LMFDB - Embedded newform 1859.2.a.s.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.149116 q^{2} -3.21882 q^{3} -1.97776 q^{4} -1.07607 q^{5} +0.479977 q^{6} +3.58386 q^{7} +0.593149 q^{8} +7.36077 q^{9} +O(q^{10})$	\(q-0.149116 q^{2} -3.21882 q^{3} -1.97776 q^{4} -1.07607 q^{5} +0.479977 q^{6} +3.58386 q^{7} +0.593149 q^{8} +7.36077 q^{9} +0.160459 q^{10} -1.00000 q^{11} +6.36606 q^{12} -0.534411 q^{14} +3.46366 q^{15} +3.86708 q^{16} -5.78160 q^{17} -1.09761 q^{18} +7.32598 q^{19} +2.12820 q^{20} -11.5358 q^{21} +0.149116 q^{22} -5.23635 q^{23} -1.90924 q^{24} -3.84208 q^{25} -14.0365 q^{27} -7.08803 q^{28} -3.62640 q^{29} -0.516487 q^{30} +2.65097 q^{31} -1.76294 q^{32} +3.21882 q^{33} +0.862129 q^{34} -3.85647 q^{35} -14.5579 q^{36} +3.91220 q^{37} -1.09242 q^{38} -0.638267 q^{40} +1.04212 q^{41} +1.72017 q^{42} -1.21675 q^{43} +1.97776 q^{44} -7.92067 q^{45} +0.780824 q^{46} -11.9180 q^{47} -12.4474 q^{48} +5.84406 q^{49} +0.572916 q^{50} +18.6099 q^{51} +0.145014 q^{53} +2.09307 q^{54} +1.07607 q^{55} +2.12576 q^{56} -23.5810 q^{57} +0.540755 q^{58} +2.35799 q^{59} -6.85029 q^{60} +9.46701 q^{61} -0.395303 q^{62} +26.3800 q^{63} -7.47128 q^{64} -0.479977 q^{66} +5.14020 q^{67} +11.4346 q^{68} +16.8549 q^{69} +0.575061 q^{70} +0.0702735 q^{71} +4.36603 q^{72} +10.7002 q^{73} -0.583372 q^{74} +12.3670 q^{75} -14.4891 q^{76} -3.58386 q^{77} +2.20655 q^{79} -4.16123 q^{80} +23.0986 q^{81} -0.155397 q^{82} +3.82400 q^{83} +22.8151 q^{84} +6.22138 q^{85} +0.181438 q^{86} +11.6727 q^{87} -0.593149 q^{88} -10.4246 q^{89} +1.18110 q^{90} +10.3563 q^{92} -8.53299 q^{93} +1.77717 q^{94} -7.88323 q^{95} +5.67458 q^{96} -11.8987 q^{97} -0.871443 q^{98} -7.36077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.149116	−0.105441	−0.0527205	−	0.998609i	$-0.516789\pi$
$2$	−0.149116	−0.105441	−0.0527205	+	0.998609i	$0.516789\pi$
$3$	−3.21882	−1.85838	−0.929192	−	0.369598i	$-0.879495\pi$
$3$	−3.21882	−1.85838	−0.929192	+	0.369598i	$0.879495\pi$
$4$	−1.97776	−0.988882
$5$	−1.07607	−0.481231	−0.240616	−	0.970621i	$-0.577349\pi$
$5$	−1.07607	−0.481231	−0.240616	+	0.970621i	$0.577349\pi$
$6$	0.479977	0.195950
$7$	3.58386	1.35457	0.677286	−	0.735720i	$-0.263156\pi$
$7$	3.58386	1.35457	0.677286	+	0.735720i	$0.263156\pi$
$8$	0.593149	0.209710
$9$	7.36077	2.45359
$10$	0.160459	0.0507415
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	6.36606	1.83772
$13$	0	0
$13$	0	0
$14$	−0.534411	−0.142827
$15$	3.46366	0.894312
$16$	3.86708	0.966770
$17$	−5.78160	−1.40224	−0.701121	−	0.713042i	$-0.747317\pi$
$17$	−5.78160	−1.40224	−0.701121	+	0.713042i	$0.747317\pi$
$18$	−1.09761	−0.258709
$19$	7.32598	1.68070	0.840348	−	0.542048i	$-0.182351\pi$
$19$	7.32598	1.68070	0.840348	+	0.542048i	$0.182351\pi$
$20$	2.12820	0.475881
$21$	−11.5358	−2.51731
$22$	0.149116	0.0317916
$23$	−5.23635	−1.09186	−0.545928	−	0.837832i	$-0.683823\pi$
$23$	−5.23635	−1.09186	−0.545928	+	0.837832i	$0.683823\pi$
$24$	−1.90924	−0.389721
$25$	−3.84208	−0.768417
$26$	0	0
$27$	−14.0365	−2.70133
$28$	−7.08803	−1.33951
$29$	−3.62640	−0.673406	−0.336703	−	0.941611i	$-0.609312\pi$
$29$	−3.62640	−0.673406	−0.336703	+	0.941611i	$0.609312\pi$
$30$	−0.516487	−0.0942971
$31$	2.65097	0.476129	0.238064	−	0.971249i	$-0.423487\pi$
$31$	2.65097	0.476129	0.238064	+	0.971249i	$0.423487\pi$
$32$	−1.76294	−0.311647
$33$	3.21882	0.560324
$34$	0.862129	0.147854
$35$	−3.85647	−0.651862
$36$	−14.5579	−2.42631
$37$	3.91220	0.643161	0.321581	−	0.946882i	$-0.395786\pi$
$37$	3.91220	0.643161	0.321581	+	0.946882i	$0.395786\pi$
$38$	−1.09242	−0.177214
$39$	0	0
$40$	−0.638267	−0.100919
$41$	1.04212	0.162752	0.0813762	−	0.996683i	$-0.474068\pi$
$41$	1.04212	0.162752	0.0813762	+	0.996683i	$0.474068\pi$
$42$	1.72017	0.265428
$43$	−1.21675	−0.185553	−0.0927766	−	0.995687i	$-0.529574\pi$
$43$	−1.21675	−0.185553	−0.0927766	+	0.995687i	$0.529574\pi$
$44$	1.97776	0.298159
$45$	−7.92067	−1.18074
$46$	0.780824	0.115126
$47$	−11.9180	−1.73843	−0.869213	−	0.494438i	$-0.835374\pi$
$47$	−11.9180	−1.73843	−0.869213	+	0.494438i	$0.835374\pi$
$48$	−12.4474	−1.79663
$49$	5.84406	0.834866
$50$	0.572916	0.0810226
$51$	18.6099	2.60591
$52$	0	0
$53$	0.145014	0.0199192	0.00995961	−	0.999950i	$-0.496830\pi$
$53$	0.145014	0.0199192	0.00995961	+	0.999950i	$0.496830\pi$
$54$	2.09307	0.284831
$55$	1.07607	0.145097
$56$	2.12576	0.284067
$57$	−23.5810	−3.12338
$58$	0.540755	0.0710046
$59$	2.35799	0.306984	0.153492	−	0.988150i	$-0.450948\pi$
$59$	2.35799	0.306984	0.153492	+	0.988150i	$0.450948\pi$
$60$	−6.85029	−0.884369
$61$	9.46701	1.21213	0.606063	−	0.795416i	$-0.292748\pi$
$61$	9.46701	1.21213	0.606063	+	0.795416i	$0.292748\pi$
$62$	−0.395303	−0.0502035
$63$	26.3800	3.32356
$64$	−7.47128	−0.933910
$65$	0	0
$66$	−0.479977	−0.0590811
$67$	5.14020	0.627976	0.313988	−	0.949427i	$-0.398335\pi$
$67$	5.14020	0.627976	0.313988	+	0.949427i	$0.398335\pi$
$68$	11.4346	1.38665
$69$	16.8549	2.02909
$70$	0.575061	0.0687330
$71$	0.0702735	0.00833993	0.00416996	−	0.999991i	$-0.498673\pi$
$71$	0.0702735	0.00833993	0.00416996	+	0.999991i	$0.498673\pi$
$72$	4.36603	0.514542
$73$	10.7002	1.25237	0.626183	−	0.779676i	$-0.284616\pi$
$73$	10.7002	1.25237	0.626183	+	0.779676i	$0.284616\pi$
$74$	−0.583372	−0.0678156
$75$	12.3670	1.42801
$76$	−14.4891	−1.66201
$77$	−3.58386	−0.408419
$78$	0	0
$79$	2.20655	0.248257	0.124128	−	0.992266i	$-0.460387\pi$
