364
$111$	−2.32820	−0.220983
$112$	−25.9923	−2.45604
$113$	−14.6554	−1.37866	−0.689332	−	0.724446i	$-0.742096\pi$
$113$	−14.6554	−1.37866	−0.689332	+	0.724446i	$0.742096\pi$
$114$	−1.89577	−0.177555
$115$	2.78697	0.259887
$116$	45.4125	4.21645
$117$	−2.38226	−0.220240
$118$	−26.6722	−2.45537
$119$	−5.10420	−0.467902
$120$	−26.4999	−2.41910
$121$	−9.81784	−0.892531
$122$	−34.9434	−3.16362
$123$	−4.13476	−0.372819
$124$	0	0
$125$	19.0595	1.70473
$126$	−8.00392	−0.713046
$127$	14.0236	1.24440	0.622198	−	0.782860i	$-0.286240\pi$
$127$	14.0236	1.24440	0.622198	+	0.782860i	$0.286240\pi$
$128$	−6.42074	−0.567519
$129$	−7.57178	−0.666658
$130$	−23.7529	−2.08326
$131$	−13.8383	−1.20906	−0.604530	−	0.796582i	$-0.706639\pi$
$131$	−13.8383	−1.20906	−0.604530	+	0.796582i	$0.706639\pi$
$132$	−5.06425	−0.440787
$133$	−2.27908	−0.197621
$134$	6.82991	0.590014
$135$	−3.86423	−0.332580
$136$	11.2842	0.967612
$137$	−5.65526	−0.483162	−0.241581	−	0.970381i	$-0.577666\pi$
$137$	−5.65526	−0.483162	−0.241581	+	0.970381i	$0.577666\pi$
$138$	−1.86095	−0.158414
$139$	5.65555	0.479697	0.239849	−	0.970810i	$-0.422902\pi$
$139$	5.65555	0.479697	0.239849	+	0.970810i	$0.422902\pi$
$140$	−55.8315	−4.71862
$141$	−1.61129	−0.135695
$142$	−19.3827	−1.62656
$143$	−2.59016	−0.216600
$144$	8.37926	0.698271
$145$	37.6757	3.12879
$146$	4.52613	0.374585
$147$	−2.62226	−0.216280
$148$	10.8442	0.891390
$149$	16.8713	1.38215	0.691075	−	0.722783i	$-0.257137\pi$
$149$	16.8713	1.38215	0.691075	+	0.722783i	$0.257137\pi$
$150$	−25.6279	−2.09251
$151$	−4.51447	−0.367382	−0.183691	−	0.982984i	$-0.558805\pi$
$151$	−4.51447	−0.367382	−0.183691	+	0.982984i	$0.558805\pi$
$152$	5.03851	0.408677
$153$	1.64547	0.133028
$154$	−8.70243	−0.701261
$155$	0	0
$156$	11.0960	0.888390
$157$	−7.86426	−0.627636	−0.313818	−	0.949483i	$-0.601608\pi$
$157$	−7.86426	−0.627636	−0.313818	+	0.949483i	$0.601608\pi$
$158$	−28.4688	−2.26485
$159$	−3.10341	−0.246117
$160$	30.5476	2.41500
$161$	−2.23722	−0.176317
$162$	2.58026	0.202725
$163$	13.0213	1.01990	0.509952	−	0.860203i	$-0.329663\pi$
$163$	13.0213	1.01990	0.509952	+	0.860203i	$0.329663\pi$
$164$	19.2587	1.50385
$165$	−4.20147	−0.327084
$166$	−28.1473	−2.18465
$167$	−21.2748	−1.64629	−0.823147	−	0.567828i	$-0.807784\pi$
$167$	−21.2748	−1.64629	−0.823147	+	0.567828i	$0.807784\pi$
$168$	21.2726	1.64121
$169$	−7.32486	−0.563451
$170$	16.4065	1.25832
$171$	0.734719	0.0561854
$172$	35.2676	2.68913
$173$	−12.7005	−0.965602	−0.482801	−	0.875730i	$-0.660381\pi$
$173$	−12.7005	−0.965602	−0.482801	+	0.875730i	$0.660381\pi$
$174$	−25.1572	−1.90716
$175$	−30.8097	−2.32900
$176$	9.11052	0.686731
$177$	10.3370	0.776976
$178$	−15.8494	−1.18796
$179$	−15.2940	−1.14312	−0.571562	−	0.820559i	$-0.693662\pi$
$179$	−15.2940	−1.14312	−0.571562	+	0.820559i	$0.693662\pi$
$180$	17.9987	1.34154
$181$	17.0478	1.26715	0.633576	−	0.773681i	$-0.281586\pi$
$181$	17.0478	1.26715	0.633576	+	0.773681i	$0.281586\pi$
$182$	19.0674	1.41337
$183$	13.5425	1.00109
$184$	4.94596	0.364621
$185$	8.99671	0.661451
$186$	0	0
$187$	1.78907	0.130830
$188$	7.50502	0.547360
$189$	3.10198	0.225636
$190$	7.32569	0.531462
$191$	−9.61692	−0.695856	−0.347928	−	0.937521i	$-0.613115\pi$
$191$	−9.61692	−0.695856	−0.347928	+	0.937521i	$0.613115\pi$
$192$	−3.63904	−0.262625
$193$	9.90492	0.712971	0.356486	−	0.934301i	$-0.383975\pi$
$193$	9.90492	0.712971	0.356486	+	0.934301i	$0.383975\pi$
$194$	31.2748	2.24540
$195$	9.20559	0.659226
$196$	12.2139	0.872418
$197$	−22.5567	−1.60710	−0.803549	−	0.595239i	$-0.797058\pi$
$197$	−22.5567	−1.60710	−0.803549	+	0.595239i	$0.797058\pi$
$198$	2.80545	0.199374
$199$	7.96086	0.564331	0.282165	−	0.959366i	$-0.408947\pi$
$199$	7.96086	0.564331	0.282165	+	0.959366i	$0.408947\pi$
$200$	68.1131	4.81632
$201$	−2.64698	−0.186704
$202$	24.9438	1.75504
$203$	−30.2438	−2.12270
$204$	−7.66421	−0.536602
$205$	15.9777	1.11593
$206$	−14.4224	−1.00485
$207$	0.721223	0.0501285
$208$	−19.9615	−1.38408
$209$	0.798838	0.0552568
$210$	30.9290	2.13430
$211$	7.35729	0.506496	0.253248	−	0.967401i	$-0.418501\pi$
$211$	7.35729	0.506496	0.253248	+	0.967401i	$0.418501\pi$
$212$	14.4550	0.992772
$213$	7.51190	0.514707
$214$	−10.8020	−0.738413
$215$	29.2591	1.99546
$216$	−6.85774	−0.466610
$217$	0	0
$218$	−14.0981	−0.954844
$219$	−1.75413	−0.118533
$220$	19.5694	1.31937
$221$	−3.91993	−0.263683
$222$	−6.00738	−0.403189
$223$	23.4532	1.57054	0.785271	−	0.619152i	$-0.212524\pi$
$223$	23.4532	1.57054	0.785271	+	0.619152i	$0.212524\pi$
$224$	−24.5218	−1.63843
$225$	9.93229	0.662152
$226$	−37.8148	−2.51540
$227$	2.89323	0.192031	0.0960153	−	0.995380i	$-0.469390\pi$
