LMFDB - Embedded newform 5577.2.a.q.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.503376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 6x^{2} + 3x - 1 $ x^5 - x^4 - 6x^3 + 6x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.547285$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.547285 q^{2} -1.00000 q^{3} -1.70048 q^{4} -0.955178 q^{5} -0.547285 q^{6} -4.37449 q^{7} -2.02522 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.547285 q^{2} -1.00000 q^{3} -1.70048 q^{4} -0.955178 q^{5} -0.547285 q^{6} -4.37449 q^{7} -2.02522 q^{8} +1.00000 q^{9} -0.522755 q^{10} +1.00000 q^{11} +1.70048 q^{12} -2.39409 q^{14} +0.955178 q^{15} +2.29259 q^{16} -6.30513 q^{17} +0.547285 q^{18} +7.97346 q^{19} +1.62426 q^{20} +4.37449 q^{21} +0.547285 q^{22} +6.15686 q^{23} +2.02522 q^{24} -4.08764 q^{25} -1.00000 q^{27} +7.43872 q^{28} +6.17716 q^{29} +0.522755 q^{30} -2.39535 q^{31} +5.30513 q^{32} -1.00000 q^{33} -3.45071 q^{34} +4.17841 q^{35} -1.70048 q^{36} -4.57944 q^{37} +4.36376 q^{38} +1.93444 q^{40} -3.13233 q^{41} +2.39409 q^{42} +5.21056 q^{43} -1.70048 q^{44} -0.955178 q^{45} +3.36956 q^{46} -3.67401 q^{47} -2.29259 q^{48} +12.1361 q^{49} -2.23710 q^{50} +6.30513 q^{51} +0.617769 q^{53} -0.547285 q^{54} -0.955178 q^{55} +8.85928 q^{56} -7.97346 q^{57} +3.38067 q^{58} +13.0554 q^{59} -1.62426 q^{60} +0.890818 q^{61} -1.31094 q^{62} -4.37449 q^{63} -1.68175 q^{64} -0.547285 q^{66} -3.32587 q^{67} +10.7217 q^{68} -6.15686 q^{69} +2.28678 q^{70} +1.81660 q^{71} -2.02522 q^{72} +8.42492 q^{73} -2.50626 q^{74} +4.08764 q^{75} -13.5587 q^{76} -4.37449 q^{77} +16.9645 q^{79} -2.18983 q^{80} +1.00000 q^{81} -1.71428 q^{82} -11.8778 q^{83} -7.43872 q^{84} +6.02252 q^{85} +2.85166 q^{86} -6.17716 q^{87} -2.02522 q^{88} +10.0552 q^{89} -0.522755 q^{90} -10.4696 q^{92} +2.39535 q^{93} -2.01073 q^{94} -7.61607 q^{95} -5.30513 q^{96} -7.46849 q^{97} +6.64192 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 5 q^{3} + 3 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - q^2 - 5 * q^3 + 3 * q^4 + 2 * q^5 + q^6 - 6 * q^7 + 3 * q^8 + 5 * q^9	$ 5 q - q^{2} - 5 q^{3} + 3 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} + 3 q^{8} + 5 q^{9} + 5 q^{11} - 3 q^{12} - 16 q^{14} - 2 q^{15} + 3 q^{16} - 10 q^{17} - q^{18} + 18 q^{20} + 6 q^{21} - q^{22} - 4 q^{23} - 3 q^{24} + 7 q^{25} - 5 q^{27} - 12 q^{28} + 4 q^{29} - 22 q^{31} + 5 q^{32} - 5 q^{33} + 20 q^{34} + 3 q^{36} - 26 q^{37} - 10 q^{40} + 18 q^{41} + 16 q^{42} + 12 q^{43} + 3 q^{44} + 2 q^{45} + 22 q^{46} - 14 q^{47} - 3 q^{48} + 13 q^{49} - 37 q^{50} + 10 q^{51} - 2 q^{53} + q^{54} + 2 q^{55} - 8 q^{56} - 14 q^{58} + 18 q^{59} - 18 q^{60} + 18 q^{61} - 12 q^{62} - 6 q^{63} - 25 q^{64} + q^{66} - 8 q^{67} - 6 q^{68} + 4 q^{69} - 24 q^{70} + 4 q^{71} + 3 q^{72} + 12 q^{74} - 7 q^{75} - 58 q^{76} - 6 q^{77} + 18 q^{79} + 16 q^{80} + 5 q^{81} + 10 q^{82} - 34 q^{83} + 12 q^{84} - 12 q^{85} - 46 q^{86} - 4 q^{87} + 3 q^{88} - 10 q^{89} - 4 q^{92} + 22 q^{93} - 16 q^{94} - 22 q^{95} - 5 q^{96} + 4 q^{97} + 69 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q - q^2 - 5 * q^3 + 3 * q^4 + 2 * q^5 + q^6 - 6 * q^7 + 3 * q^8 + 5 * q^9 + 5 * q^11 - 3 * q^12 - 16 * q^14 - 2 * q^15 + 3 * q^16 - 10 * q^17 - q^18 + 18 * q^20 + 6 * q^21 - q^22 - 4 * q^23 - 3 * q^24 + 7 * q^25 - 5 * q^27 - 12 * q^28 + 4 * q^29 - 22 * q^31 + 5 * q^32 - 5 * q^33 + 20 * q^34 + 3 * q^36 - 26 * q^37 - 10 * q^40 + 18 * q^41 + 16 * q^42 + 12 * q^43 + 3 * q^44 + 2 * q^45 + 22 * q^46 - 14 * q^47 - 3 * q^48 + 13 * q^49 - 37 * q^50 + 10 * q^51 - 2 * q^53 + q^54 + 2 * q^55 - 8 * q^56 - 14 * q^58 + 18 * q^59 - 18 * q^60 + 18 * q^61 - 12 * q^62 - 6 * q^63 - 25 * q^64 + q^66 - 8 * q^67 - 6 * q^68 + 4 * q^69 - 24 * q^70 + 4 * q^71 + 3 * q^72 + 12 * q^74 - 7 * q^75 - 58 * q^76 - 6 * q^77 + 18 * q^79 + 16 * q^80 + 5 * q^81 + 10 * q^82 - 34 * q^83 + 12 * q^84 - 12 * q^85 - 46 * q^86 - 4 * q^87 + 3 * q^88 - 10 * q^89 - 4 * q^92 + 22 * q^93 - 16 * q^94 - 22 * q^95 - 5 * q^96 + 4 * q^97 + 69 * q^98 + 5 * 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 $

$2$	0.547285	0.386989	0.193495	−	0.981101i	$-0.438018\pi$
$2$	0.547285	0.386989	0.193495	+	0.981101i	$0.438018\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.70048	−0.850239
$5$	−0.955178	−0.427168	−0.213584	−	0.976925i	$-0.568514\pi$
$5$	−0.955178	−0.427168	−0.213584	+	0.976925i	$0.568514\pi$
$6$	−0.547285	−0.223428
$7$	−4.37449	−1.65340	−0.826700	−	0.562643i	$-0.809785\pi$
$7$	−4.37449	−1.65340	−0.826700	+	0.562643i	$0.809785\pi$
$8$	−2.02522	−0.716022
$9$	1.00000	0.333333
$10$	−0.522755	−0.165309
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.70048	0.490886
$13$	0	0
$13$	0	0
$14$	−2.39409	−0.639848
$15$	0.955178	0.246626
$16$	2.29259	0.573147
$17$	−6.30513	−1.52922	−0.764610	−	0.644494i	$-0.777068\pi$
$17$	−6.30513	−1.52922	−0.764610	+	0.644494i	$0.777068\pi$
$18$	0.547285	0.128996
$19$	7.97346	1.82924	0.914619	−	0.404318i	$-0.132491\pi$
$19$	7.97346	1.82924	0.914619	+	0.404318i	$0.132491\pi$
$20$	1.62426	0.363195
$21$	4.37449	0.954591
$22$	0.547285	0.116682
$23$	6.15686	1.28380	0.641898	−	0.766790i	$-0.278147\pi$
$23$	6.15686	1.28380	0.641898	+	0.766790i	$0.278147\pi$
$24$	2.02522	0.413396
$25$	−4.08764	−0.817527
$26$	0	0
$27$	−1.00000	−0.192450
$28$	7.43872	1.40579
$29$	6.17716	1.14707	0.573535	−	0.819181i	$-0.305572\pi$
$29$	6.17716	1.14707	0.573535	+	0.819181i	$0.305572\pi$
$30$	0.522755	0.0954415
$31$	−2.39535	−0.430217	−0.215108	−	0.976590i	$-0.569010\pi$
$31$	−2.39535	−0.430217	−0.215108	+	0.976590i	$0.569010\pi$
$32$	5.30513	0.937824
$33$	−1.00000	−0.174078
$34$	−3.45071	−0.591791
$35$	4.17841	0.706280
$36$	−1.70048	−0.283413
$37$	−4.57944	−0.752855	−0.376427	−	0.926446i	$-0.622848\pi$
$37$	−4.57944	−0.752855	−0.376427	+	0.926446i	$0.622848\pi$
$38$	4.36376	0.707895
$39$	0	0
$40$	1.93444	0.305862
$41$	−3.13233	−0.489188	−0.244594	−	0.969626i	$-0.578655\pi$
$41$	−3.13233	−0.489188	−0.244594	+	0.969626i	$0.578655\pi$
