LMFDB - Embedded newform 8021.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27005 q^{2} +2.30637 q^{3} +3.15311 q^{4} -4.44364 q^{5} -5.23557 q^{6} +0.498318 q^{7} -2.61762 q^{8} +2.31934 q^{9} +O(q^{10})$	\(q-2.27005 q^{2} +2.30637 q^{3} +3.15311 q^{4} -4.44364 q^{5} -5.23557 q^{6} +0.498318 q^{7} -2.61762 q^{8} +2.31934 q^{9} +10.0873 q^{10} -3.28979 q^{11} +7.27224 q^{12} -1.00000 q^{13} -1.13120 q^{14} -10.2487 q^{15} -0.364111 q^{16} +5.28419 q^{17} -5.26502 q^{18} -2.63198 q^{19} -14.0113 q^{20} +1.14931 q^{21} +7.46797 q^{22} +5.79367 q^{23} -6.03719 q^{24} +14.7459 q^{25} +2.27005 q^{26} -1.56985 q^{27} +1.57125 q^{28} +2.59460 q^{29} +23.2650 q^{30} -6.87630 q^{31} +6.06178 q^{32} -7.58747 q^{33} -11.9954 q^{34} -2.21434 q^{35} +7.31315 q^{36} -6.70609 q^{37} +5.97472 q^{38} -2.30637 q^{39} +11.6317 q^{40} +6.83211 q^{41} -2.60898 q^{42} -3.68185 q^{43} -10.3731 q^{44} -10.3063 q^{45} -13.1519 q^{46} +9.76877 q^{47} -0.839775 q^{48} -6.75168 q^{49} -33.4739 q^{50} +12.1873 q^{51} -3.15311 q^{52} -6.25210 q^{53} +3.56362 q^{54} +14.6186 q^{55} -1.30441 q^{56} -6.07033 q^{57} -5.88987 q^{58} +3.10847 q^{59} -32.3152 q^{60} -2.90363 q^{61} +15.6095 q^{62} +1.15577 q^{63} -13.0323 q^{64} +4.44364 q^{65} +17.2239 q^{66} +8.92400 q^{67} +16.6616 q^{68} +13.3623 q^{69} +5.02666 q^{70} +12.3650 q^{71} -6.07115 q^{72} -8.32314 q^{73} +15.2231 q^{74} +34.0095 q^{75} -8.29893 q^{76} -1.63936 q^{77} +5.23557 q^{78} +9.29159 q^{79} +1.61798 q^{80} -10.5787 q^{81} -15.5092 q^{82} -13.4748 q^{83} +3.62389 q^{84} -23.4810 q^{85} +8.35796 q^{86} +5.98411 q^{87} +8.61141 q^{88} -0.889794 q^{89} +23.3958 q^{90} -0.498318 q^{91} +18.2681 q^{92} -15.8593 q^{93} -22.1756 q^{94} +11.6956 q^{95} +13.9807 q^{96} +2.01867 q^{97} +15.3266 q^{98} -7.63015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) $ 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * 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 $

$2$	−2.27005	−1.60517	−0.802583	−	0.596541i	$-0.796541\pi$
$2$	−2.27005	−1.60517	−0.802583	+	0.596541i	$0.796541\pi$
$3$	2.30637	1.33158	0.665792	−	0.746138i	$-0.268094\pi$
$3$	2.30637	1.33158	0.665792	+	0.746138i	$0.268094\pi$
$4$	3.15311	1.57656
$5$	−4.44364	−1.98726	−0.993628	−	0.112713i	$-0.964046\pi$
$5$	−4.44364	−1.98726	−0.993628	+	0.112713i	$0.964046\pi$
$6$	−5.23557	−2.13741
$7$	0.498318	0.188346	0.0941732	−	0.995556i	$-0.469979\pi$
$7$	0.498318	0.188346	0.0941732	+	0.995556i	$0.469979\pi$
$8$	−2.61762	−0.925467
$9$	2.31934	0.773115
$10$	10.0873	3.18987
$11$	−3.28979	−0.991909	−0.495954	−	0.868349i	$-0.665182\pi$
$11$	−3.28979	−0.991909	−0.495954	+	0.868349i	$0.665182\pi$
$12$	7.27224	2.09932
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.13120	−0.302327
$15$	−10.2487	−2.64620
$16$	−0.364111	−0.0910278
$17$	5.28419	1.28160	0.640802	−	0.767706i	$-0.278602\pi$
$17$	5.28419	1.28160	0.640802	+	0.767706i	$0.278602\pi$
$18$	−5.26502	−1.24098
$19$	−2.63198	−0.603818	−0.301909	−	0.953337i	$-0.597624\pi$
$19$	−2.63198	−0.603818	−0.301909	+	0.953337i	$0.597624\pi$
$20$	−14.0113	−3.13302
$21$	1.14931	0.250799
$22$	7.46797	1.59218
$23$	5.79367	1.20806	0.604032	−	0.796960i	$-0.293560\pi$
$23$	5.79367	1.20806	0.604032	+	0.796960i	$0.293560\pi$
$24$	−6.03719	−1.23234
$25$	14.7459	2.94918
$26$	2.27005	0.445193
$27$	−1.56985	−0.302117
$28$	1.57125	0.296939
$29$	2.59460	0.481805	0.240903	−	0.970549i	$-0.422557\pi$
$29$	2.59460	0.481805	0.240903	+	0.970549i	$0.422557\pi$
$30$	23.2650	4.24758
$31$	−6.87630	−1.23502	−0.617510	−	0.786563i	$-0.711858\pi$
$31$	−6.87630	−1.23502	−0.617510	+	0.786563i	$0.711858\pi$
$32$	6.06178	1.07158
$33$	−7.58747	−1.32081
$34$	−11.9954	−2.05719
$35$	−2.21434	−0.374293
$36$	7.31315	1.21886
$37$	−6.70609	−1.10247	−0.551237	−	0.834348i	$-0.685844\pi$
$37$	−6.70609	−1.10247	−0.551237	+	0.834348i	$0.685844\pi$
$38$	5.97472	0.969228
$39$	−2.30637	−0.369315
$40$	11.6317	1.83914
$41$	6.83211	1.06700	0.533498	−	0.845801i	$-0.320877\pi$
$41$	6.83211	1.06700	0.533498	+	0.845801i	$0.320877\pi$
$42$	−2.60898	−0.402574
$43$	−3.68185	−0.561476	−0.280738	−	0.959784i	$-0.590579\pi$
$43$	−3.68185	−0.561476	−0.280738	+	0.959784i	$0.590579\pi$
$44$	−10.3731	−1.56380
$45$	−10.3063	−1.53638
$46$	−13.1519	−1.93914
$47$	9.76877	1.42492	0.712460	−	0.701712i	$-0.247581\pi$
$47$	9.76877	1.42492	0.712460	+	0.701712i	$0.247581\pi$
$48$	−0.839775	−0.121211
$49$	−6.75168	−0.964526
$50$	−33.4739	−4.73393
$51$	12.1873	1.70656
$52$	−3.15311	−0.437258
$53$	−6.25210	−0.858792	−0.429396	−	0.903116i	$-0.641273\pi$
$53$	−6.25210	−0.858792	−0.429396	+	0.903116i	$0.641273\pi$
$54$	3.56362	0.484948
$55$	14.6186	1.97118
$56$	−1.30441	−0.174308
$57$	−6.07033	−0.804034
$58$	−5.88987	−0.773377
$59$	3.10847	0.404688	0.202344	−	0.979314i	$-0.435144\pi$
$59$	3.10847	0.404688	0.202344	+	0.979314i	$0.435144\pi$
$60$	−32.3152	−4.17188
$61$	−2.90363	−0.371771	−0.185886	−	0.982571i	$-0.559515\pi$
$61$	−2.90363	−0.371771	−0.185886	+	0.982571i	$0.559515\pi$
$62$	15.6095	1.98241
$63$	1.15577	0.145613
$64$	−13.0323	−1.62904
$65$	4.44364	0.551165
$66$	17.2239	2.12012
$67$	8.92400	1.09024	0.545120	−	0.838358i	$-0.316484\pi$
$67$	8.92400	1.09024	0.545120	+	0.838358i	$0.316484\pi$
$68$	16.6616	2.02052
$69$	13.3623	1.60864
$70$	5.02666	0.600801
$71$	12.3650	1.46745	0.733727	−	0.679444i	$-0.237779\pi$
$71$	12.3650	1.46745	0.733727	+	0.679444i	$0.237779\pi$
$72$	−6.07115	−0.715492
$73$	−8.32314	−0.974150	−0.487075	−	0.873360i	$-0.661936\pi$
$73$	−8.32314	−0.974150	−0.487075	+	0.873360i	$0.661936\pi$
$74$	15.2231	1.76965
$75$	34.0095	3.92708
$76$	−8.29893	−0.951953
$77$	−1.63936	−0.186823
$78$	5.23557	0.592811
$79$	9.29159	1.04539	0.522693	−	0.852521i	$-0.324928\pi$
$79$	9.29159	1.04539	0.522693	+	0.852521i	$0.324928\pi$
