LMFDB - Embedded newform 8021.2.a.b.1.19

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			1.19
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)

$f(q)$	$=$	$q-2.13500 q^{2} +1.79448 q^{3} +2.55821 q^{4} +1.65943 q^{5} -3.83121 q^{6} -2.70571 q^{7} -1.19178 q^{8} +0.220161 q^{9} +O(q^{10})$	\(q-2.13500 q^{2} +1.79448 q^{3} +2.55821 q^{4} +1.65943 q^{5} -3.83121 q^{6} -2.70571 q^{7} -1.19178 q^{8} +0.220161 q^{9} -3.54288 q^{10} +4.44641 q^{11} +4.59066 q^{12} -1.00000 q^{13} +5.77668 q^{14} +2.97782 q^{15} -2.57198 q^{16} +1.33965 q^{17} -0.470044 q^{18} +0.897098 q^{19} +4.24518 q^{20} -4.85534 q^{21} -9.49308 q^{22} +2.33749 q^{23} -2.13863 q^{24} -2.24629 q^{25} +2.13500 q^{26} -4.98837 q^{27} -6.92178 q^{28} -9.67980 q^{29} -6.35763 q^{30} +0.587081 q^{31} +7.87472 q^{32} +7.97901 q^{33} -2.86014 q^{34} -4.48994 q^{35} +0.563219 q^{36} +7.82945 q^{37} -1.91530 q^{38} -1.79448 q^{39} -1.97768 q^{40} +1.35262 q^{41} +10.3661 q^{42} +2.76377 q^{43} +11.3749 q^{44} +0.365342 q^{45} -4.99053 q^{46} -8.01765 q^{47} -4.61536 q^{48} +0.320859 q^{49} +4.79582 q^{50} +2.40397 q^{51} -2.55821 q^{52} -4.23098 q^{53} +10.6501 q^{54} +7.37852 q^{55} +3.22461 q^{56} +1.60982 q^{57} +20.6663 q^{58} -7.72599 q^{59} +7.61789 q^{60} -6.04817 q^{61} -1.25342 q^{62} -0.595692 q^{63} -11.6686 q^{64} -1.65943 q^{65} -17.0352 q^{66} +6.44800 q^{67} +3.42710 q^{68} +4.19458 q^{69} +9.58600 q^{70} -10.8324 q^{71} -0.262384 q^{72} -9.63811 q^{73} -16.7158 q^{74} -4.03092 q^{75} +2.29497 q^{76} -12.0307 q^{77} +3.83121 q^{78} +0.348852 q^{79} -4.26802 q^{80} -9.61201 q^{81} -2.88784 q^{82} -13.7081 q^{83} -12.4210 q^{84} +2.22305 q^{85} -5.90064 q^{86} -17.3702 q^{87} -5.29915 q^{88} -3.66596 q^{89} -0.780005 q^{90} +2.70571 q^{91} +5.97979 q^{92} +1.05351 q^{93} +17.1177 q^{94} +1.48867 q^{95} +14.1310 q^{96} -5.88355 q^{97} -0.685032 q^{98} +0.978928 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.13500	−1.50967	−0.754835	−	0.655914i	$-0.772283\pi$
$2$	−2.13500	−1.50967	−0.754835	+	0.655914i	$0.772283\pi$
$3$	1.79448	1.03604	0.518022	−	0.855367i	$-0.326669\pi$
$3$	1.79448	1.03604	0.518022	+	0.855367i	$0.326669\pi$
$4$	2.55821	1.27911
$5$	1.65943	0.742120	0.371060	−	0.928609i	$-0.378994\pi$
$5$	1.65943	0.742120	0.371060	+	0.928609i	$0.378994\pi$
$6$	−3.83121	−1.56409
$7$	−2.70571	−1.02266	−0.511331	−	0.859384i	$-0.670847\pi$
$7$	−2.70571	−1.02266	−0.511331	+	0.859384i	$0.670847\pi$
$8$	−1.19178	−0.421358
$9$	0.220161	0.0733871
$10$	−3.54288	−1.12036
$11$	4.44641	1.34064	0.670322	−	0.742070i	$-0.266156\pi$
$11$	4.44641	1.34064	0.670322	+	0.742070i	$0.266156\pi$
$12$	4.59066	1.32521
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.77668	1.54388
$15$	2.97782	0.768869
$16$	−2.57198	−0.642994
$17$	1.33965	0.324912	0.162456	−	0.986716i	$-0.448058\pi$
$17$	1.33965	0.324912	0.162456	+	0.986716i	$0.448058\pi$
$18$	−0.470044	−0.110790
$19$	0.897098	0.205808	0.102904	−	0.994691i	$-0.467187\pi$
$19$	0.897098	0.205808	0.102904	+	0.994691i	$0.467187\pi$
$20$	4.24518	0.949250
$21$	−4.85534	−1.05952
$22$	−9.49308	−2.02393
$23$	2.33749	0.487400	0.243700	−	0.969851i	$-0.421639\pi$
$23$	2.33749	0.487400	0.243700	+	0.969851i	$0.421639\pi$
$24$	−2.13863	−0.436546
$25$	−2.24629	−0.449258
$26$	2.13500	0.418707
$27$	−4.98837	−0.960012
$28$	−6.92178	−1.30809
$29$	−9.67980	−1.79749	−0.898747	−	0.438468i	$-0.855521\pi$
$29$	−9.67980	−1.79749	−0.898747	+	0.438468i	$0.855521\pi$
$30$	−6.35763	−1.16074
$31$	0.587081	0.105443	0.0527214	−	0.998609i	$-0.483210\pi$
$31$	0.587081	0.105443	0.0527214	+	0.998609i	$0.483210\pi$
$32$	7.87472	1.39207
$33$	7.97901	1.38897
$34$	−2.86014	−0.490510
$35$	−4.48994	−0.758938
$36$	0.563219	0.0938699
$37$	7.82945	1.28715	0.643577	−	0.765382i	$-0.277450\pi$
$37$	7.82945	1.28715	0.643577	+	0.765382i	$0.277450\pi$
$38$	−1.91530	−0.310703
$39$	−1.79448	−0.287347
$40$	−1.97768	−0.312698
$41$	1.35262	0.211244	0.105622	−	0.994406i	$-0.466317\pi$
$41$	1.35262	0.211244	0.105622	+	0.994406i	$0.466317\pi$
$42$	10.3661	1.59953
$43$	2.76377	0.421471	0.210735	−	0.977543i	$-0.432414\pi$
$43$	2.76377	0.421471	0.210735	+	0.977543i	$0.432414\pi$
$44$	11.3749	1.71483
$45$	0.365342	0.0544620
