LMFDB - Embedded newform 5239.2.a.u.1.45

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			1.45
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)

$f(q)$	$=$	$q+2.08695 q^{2} -0.777360 q^{3} +2.35535 q^{4} -3.75976 q^{5} -1.62231 q^{6} -3.38901 q^{7} +0.741587 q^{8} -2.39571 q^{9} +O(q^{10})$	\(q+2.08695 q^{2} -0.777360 q^{3} +2.35535 q^{4} -3.75976 q^{5} -1.62231 q^{6} -3.38901 q^{7} +0.741587 q^{8} -2.39571 q^{9} -7.84641 q^{10} -6.13105 q^{11} -1.83095 q^{12} -7.07268 q^{14} +2.92268 q^{15} -3.16304 q^{16} +5.82574 q^{17} -4.99972 q^{18} -3.74392 q^{19} -8.85552 q^{20} +2.63448 q^{21} -12.7952 q^{22} -2.96112 q^{23} -0.576481 q^{24} +9.13576 q^{25} +4.19441 q^{27} -7.98229 q^{28} -3.91027 q^{29} +6.09948 q^{30} -1.00000 q^{31} -8.08427 q^{32} +4.76604 q^{33} +12.1580 q^{34} +12.7418 q^{35} -5.64273 q^{36} -0.194746 q^{37} -7.81336 q^{38} -2.78819 q^{40} +10.8929 q^{41} +5.49802 q^{42} -1.93827 q^{43} -14.4407 q^{44} +9.00729 q^{45} -6.17969 q^{46} -12.5150 q^{47} +2.45882 q^{48} +4.48538 q^{49} +19.0658 q^{50} -4.52870 q^{51} -11.0790 q^{53} +8.75351 q^{54} +23.0513 q^{55} -2.51325 q^{56} +2.91037 q^{57} -8.16052 q^{58} +2.97981 q^{59} +6.88393 q^{60} +6.93601 q^{61} -2.08695 q^{62} +8.11909 q^{63} -10.5454 q^{64} +9.94646 q^{66} -11.5615 q^{67} +13.7216 q^{68} +2.30185 q^{69} +26.5915 q^{70} -5.82822 q^{71} -1.77663 q^{72} -0.957932 q^{73} -0.406424 q^{74} -7.10177 q^{75} -8.81822 q^{76} +20.7782 q^{77} +3.67451 q^{79} +11.8922 q^{80} +3.92657 q^{81} +22.7328 q^{82} +1.70677 q^{83} +6.20511 q^{84} -21.9034 q^{85} -4.04507 q^{86} +3.03969 q^{87} -4.54671 q^{88} +10.1569 q^{89} +18.7977 q^{90} -6.97445 q^{92} +0.777360 q^{93} -26.1181 q^{94} +14.0762 q^{95} +6.28439 q^{96} -5.54067 q^{97} +9.36075 q^{98} +14.6882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.08695	1.47569	0.737847	−	0.674968i	$-0.235843\pi$
$2$	2.08695	1.47569	0.737847	+	0.674968i	$0.235843\pi$
$3$	−0.777360	−0.448809	−0.224405	−	0.974496i	$-0.572044\pi$
$3$	−0.777360	−0.448809	−0.224405	+	0.974496i	$0.572044\pi$
$4$	2.35535	1.17767
$5$	−3.75976	−1.68141	−0.840707	−	0.541491i	$-0.817860\pi$
$5$	−3.75976	−1.68141	−0.840707	+	0.541491i	$0.817860\pi$
$6$	−1.62231	−0.662305
$7$	−3.38901	−1.28092	−0.640462	−	0.767989i	$-0.721257\pi$
$7$	−3.38901	−1.28092	−0.640462	+	0.767989i	$0.721257\pi$
$8$	0.741587	0.262191
$9$	−2.39571	−0.798570
$10$	−7.84641	−2.48125
$11$	−6.13105	−1.84858	−0.924291	−	0.381689i	$-0.875343\pi$
$11$	−6.13105	−1.84858	−0.924291	+	0.381689i	$0.875343\pi$
$12$	−1.83095	−0.528550
$13$	0	0
$13$	0	0
$14$	−7.07268	−1.89025
$15$	2.92268	0.754634
$16$	−3.16304	−0.790760
$17$	5.82574	1.41295	0.706475	−	0.707738i	$-0.250284\pi$
$17$	5.82574	1.41295	0.706475	+	0.707738i	$0.250284\pi$
$18$	−4.99972	−1.17845
$19$	−3.74392	−0.858914	−0.429457	−	0.903087i	$-0.641295\pi$
$19$	−3.74392	−0.858914	−0.429457	+	0.903087i	$0.641295\pi$
$20$	−8.85552	−1.98016
$21$	2.63448	0.574891
$22$	−12.7952	−2.72794
$23$	−2.96112	−0.617435	−0.308718	−	0.951154i	$-0.599900\pi$
$23$	−2.96112	−0.617435	−0.308718	+	0.951154i	$0.599900\pi$
$24$	−0.576481	−0.117674
$25$	9.13576	1.82715
$26$	0	0
$27$	4.19441	0.807215
$28$	−7.98229	−1.50851
$29$	−3.91027	−0.726119	−0.363059	−	0.931766i	$-0.618268\pi$
$29$	−3.91027	−0.726119	−0.363059	+	0.931766i	$0.618268\pi$
$30$	6.09948	1.11361
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−8.08427	−1.42911
$33$	4.76604	0.829660
$34$	12.1580	2.08508
$35$	12.7418	2.15376
$36$	−5.64273	−0.940455
$37$	−0.194746	−0.0320160	−0.0160080	−	0.999872i	$-0.505096\pi$
$37$	−0.194746	−0.0320160	−0.0160080	+	0.999872i	$0.505096\pi$
$38$	−7.81336	−1.26749
$39$	0	0
$40$	−2.78819	−0.440851
$41$	10.8929	1.70118	0.850590	−	0.525829i	$-0.176245\pi$
$41$	10.8929	1.70118	0.850590	+	0.525829i	$0.176245\pi$
$42$	5.49802	0.848363
$43$	−1.93827	−0.295583	−0.147792	−	0.989019i	$-0.547217\pi$
$43$	−1.93827	−0.295583	−0.147792	+	0.989019i	$0.547217\pi$
$44$	−14.4407	−2.17702
$45$	9.00729	1.34273
$46$	−6.17969	−0.911145
$47$	−12.5150	−1.82550	−0.912751	−	0.408517i	$-0.866046\pi$
$47$	−12.5150	−1.82550	−0.912751	+	0.408517i	$0.866046\pi$
$48$	2.45882	0.354900
$49$	4.48538	0.640769
$50$	19.0658	2.69632
$51$	−4.52870	−0.634145
$52$	0	0
$53$	−11.0790	−1.52182	−0.760910	−	0.648858i	$-0.775247\pi$
$53$	−11.0790	−1.52182	−0.760910	+	0.648858i	$0.775247\pi$
$54$	8.75351	1.19120
$55$	23.0513	3.10823
$56$	−2.51325	−0.335847
$57$	2.91037	0.385488
$58$	−8.16052	−1.07153
$59$	2.97981	0.387938	0.193969	−	0.981008i	$-0.437864\pi$
$59$	2.97981	0.387938	0.193969	+	0.981008i	$0.437864\pi$
$60$	6.88393	0.888712
$61$	6.93601	0.888065	0.444032	−	0.896011i	$-0.353547\pi$
$61$	6.93601	0.888065	0.444032	+	0.896011i	$0.353547\pi$
$62$	−2.08695	−0.265042
$63$	8.11909	1.02291
$64$	−10.5454	−1.31817
$65$	0	0
$66$	9.94646	1.22432
$67$	−11.5615	−1.41246	−0.706229	−	0.707983i	$-0.749605\pi$
$67$	−11.5615	−1.41246	−0.706229	+	0.707983i	$0.749605\pi$
$68$	13.7216	1.66399
$69$	2.30185	0.277111
$70$	26.5915	3.17830
$71$	−5.82822	−0.691683	−0.345841	−	0.938293i	$-0.612406\pi$
$71$	−5.82822	−0.691683	−0.345841	+	0.938293i	$0.612406\pi$
$72$	−1.77663	−0.209378
$73$	−0.957932	−0.112117	−0.0560587	−	0.998427i	$-0.517853\pi$
$73$	−0.957932	−0.112117	−0.0560587	+	0.998427i	$0.517853\pi$
$74$	−0.406424	−0.0472459
$75$	−7.10177	−0.820042
