LMFDB - Embedded newform 5239.2.a.v.1.20

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			1.20
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)

$f(q)$	$=$	$q-1.14077 q^{2} -3.37823 q^{3} -0.698640 q^{4} +2.91767 q^{5} +3.85379 q^{6} +1.13950 q^{7} +3.07853 q^{8} +8.41243 q^{9} +O(q^{10})$	\(q-1.14077 q^{2} -3.37823 q^{3} -0.698640 q^{4} +2.91767 q^{5} +3.85379 q^{6} +1.13950 q^{7} +3.07853 q^{8} +8.41243 q^{9} -3.32839 q^{10} -3.36564 q^{11} +2.36017 q^{12} -1.29991 q^{14} -9.85655 q^{15} -2.11462 q^{16} -2.07592 q^{17} -9.59667 q^{18} +6.06940 q^{19} -2.03840 q^{20} -3.84950 q^{21} +3.83943 q^{22} -5.19484 q^{23} -10.4000 q^{24} +3.51279 q^{25} -18.2844 q^{27} -0.796103 q^{28} +6.22325 q^{29} +11.2441 q^{30} +1.00000 q^{31} -3.74476 q^{32} +11.3699 q^{33} +2.36815 q^{34} +3.32469 q^{35} -5.87727 q^{36} +9.20792 q^{37} -6.92380 q^{38} +8.98214 q^{40} +12.7603 q^{41} +4.39140 q^{42} -8.90654 q^{43} +2.35137 q^{44} +24.5447 q^{45} +5.92613 q^{46} +5.33535 q^{47} +7.14367 q^{48} -5.70153 q^{49} -4.00729 q^{50} +7.01294 q^{51} +0.413187 q^{53} +20.8584 q^{54} -9.81982 q^{55} +3.50800 q^{56} -20.5038 q^{57} -7.09931 q^{58} +2.53271 q^{59} +6.88619 q^{60} +0.648764 q^{61} -1.14077 q^{62} +9.58600 q^{63} +8.50116 q^{64} -12.9705 q^{66} +2.70298 q^{67} +1.45032 q^{68} +17.5494 q^{69} -3.79272 q^{70} -2.56026 q^{71} +25.8979 q^{72} +3.00395 q^{73} -10.5041 q^{74} -11.8670 q^{75} -4.24033 q^{76} -3.83516 q^{77} -0.926660 q^{79} -6.16976 q^{80} +36.5317 q^{81} -14.5566 q^{82} +13.8393 q^{83} +2.68942 q^{84} -6.05685 q^{85} +10.1603 q^{86} -21.0236 q^{87} -10.3612 q^{88} +11.3360 q^{89} -27.9999 q^{90} +3.62933 q^{92} -3.37823 q^{93} -6.08642 q^{94} +17.7085 q^{95} +12.6507 q^{96} -8.11106 q^{97} +6.50415 q^{98} -28.3132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.14077	−0.806647	−0.403324	−	0.915057i	$-0.632145\pi$
$2$	−1.14077	−0.806647	−0.403324	+	0.915057i	$0.632145\pi$
$3$	−3.37823	−1.95042	−0.975211	−	0.221278i	$-0.928977\pi$
$3$	−3.37823	−1.95042	−0.975211	+	0.221278i	$0.928977\pi$
$4$	−0.698640	−0.349320
$5$	2.91767	1.30482	0.652410	−	0.757866i	$-0.273758\pi$
$5$	2.91767	1.30482	0.652410	+	0.757866i	$0.273758\pi$
$6$	3.85379	1.57330
$7$	1.13950	0.430692	0.215346	−	0.976538i	$-0.430912\pi$
$7$	1.13950	0.430692	0.215346	+	0.976538i	$0.430912\pi$
$8$	3.07853	1.08843
$9$	8.41243	2.80414
$10$	−3.32839	−1.05253
$11$	−3.36564	−1.01478	−0.507389	−	0.861717i	$-0.669389\pi$
$11$	−3.36564	−1.01478	−0.507389	+	0.861717i	$0.669389\pi$
$12$	2.36017	0.681322
$13$	0	0
$13$	0	0
$14$	−1.29991	−0.347416
$15$	−9.85655	−2.54495
$16$	−2.11462	−0.528655
$17$	−2.07592	−0.503485	−0.251743	−	0.967794i	$-0.581004\pi$
$17$	−2.07592	−0.503485	−0.251743	+	0.967794i	$0.581004\pi$
$18$	−9.59667	−2.26196
$19$	6.06940	1.39242	0.696208	−	0.717840i	$-0.254869\pi$
$19$	6.06940	1.39242	0.696208	+	0.717840i	$0.254869\pi$
$20$	−2.03840	−0.455800
$21$	−3.84950	−0.840031
$22$	3.83943	0.818568
$23$	−5.19484	−1.08320	−0.541600	−	0.840636i	$-0.682181\pi$
$23$	−5.19484	−1.08320	−0.541600	+	0.840636i	$0.682181\pi$
$24$	−10.4000	−2.12289
$25$	3.51279	0.702558
$26$	0	0
$27$	−18.2844	−3.51884
$28$	−0.796103	−0.150449
$29$	6.22325	1.15563	0.577815	−	0.816168i	$-0.303906\pi$
$29$	6.22325	1.15563	0.577815	+	0.816168i	$0.303906\pi$
$30$	11.2441	2.05288
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−3.74476	−0.661987
$33$	11.3699	1.97925
$34$	2.36815	0.406135
$35$	3.32469	0.561976
$36$	−5.87727	−0.979544
$37$	9.20792	1.51377	0.756887	−	0.653546i	$-0.226720\pi$
$37$	9.20792	1.51377	0.756887	+	0.653546i	$0.226720\pi$
$38$	−6.92380	−1.12319
$39$	0	0
$40$	8.98214	1.42020
$41$	12.7603	1.99282	0.996411	−	0.0846473i	$-0.0269763\pi$
$41$	12.7603	1.99282	0.996411	+	0.0846473i	$0.0269763\pi$
$42$	4.39140	0.677608
$43$	−8.90654	−1.35824	−0.679118	−	0.734030i	$-0.737637\pi$
$43$	−8.90654	−1.35824	−0.679118	+	0.734030i	$0.737637\pi$
$44$	2.35137	0.354483
$45$	24.5447	3.65891
$46$	5.92613	0.873760
$47$	5.33535	0.778241	0.389121	−	0.921187i	$-0.372779\pi$
$47$	5.33535	0.778241	0.389121	+	0.921187i	$0.372779\pi$
$48$	7.14367	1.03110
$49$	−5.70153	−0.814505
$50$	−4.00729	−0.566716
$51$	7.01294	0.982008
$52$	0	0
$53$	0.413187	0.0567556	0.0283778	−	0.999597i	$-0.490966\pi$
$53$	0.413187	0.0567556	0.0283778	+	0.999597i	$0.490966\pi$
$54$	20.8584	2.83846
$55$	−9.81982	−1.32410
$56$	3.50800	0.468776
$57$	−20.5038	−2.71580
$58$	−7.09931	−0.932185
$59$	2.53271	0.329731	0.164866	−	0.986316i	$-0.447281\pi$
$59$	2.53271	0.329731	0.164866	+	0.986316i	$0.447281\pi$
$60$	6.88619	0.889003
$61$	0.648764	0.0830657	0.0415329	−	0.999137i	$-0.486776\pi$
$61$	0.648764	0.0830657	0.0415329	+	0.999137i	$0.486776\pi$
$62$	−1.14077	−0.144878
$63$	9.58600	1.20772
$64$	8.50116	1.06265
$65$	0	0
$66$	−12.9705	−1.59655
$67$	2.70298	0.330221	0.165111	−	0.986275i	$-0.447202\pi$
$67$	2.70298	0.330221	0.165111	+	0.986275i	$0.447202\pi$
$68$	1.45032	0.175878
$69$	17.5494	2.11270
$70$	−3.79272	−0.453316
$71$	−2.56026	−0.303847	−0.151923	−	0.988392i	$-0.548547\pi$
$71$	−2.56026	−0.303847	−0.151923	+	0.988392i	$0.548547\pi$
$72$	25.8979	3.05210
$73$	3.00395	0.351586	0.175793	−	0.984427i	$-0.443751\pi$
$73$	3.00395	0.351586	0.175793	+	0.984427i	$0.443751\pi$
$74$	−10.5041	−1.22108
$75$	−11.8670	−1.37028
$76$	−4.24033	−0.486399
$77$	−3.83516	−0.437057
$78$	0	0
