LMFDB - Embedded newform 8041.2.a.f.1.10

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:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.99436 q^{2} -0.822682 q^{3} +1.97746 q^{4} -2.77484 q^{5} +1.64072 q^{6} +2.78471 q^{7} +0.0449503 q^{8} -2.32319 q^{9} +O(q^{10})$	\(q-1.99436 q^{2} -0.822682 q^{3} +1.97746 q^{4} -2.77484 q^{5} +1.64072 q^{6} +2.78471 q^{7} +0.0449503 q^{8} -2.32319 q^{9} +5.53402 q^{10} -1.00000 q^{11} -1.62682 q^{12} -1.85048 q^{13} -5.55370 q^{14} +2.28281 q^{15} -4.04457 q^{16} +1.00000 q^{17} +4.63328 q^{18} +7.76569 q^{19} -5.48714 q^{20} -2.29093 q^{21} +1.99436 q^{22} +3.66215 q^{23} -0.0369799 q^{24} +2.69974 q^{25} +3.69053 q^{26} +4.37930 q^{27} +5.50665 q^{28} +5.63244 q^{29} -4.55274 q^{30} +8.12430 q^{31} +7.97642 q^{32} +0.822682 q^{33} -1.99436 q^{34} -7.72711 q^{35} -4.59403 q^{36} -11.9732 q^{37} -15.4876 q^{38} +1.52236 q^{39} -0.124730 q^{40} +6.89728 q^{41} +4.56893 q^{42} -1.00000 q^{43} -1.97746 q^{44} +6.44649 q^{45} -7.30363 q^{46} +8.06254 q^{47} +3.32740 q^{48} +0.754590 q^{49} -5.38424 q^{50} -0.822682 q^{51} -3.65926 q^{52} -0.364574 q^{53} -8.73388 q^{54} +2.77484 q^{55} +0.125174 q^{56} -6.38870 q^{57} -11.2331 q^{58} +10.8457 q^{59} +4.51417 q^{60} -1.10202 q^{61} -16.2028 q^{62} -6.46941 q^{63} -7.81869 q^{64} +5.13480 q^{65} -1.64072 q^{66} -12.2315 q^{67} +1.97746 q^{68} -3.01279 q^{69} +15.4106 q^{70} +4.56159 q^{71} -0.104428 q^{72} +1.34391 q^{73} +23.8789 q^{74} -2.22103 q^{75} +15.3564 q^{76} -2.78471 q^{77} -3.03613 q^{78} -10.0769 q^{79} +11.2230 q^{80} +3.36681 q^{81} -13.7556 q^{82} -1.45688 q^{83} -4.53022 q^{84} -2.77484 q^{85} +1.99436 q^{86} -4.63371 q^{87} -0.0449503 q^{88} -7.60720 q^{89} -12.8566 q^{90} -5.15306 q^{91} +7.24176 q^{92} -6.68372 q^{93} -16.0796 q^{94} -21.5486 q^{95} -6.56206 q^{96} +8.66058 q^{97} -1.50492 q^{98} +2.32319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	−1.99436	−1.41022	−0.705112	−	0.709096i	$-0.749103\pi$
$2$	−1.99436	−1.41022	−0.705112	+	0.709096i	$0.749103\pi$
$3$	−0.822682	−0.474976	−0.237488	−	0.971390i	$-0.576324\pi$
$3$	−0.822682	−0.474976	−0.237488	+	0.971390i	$0.576324\pi$
$4$	1.97746	0.988731
$5$	−2.77484	−1.24095	−0.620473	−	0.784228i	$-0.713059\pi$
$5$	−2.77484	−1.24095	−0.620473	+	0.784228i	$0.713059\pi$
$6$	1.64072	0.669822
$7$	2.78471	1.05252	0.526260	−	0.850324i	$-0.323594\pi$
$7$	2.78471	1.05252	0.526260	+	0.850324i	$0.323594\pi$
$8$	0.0449503	0.0158923
$9$	−2.32319	−0.774398
$10$	5.53402	1.75001
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.62682	−0.469623
$13$	−1.85048	−0.513232	−0.256616	−	0.966513i	$-0.582608\pi$
$13$	−1.85048	−0.513232	−0.256616	+	0.966513i	$0.582608\pi$
$14$	−5.55370	−1.48429
$15$	2.28281	0.589420
$16$	−4.04457	−1.01114
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.63328	1.09207
$19$	7.76569	1.78157	0.890786	−	0.454423i	$-0.150155\pi$
$19$	7.76569	1.78157	0.890786	+	0.454423i	$0.150155\pi$
$20$	−5.48714	−1.22696
$21$	−2.29093	−0.499922
$22$	1.99436	0.425198
$23$	3.66215	0.763611	0.381805	−	0.924243i	$-0.375302\pi$
$23$	3.66215	0.763611	0.381805	+	0.924243i	$0.375302\pi$
$24$	−0.0369799	−0.00754848
$25$	2.69974	0.539947
$26$	3.69053	0.723772
$27$	4.37930	0.842796
$28$	5.50665	1.04066
$29$	5.63244	1.04592	0.522959	−	0.852358i	$-0.324828\pi$
$29$	5.63244	1.04592	0.522959	+	0.852358i	$0.324828\pi$
$30$	−4.55274	−0.831213
$31$	8.12430	1.45917	0.729584	−	0.683892i	$-0.239714\pi$
$31$	8.12430	1.45917	0.729584	+	0.683892i	$0.239714\pi$
$32$	7.97642	1.41004
$33$	0.822682	0.143211
$34$	−1.99436	−0.342029
$35$	−7.72711	−1.30612
$36$	−4.59403	−0.765671
$37$	−11.9732	−1.96839	−0.984193	−	0.177101i	$-0.943328\pi$
$37$	−11.9732	−1.96839	−0.984193	+	0.177101i	$0.943328\pi$
$38$	−15.4876	−2.51241
$39$	1.52236	0.243773
$40$	−0.124730	−0.0197215
$41$	6.89728	1.07717	0.538587	−	0.842570i	$-0.318958\pi$
$41$	6.89728	1.07717	0.538587	+	0.842570i	$0.318958\pi$
$42$	4.56893	0.705001
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.97746	−0.298113
$45$	6.44649	0.960986
$46$	−7.30363	−1.07686
$47$	8.06254	1.17604	0.588021	−	0.808845i	$-0.299907\pi$
$47$	8.06254	1.17604	0.588021	+	0.808845i	$0.299907\pi$
$48$	3.32740	0.480268
$49$	0.754590	0.107799
$50$	−5.38424	−0.761447
$51$	−0.822682	−0.115199
$52$	−3.65926	−0.507448
$53$	−0.364574	−0.0500782	−0.0250391	−	0.999686i	$-0.507971\pi$
$53$	−0.364574	−0.0500782	−0.0250391	+	0.999686i	$0.507971\pi$
$54$	−8.73388	−1.18853
$55$	2.77484	0.374159
$56$	0.125174	0.0167270
$57$	−6.38870	−0.846204
$58$	−11.2331	−1.47498
$59$	10.8457	1.41199	0.705995	−	0.708217i	$-0.250500\pi$
$59$	10.8457	1.41199	0.705995	+	0.708217i	$0.250500\pi$
$60$	4.51417	0.582777
$61$	−1.10202	−0.141099	−0.0705496	−	0.997508i	$-0.522475\pi$
$61$	−1.10202	−0.141099	−0.0705496	+	0.997508i	$0.522475\pi$
$62$	−16.2028	−2.05775
$63$	−6.46941	−0.815069
$64$	−7.81869	−0.977336
$65$	5.13480	0.636893
$66$	−1.64072	−0.201959
$67$	−12.2315	−1.49431	−0.747156	−	0.664649i	$-0.768581\pi$
$67$	−12.2315	−1.49431	−0.747156	+	0.664649i	$0.768581\pi$
$68$	1.97746	0.239802
$69$	−3.01279	−0.362697
$70$	15.4106	1.84192
$71$	4.56159	0.541361	0.270681	−	0.962669i	$-0.412751\pi$
$71$	4.56159	0.541361	0.270681	+	0.962669i	$0.412751\pi$
$72$	−0.104428	−0.0123070
$73$	1.34391	0.157292	0.0786461	−	0.996903i	$-0.474940\pi$
$73$	1.34391	0.157292	0.0786461	+	0.996903i	$0.474940\pi$
$74$	23.8789	2.77586
$75$	−2.22103	−0.256462
$76$	15.3564	1.76149
$77$	−2.78471	−0.317347
$78$	−3.03613	−0.343774
