LMFDB - Embedded newform 2667.2.a.q.1.14

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 = [19,4,19,22] 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:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 $ x^19 - 4x^18 - 22x^17 + 101x^16 + 178x^15 - 1035x^14 - 583x^13 + 5572x^12 + 21x^11 - 17032x^10 + 4985x^9 + 29792x^8 - 13249x^7 - 28600x^6 + 14000x^5 + 13725x^4 - 5723x^3 - 2913x^2 + 608x + 210
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$1.49024$ 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)

$f(q)$	$=$	\(q+1.49024 q^{2} +1.00000 q^{3} +0.220813 q^{4} +2.04744 q^{5} +1.49024 q^{6} +1.00000 q^{7} -2.65141 q^{8} +1.00000 q^{9} +3.05118 q^{10} -1.77527 q^{11} +0.220813 q^{12} -4.05756 q^{13} +1.49024 q^{14} +2.04744 q^{15} -4.39287 q^{16} +7.64794 q^{17} +1.49024 q^{18} +3.24885 q^{19} +0.452102 q^{20} +1.00000 q^{21} -2.64557 q^{22} +6.77465 q^{23} -2.65141 q^{24} -0.807977 q^{25} -6.04673 q^{26} +1.00000 q^{27} +0.220813 q^{28} +6.90210 q^{29} +3.05118 q^{30} -1.66081 q^{31} -1.24359 q^{32} -1.77527 q^{33} +11.3973 q^{34} +2.04744 q^{35} +0.220813 q^{36} +9.03684 q^{37} +4.84157 q^{38} -4.05756 q^{39} -5.42862 q^{40} +9.40281 q^{41} +1.49024 q^{42} +2.27572 q^{43} -0.392001 q^{44} +2.04744 q^{45} +10.0958 q^{46} -1.14335 q^{47} -4.39287 q^{48} +1.00000 q^{49} -1.20408 q^{50} +7.64794 q^{51} -0.895961 q^{52} +0.909120 q^{53} +1.49024 q^{54} -3.63476 q^{55} -2.65141 q^{56} +3.24885 q^{57} +10.2858 q^{58} -0.510997 q^{59} +0.452102 q^{60} -14.6668 q^{61} -2.47501 q^{62} +1.00000 q^{63} +6.93248 q^{64} -8.30762 q^{65} -2.64557 q^{66} -0.730117 q^{67} +1.68876 q^{68} +6.77465 q^{69} +3.05118 q^{70} -2.37985 q^{71} -2.65141 q^{72} +3.42990 q^{73} +13.4671 q^{74} -0.807977 q^{75} +0.717389 q^{76} -1.77527 q^{77} -6.04673 q^{78} -7.04927 q^{79} -8.99415 q^{80} +1.00000 q^{81} +14.0124 q^{82} +1.32633 q^{83} +0.220813 q^{84} +15.6587 q^{85} +3.39137 q^{86} +6.90210 q^{87} +4.70696 q^{88} -3.63475 q^{89} +3.05118 q^{90} -4.05756 q^{91} +1.49593 q^{92} -1.66081 q^{93} -1.70387 q^{94} +6.65185 q^{95} -1.24359 q^{96} -9.35645 q^{97} +1.49024 q^{98} -1.77527 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) $ 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * 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 $

$2$	1.49024	1.05376	0.526879	−	0.849940i	$-0.323362\pi$
$2$	1.49024	1.05376	0.526879	+	0.849940i	$0.323362\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.220813	0.110406
$5$	2.04744	0.915644	0.457822	−	0.889044i	$-0.348630\pi$
$5$	2.04744	0.915644	0.457822	+	0.889044i	$0.348630\pi$
$6$	1.49024	0.608388
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.65141	−0.937417
$9$	1.00000	0.333333
$10$	3.05118	0.964868
$11$	−1.77527	−0.535263	−0.267631	−	0.963521i	$-0.586241\pi$
$11$	−1.77527	−0.535263	−0.267631	+	0.963521i	$0.586241\pi$
$12$	0.220813	0.0637431
$13$	−4.05756	−1.12536	−0.562682	−	0.826673i	$-0.690231\pi$
$13$	−4.05756	−1.12536	−0.562682	+	0.826673i	$0.690231\pi$
$14$	1.49024	0.398283
$15$	2.04744	0.528648
$16$	−4.39287	−1.09822
$17$	7.64794	1.85490	0.927449	−	0.373949i	$-0.121996\pi$
$17$	7.64794	1.85490	0.927449	+	0.373949i	$0.121996\pi$
$18$	1.49024	0.351253
$19$	3.24885	0.745338	0.372669	−	0.927964i	$-0.378443\pi$
$19$	3.24885	0.745338	0.372669	+	0.927964i	$0.378443\pi$
$20$	0.452102	0.101093
$21$	1.00000	0.218218
$22$	−2.64557	−0.564037
$23$	6.77465	1.41261	0.706306	−	0.707906i	$-0.250360\pi$
$23$	6.77465	1.41261	0.706306	+	0.707906i	$0.250360\pi$
$24$	−2.65141	−0.541218
$25$	−0.807977	−0.161595
$26$	−6.04673	−1.18586
$27$	1.00000	0.192450
$28$	0.220813	0.0417297
$29$	6.90210	1.28169	0.640844	−	0.767671i	$-0.278585\pi$
$29$	6.90210	1.28169	0.640844	+	0.767671i	$0.278585\pi$
$30$	3.05118	0.557067
$31$	−1.66081	−0.298291	−0.149145	−	0.988815i	$-0.547652\pi$
$31$	−1.66081	−0.298291	−0.149145	+	0.988815i	$0.547652\pi$
$32$	−1.24359	−0.219838
$33$	−1.77527	−0.309034
$34$	11.3973	1.95461
$35$	2.04744	0.346081
$36$	0.220813	0.0368021
$37$	9.03684	1.48565	0.742824	−	0.669487i	$-0.233486\pi$
$37$	9.03684	1.48565	0.742824	+	0.669487i	$0.233486\pi$
$38$	4.84157	0.785406
$39$	−4.05756	−0.649729
$40$	−5.42862	−0.858340
$41$	9.40281	1.46847	0.734236	−	0.678894i	$-0.237540\pi$
$41$	9.40281	1.46847	0.734236	+	0.678894i	$0.237540\pi$
$42$	1.49024	0.229949
$43$	2.27572	0.347045	0.173522	−	0.984830i	$-0.444485\pi$
$43$	2.27572	0.347045	0.173522	+	0.984830i	$0.444485\pi$
$44$	−0.392001	−0.0590964
$45$	2.04744	0.305215
$46$	10.0958	1.48855
$47$	−1.14335	−0.166775	−0.0833875	−	0.996517i	$-0.526574\pi$
$47$	−1.14335	−0.166775	−0.0833875	+	0.996517i	$0.526574\pi$
$48$	−4.39287	−0.634056
$49$	1.00000	0.142857
$50$	−1.20408	−0.170282
$51$	7.64794	1.07093
$52$	−0.895961	−0.124247
$53$	0.909120	0.124877	0.0624386	−	0.998049i	$-0.480112\pi$
$53$	0.909120	0.124877	0.0624386	+	0.998049i	$0.480112\pi$
$54$	1.49024	0.202796
$55$	−3.63476	−0.490110
$56$	−2.65141	−0.354310
$57$	3.24885	0.430321
$58$	10.2858	1.35059
$59$	−0.510997	−0.0665261	−0.0332631	−	0.999447i	$-0.510590\pi$
$59$	−0.510997	−0.0665261	−0.0332631	+	0.999447i	$0.510590\pi$
$60$	0.452102	0.0583661
$61$	−14.6668	−1.87789	−0.938943	−	0.344074i	$-0.888193\pi$
$61$	−14.6668	−1.87789	−0.938943	+	0.344074i	$0.888193\pi$
$62$	−2.47501	−0.314326
$63$	1.00000	0.125988
$64$	6.93248	0.866560
$65$	−8.30762	−1.03043
$66$	−2.64557	−0.325647
$67$	−0.730117	−0.0891980	−0.0445990	−	0.999005i	$-0.514201\pi$
$67$	−0.730117	−0.0891980	−0.0445990	+	0.999005i	$0.514201\pi$
$68$	1.68876	0.204793
$69$	6.77465	0.815572
$70$	3.05118	0.364686