$42$	2.39409	0.369416
$43$	5.21056	0.794603	0.397302	−	0.917688i	$-0.369947\pi$
$43$	5.21056	0.794603	0.397302	+	0.917688i	$0.369947\pi$
$44$	−1.70048	−0.256357
$45$	−0.955178	−0.142389
$46$	3.36956	0.496815
$47$	−3.67401	−0.535909	−0.267955	−	0.963432i	$-0.586348\pi$
$47$	−3.67401	−0.535909	−0.267955	+	0.963432i	$0.586348\pi$
$48$	−2.29259	−0.330906
$49$	12.1361	1.73373
$50$	−2.23710	−0.316374
$51$	6.30513	0.882895
$52$	0	0
$53$	0.617769	0.0848570	0.0424285	−	0.999100i	$-0.486491\pi$
$53$	0.617769	0.0848570	0.0424285	+	0.999100i	$0.486491\pi$
$54$	−0.547285	−0.0744761
$55$	−0.955178	−0.128796
$56$	8.85928	1.18387
$57$	−7.97346	−1.05611
$58$	3.38067	0.443903
$59$	13.0554	1.69966	0.849832	−	0.527054i	$-0.176704\pi$
$59$	13.0554	1.69966	0.849832	+	0.527054i	$0.176704\pi$
$60$	−1.62426	−0.209691
$61$	0.890818	0.114058	0.0570288	−	0.998373i	$-0.481837\pi$
$61$	0.890818	0.114058	0.0570288	+	0.998373i	$0.481837\pi$
$62$	−1.31094	−0.166489
$63$	−4.37449	−0.551133
$64$	−1.68175	−0.210219
$65$	0	0
$66$	−0.547285	−0.0673661
$67$	−3.32587	−0.406320	−0.203160	−	0.979146i	$-0.565121\pi$
$67$	−3.32587	−0.406320	−0.203160	+	0.979146i	$0.565121\pi$
$68$	10.7217	1.30020
$69$	−6.15686	−0.741199
$70$	2.28678	0.273323
$71$	1.81660	0.215590	0.107795	−	0.994173i	$-0.465621\pi$
$71$	1.81660	0.215590	0.107795	+	0.994173i	$0.465621\pi$
$72$	−2.02522	−0.238674
$73$	8.42492	0.986062	0.493031	−	0.870012i	$-0.335889\pi$
$73$	8.42492	0.986062	0.493031	+	0.870012i	$0.335889\pi$
$74$	−2.50626	−0.291347
$75$	4.08764	0.472000
$76$	−13.5587	−1.55529
$77$	−4.37449	−0.498519
$78$	0	0
$79$	16.9645	1.90865	0.954325	−	0.298769i	$-0.0965760\pi$
$79$	16.9645	1.90865	0.954325	+	0.298769i	$0.0965760\pi$
$80$	−2.18983	−0.244830
$81$	1.00000	0.111111
$82$	−1.71428	−0.189311
$83$	−11.8778	−1.30375	−0.651877	−	0.758325i	$-0.726018\pi$
$83$	−11.8778	−1.30375	−0.651877	+	0.758325i	$0.726018\pi$
$84$	−7.43872	−0.811631
$85$	6.02252	0.653234
$86$	2.85166	0.307503
$87$	−6.17716	−0.662261
$88$	−2.02522	−0.215889
$89$	10.0552	1.06585	0.532926	−	0.846162i	$-0.321092\pi$
$89$	10.0552	1.06585	0.532926	+	0.846162i	$0.321092\pi$
$90$	−0.522755	−0.0551032
$91$	0	0
$92$	−10.4696	−1.09153
$93$	2.39535	0.248386
$94$	−2.01073	−0.207391
$95$	−7.61607	−0.781392
$96$	−5.30513	−0.541453
$97$	−7.46849	−0.758310	−0.379155	−	0.925333i	$-0.623785\pi$
$97$	−7.46849	−0.758310	−0.379155	+	0.925333i	$0.623785\pi$
$98$	6.64192	0.670936
$99$	1.00000	0.100504
$100$	6.95094	0.695094
$101$	10.3305	1.02792	0.513960	−	0.857814i	$-0.328178\pi$
$101$	10.3305	1.02792	0.513960	+	0.857814i	$0.328178\pi$
$102$	3.45071	0.341671
$103$	−3.50682	−0.345537	−0.172769	−	0.984962i	$-0.555271\pi$
$103$	−3.50682	−0.345537	−0.172769	+	0.984962i	$0.555271\pi$
$104$	0	0
$105$	−4.17841	−0.407771
$106$	0.338096	0.0328387
$107$	−13.3341	−1.28906	−0.644530	−	0.764579i	$-0.722947\pi$
$107$	−13.3341	−1.28906	−0.644530	+	0.764579i	$0.722947\pi$
$108$	1.70048	0.163629
$109$	−10.3491	−0.991268	−0.495634	−	0.868531i	$-0.665064\pi$
$109$	−10.3491	−0.991268	−0.495634	+	0.868531i	$0.665064\pi$
$110$	−0.522755	−0.0498427
$111$	4.57944	0.434661
$112$	−10.0289	−0.947641
$113$	−2.19802	−0.206772	−0.103386	−	0.994641i	$-0.532968\pi$
$113$	−2.19802	−0.206772	−0.103386	+	0.994641i	$0.532968\pi$
$114$	−4.36376	−0.408703
$115$	−5.88090	−0.548397
$116$	−10.5041	−0.975283
$117$	0	0
$118$	7.14500	0.657751
$119$	27.5817	2.52841
$120$	−1.93444	−0.176590
$121$	1.00000	0.0909091
$122$	0.487531	0.0441390
$123$	3.13233	0.282433
$124$	4.07324	0.365787
$125$	8.68031	0.776390
$126$	−2.39409	−0.213283
$127$	−11.2742	−1.00043	−0.500213	−	0.865902i	$-0.666745\pi$
$127$	−11.2742	−1.00043	−0.500213	+	0.865902i	$0.666745\pi$
$128$	−11.5307	−1.01918
$129$	−5.21056	−0.458764
$130$	0	0
$131$	−13.1311	−1.14727	−0.573636	−	0.819110i	$-0.694468\pi$
$131$	−13.1311	−1.14727	−0.573636	+	0.819110i	$0.694468\pi$
$132$	1.70048	0.148008
$133$	−34.8798	−3.02446
$134$	−1.82020	−0.157241
$135$	0.955178	0.0822086
$136$	12.7693	1.09496
$137$	−12.4741	−1.06573	−0.532867	−	0.846199i	$-0.678885\pi$
$137$	−12.4741	−1.06573	−0.532867	+	0.846199i	$0.678885\pi$
$138$	−3.36956	−0.286836
$139$	−7.61482	−0.645880	−0.322940	−	0.946419i	$-0.604671\pi$
$139$	−7.61482	−0.645880	−0.322940	+	0.946419i	$0.604671\pi$
$140$	−7.10530	−0.600507
$141$	3.67401	0.309407
$142$	0.994196	0.0834311
$143$	0	0
$144$	2.29259	0.191049
$145$	−5.90028	−0.489992
$146$	4.61083	0.381595
$147$	−12.1361	−1.00097
$148$	7.78724	0.640107
$149$	−20.6278	−1.68989	−0.844947	−	0.534849i	$-0.820368\pi$
$149$	−20.6278	−1.68989	−0.844947	+	0.534849i	$0.820368\pi$
$150$	2.23710	0.182659
$151$	−4.38336	−0.356713	−0.178356	−	0.983966i	$-0.557078\pi$
$151$	−4.38336	−0.356713	−0.178356	+	0.983966i	$0.557078\pi$
$152$	−16.1480	−1.30977
$153$	−6.30513	−0.509740
$154$	−2.39409	−0.192921
$155$	2.28798	0.183775
$156$	0	0
$157$	12.3964	0.989344	0.494672	−	0.869080i	$-0.335288\pi$
$157$	12.3964	0.989344	0.494672	+	0.869080i	$0.335288\pi$
$158$	9.28440	0.738627
$159$	−0.617769	−0.0489922
$160$	−5.06734	−0.400609
$161$	−26.9331	−2.12263
$162$	0.547285	0.0429988
$163$	−1.15407	−0.0903939	−0.0451970	−	0.998978i	$-0.514392\pi$
$163$	−1.15407	−0.0903939	−0.0451970	+	0.998978i	$0.514392\pi$
$164$	5.32647	0.415927
$165$	0.955178	0.0743605
$166$	−6.50052	−0.504538
$167$	−11.6820	−0.903981	−0.451990	−	0.892023i	$-0.649286\pi$
$167$	−11.6820	−0.903981	−0.451990	+	0.892023i	$0.649286\pi$
$168$	−8.85928	−0.683509
$169$	0	0
$170$	3.29604	0.252794
$171$	7.97346	0.609746
$172$	−8.86045	−0.675603
$173$	9.14601	0.695358	0.347679	−	0.937614i	$-0.386970\pi$
$173$	9.14601	0.695358	0.347679	+	0.937614i	$0.386970\pi$
$174$	−3.38067	−0.256288
$175$	17.8813	1.35170
$176$	2.29259	0.172810
$177$	−13.0554	−0.981301
$178$	5.50308	0.412473
$179$	−14.1243	−1.05570	−0.527849	−	0.849338i	$-0.677001\pi$
$179$	−14.1243	−1.05570	−0.527849	+	0.849338i	$0.677001\pi$
$180$	1.62426	0.121065
$181$	2.52918	0.187992	0.0939961	−	0.995573i	$-0.470036\pi$
