LMFDB - Embedded newform 8041.2.a.h.1.8

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:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-2.56683 q^{2} -0.396689 q^{3} +4.58863 q^{4} +1.36693 q^{5} +1.01823 q^{6} +2.28939 q^{7} -6.64457 q^{8} -2.84264 q^{9} +O(q^{10})$	\(q-2.56683 q^{2} -0.396689 q^{3} +4.58863 q^{4} +1.36693 q^{5} +1.01823 q^{6} +2.28939 q^{7} -6.64457 q^{8} -2.84264 q^{9} -3.50868 q^{10} -1.00000 q^{11} -1.82026 q^{12} +3.43528 q^{13} -5.87649 q^{14} -0.542245 q^{15} +7.87823 q^{16} -1.00000 q^{17} +7.29657 q^{18} +7.13352 q^{19} +6.27232 q^{20} -0.908177 q^{21} +2.56683 q^{22} +1.74740 q^{23} +2.63582 q^{24} -3.13151 q^{25} -8.81779 q^{26} +2.31771 q^{27} +10.5052 q^{28} +4.01171 q^{29} +1.39185 q^{30} -3.88923 q^{31} -6.93296 q^{32} +0.396689 q^{33} +2.56683 q^{34} +3.12944 q^{35} -13.0438 q^{36} -5.86698 q^{37} -18.3106 q^{38} -1.36274 q^{39} -9.08265 q^{40} -11.0647 q^{41} +2.33114 q^{42} -1.00000 q^{43} -4.58863 q^{44} -3.88568 q^{45} -4.48529 q^{46} -6.49267 q^{47} -3.12521 q^{48} -1.75868 q^{49} +8.03805 q^{50} +0.396689 q^{51} +15.7632 q^{52} -12.1339 q^{53} -5.94917 q^{54} -1.36693 q^{55} -15.2120 q^{56} -2.82979 q^{57} -10.2974 q^{58} +3.66160 q^{59} -2.48816 q^{60} +0.881663 q^{61} +9.98300 q^{62} -6.50792 q^{63} +2.03929 q^{64} +4.69578 q^{65} -1.01823 q^{66} +12.9552 q^{67} -4.58863 q^{68} -0.693176 q^{69} -8.03274 q^{70} +12.8152 q^{71} +18.8881 q^{72} +5.58943 q^{73} +15.0595 q^{74} +1.24223 q^{75} +32.7331 q^{76} -2.28939 q^{77} +3.49792 q^{78} -7.71165 q^{79} +10.7690 q^{80} +7.60851 q^{81} +28.4013 q^{82} -15.5308 q^{83} -4.16728 q^{84} -1.36693 q^{85} +2.56683 q^{86} -1.59140 q^{87} +6.64457 q^{88} +3.99113 q^{89} +9.97390 q^{90} +7.86471 q^{91} +8.01819 q^{92} +1.54281 q^{93} +16.6656 q^{94} +9.75102 q^{95} +2.75023 q^{96} -9.65669 q^{97} +4.51423 q^{98} +2.84264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.56683	−1.81502	−0.907512	−	0.420026i	$-0.862021\pi$
$2$	−2.56683	−1.81502	−0.907512	+	0.420026i	$0.862021\pi$
$3$	−0.396689	−0.229028	−0.114514	−	0.993422i	$-0.536531\pi$
$3$	−0.396689	−0.229028	−0.114514	+	0.993422i	$0.536531\pi$
$4$	4.58863	2.29431
$5$	1.36693	0.611309	0.305655	−	0.952142i	$-0.401125\pi$
$5$	1.36693	0.611309	0.305655	+	0.952142i	$0.401125\pi$
$6$	1.01823	0.415692
$7$	2.28939	0.865309	0.432655	−	0.901560i	$-0.357577\pi$
$7$	2.28939	0.865309	0.432655	+	0.901560i	$0.357577\pi$
$8$	−6.64457	−2.34921
$9$	−2.84264	−0.947546
$10$	−3.50868	−1.10954
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.82026	−0.525463
$13$	3.43528	0.952775	0.476388	−	0.879235i	$-0.341946\pi$
$13$	3.43528	0.952775	0.476388	+	0.879235i	$0.341946\pi$
$14$	−5.87649	−1.57056
$15$	−0.542245	−0.140007
$16$	7.87823	1.96956
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	7.29657	1.71982
$19$	7.13352	1.63654	0.818271	−	0.574832i	$-0.194933\pi$
$19$	7.13352	1.63654	0.818271	+	0.574832i	$0.194933\pi$
$20$	6.27232	1.40253
$21$	−0.908177	−0.198180
$22$	2.56683	0.547250
$23$	1.74740	0.364359	0.182180	−	0.983265i	$-0.441685\pi$
$23$	1.74740	0.364359	0.182180	+	0.983265i	$0.441685\pi$
$24$	2.63582	0.538035
$25$	−3.13151	−0.626301
$26$	−8.81779	−1.72931
$27$	2.31771	0.446043
$28$	10.5052	1.98529
$29$	4.01171	0.744955	0.372478	−	0.928041i	$-0.378508\pi$
$29$	4.01171	0.744955	0.372478	+	0.928041i	$0.378508\pi$
$30$	1.39185	0.254116
$31$	−3.88923	−0.698526	−0.349263	−	0.937025i	$-0.613568\pi$
$31$	−3.88923	−0.698526	−0.349263	+	0.937025i	$0.613568\pi$
$32$	−6.93296	−1.22559
$33$	0.396689	0.0690546
$34$	2.56683	0.440208
$35$	3.12944	0.528972
$36$	−13.0438	−2.17397
$37$	−5.86698	−0.964525	−0.482263	−	0.876027i	$-0.660185\pi$
$37$	−5.86698	−0.964525	−0.482263	+	0.876027i	$0.660185\pi$
$38$	−18.3106	−2.97036
$39$	−1.36274	−0.218213
$40$	−9.08265	−1.43609
$41$	−11.0647	−1.72802	−0.864010	−	0.503475i	$-0.832055\pi$
$41$	−11.0647	−1.72802	−0.864010	+	0.503475i	$0.832055\pi$
$42$	2.33114	0.359702
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−4.58863	−0.691761
$45$	−3.88568	−0.579244
$46$	−4.48529	−0.661320
$47$	−6.49267	−0.947054	−0.473527	−	0.880779i	$-0.657019\pi$
$47$	−6.49267	−0.947054	−0.473527	+	0.880779i	$0.657019\pi$
$48$	−3.12521	−0.451085
$49$	−1.75868	−0.251240
$50$	8.03805	1.13675
$51$	0.396689	0.0555475
$52$	15.7632	2.18596
$53$	−12.1339	−1.66672	−0.833359	−	0.552732i	$-0.813585\pi$
$53$	−12.1339	−1.66672	−0.833359	+	0.552732i	$0.813585\pi$
$54$	−5.94917	−0.809579
$55$	−1.36693	−0.184317
$56$	−15.2120	−2.03279
$57$	−2.82979	−0.374815
$58$	−10.2974	−1.35211
$59$	3.66160	0.476699	0.238350	−	0.971179i	$-0.423394\pi$
$59$	3.66160	0.476699	0.238350	+	0.971179i	$0.423394\pi$
$60$	−2.48816	−0.321220
$61$	0.881663	0.112885	0.0564427	−	0.998406i	$-0.482024\pi$
$61$	0.881663	0.112885	0.0564427	+	0.998406i	$0.482024\pi$
$62$	9.98300	1.26784
$63$	−6.50792	−0.819920
$64$	2.03929	0.254911
$65$	4.69578	0.582440
$66$	−1.01823	−0.125336
$67$	12.9552	1.58273	0.791364	−	0.611346i	$-0.209372\pi$
$67$	12.9552	1.58273	0.791364	+	0.611346i	$0.209372\pi$
$68$	−4.58863	−0.556453
$69$	−0.693176	−0.0834486
$70$	−8.03274	−0.960096
$71$	12.8152	1.52089	0.760444	−	0.649404i	$-0.224982\pi$
$71$	12.8152	1.52089	0.760444	+	0.649404i	$0.224982\pi$
$72$	18.8881	2.22598
$73$	5.58943	0.654193	0.327096	−	0.944991i	$-0.393930\pi$
$73$	5.58943	0.654193	0.327096	+	0.944991i	$0.393930\pi$
$74$	15.0595	1.75064
$75$	1.24223	0.143441
$76$	32.7331	3.75474
$77$	−2.28939	−0.260901
$78$	3.49792	0.396061
