LMFDB - Embedded newform 8041.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.63329 q^{2} -0.751907 q^{3} +4.93424 q^{4} +0.880982 q^{5} +1.97999 q^{6} -0.474275 q^{7} -7.72671 q^{8} -2.43464 q^{9} +O(q^{10})$	\(q-2.63329 q^{2} -0.751907 q^{3} +4.93424 q^{4} +0.880982 q^{5} +1.97999 q^{6} -0.474275 q^{7} -7.72671 q^{8} -2.43464 q^{9} -2.31989 q^{10} -1.00000 q^{11} -3.71009 q^{12} +1.67108 q^{13} +1.24891 q^{14} -0.662417 q^{15} +10.4782 q^{16} +1.00000 q^{17} +6.41111 q^{18} -5.38462 q^{19} +4.34698 q^{20} +0.356611 q^{21} +2.63329 q^{22} -6.05594 q^{23} +5.80977 q^{24} -4.22387 q^{25} -4.40046 q^{26} +4.08634 q^{27} -2.34019 q^{28} -2.82389 q^{29} +1.74434 q^{30} +0.261708 q^{31} -12.1388 q^{32} +0.751907 q^{33} -2.63329 q^{34} -0.417828 q^{35} -12.0131 q^{36} -0.476486 q^{37} +14.1793 q^{38} -1.25650 q^{39} -6.80710 q^{40} +1.06104 q^{41} -0.939062 q^{42} -1.00000 q^{43} -4.93424 q^{44} -2.14487 q^{45} +15.9471 q^{46} +9.77914 q^{47} -7.87866 q^{48} -6.77506 q^{49} +11.1227 q^{50} -0.751907 q^{51} +8.24553 q^{52} +1.50582 q^{53} -10.7605 q^{54} -0.880982 q^{55} +3.66459 q^{56} +4.04874 q^{57} +7.43614 q^{58} -9.57681 q^{59} -3.26852 q^{60} -2.96557 q^{61} -0.689155 q^{62} +1.15469 q^{63} +11.0087 q^{64} +1.47220 q^{65} -1.97999 q^{66} -10.9122 q^{67} +4.93424 q^{68} +4.55351 q^{69} +1.10026 q^{70} +5.99742 q^{71} +18.8117 q^{72} -6.44053 q^{73} +1.25473 q^{74} +3.17596 q^{75} -26.5690 q^{76} +0.474275 q^{77} +3.30874 q^{78} +1.26215 q^{79} +9.23114 q^{80} +4.23135 q^{81} -2.79404 q^{82} -3.16769 q^{83} +1.75960 q^{84} +0.880982 q^{85} +2.63329 q^{86} +2.12331 q^{87} +7.72671 q^{88} -6.83320 q^{89} +5.64807 q^{90} -0.792554 q^{91} -29.8815 q^{92} -0.196780 q^{93} -25.7513 q^{94} -4.74376 q^{95} +9.12729 q^{96} -3.79744 q^{97} +17.8407 q^{98} +2.43464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.63329	−1.86202	−0.931010	−	0.364993i	$-0.881071\pi$
$2$	−2.63329	−1.86202	−0.931010	+	0.364993i	$0.881071\pi$
$3$	−0.751907	−0.434114	−0.217057	−	0.976159i	$-0.569646\pi$
$3$	−0.751907	−0.434114	−0.217057	+	0.976159i	$0.569646\pi$
$4$	4.93424	2.46712
$5$	0.880982	0.393987	0.196994	−	0.980405i	$-0.436882\pi$
$5$	0.880982	0.393987	0.196994	+	0.980405i	$0.436882\pi$
$6$	1.97999	0.808329
$7$	−0.474275	−0.179259	−0.0896296	−	0.995975i	$-0.528568\pi$
$7$	−0.474275	−0.179259	−0.0896296	+	0.995975i	$0.528568\pi$
$8$	−7.72671	−2.73181
$9$	−2.43464	−0.811545
$10$	−2.31989	−0.733612
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.71009	−1.07101
$13$	1.67108	0.463475	0.231738	−	0.972778i	$-0.425559\pi$
$13$	1.67108	0.463475	0.231738	+	0.972778i	$0.425559\pi$
$14$	1.24891	0.333784
$15$	−0.662417	−0.171035
$16$	10.4782	2.61956
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.41111	1.51111
$19$	−5.38462	−1.23532	−0.617659	−	0.786446i	$-0.711919\pi$
$19$	−5.38462	−1.23532	−0.617659	+	0.786446i	$0.711919\pi$
$20$	4.34698	0.972014
$21$	0.356611	0.0778189
$22$	2.63329	0.561420
$23$	−6.05594	−1.26275	−0.631375	−	0.775477i	$-0.717509\pi$
$23$	−6.05594	−1.26275	−0.631375	+	0.775477i	$0.717509\pi$
$24$	5.80977	1.18592
$25$	−4.22387	−0.844774
$26$	−4.40046	−0.863000
$27$	4.08634	0.786417
$28$	−2.34019	−0.442254
$29$	−2.82389	−0.524384	−0.262192	−	0.965016i	$-0.584445\pi$
$29$	−2.82389	−0.524384	−0.262192	+	0.965016i	$0.584445\pi$
$30$	1.74434	0.318471
$31$	0.261708	0.0470042	0.0235021	−	0.999724i	$-0.492518\pi$
$31$	0.261708	0.0470042	0.0235021	+	0.999724i	$0.492518\pi$
$32$	−12.1388	−2.14587
$33$	0.751907	0.130890
$34$	−2.63329	−0.451606
$35$	−0.417828	−0.0706258
$36$	−12.0131	−2.00218
$37$	−0.476486	−0.0783339	−0.0391669	−	0.999233i	$-0.512470\pi$
$37$	−0.476486	−0.0783339	−0.0391669	+	0.999233i	$0.512470\pi$
$38$	14.1793	2.30019
$39$	−1.25650	−0.201201
$40$	−6.80710	−1.07630
$41$	1.06104	0.165707	0.0828536	−	0.996562i	$-0.473597\pi$
$41$	1.06104	0.165707	0.0828536	+	0.996562i	$0.473597\pi$
$42$	−0.939062	−0.144900
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−4.93424	−0.743864
$45$	−2.14487	−0.319738
$46$	15.9471	2.35127
$47$	9.77914	1.42643	0.713217	−	0.700943i	$-0.247237\pi$
$47$	9.77914	1.42643	0.713217	+	0.700943i	$0.247237\pi$
$48$	−7.87866	−1.13719
$49$	−6.77506	−0.967866
$50$	11.1227	1.57299
$51$	−0.751907	−0.105288
$52$	8.24553	1.14345
$53$	1.50582	0.206840	0.103420	−	0.994638i	$-0.467021\pi$
$53$	1.50582	0.206840	0.103420	+	0.994638i	$0.467021\pi$
$54$	−10.7605	−1.46432
$55$	−0.880982	−0.118792
$56$	3.66459	0.489701
$57$	4.04874	0.536269
$58$	7.43614	0.976413
$59$	−9.57681	−1.24679	−0.623397	−	0.781905i	$-0.714248\pi$
$59$	−9.57681	−1.24679	−0.623397	+	0.781905i	$0.714248\pi$
$60$	−3.26852	−0.421965
$61$	−2.96557	−0.379702	−0.189851	−	0.981813i	$-0.560800\pi$
$61$	−2.96557	−0.379702	−0.189851	+	0.981813i	$0.560800\pi$
$62$	−0.689155	−0.0875228
$63$	1.15469	0.145477
$64$	11.0087	1.37609
$65$	1.47220	0.182603
$66$	−1.97999	−0.243720
$67$	−10.9122	−1.33313	−0.666567	−	0.745445i	$-0.732237\pi$
$67$	−10.9122	−1.33313	−0.666567	+	0.745445i	$0.732237\pi$
$68$	4.93424	0.598364
$69$	4.55351	0.548178
$70$	1.10026	0.131507
$71$	5.99742	0.711762	0.355881	−	0.934531i	$-0.384181\pi$
$71$	5.99742	0.711762	0.355881	+	0.934531i	$0.384181\pi$
$72$	18.8117	2.21698
$73$	−6.44053	−0.753807	−0.376903	−	0.926253i	$-0.623011\pi$
$73$	−6.44053	−0.753807	−0.376903	+	0.926253i	$0.623011\pi$
$74$	1.25473	0.145859
$75$	3.17596	0.366728
$76$	−26.5690	−3.04768
$77$	0.474275	0.0540487
$78$	3.30874	0.374641
$79$	1.26215	0.142003	0.0710016	−	0.997476i	$-0.477380\pi$