$79$	2.20655	0.248257	0.124128	+	0.992266i	$0.460387\pi$
$80$	−4.16123	−0.465240
$81$	23.0986	2.56651
$82$	−0.155397	−0.0171608
$83$	3.82400	0.419738	0.209869	−	0.977730i	$-0.432696\pi$
$83$	3.82400	0.419738	0.209869	+	0.977730i	$0.432696\pi$
$84$	22.8151	2.48933
$85$	6.22138	0.674803
$86$	0.181438	0.0195649
$87$	11.6727	1.25145
$88$	−0.593149	−0.0632298
$89$	−10.4246	−1.10501	−0.552504	−	0.833510i	$-0.686328\pi$
$89$	−10.4246	−1.10501	−0.552504	+	0.833510i	$0.686328\pi$
$90$	1.18110	0.124499
$91$	0	0
$92$	10.3563	1.07972
$93$	−8.53299	−0.884830
$94$	1.77717	0.183301
$95$	−7.88323	−0.808803
$96$	5.67458	0.579159
$97$	−11.8987	−1.20813	−0.604065	−	0.796935i	$-0.706453\pi$
$97$	−11.8987	−1.20813	−0.604065	+	0.796935i	$0.706453\pi$
$98$	−0.871443	−0.0880291
$99$	−7.36077	−0.739785
$100$	7.59874	0.759874
$101$	8.30901	0.826778	0.413389	−	0.910555i	$-0.364345\pi$
$101$	8.30901	0.826778	0.413389	+	0.910555i	$0.364345\pi$
$102$	−2.77503	−0.274769
$103$	0.278096	0.0274016	0.0137008	−	0.999906i	$-0.495639\pi$
$103$	0.278096	0.0274016	0.0137008	+	0.999906i	$0.495639\pi$
$104$	0	0
$105$	12.4133	1.21141
$106$	−0.0216239	−0.00210030
$107$	−9.10157	−0.879882	−0.439941	−	0.898027i	$-0.645001\pi$
$107$	−9.10157	−0.879882	−0.439941	+	0.898027i	$0.645001\pi$
$108$	27.7609	2.67130
$109$	−0.848663	−0.0812872	−0.0406436	−	0.999174i	$-0.512941\pi$
$109$	−0.848663	−0.0812872	−0.0406436	+	0.999174i	$0.512941\pi$
$110$	−0.160459	−0.0152991
$111$	−12.5926	−1.19524
$112$	13.8591	1.30956
$113$	15.6738	1.47446	0.737231	−	0.675640i	$-0.236133\pi$
$113$	15.6738	1.47446	0.737231	+	0.675640i	$0.236133\pi$
$114$	3.51630	0.329332
$115$	5.63466	0.525435
$116$	7.17217	0.665919
$117$	0	0
$118$	−0.351614	−0.0323687
$119$	−20.7204	−1.89944
$120$	2.05446	0.187546
$121$	1.00000	0.0909091
$122$	−1.41168	−0.127808
$123$	−3.35440	−0.302456
$124$	−5.24300	−0.470835
$125$	9.51466	0.851017
$126$	−3.93368	−0.350440
$127$	−21.4994	−1.90776	−0.953882	−	0.300183i	$-0.902952\pi$
$127$	−21.4994	−1.90776	−0.953882	+	0.300183i	$0.902952\pi$
$128$	4.63997	0.410119
$129$	3.91651	0.344829
$130$	0	0
$131$	10.2612	0.896524	0.448262	−	0.893902i	$-0.352043\pi$
$131$	10.2612	0.896524	0.448262	+	0.893902i	$0.352043\pi$
$132$	−6.36606	−0.554094
$133$	26.2553	2.27662
$134$	−0.766487	−0.0662144
$135$	15.1042	1.29996
$136$	−3.42935	−0.294064
$137$	13.7245	1.17256	0.586282	−	0.810107i	$-0.300591\pi$
$137$	13.7245	1.17256	0.586282	+	0.810107i	$0.300591\pi$
$138$	−2.51333	−0.213949
$139$	−6.42879	−0.545283	−0.272642	−	0.962116i	$-0.587897\pi$
$139$	−6.42879	−0.545283	−0.272642	+	0.962116i	$0.587897\pi$
$140$	7.62719	0.644615
$141$	38.3620	3.23066
$142$	−0.0104789	−0.000879370 0
$143$	0	0
$144$	28.4647	2.37206
$145$	3.90225	0.324064
$146$	−1.59557	−0.132051
$147$	−18.8109	−1.55150
$148$	−7.73741	−0.636011
$149$	−3.00186	−0.245922	−0.122961	−	0.992411i	$-0.539239\pi$
$149$	−3.00186	−0.245922	−0.122961	+	0.992411i	$0.539239\pi$
$150$	−1.84411	−0.150571
$151$	23.4105	1.90512	0.952560	−	0.304352i	$-0.0984400\pi$
$151$	23.4105	1.90512	0.952560	+	0.304352i	$0.0984400\pi$
$152$	4.34539	0.352458
$153$	−42.5570	−3.44053
$154$	0.534411	0.0430641
$155$	−2.85262	−0.229128
$156$	0	0
$157$	10.1431	0.809508	0.404754	−	0.914426i	$-0.367357\pi$
$157$	10.1431	0.809508	0.404754	+	0.914426i	$0.367357\pi$
$158$	−0.329032	−0.0261764
$159$	−0.466773	−0.0370175
$160$	1.89704	0.149974
$161$	−18.7664	−1.47900
$162$	−3.44438	−0.270616
$163$	0.616582	0.0482944	0.0241472	−	0.999708i	$-0.492313\pi$
$163$	0.616582	0.0482944	0.0241472	+	0.999708i	$0.492313\pi$
$164$	−2.06108	−0.160943
$165$	−3.46366	−0.269645
$166$	−0.570219	−0.0442576
$167$	−7.60997	−0.588877	−0.294439	−	0.955670i	$-0.595133\pi$
$167$	−7.60997	−0.588877	−0.294439	+	0.955670i	$0.595133\pi$
$168$	−6.84243	−0.527905
$169$	0	0
$170$	−0.927707	−0.0711519
$171$	53.9249	4.12374
$172$	2.40645	0.183490
$173$	20.9159	1.59020	0.795102	−	0.606475i	$-0.207417\pi$
$173$	20.9159	1.59020	0.795102	+	0.606475i	$0.207417\pi$
$174$	−1.74059	−0.131954
$175$	−13.7695	−1.04088
$176$	−3.86708	−0.291492
$177$	−7.58992	−0.570494
$178$	1.55448	0.116513
$179$	12.3488	0.922995	0.461498	−	0.887141i	$-0.347312\pi$
$179$	12.3488	0.922995	0.461498	+	0.887141i	$0.347312\pi$
$180$	15.6652	1.16762
$181$	4.12806	0.306836	0.153418	−	0.988161i	$-0.450972\pi$
$181$	4.12806	0.306836	0.153418	+	0.988161i	$0.450972\pi$
$182$	0	0
$183$	−30.4726	−2.25260
$184$	−3.10594	−0.228973
$185$	−4.20978	−0.309509
$186$	1.27241	0.0932973
$187$	5.78160	0.422792
$188$	23.5711	1.71910
$189$	−50.3049	−3.65914
$190$	1.17552	0.0852809
$191$	3.93901	0.285017	0.142508	−	0.989794i	$-0.454483\pi$
$191$	3.93901	0.285017	0.142508	+	0.989794i	$0.454483\pi$
$192$	24.0487	1.73556
$193$	5.12303	0.368763	0.184382	−	0.982855i	$-0.440972\pi$
$193$	5.12303	0.368763	0.184382	+	0.982855i	$0.440972\pi$
$194$	1.77429	0.127386
$195$	0	0
$196$	−11.5582	−0.825584
$197$	5.39700	0.384520	0.192260	−	0.981344i	$-0.438418\pi$
$197$	5.39700	0.384520	0.192260	+	0.981344i	$0.438418\pi$
$198$	1.09761	0.0780037
$199$	−5.09868	−0.361436	−0.180718	−	0.983535i	$-0.557842\pi$
$199$	−5.09868	−0.361436	−0.180718	+	0.983535i	$0.557842\pi$
$200$	−2.27893	−0.161144
$201$	−16.5454	−1.16702
$202$	−1.23901	−0.0871762
$203$	−12.9965	−0.912177
$204$	−36.8060	−2.57693
$205$	−1.12139	−0.0783215
$206$	−0.0414686	−0.00288925
$207$	−38.5436	−2.67897
$208$	0	0
