LMFDB - Embedded newform 5239.2.a.u.1.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, 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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34960 q^{2} -0.719767 q^{3} -0.178593 q^{4} +1.05805 q^{5} -0.971394 q^{6} +4.17946 q^{7} -2.94022 q^{8} -2.48194 q^{9} +O(q^{10})$	\(q+1.34960 q^{2} -0.719767 q^{3} -0.178593 q^{4} +1.05805 q^{5} -0.971394 q^{6} +4.17946 q^{7} -2.94022 q^{8} -2.48194 q^{9} +1.42793 q^{10} -3.06250 q^{11} +0.128545 q^{12} +5.64057 q^{14} -0.761547 q^{15} -3.61092 q^{16} -1.86776 q^{17} -3.34961 q^{18} +0.128964 q^{19} -0.188960 q^{20} -3.00823 q^{21} -4.13314 q^{22} +6.21114 q^{23} +2.11627 q^{24} -3.88054 q^{25} +3.94572 q^{27} -0.746422 q^{28} -0.0335114 q^{29} -1.02778 q^{30} -1.00000 q^{31} +1.00716 q^{32} +2.20429 q^{33} -2.52072 q^{34} +4.42206 q^{35} +0.443257 q^{36} +4.89642 q^{37} +0.174049 q^{38} -3.11089 q^{40} +12.1005 q^{41} -4.05990 q^{42} +3.13004 q^{43} +0.546942 q^{44} -2.62600 q^{45} +8.38252 q^{46} +6.83903 q^{47} +2.59902 q^{48} +10.4678 q^{49} -5.23715 q^{50} +1.34435 q^{51} -7.95659 q^{53} +5.32512 q^{54} -3.24027 q^{55} -12.2885 q^{56} -0.0928239 q^{57} -0.0452268 q^{58} -0.0610191 q^{59} +0.136007 q^{60} -7.83308 q^{61} -1.34960 q^{62} -10.3731 q^{63} +8.58109 q^{64} +2.97490 q^{66} -7.23765 q^{67} +0.333569 q^{68} -4.47057 q^{69} +5.96799 q^{70} +9.19019 q^{71} +7.29743 q^{72} +14.5546 q^{73} +6.60818 q^{74} +2.79308 q^{75} -0.0230321 q^{76} -12.7996 q^{77} +8.49526 q^{79} -3.82052 q^{80} +4.60581 q^{81} +16.3308 q^{82} +13.2849 q^{83} +0.537250 q^{84} -1.97618 q^{85} +4.22429 q^{86} +0.0241204 q^{87} +9.00442 q^{88} +13.7328 q^{89} -3.54404 q^{90} -1.10927 q^{92} +0.719767 q^{93} +9.22992 q^{94} +0.136450 q^{95} -0.724920 q^{96} -7.54450 q^{97} +14.1274 q^{98} +7.60093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) $ 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9} - 6 q^{10} + 7 q^{11} + 5 q^{12} + 38 q^{14} - 4 q^{15} + 76 q^{16} + 62 q^{17} + 9 q^{18} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 15 q^{22} + 38 q^{23} + 99 q^{24} + 87 q^{25} + 25 q^{27} - 19 q^{28} + 95 q^{29} + 41 q^{30} - 54 q^{31} - 9 q^{32} - 12 q^{33} - 7 q^{34} + 53 q^{35} + 97 q^{36} + 24 q^{37} - 16 q^{38} - 28 q^{40} - 22 q^{41} + 11 q^{42} + 11 q^{43} + 24 q^{44} - 8 q^{45} - 9 q^{46} - 45 q^{47} + 2 q^{48} + 105 q^{49} - 6 q^{50} + 58 q^{51} + 56 q^{53} - 50 q^{54} + q^{55} + 91 q^{56} + 51 q^{57} - 25 q^{58} - 36 q^{59} - 100 q^{60} + 48 q^{61} + 2 q^{62} + 56 q^{63} + 90 q^{64} - 24 q^{66} - 26 q^{67} + 140 q^{68} + 47 q^{69} + 24 q^{70} - 40 q^{71} - 7 q^{72} - 9 q^{73} + 114 q^{74} + 18 q^{75} + 67 q^{76} + 65 q^{77} + 33 q^{79} - 53 q^{80} + 210 q^{81} - 6 q^{82} + 41 q^{83} + 37 q^{84} - 37 q^{85} + 42 q^{86} - 16 q^{87} - 22 q^{88} + 24 q^{89} - 40 q^{90} + 87 q^{92} - 7 q^{93} - 4 q^{94} + 61 q^{95} + 200 q^{96} - 28 q^{97} - 68 q^{98} - 39 q^{99}+O(q^{100}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9 - 6 * q^10 + 7 * q^11 + 5 * q^12 + 38 * q^14 - 4 * q^15 + 76 * q^16 + 62 * q^17 + 9 * q^18 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 15 * q^22 + 38 * q^23 + 99 * q^24 + 87 * q^25 + 25 * q^27 - 19 * q^28 + 95 * q^29 + 41 * q^30 - 54 * q^31 - 9 * q^32 - 12 * q^33 - 7 * q^34 + 53 * q^35 + 97 * q^36 + 24 * q^37 - 16 * q^38 - 28 * q^40 - 22 * q^41 + 11 * q^42 + 11 * q^43 + 24 * q^44 - 8 * q^45 - 9 * q^46 - 45 * q^47 + 2 * q^48 + 105 * q^49 - 6 * q^50 + 58 * q^51 + 56 * q^53 - 50 * q^54 + q^55 + 91 * q^56 + 51 * q^57 - 25 * q^58 - 36 * q^59 - 100 * q^60 + 48 * q^61 + 2 * q^62 + 56 * q^63 + 90 * q^64 - 24 * q^66 - 26 * q^67 + 140 * q^68 + 47 * q^69 + 24 * q^70 - 40 * q^71 - 7 * q^72 - 9 * q^73 + 114 * q^74 + 18 * q^75 + 67 * q^76 + 65 * q^77 + 33 * q^79 - 53 * q^80 + 210 * q^81 - 6 * q^82 + 41 * q^83 + 37 * q^84 - 37 * q^85 + 42 * q^86 - 16 * q^87 - 22 * q^88 + 24 * q^89 - 40 * q^90 + 87 * q^92 - 7 * q^93 - 4 * q^94 + 61 * q^95 + 200 * q^96 - 28 * q^97 - 68 * q^98 - 39 * 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 $

$2$	1.34960	0.954308	0.477154	−	0.878820i	$-0.341668\pi$
$2$	1.34960	0.954308	0.477154	+	0.878820i	$0.341668\pi$
$3$	−0.719767	−0.415558	−0.207779	−	0.978176i	$-0.566623\pi$
$3$	−0.719767	−0.415558	−0.207779	+	0.978176i	$0.566623\pi$
$4$	−0.178593	−0.0892966
$5$	1.05805	0.473173	0.236586	−	0.971610i	$-0.423971\pi$
$5$	1.05805	0.473173	0.236586	+	0.971610i	$0.423971\pi$
$6$	−0.971394	−0.396570
$7$	4.17946	1.57969	0.789843	−	0.613309i	$-0.210162\pi$
$7$	4.17946	1.57969	0.789843	+	0.613309i	$0.210162\pi$
$8$	−2.94022	−1.03952
$9$	−2.48194	−0.827312
$10$	1.42793	0.451553
$11$	−3.06250	−0.923379	−0.461689	−	0.887042i	$-0.652757\pi$
$11$	−3.06250	−0.923379	−0.461689	+	0.887042i	$0.652757\pi$
$12$	0.128545	0.0371079
$13$	0	0
$13$	0	0
$14$	5.64057	1.50751
$15$	−0.761547	−0.196631
$16$	−3.61092	−0.902730
$17$	−1.86776	−0.452998	−0.226499	−	0.974011i	$-0.572728\pi$
$17$	−1.86776	−0.452998	−0.226499	+	0.974011i	$0.572728\pi$
$18$	−3.34961	−0.789510
$19$	0.128964	0.0295863	0.0147932	−	0.999891i	$-0.495291\pi$
$19$	0.128964	0.0295863	0.0147932	+	0.999891i	$0.495291\pi$
$20$	−0.188960	−0.0422527
$21$	−3.00823	−0.656450
$22$	−4.13314	−0.881188
$23$	6.21114	1.29511	0.647556	−	0.762018i	$-0.275791\pi$
$23$	6.21114	1.29511	0.647556	+	0.762018i	$0.275791\pi$
$24$	2.11627	0.431982
$25$	−3.88054	−0.776107
$26$	0	0
$27$	3.94572	0.759353
$28$	−0.746422	−0.141061
$29$	−0.0335114	−0.00622290	−0.00311145	−	0.999995i	$-0.500990\pi$
$29$	−0.0335114	−0.00622290	−0.00311145	+	0.999995i	$0.500990\pi$
$30$	−1.02778	−0.187646
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00716	0.178042
$33$	2.20429	0.383717
$34$	−2.52072	−0.432300
$35$	4.42206	0.747465
$36$	0.443257	0.0738761
$37$	4.89642	0.804966	0.402483	−	0.915427i	$-0.368147\pi$
$37$	4.89642	0.804966	0.402483	+	0.915427i	$0.368147\pi$
$38$	0.174049	0.0282345
$39$	0	0
$40$	−3.11089	−0.491875
