LMFDB - Embedded newform 2667.2.a.o.1.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2667,2,Mod(1,2667)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2667, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("2667.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16,5,-16,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	yes
Analytic conductor:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 13 x^{14} + 98 x^{13} + 9 x^{12} - 712 x^{11} + 565 x^{10} + 2282 x^{9} - 3082 x^{8} + \cdots + 4 $ x^16 - 5x^15 - 13x^14 + 98x^13 + 9x^12 - 712x^11 + 565x^10 + 2282x^9 - 3082x^8 - 2747x^7 + 5821x^6 - 158x^5 - 3341x^4 + 1002x^3 + 416x^2 - 148*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.62936$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.62936 q^{2} -1.00000 q^{3} +4.91351 q^{4} -0.281520 q^{5} -2.62936 q^{6} -1.00000 q^{7} +7.66067 q^{8} +1.00000 q^{9} -0.740216 q^{10} +5.88693 q^{11} -4.91351 q^{12} +0.529744 q^{13} -2.62936 q^{14} +0.281520 q^{15} +10.3156 q^{16} -4.53224 q^{17} +2.62936 q^{18} +6.62793 q^{19} -1.38325 q^{20} +1.00000 q^{21} +15.4788 q^{22} +6.22430 q^{23} -7.66067 q^{24} -4.92075 q^{25} +1.39289 q^{26} -1.00000 q^{27} -4.91351 q^{28} -8.13724 q^{29} +0.740216 q^{30} -6.74165 q^{31} +11.8020 q^{32} -5.88693 q^{33} -11.9169 q^{34} +0.281520 q^{35} +4.91351 q^{36} +4.51976 q^{37} +17.4272 q^{38} -0.529744 q^{39} -2.15663 q^{40} -1.07598 q^{41} +2.62936 q^{42} +10.0962 q^{43} +28.9255 q^{44} -0.281520 q^{45} +16.3659 q^{46} +5.97230 q^{47} -10.3156 q^{48} +1.00000 q^{49} -12.9384 q^{50} +4.53224 q^{51} +2.60290 q^{52} +2.38641 q^{53} -2.62936 q^{54} -1.65729 q^{55} -7.66067 q^{56} -6.62793 q^{57} -21.3957 q^{58} +8.68072 q^{59} +1.38325 q^{60} -1.42983 q^{61} -17.7262 q^{62} -1.00000 q^{63} +10.4006 q^{64} -0.149133 q^{65} -15.4788 q^{66} -11.3904 q^{67} -22.2692 q^{68} -6.22430 q^{69} +0.740216 q^{70} +11.1525 q^{71} +7.66067 q^{72} +7.79261 q^{73} +11.8841 q^{74} +4.92075 q^{75} +32.5664 q^{76} -5.88693 q^{77} -1.39289 q^{78} +5.38043 q^{79} -2.90405 q^{80} +1.00000 q^{81} -2.82915 q^{82} +5.24596 q^{83} +4.91351 q^{84} +1.27591 q^{85} +26.5466 q^{86} +8.13724 q^{87} +45.0979 q^{88} -13.2313 q^{89} -0.740216 q^{90} -0.529744 q^{91} +30.5832 q^{92} +6.74165 q^{93} +15.7033 q^{94} -1.86589 q^{95} -11.8020 q^{96} +10.8359 q^{97} +2.62936 q^{98} +5.88693 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * 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 $

$2$	2.62936	1.85924	0.929618	−	0.368525i	$-0.120137\pi$
$2$	2.62936	1.85924	0.929618	+	0.368525i	$0.120137\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.91351	2.45676
$5$	−0.281520	−0.125900	−0.0629498	−	0.998017i	$-0.520051\pi$
$5$	−0.281520	−0.125900	−0.0629498	+	0.998017i	$0.520051\pi$
$6$	−2.62936	−1.07343
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	7.66067	2.70846
$9$	1.00000	0.333333
$10$	−0.740216	−0.234077
$11$	5.88693	1.77498	0.887489	−	0.460829i	$-0.152448\pi$
$11$	5.88693	1.77498	0.887489	+	0.460829i	$0.152448\pi$
$12$	−4.91351	−1.41841
$13$	0.529744	0.146924	0.0734622	−	0.997298i	$-0.476595\pi$
$13$	0.529744	0.146924	0.0734622	+	0.997298i	$0.476595\pi$
$14$	−2.62936	−0.702725
$15$	0.281520	0.0726881
$16$	10.3156	2.57890
$17$	−4.53224	−1.09923	−0.549614	−	0.835419i	$-0.685225\pi$
$17$	−4.53224	−1.09923	−0.549614	+	0.835419i	$0.685225\pi$
$18$	2.62936	0.619745
$19$	6.62793	1.52055	0.760275	−	0.649601i	$-0.225064\pi$
$19$	6.62793	1.52055	0.760275	+	0.649601i	$0.225064\pi$
$20$	−1.38325	−0.309305
$21$	1.00000	0.218218
$22$	15.4788	3.30010
$23$	6.22430	1.29786	0.648928	−	0.760850i	$-0.275218\pi$
$23$	6.22430	1.29786	0.648928	+	0.760850i	$0.275218\pi$
$24$	−7.66067	−1.56373
$25$	−4.92075	−0.984149
$26$	1.39289	0.273167
$27$	−1.00000	−0.192450
$28$	−4.91351	−0.928567
$29$	−8.13724	−1.51105	−0.755523	−	0.655122i	$-0.772617\pi$
$29$	−8.13724	−1.51105	−0.755523	+	0.655122i	$0.772617\pi$
$30$	0.740216	0.135144
$31$	−6.74165	−1.21084	−0.605418	−	0.795908i	$-0.706994\pi$
$31$	−6.74165	−1.21084	−0.605418	+	0.795908i	$0.706994\pi$
$32$	11.8020	2.08633
$33$	−5.88693	−1.02478
$34$	−11.9169	−2.04372
$35$	0.281520	0.0475855
$36$	4.91351	0.818919
$37$	4.51976	0.743045	0.371522	−	0.928424i	$-0.378836\pi$
$37$	4.51976	0.743045	0.371522	+	0.928424i	$0.378836\pi$
$38$	17.4272	2.82706
$39$	−0.529744	−0.0848269
$40$	−2.15663	−0.340993
$41$	−1.07598	−0.168041	−0.0840203	−	0.996464i	$-0.526776\pi$
$41$	−1.07598	−0.168041	−0.0840203	+	0.996464i	$0.526776\pi$
$42$	2.62936	0.405718
$43$	10.0962	1.53966	0.769829	−	0.638250i	$-0.220341\pi$
$43$	10.0962	1.53966	0.769829	+	0.638250i	$0.220341\pi$
$44$	28.9255	4.36069
$45$	−0.281520	−0.0419665
$46$	16.3659	2.41302
$47$	5.97230	0.871149	0.435575	−	0.900153i	$-0.356545\pi$
$47$	5.97230	0.871149	0.435575	+	0.900153i	$0.356545\pi$
$48$	−10.3156	−1.48893
$49$	1.00000	0.142857
$50$	−12.9384	−1.82977
$51$	4.53224	0.634640
$52$	2.60290	0.360958
$53$	2.38641	0.327799	0.163900	−	0.986477i	$-0.447593\pi$
$53$	2.38641	0.327799	0.163900	+	0.986477i	$0.447593\pi$
$54$	−2.62936	−0.357810
$55$	−1.65729	−0.223469
$56$	−7.66067	−1.02370
$57$	−6.62793	−0.877890
$58$	−21.3957	−2.80939
$59$	8.68072	1.13013	0.565067	−	0.825045i	$-0.308850\pi$
$59$	8.68072	1.13013	0.565067	+	0.825045i	$0.308850\pi$
$60$	1.38325	0.178577
$61$	−1.42983	−0.183071	−0.0915355	−	0.995802i	$-0.529178\pi$
$61$	−1.42983	−0.183071	−0.0915355	+	0.995802i	$0.529178\pi$
$62$	−17.7262	−2.25123
$63$	−1.00000	−0.125988
$64$	10.4006	1.30007
$65$	−0.149133	−0.0184977
$66$	−15.4788	−1.90531