$46$	−4.99053	−0.735813
$47$	−8.01765	−1.16950	−0.584748	−	0.811215i	$-0.698806\pi$
$47$	−8.01765	−1.16950	−0.584748	+	0.811215i	$0.698806\pi$
$48$	−4.61536	−0.666170
$49$	0.320859	0.0458370
$50$	4.79582	0.678231
$51$	2.40397	0.336623
$52$	−2.55821	−0.354760
$53$	−4.23098	−0.581170	−0.290585	−	0.956849i	$-0.593850\pi$
$53$	−4.23098	−0.581170	−0.290585	+	0.956849i	$0.593850\pi$
$54$	10.6501	1.44930
$55$	7.37852	0.994919
$56$	3.22461	0.430907
$57$	1.60982	0.213226
$58$	20.6663	2.71362
$59$	−7.72599	−1.00584	−0.502919	−	0.864333i	$-0.667741\pi$
$59$	−7.72599	−1.00584	−0.502919	+	0.864333i	$0.667741\pi$
$60$	7.61789	0.983465
$61$	−6.04817	−0.774388	−0.387194	−	0.921998i	$-0.626556\pi$
$61$	−6.04817	−0.774388	−0.387194	+	0.921998i	$0.626556\pi$
$62$	−1.25342	−0.159184
$63$	−0.595692	−0.0750502
$64$	−11.6686	−1.45857
$65$	−1.65943	−0.205827
$66$	−17.0352	−2.09688
$67$	6.44800	0.787748	0.393874	−	0.919164i	$-0.371135\pi$
$67$	6.44800	0.787748	0.393874	+	0.919164i	$0.371135\pi$
$68$	3.42710	0.415597
$69$	4.19458	0.504968
$70$	9.58600	1.14575
$71$	−10.8324	−1.28557	−0.642785	−	0.766047i	$-0.722221\pi$
$71$	−10.8324	−1.28557	−0.642785	+	0.766047i	$0.722221\pi$
$72$	−0.262384	−0.0309222
$73$	−9.63811	−1.12806	−0.564028	−	0.825756i	$-0.690749\pi$
$73$	−9.63811	−1.12806	−0.564028	+	0.825756i	$0.690749\pi$
$74$	−16.7158	−1.94318
$75$	−4.03092	−0.465451
$76$	2.29497	0.263251
$77$	−12.0307	−1.37103
$78$	3.83121	0.433799
$79$	0.348852	0.0392489	0.0196244	−	0.999807i	$-0.493753\pi$
$79$	0.348852	0.0392489	0.0196244	+	0.999807i	$0.493753\pi$
$80$	−4.26802	−0.477179
$81$	−9.61201	−1.06800
$82$	−2.88784	−0.318909
$83$	−13.7081	−1.50466	−0.752332	−	0.658784i	$-0.771071\pi$
$83$	−13.7081	−1.50466	−0.752332	+	0.658784i	$0.771071\pi$
$84$	−12.4210	−1.35524
$85$	2.22305	0.241124
$86$	−5.90064	−0.636282
$87$	−17.3702	−1.86228
$88$	−5.29915	−0.564892
$89$	−3.66596	−0.388591	−0.194296	−	0.980943i	$-0.562242\pi$
$89$	−3.66596	−0.388591	−0.194296	+	0.980943i	$0.562242\pi$
$90$	−0.780005	−0.0822198
$91$	2.70571	0.283635
$92$	5.97979	0.623436
$93$	1.05351	0.109243
$94$	17.1177	1.76555
$95$	1.48867	0.152735
$96$	14.1310	1.44224
$97$	−5.88355	−0.597384	−0.298692	−	0.954350i	$-0.596550\pi$
$97$	−5.88355	−0.597384	−0.298692	+	0.954350i	$0.596550\pi$
$98$	−0.685032	−0.0691987
$99$	0.978928	0.0983860
$100$	−5.74648	−0.574648
$101$	11.8673	1.18084	0.590420	−	0.807096i	$-0.298962\pi$
$101$	11.8673	1.18084	0.590420	+	0.807096i	$0.298962\pi$
$102$	−5.13247	−0.508190
$103$	−0.577308	−0.0568838	−0.0284419	−	0.999595i	$-0.509055\pi$
$103$	−0.577308	−0.0568838	−0.0284419	+	0.999595i	$0.509055\pi$
$104$	1.19178	0.116864
$105$	−8.05711	−0.786293
$106$	9.03313	0.877375
$107$	7.83814	0.757741	0.378871	−	0.925450i	$-0.376313\pi$
$107$	7.83814	0.757741	0.378871	+	0.925450i	$0.376313\pi$
$108$	−12.7613	−1.22796
$109$	19.9972	1.91539	0.957694	−	0.287789i	$-0.0929203\pi$
$109$	19.9972	1.91539	0.957694	+	0.287789i	$0.0929203\pi$
$110$	−15.7531	−1.50200
$111$	14.0498	1.33355
$112$	6.95902	0.657565
$113$	14.7167	1.38443	0.692215	−	0.721692i	$-0.256635\pi$
$113$	14.7167	1.38443	0.692215	+	0.721692i	$0.256635\pi$
$114$	−3.43697	−0.321902
$115$	3.87890	0.361709
$116$	−24.7630	−2.29919
$117$	−0.220161	−0.0203539
$118$	16.4950	1.51849
$119$	−3.62469	−0.332275
$120$	−3.54891	−0.323969
$121$	8.77060	0.797327
$122$	12.9128	1.16907
$123$	2.42725	0.218858
$124$	1.50188	0.134873
$125$	−12.0247	−1.07552
$126$	1.27180	0.113301
$127$	−10.0315	−0.890150	−0.445075	−	0.895493i	$-0.646823\pi$
$127$	−10.0315	−0.890150	−0.445075	+	0.895493i	$0.646823\pi$
$128$	9.16289	0.809893
$129$	4.95953	0.436662
$130$	3.54288	0.310731
$131$	−5.34568	−0.467054	−0.233527	−	0.972350i	$-0.575027\pi$
$131$	−5.34568	−0.467054	−0.233527	+	0.972350i	$0.575027\pi$
$132$	20.4120	1.77664
$133$	−2.42728	−0.210472
$134$	−13.7665	−1.18924
$135$	−8.27785	−0.712444
$136$	−1.59657	−0.136904
$137$	−14.9779	−1.27965	−0.639823	−	0.768522i	$-0.720993\pi$
$137$	−14.9779	−1.27965	−0.639823	+	0.768522i	$0.720993\pi$
$138$	−8.95541	−0.762335
$139$	0.151130	0.0128187	0.00640933	−	0.999979i	$-0.497960\pi$
$139$	0.151130	0.0128187	0.00640933	+	0.999979i	$0.497960\pi$
