LMFDB - Embedded newform 1859.2.a.s.1.19

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			1.19
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)

$f(q)$	$=$	$q+2.68347 q^{2} +3.12668 q^{3} +5.20101 q^{4} -2.33476 q^{5} +8.39034 q^{6} -0.266736 q^{7} +8.58980 q^{8} +6.77612 q^{9} +O(q^{10})$	\(q+2.68347 q^{2} +3.12668 q^{3} +5.20101 q^{4} -2.33476 q^{5} +8.39034 q^{6} -0.266736 q^{7} +8.58980 q^{8} +6.77612 q^{9} -6.26526 q^{10} -1.00000 q^{11} +16.2619 q^{12} -0.715776 q^{14} -7.30005 q^{15} +12.6484 q^{16} -1.53629 q^{17} +18.1835 q^{18} -7.55923 q^{19} -12.1431 q^{20} -0.833996 q^{21} -2.68347 q^{22} -3.95510 q^{23} +26.8575 q^{24} +0.451118 q^{25} +11.8067 q^{27} -1.38729 q^{28} +1.08736 q^{29} -19.5895 q^{30} +3.25139 q^{31} +16.7621 q^{32} -3.12668 q^{33} -4.12259 q^{34} +0.622764 q^{35} +35.2426 q^{36} -3.44806 q^{37} -20.2850 q^{38} -20.0551 q^{40} +6.30467 q^{41} -2.23800 q^{42} +2.45816 q^{43} -5.20101 q^{44} -15.8206 q^{45} -10.6134 q^{46} +6.48085 q^{47} +39.5476 q^{48} -6.92885 q^{49} +1.21056 q^{50} -4.80349 q^{51} +5.06393 q^{53} +31.6829 q^{54} +2.33476 q^{55} -2.29120 q^{56} -23.6353 q^{57} +2.91791 q^{58} -10.8892 q^{59} -37.9676 q^{60} +9.66466 q^{61} +8.72501 q^{62} -1.80743 q^{63} +19.6837 q^{64} -8.39034 q^{66} -6.41989 q^{67} -7.99026 q^{68} -12.3663 q^{69} +1.67117 q^{70} -13.0818 q^{71} +58.2055 q^{72} +1.49954 q^{73} -9.25276 q^{74} +1.41050 q^{75} -39.3156 q^{76} +0.266736 q^{77} -3.63953 q^{79} -29.5311 q^{80} +16.5874 q^{81} +16.9184 q^{82} +9.17706 q^{83} -4.33762 q^{84} +3.58688 q^{85} +6.59640 q^{86} +3.39984 q^{87} -8.58980 q^{88} +8.10322 q^{89} -42.4542 q^{90} -20.5705 q^{92} +10.1661 q^{93} +17.3912 q^{94} +17.6490 q^{95} +52.4097 q^{96} +12.7243 q^{97} -18.5934 q^{98} -6.77612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.68347	1.89750	0.948750	−	0.316029i	$-0.102350\pi$
$2$	2.68347	1.89750	0.948750	+	0.316029i	$0.102350\pi$
$3$	3.12668	1.80519	0.902594	−	0.430492i	$-0.141660\pi$
$3$	3.12668	1.80519	0.902594	+	0.430492i	$0.141660\pi$
$4$	5.20101	2.60050
$5$	−2.33476	−1.04414	−0.522069	−	0.852903i	$-0.674840\pi$
$5$	−2.33476	−1.04414	−0.522069	+	0.852903i	$0.674840\pi$
$6$	8.39034	3.42534
$7$	−0.266736	−0.100817	−0.0504083	−	0.998729i	$-0.516052\pi$
$7$	−0.266736	−0.100817	−0.0504083	+	0.998729i	$0.516052\pi$
$8$	8.58980	3.03695
$9$	6.77612	2.25871
$10$	−6.26526	−1.98125
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	16.2619	4.69440
$13$	0	0
$13$	0	0
$14$	−0.715776	−0.191299
$15$	−7.30005	−1.88487
$16$	12.6484	3.16211
$17$	−1.53629	−0.372605	−0.186303	−	0.982492i	$-0.559650\pi$
$17$	−1.53629	−0.372605	−0.186303	+	0.982492i	$0.559650\pi$
$18$	18.1835	4.28589
$19$	−7.55923	−1.73421	−0.867103	−	0.498129i	$-0.834021\pi$
$19$	−7.55923	−1.73421	−0.867103	+	0.498129i	$0.834021\pi$
$20$	−12.1431	−2.71528
$21$	−0.833996	−0.181993
$22$	−2.68347	−0.572118
$23$	−3.95510	−0.824696	−0.412348	−	0.911026i	$-0.635291\pi$
$23$	−3.95510	−0.824696	−0.412348	+	0.911026i	$0.635291\pi$
$24$	26.8575	5.48227
$25$	0.451118	0.0902236
$26$	0	0
$27$	11.8067	2.27220
$28$	−1.38729	−0.262174
$29$	1.08736	0.201919	0.100959	−	0.994891i	$-0.467809\pi$
$29$	1.08736	0.201919	0.100959	+	0.994891i	$0.467809\pi$
$30$	−19.5895	−3.57653
$31$	3.25139	0.583967	0.291984	−	0.956423i	$-0.405685\pi$
$31$	3.25139	0.583967	0.291984	+	0.956423i	$0.405685\pi$
$32$	16.7621	2.96315
$33$	−3.12668	−0.544285
$34$	−4.12259	−0.707018
$35$	0.622764	0.105266
$36$	35.2426	5.87377
$37$	−3.44806	−0.566857	−0.283429	−	0.958993i	$-0.591472\pi$
$37$	−3.44806	−0.566857	−0.283429	+	0.958993i	$0.591472\pi$
$38$	−20.2850	−3.29066
$39$	0	0
$40$	−20.0551	−3.17100
$41$	6.30467	0.984624	0.492312	−	0.870419i	$-0.336152\pi$
$41$	6.30467	0.984624	0.492312	+	0.870419i	$0.336152\pi$
$42$	−2.23800	−0.345331
$43$	2.45816	0.374866	0.187433	−	0.982277i	$-0.439983\pi$
$43$	2.45816	0.374866	0.187433	+	0.982277i	$0.439983\pi$
$44$	−5.20101	−0.784081
$45$	−15.8206	−2.35840
$46$	−10.6134	−1.56486
$47$	6.48085	0.945329	0.472664	−	0.881243i	$-0.343292\pi$
$47$	6.48085	0.945329	0.472664	+	0.881243i	$0.343292\pi$
$48$	39.5476	5.70821
$49$	−6.92885	−0.989836
$50$	1.21056	0.171199
$51$	−4.80349	−0.672623
$52$	0	0
$53$	5.06393	0.695584	0.347792	−	0.937572i	$-0.386932\pi$
$53$	5.06393	0.695584	0.347792	+	0.937572i	$0.386932\pi$
$54$	31.6829	4.31150
$55$	2.33476	0.314819
$56$	−2.29120	−0.306175
$57$	−23.6353	−3.13057
$58$	2.91791	0.383140
$59$	−10.8892	−1.41766	−0.708828	−	0.705381i	$-0.750776\pi$
$59$	−10.8892	−1.41766	−0.708828	+	0.705381i	$0.750776\pi$
$60$	−37.9676	−4.90160
$61$	9.66466	1.23743	0.618716	−	0.785614i	$-0.287653\pi$
$61$	9.66466	1.23743	0.618716	+	0.785614i	$0.287653\pi$
$62$	8.72501	1.10808
$63$	−1.80743	−0.227715
$64$	19.6837	2.46047
$65$	0	0
$66$	−8.39034	−1.03278
$67$	−6.41989	−0.784314	−0.392157	−	0.919898i	$-0.628271\pi$
$67$	−6.41989	−0.784314	−0.392157	+	0.919898i	$0.628271\pi$
$68$	−7.99026	−0.968961
$69$	−12.3663	−1.48873
$70$	1.67117	0.199743
$71$	−13.0818	−1.55252	−0.776262	−	0.630411i	$-0.782886\pi$
$71$	−13.0818	−1.55252	−0.776262	+	0.630411i	$0.782886\pi$
$72$	58.2055	6.85958
$73$	1.49954	0.175508	0.0877540	−	0.996142i	$-0.472031\pi$
$73$	1.49954	0.175508	0.0877540	+	0.996142i	$0.472031\pi$
$74$	−9.25276	−1.07561
$75$	1.41050	0.162871
$76$	−39.3156	−4.50981
$77$	0.266736	0.0303973
