LMFDB - Embedded newform 2667.2.a.o.1.7

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			1.7
Root			$0.0296587$ 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)

$f(q)$	$=$	\(q+0.0296587 q^{2} -1.00000 q^{3} -1.99912 q^{4} +3.07938 q^{5} -0.0296587 q^{6} -1.00000 q^{7} -0.118609 q^{8} +1.00000 q^{9} +0.0913304 q^{10} -4.20887 q^{11} +1.99912 q^{12} -6.43617 q^{13} -0.0296587 q^{14} -3.07938 q^{15} +3.99472 q^{16} -0.978108 q^{17} +0.0296587 q^{18} +0.452098 q^{19} -6.15605 q^{20} +1.00000 q^{21} -0.124830 q^{22} +1.87821 q^{23} +0.118609 q^{24} +4.48258 q^{25} -0.190888 q^{26} -1.00000 q^{27} +1.99912 q^{28} +6.69207 q^{29} -0.0913304 q^{30} -1.28170 q^{31} +0.355696 q^{32} +4.20887 q^{33} -0.0290094 q^{34} -3.07938 q^{35} -1.99912 q^{36} +6.10620 q^{37} +0.0134086 q^{38} +6.43617 q^{39} -0.365241 q^{40} -3.48251 q^{41} +0.0296587 q^{42} +4.11590 q^{43} +8.41404 q^{44} +3.07938 q^{45} +0.0557052 q^{46} -0.343427 q^{47} -3.99472 q^{48} +1.00000 q^{49} +0.132948 q^{50} +0.978108 q^{51} +12.8667 q^{52} +2.22047 q^{53} -0.0296587 q^{54} -12.9607 q^{55} +0.118609 q^{56} -0.452098 q^{57} +0.198478 q^{58} +1.48973 q^{59} +6.15605 q^{60} +7.08310 q^{61} -0.0380136 q^{62} -1.00000 q^{63} -7.97890 q^{64} -19.8194 q^{65} +0.124830 q^{66} +0.989393 q^{67} +1.95535 q^{68} -1.87821 q^{69} -0.0913304 q^{70} -8.17613 q^{71} -0.118609 q^{72} +9.17564 q^{73} +0.181102 q^{74} -4.48258 q^{75} -0.903798 q^{76} +4.20887 q^{77} +0.190888 q^{78} +9.02266 q^{79} +12.3013 q^{80} +1.00000 q^{81} -0.103287 q^{82} -5.68319 q^{83} -1.99912 q^{84} -3.01197 q^{85} +0.122072 q^{86} -6.69207 q^{87} +0.499209 q^{88} +2.01684 q^{89} +0.0913304 q^{90} +6.43617 q^{91} -3.75476 q^{92} +1.28170 q^{93} -0.0101856 q^{94} +1.39218 q^{95} -0.355696 q^{96} +10.8384 q^{97} +0.0296587 q^{98} -4.20887 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.0296587	0.0209719	0.0104859	−	0.999945i	$-0.496662\pi$
$2$	0.0296587	0.0209719	0.0104859	+	0.999945i	$0.496662\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99912	−0.999560
$5$	3.07938	1.37714	0.688570	−	0.725170i	$-0.258239\pi$
$5$	3.07938	1.37714	0.688570	+	0.725170i	$0.258239\pi$
$6$	−0.0296587	−0.0121081
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.118609	−0.0419345
$9$	1.00000	0.333333
$10$	0.0913304	0.0288812
$11$	−4.20887	−1.26902	−0.634511	−	0.772913i	$-0.718799\pi$
$11$	−4.20887	−1.26902	−0.634511	+	0.772913i	$0.718799\pi$
$12$	1.99912	0.577096
$13$	−6.43617	−1.78507	−0.892536	−	0.450977i	$-0.851076\pi$
$13$	−6.43617	−1.78507	−0.892536	+	0.450977i	$0.851076\pi$
$14$	−0.0296587	−0.00792662
$15$	−3.07938	−0.795093
$16$	3.99472	0.998681
$17$	−0.978108	−0.237226	−0.118613	−	0.992941i	$-0.537845\pi$
$17$	−0.978108	−0.237226	−0.118613	+	0.992941i	$0.537845\pi$
$18$	0.0296587	0.00699062
$19$	0.452098	0.103718	0.0518592	−	0.998654i	$-0.483485\pi$
$19$	0.452098	0.103718	0.0518592	+	0.998654i	$0.483485\pi$
$20$	−6.15605	−1.37654
$21$	1.00000	0.218218
$22$	−0.124830	−0.0266138
$23$	1.87821	0.391633	0.195817	−	0.980641i	$-0.437264\pi$
$23$	1.87821	0.391633	0.195817	+	0.980641i	$0.437264\pi$
$24$	0.118609	0.0242109
$25$	4.48258	0.896517
$26$	−0.190888	−0.0374363
$27$	−1.00000	−0.192450
$28$	1.99912	0.377798
$29$	6.69207	1.24269	0.621343	−	0.783539i	$-0.286587\pi$
$29$	6.69207	1.24269	0.621343	+	0.783539i	$0.286587\pi$
$30$	−0.0913304	−0.0166746
$31$	−1.28170	−0.230200	−0.115100	−	0.993354i	$-0.536719\pi$
$31$	−1.28170	−0.230200	−0.115100	+	0.993354i	$0.536719\pi$
$32$	0.355696	0.0628787
$33$	4.20887	0.732671
$34$	−0.0290094	−0.00497507
$35$	−3.07938	−0.520510
$36$	−1.99912	−0.333187
$37$	6.10620	1.00385	0.501927	−	0.864910i	$-0.332625\pi$
$37$	6.10620	1.00385	0.501927	+	0.864910i	$0.332625\pi$
$38$	0.0134086	0.00217517
$39$	6.43617	1.03061
$40$	−0.365241	−0.0577497
$41$	−3.48251	−0.543877	−0.271939	−	0.962315i	$-0.587665\pi$
$41$	−3.48251	−0.543877	−0.271939	+	0.962315i	$0.587665\pi$
$42$	0.0296587	0.00457643
$43$	4.11590	0.627669	0.313835	−	0.949478i	$-0.398386\pi$
$43$	4.11590	0.627669	0.313835	+	0.949478i	$0.398386\pi$
$44$	8.41404	1.26846
$45$	3.07938	0.459047
$46$	0.0557052	0.00821328
$47$	−0.343427	−0.0500940	−0.0250470	−	0.999686i	$-0.507974\pi$
$47$	−0.343427	−0.0500940	−0.0250470	+	0.999686i	$0.507974\pi$
$48$	−3.99472	−0.576589
$49$	1.00000	0.142857
$50$	0.132948	0.0188016
$51$	0.978108	0.136962
$52$	12.8667	1.78429
$53$	2.22047	0.305005	0.152503	−	0.988303i	$-0.451267\pi$
$53$	2.22047	0.305005	0.152503	+	0.988303i	$0.451267\pi$
$54$	−0.0296587	−0.00403604
$55$	−12.9607	−1.74762
$56$	0.118609	0.0158497
$57$	−0.452098	−0.0598818
$58$	0.198478	0.0260614
$59$	1.48973	0.193946	0.0969729	−	0.995287i	$-0.469084\pi$
$59$	1.48973	0.193946	0.0969729	+	0.995287i	$0.469084\pi$
$60$	6.15605	0.794743
$61$	7.08310	0.906898	0.453449	−	0.891282i	$-0.350193\pi$
$61$	7.08310	0.906898	0.453449	+	0.891282i	$0.350193\pi$
$62$	−0.0380136	−0.00482773
$63$	−1.00000	−0.125988
$64$	−7.97890	−0.997362
$65$	−19.8194	−2.45829
$66$	0.124830	0.0153655
$67$	0.989393	0.120874	0.0604368	−	0.998172i	$-0.480751\pi$
$67$	0.989393	0.120874	0.0604368	+	0.998172i	$0.480751\pi$
$68$	1.95535	0.237122
$69$	−1.87821	−0.226110
$70$	−0.0913304	−0.0109161
$71$	−8.17613	−0.970328	−0.485164	−	0.874423i	$-0.661240\pi$
$71$	−8.17613	−0.970328	−0.485164	+	0.874423i	$0.661240\pi$
$72$	−0.118609	−0.0139782
$73$	9.17564	1.07393	0.536964	−	0.843605i	$-0.319571\pi$
$73$	9.17564	1.07393	0.536964	+	0.843605i	$0.319571\pi$
$74$	0.181102	0.0210527
$75$	−4.48258	−0.517604
$76$	−0.903798	−0.103673
$77$	4.20887	0.479646
$78$	0.190888	0.0216138
$79$	9.02266	1.01513	0.507564	−	0.861614i	$-0.330546\pi$