$79$	1.26215	0.142003	0.0710016	+	0.997476i	$0.477380\pi$
$80$	9.23114	1.03207
$81$	4.23135	0.470150
$82$	−2.79404	−0.308550
$83$	−3.16769	−0.347699	−0.173850	−	0.984772i	$-0.555621\pi$
$83$	−3.16769	−0.347699	−0.173850	+	0.984772i	$0.555621\pi$
$84$	1.75960	0.191989
$85$	0.880982	0.0955559
$86$	2.63329	0.283955
$87$	2.12331	0.227642
$88$	7.72671	0.823670
$89$	−6.83320	−0.724318	−0.362159	−	0.932116i	$-0.617960\pi$
$89$	−6.83320	−0.724318	−0.362159	+	0.932116i	$0.617960\pi$
$90$	5.64807	0.595359
$91$	−0.792554	−0.0830822
$92$	−29.8815	−3.11536
$93$	−0.196780	−0.0204052
$94$	−25.7513	−2.65605
$95$	−4.74376	−0.486699
$96$	9.12729	0.931550
$97$	−3.79744	−0.385572	−0.192786	−	0.981241i	$-0.561752\pi$
$97$	−3.79744	−0.385572	−0.192786	+	0.981241i	$0.561752\pi$
$98$	17.8407	1.80219
$99$	2.43464	0.244690
$100$	−20.8416	−2.08416
$101$	8.97850	0.893394	0.446697	−	0.894685i	$-0.352600\pi$
$101$	8.97850	0.893394	0.446697	+	0.894685i	$0.352600\pi$
$102$	1.97999	0.196049
$103$	−3.12019	−0.307441	−0.153721	−	0.988114i	$-0.549126\pi$
$103$	−3.12019	−0.307441	−0.153721	+	0.988114i	$0.549126\pi$
$104$	−12.9120	−1.26612
$105$	0.314168	0.0306597
$106$	−3.96527	−0.385141
$107$	4.93516	0.477100	0.238550	−	0.971130i	$-0.423328\pi$
$107$	4.93516	0.477100	0.238550	+	0.971130i	$0.423328\pi$
$108$	20.1630	1.94018
$109$	−1.62584	−0.155727	−0.0778634	−	0.996964i	$-0.524810\pi$
$109$	−1.62584	−0.155727	−0.0778634	+	0.996964i	$0.524810\pi$
$110$	2.31989	0.221192
$111$	0.358274	0.0340058
$112$	−4.96957	−0.469580
$113$	5.03982	0.474107	0.237053	−	0.971497i	$-0.423818\pi$
$113$	5.03982	0.474107	0.237053	+	0.971497i	$0.423818\pi$
$114$	−10.6615	−0.998543
$115$	−5.33518	−0.497508
$116$	−13.9338	−1.29372
$117$	−4.06848	−0.376131
$118$	25.2186	2.32156
$119$	−0.474275	−0.0434767
$120$	5.11831	0.467235
$121$	1.00000	0.0909091
$122$	7.80921	0.707012
$123$	−0.797807	−0.0719358
$124$	1.29133	0.115965
$125$	−8.12607	−0.726817
$126$	−3.04063	−0.270881
$127$	−21.2974	−1.88984	−0.944920	−	0.327301i	$-0.893861\pi$
$127$	−21.2974	−1.88984	−0.944920	+	0.327301i	$0.893861\pi$
$128$	−4.71142	−0.416434
$129$	0.751907	0.0662018
$130$	−3.87672	−0.340011
$131$	18.5474	1.62050	0.810248	−	0.586087i	$-0.199332\pi$
$131$	18.5474	1.62050	0.810248	+	0.586087i	$0.199332\pi$
$132$	3.71009	0.322922
$133$	2.55379	0.221442
$134$	28.7349	2.48232
$135$	3.60000	0.309838
$136$	−7.72671	−0.662560
$137$	−13.8272	−1.18134	−0.590669	−	0.806914i	$-0.701136\pi$
$137$	−13.8272	−1.18134	−0.590669	+	0.806914i	$0.701136\pi$
$138$	−11.9907	−1.02072
$139$	18.1451	1.53905	0.769523	−	0.638619i	$-0.220494\pi$
$139$	18.1451	1.53905	0.769523	+	0.638619i	$0.220494\pi$
$140$	−2.06166	−0.174242
$141$	−7.35301	−0.619235
$142$	−15.7930	−1.32532
$143$	−1.67108	−0.139743
$144$	−25.5107	−2.12589
$145$	−2.48780	−0.206600
$146$	16.9598	1.40360
$147$	5.09422	0.420164
$148$	−2.35110	−0.193259
$149$	6.88287	0.563867	0.281933	−	0.959434i	$-0.409024\pi$
$149$	6.88287	0.563867	0.281933	+	0.959434i	$0.409024\pi$
$150$	−8.36324	−0.682855
$151$	0.799440	0.0650575	0.0325288	−	0.999471i	$-0.489644\pi$
$151$	0.799440	0.0650575	0.0325288	+	0.999471i	$0.489644\pi$
$152$	41.6054	3.37465
$153$	−2.43464	−0.196829
$154$	−1.24891	−0.100640
$155$	0.230560	0.0185191
$156$	−6.19987	−0.496387
$157$	−15.4543	−1.23339	−0.616694	−	0.787203i	$-0.711528\pi$
$157$	−15.4543	−1.23339	−0.616694	+	0.787203i	$0.711528\pi$
$158$	−3.32362	−0.264413
$159$	−1.13224	−0.0897923
$160$	−10.6941	−0.845443
$161$	2.87218	0.226360
$162$	−11.1424	−0.875430
$163$	−12.2482	−0.959355	−0.479677	−	0.877445i	$-0.659246\pi$
$163$	−12.2482	−0.959355	−0.479677	+	0.877445i	$0.659246\pi$
$164$	5.23544	0.408819
$165$	0.662417	0.0515691
$166$	8.34147	0.647423
$167$	16.5462	1.28038	0.640191	−	0.768216i	$-0.278855\pi$
$167$	16.5462	1.28038	0.640191	+	0.768216i	$0.278855\pi$
$168$	−2.75543	−0.212586
$169$	−10.2075	−0.785191
$170$	−2.31989	−0.177927
$171$	13.1096	1.00252
$172$	−4.93424	−0.376232
$173$	−17.2655	−1.31267	−0.656336	−	0.754468i	$-0.727895\pi$
$173$	−17.2655	−1.31267	−0.656336	+	0.754468i	$0.727895\pi$
$174$	−5.59129	−0.423875
$175$	2.00328	0.151434
$176$	−10.4782	−0.789827
$177$	7.20088	0.541251
$178$	17.9938	1.34869
$179$	14.7000	1.09873	0.549363	−	0.835584i	$-0.314870\pi$
$179$	14.7000	1.09873	0.549363	+	0.835584i	$0.314870\pi$
$180$	−10.5833	−0.788833
$181$	5.52793	0.410888	0.205444	−	0.978669i	$-0.434136\pi$
$181$	5.52793	0.410888	0.205444	+	0.978669i	$0.434136\pi$
$182$	2.08703	0.154701
$183$	2.22983	0.164834
$184$	46.7925	3.44959
$185$	−0.419776	−0.0308626
$186$	0.518181	0.0379949
$187$	−1.00000	−0.0731272
$188$	48.2526	3.51918
$189$	−1.93805	−0.140972
$190$	12.4917	0.906244
$191$	6.10212	0.441534	0.220767	−	0.975327i	$-0.429144\pi$
$191$	6.10212	0.441534	0.220767	+	0.975327i	$0.429144\pi$
$192$	−8.27751	−0.597378
$193$	27.3864	1.97132	0.985660	−	0.168744i	$-0.0539713\pi$
$193$	27.3864	1.97132	0.985660	+	0.168744i	$0.0539713\pi$
$194$	9.99977	0.717942
$195$	−1.10695	−0.0792707
$196$	−33.4298	−2.38784
$197$	11.0940	0.790418	0.395209	−	0.918591i	$-0.370672\pi$
$197$	11.0940	0.790418	0.395209	+	0.918591i	$0.370672\pi$
$198$	−6.41111	−0.455618
$199$	9.97683	0.707239	0.353619	−	0.935389i	$-0.384951\pi$
$199$	9.97683	0.707239	0.353619	+	0.935389i	$0.384951\pi$
$200$	32.6366	2.30776
$201$	8.20494	0.578732
$202$	−23.6430	−1.66352
$203$	1.33930	0.0940006
$204$	−3.71009	−0.259758
$205$	0.934761	0.0652865
$206$	8.21638	0.572462
$207$	14.7440	1.02478
$208$	17.5100	1.21410
