LMFDB - Embedded newform 8021.2.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.42591 q^{2} -2.98941 q^{3} +3.88502 q^{4} -2.94726 q^{5} +7.25203 q^{6} -3.20190 q^{7} -4.57289 q^{8} +5.93657 q^{9} +O(q^{10})$	\(q-2.42591 q^{2} -2.98941 q^{3} +3.88502 q^{4} -2.94726 q^{5} +7.25203 q^{6} -3.20190 q^{7} -4.57289 q^{8} +5.93657 q^{9} +7.14978 q^{10} -5.65825 q^{11} -11.6139 q^{12} -1.00000 q^{13} +7.76751 q^{14} +8.81056 q^{15} +3.32335 q^{16} -1.76495 q^{17} -14.4016 q^{18} -6.89220 q^{19} -11.4502 q^{20} +9.57179 q^{21} +13.7264 q^{22} +3.29144 q^{23} +13.6702 q^{24} +3.68634 q^{25} +2.42591 q^{26} -8.77860 q^{27} -12.4395 q^{28} -8.24517 q^{29} -21.3736 q^{30} -3.85405 q^{31} +1.08363 q^{32} +16.9148 q^{33} +4.28160 q^{34} +9.43683 q^{35} +23.0637 q^{36} -8.08337 q^{37} +16.7198 q^{38} +2.98941 q^{39} +13.4775 q^{40} +3.44946 q^{41} -23.2203 q^{42} -9.67049 q^{43} -21.9824 q^{44} -17.4966 q^{45} -7.98472 q^{46} +1.48450 q^{47} -9.93487 q^{48} +3.25217 q^{49} -8.94271 q^{50} +5.27615 q^{51} -3.88502 q^{52} +7.52813 q^{53} +21.2961 q^{54} +16.6763 q^{55} +14.6419 q^{56} +20.6036 q^{57} +20.0020 q^{58} -12.4699 q^{59} +34.2292 q^{60} -4.95423 q^{61} +9.34956 q^{62} -19.0083 q^{63} -9.27549 q^{64} +2.94726 q^{65} -41.0338 q^{66} +13.8145 q^{67} -6.85686 q^{68} -9.83946 q^{69} -22.8929 q^{70} -6.71433 q^{71} -27.1473 q^{72} -12.7151 q^{73} +19.6095 q^{74} -11.0200 q^{75} -26.7764 q^{76} +18.1172 q^{77} -7.25203 q^{78} -9.01022 q^{79} -9.79479 q^{80} +8.43313 q^{81} -8.36807 q^{82} +4.43587 q^{83} +37.1866 q^{84} +5.20176 q^{85} +23.4597 q^{86} +24.6482 q^{87} +25.8745 q^{88} +3.26017 q^{89} +42.4451 q^{90} +3.20190 q^{91} +12.7873 q^{92} +11.5213 q^{93} -3.60126 q^{94} +20.3131 q^{95} -3.23941 q^{96} +5.56715 q^{97} -7.88946 q^{98} -33.5906 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.42591	−1.71537	−0.857687	−	0.514171i	$-0.828100\pi$
$2$	−2.42591	−1.71537	−0.857687	+	0.514171i	$0.828100\pi$
$3$	−2.98941	−1.72594	−0.862968	−	0.505258i	$-0.831397\pi$
$3$	−2.98941	−1.72594	−0.862968	+	0.505258i	$0.831397\pi$
$4$	3.88502	1.94251
$5$	−2.94726	−1.31805	−0.659027	−	0.752119i	$-0.729032\pi$
$5$	−2.94726	−1.31805	−0.659027	+	0.752119i	$0.729032\pi$
$6$	7.25203	2.96063
$7$	−3.20190	−1.21020	−0.605102	−	0.796148i	$-0.706868\pi$
$7$	−3.20190	−1.21020	−0.605102	+	0.796148i	$0.706868\pi$
$8$	−4.57289	−1.61676
$9$	5.93657	1.97886
$10$	7.14978	2.26096
$11$	−5.65825	−1.70603	−0.853013	−	0.521889i	$-0.825227\pi$
$11$	−5.65825	−1.70603	−0.853013	+	0.521889i	$0.825227\pi$
$12$	−11.6139	−3.35265
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	7.76751	2.07595
$15$	8.81056	2.27488
$16$	3.32335	0.830839
$17$	−1.76495	−0.428063	−0.214031	−	0.976827i	$-0.568659\pi$
$17$	−1.76495	−0.428063	−0.214031	+	0.976827i	$0.568659\pi$
$18$	−14.4016	−3.39448
$19$	−6.89220	−1.58118	−0.790590	−	0.612346i	$-0.790226\pi$
$19$	−6.89220	−1.58118	−0.790590	+	0.612346i	$0.790226\pi$
$20$	−11.4502	−2.56034
$21$	9.57179	2.08874
$22$	13.7264	2.92648
$23$	3.29144	0.686312	0.343156	−	0.939278i	$-0.388504\pi$
$23$	3.29144	0.686312	0.343156	+	0.939278i	$0.388504\pi$
$24$	13.6702	2.79042
$25$	3.68634	0.737268
$26$	2.42591	0.475759
$27$	−8.77860	−1.68944
$28$	−12.4395	−2.35084
$29$	−8.24517	−1.53109	−0.765545	−	0.643382i	$-0.777531\pi$
$29$	−8.24517	−1.53109	−0.765545	+	0.643382i	$0.777531\pi$
$30$	−21.3736	−3.90227
$31$	−3.85405	−0.692207	−0.346104	−	0.938196i	$-0.612495\pi$
$31$	−3.85405	−0.692207	−0.346104	+	0.938196i	$0.612495\pi$
$32$	1.08363	0.191560
$33$	16.9148	2.94449
$34$	4.28160	0.734288
$35$	9.43683	1.59512
$36$	23.0637	3.84395
$37$	−8.08337	−1.32890	−0.664449	−	0.747334i	$-0.731334\pi$
$37$	−8.08337	−1.32890	−0.664449	+	0.747334i	$0.731334\pi$
$38$	16.7198	2.71232
$39$	2.98941	0.478689
$40$	13.4775	2.13098
$41$	3.44946	0.538715	0.269358	−	0.963040i	$-0.413189\pi$
$41$	3.44946	0.538715	0.269358	+	0.963040i	$0.413189\pi$
$42$	−23.2203	−3.58297
$43$	−9.67049	−1.47474	−0.737368	−	0.675491i	$-0.763932\pi$
$43$	−9.67049	−1.47474	−0.737368	+	0.675491i	$0.763932\pi$
$44$	−21.9824	−3.31398
$45$	−17.4966	−2.60824
$46$	−7.98472	−1.17728
$47$	1.48450	0.216537	0.108268	−	0.994122i	$-0.465469\pi$
$47$	1.48450	0.216537	0.108268	+	0.994122i	$0.465469\pi$
$48$	−9.93487	−1.43397
$49$	3.25217	0.464596
$50$	−8.94271	−1.26469
$51$	5.27615	0.738809
$52$	−3.88502	−0.538756
$53$	7.52813	1.03407	0.517034	−	0.855965i	$-0.327036\pi$
$53$	7.52813	1.03407	0.517034	+	0.855965i	$0.327036\pi$
$54$	21.2961	2.89803
$55$	16.6763	2.24864
$56$	14.6419	1.95661
$57$	20.6036	2.72902
$58$	20.0020	2.62639
$59$	−12.4699	−1.62344	−0.811718	−	0.584049i	$-0.801468\pi$
$59$	−12.4699	−1.62344	−0.811718	+	0.584049i	$0.801468\pi$
$60$	34.2292	4.41898
$61$	−4.95423	−0.634325	−0.317162	−	0.948371i	$-0.602730\pi$
$61$	−4.95423	−0.634325	−0.317162	+	0.948371i	$0.602730\pi$
$62$	9.34956	1.18740
$63$	−19.0083	−2.39482
$64$	−9.27549	−1.15944
$65$	2.94726	0.365563
$66$	−41.0338	−5.05091
$67$	13.8145	1.68771	0.843855	−	0.536572i	$-0.180281\pi$
$67$	13.8145	1.68771	0.843855	+	0.536572i	$0.180281\pi$
$68$	−6.85686	−0.831517
$69$	−9.83946	−1.18453
$70$	−22.8929	−2.73622
$71$	−6.71433	−0.796844	−0.398422	−	0.917202i	$-0.630442\pi$
$71$	−6.71433	−0.796844	−0.398422	+	0.917202i	$0.630442\pi$
$72$	−27.1473	−3.19934
$73$	−12.7151	−1.48819	−0.744097	−	0.668072i	$-0.767120\pi$
$73$	−12.7151	−1.48819	−0.744097	+	0.668072i	$0.767120\pi$
$74$	19.6095	2.27956
$75$	−11.0200	−1.27248
