LMFDB - Embedded newform 5766.2.a.bg.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5766,2,Mod(1,5766)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5766, 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("5766.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5766 = 2 \cdot 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5766.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,4,4,4,-3] 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:	$46.0417418055$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{15})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 4x + 1 $ x^4 - x^3 - 4x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 186)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.82709$ of defining polynomial
Character	$\chi$	$=$	5766.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.720227 q^{5} +1.00000 q^{6} -1.66174 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.720227 q^{10} -1.40898 q^{11} +1.00000 q^{12} -2.78339 q^{13} -1.66174 q^{14} -0.720227 q^{15} +1.00000 q^{16} -0.425671 q^{17} +1.00000 q^{18} -2.30678 q^{19} -0.720227 q^{20} -1.66174 q^{21} -1.40898 q^{22} +5.86889 q^{23} +1.00000 q^{24} -4.48127 q^{25} -2.78339 q^{26} +1.00000 q^{27} -1.66174 q^{28} +0.243625 q^{29} -0.720227 q^{30} +1.00000 q^{32} -1.40898 q^{33} -0.425671 q^{34} +1.19683 q^{35} +1.00000 q^{36} -2.76958 q^{37} -2.30678 q^{38} -2.78339 q^{39} -0.720227 q^{40} +5.05560 q^{41} -1.66174 q^{42} +2.84029 q^{43} -1.40898 q^{44} -0.720227 q^{45} +5.86889 q^{46} -6.89025 q^{47} +1.00000 q^{48} -4.23862 q^{49} -4.48127 q^{50} -0.425671 q^{51} -2.78339 q^{52} -4.79659 q^{53} +1.00000 q^{54} +1.01478 q^{55} -1.66174 q^{56} -2.30678 q^{57} +0.243625 q^{58} -12.0770 q^{59} -0.720227 q^{60} -2.61994 q^{61} -1.66174 q^{63} +1.00000 q^{64} +2.00467 q^{65} -1.40898 q^{66} -5.24927 q^{67} -0.425671 q^{68} +5.86889 q^{69} +1.19683 q^{70} +10.7739 q^{71} +1.00000 q^{72} -5.93960 q^{73} -2.76958 q^{74} -4.48127 q^{75} -2.30678 q^{76} +2.34135 q^{77} -2.78339 q^{78} -13.3939 q^{79} -0.720227 q^{80} +1.00000 q^{81} +5.05560 q^{82} -5.99342 q^{83} -1.66174 q^{84} +0.306580 q^{85} +2.84029 q^{86} +0.243625 q^{87} -1.40898 q^{88} +0.595693 q^{89} -0.720227 q^{90} +4.62526 q^{91} +5.86889 q^{92} -6.89025 q^{94} +1.66141 q^{95} +1.00000 q^{96} +5.23416 q^{97} -4.23862 q^{98} -1.40898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} + 4 q^{8} + 4 q^{9} - 3 q^{10} - 3 q^{11} + 4 q^{12} + 4 q^{13} - 11 q^{14} - 3 q^{15} + 4 q^{16} - 15 q^{17} + 4 q^{18} - 2 q^{19} - 3 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 + 4 * q^8 + 4 * q^9 - 3 * q^10 - 3 * q^11 + 4 * q^12 + 4 * q^13 - 11 * q^14 - 3 * q^15 + 4 * q^16 - 15 * q^17 + 4 * q^18 - 2 * q^19 - 3 * q^20 - 11 * q^21 - 3 * q^22 - 3 * q^23 + 4 * q^24 + q^25 + 4 * q^26 + 4 * q^27 - 11 * q^28 + 9 * q^29 - 3 * q^30 + 4 * q^32 - 3 * q^33 - 15 * q^34 - 3 * q^35 + 4 * q^36 - 8 * q^37 - 2 * q^38 + 4 * q^39 - 3 * q^40 - 12 * q^41 - 11 * q^42 + 10 * q^43 - 3 * q^44 - 3 * q^45 - 3 * q^46 - 6 * q^47 + 4 * q^48 + 11 * q^49 + q^50 - 15 * q^51 + 4 * q^52 - 9 * q^53 + 4 * q^54 - 9 * q^55 - 11 * q^56 - 2 * q^57 + 9 * q^58 - 21 * q^59 - 3 * q^60 - 35 * q^61 - 11 * q^63 + 4 * q^64 - 3 * q^65 - 3 * q^66 - 17 * q^67 - 15 * q^68 - 3 * q^69 - 3 * q^70 - 18 * q^71 + 4 * q^72 + q^73 - 8 * q^74 + q^75 - 2 * q^76 + 12 * q^77 + 4 * q^78 - 17 * q^79 - 3 * q^80 + 4 * q^81 - 12 * q^82 - 6 * q^83 - 11 * q^84 + 15 * q^85 + 10 * q^86 + 9 * q^87 - 3 * q^88 - 6 * q^89 - 3 * q^90 - 16 * q^91 - 3 * q^92 - 6 * q^94 - 36 * q^95 + 4 * q^96 - 17 * q^97 + 11 * q^98 - 3 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.720227	−0.322095	−0.161048	−	0.986947i	$-0.551487\pi$
$5$	−0.720227	−0.322095	−0.161048	+	0.986947i	$0.551487\pi$
$6$	1.00000	0.408248
$7$	−1.66174	−0.628078	−0.314039	−	0.949410i	$-0.601682\pi$
$7$	−1.66174	−0.628078	−0.314039	+	0.949410i	$0.601682\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.720227	−0.227756
$11$	−1.40898	−0.424823	−0.212411	−	0.977180i	$-0.568132\pi$
$11$	−1.40898	−0.424823	−0.212411	+	0.977180i	$0.568132\pi$
$12$	1.00000	0.288675
$13$	−2.78339	−0.771972	−0.385986	−	0.922505i	$-0.626139\pi$
$13$	−2.78339	−0.771972	−0.385986	+	0.922505i	$0.626139\pi$
$14$	−1.66174	−0.444118
$15$	−0.720227	−0.185962
$16$	1.00000	0.250000
$17$	−0.425671	−0.103240	−0.0516202	−	0.998667i	$-0.516439\pi$
$17$	−0.425671	−0.103240	−0.0516202	+	0.998667i	$0.516439\pi$
$18$	1.00000	0.235702
$19$	−2.30678	−0.529213	−0.264606	−	0.964357i	$-0.585242\pi$
$19$	−2.30678	−0.529213	−0.264606	+	0.964357i	$0.585242\pi$
$20$	−0.720227	−0.161048
$21$	−1.66174	−0.362621
$22$	−1.40898	−0.300395
$23$	5.86889	1.22375	0.611874	−	0.790956i	$-0.290416\pi$
$23$	5.86889	1.22375	0.611874	+	0.790956i	$0.290416\pi$
$24$	1.00000	0.204124
$25$	−4.48127	−0.896255
$26$	−2.78339	−0.545867
$27$	1.00000	0.192450
$28$	−1.66174	−0.314039
$29$	0.243625	0.0452400	0.0226200	−	0.999744i	$-0.492799\pi$
$29$	0.243625	0.0452400	0.0226200	+	0.999744i	$0.492799\pi$
$30$	−0.720227	−0.131495
$31$	0	0
$31$	0	0
$32$	1.00000	0.176777
$33$	−1.40898	−0.245271
$34$	−0.425671	−0.0730019
$35$	1.19683	0.202301
$36$	1.00000	0.166667
$37$	−2.76958	−0.455316	−0.227658	−	0.973741i	$-0.573107\pi$
$37$	−2.76958	−0.455316	−0.227658	+	0.973741i	$0.573107\pi$
$38$	−2.30678	−0.374210
$39$	−2.78339	−0.445698
$40$	−0.720227	−0.113878
$41$	5.05560	0.789552	0.394776	−	0.918777i	$-0.370822\pi$
$41$	5.05560	0.789552	0.394776	+	0.918777i	$0.370822\pi$
$42$	−1.66174	−0.256412
$43$	2.84029	0.433141	0.216570	−	0.976267i	$-0.430513\pi$
$43$	2.84029	0.433141	0.216570	+	0.976267i	$0.430513\pi$
$44$	−1.40898	−0.212411
$45$	−0.720227	−0.107365
$46$	5.86889	0.865320
$47$	−6.89025	−1.00505	−0.502523	−	0.864564i	$-0.667595\pi$
$47$	−6.89025	−1.00505	−0.502523	+	0.864564i	$0.667595\pi$
$48$	1.00000	0.144338
$49$	−4.23862	−0.605518
$50$	−4.48127	−0.633748