$76$	−8.81822	−1.01152
$77$	20.7782	2.36789
$78$	0	0
$79$	3.67451	0.413415	0.206707	−	0.978403i	$-0.433725\pi$
$79$	3.67451	0.413415	0.206707	+	0.978403i	$0.433725\pi$
$80$	11.8922	1.32959
$81$	3.92657	0.436285
$82$	22.7328	2.51042
$83$	1.70677	0.187342	0.0936710	−	0.995603i	$-0.470140\pi$
$83$	1.70677	0.187342	0.0936710	+	0.995603i	$0.470140\pi$
$84$	6.20511	0.677033
$85$	−21.9034	−2.37575
$86$	−4.04507	−0.436191
$87$	3.03969	0.325889
$88$	−4.54671	−0.484681
$89$	10.1569	1.07663	0.538313	−	0.842745i	$-0.319062\pi$
$89$	10.1569	1.07663	0.538313	+	0.842745i	$0.319062\pi$
$90$	18.7977	1.98145
$91$	0	0
$92$	−6.97445	−0.727137
$93$	0.777360	0.0806085
$94$	−26.1181	−2.69388
$95$	14.0762	1.44419
$96$	6.28439	0.641398
$97$	−5.54067	−0.562570	−0.281285	−	0.959624i	$-0.590761\pi$
$97$	−5.54067	−0.562570	−0.281285	+	0.959624i	$0.590761\pi$
$98$	9.36075	0.945578
$99$	14.6882	1.47622
$100$	21.5179	2.15179
$101$	2.02093	0.201090	0.100545	−	0.994933i	$-0.467941\pi$
$101$	2.02093	0.201090	0.100545	+	0.994933i	$0.467941\pi$
$102$	−9.45115	−0.935804
$103$	−1.41569	−0.139492	−0.0697462	−	0.997565i	$-0.522219\pi$
$103$	−1.41569	−0.139492	−0.0697462	+	0.997565i	$0.522219\pi$
$104$	0	0
$105$	−9.90500	−0.966629
$106$	−23.1213	−2.24574
$107$	11.7763	1.13846	0.569228	−	0.822179i	$-0.307242\pi$
$107$	11.7763	1.13846	0.569228	+	0.822179i	$0.307242\pi$
$108$	9.87929	0.950635
$109$	−6.86754	−0.657791	−0.328896	−	0.944366i	$-0.606676\pi$
$109$	−6.86754	−0.657791	−0.328896	+	0.944366i	$0.606676\pi$
$110$	48.1067	4.58680
$111$	0.151388	0.0143691
$112$	10.7196	1.01290
$113$	5.44938	0.512635	0.256317	−	0.966593i	$-0.417491\pi$
$113$	5.44938	0.512635	0.256317	+	0.966593i	$0.417491\pi$
$114$	6.07379	0.568863
$115$	11.1331	1.03816
$116$	−9.21004	−0.855131
$117$	0	0
$118$	6.21870	0.572478
$119$	−19.7435	−1.80988
$120$	2.16743	0.197858
$121$	26.5898	2.41726
$122$	14.4751	1.31051
$123$	−8.46768	−0.763505
$124$	−2.35535	−0.211516
$125$	−15.5494	−1.39078
$126$	16.9441	1.50950
$127$	−3.18294	−0.282441	−0.141220	−	0.989978i	$-0.545103\pi$
$127$	−3.18294	−0.282441	−0.141220	+	0.989978i	$0.545103\pi$
$128$	−5.83906	−0.516105
$129$	1.50673	0.132661
$130$	0	0
$131$	−5.85201	−0.511292	−0.255646	−	0.966770i	$-0.582288\pi$
$131$	−5.85201	−0.511292	−0.255646	+	0.966770i	$0.582288\pi$
$132$	11.2257	0.977069
$133$	12.6882	1.10020
$134$	−24.1282	−2.08436
$135$	−15.7700	−1.35726
$136$	4.32030	0.370462
$137$	12.2399	1.04572	0.522861	−	0.852418i	$-0.324865\pi$
$137$	12.2399	1.04572	0.522861	+	0.852418i	$0.324865\pi$
$138$	4.80384	0.408930
$139$	−21.4151	−1.81641	−0.908204	−	0.418529i	$-0.862546\pi$
$139$	−21.4151	−1.81641	−0.908204	+	0.418529i	$0.862546\pi$
$140$	30.0114	2.53643
$141$	9.72867	0.819302
$142$	−12.1632	−1.02071
$143$	0	0
$144$	7.57773	0.631477
$145$	14.7017	1.22091
$146$	−1.99915	−0.165451
$147$	−3.48676	−0.287583
$148$	−0.458694	−0.0377044
$149$	−5.77298	−0.472941	−0.236471	−	0.971639i	$-0.575991\pi$
$149$	−5.77298	−0.472941	−0.236471	+	0.971639i	$0.575991\pi$
$150$	−14.8210	−1.21013
$151$	−14.5117	−1.18095	−0.590473	−	0.807057i	$-0.701059\pi$
$151$	−14.5117	−1.18095	−0.590473	+	0.807057i	$0.701059\pi$
$152$	−2.77644	−0.225199
$153$	−13.9568	−1.12834
$154$	43.3630	3.49429
$155$	3.75976	0.301991
$156$	0	0
$157$	−20.9237	−1.66990	−0.834948	−	0.550330i	$-0.814502\pi$
$157$	−20.9237	−1.66990	−0.834948	+	0.550330i	$0.814502\pi$
$158$	7.66851	0.610074
$159$	8.61238	0.683006
$160$	30.3949	2.40292
$161$	10.0352	0.790888
$162$	8.19453	0.643823
$163$	17.7390	1.38942	0.694712	−	0.719288i	$-0.255532\pi$
$163$	17.7390	1.38942	0.694712	+	0.719288i	$0.255532\pi$
$164$	25.6565	2.00343
$165$	−17.9191	−1.39500
$166$	3.56193	0.276459
$167$	−15.0404	−1.16386	−0.581931	−	0.813238i	$-0.697703\pi$
$167$	−15.0404	−1.16386	−0.581931	+	0.813238i	$0.697703\pi$
$168$	1.95370	0.150731
$169$	0	0
$170$	−45.7111	−3.50588
$171$	8.96935	0.685903
$172$	−4.56530	−0.348101
$173$	−3.89614	−0.296218	−0.148109	−	0.988971i	$-0.547319\pi$
$173$	−3.89614	−0.296218	−0.148109	+	0.988971i	$0.547319\pi$
$174$	6.34367	0.480912
$175$	−30.9612	−2.34044
$176$	19.3928	1.46178
$177$	−2.31638	−0.174110
$178$	21.1968	1.58877
$179$	−5.19912	−0.388601	−0.194300	−	0.980942i	$-0.562244\pi$
$179$	−5.19912	−0.388601	−0.194300	+	0.980942i	$0.562244\pi$
$180$	21.2153	1.58129
$181$	0.376634	0.0279949	0.0139975	−	0.999902i	$-0.495544\pi$
$181$	0.376634	0.0279949	0.0139975	+	0.999902i	$0.495544\pi$
$182$	0	0
$183$	−5.39178	−0.398572
$184$	−2.19593	−0.161886
$185$	0.732197	0.0538322
$186$	1.62231	0.118953
$187$	−35.7179	−2.61195
$188$	−29.4772	−2.14984
$189$	−14.2149	−1.03398
$190$	29.3763	2.13118
$191$	15.6714	1.13394	0.566970	−	0.823738i	$-0.308115\pi$
$191$	15.6714	1.13394	0.566970	+	0.823738i	$0.308115\pi$
$192$	8.19754	0.591606
$193$	19.6169	1.41205	0.706027	−	0.708185i	$-0.250486\pi$
$193$	19.6169	1.41205	0.706027	+	0.708185i	$0.250486\pi$
$194$	−11.5631	−0.830182
$195$	0	0
$196$	10.5646	0.754616
$197$	−5.57806	−0.397420	−0.198710	−	0.980058i	$-0.563675\pi$
$197$	−5.57806	−0.397420	−0.198710	+	0.980058i	$0.563675\pi$
$198$	30.6536	2.17845
$199$	−20.3862	−1.44514	−0.722571	−	0.691297i	$-0.757040\pi$
$199$	−20.3862	−1.44514	−0.722571	+	0.691297i	$0.757040\pi$
$200$	6.77496	0.479062
$201$	8.98743	0.633924
$202$	4.21757	0.296747
$203$	13.2519	0.930104
$204$	−10.6667	−0.746815
$205$	−40.9545	−2.86039