$227$	2.89323	0.192031	0.0960153	+	0.995380i	$0.469390\pi$
$228$	−3.42215	−0.226637
$229$	−6.05191	−0.399921	−0.199961	−	0.979804i	$-0.564081\pi$
$229$	−6.05191	−0.399921	−0.199961	+	0.979804i	$0.564081\pi$
$230$	7.19113	0.474169
$231$	3.37269	0.221907
$232$	66.8620	4.38970
$233$	23.3961	1.53273	0.766366	−	0.642404i	$-0.222063\pi$
$233$	23.3961	1.53273	0.766366	+	0.642404i	$0.222063\pi$
$234$	−6.14685	−0.401832
$235$	6.22640	0.406166
$236$	−48.1473	−3.13412
$237$	11.0333	0.716688
$238$	−13.1702	−0.853697
$239$	10.3681	0.670654	0.335327	−	0.942102i	$-0.391153\pi$
$239$	10.3681	0.670654	0.335327	+	0.942102i	$0.391153\pi$
$240$	−32.3794	−2.09008
$241$	−8.27977	−0.533347	−0.266674	−	0.963787i	$-0.585925\pi$
$241$	−8.27977	−0.533347	−0.266674	+	0.963787i	$0.585925\pi$
$242$	−25.3326	−1.62844
$243$	−1.00000	−0.0641500
$244$	−63.0780	−4.03816
$245$	10.1330	0.647374
$246$	−10.6688	−0.680216
$247$	−1.75029	−0.111368
$248$	0	0
$249$	10.9087	0.691310
$250$	49.1785	3.11032
$251$	6.90761	0.436004	0.218002	−	0.975948i	$-0.430046\pi$
$251$	6.90761	0.436004	0.218002	+	0.975948i	$0.430046\pi$
$252$	−14.4483	−0.910156
$253$	0.784165	0.0493000
$254$	36.1847	2.27043
$255$	−6.35847	−0.398183
$256$	−23.8453	−1.49033
$257$	24.6807	1.53954	0.769769	−	0.638323i	$-0.220372\pi$
$257$	24.6807	1.53954	0.769769	+	0.638323i	$0.220372\pi$
$258$	−19.5372	−1.21633
$259$	−7.22203	−0.448755
$260$	−42.8775	−2.65915
$261$	9.74985	0.603501
$262$	−35.7066	−2.20596
$263$	23.5751	1.45371	0.726853	−	0.686793i	$-0.240982\pi$
$263$	23.5751	1.45371	0.726853	+	0.686793i	$0.240982\pi$
$264$	−7.45622	−0.458899
$265$	11.9923	0.736682
$266$	−5.88063	−0.360565
$267$	6.14254	0.375918
$268$	12.3290	0.753114
$269$	−0.946528	−0.0577108	−0.0288554	−	0.999584i	$-0.509186\pi$
$269$	−0.946528	−0.0577108	−0.0288554	+	0.999584i	$0.509186\pi$
$270$	−9.97074	−0.606800
$271$	−31.2388	−1.89762	−0.948812	−	0.315841i	$-0.897713\pi$
$271$	−31.2388	−1.89762	−0.948812	+	0.315841i	$0.897713\pi$
$272$	13.7878	0.836009
$273$	−7.38970	−0.447245
$274$	−14.5921	−0.881540
$275$	10.7991	0.651209
$276$	−3.35929	−0.202205
$277$	−27.6624	−1.66207	−0.831037	−	0.556217i	$-0.812252\pi$
$277$	−27.6624	−1.66207	−0.831037	+	0.556217i	$0.812252\pi$
$278$	14.5928	0.875219
$279$	0	0
$280$	−82.2021	−4.91251
$281$	−8.27017	−0.493357	−0.246679	−	0.969097i	$-0.579339\pi$
$281$	−8.27017	−0.493357	−0.246679	+	0.969097i	$0.579339\pi$
$282$	−4.15756	−0.247579
$283$	0.824691	0.0490228	0.0245114	−	0.999700i	$-0.492197\pi$
$283$	0.824691	0.0490228	0.0245114	+	0.999700i	$0.492197\pi$
$284$	−34.9887	−2.07620
$285$	−2.83912	−0.168175
$286$	−6.68329	−0.395191
$287$	−12.8259	−0.757090
$288$	7.90522	0.465819
$289$	−14.2924	−0.840731
$290$	97.2132	5.70856
$291$	−12.1208	−0.710532
$292$	8.17035	0.478134
$293$	−3.52533	−0.205952	−0.102976	−	0.994684i	$-0.532837\pi$
$293$	−3.52533	−0.205952	−0.102976	+	0.994684i	$0.532837\pi$
$294$	−6.76611	−0.394608
$295$	−39.9446	−2.32566
$296$	15.9662	0.928017
$297$	−1.08727	−0.0630898
$298$	43.5324	2.52176
$299$	−1.71814	−0.0993625
$300$	−46.2623	−2.67095
$301$	−23.4875	−1.35380
$302$	−11.6485	−0.670297
$303$	−9.66716	−0.555364
$304$	6.15640	0.353094
$305$	−52.3315	−2.99650
$306$	4.24575	0.242713
$307$	−8.90949	−0.508492	−0.254246	−	0.967140i	$-0.581827\pi$
$307$	−8.90949	−0.508492	−0.254246	+	0.967140i	$0.581827\pi$
$308$	−15.7092	−0.895114
$309$	5.58949	0.317975
$310$	0	0
$311$	−26.1174	−1.48098	−0.740491	−	0.672066i	$-0.765407\pi$
$311$	−26.1174	−1.48098	−0.740491	+	0.672066i	$0.765407\pi$
$312$	16.3369	0.924894
$313$	5.07685	0.286961	0.143480	−	0.989653i	$-0.454171\pi$
$313$	5.07685	0.286961	0.143480	+	0.989653i	$0.454171\pi$
$314$	−20.2919	−1.14514
$315$	−11.9868	−0.675377
$316$	−51.3904	−2.89094
$317$	5.58200	0.313516	0.156758	−	0.987637i	$-0.449896\pi$
$317$	5.58200	0.313516	0.156758	+	0.987637i	$0.449896\pi$
$318$	−8.00763	−0.449045
$319$	10.6007	0.593527
$320$	14.0621	0.786096
$321$	4.18641	0.233663
$322$	−5.77261	−0.321695
$323$	1.20896	0.0672682
$324$	4.65777	0.258765
$325$	−23.6612	−1.31249
$326$	33.5983	1.86084
$327$	5.46382	0.302150
$328$	28.3551	1.56565
$329$	−4.99819	−0.275559
$330$	−10.8409	−0.596772
$331$	3.69260	0.202963	0.101482	−	0.994837i	$-0.467642\pi$
$331$	3.69260	0.202963	0.101482	+	0.994837i	$0.467642\pi$
$332$	−50.8101	−2.78857
$333$	2.32820	0.127585
$334$	−54.8947	−3.00370
$335$	10.2285	0.558845
$336$	25.9923	1.41799
$337$	32.9508	1.79494	0.897472	−	0.441072i	$-0.145402\pi$
$337$	32.9508	1.79494	0.897472	+	0.441072i	$0.145402\pi$
$338$	−18.9001	−1.02803
$339$	14.6554	0.795972
$340$	29.6163	1.60617
$341$	0	0