$209$	−7.32598	−0.506749
$210$	−1.85102	−0.127732
$211$	−4.67412	−0.321780	−0.160890	−	0.986972i	$-0.551436\pi$
$211$	−4.67412	−0.321780	−0.160890	+	0.986972i	$0.551436\pi$
$212$	−0.286804	−0.0196978
$213$	−0.226197	−0.0154988
$214$	1.35719	0.0927757
$215$	1.30931	0.0892940
$216$	−8.32574	−0.566495
$217$	9.50072	0.644951
$218$	0.126549	0.00857100
$219$	−34.4420	−2.32738
$220$	−2.12820	−0.143483
$221$	0	0
$222$	1.87777	0.126027
$223$	1.69577	0.113557	0.0567786	−	0.998387i	$-0.481917\pi$
$223$	1.69577	0.113557	0.0567786	+	0.998387i	$0.481917\pi$
$224$	−6.31814	−0.422148
$225$	−28.2807	−1.88538
$226$	−2.33721	−0.155469
$227$	−14.5217	−0.963836	−0.481918	−	0.876216i	$-0.660060\pi$
$227$	−14.5217	−0.963836	−0.481918	+	0.876216i	$0.660060\pi$
$228$	46.6376	3.08865
$229$	9.18634	0.607050	0.303525	−	0.952823i	$-0.401836\pi$
$229$	9.18634	0.607050	0.303525	+	0.952823i	$0.401836\pi$
$230$	−0.840218	−0.0554023
$231$	11.5358	0.758999
$232$	−2.15099	−0.141220
$233$	24.6516	1.61498	0.807491	−	0.589880i	$-0.200825\pi$
$233$	24.6516	1.61498	0.807491	+	0.589880i	$0.200825\pi$
$234$	0	0
$235$	12.8246	0.836585
$236$	−4.66354	−0.303571
$237$	−7.10249	−0.461356
$238$	3.08975	0.200279
$239$	7.91543	0.512006	0.256003	−	0.966676i	$-0.417594\pi$
$239$	7.91543	0.512006	0.256003	+	0.966676i	$0.417594\pi$
$240$	13.3942	0.864594
$241$	−24.3689	−1.56974	−0.784871	−	0.619660i	$-0.787271\pi$
$241$	−24.3689	−1.56974	−0.784871	+	0.619660i	$0.787271\pi$
$242$	−0.149116	−0.00958554
$243$	−32.2407	−2.06824
$244$	−18.7235	−1.19865
$245$	−6.28859	−0.401763
$246$	0.500195	0.0318913
$247$	0	0
$248$	1.57242	0.0998488
$249$	−12.3087	−0.780034
$250$	−1.41879	−0.0897321
$251$	9.17729	0.579265	0.289633	−	0.957138i	$-0.406467\pi$
$251$	9.17729	0.579265	0.289633	+	0.957138i	$0.406467\pi$
$252$	−52.1734	−3.28661
$253$	5.23635	0.329207
$254$	3.20591	0.201156
$255$	−20.0255	−1.25404
$256$	14.2507	0.890666
$257$	13.4037	0.836100	0.418050	−	0.908424i	$-0.362714\pi$
$257$	13.4037	0.836100	0.418050	+	0.908424i	$0.362714\pi$
$258$	−0.584014	−0.0363591
$259$	14.0208	0.871209
$260$	0	0
$261$	−26.6931	−1.65226
$262$	−1.53011	−0.0945303
$263$	−21.9734	−1.35494	−0.677468	−	0.735552i	$-0.736923\pi$
$263$	−21.9734	−1.35494	−0.677468	+	0.735552i	$0.736923\pi$
$264$	1.90924	0.117505
$265$	−0.156045	−0.00958575
$266$	−3.91509	−0.240049
$267$	33.5550	2.05353
$268$	−10.1661	−0.620994
$269$	20.4798	1.24868	0.624339	−	0.781154i	$-0.285369\pi$
$269$	20.4798	1.24868	0.624339	+	0.781154i	$0.285369\pi$
$270$	−2.25228	−0.137069
$271$	−15.0426	−0.913775	−0.456888	−	0.889524i	$-0.651036\pi$
$271$	−15.0426	−0.913775	−0.456888	+	0.889524i	$0.651036\pi$
$272$	−22.3579	−1.35565
$273$	0	0
$274$	−2.04654	−0.123636
$275$	3.84208	0.231686
$276$	−33.3349	−2.00653
$277$	−16.4731	−0.989771	−0.494886	−	0.868958i	$-0.664790\pi$
$277$	−16.4731	−0.989771	−0.494886	+	0.868958i	$0.664790\pi$
$278$	0.958636	0.0574952
$279$	19.5132	1.16822
$280$	−2.28746	−0.136702
$281$	−19.0800	−1.13822	−0.569109	−	0.822262i	$-0.692712\pi$
$281$	−19.0800	−1.13822	−0.569109	+	0.822262i	$0.692712\pi$
$282$	−5.72039	−0.340644
$283$	22.0454	1.31046	0.655232	−	0.755428i	$-0.272571\pi$
$283$	22.0454	1.31046	0.655232	+	0.755428i	$0.272571\pi$
$284$	−0.138984	−0.00824721
$285$	25.3747	1.50307
$286$	0	0
$287$	3.73483	0.220460
$288$	−12.9766	−0.764654
$289$	16.4268	0.966285
$290$	−0.581887	−0.0341696
$291$	38.2997	2.24517
$292$	−21.1625	−1.23844
$293$	22.6759	1.32474	0.662369	−	0.749177i	$-0.269551\pi$
$293$	22.6759	1.32474	0.662369	+	0.749177i	$0.269551\pi$
$294$	2.80501	0.163592
$295$	−2.53735	−0.147730
$296$	2.32051	0.134877
$297$	14.0365	0.814481
$298$	0.447626	0.0259303
$299$	0	0
$300$	−24.4589	−1.41214
$301$	−4.36068	−0.251345
$302$	−3.49088	−0.200878
$303$	−26.7452	−1.53647
$304$	28.3302	1.62485
$305$	−10.1871	−0.583313
$306$	6.34593	0.362773
$307$	21.0536	1.20159	0.600796	−	0.799402i	$-0.294850\pi$
$307$	21.0536	1.20159	0.600796	+	0.799402i	$0.294850\pi$
$308$	7.08803	0.403878
$309$	−0.895139	−0.0509227
$310$	0.425371	0.0241595
$311$	27.9213	1.58327	0.791636	−	0.610993i	$-0.209229\pi$
$311$	27.9213	1.58327	0.791636	+	0.610993i	$0.209229\pi$
$312$	0	0
$313$	4.67710	0.264365	0.132183	−	0.991225i	$-0.457801\pi$
$313$	4.67710	0.264365	0.132183	+	0.991225i	$0.457801\pi$
$314$	−1.51250	−0.0853554
$315$	−28.3866	−1.59940
$316$	−4.36404	−0.245497
$317$	25.4219	1.42784	0.713919	−	0.700228i	$-0.246919\pi$
$317$	25.4219	1.42784	0.713919	+	0.700228i	$0.246919\pi$
$318$	0.0696034	0.00390317
$319$	3.62640	0.203040
$320$	8.03959	0.449426
$321$	29.2963	1.63516
$322$	2.79837	0.155947
$323$	−42.3559	−2.35674
$324$	−45.6836	−2.53798
$325$	0	0
$326$	−0.0919422	−0.00509221
$327$	2.73169	0.151063
$328$	0.618134	0.0341307
$329$	−42.7126	−2.35482
$330$	0.516487	0.0284317
$331$	−31.0792	−1.70827	−0.854133	−	0.520054i	$-0.825912\pi$
$331$	−31.0792	−1.70827	−0.854133	+	0.520054i	$0.825912\pi$
$332$	−7.56296	−0.415072
$333$	28.7968	1.57805
$334$	1.13477	0.0620918
$335$	−5.53119	−0.302201
$336$	−44.6098	−2.43367
$337$	−11.1008	−0.604698	−0.302349	−	0.953197i	$-0.597771\pi$
$337$	−11.1008	−0.604698	−0.302349	+	0.953197i	$0.597771\pi$
$338$	0	0
$339$	−50.4509	−2.74012
$340$	−12.3044	−0.667301
$341$	−2.65097	−0.143558
$342$	−8.04106	−0.434811
$343$	−4.14273	−0.223686
$344$	−0.721716	−0.0389123
$345$	−18.1369	−0.976459
$346$	−3.11889	−0.167673