$67$	−11.3904	−1.39155	−0.695776	−	0.718258i	$-0.744940\pi$
$67$	−11.3904	−1.39155	−0.695776	+	0.718258i	$0.744940\pi$
$68$	−22.2692	−2.70054
$69$	−6.22430	−0.749318
$70$	0.740216	0.0884728
$71$	11.1525	1.32356	0.661779	−	0.749699i	$-0.269802\pi$
$71$	11.1525	1.32356	0.661779	+	0.749699i	$0.269802\pi$
$72$	7.66067	0.902818
$73$	7.79261	0.912056	0.456028	−	0.889965i	$-0.349272\pi$
$73$	7.79261	0.912056	0.456028	+	0.889965i	$0.349272\pi$
$74$	11.8841	1.38150
$75$	4.92075	0.568199
$76$	32.5664	3.73562
$77$	−5.88693	−0.670878
$78$	−1.39289	−0.157713
$79$	5.38043	0.605346	0.302673	−	0.953095i	$-0.402121\pi$
$79$	5.38043	0.605346	0.302673	+	0.953095i	$0.402121\pi$
$80$	−2.90405	−0.324682
$81$	1.00000	0.111111
$82$	−2.82915	−0.312427
$83$	5.24596	0.575819	0.287910	−	0.957658i	$-0.407040\pi$
$83$	5.24596	0.575819	0.287910	+	0.957658i	$0.407040\pi$
$84$	4.91351	0.536108
$85$	1.27591	0.138392
$86$	26.5466	2.86259
$87$	8.13724	0.872403
$88$	45.0979	4.80745
$89$	−13.2313	−1.40251	−0.701257	−	0.712909i	$-0.747377\pi$
$89$	−13.2313	−1.40251	−0.701257	+	0.712909i	$0.747377\pi$
$90$	−0.740216	−0.0780256
$91$	−0.529744	−0.0555322
$92$	30.5832	3.18852
$93$	6.74165	0.699076
$94$	15.7033	1.61967
$95$	−1.86589	−0.191437
$96$	−11.8020	−1.20454
$97$	10.8359	1.10022	0.550109	−	0.835093i	$-0.314586\pi$
$97$	10.8359	1.10022	0.550109	+	0.835093i	$0.314586\pi$
$98$	2.62936	0.265605
$99$	5.88693	0.591659
$100$	−24.1782	−2.41782
$101$	−10.8706	−1.08167	−0.540834	−	0.841129i	$-0.681891\pi$
$101$	−10.8706	−1.08167	−0.540834	+	0.841129i	$0.681891\pi$
$102$	11.9169	1.17995
$103$	6.93370	0.683198	0.341599	−	0.939846i	$-0.389032\pi$
$103$	6.93370	0.683198	0.341599	+	0.939846i	$0.389032\pi$
$104$	4.05819	0.397938
$105$	−0.281520	−0.0274735
$106$	6.27473	0.609456
$107$	−18.2465	−1.76395	−0.881976	−	0.471295i	$-0.843787\pi$
$107$	−18.2465	−1.76395	−0.881976	+	0.471295i	$0.843787\pi$
$108$	−4.91351	−0.472803
$109$	−3.90960	−0.374472	−0.187236	−	0.982315i	$-0.559953\pi$
$109$	−3.90960	−0.374472	−0.187236	+	0.982315i	$0.559953\pi$
$110$	−4.35760	−0.415481
$111$	−4.51976	−0.428997
$112$	−10.3156	−0.974732
$113$	7.61713	0.716559	0.358280	−	0.933614i	$-0.383363\pi$
$113$	7.61713	0.716559	0.358280	+	0.933614i	$0.383363\pi$
$114$	−17.4272	−1.63221
$115$	−1.75226	−0.163400
$116$	−39.9824	−3.71228
$117$	0.529744	0.0489748
$118$	22.8247	2.10118
$119$	4.53224	0.415469
$120$	2.15663	0.196873
$121$	23.6560	2.15054
$122$	−3.75953	−0.340372
$123$	1.07598	0.0970182
$124$	−33.1252	−2.97473
$125$	2.79289	0.249803
$126$	−2.62936	−0.234242
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	3.74276	0.330816
$129$	−10.0962	−0.888922
$130$	−0.392125	−0.0343916
$131$	−7.91736	−0.691743	−0.345872	−	0.938282i	$-0.612417\pi$
$131$	−7.91736	−0.691743	−0.345872	+	0.938282i	$0.612417\pi$
$132$	−28.9255	−2.51764
$133$	−6.62793	−0.574714
$134$	−29.9493	−2.58722
$135$	0.281520	0.0242294
$136$	−34.7200	−2.97721
$137$	−15.2967	−1.30688	−0.653442	−	0.756976i	$-0.726676\pi$
$137$	−15.2967	−1.30688	−0.653442	+	0.756976i	$0.726676\pi$
$138$	−16.3659	−1.39316
$139$	−18.8442	−1.59834	−0.799171	−	0.601103i	$-0.794728\pi$
$139$	−18.8442	−1.59834	−0.799171	+	0.601103i	$0.794728\pi$
$140$	1.38325	0.116906
$141$	−5.97230	−0.502958
$142$	29.3239	2.46081
$143$	3.11857	0.260788
$144$	10.3156	0.859633
$145$	2.29079	0.190240
$146$	20.4896	1.69573
$147$	−1.00000	−0.0824786
$148$	22.2079	1.82548
$149$	1.80216	0.147639	0.0738193	−	0.997272i	$-0.476481\pi$
$149$	1.80216	0.147639	0.0738193	+	0.997272i	$0.476481\pi$
$150$	12.9384	1.05642
$151$	−18.6785	−1.52003	−0.760015	−	0.649905i	$-0.774809\pi$
$151$	−18.6785	−1.52003	−0.760015	+	0.649905i	$0.774809\pi$
$152$	50.7744	4.11834
$153$	−4.53224	−0.366409
$154$	−15.4788	−1.24732
$155$	1.89791	0.152444
$156$	−2.60290	−0.208399
$157$	5.60729	0.447510	0.223755	−	0.974645i	$-0.428168\pi$
$157$	5.60729	0.447510	0.223755	+	0.974645i	$0.428168\pi$
$158$	14.1471	1.12548
$159$	−2.38641	−0.189255
$160$	−3.32251	−0.262668
$161$	−6.22430	−0.490544
$162$	2.62936	0.206582
$163$	−11.0862	−0.868340	−0.434170	−	0.900831i	$-0.642958\pi$
$163$	−11.0862	−0.868340	−0.434170	+	0.900831i	$0.642958\pi$
$164$	−5.28686	−0.412835
$165$	1.65729	0.129020
$166$	13.7935	1.07058
$167$	−14.5847	−1.12860	−0.564298	−	0.825571i	$-0.690853\pi$
$167$	−14.5847	−1.12860	−0.564298	+	0.825571i	$0.690853\pi$
$168$	7.66067	0.591033
$169$	−12.7194	−0.978413
$170$	3.35483	0.257304
$171$	6.62793	0.506850
$172$	49.6079	3.78257
$173$	0.735687	0.0559333	0.0279666	−	0.999609i	$-0.491097\pi$
$173$	0.735687	0.0559333	0.0279666	+	0.999609i	$0.491097\pi$
$174$	21.3957	1.62200
$175$	4.92075	0.371973
$176$	60.7272	4.57749
$177$	−8.68072	−0.652483
$178$	−34.7898	−2.60760
$179$	−6.14587	−0.459364	−0.229682	−	0.973266i	$-0.573769\pi$
$179$	−6.14587	−0.459364	−0.229682	+	0.973266i	$0.573769\pi$
$180$	−1.38325	−0.103102
$181$	−26.5200	−1.97122	−0.985609	−	0.169039i	$-0.945934\pi$
$181$	−26.5200	−1.97122	−0.985609	+	0.169039i	$0.945934\pi$
$182$	−1.39289	−0.103248
$183$	1.42983	0.105696
$184$	47.6823	3.51519
$185$	−1.27240	−0.0935490
$186$	17.7262	1.29975
$187$	−26.6810	−1.95111
$188$	29.3450	2.14020
$189$	1.00000	0.0727393
$190$	−4.90610	−0.355926
$191$	3.47889	0.251724	0.125862	−	0.992048i	$-0.459830\pi$
$191$	3.47889	0.251724	0.125862	+	0.992048i	$0.459830\pi$
$192$	−10.4006	−0.750598
$193$	−19.7817	−1.42392	−0.711958	−	0.702222i	$-0.752191\pi$
$193$	−19.7817	−1.42392	−0.711958	+	0.702222i	$0.752191\pi$
$194$	28.4914	2.04557
$195$	0.149133	0.0106797
$196$	4.91351	0.350965
$197$	−4.07163	−0.290092	−0.145046	−	0.989425i	$-0.546333\pi$