$209$	5.38462	0.372462
$210$	−0.827297	−0.0570889
$211$	−7.48680	−0.515413	−0.257706	−	0.966223i	$-0.582967\pi$
$211$	−7.48680	−0.515413	−0.257706	+	0.966223i	$0.582967\pi$
$212$	7.43008	0.510300
$213$	−4.50950	−0.308986
$214$	−12.9957	−0.888370
$215$	−0.880982	−0.0600825
$216$	−31.5740	−2.14834
$217$	−0.124122	−0.00842593
$218$	4.28130	0.289967
$219$	4.84268	0.327238
$220$	−4.34698	−0.293073
$221$	1.67108	0.112409
$222$	−0.943440	−0.0633196
$223$	21.1505	1.41634	0.708169	−	0.706042i	$-0.249521\pi$
$223$	21.1505	1.41634	0.708169	+	0.706042i	$0.249521\pi$
$224$	5.75715	0.384666
$225$	10.2836	0.685572
$226$	−13.2713	−0.882796
$227$	4.71666	0.313056	0.156528	−	0.987674i	$-0.449970\pi$
$227$	4.71666	0.313056	0.156528	+	0.987674i	$0.449970\pi$
$228$	19.9774	1.32304
$229$	16.4658	1.08809	0.544046	−	0.839055i	$-0.316892\pi$
$229$	16.4658	1.08809	0.544046	+	0.839055i	$0.316892\pi$
$230$	14.0491	0.926369
$231$	−0.356611	−0.0234633
$232$	21.8194	1.43251
$233$	−6.74642	−0.441973	−0.220986	−	0.975277i	$-0.570928\pi$
$233$	−6.74642	−0.441973	−0.220986	+	0.975277i	$0.570928\pi$
$234$	10.7135	0.700364
$235$	8.61525	0.561997
$236$	−47.2543	−3.07599
$237$	−0.949021	−0.0616456
$238$	1.24891	0.0809546
$239$	−3.89547	−0.251977	−0.125989	−	0.992032i	$-0.540210\pi$
$239$	−3.89547	−0.251977	−0.125989	+	0.992032i	$0.540210\pi$
$240$	−6.94096	−0.448037
$241$	9.06449	0.583895	0.291948	−	0.956434i	$-0.405697\pi$
$241$	9.06449	0.583895	0.291948	+	0.956434i	$0.405697\pi$
$242$	−2.63329	−0.169275
$243$	−15.4406	−0.990516
$244$	−14.6328	−0.936770
$245$	−5.96871	−0.381327
$246$	2.10086	0.133946
$247$	−8.99816	−0.572539
$248$	−2.02215	−0.128406
$249$	2.38181	0.150941
$250$	21.3983	1.35335
$251$	15.0932	0.952676	0.476338	−	0.879262i	$-0.341964\pi$
$251$	15.0932	0.952676	0.476338	+	0.879262i	$0.341964\pi$
$252$	5.69750	0.358909
$253$	6.05594	0.380734
$254$	56.0824	3.51892
$255$	−0.662417	−0.0414822
$256$	−9.61083	−0.600677
$257$	9.90056	0.617580	0.308790	−	0.951130i	$-0.400076\pi$
$257$	9.90056	0.617580	0.308790	+	0.951130i	$0.400076\pi$
$258$	−1.97999	−0.123269
$259$	0.225986	0.0140421
$260$	7.26416	0.450504
$261$	6.87515	0.425561
$262$	−48.8408	−3.01740
$263$	−13.7161	−0.845773	−0.422886	−	0.906183i	$-0.638983\pi$
$263$	−13.7161	−0.845773	−0.422886	+	0.906183i	$0.638983\pi$
$264$	−5.80977	−0.357567
$265$	1.32660	0.0814925
$266$	−6.72489	−0.412329
$267$	5.13793	0.314436
$268$	−53.8432	−3.28900
$269$	−13.4423	−0.819594	−0.409797	−	0.912177i	$-0.634400\pi$
$269$	−13.4423	−0.819594	−0.409797	+	0.912177i	$0.634400\pi$
$270$	−9.47985	−0.576925
$271$	12.9010	0.783682	0.391841	−	0.920033i	$-0.371838\pi$
$271$	12.9010	0.783682	0.391841	+	0.920033i	$0.371838\pi$
$272$	10.4782	0.635336
$273$	0.595927	0.0360671
$274$	36.4111	2.19967
$275$	4.22387	0.254709
$276$	22.4681	1.35242
$277$	−8.76626	−0.526713	−0.263357	−	0.964699i	$-0.584830\pi$
$277$	−8.76626	−0.526713	−0.263357	+	0.964699i	$0.584830\pi$
$278$	−47.7814	−2.86574
$279$	−0.637164	−0.0381460
$280$	3.22844	0.192936
$281$	−19.9271	−1.18875	−0.594375	−	0.804188i	$-0.702601\pi$
$281$	−19.9271	−1.18875	−0.594375	+	0.804188i	$0.702601\pi$
$282$	19.3626	1.15303
$283$	27.3340	1.62484	0.812419	−	0.583074i	$-0.198150\pi$
$283$	27.3340	1.62484	0.812419	+	0.583074i	$0.198150\pi$
$284$	29.5927	1.75600
$285$	3.56687	0.211283
$286$	4.40046	0.260204
$287$	−0.503227	−0.0297045
$288$	29.5537	1.74147
$289$	1.00000	0.0588235
$290$	6.55111	0.384694
$291$	2.85532	0.167382
$292$	−31.7791	−1.85973
$293$	4.72738	0.276176	0.138088	−	0.990420i	$-0.455904\pi$
$293$	4.72738	0.276176	0.138088	+	0.990420i	$0.455904\pi$
$294$	−13.4146	−0.782354
$295$	−8.43700	−0.491221
$296$	3.68167	0.213993
$297$	−4.08634	−0.237114
$298$	−18.1246	−1.04993
$299$	−10.1200	−0.585254
$300$	15.6709	0.904762
$301$	0.474275	0.0273368
$302$	−2.10516	−0.121138
$303$	−6.75100	−0.387835
$304$	−56.4213	−3.23599
$305$	−2.61261	−0.149598
$306$	6.41111	0.366499
$307$	−17.6955	−1.00994	−0.504969	−	0.863138i	$-0.668496\pi$
$307$	−17.6955	−1.00994	−0.504969	+	0.863138i	$0.668496\pi$
$308$	2.34019	0.133345
$309$	2.34609	0.133465
$310$	−0.607133	−0.0344829
$311$	−5.40132	−0.306281	−0.153140	−	0.988204i	$-0.548939\pi$
$311$	−5.40132	−0.306281	−0.153140	+	0.988204i	$0.548939\pi$
$312$	9.70862	0.549642
$313$	26.0851	1.47442	0.737209	−	0.675664i	$-0.236143\pi$
$313$	26.0851	1.47442	0.737209	+	0.675664i	$0.236143\pi$
$314$	40.6957	2.29659
$315$	1.01726	0.0573160
$316$	6.22776	0.350339
$317$	−27.4498	−1.54173	−0.770867	−	0.636996i	$-0.780177\pi$
$317$	−27.4498	−1.54173	−0.770867	+	0.636996i	$0.780177\pi$
$318$	2.98152	0.167195
$319$	2.82389	0.158108
$320$	9.69846	0.542160
$321$	−3.71078	−0.207116
$322$	−7.56330	−0.421486
$323$	−5.38462	−0.299608
$324$	20.8785	1.15992
$325$	−7.05844	−0.391532
$326$	32.2532	1.78634
$327$	1.22248	0.0676032
$328$	−8.19838	−0.452680
$329$	−4.63800	−0.255701
$330$	−1.74434	−0.0960227
$331$	−0.151011	−0.00830030	−0.00415015	−	0.999991i	$-0.501321\pi$
$331$	−0.151011	−0.00830030	−0.00415015	+	0.999991i	$0.501321\pi$
$332$	−15.6302	−0.857816
$333$	1.16007	0.0635715
$334$	−43.5710	−2.38410
$335$	−9.61343	−0.525238
$336$	3.73665	0.203851
$337$	−33.3852	−1.81861	−0.909304	−	0.416133i	$-0.863385\pi$
$337$	−33.3852	−1.81861	−0.909304	+	0.416133i	$0.863385\pi$
$338$	26.8793	1.46204
$339$	−3.78948	−0.205816
$340$	4.34698	0.235748
$341$	−0.261708	−0.0141723
$342$	−34.5214	−1.86670
$343$	6.53317	0.352758
$344$	7.72671	0.416596
$345$	4.01156	0.215975
$346$	45.4652	2.44422