$78$	0	0
$79$	−3.63953	−0.409479	−0.204739	−	0.978817i	$-0.565635\pi$
$79$	−3.63953	−0.409479	−0.204739	+	0.978817i	$0.565635\pi$
$80$	−29.5311	−3.30168
$81$	16.5874	1.84304
$82$	16.9184	1.86832
$83$	9.17706	1.00731	0.503657	−	0.863904i	$-0.331988\pi$
$83$	9.17706	1.00731	0.503657	+	0.863904i	$0.331988\pi$
$84$	−4.33762	−0.473273
$85$	3.58688	0.389051
$86$	6.59640	0.711308
$87$	3.39984	0.364501
$88$	−8.58980	−0.915676
$89$	8.10322	0.858939	0.429470	−	0.903081i	$-0.358701\pi$
$89$	8.10322	0.858939	0.429470	+	0.903081i	$0.358701\pi$
$90$	−42.4542	−4.47506
$91$	0	0
$92$	−20.5705	−2.14462
$93$	10.1661	1.05417
$94$	17.3912	1.79376
$95$	17.6490	1.81075
$96$	52.4097	5.34905
$97$	12.7243	1.29195	0.645977	−	0.763357i	$-0.276450\pi$
$97$	12.7243	1.29195	0.645977	+	0.763357i	$0.276450\pi$
$98$	−18.5934	−1.87821
$99$	−6.77612	−0.681025
$100$	2.34627	0.234627
$101$	12.5430	1.24807	0.624037	−	0.781395i	$-0.285492\pi$
$101$	12.5430	1.24807	0.624037	+	0.781395i	$0.285492\pi$
$102$	−12.8900	−1.27630
$103$	−4.78743	−0.471719	−0.235860	−	0.971787i	$-0.575791\pi$
$103$	−4.78743	−0.471719	−0.235860	+	0.971787i	$0.575791\pi$
$104$	0	0
$105$	1.94718	0.190026
$106$	13.5889	1.31987
$107$	−20.0718	−1.94041	−0.970206	−	0.242283i	$-0.922104\pi$
$107$	−20.0718	−1.94041	−0.970206	+	0.242283i	$0.922104\pi$
$108$	61.4067	5.90886
$109$	5.37319	0.514658	0.257329	−	0.966324i	$-0.417158\pi$
$109$	5.37319	0.514658	0.257329	+	0.966324i	$0.417158\pi$
$110$	6.26526	0.597369
$111$	−10.7810	−1.02328
$112$	−3.37379	−0.318793
$113$	−15.1793	−1.42795	−0.713976	−	0.700170i	$-0.753108\pi$
$113$	−15.1793	−1.42795	−0.713976	+	0.700170i	$0.753108\pi$
$114$	−63.4245	−5.94025
$115$	9.23423	0.861096
$116$	5.65539	0.525090
$117$	0	0
$118$	−29.2209	−2.69000
$119$	0.409783	0.0375648
$120$	−62.7060	−5.72425
$121$	1.00000	0.0909091
$122$	25.9348	2.34803
$123$	19.7127	1.77743
$124$	16.9105	1.51861
$125$	10.6206	0.949932
$126$	−4.85018	−0.432089
$127$	21.0600	1.86877	0.934387	−	0.356260i	$-0.115948\pi$
$127$	21.0600	1.86877	0.934387	+	0.356260i	$0.115948\pi$
$128$	19.2964	1.70558
$129$	7.68588	0.676704
$130$	0	0
$131$	3.77616	0.329925	0.164962	−	0.986300i	$-0.447250\pi$
$131$	3.77616	0.329925	0.164962	+	0.986300i	$0.447250\pi$
$132$	−16.2619	−1.41541
$133$	2.01632	0.174837
$134$	−17.2276	−1.48824
$135$	−27.5658	−2.37249
$136$	−13.1964	−1.13158
$137$	−2.81943	−0.240880	−0.120440	−	0.992721i	$-0.538431\pi$
$137$	−2.81943	−0.240880	−0.120440	+	0.992721i	$0.538431\pi$
$138$	−33.1847	−2.82487
$139$	−1.84271	−0.156296	−0.0781482	−	0.996942i	$-0.524901\pi$
$139$	−1.84271	−0.156296	−0.0781482	+	0.996942i	$0.524901\pi$
$140$	3.23900	0.273745
$141$	20.2635	1.70650
$142$	−35.1046	−2.94591
$143$	0	0
$144$	85.7074	7.14228
$145$	−2.53874	−0.210831
$146$	4.02397	0.333026
$147$	−21.6643	−1.78684
$148$	−17.9334	−1.47411
$149$	5.43166	0.444979	0.222490	−	0.974935i	$-0.428582\pi$
$149$	5.43166	0.444979	0.222490	+	0.974935i	$0.428582\pi$
$150$	3.78504	0.309047
$151$	−6.87113	−0.559165	−0.279582	−	0.960122i	$-0.590196\pi$
$151$	−6.87113	−0.559165	−0.279582	+	0.960122i	$0.590196\pi$
$152$	−64.9323	−5.26670
$153$	−10.4101	−0.841606
$154$	0.715776	0.0576789
$155$	−7.59123	−0.609742
$156$	0	0
$157$	5.36679	0.428317	0.214158	−	0.976799i	$-0.431299\pi$
$157$	5.36679	0.428317	0.214158	+	0.976799i	$0.431299\pi$
$158$	−9.76656	−0.776985
$159$	15.8333	1.25566
$160$	−39.1356	−3.09394
$161$	1.05497	0.0831430
$162$	44.5118	3.49718
$163$	4.34355	0.340213	0.170106	−	0.985426i	$-0.445589\pi$
$163$	4.34355	0.340213	0.170106	+	0.985426i	$0.445589\pi$
$164$	32.7906	2.56052
$165$	7.30005	0.568308
$166$	24.6264	1.91138
$167$	16.6380	1.28749	0.643745	−	0.765240i	$-0.277380\pi$
$167$	16.6380	1.28749	0.643745	+	0.765240i	$0.277380\pi$
$168$	−7.16386	−0.552704
$169$	0	0
$170$	9.62527	0.738224
$171$	−51.2222	−3.91706
$172$	12.7849	0.974840
$173$	−2.66992	−0.202990	−0.101495	−	0.994836i	$-0.532363\pi$
$173$	−2.66992	−0.202990	−0.101495	+	0.994836i	$0.532363\pi$
$174$	9.12336	0.691640
$175$	−0.120329	−0.00909604
$176$	−12.6484	−0.953413
$177$	−34.0471	−2.55914
$178$	21.7447	1.62984
$179$	−22.7448	−1.70002	−0.850011	−	0.526764i	$-0.823405\pi$
$179$	−22.7448	−1.70002	−0.850011	+	0.526764i	$0.823405\pi$
$180$	−82.2832	−6.13302
$181$	20.4550	1.52041	0.760203	−	0.649685i	$-0.225099\pi$
$181$	20.4550	1.52041	0.760203	+	0.649685i	$0.225099\pi$
$182$	0	0
$183$	30.2183	2.23380
$184$	−33.9735	−2.50456
$185$	8.05040	0.591877
$186$	27.2803	2.00029
$187$	1.53629	0.112345
$188$	33.7069	2.45833
$189$	−3.14927	−0.229075
$190$	47.3606	3.43590
$191$	−7.69998	−0.557151	−0.278575	−	0.960414i	$-0.589862\pi$
$191$	−7.69998	−0.557151	−0.278575	+	0.960414i	$0.589862\pi$
$192$	61.5447	4.44161
$193$	−7.54943	−0.543420	−0.271710	−	0.962379i	$-0.587589\pi$
$193$	−7.54943	−0.543420	−0.271710	+	0.962379i	$0.587589\pi$
$194$	34.1452	2.45148
$195$	0	0
$196$	−36.0370	−2.57407
$197$	18.8155	1.34055	0.670275	−	0.742113i	$-0.266176\pi$
$197$	18.8155	1.34055	0.670275	+	0.742113i	$0.266176\pi$
$198$	−18.1835	−1.29224
$199$	9.03481	0.640461	0.320230	−	0.947340i	$-0.396240\pi$
$199$	9.03481	0.640461	0.320230	+	0.947340i	$0.396240\pi$
$200$	3.87501	0.274005
$201$	−20.0729	−1.41584
$202$	33.6587	2.36822
$203$	−0.290039	−0.0203567
$204$	−24.9830	−1.74916
$205$	−14.7199	−1.02808
$206$	−12.8469	−0.895087