$197$	−4.07163	−0.290092	−0.145046	+	0.989425i	$0.546333\pi$
$198$	15.4788	1.10003
$199$	4.28232	0.303566	0.151783	−	0.988414i	$-0.451499\pi$
$199$	4.28232	0.303566	0.151783	+	0.988414i	$0.451499\pi$
$200$	−37.6962	−2.66552
$201$	11.3904	0.803413
$202$	−28.5828	−2.01108
$203$	8.13724	0.571122
$204$	22.2692	1.55916
$205$	0.302911	0.0211562
$206$	18.2312	1.27023
$207$	6.22430	0.432619
$208$	5.46462	0.378903
$209$	39.0182	2.69894
$210$	−0.740216	−0.0510798
$211$	−18.9882	−1.30720	−0.653601	−	0.756839i	$-0.726743\pi$
$211$	−18.9882	−1.30720	−0.653601	+	0.756839i	$0.726743\pi$
$212$	11.7257	0.805323
$213$	−11.1525	−0.764156
$214$	−47.9764	−3.27960
$215$	−2.84229	−0.193842
$216$	−7.66067	−0.521242
$217$	6.74165	0.457653
$218$	−10.2797	−0.696231
$219$	−7.79261	−0.526576
$220$	−8.14311	−0.549009
$221$	−2.40092	−0.161504
$222$	−11.8841	−0.797607
$223$	−18.8389	−1.26155	−0.630773	−	0.775968i	$-0.717262\pi$
$223$	−18.8389	−1.26155	−0.630773	+	0.775968i	$0.717262\pi$
$224$	−11.8020	−0.788557
$225$	−4.92075	−0.328050
$226$	20.0281	1.33225
$227$	−9.90495	−0.657414	−0.328707	−	0.944432i	$-0.606613\pi$
$227$	−9.90495	−0.657414	−0.328707	+	0.944432i	$0.606613\pi$
$228$	−32.5664	−2.15676
$229$	0.0909386	0.00600939	0.00300469	−	0.999995i	$-0.499044\pi$
$229$	0.0909386	0.00600939	0.00300469	+	0.999995i	$0.499044\pi$
$230$	−4.60733	−0.303798
$231$	5.88693	0.387332
$232$	−62.3367	−4.09260
$233$	−9.23810	−0.605208	−0.302604	−	0.953116i	$-0.597856\pi$
$233$	−9.23810	−0.605208	−0.302604	+	0.953116i	$0.597856\pi$
$234$	1.39289	0.0910557
$235$	−1.68132	−0.109677
$236$	42.6528	2.77646
$237$	−5.38043	−0.349496
$238$	11.9169	0.772455
$239$	22.8712	1.47942	0.739708	−	0.672928i	$-0.234964\pi$
$239$	22.8712	1.47942	0.739708	+	0.672928i	$0.234964\pi$
$240$	2.90405	0.187455
$241$	25.5928	1.64857	0.824287	−	0.566171i	$-0.191576\pi$
$241$	25.5928	1.64857	0.824287	+	0.566171i	$0.191576\pi$
$242$	62.2000	3.99837
$243$	−1.00000	−0.0641500
$244$	−7.02549	−0.449761
$245$	−0.281520	−0.0179856
$246$	2.82915	0.180380
$247$	3.51110	0.223406
$248$	−51.6455	−3.27949
$249$	−5.24596	−0.332449
$250$	7.34350	0.464444
$251$	−10.2062	−0.644207	−0.322103	−	0.946705i	$-0.604390\pi$
$251$	−10.2062	−0.644207	−0.322103	+	0.946705i	$0.604390\pi$
$252$	−4.91351	−0.309522
$253$	36.6420	2.30367
$254$	2.62936	0.164980
$255$	−1.27591	−0.0799009
$256$	−10.9601	−0.685008
$257$	−13.3777	−0.834479	−0.417240	−	0.908797i	$-0.637002\pi$
$257$	−13.3777	−0.834479	−0.417240	+	0.908797i	$0.637002\pi$
$258$	−26.5466	−1.65272
$259$	−4.51976	−0.280845
$260$	−0.732769	−0.0454444
$261$	−8.13724	−0.503682
$262$	−20.8176	−1.28611
$263$	14.5895	0.899629	0.449815	−	0.893122i	$-0.351490\pi$
$263$	14.5895	0.899629	0.449815	+	0.893122i	$0.351490\pi$
$264$	−45.0979	−2.77558
$265$	−0.671823	−0.0412697
$266$	−17.4272	−1.06853
$267$	13.2313	0.809742
$268$	−55.9667	−3.41871
$269$	−0.998325	−0.0608689	−0.0304345	−	0.999537i	$-0.509689\pi$
$269$	−0.998325	−0.0608689	−0.0304345	+	0.999537i	$0.509689\pi$
$270$	0.740216	0.0450481
$271$	22.3880	1.35997	0.679987	−	0.733224i	$-0.261985\pi$
$271$	22.3880	1.35997	0.679987	+	0.733224i	$0.261985\pi$
$272$	−46.7527	−2.83480
$273$	0.529744	0.0320615
$274$	−40.2205	−2.42981
$275$	−28.9681	−1.74684
$276$	−30.5832	−1.84089
$277$	−7.05775	−0.424059	−0.212030	−	0.977263i	$-0.568007\pi$
$277$	−7.05775	−0.424059	−0.212030	+	0.977263i	$0.568007\pi$
$278$	−49.5481	−2.97170
$279$	−6.74165	−0.403612
$280$	2.15663	0.128883
$281$	24.0591	1.43524	0.717622	−	0.696433i	$-0.245231\pi$
$281$	24.0591	1.43524	0.717622	+	0.696433i	$0.245231\pi$
$282$	−15.7033	−0.935118
$283$	−11.0668	−0.657851	−0.328926	−	0.944356i	$-0.606687\pi$
$283$	−11.0668	−0.657851	−0.328926	+	0.944356i	$0.606687\pi$
$284$	54.7980	3.25166
$285$	1.86589	0.110526
$286$	8.19982	0.484866
$287$	1.07598	0.0635133
$288$	11.8020	0.695442
$289$	3.54115	0.208303
$290$	6.02331	0.353701
$291$	−10.8359	−0.635212
$292$	38.2891	2.24070
$293$	22.6626	1.32396	0.661982	−	0.749519i	$-0.269715\pi$
$293$	22.6626	1.32396	0.661982	+	0.749519i	$0.269715\pi$
$294$	−2.62936	−0.153347
$295$	−2.44379	−0.142283
$296$	34.6244	2.01250
$297$	−5.88693	−0.341595
$298$	4.73852	0.274495
$299$	3.29728	0.190687
$300$	24.1782	1.39593
$301$	−10.0962	−0.581936
$302$	−49.1123	−2.82610
$303$	10.8706	0.624502
$304$	68.3710	3.92135
$305$	0.402526	0.0230486
$306$	−11.9169	−0.681242
$307$	17.4088	0.993572	0.496786	−	0.867873i	$-0.334513\pi$
$307$	17.4088	0.993572	0.496786	+	0.867873i	$0.334513\pi$
$308$	−28.9255	−1.64819
$309$	−6.93370	−0.394444
$310$	4.99028	0.283429
$311$	−15.7117	−0.890930	−0.445465	−	0.895299i	$-0.646962\pi$
$311$	−15.7117	−0.890930	−0.445465	+	0.895299i	$0.646962\pi$
$312$	−4.05819	−0.229750
$313$	−13.9048	−0.785945	−0.392973	−	0.919550i	$-0.628553\pi$
$313$	−13.9048	−0.785945	−0.392973	+	0.919550i	$0.628553\pi$
$314$	14.7436	0.832027
$315$	0.281520	0.0158618
$316$	26.4368	1.48719
$317$	17.5737	0.987036	0.493518	−	0.869735i	$-0.335711\pi$
$317$	17.5737	0.987036	0.493518	+	0.869735i	$0.335711\pi$
$318$	−6.27473	−0.351869
$319$	−47.9034	−2.68207
$320$	−2.92797	−0.163679
$321$	18.2465	1.01842
$322$	−16.3659	−0.912036
$323$	−30.0393	−1.67143
$324$	4.91351	0.272973
$325$	−2.60673	−0.144596
$326$	−29.1496	−1.61445
$327$	3.90960	0.216201
$328$	−8.24276	−0.455130
$329$	−5.97230	−0.329263
$330$	4.35760	0.239878
$331$	23.1601	1.27299	0.636497	−	0.771279i	$-0.280383\pi$
$331$	23.1601	1.27299	0.636497	+	0.771279i	$0.280383\pi$
$332$	25.7761	1.41465
$333$	4.51976	0.247682
$334$	−38.3483	−2.09833
$335$	3.20661	0.175196