$79$	9.02266	1.01513	0.507564	+	0.861614i	$0.330546\pi$
$80$	12.3013	1.37532
$81$	1.00000	0.111111
$82$	−0.103287	−0.0114061
$83$	−5.68319	−0.623811	−0.311906	−	0.950113i	$-0.600967\pi$
$83$	−5.68319	−0.623811	−0.311906	+	0.950113i	$0.600967\pi$
$84$	−1.99912	−0.218122
$85$	−3.01197	−0.326694
$86$	0.122072	0.0131634
$87$	−6.69207	−0.717465
$88$	0.499209	0.0532158
$89$	2.01684	0.213785	0.106892	−	0.994271i	$-0.465910\pi$
$89$	2.01684	0.213785	0.106892	+	0.994271i	$0.465910\pi$
$90$	0.0913304	0.00962707
$91$	6.43617	0.674694
$92$	−3.75476	−0.391461
$93$	1.28170	0.132906
$94$	−0.0101856	−0.00105056
$95$	1.39218	0.142835
$96$	−0.355696	−0.0363030
$97$	10.8384	1.10047	0.550235	−	0.835010i	$-0.314538\pi$
$97$	10.8384	1.10047	0.550235	+	0.835010i	$0.314538\pi$
$98$	0.0296587	0.00299598
$99$	−4.20887	−0.423008
$100$	−8.96122	−0.896122
$101$	9.76783	0.971936	0.485968	−	0.873977i	$-0.338467\pi$
$101$	9.76783	0.971936	0.485968	+	0.873977i	$0.338467\pi$
$102$	0.0290094	0.00287236
$103$	6.28650	0.619428	0.309714	−	0.950830i	$-0.399767\pi$
$103$	6.28650	0.619428	0.309714	+	0.950830i	$0.399767\pi$
$104$	0.763385	0.0748561
$105$	3.07938	0.300517
$106$	0.0658563	0.00639653
$107$	−14.2861	−1.38109	−0.690545	−	0.723289i	$-0.742629\pi$
$107$	−14.2861	−1.38109	−0.690545	+	0.723289i	$0.742629\pi$
$108$	1.99912	0.192365
$109$	−6.40981	−0.613948	−0.306974	−	0.951718i	$-0.599317\pi$
$109$	−6.40981	−0.613948	−0.306974	+	0.951718i	$0.599317\pi$
$110$	−0.384398	−0.0366509
$111$	−6.10620	−0.579575
$112$	−3.99472	−0.377466
$113$	8.85904	0.833388	0.416694	−	0.909047i	$-0.363189\pi$
$113$	8.85904	0.833388	0.416694	+	0.909047i	$0.363189\pi$
$114$	−0.0134086	−0.00125583
$115$	5.78372	0.539334
$116$	−13.3783	−1.24214
$117$	−6.43617	−0.595024
$118$	0.0441833	0.00406740
$119$	0.978108	0.0896630
$120$	0.365241	0.0333418
$121$	6.71461	0.610419
$122$	0.210075	0.0190193
$123$	3.48251	0.314008
$124$	2.56228	0.230099
$125$	−1.59332	−0.142511
$126$	−0.0296587	−0.00264221
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−0.948035	−0.0837952
$129$	−4.11590	−0.362385
$130$	−0.587817	−0.0515550
$131$	4.30603	0.376220	0.188110	−	0.982148i	$-0.439764\pi$
$131$	4.30603	0.376220	0.188110	+	0.982148i	$0.439764\pi$
$132$	−8.41404	−0.732349
$133$	−0.452098	−0.0392019
$134$	0.0293441	0.00253494
$135$	−3.07938	−0.265031
$136$	0.116012	0.00994795
$137$	3.16745	0.270614	0.135307	−	0.990804i	$-0.456798\pi$
$137$	3.16745	0.270614	0.135307	+	0.990804i	$0.456798\pi$
$138$	−0.0557052	−0.00474194
$139$	7.21212	0.611724	0.305862	−	0.952076i	$-0.401055\pi$
$139$	7.21212	0.611724	0.305862	+	0.952076i	$0.401055\pi$
$140$	6.15605	0.520281
$141$	0.343427	0.0289218
$142$	−0.242493	−0.0203496
$143$	27.0890	2.26530
$144$	3.99472	0.332894
$145$	20.6074	1.71135
$146$	0.272138	0.0225223
$147$	−1.00000	−0.0824786
$148$	−12.2070	−1.00341
$149$	8.99048	0.736529	0.368264	−	0.929721i	$-0.379952\pi$
$149$	8.99048	0.736529	0.368264	+	0.929721i	$0.379952\pi$
$150$	−0.132948	−0.0108551
$151$	−2.86869	−0.233451	−0.116725	−	0.993164i	$-0.537240\pi$
$151$	−2.86869	−0.233451	−0.116725	+	0.993164i	$0.537240\pi$
$152$	−0.0536227	−0.00434938
$153$	−0.978108	−0.0790753
$154$	0.124830	0.0100591
$155$	−3.94685	−0.317018
$156$	−12.8667	−1.03016
$157$	−0.748120	−0.0597065	−0.0298532	−	0.999554i	$-0.509504\pi$
$157$	−0.748120	−0.0597065	−0.0298532	+	0.999554i	$0.509504\pi$
$158$	0.267600	0.0212891
$159$	−2.22047	−0.176095
$160$	1.09532	0.0865928
$161$	−1.87821	−0.148023
$162$	0.0296587	0.00233021
$163$	13.1598	1.03075	0.515376	−	0.856964i	$-0.327652\pi$
$163$	13.1598	1.03075	0.515376	+	0.856964i	$0.327652\pi$
$164$	6.96196	0.543638
$165$	12.9607	1.00899
$166$	−0.168556	−0.0130825
$167$	20.0284	1.54984	0.774921	−	0.632058i	$-0.217789\pi$
$167$	20.0284	1.54984	0.774921	+	0.632058i	$0.217789\pi$
$168$	−0.118609	−0.00915086
$169$	28.4242	2.18648
$170$	−0.0893309	−0.00685137
$171$	0.452098	0.0345728
$172$	−8.22818	−0.627393
$173$	14.6850	1.11648	0.558240	−	0.829680i	$-0.311477\pi$
$173$	14.6850	1.11648	0.558240	+	0.829680i	$0.311477\pi$
$174$	−0.198478	−0.0150466
$175$	−4.48258	−0.338851
$176$	−16.8133	−1.26735
$177$	−1.48973	−0.111975
$178$	0.0598168	0.00448346
$179$	1.42580	0.106569	0.0532846	−	0.998579i	$-0.483031\pi$
$179$	1.42580	0.106569	0.0532846	+	0.998579i	$0.483031\pi$
$180$	−6.15605	−0.458845
$181$	−16.0798	−1.19520	−0.597600	−	0.801794i	$-0.703879\pi$
$181$	−16.0798	−1.19520	−0.597600	+	0.801794i	$0.703879\pi$
$182$	0.190888	0.0141496
$183$	−7.08310	−0.523598
$184$	−0.222772	−0.0164229
$185$	18.8033	1.38245
$186$	0.0380136	0.00278729
$187$	4.11673	0.301045
$188$	0.686553	0.0500720
$189$	1.00000	0.0727393
$190$	0.0412903	0.00299551
$191$	8.95356	0.647857	0.323929	−	0.946082i	$-0.394996\pi$
$191$	8.95356	0.647857	0.323929	+	0.946082i	$0.394996\pi$
$192$	7.97890	0.575827
$193$	4.34936	0.313074	0.156537	−	0.987672i	$-0.449967\pi$
$193$	4.34936	0.313074	0.156537	+	0.987672i	$0.449967\pi$
$194$	0.321452	0.0230789
$195$	19.8194	1.41930
$196$	−1.99912	−0.142794
$197$	12.1307	0.864278	0.432139	−	0.901807i	$-0.357759\pi$
$197$	12.1307	0.864278	0.432139	+	0.901807i	$0.357759\pi$
$198$	−0.124830	−0.00887126
$199$	−15.3936	−1.09122	−0.545612	−	0.838038i	$-0.683703\pi$
$199$	−15.3936	−1.09122	−0.545612	+	0.838038i	$0.683703\pi$
$200$	−0.531673	−0.0375950
$201$	−0.989393	−0.0697864
$202$	0.289701	0.0203833
$203$	−6.69207	−0.469691
$204$	−1.95535	−0.136902
$205$	−10.7240	−0.748995
$206$	0.186449	0.0129905
$207$	1.87821	0.130544
$208$	−25.7107	−1.78272
$209$	−1.90282	−0.131621
$210$	0.0913304	0.00630239
$211$	19.6993	1.35616	0.678078	−	0.734990i	$-0.262813\pi$