$207$	−26.8002	−1.86275
$208$	0	0
$209$	7.55923	0.522883
$210$	5.22521	0.360573
$211$	−11.2951	−0.777585	−0.388793	−	0.921325i	$-0.627108\pi$
$211$	−11.2951	−0.777585	−0.388793	+	0.921325i	$0.627108\pi$
$212$	26.3375	1.80887
$213$	−40.9026	−2.80260
$214$	−53.8620	−3.68193
$215$	−5.73922	−0.391412
$216$	101.417	6.90057
$217$	−0.867262	−0.0588736
$218$	14.4188	0.976563
$219$	4.68858	0.316825
$220$	12.1431	0.818689
$221$	0	0
$222$	−28.9304	−1.94168
$223$	−25.9591	−1.73835	−0.869176	−	0.494503i	$-0.835350\pi$
$223$	−25.9591	−1.73835	−0.869176	+	0.494503i	$0.835350\pi$
$224$	−4.47105	−0.298735
$225$	3.05683	0.203789
$226$	−40.7333	−2.70954
$227$	10.0343	0.665999	0.332999	−	0.942927i	$-0.391939\pi$
$227$	10.0343	0.665999	0.332999	+	0.942927i	$0.391939\pi$
$228$	−122.927	−8.14105
$229$	2.98115	0.197000	0.0985001	−	0.995137i	$-0.468596\pi$
$229$	2.98115	0.197000	0.0985001	+	0.995137i	$0.468596\pi$
$230$	24.7798	1.63393
$231$	0.833996	0.0548729
$232$	9.34024	0.613217
$233$	−3.75063	−0.245712	−0.122856	−	0.992425i	$-0.539205\pi$
$233$	−3.75063	−0.245712	−0.122856	+	0.992425i	$0.539205\pi$
$234$	0	0
$235$	−15.1312	−0.987053
$236$	−56.6349	−3.68662
$237$	−11.3796	−0.739186
$238$	1.09964	0.0712791
$239$	−8.17311	−0.528675	−0.264337	−	0.964430i	$-0.585153\pi$
$239$	−8.17311	−0.528675	−0.264337	+	0.964430i	$0.585153\pi$
$240$	−92.3343	−5.96016
$241$	−4.62614	−0.297996	−0.148998	−	0.988838i	$-0.547605\pi$
$241$	−4.62614	−0.297996	−0.148998	+	0.988838i	$0.547605\pi$
$242$	2.68347	0.172500
$243$	16.4434	1.05484
$244$	50.2660	3.21795
$245$	16.1772	1.03353
$246$	52.8984	3.37268
$247$	0	0
$248$	27.9288	1.77348
$249$	28.6937	1.81839
$250$	28.4999	1.80249
$251$	−12.9557	−0.817758	−0.408879	−	0.912589i	$-0.634080\pi$
$251$	−12.9557	−0.817758	−0.408879	+	0.912589i	$0.634080\pi$
$252$	−9.40046	−0.592173
$253$	3.95510	0.248655
$254$	56.5139	3.54600
$255$	11.2150	0.702311
$256$	12.4139	0.775871
$257$	−0.638721	−0.0398423	−0.0199211	−	0.999802i	$-0.506342\pi$
$257$	−0.638721	−0.0398423	−0.0199211	+	0.999802i	$0.506342\pi$
$258$	20.6248	1.28405
$259$	0.919719	0.0571486
$260$	0	0
$261$	7.36811	0.456074
$262$	10.1332	0.626032
$263$	14.5476	0.897046	0.448523	−	0.893771i	$-0.351950\pi$
$263$	14.5476	0.897046	0.448523	+	0.893771i	$0.351950\pi$
$264$	−26.8575	−1.65297
$265$	−11.8231	−0.726285
$266$	5.41072	0.331752
$267$	25.3362	1.55055
$268$	−33.3899	−2.03961
$269$	−14.9672	−0.912564	−0.456282	−	0.889835i	$-0.650819\pi$
$269$	−14.9672	−0.912564	−0.456282	+	0.889835i	$0.650819\pi$
$270$	−73.9721	−4.50180
$271$	21.3675	1.29799	0.648993	−	0.760795i	$-0.275191\pi$
$271$	21.3675	1.29799	0.648993	+	0.760795i	$0.275191\pi$
$272$	−19.4317	−1.17822
$273$	0	0
$274$	−7.56586	−0.457070
$275$	−0.451118	−0.0272035
$276$	−64.3174	−3.87145
$277$	23.9016	1.43611	0.718055	−	0.695986i	$-0.245032\pi$
$277$	23.9016	1.43611	0.718055	+	0.695986i	$0.245032\pi$
$278$	−4.94485	−0.296572
$279$	22.0318	1.31901
$280$	5.34942	0.319689
$281$	−19.5972	−1.16907	−0.584535	−	0.811368i	$-0.698723\pi$
$281$	−19.5972	−1.16907	−0.584535	+	0.811368i	$0.698723\pi$
$282$	54.3765	3.23808
$283$	−1.39789	−0.0830957	−0.0415479	−	0.999137i	$-0.513229\pi$
$283$	−1.39789	−0.0830957	−0.0415479	+	0.999137i	$0.513229\pi$
$284$	−68.0385	−4.03734
$285$	55.1828	3.26875
$286$	0	0
$287$	−1.68168	−0.0992664
$288$	113.582	6.69289
$289$	−14.6398	−0.861165
$290$	−6.81263	−0.400051
$291$	39.7847	2.33222
$292$	7.79912	0.456409
$293$	−20.0795	−1.17306	−0.586529	−	0.809928i	$-0.699506\pi$
$293$	−20.0795	−1.17306	−0.586529	+	0.809928i	$0.699506\pi$
$294$	−58.1355	−3.39053
$295$	25.4238	1.48023
$296$	−29.6181	−1.72152
$297$	−11.8067	−0.685094
$298$	14.5757	0.844347
$299$	0	0
$300$	7.33603	0.423546
$301$	−0.655679	−0.0377927
$302$	−18.4385	−1.06101
$303$	39.2179	2.25301
$304$	−95.6125	−5.48375
$305$	−22.5647	−1.29205
$306$	−27.9351	−1.59695
$307$	−4.32372	−0.246768	−0.123384	−	0.992359i	$-0.539375\pi$
$307$	−4.32372	−0.246768	−0.123384	+	0.992359i	$0.539375\pi$
$308$	1.38729	0.0790483
$309$	−14.9687	−0.851542
$310$	−20.3708	−1.15699
$311$	−25.3775	−1.43902	−0.719512	−	0.694480i	$-0.755634\pi$
$311$	−25.3775	−1.43902	−0.719512	+	0.694480i	$0.755634\pi$
$312$	0	0
$313$	21.1230	1.19394	0.596972	−	0.802262i	$-0.296370\pi$
$313$	21.1230	1.19394	0.596972	+	0.802262i	$0.296370\pi$
$314$	14.4016	0.812731
$315$	4.21992	0.237766
$316$	−18.9292	−1.06485
$317$	−21.0836	−1.18417	−0.592087	−	0.805874i	$-0.701696\pi$
$317$	−21.0836	−1.18417	−0.592087	+	0.805874i	$0.701696\pi$
$318$	42.4881	2.38261
$319$	−1.08736	−0.0608807
$320$	−45.9568	−2.56907
$321$	−62.7580	−3.50281
$322$	2.83097	0.157764
$323$	11.6132	0.646175
$324$	86.2712	4.79284
$325$	0	0
$326$	11.6558	0.645553
$327$	16.8002	0.929055
$328$	54.1559	2.99026
$329$	−1.72867	−0.0953048
$330$	19.5895	1.07836
$331$	28.2148	1.55083	0.775413	−	0.631454i	$-0.217542\pi$
$331$	28.2148	1.55083	0.775413	+	0.631454i	$0.217542\pi$
$332$	47.7300	2.61952
$333$	−23.3644	−1.28036
$334$	44.6477	2.44301
$335$	14.9889	0.818932
$336$	−10.5488	−0.575482
$337$	−7.49761	−0.408421	−0.204211	−	0.978927i	$-0.565463\pi$
$337$	−7.49761	−0.408421	−0.204211	+	0.978927i	$0.565463\pi$
$338$	0	0
$339$	−47.4609	−2.57772
$340$	18.6554	1.01173
$341$	−3.25139	−0.176073
$342$	−137.453	−7.43262
$343$	3.71532	0.200608
$344$	21.1151	1.13845
$345$	28.8725	1.55444
$346$	−7.16464	−0.385174