$206$	−2.95447	−0.205848
$207$	7.09398	0.493065
$208$	0	0
$209$	22.9542	1.58777
$210$	−20.6712	−1.42645
$211$	−27.3393	−1.88212	−0.941058	−	0.338244i	$-0.890167\pi$
$211$	−27.3393	−1.88212	−0.941058	+	0.338244i	$0.890167\pi$
$212$	−26.0949	−1.79221
$213$	4.53063	0.310434
$214$	24.5765	1.68001
$215$	7.28742	0.496998
$216$	3.11052	0.211644
$217$	3.38901	0.230061
$218$	−14.3322	−0.970698
$219$	0.744658	0.0503194
$220$	54.2937	3.66048
$221$	0	0
$222$	0.315938	0.0212044
$223$	−3.76500	−0.252123	−0.126061	−	0.992022i	$-0.540234\pi$
$223$	−3.76500	−0.252123	−0.126061	+	0.992022i	$0.540234\pi$
$224$	27.3976	1.83058
$225$	−21.8866	−1.45911
$226$	11.3726	0.756492
$227$	14.8294	0.984262	0.492131	−	0.870521i	$-0.336218\pi$
$227$	14.8294	0.984262	0.492131	+	0.870521i	$0.336218\pi$
$228$	6.85494	0.453979
$229$	−11.4560	−0.757033	−0.378517	−	0.925595i	$-0.623566\pi$
$229$	−11.4560	−0.757033	−0.378517	+	0.925595i	$0.623566\pi$
$230$	23.2341	1.53201
$231$	−16.1521	−1.06273
$232$	−2.89981	−0.190382
$233$	8.11175	0.531418	0.265709	−	0.964053i	$-0.414394\pi$
$233$	8.11175	0.531418	0.265709	+	0.964053i	$0.414394\pi$
$234$	0	0
$235$	47.0534	3.06942
$236$	7.01848	0.456864
$237$	−2.85642	−0.185544
$238$	−41.2036	−2.67083
$239$	−6.61238	−0.427719	−0.213860	−	0.976864i	$-0.568604\pi$
$239$	−6.61238	−0.427719	−0.213860	+	0.976864i	$0.568604\pi$
$240$	−9.24456	−0.596734
$241$	24.8162	1.59855	0.799276	−	0.600964i	$-0.205217\pi$
$241$	24.8162	1.59855	0.799276	+	0.600964i	$0.205217\pi$
$242$	55.4915	3.56713
$243$	−15.6356	−1.00302
$244$	16.3367	1.04585
$245$	−16.8639	−1.07740
$246$	−17.6716	−1.12670
$247$	0	0
$248$	−0.741587	−0.0470909
$249$	−1.32677	−0.0840808
$250$	−32.4508	−2.05237
$251$	−26.5389	−1.67512	−0.837560	−	0.546346i	$-0.816018\pi$
$251$	−26.5389	−1.67512	−0.837560	+	0.546346i	$0.816018\pi$
$252$	19.1233	1.20465
$253$	18.1548	1.14138
$254$	−6.64263	−0.416796
$255$	17.0268	1.06626
$256$	8.90491	0.556557
$257$	−14.0558	−0.876775	−0.438387	−	0.898786i	$-0.644450\pi$
$257$	−14.0558	−0.876775	−0.438387	+	0.898786i	$0.644450\pi$
$258$	3.14447	0.195766
$259$	0.659996	0.0410101
$260$	0	0
$261$	9.36788	0.579857
$262$	−12.2128	−0.754511
$263$	1.30089	0.0802161	0.0401080	−	0.999195i	$-0.487230\pi$
$263$	1.30089	0.0802161	0.0401080	+	0.999195i	$0.487230\pi$
$264$	3.53443	0.217529
$265$	41.6544	2.55881
$266$	26.4795	1.62356
$267$	−7.89554	−0.483199
$268$	−27.2313	−1.66341
$269$	22.3304	1.36151	0.680755	−	0.732511i	$-0.261652\pi$
$269$	22.3304	1.36151	0.680755	+	0.732511i	$0.261652\pi$
$270$	−32.9111	−2.00290
$271$	−8.62028	−0.523645	−0.261822	−	0.965116i	$-0.584323\pi$
$271$	−8.62028	−0.523645	−0.261822	+	0.965116i	$0.584323\pi$
$272$	−18.4270	−1.11730
$273$	0	0
$274$	25.5439	1.54317
$275$	−56.0118	−3.37764
$276$	5.42166	0.326346
$277$	5.71628	0.343458	0.171729	−	0.985144i	$-0.445065\pi$
$277$	5.71628	0.343458	0.171729	+	0.985144i	$0.445065\pi$
$278$	−44.6922	−2.68046
$279$	2.39571	0.143427
$280$	9.44919	0.564697
$281$	−7.48838	−0.446719	−0.223360	−	0.974736i	$-0.571702\pi$
$281$	−7.48838	−0.446719	−0.223360	+	0.974736i	$0.571702\pi$
$282$	20.3032	1.20904
$283$	15.8302	0.941009	0.470504	−	0.882398i	$-0.344072\pi$
$283$	15.8302	0.941009	0.470504	+	0.882398i	$0.344072\pi$
$284$	−13.7275	−0.814576
$285$	−10.9423	−0.648165
$286$	0	0
$287$	−36.9160	−2.17908
$288$	19.3676	1.14124
$289$	16.9393	0.996427
$290$	30.6816	1.80168
$291$	4.30710	0.252487
$292$	−2.25626	−0.132038
$293$	21.4270	1.25178	0.625888	−	0.779913i	$-0.284737\pi$
$293$	21.4270	1.25178	0.625888	+	0.779913i	$0.284737\pi$
$294$	−7.27667	−0.424384
$295$	−11.2033	−0.652284
$296$	−0.144421	−0.00839431
$297$	−25.7162	−1.49220
$298$	−12.0479	−0.697917
$299$	0	0
$300$	−16.7271	−0.965742
$301$	6.56882	0.378620
$302$	−30.2852	−1.74272
$303$	−1.57099	−0.0902510
$304$	11.8422	0.679194
$305$	−26.0777	−1.49320
$306$	−29.1271	−1.66508
$307$	16.8265	0.960337	0.480168	−	0.877176i	$-0.340576\pi$
$307$	16.8265	0.960337	0.480168	+	0.877176i	$0.340576\pi$
$308$	48.9398	2.78861
$309$	1.10050	0.0626054
$310$	7.84641	0.445646
$311$	−25.3356	−1.43665	−0.718325	−	0.695707i	$-0.755091\pi$
$311$	−25.3356	−1.43665	−0.718325	+	0.695707i	$0.755091\pi$
$312$	0	0
$313$	−17.2271	−0.973735	−0.486868	−	0.873476i	$-0.661861\pi$
$313$	−17.2271	−0.973735	−0.486868	+	0.873476i	$0.661861\pi$
$314$	−43.6667	−2.46425
$315$	−30.5258	−1.71993
$316$	8.65475	0.486868
$317$	−13.6538	−0.766871	−0.383436	−	0.923568i	$-0.625259\pi$
$317$	−13.6538	−0.766871	−0.383436	+	0.923568i	$0.625259\pi$
$318$	17.9736	1.00791
$319$	23.9741	1.34229
$320$	39.6480	2.21639
$321$	−9.15442	−0.510950
$322$	20.9430	1.16711
$323$	−21.8111	−1.21360
$324$	9.24842	0.513801
$325$	0	0
$326$	37.0203	2.05036
$327$	5.33855	0.295223
$328$	8.07802	0.446034
$329$	42.4135	2.33833
$330$	−37.3963	−2.05860
$331$	−20.9509	−1.15157	−0.575783	−	0.817602i	$-0.695303\pi$
$331$	−20.9509	−1.15157	−0.575783	+	0.817602i	$0.695303\pi$
$332$	4.02003	0.220628
$333$	0.466555	0.0255671
$334$	−31.3885	−1.71750
$335$	43.4683	2.37493
$336$	−8.33296	−0.454600
$337$	−33.6709	−1.83417	−0.917086	−	0.398689i	$-0.869465\pi$
$337$	−33.6709	−1.83417	−0.917086	+	0.398689i	$0.869465\pi$
$338$	0	0
$339$	−4.23613	−0.230075
$340$	−51.5900	−2.79786
$341$	6.13105	0.332015
$342$	18.7186	1.01218
$343$	8.52207	0.460148
$344$	−1.43740	−0.0774993
$345$	−8.65440	−0.465937