$79$	−7.71165	−0.867629	−0.433814	−	0.901002i	$-0.642833\pi$
$79$	−7.71165	−0.867629	−0.433814	+	0.901002i	$0.642833\pi$
$80$	10.7690	1.20401
$81$	7.60851	0.845389
$82$	28.4013	3.13640
$83$	−15.5308	−1.70472	−0.852361	−	0.522953i	$-0.824830\pi$
$83$	−15.5308	−1.70472	−0.852361	+	0.522953i	$0.824830\pi$
$84$	−4.16728	−0.454688
$85$	−1.36693	−0.148264
$86$	2.56683	0.276789
$87$	−1.59140	−0.170616
$88$	6.64457	0.708313
$89$	3.99113	0.423058	0.211529	−	0.977372i	$-0.432156\pi$
$89$	3.99113	0.423058	0.211529	+	0.977372i	$0.432156\pi$
$90$	9.97390	1.05134
$91$	7.86471	0.824445
$92$	8.01819	0.835954
$93$	1.54281	0.159982
$94$	16.6656	1.71893
$95$	9.75102	1.00043
$96$	2.75023	0.280694
$97$	−9.65669	−0.980489	−0.490244	−	0.871585i	$-0.663092\pi$
$97$	−9.65669	−0.980489	−0.490244	+	0.871585i	$0.663092\pi$
$98$	4.51423	0.456006
$99$	2.84264	0.285696
$100$	−14.3693	−1.43693
$101$	−15.6696	−1.55918	−0.779592	−	0.626288i	$-0.784573\pi$
$101$	−15.6696	−1.55918	−0.779592	+	0.626288i	$0.784573\pi$
$102$	−1.01823	−0.100820
$103$	−1.05668	−0.104118	−0.0520590	−	0.998644i	$-0.516578\pi$
$103$	−1.05668	−0.104118	−0.0520590	+	0.998644i	$0.516578\pi$
$104$	−22.8259	−2.23827
$105$	−1.24141	−0.121149
$106$	31.1457	3.02513
$107$	8.29716	0.802117	0.401059	−	0.916052i	$-0.368642\pi$
$107$	8.29716	0.802117	0.401059	+	0.916052i	$0.368642\pi$
$108$	10.6351	1.02336
$109$	−18.0907	−1.73278	−0.866389	−	0.499370i	$-0.833565\pi$
$109$	−18.0907	−1.73278	−0.866389	+	0.499370i	$0.833565\pi$
$110$	3.50868	0.334539
$111$	2.32736	0.220904
$112$	18.0364	1.70428
$113$	−7.97870	−0.750573	−0.375286	−	0.926909i	$-0.622456\pi$
$113$	−7.97870	−0.750573	−0.375286	+	0.926909i	$0.622456\pi$
$114$	7.26359	0.680298
$115$	2.38858	0.222736
$116$	18.4082	1.70916
$117$	−9.76526	−0.902798
$118$	−9.39870	−0.865221
$119$	−2.28939	−0.209868
$120$	3.60298	0.328906
$121$	1.00000	0.0909091
$122$	−2.26308	−0.204890
$123$	4.38925	0.395766
$124$	−17.8462	−1.60264
$125$	−11.1152	−0.994173
$126$	16.7047	1.48818
$127$	−15.3706	−1.36392	−0.681958	−	0.731391i	$-0.738872\pi$
$127$	−15.3706	−1.36392	−0.681958	+	0.731391i	$0.738872\pi$
$128$	8.63142	0.762917
$129$	0.396689	0.0349265
$130$	−12.0533	−1.05714
$131$	2.80522	0.245093	0.122547	−	0.992463i	$-0.460894\pi$
$131$	2.80522	0.245093	0.122547	+	0.992463i	$0.460894\pi$
$132$	1.82026	0.158433
$133$	16.3314	1.41612
$134$	−33.2538	−2.87269
$135$	3.16814	0.272670
$136$	6.64457	0.569767
$137$	−19.0822	−1.63030	−0.815151	−	0.579249i	$-0.803346\pi$
$137$	−19.0822	−1.63030	−0.815151	+	0.579249i	$0.803346\pi$
$138$	1.77927	0.151461
$139$	16.8868	1.43232	0.716159	−	0.697937i	$-0.245898\pi$
$139$	16.8868	1.43232	0.716159	+	0.697937i	$0.245898\pi$
$140$	14.3598	1.21363
$141$	2.57557	0.216902
$142$	−32.8945	−2.76045
$143$	−3.43528	−0.287273
$144$	−22.3950	−1.86625
$145$	5.48372	0.455398
$146$	−14.3471	−1.18738
$147$	0.697648	0.0575410
$148$	−26.9214	−2.21292
$149$	−19.4200	−1.59095	−0.795476	−	0.605985i	$-0.792779\pi$
$149$	−19.4200	−1.59095	−0.795476	+	0.605985i	$0.792779\pi$
$150$	−3.18860	−0.260348
$151$	−0.718907	−0.0585039	−0.0292519	−	0.999572i	$-0.509313\pi$
$151$	−0.718907	−0.0585039	−0.0292519	+	0.999572i	$0.509313\pi$
$152$	−47.3992	−3.84458
$153$	2.84264	0.229814
$154$	5.87649	0.473541
$155$	−5.31630	−0.427015
$156$	−6.25309	−0.500648
$157$	23.6063	1.88399	0.941995	−	0.335627i	$-0.108948\pi$
$157$	23.6063	1.88399	0.941995	+	0.335627i	$0.108948\pi$
$158$	19.7945	1.57477
$159$	4.81338	0.381726
$160$	−9.47687	−0.749212
$161$	4.00050	0.315283
$162$	−19.5298	−1.53440
$163$	13.1963	1.03362	0.516808	−	0.856102i	$-0.327120\pi$
$163$	13.1963	1.03362	0.516808	+	0.856102i	$0.327120\pi$
$164$	−50.7719	−3.96462
$165$	0.542245	0.0422137
$166$	39.8649	3.09411
$167$	−13.1804	−1.01993	−0.509964	−	0.860196i	$-0.670341\pi$
$167$	−13.1804	−1.01993	−0.509964	+	0.860196i	$0.670341\pi$
$168$	6.03444	0.465567
$169$	−1.19885	−0.0922195
$170$	3.50868	0.269103
$171$	−20.2780	−1.55070
$172$	−4.58863	−0.349879
$173$	−8.84334	−0.672346	−0.336173	−	0.941800i	$-0.609133\pi$
$173$	−8.84334	−0.672346	−0.336173	+	0.941800i	$0.609133\pi$
$174$	4.08485	0.309672
$175$	−7.16925	−0.541944
$176$	−7.87823	−0.593844
$177$	−1.45251	−0.109178
$178$	−10.2445	−0.767861
$179$	−16.8876	−1.26224	−0.631118	−	0.775686i	$-0.717404\pi$
$179$	−16.8876	−1.26224	−0.631118	+	0.775686i	$0.717404\pi$
$180$	−17.8299	−1.32897
$181$	0.970786	0.0721580	0.0360790	−	0.999349i	$-0.488513\pi$
$181$	0.970786	0.0721580	0.0360790	+	0.999349i	$0.488513\pi$
$182$	−20.1874	−1.49639
$183$	−0.349746	−0.0258539
$184$	−11.6107	−0.855955
$185$	−8.01974	−0.589623
$186$	−3.96014	−0.290372
$187$	1.00000	0.0731272
$188$	−29.7924	−2.17284
$189$	5.30615	0.385965
$190$	−25.0292	−1.81581
$191$	−3.48830	−0.252404	−0.126202	−	0.992005i	$-0.540279\pi$
$191$	−3.48830	−0.252404	−0.126202	+	0.992005i	$0.540279\pi$
$192$	−0.808962	−0.0583818
$193$	16.2702	1.17115	0.585577	−	0.810617i	$-0.300868\pi$
$193$	16.2702	1.17115	0.585577	+	0.810617i	$0.300868\pi$
$194$	24.7871	1.77961
$195$	−1.86276	−0.133395
$196$	−8.06991	−0.576422
$197$	13.8812	0.988992	0.494496	−	0.869180i	$-0.335353\pi$
$197$	13.8812	0.988992	0.494496	+	0.869180i	$0.335353\pi$
$198$	−7.29657	−0.518545
$199$	−4.35500	−0.308718	−0.154359	−	0.988015i	$-0.549331\pi$
$199$	−4.35500	−0.308718	−0.154359	+	0.988015i	$0.549331\pi$
$200$	20.8075	1.47131
$201$	−5.13917	−0.362489
$202$	40.2212	2.82996
$203$	9.18437	0.644617
$204$	1.82026	0.127443
$205$	−15.1247	−1.05635
$206$	2.71233	0.188977