$347$	4.83227	0.259410	0.129705	−	0.991553i	$-0.458597\pi$
$347$	4.83227	0.259410	0.129705	+	0.991553i	$0.458597\pi$
$348$	−23.0859	−1.23753
$349$	6.80301	0.364157	0.182078	−	0.983284i	$-0.441718\pi$
$349$	6.80301	0.364157	0.182078	+	0.983284i	$0.441718\pi$
$350$	2.05325	0.109751
$351$	0	0
$352$	1.76294	0.0939651
$353$	26.6753	1.41978	0.709892	−	0.704310i	$-0.248744\pi$
$353$	26.6753	1.41978	0.709892	+	0.704310i	$0.248744\pi$
$354$	1.13178	0.0601534
$355$	−0.0756189	−0.00401343
$356$	20.6175	1.09272
$357$	66.6953	3.52989
$358$	−1.84141	−0.0973215
$359$	16.3829	0.864657	0.432329	−	0.901716i	$-0.357692\pi$
$359$	16.3829	0.864657	0.432329	+	0.901716i	$0.357692\pi$
$360$	−4.69813	−0.247613
$361$	34.6700	1.82474
$362$	−0.615560	−0.0323531
$363$	−3.21882	−0.168944
$364$	0	0
$365$	−11.5141	−0.602678
$366$	4.54395	0.237516
$367$	−11.0696	−0.577830	−0.288915	−	0.957355i	$-0.593294\pi$
$367$	−11.0696	−0.577830	−0.288915	+	0.957355i	$0.593294\pi$
$368$	−20.2494	−1.05557
$369$	7.67083	0.399328
$370$	0.627746	0.0326350
$371$	0.519710	0.0269820
$372$	16.8762	0.874993
$373$	−20.2838	−1.05026	−0.525128	−	0.851023i	$-0.675982\pi$
$373$	−20.2838	−1.05026	−0.525128	+	0.851023i	$0.675982\pi$
$374$	−0.862129	−0.0445796
$375$	−30.6259	−1.58152
$376$	−7.06917	−0.364565
$377$	0	0
$378$	7.50127	0.385824
$379$	−21.9402	−1.12699	−0.563496	−	0.826119i	$-0.690544\pi$
$379$	−21.9402	−1.12699	−0.563496	+	0.826119i	$0.690544\pi$
$380$	15.5912	0.799811
$381$	69.2026	3.54536
$382$	−0.587369	−0.0300524
$383$	25.2157	1.28846	0.644230	−	0.764832i	$-0.277178\pi$
$383$	25.2157	1.28846	0.644230	+	0.764832i	$0.277178\pi$
$384$	−14.9352	−0.762159
$385$	3.85647	0.196544
$386$	−0.763925	−0.0388828
$387$	−8.95625	−0.455272
$388$	23.5328	1.19470
$389$	−10.8999	−0.552649	−0.276324	−	0.961064i	$-0.589116\pi$
$389$	−10.8999	−0.552649	−0.276324	+	0.961064i	$0.589116\pi$
$390$	0	0
$391$	30.2745	1.53105
$392$	3.46640	0.175079
$393$	−33.0289	−1.66609
$394$	−0.804779	−0.0405442
$395$	−2.37440	−0.119469
$396$	14.5579	0.731560
$397$	31.5621	1.58405	0.792027	−	0.610486i	$-0.209026\pi$
$397$	31.5621	1.58405	0.792027	+	0.610486i	$0.209026\pi$
$398$	0.760295	0.0381102
$399$	−84.5109	−4.23084
$400$	−14.8576	−0.742882
$401$	33.6361	1.67971	0.839854	−	0.542812i	$-0.182640\pi$
$401$	33.6361	1.67971	0.839854	+	0.542812i	$0.182640\pi$
$402$	2.46718	0.123052
$403$	0	0
$404$	−16.4333	−0.817586
$405$	−24.8556	−1.23509
$406$	1.93799	0.0961808
$407$	−3.91220	−0.193920
$408$	11.0384	0.546484
$409$	29.0107	1.43449	0.717244	−	0.696822i	$-0.245403\pi$
$409$	29.0107	1.43449	0.717244	+	0.696822i	$0.245403\pi$
$410$	0.167218	0.00825830
$411$	−44.1767	−2.17907
$412$	−0.550008	−0.0270970
$413$	8.45070	0.415832
$414$	5.74747	0.282473
$415$	−4.11487	−0.201991
$416$	0	0
$417$	20.6931	1.01335
$418$	1.09242	0.0534321
$419$	16.9025	0.825743	0.412871	−	0.910789i	$-0.364526\pi$
$419$	16.9025	0.825743	0.412871	+	0.910789i	$0.364526\pi$
$420$	−24.5505	−1.19794
$421$	9.39424	0.457847	0.228924	−	0.973444i	$-0.426479\pi$
$421$	9.39424	0.457847	0.228924	+	0.973444i	$0.426479\pi$
$422$	0.696987	0.0339288
$423$	−87.7260	−4.26538
$424$	0.0860149	0.00417725
$425$	22.2134	1.07751
$426$	0.0337297	0.00163421
$427$	33.9285	1.64191
$428$	18.0008	0.870100
$429$	0	0
$430$	−0.195239	−0.00941524
$431$	−5.72759	−0.275888	−0.137944	−	0.990440i	$-0.544049\pi$
$431$	−5.72759	−0.275888	−0.137944	+	0.990440i	$0.544049\pi$
$432$	−54.2803	−2.61156
$433$	19.2956	0.927289	0.463644	−	0.886021i	$-0.346542\pi$
$433$	19.2956	0.927289	0.463644	+	0.886021i	$0.346542\pi$
$434$	−1.41671	−0.0680042
$435$	−12.5606	−0.602235
$436$	1.67846	0.0803834
$437$	−38.3614	−1.83508
$438$	5.13586	0.245401
$439$	24.0666	1.14864	0.574318	−	0.818632i	$-0.305267\pi$
$439$	24.0666	1.14864	0.574318	+	0.818632i	$0.305267\pi$
$440$	0.638267	0.0304282
$441$	43.0168	2.04842
$442$	0	0
$443$	−4.19960	−0.199529	−0.0997646	−	0.995011i	$-0.531809\pi$
$443$	−4.19960	−0.199529	−0.0997646	+	0.995011i	$0.531809\pi$
$444$	24.9053	1.18195
$445$	11.2176	0.531764
$446$	−0.252866	−0.0119736
$447$	9.66244	0.457018
$448$	−26.7760	−1.26505
$449$	8.18012	0.386044	0.193022	−	0.981194i	$-0.438171\pi$
$449$	8.18012	0.386044	0.193022	+	0.981194i	$0.438171\pi$
$450$	4.21711	0.198796
$451$	−1.04212	−0.0490717
$452$	−30.9990	−1.45807
$453$	−75.3541	−3.54044
$454$	2.16541	0.101628
$455$	0	0
$456$	−13.9870	−0.655002
$457$	−17.6613	−0.826160	−0.413080	−	0.910695i	$-0.635547\pi$
$457$	−17.6613	−0.826160	−0.413080	+	0.910695i	$0.635547\pi$
$458$	−1.36983	−0.0640080
$459$	81.1534	3.78792
$460$	−11.1440	−0.519593
$461$	34.4679	1.60533	0.802666	−	0.596429i	$-0.203414\pi$
$461$	34.4679	1.60533	0.802666	+	0.596429i	$0.203414\pi$
$462$	−1.72017	−0.0800296
$463$	0.882146	0.0409968	0.0204984	−	0.999790i	$-0.493475\pi$
$463$	0.882146	0.0409968	0.0204984	+	0.999790i	$0.493475\pi$
$464$	−14.0236	−0.651029
$465$	9.18206	0.425808
$466$	−3.67595	−0.170285
$467$	−21.6018	−0.999612	−0.499806	−	0.866137i	$-0.666595\pi$
$467$	−21.6018	−0.999612	−0.499806	+	0.866137i	$0.666595\pi$
$468$	0	0
$469$	18.4218	0.850638
$470$	−1.91235	−0.0882103
$471$	−32.6488	−1.50438
$472$	1.39864	0.0643775
$473$	1.21675	0.0559464
$474$	1.05909	0.0486458
$475$	−28.1470	−1.29147
$476$	40.9801	1.87832
$477$	1.06742	0.0488736
$478$	−1.18032	−0.0539865
$479$	−6.49086	−0.296575	−0.148287	−	0.988944i	$-0.547376\pi$