$80$	1.61798	0.180895
$81$	−10.5787	−1.17541
$82$	−15.5092	−1.71271
$83$	−13.4748	−1.47905	−0.739526	−	0.673128i	$-0.764950\pi$
$83$	−13.4748	−1.47905	−0.739526	+	0.673128i	$0.764950\pi$
$84$	3.62389	0.395399
$85$	−23.4810	−2.54687
$86$	8.35796	0.901262
$87$	5.98411	0.641564
$88$	8.61141	0.917979
$89$	−0.889794	−0.0943179	−0.0471590	−	0.998887i	$-0.515017\pi$
$89$	−0.889794	−0.0943179	−0.0471590	+	0.998887i	$0.515017\pi$
$90$	23.3958	2.46614
$91$	−0.498318	−0.0522379
$92$	18.2681	1.90458
$93$	−15.8593	−1.64453
$94$	−22.1756	−2.28723
$95$	11.6956	1.19994
$96$	13.9807	1.42690
$97$	2.01867	0.204965	0.102482	−	0.994735i	$-0.467321\pi$
$97$	2.01867	0.204965	0.102482	+	0.994735i	$0.467321\pi$
$98$	15.3266	1.54822
$99$	−7.63015	−0.766859
$100$	46.4955	4.64955
$101$	0.695565	0.0692113	0.0346057	−	0.999401i	$-0.488982\pi$
$101$	0.695565	0.0692113	0.0346057	+	0.999401i	$0.488982\pi$
$102$	−27.6657	−2.73931
$103$	13.3981	1.32015	0.660076	−	0.751199i	$-0.270524\pi$
$103$	13.3981	1.32015	0.660076	+	0.751199i	$0.270524\pi$
$104$	2.61762	0.256678
$105$	−5.10710	−0.498402
$106$	14.1926	1.37850
$107$	16.9757	1.64110	0.820549	−	0.571576i	$-0.193668\pi$
$107$	16.9757	1.64110	0.820549	+	0.571576i	$0.193668\pi$
$108$	−4.94990	−0.476304
$109$	18.6137	1.78287	0.891437	−	0.453145i	$-0.149698\pi$
$109$	18.6137	1.78287	0.891437	+	0.453145i	$0.149698\pi$
$110$	−33.1850	−3.16406
$111$	−15.4667	−1.46804
$112$	−0.181443	−0.0171448
$113$	−12.5299	−1.17872	−0.589358	−	0.807872i	$-0.700619\pi$
$113$	−12.5299	−1.17872	−0.589358	+	0.807872i	$0.700619\pi$
$114$	13.7799	1.29061
$115$	−25.7450	−2.40073
$116$	8.18107	0.759593
$117$	−2.31934	−0.214423
$118$	−7.05637	−0.649592
$119$	2.63321	0.241386
$120$	26.8271	2.44897
$121$	−0.177287	−0.0161170
$122$	6.59137	0.596754
$123$	15.7574	1.42080
$124$	−21.6817	−1.94708
$125$	−43.3073	−3.87353
$126$	−2.62365	−0.233734
$127$	−17.8268	−1.58188	−0.790938	−	0.611897i	$-0.790407\pi$
$127$	−17.8268	−1.58188	−0.790938	+	0.611897i	$0.790407\pi$
$128$	17.4604	1.54329
$129$	−8.49170	−0.747653
$130$	−10.0873	−0.884712
$131$	−10.6028	−0.926372	−0.463186	−	0.886261i	$-0.653294\pi$
$131$	−10.6028	−0.926372	−0.463186	+	0.886261i	$0.653294\pi$
$132$	−23.9241	−2.08233
$133$	−1.31156	−0.113727
$134$	−20.2579	−1.75002
$135$	6.97582	0.600383
$136$	−13.8320	−1.18608
$137$	8.57412	0.732536	0.366268	−	0.930509i	$-0.380635\pi$
$137$	8.57412	0.732536	0.366268	+	0.930509i	$0.380635\pi$
$138$	−30.3331	−2.58213
$139$	9.43647	0.800391	0.400196	−	0.916430i	$-0.368942\pi$
$139$	9.43647	0.800391	0.400196	+	0.916430i	$0.368942\pi$
$140$	−6.98207	−0.590093
$141$	22.5304	1.89740
$142$	−28.0691	−2.35551
$143$	3.28979	0.275106
$144$	−0.844499	−0.0703749
$145$	−11.5295	−0.957470
$146$	18.8939	1.56367
$147$	−15.5719	−1.28435
$148$	−21.1451	−1.73811
$149$	−12.3317	−1.01025	−0.505125	−	0.863046i	$-0.668554\pi$
$149$	−12.3317	−1.01025	−0.505125	+	0.863046i	$0.668554\pi$
$150$	−77.2033	−6.30362
$151$	7.42194	0.603989	0.301994	−	0.953310i	$-0.402348\pi$
$151$	7.42194	0.603989	0.301994	+	0.953310i	$0.402348\pi$
$152$	6.88952	0.558814
$153$	12.2558	0.990826
$154$	3.72143	0.299881
$155$	30.5558	2.45430
$156$	−7.27224	−0.582245
$157$	4.03280	0.321853	0.160926	−	0.986966i	$-0.448552\pi$
$157$	4.03280	0.321853	0.160926	+	0.986966i	$0.448552\pi$
$158$	−21.0923	−1.67802
$159$	−14.4197	−1.14355
$160$	−26.9364	−2.12951
$161$	2.88709	0.227534
$162$	24.0141	1.88672
$163$	−4.78095	−0.374473	−0.187236	−	0.982315i	$-0.559953\pi$
$163$	−4.78095	−0.374473	−0.187236	+	0.982315i	$0.559953\pi$
$164$	21.5424	1.68218
$165$	33.7160	2.62479
$166$	30.5884	2.37412
$167$	7.66928	0.593467	0.296733	−	0.954960i	$-0.404103\pi$
$167$	7.66928	0.593467	0.296733	+	0.954960i	$0.404103\pi$
$168$	−3.00844	−0.232106
$169$	1.00000	0.0769231
$170$	53.3030	4.08815
$171$	−6.10447	−0.466821
$172$	−11.6093	−0.885199
$173$	2.29144	0.174215	0.0871074	−	0.996199i	$-0.472238\pi$
$173$	2.29144	0.174215	0.0871074	+	0.996199i	$0.472238\pi$
$174$	−13.5842	−1.02982
$175$	7.34815	0.555468
$176$	1.19785	0.0902912
$177$	7.16928	0.538876
$178$	2.01987	0.151396
$179$	3.96875	0.296638	0.148319	−	0.988940i	$-0.452614\pi$
$179$	3.96875	0.296638	0.148319	+	0.988940i	$0.452614\pi$
$180$	−32.4970	−2.42218
$181$	−2.76324	−0.205390	−0.102695	−	0.994713i	$-0.532747\pi$
$181$	−2.76324	−0.205390	−0.102695	+	0.994713i	$0.532747\pi$
$182$	1.13120	0.0838505
$183$	−6.69684	−0.495045
$184$	−15.1656	−1.11802
$185$	29.7995	2.19090
$186$	36.0013	2.63975
$187$	−17.3839	−1.27123
$188$	30.8020	2.24647
$189$	−0.782282	−0.0569027
$190$	−26.5495	−1.92610
$191$	9.02253	0.652848	0.326424	−	0.945224i	$-0.394156\pi$
$191$	9.02253	0.652848	0.326424	+	0.945224i	$0.394156\pi$
$192$	−30.0573	−2.16920
$193$	−2.00847	−0.144573	−0.0722866	−	0.997384i	$-0.523030\pi$
$193$	−2.00847	−0.144573	−0.0722866	+	0.997384i	$0.523030\pi$
$194$	−4.58247	−0.329002
$195$	10.2487	0.733923
$196$	−21.2888	−1.52063
$197$	15.6592	1.11567	0.557834	−	0.829952i	$-0.311632\pi$
$197$	15.6592	1.11567	0.557834	+	0.829952i	$0.311632\pi$
$198$	17.3208	1.23094
$199$	1.92504	0.136462	0.0682311	−	0.997670i	$-0.478264\pi$
$199$	1.92504	0.136462	0.0682311	+	0.997670i	$0.478264\pi$
$200$	−38.5992	−2.72937
$201$	20.5820	1.45175
$202$	−1.57897	−0.111096
$203$	1.29294	0.0907463
$204$	38.4279	2.69049
$205$	−30.3594	−2.12040
$206$	−30.4143	−2.11906
$207$	13.4375	0.933971
$208$	0.364111	0.0252466
$209$	8.65867	0.598933
$210$	11.5933	0.800017
$211$	−20.0622	−1.38114	−0.690569	−	0.723267i	$-0.742640\pi$
$211$	−20.0622	−1.38114	−0.690569	+	0.723267i	$0.742640\pi$
$212$	−19.7136	−1.35393
$213$	28.5182	1.95404
$214$	−38.5355	−2.63423
$215$	16.3608	1.11580
$216$	4.10925	0.279599
$217$	−3.42658	−0.232612
$218$	−42.2541	−2.86181
$219$	−19.1962	−1.29716
$220$	46.0942	3.10767