$41$	12.1005	1.88978	0.944890	−	0.327388i	$-0.106169\pi$
$41$	12.1005	1.88978	0.944890	+	0.327388i	$0.106169\pi$
$42$	−4.05990	−0.626456
$43$	3.13004	0.477327	0.238663	−	0.971102i	$-0.423291\pi$
$43$	3.13004	0.477327	0.238663	+	0.971102i	$0.423291\pi$
$44$	0.546942	0.0824546
$45$	−2.62600	−0.391462
$46$	8.38252	1.23594
$47$	6.83903	0.997575	0.498787	−	0.866724i	$-0.333779\pi$
$47$	6.83903	0.997575	0.498787	+	0.866724i	$0.333779\pi$
$48$	2.59902	0.375136
$49$	10.4678	1.49541
$50$	−5.23715	−0.740645
$51$	1.34435	0.188247
$52$	0	0
$53$	−7.95659	−1.09292	−0.546461	−	0.837485i	$-0.684025\pi$
$53$	−7.95659	−1.09292	−0.546461	+	0.837485i	$0.684025\pi$
$54$	5.32512	0.724657
$55$	−3.24027	−0.436918
$56$	−12.2885	−1.64212
$57$	−0.0928239	−0.0122948
$58$	−0.0452268	−0.00593856
$59$	−0.0610191	−0.00794401	−0.00397201	−	0.999992i	$-0.501264\pi$
$59$	−0.0610191	−0.00794401	−0.00397201	+	0.999992i	$0.501264\pi$
$60$	0.136007	0.0175584
$61$	−7.83308	−1.00292	−0.501461	−	0.865180i	$-0.667204\pi$
$61$	−7.83308	−1.00292	−0.501461	+	0.865180i	$0.667204\pi$
$62$	−1.34960	−0.171399
$63$	−10.3731	−1.30689
$64$	8.58109	1.07264
$65$	0	0
$66$	2.97490	0.366184
$67$	−7.23765	−0.884219	−0.442110	−	0.896961i	$-0.645770\pi$
$67$	−7.23765	−0.884219	−0.442110	+	0.896961i	$0.645770\pi$
$68$	0.333569	0.0404512
$69$	−4.47057	−0.538194
$70$	5.96799	0.713311
$71$	9.19019	1.09068	0.545338	−	0.838216i	$-0.316401\pi$
$71$	9.19019	1.09068	0.545338	+	0.838216i	$0.316401\pi$
$72$	7.29743	0.860011
$73$	14.5546	1.70349	0.851743	−	0.523960i	$-0.175546\pi$
$73$	14.5546	1.70349	0.851743	+	0.523960i	$0.175546\pi$
$74$	6.60818	0.768185
$75$	2.79308	0.322517
$76$	−0.0230321	−0.00264196
$77$	−12.7996	−1.45865
$78$	0	0
$79$	8.49526	0.955791	0.477896	−	0.878417i	$-0.341400\pi$
$79$	8.49526	0.955791	0.477896	+	0.878417i	$0.341400\pi$
$80$	−3.82052	−0.427147
$81$	4.60581	0.511757
$82$	16.3308	1.80343
$83$	13.2849	1.45821	0.729106	−	0.684401i	$-0.239936\pi$
$83$	13.2849	1.45821	0.729106	+	0.684401i	$0.239936\pi$
$84$	0.537250	0.0586188
$85$	−1.97618	−0.214347
$86$	4.22429	0.455517
$87$	0.0241204	0.00258597
$88$	9.00442	0.959875
$89$	13.7328	1.45567	0.727835	−	0.685752i	$-0.240527\pi$
$89$	13.7328	1.45567	0.727835	+	0.685752i	$0.240527\pi$
$90$	−3.54404	−0.373575
$91$	0	0
$92$	−1.10927	−0.115649
$93$	0.719767	0.0746364
$94$	9.22992	0.951993
$95$	0.136450	0.0139995
$96$	−0.724920	−0.0739869
$97$	−7.54450	−0.766027	−0.383014	−	0.923743i	$-0.625114\pi$
$97$	−7.54450	−0.766027	−0.383014	+	0.923743i	$0.625114\pi$
$98$	14.1274	1.42708
$99$	7.60093	0.763922
$100$	0.693037	0.0693037
$101$	0.931102	0.0926481	0.0463241	−	0.998926i	$-0.485249\pi$
$101$	0.931102	0.0926481	0.0463241	+	0.998926i	$0.485249\pi$
$102$	1.81433	0.179646
$103$	13.9637	1.37589	0.687944	−	0.725764i	$-0.258514\pi$
$103$	13.9637	1.37589	0.687944	+	0.725764i	$0.258514\pi$
$104$	0	0
$105$	−3.18285	−0.310615
$106$	−10.7382	−1.04298
$107$	1.26699	0.122484	0.0612422	−	0.998123i	$-0.480494\pi$
$107$	1.26699	0.122484	0.0612422	+	0.998123i	$0.480494\pi$
$108$	−0.704678	−0.0678077
$109$	8.47485	0.811743	0.405872	−	0.913930i	$-0.366968\pi$
$109$	8.47485	0.811743	0.405872	+	0.913930i	$0.366968\pi$
$110$	−4.37305	−0.416954
$111$	−3.52428	−0.334510
$112$	−15.0917	−1.42603
$113$	−16.2832	−1.53179	−0.765896	−	0.642965i	$-0.777704\pi$
$113$	−16.2832	−1.53179	−0.765896	+	0.642965i	$0.777704\pi$
$114$	−0.125275	−0.0117330
$115$	6.57168	0.612812
$116$	0.00598490	0.000555684 0
$117$	0	0
$118$	−0.0823511	−0.00758103
$119$	−7.80622	−0.715595
$120$	2.23912	0.204402
$121$	−1.62109	−0.147371
$122$	−10.5715	−0.957097
$123$	−8.70954	−0.785312
$124$	0.178593	0.0160381
$125$	−9.39602	−0.840406
$126$	−13.9995	−1.24718
$127$	−1.99088	−0.176662	−0.0883311	−	0.996091i	$-0.528153\pi$
$127$	−1.99088	−0.176662	−0.0883311	+	0.996091i	$0.528153\pi$
$128$	9.56668	0.845583
$129$	−2.25290	−0.198357
$130$	0	0
$131$	−3.92459	−0.342893	−0.171447	−	0.985193i	$-0.554844\pi$
$131$	−3.92459	−0.342893	−0.171447	+	0.985193i	$0.554844\pi$
$132$	−0.393671	−0.0342646
$133$	0.538999	0.0467371
$134$	−9.76789	−0.843817
$135$	4.17475	0.359306
$136$	5.49162	0.470903
$137$	−0.942996	−0.0805656	−0.0402828	−	0.999188i	$-0.512826\pi$
$137$	−0.942996	−0.0805656	−0.0402828	+	0.999188i	$0.512826\pi$
$138$	−6.03346	−0.513603
$139$	−5.90296	−0.500683	−0.250341	−	0.968158i	$-0.580543\pi$
$139$	−5.90296	−0.500683	−0.250341	+	0.968158i	$0.580543\pi$
$140$	−0.789750	−0.0667460
$141$	−4.92251	−0.414550
$142$	12.4030	1.04084
$143$	0	0
$144$	8.96207	0.746839
$145$	−0.0354566	−0.00294451
$146$	19.6428	1.62565
$147$	−7.53441	−0.621428
$148$	−0.874467	−0.0718807
$149$	−19.3176	−1.58256	−0.791281	−	0.611452i	$-0.790586\pi$
$149$	−19.3176	−1.58256	−0.791281	+	0.611452i	$0.790586\pi$
$150$	3.76953	0.307781
$151$	0.906605	0.0737785	0.0368892	−	0.999319i	$-0.488255\pi$
$151$	0.906605	0.0737785	0.0368892	+	0.999319i	$0.488255\pi$
$152$	−0.379182	−0.0307557
$153$	4.63566	0.374771
$154$	−17.2743	−1.39200
$155$	−1.05805	−0.0849844
$156$	0	0
$157$	−13.8070	−1.10192	−0.550959	−	0.834532i	$-0.685738\pi$
$157$	−13.8070	−1.10192	−0.550959	+	0.834532i	$0.685738\pi$
$158$	11.4652	0.912119
$159$	5.72689	0.454172
$160$	1.06562	0.0842449
$161$	25.9592	2.04587
$162$	6.21598	0.488373
$163$	9.22932	0.722896	0.361448	−	0.932392i	$-0.382282\pi$
$163$	9.22932	0.722896	0.361448	+	0.932392i	$0.382282\pi$
$164$	−2.16107	−0.168751
$165$	2.33224	0.181565
$166$	17.9293	1.39158
$167$	8.30766	0.642866	0.321433	−	0.946932i	$-0.395836\pi$
$167$	8.30766	0.642866	0.321433	+	0.946932i	$0.395836\pi$
$168$	8.84487	0.682396
$169$	0	0
$170$	−2.66704	−0.204553
$171$	−0.320080	−0.0244771
$172$	−0.559004	−0.0426237
$173$	6.41721	0.487892	0.243946	−	0.969789i	$-0.421558\pi$
$173$	6.41721	0.487892	0.243946	+	0.969789i	$0.421558\pi$
$174$	0.0325527	0.00246782
$175$	−16.2185	−1.22601
$176$	11.0584	0.833561
$177$	0.0439196	0.00330120
$178$	18.5337	1.38916
$179$	13.5729	1.01448	0.507242	−	0.861804i	$-0.330665\pi$
