LMFDB - Embedded newform 8041.2.a.d.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:	$62$
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)

$f(q)$	$=$	$q-2.25455 q^{2} +2.07382 q^{3} +3.08298 q^{4} +1.31329 q^{5} -4.67552 q^{6} -0.325302 q^{7} -2.44162 q^{8} +1.30073 q^{9} +O(q^{10})$	\(q-2.25455 q^{2} +2.07382 q^{3} +3.08298 q^{4} +1.31329 q^{5} -4.67552 q^{6} -0.325302 q^{7} -2.44162 q^{8} +1.30073 q^{9} -2.96087 q^{10} +1.00000 q^{11} +6.39354 q^{12} -3.54069 q^{13} +0.733408 q^{14} +2.72352 q^{15} -0.661206 q^{16} -1.00000 q^{17} -2.93255 q^{18} +5.22856 q^{19} +4.04883 q^{20} -0.674617 q^{21} -2.25455 q^{22} -1.98649 q^{23} -5.06348 q^{24} -3.27528 q^{25} +7.98264 q^{26} -3.52398 q^{27} -1.00290 q^{28} +0.424618 q^{29} -6.14030 q^{30} -5.82810 q^{31} +6.37396 q^{32} +2.07382 q^{33} +2.25455 q^{34} -0.427215 q^{35} +4.01011 q^{36} +7.52448 q^{37} -11.7880 q^{38} -7.34274 q^{39} -3.20655 q^{40} +5.24681 q^{41} +1.52096 q^{42} +1.00000 q^{43} +3.08298 q^{44} +1.70823 q^{45} +4.47864 q^{46} -7.13969 q^{47} -1.37122 q^{48} -6.89418 q^{49} +7.38426 q^{50} -2.07382 q^{51} -10.9159 q^{52} -9.02173 q^{53} +7.94498 q^{54} +1.31329 q^{55} +0.794264 q^{56} +10.8431 q^{57} -0.957320 q^{58} +0.0984967 q^{59} +8.39655 q^{60} -0.224215 q^{61} +13.1397 q^{62} -0.423129 q^{63} -13.0480 q^{64} -4.64994 q^{65} -4.67552 q^{66} +11.7607 q^{67} -3.08298 q^{68} -4.11963 q^{69} +0.963175 q^{70} +0.278786 q^{71} -3.17589 q^{72} -14.0167 q^{73} -16.9643 q^{74} -6.79233 q^{75} +16.1195 q^{76} -0.325302 q^{77} +16.5546 q^{78} -2.68260 q^{79} -0.868353 q^{80} -11.2103 q^{81} -11.8292 q^{82} +12.3668 q^{83} -2.07983 q^{84} -1.31329 q^{85} -2.25455 q^{86} +0.880581 q^{87} -2.44162 q^{88} +6.90487 q^{89} -3.85128 q^{90} +1.15179 q^{91} -6.12431 q^{92} -12.0864 q^{93} +16.0968 q^{94} +6.86659 q^{95} +13.2184 q^{96} -6.24062 q^{97} +15.5432 q^{98} +1.30073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.25455	−1.59420	−0.797102	−	0.603844i	$-0.793635\pi$
$2$	−2.25455	−1.59420	−0.797102	+	0.603844i	$0.793635\pi$
$3$	2.07382	1.19732	0.598660	−	0.801003i	$-0.295700\pi$
$3$	2.07382	1.19732	0.598660	+	0.801003i	$0.295700\pi$
$4$	3.08298	1.54149
$5$	1.31329	0.587320	0.293660	−	0.955910i	$-0.405127\pi$
$5$	1.31329	0.587320	0.293660	+	0.955910i	$0.405127\pi$
$6$	−4.67552	−1.90877
$7$	−0.325302	−0.122953	−0.0614763	−	0.998109i	$-0.519581\pi$
$7$	−0.325302	−0.122953	−0.0614763	+	0.998109i	$0.519581\pi$
$8$	−2.44162	−0.863244
$9$	1.30073	0.433576
$10$	−2.96087	−0.936308
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	6.39354	1.84566
$13$	−3.54069	−0.982009	−0.491005	−	0.871157i	$-0.663370\pi$
$13$	−3.54069	−0.982009	−0.491005	+	0.871157i	$0.663370\pi$
$14$	0.733408	0.196011
$15$	2.72352	0.703210
$16$	−0.661206	−0.165302
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.93255	−0.691209
$19$	5.22856	1.19951	0.599756	−	0.800183i	$-0.295264\pi$
$19$	5.22856	1.19951	0.599756	+	0.800183i	$0.295264\pi$
$20$	4.04883	0.905347
$21$	−0.674617	−0.147214
$22$	−2.25455	−0.480671
$23$	−1.98649	−0.414212	−0.207106	−	0.978318i	$-0.566405\pi$
$23$	−1.98649	−0.414212	−0.207106	+	0.978318i	$0.566405\pi$
$24$	−5.06348	−1.03358
$25$	−3.27528	−0.655055
$26$	7.98264	1.56552
$27$	−3.52398	−0.678191
$28$	−1.00290	−0.189530
$29$	0.424618	0.0788495	0.0394248	−	0.999223i	$-0.487447\pi$
$29$	0.424618	0.0788495	0.0394248	+	0.999223i	$0.487447\pi$
$30$	−6.14030	−1.12106
$31$	−5.82810	−1.04676	−0.523379	−	0.852100i	$-0.675329\pi$
$31$	−5.82810	−1.04676	−0.523379	+	0.852100i	$0.675329\pi$
$32$	6.37396	1.12677
$33$	2.07382	0.361006
$34$	2.25455	0.386651
$35$	−0.427215	−0.0722124
$36$	4.01011	0.668352
$37$	7.52448	1.23702	0.618508	−	0.785778i	$-0.287737\pi$
$37$	7.52448	1.23702	0.618508	+	0.785778i	$0.287737\pi$
$38$	−11.7880	−1.91227
$39$	−7.34274	−1.17578
$40$	−3.20655	−0.507000
$41$	5.24681	0.819414	0.409707	−	0.912217i	$-0.365631\pi$
$41$	5.24681	0.819414	0.409707	+	0.912217i	$0.365631\pi$
$42$	1.52096	0.234689
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.08298	0.464776
$45$	1.70823	0.254648
$46$	4.47864	0.660339
$47$	−7.13969	−1.04143	−0.520716	−	0.853730i	$-0.674335\pi$
$47$	−7.13969	−1.04143	−0.520716	+	0.853730i	$0.674335\pi$
$48$	−1.37122	−0.197919
$49$	−6.89418	−0.984883
$50$	7.38426	1.04429
$51$	−2.07382	−0.290393
$52$	−10.9159	−1.51376
$53$	−9.02173	−1.23923	−0.619615	−	0.784906i	$-0.712711\pi$
$53$	−9.02173	−1.23923	−0.619615	+	0.784906i	$0.712711\pi$
$54$	7.94498	1.08118
$55$	1.31329	0.177084
$56$	0.794264	0.106138
$57$	10.8431	1.43620
$58$	−0.957320	−0.125702
$59$	0.0984967	0.0128232	0.00641159	−	0.999979i	$-0.497959\pi$
$59$	0.0984967	0.0128232	0.00641159	+	0.999979i	$0.497959\pi$
$60$	8.39655	1.08399
$61$	−0.224215	−0.0287078	−0.0143539	−	0.999897i	$-0.504569\pi$
$61$	−0.224215	−0.0287078	−0.0143539	+	0.999897i	$0.504569\pi$
$62$	13.1397	1.66875
$63$	−0.423129	−0.0533093
$64$	−13.0480	−1.63100
$65$	−4.64994	−0.576754
$66$	−4.67552	−0.575517
$67$	11.7607	1.43679	0.718397	−	0.695633i	$-0.244876\pi$
$67$	11.7607	1.43679	0.718397	+	0.695633i	$0.244876\pi$
$68$	−3.08298	−0.373866
$69$	−4.11963	−0.495945
$70$	0.963175	0.115121
$71$	0.278786	0.0330858	0.0165429	−	0.999863i	$-0.494734\pi$
$71$	0.278786	0.0330858	0.0165429	+	0.999863i	$0.494734\pi$
$72$	−3.17589	−0.374282
$73$	−14.0167	−1.64053	−0.820265	−	0.571984i	$-0.806174\pi$
$73$	−14.0167	−1.64053	−0.820265	+	0.571984i	$0.806174\pi$
$74$	−16.9643	−1.97206
$75$	−6.79233	−0.784311
$76$	16.1195	1.84904
$77$	−0.325302	−0.0370716
$78$	16.5546	1.87443