$79$	−0.926660	−0.104257	−0.0521287	−	0.998640i	$-0.516601\pi$
$79$	−0.926660	−0.104257	−0.0521287	+	0.998640i	$0.516601\pi$
$80$	−6.16976	−0.689800
$81$	36.5317	4.05908
$82$	−14.5566	−1.60750
$83$	13.8393	1.51906	0.759528	−	0.650474i	$-0.225430\pi$
$83$	13.8393	1.51906	0.759528	+	0.650474i	$0.225430\pi$
$84$	2.68942	0.293440
$85$	−6.05685	−0.656958
$86$	10.1603	1.09562
$87$	−21.0236	−2.25396
$88$	−10.3612	−1.10451
$89$	11.3360	1.20161	0.600805	−	0.799396i	$-0.294847\pi$
$89$	11.3360	1.20161	0.600805	+	0.799396i	$0.294847\pi$
$90$	−27.9999	−2.95145
$91$	0	0
$92$	3.62933	0.378383
$93$	−3.37823	−0.350306
$94$	−6.08642	−0.627766
$95$	17.7085	1.81685
$96$	12.6507	1.29115
$97$	−8.11106	−0.823554	−0.411777	−	0.911285i	$-0.635092\pi$
$97$	−8.11106	−0.823554	−0.411777	+	0.911285i	$0.635092\pi$
$98$	6.50415	0.657018
$99$	−28.3132	−2.84559
$100$	−2.45418	−0.245418
$101$	2.09017	0.207980	0.103990	−	0.994578i	$-0.466839\pi$
$101$	2.09017	0.207980	0.103990	+	0.994578i	$0.466839\pi$
$102$	−8.00016	−0.792134
$103$	15.5394	1.53114	0.765570	−	0.643353i	$-0.222457\pi$
$103$	15.5394	1.53114	0.765570	+	0.643353i	$0.222457\pi$
$104$	0	0
$105$	−11.2316	−1.09609
$106$	−0.471352	−0.0457817
$107$	−17.9932	−1.73947	−0.869736	−	0.493517i	$-0.835711\pi$
$107$	−17.9932	−1.73947	−0.869736	+	0.493517i	$0.835711\pi$
$108$	12.7742	1.22920
$109$	−6.76445	−0.647916	−0.323958	−	0.946071i	$-0.605014\pi$
$109$	−6.76445	−0.647916	−0.323958	+	0.946071i	$0.605014\pi$
$110$	11.2022	1.06808
$111$	−31.1065	−2.95250
$112$	−2.40962	−0.227687
$113$	−2.54714	−0.239615	−0.119807	−	0.992797i	$-0.538228\pi$
$113$	−2.54714	−0.239615	−0.119807	+	0.992797i	$0.538228\pi$
$114$	23.3902	2.19069
$115$	−15.1568	−1.41338
$116$	−4.34782	−0.403685
$117$	0	0
$118$	−2.88925	−0.265977
$119$	−2.36552	−0.216847
$120$	−30.3437	−2.76999
$121$	0.327526	0.0297751
$122$	−0.740092	−0.0670047
$123$	−43.1072	−3.88684
$124$	−0.698640	−0.0627398
$125$	−4.33919	−0.388109
$126$	−10.9354	−0.974206
$127$	−11.8274	−1.04951	−0.524754	−	0.851254i	$-0.675843\pi$
$127$	−11.8274	−1.04951	−0.524754	+	0.851254i	$0.675843\pi$
$128$	−2.20836	−0.195193
$129$	30.0883	2.64913
$130$	0	0
$131$	−12.1927	−1.06528	−0.532639	−	0.846342i	$-0.678800\pi$
$131$	−12.1927	−1.06528	−0.532639	+	0.846342i	$0.678800\pi$
$132$	−7.94347	−0.691390
$133$	6.91610	0.599702
$134$	−3.08348	−0.266372
$135$	−53.3479	−4.59146
$136$	−6.39079	−0.548006
$137$	−10.2404	−0.874901	−0.437450	−	0.899243i	$-0.644118\pi$
$137$	−10.2404	−0.874901	−0.437450	+	0.899243i	$0.644118\pi$
$138$	−20.0198	−1.70420
$139$	5.50365	0.466814	0.233407	−	0.972379i	$-0.425013\pi$
$139$	5.50365	0.466814	0.233407	+	0.972379i	$0.425013\pi$
$140$	−2.32276	−0.196309
$141$	−18.0240	−1.51790
$142$	2.92067	0.245097
$143$	0	0
$144$	−17.7891	−1.48243
$145$	18.1574	1.50789
$146$	−3.42682	−0.283606
$147$	19.2611	1.58863
$148$	−6.43303	−0.528791
$149$	8.59247	0.703923	0.351961	−	0.936015i	$-0.385515\pi$
$149$	8.59247	0.703923	0.351961	+	0.936015i	$0.385515\pi$
$150$	13.5375	1.10534
$151$	7.41951	0.603791	0.301896	−	0.953341i	$-0.402381\pi$
$151$	7.41951	0.603791	0.301896	+	0.953341i	$0.402381\pi$
$152$	18.6848	1.51554
$153$	−17.4636	−1.41185
$154$	4.37504	0.352551
$155$	2.91767	0.234353
$156$	0	0
$157$	−2.94699	−0.235195	−0.117598	−	0.993061i	$-0.537519\pi$
$157$	−2.94699	−0.235195	−0.117598	+	0.993061i	$0.537519\pi$
$158$	1.05711	0.0840990
$159$	−1.39584	−0.110697
$160$	−10.9260	−0.863775
$161$	−5.91954	−0.466525
$162$	−41.6744	−3.27425
$163$	−7.96268	−0.623685	−0.311843	−	0.950134i	$-0.600946\pi$
$163$	−7.96268	−0.623685	−0.311843	+	0.950134i	$0.600946\pi$
$164$	−8.91485	−0.696133
$165$	33.1736	2.58256
$166$	−15.7874	−1.22534
$167$	11.4385	0.885139	0.442569	−	0.896734i	$-0.354067\pi$
$167$	11.4385	0.885139	0.442569	+	0.896734i	$0.354067\pi$
$168$	−11.8508	−0.914311
$169$	0	0
$170$	6.90949	0.529933
$171$	51.0584	3.90454
$172$	6.22247	0.474459
$173$	−9.39653	−0.714405	−0.357202	−	0.934027i	$-0.616269\pi$
$173$	−9.39653	−0.714405	−0.357202	+	0.934027i	$0.616269\pi$
$174$	23.9831	1.81815
$175$	4.00284	0.302586
$176$	7.11705	0.536468
$177$	−8.55609	−0.643115
$178$	−12.9317	−0.969275
$179$	−17.7155	−1.32412	−0.662059	−	0.749452i	$-0.730317\pi$
$179$	−17.7155	−1.32412	−0.662059	+	0.749452i	$0.730317\pi$
$180$	−17.1479	−1.27813
$181$	−6.71383	−0.499035	−0.249518	−	0.968370i	$-0.580272\pi$
$181$	−6.71383	−0.499035	−0.249518	+	0.968370i	$0.580272\pi$
$182$	0	0
$183$	−2.19167	−0.162013
$184$	−15.9925	−1.17898
$185$	26.8657	1.97520
$186$	3.85379	0.282573
$187$	6.98680	0.510926
$188$	−3.72749	−0.271855
$189$	−20.8352	−1.51554
$190$	−20.2014	−1.46556
$191$	24.7388	1.79004	0.895019	−	0.446028i	$-0.147162\pi$
$191$	24.7388	1.79004	0.895019	+	0.446028i	$0.147162\pi$
$192$	−28.7189	−2.07261
$193$	−1.22741	−0.0883506	−0.0441753	−	0.999024i	$-0.514066\pi$
$193$	−1.22741	−0.0883506	−0.0441753	+	0.999024i	$0.514066\pi$
$194$	9.25287	0.664317
$195$	0	0
$196$	3.98332	0.284523
$197$	−1.36218	−0.0970515	−0.0485258	−	0.998822i	$-0.515452\pi$
$197$	−1.36218	−0.0970515	−0.0485258	+	0.998822i	$0.515452\pi$
$198$	32.2989	2.29538
$199$	18.4676	1.30913	0.654566	−	0.756005i	$-0.272851\pi$
$199$	18.4676	1.30913	0.654566	+	0.756005i	$0.272851\pi$
$200$	10.8142	0.764682
$201$	−9.13128	−0.644071
$202$	−2.38441	−0.167766
$203$	7.09142	0.497720
$204$	−4.89952	−0.343035
$205$	37.2303	2.60028