$179$	13.5729	1.01448	0.507242	+	0.861804i	$0.330665\pi$
$180$	0.468987	0.0349562
$181$	12.3745	0.919788	0.459894	−	0.887974i	$-0.347887\pi$
$181$	12.3745	0.919788	0.459894	+	0.887974i	$0.347887\pi$
$182$	0	0
$183$	5.63799	0.416772
$184$	−18.2621	−1.34630
$185$	5.18064	0.380888
$186$	0.971394	0.0712261
$187$	5.72002	0.418289
$188$	−1.22140	−0.0890800
$189$	16.4909	1.19954
$190$	0.184152	0.0133598
$191$	−19.5118	−1.41183	−0.705913	−	0.708299i	$-0.749463\pi$
$191$	−19.5118	−1.41183	−0.705913	+	0.708299i	$0.749463\pi$
$192$	−6.17639	−0.445742
$193$	19.1950	1.38168	0.690841	−	0.723006i	$-0.257240\pi$
$193$	19.1950	1.38168	0.690841	+	0.723006i	$0.257240\pi$
$194$	−10.1820	−0.731026
$195$	0	0
$196$	−1.86949	−0.133535
$197$	−23.4892	−1.67353	−0.836767	−	0.547559i	$-0.815557\pi$
$197$	−23.4892	−1.67353	−0.836767	+	0.547559i	$0.815557\pi$
$198$	10.2582	0.729017
$199$	1.81419	0.128605	0.0643024	−	0.997930i	$-0.479518\pi$
$199$	1.81419	0.128605	0.0643024	+	0.997930i	$0.479518\pi$
$200$	11.4096	0.806782
$201$	5.20942	0.367444
$202$	1.25661	0.0884148
$203$	−0.140059	−0.00983023
$204$	−0.240092	−0.0168098
$205$	12.8029	0.894193
$206$	18.8454	1.31302
$207$	−15.4156	−1.07146
$208$	0	0
$209$	−0.394952	−0.0273194
$210$	−4.29556	−0.296422
$211$	14.7215	1.01347	0.506734	−	0.862103i	$-0.330853\pi$
$211$	14.7215	1.01347	0.506734	+	0.862103i	$0.330853\pi$
$212$	1.42099	0.0975942
$213$	−6.61480	−0.453238
$214$	1.70992	0.116888
$215$	3.31173	0.225858
$216$	−11.6013	−0.789366
$217$	−4.17946	−0.283720
$218$	11.4376	0.774653
$219$	−10.4759	−0.707896
$220$	0.578690	0.0390153
$221$	0	0
$222$	−4.75635	−0.319225
$223$	13.2852	0.889641	0.444821	−	0.895620i	$-0.353267\pi$
$223$	13.2852	0.889641	0.444821	+	0.895620i	$0.353267\pi$
$224$	4.20938	0.281251
$225$	9.63124	0.642083
$226$	−21.9757	−1.46180
$227$	−1.32474	−0.0879258	−0.0439629	−	0.999033i	$-0.513998\pi$
$227$	−1.32474	−0.0879258	−0.0439629	+	0.999033i	$0.513998\pi$
$228$	0.0165777	0.00109789
$229$	−17.6330	−1.16522	−0.582611	−	0.812751i	$-0.697969\pi$
$229$	−17.6330	−1.16522	−0.582611	+	0.812751i	$0.697969\pi$
$230$	8.86910	0.584811
$231$	9.21272	0.606153
$232$	0.0985307	0.00646886
$233$	29.2967	1.91929	0.959645	−	0.281214i	$-0.0907369\pi$
$233$	29.2967	1.91929	0.959645	+	0.281214i	$0.0907369\pi$
$234$	0	0
$235$	7.23601	0.472025
$236$	0.0108976	0.000709373 0
$237$	−6.11461	−0.397186
$238$	−10.5352	−0.682898
$239$	−21.0876	−1.36404	−0.682022	−	0.731331i	$-0.738899\pi$
$239$	−21.0876	−1.36404	−0.682022	+	0.731331i	$0.738899\pi$
$240$	2.74988	0.177504
$241$	9.61141	0.619125	0.309563	−	0.950879i	$-0.399817\pi$
$241$	9.61141	0.619125	0.309563	+	0.950879i	$0.399817\pi$
$242$	−2.18781	−0.140638
$243$	−15.1523	−0.972018
$244$	1.39893	0.0895576
$245$	11.0755	0.707586
$246$	−11.7543	−0.749430
$247$	0	0
$248$	2.94022	0.186704
$249$	−9.56206	−0.605971
$250$	−12.6808	−0.802006
$251$	−5.52531	−0.348754	−0.174377	−	0.984679i	$-0.555791\pi$
$251$	−5.52531	−0.348754	−0.174377	+	0.984679i	$0.555791\pi$
$252$	1.85257	0.116701
$253$	−19.0216	−1.19588
$254$	−2.68688	−0.168590
$255$	1.42239	0.0890734
$256$	−4.25104	−0.265690
$257$	6.62882	0.413494	0.206747	−	0.978394i	$-0.433712\pi$
$257$	6.62882	0.413494	0.206747	+	0.978394i	$0.433712\pi$
$258$	−3.04050	−0.189294
$259$	20.4644	1.27159
$260$	0	0
$261$	0.0831730	0.00514828
$262$	−5.29661	−0.327226
$263$	−0.731398	−0.0450999	−0.0225500	−	0.999746i	$-0.507178\pi$
$263$	−0.731398	−0.0450999	−0.0225500	+	0.999746i	$0.507178\pi$
$264$	−6.48109	−0.398883
$265$	−8.41845	−0.517141
$266$	0.727430	0.0446016
$267$	−9.88439	−0.604915
$268$	1.29259	0.0789578
$269$	16.0183	0.976652	0.488326	−	0.872661i	$-0.337608\pi$
$269$	16.0183	0.976652	0.488326	+	0.872661i	$0.337608\pi$
$270$	5.63423	0.342888
$271$	25.7879	1.56650	0.783252	−	0.621704i	$-0.213559\pi$
$271$	25.7879	1.56650	0.783252	+	0.621704i	$0.213559\pi$
$272$	6.74433	0.408935
$273$	0	0
$274$	−1.27266	−0.0768844
$275$	11.8841	0.716641
$276$	0.798414	0.0480589
$277$	7.74384	0.465282	0.232641	−	0.972563i	$-0.425263\pi$
$277$	7.74384	0.465282	0.232641	+	0.972563i	$0.425263\pi$
$278$	−7.96661	−0.477805
$279$	2.48194	0.148590
$280$	−13.0018	−0.777008
$281$	−1.30214	−0.0776790	−0.0388395	−	0.999245i	$-0.512366\pi$
$281$	−1.30214	−0.0776790	−0.0388395	+	0.999245i	$0.512366\pi$
$282$	−6.64339	−0.395608
$283$	−6.03063	−0.358484	−0.179242	−	0.983805i	$-0.557364\pi$
$283$	−6.03063	−0.358484	−0.179242	+	0.983805i	$0.557364\pi$
$284$	−1.64131	−0.0973936
$285$	−0.0982120	−0.00581758
$286$	0	0
$287$	50.5735	2.98526
$288$	−2.49971	−0.147297
$289$	−13.5115	−0.794792
$290$	−0.0478520	−0.00280997
$291$	5.43028	0.318329
$292$	−2.59935	−0.152115
$293$	5.42982	0.317214	0.158607	−	0.987342i	$-0.449300\pi$
$293$	5.42982	0.317214	0.158607	+	0.987342i	$0.449300\pi$
$294$	−10.1684	−0.593033
$295$	−0.0645611	−0.00375889
$296$	−14.3965	−0.836782
$297$	−12.0838	−0.701171
$298$	−26.0710	−1.51025
$299$	0	0
$300$	−0.498825	−0.0287997
$301$	13.0819	0.754027
$302$	1.22355	0.0704074
$303$	−0.670176	−0.0385006
$304$	−0.465678	−0.0267085
$305$	−8.28776	−0.474556
$306$	6.25626	0.357647
$307$	−7.28313	−0.415670	−0.207835	−	0.978164i	$-0.566642\pi$
$307$	−7.28313	−0.415670	−0.207835	+	0.978164i	$0.566642\pi$
$308$	2.28592	0.130252
$309$	−10.0506	−0.571761
$310$	−1.42793	−0.0811013
$311$	9.80090	0.555758	0.277879	−	0.960616i	$-0.410369\pi$
$311$	9.80090	0.555758	0.277879	+	0.960616i	$0.410369\pi$
$312$	0	0
$313$	13.5740	0.767250	0.383625	−	0.923489i	$-0.374676\pi$
$313$	13.5740	0.767250	0.383625	+	0.923489i	$0.374676\pi$
$314$	−18.6339	−1.05157
$315$	−10.9753	−0.618386
$316$	−1.51720	−0.0853489
$317$	25.5803	1.43673	0.718366	−	0.695666i	$-0.244890\pi$
$317$	25.5803	1.43673	0.718366	+	0.695666i	$0.244890\pi$
$318$	7.72898	0.433420
$319$	0.102629	0.00574610
$320$	9.07920	0.507543
$321$	−0.911937	−0.0508994
$322$	35.0344	1.95239
$323$	−0.240873	−0.0134026
$324$	−0.822566	−0.0456981
$325$	0	0
$326$	12.4558	0.689866
$327$	−6.09992	−0.337326
$328$	−35.5781	−1.96447