$336$	10.3156	0.562762
$337$	−6.95439	−0.378830	−0.189415	−	0.981897i	$-0.560659\pi$
$337$	−6.95439	−0.378830	−0.189415	+	0.981897i	$0.560659\pi$
$338$	−33.4438	−1.81910
$339$	−7.61713	−0.413706
$340$	6.26922	0.339996
$341$	−39.6876	−2.14921
$342$	17.4272	0.942354
$343$	−1.00000	−0.0539949
$344$	77.3438	4.17010
$345$	1.75226	0.0943388
$346$	1.93438	0.103993
$347$	19.6511	1.05493	0.527463	−	0.849578i	$-0.323143\pi$
$347$	19.6511	1.05493	0.527463	+	0.849578i	$0.323143\pi$
$348$	39.9824	2.14328
$349$	−15.6440	−0.837404	−0.418702	−	0.908124i	$-0.637515\pi$
$349$	−15.6440	−0.837404	−0.418702	+	0.908124i	$0.637515\pi$
$350$	12.9384	0.691586
$351$	−0.529744	−0.0282756
$352$	69.4779	3.70318
$353$	−28.9684	−1.54183	−0.770916	−	0.636937i	$-0.780201\pi$
$353$	−28.9684	−1.54183	−0.770916	+	0.636937i	$0.780201\pi$
$354$	−22.8247	−1.21312
$355$	−3.13965	−0.166635
$356$	−65.0121	−3.44564
$357$	−4.53224	−0.239871
$358$	−16.1597	−0.854066
$359$	1.84320	0.0972803	0.0486401	−	0.998816i	$-0.484511\pi$
$359$	1.84320	0.0972803	0.0486401	+	0.998816i	$0.484511\pi$
$360$	−2.15663	−0.113664
$361$	24.9294	1.31207
$362$	−69.7306	−3.66496
$363$	−23.6560	−1.24162
$364$	−2.60290	−0.136429
$365$	−2.19378	−0.114827
$366$	3.75953	0.196514
$367$	32.0796	1.67454	0.837270	−	0.546790i	$-0.184150\pi$
$367$	32.0796	1.67454	0.837270	+	0.546790i	$0.184150\pi$
$368$	64.2074	3.34704
$369$	−1.07598	−0.0560135
$370$	−3.34560	−0.173930
$371$	−2.38641	−0.123896
$372$	33.1252	1.71746
$373$	−3.41982	−0.177072	−0.0885359	−	0.996073i	$-0.528219\pi$
$373$	−3.41982	−0.177072	−0.0885359	+	0.996073i	$0.528219\pi$
$374$	−70.1538	−3.62757
$375$	−2.79289	−0.144224
$376$	45.7518	2.35947
$377$	−4.31065	−0.222010
$378$	2.62936	0.135239
$379$	−11.9019	−0.611360	−0.305680	−	0.952134i	$-0.598884\pi$
$379$	−11.9019	−0.611360	−0.305680	+	0.952134i	$0.598884\pi$
$380$	−9.16809	−0.470313
$381$	−1.00000	−0.0512316
$382$	9.14725	0.468014
$383$	1.97154	0.100741	0.0503705	−	0.998731i	$-0.483960\pi$
$383$	1.97154	0.100741	0.0503705	+	0.998731i	$0.483960\pi$
$384$	−3.74276	−0.190997
$385$	1.65729	0.0844633
$386$	−52.0131	−2.64740
$387$	10.0962	0.513220
$388$	53.2423	2.70297
$389$	15.1519	0.768233	0.384116	−	0.923285i	$-0.374506\pi$
$389$	15.1519	0.768233	0.384116	+	0.923285i	$0.374506\pi$
$390$	0.392125	0.0198560
$391$	−28.2100	−1.42664
$392$	7.66067	0.386922
$393$	7.91736	0.399378
$394$	−10.7058	−0.539349
$395$	−1.51470	−0.0762127
$396$	28.9255	1.45356
$397$	20.2999	1.01882	0.509412	−	0.860523i	$-0.329863\pi$
$397$	20.2999	1.01882	0.509412	+	0.860523i	$0.329863\pi$
$398$	11.2598	0.564400
$399$	6.62793	0.331811
$400$	−50.7604	−2.53802
$401$	8.93416	0.446151	0.223075	−	0.974801i	$-0.428390\pi$
$401$	8.93416	0.446151	0.223075	+	0.974801i	$0.428390\pi$
$402$	29.9493	1.49374
$403$	−3.57134	−0.177901
$404$	−53.4130	−2.65740
$405$	−0.281520	−0.0139888
$406$	21.3957	1.06185
$407$	26.6076	1.31889
$408$	34.7200	1.71889
$409$	35.0206	1.73166	0.865828	−	0.500341i	$-0.166792\pi$
$409$	35.0206	1.73166	0.865828	+	0.500341i	$0.166792\pi$
$410$	0.796461	0.0393344
$411$	15.2967	0.754530
$412$	34.0688	1.67845
$413$	−8.68072	−0.427150
$414$	16.3659	0.804340
$415$	−1.47684	−0.0724954
$416$	6.25206	0.306532
$417$	18.8442	0.922804
$418$	102.593	5.01797
$419$	0.262864	0.0128418	0.00642088	−	0.999979i	$-0.497956\pi$
$419$	0.262864	0.0128418	0.00642088	+	0.999979i	$0.497956\pi$
$420$	−1.38325	−0.0674958
$421$	−16.5395	−0.806087	−0.403044	−	0.915181i	$-0.632048\pi$
$421$	−16.5395	−0.806087	−0.403044	+	0.915181i	$0.632048\pi$
$422$	−49.9268	−2.43040
$423$	5.97230	0.290383
$424$	18.2815	0.887829
$425$	22.3020	1.08180
$426$	−29.3239	−1.42075
$427$	1.42983	0.0691944
$428$	−89.6542	−4.33360
$429$	−3.11857	−0.150566
$430$	−7.47338	−0.360399
$431$	−1.16723	−0.0562235	−0.0281118	−	0.999605i	$-0.508949\pi$
$431$	−1.16723	−0.0562235	−0.0281118	+	0.999605i	$0.508949\pi$
$432$	−10.3156	−0.496309
$433$	20.2215	0.971784	0.485892	−	0.874019i	$-0.338495\pi$
$433$	20.2215	0.971784	0.485892	+	0.874019i	$0.338495\pi$
$434$	17.7262	0.850884
$435$	−2.29079	−0.109835
$436$	−19.2099	−0.919986
$437$	41.2542	1.97346
$438$	−20.4896	−0.979029
$439$	7.60899	0.363157	0.181579	−	0.983376i	$-0.441879\pi$
$439$	7.60899	0.363157	0.181579	+	0.983376i	$0.441879\pi$
$440$	−12.6959	−0.605255
$441$	1.00000	0.0476190
$442$	−6.31288	−0.300273
$443$	−26.1266	−1.24131	−0.620656	−	0.784083i	$-0.713133\pi$
$443$	−26.1266	−1.24131	−0.620656	+	0.784083i	$0.713133\pi$
$444$	−22.2079	−1.05394
$445$	3.72487	0.176576
$446$	−49.5341	−2.34551
$447$	−1.80216	−0.0852392
$448$	−10.4006	−0.491382
$449$	5.83016	0.275142	0.137571	−	0.990492i	$-0.456070\pi$
$449$	5.83016	0.275142	0.137571	+	0.990492i	$0.456070\pi$
$450$	−12.9384	−0.609922
$451$	−6.33425	−0.298268
$452$	37.4269	1.76041
$453$	18.6785	0.877590
$454$	−26.0436	−1.22229
$455$	0.149133	0.00699148
$456$	−50.7744	−2.37773
$457$	−35.6020	−1.66539	−0.832696	−	0.553730i	$-0.813204\pi$
$457$	−35.6020	−1.66539	−0.832696	+	0.553730i	$0.813204\pi$
$458$	0.239110	0.0111729
$459$	4.53224	0.211547
$460$	−8.60978	−0.401433
$461$	0.628045	0.0292510	0.0146255	−	0.999893i	$-0.495344\pi$
$461$	0.628045	0.0292510	0.0146255	+	0.999893i	$0.495344\pi$
$462$	15.4788	0.720141
$463$	−32.3183	−1.50196	−0.750979	−	0.660327i	$-0.770418\pi$
$463$	−32.3183	−1.50196	−0.750979	+	0.660327i	$0.770418\pi$
$464$	−83.9404	−3.89684
$465$	−1.89791	−0.0880134
$466$	−24.2902	−1.12522
$467$	42.6554	1.97386	0.986929	−	0.161157i	$-0.0515224\pi$
$467$	42.6554	1.97386	0.986929	+	0.161157i	$0.0515224\pi$
$468$	2.60290	0.120319
$469$	11.3904	0.525958