$79$	−2.68260	−0.301816	−0.150908	−	0.988548i	$-0.548220\pi$
$79$	−2.68260	−0.301816	−0.150908	+	0.988548i	$0.548220\pi$
$80$	−0.868353	−0.0970848
$81$	−11.2103	−1.24559
$82$	−11.8292	−1.30631
$83$	12.3668	1.35744	0.678719	−	0.734398i	$-0.262536\pi$
$83$	12.3668	1.35744	0.678719	+	0.734398i	$0.262536\pi$
$84$	−2.07983	−0.226928
$85$	−1.31329	−0.142446
$86$	−2.25455	−0.243114
$87$	0.880581	0.0944081
$88$	−2.44162	−0.260278
$89$	6.90487	0.731914	0.365957	−	0.930632i	$-0.380742\pi$
$89$	6.90487	0.731914	0.365957	+	0.930632i	$0.380742\pi$
$90$	−3.85128	−0.405961
$91$	1.15179	0.120741
$92$	−6.12431	−0.638504
$93$	−12.0864	−1.25330
$94$	16.0968	1.66025
$95$	6.86659	0.704498
$96$	13.2184	1.34910
$97$	−6.24062	−0.633639	−0.316820	−	0.948486i	$-0.602615\pi$
$97$	−6.24062	−0.633639	−0.316820	+	0.948486i	$0.602615\pi$
$98$	15.5432	1.57010
$99$	1.30073	0.130728
$100$	−10.0976	−1.00976
$101$	−16.3688	−1.62876	−0.814380	−	0.580332i	$-0.802923\pi$
$101$	−16.3688	−1.62876	−0.814380	+	0.580332i	$0.802923\pi$
$102$	4.67552	0.462946
$103$	−2.95430	−0.291095	−0.145548	−	0.989351i	$-0.546494\pi$
$103$	−2.95430	−0.291095	−0.145548	+	0.989351i	$0.546494\pi$
$104$	8.64501	0.847713
$105$	−0.885966	−0.0864614
$106$	20.3399	1.97559
$107$	16.8977	1.63356	0.816781	−	0.576948i	$-0.195757\pi$
$107$	16.8977	1.63356	0.816781	+	0.576948i	$0.195757\pi$
$108$	−10.8644	−1.04542
$109$	−0.557419	−0.0533910	−0.0266955	−	0.999644i	$-0.508498\pi$
$109$	−0.557419	−0.0533910	−0.0266955	+	0.999644i	$0.508498\pi$
$110$	−2.96087	−0.282307
$111$	15.6044	1.48111
$112$	0.215091	0.0203242
$113$	−8.82213	−0.829916	−0.414958	−	0.909841i	$-0.636204\pi$
$113$	−8.82213	−0.829916	−0.414958	+	0.909841i	$0.636204\pi$
$114$	−24.4462	−2.28960
$115$	−2.60884	−0.243275
$116$	1.30909	0.121546
$117$	−4.60547	−0.425776
$118$	−0.222065	−0.0204428
$119$	0.325302	0.0298204
$120$	−6.64981	−0.607042
$121$	1.00000	0.0909091
$122$	0.505504	0.0457662
$123$	10.8809	0.981101
$124$	−17.9679	−1.61357
$125$	−10.8678	−0.972047
$126$	0.953964	0.0849859
$127$	4.17182	0.370189	0.185095	−	0.982721i	$-0.440741\pi$
$127$	4.17182	0.370189	0.185095	+	0.982721i	$0.440741\pi$
$128$	16.6693	1.47338
$129$	2.07382	0.182590
$130$	10.4835	0.919463
$131$	−18.4481	−1.61182	−0.805910	−	0.592038i	$-0.798324\pi$
$131$	−18.4481	−1.61182	−0.805910	+	0.592038i	$0.798324\pi$
$132$	6.39354	0.556486
$133$	−1.70086	−0.147483
$134$	−26.5150	−2.29054
$135$	−4.62800	−0.398315
$136$	2.44162	0.209367
$137$	−15.2031	−1.29889	−0.649446	−	0.760408i	$-0.724999\pi$
$137$	−15.2031	−1.29889	−0.649446	+	0.760408i	$0.724999\pi$
$138$	9.28789	0.790638
$139$	−5.22427	−0.443116	−0.221558	−	0.975147i	$-0.571114\pi$
$139$	−5.22427	−0.443116	−0.221558	+	0.975147i	$0.571114\pi$
$140$	−1.31709	−0.111315
$141$	−14.8064	−1.24693
$142$	−0.628535	−0.0527455
$143$	−3.54069	−0.296087
$144$	−0.860049	−0.0716708
$145$	0.557645	0.0463099
$146$	31.6013	2.61534
$147$	−14.2973	−1.17922
$148$	23.1978	1.90685
$149$	18.3752	1.50536	0.752678	−	0.658388i	$-0.228762\pi$
$149$	18.3752	1.50536	0.752678	+	0.658388i	$0.228762\pi$
$150$	15.3136	1.25035
$151$	−1.89912	−0.154548	−0.0772739	−	0.997010i	$-0.524622\pi$
$151$	−1.89912	−0.154548	−0.0772739	+	0.997010i	$0.524622\pi$
$152$	−12.7662	−1.03547
$153$	−1.30073	−0.105158
$154$	0.733408	0.0590997
$155$	−7.65397	−0.614782
$156$	−22.6375	−1.81245
$157$	−7.88912	−0.629621	−0.314810	−	0.949155i	$-0.601941\pi$
$157$	−7.88912	−0.629621	−0.314810	+	0.949155i	$0.601941\pi$
$158$	6.04805	0.481157
$159$	−18.7094	−1.48375
$160$	8.37084	0.661773
$161$	0.646210	0.0509285
$162$	25.2741	1.98572
$163$	2.94099	0.230356	0.115178	−	0.993345i	$-0.463256\pi$
$163$	2.94099	0.230356	0.115178	+	0.993345i	$0.463256\pi$
$164$	16.1758	1.26312
$165$	2.72352	0.212026
$166$	−27.8816	−2.16403
$167$	13.9539	1.07978	0.539892	−	0.841734i	$-0.318465\pi$
$167$	13.9539	1.07978	0.539892	+	0.841734i	$0.318465\pi$
$168$	1.64716	0.127081
$169$	−0.463547	−0.0356575
$170$	2.96087	0.227088
$171$	6.80093	0.520080
$172$	3.08298	0.235075
$173$	−7.60582	−0.578260	−0.289130	−	0.957290i	$-0.593366\pi$
$173$	−7.60582	−0.578260	−0.289130	+	0.957290i	$0.593366\pi$
$174$	−1.98531	−0.150506
$175$	1.06545	0.0805407
$176$	−0.661206	−0.0498403
$177$	0.204264	0.0153535
$178$	−15.5673	−1.16682
$179$	−2.52249	−0.188540	−0.0942700	−	0.995547i	$-0.530052\pi$
$179$	−2.52249	−0.188540	−0.0942700	+	0.995547i	$0.530052\pi$
$180$	5.26643	0.392537
$181$	24.4917	1.82046	0.910228	−	0.414108i	$-0.135906\pi$
$181$	24.4917	1.82046	0.910228	+	0.414108i	$0.135906\pi$
$182$	−2.59677	−0.192485
$183$	−0.464982	−0.0343725
$184$	4.85026	0.357566
$185$	9.88180	0.726524
$186$	27.2494	1.99802
$187$	−1.00000	−0.0731272
$188$	−22.0115	−1.60535
$189$	1.14636	0.0833853
$190$	−15.4811	−1.12311
$191$	−4.75117	−0.343783	−0.171891	−	0.985116i	$-0.554988\pi$
$191$	−4.75117	−0.343783	−0.171891	+	0.985116i	$0.554988\pi$
$192$	−27.0592	−1.95283
$193$	9.58513	0.689952	0.344976	−	0.938611i	$-0.387887\pi$
$193$	9.58513	0.689952	0.344976	+	0.938611i	$0.387887\pi$
$194$	14.0698	1.01015
$195$	−9.64313	−0.690559
$196$	−21.2546	−1.51819
$197$	−5.15260	−0.367108	−0.183554	−	0.983010i	$-0.558760\pi$
$197$	−5.15260	−0.367108	−0.183554	+	0.983010i	$0.558760\pi$
$198$	−2.93255	−0.208407
$199$	−26.5657	−1.88319	−0.941595	−	0.336748i	$-0.890673\pi$
$199$	−26.5657	−1.88319	−0.941595	+	0.336748i	$0.890673\pi$
$200$	7.99699	0.565472
$201$	24.3895	1.72030
$202$	36.9043	2.59658
$203$	−0.138129	−0.00969475
$204$	−6.39354	−0.447637
$205$	6.89056	0.481258
$206$	6.66060	0.464066
