LMFDB - Embedded newform 4598.2.a.bf.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.73205 q^{5} -1.00000 q^{6} -3.73205 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.73205 q^{5} -1.00000 q^{6} -3.73205 q^{7} +1.00000 q^{8} -2.00000 q^{9} +2.73205 q^{10} -1.00000 q^{12} -3.46410 q^{13} -3.73205 q^{14} -2.73205 q^{15} +1.00000 q^{16} +0.535898 q^{17} -2.00000 q^{18} -1.00000 q^{19} +2.73205 q^{20} +3.73205 q^{21} -1.00000 q^{23} -1.00000 q^{24} +2.46410 q^{25} -3.46410 q^{26} +5.00000 q^{27} -3.73205 q^{28} +1.73205 q^{29} -2.73205 q^{30} +5.46410 q^{31} +1.00000 q^{32} +0.535898 q^{34} -10.1962 q^{35} -2.00000 q^{36} +0.464102 q^{37} -1.00000 q^{38} +3.46410 q^{39} +2.73205 q^{40} +7.26795 q^{41} +3.73205 q^{42} +8.92820 q^{43} -5.46410 q^{45} -1.00000 q^{46} +5.53590 q^{47} -1.00000 q^{48} +6.92820 q^{49} +2.46410 q^{50} -0.535898 q^{51} -3.46410 q^{52} +3.92820 q^{53} +5.00000 q^{54} -3.73205 q^{56} +1.00000 q^{57} +1.73205 q^{58} +11.3923 q^{59} -2.73205 q^{60} -4.73205 q^{61} +5.46410 q^{62} +7.46410 q^{63} +1.00000 q^{64} -9.46410 q^{65} +14.0000 q^{67} +0.535898 q^{68} +1.00000 q^{69} -10.1962 q^{70} +3.80385 q^{71} -2.00000 q^{72} -2.00000 q^{73} +0.464102 q^{74} -2.46410 q^{75} -1.00000 q^{76} +3.46410 q^{78} -8.19615 q^{79} +2.73205 q^{80} +1.00000 q^{81} +7.26795 q^{82} +14.1962 q^{83} +3.73205 q^{84} +1.46410 q^{85} +8.92820 q^{86} -1.73205 q^{87} +1.80385 q^{89} -5.46410 q^{90} +12.9282 q^{91} -1.00000 q^{92} -5.46410 q^{93} +5.53590 q^{94} -2.73205 q^{95} -1.00000 q^{96} +6.53590 q^{97} +6.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 2 q^{10} - 2 q^{12} - 4 q^{14} - 2 q^{15} + 2 q^{16} + 8 q^{17} - 4 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{21} - 2 q^{23} - 2 q^{24} - 2 q^{25} + 10 q^{27} - 4 q^{28} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 8 q^{34} - 10 q^{35} - 4 q^{36} - 6 q^{37} - 2 q^{38} + 2 q^{40} + 18 q^{41} + 4 q^{42} + 4 q^{43} - 4 q^{45} - 2 q^{46} + 18 q^{47} - 2 q^{48} - 2 q^{50} - 8 q^{51} - 6 q^{53} + 10 q^{54} - 4 q^{56} + 2 q^{57} + 2 q^{59} - 2 q^{60} - 6 q^{61} + 4 q^{62} + 8 q^{63} + 2 q^{64} - 12 q^{65} + 28 q^{67} + 8 q^{68} + 2 q^{69} - 10 q^{70} + 18 q^{71} - 4 q^{72} - 4 q^{73} - 6 q^{74} + 2 q^{75} - 2 q^{76} - 6 q^{79} + 2 q^{80} + 2 q^{81} + 18 q^{82} + 18 q^{83} + 4 q^{84} - 4 q^{85} + 4 q^{86} + 14 q^{89} - 4 q^{90} + 12 q^{91} - 2 q^{92} - 4 q^{93} + 18 q^{94} - 2 q^{95} - 2 q^{96} + 20 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 2 * q^10 - 2 * q^12 - 4 * q^14 - 2 * q^15 + 2 * q^16 + 8 * q^17 - 4 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^21 - 2 * q^23 - 2 * q^24 - 2 * q^25 + 10 * q^27 - 4 * q^28 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 8 * q^34 - 10 * q^35 - 4 * q^36 - 6 * q^37 - 2 * q^38 + 2 * q^40 + 18 * q^41 + 4 * q^42 + 4 * q^43 - 4 * q^45 - 2 * q^46 + 18 * q^47 - 2 * q^48 - 2 * q^50 - 8 * q^51 - 6 * q^53 + 10 * q^54 - 4 * q^56 + 2 * q^57 + 2 * q^59 - 2 * q^60 - 6 * q^61 + 4 * q^62 + 8 * q^63 + 2 * q^64 - 12 * q^65 + 28 * q^67 + 8 * q^68 + 2 * q^69 - 10 * q^70 + 18 * q^71 - 4 * q^72 - 4 * q^73 - 6 * q^74 + 2 * q^75 - 2 * q^76 - 6 * q^79 + 2 * q^80 + 2 * q^81 + 18 * q^82 + 18 * q^83 + 4 * q^84 - 4 * q^85 + 4 * q^86 + 14 * q^89 - 4 * q^90 + 12 * q^91 - 2 * q^92 - 4 * q^93 + 18 * q^94 - 2 * q^95 - 2 * q^96 + 20 * q^97

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	2.73205	1.22181	0.610905	−	0.791704i	$-0.290806\pi$
$5$	2.73205	1.22181	0.610905	+	0.791704i	$0.290806\pi$
$6$	−1.00000	−0.408248
$7$	−3.73205	−1.41058	−0.705291	−	0.708918i	$-0.749184\pi$
$7$	−3.73205	−1.41058	−0.705291	+	0.708918i	$0.749184\pi$
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	2.73205	0.863950
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	−3.46410	−0.960769	−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410	−0.960769	−0.480384	+	0.877058i	$0.659503\pi$
$14$	−3.73205	−0.997433
$15$	−2.73205	−0.705412
$16$	1.00000	0.250000
$17$	0.535898	0.129974	0.0649872	−	0.997886i	$-0.479299\pi$
$17$	0.535898	0.129974	0.0649872	+	0.997886i	$0.479299\pi$
$18$	−2.00000	−0.471405
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.73205	0.610905
$21$	3.73205	0.814400
$22$	0	0
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	−1.00000	−0.204124
$25$	2.46410	0.492820
$26$	−3.46410	−0.679366
$27$	5.00000	0.962250
$28$	−3.73205	−0.705291
$29$	1.73205	0.321634	0.160817	−	0.986984i	$-0.448587\pi$
$29$	1.73205	0.321634	0.160817	+	0.986984i	$0.448587\pi$
$30$	−2.73205	−0.498802
$31$	5.46410	0.981382	0.490691	−	0.871334i	$-0.336744\pi$
$31$	5.46410	0.981382	0.490691	+	0.871334i	$0.336744\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	0.535898	0.0919058
$35$	−10.1962	−1.72346
$36$	−2.00000	−0.333333
$37$	0.464102	0.0762978	0.0381489	−	0.999272i	$-0.487854\pi$
$37$	0.464102	0.0762978	0.0381489	+	0.999272i	$0.487854\pi$
$38$	−1.00000	−0.162221
$39$	3.46410	0.554700
$40$	2.73205	0.431975
$41$	7.26795	1.13506	0.567531	−	0.823352i	$-0.307899\pi$
$41$	7.26795	1.13506	0.567531	+	0.823352i	$0.307899\pi$
$42$	3.73205	0.575868
$43$	8.92820	1.36154	0.680769	−	0.732498i	$-0.261646\pi$
$43$	8.92820	1.36154	0.680769	+	0.732498i	$0.261646\pi$
$44$	0	0
$45$	−5.46410	−0.814540
$46$	−1.00000	−0.147442
$47$	5.53590	0.807494	0.403747	−	0.914871i	$-0.367708\pi$
$47$	5.53590	0.807494	0.403747	+	0.914871i	$0.367708\pi$
$48$	−1.00000	−0.144338
$49$	6.92820	0.989743
$50$	2.46410	0.348477
$51$	−0.535898	−0.0750408
$52$	−3.46410	−0.480384
$53$	3.92820	0.539580	0.269790	−	0.962919i	$-0.413046\pi$
$53$	3.92820	0.539580	0.269790	+	0.962919i	$0.413046\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	−3.73205	−0.498716
