LMFDB - Embedded newform 8041.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.57436 q^{2} +0.0662834 q^{3} +0.478605 q^{4} -1.53153 q^{5} -0.104354 q^{6} +0.748849 q^{7} +2.39522 q^{8} -2.99561 q^{9} +O(q^{10})$	\(q-1.57436 q^{2} +0.0662834 q^{3} +0.478605 q^{4} -1.53153 q^{5} -0.104354 q^{6} +0.748849 q^{7} +2.39522 q^{8} -2.99561 q^{9} +2.41117 q^{10} +1.00000 q^{11} +0.0317236 q^{12} +4.41544 q^{13} -1.17896 q^{14} -0.101515 q^{15} -4.72815 q^{16} +1.00000 q^{17} +4.71616 q^{18} +3.65264 q^{19} -0.732997 q^{20} +0.0496363 q^{21} -1.57436 q^{22} +7.78026 q^{23} +0.158763 q^{24} -2.65443 q^{25} -6.95148 q^{26} -0.397409 q^{27} +0.358403 q^{28} -1.97743 q^{29} +0.159821 q^{30} -9.64484 q^{31} +2.65336 q^{32} +0.0662834 q^{33} -1.57436 q^{34} -1.14688 q^{35} -1.43371 q^{36} +2.75250 q^{37} -5.75056 q^{38} +0.292670 q^{39} -3.66834 q^{40} -7.81802 q^{41} -0.0781453 q^{42} -1.00000 q^{43} +0.478605 q^{44} +4.58785 q^{45} -12.2489 q^{46} -7.41589 q^{47} -0.313398 q^{48} -6.43922 q^{49} +4.17902 q^{50} +0.0662834 q^{51} +2.11325 q^{52} +1.83475 q^{53} +0.625664 q^{54} -1.53153 q^{55} +1.79366 q^{56} +0.242109 q^{57} +3.11319 q^{58} +0.654773 q^{59} -0.0485855 q^{60} -4.71238 q^{61} +15.1844 q^{62} -2.24326 q^{63} +5.27896 q^{64} -6.76236 q^{65} -0.104354 q^{66} -2.78101 q^{67} +0.478605 q^{68} +0.515702 q^{69} +1.80560 q^{70} +6.71561 q^{71} -7.17514 q^{72} -15.2160 q^{73} -4.33341 q^{74} -0.175944 q^{75} +1.74817 q^{76} +0.748849 q^{77} -0.460768 q^{78} +8.77145 q^{79} +7.24128 q^{80} +8.96048 q^{81} +12.3084 q^{82} +7.52105 q^{83} +0.0237562 q^{84} -1.53153 q^{85} +1.57436 q^{86} -0.131071 q^{87} +2.39522 q^{88} +4.64389 q^{89} -7.22292 q^{90} +3.30650 q^{91} +3.72368 q^{92} -0.639293 q^{93} +11.6753 q^{94} -5.59411 q^{95} +0.175874 q^{96} +0.397363 q^{97} +10.1376 q^{98} -2.99561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.57436	−1.11324	−0.556620	−	0.830767i	$-0.687902\pi$
$2$	−1.57436	−1.11324	−0.556620	+	0.830767i	$0.687902\pi$
$3$	0.0662834	0.0382687	0.0191344	−	0.999817i	$-0.493909\pi$
$3$	0.0662834	0.0382687	0.0191344	+	0.999817i	$0.493909\pi$
$4$	0.478605	0.239303
$5$	−1.53153	−0.684919	−0.342460	−	0.939533i	$-0.611260\pi$
$5$	−1.53153	−0.684919	−0.342460	+	0.939533i	$0.611260\pi$
$6$	−0.104354	−0.0426023
$7$	0.748849	0.283038	0.141519	−	0.989936i	$-0.454801\pi$
$7$	0.748849	0.283038	0.141519	+	0.989936i	$0.454801\pi$
$8$	2.39522	0.846838
$9$	−2.99561	−0.998536
$10$	2.41117	0.762479
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.0317236	0.00915781
$13$	4.41544	1.22462	0.612311	−	0.790617i	$-0.290240\pi$
$13$	4.41544	1.22462	0.612311	+	0.790617i	$0.290240\pi$
$14$	−1.17896	−0.315090
$15$	−0.101515	−0.0262110
$16$	−4.72815	−1.18204
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.71616	1.11161
$19$	3.65264	0.837972	0.418986	−	0.907993i	$-0.362386\pi$
$19$	3.65264	0.837972	0.418986	+	0.907993i	$0.362386\pi$
$20$	−0.732997	−0.163903
$21$	0.0496363	0.0108315
$22$	−1.57436	−0.335654
$23$	7.78026	1.62230	0.811148	−	0.584840i	$-0.198843\pi$
$23$	7.78026	1.62230	0.811148	+	0.584840i	$0.198843\pi$
$24$	0.158763	0.0324074
$25$	−2.65443	−0.530886
$26$	−6.95148	−1.36330
$27$	−0.397409	−0.0764814
$28$	0.358403	0.0677319
$29$	−1.97743	−0.367200	−0.183600	−	0.983001i	$-0.558775\pi$
$29$	−1.97743	−0.367200	−0.183600	+	0.983001i	$0.558775\pi$
$30$	0.159821	0.0291791
$31$	−9.64484	−1.73227	−0.866133	−	0.499814i	$-0.833402\pi$
$31$	−9.64484	−1.73227	−0.866133	+	0.499814i	$0.833402\pi$
$32$	2.65336	0.469052
$33$	0.0662834	0.0115385
$34$	−1.57436	−0.270000
$35$	−1.14688	−0.193859
$36$	−1.43371	−0.238952
$37$	2.75250	0.452507	0.226254	−	0.974068i	$-0.427352\pi$
$37$	2.75250	0.452507	0.226254	+	0.974068i	$0.427352\pi$
$38$	−5.75056	−0.932864
$39$	0.292670	0.0468647
$40$	−3.66834	−0.580016
$41$	−7.81802	−1.22097	−0.610485	−	0.792028i	$-0.709025\pi$
$41$	−7.81802	−1.22097	−0.610485	+	0.792028i	$0.709025\pi$
$42$	−0.0781453	−0.0120581
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.478605	0.0721525
$45$	4.58785	0.683916
$46$	−12.2489	−1.80601
$47$	−7.41589	−1.08172	−0.540859	−	0.841113i	$-0.681901\pi$
$47$	−7.41589	−1.08172	−0.540859	+	0.841113i	$0.681901\pi$
$48$	−0.313398	−0.0452350
$49$	−6.43922	−0.919889
$50$	4.17902	0.591003
$51$	0.0662834	0.00928153
$52$	2.11325	0.293055
$53$	1.83475	0.252023	0.126011	−	0.992029i	$-0.459782\pi$
$53$	1.83475	0.252023	0.126011	+	0.992029i	$0.459782\pi$
$54$	0.625664	0.0851421
$55$	−1.53153	−0.206511
$56$	1.79366	0.239688
$57$	0.242109	0.0320681
$58$	3.11319	0.408782
$59$	0.654773	0.0852442	0.0426221	−	0.999091i	$-0.486429\pi$
$59$	0.654773	0.0852442	0.0426221	+	0.999091i	$0.486429\pi$
$60$	−0.0485855	−0.00627236
$61$	−4.71238	−0.603358	−0.301679	−	0.953409i	$-0.597547\pi$
$61$	−4.71238	−0.603358	−0.301679	+	0.953409i	$0.597547\pi$
$62$	15.1844	1.92843
$63$	−2.24326	−0.282624
$64$	5.27896	0.659870
$65$	−6.76236	−0.838767
$66$	−0.104354	−0.0128451
$67$	−2.78101	−0.339755	−0.169877	−	0.985465i	$-0.554337\pi$
$67$	−2.78101	−0.339755	−0.169877	+	0.985465i	$0.554337\pi$
$68$	0.478605	0.0580394
$69$	0.515702	0.0620832
$70$	1.80560	0.215811
$71$	6.71561	0.796997	0.398498	−	0.917169i	$-0.369531\pi$
$71$	6.71561	0.796997	0.398498	+	0.917169i	$0.369531\pi$
$72$	−7.17514	−0.845598
$73$	−15.2160	−1.78090	−0.890451	−	0.455080i	$-0.849611\pi$
$73$	−15.2160	−1.78090	−0.890451	+	0.455080i	$0.849611\pi$
$74$	−4.33341	−0.503749
$75$	−0.175944	−0.0203163
$76$	1.74817	0.200529
$77$	0.748849	0.0853393
$78$	−0.460768	−0.0521717
$79$	8.77145	0.986866	0.493433	−	0.869784i	$-0.335742\pi$
