LMFDB - Embedded newform 2667.2.a.o.1.11

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			1.11
Root			$1.55853$ 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)

$f(q)$	$=$	\(q+1.55853 q^{2} -1.00000 q^{3} +0.429028 q^{4} -1.78044 q^{5} -1.55853 q^{6} -1.00000 q^{7} -2.44841 q^{8} +1.00000 q^{9} -2.77487 q^{10} +0.515364 q^{11} -0.429028 q^{12} -5.03536 q^{13} -1.55853 q^{14} +1.78044 q^{15} -4.67399 q^{16} -0.0785962 q^{17} +1.55853 q^{18} +4.96243 q^{19} -0.763858 q^{20} +1.00000 q^{21} +0.803212 q^{22} +1.02045 q^{23} +2.44841 q^{24} -1.83005 q^{25} -7.84779 q^{26} -1.00000 q^{27} -0.429028 q^{28} +4.62457 q^{29} +2.77487 q^{30} +2.09705 q^{31} -2.38775 q^{32} -0.515364 q^{33} -0.122495 q^{34} +1.78044 q^{35} +0.429028 q^{36} +5.01414 q^{37} +7.73411 q^{38} +5.03536 q^{39} +4.35924 q^{40} -2.22133 q^{41} +1.55853 q^{42} +10.4993 q^{43} +0.221106 q^{44} -1.78044 q^{45} +1.59040 q^{46} +10.2871 q^{47} +4.67399 q^{48} +1.00000 q^{49} -2.85219 q^{50} +0.0785962 q^{51} -2.16031 q^{52} -2.98505 q^{53} -1.55853 q^{54} -0.917572 q^{55} +2.44841 q^{56} -4.96243 q^{57} +7.20755 q^{58} -10.5275 q^{59} +0.763858 q^{60} -3.21732 q^{61} +3.26832 q^{62} -1.00000 q^{63} +5.62659 q^{64} +8.96515 q^{65} -0.803212 q^{66} +6.73590 q^{67} -0.0337200 q^{68} -1.02045 q^{69} +2.77487 q^{70} +7.69793 q^{71} -2.44841 q^{72} -7.37692 q^{73} +7.81471 q^{74} +1.83005 q^{75} +2.12902 q^{76} -0.515364 q^{77} +7.84779 q^{78} -3.98213 q^{79} +8.32175 q^{80} +1.00000 q^{81} -3.46202 q^{82} -4.54247 q^{83} +0.429028 q^{84} +0.139936 q^{85} +16.3635 q^{86} -4.62457 q^{87} -1.26182 q^{88} +6.80807 q^{89} -2.77487 q^{90} +5.03536 q^{91} +0.437801 q^{92} -2.09705 q^{93} +16.0329 q^{94} -8.83529 q^{95} +2.38775 q^{96} +6.33552 q^{97} +1.55853 q^{98} +0.515364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.55853	1.10205	0.551025	−	0.834489i	$-0.314237\pi$
$2$	1.55853	1.10205	0.551025	+	0.834489i	$0.314237\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.429028	0.214514
$5$	−1.78044	−0.796235	−0.398118	−	0.917334i	$-0.630336\pi$
$5$	−1.78044	−0.796235	−0.398118	+	0.917334i	$0.630336\pi$
$6$	−1.55853	−0.636269
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.44841	−0.865645
$9$	1.00000	0.333333
$10$	−2.77487	−0.877491
$11$	0.515364	0.155388	0.0776940	−	0.996977i	$-0.475244\pi$
$11$	0.515364	0.155388	0.0776940	+	0.996977i	$0.475244\pi$
$12$	−0.429028	−0.123850
$13$	−5.03536	−1.39656	−0.698279	−	0.715825i	$-0.746051\pi$
$13$	−5.03536	−1.39656	−0.698279	+	0.715825i	$0.746051\pi$
$14$	−1.55853	−0.416536
$15$	1.78044	0.459707
$16$	−4.67399	−1.16850
$17$	−0.0785962	−0.0190624	−0.00953119	−	0.999955i	$-0.503034\pi$
$17$	−0.0785962	−0.0190624	−0.00953119	+	0.999955i	$0.503034\pi$
$18$	1.55853	0.367350
$19$	4.96243	1.13846	0.569230	−	0.822179i	$-0.307242\pi$
$19$	4.96243	1.13846	0.569230	+	0.822179i	$0.307242\pi$
$20$	−0.763858	−0.170804
$21$	1.00000	0.218218
$22$	0.803212	0.171245
$23$	1.02045	0.212778	0.106389	−	0.994325i	$-0.466071\pi$
$23$	1.02045	0.212778	0.106389	+	0.994325i	$0.466071\pi$
$24$	2.44841	0.499780
$25$	−1.83005	−0.366009
$26$	−7.84779	−1.53908
$27$	−1.00000	−0.192450
$28$	−0.429028	−0.0810788
$29$	4.62457	0.858761	0.429380	−	0.903124i	$-0.358732\pi$
$29$	4.62457	0.858761	0.429380	+	0.903124i	$0.358732\pi$
$30$	2.77487	0.506620
$31$	2.09705	0.376641	0.188321	−	0.982108i	$-0.439696\pi$
$31$	2.09705	0.376641	0.188321	+	0.982108i	$0.439696\pi$
$32$	−2.38775	−0.422099
$33$	−0.515364	−0.0897133
$34$	−0.122495	−0.0210077
$35$	1.78044	0.300949
$36$	0.429028	0.0715047
$37$	5.01414	0.824320	0.412160	−	0.911112i	$-0.364774\pi$
$37$	5.01414	0.824320	0.412160	+	0.911112i	$0.364774\pi$
$38$	7.73411	1.25464
$39$	5.03536	0.806303
$40$	4.35924	0.689257
$41$	−2.22133	−0.346914	−0.173457	−	0.984841i	$-0.555494\pi$
$41$	−2.22133	−0.346914	−0.173457	+	0.984841i	$0.555494\pi$
$42$	1.55853	0.240487
$43$	10.4993	1.60113	0.800565	−	0.599247i	$-0.204533\pi$
$43$	10.4993	1.60113	0.800565	+	0.599247i	$0.204533\pi$
$44$	0.221106	0.0333329
$45$	−1.78044	−0.265412
$46$	1.59040	0.234492
$47$	10.2871	1.50053	0.750267	−	0.661135i	$-0.229925\pi$
$47$	10.2871	1.50053	0.750267	+	0.661135i	$0.229925\pi$
$48$	4.67399	0.674633
$49$	1.00000	0.142857
$50$	−2.85219	−0.403360
$51$	0.0785962	0.0110057
$52$	−2.16031	−0.299582
$53$	−2.98505	−0.410029	−0.205014	−	0.978759i	$-0.565724\pi$
$53$	−2.98505	−0.410029	−0.205014	+	0.978759i	$0.565724\pi$
$54$	−1.55853	−0.212090
$55$	−0.917572	−0.123725
$56$	2.44841	0.327183
$57$	−4.96243	−0.657290
$58$	7.20755	0.946397
$59$	−10.5275	−1.37057	−0.685283	−	0.728277i	$-0.740322\pi$
$59$	−10.5275	−1.37057	−0.685283	+	0.728277i	$0.740322\pi$
$60$	0.763858	0.0986136
$61$	−3.21732	−0.411936	−0.205968	−	0.978559i	$-0.566034\pi$
$61$	−3.21732	−0.411936	−0.205968	+	0.978559i	$0.566034\pi$
$62$	3.26832	0.415078
$63$	−1.00000	−0.125988
$64$	5.62659	0.703324
$65$	8.96515	1.11199
$66$	−0.803212	−0.0988685
$67$	6.73590	0.822921	0.411461	−	0.911428i	$-0.365019\pi$
$67$	6.73590	0.822921	0.411461	+	0.911428i	$0.365019\pi$
$68$	−0.0337200	−0.00408915
$69$	−1.02045	−0.122847
$70$	2.77487	0.331661
$71$	7.69793	0.913577	0.456788	−	0.889575i	$-0.349000\pi$
$71$	7.69793	0.913577	0.456788	+	0.889575i	$0.349000\pi$
$72$	−2.44841	−0.288548
$73$	−7.37692	−0.863403	−0.431701	−	0.902017i	$-0.642087\pi$
$73$	−7.37692	−0.863403	−0.431701	+	0.902017i	$0.642087\pi$
$74$	7.81471	0.908442
$75$	1.83005	0.211315
$76$	2.12902	0.244216
$77$	−0.515364	−0.0587311
$78$	7.84779	0.888587
$79$	−3.98213	−0.448025	−0.224012	−	0.974586i	$-0.571916\pi$