$76$	−26.7764	−3.07146
$77$	18.1172	2.06464
$78$	−7.25203	−0.821130
$79$	−9.01022	−1.01373	−0.506864	−	0.862026i	$-0.669196\pi$
$79$	−9.01022	−1.01373	−0.506864	+	0.862026i	$0.669196\pi$
$80$	−9.79479	−1.09509
$81$	8.43313	0.937014
$82$	−8.36807	−0.924099
$83$	4.43587	0.486900	0.243450	−	0.969913i	$-0.421721\pi$
$83$	4.43587	0.486900	0.243450	+	0.969913i	$0.421721\pi$
$84$	37.1866	4.05739
$85$	5.20176	0.564210
$86$	23.4597	2.52973
$87$	24.6482	2.64256
$88$	25.8745	2.75824
$89$	3.26017	0.345577	0.172789	−	0.984959i	$-0.444722\pi$
$89$	3.26017	0.345577	0.172789	+	0.984959i	$0.444722\pi$
$90$	42.4451	4.47411
$91$	3.20190	0.335650
$92$	12.7873	1.33317
$93$	11.5213	1.19471
$94$	−3.60126	−0.371442
$95$	20.3131	2.08408
$96$	−3.23941	−0.330621
$97$	5.56715	0.565258	0.282629	−	0.959229i	$-0.408793\pi$
$97$	5.56715	0.565258	0.282629	+	0.959229i	$0.408793\pi$
$98$	−7.88946	−0.796956
$99$	−33.5906	−3.37598
$100$	14.3215	1.43215
$101$	4.27427	0.425306	0.212653	−	0.977128i	$-0.431790\pi$
$101$	4.27427	0.425306	0.212653	+	0.977128i	$0.431790\pi$
$102$	−12.7995	−1.26733
$103$	−14.9993	−1.47792	−0.738961	−	0.673748i	$-0.764683\pi$
$103$	−14.9993	−1.47792	−0.738961	+	0.673748i	$0.764683\pi$
$104$	4.57289	0.448409
$105$	−28.2106	−2.75307
$106$	−18.2625	−1.77381
$107$	−3.09939	−0.299630	−0.149815	−	0.988714i	$-0.547868\pi$
$107$	−3.09939	−0.299630	−0.149815	+	0.988714i	$0.547868\pi$
$108$	−34.1051	−3.28176
$109$	−8.87468	−0.850040	−0.425020	−	0.905184i	$-0.639733\pi$
$109$	−8.87468	−0.850040	−0.425020	+	0.905184i	$0.639733\pi$
$110$	−40.4552	−3.85725
$111$	24.1645	2.29359
$112$	−10.6411	−1.00549
$113$	−17.2815	−1.62570	−0.812851	−	0.582472i	$-0.802086\pi$
$113$	−17.2815	−1.62570	−0.812851	+	0.582472i	$0.802086\pi$
$114$	−49.9825	−4.68129
$115$	−9.70072	−0.904597
$116$	−32.0327	−2.97416
$117$	−5.93657	−0.548836
$118$	30.2507	2.78480
$119$	5.65119	0.518044
$120$	−40.2897	−3.67793
$121$	21.0158	1.91053
$122$	12.0185	1.08810
$123$	−10.3119	−0.929788
$124$	−14.9731	−1.34462
$125$	3.87170	0.346295
$126$	46.1124	4.10802
$127$	13.7508	1.22019	0.610093	−	0.792330i	$-0.291132\pi$
$127$	13.7508	1.22019	0.610093	+	0.792330i	$0.291132\pi$
$128$	20.3342	1.79731
$129$	28.9091	2.54530
$130$	−7.14978	−0.627077
$131$	2.15378	0.188176	0.0940881	−	0.995564i	$-0.470006\pi$
$131$	2.15378	0.188176	0.0940881	+	0.995564i	$0.470006\pi$
$132$	65.7145	5.71971
$133$	22.0682	1.91355
$134$	−33.5127	−2.89505
$135$	25.8728	2.22678
$136$	8.07091	0.692075
$137$	2.65167	0.226547	0.113274	−	0.993564i	$-0.463866\pi$
$137$	2.65167	0.226547	0.113274	+	0.993564i	$0.463866\pi$
$138$	23.8696	2.03192
$139$	−8.34932	−0.708180	−0.354090	−	0.935211i	$-0.615209\pi$
$139$	−8.34932	−0.708180	−0.354090	+	0.935211i	$0.615209\pi$
$140$	36.6623	3.09853
$141$	−4.43778	−0.373729
$142$	16.2883	1.36689
$143$	5.65825	0.473167
$144$	19.7293	1.64411
$145$	24.3007	2.01806
$146$	30.8457	2.55281
$147$	−9.72207	−0.801862
$148$	−31.4041	−2.58140
$149$	−10.8349	−0.887631	−0.443816	−	0.896118i	$-0.646375\pi$
$149$	−10.8349	−0.887631	−0.443816	+	0.896118i	$0.646375\pi$
$150$	26.7334	2.18278
$151$	−4.79513	−0.390222	−0.195111	−	0.980781i	$-0.562507\pi$
$151$	−4.79513	−0.390222	−0.195111	+	0.980781i	$0.562507\pi$
$152$	31.5173	2.55639
$153$	−10.4777	−0.847075
$154$	−43.9505	−3.54163
$155$	11.3589	0.912367
$156$	11.6139	0.929858
$157$	18.1551	1.44893	0.724467	−	0.689309i	$-0.242086\pi$
$157$	18.1551	1.44893	0.724467	+	0.689309i	$0.242086\pi$
$158$	21.8579	1.73893
$159$	−22.5046	−1.78473
$160$	−3.19373	−0.252487
$161$	−10.5389	−0.830578
$162$	−20.4580	−1.60733
$163$	−24.0049	−1.88021	−0.940105	−	0.340885i	$-0.889273\pi$
$163$	−24.0049	−1.88021	−0.940105	+	0.340885i	$0.889273\pi$
$164$	13.4012	1.04646
$165$	−49.8524	−3.88100
$166$	−10.7610	−0.835216
$167$	19.9355	1.54266	0.771329	−	0.636437i	$-0.219592\pi$
$167$	19.9355	1.54266	0.771329	+	0.636437i	$0.219592\pi$
$168$	−43.7707	−3.37699
$169$	1.00000	0.0769231
$170$	−12.6190	−0.967832
$171$	−40.9160	−3.12893
$172$	−37.5701	−2.86469
$173$	23.4698	1.78437	0.892187	−	0.451667i	$-0.149170\pi$
$173$	23.4698	1.78437	0.892187	+	0.451667i	$0.149170\pi$
$174$	−59.7942	−4.53299
$175$	−11.8033	−0.892245
$176$	−18.8044	−1.41743
$177$	37.2775	2.80195
$178$	−7.90886	−0.592794
$179$	18.8323	1.40759	0.703795	−	0.710403i	$-0.251487\pi$
$179$	18.8323	1.40759	0.703795	+	0.710403i	$0.251487\pi$
$180$	−67.9747	−5.06654
$181$	−6.90200	−0.513022	−0.256511	−	0.966541i	$-0.582573\pi$
$181$	−6.90200	−0.513022	−0.256511	+	0.966541i	$0.582573\pi$
$182$	−7.76751	−0.575766
$183$	14.8102	1.09480
$184$	−15.0514	−1.10960
$185$	23.8238	1.75156
$186$	−27.9497	−2.04937
$187$	9.98652	0.730286
$188$	5.76732	0.420625
$189$	28.1082	2.04457
$190$	−49.2777	−3.57498
$191$	−12.8869	−0.932464	−0.466232	−	0.884663i	$-0.654389\pi$
$191$	−12.8869	−0.932464	−0.466232	+	0.884663i	$0.654389\pi$
$192$	27.7282	2.00111
$193$	−4.32141	−0.311062	−0.155531	−	0.987831i	$-0.549709\pi$
$193$	−4.32141	−0.311062	−0.155531	+	0.987831i	$0.549709\pi$
$194$	−13.5054	−0.969629
$195$	−8.81056	−0.630938
$196$	12.6348	0.902482
$197$	−22.0624	−1.57188	−0.785939	−	0.618304i	$-0.787820\pi$
$197$	−22.0624	−1.57188	−0.785939	+	0.618304i	$0.787820\pi$
$198$	81.4876	5.79107
$199$	−9.98704	−0.707962	−0.353981	−	0.935253i	$-0.615172\pi$
$199$	−9.98704	−0.707962	−0.353981	+	0.935253i	$0.615172\pi$
$200$	−16.8572	−1.19199
$201$	−41.2972	−2.91288
$202$	−10.3690	−0.729560
$203$	26.4002	1.85293