$79$	8.77145	0.986866	0.493433	+	0.869784i	$0.335742\pi$
$80$	7.24128	0.809600
$81$	8.96048	0.995609
$82$	12.3084	1.35923
$83$	7.52105	0.825543	0.412771	−	0.910835i	$-0.364561\pi$
$83$	7.52105	0.825543	0.412771	+	0.910835i	$0.364561\pi$
$84$	0.0237562	0.00259201
$85$	−1.53153	−0.166117
$86$	1.57436	0.169767
$87$	−0.131071	−0.0140523
$88$	2.39522	0.255331
$89$	4.64389	0.492251	0.246126	−	0.969238i	$-0.420842\pi$
$89$	4.64389	0.492251	0.246126	+	0.969238i	$0.420842\pi$
$90$	−7.22292	−0.761363
$91$	3.30650	0.346615
$92$	3.72368	0.388220
$93$	−0.639293	−0.0662916
$94$	11.6753	1.20421
$95$	−5.59411	−0.573943
$96$	0.175874	0.0179500
$97$	0.397363	0.0403461	0.0201731	−	0.999797i	$-0.493578\pi$
$97$	0.397363	0.0403461	0.0201731	+	0.999797i	$0.493578\pi$
$98$	10.1376	1.02406
$99$	−2.99561	−0.301070
$100$	−1.27042	−0.127042
$101$	−4.98740	−0.496265	−0.248132	−	0.968726i	$-0.579817\pi$
$101$	−4.98740	−0.496265	−0.248132	+	0.968726i	$0.579817\pi$
$102$	−0.104354	−0.0103326
$103$	19.0528	1.87733	0.938664	−	0.344834i	$-0.112065\pi$
$103$	19.0528	1.87733	0.938664	+	0.344834i	$0.112065\pi$
$104$	10.5759	1.03706
$105$	−0.0760192	−0.00741872
$106$	−2.88856	−0.280562
$107$	−14.5226	−1.40395	−0.701977	−	0.712200i	$-0.747699\pi$
$107$	−14.5226	−1.40395	−0.701977	+	0.712200i	$0.747699\pi$
$108$	−0.190202	−0.0183022
$109$	13.2323	1.26742	0.633711	−	0.773570i	$-0.281531\pi$
$109$	13.2323	1.26742	0.633711	+	0.773570i	$0.281531\pi$
$110$	2.41117	0.229896
$111$	0.182445	0.0173169
$112$	−3.54067	−0.334562
$113$	8.38498	0.788793	0.394396	−	0.918940i	$-0.370954\pi$
$113$	8.38498	0.788793	0.394396	+	0.918940i	$0.370954\pi$
$114$	−0.381166	−0.0356995
$115$	−11.9157	−1.11114
$116$	−0.946410	−0.0878719
$117$	−13.2269	−1.22283
$118$	−1.03085	−0.0948972
$119$	0.748849	0.0686469
$120$	−0.243150	−0.0221965
$121$	1.00000	0.0909091
$122$	7.41898	0.671683
$123$	−0.518205	−0.0467249
$124$	−4.61607	−0.414536
$125$	11.7230	1.04853
$126$	3.53169	0.314628
$127$	−6.80270	−0.603642	−0.301821	−	0.953365i	$-0.597595\pi$
$127$	−6.80270	−0.603642	−0.301821	+	0.953365i	$0.597595\pi$
$128$	−13.6177	−1.20365
$129$	−0.0662834	−0.00583593
$130$	10.6464	0.933749
$131$	12.2253	1.06813	0.534065	−	0.845444i	$-0.320664\pi$
$131$	12.2253	1.06813	0.534065	+	0.845444i	$0.320664\pi$
$132$	0.0317236	0.00276118
$133$	2.73527	0.237178
$134$	4.37831	0.378228
$135$	0.608642	0.0523836
$136$	2.39522	0.205388
$137$	−15.0830	−1.28863	−0.644315	−	0.764760i	$-0.722858\pi$
$137$	−15.0830	−1.28863	−0.644315	+	0.764760i	$0.722858\pi$
$138$	−0.811900	−0.0691135
$139$	13.5049	1.14547	0.572737	−	0.819739i	$-0.305881\pi$
$139$	13.5049	1.14547	0.572737	+	0.819739i	$0.305881\pi$
$140$	−0.548904	−0.0463909
$141$	−0.491550	−0.0413960
$142$	−10.5728	−0.887249
$143$	4.41544	0.369237
$144$	14.1637	1.18031
$145$	3.02849	0.251502
$146$	23.9555	1.98257
$147$	−0.426814	−0.0352030
$148$	1.31736	0.108286
$149$	−7.22526	−0.591916	−0.295958	−	0.955201i	$-0.595639\pi$
$149$	−7.22526	−0.591916	−0.295958	+	0.955201i	$0.595639\pi$
$150$	0.277000	0.0226169
$151$	7.37692	0.600325	0.300163	−	0.953888i	$-0.402959\pi$
$151$	7.37692	0.600325	0.300163	+	0.953888i	$0.402959\pi$
$152$	8.74887	0.709627
$153$	−2.99561	−0.242180
$154$	−1.17896	−0.0950031
$155$	14.7713	1.18646
$156$	0.140073	0.0112149
$157$	1.07088	0.0854654	0.0427327	−	0.999087i	$-0.486394\pi$
$157$	1.07088	0.0854654	0.0427327	+	0.999087i	$0.486394\pi$
$158$	−13.8094	−1.09862
$159$	0.121614	0.00964458
$160$	−4.06369	−0.321263
$161$	5.82624	0.459172
$162$	−14.1070	−1.10835
$163$	−19.5174	−1.52872	−0.764360	−	0.644790i	$-0.776945\pi$
$163$	−19.5174	−1.52872	−0.764360	+	0.644790i	$0.776945\pi$
$164$	−3.74175	−0.292181
$165$	−0.101515	−0.00790291
$166$	−11.8408	−0.919027
$167$	−11.4638	−0.887096	−0.443548	−	0.896251i	$-0.646280\pi$
$167$	−11.4638	−0.887096	−0.443548	+	0.896251i	$0.646280\pi$
$168$	0.118890	0.00917255
$169$	6.49608	0.499699
$170$	2.41117	0.184928
$171$	−10.9419	−0.836745
$172$	−0.478605	−0.0364933
$173$	−15.4968	−1.17820	−0.589098	−	0.808061i	$-0.700517\pi$
$173$	−15.4968	−1.17820	−0.589098	+	0.808061i	$0.700517\pi$
$174$	0.206353	0.0156436
$175$	−1.98777	−0.150261
$176$	−4.72815	−0.356398
$177$	0.0434006	0.00326219
$178$	−7.31114	−0.547993
$179$	−16.7345	−1.25080	−0.625398	−	0.780306i	$-0.715064\pi$
$179$	−16.7345	−1.25080	−0.625398	+	0.780306i	$0.715064\pi$
$180$	2.19577	0.163663
$181$	−0.204793	−0.0152221	−0.00761107	−	0.999971i	$-0.502423\pi$
$181$	−0.204793	−0.0152221	−0.00761107	+	0.999971i	$0.502423\pi$
$182$	−5.20561	−0.385866
$183$	−0.312352	−0.0230898
$184$	18.6354	1.37382
$185$	−4.21552	−0.309931
$186$	1.00648	0.0737984
$187$	1.00000	0.0731272
$188$	−3.54928	−0.258858
$189$	−0.297600	−0.0216472
$190$	8.80713	0.638936
$191$	18.6287	1.34792	0.673962	−	0.738766i	$-0.264591\pi$
$191$	18.6287	1.34792	0.673962	+	0.738766i	$0.264591\pi$
$192$	0.349907	0.0252524
$193$	12.9249	0.930355	0.465178	−	0.885217i	$-0.345990\pi$
$193$	12.9249	0.930355	0.465178	+	0.885217i	$0.345990\pi$
$194$	−0.625592	−0.0449149
$195$	−0.448232	−0.0320986
$196$	−3.08185	−0.220132
$197$	−23.2921	−1.65949	−0.829745	−	0.558142i	$-0.811514\pi$
$197$	−23.2921	−1.65949	−0.829745	+	0.558142i	$0.811514\pi$
$198$	4.71616	0.335163
$199$	22.6905	1.60849	0.804244	−	0.594299i	$-0.202571\pi$
$199$	22.6905	1.60849	0.804244	+	0.594299i	$0.202571\pi$
$200$	−6.35794	−0.449574
$201$	−0.184335	−0.0130020
$202$	7.85195	0.552461
$203$	−1.48080	−0.103932
$204$	0.0317236	0.00222110
$205$	11.9735	0.836265
$206$	−29.9959	−2.08992
$207$	−23.3066	−1.61992
$208$	−20.8768	−1.44755
$209$	3.65264	0.252658