$140$	−11.4862	−0.970762
$141$	−14.3875	−1.21165
$142$	23.1271	1.94079
$143$	−4.44641	−0.371828
$144$	−0.566249	−0.0471874
$145$	−16.0630	−1.33396
$146$	20.5773	1.70299
$147$	0.575775	0.0474891
$148$	20.0294	1.64641
$149$	12.6218	1.03401	0.517007	−	0.855981i	$-0.327046\pi$
$149$	12.6218	1.03401	0.517007	+	0.855981i	$0.327046\pi$
$150$	8.60600	0.702677
$151$	12.9654	1.05511	0.527556	−	0.849520i	$-0.323109\pi$
$151$	12.9654	1.05511	0.527556	+	0.849520i	$0.323109\pi$
$152$	−1.06914	−0.0867190
$153$	0.294938	0.0238444
$154$	25.6855	2.06980
$155$	0.974221	0.0782513
$156$	−4.59066	−0.367547
$157$	3.01142	0.240337	0.120169	−	0.992753i	$-0.461656\pi$
$157$	3.01142	0.240337	0.120169	+	0.992753i	$0.461656\pi$
$158$	−0.744797	−0.0592529
$159$	−7.59241	−0.602117
$160$	13.0676	1.03308
$161$	−6.32456	−0.498445
$162$	20.5216	1.61233
$163$	−7.42805	−0.581810	−0.290905	−	0.956752i	$-0.593956\pi$
$163$	−7.42805	−0.581810	−0.290905	+	0.956752i	$0.593956\pi$
$164$	3.46029	0.270203
$165$	13.2406	1.03078
$166$	29.2669	2.27155
$167$	−10.9788	−0.849566	−0.424783	−	0.905295i	$-0.639650\pi$
$167$	−10.9788	−0.849566	−0.424783	+	0.905295i	$0.639650\pi$
$168$	5.78650	0.446439
$169$	1.00000	0.0769231
$170$	−4.74621	−0.364018
$171$	0.197506	0.0151037
$172$	7.07031	0.539106
$173$	11.1358	0.846637	0.423319	−	0.905981i	$-0.360865\pi$
$173$	11.1358	0.846637	0.423319	+	0.905981i	$0.360865\pi$
$174$	37.0854	2.81143
$175$	6.07780	0.459438
$176$	−11.4361	−0.862026
$177$	−13.8641	−1.04209
$178$	7.82682	0.586645
$179$	17.2180	1.28693	0.643466	−	0.765475i	$-0.277496\pi$
$179$	17.2180	1.28693	0.643466	+	0.765475i	$0.277496\pi$
$180$	0.934623	0.0696627
$181$	−23.5654	−1.75160	−0.875801	−	0.482673i	$-0.839666\pi$
$181$	−23.5654	−1.75160	−0.875801	+	0.482673i	$0.839666\pi$
$182$	−5.77668	−0.428196
$183$	−10.8533	−0.802300
$184$	−2.78577	−0.205370
$185$	12.9924	0.955223
$186$	−2.24923	−0.164922
$187$	5.95663	0.435592
$188$	−20.5109	−1.49591
$189$	13.4971	0.981767
$190$	−3.17831	−0.230579
$191$	22.1929	1.60583	0.802913	−	0.596097i	$-0.203283\pi$
$191$	22.1929	1.60583	0.802913	+	0.596097i	$0.203283\pi$
$192$	−20.9390	−1.51114
$193$	−21.6436	−1.55794	−0.778970	−	0.627061i	$-0.784258\pi$
$193$	−21.6436	−1.55794	−0.778970	+	0.627061i	$0.784258\pi$
$194$	12.5614	0.901853
$195$	−2.97782	−0.213246
$196$	0.820825	0.0586303
$197$	−27.9774	−1.99331	−0.996655	−	0.0817260i	$-0.973957\pi$
$197$	−27.9774	−1.99331	−0.996655	+	0.0817260i	$0.973957\pi$
$198$	−2.09001	−0.148530
$199$	4.60481	0.326426	0.163213	−	0.986591i	$-0.447814\pi$
$199$	4.60481	0.326426	0.163213	+	0.986591i	$0.447814\pi$
$200$	2.67708	0.189298
$201$	11.5708	0.816142
$202$	−25.3366	−1.78268
$203$	26.1907	1.83823
$204$	6.14987	0.430577
$205$	2.24458	0.156768
$206$	1.23255	0.0858759
$207$	0.514624	0.0357688
$208$	2.57198	0.178334
$209$	3.98887	0.275916
$210$	17.2019	1.18704
$211$	−1.57066	−0.108129	−0.0540645	−	0.998537i	$-0.517218\pi$
$211$	−1.57066	−0.108129	−0.0540645	+	0.998537i	$0.517218\pi$
$212$	−10.8237	−0.743378
$213$	−19.4385	−1.33191
$214$	−16.7344	−1.14394
$215$	4.58628	0.312782
$216$	5.94504	0.404509
$217$	−1.58847	−0.107832
$218$	−42.6940	−2.89160
$219$	−17.2954	−1.16871
$220$	18.8758	1.27261
$221$	−1.33965	−0.0901144
$222$	−29.9963	−2.01322
$223$	−13.0081	−0.871088	−0.435544	−	0.900167i	$-0.643444\pi$
$223$	−13.0081	−0.871088	−0.435544	+	0.900167i	$0.643444\pi$
$224$	−21.3067	−1.42361
$225$	−0.494545	−0.0329697
$226$	−31.4201	−2.09003
$227$	−18.2743	−1.21291	−0.606455	−	0.795118i	$-0.707409\pi$
$227$	−18.2743	−1.21291	−0.606455	+	0.795118i	$0.707409\pi$
$228$	4.11827	0.272739
$229$	−15.2642	−1.00869	−0.504344	−	0.863503i	$-0.668266\pi$
$229$	−15.2642	−1.00869	−0.504344	+	0.863503i	$0.668266\pi$
$230$	−8.28144	−0.546062
$231$	−21.5889	−1.42044
$232$	11.5362	0.757389
$233$	−14.9653	−0.980412	−0.490206	−	0.871607i	$-0.663078\pi$
$233$	−14.9653	−0.980412	−0.490206	+	0.871607i	$0.663078\pi$
$234$	0.470044	0.0307277
$235$	−13.3047	−0.867906
$236$	−19.7647	−1.28657
$237$	0.626007	0.0406636
$238$	7.73871	0.501626
$239$	−13.1012	−0.847448	−0.423724	−	0.905791i	$-0.639277\pi$
$239$	−13.1012	−0.847448	−0.423724	+	0.905791i	$0.639277\pi$
$240$	−7.65887	−0.494378