$347$	22.1568	1.18944	0.594720	−	0.803933i	$-0.297263\pi$
$347$	22.1568	1.18944	0.594720	+	0.803933i	$0.297263\pi$
$348$	17.6826	0.947886
$349$	32.7247	1.75171	0.875856	−	0.482573i	$-0.160298\pi$
$349$	32.7247	1.75171	0.875856	+	0.482573i	$0.160298\pi$
$350$	−0.322900	−0.0172597
$351$	0	0
$352$	−16.7621	−0.893424
$353$	8.19679	0.436271	0.218135	−	0.975919i	$-0.430003\pi$
$353$	8.19679	0.436271	0.218135	+	0.975919i	$0.430003\pi$
$354$	−91.3644	−4.85596
$355$	30.5429	1.62105
$356$	42.1449	2.23367
$357$	1.28126	0.0678115
$358$	−61.0348	−3.22579
$359$	−15.1960	−0.802017	−0.401008	−	0.916074i	$-0.631340\pi$
$359$	−15.1960	−0.802017	−0.401008	+	0.916074i	$0.631340\pi$
$360$	−135.896	−7.16235
$361$	38.1420	2.00747
$362$	54.8903	2.88497
$363$	3.12668	0.164108
$364$	0	0
$365$	−3.50107	−0.183254
$366$	81.0898	4.23863
$367$	11.8602	0.619099	0.309549	−	0.950883i	$-0.399822\pi$
$367$	11.8602	0.619099	0.309549	+	0.950883i	$0.399822\pi$
$368$	−50.0259	−2.60778
$369$	42.7212	2.22398
$370$	21.6030	1.12309
$371$	−1.35073	−0.0701264
$372$	52.8737	2.74137
$373$	−31.4345	−1.62762	−0.813810	−	0.581132i	$-0.802610\pi$
$373$	−31.4345	−1.62762	−0.813810	+	0.581132i	$0.802610\pi$
$374$	4.12259	0.213174
$375$	33.2071	1.71481
$376$	55.6692	2.87092
$377$	0	0
$378$	−8.45096	−0.434670
$379$	27.8846	1.43233	0.716167	−	0.697929i	$-0.245895\pi$
$379$	27.8846	1.43233	0.716167	+	0.697929i	$0.245895\pi$
$380$	91.7926	4.70886
$381$	65.8479	3.37349
$382$	−20.6626	−1.05719
$383$	20.0951	1.02681	0.513406	−	0.858146i	$-0.328383\pi$
$383$	20.0951	1.02681	0.513406	+	0.858146i	$0.328383\pi$
$384$	60.3338	3.07889
$385$	−0.622764	−0.0317390
$386$	−20.2587	−1.03114
$387$	16.6568	0.846712
$388$	66.1790	3.35973
$389$	−1.80049	−0.0912883	−0.0456441	−	0.998958i	$-0.514534\pi$
$389$	−1.80049	−0.0912883	−0.0456441	+	0.998958i	$0.514534\pi$
$390$	0	0
$391$	6.07619	0.307286
$392$	−59.5174	−3.00609
$393$	11.8068	0.595576
$394$	50.4908	2.54369
$395$	8.49743	0.427552
$396$	−35.2426	−1.77101
$397$	4.76541	0.239169	0.119584	−	0.992824i	$-0.461844\pi$
$397$	4.76541	0.239169	0.119584	+	0.992824i	$0.461844\pi$
$398$	24.2446	1.21527
$399$	6.30437	0.315613
$400$	5.70594	0.285297
$401$	−29.3417	−1.46526	−0.732628	−	0.680629i	$-0.761706\pi$
$401$	−29.3417	−1.46526	−0.732628	+	0.680629i	$0.761706\pi$
$402$	−53.8651	−2.68655
$403$	0	0
$404$	65.2361	3.24562
$405$	−38.7277	−1.92439
$406$	−0.778310	−0.0386269
$407$	3.44806	0.170914
$408$	−41.2610	−2.04272
$409$	−12.2591	−0.606172	−0.303086	−	0.952963i	$-0.598017\pi$
$409$	−12.2591	−0.606172	−0.303086	+	0.952963i	$0.598017\pi$
$410$	−39.5004	−1.95079
$411$	−8.81546	−0.434834
$412$	−24.8994	−1.22671
$413$	2.90454	0.142923
$414$	−71.9176	−3.53456
$415$	−21.4263	−1.05177
$416$	0	0
$417$	−5.76155	−0.282144
$418$	20.2850	0.992170
$419$	36.1583	1.76645	0.883224	−	0.468951i	$-0.155368\pi$
$419$	36.1583	1.76645	0.883224	+	0.468951i	$0.155368\pi$
$420$	10.1273	0.494162
$421$	−1.38467	−0.0674849	−0.0337424	−	0.999431i	$-0.510743\pi$
$421$	−1.38467	−0.0674849	−0.0337424	+	0.999431i	$0.510743\pi$
$422$	−30.3100	−1.47547
$423$	43.9150	2.13522
$424$	43.4981	2.11245
$425$	−0.693049	−0.0336178
$426$	−109.761	−5.31792
$427$	−2.57791	−0.124754
$428$	−104.393	−5.04604
$429$	0	0
$430$	−15.4010	−0.742704
$431$	0.0306402	0.00147589	0.000737943	−	1.00000i	$-0.499765\pi$
$431$	0.0306402	0.00147589	0.000737943		1.00000i	$0.499765\pi$
$432$	149.336	7.18495
$433$	13.5388	0.650631	0.325315	−	0.945606i	$-0.394530\pi$
$433$	13.5388	0.650631	0.325315	+	0.945606i	$0.394530\pi$
$434$	−2.32727	−0.111713
$435$	−7.93782	−0.380589
$436$	27.9460	1.33837
$437$	29.8975	1.43019
$438$	12.5817	0.601175
$439$	15.5973	0.744417	0.372208	−	0.928149i	$-0.378601\pi$
$439$	15.5973	0.744417	0.372208	+	0.928149i	$0.378601\pi$
$440$	20.0551	0.956092
$441$	−46.9507	−2.23575
$442$	0	0
$443$	16.3311	0.775914	0.387957	−	0.921677i	$-0.373181\pi$
$443$	16.3311	0.775914	0.387957	+	0.921677i	$0.373181\pi$
$444$	−56.0719	−2.66105
$445$	−18.9191	−0.896851
$446$	−69.6605	−3.29852
$447$	16.9831	0.803271
$448$	−5.25035	−0.248056
$449$	2.94124	0.138806	0.0694029	−	0.997589i	$-0.477891\pi$
$449$	2.94124	0.138806	0.0694029	+	0.997589i	$0.477891\pi$
$450$	8.20291	0.386689
$451$	−6.30467	−0.296875
$452$	−78.9479	−3.71340
$453$	−21.4838	−1.00940
$454$	26.9267	1.26373
$455$	0	0
$456$	−203.022	−9.50739
$457$	25.6418	1.19947	0.599735	−	0.800199i	$-0.295273\pi$
$457$	25.6418	1.19947	0.599735	+	0.800199i	$0.295273\pi$
$458$	7.99983	0.373808
$459$	−18.1385	−0.846634
$460$	48.0273	2.23928
$461$	−25.4408	−1.18490	−0.592449	−	0.805608i	$-0.701839\pi$
$461$	−25.4408	−1.18490	−0.592449	+	0.805608i	$0.701839\pi$
$462$	2.23800	0.104121
$463$	10.6067	0.492934	0.246467	−	0.969151i	$-0.420730\pi$
$463$	10.6067	0.492934	0.246467	+	0.969151i	$0.420730\pi$
$464$	13.7535	0.638489
$465$	−23.7353	−1.10070
$466$	−10.0647	−0.466238
$467$	−5.17505	−0.239473	−0.119736	−	0.992806i	$-0.538205\pi$
$467$	−5.17505	−0.239473	−0.119736	+	0.992806i	$0.538205\pi$
$468$	0	0
$469$	1.71241	0.0790719
$470$	−40.6042	−1.87293
$471$	16.7802	0.773193
$472$	−93.5363	−4.30536
$473$	−2.45816	−0.113026
$474$	−30.5369	−1.40261
$475$	−3.41011	−0.156466
$476$	2.13129	0.0976873
$477$	34.3138	1.57112
$478$	−21.9323	−1.00316
$479$	−17.9210	−0.818829	−0.409415	−	0.912348i	$-0.634267\pi$