$207$	−4.96724	−0.345247
$208$	27.0639	1.87655
$209$	−7.13352	−0.493436
$210$	3.18650	0.219889
$211$	−15.4930	−1.06658	−0.533290	−	0.845932i	$-0.679045\pi$
$211$	−15.4930	−1.06658	−0.533290	+	0.845932i	$0.679045\pi$
$212$	−55.6779	−3.82397
$213$	−5.08365	−0.348326
$214$	−21.2974	−1.45586
$215$	−1.36693	−0.0932238
$216$	−15.4002	−1.04785
$217$	−8.90397	−0.604441
$218$	46.4359	3.14503
$219$	−2.21726	−0.149829
$220$	−6.27232	−0.422880
$221$	−3.43528	−0.231082
$222$	−5.97395	−0.400946
$223$	14.1150	0.945210	0.472605	−	0.881274i	$-0.343314\pi$
$223$	14.1150	0.945210	0.472605	+	0.881274i	$0.343314\pi$
$224$	−15.8723	−1.06051
$225$	8.90174	0.593449
$226$	20.4800	1.36231
$227$	−13.1131	−0.870349	−0.435174	−	0.900346i	$-0.643313\pi$
$227$	−13.1131	−0.870349	−0.435174	+	0.900346i	$0.643313\pi$
$228$	−12.9848	−0.859942
$229$	−22.3936	−1.47981	−0.739906	−	0.672710i	$-0.765130\pi$
$229$	−22.3936	−1.47981	−0.739906	+	0.672710i	$0.765130\pi$
$230$	−6.13108	−0.404271
$231$	0.908177	0.0597536
$232$	−26.6560	−1.75006
$233$	22.7776	1.49221	0.746105	−	0.665828i	$-0.231921\pi$
$233$	22.7776	1.49221	0.746105	+	0.665828i	$0.231921\pi$
$234$	25.0658	1.63860
$235$	−8.87502	−0.578943
$236$	16.8017	1.09370
$237$	3.05913	0.198712
$238$	5.87649	0.380916
$239$	2.61874	0.169392	0.0846962	−	0.996407i	$-0.473008\pi$
$239$	2.61874	0.169392	0.0846962	+	0.996407i	$0.473008\pi$
$240$	−4.27193	−0.275752
$241$	19.8424	1.27816	0.639082	−	0.769139i	$-0.279315\pi$
$241$	19.8424	1.27816	0.639082	+	0.769139i	$0.279315\pi$
$242$	−2.56683	−0.165002
$243$	−9.97133	−0.639661
$244$	4.04562	0.258994
$245$	−2.40399	−0.153585
$246$	−11.2665	−0.718324
$247$	24.5056	1.55926
$248$	25.8422	1.64098
$249$	6.16088	0.390430
$250$	28.5308	1.80445
$251$	27.8090	1.75529	0.877644	−	0.479312i	$-0.159114\pi$
$251$	27.8090	1.75529	0.877644	+	0.479312i	$0.159114\pi$
$252$	−29.8624	−1.88115
$253$	−1.74740	−0.109858
$254$	39.4536	2.47554
$255$	0.542245	0.0339567
$256$	−26.2340	−1.63962
$257$	17.4490	1.08844	0.544220	−	0.838943i	$-0.316826\pi$
$257$	17.4490	1.08844	0.544220	+	0.838943i	$0.316826\pi$
$258$	−1.01823	−0.0633924
$259$	−13.4318	−0.834613
$260$	21.5472	1.33630
$261$	−11.4038	−0.705879
$262$	−7.20053	−0.444850
$263$	−11.6025	−0.715438	−0.357719	−	0.933829i	$-0.616445\pi$
$263$	−11.6025	−0.715438	−0.357719	+	0.933829i	$0.616445\pi$
$264$	−2.63582	−0.162224
$265$	−16.5862	−1.01888
$266$	−41.9201	−2.57028
$267$	−1.58323	−0.0968924
$268$	59.4465	3.63127
$269$	−18.2121	−1.11041	−0.555205	−	0.831713i	$-0.687360\pi$
$269$	−18.2121	−1.11041	−0.555205	+	0.831713i	$0.687360\pi$
$270$	−8.13209	−0.494903
$271$	13.8548	0.841620	0.420810	−	0.907149i	$-0.361746\pi$
$271$	13.8548	0.841620	0.420810	+	0.907149i	$0.361746\pi$
$272$	−7.87823	−0.477688
$273$	−3.11984	−0.188821
$274$	48.9808	2.95904
$275$	3.13151	0.188837
$276$	−3.18072	−0.191457
$277$	−17.9071	−1.07593	−0.537967	−	0.842966i	$-0.680807\pi$
$277$	−17.9071	−1.07593	−0.537967	+	0.842966i	$0.680807\pi$
$278$	−43.3456	−2.59969
$279$	11.0557	0.661886
$280$	−20.7938	−1.24266
$281$	12.7567	0.761002	0.380501	−	0.924780i	$-0.375752\pi$
$281$	12.7567	0.761002	0.380501	+	0.924780i	$0.375752\pi$
$282$	−6.61106	−0.393683
$283$	−0.877722	−0.0521752	−0.0260876	−	0.999660i	$-0.508305\pi$
$283$	−0.877722	−0.0521752	−0.0260876	+	0.999660i	$0.508305\pi$
$284$	58.8043	3.48939
$285$	−3.86812	−0.229128
$286$	8.81779	0.521407
$287$	−25.3315	−1.49527
$288$	19.7079	1.16130
$289$	1.00000	0.0588235
$290$	−14.0758	−0.826558
$291$	3.83070	0.224560
$292$	25.6478	1.50092
$293$	−19.5172	−1.14021	−0.570104	−	0.821573i	$-0.693097\pi$
$293$	−19.5172	−1.14021	−0.570104	+	0.821573i	$0.693097\pi$
$294$	−1.79074	−0.104438
$295$	5.00514	0.291411
$296$	38.9835	2.26587
$297$	−2.31771	−0.134487
$298$	49.8480	2.88762
$299$	6.00282	0.347152
$300$	5.70014	0.329098
$301$	−2.28939	−0.131958
$302$	1.84531	0.106186
$303$	6.21595	0.357097
$304$	56.1995	3.22326
$305$	1.20517	0.0690078
$306$	−7.29657	−0.417117
$307$	17.0209	0.971436	0.485718	−	0.874115i	$-0.338558\pi$
$307$	17.0209	0.971436	0.485718	+	0.874115i	$0.338558\pi$
$308$	−10.5052	−0.598588
$309$	0.419174	0.0238460
$310$	13.6460	0.775043
$311$	−20.2391	−1.14766	−0.573828	−	0.818976i	$-0.694542\pi$
$311$	−20.2391	−1.14766	−0.573828	+	0.818976i	$0.694542\pi$
$312$	9.05479	0.512627
$313$	−1.22624	−0.0693114	−0.0346557	−	0.999399i	$-0.511033\pi$
$313$	−1.22624	−0.0693114	−0.0346557	+	0.999399i	$0.511033\pi$
$314$	−60.5935	−3.41949
$315$	−8.89586	−0.501225
$316$	−35.3859	−1.99061
$317$	−2.26653	−0.127301	−0.0636505	−	0.997972i	$-0.520274\pi$
$317$	−2.26653	−0.127301	−0.0636505	+	0.997972i	$0.520274\pi$
$318$	−12.3551	−0.692841
$319$	−4.01171	−0.224612
$320$	2.78756	0.155829
$321$	−3.29139	−0.183708
$322$	−10.2686	−0.572247
$323$	−7.13352	−0.396920
$324$	34.9126	1.93959
$325$	−10.7576	−0.596724
$326$	−33.8727	−1.87604
$327$	7.17639	0.396855
$328$	73.5203	4.05948
$329$	−14.8643	−0.819494
$330$	−1.39185	−0.0766190
$331$	−12.9631	−0.712517	−0.356259	−	0.934387i	$-0.615948\pi$
$331$	−12.9631	−0.712517	−0.356259	+	0.934387i	$0.615948\pi$
$332$	−71.2648	−3.91117
$333$	16.6777	0.913932
$334$	33.8318	1.85119
$335$	17.7088	0.967536
$336$	−7.15482	−0.390328
$337$	−21.2643	−1.15834	−0.579169	−	0.815208i	$-0.696623\pi$
$337$	−21.2643	−1.15834	−0.579169	+	0.815208i	$0.696623\pi$
$338$	3.07725	0.167381
$339$	3.16506	0.171902
$340$	−6.27232	−0.340165
$341$	3.88923	0.210614
$342$	52.0503	2.81456
$343$	−20.0521	−1.08271
$344$	6.64457	0.358251
$345$	−0.947522	−0.0510129