$71$	−2.37985	−0.282437	−0.141218	−	0.989978i	$-0.545102\pi$
$71$	−2.37985	−0.282437	−0.141218	+	0.989978i	$0.545102\pi$
$72$	−2.65141	−0.312472
$73$	3.42990	0.401439	0.200720	−	0.979649i	$-0.435672\pi$
$73$	3.42990	0.401439	0.200720	+	0.979649i	$0.435672\pi$
$74$	13.4671	1.56551
$75$	−0.807977	−0.0932971
$76$	0.717389	0.0822901
$77$	−1.77527	−0.202310
$78$	−6.04673	−0.684658
$79$	−7.04927	−0.793104	−0.396552	−	0.918012i	$-0.629793\pi$
$79$	−7.04927	−0.793104	−0.396552	+	0.918012i	$0.629793\pi$
$80$	−8.99415	−1.00558
$81$	1.00000	0.111111
$82$	14.0124	1.54741
$83$	1.32633	0.145584	0.0727920	−	0.997347i	$-0.476809\pi$
$83$	1.32633	0.145584	0.0727920	+	0.997347i	$0.476809\pi$
$84$	0.220813	0.0240926
$85$	15.6587	1.69843
$86$	3.39137	0.365701
$87$	6.90210	0.739982
$88$	4.70696	0.501764
$89$	−3.63475	−0.385283	−0.192641	−	0.981269i	$-0.561705\pi$
$89$	−3.63475	−0.385283	−0.192641	+	0.981269i	$0.561705\pi$
$90$	3.05118	0.321623
$91$	−4.05756	−0.425348
$92$	1.49593	0.155961
$93$	−1.66081	−0.172218
$94$	−1.70387	−0.175741
$95$	6.65185	0.682465
$96$	−1.24359	−0.126924
$97$	−9.35645	−0.950004	−0.475002	−	0.879985i	$-0.657553\pi$
$97$	−9.35645	−0.950004	−0.475002	+	0.879985i	$0.657553\pi$
$98$	1.49024	0.150537
$99$	−1.77527	−0.178421
$100$	−0.178412	−0.0178412
$101$	1.21116	0.120515	0.0602573	−	0.998183i	$-0.480808\pi$
$101$	1.21116	0.120515	0.0602573	+	0.998183i	$0.480808\pi$
$102$	11.3973	1.12850
$103$	−8.69531	−0.856774	−0.428387	−	0.903595i	$-0.640918\pi$
$103$	−8.69531	−0.856774	−0.428387	+	0.903595i	$0.640918\pi$
$104$	10.7583	1.05494
$105$	2.04744	0.199810
$106$	1.35481	0.131590
$107$	−17.3884	−1.68100	−0.840499	−	0.541813i	$-0.817738\pi$
$107$	−17.3884	−1.68100	−0.840499	+	0.541813i	$0.817738\pi$
$108$	0.220813	0.0212477
$109$	13.0624	1.25115	0.625576	−	0.780164i	$-0.284864\pi$
$109$	13.0624	1.25115	0.625576	+	0.780164i	$0.284864\pi$
$110$	−5.41665	−0.516458
$111$	9.03684	0.857739
$112$	−4.39287	−0.415087
$113$	−12.6936	−1.19411	−0.597057	−	0.802199i	$-0.703663\pi$
$113$	−12.6936	−1.19411	−0.597057	+	0.802199i	$0.703663\pi$
$114$	4.84157	0.453455
$115$	13.8707	1.29345
$116$	1.52407	0.141506
$117$	−4.05756	−0.375121
$118$	−0.761508	−0.0701025
$119$	7.64794	0.701086
$120$	−5.42862	−0.495563
$121$	−7.84843	−0.713494
$122$	−21.8570	−1.97884
$123$	9.40281	0.847823
$124$	−0.366729	−0.0329332
$125$	−11.8915	−1.06361
$126$	1.49024	0.132761
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	12.8182	1.13298
$129$	2.27572	0.200366
$130$	−12.3803	−1.08583
$131$	−10.1857	−0.889928	−0.444964	−	0.895548i	$-0.646784\pi$
$131$	−10.1857	−0.889928	−0.444964	+	0.895548i	$0.646784\pi$
$132$	−0.392001	−0.0341193
$133$	3.24885	0.281711
$134$	−1.08805	−0.0939931
$135$	2.04744	0.176216
$136$	−20.2779	−1.73881
$137$	5.48349	0.468486	0.234243	−	0.972178i	$-0.424739\pi$
$137$	5.48349	0.468486	0.234243	+	0.972178i	$0.424739\pi$
$138$	10.0958	0.859416
$139$	−9.95792	−0.844620	−0.422310	−	0.906451i	$-0.638781\pi$
$139$	−9.95792	−0.844620	−0.422310	+	0.906451i	$0.638781\pi$
$140$	0.452102	0.0382096
$141$	−1.14335	−0.0962876
$142$	−3.54655	−0.297620
$143$	7.20324	0.602366
$144$	−4.39287	−0.366072
$145$	14.1317	1.17357
$146$	5.11137	0.423020
$147$	1.00000	0.0824786
$148$	1.99545	0.164025
$149$	−4.47456	−0.366571	−0.183285	−	0.983060i	$-0.558673\pi$
$149$	−4.47456	−0.366571	−0.183285	+	0.983060i	$0.558673\pi$
$150$	−1.20408	−0.0983126
$151$	−14.0817	−1.14595	−0.572977	−	0.819571i	$-0.694212\pi$
$151$	−14.0817	−1.14595	−0.572977	+	0.819571i	$0.694212\pi$
$152$	−8.61406	−0.698693
$153$	7.64794	0.618300
$154$	−2.64557	−0.213186
$155$	−3.40042	−0.273128
$156$	−0.895961	−0.0717343
$157$	−5.58675	−0.445871	−0.222936	−	0.974833i	$-0.571564\pi$
$157$	−5.58675	−0.445871	−0.222936	+	0.974833i	$0.571564\pi$
$158$	−10.5051	−0.835740
$159$	0.909120	0.0720979
$160$	−2.54619	−0.201294
$161$	6.77465	0.533917
$162$	1.49024	0.117084
$163$	−12.1815	−0.954127	−0.477064	−	0.878869i	$-0.658299\pi$
$163$	−12.1815	−0.954127	−0.477064	+	0.878869i	$0.658299\pi$
$164$	2.07626	0.162129
$165$	−3.63476	−0.282965
$166$	1.97655	0.153410
$167$	6.23754	0.482676	0.241338	−	0.970441i	$-0.422414\pi$
$167$	6.23754	0.482676	0.241338	+	0.970441i	$0.422414\pi$
$168$	−2.65141	−0.204561
$169$	3.46378	0.266445
$170$	23.3353	1.78973
$171$	3.24885	0.248446
$172$	0.502509	0.0383159
$173$	−13.5405	−1.02946	−0.514731	−	0.857352i	$-0.672108\pi$
$173$	−13.5405	−1.02946	−0.514731	+	0.857352i	$0.672108\pi$
$174$	10.2858	0.779763
$175$	−0.807977	−0.0610773
$176$	7.79851	0.587834
$177$	−0.510997	−0.0384089
$178$	−5.41664	−0.405995
$179$	10.0729	0.752887	0.376443	−	0.926440i	$-0.377147\pi$
$179$	10.0729	0.752887	0.376443	+	0.926440i	$0.377147\pi$
$180$	0.452102	0.0336977
$181$	15.0581	1.11926	0.559630	−	0.828742i	$-0.310943\pi$
$181$	15.0581	1.11926	0.559630	+	0.828742i	$0.310943\pi$
$182$	−6.04673	−0.448214
$183$	−14.6668	−1.08420
$184$	−17.9624	−1.32421
$185$	18.5024	1.36032
$186$	−2.47501	−0.181476
$187$	−13.5771	−0.992858
$188$	−0.252467	−0.0184130
$189$	1.00000	0.0727393
$190$	9.91284	0.719153
$191$	4.76684	0.344916	0.172458	−	0.985017i	$-0.444829\pi$
$191$	4.76684	0.344916	0.172458	+	0.985017i	$0.444829\pi$
$192$	6.93248	0.500309
$193$	−7.71655	−0.555449	−0.277725	−	0.960661i	$-0.589580\pi$
$193$	−7.71655	−0.555449	−0.277725	+	0.960661i	$0.589580\pi$
$194$	−13.9434	−1.00107
$195$	−8.30762	−0.594921
$196$	0.220813	0.0157723
$197$	−2.00654	−0.142960	−0.0714799	−	0.997442i	$-0.522772\pi$
$197$	−2.00654	−0.142960	−0.0714799	+	0.997442i	$0.522772\pi$
$198$	−2.64557	−0.188012