$79$	−10.0769	−1.13374	−0.566869	−	0.823808i	$-0.691845\pi$
$79$	−10.0769	−1.13374	−0.566869	+	0.823808i	$0.691845\pi$
$80$	11.2230	1.25477
$81$	3.36681	0.374090
$82$	−13.7556	−1.51906
$83$	−1.45688	−0.159913	−0.0799567	−	0.996798i	$-0.525478\pi$
$83$	−1.45688	−0.159913	−0.0799567	+	0.996798i	$0.525478\pi$
$84$	−4.53022	−0.494288
$85$	−2.77484	−0.300974
$86$	1.99436	0.215057
$87$	−4.63371	−0.496786
$88$	−0.0449503	−0.00479172
$89$	−7.60720	−0.806361	−0.403181	−	0.915120i	$-0.632095\pi$
$89$	−7.60720	−0.806361	−0.403181	+	0.915120i	$0.632095\pi$
$90$	−12.8566	−1.35521
$91$	−5.15306	−0.540187
$92$	7.24176	0.755006
$93$	−6.68372	−0.693069
$94$	−16.0796	−1.65848
$95$	−21.5486	−2.21083
$96$	−6.56206	−0.669737
$97$	8.66058	0.879349	0.439674	−	0.898157i	$-0.355094\pi$
$97$	8.66058	0.879349	0.439674	+	0.898157i	$0.355094\pi$
$98$	−1.50492	−0.152020
$99$	2.32319	0.233490
$100$	5.33863	0.533863
$101$	−2.69157	−0.267822	−0.133911	−	0.990993i	$-0.542754\pi$
$101$	−2.69157	−0.267822	−0.133911	+	0.990993i	$0.542754\pi$
$102$	1.64072	0.162456
$103$	−6.29909	−0.620668	−0.310334	−	0.950628i	$-0.600441\pi$
$103$	−6.29909	−0.620668	−0.310334	+	0.950628i	$0.600441\pi$
$104$	−0.0831799	−0.00815646
$105$	6.35696	0.620376
$106$	0.727092	0.0706214
$107$	5.38822	0.520899	0.260449	−	0.965488i	$-0.416129\pi$
$107$	5.38822	0.520899	0.260449	+	0.965488i	$0.416129\pi$
$108$	8.65989	0.833298
$109$	9.31639	0.892348	0.446174	−	0.894946i	$-0.352786\pi$
$109$	9.31639	0.892348	0.446174	+	0.894946i	$0.352786\pi$
$110$	−5.53402	−0.527648
$111$	9.85016	0.934936
$112$	−11.2629	−1.06425
$113$	16.0844	1.51310	0.756548	−	0.653938i	$-0.226884\pi$
$113$	16.0844	1.51310	0.756548	+	0.653938i	$0.226884\pi$
$114$	12.7413	1.19334
$115$	−10.1619	−0.947600
$116$	11.1379	1.03413
$117$	4.29903	0.397446
$118$	−21.6302	−1.99122
$119$	2.78471	0.255274
$120$	0.102613	0.00936726
$121$	1.00000	0.0909091
$122$	2.19782	0.198981
$123$	−5.67427	−0.511632
$124$	16.0655	1.44272
$125$	6.38286	0.570900
$126$	12.9023	1.14943
$127$	2.27361	0.201750	0.100875	−	0.994899i	$-0.467836\pi$
$127$	2.27361	0.201750	0.100875	+	0.994899i	$0.467836\pi$
$128$	−0.359580	−0.0317827
$129$	0.822682	0.0724331
$130$	−10.2406	−0.898162
$131$	5.50061	0.480590	0.240295	−	0.970700i	$-0.422756\pi$
$131$	5.50061	0.480590	0.240295	+	0.970700i	$0.422756\pi$
$132$	1.62682	0.141597
$133$	21.6252	1.87514
$134$	24.3939	2.10731
$135$	−12.1519	−1.04586
$136$	0.0449503	0.00385446
$137$	9.72908	0.831211	0.415606	−	0.909545i	$-0.363570\pi$
$137$	9.72908	0.831211	0.415606	+	0.909545i	$0.363570\pi$
$138$	6.00857	0.511484
$139$	3.37891	0.286595	0.143298	−	0.989680i	$-0.454229\pi$
$139$	3.37891	0.286595	0.143298	+	0.989680i	$0.454229\pi$
$140$	−15.2801	−1.29140
$141$	−6.63291	−0.558592
$142$	−9.09744	−0.763440
$143$	1.85048	0.154745
$144$	9.39632	0.783027
$145$	−15.6291	−1.29793
$146$	−2.68023	−0.221817
$147$	−0.620788	−0.0512017
$148$	−23.6766	−1.94620
$149$	−16.4291	−1.34593	−0.672963	−	0.739676i	$-0.734979\pi$
$149$	−16.4291	−1.34593	−0.672963	+	0.739676i	$0.734979\pi$
$150$	4.42952	0.361669
$151$	−8.03807	−0.654128	−0.327064	−	0.945002i	$-0.606059\pi$
$151$	−8.03807	−0.654128	−0.327064	+	0.945002i	$0.606059\pi$
$152$	0.349070	0.0283134
$153$	−2.32319	−0.187819
$154$	5.55370	0.447530
$155$	−22.5436	−1.81075
$156$	3.01041	0.241026
$157$	6.23855	0.497891	0.248945	−	0.968518i	$-0.419916\pi$
$157$	6.23855	0.497891	0.248945	+	0.968518i	$0.419916\pi$
$158$	20.0969	1.59882
$159$	0.299929	0.0237859
$160$	−22.1333	−1.74979
$161$	10.1980	0.803716
$162$	−6.71462	−0.527550
$163$	−11.1975	−0.877054	−0.438527	−	0.898718i	$-0.644500\pi$
$163$	−11.1975	−0.877054	−0.438527	+	0.898718i	$0.644500\pi$
$164$	13.6391	1.06504
$165$	−2.28281	−0.177717
$166$	2.90554	0.225514
$167$	2.54424	0.196879	0.0984396	−	0.995143i	$-0.468615\pi$
$167$	2.54424	0.196879	0.0984396	+	0.995143i	$0.468615\pi$
$168$	−0.102978	−0.00794493
$169$	−9.57571	−0.736593
$170$	5.53402	0.424440
$171$	−18.0412	−1.37965
$172$	−1.97746	−0.150780
$173$	16.4828	1.25317	0.626584	−	0.779354i	$-0.284453\pi$
$173$	16.4828	1.25317	0.626584	+	0.779354i	$0.284453\pi$
$174$	9.24127	0.700579
$175$	7.51798	0.568306
$176$	4.04457	0.304871
$177$	−8.92256	−0.670661
$178$	15.1715	1.13715
$179$	−15.0662	−1.12610	−0.563051	−	0.826422i	$-0.690372\pi$
$179$	−15.0662	−1.12610	−0.563051	+	0.826422i	$0.690372\pi$
$180$	12.7477	0.950156
$181$	−17.2293	−1.28064	−0.640322	−	0.768107i	$-0.721199\pi$
$181$	−17.2293	−1.28064	−0.640322	+	0.768107i	$0.721199\pi$
$182$	10.2770	0.761785
$183$	0.906612	0.0670187
$184$	0.164615	0.0121356
$185$	33.2238	2.44266
$186$	13.3297	0.977383
$187$	−1.00000	−0.0731272
$188$	15.9434	1.16279
$189$	12.1951	0.887060
$190$	42.9755	3.11777
$191$	16.3704	1.18452	0.592261	−	0.805746i	$-0.298235\pi$
$191$	16.3704	1.18452	0.592261	+	0.805746i	$0.298235\pi$
$192$	6.43229	0.464211
$193$	−3.53270	−0.254289	−0.127145	−	0.991884i	$-0.540581\pi$
$193$	−3.53270	−0.254289	−0.127145	+	0.991884i	$0.540581\pi$
$194$	−17.2723	−1.24008
$195$	−4.22431	−0.302509
$196$	1.49217	0.106584
$197$	−4.37844	−0.311951	−0.155975	−	0.987761i	$-0.549852\pi$
$197$	−4.37844	−0.311951	−0.155975	+	0.987761i	$0.549852\pi$
$198$	−4.63328	−0.329273
$199$	12.2441	0.867962	0.433981	−	0.900922i	$-0.357108\pi$
$199$	12.2441	0.867962	0.433981	+	0.900922i	$0.357108\pi$
$200$	0.121354	0.00858103
$201$	10.0626	0.709762
$202$	5.36796	0.377688
$203$	15.6847	1.10085
$204$	−1.62682	−0.113900
$205$	−19.1389	−1.33672
$206$	12.5626	0.875281
$207$	−8.50788	−0.591339
$208$	7.48441	0.518951