$329$	28.5834	1.57585
$330$	3.14758	0.173269
$331$	8.89679	0.489012	0.244506	−	0.969648i	$-0.421374\pi$
$331$	8.89679	0.489012	0.244506	+	0.969648i	$0.421374\pi$
$332$	−2.37260	−0.130213
$333$	−12.1526	−0.665958
$334$	11.2120	0.613492
$335$	−7.65777	−0.418389
$336$	10.8625	0.592597
$337$	12.0300	0.655313	0.327657	−	0.944797i	$-0.393741\pi$
$337$	12.0300	0.655313	0.327657	+	0.944797i	$0.393741\pi$
$338$	0	0
$339$	11.7201	0.636548
$340$	0.352932	0.0191404
$341$	3.06250	0.165844
$342$	−0.431978	−0.0233587
$343$	14.4937	0.782587
$344$	−9.20301	−0.496193
$345$	−4.73008	−0.254659
$346$	8.66064	0.465599
$347$	25.2210	1.35393	0.676967	−	0.736013i	$-0.263294\pi$
$347$	25.2210	1.35393	0.676967	+	0.736013i	$0.263294\pi$
$348$	−0.00430773	−0.000230919 0
$349$	−19.9257	−1.06660	−0.533300	−	0.845926i	$-0.679048\pi$
$349$	−19.9257	−1.06660	−0.533300	+	0.845926i	$0.679048\pi$
$350$	−21.8884	−1.16999
$351$	0	0
$352$	−3.08443	−0.164401
$353$	27.9536	1.48782	0.743909	−	0.668281i	$-0.232970\pi$
$353$	27.9536	1.48782	0.743909	+	0.668281i	$0.232970\pi$
$354$	0.0592736	0.00315036
$355$	9.72366	0.516078
$356$	−2.45258	−0.129986
$357$	5.61866	0.297371
$358$	18.3179	0.968130
$359$	8.24032	0.434907	0.217454	−	0.976071i	$-0.430225\pi$
$359$	8.24032	0.434907	0.217454	+	0.976071i	$0.430225\pi$
$360$	7.72103	0.406934
$361$	−18.9834	−0.999125
$362$	16.7005	0.877761
$363$	1.16680	0.0612413
$364$	0	0
$365$	15.3994	0.806043
$366$	7.60900	0.397729
$367$	−5.67733	−0.296354	−0.148177	−	0.988961i	$-0.547341\pi$
$367$	−5.67733	−0.296354	−0.148177	+	0.988961i	$0.547341\pi$
$368$	−22.4279	−1.16914
$369$	−30.0326	−1.56344
$370$	6.99176	0.363484
$371$	−33.2542	−1.72647
$372$	−0.128545	−0.00666477
$373$	−37.5687	−1.94523	−0.972616	−	0.232419i	$-0.925336\pi$
$373$	−37.5687	−1.94523	−0.972616	+	0.232419i	$0.925336\pi$
$374$	7.71971	0.399177
$375$	6.76295	0.349237
$376$	−20.1082	−1.03700
$377$	0	0
$378$	22.2561	1.14473
$379$	12.7897	0.656962	0.328481	−	0.944511i	$-0.393463\pi$
$379$	12.7897	0.656962	0.328481	+	0.944511i	$0.393463\pi$
$380$	−0.0243690	−0.00125010
$381$	1.43297	0.0734133
$382$	−26.3330	−1.34732
$383$	30.1708	1.54166	0.770829	−	0.637042i	$-0.219842\pi$
$383$	30.1708	1.54166	0.770829	+	0.637042i	$0.219842\pi$
$384$	−6.88578	−0.351389
$385$	−13.5426	−0.690193
$386$	25.9054	1.31855
$387$	−7.76856	−0.394898
$388$	1.34740	0.0684036
$389$	5.39857	0.273718	0.136859	−	0.990591i	$-0.456299\pi$
$389$	5.39857	0.273718	0.136859	+	0.990591i	$0.456299\pi$
$390$	0	0
$391$	−11.6009	−0.586684
$392$	−30.7778	−1.55451
$393$	2.82479	0.142492
$394$	−31.7009	−1.59707
$395$	8.98838	0.452255
$396$	−1.35747	−0.0682157
$397$	34.6774	1.74041	0.870205	−	0.492690i	$-0.163986\pi$
$397$	34.6774	1.74041	0.870205	+	0.492690i	$0.163986\pi$
$398$	2.44843	0.122729
$399$	−0.387953	−0.0194220
$400$	14.0123	0.700615
$401$	−6.98239	−0.348684	−0.174342	−	0.984685i	$-0.555780\pi$
$401$	−6.98239	−0.348684	−0.174342	+	0.984685i	$0.555780\pi$
$402$	7.03060	0.350655
$403$	0	0
$404$	−0.166288	−0.00827316
$405$	4.87316	0.242149
$406$	−0.189023	−0.00938107
$407$	−14.9953	−0.743289
$408$	−3.95269	−0.195687
$409$	−4.31811	−0.213517	−0.106758	−	0.994285i	$-0.534047\pi$
$409$	−4.31811	−0.213517	−0.106758	+	0.994285i	$0.534047\pi$
$410$	17.2787	0.853335
$411$	0.678737	0.0334796
$412$	−2.49383	−0.122862
$413$	−0.255027	−0.0125490
$414$	−20.8049	−1.02250
$415$	14.0561	0.689986
$416$	0	0
$417$	4.24876	0.208063
$418$	−0.533025	−0.0260711
$419$	32.1294	1.56962	0.784811	−	0.619735i	$-0.212760\pi$
$419$	32.1294	1.56962	0.784811	+	0.619735i	$0.212760\pi$
$420$	0.568436	0.0277368
$421$	−28.9593	−1.41139	−0.705694	−	0.708517i	$-0.749365\pi$
$421$	−28.9593	−1.41139	−0.705694	+	0.708517i	$0.749365\pi$
$422$	19.8680	0.967160
$423$	−16.9740	−0.825305
$424$	23.3941	1.13612
$425$	7.24791	0.351575
$426$	−8.92730	−0.432529
$427$	−32.7380	−1.58430
$428$	−0.226276	−0.0109374
$429$	0	0
$430$	4.46950	0.215538
$431$	3.08215	0.148462	0.0742309	−	0.997241i	$-0.476350\pi$
$431$	3.08215	0.148462	0.0742309	+	0.997241i	$0.476350\pi$
$432$	−14.2477	−0.685491
$433$	13.9241	0.669149	0.334574	−	0.942369i	$-0.391407\pi$
$433$	13.9241	0.669149	0.334574	+	0.942369i	$0.391407\pi$
$434$	−5.64057	−0.270756
$435$	0.0255205	0.00122361
$436$	−1.51355	−0.0724859
$437$	0.801012	0.0383176
$438$	−14.1382	−0.675551
$439$	−16.3135	−0.778600	−0.389300	−	0.921111i	$-0.627283\pi$
$439$	−16.3135	−0.778600	−0.389300	+	0.921111i	$0.627283\pi$
$440$	9.52710	0.454187
$441$	−25.9805	−1.23717
$442$	0	0
$443$	15.2254	0.723380	0.361690	−	0.932298i	$-0.382200\pi$
$443$	15.2254	0.723380	0.361690	+	0.932298i	$0.382200\pi$
$444$	0.629412	0.0298706
$445$	14.5299	0.688784
$446$	17.9296	0.848992
$447$	13.9042	0.657646
$448$	35.8643	1.69443
$449$	−35.2699	−1.66449	−0.832244	−	0.554409i	$-0.812944\pi$
$449$	−35.2699	−1.66449	−0.832244	+	0.554409i	$0.812944\pi$
$450$	12.9983	0.612745
$451$	−37.0578	−1.74498
$452$	2.90806	0.136784
$453$	−0.652544	−0.0306592
$454$	−1.78786	−0.0839083
$455$	0	0
$456$	0.272923	0.0127808
$457$	−34.1470	−1.59733	−0.798664	−	0.601778i	$-0.794459\pi$
$457$	−34.1470	−1.59733	−0.798664	+	0.601778i	$0.794459\pi$
$458$	−23.7974	−1.11198
$459$	−7.36965	−0.343986
$460$	−1.17366	−0.0547220
$461$	−38.5290	−1.79448	−0.897238	−	0.441547i	$-0.854430\pi$
$461$	−38.5290	−1.79448	−0.897238	+	0.441547i	$0.854430\pi$
$462$	12.4334	0.578456
$463$	−4.98324	−0.231591	−0.115795	−	0.993273i	$-0.536942\pi$
$463$	−4.98324	−0.231591	−0.115795	+	0.993273i	$0.536942\pi$
$464$	0.121007	0.00561760
$465$	0.761547	0.0353159
$466$	39.5387	1.83159
$467$	−31.1638	−1.44209	−0.721045	−	0.692889i	$-0.756338\pi$
$467$	−31.1638	−1.44209	−0.721045	+	0.692889i	$0.756338\pi$
$468$	0	0
$469$	−30.2494	−1.39679
$470$	9.76568	0.450457
$471$	9.93782	0.457911
$472$	0.179410	0.00825800
$473$	−9.58576	−0.440754
$474$	−8.25224	−0.379038
$475$	−0.500449	−0.0229622
$476$	1.39414	0.0639002
$477$	19.7477	0.904187
$478$	−28.4597	−1.30172