$211$	19.6993	1.35616	0.678078	+	0.734990i	$0.262813\pi$
$212$	−4.43899	−0.304871
$213$	8.17613	0.560219
$214$	−0.423707	−0.0289640
$215$	12.6744	0.864389
$216$	0.118609	0.00807030
$217$	1.28170	0.0870076
$218$	−0.190107	−0.0128756
$219$	−9.17564	−0.620033
$220$	25.9100	1.74685
$221$	6.29526	0.423465
$222$	−0.181102	−0.0121548
$223$	−10.1764	−0.681462	−0.340731	−	0.940161i	$-0.610675\pi$
$223$	−10.1764	−0.681462	−0.340731	+	0.940161i	$0.610675\pi$
$224$	−0.355696	−0.0237659
$225$	4.48258	0.298839
$226$	0.262747	0.0174777
$227$	−3.99422	−0.265105	−0.132553	−	0.991176i	$-0.542317\pi$
$227$	−3.99422	−0.265105	−0.132553	+	0.991176i	$0.542317\pi$
$228$	0.903798	0.0598555
$229$	−10.8957	−0.720010	−0.360005	−	0.932950i	$-0.617225\pi$
$229$	−10.8957	−0.720010	−0.360005	+	0.932950i	$0.617225\pi$
$230$	0.171537	0.0113108
$231$	−4.20887	−0.276924
$232$	−0.793737	−0.0521114
$233$	25.3409	1.66014	0.830070	−	0.557660i	$-0.188301\pi$
$233$	25.3409	1.66014	0.830070	+	0.557660i	$0.188301\pi$
$234$	−0.190888	−0.0124788
$235$	−1.05754	−0.0689865
$236$	−2.97814	−0.193860
$237$	−9.02266	−0.586085
$238$	0.0290094	0.00188040
$239$	2.55633	0.165355	0.0826776	−	0.996576i	$-0.473653\pi$
$239$	2.55633	0.165355	0.0826776	+	0.996576i	$0.473653\pi$
$240$	−12.3013	−0.794044
$241$	14.5627	0.938065	0.469032	−	0.883181i	$-0.344603\pi$
$241$	14.5627	0.938065	0.469032	+	0.883181i	$0.344603\pi$
$242$	0.199147	0.0128016
$243$	−1.00000	−0.0641500
$244$	−14.1600	−0.906499
$245$	3.07938	0.196734
$246$	0.103287	0.00658532
$247$	−2.90978	−0.185145
$248$	0.152021	0.00965334
$249$	5.68319	0.360158
$250$	−0.0472559	−0.00298873
$251$	−6.85143	−0.432458	−0.216229	−	0.976343i	$-0.569376\pi$
$251$	−6.85143	−0.432458	−0.216229	+	0.976343i	$0.569376\pi$
$252$	1.99912	0.125933
$253$	−7.90514	−0.496992
$254$	0.0296587	0.00186095
$255$	3.01197	0.188617
$256$	15.9297	0.995605
$257$	6.82464	0.425709	0.212855	−	0.977084i	$-0.431724\pi$
$257$	6.82464	0.425709	0.212855	+	0.977084i	$0.431724\pi$
$258$	−0.122072	−0.00759989
$259$	−6.10620	−0.379421
$260$	39.6214	2.45721
$261$	6.69207	0.414229
$262$	0.127711	0.00789003
$263$	9.84480	0.607056	0.303528	−	0.952822i	$-0.401835\pi$
$263$	9.84480	0.607056	0.303528	+	0.952822i	$0.401835\pi$
$264$	−0.499209	−0.0307242
$265$	6.83768	0.420035
$266$	−0.0134086	−0.000822136 0
$267$	−2.01684	−0.123429
$268$	−1.97792	−0.120820
$269$	4.81113	0.293340	0.146670	−	0.989186i	$-0.453145\pi$
$269$	4.81113	0.293340	0.146670	+	0.989186i	$0.453145\pi$
$270$	−0.0913304	−0.00555819
$271$	−25.2057	−1.53114	−0.765568	−	0.643356i	$-0.777542\pi$
$271$	−25.2057	−1.53114	−0.765568	+	0.643356i	$0.777542\pi$
$272$	−3.90727	−0.236913
$273$	−6.43617	−0.389535
$274$	0.0939424	0.00567527
$275$	−18.8666	−1.13770
$276$	3.75476	0.226010
$277$	20.4070	1.22614	0.613070	−	0.790028i	$-0.289934\pi$
$277$	20.4070	1.22614	0.613070	+	0.790028i	$0.289934\pi$
$278$	0.213902	0.0128290
$279$	−1.28170	−0.0767335
$280$	0.365241	0.0218273
$281$	−16.1617	−0.964126	−0.482063	−	0.876136i	$-0.660112\pi$
$281$	−16.1617	−0.964126	−0.482063	+	0.876136i	$0.660112\pi$
$282$	0.0101856	0.000606544 0
$283$	3.55148	0.211114	0.105557	−	0.994413i	$-0.466338\pi$
$283$	3.55148	0.211114	0.105557	+	0.994413i	$0.466338\pi$
$284$	16.3451	0.969901
$285$	−1.39218	−0.0824657
$286$	0.803424	0.0475075
$287$	3.48251	0.205566
$288$	0.355696	0.0209596
$289$	−16.0433	−0.943724
$290$	0.611189	0.0358903
$291$	−10.8384	−0.635357
$292$	−18.3432	−1.07346
$293$	21.0187	1.22793	0.613963	−	0.789335i	$-0.289574\pi$
$293$	21.0187	1.22793	0.613963	+	0.789335i	$0.289574\pi$
$294$	−0.0296587	−0.00172973
$295$	4.58743	0.267091
$296$	−0.724249	−0.0420961
$297$	4.20887	0.244224
$298$	0.266646	0.0154464
$299$	−12.0885	−0.699094
$300$	8.96122	0.517376
$301$	−4.11590	−0.237237
$302$	−0.0850816	−0.00489590
$303$	−9.76783	−0.561147
$304$	1.80601	0.103582
$305$	21.8116	1.24893
$306$	−0.0290094	−0.00165836
$307$	16.9198	0.965666	0.482833	−	0.875712i	$-0.339608\pi$
$307$	16.9198	0.965666	0.482833	+	0.875712i	$0.339608\pi$
$308$	−8.41404	−0.479435
$309$	−6.28650	−0.357627
$310$	−0.117058	−0.00664846
$311$	13.5782	0.769948	0.384974	−	0.922927i	$-0.374210\pi$
$311$	13.5782	0.769948	0.384974	+	0.922927i	$0.374210\pi$
$312$	−0.763385	−0.0432182
$313$	−31.4249	−1.77624	−0.888120	−	0.459612i	$-0.847989\pi$
$313$	−31.4249	−1.77624	−0.888120	+	0.459612i	$0.847989\pi$
$314$	−0.0221883	−0.00125216
$315$	−3.07938	−0.173503
$316$	−18.0374	−1.01468
$317$	−17.5662	−0.986614	−0.493307	−	0.869855i	$-0.664212\pi$
$317$	−17.5662	−0.986614	−0.493307	+	0.869855i	$0.664212\pi$
$318$	−0.0658563	−0.00369304
$319$	−28.1661	−1.57700
$320$	−24.5701	−1.37351
$321$	14.2861	0.797373
$322$	−0.0557052	−0.00310433
$323$	−0.442200	−0.0246047
$324$	−1.99912	−0.111062
$325$	−28.8507	−1.60035
$326$	0.390301	0.0216168
$327$	6.40981	0.354463
$328$	0.413056	0.0228072
$329$	0.343427	0.0189338
$330$	0.384398	0.0211604
$331$	26.2992	1.44553	0.722766	−	0.691093i	$-0.242870\pi$
$331$	26.2992	1.44553	0.722766	+	0.691093i	$0.242870\pi$
$332$	11.3614	0.623537
$333$	6.10620	0.334618
$334$	0.594015	0.0325031
$335$	3.04672	0.166460
$336$	3.99472	0.217930
$337$	−1.31181	−0.0714590	−0.0357295	−	0.999361i	$-0.511375\pi$
$337$	−1.31181	−0.0714590	−0.0357295	+	0.999361i	$0.511375\pi$
$338$	0.843026	0.0458546
$339$	−8.85904	−0.481157
$340$	6.02128	0.326550
$341$	5.39452	0.292130
$342$	0.0134086	0.000725056 0
$343$	−1.00000	−0.0539949
$344$	−0.488182	−0.0263210
$345$	−5.78372	−0.311385
$346$	0.435538	0.0234146
$347$	−12.5440	−0.673397	−0.336699	−	0.941612i	$-0.609310\pi$
$347$	−12.5440	−0.673397	−0.336699	+	0.941612i	$0.609310\pi$