$79$	−3.98213	−0.448025	−0.224012	+	0.974586i	$0.571916\pi$
$80$	8.32175	0.930399
$81$	1.00000	0.111111
$82$	−3.46202	−0.382316
$83$	−4.54247	−0.498601	−0.249301	−	0.968426i	$-0.580201\pi$
$83$	−4.54247	−0.498601	−0.249301	+	0.968426i	$0.580201\pi$
$84$	0.429028	0.0468108
$85$	0.139936	0.0151781
$86$	16.3635	1.76452
$87$	−4.62457	−0.495806
$88$	−1.26182	−0.134511
$89$	6.80807	0.721654	0.360827	−	0.932633i	$-0.382494\pi$
$89$	6.80807	0.721654	0.360827	+	0.932633i	$0.382494\pi$
$90$	−2.77487	−0.292497
$91$	5.03536	0.527850
$92$	0.437801	0.0456439
$93$	−2.09705	−0.217454
$94$	16.0329	1.65366
$95$	−8.83529	−0.906482
$96$	2.38775	0.243699
$97$	6.33552	0.643274	0.321637	−	0.946863i	$-0.395767\pi$
$97$	6.33552	0.643274	0.321637	+	0.946863i	$0.395767\pi$
$98$	1.55853	0.157436
$99$	0.515364	0.0517960
$100$	−0.785142	−0.0785142
$101$	6.44299	0.641102	0.320551	−	0.947231i	$-0.396132\pi$
$101$	6.44299	0.641102	0.320551	+	0.947231i	$0.396132\pi$
$102$	0.122495	0.0121288
$103$	9.00401	0.887191	0.443596	−	0.896227i	$-0.353703\pi$
$103$	9.00401	0.887191	0.443596	+	0.896227i	$0.353703\pi$
$104$	12.3286	1.20892
$105$	−1.78044	−0.173753
$106$	−4.65231	−0.451872
$107$	17.9368	1.73401	0.867006	−	0.498298i	$-0.166041\pi$
$107$	17.9368	1.73401	0.867006	+	0.498298i	$0.166041\pi$
$108$	−0.429028	−0.0412833
$109$	11.0874	1.06198	0.530991	−	0.847378i	$-0.321820\pi$
$109$	11.0874	1.06198	0.530991	+	0.847378i	$0.321820\pi$
$110$	−1.43007	−0.136352
$111$	−5.01414	−0.475921
$112$	4.67399	0.441651
$113$	−8.93713	−0.840734	−0.420367	−	0.907354i	$-0.638099\pi$
$113$	−8.93713	−0.840734	−0.420367	+	0.907354i	$0.638099\pi$
$114$	−7.73411	−0.724366
$115$	−1.81684	−0.169421
$116$	1.98407	0.184216
$117$	−5.03536	−0.465520
$118$	−16.4075	−1.51043
$119$	0.0785962	0.00720490
$120$	−4.35924	−0.397943
$121$	−10.7344	−0.975855
$122$	−5.01431	−0.453974
$123$	2.22133	0.200291
$124$	0.899694	0.0807949
$125$	12.1605	1.08766
$126$	−1.55853	−0.138845
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	13.5447	1.19720
$129$	−10.4993	−0.924412
$130$	13.9725	1.22547
$131$	−9.58473	−0.837422	−0.418711	−	0.908120i	$-0.637518\pi$
$131$	−9.58473	−0.837422	−0.418711	+	0.908120i	$0.637518\pi$
$132$	−0.221106	−0.0192448
$133$	−4.96243	−0.430297
$134$	10.4981	0.906900
$135$	1.78044	0.153236
$136$	0.192436	0.0165012
$137$	14.3286	1.22418	0.612088	−	0.790790i	$-0.290330\pi$
$137$	14.3286	1.22418	0.612088	+	0.790790i	$0.290330\pi$
$138$	−1.59040	−0.135384
$139$	−10.1363	−0.859752	−0.429876	−	0.902888i	$-0.641443\pi$
$139$	−10.1363	−0.859752	−0.429876	+	0.902888i	$0.641443\pi$
$140$	0.763858	0.0645578
$141$	−10.2871	−0.866333
$142$	11.9975	1.00681
$143$	−2.59504	−0.217008
$144$	−4.67399	−0.389499
$145$	−8.23375	−0.683776
$146$	−11.4972	−0.951513
$147$	−1.00000	−0.0824786
$148$	2.15121	0.176828
$149$	0.914867	0.0749489	0.0374744	−	0.999298i	$-0.488069\pi$
$149$	0.914867	0.0749489	0.0374744	+	0.999298i	$0.488069\pi$
$150$	2.85219	0.232880
$151$	0.363833	0.0296083	0.0148042	−	0.999890i	$-0.495288\pi$
$151$	0.363833	0.0296083	0.0148042	+	0.999890i	$0.495288\pi$
$152$	−12.1501	−0.985501
$153$	−0.0785962	−0.00635413
$154$	−0.803212	−0.0647246
$155$	−3.73366	−0.299895
$156$	2.16031	0.172964
$157$	−7.86274	−0.627515	−0.313757	−	0.949503i	$-0.601588\pi$
$157$	−7.86274	−0.627515	−0.313757	+	0.949503i	$0.601588\pi$
$158$	−6.20629	−0.493746
$159$	2.98505	0.236730
$160$	4.25124	0.336090
$161$	−1.02045	−0.0804225
$162$	1.55853	0.122450
$163$	−5.02780	−0.393808	−0.196904	−	0.980423i	$-0.563089\pi$
$163$	−5.02780	−0.393808	−0.196904	+	0.980423i	$0.563089\pi$
$164$	−0.953014	−0.0744179
$165$	0.917572	0.0714329
$166$	−7.07960	−0.549484
$167$	4.92702	0.381264	0.190632	−	0.981662i	$-0.438946\pi$
$167$	4.92702	0.381264	0.190632	+	0.981662i	$0.438946\pi$
$168$	−2.44841	−0.188899
$169$	12.3549	0.950376
$170$	0.218094	0.0167271
$171$	4.96243	0.379486
$172$	4.50450	0.343465
$173$	−0.354038	−0.0269170	−0.0134585	−	0.999909i	$-0.504284\pi$
$173$	−0.354038	−0.0269170	−0.0134585	+	0.999909i	$0.504284\pi$
$174$	−7.20755	−0.546403
$175$	1.83005	0.138338
$176$	−2.40881	−0.181571
$177$	10.5275	0.791297
$178$	10.6106	0.795299
$179$	24.4892	1.83041	0.915203	−	0.402994i	$-0.132030\pi$
$179$	24.4892	1.83041	0.915203	+	0.402994i	$0.132030\pi$
$180$	−0.763858	−0.0569346
$181$	−1.28210	−0.0952977	−0.0476488	−	0.998864i	$-0.515173\pi$
$181$	−1.28210	−0.0952977	−0.0476488	+	0.998864i	$0.515173\pi$
$182$	7.84779	0.581717
$183$	3.21732	0.237831
$184$	−2.49848	−0.184190
$185$	−8.92736	−0.656353
$186$	−3.26832	−0.239645
$187$	−0.0405056	−0.00296207
$188$	4.41347	0.321886
$189$	1.00000	0.0727393
$190$	−13.7701	−0.998988
$191$	7.18855	0.520146	0.260073	−	0.965589i	$-0.416253\pi$
$191$	7.18855	0.520146	0.260073	+	0.965589i	$0.416253\pi$
$192$	−5.62659	−0.406064
$193$	19.5323	1.40597	0.702983	−	0.711207i	$-0.251851\pi$
$193$	19.5323	1.40597	0.702983	+	0.711207i	$0.251851\pi$
$194$	9.87412	0.708921
$195$	−8.96515	−0.642007
$196$	0.429028	0.0306449
$197$	0.445897	0.0317688	0.0158844	−	0.999874i	$-0.494944\pi$
$197$	0.445897	0.0317688	0.0158844	+	0.999874i	$0.494944\pi$
$198$	0.803212	0.0570818
$199$	−0.902735	−0.0639932	−0.0319966	−	0.999488i	$-0.510187\pi$
$199$	−0.902735	−0.0639932	−0.0319966	+	0.999488i	$0.510187\pi$
$200$	4.48071	0.316834
$201$	−6.73590	−0.475114
$202$	10.0416	0.706526
$203$	−4.62457	−0.324581
$204$	0.0337200	0.00236087
$205$	3.95494	0.276225
$206$	14.0331	0.977729
$207$	1.02045	0.0709260
$208$	23.5352	1.63188
$209$	2.55745	0.176903
$210$	−2.77487	−0.191484