$346$	−8.13103	−0.437127
$347$	−13.4327	−0.721103	−0.360552	−	0.932739i	$-0.617412\pi$
$347$	−13.4327	−0.721103	−0.360552	+	0.932739i	$0.617412\pi$
$348$	7.15952	0.383790
$349$	−14.6474	−0.784055	−0.392028	−	0.919953i	$-0.628226\pi$
$349$	−14.6474	−0.784055	−0.392028	+	0.919953i	$0.628226\pi$
$350$	−64.6143	−3.45378
$351$	0	0
$352$	49.5651	2.64183
$353$	−32.1732	−1.71241	−0.856204	−	0.516638i	$-0.827183\pi$
$353$	−32.1732	−1.71241	−0.856204	+	0.516638i	$0.827183\pi$
$354$	−4.83417	−0.256933
$355$	21.9127	1.16300
$356$	23.9229	1.26791
$357$	15.3478	0.812292
$358$	−10.8503	−0.573456
$359$	25.0403	1.32157	0.660787	−	0.750573i	$-0.270223\pi$
$359$	25.0403	1.32157	0.660787	+	0.750573i	$0.270223\pi$
$360$	6.67969	0.352051
$361$	−4.98307	−0.262267
$362$	0.786014	0.0413120
$363$	−20.6699	−1.08489
$364$	0	0
$365$	3.60159	0.188516
$366$	−11.2524	−0.588170
$367$	1.37121	0.0715767	0.0357883	−	0.999359i	$-0.488606\pi$
$367$	1.37121	0.0715767	0.0357883	+	0.999359i	$0.488606\pi$
$368$	9.36612	0.488243
$369$	−26.0962	−1.35851
$370$	1.52806	0.0794399
$371$	37.5469	1.94934
$372$	1.83095	0.0949304
$373$	−17.8997	−0.926812	−0.463406	−	0.886146i	$-0.653373\pi$
$373$	−17.8997	−0.926812	−0.463406	+	0.886146i	$0.653373\pi$
$374$	−74.5414	−3.85444
$375$	12.0875	0.624197
$376$	−9.28097	−0.478630
$377$	0	0
$378$	−29.6657	−1.52584
$379$	7.29130	0.374529	0.187264	−	0.982310i	$-0.440038\pi$
$379$	7.29130	0.374529	0.187264	+	0.982310i	$0.440038\pi$
$380$	33.1544	1.70078
$381$	2.47429	0.126762
$382$	32.7053	1.67335
$383$	3.53542	0.180651	0.0903257	−	0.995912i	$-0.471209\pi$
$383$	3.53542	0.180651	0.0903257	+	0.995912i	$0.471209\pi$
$384$	4.53905	0.231633
$385$	−78.1209	−3.98141
$386$	40.9394	2.08376
$387$	4.64354	0.236044
$388$	−13.0502	−0.662524
$389$	19.4621	0.986766	0.493383	−	0.869812i	$-0.335760\pi$
$389$	19.4621	0.986766	0.493383	+	0.869812i	$0.335760\pi$
$390$	0	0
$391$	−17.2507	−0.872405
$392$	3.32630	0.168004
$393$	4.54912	0.229473
$394$	−11.6411	−0.586471
$395$	−13.8153	−0.695122
$396$	34.5959	1.73851
$397$	7.06697	0.354681	0.177341	−	0.984150i	$-0.443251\pi$
$397$	7.06697	0.354681	0.177341	+	0.984150i	$0.443251\pi$
$398$	−42.5450	−2.13259
$399$	−9.86328	−0.493782
$400$	−28.8968	−1.44484
$401$	−18.5362	−0.925656	−0.462828	−	0.886448i	$-0.653165\pi$
$401$	−18.5362	−0.925656	−0.462828	+	0.886448i	$0.653165\pi$
$402$	18.7563	0.935478
$403$	0	0
$404$	4.75999	0.236818
$405$	−14.7629	−0.733576
$406$	27.6561	1.37255
$407$	1.19400	0.0591843
$408$	−3.35843	−0.166267
$409$	21.0298	1.03985	0.519927	−	0.854210i	$-0.325959\pi$
$409$	21.0298	1.03985	0.519927	+	0.854210i	$0.325959\pi$
$410$	−85.4699	−4.22106
$411$	−9.51478	−0.469330
$412$	−3.33445	−0.164276
$413$	−10.0986	−0.496919
$414$	14.8048	0.727614
$415$	−6.41702	−0.314999
$416$	0	0
$417$	16.6473	0.815220
$418$	47.9041	2.34307
$419$	14.0379	0.685794	0.342897	−	0.939373i	$-0.388592\pi$
$419$	14.0379	0.685794	0.342897	+	0.939373i	$0.388592\pi$
$420$	−23.3297	−1.13837
$421$	−26.7405	−1.30325	−0.651627	−	0.758540i	$-0.725913\pi$
$421$	−26.7405	−1.30325	−0.651627	+	0.758540i	$0.725913\pi$
$422$	−57.0557	−2.77743
$423$	29.9823	1.45779
$424$	−8.21606	−0.399007
$425$	53.2226	2.58167
$426$	9.45518	0.458105
$427$	−23.5062	−1.13754
$428$	27.7372	1.34073
$429$	0	0
$430$	15.2085	0.733417
$431$	7.30729	0.351980	0.175990	−	0.984392i	$-0.443687\pi$
$431$	7.30729	0.351980	0.175990	+	0.984392i	$0.443687\pi$
$432$	−13.2671	−0.638313
$433$	35.1066	1.68711	0.843557	−	0.537040i	$-0.180457\pi$
$433$	35.1066	1.68711	0.843557	+	0.537040i	$0.180457\pi$
$434$	7.07268	0.339500
$435$	−11.4285	−0.547954
$436$	−16.1754	−0.774663
$437$	11.0862	0.530324
$438$	1.55406	0.0742560
$439$	4.09417	0.195404	0.0977020	−	0.995216i	$-0.468851\pi$
$439$	4.09417	0.195404	0.0977020	+	0.995216i	$0.468851\pi$
$440$	17.0945	0.814949
$441$	−10.7457	−0.511699
$442$	0	0
$443$	10.7169	0.509174	0.254587	−	0.967050i	$-0.418060\pi$
$443$	10.7169	0.509174	0.254587	+	0.967050i	$0.418060\pi$
$444$	0.356571	0.0169221
$445$	−38.1873	−1.81025
$446$	−7.85735	−0.372056
$447$	4.48769	0.212260
$448$	35.7383	1.68848
$449$	16.4588	0.776739	0.388369	−	0.921504i	$-0.373038\pi$
$449$	16.4588	0.776739	0.388369	+	0.921504i	$0.373038\pi$
$450$	−45.6762	−2.15320
$451$	−66.7848	−3.14477
$452$	12.8352	0.603716
$453$	11.2808	0.530019
$454$	30.9482	1.45247
$455$	0	0
$456$	2.15830	0.101071
$457$	−2.02713	−0.0948253	−0.0474127	−	0.998875i	$-0.515098\pi$
$457$	−2.02713	−0.0948253	−0.0474127	+	0.998875i	$0.515098\pi$
$458$	−23.9080	−1.11715
$459$	24.4356	1.14055
$460$	26.2222	1.22262
$461$	−0.683626	−0.0318396	−0.0159198	−	0.999873i	$-0.505068\pi$
$461$	−0.683626	−0.0318396	−0.0159198	+	0.999873i	$0.505068\pi$
$462$	−33.7087	−1.56827
$463$	−6.65175	−0.309133	−0.154567	−	0.987982i	$-0.549398\pi$
$463$	−6.65175	−0.309133	−0.154567	+	0.987982i	$0.549398\pi$
$464$	12.3683	0.574185
$465$	−2.92268	−0.135536
$466$	16.9288	0.784211
$467$	21.2436	0.983035	0.491517	−	0.870868i	$-0.336442\pi$
$467$	21.2436	0.983035	0.491517	+	0.870868i	$0.336442\pi$
$468$	0	0
$469$	39.1819	1.80925
$470$	98.1978	4.52953
$471$	16.2653	0.749464
$472$	2.20979	0.101714
$473$	11.8836	0.546410
$474$	−5.96119	−0.273807
$475$	−34.2035	−1.56937
$476$	−46.5027	−2.13145
$477$	26.5421	1.21528
$478$	−13.7997	−0.631183
$479$	23.9416	1.09392	0.546960	−	0.837159i	$-0.315785\pi$