$57$	1.00000	0.132453
$58$	1.73205	0.227429
$59$	11.3923	1.48315	0.741576	−	0.670869i	$-0.234079\pi$
$59$	11.3923	1.48315	0.741576	+	0.670869i	$0.234079\pi$
$60$	−2.73205	−0.352706
$61$	−4.73205	−0.605877	−0.302939	−	0.953010i	$-0.597968\pi$
$61$	−4.73205	−0.605877	−0.302939	+	0.953010i	$0.597968\pi$
$62$	5.46410	0.693942
$63$	7.46410	0.940388
$64$	1.00000	0.125000
$65$	−9.46410	−1.17388
$66$	0	0
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	0.535898	0.0649872
$69$	1.00000	0.120386
$70$	−10.1962	−1.21867
$71$	3.80385	0.451434	0.225717	−	0.974193i	$-0.427528\pi$
$71$	3.80385	0.451434	0.225717	+	0.974193i	$0.427528\pi$
$72$	−2.00000	−0.235702
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	0.464102	0.0539507
$75$	−2.46410	−0.284530
$76$	−1.00000	−0.114708
$77$	0	0
$78$	3.46410	0.392232
$79$	−8.19615	−0.922139	−0.461070	−	0.887364i	$-0.652534\pi$
$79$	−8.19615	−0.922139	−0.461070	+	0.887364i	$0.652534\pi$
$80$	2.73205	0.305453
$81$	1.00000	0.111111
$82$	7.26795	0.802611
$83$	14.1962	1.55823	0.779115	−	0.626881i	$-0.215669\pi$
$83$	14.1962	1.55823	0.779115	+	0.626881i	$0.215669\pi$
$84$	3.73205	0.407200
$85$	1.46410	0.158804
$86$	8.92820	0.962753
$87$	−1.73205	−0.185695
$88$	0	0
$89$	1.80385	0.191207	0.0956037	−	0.995419i	$-0.469522\pi$
$89$	1.80385	0.191207	0.0956037	+	0.995419i	$0.469522\pi$
$90$	−5.46410	−0.575967
$91$	12.9282	1.35524
$92$	−1.00000	−0.104257
$93$	−5.46410	−0.566601
$94$	5.53590	0.570984
$95$	−2.73205	−0.280302
$96$	−1.00000	−0.102062
$97$	6.53590	0.663620	0.331810	−	0.943346i	$-0.392341\pi$
$97$	6.53590	0.663620	0.331810	+	0.943346i	$0.392341\pi$
$98$	6.92820	0.699854
$99$	0	0
$100$	2.46410	0.246410
$101$	−14.5885	−1.45161	−0.725803	−	0.687903i	$-0.758532\pi$
$101$	−14.5885	−1.45161	−0.725803	+	0.687903i	$0.758532\pi$
$102$	−0.535898	−0.0530618
$103$	0.732051	0.0721311	0.0360656	−	0.999349i	$-0.488517\pi$
$103$	0.732051	0.0721311	0.0360656	+	0.999349i	$0.488517\pi$
$104$	−3.46410	−0.339683
$105$	10.1962	0.995043
$106$	3.92820	0.381541
$107$	13.1962	1.27572	0.637860	−	0.770152i	$-0.279820\pi$
$107$	13.1962	1.27572	0.637860	+	0.770152i	$0.279820\pi$
$108$	5.00000	0.481125
$109$	−18.1244	−1.73600	−0.867999	−	0.496566i	$-0.834594\pi$
$109$	−18.1244	−1.73600	−0.867999	+	0.496566i	$0.834594\pi$
$110$	0	0
$111$	−0.464102	−0.0440506
$112$	−3.73205	−0.352646
$113$	−1.26795	−0.119279	−0.0596393	−	0.998220i	$-0.518995\pi$
$113$	−1.26795	−0.119279	−0.0596393	+	0.998220i	$0.518995\pi$
$114$	1.00000	0.0936586
$115$	−2.73205	−0.254765
$116$	1.73205	0.160817
$117$	6.92820	0.640513
$118$	11.3923	1.04875
$119$	−2.00000	−0.183340
$120$	−2.73205	−0.249401
$121$	0	0
$122$	−4.73205	−0.428420
$123$	−7.26795	−0.655329
$124$	5.46410	0.490691
$125$	−6.92820	−0.619677
$126$	7.46410	0.664955
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	1.00000	0.0883883
$129$	−8.92820	−0.786084
$130$	−9.46410	−0.830057
$131$	7.07180	0.617866	0.308933	−	0.951084i	$-0.400028\pi$
$131$	7.07180	0.617866	0.308933	+	0.951084i	$0.400028\pi$
$132$	0	0
$133$	3.73205	0.323610
$134$	14.0000	1.20942
$135$	13.6603	1.17569
$136$	0.535898	0.0459529
$137$	2.53590	0.216656	0.108328	−	0.994115i	$-0.465450\pi$
$137$	2.53590	0.216656	0.108328	+	0.994115i	$0.465450\pi$
$138$	1.00000	0.0851257
$139$	13.4641	1.14201	0.571005	−	0.820947i	$-0.306554\pi$
$139$	13.4641	1.14201	0.571005	+	0.820947i	$0.306554\pi$
$140$	−10.1962	−0.861732
$141$	−5.53590	−0.466207
$142$	3.80385	0.319212
$143$	0	0
$144$	−2.00000	−0.166667
$145$	4.73205	0.392975
$146$	−2.00000	−0.165521
$147$	−6.92820	−0.571429
$148$	0.464102	0.0381489
$149$	23.3205	1.91049	0.955245	−	0.295815i	$-0.0955912\pi$
$149$	23.3205	1.91049	0.955245	+	0.295815i	$0.0955912\pi$
$150$	−2.46410	−0.201193
$151$	17.2679	1.40525	0.702623	−	0.711562i	$-0.252012\pi$
$151$	17.2679	1.40525	0.702623	+	0.711562i	$0.252012\pi$
$152$	−1.00000	−0.0811107
$153$	−1.07180	−0.0866496
$154$	0	0
$155$	14.9282	1.19906
$156$	3.46410	0.277350
$157$	−8.73205	−0.696894	−0.348447	−	0.937329i	$-0.613291\pi$
$157$	−8.73205	−0.696894	−0.348447	+	0.937329i	$0.613291\pi$
$158$	−8.19615	−0.652051
$159$	−3.92820	−0.311527
$160$	2.73205	0.215988
$161$	3.73205	0.294127
$162$	1.00000	0.0785674
$163$	−17.3205	−1.35665	−0.678323	−	0.734763i	$-0.737293\pi$
$163$	−17.3205	−1.35665	−0.678323	+	0.734763i	$0.737293\pi$
$164$	7.26795	0.567531
$165$	0	0
$166$	14.1962	1.10184
$167$	−3.46410	−0.268060	−0.134030	−	0.990977i	$-0.542792\pi$
$167$	−3.46410	−0.268060	−0.134030	+	0.990977i	$0.542792\pi$
$168$	3.73205	0.287934
$169$	−1.00000	−0.0769231
$170$	1.46410	0.112291
$171$	2.00000	0.152944
$172$	8.92820	0.680769
$173$	−20.1244	−1.53003	−0.765013	−	0.644015i	$-0.777268\pi$
$173$	−20.1244	−1.53003	−0.765013	+	0.644015i	$0.777268\pi$
$174$	−1.73205	−0.131306
$175$	−9.19615	−0.695164
$176$	0	0
$177$	−11.3923	−0.856298
$178$	1.80385	0.135204
$179$	−15.9282	−1.19053	−0.595265	−	0.803530i	$-0.702953\pi$
$179$	−15.9282	−1.19053	−0.595265	+	0.803530i	$0.702953\pi$
$180$	−5.46410	−0.407270
$181$	3.60770	0.268158	0.134079	−	0.990971i	$-0.457192\pi$
$181$	3.60770	0.268158	0.134079	+	0.990971i	$0.457192\pi$
$182$	12.9282	0.958302
$183$	4.73205	0.349803
$184$	−1.00000	−0.0737210
$185$	1.26795	0.0932215
$186$	−5.46410	−0.400647
$187$	0	0
$188$	5.53590	0.403747
$189$	−18.6603	−1.35733
$190$	−2.73205	−0.198204
$191$	3.39230	0.245459	0.122729	−	0.992440i	$-0.460835\pi$
$191$	3.39230	0.245459	0.122729	+	0.992440i	$0.460835\pi$
$192$	−1.00000	−0.0721688
$193$	−19.4641	−1.40106	−0.700528	−	0.713625i	$-0.747052\pi$
$193$	−19.4641	−1.40106	−0.700528	+	0.713625i	$0.747052\pi$
$194$	6.53590	0.469250
$195$	9.46410	0.677738
$196$	6.92820	0.494872