$211$	−7.09394	−0.488367	−0.244184	−	0.969729i	$-0.578520\pi$
$211$	−7.09394	−0.488367	−0.244184	+	0.969729i	$0.578520\pi$
$212$	−1.28067	−0.0879570
$213$	−7.69793	−0.527454
$214$	27.9550	1.91097
$215$	−18.6933	−1.27488
$216$	2.44841	0.166593
$217$	−2.09705	−0.142357
$218$	17.2801	1.17036
$219$	7.37692	0.498486
$220$	−0.393665	−0.0265409
$221$	0.395761	0.0266217
$222$	−7.81471	−0.524489
$223$	−14.1415	−0.946983	−0.473492	−	0.880798i	$-0.657007\pi$
$223$	−14.1415	−0.946983	−0.473492	+	0.880798i	$0.657007\pi$
$224$	2.38775	0.159538
$225$	−1.83005	−0.122003
$226$	−13.9288	−0.926531
$227$	4.17585	0.277161	0.138580	−	0.990351i	$-0.455746\pi$
$227$	4.17585	0.277161	0.138580	+	0.990351i	$0.455746\pi$
$228$	−2.12902	−0.140998
$229$	−6.56707	−0.433964	−0.216982	−	0.976176i	$-0.569621\pi$
$229$	−6.56707	−0.433964	−0.216982	+	0.976176i	$0.569621\pi$
$230$	−2.83161	−0.186711
$231$	0.515364	0.0339084
$232$	−11.3229	−0.743382
$233$	13.1952	0.864449	0.432224	−	0.901766i	$-0.357729\pi$
$233$	13.1952	0.864449	0.432224	+	0.901766i	$0.357729\pi$
$234$	−7.84779	−0.513026
$235$	−18.3156	−1.19478
$236$	−4.51661	−0.294006
$237$	3.98213	0.258667
$238$	0.122495	0.00794016
$239$	−15.5726	−1.00731	−0.503653	−	0.863906i	$-0.668011\pi$
$239$	−15.5726	−1.00731	−0.503653	+	0.863906i	$0.668011\pi$
$240$	−8.32175	−0.537166
$241$	−27.5918	−1.77735	−0.888673	−	0.458541i	$-0.848372\pi$
$241$	−27.5918	−1.77735	−0.888673	+	0.458541i	$0.848372\pi$
$242$	−16.7299	−1.07544
$243$	−1.00000	−0.0641500
$244$	−1.38032	−0.0883661
$245$	−1.78044	−0.113748
$246$	3.46202	0.220730
$247$	−24.9876	−1.58992
$248$	−5.13444	−0.326038
$249$	4.54247	0.287868
$250$	18.9525	1.19866
$251$	−22.0431	−1.39135	−0.695676	−	0.718356i	$-0.744895\pi$
$251$	−22.0431	−1.39135	−0.695676	+	0.718356i	$0.744895\pi$
$252$	−0.429028	−0.0270263
$253$	0.525902	0.0330631
$254$	1.55853	0.0977911
$255$	−0.139936	−0.00876311
$256$	9.85675	0.616047
$257$	−1.48239	−0.0924692	−0.0462346	−	0.998931i	$-0.514722\pi$
$257$	−1.48239	−0.0924692	−0.0462346	+	0.998931i	$0.514722\pi$
$258$	−16.3635	−1.01875
$259$	−5.01414	−0.311564
$260$	3.84630	0.238538
$261$	4.62457	0.286254
$262$	−14.9381	−0.922881
$263$	2.26700	0.139789	0.0698946	−	0.997554i	$-0.477734\pi$
$263$	2.26700	0.139789	0.0698946	+	0.997554i	$0.477734\pi$
$264$	1.26182	0.0776598
$265$	5.31470	0.326479
$266$	−7.73411	−0.474209
$267$	−6.80807	−0.416647
$268$	2.88989	0.176528
$269$	21.6954	1.32279	0.661396	−	0.750036i	$-0.269964\pi$
$269$	21.6954	1.32279	0.661396	+	0.750036i	$0.269964\pi$
$270$	2.77487	0.168873
$271$	22.5226	1.36815	0.684077	−	0.729410i	$-0.260205\pi$
$271$	22.5226	1.36815	0.684077	+	0.729410i	$0.260205\pi$
$272$	0.367358	0.0222744
$273$	−5.03536	−0.304754
$274$	22.3316	1.34910
$275$	−0.943139	−0.0568734
$276$	−0.437801	−0.0263525
$277$	7.27304	0.436994	0.218497	−	0.975838i	$-0.429885\pi$
$277$	7.27304	0.436994	0.218497	+	0.975838i	$0.429885\pi$
$278$	−15.7978	−0.947490
$279$	2.09705	0.125547
$280$	−4.35924	−0.260515
$281$	−17.9035	−1.06803	−0.534016	−	0.845474i	$-0.679318\pi$
$281$	−17.9035	−1.06803	−0.534016	+	0.845474i	$0.679318\pi$
$282$	−16.0329	−0.954743
$283$	12.0940	0.718916	0.359458	−	0.933161i	$-0.382962\pi$
$283$	12.0940	0.718916	0.359458	+	0.933161i	$0.382962\pi$
$284$	3.30263	0.195975
$285$	8.83529	0.523357
$286$	−4.04446	−0.239154
$287$	2.22133	0.131121
$288$	−2.38775	−0.140700
$289$	−16.9938	−0.999637
$290$	−12.8326	−0.753555
$291$	−6.33552	−0.371395
$292$	−3.16491	−0.185212
$293$	23.2269	1.35693	0.678465	−	0.734632i	$-0.262645\pi$
$293$	23.2269	1.35693	0.678465	+	0.734632i	$0.262645\pi$
$294$	−1.55853	−0.0908956
$295$	18.7436	1.09129
$296$	−12.2767	−0.713568
$297$	−0.515364	−0.0299044
$298$	1.42585	0.0825974
$299$	−5.13832	−0.297157
$300$	0.785142	0.0453302
$301$	−10.4993	−0.605170
$302$	0.567046	0.0326298
$303$	−6.44299	−0.370140
$304$	−23.1943	−1.33029
$305$	5.72824	0.327998
$306$	−0.122495	−0.00700257
$307$	−3.68668	−0.210410	−0.105205	−	0.994451i	$-0.533550\pi$
$307$	−3.68668	−0.210410	−0.105205	+	0.994451i	$0.533550\pi$
$308$	−0.221106	−0.0125987
$309$	−9.00401	−0.512220
$310$	−5.81904	−0.330499
$311$	−12.1597	−0.689513	−0.344756	−	0.938692i	$-0.612038\pi$
$311$	−12.1597	−0.689513	−0.344756	+	0.938692i	$0.612038\pi$
$312$	−12.3286	−0.697972
$313$	27.8377	1.57348	0.786741	−	0.617283i	$-0.211767\pi$
$313$	27.8377	1.57348	0.786741	+	0.617283i	$0.211767\pi$
$314$	−12.2543	−0.691553
$315$	1.78044	0.100316
$316$	−1.70845	−0.0961077
$317$	−23.2275	−1.30458	−0.652292	−	0.757967i	$-0.726193\pi$
$317$	−23.2275	−1.30458	−0.652292	+	0.757967i	$0.726193\pi$
$318$	4.65231	0.260888
$319$	2.38333	0.133441
$320$	−10.0178	−0.560012
$321$	−17.9368	−1.00113
$322$	−1.59040	−0.0886297
$323$	−0.390028	−0.0217017
$324$	0.429028	0.0238349
$325$	9.21494	0.511153
$326$	−7.83600	−0.433996
$327$	−11.0874	−0.613135
$328$	5.43873	0.300304
$329$	−10.2871	−0.567148
$330$	1.43007	0.0787226
$331$	−16.1213	−0.886109	−0.443054	−	0.896495i	$-0.646105\pi$
$331$	−16.1213	−0.886109	−0.443054	+	0.896495i	$0.646105\pi$
$332$	−1.94885	−0.106957
$333$	5.01414	0.274773
$334$	7.67893	0.420172
$335$	−11.9928	−0.655239
$336$	−4.67399	−0.254987
$337$	32.7239	1.78258	0.891292	−	0.453430i	$-0.149800\pi$
$337$	32.7239	1.78258	0.891292	+	0.453430i	$0.149800\pi$
$338$	19.2555	1.04736
$339$	8.93713	0.485398
$340$	0.0600364	0.00325593
$341$	1.08074	0.0585255
$342$	7.73411	0.418213
$343$	−1.00000	−0.0539949
$344$	−25.7066	−1.38601
$345$	1.81684	0.0978155
$346$	−0.551781	−0.0296639
$347$	32.5547	1.74763	0.873814	−	0.486260i	$-0.161639\pi$