$479$	23.9416	1.09392	0.546960	+	0.837159i	$0.315785\pi$
$480$	−23.6278	−1.07845
$481$	0	0
$482$	51.7901	2.35897
$483$	−7.80100	−0.354958
$484$	62.6282	2.84674
$485$	20.8316	0.945913
$486$	−32.6306	−1.48016
$487$	30.0710	1.36265	0.681324	−	0.731982i	$-0.261405\pi$
$487$	30.0710	1.36265	0.681324	+	0.731982i	$0.261405\pi$
$488$	5.14366	0.232842
$489$	−13.7896	−0.623586
$490$	−35.1941	−1.58991
$491$	25.6777	1.15882	0.579410	−	0.815036i	$-0.303283\pi$
$491$	25.6777	1.15882	0.579410	+	0.815036i	$0.303283\pi$
$492$	−19.9443	−0.899159
$493$	−22.7802	−1.02597
$494$	0	0
$495$	−55.2242	−2.48214
$496$	3.16304	0.142025
$497$	19.7519	0.885994
$498$	−2.76890	−0.124077
$499$	−8.29099	−0.371156	−0.185578	−	0.982630i	$-0.559416\pi$
$499$	−8.29099	−0.371156	−0.185578	+	0.982630i	$0.559416\pi$
$500$	−36.6243	−1.63789
$501$	11.6918	0.522352
$502$	−55.3852	−2.47196
$503$	20.7501	0.925202	0.462601	−	0.886567i	$-0.346916\pi$
$503$	20.7501	0.925202	0.462601	+	0.886567i	$0.346916\pi$
$504$	6.02101	0.268197
$505$	−7.59820	−0.338115
$506$	37.8880	1.68433
$507$	0	0
$508$	−7.49693	−0.332623
$509$	−29.8505	−1.32310	−0.661550	−	0.749901i	$-0.730101\pi$
$509$	−29.8505	−1.32310	−0.661550	+	0.749901i	$0.730101\pi$
$510$	35.5340	1.57347
$511$	3.24644	0.143614
$512$	30.2622	1.33741
$513$	−15.7035	−0.693328
$514$	−29.3336	−1.29385
$515$	5.32266	0.234544
$516$	3.54888	0.156231
$517$	76.7302	3.37459
$518$	1.37738	0.0605184
$519$	3.02870	0.132945
$520$	0	0
$521$	17.0269	0.745963	0.372981	−	0.927839i	$-0.378335\pi$
$521$	17.0269	0.745963	0.372981	+	0.927839i	$0.378335\pi$
$522$	19.5503	0.855692
$523$	−16.7914	−0.734235	−0.367118	−	0.930175i	$-0.619655\pi$
$523$	−16.7914	−0.734235	−0.367118	+	0.930175i	$0.619655\pi$
$524$	−13.7835	−0.602135
$525$	24.0680	1.05041
$526$	2.71488	0.118374
$527$	−5.82574	−0.253773
$528$	−15.0752	−0.656062
$529$	−14.2318	−0.618774
$530$	86.9304	3.77602
$531$	−7.13876	−0.309796
$532$	29.8850	1.29568
$533$	0	0
$534$	−16.4776	−0.713054
$535$	−44.2760	−1.91422
$536$	−8.57384	−0.370334
$537$	4.04159	0.174408
$538$	46.6024	2.00917
$539$	−27.5001	−1.18451
$540$	−37.1437	−1.59841
$541$	0.615194	0.0264492	0.0132246	−	0.999913i	$-0.495790\pi$
$541$	0.615194	0.0264492	0.0132246	+	0.999913i	$0.495790\pi$
$542$	−17.9901	−0.772740
$543$	−0.292780	−0.0125644
$544$	−47.0968	−2.01926
$545$	25.8203	1.10602
$546$	0	0
$547$	25.1095	1.07361	0.536803	−	0.843708i	$-0.319632\pi$
$547$	25.1095	1.07361	0.536803	+	0.843708i	$0.319632\pi$
$548$	28.8291	1.23152
$549$	−16.6167	−0.709182
$550$	−116.894	−4.98436
$551$	14.6397	0.623674
$552$	1.70703	0.0726558
$553$	−12.4530	−0.529554
$554$	11.9296	0.506839
$555$	−0.569181	−0.0241604
$556$	−50.4400	−2.13913
$557$	9.82580	0.416333	0.208166	−	0.978093i	$-0.433250\pi$
$557$	9.82580	0.416333	0.208166	+	0.978093i	$0.433250\pi$
$558$	4.99972	0.211655
$559$	0	0
$560$	−40.3029	−1.70311
$561$	27.7657	1.17227
$562$	−15.6278	−0.659221
$563$	4.63482	0.195335	0.0976673	−	0.995219i	$-0.468862\pi$
$563$	4.63482	0.195335	0.0976673	+	0.995219i	$0.468862\pi$
$564$	22.9144	0.964869
$565$	−20.4883	−0.861951
$566$	33.0368	1.38864
$567$	−13.3072	−0.558848
$568$	−4.32214	−0.181353
$569$	−17.9924	−0.754279	−0.377139	−	0.926156i	$-0.623092\pi$
$569$	−17.9924	−0.754279	−0.377139	+	0.926156i	$0.623092\pi$
$570$	−22.8360	−0.956494
$571$	10.6054	0.443824	0.221912	−	0.975067i	$-0.428770\pi$
$571$	10.6054	0.443824	0.221912	+	0.975067i	$0.428770\pi$
$572$	0	0
$573$	−12.1823	−0.508923
$574$	−77.0418	−3.21566
$575$	−27.0520	−1.12815
$576$	25.2636	1.05265
$577$	−21.0899	−0.877983	−0.438991	−	0.898491i	$-0.644664\pi$
$577$	−21.0899	−0.877983	−0.438991	+	0.898491i	$0.644664\pi$
$578$	35.3513	1.47042
$579$	−15.2494	−0.633743
$580$	34.6275	1.43783
$581$	−5.78425	−0.239971
$582$	8.98869	0.372593
$583$	67.9260	2.81321
$584$	−0.710391	−0.0293962
$585$	0	0
$586$	44.7169	1.84724
$587$	−22.3527	−0.922594	−0.461297	−	0.887246i	$-0.652616\pi$
$587$	−22.3527	−0.922594	−0.461297	+	0.887246i	$0.652616\pi$
$588$	−8.21252	−0.338678
$589$	3.74392	0.154265
$590$	−23.3808	−0.962572
$591$	4.33616	0.178366
$592$	0.615989	0.0253170
$593$	−45.6675	−1.87534	−0.937671	−	0.347526i	$-0.887022\pi$
$593$	−45.6675	−1.87534	−0.937671	+	0.347526i	$0.887022\pi$
$594$	−53.6682	−2.20203
$595$	74.2307	3.04316
$596$	−13.5974	−0.556970
$597$	15.8474	0.648593
$598$	0	0
$599$	12.8783	0.526192	0.263096	−	0.964770i	$-0.415256\pi$
$599$	12.8783	0.526192	0.263096	+	0.964770i	$0.415256\pi$
$600$	−5.26659	−0.215008
$601$	22.0506	0.899463	0.449732	−	0.893164i	$-0.351520\pi$
$601$	22.0506	0.899463	0.449732	+	0.893164i	$0.351520\pi$
$602$	13.7088	0.558728
$603$	27.6979	1.12795
$604$	−34.1801	−1.39077
$605$	−99.9712	−4.06441
$606$	−3.27857	−0.133183
$607$	6.20250	0.251752	0.125876	−	0.992046i	$-0.459826\pi$
$607$	6.20250	0.251752	0.125876	+	0.992046i	$0.459826\pi$
$608$	30.2668	1.22748
$609$	−10.3015	−0.417439
$610$	−54.4228	−2.20351
$611$	0	0
$612$	−32.8731	−1.32882
$613$	48.4901	1.95850	0.979248	−	0.202666i	$-0.0649607\pi$
$613$	48.4901	1.95850	0.979248	+	0.202666i	$0.0649607\pi$
$614$	35.1159	1.41716
$615$	31.8364	1.28377
$616$	15.4088	0.620840
$617$	30.2695	1.21861	0.609303	−	0.792938i	$-0.291449\pi$
$617$	30.2695	1.21861	0.609303	+	0.792938i	$0.291449\pi$
$618$	2.29669	0.0923865
$619$	35.2759	1.41786	0.708929	−	0.705280i	$-0.249179\pi$