$197$	−18.9282	−1.34858	−0.674289	−	0.738467i	$-0.735550\pi$
$197$	−18.9282	−1.34858	−0.674289	+	0.738467i	$0.735550\pi$
$198$	0	0
$199$	3.07180	0.217754	0.108877	−	0.994055i	$-0.465275\pi$
$199$	3.07180	0.217754	0.108877	+	0.994055i	$0.465275\pi$
$200$	2.46410	0.174238
$201$	−14.0000	−0.987484
$202$	−14.5885	−1.02644
$203$	−6.46410	−0.453691
$204$	−0.535898	−0.0375204
$205$	19.8564	1.38683
$206$	0.732051	0.0510044
$207$	2.00000	0.139010
$208$	−3.46410	−0.240192
$209$	0	0
$210$	10.1962	0.703601
$211$	−20.1244	−1.38542	−0.692709	−	0.721217i	$-0.743583\pi$
$211$	−20.1244	−1.38542	−0.692709	+	0.721217i	$0.743583\pi$
$212$	3.92820	0.269790
$213$	−3.80385	−0.260635
$214$	13.1962	0.902070
$215$	24.3923	1.66354
$216$	5.00000	0.340207
$217$	−20.3923	−1.38432
$218$	−18.1244	−1.22754
$219$	2.00000	0.135147
$220$	0	0
$221$	−1.85641	−0.124875
$222$	−0.464102	−0.0311485
$223$	−11.1244	−0.744942	−0.372471	−	0.928044i	$-0.621489\pi$
$223$	−11.1244	−0.744942	−0.372471	+	0.928044i	$0.621489\pi$
$224$	−3.73205	−0.249358
$225$	−4.92820	−0.328547
$226$	−1.26795	−0.0843427
$227$	12.3923	0.822506	0.411253	−	0.911521i	$-0.365091\pi$
$227$	12.3923	0.822506	0.411253	+	0.911521i	$0.365091\pi$
$228$	1.00000	0.0662266
$229$	8.39230	0.554579	0.277290	−	0.960786i	$-0.410564\pi$
$229$	8.39230	0.554579	0.277290	+	0.960786i	$0.410564\pi$
$230$	−2.73205	−0.180146
$231$	0	0
$232$	1.73205	0.113715
$233$	11.7321	0.768592	0.384296	−	0.923210i	$-0.374444\pi$
$233$	11.7321	0.768592	0.384296	+	0.923210i	$0.374444\pi$
$234$	6.92820	0.452911
$235$	15.1244	0.986604
$236$	11.3923	0.741576
$237$	8.19615	0.532397
$238$	−2.00000	−0.129641
$239$	−10.1244	−0.654890	−0.327445	−	0.944870i	$-0.606188\pi$
$239$	−10.1244	−0.654890	−0.327445	+	0.944870i	$0.606188\pi$
$240$	−2.73205	−0.176353
$241$	−14.7321	−0.948975	−0.474487	−	0.880262i	$-0.657367\pi$
$241$	−14.7321	−0.948975	−0.474487	+	0.880262i	$0.657367\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	−4.73205	−0.302939
$245$	18.9282	1.20928
$246$	−7.26795	−0.463388
$247$	3.46410	0.220416
$248$	5.46410	0.346971
$249$	−14.1962	−0.899645
$250$	−6.92820	−0.438178
$251$	15.4641	0.976085	0.488043	−	0.872820i	$-0.337711\pi$
$251$	15.4641	0.976085	0.488043	+	0.872820i	$0.337711\pi$
$252$	7.46410	0.470194
$253$	0	0
$254$	−4.00000	−0.250982
$255$	−1.46410	−0.0916856
$256$	1.00000	0.0625000
$257$	31.3205	1.95372	0.976860	−	0.213881i	$-0.0686104\pi$
$257$	31.3205	1.95372	0.976860	+	0.213881i	$0.0686104\pi$
$258$	−8.92820	−0.555846
$259$	−1.73205	−0.107624
$260$	−9.46410	−0.586939
$261$	−3.46410	−0.214423
$262$	7.07180	0.436897
$263$	16.7846	1.03498	0.517492	−	0.855688i	$-0.326866\pi$
$263$	16.7846	1.03498	0.517492	+	0.855688i	$0.326866\pi$
$264$	0	0
$265$	10.7321	0.659265
$266$	3.73205	0.228827
$267$	−1.80385	−0.110394
$268$	14.0000	0.855186
$269$	11.7846	0.718520	0.359260	−	0.933237i	$-0.383029\pi$
$269$	11.7846	0.718520	0.359260	+	0.933237i	$0.383029\pi$
$270$	13.6603	0.831337
$271$	−27.3205	−1.65960	−0.829801	−	0.558059i	$-0.811546\pi$
$271$	−27.3205	−1.65960	−0.829801	+	0.558059i	$0.811546\pi$
$272$	0.535898	0.0324936
$273$	−12.9282	−0.782450
$274$	2.53590	0.153199
$275$	0	0
$276$	1.00000	0.0601929
$277$	9.12436	0.548229	0.274115	−	0.961697i	$-0.411615\pi$
$277$	9.12436	0.548229	0.274115	+	0.961697i	$0.411615\pi$
$278$	13.4641	0.807523
$279$	−10.9282	−0.654254
$280$	−10.1962	−0.609337
$281$	22.0526	1.31555	0.657773	−	0.753216i	$-0.271499\pi$
$281$	22.0526	1.31555	0.657773	+	0.753216i	$0.271499\pi$
$282$	−5.53590	−0.329658
$283$	−14.5359	−0.864069	−0.432035	−	0.901857i	$-0.642204\pi$
$283$	−14.5359	−0.864069	−0.432035	+	0.901857i	$0.642204\pi$
$284$	3.80385	0.225717
$285$	2.73205	0.161833
$286$	0	0
$287$	−27.1244	−1.60110
$288$	−2.00000	−0.117851
$289$	−16.7128	−0.983107
$290$	4.73205	0.277876
$291$	−6.53590	−0.383141
$292$	−2.00000	−0.117041
$293$	12.1244	0.708312	0.354156	−	0.935186i	$-0.384768\pi$
$293$	12.1244	0.708312	0.354156	+	0.935186i	$0.384768\pi$
$294$	−6.92820	−0.404061
$295$	31.1244	1.81213
$296$	0.464102	0.0269754
$297$	0	0
$298$	23.3205	1.35092
$299$	3.46410	0.200334
$300$	−2.46410	−0.142265
$301$	−33.3205	−1.92056
$302$	17.2679	0.993659
$303$	14.5885	0.838085
$304$	−1.00000	−0.0573539
$305$	−12.9282	−0.740267
$306$	−1.07180	−0.0612705
$307$	15.5885	0.889680	0.444840	−	0.895610i	$-0.353260\pi$
$307$	15.5885	0.889680	0.444840	+	0.895610i	$0.353260\pi$
$308$	0	0
$309$	−0.732051	−0.0416449
$310$	14.9282	0.847865
$311$	−22.3923	−1.26975	−0.634876	−	0.772614i	$-0.718949\pi$
$311$	−22.3923	−1.26975	−0.634876	+	0.772614i	$0.718949\pi$
$312$	3.46410	0.196116
$313$	20.4641	1.15670	0.578350	−	0.815789i	$-0.303697\pi$
$313$	20.4641	1.15670	0.578350	+	0.815789i	$0.303697\pi$
$314$	−8.73205	−0.492778
$315$	20.3923	1.14898
$316$	−8.19615	−0.461070
$317$	20.7846	1.16738	0.583690	−	0.811977i	$-0.301608\pi$
$317$	20.7846	1.16738	0.583690	+	0.811977i	$0.301608\pi$
$318$	−3.92820	−0.220283
$319$	0	0
$320$	2.73205	0.152726
$321$	−13.1962	−0.736537
$322$	3.73205	0.207979
$323$	−0.535898	−0.0298182
$324$	1.00000	0.0555556
$325$	−8.53590	−0.473486
$326$	−17.3205	−0.959294
$327$	18.1244	1.00228
$328$	7.26795	0.401305
$329$	−20.6603	−1.13904
$330$	0	0
$331$	−19.7846	−1.08746	−0.543730	−	0.839260i	$-0.682989\pi$
$331$	−19.7846	−1.08746	−0.543730	+	0.839260i	$0.682989\pi$
$332$	14.1962	0.779115
$333$	−0.928203	−0.0508652
$334$	−3.46410	−0.189547
$335$	38.2487	2.08975
$336$	3.73205	0.203600
$337$	13.8038	0.751943	0.375972	−	0.926631i	$-0.377309\pi$
$337$	13.8038	0.751943	0.375972	+	0.926631i	$0.377309\pi$
$338$	−1.00000	−0.0543928
$339$	1.26795	0.0688655
$340$	1.46410	0.0794021
$341$	0	0
$342$	2.00000	0.108148