$181$	2.52918	0.187992	0.0939961	+	0.995573i	$0.470036\pi$
$182$	0	0
$183$	−0.890818	−0.0658512
$184$	−12.4690	−0.919226
$185$	4.37418	0.321596
$186$	1.31094	0.0961226
$187$	−6.30513	−0.461077
$188$	6.24757	0.455651
$189$	4.37449	0.318197
$190$	−4.16816	−0.302390
$191$	2.92327	0.211520	0.105760	−	0.994392i	$-0.466272\pi$
$191$	2.92327	0.211520	0.105760	+	0.994392i	$0.466272\pi$
$192$	1.68175	0.121370
$193$	0.578869	0.0416679	0.0208339	−	0.999783i	$-0.493368\pi$
$193$	0.578869	0.0416679	0.0208339	+	0.999783i	$0.493368\pi$
$194$	−4.08739	−0.293458
$195$	0	0
$196$	−20.6372	−1.47409
$197$	13.9481	0.993762	0.496881	−	0.867819i	$-0.334478\pi$
$197$	13.9481	0.993762	0.496881	+	0.867819i	$0.334478\pi$
$198$	0.547285	0.0388939
$199$	16.4750	1.16788	0.583942	−	0.811795i	$-0.301509\pi$
$199$	16.4750	1.16788	0.583942	+	0.811795i	$0.301509\pi$
$200$	8.27835	0.585368
$201$	3.32587	0.234589
$202$	5.65372	0.397794
$203$	−27.0219	−1.89656
$204$	−10.7217	−0.750672
$205$	2.99194	0.208966
$206$	−1.91923	−0.133719
$207$	6.15686	0.427932
$208$	0	0
$209$	7.97346	0.551536
$210$	−2.28678	−0.157803
$211$	18.3150	1.26086	0.630428	−	0.776248i	$-0.282880\pi$
$211$	18.3150	1.26086	0.630428	+	0.776248i	$0.282880\pi$
$212$	−1.05050	−0.0721488
$213$	−1.81660	−0.124471
$214$	−7.29758	−0.498852
$215$	−4.97701	−0.339429
$216$	2.02522	0.137799
$217$	10.4784	0.711321
$218$	−5.66393	−0.383610
$219$	−8.42492	−0.569303
$220$	1.62426	0.109508
$221$	0	0
$222$	2.50626	0.168209
$223$	−13.5671	−0.908518	−0.454259	−	0.890870i	$-0.650096\pi$
$223$	−13.5671	−0.908518	−0.454259	+	0.890870i	$0.650096\pi$
$224$	−23.2072	−1.55060
$225$	−4.08764	−0.272509
$226$	−1.20294	−0.0800185
$227$	0.374486	0.0248555	0.0124278	−	0.999923i	$-0.496044\pi$
$227$	0.374486	0.0248555	0.0124278	+	0.999923i	$0.496044\pi$
$228$	13.5587	0.897947
$229$	−15.5719	−1.02902	−0.514509	−	0.857485i	$-0.672026\pi$
$229$	−15.5719	−1.02902	−0.514509	+	0.857485i	$0.672026\pi$
$230$	−3.21853	−0.212224
$231$	4.37449	0.287820
$232$	−12.5101	−0.821327
$233$	−13.8177	−0.905227	−0.452613	−	0.891707i	$-0.649508\pi$
$233$	−13.8177	−0.905227	−0.452613	+	0.891707i	$0.649508\pi$
$234$	0	0
$235$	3.50933	0.228923
$236$	−22.2004	−1.44512
$237$	−16.9645	−1.10196
$238$	15.0951	0.978468
$239$	10.7640	0.696265	0.348132	−	0.937445i	$-0.386816\pi$
$239$	10.7640	0.696265	0.348132	+	0.937445i	$0.386816\pi$
$240$	2.18983	0.141353
$241$	11.4930	0.740326	0.370163	−	0.928967i	$-0.379302\pi$
$241$	11.4930	0.740326	0.370163	+	0.928967i	$0.379302\pi$
$242$	0.547285	0.0351808
$243$	−1.00000	−0.0641500
$244$	−1.51482	−0.0969762
$245$	−11.5922	−0.740596
$246$	1.71428	0.109298
$247$	0	0
$248$	4.85110	0.308045
$249$	11.8778	0.752722
$250$	4.75060	0.300454
$251$	−7.14001	−0.450674	−0.225337	−	0.974281i	$-0.572348\pi$
$251$	−7.14001	−0.450674	−0.225337	+	0.974281i	$0.572348\pi$
$252$	7.43872	0.468595
$253$	6.15686	0.387079
$254$	−6.17022	−0.387154
$255$	−6.02252	−0.377145
$256$	−2.94706	−0.184191
$257$	6.59154	0.411169	0.205584	−	0.978639i	$-0.434090\pi$
$257$	6.59154	0.411169	0.205584	+	0.978639i	$0.434090\pi$
$258$	−2.85166	−0.177537
$259$	20.0327	1.24477
$260$	0	0
$261$	6.17716	0.382356
$262$	−7.18648	−0.443982
$263$	31.2573	1.92741	0.963705	−	0.266968i	$-0.0860220\pi$
$263$	31.2573	1.92741	0.963705	+	0.266968i	$0.0860220\pi$
$264$	2.02522	0.124644
$265$	−0.590079	−0.0362482
$266$	−19.0892	−1.17043
$267$	−10.0552	−0.615370
$268$	5.65557	0.345469
$269$	−19.2067	−1.17105	−0.585525	−	0.810654i	$-0.699112\pi$
$269$	−19.2067	−1.17105	−0.585525	+	0.810654i	$0.699112\pi$
$270$	0.522755	0.0318138
$271$	−10.6834	−0.648969	−0.324485	−	0.945891i	$-0.605191\pi$
$271$	−10.6834	−0.648969	−0.324485	+	0.945891i	$0.605191\pi$
$272$	−14.4551	−0.876467
$273$	0	0
$274$	−6.82689	−0.412428
$275$	−4.08764	−0.246494
$276$	10.4696	0.630197
$277$	−2.65933	−0.159784	−0.0798918	−	0.996804i	$-0.525457\pi$
$277$	−2.65933	−0.159784	−0.0798918	+	0.996804i	$0.525457\pi$
$278$	−4.16748	−0.249949
$279$	−2.39535	−0.143406
$280$	−8.46219	−0.505713
$281$	−33.4876	−1.99770	−0.998852	−	0.0479021i	$-0.984746\pi$
$281$	−33.4876	−1.99770	−0.998852	+	0.0479021i	$0.984746\pi$
$282$	2.01073	0.119737
$283$	−5.70923	−0.339379	−0.169689	−	0.985498i	$-0.554276\pi$
$283$	−5.70923	−0.339379	−0.169689	+	0.985498i	$0.554276\pi$
$284$	−3.08908	−0.183303
$285$	7.61607	0.451137
$286$	0	0
$287$	13.7024	0.808824
$288$	5.30513	0.312608
$289$	22.7547	1.33851
$290$	−3.22914	−0.189621
$291$	7.46849	0.437811
$292$	−14.3264	−0.838389
$293$	9.43872	0.551416	0.275708	−	0.961241i	$-0.411088\pi$
$293$	9.43872	0.551416	0.275708	+	0.961241i	$0.411088\pi$
$294$	−6.64192	−0.387365
$295$	−12.4702	−0.726042
$296$	9.27435	0.539061
$297$	−1.00000	−0.0580259
$298$	−11.2893	−0.653971
$299$	0	0
$300$	−6.95094	−0.401313
$301$	−22.7935	−1.31380
$302$	−2.39895	−0.138044
$303$	−10.3305	−0.593470
$304$	18.2798	1.04842
$305$	−0.850889	−0.0487218
$306$	−3.45071	−0.197264
$307$	27.6352	1.57722	0.788612	−	0.614891i	$-0.210800\pi$
$307$	27.6352	1.57722	0.788612	+	0.614891i	$0.210800\pi$
$308$	7.43872	0.423861
$309$	3.50682	0.199496
$310$	1.25218	0.0711189
$311$	2.04350	0.115876	0.0579381	−	0.998320i	$-0.481547\pi$
$311$	2.04350	0.115876	0.0579381	+	0.998320i	$0.481547\pi$
$312$	0	0
$313$	−8.31567	−0.470029	−0.235015	−	0.971992i	$-0.575514\pi$
$313$	−8.31567	−0.470029	−0.235015	+	0.971992i	$0.575514\pi$
$314$	6.78439	0.382865
$315$	4.17841	0.235427
$316$	−28.8477	−1.62281
$317$	−15.1498	−0.850898	−0.425449	−	0.904982i	$-0.639884\pi$
$317$	−15.1498	−0.850898	−0.425449	+	0.904982i	$0.639884\pi$
$318$	−0.338096	−0.0189595
$319$	6.17716	0.345854
$320$	1.60637	0.0897989
$321$	13.3341	0.744239
$322$	−14.7401	−0.821433
$323$	−50.2737	−2.79731
$324$	−1.70048	−0.0944711
$325$	0	0
$326$	−0.631607	−0.0349815
$327$	10.3491	0.572309
$328$	6.34366	0.350270
$329$	16.0719	0.886072
$330$	0.522755	0.0287767
$331$	−25.9100	−1.42414	−0.712071	−	0.702107i	$-0.752243\pi$