$241$	19.5942	1.26218	0.631088	−	0.775711i	$-0.282609\pi$
$241$	19.5942	1.26218	0.631088	+	0.775711i	$0.282609\pi$
$242$	−18.7252	−1.20370
$243$	−2.28347	−0.146485
$244$	−15.4725	−0.990525
$245$	0.532443	0.0340165
$246$	−5.18218	−0.330404
$247$	−0.897098	−0.0570810
$248$	−0.699672	−0.0444292
$249$	−24.5990	−1.55890
$250$	25.6727	1.62369
$251$	−6.74207	−0.425556	−0.212778	−	0.977101i	$-0.568251\pi$
$251$	−6.74207	−0.425556	−0.212778	+	0.977101i	$0.568251\pi$
$252$	−1.52391	−0.0959971
$253$	10.3934	0.653430
$254$	21.4172	1.34383
$255$	3.98922	0.249815
$256$	3.77437	0.235898
$257$	−24.1655	−1.50740	−0.753700	−	0.657218i	$-0.771733\pi$
$257$	−24.1655	−1.50740	−0.753700	+	0.657218i	$0.771733\pi$
$258$	−10.5886	−0.659216
$259$	−21.1842	−1.31632
$260$	−4.24518	−0.263275
$261$	−2.13112	−0.131913
$262$	11.4130	0.705098
$263$	8.37857	0.516645	0.258322	−	0.966059i	$-0.416830\pi$
$263$	8.37857	0.516645	0.258322	+	0.966059i	$0.416830\pi$
$264$	−9.50923	−0.585252
$265$	−7.02102	−0.431298
$266$	5.18225	0.317744
$267$	−6.57850	−0.402598
$268$	16.4953	1.00761
$269$	−12.4014	−0.756128	−0.378064	−	0.925779i	$-0.623410\pi$
$269$	−12.4014	−0.756128	−0.378064	+	0.925779i	$0.623410\pi$
$270$	17.6732	1.07556
$271$	−13.8550	−0.841630	−0.420815	−	0.907146i	$-0.638256\pi$
$271$	−13.8550	−0.841630	−0.420815	+	0.907146i	$0.638256\pi$
$272$	−3.44554	−0.208917
$273$	4.85534	0.293859
$274$	31.9777	1.93185
$275$	−9.98793	−0.602295
$276$	10.7306	0.645907
$277$	32.9885	1.98209	0.991043	−	0.133542i	$-0.0426351\pi$
$277$	32.9885	1.98209	0.991043	+	0.133542i	$0.0426351\pi$
$278$	−0.322661	−0.0193519
$279$	0.129252	0.00773814
$280$	5.35102	0.319785
$281$	13.1229	0.782845	0.391422	−	0.920211i	$-0.371983\pi$
$281$	13.1229	0.782845	0.391422	+	0.920211i	$0.371983\pi$
$282$	30.7173	1.82919
$283$	25.5614	1.51947	0.759734	−	0.650234i	$-0.225329\pi$
$283$	25.5614	1.51947	0.759734	+	0.650234i	$0.225329\pi$
$284$	−27.7116	−1.64438
$285$	2.67139	0.158240
$286$	9.49308	0.561338
$287$	−3.65980	−0.216031
$288$	1.73371	0.102160
$289$	−15.2053	−0.894432
$290$	34.2944	2.01384
$291$	−10.5579	−0.618916
$292$	−24.6563	−1.44290
$293$	8.48163	0.495502	0.247751	−	0.968824i	$-0.420308\pi$
$293$	8.48163	0.495502	0.247751	+	0.968824i	$0.420308\pi$
$294$	−1.22928	−0.0716929
$295$	−12.8208	−0.746453
$296$	−9.33099	−0.542353
$297$	−22.1803	−1.28703
$298$	−26.9474	−1.56102
$299$	−2.33749	−0.135180
$300$	−10.3119	−0.595361
$301$	−7.47795	−0.431022
$302$	−27.6811	−1.59287
$303$	21.2956	1.22340
$304$	−2.30731	−0.132333
$305$	−10.0365	−0.574689
$306$	−0.629693	−0.0359971
$307$	−1.53611	−0.0876704	−0.0438352	−	0.999039i	$-0.513958\pi$
$307$	−1.53611	−0.0876704	−0.0438352	+	0.999039i	$0.513958\pi$
$308$	−30.7771	−1.75369
$309$	−1.03597	−0.0589342
$310$	−2.07996	−0.118134
$311$	−7.32808	−0.415537	−0.207769	−	0.978178i	$-0.566620\pi$
$311$	−7.32808	−0.415537	−0.207769	+	0.978178i	$0.566620\pi$
$312$	2.13863	0.121076
$313$	20.7805	1.17458	0.587291	−	0.809376i	$-0.300194\pi$
$313$	20.7805	1.17458	0.587291	+	0.809376i	$0.300194\pi$
$314$	−6.42937	−0.362830
$315$	−0.988510	−0.0556962
$316$	0.892436	0.0502035
$317$	24.9087	1.39901	0.699506	−	0.714627i	$-0.253403\pi$
$317$	24.9087	1.39901	0.699506	+	0.714627i	$0.253403\pi$
$318$	16.2098	0.908999
$319$	−43.0404	−2.40980
$320$	−19.3632	−1.08243
$321$	14.0654	0.785053
$322$	13.5029	0.752488
$323$	1.20179	0.0668696
$324$	−24.5896	−1.36609
$325$	2.24629	0.124602
$326$	15.8589	0.878341
$327$	35.8847	1.98443
$328$	−1.61203	−0.0890094
$329$	21.6934	1.19600
$330$	−28.2687	−1.55614
$331$	−4.55976	−0.250627	−0.125314	−	0.992117i	$-0.539994\pi$
$331$	−4.55976	−0.250627	−0.125314	+	0.992117i	$0.539994\pi$
$332$	−35.0683	−1.92463
$333$	1.72374	0.0944604
$334$	23.4397	1.28256
$335$	10.7000	0.584604
$336$	12.4878	0.681266
$337$	−15.5224	−0.845558	−0.422779	−	0.906233i	$-0.638945\pi$
$337$	−15.5224	−0.845558	−0.422779	+	0.906233i	$0.638945\pi$
$338$	−2.13500	−0.116129
$339$	26.4088	1.43433
$340$	5.68704	0.308423
$341$	2.61041	0.141361
$342$	−0.421675	−0.0228016
$343$	18.0718	0.975786
$344$	−3.29381	−0.177590
$345$	6.96061	0.374747
$346$	−23.7748	−1.27814
$347$	−13.7609	−0.738724	−0.369362	−	0.929286i	$-0.620424\pi$