$207$	−2.58389	−0.179593
$208$	2.34112	0.162328
$209$	5.22856	0.361667
$210$	1.99745	0.137837
$211$	−4.08796	−0.281427	−0.140713	−	0.990050i	$-0.544940\pi$
$211$	−4.08796	−0.281427	−0.140713	+	0.990050i	$0.544940\pi$
$212$	−27.8138	−1.91026
$213$	0.578151	0.0396143
$214$	−38.0966	−2.60423
$215$	1.31329	0.0895654
$216$	8.60424	0.585444
$217$	1.89589	0.128702
$218$	1.25673	0.0851162
$219$	−29.0681	−1.96424
$220$	4.04883	0.272972
$221$	3.54069	0.238172
$222$	−35.1809	−2.36118
$223$	0.684309	0.0458247	0.0229123	−	0.999737i	$-0.492706\pi$
$223$	0.684309	0.0458247	0.0229123	+	0.999737i	$0.492706\pi$
$224$	−2.07346	−0.138539
$225$	−4.26025	−0.284016
$226$	19.8899	1.32306
$227$	−6.52355	−0.432983	−0.216492	−	0.976284i	$-0.569461\pi$
$227$	−6.52355	−0.432983	−0.216492	+	0.976284i	$0.569461\pi$
$228$	33.4290	2.21389
$229$	−19.6404	−1.29787	−0.648937	−	0.760842i	$-0.724786\pi$
$229$	−19.6404	−1.29787	−0.648937	+	0.760842i	$0.724786\pi$
$230$	5.88174	0.387830
$231$	−0.674617	−0.0443866
$232$	−1.03676	−0.0680664
$233$	−10.8315	−0.709595	−0.354798	−	0.934943i	$-0.615450\pi$
$233$	−10.8315	−0.709595	−0.354798	+	0.934943i	$0.615450\pi$
$234$	10.3832	0.678774
$235$	−9.37647	−0.611653
$236$	0.303663	0.0197668
$237$	−5.56323	−0.361371
$238$	−0.733408	−0.0475398
$239$	−11.5067	−0.744307	−0.372154	−	0.928171i	$-0.621381\pi$
$239$	−11.5067	−0.744307	−0.372154	+	0.928171i	$0.621381\pi$
$240$	−1.80081	−0.116242
$241$	−10.1150	−0.651566	−0.325783	−	0.945445i	$-0.605628\pi$
$241$	−10.1150	−0.651566	−0.325783	+	0.945445i	$0.605628\pi$
$242$	−2.25455	−0.144928
$243$	−12.6762	−0.813177
$244$	−0.691251	−0.0442528
$245$	−9.05404	−0.578441
$246$	−24.5316	−1.56408
$247$	−18.5127	−1.17793
$248$	14.2300	0.903607
$249$	25.6466	1.62529
$250$	24.5020	1.54964
$251$	−24.3533	−1.53717	−0.768584	−	0.639749i	$-0.779038\pi$
$251$	−24.3533	−1.53717	−0.768584	+	0.639749i	$0.779038\pi$
$252$	−1.30450	−0.0821756
$253$	−1.98649	−0.124890
$254$	−9.40556	−0.590157
$255$	−2.72352	−0.170553
$256$	−11.4858	−0.717865
$257$	−4.70560	−0.293528	−0.146764	−	0.989172i	$-0.546886\pi$
$257$	−4.70560	−0.293528	−0.146764	+	0.989172i	$0.546886\pi$
$258$	−4.67552	−0.291085
$259$	−2.44773	−0.152094
$260$	−14.3356	−0.889059
$261$	0.552312	0.0341873
$262$	41.5921	2.56957
$263$	−9.53630	−0.588034	−0.294017	−	0.955800i	$-0.594992\pi$
$263$	−9.53630	−0.588034	−0.294017	+	0.955800i	$0.594992\pi$
$264$	−5.06348	−0.311636
$265$	−11.8481	−0.727824
$266$	3.83466	0.235118
$267$	14.3194	0.876336
$268$	36.2579	2.21480
$269$	−26.7296	−1.62973	−0.814867	−	0.579648i	$-0.803190\pi$
$269$	−26.7296	−1.62973	−0.814867	+	0.579648i	$0.803190\pi$
$270$	10.4340	0.634996
$271$	−21.7486	−1.32113	−0.660567	−	0.750767i	$-0.729684\pi$
$271$	−21.7486	−1.32113	−0.660567	+	0.750767i	$0.729684\pi$
$272$	0.661206	0.0400915
$273$	2.38861	0.144565
$274$	34.2762	2.07070
$275$	−3.27528	−0.197507
$276$	−12.7007	−0.764493
$277$	−29.6604	−1.78212	−0.891060	−	0.453886i	$-0.850037\pi$
$277$	−29.6604	−1.78212	−0.891060	+	0.453886i	$0.850037\pi$
$278$	11.7783	0.706418
$279$	−7.58078	−0.453849
$280$	1.04310	0.0623369
$281$	2.49934	0.149098	0.0745492	−	0.997217i	$-0.476248\pi$
$281$	2.49934	0.149098	0.0745492	+	0.997217i	$0.476248\pi$
$282$	33.3818	1.98786
$283$	15.1833	0.902554	0.451277	−	0.892384i	$-0.350969\pi$
$283$	15.1833	0.902554	0.451277	+	0.892384i	$0.350969\pi$
$284$	0.859490	0.0510013
$285$	14.2401	0.843509
$286$	7.98264	0.472023
$287$	−1.70680	−0.100749
$288$	8.29079	0.488540
$289$	1.00000	0.0588235
$290$	−1.25724	−0.0738274
$291$	−12.9419	−0.758669
$292$	−43.2132	−2.52886
$293$	6.97776	0.407645	0.203823	−	0.979008i	$-0.434663\pi$
$293$	6.97776	0.407645	0.203823	+	0.979008i	$0.434663\pi$
$294$	32.2339	1.87992
$295$	0.129354	0.00753131
$296$	−18.3719	−1.06785
$297$	−3.52398	−0.204482
$298$	−41.4278	−2.39985
$299$	7.03355	0.406760
$300$	−20.9406	−1.20901
$301$	−0.325302	−0.0187501
$302$	4.28164	0.246381
$303$	−33.9460	−1.95015
$304$	−3.45715	−0.198281
$305$	−0.294459	−0.0168607
$306$	2.93255	0.167643
$307$	24.5376	1.40043	0.700217	−	0.713930i	$-0.253087\pi$
$307$	24.5376	1.40043	0.700217	+	0.713930i	$0.253087\pi$
$308$	−1.00290	−0.0571454
$309$	−6.12668	−0.348534
$310$	17.2562	0.980088
$311$	7.57324	0.429439	0.214719	−	0.976676i	$-0.431116\pi$
$311$	7.57324	0.429439	0.214719	+	0.976676i	$0.431116\pi$
$312$	17.9282	1.01498
$313$	13.1084	0.740932	0.370466	−	0.928846i	$-0.379198\pi$
$313$	13.1084	0.740932	0.370466	+	0.928846i	$0.379198\pi$
$314$	17.7864	1.00374
$315$	−0.555690	−0.0313096
$316$	−8.27040	−0.465246
$317$	−4.28748	−0.240809	−0.120404	−	0.992725i	$-0.538419\pi$
$317$	−4.28748	−0.240809	−0.120404	+	0.992725i	$0.538419\pi$
$318$	42.1813	2.36541
$319$	0.424618	0.0237740
$320$	−17.1357	−0.957917
$321$	35.0428	1.95590
$322$	−1.45691	−0.0811904
$323$	−5.22856	−0.290925
$324$	−34.5611	−1.92006
$325$	11.5967	0.643271
$326$	−6.63059	−0.367234
$327$	−1.15599	−0.0639262
$328$	−12.8107	−0.707354
$329$	2.32255	0.128047
$330$	−6.14030	−0.338012
$331$	8.90844	0.489652	0.244826	−	0.969567i	$-0.421269\pi$
$331$	8.90844	0.489652	0.244826	+	0.969567i	$0.421269\pi$
$332$	38.1267	2.09247
$333$	9.78730	0.536341
$334$	−31.4597	−1.72140
$335$	15.4451	0.843858
$336$	0.446061	0.0243346
$337$	11.3994	0.620967	0.310484	−	0.950579i	$-0.399509\pi$
$337$	11.3994	0.620967	0.310484	+	0.950579i	$0.399509\pi$
$338$	1.04509	0.0568453
$339$	−18.2955	−0.993675
$340$	−4.04883	−0.219579
$341$	−5.82810	−0.315609
$342$	−15.3330	−0.829114
$343$	4.51980	0.244046
$344$	−2.44162	−0.131643
$345$	−5.41025	−0.291278