$204$	20.4980	1.43514
$205$	−10.1665	−0.710056
$206$	36.3868	2.53519
$207$	19.5398	1.35811
$208$	−3.32335	−0.230433
$209$	38.9978	2.69754
$210$	68.4362	4.72254
$211$	1.85298	0.127564	0.0637822	−	0.997964i	$-0.479684\pi$
$211$	1.85298	0.127564	0.0637822	+	0.997964i	$0.479684\pi$
$212$	29.2469	2.00869
$213$	20.0719	1.37530
$214$	7.51884	0.513977
$215$	28.5015	1.94378
$216$	40.1436	2.73142
$217$	12.3403	0.837713
$218$	21.5291	1.45814
$219$	38.0107	2.56853
$220$	64.7879	4.36800
$221$	1.76495	0.118723
$222$	−58.6208	−3.93437
$223$	−7.75689	−0.519440	−0.259720	−	0.965684i	$-0.583630\pi$
$223$	−7.75689	−0.519440	−0.259720	+	0.965684i	$0.583630\pi$
$224$	−3.46967	−0.231827
$225$	21.8842	1.45895
$226$	41.9232	2.78869
$227$	−27.2190	−1.80659	−0.903295	−	0.429020i	$-0.858859\pi$
$227$	−27.2190	−1.80659	−0.903295	+	0.429020i	$0.858859\pi$
$228$	80.0455	5.30114
$229$	22.7149	1.50104	0.750520	−	0.660848i	$-0.229803\pi$
$229$	22.7149	1.50104	0.750520	+	0.660848i	$0.229803\pi$
$230$	23.5330	1.55172
$231$	−54.1596	−3.56344
$232$	37.7042	2.47541
$233$	7.83708	0.513425	0.256712	−	0.966488i	$-0.417361\pi$
$233$	7.83708	0.513425	0.256712	+	0.966488i	$0.417361\pi$
$234$	14.4016	0.941459
$235$	−4.37521	−0.285407
$236$	−48.4457	−3.15354
$237$	26.9352	1.74963
$238$	−13.7093	−0.888639
$239$	24.2706	1.56993	0.784967	−	0.619537i	$-0.212680\pi$
$239$	24.2706	1.56993	0.784967	+	0.619537i	$0.212680\pi$
$240$	29.2806	1.89006
$241$	18.9268	1.21919	0.609593	−	0.792715i	$-0.291333\pi$
$241$	18.9268	1.21919	0.609593	+	0.792715i	$0.291333\pi$
$242$	−50.9823	−3.27727
$243$	1.12573	0.0722155
$244$	−19.2473	−1.23218
$245$	−9.58499	−0.612362
$246$	25.0156	1.59494
$247$	6.89220	0.438540
$248$	17.6241	1.11913
$249$	−13.2606	−0.840358
$250$	−9.39238	−0.594027
$251$	13.1391	0.829331	0.414666	−	0.909974i	$-0.363899\pi$
$251$	13.1391	0.829331	0.414666	+	0.909974i	$0.363899\pi$
$252$	−73.8477	−4.65197
$253$	−18.6238	−1.17087
$254$	−33.3581	−2.09308
$255$	−15.5502	−0.973791
$256$	−30.7779	−1.92362
$257$	4.05563	0.252983	0.126492	−	0.991968i	$-0.459628\pi$
$257$	4.05563	0.252983	0.126492	+	0.991968i	$0.459628\pi$
$258$	−70.1307	−4.36615
$259$	25.8821	1.60824
$260$	11.4502	0.710109
$261$	−48.9480	−3.02981
$262$	−5.22486	−0.322793
$263$	12.3316	0.760401	0.380201	−	0.924904i	$-0.375855\pi$
$263$	12.3316	0.760401	0.380201	+	0.924904i	$0.375855\pi$
$264$	−77.3496	−4.76054
$265$	−22.1873	−1.36296
$266$	−53.5353	−3.28246
$267$	−9.74598	−0.596444
$268$	53.6696	3.27839
$269$	13.8500	0.844452	0.422226	−	0.906490i	$-0.361249\pi$
$269$	13.8500	0.844452	0.422226	+	0.906490i	$0.361249\pi$
$270$	−62.7650	−3.81976
$271$	6.14725	0.373419	0.186709	−	0.982415i	$-0.440218\pi$
$271$	6.14725	0.373419	0.186709	+	0.982415i	$0.440218\pi$
$272$	−5.86555	−0.355651
$273$	−9.57179	−0.579311
$274$	−6.43270	−0.388614
$275$	−20.8582	−1.25780
$276$	−38.2265	−2.30097
$277$	−6.07646	−0.365099	−0.182550	−	0.983197i	$-0.558435\pi$
$277$	−6.07646	−0.365099	−0.182550	+	0.983197i	$0.558435\pi$
$278$	20.2547	1.21479
$279$	−22.8798	−1.36978
$280$	−43.1536	−2.57892
$281$	30.1840	1.80062	0.900312	−	0.435245i	$-0.143338\pi$
$281$	30.1840	1.80062	0.900312	+	0.435245i	$0.143338\pi$
$282$	10.7656	0.641085
$283$	20.6513	1.22759	0.613797	−	0.789464i	$-0.289642\pi$
$283$	20.6513	1.22759	0.613797	+	0.789464i	$0.289642\pi$
$284$	−26.0853	−1.54788
$285$	−60.7242	−3.59699
$286$	−13.7264	−0.811658
$287$	−11.0448	−0.651956
$288$	6.43303	0.379070
$289$	−13.8850	−0.816762
$290$	−58.9511	−3.46173
$291$	−16.6425	−0.975599
$292$	−49.3986	−2.89083
$293$	−4.23432	−0.247372	−0.123686	−	0.992321i	$-0.539472\pi$
$293$	−4.23432	−0.247372	−0.123686	+	0.992321i	$0.539472\pi$
$294$	23.5848	1.37549
$295$	36.7519	2.13978
$296$	36.9643	2.14851
$297$	49.6715	2.88223
$298$	26.2845	1.52262
$299$	−3.29144	−0.190349
$300$	−42.8129	−2.47180
$301$	30.9640	1.78473
$302$	11.6325	0.669377
$303$	−12.7776	−0.734051
$304$	−22.9052	−1.31371
$305$	14.6014	0.836074
$306$	25.4180	1.45305
$307$	−0.361536	−0.0206340	−0.0103170	−	0.999947i	$-0.503284\pi$
$307$	−0.361536	−0.0206340	−0.0103170	+	0.999947i	$0.503284\pi$
$308$	70.3856	4.01059
$309$	44.8390	2.55080
$310$	−27.5556	−1.56505
$311$	−29.8977	−1.69534	−0.847672	−	0.530521i	$-0.821996\pi$
$311$	−29.8977	−1.69534	−0.847672	+	0.530521i	$0.821996\pi$
$312$	−13.6702	−0.773925
$313$	12.9572	0.732383	0.366191	−	0.930540i	$-0.380662\pi$
$313$	12.9572	0.732383	0.366191	+	0.930540i	$0.380662\pi$
$314$	−44.0426	−2.48547
$315$	56.0224	3.15650
$316$	−35.0049	−1.96918
$317$	3.53059	0.198298	0.0991488	−	0.995073i	$-0.468388\pi$
$317$	3.53059	0.198298	0.0991488	+	0.995073i	$0.468388\pi$
$318$	54.5942	3.06149
$319$	46.6532	2.61208
$320$	27.3373	1.52820
$321$	9.26536	0.517142
$322$	25.5663	1.42475
$323$	12.1644	0.676844
$324$	32.7629	1.82016
$325$	−3.68634	−0.204481
$326$	58.2337	3.22527
$327$	26.5300	1.46711
$328$	−15.7740	−0.870974
$329$	−4.75323	−0.262054
$330$	120.937	6.65737
$331$	−34.5284	−1.89785	−0.948926	−	0.315498i	$-0.897828\pi$
$331$	−34.5284	−1.89785	−0.948926	+	0.315498i	$0.897828\pi$
$332$	17.2334	0.945808
$333$	−47.9875	−2.62970
$334$	−48.3617	−2.64624
$335$	−40.7149	−2.22449
$336$	31.8105	1.73540
$337$	28.9478	1.57689	0.788444	−	0.615106i	$-0.210887\pi$
$337$	28.9478	1.57689	0.788444	+	0.615106i	$0.210887\pi$
$338$	−2.42591	−0.131952
$339$	51.6613	2.80586
$340$	20.2090	1.09598
$341$	21.8072	1.18092
$342$	99.2585	5.36728
$343$	12.0002	0.647949
$344$	44.2221	2.38429