$346$	22.6994	1.22032
$347$	−21.6569	−1.16261	−0.581303	−	0.813687i	$-0.697457\pi$
$347$	−21.6569	−1.16261	−0.581303	+	0.813687i	$0.697457\pi$
$348$	−7.30233	−0.391446
$349$	−8.94342	−0.478730	−0.239365	−	0.970930i	$-0.576939\pi$
$349$	−8.94342	−0.478730	−0.239365	+	0.970930i	$0.576939\pi$
$350$	18.4023	0.983642
$351$	7.96198	0.424979
$352$	6.93296	0.369528
$353$	28.9580	1.54128	0.770639	−	0.637272i	$-0.219937\pi$
$353$	28.9580	1.54128	0.770639	+	0.637272i	$0.219937\pi$
$354$	3.72836	0.198160
$355$	17.5175	0.929732
$356$	18.3138	0.970628
$357$	0.908177	0.0480658
$358$	43.3476	2.29099
$359$	−23.9761	−1.26541	−0.632704	−	0.774394i	$-0.718055\pi$
$359$	−23.9761	−1.26541	−0.632704	+	0.774394i	$0.718055\pi$
$360$	25.8187	1.36076
$361$	31.8871	1.67827
$362$	−2.49185	−0.130968
$363$	−0.396689	−0.0208208
$364$	36.0882	1.89154
$365$	7.64035	0.399914
$366$	0.897738	0.0469255
$367$	−11.1622	−0.582663	−0.291332	−	0.956622i	$-0.594098\pi$
$367$	−11.1622	−0.582663	−0.291332	+	0.956622i	$0.594098\pi$
$368$	13.7665	0.717626
$369$	31.4530	1.63738
$370$	20.5853	1.07018
$371$	−27.7792	−1.44223
$372$	7.07939	0.367049
$373$	−3.11384	−0.161228	−0.0806142	−	0.996745i	$-0.525688\pi$
$373$	−3.11384	−0.161228	−0.0806142	+	0.996745i	$0.525688\pi$
$374$	−2.56683	−0.132728
$375$	4.40927	0.227694
$376$	43.1410	2.22483
$377$	13.7813	0.709775
$378$	−13.6200	−0.700536
$379$	26.7100	1.37200	0.686000	−	0.727601i	$-0.259365\pi$
$379$	26.7100	1.37200	0.686000	+	0.727601i	$0.259365\pi$
$380$	44.7438	2.29531
$381$	6.09733	0.312376
$382$	8.95387	0.458120
$383$	14.3074	0.731072	0.365536	−	0.930797i	$-0.380886\pi$
$383$	14.3074	0.731072	0.365536	+	0.930797i	$0.380886\pi$
$384$	−3.42399	−0.174730
$385$	−3.12944	−0.159491
$386$	−41.7629	−2.12567
$387$	2.84264	0.144499
$388$	−44.3109	−2.24955
$389$	19.3964	0.983437	0.491718	−	0.870754i	$-0.336369\pi$
$389$	19.3964	0.983437	0.491718	+	0.870754i	$0.336369\pi$
$390$	4.78140	0.242116
$391$	−1.74740	−0.0883701
$392$	11.6857	0.590215
$393$	−1.11280	−0.0561333
$394$	−35.6306	−1.79504
$395$	−10.5413	−0.530389
$396$	13.0438	0.655476
$397$	−21.0682	−1.05738	−0.528691	−	0.848814i	$-0.677317\pi$
$397$	−21.0682	−1.05738	−0.528691	+	0.848814i	$0.677317\pi$
$398$	11.1786	0.560331
$399$	−6.47850	−0.324331
$400$	−24.6707	−1.23354
$401$	−7.78562	−0.388795	−0.194398	−	0.980923i	$-0.562275\pi$
$401$	−7.78562	−0.388795	−0.194398	+	0.980923i	$0.562275\pi$
$402$	13.1914	0.657927
$403$	−13.3606	−0.665538
$404$	−71.9019	−3.57725
$405$	10.4003	0.516794
$406$	−23.5747	−1.16999
$407$	5.86698	0.290815
$408$	−2.63582	−0.130493
$409$	−11.5107	−0.569168	−0.284584	−	0.958651i	$-0.591855\pi$
$409$	−11.5107	−0.569168	−0.284584	+	0.958651i	$0.591855\pi$
$410$	38.8226	1.91731
$411$	7.56969	0.373385
$412$	−4.84872	−0.238879
$413$	8.38283	0.412492
$414$	12.7501	0.626632
$415$	−21.2294	−1.04211
$416$	−23.8167	−1.16771
$417$	−6.69880	−0.328042
$418$	18.3106	0.895598
$419$	35.5773	1.73806	0.869032	−	0.494756i	$-0.164743\pi$
$419$	35.5773	1.73806	0.869032	+	0.494756i	$0.164743\pi$
$420$	−5.69638	−0.277955
$421$	27.6450	1.34734	0.673669	−	0.739034i	$-0.264718\pi$
$421$	27.6450	1.34734	0.673669	+	0.739034i	$0.264718\pi$
$422$	39.7679	1.93587
$423$	18.4563	0.897377
$424$	80.6244	3.91547
$425$	3.13151	0.151900
$426$	13.0489	0.632221
$427$	2.01847	0.0976807
$428$	38.0726	1.84031
$429$	1.36274	0.0657935
$430$	3.50868	0.169203
$431$	26.5752	1.28008	0.640041	−	0.768341i	$-0.278917\pi$
$431$	26.5752	1.28008	0.640041	+	0.768341i	$0.278917\pi$
$432$	18.2594	0.878508
$433$	24.9710	1.20003	0.600015	−	0.799989i	$-0.295161\pi$
$433$	24.9710	1.20003	0.600015	+	0.799989i	$0.295161\pi$
$434$	22.8550	1.09708
$435$	−2.17533	−0.104299
$436$	−83.0116	−3.97553
$437$	12.4652	0.596289
$438$	5.69134	0.271943
$439$	−8.10063	−0.386622	−0.193311	−	0.981138i	$-0.561923\pi$
$439$	−8.10063	−0.386622	−0.193311	+	0.981138i	$0.561923\pi$
$440$	9.08265	0.432998
$441$	4.99929	0.238061
$442$	8.81779	0.419419
$443$	−15.8279	−0.752006	−0.376003	−	0.926618i	$-0.622702\pi$
$443$	−15.8279	−0.752006	−0.376003	+	0.926618i	$0.622702\pi$
$444$	10.6794	0.506822
$445$	5.45558	0.258620
$446$	−36.2308	−1.71558
$447$	7.70371	0.364373
$448$	4.66873	0.220577
$449$	38.9062	1.83610	0.918048	−	0.396470i	$-0.129765\pi$
$449$	38.9062	1.83610	0.918048	+	0.396470i	$0.129765\pi$
$450$	−22.8493	−1.07712
$451$	11.0647	0.521018
$452$	−36.6113	−1.72205
$453$	0.285182	0.0133990
$454$	33.6592	1.57970
$455$	10.7505	0.503991
$456$	18.8027	0.880518
$457$	−24.1022	−1.12745	−0.563727	−	0.825961i	$-0.690633\pi$
$457$	−24.1022	−1.12745	−0.563727	+	0.825961i	$0.690633\pi$
$458$	57.4807	2.68589
$459$	−2.31771	−0.108181
$460$	10.9603	0.511026
$461$	−32.8960	−1.53212	−0.766059	−	0.642770i	$-0.777785\pi$
$461$	−32.8960	−1.53212	−0.766059	+	0.642770i	$0.777785\pi$
$462$	−2.33114	−0.108454
$463$	−6.89626	−0.320496	−0.160248	−	0.987077i	$-0.551229\pi$
$463$	−6.89626	−0.320496	−0.160248	+	0.987077i	$0.551229\pi$
$464$	31.6052	1.46723
$465$	2.10892	0.0977986
$466$	−58.4663	−2.70840
$467$	15.4114	0.713155	0.356577	−	0.934266i	$-0.383944\pi$
$467$	15.4114	0.713155	0.356577	+	0.934266i	$0.383944\pi$
$468$	−44.8091	−2.07130
$469$	29.6595	1.36955
$470$	22.7807	1.05079
$471$	−9.36436	−0.431487
$472$	−24.3297	−1.11987
$473$	1.00000	0.0459800
$474$	−7.85226	−0.360666
$475$	−22.3387	−1.02497
$476$	−10.5052	−0.481504
$477$	34.4923	1.57929
$478$	−6.72187	−0.307451
$479$	1.14098	0.0521327	0.0260663	−	0.999660i	$-0.491702\pi$