$221$	−5.28419	−0.355453
$222$	35.1102	2.35644
$223$	−13.2358	−0.886331	−0.443166	−	0.896440i	$-0.646145\pi$
$223$	−13.2358	−0.886331	−0.443166	+	0.896440i	$0.646145\pi$
$224$	3.02069	0.201829
$225$	34.2009	2.28006
$226$	28.4435	1.89203
$227$	11.1411	0.739462	0.369731	−	0.929139i	$-0.379450\pi$
$227$	11.1411	0.739462	0.369731	+	0.929139i	$0.379450\pi$
$228$	−19.1404	−1.26761
$229$	14.3607	0.948979	0.474490	−	0.880261i	$-0.342633\pi$
$229$	14.3607	0.948979	0.474490	+	0.880261i	$0.342633\pi$
$230$	58.4423	3.85357
$231$	−3.78097	−0.248770
$232$	−6.79167	−0.445895
$233$	8.76137	0.573976	0.286988	−	0.957934i	$-0.407346\pi$
$233$	8.76137	0.573976	0.286988	+	0.957934i	$0.407346\pi$
$234$	5.26502	0.344185
$235$	−43.4089	−2.83168
$236$	9.80135	0.638014
$237$	21.4298	1.39202
$238$	−5.97750	−0.387464
$239$	−22.3127	−1.44329	−0.721643	−	0.692265i	$-0.756613\pi$
$239$	−22.3127	−1.44329	−0.721643	+	0.692265i	$0.756613\pi$
$240$	3.73166	0.240877
$241$	−16.0517	−1.03398	−0.516991	−	0.855991i	$-0.672948\pi$
$241$	−16.0517	−1.03398	−0.516991	+	0.855991i	$0.672948\pi$
$242$	0.402451	0.0258705
$243$	−19.6888	−1.26304
$244$	−9.15546	−0.586118
$245$	30.0020	1.91676
$246$	−35.7700	−2.28061
$247$	2.63198	0.167469
$248$	17.9995	1.14297
$249$	−31.0779	−1.96948
$250$	98.3097	6.21765
$251$	4.99786	0.315462	0.157731	−	0.987482i	$-0.449582\pi$
$251$	4.99786	0.315462	0.157731	+	0.987482i	$0.449582\pi$
$252$	3.64427	0.229568
$253$	−19.0599	−1.19829
$254$	40.4677	2.53917
$255$	−54.1559	−3.39137
$256$	−13.5713	−0.848204
$257$	−26.8411	−1.67430	−0.837151	−	0.546972i	$-0.815781\pi$
$257$	−26.8411	−1.67430	−0.837151	+	0.546972i	$0.815781\pi$
$258$	19.2766	1.20011
$259$	−3.34177	−0.207647
$260$	14.0113	0.868943
$261$	6.01777	0.372491
$262$	24.0689	1.48698
$263$	−26.9933	−1.66448	−0.832240	−	0.554415i	$-0.812942\pi$
$263$	−26.9933	−1.66448	−0.832240	+	0.554415i	$0.812942\pi$
$264$	19.8611	1.22237
$265$	27.7821	1.70664
$266$	2.97731	0.182551
$267$	−2.05219	−0.125592
$268$	28.1384	1.71882
$269$	8.12264	0.495246	0.247623	−	0.968856i	$-0.420351\pi$
$269$	8.12264	0.495246	0.247623	+	0.968856i	$0.420351\pi$
$270$	−15.8354	−0.963715
$271$	18.5338	1.12585	0.562923	−	0.826509i	$-0.309677\pi$
$271$	18.5338	1.12585	0.562923	+	0.826509i	$0.309677\pi$
$272$	−1.92403	−0.116662
$273$	−1.14931	−0.0695591
$274$	−19.4636	−1.17584
$275$	−48.5110	−2.92532
$276$	42.1330	2.53611
$277$	−9.42652	−0.566385	−0.283192	−	0.959063i	$-0.591394\pi$
$277$	−9.42652	−0.566385	−0.283192	+	0.959063i	$0.591394\pi$
$278$	−21.4212	−1.28476
$279$	−15.9485	−0.954812
$280$	5.79630	0.346395
$281$	−17.4481	−1.04087	−0.520433	−	0.853903i	$-0.674229\pi$
$281$	−17.4481	−1.04087	−0.520433	+	0.853903i	$0.674229\pi$
$282$	−51.1450	−3.04564
$283$	−20.6897	−1.22988	−0.614938	−	0.788576i	$-0.710819\pi$
$283$	−20.6897	−1.22988	−0.614938	+	0.788576i	$0.710819\pi$
$284$	38.9882	2.31352
$285$	26.9743	1.59782
$286$	−7.46797	−0.441591
$287$	3.40456	0.200965
$288$	14.0594	0.828456
$289$	10.9226	0.642508
$290$	26.1724	1.53690
$291$	4.65580	0.272928
$292$	−26.2438	−1.53580
$293$	−6.21621	−0.363155	−0.181577	−	0.983377i	$-0.558120\pi$
$293$	−6.21621	−0.363155	−0.181577	+	0.983377i	$0.558120\pi$
$294$	35.3489	2.06159
$295$	−13.8129	−0.804219
$296$	17.5540	1.02030
$297$	5.16446	0.299672
$298$	27.9935	1.62162
$299$	−5.79367	−0.335056
$300$	107.236	6.19127
$301$	−1.83473	−0.105752
$302$	−16.8481	−0.969502
$303$	1.60423	0.0921606
$304$	0.958334	0.0549642
$305$	12.9027	0.738804
$306$	−27.8213	−1.59044
$307$	−16.9537	−0.967597	−0.483799	−	0.875179i	$-0.660743\pi$
$307$	−16.9537	−0.967597	−0.483799	+	0.875179i	$0.660743\pi$
$308$	−5.16909	−0.294536
$309$	30.9009	1.75789
$310$	−69.3631	−3.93956
$311$	1.61500	0.0915780	0.0457890	−	0.998951i	$-0.485420\pi$
$311$	1.61500	0.0915780	0.0457890	+	0.998951i	$0.485420\pi$
$312$	6.03719	0.341789
$313$	4.86086	0.274752	0.137376	−	0.990519i	$-0.456133\pi$
$313$	4.86086	0.274752	0.137376	+	0.990519i	$0.456133\pi$
$314$	−9.15465	−0.516627
$315$	−5.13583	−0.289371
$316$	29.2974	1.64811
$317$	−17.4738	−0.981427	−0.490713	−	0.871321i	$-0.663264\pi$
$317$	−17.4738	−0.981427	−0.490713	+	0.871321i	$0.663264\pi$
$318$	32.7333	1.83559
$319$	−8.53569	−0.477907
$320$	57.9109	3.23731
$321$	39.1521	2.18526
$322$	−6.55382	−0.365230
$323$	−13.9079	−0.773856
$324$	−33.3557	−1.85310
$325$	−14.7459	−0.817956
$326$	10.8530	0.601091
$327$	42.9302	2.37405
$328$	−17.8839	−0.987471
$329$	4.86795	0.268379
$330$	−76.5368	−4.21321
$331$	−14.4563	−0.794589	−0.397295	−	0.917691i	$-0.630051\pi$
$331$	−14.4563	−0.794589	−0.397295	+	0.917691i	$0.630051\pi$
$332$	−42.4876	−2.33181
$333$	−15.5537	−0.852339
$334$	−17.4096	−0.952612
$335$	−39.6550	−2.16658
$336$	−0.418475	−0.0228297
$337$	−15.9979	−0.871461	−0.435731	−	0.900077i	$-0.643510\pi$
$337$	−15.9979	−0.871461	−0.435731	+	0.900077i	$0.643510\pi$
$338$	−2.27005	−0.123474
$339$	−28.8986	−1.56956
$340$	−74.0383	−4.01529
$341$	22.6216	1.22503
$342$	13.8574	0.749324
$343$	−6.85271	−0.370011
$344$	9.63766	0.519628
$345$	−59.3774	−3.19677
$346$	−5.20167	−0.279644
$347$	−28.9468	−1.55394	−0.776972	−	0.629535i	$-0.783246\pi$
$347$	−28.9468	−1.55394	−0.776972	+	0.629535i	$0.783246\pi$
$348$	18.8686	1.01146
$349$	−12.8260	−0.686561	−0.343281	−	0.939233i	$-0.611538\pi$
$349$	−12.8260	−0.686561	−0.343281	+	0.939233i	$0.611538\pi$
$350$	−16.6807	−0.891618
$351$	1.56985	0.0837922
$352$	−19.9420	−1.06291
$353$	−3.42101	−0.182082	−0.0910409	−	0.995847i	$-0.529019\pi$
$353$	−3.42101	−0.182082	−0.0910409	+	0.995847i	$0.529019\pi$
$354$	−16.2746	−0.864986
$355$	−54.9455	−2.91621
$356$	−2.80562	−0.148697
$357$	6.07315	0.321425
$358$	−9.00924	−0.476153
$359$	14.4262	0.761387	0.380693	−	0.924701i	$-0.375685\pi$
$359$	14.4262	0.761387	0.380693	+	0.924701i	$0.375685\pi$