$345$	28.9994	1.56128
$346$	−56.9355	−3.06087
$347$	24.9308	1.33836	0.669179	−	0.743101i	$-0.266646\pi$
$347$	24.9308	1.33836	0.669179	+	0.743101i	$0.266646\pi$
$348$	95.7588	5.13321
$349$	15.9001	0.851112	0.425556	−	0.904932i	$-0.360079\pi$
$349$	15.9001	0.851112	0.425556	+	0.904932i	$0.360079\pi$
$350$	28.6337	1.53053
$351$	8.77860	0.468567
$352$	−6.13144	−0.326807
$353$	19.5796	1.04212	0.521058	−	0.853521i	$-0.325538\pi$
$353$	19.5796	1.04212	0.521058	+	0.853521i	$0.325538\pi$
$354$	−90.4317	−4.80639
$355$	19.7889	1.05028
$356$	12.6658	0.671288
$357$	−16.8937	−0.894110
$358$	−45.6854	−2.41455
$359$	−10.8831	−0.574388	−0.287194	−	0.957873i	$-0.592722\pi$
$359$	−10.8831	−0.574388	−0.287194	+	0.957873i	$0.592722\pi$
$360$	80.0100	4.21690
$361$	28.5025	1.50013
$362$	16.7436	0.880025
$363$	−62.8248	−3.29745
$364$	12.4395	0.652005
$365$	37.4748	1.96152
$366$	−35.9282	−1.87800
$367$	−9.22999	−0.481802	−0.240901	−	0.970550i	$-0.577443\pi$
$367$	−9.22999	−0.481802	−0.240901	+	0.970550i	$0.577443\pi$
$368$	10.9386	0.570215
$369$	20.4780	1.06604
$370$	−57.7943	−3.00458
$371$	−24.1043	−1.25143
$372$	44.7606	2.32073
$373$	−3.41141	−0.176636	−0.0883180	−	0.996092i	$-0.528149\pi$
$373$	−3.41141	−0.176636	−0.0883180	+	0.996092i	$0.528149\pi$
$374$	−24.2264	−1.25272
$375$	−11.5741	−0.597684
$376$	−6.78846	−0.350088
$377$	8.24517	0.424648
$378$	−68.1879	−3.50721
$379$	−15.2146	−0.781520	−0.390760	−	0.920493i	$-0.627788\pi$
$379$	−15.2146	−0.781520	−0.390760	+	0.920493i	$0.627788\pi$
$380$	78.9169	4.04835
$381$	−41.1067	−2.10596
$382$	31.2624	1.59953
$383$	−16.1450	−0.824968	−0.412484	−	0.910965i	$-0.635339\pi$
$383$	−16.1450	−0.824968	−0.412484	+	0.910965i	$0.635339\pi$
$384$	−60.7873	−3.10204
$385$	−53.3960	−2.72131
$386$	10.4833	0.533588
$387$	−57.4095	−2.91829
$388$	21.6285	1.09802
$389$	32.9710	1.67170	0.835848	−	0.548961i	$-0.184976\pi$
$389$	32.9710	1.67170	0.835848	+	0.548961i	$0.184976\pi$
$390$	21.3736	1.08229
$391$	−5.80922	−0.293785
$392$	−14.8718	−0.751140
$393$	−6.43852	−0.324780
$394$	53.5212	2.69636
$395$	26.5555	1.33615
$396$	−130.500	−6.55788
$397$	5.02348	0.252121	0.126061	−	0.992023i	$-0.459767\pi$
$397$	5.02348	0.252121	0.126061	+	0.992023i	$0.459767\pi$
$398$	24.2276	1.21442
$399$	−65.9707	−3.30267
$400$	12.2510	0.612551
$401$	−15.7654	−0.787286	−0.393643	−	0.919263i	$-0.628785\pi$
$401$	−15.7654	−0.787286	−0.393643	+	0.919263i	$0.628785\pi$
$402$	100.183	4.99668
$403$	3.85405	0.191984
$404$	16.6057	0.826162
$405$	−24.8546	−1.23504
$406$	−64.0445	−3.17847
$407$	45.7377	2.26713
$408$	−24.1273	−1.19448
$409$	−11.1276	−0.550227	−0.275113	−	0.961412i	$-0.588715\pi$
$409$	−11.1276	−0.550227	−0.275113	+	0.961412i	$0.588715\pi$
$410$	24.6629	1.21801
$411$	−7.92692	−0.391006
$412$	−58.2725	−2.87088
$413$	39.9272	1.96469
$414$	−47.4018	−2.32967
$415$	−13.0737	−0.641761
$416$	−1.08363	−0.0531293
$417$	24.9595	1.22227
$418$	−94.6051	−4.62728
$419$	23.9065	1.16791	0.583954	−	0.811786i	$-0.301505\pi$
$419$	23.9065	1.16791	0.583954	+	0.811786i	$0.301505\pi$
$420$	−109.599	−5.34787
$421$	−35.5817	−1.73415	−0.867074	−	0.498180i	$-0.834002\pi$
$421$	−35.5817	−1.73415	−0.867074	+	0.498180i	$0.834002\pi$
$422$	−4.49515	−0.218821
$423$	8.81284	0.428495
$424$	−34.4253	−1.67184
$425$	−6.50620	−0.315597
$426$	−48.6925	−2.35916
$427$	15.8630	0.767663
$428$	−12.0412	−0.582034
$429$	−16.9148	−0.816655
$430$	−69.1419	−3.33432
$431$	3.11899	0.150236	0.0751182	−	0.997175i	$-0.476067\pi$
$431$	3.11899	0.150236	0.0751182	+	0.997175i	$0.476067\pi$
$432$	−29.1744	−1.40365
$433$	35.8461	1.72265	0.861327	−	0.508051i	$-0.169634\pi$
$433$	35.8461	1.72265	0.861327	+	0.508051i	$0.169634\pi$
$434$	−29.9364	−1.43699
$435$	−72.6446	−3.48304
$436$	−34.4783	−1.65121
$437$	−22.6853	−1.08518
$438$	−92.2105	−4.40599
$439$	−0.968038	−0.0462019	−0.0231010	−	0.999733i	$-0.507354\pi$
$439$	−0.968038	−0.0462019	−0.0231010	+	0.999733i	$0.507354\pi$
$440$	−76.2590	−3.63551
$441$	19.3067	0.919368
$442$	−4.28160	−0.203655
$443$	1.20030	0.0570279	0.0285140	−	0.999593i	$-0.490922\pi$
$443$	1.20030	0.0570279	0.0285140	+	0.999593i	$0.490922\pi$
$444$	93.8796	4.45533
$445$	−9.60856	−0.455490
$446$	18.8175	0.891034
$447$	32.3900	1.53199
$448$	29.6992	1.40316
$449$	−2.64582	−0.124864	−0.0624319	−	0.998049i	$-0.519886\pi$
$449$	−2.64582	−0.124864	−0.0624319	+	0.998049i	$0.519886\pi$
$450$	−53.0890	−2.50264
$451$	−19.5179	−0.919063
$452$	−67.1388	−3.15794
$453$	14.3346	0.673498
$454$	66.0308	3.09898
$455$	−9.43683	−0.442406
$456$	−94.2180	−4.41216
$457$	21.7497	1.01741	0.508704	−	0.860941i	$-0.330125\pi$
$457$	21.7497	1.01741	0.508704	+	0.860941i	$0.330125\pi$
$458$	−55.1041	−2.57485
$459$	15.4938	0.723188
$460$	−37.6875	−1.75719
$461$	−30.0922	−1.40153	−0.700767	−	0.713391i	$-0.747159\pi$
$461$	−30.0922	−1.40153	−0.700767	+	0.713391i	$0.747159\pi$
$462$	131.386	6.11263
$463$	21.8255	1.01432	0.507159	−	0.861852i	$-0.330696\pi$
$463$	21.8255	1.01432	0.507159	+	0.861852i	$0.330696\pi$
$464$	−27.4016	−1.27209
$465$	−33.9563	−1.57469
$466$	−19.0120	−0.880716
$467$	−0.177312	−0.00820500	−0.00410250	−	0.999992i	$-0.501306\pi$
$467$	−0.177312	−0.00820500	−0.00410250	+	0.999992i	$0.501306\pi$
$468$	−23.0637	−1.06612
$469$	−44.2327	−2.04247
$470$	10.6139	0.489580
$471$	−54.2730	−2.50077
$472$	57.0232	2.62471
$473$	54.7181	2.51594
$474$	−65.3424	−3.00127
$475$	−25.4070	−1.16575
$476$	21.9550	1.00631
$477$	44.6912	2.04627
$478$	−58.8782	−2.69303