$331$	−25.9100	−1.42414	−0.712071	+	0.702107i	$0.752243\pi$
$332$	20.1979	1.10850
$333$	−4.57944	−0.250952
$334$	−6.39339	−0.349831
$335$	3.17680	0.173567
$336$	10.0289	0.547121
$337$	−8.86485	−0.482899	−0.241449	−	0.970413i	$-0.577623\pi$
$337$	−8.86485	−0.482899	−0.241449	+	0.970413i	$0.577623\pi$
$338$	0	0
$339$	2.19802	0.119380
$340$	−10.2412	−0.555405
$341$	−2.39535	−0.129715
$342$	4.36376	0.235965
$343$	−22.4679	−1.21315
$344$	−10.5525	−0.568954
$345$	5.88090	0.316617
$346$	5.00548	0.269096
$347$	11.7646	0.631558	0.315779	−	0.948833i	$-0.397734\pi$
$347$	11.7646	0.631558	0.315779	+	0.948833i	$0.397734\pi$
$348$	10.5041	0.563080
$349$	−32.0398	−1.71505	−0.857526	−	0.514441i	$-0.827999\pi$
$349$	−32.0398	−1.71505	−0.857526	+	0.514441i	$0.827999\pi$
$350$	9.78617	0.523093
$351$	0	0
$352$	5.30513	0.282765
$353$	32.5832	1.73423	0.867115	−	0.498108i	$-0.165972\pi$
$353$	32.5832	1.73423	0.867115	+	0.498108i	$0.165972\pi$
$354$	−7.14500	−0.379753
$355$	−1.73517	−0.0920933
$356$	−17.0987	−0.906230
$357$	−27.5817	−1.45978
$358$	−7.73000	−0.408543
$359$	−35.3920	−1.86792	−0.933959	−	0.357379i	$-0.883670\pi$
$359$	−35.3920	−1.86792	−0.933959	+	0.357379i	$0.883670\pi$
$360$	1.93444	0.101954
$361$	44.5761	2.34611
$362$	1.38418	0.0727509
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−8.04730	−0.421215
$366$	−0.487531	−0.0254837
$367$	5.80933	0.303244	0.151622	−	0.988439i	$-0.451550\pi$
$367$	5.80933	0.303244	0.151622	+	0.988439i	$0.451550\pi$
$368$	14.1151	0.735803
$369$	−3.13233	−0.163063
$370$	2.39392	0.124454
$371$	−2.70242	−0.140303
$372$	−4.07324	−0.211187
$373$	3.47511	0.179934	0.0899672	−	0.995945i	$-0.471324\pi$
$373$	3.47511	0.179934	0.0899672	+	0.995945i	$0.471324\pi$
$374$	−3.45071	−0.178432
$375$	−8.68031	−0.448249
$376$	7.44066	0.383723
$377$	0	0
$378$	2.39409	0.123139
$379$	10.2421	0.526102	0.263051	−	0.964782i	$-0.415271\pi$
$379$	10.2421	0.526102	0.263051	+	0.964782i	$0.415271\pi$
$380$	12.9510	0.664371
$381$	11.2742	0.577597
$382$	1.59986	0.0818560
$383$	−23.2952	−1.19033	−0.595164	−	0.803604i	$-0.702913\pi$
$383$	−23.2952	−1.19033	−0.595164	+	0.803604i	$0.702913\pi$
$384$	11.5307	0.588422
$385$	4.17841	0.212952
$386$	0.316806	0.0161250
$387$	5.21056	0.264868
$388$	12.7000	0.644745
$389$	2.88009	0.146026	0.0730131	−	0.997331i	$-0.476738\pi$
$389$	2.88009	0.146026	0.0730131	+	0.997331i	$0.476738\pi$
$390$	0	0
$391$	−38.8199	−1.96320
$392$	−24.5783	−1.24139
$393$	13.1311	0.662378
$394$	7.63360	0.384575
$395$	−16.2041	−0.815315
$396$	−1.70048	−0.0854523
$397$	−10.6070	−0.532352	−0.266176	−	0.963924i	$-0.585760\pi$
$397$	−10.6070	−0.532352	−0.266176	+	0.963924i	$0.585760\pi$
$398$	9.01655	0.451959
$399$	34.8798	1.74617
$400$	−9.37126	−0.468563
$401$	28.5679	1.42661	0.713305	−	0.700853i	$-0.247197\pi$
$401$	28.5679	1.42661	0.713305	+	0.700853i	$0.247197\pi$
$402$	1.82020	0.0907833
$403$	0	0
$404$	−17.5668	−0.873979
$405$	−0.955178	−0.0474632
$406$	−14.7887	−0.733950
$407$	−4.57944	−0.226994
$408$	−12.7693	−0.632173
$409$	−1.20414	−0.0595409	−0.0297704	−	0.999557i	$-0.509478\pi$
$409$	−1.20414	−0.0595409	−0.0297704	+	0.999557i	$0.509478\pi$
$410$	1.63744	0.0808675
$411$	12.4741	0.615302
$412$	5.96327	0.293789
$413$	−57.1105	−2.81022
$414$	3.36956	0.165605
$415$	11.3454	0.556922
$416$	0	0
$417$	7.61482	0.372899
$418$	4.36376	0.213438
$419$	4.27522	0.208858	0.104429	−	0.994532i	$-0.466698\pi$
$419$	4.27522	0.208858	0.104429	+	0.994532i	$0.466698\pi$
$420$	7.10530	0.346703
$421$	−16.5321	−0.805725	−0.402862	−	0.915261i	$-0.631985\pi$
$421$	−16.5321	−0.805725	−0.402862	+	0.915261i	$0.631985\pi$
$422$	10.0235	0.487937
$423$	−3.67401	−0.178636
$424$	−1.25112	−0.0607595
$425$	25.7731	1.25018
$426$	−0.994196	−0.0481689
$427$	−3.89687	−0.188583
$428$	22.6744	1.09601
$429$	0	0
$430$	−2.72385	−0.131355
$431$	−17.3415	−0.835310	−0.417655	−	0.908606i	$-0.637148\pi$
$431$	−17.3415	−0.835310	−0.417655	+	0.908606i	$0.637148\pi$
$432$	−2.29259	−0.110302
$433$	−5.31382	−0.255366	−0.127683	−	0.991815i	$-0.540754\pi$
$433$	−5.31382	−0.255366	−0.127683	+	0.991815i	$0.540754\pi$
$434$	5.73468	0.275273
$435$	5.90028	0.282897
$436$	17.5985	0.842815
$437$	49.0915	2.34837
$438$	−4.61083	−0.220314
$439$	32.9098	1.57070	0.785349	−	0.619054i	$-0.212484\pi$
$439$	32.9098	1.57070	0.785349	+	0.619054i	$0.212484\pi$
$440$	1.93444	0.0922209
$441$	12.1361	0.577911
$442$	0	0
$443$	−14.6797	−0.697451	−0.348726	−	0.937225i	$-0.613385\pi$
$443$	−14.6797	−0.697451	−0.348726	+	0.937225i	$0.613385\pi$
$444$	−7.78724	−0.369566
$445$	−9.60454	−0.455299
$446$	−7.42505	−0.351586
$447$	20.6278	0.975661
$448$	7.35680	0.347576
$449$	24.7121	1.16623	0.583117	−	0.812388i	$-0.301833\pi$
$449$	24.7121	1.16623	0.583117	+	0.812388i	$0.301833\pi$
$450$	−2.23710	−0.105458
$451$	−3.13233	−0.147496
$452$	3.73768	0.175806
$453$	4.38336	0.205948
$454$	0.204951	0.00961881
$455$	0	0
$456$	16.1480	0.756199
$457$	−19.1273	−0.894735	−0.447368	−	0.894350i	$-0.647638\pi$
$457$	−19.1273	−0.894735	−0.447368	+	0.894350i	$0.647638\pi$
$458$	−8.52225	−0.398219
$459$	6.30513	0.294298
$460$	10.0003	0.466268
$461$	33.9286	1.58021	0.790106	−	0.612970i	$-0.210025\pi$
$461$	33.9286	1.58021	0.790106	+	0.612970i	$0.210025\pi$
$462$	2.39409	0.111383
$463$	−30.9206	−1.43700	−0.718500	−	0.695527i	$-0.755171\pi$
$463$	−30.9206	−1.43700	−0.718500	+	0.695527i	$0.755171\pi$
$464$	14.1617	0.657439
$465$	−2.28798	−0.106103
$466$	−7.56222	−0.350313
$467$	17.2553	0.798481	0.399240	−	0.916846i	$-0.369274\pi$
$467$	17.2553	0.798481	0.399240	+	0.916846i	$0.369274\pi$
$468$	0	0
$469$	14.5490	0.671809
$470$	1.92060	0.0885908
$471$	−12.3964	−0.571198
$472$	−26.4399	−1.21700
$473$	5.21056	0.239582
$474$	−9.28440	−0.426447
$475$	−32.5926	−1.49545
$476$	−46.9021	−2.14976
$477$	0.617769	0.0282857
$478$	5.89097	0.269447
$479$	30.2952	1.38422	0.692111	−	0.721791i	$-0.256681\pi$
$479$	30.2952	1.38422	0.692111	+	0.721791i	$0.256681\pi$
$480$	5.06734	0.231292
$481$	0	0
$482$	6.28992	0.286498
$483$	26.9331	1.22550