$479$	1.14098	0.0521327	0.0260663	+	0.999660i	$0.491702\pi$
$480$	3.75937	0.171591
$481$	−20.1547	−0.918976
$482$	−50.9322	−2.31990
$483$	−1.58695	−0.0722088
$484$	4.58863	0.208574
$485$	−13.2000	−0.599382
$486$	25.5947	1.16100
$487$	18.8211	0.852867	0.426434	−	0.904519i	$-0.359770\pi$
$487$	18.8211	0.852867	0.426434	+	0.904519i	$0.359770\pi$
$488$	−5.85826	−0.265191
$489$	−5.23483	−0.236727
$490$	6.17063	0.278761
$491$	−29.0439	−1.31073	−0.655367	−	0.755311i	$-0.727486\pi$
$491$	−29.0439	−1.31073	−0.655367	+	0.755311i	$0.727486\pi$
$492$	20.1406	0.908010
$493$	−4.01171	−0.180678
$494$	−62.9019	−2.83009
$495$	3.88568	0.174649
$496$	−30.6402	−1.37579
$497$	29.3391	1.31604
$498$	−15.8139	−0.708640
$499$	−16.1008	−0.720772	−0.360386	−	0.932803i	$-0.617355\pi$
$499$	−16.1008	−0.720772	−0.360386	+	0.932803i	$0.617355\pi$
$500$	−51.0034	−2.28094
$501$	5.22851	0.233593
$502$	−71.3810	−3.18589
$503$	0.807172	0.0359900	0.0179950	−	0.999838i	$-0.494272\pi$
$503$	0.807172	0.0359900	0.0179950	+	0.999838i	$0.494272\pi$
$504$	43.2423	1.92616
$505$	−21.4192	−0.953143
$506$	4.48529	0.199396
$507$	0.475572	0.0211209
$508$	−70.5297	−3.12925
$509$	−21.3226	−0.945106	−0.472553	−	0.881302i	$-0.656668\pi$
$509$	−21.3226	−0.945106	−0.472553	+	0.881302i	$0.656668\pi$
$510$	−1.39185	−0.0616323
$511$	12.7964	0.566079
$512$	50.0754	2.21304
$513$	16.5334	0.729969
$514$	−44.7887	−1.97554
$515$	−1.44441	−0.0636483
$516$	1.82026	0.0801323
$517$	6.49267	0.285547
$518$	34.4772	1.51484
$519$	3.50805	0.153986
$520$	−31.2014	−1.36827
$521$	−23.8461	−1.04472	−0.522359	−	0.852725i	$-0.674948\pi$
$521$	−23.8461	−1.04472	−0.522359	+	0.852725i	$0.674948\pi$
$522$	29.2717	1.28119
$523$	17.6124	0.770138	0.385069	−	0.922888i	$-0.374178\pi$
$523$	17.6124	0.770138	0.385069	+	0.922888i	$0.374178\pi$
$524$	12.8721	0.562320
$525$	2.84396	0.124121
$526$	29.7816	1.29854
$527$	3.88923	0.169417
$528$	3.12521	0.136007
$529$	−19.9466	−0.867242
$530$	42.5739	1.84929
$531$	−10.4086	−0.451694
$532$	74.9389	3.24901
$533$	−38.0104	−1.64641
$534$	4.06390	0.175862
$535$	11.3416	0.490342
$536$	−86.0815	−3.71816
$537$	6.69911	0.289088
$538$	46.7474	2.01542
$539$	1.75868	0.0757516
$540$	14.5374	0.625591
$541$	23.3393	1.00344	0.501718	−	0.865031i	$-0.332702\pi$
$541$	23.3393	1.00344	0.501718	+	0.865031i	$0.332702\pi$
$542$	−35.5630	−1.52756
$543$	−0.385100	−0.0165262
$544$	6.93296	0.297248
$545$	−24.7287	−1.05926
$546$	8.00811	0.342715
$547$	−21.5656	−0.922077	−0.461039	−	0.887380i	$-0.652523\pi$
$547$	−21.5656	−0.922077	−0.461039	+	0.887380i	$0.652523\pi$
$548$	−87.5610	−3.74042
$549$	−2.50625	−0.106964
$550$	−8.03805	−0.342743
$551$	28.6176	1.21915
$552$	4.60585	0.196038
$553$	−17.6550	−0.750767
$554$	45.9645	1.95284
$555$	3.18134	0.135040
$556$	77.4872	3.28619
$557$	38.0157	1.61078	0.805388	−	0.592748i	$-0.201957\pi$
$557$	38.0157	1.61078	0.805388	+	0.592748i	$0.201957\pi$
$558$	−28.3780	−1.20134
$559$	−3.43528	−0.145297
$560$	24.6544	1.04184
$561$	−0.396689	−0.0167482
$562$	−32.7444	−1.38124
$563$	5.39845	0.227517	0.113759	−	0.993508i	$-0.463711\pi$
$563$	5.39845	0.227517	0.113759	+	0.993508i	$0.463711\pi$
$564$	11.8183	0.497641
$565$	−10.9063	−0.458832
$566$	2.25297	0.0946992
$567$	17.4189	0.731523
$568$	−85.1516	−3.57288
$569$	−5.12835	−0.214992	−0.107496	−	0.994206i	$-0.534283\pi$
$569$	−5.12835	−0.214992	−0.107496	+	0.994206i	$0.534283\pi$
$570$	9.92881	0.415872
$571$	1.21537	0.0508615	0.0254308	−	0.999677i	$-0.491904\pi$
$571$	1.21537	0.0508615	0.0254308	+	0.999677i	$0.491904\pi$
$572$	−15.7632	−0.659093
$573$	1.38377	0.0578077
$574$	65.0217	2.71395
$575$	−5.47201	−0.228198
$576$	−5.79696	−0.241540
$577$	21.9805	0.915060	0.457530	−	0.889194i	$-0.348734\pi$
$577$	21.9805	0.915060	0.457530	+	0.889194i	$0.348734\pi$
$578$	−2.56683	−0.106766
$579$	−6.45420	−0.268228
$580$	25.1627	1.04483
$581$	−35.5560	−1.47511
$582$	−9.83276	−0.407581
$583$	12.1339	0.502534
$584$	−37.1393	−1.53684
$585$	−13.3484	−0.551889
$586$	50.0974	2.06950
$587$	5.34725	0.220705	0.110352	−	0.993893i	$-0.464802\pi$
$587$	5.34725	0.220705	0.110352	+	0.993893i	$0.464802\pi$
$588$	3.20124	0.132017
$589$	−27.7439	−1.14317
$590$	−12.8474	−0.528917
$591$	−5.50650	−0.226507
$592$	−46.2214	−1.89969
$593$	38.7605	1.59170	0.795850	−	0.605493i	$-0.207024\pi$
$593$	38.7605	1.59170	0.795850	+	0.605493i	$0.207024\pi$
$594$	5.94917	0.244097
$595$	−3.12944	−0.128294
$596$	−89.1113	−3.65014
$597$	1.72758	0.0707052
$598$	−15.4082	−0.630090
$599$	32.2114	1.31612	0.658060	−	0.752965i	$-0.271377\pi$
$599$	32.2114	1.31612	0.658060	+	0.752965i	$0.271377\pi$
$600$	−8.25410	−0.336972
$601$	3.77744	0.154085	0.0770426	−	0.997028i	$-0.475452\pi$
$601$	3.77744	0.154085	0.0770426	+	0.997028i	$0.475452\pi$
$602$	5.87649	0.239508
$603$	−36.8269	−1.49971
$604$	−3.29880	−0.134226
$605$	1.36693	0.0555736
$606$	−15.9553	−0.648140
$607$	−20.2765	−0.822998	−0.411499	−	0.911410i	$-0.634995\pi$
$607$	−20.2765	−0.822998	−0.411499	+	0.911410i	$0.634995\pi$
$608$	−49.4564	−2.00572
$609$	−3.64334	−0.147635
$610$	−3.09347	−0.125251
$611$	−22.3041	−0.902329
$612$	13.0438	0.527264
$613$	−2.74123	−0.110717	−0.0553586	−	0.998467i	$-0.517630\pi$
$613$	−2.74123	−0.110717	−0.0553586	+	0.998467i	$0.517630\pi$
$614$	−43.6899	−1.76318
$615$	5.99980	0.241935
$616$	15.2120	0.612910
$617$	−41.7514	−1.68085	−0.840424	−	0.541929i	$-0.817694\pi$
$617$	−41.7514	−1.68085	−0.840424	+	0.541929i	$0.817694\pi$
$618$	−1.07595	−0.0432810
$619$	8.21477	0.330179	0.165090	−	0.986279i	$-0.447209\pi$