$343$	0.267949	0.0144679
$344$	8.92820	0.481376
$345$	2.73205	0.147089
$346$	−20.1244	−1.08189
$347$	28.0526	1.50594	0.752970	−	0.658055i	$-0.228620\pi$
$347$	28.0526	1.50594	0.752970	+	0.658055i	$0.228620\pi$
$348$	−1.73205	−0.0928477
$349$	−26.7846	−1.43375	−0.716874	−	0.697203i	$-0.754428\pi$
$349$	−26.7846	−1.43375	−0.716874	+	0.697203i	$0.754428\pi$
$350$	−9.19615	−0.491555
$351$	−17.3205	−0.924500
$352$	0	0
$353$	0.464102	0.0247016	0.0123508	−	0.999924i	$-0.496069\pi$
$353$	0.464102	0.0247016	0.0123508	+	0.999924i	$0.496069\pi$
$354$	−11.3923	−0.605494
$355$	10.3923	0.551566
$356$	1.80385	0.0956037
$357$	2.00000	0.105851
$358$	−15.9282	−0.841832
$359$	−7.60770	−0.401519	−0.200759	−	0.979641i	$-0.564341\pi$
$359$	−7.60770	−0.401519	−0.200759	+	0.979641i	$0.564341\pi$
$360$	−5.46410	−0.287983
$361$	1.00000	0.0526316
$362$	3.60770	0.189616
$363$	0	0
$364$	12.9282	0.677622
$365$	−5.46410	−0.286004
$366$	4.73205	0.247348
$367$	4.85641	0.253502	0.126751	−	0.991935i	$-0.459545\pi$
$367$	4.85641	0.253502	0.126751	+	0.991935i	$0.459545\pi$
$368$	−1.00000	−0.0521286
$369$	−14.5359	−0.756709
$370$	1.26795	0.0659175
$371$	−14.6603	−0.761122
$372$	−5.46410	−0.283300
$373$	27.1962	1.40816	0.704082	−	0.710119i	$-0.251359\pi$
$373$	27.1962	1.40816	0.704082	+	0.710119i	$0.251359\pi$
$374$	0	0
$375$	6.92820	0.357771
$376$	5.53590	0.285492
$377$	−6.00000	−0.309016
$378$	−18.6603	−0.959780
$379$	10.0718	0.517353	0.258677	−	0.965964i	$-0.416714\pi$
$379$	10.0718	0.517353	0.258677	+	0.965964i	$0.416714\pi$
$380$	−2.73205	−0.140151
$381$	4.00000	0.204926
$382$	3.39230	0.173565
$383$	26.5359	1.35592	0.677961	−	0.735098i	$-0.262864\pi$
$383$	26.5359	1.35592	0.677961	+	0.735098i	$0.262864\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−19.4641	−0.990697
$387$	−17.8564	−0.907692
$388$	6.53590	0.331810
$389$	30.5885	1.55090	0.775448	−	0.631411i	$-0.217524\pi$
$389$	30.5885	1.55090	0.775448	+	0.631411i	$0.217524\pi$
$390$	9.46410	0.479233
$391$	−0.535898	−0.0271015
$392$	6.92820	0.349927
$393$	−7.07180	−0.356725
$394$	−18.9282	−0.953589
$395$	−22.3923	−1.12668
$396$	0	0
$397$	26.3923	1.32459	0.662296	−	0.749242i	$-0.269582\pi$
$397$	26.3923	1.32459	0.662296	+	0.749242i	$0.269582\pi$
$398$	3.07180	0.153975
$399$	−3.73205	−0.186836
$400$	2.46410	0.123205
$401$	22.0526	1.10125	0.550626	−	0.834752i	$-0.314389\pi$
$401$	22.0526	1.10125	0.550626	+	0.834752i	$0.314389\pi$
$402$	−14.0000	−0.698257
$403$	−18.9282	−0.942881
$404$	−14.5885	−0.725803
$405$	2.73205	0.135757
$406$	−6.46410	−0.320808
$407$	0	0
$408$	−0.535898	−0.0265309
$409$	−6.53590	−0.323179	−0.161590	−	0.986858i	$-0.551662\pi$
$409$	−6.53590	−0.323179	−0.161590	+	0.986858i	$0.551662\pi$
$410$	19.8564	0.980638
$411$	−2.53590	−0.125087
$412$	0.732051	0.0360656
$413$	−42.5167	−2.09211
$414$	2.00000	0.0982946
$415$	38.7846	1.90386
$416$	−3.46410	−0.169842
$417$	−13.4641	−0.659340
$418$	0	0
$419$	26.4449	1.29192	0.645958	−	0.763373i	$-0.276458\pi$
$419$	26.4449	1.29192	0.645958	+	0.763373i	$0.276458\pi$
$420$	10.1962	0.497521
$421$	−36.3205	−1.77015	−0.885077	−	0.465445i	$-0.845894\pi$
$421$	−36.3205	−1.77015	−0.885077	+	0.465445i	$0.845894\pi$
$422$	−20.1244	−0.979638
$423$	−11.0718	−0.538329
$424$	3.92820	0.190770
$425$	1.32051	0.0640541
$426$	−3.80385	−0.184297
$427$	17.6603	0.854640
$428$	13.1962	0.637860
$429$	0	0
$430$	24.3923	1.17630
$431$	−6.33975	−0.305375	−0.152687	−	0.988275i	$-0.548793\pi$
$431$	−6.33975	−0.305375	−0.152687	+	0.988275i	$0.548793\pi$
$432$	5.00000	0.240563
$433$	−22.7846	−1.09496	−0.547479	−	0.836819i	$-0.684412\pi$
$433$	−22.7846	−1.09496	−0.547479	+	0.836819i	$0.684412\pi$
$434$	−20.3923	−0.978862
$435$	−4.73205	−0.226884
$436$	−18.1244	−0.867999
$437$	1.00000	0.0478365
$438$	2.00000	0.0955637
$439$	−10.5359	−0.502851	−0.251425	−	0.967877i	$-0.580899\pi$
$439$	−10.5359	−0.502851	−0.251425	+	0.967877i	$0.580899\pi$
$440$	0	0
$441$	−13.8564	−0.659829
$442$	−1.85641	−0.0883003
$443$	18.0000	0.855206	0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000	0.855206	0.427603	+	0.903967i	$0.359358\pi$
$444$	−0.464102	−0.0220253
$445$	4.92820	0.233619
$446$	−11.1244	−0.526754
$447$	−23.3205	−1.10302
$448$	−3.73205	−0.176323
$449$	0.143594	0.00677660	0.00338830	−	0.999994i	$-0.498921\pi$
$449$	0.143594	0.00677660	0.00338830	+	0.999994i	$0.498921\pi$
$450$	−4.92820	−0.232318
$451$	0	0
$452$	−1.26795	−0.0596393
$453$	−17.2679	−0.811319
$454$	12.3923	0.581600
$455$	35.3205	1.65585
$456$	1.00000	0.0468293
$457$	−33.4449	−1.56448	−0.782242	−	0.622974i	$-0.785924\pi$
$457$	−33.4449	−1.56448	−0.782242	+	0.622974i	$0.785924\pi$
$458$	8.39230	0.392147
$459$	2.67949	0.125068
$460$	−2.73205	−0.127383
$461$	17.8038	0.829208	0.414604	−	0.910002i	$-0.363920\pi$
$461$	17.8038	0.829208	0.414604	+	0.910002i	$0.363920\pi$
$462$	0	0
$463$	26.0000	1.20832	0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000	1.20832	0.604161	+	0.796862i	$0.293508\pi$
$464$	1.73205	0.0804084
$465$	−14.9282	−0.692279
$466$	11.7321	0.543477
$467$	−21.7128	−1.00475	−0.502375	−	0.864650i	$-0.667540\pi$
$467$	−21.7128	−1.00475	−0.502375	+	0.864650i	$0.667540\pi$
$468$	6.92820	0.320256
$469$	−52.2487	−2.41262
$470$	15.1244	0.697635
$471$	8.73205	0.402352
$472$	11.3923	0.524373
$473$	0	0
$474$	8.19615	0.376462
$475$	−2.46410	−0.113061
$476$	−2.00000	−0.0916698
$477$	−7.85641	−0.359720
$478$	−10.1244	−0.463077
$479$	28.2679	1.29160	0.645798	−	0.763508i	$-0.276525\pi$
$479$	28.2679	1.29160	0.645798	+	0.763508i	$0.276525\pi$
$480$	−2.73205	−0.124700
$481$	−1.60770	−0.0733046
$482$	−14.7321	−0.671027
$483$	−3.73205	−0.169814
$484$	0	0
$485$	17.8564	0.810818
$486$	−16.0000	−0.725775