$348$	13.3783	0.717150
$349$	−10.9299	−0.585067	−0.292533	−	0.956255i	$-0.594498\pi$
$349$	−10.9299	−0.585067	−0.292533	+	0.956255i	$0.594498\pi$
$350$	−0.132948	−0.00710634
$351$	6.43617	0.343537
$352$	−1.49708	−0.0797945
$353$	24.2674	1.29162	0.645810	−	0.763498i	$-0.276520\pi$
$353$	24.2674	1.29162	0.645810	+	0.763498i	$0.276520\pi$
$354$	−0.0441833	−0.00234832
$355$	−25.1774	−1.33628
$356$	−4.03191	−0.213691
$357$	−0.978108	−0.0517669
$358$	0.0422873	0.00223496
$359$	8.77538	0.463147	0.231573	−	0.972817i	$-0.425613\pi$
$359$	8.77538	0.463147	0.231573	+	0.972817i	$0.425613\pi$
$360$	−0.365241	−0.0192499
$361$	−18.7956	−0.989243
$362$	−0.476905	−0.0250656
$363$	−6.71461	−0.352426
$364$	−12.8667	−0.674397
$365$	28.2553	1.47895
$366$	−0.210075	−0.0109808
$367$	−28.2522	−1.47475	−0.737376	−	0.675483i	$-0.763935\pi$
$367$	−28.2522	−1.47475	−0.737376	+	0.675483i	$0.763935\pi$
$368$	7.50292	0.391117
$369$	−3.48251	−0.181292
$370$	0.557682	0.0289925
$371$	−2.22047	−0.115281
$372$	−2.56228	−0.132848
$373$	16.7923	0.869475	0.434737	−	0.900557i	$-0.356841\pi$
$373$	16.7923	0.869475	0.434737	+	0.900557i	$0.356841\pi$
$374$	0.122097	0.00631348
$375$	1.59332	0.0822789
$376$	0.0407335	0.00210067
$377$	−43.0713	−2.21828
$378$	0.0296587	0.00152548
$379$	−25.8015	−1.32533	−0.662666	−	0.748915i	$-0.730575\pi$
$379$	−25.8015	−1.32533	−0.662666	+	0.748915i	$0.730575\pi$
$380$	−2.78314	−0.142772
$381$	−1.00000	−0.0512316
$382$	0.265551	0.0135868
$383$	−14.3700	−0.734272	−0.367136	−	0.930167i	$-0.619662\pi$
$383$	−14.3700	−0.734272	−0.367136	+	0.930167i	$0.619662\pi$
$384$	0.948035	0.0483792
$385$	12.9607	0.660539
$386$	0.128996	0.00656575
$387$	4.11590	0.209223
$388$	−21.6672	−1.09999
$389$	−22.5454	−1.14309	−0.571547	−	0.820569i	$-0.693657\pi$
$389$	−22.5454	−1.14309	−0.571547	+	0.820569i	$0.693657\pi$
$390$	0.587817	0.0297653
$391$	−1.83709	−0.0929056
$392$	−0.118609	−0.00599064
$393$	−4.30603	−0.217211
$394$	0.359781	0.0181255
$395$	27.7842	1.39797
$396$	8.41404	0.422822
$397$	0.445695	0.0223688	0.0111844	−	0.999937i	$-0.496440\pi$
$397$	0.445695	0.0223688	0.0111844	+	0.999937i	$0.496440\pi$
$398$	−0.456554	−0.0228850
$399$	0.452098	0.0226332
$400$	17.9067	0.895334
$401$	6.19494	0.309361	0.154680	−	0.987965i	$-0.450565\pi$
$401$	6.19494	0.309361	0.154680	+	0.987965i	$0.450565\pi$
$402$	−0.0293441	−0.00146355
$403$	8.24924	0.410924
$404$	−19.5271	−0.971508
$405$	3.07938	0.153016
$406$	−0.198478	−0.00985030
$407$	−25.7002	−1.27391
$408$	−0.116012	−0.00574345
$409$	−26.3504	−1.30294	−0.651472	−	0.758673i	$-0.725848\pi$
$409$	−26.3504	−1.30294	−0.651472	+	0.758673i	$0.725848\pi$
$410$	−0.318059	−0.0157078
$411$	−3.16745	−0.156239
$412$	−12.5675	−0.619155
$413$	−1.48973	−0.0733046
$414$	0.0557052	0.00273776
$415$	−17.5007	−0.859076
$416$	−2.28932	−0.112243
$417$	−7.21212	−0.353179
$418$	−0.0564352	−0.00276034
$419$	6.10307	0.298154	0.149077	−	0.988826i	$-0.452370\pi$
$419$	6.10307	0.298154	0.149077	+	0.988826i	$0.452370\pi$
$420$	−6.15605	−0.300385
$421$	10.1315	0.493777	0.246888	−	0.969044i	$-0.420592\pi$
$421$	10.1315	0.493777	0.246888	+	0.969044i	$0.420592\pi$
$422$	0.584256	0.0284411
$423$	−0.343427	−0.0166980
$424$	−0.263367	−0.0127902
$425$	−4.38445	−0.212677
$426$	0.242493	0.0117488
$427$	−7.08310	−0.342775
$428$	28.5597	1.38048
$429$	−27.0890	−1.30787
$430$	0.375907	0.0181278
$431$	−39.8669	−1.92032	−0.960160	−	0.279451i	$-0.909847\pi$
$431$	−39.8669	−1.92032	−0.960160	+	0.279451i	$0.909847\pi$
$432$	−3.99472	−0.192196
$433$	13.2786	0.638128	0.319064	−	0.947733i	$-0.396632\pi$
$433$	13.2786	0.638128	0.319064	+	0.947733i	$0.396632\pi$
$434$	0.0380136	0.00182471
$435$	−20.6074	−0.988050
$436$	12.8140	0.613678
$437$	0.849134	0.0406196
$438$	−0.272138	−0.0130032
$439$	−12.8890	−0.615158	−0.307579	−	0.951523i	$-0.599519\pi$
$439$	−12.8890	−0.615158	−0.307579	+	0.951523i	$0.599519\pi$
$440$	1.53725	0.0732857
$441$	1.00000	0.0476190
$442$	0.186709	0.00888085
$443$	−25.3649	−1.20512	−0.602561	−	0.798073i	$-0.705853\pi$
$443$	−25.3649	−1.20512	−0.602561	+	0.798073i	$0.705853\pi$
$444$	12.2070	0.579320
$445$	6.21062	0.294411
$446$	−0.301819	−0.0142915
$447$	−8.99048	−0.425235
$448$	7.97890	0.376967
$449$	23.2619	1.09780	0.548899	−	0.835889i	$-0.315047\pi$
$449$	23.2619	1.09780	0.548899	+	0.835889i	$0.315047\pi$
$450$	0.132948	0.00626721
$451$	14.6575	0.690192
$452$	−17.7103	−0.833022
$453$	2.86869	0.134783
$454$	−0.118463	−0.00555975
$455$	19.8194	0.929148
$456$	0.0536227	0.00251111
$457$	−38.4218	−1.79730	−0.898649	−	0.438669i	$-0.855450\pi$
$457$	−38.4218	−1.79730	−0.898649	+	0.438669i	$0.855450\pi$
$458$	−0.323153	−0.0150999
$459$	0.978108	0.0456542
$460$	−11.5623	−0.539097
$461$	14.8206	0.690262	0.345131	−	0.938555i	$-0.387834\pi$
$461$	14.8206	0.690262	0.345131	+	0.938555i	$0.387834\pi$
$462$	−0.124830	−0.00580760
$463$	35.2074	1.63623	0.818114	−	0.575056i	$-0.195020\pi$
$463$	35.2074	1.63623	0.818114	+	0.575056i	$0.195020\pi$
$464$	26.7330	1.24105
$465$	3.94685	0.183031
$466$	0.751579	0.0348162
$467$	23.2168	1.07435	0.537173	−	0.843472i	$-0.319492\pi$
$467$	23.2168	1.07435	0.537173	+	0.843472i	$0.319492\pi$
$468$	12.8667	0.594762
$469$	−0.989393	−0.0456859
$470$	−0.0313654	−0.00144678
$471$	0.748120	0.0344715
$472$	−0.176694	−0.00813302
$473$	−17.3233	−0.796527
$474$	−0.267600	−0.0122913
$475$	2.02657	0.0929852
$476$	−1.95535	−0.0896235
$477$	2.22047	0.101668
$478$	0.0758174	0.00346781
$479$	−28.7854	−1.31524	−0.657620	−	0.753350i	$-0.728437\pi$
$479$	−28.7854	−1.31524	−0.657620	+	0.753350i	$0.728437\pi$
$480$	−1.09532	−0.0499944
$481$	−39.3006	−1.79195