$347$	32.5547	1.74763	0.873814	+	0.486260i	$0.161639\pi$
$348$	−1.98407	−0.106357
$349$	−16.9971	−0.909832	−0.454916	−	0.890534i	$-0.650331\pi$
$349$	−16.9971	−0.909832	−0.454916	+	0.890534i	$0.650331\pi$
$350$	2.85219	0.152456
$351$	5.03536	0.268768
$352$	−1.23056	−0.0655890
$353$	−16.4266	−0.874298	−0.437149	−	0.899389i	$-0.644012\pi$
$353$	−16.4266	−0.874298	−0.437149	+	0.899389i	$0.644012\pi$
$354$	16.4075	0.872049
$355$	−13.7057	−0.727422
$356$	2.92086	0.154805
$357$	−0.0785962	−0.00415975
$358$	38.1672	2.01720
$359$	−20.0155	−1.05638	−0.528190	−	0.849126i	$-0.677129\pi$
$359$	−20.0155	−1.05638	−0.528190	+	0.849126i	$0.677129\pi$
$360$	4.35924	0.229752
$361$	5.62570	0.296089
$362$	−1.99819	−0.105023
$363$	10.7344	0.563410
$364$	2.16031	0.113231
$365$	13.1341	0.687472
$366$	5.01431	0.262102
$367$	−3.06255	−0.159864	−0.0799319	−	0.996800i	$-0.525470\pi$
$367$	−3.06255	−0.159864	−0.0799319	+	0.996800i	$0.525470\pi$
$368$	−4.76956	−0.248631
$369$	−2.22133	−0.115638
$370$	−13.9136	−0.723333
$371$	2.98505	0.154976
$372$	−0.899694	−0.0466470
$373$	−18.7049	−0.968501	−0.484250	−	0.874929i	$-0.660908\pi$
$373$	−18.7049	−0.968501	−0.484250	+	0.874929i	$0.660908\pi$
$374$	−0.0631294	−0.00326434
$375$	−12.1605	−0.627964
$376$	−25.1872	−1.29893
$377$	−23.2864	−1.19931
$378$	1.55853	0.0801623
$379$	−11.0442	−0.567300	−0.283650	−	0.958928i	$-0.591545\pi$
$379$	−11.0442	−0.567300	−0.283650	+	0.958928i	$0.591545\pi$
$380$	−3.79059	−0.194453
$381$	−1.00000	−0.0512316
$382$	11.2036	0.573226
$383$	5.24124	0.267815	0.133907	−	0.990994i	$-0.457248\pi$
$383$	5.24124	0.267815	0.133907	+	0.990994i	$0.457248\pi$
$384$	−13.5447	−0.691202
$385$	0.917572	0.0467638
$386$	30.4418	1.54944
$387$	10.4993	0.533710
$388$	2.71812	0.137992
$389$	29.4180	1.49155	0.745776	−	0.666197i	$-0.232079\pi$
$389$	29.4180	1.49155	0.745776	+	0.666197i	$0.232079\pi$
$390$	−13.9725	−0.707524
$391$	−0.0802033	−0.00405606
$392$	−2.44841	−0.123664
$393$	9.58473	0.483486
$394$	0.694945	0.0350108
$395$	7.08993	0.356733
$396$	0.221106	0.0111110
$397$	11.1886	0.561541	0.280770	−	0.959775i	$-0.409410\pi$
$397$	11.1886	0.561541	0.280770	+	0.959775i	$0.409410\pi$
$398$	−1.40694	−0.0705237
$399$	4.96243	0.248432
$400$	8.55362	0.427681
$401$	−10.9819	−0.548411	−0.274205	−	0.961671i	$-0.588415\pi$
$401$	−10.9819	−0.548411	−0.274205	+	0.961671i	$0.588415\pi$
$402$	−10.4981	−0.523599
$403$	−10.5594	−0.526002
$404$	2.76423	0.137525
$405$	−1.78044	−0.0884706
$406$	−7.20755	−0.357705
$407$	2.58411	0.128089
$408$	−0.192436	−0.00952700
$409$	−20.2531	−1.00145	−0.500725	−	0.865607i	$-0.666933\pi$
$409$	−20.2531	−1.00145	−0.500725	+	0.865607i	$0.666933\pi$
$410$	6.16391	0.304414
$411$	−14.3286	−0.706778
$412$	3.86298	0.190315
$413$	10.5275	0.518025
$414$	1.59040	0.0781640
$415$	8.08759	0.397004
$416$	12.0232	0.589485
$417$	10.1363	0.496378
$418$	3.98588	0.194956
$419$	−1.17174	−0.0572431	−0.0286216	−	0.999590i	$-0.509112\pi$
$419$	−1.17174	−0.0572431	−0.0286216	+	0.999590i	$0.509112\pi$
$420$	−0.763858	−0.0372725
$421$	−23.9827	−1.16885	−0.584423	−	0.811449i	$-0.698679\pi$
$421$	−23.9827	−1.16885	−0.584423	+	0.811449i	$0.698679\pi$
$422$	−11.0562	−0.538205
$423$	10.2871	0.500178
$424$	7.30864	0.354939
$425$	0.143835	0.00697701
$426$	−11.9975	−0.581280
$427$	3.21732	0.155697
$428$	7.69538	0.371970
$429$	2.59504	0.125290
$430$	−29.1342	−1.40498
$431$	21.8335	1.05168	0.525841	−	0.850583i	$-0.323751\pi$
$431$	21.8335	1.05168	0.525841	+	0.850583i	$0.323751\pi$
$432$	4.67399	0.224878
$433$	37.4203	1.79830	0.899152	−	0.437637i	$-0.144185\pi$
$433$	37.4203	1.79830	0.899152	+	0.437637i	$0.144185\pi$
$434$	−3.26832	−0.156885
$435$	8.23375	0.394778
$436$	4.75682	0.227810
$437$	5.06390	0.242239
$438$	11.4972	0.549356
$439$	−31.4000	−1.49864	−0.749319	−	0.662209i	$-0.769619\pi$
$439$	−31.4000	−1.49864	−0.749319	+	0.662209i	$0.769619\pi$
$440$	2.24660	0.107102
$441$	1.00000	0.0476190
$442$	0.616806	0.0293385
$443$	40.6534	1.93150	0.965750	−	0.259473i	$-0.0835489\pi$
$443$	40.6534	1.93150	0.965750	+	0.259473i	$0.0835489\pi$
$444$	−2.15121	−0.102092
$445$	−12.1213	−0.574607
$446$	−22.0400	−1.04362
$447$	−0.914867	−0.0432717
$448$	−5.62659	−0.265832
$449$	−20.9174	−0.987155	−0.493578	−	0.869702i	$-0.664311\pi$
$449$	−20.9174	−0.987155	−0.493578	+	0.869702i	$0.664311\pi$
$450$	−2.85219	−0.134453
$451$	−1.14479	−0.0539062
$452$	−3.83428	−0.180350
$453$	−0.363833	−0.0170944
$454$	6.50820	0.305445
$455$	−8.96515	−0.420292
$456$	12.1501	0.568979
$457$	38.7768	1.81390	0.906951	−	0.421236i	$-0.138404\pi$
$457$	38.7768	1.81390	0.906951	+	0.421236i	$0.138404\pi$
$458$	−10.2350	−0.478251
$459$	0.0785962	0.00366856
$460$	−0.779477	−0.0363433
$461$	28.3743	1.32152	0.660761	−	0.750596i	$-0.270234\pi$
$461$	28.3743	1.32152	0.660761	+	0.750596i	$0.270234\pi$
$462$	0.803212	0.0373688
$463$	6.90362	0.320838	0.160419	−	0.987049i	$-0.448715\pi$
$463$	6.90362	0.320838	0.160419	+	0.987049i	$0.448715\pi$
$464$	−21.6152	−1.00346
$465$	3.73366	0.173145
$466$	20.5652	0.952666
$467$	−9.72062	−0.449816	−0.224908	−	0.974380i	$-0.572208\pi$
$467$	−9.72062	−0.449816	−0.224908	+	0.974380i	$0.572208\pi$
$468$	−2.16031	−0.0998606
$469$	−6.73590	−0.311035
$470$	−28.5455	−1.31670
$471$	7.86274	0.362296
$472$	25.7757	1.18642
$473$	5.41096	0.248796
$474$	6.20629	0.285064
$475$	−9.08147	−0.416686
$476$	0.0337200	0.00154555
$477$	−2.98505	−0.136676
$478$	−24.2704	−1.11010
$479$	38.8371	1.77451	0.887256	−	0.461277i	$-0.152609\pi$
$479$	38.8371	1.77451	0.887256	+	0.461277i	$0.152609\pi$