$347$	−13.7609	−0.738724	−0.369362	+	0.929286i	$0.620424\pi$
$348$	−44.4367	−2.38206
$349$	−24.3931	−1.30573	−0.652866	−	0.757473i	$-0.726434\pi$
$349$	−24.3931	−1.30573	−0.652866	+	0.757473i	$0.726434\pi$
$350$	−12.9761	−0.693601
$351$	4.98837	0.266259
$352$	35.0143	1.86627
$353$	1.89831	0.101037	0.0505184	−	0.998723i	$-0.483913\pi$
$353$	1.89831	0.101037	0.0505184	+	0.998723i	$0.483913\pi$
$354$	29.5999	1.57322
$355$	−17.9756	−0.954047
$356$	−9.37831	−0.497050
$357$	−6.50445	−0.344252
$358$	−36.7603	−1.94284
$359$	23.4274	1.23645	0.618226	−	0.786000i	$-0.287851\pi$
$359$	23.4274	1.23645	0.618226	+	0.786000i	$0.287851\pi$
$360$	−0.435408	−0.0229480
$361$	−18.1952	−0.957643
$362$	50.3120	2.64434
$363$	15.7387	0.826066
$364$	6.92178	0.362800
$365$	−15.9938	−0.837153
$366$	23.1718	1.21121
$367$	15.7689	0.823129	0.411565	−	0.911381i	$-0.364982\pi$
$367$	15.7689	0.823129	0.411565	+	0.911381i	$0.364982\pi$
$368$	−6.01196	−0.313395
$369$	0.297795	0.0155026
$370$	−27.7388	−1.44207
$371$	11.4478	0.594340
$372$	2.69509	0.139734
$373$	−5.35894	−0.277476	−0.138738	−	0.990329i	$-0.544305\pi$
$373$	−5.35894	−0.277476	−0.138738	+	0.990329i	$0.544305\pi$
$374$	−12.7174	−0.657600
$375$	−21.5781	−1.11429
$376$	9.55529	0.492776
$377$	9.67980	0.498535
$378$	−28.8162	−1.48215
$379$	−28.2030	−1.44869	−0.724345	−	0.689438i	$-0.757858\pi$
$379$	−28.2030	−1.44869	−0.724345	+	0.689438i	$0.757858\pi$
$380$	3.80834	0.195364
$381$	−18.0013	−0.922235
$382$	−47.3819	−2.42427
$383$	22.1036	1.12944	0.564721	−	0.825282i	$-0.308984\pi$
$383$	22.1036	1.12944	0.564721	+	0.825282i	$0.308984\pi$
$384$	16.4426	0.839084
$385$	−19.9641	−1.01747
$386$	46.2090	2.35198
$387$	0.608475	0.0309305
$388$	−15.0514	−0.764117
$389$	−2.37405	−0.120369	−0.0601846	−	0.998187i	$-0.519169\pi$
$389$	−2.37405	−0.120369	−0.0601846	+	0.998187i	$0.519169\pi$
$390$	6.35763	0.321931
$391$	3.13141	0.158362
$392$	−0.382393	−0.0193138
$393$	−9.59272	−0.483889
$394$	59.7317	3.00924
$395$	0.578895	0.0291274
$396$	2.50431	0.125846
$397$	28.7958	1.44522	0.722610	−	0.691256i	$-0.242942\pi$
$397$	28.7958	1.44522	0.722610	+	0.691256i	$0.242942\pi$
$398$	−9.83126	−0.492796
$399$	−4.35572	−0.218059
$400$	5.77740	0.288870
$401$	−20.1925	−1.00836	−0.504181	−	0.863598i	$-0.668206\pi$
$401$	−20.1925	−1.00836	−0.504181	+	0.863598i	$0.668206\pi$
$402$	−24.7036	−1.23211
$403$	−0.587081	−0.0292446
$404$	30.3591	1.51042
$405$	−15.9505	−0.792585
$406$	−55.9171	−2.77512
$407$	34.8130	1.72561
$408$	−2.86501	−0.141839
$409$	−29.5041	−1.45889	−0.729443	−	0.684042i	$-0.760220\pi$
$409$	−29.5041	−1.45889	−0.729443	+	0.684042i	$0.760220\pi$
$410$	−4.79218	−0.236669
$411$	−26.8775	−1.32577
$412$	−1.47688	−0.0727605
$413$	20.9043	1.02863
$414$	−1.09872	−0.0539992
$415$	−22.7477	−1.11664
$416$	−7.87472	−0.386090
$417$	0.271199	0.0132807
$418$	−8.51622	−0.416542
$419$	−1.83885	−0.0898339	−0.0449170	−	0.998991i	$-0.514302\pi$
$419$	−1.83885	−0.0898339	−0.0449170	+	0.998991i	$0.514302\pi$
$420$	−20.6118	−1.00575
$421$	−11.0496	−0.538526	−0.269263	−	0.963067i	$-0.586780\pi$
$421$	−11.0496	−0.538526	−0.269263	+	0.963067i	$0.586780\pi$
$422$	3.35336	0.163239
$423$	−1.76518	−0.0858258
$424$	5.04240	0.244881
$425$	−3.00923	−0.145969
$426$	41.5012	2.01074
$427$	16.3646	0.791937
$428$	20.0516	0.969231
$429$	−7.97901	−0.385230
$430$	−9.79170	−0.472198
$431$	−15.3156	−0.737726	−0.368863	−	0.929484i	$-0.620253\pi$
$431$	−15.3156	−0.737726	−0.368863	+	0.929484i	$0.620253\pi$
$432$	12.8300	0.617282
$433$	−21.0243	−1.01036	−0.505182	−	0.863013i	$-0.668575\pi$
$433$	−21.0243	−1.01036	−0.505182	+	0.863013i	$0.668575\pi$
$434$	3.39138	0.162791
$435$	−28.8247	−1.38204
$436$	51.1572	2.44998
$437$	2.09695	0.100311
$438$	36.9256	1.76437
$439$	24.3870	1.16393	0.581963	−	0.813215i	$-0.302285\pi$
$439$	24.3870	1.16393	0.581963	+	0.813215i	$0.302285\pi$
$440$	−8.79358	−0.419217
$441$	0.0706407	0.00336384
$442$	2.86014	0.136043
$443$	−28.9180	−1.37393	−0.686967	−	0.726689i	$-0.741058\pi$
$443$	−28.9180	−1.37393	−0.686967	+	0.726689i	$0.741058\pi$
$444$	35.9424	1.70575
$445$	−6.08341	−0.288381
$446$	27.7723	1.31506
$447$	22.6495	1.07128
$448$	31.5717	1.49162
$449$	14.5931	0.688692	0.344346	−	0.938843i	$-0.388101\pi$