$199$	11.5326	0.817525	0.408762	−	0.912641i	$-0.365960\pi$
$199$	11.5326	0.817525	0.408762	+	0.912641i	$0.365960\pi$
$200$	2.14228	0.151482
$201$	−0.730117	−0.0514985
$202$	1.80491	0.126993
$203$	6.90210	0.484432
$204$	1.68876	0.118237
$205$	19.2517	1.34460
$206$	−12.9581	−0.902833
$207$	6.77465	0.470871
$208$	17.8243	1.23589
$209$	−5.76758	−0.398952
$210$	3.05118	0.210551
$211$	20.5078	1.41181	0.705906	−	0.708306i	$-0.250540\pi$
$211$	20.5078	1.41181	0.705906	+	0.708306i	$0.250540\pi$
$212$	0.200745	0.0137872
$213$	−2.37985	−0.163065
$214$	−25.9129	−1.77137
$215$	4.65942	0.317769
$216$	−2.65141	−0.180406
$217$	−1.66081	−0.112743
$218$	19.4661	1.31841
$219$	3.42990	0.231771
$220$	−0.802600	−0.0541113
$221$	−31.0320	−2.08744
$222$	13.4671	0.903849
$223$	−1.44549	−0.0967969	−0.0483985	−	0.998828i	$-0.515412\pi$
$223$	−1.44549	−0.0967969	−0.0483985	+	0.998828i	$0.515412\pi$
$224$	−1.24359	−0.0830911
$225$	−0.807977	−0.0538651
$226$	−18.9165	−1.25831
$227$	23.4362	1.55551	0.777757	−	0.628565i	$-0.216357\pi$
$227$	23.4362	1.55551	0.777757	+	0.628565i	$0.216357\pi$
$228$	0.717389	0.0475102
$229$	17.5045	1.15673	0.578364	−	0.815779i	$-0.303691\pi$
$229$	17.5045	1.15673	0.578364	+	0.815779i	$0.303691\pi$
$230$	20.6707	1.36298
$231$	−1.77527	−0.116804
$232$	−18.3003	−1.20147
$233$	24.5272	1.60683	0.803415	−	0.595419i	$-0.203014\pi$
$233$	24.5272	1.60683	0.803415	+	0.595419i	$0.203014\pi$
$234$	−6.04673	−0.395287
$235$	−2.34095	−0.152707
$236$	−0.112835	−0.00734491
$237$	−7.04927	−0.457899
$238$	11.3973	0.738775
$239$	12.9074	0.834908	0.417454	−	0.908698i	$-0.362923\pi$
$239$	12.9074	0.834908	0.417454	+	0.908698i	$0.362923\pi$
$240$	−8.99415	−0.580570
$241$	−17.5870	−1.13288	−0.566440	−	0.824103i	$-0.691680\pi$
$241$	−17.5870	−1.13288	−0.566440	+	0.824103i	$0.691680\pi$
$242$	−11.6960	−0.751850
$243$	1.00000	0.0641500
$244$	−3.23861	−0.207330
$245$	2.04744	0.130806
$246$	14.0124	0.893400
$247$	−13.1824	−0.838777
$248$	4.40350	0.279623
$249$	1.32633	0.0840530
$250$	−17.7212	−1.12079
$251$	10.2258	0.645445	0.322722	−	0.946494i	$-0.395402\pi$
$251$	10.2258	0.645445	0.322722	+	0.946494i	$0.395402\pi$
$252$	0.220813	0.0139099
$253$	−12.0268	−0.756119
$254$	1.49024	0.0935059
$255$	15.6587	0.980588
$256$	5.23728	0.327330
$257$	13.1251	0.818723	0.409361	−	0.912372i	$-0.365752\pi$
$257$	13.1251	0.818723	0.409361	+	0.912372i	$0.365752\pi$
$258$	3.39137	0.211138
$259$	9.03684	0.561522
$260$	−1.83443	−0.113766
$261$	6.90210	0.427229
$262$	−15.1791	−0.937769
$263$	−6.65987	−0.410665	−0.205333	−	0.978692i	$-0.565828\pi$
$263$	−6.65987	−0.410665	−0.205333	+	0.978692i	$0.565828\pi$
$264$	4.70696	0.289694
$265$	1.86137	0.114343
$266$	4.84157	0.296856
$267$	−3.63475	−0.222443
$268$	−0.161219	−0.00984802
$269$	7.74043	0.471942	0.235971	−	0.971760i	$-0.424173\pi$
$269$	7.74043	0.471942	0.235971	+	0.971760i	$0.424173\pi$
$270$	3.05118	0.185689
$271$	6.03897	0.366842	0.183421	−	0.983034i	$-0.441283\pi$
$271$	6.03897	0.366842	0.183421	+	0.983034i	$0.441283\pi$
$272$	−33.5964	−2.03708
$273$	−4.05756	−0.245575
$274$	8.17171	0.493671
$275$	1.43437	0.0864959
$276$	1.49593	0.0900444
$277$	−22.9334	−1.37794	−0.688968	−	0.724792i	$-0.741936\pi$
$277$	−22.9334	−1.37794	−0.688968	+	0.724792i	$0.741936\pi$
$278$	−14.8397	−0.890025
$279$	−1.66081	−0.0994302
$280$	−5.42862	−0.324422
$281$	−25.2804	−1.50810	−0.754052	−	0.656814i	$-0.771904\pi$
$281$	−25.2804	−1.50810	−0.754052	+	0.656814i	$0.771904\pi$
$282$	−1.70387	−0.101464
$283$	−13.0595	−0.776308	−0.388154	−	0.921594i	$-0.626887\pi$
$283$	−13.0595	−0.776308	−0.388154	+	0.921594i	$0.626887\pi$
$284$	−0.525502	−0.0311828
$285$	6.65185	0.394021
$286$	10.7346	0.634748
$287$	9.40281	0.555030
$288$	−1.24359	−0.0732795
$289$	41.4910	2.44065
$290$	21.0595	1.23666
$291$	−9.35645	−0.548485
$292$	0.757366	0.0443215
$293$	−3.00348	−0.175465	−0.0877327	−	0.996144i	$-0.527962\pi$
$293$	−3.00348	−0.175465	−0.0877327	+	0.996144i	$0.527962\pi$
$294$	1.49024	0.0869125
$295$	−1.04624	−0.0609143
$296$	−23.9604	−1.39267
$297$	−1.77527	−0.103011
$298$	−6.66817	−0.386277
$299$	−27.4885	−1.58970
$300$	−0.178412	−0.0103006
$301$	2.27572	0.131171
$302$	−20.9851	−1.20756
$303$	1.21116	0.0695791
$304$	−14.2718	−0.818543
$305$	−30.0293	−1.71947
$306$	11.3973	0.651538
$307$	2.33304	0.133153	0.0665767	−	0.997781i	$-0.478792\pi$
$307$	2.33304	0.133153	0.0665767	+	0.997781i	$0.478792\pi$
$308$	−0.392001	−0.0223363
$309$	−8.69531	−0.494659
$310$	−5.06744	−0.287811
$311$	−0.675512	−0.0383047	−0.0191524	−	0.999817i	$-0.506097\pi$
$311$	−0.675512	−0.0383047	−0.0191524	+	0.999817i	$0.506097\pi$
$312$	10.7583	0.609067
$313$	−6.63228	−0.374879	−0.187439	−	0.982276i	$-0.560019\pi$
$313$	−6.63228	−0.374879	−0.187439	+	0.982276i	$0.560019\pi$
$314$	−8.32560	−0.469841
$315$	2.04744	0.115360
$316$	−1.55657	−0.0875638
$317$	−4.68652	−0.263221	−0.131611	−	0.991301i	$-0.542015\pi$
$317$	−4.68652	−0.263221	−0.131611	+	0.991301i	$0.542015\pi$
$318$	1.35481	0.0759737
$319$	−12.2531	−0.686039
$320$	14.1939	0.793461
$321$	−17.3884	−0.970525
$322$	10.0958	0.562620
$323$	24.8471	1.38253
$324$	0.220813	0.0122674
$325$	3.27841	0.181854
$326$	−18.1533	−1.00542
$327$	13.0624	0.722352
$328$	−24.9308	−1.37657
$329$	−1.14335	−0.0630350
$330$	−5.41665	−0.298177
$331$	−6.07509	−0.333917	−0.166959	−	0.985964i	$-0.553395\pi$
$331$	−6.07509	−0.333917	−0.166959	+	0.985964i	$0.553395\pi$
$332$	0.292871	0.0160734
$333$	9.03684	0.495216
$334$	9.29543	0.508623
$335$	−1.49487	−0.0816736
$336$	−4.39287	−0.239651
$337$	5.31829	0.289706	0.144853	−	0.989453i	$-0.453729\pi$
$337$	5.31829	0.289706	0.144853	+	0.989453i	$0.453729\pi$