$342$	1.89577	0.102511
$343$	13.5797	0.733233
$344$	51.9253	2.79963
$345$	−2.78697	−0.150046
$346$	−32.7707	−1.76176
$347$	7.70902	0.413842	0.206921	−	0.978358i	$-0.433656\pi$
$347$	7.70902	0.413842	0.206921	+	0.978358i	$0.433656\pi$
$348$	−45.4125	−2.43437
$349$	25.5894	1.36977	0.684886	−	0.728651i	$-0.259852\pi$
$349$	25.5894	1.36977	0.684886	+	0.728651i	$0.259852\pi$
$350$	−79.4972	−4.24931
$351$	2.38226	0.127155
$352$	8.59511	0.458121
$353$	7.98710	0.425111	0.212555	−	0.977149i	$-0.431821\pi$
$353$	7.98710	0.425111	0.212555	+	0.977149i	$0.431821\pi$
$354$	26.6722	1.41761
$355$	−29.0277	−1.54063
$356$	−28.6105	−1.51636
$357$	5.10420	0.270143
$358$	−39.4625	−2.08566
$359$	4.71728	0.248968	0.124484	−	0.992222i	$-0.460272\pi$
$359$	4.71728	0.248968	0.124484	+	0.992222i	$0.460272\pi$
$360$	26.4999	1.39667
$361$	−18.4602	−0.971589
$362$	43.9878	2.31195
$363$	9.81784	0.515303
$364$	34.4195	1.80407
$365$	6.77838	0.354797
$366$	34.9434	1.82652
$367$	−24.4913	−1.27843	−0.639217	−	0.769027i	$-0.720741\pi$
$367$	−24.4913	−1.27843	−0.639217	+	0.769027i	$0.720741\pi$
$368$	6.04332	0.315030
$369$	4.13476	0.215247
$370$	23.2139	1.20683
$371$	−9.62671	−0.499794
$372$	0	0
$373$	1.58686	0.0821647	0.0410824	−	0.999156i	$-0.486919\pi$
$373$	1.58686	0.0821647	0.0410824	+	0.999156i	$0.486919\pi$
$374$	4.61627	0.238702
$375$	−19.0595	−0.984228
$376$	11.0498	0.569851
$377$	−23.2266	−1.19623
$378$	8.00392	0.411677
$379$	7.67520	0.394249	0.197124	−	0.980378i	$-0.436840\pi$
$379$	7.67520	0.394249	0.197124	+	0.980378i	$0.436840\pi$
$380$	13.2240	0.678376
$381$	−14.0236	−0.718453
$382$	−24.8142	−1.26961
$383$	11.7282	0.599281	0.299641	−	0.954052i	$-0.403133\pi$
$383$	11.7282	0.599281	0.299641	+	0.954052i	$0.403133\pi$
$384$	6.42074	0.327657
$385$	−13.0328	−0.664215
$386$	25.5573	1.30083
$387$	7.57178	0.384895
$388$	56.4557	2.86611
$389$	4.61015	0.233744	0.116872	−	0.993147i	$-0.462713\pi$
$389$	4.61015	0.233744	0.116872	+	0.993147i	$0.462713\pi$
$390$	23.7529	1.20277
$391$	1.18675	0.0600165
$392$	17.9828	0.908266
$393$	13.8383	0.698052
$394$	−58.2022	−2.93219
$395$	−42.6351	−2.14521
$396$	5.06425	0.254488
$397$	32.1078	1.61145	0.805723	−	0.592293i	$-0.201777\pi$
$397$	32.1078	1.61145	0.805723	+	0.592293i	$0.201777\pi$
$398$	20.5411	1.02963
$399$	2.27908	0.114097
$400$	83.2252	4.16126
$401$	−2.47207	−0.123449	−0.0617246	−	0.998093i	$-0.519660\pi$
$401$	−2.47207	−0.123449	−0.0617246	+	0.998093i	$0.519660\pi$
$402$	−6.82991	−0.340645
$403$	0	0
$404$	45.0274	2.24019
$405$	3.86423	0.192015
$406$	−78.0370	−3.87291
$407$	2.53139	0.125476
$408$	−11.2842	−0.558651
$409$	−20.3157	−1.00455	−0.502274	−	0.864708i	$-0.667503\pi$
$409$	−20.3157	−1.00455	−0.502274	+	0.864708i	$0.667503\pi$
$410$	41.2266	2.03604
$411$	5.65526	0.278954
$412$	−26.0345	−1.28263
$413$	32.0651	1.57782
$414$	1.86095	0.0914606
$415$	−42.1537	−2.06924
$416$	−18.8323	−0.923327
$417$	−5.65555	−0.276953
$418$	2.06121	0.100817
$419$	−14.0955	−0.688609	−0.344305	−	0.938858i	$-0.611885\pi$
$419$	−14.0955	−0.688609	−0.344305	+	0.938858i	$0.611885\pi$
$420$	55.8315	2.72430
$421$	−7.71964	−0.376232	−0.188116	−	0.982147i	$-0.560238\pi$
$421$	−7.71964	−0.376232	−0.188116	+	0.982147i	$0.560238\pi$
$422$	18.9837	0.924114
$423$	1.61129	0.0783437
$424$	21.2824	1.03357
$425$	16.3433	0.792765
$426$	19.3827	0.939095
$427$	42.0087	2.03294
$428$	−19.4993	−0.942535
$429$	2.59016	0.125054
$430$	75.4963	3.64075
$431$	26.2177	1.26286	0.631431	−	0.775432i	$-0.282468\pi$
$431$	26.2177	1.26286	0.631431	+	0.775432i	$0.282468\pi$
$432$	−8.37926	−0.403147
$433$	−22.6643	−1.08918	−0.544589	−	0.838703i	$-0.683315\pi$
$433$	−22.6643	−1.08918	−0.544589	+	0.838703i	$0.683315\pi$
$434$	0	0
$435$	−37.6757	−1.80641
$436$	−25.4492	−1.21880
$437$	0.529896	0.0253484
$438$	−4.52613	−0.216267
$439$	22.0685	1.05327	0.526636	−	0.850091i	$-0.323453\pi$
$439$	22.0685	1.05327	0.526636	+	0.850091i	$0.323453\pi$
$440$	28.8126	1.37359
$441$	2.62226	0.124869
$442$	−10.1145	−0.481095
$443$	−4.25435	−0.202130	−0.101065	−	0.994880i	$-0.532225\pi$
$443$	−4.25435	−0.202130	−0.101065	+	0.994880i	$0.532225\pi$
$444$	−10.8442	−0.514644
$445$	−23.7362	−1.12520
$446$	60.5155	2.86549
$447$	−16.8713	−0.797985
$448$	−11.2882	−0.533319
$449$	−31.8722	−1.50414	−0.752071	−	0.659082i	$-0.770945\pi$
$449$	−31.8722	−1.50414	−0.752071	+	0.659082i	$0.770945\pi$
$450$	25.6279	1.20811
$451$	4.49560	0.211690
$452$	−68.2614	−3.21075
$453$	4.51447	0.212108
$454$	7.46531	0.350364
$455$	28.5555	1.33870
$456$	−5.03851	−0.235950
$457$	8.27886	0.387269	0.193634	−	0.981074i	$-0.437972\pi$
$457$	8.27886	0.387269	0.193634	+	0.981074i	$0.437972\pi$