$347$	6.42839	0.345094	0.172547	−	0.985001i	$-0.444800\pi$
$347$	6.42839	0.345094	0.172547	+	0.985001i	$0.444800\pi$
$348$	10.4769	0.561621
$349$	19.2250	1.02909	0.514546	−	0.857463i	$-0.327961\pi$
$349$	19.2250	1.02909	0.514546	+	0.857463i	$0.327961\pi$
$350$	−5.27522	−0.281972
$351$	6.82862	0.364485
$352$	12.1388	0.647003
$353$	−14.3192	−0.762134	−0.381067	−	0.924547i	$-0.624443\pi$
$353$	−14.3192	−0.762134	−0.381067	+	0.924547i	$0.624443\pi$
$354$	−18.9620	−1.00782
$355$	5.28362	0.280425
$356$	−33.7166	−1.78698
$357$	0.356611	0.0188739
$358$	−38.7093	−2.04585
$359$	−8.02571	−0.423581	−0.211790	−	0.977315i	$-0.567929\pi$
$359$	−8.02571	−0.423581	−0.211790	+	0.977315i	$0.567929\pi$
$360$	16.5728	0.873463
$361$	9.99417	0.526009
$362$	−14.5567	−0.765081
$363$	−0.751907	−0.0394649
$364$	−3.91065	−0.204974
$365$	−5.67399	−0.296990
$366$	−5.87180	−0.306924
$367$	−11.7891	−0.615388	−0.307694	−	0.951485i	$-0.599557\pi$
$367$	−11.7891	−0.615388	−0.307694	+	0.951485i	$0.599557\pi$
$368$	−63.4556	−3.30785
$369$	−2.58325	−0.134479
$370$	1.10539	0.0574667
$371$	−0.714174	−0.0370781
$372$	−0.970962	−0.0503420
$373$	−15.4025	−0.797510	−0.398755	−	0.917058i	$-0.630558\pi$
$373$	−15.4025	−0.797510	−0.398755	+	0.917058i	$0.630558\pi$
$374$	2.63329	0.136164
$375$	6.11005	0.315522
$376$	−75.5606	−3.89674
$377$	−4.71896	−0.243039
$378$	5.10346	0.262494
$379$	−19.0118	−0.976569	−0.488285	−	0.872684i	$-0.662377\pi$
$379$	−19.0118	−0.976569	−0.488285	+	0.872684i	$0.662377\pi$
$380$	−23.4068	−1.20075
$381$	16.0137	0.820406
$382$	−16.0687	−0.822145
$383$	25.1112	1.28312	0.641561	−	0.767072i	$-0.278287\pi$
$383$	25.1112	1.28312	0.641561	+	0.767072i	$0.278287\pi$
$384$	3.54255	0.180780
$385$	0.417828	0.0212945
$386$	−72.1166	−3.67064
$387$	2.43464	0.123759
$388$	−18.7375	−0.951251
$389$	−10.8713	−0.551198	−0.275599	−	0.961273i	$-0.588876\pi$
$389$	−10.8713	−0.551198	−0.275599	+	0.961273i	$0.588876\pi$
$390$	2.91494	0.147604
$391$	−6.05594	−0.306262
$392$	52.3490	2.64402
$393$	−13.9459	−0.703480
$394$	−29.2139	−1.47177
$395$	1.11193	0.0559474
$396$	12.0131	0.603680
$397$	−24.3574	−1.22246	−0.611230	−	0.791453i	$-0.709325\pi$
$397$	−24.3574	−1.22246	−0.611230	+	0.791453i	$0.709325\pi$
$398$	−26.2719	−1.31689
$399$	−1.92022	−0.0961311
$400$	−44.2587	−2.21294
$401$	16.3498	0.816469	0.408235	−	0.912877i	$-0.366145\pi$
$401$	16.3498	0.816469	0.408235	+	0.912877i	$0.366145\pi$
$402$	−21.6060	−1.07761
$403$	0.437337	0.0217853
$404$	44.3020	2.20411
$405$	3.72775	0.185233
$406$	−3.52678	−0.175031
$407$	0.476486	0.0236186
$408$	5.80977	0.287627
$409$	22.8005	1.12741	0.563707	−	0.825975i	$-0.309375\pi$
$409$	22.8005	1.12741	0.563707	+	0.825975i	$0.309375\pi$
$410$	−2.46150	−0.121565
$411$	10.3968	0.512835
$412$	−15.3958	−0.758495
$413$	4.54204	0.223499
$414$	−38.8253	−1.90816
$415$	−2.79068	−0.136989
$416$	−20.2850	−0.994555
$417$	−13.6434	−0.668122
$418$	−14.1793	−0.693532
$419$	5.19595	0.253839	0.126919	−	0.991913i	$-0.459491\pi$
$419$	5.19595	0.253839	0.126919	+	0.991913i	$0.459491\pi$
$420$	1.55018	0.0756410
$421$	−4.31217	−0.210162	−0.105081	−	0.994464i	$-0.533510\pi$
$421$	−4.31217	−0.210162	−0.105081	+	0.994464i	$0.533510\pi$
$422$	19.7149	0.959709
$423$	−23.8086	−1.15762
$424$	−11.6350	−0.565048
$425$	−4.22387	−0.204888
$426$	11.8748	0.575338
$427$	1.40649	0.0680650
$428$	24.3513	1.17706
$429$	1.25650	0.0606644
$430$	2.31989	0.111875
$431$	15.2180	0.733025	0.366512	−	0.930413i	$-0.380552\pi$
$431$	15.2180	0.733025	0.366512	+	0.930413i	$0.380552\pi$
$432$	42.8177	2.06007
$433$	−14.2964	−0.687042	−0.343521	−	0.939145i	$-0.611620\pi$
$433$	−14.2964	−0.687042	−0.343521	+	0.939145i	$0.611620\pi$
$434$	0.326849	0.0156893
$435$	1.87059	0.0896881
$436$	−8.02226	−0.384197
$437$	32.6090	1.55990
$438$	−12.7522	−0.609324
$439$	−34.5861	−1.65071	−0.825353	−	0.564617i	$-0.809024\pi$
$439$	−34.5861	−1.65071	−0.825353	+	0.564617i	$0.809024\pi$
$440$	6.80710	0.324516
$441$	16.4948	0.785467
$442$	−4.40046	−0.209308
$443$	−18.8076	−0.893575	−0.446787	−	0.894640i	$-0.647432\pi$
$443$	−18.8076	−0.893575	−0.446787	+	0.894640i	$0.647432\pi$
$444$	1.76781	0.0838965
$445$	−6.01993	−0.285372
$446$	−55.6954	−2.63725
$447$	−5.17528	−0.244783
$448$	−5.22115	−0.246676
$449$	14.5740	0.687791	0.343895	−	0.939008i	$-0.388253\pi$
$449$	14.5740	0.687791	0.343895	+	0.939008i	$0.388253\pi$
$450$	−27.0797	−1.27655
$451$	−1.06104	−0.0499626
$452$	24.8677	1.16968
$453$	−0.601105	−0.0282424
$454$	−12.4204	−0.582916
$455$	−0.698226	−0.0327333
$456$	−31.2834	−1.46498
$457$	−8.89142	−0.415923	−0.207961	−	0.978137i	$-0.566683\pi$
$457$	−8.89142	−0.415923	−0.207961	+	0.978137i	$0.566683\pi$
$458$	−43.3594	−2.02605
$459$	4.08634	0.190734
$460$	−26.3250	−1.22741
$461$	32.5359	1.51535	0.757674	−	0.652633i	$-0.226336\pi$
$461$	32.5359	1.51535	0.757674	+	0.652633i	$0.226336\pi$
$462$	0.939062	0.0436891
$463$	−11.2408	−0.522403	−0.261201	−	0.965284i	$-0.584119\pi$
$463$	−11.2408	−0.522403	−0.261201	+	0.965284i	$0.584119\pi$
$464$	−29.5894	−1.37365
$465$	−0.173360	−0.00803938
$466$	17.7653	0.822962
$467$	−21.5602	−0.997687	−0.498844	−	0.866692i	$-0.666242\pi$
$467$	−21.5602	−0.997687	−0.498844	+	0.866692i	$0.666242\pi$
$468$	−20.0749	−0.927960
$469$	5.17537	0.238976
$470$	−22.6865	−1.04645
$471$	11.6202	0.535431
$472$	73.9973	3.40600
$473$	1.00000	0.0459800
$474$	2.49905	0.114785
$475$	22.7440	1.04356
$476$	−2.34019	−0.107262
$477$	−3.66613	−0.167860
$478$	10.2579	0.469187
$479$	18.2596	0.834304	0.417152	−	0.908837i	$-0.363028\pi$