$619$	8.21477	0.330179	0.165090	+	0.986279i	$0.447209\pi$
$620$	−24.3945	−0.979707
$621$	4.04997	0.162520
$622$	51.9505	2.08302
$623$	9.13726	0.366076
$624$	−10.7360	−0.429782
$625$	0.463852	0.0185541
$626$	3.14756	0.125802
$627$	2.82979	0.113011
$628$	108.321	4.32246
$629$	5.86698	0.233932
$630$	22.8342	0.909735
$631$	−31.1797	−1.24124	−0.620622	−	0.784110i	$-0.713120\pi$
$631$	−31.1797	−1.24124	−0.620622	+	0.784110i	$0.713120\pi$
$632$	51.2406	2.03824
$633$	6.14589	0.244277
$634$	5.81780	0.231054
$635$	−21.0105	−0.833775
$636$	22.0868	0.875798
$637$	−6.04155	−0.239375
$638$	10.2974	0.407677
$639$	−36.4290	−1.44111
$640$	11.7985	0.466378
$641$	36.3633	1.43626	0.718132	−	0.695907i	$-0.244997\pi$
$641$	36.3633	1.43626	0.718132	+	0.695907i	$0.244997\pi$
$642$	8.44845	0.333434
$643$	11.6175	0.458148	0.229074	−	0.973409i	$-0.426430\pi$
$643$	11.6175	0.458148	0.229074	+	0.973409i	$0.426430\pi$
$644$	18.3568	0.723358
$645$	0.542245	0.0213509
$646$	18.3106	0.720419
$647$	−6.68042	−0.262634	−0.131317	−	0.991340i	$-0.541921\pi$
$647$	−6.68042	−0.262634	−0.131317	+	0.991340i	$0.541921\pi$
$648$	−50.5552	−1.98600
$649$	−3.66160	−0.143730
$650$	27.6129	1.08307
$651$	3.53211	0.138434
$652$	60.5529	2.37144
$653$	−31.8130	−1.24494	−0.622469	−	0.782645i	$-0.713870\pi$
$653$	−31.8130	−1.24494	−0.622469	+	0.782645i	$0.713870\pi$
$654$	−18.4206	−0.720302
$655$	3.83454	0.149828
$656$	−87.1705	−3.40344
$657$	−15.8887	−0.619878
$658$	38.1541	1.48740
$659$	5.15257	0.200716	0.100358	−	0.994951i	$-0.468001\pi$
$659$	5.15257	0.200716	0.100358	+	0.994951i	$0.468001\pi$
$660$	2.48816	0.0968515
$661$	−40.0736	−1.55868	−0.779342	−	0.626599i	$-0.784447\pi$
$661$	−40.0736	−1.55868	−0.779342	+	0.626599i	$0.784447\pi$
$662$	33.2741	1.29324
$663$	1.36274	0.0529243
$664$	103.195	4.00475
$665$	22.3239	0.865684
$666$	−42.8088	−1.65881
$667$	7.01007	0.271431
$668$	−60.4798	−2.34003
$669$	−5.59926	−0.216480
$670$	−45.4555	−1.75610
$671$	−0.881663	−0.0340362
$672$	6.29635	0.242887
$673$	22.7972	0.878767	0.439384	−	0.898299i	$-0.355197\pi$
$673$	22.7972	0.878767	0.439384	+	0.898299i	$0.355197\pi$
$674$	54.5818	2.10241
$675$	−7.25792	−0.279357
$676$	−5.50109	−0.211580
$677$	8.65040	0.332462	0.166231	−	0.986087i	$-0.446840\pi$
$677$	8.65040	0.332462	0.166231	+	0.986087i	$0.446840\pi$
$678$	−8.12417	−0.312007
$679$	−22.1080	−0.848426
$680$	9.08265	0.348304
$681$	5.20183	0.199335
$682$	−9.98300	−0.382269
$683$	−33.3807	−1.27728	−0.638639	−	0.769506i	$-0.720502\pi$
$683$	−33.3807	−1.27728	−0.638639	+	0.769506i	$0.720502\pi$
$684$	−93.0482	−3.55779
$685$	−26.0840	−0.996618
$686$	51.4703	1.96514
$687$	8.88330	0.338919
$688$	−7.87823	−0.300355
$689$	−41.6833	−1.58801
$690$	2.43213	0.0925896
$691$	40.0861	1.52495	0.762474	−	0.647019i	$-0.223984\pi$
$691$	40.0861	1.52495	0.762474	+	0.647019i	$0.223984\pi$
$692$	−40.5788	−1.54257
$693$	6.50792	0.247215
$694$	55.5897	2.11016
$695$	23.0830	0.875590
$696$	10.5742	0.400812
$697$	11.0647	0.419106
$698$	22.9562	0.868907
$699$	−9.03562	−0.341759
$700$	−32.8970	−1.24339
$701$	−20.0289	−0.756483	−0.378241	−	0.925707i	$-0.623471\pi$
$701$	−20.0289	−0.756483	−0.378241	+	0.925707i	$0.623471\pi$
$702$	−20.4371	−0.771347
$703$	−41.8522	−1.57849
$704$	−2.03929	−0.0768585
$705$	3.52062	0.132594
$706$	−74.3303	−2.79746
$707$	−35.8739	−1.34918
$708$	−6.66504	−0.250488
$709$	−5.93863	−0.223030	−0.111515	−	0.993763i	$-0.535570\pi$
$709$	−5.93863	−0.223030	−0.111515	+	0.993763i	$0.535570\pi$
$710$	−44.9645	−1.68749
$711$	21.9214	0.822118
$712$	−26.5193	−0.993853
$713$	−6.79606	−0.254514
$714$	−2.33114	−0.0872406
$715$	−4.69578	−0.175612
$716$	−77.4908	−2.89597
$717$	−1.03883	−0.0387957
$718$	61.5425	2.29675
$719$	6.94752	0.259099	0.129549	−	0.991573i	$-0.458647\pi$
$719$	6.94752	0.259099	0.129549	+	0.991573i	$0.458647\pi$
$720$	−30.6123	−1.14085
$721$	−2.41916	−0.0900943
$722$	−81.8489	−3.04610
$723$	−7.87127	−0.292736
$724$	4.45457	0.165553
$725$	−12.5627	−0.466566
$726$	1.01823	0.0377902
$727$	4.67539	0.173400	0.0867002	−	0.996234i	$-0.472368\pi$
$727$	4.67539	0.173400	0.0867002	+	0.996234i	$0.472368\pi$
$728$	−52.2576	−1.93679
$729$	−18.8700	−0.698889
$730$	−19.6115	−0.725854
$731$	1.00000	0.0369863
$732$	−1.60485	−0.0593170
$733$	−18.0195	−0.665567	−0.332783	−	0.943003i	$-0.607988\pi$
$733$	−18.0195	−0.665567	−0.332783	+	0.943003i	$0.607988\pi$
$734$	28.6515	1.05755
$735$	0.953635	0.0351754
$736$	−12.1147	−0.446553
$737$	−12.9552	−0.477210
$738$	−80.7346	−2.97188
$739$	10.0029	0.367963	0.183982	−	0.982930i	$-0.441101\pi$
$739$	10.0029	0.367963	0.183982	+	0.982930i	$0.441101\pi$
$740$	−36.7996	−1.35278
$741$	−9.72111	−0.357114
$742$	71.3046	2.61768
$743$	−25.5199	−0.936234	−0.468117	−	0.883667i	$-0.655067\pi$
$743$	−25.5199	−0.936234	−0.468117	+	0.883667i	$0.655067\pi$
$744$	−10.2513	−0.375832
$745$	−26.5458	−0.972563
$746$	7.99270	0.292633
$747$	44.1483	1.61530
$748$	4.58863	0.167777
$749$	18.9955	0.694079
$750$	−11.3179	−0.413270
$751$	−25.0123	−0.912713	−0.456357	−	0.889797i	$-0.650846\pi$
$751$	−25.0123	−0.912713	−0.456357	+	0.889797i	$0.650846\pi$
$752$	−51.1508	−1.86528
$753$	−11.0315	−0.402011
$754$	−35.3744	−1.28826
$755$	−0.982695	−0.0357639
$756$	24.3479	0.885525
$757$	28.3454	1.03023	0.515115	−	0.857121i	$-0.327749\pi$
$757$	28.3454	1.03023	0.515115	+	0.857121i	$0.327749\pi$
$758$	−68.5601	−2.49021
$759$	0.693176	0.0251607
$760$	−64.7913	−2.35023
$761$	−2.77812	−0.100707	−0.0503534	−	0.998731i	$-0.516035\pi$
$761$	−2.77812	−0.100707	−0.0503534	+	0.998731i	$0.516035\pi$