$484$	−1.70048	−0.0772945
$485$	7.13373	0.323926
$486$	−0.547285	−0.0248254
$487$	0.563260	0.0255237	0.0127619	−	0.999919i	$-0.495938\pi$
$487$	0.563260	0.0255237	0.0127619	+	0.999919i	$0.495938\pi$
$488$	−1.80410	−0.0816678
$489$	1.15407	0.0521890
$490$	−6.34422	−0.286602
$491$	7.33979	0.331240	0.165620	−	0.986190i	$-0.447037\pi$
$491$	7.33979	0.331240	0.165620	+	0.986190i	$0.447037\pi$
$492$	−5.32647	−0.240136
$493$	−38.9478	−1.75412
$494$	0	0
$495$	−0.955178	−0.0429320
$496$	−5.49154	−0.246577
$497$	−7.94667	−0.356457
$498$	6.50052	0.291295
$499$	−33.8165	−1.51383	−0.756917	−	0.653511i	$-0.773295\pi$
$499$	−33.8165	−1.51383	−0.756917	+	0.653511i	$0.773295\pi$
$500$	−14.7607	−0.660118
$501$	11.6820	0.521913
$502$	−3.90762	−0.174406
$503$	−15.1318	−0.674692	−0.337346	−	0.941381i	$-0.609529\pi$
$503$	−15.1318	−0.674692	−0.337346	+	0.941381i	$0.609529\pi$
$504$	8.85928	0.394624
$505$	−9.86744	−0.439095
$506$	3.36956	0.149795
$507$	0	0
$508$	19.1716	0.850602
$509$	7.59020	0.336430	0.168215	−	0.985750i	$-0.446200\pi$
$509$	7.59020	0.336430	0.168215	+	0.985750i	$0.446200\pi$
$510$	−3.29604	−0.145951
$511$	−36.8547	−1.63036
$512$	21.4484	0.947896
$513$	−7.97346	−0.352037
$514$	3.60745	0.159118
$515$	3.34964	0.147603
$516$	8.86045	0.390060
$517$	−3.67401	−0.161583
$518$	10.9636	0.481713
$519$	−9.14601	−0.401465
$520$	0	0
$521$	26.6667	1.16829	0.584144	−	0.811650i	$-0.301430\pi$
$521$	26.6667	1.16829	0.584144	+	0.811650i	$0.301430\pi$
$522$	3.38067	0.147968
$523$	38.5709	1.68659	0.843293	−	0.537454i	$-0.180614\pi$
$523$	38.5709	1.68659	0.843293	+	0.537454i	$0.180614\pi$
$524$	22.3292	0.975457
$525$	−17.8813	−0.780404
$526$	17.1067	0.745887
$527$	15.1030	0.657896
$528$	−2.29259	−0.0997720
$529$	14.9070	0.648130
$530$	−0.322941	−0.0140277
$531$	13.0554	0.566554
$532$	59.3124	2.57152
$533$	0	0
$534$	−5.50308	−0.238142
$535$	12.7365	0.550646
$536$	6.73561	0.290934
$537$	14.1243	0.609507
$538$	−10.5115	−0.453184
$539$	12.1361	0.522740
$540$	−1.62426	−0.0698970
$541$	−22.1465	−0.952154	−0.476077	−	0.879404i	$-0.657942\pi$
$541$	−22.1465	−0.952154	−0.476077	+	0.879404i	$0.657942\pi$
$542$	−5.84686	−0.251144
$543$	−2.52918	−0.108537
$544$	−33.4496	−1.43414
$545$	9.88527	0.423438
$546$	0	0
$547$	−36.0573	−1.54170	−0.770849	−	0.637018i	$-0.780168\pi$
$547$	−36.0573	−1.54170	−0.770849	+	0.637018i	$0.780168\pi$
$548$	21.2119	0.906129
$549$	0.890818	0.0380192
$550$	−2.23710	−0.0953904
$551$	49.2533	2.09826
$552$	12.4690	0.530715
$553$	−74.2108	−3.15576
$554$	−1.45541	−0.0618345
$555$	−4.37418	−0.185673
$556$	12.9488	0.549153
$557$	20.9181	0.886326	0.443163	−	0.896441i	$-0.353856\pi$
$557$	20.9181	0.886326	0.443163	+	0.896441i	$0.353856\pi$
$558$	−1.31094	−0.0554964
$559$	0	0
$560$	9.57937	0.404802
$561$	6.30513	0.266203
$562$	−18.3273	−0.773090
$563$	22.2118	0.936117	0.468059	−	0.883697i	$-0.344954\pi$
$563$	22.2118	0.936117	0.468059	+	0.883697i	$0.344954\pi$
$564$	−6.24757	−0.263070
$565$	2.09950	0.0883265
$566$	−3.12458	−0.131336
$567$	−4.37449	−0.183711
$568$	−3.67900	−0.154367
$569$	9.66437	0.405152	0.202576	−	0.979267i	$-0.435069\pi$
$569$	9.66437	0.405152	0.202576	+	0.979267i	$0.435069\pi$
$570$	4.16816	0.174585
$571$	−27.9479	−1.16958	−0.584792	−	0.811183i	$-0.698824\pi$
$571$	−27.9479	−1.16958	−0.584792	+	0.811183i	$0.698824\pi$
$572$	0	0
$573$	−2.92327	−0.122121
$574$	7.49909	0.313006
$575$	−25.1670	−1.04954
$576$	−1.68175	−0.0700730
$577$	−1.39111	−0.0579125	−0.0289563	−	0.999581i	$-0.509218\pi$
$577$	−1.39111	−0.0579125	−0.0289563	+	0.999581i	$0.509218\pi$
$578$	12.4533	0.517989
$579$	−0.578869	−0.0240570
$580$	10.0333	0.416610
$581$	51.9591	2.15563
$582$	4.08739	0.169428
$583$	0.617769	0.0255854
$584$	−17.0623	−0.706043
$585$	0	0
$586$	5.16567	0.213392
$587$	17.9218	0.739713	0.369856	−	0.929089i	$-0.379407\pi$
$587$	17.9218	0.739713	0.369856	+	0.929089i	$0.379407\pi$
$588$	20.6372	0.851065
$589$	−19.0992	−0.786969
$590$	−6.82475	−0.280970
$591$	−13.9481	−0.573749
$592$	−10.4988	−0.431496
$593$	11.1399	0.457462	0.228731	−	0.973490i	$-0.426542\pi$
$593$	11.1399	0.457462	0.228731	+	0.973490i	$0.426542\pi$
$594$	−0.547285	−0.0224554
$595$	−26.3454	−1.08006
$596$	35.0771	1.43682
$597$	−16.4750	−0.674279
$598$	0	0
$599$	−13.5965	−0.555537	−0.277768	−	0.960648i	$-0.589595\pi$
$599$	−13.5965	−0.555537	−0.277768	+	0.960648i	$0.589595\pi$
$600$	−8.27835	−0.337962
$601$	25.3091	1.03238	0.516189	−	0.856475i	$-0.327350\pi$
$601$	25.3091	1.03238	0.516189	+	0.856475i	$0.327350\pi$
$602$	−12.4746	−0.508425
$603$	−3.32587	−0.135440
$604$	7.45381	0.303291
$605$	−0.955178	−0.0388335
$606$	−5.65372	−0.229666
$607$	−37.7004	−1.53021	−0.765107	−	0.643903i	$-0.777314\pi$
$607$	−37.7004	−1.53021	−0.765107	+	0.643903i	$0.777314\pi$
$608$	42.3003	1.71550
$609$	27.0219	1.09498
$610$	−0.465679	−0.0188548
$611$	0	0
$612$	10.7217	0.433401
$613$	−3.16757	−0.127937	−0.0639686	−	0.997952i	$-0.520376\pi$
$613$	−3.16757	−0.127937	−0.0639686	+	0.997952i	$0.520376\pi$
$614$	15.1243	0.610369
$615$	−2.99194	−0.120646
$616$	8.85928	0.356951
$617$	−23.0775	−0.929065	−0.464533	−	0.885556i	$-0.653778\pi$
$617$	−23.0775	−0.929065	−0.464533	+	0.885556i	$0.653778\pi$
$618$	1.91923	0.0772028
$619$	28.0983	1.12937	0.564684	−	0.825307i	$-0.308998\pi$
$619$	28.0983	1.12937	0.564684	+	0.825307i	$0.308998\pi$
$620$	−3.89066	−0.156253
$621$	−6.15686	−0.247066
$622$	1.11838	0.0448428
$623$	−43.9865	−1.76228
$624$	0	0
$625$	12.1469	0.485878
$626$	−4.55104	−0.181896
$627$	−7.97346	−0.318429
$628$	−21.0799	−0.841179
$629$	28.8740	1.15128
$630$	2.28678	0.0911076
$631$	−47.0147	−1.87162	−0.935812	−	0.352499i	$-0.885332\pi$
$631$	−47.0147	−1.87162	−0.935812	+	0.352499i	$0.885332\pi$
$632$	−34.3567	−1.36664
$633$	−18.3150	−0.727955
$634$	−8.29126	−0.329288
$635$	10.7689	0.427351
$636$	1.05050	0.0416551
$637$	0	0
$638$	3.38067	0.133842
$639$	1.81660	0.0718634
$640$	11.0138	0.435360
$641$	43.5686	1.72085	0.860427	−	0.509573i	$-0.170197\pi$
