LMFDB - Embedded newform 483.2.a.j.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(1,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,2,-4,4,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.15317.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 2 $ x^4 - 2x^3 - 4x^2 + 5*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.32973$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.32973 q^{2} -1.00000 q^{3} -0.231826 q^{4} +3.17434 q^{5} -1.32973 q^{6} -1.00000 q^{7} -2.96772 q^{8} +1.00000 q^{9} +4.22101 q^{10} +5.06562 q^{11} +0.231826 q^{12} +4.07644 q^{13} -1.32973 q^{14} -3.17434 q^{15} -3.48261 q^{16} +4.22101 q^{17} +1.32973 q^{18} -5.06562 q^{19} -0.735894 q^{20} +1.00000 q^{21} +6.73589 q^{22} +1.00000 q^{23} +2.96772 q^{24} +5.07644 q^{25} +5.42055 q^{26} -1.00000 q^{27} +0.231826 q^{28} +6.68466 q^{29} -4.22101 q^{30} -2.22101 q^{31} +1.30452 q^{32} -5.06562 q^{33} +5.61279 q^{34} -3.17434 q^{35} -0.231826 q^{36} -1.91023 q^{37} -6.73589 q^{38} -4.07644 q^{39} -9.42055 q^{40} -1.37639 q^{41} +1.32973 q^{42} -3.39535 q^{43} -1.17434 q^{44} +3.17434 q^{45} +1.32973 q^{46} -5.81484 q^{47} +3.48261 q^{48} +1.00000 q^{49} +6.75028 q^{50} -4.22101 q^{51} -0.945023 q^{52} -6.57594 q^{53} -1.32973 q^{54} +16.0800 q^{55} +2.96772 q^{56} +5.06562 q^{57} +8.88877 q^{58} -5.67027 q^{59} +0.735894 q^{60} -14.4862 q^{61} -2.95333 q^{62} -1.00000 q^{63} +8.69987 q^{64} +12.9400 q^{65} -6.73589 q^{66} +13.8842 q^{67} -0.978538 q^{68} -1.00000 q^{69} -4.22101 q^{70} -2.95333 q^{71} -2.96772 q^{72} -2.02520 q^{73} -2.54009 q^{74} -5.07644 q^{75} +1.17434 q^{76} -5.06562 q^{77} -5.42055 q^{78} +7.14831 q^{79} -11.0550 q^{80} +1.00000 q^{81} -1.83023 q^{82} -12.7226 q^{83} -0.231826 q^{84} +13.3989 q^{85} -4.51489 q^{86} -6.68466 q^{87} -15.0333 q^{88} -17.0629 q^{89} +4.22101 q^{90} -4.07644 q^{91} -0.231826 q^{92} +2.22101 q^{93} -7.73215 q^{94} -16.0800 q^{95} -1.30452 q^{96} +2.08977 q^{97} +1.32973 q^{98} +5.06562 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} + 4 q^{9} + 2 q^{10} + q^{11} - 4 q^{12} + 7 q^{13} - 2 q^{14} - 5 q^{15} + 8 q^{16} + 2 q^{17} + 2 q^{18} - q^{19} + 13 q^{20}+ \cdots + q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 + 4 * q^9 + 2 * q^10 + q^11 - 4 * q^12 + 7 * q^13 - 2 * q^14 - 5 * q^15 + 8 * q^16 + 2 * q^17 + 2 * q^18 - q^19 + 13 * q^20 + 4 * q^21 + 11 * q^22 + 4 * q^23 - 9 * q^24 + 11 * q^25 - 19 * q^26 - 4 * q^27 - 4 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 20 * q^32 - q^33 + 23 * q^34 - 5 * q^35 + 4 * q^36 + 16 * q^37 - 11 * q^38 - 7 * q^39 + 3 * q^40 + 5 * q^41 + 2 * q^42 + 9 * q^43 + 3 * q^44 + 5 * q^45 + 2 * q^46 - 21 * q^47 - 8 * q^48 + 4 * q^49 - 17 * q^50 - 2 * q^51 - 24 * q^52 + 10 * q^53 - 2 * q^54 + 17 * q^55 - 9 * q^56 + q^57 + q^58 - 26 * q^59 - 13 * q^60 + 2 * q^61 - 19 * q^62 - 4 * q^63 + 27 * q^64 + 26 * q^65 - 11 * q^66 + 5 * q^67 + 7 * q^68 - 4 * q^69 - 2 * q^70 - 19 * q^71 + 9 * q^72 + 10 * q^73 + 9 * q^74 - 11 * q^75 - 3 * q^76 - q^77 + 19 * q^78 - 6 * q^79 - 24 * q^80 + 4 * q^81 - 31 * q^82 - 2 * q^83 + 4 * q^84 - 7 * q^85 - 17 * q^86 - 2 * q^87 - 20 * q^88 - 17 * q^89 + 2 * q^90 - 7 * q^91 + 4 * q^92 - 6 * q^93 - 44 * q^94 - 17 * q^95 - 20 * q^96 + 32 * q^97 + 2 * q^98 + 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 $

$2$	1.32973	0.940259	0.470130	−	0.882597i	$-0.344207\pi$
$2$	1.32973	0.940259	0.470130	+	0.882597i	$0.344207\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.231826	−0.115913
$5$	3.17434	1.41961	0.709804	−	0.704399i	$-0.248783\pi$
$5$	3.17434	1.41961	0.709804	+	0.704399i	$0.248783\pi$
$6$	−1.32973	−0.542859
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.96772	−1.04925
$9$	1.00000	0.333333
$10$	4.22101	1.33480
$11$	5.06562	1.52734	0.763671	−	0.645606i	$-0.223395\pi$
$11$	5.06562	1.52734	0.763671	+	0.645606i	$0.223395\pi$
$12$	0.231826	0.0669223
$13$	4.07644	1.13060	0.565300	−	0.824885i	$-0.308760\pi$
$13$	4.07644	1.13060	0.565300	+	0.824885i	$0.308760\pi$
$14$	−1.32973	−0.355385
$15$	−3.17434	−0.819611
$16$	−3.48261	−0.870651
$17$	4.22101	1.02374	0.511872	−	0.859062i	$-0.328952\pi$
$17$	4.22101	1.02374	0.511872	+	0.859062i	$0.328952\pi$
$18$	1.32973	0.313420
$19$	−5.06562	−1.16213	−0.581067	−	0.813856i	$-0.697364\pi$
$19$	−5.06562	−1.16213	−0.581067	+	0.813856i	$0.697364\pi$
$20$	−0.735894	−0.164551
$21$	1.00000	0.218218
$22$	6.73589	1.43610
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.96772	0.605783
$25$	5.07644	1.01529
$26$	5.42055	1.06306
$27$	−1.00000	−0.192450
$28$	0.231826	0.0438109
$29$	6.68466	1.24131	0.620655	−	0.784084i	$-0.286867\pi$
$29$	6.68466	1.24131	0.620655	+	0.784084i	$0.286867\pi$
$30$	−4.22101	−0.770647
$31$	−2.22101	−0.398905	−0.199452	−	0.979908i	$-0.563916\pi$
$31$	−2.22101	−0.398905	−0.199452	+	0.979908i	$0.563916\pi$
$32$	1.30452	0.230609
$33$	−5.06562	−0.881811
$34$	5.61279	0.962585
$35$	−3.17434	−0.536562
$36$	−0.231826	−0.0386376
$37$	−1.91023	−0.314041	−0.157020	−	0.987595i	$-0.550189\pi$
$37$	−1.91023	−0.314041	−0.157020	+	0.987595i	$0.550189\pi$
$38$	−6.73589	−1.09271
$39$	−4.07644	−0.652753
$40$	−9.42055	−1.48952
$41$	−1.37639	−0.214957	−0.107478	−	0.994207i	$-0.534278\pi$
$41$	−1.37639	−0.214957	−0.107478	+	0.994207i	$0.534278\pi$
$42$	1.32973	0.205181
$43$	−3.39535	−0.517786	−0.258893	−	0.965906i	$-0.583358\pi$
$43$	−3.39535	−0.517786	−0.258893	+	0.965906i	$0.583358\pi$
$44$	−1.17434	−0.177039
$45$	3.17434	0.473203
$46$	1.32973	0.196058
$47$	−5.81484	−0.848182	−0.424091	−	0.905620i	$-0.639406\pi$
$47$	−5.81484	−0.848182	−0.424091	+	0.905620i	$0.639406\pi$
$48$	3.48261	0.502671
$49$	1.00000	0.142857
$50$	6.75028	0.954634
$51$	−4.22101	−0.591059
$52$	−0.945023	−0.131051
$53$	−6.57594	−0.903275	−0.451637	−	0.892202i	$-0.649160\pi$
$53$	−6.57594	−0.903275	−0.451637	+	0.892202i	$0.649160\pi$
$54$	−1.32973	−0.180953