$51$	−0.425671	−0.0596058
$52$	−2.78339	−0.385986
$53$	−4.79659	−0.658862	−0.329431	−	0.944180i	$-0.606857\pi$
$53$	−4.79659	−0.658862	−0.329431	+	0.944180i	$0.606857\pi$
$54$	1.00000	0.136083
$55$	1.01478	0.136833
$56$	−1.66174	−0.222059
$57$	−2.30678	−0.305541
$58$	0.243625	0.0319895
$59$	−12.0770	−1.57229	−0.786144	−	0.618044i	$-0.787925\pi$
$59$	−12.0770	−1.57229	−0.786144	+	0.618044i	$0.787925\pi$
$60$	−0.720227	−0.0929809
$61$	−2.61994	−0.335449	−0.167725	−	0.985834i	$-0.553642\pi$
$61$	−2.61994	−0.335449	−0.167725	+	0.985834i	$0.553642\pi$
$62$	0	0
$63$	−1.66174	−0.209359
$64$	1.00000	0.125000
$65$	2.00467	0.248649
$66$	−1.40898	−0.173433
$67$	−5.24927	−0.641301	−0.320650	−	0.947198i	$-0.603901\pi$
$67$	−5.24927	−0.641301	−0.320650	+	0.947198i	$0.603901\pi$
$68$	−0.425671	−0.0516202
$69$	5.86889	0.706531
$70$	1.19683	0.143048
$71$	10.7739	1.27863	0.639314	−	0.768945i	$-0.279218\pi$
$71$	10.7739	1.27863	0.639314	+	0.768945i	$0.279218\pi$
$72$	1.00000	0.117851
$73$	−5.93960	−0.695178	−0.347589	−	0.937647i	$-0.613000\pi$
$73$	−5.93960	−0.695178	−0.347589	+	0.937647i	$0.613000\pi$
$74$	−2.76958	−0.321957
$75$	−4.48127	−0.517453
$76$	−2.30678	−0.264606
$77$	2.34135	0.266822
$78$	−2.78339	−0.315156
$79$	−13.3939	−1.50693	−0.753464	−	0.657490i	$-0.771618\pi$
$79$	−13.3939	−1.50693	−0.753464	+	0.657490i	$0.771618\pi$
$80$	−0.720227	−0.0805239
$81$	1.00000	0.111111
$82$	5.05560	0.558298
$83$	−5.99342	−0.657863	−0.328932	−	0.944354i	$-0.606689\pi$
$83$	−5.99342	−0.657863	−0.328932	+	0.944354i	$0.606689\pi$
$84$	−1.66174	−0.181311
$85$	0.306580	0.0332532
$86$	2.84029	0.306277
$87$	0.243625	0.0261193
$88$	−1.40898	−0.150197
$89$	0.595693	0.0631434	0.0315717	−	0.999501i	$-0.489949\pi$
$89$	0.595693	0.0631434	0.0315717	+	0.999501i	$0.489949\pi$
$90$	−0.720227	−0.0759186
$91$	4.62526	0.484859
$92$	5.86889	0.611874
$93$	0	0
$94$	−6.89025	−0.710675
$95$	1.66141	0.170457
$96$	1.00000	0.102062
$97$	5.23416	0.531448	0.265724	−	0.964049i	$-0.414389\pi$
$97$	5.23416	0.531448	0.265724	+	0.964049i	$0.414389\pi$
$98$	−4.23862	−0.428166
$99$	−1.40898	−0.141608
$100$	−4.48127	−0.448127
$101$	−9.92173	−0.987249	−0.493624	−	0.869675i	$-0.664328\pi$
$101$	−9.92173	−0.987249	−0.493624	+	0.869675i	$0.664328\pi$
$102$	−0.425671	−0.0421477
$103$	−18.3111	−1.80425	−0.902124	−	0.431476i	$-0.857993\pi$
$103$	−18.3111	−1.80425	−0.902124	+	0.431476i	$0.857993\pi$
$104$	−2.78339	−0.272933
$105$	1.19683	0.116799
$106$	−4.79659	−0.465886
$107$	−4.47193	−0.432318	−0.216159	−	0.976358i	$-0.569353\pi$
$107$	−4.47193	−0.432318	−0.216159	+	0.976358i	$0.569353\pi$
$108$	1.00000	0.0962250
$109$	−9.84187	−0.942681	−0.471340	−	0.881951i	$-0.656230\pi$
$109$	−9.84187	−0.942681	−0.471340	+	0.881951i	$0.656230\pi$
$110$	1.01478	0.0967558
$111$	−2.76958	−0.262877
$112$	−1.66174	−0.157020
$113$	−10.9786	−1.03278	−0.516392	−	0.856353i	$-0.672725\pi$
$113$	−10.9786	−1.03278	−0.516392	+	0.856353i	$0.672725\pi$
$114$	−2.30678	−0.216050
$115$	−4.22693	−0.394163
$116$	0.243625	0.0226200
$117$	−2.78339	−0.257324
$118$	−12.0770	−1.11177
$119$	0.707354	0.0648430
$120$	−0.720227	−0.0657474
$121$	−9.01478	−0.819526
$122$	−2.61994	−0.237199
$123$	5.05560	0.455848
$124$	0	0
$125$	6.82867	0.610775
$126$	−1.66174	−0.148039
$127$	16.3333	1.44934	0.724671	−	0.689095i	$-0.241992\pi$
$127$	16.3333	1.44934	0.724671	+	0.689095i	$0.241992\pi$
$128$	1.00000	0.0883883
$129$	2.84029	0.250074
$130$	2.00467	0.175821
$131$	7.12185	0.622239	0.311120	−	0.950371i	$-0.399296\pi$
$131$	7.12185	0.622239	0.311120	+	0.950371i	$0.399296\pi$
$132$	−1.40898	−0.122636
$133$	3.83327	0.332387
$134$	−5.24927	−0.453468
$135$	−0.720227	−0.0619873
$136$	−0.425671	−0.0365010
$137$	−14.4967	−1.23853	−0.619267	−	0.785181i	$-0.712570\pi$
$137$	−14.4967	−1.23853	−0.619267	+	0.785181i	$0.712570\pi$
$138$	5.86889	0.499593
$139$	20.5545	1.74341	0.871707	−	0.490028i	$-0.163013\pi$
$139$	20.5545	1.74341	0.871707	+	0.490028i	$0.163013\pi$
$140$	1.19683	0.101151
$141$	−6.89025	−0.580264
$142$	10.7739	0.904127
$143$	3.92173	0.327951
$144$	1.00000	0.0833333
$145$	−0.175465	−0.0145716
$146$	−5.93960	−0.491565
$147$	−4.23862	−0.349596
$148$	−2.76958	−0.227658
$149$	−20.4312	−1.67379	−0.836894	−	0.547365i	$-0.815631\pi$
$149$	−20.4312	−1.67379	−0.836894	+	0.547365i	$0.815631\pi$
$150$	−4.48127	−0.365894
$151$	1.05029	0.0854710	0.0427355	−	0.999086i	$-0.486393\pi$
$151$	1.05029	0.0854710	0.0427355	+	0.999086i	$0.486393\pi$
$152$	−2.30678	−0.187105
$153$	−0.425671	−0.0344134
$154$	2.34135	0.188672
$155$	0	0
$156$	−2.78339	−0.222849
$157$	14.5822	1.16378	0.581892	−	0.813266i	$-0.302313\pi$
$157$	14.5822	1.16378	0.581892	+	0.813266i	$0.302313\pi$
$158$	−13.3939	−1.06556
$159$	−4.79659	−0.380394
$160$	−0.720227	−0.0569390
$161$	−9.75255	−0.768609
$162$	1.00000	0.0785674
$163$	4.88932	0.382961	0.191480	−	0.981496i	$-0.438671\pi$
$163$	4.88932	0.382961	0.191480	+	0.981496i	$0.438671\pi$
$164$	5.05560	0.394776
$165$	1.01478	0.0790008
$166$	−5.99342	−0.465180
$167$	12.4920	0.966659	0.483330	−	0.875438i	$-0.339427\pi$
$167$	12.4920	0.966659	0.483330	+	0.875438i	$0.339427\pi$
$168$	−1.66174	−0.128206
$169$	−5.25276	−0.404059
$170$	0.306580	0.0235136
$171$	−2.30678	−0.176404
$172$	2.84029	0.216570
$173$	−5.08708	−0.386763	−0.193382	−	0.981124i	$-0.561946\pi$
$173$	−5.08708	−0.386763	−0.193382	+	0.981124i	$0.561946\pi$
$174$	0.243625	0.0184692
$175$	7.44670	0.562918
$176$	−1.40898	−0.106206
$177$	−12.0770	−0.907760
$178$	0.595693	0.0446491
$179$	14.1982	1.06122	0.530612	−	0.847615i	$-0.321962\pi$
$179$	14.1982	1.06122	0.530612	+	0.847615i	$0.321962\pi$
$180$	−0.720227	−0.0536826
$181$	16.8223	1.25039	0.625196	−	0.780468i	$-0.285019\pi$
$181$	16.8223	1.25039	0.625196	+	0.780468i	$0.285019\pi$
$182$	4.62526	0.342847
$183$	−2.61994	−0.193672
$184$	5.86889	0.432660
$185$	1.99473	0.146655
$186$	0	0
$187$	0.599760	0.0438588