$479$	−17.9210	−0.818829	−0.409415	+	0.912348i	$0.634267\pi$
$480$	−122.364	−5.58514
$481$	0	0
$482$	−12.4141	−0.565447
$483$	3.29854	0.150089
$484$	5.20101	0.236409
$485$	−29.7081	−1.34898
$486$	44.1253	2.00156
$487$	−6.46395	−0.292910	−0.146455	−	0.989217i	$-0.546786\pi$
$487$	−6.46395	−0.292910	−0.146455	+	0.989217i	$0.546786\pi$
$488$	83.0175	3.75803
$489$	13.5809	0.614148
$490$	43.4111	1.96111
$491$	16.7077	0.754007	0.377004	−	0.926212i	$-0.376954\pi$
$491$	16.7077	0.754007	0.377004	+	0.926212i	$0.376954\pi$
$492$	102.526	4.62222
$493$	−1.67051	−0.0752359
$494$	0	0
$495$	15.8206	0.711084
$496$	41.1251	1.84657
$497$	3.48938	0.156520
$498$	76.9987	3.45040
$499$	18.7254	0.838264	0.419132	−	0.907925i	$-0.362335\pi$
$499$	18.7254	0.838264	0.419132	+	0.907925i	$0.362335\pi$
$500$	55.2376	2.47030
$501$	52.0218	2.32416
$502$	−34.7663	−1.55169
$503$	−38.7263	−1.72672	−0.863359	−	0.504590i	$-0.831644\pi$
$503$	−38.7263	−1.72672	−0.863359	+	0.504590i	$0.831644\pi$
$504$	−15.5255	−0.691559
$505$	−29.2849	−1.30316
$506$	10.6134	0.471823
$507$	0	0
$508$	109.533	4.85975
$509$	−10.4846	−0.464721	−0.232360	−	0.972630i	$-0.574645\pi$
$509$	−10.4846	−0.464721	−0.232360	+	0.972630i	$0.574645\pi$
$510$	30.0951	1.33263
$511$	−0.399981	−0.0176941
$512$	−5.28047	−0.233366
$513$	−89.2496	−3.94046
$514$	−1.71399	−0.0756007
$515$	11.1775	0.492540
$516$	39.9743	1.75977
$517$	−6.48085	−0.285027
$518$	2.46804	0.108439
$519$	−8.34797	−0.366435
$520$	0	0
$521$	−8.86293	−0.388292	−0.194146	−	0.980973i	$-0.562194\pi$
$521$	−8.86293	−0.388292	−0.194146	+	0.980973i	$0.562194\pi$
$522$	19.7721	0.865401
$523$	−38.3068	−1.67504	−0.837520	−	0.546407i	$-0.815995\pi$
$523$	−38.3068	−1.67504	−0.837520	+	0.546407i	$0.815995\pi$
$524$	19.6398	0.857970
$525$	−0.376231	−0.0164201
$526$	39.0382	1.70214
$527$	−4.99508	−0.217589
$528$	−39.5476	−1.72109
$529$	−7.35715	−0.319876
$530$	−31.7268	−1.37813
$531$	−73.7867	−3.20207
$532$	10.4869	0.454663
$533$	0	0
$534$	67.9888	2.94216
$535$	46.8628	2.02606
$536$	−55.1456	−2.38193
$537$	−71.1155	−3.06886
$538$	−40.1639	−1.73159
$539$	6.92885	0.298447
$540$	−143.370	−6.16967
$541$	18.3574	0.789245	0.394623	−	0.918843i	$-0.370875\pi$
$541$	18.3574	0.789245	0.394623	+	0.918843i	$0.370875\pi$
$542$	57.3391	2.46293
$543$	63.9561	2.74462
$544$	−25.7515	−1.10409
$545$	−12.5451	−0.537374
$546$	0	0
$547$	−1.64398	−0.0702916	−0.0351458	−	0.999382i	$-0.511190\pi$
$547$	−1.64398	−0.0702916	−0.0351458	+	0.999382i	$0.511190\pi$
$548$	−14.6639	−0.626410
$549$	65.4889	2.79500
$550$	−1.21056	−0.0516185
$551$	−8.21964	−0.350168
$552$	−106.224	−4.52121
$553$	0.970791	0.0412822
$554$	64.1393	2.72502
$555$	25.1710	1.06845
$556$	−9.58393	−0.406449
$557$	−7.76685	−0.329092	−0.164546	−	0.986369i	$-0.552616\pi$
$557$	−7.76685	−0.329092	−0.164546	+	0.986369i	$0.552616\pi$
$558$	59.1217	2.50282
$559$	0	0
$560$	7.87700	0.332864
$561$	4.80349	0.202803
$562$	−52.5885	−2.21831
$563$	−45.9808	−1.93786	−0.968930	−	0.247333i	$-0.920446\pi$
$563$	−45.9808	−1.93786	−0.968930	+	0.247333i	$0.920446\pi$
$564$	105.391	4.43775
$565$	35.4402	1.49098
$566$	−3.75119	−0.157674
$567$	−4.42445	−0.185809
$568$	−112.370	−4.71494
$569$	29.8201	1.25012	0.625061	−	0.780576i	$-0.285074\pi$
$569$	29.8201	1.25012	0.625061	+	0.780576i	$0.285074\pi$
$570$	148.081	6.20244
$571$	27.3401	1.14415	0.572075	−	0.820202i	$-0.306139\pi$
$571$	27.3401	1.14415	0.572075	+	0.820202i	$0.306139\pi$
$572$	0	0
$573$	−24.0753	−1.00576
$574$	−4.51273	−0.188358
$575$	−1.78422	−0.0744071
$576$	133.379	5.55747
$577$	40.3312	1.67901	0.839504	−	0.543353i	$-0.182846\pi$
$577$	40.3312	1.67901	0.839504	+	0.543353i	$0.182846\pi$
$578$	−39.2855	−1.63406
$579$	−23.6046	−0.980975
$580$	−13.2040	−0.548266
$581$	−2.44785	−0.101554
$582$	106.761	4.42538
$583$	−5.06393	−0.209726
$584$	12.8807	0.533009
$585$	0	0
$586$	−53.8827	−2.22588
$587$	−6.46283	−0.266750	−0.133375	−	0.991066i	$-0.542581\pi$
$587$	−6.46283	−0.266750	−0.133375	+	0.991066i	$0.542581\pi$
$588$	−112.676	−4.64668
$589$	−24.5780	−1.01272
$590$	68.2239	2.80873
$591$	58.8300	2.41994
$592$	−43.6126	−1.79247
$593$	−18.4337	−0.756983	−0.378492	−	0.925605i	$-0.623557\pi$
$593$	−18.4337	−0.756983	−0.378492	+	0.925605i	$0.623557\pi$
$594$	−31.6829	−1.29997
$595$	−0.956747	−0.0392228
$596$	28.2501	1.15717
$597$	28.2490	1.15615
$598$	0	0
$599$	−9.81967	−0.401221	−0.200610	−	0.979671i	$-0.564293\pi$
$599$	−9.81967	−0.401221	−0.200610	+	0.979671i	$0.564293\pi$
$600$	12.1159	0.494631
$601$	15.7357	0.641872	0.320936	−	0.947101i	$-0.396003\pi$
$601$	15.7357	0.641872	0.320936	+	0.947101i	$0.396003\pi$
$602$	−1.75949	−0.0717116
$603$	−43.5019	−1.77153
$604$	−35.7368	−1.45411
$605$	−2.33476	−0.0949216
$606$	105.240	4.27508
$607$	20.9871	0.851839	0.425919	−	0.904761i	$-0.359951\pi$
$607$	20.9871	0.851839	0.425919	+	0.904761i	$0.359951\pi$
$608$	−126.709	−5.13872
$609$	−0.906858	−0.0367477
$610$	−60.5516	−2.45166
$611$	0	0
$612$	−54.1429	−2.18860
$613$	1.66482	0.0672413	0.0336206	−	0.999435i	$-0.489296\pi$
$613$	1.66482	0.0672413	0.0336206	+	0.999435i	$0.489296\pi$
$614$	−11.6026	−0.468241
$615$	−46.0244	−1.85588
$616$	2.29120	0.0923153
$617$	10.5682	0.425462	0.212731	−	0.977111i	$-0.431764\pi$
$617$	10.5682	0.425462	0.212731	+	0.977111i	$0.431764\pi$
$618$	−40.1682	−1.61580
$619$	−28.5798	−1.14872	−0.574359	−	0.818603i	$-0.694749\pi$