$480$	−4.25124	−0.194042
$481$	−25.2480	−1.15121
$482$	−43.0028	−1.95872
$483$	1.02045	0.0464320
$484$	−4.60536	−0.209335
$485$	−11.2800	−0.512198
$486$	−1.55853	−0.0706965
$487$	−8.67843	−0.393257	−0.196629	−	0.980478i	$-0.562999\pi$
$487$	−8.67843	−0.393257	−0.196629	+	0.980478i	$0.562999\pi$
$488$	7.87733	0.356590
$489$	5.02780	0.227365
$490$	−2.77487	−0.125356
$491$	−8.02175	−0.362017	−0.181008	−	0.983482i	$-0.557936\pi$
$491$	−8.02175	−0.362017	−0.181008	+	0.983482i	$0.557936\pi$
$492$	0.953014	0.0429652
$493$	−0.363474	−0.0163700
$494$	−38.9441	−1.75218
$495$	−0.917572	−0.0412418
$496$	−9.80159	−0.440105
$497$	−7.69793	−0.345299
$498$	7.07960	0.317245
$499$	3.20665	0.143549	0.0717746	−	0.997421i	$-0.477134\pi$
$499$	3.20665	0.143549	0.0717746	+	0.997421i	$0.477134\pi$
$500$	5.21718	0.233320
$501$	−4.92702	−0.220123
$502$	−34.3550	−1.53334
$503$	−6.43794	−0.287053	−0.143527	−	0.989646i	$-0.545844\pi$
$503$	−6.43794	−0.287053	−0.143527	+	0.989646i	$0.545844\pi$
$504$	2.44841	0.109061
$505$	−11.4713	−0.510468
$506$	0.819635	0.0364372
$507$	−12.3549	−0.548700
$508$	0.429028	0.0190351
$509$	35.6794	1.58146	0.790732	−	0.612163i	$-0.209700\pi$
$509$	35.6794	1.58146	0.790732	+	0.612163i	$0.209700\pi$
$510$	−0.218094	−0.00965738
$511$	7.37692	0.326336
$512$	−11.7274	−0.518283
$513$	−4.96243	−0.219097
$514$	−2.31036	−0.101906
$515$	−16.0311	−0.706413
$516$	−4.50450	−0.198300
$517$	5.30162	0.233165
$518$	−7.81471	−0.343359
$519$	0.354038	0.0155406
$520$	−21.9504	−0.962588
$521$	27.0870	1.18670	0.593351	−	0.804944i	$-0.297805\pi$
$521$	27.0870	1.18670	0.593351	+	0.804944i	$0.297805\pi$
$522$	7.20755	0.315466
$523$	−10.9602	−0.479257	−0.239628	−	0.970865i	$-0.577026\pi$
$523$	−10.9602	−0.479257	−0.239628	+	0.970865i	$0.577026\pi$
$524$	−4.11212	−0.179639
$525$	−1.83005	−0.0798697
$526$	3.53319	0.154055
$527$	−0.164820	−0.00717968
$528$	2.40881	0.104830
$529$	−21.9587	−0.954726
$530$	8.28314	0.359797
$531$	−10.5275	−0.456856
$532$	−2.12902	−0.0923049
$533$	11.1852	0.484485
$534$	−10.6106	−0.459166
$535$	−31.9353	−1.38068
$536$	−16.4923	−0.712357
$537$	−24.4892	−1.05679
$538$	33.8130	1.45778
$539$	0.515364	0.0221983
$540$	0.763858	0.0328712
$541$	8.76283	0.376743	0.188372	−	0.982098i	$-0.439679\pi$
$541$	8.76283	0.376743	0.188372	+	0.982098i	$0.439679\pi$
$542$	35.1023	1.50777
$543$	1.28210	0.0550201
$544$	0.187668	0.00804620
$545$	−19.7404	−0.845587
$546$	−7.84779	−0.335854
$547$	−15.1052	−0.645851	−0.322925	−	0.946424i	$-0.604666\pi$
$547$	−15.1052	−0.645851	−0.322925	+	0.946424i	$0.604666\pi$
$548$	6.14738	0.262603
$549$	−3.21732	−0.137312
$550$	−1.46991	−0.0626773
$551$	22.9491	0.977664
$552$	2.49848	0.106342
$553$	3.98213	0.169337
$554$	11.3353	0.481590
$555$	8.92736	0.378945
$556$	−4.34877	−0.184429
$557$	30.1447	1.27727	0.638636	−	0.769509i	$-0.279499\pi$
$557$	30.1447	1.27727	0.638636	+	0.769509i	$0.279499\pi$
$558$	3.26832	0.138359
$559$	−52.8678	−2.23607
$560$	−8.32175	−0.351658
$561$	0.0405056	0.00171015
$562$	−27.9032	−1.17703
$563$	17.7284	0.747165	0.373582	−	0.927597i	$-0.378129\pi$
$563$	17.7284	0.747165	0.373582	+	0.927597i	$0.378129\pi$
$564$	−4.41347	−0.185841
$565$	15.9120	0.669423
$566$	18.8490	0.792281
$567$	−1.00000	−0.0419961
$568$	−18.8477	−0.790833
$569$	−11.0414	−0.462878	−0.231439	−	0.972849i	$-0.574343\pi$
$569$	−11.0414	−0.462878	−0.231439	+	0.972849i	$0.574343\pi$
$570$	13.7701	0.576766
$571$	20.2102	0.845772	0.422886	−	0.906183i	$-0.361017\pi$
$571$	20.2102	0.845772	0.422886	+	0.906183i	$0.361017\pi$
$572$	−1.11335	−0.0465514
$573$	−7.18855	−0.300306
$574$	3.46202	0.144502
$575$	−1.86747	−0.0778787
$576$	5.62659	0.234441
$577$	10.6062	0.441544	0.220772	−	0.975325i	$-0.429142\pi$
$577$	10.6062	0.441544	0.220772	+	0.975325i	$0.429142\pi$
$578$	−26.4855	−1.10165
$579$	−19.5323	−0.811735
$580$	−3.53251	−0.146680
$581$	4.54247	0.188454
$582$	−9.87412	−0.409296
$583$	−1.53839	−0.0637135
$584$	18.0617	0.747400
$585$	8.96515	0.370663
$586$	36.1999	1.49541
$587$	−1.49954	−0.0618924	−0.0309462	−	0.999521i	$-0.509852\pi$
$587$	−1.49954	−0.0618924	−0.0309462	+	0.999521i	$0.509852\pi$
$588$	−0.429028	−0.0176928
$589$	10.4065	0.428791
$590$	29.2125	1.20266
$591$	−0.445897	−0.0183417
$592$	−23.4361	−0.963216
$593$	27.4075	1.12549	0.562745	−	0.826631i	$-0.309745\pi$
$593$	27.4075	1.12549	0.562745	+	0.826631i	$0.309745\pi$
$594$	−0.803212	−0.0329562
$595$	−0.139936	−0.00573680
$596$	0.392504	0.0160776
$597$	0.902735	0.0369465
$598$	−8.00825	−0.327482
$599$	11.0899	0.453120	0.226560	−	0.973997i	$-0.427252\pi$
$599$	11.0899	0.453120	0.226560	+	0.973997i	$0.427252\pi$
$600$	−4.48071	−0.182924
$601$	−23.0051	−0.938399	−0.469199	−	0.883092i	$-0.655457\pi$
$601$	−23.0051	−0.938399	−0.469199	+	0.883092i	$0.655457\pi$
$602$	−16.3635	−0.666927
$603$	6.73590	0.274307
$604$	0.156095	0.00635140
$605$	19.1119	0.777010
$606$	−10.0416	−0.407913
$607$	−31.3846	−1.27386	−0.636930	−	0.770922i	$-0.719796\pi$
$607$	−31.3846	−1.27386	−0.636930	+	0.770922i	$0.719796\pi$
$608$	−11.8490	−0.480542
$609$	4.62457	0.187397
$610$	8.92765	0.361470
$611$	−51.7995	−2.09558
$612$	−0.0337200	−0.00136305
$613$	2.27107	0.0917275	0.0458637	−	0.998948i	$-0.485396\pi$
$613$	2.27107	0.0917275	0.0458637	+	0.998948i	$0.485396\pi$
$614$	−5.74581	−0.231882
$615$	−3.95494	−0.159478
$616$	1.26182	0.0508403
$617$	−21.4443	−0.863314	−0.431657	−	0.902038i	$-0.642071\pi$
$617$	−21.4443	−0.863314	−0.431657	+	0.902038i	$0.642071\pi$
$618$	−14.0331	−0.564492
$619$	29.7159	1.19438	0.597191	−	0.802099i	$-0.296284\pi$