$346$	17.1477	0.921865
$347$	−22.0429	−1.18333	−0.591663	−	0.806186i	$-0.701528\pi$
$347$	−22.0429	−1.18333	−0.591663	+	0.806186i	$0.701528\pi$
$348$	2.71481	0.145529
$349$	−1.37949	−0.0738422	−0.0369211	−	0.999318i	$-0.511755\pi$
$349$	−1.37949	−0.0738422	−0.0369211	+	0.999318i	$0.511755\pi$
$350$	−2.40211	−0.128398
$351$	12.4773	0.665990
$352$	6.37396	0.339733
$353$	12.0503	0.641375	0.320688	−	0.947185i	$-0.396086\pi$
$353$	12.0503	0.641375	0.320688	+	0.947185i	$0.396086\pi$
$354$	−0.460524	−0.0244766
$355$	0.366126	0.0194319
$356$	21.2875	1.12824
$357$	0.674617	0.0357045
$358$	5.68707	0.300571
$359$	−15.7103	−0.829159	−0.414579	−	0.910013i	$-0.636071\pi$
$359$	−15.7103	−0.829159	−0.414579	+	0.910013i	$0.636071\pi$
$360$	−4.17085	−0.219823
$361$	8.33780	0.438831
$362$	−55.2177	−2.90218
$363$	2.07382	0.108847
$364$	3.55095	0.186120
$365$	−18.4079	−0.963516
$366$	1.04832	0.0547968
$367$	14.7856	0.771803	0.385902	−	0.922540i	$-0.373890\pi$
$367$	14.7856	0.771803	0.385902	+	0.922540i	$0.373890\pi$
$368$	1.31348	0.0684699
$369$	6.82467	0.355278
$370$	−22.2790	−1.15823
$371$	2.93478	0.152366
$372$	−37.2622	−1.93195
$373$	21.2815	1.10191	0.550957	−	0.834534i	$-0.314263\pi$
$373$	21.2815	1.10191	0.550957	+	0.834534i	$0.314263\pi$
$374$	2.25455	0.116580
$375$	−22.5379	−1.16385
$376$	17.4324	0.899009
$377$	−1.50344	−0.0774310
$378$	−2.58452	−0.132933
$379$	−7.57927	−0.389321	−0.194660	−	0.980871i	$-0.562360\pi$
$379$	−7.57927	−0.389321	−0.194660	+	0.980871i	$0.562360\pi$
$380$	21.1696	1.08598
$381$	8.65160	0.443235
$382$	10.7117	0.548060
$383$	−12.4305	−0.635171	−0.317585	−	0.948230i	$-0.602872\pi$
$383$	−12.4305	−0.635171	−0.317585	+	0.948230i	$0.602872\pi$
$384$	34.5692	1.76410
$385$	−0.427215	−0.0217729
$386$	−21.6101	−1.09993
$387$	1.30073	0.0661197
$388$	−19.2397	−0.976747
$389$	−8.68606	−0.440401	−0.220200	−	0.975455i	$-0.570671\pi$
$389$	−8.68606	−0.440401	−0.220200	+	0.975455i	$0.570671\pi$
$390$	21.7409	1.10089
$391$	1.98649	0.100461
$392$	16.8330	0.850194
$393$	−38.2581	−1.92987
$394$	11.6168	0.585245
$395$	−3.52302	−0.177263
$396$	4.01011	0.201516
$397$	7.48503	0.375663	0.187832	−	0.982201i	$-0.439854\pi$
$397$	7.48503	0.375663	0.187832	+	0.982201i	$0.439854\pi$
$398$	59.8935	3.00219
$399$	−3.52727	−0.176585
$400$	2.16563	0.108282
$401$	31.7349	1.58477	0.792383	−	0.610024i	$-0.208840\pi$
$401$	31.7349	1.58477	0.792383	+	0.610024i	$0.208840\pi$
$402$	−54.9873	−2.74252
$403$	20.6355	1.02793
$404$	−50.4648	−2.51072
$405$	−14.7223	−0.731558
$406$	0.311418	0.0154554
$407$	7.52448	0.372975
$408$	5.06348	0.250680
$409$	17.1220	0.846629	0.423315	−	0.905983i	$-0.360866\pi$
$409$	17.1220	0.846629	0.423315	+	0.905983i	$0.360866\pi$
$410$	−15.5351	−0.767224
$411$	−31.5286	−1.55519
$412$	−9.10803	−0.448720
$413$	−0.0320412	−0.00157664
$414$	5.82549	0.286307
$415$	16.2412	0.797250
$416$	−22.5682	−1.10650
$417$	−10.8342	−0.530552
$418$	−11.7880	−0.576571
$419$	6.19243	0.302520	0.151260	−	0.988494i	$-0.451667\pi$
$419$	6.19243	0.302520	0.151260	+	0.988494i	$0.451667\pi$
$420$	−2.73141	−0.133279
$421$	−12.2466	−0.596862	−0.298431	−	0.954431i	$-0.596463\pi$
$421$	−12.2466	−0.596862	−0.298431	+	0.954431i	$0.596463\pi$
$422$	9.21649	0.448651
$423$	−9.28680	−0.451540
$424$	22.0276	1.06976
$425$	3.27528	0.158874
$426$	−1.30347	−0.0631532
$427$	0.0729377	0.00352970
$428$	52.0952	2.51812
$429$	−7.34274	−0.354511
$430$	−2.96087	−0.142786
$431$	−23.0747	−1.11147	−0.555735	−	0.831359i	$-0.687563\pi$
$431$	−23.0747	−1.11147	−0.555735	+	0.831359i	$0.687563\pi$
$432$	2.33008	0.112106
$433$	−18.7038	−0.898849	−0.449424	−	0.893318i	$-0.648371\pi$
$433$	−18.7038	−0.898849	−0.449424	+	0.893318i	$0.648371\pi$
$434$	−4.27438	−0.205177
$435$	1.15645	0.0554478
$436$	−1.71851	−0.0823017
$437$	−10.3865	−0.496853
$438$	65.5354	3.13140
$439$	−6.12026	−0.292104	−0.146052	−	0.989277i	$-0.546657\pi$
$439$	−6.12026	−0.292104	−0.146052	+	0.989277i	$0.546657\pi$
$440$	−3.20655	−0.152866
$441$	−8.96745	−0.427022
$442$	−7.98264	−0.379695
$443$	−2.57359	−0.122275	−0.0611375	−	0.998129i	$-0.519473\pi$
$443$	−2.57359	−0.122275	−0.0611375	+	0.998129i	$0.519473\pi$
$444$	48.1080	2.28311
$445$	9.06807	0.429868
$446$	−1.54281	−0.0730539
$447$	38.1069	1.80239
$448$	4.24453	0.200535
$449$	−35.0213	−1.65276	−0.826378	−	0.563116i	$-0.809602\pi$
$449$	−35.0213	−1.65276	−0.826378	+	0.563116i	$0.809602\pi$
$450$	9.60492	0.452780
$451$	5.24681	0.247063
$452$	−27.1984	−1.27931
$453$	−3.93842	−0.185043
$454$	14.7076	0.690264
$455$	1.51263	0.0709133
$456$	−26.4747	−1.23979
$457$	23.2333	1.08681	0.543405	−	0.839471i	$-0.317135\pi$
$457$	23.2333	1.08681	0.543405	+	0.839471i	$0.317135\pi$
$458$	44.2802	2.06908
$459$	3.52398	0.164485
$460$	−8.04298	−0.375006
$461$	6.53965	0.304582	0.152291	−	0.988336i	$-0.451335\pi$
$461$	6.53965	0.304582	0.152291	+	0.988336i	$0.451335\pi$
$462$	1.52096	0.0707613
$463$	10.5315	0.489438	0.244719	−	0.969594i	$-0.421304\pi$
$463$	10.5315	0.489438	0.244719	+	0.969594i	$0.421304\pi$
$464$	−0.280760	−0.0130339
$465$	−15.8730	−0.736091
$466$	24.4201	1.13124
$467$	−12.0092	−0.555719	−0.277859	−	0.960622i	$-0.589625\pi$
$467$	−12.0092	−0.555719	−0.277859	+	0.960622i	$0.589625\pi$
$468$	−14.1986	−0.656328
$469$	−3.82577	−0.176657
$470$	21.1397	0.975100
$471$	−16.3606	−0.753858
$472$	−0.240492	−0.0110695
$473$	1.00000	0.0459800
$474$	12.5426	0.576099
$475$	−17.1250	−0.785748
$476$	1.00290	0.0459678
$477$	−11.7348	−0.537300
$478$	25.9424	1.18658
$479$	25.4205	1.16149	0.580745	−	0.814085i	$-0.302761\pi$