$619$	−28.5798	−1.14872	−0.574359	+	0.818603i	$0.694749\pi$
$620$	−39.4820	−1.58564
$621$	−46.6967	−1.87388
$622$	−68.0996	−2.73055
$623$	−2.16142	−0.0865953
$624$	0	0
$625$	−27.0521	−1.08208
$626$	56.6830	2.26551
$627$	23.6353	0.943902
$628$	27.9127	1.11384
$629$	5.29722	0.211214
$630$	11.3240	0.451160
$631$	−22.7451	−0.905469	−0.452735	−	0.891645i	$-0.649552\pi$
$631$	−22.7451	−0.905469	−0.452735	+	0.891645i	$0.649552\pi$
$632$	−31.2628	−1.24357
$633$	−35.3161	−1.40369
$634$	−56.5772	−2.24697
$635$	−49.1701	−1.95126
$636$	82.3489	3.26535
$637$	0	0
$638$	−2.91791	−0.115521
$639$	−88.6437	−3.50669
$640$	−45.0526	−1.78086
$641$	−10.4900	−0.414329	−0.207165	−	0.978306i	$-0.566424\pi$
$641$	−10.4900	−0.414329	−0.207165	+	0.978306i	$0.566424\pi$
$642$	−168.409	−6.64658
$643$	−35.6282	−1.40504	−0.702520	−	0.711664i	$-0.747942\pi$
$643$	−35.6282	−1.40504	−0.702520	+	0.711664i	$0.747942\pi$
$644$	5.48689	0.216214
$645$	−17.9447	−0.706572
$646$	31.1636	1.22612
$647$	4.37246	0.171899	0.0859495	−	0.996299i	$-0.472608\pi$
$647$	4.37246	0.171899	0.0859495	+	0.996299i	$0.472608\pi$
$648$	142.482	5.59724
$649$	10.8892	0.427440
$650$	0	0
$651$	−2.71165	−0.106278
$652$	22.5908	0.884724
$653$	−23.0934	−0.903716	−0.451858	−	0.892090i	$-0.649239\pi$
$653$	−23.0934	−0.903716	−0.451858	+	0.892090i	$0.649239\pi$
$654$	45.0829	1.76288
$655$	−8.81644	−0.344487
$656$	79.7443	3.11349
$657$	10.1611	0.396421
$658$	−4.63884	−0.180841
$659$	30.0102	1.16903	0.584516	−	0.811383i	$-0.301285\pi$
$659$	30.0102	1.16903	0.584516	+	0.811383i	$0.301285\pi$
$660$	37.9676	1.47789
$661$	35.0403	1.36291	0.681455	−	0.731860i	$-0.261347\pi$
$661$	35.0403	1.36291	0.681455	+	0.731860i	$0.261347\pi$
$662$	75.7136	2.94269
$663$	0	0
$664$	78.8291	3.05916
$665$	−4.70762	−0.182554
$666$	−62.6977	−2.42949
$667$	−4.30064	−0.166521
$668$	86.5346	3.34812
$669$	−81.1659	−3.13805
$670$	40.2223	1.55392
$671$	−9.66466	−0.373100
$672$	−13.9795	−0.539273
$673$	−12.4420	−0.479606	−0.239803	−	0.970822i	$-0.577083\pi$
$673$	−12.4420	−0.479606	−0.239803	+	0.970822i	$0.577083\pi$
$674$	−20.1196	−0.774978
$675$	5.32622	0.205006
$676$	0	0
$677$	29.5713	1.13652	0.568259	−	0.822849i	$-0.307617\pi$
$677$	29.5713	1.13652	0.568259	+	0.822849i	$0.307617\pi$
$678$	−127.360	−4.89123
$679$	−3.39401	−0.130250
$680$	30.8105	1.18153
$681$	31.3740	1.20225
$682$	−8.72501	−0.334098
$683$	−13.5278	−0.517628	−0.258814	−	0.965927i	$-0.583332\pi$
$683$	−13.5278	−0.517628	−0.258814	+	0.965927i	$0.583332\pi$
$684$	−266.407	−10.1863
$685$	6.58271	0.251512
$686$	9.96994	0.380654
$687$	9.32111	0.355622
$688$	31.0919	1.18537
$689$	0	0
$690$	77.4784	2.94955
$691$	−5.92854	−0.225532	−0.112766	−	0.993622i	$-0.535971\pi$
$691$	−5.92854	−0.225532	−0.112766	+	0.993622i	$0.535971\pi$
$692$	−13.8863	−0.527876
$693$	1.80743	0.0686586
$694$	59.4571	2.25696
$695$	4.30229	0.163195
$696$	29.2039	1.10697
$697$	−9.68581	−0.366876
$698$	87.8156	3.32387
$699$	−11.7270	−0.443556
$700$	−0.625833	−0.0236543
$701$	0.404230	0.0152675	0.00763377	−	0.999971i	$-0.497570\pi$
$701$	0.404230	0.0152675	0.00763377	+	0.999971i	$0.497570\pi$
$702$	0	0
$703$	26.0647	0.983047
$704$	−19.6837	−0.741858
$705$	−47.3105	−1.78182
$706$	21.9958	0.827824
$707$	−3.34566	−0.125826
$708$	−177.079	−6.65505
$709$	−22.1763	−0.832849	−0.416425	−	0.909170i	$-0.636717\pi$
$709$	−22.1763	−0.832849	−0.416425	+	0.909170i	$0.636717\pi$
$710$	81.9609	3.07594
$711$	−24.6619	−0.924892
$712$	69.6050	2.60856
$713$	−12.8596	−0.481596
$714$	3.43822	0.128672
$715$	0	0
$716$	−118.296	−4.42091
$717$	−25.5547	−0.954358
$718$	−40.7781	−1.52183
$719$	8.69164	0.324144	0.162072	−	0.986779i	$-0.448182\pi$
$719$	8.69164	0.324144	0.162072	+	0.986779i	$0.448182\pi$
$720$	−200.106	−7.45752
$721$	1.27698	0.0475571
$722$	102.353	3.80918
$723$	−14.4645	−0.537939
$724$	106.386	3.95382
$725$	0.490530	0.0182178
$726$	8.39034	0.311395
$727$	−24.2296	−0.898627	−0.449314	−	0.893374i	$-0.648331\pi$
$727$	−24.2296	−0.898627	−0.449314	+	0.893374i	$0.648331\pi$
$728$	0	0
$729$	1.65092	0.0611451
$730$	−9.39502	−0.347725
$731$	−3.77645	−0.139677
$732$	157.165	5.80900
$733$	−6.69006	−0.247103	−0.123552	−	0.992338i	$-0.539428\pi$
$733$	−6.69006	−0.247103	−0.123552	+	0.992338i	$0.539428\pi$
$734$	31.8266	1.17474
$735$	50.5810	1.86571
$736$	−66.2959	−2.44370
$737$	6.41989	0.236480
$738$	114.641	4.21999
$739$	32.0479	1.17890	0.589450	−	0.807805i	$-0.299345\pi$
$739$	32.0479	1.17890	0.589450	+	0.807805i	$0.299345\pi$
$740$	41.8702	1.53918
$741$	0	0
$742$	−3.62464	−0.133065
$743$	27.7046	1.01638	0.508191	−	0.861244i	$-0.330314\pi$
$743$	27.7046	1.01638	0.508191	+	0.861244i	$0.330314\pi$
$744$	87.3244	3.20147
$745$	−12.6816	−0.464619
$746$	−84.3536	−3.08841
$747$	62.1848	2.27522
$748$	7.99026	0.292153
$749$	5.35385	0.195626
$750$	89.1102	3.25384
$751$	30.0879	1.09792	0.548961	−	0.835848i	$-0.315023\pi$
$751$	30.0879	1.09792	0.548961	+	0.835848i	$0.315023\pi$
$752$	81.9727	2.98924
$753$	−40.5084	−1.47621
$754$	0	0
$755$	16.0425	0.583845
$756$	−16.3794	−0.595711
$757$	−18.0765	−0.657003	−0.328502	−	0.944503i	$-0.606544\pi$
$757$	−18.0765	−0.657003	−0.328502	+	0.944503i	$0.606544\pi$
$758$	74.8274	2.71785
$759$	12.3663	0.448870
$760$	151.601	5.49916
$761$	−28.5069	−1.03337	−0.516687	−	0.856174i	$-0.672835\pi$
$761$	−28.5069	−1.03337	−0.516687	+	0.856174i	$0.672835\pi$