$458$	−15.6155	−0.729666
$459$	−1.64547	−0.0768039
$460$	12.9811	0.605246
$461$	11.2601	0.524434	0.262217	−	0.965009i	$-0.415546\pi$
$461$	11.2601	0.524434	0.262217	+	0.965009i	$0.415546\pi$
$462$	8.70243	0.404874
$463$	20.4729	0.951458	0.475729	−	0.879592i	$-0.342184\pi$
$463$	20.4729	0.951458	0.475729	+	0.879592i	$0.342184\pi$
$464$	81.6965	3.79266
$465$	0	0
$466$	60.3682	2.79650
$467$	−23.9348	−1.10757	−0.553786	−	0.832659i	$-0.686817\pi$
$467$	−23.9348	−1.10757	−0.553786	+	0.832659i	$0.686817\pi$
$468$	−11.0960	−0.512912
$469$	−8.21087	−0.379143
$470$	16.0658	0.741059
$471$	7.86426	0.362366
$472$	−70.8885	−3.26291
$473$	8.23258	0.378534
$474$	28.4688	1.30761
$475$	7.29744	0.334829
$476$	−23.7742	−1.08969
$477$	3.10341	0.142096
$478$	26.7524	1.22362
$479$	16.7678	0.766141	0.383070	−	0.923719i	$-0.374867\pi$
$479$	16.7678	0.766141	0.383070	+	0.923719i	$0.374867\pi$
$480$	−30.5476	−1.39430
$481$	−5.54637	−0.252893
$482$	−21.3640	−0.973104
$483$	2.23722	0.101797
$484$	−45.7292	−2.07860
$485$	46.8375	2.12678
$486$	−2.58026	−0.117043
$487$	3.68419	0.166946	0.0834732	−	0.996510i	$-0.473399\pi$
$487$	3.68419	0.166946	0.0834732	+	0.996510i	$0.473399\pi$
$488$	−92.8713	−4.20409
$489$	−13.0213	−0.588841
$490$	26.1458	1.18115
$491$	3.86352	0.174358	0.0871791	−	0.996193i	$-0.472215\pi$
$491$	3.86352	0.174358	0.0871791	+	0.996193i	$0.472215\pi$
$492$	−19.2587	−0.868251
$493$	16.0431	0.722544
$494$	−4.51621	−0.203194
$495$	4.20147	0.188842
$496$	0	0
$497$	23.3017	1.04523
$498$	28.1473	1.26131
$499$	27.2696	1.22075	0.610377	−	0.792111i	$-0.291018\pi$
$499$	27.2696	1.22075	0.610377	+	0.792111i	$0.291018\pi$
$500$	88.7747	3.97012
$501$	21.2748	0.950489
$502$	17.8235	0.795500
$503$	−10.3585	−0.461865	−0.230932	−	0.972970i	$-0.574178\pi$
$503$	−10.3585	−0.461865	−0.230932	+	0.972970i	$0.574178\pi$
$504$	−21.2726	−0.947555
$505$	37.3561	1.66233
$506$	2.02335	0.0899490
$507$	7.32486	0.325308
$508$	65.3188	2.89806
$509$	−28.6661	−1.27060	−0.635302	−	0.772264i	$-0.719124\pi$
$509$	−28.6661	−1.27060	−0.635302	+	0.772264i	$0.719124\pi$
$510$	−16.4065	−0.726494
$511$	−5.44128	−0.240708
$512$	−48.6857	−2.15162
$513$	−0.734719	−0.0324386
$514$	63.6826	2.80892
$515$	−21.5991	−0.951769
$516$	−35.2676	−1.55257
$517$	1.75191	0.0770489
$518$	−18.6347	−0.818764
$519$	12.7005	0.557491
$520$	−63.1295	−2.76841
$521$	−8.78711	−0.384970	−0.192485	−	0.981300i	$-0.561655\pi$
$521$	−8.78711	−0.384970	−0.192485	+	0.981300i	$0.561655\pi$
$522$	25.1572	1.10110
$523$	−36.7643	−1.60759	−0.803795	−	0.594906i	$-0.797189\pi$
$523$	−36.7643	−1.60759	−0.803795	+	0.594906i	$0.797189\pi$
$524$	−64.4557	−2.81576
$525$	30.8097	1.34465
$526$	60.8301	2.65232
$527$	0	0
$528$	−9.11052	−0.396484
$529$	−22.4798	−0.977384
$530$	30.9433	1.34409
$531$	−10.3370	−0.448588
$532$	−10.6154	−0.460237
$533$	−9.85005	−0.426653
$534$	15.8494	0.685870
$535$	−16.1773	−0.699404
$536$	18.1523	0.784060
$537$	15.2940	0.659983
$538$	−2.44229	−0.105295
$539$	2.85110	0.122806
$540$	−17.9987	−0.774540
$541$	6.05265	0.260224	0.130112	−	0.991499i	$-0.458466\pi$
$541$	6.05265	0.260224	0.130112	+	0.991499i	$0.458466\pi$
$542$	−80.6045	−3.46226
$543$	−17.0478	−0.731590
$544$	13.0078	0.557704
$545$	−21.1135	−0.904402
$546$	−19.0674	−0.816009
$547$	−3.89390	−0.166491	−0.0832456	−	0.996529i	$-0.526529\pi$
$547$	−3.89390	−0.166491	−0.0832456	+	0.996529i	$0.526529\pi$
$548$	−26.3409	−1.12523
$549$	−13.5425	−0.577982
$550$	27.8645	1.18815
$551$	7.16340	0.305171
$552$	−4.94596	−0.210514
$553$	34.2249	1.45539
$554$	−71.3764	−3.03249
$555$	−8.99671	−0.381889
$556$	26.3422	1.11716
$557$	−36.1880	−1.53334	−0.766668	−	0.642044i	$-0.778087\pi$
$557$	−36.1880	−1.53334	−0.766668	+	0.642044i	$0.778087\pi$
$558$	0	0
$559$	−18.0379	−0.762923
$560$	−100.440	−4.24437
$561$	−1.78907	−0.0755346
$562$	−21.3392	−0.900141
$563$	10.9590	0.461866	0.230933	−	0.972970i	$-0.425822\pi$
$563$	10.9590	0.461866	0.230933	+	0.972970i	$0.425822\pi$
$564$	−7.50502	−0.316018
$565$	−56.6318	−2.38252
$566$	2.12792	0.0894432
$567$	−3.10198	−0.130271
$568$	−51.5147	−2.16151
$569$	−5.73959	−0.240616	−0.120308	−	0.992737i	$-0.538388\pi$
$569$	−5.73959	−0.240616	−0.120308	+	0.992737i	$0.538388\pi$
$570$	−7.32569	−0.306840
$571$	20.8084	0.870804	0.435402	−	0.900236i	$-0.356606\pi$
$571$	20.8084	0.870804	0.435402	+	0.900236i	$0.356606\pi$
$572$	−12.0643	−0.504436
$573$	9.61692	0.401753
$574$	−33.0943	−1.38133
$575$	7.16340	0.298734
$576$	3.63904	0.151627
$577$	2.23922	0.0932200	0.0466100	−	0.998913i	$-0.485158\pi$
$577$	2.23922	0.0932200	0.0466100	+	0.998913i	$0.485158\pi$
$578$	−36.8783	−1.53393