$206$	−17.7269	−1.23509
$207$	−43.7013	−3.03745
$208$	0	0
$209$	−20.4274	−1.41299
$210$	12.8127	0.884158
$211$	−7.80102	−0.537045	−0.268522	−	0.963273i	$-0.586535\pi$
$211$	−7.80102	−0.537045	−0.268522	+	0.963273i	$0.586535\pi$
$212$	−0.288669	−0.0198259
$213$	8.64914	0.592629
$214$	20.5262	1.40314
$215$	−25.9863	−1.77225
$216$	−56.2892	−3.83000
$217$	1.13950	0.0773545
$218$	7.71669	0.522640
$219$	−10.1480	−0.685740
$220$	6.86052	0.462536
$221$	0	0
$222$	35.4854	2.38162
$223$	22.0365	1.47567	0.737837	−	0.674978i	$-0.235847\pi$
$223$	22.0365	1.47567	0.737837	+	0.674978i	$0.235847\pi$
$224$	−4.26717	−0.285112
$225$	29.5511	1.97007
$226$	2.90571	0.193285
$227$	17.3601	1.15223	0.576115	−	0.817369i	$-0.304568\pi$
$227$	17.3601	1.15223	0.576115	+	0.817369i	$0.304568\pi$
$228$	14.3248	0.948683
$229$	1.25868	0.0831760	0.0415880	−	0.999135i	$-0.486758\pi$
$229$	1.25868	0.0831760	0.0415880	+	0.999135i	$0.486758\pi$
$230$	17.2905	1.14010
$231$	12.9560	0.852445
$232$	19.1585	1.25782
$233$	5.72942	0.375347	0.187674	−	0.982231i	$-0.439905\pi$
$233$	5.72942	0.375347	0.187674	+	0.982231i	$0.439905\pi$
$234$	0	0
$235$	15.5668	1.01547
$236$	−1.76946	−0.115182
$237$	3.13047	0.203346
$238$	2.69852	0.174919
$239$	−15.9398	−1.03106	−0.515529	−	0.856872i	$-0.672404\pi$
$239$	−15.9398	−1.03106	−0.515529	+	0.856872i	$0.672404\pi$
$240$	20.8429	1.34540
$241$	6.29828	0.405708	0.202854	−	0.979209i	$-0.434978\pi$
$241$	6.29828	0.405708	0.202854	+	0.979209i	$0.434978\pi$
$242$	−0.373632	−0.0240180
$243$	−68.5593	−4.39808
$244$	−0.453253	−0.0290165
$245$	−16.6352	−1.06278
$246$	49.1754	3.13531
$247$	0	0
$248$	3.07853	0.195487
$249$	−46.7522	−2.96280
$250$	4.95002	0.313067
$251$	−16.4679	−1.03944	−0.519722	−	0.854336i	$-0.673964\pi$
$251$	−16.4679	−1.03944	−0.519722	+	0.854336i	$0.673964\pi$
$252$	−6.69716	−0.421882
$253$	17.4840	1.09921
$254$	13.4923	0.846583
$255$	20.4614	1.28134
$256$	−14.4831	−0.905194
$257$	−14.9187	−0.930603	−0.465301	−	0.885152i	$-0.654054\pi$
$257$	−14.9187	−0.930603	−0.465301	+	0.885152i	$0.654054\pi$
$258$	−34.3239	−2.13691
$259$	10.4925	0.651970
$260$	0	0
$261$	52.3527	3.24055
$262$	13.9091	0.859304
$263$	7.86024	0.484683	0.242342	−	0.970191i	$-0.422085\pi$
$263$	7.86024	0.484683	0.242342	+	0.970191i	$0.422085\pi$
$264$	35.0026	2.15426
$265$	1.20554	0.0740559
$266$	−7.88969	−0.483748
$267$	−38.2955	−2.34365
$268$	−1.88841	−0.115353
$269$	31.0076	1.89057	0.945283	−	0.326253i	$-0.105786\pi$
$269$	31.0076	1.89057	0.945283	+	0.326253i	$0.105786\pi$
$270$	60.8578	3.70369
$271$	−10.8133	−0.656858	−0.328429	−	0.944529i	$-0.606519\pi$
$271$	−10.8133	−0.656858	−0.328429	+	0.944529i	$0.606519\pi$
$272$	4.38979	0.266170
$273$	0	0
$274$	11.6820	0.705736
$275$	−11.8228	−0.712940
$276$	−12.2607	−0.738007
$277$	−23.5804	−1.41681	−0.708404	−	0.705807i	$-0.750585\pi$
$277$	−23.5804	−1.41681	−0.708404	+	0.705807i	$0.750585\pi$
$278$	−6.27841	−0.376554
$279$	8.41243	0.503639
$280$	10.2352	0.611669
$281$	−17.3565	−1.03540	−0.517702	−	0.855561i	$-0.673212\pi$
$281$	−17.3565	−1.03540	−0.517702	+	0.855561i	$0.673212\pi$
$282$	20.5613	1.22441
$283$	30.1166	1.79024	0.895122	−	0.445822i	$-0.147089\pi$
$283$	30.1166	1.79024	0.895122	+	0.445822i	$0.147089\pi$
$284$	1.78870	0.106140
$285$	−59.8234	−3.54363
$286$	0	0
$287$	14.5404	0.858292
$288$	−31.5026	−1.85631
$289$	−12.6905	−0.746503
$290$	−20.7134	−1.21633
$291$	27.4010	1.60628
$292$	−2.09868	−0.122816
$293$	15.1208	0.883364	0.441682	−	0.897172i	$-0.354382\pi$
$293$	15.1208	0.883364	0.441682	+	0.897172i	$0.354382\pi$
$294$	−21.9725	−1.28146
$295$	7.38962	0.430240
$296$	28.3469	1.64763
$297$	61.5388	3.57085
$298$	−9.80205	−0.567817
$299$	0	0
$300$	8.29077	0.478668
$301$	−10.1490	−0.584981
$302$	−8.46397	−0.487047
$303$	−7.06107	−0.405648
$304$	−12.8345	−0.736108
$305$	1.89288	0.108386
$306$	19.9219	1.13886
$307$	−4.21725	−0.240691	−0.120345	−	0.992732i	$-0.538400\pi$
$307$	−4.21725	−0.240691	−0.120345	+	0.992732i	$0.538400\pi$
$308$	2.67940	0.152673
$309$	−52.4956	−2.98637
$310$	−3.32839	−0.189040
$311$	−16.3930	−0.929562	−0.464781	−	0.885426i	$-0.653867\pi$
$311$	−16.3930	−0.929562	−0.464781	+	0.885426i	$0.653867\pi$
$312$	0	0
$313$	21.8252	1.23363	0.616816	−	0.787107i	$-0.288422\pi$
$313$	21.8252	1.23363	0.616816	+	0.787107i	$0.288422\pi$
$314$	3.36184	0.189720
$315$	27.9688	1.57586
$316$	0.647402	0.0364192
$317$	27.7658	1.55948	0.779741	−	0.626102i	$-0.215351\pi$
$317$	27.7658	1.55948	0.779741	+	0.626102i	$0.215351\pi$
$318$	1.59233	0.0892937
$319$	−20.9452	−1.17271
$320$	24.8036	1.38656
$321$	60.7853	3.39270
$322$	6.75284	0.376321
$323$	−12.5996	−0.701061
$324$	−25.5225	−1.41792
$325$	0	0
$326$	9.08360	0.503094
$327$	22.8518	1.26371
$328$	39.2830	2.16904
$329$	6.07965	0.335182
$330$	−37.8435	−2.08322
$331$	18.1162	0.995756	0.497878	−	0.867247i	$-0.334113\pi$
$331$	18.1162	0.995756	0.497878	+	0.867247i	$0.334113\pi$
$332$	−9.66867	−0.530637
$333$	77.4610	4.24484
$334$	−13.0487	−0.713995
$335$	7.88639	0.430880
$336$	8.14024	0.444087
$337$	14.0743	0.766674	0.383337	−	0.923608i	$-0.374775\pi$
$337$	14.0743	0.766674	0.383337	+	0.923608i	$0.374775\pi$
$338$	0	0
$339$	8.60483	0.467350
$340$	4.23156	0.229489
$341$	−3.36564	−0.182260
$342$	−58.2460	−3.14958
$343$	−14.4734	−0.781492
$344$	−27.4191	−1.47834
$345$	51.2032	2.75669
$346$	10.7193	0.576273