$482$	0.431910	0.0196730
$483$	1.87821	0.0854614
$484$	−13.4233	−0.610151
$485$	33.3755	1.51550
$486$	−0.0296587	−0.00134535
$487$	40.6311	1.84117	0.920584	−	0.390544i	$-0.127713\pi$
$487$	40.6311	1.84117	0.920584	+	0.390544i	$0.127713\pi$
$488$	−0.840117	−0.0380303
$489$	−13.1598	−0.595105
$490$	0.0913304	0.00412589
$491$	6.94851	0.313582	0.156791	−	0.987632i	$-0.449885\pi$
$491$	6.94851	0.313582	0.156791	+	0.987632i	$0.449885\pi$
$492$	−6.96196	−0.313869
$493$	−6.54556	−0.294797
$494$	−0.0863002	−0.00388283
$495$	−12.9607	−0.582541
$496$	−5.12004	−0.229897
$497$	8.17613	0.366750
$498$	0.168556	0.00755317
$499$	5.09072	0.227892	0.113946	−	0.993487i	$-0.463651\pi$
$499$	5.09072	0.227892	0.113946	+	0.993487i	$0.463651\pi$
$500$	3.18525	0.142449
$501$	−20.0284	−0.894802
$502$	−0.203204	−0.00906946
$503$	−34.4535	−1.53621	−0.768104	−	0.640325i	$-0.778799\pi$
$503$	−34.4535	−1.53621	−0.768104	+	0.640325i	$0.778799\pi$
$504$	0.118609	0.00528325
$505$	30.0789	1.33849
$506$	−0.234456	−0.0104228
$507$	−28.4242	−1.26236
$508$	−1.99912	−0.0886966
$509$	33.6813	1.49290	0.746450	−	0.665442i	$-0.231757\pi$
$509$	33.6813	1.49290	0.746450	+	0.665442i	$0.231757\pi$
$510$	0.0893309	0.00395564
$511$	−9.17564	−0.405907
$512$	2.36852	0.104675
$513$	−0.452098	−0.0199606
$514$	0.202410	0.00892792
$515$	19.3585	0.853039
$516$	8.22818	0.362226
$517$	1.44544	0.0635705
$518$	−0.181102	−0.00795717
$519$	−14.6850	−0.644600
$520$	2.35075	0.103087
$521$	36.6294	1.60476	0.802382	−	0.596811i	$-0.203566\pi$
$521$	36.6294	1.60476	0.802382	+	0.596811i	$0.203566\pi$
$522$	0.198478	0.00868715
$523$	−28.7191	−1.25580	−0.627900	−	0.778294i	$-0.716085\pi$
$523$	−28.7191	−1.25580	−0.627900	+	0.778294i	$0.716085\pi$
$524$	−8.60828	−0.376055
$525$	4.48258	0.195636
$526$	0.291984	0.0127311
$527$	1.25364	0.0546095
$528$	16.8133	0.731704
$529$	−19.4723	−0.846623
$530$	0.202797	0.00880892
$531$	1.48973	0.0646486
$532$	0.903798	0.0391846
$533$	22.4140	0.970859
$534$	−0.0598168	−0.00258853
$535$	−43.9924	−1.90196
$536$	−0.117351	−0.00506877
$537$	−1.42580	−0.0615278
$538$	0.142692	0.00615188
$539$	−4.20887	−0.181289
$540$	6.15605	0.264914
$541$	4.29971	0.184859	0.0924294	−	0.995719i	$-0.470537\pi$
$541$	4.29971	0.184859	0.0924294	+	0.995719i	$0.470537\pi$
$542$	−0.747567	−0.0321107
$543$	16.0798	0.690050
$544$	−0.347909	−0.0149165
$545$	−19.7382	−0.845493
$546$	−0.190888	−0.00816926
$547$	−19.4300	−0.830767	−0.415383	−	0.909646i	$-0.636353\pi$
$547$	−19.4300	−0.830767	−0.415383	+	0.909646i	$0.636353\pi$
$548$	−6.33212	−0.270495
$549$	7.08310	0.302299
$550$	−0.559559	−0.0238597
$551$	3.02547	0.128889
$552$	0.222772	0.00948179
$553$	−9.02266	−0.383682
$554$	0.605246	0.0257144
$555$	−18.8033	−0.798157
$556$	−14.4179	−0.611455
$557$	−39.6587	−1.68039	−0.840197	−	0.542281i	$-0.817561\pi$
$557$	−39.6587	−1.68039	−0.840197	+	0.542281i	$0.817561\pi$
$558$	−0.0380136	−0.00160924
$559$	−26.4906	−1.12043
$560$	−12.3013	−0.519824
$561$	−4.11673	−0.173809
$562$	−0.479335	−0.0202195
$563$	1.06429	0.0448545	0.0224272	−	0.999748i	$-0.492861\pi$
$563$	1.06429	0.0448545	0.0224272	+	0.999748i	$0.492861\pi$
$564$	−0.686553	−0.0289091
$565$	27.2804	1.14769
$566$	0.105332	0.00442745
$567$	−1.00000	−0.0419961
$568$	0.969760	0.0406902
$569$	4.34569	0.182181	0.0910903	−	0.995843i	$-0.470965\pi$
$569$	4.34569	0.182181	0.0910903	+	0.995843i	$0.470965\pi$
$570$	−0.0412903	−0.00172946
$571$	0.617402	0.0258374	0.0129187	−	0.999917i	$-0.495888\pi$
$571$	0.617402	0.0258374	0.0129187	+	0.999917i	$0.495888\pi$
$572$	−54.1542	−2.26430
$573$	−8.95356	−0.374041
$574$	0.103287	0.00431111
$575$	8.41922	0.351106
$576$	−7.97890	−0.332454
$577$	−45.6275	−1.89950	−0.949748	−	0.313015i	$-0.898661\pi$
$577$	−45.6275	−1.89950	−0.949748	+	0.313015i	$0.898661\pi$
$578$	−0.475823	−0.0197916
$579$	−4.34936	−0.180753
$580$	−41.1967	−1.71060
$581$	5.68319	0.235778
$582$	−0.321452	−0.0133246
$583$	−9.34569	−0.387059
$584$	−1.08831	−0.0450346
$585$	−19.8194	−0.819432
$586$	0.623388	0.0257519
$587$	−38.7194	−1.59812	−0.799061	−	0.601250i	$-0.794669\pi$
$587$	−38.7194	−1.59812	−0.799061	+	0.601250i	$0.794669\pi$
$588$	1.99912	0.0824423
$589$	−0.579455	−0.0238760
$590$	0.136057	0.00560139
$591$	−12.1307	−0.498991
$592$	24.3926	1.00253
$593$	30.6824	1.25998	0.629988	−	0.776605i	$-0.283060\pi$
$593$	30.6824	1.25998	0.629988	+	0.776605i	$0.283060\pi$
$594$	0.124830	0.00512182
$595$	3.01197	0.123479
$596$	−17.9731	−0.736205
$597$	15.3936	0.630018
$598$	−0.358528	−0.0146613
$599$	36.2093	1.47947	0.739736	−	0.672897i	$-0.234950\pi$
$599$	36.2093	1.47947	0.739736	+	0.672897i	$0.234950\pi$
$600$	0.531673	0.0217055
$601$	40.5462	1.65391	0.826956	−	0.562266i	$-0.190070\pi$
$601$	40.5462	1.65391	0.826956	+	0.562266i	$0.190070\pi$
$602$	−0.122072	−0.00497529
$603$	0.989393	0.0402912
$604$	5.73486	0.233348
$605$	20.6768	0.840633
$606$	−0.289701	−0.0117683
$607$	33.8247	1.37290	0.686451	−	0.727176i	$-0.259168\pi$
$607$	33.8247	1.37290	0.686451	+	0.727176i	$0.259168\pi$
$608$	0.160809	0.00652167
$609$	6.69207	0.271176
$610$	0.646902	0.0261923
$611$	2.21036	0.0894214
$612$	1.95535	0.0790405
$613$	5.81836	0.235001	0.117501	−	0.993073i	$-0.462512\pi$
$613$	5.81836	0.235001	0.117501	+	0.993073i	$0.462512\pi$
$614$	0.501820	0.0202518
$615$	10.7240	0.432433
$616$	−0.499209	−0.0201137
$617$	43.1946	1.73895	0.869474	−	0.493979i	$-0.164458\pi$
$617$	43.1946	1.73895	0.869474	+	0.493979i	$0.164458\pi$
$618$	−0.186449	−0.00750010
$619$	−0.582136	−0.0233980	−0.0116990	−	0.999932i	$-0.503724\pi$
$619$	−0.582136	−0.0233980	−0.0116990	+	0.999932i	$0.503724\pi$
$620$	7.89022	0.316879