$619$	35.2759	1.41786	0.708929	+	0.705280i	$0.249179\pi$
$620$	8.85552	0.355646
$621$	−12.4201	−0.498403
$622$	−52.8741	−2.12006
$623$	−34.4217	−1.37908
$624$	0	0
$625$	12.7833	0.511332
$626$	−35.9521	−1.43693
$627$	−17.8437	−0.712607
$628$	−49.2826	−1.96659
$629$	−1.13454	−0.0452371
$630$	−63.7057	−2.53809
$631$	0.729716	0.0290496	0.0145248	−	0.999895i	$-0.495376\pi$
$631$	0.729716	0.0290496	0.0145248	+	0.999895i	$0.495376\pi$
$632$	2.72497	0.108394
$633$	21.2525	0.844711
$634$	−28.4947	−1.13167
$635$	11.9671	0.474899
$636$	20.2851	0.804358
$637$	0	0
$638$	50.0326	1.98081
$639$	13.9627	0.552357
$640$	21.9534	0.867786
$641$	−3.25389	−0.128521	−0.0642604	−	0.997933i	$-0.520469\pi$
$641$	−3.25389	−0.128521	−0.0642604	+	0.997933i	$0.520469\pi$
$642$	−19.1048	−0.754005
$643$	16.1745	0.637861	0.318931	−	0.947778i	$-0.396676\pi$
$643$	16.1745	0.637861	0.318931	+	0.947778i	$0.396676\pi$
$644$	23.6365	0.931408
$645$	−5.66495	−0.223057
$646$	−45.5186	−1.79091
$647$	36.9033	1.45082	0.725409	−	0.688318i	$-0.241651\pi$
$647$	36.9033	1.45082	0.725409	+	0.688318i	$0.241651\pi$
$648$	2.91189	0.114390
$649$	−18.2694	−0.717135
$650$	0	0
$651$	−2.63448	−0.103253
$652$	41.7814	1.63629
$653$	−4.04254	−0.158197	−0.0790984	−	0.996867i	$-0.525204\pi$
$653$	−4.04254	−0.158197	−0.0790984	+	0.996867i	$0.525204\pi$
$654$	11.1413	0.435658
$655$	22.0021	0.859693
$656$	−34.4546	−1.34522
$657$	2.29493	0.0895337
$658$	88.5146	3.45066
$659$	−15.9816	−0.622554	−0.311277	−	0.950319i	$-0.600757\pi$
$659$	−15.9816	−0.622554	−0.311277	+	0.950319i	$0.600757\pi$
$660$	−42.2057	−1.64286
$661$	8.01530	0.311759	0.155880	−	0.987776i	$-0.450179\pi$
$661$	8.01530	0.311759	0.155880	+	0.987776i	$0.450179\pi$
$662$	−43.7234	−1.69936
$663$	0	0
$664$	1.26572	0.0491193
$665$	−47.7044	−1.84990
$666$	0.973676	0.0377292
$667$	11.5788	0.448331
$668$	−35.4254	−1.37065
$669$	2.92676	0.113155
$670$	90.7160	3.50467
$671$	−42.5250	−1.64166
$672$	−21.2978	−0.821582
$673$	−29.2851	−1.12886	−0.564429	−	0.825482i	$-0.690903\pi$
$673$	−29.2851	−1.12886	−0.564429	+	0.825482i	$0.690903\pi$
$674$	−70.2694	−2.70668
$675$	38.3191	1.47490
$676$	0	0
$677$	−49.5315	−1.90365	−0.951825	−	0.306643i	$-0.900794\pi$
$677$	−49.5315	−1.90365	−0.951825	+	0.306643i	$0.900794\pi$
$678$	−8.84058	−0.339521
$679$	18.7774	0.720610
$680$	−16.2433	−0.622900
$681$	−11.5278	−0.441746
$682$	12.7952	0.489953
$683$	−5.72116	−0.218914	−0.109457	−	0.993992i	$-0.534911\pi$
$683$	−5.72116	−0.218914	−0.109457	+	0.993992i	$0.534911\pi$
$684$	21.1259	0.807770
$685$	−46.0189	−1.75829
$686$	17.7851	0.679038
$687$	8.90543	0.339763
$688$	6.13082	0.233735
$689$	0	0
$690$	−18.0613	−0.687581
$691$	1.74998	0.0665723	0.0332862	−	0.999446i	$-0.489403\pi$
$691$	1.74998	0.0665723	0.0332862	+	0.999446i	$0.489403\pi$
$692$	−9.17675	−0.348848
$693$	−49.7785	−1.89093
$694$	−28.0333	−1.06413
$695$	80.5156	3.05413
$696$	2.25419	0.0854450
$697$	63.4590	2.40368
$698$	−30.5683	−1.15703
$699$	−6.30575	−0.238505
$700$	−72.9242	−2.75628
$701$	31.6370	1.19491	0.597456	−	0.801902i	$-0.296178\pi$
$701$	31.6370	1.19491	0.597456	+	0.801902i	$0.296178\pi$
$702$	0	0
$703$	0.729113	0.0274990
$704$	64.6541	2.43674
$705$	−36.5774	−1.37758
$706$	−67.1438	−2.52699
$707$	−6.84895	−0.257581
$708$	−5.45589	−0.205045
$709$	24.4029	0.916472	0.458236	−	0.888831i	$-0.348482\pi$
$709$	24.4029	0.916472	0.458236	+	0.888831i	$0.348482\pi$
$710$	45.7306	1.71624
$711$	−8.80307	−0.330141
$712$	7.53220	0.282281
$713$	2.96112	0.110895
$714$	32.0300	1.19869
$715$	0	0
$716$	−12.2457	−0.457645
$717$	5.14020	0.191964
$718$	52.2577	1.95024
$719$	−26.4700	−0.987163	−0.493581	−	0.869700i	$-0.664312\pi$
$719$	−26.4700	−0.987163	−0.493581	+	0.869700i	$0.664312\pi$
$720$	−28.4904	−1.06177
$721$	4.79779	0.178679
$722$	−10.3994	−0.387026
$723$	−19.2911	−0.717444
$724$	0.887102	0.0329689
$725$	−35.7233	−1.32673
$726$	−43.1369	−1.60096
$727$	−19.1090	−0.708715	−0.354358	−	0.935110i	$-0.615300\pi$
$727$	−19.1090	−0.708715	−0.354358	+	0.935110i	$0.615300\pi$
$728$	0	0
$729$	0.374787	0.0138810
$730$	7.51633	0.278192
$731$	−11.2919	−0.417645
$732$	−12.6995	−0.469387
$733$	−11.0517	−0.408203	−0.204102	−	0.978950i	$-0.565427\pi$
$733$	−11.0517	−0.408203	−0.204102	+	0.978950i	$0.565427\pi$
$734$	2.86165	0.105625
$735$	13.1093	0.483546
$736$	23.9384	0.882383
$737$	70.8840	2.61105
$738$	−54.4613	−2.00475
$739$	−29.6707	−1.09146	−0.545728	−	0.837963i	$-0.683747\pi$
$739$	−29.6707	−1.09146	−0.545728	+	0.837963i	$0.683747\pi$
$740$	1.72458	0.0633967
$741$	0	0
$742$	78.3583	2.87662
$743$	51.2497	1.88017	0.940085	−	0.340939i	$-0.110745\pi$
$743$	51.2497	1.88017	0.940085	+	0.340939i	$0.110745\pi$
$744$	0.576481	0.0211348
$745$	21.7050	0.795210
$746$	−37.3557	−1.36769
$747$	−4.08892	−0.149606
$748$	−84.1281	−3.07603
$749$	−39.9099	−1.45828
$750$	25.2260	0.921123
$751$	−10.5293	−0.384218	−0.192109	−	0.981374i	$-0.561533\pi$
$751$	−10.5293	−0.384218	−0.192109	+	0.981374i	$0.561533\pi$
$752$	39.5854	1.44353
$753$	20.6303	0.751809
$754$	0	0
$755$	54.5605	1.98566
$756$	−33.4810	−1.21769
$757$	−26.8331	−0.975264	−0.487632	−	0.873049i	$-0.662139\pi$
$757$	−26.8331	−0.975264	−0.487632	+	0.873049i	$0.662139\pi$
$758$	15.2165	0.552690
$759$	−14.1128	−0.512262
$760$	10.4387	0.378653
$761$	0.179312	0.00650005	0.00325002	−	0.999995i	$-0.498965\pi$
$761$	0.179312	0.00650005	0.00325002	+	0.999995i	$0.498965\pi$