$360$	26.9780	1.42187
$361$	−12.0727	−0.635404
$362$	6.27269	0.329685
$363$	−0.408890	−0.0214612
$364$	−1.57125	−0.0823560
$365$	36.9850	1.93588
$366$	15.2021	0.794628
$367$	−33.3488	−1.74079	−0.870396	−	0.492353i	$-0.836137\pi$
$367$	−33.3488	−1.74079	−0.870396	+	0.492353i	$0.836137\pi$
$368$	−2.10954	−0.109967
$369$	15.8460	0.824911
$370$	−67.6461	−3.51676
$371$	−3.11553	−0.161750
$372$	−50.0061	−2.59270
$373$	−19.1945	−0.993854	−0.496927	−	0.867792i	$-0.665538\pi$
$373$	−19.1945	−0.993854	−0.496927	+	0.867792i	$0.665538\pi$
$374$	39.4622	2.04054
$375$	−99.8827	−5.15792
$376$	−25.5709	−1.31872
$377$	−2.59460	−0.133629
$378$	1.77582	0.0913382
$379$	6.68157	0.343209	0.171605	−	0.985166i	$-0.445105\pi$
$379$	6.68157	0.343209	0.171605	+	0.985166i	$0.445105\pi$
$380$	36.8775	1.89177
$381$	−41.1153	−2.10640
$382$	−20.4816	−1.04793
$383$	−3.81822	−0.195102	−0.0975511	−	0.995231i	$-0.531101\pi$
$383$	−3.81822	−0.195102	−0.0975511	+	0.995231i	$0.531101\pi$
$384$	40.2701	2.05502
$385$	7.28473	0.371264
$386$	4.55933	0.232064
$387$	−8.53947	−0.434086
$388$	6.36509	0.323138
$389$	−11.3428	−0.575100	−0.287550	−	0.957766i	$-0.592841\pi$
$389$	−11.3428	−0.575100	−0.287550	+	0.957766i	$0.592841\pi$
$390$	−23.2650	−1.17807
$391$	30.6148	1.54826
$392$	17.6733	0.892637
$393$	−24.4540	−1.23354
$394$	−35.5470	−1.79083
$395$	−41.2885	−2.07745
$396$	−24.0587	−1.20900
$397$	−12.9410	−0.649490	−0.324745	−	0.945802i	$-0.605278\pi$
$397$	−12.9410	−0.649490	−0.324745	+	0.945802i	$0.605278\pi$
$398$	−4.36992	−0.219044
$399$	−3.02495	−0.151437
$400$	−5.36915	−0.268458
$401$	0.584183	0.0291727	0.0145864	−	0.999894i	$-0.495357\pi$
$401$	0.584183	0.0291727	0.0145864	+	0.999894i	$0.495357\pi$
$402$	−46.7222	−2.33029
$403$	6.87630	0.342533
$404$	2.19319	0.109115
$405$	47.0078	2.33584
$406$	−2.93503	−0.145663
$407$	22.0616	1.09355
$408$	−31.9017	−1.57937
$409$	−28.7036	−1.41930	−0.709651	−	0.704554i	$-0.751147\pi$
$409$	−28.7036	−1.41930	−0.709651	+	0.704554i	$0.751147\pi$
$410$	68.9173	3.40358
$411$	19.7751	0.975433
$412$	42.2456	2.08129
$413$	1.54901	0.0762216
$414$	−30.5038	−1.49918
$415$	59.8771	2.93925
$416$	−6.06178	−0.297203
$417$	21.7640	1.06579
$418$	−19.6556	−0.961386
$419$	14.1976	0.693599	0.346799	−	0.937939i	$-0.387268\pi$
$419$	14.1976	0.693599	0.346799	+	0.937939i	$0.387268\pi$
$420$	−16.1032	−0.785758
$421$	18.7519	0.913910	0.456955	−	0.889490i	$-0.348940\pi$
$421$	18.7519	0.913910	0.456955	+	0.889490i	$0.348940\pi$
$422$	45.5421	2.21695
$423$	22.6571	1.10163
$424$	16.3656	0.794784
$425$	77.9202	3.77968
$426$	−64.7377	−3.13655
$427$	−1.44693	−0.0700218
$428$	53.5261	2.58728
$429$	7.58747	0.366327
$430$	−37.1398	−1.79104
$431$	9.05020	0.435933	0.217966	−	0.975956i	$-0.430058\pi$
$431$	9.05020	0.435933	0.217966	+	0.975956i	$0.430058\pi$
$432$	0.571598	0.0275010
$433$	−31.4977	−1.51368	−0.756842	−	0.653598i	$-0.773259\pi$
$433$	−31.4977	−1.51368	−0.756842	+	0.653598i	$0.773259\pi$
$434$	7.77850	0.373380
$435$	−26.5912	−1.27495
$436$	58.6912	2.81080
$437$	−15.2488	−0.729451
$438$	43.5764	2.08216
$439$	16.6664	0.795442	0.397721	−	0.917506i	$-0.369801\pi$
$439$	16.6664	0.795442	0.397721	+	0.917506i	$0.369801\pi$
$440$	−38.2660	−1.82426
$441$	−15.6595	−0.745689
$442$	11.9954	0.570561
$443$	23.6377	1.12306	0.561531	−	0.827456i	$-0.310212\pi$
$443$	23.6377	1.12306	0.561531	+	0.827456i	$0.310212\pi$
$444$	−48.7683	−2.31444
$445$	3.95392	0.187434
$446$	30.0458	1.42271
$447$	−28.4414	−1.34523
$448$	−6.49423	−0.306824
$449$	−37.8711	−1.78725	−0.893623	−	0.448818i	$-0.851845\pi$
$449$	−37.8711	−1.78725	−0.893623	+	0.448818i	$0.851845\pi$
$450$	−77.6375	−3.65987
$451$	−22.4762	−1.05836
$452$	−39.5082	−1.85831
$453$	17.1177	0.804261
$454$	−25.2908	−1.18696
$455$	2.21434	0.103810
$456$	15.8898	0.744108
$457$	31.4164	1.46960	0.734799	−	0.678285i	$-0.237276\pi$
$457$	31.4164	1.46960	0.734799	+	0.678285i	$0.237276\pi$
$458$	−32.5994	−1.52327
$459$	−8.29536	−0.387194
$460$	−81.1767	−3.78488
$461$	11.4981	0.535518	0.267759	−	0.963486i	$-0.413717\pi$
$461$	11.4981	0.535518	0.267759	+	0.963486i	$0.413717\pi$
$462$	8.58298	0.399317
$463$	10.5156	0.488700	0.244350	−	0.969687i	$-0.421426\pi$
$463$	10.5156	0.488700	0.244350	+	0.969687i	$0.421426\pi$
$464$	−0.944723	−0.0438577
$465$	70.4730	3.26810
$466$	−19.8887	−0.921327
$467$	0.554975	0.0256812	0.0128406	−	0.999918i	$-0.495913\pi$
$467$	0.554975	0.0256812	0.0128406	+	0.999918i	$0.495913\pi$
$468$	−7.31315	−0.338050
$469$	4.44699	0.205343
$470$	98.5401	4.54532
$471$	9.30114	0.428574
$472$	−8.13678	−0.374526
$473$	12.1125	0.556933
$474$	−48.6467	−2.23442
$475$	−38.8110	−1.78077
$476$	8.30279	0.380558
$477$	−14.5008	−0.663944
$478$	50.6508	2.31671
$479$	2.97561	0.135959	0.0679796	−	0.997687i	$-0.478345\pi$
$479$	2.97561	0.135959	0.0679796	+	0.997687i	$0.478345\pi$
$480$	−62.1252	−2.83562
$481$	6.70609	0.305772
$482$	36.4382	1.65971
$483$	6.65869	0.302981
$484$	−0.559007	−0.0254094
$485$	−8.97023	−0.407317
$486$	44.6945	2.02738
$487$	3.31452	0.150195	0.0750976	−	0.997176i	$-0.476073\pi$
$487$	3.31452	0.150195	0.0750976	+	0.997176i	$0.476073\pi$
$488$	7.60058	0.344062
$489$	−11.0266	−0.498642
$490$	−68.1060	−3.07671
$491$	0.712709	0.0321641	0.0160820	−	0.999871i	$-0.494881\pi$
$491$	0.712709	0.0321641	0.0160820	+	0.999871i	$0.494881\pi$
$492$	49.6848	2.23996
$493$	13.7104	0.617484
$494$	−5.97472	−0.268816
$495$	33.9056	1.52394
$496$	2.50374	0.112421
$497$	6.16170	0.276390
$498$	70.5482	3.16134
$499$	−28.0541	−1.25587	−0.627936	−	0.778265i	$-0.716100\pi$
$499$	−28.0541	−1.25587	−0.627936	+	0.778265i	$0.716100\pi$
$500$	−136.553	−6.10683
$501$	17.6882	0.790251
$502$	−11.3454	−0.506369
$503$	−25.4851	−1.13632	−0.568162	−	0.822916i	$-0.692345\pi$
$503$	−25.4851	−1.13632	−0.568162	+	0.822916i	$0.692345\pi$