$55$	16.0800	2.16823
$56$	2.96772	0.396578
$57$	5.06562	0.670958
$58$	8.88877	1.16715
$59$	−5.67027	−0.738207	−0.369103	−	0.929388i	$-0.620335\pi$
$59$	−5.67027	−0.738207	−0.369103	+	0.929388i	$0.620335\pi$
$60$	0.735894	0.0950035
$61$	−14.4862	−1.85476	−0.927382	−	0.374115i	$-0.877946\pi$
$61$	−14.4862	−1.85476	−0.927382	+	0.374115i	$0.877946\pi$
$62$	−2.95333	−0.375074
$63$	−1.00000	−0.125988
$64$	8.69987	1.08748
$65$	12.9400	1.60501
$66$	−6.73589	−0.829131
$67$	13.8842	1.69623	0.848113	−	0.529816i	$-0.177739\pi$
$67$	13.8842	1.69623	0.848113	+	0.529816i	$0.177739\pi$
$68$	−0.978538	−0.118665
$69$	−1.00000	−0.120386
$70$	−4.22101	−0.504507
$71$	−2.95333	−0.350496	−0.175248	−	0.984524i	$-0.556073\pi$
$71$	−2.95333	−0.350496	−0.175248	+	0.984524i	$0.556073\pi$
$72$	−2.96772	−0.349749
$73$	−2.02520	−0.237032	−0.118516	−	0.992952i	$-0.537814\pi$
$73$	−2.02520	−0.237032	−0.118516	+	0.992952i	$0.537814\pi$
$74$	−2.54009	−0.295280
$75$	−5.07644	−0.586177
$76$	1.17434	0.134706
$77$	−5.06562	−0.577281
$78$	−5.42055	−0.613757
$79$	7.14831	0.804248	0.402124	−	0.915585i	$-0.368272\pi$
$79$	7.14831	0.804248	0.402124	+	0.915585i	$0.368272\pi$
$80$	−11.0550	−1.23598
$81$	1.00000	0.111111
$82$	−1.83023	−0.202115
$83$	−12.7226	−1.39648	−0.698242	−	0.715862i	$-0.746034\pi$
$83$	−12.7226	−1.39648	−0.698242	+	0.715862i	$0.746034\pi$
$84$	−0.231826	−0.0252943
$85$	13.3989	1.45332
$86$	−4.51489	−0.486853
$87$	−6.68466	−0.716671
$88$	−15.0333	−1.60256
$89$	−17.0629	−1.80867	−0.904334	−	0.426826i	$-0.859632\pi$
$89$	−17.0629	−1.80867	−0.904334	+	0.426826i	$0.859632\pi$
$90$	4.22101	0.444933
$91$	−4.07644	−0.427327
$92$	−0.231826	−0.0241695
$93$	2.22101	0.230308
$94$	−7.73215	−0.797511
$95$	−16.0800	−1.64977
$96$	−1.30452	−0.133142
$97$	2.08977	0.212184	0.106092	−	0.994356i	$-0.466166\pi$
$97$	2.08977	0.212184	0.106092	+	0.994356i	$0.466166\pi$
$98$	1.32973	0.134323
$99$	5.06562	0.509114
$100$	−1.17685	−0.117685
$101$	13.4312	1.33645	0.668227	−	0.743957i	$-0.267054\pi$
$101$	13.4312	1.33645	0.668227	+	0.743957i	$0.267054\pi$
$102$	−5.61279	−0.555749
$103$	2.72964	0.268960	0.134480	−	0.990916i	$-0.457064\pi$
$103$	2.72964	0.268960	0.134480	+	0.990916i	$0.457064\pi$
$104$	−12.0977	−1.18628
$105$	3.17434	0.309784
$106$	−8.74420	−0.849312
$107$	−2.36558	−0.228689	−0.114344	−	0.993441i	$-0.536477\pi$
$107$	−2.36558	−0.228689	−0.114344	+	0.993441i	$0.536477\pi$
$108$	0.231826	0.0223074
$109$	−18.1179	−1.73538	−0.867691	−	0.497104i	$-0.834397\pi$
$109$	−18.1179	−1.73538	−0.867691	+	0.497104i	$0.834397\pi$
$110$	21.3820	2.03870
$111$	1.91023	0.181311
$112$	3.48261	0.329075
$113$	−6.08001	−0.571959	−0.285979	−	0.958236i	$-0.592319\pi$
$113$	−6.08001	−0.571959	−0.285979	+	0.958236i	$0.592319\pi$
$114$	6.73589	0.630874
$115$	3.17434	0.296009
$116$	−1.54968	−0.143884
$117$	4.07644	0.376867
$118$	−7.53992	−0.694106
$119$	−4.22101	−0.386939
$120$	9.42055	0.859975
$121$	14.6605	1.33277
$122$	−19.2627	−1.74396
$123$	1.37639	0.124105
$124$	0.514886	0.0462382
$125$	0.242644	0.0217027
$126$	−1.32973	−0.118462
$127$	5.42763	0.481624	0.240812	−	0.970572i	$-0.422586\pi$
$127$	5.42763	0.481624	0.240812	+	0.970572i	$0.422586\pi$
$128$	8.95941	0.791907
$129$	3.39535	0.298944
$130$	17.2067	1.50913
$131$	−0.585698	−0.0511727	−0.0255863	−	0.999673i	$-0.508145\pi$
$131$	−0.585698	−0.0511727	−0.0255863	+	0.999673i	$0.508145\pi$
$132$	1.17434	0.102213
$133$	5.06562	0.439245
$134$	18.4622	1.59489
$135$	−3.17434	−0.273204
$136$	−12.5268	−1.07416
$137$	19.6605	1.67971	0.839856	−	0.542810i	$-0.182640\pi$
$137$	19.6605	1.67971	0.839856	+	0.542810i	$0.182640\pi$
$138$	−1.32973	−0.113194
$139$	−9.98667	−0.847059	−0.423529	−	0.905882i	$-0.639209\pi$
$139$	−9.98667	−0.847059	−0.423529	+	0.905882i	$0.639209\pi$
$140$	0.735894	0.0621944
$141$	5.81484	0.489698
$142$	−3.92713	−0.329557
$143$	20.6497	1.72681
$144$	−3.48261	−0.290217
$145$	21.2194	1.76217
$146$	−2.69297	−0.222872
$147$	−1.00000	−0.0824786
$148$	0.442841	0.0364013
$149$	2.01064	0.164718	0.0823592	−	0.996603i	$-0.473755\pi$
$149$	2.01064	0.164718	0.0823592	+	0.996603i	$0.473755\pi$
$150$	−6.75028	−0.551158
$151$	−7.43951	−0.605418	−0.302709	−	0.953083i	$-0.597891\pi$
$151$	−7.43951	−0.605418	−0.302709	+	0.953083i	$0.597891\pi$
$152$	15.0333	1.21936
$153$	4.22101	0.341248
$154$	−6.73589	−0.542794
$155$	−7.05023	−0.566288
$156$	0.945023	0.0756624
$157$	17.5041	1.39698	0.698488	−	0.715621i	$-0.253856\pi$
$157$	17.5041	1.39698	0.698488	+	0.715621i	$0.253856\pi$
$158$	9.50530	0.756201
$159$	6.57594	0.521506
$160$	4.14100	0.327375
$161$	−1.00000	−0.0788110
$162$	1.32973	0.104473
$163$	−3.95439	−0.309732	−0.154866	−	0.987935i	$-0.549495\pi$
$163$	−3.95439	−0.309732	−0.154866	+	0.987935i	$0.549495\pi$
$164$	0.319083	0.0249162
$165$	−16.0800	−1.25183
$166$	−16.9175	−1.31306
$167$	−3.08726	−0.238899	−0.119450	−	0.992840i	$-0.538113\pi$
$167$	−3.08726	−0.238899	−0.119450	+	0.992840i	$0.538113\pi$
$168$	−2.96772	−0.228965
$169$	3.61736	0.278258
$170$	17.8169	1.36649
$171$	−5.06562	−0.387378
$172$	0.787129	0.0600180
$173$	−23.9265	−1.81910	−0.909549	−	0.415596i	$-0.863573\pi$
$173$	−23.9265	−1.81910	−0.909549	+	0.415596i	$0.863573\pi$
$174$	−8.88877	−0.673856
$175$	−5.07644	−0.383743
$176$	−17.6416	−1.32978
$177$	5.67027	0.426204
$178$	−22.6891	−1.70062
$179$	−17.5014	−1.30811	−0.654057	−	0.756445i	$-0.726935\pi$
$179$	−17.5014	−1.30811	−0.654057	+	0.756445i	$0.726935\pi$
$180$	−0.735894	−0.0548503
$181$	14.9738	1.11299	0.556497	−	0.830850i	$-0.312145\pi$
$181$	14.9738	1.11299	0.556497	+	0.830850i	$0.312145\pi$
$182$	−5.42055	−0.401798
$183$	14.4862	1.07085
$184$	−2.96772	−0.218783
$185$	−6.06373	−0.445815
$186$	2.95333	0.216549
$187$	21.3820	1.56361
$188$	1.34803	0.0983151
$189$	1.00000	0.0727393
$190$	−21.3820	−1.55121
$191$	15.4395	1.11716	0.558582	−	0.829449i	$-0.311346\pi$
$191$	15.4395	1.11716	0.558582	+	0.829449i	$0.311346\pi$