$619$	29.7159	1.19438	0.597191	+	0.802099i	$0.296284\pi$
$620$	−1.60185	−0.0643318
$621$	−1.02045	−0.0409492
$622$	−18.9513	−0.759878
$623$	−6.80807	−0.272760
$624$	−23.5352	−0.942164
$625$	−12.5007	−0.500028
$626$	43.3861	1.73406
$627$	−2.55745	−0.102135
$628$	−3.37334	−0.134611
$629$	−0.394093	−0.0157135
$630$	2.77487	0.110554
$631$	30.4100	1.21060	0.605302	−	0.795996i	$-0.293052\pi$
$631$	30.4100	1.21060	0.605302	+	0.795996i	$0.293052\pi$
$632$	9.74990	0.387830
$633$	7.09394	0.281959
$634$	−36.2008	−1.43772
$635$	−1.78044	−0.0706545
$636$	1.28067	0.0507820
$637$	−5.03536	−0.199508
$638$	3.71451	0.147059
$639$	7.69793	0.304526
$640$	−24.1155	−0.953251
$641$	20.0927	0.793612	0.396806	−	0.917902i	$-0.370119\pi$
$641$	20.0927	0.793612	0.396806	+	0.917902i	$0.370119\pi$
$642$	−27.9550	−1.10330
$643$	−1.91571	−0.0755484	−0.0377742	−	0.999286i	$-0.512027\pi$
$643$	−1.91571	−0.0755484	−0.0377742	+	0.999286i	$0.512027\pi$
$644$	−0.437801	−0.0172518
$645$	18.6933	0.736050
$646$	−0.607872	−0.0239164
$647$	2.27974	0.0896259	0.0448130	−	0.998995i	$-0.485731\pi$
$647$	2.27974	0.0896259	0.0448130	+	0.998995i	$0.485731\pi$
$648$	−2.44841	−0.0961827
$649$	−5.42550	−0.212970
$650$	14.3618	0.563316
$651$	2.09705	0.0821899
$652$	−2.15707	−0.0844774
$653$	16.9385	0.662856	0.331428	−	0.943481i	$-0.392470\pi$
$653$	16.9385	0.662856	0.331428	+	0.943481i	$0.392470\pi$
$654$	−17.2801	−0.675706
$655$	17.0650	0.666785
$656$	10.3825	0.405368
$657$	−7.37692	−0.287801
$658$	−16.0329	−0.625026
$659$	26.4392	1.02992	0.514962	−	0.857213i	$-0.327806\pi$
$659$	26.4392	1.02992	0.514962	+	0.857213i	$0.327806\pi$
$660$	0.393665	0.0153234
$661$	5.49530	0.213743	0.106871	−	0.994273i	$-0.465917\pi$
$661$	5.49530	0.213743	0.106871	+	0.994273i	$0.465917\pi$
$662$	−25.1256	−0.976536
$663$	−0.395761	−0.0153701
$664$	11.1219	0.431612
$665$	8.83529	0.342618
$666$	7.81471	0.302814
$667$	4.71913	0.182725
$668$	2.11383	0.0817866
$669$	14.1415	0.546741
$670$	−18.6913	−0.722106
$671$	−1.65809	−0.0640099
$672$	−2.38775	−0.0921094
$673$	4.88115	0.188154	0.0940772	−	0.995565i	$-0.470010\pi$
$673$	4.88115	0.188154	0.0940772	+	0.995565i	$0.470010\pi$
$674$	51.0013	1.96450
$675$	1.83005	0.0704385
$676$	5.30060	0.203869
$677$	36.6675	1.40925	0.704624	−	0.709581i	$-0.251116\pi$
$677$	36.6675	1.40925	0.704624	+	0.709581i	$0.251116\pi$
$678$	13.9288	0.534933
$679$	−6.33552	−0.243135
$680$	−0.342620	−0.0131389
$681$	−4.17585	−0.160019
$682$	1.68438	0.0644981
$683$	−16.8378	−0.644281	−0.322141	−	0.946692i	$-0.604402\pi$
$683$	−16.8378	−0.644281	−0.322141	+	0.946692i	$0.604402\pi$
$684$	2.12902	0.0814052
$685$	−25.5112	−0.974732
$686$	−1.55853	−0.0595051
$687$	6.56707	0.250550
$688$	−49.0737	−1.87092
$689$	15.0308	0.572629
$690$	2.83161	0.107798
$691$	9.26464	0.352443	0.176222	−	0.984350i	$-0.443612\pi$
$691$	9.26464	0.352443	0.176222	+	0.984350i	$0.443612\pi$
$692$	−0.151892	−0.00577408
$693$	−0.515364	−0.0195770
$694$	50.7376	1.92597
$695$	18.0471	0.684565
$696$	11.3229	0.429192
$697$	0.174588	0.00661300
$698$	−26.4905	−1.00268
$699$	−13.1952	−0.499090
$700$	0.785142	0.0296756
$701$	19.4041	0.732882	0.366441	−	0.930441i	$-0.380576\pi$
$701$	19.4041	0.732882	0.366441	+	0.930441i	$0.380576\pi$
$702$	7.84779	0.296196
$703$	24.8823	0.938454
$704$	2.89974	0.109288
$705$	18.3156	0.689805
$706$	−25.6014	−0.963520
$707$	−6.44299	−0.242314
$708$	4.51661	0.169744
$709$	15.2697	0.573466	0.286733	−	0.958011i	$-0.407431\pi$
$709$	15.2697	0.573466	0.286733	+	0.958011i	$0.407431\pi$
$710$	−21.3608	−0.801655
$711$	−3.98213	−0.149342
$712$	−16.6690	−0.624696
$713$	2.13993	0.0801410
$714$	−0.122495	−0.00458426
$715$	4.62031	0.172790
$716$	10.5065	0.392648
$717$	15.5726	0.581569
$718$	−31.1949	−1.16418
$719$	−32.2131	−1.20135	−0.600673	−	0.799495i	$-0.705101\pi$
$719$	−32.2131	−1.20135	−0.600673	+	0.799495i	$0.705101\pi$
$720$	8.32175	0.310133
$721$	−9.00401	−0.335327
$722$	8.76784	0.326305
$723$	27.5918	1.02615
$724$	−0.550057	−0.0204427
$725$	−8.46317	−0.314314
$726$	16.7299	0.620906
$727$	−24.3075	−0.901516	−0.450758	−	0.892646i	$-0.648846\pi$
$727$	−24.3075	−0.901516	−0.450758	+	0.892646i	$0.648846\pi$
$728$	−12.3286	−0.456930
$729$	1.00000	0.0370370
$730$	20.4700	0.757629
$731$	−0.825206	−0.0305213
$732$	1.38032	0.0510182
$733$	31.6574	1.16929	0.584647	−	0.811288i	$-0.301233\pi$
$733$	31.6574	1.16929	0.584647	+	0.811288i	$0.301233\pi$
$734$	−4.77309	−0.176178
$735$	1.78044	0.0656724
$736$	−2.43657	−0.0898133
$737$	3.47144	0.127872
$738$	−3.46202	−0.127439
$739$	−15.9162	−0.585487	−0.292743	−	0.956191i	$-0.594568\pi$
$739$	−15.9162	−0.585487	−0.292743	+	0.956191i	$0.594568\pi$
$740$	−3.83009	−0.140797
$741$	24.9876	0.917944
$742$	4.65231	0.170792
$743$	12.7798	0.468847	0.234423	−	0.972135i	$-0.424680\pi$
$743$	12.7798	0.468847	0.234423	+	0.972135i	$0.424680\pi$
$744$	5.13444	0.188238
$745$	−1.62886	−0.0596769
$746$	−29.1522	−1.06734
$747$	−4.54247	−0.166200
$748$	−0.0173781	−0.000635405 0
$749$	−17.9368	−0.655395
$750$	−18.9525	−0.692047
$751$	21.2634	0.775913	0.387956	−	0.921678i	$-0.373181\pi$
$751$	21.2634	0.775913	0.387956	+	0.921678i	$0.373181\pi$
$752$	−48.0820	−1.75337
$753$	22.0431	0.803297
$754$	−36.2926	−1.32170
$755$	−0.647782	−0.0235752
$756$	0.429028	0.0156036
$757$	−12.8093	−0.465563	−0.232782	−	0.972529i	$-0.574783\pi$
$757$	−12.8093	−0.465563	−0.232782	+	0.972529i	$0.574783\pi$
$758$	−17.2127	−0.625193
$759$	−0.525902	−0.0190890
$760$	21.6324	0.784691
$761$	−39.8743	−1.44544	−0.722720	−	0.691141i	$-0.757109\pi$
$761$	−39.8743	−1.44544	−0.722720	+	0.691141i	$0.757109\pi$