$470$	−4.42079	−0.203916
$471$	−5.60729	−0.258370
$472$	66.5001	3.06092
$473$	59.4358	2.73286
$474$	−14.1471	−0.649796
$475$	−32.6143	−1.49645
$476$	22.2692	1.02071
$477$	2.38641	0.109266
$478$	60.1366	2.75058
$479$	−0.329133	−0.0150385	−0.00751925	−	0.999972i	$-0.502393\pi$
$479$	−0.329133	−0.0150385	−0.00751925	+	0.999972i	$0.502393\pi$
$480$	3.32251	0.151651
$481$	2.39432	0.109171
$482$	67.2925	3.06509
$483$	6.22430	0.283215
$484$	116.234	5.28337
$485$	−3.05052	−0.138517
$486$	−2.62936	−0.119270
$487$	1.30116	0.0589612	0.0294806	−	0.999565i	$-0.490615\pi$
$487$	1.30116	0.0589612	0.0294806	+	0.999565i	$0.490615\pi$
$488$	−10.9535	−0.495840
$489$	11.0862	0.501336
$490$	−0.740216	−0.0334396
$491$	−26.3888	−1.19091	−0.595456	−	0.803388i	$-0.703028\pi$
$491$	−26.3888	−1.19091	−0.595456	+	0.803388i	$0.703028\pi$
$492$	5.28686	0.238350
$493$	36.8799	1.66099
$494$	9.23194	0.415365
$495$	−1.65729	−0.0744896
$496$	−69.5441	−3.12262
$497$	−11.1525	−0.500258
$498$	−13.7935	−0.618102
$499$	−21.1126	−0.945128	−0.472564	−	0.881296i	$-0.656672\pi$
$499$	−21.1126	−0.945128	−0.472564	+	0.881296i	$0.656672\pi$
$500$	13.7229	0.613707
$501$	14.5847	0.651595
$502$	−26.8356	−1.19773
$503$	−1.06969	−0.0476951	−0.0238475	−	0.999716i	$-0.507592\pi$
$503$	−1.06969	−0.0476951	−0.0238475	+	0.999716i	$0.507592\pi$
$504$	−7.66067	−0.341233
$505$	3.06030	0.136182
$506$	96.3450	4.28306
$507$	12.7194	0.564887
$508$	4.91351	0.218002
$509$	22.5239	0.998354	0.499177	−	0.866500i	$-0.333636\pi$
$509$	22.5239	0.998354	0.499177	+	0.866500i	$0.333636\pi$
$510$	−3.35483	−0.148555
$511$	−7.79261	−0.344725
$512$	−36.3036	−1.60441
$513$	−6.62793	−0.292630
$514$	−35.1748	−1.55149
$515$	−1.95197	−0.0860143
$516$	−49.6079	−2.18387
$517$	35.1585	1.54627
$518$	−11.8841	−0.522156
$519$	−0.735687	−0.0322931
$520$	−1.14246	−0.0501003
$521$	1.86602	0.0817516	0.0408758	−	0.999164i	$-0.486985\pi$
$521$	1.86602	0.0817516	0.0408758	+	0.999164i	$0.486985\pi$
$522$	−21.3957	−0.936464
$523$	−10.3257	−0.451513	−0.225757	−	0.974184i	$-0.572485\pi$
$523$	−10.3257	−0.451513	−0.225757	+	0.974184i	$0.572485\pi$
$524$	−38.9021	−1.69945
$525$	−4.92075	−0.214759
$526$	38.3611	1.67262
$527$	30.5547	1.33098
$528$	−60.7272	−2.64281
$529$	15.7419	0.684431
$530$	−1.76646	−0.0767302
$531$	8.68072	0.376711
$532$	−32.5664	−1.41193
$533$	−0.569996	−0.0246893
$534$	34.7898	1.50550
$535$	5.13674	0.222081
$536$	−87.2577	−3.76896
$537$	6.14587	0.265214
$538$	−2.62495	−0.113170
$539$	5.88693	0.253568
$540$	1.38325	0.0595257
$541$	−14.9035	−0.640752	−0.320376	−	0.947291i	$-0.603809\pi$
$541$	−14.9035	−0.640752	−0.320376	+	0.947291i	$0.603809\pi$
$542$	58.8660	2.52851
$543$	26.5200	1.13808
$544$	−53.4896	−2.29335
$545$	1.10063	0.0471458
$546$	1.39289	0.0596100
$547$	0.550788	0.0235500	0.0117750	−	0.999931i	$-0.496252\pi$
$547$	0.550788	0.0235500	0.0117750	+	0.999931i	$0.496252\pi$
$548$	−75.1605	−3.21070
$549$	−1.42983	−0.0610237
$550$	−76.1675	−3.24779
$551$	−53.9330	−2.29762
$552$	−47.6823	−2.02949
$553$	−5.38043	−0.228799
$554$	−18.5573	−0.788426
$555$	1.27240	0.0540105
$556$	−92.5912	−3.92674
$557$	26.6367	1.12863	0.564317	−	0.825558i	$-0.309140\pi$
$557$	26.6367	1.12863	0.564317	+	0.825558i	$0.309140\pi$
$558$	−17.7262	−0.750409
$559$	5.34841	0.226214
$560$	2.90405	0.122718
$561$	26.6810	1.12647
$562$	63.2599	2.66846
$563$	33.1928	1.39891	0.699454	−	0.714677i	$-0.253426\pi$
$563$	33.1928	1.39891	0.699454	+	0.714677i	$0.253426\pi$
$564$	−29.3450	−1.23565
$565$	−2.14437	−0.0902144
$566$	−29.0985	−1.22310
$567$	−1.00000	−0.0419961
$568$	85.4356	3.58480
$569$	25.8211	1.08248	0.541239	−	0.840869i	$-0.317955\pi$
$569$	25.8211	1.08248	0.541239	+	0.840869i	$0.317955\pi$
$570$	4.90610	0.205494
$571$	−33.0630	−1.38365	−0.691823	−	0.722068i	$-0.743192\pi$
$571$	−33.0630	−1.38365	−0.691823	+	0.722068i	$0.743192\pi$
$572$	15.3231	0.640692
$573$	−3.47889	−0.145333
$574$	2.82915	0.118086
$575$	−30.6282	−1.27728
$576$	10.4006	0.433358
$577$	−37.5968	−1.56518	−0.782588	−	0.622540i	$-0.786101\pi$
$577$	−37.5968	−1.56518	−0.782588	+	0.622540i	$0.786101\pi$
$578$	9.31096	0.387285
$579$	19.7817	0.822098
$580$	11.2558	0.467374
$581$	−5.24596	−0.217639
$582$	−28.4914	−1.18101
$583$	14.0487	0.581836
$584$	59.6966	2.47026
$585$	−0.149133	−0.00616591
$586$	59.5881	2.46156
$587$	−0.355126	−0.0146576	−0.00732880	−	0.999973i	$-0.502333\pi$
$587$	−0.355126	−0.0146576	−0.00732880	+	0.999973i	$0.502333\pi$
$588$	−4.91351	−0.202630
$589$	−44.6831	−1.84114
$590$	−6.42561	−0.264538
$591$	4.07163	0.167484
$592$	46.6241	1.91624
$593$	−7.40159	−0.303947	−0.151973	−	0.988385i	$-0.548563\pi$
$593$	−7.40159	−0.303947	−0.151973	+	0.988385i	$0.548563\pi$
$594$	−15.4788	−0.635105
$595$	−1.27591	−0.0523074
$596$	8.85494	0.362712
$597$	−4.28232	−0.175264
$598$	8.66974	0.354532
$599$	25.6275	1.04711	0.523556	−	0.851991i	$-0.324605\pi$
$599$	25.6275	1.04711	0.523556	+	0.851991i	$0.324605\pi$
$600$	37.6962	1.53894
$601$	−5.51196	−0.224837	−0.112419	−	0.993661i	$-0.535860\pi$
$601$	−5.51196	−0.224837	−0.112419	+	0.993661i	$0.535860\pi$
$602$	−26.5466	−1.08196
$603$	−11.3904	−0.463851
$604$	−91.7768	−3.73435
$605$	−6.65963	−0.270753
$606$	28.5828	1.16110
$607$	21.3164	0.865208	0.432604	−	0.901584i	$-0.357595\pi$
$607$	21.3164	0.865208	0.432604	+	0.901584i	$0.357595\pi$
$608$	78.2231	3.17237
$609$	−8.13724	−0.329737
$610$	1.05838	0.0428527
$611$	3.16379	0.127993
$612$	−22.2692	−0.900179
$613$	47.7819	1.92989	0.964946	−	0.262447i	$-0.0845295\pi$
$613$	47.7819	1.92989	0.964946	+	0.262447i	$0.0845295\pi$
$614$	45.7739	1.84728