$188$	−6.89025	−0.502523
$189$	−1.66174	−0.120874
$190$	1.66141	0.120531
$191$	−24.4881	−1.77190	−0.885948	−	0.463784i	$-0.846491\pi$
$191$	−24.4881	−1.77190	−0.885948	+	0.463784i	$0.846491\pi$
$192$	1.00000	0.0721688
$193$	11.9999	0.863770	0.431885	−	0.901929i	$-0.357849\pi$
$193$	11.9999	0.863770	0.431885	+	0.901929i	$0.357849\pi$
$194$	5.23416	0.375791
$195$	2.00467	0.143557
$196$	−4.23862	−0.302759
$197$	13.4024	0.954881	0.477441	−	0.878664i	$-0.341565\pi$
$197$	13.4024	0.954881	0.477441	+	0.878664i	$0.341565\pi$
$198$	−1.40898	−0.100132
$199$	−1.04337	−0.0739629	−0.0369814	−	0.999316i	$-0.511774\pi$
$199$	−1.04337	−0.0739629	−0.0369814	+	0.999316i	$0.511774\pi$
$200$	−4.48127	−0.316874
$201$	−5.24927	−0.370255
$202$	−9.92173	−0.698090
$203$	−0.404841	−0.0284143
$204$	−0.425671	−0.0298029
$205$	−3.64118	−0.254311
$206$	−18.3111	−1.27580
$207$	5.86889	0.407916
$208$	−2.78339	−0.192993
$209$	3.25021	0.224821
$210$	1.19683	0.0825891
$211$	−16.4020	−1.12916	−0.564581	−	0.825378i	$-0.690962\pi$
$211$	−16.4020	−1.12916	−0.564581	+	0.825378i	$0.690962\pi$
$212$	−4.79659	−0.329431
$213$	10.7739	0.738217
$214$	−4.47193	−0.305695
$215$	−2.04566	−0.139513
$216$	1.00000	0.0680414
$217$	0	0
$218$	−9.84187	−0.666576
$219$	−5.93960	−0.401361
$220$	1.01478	0.0684167
$221$	1.18481	0.0796987
$222$	−2.76958	−0.185882
$223$	−21.8525	−1.46335	−0.731675	−	0.681654i	$-0.761261\pi$
$223$	−21.8525	−1.46335	−0.731675	+	0.681654i	$0.761261\pi$
$224$	−1.66174	−0.111030
$225$	−4.48127	−0.298752
$226$	−10.9786	−0.730288
$227$	11.5429	0.766126	0.383063	−	0.923722i	$-0.374869\pi$
$227$	11.5429	0.766126	0.383063	+	0.923722i	$0.374869\pi$
$228$	−2.30678	−0.152770
$229$	20.8613	1.37856	0.689278	−	0.724497i	$-0.257928\pi$
$229$	20.8613	1.37856	0.689278	+	0.724497i	$0.257928\pi$
$230$	−4.22693	−0.278716
$231$	2.34135	0.154050
$232$	0.243625	0.0159948
$233$	−27.4079	−1.79555	−0.897776	−	0.440452i	$-0.854818\pi$
$233$	−27.4079	−1.79555	−0.897776	+	0.440452i	$0.854818\pi$
$234$	−2.78339	−0.181956
$235$	4.96255	0.323721
$236$	−12.0770	−0.786144
$237$	−13.3939	−0.870025
$238$	0.707354	0.0458509
$239$	4.70353	0.304246	0.152123	−	0.988362i	$-0.451389\pi$
$239$	4.70353	0.304246	0.152123	+	0.988362i	$0.451389\pi$
$240$	−0.720227	−0.0464905
$241$	11.3375	0.730315	0.365157	−	0.930946i	$-0.381015\pi$
$241$	11.3375	0.730315	0.365157	+	0.930946i	$0.381015\pi$
$242$	−9.01478	−0.579492
$243$	1.00000	0.0641500
$244$	−2.61994	−0.167725
$245$	3.05277	0.195034
$246$	5.05560	0.322333
$247$	6.42067	0.408537
$248$	0	0
$249$	−5.99342	−0.379818
$250$	6.82867	0.431883
$251$	1.01072	0.0637959	0.0318979	−	0.999491i	$-0.489845\pi$
$251$	1.01072	0.0637959	0.0318979	+	0.999491i	$0.489845\pi$
$252$	−1.66174	−0.104680
$253$	−8.26913	−0.519875
$254$	16.3333	1.02484
$255$	0.306580	0.0191988
$256$	1.00000	0.0625000
$257$	30.6255	1.91037	0.955183	−	0.296015i	$-0.0956578\pi$
$257$	30.6255	1.91037	0.955183	+	0.296015i	$0.0956578\pi$
$258$	2.84029	0.176829
$259$	4.60232	0.285974
$260$	2.00467	0.124324
$261$	0.243625	0.0150800
$262$	7.12185	0.439989
$263$	−5.84536	−0.360441	−0.180220	−	0.983626i	$-0.557681\pi$
$263$	−5.84536	−0.360441	−0.180220	+	0.983626i	$0.557681\pi$
$264$	−1.40898	−0.0867165
$265$	3.45463	0.212217
$266$	3.83327	0.235033
$267$	0.595693	0.0364558
$268$	−5.24927	−0.320650
$269$	0.455772	0.0277889	0.0138945	−	0.999903i	$-0.495577\pi$
$269$	0.455772	0.0277889	0.0138945	+	0.999903i	$0.495577\pi$
$270$	−0.720227	−0.0438316
$271$	−2.57551	−0.156451	−0.0782255	−	0.996936i	$-0.524925\pi$
$271$	−2.57551	−0.156451	−0.0782255	+	0.996936i	$0.524925\pi$
$272$	−0.425671	−0.0258101
$273$	4.62526	0.279934
$274$	−14.4967	−0.875775
$275$	6.31401	0.380749
$276$	5.86889	0.353265
$277$	23.4233	1.40737	0.703685	−	0.710512i	$-0.251537\pi$
$277$	23.4233	1.40737	0.703685	+	0.710512i	$0.251537\pi$
$278$	20.5545	1.23278
$279$	0	0
$280$	1.19683	0.0715242
$281$	29.3381	1.75017	0.875083	−	0.483973i	$-0.160807\pi$
$281$	29.3381	1.75017	0.875083	+	0.483973i	$0.160807\pi$
$282$	−6.89025	−0.410308
$283$	−10.8881	−0.647232	−0.323616	−	0.946188i	$-0.604899\pi$
$283$	−10.8881	−0.647232	−0.323616	+	0.946188i	$0.604899\pi$
$284$	10.7739	0.639314
$285$	1.66141	0.0984133
$286$	3.92173	0.231897
$287$	−8.40109	−0.495901
$288$	1.00000	0.0589256
$289$	−16.8188	−0.989341
$290$	−0.175465	−0.0103037
$291$	5.23416	0.306832
$292$	−5.93960	−0.347589
$293$	11.0321	0.644501	0.322251	−	0.946654i	$-0.395561\pi$
$293$	11.0321	0.644501	0.322251	+	0.946654i	$0.395561\pi$
$294$	−4.23862	−0.247202
$295$	8.69816	0.506426
$296$	−2.76958	−0.160979
$297$	−1.40898	−0.0817571
$298$	−20.4312	−1.18355
$299$	−16.3354	−0.944699
$300$	−4.48127	−0.258726
$301$	−4.71983	−0.272046
$302$	1.05029	0.0604371
$303$	−9.92173	−0.569988
$304$	−2.30678	−0.132303
$305$	1.88696	0.108047
$306$	−0.425671	−0.0243340
$307$	−7.53042	−0.429784	−0.214892	−	0.976638i	$-0.568940\pi$
$307$	−7.53042	−0.429784	−0.214892	+	0.976638i	$0.568940\pi$
$308$	2.34135	0.133411
$309$	−18.3111	−1.04168
$310$	0	0
$311$	−13.9560	−0.791370	−0.395685	−	0.918386i	$-0.629493\pi$
$311$	−13.9560	−0.791370	−0.395685	+	0.918386i	$0.629493\pi$
$312$	−2.78339	−0.157578
$313$	25.0900	1.41817	0.709087	−	0.705121i	$-0.249108\pi$
$313$	25.0900	1.41817	0.709087	+	0.705121i	$0.249108\pi$
$314$	14.5822	0.822919
$315$	1.19683	0.0674337
$316$	−13.3939	−0.753464
$317$	−13.7846	−0.774218	−0.387109	−	0.922034i	$-0.626526\pi$
$317$	−13.7846	−0.774218	−0.387109	+	0.922034i	$0.626526\pi$
$318$	−4.79659	−0.268979
$319$	−0.343262	−0.0192190
$320$	−0.720227	−0.0402619
$321$	−4.47193	−0.249599
$322$	−9.75255	−0.543489
$323$	0.981931	0.0546361
$324$	1.00000	0.0555556
$325$	12.4731	0.691884
$326$	4.88932	0.270794
$327$	−9.84187	−0.544257
$328$	5.05560	0.279149
$329$	11.4498	0.631248
$330$	1.01478	0.0558620
$331$	0.362785	0.0199405	0.00997024	−	0.999950i	$-0.496826\pi$