$487$	−35.1769	−1.59402	−0.797009	−	0.603967i	$-0.793586\pi$
$487$	−35.1769	−1.59402	−0.797009	+	0.603967i	$0.793586\pi$
$488$	−4.73205	−0.214210
$489$	17.3205	0.783260
$490$	18.9282	0.855089
$491$	−24.3923	−1.10081	−0.550405	−	0.834898i	$-0.685527\pi$
$491$	−24.3923	−1.10081	−0.550405	+	0.834898i	$0.685527\pi$
$492$	−7.26795	−0.327664
$493$	0.928203	0.0418042
$494$	3.46410	0.155857
$495$	0	0
$496$	5.46410	0.245345
$497$	−14.1962	−0.636784
$498$	−14.1962	−0.636145
$499$	24.7321	1.10716	0.553579	−	0.832796i	$-0.313262\pi$
$499$	24.7321	1.10716	0.553579	+	0.832796i	$0.313262\pi$
$500$	−6.92820	−0.309839
$501$	3.46410	0.154765
$502$	15.4641	0.690197
$503$	−16.6603	−0.742844	−0.371422	−	0.928464i	$-0.621130\pi$
$503$	−16.6603	−0.742844	−0.371422	+	0.928464i	$0.621130\pi$
$504$	7.46410	0.332478
$505$	−39.8564	−1.77359
$506$	0	0
$507$	1.00000	0.0444116
$508$	−4.00000	−0.177471
$509$	20.0718	0.889667	0.444833	−	0.895613i	$-0.353263\pi$
$509$	20.0718	0.889667	0.444833	+	0.895613i	$0.353263\pi$
$510$	−1.46410	−0.0648315
$511$	7.46410	0.330192
$512$	1.00000	0.0441942
$513$	−5.00000	−0.220755
$514$	31.3205	1.38149
$515$	2.00000	0.0881305
$516$	−8.92820	−0.393042
$517$	0	0
$518$	−1.73205	−0.0761019
$519$	20.1244	0.883361
$520$	−9.46410	−0.415028
$521$	17.3205	0.758825	0.379413	−	0.925228i	$-0.376126\pi$
$521$	17.3205	0.758825	0.379413	+	0.925228i	$0.376126\pi$
$522$	−3.46410	−0.151620
$523$	−26.6603	−1.16577	−0.582886	−	0.812554i	$-0.698076\pi$
$523$	−26.6603	−1.16577	−0.582886	+	0.812554i	$0.698076\pi$
$524$	7.07180	0.308933
$525$	9.19615	0.401353
$526$	16.7846	0.731844
$527$	2.92820	0.127555
$528$	0	0
$529$	−22.0000	−0.956522
$530$	10.7321	0.466170
$531$	−22.7846	−0.988768
$532$	3.73205	0.161805
$533$	−25.1769	−1.09053
$534$	−1.80385	−0.0780601
$535$	36.0526	1.55869
$536$	14.0000	0.604708
$537$	15.9282	0.687353
$538$	11.7846	0.508071
$539$	0	0
$540$	13.6603	0.587844
$541$	35.1769	1.51237	0.756187	−	0.654356i	$-0.227060\pi$
$541$	35.1769	1.51237	0.756187	+	0.654356i	$0.227060\pi$
$542$	−27.3205	−1.17352
$543$	−3.60770	−0.154821
$544$	0.535898	0.0229765
$545$	−49.5167	−2.12106
$546$	−12.9282	−0.553276
$547$	15.1962	0.649741	0.324870	−	0.945759i	$-0.394679\pi$
$547$	15.1962	0.649741	0.324870	+	0.945759i	$0.394679\pi$
$548$	2.53590	0.108328
$549$	9.46410	0.403918
$550$	0	0
$551$	−1.73205	−0.0737878
$552$	1.00000	0.0425628
$553$	30.5885	1.30075
$554$	9.12436	0.387657
$555$	−1.26795	−0.0538214
$556$	13.4641	0.571005
$557$	39.1769	1.65998	0.829990	−	0.557779i	$-0.188346\pi$
$557$	39.1769	1.65998	0.829990	+	0.557779i	$0.188346\pi$
$558$	−10.9282	−0.462628
$559$	−30.9282	−1.30812
$560$	−10.1962	−0.430866
$561$	0	0
$562$	22.0526	0.930231
$563$	7.33975	0.309333	0.154667	−	0.987967i	$-0.450570\pi$
$563$	7.33975	0.309333	0.154667	+	0.987967i	$0.450570\pi$
$564$	−5.53590	−0.233103
$565$	−3.46410	−0.145736
$566$	−14.5359	−0.610989
$567$	−3.73205	−0.156731
$568$	3.80385	0.159606
$569$	15.7128	0.658715	0.329358	−	0.944205i	$-0.393168\pi$
$569$	15.7128	0.658715	0.329358	+	0.944205i	$0.393168\pi$
$570$	2.73205	0.114433
$571$	28.9808	1.21281	0.606404	−	0.795157i	$-0.292612\pi$
$571$	28.9808	1.21281	0.606404	+	0.795157i	$0.292612\pi$
$572$	0	0
$573$	−3.39230	−0.141716
$574$	−27.1244	−1.13215
$575$	−2.46410	−0.102760
$576$	−2.00000	−0.0833333
$577$	29.1769	1.21465	0.607325	−	0.794453i	$-0.292242\pi$
$577$	29.1769	1.21465	0.607325	+	0.794453i	$0.292242\pi$
$578$	−16.7128	−0.695161
$579$	19.4641	0.808900
$580$	4.73205	0.196488
$581$	−52.9808	−2.19801
$582$	−6.53590	−0.270922
$583$	0	0
$584$	−2.00000	−0.0827606
$585$	18.9282	0.782585
$586$	12.1244	0.500853
$587$	41.3731	1.70765	0.853825	−	0.520561i	$-0.174277\pi$
$587$	41.3731	1.70765	0.853825	+	0.520561i	$0.174277\pi$
$588$	−6.92820	−0.285714
$589$	−5.46410	−0.225144
$590$	31.1244	1.28137
$591$	18.9282	0.778602
$592$	0.464102	0.0190745
$593$	26.1244	1.07280	0.536399	−	0.843964i	$-0.319784\pi$
$593$	26.1244	1.07280	0.536399	+	0.843964i	$0.319784\pi$
$594$	0	0
$595$	−5.46410	−0.224006
$596$	23.3205	0.955245
$597$	−3.07180	−0.125720
$598$	3.46410	0.141658
$599$	−40.3923	−1.65038	−0.825192	−	0.564852i	$-0.808933\pi$
$599$	−40.3923	−1.65038	−0.825192	+	0.564852i	$0.808933\pi$
$600$	−2.46410	−0.100597
$601$	−22.7846	−0.929404	−0.464702	−	0.885467i	$-0.653838\pi$
$601$	−22.7846	−0.929404	−0.464702	+	0.885467i	$0.653838\pi$
$602$	−33.3205	−1.35804
$603$	−28.0000	−1.14025
$604$	17.2679	0.702623
$605$	0	0
$606$	14.5885	0.592616
$607$	−6.73205	−0.273246	−0.136623	−	0.990623i	$-0.543625\pi$
$607$	−6.73205	−0.273246	−0.136623	+	0.990623i	$0.543625\pi$
$608$	−1.00000	−0.0405554
$609$	6.46410	0.261939
$610$	−12.9282	−0.523448
$611$	−19.1769	−0.775815
$612$	−1.07180	−0.0433248
$613$	−11.8038	−0.476753	−0.238376	−	0.971173i	$-0.576615\pi$
$613$	−11.8038	−0.476753	−0.238376	+	0.971173i	$0.576615\pi$
$614$	15.5885	0.629099
$615$	−19.8564	−0.800688
$616$	0	0
$617$	11.9282	0.480211	0.240106	−	0.970747i	$-0.422818\pi$
$617$	11.9282	0.480211	0.240106	+	0.970747i	$0.422818\pi$
$618$	−0.732051	−0.0294474
$619$	13.6077	0.546939	0.273470	−	0.961881i	$-0.411829\pi$
$619$	13.6077	0.546939	0.273470	+	0.961881i	$0.411829\pi$
$620$	14.9282	0.599531
$621$	−5.00000	−0.200643
$622$	−22.3923	−0.897850
$623$	−6.73205	−0.269714
$624$	3.46410	0.138675
$625$	−31.2487	−1.24995
$626$	20.4641	0.817910
$627$	0	0
$628$	−8.73205	−0.348447
$629$	0.248711	0.00991677
$630$	20.3923	0.812449
$631$	27.2487	1.08475	0.542377	−	0.840135i	$-0.317524\pi$
$631$	27.2487	1.08475	0.542377	+	0.840135i	$0.317524\pi$
$632$	−8.19615	−0.326025
$633$	20.1244	0.799871
$634$	20.7846	0.825462
$635$	−10.9282	−0.433673
$636$	−3.92820	−0.155763
$637$	−24.0000	−0.950915