$504$	−3.02536	−0.134760
$505$	−3.09084	−0.137541
$506$	43.2670	1.92345
$507$	2.30637	0.102429
$508$	−56.2100	−2.49391
$509$	23.4992	1.04158	0.520792	−	0.853684i	$-0.325637\pi$
$509$	23.4992	1.04158	0.520792	+	0.853684i	$0.325637\pi$
$510$	122.936	5.44372
$511$	−4.14757	−0.183478
$512$	−4.11337	−0.181787
$513$	4.13181	0.182424
$514$	60.9306	2.68753
$515$	−59.5362	−2.62348
$516$	−26.7753	−1.17872
$517$	−32.1372	−1.41339
$518$	7.58597	0.333308
$519$	5.28490	0.231982
$520$	−11.6317	−0.510086
$521$	−3.74919	−0.164255	−0.0821275	−	0.996622i	$-0.526171\pi$
$521$	−3.74919	−0.164255	−0.0821275	+	0.996622i	$0.526171\pi$
$522$	−13.6606	−0.597909
$523$	45.0851	1.97143	0.985717	−	0.168411i	$-0.0538637\pi$
$523$	45.0851	1.97143	0.985717	+	0.168411i	$0.0538637\pi$
$524$	−33.4319	−1.46048
$525$	16.9476	0.739652
$526$	61.2761	2.67177
$527$	−36.3357	−1.58281
$528$	2.76268	0.120230
$529$	10.5666	0.459417
$530$	−63.0666	−2.73944
$531$	7.20961	0.312870
$532$	−4.13551	−0.179297
$533$	−6.83211	−0.295932
$534$	4.65858	0.201596
$535$	−75.4337	−3.26128
$536$	−23.3596	−1.00898
$537$	9.15340	0.394998
$538$	−18.4388	−0.794952
$539$	22.2116	0.956721
$540$	21.9956	0.946538
$541$	−23.9432	−1.02940	−0.514700	−	0.857370i	$-0.672097\pi$
$541$	−23.9432	−1.02940	−0.514700	+	0.857370i	$0.672097\pi$
$542$	−42.0725	−1.80717
$543$	−6.37306	−0.273494
$544$	32.0316	1.37334
$545$	−82.7128	−3.54303
$546$	2.60898	0.111654
$547$	−34.3576	−1.46903	−0.734513	−	0.678595i	$-0.762589\pi$
$547$	−34.3576	−1.46903	−0.734513	+	0.678595i	$0.762589\pi$
$548$	27.0351	1.15488
$549$	−6.73451	−0.287422
$550$	110.122	4.69562
$551$	−6.82895	−0.290923
$552$	−34.9775	−1.48874
$553$	4.63016	0.196895
$554$	21.3986	0.909141
$555$	68.7286	2.91737
$556$	29.7543	1.26186
$557$	−3.95604	−0.167623	−0.0838113	−	0.996482i	$-0.526709\pi$
$557$	−3.95604	−0.167623	−0.0838113	+	0.996482i	$0.526709\pi$
$558$	36.2038	1.53263
$559$	3.68185	0.155726
$560$	0.806267	0.0340710
$561$	−40.0936	−1.69275
$562$	39.6080	1.67076
$563$	−11.6213	−0.489780	−0.244890	−	0.969551i	$-0.578752\pi$
$563$	−11.6213	−0.489780	−0.244890	+	0.969551i	$0.578752\pi$
$564$	71.0408	2.99136
$565$	55.6784	2.34241
$566$	46.9666	1.97415
$567$	−5.27154	−0.221384
$568$	−32.3668	−1.35808
$569$	−27.3742	−1.14759	−0.573794	−	0.819000i	$-0.694529\pi$
$569$	−27.3742	−1.14759	−0.573794	+	0.819000i	$0.694529\pi$
$570$	−61.2330	−2.56477
$571$	8.83967	0.369929	0.184964	−	0.982745i	$-0.440783\pi$
$571$	8.83967	0.369929	0.184964	+	0.982745i	$0.440783\pi$
$572$	10.3731	0.433720
$573$	20.8093	0.869321
$574$	−7.72852	−0.322582
$575$	85.4329	3.56280
$576$	−30.2264	−1.25943
$577$	−12.5007	−0.520412	−0.260206	−	0.965553i	$-0.583790\pi$
$577$	−12.5007	−0.520412	−0.260206	+	0.965553i	$0.583790\pi$
$578$	−24.7949	−1.03133
$579$	−4.63229	−0.192511
$580$	−36.3537	−1.50951
$581$	−6.71474	−0.278574
$582$	−10.5689	−0.438094
$583$	20.5681	0.851843
$584$	21.7868	0.901544
$585$	10.3063	0.426114
$586$	14.1111	0.582923
$587$	10.4553	0.431535	0.215767	−	0.976445i	$-0.430775\pi$
$587$	10.4553	0.431535	0.215767	+	0.976445i	$0.430775\pi$
$588$	−49.0998	−2.02484
$589$	18.0983	0.745728
$590$	31.3560	1.29090
$591$	36.1158	1.48561
$592$	2.44176	0.100356
$593$	2.20725	0.0906410	0.0453205	−	0.998972i	$-0.485569\pi$
$593$	2.20725	0.0906410	0.0453205	+	0.998972i	$0.485569\pi$
$594$	−11.7236	−0.481024
$595$	−11.7010	−0.479695
$596$	−38.8832	−1.59272
$597$	4.43985	0.181711
$598$	13.1519	0.537821
$599$	31.9415	1.30509	0.652547	−	0.757748i	$-0.273701\pi$
$599$	31.9415	1.30509	0.652547	+	0.757748i	$0.273701\pi$
$600$	−89.0240	−3.63439
$601$	0.815718	0.0332739	0.0166369	−	0.999862i	$-0.494704\pi$
$601$	0.815718	0.0332739	0.0166369	+	0.999862i	$0.494704\pi$
$602$	4.16492	0.169750
$603$	20.6978	0.842880
$604$	23.4022	0.952222
$605$	0.787801	0.0320287
$606$	−3.64168	−0.147933
$607$	−19.8420	−0.805363	−0.402682	−	0.915340i	$-0.631922\pi$
$607$	−19.8420	−0.805363	−0.402682	+	0.915340i	$0.631922\pi$
$608$	−15.9545	−0.647041
$609$	2.98199	0.120836
$610$	−29.2897	−1.18590
$611$	−9.76877	−0.395202
$612$	38.6440	1.56209
$613$	−30.9669	−1.25074	−0.625370	−	0.780328i	$-0.715052\pi$
$613$	−30.9669	−1.25074	−0.625370	+	0.780328i	$0.715052\pi$
$614$	38.4856	1.55315
$615$	−70.0201	−2.82348
$616$	4.29122	0.172898
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−70.1465	−2.82171
$619$	15.1048	0.607113	0.303557	−	0.952813i	$-0.401826\pi$
$619$	15.1048	0.607113	0.303557	+	0.952813i	$0.401826\pi$
$620$	96.3458	3.86934
$621$	−9.09516	−0.364976
$622$	−3.66611	−0.146998
$623$	−0.443400	−0.0177645
$624$	0.839775	0.0336179
$625$	118.713	4.74850
$626$	−11.0344	−0.441022
$627$	19.9701	0.797529
$628$	12.7159	0.507419
$629$	−35.4363	−1.41294
$630$	11.6586	0.464488
$631$	−3.00642	−0.119684	−0.0598419	−	0.998208i	$-0.519060\pi$
$631$	−3.00642	−0.119684	−0.0598419	+	0.998208i	$0.519060\pi$
$632$	−24.3218	−0.967470
$633$	−46.2708	−1.83910
$634$	39.6664	1.57535
$635$	79.2160	3.14359
$636$	−45.4668	−1.80287
$637$	6.75168	0.267511
$638$	19.3764	0.767120
$639$	28.6787	1.13451
$640$	−77.5876	−3.06692
$641$	13.2871	0.524808	0.262404	−	0.964958i	$-0.415485\pi$
$641$	13.2871	0.524808	0.262404	+	0.964958i	$0.415485\pi$
$642$	−88.8772	−3.50770
$643$	2.26392	0.0892801	0.0446401	−	0.999003i	$-0.485786\pi$
$643$	2.26392	0.0892801	0.0446401	+	0.999003i	$0.485786\pi$
$644$	9.10331	0.358721
$645$	37.7340	1.48578
$646$	31.5716	1.24217
$647$	10.6817	0.419940	0.209970	−	0.977708i	$-0.432663\pi$
$647$	10.6817	0.419940	0.209970	+	0.977708i	$0.432663\pi$
$648$	27.6909	1.08780
$649$	−10.2262	−0.401414
$650$	33.4739	1.31296
$651$	−7.90297	−0.309742
$652$	−15.0749	−0.590377
$653$	−38.8097	−1.51874	−0.759371	−	0.650658i	$-0.774493\pi$
$653$	−38.8097	−1.51874	−0.759371	+	0.650658i	$0.774493\pi$
$654$	−97.4535	−3.81073
