LMFDB - Embedded newform 1859.2.a.t.1.12

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			1.12
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	$-0.483211\pi$
$2$	0.149116	0.105441	0.0527205	+	0.998609i	$0.483211\pi$
$3$	−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	$-0.422651\pi$
$5$	1.07607	0.481231	0.240616	+	0.970621i	$0.422651\pi$
$6$	−0.479977	−0.195950
$7$	−3.58386	−1.35457	−0.677286	−	0.735720i	$-0.736844\pi$
$7$	−3.58386	−1.35457	−0.677286	+	0.735720i	$0.736844\pi$
$8$	−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	$-0.817649\pi$
$19$	−7.32598	−1.68070	−0.840348	+	0.542048i	$0.817649\pi$
$20$	−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	$-0.576513\pi$
$31$	−2.65097	−0.476129	−0.238064	+	0.971249i	$0.576513\pi$
$32$	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	$-0.604214\pi$
$37$	−3.91220	−0.643161	−0.321581	+	0.946882i	$0.604214\pi$
$38$	−1.09242	−0.177214
$39$	0	0
$40$	−0.638267	−0.100919
$41$	−1.04212	−0.162752	−0.0813762	−	0.996683i	$-0.525932\pi$
$41$	−1.04212	−0.162752	−0.0813762	+	0.996683i	$0.525932\pi$
$42$	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	$-0.164626\pi$
$47$	11.9180	1.73843	0.869213	+	0.494438i	$0.164626\pi$
$48$	−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	$-0.549052\pi$
$59$	−2.35799	−0.306984	−0.153492	+	0.988150i	$0.549052\pi$
$60$	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	$-0.601665\pi$
$67$	−5.14020	−0.627976	−0.313988	+	0.949427i	$0.601665\pi$
$68$	11.4346	1.38665
$69$	16.8549	2.02909
$70$	−0.575061	−0.0687330
$71$	−0.0702735	−0.00833993	−0.00416996	−	0.999991i	$-0.501327\pi$
$71$	−0.0702735	−0.00833993	−0.00416996	+	0.999991i	$0.501327\pi$
$72$	−4.36603	−0.514542
$73$	−10.7002	−1.25237	−0.626183	−	0.779676i	$-0.715384\pi$
$73$	−10.7002	−1.25237	−0.626183	+	0.779676i	$0.715384\pi$
$74$	−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	$-0.567304\pi$
$83$	−3.82400	−0.419738	−0.209869	+	0.977730i	$0.567304\pi$
$84$	−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	$-0.313672\pi$
$89$	10.4246	1.10501	0.552504	+	0.833510i	$0.313672\pi$
$90$	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	$-0.293547\pi$
$97$	11.8987	1.20813	0.604065	+	0.796935i	$0.293547\pi$
$98$	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	$-0.487059\pi$
$109$	0.848663	0.0812872	0.0406436	+	0.999174i	$0.487059\pi$
$110$	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	$-0.699409\pi$
$137$	−13.7245	−1.17256	−0.586282	+	0.810107i	$0.699409\pi$
$138$	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	$-0.460761\pi$
$149$	3.00186	0.245922	0.122961	+	0.992411i	$0.460761\pi$
$150$	1.84411	0.150571
$151$	−23.4105	−1.90512	−0.952560	−	0.304352i	$-0.901560\pi$
$151$	−23.4105	−1.90512	−0.952560	+	0.304352i	$0.901560\pi$
$152$	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	$-0.507687\pi$
$163$	−0.616582	−0.0482944	−0.0241472	+	0.999708i	$0.507687\pi$
$164$	2.06108	0.160943
$165$	−3.46366	−0.269645
$166$	−0.570219	−0.0442576
$167$	7.60997	0.588877	0.294439	−	0.955670i	$-0.404867\pi$
$167$	7.60997	0.588877	0.294439	+	0.955670i	$0.404867\pi$
$168$	−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	$-0.559028\pi$
$193$	−5.12303	−0.368763	−0.184382	+	0.982855i	$0.559028\pi$
$194$	1.77429	0.127386
$195$	0	0
$196$	−11.5582	−0.825584
$197$	−5.39700	−0.384520	−0.192260	−	0.981344i	$-0.561582\pi$
$197$	−5.39700	−0.384520	−0.192260	+	0.981344i	$0.561582\pi$
$198$	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	$-0.518083\pi$
$223$	−1.69577	−0.113557	−0.0567786	+	0.998387i	$0.518083\pi$
$224$	−6.31814	−0.422148
$225$	−28.2807	−1.88538
$226$	2.33721	0.155469
$227$	14.5217	0.963836	0.481918	−	0.876216i	$-0.339940\pi$
$227$	14.5217	0.963836	0.481918	+	0.876216i	$0.339940\pi$
$228$	−46.6376	−3.08865
$229$	−9.18634	−0.607050	−0.303525	−	0.952823i	$-0.598164\pi$
$229$	−9.18634	−0.607050	−0.303525	+	0.952823i	$0.598164\pi$
$230$	−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	$-0.582406\pi$
$239$	−7.91543	−0.512006	−0.256003	+	0.966676i	$0.582406\pi$
$240$	−13.3942	−0.864594
$241$	24.3689	1.56974	0.784871	−	0.619660i	$-0.212729\pi$
$241$	24.3689	1.56974	0.784871	+	0.619660i	$0.212729\pi$
$242$	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	$-0.348964\pi$