$579$	−9.90492	−0.411634
$580$	175.485	7.28660
$581$	33.8385	1.40386
$582$	−31.2748	−1.29638
$583$	3.37425	0.139747
$584$	12.0294	0.497780
$585$	−9.20559	−0.380604
$586$	−9.09629	−0.375764
$587$	10.8329	0.447123	0.223561	−	0.974690i	$-0.428232\pi$
$587$	10.8329	0.447123	0.223561	+	0.974690i	$0.428232\pi$
$588$	−12.2139	−0.503691
$589$	0	0
$590$	−103.068	−4.24322
$591$	22.5567	0.927858
$592$	19.5086	0.801799
$593$	7.75050	0.318275	0.159138	−	0.987256i	$-0.449129\pi$
$593$	7.75050	0.318275	0.159138	+	0.987256i	$0.449129\pi$
$594$	−2.80545	−0.115109
$595$	−19.7238	−0.808598
$596$	78.5825	3.21887
$597$	−7.96086	−0.325817
$598$	−4.43325	−0.181289
$599$	−7.98293	−0.326174	−0.163087	−	0.986612i	$-0.552145\pi$
$599$	−7.98293	−0.326174	−0.163087	+	0.986612i	$0.552145\pi$
$600$	−68.1131	−2.78070
$601$	−25.6884	−1.04785	−0.523927	−	0.851763i	$-0.675533\pi$
$601$	−25.6884	−1.04785	−0.523927	+	0.851763i	$0.675533\pi$
$602$	−60.6039	−2.47003
$603$	2.64698	0.107793
$604$	−21.0273	−0.855590
$605$	−37.9384	−1.54242
$606$	−24.9438	−1.01327
$607$	−17.6504	−0.716408	−0.358204	−	0.933643i	$-0.616611\pi$
$607$	−17.6504	−0.716408	−0.358204	+	0.933643i	$0.616611\pi$
$608$	5.80811	0.235550
$609$	30.2438	1.22554
$610$	−135.029	−5.46717
$611$	−3.83851	−0.155289
$612$	7.66421	0.309807
$613$	42.4045	1.71270	0.856351	−	0.516393i	$-0.172726\pi$
$613$	42.4045	1.71270	0.856351	+	0.516393i	$0.172726\pi$
$614$	−22.9889	−0.927755
$615$	−15.9777	−0.644282
$616$	−23.1290	−0.931895
$617$	34.0867	1.37228	0.686140	−	0.727469i	$-0.259304\pi$
$617$	34.0867	1.37228	0.686140	+	0.727469i	$0.259304\pi$
$618$	14.4224	0.580152
$619$	6.20601	0.249441	0.124720	−	0.992192i	$-0.460197\pi$
$619$	6.20601	0.249441	0.124720	+	0.992192i	$0.460197\pi$
$620$	0	0
$621$	−0.721223	−0.0289417
$622$	−67.3898	−2.70209
$623$	19.0540	0.763383
$624$	19.9615	0.799101
$625$	23.9889	0.959555
$626$	13.0996	0.523566
$627$	−0.798838	−0.0319025
$628$	−36.6299	−1.46169
$629$	3.83098	0.152751
$630$	−30.9290	−1.23224
$631$	−20.7176	−0.824754	−0.412377	−	0.911013i	$-0.635301\pi$
$631$	−20.7176	−0.824754	−0.412377	+	0.911013i	$0.635301\pi$
$632$	−75.6633	−3.00973
$633$	−7.35729	−0.292426
$634$	14.4030	0.572017
$635$	54.1906	2.15049
$636$	−14.4550	−0.573177
$637$	−6.24688	−0.247510
$638$	27.3527	1.08290
$639$	−7.51190	−0.297166
$640$	−24.8112	−0.980750
$641$	39.5010	1.56019	0.780097	−	0.625659i	$-0.215170\pi$
$641$	39.5010	1.56019	0.780097	+	0.625659i	$0.215170\pi$
$642$	10.8020	0.426323
$643$	−31.5689	−1.24496	−0.622478	−	0.782637i	$-0.713874\pi$
$643$	−31.5689	−1.24496	−0.622478	+	0.782637i	$0.713874\pi$
$644$	−10.4204	−0.410623
$645$	−29.2591	−1.15208
$646$	3.11943	0.122732
$647$	27.1258	1.06643	0.533213	−	0.845981i	$-0.320984\pi$
$647$	27.1258	1.06643	0.533213	+	0.845981i	$0.320984\pi$
$648$	6.85774	0.269398
$649$	−11.2391	−0.441174
$650$	−61.0523	−2.39467
$651$	0	0
$652$	60.6500	2.37524
$653$	−0.530714	−0.0207685	−0.0103842	−	0.999946i	$-0.503305\pi$
$653$	−0.530714	−0.0207685	−0.0103842	+	0.999946i	$0.503305\pi$
$654$	14.0981	0.551280
$655$	−53.4745	−2.08942
$656$	34.6462	1.35271
$657$	1.75413	0.0684353
$658$	−12.8966	−0.502764
$659$	−15.8184	−0.616196	−0.308098	−	0.951355i	$-0.599692\pi$
$659$	−15.8184	−0.616196	−0.308098	+	0.951355i	$0.599692\pi$
$660$	−19.5694	−0.761740
$661$	40.0483	1.55770	0.778849	−	0.627212i	$-0.215804\pi$
$661$	40.0483	1.55770	0.778849	+	0.627212i	$0.215804\pi$
$662$	9.52788	0.370311
$663$	3.91993	0.152237
$664$	−74.8090	−2.90315
$665$	−8.80690	−0.341517
$666$	6.00738	0.232781
$667$	7.03182	0.272273
$668$	−99.0931	−3.83403
$669$	−23.4532	−0.906753
$670$	26.3923	1.01963
$671$	−14.7244	−0.568430
$672$	24.5218	0.945949
$673$	14.4709	0.557811	0.278905	−	0.960319i	$-0.410028\pi$
$673$	14.4709	0.557811	0.278905	+	0.960319i	$0.410028\pi$
$674$	85.0217	3.27491
$675$	−9.93229	−0.382294
$676$	−34.1175	−1.31221
$677$	26.3074	1.01108	0.505538	−	0.862804i	$-0.331294\pi$
$677$	26.3074	1.01108	0.505538	+	0.862804i	$0.331294\pi$
$678$	37.8148	1.45227
$679$	−37.5983	−1.44289
$680$	43.6048	1.67217
$681$	−2.89323	−0.110869
$682$	0	0
$683$	4.22266	0.161575	0.0807877	−	0.996731i	$-0.474256\pi$
$683$	4.22266	0.161575	0.0807877	+	0.996731i	$0.474256\pi$
$684$	3.42215	0.130849
$685$	−21.8532	−0.834970
$686$	35.0391	1.33780
$687$	6.05191	0.230895
$688$	63.4459	2.41885
$689$	−7.39312	−0.281656
$690$	−7.19113	−0.273762
$691$	−35.0184	−1.33216	−0.666081	−	0.745879i	$-0.732030\pi$
$691$	−35.0184	−1.33216	−0.666081	+	0.745879i	$0.732030\pi$
$692$	−59.1560	−2.24878
$693$	−3.37269	−0.128118
$694$	19.8913	0.755064
$695$	21.8543	0.828983