$479$	0.0721194	0.00329522	0.00164761	−	0.999999i	$-0.499476\pi$
$479$	0.0721194	0.00329522	0.00164761	+	0.999999i	$0.499476\pi$
$480$	−0.767000	−0.0350086
$481$	0	0
$482$	12.9715	0.590836
$483$	−18.6846	−0.850177
$484$	0.289515	0.0131598
$485$	−7.98243	−0.362464
$486$	−20.4494	−0.927604
$487$	−14.6965	−0.665961	−0.332981	−	0.942934i	$-0.608054\pi$
$487$	−14.6965	−0.665961	−0.332981	+	0.942934i	$0.608054\pi$
$488$	23.0310	1.04256
$489$	−6.64296	−0.300405
$490$	14.9474	0.675255
$491$	19.1533	0.864378	0.432189	−	0.901783i	$-0.357741\pi$
$491$	19.1533	0.864378	0.432189	+	0.901783i	$0.357741\pi$
$492$	1.55546	0.0701257
$493$	0.0625912	0.00281896
$494$	0	0
$495$	8.04214	0.361467
$496$	3.61092	0.162135
$497$	38.4100	1.72292
$498$	−12.9049	−0.578283
$499$	−38.7077	−1.73280	−0.866398	−	0.499355i	$-0.833570\pi$
$499$	−38.7077	−1.73280	−0.866398	+	0.499355i	$0.833570\pi$
$500$	1.67807	0.0750454
$501$	−5.97958	−0.267148
$502$	−7.45693	−0.332819
$503$	1.63371	0.0728437	0.0364218	−	0.999337i	$-0.488404\pi$
$503$	1.63371	0.0728437	0.0364218	+	0.999337i	$0.488404\pi$
$504$	30.4993	1.35855
$505$	0.985150	0.0438386
$506$	−25.6715	−1.14124
$507$	0	0
$508$	0.355558	0.0157753
$509$	38.4578	1.70461	0.852306	−	0.523044i	$-0.175204\pi$
$509$	38.4578	1.70461	0.852306	+	0.523044i	$0.175204\pi$
$510$	1.91965	0.0850034
$511$	60.8303	2.69097
$512$	−24.8705	−1.09913
$513$	0.508855	0.0224665
$514$	8.94622	0.394601
$515$	14.7743	0.651033
$516$	0.402353	0.0177126
$517$	−20.9445	−0.921139
$518$	27.6186	1.21349
$519$	−4.61890	−0.202747
$520$	0	0
$521$	−7.61280	−0.333523	−0.166761	−	0.985997i	$-0.553331\pi$
$521$	−7.61280	−0.333523	−0.166761	+	0.985997i	$0.553331\pi$
$522$	0.112250	0.00491304
$523$	41.7463	1.82544	0.912719	−	0.408587i	$-0.133978\pi$
$523$	41.7463	1.82544	0.912719	+	0.408587i	$0.133978\pi$
$524$	0.700905	0.0306192
$525$	11.6736	0.509476
$526$	−0.987091	−0.0430392
$527$	1.86776	0.0813609
$528$	−7.95950	−0.346393
$529$	15.5783	0.677316
$530$	−11.3615	−0.493512
$531$	0.151446	0.00657218
$532$	−0.0962615	−0.00417346
$533$	0	0
$534$	−13.3399	−0.577275
$535$	1.34053	0.0579563
$536$	21.2803	0.919167
$537$	−9.76930	−0.421576
$538$	21.6182	0.932027
$539$	−32.0578	−1.38083
$540$	−0.745582	−0.0320848
$541$	−36.3813	−1.56415	−0.782076	−	0.623183i	$-0.785839\pi$
$541$	−36.3813	−1.56415	−0.782076	+	0.623183i	$0.785839\pi$
$542$	34.8033	1.49493
$543$	−8.90675	−0.382225
$544$	−1.88113	−0.0806529
$545$	8.96679	0.384095
$546$	0	0
$547$	8.27495	0.353811	0.176906	−	0.984228i	$-0.443391\pi$
$547$	8.27495	0.353811	0.176906	+	0.984228i	$0.443391\pi$
$548$	0.168413	0.00719423
$549$	19.4412	0.829730
$550$	16.0388	0.683896
$551$	−0.00432175	−0.000184113 0
$552$	13.1445	0.559465
$553$	35.5056	1.50985
$554$	10.4510	0.444022
$555$	−3.72885	−0.158281
$556$	1.05423	0.0447093
$557$	36.5488	1.54862	0.774310	−	0.632806i	$-0.218097\pi$
$557$	36.5488	1.54862	0.774310	+	0.632806i	$0.218097\pi$
$558$	3.34961	0.141800
$559$	0	0
$560$	−15.9677	−0.674758
$561$	−4.11708	−0.173823
$562$	−1.75736	−0.0741297
$563$	8.13854	0.342998	0.171499	−	0.985184i	$-0.445139\pi$
$563$	8.13854	0.342998	0.171499	+	0.985184i	$0.445139\pi$
$564$	0.879126	0.0370179
$565$	−17.2284	−0.724802
$566$	−8.13891	−0.342104
$567$	19.2498	0.808415
$568$	−27.0212	−1.13378
$569$	2.04819	0.0858647	0.0429323	−	0.999078i	$-0.486330\pi$
$569$	2.04819	0.0858647	0.0429323	+	0.999078i	$0.486330\pi$
$570$	−0.132546	−0.00555176
$571$	−19.6963	−0.824265	−0.412132	−	0.911124i	$-0.635216\pi$
$571$	−19.6963	−0.824265	−0.412132	+	0.911124i	$0.635216\pi$
$572$	0	0
$573$	14.0440	0.586695
$574$	68.2537	2.84886
$575$	−24.1026	−1.00515
$576$	−21.2977	−0.887405
$577$	−15.2467	−0.634727	−0.317364	−	0.948304i	$-0.602798\pi$
$577$	−15.2467	−0.634727	−0.317364	+	0.948304i	$0.602798\pi$
$578$	−18.2350	−0.758477
$579$	−13.8159	−0.574169
$580$	0.00633231	0.000262935 0
$581$	55.5238	2.30352
$582$	7.32868	0.303783
$583$	24.3671	1.00918
$584$	−42.7937	−1.77081
$585$	0	0
$586$	7.32806	0.302719
$587$	−34.0944	−1.40723	−0.703613	−	0.710583i	$-0.748431\pi$
$587$	−34.0944	−1.40723	−0.703613	+	0.710583i	$0.748431\pi$
$588$	1.34559	0.0554914
$589$	−0.128964	−0.00531386
$590$	−0.0871313	−0.00358714
$591$	16.9067	0.695450
$592$	−17.6806	−0.726666
$593$	2.87444	0.118039	0.0590195	−	0.998257i	$-0.481203\pi$
$593$	2.87444	0.118039	0.0590195	+	0.998257i	$0.481203\pi$
$594$	−16.3082	−0.669133
$595$	−8.25935	−0.338600
$596$	3.45000	0.141317
$597$	−1.30580	−0.0534427
$598$	0	0
$599$	−19.6810	−0.804145	−0.402072	−	0.915608i	$-0.631710\pi$
$599$	−19.6810	−0.804145	−0.402072	+	0.915608i	$0.631710\pi$
$600$	−8.21227	−0.335265
$601$	21.3371	0.870360	0.435180	−	0.900344i	$-0.356685\pi$
$601$	21.3371	0.870360	0.435180	+	0.900344i	$0.356685\pi$
$602$	17.6552	0.719574
$603$	17.9634	0.731525
$604$	−0.161913	−0.00658816
$605$	−1.71518	−0.0697322
$606$	−0.904467	−0.0367415
$607$	−37.9147	−1.53891	−0.769455	−	0.638701i	$-0.779472\pi$
$607$	−37.9147	−1.53891	−0.769455	+	0.638701i	$0.779472\pi$
$608$	0.129887	0.00526762
$609$	0.100810	0.00408503
$610$	−11.1851	−0.452872
$611$	0	0
$612$	−0.827897	−0.0334658
$613$	−34.8521	−1.40766	−0.703832	−	0.710366i	$-0.748529\pi$
$613$	−34.8521	−1.40766	−0.703832	+	0.710366i	$0.748529\pi$
$614$	−9.82928	−0.396677
$615$	−9.21510	−0.371589
$616$	37.6336	1.51630
$617$	−11.6812	−0.470269	−0.235135	−	0.971963i	$-0.575553\pi$
$617$	−11.6812	−0.470269	−0.235135	+	0.971963i	$0.575553\pi$
$618$	−13.5643	−0.545636
$619$	−33.3219	−1.33932	−0.669660	−	0.742668i	$-0.733560\pi$
$619$	−33.3219	−1.33932	−0.669660	+	0.742668i	$0.733560\pi$
$620$	0.188960	0.00758882
$621$	24.5074	0.983448
$622$	13.2272	0.530364
$623$	57.3955	2.29950
$624$	0	0
$625$	9.46125	0.378450
$626$	18.3195	0.732193
$627$	0.284273	0.0113528
$628$	2.46584	0.0983976
$629$	−9.14533	−0.364648
$630$	−14.8122	−0.590131
$631$	−42.2418	−1.68162	−0.840809	−	0.541332i	$-0.817920\pi$
$631$	−42.2418	−1.68162	−0.840809	+	0.541332i	$0.817920\pi$
$632$	−24.9779	−0.993568
$633$	−10.5960	−0.421154