$762$	5.16372	0.187062
$763$	23.2742	0.842581
$764$	36.9115	1.33541
$765$	52.4741	1.89721
$766$	7.37823	0.266586
$767$	0	0
$768$	−6.92232	−0.249788
$769$	−10.6872	−0.385392	−0.192696	−	0.981259i	$-0.561723\pi$
$769$	−10.6872	−0.385392	−0.192696	+	0.981259i	$0.561723\pi$
$770$	−163.034	−5.87534
$771$	10.9264	0.393504
$772$	46.2046	1.66294
$773$	10.1272	0.364250	0.182125	−	0.983275i	$-0.441703\pi$
$773$	10.1272	0.364250	0.182125	+	0.983275i	$0.441703\pi$
$774$	9.69081	0.348329
$775$	−9.13576	−0.328166
$776$	−4.10889	−0.147501
$777$	−0.513055	−0.0184057
$778$	40.6163	1.45616
$779$	−40.7820	−1.46117
$780$	0	0
$781$	35.7331	1.27863
$782$	−36.0013	−1.28740
$783$	−16.4013	−0.586134
$784$	−14.1874	−0.506694
$785$	78.6681	2.80778
$786$	9.49376	0.338631
$787$	0.839639	0.0299299	0.0149649	−	0.999888i	$-0.495236\pi$
$787$	0.839639	0.0299299	0.0149649	+	0.999888i	$0.495236\pi$
$788$	−13.1383	−0.468031
$789$	−1.01126	−0.0360017
$790$	−28.8317	−1.02579
$791$	−18.4680	−0.656647
$792$	10.8926	0.387052
$793$	0	0
$794$	14.7484	0.523401
$795$	−32.3804	−1.14842
$796$	−48.0166	−1.70190
$797$	−6.52897	−0.231268	−0.115634	−	0.993292i	$-0.536890\pi$
$797$	−6.52897	−0.231268	−0.115634	+	0.993292i	$0.536890\pi$
$798$	−20.5841	−0.728671
$799$	−72.9092	−2.57934
$800$	−73.8559	−2.61120
$801$	−24.3329	−0.859761
$802$	−38.6841	−1.36598
$803$	5.87313	0.207258
$804$	21.1685	0.746555
$805$	−37.7301	−1.32981
$806$	0	0
$807$	−17.3588	−0.611058
$808$	1.49870	0.0527239
$809$	33.0760	1.16289	0.581446	−	0.813585i	$-0.302487\pi$
$809$	33.0760	1.16289	0.581446	+	0.813585i	$0.302487\pi$
$810$	−30.8094	−1.08253
$811$	−34.6275	−1.21594	−0.607969	−	0.793961i	$-0.708015\pi$
$811$	−34.6275	−1.21594	−0.607969	+	0.793961i	$0.708015\pi$
$812$	31.2129	1.09536
$813$	6.70106	0.235017
$814$	2.49181	0.0873379
$815$	−66.6942	−2.33620
$816$	14.3244	0.501456
$817$	7.25673	0.253881
$818$	43.8880	1.53451
$819$	0	0
$820$	−96.4621	−3.36860
$821$	10.9430	0.381914	0.190957	−	0.981598i	$-0.438841\pi$
$821$	10.9430	0.381914	0.190957	+	0.981598i	$0.438841\pi$
$822$	−19.8568	−0.692587
$823$	35.8487	1.24961	0.624803	−	0.780782i	$-0.285179\pi$
$823$	35.8487	1.24961	0.624803	+	0.780782i	$0.285179\pi$
$824$	−1.04986	−0.0365736
$825$	43.5414	1.51592
$826$	−21.0752	−0.733301
$827$	18.6209	0.647511	0.323756	−	0.946141i	$-0.395054\pi$
$827$	18.6209	0.647511	0.323756	+	0.946141i	$0.395054\pi$
$828$	16.7088	0.580670
$829$	43.7979	1.52117	0.760583	−	0.649241i	$-0.224913\pi$
$829$	43.7979	1.52117	0.760583	+	0.649241i	$0.224913\pi$
$830$	−13.3920	−0.464843
$831$	−4.44361	−0.154147
$832$	0	0
$833$	26.1307	0.905374
$834$	34.7419	1.20302
$835$	56.5483	1.95693
$836$	54.0650	1.86988
$837$	−4.19441	−0.144980
$838$	29.2963	1.01202
$839$	−18.2289	−0.629331	−0.314665	−	0.949203i	$-0.601892\pi$
$839$	−18.2289	−0.629331	−0.314665	+	0.949203i	$0.601892\pi$
$840$	−7.34543	−0.253441
$841$	−13.7098	−0.472751
$842$	−55.8061	−1.92320
$843$	5.82117	0.200492
$844$	−64.3936	−2.21652
$845$	0	0
$846$	62.5715	2.15125
$847$	−90.1131	−3.09632
$848$	35.0433	1.20339
$849$	−12.3058	−0.422333
$850$	111.073	3.80976
$851$	0.576665	0.0197678
$852$	10.6712	0.365589
$853$	−42.6315	−1.45968	−0.729838	−	0.683620i	$-0.760405\pi$
$853$	−42.6315	−1.45968	−0.729838	+	0.683620i	$0.760405\pi$
$854$	−49.0562	−1.67867
$855$	−33.7226	−1.15329
$856$	8.73315	0.298493
$857$	0.724671	0.0247543	0.0123771	−	0.999923i	$-0.496060\pi$
$857$	0.724671	0.0247543	0.0123771	+	0.999923i	$0.496060\pi$
$858$	0	0
$859$	13.4610	0.459282	0.229641	−	0.973275i	$-0.426245\pi$
$859$	13.4610	0.459282	0.229641	+	0.973275i	$0.426245\pi$
$860$	17.1644	0.585301
$861$	28.6971	0.977993
$862$	15.2499	0.519414
$863$	−10.0222	−0.341161	−0.170580	−	0.985344i	$-0.554564\pi$
$863$	−10.0222	−0.341161	−0.170580	+	0.985344i	$0.554564\pi$
$864$	−33.9087	−1.15360
$865$	14.6485	0.498065
$866$	73.2655	2.48966
$867$	−13.1679	−0.447205
$868$	7.98229	0.270936
$869$	−22.5286	−0.764231
$870$	−23.8506	−0.808612
$871$	0	0
$872$	−5.09288	−0.172467
$873$	13.2739	0.449252
$874$	23.1363	0.782595
$875$	52.6972	1.78149
$876$	1.75393	0.0592597
$877$	−25.6391	−0.865772	−0.432886	−	0.901449i	$-0.642505\pi$
$877$	−25.6391	−0.865772	−0.432886	+	0.901449i	$0.642505\pi$
$878$	8.54431	0.288356
$879$	−16.6565	−0.561809
$880$	−72.9120	−2.45786
$881$	54.9111	1.85000	0.925000	−	0.379966i	$-0.124064\pi$
$881$	54.9111	1.85000	0.925000	+	0.379966i	$0.124064\pi$
$882$	−22.4257	−0.755111
$883$	23.3276	0.785035	0.392517	−	0.919745i	$-0.371604\pi$
$883$	23.3276	0.785035	0.392517	+	0.919745i	$0.371604\pi$
$884$	0	0
$885$	8.70904	0.292751
$886$	22.3656	0.751386
$887$	−6.16098	−0.206865	−0.103433	−	0.994636i	$-0.532983\pi$
$887$	−6.16098	−0.206865	−0.103433	+	0.994636i	$0.532983\pi$
$888$	0.112267	0.00376744
$889$	10.7870	0.361785
$890$	−79.6949	−2.67138
$891$	−24.0740	−0.806509
$892$	−8.86787	−0.296918
$893$	46.8552	1.56795
$894$	9.36556	0.313231
$895$	19.5474	0.653399
$896$	19.7886	0.661091
$897$	0	0
$898$	34.3486	1.14623
$899$	3.91027	0.130415
$900$	−51.5506	−1.71835
$901$	−64.5435	−2.15025
$902$	−139.376	−4.64072
$903$	−5.10634	−0.169928
$904$	4.04119	0.134408
$905$	−1.41605	−0.0470711
$906$	23.5425	0.782146
$907$	7.71561	0.256193	0.128096	−	0.991762i	$-0.459113\pi$
$907$	7.71561	0.256193	0.128096	+	0.991762i	$0.459113\pi$
$908$	34.9284	1.15914