$479$	−6.49086	−0.296575	−0.148287	+	0.988944i	$0.547376\pi$
$480$	−6.10622	−0.278710
$481$	0	0
$482$	3.63380	0.165515
$483$	60.4055	2.74854
$484$	−1.97776	−0.0898984
$485$	12.8038	0.581390
$486$	4.80760	0.218077
$487$	10.8211	0.490353	0.245176	−	0.969479i	$-0.421154\pi$
$487$	10.8211	0.490353	0.245176	+	0.969479i	$0.421154\pi$
$488$	5.61534	0.254195
$489$	−1.98466	−0.0897496
$490$	0.937730	0.0423623
$491$	11.3336	0.511480	0.255740	−	0.966746i	$-0.417681\pi$
$491$	11.3336	0.511480	0.255740	+	0.966746i	$0.417681\pi$
$492$	6.63422	0.299094
$493$	20.9664	0.944279
$494$	0	0
$495$	7.92067	0.356008
$496$	10.2515	0.460307
$497$	0.251850	0.0112970
$498$	1.83543	0.0822476
$499$	16.4178	0.734961	0.367481	−	0.930031i	$-0.380220\pi$
$499$	16.4178	0.734961	0.367481	+	0.930031i	$0.380220\pi$
$500$	−18.8178	−0.841556
$501$	24.4951	1.09436
$502$	−1.36848	−0.0610783
$503$	−30.5761	−1.36332	−0.681661	−	0.731668i	$-0.738742\pi$
$503$	−30.5761	−1.36332	−0.681661	+	0.731668i	$0.738742\pi$
$504$	15.6472	0.696984
$505$	−8.94104	−0.397871
$506$	−0.780824	−0.0347119
$507$	0	0
$508$	42.5207	1.88655
$509$	21.3391	0.945840	0.472920	−	0.881105i	$-0.343200\pi$
$509$	21.3391	0.945840	0.472920	+	0.881105i	$0.343200\pi$
$510$	2.98612	0.132227
$511$	38.3481	1.69642
$512$	−11.4049	−0.504032
$513$	−102.831	−4.54011
$514$	−1.99871	−0.0881592
$515$	−0.299249	−0.0131865
$516$	−7.74593	−0.340995
$517$	11.9180	0.524155
$518$	−2.09072	−0.0918611
$519$	−67.3243	−2.95521
$520$	0	0
$521$	−19.2230	−0.842175	−0.421087	−	0.907020i	$-0.638351\pi$
$521$	−19.2230	−0.842175	−0.421087	+	0.907020i	$0.638351\pi$
$522$	3.98037	0.174216
$523$	−17.2005	−0.752127	−0.376063	−	0.926594i	$-0.622723\pi$
$523$	−17.2005	−0.752127	−0.376063	+	0.926594i	$0.622723\pi$
$524$	−20.2942	−0.886556
$525$	44.3214	1.93435
$526$	3.27658	0.142866
$527$	−15.3269	−0.667648
$528$	12.4474	0.541704
$529$	4.41940	0.192148
$530$	0.0232688	0.00101073
$531$	17.3566	0.753212
$532$	−51.9268	−2.25131
$533$	0	0
$534$	−5.00358	−0.216526
$535$	9.79389	0.423427
$536$	3.04890	0.131693
$537$	−39.7486	−1.71528
$538$	−3.05387	−0.131662
$539$	−5.84406	−0.251722
$540$	−29.8726	−1.28551
$541$	7.08996	0.304821	0.152411	−	0.988317i	$-0.451296\pi$
$541$	7.08996	0.304821	0.152411	+	0.988317i	$0.451296\pi$
$542$	2.24310	0.0963493
$543$	−13.2875	−0.570220
$544$	10.1926	0.437005
$545$	0.913217	0.0391179
$546$	0	0
$547$	37.7944	1.61597	0.807986	−	0.589202i	$-0.200558\pi$
$547$	37.7944	1.61597	0.807986	+	0.589202i	$0.200558\pi$
$548$	−27.1438	−1.15953
$549$	69.6845	2.97406
$550$	−0.572916	−0.0244292
$551$	−26.5669	−1.13179
$552$	9.99743	0.425519
$553$	7.90798	0.336282
$554$	2.45640	0.104362
$555$	13.5505	0.575187
$556$	12.7146	0.539221
$557$	−37.9585	−1.60835	−0.804176	−	0.594391i	$-0.797393\pi$
$557$	−37.9585	−1.60835	−0.804176	+	0.594391i	$0.797393\pi$
$558$	−2.90973	−0.123179
$559$	0	0
$560$	−14.9133	−0.630201
$561$	−18.6099	−0.785710
$562$	2.84514	0.120015
$563$	4.28580	0.180625	0.0903125	−	0.995913i	$-0.471213\pi$
$563$	4.28580	0.180625	0.0903125	+	0.995913i	$0.471213\pi$
$564$	−75.8710	−3.19474
$565$	−16.8660	−0.709557
$566$	−3.28732	−0.138177
$567$	82.7823	3.47653
$568$	0.0416826	0.00174896
$569$	−28.5526	−1.19699	−0.598493	−	0.801128i	$-0.704234\pi$
$569$	−28.5526	−1.19699	−0.598493	+	0.801128i	$0.704234\pi$
$570$	−3.78377	−0.158485
$571$	12.3136	0.515310	0.257655	−	0.966237i	$-0.417050\pi$
$571$	12.3136	0.515310	0.257655	+	0.966237i	$0.417050\pi$
$572$	0	0
$573$	−12.6789	−0.529670
$574$	−0.556923	−0.0232455
$575$	20.1185	0.839000
$576$	−54.9944	−2.29143
$577$	−16.5468	−0.688854	−0.344427	−	0.938813i	$-0.611927\pi$
$577$	−16.5468	−0.688854	−0.344427	+	0.938813i	$0.611927\pi$
$578$	−2.44951	−0.101886
$579$	−16.4901	−0.685304
$580$	−7.71772	−0.320461
$581$	13.7047	0.568566
$582$	−5.71110	−0.236733
$583$	−0.145014	−0.00600587
$584$	6.34682	0.262633
$585$	0	0
$586$	−3.38134	−0.139682
$587$	−28.2129	−1.16447	−0.582235	−	0.813021i	$-0.697822\pi$
$587$	−28.2129	−1.16447	−0.582235	+	0.813021i	$0.697822\pi$
$588$	37.2036	1.53425
$589$	19.4210	0.800227
$590$	0.378359	0.0155768
$591$	−17.3719	−0.714586
$592$	15.1288	0.621789
$593$	32.5980	1.33864	0.669320	−	0.742974i	$-0.266586\pi$
$593$	32.5980	1.33864	0.669320	+	0.742974i	$0.266586\pi$
$594$	−2.09307	−0.0858797
$595$	22.2965	0.914069
$596$	5.93698	0.243188
$597$	16.4117	0.671687
$598$	0	0
$599$	9.75703	0.398661	0.199331	−	0.979932i	$-0.436123\pi$
$599$	9.75703	0.398661	0.199331	+	0.979932i	$0.436123\pi$
$600$	7.33544	0.299468
$601$	21.9155	0.893950	0.446975	−	0.894546i	$-0.352501\pi$
$601$	21.9155	0.893950	0.446975	+	0.894546i	$0.352501\pi$
$602$	0.650247	0.0265021
$603$	37.8358	1.54079
$604$	−46.3004	−1.88394
$605$	−1.07607	−0.0437483
$606$	3.98814	0.162007
$607$	35.3675	1.43552	0.717762	−	0.696289i	$-0.245167\pi$
$607$	35.3675	1.43552	0.717762	+	0.696289i	$0.245167\pi$
$608$	−12.9153	−0.523783
$609$	41.8334	1.69517
$610$	1.51906	0.0615051
$611$	0	0
$612$	84.1677	3.40228
$613$	−29.9389	−1.20922	−0.604611	−	0.796521i	$-0.706672\pi$
$613$	−29.9389	−1.20922	−0.604611	+	0.796521i	$0.706672\pi$
$614$	−3.13943	−0.126697
$615$	3.60956	0.145551
$616$	−2.12576	−0.0856494
$617$	12.1838	0.490499	0.245250	−	0.969460i	$-0.421130\pi$
$617$	12.1838	0.490499	0.245250	+	0.969460i	$0.421130\pi$
$618$	0.133480	0.00536934
$619$	15.3580	0.617288	0.308644	−	0.951178i	$-0.400125\pi$
$619$	15.3580	0.617288	0.308644	+	0.951178i	$0.400125\pi$