$655$	47.1151	1.84094
$656$	−2.48765	−0.0971263
$657$	−19.3042	−0.753130
$658$	−11.0505	−0.430792
$659$	−38.0983	−1.48410	−0.742049	−	0.670345i	$-0.766146\pi$
$659$	−38.0983	−1.48410	−0.742049	+	0.670345i	$0.766146\pi$
$660$	106.310	4.13812
$661$	49.1721	1.91257	0.956286	−	0.292433i	$-0.0944647\pi$
$661$	49.1721	1.91257	0.956286	+	0.292433i	$0.0944647\pi$
$662$	32.8164	1.27545
$663$	−12.1873	−0.473315
$664$	35.2719	1.36881
$665$	5.82812	0.226005
$666$	35.3077	1.36815
$667$	15.0323	0.582051
$668$	24.1821	0.935633
$669$	−30.5265	−1.18022
$670$	90.0187	3.47773
$671$	9.55232	0.368763
$672$	6.96684	0.268752
$673$	22.3448	0.861330	0.430665	−	0.902512i	$-0.358279\pi$
$673$	22.3448	0.861330	0.430665	+	0.902512i	$0.358279\pi$
$674$	36.3160	1.39884
$675$	−23.1488	−0.890998
$676$	3.15311	0.121274
$677$	16.2088	0.622956	0.311478	−	0.950253i	$-0.399176\pi$
$677$	16.2088	0.622956	0.311478	+	0.950253i	$0.399176\pi$
$678$	65.6012	2.51940
$679$	1.00594	0.0386044
$680$	61.4643	2.35705
$681$	25.6955	0.984655
$682$	−51.3520	−1.96637
$683$	−18.4977	−0.707795	−0.353898	−	0.935284i	$-0.615144\pi$
$683$	−18.4977	−0.707795	−0.353898	+	0.935284i	$0.615144\pi$
$684$	−19.2481	−0.735969
$685$	−38.1003	−1.45574
$686$	15.5560	0.593930
$687$	33.1210	1.26364
$688$	1.34060	0.0511099
$689$	6.25210	0.238186
$690$	134.789	5.13135
$691$	−24.7479	−0.941455	−0.470728	−	0.882279i	$-0.656009\pi$
$691$	−24.7479	−0.941455	−0.470728	+	0.882279i	$0.656009\pi$
$692$	7.22516	0.274659
$693$	−3.80224	−0.144435
$694$	65.7105	2.49434
$695$	−41.9323	−1.59058
$696$	−15.6641	−0.593747
$697$	36.1022	1.36747
$698$	29.1157	1.10204
$699$	20.2070	0.764297
$700$	23.1696	0.875727
$701$	−9.33065	−0.352414	−0.176207	−	0.984353i	$-0.556383\pi$
$701$	−9.33065	−0.352414	−0.176207	+	0.984353i	$0.556383\pi$
$702$	−3.56362	−0.134500
$703$	17.6503	0.665695
$704$	42.8735	1.61586
$705$	−100.117	−3.77062
$706$	7.76584	0.292271
$707$	0.346613	0.0130357
$708$	22.6055	0.849568
$709$	−43.6689	−1.64002	−0.820010	−	0.572350i	$-0.806032\pi$
$709$	−43.6689	−1.64002	−0.820010	+	0.572350i	$0.806032\pi$
$710$	124.729	4.68099
$711$	21.5504	0.808203
$712$	2.32914	0.0872882
$713$	−39.8390	−1.49198
$714$	−13.7863	−0.515940
$715$	−14.6186	−0.546706
$716$	12.5139	0.467666
$717$	−51.4613	−1.92186
$718$	−32.7482	−1.22215
$719$	−7.09429	−0.264573	−0.132286	−	0.991212i	$-0.542232\pi$
$719$	−7.09429	−0.264573	−0.132286	+	0.991212i	$0.542232\pi$
$720$	3.75265	0.139853
$721$	6.67650	0.248646
$722$	27.4055	1.01993
$723$	−37.0212	−1.37683
$724$	−8.71281	−0.323809
$725$	38.2598	1.42093
$726$	0.928200	0.0344487
$727$	1.77296	0.0657556	0.0328778	−	0.999459i	$-0.489533\pi$
$727$	1.77296	0.0657556	0.0328778	+	0.999459i	$0.489533\pi$
$728$	1.30441	0.0483445
$729$	−13.6737	−0.506431
$730$	−83.9577	−3.10742
$731$	−19.4556	−0.719590
$732$	−21.1159	−0.780465
$733$	33.2204	1.22702	0.613512	−	0.789686i	$-0.289756\pi$
$733$	33.2204	1.22702	0.613512	+	0.789686i	$0.289756\pi$
$734$	75.7032	2.79426
$735$	69.1958	2.55232
$736$	35.1200	1.29454
$737$	−29.3581	−1.08142
$738$	−35.9712	−1.32412
$739$	−37.4762	−1.37859	−0.689293	−	0.724483i	$-0.742079\pi$
$739$	−37.4762	−1.37859	−0.689293	+	0.724483i	$0.742079\pi$
$740$	93.9610	3.45407
$741$	6.07033	0.222999
$742$	7.07240	0.259636
$743$	18.7026	0.686133	0.343067	−	0.939311i	$-0.388534\pi$
$743$	18.7026	0.686133	0.343067	+	0.939311i	$0.388534\pi$
$744$	41.5135	1.52196
$745$	54.7975	2.00763
$746$	43.5724	1.59530
$747$	−31.2527	−1.14348
$748$	−54.8133	−2.00417
$749$	8.45927	0.309095
$750$	226.738	8.27932
$751$	−19.1499	−0.698791	−0.349395	−	0.936975i	$-0.613613\pi$
$751$	−19.1499	−0.698791	−0.349395	+	0.936975i	$0.613613\pi$
$752$	−3.55692	−0.129707
$753$	11.5269	0.420064
$754$	5.88987	0.214496
$755$	−32.9804	−1.20028
$756$	−2.46662	−0.0897102
$757$	21.2574	0.772613	0.386306	−	0.922371i	$-0.373751\pi$
$757$	21.2574	0.772613	0.386306	+	0.922371i	$0.373751\pi$
$758$	−15.1675	−0.550908
$759$	−43.9593	−1.59562
$760$	−30.6145	−1.11051
$761$	1.54718	0.0560852	0.0280426	−	0.999607i	$-0.491073\pi$
$761$	1.54718	0.0560852	0.0280426	+	0.999607i	$0.491073\pi$
$762$	93.3336	3.38112
$763$	9.27556	0.335798
$764$	28.4491	1.02925
$765$	−54.4605	−1.96903
$766$	8.66755	0.313171
$767$	−3.10847	−0.112240
$768$	−31.3003	−1.12945
$769$	5.44570	0.196377	0.0981885	−	0.995168i	$-0.468695\pi$
$769$	5.44570	0.196377	0.0981885	+	0.995168i	$0.468695\pi$
$770$	−16.5367	−0.595940
$771$	−61.9055	−2.22947
$772$	−6.33294	−0.227928
$773$	−52.5490	−1.89006	−0.945029	−	0.326987i	$-0.893967\pi$
$773$	−52.5490	−1.89006	−0.945029	+	0.326987i	$0.893967\pi$
$774$	19.3850	0.696779
$775$	−101.397	−3.64230
$776$	−5.28410	−0.189688
$777$	−7.70735	−0.276500
$778$	25.7486	0.923131
$779$	−17.9820	−0.644272
$780$	32.3152	1.15707
$781$	−40.6782	−1.45558
$782$	−69.4971	−2.48521
$783$	−4.07312	−0.145562
$784$	2.45836	0.0877986
$785$	−17.9203	−0.639603
$786$	55.5118	1.98004
$787$	40.2010	1.43301	0.716506	−	0.697581i	$-0.245740\pi$
$787$	40.2010	1.43301	0.716506	+	0.697581i	$0.245740\pi$
$788$	49.3751	1.75891
$789$	−62.2566	−2.21639
$790$	93.7267	3.33465
$791$	−6.24388	−0.222007
$792$	19.9728	0.709703
$793$	2.90363	0.103111
$794$	29.3767	1.04254
$795$	64.0757	2.27253
$796$	6.06985	0.215140
$797$	51.7942	1.83464	0.917322	−	0.398146i	$-0.130346\pi$
$797$	51.7942	1.83464	0.917322	+	0.398146i	$0.130346\pi$
$798$	6.86678	0.243081
$799$	51.6200	1.82618
$800$	89.3865	3.16029
$801$	−2.06374	−0.0729186
$802$	−1.32612	−0.0468270
$803$	27.3814	0.966268
$804$	64.8975	2.28876
$805$	−12.8292	−0.452169
$806$	−15.6095	−0.549822
$807$	18.7338	0.659462
$808$	−1.82072	−0.0640528
$809$	31.4624	1.10616	0.553080	−	0.833128i	$-0.313452\pi$
$809$	31.4624	1.10616	0.553080	+	0.833128i	$0.313452\pi$
$810$	−106.710	−3.74940