$338$	5.16187	0.280769
$339$	−12.6936	−0.689422
$340$	3.45765	0.187517
$341$	2.94838	0.159664
$342$	4.84157	0.261802
$343$	1.00000	0.0539949
$344$	−6.03389	−0.325325
$345$	13.8707	0.746774
$346$	−20.1785	−1.08480
$347$	−14.5110	−0.778993	−0.389496	−	0.921028i	$-0.627351\pi$
$347$	−14.5110	−0.778993	−0.389496	+	0.921028i	$0.627351\pi$
$348$	1.52407	0.0816988
$349$	19.6940	1.05419	0.527097	−	0.849805i	$-0.323281\pi$
$349$	19.6940	1.05419	0.527097	+	0.849805i	$0.323281\pi$
$350$	−1.20408	−0.0643607
$351$	−4.05756	−0.216576
$352$	2.20771	0.117671
$353$	17.7743	0.946033	0.473016	−	0.881054i	$-0.343165\pi$
$353$	17.7743	0.946033	0.473016	+	0.881054i	$0.343165\pi$
$354$	−0.761508	−0.0404737
$355$	−4.87262	−0.258612
$356$	−0.802599	−0.0425376
$357$	7.64794	0.404772
$358$	15.0111	0.793360
$359$	−14.7077	−0.776245	−0.388123	−	0.921608i	$-0.626876\pi$
$359$	−14.7077	−0.776245	−0.388123	+	0.921608i	$0.626876\pi$
$360$	−5.42862	−0.286113
$361$	−8.44494	−0.444471
$362$	22.4402	1.17943
$363$	−7.84843	−0.411936
$364$	−0.895961	−0.0469611
$365$	7.02252	0.367576
$366$	−21.8570	−1.14248
$367$	−13.9272	−0.726995	−0.363498	−	0.931595i	$-0.618417\pi$
$367$	−13.9272	−0.726995	−0.363498	+	0.931595i	$0.618417\pi$
$368$	−29.7601	−1.55135
$369$	9.40281	0.489491
$370$	27.5730	1.43345
$371$	0.909120	0.0471991
$372$	−0.366729	−0.0190140
$373$	29.6120	1.53325	0.766627	−	0.642093i	$-0.221934\pi$
$373$	29.6120	1.53325	0.766627	+	0.642093i	$0.221934\pi$
$374$	−20.2332	−1.04623
$375$	−11.8915	−0.614075
$376$	3.03150	0.156338
$377$	−28.0057	−1.44237
$378$	1.49024	0.0766496
$379$	−16.3108	−0.837829	−0.418914	−	0.908026i	$-0.637589\pi$
$379$	−16.3108	−0.837829	−0.418914	+	0.908026i	$0.637589\pi$
$380$	1.46881	0.0753485
$381$	1.00000	0.0512316
$382$	7.10373	0.363458
$383$	−30.7897	−1.57328	−0.786640	−	0.617412i	$-0.788181\pi$
$383$	−30.7897	−1.57328	−0.786640	+	0.617412i	$0.788181\pi$
$384$	12.8182	0.654128
$385$	−3.63476	−0.185244
$386$	−11.4995	−0.585309
$387$	2.27572	0.115682
$388$	−2.06602	−0.104886
$389$	3.20667	0.162585	0.0812923	−	0.996690i	$-0.474095\pi$
$389$	3.20667	0.162585	0.0812923	+	0.996690i	$0.474095\pi$
$390$	−12.3803	−0.626903
$391$	51.8121	2.62025
$392$	−2.65141	−0.133917
$393$	−10.1857	−0.513800
$394$	−2.99022	−0.150645
$395$	−14.4330	−0.726202
$396$	−0.392001	−0.0196988
$397$	34.4082	1.72690	0.863449	−	0.504435i	$-0.168299\pi$
$397$	34.4082	1.72690	0.863449	+	0.504435i	$0.168299\pi$
$398$	17.1863	0.861474
$399$	3.24885	0.162646
$400$	3.54933	0.177467
$401$	−6.69898	−0.334531	−0.167266	−	0.985912i	$-0.553494\pi$
$401$	−6.69898	−0.334531	−0.167266	+	0.985912i	$0.553494\pi$
$402$	−1.08805	−0.0542669
$403$	6.73884	0.335686
$404$	0.267439	0.0133056
$405$	2.04744	0.101738
$406$	10.2858	0.510474
$407$	−16.0428	−0.795212
$408$	−20.2779	−1.00390
$409$	−28.8318	−1.42564	−0.712820	−	0.701347i	$-0.752582\pi$
$409$	−28.8318	−1.42564	−0.712820	+	0.701347i	$0.752582\pi$
$410$	28.6897	1.41688
$411$	5.48349	0.270481
$412$	−1.92003	−0.0945933
$413$	−0.510997	−0.0251445
$414$	10.0958	0.496184
$415$	2.71559	0.133303
$416$	5.04595	0.247398
$417$	−9.95792	−0.487642
$418$	−8.59507	−0.420399
$419$	26.8706	1.31272	0.656358	−	0.754450i	$-0.272096\pi$
$419$	26.8706	1.31272	0.656358	+	0.754450i	$0.272096\pi$
$420$	0.452102	0.0220603
$421$	35.8612	1.74777	0.873884	−	0.486135i	$-0.161594\pi$
$421$	35.8612	1.74777	0.873884	+	0.486135i	$0.161594\pi$
$422$	30.5615	1.48771
$423$	−1.14335	−0.0555917
$424$	−2.41045	−0.117062
$425$	−6.17936	−0.299743
$426$	−3.54655	−0.171831
$427$	−14.6668	−0.709774
$428$	−3.83958	−0.185593
$429$	7.20324	0.347776
$430$	6.94364	0.334852
$431$	−25.9119	−1.24813	−0.624066	−	0.781372i	$-0.714520\pi$
$431$	−25.9119	−1.24813	−0.624066	+	0.781372i	$0.714520\pi$
$432$	−4.39287	−0.211352
$433$	17.2601	0.829468	0.414734	−	0.909943i	$-0.363875\pi$
$433$	17.2601	0.829468	0.414734	+	0.909943i	$0.363875\pi$
$434$	−2.47501	−0.118804
$435$	14.1317	0.677561
$436$	2.88434	0.138135
$437$	22.0099	1.05287
$438$	5.11137	0.244231
$439$	32.7590	1.56350	0.781752	−	0.623590i	$-0.214327\pi$
$439$	32.7590	1.56350	0.781752	+	0.623590i	$0.214327\pi$
$440$	9.63724	0.459438
$441$	1.00000	0.0476190
$442$	−46.2451	−2.19965
$443$	−25.1899	−1.19681	−0.598404	−	0.801195i	$-0.704198\pi$
$443$	−25.1899	−1.19681	−0.598404	+	0.801195i	$0.704198\pi$
$444$	1.99545	0.0946998
$445$	−7.44194	−0.352782
$446$	−2.15412	−0.102001
$447$	−4.47456	−0.211640
$448$	6.93248	0.327529
$449$	−38.5015	−1.81700	−0.908500	−	0.417885i	$-0.862771\pi$
$449$	−38.5015	−1.81700	−0.908500	+	0.417885i	$0.862771\pi$
$450$	−1.20408	−0.0567608
$451$	−16.6925	−0.786018
$452$	−2.80291	−0.131838
$453$	−14.0817	−0.661617
$454$	34.9255	1.63914
$455$	−8.30762	−0.389467
$456$	−8.61406	−0.403390
$457$	−23.8848	−1.11729	−0.558643	−	0.829408i	$-0.688678\pi$
$457$	−23.8848	−1.11729	−0.558643	+	0.829408i	$0.688678\pi$
$458$	26.0859	1.21891
$459$	7.64794	0.356975
$460$	3.06283	0.142805
$461$	−22.5033	−1.04808	−0.524041	−	0.851693i	$-0.675576\pi$
$461$	−22.5033	−1.04808	−0.524041	+	0.851693i	$0.675576\pi$
$462$	−2.64557	−0.123083
$463$	−7.25600	−0.337215	−0.168607	−	0.985683i	$-0.553927\pi$
$463$	−7.25600	−0.337215	−0.168607	+	0.985683i	$0.553927\pi$
$464$	−30.3200	−1.40757
$465$	−3.40042	−0.157691
$466$	36.5514	1.69321
$467$	−3.02312	−0.139893	−0.0699465	−	0.997551i	$-0.522283\pi$
$467$	−3.02312	−0.139893	−0.0699465	+	0.997551i	$0.522283\pi$
$468$	−0.895961	−0.0414158
$469$	−0.730117	−0.0337137
$470$	−3.48857	−0.160916
$471$	−5.58675	−0.257424
$472$	1.35486	0.0623627
$473$	−4.04001	−0.185760