$634$	34.5230	1.37108
$635$	−2.10645	−0.0835918
$636$	−1.02278	−0.0405560
$637$	0	0
$638$	0.138507	0.00548355
$639$	−22.8095	−0.902329
$640$	10.1220	0.400107
$641$	23.7789	0.939211	0.469605	−	0.882876i	$-0.344396\pi$
$641$	23.7789	0.939211	0.469605	+	0.882876i	$0.344396\pi$
$642$	−1.23075	−0.0485737
$643$	40.4037	1.59337	0.796683	−	0.604397i	$-0.206586\pi$
$643$	40.4037	1.59337	0.796683	+	0.604397i	$0.206586\pi$
$644$	−4.63613	−0.182689
$645$	−2.38368	−0.0938571
$646$	−0.325082	−0.0127902
$647$	−5.18693	−0.203919	−0.101960	−	0.994789i	$-0.532511\pi$
$647$	−5.18693	−0.203919	−0.101960	+	0.994789i	$0.532511\pi$
$648$	−13.5421	−0.531984
$649$	0.186871	0.00733533
$650$	0	0
$651$	3.00823	0.117902
$652$	−1.64829	−0.0645522
$653$	8.39430	0.328494	0.164247	−	0.986419i	$-0.447481\pi$
$653$	8.39430	0.328494	0.164247	+	0.986419i	$0.447481\pi$
$654$	−8.23242	−0.321913
$655$	−4.15240	−0.162248
$656$	−43.6939	−1.70596
$657$	−36.1235	−1.40931
$658$	38.5760	1.50385
$659$	−4.50177	−0.175364	−0.0876820	−	0.996149i	$-0.527946\pi$
$659$	−4.50177	−0.175364	−0.0876820	+	0.996149i	$0.527946\pi$
$660$	−0.416522	−0.0162131
$661$	−36.2163	−1.40865	−0.704325	−	0.709878i	$-0.748750\pi$
$661$	−36.2163	−1.40865	−0.704325	+	0.709878i	$0.748750\pi$
$662$	12.0071	0.466668
$663$	0	0
$664$	−39.0606	−1.51585
$665$	0.570286	0.0221147
$666$	−16.4011	−0.635529
$667$	−0.208144	−0.00805936
$668$	−1.48369	−0.0574057
$669$	−9.56223	−0.369697
$670$	−10.3349	−0.399271
$671$	23.9888	0.926078
$672$	−3.02977	−0.116876
$673$	−25.6541	−0.988893	−0.494446	−	0.869208i	$-0.664629\pi$
$673$	−25.6541	−0.988893	−0.494446	+	0.869208i	$0.664629\pi$
$674$	16.2356	0.625371
$675$	−15.3115	−0.589340
$676$	0	0
$677$	−13.3480	−0.513006	−0.256503	−	0.966543i	$-0.582570\pi$
$677$	−13.3480	−0.513006	−0.256503	+	0.966543i	$0.582570\pi$
$678$	15.8174	0.607463
$679$	−31.5319	−1.21008
$680$	5.81039	0.222818
$681$	0.953501	0.0365382
$682$	4.13314	0.158266
$683$	−11.4867	−0.439525	−0.219763	−	0.975553i	$-0.570528\pi$
$683$	−11.4867	−0.439525	−0.219763	+	0.975553i	$0.570528\pi$
$684$	0.0571641	0.00218572
$685$	−0.997734	−0.0381215
$686$	19.5607	0.746829
$687$	12.6917	0.484217
$688$	−11.3023	−0.430897
$689$	0	0
$690$	−6.38369	−0.243023
$691$	5.53506	0.210563	0.105282	−	0.994442i	$-0.466426\pi$
$691$	5.53506	0.210563	0.105282	+	0.994442i	$0.466426\pi$
$692$	−1.14607	−0.0435671
$693$	31.7678	1.20676
$694$	34.0382	1.29207
$695$	−6.24561	−0.236910
$696$	−0.0709191	−0.00268818
$697$	−22.6008	−0.856067
$698$	−26.8917	−1.01787
$699$	−21.0868	−0.797576
$700$	2.89652	0.109478
$701$	8.93898	0.337621	0.168810	−	0.985649i	$-0.446007\pi$
$701$	8.93898	0.337621	0.168810	+	0.985649i	$0.446007\pi$
$702$	0	0
$703$	0.631460	0.0238160
$704$	−26.2796	−0.990450
$705$	−5.20824	−0.196154
$706$	37.7260	1.41984
$707$	3.89150	0.146355
$708$	−0.00784373	−0.000294786 0
$709$	8.70965	0.327098	0.163549	−	0.986535i	$-0.447706\pi$
$709$	8.70965	0.327098	0.163549	+	0.986535i	$0.447706\pi$
$710$	13.1230	0.492497
$711$	−21.0847	−0.790737
$712$	−40.3773	−1.51320
$713$	−6.21114	−0.232609
$714$	7.58291	0.283783
$715$	0	0
$716$	−2.42402	−0.0905899
$717$	15.1782	0.566839
$718$	11.1211	0.415036
$719$	−17.1593	−0.639933	−0.319966	−	0.947429i	$-0.603672\pi$
$719$	−17.1593	−0.639933	−0.319966	+	0.947429i	$0.603672\pi$
$720$	9.48229	0.353384
$721$	58.3608	2.17347
$722$	−25.6199	−0.953472
$723$	−6.91797	−0.257282
$724$	−2.21000	−0.0821340
$725$	0.130042	0.00482964
$726$	1.57471	0.0584431
$727$	20.7939	0.771204	0.385602	−	0.922665i	$-0.373994\pi$
$727$	20.7939	0.771204	0.385602	+	0.922665i	$0.373994\pi$
$728$	0	0
$729$	−2.91134	−0.107827
$730$	20.7830	0.769213
$731$	−5.84617	−0.216228
$732$	−1.00691	−0.0372163
$733$	17.4042	0.642838	0.321419	−	0.946937i	$-0.395840\pi$
$733$	17.4042	0.642838	0.321419	+	0.946937i	$0.395840\pi$
$734$	−7.66210	−0.282813
$735$	−7.97176	−0.294043
$736$	6.25561	0.230585
$737$	22.1653	0.816469
$738$	−40.5319	−1.49200
$739$	−19.8578	−0.730480	−0.365240	−	0.930913i	$-0.619013\pi$
$739$	−19.8578	−0.730480	−0.365240	+	0.930913i	$0.619013\pi$
$740$	−0.925227	−0.0340120
$741$	0	0
$742$	−44.8797	−1.64759
$743$	−12.5529	−0.460521	−0.230260	−	0.973129i	$-0.573958\pi$
$743$	−12.5529	−0.460521	−0.230260	+	0.973129i	$0.573958\pi$
$744$	−2.11627	−0.0775863
$745$	−20.4390	−0.748826
$746$	−50.7025	−1.85635
$747$	−32.9724	−1.20640
$748$	−1.02156	−0.0373518
$749$	5.29533	0.193487
$750$	9.12724	0.333280
$751$	−54.7715	−1.99864	−0.999321	−	0.0368438i	$-0.988270\pi$
$751$	−54.7715	−1.99864	−0.999321	+	0.0368438i	$0.988270\pi$
$752$	−24.6952	−0.900540
$753$	3.97693	0.144927
$754$	0	0
$755$	0.959230	0.0349100
$756$	−2.94517	−0.107115
$757$	−7.63390	−0.277459	−0.138729	−	0.990330i	$-0.544302\pi$
$757$	−7.63390	−0.277459	−0.138729	+	0.990330i	$0.544302\pi$
$758$	17.2609	0.626944
$759$	13.6911	0.496957
$760$	−0.401192	−0.0145528
$761$	−7.67824	−0.278336	−0.139168	−	0.990269i	$-0.544443\pi$
$761$	−7.67824	−0.278336	−0.139168	+	0.990269i	$0.544443\pi$
$762$	1.93393	0.0700589
$763$	35.4203	1.28230
$764$	3.48468	0.126071
$765$	4.90475	0.177331
$766$	40.7184	1.47122
$767$	0	0
$768$	3.05976	0.110410
$769$	45.3585	1.63567	0.817835	−	0.575453i	$-0.195174\pi$
$769$	45.3585	1.63567	0.817835	+	0.575453i	$0.195174\pi$
$770$	−18.2770	−0.658657
$771$	−4.77120	−0.171831
$772$	−3.42809	−0.123380
$773$	8.43921	0.303537	0.151769	−	0.988416i	$-0.451503\pi$
$773$	8.43921	0.303537	0.151769	+	0.988416i	$0.451503\pi$
$774$	−10.4844	−0.376855
$775$	3.88054	0.139393
$776$	22.1825	0.796304
$777$	−14.7296	−0.528420
$778$	7.28588	0.261211
$779$	1.56053	0.0559116
$780$	0	0
$781$	−28.1450	−1.00711
$782$	−15.6565	−0.559877
$783$	−0.132226	−0.00472538
$784$	−37.7985	−1.34995
$785$	−14.6085	−0.521398
$786$	3.81232	0.135981
$787$	−15.9392	−0.568170	−0.284085	−	0.958799i	$-0.591690\pi$
$787$	−15.9392	−0.568170	−0.284085	+	0.958799i	$0.591690\pi$
$788$	4.19501	0.149441
$789$	0.526436	0.0187416
$790$	12.1307	0.431590
$791$	−68.0548	−2.41975