$331$	0.362785	0.0199405	0.00997024	+	0.999950i	$0.496826\pi$
$332$	−5.99342	−0.328932
$333$	−2.76958	−0.151772
$334$	12.4920	0.683531
$335$	3.78067	0.206560
$336$	−1.66174	−0.0906553
$337$	−13.4133	−0.730670	−0.365335	−	0.930876i	$-0.619046\pi$
$337$	−13.4133	−0.730670	−0.365335	+	0.930876i	$0.619046\pi$
$338$	−5.25276	−0.285713
$339$	−10.9786	−0.596278
$340$	0.306580	0.0166266
$341$	0	0
$342$	−2.30678	−0.124737
$343$	18.6757	1.00839
$344$	2.84029	0.153138
$345$	−4.22693	−0.227570
$346$	−5.08708	−0.273483
$347$	−35.3404	−1.89717	−0.948585	−	0.316523i	$-0.897485\pi$
$347$	−35.3404	−1.89717	−0.948585	+	0.316523i	$0.897485\pi$
$348$	0.243625	0.0130597
$349$	31.0104	1.65995	0.829974	−	0.557802i	$-0.188355\pi$
$349$	31.0104	1.65995	0.829974	+	0.557802i	$0.188355\pi$
$350$	7.44670	0.398043
$351$	−2.78339	−0.148566
$352$	−1.40898	−0.0750987
$353$	24.3174	1.29428	0.647142	−	0.762370i	$-0.275964\pi$
$353$	24.3174	1.29428	0.647142	+	0.762370i	$0.275964\pi$
$354$	−12.0770	−0.641884
$355$	−7.75967	−0.411841
$356$	0.595693	0.0315717
$357$	0.707354	0.0374371
$358$	14.1982	0.750399
$359$	−19.4298	−1.02547	−0.512733	−	0.858548i	$-0.671367\pi$
$359$	−19.4298	−1.02547	−0.512733	+	0.858548i	$0.671367\pi$
$360$	−0.720227	−0.0379593
$361$	−13.6787	−0.719934
$362$	16.8223	0.884160
$363$	−9.01478	−0.473153
$364$	4.62526	0.242430
$365$	4.27786	0.223914
$366$	−2.61994	−0.136947
$367$	19.2691	1.00584	0.502920	−	0.864333i	$-0.332259\pi$
$367$	19.2691	1.00584	0.502920	+	0.864333i	$0.332259\pi$
$368$	5.86889	0.305937
$369$	5.05560	0.263184
$370$	1.99473	0.103701
$371$	7.97068	0.413817
$372$	0	0
$373$	−4.38573	−0.227084	−0.113542	−	0.993533i	$-0.536220\pi$
$373$	−4.38573	−0.227084	−0.113542	+	0.993533i	$0.536220\pi$
$374$	0.599760	0.0310129
$375$	6.82867	0.352631
$376$	−6.89025	−0.355338
$377$	−0.678102	−0.0349240
$378$	−1.66174	−0.0854706
$379$	12.8066	0.657830	0.328915	−	0.944360i	$-0.393317\pi$
$379$	12.8066	0.657830	0.328915	+	0.944360i	$0.393317\pi$
$380$	1.66141	0.0852285
$381$	16.3333	0.836778
$382$	−24.4881	−1.25292
$383$	−28.1219	−1.43696	−0.718480	−	0.695548i	$-0.755162\pi$
$383$	−28.1219	−1.43696	−0.718480	+	0.695548i	$0.755162\pi$
$384$	1.00000	0.0510310
$385$	−1.68631	−0.0859421
$386$	11.9999	0.610777
$387$	2.84029	0.144380
$388$	5.23416	0.265724
$389$	2.34679	0.118987	0.0594936	−	0.998229i	$-0.481051\pi$
$389$	2.34679	0.118987	0.0594936	+	0.998229i	$0.481051\pi$
$390$	2.00467	0.101510
$391$	−2.49821	−0.126340
$392$	−4.23862	−0.214083
$393$	7.12185	0.359250
$394$	13.4024	0.675203
$395$	9.64662	0.485374
$396$	−1.40898	−0.0708038
$397$	22.5740	1.13295	0.566477	−	0.824077i	$-0.308306\pi$
$397$	22.5740	1.13295	0.566477	+	0.824077i	$0.308306\pi$
$398$	−1.04337	−0.0522996
$399$	3.83327	0.191904
$400$	−4.48127	−0.224064
$401$	−21.0980	−1.05358	−0.526791	−	0.849995i	$-0.676605\pi$
$401$	−21.0980	−1.05358	−0.526791	+	0.849995i	$0.676605\pi$
$402$	−5.24927	−0.261810
$403$	0	0
$404$	−9.92173	−0.493624
$405$	−0.720227	−0.0357884
$406$	−0.404841	−0.0200919
$407$	3.90227	0.193428
$408$	−0.425671	−0.0210738
$409$	−21.4312	−1.05970	−0.529852	−	0.848090i	$-0.677753\pi$
$409$	−21.4312	−1.05970	−0.529852	+	0.848090i	$0.677753\pi$
$410$	−3.64118	−0.179825
$411$	−14.4967	−0.715067
$412$	−18.3111	−0.902124
$413$	20.0688	0.987519
$414$	5.86889	0.288440
$415$	4.31662	0.211895
$416$	−2.78339	−0.136467
$417$	20.5545	1.00656
$418$	3.25021	0.158973
$419$	12.3561	0.603637	0.301818	−	0.953365i	$-0.402406\pi$
$419$	12.3561	0.603637	0.301818	+	0.953365i	$0.402406\pi$
$420$	1.19683	0.0583993
$421$	23.9422	1.16687	0.583435	−	0.812160i	$-0.301708\pi$
$421$	23.9422	1.16687	0.583435	+	0.812160i	$0.301708\pi$
$422$	−16.4020	−0.798438
$423$	−6.89025	−0.335015
$424$	−4.79659	−0.232943
$425$	1.90755	0.0925296
$426$	10.7739	0.521998
$427$	4.35366	0.210689
$428$	−4.47193	−0.216159
$429$	3.92173	0.189343
$430$	−2.04566	−0.0986504
$431$	12.6020	0.607016	0.303508	−	0.952829i	$-0.401842\pi$
$431$	12.6020	0.607016	0.303508	+	0.952829i	$0.401842\pi$
$432$	1.00000	0.0481125
$433$	−16.5682	−0.796215	−0.398107	−	0.917339i	$-0.630333\pi$
$433$	−16.5682	−0.796215	−0.398107	+	0.917339i	$0.630333\pi$
$434$	0	0
$435$	−0.175465	−0.00841292
$436$	−9.84187	−0.471340
$437$	−13.5383	−0.647622
$438$	−5.93960	−0.283805
$439$	−16.3339	−0.779573	−0.389786	−	0.920905i	$-0.627451\pi$
$439$	−16.3339	−0.779573	−0.389786	+	0.920905i	$0.627451\pi$
$440$	1.01478	0.0483779
$441$	−4.23862	−0.201839
$442$	1.18481	0.0563555
$443$	13.4178	0.637498	0.318749	−	0.947839i	$-0.396737\pi$
$443$	13.4178	0.637498	0.318749	+	0.947839i	$0.396737\pi$
$444$	−2.76958	−0.131438
$445$	−0.429035	−0.0203382
$446$	−21.8525	−1.03474
$447$	−20.4312	−0.966362
$448$	−1.66174	−0.0785098
$449$	5.10431	0.240887	0.120444	−	0.992720i	$-0.461568\pi$
$449$	5.10431	0.240887	0.120444	+	0.992720i	$0.461568\pi$
$450$	−4.48127	−0.211249
$451$	−7.12323	−0.335420
$452$	−10.9786	−0.516392
$453$	1.05029	0.0493467
$454$	11.5429	0.541733
$455$	−3.33124	−0.156171
$456$	−2.30678	−0.108025
$457$	−38.1315	−1.78372	−0.891858	−	0.452315i	$-0.850598\pi$
$457$	−38.1315	−1.78372	−0.891858	+	0.452315i	$0.850598\pi$
$458$	20.8613	0.974786
$459$	−0.425671	−0.0198686
$460$	−4.22693	−0.197082
$461$	−13.6508	−0.635779	−0.317890	−	0.948128i	$-0.602974\pi$
$461$	−13.6508	−0.635779	−0.317890	+	0.948128i	$0.602974\pi$
$462$	2.34135	0.108930
$463$	31.3505	1.45698	0.728490	−	0.685056i	$-0.240222\pi$
$463$	31.3505	1.45698	0.728490	+	0.685056i	$0.240222\pi$
$464$	0.243625	0.0113100
$465$	0	0
$466$	−27.4079	−1.26965
$467$	−6.51144	−0.301314	−0.150657	−	0.988586i	$-0.548139\pi$
$467$	−6.51144	−0.301314	−0.150657	+	0.988586i	$0.548139\pi$
$468$	−2.78339	−0.128662
$469$	8.72292	0.402787
$470$	4.96255	0.228905
$471$	14.5822	0.671910
$472$	−12.0770	−0.555887
$473$	−4.00191	−0.184008
$474$	−13.3939	−0.615201
$475$	10.3373	0.474309
$476$	0.707354	0.0324215
$477$	−4.79659	−0.219621
$478$	4.70353	0.215135