$209$	−7.76569	−0.537164
$210$	−12.6781	−0.874869
$211$	−12.6960	−0.874027	−0.437013	−	0.899455i	$-0.643964\pi$
$211$	−12.6960	−0.874027	−0.437013	+	0.899455i	$0.643964\pi$
$212$	−0.720932	−0.0495138
$213$	−3.75274	−0.257133
$214$	−10.7460	−0.734584
$215$	2.77484	0.189243
$216$	0.196851	0.0133940
$217$	22.6238	1.53580
$218$	−18.5802	−1.25841
$219$	−1.10561	−0.0747100
$220$	5.48714	0.369943
$221$	−1.85048	−0.124477
$222$	−19.6447	−1.31847
$223$	6.95311	0.465615	0.232807	−	0.972523i	$-0.425209\pi$
$223$	6.95311	0.465615	0.232807	+	0.972523i	$0.425209\pi$
$224$	22.2120	1.48410
$225$	−6.27201	−0.418134
$226$	−32.0781	−2.13380
$227$	−11.7832	−0.782075	−0.391038	−	0.920375i	$-0.627884\pi$
$227$	−11.7832	−0.782075	−0.391038	+	0.920375i	$0.627884\pi$
$228$	−12.6334	−0.836667
$229$	0.753178	0.0497714	0.0248857	−	0.999690i	$-0.492078\pi$
$229$	0.753178	0.0497714	0.0248857	+	0.999690i	$0.492078\pi$
$230$	20.2664	1.33633
$231$	2.29093	0.150732
$232$	0.253180	0.0166221
$233$	−7.32679	−0.479994	−0.239997	−	0.970774i	$-0.577146\pi$
$233$	−7.32679	−0.479994	−0.239997	+	0.970774i	$0.577146\pi$
$234$	−8.57381	−0.560487
$235$	−22.3723	−1.45941
$236$	21.4469	1.39608
$237$	8.29007	0.538498
$238$	−5.55370	−0.359993
$239$	2.46250	0.159286	0.0796428	−	0.996823i	$-0.474622\pi$
$239$	2.46250	0.159286	0.0796428	+	0.996823i	$0.474622\pi$
$240$	−9.23299	−0.595987
$241$	−17.5998	−1.13371	−0.566853	−	0.823819i	$-0.691839\pi$
$241$	−17.5998	−1.13371	−0.566853	+	0.823819i	$0.691839\pi$
$242$	−1.99436	−0.128202
$243$	−15.9077	−1.02048
$244$	−2.17920	−0.139509
$245$	−2.09387	−0.133772
$246$	11.3165	0.721515
$247$	−14.3703	−0.914360
$248$	0.365190	0.0231896
$249$	1.19855	0.0759551
$250$	−12.7297	−0.805097
$251$	−14.7822	−0.933043	−0.466521	−	0.884510i	$-0.654493\pi$
$251$	−14.7822	−0.933043	−0.466521	+	0.884510i	$0.654493\pi$
$252$	−12.7930	−0.805884
$253$	−3.66215	−0.230237
$254$	−4.53439	−0.284513
$255$	2.28281	0.142955
$256$	16.3545	1.02216
$257$	8.05443	0.502422	0.251211	−	0.967932i	$-0.419171\pi$
$257$	8.05443	0.502422	0.251211	+	0.967932i	$0.419171\pi$
$258$	−1.64072	−0.102147
$259$	−33.3419	−2.07177
$260$	10.1539	0.629716
$261$	−13.0853	−0.809957
$262$	−10.9702	−0.677740
$263$	−32.0538	−1.97652	−0.988261	−	0.152774i	$-0.951179\pi$
$263$	−32.0538	−1.97652	−0.988261	+	0.152774i	$0.951179\pi$
$264$	0.0369799	0.00227595
$265$	1.01164	0.0621443
$266$	−43.1283	−2.64437
$267$	6.25831	0.383002
$268$	−24.1873	−1.47747
$269$	21.5849	1.31606	0.658029	−	0.752993i	$-0.271391\pi$
$269$	21.5849	1.31606	0.658029	+	0.752993i	$0.271391\pi$
$270$	24.2351	1.47490
$271$	−19.6159	−1.19158	−0.595791	−	0.803140i	$-0.703161\pi$
$271$	−19.6159	−1.19158	−0.595791	+	0.803140i	$0.703161\pi$
$272$	−4.04457	−0.245238
$273$	4.23933	0.256576
$274$	−19.4033	−1.17219
$275$	−2.69974	−0.162800
$276$	−5.95767	−0.358609
$277$	−27.5138	−1.65314	−0.826571	−	0.562832i	$-0.809712\pi$
$277$	−27.5138	−1.65314	−0.826571	+	0.562832i	$0.809712\pi$
$278$	−6.73875	−0.404163
$279$	−18.8743	−1.12998
$280$	−0.347336	−0.0207573
$281$	7.95788	0.474728	0.237364	−	0.971421i	$-0.423717\pi$
$281$	7.95788	0.474728	0.237364	+	0.971421i	$0.423717\pi$
$282$	13.2284	0.787740
$283$	20.8743	1.24085	0.620424	−	0.784267i	$-0.286961\pi$
$283$	20.8743	1.24085	0.620424	+	0.784267i	$0.286961\pi$
$284$	9.02037	0.535260
$285$	17.7276	1.05009
$286$	−3.69053	−0.218225
$287$	19.2069	1.13375
$288$	−18.5308	−1.09194
$289$	1.00000	0.0588235
$290$	31.1701	1.83037
$291$	−7.12491	−0.417669
$292$	2.65752	0.155520
$293$	−8.96761	−0.523893	−0.261947	−	0.965082i	$-0.584364\pi$
$293$	−8.96761	−0.523893	−0.261947	+	0.965082i	$0.584364\pi$
$294$	1.23807	0.0722059
$295$	−30.0951	−1.75220
$296$	−0.538200	−0.0312823
$297$	−4.37930	−0.254113
$298$	32.7655	1.89806
$299$	−6.77675	−0.391910
$300$	−4.39199	−0.253572
$301$	−2.78471	−0.160508
$302$	16.0308	0.922467
$303$	2.21431	0.127209
$304$	−31.4089	−1.80142
$305$	3.05793	0.175096
$306$	4.63328	0.264867
$307$	−6.61565	−0.377575	−0.188788	−	0.982018i	$-0.560456\pi$
$307$	−6.61565	−0.377575	−0.188788	+	0.982018i	$0.560456\pi$
$308$	−5.50665	−0.313770
$309$	5.18215	0.294802
$310$	44.9601	2.55356
$311$	−1.37891	−0.0781906	−0.0390953	−	0.999235i	$-0.512448\pi$
$311$	−1.37891	−0.0781906	−0.0390953	+	0.999235i	$0.512448\pi$
$312$	0.0684306	0.00387412
$313$	0.929520	0.0525396	0.0262698	−	0.999655i	$-0.491637\pi$
$313$	0.929520	0.0525396	0.0262698	+	0.999655i	$0.491637\pi$
$314$	−12.4419	−0.702137
$315$	17.9516	1.01146
$316$	−19.9266	−1.12096
$317$	−9.48830	−0.532916	−0.266458	−	0.963847i	$-0.585853\pi$
$317$	−9.48830	−0.532916	−0.266458	+	0.963847i	$0.585853\pi$
$318$	−0.598166	−0.0335435
$319$	−5.63244	−0.315356
$320$	21.6956	1.21282
$321$	−4.43279	−0.247414
$322$	−20.3385	−1.13342
$323$	7.76569	0.432095
$324$	6.65774	0.369874
$325$	−4.99582	−0.277118
$326$	22.3318	1.23684
$327$	−7.66443	−0.423844
$328$	0.310035	0.0171188
$329$	22.4518	1.23781
$330$	4.55274	0.250620
$331$	27.1498	1.49229	0.746145	−	0.665783i	$-0.231902\pi$
$331$	27.1498	1.49229	0.746145	+	0.665783i	$0.231902\pi$
$332$	−2.88093	−0.158111
$333$	27.8161	1.52431
$334$	−5.07412	−0.277644
$335$	33.9404	1.85436
$336$	9.26582	0.505492
$337$	0.00936771	0.000510292 0	0.000255146	−	1.00000i	$-0.499919\pi$
$337$	0.00936771	0.000510292 0	0.000255146		1.00000i	$0.499919\pi$
$338$	19.0974	1.03876
$339$	−13.2324	−0.718684
$340$	−5.48714	−0.297582
$341$	−8.12430	−0.439956
$342$	35.9806	1.94561
$343$	−17.3916	−0.939060
$344$	−0.0449503	−0.00242356
$345$	8.36000	0.450087
$346$	−32.8727	−1.76725