$641$	43.5686	1.72085	0.860427	+	0.509573i	$0.170197\pi$
$642$	7.29758	0.288013
$643$	−4.29183	−0.169253	−0.0846267	−	0.996413i	$-0.526970\pi$
$643$	−4.29183	−0.169253	−0.0846267	+	0.996413i	$0.526970\pi$
$644$	45.7992	1.80474
$645$	4.97701	0.195970
$646$	−27.5141	−1.08253
$647$	−34.9754	−1.37503	−0.687513	−	0.726173i	$-0.741297\pi$
$647$	−34.9754	−1.37503	−0.687513	+	0.726173i	$0.741297\pi$
$648$	−2.02522	−0.0795580
$649$	13.0554	0.512468
$650$	0	0
$651$	−10.4784	−0.410681
$652$	1.96248	0.0768565
$653$	−26.6555	−1.04311	−0.521555	−	0.853218i	$-0.674648\pi$
$653$	−26.6555	−1.04311	−0.521555	+	0.853218i	$0.674648\pi$
$654$	5.66393	0.221477
$655$	12.5426	0.490079
$656$	−7.18115	−0.280377
$657$	8.42492	0.328687
$658$	8.79591	0.342900
$659$	−38.0227	−1.48115	−0.740577	−	0.671971i	$-0.765448\pi$
$659$	−38.0227	−1.48115	−0.740577	+	0.671971i	$0.765448\pi$
$660$	−1.62426	−0.0632242
$661$	−7.43138	−0.289047	−0.144524	−	0.989501i	$-0.546165\pi$
$661$	−7.43138	−0.289047	−0.144524	+	0.989501i	$0.546165\pi$
$662$	−14.1802	−0.551128
$663$	0	0
$664$	24.0550	0.933517
$665$	33.3164	1.29195
$666$	−2.50626	−0.0971155
$667$	38.0319	1.47260
$668$	19.8650	0.768600
$669$	13.5671	0.524533
$670$	1.73861	0.0671685
$671$	0.890818	0.0343896
$672$	23.2072	0.895238
$673$	30.2624	1.16653	0.583265	−	0.812282i	$-0.301775\pi$
$673$	30.2624	1.16653	0.583265	+	0.812282i	$0.301775\pi$
$674$	−4.85160	−0.186877
$675$	4.08764	0.157333
$676$	0	0
$677$	−1.58564	−0.0609412	−0.0304706	−	0.999536i	$-0.509701\pi$
$677$	−1.58564	−0.0609412	−0.0304706	+	0.999536i	$0.509701\pi$
$678$	1.20294	0.0461987
$679$	32.6708	1.25379
$680$	−12.1969	−0.467730
$681$	−0.374486	−0.0143503
$682$	−1.31094	−0.0501984
$683$	−7.72684	−0.295659	−0.147830	−	0.989013i	$-0.547229\pi$
$683$	−7.72684	−0.295659	−0.147830	+	0.989013i	$0.547229\pi$
$684$	−13.5587	−0.518430
$685$	11.9150	0.455248
$686$	−12.2964	−0.469477
$687$	15.5719	0.594104
$688$	11.9457	0.455424
$689$	0	0
$690$	3.21853	0.122527
$691$	−38.7247	−1.47316	−0.736578	−	0.676353i	$-0.763559\pi$
$691$	−38.7247	−1.47316	−0.736578	+	0.676353i	$0.763559\pi$
$692$	−15.5526	−0.591221
$693$	−4.37449	−0.166173
$694$	6.43861	0.244406
$695$	7.27350	0.275900
$696$	12.5101	0.474194
$697$	19.7498	0.748076
$698$	−17.5349	−0.663706
$699$	13.8177	0.522633
$700$	−30.4068	−1.14927
$701$	30.1810	1.13992	0.569960	−	0.821673i	$-0.306959\pi$
$701$	30.1810	1.13992	0.569960	+	0.821673i	$0.306959\pi$
$702$	0	0
$703$	−36.5140	−1.37715
$704$	−1.68175	−0.0633834
$705$	−3.50933	−0.132169
$706$	17.8323	0.671128
$707$	−45.1905	−1.69956
$708$	22.2004	0.834341
$709$	−5.86817	−0.220384	−0.110192	−	0.993910i	$-0.535147\pi$
$709$	−5.86817	−0.220384	−0.110192	+	0.993910i	$0.535147\pi$
$710$	−0.949634	−0.0356391
$711$	16.9645	0.636217
$712$	−20.3640	−0.763175
$713$	−14.7478	−0.552310
$714$	−15.0951	−0.564919
$715$	0	0
$716$	24.0180	0.897596
$717$	−10.7640	−0.401989
$718$	−19.3695	−0.722864
$719$	−12.9294	−0.482185	−0.241093	−	0.970502i	$-0.577506\pi$
$719$	−12.9294	−0.482185	−0.241093	+	0.970502i	$0.577506\pi$
$720$	−2.18983	−0.0816100
$721$	15.3405	0.571311
$722$	24.3958	0.907918
$723$	−11.4930	−0.427427
$724$	−4.30081	−0.159838
$725$	−25.2500	−0.937760
$726$	−0.547285	−0.0203117
$727$	35.9583	1.33362	0.666809	−	0.745228i	$-0.267660\pi$
$727$	35.9583	1.33362	0.666809	+	0.745228i	$0.267660\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.40417	−0.163005
$731$	−32.8533	−1.21512
$732$	1.51482	0.0559892
$733$	−10.2262	−0.377712	−0.188856	−	0.982005i	$-0.560478\pi$
$733$	−10.2262	−0.377712	−0.188856	+	0.982005i	$0.560478\pi$
$734$	3.17936	0.117352
$735$	11.5922	0.427583
$736$	32.6630	1.20397
$737$	−3.32587	−0.122510
$738$	−1.71428	−0.0631035
$739$	−41.5569	−1.52870	−0.764348	−	0.644803i	$-0.776939\pi$
$739$	−41.5569	−1.52870	−0.764348	+	0.644803i	$0.776939\pi$
$740$	−7.43819	−0.273433
$741$	0	0
$742$	−1.47899	−0.0542956
$743$	−10.9762	−0.402678	−0.201339	−	0.979522i	$-0.564529\pi$
$743$	−10.9762	−0.402678	−0.201339	+	0.979522i	$0.564529\pi$
$744$	−4.85110	−0.177850
$745$	19.7032	0.721870
$746$	1.90188	0.0696327
$747$	−11.8778	−0.434585
$748$	10.7217	0.392026
$749$	58.3300	2.13133
$750$	−4.75060	−0.173467
$751$	−5.26951	−0.192287	−0.0961435	−	0.995367i	$-0.530651\pi$
$751$	−5.26951	−0.192287	−0.0961435	+	0.995367i	$0.530651\pi$
$752$	−8.42298	−0.307154
$753$	7.14001	0.260196
$754$	0	0
$755$	4.18689	0.152376
$756$	−7.43872	−0.270544
$757$	−35.5804	−1.29319	−0.646596	−	0.762833i	$-0.723808\pi$
$757$	−35.5804	−1.29319	−0.646596	+	0.762833i	$0.723808\pi$
$758$	5.60536	0.203596
$759$	−6.15686	−0.223480
$760$	15.4242	0.559494
$761$	−21.0809	−0.764181	−0.382091	−	0.924125i	$-0.624796\pi$
$761$	−21.0809	−0.764181	−0.382091	+	0.924125i	$0.624796\pi$
$762$	6.17022	0.223524
$763$	45.2722	1.63896
$764$	−4.97096	−0.179843
$765$	6.02252	0.217745
$766$	−12.7491	−0.460644
$767$	0	0
$768$	2.94706	0.106343
$769$	39.0584	1.40848	0.704242	−	0.709960i	$-0.251287\pi$
$769$	39.0584	1.40848	0.704242	+	0.709960i	$0.251287\pi$
$770$	2.28678	0.0824099
$771$	−6.59154	−0.237389
$772$	−0.984354	−0.0354277
$773$	−1.22434	−0.0440366	−0.0220183	−	0.999758i	$-0.507009\pi$
$773$	−1.22434	−0.0440366	−0.0220183	+	0.999758i	$0.507009\pi$
$774$	2.85166	0.102501
$775$	9.79130	0.351714
$776$	15.1253	0.542967
$777$	−20.0327	−0.718669
$778$	1.57623	0.0565106
$779$	−24.9755	−0.894842
$780$	0	0
$781$	1.81660	0.0650029
$782$	−21.2455	−0.759739
$783$	−6.17716	−0.220754
$784$	27.8231	0.993683
$785$	−11.8408	−0.422616
$786$	7.18648	0.256333
$787$	−18.5952	−0.662849	−0.331424	−	0.943482i	$-0.607529\pi$
$787$	−18.5952	−0.662849	−0.331424	+	0.943482i	$0.607529\pi$
$788$	−23.7185	−0.844936
$789$	−31.2573	−1.11279
$790$	−8.86825	−0.315518
$791$	9.61519	0.341877
$792$	−2.02522	−0.0719630
$793$	0	0
$794$	−5.80508	−0.206014
$795$	0.590079	0.0209279
$796$	−28.0155	−0.992982
$797$	−43.4546	−1.53924	−0.769621	−	0.638501i	$-0.779555\pi$
$797$	−43.4546	−1.53924	−0.769621	+	0.638501i	$0.779555\pi$
$798$	19.0892	0.675750