$479$	12.6740	0.579091	0.289546	−	0.957164i	$-0.406496\pi$
$479$	12.6740	0.579091	0.289546	+	0.957164i	$0.406496\pi$
$480$	−0.720227	−0.0328737
$481$	7.70881	0.351491
$482$	11.3375	0.516410
$483$	−9.75255	−0.443757
$484$	−9.01478	−0.409763
$485$	−3.76978	−0.171177
$486$	1.00000	0.0453609
$487$	15.2003	0.688792	0.344396	−	0.938824i	$-0.388084\pi$
$487$	15.2003	0.688792	0.344396	+	0.938824i	$0.388084\pi$
$488$	−2.61994	−0.118599
$489$	4.88932	0.221103
$490$	3.05277	0.137910
$491$	−26.8000	−1.20947	−0.604734	−	0.796427i	$-0.706721\pi$
$491$	−26.8000	−1.20947	−0.604734	+	0.796427i	$0.706721\pi$
$492$	5.05560	0.227924
$493$	−0.103704	−0.00467059
$494$	6.42067	0.288880
$495$	1.01478	0.0456111
$496$	0	0
$497$	−17.9034	−0.803079
$498$	−5.99342	−0.268572
$499$	32.0535	1.43491	0.717456	−	0.696604i	$-0.245307\pi$
$499$	32.0535	1.43491	0.717456	+	0.696604i	$0.245307\pi$
$500$	6.82867	0.305387
$501$	12.4920	0.558101
$502$	1.01072	0.0451105
$503$	11.6737	0.520504	0.260252	−	0.965541i	$-0.416194\pi$
$503$	11.6737	0.520504	0.260252	+	0.965541i	$0.416194\pi$
$504$	−1.66174	−0.0740197
$505$	7.14590	0.317988
$506$	−8.26913	−0.367607
$507$	−5.25276	−0.233283
$508$	16.3333	0.724671
$509$	−18.2946	−0.810892	−0.405446	−	0.914119i	$-0.632884\pi$
$509$	−18.2946	−0.810892	−0.405446	+	0.914119i	$0.632884\pi$
$510$	0.306580	0.0135756
$511$	9.87007	0.436626
$512$	1.00000	0.0441942
$513$	−2.30678	−0.101847
$514$	30.6255	1.35083
$515$	13.1882	0.581140
$516$	2.84029	0.125037
$517$	9.70820	0.426966
$518$	4.60232	0.202214
$519$	−5.08708	−0.223298
$520$	2.00467	0.0879106
$521$	26.7701	1.17282	0.586410	−	0.810015i	$-0.300541\pi$
$521$	26.7701	1.17282	0.586410	+	0.810015i	$0.300541\pi$
$522$	0.243625	0.0106632
$523$	23.7051	1.03655	0.518276	−	0.855213i	$-0.326574\pi$
$523$	23.7051	1.03655	0.518276	+	0.855213i	$0.326574\pi$
$524$	7.12185	0.311120
$525$	7.44670	0.325001
$526$	−5.84536	−0.254870
$527$	0	0
$528$	−1.40898	−0.0613179
$529$	11.4438	0.497557
$530$	3.45463	0.150060
$531$	−12.0770	−0.524096
$532$	3.83327	0.166193
$533$	−14.0717	−0.609513
$534$	0.595693	0.0257782
$535$	3.22081	0.139248
$536$	−5.24927	−0.226734
$537$	14.1982	0.612698
$538$	0.455772	0.0196497
$539$	5.97212	0.257238
$540$	−0.720227	−0.0309936
$541$	−13.3550	−0.574174	−0.287087	−	0.957904i	$-0.592687\pi$
$541$	−13.3550	−0.574174	−0.287087	+	0.957904i	$0.592687\pi$
$542$	−2.57551	−0.110628
$543$	16.8223	0.721914
$544$	−0.425671	−0.0182505
$545$	7.08839	0.303633
$546$	4.62526	0.197943
$547$	0.974196	0.0416536	0.0208268	−	0.999783i	$-0.493370\pi$
$547$	0.974196	0.0416536	0.0208268	+	0.999783i	$0.493370\pi$
$548$	−14.4967	−0.619267
$549$	−2.61994	−0.111816
$550$	6.31401	0.269230
$551$	−0.561990	−0.0239416
$552$	5.86889	0.249796
$553$	22.2571	0.946468
$554$	23.4233	0.995161
$555$	1.99473	0.0846714
$556$	20.5545	0.871707
$557$	−4.59258	−0.194594	−0.0972969	−	0.995255i	$-0.531020\pi$
$557$	−4.59258	−0.194594	−0.0972969	+	0.995255i	$0.531020\pi$
$558$	0	0
$559$	−7.90564	−0.334373
$560$	1.19683	0.0505753
$561$	0.599760	0.0253219
$562$	29.3381	1.23755
$563$	−30.3395	−1.27866	−0.639329	−	0.768933i	$-0.720788\pi$
$563$	−30.3395	−1.27866	−0.639329	+	0.768933i	$0.720788\pi$
$564$	−6.89025	−0.290132
$565$	7.90711	0.332655
$566$	−10.8881	−0.457662
$567$	−1.66174	−0.0697865
$568$	10.7739	0.452064
$569$	30.9486	1.29743	0.648717	−	0.761030i	$-0.275306\pi$
$569$	30.9486	1.29743	0.648717	+	0.761030i	$0.275306\pi$
$570$	1.66141	0.0695887
$571$	38.2386	1.60023	0.800117	−	0.599844i	$-0.204771\pi$
$571$	38.2386	1.60023	0.800117	+	0.599844i	$0.204771\pi$
$572$	3.92173	0.163976
$573$	−24.4881	−1.02301
$574$	−8.40109	−0.350655
$575$	−26.3001	−1.09679
$576$	1.00000	0.0416667
$577$	−21.6380	−0.900802	−0.450401	−	0.892826i	$-0.648719\pi$
$577$	−21.6380	−0.900802	−0.450401	+	0.892826i	$0.648719\pi$
$578$	−16.8188	−0.699570
$579$	11.9999	0.498698
$580$	−0.175465	−0.00728580
$581$	9.95950	0.413190
$582$	5.23416	0.216963
$583$	6.75829	0.279900
$584$	−5.93960	−0.245782
$585$	2.00467	0.0828829
$586$	11.0321	0.455731
$587$	−42.2673	−1.74456	−0.872279	−	0.489009i	$-0.837359\pi$
$587$	−42.2673	−1.74456	−0.872279	+	0.489009i	$0.837359\pi$
$588$	−4.23862	−0.174798
$589$	0	0
$590$	8.69816	0.358098
$591$	13.4024	0.551301
$592$	−2.76958	−0.113829
$593$	−9.58437	−0.393583	−0.196792	−	0.980445i	$-0.563052\pi$
$593$	−9.58437	−0.393583	−0.196792	+	0.980445i	$0.563052\pi$
$594$	−1.40898	−0.0578110
$595$	−0.509455	−0.0208856
$596$	−20.4312	−0.836894
$597$	−1.04337	−0.0427025
$598$	−16.3354	−0.668003
$599$	35.9741	1.46986	0.734931	−	0.678142i	$-0.237214\pi$
$599$	35.9741	1.46986	0.734931	+	0.678142i	$0.237214\pi$
$600$	−4.48127	−0.182947
$601$	−18.2067	−0.742669	−0.371334	−	0.928499i	$-0.621100\pi$
$601$	−18.2067	−0.742669	−0.371334	+	0.928499i	$0.621100\pi$
$602$	−4.71983	−0.192366
$603$	−5.24927	−0.213767
$604$	1.05029	0.0427355
$605$	6.49269	0.263965
$606$	−9.92173	−0.403043
$607$	19.8432	0.805410	0.402705	−	0.915330i	$-0.368070\pi$
$607$	19.8432	0.805410	0.402705	+	0.915330i	$0.368070\pi$
$608$	−2.30678	−0.0935524
$609$	−0.404841	−0.0164050
$610$	1.88696	0.0764006
$611$	19.1782	0.775868
$612$	−0.425671	−0.0172067
$613$	−21.7481	−0.878397	−0.439199	−	0.898390i	$-0.644738\pi$
$613$	−21.7481	−0.878397	−0.439199	+	0.898390i	$0.644738\pi$
$614$	−7.53042	−0.303903
$615$	−3.64118	−0.146827
$616$	2.34135	0.0943358
$617$	0.675876	0.0272098	0.0136049	−	0.999907i	$-0.495669\pi$
$617$	0.675876	0.0272098	0.0136049	+	0.999907i	$0.495669\pi$
$618$	−18.3111	−0.736581
$619$	10.7141	0.430634	0.215317	−	0.976544i	$-0.430921\pi$
$619$	10.7141	0.430634	0.215317	+	0.976544i	$0.430921\pi$
$620$	0	0
$621$	5.86889	0.235510
$622$	−13.9560	−0.559583
$623$	−0.989887	−0.0396590
$624$	−2.78339	−0.111425
$625$	17.4882	0.699527
$626$	25.0900	1.00280
$627$	3.25021	0.129801
$628$	14.5822	0.581892
$629$	1.17893	0.0470070
$630$	1.19683	0.0476828