$638$	0	0
$639$	−7.60770	−0.300956
$640$	2.73205	0.107994
$641$	−44.1962	−1.74564	−0.872822	−	0.488040i	$-0.837712\pi$
$641$	−44.1962	−1.74564	−0.872822	+	0.488040i	$0.837712\pi$
$642$	−13.1962	−0.520811
$643$	37.7128	1.48725	0.743624	−	0.668598i	$-0.233105\pi$
$643$	37.7128	1.48725	0.743624	+	0.668598i	$0.233105\pi$
$644$	3.73205	0.147063
$645$	−24.3923	−0.960446
$646$	−0.535898	−0.0210846
$647$	−30.8564	−1.21309	−0.606545	−	0.795049i	$-0.707445\pi$
$647$	−30.8564	−1.21309	−0.606545	+	0.795049i	$0.707445\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−8.53590	−0.334805
$651$	20.3923	0.799237
$652$	−17.3205	−0.678323
$653$	−37.3205	−1.46046	−0.730232	−	0.683199i	$-0.760588\pi$
$653$	−37.3205	−1.46046	−0.730232	+	0.683199i	$0.760588\pi$
$654$	18.1244	0.708718
$655$	19.3205	0.754915
$656$	7.26795	0.283766
$657$	4.00000	0.156055
$658$	−20.6603	−0.805421
$659$	17.3205	0.674711	0.337356	−	0.941377i	$-0.390468\pi$
$659$	17.3205	0.674711	0.337356	+	0.941377i	$0.390468\pi$
$660$	0	0
$661$	−29.2487	−1.13764	−0.568822	−	0.822461i	$-0.692600\pi$
$661$	−29.2487	−1.13764	−0.568822	+	0.822461i	$0.692600\pi$
$662$	−19.7846	−0.768951
$663$	1.85641	0.0720969
$664$	14.1962	0.550918
$665$	10.1962	0.395390
$666$	−0.928203	−0.0359671
$667$	−1.73205	−0.0670653
$668$	−3.46410	−0.134030
$669$	11.1244	0.430092
$670$	38.2487	1.47768
$671$	0	0
$672$	3.73205	0.143967
$673$	−16.5885	−0.639438	−0.319719	−	0.947512i	$-0.603589\pi$
$673$	−16.5885	−0.639438	−0.319719	+	0.947512i	$0.603589\pi$
$674$	13.8038	0.531704
$675$	12.3205	0.474217
$676$	−1.00000	−0.0384615
$677$	−19.3397	−0.743287	−0.371643	−	0.928376i	$-0.621206\pi$
$677$	−19.3397	−0.743287	−0.371643	+	0.928376i	$0.621206\pi$
$678$	1.26795	0.0486953
$679$	−24.3923	−0.936091
$680$	1.46410	0.0561457
$681$	−12.3923	−0.474874
$682$	0	0
$683$	18.7846	0.718773	0.359387	−	0.933189i	$-0.382986\pi$
$683$	18.7846	0.718773	0.359387	+	0.933189i	$0.382986\pi$
$684$	2.00000	0.0764719
$685$	6.92820	0.264713
$686$	0.267949	0.0102303
$687$	−8.39230	−0.320186
$688$	8.92820	0.340385
$689$	−13.6077	−0.518412
$690$	2.73205	0.104007
$691$	−10.0526	−0.382417	−0.191209	−	0.981549i	$-0.561241\pi$
$691$	−10.0526	−0.382417	−0.191209	+	0.981549i	$0.561241\pi$
$692$	−20.1244	−0.765013
$693$	0	0
$694$	28.0526	1.06486
$695$	36.7846	1.39532
$696$	−1.73205	−0.0656532
$697$	3.89488	0.147529
$698$	−26.7846	−1.01381
$699$	−11.7321	−0.443747
$700$	−9.19615	−0.347582
$701$	2.53590	0.0957796	0.0478898	−	0.998853i	$-0.484750\pi$
$701$	2.53590	0.0957796	0.0478898	+	0.998853i	$0.484750\pi$
$702$	−17.3205	−0.653720
$703$	−0.464102	−0.0175039
$704$	0	0
$705$	−15.1244	−0.569616
$706$	0.464102	0.0174667
$707$	54.4449	2.04761
$708$	−11.3923	−0.428149
$709$	−17.8564	−0.670611	−0.335306	−	0.942109i	$-0.608840\pi$
$709$	−17.8564	−0.670611	−0.335306	+	0.942109i	$0.608840\pi$
$710$	10.3923	0.390016
$711$	16.3923	0.614759
$712$	1.80385	0.0676020
$713$	−5.46410	−0.204632
$714$	2.00000	0.0748481
$715$	0	0
$716$	−15.9282	−0.595265
$717$	10.1244	0.378101
$718$	−7.60770	−0.283917
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	−5.46410	−0.203635
$721$	−2.73205	−0.101747
$722$	1.00000	0.0372161
$723$	14.7321	0.547891
$724$	3.60770	0.134079
$725$	4.26795	0.158508
$726$	0	0
$727$	6.32051	0.234415	0.117207	−	0.993107i	$-0.462606\pi$
$727$	6.32051	0.234415	0.117207	+	0.993107i	$0.462606\pi$
$728$	12.9282	0.479151
$729$	13.0000	0.481481
$730$	−5.46410	−0.202235
$731$	4.78461	0.176965
$732$	4.73205	0.174902
$733$	−18.9282	−0.699129	−0.349565	−	0.936912i	$-0.613670\pi$
$733$	−18.9282	−0.699129	−0.349565	+	0.936912i	$0.613670\pi$
$734$	4.85641	0.179253
$735$	−18.9282	−0.698177
$736$	−1.00000	−0.0368605
$737$	0	0
$738$	−14.5359	−0.535074
$739$	14.3397	0.527496	0.263748	−	0.964592i	$-0.415041\pi$
$739$	14.3397	0.527496	0.263748	+	0.964592i	$0.415041\pi$
$740$	1.26795	0.0466107
$741$	−3.46410	−0.127257
$742$	−14.6603	−0.538195
$743$	19.4641	0.714069	0.357034	−	0.934091i	$-0.383788\pi$
$743$	19.4641	0.714069	0.357034	+	0.934091i	$0.383788\pi$
$744$	−5.46410	−0.200324
$745$	63.7128	2.33426
$746$	27.1962	0.995722
$747$	−28.3923	−1.03882
$748$	0	0
$749$	−49.2487	−1.79951
$750$	6.92820	0.252982
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	5.53590	0.201873
$753$	−15.4641	−0.563543
$754$	−6.00000	−0.218507
$755$	47.1769	1.71694
$756$	−18.6603	−0.678667
$757$	51.3731	1.86719	0.933593	−	0.358335i	$-0.116656\pi$
$757$	51.3731	1.86719	0.933593	+	0.358335i	$0.116656\pi$
$758$	10.0718	0.365824
$759$	0	0
$760$	−2.73205	−0.0991019
$761$	−44.7654	−1.62274	−0.811372	−	0.584531i	$-0.801279\pi$
$761$	−44.7654	−1.62274	−0.811372	+	0.584531i	$0.801279\pi$
$762$	4.00000	0.144905
$763$	67.6410	2.44877
$764$	3.39230	0.122729
$765$	−2.92820	−0.105869
$766$	26.5359	0.958781
$767$	−39.4641	−1.42497
$768$	−1.00000	−0.0360844
$769$	3.58846	0.129403	0.0647015	−	0.997905i	$-0.479390\pi$
$769$	3.58846	0.129403	0.0647015	+	0.997905i	$0.479390\pi$
$770$	0	0
$771$	−31.3205	−1.12798
$772$	−19.4641	−0.700528
$773$	27.3923	0.985233	0.492616	−	0.870247i	$-0.336041\pi$
$773$	27.3923	0.985233	0.492616	+	0.870247i	$0.336041\pi$
$774$	−17.8564	−0.641835
$775$	13.4641	0.483645
$776$	6.53590	0.234625
$777$	1.73205	0.0621370
$778$	30.5885	1.09665
$779$	−7.26795	−0.260401
$780$	9.46410	0.338869
$781$	0	0
$782$	−0.535898	−0.0191637
$783$	8.66025	0.309492
$784$	6.92820	0.247436
$785$	−23.8564	−0.851472
$786$	−7.07180	−0.252243
$787$	−25.0526	−0.893027	−0.446514	−	0.894777i	$-0.647335\pi$
$787$	−25.0526	−0.893027	−0.446514	+	0.894777i	$0.647335\pi$
$788$	−18.9282	−0.674289
$789$	−16.7846	−0.597548
$790$	−22.3923	−0.796682
$791$	4.73205	0.168252
$792$	0	0
$793$	16.3923	0.582108