$762$	−1.55853	−0.0564597
$763$	−11.0874	−0.401391
$764$	3.08409	0.111579
$765$	0.139936	0.00505938
$766$	8.16864	0.295145
$767$	53.0099	1.91408
$768$	−9.85675	−0.355675
$769$	5.50092	0.198368	0.0991842	−	0.995069i	$-0.468377\pi$
$769$	5.50092	0.198368	0.0991842	+	0.995069i	$0.468377\pi$
$770$	1.43007	0.0515361
$771$	1.48239	0.0533871
$772$	8.37991	0.301600
$773$	34.0279	1.22390	0.611949	−	0.790897i	$-0.290386\pi$
$773$	34.0279	1.22390	0.611949	+	0.790897i	$0.290386\pi$
$774$	16.3635	0.588175
$775$	−3.83770	−0.137854
$776$	−15.5120	−0.556847
$777$	5.01414	0.179881
$778$	45.8489	1.64376
$779$	−11.0232	−0.394947
$780$	−3.84630	−0.137720
$781$	3.96723	0.141959
$782$	−0.125000	−0.00446998
$783$	−4.62457	−0.165269
$784$	−4.67399	−0.166928
$785$	13.9991	0.499650
$786$	14.9381	0.532826
$787$	−20.5802	−0.733605	−0.366803	−	0.930299i	$-0.619548\pi$
$787$	−20.5802	−0.733605	−0.366803	+	0.930299i	$0.619548\pi$
$788$	0.191302	0.00681487
$789$	−2.26700	−0.0807073
$790$	11.0499	0.393138
$791$	8.93713	0.317768
$792$	−1.26182	−0.0448369
$793$	16.2004	0.575292
$794$	17.4378	0.618846
$795$	−5.31470	−0.188493
$796$	−0.387299	−0.0137274
$797$	−3.94676	−0.139801	−0.0699007	−	0.997554i	$-0.522268\pi$
$797$	−3.94676	−0.139801	−0.0699007	+	0.997554i	$0.522268\pi$
$798$	7.73411	0.273785
$799$	−0.808530	−0.0286037
$800$	4.36969	0.154492
$801$	6.80807	0.240551
$802$	−17.1157	−0.604376
$803$	−3.80179	−0.134162
$804$	−2.88989	−0.101919
$805$	1.81684	0.0640353
$806$	−16.4572	−0.579680
$807$	−21.6954	−0.763715
$808$	−15.7751	−0.554966
$809$	23.5792	0.828999	0.414500	−	0.910049i	$-0.363957\pi$
$809$	23.5792	0.828999	0.414500	+	0.910049i	$0.363957\pi$
$810$	−2.77487	−0.0974990
$811$	−29.0528	−1.02018	−0.510091	−	0.860121i	$-0.670388\pi$
$811$	−29.0528	−1.02018	−0.510091	+	0.860121i	$0.670388\pi$
$812$	−1.98407	−0.0696273
$813$	−22.5226	−0.789904
$814$	4.02742	0.141161
$815$	8.95168	0.313564
$816$	−0.367358	−0.0128601
$817$	52.1021	1.82282
$818$	−31.5651	−1.10365
$819$	5.03536	0.175950
$820$	1.69678	0.0592542
$821$	12.1475	0.423951	0.211976	−	0.977275i	$-0.432010\pi$
$821$	12.1475	0.423951	0.211976	+	0.977275i	$0.432010\pi$
$822$	−22.3316	−0.778905
$823$	−30.1618	−1.05138	−0.525688	−	0.850678i	$-0.676192\pi$
$823$	−30.1618	−1.05138	−0.525688	+	0.850678i	$0.676192\pi$
$824$	−22.0455	−0.767992
$825$	0.943139	0.0328359
$826$	16.4075	0.570890
$827$	0.711655	0.0247467	0.0123733	−	0.999923i	$-0.496061\pi$
$827$	0.711655	0.0247467	0.0123733	+	0.999923i	$0.496061\pi$
$828$	0.437801	0.0152146
$829$	22.9180	0.795976	0.397988	−	0.917391i	$-0.369709\pi$
$829$	22.9180	0.795976	0.397988	+	0.917391i	$0.369709\pi$
$830$	12.6048	0.437518
$831$	−7.27304	−0.252299
$832$	−28.3319	−0.982233
$833$	−0.0785962	−0.00272320
$834$	15.7978	0.547034
$835$	−8.77225	−0.303576
$836$	1.09722	0.0379482
$837$	−2.09705	−0.0724847
$838$	−1.82619	−0.0630848
$839$	16.7052	0.576729	0.288364	−	0.957521i	$-0.406889\pi$
$839$	16.7052	0.576729	0.288364	+	0.957521i	$0.406889\pi$
$840$	4.35924	0.150408
$841$	−7.61336	−0.262530
$842$	−37.3779	−1.28813
$843$	17.9035	0.616629
$844$	−3.04350	−0.104762
$845$	−21.9971	−0.756723
$846$	16.0329	0.551221
$847$	10.7344	0.368838
$848$	13.9521	0.479118
$849$	−12.0940	−0.415066
$850$	0.224171	0.00768901
$851$	5.11667	0.175397
$852$	−3.30263	−0.113146
$853$	43.1401	1.47709	0.738544	−	0.674205i	$-0.235514\pi$
$853$	43.1401	1.47709	0.738544	+	0.674205i	$0.235514\pi$
$854$	5.01431	0.171586
$855$	−8.83529	−0.302161
$856$	−43.9166	−1.50104
$857$	40.8276	1.39465	0.697323	−	0.716757i	$-0.254375\pi$
$857$	40.8276	1.39465	0.697323	+	0.716757i	$0.254375\pi$
$858$	4.04446	0.138076
$859$	−14.5718	−0.497185	−0.248592	−	0.968608i	$-0.579968\pi$
$859$	−14.5718	−0.497185	−0.248592	+	0.968608i	$0.579968\pi$
$860$	−8.01998	−0.273479
$861$	−2.22133	−0.0757027
$862$	34.0282	1.15901
$863$	7.00504	0.238454	0.119227	−	0.992867i	$-0.461958\pi$
$863$	7.00504	0.238454	0.119227	+	0.992867i	$0.461958\pi$
$864$	2.38775	0.0812329
$865$	0.630342	0.0214323
$866$	58.3208	1.98182
$867$	16.9938	0.577140
$868$	−0.899694	−0.0305376
$869$	−2.05224	−0.0696176
$870$	12.8326	0.435065
$871$	−33.9177	−1.14926
$872$	−27.1466	−0.919299
$873$	6.33552	0.214425
$874$	7.89226	0.266960
$875$	−12.1605	−0.411099
$876$	3.16491	0.106932
$877$	−54.4272	−1.83787	−0.918937	−	0.394404i	$-0.870951\pi$
$877$	−54.4272	−1.83787	−0.918937	+	0.394404i	$0.870951\pi$
$878$	−48.9379	−1.65157
$879$	−23.2269	−0.783424
$880$	4.28872	0.144573
$881$	−17.1113	−0.576494	−0.288247	−	0.957556i	$-0.593072\pi$
$881$	−17.1113	−0.576494	−0.288247	+	0.957556i	$0.593072\pi$
$882$	1.55853	0.0524786
$883$	−27.0710	−0.911011	−0.455505	−	0.890233i	$-0.650541\pi$
$883$	−27.0710	−0.911011	−0.455505	+	0.890233i	$0.650541\pi$
$884$	0.169793	0.00571074
$885$	−18.7436	−0.630059
$886$	63.3597	2.12861
$887$	−1.70221	−0.0571546	−0.0285773	−	0.999592i	$-0.509098\pi$
$887$	−1.70221	−0.0571546	−0.0285773	+	0.999592i	$0.509098\pi$
$888$	12.2767	0.411979
$889$	−1.00000	−0.0335389
$890$	−18.8915	−0.633245
$891$	0.515364	0.0172653
$892$	−6.06710	−0.203141
$893$	51.0492	1.70830
$894$	−1.42585	−0.0476876
$895$	−43.6014	−1.45743
$896$	−13.5447	−0.452498
$897$	5.13832	0.171564
$898$	−32.6005	−1.08789
$899$	9.69795	0.323445
$900$	−0.785142	−0.0261714
$901$	0.234614	0.00781612
$902$	−1.78420	−0.0594073
$903$	10.4993	0.349395
$904$	21.8818	0.727777
$905$	2.28270	0.0758794
$906$	−0.567046	−0.0188388
$907$	11.0234	0.366026	0.183013	−	0.983111i	$-0.441415\pi$
$907$	11.0234	0.366026	0.183013	+	0.983111i	$0.441415\pi$