$479$	18.2596	0.834304	0.417152	+	0.908837i	$0.363028\pi$
$480$	8.04098	0.367019
$481$	−0.796249	−0.0363058
$482$	−23.8695	−1.08722
$483$	−2.15962	−0.0982659
$484$	4.93424	0.224284
$485$	−3.34548	−0.151910
$486$	40.6597	1.84436
$487$	−24.6964	−1.11910	−0.559551	−	0.828796i	$-0.689026\pi$
$487$	−24.6964	−1.11910	−0.559551	+	0.828796i	$0.689026\pi$
$488$	22.9141	1.03727
$489$	9.20953	0.416469
$490$	15.7174	0.710038
$491$	26.3374	1.18859	0.594295	−	0.804247i	$-0.297431\pi$
$491$	26.3374	1.18859	0.594295	+	0.804247i	$0.297431\pi$
$492$	−3.93657	−0.177474
$493$	−2.82389	−0.127182
$494$	23.6948	1.06608
$495$	2.14487	0.0964047
$496$	2.74224	0.123130
$497$	−2.84443	−0.127590
$498$	−6.27201	−0.281056
$499$	−18.8192	−0.842463	−0.421231	−	0.906953i	$-0.638402\pi$
$499$	−18.8192	−0.842463	−0.421231	+	0.906953i	$0.638402\pi$
$500$	−40.0959	−1.79315
$501$	−12.4412	−0.555832
$502$	−39.7449	−1.77390
$503$	0.241316	0.0107598	0.00537988	−	0.999986i	$-0.498288\pi$
$503$	0.241316	0.0107598	0.00537988	+	0.999986i	$0.498288\pi$
$504$	−8.92194	−0.397415
$505$	7.90989	0.351986
$506$	−15.9471	−0.708934
$507$	7.67508	0.340862
$508$	−105.087	−4.66246
$509$	−40.0209	−1.77389	−0.886947	−	0.461872i	$-0.847178\pi$
$509$	−40.0209	−1.77389	−0.886947	+	0.461872i	$0.847178\pi$
$510$	1.74434	0.0772406
$511$	3.05458	0.135127
$512$	34.7310	1.53491
$513$	−22.0034	−0.971475
$514$	−26.0711	−1.14995
$515$	−2.74883	−0.121128
$516$	3.71009	0.163328
$517$	−9.77914	−0.430086
$518$	−0.595087	−0.0261466
$519$	12.9821	0.569850
$520$	−11.3752	−0.498837
$521$	28.9343	1.26764	0.633818	−	0.773483i	$-0.281487\pi$
$521$	28.9343	1.26764	0.633818	+	0.773483i	$0.281487\pi$
$522$	−18.1043	−0.792403
$523$	20.4141	0.892646	0.446323	−	0.894872i	$-0.352733\pi$
$523$	20.4141	0.892646	0.446323	+	0.894872i	$0.352733\pi$
$524$	91.5174	3.99796
$525$	−1.50628	−0.0657394
$526$	36.1186	1.57485
$527$	0.261708	0.0114002
$528$	7.87866	0.342875
$529$	13.6744	0.594540
$530$	−3.49333	−0.151741
$531$	23.3160	1.01183
$532$	12.6010	0.546324
$533$	1.77309	0.0768012
$534$	−13.5297	−0.585487
$535$	4.34779	0.187971
$536$	84.3152	3.64186
$537$	−11.0530	−0.476972
$538$	35.3976	1.52610
$539$	6.77506	0.291823
$540$	17.7632	0.764408
$541$	−39.5385	−1.69989	−0.849947	−	0.526868i	$-0.823366\pi$
$541$	−39.5385	−1.69989	−0.849947	+	0.526868i	$0.823366\pi$
$542$	−33.9722	−1.45923
$543$	−4.15649	−0.178372
$544$	−12.1388	−0.520449
$545$	−1.43233	−0.0613544
$546$	−1.56925	−0.0671578
$547$	−2.55889	−0.109410	−0.0547052	−	0.998503i	$-0.517422\pi$
$547$	−2.55889	−0.109410	−0.0547052	+	0.998503i	$0.517422\pi$
$548$	−68.2267	−2.91450
$549$	7.22007	0.308145
$550$	−11.1227	−0.474273
$551$	15.2056	0.647780
$552$	−35.1836	−1.49752
$553$	−0.598607	−0.0254554
$554$	23.0841	0.980751
$555$	0.315633	0.0133979
$556$	89.5322	3.79701
$557$	19.4305	0.823299	0.411649	−	0.911342i	$-0.364953\pi$
$557$	19.4305	0.823299	0.411649	+	0.911342i	$0.364953\pi$
$558$	1.67784	0.0710287
$559$	−1.67108	−0.0706793
$560$	−4.37810	−0.185008
$561$	0.751907	0.0317456
$562$	52.4739	2.21348
$563$	37.0039	1.55953	0.779765	−	0.626072i	$-0.215338\pi$
$563$	37.0039	1.55953	0.779765	+	0.626072i	$0.215338\pi$
$564$	−36.2815	−1.52773
$565$	4.43999	0.186792
$566$	−71.9785	−3.02548
$567$	−2.00683	−0.0842788
$568$	−46.3403	−1.94440
$569$	21.7362	0.911228	0.455614	−	0.890177i	$-0.349420\pi$
$569$	21.7362	0.911228	0.455614	+	0.890177i	$0.349420\pi$
$570$	−9.39261	−0.393413
$571$	36.5069	1.52777	0.763883	−	0.645354i	$-0.223290\pi$
$571$	36.5069	1.52777	0.763883	+	0.645354i	$0.223290\pi$
$572$	−8.24553	−0.344763
$573$	−4.58823	−0.191676
$574$	1.32514	0.0553104
$575$	25.5795	1.06674
$576$	−26.8021	−1.11676
$577$	12.3175	0.512786	0.256393	−	0.966573i	$-0.417466\pi$
$577$	12.3175	0.512786	0.256393	+	0.966573i	$0.417466\pi$
$578$	−2.63329	−0.109531
$579$	−20.5921	−0.855777
$580$	−12.2754	−0.509708
$581$	1.50236	0.0623283
$582$	−7.51891	−0.311669
$583$	−1.50582	−0.0623647
$584$	49.7641	2.05925
$585$	−3.58426	−0.148191
$586$	−12.4486	−0.514246
$587$	−4.25985	−0.175823	−0.0879114	−	0.996128i	$-0.528019\pi$
$587$	−4.25985	−0.175823	−0.0879114	+	0.996128i	$0.528019\pi$
$588$	25.1361	1.03660
$589$	−1.40920	−0.0580651
$590$	22.2171	0.914664
$591$	−8.34169	−0.343131
$592$	−4.99274	−0.205200
$593$	−44.0680	−1.80966	−0.904829	−	0.425775i	$-0.860001\pi$
$593$	−44.0680	−1.80966	−0.904829	+	0.425775i	$0.860001\pi$
$594$	10.7605	0.441510
$595$	−0.417828	−0.0171293
$596$	33.9617	1.39113
$597$	−7.50166	−0.307022
$598$	26.6489	1.08975
$599$	−8.54084	−0.348969	−0.174485	−	0.984660i	$-0.555826\pi$
$599$	−8.54084	−0.348969	−0.174485	+	0.984660i	$0.555826\pi$
$600$	−24.5397	−1.00183
$601$	−20.1317	−0.821190	−0.410595	−	0.911818i	$-0.634679\pi$
$601$	−20.1317	−0.821190	−0.410595	+	0.911818i	$0.634679\pi$
$602$	−1.24891	−0.0509016
$603$	26.5671	1.08190
$604$	3.94463	0.160505
$605$	0.880982	0.0358170
$606$	17.7774	0.722156
$607$	18.5437	0.752666	0.376333	−	0.926485i	$-0.377185\pi$
$607$	18.5437	0.752666	0.376333	+	0.926485i	$0.377185\pi$
$608$	65.3631	2.65082
$609$	−1.00703	−0.0408070
$610$	6.87977	0.278554
$611$	16.3418	0.661117
$612$	−12.0131	−0.485600
$613$	48.8602	1.97345	0.986723	−	0.162415i	$-0.0519283\pi$
$613$	48.8602	1.97345	0.986723	+	0.162415i	$0.0519283\pi$
$614$	46.5975	1.88052
$615$	−0.702854	−0.0283418
$616$	−3.66459	−0.147651
$617$	38.7311	1.55926	0.779628	−	0.626242i	$-0.215408\pi$
$617$	38.7311	1.55926	0.779628	+	0.626242i	$0.215408\pi$
$618$	−6.17796	−0.248514
$619$	−27.9716	−1.12427	−0.562136	−	0.827045i	$-0.690020\pi$