$762$	176.701	6.40119
$763$	−1.43322	−0.0518861
$764$	−40.0476	−1.44887
$765$	24.3051	0.878752
$766$	53.9246	1.94838
$767$	0	0
$768$	38.8144	1.40059
$769$	−15.3331	−0.552927	−0.276464	−	0.961024i	$-0.589163\pi$
$769$	−15.3331	−0.552927	−0.276464	+	0.961024i	$0.589163\pi$
$770$	−1.67117	−0.0602247
$771$	−1.99707	−0.0719228
$772$	−39.2646	−1.41316
$773$	−22.6186	−0.813536	−0.406768	−	0.913532i	$-0.633344\pi$
$773$	−22.6186	−0.813536	−0.406768	+	0.913532i	$0.633344\pi$
$774$	44.6980	1.60664
$775$	1.46676	0.0526877
$776$	109.299	3.92360
$777$	2.87567	0.103164
$778$	−4.83155	−0.173219
$779$	−47.6585	−1.70754
$780$	0	0
$781$	13.0818	0.468103
$782$	16.3053	0.583075
$783$	12.8382	0.458799
$784$	−87.6392	−3.12997
$785$	−12.5302	−0.447222
$786$	31.6833	1.13011
$787$	13.6903	0.488008	0.244004	−	0.969774i	$-0.421539\pi$
$787$	13.6903	0.488008	0.244004	+	0.969774i	$0.421539\pi$
$788$	97.8596	3.48610
$789$	45.4858	1.61934
$790$	22.8026	0.811280
$791$	4.04887	0.143961
$792$	−58.2055	−2.06824
$793$	0	0
$794$	12.7878	0.453823
$795$	−36.9669	−1.31108
$796$	46.9901	1.66552
$797$	33.7231	1.19453	0.597266	−	0.802043i	$-0.296254\pi$
$797$	33.7231	1.19453	0.597266	+	0.802043i	$0.296254\pi$
$798$	16.9176	0.598876
$799$	−9.95647	−0.352234
$800$	7.56170	0.267346
$801$	54.9083	1.94009
$802$	−78.7376	−2.78032
$803$	−1.49954	−0.0529176
$804$	−104.399	−3.68188
$805$	−2.46310	−0.0868128
$806$	0	0
$807$	−46.7975	−1.64735
$808$	107.742	3.79034
$809$	−5.96962	−0.209881	−0.104940	−	0.994479i	$-0.533465\pi$
$809$	−5.96962	−0.209881	−0.104940	+	0.994479i	$0.533465\pi$
$810$	−103.924	−3.65153
$811$	34.4025	1.20803	0.604017	−	0.796971i	$-0.293566\pi$
$811$	34.4025	1.20803	0.604017	+	0.796971i	$0.293566\pi$
$812$	−1.50849	−0.0529377
$813$	66.8094	2.34311
$814$	9.25276	0.324309
$815$	−10.1411	−0.355229
$816$	−60.7567	−2.12691
$817$	−18.5818	−0.650095
$818$	−32.8968	−1.15021
$819$	0	0
$820$	−76.5583	−2.67353
$821$	43.5132	1.51862	0.759311	−	0.650728i	$-0.225536\pi$
$821$	43.5132	1.51862	0.759311	+	0.650728i	$0.225536\pi$
$822$	−23.6560	−0.825098
$823$	−51.6931	−1.80191	−0.900953	−	0.433916i	$-0.857132\pi$
$823$	−51.6931	−1.80191	−0.900953	+	0.433916i	$0.857132\pi$
$824$	−41.1231	−1.43259
$825$	−1.41050	−0.0491074
$826$	7.79425	0.271197
$827$	48.9877	1.70347	0.851734	−	0.523974i	$-0.175551\pi$
$827$	48.9877	1.70347	0.851734	+	0.523974i	$0.175551\pi$
$828$	−139.388	−4.84408
$829$	41.8011	1.45181	0.725906	−	0.687794i	$-0.241421\pi$
$829$	41.8011	1.45181	0.725906	+	0.687794i	$0.241421\pi$
$830$	−57.4967	−1.99574
$831$	74.7327	2.59245
$832$	0	0
$833$	10.6447	0.368818
$834$	−15.4609	−0.535369
$835$	−38.8459	−1.34432
$836$	39.3156	1.35976
$837$	38.3882	1.32689
$838$	97.0297	3.35183
$839$	−30.6863	−1.05941	−0.529705	−	0.848182i	$-0.677697\pi$
$839$	−30.6863	−1.05941	−0.529705	+	0.848182i	$0.677697\pi$
$840$	16.7259	0.577099
$841$	−27.8176	−0.959229
$842$	−3.71573	−0.128052
$843$	−61.2741	−2.11039
$844$	−58.7458	−2.02211
$845$	0	0
$846$	117.844	4.05158
$847$	−0.266736	−0.00916514
$848$	64.0508	2.19951
$849$	−4.37074	−0.150003
$850$	−1.85978	−0.0637898
$851$	13.6374	0.467485
$852$	−212.734	−7.28816
$853$	41.4726	1.42000	0.709998	−	0.704204i	$-0.248696\pi$
$853$	41.4726	1.42000	0.709998	+	0.704204i	$0.248696\pi$
$854$	−6.91774	−0.236720
$855$	119.592	4.08995
$856$	−172.412	−5.89294
$857$	−24.1190	−0.823890	−0.411945	−	0.911209i	$-0.635150\pi$
$857$	−24.1190	−0.823890	−0.411945	+	0.911209i	$0.635150\pi$
$858$	0	0
$859$	−47.9287	−1.63531	−0.817653	−	0.575712i	$-0.804725\pi$
$859$	−47.9287	−1.63531	−0.817653	+	0.575712i	$0.804725\pi$
$860$	−29.8497	−1.01787
$861$	−5.25807	−0.179195
$862$	0.0822220	0.00280049
$863$	32.9887	1.12295	0.561474	−	0.827495i	$-0.310235\pi$
$863$	32.9887	1.12295	0.561474	+	0.827495i	$0.310235\pi$
$864$	197.905	6.73288
$865$	6.23363	0.211950
$866$	36.3308	1.23457
$867$	−45.7740	−1.55457
$868$	−4.51063	−0.153101
$869$	3.63953	0.123462
$870$	−21.3009	−0.722168
$871$	0	0
$872$	46.1546	1.56299
$873$	86.2211	2.91814
$874$	80.2291	2.71379
$875$	−2.83288	−0.0957688
$876$	24.3853	0.823904
$877$	8.41464	0.284142	0.142071	−	0.989856i	$-0.454624\pi$
$877$	8.41464	0.284142	0.142071	+	0.989856i	$0.454624\pi$
$878$	41.8548	1.41253
$879$	−62.7822	−2.11759
$880$	29.5311	0.995494
$881$	−20.8178	−0.701369	−0.350684	−	0.936494i	$-0.614051\pi$
$881$	−20.8178	−0.701369	−0.350684	+	0.936494i	$0.614051\pi$
$882$	−125.991	−4.24233
$883$	42.2995	1.42349	0.711746	−	0.702437i	$-0.247905\pi$
$883$	42.2995	1.42349	0.711746	+	0.702437i	$0.247905\pi$
$884$	0	0
$885$	79.4919	2.67209
$886$	43.8240	1.47230
$887$	−34.4350	−1.15622	−0.578108	−	0.815961i	$-0.696209\pi$
$887$	−34.4350	−1.15622	−0.578108	+	0.815961i	$0.696209\pi$
$888$	−92.6063	−3.10766
$889$	−5.61745	−0.188403
$890$	−50.7688	−1.70177
$891$	−16.5874	−0.555699
$892$	−135.014	−4.52059
$893$	−48.9902	−1.63940
$894$	45.5735	1.52421
$895$	53.1036	1.77506
$896$	−5.14705	−0.171951
$897$	0	0
$898$	7.89273	0.263384
$899$	3.53545	0.117914
$900$	15.8986	0.529953
$901$	−7.77966	−0.259178
$902$	−16.9184	−0.563321
$903$	−2.05010	−0.0682230
$904$	−130.388	−4.33663
$905$	−47.7575	−1.58751
$906$	−57.6512	−1.91533
$907$	−8.62987	−0.286550	−0.143275	−	0.989683i	$-0.545763\pi$
$907$	−8.62987	−0.286550	−0.143275	+	0.989683i	$0.545763\pi$
$908$	52.1884	1.73193
$909$	84.9927	2.81903
$910$	0	0