$210$	0.119682	0.00825881
$211$	22.6052	1.55620	0.778102	−	0.628138i	$-0.216183\pi$
$211$	22.6052	1.55620	0.778102	+	0.628138i	$0.216183\pi$
$212$	0.878122	0.0603097
$213$	0.445134	0.0305001
$214$	22.8638	1.56294
$215$	1.53153	0.104449
$216$	−0.951882	−0.0647674
$217$	−7.22254	−0.490298
$218$	−20.8323	−1.41094
$219$	−1.00857	−0.0681528
$220$	−0.732997	−0.0494186
$221$	4.41544	0.297014
$222$	−0.287233	−0.0192778
$223$	8.15369	0.546011	0.273006	−	0.962012i	$-0.411982\pi$
$223$	8.15369	0.546011	0.273006	+	0.962012i	$0.411982\pi$
$224$	1.98697	0.132760
$225$	7.95162	0.530108
$226$	−13.2010	−0.878116
$227$	−2.27841	−0.151224	−0.0756118	−	0.997137i	$-0.524091\pi$
$227$	−2.27841	−0.151224	−0.0756118	+	0.997137i	$0.524091\pi$
$228$	0.115875	0.00767399
$229$	2.90494	0.191964	0.0959820	−	0.995383i	$-0.469401\pi$
$229$	2.90494	0.191964	0.0959820	+	0.995383i	$0.469401\pi$
$230$	18.7595	1.23697
$231$	0.0496363	0.00326583
$232$	−4.73639	−0.310959
$233$	−3.54194	−0.232040	−0.116020	−	0.993247i	$-0.537014\pi$
$233$	−3.54194	−0.232040	−0.116020	+	0.993247i	$0.537014\pi$
$234$	20.8239	1.36130
$235$	11.3576	0.740890
$236$	0.313378	0.0203992
$237$	0.581402	0.0377661
$238$	−1.17896	−0.0764205
$239$	−24.9218	−1.61206	−0.806029	−	0.591877i	$-0.798387\pi$
$239$	−24.9218	−1.61206	−0.806029	+	0.591877i	$0.798387\pi$
$240$	0.479977	0.0309824
$241$	2.39486	0.154266	0.0771331	−	0.997021i	$-0.475423\pi$
$241$	2.39486	0.154266	0.0771331	+	0.997021i	$0.475423\pi$
$242$	−1.57436	−0.101204
$243$	1.78616	0.114582
$244$	−2.25537	−0.144385
$245$	9.86184	0.630050
$246$	0.815840	0.0520161
$247$	16.1280	1.02620
$248$	−23.1015	−1.46695
$249$	0.498521	0.0315925
$250$	−18.4561	−1.16727
$251$	−20.0929	−1.26825	−0.634127	−	0.773229i	$-0.718640\pi$
$251$	−20.0929	−1.26825	−0.634127	+	0.773229i	$0.718640\pi$
$252$	−1.07364	−0.0676327
$253$	7.78026	0.489141
$254$	10.7099	0.671999
$255$	−0.101515	−0.00635710
$256$	10.8812	0.680076
$257$	−14.8832	−0.928390	−0.464195	−	0.885733i	$-0.653656\pi$
$257$	−14.8832	−0.928390	−0.464195	+	0.885733i	$0.653656\pi$
$258$	0.104354	0.00649678
$259$	2.06120	0.128077
$260$	−3.23650	−0.200719
$261$	5.92361	0.366662
$262$	−19.2470	−1.18908
$263$	−9.52105	−0.587093	−0.293547	−	0.955945i	$-0.594836\pi$
$263$	−9.52105	−0.587093	−0.293547	+	0.955945i	$0.594836\pi$
$264$	0.158763	0.00977121
$265$	−2.80997	−0.172615
$266$	−4.30630	−0.264036
$267$	0.307813	0.0188378
$268$	−1.33101	−0.0813042
$269$	−30.5338	−1.86168	−0.930840	−	0.365427i	$-0.880923\pi$
$269$	−30.5338	−1.86168	−0.930840	+	0.365427i	$0.880923\pi$
$270$	−0.958221	−0.0583155
$271$	−7.35503	−0.446786	−0.223393	−	0.974728i	$-0.571713\pi$
$271$	−7.35503	−0.446786	−0.223393	+	0.974728i	$0.571713\pi$
$272$	−4.72815	−0.286686
$273$	0.219166	0.0132645
$274$	23.7461	1.43455
$275$	−2.65443	−0.160068
$276$	0.246818	0.0148567
$277$	−29.8090	−1.79105	−0.895523	−	0.445014i	$-0.853199\pi$
$277$	−29.8090	−1.79105	−0.895523	+	0.445014i	$0.853199\pi$
$278$	−21.2616	−1.27519
$279$	28.8922	1.72973
$280$	−2.74704	−0.164167
$281$	8.48930	0.506429	0.253215	−	0.967410i	$-0.418512\pi$
$281$	8.48930	0.506429	0.253215	+	0.967410i	$0.418512\pi$
$282$	0.773876	0.0460837
$283$	−8.21395	−0.488268	−0.244134	−	0.969741i	$-0.578504\pi$
$283$	−8.21395	−0.488268	−0.244134	+	0.969741i	$0.578504\pi$
$284$	3.21413	0.190723
$285$	−0.370796	−0.0219641
$286$	−6.95148	−0.411050
$287$	−5.85452	−0.345581
$288$	−7.94842	−0.468365
$289$	1.00000	0.0588235
$290$	−4.76793	−0.279982
$291$	0.0263386	0.00154399
$292$	−7.28247	−0.426175
$293$	21.0195	1.22797	0.613985	−	0.789318i	$-0.289565\pi$
$293$	21.0195	1.22797	0.613985	+	0.789318i	$0.289565\pi$
$294$	0.671958	0.0391894
$295$	−1.00280	−0.0583854
$296$	6.59283	0.383201
$297$	−0.397409	−0.0230600
$298$	11.3751	0.658944
$299$	34.3533	1.98670
$300$	−0.0842080	−0.00486175
$301$	−0.748849	−0.0431630
$302$	−11.6139	−0.668306
$303$	−0.330582	−0.0189914
$304$	−17.2702	−0.990514
$305$	7.21713	0.413252
$306$	4.71616	0.269605
$307$	−22.8808	−1.30588	−0.652938	−	0.757412i	$-0.726464\pi$
$307$	−22.8808	−1.30588	−0.652938	+	0.757412i	$0.726464\pi$
$308$	0.358403	0.0204219
$309$	1.26288	0.0718429
$310$	−23.2554	−1.32082
$311$	14.3396	0.813124	0.406562	−	0.913623i	$-0.366728\pi$
$311$	14.3396	0.813124	0.406562	+	0.913623i	$0.366728\pi$
$312$	0.701009	0.0396868
$313$	4.33338	0.244937	0.122469	−	0.992472i	$-0.460919\pi$
$313$	4.33338	0.244937	0.122469	+	0.992472i	$0.460919\pi$
$314$	−1.68595	−0.0951435
$315$	3.43561	0.193575
$316$	4.19807	0.236160
$317$	33.7270	1.89430	0.947150	−	0.320792i	$-0.103949\pi$
$317$	33.7270	1.89430	0.947150	+	0.320792i	$0.103949\pi$
$318$	−0.191463	−0.0107367
$319$	−1.97743	−0.110715
$320$	−8.08486	−0.451957
$321$	−0.962608	−0.0537275
$322$	−9.17260	−0.511169
$323$	3.65264	0.203238
$324$	4.28853	0.238252
$325$	−11.7205	−0.650134
$326$	30.7274	1.70183
$327$	0.877079	0.0485026
$328$	−18.7259	−1.03396
$329$	−5.55338	−0.306168
$330$	0.159821	0.00879783
$331$	4.35255	0.239238	0.119619	−	0.992820i	$-0.461833\pi$
$331$	4.35255	0.239238	0.119619	+	0.992820i	$0.461833\pi$
$332$	3.59962	0.197555
$333$	−8.24539	−0.451845
$334$	18.0482	0.987551
$335$	4.25919	0.232704
$336$	−0.234688	−0.0128033
$337$	−9.32870	−0.508167	−0.254083	−	0.967182i	$-0.581774\pi$
$337$	−9.32870	−0.508167	−0.254083	+	0.967182i	$0.581774\pi$
$338$	−10.2272	−0.556284
$339$	0.555785	0.0301861
$340$	−0.732997	−0.0397523
$341$	−9.64484	−0.522298
$342$	17.2264	0.931498
$343$	−10.0640	−0.543403
$344$	−2.39522	−0.129142
$345$	−0.789811	−0.0425220
$346$	24.3975	1.31162
$347$	24.8934	1.33635	0.668174	−	0.744005i	$-0.267076\pi$