$479$	25.4205	1.16149	0.580745	+	0.814085i	$0.302761\pi$
$480$	17.3596	0.792355
$481$	−26.6418	−1.21476
$482$	22.8048	1.03873
$483$	1.34012	0.0609777
$484$	3.08298	0.140135
$485$	−8.19573	−0.372149
$486$	28.5790	1.29637
$487$	31.9900	1.44961	0.724803	−	0.688956i	$-0.241931\pi$
$487$	31.9900	1.44961	0.724803	+	0.688956i	$0.241931\pi$
$488$	0.547449	0.0247819
$489$	6.09908	0.275810
$490$	20.4127	0.922153
$491$	−24.1436	−1.08958	−0.544792	−	0.838571i	$-0.683391\pi$
$491$	−24.1436	−1.08958	−0.544792	+	0.838571i	$0.683391\pi$
$492$	33.5457	1.51236
$493$	−0.424618	−0.0191238
$494$	41.7377	1.87787
$495$	1.70823	0.0767792
$496$	3.85358	0.173031
$497$	−0.0906895	−0.00406798
$498$	−57.8215	−2.59104
$499$	6.08353	0.272336	0.136168	−	0.990686i	$-0.456521\pi$
$499$	6.08353	0.272336	0.136168	+	0.990686i	$0.456521\pi$
$500$	−33.5052	−1.49840
$501$	28.9378	1.29285
$502$	54.9057	2.45056
$503$	−8.19577	−0.365431	−0.182716	−	0.983166i	$-0.558489\pi$
$503$	−8.19577	−0.365431	−0.182716	+	0.983166i	$0.558489\pi$
$504$	1.03312	0.0460189
$505$	−21.4970	−0.956603
$506$	4.47864	0.199100
$507$	−0.961314	−0.0426934
$508$	12.8616	0.570642
$509$	18.0880	0.801736	0.400868	−	0.916136i	$-0.368709\pi$
$509$	18.0880	0.801736	0.400868	+	0.916136i	$0.368709\pi$
$510$	6.14030	0.271897
$511$	4.55966	0.201707
$512$	−7.44333	−0.328952
$513$	−18.4253	−0.813499
$514$	10.6090	0.467943
$515$	−3.87984	−0.170966
$516$	6.39354	0.281460
$517$	−7.13969	−0.314003
$518$	5.51851	0.242469
$519$	−15.7731	−0.692362
$520$	11.3534	0.497879
$521$	23.4661	1.02807	0.514035	−	0.857769i	$-0.328150\pi$
$521$	23.4661	1.02807	0.514035	+	0.857769i	$0.328150\pi$
$522$	−1.24521	−0.0545015
$523$	27.5348	1.20401	0.602007	−	0.798491i	$-0.294368\pi$
$523$	27.5348	1.20401	0.602007	+	0.798491i	$0.294368\pi$
$524$	−56.8751	−2.48460
$525$	2.20956	0.0964330
$526$	21.5000	0.937446
$527$	5.82810	0.253876
$528$	−1.37122	−0.0596748
$529$	−19.0538	−0.828428
$530$	26.7121	1.16030
$531$	0.128117	0.00555982
$532$	−5.24371	−0.227344
$533$	−18.5773	−0.804672
$534$	−32.2839	−1.39706
$535$	22.1915	0.959423
$536$	−28.7151	−1.24030
$537$	−5.23119	−0.225743
$538$	60.2632	2.59813
$539$	−6.89418	−0.296953
$540$	−14.2680	−0.613998
$541$	−3.29811	−0.141797	−0.0708984	−	0.997484i	$-0.522587\pi$
$541$	−3.29811	−0.141797	−0.0708984	+	0.997484i	$0.522587\pi$
$542$	49.0333	2.10616
$543$	50.7914	2.17967
$544$	−6.37396	−0.273281
$545$	−0.732051	−0.0313576
$546$	−5.38522	−0.230466
$547$	−9.36368	−0.400362	−0.200181	−	0.979759i	$-0.564153\pi$
$547$	−9.36368	−0.400362	−0.200181	+	0.979759i	$0.564153\pi$
$548$	−46.8709	−2.00223
$549$	−0.291643	−0.0124470
$550$	7.38426	0.314866
$551$	2.22014	0.0945810
$552$	10.0586	0.428121
$553$	0.872655	0.0371091
$554$	66.8707	2.84106
$555$	20.4931	0.869882
$556$	−16.1063	−0.683059
$557$	−14.7220	−0.623789	−0.311895	−	0.950117i	$-0.600964\pi$
$557$	−14.7220	−0.623789	−0.311895	+	0.950117i	$0.600964\pi$
$558$	17.0912	0.723529
$559$	−3.54069	−0.149755
$560$	0.282477	0.0119368
$561$	−2.07382	−0.0875567
$562$	−5.63488	−0.237693
$563$	−11.3946	−0.480223	−0.240112	−	0.970745i	$-0.577184\pi$
$563$	−11.3946	−0.480223	−0.240112	+	0.970745i	$0.577184\pi$
$564$	−45.6479	−1.92212
$565$	−11.5860	−0.487426
$566$	−34.2315	−1.43886
$567$	3.64673	0.153148
$568$	−0.680689	−0.0285611
$569$	39.7435	1.66613	0.833066	−	0.553173i	$-0.186583\pi$
$569$	39.7435	1.66613	0.833066	+	0.553173i	$0.186583\pi$
$570$	−32.1049	−1.34473
$571$	27.2361	1.13979	0.569897	−	0.821716i	$-0.306983\pi$
$571$	27.2361	1.13979	0.569897	+	0.821716i	$0.306983\pi$
$572$	−10.9159	−0.456415
$573$	−9.85307	−0.411618
$574$	3.84805	0.160614
$575$	6.50631	0.271332
$576$	−16.9719	−0.707161
$577$	4.27206	0.177848	0.0889241	−	0.996038i	$-0.471657\pi$
$577$	4.27206	0.177848	0.0889241	+	0.996038i	$0.471657\pi$
$578$	−2.25455	−0.0937767
$579$	19.8778	0.826094
$580$	1.71921	0.0713862
$581$	−4.02296	−0.166900
$582$	29.1782	1.20947
$583$	−9.02173	−0.373642
$584$	34.2235	1.41618
$585$	−6.04830	−0.250067
$586$	−15.7317	−0.649870
$587$	−0.194556	−0.00803017	−0.00401509	−	0.999992i	$-0.501278\pi$
$587$	−0.194556	−0.00803017	−0.00401509	+	0.999992i	$0.501278\pi$
$588$	−44.0782	−1.81775
$589$	−30.4726	−1.25560
$590$	−0.291636	−0.0120064
$591$	−10.6856	−0.439545
$592$	−4.97523	−0.204481
$593$	−23.5786	−0.968258	−0.484129	−	0.874997i	$-0.660864\pi$
$593$	−23.5786	−0.968258	−0.484129	+	0.874997i	$0.660864\pi$
$594$	7.94498	0.325987
$595$	0.427215	0.0175141
$596$	56.6504	2.32049
$597$	−55.0924	−2.25478
$598$	−15.8575	−0.648459
$599$	22.7353	0.928938	0.464469	−	0.885590i	$-0.346245\pi$
$599$	22.7353	0.928938	0.464469	+	0.885590i	$0.346245\pi$
$600$	16.5843	0.677052
$601$	−10.7132	−0.436999	−0.218500	−	0.975837i	$-0.570116\pi$
$601$	−10.7132	−0.436999	−0.218500	+	0.975837i	$0.570116\pi$
$602$	0.733408	0.0298915
$603$	15.2974	0.622960
$604$	−5.85493	−0.238234
$605$	1.31329	0.0533927
$606$	76.5329	3.10894
$607$	9.43946	0.383136	0.191568	−	0.981479i	$-0.438643\pi$
$607$	9.43946	0.383136	0.191568	+	0.981479i	$0.438643\pi$
$608$	33.3266	1.35157
$609$	−0.286454	−0.0116077
$610$	0.663872	0.0268794
$611$	25.2794	1.02270
$612$	−4.01011	−0.162099
$613$	29.3134	1.18396	0.591978	−	0.805954i	$-0.298347\pi$
$613$	29.3134	1.18396	0.591978	+	0.805954i	$0.298347\pi$
$614$	−55.3211	−2.23258
$615$	14.2898	0.576220
$616$	0.794264	0.0320018
$617$	9.08556	0.365771	0.182885	−	0.983134i	$-0.441456\pi$
$617$	9.08556	0.365771	0.182885	+	0.983134i	$0.441456\pi$
$618$	13.8129	0.555635
$619$	−23.6629	−0.951093	−0.475546	−	0.879691i	$-0.657750\pi$