$449$	14.5931	0.688692	0.344346	+	0.938843i	$0.388101\pi$
$450$	1.05585	0.0497734
$451$	6.01431	0.283203
$452$	37.6484	1.77083
$453$	23.2662	1.09314
$454$	39.0156	1.83110
$455$	4.48994	0.210492
$456$	−1.91856	−0.0898447
$457$	−32.9034	−1.53916	−0.769579	−	0.638552i	$-0.779534\pi$
$457$	−32.9034	−1.53916	−0.769579	+	0.638552i	$0.779534\pi$
$458$	32.5891	1.52279
$459$	−6.68265	−0.311919
$460$	9.92305	0.462664
$461$	−12.8861	−0.600168	−0.300084	−	0.953913i	$-0.597015\pi$
$461$	−12.8861	−0.600168	−0.300084	+	0.953913i	$0.597015\pi$
$462$	46.0922	2.14440
$463$	−20.6666	−0.960458	−0.480229	−	0.877143i	$-0.659446\pi$
$463$	−20.6666	−0.960458	−0.480229	+	0.877143i	$0.659446\pi$
$464$	24.8962	1.15578
$465$	1.74822	0.0810718
$466$	31.9509	1.48010
$467$	14.2968	0.661579	0.330789	−	0.943705i	$-0.392685\pi$
$467$	14.2968	0.661579	0.330789	+	0.943705i	$0.392685\pi$
$468$	−0.563219	−0.0260348
$469$	−17.4464	−0.805600
$470$	28.4056	1.31025
$471$	5.40393	0.249000
$472$	9.20769	0.423818
$473$	12.2889	0.565042
$474$	−1.33652	−0.0613886
$475$	−2.01514	−0.0924609
$476$	−9.27274	−0.425015
$477$	−0.931498	−0.0426503
$478$	27.9711	1.27937
$479$	35.9546	1.64281	0.821404	−	0.570347i	$-0.193191\pi$
$479$	35.9546	1.64281	0.821404	+	0.570347i	$0.193191\pi$
$480$	23.4495	1.07032
$481$	−7.82945	−0.356992
$482$	−41.8336	−1.90547
$483$	−11.3493	−0.516411
$484$	22.4371	1.01987
$485$	−9.76334	−0.443331
$486$	4.87520	0.221144
$487$	−32.9217	−1.49182	−0.745912	−	0.666044i	$-0.767986\pi$
$487$	−32.9217	−1.49182	−0.745912	+	0.666044i	$0.767986\pi$
$488$	7.20809	0.326295
$489$	−13.3295	−0.602780
$490$	−1.13676	−0.0513538
$491$	6.73826	0.304093	0.152047	−	0.988373i	$-0.451414\pi$
$491$	6.73826	0.304093	0.152047	+	0.988373i	$0.451414\pi$
$492$	6.20943	0.279943
$493$	−12.9675	−0.584028
$494$	1.91530	0.0861735
$495$	1.62446	0.0730142
$496$	−1.50996	−0.0677991
$497$	29.3093	1.31470
$498$	52.5188	2.35342
$499$	16.3941	0.733903	0.366951	−	0.930240i	$-0.380402\pi$
$499$	16.3941	0.733903	0.366951	+	0.930240i	$0.380402\pi$
$500$	−30.7618	−1.37571
$501$	−19.7013	−0.880187
$502$	14.3943	0.642449
$503$	25.4313	1.13392	0.566962	−	0.823744i	$-0.308119\pi$
$503$	25.4313	1.13392	0.566962	+	0.823744i	$0.308119\pi$
$504$	0.709935	0.0316230
$505$	19.6930	0.876325
$506$	−22.1900	−0.986464
$507$	1.79448	0.0796957
$508$	−25.6627	−1.13860
$509$	−34.9694	−1.54999	−0.774996	−	0.631966i	$-0.782248\pi$
$509$	−34.9694	−1.54999	−0.774996	+	0.631966i	$0.782248\pi$
$510$	−8.51698	−0.377138
$511$	26.0779	1.15362
$512$	−26.3841	−1.16602
$513$	−4.47505	−0.197578
$514$	51.5932	2.27568
$515$	−0.958003	−0.0422146
$516$	12.6875	0.558537
$517$	−35.6498	−1.56788
$518$	45.2282	1.98721
$519$	19.9829	0.877153
$520$	1.97768	0.0867270
$521$	−6.42922	−0.281669	−0.140835	−	0.990033i	$-0.544979\pi$
$521$	−6.42922	−0.281669	−0.140835	+	0.990033i	$0.544979\pi$
$522$	4.54993	0.199145
$523$	8.52713	0.372865	0.186433	−	0.982468i	$-0.440307\pi$
$523$	8.52713	0.372865	0.186433	+	0.982468i	$0.440307\pi$
$524$	−13.6754	−0.597412
$525$	10.9065	0.475998
$526$	−17.8882	−0.779963
$527$	0.786481	0.0342597
$528$	−20.5218	−0.893097
$529$	−17.5362	−0.762442
$530$	14.9899	0.651118
$531$	−1.70096	−0.0738156
$532$	−6.20951	−0.269216
$533$	−1.35262	−0.0585885
$534$	14.0451	0.607790
$535$	13.0068	0.562335
$536$	−7.68460	−0.331924
$537$	30.8973	1.33332
$538$	26.4770	1.14150
$539$	1.42667	0.0614511
$540$	−21.1765	−0.911292
$541$	29.5402	1.27003	0.635015	−	0.772499i	$-0.280994\pi$
$541$	29.5402	1.27003	0.635015	+	0.772499i	$0.280994\pi$
$542$	29.5803	1.27058
$543$	−42.2876	−1.81474
$544$	10.5493	0.452300
$545$	33.1840	1.42145
$546$	−10.3661	−0.443630
$547$	28.2200	1.20660	0.603300	−	0.797514i	$-0.293852\pi$
$547$	28.2200	1.20660	0.603300	+	0.797514i	$0.293852\pi$
$548$	−38.3166	−1.63680
$549$	−1.33157	−0.0568301
$550$	21.3242	0.909267
$551$	−8.68373	−0.369939
$552$	−4.99902	−0.212772
$553$	−0.943891	−0.0401383
$554$	−70.4303	−2.99230
$555$	23.3147	0.989653
$556$	0.386622	0.0163964
$557$	22.3724	0.947950	0.473975	−	0.880538i	$-0.342819\pi$
$557$	22.3724	0.947950	0.473975	+	0.880538i	$0.342819\pi$
$558$	−0.275954	−0.0116821
$559$	−2.76377	−0.116895
$560$	11.5480	0.487992