$347$	−8.57669	−0.460421	−0.230210	−	0.973141i	$-0.573941\pi$
$347$	−8.57669	−0.460421	−0.230210	+	0.973141i	$0.573941\pi$
$348$	−9.16298	−0.491187
$349$	18.3131	0.980280	0.490140	−	0.871644i	$-0.336946\pi$
$349$	18.3131	0.980280	0.490140	+	0.871644i	$0.336946\pi$
$350$	−14.9935	−0.801438
$351$	−8.10382	−0.432550
$352$	−7.97642	−0.425144
$353$	−0.576334	−0.0306751	−0.0153376	−	0.999882i	$-0.504882\pi$
$353$	−0.576334	−0.0306751	−0.0153376	+	0.999882i	$0.504882\pi$
$354$	17.7948	0.945782
$355$	−12.6577	−0.671800
$356$	−15.0429	−0.797274
$357$	−2.29093	−0.121249
$358$	30.0474	1.58805
$359$	9.58555	0.505906	0.252953	−	0.967479i	$-0.418598\pi$
$359$	9.58555	0.505906	0.252953	+	0.967479i	$0.418598\pi$
$360$	0.289772	0.0152723
$361$	41.3060	2.17400
$362$	34.3614	1.80599
$363$	−0.822682	−0.0431796
$364$	−10.1900	−0.534099
$365$	−3.72912	−0.195191
$366$	−1.80811	−0.0945113
$367$	22.1502	1.15623	0.578117	−	0.815954i	$-0.303788\pi$
$367$	22.1502	1.15623	0.578117	+	0.815954i	$0.303788\pi$
$368$	−14.8118	−0.772119
$369$	−16.0237	−0.834161
$370$	−66.2601	−3.44470
$371$	−1.01523	−0.0527083
$372$	−13.2168	−0.685259
$373$	−3.36270	−0.174114	−0.0870571	−	0.996203i	$-0.527746\pi$
$373$	−3.36270	−0.174114	−0.0870571	+	0.996203i	$0.527746\pi$
$374$	1.99436	0.103126
$375$	−5.25107	−0.271164
$376$	0.362414	0.0186901
$377$	−10.4227	−0.536799
$378$	−24.3213	−1.25095
$379$	−5.60141	−0.287725	−0.143862	−	0.989598i	$-0.545952\pi$
$379$	−5.60141	−0.287725	−0.143862	+	0.989598i	$0.545952\pi$
$380$	−42.6114	−2.18592
$381$	−1.87046	−0.0958266
$382$	−32.6485	−1.67044
$383$	−22.3275	−1.14088	−0.570440	−	0.821339i	$-0.693227\pi$
$383$	−22.3275	−1.14088	−0.570440	+	0.821339i	$0.693227\pi$
$384$	0.295820	0.0150960
$385$	7.72711	0.393810
$386$	7.04547	0.358605
$387$	2.32319	0.118095
$388$	17.1260	0.869439
$389$	25.8288	1.30957	0.654786	−	0.755815i	$-0.272759\pi$
$389$	25.8288	1.30957	0.654786	+	0.755815i	$0.272759\pi$
$390$	8.42478	0.426605
$391$	3.66215	0.185203
$392$	0.0339191	0.00171317
$393$	−4.52525	−0.228269
$394$	8.73217	0.439920
$395$	27.9617	1.40691
$396$	4.59403	0.230858
$397$	24.0066	1.20486	0.602429	−	0.798172i	$-0.294200\pi$
$397$	24.0066	1.20486	0.602429	+	0.798172i	$0.294200\pi$
$398$	−24.4191	−1.22402
$399$	−17.7906	−0.890646
$400$	−10.9193	−0.545964
$401$	−27.2565	−1.36112	−0.680561	−	0.732691i	$-0.738264\pi$
$401$	−27.2565	−1.36112	−0.680561	+	0.732691i	$0.738264\pi$
$402$	−20.0684	−1.00092
$403$	−15.0339	−0.748891
$404$	−5.32248	−0.264803
$405$	−9.34236	−0.464226
$406$	−31.2809	−1.55244
$407$	11.9732	0.593491
$408$	−0.0369799	−0.00183078
$409$	6.27982	0.310517	0.155258	−	0.987874i	$-0.450379\pi$
$409$	6.27982	0.310517	0.155258	+	0.987874i	$0.450379\pi$
$410$	38.1697	1.88507
$411$	−8.00394	−0.394805
$412$	−12.4562	−0.613673
$413$	30.2021	1.48615
$414$	16.9678	0.833920
$415$	4.04261	0.198444
$416$	−14.7602	−0.723680
$417$	−2.77977	−0.136126
$418$	15.4876	0.757521
$419$	−11.6102	−0.567195	−0.283598	−	0.958943i	$-0.591528\pi$
$419$	−11.6102	−0.567195	−0.283598	+	0.958943i	$0.591528\pi$
$420$	12.5706	0.613385
$421$	21.2266	1.03452	0.517260	−	0.855828i	$-0.326952\pi$
$421$	21.2266	1.03452	0.517260	+	0.855828i	$0.326952\pi$
$422$	25.3203	1.23257
$423$	−18.7308	−0.910725
$424$	−0.0163877	−0.000795859 0
$425$	2.69974	0.130957
$426$	7.48430	0.362616
$427$	−3.06880	−0.148510
$428$	10.6550	0.515029
$429$	−1.52236	−0.0735003
$430$	−5.53402	−0.266874
$431$	−15.4430	−0.743866	−0.371933	−	0.928260i	$-0.621305\pi$
$431$	−15.4430	−0.743866	−0.371933	+	0.928260i	$0.621305\pi$
$432$	−17.7124	−0.852187
$433$	−2.95186	−0.141857	−0.0709286	−	0.997481i	$-0.522596\pi$
$433$	−2.95186	−0.141857	−0.0709286	+	0.997481i	$0.522596\pi$
$434$	−45.1199	−2.16583
$435$	12.8578	0.616485
$436$	18.4228	0.882292
$437$	28.4391	1.36043
$438$	2.20498	0.105358
$439$	30.0024	1.43194	0.715968	−	0.698133i	$-0.245986\pi$
$439$	30.0024	1.43194	0.715968	+	0.698133i	$0.245986\pi$
$440$	0.124730	0.00594627
$441$	−1.75306	−0.0834790
$442$	3.69053	0.175540
$443$	3.03331	0.144117	0.0720584	−	0.997400i	$-0.477043\pi$
$443$	3.03331	0.144117	0.0720584	+	0.997400i	$0.477043\pi$
$444$	19.4783	0.924399
$445$	21.1088	1.00065
$446$	−13.8670	−0.656621
$447$	13.5160	0.639283
$448$	−21.7727	−1.02867
$449$	23.8687	1.12643	0.563216	−	0.826309i	$-0.309564\pi$
$449$	23.8687	1.12643	0.563216	+	0.826309i	$0.309564\pi$
$450$	12.5086	0.589663
$451$	−6.89728	−0.324780
$452$	31.8063	1.49604
$453$	6.61278	0.310695
$454$	23.4998	1.10290
$455$	14.2989	0.670343
$456$	−0.287174	−0.0134482
$457$	−11.1348	−0.520863	−0.260432	−	0.965492i	$-0.583865\pi$
$457$	−11.1348	−0.520863	−0.260432	+	0.965492i	$0.583865\pi$
$458$	−1.50211	−0.0701888
$459$	4.37930	0.204408
$460$	−20.0947	−0.936921
$461$	15.7739	0.734664	0.367332	−	0.930090i	$-0.380271\pi$
$461$	15.7739	0.734664	0.367332	+	0.930090i	$0.380271\pi$
$462$	−4.56893	−0.212566
$463$	31.0474	1.44290	0.721448	−	0.692469i	$-0.243477\pi$
$463$	31.0474	1.44290	0.721448	+	0.692469i	$0.243477\pi$
$464$	−22.7808	−1.05757
$465$	18.5463	0.860062
$466$	14.6122	0.676899
$467$	−15.8740	−0.734559	−0.367280	−	0.930111i	$-0.619711\pi$
$467$	−15.8740	−0.734559	−0.367280	+	0.930111i	$0.619711\pi$
$468$	8.50117	0.392967
$469$	−34.0610	−1.57279
$470$	44.6183	2.05809
$471$	−5.13235	−0.236486
$472$	0.487518	0.0224398
$473$	1.00000	0.0459800
$474$	−16.5334	−0.759403
$475$	20.9653	0.961955
$476$	5.50665	0.252397
$477$	0.846977	0.0387804
$478$	−4.91110	−0.224628
$479$	26.4128	1.20683	0.603417	−	0.797426i	$-0.293806\pi$