$474$	−10.5051	−0.482515
$475$	−2.62500	−0.120443
$476$	1.68876	0.0774043
$477$	0.909120	0.0416257
$478$	19.2351	0.879791
$479$	12.8660	0.587862	0.293931	−	0.955827i	$-0.405036\pi$
$479$	12.8660	0.587862	0.293931	+	0.955827i	$0.405036\pi$
$480$	−2.54619	−0.116217
$481$	−36.6675	−1.67189
$482$	−26.2089	−1.19378
$483$	6.77465	0.308257
$484$	−1.73303	−0.0787743
$485$	−19.1568	−0.869866
$486$	1.49024	0.0675986
$487$	−38.6527	−1.75152	−0.875761	−	0.482745i	$-0.839640\pi$
$487$	−38.6527	−1.75152	−0.875761	+	0.482745i	$0.839640\pi$
$488$	38.8876	1.76036
$489$	−12.1815	−0.550866
$490$	3.05118	0.137838
$491$	−17.5142	−0.790404	−0.395202	−	0.918594i	$-0.629325\pi$
$491$	−17.5142	−0.790404	−0.395202	+	0.918594i	$0.629325\pi$
$492$	2.07626	0.0936051
$493$	52.7869	2.37740
$494$	−19.6450	−0.883868
$495$	−3.63476	−0.163370
$496$	7.29573	0.327588
$497$	−2.37985	−0.106751
$498$	1.97655	0.0885715
$499$	8.34272	0.373471	0.186736	−	0.982410i	$-0.440209\pi$
$499$	8.34272	0.373471	0.186736	+	0.982410i	$0.440209\pi$
$500$	−2.62580	−0.117429
$501$	6.23754	0.278673
$502$	15.2388	0.680143
$503$	−20.6604	−0.921203	−0.460602	−	0.887607i	$-0.652366\pi$
$503$	−20.6604	−0.921203	−0.460602	+	0.887607i	$0.652366\pi$
$504$	−2.65141	−0.118103
$505$	2.47977	0.110349
$506$	−17.9228	−0.796766
$507$	3.46378	0.153832
$508$	0.220813	0.00979698
$509$	−23.3833	−1.03644	−0.518222	−	0.855246i	$-0.673406\pi$
$509$	−23.3833	−1.03644	−0.518222	+	0.855246i	$0.673406\pi$
$510$	23.3353	1.03330
$511$	3.42990	0.151730
$512$	−17.8317	−0.788056
$513$	3.24885	0.143440
$514$	19.5596	0.862736
$515$	−17.8031	−0.784500
$516$	0.502509	0.0221217
$517$	2.02975	0.0892684
$518$	13.4671	0.591708
$519$	−13.5405	−0.594360
$520$	22.0269	0.965946
$521$	17.6114	0.771568	0.385784	−	0.922589i	$-0.373931\pi$
$521$	17.6114	0.771568	0.385784	+	0.922589i	$0.373931\pi$
$522$	10.2858	0.450196
$523$	−26.6248	−1.16422	−0.582110	−	0.813110i	$-0.697773\pi$
$523$	−26.6248	−1.16422	−0.582110	+	0.813110i	$0.697773\pi$
$524$	−2.24913	−0.0982538
$525$	−0.807977	−0.0352630
$526$	−9.92481	−0.432742
$527$	−12.7018	−0.553299
$528$	7.79851	0.339386
$529$	22.8959	0.995474
$530$	2.77389	0.120490
$531$	−0.510997	−0.0221754
$532$	0.717389	0.0311027
$533$	−38.1525	−1.65257
$534$	−5.41664	−0.234401
$535$	−35.6017	−1.53920
$536$	1.93584	0.0836157
$537$	10.0729	0.434679
$538$	11.5351	0.497313
$539$	−1.77527	−0.0764661
$540$	0.452102	0.0194554
$541$	27.4985	1.18225	0.591126	−	0.806579i	$-0.298684\pi$
$541$	27.4985	1.18225	0.591126	+	0.806579i	$0.298684\pi$
$542$	8.99952	0.386562
$543$	15.0581	0.646206
$544$	−9.51094	−0.407778
$545$	26.7445	1.14561
$546$	−6.04673	−0.258776
$547$	10.0299	0.428846	0.214423	−	0.976741i	$-0.431213\pi$
$547$	10.0299	0.428846	0.214423	+	0.976741i	$0.431213\pi$
$548$	1.21082	0.0517239
$549$	−14.6668	−0.625962
$550$	2.13756	0.0911458
$551$	22.4239	0.955291
$552$	−17.9624	−0.764531
$553$	−7.04927	−0.299765
$554$	−34.1763	−1.45201
$555$	18.5024	0.785384
$556$	−2.19884	−0.0932514
$557$	−32.2636	−1.36705	−0.683527	−	0.729925i	$-0.739555\pi$
$557$	−32.2636	−1.36705	−0.683527	+	0.729925i	$0.739555\pi$
$558$	−2.47501	−0.104775
$559$	−9.23388	−0.390552
$560$	−8.99415	−0.380072
$561$	−13.5771	−0.573227
$562$	−37.6739	−1.58918
$563$	5.87677	0.247676	0.123838	−	0.992302i	$-0.460480\pi$
$563$	5.87677	0.247676	0.123838	+	0.992302i	$0.460480\pi$
$564$	−0.252467	−0.0106308
$565$	−25.9894	−1.09338
$566$	−19.4618	−0.818041
$567$	1.00000	0.0419961
$568$	6.30998	0.264761
$569$	−33.2432	−1.39363	−0.696813	−	0.717253i	$-0.745399\pi$
$569$	−33.2432	−1.39363	−0.696813	+	0.717253i	$0.745399\pi$
$570$	9.91284	0.415203
$571$	43.6479	1.82661	0.913305	−	0.407277i	$-0.133522\pi$
$571$	43.6479	1.82661	0.913305	+	0.407277i	$0.133522\pi$
$572$	1.59057	0.0665050
$573$	4.76684	0.199138
$574$	14.0124	0.584868
$575$	−5.47376	−0.228272
$576$	6.93248	0.288853
$577$	−11.2681	−0.469099	−0.234549	−	0.972104i	$-0.575361\pi$
$577$	−11.2681	−0.469099	−0.234549	+	0.972104i	$0.575361\pi$
$578$	61.8316	2.57185
$579$	−7.71655	−0.320689
$580$	3.12045	0.129570
$581$	1.32633	0.0550256
$582$	−13.9434	−0.577971
$583$	−1.61393	−0.0668421
$584$	−9.09409	−0.376316
$585$	−8.30762	−0.343478
$586$	−4.47591	−0.184898
$587$	−11.3396	−0.468037	−0.234018	−	0.972232i	$-0.575188\pi$
$587$	−11.3396	−0.468037	−0.234018	+	0.972232i	$0.575188\pi$
$588$	0.220813	0.00910616
$589$	−5.39574	−0.222328
$590$	−1.55914	−0.0641889
$591$	−2.00654	−0.0825379
$592$	−39.6976	−1.63156
$593$	12.6697	0.520283	0.260141	−	0.965571i	$-0.416231\pi$
$593$	12.6697	0.520283	0.260141	+	0.965571i	$0.416231\pi$
$594$	−2.64557	−0.108549
$595$	15.6587	0.641945
$596$	−0.988041	−0.0404717
$597$	11.5326	0.471998
$598$	−40.9645	−1.67516
$599$	11.1486	0.455520	0.227760	−	0.973717i	$-0.426860\pi$
$599$	11.1486	0.455520	0.227760	+	0.973717i	$0.426860\pi$
$600$	2.14228	0.0874583
$601$	35.8081	1.46064	0.730322	−	0.683104i	$-0.239370\pi$
$601$	35.8081	1.46064	0.730322	+	0.683104i	$0.239370\pi$
$602$	3.39137	0.138222
$603$	−0.730117	−0.0297327
$604$	−3.10942	−0.126521
$605$	−16.0692	−0.653307
$606$	1.80491	0.0733196
$607$	−5.95533	−0.241719	−0.120860	−	0.992670i	$-0.538565\pi$
$607$	−5.95533	−0.241719	−0.120860	+	0.992670i	$0.538565\pi$
$608$	−4.04026	−0.163854
$609$	6.90210	0.279687
$610$	−44.7509	−1.81191
$611$	4.63922	0.187683
$612$	1.68876	0.0682642
$613$	17.0813	0.689908	0.344954	−	0.938620i	$-0.387894\pi$
$613$	17.0813	0.689908	0.344954	+	0.938620i	$0.387894\pi$
$614$	3.47678	0.140311
$615$	19.2517	0.776304
$616$	4.70696	0.189649
$617$	23.2365	0.935465	0.467732	−	0.883870i	$-0.345071\pi$