$911$	43.0264	1.42553	0.712763	−	0.701405i	$-0.247443\pi$
$911$	43.0264	1.42553	0.712763	+	0.701405i	$0.247443\pi$
$912$	−298.950	−9.89921
$913$	−9.17706	−0.303716
$914$	68.8088	2.27599
$915$	−70.5525	−2.33239
$916$	15.5050	0.512300
$917$	−1.00724	−0.0332619
$918$	−48.6742	−1.60649
$919$	−39.5049	−1.30315	−0.651574	−	0.758585i	$-0.725891\pi$
$919$	−39.5049	−1.30315	−0.651574	+	0.758585i	$0.725891\pi$
$920$	79.3202	2.61511
$921$	−13.5189	−0.445462
$922$	−68.2697	−2.24834
$923$	0	0
$924$	4.33762	0.142697
$925$	−1.55548	−0.0511439
$926$	28.4627	0.935341
$927$	−32.4402	−1.06548
$928$	18.2265	0.598315
$929$	−23.8514	−0.782539	−0.391269	−	0.920276i	$-0.627964\pi$
$929$	−23.8514	−0.782539	−0.391269	+	0.920276i	$0.627964\pi$
$930$	−63.6930	−2.08858
$931$	52.3768	1.71658
$932$	−19.5070	−0.638974
$933$	−79.3472	−2.59771
$934$	−13.8871	−0.454399
$935$	−3.58688	−0.117303
$936$	0	0
$937$	−21.8554	−0.713985	−0.356993	−	0.934107i	$-0.616198\pi$
$937$	−21.8554	−0.713985	−0.356993	+	0.934107i	$0.616198\pi$
$938$	4.59521	0.150039
$939$	66.0449	2.15529
$940$	−78.6977	−2.56683
$941$	14.3904	0.469112	0.234556	−	0.972103i	$-0.424636\pi$
$941$	14.3904	0.469112	0.234556	+	0.972103i	$0.424636\pi$
$942$	45.0292	1.46713
$943$	−24.9356	−0.812016
$944$	−137.732	−4.48279
$945$	7.35279	0.239186
$946$	−6.59640	−0.214467
$947$	18.5363	0.602349	0.301175	−	0.953569i	$-0.402621\pi$
$947$	18.5363	0.602349	0.301175	+	0.953569i	$0.402621\pi$
$948$	−59.1855	−1.92226
$949$	0	0
$950$	−9.15091	−0.296895
$951$	−65.9216	−2.13766
$952$	3.51996	0.114082
$953$	15.7252	0.509388	0.254694	−	0.967022i	$-0.418025\pi$
$953$	15.7252	0.509388	0.254694	+	0.967022i	$0.418025\pi$
$954$	92.0799	2.98120
$955$	17.9776	0.581742
$956$	−42.5084	−1.37482
$957$	−3.39984	−0.109901
$958$	−48.0903	−1.55373
$959$	0.752043	0.0242847
$960$	−143.692	−4.63765
$961$	−20.4284	−0.658982
$962$	0	0
$963$	−136.009	−4.38282
$964$	−24.0606	−0.774939
$965$	17.6261	0.567405
$966$	8.85153	0.284793
$967$	−40.7288	−1.30975	−0.654874	−	0.755738i	$-0.727278\pi$
$967$	−40.7288	−1.30975	−0.654874	+	0.755738i	$0.727278\pi$
$968$	8.58980	0.276087
$969$	36.3107	1.16647
$970$	−79.7209	−2.55968
$971$	51.9398	1.66683	0.833414	−	0.552649i	$-0.186383\pi$
$971$	51.9398	1.66683	0.833414	+	0.552649i	$0.186383\pi$
$972$	85.5221	2.74312
$973$	0.491516	0.0157573
$974$	−17.3458	−0.555796
$975$	0	0
$976$	122.243	3.91290
$977$	−6.50233	−0.208028	−0.104014	−	0.994576i	$-0.533169\pi$
$977$	−6.50233	−0.208028	−0.104014	+	0.994576i	$0.533169\pi$
$978$	36.4438	1.16535
$979$	−8.10322	−0.258980
$980$	84.1379	2.68769
$981$	36.4093	1.16246
$982$	44.8345	1.43073
$983$	10.4399	0.332981	0.166491	−	0.986043i	$-0.446756\pi$
$983$	10.4399	0.332981	0.166491	+	0.986043i	$0.446756\pi$
$984$	169.328	5.39798
$985$	−43.9298	−1.39972
$986$	−4.48276	−0.142760
$987$	−5.40500	−0.172043
$988$	0	0
$989$	−9.72228	−0.309151
$990$	42.4542	1.34928
$991$	−25.3194	−0.804296	−0.402148	−	0.915575i	$-0.631736\pi$
$991$	−25.3194	−0.804296	−0.402148	+	0.915575i	$0.631736\pi$
$992$	54.5002	1.73038
$993$	88.2186	2.79953
$994$	9.36364	0.296997
$995$	−21.0941	−0.668729
$996$	149.236	4.72873
$997$	−21.2428	−0.672766	−0.336383	−	0.941725i	$-0.609204\pi$
$997$	−21.2428	−0.672766	−0.336383	+	0.941725i	$0.609204\pi$
$998$	50.2490	1.59060
$999$	−40.7102	−1.28801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.19	✓	21
13.12	even	2		1859.2.a.t.1.3	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.19	✓	21	1.1	even	1	trivial
1859.2.a.t.1.3	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)

\(f(q)\)	\(=\)	\(q+2.68347 q^{2} +3.12668 q^{3} +5.20101 q^{4} -2.33476 q^{5} +8.39034 q^{6} -0.266736 q^{7} +8.58980 q^{8} +6.77612 q^{9} +O(q^{10})\)	\(q+2.68347 q^{2} +3.12668 q^{3} +5.20101 q^{4} -2.33476 q^{5} +8.39034 q^{6} -0.266736 q^{7} +8.58980 q^{8} +6.77612 q^{9} -6.26526 q^{10} -1.00000 q^{11} +16.2619 q^{12} -0.715776 q^{14} -7.30005 q^{15} +12.6484 q^{16} -1.53629 q^{17} +18.1835 q^{18} -7.55923 q^{19} -12.1431 q^{20} -0.833996 q^{21} -2.68347 q^{22} -3.95510 q^{23} +26.8575 q^{24} +0.451118 q^{25} +11.8067 q^{27} -1.38729 q^{28} +1.08736 q^{29} -19.5895 q^{30} +3.25139 q^{31} +16.7621 q^{32} -3.12668 q^{33} -4.12259 q^{34} +0.622764 q^{35} +35.2426 q^{36} -3.44806 q^{37} -20.2850 q^{38} -20.0551 q^{40} +6.30467 q^{41} -2.23800 q^{42} +2.45816 q^{43} -5.20101 q^{44} -15.8206 q^{45} -10.6134 q^{46} +6.48085 q^{47} +39.5476 q^{48} -6.92885 q^{49} +1.21056 q^{50} -4.80349 q^{51} +5.06393 q^{53} +31.6829 q^{54} +2.33476 q^{55} -2.29120 q^{56} -23.6353 q^{57} +2.91791 q^{58} -10.8892 q^{59} -37.9676 q^{60} +9.66466 q^{61} +8.72501 q^{62} -1.80743 q^{63} +19.6837 q^{64} -8.39034 q^{66} -6.41989 q^{67} -7.99026 q^{68} -12.3663 q^{69} +1.67117 q^{70} -13.0818 q^{71} +58.2055 q^{72} +1.49954 q^{73} -9.25276 q^{74} +1.41050 q^{75} -39.3156 q^{76} +0.266736 q^{77} -3.63953 q^{79} -29.5311 q^{80} +16.5874 q^{81} +16.9184 q^{82} +9.17706 q^{83} -4.33762 q^{84} +3.58688 q^{85} +6.59640 q^{86} +3.39984 q^{87} -8.58980 q^{88} +8.10322 q^{89} -42.4542 q^{90} -20.5705 q^{92} +10.1661 q^{93} +17.3912 q^{94} +17.6490 q^{95} +52.4097 q^{96} +12.7243 q^{97} -18.5934 q^{98} -6.77612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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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