$561$	10.6891	0.451292
$562$	−28.0173	−1.18184
$563$	32.5481	1.37174	0.685870	−	0.727724i	$-0.259422\pi$
$563$	32.5481	1.37174	0.685870	+	0.727724i	$0.259422\pi$
$564$	−36.8063	−1.54983
$565$	24.4213	1.02741
$566$	−54.5735	−2.29390
$567$	26.0073	1.09220
$568$	12.9099	0.541685
$569$	−19.3413	−0.810829	−0.405414	−	0.914133i	$-0.632873\pi$
$569$	−19.3413	−0.810829	−0.405414	+	0.914133i	$0.632873\pi$
$570$	−5.70342	−0.238890
$571$	−42.1645	−1.76453	−0.882264	−	0.470755i	$-0.843982\pi$
$571$	−42.1645	−1.76453	−0.882264	+	0.470755i	$0.843982\pi$
$572$	−11.3749	−0.475607
$573$	39.8248	1.66371
$574$	7.81366	0.326136
$575$	−5.25067	−0.218968
$576$	−2.56896	−0.107040
$577$	−22.1916	−0.923849	−0.461925	−	0.886919i	$-0.652841\pi$
$577$	−22.1916	−0.923849	−0.461925	+	0.886919i	$0.652841\pi$
$578$	32.4634	1.35030
$579$	−38.8390	−1.61409
$580$	−41.0925	−1.70627
$581$	37.0903	1.53876
$582$	22.5411	0.934359
$583$	−18.8127	−0.779142
$584$	11.4865	0.475315
$585$	−0.365342	−0.0151051
$586$	−18.1083	−0.748045
$587$	16.1578	0.666905	0.333453	−	0.942767i	$-0.391786\pi$
$587$	16.1578	0.666905	0.333453	+	0.942767i	$0.391786\pi$
$588$	1.47295	0.0607436
$589$	0.526669	0.0217010
$590$	27.3723	1.12690
$591$	−50.2050	−2.06516
$592$	−20.1371	−0.827632
$593$	6.85297	0.281418	0.140709	−	0.990051i	$-0.455062\pi$
$593$	6.85297	0.281418	0.140709	+	0.990051i	$0.455062\pi$
$594$	47.3550	1.94300
$595$	−6.01493	−0.246588
$596$	32.2891	1.32261
$597$	8.26324	0.338192
$598$	4.99053	0.204078
$599$	−1.97609	−0.0807408	−0.0403704	−	0.999185i	$-0.512854\pi$
$599$	−1.97609	−0.0807408	−0.0403704	+	0.999185i	$0.512854\pi$
$600$	4.80397	0.196121
$601$	9.19917	0.375242	0.187621	−	0.982241i	$-0.439922\pi$
$601$	9.19917	0.375242	0.187621	+	0.982241i	$0.439922\pi$
$602$	15.9654	0.650701
$603$	1.41960	0.0578105
$604$	33.1683	1.34960
$605$	14.5542	0.591713
$606$	−45.4661	−1.84693
$607$	−24.1248	−0.979197	−0.489599	−	0.871948i	$-0.662857\pi$
$607$	−24.1248	−0.979197	−0.489599	+	0.871948i	$0.662857\pi$
$608$	7.06439	0.286499
$609$	46.9987	1.90449
$610$	21.4279	0.867591
$611$	8.01765	0.324360
$612$	0.754515	0.0304995
$613$	−1.23710	−0.0499660	−0.0249830	−	0.999688i	$-0.507953\pi$
$613$	−1.23710	−0.0499660	−0.0249830	+	0.999688i	$0.507953\pi$
$614$	3.27959	0.132353
$615$	4.02786	0.162419
$616$	14.3380	0.577693
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	2.21179	0.0889712
$619$	26.3223	1.05798	0.528991	−	0.848627i	$-0.322571\pi$
$619$	26.3223	1.05798	0.528991	+	0.848627i	$0.322571\pi$
$620$	2.49226	0.100092
$621$	−11.6602	−0.467909
$622$	15.6454	0.627324
$623$	9.91903	0.397397
$624$	4.61536	0.184762
$625$	−8.72275	−0.348910
$626$	−44.3662	−1.77323
$627$	7.15795	0.285861
$628$	7.70384	0.307417
$629$	10.4887	0.418212
$630$	2.11047	0.0840830
$631$	5.93215	0.236155	0.118078	−	0.993004i	$-0.462327\pi$
$631$	5.93215	0.236155	0.118078	+	0.993004i	$0.462327\pi$
$632$	−0.415755	−0.0165378
$633$	−2.81853	−0.112026
$634$	−53.1800	−2.11205
$635$	−16.6466	−0.660599
$636$	−19.4230	−0.770172
$637$	−0.320859	−0.0127129
$638$	91.8911	3.63800
$639$	−2.38488	−0.0943442
$640$	15.2052	0.601038
$641$	−19.3478	−0.764191	−0.382095	−	0.924123i	$-0.624797\pi$
$641$	−19.3478	−0.764191	−0.382095	+	0.924123i	$0.624797\pi$
$642$	−30.0296	−1.18517
$643$	31.3140	1.23491	0.617453	−	0.786608i	$-0.288165\pi$
$643$	31.3140	1.23491	0.617453	+	0.786608i	$0.288165\pi$
$644$	−16.1796	−0.637564
$645$	8.23000	0.324056
$646$	−2.56583	−0.100951
$647$	−11.9342	−0.469182	−0.234591	−	0.972094i	$-0.575375\pi$
$647$	−11.9342	−0.469182	−0.234591	+	0.972094i	$0.575375\pi$
$648$	11.4554	0.450011
$649$	−34.3530	−1.34847
$650$	−4.79582	−0.188107
$651$	−2.85048	−0.111719
$652$	−19.0025	−0.744196
$653$	41.8600	1.63811	0.819055	−	0.573715i	$-0.194498\pi$
$653$	41.8600	1.63811	0.819055	+	0.573715i	$0.194498\pi$
$654$	−76.6136	−2.99583
$655$	−8.87079	−0.346610
$656$	−3.47891	−0.135829
$657$	−2.12194	−0.0827847
$658$	−46.3154	−1.80556
$659$	−43.0800	−1.67816	−0.839079	−	0.544009i	$-0.816906\pi$
$659$	−43.0800	−1.67816	−0.839079	+	0.544009i	$0.816906\pi$
$660$	33.8723	1.31848
$661$	21.9823	0.855012	0.427506	−	0.904012i	$-0.359392\pi$
$661$	21.9823	0.855012	0.427506	+	0.904012i	$0.359392\pi$