$792$	−22.3484	−0.794116
$793$	0	0
$794$	46.8005	1.66089
$795$	6.05932	0.214902
$796$	−0.324003	−0.0114840
$797$	28.9014	1.02374	0.511869	−	0.859063i	$-0.328953\pi$
$797$	28.9014	1.02374	0.511869	+	0.859063i	$0.328953\pi$
$798$	−0.523580	−0.0185345
$799$	−12.7737	−0.451900
$800$	−3.90832	−0.138180
$801$	−34.0838	−1.20429
$802$	−9.42340	−0.332752
$803$	−44.5734	−1.57296
$804$	−0.930367	−0.0328115
$805$	27.4660	0.968051
$806$	0	0
$807$	−11.5294	−0.405855
$808$	−2.73764	−0.0963100
$809$	−13.9216	−0.489456	−0.244728	−	0.969592i	$-0.578699\pi$
$809$	−13.9216	−0.489456	−0.244728	+	0.969592i	$0.578699\pi$
$810$	6.57680	0.231085
$811$	−0.213219	−0.00748714	−0.00374357	−	0.999993i	$-0.501192\pi$
$811$	−0.213219	−0.00748714	−0.00374357	+	0.999993i	$0.501192\pi$
$812$	0.0250136	0.000877806 0
$813$	−18.5613	−0.650973
$814$	−20.2376	−0.709326
$815$	9.76506	0.342055
$816$	−4.85434	−0.169936
$817$	0.403662	0.0141224
$818$	−5.82770	−0.203761
$819$	0	0
$820$	−2.28651	−0.0798484
$821$	−14.7359	−0.514286	−0.257143	−	0.966373i	$-0.582781\pi$
$821$	−14.7359	−0.514286	−0.257143	+	0.966373i	$0.582781\pi$
$822$	0.916021	0.0319499
$823$	6.26795	0.218487	0.109243	−	0.994015i	$-0.465157\pi$
$823$	6.26795	0.218487	0.109243	+	0.994015i	$0.465157\pi$
$824$	−41.0564	−1.43027
$825$	−8.55382	−0.297806
$826$	−0.344183	−0.0119757
$827$	−20.1160	−0.699504	−0.349752	−	0.936842i	$-0.613734\pi$
$827$	−20.1160	−0.699504	−0.349752	+	0.936842i	$0.613734\pi$
$828$	2.75313	0.0956779
$829$	56.2720	1.95441	0.977203	−	0.212306i	$-0.0680973\pi$
$829$	56.2720	1.95441	0.977203	+	0.212306i	$0.0680973\pi$
$830$	18.9700	0.658459
$831$	−5.57376	−0.193351
$832$	0	0
$833$	−19.5514	−0.677417
$834$	5.73410	0.198556
$835$	8.78989	0.304187
$836$	0.0705357	0.00243953
$837$	−3.94572	−0.136384
$838$	43.3617	1.49790
$839$	−35.7681	−1.23485	−0.617427	−	0.786629i	$-0.711825\pi$
$839$	−35.7681	−1.23485	−0.617427	+	0.786629i	$0.711825\pi$
$840$	9.35828	0.322891
$841$	−28.9989	−0.999961
$842$	−39.0833	−1.34690
$843$	0.937235	0.0322801
$844$	−2.62915	−0.0904992
$845$	0	0
$846$	−22.9081	−0.787595
$847$	−6.77525	−0.232800
$848$	28.7306	0.986613
$849$	4.34065	0.148971
$850$	9.78175	0.335511
$851$	30.4123	1.04252
$852$	1.18136	0.0404727
$853$	−33.0374	−1.13118	−0.565590	−	0.824687i	$-0.691351\pi$
$853$	−33.0374	−1.13118	−0.565590	+	0.824687i	$0.691351\pi$
$854$	−44.1830	−1.51191
$855$	−0.338660	−0.0115819
$856$	−3.72523	−0.127326
$857$	20.5060	0.700472	0.350236	−	0.936662i	$-0.386101\pi$
$857$	20.5060	0.700472	0.350236	+	0.936662i	$0.386101\pi$
$858$	0	0
$859$	32.1424	1.09669	0.548343	−	0.836254i	$-0.315259\pi$
$859$	32.1424	1.09669	0.548343	+	0.836254i	$0.315259\pi$
$860$	−0.591453	−0.0201684
$861$	−36.4011	−1.24055
$862$	4.15965	0.141678
$863$	53.0910	1.80724	0.903619	−	0.428338i	$-0.140901\pi$
$863$	53.0910	1.80724	0.903619	+	0.428338i	$0.140901\pi$
$864$	3.97397	0.135197
$865$	6.78971	0.230857
$866$	18.7919	0.638574
$867$	9.72511	0.330282
$868$	0.746422	0.0253352
$869$	−26.0167	−0.882557
$870$	0.0344423	0.00116770
$871$	0	0
$872$	−24.9179	−0.843827
$873$	18.7250	0.633744
$874$	1.08104	0.0365668
$875$	−39.2703	−1.32758
$876$	1.87093	0.0632127
$877$	41.9810	1.41760	0.708798	−	0.705411i	$-0.249238\pi$
$877$	41.9810	1.41760	0.708798	+	0.705411i	$0.249238\pi$
$878$	−22.0166	−0.743024
$879$	−3.90821	−0.131821
$880$	11.7004	0.394419
$881$	−7.21948	−0.243230	−0.121615	−	0.992577i	$-0.538807\pi$
$881$	−7.21948	−0.243230	−0.121615	+	0.992577i	$0.538807\pi$
$882$	−35.0632	−1.18064
$883$	−56.8942	−1.91464	−0.957321	−	0.289028i	$-0.906668\pi$
$883$	−56.8942	−1.91464	−0.957321	+	0.289028i	$0.906668\pi$
$884$	0	0
$885$	0.0464689	0.00156204
$886$	20.5481	0.690327
$887$	−24.9575	−0.837990	−0.418995	−	0.907989i	$-0.637617\pi$
$887$	−24.9575	−0.837990	−0.418995	+	0.907989i	$0.637617\pi$
$888$	10.3621	0.347731
$889$	−8.32080	−0.279071
$890$	19.6095	0.657312
$891$	−14.1053	−0.472545
$892$	−2.37264	−0.0794419
$893$	0.881987	0.0295146
$894$	18.7650	0.627597
$895$	14.3607	0.480026
$896$	39.9835	1.33576
$897$	0	0
$898$	−47.6001	−1.58843
$899$	0.0335114	0.00111767
$900$	−1.72007	−0.0573358
$901$	14.8610	0.495092
$902$	−50.0130	−1.66525
$903$	−9.41590	−0.313342
$904$	47.8761	1.59233
$905$	13.0928	0.435219
$906$	−0.880670	−0.0292583
$907$	22.1747	0.736300	0.368150	−	0.929766i	$-0.379991\pi$
$907$	22.1747	0.736300	0.368150	+	0.929766i	$0.379991\pi$
$908$	0.236589	0.00785147
$909$	−2.31094	−0.0766489
$910$	0	0
$911$	−36.4810	−1.20867	−0.604336	−	0.796730i	$-0.706561\pi$
$911$	−36.4810	−1.20867	−0.604336	+	0.796730i	$0.706561\pi$
$912$	0.335179	0.0110989
$913$	−40.6851	−1.34648
$914$	−46.0846	−1.52434
$915$	5.96526	0.197205
$916$	3.14913	0.104050
$917$	−16.4027	−0.541663
$918$	−9.94604	−0.328268
$919$	13.1818	0.434828	0.217414	−	0.976080i	$-0.430238\pi$
$919$	13.1818	0.434828	0.217414	+	0.976080i	$0.430238\pi$
$920$	−19.3222	−0.637033
$921$	5.24216	0.172735
$922$	−51.9986	−1.71248
$923$	0	0
$924$	−1.64533	−0.0541274
$925$	−19.0007	−0.624740
$926$	−6.72536	−0.221009
$927$	−34.6571	−1.13829
$928$	−0.0337513	−0.00110794
$929$	−29.6646	−0.973263	−0.486631	−	0.873607i	$-0.661774\pi$
$929$	−29.6646	−0.973263	−0.486631	+	0.873607i	$0.661774\pi$
$930$	1.02778	0.0337022
$931$	1.34997	0.0442436
$932$	−5.23219	−0.171386
$933$	−7.05436	−0.230949
$934$	−42.0585	−1.37620
$935$	6.05205	0.197923
$936$	0	0
$937$	5.23050	0.170873	0.0854366	−	0.996344i	$-0.472772\pi$
$937$	5.23050	0.170873	0.0854366	+	0.996344i	$0.472772\pi$
$938$	−40.8245	−1.33297
$939$	−9.77014	−0.318837
$940$	−1.29230	−0.0421503
$941$	10.7268	0.349684	0.174842	−	0.984597i	$-0.444059\pi$
$941$	10.7268	0.349684	0.174842	+	0.984597i	$0.444059\pi$
$942$	13.4120	0.436988
$943$	75.1579	2.44748
$944$	0.220335	0.00717130
$945$	17.4482	0.567590
$946$	−12.9369	−0.420615
$947$	−11.9062	−0.386898	−0.193449	−	0.981110i	$-0.561967\pi$
$947$	−11.9062	−0.386898	−0.193449	+	0.981110i	$0.561967\pi$
$948$	1.09203	0.0354674
$949$	0	0
$950$	−0.675403	−0.0219130