$192$	−8.69987	−0.627859
$193$	17.4395	1.25532	0.627662	−	0.778486i	$-0.284012\pi$
$193$	17.4395	1.25532	0.627662	+	0.778486i	$0.284012\pi$
$194$	2.77882	0.199508
$195$	−12.9400	−0.926653
$196$	−0.231826	−0.0165590
$197$	22.1698	1.57953	0.789765	−	0.613409i	$-0.210202\pi$
$197$	22.1698	1.57953	0.789765	+	0.613409i	$0.210202\pi$
$198$	6.73589	0.478699
$199$	14.9246	1.05798	0.528989	−	0.848629i	$-0.322571\pi$
$199$	14.9246	1.05798	0.528989	+	0.848629i	$0.322571\pi$
$200$	−15.0654	−1.06529
$201$	−13.8842	−0.979316
$202$	17.8598	1.25661
$203$	−6.68466	−0.469171
$204$	0.978538	0.0685113
$205$	−4.36914	−0.305154
$206$	3.62968	0.252892
$207$	1.00000	0.0695048
$208$	−14.1966	−0.984359
$209$	−25.6605	−1.77497
$210$	4.22101	0.291277
$211$	−3.70880	−0.255325	−0.127662	−	0.991818i	$-0.540747\pi$
$211$	−3.70880	−0.255325	−0.127662	+	0.991818i	$0.540747\pi$
$212$	1.52447	0.104701
$213$	2.95333	0.202359
$214$	−3.14557	−0.215027
$215$	−10.7780	−0.735053
$216$	2.96772	0.201928
$217$	2.22101	0.150772
$218$	−24.0919	−1.63171
$219$	2.02520	0.136851
$220$	−3.72776	−0.251325
$221$	17.2067	1.15745
$222$	2.54009	0.170480
$223$	5.71883	0.382961	0.191480	−	0.981496i	$-0.438671\pi$
$223$	5.71883	0.382961	0.191480	+	0.981496i	$0.438671\pi$
$224$	−1.30452	−0.0871621
$225$	5.07644	0.338429
$226$	−8.08475	−0.537790
$227$	26.5437	1.76176	0.880882	−	0.473336i	$-0.156950\pi$
$227$	26.5437	1.76176	0.880882	+	0.473336i	$0.156950\pi$
$228$	−1.17434	−0.0777726
$229$	−3.70818	−0.245044	−0.122522	−	0.992466i	$-0.539098\pi$
$229$	−3.70818	−0.245044	−0.122522	+	0.992466i	$0.539098\pi$
$230$	4.22101	0.278325
$231$	5.06562	0.333293
$232$	−19.8382	−1.30244
$233$	22.1950	1.45404	0.727021	−	0.686616i	$-0.240904\pi$
$233$	22.1950	1.45404	0.727021	+	0.686616i	$0.240904\pi$
$234$	5.42055	0.354353
$235$	−18.4583	−1.20409
$236$	1.31451	0.0855676
$237$	−7.14831	−0.464333
$238$	−5.61279	−0.363823
$239$	−20.2921	−1.31259	−0.656293	−	0.754506i	$-0.727876\pi$
$239$	−20.2921	−1.31259	−0.656293	+	0.754506i	$0.727876\pi$
$240$	11.0550	0.713596
$241$	14.5158	0.935043	0.467522	−	0.883982i	$-0.345147\pi$
$241$	14.5158	0.935043	0.467522	+	0.883982i	$0.345147\pi$
$242$	19.4945	1.25315
$243$	−1.00000	−0.0641500
$244$	3.35827	0.214991
$245$	3.17434	0.202801
$246$	1.83023	0.116691
$247$	−20.6497	−1.31391
$248$	6.59133	0.418550
$249$	12.7226	0.806260
$250$	0.322650	0.0204062
$251$	4.03791	0.254871	0.127435	−	0.991847i	$-0.459325\pi$
$251$	4.03791	0.254871	0.127435	+	0.991847i	$0.459325\pi$
$252$	0.231826	0.0146036
$253$	5.06562	0.318473
$254$	7.21727	0.452852
$255$	−13.3989	−0.839073
$256$	−5.48617	−0.342886
$257$	−16.7676	−1.04593	−0.522966	−	0.852354i	$-0.675174\pi$
$257$	−16.7676	−1.04593	−0.522966	+	0.852354i	$0.675174\pi$
$258$	4.51489	0.281085
$259$	1.91023	0.118696
$260$	−2.99983	−0.186041
$261$	6.68466	0.413770
$262$	−0.778818	−0.0481156
$263$	−22.0308	−1.35848	−0.679240	−	0.733917i	$-0.737690\pi$
$263$	−22.0308	−1.35848	−0.679240	+	0.733917i	$0.737690\pi$
$264$	15.0333	0.925238
$265$	−20.8743	−1.28230
$266$	6.73589	0.413004
$267$	17.0629	1.04423
$268$	−3.21871	−0.196614
$269$	−17.9902	−1.09688	−0.548442	−	0.836188i	$-0.684779\pi$
$269$	−17.9902	−1.09688	−0.548442	+	0.836188i	$0.684779\pi$
$270$	−4.22101	−0.256882
$271$	0.940007	0.0571014	0.0285507	−	0.999592i	$-0.490911\pi$
$271$	0.940007	0.0571014	0.0285507	+	0.999592i	$0.490911\pi$
$272$	−14.7001	−0.891325
$273$	4.07644	0.246717
$274$	26.1431	1.57936
$275$	25.7153	1.55069
$276$	0.231826	0.0139543
$277$	3.73339	0.224317	0.112159	−	0.993690i	$-0.464223\pi$
$277$	3.73339	0.224317	0.112159	+	0.993690i	$0.464223\pi$
$278$	−13.2796	−0.796455
$279$	−2.22101	−0.132968
$280$	9.42055	0.562986
$281$	21.7180	1.29559	0.647794	−	0.761816i	$-0.275692\pi$
$281$	21.7180	1.29559	0.647794	+	0.761816i	$0.275692\pi$
$282$	7.73215	0.460443
$283$	−24.0534	−1.42982	−0.714912	−	0.699215i	$-0.753533\pi$
$283$	−24.0534	−1.42982	−0.714912	+	0.699215i	$0.753533\pi$
$284$	0.684658	0.0406270
$285$	16.0800	0.952497
$286$	27.4585	1.62365
$287$	1.37639	0.0812459
$288$	1.30452	0.0768698
$289$	0.816901	0.0480530
$290$	28.2160	1.65690
$291$	−2.08977	−0.122504
$292$	0.469494	0.0274751
$293$	24.0021	1.40222	0.701109	−	0.713054i	$-0.252688\pi$
$293$	24.0021	1.40222	0.701109	+	0.713054i	$0.252688\pi$
$294$	−1.32973	−0.0775513
$295$	−17.9994	−1.04796
$296$	5.66904	0.329506
$297$	−5.06562	−0.293937
$298$	2.67361	0.154878
$299$	4.07644	0.235747
$300$	1.17685	0.0679454
$301$	3.39535	0.195705
$302$	−9.89251	−0.569250
$303$	−13.4312	−0.771602
$304$	17.6416	1.01181
$305$	−45.9840	−2.63304
$306$	5.61279	0.320862
$307$	31.9678	1.82450	0.912249	−	0.409637i	$-0.134345\pi$
$307$	31.9678	1.82450	0.912249	+	0.409637i	$0.134345\pi$
$308$	1.17434	0.0669143
$309$	−2.72964	−0.155284
$310$	−9.37489	−0.532458
$311$	−21.1889	−1.20151	−0.600756	−	0.799432i	$-0.705134\pi$
$311$	−21.1889	−1.20151	−0.600756	+	0.799432i	$0.705134\pi$
$312$	12.0977	0.684899
$313$	−14.3935	−0.813567	−0.406783	−	0.913525i	$-0.633350\pi$
$313$	−14.3935	−0.813567	−0.406783	+	0.913525i	$0.633350\pi$
$314$	23.2756	1.31352
$315$	−3.17434	−0.178854
$316$	−1.65716	−0.0932226
$317$	−24.3516	−1.36772	−0.683862	−	0.729612i	$-0.739701\pi$
$317$	−24.3516	−1.36772	−0.683862	+	0.729612i	$0.739701\pi$
$318$	8.74420	0.490351
$319$	33.8619	1.89590
$320$	27.6164	1.54380
$321$	2.36558	0.132034
$322$	−1.32973	−0.0741028
$323$	−21.3820	−1.18973
$324$	−0.231826	−0.0128792
$325$	20.6938	1.14789
$326$	−5.25826	−0.291228
$327$	18.1179	1.00192
$328$	4.08475	0.225543
$329$	5.81484	0.320583
$330$	−21.3820	−1.17704
$331$	−9.09082	−0.499677	−0.249838	−	0.968288i	$-0.580378\pi$
$331$	−9.09082	−0.499677	−0.249838	+	0.968288i	$0.580378\pi$
$332$	2.94942	0.161870
$333$	−1.91023	−0.104680
$334$	−4.10521	−0.224627
$335$	44.0732	2.40798
$336$	−3.48261	−0.189992
$337$	−35.4620	−1.93174	−0.965870	−	0.259028i	$-0.916598\pi$