$271$	15.0426	0.913775	0.456888	+	0.889524i	$0.348964\pi$
$272$	−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	$-0.307288\pi$
$281$	19.0800	1.13822	0.569109	+	0.822262i	$0.307288\pi$
$282$	−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	$-0.730449\pi$
$293$	−22.6759	−1.32474	−0.662369	+	0.749177i	$0.730449\pi$
$294$	−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	$-0.705150\pi$
$307$	−21.0536	−1.20159	−0.600796	+	0.799402i	$0.705150\pi$
$308$	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	$-0.753081\pi$
$317$	−25.4219	−1.42784	−0.713919	+	0.700228i	$0.753081\pi$
$318$	−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	$-0.174088\pi$
$331$	31.0792	1.70827	0.854133	+	0.520054i	$0.174088\pi$
$332$	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	$-0.558282\pi$
$349$	−6.80301	−0.364157	−0.182078	+	0.983284i	$0.558282\pi$
$350$	2.05325	0.109751
$351$	0	0
$352$	1.76294	0.0939651
$353$	−26.6753	−1.41978	−0.709892	−	0.704310i	$-0.751256\pi$
$353$	−26.6753	−1.41978	−0.709892	+	0.704310i	$0.751256\pi$
$354$	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	$-0.642308\pi$
$359$	−16.3829	−0.864657	−0.432329	+	0.901716i	$0.642308\pi$
$360$	−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	$-0.309456\pi$
$379$	21.9402	1.12699	0.563496	+	0.826119i	$0.309456\pi$
$380$	15.5912	0.799811
$381$	69.2026	3.54536
$382$	0.587369	0.0300524
$383$	−25.2157	−1.28846	−0.644230	−	0.764832i	$-0.722822\pi$
$383$	−25.2157	−1.28846	−0.644230	+	0.764832i	$0.722822\pi$
$384$	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	$-0.790974\pi$
$397$	−31.5621	−1.58405	−0.792027	+	0.610486i	$0.790974\pi$
$398$	−0.760295	−0.0381102
$399$	−84.5109	−4.23084
$400$	−14.8576	−0.742882
$401$	−33.6361	−1.67971	−0.839854	−	0.542812i	$-0.817360\pi$
$401$	−33.6361	−1.67971	−0.839854	+	0.542812i	$0.817360\pi$
$402$	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	$-0.754597\pi$
$409$	−29.0107	−1.43449	−0.717244	+	0.696822i	$0.754597\pi$
$410$	−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	$-0.573521\pi$
$421$	−9.39424	−0.457847	−0.228924	+	0.973444i	$0.573521\pi$
$422$	−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	$-0.455951\pi$
$431$	5.72759	0.275888	0.137944	+	0.990440i	$0.455951\pi$
$432$	−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	$-0.561829\pi$
$449$	−8.18012	−0.386044	−0.193022	+	0.981194i	$0.561829\pi$
$450$	−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	$-0.364453\pi$
$457$	17.6613	0.826160	0.413080	+	0.910695i	$0.364453\pi$
$458$	−1.36983	−0.0640080
$459$	81.1534	3.78792
$460$	11.1440	0.519593
$461$	−34.4679	−1.60533	−0.802666	−	0.596429i	$-0.796586\pi$
$461$	−34.4679	−1.60533	−0.802666	+	0.596429i	$0.796586\pi$
$462$	1.72017	0.0800296
$463$	−0.882146	−0.0409968	−0.0204984	−	0.999790i	$-0.506525\pi$
$463$	−0.882146	−0.0409968	−0.0204984	+	0.999790i	$0.506525\pi$
$464$	−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	$-0.452624\pi$
$479$	6.49086	0.296575	0.148287	+	0.988944i	$0.452624\pi$
$480$	−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	$-0.578846\pi$
$487$	−10.8211	−0.490353	−0.245176	+	0.969479i	$0.578846\pi$
$488$	−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	$-0.619780\pi$
$499$	−16.4178	−0.734961	−0.367481	+	0.930031i	$0.619780\pi$
$500$	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	$-0.656800\pi$
$509$	−21.3391	−0.945840	−0.472920	+	0.881105i	$0.656800\pi$
$510$	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	$-0.548704\pi$
$541$	−7.08996	−0.304821	−0.152411	+	0.988317i	$0.548704\pi$
$542$	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	$-0.202607\pi$
$557$	37.9585	1.60835	0.804176	+	0.594391i	$0.202607\pi$
$558$	−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	$-0.388073\pi$
$577$	16.5468	0.688854	0.344427	+	0.938813i	$0.388073\pi$
$578$	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	$-0.302178\pi$
$587$	28.2129	1.16447	0.582235	+	0.813021i	$0.302178\pi$
$588$	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	$-0.733414\pi$
$593$	−32.5980	−1.33864	−0.669320	+	0.742974i	$0.733414\pi$
$594$	−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	$-0.293328\pi$
$613$	29.9389	1.20922	0.604611	+	0.796521i	$0.293328\pi$