$631$	−23.8780	−0.950567	−0.475283	−	0.879833i	$-0.657654\pi$
$631$	−23.8780	−0.950567	−0.475283	+	0.879833i	$0.657654\pi$
$632$	−13.3939	−0.532779
$633$	−16.4020	−0.651922
$634$	−13.7846	−0.547455
$635$	−11.7637	−0.466827
$636$	−4.79659	−0.190197
$637$	11.7977	0.467443
$638$	−0.343262	−0.0135899
$639$	10.7739	0.426210
$640$	−0.720227	−0.0284695
$641$	3.70300	0.146260	0.0731298	−	0.997322i	$-0.476701\pi$
$641$	3.70300	0.146260	0.0731298	+	0.997322i	$0.476701\pi$
$642$	−4.47193	−0.176493
$643$	−15.2231	−0.600339	−0.300170	−	0.953886i	$-0.597043\pi$
$643$	−15.2231	−0.600339	−0.300170	+	0.953886i	$0.597043\pi$
$644$	−9.75255	−0.384304
$645$	−2.04566	−0.0805477
$646$	0.981931	0.0386335
$647$	−7.43908	−0.292460	−0.146230	−	0.989251i	$-0.546714\pi$
$647$	−7.43908	−0.292460	−0.146230	+	0.989251i	$0.546714\pi$
$648$	1.00000	0.0392837
$649$	17.0162	0.667943
$650$	12.4731	0.489236
$651$	0	0
$652$	4.88932	0.191480
$653$	9.46780	0.370503	0.185252	−	0.982691i	$-0.440690\pi$
$653$	9.46780	0.370503	0.185252	+	0.982691i	$0.440690\pi$
$654$	−9.84187	−0.384848
$655$	−5.12935	−0.200420
$656$	5.05560	0.197388
$657$	−5.93960	−0.231726
$658$	11.4498	0.446359
$659$	−21.9987	−0.856947	−0.428474	−	0.903554i	$-0.640949\pi$
$659$	−21.9987	−0.856947	−0.428474	+	0.903554i	$0.640949\pi$
$660$	1.01478	0.0395004
$661$	18.9918	0.738695	0.369347	−	0.929291i	$-0.379581\pi$
$661$	18.9918	0.738695	0.369347	+	0.929291i	$0.379581\pi$
$662$	0.362785	0.0141000
$663$	1.18481	0.0460141
$664$	−5.99342	−0.232590
$665$	−2.76083	−0.107060
$666$	−2.76958	−0.107319
$667$	1.42981	0.0553623
$668$	12.4920	0.483330
$669$	−21.8525	−0.844865
$670$	3.78067	0.146060
$671$	3.69144	0.142507
$672$	−1.66174	−0.0641030
$673$	15.8404	0.610601	0.305301	−	0.952256i	$-0.401243\pi$
$673$	15.8404	0.610601	0.305301	+	0.952256i	$0.401243\pi$
$674$	−13.4133	−0.516662
$675$	−4.48127	−0.172484
$676$	−5.25276	−0.202029
$677$	36.2335	1.39257	0.696284	−	0.717766i	$-0.254835\pi$
$677$	36.2335	1.39257	0.696284	+	0.717766i	$0.254835\pi$
$678$	−10.9786	−0.421632
$679$	−8.69780	−0.333791
$680$	0.306580	0.0117568
$681$	11.5429	0.442323
$682$	0	0
$683$	21.4383	0.820312	0.410156	−	0.912015i	$-0.365474\pi$
$683$	21.4383	0.820312	0.410156	+	0.912015i	$0.365474\pi$
$684$	−2.30678	−0.0882021
$685$	10.4409	0.398926
$686$	18.6757	0.713040
$687$	20.8613	0.795909
$688$	2.84029	0.108285
$689$	13.3508	0.508624
$690$	−4.22693	−0.160917
$691$	−25.0515	−0.953002	−0.476501	−	0.879174i	$-0.658095\pi$
$691$	−25.0515	−0.953002	−0.476501	+	0.879174i	$0.658095\pi$
$692$	−5.08708	−0.193382
$693$	2.34135	0.0889406
$694$	−35.3404	−1.34150
$695$	−14.8039	−0.561546
$696$	0.243625	0.00923458
$697$	−2.15202	−0.0815137
$698$	31.0104	1.17376
$699$	−27.4079	−1.03666
$700$	7.44670	0.281459
$701$	2.41580	0.0912437	0.0456218	−	0.998959i	$-0.485473\pi$
$701$	2.41580	0.0912437	0.0456218	+	0.998959i	$0.485473\pi$
$702$	−2.78339	−0.105052
$703$	6.38882	0.240959
$704$	−1.40898	−0.0531028
$705$	4.96255	0.186900
$706$	24.3174	0.915196
$707$	16.4873	0.620069
$708$	−12.0770	−0.453880
$709$	−36.1246	−1.35669	−0.678344	−	0.734744i	$-0.737302\pi$
$709$	−36.1246	−1.35669	−0.678344	+	0.734744i	$0.737302\pi$
$710$	−7.75967	−0.291215
$711$	−13.3939	−0.502309
$712$	0.595693	0.0223246
$713$	0	0
$714$	0.707354	0.0264720
$715$	−2.82453	−0.105632
$716$	14.1982	0.530612
$717$	4.70353	0.175657
$718$	−19.4298	−0.725114
$719$	26.4602	0.986797	0.493399	−	0.869803i	$-0.335754\pi$
$719$	26.4602	0.986797	0.493399	+	0.869803i	$0.335754\pi$
$720$	−0.720227	−0.0268413
$721$	30.4283	1.13321
$722$	−13.6787	−0.509070
$723$	11.3375	0.421647
$724$	16.8223	0.625196
$725$	−1.09175	−0.0405466
$726$	−9.01478	−0.334570
$727$	−7.08103	−0.262621	−0.131310	−	0.991341i	$-0.541918\pi$
$727$	−7.08103	−0.262621	−0.131310	+	0.991341i	$0.541918\pi$
$728$	4.62526	0.171424
$729$	1.00000	0.0370370
$730$	4.27786	0.158331
$731$	−1.20903	−0.0447176
$732$	−2.61994	−0.0968359
$733$	26.8470	0.991616	0.495808	−	0.868432i	$-0.334872\pi$
$733$	26.8470	0.991616	0.495808	+	0.868432i	$0.334872\pi$
$734$	19.2691	0.711236
$735$	3.05277	0.112603
$736$	5.86889	0.216330
$737$	7.39610	0.272439
$738$	5.05560	0.186099
$739$	23.4062	0.861010	0.430505	−	0.902588i	$-0.358336\pi$
$739$	23.4062	0.861010	0.430505	+	0.902588i	$0.358336\pi$
$740$	1.99473	0.0733276
$741$	6.42067	0.235869
$742$	7.97068	0.292613
$743$	−15.2912	−0.560979	−0.280490	−	0.959857i	$-0.590497\pi$
$743$	−15.2912	−0.560979	−0.280490	+	0.959857i	$0.590497\pi$
$744$	0	0
$745$	14.7151	0.539120
$746$	−4.38573	−0.160573
$747$	−5.99342	−0.219288
$748$	0.599760	0.0219294
$749$	7.43118	0.271530
$750$	6.82867	0.249348
$751$	−21.2551	−0.775610	−0.387805	−	0.921741i	$-0.626767\pi$
$751$	−21.2551	−0.775610	−0.387805	+	0.921741i	$0.626767\pi$
$752$	−6.89025	−0.251262
$753$	1.01072	0.0368326
$754$	−0.678102	−0.0246950
$755$	−0.756444	−0.0275298
$756$	−1.66174	−0.0604369
$757$	48.8803	1.77659	0.888293	−	0.459278i	$-0.151892\pi$
$757$	48.8803	1.77659	0.888293	+	0.459278i	$0.151892\pi$
$758$	12.8066	0.465156
$759$	−8.26913	−0.300150
$760$	1.66141	0.0602656
$761$	−22.5878	−0.818807	−0.409404	−	0.912353i	$-0.634263\pi$
$761$	−22.5878	−0.818807	−0.409404	+	0.912353i	$0.634263\pi$
$762$	16.3333	0.591692
$763$	16.3546	0.592077
$764$	−24.4881	−0.885948
$765$	0.306580	0.0110844
$766$	−28.1219	−1.01608
$767$	33.6149	1.21376
$768$	1.00000	0.0360844
$769$	−46.7012	−1.68409	−0.842044	−	0.539408i	$-0.818648\pi$
$769$	−46.7012	−1.68409	−0.842044	+	0.539408i	$0.818648\pi$
$770$	−1.68631	−0.0607702
$771$	30.6255	1.10295
$772$	11.9999	0.431885
$773$	−26.3710	−0.948499	−0.474249	−	0.880391i	$-0.657280\pi$
$773$	−26.3710	−0.948499	−0.474249	+	0.880391i	$0.657280\pi$
$774$	2.84029	0.102092
$775$	0	0
$776$	5.23416	0.187895
$777$	4.60232	0.165107
$778$	2.34679	0.0841367
$779$	−11.6622	−0.417841
$780$	2.00467	0.0717787
$781$	−15.1802	−0.543190
$782$	−2.49821	−0.0893359