$696$	−66.8620	−2.53440
$697$	6.80362	0.257705
$698$	66.0275	2.49918
$699$	−23.3961	−0.884923
$700$	−143.504	−5.42396
$701$	−15.6483	−0.591028	−0.295514	−	0.955338i	$-0.595491\pi$
$701$	−15.6483	−0.591028	−0.295514	+	0.955338i	$0.595491\pi$
$702$	6.14685	0.231998
$703$	1.71057	0.0645155
$704$	3.95663	0.149121
$705$	−6.22640	−0.234500
$706$	20.6088	0.775624
$707$	−29.9873	−1.12779
$708$	48.1473	1.80949
$709$	−37.3127	−1.40131	−0.700653	−	0.713502i	$-0.747108\pi$
$709$	−37.3127	−1.40131	−0.700653	+	0.713502i	$0.747108\pi$
$710$	−74.8992	−2.81092
$711$	−11.0333	−0.413780
$712$	−42.1240	−1.57866
$713$	0	0
$714$	13.1702	0.492882
$715$	−10.0090	−0.374314
$716$	−71.2357	−2.66220
$717$	−10.3681	−0.387203
$718$	12.1718	0.454248
$719$	−35.4757	−1.32302	−0.661511	−	0.749936i	$-0.730084\pi$
$719$	−35.4757	−1.32302	−0.661511	+	0.749936i	$0.730084\pi$
$720$	32.3794	1.20671
$721$	17.3385	0.645718
$722$	−47.6322	−1.77269
$723$	8.27977	0.307928
$724$	79.4046	2.95105
$725$	96.8383	3.59648
$726$	25.3326	0.940182
$727$	−7.27678	−0.269881	−0.134940	−	0.990854i	$-0.543084\pi$
$727$	−7.27678	−0.269881	−0.134940	+	0.990854i	$0.543084\pi$
$728$	50.6767	1.87820
$729$	1.00000	0.0370370
$730$	17.4900	0.647335
$731$	12.4591	0.460818
$732$	63.0780	2.33143
$733$	2.48708	0.0918624	0.0459312	−	0.998945i	$-0.485374\pi$
$733$	2.48708	0.0918624	0.0459312	+	0.998945i	$0.485374\pi$
$734$	−63.1939	−2.33253
$735$	−10.1330	−0.373761
$736$	5.70143	0.210157
$737$	2.87798	0.106012
$738$	10.6688	0.392723
$739$	12.5592	0.461997	0.230998	−	0.972954i	$-0.425801\pi$
$739$	12.5592	0.461997	0.230998	+	0.972954i	$0.425801\pi$
$740$	41.9046	1.54044
$741$	1.75029	0.0642985
$742$	−24.8395	−0.911886
$743$	16.9054	0.620198	0.310099	−	0.950704i	$-0.399638\pi$
$743$	16.9054	0.620198	0.310099	+	0.950704i	$0.399638\pi$
$744$	0	0
$745$	65.1946	2.38854
$746$	4.09453	0.149911
$747$	−10.9087	−0.399128
$748$	8.33307	0.304687
$749$	12.9861	0.474503
$750$	−49.1785	−1.79575
$751$	42.2094	1.54024	0.770121	−	0.637898i	$-0.220196\pi$
$751$	42.2094	1.54024	0.770121	+	0.637898i	$0.220196\pi$
$752$	13.5014	0.492346
$753$	−6.90761	−0.251727
$754$	−59.9309	−2.18255
$755$	−17.4449	−0.634887
$756$	14.4483	0.525479
$757$	−11.0364	−0.401125	−0.200563	−	0.979681i	$-0.564277\pi$
$757$	−11.0364	−0.401125	−0.200563	+	0.979681i	$0.564277\pi$
$758$	19.8041	0.719316
$759$	−0.784165	−0.0284634
$760$	19.4700	0.706250
$761$	15.2318	0.552153	0.276076	−	0.961136i	$-0.410966\pi$
$761$	15.2318	0.552153	0.276076	+	0.961136i	$0.410966\pi$
$762$	−36.1847	−1.31083
$763$	16.9486	0.613582
$764$	−44.7934	−1.62057
$765$	6.35847	0.229891
$766$	30.2618	1.09340
$767$	24.6254	0.889171
$768$	23.8453	0.860443
$769$	15.7615	0.568374	0.284187	−	0.958769i	$-0.408276\pi$
$769$	15.7615	0.568374	0.284187	+	0.958769i	$0.408276\pi$
$770$	−33.6282	−1.21188
$771$	−24.6807	−0.888852
$772$	46.1348	1.66043
$773$	21.2826	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$773$	21.2826	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$774$	19.5372	0.702250
$775$	0	0
$776$	83.1211	2.98387
$777$	7.22203	0.259089
$778$	11.8954	0.426471
$779$	3.03789	0.108844
$780$	42.8775	1.53526
$781$	−8.16747	−0.292255
$782$	3.06213	0.109502
$783$	−9.74985	−0.348431
$784$	21.9726	0.784734
$785$	−30.3893	−1.08464
$786$	35.7066	1.27361
$787$	−2.57212	−0.0916861	−0.0458430	−	0.998949i	$-0.514597\pi$
$787$	−2.57212	−0.0916861	−0.0458430	+	0.998949i	$0.514597\pi$
$788$	−105.064	−3.74274
$789$	−23.5751	−0.839297
$790$	−110.010	−3.91398
$791$	45.4607	1.61640
$792$	7.45622	0.264945
$793$	32.2618	1.14565
$794$	82.8467	2.94012
$795$	−11.9923	−0.425323
$796$	37.0799	1.31426
$797$	32.2854	1.14361	0.571804	−	0.820390i	$-0.306244\pi$
$797$	32.2854	1.14361	0.571804	+	0.820390i	$0.306244\pi$
$798$	5.88063	0.208172
$799$	2.65133	0.0937973
$800$	78.5169	2.77599
$801$	−6.14254	−0.217036
$802$	−6.37859	−0.225236
$803$	1.90722	0.0673043
$804$	−12.3290	−0.434811
$805$	−8.64513	−0.304701
$806$	0	0
$807$	0.946528	0.0333194
$808$	66.2949	2.33224
$809$	9.25895	0.325527	0.162764	−	0.986665i	$-0.447959\pi$
$809$	9.25895	0.325527	0.162764	+	0.986665i	$0.447959\pi$
$810$	9.97074	0.350336
$811$	−49.5206	−1.73890	−0.869452	−	0.494018i	$-0.835528\pi$
$811$	−49.5206	−1.73890	−0.869452	+	0.494018i	$0.835528\pi$
$812$	−140.869	−4.94352
$813$	31.2388	1.09559
$814$	6.53165	0.228934
$815$	50.3171	1.76253
$816$	−13.7878	−0.482670
$817$	5.56313	0.194629
$818$	−52.4200	−1.83282
$819$	7.38970	0.258217
$820$	74.4202	2.59887
$821$	13.7928	0.481373	0.240686	−	0.970603i	$-0.422627\pi$
$821$	13.7928	0.481373	0.240686	+	0.970603i	$0.422627\pi$
$822$	14.5921	0.508957