$347$	24.8934	1.33635	0.668174	+	0.744005i	$0.267076\pi$
$348$	−0.0627312	−0.00336275
$349$	−8.11704	−0.434495	−0.217248	−	0.976117i	$-0.569708\pi$
$349$	−8.11704	−0.434495	−0.217248	+	0.976117i	$0.569708\pi$
$350$	3.12946	0.167277
$351$	−1.75473	−0.0936608
$352$	2.65336	0.141425
$353$	9.97870	0.531112	0.265556	−	0.964095i	$-0.414444\pi$
$353$	9.97870	0.531112	0.265556	+	0.964095i	$0.414444\pi$
$354$	−0.0683281	−0.00363160
$355$	−10.2851	−0.545879
$356$	2.22259	0.117797
$357$	0.0496363	0.00262703
$358$	26.3461	1.39244
$359$	−24.7301	−1.30520	−0.652602	−	0.757701i	$-0.726322\pi$
$359$	−24.7301	−1.30520	−0.652602	+	0.757701i	$0.726322\pi$
$360$	10.9889	0.579167
$361$	−5.65825	−0.297803
$362$	0.322417	0.0169459
$363$	0.0662834	0.00347898
$364$	1.58251	0.0829459
$365$	23.3037	1.21977
$366$	0.491755	0.0257044
$367$	11.3529	0.592617	0.296308	−	0.955092i	$-0.404244\pi$
$367$	11.3529	0.592617	0.296308	+	0.955092i	$0.404244\pi$
$368$	−36.7862	−1.91761
$369$	23.4197	1.21918
$370$	6.63674	0.345028
$371$	1.37395	0.0713321
$372$	−0.305969	−0.0158638
$373$	18.9298	0.980146	0.490073	−	0.871681i	$-0.336970\pi$
$373$	18.9298	0.980146	0.490073	+	0.871681i	$0.336970\pi$
$374$	−1.57436	−0.0814082
$375$	0.777037	0.0401260
$376$	−17.7627	−0.916041
$377$	−8.73123	−0.449681
$378$	0.468528	0.0240985
$379$	−10.4228	−0.535384	−0.267692	−	0.963505i	$-0.586261\pi$
$379$	−10.4228	−0.535384	−0.267692	+	0.963505i	$0.586261\pi$
$380$	−2.67737	−0.137346
$381$	−0.450906	−0.0231006
$382$	−29.3282	−1.50056
$383$	32.9759	1.68499	0.842495	−	0.538704i	$-0.181086\pi$
$383$	32.9759	1.68499	0.842495	+	0.538704i	$0.181086\pi$
$384$	−0.902626	−0.0460620
$385$	−1.14688	−0.0584505
$386$	−20.3484	−1.03571
$387$	2.99561	0.152275
$388$	0.190180	0.00965494
$389$	−5.93940	−0.301140	−0.150570	−	0.988599i	$-0.548111\pi$
$389$	−5.93940	−0.301140	−0.150570	+	0.988599i	$0.548111\pi$
$390$	0.705678	0.0357334
$391$	7.78026	0.393465
$392$	−15.4234	−0.778998
$393$	0.810334	0.0408759
$394$	36.6701	1.84741
$395$	−13.4337	−0.675923
$396$	−1.43371	−0.0720468
$397$	−27.1087	−1.36055	−0.680275	−	0.732957i	$-0.738139\pi$
$397$	−27.1087	−1.36055	−0.680275	+	0.732957i	$0.738139\pi$
$398$	−35.7230	−1.79063
$399$	0.181303	0.00907651
$400$	12.5505	0.627526
$401$	−14.5388	−0.726032	−0.363016	−	0.931783i	$-0.618253\pi$
$401$	−14.5388	−0.726032	−0.363016	+	0.931783i	$0.618253\pi$
$402$	0.290209	0.0144743
$403$	−42.5862	−2.12137
$404$	−2.38700	−0.118757
$405$	−13.7232	−0.681912
$406$	2.33131	0.115701
$407$	2.75250	0.136436
$408$	0.158763	0.00785996
$409$	−23.8584	−1.17972	−0.589860	−	0.807505i	$-0.700817\pi$
$409$	−23.8584	−1.17972	−0.589860	+	0.807505i	$0.700817\pi$
$410$	−18.8506	−0.930964
$411$	−0.999755	−0.0493143
$412$	9.11877	0.449249
$413$	0.490327	0.0241274
$414$	36.6930	1.80336
$415$	−11.5187	−0.565430
$416$	11.7157	0.574411
$417$	0.895154	0.0438359
$418$	−5.75056	−0.281269
$419$	−29.2030	−1.42666	−0.713330	−	0.700829i	$-0.752814\pi$
$419$	−29.2030	−1.42666	−0.713330	+	0.700829i	$0.752814\pi$
$420$	−0.0363832	−0.00177532
$421$	5.00470	0.243914	0.121957	−	0.992535i	$-0.461083\pi$
$421$	5.00470	0.243914	0.121957	+	0.992535i	$0.461083\pi$
$422$	−35.5887	−1.73243
$423$	22.2151	1.08013
$424$	4.39464	0.213422
$425$	−2.65443	−0.128759
$426$	−0.700800	−0.0339539
$427$	−3.52886	−0.170774
$428$	−6.95060	−0.335970
$429$	0.292670	0.0141302
$430$	−2.41117	−0.116277
$431$	−22.6134	−1.08925	−0.544626	−	0.838679i	$-0.683328\pi$
$431$	−22.6134	−1.08925	−0.544626	+	0.838679i	$0.683328\pi$
$432$	1.87901	0.0904039
$433$	9.87510	0.474567	0.237283	−	0.971440i	$-0.423743\pi$
$433$	9.87510	0.474567	0.237283	+	0.971440i	$0.423743\pi$
$434$	11.3709	0.545819
$435$	0.200738	0.00962467
$436$	6.33303	0.303297
$437$	28.4185	1.35944
$438$	1.58785	0.0758704
$439$	31.8194	1.51866	0.759329	−	0.650707i	$-0.225527\pi$
$439$	31.8194	1.51866	0.759329	+	0.650707i	$0.225527\pi$
$440$	−3.66834	−0.174881
$441$	19.2894	0.918542
$442$	−6.95148	−0.330648
$443$	−27.9032	−1.32572	−0.662861	−	0.748743i	$-0.730658\pi$
$443$	−27.9032	−1.32572	−0.662861	+	0.748743i	$0.730658\pi$
$444$	0.0873190	0.00414398
$445$	−7.11224	−0.337152
$446$	−12.8368	−0.607842
$447$	−0.478914	−0.0226519
$448$	3.95314	0.186768
$449$	−33.9503	−1.60221	−0.801106	−	0.598522i	$-0.795755\pi$
$449$	−33.9503	−1.60221	−0.801106	+	0.598522i	$0.795755\pi$
$450$	−12.5187	−0.590137
$451$	−7.81802	−0.368136
$452$	4.01310	0.188760
$453$	0.488967	0.0229737
$454$	3.58704	0.168348
$455$	−5.06399	−0.237403
$456$	0.579905	0.0271565
$457$	−10.2848	−0.481101	−0.240551	−	0.970637i	$-0.577328\pi$
$457$	−10.2848	−0.481101	−0.240551	+	0.970637i	$0.577328\pi$
$458$	−4.57342	−0.213702
$459$	−0.397409	−0.0185495
$460$	−5.70291	−0.265899
$461$	−33.4198	−1.55651	−0.778257	−	0.627946i	$-0.783896\pi$
$461$	−33.4198	−1.55651	−0.778257	+	0.627946i	$0.783896\pi$
$462$	−0.0781453	−0.00363565
$463$	1.05640	0.0490952	0.0245476	−	0.999699i	$-0.492185\pi$
$463$	1.05640	0.0490952	0.0245476	+	0.999699i	$0.492185\pi$
$464$	9.34959	0.434044
$465$	0.979094	0.0454044
$466$	5.57628	0.258316
$467$	−18.3950	−0.851220	−0.425610	−	0.904907i	$-0.639940\pi$
$467$	−18.3950	−0.851220	−0.425610	+	0.904907i	$0.639940\pi$
$468$	−6.33047	−0.292626
$469$	−2.08256	−0.0961636
$470$	−17.8810	−0.824788
$471$	0.0709814	0.00327065
$472$	1.56833	0.0721881
$473$	−1.00000	−0.0459800
$474$	−0.915335	−0.0420427
$475$	−9.69566	−0.444867
$476$	0.358403	0.0164274
$477$	−5.49620	−0.251654
$478$	39.2359	1.79461
$479$	8.80519	0.402319	0.201160	−	0.979558i	$-0.435529\pi$
$479$	8.80519	0.402319	0.201160	+	0.979558i	$0.435529\pi$