$617$	23.2365	0.935465	0.467732	+	0.883870i	$0.345071\pi$
$618$	−12.9581	−0.521251
$619$	−48.1408	−1.93494	−0.967470	−	0.252984i	$-0.918588\pi$
$619$	−48.1408	−1.93494	−0.967470	+	0.252984i	$0.918588\pi$
$620$	−0.750856	−0.0301551
$621$	6.77465	0.271857
$622$	−1.00667	−0.0403639
$623$	−3.63475	−0.145623
$624$	17.8243	0.713544
$625$	−20.3073	−0.812292
$626$	−9.88369	−0.395032
$627$	−5.76758	−0.230335
$628$	−1.23363	−0.0492270
$629$	69.1132	2.75573
$630$	3.05118	0.121562
$631$	−18.0853	−0.719963	−0.359982	−	0.932959i	$-0.617217\pi$
$631$	−18.0853	−0.719963	−0.359982	+	0.932959i	$0.617217\pi$
$632$	18.6905	0.743469
$633$	20.5078	0.815110
$634$	−6.98403	−0.277371
$635$	2.04744	0.0812503
$636$	0.200745	0.00796007
$637$	−4.05756	−0.160766
$638$	−18.2600	−0.722920
$639$	−2.37985	−0.0941456
$640$	26.2446	1.03741
$641$	−12.7420	−0.503280	−0.251640	−	0.967821i	$-0.580970\pi$
$641$	−12.7420	−0.503280	−0.251640	+	0.967821i	$0.580970\pi$
$642$	−25.9129	−1.02270
$643$	−4.19773	−0.165542	−0.0827712	−	0.996569i	$-0.526377\pi$
$643$	−4.19773	−0.165542	−0.0827712	+	0.996569i	$0.526377\pi$
$644$	1.49593	0.0589479
$645$	4.65942	0.183464
$646$	37.0281	1.45685
$647$	−21.9409	−0.862587	−0.431293	−	0.902212i	$-0.641943\pi$
$647$	−21.9409	−0.862587	−0.431293	+	0.902212i	$0.641943\pi$
$648$	−2.65141	−0.104157
$649$	0.907155	0.0356090
$650$	4.88562	0.191630
$651$	−1.66081	−0.0650924
$652$	−2.68983	−0.105342
$653$	−1.77511	−0.0694654	−0.0347327	−	0.999397i	$-0.511058\pi$
$653$	−1.77511	−0.0694654	−0.0347327	+	0.999397i	$0.511058\pi$
$654$	19.4661	0.761185
$655$	−20.8546	−0.814858
$656$	−41.3053	−1.61270
$657$	3.42990	0.133813
$658$	−1.70387	−0.0664237
$659$	−14.8065	−0.576780	−0.288390	−	0.957513i	$-0.593120\pi$
$659$	−14.8065	−0.576780	−0.288390	+	0.957513i	$0.593120\pi$
$660$	−0.802600	−0.0312412
$661$	−22.5004	−0.875164	−0.437582	−	0.899179i	$-0.644165\pi$
$661$	−22.5004	−0.875164	−0.437582	+	0.899179i	$0.644165\pi$
$662$	−9.05334	−0.351868
$663$	−31.0320	−1.20518
$664$	−3.51666	−0.136473
$665$	6.65185	0.257947
$666$	13.4671	0.521838
$667$	46.7593	1.81053
$668$	1.37733	0.0532905
$669$	−1.44549	−0.0558857
$670$	−2.22772	−0.0860643
$671$	26.0374	1.00516
$672$	−1.24359	−0.0479727
$673$	32.2028	1.24133	0.620663	−	0.784077i	$-0.286864\pi$
$673$	32.2028	1.24133	0.620663	+	0.784077i	$0.286864\pi$
$674$	7.92553	0.305280
$675$	−0.807977	−0.0310990
$676$	0.764848	0.0294172
$677$	38.5853	1.48296	0.741478	−	0.670978i	$-0.234125\pi$
$677$	38.5853	1.48296	0.741478	+	0.670978i	$0.234125\pi$
$678$	−18.9165	−0.726484
$679$	−9.35645	−0.359068
$680$	−41.5178	−1.59213
$681$	23.4362	0.898077
$682$	4.39380	0.168247
$683$	37.7291	1.44366	0.721831	−	0.692069i	$-0.243301\pi$
$683$	37.7291	1.44366	0.721831	+	0.692069i	$0.243301\pi$
$684$	0.717389	0.0274300
$685$	11.2271	0.428967
$686$	1.49024	0.0568976
$687$	17.5045	0.667837
$688$	−9.99695	−0.381130
$689$	−3.68881	−0.140532
$690$	20.6707	0.786919
$691$	40.9255	1.55688	0.778439	−	0.627720i	$-0.216012\pi$
$691$	40.9255	1.55688	0.778439	+	0.627720i	$0.216012\pi$
$692$	−2.98991	−0.113659
$693$	−1.77527	−0.0674368
$694$	−21.6249	−0.820870
$695$	−20.3883	−0.773372
$696$	−18.3003	−0.693672
$697$	71.9122	2.72387
$698$	29.3487	1.11087
$699$	24.5272	0.927704
$700$	−0.178412	−0.00674332
$701$	18.9250	0.714788	0.357394	−	0.933954i	$-0.383665\pi$
$701$	18.9250	0.714788	0.357394	+	0.933954i	$0.383665\pi$
$702$	−6.04673	−0.228219
$703$	29.3594	1.10731
$704$	−12.3070	−0.463837
$705$	−2.34095	−0.0881652
$706$	26.4880	0.996890
$707$	1.21116	0.0455502
$708$	−0.112835	−0.00424059
$709$	−9.73734	−0.365693	−0.182847	−	0.983141i	$-0.558531\pi$
$709$	−9.73734	−0.365693	−0.182847	+	0.983141i	$0.558531\pi$
$710$	−7.26136	−0.272514
$711$	−7.04927	−0.264368
$712$	9.63722	0.361170
$713$	−11.2514	−0.421369
$714$	11.3973	0.426532
$715$	14.7482	0.551553
$716$	2.22423	0.0831235
$717$	12.9074	0.482034
$718$	−21.9181	−0.817975
$719$	−33.4897	−1.24896	−0.624478	−	0.781042i	$-0.714688\pi$
$719$	−33.4897	−1.24896	−0.624478	+	0.781042i	$0.714688\pi$
$720$	−8.99415	−0.335192
$721$	−8.69531	−0.323830
$722$	−12.5850	−0.468365
$723$	−17.5870	−0.654069
$724$	3.32502	0.123574
$725$	−5.57673	−0.207115
$726$	−11.6960	−0.434081
$727$	7.63222	0.283063	0.141532	−	0.989934i	$-0.454797\pi$
$727$	7.63222	0.283063	0.141532	+	0.989934i	$0.454797\pi$
$728$	10.7583	0.398728
$729$	1.00000	0.0370370
$730$	10.4652	0.387336
$731$	17.4046	0.643733
$732$	−3.23861	−0.119702
$733$	41.0907	1.51772	0.758859	−	0.651254i	$-0.225757\pi$
$733$	41.0907	1.51772	0.758859	+	0.651254i	$0.225757\pi$
$734$	−20.7549	−0.766077
$735$	2.04744	0.0755211
$736$	−8.42491	−0.310546
$737$	1.29615	0.0477443
$738$	14.0124	0.515805
$739$	−40.6018	−1.49356	−0.746781	−	0.665070i	$-0.768402\pi$
$739$	−40.6018	−1.49356	−0.746781	+	0.665070i	$0.768402\pi$
$740$	4.08557	0.150189
$741$	−13.1824	−0.484268
$742$	1.35481	0.0497365
$743$	−18.3986	−0.674977	−0.337489	−	0.941330i	$-0.609577\pi$
$743$	−18.3986	−0.674977	−0.337489	+	0.941330i	$0.609577\pi$
$744$	4.40350	0.161440
$745$	−9.16141	−0.335648
$746$	44.1290	1.61568
$747$	1.32633	0.0485280
$748$	−2.99800	−0.109618
$749$	−17.3884	−0.635358
$750$	−17.7212	−0.647086
$751$	32.7553	1.19526	0.597630	−	0.801772i	$-0.296109\pi$
$751$	32.7553	1.19526	0.597630	+	0.801772i	$0.296109\pi$
$752$	5.02259	0.183155
$753$	10.2258	0.372648
$754$	−41.7351	−1.51990
$755$	−28.8315	−1.04929
$756$	0.220813	0.00803088
$757$	−46.5385	−1.69147	−0.845735	−	0.533604i	$-0.820837\pi$
$757$	−46.5385	−1.69147	−0.845735	+	0.533604i	$0.820837\pi$
$758$	−24.3070	−0.882869
$759$	−12.0268	−0.436545