$620$	5.64181	0.226581
$621$	73.5001	2.94946
$622$	−4.16352	−0.166942
$623$	−37.3604	−1.49681
$624$	0	0
$625$	8.97202	0.358881
$626$	−0.697430	−0.0278749
$627$	23.5810	0.941733
$628$	−20.0607	−0.800508
$629$	−22.6187	−0.901869
$630$	4.23290	0.168643
$631$	−40.1765	−1.59940	−0.799701	−	0.600398i	$-0.795009\pi$
$631$	−40.1765	−1.59940	−0.799701	+	0.600398i	$0.795009\pi$
$632$	1.30881	0.0520618
$633$	15.0451	0.597990
$634$	−3.79082	−0.150553
$635$	23.1348	0.918075
$636$	0.923168	0.0366060
$637$	0	0
$638$	−0.540755	−0.0214087
$639$	0.517267	0.0204628
$640$	−4.99291	−0.197362
$641$	−12.9238	−0.510458	−0.255229	−	0.966881i	$-0.582151\pi$
$641$	−12.9238	−0.510458	−0.255229	+	0.966881i	$0.582151\pi$
$642$	−4.36855	−0.172413
$643$	−30.9303	−1.21977	−0.609885	−	0.792490i	$-0.708784\pi$
$643$	−30.9303	−1.21977	−0.609885	+	0.792490i	$0.708784\pi$
$644$	37.1154	1.46255
$645$	−4.21442	−0.165942
$646$	6.31594	0.248497
$647$	20.0880	0.789740	0.394870	−	0.918737i	$-0.370790\pi$
$647$	20.0880	0.789740	0.394870	+	0.918737i	$0.370790\pi$
$648$	13.7009	0.538223
$649$	−2.35799	−0.0925591
$650$	0	0
$651$	−30.5811	−1.19857
$652$	−1.21945	−0.0477575
$653$	28.1012	1.09968	0.549842	−	0.835269i	$-0.314688\pi$
$653$	28.1012	1.09968	0.549842	+	0.835269i	$0.314688\pi$
$654$	−0.407339	−0.0159282
$655$	−11.0417	−0.431435
$656$	4.02998	0.157344
$657$	78.7619	3.07279
$658$	6.36914	0.248295
$659$	−26.3236	−1.02542	−0.512711	−	0.858561i	$-0.671359\pi$
$659$	−26.3236	−1.02542	−0.512711	+	0.858561i	$0.671359\pi$
$660$	6.85029	0.266647
$661$	−9.22306	−0.358735	−0.179368	−	0.983782i	$-0.557405\pi$
$661$	−9.22306	−0.358735	−0.179368	+	0.983782i	$0.557405\pi$
$662$	4.63441	0.180121
$663$	0	0
$664$	2.26820	0.0880231
$665$	−28.2524	−1.09558
$666$	−4.29406	−0.166392
$667$	18.9891	0.735262
$668$	15.0507	0.582330
$669$	−5.45837	−0.211033
$670$	0.824790	0.0318644
$671$	−9.46701	−0.365470
$672$	20.3369	0.784513
$673$	2.33710	0.0900884	0.0450442	−	0.998985i	$-0.485657\pi$
$673$	2.33710	0.0900884	0.0450442	+	0.998985i	$0.485657\pi$
$674$	1.65530	0.0637600
$675$	53.9294	2.07575
$676$	0	0
$677$	2.49884	0.0960382	0.0480191	−	0.998846i	$-0.484709\pi$
$677$	2.49884	0.0960382	0.0480191	+	0.998846i	$0.484709\pi$
$678$	7.52304	0.288921
$679$	−42.6433	−1.63650
$680$	3.69020	0.141513
$681$	46.7425	1.79118
$682$	0.395303	0.0151369
$683$	−47.0092	−1.79876	−0.899379	−	0.437170i	$-0.855981\pi$
$683$	−47.0092	−1.79876	−0.899379	+	0.437170i	$0.855981\pi$
$684$	−106.651	−4.07789
$685$	−14.7685	−0.564274
$686$	0.617747	0.0235857
$687$	−29.5691	−1.12813
$688$	−4.70529	−0.179387
$689$	0	0
$690$	2.70451	0.102959
$691$	43.9719	1.67277	0.836385	−	0.548143i	$-0.184665\pi$
$691$	43.9719	1.67277	0.836385	+	0.548143i	$0.184665\pi$
$692$	−41.3667	−1.57253
$693$	−26.3800	−1.00209
$694$	−0.720569	−0.0273524
$695$	6.91780	0.262407
$696$	6.92365	0.262440
$697$	−6.02514	−0.228218
$698$	−1.01444	−0.0383970
$699$	−79.3490	−3.00125
$700$	27.2328	1.02930
$701$	8.08400	0.305328	0.152664	−	0.988278i	$-0.451215\pi$
$701$	8.08400	0.305328	0.152664	+	0.988278i	$0.451215\pi$
$702$	0	0
$703$	28.6607	1.08096
$704$	7.47128	0.281584
$705$	−41.2800	−1.55470
$706$	−3.97772	−0.149703
$707$	29.7783	1.11993
$708$	15.0111	0.564151
$709$	−23.1084	−0.867855	−0.433927	−	0.900948i	$-0.642873\pi$
$709$	−23.1084	−0.867855	−0.433927	+	0.900948i	$0.642873\pi$
$710$	0.0112760	0.000423180 0
$711$	16.2419	0.609120
$712$	−6.18335	−0.231731
$713$	−13.8814	−0.519864
$714$	−9.94533	−0.372195
$715$	0	0
$716$	−24.4231	−0.912734
$717$	−25.4783	−0.951504
$718$	−2.44296	−0.0911703
$719$	−0.262823	−0.00980164	−0.00490082	−	0.999988i	$-0.501560\pi$
$719$	−0.262823	−0.00980164	−0.00490082	+	0.999988i	$0.501560\pi$
$720$	−30.6299	−1.14151
$721$	0.996657	0.0371174
$722$	−5.16985	−0.192402
$723$	78.4391	2.91718
$724$	−8.16433	−0.303425
$725$	13.9329	0.517456
$726$	0.479977	0.0178136
$727$	−33.8486	−1.25537	−0.627687	−	0.778466i	$-0.715998\pi$
$727$	−33.8486	−1.25537	−0.627687	+	0.778466i	$0.715998\pi$
$728$	0	0
$729$	34.4809	1.27707
$730$	1.71694	0.0635469
$731$	7.03478	0.260191
$732$	60.2675	2.22755
$733$	−34.3896	−1.27021	−0.635105	−	0.772426i	$-0.719043\pi$
$733$	−34.3896	−1.27021	−0.635105	+	0.772426i	$0.719043\pi$
$734$	1.65066	0.0609269
$735$	20.2418	0.746631
$736$	9.23138	0.340273
$737$	−5.14020	−0.189342
$738$	−1.14384	−0.0421055
$739$	39.6452	1.45837	0.729186	−	0.684315i	$-0.239899\pi$
$739$	39.6452	1.45837	0.729186	+	0.684315i	$0.239899\pi$
$740$	8.32596	0.306068
$741$	0	0
$742$	−0.0774972	−0.00284501
$743$	−0.204133	−0.00748891	−0.00374445	−	0.999993i	$-0.501192\pi$
$743$	−0.204133	−0.00748891	−0.00374445	+	0.999993i	$0.501192\pi$
$744$	−5.06133	−0.185557
$745$	3.23020	0.118345
$746$	3.02464	0.110740
$747$	28.1476	1.02987
$748$	−11.4346	−0.418092
$749$	−32.6188	−1.19186
$750$	4.56682	0.166757
$751$	−19.3915	−0.707605	−0.353802	−	0.935320i	$-0.615111\pi$
$751$	−19.3915	−0.707605	−0.353802	+	0.935320i	$0.615111\pi$
$752$	−46.0881	−1.68066
$753$	−29.5400	−1.07650
$754$	0	0
$755$	−25.1912	−0.916803
$756$	99.4913	3.61846
$757$	17.5291	0.637107	0.318553	−	0.947905i	$-0.396803\pi$
$757$	17.5291	0.637107	0.318553	+	0.947905i	$0.396803\pi$
$758$	3.27163	0.118831
$759$	−16.8549	−0.611792
$760$	−4.67593	−0.169614
$761$	10.7721	0.390487	0.195244	−	0.980755i	$-0.437450\pi$
$761$	10.7721	0.390487	0.195244	+	0.980755i	$0.437450\pi$