$794$	26.3923	0.936628
$795$	−10.7321	−0.380627
$796$	3.07180	0.108877
$797$	32.3923	1.14739	0.573697	−	0.819068i	$-0.305509\pi$
$797$	32.3923	1.14739	0.573697	+	0.819068i	$0.305509\pi$
$798$	−3.73205	−0.132113
$799$	2.96668	0.104954
$800$	2.46410	0.0871191
$801$	−3.60770	−0.127472
$802$	22.0526	0.778703
$803$	0	0
$804$	−14.0000	−0.493742
$805$	10.1962	0.359367
$806$	−18.9282	−0.666718
$807$	−11.7846	−0.414838
$808$	−14.5885	−0.513220
$809$	8.80385	0.309527	0.154763	−	0.987952i	$-0.450538\pi$
$809$	8.80385	0.309527	0.154763	+	0.987952i	$0.450538\pi$
$810$	2.73205	0.0959945
$811$	46.7654	1.64215	0.821077	−	0.570817i	$-0.193374\pi$
$811$	46.7654	1.64215	0.821077	+	0.570817i	$0.193374\pi$
$812$	−6.46410	−0.226845
$813$	27.3205	0.958172
$814$	0	0
$815$	−47.3205	−1.65757
$816$	−0.535898	−0.0187602
$817$	−8.92820	−0.312358
$818$	−6.53590	−0.228522
$819$	−25.8564	−0.903496
$820$	19.8564	0.693416
$821$	3.94744	0.137767	0.0688833	−	0.997625i	$-0.478056\pi$
$821$	3.94744	0.137767	0.0688833	+	0.997625i	$0.478056\pi$
$822$	−2.53590	−0.0884496
$823$	−28.4641	−0.992196	−0.496098	−	0.868266i	$-0.665234\pi$
$823$	−28.4641	−0.992196	−0.496098	+	0.868266i	$0.665234\pi$
$824$	0.732051	0.0255022
$825$	0	0
$826$	−42.5167	−1.47934
$827$	13.3205	0.463199	0.231600	−	0.972811i	$-0.425604\pi$
$827$	13.3205	0.463199	0.231600	+	0.972811i	$0.425604\pi$
$828$	2.00000	0.0695048
$829$	−50.6410	−1.75884	−0.879418	−	0.476051i	$-0.842068\pi$
$829$	−50.6410	−1.75884	−0.879418	+	0.476051i	$0.842068\pi$
$830$	38.7846	1.34623
$831$	−9.12436	−0.316520
$832$	−3.46410	−0.120096
$833$	3.71281	0.128641
$834$	−13.4641	−0.466224
$835$	−9.46410	−0.327519
$836$	0	0
$837$	27.3205	0.944335
$838$	26.4449	0.913523
$839$	−36.9808	−1.27672	−0.638359	−	0.769739i	$-0.720386\pi$
$839$	−36.9808	−1.27672	−0.638359	+	0.769739i	$0.720386\pi$
$840$	10.1962	0.351801
$841$	−26.0000	−0.896552
$842$	−36.3205	−1.25169
$843$	−22.0526	−0.759530
$844$	−20.1244	−0.692709
$845$	−2.73205	−0.0939854
$846$	−11.0718	−0.380656
$847$	0	0
$848$	3.92820	0.134895
$849$	14.5359	0.498871
$850$	1.32051	0.0452931
$851$	−0.464102	−0.0159092
$852$	−3.80385	−0.130318
$853$	−22.1051	−0.756865	−0.378432	−	0.925629i	$-0.623537\pi$
$853$	−22.1051	−0.756865	−0.378432	+	0.925629i	$0.623537\pi$
$854$	17.6603	0.604321
$855$	5.46410	0.186868
$856$	13.1962	0.451035
$857$	23.4641	0.801518	0.400759	−	0.916183i	$-0.368746\pi$
$857$	23.4641	0.801518	0.400759	+	0.916183i	$0.368746\pi$
$858$	0	0
$859$	−58.0526	−1.98073	−0.990364	−	0.138490i	$-0.955775\pi$
$859$	−58.0526	−1.98073	−0.990364	+	0.138490i	$0.955775\pi$
$860$	24.3923	0.831771
$861$	27.1244	0.924396
$862$	−6.33975	−0.215933
$863$	−29.0718	−0.989615	−0.494808	−	0.869002i	$-0.664762\pi$
$863$	−29.0718	−0.989615	−0.494808	+	0.869002i	$0.664762\pi$
$864$	5.00000	0.170103
$865$	−54.9808	−1.86940
$866$	−22.7846	−0.774253
$867$	16.7128	0.567597
$868$	−20.3923	−0.692160
$869$	0	0
$870$	−4.73205	−0.160432
$871$	−48.4974	−1.64327
$872$	−18.1244	−0.613768
$873$	−13.0718	−0.442413
$874$	1.00000	0.0338255
$875$	25.8564	0.874106
$876$	2.00000	0.0675737
$877$	−10.1436	−0.342525	−0.171262	−	0.985225i	$-0.554785\pi$
$877$	−10.1436	−0.342525	−0.171262	+	0.985225i	$0.554785\pi$
$878$	−10.5359	−0.355569
$879$	−12.1244	−0.408944
$880$	0	0
$881$	−20.4641	−0.689453	−0.344727	−	0.938703i	$-0.612028\pi$
$881$	−20.4641	−0.689453	−0.344727	+	0.938703i	$0.612028\pi$
$882$	−13.8564	−0.466569
$883$	6.58846	0.221719	0.110860	−	0.993836i	$-0.464640\pi$
$883$	6.58846	0.221719	0.110860	+	0.993836i	$0.464640\pi$
$884$	−1.85641	−0.0624377
$885$	−31.1244	−1.04623
$886$	18.0000	0.604722
$887$	−12.3397	−0.414328	−0.207164	−	0.978306i	$-0.566423\pi$
$887$	−12.3397	−0.414328	−0.207164	+	0.978306i	$0.566423\pi$
$888$	−0.464102	−0.0155742
$889$	14.9282	0.500676
$890$	4.92820	0.165194
$891$	0	0
$892$	−11.1244	−0.372471
$893$	−5.53590	−0.185252
$894$	−23.3205	−0.779954
$895$	−43.5167	−1.45460
$896$	−3.73205	−0.124679
$897$	−3.46410	−0.115663
$898$	0.143594	0.00479178
$899$	9.46410	0.315645
$900$	−4.92820	−0.164273
$901$	2.10512	0.0701316
$902$	0	0
$903$	33.3205	1.10884
$904$	−1.26795	−0.0421714
$905$	9.85641	0.327638
$906$	−17.2679	−0.573689
$907$	−19.2487	−0.639143	−0.319571	−	0.947562i	$-0.603539\pi$
$907$	−19.2487	−0.639143	−0.319571	+	0.947562i	$0.603539\pi$
$908$	12.3923	0.411253
$909$	29.1769	0.967737
$910$	35.3205	1.17086
$911$	−26.5885	−0.880915	−0.440457	−	0.897773i	$-0.645184\pi$
$911$	−26.5885	−0.880915	−0.440457	+	0.897773i	$0.645184\pi$
$912$	1.00000	0.0331133
$913$	0	0
$914$	−33.4449	−1.10626
$915$	12.9282	0.427393
$916$	8.39230	0.277290
$917$	−26.3923	−0.871551
$918$	2.67949	0.0884364
$919$	−22.1051	−0.729181	−0.364590	−	0.931168i	$-0.618791\pi$
$919$	−22.1051	−0.729181	−0.364590	+	0.931168i	$0.618791\pi$
$920$	−2.73205	−0.0900730
$921$	−15.5885	−0.513657
$922$	17.8038	0.586338
$923$	−13.1769	−0.433723
$924$	0	0
$925$	1.14359	0.0376011
$926$	26.0000	0.854413
$927$	−1.46410	−0.0480874
$928$	1.73205	0.0568574
$929$	32.0333	1.05098	0.525490	−	0.850800i	$-0.323882\pi$
$929$	32.0333	1.05098	0.525490	+	0.850800i	$0.323882\pi$
$930$	−14.9282	−0.489515
$931$	−6.92820	−0.227063
$932$	11.7321	0.384296
$933$	22.3923	0.733091
$934$	−21.7128	−0.710465
$935$	0	0
$936$	6.92820	0.226455
$937$	−54.1244	−1.76817	−0.884083	−	0.467330i	$-0.845216\pi$
$937$	−54.1244	−1.76817	−0.884083	+	0.467330i	$0.845216\pi$
$938$	−52.2487	−1.70598
$939$	−20.4641	−0.667821
$940$	15.1244	0.493302
$941$	24.2487	0.790485	0.395243	−	0.918577i	$-0.370660\pi$
$941$	24.2487	0.790485	0.395243	+	0.918577i	$0.370660\pi$
$942$	8.73205	0.284506
$943$	−7.26795	−0.236677
$944$	11.3923	0.370788
$945$	−50.9808	−1.65840