$480$	−0.269355	−0.0122943
$481$	12.1535	0.554151
$482$	−3.77036	−0.171735
$483$	0.386183	0.0175719
$484$	0.478605	0.0217548
$485$	−0.608572	−0.0276338
$486$	−2.81205	−0.127557
$487$	18.7239	0.848460	0.424230	−	0.905554i	$-0.360545\pi$
$487$	18.7239	0.848460	0.424230	+	0.905554i	$0.360545\pi$
$488$	−11.2872	−0.510947
$489$	−1.29368	−0.0585021
$490$	−15.5261	−0.701397
$491$	14.3146	0.646008	0.323004	−	0.946398i	$-0.395307\pi$
$491$	14.3146	0.646008	0.323004	+	0.946398i	$0.395307\pi$
$492$	−0.248016	−0.0111814
$493$	−1.97743	−0.0890591
$494$	−25.3912	−1.14241
$495$	4.58785	0.206209
$496$	45.6022	2.04760
$497$	5.02898	0.225581
$498$	−0.784851	−0.0351700
$499$	25.3620	1.13536	0.567679	−	0.823250i	$-0.307841\pi$
$499$	25.3620	1.13536	0.567679	+	0.823250i	$0.307841\pi$
$500$	5.61067	0.250917
$501$	−0.759860	−0.0339480
$502$	31.6335	1.41187
$503$	0.591845	0.0263891	0.0131945	−	0.999913i	$-0.495800\pi$
$503$	0.591845	0.0263891	0.0131945	+	0.999913i	$0.495800\pi$
$504$	−5.37310	−0.239337
$505$	7.63833	0.339901
$506$	−12.2489	−0.544531
$507$	0.430582	0.0191228
$508$	−3.25581	−0.144453
$509$	5.43464	0.240886	0.120443	−	0.992720i	$-0.461568\pi$
$509$	5.43464	0.240886	0.120443	+	0.992720i	$0.461568\pi$
$510$	0.159821	0.00707698
$511$	−11.3945	−0.504064
$512$	10.1044	0.446558
$513$	−1.45159	−0.0640893
$514$	23.4315	1.03352
$515$	−29.1798	−1.28582
$516$	−0.0317236	−0.00139655
$517$	−7.41589	−0.326150
$518$	−3.24508	−0.142580
$519$	−1.02718	−0.0450881
$520$	−16.1973	−0.710300
$521$	−39.4921	−1.73018	−0.865091	−	0.501615i	$-0.832740\pi$
$521$	−39.4921	−1.73018	−0.865091	+	0.501615i	$0.832740\pi$
$522$	−9.32589	−0.408183
$523$	−5.51906	−0.241332	−0.120666	−	0.992693i	$-0.538503\pi$
$523$	−5.51906	−0.241332	−0.120666	+	0.992693i	$0.538503\pi$
$524$	5.85109	0.255606
$525$	−0.131756	−0.00575030
$526$	14.9895	0.653575
$527$	−9.64484	−0.420136
$528$	−0.313398	−0.0136389
$529$	37.5325	1.63185
$530$	4.42390	0.192162
$531$	−1.96144	−0.0851194
$532$	1.30912	0.0567574
$533$	−34.5200	−1.49523
$534$	−0.484607	−0.0209710
$535$	22.2418	0.961595
$536$	−6.66114	−0.287717
$537$	−1.10922	−0.0478664
$538$	48.0712	2.07250
$539$	−6.43922	−0.277357
$540$	0.291300	0.0125355
$541$	−23.7232	−1.01994	−0.509970	−	0.860192i	$-0.670344\pi$
$541$	−23.7232	−1.01994	−0.509970	+	0.860192i	$0.670344\pi$
$542$	11.5795	0.497380
$543$	−0.0135744	−0.000582532 0
$544$	2.65336	0.113762
$545$	−20.2656	−0.868081
$546$	−0.345046	−0.0147666
$547$	1.11122	0.0475124	0.0237562	−	0.999718i	$-0.492437\pi$
$547$	1.11122	0.0475124	0.0237562	+	0.999718i	$0.492437\pi$
$548$	−7.21882	−0.308373
$549$	14.1164	0.602475
$550$	4.17902	0.178194
$551$	−7.22284	−0.307703
$552$	1.23522	0.0525745
$553$	6.56850	0.279321
$554$	46.9300	1.99386
$555$	−0.279419	−0.0118607
$556$	6.46354	0.274115
$557$	25.7521	1.09115	0.545577	−	0.838061i	$-0.316311\pi$
$557$	25.7521	1.09115	0.545577	+	0.838061i	$0.316311\pi$
$558$	−45.4866	−1.92560
$559$	−4.41544	−0.186753
$560$	5.42263	0.229148
$561$	0.0662834	0.00279849
$562$	−13.3652	−0.563777
$563$	27.1146	1.14274	0.571371	−	0.820692i	$-0.306412\pi$
$563$	27.1146	1.14274	0.571371	+	0.820692i	$0.306412\pi$
$564$	−0.235259	−0.00990617
$565$	−12.8418	−0.540259
$566$	12.9317	0.543560
$567$	6.71005	0.281796
$568$	16.0854	0.674928
$569$	28.8996	1.21153	0.605767	−	0.795642i	$-0.292866\pi$
$569$	28.8996	1.21153	0.605767	+	0.795642i	$0.292866\pi$
$570$	0.583766	0.0244513
$571$	−25.1193	−1.05121	−0.525604	−	0.850729i	$-0.676161\pi$
$571$	−25.1193	−1.05121	−0.525604	+	0.850729i	$0.676161\pi$
$572$	2.11325	0.0883595
$573$	1.23477	0.0515834
$574$	9.21711	0.384715
$575$	−20.6521	−0.861254
$576$	−15.8137	−0.658903
$577$	−42.4064	−1.76540	−0.882700	−	0.469936i	$-0.844277\pi$
$577$	−42.4064	−1.76540	−0.882700	+	0.469936i	$0.844277\pi$
$578$	−1.57436	−0.0654847
$579$	0.856707	0.0356035
$580$	1.44945	0.0601852
$581$	5.63214	0.233660
$582$	−0.0414664	−0.00171884
$583$	1.83475	0.0759877
$584$	−36.4457	−1.50814
$585$	20.2574	0.837539
$586$	−33.0922	−1.36703
$587$	−12.3155	−0.508316	−0.254158	−	0.967163i	$-0.581798\pi$
$587$	−12.3155	−0.508316	−0.254158	+	0.967163i	$0.581798\pi$
$588$	−0.204275	−0.00842417
$589$	−35.2291	−1.45159
$590$	1.57877	0.0649970
$591$	−1.54388	−0.0635066
$592$	−13.0142	−0.534880
$593$	−26.4521	−1.08626	−0.543128	−	0.839650i	$-0.682760\pi$
$593$	−26.4521	−1.08626	−0.543128	+	0.839650i	$0.682760\pi$
$594$	0.625664	0.0256713
$595$	−1.14688	−0.0470176
$596$	−3.45805	−0.141647
$597$	1.50400	0.0615548
$598$	−54.0843	−2.21167
$599$	−13.8622	−0.566394	−0.283197	−	0.959062i	$-0.591395\pi$
$599$	−13.8622	−0.566394	−0.283197	+	0.959062i	$0.591395\pi$
$600$	−0.421426	−0.0172046
$601$	4.11559	0.167878	0.0839392	−	0.996471i	$-0.473250\pi$
$601$	4.11559	0.167878	0.0839392	+	0.996471i	$0.473250\pi$
$602$	1.17896	0.0480507
$603$	8.33082	0.339257
$604$	3.53063	0.143659
$605$	−1.53153	−0.0622654
$606$	0.520454	0.0211420
$607$	4.90299	0.199006	0.0995032	−	0.995037i	$-0.468275\pi$
$607$	4.90299	0.199006	0.0995032	+	0.995037i	$0.468275\pi$
$608$	9.69175	0.393052
$609$	−0.0981524	−0.00397733
$610$	−11.3624	−0.460048
$611$	−32.7444	−1.32470
$612$	−1.43371	−0.0579544
$613$	35.9706	1.45284	0.726419	−	0.687252i	$-0.241183\pi$
$613$	35.9706	1.45284	0.726419	+	0.687252i	$0.241183\pi$
$614$	36.0226	1.45375
$615$	0.793644	0.0320028
$616$	1.79366	0.0722686
$617$	−26.2403	−1.05639	−0.528197	−	0.849122i	$-0.677132\pi$
$617$	−26.2403	−1.05639	−0.528197	+	0.849122i	$0.677132\pi$
$618$	−1.98823	−0.0799784
$619$	33.6415	1.35217	0.676084	−	0.736825i	$-0.263676\pi$