$762$	−15.6508	−0.566969
$763$	−41.4168	−1.49939
$764$	−16.0065	−0.579094
$765$	3.88568	0.140487
$766$	−36.7246	−1.32691
$767$	12.5786	0.454187
$768$	10.4067	0.375520
$769$	−37.4140	−1.34918	−0.674592	−	0.738191i	$-0.735680\pi$
$769$	−37.4140	−1.34918	−0.674592	+	0.738191i	$0.735680\pi$
$770$	8.03274	0.289480
$771$	−6.92183	−0.249284
$772$	74.6578	2.68699
$773$	−47.9153	−1.72339	−0.861697	−	0.507423i	$-0.830598\pi$
$773$	−47.9153	−1.72339	−0.861697	+	0.507423i	$0.830598\pi$
$774$	−7.29657	−0.262270
$775$	12.1791	0.437488
$776$	64.1645	2.30337
$777$	5.32825	0.191150
$778$	−49.7873	−1.78496
$779$	−78.9305	−2.82798
$780$	−8.54753	−0.306051
$781$	−12.8152	−0.458565
$782$	4.48529	0.160394
$783$	9.29797	0.332282
$784$	−13.8553	−0.494831
$785$	32.2682	1.15170
$786$	2.85637	0.101883
$787$	30.4320	1.08479	0.542393	−	0.840125i	$-0.317519\pi$
$787$	30.4320	1.08479	0.542393	+	0.840125i	$0.317519\pi$
$788$	63.6955	2.26906
$789$	4.60256	0.163856
$790$	27.0577	0.962669
$791$	−18.2664	−0.649478
$792$	−18.8881	−0.671159
$793$	3.02876	0.107554
$794$	54.0785	1.91917
$795$	6.57954	0.233352
$796$	−19.9835	−0.708296
$797$	−15.3009	−0.541985	−0.270992	−	0.962582i	$-0.587352\pi$
$797$	−15.3009	−0.541985	−0.270992	+	0.962582i	$0.587352\pi$
$798$	16.6292	0.588668
$799$	6.49267	0.229694
$800$	21.7106	0.767586
$801$	−11.3453	−0.400867
$802$	19.9844	0.705673
$803$	−5.58943	−0.197247
$804$	−23.5817	−0.831664
$805$	5.46839	0.192736
$806$	34.2944	1.20797
$807$	7.22453	0.254315
$808$	104.118	3.66285
$809$	4.49586	0.158066	0.0790330	−	0.996872i	$-0.474817\pi$
$809$	4.49586	0.158066	0.0790330	+	0.996872i	$0.474817\pi$
$810$	−26.6958	−0.937994
$811$	−4.95452	−0.173977	−0.0869883	−	0.996209i	$-0.527724\pi$
$811$	−4.95452	−0.173977	−0.0869883	+	0.996209i	$0.527724\pi$
$812$	42.1437	1.47895
$813$	−5.49605	−0.192755
$814$	−15.0595	−0.527837
$815$	18.0384	0.631858
$816$	3.12521	0.109404
$817$	−7.13352	−0.249570
$818$	29.5460	1.03305
$819$	−22.3565	−0.781200
$820$	−69.4016	−2.42361
$821$	10.0996	0.352479	0.176240	−	0.984347i	$-0.443607\pi$
$821$	10.0996	0.352479	0.176240	+	0.984347i	$0.443607\pi$
$822$	−19.4301	−0.677703
$823$	35.5363	1.23872	0.619358	−	0.785109i	$-0.287393\pi$
$823$	35.5363	1.23872	0.619358	+	0.785109i	$0.287393\pi$
$824$	7.02120	0.244595
$825$	−1.24223	−0.0432490
$826$	−21.5173	−0.748683
$827$	32.2265	1.12063	0.560313	−	0.828281i	$-0.310681\pi$
$827$	32.2265	1.12063	0.560313	+	0.828281i	$0.310681\pi$
$828$	−22.7928	−0.792104
$829$	−40.8378	−1.41836	−0.709178	−	0.705029i	$-0.750934\pi$
$829$	−40.8378	−1.41836	−0.709178	+	0.705029i	$0.750934\pi$
$830$	54.4924	1.89146
$831$	7.10354	0.246419
$832$	7.00552	0.242873
$833$	1.75868	0.0609346
$834$	17.1947	0.595403
$835$	−18.0166	−0.623492
$836$	−32.7331	−1.13210
$837$	−9.01410	−0.311573
$838$	−91.3209	−3.15463
$839$	−34.4923	−1.19081	−0.595404	−	0.803427i	$-0.703008\pi$
$839$	−34.4923	−1.19081	−0.595404	+	0.803427i	$0.703008\pi$
$840$	8.24865	0.284605
$841$	−12.9062	−0.445042
$842$	−70.9602	−2.44545
$843$	−5.06045	−0.174291
$844$	−71.0915	−2.44707
$845$	−1.63875	−0.0563746
$846$	−47.3743	−1.62876
$847$	2.28939	0.0786645
$848$	−95.5936	−3.28270
$849$	0.348183	0.0119496
$850$	−8.03805	−0.275703
$851$	−10.2520	−0.351434
$852$	−23.3270	−0.799169
$853$	26.2253	0.897937	0.448969	−	0.893547i	$-0.351791\pi$
$853$	26.2253	0.897937	0.448969	+	0.893547i	$0.351791\pi$
$854$	−5.18108	−0.177293
$855$	−27.7186	−0.947957
$856$	−55.1310	−1.88434
$857$	−17.2026	−0.587631	−0.293815	−	0.955862i	$-0.594925\pi$
$857$	−17.2026	−0.587631	−0.293815	+	0.955862i	$0.594925\pi$
$858$	−3.49792	−0.119417
$859$	17.9694	0.613110	0.306555	−	0.951853i	$-0.400824\pi$
$859$	17.9694	0.613110	0.306555	+	0.951853i	$0.400824\pi$
$860$	−6.27232	−0.213884
$861$	10.0487	0.342460
$862$	−68.2140	−2.32338
$863$	20.3707	0.693426	0.346713	−	0.937971i	$-0.387298\pi$
$863$	20.3707	0.693426	0.346713	+	0.937971i	$0.387298\pi$
$864$	−16.0686	−0.546664
$865$	−12.0882	−0.411012
$866$	−64.0963	−2.17808
$867$	−0.396689	−0.0134723
$868$	−40.8570	−1.38678
$869$	7.71165	0.261600
$870$	5.58370	0.189305
$871$	44.5047	1.50798
$872$	120.205	4.07066
$873$	27.4505	0.929058
$874$	−31.9959	−1.08228
$875$	−25.4470	−0.860267
$876$	−10.1742	−0.343754
$877$	25.3976	0.857616	0.428808	−	0.903396i	$-0.358934\pi$
$877$	25.3976	0.857616	0.428808	+	0.903396i	$0.358934\pi$
$878$	20.7930	0.701728
$879$	7.74225	0.261140
$880$	−10.7690	−0.363022
$881$	−17.3914	−0.585932	−0.292966	−	0.956123i	$-0.594642\pi$
$881$	−17.3914	−0.585932	−0.292966	+	0.956123i	$0.594642\pi$
$882$	−12.8323	−0.432087
$883$	−23.4499	−0.789151	−0.394576	−	0.918864i	$-0.629108\pi$
$883$	−23.4499	−0.789151	−0.394576	+	0.918864i	$0.629108\pi$
$884$	−15.7632	−0.530174
$885$	−1.98548	−0.0667413
$886$	40.6275	1.36491
$887$	−39.7708	−1.33537	−0.667686	−	0.744443i	$-0.732715\pi$
$887$	−39.7708	−1.33537	−0.667686	+	0.744443i	$0.732715\pi$
$888$	−15.4643	−0.518949
$889$	−35.1893	−1.18021
$890$	−14.0036	−0.469401
$891$	−7.60851	−0.254895
$892$	64.7684	2.16861
$893$	−46.3156	−1.54989
$894$	−19.7741	−0.661346
$895$	−23.0841	−0.771617
$896$	19.7607	0.660159
$897$	−2.38125	−0.0795077
$898$	−99.8656	−3.33256
$899$	−15.6024	−0.520371
$900$	40.8467	1.36156
$901$	12.1339	0.404238
$902$	−28.4013	−0.945660
$903$	0.908177	0.0302222
$904$	53.0150	1.76325
$905$	1.32700	0.0441108
$906$	−0.732015	−0.0243196
$907$	16.9334	0.562263	0.281132	−	0.959669i	$-0.409290\pi$
$907$	16.9334	0.562263	0.281132	+	0.959669i	$0.409290\pi$