$337$	−35.4620	−1.93174	−0.965870	+	0.259028i	$0.916598\pi$
$338$	4.81010	0.261635
$339$	6.08001	0.330221
$340$	−3.10621	−0.168458
$341$	−11.2508	−0.609264
$342$	−6.73589	−0.364235
$343$	−1.00000	−0.0539949
$344$	10.0764	0.543285
$345$	−3.17434	−0.170901
$346$	−31.8157	−1.71042
$347$	−0.799628	−0.0429263	−0.0214631	−	0.999770i	$-0.506832\pi$
$347$	−0.799628	−0.0429263	−0.0214631	+	0.999770i	$0.506832\pi$
$348$	1.54968	0.0830713
$349$	1.20311	0.0644011	0.0322006	−	0.999481i	$-0.489748\pi$
$349$	1.20311	0.0644011	0.0322006	+	0.999481i	$0.489748\pi$
$350$	−6.75028	−0.360818
$351$	−4.07644	−0.217584
$352$	6.60822	0.352219
$353$	−1.03334	−0.0549991	−0.0274996	−	0.999622i	$-0.508754\pi$
$353$	−1.03334	−0.0549991	−0.0274996	+	0.999622i	$0.508754\pi$
$354$	7.53992	0.400742
$355$	−9.37489	−0.497567
$356$	3.95563	0.209648
$357$	4.22101	0.223399
$358$	−23.2721	−1.22997
$359$	12.2329	0.645627	0.322813	−	0.946463i	$-0.395371\pi$
$359$	12.2329	0.645627	0.322813	+	0.946463i	$0.395371\pi$
$360$	−9.42055	−0.496507
$361$	6.66051	0.350553
$362$	19.9111	1.04650
$363$	−14.6605	−0.769477
$364$	0.945023	0.0495327
$365$	−6.42869	−0.336493
$366$	19.2627	1.00688
$367$	−20.0388	−1.04602	−0.523008	−	0.852328i	$-0.675190\pi$
$367$	−20.0388	−1.04602	−0.523008	+	0.852328i	$0.675190\pi$
$368$	−3.48261	−0.181543
$369$	−1.37639	−0.0716522
$370$	−8.06311	−0.419181
$371$	6.57594	0.341406
$372$	−0.514886	−0.0266956
$373$	−25.6803	−1.32968	−0.664838	−	0.746988i	$-0.731499\pi$
$373$	−25.6803	−1.32968	−0.664838	+	0.746988i	$0.731499\pi$
$374$	28.4323	1.47020
$375$	−0.242644	−0.0125301
$376$	17.2568	0.889952
$377$	27.2496	1.40343
$378$	1.32973	0.0683938
$379$	10.7782	0.553639	0.276819	−	0.960922i	$-0.410720\pi$
$379$	10.7782	0.553639	0.276819	+	0.960922i	$0.410720\pi$
$380$	3.72776	0.191230
$381$	−5.42763	−0.278066
$382$	20.5303	1.05042
$383$	16.2877	0.832262	0.416131	−	0.909305i	$-0.363386\pi$
$383$	16.2877	0.832262	0.416131	+	0.909305i	$0.363386\pi$
$384$	−8.95941	−0.457208
$385$	−16.0800	−0.819513
$386$	23.1898	1.18033
$387$	−3.39535	−0.172595
$388$	−0.484461	−0.0245948
$389$	22.2160	1.12640	0.563198	−	0.826322i	$-0.309571\pi$
$389$	22.2160	1.12640	0.563198	+	0.826322i	$0.309571\pi$
$390$	−17.2067	−0.871294
$391$	4.22101	0.213466
$392$	−2.96772	−0.149892
$393$	0.585698	0.0295445
$394$	29.4797	1.48517
$395$	22.6912	1.14172
$396$	−1.17434	−0.0590128
$397$	−25.3518	−1.27237	−0.636185	−	0.771536i	$-0.719489\pi$
$397$	−25.3518	−1.27237	−0.636185	+	0.771536i	$0.719489\pi$
$398$	19.8457	0.994774
$399$	−5.06562	−0.253598
$400$	−17.6792	−0.883962
$401$	−37.3622	−1.86578	−0.932891	−	0.360160i	$-0.882722\pi$
$401$	−37.3622	−1.86578	−0.932891	+	0.360160i	$0.882722\pi$
$402$	−18.4622	−0.920811
$403$	−9.05380	−0.451002
$404$	−3.11370	−0.154912
$405$	3.17434	0.157734
$406$	−8.88877	−0.441142
$407$	−9.67652	−0.479647
$408$	12.5268	0.620167
$409$	−29.7899	−1.47302	−0.736508	−	0.676429i	$-0.763527\pi$
$409$	−29.7899	−1.47302	−0.736508	+	0.676429i	$0.763527\pi$
$410$	−5.80977	−0.286924
$411$	−19.6605	−0.969782
$412$	−0.632801	−0.0311759
$413$	5.67027	0.279016
$414$	1.32973	0.0653525
$415$	−40.3858	−1.98246
$416$	5.31781	0.260727
$417$	9.98667	0.489050
$418$	−34.1215	−1.66894
$419$	−2.46784	−0.120562	−0.0602809	−	0.998181i	$-0.519200\pi$
$419$	−2.46784	−0.120562	−0.0602809	+	0.998181i	$0.519200\pi$
$420$	−0.735894	−0.0359079
$421$	−15.1942	−0.740519	−0.370260	−	0.928928i	$-0.620731\pi$
$421$	−15.1942	−0.740519	−0.370260	+	0.928928i	$0.620731\pi$
$422$	−4.93170	−0.240071
$423$	−5.81484	−0.282727
$424$	19.5155	0.947758
$425$	21.4277	1.03940
$426$	3.92713	0.190270
$427$	14.4862	0.701035
$428$	0.548401	0.0265080
$429$	−20.6497	−0.996977
$430$	−14.3318	−0.691140
$431$	−15.3289	−0.738369	−0.369184	−	0.929356i	$-0.620363\pi$
$431$	−15.3289	−0.738369	−0.369184	+	0.929356i	$0.620363\pi$
$432$	3.48261	0.167557
$433$	−1.93895	−0.0931799	−0.0465899	−	0.998914i	$-0.514835\pi$
$433$	−1.93895	−0.0931799	−0.0465899	+	0.998914i	$0.514835\pi$
$434$	2.95333	0.141765
$435$	−21.2194	−1.01739
$436$	4.20020	0.201153
$437$	−5.06562	−0.242322
$438$	2.69297	0.128675
$439$	4.04649	0.193129	0.0965643	−	0.995327i	$-0.469215\pi$
$439$	4.04649	0.193129	0.0965643	+	0.995327i	$0.469215\pi$
$440$	−47.7209	−2.27501
$441$	1.00000	0.0476190
$442$	22.8802	1.08830
$443$	17.8871	0.849844	0.424922	−	0.905230i	$-0.360302\pi$
$443$	17.8871	0.849844	0.424922	+	0.905230i	$0.360302\pi$
$444$	−0.442841	−0.0210163
$445$	−54.1636	−2.56760
$446$	7.60448	0.360082
$447$	−2.01064	−0.0951002
$448$	−8.69987	−0.411030
$449$	33.1765	1.56569	0.782847	−	0.622214i	$-0.213767\pi$
$449$	33.1765	1.56569	0.782847	+	0.622214i	$0.213767\pi$
$450$	6.75028	0.318211
$451$	−6.97229	−0.328312
$452$	1.40950	0.0662974
$453$	7.43951	0.349538
$454$	35.2958	1.65652
$455$	−12.9400	−0.606637
$456$	−15.0333	−0.704001
$457$	29.0828	1.36043	0.680217	−	0.733010i	$-0.261885\pi$
$457$	29.0828	1.36043	0.680217	+	0.733010i	$0.261885\pi$
$458$	−4.93087	−0.230404
$459$	−4.22101	−0.197020
$460$	−0.735894	−0.0343112
$461$	−33.3560	−1.55354	−0.776772	−	0.629782i	$-0.783144\pi$
$461$	−33.3560	−1.55354	−0.776772	+	0.629782i	$0.783144\pi$
$462$	6.73589	0.313382
$463$	−1.87795	−0.0872759	−0.0436380	−	0.999047i	$-0.513895\pi$
$463$	−1.87795	−0.0872759	−0.0436380	+	0.999047i	$0.513895\pi$
$464$	−23.2800	−1.08075
$465$	7.05023	0.326947
$466$	29.5133	1.36718
$467$	12.9275	0.598214	0.299107	−	0.954220i	$-0.403311\pi$
$467$	12.9275	0.598214	0.299107	+	0.954220i	$0.403311\pi$
$468$	−0.945023	−0.0436837
$469$	−13.8842	−0.641113
$470$	−24.5445	−1.13215
$471$	−17.5041	−0.806545
$472$	16.8278	0.774561
$473$	−17.1995	−0.790836
$474$	−9.50530	−0.436593
$475$	−25.7153	−1.17990
$476$	0.978538	0.0448512
$477$	−6.57594	−0.301092
$478$	−26.9829	−1.23417
$479$	−43.3983	−1.98292	−0.991459	−	0.130416i	$-0.958369\pi$