$479$	26.4128	1.20683	0.603417	+	0.797426i	$0.293806\pi$
$480$	18.2087	0.831108
$481$	22.1563	1.01024
$482$	35.1004	1.59878
$483$	−8.38972	−0.381746
$484$	1.97746	0.0898846
$485$	−24.0317	−1.09122
$486$	31.7257	1.43910
$487$	9.40318	0.426099	0.213049	−	0.977041i	$-0.431660\pi$
$487$	9.40318	0.426099	0.213049	+	0.977041i	$0.431660\pi$
$488$	−0.0495361	−0.00224240
$489$	9.21196	0.416579
$490$	4.17592	0.188649
$491$	12.4129	0.560185	0.280092	−	0.959973i	$-0.409635\pi$
$491$	12.4129	0.560185	0.280092	+	0.959973i	$0.409635\pi$
$492$	−11.2207	−0.505866
$493$	5.63244	0.253672
$494$	28.6595	1.28945
$495$	−6.44649	−0.289748
$496$	−32.8593	−1.47543
$497$	12.7027	0.569793
$498$	−2.39034	−0.107114
$499$	−19.0506	−0.852823	−0.426412	−	0.904529i	$-0.640222\pi$
$499$	−19.0506	−0.852823	−0.426412	+	0.904529i	$0.640222\pi$
$500$	12.6219	0.564467
$501$	−2.09310	−0.0935129
$502$	29.4810	1.31580
$503$	35.5094	1.58328	0.791642	−	0.610985i	$-0.209227\pi$
$503$	35.5094	1.58328	0.791642	+	0.610985i	$0.209227\pi$
$504$	−0.290802	−0.0129534
$505$	7.46869	0.332352
$506$	7.30363	0.324686
$507$	7.87777	0.349864
$508$	4.49598	0.199477
$509$	−4.71280	−0.208891	−0.104446	−	0.994531i	$-0.533307\pi$
$509$	−4.71280	−0.208891	−0.104446	+	0.994531i	$0.533307\pi$
$510$	−4.55274	−0.201599
$511$	3.74238	0.165553
$512$	−31.8976	−1.40969
$513$	34.0083	1.50150
$514$	−16.0634	−0.708527
$515$	17.4790	0.770216
$516$	1.62682	0.0716169
$517$	−8.06254	−0.354590
$518$	66.4957	2.92165
$519$	−13.5601	−0.595224
$520$	0.230811	0.0101217
$521$	17.2240	0.754598	0.377299	−	0.926092i	$-0.376853\pi$
$521$	17.2240	0.754598	0.377299	+	0.926092i	$0.376853\pi$
$522$	26.0967	1.14222
$523$	38.0092	1.66202	0.831012	−	0.556254i	$-0.187762\pi$
$523$	38.0092	1.66202	0.831012	+	0.556254i	$0.187762\pi$
$524$	10.8772	0.475174
$525$	−6.18491	−0.269931
$526$	63.9267	2.78734
$527$	8.12430	0.353900
$528$	−3.32740	−0.144806
$529$	−9.58866	−0.416898
$530$	−2.01756	−0.0876373
$531$	−25.1967	−1.09344
$532$	42.7629	1.85401
$533$	−12.7633	−0.552840
$534$	−12.4813	−0.540119
$535$	−14.9514	−0.646407
$536$	−0.549809	−0.0237481
$537$	12.3947	0.534871
$538$	−43.0481	−1.85593
$539$	−0.754590	−0.0325025
$540$	−24.0298	−1.03408
$541$	−28.5883	−1.22911	−0.614553	−	0.788876i	$-0.710663\pi$
$541$	−28.5883	−1.22911	−0.614553	+	0.788876i	$0.710663\pi$
$542$	39.1211	1.68040
$543$	14.1742	0.608275
$544$	7.97642	0.341986
$545$	−25.8515	−1.10736
$546$	−8.45474	−0.361829
$547$	−5.58772	−0.238914	−0.119457	−	0.992839i	$-0.538115\pi$
$547$	−5.58772	−0.238914	−0.119457	+	0.992839i	$0.538115\pi$
$548$	19.2389	0.821844
$549$	2.56020	0.109267
$550$	5.38424	0.229585
$551$	43.7398	1.86338
$552$	−0.135426	−0.00576410
$553$	−28.0612	−1.19328
$554$	54.8723	2.33130
$555$	−27.3326	−1.16020
$556$	6.68166	0.283365
$557$	24.5544	1.04040	0.520201	−	0.854044i	$-0.325857\pi$
$557$	24.5544	1.04040	0.520201	+	0.854044i	$0.325857\pi$
$558$	37.6421	1.59352
$559$	1.85048	0.0782672
$560$	31.2529	1.32067
$561$	0.822682	0.0347337
$562$	−15.8709	−0.669472
$563$	9.34456	0.393826	0.196913	−	0.980421i	$-0.436908\pi$
$563$	9.34456	0.393826	0.196913	+	0.980421i	$0.436908\pi$
$564$	−13.1163	−0.552297
$565$	−44.6317	−1.87767
$566$	−41.6308	−1.74987
$567$	9.37558	0.393737
$568$	0.205045	0.00860350
$569$	15.8004	0.662385	0.331193	−	0.943563i	$-0.392549\pi$
$569$	15.8004	0.662385	0.331193	+	0.943563i	$0.392549\pi$
$570$	−35.3552	−1.48087
$571$	−0.593947	−0.0248559	−0.0124280	−	0.999923i	$-0.503956\pi$
$571$	−0.593947	−0.0248559	−0.0124280	+	0.999923i	$0.503956\pi$
$572$	3.65926	0.153001
$573$	−13.4677	−0.562620
$574$	−38.3054	−1.59884
$575$	9.88684	0.412310
$576$	18.1643	0.756847
$577$	19.3114	0.803946	0.401973	−	0.915652i	$-0.368325\pi$
$577$	19.3114	0.803946	0.401973	+	0.915652i	$0.368325\pi$
$578$	−1.99436	−0.0829543
$579$	2.90629	0.120781
$580$	−30.9060	−1.28330
$581$	−4.05699	−0.168312
$582$	14.2096	0.589007
$583$	0.364574	0.0150991
$584$	0.0604090	0.00249974
$585$	−11.9291	−0.493209
$586$	17.8846	0.738807
$587$	−45.6346	−1.88354	−0.941770	−	0.336257i	$-0.890839\pi$
$587$	−45.6346	−1.88354	−0.941770	+	0.336257i	$0.890839\pi$
$588$	−1.22758	−0.0506247
$589$	63.0908	2.59961
$590$	60.0203	2.47100
$591$	3.60206	0.148169
$592$	48.4265	1.99032
$593$	−11.3225	−0.464961	−0.232480	−	0.972601i	$-0.574684\pi$
$593$	−11.3225	−0.464961	−0.232480	+	0.972601i	$0.574684\pi$
$594$	8.73388	0.358356
$595$	−7.72711	−0.316781
$596$	−32.4880	−1.33076
$597$	−10.0730	−0.412261
$598$	13.5153	0.552680
$599$	−48.0216	−1.96211	−0.981054	−	0.193735i	$-0.937940\pi$
$599$	−48.0216	−1.96211	−0.981054	+	0.193735i	$0.937940\pi$
$600$	−0.0998359	−0.00407578
$601$	24.9410	1.01737	0.508683	−	0.860954i	$-0.330133\pi$
$601$	24.9410	1.01737	0.508683	+	0.860954i	$0.330133\pi$
$602$	5.55370	0.226352
$603$	28.4161	1.15719
$604$	−15.8950	−0.646757
$605$	−2.77484	−0.112813
$606$	−4.41613	−0.179393
$607$	−9.23136	−0.374689	−0.187345	−	0.982294i	$-0.559988\pi$
$607$	−9.23136	−0.374689	−0.187345	+	0.982294i	$0.559988\pi$
$608$	61.9424	2.51210
$609$	−12.9035	−0.522877
$610$	−6.09860	−0.246925
$611$	−14.9196	−0.603583
$612$	−4.59403	−0.185702
$613$	13.5492	0.547246	0.273623	−	0.961837i	$-0.411778\pi$
$613$	13.5492	0.547246	0.273623	+	0.961837i	$0.411778\pi$
$614$	13.1940	0.532466
$615$	15.7452	0.634908
$616$	−0.125174	−0.00504338
$617$	−17.3104	−0.696892	−0.348446	−	0.937329i	$-0.613291\pi$
$617$	−17.3104	−0.696892	−0.348446	+	0.937329i	$0.613291\pi$
$618$	−10.3351	−0.415737
$619$	−17.8318	−0.716719	−0.358359	−	0.933584i	$-0.616664\pi$