$946$	0	0
$947$	−31.7128	−1.03053	−0.515264	−	0.857032i	$-0.672306\pi$
$947$	−31.7128	−1.03053	−0.515264	+	0.857032i	$0.672306\pi$
$948$	8.19615	0.266199
$949$	6.92820	0.224899
$950$	−2.46410	−0.0799460
$951$	−20.7846	−0.673987
$952$	−2.00000	−0.0648204
$953$	−36.9808	−1.19792	−0.598962	−	0.800777i	$-0.704420\pi$
$953$	−36.9808	−1.19792	−0.598962	+	0.800777i	$0.704420\pi$
$954$	−7.85641	−0.254361
$955$	9.26795	0.299904
$956$	−10.1244	−0.327445
$957$	0	0
$958$	28.2679	0.913296
$959$	−9.46410	−0.305612
$960$	−2.73205	−0.0881766
$961$	−1.14359	−0.0368901
$962$	−1.60770	−0.0518342
$963$	−26.3923	−0.850480
$964$	−14.7321	−0.474487
$965$	−53.1769	−1.71183
$966$	−3.73205	−0.120077
$967$	36.5167	1.17430	0.587148	−	0.809479i	$-0.300251\pi$
$967$	36.5167	1.17430	0.587148	+	0.809479i	$0.300251\pi$
$968$	0	0
$969$	0.535898	0.0172155
$970$	17.8564	0.573335
$971$	13.5359	0.434388	0.217194	−	0.976128i	$-0.430310\pi$
$971$	13.5359	0.434388	0.217194	+	0.976128i	$0.430310\pi$
$972$	−16.0000	−0.513200
$973$	−50.2487	−1.61090
$974$	−35.1769	−1.12714
$975$	8.53590	0.273368
$976$	−4.73205	−0.151469
$977$	−27.4641	−0.878654	−0.439327	−	0.898327i	$-0.644783\pi$
$977$	−27.4641	−0.878654	−0.439327	+	0.898327i	$0.644783\pi$
$978$	17.3205	0.553849
$979$	0	0
$980$	18.9282	0.604639
$981$	36.2487	1.15733
$982$	−24.3923	−0.778390
$983$	−40.9808	−1.30708	−0.653542	−	0.756891i	$-0.726718\pi$
$983$	−40.9808	−1.30708	−0.653542	+	0.756891i	$0.726718\pi$
$984$	−7.26795	−0.231694
$985$	−51.7128	−1.64771
$986$	0.928203	0.0295600
$987$	20.6603	0.657623
$988$	3.46410	0.110208
$989$	−8.92820	−0.283900
$990$	0	0
$991$	22.0526	0.700523	0.350261	−	0.936652i	$-0.386093\pi$
$991$	22.0526	0.700523	0.350261	+	0.936652i	$0.386093\pi$
$992$	5.46410	0.173485
$993$	19.7846	0.627846
$994$	−14.1962	−0.450275
$995$	8.39230	0.266054
$996$	−14.1962	−0.449822
$997$	−27.6603	−0.876009	−0.438005	−	0.898973i	$-0.644315\pi$
$997$	−27.6603	−0.876009	−0.438005	+	0.898973i	$0.644315\pi$
$998$	24.7321	0.782879
$999$	2.32051	0.0734176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bf.1.2	yes	2
11.10	odd	2		4598.2.a.w.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.w.1.2	✓	2	11.10	odd	2
4598.2.a.bf.1.2	yes	2	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.73205 q^{5} -1.00000 q^{6} -3.73205 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.73205 q^{5} -1.00000 q^{6} -3.73205 q^{7} +1.00000 q^{8} -2.00000 q^{9} +2.73205 q^{10} -1.00000 q^{12} -3.46410 q^{13} -3.73205 q^{14} -2.73205 q^{15} +1.00000 q^{16} +0.535898 q^{17} -2.00000 q^{18} -1.00000 q^{19} +2.73205 q^{20} +3.73205 q^{21} -1.00000 q^{23} -1.00000 q^{24} +2.46410 q^{25} -3.46410 q^{26} +5.00000 q^{27} -3.73205 q^{28} +1.73205 q^{29} -2.73205 q^{30} +5.46410 q^{31} +1.00000 q^{32} +0.535898 q^{34} -10.1962 q^{35} -2.00000 q^{36} +0.464102 q^{37} -1.00000 q^{38} +3.46410 q^{39} +2.73205 q^{40} +7.26795 q^{41} +3.73205 q^{42} +8.92820 q^{43} -5.46410 q^{45} -1.00000 q^{46} +5.53590 q^{47} -1.00000 q^{48} +6.92820 q^{49} +2.46410 q^{50} -0.535898 q^{51} -3.46410 q^{52} +3.92820 q^{53} +5.00000 q^{54} -3.73205 q^{56} +1.00000 q^{57} +1.73205 q^{58} +11.3923 q^{59} -2.73205 q^{60} -4.73205 q^{61} +5.46410 q^{62} +7.46410 q^{63} +1.00000 q^{64} -9.46410 q^{65} +14.0000 q^{67} +0.535898 q^{68} +1.00000 q^{69} -10.1962 q^{70} +3.80385 q^{71} -2.00000 q^{72} -2.00000 q^{73} +0.464102 q^{74} -2.46410 q^{75} -1.00000 q^{76} +3.46410 q^{78} -8.19615 q^{79} +2.73205 q^{80} +1.00000 q^{81} +7.26795 q^{82} +14.1962 q^{83} +3.73205 q^{84} +1.46410 q^{85} +8.92820 q^{86} -1.73205 q^{87} +1.80385 q^{89} -5.46410 q^{90} +12.9282 q^{91} -1.00000 q^{92} -5.46410 q^{93} +5.53590 q^{94} -2.73205 q^{95} -1.00000 q^{96} +6.53590 q^{97} +6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 4 q^{7} + 2 q^{8} - 4 q^{9} + 2 q^{10} - 2 q^{12} - 4 q^{14} - 2 q^{15} + 2 q^{16} + 8 q^{17} - 4 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{21} - 2 q^{23} - 2 q^{24} - 2 q^{25} + 10 q^{27} - 4 q^{28} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 8 q^{34} - 10 q^{35} - 4 q^{36} - 6 q^{37} - 2 q^{38} + 2 q^{40} + 18 q^{41} + 4 q^{42} + 4 q^{43} - 4 q^{45} - 2 q^{46} + 18 q^{47} - 2 q^{48} - 2 q^{50} - 8 q^{51} - 6 q^{53} + 10 q^{54} - 4 q^{56} + 2 q^{57} + 2 q^{59} - 2 q^{60} - 6 q^{61} + 4 q^{62} + 8 q^{63} + 2 q^{64} - 12 q^{65} + 28 q^{67} + 8 q^{68} + 2 q^{69} - 10 q^{70} + 18 q^{71} - 4 q^{72} - 4 q^{73} - 6 q^{74} + 2 q^{75} - 2 q^{76} - 6 q^{79} + 2 q^{80} + 2 q^{81} + 18 q^{82} + 18 q^{83} + 4 q^{84} - 4 q^{85} + 4 q^{86} + 14 q^{89} - 4 q^{90} + 12 q^{91} - 2 q^{92} - 4 q^{93} + 18 q^{94} - 2 q^{95} - 2 q^{96} + 20 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 4 * q^7 + 2 * q^8 - 4 * q^9 + 2 * q^10 - 2 * q^12 - 4 * q^14 - 2 * q^15 + 2 * q^16 + 8 * q^17 - 4 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^21 - 2 * q^23 - 2 * q^24 - 2 * q^25 + 10 * q^27 - 4 * q^28 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 8 * q^34 - 10 * q^35 - 4 * q^36 - 6 * q^37 - 2 * q^38 + 2 * q^40 + 18 * q^41 + 4 * q^42 + 4 * q^43 - 4 * q^45 - 2 * q^46 + 18 * q^47 - 2 * q^48 - 2 * q^50 - 8 * q^51 - 6 * q^53 + 10 * q^54 - 4 * q^56 + 2 * q^57 + 2 * q^59 - 2 * q^60 - 6 * q^61 + 4 * q^62 + 8 * q^63 + 2 * q^64 - 12 * q^65 + 28 * q^67 + 8 * q^68 + 2 * q^69 - 10 * q^70 + 18 * q^71 - 4 * q^72 - 4 * q^73 - 6 * q^74 + 2 * q^75 - 2 * q^76 - 6 * q^79 + 2 * q^80 + 2 * q^81 + 18 * q^82 + 18 * q^83 + 4 * q^84 - 4 * q^85 + 4 * q^86 + 14 * q^89 - 4 * q^90 + 12 * q^91 - 2 * q^92 - 4 * q^93 + 18 * q^94 - 2 * q^95 - 2 * q^96 + 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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