$479$	−43.3983	−1.98292	−0.991459	+	0.130416i	$0.958369\pi$
$480$	−4.14100	−0.189010
$481$	−7.78695	−0.355055
$482$	19.3020	0.879183
$483$	1.00000	0.0455016
$484$	−3.39868	−0.154486
$485$	6.63363	0.301218
$486$	−1.32973	−0.0603176
$487$	16.9992	0.770307	0.385154	−	0.922852i	$-0.374148\pi$
$487$	16.9992	0.770307	0.385154	+	0.922852i	$0.374148\pi$
$488$	42.9909	1.94611
$489$	3.95439	0.178824
$490$	4.22101	0.190686
$491$	10.9480	0.494075	0.247037	−	0.969006i	$-0.420543\pi$
$491$	10.9480	0.494075	0.247037	+	0.969006i	$0.420543\pi$
$492$	−0.319083	−0.0143854
$493$	28.2160	1.27078
$494$	−27.4585	−1.23541
$495$	16.0800	0.722743
$496$	7.73489	0.347307
$497$	2.95333	0.132475
$498$	16.9175	0.758093
$499$	30.3588	1.35904	0.679522	−	0.733655i	$-0.262187\pi$
$499$	30.3588	1.35904	0.679522	+	0.733655i	$0.262187\pi$
$500$	−0.0562511	−0.00251563
$501$	3.08726	0.137929
$502$	5.36932	0.239644
$503$	25.5951	1.14123	0.570614	−	0.821219i	$-0.306705\pi$
$503$	25.5951	1.14123	0.570614	+	0.821219i	$0.306705\pi$
$504$	2.96772	0.132193
$505$	42.6352	1.89724
$506$	6.73589	0.299447
$507$	−3.61736	−0.160652
$508$	−1.25826	−0.0558264
$509$	−8.95422	−0.396889	−0.198444	−	0.980112i	$-0.563589\pi$
$509$	−8.95422	−0.396889	−0.198444	+	0.980112i	$0.563589\pi$
$510$	−17.8169	−0.788946
$511$	2.02520	0.0895898
$512$	−25.2139	−1.11431
$513$	5.06562	0.223653
$514$	−22.2963	−0.983446
$515$	8.66482	0.381818
$516$	−0.787129	−0.0346514
$517$	−29.4558	−1.29546
$518$	2.54009	0.111605
$519$	23.9265	1.05026
$520$	−38.4023	−1.68405
$521$	15.9405	0.698364	0.349182	−	0.937055i	$-0.386459\pi$
$521$	15.9405	0.698364	0.349182	+	0.937055i	$0.386459\pi$
$522$	8.88877	0.389051
$523$	28.1102	1.22917	0.614587	−	0.788849i	$-0.289323\pi$
$523$	28.1102	1.22917	0.614587	+	0.788849i	$0.289323\pi$
$524$	0.135780	0.00593157
$525$	5.07644	0.221554
$526$	−29.2950	−1.27732
$527$	−9.37489	−0.408376
$528$	17.6416	0.767750
$529$	1.00000	0.0434783
$530$	−27.7571	−1.20569
$531$	−5.67027	−0.246069
$532$	−1.17434	−0.0509141
$533$	−5.61078	−0.243030
$534$	22.6891	0.981851
$535$	−7.50914	−0.324648
$536$	−41.2044	−1.77976
$537$	17.5014	0.755241
$538$	−23.9221	−1.03136
$539$	5.06562	0.218192
$540$	0.735894	0.0316678
$541$	31.5707	1.35733	0.678666	−	0.734447i	$-0.262558\pi$
$541$	31.5707	1.35733	0.678666	+	0.734447i	$0.262558\pi$
$542$	1.24995	0.0536901
$543$	−14.9738	−0.642587
$544$	5.50640	0.236085
$545$	−57.5124	−2.46356
$546$	5.42055	0.231978
$547$	−37.7639	−1.61467	−0.807333	−	0.590096i	$-0.799090\pi$
$547$	−37.7639	−1.61467	−0.807333	+	0.590096i	$0.799090\pi$
$548$	−4.55781	−0.194700
$549$	−14.4862	−0.618255
$550$	34.1944	1.45805
$551$	−33.8619	−1.44257
$552$	2.96772	0.126315
$553$	−7.14831	−0.303977
$554$	4.96438	0.210916
$555$	6.06373	0.257391
$556$	2.31517	0.0981849
$557$	11.1660	0.473120	0.236560	−	0.971617i	$-0.423980\pi$
$557$	11.1660	0.473120	0.236560	+	0.971617i	$0.423980\pi$
$558$	−2.95333	−0.125025
$559$	−13.8409	−0.585409
$560$	11.0550	0.467158
$561$	−21.3820	−0.902750
$562$	28.8790	1.21819
$563$	−22.5943	−0.952235	−0.476117	−	0.879382i	$-0.657956\pi$
$563$	−22.5943	−0.952235	−0.476117	+	0.879382i	$0.657956\pi$
$564$	−1.34803	−0.0567623
$565$	−19.3000	−0.811958
$566$	−31.9844	−1.34440
$567$	−1.00000	−0.0419961
$568$	8.76466	0.367757
$569$	−40.4210	−1.69454	−0.847268	−	0.531166i	$-0.821754\pi$
$569$	−40.4210	−1.69454	−0.847268	+	0.531166i	$0.821754\pi$
$570$	21.3820	0.895594
$571$	−17.1859	−0.719206	−0.359603	−	0.933105i	$-0.617088\pi$
$571$	−17.1859	−0.719206	−0.359603	+	0.933105i	$0.617088\pi$
$572$	−4.78713	−0.200160
$573$	−15.4395	−0.644995
$574$	1.83023	0.0763922
$575$	5.07644	0.211702
$576$	8.69987	0.362495
$577$	31.1465	1.29665	0.648323	−	0.761365i	$-0.275471\pi$
$577$	31.1465	1.29665	0.648323	+	0.761365i	$0.275471\pi$
$578$	1.08626	0.0451823
$579$	−17.4395	−0.724761
$580$	−4.91920	−0.204259
$581$	12.7226	0.527821
$582$	−2.77882	−0.115186
$583$	−33.3112	−1.37961
$584$	6.01024	0.248705
$585$	12.9400	0.535003
$586$	31.9163	1.31845
$587$	−11.0144	−0.454612	−0.227306	−	0.973823i	$-0.572992\pi$
$587$	−11.0144	−0.454612	−0.227306	+	0.973823i	$0.572992\pi$
$588$	0.231826	0.00956033
$589$	11.2508	0.463580
$590$	−23.9343	−0.985358
$591$	−22.1698	−0.911943
$592$	6.65259	0.273420
$593$	−11.6009	−0.476392	−0.238196	−	0.971217i	$-0.576556\pi$
$593$	−11.6009	−0.476392	−0.238196	+	0.971217i	$0.576556\pi$
$594$	−6.73589	−0.276377
$595$	−13.3989	−0.549302
$596$	−0.466119	−0.0190930
$597$	−14.9246	−0.610824
$598$	5.42055	0.221663
$599$	−10.1410	−0.414350	−0.207175	−	0.978304i	$-0.566427\pi$
$599$	−10.1410	−0.414350	−0.207175	+	0.978304i	$0.566427\pi$
$600$	15.0654	0.615044
$601$	39.1210	1.59578	0.797890	−	0.602803i	$-0.205949\pi$
$601$	39.1210	1.59578	0.797890	+	0.602803i	$0.205949\pi$
$602$	4.51489	0.184013
$603$	13.8842	0.565408
$604$	1.72467	0.0701758
$605$	46.5375	1.89202
$606$	−17.8598	−0.725506
$607$	13.8211	0.560981	0.280490	−	0.959857i	$-0.409503\pi$
$607$	13.8211	0.560981	0.280490	+	0.959857i	$0.409503\pi$
$608$	−6.60822	−0.267999
$609$	6.68466	0.270876
$610$	−61.1462	−2.47574
$611$	−23.7038	−0.958955
$612$	−0.978538	−0.0395550
$613$	41.6282	1.68135	0.840674	−	0.541541i	$-0.182159\pi$
$613$	41.6282	1.68135	0.840674	+	0.541541i	$0.182159\pi$
$614$	42.5084	1.71550
$615$	4.36914	0.176181
$616$	15.0333	0.605711
$617$	2.31552	0.0932192	0.0466096	−	0.998913i	$-0.485158\pi$
$617$	2.31552	0.0932192	0.0466096	+	0.998913i	$0.485158\pi$
$618$	−3.62968	−0.146007
$619$	18.3318	0.736817	0.368408	−	0.929664i	$-0.379903\pi$
$619$	18.3318	0.736817	0.368408	+	0.929664i	$0.379903\pi$
$620$	1.63442	0.0656401
$621$	−1.00000	−0.0401286
$622$	−28.1755	−1.12973
$623$	17.0629	0.683612
$624$	14.1966	0.568320
$625$	−24.6120	−0.984478
$626$	−19.1394	−0.764963
$627$	25.6605	1.02478
$628$	−4.05789	−0.161928
$629$	−8.06311	−0.321497
$630$	−4.22101	−0.168169
$631$	37.9644	1.51134	0.755670	−	0.654953i	$-0.227312\pi$