$347$	19.7318	1.05926	0.529629	−	0.848229i	$-0.322331\pi$
$347$	19.7318	1.05926	0.529629	+	0.848229i	$0.322331\pi$
$348$	14.6879	0.787355
$349$	15.6464	0.837535	0.418767	−	0.908094i	$-0.362462\pi$
$349$	15.6464	0.837535	0.418767	+	0.908094i	$0.362462\pi$
$350$	−4.56632	−0.244080
$351$	0	0
$352$	12.6035	0.671770
$353$	−19.1115	−1.01720	−0.508600	−	0.861003i	$-0.669837\pi$
$353$	−19.1115	−1.01720	−0.508600	+	0.861003i	$0.669837\pi$
$354$	9.76054	0.518767
$355$	−7.46999	−0.396466
$356$	−7.91976	−0.419746
$357$	7.99127	0.422943
$358$	20.2093	1.06810
$359$	5.21273	0.275117	0.137559	−	0.990494i	$-0.456074\pi$
$359$	5.21273	0.275117	0.137559	+	0.990494i	$0.456074\pi$
$360$	75.5616	3.98245
$361$	17.8376	0.938822
$362$	7.65895	0.402545
$363$	−1.10646	−0.0580739
$364$	0	0
$365$	8.76453	0.458756
$366$	2.50020	0.130688
$367$	−30.8444	−1.61006	−0.805031	−	0.593233i	$-0.797851\pi$
$367$	−30.8444	−1.61006	−0.805031	+	0.593233i	$0.797851\pi$
$368$	10.9851	0.572639
$369$	107.345	5.58816
$370$	−30.6476	−1.59329
$371$	0.470828	0.0244442
$372$	2.36017	0.122369
$373$	22.2465	1.15188	0.575941	−	0.817491i	$-0.304636\pi$
$373$	22.2465	1.15188	0.575941	+	0.817491i	$0.304636\pi$
$374$	−7.97035	−0.412137
$375$	14.6588	0.756976
$376$	16.4251	0.847058
$377$	0	0
$378$	23.7682	1.22250
$379$	−8.05156	−0.413581	−0.206790	−	0.978385i	$-0.566302\pi$
$379$	−8.05156	−0.413581	−0.206790	+	0.978385i	$0.566302\pi$
$380$	−12.3719	−0.634664
$381$	39.9555	2.04698
$382$	−28.2213	−1.44393
$383$	−23.7303	−1.21256	−0.606282	−	0.795250i	$-0.707340\pi$
$383$	−23.7303	−1.21256	−0.606282	+	0.795250i	$0.707340\pi$
$384$	7.46033	0.380708
$385$	−11.1897	−0.570281
$386$	1.40019	0.0712678
$387$	−74.9257	−3.80869
$388$	5.66672	0.287684
$389$	1.74252	0.0883495	0.0441747	−	0.999024i	$-0.485934\pi$
$389$	1.74252	0.0883495	0.0441747	+	0.999024i	$0.485934\pi$
$390$	0	0
$391$	10.7841	0.545375
$392$	−17.5523	−0.886528
$393$	41.1896	2.07774
$394$	1.55394	0.0782864
$395$	−2.70369	−0.136037
$396$	19.7808	0.994020
$397$	−21.8240	−1.09531	−0.547657	−	0.836703i	$-0.684480\pi$
$397$	−21.8240	−1.09531	−0.547657	+	0.836703i	$0.684480\pi$
$398$	−21.0673	−1.05601
$399$	−23.3642	−1.16967
$400$	−7.42822	−0.371411
$401$	−16.3502	−0.816491	−0.408245	−	0.912872i	$-0.633859\pi$
$401$	−16.3502	−0.816491	−0.408245	+	0.912872i	$0.633859\pi$
$402$	10.4167	0.519538
$403$	0	0
$404$	−1.46028	−0.0726515
$405$	106.588	5.29638
$406$	−8.08969	−0.401484
$407$	−30.9905	−1.53614
$408$	21.5896	1.06884
$409$	−15.1332	−0.748290	−0.374145	−	0.927370i	$-0.622064\pi$
$409$	−15.1332	−0.748290	−0.374145	+	0.927370i	$0.622064\pi$
$410$	−42.4712	−2.09751
$411$	34.5946	1.70643
$412$	−10.8564	−0.534858
$413$	2.88604	0.142013
$414$	49.8532	2.45015
$415$	40.3784	1.98210
$416$	0	0
$417$	−18.5926	−0.910483
$418$	23.3030	1.13979
$419$	3.35408	0.163858	0.0819288	−	0.996638i	$-0.473892\pi$
$419$	3.35408	0.163858	0.0819288	+	0.996638i	$0.473892\pi$
$420$	7.84683	0.382886
$421$	15.6796	0.764175	0.382087	−	0.924126i	$-0.375205\pi$
$421$	15.6796	0.764175	0.382087	+	0.924126i	$0.375205\pi$
$422$	8.89919	0.433206
$423$	44.8833	2.18230
$424$	1.27201	0.0617742
$425$	−7.29228	−0.353727
$426$	−9.86669	−0.478043
$427$	0.739269	0.0357757
$428$	12.5708	0.607633
$429$	0	0
$430$	29.6445	1.42958
$431$	35.8427	1.72648	0.863241	−	0.504792i	$-0.168431\pi$
$431$	35.8427	1.72648	0.863241	+	0.504792i	$0.168431\pi$
$432$	38.6647	1.86025
$433$	−30.9694	−1.48829	−0.744147	−	0.668016i	$-0.767144\pi$
$433$	−30.9694	−1.48829	−0.744147	+	0.668016i	$0.767144\pi$
$434$	−1.29991	−0.0623978
$435$	−61.3398	−2.94102
$436$	4.72591	0.226330
$437$	−31.5296	−1.50826
$438$	11.5766	0.553151
$439$	18.7150	0.893217	0.446608	−	0.894730i	$-0.352632\pi$
$439$	18.7150	0.893217	0.446608	+	0.894730i	$0.352632\pi$
$440$	−30.2306	−1.44119
$441$	−47.9638	−2.28399
$442$	0	0
$443$	22.4081	1.06464	0.532320	−	0.846543i	$-0.321320\pi$
$443$	22.4081	1.06464	0.532320	+	0.846543i	$0.321320\pi$
$444$	21.7322	1.03137
$445$	33.0746	1.56789
$446$	−25.1386	−1.19035
$447$	−29.0273	−1.37295
$448$	9.68710	0.457673
$449$	−6.08518	−0.287177	−0.143589	−	0.989637i	$-0.545864\pi$
$449$	−6.08518	−0.287177	−0.143589	+	0.989637i	$0.545864\pi$
$450$	−33.7111	−1.58915
$451$	−42.9465	−2.02227
$452$	1.77954	0.0837023
$453$	−25.0648	−1.17765
$454$	−19.8039	−0.929443
$455$	0	0
$456$	−63.1217	−2.95594
$457$	14.1539	0.662093	0.331047	−	0.943614i	$-0.392598\pi$
$457$	14.1539	0.662093	0.331047	+	0.943614i	$0.392598\pi$
$458$	−1.43587	−0.0670937
$459$	37.9571	1.77168
$460$	10.5892	0.493723
$461$	6.61349	0.308021	0.154010	−	0.988069i	$-0.450781\pi$
$461$	6.61349	0.308021	0.154010	+	0.988069i	$0.450781\pi$
$462$	−14.7799	−0.687622
$463$	−14.7433	−0.685180	−0.342590	−	0.939485i	$-0.611304\pi$
$463$	−14.7433	−0.685180	−0.342590	+	0.939485i	$0.611304\pi$
$464$	−13.1598	−0.610929
$465$	−9.85655	−0.457087
$466$	−6.53596	−0.302773
$467$	0.638111	0.0295282	0.0147641	−	0.999891i	$-0.495300\pi$
$467$	0.638111	0.0295282	0.0147641	+	0.999891i	$0.495300\pi$
$468$	0	0
$469$	3.08005	0.142224
$470$	−17.7582	−0.819123
$471$	9.95560	0.458730
$472$	7.79704	0.358888
$473$	29.9762	1.37831
$474$	−3.57115	−0.164028
$475$	21.3205	0.978253
$476$	1.65265	0.0757490
$477$	3.47591	0.159151
$478$	18.1836	0.831699
$479$	26.1477	1.19472	0.597359	−	0.801974i	$-0.296217\pi$
$479$	26.1477	1.19472	0.597359	+	0.801974i	$0.296217\pi$
$480$	36.9105	1.68472