$783$	0.243625	0.00870644
$784$	−4.23862	−0.151379
$785$	−10.5025	−0.374849
$786$	7.12185	0.254028
$787$	−5.23167	−0.186489	−0.0932445	−	0.995643i	$-0.529724\pi$
$787$	−5.23167	−0.186489	−0.0932445	+	0.995643i	$0.529724\pi$
$788$	13.4024	0.477441
$789$	−5.84536	−0.208100
$790$	9.64662	0.343212
$791$	18.2436	0.648669
$792$	−1.40898	−0.0500658
$793$	7.29232	0.258958
$794$	22.5740	0.801120
$795$	3.45463	0.122523
$796$	−1.04337	−0.0369814
$797$	37.0158	1.31117	0.655583	−	0.755123i	$-0.272423\pi$
$797$	37.0158	1.31117	0.655583	+	0.755123i	$0.272423\pi$
$798$	3.83327	0.135696
$799$	2.93298	0.103761
$800$	−4.48127	−0.158437
$801$	0.595693	0.0210478
$802$	−21.0980	−0.744995
$803$	8.36876	0.295327
$804$	−5.24927	−0.185128
$805$	7.02406	0.247565
$806$	0	0
$807$	0.455772	0.0160440
$808$	−9.92173	−0.349045
$809$	−23.1764	−0.814839	−0.407419	−	0.913241i	$-0.633571\pi$
$809$	−23.1764	−0.814839	−0.407419	+	0.913241i	$0.633571\pi$
$810$	−0.720227	−0.0253062
$811$	−25.2396	−0.886281	−0.443140	−	0.896452i	$-0.646136\pi$
$811$	−25.2396	−0.886281	−0.443140	+	0.896452i	$0.646136\pi$
$812$	−0.404841	−0.0142071
$813$	−2.57551	−0.0903271
$814$	3.90227	0.136775
$815$	−3.52142	−0.123350
$816$	−0.425671	−0.0149015
$817$	−6.55195	−0.229224
$818$	−21.4312	−0.749324
$819$	4.62526	0.161620
$820$	−3.64118	−0.127156
$821$	12.6943	0.443036	0.221518	−	0.975156i	$-0.428899\pi$
$821$	12.6943	0.443036	0.221518	+	0.975156i	$0.428899\pi$
$822$	−14.4967	−0.505629
$823$	−12.2905	−0.428421	−0.214211	−	0.976788i	$-0.568718\pi$
$823$	−12.2905	−0.428421	−0.214211	+	0.976788i	$0.568718\pi$
$824$	−18.3111	−0.637898
$825$	6.31401	0.219826
$826$	20.0688	0.698282
$827$	−28.8402	−1.00287	−0.501437	−	0.865194i	$-0.667195\pi$
$827$	−28.8402	−1.00287	−0.501437	+	0.865194i	$0.667195\pi$
$828$	5.86889	0.203958
$829$	−28.8464	−1.00188	−0.500939	−	0.865483i	$-0.667012\pi$
$829$	−28.8464	−1.00188	−0.500939	+	0.865483i	$0.667012\pi$
$830$	4.31662	0.149832
$831$	23.4233	0.812545
$832$	−2.78339	−0.0964966
$833$	1.80426	0.0625139
$834$	20.5545	0.711746
$835$	−8.99707	−0.311356
$836$	3.25021	0.112411
$837$	0	0
$838$	12.3561	0.426836
$839$	−19.3028	−0.666405	−0.333203	−	0.942855i	$-0.608129\pi$
$839$	−19.3028	−0.666405	−0.333203	+	0.942855i	$0.608129\pi$
$840$	1.19683	0.0412945
$841$	−28.9406	−0.997953
$842$	23.9422	0.825101
$843$	29.3381	1.01046
$844$	−16.4020	−0.564581
$845$	3.78318	0.130145
$846$	−6.89025	−0.236892
$847$	14.9802	0.514726
$848$	−4.79659	−0.164716
$849$	−10.8881	−0.373680
$850$	1.90755	0.0654283
$851$	−16.2543	−0.557192
$852$	10.7739	0.369108
$853$	−5.20072	−0.178069	−0.0890346	−	0.996029i	$-0.528378\pi$
$853$	−5.20072	−0.178069	−0.0890346	+	0.996029i	$0.528378\pi$
$854$	4.35366	0.148979
$855$	1.66141	0.0568190
$856$	−4.47193	−0.152847
$857$	6.71771	0.229473	0.114736	−	0.993396i	$-0.463398\pi$
$857$	6.71771	0.229473	0.114736	+	0.993396i	$0.463398\pi$
$858$	3.92173	0.133886
$859$	47.7349	1.62869	0.814347	−	0.580378i	$-0.197095\pi$
$859$	47.7349	1.62869	0.814347	+	0.580378i	$0.197095\pi$
$860$	−2.04566	−0.0697563
$861$	−8.40109	−0.286308
$862$	12.6020	0.429225
$863$	−34.0093	−1.15769	−0.578846	−	0.815437i	$-0.696497\pi$
$863$	−34.0093	−1.15769	−0.578846	+	0.815437i	$0.696497\pi$
$864$	1.00000	0.0340207
$865$	3.66385	0.124575
$866$	−16.5682	−0.563009
$867$	−16.8188	−0.571197
$868$	0	0
$869$	18.8716	0.640177
$870$	−0.175465	−0.00594883
$871$	14.6108	0.495066
$872$	−9.84187	−0.333288
$873$	5.23416	0.177149
$874$	−13.5383	−0.457938
$875$	−11.3475	−0.383614
$876$	−5.93960	−0.200681
$877$	−12.9499	−0.437288	−0.218644	−	0.975805i	$-0.570163\pi$
$877$	−12.9499	−0.437288	−0.218644	+	0.975805i	$0.570163\pi$
$878$	−16.3339	−0.551241
$879$	11.0321	0.372103
$880$	1.01478	0.0342083
$881$	46.3994	1.56323	0.781617	−	0.623759i	$-0.214395\pi$
$881$	46.3994	1.56323	0.781617	+	0.623759i	$0.214395\pi$
$882$	−4.23862	−0.142722
$883$	18.3961	0.619078	0.309539	−	0.950887i	$-0.399825\pi$
$883$	18.3961	0.619078	0.309539	+	0.950887i	$0.399825\pi$
$884$	1.18481	0.0398493
$885$	8.69816	0.292385
$886$	13.4178	0.450779
$887$	−1.15541	−0.0387948	−0.0193974	−	0.999812i	$-0.506175\pi$
$887$	−1.15541	−0.0387948	−0.0193974	+	0.999812i	$0.506175\pi$
$888$	−2.76958	−0.0929410
$889$	−27.1416	−0.910300
$890$	−0.429035	−0.0143813
$891$	−1.40898	−0.0472025
$892$	−21.8525	−0.731675
$893$	15.8943	0.531883
$894$	−20.4312	−0.683321
$895$	−10.2259	−0.341815
$896$	−1.66174	−0.0555148
$897$	−16.3354	−0.545422
$898$	5.10431	0.170333
$899$	0	0
$900$	−4.48127	−0.149376
$901$	2.04177	0.0680212
$902$	−7.12323	−0.237178
$903$	−4.71983	−0.157066
$904$	−10.9786	−0.365144
$905$	−12.1159	−0.402745
$906$	1.05029	0.0348934
$907$	4.42201	0.146830	0.0734152	−	0.997301i	$-0.476610\pi$
$907$	4.42201	0.146830	0.0734152	+	0.997301i	$0.476610\pi$
$908$	11.5429	0.383063
$909$	−9.92173	−0.329083
$910$	−3.33124	−0.110429
$911$	−11.3713	−0.376747	−0.188374	−	0.982097i	$-0.560322\pi$
$911$	−11.3713	−0.376747	−0.188374	+	0.982097i	$0.560322\pi$
$912$	−2.30678	−0.0763852
$913$	8.44459	0.279475
$914$	−38.1315	−1.26128
$915$	1.88696	0.0623808
$916$	20.8613	0.689278
$917$	−11.8347	−0.390815
$918$	−0.425671	−0.0140492
$919$	23.4042	0.772033	0.386016	−	0.922492i	$-0.373851\pi$
$919$	23.4042	0.772033	0.386016	+	0.922492i	$0.373851\pi$
$920$	−4.22693	−0.139358
$921$	−7.53042	−0.248136
$922$	−13.6508	−0.449564
$923$	−29.9880	−0.987066
$924$	2.34135	0.0770248
$925$	12.4112	0.408079
$926$	31.3505	1.03024
$927$	−18.3111	−0.601416
$928$	0.243625	0.00799738
$929$	−33.5711	−1.10143	−0.550716	−	0.834692i	$-0.685645\pi$
$929$	−33.5711	−1.10143	−0.550716	+	0.834692i	$0.685645\pi$
$930$	0	0
$931$	9.77759	0.320448
$932$	−27.4079	−0.897776
$933$	−13.9560	−0.456898
$934$	−6.51144	−0.213061
$935$	−0.431964	−0.0141267
$936$	−2.78339	−0.0909778
$937$	5.57092	0.181994	0.0909971	−	0.995851i	$-0.470995\pi$
$937$	5.57092	0.181994	0.0909971	+	0.995851i	$0.470995\pi$