$621$	−1.87821	−0.0753699
$622$	0.402711	0.0161472
$623$	−2.01684	−0.0808030
$624$	25.7107	1.02925
$625$	−27.3194	−1.09277
$626$	−0.932021	−0.0372511
$627$	1.90282	0.0759914
$628$	1.49558	0.0596802
$629$	−5.97253	−0.238140
$630$	−0.0913304	−0.00363869
$631$	−30.1214	−1.19911	−0.599557	−	0.800332i	$-0.704657\pi$
$631$	−30.1214	−1.19911	−0.599557	+	0.800332i	$0.704657\pi$
$632$	−1.07017	−0.0425689
$633$	−19.6993	−0.782977
$634$	−0.520989	−0.0206911
$635$	3.07938	0.122201
$636$	4.43899	0.176017
$637$	−6.43617	−0.255010
$638$	−0.835369	−0.0330726
$639$	−8.17613	−0.323443
$640$	−2.91936	−0.115398
$641$	31.1460	1.23019	0.615096	−	0.788452i	$-0.289117\pi$
$641$	31.1460	1.23019	0.615096	+	0.788452i	$0.289117\pi$
$642$	0.423707	0.0167224
$643$	2.91383	0.114910	0.0574551	−	0.998348i	$-0.481701\pi$
$643$	2.91383	0.114910	0.0574551	+	0.998348i	$0.481701\pi$
$644$	3.75476	0.147958
$645$	−12.6744	−0.499055
$646$	−0.0131151	−0.000516006 0
$647$	−18.7263	−0.736206	−0.368103	−	0.929785i	$-0.619993\pi$
$647$	−18.7263	−0.736206	−0.368103	+	0.929785i	$0.619993\pi$
$648$	−0.118609	−0.00465939
$649$	−6.27007	−0.246122
$650$	−0.855672	−0.0335622
$651$	−1.28170	−0.0502338
$652$	−26.3079	−1.03030
$653$	13.6677	0.534857	0.267429	−	0.963578i	$-0.413826\pi$
$653$	13.6677	0.534857	0.267429	+	0.963578i	$0.413826\pi$
$654$	0.190107	0.00743375
$655$	13.2599	0.518108
$656$	−13.9117	−0.543160
$657$	9.17564	0.357976
$658$	0.0101856	0.000397076 0
$659$	−6.46273	−0.251752	−0.125876	−	0.992046i	$-0.540174\pi$
$659$	−6.46273	−0.251752	−0.125876	+	0.992046i	$0.540174\pi$
$660$	−25.9100	−1.00855
$661$	−27.1580	−1.05632	−0.528162	−	0.849144i	$-0.677118\pi$
$661$	−27.1580	−1.05632	−0.528162	+	0.849144i	$0.677118\pi$
$662$	0.779998	0.0303155
$663$	−6.29526	−0.244488
$664$	0.674076	0.0261592
$665$	−1.39218	−0.0539865
$666$	0.181102	0.00701756
$667$	12.5691	0.486677
$668$	−40.0391	−1.54916
$669$	10.1764	0.393442
$670$	0.0903617	0.00349098
$671$	−29.8119	−1.15087
$672$	0.355696	0.0137213
$673$	−1.23799	−0.0477211	−0.0238606	−	0.999715i	$-0.507596\pi$
$673$	−1.23799	−0.0477211	−0.0238606	+	0.999715i	$0.507596\pi$
$674$	−0.0389066	−0.00149863
$675$	−4.48258	−0.172535
$676$	−56.8235	−2.18552
$677$	−3.72439	−0.143140	−0.0715700	−	0.997436i	$-0.522801\pi$
$677$	−3.72439	−0.143140	−0.0715700	+	0.997436i	$0.522801\pi$
$678$	−0.262747	−0.0100908
$679$	−10.8384	−0.415939
$680$	0.357245	0.0136997
$681$	3.99422	0.153059
$682$	0.159994	0.00612650
$683$	1.26391	0.0483621	0.0241811	−	0.999708i	$-0.492302\pi$
$683$	1.26391	0.0483621	0.0241811	+	0.999708i	$0.492302\pi$
$684$	−0.903798	−0.0345576
$685$	9.75379	0.372673
$686$	−0.0296587	−0.00113237
$687$	10.8957	0.415698
$688$	16.4419	0.626841
$689$	−14.2913	−0.544456
$690$	−0.171537	−0.00653032
$691$	−9.08197	−0.345495	−0.172747	−	0.984966i	$-0.555264\pi$
$691$	−9.08197	−0.345495	−0.172747	+	0.984966i	$0.555264\pi$
$692$	−29.3571	−1.11599
$693$	4.20887	0.159882
$694$	−0.372038	−0.0141224
$695$	22.2089	0.842430
$696$	0.793737	0.0300865
$697$	3.40627	0.129022
$698$	−0.324168	−0.0122699
$699$	−25.3409	−0.958482
$700$	8.96122	0.338702
$701$	11.3303	0.427941	0.213971	−	0.976840i	$-0.431360\pi$
$701$	11.3303	0.427941	0.213971	+	0.976840i	$0.431360\pi$
$702$	0.190888	0.00720461
$703$	2.76060	0.104118
$704$	33.5822	1.26568
$705$	1.05754	0.0398294
$706$	0.719738	0.0270877
$707$	−9.76783	−0.367357
$708$	2.97814	0.111925
$709$	19.1018	0.717383	0.358691	−	0.933456i	$-0.383223\pi$
$709$	19.1018	0.717383	0.358691	+	0.933456i	$0.383223\pi$
$710$	−0.746729	−0.0280242
$711$	9.02266	0.338376
$712$	−0.239215	−0.00896495
$713$	−2.40730	−0.0901542
$714$	−0.0290094	−0.00108565
$715$	83.4174	3.11963
$716$	−2.85035	−0.106522
$717$	−2.55633	−0.0954679
$718$	0.260266	0.00971305
$719$	16.5348	0.616645	0.308322	−	0.951282i	$-0.400232\pi$
$719$	16.5348	0.616645	0.308322	+	0.951282i	$0.400232\pi$
$720$	12.3013	0.458441
$721$	−6.28650	−0.234122
$722$	−0.557453	−0.0207463
$723$	−14.5627	−0.541592
$724$	32.1454	1.19468
$725$	29.9978	1.11409
$726$	−0.199147	−0.00739102
$727$	−13.6415	−0.505934	−0.252967	−	0.967475i	$-0.581406\pi$
$727$	−13.6415	−0.505934	−0.252967	+	0.967475i	$0.581406\pi$
$728$	−0.763385	−0.0282929
$729$	1.00000	0.0370370
$730$	0.838015	0.0310163
$731$	−4.02579	−0.148899
$732$	14.1600	0.523368
$733$	42.7851	1.58030	0.790152	−	0.612911i	$-0.210002\pi$
$733$	42.7851	1.58030	0.790152	+	0.612911i	$0.210002\pi$
$734$	−0.837922	−0.0309283
$735$	−3.07938	−0.113585
$736$	0.668070	0.0246254
$737$	−4.16423	−0.153391
$738$	−0.103287	−0.00380204
$739$	24.3103	0.894270	0.447135	−	0.894467i	$-0.352444\pi$
$739$	24.3103	0.894270	0.447135	+	0.894467i	$0.352444\pi$
$740$	−37.5901	−1.38184
$741$	2.90978	0.106893
$742$	−0.0658563	−0.00241766
$743$	−31.4154	−1.15252	−0.576260	−	0.817266i	$-0.695489\pi$
$743$	−31.4154	−1.15252	−0.576260	+	0.817266i	$0.695489\pi$
$744$	−0.152021	−0.00557336
$745$	27.6851	1.01430
$746$	0.498039	0.0182345
$747$	−5.68319	−0.207937
$748$	−8.22984	−0.300913
$749$	14.2861	0.522003
$750$	0.0472559	0.00172554
$751$	5.27111	0.192345	0.0961727	−	0.995365i	$-0.469340\pi$
$751$	5.27111	0.192345	0.0961727	+	0.995365i	$0.469340\pi$
$752$	−1.37190	−0.0500279
$753$	6.85143	0.249680
$754$	−1.27744	−0.0465215
$755$	−8.83379	−0.321495
$756$	−1.99912	−0.0727073
$757$	44.1949	1.60629	0.803145	−	0.595784i	$-0.203158\pi$
$757$	44.1949	1.60629	0.803145	+	0.595784i	$0.203158\pi$
$758$	−0.765238	−0.0277947
$759$	7.90514	0.286938
$760$	−0.165125	−0.00598970
$761$	43.9305	1.59248	0.796240	−	0.604981i	$-0.206819\pi$
$761$	43.9305	1.59248	0.796240	+	0.604981i	$0.206819\pi$
$762$	−0.0296587	−0.00107442