$799$	23.1651	0.819522
$800$	−21.6855	−0.766697
$801$	10.0552	0.355284
$802$	15.6348	0.552083
$803$	8.42492	0.297309
$804$	−5.65557	−0.199457
$805$	25.7259	0.906719
$806$	0	0
$807$	19.2067	0.676107
$808$	−20.9215	−0.736014
$809$	−16.7906	−0.590325	−0.295162	−	0.955447i	$-0.595374\pi$
$809$	−16.7906	−0.590325	−0.295162	+	0.955447i	$0.595374\pi$
$810$	−0.522755	−0.0183677
$811$	−41.8130	−1.46825	−0.734126	−	0.679013i	$-0.762408\pi$
$811$	−41.8130	−1.46825	−0.734126	+	0.679013i	$0.762408\pi$
$812$	45.9501	1.61253
$813$	10.6834	0.374683
$814$	−2.50626	−0.0878443
$815$	1.10234	0.0386134
$816$	14.4551	0.506028
$817$	41.5462	1.45352
$818$	−0.659008	−0.0230417
$819$	0	0
$820$	−5.08772	−0.177671
$821$	26.6996	0.931822	0.465911	−	0.884832i	$-0.345727\pi$
$821$	26.6996	0.931822	0.465911	+	0.884832i	$0.345727\pi$
$822$	6.82689	0.238115
$823$	24.2092	0.843878	0.421939	−	0.906624i	$-0.361350\pi$
$823$	24.2092	0.843878	0.421939	+	0.906624i	$0.361350\pi$
$824$	7.10207	0.247412
$825$	4.08764	0.142313
$826$	−31.2557	−1.08753
$827$	11.6768	0.406043	0.203022	−	0.979174i	$-0.434924\pi$
$827$	11.6768	0.406043	0.203022	+	0.979174i	$0.434924\pi$
$828$	−10.4696	−0.363844
$829$	−47.7326	−1.65782	−0.828911	−	0.559380i	$-0.811039\pi$
$829$	−47.7326	−1.65782	−0.828911	+	0.559380i	$0.811039\pi$
$830$	6.20915	0.215523
$831$	2.65933	0.0922510
$832$	0	0
$833$	−76.5199	−2.65126
$834$	4.16748	0.144308
$835$	11.1584	0.386152
$836$	−13.5587	−0.468937
$837$	2.39535	0.0827953
$838$	2.33977	0.0808259
$839$	−16.9518	−0.585243	−0.292621	−	0.956228i	$-0.594528\pi$
$839$	−16.9518	−0.585243	−0.292621	+	0.956228i	$0.594528\pi$
$840$	8.46219	0.291973
$841$	9.15726	0.315768
$842$	−9.04777	−0.311807
$843$	33.4876	1.15337
$844$	−31.1442	−1.07203
$845$	0	0
$846$	−2.01073	−0.0691303
$847$	−4.37449	−0.150309
$848$	1.41629	0.0486355
$849$	5.70923	0.195940
$850$	14.1052	0.483805
$851$	−28.1950	−0.966511
$852$	3.08908	0.105830
$853$	−25.0979	−0.859336	−0.429668	−	0.902987i	$-0.641369\pi$
$853$	−25.0979	−0.859336	−0.429668	+	0.902987i	$0.641369\pi$
$854$	−2.13270	−0.0729795
$855$	−7.61607	−0.260464
$856$	27.0045	0.922996
$857$	21.5163	0.734983	0.367492	−	0.930027i	$-0.380217\pi$
$857$	21.5163	0.734983	0.367492	+	0.930027i	$0.380217\pi$
$858$	0	0
$859$	−11.0033	−0.375428	−0.187714	−	0.982224i	$-0.560108\pi$
$859$	−11.0033	−0.375428	−0.187714	+	0.982224i	$0.560108\pi$
$860$	8.46331	0.288596
$861$	−13.7024	−0.466975
$862$	−9.49074	−0.323256
$863$	−37.6567	−1.28185	−0.640924	−	0.767604i	$-0.721449\pi$
$863$	−37.6567	−1.28185	−0.640924	+	0.767604i	$0.721449\pi$
$864$	−5.30513	−0.180484
$865$	−8.73606	−0.297035
$866$	−2.90818	−0.0988238
$867$	−22.7547	−0.772790
$868$	−17.8183	−0.604793
$869$	16.9645	0.575480
$870$	3.22914	0.109478
$871$	0	0
$872$	20.9593	0.709770
$873$	−7.46849	−0.252770
$874$	26.8671	0.908792
$875$	−37.9719	−1.28368
$876$	14.3264	0.484044
$877$	10.2307	0.345466	0.172733	−	0.984969i	$-0.444740\pi$
$877$	10.2307	0.345466	0.172733	+	0.984969i	$0.444740\pi$
$878$	18.0110	0.607843
$879$	−9.43872	−0.318360
$880$	−2.18983	−0.0738191
$881$	−33.1131	−1.11561	−0.557805	−	0.829972i	$-0.688356\pi$
$881$	−33.1131	−1.11561	−0.557805	+	0.829972i	$0.688356\pi$
$882$	6.64192	0.223645
$883$	−5.00333	−0.168375	−0.0841877	−	0.996450i	$-0.526830\pi$
$883$	−5.00333	−0.168375	−0.0841877	+	0.996450i	$0.526830\pi$
$884$	0	0
$885$	12.4702	0.419181
$886$	−8.03396	−0.269906
$887$	2.24511	0.0753835	0.0376917	−	0.999289i	$-0.488000\pi$
$887$	2.24511	0.0753835	0.0376917	+	0.999289i	$0.488000\pi$
$888$	−9.27435	−0.311227
$889$	49.3190	1.65411
$890$	−5.25642	−0.176196
$891$	1.00000	0.0335013
$892$	23.0705	0.772458
$893$	−29.2946	−0.980305
$894$	11.2893	0.377570
$895$	13.4912	0.450961
$896$	50.4407	1.68511
$897$	0	0
$898$	13.5245	0.451320
$899$	−14.7964	−0.493488
$900$	6.95094	0.231698
$901$	−3.89511	−0.129765
$902$	−1.71428	−0.0570793
$903$	22.7935	0.758521
$904$	4.45146	0.148053
$905$	−2.41581	−0.0803044
$906$	2.39895	0.0796997
$907$	−14.8281	−0.492360	−0.246180	−	0.969224i	$-0.579175\pi$
$907$	−14.8281	−0.492360	−0.246180	+	0.969224i	$0.579175\pi$
$908$	−0.636806	−0.0211331
$909$	10.3305	0.342640
$910$	0	0
$911$	43.6416	1.44591	0.722956	−	0.690895i	$-0.242783\pi$
$911$	43.6416	1.44591	0.722956	+	0.690895i	$0.242783\pi$
$912$	−18.2798	−0.605306
$913$	−11.8778	−0.393096
$914$	−10.4681	−0.346253
$915$	0.850889	0.0281295
$916$	26.4796	0.874912
$917$	57.4420	1.89690
$918$	3.45071	0.113890
$919$	−19.5795	−0.645868	−0.322934	−	0.946422i	$-0.604669\pi$
$919$	−19.5795	−0.645868	−0.322934	+	0.946422i	$0.604669\pi$
$920$	11.9101	0.392664
$921$	−27.6352	−0.910611
$922$	18.5686	0.611525
$923$	0	0
$924$	−7.43872	−0.244716
$925$	18.7191	0.615479
$926$	−16.9224	−0.556104
$927$	−3.50682	−0.115179
$928$	32.7706	1.07575
$929$	−20.4642	−0.671410	−0.335705	−	0.941967i	$-0.608975\pi$
$929$	−20.4642	−0.671410	−0.335705	+	0.941967i	$0.608975\pi$
$930$	−1.25218	−0.0410605
$931$	96.7669	3.17141
$932$	23.4967	0.769660
$933$	−2.04350	−0.0669012
$934$	9.44358	0.309003
$935$	6.02252	0.196958
$936$	0	0
$937$	−4.95499	−0.161872	−0.0809362	−	0.996719i	$-0.525791\pi$
$937$	−4.95499	−0.161872	−0.0809362	+	0.996719i	$0.525791\pi$
$938$	7.96243	0.259983
$939$	8.31567	0.271372
$940$	−5.96754	−0.194640
$941$	−23.7965	−0.775744	−0.387872	−	0.921713i	$-0.626790\pi$
$941$	−23.7965	−0.775744	−0.387872	+	0.921713i	$0.626790\pi$
$942$	−6.78439	−0.221047
$943$	−19.2854	−0.628018
$944$	29.9305	0.974156
$945$	−4.17841	−0.135924
$946$	2.85166	0.0927156
$947$	40.0504	1.30146	0.650731	−	0.759308i	$-0.274462\pi$
$947$	40.0504	1.30146	0.650731	+	0.759308i	$0.274462\pi$
$948$	28.8477	0.936930
$949$	0	0
$950$	−17.8374	−0.578723
$951$	15.1498	0.491266
$952$	−55.8590	−1.81040
$953$	28.4952	0.923049	0.461524	−	0.887128i	$-0.347303\pi$
$953$	28.4952	0.923049	0.461524	+	0.887128i	$0.347303\pi$
$954$	0.338096	0.0109462
$955$	−2.79224	−0.0903548
$956$	−18.3039	−0.591992
$957$	−6.17716	−0.199679
$958$	16.5801	0.535679