$909$	−4.84156	−0.160585
$910$	0	0
$911$	6.91880	0.229230	0.114615	−	0.993410i	$-0.463437\pi$
$911$	6.91880	0.229230	0.114615	+	0.993410i	$0.463437\pi$
$912$	−9.20562	−0.304829
$913$	−10.4643	−0.346317
$914$	−4.23052	−0.139933
$915$	20.2718	0.670164
$916$	−26.9828	−0.891537
$917$	19.8325	0.654927
$918$	50.9957	1.68311
$919$	8.07910	0.266505	0.133252	−	0.991082i	$-0.457458\pi$
$919$	8.07910	0.266505	0.133252	+	0.991082i	$0.457458\pi$
$920$	8.25614	0.272197
$921$	−13.0802	−0.431008
$922$	−1.42669	−0.0469856
$923$	0	0
$924$	−38.0439	−1.25155
$925$	−1.77915	−0.0584982
$926$	−13.8818	−0.456186
$927$	3.39159	0.111394
$928$	31.6117	1.03770
$929$	5.39980	0.177162	0.0885808	−	0.996069i	$-0.471767\pi$
$929$	5.39980	0.177162	0.0885808	+	0.996069i	$0.471767\pi$
$930$	−6.09948	−0.200010
$931$	−16.7929	−0.550365
$932$	19.1060	0.625837
$933$	19.6949	0.644782
$934$	44.3342	1.45066
$935$	134.291	4.39177
$936$	0	0
$937$	−26.3458	−0.860680	−0.430340	−	0.902667i	$-0.641606\pi$
$937$	−26.3458	−0.860680	−0.430340	+	0.902667i	$0.641606\pi$
$938$	81.7706	2.66990
$939$	13.3917	0.437021
$940$	110.827	3.61478
$941$	−10.0672	−0.328182	−0.164091	−	0.986445i	$-0.552469\pi$
$941$	−10.0672	−0.328182	−0.164091	+	0.986445i	$0.552469\pi$
$942$	33.9448	1.10598
$943$	−32.2550	−1.05037
$944$	−9.42525	−0.306766
$945$	53.4445	1.73855
$946$	24.8005	0.806334
$947$	−19.4706	−0.632709	−0.316354	−	0.948641i	$-0.602459\pi$
$947$	−19.4706	−0.632709	−0.316354	+	0.948641i	$0.602459\pi$
$948$	−6.72786	−0.218511
$949$	0	0
$950$	−71.3810	−2.31590
$951$	10.6139	0.344179
$952$	−14.6415	−0.474534
$953$	−41.5957	−1.34742	−0.673708	−	0.738997i	$-0.735300\pi$
$953$	−41.5957	−1.34742	−0.673708	+	0.738997i	$0.735300\pi$
$954$	55.3920	1.79338
$955$	−58.9205	−1.90662
$956$	−15.5744	−0.503714
$957$	−18.6365	−0.602432
$958$	49.9648	1.61429
$959$	−41.4810	−1.33949
$960$	−30.8207	−0.994735
$961$	1.00000	0.0322581
$962$	0	0
$963$	−28.2126	−0.909138
$964$	58.4507	1.88257
$965$	−73.7547	−2.37425
$966$	−16.2803	−0.523809
$967$	−25.7515	−0.828112	−0.414056	−	0.910251i	$-0.635888\pi$
$967$	−25.7515	−0.828112	−0.414056	+	0.910251i	$0.635888\pi$
$968$	19.7187	0.633782
$969$	16.9551	0.544676
$970$	43.4744	1.39588
$971$	−40.9577	−1.31440	−0.657198	−	0.753718i	$-0.728258\pi$
$971$	−40.9577	−1.31440	−0.657198	+	0.753718i	$0.728258\pi$
$972$	−36.8272	−1.18123
$973$	72.5760	2.32668
$974$	62.7566	2.01085
$975$	0	0
$976$	−21.9389	−0.702246
$977$	18.4990	0.591836	0.295918	−	0.955213i	$-0.404375\pi$
$977$	18.4990	0.591836	0.295918	+	0.955213i	$0.404375\pi$
$978$	−28.7781	−0.920222
$979$	−62.2723	−1.99023
$980$	−39.7204	−1.26882
$981$	16.4526	0.525292
$982$	53.5881	1.71006
$983$	14.6460	0.467135	0.233567	−	0.972341i	$-0.424960\pi$
$983$	14.6460	0.467135	0.233567	+	0.972341i	$0.424960\pi$
$984$	−6.27953	−0.200184
$985$	20.9721	0.668228
$986$	−47.5411	−1.51402
$987$	−32.9705	−1.04946
$988$	0	0
$989$	5.73944	0.182504
$990$	−115.250	−3.66288
$991$	17.0764	0.542450	0.271225	−	0.962516i	$-0.412571\pi$
$991$	17.0764	0.542450	0.271225	+	0.962516i	$0.412571\pi$
$992$	8.08427	0.256676
$993$	16.2864	0.516833
$994$	41.2212	1.30746
$995$	76.6472	2.42988
$996$	−3.12501	−0.0990196
$997$	6.41668	0.203218	0.101609	−	0.994824i	$-0.467601\pi$
$997$	6.41668	0.203218	0.101609	+	0.994824i	$0.467601\pi$
$998$	−17.3029	−0.547712
$999$	−0.816845	−0.0258438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.u.1.45	✓	54
13.12	even	2		5239.2.a.v.1.10	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.45	✓	54	1.1	even	1	trivial
5239.2.a.v.1.10	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)

\(f(q)\)	\(=\)	\(q+2.08695 q^{2} -0.777360 q^{3} +2.35535 q^{4} -3.75976 q^{5} -1.62231 q^{6} -3.38901 q^{7} +0.741587 q^{8} -2.39571 q^{9} +O(q^{10})\)	\(q+2.08695 q^{2} -0.777360 q^{3} +2.35535 q^{4} -3.75976 q^{5} -1.62231 q^{6} -3.38901 q^{7} +0.741587 q^{8} -2.39571 q^{9} -7.84641 q^{10} -6.13105 q^{11} -1.83095 q^{12} -7.07268 q^{14} +2.92268 q^{15} -3.16304 q^{16} +5.82574 q^{17} -4.99972 q^{18} -3.74392 q^{19} -8.85552 q^{20} +2.63448 q^{21} -12.7952 q^{22} -2.96112 q^{23} -0.576481 q^{24} +9.13576 q^{25} +4.19441 q^{27} -7.98229 q^{28} -3.91027 q^{29} +6.09948 q^{30} -1.00000 q^{31} -8.08427 q^{32} +4.76604 q^{33} +12.1580 q^{34} +12.7418 q^{35} -5.64273 q^{36} -0.194746 q^{37} -7.81336 q^{38} -2.78819 q^{40} +10.8929 q^{41} +5.49802 q^{42} -1.93827 q^{43} -14.4407 q^{44} +9.00729 q^{45} -6.17969 q^{46} -12.5150 q^{47} +2.45882 q^{48} +4.48538 q^{49} +19.0658 q^{50} -4.52870 q^{51} -11.0790 q^{53} +8.75351 q^{54} +23.0513 q^{55} -2.51325 q^{56} +2.91037 q^{57} -8.16052 q^{58} +2.97981 q^{59} +6.88393 q^{60} +6.93601 q^{61} -2.08695 q^{62} +8.11909 q^{63} -10.5454 q^{64} +9.94646 q^{66} -11.5615 q^{67} +13.7216 q^{68} +2.30185 q^{69} +26.5915 q^{70} -5.82822 q^{71} -1.77663 q^{72} -0.957932 q^{73} -0.406424 q^{74} -7.10177 q^{75} -8.81822 q^{76} +20.7782 q^{77} +3.67451 q^{79} +11.8922 q^{80} +3.92657 q^{81} +22.7328 q^{82} +1.70677 q^{83} +6.20511 q^{84} -21.9034 q^{85} -4.04507 q^{86} +3.03969 q^{87} -4.54671 q^{88} +10.1569 q^{89} +18.7977 q^{90} -6.97445 q^{92} +0.777360 q^{93} -26.1181 q^{94} +14.0762 q^{95} +6.28439 q^{96} -5.54067 q^{97} +9.36075 q^{98} +14.6882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

Properties

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