$763$	6.40981	0.232051
$764$	−17.8993	−0.647572
$765$	−3.01197	−0.108898
$766$	−0.426195	−0.0153990
$767$	−9.58812	−0.346207
$768$	−15.9297	−0.574813
$769$	7.00950	0.252769	0.126385	−	0.991981i	$-0.459663\pi$
$769$	7.00950	0.252769	0.126385	+	0.991981i	$0.459663\pi$
$770$	0.384398	0.0138527
$771$	−6.82464	−0.245783
$772$	−8.69490	−0.312936
$773$	25.2979	0.909902	0.454951	−	0.890516i	$-0.349657\pi$
$773$	25.2979	0.909902	0.454951	+	0.890516i	$0.349657\pi$
$774$	0.122072	0.00438780
$775$	−5.74533	−0.206378
$776$	−1.28553	−0.0461477
$777$	6.10620	0.219059
$778$	−0.668666	−0.0239728
$779$	−1.57444	−0.0564100
$780$	−39.6214	−1.41867
$781$	34.4123	1.23137
$782$	−0.0544856	−0.00194840
$783$	−6.69207	−0.239155
$784$	3.99472	0.142669
$785$	−2.30375	−0.0822242
$786$	−0.127711	−0.00455531
$787$	32.8781	1.17198	0.585989	−	0.810319i	$-0.300706\pi$
$787$	32.8781	1.17198	0.585989	+	0.810319i	$0.300706\pi$
$788$	−24.2508	−0.863898
$789$	−9.84480	−0.350484
$790$	0.824043	0.0293181
$791$	−8.85904	−0.314991
$792$	0.499209	0.0177386
$793$	−45.5880	−1.61888
$794$	0.0132187	0.000469115 0
$795$	−6.83768	−0.242507
$796$	30.7737	1.09074
$797$	−9.58152	−0.339395	−0.169697	−	0.985496i	$-0.554279\pi$
$797$	−9.58152	−0.339395	−0.169697	+	0.985496i	$0.554279\pi$
$798$	0.0134086	0.000474660 0
$799$	0.335909	0.0118836
$800$	1.59443	0.0563718
$801$	2.01684	0.0712615
$802$	0.183734	0.00648787
$803$	−38.6191	−1.36284
$804$	1.97792	0.0697557
$805$	−5.78372	−0.203849
$806$	0.244662	0.00861784
$807$	−4.81113	−0.169360
$808$	−1.15855	−0.0407576
$809$	−7.62861	−0.268208	−0.134104	−	0.990967i	$-0.542816\pi$
$809$	−7.62861	−0.268208	−0.134104	+	0.990967i	$0.542816\pi$
$810$	0.0913304	0.00320902
$811$	53.0396	1.86247	0.931236	−	0.364416i	$-0.118731\pi$
$811$	53.0396	1.86247	0.931236	+	0.364416i	$0.118731\pi$
$812$	13.3783	0.469485
$813$	25.2057	0.884001
$814$	−0.762235	−0.0267163
$815$	40.5239	1.41949
$816$	3.90727	0.136782
$817$	1.86079	0.0651008
$818$	−0.781518	−0.0273251
$819$	6.43617	0.224898
$820$	21.4385	0.748666
$821$	29.2651	1.02136	0.510679	−	0.859772i	$-0.329394\pi$
$821$	29.2651	1.02136	0.510679	+	0.859772i	$0.329394\pi$
$822$	−0.0939424	−0.00327662
$823$	5.28174	0.184110	0.0920550	−	0.995754i	$-0.470656\pi$
$823$	5.28174	0.184110	0.0920550	+	0.995754i	$0.470656\pi$
$824$	−0.745634	−0.0259754
$825$	18.8666	0.656851
$826$	−0.0441833	−0.00153733
$827$	23.0353	0.801014	0.400507	−	0.916294i	$-0.368834\pi$
$827$	23.0353	0.801014	0.400507	+	0.916294i	$0.368834\pi$
$828$	−3.75476	−0.130487
$829$	−22.6811	−0.787748	−0.393874	−	0.919164i	$-0.628865\pi$
$829$	−22.6811	−0.787748	−0.393874	+	0.919164i	$0.628865\pi$
$830$	−0.519048	−0.0180164
$831$	−20.4070	−0.707913
$832$	51.3535	1.78036
$833$	−0.978108	−0.0338894
$834$	−0.213902	−0.00740682
$835$	61.6750	2.13435
$836$	3.80397	0.131563
$837$	1.28170	0.0443021
$838$	0.181009	0.00625285
$839$	−39.4521	−1.36204	−0.681018	−	0.732267i	$-0.738462\pi$
$839$	−39.4521	−1.36204	−0.681018	+	0.732267i	$0.738462\pi$
$840$	−0.365241	−0.0126020
$841$	15.7838	0.544269
$842$	0.300486	0.0103554
$843$	16.1617	0.556639
$844$	−39.3813	−1.35556
$845$	87.5290	3.01109
$846$	−0.0101856	−0.000350188 0
$847$	−6.71461	−0.230717
$848$	8.87017	0.304603
$849$	−3.55148	−0.121887
$850$	−0.130037	−0.00446023
$851$	11.4687	0.393143
$852$	−16.3451	−0.559973
$853$	53.5165	1.83237	0.916186	−	0.400754i	$-0.131252\pi$
$853$	53.5165	1.83237	0.916186	+	0.400754i	$0.131252\pi$
$854$	−0.210075	−0.00718864
$855$	1.39218	0.0476116
$856$	1.69446	0.0579153
$857$	15.6792	0.535593	0.267796	−	0.963476i	$-0.413705\pi$
$857$	15.6792	0.535593	0.267796	+	0.963476i	$0.413705\pi$
$858$	−0.803424	−0.0274285
$859$	−31.0758	−1.06029	−0.530146	−	0.847907i	$-0.677863\pi$
$859$	−31.0758	−1.06029	−0.530146	+	0.847907i	$0.677863\pi$
$860$	−25.3377	−0.864009
$861$	−3.48251	−0.118684
$862$	−1.18240	−0.0402727
$863$	−27.3878	−0.932291	−0.466145	−	0.884708i	$-0.654358\pi$
$863$	−27.3878	−0.932291	−0.466145	+	0.884708i	$0.654358\pi$
$864$	−0.355696	−0.0121010
$865$	45.2207	1.53755
$866$	0.393825	0.0133827
$867$	16.0433	0.544859
$868$	−2.56228	−0.0869693
$869$	−37.9752	−1.28822
$870$	−0.611189	−0.0207213
$871$	−6.36790	−0.215768
$872$	0.760259	0.0257456
$873$	10.8384	0.366824
$874$	0.0251842	0.000851868 0
$875$	1.59332	0.0538642
$876$	18.3432	0.619760
$877$	−17.1942	−0.580608	−0.290304	−	0.956935i	$-0.593756\pi$
$877$	−17.1942	−0.580608	−0.290304	+	0.956935i	$0.593756\pi$
$878$	−0.382270	−0.0129010
$879$	−21.0187	−0.708944
$880$	−51.7745	−1.74532
$881$	−56.6431	−1.90835	−0.954177	−	0.299241i	$-0.903266\pi$
$881$	−56.6431	−1.90835	−0.954177	+	0.299241i	$0.903266\pi$
$882$	0.0296587	0.000998660 0
$883$	9.71797	0.327036	0.163518	−	0.986540i	$-0.447716\pi$
$883$	9.71797	0.327036	0.163518	+	0.986540i	$0.447716\pi$
$884$	−12.5850	−0.423279
$885$	−4.58743	−0.154205
$886$	−0.752289	−0.0252737
$887$	−37.9696	−1.27489	−0.637447	−	0.770494i	$-0.720010\pi$
$887$	−37.9696	−1.27489	−0.637447	+	0.770494i	$0.720010\pi$
$888$	0.724249	0.0243042
$889$	−1.00000	−0.0335389
$890$	0.184199	0.00617436
$891$	−4.20887	−0.141003
$892$	20.3438	0.681162
$893$	−0.155263	−0.00519567
$894$	−0.266646	−0.00891797
$895$	4.39058	0.146761
$896$	0.948035	0.0316716
$897$	12.0885	0.403622
$898$	0.689918	0.0230229
$899$	−8.57724	−0.286067
$900$	−8.96122	−0.298707
$901$	−2.17186	−0.0723552
$902$	0.434721	0.0144746
$903$	4.11590	0.136969
$904$	−1.05076	−0.0349477
$905$	−49.5158	−1.64596
$906$	0.0850816	0.00282665
$907$	−40.9254	−1.35891	−0.679453	−	0.733719i	$-0.737783\pi$
$907$	−40.9254	−1.35891	−0.679453	+	0.733719i	$0.737783\pi$
$908$	7.98492	0.264989