$615$	−0.302911	−0.0122145
$616$	−45.0979	−1.81704
$617$	−23.6397	−0.951700	−0.475850	−	0.879526i	$-0.657860\pi$
$617$	−23.6397	−0.951700	−0.475850	+	0.879526i	$0.657860\pi$
$618$	−18.2312	−0.733365
$619$	−37.9034	−1.52347	−0.761734	−	0.647890i	$-0.775652\pi$
$619$	−37.9034	−1.52347	−0.761734	+	0.647890i	$0.775652\pi$
$620$	9.32540	0.374517
$621$	−6.22430	−0.249773
$622$	−41.3117	−1.65645
$623$	13.2313	0.530100
$624$	−5.46462	−0.218760
$625$	23.8175	0.952699
$626$	−36.5607	−1.46126
$627$	−39.0182	−1.55824
$628$	27.5515	1.09942
$629$	−20.4846	−0.816776
$630$	0.740216	0.0294909
$631$	−21.3232	−0.848862	−0.424431	−	0.905460i	$-0.639526\pi$
$631$	−21.3232	−0.848862	−0.424431	+	0.905460i	$0.639526\pi$
$632$	41.2177	1.63955
$633$	18.9882	0.754714
$634$	46.2075	1.83513
$635$	−0.281520	−0.0111718
$636$	−11.7257	−0.464953
$637$	0.529744	0.0209892
$638$	−125.955	−4.98661
$639$	11.1525	0.441186
$640$	−1.05366	−0.0416496
$641$	15.0762	0.595474	0.297737	−	0.954648i	$-0.403768\pi$
$641$	15.0762	0.595474	0.297737	+	0.954648i	$0.403768\pi$
$642$	47.9764	1.89348
$643$	9.56577	0.377237	0.188619	−	0.982050i	$-0.439599\pi$
$643$	9.56577	0.377237	0.188619	+	0.982050i	$0.439599\pi$
$644$	−30.5832	−1.20515
$645$	2.84229	0.111915
$646$	−78.9841	−3.10759
$647$	−19.8265	−0.779461	−0.389730	−	0.920929i	$-0.627432\pi$
$647$	−19.8265	−0.779461	−0.389730	+	0.920929i	$0.627432\pi$
$648$	7.66067	0.300939
$649$	51.1028	2.00596
$650$	−6.85403	−0.268837
$651$	−6.74165	−0.264226
$652$	−54.4723	−2.13330
$653$	39.0463	1.52800	0.764000	−	0.645216i	$-0.223233\pi$
$653$	39.0463	1.52800	0.764000	+	0.645216i	$0.223233\pi$
$654$	10.2797	0.401969
$655$	2.22890	0.0870901
$656$	−11.0994	−0.433360
$657$	7.79261	0.304019
$658$	−15.7033	−0.612178
$659$	0.346451	0.0134958	0.00674790	−	0.999977i	$-0.497852\pi$
$659$	0.346451	0.0134958	0.00674790	+	0.999977i	$0.497852\pi$
$660$	8.14311	0.316970
$661$	−44.3391	−1.72459	−0.862295	−	0.506407i	$-0.830974\pi$
$661$	−44.3391	−1.72459	−0.862295	+	0.506407i	$0.830974\pi$
$662$	60.8962	2.36680
$663$	2.40092	0.0932441
$664$	40.1876	1.55958
$665$	1.86589	0.0723562
$666$	11.8841	0.460498
$667$	−50.6486	−1.96112
$668$	−71.6620	−2.77269
$669$	18.8389	0.728353
$670$	8.43132	0.325730
$671$	−8.41732	−0.324947
$672$	11.8020	0.455274
$673$	12.6656	0.488221	0.244111	−	0.969747i	$-0.421504\pi$
$673$	12.6656	0.488221	0.244111	+	0.969747i	$0.421504\pi$
$674$	−18.2856	−0.704333
$675$	4.92075	0.189400
$676$	−62.4968	−2.40372
$677$	37.1876	1.42923	0.714617	−	0.699516i	$-0.246601\pi$
$677$	37.1876	1.42923	0.714617	+	0.699516i	$0.246601\pi$
$678$	−20.0281	−0.769176
$679$	−10.8359	−0.415844
$680$	9.77436	0.374829
$681$	9.90495	0.379558
$682$	−104.353	−3.99588
$683$	25.3023	0.968166	0.484083	−	0.875022i	$-0.339153\pi$
$683$	25.3023	0.968166	0.484083	+	0.875022i	$0.339153\pi$
$684$	32.5664	1.24521
$685$	4.30632	0.164536
$686$	−2.62936	−0.100389
$687$	−0.0909386	−0.00346952
$688$	104.149	3.97062
$689$	1.26419	0.0481617
$690$	4.60733	0.175398
$691$	−29.3373	−1.11604	−0.558021	−	0.829827i	$-0.688439\pi$
$691$	−29.3373	−1.11604	−0.558021	+	0.829827i	$0.688439\pi$
$692$	3.61481	0.137414
$693$	−5.88693	−0.223626
$694$	51.6697	1.96136
$695$	5.30501	0.201231
$696$	62.3367	2.36287
$697$	4.87661	0.184715
$698$	−41.1336	−1.55693
$699$	9.23810	0.349417
$700$	24.1782	0.913849
$701$	−2.53580	−0.0957758	−0.0478879	−	0.998853i	$-0.515249\pi$
$701$	−2.53580	−0.0957758	−0.0478879	+	0.998853i	$0.515249\pi$
$702$	−1.39289	−0.0525711
$703$	29.9567	1.12984
$704$	61.2276	2.30760
$705$	1.68132	0.0633222
$706$	−76.1683	−2.86663
$707$	10.8706	0.408832
$708$	−42.6528	−1.60299
$709$	−44.3690	−1.66631	−0.833157	−	0.553036i	$-0.813469\pi$
$709$	−44.3690	−1.66631	−0.833157	+	0.553036i	$0.813469\pi$
$710$	−8.25526	−0.309814
$711$	5.38043	0.201782
$712$	−101.360	−3.79865
$713$	−41.9620	−1.57149
$714$	−11.9169	−0.445977
$715$	−0.877939	−0.0328330
$716$	−30.1978	−1.12855
$717$	−22.8712	−0.854141
$718$	4.84642	0.180867
$719$	13.3006	0.496027	0.248013	−	0.968757i	$-0.420222\pi$
$719$	13.3006	0.496027	0.248013	+	0.968757i	$0.420222\pi$
$720$	−2.90405	−0.108227
$721$	−6.93370	−0.258224
$722$	65.5483	2.43946
$723$	−25.5928	−0.951805
$724$	−130.307	−4.84281
$725$	40.0413	1.48710
$726$	−62.2000	−2.30846
$727$	12.3531	0.458152	0.229076	−	0.973408i	$-0.426430\pi$
$727$	12.3531	0.458152	0.229076	+	0.973408i	$0.426430\pi$
$728$	−4.05819	−0.150407
$729$	1.00000	0.0370370
$730$	−5.76822	−0.213491
$731$	−45.7584	−1.69244
$732$	7.02549	0.259670
$733$	34.3503	1.26876	0.634379	−	0.773022i	$-0.281256\pi$
$733$	34.3503	1.26876	0.634379	+	0.773022i	$0.281256\pi$
$734$	84.3486	3.11336
$735$	0.281520	0.0103840
$736$	73.4595	2.70775
$737$	−67.0543	−2.46998
$738$	−2.82915	−0.104142
$739$	13.5112	0.497016	0.248508	−	0.968630i	$-0.420060\pi$
$739$	13.5112	0.497016	0.248508	+	0.968630i	$0.420060\pi$
$740$	−6.25197	−0.229827
$741$	−3.51110	−0.128984
$742$	−6.27473	−0.230353
$743$	−41.3180	−1.51581	−0.757905	−	0.652365i	$-0.773777\pi$
$743$	−41.3180	−1.51581	−0.757905	+	0.652365i	$0.773777\pi$
$744$	51.6455	1.89342
$745$	−0.507344	−0.0185876
$746$	−8.99194	−0.329218
$747$	5.24596	0.191940
$748$	−131.097	−4.79339
$749$	18.2465	0.666711
$750$	−7.34350	−0.268147
$751$	−4.93707	−0.180156	−0.0900781	−	0.995935i	$-0.528712\pi$
$751$	−4.93707	−0.180156	−0.0900781	+	0.995935i	$0.528712\pi$
$752$	61.6078	2.24661
$753$	10.2062	0.371933
$754$	−11.3342	−0.412768
$755$	5.25836	0.191371
$756$	4.91351	0.178703
$757$	−23.7869	−0.864550	−0.432275	−	0.901742i	$-0.642289\pi$
$757$	−23.7869	−0.864550	−0.432275	+	0.901742i	$0.642289\pi$