$619$	−23.6629	−0.951093	−0.475546	+	0.879691i	$0.657750\pi$
$620$	−23.5970	−0.947679
$621$	7.00037	0.280915
$622$	−17.0742	−0.684613
$623$	−2.24617	−0.0899907
$624$	4.85507	0.194358
$625$	2.10383	0.0841531
$626$	−29.5535	−1.18120
$627$	10.8431	0.433031
$628$	−24.3220	−0.970553
$629$	−7.52448	−0.300021
$630$	1.25283	0.0499139
$631$	22.6880	0.903196	0.451598	−	0.892222i	$-0.350854\pi$
$631$	22.6880	0.903196	0.451598	+	0.892222i	$0.350854\pi$
$632$	6.54990	0.260541
$633$	−8.47768	−0.336958
$634$	9.66631	0.383898
$635$	5.47880	0.217419
$636$	−57.6808	−2.28719
$637$	24.4101	0.967164
$638$	−0.957320	−0.0379007
$639$	0.362624	0.0143452
$640$	21.8916	0.865343
$641$	−2.39573	−0.0946255	−0.0473128	−	0.998880i	$-0.515066\pi$
$641$	−2.39573	−0.0946255	−0.0473128	+	0.998880i	$0.515066\pi$
$642$	−79.0055	−3.11810
$643$	14.1495	0.558003	0.279001	−	0.960291i	$-0.409997\pi$
$643$	14.1495	0.558003	0.279001	+	0.960291i	$0.409997\pi$
$644$	1.99225	0.0785056
$645$	2.72352	0.107239
$646$	11.7880	0.463793
$647$	29.6761	1.16669	0.583343	−	0.812226i	$-0.301744\pi$
$647$	29.6761	1.16669	0.583343	+	0.812226i	$0.301744\pi$
$648$	27.3713	1.07525
$649$	0.0984967	0.00386634
$650$	−26.1454	−1.02551
$651$	3.93174	0.154097
$652$	9.06699	0.355091
$653$	−49.8595	−1.95115	−0.975577	−	0.219657i	$-0.929506\pi$
$653$	−49.8595	−1.95115	−0.975577	+	0.219657i	$0.929506\pi$
$654$	2.60622	0.101911
$655$	−24.2277	−0.946654
$656$	−3.46922	−0.135450
$657$	−18.2319	−0.711294
$658$	−5.23631	−0.204132
$659$	−10.1834	−0.396690	−0.198345	−	0.980132i	$-0.563557\pi$
$659$	−10.1834	−0.396690	−0.198345	+	0.980132i	$0.563557\pi$
$660$	8.39655	0.326835
$661$	17.6302	0.685733	0.342867	−	0.939384i	$-0.388602\pi$
$661$	17.6302	0.685733	0.342867	+	0.939384i	$0.388602\pi$
$662$	−20.0845	−0.780606
$663$	7.34274	0.285169
$664$	−30.1952	−1.17180
$665$	−2.23372	−0.0866198
$666$	−22.0659	−0.855037
$667$	−0.843500	−0.0326604
$668$	43.0195	1.66447
$669$	1.41913	0.0548668
$670$	−34.8218	−1.34528
$671$	−0.224215	−0.00865574
$672$	−4.29998	−0.165876
$673$	−2.06113	−0.0794508	−0.0397254	−	0.999211i	$-0.512648\pi$
$673$	−2.06113	−0.0794508	−0.0397254	+	0.999211i	$0.512648\pi$
$674$	−25.7006	−0.989949
$675$	11.5420	0.444253
$676$	−1.42911	−0.0549656
$677$	−9.07207	−0.348668	−0.174334	−	0.984687i	$-0.555777\pi$
$677$	−9.07207	−0.348668	−0.174334	+	0.984687i	$0.555777\pi$
$678$	41.2480	1.58412
$679$	2.03009	0.0779075
$680$	3.20655	0.122966
$681$	−13.5287	−0.518420
$682$	13.1397	0.503146
$683$	33.2896	1.27379	0.636895	−	0.770951i	$-0.280219\pi$
$683$	33.2896	1.27379	0.636895	+	0.770951i	$0.280219\pi$
$684$	20.9671	0.801697
$685$	−19.9661	−0.762865
$686$	−10.1901	−0.389060
$687$	−40.7307	−1.55397
$688$	−0.661206	−0.0252082
$689$	31.9431	1.21693
$690$	12.1977	0.464357
$691$	−0.528484	−0.0201045	−0.0100522	−	0.999949i	$-0.503200\pi$
$691$	−0.528484	−0.0201045	−0.0100522	+	0.999949i	$0.503200\pi$
$692$	−23.4486	−0.891381
$693$	−0.423129	−0.0160733
$694$	49.6968	1.88646
$695$	−6.86096	−0.260251
$696$	−2.15004	−0.0814972
$697$	−5.24681	−0.198737
$698$	3.11012	0.117720
$699$	−22.4626	−0.849613
$700$	3.28477	0.124153
$701$	−40.2495	−1.52020	−0.760102	−	0.649804i	$-0.774851\pi$
$701$	−40.2495	−1.52020	−0.760102	+	0.649804i	$0.774851\pi$
$702$	−28.1307	−1.06172
$703$	39.3422	1.48382
$704$	−13.0480	−0.491764
$705$	−19.4451	−0.732345
$706$	−27.1681	−1.02248
$707$	5.32481	0.200260
$708$	0.629743	0.0236672
$709$	−19.5235	−0.733222	−0.366611	−	0.930374i	$-0.619482\pi$
$709$	−19.5235	−0.733222	−0.366611	+	0.930374i	$0.619482\pi$
$710$	−0.825447	−0.0309785
$711$	−3.48933	−0.130860
$712$	−16.8591	−0.631820
$713$	11.5775	0.433580
$714$	−1.52096	−0.0569203
$715$	−4.64994	−0.173898
$716$	−7.77679	−0.290632
$717$	−23.8628	−0.891174
$718$	35.4196	1.32185
$719$	−26.8303	−1.00060	−0.500301	−	0.865852i	$-0.666777\pi$
$719$	−26.8303	−1.00060	−0.500301	+	0.865852i	$0.666777\pi$
$720$	−1.12949	−0.0420937
$721$	0.961038	0.0357909
$722$	−18.7979	−0.699587
$723$	−20.9767	−0.780133
$724$	75.5074	2.80621
$725$	−1.39074	−0.0516508
$726$	−4.67552	−0.173525
$727$	30.6278	1.13592	0.567961	−	0.823055i	$-0.307732\pi$
$727$	30.6278	1.13592	0.567961	+	0.823055i	$0.307732\pi$
$728$	−2.81224	−0.104228
$729$	7.34278	0.271955
$730$	41.5016	1.53604
$731$	−1.00000	−0.0369863
$732$	−1.43353	−0.0529848
$733$	29.0359	1.07247	0.536233	−	0.844070i	$-0.319847\pi$
$733$	29.0359	1.07247	0.536233	+	0.844070i	$0.319847\pi$
$734$	−33.3349	−1.23041
$735$	−18.7764	−0.692579
$736$	−12.6618	−0.466721
$737$	11.7607	0.433210
$738$	−15.3865	−0.566386
$739$	16.6320	0.611820	0.305910	−	0.952060i	$-0.401039\pi$
$739$	16.6320	0.611820	0.305910	+	0.952060i	$0.401039\pi$
$740$	30.4654	1.11993
$741$	−38.3919	−1.41036
$742$	−6.61660	−0.242903
$743$	40.0253	1.46839	0.734193	−	0.678940i	$-0.237561\pi$
$743$	40.0253	1.46839	0.734193	+	0.678940i	$0.237561\pi$
$744$	29.5105	1.08191
$745$	24.1319	0.884126
$746$	−47.9801	−1.75668
$747$	16.0859	0.588552
$748$	−3.08298	−0.112725
$749$	−5.49685	−0.200850
$750$	50.8127	1.85542
$751$	8.24102	0.300719	0.150360	−	0.988631i	$-0.451957\pi$
$751$	8.24102	0.300719	0.150360	+	0.988631i	$0.451957\pi$
$752$	4.72081	0.172150
$753$	−50.5044	−1.84048
$754$	3.38957	0.123441
$755$	−2.49408	−0.0907690
$756$	3.53420	0.128537
$757$	−23.8527	−0.866941	−0.433471	−	0.901168i	$-0.642711\pi$
$757$	−23.8527	−0.866941	−0.433471	+	0.901168i	$0.642711\pi$
$758$	17.0878	0.620657
$759$	−4.11963	−0.149533
$760$	−16.7656	−0.608153
$761$	−22.2992	−0.808344	−0.404172	−	0.914683i	$-0.632440\pi$
$761$	−22.2992	−0.808344	−0.404172	+	0.914683i	$0.632440\pi$