$479$	22.5051	1.02829	0.514143	−	0.857705i	$-0.328110\pi$
$479$	22.5051	1.02829	0.514143	+	0.857705i	$0.328110\pi$
$480$	9.54738	0.435776
$481$	8.08337	0.368570
$482$	−45.9148	−2.09136
$483$	31.5050	1.43353
$484$	81.6468	3.71122
$485$	−16.4078	−0.745041
$486$	−2.73091	−0.123877
$487$	−31.3736	−1.42167	−0.710837	−	0.703357i	$-0.751684\pi$
$487$	−31.3736	−1.42167	−0.710837	+	0.703357i	$0.751684\pi$
$488$	22.6552	1.02555
$489$	71.7605	3.24512
$490$	23.2523	1.05043
$491$	−9.39729	−0.424094	−0.212047	−	0.977260i	$-0.568013\pi$
$491$	−9.39729	−0.424094	−0.212047	+	0.977260i	$0.568013\pi$
$492$	−40.0618	−1.80612
$493$	14.5523	0.655403
$494$	−16.7198	−0.752261
$495$	99.0002	4.44973
$496$	−12.8084	−0.575113
$497$	21.4986	0.964344
$498$	32.1690	1.44153
$499$	−27.5852	−1.23489	−0.617443	−	0.786616i	$-0.711831\pi$
$499$	−27.5852	−1.23489	−0.617443	+	0.786616i	$0.711831\pi$
$500$	15.0416	0.672683
$501$	−59.5955	−2.66253
$502$	−31.8742	−1.42261
$503$	−0.927256	−0.0413443	−0.0206722	−	0.999786i	$-0.506581\pi$
$503$	−0.927256	−0.0413443	−0.0206722	+	0.999786i	$0.506581\pi$
$504$	86.9228	3.87185
$505$	−12.5974	−0.560577
$506$	45.1795	2.00848
$507$	−2.98941	−0.132764
$508$	53.4221	2.37022
$509$	−34.8542	−1.54489	−0.772443	−	0.635084i	$-0.780965\pi$
$509$	−34.8542	−1.54489	−0.772443	+	0.635084i	$0.780965\pi$
$510$	37.7233	1.67042
$511$	40.7126	1.80102
$512$	33.9959	1.50242
$513$	60.5039	2.67131
$514$	−9.83858	−0.433961
$515$	44.2068	1.94798
$516$	112.312	4.94428
$517$	−8.39968	−0.369417
$518$	−62.7877	−2.75873
$519$	−70.1607	−3.07971
$520$	−13.4775	−0.591027
$521$	18.0303	0.789924	0.394962	−	0.918698i	$-0.370758\pi$
$521$	18.0303	0.789924	0.394962	+	0.918698i	$0.370758\pi$
$522$	118.743	5.19725
$523$	−5.15494	−0.225410	−0.112705	−	0.993629i	$-0.535951\pi$
$523$	−5.15494	−0.225410	−0.112705	+	0.993629i	$0.535951\pi$
$524$	8.36747	0.365535
$525$	35.2849	1.53996
$526$	−29.9154	−1.30437
$527$	6.80219	0.296308
$528$	56.2140	2.44640
$529$	−12.1664	−0.528975
$530$	53.8244	2.33798
$531$	−74.0281	−3.21255
$532$	85.7353	3.71710
$533$	−3.44946	−0.149413
$534$	23.6428	1.02313
$535$	9.13472	0.394928
$536$	−63.1722	−2.72862
$537$	−56.2974	−2.42941
$538$	−33.5989	−1.44855
$539$	−18.4016	−0.792612
$540$	100.516	4.32554
$541$	13.1723	0.566323	0.283162	−	0.959072i	$-0.408617\pi$
$541$	13.1723	0.566323	0.283162	+	0.959072i	$0.408617\pi$
$542$	−14.9127	−0.640553
$543$	20.6329	0.885443
$544$	−1.91255	−0.0819998
$545$	26.1560	1.12040
$546$	23.2203	0.993736
$547$	4.06526	0.173818	0.0869089	−	0.996216i	$-0.472301\pi$
$547$	4.06526	0.173818	0.0869089	+	0.996216i	$0.472301\pi$
$548$	10.3018	0.440071
$549$	−29.4111	−1.25524
$550$	50.6001	2.15760
$551$	56.8274	2.42093
$552$	44.9947	1.91510
$553$	28.8498	1.22682
$554$	14.7409	0.626282
$555$	−71.2190	−3.02308
$556$	−32.4373	−1.37565
$557$	−5.92882	−0.251212	−0.125606	−	0.992080i	$-0.540088\pi$
$557$	−5.92882	−0.251212	−0.125606	+	0.992080i	$0.540088\pi$
$558$	55.5043	2.34968
$559$	9.67049	0.409018
$560$	31.3619	1.32528
$561$	−29.8538	−1.26043
$562$	−73.2235	−3.08875
$563$	−4.52983	−0.190909	−0.0954547	−	0.995434i	$-0.530431\pi$
$563$	−4.52983	−0.190909	−0.0954547	+	0.995434i	$0.530431\pi$
$564$	−17.2409	−0.725972
$565$	50.9329	2.14276
$566$	−50.0982	−2.10578
$567$	−27.0020	−1.13398
$568$	30.7039	1.28831
$569$	13.1403	0.550872	0.275436	−	0.961319i	$-0.411178\pi$
$569$	13.1403	0.550872	0.275436	+	0.961319i	$0.411178\pi$
$570$	147.311	6.17019
$571$	−2.27650	−0.0952687	−0.0476344	−	0.998865i	$-0.515168\pi$
$571$	−2.27650	−0.0952687	−0.0476344	+	0.998865i	$0.515168\pi$
$572$	21.9824	0.919132
$573$	38.5242	1.60937
$574$	26.7937	1.11835
$575$	12.1334	0.505996
$576$	−55.0646	−2.29436
$577$	3.71045	0.154468	0.0772341	−	0.997013i	$-0.475391\pi$
$577$	3.71045	0.154468	0.0772341	+	0.997013i	$0.475391\pi$
$578$	33.6836	1.40105
$579$	12.9185	0.536873
$580$	94.4086	3.92010
$581$	−14.2032	−0.589249
$582$	40.3731	1.67352
$583$	−42.5960	−1.76415
$584$	58.1449	2.40605
$585$	17.4966	0.723396
$586$	10.2721	0.424335
$587$	−32.4012	−1.33734	−0.668670	−	0.743559i	$-0.733136\pi$
$587$	−32.4012	−1.33734	−0.668670	+	0.743559i	$0.733136\pi$
$588$	−37.7704	−1.55763
$589$	26.5629	1.09450
$590$	−89.1567	−3.67052
$591$	65.9534	2.71296
$592$	−26.8639	−1.10410
$593$	−32.0052	−1.31430	−0.657148	−	0.753762i	$-0.728237\pi$
$593$	−32.0052	−1.31430	−0.657148	+	0.753762i	$0.728237\pi$
$594$	−120.498	−4.94411
$595$	−16.6555	−0.682810
$596$	−42.0939	−1.72423
$597$	29.8553	1.22190
$598$	7.98472	0.326520
$599$	−2.25459	−0.0921200	−0.0460600	−	0.998939i	$-0.514667\pi$
$599$	−2.25459	−0.0921200	−0.0460600	+	0.998939i	$0.514667\pi$
$600$	50.3931	2.05729
$601$	19.1056	0.779332	0.389666	−	0.920956i	$-0.372590\pi$
$601$	19.1056	0.779332	0.389666	+	0.920956i	$0.372590\pi$
$602$	−75.1157	−3.06149
$603$	82.0107	3.33973
$604$	−18.6292	−0.758011
$605$	−61.9390	−2.51818
$606$	30.9972	1.25917
$607$	26.3010	1.06753	0.533763	−	0.845634i	$-0.320777\pi$
$607$	26.3010	1.06753	0.533763	+	0.845634i	$0.320777\pi$
$608$	−7.46859	−0.302891
$609$	−78.9211	−3.19804
$610$	−35.4217	−1.43418
$611$	−1.48450	−0.0600565
$612$	−40.7062	−1.64545
$613$	−16.1680	−0.653020	−0.326510	−	0.945194i	$-0.605873\pi$
$613$	−16.1680	−0.653020	−0.326510	+	0.945194i	$0.605873\pi$
$614$	0.877053	0.0353950
$615$	30.3917	1.22551
$616$	−82.8477	−3.33803
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−108.775	−4.37558
$619$	−28.6686	−1.15229	−0.576145	−	0.817348i	$-0.695444\pi$