$758$	−31.2944	−1.13666
$759$	−36.6420	−1.33002
$760$	−14.2940	−0.518498
$761$	−44.1026	−1.59872	−0.799359	−	0.600854i	$-0.794827\pi$
$761$	−44.1026	−1.59872	−0.799359	+	0.600854i	$0.794827\pi$
$762$	−2.62936	−0.0952515
$763$	3.90960	0.141537
$764$	17.0936	0.618424
$765$	1.27591	0.0461308
$766$	5.18389	0.187301
$767$	4.59856	0.166044
$768$	10.9601	0.395489
$769$	−48.0338	−1.73214	−0.866072	−	0.499920i	$-0.833363\pi$
$769$	−48.0338	−1.73214	−0.866072	+	0.499920i	$0.833363\pi$
$770$	4.35760	0.157037
$771$	13.3777	0.481787
$772$	−97.1975	−3.49822
$773$	22.0762	0.794025	0.397013	−	0.917813i	$-0.370047\pi$
$773$	22.0762	0.794025	0.397013	+	0.917813i	$0.370047\pi$
$774$	26.5466	0.954196
$775$	33.1739	1.19164
$776$	83.0102	2.97989
$777$	4.51976	0.162146
$778$	39.8398	1.42833
$779$	−7.13155	−0.255514
$780$	0.732769	0.0262373
$781$	65.6540	2.34929
$782$	−74.1741	−2.65246
$783$	8.13724	0.290801
$784$	10.3156	0.368414
$785$	−1.57856	−0.0563413
$786$	20.8176	0.742538
$787$	45.8301	1.63367	0.816834	−	0.576873i	$-0.195727\pi$
$787$	45.8301	1.63367	0.816834	+	0.576873i	$0.195727\pi$
$788$	−20.0060	−0.712685
$789$	−14.5895	−0.519401
$790$	−3.98268	−0.141697
$791$	−7.61713	−0.270834
$792$	45.0979	1.60248
$793$	−0.757444	−0.0268976
$794$	53.3757	1.89423
$795$	0.671823	0.0238271
$796$	21.0413	0.745788
$797$	−17.3092	−0.613124	−0.306562	−	0.951851i	$-0.599179\pi$
$797$	−17.3092	−0.613124	−0.306562	+	0.951851i	$0.599179\pi$
$798$	17.4272	0.616916
$799$	−27.0679	−0.957592
$800$	−58.0749	−2.05326
$801$	−13.2313	−0.467504
$802$	23.4911	0.829499
$803$	45.8746	1.61888
$804$	55.9667	1.97379
$805$	1.75226	0.0617592
$806$	−9.39034	−0.330761
$807$	0.998325	0.0351427
$808$	−83.2764	−2.92965
$809$	−20.2565	−0.712179	−0.356090	−	0.934452i	$-0.615890\pi$
$809$	−20.2565	−0.712179	−0.356090	+	0.934452i	$0.615890\pi$
$810$	−0.740216	−0.0260085
$811$	19.1975	0.674116	0.337058	−	0.941484i	$-0.390568\pi$
$811$	19.1975	0.674116	0.337058	+	0.941484i	$0.390568\pi$
$812$	39.9824	1.40311
$813$	−22.3880	−0.785181
$814$	69.9607	2.45212
$815$	3.12099	0.109324
$816$	46.7527	1.63667
$817$	66.9170	2.34113
$818$	92.0816	3.21956
$819$	−0.529744	−0.0185107
$820$	1.48836	0.0519757
$821$	26.4827	0.924252	0.462126	−	0.886814i	$-0.347087\pi$
$821$	26.4827	0.924252	0.462126	+	0.886814i	$0.347087\pi$
$822$	40.2205	1.40285
$823$	−49.4957	−1.72531	−0.862657	−	0.505790i	$-0.831201\pi$
$823$	−49.4957	−1.72531	−0.862657	+	0.505790i	$0.831201\pi$
$824$	53.1168	1.85041
$825$	28.9681	1.00854
$826$	−22.8247	−0.794173
$827$	27.5998	0.959738	0.479869	−	0.877340i	$-0.340684\pi$
$827$	27.5998	0.959738	0.479869	+	0.877340i	$0.340684\pi$
$828$	30.5832	1.06284
$829$	−5.45427	−0.189435	−0.0947173	−	0.995504i	$-0.530195\pi$
$829$	−5.45427	−0.189435	−0.0947173	+	0.995504i	$0.530195\pi$
$830$	−3.88315	−0.134786
$831$	7.05775	0.244831
$832$	5.50965	0.191013
$833$	−4.53224	−0.157033
$834$	49.5481	1.71571
$835$	4.10588	0.142090
$836$	191.716	6.63065
$837$	6.74165	0.233025
$838$	0.691164	0.0238759
$839$	35.7462	1.23410	0.617049	−	0.786925i	$-0.288328\pi$
$839$	35.7462	1.23410	0.617049	+	0.786925i	$0.288328\pi$
$840$	−2.15663	−0.0744108
$841$	37.2146	1.28326
$842$	−43.4883	−1.49871
$843$	−24.0591	−0.828638
$844$	−93.2989	−3.21148
$845$	3.58076	0.123182
$846$	15.7033	0.539891
$847$	−23.6560	−0.812830
$848$	24.6173	0.845361
$849$	11.0668	0.379811
$850$	58.6399	2.01133
$851$	28.1324	0.964365
$852$	−54.7980	−1.87735
$853$	−37.4691	−1.28292	−0.641458	−	0.767158i	$-0.721670\pi$
$853$	−37.4691	−1.28292	−0.641458	+	0.767158i	$0.721670\pi$
$854$	3.75953	0.128649
$855$	−1.86589	−0.0638122
$856$	−139.780	−4.77758
$857$	−22.1488	−0.756588	−0.378294	−	0.925686i	$-0.623489\pi$
$857$	−22.1488	−0.756588	−0.378294	+	0.925686i	$0.623489\pi$
$858$	−8.19982	−0.279937
$859$	−6.66621	−0.227448	−0.113724	−	0.993512i	$-0.536278\pi$
$859$	−6.66621	−0.227448	−0.113724	+	0.993512i	$0.536278\pi$
$860$	−13.9656	−0.476224
$861$	−1.07598	−0.0366694
$862$	−3.06906	−0.104533
$863$	19.6229	0.667972	0.333986	−	0.942578i	$-0.391606\pi$
$863$	19.6229	0.667972	0.333986	+	0.942578i	$0.391606\pi$
$864$	−11.8020	−0.401514
$865$	−0.207111	−0.00704197
$866$	53.1696	1.80678
$867$	−3.54115	−0.120264
$868$	33.1252	1.12434
$869$	31.6742	1.07447
$870$	−6.02331	−0.204209
$871$	−6.03397	−0.204453
$872$	−29.9501	−1.01424
$873$	10.8359	0.366740
$874$	108.472	3.66912
$875$	−2.79289	−0.0944168
$876$	−38.2891	−1.29367
$877$	48.6407	1.64248	0.821241	−	0.570582i	$-0.193282\pi$
$877$	48.6407	1.64248	0.821241	+	0.570582i	$0.193282\pi$
$878$	20.0067	0.675195
$879$	−22.6626	−0.764392
$880$	−17.0959	−0.576304
$881$	−9.08797	−0.306182	−0.153091	−	0.988212i	$-0.548923\pi$
$881$	−9.08797	−0.306182	−0.153091	+	0.988212i	$0.548923\pi$
$882$	2.62936	0.0885350
$883$	4.29728	0.144615	0.0723075	−	0.997382i	$-0.476964\pi$
$883$	4.29728	0.144615	0.0723075	+	0.997382i	$0.476964\pi$
$884$	−11.7970	−0.396775
$885$	2.44379	0.0821473
$886$	−68.6961	−2.30789
$887$	22.8510	0.767261	0.383630	−	0.923487i	$-0.374674\pi$
$887$	22.8510	0.767261	0.383630	+	0.923487i	$0.374674\pi$
$888$	−34.6244	−1.16192
$889$	−1.00000	−0.0335389
$890$	9.79401	0.328296
$891$	5.88693	0.197220
$892$	−92.5652	−3.09931
$893$	39.5840	1.32463
$894$	−4.73852	−0.158480
$895$	1.73019	0.0578337
$896$	−3.74276	−0.125037
$897$	−3.29728	−0.110093
$898$	15.3296	0.511554
$899$	54.8584	1.82963
$900$	−24.1782	−0.805939
$901$	−10.8158	−0.360326
$902$	−16.6550	−0.554551
$903$	10.0962	0.335981
$904$	58.3523	1.94077
$905$	7.46592	0.248176
$906$	49.1123	1.63165