$938$	8.72292	0.284813
$939$	25.0900	0.818783
$940$	4.96255	0.161860
$941$	44.4642	1.44949	0.724746	−	0.689017i	$-0.241957\pi$
$941$	44.4642	1.44949	0.724746	+	0.689017i	$0.241957\pi$
$942$	14.5822	0.475112
$943$	29.6707	0.966213
$944$	−12.0770	−0.393072
$945$	1.19683	0.0389329
$946$	−4.00191	−0.130113
$947$	−33.4274	−1.08624	−0.543122	−	0.839654i	$-0.682758\pi$
$947$	−33.4274	−1.08624	−0.543122	+	0.839654i	$0.682758\pi$
$948$	−13.3939	−0.435012
$949$	16.5322	0.536658
$950$	10.3373	0.335387
$951$	−13.7846	−0.446995
$952$	0.707354	0.0229255
$953$	−26.5754	−0.860862	−0.430431	−	0.902623i	$-0.641638\pi$
$953$	−26.5754	−0.860862	−0.430431	+	0.902623i	$0.641638\pi$
$954$	−4.79659	−0.155295
$955$	17.6370	0.570720
$956$	4.70353	0.152123
$957$	−0.343262	−0.0110961
$958$	12.6740	0.409479
$959$	24.0897	0.777896
$960$	−0.720227	−0.0232452
$961$	0	0
$962$	7.70881	0.248542
$963$	−4.47193	−0.144106
$964$	11.3375	0.365157
$965$	−8.64264	−0.278216
$966$	−9.75255	−0.313783
$967$	32.0091	1.02934	0.514671	−	0.857388i	$-0.327914\pi$
$967$	32.0091	1.02934	0.514671	+	0.857388i	$0.327914\pi$
$968$	−9.01478	−0.289746
$969$	0.981931	0.0315442
$970$	−3.76978	−0.121040
$971$	40.8982	1.31248	0.656242	−	0.754550i	$-0.272145\pi$
$971$	40.8982	1.31248	0.656242	+	0.754550i	$0.272145\pi$
$972$	1.00000	0.0320750
$973$	−34.1563	−1.09500
$974$	15.2003	0.487050
$975$	12.4731	0.399459
$976$	−2.61994	−0.0838624
$977$	−42.5796	−1.36224	−0.681121	−	0.732171i	$-0.738507\pi$
$977$	−42.5796	−1.36224	−0.681121	+	0.732171i	$0.738507\pi$
$978$	4.88932	0.156343
$979$	−0.839318	−0.0268247
$980$	3.05277	0.0975172
$981$	−9.84187	−0.314227
$982$	−26.8000	−0.855223
$983$	−21.4225	−0.683270	−0.341635	−	0.939833i	$-0.610981\pi$
$983$	−21.4225	−0.683270	−0.341635	+	0.939833i	$0.610981\pi$
$984$	5.05560	0.161167
$985$	−9.65277	−0.307563
$986$	−0.103704	−0.00330261
$987$	11.4498	0.364451
$988$	6.42067	0.204269
$989$	16.6694	0.530055
$990$	1.01478	0.0322519
$991$	−6.00211	−0.190663	−0.0953317	−	0.995446i	$-0.530391\pi$
$991$	−6.00211	−0.190663	−0.0953317	+	0.995446i	$0.530391\pi$
$992$	0	0
$993$	0.362785	0.0115126
$994$	−17.9034	−0.567863
$995$	0.751467	0.0238231
$996$	−5.99342	−0.189909
$997$	36.1833	1.14594	0.572968	−	0.819578i	$-0.305792\pi$
$997$	36.1833	1.14594	0.572968	+	0.819578i	$0.305792\pi$
$998$	32.0535	1.01464
$999$	−2.76958	−0.0876256

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5766.2.a.bg.1.3		4
31.18	even	15		186.2.m.a.169.1	✓	8
31.19	even	15		186.2.m.a.175.1	yes	8
31.30	odd	2		5766.2.a.bc.1.3		4
93.50	odd	30		558.2.ba.e.361.1		8
93.80	odd	30		558.2.ba.e.541.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.m.a.169.1	✓	8	31.18	even	15
186.2.m.a.175.1	yes	8	31.19	even	15
558.2.ba.e.361.1		8	93.50	odd	30
558.2.ba.e.541.1		8	93.80	odd	30
5766.2.a.bc.1.3		4	31.30	odd	2
5766.2.a.bg.1.3		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5766 = 2 \cdot 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5766.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.720227 q^{5} +1.00000 q^{6} -1.66174 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.720227 q^{10} -1.40898 q^{11} +1.00000 q^{12} -2.78339 q^{13} -1.66174 q^{14} -0.720227 q^{15} +1.00000 q^{16} -0.425671 q^{17} +1.00000 q^{18} -2.30678 q^{19} -0.720227 q^{20} -1.66174 q^{21} -1.40898 q^{22} +5.86889 q^{23} +1.00000 q^{24} -4.48127 q^{25} -2.78339 q^{26} +1.00000 q^{27} -1.66174 q^{28} +0.243625 q^{29} -0.720227 q^{30} +1.00000 q^{32} -1.40898 q^{33} -0.425671 q^{34} +1.19683 q^{35} +1.00000 q^{36} -2.76958 q^{37} -2.30678 q^{38} -2.78339 q^{39} -0.720227 q^{40} +5.05560 q^{41} -1.66174 q^{42} +2.84029 q^{43} -1.40898 q^{44} -0.720227 q^{45} +5.86889 q^{46} -6.89025 q^{47} +1.00000 q^{48} -4.23862 q^{49} -4.48127 q^{50} -0.425671 q^{51} -2.78339 q^{52} -4.79659 q^{53} +1.00000 q^{54} +1.01478 q^{55} -1.66174 q^{56} -2.30678 q^{57} +0.243625 q^{58} -12.0770 q^{59} -0.720227 q^{60} -2.61994 q^{61} -1.66174 q^{63} +1.00000 q^{64} +2.00467 q^{65} -1.40898 q^{66} -5.24927 q^{67} -0.425671 q^{68} +5.86889 q^{69} +1.19683 q^{70} +10.7739 q^{71} +1.00000 q^{72} -5.93960 q^{73} -2.76958 q^{74} -4.48127 q^{75} -2.30678 q^{76} +2.34135 q^{77} -2.78339 q^{78} -13.3939 q^{79} -0.720227 q^{80} +1.00000 q^{81} +5.05560 q^{82} -5.99342 q^{83} -1.66174 q^{84} +0.306580 q^{85} +2.84029 q^{86} +0.243625 q^{87} -1.40898 q^{88} +0.595693 q^{89} -0.720227 q^{90} +4.62526 q^{91} +5.86889 q^{92} -6.89025 q^{94} +1.66141 q^{95} +1.00000 q^{96} +5.23416 q^{97} -4.23862 q^{98} -1.40898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} + 4 q^{8} + 4 q^{9} - 3 q^{10} - 3 q^{11} + 4 q^{12} + 4 q^{13} - 11 q^{14} - 3 q^{15} + 4 q^{16} - 15 q^{17} + 4 q^{18} - 2 q^{19} - 3 q^{20}+ \cdots - 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 + 4 * q^8 + 4 * q^9 - 3 * q^10 - 3 * q^11 + 4 * q^12 + 4 * q^13 - 11 * q^14 - 3 * q^15 + 4 * q^16 - 15 * q^17 + 4 * q^18 - 2 * q^19 - 3 * q^20 - 11 * q^21 - 3 * q^22 - 3 * q^23 + 4 * q^24 + q^25 + 4 * q^26 + 4 * q^27 - 11 * q^28 + 9 * q^29 - 3 * q^30 + 4 * q^32 - 3 * q^33 - 15 * q^34 - 3 * q^35 + 4 * q^36 - 8 * q^37 - 2 * q^38 + 4 * q^39 - 3 * q^40 - 12 * q^41 - 11 * q^42 + 10 * q^43 - 3 * q^44 - 3 * q^45 - 3 * q^46 - 6 * q^47 + 4 * q^48 + 11 * q^49 + q^50 - 15 * q^51 + 4 * q^52 - 9 * q^53 + 4 * q^54 - 9 * q^55 - 11 * q^56 - 2 * q^57 + 9 * q^58 - 21 * q^59 - 3 * q^60 - 35 * q^61 - 11 * q^63 + 4 * q^64 - 3 * q^65 - 3 * q^66 - 17 * q^67 - 15 * q^68 - 3 * q^69 - 3 * q^70 - 18 * q^71 + 4 * q^72 + q^73 - 8 * q^74 + q^75 - 2 * q^76 + 12 * q^77 + 4 * q^78 - 17 * q^79 - 3 * q^80 + 4 * q^81 - 12 * q^82 - 6 * q^83 - 11 * q^84 + 15 * q^85 + 10 * q^86 + 9 * q^87 - 3 * q^88 - 6 * q^89 - 3 * q^90 - 16 * q^91 - 3 * q^92 - 6 * q^94 - 36 * q^95 + 4 * q^96 - 17 * q^97 + 11 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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