$760$	−17.6368	−0.639754
$761$	−11.4405	−0.414718	−0.207359	−	0.978265i	$-0.566487\pi$
$761$	−11.4405	−0.414718	−0.207359	+	0.978265i	$0.566487\pi$
$762$	1.49024	0.0539857
$763$	13.0624	0.472891
$764$	1.05258	0.0380810
$765$	15.6587	0.566143
$766$	−45.8840	−1.65786
$767$	2.07340	0.0748662
$768$	5.23728	0.188984
$769$	−1.29466	−0.0466867	−0.0233434	−	0.999728i	$-0.507431\pi$
$769$	−1.29466	−0.0466867	−0.0233434	+	0.999728i	$0.507431\pi$
$770$	−5.41665	−0.195203
$771$	13.1251	0.472690
$772$	−1.70391	−0.0613251
$773$	34.0700	1.22541	0.612706	−	0.790311i	$-0.290081\pi$
$773$	34.0700	1.22541	0.612706	+	0.790311i	$0.290081\pi$
$774$	3.39137	0.121900
$775$	1.34190	0.0482024
$776$	24.8078	0.890549
$777$	9.03684	0.324195
$778$	4.77870	0.171325
$779$	30.5484	1.09451
$780$	−1.83443	−0.0656831
$781$	4.22487	0.151178
$782$	77.2125	2.76111
$783$	6.90210	0.246661
$784$	−4.39287	−0.156888
$785$	−11.4386	−0.408260
$786$	−15.1791	−0.541421
$787$	33.5028	1.19424	0.597122	−	0.802150i	$-0.296311\pi$
$787$	33.5028	1.19424	0.597122	+	0.802150i	$0.296311\pi$
$788$	−0.443069	−0.0157837
$789$	−6.65987	−0.237098
$790$	−21.5086	−0.765241
$791$	−12.6936	−0.451333
$792$	4.70696	0.167255
$793$	59.5112	2.11330
$794$	51.2765	1.81973
$795$	1.86137	0.0660160
$796$	2.54655	0.0902600
$797$	19.4492	0.688927	0.344464	−	0.938800i	$-0.388061\pi$
$797$	19.4492	0.688927	0.344464	+	0.938800i	$0.388061\pi$
$798$	4.84157	0.171390
$799$	−8.74429	−0.309351
$800$	1.00479	0.0355249
$801$	−3.63475	−0.128428
$802$	−9.98309	−0.352515
$803$	−6.08898	−0.214876
$804$	−0.161219	−0.00568576
$805$	13.8707	0.488878
$806$	10.0425	0.353732
$807$	7.74043	0.272476
$808$	−3.21128	−0.112972
$809$	−16.3351	−0.574311	−0.287156	−	0.957884i	$-0.592710\pi$
$809$	−16.3351	−0.574311	−0.287156	+	0.957884i	$0.592710\pi$
$810$	3.05118	0.107208
$811$	−32.0347	−1.12489	−0.562445	−	0.826835i	$-0.690139\pi$
$811$	−32.0347	−1.12489	−0.562445	+	0.826835i	$0.690139\pi$
$812$	1.52407	0.0534844
$813$	6.03897	0.211796
$814$	−23.9076	−0.837961
$815$	−24.9409	−0.873641
$816$	−33.5964	−1.17611
$817$	7.39350	0.258666
$818$	−42.9663	−1.50228
$819$	−4.05756	−0.141783
$820$	4.25103	0.148452
$821$	21.7526	0.759171	0.379586	−	0.925157i	$-0.376067\pi$
$821$	21.7526	0.759171	0.379586	+	0.925157i	$0.376067\pi$
$822$	8.17171	0.285021
$823$	−19.0673	−0.664643	−0.332322	−	0.943166i	$-0.607832\pi$
$823$	−19.0673	−0.664643	−0.332322	+	0.943166i	$0.607832\pi$
$824$	23.0549	0.803154
$825$	1.43437	0.0499385
$826$	−0.761508	−0.0264962
$827$	16.0124	0.556807	0.278403	−	0.960464i	$-0.410195\pi$
$827$	16.0124	0.556807	0.278403	+	0.960464i	$0.410195\pi$
$828$	1.49593	0.0519871
$829$	8.10746	0.281584	0.140792	−	0.990039i	$-0.455035\pi$
$829$	8.10746	0.281584	0.140792	+	0.990039i	$0.455035\pi$
$830$	4.04688	0.140469
$831$	−22.9334	−0.795552
$832$	−28.1290	−0.975196
$833$	7.64794	0.264986
$834$	−14.8397	−0.513856
$835$	12.7710	0.441959
$836$	−1.27356	−0.0440468
$837$	−1.66081	−0.0574061
$838$	40.0436	1.38328
$839$	13.7923	0.476161	0.238081	−	0.971245i	$-0.423482\pi$
$839$	13.7923	0.476161	0.238081	+	0.971245i	$0.423482\pi$
$840$	−5.42862	−0.187305
$841$	18.6389	0.642722
$842$	53.4418	1.84172
$843$	−25.2804	−0.870705
$844$	4.52837	0.155873
$845$	7.09190	0.243969
$846$	−1.70387	−0.0585802
$847$	−7.84843	−0.269675
$848$	−3.99364	−0.137142
$849$	−13.0595	−0.448202
$850$	−9.20872	−0.315857
$851$	61.2214	2.09864
$852$	−0.525502	−0.0180034
$853$	0.711300	0.0243545	0.0121772	−	0.999926i	$-0.496124\pi$
$853$	0.711300	0.0243545	0.0121772	+	0.999926i	$0.496124\pi$
$854$	−21.8570	−0.747930
$855$	6.65185	0.227488
$856$	46.1038	1.57580
$857$	−7.40150	−0.252831	−0.126415	−	0.991977i	$-0.540347\pi$
$857$	−7.40150	−0.252831	−0.126415	+	0.991977i	$0.540347\pi$
$858$	10.7346	0.366472
$859$	−17.0089	−0.580335	−0.290167	−	0.956976i	$-0.593711\pi$
$859$	−17.0089	−0.580335	−0.290167	+	0.956976i	$0.593711\pi$
$860$	1.02886	0.0350838
$861$	9.40281	0.320447
$862$	−38.6149	−1.31523
$863$	18.4171	0.626927	0.313464	−	0.949600i	$-0.398511\pi$
$863$	18.4171	0.626927	0.313464	+	0.949600i	$0.398511\pi$
$864$	−1.24359	−0.0423079
$865$	−27.7233	−0.942621
$866$	25.7217	0.874059
$867$	41.4910	1.40911
$868$	−0.366729	−0.0124476
$869$	12.5143	0.424519
$870$	21.0595	0.713985
$871$	2.96249	0.100380
$872$	−34.6338	−1.17285
$873$	−9.35645	−0.316668
$874$	32.7999	1.10947
$875$	−11.8915	−0.402006
$876$	0.757366	0.0255890
$877$	11.4975	0.388242	0.194121	−	0.980978i	$-0.437815\pi$
$877$	11.4975	0.388242	0.194121	+	0.980978i	$0.437815\pi$
$878$	48.8188	1.64755
$879$	−3.00348	−0.101305
$880$	15.9670	0.538247
$881$	25.7078	0.866119	0.433060	−	0.901365i	$-0.357434\pi$
$881$	25.7078	0.866119	0.433060	+	0.901365i	$0.357434\pi$
$882$	1.49024	0.0501790
$883$	−49.3302	−1.66009	−0.830047	−	0.557693i	$-0.811687\pi$
$883$	−49.3302	−1.66009	−0.830047	+	0.557693i	$0.811687\pi$
$884$	−6.85226	−0.230466
$885$	−1.04624	−0.0351689
$886$	−37.5390	−1.26115
$887$	−9.71012	−0.326034	−0.163017	−	0.986623i	$-0.552123\pi$
$887$	−9.71012	−0.326034	−0.163017	+	0.986623i	$0.552123\pi$
$888$	−23.9604	−0.804059
$889$	1.00000	0.0335389
$890$	−11.0903	−0.371747
$891$	−1.77527	−0.0594736
$892$	−0.319182	−0.0106870
$893$	−3.71458	−0.124304
$894$	−6.66817	−0.223017
$895$	20.6238	0.689376
$896$	12.8182	0.428227
$897$	−27.4885	−0.917816
$898$	−57.3765	−1.91468
$899$	−11.4631	−0.382315
$900$	−0.178412	−0.00594705
$901$	6.95290	0.231635
$902$	−24.8758	−0.828273
$903$	2.27572	0.0757313
$904$	33.6560	1.11938
$905$	30.8306	1.02484
$906$	−20.9851	−0.697184
$907$	8.87266	0.294612	0.147306	−	0.989091i	$-0.452940\pi$