$619$	−28.6686	−1.15229	−0.576145	+	0.817348i	$0.695444\pi$
$620$	44.1295	1.77228
$621$	−28.8942	−1.15949
$622$	72.5290	2.90815
$623$	−10.4387	−0.418219
$624$	9.93487	0.397713
$625$	−29.8426	−1.19370
$626$	−31.4329	−1.25631
$627$	−116.580	−4.65577
$628$	70.5329	2.81457
$629$	14.2667	0.568852
$630$	−135.905	−5.41459
$631$	−10.0642	−0.400650	−0.200325	−	0.979729i	$-0.564200\pi$
$631$	−10.0642	−0.400650	−0.200325	+	0.979729i	$0.564200\pi$
$632$	41.2027	1.63896
$633$	−5.53931	−0.220168
$634$	−8.56487	−0.340155
$635$	−40.5272	−1.60827
$636$	−87.4311	−3.46687
$637$	−3.25217	−0.128856
$638$	−113.176	−4.48070
$639$	−39.8601	−1.57684
$640$	−59.9302	−2.36895
$641$	23.4477	0.926128	0.463064	−	0.886325i	$-0.346750\pi$
$641$	23.4477	0.926128	0.463064	+	0.886325i	$0.346750\pi$
$642$	−22.4769	−0.887092
$643$	33.4021	1.31725	0.658626	−	0.752471i	$-0.271138\pi$
$643$	33.4021	1.31725	0.658626	+	0.752471i	$0.271138\pi$
$644$	−40.9437	−1.61341
$645$	−85.2025	−3.35485
$646$	−29.5097	−1.16104
$647$	−9.38403	−0.368924	−0.184462	−	0.982840i	$-0.559054\pi$
$647$	−9.38403	−0.368924	−0.184462	+	0.982840i	$0.559054\pi$
$648$	−38.5638	−1.51493
$649$	70.5575	2.76963
$650$	8.94271	0.350762
$651$	−36.8901	−1.44584
$652$	−93.2596	−3.65233
$653$	−31.9485	−1.25024	−0.625120	−	0.780529i	$-0.714950\pi$
$653$	−31.9485	−1.25024	−0.625120	+	0.780529i	$0.714950\pi$
$654$	−64.3594	−2.51665
$655$	−6.34774	−0.248027
$656$	11.4638	0.447586
$657$	−75.4842	−2.94492
$658$	11.5309	0.449521
$659$	−49.3334	−1.92176	−0.960879	−	0.276968i	$-0.910670\pi$
$659$	−49.3334	−1.92176	−0.960879	+	0.276968i	$0.910670\pi$
$660$	−193.678	−7.53889
$661$	20.8779	0.812055	0.406027	−	0.913861i	$-0.366914\pi$
$661$	20.8779	0.812055	0.406027	+	0.913861i	$0.366914\pi$
$662$	83.7627	3.25553
$663$	−5.27615	−0.204909
$664$	−20.2847	−0.787200
$665$	−65.0406	−2.52217
$666$	116.413	4.51092
$667$	−27.1385	−1.05081
$668$	77.4500	2.99663
$669$	23.1885	0.896520
$670$	98.7706	3.81584
$671$	28.0323	1.08217
$672$	10.3723	0.400119
$673$	−16.8584	−0.649843	−0.324922	−	0.945741i	$-0.605338\pi$
$673$	−16.8584	−0.649843	−0.324922	+	0.945741i	$0.605338\pi$
$674$	−70.2247	−2.70496
$675$	−32.3609	−1.24557
$676$	3.88502	0.149424
$677$	10.5616	0.405917	0.202959	−	0.979187i	$-0.434944\pi$
$677$	10.5616	0.405917	0.202959	+	0.979187i	$0.434944\pi$
$678$	−125.326	−4.81310
$679$	−17.8254	−0.684078
$680$	−23.7871	−0.912192
$681$	81.3688	3.11806
$682$	−52.9021	−2.02573
$683$	1.79449	0.0686642	0.0343321	−	0.999410i	$-0.489070\pi$
$683$	1.79449	0.0686642	0.0343321	+	0.999410i	$0.489070\pi$
$684$	−158.960	−6.07798
$685$	−7.81515	−0.298602
$686$	−29.1113	−1.11148
$687$	−67.9040	−2.59070
$688$	−32.1385	−1.22527
$689$	−7.52813	−0.286799
$690$	−70.3499	−2.67818
$691$	19.1405	0.728140	0.364070	−	0.931372i	$-0.381387\pi$
$691$	19.1405	0.728140	0.364070	+	0.931372i	$0.381387\pi$
$692$	91.1806	3.46617
$693$	107.554	4.08563
$694$	−60.4799	−2.29579
$695$	24.6076	0.933420
$696$	−112.713	−4.27239
$697$	−6.08812	−0.230604
$698$	−38.5721	−1.45998
$699$	−23.4283	−0.886138
$700$	−45.8561	−1.73320
$701$	17.2808	0.652687	0.326343	−	0.945251i	$-0.394183\pi$
$701$	17.2808	0.652687	0.326343	+	0.945251i	$0.394183\pi$
$702$	−21.2961	−0.803768
$703$	55.7122	2.10123
$704$	52.4830	1.97803
$705$	13.0793	0.492595
$706$	−47.4982	−1.78762
$707$	−13.6858	−0.514708
$708$	144.824	5.44282
$709$	−18.5684	−0.697351	−0.348676	−	0.937243i	$-0.613369\pi$
$709$	−18.5684	−0.697351	−0.348676	+	0.937243i	$0.613369\pi$
$710$	−48.0059	−1.80163
$711$	−53.4898	−2.00602
$712$	−14.9084	−0.558715
$713$	−12.6854	−0.475070
$714$	40.9826	1.53373
$715$	−16.6763	−0.623659
$716$	73.1638	2.73426
$717$	−72.5548	−2.70961
$718$	26.4014	0.985290
$719$	−27.9682	−1.04304	−0.521519	−	0.853239i	$-0.674635\pi$
$719$	−27.9682	−1.04304	−0.521519	+	0.853239i	$0.674635\pi$
$720$	−58.1474	−2.16703
$721$	48.0262	1.78859
$722$	−69.1443	−2.57329
$723$	−56.5801	−2.10424
$724$	−26.8144	−0.996551
$725$	−30.3945	−1.12882
$726$	152.407	5.65636
$727$	−26.8999	−0.997663	−0.498831	−	0.866699i	$-0.666237\pi$
$727$	−26.8999	−0.997663	−0.498831	+	0.866699i	$0.666237\pi$
$728$	−14.6419	−0.542666
$729$	−28.6647	−1.06165
$730$	−90.9103	−3.36474
$731$	17.0679	0.631280
$732$	57.5381	2.12667
$733$	39.6699	1.46524	0.732621	−	0.680636i	$-0.238297\pi$
$733$	39.6699	1.46524	0.732621	+	0.680636i	$0.238297\pi$
$734$	22.3911	0.826471
$735$	28.6534	1.05690
$736$	3.56670	0.131470
$737$	−78.1659	−2.87928
$738$	−49.6776	−1.82866
$739$	13.4793	0.495844	0.247922	−	0.968780i	$-0.420252\pi$
$739$	13.4793	0.495844	0.247922	+	0.968780i	$0.420252\pi$
$740$	92.5559	3.40242
$741$	−20.6036	−0.756893
$742$	58.4748	2.14668
$743$	14.2498	0.522774	0.261387	−	0.965234i	$-0.415820\pi$
$743$	14.2498	0.522774	0.261387	+	0.965234i	$0.415820\pi$
$744$	−52.6857	−1.93155
$745$	31.9333	1.16995
$746$	8.27576	0.302997
$747$	26.3338	0.963505
$748$	38.7978	1.41859
$749$	9.92395	0.362613
$750$	28.0777	1.02525
$751$	−14.9570	−0.545788	−0.272894	−	0.962044i	$-0.587981\pi$
$751$	−14.9570	−0.545788	−0.272894	+	0.962044i	$0.587981\pi$
$752$	4.93352	0.179907
$753$	−39.2781	−1.43137
$754$	−20.0020	−0.728430
$755$	14.1325	0.514334
$756$	109.201	3.97160
$757$	−11.1966	−0.406947	−0.203473	−	0.979080i	$-0.565223\pi$
$757$	−11.1966	−0.406947	−0.203473	+	0.979080i	$0.565223\pi$
$758$	36.9091	1.34060
$759$	55.6741	2.02084
$760$	−92.8896	−3.36946
$761$	−46.4765	−1.68477	−0.842385	−	0.538876i	$-0.818849\pi$