$908$	1.79156	0.0594549
$909$	6.44299	0.213701
$910$	−13.9725	−0.463183
$911$	30.6668	1.01604	0.508018	−	0.861346i	$-0.330378\pi$
$911$	30.6668	1.01604	0.508018	+	0.861346i	$0.330378\pi$
$912$	23.1943	0.768042
$913$	−2.34103	−0.0774767
$914$	60.4350	1.99901
$915$	−5.72824	−0.189370
$916$	−2.81746	−0.0930916
$917$	9.58473	0.316516
$918$	0.122495	0.00404293
$919$	37.9535	1.25197	0.625985	−	0.779835i	$-0.284697\pi$
$919$	37.9535	1.25197	0.625985	+	0.779835i	$0.284697\pi$
$920$	4.44838	0.146659
$921$	3.68668	0.121480
$922$	44.2223	1.45638
$923$	−38.7619	−1.27586
$924$	0.221106	0.00727384
$925$	−9.17611	−0.301709
$926$	10.7595	0.353580
$927$	9.00401	0.295730
$928$	−11.0423	−0.362482
$929$	−0.956910	−0.0313952	−0.0156976	−	0.999877i	$-0.504997\pi$
$929$	−0.956910	−0.0313952	−0.0156976	+	0.999877i	$0.504997\pi$
$930$	5.81904	0.190814
$931$	4.96243	0.162637
$932$	5.66113	0.185437
$933$	12.1597	0.398090
$934$	−15.1499	−0.495720
$935$	0.0721177	0.00235850
$936$	12.3286	0.402974
$937$	2.47200	0.0807567	0.0403783	−	0.999184i	$-0.487144\pi$
$937$	2.47200	0.0807567	0.0403783	+	0.999184i	$0.487144\pi$
$938$	−10.4981	−0.342776
$939$	−27.8377	−0.908450
$940$	−7.85791	−0.256297
$941$	8.23741	0.268532	0.134266	−	0.990945i	$-0.457132\pi$
$941$	8.23741	0.268532	0.134266	+	0.990945i	$0.457132\pi$
$942$	12.2543	0.399268
$943$	−2.26675	−0.0738156
$944$	49.2055	1.60150
$945$	−1.78044	−0.0579176
$946$	8.43317	0.274186
$947$	−9.38242	−0.304888	−0.152444	−	0.988312i	$-0.548714\pi$
$947$	−9.38242	−0.304888	−0.152444	+	0.988312i	$0.548714\pi$
$948$	1.70845	0.0554878
$949$	37.1455	1.20579
$950$	−14.1538	−0.459209
$951$	23.2275	0.753202
$952$	−0.192436	−0.00623689
$953$	−3.12669	−0.101283	−0.0506417	−	0.998717i	$-0.516127\pi$
$953$	−3.12669	−0.101283	−0.0506417	+	0.998717i	$0.516127\pi$
$954$	−4.65231	−0.150624
$955$	−12.7988	−0.414158
$956$	−6.68108	−0.216082
$957$	−2.38333	−0.0770423
$958$	60.5289	1.95560
$959$	−14.3286	−0.462695
$960$	10.0178	0.323323
$961$	−26.6024	−0.858141
$962$	−39.3499	−1.26869
$963$	17.9368	0.578004
$964$	−11.8377	−0.381266
$965$	−34.7760	−1.11948
$966$	1.59040	0.0511704
$967$	−26.6441	−0.856817	−0.428408	−	0.903585i	$-0.640926\pi$
$967$	−26.6441	−0.856817	−0.428408	+	0.903585i	$0.640926\pi$
$968$	26.2822	0.844743
$969$	0.390028	0.0125295
$970$	−17.5802	−0.564468
$971$	47.1816	1.51413	0.757064	−	0.653341i	$-0.226633\pi$
$971$	47.1816	1.51413	0.757064	+	0.653341i	$0.226633\pi$
$972$	−0.429028	−0.0137611
$973$	10.1363	0.324956
$974$	−13.5256	−0.433389
$975$	−9.21494	−0.295114
$976$	15.0377	0.481346
$977$	32.3530	1.03507	0.517533	−	0.855663i	$-0.326851\pi$
$977$	32.3530	1.03507	0.517533	+	0.855663i	$0.326851\pi$
$978$	7.83600	0.250568
$979$	3.50863	0.112136
$980$	−0.763858	−0.0244005
$981$	11.0874	0.353994
$982$	−12.5022	−0.398960
$983$	−19.9109	−0.635058	−0.317529	−	0.948249i	$-0.602853\pi$
$983$	−19.9109	−0.635058	−0.317529	+	0.948249i	$0.602853\pi$
$984$	−5.43873	−0.173380
$985$	−0.793891	−0.0252955
$986$	−0.566486	−0.0180406
$987$	10.2871	0.327443
$988$	−10.7204	−0.341062
$989$	10.7140	0.340685
$990$	−1.43007	−0.0454505
$991$	22.2465	0.706684	0.353342	−	0.935494i	$-0.385045\pi$
$991$	22.2465	0.706684	0.353342	+	0.935494i	$0.385045\pi$
$992$	−5.00723	−0.158980
$993$	16.1213	0.511595
$994$	−11.9975	−0.380537
$995$	1.60726	0.0509536
$996$	1.94885	0.0617517
$997$	33.9575	1.07544	0.537722	−	0.843122i	$-0.319285\pi$
$997$	33.9575	1.07544	0.537722	+	0.843122i	$0.319285\pi$
$998$	4.99767	0.158198
$999$	−5.01414	−0.158640

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.11	✓	16
3.2	odd	2		8001.2.a.r.1.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.11	✓	16	1.1	even	1	trivial
8001.2.a.r.1.6		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)

\(f(q)\)	\(=\)	\(q+1.55853 q^{2} -1.00000 q^{3} +0.429028 q^{4} -1.78044 q^{5} -1.55853 q^{6} -1.00000 q^{7} -2.44841 q^{8} +1.00000 q^{9} -2.77487 q^{10} +0.515364 q^{11} -0.429028 q^{12} -5.03536 q^{13} -1.55853 q^{14} +1.78044 q^{15} -4.67399 q^{16} -0.0785962 q^{17} +1.55853 q^{18} +4.96243 q^{19} -0.763858 q^{20} +1.00000 q^{21} +0.803212 q^{22} +1.02045 q^{23} +2.44841 q^{24} -1.83005 q^{25} -7.84779 q^{26} -1.00000 q^{27} -0.429028 q^{28} +4.62457 q^{29} +2.77487 q^{30} +2.09705 q^{31} -2.38775 q^{32} -0.515364 q^{33} -0.122495 q^{34} +1.78044 q^{35} +0.429028 q^{36} +5.01414 q^{37} +7.73411 q^{38} +5.03536 q^{39} +4.35924 q^{40} -2.22133 q^{41} +1.55853 q^{42} +10.4993 q^{43} +0.221106 q^{44} -1.78044 q^{45} +1.59040 q^{46} +10.2871 q^{47} +4.67399 q^{48} +1.00000 q^{49} -2.85219 q^{50} +0.0785962 q^{51} -2.16031 q^{52} -2.98505 q^{53} -1.55853 q^{54} -0.917572 q^{55} +2.44841 q^{56} -4.96243 q^{57} +7.20755 q^{58} -10.5275 q^{59} +0.763858 q^{60} -3.21732 q^{61} +3.26832 q^{62} -1.00000 q^{63} +5.62659 q^{64} +8.96515 q^{65} -0.803212 q^{66} +6.73590 q^{67} -0.0337200 q^{68} -1.02045 q^{69} +2.77487 q^{70} +7.69793 q^{71} -2.44841 q^{72} -7.37692 q^{73} +7.81471 q^{74} +1.83005 q^{75} +2.12902 q^{76} -0.515364 q^{77} +7.84779 q^{78} -3.98213 q^{79} +8.32175 q^{80} +1.00000 q^{81} -3.46202 q^{82} -4.54247 q^{83} +0.429028 q^{84} +0.139936 q^{85} +16.3635 q^{86} -4.62457 q^{87} -1.26182 q^{88} +6.80807 q^{89} -2.77487 q^{90} +5.03536 q^{91} +0.437801 q^{92} -2.09705 q^{93} +16.0329 q^{94} -8.83529 q^{95} +2.38775 q^{96} +6.33552 q^{97} +1.55853 q^{98} +0.515364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) \) 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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