$619$	33.6415	1.35217	0.676084	+	0.736825i	$0.263676\pi$
$620$	7.06964	0.283924
$621$	−3.09195	−0.124076
$622$	−22.5757	−0.905202
$623$	3.47757	0.139326
$624$	−1.38379	−0.0553958
$625$	−4.68187	−0.187275
$626$	−6.82230	−0.272674
$627$	0.242109	0.00966890
$628$	0.512528	0.0204521
$629$	2.75250	0.109749
$630$	−5.40888	−0.215495
$631$	−1.15088	−0.0458158	−0.0229079	−	0.999738i	$-0.507292\pi$
$631$	−1.15088	−0.0458158	−0.0229079	+	0.999738i	$0.507292\pi$
$632$	21.0096	0.835716
$633$	1.49835	0.0595540
$634$	−53.0985	−2.10881
$635$	10.4185	0.413446
$636$	0.0582049	0.00230798
$637$	−28.4320	−1.12652
$638$	3.11319	0.123252
$639$	−20.1173	−0.795830
$640$	20.8558	0.824400
$641$	−25.6555	−1.01333	−0.506665	−	0.862143i	$-0.669122\pi$
$641$	−25.6555	−1.01333	−0.506665	+	0.862143i	$0.669122\pi$
$642$	1.51549	0.0598116
$643$	−43.8943	−1.73102	−0.865512	−	0.500889i	$-0.833007\pi$
$643$	−43.8943	−1.73102	−0.865512	+	0.500889i	$0.833007\pi$
$644$	2.78847	0.109881
$645$	0.101515	0.00399714
$646$	−5.75056	−0.226253
$647$	38.3558	1.50792	0.753961	−	0.656920i	$-0.228141\pi$
$647$	38.3558	1.50792	0.753961	+	0.656920i	$0.228141\pi$
$648$	21.4623	0.843120
$649$	0.654773	0.0257021
$650$	18.4522	0.723755
$651$	−0.478734	−0.0187631
$652$	−9.34112	−0.365827
$653$	−16.0667	−0.628737	−0.314369	−	0.949301i	$-0.601793\pi$
$653$	−16.0667	−0.628737	−0.314369	+	0.949301i	$0.601793\pi$
$654$	−1.38084	−0.0539950
$655$	−18.7234	−0.731582
$656$	36.9647	1.44323
$657$	45.5812	1.77829
$658$	8.74302	0.340838
$659$	−5.92980	−0.230992	−0.115496	−	0.993308i	$-0.536846\pi$
$659$	−5.92980	−0.230992	−0.115496	+	0.993308i	$0.536846\pi$
$660$	−0.0485855	−0.00189119
$661$	−27.0708	−1.05293	−0.526466	−	0.850196i	$-0.676483\pi$
$661$	−27.0708	−1.05293	−0.526466	+	0.850196i	$0.676483\pi$
$662$	−6.85247	−0.266329
$663$	0.292670	0.0113664
$664$	18.0146	0.699101
$665$	−4.18914	−0.162448
$666$	12.9812	0.503012
$667$	−15.3849	−0.595707
$668$	−5.48664	−0.212285
$669$	0.540454	0.0208952
$670$	−6.70549	−0.259056
$671$	−4.71238	−0.181919
$672$	0.131703	0.00508055
$673$	13.5464	0.522175	0.261087	−	0.965315i	$-0.415919\pi$
$673$	13.5464	0.522175	0.261087	+	0.965315i	$0.415919\pi$
$674$	14.6867	0.565712
$675$	1.05489	0.0406029
$676$	3.10906	0.119579
$677$	31.4910	1.21030	0.605148	−	0.796113i	$-0.293114\pi$
$677$	31.4910	1.21030	0.605148	+	0.796113i	$0.293114\pi$
$678$	−0.875005	−0.0336044
$679$	0.297565	0.0114195
$680$	−3.66834	−0.140675
$681$	−0.151021	−0.00578713
$682$	15.1844	0.581442
$683$	−9.30767	−0.356148	−0.178074	−	0.984017i	$-0.556987\pi$
$683$	−9.30767	−0.356148	−0.178074	+	0.984017i	$0.556987\pi$
$684$	−5.23683	−0.200235
$685$	23.1001	0.882608
$686$	15.8443	0.604937
$687$	0.192549	0.00734622
$688$	4.72815	0.180259
$689$	8.10123	0.308632
$690$	1.24345	0.0473372
$691$	19.0010	0.722832	0.361416	−	0.932405i	$-0.382293\pi$
$691$	19.0010	0.722832	0.361416	+	0.932405i	$0.382293\pi$
$692$	−7.41683	−0.281946
$693$	−2.24326	−0.0852143
$694$	−39.1912	−1.48768
$695$	−20.6832	−0.784558
$696$	−0.313944	−0.0119000
$697$	−7.81802	−0.296129
$698$	12.7791	0.483697
$699$	−0.234772	−0.00887988
$700$	−0.951356	−0.0359579
$701$	−19.9530	−0.753614	−0.376807	−	0.926292i	$-0.622978\pi$
$701$	−19.9530	−0.753614	−0.376807	+	0.926292i	$0.622978\pi$
$702$	2.76258	0.104267
$703$	10.0539	0.379189
$704$	5.27896	0.198958
$705$	0.752822	0.0283529
$706$	−15.7100	−0.591255
$707$	−3.73481	−0.140462
$708$	0.0207718	0.000780650 0
$709$	8.55811	0.321406	0.160703	−	0.987003i	$-0.448624\pi$
$709$	8.55811	0.321406	0.160703	+	0.987003i	$0.448624\pi$
$710$	16.1925	0.607694
$711$	−26.2758	−0.985421
$712$	11.1231	0.416857
$713$	−75.0394	−2.81025
$714$	−0.0781453	−0.00292451
$715$	−6.76236	−0.252898
$716$	−8.00923	−0.299319
$717$	−1.65190	−0.0616914
$718$	38.9340	1.45300
$719$	9.96129	0.371493	0.185747	−	0.982598i	$-0.440530\pi$
$719$	9.96129	0.371493	0.185747	+	0.982598i	$0.440530\pi$
$720$	−21.6920	−0.808414
$721$	14.2677	0.531356
$722$	8.90812	0.331526
$723$	0.158739	0.00590357
$724$	−0.0980150	−0.00364270
$725$	5.24895	0.194941
$726$	−0.104354	−0.00387293
$727$	30.6497	1.13673	0.568367	−	0.822775i	$-0.307575\pi$
$727$	30.6497	1.13673	0.568367	+	0.822775i	$0.307575\pi$
$728$	7.91979	0.293527
$729$	−26.7630	−0.991224
$730$	−36.6885	−1.35790
$731$	−1.00000	−0.0369863
$732$	−0.149494	−0.00552544
$733$	−25.4978	−0.941782	−0.470891	−	0.882191i	$-0.656068\pi$
$733$	−25.4978	−0.941782	−0.470891	+	0.882191i	$0.656068\pi$
$734$	−17.8735	−0.659724
$735$	0.653676	0.0241112
$736$	20.6438	0.760942
$737$	−2.78101	−0.102440
$738$	−36.8710	−1.35724
$739$	−26.8844	−0.988960	−0.494480	−	0.869189i	$-0.664641\pi$
$739$	−26.8844	−0.988960	−0.494480	+	0.869189i	$0.664641\pi$
$740$	−2.01757	−0.0741673
$741$	1.06902	0.0392713
$742$	−2.16310	−0.0794097
$743$	−38.8175	−1.42408	−0.712038	−	0.702141i	$-0.752228\pi$
$743$	−38.8175	−1.42408	−0.712038	+	0.702141i	$0.752228\pi$
$744$	−1.53125	−0.0561383
$745$	11.0657	0.405415
$746$	−29.8022	−1.09114
$747$	−22.5301	−0.824334
$748$	0.478605	0.0174995
$749$	−10.8753	−0.397373
$750$	−1.22334	−0.0446699
$751$	25.1390	0.917336	0.458668	−	0.888608i	$-0.348327\pi$
$751$	25.1390	0.917336	0.458668	+	0.888608i	$0.348327\pi$
$752$	35.0634	1.27863
$753$	−1.33183	−0.0485345
$754$	13.7461	0.500603
$755$	−11.2979	−0.411174
$756$	−0.142433	−0.00518023
$757$	−17.4830	−0.635431	−0.317716	−	0.948186i	$-0.602916\pi$
$757$	−17.4830	−0.635431	−0.317716	+	0.948186i	$0.602916\pi$
$758$	16.4092	0.596011
$759$	0.515702	0.0187188
$760$	−13.3991	−0.486037
$761$	−14.1949	−0.514566	−0.257283	−	0.966336i	$-0.582827\pi$