$619$	−17.8318	−0.716719	−0.358359	+	0.933584i	$0.616664\pi$
$620$	−44.5792	−1.79034
$621$	16.0376	0.643568
$622$	2.75003	0.110266
$623$	−21.1838	−0.848712
$624$	−6.15730	−0.246489
$625$	−31.2101	−1.24840
$626$	−1.85379	−0.0740925
$627$	6.38870	0.255140
$628$	12.3365	0.492280
$629$	−11.9732	−0.477404
$630$	−35.8019	−1.42638
$631$	48.5834	1.93407	0.967036	−	0.254638i	$-0.0819564\pi$
$631$	48.5834	1.93407	0.967036	+	0.254638i	$0.0819564\pi$
$632$	−0.452959	−0.0180178
$633$	10.4448	0.415142
$634$	18.9231	0.751530
$635$	−6.30891	−0.250361
$636$	0.593098	0.0235179
$637$	−1.39636	−0.0553257
$638$	11.2331	0.444723
$639$	−10.5975	−0.419229
$640$	0.997777	0.0394406
$641$	−0.906021	−0.0357857	−0.0178928	−	0.999840i	$-0.505696\pi$
$641$	−0.906021	−0.0357857	−0.0178928	+	0.999840i	$0.505696\pi$
$642$	8.84057	0.348910
$643$	20.1717	0.795496	0.397748	−	0.917495i	$-0.369792\pi$
$643$	20.1717	0.795496	0.397748	+	0.917495i	$0.369792\pi$
$644$	20.1662	0.794658
$645$	−2.28281	−0.0898856
$646$	−15.4876	−0.609350
$647$	8.36576	0.328892	0.164446	−	0.986386i	$-0.447416\pi$
$647$	8.36576	0.328892	0.164446	+	0.986386i	$0.447416\pi$
$648$	0.151339	0.00594517
$649$	−10.8457	−0.425731
$650$	9.96345	0.390799
$651$	−18.6122	−0.729469
$652$	−22.1426	−0.867170
$653$	−35.2772	−1.38050	−0.690251	−	0.723570i	$-0.742500\pi$
$653$	−35.2772	−1.38050	−0.690251	+	0.723570i	$0.742500\pi$
$654$	15.2856	0.597715
$655$	−15.2633	−0.596387
$656$	−27.8965	−1.08918
$657$	−3.12215	−0.121807
$658$	−44.7769	−1.74559
$659$	3.95776	0.154173	0.0770863	−	0.997024i	$-0.475438\pi$
$659$	3.95776	0.154173	0.0770863	+	0.997024i	$0.475438\pi$
$660$	−4.51417	−0.175714
$661$	−12.9725	−0.504573	−0.252286	−	0.967653i	$-0.581183\pi$
$661$	−12.9725	−0.504573	−0.252286	+	0.967653i	$0.581183\pi$
$662$	−54.1465	−2.10446
$663$	1.52236	0.0591236
$664$	−0.0654873	−0.00254140
$665$	−60.0064	−2.32695
$666$	−55.4753	−2.14962
$667$	20.6268	0.798674
$668$	5.03114	0.194660
$669$	−5.72020	−0.221156
$670$	−67.6892	−2.61506
$671$	1.10202	0.0425430
$672$	−18.2734	−0.704912
$673$	−3.89394	−0.150100	−0.0750501	−	0.997180i	$-0.523912\pi$
$673$	−3.89394	−0.150100	−0.0750501	+	0.997180i	$0.523912\pi$
$674$	−0.0186826	−0.000719625 0
$675$	11.8230	0.455066
$676$	−18.9356	−0.728292
$677$	49.3712	1.89749	0.948744	−	0.316044i	$-0.102355\pi$
$677$	49.3712	1.89749	0.948744	+	0.316044i	$0.102355\pi$
$678$	26.3901	1.01351
$679$	24.1172	0.925532
$680$	−0.124730	−0.00478318
$681$	9.69379	0.371467
$682$	16.2028	0.620436
$683$	−2.13032	−0.0815145	−0.0407572	−	0.999169i	$-0.512977\pi$
$683$	−2.13032	−0.0815145	−0.0407572	+	0.999169i	$0.512977\pi$
$684$	−35.6758	−1.36410
$685$	−26.9966	−1.03149
$686$	34.6851	1.32428
$687$	−0.619626	−0.0236402
$688$	4.04457	0.154198
$689$	0.674639	0.0257017
$690$	−16.6728	−0.634724
$691$	10.5846	0.402659	0.201329	−	0.979524i	$-0.435474\pi$
$691$	10.5846	0.402659	0.201329	+	0.979524i	$0.435474\pi$
$692$	32.5942	1.23904
$693$	6.46941	0.245753
$694$	17.1050	0.649297
$695$	−9.37592	−0.355649
$696$	−0.208287	−0.00789509
$697$	6.89728	0.261253
$698$	−36.5230	−1.38241
$699$	6.02762	0.227986
$700$	14.8665	0.561901
$701$	−13.7243	−0.518359	−0.259180	−	0.965829i	$-0.583452\pi$
$701$	−13.7243	−0.518359	−0.259180	+	0.965829i	$0.583452\pi$
$702$	16.1619	0.609992
$703$	−92.9803	−3.50682
$704$	7.81869	0.294678
$705$	18.4053	0.693183
$706$	1.14942	0.0432588
$707$	−7.49524	−0.281888
$708$	−17.6440	−0.663103
$709$	33.7122	1.26609	0.633044	−	0.774116i	$-0.281805\pi$
$709$	33.7122	1.26609	0.633044	+	0.774116i	$0.281805\pi$
$710$	25.2439	0.947388
$711$	23.4106	0.877964
$712$	−0.341946	−0.0128150
$713$	29.7524	1.11424
$714$	4.56893	0.170988
$715$	−5.13480	−0.192031
$716$	−29.7928	−1.11341
$717$	−2.02585	−0.0756568
$718$	−19.1170	−0.713441
$719$	−46.5613	−1.73644	−0.868221	−	0.496177i	$-0.834737\pi$
$719$	−46.5613	−1.73644	−0.868221	+	0.496177i	$0.834737\pi$
$720$	−26.0733	−0.971694
$721$	−17.5411	−0.653266
$722$	−82.3788	−3.06582
$723$	14.4791	0.538483
$724$	−34.0703	−1.26621
$725$	15.2061	0.564741
$726$	1.64072	0.0608929
$727$	30.9604	1.14826	0.574129	−	0.818765i	$-0.305341\pi$
$727$	30.9604	1.14826	0.574129	+	0.818765i	$0.305341\pi$
$728$	−0.231632	−0.00858484
$729$	2.98656	0.110613
$730$	7.43720	0.275263
$731$	−1.00000	−0.0369863
$732$	1.79279	0.0662634
$733$	−10.5175	−0.388472	−0.194236	−	0.980955i	$-0.562223\pi$
$733$	−10.5175	−0.388472	−0.194236	+	0.980955i	$0.562223\pi$
$734$	−44.1755	−1.63055
$735$	1.72259	0.0635386
$736$	29.2108	1.07673
$737$	12.2315	0.450552
$738$	31.9570	1.17635
$739$	−3.04184	−0.111896	−0.0559479	−	0.998434i	$-0.517818\pi$
$739$	−3.04184	−0.111896	−0.0559479	+	0.998434i	$0.517818\pi$
$740$	65.6987	2.41513
$741$	11.8222	0.434299
$742$	2.02474	0.0743304
$743$	−15.4234	−0.565831	−0.282915	−	0.959145i	$-0.591302\pi$
$743$	−15.4234	−0.565831	−0.282915	+	0.959145i	$0.591302\pi$
$744$	−0.300435	−0.0110145
$745$	45.5882	1.67022
$746$	6.70643	0.245540
$747$	3.38462	0.123837
$748$	−1.97746	−0.0723031
$749$	15.0046	0.548256
$750$	10.4725	0.382402
$751$	13.6328	0.497466	0.248733	−	0.968572i	$-0.419986\pi$
$751$	13.6328	0.497466	0.248733	+	0.968572i	$0.419986\pi$
$752$	−32.6095	−1.18915
$753$	12.1610	0.443173
$754$	20.7867	0.757006
$755$	22.3043	0.811738
$756$	24.1153	0.877063
$757$	−17.6006	−0.639705	−0.319853	−	0.947467i	$-0.603633\pi$
$757$	−17.6006	−0.639705	−0.319853	+	0.947467i	$0.603633\pi$
$758$	11.1712	0.405756
$759$	3.01279	0.109357
$760$	−0.968615	−0.0351353
$761$	16.0454	0.581647	0.290823	−	0.956777i	$-0.406071\pi$