$811$	54.4481	1.91193	0.955965	−	0.293481i	$-0.0948137\pi$
$811$	54.4481	1.91193	0.955965	+	0.293481i	$0.0948137\pi$
$812$	4.07677	0.143067
$813$	42.7458	1.49916
$814$	−50.0809	−1.75534
$815$	21.2448	0.744173
$816$	−4.43753	−0.155345
$817$	9.69056	0.339030
$818$	65.1585	2.27821
$819$	−1.15577	−0.0403859
$820$	−95.7267	−3.34292
$821$	−3.30302	−0.115276	−0.0576381	−	0.998338i	$-0.518357\pi$
$821$	−3.30302	−0.115276	−0.0576381	+	0.998338i	$0.518357\pi$
$822$	−44.8904	−1.56573
$823$	41.5667	1.44893	0.724463	−	0.689314i	$-0.242088\pi$
$823$	41.5667	1.44893	0.724463	+	0.689314i	$0.242088\pi$
$824$	−35.0710	−1.22176
$825$	−111.884	−3.89531
$826$	−3.51632	−0.122348
$827$	−16.2950	−0.566633	−0.283317	−	0.959026i	$-0.591435\pi$
$827$	−16.2950	−0.566633	−0.283317	+	0.959026i	$0.591435\pi$
$828$	42.3700	1.47246
$829$	37.7920	1.31257	0.656285	−	0.754513i	$-0.272127\pi$
$829$	37.7920	1.31257	0.656285	+	0.754513i	$0.272127\pi$
$830$	−135.924	−4.71799
$831$	−21.7411	−0.754189
$832$	13.0323	0.451814
$833$	−35.6771	−1.23614
$834$	−49.4053	−1.71077
$835$	−34.0795	−1.17937
$836$	27.3017	0.944251
$837$	10.7947	0.373120
$838$	−32.2292	−1.11334
$839$	−22.7824	−0.786537	−0.393269	−	0.919424i	$-0.628656\pi$
$839$	−22.7824	−0.786537	−0.393269	+	0.919424i	$0.628656\pi$
$840$	13.3684	0.461254
$841$	−22.2680	−0.767864
$842$	−42.5676	−1.46698
$843$	−40.2417	−1.38600
$844$	−63.2583	−2.17744
$845$	−4.44364	−0.152866
$846$	−51.4327	−1.76829
$847$	−0.0883455	−0.00303559
$848$	2.27646	0.0781739
$849$	−47.7181	−1.63768
$850$	−176.882	−6.06702
$851$	−38.8529	−1.33186
$852$	89.9212	3.08065
$853$	−24.6729	−0.844783	−0.422392	−	0.906413i	$-0.638809\pi$
$853$	−24.6729	−0.844783	−0.422392	+	0.906413i	$0.638809\pi$
$854$	3.28460	0.112397
$855$	27.1261	0.927692
$856$	−44.4358	−1.51878
$857$	−27.8408	−0.951024	−0.475512	−	0.879709i	$-0.657737\pi$
$857$	−27.8408	−0.951024	−0.475512	+	0.879709i	$0.657737\pi$
$858$	−17.2239	−0.588015
$859$	−44.4215	−1.51564	−0.757821	−	0.652462i	$-0.773736\pi$
$859$	−44.4215	−1.51564	−0.757821	+	0.652462i	$0.773736\pi$
$860$	51.5874	1.75912
$861$	7.85219	0.267602
$862$	−20.5444	−0.699744
$863$	−19.9364	−0.678645	−0.339322	−	0.940670i	$-0.610198\pi$
$863$	−19.9364	−0.678645	−0.339322	+	0.940670i	$0.610198\pi$
$864$	−9.51606	−0.323743
$865$	−10.1823	−0.346209
$866$	71.5013	2.42971
$867$	25.1916	0.855553
$868$	−10.8044	−0.366725
$869$	−30.5674	−1.03693
$870$	60.3633	2.04651
$871$	−8.92400	−0.302378
$872$	−48.7237	−1.64999
$873$	4.68199	0.158461
$874$	34.6156	1.17089
$875$	−21.5808	−0.729565
$876$	−60.5279	−2.04505
$877$	−36.9509	−1.24774	−0.623871	−	0.781527i	$-0.714441\pi$
$877$	−36.9509	−1.24774	−0.623871	+	0.781527i	$0.714441\pi$
$878$	−37.8334	−1.27682
$879$	−14.3369	−0.483571
$880$	−5.32281	−0.179432
$881$	−43.9072	−1.47927	−0.739636	−	0.673007i	$-0.765003\pi$
$881$	−43.9072	−1.47927	−0.739636	+	0.673007i	$0.765003\pi$
$882$	35.5477	1.19695
$883$	21.6548	0.728742	0.364371	−	0.931254i	$-0.381284\pi$
$883$	21.6548	0.728742	0.364371	+	0.931254i	$0.381284\pi$
$884$	−16.6616	−0.560391
$885$	−31.8577	−1.07088
$886$	−53.6588	−1.80270
$887$	−14.5426	−0.488294	−0.244147	−	0.969738i	$-0.578508\pi$
$887$	−14.5426	−0.488294	−0.244147	+	0.969738i	$0.578508\pi$
$888$	40.4860	1.35862
$889$	−8.88343	−0.297941
$890$	−8.97558	−0.300862
$891$	34.8016	1.16590
$892$	−41.7338	−1.39735
$893$	−25.7112	−0.860393
$894$	64.5634	2.15932
$895$	−17.6357	−0.589496
$896$	8.70082	0.290674
$897$	−13.3623	−0.446156
$898$	85.9691	2.86883
$899$	−17.8413	−0.595039
$900$	107.839	3.59464
$901$	−33.0373	−1.10063
$902$	51.0221	1.69885
$903$	−4.23157	−0.140818
$904$	32.7985	1.09086
$905$	12.2789	0.408163
$906$	−38.8581	−1.29097
$907$	−38.6786	−1.28430	−0.642152	−	0.766578i	$-0.721958\pi$
$907$	−38.6786	−1.28430	−0.642152	+	0.766578i	$0.721958\pi$
$908$	35.1292	1.16580
$909$	1.61325	0.0535083
$910$	−5.02666	−0.166632
$911$	38.8374	1.28674	0.643369	−	0.765556i	$-0.277536\pi$
$911$	38.8374	1.28674	0.643369	+	0.765556i	$0.277536\pi$
$912$	2.21027	0.0731895
$913$	44.3293	1.46708
$914$	−71.3167	−2.35895
$915$	29.7583	0.983780
$916$	45.2808	1.49612
$917$	−5.28357	−0.174479
$918$	18.8308	0.621511
$919$	−12.8452	−0.423725	−0.211863	−	0.977299i	$-0.567953\pi$
$919$	−12.8452	−0.423725	−0.211863	+	0.977299i	$0.567953\pi$
$920$	67.3904	2.22180
$921$	−39.1015	−1.28844
$922$	−26.1011	−0.859595
$923$	−12.3650	−0.406999
$924$	−11.9218	−0.392199
$925$	−98.8875	−3.25140
$926$	−23.8708	−0.784444
$927$	31.0747	1.02063
$928$	15.7279	0.516294
$929$	54.8598	1.79989	0.899947	−	0.436000i	$-0.143605\pi$
$929$	54.8598	1.79989	0.899947	+	0.436000i	$0.143605\pi$
$930$	−159.977	−5.24585
$931$	17.7703	0.582398
$932$	27.6256	0.904906
$933$	3.72478	0.121944
$934$	−1.25982	−0.0412225
$935$	77.2476	2.52627
$936$	6.07115	0.198442
$937$	−1.11661	−0.0364780	−0.0182390	−	0.999834i	$-0.505806\pi$
$937$	−1.11661	−0.0364780	−0.0182390	+	0.999834i	$0.505806\pi$
$938$	−10.0949	−0.329609
$939$	11.2109	0.365855
$940$	−136.873	−4.46430
$941$	−28.4524	−0.927521	−0.463760	−	0.885961i	$-0.653500\pi$
$941$	−28.4524	−0.927521	−0.463760	+	0.885961i	$0.653500\pi$
$942$	−21.1140	−0.687932
$943$	39.5830	1.28900
$944$	−1.13183	−0.0368379
$945$	3.47618	0.113080
$946$	−27.4959	−0.893970
$947$	18.8246	0.611717	0.305858	−	0.952077i	$-0.401057\pi$
$947$	18.8246	0.611717	0.305858	+	0.952077i	$0.401057\pi$
$948$	67.5707	2.19459
$949$	8.32314	0.270181
$950$	88.1028	2.85843
$951$	−40.3011	−1.30685
$952$	−6.89272	−0.223394
$953$	42.0995	1.36374	0.681869	−	0.731475i	$-0.261168\pi$
$953$	42.0995	1.36374	0.681869	+	0.731475i	$0.261168\pi$
$954$	32.9174	1.06574
$955$	−40.0929	−1.29737
$956$	−70.3543	−2.27542
$957$	−19.6865	−0.636373
$958$	−6.75478	−0.218237
$959$	4.27264	0.137971
$960$	133.564	4.31076
$961$	16.2835	0.525274
$962$	−15.2231	−0.490814