$761$	−14.1949	−0.514566	−0.257283	+	0.966336i	$0.582827\pi$
$762$	0.709888	0.0257165
$763$	9.90898	0.358729
$764$	8.91579	0.322562
$765$	4.58785	0.165874
$766$	−51.9159	−1.87580
$767$	2.89111	0.104392
$768$	0.721244	0.0260256
$769$	−5.42617	−0.195673	−0.0978364	−	0.995203i	$-0.531192\pi$
$769$	−5.42617	−0.195673	−0.0978364	+	0.995203i	$0.531192\pi$
$770$	1.80560	0.0650695
$771$	−0.986510	−0.0355283
$772$	6.18593	0.222637
$773$	−35.9559	−1.29324	−0.646622	−	0.762811i	$-0.723819\pi$
$773$	−35.9559	−1.29324	−0.646622	+	0.762811i	$0.723819\pi$
$774$	−4.71616	−0.169519
$775$	25.6015	0.919635
$776$	0.951773	0.0341666
$777$	0.136624	0.00490134
$778$	9.35075	0.335241
$779$	−28.5564	−1.02314
$780$	−0.214526	−0.00768127
$781$	6.71561	0.240304
$782$	−12.2489	−0.438021
$783$	0.785850	0.0280840
$784$	30.4456	1.08734
$785$	−1.64008	−0.0585369
$786$	−1.27576	−0.0455047
$787$	43.0818	1.53570	0.767851	−	0.640629i	$-0.221326\pi$
$787$	43.0818	1.53570	0.767851	+	0.640629i	$0.221326\pi$
$788$	−11.1477	−0.397121
$789$	−0.631087	−0.0224673
$790$	21.1495	0.752465
$791$	6.27909	0.223259
$792$	−7.17514	−0.254957
$793$	−20.8072	−0.738886
$794$	42.6789	1.51462
$795$	−0.186254	−0.00660576
$796$	10.8598	0.384916
$797$	36.0817	1.27808	0.639039	−	0.769174i	$-0.279332\pi$
$797$	36.0817	1.27808	0.639039	+	0.769174i	$0.279332\pi$
$798$	−0.285436	−0.0101043
$799$	−7.41589	−0.262355
$800$	−7.04315	−0.249013
$801$	−13.9113	−0.491530
$802$	22.8893	0.808248
$803$	−15.2160	−0.536962
$804$	−0.0882236	−0.00311141
$805$	−8.92305	−0.314496
$806$	67.0460	2.36159
$807$	−2.02389	−0.0712441
$808$	−11.9459	−0.420256
$809$	−11.6159	−0.408392	−0.204196	−	0.978930i	$-0.565458\pi$
$809$	−11.6159	−0.408392	−0.204196	+	0.978930i	$0.565458\pi$
$810$	21.6052	0.759131
$811$	2.85027	0.100086	0.0500432	−	0.998747i	$-0.484064\pi$
$811$	2.85027	0.100086	0.0500432	+	0.998747i	$0.484064\pi$
$812$	−0.708718	−0.0248711
$813$	−0.487516	−0.0170979
$814$	−4.33341	−0.151886
$815$	29.8914	1.04705
$816$	−0.313398	−0.0109711
$817$	−3.65264	−0.127790
$818$	37.5616	1.31331
$819$	−9.90497	−0.346108
$820$	5.73058	0.200121
$821$	−3.39888	−0.118622	−0.0593109	−	0.998240i	$-0.518890\pi$
$821$	−3.39888	−0.118622	−0.0593109	+	0.998240i	$0.518890\pi$
$822$	1.57397	0.0548986
$823$	9.49847	0.331096	0.165548	−	0.986202i	$-0.447061\pi$
$823$	9.49847	0.331096	0.165548	+	0.986202i	$0.447061\pi$
$824$	45.6356	1.58979
$825$	−0.175944	−0.00612560
$826$	−0.771950	−0.0268596
$827$	−15.3161	−0.532593	−0.266296	−	0.963891i	$-0.585800\pi$
$827$	−15.3161	−0.532593	−0.266296	+	0.963891i	$0.585800\pi$
$828$	−11.1547	−0.387651
$829$	16.0184	0.556341	0.278170	−	0.960532i	$-0.410272\pi$
$829$	16.0184	0.556341	0.278170	+	0.960532i	$0.410272\pi$
$830$	18.1345	0.629459
$831$	−1.97584	−0.0685411
$832$	23.3089	0.808091
$833$	−6.43922	−0.223106
$834$	−1.40929	−0.0487998
$835$	17.5571	0.607589
$836$	1.74817	0.0604618
$837$	3.83295	0.132486
$838$	45.9760	1.58821
$839$	12.9007	0.445381	0.222690	−	0.974889i	$-0.428516\pi$
$839$	12.9007	0.445381	0.222690	+	0.974889i	$0.428516\pi$
$840$	−0.182083	−0.00628246
$841$	−25.0898	−0.865164
$842$	−7.87920	−0.271535
$843$	0.562700	0.0193804
$844$	10.8190	0.372404
$845$	−9.94892	−0.342253
$846$	−34.9745	−1.20245
$847$	0.748849	0.0257308
$848$	−8.67498	−0.297900
$849$	−0.544448	−0.0186854
$850$	4.17902	0.143339
$851$	21.4151	0.734101
$852$	0.213043	0.00729875
$853$	−31.7452	−1.08693	−0.543467	−	0.839431i	$-0.682889\pi$
$853$	−31.7452	−1.08693	−0.543467	+	0.839431i	$0.682889\pi$
$854$	5.55570	0.190112
$855$	16.7577	0.573103
$856$	−34.7849	−1.18892
$857$	27.4418	0.937396	0.468698	−	0.883359i	$-0.344723\pi$
$857$	27.4418	0.937396	0.468698	+	0.883359i	$0.344723\pi$
$858$	−0.460768	−0.0157304
$859$	26.6237	0.908387	0.454194	−	0.890903i	$-0.349927\pi$
$859$	26.6237	0.908387	0.454194	+	0.890903i	$0.349927\pi$
$860$	0.732997	0.0249950
$861$	−0.388057	−0.0132250
$862$	35.6017	1.21260
$863$	−10.0400	−0.341767	−0.170883	−	0.985291i	$-0.554662\pi$
$863$	−10.0400	−0.341767	−0.170883	+	0.985291i	$0.554662\pi$
$864$	−1.05447	−0.0358738
$865$	23.7337	0.806969
$866$	−15.5469	−0.528307
$867$	0.0662834	0.00225110
$868$	−3.45675	−0.117330
$869$	8.77145	0.297551
$870$	−0.316034	−0.0107146
$871$	−12.2794	−0.416071
$872$	31.6942	1.07330
$873$	−1.19034	−0.0402870
$874$	−44.7408	−1.51338
$875$	8.77873	0.296775
$876$	−0.482707	−0.0163092
$877$	15.6583	0.528742	0.264371	−	0.964421i	$-0.414836\pi$
$877$	15.6583	0.528742	0.264371	+	0.964421i	$0.414836\pi$
$878$	−50.0952	−1.69063
$879$	1.39324	0.0469929
$880$	7.24128	0.244104
$881$	33.9071	1.14236	0.571180	−	0.820825i	$-0.306486\pi$
$881$	33.9071	1.14236	0.571180	+	0.820825i	$0.306486\pi$
$882$	−30.3684	−1.02256
$883$	−43.2083	−1.45408	−0.727038	−	0.686598i	$-0.759103\pi$
$883$	−43.2083	−1.45408	−0.727038	+	0.686598i	$0.759103\pi$
$884$	2.11325	0.0710764
$885$	−0.0664691	−0.00223434
$886$	43.9297	1.47585
$887$	38.9446	1.30763	0.653816	−	0.756653i	$-0.273167\pi$
$887$	38.9446	1.30763	0.653816	+	0.756653i	$0.273167\pi$
$888$	0.436995	0.0146646
$889$	−5.09420	−0.170854
$890$	11.1972	0.375331
$891$	8.96048	0.300187
$892$	3.90240	0.130662
$893$	−27.0875	−0.906450
$894$	0.753983	0.0252170
$895$	25.6294	0.856695
$896$	−10.1976	−0.340678
$897$	2.27705	0.0760285
$898$	53.4499	1.78365
$899$	19.0720	0.636088
$900$	3.80569	0.126856
$901$	1.83475	0.0611245
$902$	12.3084	0.409824
$903$	−0.0496363	−0.00165179
$904$	20.0839	0.667980
$905$	0.313646	0.0104259
$906$	−0.769810	−0.0255752
$907$	−6.06370	−0.201342	−0.100671	−	0.994920i	$-0.532099\pi$
$907$	−6.06370	−0.201342	−0.100671	+	0.994920i	$0.532099\pi$