$908$	−60.1712	−1.99685
$909$	44.5430	1.47740
$910$	−27.5947	−0.914756
$911$	−52.2258	−1.73032	−0.865158	−	0.501499i	$-0.832782\pi$
$911$	−52.2258	−1.73032	−0.865158	+	0.501499i	$0.832782\pi$
$912$	−22.2937	−0.738219
$913$	15.5308	0.513993
$914$	61.8664	2.04636
$915$	−0.478077	−0.0158048
$916$	−102.756	−3.39515
$917$	6.42225	0.212081
$918$	5.94917	0.196352
$919$	−32.3241	−1.06627	−0.533137	−	0.846029i	$-0.678987\pi$
$919$	−32.3241	−1.06627	−0.533137	+	0.846029i	$0.678987\pi$
$920$	−15.8711	−0.523253
$921$	−6.75202	−0.222486
$922$	84.4384	2.78083
$923$	44.0239	1.44906
$924$	4.16728	0.137094
$925$	18.3725	0.604083
$926$	17.7015	0.581709
$927$	3.00377	0.0986566
$928$	−27.8130	−0.913007
$929$	56.5927	1.85674	0.928372	−	0.371651i	$-0.121208\pi$
$929$	56.5927	1.85674	0.928372	+	0.371651i	$0.121208\pi$
$930$	−5.41323	−0.177507
$931$	−12.5456	−0.411164
$932$	104.518	3.42360
$933$	8.02864	0.262846
$934$	−39.5585	−1.29439
$935$	1.36693	0.0447034
$936$	64.8859	2.12086
$937$	58.8594	1.92285	0.961426	−	0.275064i	$-0.0886991\pi$
$937$	58.8594	1.92285	0.961426	+	0.275064i	$0.0886991\pi$
$938$	−76.1309	−2.48576
$939$	0.486437	0.0158743
$940$	−40.7242	−1.32828
$941$	−54.4274	−1.77428	−0.887141	−	0.461498i	$-0.847312\pi$
$941$	−54.4274	−1.77428	−0.887141	+	0.461498i	$0.847312\pi$
$942$	24.0367	0.783160
$943$	−19.3346	−0.629620
$944$	28.8469	0.938887
$945$	7.25313	0.235944
$946$	−2.56683	−0.0834549
$947$	40.1751	1.30551	0.652757	−	0.757567i	$-0.273612\pi$
$947$	40.1751	1.30551	0.652757	+	0.757567i	$0.273612\pi$
$948$	14.0372	0.455906
$949$	19.2012	0.623299
$950$	57.3396	1.86034
$951$	0.899107	0.0291555
$952$	15.2120	0.493025
$953$	27.4861	0.890362	0.445181	−	0.895441i	$-0.353139\pi$
$953$	27.4861	0.890362	0.445181	+	0.895441i	$0.353139\pi$
$954$	−88.5358	−2.86645
$955$	−4.76825	−0.154297
$956$	12.0164	0.388639
$957$	1.59140	0.0514426
$958$	−2.92870	−0.0946221
$959$	−43.6866	−1.41072
$960$	−1.10579	−0.0356893
$961$	−15.8739	−0.512061
$962$	51.7338	1.66796
$963$	−23.5858	−0.760043
$964$	91.0495	2.93251
$965$	22.2402	0.715938
$966$	4.07344	0.131061
$967$	10.0757	0.324014	0.162007	−	0.986790i	$-0.448203\pi$
$967$	10.0757	0.324014	0.162007	+	0.986790i	$0.448203\pi$
$968$	−6.64457	−0.213564
$969$	2.82979	0.0909059
$970$	33.8822	1.08789
$971$	−45.5004	−1.46018	−0.730088	−	0.683353i	$-0.760521\pi$
$971$	−45.5004	−1.46018	−0.730088	+	0.683353i	$0.760521\pi$
$972$	−45.7547	−1.46758
$973$	38.6605	1.23940
$974$	−48.3107	−1.54797
$975$	4.26742	0.136667
$976$	6.94594	0.222334
$977$	50.1739	1.60520	0.802602	−	0.596514i	$-0.203448\pi$
$977$	50.1739	1.60520	0.802602	+	0.596514i	$0.203448\pi$
$978$	13.4369	0.429665
$979$	−3.99113	−0.127557
$980$	−11.0310	−0.352372
$981$	51.4254	1.64189
$982$	74.5509	2.37901
$983$	−15.9413	−0.508449	−0.254225	−	0.967145i	$-0.581820\pi$
$983$	−15.9413	−0.508449	−0.254225	+	0.967145i	$0.581820\pi$
$984$	−29.1647	−0.929736
$985$	18.9746	0.604580
$986$	10.2974	0.327935
$987$	5.89649	0.187687
$988$	112.447	3.57742
$989$	−1.74740	−0.0555642
$990$	−9.97390	−0.316991
$991$	−36.5288	−1.16038	−0.580188	−	0.814483i	$-0.697021\pi$
$991$	−36.5288	−1.16038	−0.580188	+	0.814483i	$0.697021\pi$
$992$	26.9639	0.856104
$993$	5.14232	0.163187
$994$	−75.3085	−2.38864
$995$	−5.95298	−0.188722
$996$	28.2700	0.895768
$997$	−24.2386	−0.767645	−0.383823	−	0.923407i	$-0.625393\pi$
$997$	−24.2386	−0.767645	−0.383823	+	0.923407i	$0.625393\pi$
$998$	41.3281	1.30822
$999$	−13.5979	−0.430220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.8	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.8	✓	74	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)

\(f(q)\)	\(=\)	\(q-2.56683 q^{2} -0.396689 q^{3} +4.58863 q^{4} +1.36693 q^{5} +1.01823 q^{6} +2.28939 q^{7} -6.64457 q^{8} -2.84264 q^{9} +O(q^{10})\)	\(q-2.56683 q^{2} -0.396689 q^{3} +4.58863 q^{4} +1.36693 q^{5} +1.01823 q^{6} +2.28939 q^{7} -6.64457 q^{8} -2.84264 q^{9} -3.50868 q^{10} -1.00000 q^{11} -1.82026 q^{12} +3.43528 q^{13} -5.87649 q^{14} -0.542245 q^{15} +7.87823 q^{16} -1.00000 q^{17} +7.29657 q^{18} +7.13352 q^{19} +6.27232 q^{20} -0.908177 q^{21} +2.56683 q^{22} +1.74740 q^{23} +2.63582 q^{24} -3.13151 q^{25} -8.81779 q^{26} +2.31771 q^{27} +10.5052 q^{28} +4.01171 q^{29} +1.39185 q^{30} -3.88923 q^{31} -6.93296 q^{32} +0.396689 q^{33} +2.56683 q^{34} +3.12944 q^{35} -13.0438 q^{36} -5.86698 q^{37} -18.3106 q^{38} -1.36274 q^{39} -9.08265 q^{40} -11.0647 q^{41} +2.33114 q^{42} -1.00000 q^{43} -4.58863 q^{44} -3.88568 q^{45} -4.48529 q^{46} -6.49267 q^{47} -3.12521 q^{48} -1.75868 q^{49} +8.03805 q^{50} +0.396689 q^{51} +15.7632 q^{52} -12.1339 q^{53} -5.94917 q^{54} -1.36693 q^{55} -15.2120 q^{56} -2.82979 q^{57} -10.2974 q^{58} +3.66160 q^{59} -2.48816 q^{60} +0.881663 q^{61} +9.98300 q^{62} -6.50792 q^{63} +2.03929 q^{64} +4.69578 q^{65} -1.01823 q^{66} +12.9552 q^{67} -4.58863 q^{68} -0.693176 q^{69} -8.03274 q^{70} +12.8152 q^{71} +18.8881 q^{72} +5.58943 q^{73} +15.0595 q^{74} +1.24223 q^{75} +32.7331 q^{76} -2.28939 q^{77} +3.49792 q^{78} -7.71165 q^{79} +10.7690 q^{80} +7.60851 q^{81} +28.4013 q^{82} -15.5308 q^{83} -4.16728 q^{84} -1.36693 q^{85} +2.56683 q^{86} -1.59140 q^{87} +6.64457 q^{88} +3.99113 q^{89} +9.97390 q^{90} +7.86471 q^{91} +8.01819 q^{92} +1.54281 q^{93} +16.6656 q^{94} +9.75102 q^{95} +2.75023 q^{96} -9.65669 q^{97} +4.51423 q^{98} +2.84264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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