$631$	37.9644	1.51134	0.755670	+	0.654953i	$0.227312\pi$
$632$	−21.2142	−0.843855
$633$	3.70880	0.147412
$634$	−32.3810	−1.28601
$635$	17.2291	0.683718
$636$	−1.52447	−0.0604492
$637$	4.07644	0.161514
$638$	45.0271	1.78264
$639$	−2.95333	−0.116832
$640$	28.4402	1.12420
$641$	5.55174	0.219280	0.109640	−	0.993971i	$-0.465030\pi$
$641$	5.55174	0.219280	0.109640	+	0.993971i	$0.465030\pi$
$642$	3.14557	0.124146
$643$	39.2894	1.54942	0.774711	−	0.632316i	$-0.217895\pi$
$643$	39.2894	1.54942	0.774711	+	0.632316i	$0.217895\pi$
$644$	0.231826	0.00913521
$645$	10.7780	0.424383
$646$	−28.4323	−1.11865
$647$	18.4287	0.724506	0.362253	−	0.932080i	$-0.382008\pi$
$647$	18.4287	0.724506	0.362253	+	0.932080i	$0.382008\pi$
$648$	−2.96772	−0.116583
$649$	−28.7235	−1.12749
$650$	27.5171	1.07931
$651$	−2.22101	−0.0870481
$652$	0.916730	0.0359019
$653$	42.2708	1.65418	0.827092	−	0.562067i	$-0.189994\pi$
$653$	42.2708	1.65418	0.827092	+	0.562067i	$0.189994\pi$
$654$	24.0919	0.942067
$655$	−1.85920	−0.0726451
$656$	4.79344	0.187152
$657$	−2.02520	−0.0790107
$658$	7.73215	0.301431
$659$	47.9174	1.86660	0.933298	−	0.359103i	$-0.116917\pi$
$659$	47.9174	1.86660	0.933298	+	0.359103i	$0.116917\pi$
$660$	3.72776	0.145103
$661$	17.9334	0.697528	0.348764	−	0.937211i	$-0.386602\pi$
$661$	17.9334	0.697528	0.348764	+	0.937211i	$0.386602\pi$
$662$	−12.0883	−0.469826
$663$	−17.2067	−0.668252
$664$	37.7570	1.46526
$665$	16.0800	0.623556
$666$	−2.54009	−0.0984265
$667$	6.68466	0.258831
$668$	0.715705	0.0276915
$669$	−5.71883	−0.221103
$670$	58.6053	2.26412
$671$	−73.3815	−2.83286
$672$	1.30452	0.0503231
$673$	−30.4174	−1.17251	−0.586253	−	0.810128i	$-0.699397\pi$
$673$	−30.4174	−1.17251	−0.586253	+	0.810128i	$0.699397\pi$
$674$	−47.1548	−1.81634
$675$	−5.07644	−0.195392
$676$	−0.838596	−0.0322537
$677$	31.1083	1.19559	0.597795	−	0.801649i	$-0.296044\pi$
$677$	31.1083	1.19559	0.597795	+	0.801649i	$0.296044\pi$
$678$	8.08475	0.310493
$679$	−2.08977	−0.0801978
$680$	−39.7642	−1.52489
$681$	−26.5437	−1.01716
$682$	−14.9605	−0.572866
$683$	41.1267	1.57367	0.786834	−	0.617164i	$-0.211719\pi$
$683$	41.1267	1.57367	0.786834	+	0.617164i	$0.211719\pi$
$684$	1.17434	0.0449020
$685$	62.4092	2.38453
$686$	−1.32973	−0.0507692
$687$	3.70818	0.141476
$688$	11.8247	0.450811
$689$	−26.8064	−1.02124
$690$	−4.22101	−0.160691
$691$	−15.1725	−0.577191	−0.288595	−	0.957451i	$-0.593188\pi$
$691$	−15.1725	−0.577191	−0.288595	+	0.957451i	$0.593188\pi$
$692$	5.54678	0.210857
$693$	−5.06562	−0.192427
$694$	−1.06329	−0.0403618
$695$	−31.7011	−1.20249
$696$	19.8382	0.751965
$697$	−5.80977	−0.220061
$698$	1.59981	0.0605537
$699$	−22.1950	−0.839491
$700$	1.17685	0.0444807
$701$	6.18062	0.233439	0.116719	−	0.993165i	$-0.462762\pi$
$701$	6.18062	0.233439	0.116719	+	0.993165i	$0.462762\pi$
$702$	−5.42055	−0.204586
$703$	9.67652	0.364957
$704$	44.0702	1.66096
$705$	18.4583	0.695179
$706$	−1.37406	−0.0517134
$707$	−13.4312	−0.505132
$708$	−1.31451	−0.0494025
$709$	16.8330	0.632177	0.316088	−	0.948730i	$-0.397630\pi$
$709$	16.8330	0.632177	0.316088	+	0.948730i	$0.397630\pi$
$710$	−12.4660	−0.467842
$711$	7.14831	0.268083
$712$	50.6380	1.89774
$713$	−2.22101	−0.0831774
$714$	5.61279	0.210053
$715$	65.5492	2.45140
$716$	4.05727	0.151627
$717$	20.2921	0.757822
$718$	16.2664	0.607057
$719$	−36.7510	−1.37058	−0.685290	−	0.728270i	$-0.740325\pi$
$719$	−36.7510	−1.37058	−0.685290	+	0.728270i	$0.740325\pi$
$720$	−11.0550	−0.411995
$721$	−2.72964	−0.101657
$722$	8.85667	0.329611
$723$	−14.5158	−0.539847
$724$	−3.47131	−0.129010
$725$	33.9343	1.26029
$726$	−19.4945	−0.723508
$727$	42.5612	1.57851	0.789253	−	0.614068i	$-0.210468\pi$
$727$	42.5612	1.57851	0.789253	+	0.614068i	$0.210468\pi$
$728$	12.0977	0.448372
$729$	1.00000	0.0370370
$730$	−8.54840	−0.316391
$731$	−14.3318	−0.530080
$732$	−3.35827	−0.124125
$733$	−7.67673	−0.283546	−0.141773	−	0.989899i	$-0.545280\pi$
$733$	−7.67673	−0.283546	−0.141773	+	0.989899i	$0.545280\pi$
$734$	−26.6461	−0.983527
$735$	−3.17434	−0.117087
$736$	1.30452	0.0480854
$737$	70.3321	2.59072
$738$	−1.83023	−0.0673716
$739$	30.0540	1.10555	0.552777	−	0.833329i	$-0.313568\pi$
$739$	30.0540	1.10555	0.552777	+	0.833329i	$0.313568\pi$
$740$	1.40573	0.0516756
$741$	20.6497	0.758586
$742$	8.74420	0.321010
$743$	43.6849	1.60264	0.801322	−	0.598234i	$-0.204131\pi$
$743$	43.6849	1.60264	0.801322	+	0.598234i	$0.204131\pi$
$744$	−6.59133	−0.241650
$745$	6.38247	0.233836
$746$	−34.1478	−1.25024
$747$	−12.7226	−0.465494
$748$	−4.95690	−0.181242
$749$	2.36558	0.0864362
$750$	−0.322650	−0.0117815
$751$	−35.0236	−1.27803	−0.639014	−	0.769195i	$-0.720658\pi$
$751$	−35.0236	−1.27803	−0.639014	+	0.769195i	$0.720658\pi$
$752$	20.2508	0.738471
$753$	−4.03791	−0.147150
$754$	36.2345	1.31958
$755$	−23.6155	−0.859457
$756$	−0.231826	−0.00843142
$757$	25.1809	0.915214	0.457607	−	0.889155i	$-0.348707\pi$
$757$	25.1809	0.915214	0.457607	+	0.889155i	$0.348707\pi$
$758$	14.3321	0.520564
$759$	−5.06562	−0.183870
$760$	47.7209	1.73102
$761$	−35.7236	−1.29498	−0.647490	−	0.762074i	$-0.724181\pi$
$761$	−35.7236	−1.29498	−0.647490	+	0.762074i	$0.724181\pi$
$762$	−7.21727	−0.261454
$763$	18.1179	0.655913
$764$	−3.57927	−0.129494
$765$	13.3989	0.484439
$766$	21.6582	0.782542
$767$	−23.1145	−0.834617
$768$	5.48617	0.197965
$769$	−42.1421	−1.51968	−0.759842	−	0.650107i	$-0.774724\pi$
$769$	−42.1421	−1.51968	−0.759842	+	0.650107i	$0.774724\pi$
$770$	−21.3820	−0.770555
$771$	16.7676	0.603869
$772$	−4.04292	−0.145508
$773$	12.5030	0.449702	0.224851	−	0.974393i	$-0.427810\pi$
$773$	12.5030	0.449702	0.224851	+	0.974393i	$0.427810\pi$
$774$	−4.51489	−0.162284
$775$	−11.2748	−0.405003
$776$	−6.20184	−0.222633
$777$	−1.91023	−0.0685293
$778$	29.5412	1.05910
$779$	6.97229	0.249808
$780$	2.99983	0.107411
$781$	−14.9605	−0.535328
$782$	5.61279	0.200713
$783$	−6.68466	−0.238890
$784$	−3.48261	−0.124379