$908$	−1.09046	−0.0361882
$909$	14.9403	0.495538
$910$	7.97253	0.264287
$911$	0.952680	0.0315637	0.0157819	−	0.999875i	$-0.494976\pi$
$911$	0.952680	0.0315637	0.0157819	+	0.999875i	$0.494976\pi$
$912$	−1.14473	−0.0379057
$913$	7.52105	0.248911
$914$	16.1919	0.535581
$915$	0.478376	0.0158146
$916$	1.39032	0.0459375
$917$	9.15491	0.302322
$918$	0.625664	0.0206500
$919$	1.25635	0.0414432	0.0207216	−	0.999785i	$-0.493404\pi$
$919$	1.25635	0.0414432	0.0207216	+	0.999785i	$0.493404\pi$
$920$	−28.5407	−0.940958
$921$	−1.51662	−0.0499742
$922$	52.6147	1.73277
$923$	29.6524	0.976020
$924$	0.0237562	0.000781521 0
$925$	−7.30630	−0.240230
$926$	−1.66316	−0.0546547
$927$	−57.0747	−1.87458
$928$	−5.24684	−0.172236
$929$	45.7364	1.50056	0.750282	−	0.661118i	$-0.229918\pi$
$929$	45.7364	1.50056	0.750282	+	0.661118i	$0.229918\pi$
$930$	−1.54144	−0.0505460
$931$	−23.5201	−0.770841
$932$	−1.69519	−0.0555278
$933$	0.950477	0.0311172
$934$	28.9604	0.947612
$935$	−1.53153	−0.0500863
$936$	−31.6814	−1.03554
$937$	13.6779	0.446838	0.223419	−	0.974723i	$-0.428278\pi$
$937$	13.6779	0.446838	0.223419	+	0.974723i	$0.428278\pi$
$938$	3.27869	0.107053
$939$	0.287231	0.00937343
$940$	5.43582	0.177297
$941$	−58.8745	−1.91925	−0.959626	−	0.281279i	$-0.909241\pi$
$941$	−58.8745	−1.91925	−0.959626	+	0.281279i	$0.909241\pi$
$942$	−0.111750	−0.00364102
$943$	−60.8262	−1.98077
$944$	−3.09586	−0.100762
$945$	0.455782	0.0148266
$946$	1.57436	0.0511868
$947$	−61.2079	−1.98899	−0.994494	−	0.104792i	$-0.966582\pi$
$947$	−61.2079	−1.98899	−0.994494	+	0.104792i	$0.966582\pi$
$948$	0.278262	0.00903753
$949$	−67.1854	−2.18093
$950$	15.2644	0.495244
$951$	2.23554	0.0724924
$952$	1.79366	0.0581328
$953$	−33.5577	−1.08704	−0.543521	−	0.839396i	$-0.682909\pi$
$953$	−33.5577	−1.08704	−0.543521	+	0.839396i	$0.682909\pi$
$954$	8.65298	0.280151
$955$	−28.5303	−0.923220
$956$	−11.9277	−0.385770
$957$	−0.131071	−0.00423692
$958$	−13.8625	−0.447878
$959$	−11.2949	−0.364732
$960$	−0.535892	−0.0172958
$961$	62.0230	2.00074
$962$	−19.1339	−0.616902
$963$	43.5040	1.40190
$964$	1.14619	0.0369163
$965$	−19.7948	−0.637218
$966$	−0.607991	−0.0195618
$967$	34.6796	1.11522	0.557611	−	0.830103i	$-0.311718\pi$
$967$	34.6796	1.11522	0.557611	+	0.830103i	$0.311718\pi$
$968$	2.39522	0.0769853
$969$	0.242109	0.00777766
$970$	0.958111	0.0307631
$971$	−1.24010	−0.0397969	−0.0198984	−	0.999802i	$-0.506334\pi$
$971$	−1.24010	−0.0397969	−0.0198984	+	0.999802i	$0.506334\pi$
$972$	0.854865	0.0274198
$973$	10.1132	0.324213
$974$	−29.4781	−0.944539
$975$	−0.776872	−0.0248798
$976$	22.2808	0.713192
$977$	3.49826	0.111919	0.0559596	−	0.998433i	$-0.482178\pi$
$977$	3.49826	0.111919	0.0559596	+	0.998433i	$0.482178\pi$
$978$	2.03671	0.0651269
$979$	4.64389	0.148419
$980$	4.71993	0.150773
$981$	−39.6387	−1.26557
$982$	−22.5363	−0.719162
$983$	−58.9729	−1.88094	−0.940472	−	0.339870i	$-0.889617\pi$
$983$	−58.9729	−1.88094	−0.940472	+	0.339870i	$0.889617\pi$
$984$	−1.24121	−0.0395685
$985$	35.6724	1.13662
$986$	3.11319	0.0991441
$987$	−0.368097	−0.0117167
$988$	7.71894	0.245572
$989$	−7.78026	−0.247398
$990$	−7.22292	−0.229560
$991$	−21.7815	−0.691911	−0.345956	−	0.938251i	$-0.612445\pi$
$991$	−21.7815	−0.691911	−0.345956	+	0.938251i	$0.612445\pi$
$992$	−25.5912	−0.812522
$993$	0.288502	0.00915532
$994$	−7.91743	−0.251125
$995$	−34.7511	−1.10168
$996$	0.238595	0.00756016
$997$	−20.2611	−0.641676	−0.320838	−	0.947134i	$-0.603965\pi$
$997$	−20.2611	−0.641676	−0.320838	+	0.947134i	$0.603965\pi$
$998$	−39.9289	−1.26393
$999$	−1.09387	−0.0346084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.14	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.14	✓	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.57436 q^{2} +0.0662834 q^{3} +0.478605 q^{4} -1.53153 q^{5} -0.104354 q^{6} +0.748849 q^{7} +2.39522 q^{8} -2.99561 q^{9} +O(q^{10})\)	\(q-1.57436 q^{2} +0.0662834 q^{3} +0.478605 q^{4} -1.53153 q^{5} -0.104354 q^{6} +0.748849 q^{7} +2.39522 q^{8} -2.99561 q^{9} +2.41117 q^{10} +1.00000 q^{11} +0.0317236 q^{12} +4.41544 q^{13} -1.17896 q^{14} -0.101515 q^{15} -4.72815 q^{16} +1.00000 q^{17} +4.71616 q^{18} +3.65264 q^{19} -0.732997 q^{20} +0.0496363 q^{21} -1.57436 q^{22} +7.78026 q^{23} +0.158763 q^{24} -2.65443 q^{25} -6.95148 q^{26} -0.397409 q^{27} +0.358403 q^{28} -1.97743 q^{29} +0.159821 q^{30} -9.64484 q^{31} +2.65336 q^{32} +0.0662834 q^{33} -1.57436 q^{34} -1.14688 q^{35} -1.43371 q^{36} +2.75250 q^{37} -5.75056 q^{38} +0.292670 q^{39} -3.66834 q^{40} -7.81802 q^{41} -0.0781453 q^{42} -1.00000 q^{43} +0.478605 q^{44} +4.58785 q^{45} -12.2489 q^{46} -7.41589 q^{47} -0.313398 q^{48} -6.43922 q^{49} +4.17902 q^{50} +0.0662834 q^{51} +2.11325 q^{52} +1.83475 q^{53} +0.625664 q^{54} -1.53153 q^{55} +1.79366 q^{56} +0.242109 q^{57} +3.11319 q^{58} +0.654773 q^{59} -0.0485855 q^{60} -4.71238 q^{61} +15.1844 q^{62} -2.24326 q^{63} +5.27896 q^{64} -6.76236 q^{65} -0.104354 q^{66} -2.78101 q^{67} +0.478605 q^{68} +0.515702 q^{69} +1.80560 q^{70} +6.71561 q^{71} -7.17514 q^{72} -15.2160 q^{73} -4.33341 q^{74} -0.175944 q^{75} +1.74817 q^{76} +0.748849 q^{77} -0.460768 q^{78} +8.77145 q^{79} +7.24128 q^{80} +8.96048 q^{81} +12.3084 q^{82} +7.52105 q^{83} +0.0237562 q^{84} -1.53153 q^{85} +1.57436 q^{86} -0.131071 q^{87} +2.39522 q^{88} +4.64389 q^{89} -7.22292 q^{90} +3.30650 q^{91} +3.72368 q^{92} -0.639293 q^{93} +11.6753 q^{94} -5.59411 q^{95} +0.175874 q^{96} +0.397363 q^{97} +10.1376 q^{98} -2.99561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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