$481$	0	0
$482$	−7.18489	−0.327263
$483$	19.9976	0.909921
$484$	−0.228823	−0.0104010
$485$	−23.6654	−1.07459
$486$	78.2105	3.54770
$487$	29.6645	1.34423	0.672114	−	0.740448i	$-0.265386\pi$
$487$	29.6645	1.34423	0.672114	+	0.740448i	$0.265386\pi$
$488$	1.99724	0.0904109
$489$	26.8998	1.21645
$490$	18.9769	0.857291
$491$	16.2858	0.734966	0.367483	−	0.930030i	$-0.380220\pi$
$491$	16.2858	0.734966	0.367483	+	0.930030i	$0.380220\pi$
$492$	30.1164	1.35775
$493$	−12.9190	−0.581842
$494$	0	0
$495$	−82.6086	−3.71298
$496$	−2.11462	−0.0949493
$497$	−2.91742	−0.130864
$498$	53.3336	2.38994
$499$	−4.66946	−0.209034	−0.104517	−	0.994523i	$-0.533330\pi$
$499$	−4.66946	−0.209034	−0.104517	+	0.994523i	$0.533330\pi$
$500$	3.03153	0.135574
$501$	−38.6419	−1.72639
$502$	18.7861	0.838464
$503$	20.3155	0.905823	0.452911	−	0.891556i	$-0.350385\pi$
$503$	20.3155	0.905823	0.452911	+	0.891556i	$0.350385\pi$
$504$	29.5108	1.31452
$505$	6.09842	0.271376
$506$	−19.9452	−0.886673
$507$	0	0
$508$	8.26307	0.366614
$509$	−23.4224	−1.03818	−0.519090	−	0.854720i	$-0.673729\pi$
$509$	−23.4224	−1.03818	−0.519090	+	0.854720i	$0.673729\pi$
$510$	−23.3418	−1.03359
$511$	3.42301	0.151425
$512$	20.9386	0.925365
$513$	−110.976	−4.89969
$514$	17.0188	0.750668
$515$	45.3387	1.99786
$516$	−21.0209	−0.925395
$517$	−17.9569	−0.789742
$518$	−11.9695	−0.525910
$519$	31.7436	1.39339
$520$	0	0
$521$	25.4082	1.11315	0.556576	−	0.830797i	$-0.312115\pi$
$521$	25.4082	1.11315	0.556576	+	0.830797i	$0.312115\pi$
$522$	−59.7225	−2.61398
$523$	−42.8337	−1.87299	−0.936493	−	0.350687i	$-0.885948\pi$
$523$	−42.8337	−1.87299	−0.936493	+	0.350687i	$0.885948\pi$
$524$	8.51829	0.372123
$525$	−13.5225	−0.590170
$526$	−8.96674	−0.390968
$527$	−2.07592	−0.0904286
$528$	−24.0430	−1.04634
$529$	3.98639	0.173321
$530$	−1.37525	−0.0597370
$531$	21.3063	0.924614
$532$	−4.83187	−0.209488
$533$	0	0
$534$	43.6864	1.89049
$535$	−52.4983	−2.26970
$536$	8.32120	0.359421
$537$	59.8470	2.58259
$538$	−35.3726	−1.52502
$539$	19.1893	0.826542
$540$	37.2710	1.60389
$541$	0.765891	0.0329282	0.0164641	−	0.999864i	$-0.494759\pi$
$541$	0.765891	0.0329282	0.0164641	+	0.999864i	$0.494759\pi$
$542$	12.3354	0.529853
$543$	22.6809	0.973329
$544$	7.77384	0.333301
$545$	−19.7364	−0.845415
$546$	0	0
$547$	−31.8358	−1.36120	−0.680600	−	0.732655i	$-0.738281\pi$
$547$	−31.8358	−1.36120	−0.680600	+	0.732655i	$0.738281\pi$
$548$	7.15439	0.305620
$549$	5.45769	0.232928
$550$	13.4871	0.575091
$551$	37.7714	1.60912
$552$	54.0263	2.29951
$553$	−1.05593	−0.0449028
$554$	26.8998	1.14286
$555$	−90.7584	−3.85248
$556$	−3.84507	−0.163067
$557$	17.3002	0.733032	0.366516	−	0.930412i	$-0.380551\pi$
$557$	17.3002	0.733032	0.366516	+	0.930412i	$0.380551\pi$
$558$	−9.59667	−0.406259
$559$	0	0
$560$	−7.03047	−0.297091
$561$	−23.6030	−0.996521
$562$	19.7998	0.835206
$563$	−35.9186	−1.51379	−0.756895	−	0.653537i	$-0.773285\pi$
$563$	−35.9186	−1.51379	−0.756895	+	0.653537i	$0.773285\pi$
$564$	12.5923	0.530233
$565$	−7.43171	−0.312654
$566$	−34.3561	−1.44409
$567$	41.6280	1.74821
$568$	−7.88184	−0.330715
$569$	25.5330	1.07040	0.535199	−	0.844726i	$-0.320237\pi$
$569$	25.5330	1.07040	0.535199	+	0.844726i	$0.320237\pi$
$570$	68.2448	2.85846
$571$	−6.70265	−0.280497	−0.140249	−	0.990116i	$-0.544790\pi$
$571$	−6.70265	−0.280497	−0.140249	+	0.990116i	$0.544790\pi$
$572$	0	0
$573$	−83.5734	−3.49133
$574$	−16.5873	−0.692339
$575$	−18.2484	−0.761010
$576$	71.5155	2.97981
$577$	−10.1551	−0.422762	−0.211381	−	0.977404i	$-0.567796\pi$
$577$	−10.1551	−0.422762	−0.211381	+	0.977404i	$0.567796\pi$
$578$	14.4770	0.602164
$579$	4.14646	0.172321
$580$	−12.6855	−0.526736
$581$	15.7699	0.654245
$582$	−31.2583	−1.29570
$583$	−1.39064	−0.0575943
$584$	9.24775	0.382675
$585$	0	0
$586$	−17.2493	−0.712563
$587$	18.2972	0.755206	0.377603	−	0.925968i	$-0.376748\pi$
$587$	18.2972	0.755206	0.377603	+	0.925968i	$0.376748\pi$
$588$	−13.4566	−0.554940
$589$	6.06940	0.250085
$590$	−8.42987	−0.347052
$591$	4.60177	0.189291
$592$	−19.4713	−0.800264
$593$	−41.7882	−1.71604	−0.858018	−	0.513619i	$-0.828304\pi$
$593$	−41.7882	−1.71604	−0.858018	+	0.513619i	$0.828304\pi$
$594$	−70.2018	−2.88041
$595$	−6.90180	−0.282946
$596$	−6.00305	−0.245894
$597$	−62.3877	−2.55336
$598$	0	0
$599$	−20.6797	−0.844949	−0.422475	−	0.906375i	$-0.638838\pi$
$599$	−20.6797	−0.844949	−0.422475	+	0.906375i	$0.638838\pi$
$600$	−36.5330	−1.49145
$601$	9.84016	0.401389	0.200694	−	0.979654i	$-0.435680\pi$
$601$	9.84016	0.401389	0.200694	+	0.979654i	$0.435680\pi$
$602$	11.5777	0.471873
$603$	22.7386	0.925988
$604$	−5.18357	−0.210916
$605$	0.955611	0.0388511
$606$	8.05507	0.327215
$607$	2.70635	0.109848	0.0549238	−	0.998491i	$-0.482508\pi$
$607$	2.70635	0.109848	0.0549238	+	0.998491i	$0.482508\pi$
$608$	−22.7285	−0.921761
$609$	−23.9564	−0.970764
$610$	−2.15934	−0.0874292
$611$	0	0
$612$	12.2007	0.493186
$613$	31.7108	1.28079	0.640393	−	0.768048i	$-0.278772\pi$
$613$	31.7108	1.28079	0.640393	+	0.768048i	$0.278772\pi$
$614$	4.81091	0.194153
$615$	−125.772	−5.07163
$616$	−11.8067	−0.475704
$617$	−0.765125	−0.0308028	−0.0154014	−	0.999881i	$-0.504903\pi$
$617$	−0.765125	−0.0308028	−0.0154014	+	0.999881i	$0.504903\pi$
$618$	59.8854	2.40895
$619$	−6.15492	−0.247387	−0.123694	−	0.992320i	$-0.539474\pi$
$619$	−6.15492	−0.247387	−0.123694	+	0.992320i	$0.539474\pi$