$785$	55.5639	1.98316
$786$	0.778818	0.0277795
$787$	37.5411	1.33820	0.669099	−	0.743174i	$-0.266680\pi$
$787$	37.5411	1.33820	0.669099	+	0.743174i	$0.266680\pi$
$788$	−5.13952	−0.183088
$789$	22.0308	0.784318
$790$	30.1731	1.07351
$791$	6.08001	0.216180
$792$	−15.0333	−0.534186
$793$	−59.0520	−2.09700
$794$	−33.7110	−1.19636
$795$	20.8743	0.740334
$796$	−3.45991	−0.122633
$797$	−5.97335	−0.211587	−0.105793	−	0.994388i	$-0.533738\pi$
$797$	−5.97335	−0.211587	−0.105793	+	0.994388i	$0.533738\pi$
$798$	−6.73589	−0.238448
$799$	−24.5445	−0.868321
$800$	6.62233	0.234135
$801$	−17.0629	−0.602889
$802$	−49.6816	−1.75432
$803$	−10.2589	−0.362029
$804$	3.21871	0.113515
$805$	−3.17434	−0.111881
$806$	−12.0391	−0.424059
$807$	17.9902	0.633286
$808$	−39.8600	−1.40227
$809$	38.3623	1.34875	0.674374	−	0.738390i	$-0.264414\pi$
$809$	38.3623	1.34875	0.674374	+	0.738390i	$0.264414\pi$
$810$	4.22101	0.148311
$811$	−17.7595	−0.623619	−0.311810	−	0.950145i	$-0.600935\pi$
$811$	−17.7595	−0.623619	−0.311810	+	0.950145i	$0.600935\pi$
$812$	1.54968	0.0543829
$813$	−0.940007	−0.0329675
$814$	−12.8671	−0.450993
$815$	−12.5526	−0.439698
$816$	14.7001	0.514607
$817$	17.1995	0.601736
$818$	−39.6124	−1.38502
$819$	−4.07644	−0.142442
$820$	1.01288	0.0353713
$821$	−7.09433	−0.247594	−0.123797	−	0.992308i	$-0.539507\pi$
$821$	−7.09433	−0.247594	−0.123797	+	0.992308i	$0.539507\pi$
$822$	−26.1431	−0.911846
$823$	31.6990	1.10496	0.552480	−	0.833526i	$-0.313682\pi$
$823$	31.6990	1.10496	0.552480	+	0.833526i	$0.313682\pi$
$824$	−8.10082	−0.282205
$825$	−25.7153	−0.895292
$826$	7.53992	0.262347
$827$	−49.0671	−1.70623	−0.853115	−	0.521722i	$-0.825290\pi$
$827$	−49.0671	−1.70623	−0.853115	+	0.521722i	$0.825290\pi$
$828$	−0.231826	−0.00805650
$829$	16.4384	0.570931	0.285465	−	0.958389i	$-0.407852\pi$
$829$	16.4384	0.570931	0.285465	+	0.958389i	$0.407852\pi$
$830$	−53.7020	−1.86403
$831$	−3.73339	−0.129510
$832$	35.4645	1.22951
$833$	4.22101	0.146249
$834$	13.2796	0.459833
$835$	−9.80001	−0.339143
$836$	5.94876	0.205742
$837$	2.22101	0.0767692
$838$	−3.28155	−0.113359
$839$	−6.63342	−0.229011	−0.114506	−	0.993423i	$-0.536528\pi$
$839$	−6.63342	−0.229011	−0.114506	+	0.993423i	$0.536528\pi$
$840$	−9.42055	−0.325040
$841$	15.6847	0.540850
$842$	−20.2041	−0.696280
$843$	−21.7180	−0.748008
$844$	0.859796	0.0295954
$845$	11.4827	0.395018
$846$	−7.73215	−0.265837
$847$	−14.6605	−0.503741
$848$	22.9014	0.786437
$849$	24.0534	0.825509
$850$	28.4930	0.977301
$851$	−1.91023	−0.0654820
$852$	−0.684658	−0.0234560
$853$	41.8151	1.43172	0.715861	−	0.698243i	$-0.246034\pi$
$853$	41.8151	1.43172	0.715861	+	0.698243i	$0.246034\pi$
$854$	19.2627	0.659155
$855$	−16.0800	−0.549925
$856$	7.02036	0.239951
$857$	−36.4689	−1.24575	−0.622877	−	0.782319i	$-0.714036\pi$
$857$	−36.4689	−1.24575	−0.622877	+	0.782319i	$0.714036\pi$
$858$	−27.4585	−0.937416
$859$	−34.5774	−1.17976	−0.589882	−	0.807489i	$-0.700826\pi$
$859$	−34.5774	−1.17976	−0.589882	+	0.807489i	$0.700826\pi$
$860$	2.49861	0.0852021
$861$	−1.37639	−0.0469074
$862$	−20.3833	−0.694258
$863$	−29.2710	−0.996395	−0.498198	−	0.867063i	$-0.666005\pi$
$863$	−29.2710	−0.996395	−0.498198	+	0.867063i	$0.666005\pi$
$864$	−1.30452	−0.0443808
$865$	−75.9509	−2.58241
$866$	−2.57827	−0.0876132
$867$	−0.816901	−0.0277434
$868$	−0.514886	−0.0174764
$869$	36.2106	1.22836
$870$	−28.2160	−0.956612
$871$	56.5981	1.91775
$872$	53.7689	1.82084
$873$	2.08977	0.0707279
$874$	−6.73589	−0.227845
$875$	−0.242644	−0.00820287
$876$	−0.469494	−0.0158627
$877$	−4.57140	−0.154365	−0.0771826	−	0.997017i	$-0.524592\pi$
$877$	−4.57140	−0.154365	−0.0771826	+	0.997017i	$0.524592\pi$
$878$	5.38073	0.181591
$879$	−24.0021	−0.809571
$880$	−56.0003	−1.88777
$881$	11.4285	0.385036	0.192518	−	0.981293i	$-0.438335\pi$
$881$	11.4285	0.385036	0.192518	+	0.981293i	$0.438335\pi$
$882$	1.32973	0.0447742
$883$	−18.9351	−0.637215	−0.318608	−	0.947887i	$-0.603215\pi$
$883$	−18.9351	−0.637215	−0.318608	+	0.947887i	$0.603215\pi$
$884$	−3.98895	−0.134163
$885$	17.9994	0.605042
$886$	23.7850	0.799074
$887$	−6.96926	−0.234005	−0.117002	−	0.993132i	$-0.537329\pi$
$887$	−6.96926	−0.234005	−0.117002	+	0.993132i	$0.537329\pi$
$888$	−5.66904	−0.190240
$889$	−5.42763	−0.182037
$890$	−72.0228	−2.41421
$891$	5.06562	0.169705
$892$	−1.32577	−0.0443901
$893$	29.4558	0.985700
$894$	−2.67361	−0.0894188
$895$	−55.5554	−1.85701
$896$	−8.95941	−0.299313
$897$	−4.07644	−0.136108
$898$	44.1156	1.47216
$899$	−14.8467	−0.495164
$900$	−1.17685	−0.0392283
$901$	−27.7571	−0.924723
$902$	−9.27124	−0.308699
$903$	−3.39535	−0.112990
$904$	18.0438	0.600126
$905$	47.5319	1.58001
$906$	9.89251	0.328657
$907$	41.9505	1.39294	0.696472	−	0.717584i	$-0.254752\pi$
$907$	41.9505	1.39294	0.696472	+	0.717584i	$0.254752\pi$
$908$	−6.15350	−0.204211
$909$	13.4312	0.445485
$910$	−17.2067	−0.570396
$911$	−10.6040	−0.351327	−0.175664	−	0.984450i	$-0.556207\pi$
$911$	−10.6040	−0.351327	−0.175664	+	0.984450i	$0.556207\pi$
$912$	−17.6416	−0.584170
$913$	−64.4477	−2.13291
$914$	38.6722	1.27916
$915$	45.9840	1.52019
$916$	0.859652	0.0284037
$917$	0.585698	0.0193414
$918$	−5.61279	−0.185250
$919$	2.20439	0.0727160	0.0363580	−	0.999339i	$-0.488424\pi$
$919$	2.20439	0.0727160	0.0363580	+	0.999339i	$0.488424\pi$
$920$	−9.42055	−0.310586
$921$	−31.9678	−1.05337
$922$	−44.3544	−1.46073
$923$	−12.0391	−0.396271
$924$	−1.17434	−0.0386330
$925$	−9.69719	−0.318842
$926$	−2.49717	−0.0820620
$927$	2.72964	0.0896533
$928$	8.72029	0.286258
$929$	−4.27581	−0.140285	−0.0701424	−	0.997537i	$-0.522345\pi$
$929$	−4.27581	−0.140285	−0.0701424	+	0.997537i	$0.522345\pi$
$930$	9.37489	0.307415
$931$	−5.06562	−0.166019
$932$	−5.14536	−0.168542
$933$	21.1889	0.693693
$934$	17.1901	0.562476
$935$	67.8738	2.21971
$936$	−12.0977	−0.395427
$937$	−30.6645	−1.00177	−0.500883	−	0.865515i	$-0.666991\pi$