$823$	−19.9361	−0.694928	−0.347464	−	0.937693i	$-0.612957\pi$
$823$	−19.9361	−0.694928	−0.347464	+	0.937693i	$0.612957\pi$
$824$	−38.3313	−1.33533
$825$	−10.7991	−0.375976
$826$	82.7365	2.87877
$827$	−30.6866	−1.06708	−0.533539	−	0.845775i	$-0.679138\pi$
$827$	−30.6866	−1.06708	−0.533539	+	0.845775i	$0.679138\pi$
$828$	3.35929	0.116743
$829$	27.8912	0.968700	0.484350	−	0.874874i	$-0.339056\pi$
$829$	27.8912	0.968700	0.484350	+	0.874874i	$0.339056\pi$
$830$	−108.768	−3.77538
$831$	27.6624	0.959599
$832$	−8.66913	−0.300548
$833$	4.31484	0.149500
$834$	−14.5928	−0.505308
$835$	−82.2108	−2.84502
$836$	3.72080	0.128687
$837$	0	0
$838$	−36.3701	−1.25638
$839$	−37.1177	−1.28145	−0.640723	−	0.767772i	$-0.721365\pi$
$839$	−37.1177	−1.28145	−0.640723	+	0.767772i	$0.721365\pi$
$840$	82.2021	2.83624
$841$	66.0596	2.27792
$842$	−19.9187	−0.686444
$843$	8.27017	0.284840
$844$	34.2685	1.17957
$845$	−28.3049	−0.973720
$846$	4.15756	0.142940
$847$	30.4547	1.04644
$848$	26.0043	0.892991
$849$	−0.824691	−0.0283033
$850$	42.1700	1.44642
$851$	1.67915	0.0575606
$852$	34.9887	1.19869
$853$	−18.5218	−0.634175	−0.317087	−	0.948396i	$-0.602705\pi$
$853$	−18.5218	−0.634175	−0.317087	+	0.948396i	$0.602705\pi$
$854$	108.393	3.70915
$855$	2.83912	0.0970960
$856$	−28.7093	−0.981264
$857$	55.4492	1.89411	0.947055	−	0.321072i	$-0.104043\pi$
$857$	55.4492	1.89411	0.947055	+	0.321072i	$0.104043\pi$
$858$	6.68329	0.228164
$859$	−55.6992	−1.90043	−0.950215	−	0.311594i	$-0.899137\pi$
$859$	−55.6992	−1.90043	−0.950215	+	0.311594i	$0.899137\pi$
$860$	136.282	4.64718
$861$	12.8259	0.437106
$862$	67.6486	2.30412
$863$	42.9244	1.46116	0.730581	−	0.682826i	$-0.239249\pi$
$863$	42.9244	1.46116	0.730581	+	0.682826i	$0.239249\pi$
$864$	−7.90522	−0.268941
$865$	−49.0777	−1.66869
$866$	−58.4800	−1.98723
$867$	14.2924	0.485396
$868$	0	0
$869$	−11.9962	−0.406942
$870$	−97.2132	−3.29584
$871$	−6.30578	−0.213663
$872$	−37.4695	−1.26888
$873$	12.1208	0.410226
$874$	1.36727	0.0462487
$875$	−59.1221	−1.99869
$876$	−8.17035	−0.276051
$877$	0.643758	0.0217382	0.0108691	−	0.999941i	$-0.496540\pi$
$877$	0.643758	0.0217382	0.0108691	+	0.999941i	$0.496540\pi$
$878$	56.9426	1.92172
$879$	3.52533	0.118906
$880$	35.2052	1.18677
$881$	−9.33590	−0.314534	−0.157267	−	0.987556i	$-0.550268\pi$
$881$	−9.33590	−0.314534	−0.157267	+	0.987556i	$0.550268\pi$
$882$	6.76611	0.227827
$883$	−41.2846	−1.38934	−0.694669	−	0.719330i	$-0.744449\pi$
$883$	−41.2846	−1.38934	−0.694669	+	0.719330i	$0.744449\pi$
$884$	−18.2581	−0.614087
$885$	39.9446	1.34272
$886$	−10.9774	−0.368792
$887$	−30.7616	−1.03287	−0.516437	−	0.856325i	$-0.672742\pi$
$887$	−30.7616	−1.03287	−0.516437	+	0.856325i	$0.672742\pi$
$888$	−15.9662	−0.535791
$889$	−43.5010	−1.45898
$890$	−61.2457	−2.05296
$891$	1.08727	0.0364249
$892$	109.240	3.65761
$893$	1.18385	0.0396159
$894$	−43.5324	−1.45594
$895$	−59.0994	−1.97548
$896$	19.9170	0.665380
$897$	1.71814	0.0573670
$898$	−82.2387	−2.74434
$899$	0	0
$900$	46.2623	1.54208
$901$	5.10657	0.170124
$902$	11.5998	0.386232
$903$	23.4875	0.781615
$904$	−100.503	−3.34268
$905$	65.8766	2.18981
$906$	11.6485	0.386996
$907$	32.1721	1.06826	0.534129	−	0.845403i	$-0.320640\pi$
$907$	32.1721	1.06826	0.534129	+	0.845403i	$0.320640\pi$
$908$	13.4760	0.447217
$909$	9.66716	0.320639
$910$	73.6808	2.44249
$911$	−17.3689	−0.575459	−0.287729	−	0.957712i	$-0.592900\pi$
$911$	−17.3689	−0.575459	−0.287729	+	0.957712i	$0.592900\pi$
$912$	−6.15640	−0.203859
$913$	−11.8607	−0.392532
$914$	21.3616	0.706580
$915$	52.3315	1.73003
$916$	−28.1884	−0.931370
$917$	42.9262	1.41755
$918$	−4.24575	−0.140130
$919$	47.9685	1.58233	0.791167	−	0.611600i	$-0.209474\pi$
$919$	47.9685	1.58233	0.791167	+	0.611600i	$0.209474\pi$
$920$	19.1123	0.630115
$921$	8.90949	0.293578
$922$	29.0540	0.956842
$923$	17.8953	0.589030
$924$	15.7092	0.516794
$925$	23.1244	0.760325
$926$	52.8256	1.73596
$927$	−5.58949	−0.183583
$928$	77.0747	2.53010
$929$	36.7464	1.20561	0.602805	−	0.797888i	$-0.294050\pi$
$929$	36.7464	1.20561	0.602805	+	0.797888i	$0.294050\pi$
$930$	0	0
$931$	1.92662	0.0631424
$932$	108.974	3.56955
$933$	26.1174	0.855045
$934$	−61.7582	−2.02079
$935$	6.91338	0.226092
$936$	−16.3369	−0.533988
$937$	29.8912	0.976502	0.488251	−	0.872703i	$-0.337635\pi$
$937$	29.8912	0.976502	0.488251	+	0.872703i	$0.337635\pi$
$938$	−21.1862	−0.691754
$939$	−5.07685	−0.165677
$940$	29.0011	0.945913
$941$	12.1214	0.395145	0.197573	−	0.980288i	$-0.436694\pi$
$941$	12.1214	0.395145	0.197573	+	0.980288i	$0.436694\pi$
$942$	20.2919	0.661145
$943$	2.98208	0.0971100
$944$	−86.6164	−2.81912
$945$	11.9868	0.389929