$762$	−19.5054	−0.706607
$763$	0.181329	0.00656456
$764$	−14.6478	−0.529937
$765$	−1.70823	−0.0617612
$766$	28.0252	1.01259
$767$	−0.348746	−0.0125925
$768$	−23.8196	−0.859514
$769$	19.8319	0.715157	0.357578	−	0.933883i	$-0.383602\pi$
$769$	19.8319	0.715157	0.357578	+	0.933883i	$0.383602\pi$
$770$	0.963175	0.0347104
$771$	−9.75858	−0.351447
$772$	29.5507	1.06355
$773$	−43.0339	−1.54782	−0.773910	−	0.633295i	$-0.781702\pi$
$773$	−43.0339	−1.54782	−0.773910	+	0.633295i	$0.781702\pi$
$774$	−2.93255	−0.105408
$775$	19.0887	0.685685
$776$	15.2372	0.546985
$777$	−5.07614	−0.182106
$778$	19.5831	0.702089
$779$	27.4332	0.982897
$780$	−29.7295	−1.06449
$781$	0.278786	0.00997573
$782$	−4.47864	−0.160156
$783$	−1.49635	−0.0534750
$784$	4.55847	0.162803
$785$	−10.3607	−0.369789
$786$	86.2546	3.07660
$787$	16.1532	0.575800	0.287900	−	0.957661i	$-0.407043\pi$
$787$	16.1532	0.575800	0.287900	+	0.957661i	$0.407043\pi$
$788$	−15.8853	−0.565892
$789$	−19.7766	−0.704065
$790$	7.94282	0.282593
$791$	2.86985	0.102040
$792$	−3.17589	−0.112850
$793$	0.793876	0.0281914
$794$	−16.8753	−0.598884
$795$	−24.5709	−0.871438
$796$	−81.9013	−2.90291
$797$	−30.8393	−1.09238	−0.546192	−	0.837660i	$-0.683923\pi$
$797$	−30.8393	−1.09238	−0.546192	+	0.837660i	$0.683923\pi$
$798$	7.95240	0.281512
$799$	7.13969	0.252584
$800$	−20.8765	−0.738096
$801$	8.98135	0.317341
$802$	−71.5478	−2.52644
$803$	−14.0167	−0.494638
$804$	75.1923	2.65183
$805$	0.848659	0.0299113
$806$	−46.5236	−1.63872
$807$	−55.4324	−1.95131
$808$	39.9665	1.40602
$809$	−31.3557	−1.10241	−0.551204	−	0.834371i	$-0.685831\pi$
$809$	−31.3557	−1.10241	−0.551204	+	0.834371i	$0.685831\pi$
$810$	33.1922	1.16625
$811$	41.0527	1.44156	0.720778	−	0.693166i	$-0.243785\pi$
$811$	41.0527	1.44156	0.720778	+	0.693166i	$0.243785\pi$
$812$	−0.425848	−0.0149443
$813$	−45.1027	−1.58182
$814$	−16.9643	−0.594598
$815$	3.86236	0.135293
$816$	1.37122	0.0480024
$817$	5.22856	0.182924
$818$	−38.6024	−1.34970
$819$	1.49817	0.0523502
$820$	21.2435	0.741854
$821$	1.64628	0.0574554	0.0287277	−	0.999587i	$-0.490854\pi$
$821$	1.64628	0.0574554	0.0287277	+	0.999587i	$0.490854\pi$
$822$	71.0826	2.47929
$823$	−35.7731	−1.24697	−0.623486	−	0.781835i	$-0.714284\pi$
$823$	−35.7731	−1.24697	−0.623486	+	0.781835i	$0.714284\pi$
$824$	7.21327	0.251286
$825$	−6.79233	−0.236479
$826$	0.0722383	0.00251349
$827$	−35.5788	−1.23720	−0.618599	−	0.785707i	$-0.712299\pi$
$827$	−35.5788	−1.23720	−0.618599	+	0.785707i	$0.712299\pi$
$828$	−7.96606	−0.276840
$829$	−5.52846	−0.192011	−0.0960057	−	0.995381i	$-0.530607\pi$
$829$	−5.52846	−0.192011	−0.0960057	+	0.995381i	$0.530607\pi$
$830$	−36.6166	−1.27098
$831$	−61.5103	−2.13377
$832$	46.1988	1.60165
$833$	6.89418	0.238869
$834$	24.4262	0.845809
$835$	18.3254	0.634178
$836$	16.1195	0.557505
$837$	20.5381	0.709902
$838$	−13.9611	−0.482279
$839$	39.0304	1.34748	0.673739	−	0.738969i	$-0.264687\pi$
$839$	39.0304	1.34748	0.673739	+	0.738969i	$0.264687\pi$
$840$	2.16319	0.0746373
$841$	−28.8197	−0.993783
$842$	27.6105	0.951520
$843$	5.18319	0.178518
$844$	−12.6031	−0.433816
$845$	−0.608771	−0.0209423
$846$	20.9375	0.719847
$847$	−0.325302	−0.0111775
$848$	5.96522	0.204846
$849$	31.4875	1.08065
$850$	−7.38426	−0.253278
$851$	−14.9473	−0.512388
$852$	1.78243	0.0610649
$853$	−31.3143	−1.07218	−0.536091	−	0.844160i	$-0.680100\pi$
$853$	−31.3143	−1.07218	−0.536091	+	0.844160i	$0.680100\pi$
$854$	−0.164441	−0.00562707
$855$	8.93157	0.305453
$856$	−41.2578	−1.41016
$857$	−7.47999	−0.255512	−0.127756	−	0.991806i	$-0.540777\pi$
$857$	−7.47999	−0.255512	−0.127756	+	0.991806i	$0.540777\pi$
$858$	16.5546	0.565163
$859$	10.1188	0.345250	0.172625	−	0.984988i	$-0.444775\pi$
$859$	10.1188	0.345250	0.172625	+	0.984988i	$0.444775\pi$
$860$	4.04883	0.138064
$861$	−3.53959	−0.120629
$862$	52.0231	1.77191
$863$	29.8717	1.01684	0.508422	−	0.861108i	$-0.330229\pi$
$863$	29.8717	1.01684	0.508422	+	0.861108i	$0.330229\pi$
$864$	−22.4617	−0.764164
$865$	−9.98863	−0.339624
$866$	42.1686	1.43295
$867$	2.07382	0.0704306
$868$	5.84499	0.198392
$869$	−2.68260	−0.0910010
$870$	−2.60728	−0.0883951
$871$	−41.6408	−1.41095
$872$	1.36101	0.0460895
$873$	−8.11735	−0.274731
$874$	23.4168	0.792086
$875$	3.53532	0.119516
$876$	−89.6163	−3.02785
$877$	13.7855	0.465503	0.232752	−	0.972536i	$-0.425227\pi$
$877$	13.7855	0.465503	0.232752	+	0.972536i	$0.425227\pi$
$878$	13.7984	0.465673
$879$	14.4706	0.488082
$880$	−0.868353	−0.0292722
$881$	−9.75647	−0.328704	−0.164352	−	0.986402i	$-0.552553\pi$
$881$	−9.75647	−0.328704	−0.164352	+	0.986402i	$0.552553\pi$
$882$	20.2175	0.680760
$883$	24.1636	0.813171	0.406586	−	0.913613i	$-0.366719\pi$
$883$	24.1636	0.813171	0.406586	+	0.913613i	$0.366719\pi$
$884$	10.9159	0.367140
$885$	0.268258	0.00901739
$886$	5.80228	0.194931
$887$	37.4053	1.25595	0.627973	−	0.778235i	$-0.283885\pi$
$887$	37.4053	1.25595	0.627973	+	0.778235i	$0.283885\pi$
$888$	−38.1001	−1.27855
$889$	−1.35710	−0.0455157
$890$	−20.4444	−0.685297
$891$	−11.2103	−0.375559
$892$	2.10971	0.0706382
$893$	−37.3303	−1.24921
$894$	−85.9137	−2.87339
$895$	−3.31276	−0.110733
$896$	−5.42257	−0.181155
$897$	14.5863	0.487023
$898$	78.9570	2.63483
$899$	−2.47472	−0.0825364
$900$	−13.1342	−0.437808
$901$	9.02173	0.300557
$902$	−11.8292	−0.393868
$903$	−0.674617	−0.0224499
$904$	21.5403	0.716420
$905$	32.1647	1.06919
$906$	8.87935	0.294997
$907$	−7.36050	−0.244402	−0.122201	−	0.992505i	$-0.538995\pi$
$907$	−7.36050	−0.244402	−0.122201	+	0.992505i	$0.538995\pi$
$908$	−20.1120	−0.667439