$937$	−30.6645	−1.00177	−0.500883	+	0.865515i	$0.666991\pi$
$938$	−18.4622	−0.602812
$939$	14.3935	0.469713
$940$	4.27910	0.139569
$941$	9.24521	0.301385	0.150693	−	0.988581i	$-0.451850\pi$
$941$	9.24521	0.301385	0.150693	+	0.988581i	$0.451850\pi$
$942$	−23.2756	−0.758361
$943$	−1.37639	−0.0448215
$944$	19.7473	0.642721
$945$	3.17434	0.103261
$946$	−22.8707	−0.743591
$947$	21.8800	0.711005	0.355502	−	0.934675i	$-0.384310\pi$
$947$	21.8800	0.711005	0.355502	+	0.934675i	$0.384310\pi$
$948$	1.65716	0.0538221
$949$	−8.25562	−0.267989
$950$	−34.1944	−1.10941
$951$	24.3516	0.789656
$952$	12.5268	0.405995
$953$	−38.2800	−1.24001	−0.620005	−	0.784598i	$-0.712870\pi$
$953$	−38.2800	−1.24001	−0.620005	+	0.784598i	$0.712870\pi$
$954$	−8.74420	−0.283104
$955$	49.0103	1.58593
$956$	4.70422	0.152145
$957$	−33.8619	−1.09460
$958$	−57.7079	−1.86446
$959$	−19.6605	−0.634871
$960$	−27.6164	−0.891314
$961$	−26.0671	−0.840875
$962$	−10.3545	−0.333843
$963$	−2.36558	−0.0762296
$964$	−3.36513	−0.108383
$965$	55.3589	1.78207
$966$	1.32973	0.0427833
$967$	−15.5397	−0.499723	−0.249862	−	0.968282i	$-0.580385\pi$
$967$	−15.5397	−0.499723	−0.249862	+	0.968282i	$0.580385\pi$
$968$	−43.5083	−1.39841
$969$	21.3820	0.686889
$970$	8.82092	0.283223
$971$	23.9345	0.768094	0.384047	−	0.923314i	$-0.374530\pi$
$971$	23.9345	0.768094	0.384047	+	0.923314i	$0.374530\pi$
$972$	0.231826	0.00743581
$973$	9.98667	0.320158
$974$	22.6043	0.724289
$975$	−20.6938	−0.662732
$976$	50.4496	1.61485
$977$	−8.13749	−0.260341	−0.130171	−	0.991492i	$-0.541553\pi$
$977$	−8.13749	−0.260341	−0.130171	+	0.991492i	$0.541553\pi$
$978$	5.25826	0.168141
$979$	−86.4344	−2.76245
$980$	−0.735894	−0.0235073
$981$	−18.1179	−0.578461
$982$	14.5578	0.464558
$983$	24.2119	0.772239	0.386119	−	0.922449i	$-0.373815\pi$
$983$	24.2119	0.772239	0.386119	+	0.922449i	$0.373815\pi$
$984$	−4.08475	−0.130217
$985$	70.3744	2.24232
$986$	37.5196	1.19487
$987$	−5.81484	−0.185088
$988$	4.78713	0.152299
$989$	−3.39535	−0.107966
$990$	21.3820	0.679565
$991$	36.1425	1.14810	0.574052	−	0.818819i	$-0.305371\pi$
$991$	36.1425	1.14810	0.574052	+	0.818819i	$0.305371\pi$
$992$	−2.89736	−0.0919911
$993$	9.09082	0.288489
$994$	3.92713	0.124561
$995$	47.3758	1.50191
$996$	−2.94942	−0.0934559
$997$	−0.629234	−0.0199280	−0.00996402	−	0.999950i	$-0.503172\pi$
$997$	−0.629234	−0.0199280	−0.00996402	+	0.999950i	$0.503172\pi$
$998$	40.3689	1.27785
$999$	1.91023	0.0604371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.a.j.1.3	✓	4
3.2	odd	2		1449.2.a.o.1.2		4
4.3	odd	2		7728.2.a.ce.1.3		4
7.6	odd	2		3381.2.a.x.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.j.1.3	✓	4	1.1	even	1	trivial
1449.2.a.o.1.2		4	3.2	odd	2
3381.2.a.x.1.3		4	7.6	odd	2
7728.2.a.ce.1.3		4	4.3	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+1.32973 q^{2} -1.00000 q^{3} -0.231826 q^{4} +3.17434 q^{5} -1.32973 q^{6} -1.00000 q^{7} -2.96772 q^{8} +1.00000 q^{9} +4.22101 q^{10} +5.06562 q^{11} +0.231826 q^{12} +4.07644 q^{13} -1.32973 q^{14} -3.17434 q^{15} -3.48261 q^{16} +4.22101 q^{17} +1.32973 q^{18} -5.06562 q^{19} -0.735894 q^{20} +1.00000 q^{21} +6.73589 q^{22} +1.00000 q^{23} +2.96772 q^{24} +5.07644 q^{25} +5.42055 q^{26} -1.00000 q^{27} +0.231826 q^{28} +6.68466 q^{29} -4.22101 q^{30} -2.22101 q^{31} +1.30452 q^{32} -5.06562 q^{33} +5.61279 q^{34} -3.17434 q^{35} -0.231826 q^{36} -1.91023 q^{37} -6.73589 q^{38} -4.07644 q^{39} -9.42055 q^{40} -1.37639 q^{41} +1.32973 q^{42} -3.39535 q^{43} -1.17434 q^{44} +3.17434 q^{45} +1.32973 q^{46} -5.81484 q^{47} +3.48261 q^{48} +1.00000 q^{49} +6.75028 q^{50} -4.22101 q^{51} -0.945023 q^{52} -6.57594 q^{53} -1.32973 q^{54} +16.0800 q^{55} +2.96772 q^{56} +5.06562 q^{57} +8.88877 q^{58} -5.67027 q^{59} +0.735894 q^{60} -14.4862 q^{61} -2.95333 q^{62} -1.00000 q^{63} +8.69987 q^{64} +12.9400 q^{65} -6.73589 q^{66} +13.8842 q^{67} -0.978538 q^{68} -1.00000 q^{69} -4.22101 q^{70} -2.95333 q^{71} -2.96772 q^{72} -2.02520 q^{73} -2.54009 q^{74} -5.07644 q^{75} +1.17434 q^{76} -5.06562 q^{77} -5.42055 q^{78} +7.14831 q^{79} -11.0550 q^{80} +1.00000 q^{81} -1.83023 q^{82} -12.7226 q^{83} -0.231826 q^{84} +13.3989 q^{85} -4.51489 q^{86} -6.68466 q^{87} -15.0333 q^{88} -17.0629 q^{89} +4.22101 q^{90} -4.07644 q^{91} -0.231826 q^{92} +2.22101 q^{93} -7.73215 q^{94} -16.0800 q^{95} -1.30452 q^{96} +2.08977 q^{97} +1.32973 q^{98} +5.06562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 4 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 9 q^{8} + 4 q^{9} + 2 q^{10} + q^{11} - 4 q^{12} + 7 q^{13} - 2 q^{14} - 5 q^{15} + 8 q^{16} + 2 q^{17} + 2 q^{18} - q^{19} + 13 q^{20}+ \cdots + q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 4 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 9 * q^8 + 4 * q^9 + 2 * q^10 + q^11 - 4 * q^12 + 7 * q^13 - 2 * q^14 - 5 * q^15 + 8 * q^16 + 2 * q^17 + 2 * q^18 - q^19 + 13 * q^20 + 4 * q^21 + 11 * q^22 + 4 * q^23 - 9 * q^24 + 11 * q^25 - 19 * q^26 - 4 * q^27 - 4 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 20 * q^32 - q^33 + 23 * q^34 - 5 * q^35 + 4 * q^36 + 16 * q^37 - 11 * q^38 - 7 * q^39 + 3 * q^40 + 5 * q^41 + 2 * q^42 + 9 * q^43 + 3 * q^44 + 5 * q^45 + 2 * q^46 - 21 * q^47 - 8 * q^48 + 4 * q^49 - 17 * q^50 - 2 * q^51 - 24 * q^52 + 10 * q^53 - 2 * q^54 + 17 * q^55 - 9 * q^56 + q^57 + q^58 - 26 * q^59 - 13 * q^60 + 2 * q^61 - 19 * q^62 - 4 * q^63 + 27 * q^64 + 26 * q^65 - 11 * q^66 + 5 * q^67 + 7 * q^68 - 4 * q^69 - 2 * q^70 - 19 * q^71 + 9 * q^72 + 10 * q^73 + 9 * q^74 - 11 * q^75 - 3 * q^76 - q^77 + 19 * q^78 - 6 * q^79 - 24 * q^80 + 4 * q^81 - 31 * q^82 - 2 * q^83 + 4 * q^84 - 7 * q^85 - 17 * q^86 - 2 * q^87 - 20 * q^88 - 17 * q^89 + 2 * q^90 - 7 * q^91 + 4 * q^92 - 6 * q^93 - 44 * q^94 - 17 * q^95 - 20 * q^96 + 32 * q^97 + 2 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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