$761$	−46.4765	−1.68477	−0.842385	+	0.538876i	$0.818849\pi$
$762$	99.7211	3.61251
$763$	28.4158	1.02872
$764$	−50.0659	−1.81132
$765$	30.8806	1.11649
$766$	39.1661	1.41513
$767$	12.4699	0.450260
$768$	92.0078	3.32005
$769$	−43.7403	−1.57731	−0.788657	−	0.614833i	$-0.789223\pi$
$769$	−43.7403	−1.57731	−0.788657	+	0.614833i	$0.789223\pi$
$770$	129.534	4.66807
$771$	−12.1239	−0.436633
$772$	−16.7888	−0.604241
$773$	−12.9501	−0.465784	−0.232892	−	0.972503i	$-0.574819\pi$
$773$	−12.9501	−0.465784	−0.232892	+	0.972503i	$0.574819\pi$
$774$	139.270	5.00596
$775$	−14.2073	−0.510342
$776$	−25.4579	−0.913887
$777$	−77.3723	−2.77572
$778$	−79.9846	−2.86759
$779$	−23.7744	−0.851806
$780$	−34.2292	−1.22560
$781$	37.9913	1.35944
$782$	14.0926	0.503951
$783$	72.3811	2.58669
$784$	10.8081	0.386004
$785$	−53.5078	−1.90977
$786$	15.6192	0.557120
$787$	−18.4638	−0.658165	−0.329082	−	0.944301i	$-0.606739\pi$
$787$	−18.4638	−0.658165	−0.329082	+	0.944301i	$0.606739\pi$
$788$	−85.7128	−3.05339
$789$	−36.8643	−1.31240
$790$	−64.4211	−2.29200
$791$	55.3335	1.96743
$792$	153.606	5.45815
$793$	4.95423	0.175930
$794$	−12.1865	−0.432483
$795$	66.3270	2.35238
$796$	−38.7999	−1.37522
$797$	15.0247	0.532201	0.266100	−	0.963945i	$-0.414265\pi$
$797$	15.0247	0.532201	0.266100	+	0.963945i	$0.414265\pi$
$798$	160.039	5.66531
$799$	−2.62007	−0.0926913
$800$	3.99462	0.141231
$801$	19.3542	0.683847
$802$	38.2454	1.35049
$803$	71.9454	2.53890
$804$	−160.441	−5.65830
$805$	31.0608	1.09475
$806$	−9.34956	−0.329324
$807$	−41.4035	−1.45747
$808$	−19.5458	−0.687618
$809$	21.8462	0.768072	0.384036	−	0.923318i	$-0.374534\pi$
$809$	21.8462	0.768072	0.384036	+	0.923318i	$0.374534\pi$
$810$	60.2950	2.11855
$811$	−3.65780	−0.128443	−0.0642214	−	0.997936i	$-0.520456\pi$
$811$	−3.65780	−0.128443	−0.0642214	+	0.997936i	$0.520456\pi$
$812$	102.565	3.59934
$813$	−18.3766	−0.644497
$814$	−110.955	−3.88899
$815$	70.7487	2.47822
$816$	17.5345	0.613831
$817$	66.6510	2.33182
$818$	26.9946	0.943845
$819$	19.0083	0.664204
$820$	−39.4969	−1.37929
$821$	33.1251	1.15607	0.578037	−	0.816011i	$-0.303819\pi$
$821$	33.1251	1.15607	0.578037	+	0.816011i	$0.303819\pi$
$822$	19.2300	0.670722
$823$	−48.8745	−1.70366	−0.851829	−	0.523820i	$-0.824507\pi$
$823$	−48.8745	−1.70366	−0.851829	+	0.523820i	$0.824507\pi$
$824$	68.5900	2.38945
$825$	62.3538	2.17088
$826$	−96.8597	−3.37018
$827$	−3.57195	−0.124209	−0.0621044	−	0.998070i	$-0.519781\pi$
$827$	−3.57195	−0.124209	−0.0621044	+	0.998070i	$0.519781\pi$
$828$	75.9127	2.63815
$829$	36.0916	1.25351	0.626757	−	0.779215i	$-0.284382\pi$
$829$	36.0916	1.25351	0.626757	+	0.779215i	$0.284382\pi$
$830$	31.7155	1.10086
$831$	18.1650	0.630138
$832$	9.27549	0.321570
$833$	−5.73991	−0.198876
$834$	−60.5495	−2.09666
$835$	−58.7552	−2.03331
$836$	151.507	5.23999
$837$	33.8331	1.16944
$838$	−57.9949	−2.00340
$839$	−0.243871	−0.00841935	−0.00420968	−	0.999991i	$-0.501340\pi$
$839$	−0.243871	−0.00841935	−0.00420968	+	0.999991i	$0.501340\pi$
$840$	129.004	4.45105
$841$	38.9829	1.34424
$842$	86.3179	2.97471
$843$	−90.2322	−3.10776
$844$	7.19886	0.247795
$845$	−2.94726	−0.101389
$846$	−21.3791	−0.735030
$847$	−67.2905	−2.31213
$848$	25.0186	0.859143
$849$	−61.7352	−2.11875
$850$	15.7834	0.541367
$851$	−26.6059	−0.912039
$852$	77.9797	2.67154
$853$	−41.2554	−1.41256	−0.706279	−	0.707934i	$-0.749628\pi$
$853$	−41.2554	−1.41256	−0.706279	+	0.707934i	$0.749628\pi$
$854$	−38.4821	−1.31683
$855$	120.590	4.12410
$856$	14.1732	0.484430
$857$	−8.63895	−0.295101	−0.147550	−	0.989055i	$-0.547139\pi$
$857$	−8.63895	−0.295101	−0.147550	+	0.989055i	$0.547139\pi$
$858$	41.0338	1.40087
$859$	−24.1851	−0.825185	−0.412593	−	0.910916i	$-0.635377\pi$
$859$	−24.1851	−0.825185	−0.412593	+	0.910916i	$0.635377\pi$
$860$	110.729	3.77582
$861$	33.0175	1.12523
$862$	−7.56638	−0.257712
$863$	−51.2873	−1.74584	−0.872920	−	0.487863i	$-0.837777\pi$
$863$	−51.2873	−1.74584	−0.872920	+	0.487863i	$0.837777\pi$
$864$	−9.51274	−0.323630
$865$	−69.1715	−2.35190
$866$	−86.9593	−2.95500
$867$	41.5078	1.40968
$868$	47.9423	1.62727
$869$	50.9821	1.72945
$870$	176.229	5.97472
$871$	−13.8145	−0.468086
$872$	40.5829	1.37431
$873$	33.0497	1.11856
$874$	55.0323	1.86150
$875$	−12.3968	−0.419088
$876$	147.673	4.98939
$877$	31.2186	1.05418	0.527089	−	0.849810i	$-0.323283\pi$
$877$	31.2186	1.05418	0.527089	+	0.849810i	$0.323283\pi$
$878$	2.34837	0.0792536
$879$	12.6581	0.426948
$880$	55.4214	1.86825
$881$	12.5471	0.422724	0.211362	−	0.977408i	$-0.432210\pi$
$881$	12.5471	0.422724	0.211362	+	0.977408i	$0.432210\pi$
$882$	−46.8363	−1.57706
$883$	−8.80171	−0.296201	−0.148101	−	0.988972i	$-0.547316\pi$
$883$	−8.80171	−0.296201	−0.148101	+	0.988972i	$0.547316\pi$
$884$	6.85686	0.230621
$885$	−109.866	−3.69312
$886$	−2.91181	−0.0978243
$887$	−20.5007	−0.688346	−0.344173	−	0.938906i	$-0.611841\pi$
$887$	−20.5007	−0.688346	−0.344173	+	0.938906i	$0.611841\pi$
$888$	−110.502	−3.70819
$889$	−44.0287	−1.47667
$890$	23.3095	0.781335
$891$	−47.7168	−1.59857
$892$	−30.1357	−1.00902
$893$	−10.2315	−0.342384
$894$	−78.5751	−2.62795
$895$	−55.5036	−1.85528
$896$	−65.1082	−2.17511
$897$	9.83946	0.328530
$898$	6.41850	0.214188
$899$	31.7773	1.05983
$900$	85.0206	2.83402
$901$	−13.2868	−0.442646
$902$	47.3486	1.57654
$903$	−92.5639	−3.08034
$904$	79.0262	2.62837
$905$	20.3420	0.676191
$906$	−34.7744	−1.15530
$907$	−47.3251	−1.57141	−0.785703	−	0.618604i	$-0.787699\pi$
$907$	−47.3251	−1.57141	−0.785703	+	0.618604i	$0.787699\pi$