$909$	−21.2914	−0.706192
$910$	−3.41030	−0.113050
$911$	−7.68868	−0.254737	−0.127369	−	0.991855i	$-0.540653\pi$
$911$	−7.68868	−0.254737	−0.127369	+	0.991855i	$0.540653\pi$
$912$	−7.16951	−0.237406
$913$	12.3668	0.409283
$914$	−52.3806	−1.73260
$915$	−0.610655	−0.0201876
$916$	−60.5509	−2.00066
$917$	6.00121	0.198177
$918$	−7.94498	−0.262224
$919$	0.433699	0.0143064	0.00715321	−	0.999974i	$-0.497723\pi$
$919$	0.433699	0.0143064	0.00715321	+	0.999974i	$0.497723\pi$
$920$	6.36979	0.210006
$921$	50.8865	1.67677
$922$	−14.7439	−0.485566
$923$	−0.987092	−0.0324905
$924$	−2.07983	−0.0684214
$925$	−24.6448	−0.810314
$926$	−23.7436	−0.780265
$927$	−3.84274	−0.126212
$928$	2.70650	0.0888451
$929$	−15.2402	−0.500015	−0.250008	−	0.968244i	$-0.580433\pi$
$929$	−15.2402	−0.500015	−0.250008	+	0.968244i	$0.580433\pi$
$930$	35.7863	1.17348
$931$	−36.0466	−1.18138
$932$	−33.3933	−1.09383
$933$	15.7055	0.514176
$934$	27.0753	0.885929
$935$	−1.31329	−0.0429491
$936$	11.2448	0.367548
$937$	12.4759	0.407569	0.203784	−	0.979016i	$-0.434676\pi$
$937$	12.4759	0.407569	0.203784	+	0.979016i	$0.434676\pi$
$938$	8.62537	0.281628
$939$	27.1845	0.887133
$940$	−28.9074	−0.942857
$941$	−23.3479	−0.761119	−0.380560	−	0.924756i	$-0.624269\pi$
$941$	−23.3479	−0.761119	−0.380560	+	0.924756i	$0.624269\pi$
$942$	36.8858	1.20180
$943$	−10.4227	−0.339411
$944$	−0.0651266	−0.00211969
$945$	1.50550	0.0489738
$946$	−2.25455	−0.0733016
$947$	−42.3225	−1.37530	−0.687649	−	0.726043i	$-0.741357\pi$
$947$	−42.3225	−1.37530	−0.687649	+	0.726043i	$0.741357\pi$
$948$	−17.1513	−0.557049
$949$	49.6287	1.61102
$950$	38.6090	1.25264
$951$	−8.89145	−0.288325
$952$	−0.794264	−0.0257422
$953$	−27.0693	−0.876859	−0.438430	−	0.898765i	$-0.644465\pi$
$953$	−27.0693	−0.876859	−0.438430	+	0.898765i	$0.644465\pi$
$954$	26.4567	0.856566
$955$	−6.23965	−0.201910
$956$	−35.4749	−1.14734
$957$	0.880581	0.0284651
$958$	−57.3116	−1.85165
$959$	4.94561	0.159702
$960$	−35.5364	−1.14693
$961$	2.96678	0.0957025
$962$	60.0652	1.93658
$963$	21.9793	0.708273
$964$	−31.1844	−1.00438
$965$	12.5880	0.405223
$966$	−3.02137	−0.0972109
$967$	−54.1184	−1.74033	−0.870164	−	0.492761i	$-0.835988\pi$
$967$	−54.1184	−1.74033	−0.870164	+	0.492761i	$0.835988\pi$
$968$	−2.44162	−0.0784767
$969$	−10.8431	−0.348330
$970$	18.4776	0.593281
$971$	−38.5443	−1.23695	−0.618473	−	0.785806i	$-0.712249\pi$
$971$	−38.5443	−1.23695	−0.618473	+	0.785806i	$0.712249\pi$
$972$	−39.0803	−1.25350
$973$	1.69946	0.0544823
$974$	−72.1229	−2.31097
$975$	24.0495	0.770201
$976$	0.148253	0.00474545
$977$	−33.7275	−1.07904	−0.539520	−	0.841973i	$-0.681394\pi$
$977$	−33.7275	−1.07904	−0.539520	+	0.841973i	$0.681394\pi$
$978$	−13.7506	−0.439697
$979$	6.90487	0.220680
$980$	−27.9134	−0.891660
$981$	−0.725050	−0.0231491
$982$	54.4328	1.73702
$983$	−36.5986	−1.16731	−0.583657	−	0.812000i	$-0.698379\pi$
$983$	−36.5986	−1.16731	−0.583657	+	0.812000i	$0.698379\pi$
$984$	−26.5671	−0.846929
$985$	−6.76684	−0.215610
$986$	0.957320	0.0304873
$987$	4.81656	0.153313
$988$	−57.0741	−1.81577
$989$	−1.98649	−0.0631668
$990$	−3.85128	−0.122402
$991$	−2.11266	−0.0671108	−0.0335554	−	0.999437i	$-0.510683\pi$
$991$	−2.11266	−0.0671108	−0.0335554	+	0.999437i	$0.510683\pi$
$992$	−37.1481	−1.17945
$993$	18.4745	0.586271
$994$	0.204464	0.00648519
$995$	−34.8883	−1.10603
$996$	79.0679	2.50536
$997$	2.70245	0.0855876	0.0427938	−	0.999084i	$-0.486374\pi$
$997$	2.70245	0.0855876	0.0427938	+	0.999084i	$0.486374\pi$
$998$	−13.7156	−0.434160
$999$	−26.5161	−0.838933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.8	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.8	✓	62	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)

\(f(q)\)	\(=\)	\(q-2.25455 q^{2} +2.07382 q^{3} +3.08298 q^{4} +1.31329 q^{5} -4.67552 q^{6} -0.325302 q^{7} -2.44162 q^{8} +1.30073 q^{9} +O(q^{10})\)	\(q-2.25455 q^{2} +2.07382 q^{3} +3.08298 q^{4} +1.31329 q^{5} -4.67552 q^{6} -0.325302 q^{7} -2.44162 q^{8} +1.30073 q^{9} -2.96087 q^{10} +1.00000 q^{11} +6.39354 q^{12} -3.54069 q^{13} +0.733408 q^{14} +2.72352 q^{15} -0.661206 q^{16} -1.00000 q^{17} -2.93255 q^{18} +5.22856 q^{19} +4.04883 q^{20} -0.674617 q^{21} -2.25455 q^{22} -1.98649 q^{23} -5.06348 q^{24} -3.27528 q^{25} +7.98264 q^{26} -3.52398 q^{27} -1.00290 q^{28} +0.424618 q^{29} -6.14030 q^{30} -5.82810 q^{31} +6.37396 q^{32} +2.07382 q^{33} +2.25455 q^{34} -0.427215 q^{35} +4.01011 q^{36} +7.52448 q^{37} -11.7880 q^{38} -7.34274 q^{39} -3.20655 q^{40} +5.24681 q^{41} +1.52096 q^{42} +1.00000 q^{43} +3.08298 q^{44} +1.70823 q^{45} +4.47864 q^{46} -7.13969 q^{47} -1.37122 q^{48} -6.89418 q^{49} +7.38426 q^{50} -2.07382 q^{51} -10.9159 q^{52} -9.02173 q^{53} +7.94498 q^{54} +1.31329 q^{55} +0.794264 q^{56} +10.8431 q^{57} -0.957320 q^{58} +0.0984967 q^{59} +8.39655 q^{60} -0.224215 q^{61} +13.1397 q^{62} -0.423129 q^{63} -13.0480 q^{64} -4.64994 q^{65} -4.67552 q^{66} +11.7607 q^{67} -3.08298 q^{68} -4.11963 q^{69} +0.963175 q^{70} +0.278786 q^{71} -3.17589 q^{72} -14.0167 q^{73} -16.9643 q^{74} -6.79233 q^{75} +16.1195 q^{76} -0.325302 q^{77} +16.5546 q^{78} -2.68260 q^{79} -0.868353 q^{80} -11.2103 q^{81} -11.8292 q^{82} +12.3668 q^{83} -2.07983 q^{84} -1.31329 q^{85} -2.25455 q^{86} +0.880581 q^{87} -2.44162 q^{88} +6.90487 q^{89} -3.85128 q^{90} +1.15179 q^{91} -6.12431 q^{92} -12.0864 q^{93} +16.0968 q^{94} +6.86659 q^{95} +13.2184 q^{96} -6.24062 q^{97} +15.5432 q^{98} +1.30073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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