$762$	−10.3192	−0.373826
$763$	−3.04149	−0.110109
$764$	−7.79043	−0.281848
$765$	45.7941	1.65569
$766$	−3.76006	−0.135857
$767$	0	0
$768$	−45.8703	−1.65520
$769$	12.9519	0.467059	0.233530	−	0.972350i	$-0.424972\pi$
$769$	12.9519	0.467059	0.233530	+	0.972350i	$0.424972\pi$
$770$	−0.575061	−0.0207238
$771$	−43.1440	−1.55379
$772$	−10.1321	−0.364664
$773$	19.3529	0.696077	0.348038	−	0.937480i	$-0.386848\pi$
$773$	19.3529	0.696077	0.348038	+	0.937480i	$0.386848\pi$
$774$	1.33552	0.0480043
$775$	−10.1853	−0.365865
$776$	−7.05770	−0.253357
$777$	−45.1303	−1.61904
$778$	1.62536	0.0582718
$779$	7.63458	0.273537
$780$	0	0
$781$	−0.0702735	−0.00251458
$782$	−4.51441	−0.161435
$783$	50.9020	1.81909
$784$	22.5995	0.807123
$785$	−10.9147	−0.389561
$786$	4.92513	0.175674
$787$	−21.6840	−0.772952	−0.386476	−	0.922300i	$-0.626308\pi$
$787$	−21.6840	−0.772952	−0.386476	+	0.922300i	$0.626308\pi$
$788$	−10.6740	−0.380245
$789$	70.7282	2.51799
$790$	0.354060	0.0125969
$791$	56.1726	1.99727
$792$	−4.36603	−0.155140
$793$	0	0
$794$	−4.70641	−0.167024
$795$	0.502279	0.0178140
$796$	10.0840	0.357418
$797$	−2.75951	−0.0977470	−0.0488735	−	0.998805i	$-0.515563\pi$
$797$	−2.75951	−0.0977470	−0.0488735	+	0.998805i	$0.515563\pi$
$798$	12.6019	0.446104
$799$	68.9053	2.43770
$800$	6.77337	0.239475
$801$	−76.7333	−2.71124
$802$	−5.01569	−0.177110
$803$	−10.7002	−0.377603
$804$	32.7228	1.15404
$805$	20.1938	0.711739
$806$	0	0
$807$	−65.9208	−2.32052
$808$	4.92848	0.173383
$809$	−45.8834	−1.61317	−0.806587	−	0.591115i	$-0.798688\pi$
$809$	−45.8834	−1.61317	−0.806587	+	0.591115i	$0.798688\pi$
$810$	3.70637	0.130229
$811$	−12.3618	−0.434083	−0.217042	−	0.976162i	$-0.569641\pi$
$811$	−12.3618	−0.434083	−0.217042	+	0.976162i	$0.569641\pi$
$812$	25.7041	0.902035
$813$	48.4195	1.69814
$814$	0.583372	0.0204472
$815$	−0.663482	−0.0232408
$816$	71.9659	2.51931
$817$	−8.91391	−0.311858
$818$	−4.32597	−0.151254
$819$	0	0
$820$	2.21785	0.0774507
$821$	32.6089	1.13806	0.569029	−	0.822317i	$-0.307319\pi$
$821$	32.6089	1.13806	0.569029	+	0.822317i	$0.307319\pi$
$822$	6.58745	0.229764
$823$	22.7067	0.791504	0.395752	−	0.918357i	$-0.370484\pi$
$823$	22.7067	0.791504	0.395752	+	0.918357i	$0.370484\pi$
$824$	0.164952	0.00574638
$825$	−12.3670	−0.430562
$826$	−1.26013	−0.0438457
$827$	7.61671	0.264859	0.132429	−	0.991192i	$-0.457722\pi$
$827$	7.61671	0.264859	0.132429	+	0.991192i	$0.457722\pi$
$828$	76.2302	2.64918
$829$	−7.63802	−0.265279	−0.132640	−	0.991164i	$-0.542345\pi$
$829$	−7.63802	−0.265279	−0.132640	+	0.991164i	$0.542345\pi$
$830$	0.613593	0.0212981
$831$	53.0238	1.83938
$832$	0	0
$833$	−33.7880	−1.17068
$834$	−3.08567	−0.106848
$835$	8.18882	0.283386
$836$	14.4891	0.501115
$837$	−37.2104	−1.28618
$838$	−2.52044	−0.0870671
$839$	29.8606	1.03090	0.515451	−	0.856919i	$-0.327624\pi$
$839$	29.8606	1.03090	0.515451	+	0.856919i	$0.327624\pi$
$840$	7.36291	0.254044
$841$	−15.8492	−0.546525
$842$	−1.40083	−0.0482758
$843$	61.4150	2.11525
$844$	9.24431	0.318202
$845$	0	0
$846$	13.0814	0.449746
$847$	3.58386	0.123143
$848$	0.560781	0.0192573
$849$	−70.9601	−2.43534
$850$	−3.31237	−0.113613
$851$	−20.4857	−0.702239
$852$	0.447365	0.0153265
$853$	−32.2985	−1.10588	−0.552941	−	0.833221i	$-0.686494\pi$
$853$	−32.2985	−1.10588	−0.552941	+	0.833221i	$0.686494\pi$
$854$	−5.05928	−0.173125
$855$	−58.0267	−1.98447
$856$	−5.39859	−0.184520
$857$	7.77734	0.265669	0.132834	−	0.991138i	$-0.457592\pi$
$857$	7.77734	0.265669	0.132834	+	0.991138i	$0.457592\pi$
$858$	0	0
$859$	7.28099	0.248424	0.124212	−	0.992256i	$-0.460360\pi$
$859$	7.28099	0.248424	0.124212	+	0.992256i	$0.460360\pi$
$860$	−2.58950	−0.0883012
$861$	−12.0217	−0.409699
$862$	0.854076	0.0290899
$863$	−26.3739	−0.897778	−0.448889	−	0.893588i	$-0.648180\pi$
$863$	−26.3739	−0.897778	−0.448889	+	0.893588i	$0.648180\pi$
$864$	24.7455	0.841860
$865$	−22.5069	−0.765256
$866$	−2.87729	−0.0977742
$867$	−52.8750	−1.79573
$868$	−18.7902	−0.637780
$869$	−2.20655	−0.0748522
$870$	1.87299	0.0635002
$871$	0	0
$872$	−0.503383	−0.0170467
$873$	−87.5836	−2.96426
$874$	5.72030	0.193492
$875$	34.0992	1.15276
$876$	68.1182	2.30150
$877$	29.9767	1.01224	0.506121	−	0.862462i	$-0.331079\pi$
$877$	29.9767	1.01224	0.506121	+	0.862462i	$0.331079\pi$
$878$	−3.58872	−0.121113
$879$	−72.9895	−2.46187
$880$	4.16123	0.140275
$881$	−19.1781	−0.646128	−0.323064	−	0.946377i	$-0.604713\pi$
$881$	−19.1781	−0.646128	−0.323064	+	0.946377i	$0.604713\pi$
$882$	−6.41449	−0.215987
$883$	−4.66507	−0.156992	−0.0784960	−	0.996914i	$-0.525012\pi$
$883$	−4.66507	−0.156992	−0.0784960	+	0.996914i	$0.525012\pi$
$884$	0	0
$885$	8.16725	0.274539
$886$	0.626228	0.0210385
$887$	6.43856	0.216186	0.108093	−	0.994141i	$-0.465526\pi$
$887$	6.43856	0.216186	0.108093	+	0.994141i	$0.465526\pi$
$888$	−7.46931	−0.250654
$889$	−77.0509	−2.58420
$890$	−1.67272	−0.0560698
$891$	−23.0986	−0.773833
$892$	−3.35383	−0.112295
$893$	−87.3114	−2.92176
$894$	−1.44083	−0.0481884
$895$	−13.2882	−0.444174
$896$	16.6290	0.555536
$897$	0	0
$898$	−1.21979	−0.0407048
$899$	−9.61349	−0.320628
$900$	55.9325	1.86442
$901$	−0.838413	−0.0279316
$902$	0.155397	0.00517417
$903$	14.0362	0.467096
$904$	9.29687	0.309209
$905$	−4.44206	−0.147659
$906$	11.2365	0.373308
$907$	17.1170	0.568359	0.284180	−	0.958771i	$-0.408279\pi$
$907$	17.1170	0.568359	0.284180	+	0.958771i	$0.408279\pi$
$908$	28.7204	0.953120