$908$	−105.747	−3.50932
$909$	25.3745	0.841620
$910$	22.8929	0.758891
$911$	−31.6438	−1.04840	−0.524202	−	0.851594i	$-0.675636\pi$
$911$	−31.6438	−1.04840	−0.524202	+	0.851594i	$0.675636\pi$
$912$	68.4731	2.26737
$913$	−25.0993	−0.830664
$914$	−52.7627	−1.74524
$915$	−43.6496	−1.44301
$916$	88.2477	2.91579
$917$	−6.89618	−0.227732
$918$	−37.5865	−1.24054
$919$	21.4626	0.707985	0.353993	−	0.935248i	$-0.384824\pi$
$919$	21.4626	0.707985	0.353993	+	0.935248i	$0.384824\pi$
$920$	44.3603	1.46252
$921$	1.08078	0.0356129
$922$	73.0009	2.40416
$923$	6.71433	0.221005
$924$	−210.411	−6.92202
$925$	−29.7980	−0.979753
$926$	−52.9467	−1.73994
$927$	−89.0442	−2.92460
$928$	−8.93470	−0.293296
$929$	4.48214	0.147054	0.0735271	−	0.997293i	$-0.476574\pi$
$929$	4.48214	0.147054	0.0735271	+	0.997293i	$0.476574\pi$
$930$	82.3749	2.70118
$931$	−22.4146	−0.734609
$932$	30.4473	0.997333
$933$	89.3765	2.92605
$934$	0.430141	0.0140746
$935$	−29.4329	−0.962557
$936$	27.1473	0.887336
$937$	−2.91881	−0.0953534	−0.0476767	−	0.998863i	$-0.515182\pi$
$937$	−2.91881	−0.0953534	−0.0476767	+	0.998863i	$0.515182\pi$
$938$	107.304	3.50361
$939$	−38.7343	−1.26405
$940$	−16.9978	−0.554407
$941$	12.0139	0.391643	0.195821	−	0.980640i	$-0.437263\pi$
$941$	12.0139	0.391643	0.195821	+	0.980640i	$0.437263\pi$
$942$	131.661	4.28975
$943$	11.3537	0.369727
$944$	−41.4417	−1.34881
$945$	−82.8422	−2.69486
$946$	−132.741	−4.31578
$947$	−56.2927	−1.82927	−0.914633	−	0.404285i	$-0.867521\pi$
$947$	−56.2927	−1.82927	−0.914633	+	0.404285i	$0.867521\pi$
$948$	104.644	3.39868
$949$	12.7151	0.412751
$950$	61.6350	1.99970
$951$	−10.5544	−0.342249
$952$	−25.8423	−0.837552
$953$	−54.9146	−1.77886	−0.889430	−	0.457071i	$-0.848898\pi$
$953$	−54.9146	−1.77886	−0.889430	+	0.457071i	$0.848898\pi$
$954$	−108.417	−3.51012
$955$	37.9811	1.22904
$956$	94.2918	3.04962
$957$	−139.466	−4.50828
$958$	−54.5953	−1.76390
$959$	−8.49038	−0.274169
$960$	−81.7223	−2.63758
$961$	−16.1463	−0.520849
$962$	−19.6095	−0.632236
$963$	−18.3998	−0.592924
$964$	73.5312	2.36828
$965$	12.7363	0.409997
$966$	−76.4281	−2.45903
$967$	56.5070	1.81714	0.908571	−	0.417730i	$-0.137174\pi$
$967$	56.5070	1.81714	0.908571	+	0.417730i	$0.137174\pi$
$968$	−96.1029	−3.08886
$969$	−36.3643	−1.16819
$970$	39.8038	1.27802
$971$	−17.6655	−0.566913	−0.283457	−	0.958985i	$-0.591481\pi$
$971$	−17.6655	−0.566913	−0.283457	+	0.958985i	$0.591481\pi$
$972$	4.37348	0.140279
$973$	26.7337	0.857043
$974$	76.1095	2.43870
$975$	11.0200	0.352922
$976$	−16.4647	−0.527021
$977$	32.5452	1.04121	0.520606	−	0.853797i	$-0.325706\pi$
$977$	32.5452	1.04121	0.520606	+	0.853797i	$0.325706\pi$
$978$	−174.084	−5.56660
$979$	−18.4468	−0.589564
$980$	−37.2379	−1.18952
$981$	−52.6851	−1.68211
$982$	22.7969	0.727480
$983$	55.4805	1.76955	0.884777	−	0.466014i	$-0.154311\pi$
$983$	55.4805	1.76955	0.884777	+	0.466014i	$0.154311\pi$
$984$	47.1549	1.50324
$985$	65.0235	2.07182
$986$	−35.3025	−1.12426
$987$	14.2093	0.452288
$988$	26.7764	0.851870
$989$	−31.8298	−1.01213
$990$	−240.165	−7.63295
$991$	22.1684	0.704202	0.352101	−	0.935962i	$-0.385467\pi$
$991$	22.1684	0.704202	0.352101	+	0.935962i	$0.385467\pi$
$992$	−4.17635	−0.132599
$993$	103.220	3.27557
$994$	−52.1536	−1.65421
$995$	29.4344	0.933133
$996$	−51.5178	−1.63241
$997$	−3.47880	−0.110175	−0.0550873	−	0.998482i	$-0.517544\pi$
$997$	−3.47880	−0.110175	−0.0550873	+	0.998482i	$0.517544\pi$
$998$	66.9192	2.11829
$999$	70.9607	2.24510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.13	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.42591 q^{2} -2.98941 q^{3} +3.88502 q^{4} -2.94726 q^{5} +7.25203 q^{6} -3.20190 q^{7} -4.57289 q^{8} +5.93657 q^{9} +O(q^{10})\)	\(q-2.42591 q^{2} -2.98941 q^{3} +3.88502 q^{4} -2.94726 q^{5} +7.25203 q^{6} -3.20190 q^{7} -4.57289 q^{8} +5.93657 q^{9} +7.14978 q^{10} -5.65825 q^{11} -11.6139 q^{12} -1.00000 q^{13} +7.76751 q^{14} +8.81056 q^{15} +3.32335 q^{16} -1.76495 q^{17} -14.4016 q^{18} -6.89220 q^{19} -11.4502 q^{20} +9.57179 q^{21} +13.7264 q^{22} +3.29144 q^{23} +13.6702 q^{24} +3.68634 q^{25} +2.42591 q^{26} -8.77860 q^{27} -12.4395 q^{28} -8.24517 q^{29} -21.3736 q^{30} -3.85405 q^{31} +1.08363 q^{32} +16.9148 q^{33} +4.28160 q^{34} +9.43683 q^{35} +23.0637 q^{36} -8.08337 q^{37} +16.7198 q^{38} +2.98941 q^{39} +13.4775 q^{40} +3.44946 q^{41} -23.2203 q^{42} -9.67049 q^{43} -21.9824 q^{44} -17.4966 q^{45} -7.98472 q^{46} +1.48450 q^{47} -9.93487 q^{48} +3.25217 q^{49} -8.94271 q^{50} +5.27615 q^{51} -3.88502 q^{52} +7.52813 q^{53} +21.2961 q^{54} +16.6763 q^{55} +14.6419 q^{56} +20.6036 q^{57} +20.0020 q^{58} -12.4699 q^{59} +34.2292 q^{60} -4.95423 q^{61} +9.34956 q^{62} -19.0083 q^{63} -9.27549 q^{64} +2.94726 q^{65} -41.0338 q^{66} +13.8145 q^{67} -6.85686 q^{68} -9.83946 q^{69} -22.8929 q^{70} -6.71433 q^{71} -27.1473 q^{72} -12.7151 q^{73} +19.6095 q^{74} -11.0200 q^{75} -26.7764 q^{76} +18.1172 q^{77} -7.25203 q^{78} -9.01022 q^{79} -9.79479 q^{80} +8.43313 q^{81} -8.36807 q^{82} +4.43587 q^{83} +37.1866 q^{84} +5.20176 q^{85} +23.4597 q^{86} +24.6482 q^{87} +25.8745 q^{88} +3.26017 q^{89} +42.4451 q^{90} +3.20190 q^{91} +12.7873 q^{92} +11.5213 q^{93} -3.60126 q^{94} +20.3131 q^{95} -3.23941 q^{96} +5.56715 q^{97} -7.88946 q^{98} -33.5906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 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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