$963$	39.3724	1.26876
$964$	−50.6129	−1.63013
$965$	8.92493	0.287304
$966$	−15.1155	−0.486335
$967$	24.8768	0.799985	0.399992	−	0.916519i	$-0.369013\pi$
$967$	24.8768	0.799985	0.399992	+	0.916519i	$0.369013\pi$
$968$	0.464070	0.0149158
$969$	−32.0767	−1.03045
$970$	20.3628	0.653811
$971$	−50.9236	−1.63422	−0.817108	−	0.576484i	$-0.804424\pi$
$971$	−50.9236	−1.63422	−0.817108	+	0.576484i	$0.804424\pi$
$972$	−62.0810	−1.99125
$973$	4.70236	0.150751
$974$	−7.52411	−0.241088
$975$	−34.0095	−1.08918
$976$	1.05724	0.0338415
$977$	−34.5537	−1.10547	−0.552736	−	0.833356i	$-0.686416\pi$
$977$	−34.5537	−1.10547	−0.552736	+	0.833356i	$0.686416\pi$
$978$	25.0310	0.800403
$979$	2.92723	0.0935548
$980$	94.5997	3.02188
$981$	43.1717	1.37837
$982$	−1.61788	−0.0516287
$983$	37.8371	1.20682	0.603408	−	0.797432i	$-0.293809\pi$
$983$	37.8371	1.20682	0.603408	+	0.797432i	$0.293809\pi$
$984$	−41.2468	−1.31490
$985$	−69.5836	−2.21712
$986$	−31.1232	−0.991163
$987$	11.2273	0.357369
$988$	8.29893	0.264024
$989$	−21.3314	−0.678299
$990$	−76.9674	−2.44618
$991$	−29.6720	−0.942561	−0.471281	−	0.881983i	$-0.656208\pi$
$991$	−29.6720	−0.942561	−0.471281	+	0.881983i	$0.656208\pi$
$992$	−41.6826	−1.32342
$993$	−33.3416	−1.05806
$994$	−13.9873	−0.443651
$995$	−8.55417	−0.271185
$996$	−97.9920	−3.10500
$997$	−16.2413	−0.514367	−0.257184	−	0.966363i	$-0.582795\pi$
$997$	−16.2413	−0.514367	−0.257184	+	0.966363i	$0.582795\pi$
$998$	63.6840	2.01588
$999$	10.5275	0.333076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.17	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.17	✓	140	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27005 q^{2} +2.30637 q^{3} +3.15311 q^{4} -4.44364 q^{5} -5.23557 q^{6} +0.498318 q^{7} -2.61762 q^{8} +2.31934 q^{9} +O(q^{10})\)	\(q-2.27005 q^{2} +2.30637 q^{3} +3.15311 q^{4} -4.44364 q^{5} -5.23557 q^{6} +0.498318 q^{7} -2.61762 q^{8} +2.31934 q^{9} +10.0873 q^{10} -3.28979 q^{11} +7.27224 q^{12} -1.00000 q^{13} -1.13120 q^{14} -10.2487 q^{15} -0.364111 q^{16} +5.28419 q^{17} -5.26502 q^{18} -2.63198 q^{19} -14.0113 q^{20} +1.14931 q^{21} +7.46797 q^{22} +5.79367 q^{23} -6.03719 q^{24} +14.7459 q^{25} +2.27005 q^{26} -1.56985 q^{27} +1.57125 q^{28} +2.59460 q^{29} +23.2650 q^{30} -6.87630 q^{31} +6.06178 q^{32} -7.58747 q^{33} -11.9954 q^{34} -2.21434 q^{35} +7.31315 q^{36} -6.70609 q^{37} +5.97472 q^{38} -2.30637 q^{39} +11.6317 q^{40} +6.83211 q^{41} -2.60898 q^{42} -3.68185 q^{43} -10.3731 q^{44} -10.3063 q^{45} -13.1519 q^{46} +9.76877 q^{47} -0.839775 q^{48} -6.75168 q^{49} -33.4739 q^{50} +12.1873 q^{51} -3.15311 q^{52} -6.25210 q^{53} +3.56362 q^{54} +14.6186 q^{55} -1.30441 q^{56} -6.07033 q^{57} -5.88987 q^{58} +3.10847 q^{59} -32.3152 q^{60} -2.90363 q^{61} +15.6095 q^{62} +1.15577 q^{63} -13.0323 q^{64} +4.44364 q^{65} +17.2239 q^{66} +8.92400 q^{67} +16.6616 q^{68} +13.3623 q^{69} +5.02666 q^{70} +12.3650 q^{71} -6.07115 q^{72} -8.32314 q^{73} +15.2231 q^{74} +34.0095 q^{75} -8.29893 q^{76} -1.63936 q^{77} +5.23557 q^{78} +9.29159 q^{79} +1.61798 q^{80} -10.5787 q^{81} -15.5092 q^{82} -13.4748 q^{83} +3.62389 q^{84} -23.4810 q^{85} +8.35796 q^{86} +5.98411 q^{87} +8.61141 q^{88} -0.889794 q^{89} +23.3958 q^{90} -0.498318 q^{91} +18.2681 q^{92} -15.8593 q^{93} -22.1756 q^{94} +11.6956 q^{95} +13.9807 q^{96} +2.01867 q^{97} +15.3266 q^{98} -7.63015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9} - q^{10} - 47 q^{11} - 11 q^{12} - 140 q^{13} - 12 q^{14} - 30 q^{15} + 64 q^{16} + 3 q^{17} - 22 q^{18} - 91 q^{19} - 24 q^{20} - 28 q^{21} - 12 q^{22} - 10 q^{23} - 42 q^{24} + 84 q^{25} + 6 q^{26} - 33 q^{27} - 71 q^{28} - 32 q^{29} - 45 q^{30} - 90 q^{31} - 31 q^{32} - 32 q^{33} - 78 q^{34} - 50 q^{35} + 10 q^{36} - 67 q^{37} - 8 q^{38} + 9 q^{39} - 10 q^{40} - 22 q^{41} - 30 q^{42} - 40 q^{43} - 88 q^{44} - 36 q^{45} - 77 q^{46} - 29 q^{47} - 4 q^{48} + 66 q^{49} - 45 q^{50} - 87 q^{51} - 112 q^{52} - 19 q^{53} - 82 q^{54} - 28 q^{55} - 63 q^{56} - 41 q^{57} - 96 q^{58} - 84 q^{59} - 106 q^{60} - 58 q^{61} - 3 q^{62} - 76 q^{63} - 55 q^{64} + 12 q^{65} - 56 q^{66} - 140 q^{67} - 4 q^{68} - 41 q^{69} - 106 q^{70} - 104 q^{71} - 52 q^{72} - 57 q^{73} - 24 q^{74} - 62 q^{75} - 184 q^{76} + 8 q^{77} + 18 q^{78} - 104 q^{79} - 102 q^{80} + 4 q^{81} - 37 q^{82} - 52 q^{83} - 94 q^{84} - 93 q^{85} - 79 q^{86} + 51 q^{87} - 47 q^{88} - 64 q^{89} + 22 q^{90} + 32 q^{91} - 42 q^{92} - 115 q^{93} - 43 q^{94} - 25 q^{95} - 116 q^{96} - 92 q^{97} - 36 q^{98} - 223 q^{99}+O(q^{100}) \) 140 * q - 6 * q^2 - 9 * q^3 + 112 * q^4 - 12 * q^5 - 18 * q^6 - 32 * q^7 - 15 * q^8 + 111 * q^9 - q^10 - 47 * q^11 - 11 * q^12 - 140 * q^13 - 12 * q^14 - 30 * q^15 + 64 * q^16 + 3 * q^17 - 22 * q^18 - 91 * q^19 - 24 * q^20 - 28 * q^21 - 12 * q^22 - 10 * q^23 - 42 * q^24 + 84 * q^25 + 6 * q^26 - 33 * q^27 - 71 * q^28 - 32 * q^29 - 45 * q^30 - 90 * q^31 - 31 * q^32 - 32 * q^33 - 78 * q^34 - 50 * q^35 + 10 * q^36 - 67 * q^37 - 8 * q^38 + 9 * q^39 - 10 * q^40 - 22 * q^41 - 30 * q^42 - 40 * q^43 - 88 * q^44 - 36 * q^45 - 77 * q^46 - 29 * q^47 - 4 * q^48 + 66 * q^49 - 45 * q^50 - 87 * q^51 - 112 * q^52 - 19 * q^53 - 82 * q^54 - 28 * q^55 - 63 * q^56 - 41 * q^57 - 96 * q^58 - 84 * q^59 - 106 * q^60 - 58 * q^61 - 3 * q^62 - 76 * q^63 - 55 * q^64 + 12 * q^65 - 56 * q^66 - 140 * q^67 - 4 * q^68 - 41 * q^69 - 106 * q^70 - 104 * q^71 - 52 * q^72 - 57 * q^73 - 24 * q^74 - 62 * q^75 - 184 * q^76 + 8 * q^77 + 18 * q^78 - 104 * q^79 - 102 * q^80 + 4 * q^81 - 37 * q^82 - 52 * q^83 - 94 * q^84 - 93 * q^85 - 79 * q^86 + 51 * q^87 - 47 * q^88 - 64 * q^89 + 22 * q^90 + 32 * q^91 - 42 * q^92 - 115 * q^93 - 43 * q^94 - 25 * q^95 - 116 * q^96 - 92 * q^97 - 36 * q^98 - 223 * q^99

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