$761$	16.0454	0.581647	0.290823	+	0.956777i	$0.406071\pi$
$762$	3.73037	0.135137
$763$	25.9434	0.939215
$764$	32.3719	1.17117
$765$	6.44649	0.233073
$766$	44.5289	1.60890
$767$	−20.0698	−0.724678
$768$	−13.4546	−0.485500
$769$	37.2181	1.34212	0.671059	−	0.741404i	$-0.265840\pi$
$769$	37.2181	1.34212	0.671059	+	0.741404i	$0.265840\pi$
$770$	−15.4106	−0.555361
$771$	−6.62624	−0.238638
$772$	−6.98578	−0.251424
$773$	37.3555	1.34358	0.671792	−	0.740740i	$-0.265525\pi$
$773$	37.3555	1.34358	0.671792	+	0.740740i	$0.265525\pi$
$774$	−4.63328	−0.166540
$775$	21.9335	0.787874
$776$	0.389296	0.0139749
$777$	27.4298	0.984039
$778$	−51.5118	−1.84679
$779$	53.5622	1.91906
$780$	−8.35341	−0.299100
$781$	−4.56159	−0.163227
$782$	−7.30363	−0.261177
$783$	24.6661	0.881496
$784$	−3.05199	−0.109000
$785$	−17.3110	−0.617856
$786$	9.02497	0.321910
$787$	49.5672	1.76688	0.883441	−	0.468543i	$-0.155221\pi$
$787$	49.5672	1.76688	0.883441	+	0.468543i	$0.155221\pi$
$788$	−8.65819	−0.308435
$789$	26.3701	0.938801
$790$	−55.7657	−1.98405
$791$	44.7904	1.59256
$792$	0.104428	0.00371070
$793$	2.03927	0.0724166
$794$	−47.8778	−1.69912
$795$	−0.832255	−0.0295170
$796$	24.2123	0.858181
$797$	19.7806	0.700663	0.350332	−	0.936626i	$-0.386069\pi$
$797$	19.7806	0.700663	0.350332	+	0.936626i	$0.386069\pi$
$798$	35.4809	1.25601
$799$	8.06254	0.285232
$800$	21.5342	0.761350
$801$	17.6730	0.624445
$802$	54.3591	1.91949
$803$	−1.34391	−0.0474254
$804$	19.8984	0.701763
$805$	−28.2978	−0.997368
$806$	29.9830	1.05610
$807$	−17.7576	−0.625095
$808$	−0.120987	−0.00425631
$809$	31.4162	1.10453	0.552267	−	0.833667i	$-0.313763\pi$
$809$	31.4162	1.10453	0.552267	+	0.833667i	$0.313763\pi$
$810$	18.6320	0.654662
$811$	9.08500	0.319018	0.159509	−	0.987197i	$-0.449009\pi$
$811$	9.08500	0.319018	0.159509	+	0.987197i	$0.449009\pi$
$812$	31.0159	1.08844
$813$	16.1377	0.565973
$814$	−23.8789	−0.836954
$815$	31.0712	1.08838
$816$	3.32740	0.116482
$817$	−7.76569	−0.271687
$818$	−12.5242	−0.437898
$819$	11.9715	0.418320
$820$	−37.8463	−1.32165
$821$	−30.2430	−1.05549	−0.527743	−	0.849404i	$-0.676962\pi$
$821$	−30.2430	−1.05549	−0.527743	+	0.849404i	$0.676962\pi$
$822$	15.9627	0.556764
$823$	−15.3097	−0.533662	−0.266831	−	0.963743i	$-0.585977\pi$
$823$	−15.3097	−0.533662	−0.266831	+	0.963743i	$0.585977\pi$
$824$	−0.283146	−0.00986387
$825$	2.22103	0.0773262
$826$	−60.2337	−2.09580
$827$	33.5449	1.16647	0.583236	−	0.812303i	$-0.301786\pi$
$827$	33.5449	1.16647	0.583236	+	0.812303i	$0.301786\pi$
$828$	−16.8240	−0.584675
$829$	3.74619	0.130111	0.0650553	−	0.997882i	$-0.479278\pi$
$829$	3.74619	0.130111	0.0650553	+	0.997882i	$0.479278\pi$
$830$	−8.06241	−0.279850
$831$	22.6351	0.785203
$832$	14.4684	0.501600
$833$	0.754590	0.0261450
$834$	5.54385	0.191968
$835$	−7.05986	−0.244316
$836$	−15.3564	−0.531111
$837$	35.5787	1.22978
$838$	23.1549	0.799872
$839$	−18.2309	−0.629401	−0.314701	−	0.949191i	$-0.601904\pi$
$839$	−18.2309	−0.629401	−0.314701	+	0.949191i	$0.601904\pi$
$840$	0.285748	0.00985923
$841$	2.72439	0.0939446
$842$	−42.3334	−1.45890
$843$	−6.54681	−0.225484
$844$	−25.1058	−0.864177
$845$	26.5711	0.914072
$846$	37.3560	1.28433
$847$	2.78471	0.0956836
$848$	1.47455	0.0506361
$849$	−17.1729	−0.589373
$850$	−5.38424	−0.184678
$851$	−43.8477	−1.50308
$852$	−7.42090	−0.254236
$853$	−32.0810	−1.09843	−0.549215	−	0.835681i	$-0.685073\pi$
$853$	−32.0810	−1.09843	−0.549215	+	0.835681i	$0.685073\pi$
$854$	6.12028	0.209432
$855$	50.0615	1.71207
$856$	0.242202	0.00827830
$857$	6.19255	0.211533	0.105767	−	0.994391i	$-0.466270\pi$
$857$	6.19255	0.211533	0.105767	+	0.994391i	$0.466270\pi$
$858$	3.03613	0.103652
$859$	20.2161	0.689764	0.344882	−	0.938646i	$-0.387919\pi$
$859$	20.2161	0.689764	0.344882	+	0.938646i	$0.387919\pi$
$860$	5.48714	0.187110
$861$	−15.8012	−0.538503
$862$	30.7990	1.04902
$863$	17.9996	0.612713	0.306357	−	0.951917i	$-0.400890\pi$
$863$	17.9996	0.612713	0.306357	+	0.951917i	$0.400890\pi$
$864$	34.9311	1.18838
$865$	−45.7372	−1.55511
$866$	5.88706	0.200050
$867$	−0.822682	−0.0279398
$868$	44.7377	1.51850
$869$	10.0769	0.341835
$870$	−25.6431	−0.869381
$871$	22.6341	0.766929
$872$	0.418775	0.0141815
$873$	−20.1202	−0.680966
$874$	−56.7178	−1.91851
$875$	17.7744	0.600884
$876$	−2.18630	−0.0738681
$877$	−44.1430	−1.49060	−0.745302	−	0.666727i	$-0.767695\pi$
$877$	−44.1430	−1.49060	−0.745302	+	0.666727i	$0.767695\pi$
$878$	−59.8355	−2.01935
$879$	7.37749	0.248837
$880$	−11.2230	−0.378328
$881$	56.6831	1.90970	0.954851	−	0.297085i	$-0.0960146\pi$
$881$	56.6831	1.90970	0.954851	+	0.297085i	$0.0960146\pi$
$882$	3.49622	0.117724
$883$	43.3234	1.45795	0.728974	−	0.684541i	$-0.239997\pi$
$883$	43.3234	1.45795	0.728974	+	0.684541i	$0.239997\pi$
$884$	−3.65926	−0.123074
$885$	24.7587	0.832254
$886$	−6.04950	−0.203237
$887$	−8.94154	−0.300227	−0.150114	−	0.988669i	$-0.547964\pi$
$887$	−8.94154	−0.300227	−0.150114	+	0.988669i	$0.547964\pi$
$888$	0.442768	0.0148583
$889$	6.33134	0.212346
$890$	−42.0984	−1.41114
$891$	−3.36681	−0.112792
$892$	13.7495	0.460367
$893$	62.6112	2.09520
$894$	−26.9556	−0.901531
$895$	41.8063	1.39743
$896$	−1.00132	−0.0334519
$897$	5.57511	0.186148
$898$	−47.6027	−1.58852
$899$	45.7596	1.52617
$900$	−12.4027	−0.413422
$901$	−0.364574	−0.0121457
$902$	13.7556	0.458013
$903$	2.29093	0.0762373
$904$	0.723001	0.0240466
$905$	47.8086	1.58921
$906$	−13.1882	−0.438150
$907$	−51.6159	−1.71388	−0.856940	−	0.515417i	$-0.827637\pi$
$907$	−51.6159	−1.71388	−0.856940	+	0.515417i	$0.827637\pi$
$908$	−23.3007	−0.773262