$620$	−2.03840	−0.0818641
$621$	94.9848	3.81161
$622$	18.7007	0.749829
$623$	12.9174	0.517523
$624$	0	0
$625$	−30.2243	−1.20897
$626$	−24.8975	−0.995106
$627$	69.0085	2.75593
$628$	2.05888	0.0821584
$629$	−19.1149	−0.762162
$630$	−31.9060	−1.27116
$631$	31.8837	1.26927	0.634636	−	0.772812i	$-0.281150\pi$
$631$	31.8837	1.26927	0.634636	+	0.772812i	$0.281150\pi$
$632$	−2.85275	−0.113476
$633$	26.3536	1.04746
$634$	−31.6744	−1.25795
$635$	−34.5083	−1.36942
$636$	0.975190	0.0386688
$637$	0	0
$638$	23.8937	0.945961
$639$	−21.5380	−0.852030
$640$	−6.44325	−0.254692
$641$	24.5170	0.968361	0.484181	−	0.874968i	$-0.339118\pi$
$641$	24.5170	0.968361	0.484181	+	0.874968i	$0.339118\pi$
$642$	−69.3421	−2.73672
$643$	36.9102	1.45560	0.727799	−	0.685791i	$-0.240543\pi$
$643$	36.9102	1.45560	0.727799	+	0.685791i	$0.240543\pi$
$644$	4.13563	0.162967
$645$	87.7878	3.45664
$646$	14.3733	0.565509
$647$	9.69981	0.381339	0.190669	−	0.981654i	$-0.438934\pi$
$647$	9.69981	0.381339	0.190669	+	0.981654i	$0.438934\pi$
$648$	112.464	4.41801
$649$	−8.52420	−0.334604
$650$	0	0
$651$	−3.84950	−0.150874
$652$	5.56305	0.217866
$653$	44.4135	1.73803	0.869017	−	0.494782i	$-0.164752\pi$
$653$	44.4135	1.73803	0.869017	+	0.494782i	$0.164752\pi$
$654$	−26.0687	−1.01937
$655$	−35.5742	−1.39000
$656$	−26.9832	−1.05352
$657$	25.2705	0.985897
$658$	−6.93550	−0.270374
$659$	−4.87147	−0.189766	−0.0948828	−	0.995488i	$-0.530248\pi$
$659$	−4.87147	−0.189766	−0.0948828	+	0.995488i	$0.530248\pi$
$660$	−23.1764	−0.902141
$661$	15.7653	0.613197	0.306599	−	0.951839i	$-0.400809\pi$
$661$	15.7653	0.613197	0.306599	+	0.951839i	$0.400809\pi$
$662$	−20.6664	−0.803224
$663$	0	0
$664$	42.6046	1.65338
$665$	20.1789	0.782504
$666$	−88.3653	−3.42409
$667$	−32.3288	−1.25178
$668$	−7.99141	−0.309197
$669$	−74.4444	−2.87819
$670$	−8.99657	−0.347568
$671$	−2.18351	−0.0842933
$672$	14.4155	0.556089
$673$	−22.9334	−0.884018	−0.442009	−	0.897011i	$-0.645734\pi$
$673$	−22.9334	−0.884018	−0.442009	+	0.897011i	$0.645734\pi$
$674$	−16.0555	−0.618436
$675$	−64.2294	−2.47219
$676$	0	0
$677$	19.0171	0.730888	0.365444	−	0.930833i	$-0.380917\pi$
$677$	19.0171	0.730888	0.365444	+	0.930833i	$0.380917\pi$
$678$	−9.81614	−0.376987
$679$	−9.24258	−0.354698
$680$	−18.6462	−0.715050
$681$	−58.6464	−2.24733
$682$	3.83943	0.147019
$683$	−26.6680	−1.02042	−0.510212	−	0.860049i	$-0.670433\pi$
$683$	−26.6680	−1.02042	−0.510212	+	0.860049i	$0.670433\pi$
$684$	−35.6715	−1.36393
$685$	−29.8782	−1.14159
$686$	16.5109	0.630389
$687$	−4.25211	−0.162228
$688$	18.8340	0.718038
$689$	0	0
$690$	−58.4112	−2.22368
$691$	47.9688	1.82482	0.912409	−	0.409279i	$-0.134220\pi$
$691$	47.9688	1.82482	0.912409	+	0.409279i	$0.134220\pi$
$692$	6.56479	0.249556
$693$	−32.2630	−1.22557
$694$	−22.5095	−0.854448
$695$	16.0578	0.609108
$696$	−64.7218	−2.45327
$697$	−26.4894	−1.00336
$698$	−17.8490	−0.675595
$699$	−19.3553	−0.732085
$700$	−2.79654	−0.105699
$701$	−4.22673	−0.159641	−0.0798206	−	0.996809i	$-0.525435\pi$
$701$	−4.22673	−0.159641	−0.0798206	+	0.996809i	$0.525435\pi$
$702$	0	0
$703$	55.8866	2.10780
$704$	−28.6118	−1.07835
$705$	−52.5882	−1.98059
$706$	21.8018	0.820522
$707$	2.38176	0.0895751
$708$	5.97763	0.224653
$709$	−40.8477	−1.53407	−0.767033	−	0.641607i	$-0.778268\pi$
$709$	−40.8477	−1.53407	−0.767033	+	0.641607i	$0.778268\pi$
$710$	8.52155	0.319808
$711$	−7.79547	−0.292353
$712$	34.8981	1.30786
$713$	−5.19484	−0.194548
$714$	−9.11621	−0.341166
$715$	0	0
$716$	12.3767	0.462541
$717$	53.8482	2.01100
$718$	−5.94653	−0.221923
$719$	29.2255	1.08993	0.544963	−	0.838460i	$-0.316544\pi$
$719$	29.2255	1.08993	0.544963	+	0.838460i	$0.316544\pi$
$720$	−51.9027	−1.93430
$721$	17.7072	0.659449
$722$	−20.3487	−0.757298
$723$	−21.2770	−0.791301
$724$	4.69055	0.174323
$725$	21.8610	0.811896
$726$	1.26221	0.0468452
$727$	5.76839	0.213938	0.106969	−	0.994262i	$-0.465886\pi$
$727$	5.76839	0.213938	0.106969	+	0.994262i	$0.465886\pi$
$728$	0	0
$729$	122.014	4.51903
$730$	−9.99832	−0.370055
$731$	18.4893	0.683851
$732$	1.53119	0.0565945
$733$	−20.6833	−0.763956	−0.381978	−	0.924171i	$-0.624757\pi$
$733$	−20.6833	−0.763956	−0.381978	+	0.924171i	$0.624757\pi$
$734$	35.1864	1.29875
$735$	56.1975	2.07287
$736$	19.4535	0.717064
$737$	−9.09725	−0.335101
$738$	−122.456	−4.50767
$739$	−15.7093	−0.577877	−0.288939	−	0.957348i	$-0.593302\pi$
$739$	−15.7093	−0.577877	−0.288939	+	0.957348i	$0.593302\pi$
$740$	−18.7694	−0.689978
$741$	0	0
$742$	−0.537107	−0.0197178
$743$	−27.6773	−1.01538	−0.507692	−	0.861539i	$-0.669501\pi$
$743$	−27.6773	−1.01538	−0.507692	+	0.861539i	$0.669501\pi$
$744$	−10.4000	−0.381282
$745$	25.0700	0.918493
$746$	−25.3782	−0.929162
$747$	116.422	4.25965
$748$	−4.88126	−0.178477
$749$	−20.5034	−0.749176
$750$	−16.7223	−0.610612
$751$	29.2811	1.06848	0.534241	−	0.845332i	$-0.320598\pi$
$751$	29.2811	1.06848	0.534241	+	0.845332i	$0.320598\pi$
$752$	−11.2823	−0.411421
$753$	55.6323	2.02735
$754$	0	0
$755$	21.6477	0.787840
$756$	14.5563	0.529408
$757$	−4.94846	−0.179855	−0.0899275	−	0.995948i	$-0.528664\pi$
$757$	−4.94846	−0.179855	−0.0899275	+	0.995948i	$0.528664\pi$
$758$	9.18499	0.333614
$759$	−59.0648	−2.14392
$760$	54.5162	1.97751
$761$	18.5148	0.671162	0.335581	−	0.942011i	$-0.391067\pi$
$761$	18.5148	0.671162	0.335581	+	0.942011i	$0.391067\pi$
$762$	−45.5801	−1.65119
$763$	−7.70811	−0.279052