$619$	−27.9716	−1.12427	−0.562136	+	0.827045i	$0.690020\pi$
$620$	1.13764	0.0456887
$621$	−24.7467	−0.993049
$622$	14.2233	0.570301
$623$	3.24082	0.129841
$624$	−13.1659	−0.527058
$625$	13.9604	0.558417
$626$	−68.6898	−2.74540
$627$	−4.04874	−0.161691
$628$	−76.2552	−3.04291
$629$	−0.476486	−0.0189988
$630$	−2.67874	−0.106724
$631$	34.0208	1.35435	0.677173	−	0.735824i	$-0.263205\pi$
$631$	34.0208	1.35435	0.677173	+	0.735824i	$0.263205\pi$
$632$	−9.75229	−0.387925
$633$	5.62938	0.223748
$634$	72.2834	2.87074
$635$	−18.7626	−0.744573
$636$	−5.58673	−0.221528
$637$	−11.3217	−0.448582
$638$	−7.43614	−0.294400
$639$	−14.6015	−0.577627
$640$	−4.15067	−0.164070
$641$	31.3645	1.23883	0.619413	−	0.785066i	$-0.287371\pi$
$641$	31.3645	1.23883	0.619413	+	0.785066i	$0.287371\pi$
$642$	9.77159	0.385654
$643$	−8.45804	−0.333553	−0.166776	−	0.985995i	$-0.553336\pi$
$643$	−8.45804	−0.333553	−0.166776	+	0.985995i	$0.553336\pi$
$644$	14.1720	0.558456
$645$	0.662417	0.0260826
$646$	14.1793	0.557877
$647$	−25.1898	−0.990312	−0.495156	−	0.868804i	$-0.664889\pi$
$647$	−25.1898	−0.990312	−0.495156	+	0.868804i	$0.664889\pi$
$648$	−32.6945	−1.28436
$649$	9.57681	0.375923
$650$	18.5870	0.729040
$651$	0.0933281	0.00365782
$652$	−60.4356	−2.36684
$653$	27.7442	1.08572	0.542858	−	0.839825i	$-0.317342\pi$
$653$	27.7442	1.08572	0.542858	+	0.839825i	$0.317342\pi$
$654$	−3.21915	−0.125879
$655$	16.3400	0.638455
$656$	11.1179	0.434080
$657$	15.6803	0.611748
$658$	12.2132	0.476121
$659$	43.9257	1.71110	0.855552	−	0.517717i	$-0.173218\pi$
$659$	43.9257	1.71110	0.855552	+	0.517717i	$0.173218\pi$
$660$	3.26852	0.127227
$661$	−11.3843	−0.442798	−0.221399	−	0.975183i	$-0.571062\pi$
$661$	−11.3843	−0.442798	−0.221399	+	0.975183i	$0.571062\pi$
$662$	0.397655	0.0154553
$663$	−1.25650	−0.0487984
$664$	24.4759	0.949847
$665$	2.24985	0.0872453
$666$	−3.05481	−0.118371
$667$	17.1013	0.662166
$668$	81.6428	3.15886
$669$	−15.9032	−0.614853
$670$	25.3150	0.978003
$671$	2.96557	0.114484
$672$	−4.32885	−0.166989
$673$	−6.45942	−0.248992	−0.124496	−	0.992220i	$-0.539731\pi$
$673$	−6.45942	−0.248992	−0.124496	+	0.992220i	$0.539731\pi$
$674$	87.9130	3.38628
$675$	−17.2602	−0.664345
$676$	−50.3661	−1.93716
$677$	−8.93128	−0.343257	−0.171628	−	0.985162i	$-0.554903\pi$
$677$	−8.93128	−0.343257	−0.171628	+	0.985162i	$0.554903\pi$
$678$	9.97882	0.383234
$679$	1.80103	0.0691172
$680$	−6.80710	−0.261040
$681$	−3.54649	−0.135902
$682$	0.689155	0.0263891
$683$	−2.83579	−0.108509	−0.0542543	−	0.998527i	$-0.517278\pi$
$683$	−2.83579	−0.108509	−0.0542543	+	0.998527i	$0.517278\pi$
$684$	64.6859	2.47333
$685$	−12.1815	−0.465432
$686$	−17.2038	−0.656843
$687$	−12.3808	−0.472356
$688$	−10.4782	−0.399479
$689$	2.51635	0.0958654
$690$	−10.5636	−0.402150
$691$	−35.9492	−1.36757	−0.683786	−	0.729683i	$-0.739668\pi$
$691$	−35.9492	−1.36757	−0.683786	+	0.729683i	$0.739668\pi$
$692$	−85.1922	−3.23852
$693$	−1.15469	−0.0438629
$694$	−16.9278	−0.642572
$695$	15.9855	0.606365
$696$	−16.4062	−0.621875
$697$	1.06104	0.0401899
$698$	−50.6251	−1.91619
$699$	5.07269	0.191867
$700$	9.88465	0.373605
$701$	−3.38572	−0.127877	−0.0639383	−	0.997954i	$-0.520366\pi$
$701$	−3.38572	−0.127877	−0.0639383	+	0.997954i	$0.520366\pi$
$702$	−17.9818	−0.678678
$703$	2.56570	0.0967672
$704$	−11.0087	−0.414905
$705$	−6.47787	−0.243971
$706$	37.7067	1.41911
$707$	−4.25828	−0.160149
$708$	35.5308	1.33533
$709$	−8.91364	−0.334759	−0.167379	−	0.985893i	$-0.553530\pi$
$709$	−8.91364	−0.334759	−0.167379	+	0.985893i	$0.553530\pi$
$710$	−13.9133	−0.522157
$711$	−3.07288	−0.115242
$712$	52.7982	1.97870
$713$	−1.58489	−0.0593546
$714$	−0.939062	−0.0351435
$715$	−1.47220	−0.0550570
$716$	72.5331	2.71069
$717$	2.92904	0.109387
$718$	21.1341	0.788716
$719$	0.465426	0.0173574	0.00867872	−	0.999962i	$-0.497237\pi$
$719$	0.465426	0.0173574	0.00867872	+	0.999962i	$0.497237\pi$
$720$	−22.4745	−0.837573
$721$	1.47983	0.0551117
$722$	−26.3176	−0.979440
$723$	−6.81566	−0.253477
$724$	27.2761	1.01371
$725$	11.9278	0.442986
$726$	1.97999	0.0734845
$727$	10.6991	0.396807	0.198403	−	0.980120i	$-0.436424\pi$
$727$	10.6991	0.396807	0.198403	+	0.980120i	$0.436424\pi$
$728$	6.12384	0.226964
$729$	−1.08415	−0.0401536
$730$	14.9413	0.553002
$731$	−1.00000	−0.0369863
$732$	11.0025	0.406665
$733$	−41.8283	−1.54496	−0.772482	−	0.635037i	$-0.780985\pi$
$733$	−41.8283	−1.54496	−0.772482	+	0.635037i	$0.780985\pi$
$734$	31.0443	1.14586
$735$	4.48792	0.165539
$736$	73.5121	2.70969
$737$	10.9122	0.401955
$738$	6.80247	0.250402
$739$	51.2108	1.88382	0.941909	−	0.335867i	$-0.109029\pi$
$739$	51.2108	1.88382	0.941909	+	0.335867i	$0.109029\pi$
$740$	−2.07128	−0.0761416
$741$	6.76578	0.248547
$742$	1.88063	0.0690401
$743$	48.8826	1.79333	0.896664	−	0.442713i	$-0.145984\pi$
$743$	48.8826	1.79333	0.896664	+	0.442713i	$0.145984\pi$
$744$	1.52047	0.0557430
$745$	6.06369	0.222156
$746$	40.5592	1.48498
$747$	7.71218	0.282174
$748$	−4.93424	−0.180414
$749$	−2.34062	−0.0855246
$750$	−16.0896	−0.587508
$751$	25.3448	0.924843	0.462422	−	0.886660i	$-0.346981\pi$
$751$	25.3448	0.924843	0.462422	+	0.886660i	$0.346981\pi$
$752$	102.468	3.73663
$753$	−11.3487	−0.413570
$754$	12.4264	0.452543
$755$	0.704292	0.0256318
$756$	−9.56281	−0.347796
$757$	18.9166	0.687535	0.343768	−	0.939055i	$-0.388297\pi$
$757$	18.9166	0.687535	0.343768	+	0.939055i	$0.388297\pi$
$758$	50.0636	1.81839
$759$	−4.55351	−0.165282
$760$	36.6537	1.32957
$761$	−5.97430	−0.216568	−0.108284	−	0.994120i	$-0.534536\pi$