$909$	6.25305	0.207401
$910$	−28.5171	−0.945334
$911$	−10.7665	−0.356709	−0.178354	−	0.983966i	$-0.557077\pi$
$911$	−10.7665	−0.356709	−0.178354	+	0.983966i	$0.557077\pi$
$912$	25.8395	0.855632
$913$	1.45688	0.0482157
$914$	22.2067	0.734534
$915$	−2.51570	−0.0831666
$916$	1.48938	0.0492105
$917$	15.3176	0.505831
$918$	−8.73388	−0.288261
$919$	−12.2695	−0.404732	−0.202366	−	0.979310i	$-0.564863\pi$
$919$	−12.2695	−0.404732	−0.202366	+	0.979310i	$0.564863\pi$
$920$	−0.456780	−0.0150596
$921$	5.44258	0.179339
$922$	−31.4588	−1.03604
$923$	−8.44115	−0.277844
$924$	4.53022	0.149033
$925$	−32.3246	−1.06282
$926$	−61.9196	−2.03481
$927$	14.6340	0.480644
$928$	44.9267	1.47479
$929$	55.7466	1.82899	0.914494	−	0.404600i	$-0.132589\pi$
$929$	55.7466	1.82899	0.914494	+	0.404600i	$0.132589\pi$
$930$	−36.9879	−1.21288
$931$	5.85991	0.192051
$932$	−14.4884	−0.474585
$933$	1.13440	0.0371386
$934$	31.6583	1.03589
$935$	2.77484	0.0907470
$936$	0.193243	0.00631635
$937$	40.6566	1.32819	0.664097	−	0.747647i	$-0.268816\pi$
$937$	40.6566	1.32819	0.664097	+	0.747647i	$0.268816\pi$
$938$	67.9299	2.21799
$939$	−0.764700	−0.0249550
$940$	−44.2403	−1.44296
$941$	−22.8093	−0.743562	−0.371781	−	0.928320i	$-0.621253\pi$
$941$	−22.8093	−0.743562	−0.371781	+	0.928320i	$0.621253\pi$
$942$	10.2357	0.333498
$943$	25.2589	0.822542
$944$	−43.8662	−1.42772
$945$	−33.8393	−1.10079
$946$	−1.99436	−0.0648422
$947$	−49.9903	−1.62447	−0.812233	−	0.583333i	$-0.801748\pi$
$947$	−49.9903	−1.62447	−0.812233	+	0.583333i	$0.801748\pi$
$948$	16.3933	0.532430
$949$	−2.48688	−0.0807274
$950$	−41.8124	−1.35657
$951$	7.80585	0.253122
$952$	0.125174	0.00405690
$953$	−50.1438	−1.62432	−0.812159	−	0.583437i	$-0.801708\pi$
$953$	−50.1438	−1.62432	−0.812159	+	0.583437i	$0.801708\pi$
$954$	−1.68917	−0.0546891
$955$	−45.4253	−1.46993
$956$	4.86949	0.157491
$957$	4.63371	0.149787
$958$	−52.6766	−1.70190
$959$	27.0926	0.874867
$960$	−17.8486	−0.576061
$961$	35.0043	1.12917
$962$	−44.1875	−1.42466
$963$	−12.5179	−0.403383
$964$	−34.8030	−1.12093
$965$	9.80268	0.315559
$966$	16.7321	0.538347
$967$	−27.1829	−0.874142	−0.437071	−	0.899427i	$-0.643984\pi$
$967$	−27.1829	−0.874142	−0.437071	+	0.899427i	$0.643984\pi$
$968$	0.0449503	0.00144476
$969$	−6.38870	−0.205235
$970$	47.9278	1.53887
$971$	−6.33535	−0.203311	−0.101656	−	0.994820i	$-0.532414\pi$
$971$	−6.33535	−0.203311	−0.101656	+	0.994820i	$0.532414\pi$
$972$	−31.4569	−1.00898
$973$	9.40926	0.301647
$974$	−18.7533	−0.600895
$975$	4.10998	0.131625
$976$	4.45719	0.142671
$977$	−12.9357	−0.413849	−0.206924	−	0.978357i	$-0.566345\pi$
$977$	−12.9357	−0.413849	−0.206924	+	0.978357i	$0.566345\pi$
$978$	−18.3719	−0.587470
$979$	7.60720	0.243127
$980$	−4.14054	−0.132265
$981$	−21.6438	−0.691033
$982$	−24.7557	−0.789986
$983$	22.0115	0.702059	0.351029	−	0.936364i	$-0.385832\pi$
$983$	22.0115	0.702059	0.351029	+	0.936364i	$0.385832\pi$
$984$	−0.255060	−0.00813103
$985$	12.1495	0.387114
$986$	−11.2331	−0.357735
$987$	−18.4707	−0.587929
$988$	−28.4167	−0.904055
$989$	−3.66215	−0.116450
$990$	12.8566	0.408610
$991$	45.3083	1.43926	0.719632	−	0.694356i	$-0.244310\pi$
$991$	45.3083	1.43926	0.719632	+	0.694356i	$0.244310\pi$
$992$	64.8028	2.05749
$993$	−22.3357	−0.708802
$994$	−25.3337	−0.803536
$995$	−33.9755	−1.07709
$996$	2.37009	0.0750991
$997$	0.525692	0.0166488	0.00832441	−	0.999965i	$-0.497350\pi$
$997$	0.525692	0.0166488	0.00832441	+	0.999965i	$0.497350\pi$
$998$	37.9938	1.20267
$999$	−52.4343	−1.65895

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.10	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.10	✓	66	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)

\(f(q)\)	\(=\)	\(q-1.99436 q^{2} -0.822682 q^{3} +1.97746 q^{4} -2.77484 q^{5} +1.64072 q^{6} +2.78471 q^{7} +0.0449503 q^{8} -2.32319 q^{9} +O(q^{10})\)	\(q-1.99436 q^{2} -0.822682 q^{3} +1.97746 q^{4} -2.77484 q^{5} +1.64072 q^{6} +2.78471 q^{7} +0.0449503 q^{8} -2.32319 q^{9} +5.53402 q^{10} -1.00000 q^{11} -1.62682 q^{12} -1.85048 q^{13} -5.55370 q^{14} +2.28281 q^{15} -4.04457 q^{16} +1.00000 q^{17} +4.63328 q^{18} +7.76569 q^{19} -5.48714 q^{20} -2.29093 q^{21} +1.99436 q^{22} +3.66215 q^{23} -0.0369799 q^{24} +2.69974 q^{25} +3.69053 q^{26} +4.37930 q^{27} +5.50665 q^{28} +5.63244 q^{29} -4.55274 q^{30} +8.12430 q^{31} +7.97642 q^{32} +0.822682 q^{33} -1.99436 q^{34} -7.72711 q^{35} -4.59403 q^{36} -11.9732 q^{37} -15.4876 q^{38} +1.52236 q^{39} -0.124730 q^{40} +6.89728 q^{41} +4.56893 q^{42} -1.00000 q^{43} -1.97746 q^{44} +6.44649 q^{45} -7.30363 q^{46} +8.06254 q^{47} +3.32740 q^{48} +0.754590 q^{49} -5.38424 q^{50} -0.822682 q^{51} -3.65926 q^{52} -0.364574 q^{53} -8.73388 q^{54} +2.77484 q^{55} +0.125174 q^{56} -6.38870 q^{57} -11.2331 q^{58} +10.8457 q^{59} +4.51417 q^{60} -1.10202 q^{61} -16.2028 q^{62} -6.46941 q^{63} -7.81869 q^{64} +5.13480 q^{65} -1.64072 q^{66} -12.2315 q^{67} +1.97746 q^{68} -3.01279 q^{69} +15.4106 q^{70} +4.56159 q^{71} -0.104428 q^{72} +1.34391 q^{73} +23.8789 q^{74} -2.22103 q^{75} +15.3564 q^{76} -2.78471 q^{77} -3.03613 q^{78} -10.0769 q^{79} +11.2230 q^{80} +3.36681 q^{81} -13.7556 q^{82} -1.45688 q^{83} -4.53022 q^{84} -2.77484 q^{85} +1.99436 q^{86} -4.63371 q^{87} -0.0449503 q^{88} -7.60720 q^{89} -12.8566 q^{90} -5.15306 q^{91} +7.24176 q^{92} -6.68372 q^{93} -16.0796 q^{94} -21.5486 q^{95} -6.56206 q^{96} +8.66058 q^{97} -1.50492 q^{98} +2.32319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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