$907$	8.87266	0.294612	0.147306	+	0.989091i	$0.452940\pi$
$908$	5.17501	0.171739
$909$	1.21116	0.0401715
$910$	−12.3803	−0.410404
$911$	−16.3270	−0.540938	−0.270469	−	0.962729i	$-0.587179\pi$
$911$	−16.3270	−0.540938	−0.270469	+	0.962729i	$0.587179\pi$
$912$	−14.2718	−0.472586
$913$	−2.35459	−0.0779257
$914$	−35.5941	−1.17735
$915$	−30.0293	−0.992739
$916$	3.86521	0.127710
$917$	−10.1857	−0.336361
$918$	11.3973	0.376166
$919$	−28.0448	−0.925111	−0.462556	−	0.886590i	$-0.653067\pi$
$919$	−28.0448	−0.925111	−0.462556	+	0.886590i	$0.653067\pi$
$920$	−36.7770	−1.21250
$921$	2.33304	0.0768761
$922$	−33.5353	−1.10442
$923$	9.65640	0.317844
$924$	−0.392001	−0.0128959
$925$	−7.30156	−0.240074
$926$	−10.8132	−0.355343
$927$	−8.69531	−0.285591
$928$	−8.58340	−0.281764
$929$	−50.8036	−1.66681	−0.833406	−	0.552662i	$-0.813612\pi$
$929$	−50.8036	−1.66681	−0.833406	+	0.552662i	$0.813612\pi$
$930$	−5.06744	−0.166168
$931$	3.24885	0.106477
$932$	5.41592	0.177404
$933$	−0.675512	−0.0221153
$934$	−4.50516	−0.147413
$935$	−27.7984	−0.909105
$936$	10.7583	0.351645
$937$	30.2345	0.987719	0.493860	−	0.869542i	$-0.335586\pi$
$937$	30.2345	0.987719	0.493860	+	0.869542i	$0.335586\pi$
$938$	−1.08805	−0.0355261
$939$	−6.63228	−0.216436
$940$	−0.516911	−0.0168598
$941$	22.7086	0.740280	0.370140	−	0.928976i	$-0.379310\pi$
$941$	22.7086	0.740280	0.370140	+	0.928976i	$0.379310\pi$
$942$	−8.32560	−0.271263
$943$	63.7008	2.07438
$944$	2.24474	0.0730601
$945$	2.04744	0.0666033
$946$	−6.02059	−0.195746
$947$	48.8988	1.58900	0.794499	−	0.607265i	$-0.207733\pi$
$947$	48.8988	1.58900	0.794499	+	0.607265i	$0.207733\pi$
$948$	−1.55657	−0.0505550
$949$	−13.9170	−0.451766
$950$	−3.91188	−0.126918
$951$	−4.68652	−0.151971
$952$	−20.2779	−0.657210
$953$	−43.4704	−1.40814	−0.704072	−	0.710129i	$-0.748637\pi$
$953$	−43.4704	−1.40814	−0.704072	+	0.710129i	$0.748637\pi$
$954$	1.35481	0.0438635
$955$	9.75983	0.315821
$956$	2.85011	0.0921792
$957$	−12.2531	−0.396085
$958$	19.1734	0.619464
$959$	5.48349	0.177071
$960$	14.1939	0.458105
$961$	−28.2417	−0.911023
$962$	−54.6434	−1.76177
$963$	−17.3884	−0.560333
$964$	−3.88344	−0.125077
$965$	−15.7992	−0.508594
$966$	10.0958	0.324829
$967$	5.76371	0.185348	0.0926742	−	0.995696i	$-0.470458\pi$
$967$	5.76371	0.185348	0.0926742	+	0.995696i	$0.470458\pi$
$968$	20.8094	0.668841
$969$	24.8471	0.798203
$970$	−28.5482	−0.916628
$971$	42.8223	1.37423	0.687117	−	0.726547i	$-0.258876\pi$
$971$	42.8223	1.37423	0.687117	+	0.726547i	$0.258876\pi$
$972$	0.220813	0.00708257
$973$	−9.95792	−0.319236
$974$	−57.6018	−1.84568
$975$	3.27841	0.104993
$976$	64.4291	2.06232
$977$	−35.6861	−1.14170	−0.570850	−	0.821054i	$-0.693386\pi$
$977$	−35.6861	−1.14170	−0.570850	+	0.821054i	$0.693386\pi$
$978$	−18.1533	−0.580479
$979$	6.45264	0.206227
$980$	0.452102	0.0144419
$981$	13.0624	0.417050
$982$	−26.1003	−0.832895
$983$	15.2090	0.485092	0.242546	−	0.970140i	$-0.422017\pi$
$983$	15.2090	0.485092	0.242546	+	0.970140i	$0.422017\pi$
$984$	−24.9308	−0.794763
$985$	−4.10827	−0.130900
$986$	78.6650	2.50521
$987$	−1.14335	−0.0363933
$988$	−2.91085	−0.0926063
$989$	15.4172	0.490240
$990$	−5.41665	−0.172153
$991$	−12.7220	−0.404126	−0.202063	−	0.979373i	$-0.564765\pi$
$991$	−12.7220	−0.404126	−0.202063	+	0.979373i	$0.564765\pi$
$992$	2.06538	0.0655757
$993$	−6.07509	−0.192787
$994$	−3.54655	−0.112490
$995$	23.6124	0.748562
$996$	0.292871	0.00927999
$997$	−15.9043	−0.503695	−0.251847	−	0.967767i	$-0.581038\pi$
$997$	−15.9043	−0.503695	−0.251847	+	0.967767i	$0.581038\pi$
$998$	12.4326	0.393549
$999$	9.03684	0.285913

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.q.1.14	✓	19
3.2	odd	2		8001.2.a.v.1.6		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.q.1.14	✓	19	1.1	even	1	trivial
8001.2.a.v.1.6		19	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)

\(f(q)\)	\(=\)	\(q+1.49024 q^{2} +1.00000 q^{3} +0.220813 q^{4} +2.04744 q^{5} +1.49024 q^{6} +1.00000 q^{7} -2.65141 q^{8} +1.00000 q^{9} +3.05118 q^{10} -1.77527 q^{11} +0.220813 q^{12} -4.05756 q^{13} +1.49024 q^{14} +2.04744 q^{15} -4.39287 q^{16} +7.64794 q^{17} +1.49024 q^{18} +3.24885 q^{19} +0.452102 q^{20} +1.00000 q^{21} -2.64557 q^{22} +6.77465 q^{23} -2.65141 q^{24} -0.807977 q^{25} -6.04673 q^{26} +1.00000 q^{27} +0.220813 q^{28} +6.90210 q^{29} +3.05118 q^{30} -1.66081 q^{31} -1.24359 q^{32} -1.77527 q^{33} +11.3973 q^{34} +2.04744 q^{35} +0.220813 q^{36} +9.03684 q^{37} +4.84157 q^{38} -4.05756 q^{39} -5.42862 q^{40} +9.40281 q^{41} +1.49024 q^{42} +2.27572 q^{43} -0.392001 q^{44} +2.04744 q^{45} +10.0958 q^{46} -1.14335 q^{47} -4.39287 q^{48} +1.00000 q^{49} -1.20408 q^{50} +7.64794 q^{51} -0.895961 q^{52} +0.909120 q^{53} +1.49024 q^{54} -3.63476 q^{55} -2.65141 q^{56} +3.24885 q^{57} +10.2858 q^{58} -0.510997 q^{59} +0.452102 q^{60} -14.6668 q^{61} -2.47501 q^{62} +1.00000 q^{63} +6.93248 q^{64} -8.30762 q^{65} -2.64557 q^{66} -0.730117 q^{67} +1.68876 q^{68} +6.77465 q^{69} +3.05118 q^{70} -2.37985 q^{71} -2.65141 q^{72} +3.42990 q^{73} +13.4671 q^{74} -0.807977 q^{75} +0.717389 q^{76} -1.77527 q^{77} -6.04673 q^{78} -7.04927 q^{79} -8.99415 q^{80} +1.00000 q^{81} +14.0124 q^{82} +1.32633 q^{83} +0.220813 q^{84} +15.6587 q^{85} +3.39137 q^{86} +6.90210 q^{87} +4.70696 q^{88} -3.63475 q^{89} +3.05118 q^{90} -4.05756 q^{91} +1.49593 q^{92} -1.66081 q^{93} -1.70387 q^{94} +6.65185 q^{95} -1.24359 q^{96} -9.35645 q^{97} +1.49024 q^{98} -1.77527 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20}+ \cdots - 9 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more