$951$	−18.4118	−0.597045
$952$	22.9520	0.743878
$953$	−15.5869	−0.504910	−0.252455	−	0.967609i	$-0.581238\pi$
$953$	−15.5869	−0.504910	−0.252455	+	0.967609i	$0.581238\pi$
$954$	26.6515	0.862873
$955$	−20.6444	−0.668037
$956$	3.76611	0.121805
$957$	−0.0738687	−0.00238783
$958$	0.0973319	0.00314465
$959$	−3.94121	−0.127268
$960$	−6.53491	−0.210913
$961$	1.00000	0.0322581
$962$	0	0
$963$	−3.14459	−0.101333
$964$	−1.71653	−0.0552858
$965$	20.3092	0.653775
$966$	−25.2166	−0.811331
$967$	48.0705	1.54584	0.772922	−	0.634501i	$-0.218795\pi$
$967$	48.0705	1.54584	0.772922	+	0.634501i	$0.218795\pi$
$968$	4.76635	0.153196
$969$	0.173373	0.00556954
$970$	−10.7730	−0.345902
$971$	−44.8253	−1.43851	−0.719255	−	0.694746i	$-0.755517\pi$
$971$	−44.8253	−1.43851	−0.719255	+	0.694746i	$0.755517\pi$
$972$	2.70609	0.0867979
$973$	−24.6712	−0.790921
$974$	−19.8343	−0.635532
$975$	0	0
$976$	28.2846	0.905368
$977$	21.3111	0.681803	0.340902	−	0.940099i	$-0.389268\pi$
$977$	21.3111	0.681803	0.340902	+	0.940099i	$0.389268\pi$
$978$	−8.96531	−0.286679
$979$	−42.0566	−1.34413
$980$	−1.97800	−0.0631850
$981$	−21.0340	−0.671565
$982$	25.8493	0.824883
$983$	50.4918	1.61044	0.805220	−	0.592976i	$-0.202047\pi$
$983$	50.4918	1.61044	0.805220	+	0.592976i	$0.202047\pi$
$984$	25.6079	0.816351
$985$	−24.8527	−0.791871
$986$	0.0844727	0.00269016
$987$	−20.5734	−0.654858
$988$	0	0
$989$	19.4411	0.618192
$990$	10.8536	0.344951
$991$	−25.3930	−0.806635	−0.403318	−	0.915060i	$-0.632143\pi$
$991$	−25.3930	−0.806635	−0.403318	+	0.915060i	$0.632143\pi$
$992$	−1.00716	−0.0319774
$993$	−6.40362	−0.203213
$994$	51.8380	1.64420
$995$	1.91950	0.0608523
$996$	1.70772	0.0541111
$997$	−27.2103	−0.861758	−0.430879	−	0.902410i	$-0.641796\pi$
$997$	−27.2103	−0.861758	−0.430879	+	0.902410i	$0.641796\pi$
$998$	−52.2397	−1.65362
$999$	19.3199	0.611254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.u.1.39	✓	54
13.12	even	2		5239.2.a.v.1.16	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.39	✓	54	1.1	even	1	trivial
5239.2.a.v.1.16	yes	54	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+1.34960 q^{2} -0.719767 q^{3} -0.178593 q^{4} +1.05805 q^{5} -0.971394 q^{6} +4.17946 q^{7} -2.94022 q^{8} -2.48194 q^{9} +O(q^{10})\)	\(q+1.34960 q^{2} -0.719767 q^{3} -0.178593 q^{4} +1.05805 q^{5} -0.971394 q^{6} +4.17946 q^{7} -2.94022 q^{8} -2.48194 q^{9} +1.42793 q^{10} -3.06250 q^{11} +0.128545 q^{12} +5.64057 q^{14} -0.761547 q^{15} -3.61092 q^{16} -1.86776 q^{17} -3.34961 q^{18} +0.128964 q^{19} -0.188960 q^{20} -3.00823 q^{21} -4.13314 q^{22} +6.21114 q^{23} +2.11627 q^{24} -3.88054 q^{25} +3.94572 q^{27} -0.746422 q^{28} -0.0335114 q^{29} -1.02778 q^{30} -1.00000 q^{31} +1.00716 q^{32} +2.20429 q^{33} -2.52072 q^{34} +4.42206 q^{35} +0.443257 q^{36} +4.89642 q^{37} +0.174049 q^{38} -3.11089 q^{40} +12.1005 q^{41} -4.05990 q^{42} +3.13004 q^{43} +0.546942 q^{44} -2.62600 q^{45} +8.38252 q^{46} +6.83903 q^{47} +2.59902 q^{48} +10.4678 q^{49} -5.23715 q^{50} +1.34435 q^{51} -7.95659 q^{53} +5.32512 q^{54} -3.24027 q^{55} -12.2885 q^{56} -0.0928239 q^{57} -0.0452268 q^{58} -0.0610191 q^{59} +0.136007 q^{60} -7.83308 q^{61} -1.34960 q^{62} -10.3731 q^{63} +8.58109 q^{64} +2.97490 q^{66} -7.23765 q^{67} +0.333569 q^{68} -4.47057 q^{69} +5.96799 q^{70} +9.19019 q^{71} +7.29743 q^{72} +14.5546 q^{73} +6.60818 q^{74} +2.79308 q^{75} -0.0230321 q^{76} -12.7996 q^{77} +8.49526 q^{79} -3.82052 q^{80} +4.60581 q^{81} +16.3308 q^{82} +13.2849 q^{83} +0.537250 q^{84} -1.97618 q^{85} +4.22429 q^{86} +0.0241204 q^{87} +9.00442 q^{88} +13.7328 q^{89} -3.54404 q^{90} -1.10927 q^{92} +0.719767 q^{93} +9.22992 q^{94} +0.136450 q^{95} -0.724920 q^{96} -7.54450 q^{97} +14.1274 q^{98} +7.60093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9} - 6 q^{10} + 7 q^{11} + 5 q^{12} + 38 q^{14} - 4 q^{15} + 76 q^{16} + 62 q^{17} + 9 q^{18} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 15 q^{22} + 38 q^{23} + 99 q^{24} + 87 q^{25} + 25 q^{27} - 19 q^{28} + 95 q^{29} + 41 q^{30} - 54 q^{31} - 9 q^{32} - 12 q^{33} - 7 q^{34} + 53 q^{35} + 97 q^{36} + 24 q^{37} - 16 q^{38} - 28 q^{40} - 22 q^{41} + 11 q^{42} + 11 q^{43} + 24 q^{44} - 8 q^{45} - 9 q^{46} - 45 q^{47} + 2 q^{48} + 105 q^{49} - 6 q^{50} + 58 q^{51} + 56 q^{53} - 50 q^{54} + q^{55} + 91 q^{56} + 51 q^{57} - 25 q^{58} - 36 q^{59} - 100 q^{60} + 48 q^{61} + 2 q^{62} + 56 q^{63} + 90 q^{64} - 24 q^{66} - 26 q^{67} + 140 q^{68} + 47 q^{69} + 24 q^{70} - 40 q^{71} - 7 q^{72} - 9 q^{73} + 114 q^{74} + 18 q^{75} + 67 q^{76} + 65 q^{77} + 33 q^{79} - 53 q^{80} + 210 q^{81} - 6 q^{82} + 41 q^{83} + 37 q^{84} - 37 q^{85} + 42 q^{86} - 16 q^{87} - 22 q^{88} + 24 q^{89} - 40 q^{90} + 87 q^{92} - 7 q^{93} - 4 q^{94} + 61 q^{95} + 200 q^{96} - 28 q^{97} - 68 q^{98} - 39 q^{99}+O(q^{100}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9 - 6 * q^10 + 7 * q^11 + 5 * q^12 + 38 * q^14 - 4 * q^15 + 76 * q^16 + 62 * q^17 + 9 * q^18 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 15 * q^22 + 38 * q^23 + 99 * q^24 + 87 * q^25 + 25 * q^27 - 19 * q^28 + 95 * q^29 + 41 * q^30 - 54 * q^31 - 9 * q^32 - 12 * q^33 - 7 * q^34 + 53 * q^35 + 97 * q^36 + 24 * q^37 - 16 * q^38 - 28 * q^40 - 22 * q^41 + 11 * q^42 + 11 * q^43 + 24 * q^44 - 8 * q^45 - 9 * q^46 - 45 * q^47 + 2 * q^48 + 105 * q^49 - 6 * q^50 + 58 * q^51 + 56 * q^53 - 50 * q^54 + q^55 + 91 * q^56 + 51 * q^57 - 25 * q^58 - 36 * q^59 - 100 * q^60 + 48 * q^61 + 2 * q^62 + 56 * q^63 + 90 * q^64 - 24 * q^66 - 26 * q^67 + 140 * q^68 + 47 * q^69 + 24 * q^70 - 40 * q^71 - 7 * q^72 - 9 * q^73 + 114 * q^74 + 18 * q^75 + 67 * q^76 + 65 * q^77 + 33 * q^79 - 53 * q^80 + 210 * q^81 - 6 * q^82 + 41 * q^83 + 37 * q^84 - 37 * q^85 + 42 * q^86 - 16 * q^87 - 22 * q^88 + 24 * q^89 - 40 * q^90 + 87 * q^92 - 7 * q^93 - 4 * q^94 + 61 * q^95 + 200 * q^96 - 28 * q^97 - 68 * q^98 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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