$907$	57.7685	1.91817	0.959086	−	0.283115i	$-0.0913679\pi$
$907$	57.7685	1.91817	0.959086	+	0.283115i	$0.0913679\pi$
$908$	−48.6681	−1.61511
$909$	−10.8706	−0.360556
$910$	0.392125	0.0129988
$911$	14.0228	0.464597	0.232299	−	0.972645i	$-0.425375\pi$
$911$	14.0228	0.464597	0.232299	+	0.972645i	$0.425375\pi$
$912$	−68.3710	−2.26399
$913$	30.8826	1.02207
$914$	−93.6104	−3.09636
$915$	−0.402526	−0.0133071
$916$	0.446828	0.0147636
$917$	7.91736	0.261454
$918$	11.9169	0.393315
$919$	−9.51583	−0.313898	−0.156949	−	0.987607i	$-0.550166\pi$
$919$	−9.51583	−0.313898	−0.156949	+	0.987607i	$0.550166\pi$
$920$	−13.4235	−0.442560
$921$	−17.4088	−0.573639
$922$	1.65136	0.0543845
$923$	5.90796	0.194463
$924$	28.9255	0.951580
$925$	−22.2406	−0.731267
$926$	−84.9762	−2.79249
$927$	6.93370	0.227733
$928$	−96.0360	−3.15254
$929$	11.7678	0.386088	0.193044	−	0.981190i	$-0.438164\pi$
$929$	11.7678	0.386088	0.193044	+	0.981190i	$0.438164\pi$
$930$	−4.99028	−0.163638
$931$	6.62793	0.217222
$932$	−45.3915	−1.48685
$933$	15.7117	0.514378
$934$	112.156	3.66987
$935$	7.51122	0.245643
$936$	4.05819	0.132646
$937$	−30.9966	−1.01262	−0.506308	−	0.862353i	$-0.668990\pi$
$937$	−30.9966	−1.01262	−0.506308	+	0.862353i	$0.668990\pi$
$938$	29.9493	0.977879
$939$	13.9048	0.453766
$940$	−8.26119	−0.269450
$941$	29.7890	0.971094	0.485547	−	0.874211i	$-0.338620\pi$
$941$	29.7890	0.971094	0.485547	+	0.874211i	$0.338620\pi$
$942$	−14.7436	−0.480371
$943$	−6.69725	−0.218092
$944$	89.5468	2.91450
$945$	−0.281520	−0.00915784
$946$	156.278	5.08103
$947$	−0.245881	−0.00799006	−0.00399503	−	0.999992i	$-0.501272\pi$
$947$	−0.245881	−0.00799006	−0.00399503	+	0.999992i	$0.501272\pi$
$948$	−26.4368	−0.858628
$949$	4.12809	0.134003
$950$	−85.7547	−2.78225
$951$	−17.5737	−0.569866
$952$	34.7200	1.12528
$953$	29.4515	0.954027	0.477013	−	0.878896i	$-0.341719\pi$
$953$	29.4515	0.954027	0.477013	+	0.878896i	$0.341719\pi$
$954$	6.27473	0.203152
$955$	−0.979377	−0.0316919
$956$	112.378	3.63457
$957$	47.9034	1.54850
$958$	−0.865409	−0.0279601
$959$	15.2967	0.493956
$960$	2.92797	0.0944999
$961$	14.4498	0.466122
$962$	6.29551	0.202975
$963$	−18.2465	−0.587984
$964$	125.750	4.05015
$965$	5.56894	0.179270
$966$	16.3659	0.526564
$967$	33.8225	1.08766	0.543829	−	0.839196i	$-0.316974\pi$
$967$	33.8225	1.08766	0.543829	+	0.839196i	$0.316974\pi$
$968$	181.221	5.82465
$969$	30.0393	0.965002
$970$	−8.02091	−0.257536
$971$	−55.5688	−1.78329	−0.891644	−	0.452736i	$-0.850448\pi$
$971$	−55.5688	−1.78329	−0.891644	+	0.452736i	$0.850448\pi$
$972$	−4.91351	−0.157601
$973$	18.8442	0.604117
$974$	3.42121	0.109623
$975$	2.60673	0.0834823
$976$	−14.7496	−0.472122
$977$	28.8054	0.921566	0.460783	−	0.887513i	$-0.347569\pi$
$977$	28.8054	0.921566	0.460783	+	0.887513i	$0.347569\pi$
$978$	29.1496	0.932103
$979$	−77.8917	−2.48943
$980$	−1.38325	−0.0441864
$981$	−3.90960	−0.124824
$982$	−69.3856	−2.21418
$983$	23.4017	0.746397	0.373198	−	0.927752i	$-0.378261\pi$
$983$	23.4017	0.746397	0.373198	+	0.927752i	$0.378261\pi$
$984$	8.24276	0.262770
$985$	1.14624	0.0365224
$986$	96.9703	3.08816
$987$	5.97230	0.190100
$988$	17.2519	0.548855
$989$	62.8419	1.99826
$990$	−4.35760	−0.138494
$991$	−57.4474	−1.82488	−0.912439	−	0.409213i	$-0.865803\pi$
$991$	−57.4474	−1.82488	−0.912439	+	0.409213i	$0.865803\pi$
$992$	−79.5652	−2.52620
$993$	−23.1601	−0.734964
$994$	−29.3239	−0.930097
$995$	−1.20556	−0.0382188
$996$	−25.7761	−0.816748
$997$	−31.3586	−0.993138	−0.496569	−	0.867997i	$-0.665407\pi$
$997$	−31.3586	−0.993138	−0.496569	+	0.867997i	$0.665407\pi$
$998$	−55.5125	−1.75722
$999$	−4.51976	−0.142999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.15	✓	16
3.2	odd	2		8001.2.a.r.1.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.15	✓	16	1.1	even	1	trivial
8001.2.a.r.1.2		16	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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.62936 q^{2} -1.00000 q^{3} +4.91351 q^{4} -0.281520 q^{5} -2.62936 q^{6} -1.00000 q^{7} +7.66067 q^{8} +1.00000 q^{9} -0.740216 q^{10} +5.88693 q^{11} -4.91351 q^{12} +0.529744 q^{13} -2.62936 q^{14} +0.281520 q^{15} +10.3156 q^{16} -4.53224 q^{17} +2.62936 q^{18} +6.62793 q^{19} -1.38325 q^{20} +1.00000 q^{21} +15.4788 q^{22} +6.22430 q^{23} -7.66067 q^{24} -4.92075 q^{25} +1.39289 q^{26} -1.00000 q^{27} -4.91351 q^{28} -8.13724 q^{29} +0.740216 q^{30} -6.74165 q^{31} +11.8020 q^{32} -5.88693 q^{33} -11.9169 q^{34} +0.281520 q^{35} +4.91351 q^{36} +4.51976 q^{37} +17.4272 q^{38} -0.529744 q^{39} -2.15663 q^{40} -1.07598 q^{41} +2.62936 q^{42} +10.0962 q^{43} +28.9255 q^{44} -0.281520 q^{45} +16.3659 q^{46} +5.97230 q^{47} -10.3156 q^{48} +1.00000 q^{49} -12.9384 q^{50} +4.53224 q^{51} +2.60290 q^{52} +2.38641 q^{53} -2.62936 q^{54} -1.65729 q^{55} -7.66067 q^{56} -6.62793 q^{57} -21.3957 q^{58} +8.68072 q^{59} +1.38325 q^{60} -1.42983 q^{61} -17.7262 q^{62} -1.00000 q^{63} +10.4006 q^{64} -0.149133 q^{65} -15.4788 q^{66} -11.3904 q^{67} -22.2692 q^{68} -6.22430 q^{69} +0.740216 q^{70} +11.1525 q^{71} +7.66067 q^{72} +7.79261 q^{73} +11.8841 q^{74} +4.92075 q^{75} +32.5664 q^{76} -5.88693 q^{77} -1.39289 q^{78} +5.38043 q^{79} -2.90405 q^{80} +1.00000 q^{81} -2.82915 q^{82} +5.24596 q^{83} +4.91351 q^{84} +1.27591 q^{85} +26.5466 q^{86} +8.13724 q^{87} +45.0979 q^{88} -13.2313 q^{89} -0.740216 q^{90} -0.529744 q^{91} +30.5832 q^{92} +6.74165 q^{93} +15.7033 q^{94} -1.86589 q^{95} -11.8020 q^{96} +10.8359 q^{97} +2.62936 q^{98} +5.88693 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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