$761$	−5.97430	−0.216568	−0.108284	+	0.994120i	$0.534536\pi$
$762$	−42.1688	−1.52761
$763$	0.771094	0.0279155
$764$	30.1093	1.08932
$765$	−2.14487	−0.0775479
$766$	−66.1251	−2.38920
$767$	−16.0037	−0.577858
$768$	7.22645	0.260762
$769$	20.8455	0.751710	0.375855	−	0.926679i	$-0.377349\pi$
$769$	20.8455	0.751710	0.375855	+	0.926679i	$0.377349\pi$
$770$	−1.10026	−0.0396508
$771$	−7.44431	−0.268100
$772$	135.131	4.86348
$773$	11.7755	0.423535	0.211768	−	0.977320i	$-0.432078\pi$
$773$	11.7755	0.423535	0.211768	+	0.977320i	$0.432078\pi$
$774$	−6.41111	−0.230443
$775$	−1.10542	−0.0397079
$776$	29.3417	1.05331
$777$	−0.169920	−0.00609586
$778$	28.6274	1.02634
$779$	−5.71332	−0.204701
$780$	−5.46198	−0.195570
$781$	−5.99742	−0.214604
$782$	15.9471	0.570266
$783$	−11.5394	−0.412384
$784$	−70.9907	−2.53538
$785$	−13.6150	−0.485939
$786$	36.7238	1.30989
$787$	19.2688	0.686860	0.343430	−	0.939178i	$-0.388411\pi$
$787$	19.2688	0.686860	0.343430	+	0.939178i	$0.388411\pi$
$788$	54.7406	1.95005
$789$	10.3133	0.367162
$790$	−2.92805	−0.104175
$791$	−2.39026	−0.0849880
$792$	−18.8117	−0.668446
$793$	−4.95571	−0.175982
$794$	64.1401	2.27625
$795$	−0.997482	−0.0353770
$796$	49.2281	1.74484
$797$	−28.6345	−1.01428	−0.507142	−	0.861862i	$-0.669298\pi$
$797$	−28.6345	−1.01428	−0.507142	+	0.861862i	$0.669298\pi$
$798$	5.05650	0.178998
$799$	9.77914	0.345961
$800$	51.2729	1.81277
$801$	16.6363	0.587816
$802$	−43.0538	−1.52028
$803$	6.44053	0.227281
$804$	40.4851	1.42780
$805$	2.53034	0.0891828
$806$	−1.15164	−0.0405646
$807$	10.1074	0.355797
$808$	−69.3743	−2.44058
$809$	−28.7851	−1.01203	−0.506015	−	0.862525i	$-0.668882\pi$
$809$	−28.7851	−1.01203	−0.506015	+	0.862525i	$0.668882\pi$
$810$	−9.81626	−0.344908
$811$	55.4474	1.94702	0.973511	−	0.228638i	$-0.0734274\pi$
$811$	55.4474	1.94702	0.973511	+	0.228638i	$0.0734274\pi$
$812$	6.60844	0.231911
$813$	−9.70038	−0.340207
$814$	−1.25473	−0.0439782
$815$	−10.7905	−0.377973
$816$	−7.87866	−0.275808
$817$	5.38462	0.188384
$818$	−60.0405	−2.09927
$819$	1.92958	0.0674250
$820$	4.61233	0.161070
$821$	32.7931	1.14449	0.572243	−	0.820084i	$-0.306074\pi$
$821$	32.7931	1.14449	0.572243	+	0.820084i	$0.306074\pi$
$822$	−27.3778	−0.954909
$823$	−21.1833	−0.738403	−0.369201	−	0.929349i	$-0.620369\pi$
$823$	−21.1833	−0.738403	−0.369201	+	0.929349i	$0.620369\pi$
$824$	24.1088	0.839870
$825$	−3.17596	−0.110573
$826$	−11.9605	−0.416160
$827$	1.31936	0.0458786	0.0229393	−	0.999737i	$-0.492698\pi$
$827$	1.31936	0.0458786	0.0229393	+	0.999737i	$0.492698\pi$
$828$	72.7504	2.52825
$829$	14.1083	0.490000	0.245000	−	0.969523i	$-0.421212\pi$
$829$	14.1083	0.490000	0.245000	+	0.969523i	$0.421212\pi$
$830$	7.34868	0.255077
$831$	6.59142	0.228654
$832$	18.3964	0.637782
$833$	−6.77506	−0.234742
$834$	35.9272	1.24406
$835$	14.5769	0.504454
$836$	26.5690	0.918909
$837$	1.06943	0.0369649
$838$	−13.6825	−0.472653
$839$	20.2449	0.698932	0.349466	−	0.936949i	$-0.386363\pi$
$839$	20.2449	0.698932	0.349466	+	0.936949i	$0.386363\pi$
$840$	−2.42749	−0.0837562
$841$	−21.0256	−0.725022
$842$	11.3552	0.391327
$843$	14.9833	0.516053
$844$	−36.9417	−1.27158
$845$	−8.99261	−0.309355
$846$	62.6951	2.15550
$847$	−0.474275	−0.0162963
$848$	15.7783	0.541831
$849$	−20.5526	−0.705365
$850$	11.1227	0.381505
$851$	2.88557	0.0989162
$852$	−22.2510	−0.762305
$853$	25.9237	0.887611	0.443806	−	0.896123i	$-0.353628\pi$
$853$	25.9237	0.887611	0.443806	+	0.896123i	$0.353628\pi$
$854$	−3.70371	−0.126738
$855$	11.5493	0.394978
$856$	−38.1326	−1.30334
$857$	−6.81425	−0.232770	−0.116385	−	0.993204i	$-0.537131\pi$
$857$	−6.81425	−0.232770	−0.116385	+	0.993204i	$0.537131\pi$
$858$	−3.30874	−0.112958
$859$	50.5089	1.72334	0.861670	−	0.507469i	$-0.169419\pi$
$859$	50.5089	1.72334	0.861670	+	0.507469i	$0.169419\pi$
$860$	−4.34698	−0.148231
$861$	0.378380	0.0128952
$862$	−40.0734	−1.36491
$863$	−45.4308	−1.54648	−0.773240	−	0.634113i	$-0.781365\pi$
$863$	−45.4308	−1.54648	−0.773240	+	0.634113i	$0.781365\pi$
$864$	−49.6035	−1.68754
$865$	−15.2106	−0.517176
$866$	37.6467	1.27929
$867$	−0.751907	−0.0255361
$868$	−0.612446	−0.0207878
$869$	−1.26215	−0.0428156
$870$	−4.92583	−0.167001
$871$	−18.2351	−0.617874
$872$	12.5624	0.425416
$873$	9.24538	0.312909
$874$	−85.8690	−2.90456
$875$	3.85399	0.130289
$876$	23.8949	0.807336
$877$	−22.5477	−0.761382	−0.380691	−	0.924702i	$-0.624314\pi$
$877$	−22.5477	−0.761382	−0.380691	+	0.924702i	$0.624314\pi$
$878$	91.0754	3.07365
$879$	−3.55455	−0.119892
$880$	−9.23114	−0.311182
$881$	−7.20485	−0.242738	−0.121369	−	0.992607i	$-0.538728\pi$
$881$	−7.20485	−0.242738	−0.121369	+	0.992607i	$0.538728\pi$
$882$	−43.4357	−1.46256
$883$	42.4220	1.42761	0.713807	−	0.700342i	$-0.246969\pi$
$883$	42.4220	1.42761	0.713807	+	0.700342i	$0.246969\pi$
$884$	8.24553	0.277327
$885$	6.34384	0.213246
$886$	49.5259	1.66385
$887$	−2.40755	−0.0808376	−0.0404188	−	0.999183i	$-0.512869\pi$
$887$	−2.40755	−0.0808376	−0.0404188	+	0.999183i	$0.512869\pi$
$888$	−2.76828	−0.0928974
$889$	10.1008	0.338771
$890$	15.8522	0.531368
$891$	−4.23135	−0.141756
$892$	104.361	3.49428
$893$	−52.6570	−1.76210
$894$	13.6280	0.455790
$895$	12.9504	0.432884
$896$	2.23451	0.0746497
$897$	7.60929	0.254067
$898$	−38.3777	−1.28068
$899$	−0.739036	−0.0246482
$900$	50.7417	1.69139
$901$	1.50582	0.0501662
$902$	2.79404	0.0930314
$903$	−0.356611	−0.0118673
$904$	−38.9413	−1.29517
$905$	4.87001	0.161884
$906$	1.58289	0.0525879
$907$	−12.2509	−0.406783	−0.203392	−	0.979097i	$-0.565196\pi$