$946$	21.2422	0.690644
$947$	21.4623	0.697431	0.348716	−	0.937229i	$-0.386618\pi$
$947$	21.4623	0.697431	0.348716	+	0.937229i	$0.386618\pi$
$948$	51.3904	1.66908
$949$	−4.17880	−0.135649
$950$	18.8293	0.610904
$951$	−5.58200	−0.181009
$952$	−35.0033	−1.13446
$953$	0.577941	0.0187214	0.00936068	−	0.999956i	$-0.497020\pi$
$953$	0.577941	0.0187214	0.00936068	+	0.999956i	$0.497020\pi$
$954$	8.00763	0.259257
$955$	−37.1620	−1.20253
$956$	48.2920	1.56188
$957$	−10.6007	−0.342673
$958$	43.2654	1.39784
$959$	17.5425	0.566477
$960$	−14.0621	−0.453853
$961$	0	0
$962$	−14.3111	−0.461409
$963$	−4.18641	−0.134905
$964$	−38.5652	−1.24210
$965$	38.2749	1.23211
$966$	5.77261	0.185731
$967$	36.7066	1.18040	0.590202	−	0.807256i	$-0.299048\pi$
$967$	36.7066	1.18040	0.590202	+	0.807256i	$0.299048\pi$
$968$	−67.3282	−2.16401
$969$	−1.20896	−0.0388373
$970$	120.853	3.88036
$971$	−27.4394	−0.880573	−0.440286	−	0.897857i	$-0.645123\pi$
$971$	−27.4394	−0.880573	−0.440286	+	0.897857i	$0.645123\pi$
$972$	−4.65777	−0.149398
$973$	−17.5434	−0.562415
$974$	9.50618	0.304598
$975$	23.6612	0.757766
$976$	−113.476	−3.63229
$977$	13.8245	0.442284	0.221142	−	0.975242i	$-0.429022\pi$
$977$	13.8245	0.442284	0.221142	+	0.975242i	$0.429022\pi$
$978$	−33.5983	−1.07435
$979$	−6.67861	−0.213449
$980$	47.1972	1.50766
$981$	−5.46382	−0.174446
$982$	9.96891	0.318121
$983$	12.1637	0.387963	0.193982	−	0.981005i	$-0.437860\pi$
$983$	12.1637	0.387963	0.193982	+	0.981005i	$0.437860\pi$
$984$	−28.3551	−0.903928
$985$	−87.1643	−2.77729
$986$	41.3954	1.31830
$987$	4.99819	0.159094
$988$	−8.15243	−0.259364
$989$	5.46095	0.173648
$990$	10.8409	0.344546
$991$	49.0596	1.55843	0.779214	−	0.626758i	$-0.215618\pi$
$991$	49.0596	1.55843	0.779214	+	0.626758i	$0.215618\pi$
$992$	0	0
$993$	−3.69260	−0.117181
$994$	60.1246	1.90704
$995$	30.7626	0.975241
$996$	50.8101	1.60998
$997$	57.2434	1.81292	0.906459	−	0.422295i	$-0.138775\pi$
$997$	57.2434	1.81292	0.906459	+	0.422295i	$0.138775\pi$
$998$	70.3628	2.22730
$999$	−2.32820	−0.0736611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2883.2.a.s.1.11		12
3.2	odd	2		8649.2.a.bl.1.2		12
31.22	odd	30		93.2.m.b.19.1	✓	24
31.24	odd	30		93.2.m.b.49.1	yes	24
31.30	odd	2		2883.2.a.t.1.11		12
93.53	even	30		279.2.y.d.19.3		24
93.86	even	30		279.2.y.d.235.3		24
93.92	even	2		8649.2.a.bk.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.19.1	✓	24	31.22	odd	30
93.2.m.b.49.1	yes	24	31.24	odd	30
279.2.y.d.19.3		24	93.53	even	30
279.2.y.d.235.3		24	93.86	even	30
2883.2.a.s.1.11		12	1.1	even	1	trivial
2883.2.a.t.1.11		12	31.30	odd	2
8649.2.a.bk.1.2		12	93.92	even	2
8649.2.a.bl.1.2		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)

\(f(q)\)	\(=\)	\(q+2.58026 q^{2} -1.00000 q^{3} +4.65777 q^{4} +3.86423 q^{5} -2.58026 q^{6} -3.10198 q^{7} +6.85774 q^{8} +1.00000 q^{9} +9.97074 q^{10} +1.08727 q^{11} -4.65777 q^{12} -2.38226 q^{13} -8.00392 q^{14} -3.86423 q^{15} +8.37926 q^{16} +1.64547 q^{17} +2.58026 q^{18} +0.734719 q^{19} +17.9987 q^{20} +3.10198 q^{21} +2.80545 q^{22} +0.721223 q^{23} -6.85774 q^{24} +9.93229 q^{25} -6.14685 q^{26} -1.00000 q^{27} -14.4483 q^{28} +9.74985 q^{29} -9.97074 q^{30} +7.90522 q^{32} -1.08727 q^{33} +4.24575 q^{34} -11.9868 q^{35} +4.65777 q^{36} +2.32820 q^{37} +1.89577 q^{38} +2.38226 q^{39} +26.4999 q^{40} +4.13476 q^{41} +8.00392 q^{42} +7.57178 q^{43} +5.06425 q^{44} +3.86423 q^{45} +1.86095 q^{46} +1.61129 q^{47} -8.37926 q^{48} +2.62226 q^{49} +25.6279 q^{50} -1.64547 q^{51} -11.0960 q^{52} +3.10341 q^{53} -2.58026 q^{54} +4.20147 q^{55} -21.2726 q^{56} -0.734719 q^{57} +25.1572 q^{58} -10.3370 q^{59} -17.9987 q^{60} -13.5425 q^{61} -3.10198 q^{63} +3.63904 q^{64} -9.20559 q^{65} -2.80545 q^{66} +2.64698 q^{67} +7.66421 q^{68} -0.721223 q^{69} -30.9290 q^{70} -7.51190 q^{71} +6.85774 q^{72} +1.75413 q^{73} +6.00738 q^{74} -9.93229 q^{75} +3.42215 q^{76} -3.37269 q^{77} +6.14685 q^{78} -11.0333 q^{79} +32.3794 q^{80} +1.00000 q^{81} +10.6688 q^{82} -10.9087 q^{83} +14.4483 q^{84} +6.35847 q^{85} +19.5372 q^{86} -9.74985 q^{87} +7.45622 q^{88} -6.14254 q^{89} +9.97074 q^{90} +7.38970 q^{91} +3.35929 q^{92} +4.15756 q^{94} +2.83912 q^{95} -7.90522 q^{96} +12.1208 q^{97} +6.76611 q^{98} +1.08727 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 5 q^{2} - 12 q^{3} + 13 q^{4} + 6 q^{5} - 5 q^{6} + 6 q^{7} + 24 q^{8} + 12 q^{9} + 21 q^{10} - 2 q^{11} - 13 q^{12} - 3 q^{13} + 15 q^{14} - 6 q^{15} + 19 q^{16} + 8 q^{17} + 5 q^{18} + 15 q^{19}+ \cdots - 2 q^{99}+O(q^{100}) \) 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

Related objects

Downloads

Learn more