$909$	9.76783	0.323979
$910$	0.587817	0.0194860
$911$	24.4739	0.810858	0.405429	−	0.914127i	$-0.367122\pi$
$911$	24.4739	0.810858	0.405429	+	0.914127i	$0.367122\pi$
$912$	−1.80601	−0.0598028
$913$	23.9198	0.791631
$914$	−1.13954	−0.0376927
$915$	−21.8116	−0.721068
$916$	21.7819	0.719693
$917$	−4.30603	−0.142198
$918$	0.0290094	0.000957452 0
$919$	−18.2904	−0.603346	−0.301673	−	0.953411i	$-0.597545\pi$
$919$	−18.2904	−0.603346	−0.301673	+	0.953411i	$0.597545\pi$
$920$	−0.685999	−0.0226167
$921$	−16.9198	−0.557527
$922$	0.439558	0.0144761
$923$	52.6229	1.73210
$924$	8.41404	0.276802
$925$	27.3716	0.899972
$926$	1.04421	0.0343147
$927$	6.28650	0.206476
$928$	2.38034	0.0781385
$929$	3.21214	0.105387	0.0526935	−	0.998611i	$-0.483219\pi$
$929$	3.21214	0.105387	0.0526935	+	0.998611i	$0.483219\pi$
$930$	0.117058	0.00383849
$931$	0.452098	0.0148169
$932$	−50.6596	−1.65941
$933$	−13.5782	−0.444530
$934$	0.688580	0.0225310
$935$	12.6770	0.414582
$936$	0.763385	0.0249520
$937$	0.847525	0.0276874	0.0138437	−	0.999904i	$-0.495593\pi$
$937$	0.847525	0.0276874	0.0138437	+	0.999904i	$0.495593\pi$
$938$	−0.0293441	−0.000958119 0
$939$	31.4249	1.02551
$940$	2.11416	0.0689562
$941$	20.7245	0.675601	0.337800	−	0.941218i	$-0.390317\pi$
$941$	20.7245	0.675601	0.337800	+	0.941218i	$0.390317\pi$
$942$	0.0221883	0.000722932 0
$943$	−6.54088	−0.213000
$944$	5.95104	0.193690
$945$	3.07938	0.100172
$946$	−0.513787	−0.0167046
$947$	53.5475	1.74006	0.870031	−	0.492998i	$-0.164099\pi$
$947$	53.5475	1.74006	0.870031	+	0.492998i	$0.164099\pi$
$948$	18.0374	0.585827
$949$	−59.0560	−1.91704
$950$	0.0601053	0.00195007
$951$	17.5662	0.569622
$952$	−0.116012	−0.00375997
$953$	−6.51677	−0.211099	−0.105549	−	0.994414i	$-0.533660\pi$
$953$	−6.51677	−0.211099	−0.105549	+	0.994414i	$0.533660\pi$
$954$	0.0658563	0.00213218
$955$	27.5714	0.892191
$956$	−5.11041	−0.165283
$957$	28.1661	0.910480
$958$	−0.853738	−0.0275830
$959$	−3.16745	−0.102282
$960$	24.5701	0.792995
$961$	−29.3572	−0.947008
$962$	−1.16560	−0.0375805
$963$	−14.2861	−0.460364
$964$	−29.1125	−0.937652
$965$	13.3933	0.431147
$966$	0.0557052	0.00179228
$967$	55.2012	1.77515	0.887575	−	0.460662i	$-0.152388\pi$
$967$	55.2012	1.77515	0.887575	+	0.460662i	$0.152388\pi$
$968$	−0.796411	−0.0255976
$969$	0.442200	0.0142055
$970$	0.989873	0.0317829
$971$	−37.1275	−1.19148	−0.595740	−	0.803178i	$-0.703141\pi$
$971$	−37.1275	−1.19148	−0.595740	+	0.803178i	$0.703141\pi$
$972$	1.99912	0.0641218
$973$	−7.21212	−0.231210
$974$	1.20506	0.0386127
$975$	28.8507	0.923960
$976$	28.2950	0.905702
$977$	−61.2366	−1.95913	−0.979566	−	0.201124i	$-0.935540\pi$
$977$	−61.2366	−1.95913	−0.979566	+	0.201124i	$0.935540\pi$
$978$	−0.390301	−0.0124805
$979$	−8.48862	−0.271298
$980$	−6.15605	−0.196648
$981$	−6.40981	−0.204649
$982$	0.206084	0.00657640
$983$	−48.0106	−1.53130	−0.765651	−	0.643257i	$-0.777583\pi$
$983$	−48.0106	−1.53130	−0.765651	+	0.643257i	$0.777583\pi$
$984$	−0.413056	−0.0131677
$985$	37.3551	1.19023
$986$	−0.194133	−0.00618245
$987$	−0.343427	−0.0109314
$988$	5.81699	0.185063
$989$	7.73052	0.245816
$990$	−0.384398	−0.0122170
$991$	44.1047	1.40103	0.700517	−	0.713636i	$-0.252953\pi$
$991$	44.1047	1.40103	0.700517	+	0.713636i	$0.252953\pi$
$992$	−0.455896	−0.0144747
$993$	−26.2992	−0.834579
$994$	0.242493	0.00769142
$995$	−47.4027	−1.50277
$996$	−11.3614	−0.359999
$997$	−46.7633	−1.48101	−0.740504	−	0.672052i	$-0.765413\pi$
$997$	−46.7633	−1.48101	−0.740504	+	0.672052i	$0.765413\pi$
$998$	0.150984	0.00477932
$999$	−6.10620	−0.193192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.7	✓	16
3.2	odd	2		8001.2.a.r.1.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.7	✓	16	1.1	even	1	trivial
8001.2.a.r.1.10		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)

\(f(q)\)	\(=\)	\(q+0.0296587 q^{2} -1.00000 q^{3} -1.99912 q^{4} +3.07938 q^{5} -0.0296587 q^{6} -1.00000 q^{7} -0.118609 q^{8} +1.00000 q^{9} +0.0913304 q^{10} -4.20887 q^{11} +1.99912 q^{12} -6.43617 q^{13} -0.0296587 q^{14} -3.07938 q^{15} +3.99472 q^{16} -0.978108 q^{17} +0.0296587 q^{18} +0.452098 q^{19} -6.15605 q^{20} +1.00000 q^{21} -0.124830 q^{22} +1.87821 q^{23} +0.118609 q^{24} +4.48258 q^{25} -0.190888 q^{26} -1.00000 q^{27} +1.99912 q^{28} +6.69207 q^{29} -0.0913304 q^{30} -1.28170 q^{31} +0.355696 q^{32} +4.20887 q^{33} -0.0290094 q^{34} -3.07938 q^{35} -1.99912 q^{36} +6.10620 q^{37} +0.0134086 q^{38} +6.43617 q^{39} -0.365241 q^{40} -3.48251 q^{41} +0.0296587 q^{42} +4.11590 q^{43} +8.41404 q^{44} +3.07938 q^{45} +0.0557052 q^{46} -0.343427 q^{47} -3.99472 q^{48} +1.00000 q^{49} +0.132948 q^{50} +0.978108 q^{51} +12.8667 q^{52} +2.22047 q^{53} -0.0296587 q^{54} -12.9607 q^{55} +0.118609 q^{56} -0.452098 q^{57} +0.198478 q^{58} +1.48973 q^{59} +6.15605 q^{60} +7.08310 q^{61} -0.0380136 q^{62} -1.00000 q^{63} -7.97890 q^{64} -19.8194 q^{65} +0.124830 q^{66} +0.989393 q^{67} +1.95535 q^{68} -1.87821 q^{69} -0.0913304 q^{70} -8.17613 q^{71} -0.118609 q^{72} +9.17564 q^{73} +0.181102 q^{74} -4.48258 q^{75} -0.903798 q^{76} +4.20887 q^{77} +0.190888 q^{78} +9.02266 q^{79} +12.3013 q^{80} +1.00000 q^{81} -0.103287 q^{82} -5.68319 q^{83} -1.99912 q^{84} -3.01197 q^{85} +0.122072 q^{86} -6.69207 q^{87} +0.499209 q^{88} +2.01684 q^{89} +0.0913304 q^{90} +6.43617 q^{91} -3.75476 q^{92} +1.28170 q^{93} -0.0101856 q^{94} +1.39218 q^{95} -0.355696 q^{96} +10.8384 q^{97} +0.0296587 q^{98} -4.20887 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19}+ \cdots + 11 q^{99}+O(q^{100}) \) 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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