$959$	54.5678	1.76209
$960$	−1.60637	−0.0518454
$961$	−25.2623	−0.814913
$962$	0	0
$963$	−13.3341	−0.429687
$964$	−19.5435	−0.629454
$965$	−0.552923	−0.0177992
$966$	14.7401	0.474255
$967$	−18.4660	−0.593826	−0.296913	−	0.954904i	$-0.595957\pi$
$967$	−18.4660	−0.593826	−0.296913	+	0.954904i	$0.595957\pi$
$968$	−2.02522	−0.0650929
$969$	50.2737	1.61502
$970$	3.90419	0.125356
$971$	−36.8905	−1.18387	−0.591936	−	0.805985i	$-0.701636\pi$
$971$	−36.8905	−1.18387	−0.591936	+	0.805985i	$0.701636\pi$
$972$	1.70048	0.0545429
$973$	33.3109	1.06790
$974$	0.308264	0.00987741
$975$	0	0
$976$	2.04228	0.0653717
$977$	0.0175455	0.000561330 0	0.000280665	−	1.00000i	$-0.499911\pi$
$977$	0.0175455	0.000561330 0	0.000280665		1.00000i	$0.499911\pi$
$978$	0.631607	0.0201966
$979$	10.0552	0.321367
$980$	19.7122	0.629684
$981$	−10.3491	−0.330423
$982$	4.01696	0.128186
$983$	−3.04897	−0.0972470	−0.0486235	−	0.998817i	$-0.515483\pi$
$983$	−3.04897	−0.0972470	−0.0486235	+	0.998817i	$0.515483\pi$
$984$	−6.34366	−0.202228
$985$	−13.3229	−0.424504
$986$	−21.3155	−0.678825
$987$	−16.0719	−0.511574
$988$	0	0
$989$	32.0807	1.02011
$990$	−0.522755	−0.0166142
$991$	33.7339	1.07159	0.535796	−	0.844348i	$-0.320012\pi$
$991$	33.7339	1.07159	0.535796	+	0.844348i	$0.320012\pi$
$992$	−12.7076	−0.403468
$993$	25.9100	0.822229
$994$	−4.34910	−0.137945
$995$	−15.7366	−0.498884
$996$	−20.1979	−0.639994
$997$	14.5802	0.461758	0.230879	−	0.972982i	$-0.425840\pi$
$997$	14.5802	0.461758	0.230879	+	0.972982i	$0.425840\pi$
$998$	−18.5073	−0.585837
$999$	4.57944	0.144887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.q.1.4		5
13.5	odd	4		429.2.b.a.298.4	✓	10
13.8	odd	4		429.2.b.a.298.7	yes	10
13.12	even	2		5577.2.a.t.1.2		5
39.5	even	4		1287.2.b.a.298.7		10
39.8	even	4		1287.2.b.a.298.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.a.298.4	✓	10	13.5	odd	4
429.2.b.a.298.7	yes	10	13.8	odd	4
1287.2.b.a.298.4		10	39.8	even	4
1287.2.b.a.298.7		10	39.5	even	4
5577.2.a.q.1.4		5	1.1	even	1	trivial
5577.2.a.t.1.2		5	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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+0.547285 q^{2} -1.00000 q^{3} -1.70048 q^{4} -0.955178 q^{5} -0.547285 q^{6} -4.37449 q^{7} -2.02522 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.547285 q^{2} -1.00000 q^{3} -1.70048 q^{4} -0.955178 q^{5} -0.547285 q^{6} -4.37449 q^{7} -2.02522 q^{8} +1.00000 q^{9} -0.522755 q^{10} +1.00000 q^{11} +1.70048 q^{12} -2.39409 q^{14} +0.955178 q^{15} +2.29259 q^{16} -6.30513 q^{17} +0.547285 q^{18} +7.97346 q^{19} +1.62426 q^{20} +4.37449 q^{21} +0.547285 q^{22} +6.15686 q^{23} +2.02522 q^{24} -4.08764 q^{25} -1.00000 q^{27} +7.43872 q^{28} +6.17716 q^{29} +0.522755 q^{30} -2.39535 q^{31} +5.30513 q^{32} -1.00000 q^{33} -3.45071 q^{34} +4.17841 q^{35} -1.70048 q^{36} -4.57944 q^{37} +4.36376 q^{38} +1.93444 q^{40} -3.13233 q^{41} +2.39409 q^{42} +5.21056 q^{43} -1.70048 q^{44} -0.955178 q^{45} +3.36956 q^{46} -3.67401 q^{47} -2.29259 q^{48} +12.1361 q^{49} -2.23710 q^{50} +6.30513 q^{51} +0.617769 q^{53} -0.547285 q^{54} -0.955178 q^{55} +8.85928 q^{56} -7.97346 q^{57} +3.38067 q^{58} +13.0554 q^{59} -1.62426 q^{60} +0.890818 q^{61} -1.31094 q^{62} -4.37449 q^{63} -1.68175 q^{64} -0.547285 q^{66} -3.32587 q^{67} +10.7217 q^{68} -6.15686 q^{69} +2.28678 q^{70} +1.81660 q^{71} -2.02522 q^{72} +8.42492 q^{73} -2.50626 q^{74} +4.08764 q^{75} -13.5587 q^{76} -4.37449 q^{77} +16.9645 q^{79} -2.18983 q^{80} +1.00000 q^{81} -1.71428 q^{82} -11.8778 q^{83} -7.43872 q^{84} +6.02252 q^{85} +2.85166 q^{86} -6.17716 q^{87} -2.02522 q^{88} +10.0552 q^{89} -0.522755 q^{90} -10.4696 q^{92} +2.39535 q^{93} -2.01073 q^{94} -7.61607 q^{95} -5.30513 q^{96} -7.46849 q^{97} +6.64192 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 5 q^{3} + 3 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - q^2 - 5 * q^3 + 3 * q^4 + 2 * q^5 + q^6 - 6 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q - q^{2} - 5 q^{3} + 3 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} + 3 q^{8} + 5 q^{9} + 5 q^{11} - 3 q^{12} - 16 q^{14} - 2 q^{15} + 3 q^{16} - 10 q^{17} - q^{18} + 18 q^{20} + 6 q^{21} - q^{22} - 4 q^{23} - 3 q^{24} + 7 q^{25} - 5 q^{27} - 12 q^{28} + 4 q^{29} - 22 q^{31} + 5 q^{32} - 5 q^{33} + 20 q^{34} + 3 q^{36} - 26 q^{37} - 10 q^{40} + 18 q^{41} + 16 q^{42} + 12 q^{43} + 3 q^{44} + 2 q^{45} + 22 q^{46} - 14 q^{47} - 3 q^{48} + 13 q^{49} - 37 q^{50} + 10 q^{51} - 2 q^{53} + q^{54} + 2 q^{55} - 8 q^{56} - 14 q^{58} + 18 q^{59} - 18 q^{60} + 18 q^{61} - 12 q^{62} - 6 q^{63} - 25 q^{64} + q^{66} - 8 q^{67} - 6 q^{68} + 4 q^{69} - 24 q^{70} + 4 q^{71} + 3 q^{72} + 12 q^{74} - 7 q^{75} - 58 q^{76} - 6 q^{77} + 18 q^{79} + 16 q^{80} + 5 q^{81} + 10 q^{82} - 34 q^{83} + 12 q^{84} - 12 q^{85} - 46 q^{86} - 4 q^{87} + 3 q^{88} - 10 q^{89} - 4 q^{92} + 22 q^{93} - 16 q^{94} - 22 q^{95} - 5 q^{96} + 4 q^{97} + 69 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q - q^2 - 5 * q^3 + 3 * q^4 + 2 * q^5 + q^6 - 6 * q^7 + 3 * q^8 + 5 * q^9 + 5 * q^11 - 3 * q^12 - 16 * q^14 - 2 * q^15 + 3 * q^16 - 10 * q^17 - q^18 + 18 * q^20 + 6 * q^21 - q^22 - 4 * q^23 - 3 * q^24 + 7 * q^25 - 5 * q^27 - 12 * q^28 + 4 * q^29 - 22 * q^31 + 5 * q^32 - 5 * q^33 + 20 * q^34 + 3 * q^36 - 26 * q^37 - 10 * q^40 + 18 * q^41 + 16 * q^42 + 12 * q^43 + 3 * q^44 + 2 * q^45 + 22 * q^46 - 14 * q^47 - 3 * q^48 + 13 * q^49 - 37 * q^50 + 10 * q^51 - 2 * q^53 + q^54 + 2 * q^55 - 8 * q^56 - 14 * q^58 + 18 * q^59 - 18 * q^60 + 18 * q^61 - 12 * q^62 - 6 * q^63 - 25 * q^64 + q^66 - 8 * q^67 - 6 * q^68 + 4 * q^69 - 24 * q^70 + 4 * q^71 + 3 * q^72 + 12 * q^74 - 7 * q^75 - 58 * q^76 - 6 * q^77 + 18 * q^79 + 16 * q^80 + 5 * q^81 + 10 * q^82 - 34 * q^83 + 12 * q^84 - 12 * q^85 - 46 * q^86 - 4 * q^87 + 3 * q^88 - 10 * q^89 - 4 * q^92 + 22 * q^93 - 16 * q^94 - 22 * q^95 - 5 * q^96 + 4 * q^97 + 69 * q^98 + 5 * q^99

Introduction

L-functions

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