$764$	−17.2835	−0.625296
$765$	−50.9529	−1.84221
$766$	27.0709	0.978111
$767$	0	0
$768$	48.9272	1.76551
$769$	22.0378	0.794702	0.397351	−	0.917667i	$-0.369929\pi$
$769$	22.0378	0.794702	0.397351	+	0.917667i	$0.369929\pi$
$770$	12.7649	0.460015
$771$	50.3988	1.81507
$772$	0.857515	0.0308627
$773$	−2.44881	−0.0880776	−0.0440388	−	0.999030i	$-0.514023\pi$
$773$	−2.44881	−0.0880776	−0.0440388	+	0.999030i	$0.514023\pi$
$774$	85.4731	3.07227
$775$	3.51279	0.126183
$776$	−24.9702	−0.896377
$777$	−35.4459	−1.27162
$778$	−1.98782	−0.0712669
$779$	77.4473	2.77484
$780$	0	0
$781$	8.61691	0.308337
$782$	−12.3022	−0.439925
$783$	−113.789	−4.06648
$784$	12.0566	0.430592
$785$	−8.59833	−0.306888
$786$	−46.9880	−1.67601
$787$	−29.7860	−1.06176	−0.530878	−	0.847448i	$-0.678138\pi$
$787$	−29.7860	−1.06176	−0.530878	+	0.847448i	$0.678138\pi$
$788$	0.951676	0.0339021
$789$	−26.5537	−0.945337
$790$	3.08429	0.109734
$791$	−2.90248	−0.103200
$792$	−87.1631	−3.09721
$793$	0	0
$794$	24.8962	0.883533
$795$	−4.07260	−0.144440
$796$	−12.9022	−0.457306
$797$	−18.1431	−0.642662	−0.321331	−	0.946967i	$-0.604130\pi$
$797$	−18.1431	−0.642662	−0.321331	+	0.946967i	$0.604130\pi$
$798$	26.6532	0.943513
$799$	−11.0758	−0.391833
$800$	−13.1546	−0.465084
$801$	95.3630	3.36949
$802$	18.6519	0.658620
$803$	−10.1102	−0.356781
$804$	6.37948	0.224987
$805$	−17.2713	−0.608732
$806$	0	0
$807$	−104.751	−3.68740
$808$	6.43466	0.226370
$809$	34.1959	1.20226	0.601131	−	0.799150i	$-0.294717\pi$
$809$	34.1959	1.20226	0.601131	+	0.799150i	$0.294717\pi$
$810$	−121.592	−4.27231
$811$	31.7652	1.11543	0.557713	−	0.830034i	$-0.311679\pi$
$811$	31.7652	1.11543	0.557713	+	0.830034i	$0.311679\pi$
$812$	−4.95435	−0.173864
$813$	36.5296	1.28115
$814$	35.3531	1.23913
$815$	−23.2325	−0.813798
$816$	−14.8297	−0.519144
$817$	−54.0574	−1.89123
$818$	17.2636	0.603606
$819$	0	0
$820$	−26.0106	−0.908329
$821$	3.16400	0.110424	0.0552122	−	0.998475i	$-0.482416\pi$
$821$	3.16400	0.110424	0.0552122	+	0.998475i	$0.482416\pi$
$822$	−39.4645	−1.37648
$823$	45.0016	1.56866	0.784328	−	0.620346i	$-0.213008\pi$
$823$	45.0016	1.56866	0.784328	+	0.620346i	$0.213008\pi$
$824$	47.8385	1.66653
$825$	39.9401	1.39053
$826$	−3.29231	−0.114554
$827$	5.14633	0.178955	0.0894777	−	0.995989i	$-0.471480\pi$
$827$	5.14633	0.178955	0.0894777	+	0.995989i	$0.471480\pi$
$828$	30.5315	1.06104
$829$	1.03021	0.0357806	0.0178903	−	0.999840i	$-0.494305\pi$
$829$	1.03021	0.0357806	0.0178903	+	0.999840i	$0.494305\pi$
$830$	−46.0625	−1.59885
$831$	79.6600	2.76337
$832$	0	0
$833$	11.8359	0.410091
$834$	21.2099	0.734439
$835$	33.3738	1.15495
$836$	14.2714	0.493587
$837$	−18.2844	−0.632003
$838$	−3.82624	−0.132175
$839$	30.1645	1.04139	0.520697	−	0.853742i	$-0.325672\pi$
$839$	30.1645	1.04139	0.520697	+	0.853742i	$0.325672\pi$
$840$	−34.5768	−1.19301
$841$	9.72888	0.335479
$842$	−17.8868	−0.616419
$843$	58.6343	2.01947
$844$	5.45011	0.187601
$845$	0	0
$846$	−51.2016	−1.76035
$847$	0.373217	0.0128239
$848$	−0.873734	−0.0300041
$849$	−101.741	−3.49173
$850$	8.31882	0.285333
$851$	−47.8337	−1.63972
$852$	−6.04264	−0.207017
$853$	32.1996	1.10249	0.551246	−	0.834343i	$-0.314153\pi$
$853$	32.1996	1.10249	0.551246	+	0.834343i	$0.314153\pi$
$854$	−0.843337	−0.0288584
$855$	148.972	5.09472
$856$	−55.3928	−1.89329
$857$	55.4890	1.89547	0.947734	−	0.319061i	$-0.103368\pi$
$857$	55.4890	1.89547	0.947734	+	0.319061i	$0.103368\pi$
$858$	0	0
$859$	51.5181	1.75778	0.878888	−	0.477028i	$-0.158286\pi$
$859$	51.5181	1.75778	0.878888	+	0.477028i	$0.158286\pi$
$860$	18.1551	0.619084
$861$	−49.1208	−1.67403
$862$	−40.8883	−1.39266
$863$	−12.1067	−0.412118	−0.206059	−	0.978540i	$-0.566064\pi$
$863$	−12.1067	−0.412118	−0.206059	+	0.978540i	$0.566064\pi$
$864$	68.4709	2.32943
$865$	−27.4159	−0.932170
$866$	35.3290	1.20053
$867$	42.8716	1.45600
$868$	−0.796103	−0.0270215
$869$	3.11880	0.105798
$870$	69.9747	2.37237
$871$	0	0
$872$	−20.8246	−0.705209
$873$	−68.2338	−2.30936
$874$	35.9680	1.21664
$875$	−4.94452	−0.167155
$876$	7.08982	0.239543
$877$	10.8413	0.366085	0.183042	−	0.983105i	$-0.441405\pi$
$877$	10.8413	0.366085	0.183042	+	0.983105i	$0.441405\pi$
$878$	−21.3495	−0.720511
$879$	−51.0814	−1.72293
$880$	20.7652	0.699995
$881$	−7.96978	−0.268509	−0.134254	−	0.990947i	$-0.542864\pi$
$881$	−7.96978	−0.268509	−0.134254	+	0.990947i	$0.542864\pi$
$882$	54.7157	1.84237
$883$	−25.7999	−0.868236	−0.434118	−	0.900856i	$-0.642940\pi$
$883$	−25.7999	−0.868236	−0.434118	+	0.900856i	$0.642940\pi$
$884$	0	0
$885$	−24.9638	−0.839150
$886$	−25.5625	−0.858789
$887$	11.4159	0.383307	0.191654	−	0.981463i	$-0.438615\pi$
$887$	11.4159	0.383307	0.191654	+	0.981463i	$0.438615\pi$
$888$	−95.7623	−3.21357
$889$	−13.4773	−0.452015
$890$	−37.7305	−1.26473
$891$	−122.953	−4.11907
$892$	−15.3956	−0.515483
$893$	32.3824	1.08364
$894$	33.1136	1.10748
$895$	−51.6879	−1.72774
$896$	−2.51643	−0.0840680
$897$	0	0
$898$	6.94180	0.231651
$899$	6.22325	0.207557
$900$	−20.6456	−0.688186
$901$	−0.857744	−0.0285756
$902$	48.9922	1.63126
$903$	34.2858	1.14096
$904$	−7.84145	−0.260803
$905$	−19.5887	−0.651152
$906$	28.5932	0.949946
$907$	−33.9010	−1.12566	−0.562832	−	0.826572i	$-0.690288\pi$
$907$	−33.9010	−1.12566	−0.562832	+	0.826572i	$0.690288\pi$
$908$	−12.1285	−0.402497
$909$	17.5834	0.583205
$910$	0	0
$911$	9.18348	0.304262	0.152131	−	0.988360i	$-0.451386\pi$