$909$	61.1607	2.02857
$910$	0	0
$911$	13.3331	0.441746	0.220873	−	0.975303i	$-0.429109\pi$
$911$	13.3331	0.441746	0.220873	+	0.975303i	$0.429109\pi$
$912$	−91.1895	−3.01959
$913$	−3.82400	−0.126556
$914$	2.63358	0.0871111
$915$	32.7905	1.08402
$916$	−18.1684	−0.600301
$917$	36.7747	1.21441
$918$	−12.1013	−0.399402
$919$	−3.68329	−0.121501	−0.0607503	−	0.998153i	$-0.519349\pi$
$919$	−3.68329	−0.121501	−0.0607503	+	0.998153i	$0.519349\pi$
$920$	3.34219	0.110189
$921$	−67.7676	−2.23302
$922$	−5.13972	−0.169268
$923$	0	0
$924$	−22.8151	−0.750561
$925$	−15.0310	−0.494216
$926$	−0.131542	−0.00432274
$927$	2.04700	0.0672323
$928$	6.39313	0.209865
$929$	13.0683	0.428757	0.214379	−	0.976751i	$-0.431227\pi$
$929$	13.0683	0.428757	0.214379	+	0.976751i	$0.431227\pi$
$930$	−1.36919	−0.0448976
$931$	42.8135	1.40315
$932$	−48.7551	−1.59703
$933$	−89.8736	−2.94233
$934$	3.22117	0.105400
$935$	−6.22138	−0.203461
$936$	0	0
$937$	−25.8440	−0.844287	−0.422144	−	0.906529i	$-0.638722\pi$
$937$	−25.8440	−0.844287	−0.422144	+	0.906529i	$0.638722\pi$
$938$	−2.74698	−0.0896921
$939$	−15.0547	−0.491292
$940$	−25.3640	−0.827284
$941$	24.4292	0.796370	0.398185	−	0.917305i	$-0.369640\pi$
$941$	24.4292	0.796370	0.398185	+	0.917305i	$0.369640\pi$
$942$	4.86846	0.158623
$943$	−5.45693	−0.177702
$944$	9.11853	0.296783
$945$	54.1314	1.76089
$946$	−0.181438	−0.00589904
$947$	4.16646	0.135392	0.0676959	−	0.997706i	$-0.478435\pi$
$947$	4.16646	0.135392	0.0676959	+	0.997706i	$0.478435\pi$
$948$	14.0470	0.456227
$949$	0	0
$950$	4.19717	0.136174
$951$	−81.8285	−2.65347
$952$	−12.2903	−0.398331
$953$	−39.4339	−1.27739	−0.638695	−	0.769460i	$-0.720526\pi$
$953$	−39.4339	−1.27739	−0.638695	+	0.769460i	$0.720526\pi$
$954$	−0.159169	−0.00515328
$955$	−4.23863	−0.137159
$956$	−15.6549	−0.506314
$957$	−11.6727	−0.377325
$958$	0.967892	0.0312712
$959$	49.1867	1.58832
$960$	−25.8779	−0.835207
$961$	−23.9723	−0.773301
$962$	0	0
$963$	−66.9946	−2.15887
$964$	48.1960	1.55229
$965$	−5.51271	−0.177460
$966$	−9.00742	−0.289809
$967$	5.25113	0.168865	0.0844325	−	0.996429i	$-0.473092\pi$
$967$	5.25113	0.168865	0.0844325	+	0.996429i	$0.473092\pi$
$968$	0.593149	0.0190645
$969$	136.336	4.37973
$970$	−1.90925	−0.0613023
$971$	56.9977	1.82914	0.914572	−	0.404422i	$-0.132527\pi$
$971$	56.9977	1.82914	0.914572	+	0.404422i	$0.132527\pi$
$972$	63.7644	2.04525
$973$	−23.0399	−0.738625
$974$	−1.61361	−0.0517032
$975$	0	0
$976$	36.6097	1.17185
$977$	42.9772	1.37496	0.687481	−	0.726202i	$-0.258716\pi$
$977$	42.9772	1.37496	0.687481	+	0.726202i	$0.258716\pi$
$978$	0.295945	0.00946328
$979$	10.4246	0.333173
$980$	12.4374	0.397297
$981$	−6.24681	−0.199445
$982$	−1.69003	−0.0539310
$983$	−15.5764	−0.496809	−0.248404	−	0.968656i	$-0.579906\pi$
$983$	−15.5764	−0.496809	−0.248404	+	0.968656i	$0.579906\pi$
$984$	−1.98966	−0.0634280
$985$	−5.80753	−0.185043
$986$	−3.12643	−0.0995657
$987$	137.484	4.37617
$988$	0	0
$989$	6.37135	0.202597
$990$	−1.18110	−0.0375378
$991$	12.2598	0.389446	0.194723	−	0.980858i	$-0.437619\pi$
$991$	12.2598	0.389446	0.194723	+	0.980858i	$0.437619\pi$
$992$	−4.67351	−0.148384
$993$	100.038	3.17462
$994$	−0.0375549	−0.00119117
$995$	5.48651	0.173934
$996$	24.3438	0.771362
$997$	−10.7308	−0.339848	−0.169924	−	0.985457i	$-0.554352\pi$
$997$	−10.7308	−0.339848	−0.169924	+	0.985457i	$0.554352\pi$
$998$	−2.44816	−0.0774950
$999$	−54.9136	−1.73739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.10	✓	21
13.12	even	2		1859.2.a.t.1.12	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.10	✓	21	1.1	even	1	trivial
1859.2.a.t.1.12	yes	21	13.12	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-0.149116 q^{2} -3.21882 q^{3} -1.97776 q^{4} -1.07607 q^{5} +0.479977 q^{6} +3.58386 q^{7} +0.593149 q^{8} +7.36077 q^{9} +O(q^{10})\)	\(q-0.149116 q^{2} -3.21882 q^{3} -1.97776 q^{4} -1.07607 q^{5} +0.479977 q^{6} +3.58386 q^{7} +0.593149 q^{8} +7.36077 q^{9} +0.160459 q^{10} -1.00000 q^{11} +6.36606 q^{12} -0.534411 q^{14} +3.46366 q^{15} +3.86708 q^{16} -5.78160 q^{17} -1.09761 q^{18} +7.32598 q^{19} +2.12820 q^{20} -11.5358 q^{21} +0.149116 q^{22} -5.23635 q^{23} -1.90924 q^{24} -3.84208 q^{25} -14.0365 q^{27} -7.08803 q^{28} -3.62640 q^{29} -0.516487 q^{30} +2.65097 q^{31} -1.76294 q^{32} +3.21882 q^{33} +0.862129 q^{34} -3.85647 q^{35} -14.5579 q^{36} +3.91220 q^{37} -1.09242 q^{38} -0.638267 q^{40} +1.04212 q^{41} +1.72017 q^{42} -1.21675 q^{43} +1.97776 q^{44} -7.92067 q^{45} +0.780824 q^{46} -11.9180 q^{47} -12.4474 q^{48} +5.84406 q^{49} +0.572916 q^{50} +18.6099 q^{51} +0.145014 q^{53} +2.09307 q^{54} +1.07607 q^{55} +2.12576 q^{56} -23.5810 q^{57} +0.540755 q^{58} +2.35799 q^{59} -6.85029 q^{60} +9.46701 q^{61} -0.395303 q^{62} +26.3800 q^{63} -7.47128 q^{64} -0.479977 q^{66} +5.14020 q^{67} +11.4346 q^{68} +16.8549 q^{69} +0.575061 q^{70} +0.0702735 q^{71} +4.36603 q^{72} +10.7002 q^{73} -0.583372 q^{74} +12.3670 q^{75} -14.4891 q^{76} -3.58386 q^{77} +2.20655 q^{79} -4.16123 q^{80} +23.0986 q^{81} -0.155397 q^{82} +3.82400 q^{83} +22.8151 q^{84} +6.22138 q^{85} +0.181438 q^{86} +11.6727 q^{87} -0.593149 q^{88} -10.4246 q^{89} +1.18110 q^{90} +10.3563 q^{92} -8.53299 q^{93} +1.77717 q^{94} -7.88323 q^{95} +5.67458 q^{96} -11.8987 q^{97} -0.871443 q^{98} -7.36077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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