$907$	−12.2509	−0.406783	−0.203392	+	0.979097i	$0.565196\pi$
$908$	23.2731	0.772346
$909$	−21.8594	−0.725029
$910$	1.83863	0.0609501
$911$	59.0433	1.95619	0.978096	−	0.208154i	$-0.0667454\pi$
$911$	59.0433	1.95619	0.978096	+	0.208154i	$0.0667454\pi$
$912$	42.4236	1.40479
$913$	3.16769	0.104835
$914$	23.4137	0.774457
$915$	1.96444	0.0649424
$916$	81.2463	2.68445
$917$	−8.79659	−0.290489
$918$	−10.7605	−0.355151
$919$	20.5719	0.678606	0.339303	−	0.940677i	$-0.389809\pi$
$919$	20.5719	0.678606	0.339303	+	0.940677i	$0.389809\pi$
$920$	41.2234	1.35909
$921$	13.3054	0.438428
$922$	−85.6766	−2.82161
$923$	10.0222	0.329884
$924$	−1.75960	−0.0578867
$925$	2.01262	0.0661744
$926$	29.6002	0.972724
$927$	7.59652	0.249503
$928$	34.2788	1.12526
$929$	10.9341	0.358736	0.179368	−	0.983782i	$-0.442595\pi$
$929$	10.9341	0.358736	0.179368	+	0.983782i	$0.442595\pi$
$930$	0.456508	0.0149695
$931$	36.4812	1.19562
$932$	−33.2885	−1.09040
$933$	4.06129	0.132961
$934$	56.7744	1.85771
$935$	−0.880982	−0.0288112
$936$	31.4360	1.02752
$937$	12.6479	0.413188	0.206594	−	0.978427i	$-0.433762\pi$
$937$	12.6479	0.413188	0.206594	+	0.978427i	$0.433762\pi$
$938$	−13.6283	−0.444979
$939$	−19.6136	−0.640066
$940$	42.5097	1.38651
$941$	26.0815	0.850232	0.425116	−	0.905139i	$-0.360233\pi$
$941$	26.0815	0.850232	0.425116	+	0.905139i	$0.360233\pi$
$942$	−30.5994	−0.996983
$943$	−6.42562	−0.209247
$944$	−100.348	−3.26605
$945$	−1.70739	−0.0555414
$946$	−2.63329	−0.0856158
$947$	35.5685	1.15582	0.577910	−	0.816100i	$-0.303868\pi$
$947$	35.5685	1.15582	0.577910	+	0.816100i	$0.303868\pi$
$948$	−4.68270	−0.152087
$949$	−10.7627	−0.349371
$950$	−59.8915	−1.94314
$951$	20.6397	0.669288
$952$	3.66459	0.118770
$953$	7.67470	0.248608	0.124304	−	0.992244i	$-0.460330\pi$
$953$	7.67470	0.248608	0.124304	+	0.992244i	$0.460330\pi$
$954$	9.65399	0.312559
$955$	5.37586	0.173959
$956$	−19.2212	−0.621658
$957$	−2.12331	−0.0686367
$958$	−48.0830	−1.55349
$959$	6.55790	0.211766
$960$	−7.29234	−0.235359
$961$	−30.9315	−0.997791
$962$	2.09676	0.0676022
$963$	−12.0153	−0.387188
$964$	44.7264	1.44054
$965$	24.1270	0.776675
$966$	5.68690	0.182973
$967$	−47.6770	−1.53319	−0.766594	−	0.642132i	$-0.778050\pi$
$967$	−47.6770	−1.53319	−0.766594	+	0.642132i	$0.778050\pi$
$968$	−7.72671	−0.248346
$969$	4.04874	0.130064
$970$	8.80962	0.282860
$971$	−1.03084	−0.0330814	−0.0165407	−	0.999863i	$-0.505265\pi$
$971$	−1.03084	−0.0330814	−0.0165407	+	0.999863i	$0.505265\pi$
$972$	−76.1877	−2.44372
$973$	−8.60577	−0.275888
$974$	65.0329	2.08379
$975$	5.30730	0.169969
$976$	−31.0739	−0.994651
$977$	−9.43221	−0.301763	−0.150882	−	0.988552i	$-0.548211\pi$
$977$	−9.43221	−0.301763	−0.150882	+	0.988552i	$0.548211\pi$
$978$	−24.2514	−0.775474
$979$	6.83320	0.218390
$980$	−29.4510	−0.940779
$981$	3.95832	0.126379
$982$	−69.3542	−2.21318
$983$	42.0347	1.34070	0.670349	−	0.742046i	$-0.266144\pi$
$983$	42.0347	1.34070	0.670349	+	0.742046i	$0.266144\pi$
$984$	6.16442	0.196515
$985$	9.77365	0.311414
$986$	7.43614	0.236815
$987$	3.48735	0.111004
$988$	−44.3991	−1.41252
$989$	6.05594	0.192568
$990$	−5.64807	−0.179508
$991$	8.10168	0.257358	0.128679	−	0.991686i	$-0.458926\pi$
$991$	8.10168	0.257358	0.128679	+	0.991686i	$0.458926\pi$
$992$	−3.17684	−0.100865
$993$	0.113546	0.00360327
$994$	7.49021	0.237575
$995$	8.78941	0.278643
$996$	11.7524	0.372390
$997$	24.9408	0.789882	0.394941	−	0.918706i	$-0.370765\pi$
$997$	24.9408	0.789882	0.394941	+	0.918706i	$0.370765\pi$
$998$	49.5565	1.56868
$999$	−1.94709	−0.0616031

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.3	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.3	✓	66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.63329 q^{2} -0.751907 q^{3} +4.93424 q^{4} +0.880982 q^{5} +1.97999 q^{6} -0.474275 q^{7} -7.72671 q^{8} -2.43464 q^{9} +O(q^{10})\)	\(q-2.63329 q^{2} -0.751907 q^{3} +4.93424 q^{4} +0.880982 q^{5} +1.97999 q^{6} -0.474275 q^{7} -7.72671 q^{8} -2.43464 q^{9} -2.31989 q^{10} -1.00000 q^{11} -3.71009 q^{12} +1.67108 q^{13} +1.24891 q^{14} -0.662417 q^{15} +10.4782 q^{16} +1.00000 q^{17} +6.41111 q^{18} -5.38462 q^{19} +4.34698 q^{20} +0.356611 q^{21} +2.63329 q^{22} -6.05594 q^{23} +5.80977 q^{24} -4.22387 q^{25} -4.40046 q^{26} +4.08634 q^{27} -2.34019 q^{28} -2.82389 q^{29} +1.74434 q^{30} +0.261708 q^{31} -12.1388 q^{32} +0.751907 q^{33} -2.63329 q^{34} -0.417828 q^{35} -12.0131 q^{36} -0.476486 q^{37} +14.1793 q^{38} -1.25650 q^{39} -6.80710 q^{40} +1.06104 q^{41} -0.939062 q^{42} -1.00000 q^{43} -4.93424 q^{44} -2.14487 q^{45} +15.9471 q^{46} +9.77914 q^{47} -7.87866 q^{48} -6.77506 q^{49} +11.1227 q^{50} -0.751907 q^{51} +8.24553 q^{52} +1.50582 q^{53} -10.7605 q^{54} -0.880982 q^{55} +3.66459 q^{56} +4.04874 q^{57} +7.43614 q^{58} -9.57681 q^{59} -3.26852 q^{60} -2.96557 q^{61} -0.689155 q^{62} +1.15469 q^{63} +11.0087 q^{64} +1.47220 q^{65} -1.97999 q^{66} -10.9122 q^{67} +4.93424 q^{68} +4.55351 q^{69} +1.10026 q^{70} +5.99742 q^{71} +18.8117 q^{72} -6.44053 q^{73} +1.25473 q^{74} +3.17596 q^{75} -26.5690 q^{76} +0.474275 q^{77} +3.30874 q^{78} +1.26215 q^{79} +9.23114 q^{80} +4.23135 q^{81} -2.79404 q^{82} -3.16769 q^{83} +1.75960 q^{84} +0.880982 q^{85} +2.63329 q^{86} +2.12331 q^{87} +7.72671 q^{88} -6.83320 q^{89} +5.64807 q^{90} -0.792554 q^{91} -29.8815 q^{92} -0.196780 q^{93} -25.7513 q^{94} -4.74376 q^{95} +9.12729 q^{96} -3.79744 q^{97} +17.8407 q^{98} +2.43464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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