$614$	−3.13943	−0.126697
$615$	3.60956	0.145551
$616$	2.12576	0.0856494
$617$	−12.1838	−0.490499	−0.245250	−	0.969460i	$-0.578870\pi$
$617$	−12.1838	−0.490499	−0.245250	+	0.969460i	$0.578870\pi$
$618$	−0.133480	−0.00536934
$619$	−15.3580	−0.617288	−0.308644	−	0.951178i	$-0.599875\pi$
$619$	−15.3580	−0.617288	−0.308644	+	0.951178i	$0.599875\pi$
$620$	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	$-0.204991\pi$
$631$	40.1765	1.59940	0.799701	+	0.600398i	$0.204991\pi$
$632$	−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	$-0.291216\pi$
$643$	30.9303	1.21977	0.609885	+	0.792490i	$0.291216\pi$
$644$	−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	$-0.442595\pi$
$661$	9.22306	0.358735	0.179368	+	0.983782i	$0.442595\pi$
$662$	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	$-0.144019\pi$
$683$	47.0092	1.79876	0.899379	+	0.437170i	$0.144019\pi$
$684$	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	$-0.815335\pi$
$691$	−43.9719	−1.67277	−0.836385	+	0.548143i	$0.815335\pi$
$692$	−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	$-0.357127\pi$
$709$	23.1084	0.867855	0.433927	+	0.900948i	$0.357127\pi$
$710$	−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	$-0.280957\pi$
$733$	34.3896	1.27021	0.635105	+	0.772426i	$0.280957\pi$
$734$	−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	$-0.760101\pi$
$739$	−39.6452	−1.45837	−0.729186	+	0.684315i	$0.760101\pi$
$740$	8.32596	0.306068
$741$	0	0
$742$	−0.0774972	−0.00284501
$743$	0.204133	0.00748891	0.00374445	−	0.999993i	$-0.498808\pi$
$743$	0.204133	0.00748891	0.00374445	+	0.999993i	$0.498808\pi$
$744$	−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	$-0.562550\pi$
$761$	−10.7721	−0.390487	−0.195244	+	0.980755i	$0.562550\pi$
$762$	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	$-0.575028\pi$
$769$	−12.9519	−0.467059	−0.233530	+	0.972350i	$0.575028\pi$
$770$	−0.575061	−0.0207238
$771$	−43.1440	−1.55379
$772$	10.1321	0.364664
$773$	−19.3529	−0.696077	−0.348038	−	0.937480i	$-0.613152\pi$
$773$	−19.3529	−0.696077	−0.348038	+	0.937480i	$0.613152\pi$
$774$	−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	$-0.373692\pi$
$787$	21.6840	0.772952	0.386476	+	0.922300i	$0.373692\pi$
$788$	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	$-0.430359\pi$
$811$	12.3618	0.434083	0.217042	+	0.976162i	$0.430359\pi$
$812$	−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	$-0.692681\pi$
$821$	−32.6089	−1.13806	−0.569029	+	0.822317i	$0.692681\pi$
$822$	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	$-0.542278\pi$
$827$	−7.61671	−0.264859	−0.132429	+	0.991192i	$0.542278\pi$
$828$	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	$-0.672376\pi$
$839$	−29.8606	−1.03090	−0.515451	+	0.856919i	$0.672376\pi$
$840$	−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	$-0.313506\pi$
$853$	32.2985	1.10588	0.552941	+	0.833221i	$0.313506\pi$
$854$	−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	$-0.351820\pi$
$863$	26.3739	0.897778	0.448889	+	0.893588i	$0.351820\pi$
$864$	−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	$-0.668921\pi$
$877$	−29.9767	−1.01224	−0.506121	+	0.862462i	$0.668921\pi$
$878$	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	$-0.568773\pi$
$929$	−13.0683	−0.428757	−0.214379	+	0.976751i	$0.568773\pi$
$930$	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	$-0.630360\pi$
$941$	−24.4292	−0.796370	−0.398185	+	0.917305i	$0.630360\pi$
$942$	−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	$-0.521565\pi$
$947$	−4.16646	−0.135392	−0.0676959	+	0.997706i	$0.521565\pi$
$948$	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	$-0.526908\pi$
$967$	−5.25113	−0.168865	−0.0844325	+	0.996429i	$0.526908\pi$
$968$	−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	$-0.741284\pi$
$977$	−42.9772	−1.37496	−0.687481	+	0.726202i	$0.741284\pi$
$978$	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	$-0.420094\pi$
$983$	15.5764	0.496809	0.248404	+	0.968656i	$0.420094\pi$
$984$	−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.t.1.12	yes	21
13.12	even	2		1859.2.a.s.1.10	✓	21

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

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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