$911$	9.18348	0.304262	0.152131	+	0.988360i	$0.451386\pi$
$912$	43.3578	1.43572
$913$	−46.5780	−1.54151
$914$	−16.1464	−0.534076
$915$	−6.39458	−0.211398
$916$	−0.879365	−0.0290550
$917$	−13.8936	−0.458807
$918$	−43.3004	−1.42912
$919$	−29.5067	−0.973336	−0.486668	−	0.873587i	$-0.661788\pi$
$919$	−29.5067	−0.973336	−0.486668	+	0.873587i	$0.661788\pi$
$920$	−46.6608	−1.53836
$921$	14.2468	0.469449
$922$	−7.54448	−0.248464
$923$	0	0
$924$	−9.05161	−0.297776
$925$	32.3455	1.06351
$926$	16.8187	0.552698
$927$	130.724	4.29354
$928$	−23.3046	−0.765012
$929$	34.6310	1.13621	0.568103	−	0.822958i	$-0.307678\pi$
$929$	34.6310	1.13621	0.568103	+	0.822958i	$0.307678\pi$
$930$	11.2441	0.368708
$931$	−34.6049	−1.13413
$932$	−4.00281	−0.131116
$933$	55.3793	1.81304
$934$	−0.727939	−0.0238189
$935$	20.3852	0.666667
$936$	0	0
$937$	16.9914	0.555085	0.277542	−	0.960713i	$-0.410480\pi$
$937$	16.9914	0.555085	0.277542	+	0.960713i	$0.410480\pi$
$938$	−3.51364	−0.114724
$939$	−73.7304	−2.40610
$940$	−10.8756	−0.354723
$941$	1.74044	0.0567366	0.0283683	−	0.999598i	$-0.490969\pi$
$941$	1.74044	0.0567366	0.0283683	+	0.999598i	$0.490969\pi$
$942$	−11.3571	−0.370033
$943$	−66.2877	−2.15862
$944$	−5.35573	−0.174314
$945$	−60.7902	−1.97750
$946$	−34.1960	−1.11181
$947$	−4.00295	−0.130078	−0.0650392	−	0.997883i	$-0.520717\pi$
$947$	−4.00295	−0.130078	−0.0650392	+	0.997883i	$0.520717\pi$
$948$	−2.18707	−0.0710328
$949$	0	0
$950$	−24.3218	−0.789105
$951$	−93.7992	−3.04165
$952$	−7.28233	−0.236022
$953$	−6.11078	−0.197948	−0.0989738	−	0.995090i	$-0.531556\pi$
$953$	−6.11078	−0.197948	−0.0989738	+	0.995090i	$0.531556\pi$
$954$	−3.96522	−0.128379
$955$	72.1797	2.33568
$956$	11.1362	0.360169
$957$	70.7578	2.28727
$958$	−29.8285	−0.963717
$959$	−11.6690	−0.376813
$960$	−83.7922	−2.70438
$961$	1.00000	0.0322581
$962$	0	0
$963$	−151.367	−4.87773
$964$	−4.40023	−0.141722
$965$	−3.58116	−0.115282
$966$	−22.8127	−0.733985
$967$	−15.5955	−0.501517	−0.250758	−	0.968050i	$-0.580680\pi$
$967$	−15.5955	−0.501517	−0.250758	+	0.968050i	$0.580680\pi$
$968$	1.00830	0.0324079
$969$	42.5644	1.36736
$970$	26.9968	0.866815
$971$	0.430308	0.0138092	0.00690462	−	0.999976i	$-0.497802\pi$
$971$	0.430308	0.0138092	0.00690462	+	0.999976i	$0.497802\pi$
$972$	47.8983	1.53634
$973$	6.27143	0.201053
$974$	−33.8405	−1.08432
$975$	0	0
$976$	−1.37189	−0.0439131
$977$	28.6092	0.915290	0.457645	−	0.889135i	$-0.348693\pi$
$977$	28.6092	0.915290	0.457645	+	0.889135i	$0.348693\pi$
$978$	−30.6865	−0.981246
$979$	−38.1528	−1.21937
$980$	11.6220	0.371251
$981$	−56.9055	−1.81685
$982$	−18.5783	−0.592859
$983$	38.7895	1.23719	0.618596	−	0.785709i	$-0.287702\pi$
$983$	38.7895	1.23719	0.618596	+	0.785709i	$0.287702\pi$
$984$	−132.707	−4.23054
$985$	−3.97440	−0.126635
$986$	14.7376	0.469341
$987$	−20.5385	−0.653747
$988$	0	0
$989$	46.2681	1.47124
$990$	94.2375	2.99506
$991$	−6.97614	−0.221604	−0.110802	−	0.993842i	$-0.535342\pi$
$991$	−6.97614	−0.221604	−0.110802	+	0.993842i	$0.535342\pi$
$992$	−3.74476	−0.118896
$993$	−61.2006	−1.94214
$994$	3.32811	0.105561
$995$	53.8823	1.70818
$996$	32.6630	1.03497
$997$	−51.2573	−1.62334	−0.811668	−	0.584119i	$-0.801440\pi$
$997$	−51.2573	−1.62334	−0.811668	+	0.584119i	$0.801440\pi$
$998$	5.32679	0.168616
$999$	−168.362	−5.32673

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.v.1.20	yes	54
13.12	even	2		5239.2.a.u.1.35	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.35	✓	54	13.12	even	2
5239.2.a.v.1.20	yes	54	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q-1.14077 q^{2} -3.37823 q^{3} -0.698640 q^{4} +2.91767 q^{5} +3.85379 q^{6} +1.13950 q^{7} +3.07853 q^{8} +8.41243 q^{9} +O(q^{10})\)	\(q-1.14077 q^{2} -3.37823 q^{3} -0.698640 q^{4} +2.91767 q^{5} +3.85379 q^{6} +1.13950 q^{7} +3.07853 q^{8} +8.41243 q^{9} -3.32839 q^{10} -3.36564 q^{11} +2.36017 q^{12} -1.29991 q^{14} -9.85655 q^{15} -2.11462 q^{16} -2.07592 q^{17} -9.59667 q^{18} +6.06940 q^{19} -2.03840 q^{20} -3.84950 q^{21} +3.83943 q^{22} -5.19484 q^{23} -10.4000 q^{24} +3.51279 q^{25} -18.2844 q^{27} -0.796103 q^{28} +6.22325 q^{29} +11.2441 q^{30} +1.00000 q^{31} -3.74476 q^{32} +11.3699 q^{33} +2.36815 q^{34} +3.32469 q^{35} -5.87727 q^{36} +9.20792 q^{37} -6.92380 q^{38} +8.98214 q^{40} +12.7603 q^{41} +4.39140 q^{42} -8.90654 q^{43} +2.35137 q^{44} +24.5447 q^{45} +5.92613 q^{46} +5.33535 q^{47} +7.14367 q^{48} -5.70153 q^{49} -4.00729 q^{50} +7.01294 q^{51} +0.413187 q^{53} +20.8584 q^{54} -9.81982 q^{55} +3.50800 q^{56} -20.5038 q^{57} -7.09931 q^{58} +2.53271 q^{59} +6.88619 q^{60} +0.648764 q^{61} -1.14077 q^{62} +9.58600 q^{63} +8.50116 q^{64} -12.9705 q^{66} +2.70298 q^{67} +1.45032 q^{68} +17.5494 q^{69} -3.79272 q^{70} -2.56026 q^{71} +25.8979 q^{72} +3.00395 q^{73} -10.5041 q^{74} -11.8670 q^{75} -4.24033 q^{76} -3.83516 q^{77} -0.926660 q^{79} -6.16976 q^{80} +36.5317 q^{81} -14.5566 q^{82} +13.8393 q^{83} +2.68942 q^{84} -6.05685 q^{85} +10.1603 q^{86} -21.0236 q^{87} -10.3612 q^{88} +11.3360 q^{89} -27.9999 q^{90} +3.62933 q^{92} -3.37823 q^{93} -6.08642 q^{94} +17.7085 q^{95} +12.6507 q^{96} -8.11106 q^{97} +6.50415 q^{98} -28.3132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9}+O(q^{10}) \) 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

Groups

Database

Properties

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