$662$	9.73508	0.378365
$663$	−2.40397	−0.0933625
$664$	16.3371	0.634003
$665$	−4.02791	−0.156196
$666$	−3.68018	−0.142604
$667$	−22.6264	−0.876098
$668$	−28.0861	−1.08668
$669$	−23.3428	−0.902486
$670$	−22.8445	−0.882559
$671$	−26.8926	−1.03818
$672$	−38.2345	−1.47493
$673$	22.3334	0.860890	0.430445	−	0.902617i	$-0.358357\pi$
$673$	22.3334	0.860890	0.430445	+	0.902617i	$0.358357\pi$
$674$	33.1402	1.27651
$675$	11.2053	0.431292
$676$	2.55821	0.0983928
$677$	35.9341	1.38106	0.690529	−	0.723304i	$-0.257378\pi$
$677$	35.9341	1.38106	0.690529	+	0.723304i	$0.257378\pi$
$678$	−56.3827	−2.16537
$679$	15.9192	0.610921
$680$	−2.64939	−0.101600
$681$	−32.7929	−1.25663
$682$	−5.57321	−0.213409
$683$	27.0260	1.03412	0.517060	−	0.855949i	$-0.327026\pi$
$683$	27.0260	1.03412	0.517060	+	0.855949i	$0.327026\pi$
$684$	0.505263	0.0193192
$685$	−24.8548	−0.949652
$686$	−38.5833	−1.47312
$687$	−27.3913	−1.04505
$688$	−7.10834	−0.271003
$689$	4.23098	0.161187
$690$	−14.8609	−0.565744
$691$	2.63258	0.100148	0.0500740	−	0.998746i	$-0.484054\pi$
$691$	2.63258	0.100148	0.0500740	+	0.998746i	$0.484054\pi$
$692$	28.4877	1.08294
$693$	−2.64869	−0.100616
$694$	29.3795	1.11523
$695$	0.250789	0.00951298
$696$	20.7015	0.784688
$697$	1.81203	0.0686357
$698$	52.0792	1.97123
$699$	−26.8550	−1.01575
$700$	15.5483	0.587671
$701$	−41.3862	−1.56314	−0.781568	−	0.623820i	$-0.785580\pi$
$701$	−41.3862	−1.56314	−0.781568	+	0.623820i	$0.785580\pi$
$702$	−10.6501	−0.401964
$703$	7.02378	0.264907
$704$	−51.8832	−1.95542
$705$	−23.8751	−0.899189
$706$	−4.05288	−0.152532
$707$	−32.1094	−1.20760
$708$	−35.4674	−1.33295
$709$	−40.7279	−1.52957	−0.764785	−	0.644286i	$-0.777155\pi$
$709$	−40.7279	−1.52957	−0.764785	+	0.644286i	$0.777155\pi$
$710$	38.3779	1.44030
$711$	0.0768036	0.00288036
$712$	4.36903	0.163736
$713$	1.37229	0.0513928
$714$	13.8870	0.519707
$715$	−7.37852	−0.275941
$716$	44.0472	1.64612
$717$	−23.5099	−0.877994
$718$	−50.0175	−1.86664
$719$	21.6419	0.807105	0.403553	−	0.914956i	$-0.367775\pi$
$719$	21.6419	0.807105	0.403553	+	0.914956i	$0.367775\pi$
$720$	−0.939652	−0.0350188
$721$	1.56203	0.0581729
$722$	38.8467	1.44573
$723$	35.1615	1.30767
$724$	−60.2853	−2.24048
$725$	21.7436	0.807538
$726$	−33.6020	−1.24709
$727$	−21.9253	−0.813163	−0.406582	−	0.913614i	$-0.633279\pi$
$727$	−21.9253	−0.813163	−0.406582	+	0.913614i	$0.633279\pi$
$728$	−3.22461	−0.119512
$729$	24.7384	0.916237
$730$	34.1467	1.26382
$731$	3.70247	0.136941
$732$	−27.7651	−1.02623
$733$	−8.04030	−0.296975	−0.148488	−	0.988914i	$-0.547441\pi$
$733$	−8.04030	−0.296975	−0.148488	+	0.988914i	$0.547441\pi$
$734$	−33.6665	−1.24265
$735$	0.955459	0.0352426
$736$	18.4071	0.678493
$737$	28.6705	1.05609
$738$	−0.635791	−0.0234038
$739$	−5.86682	−0.215814	−0.107907	−	0.994161i	$-0.534415\pi$
$739$	−5.86682	−0.215814	−0.107907	+	0.994161i	$0.534415\pi$
$740$	33.2374	1.22183
$741$	−1.60982	−0.0591384
$742$	−24.4410	−0.897258
$743$	27.5519	1.01078	0.505391	−	0.862891i	$-0.331348\pi$
$743$	27.5519	1.01078	0.505391	+	0.862891i	$0.331348\pi$
$744$	−1.25555	−0.0460306
$745$	20.9449	0.767363
$746$	11.4413	0.418897
$747$	−3.01800	−0.110423
$748$	15.2383	0.557168
$749$	−21.2077	−0.774913
$750$	46.0692	1.68221
$751$	−1.88921	−0.0689383	−0.0344692	−	0.999406i	$-0.510974\pi$
$751$	−1.88921	−0.0689383	−0.0344692	+	0.999406i	$0.510974\pi$
$752$	20.6212	0.751978
$753$	−12.0985	−0.440894
$754$	−20.6663	−0.752624
$755$	21.5152	0.783020
$756$	34.5284	1.25578
$757$	−43.2123	−1.57058	−0.785289	−	0.619129i	$-0.787486\pi$
$757$	−43.2123	−1.57058	−0.785289	+	0.619129i	$0.787486\pi$
$758$	60.2133	2.18704
$759$	18.6508	0.676982
$760$	−1.77417	−0.0643559
$761$	37.1049	1.34505	0.672526	−	0.740074i	$-0.265209\pi$
$761$	37.1049	1.34505	0.672526	+	0.740074i	$0.265209\pi$
$762$	38.4327	1.39227
$763$	−54.1067	−1.95879
$764$	56.7743	2.05402
$765$	0.489430	0.0176954
$766$	−47.1912	−1.70509
$767$	7.72599	0.278969
$768$	6.77304	0.244401
$769$	21.9422	0.791257	0.395628	−	0.918411i	$-0.370527\pi$
$769$	21.9422	0.791257	0.395628	+	0.918411i	$0.370527\pi$
$770$	42.6233	1.53604
$771$	−43.3645	−1.56173
$772$	−55.3689	−1.99277
$773$	13.8212	0.497114	0.248557	−	0.968617i	$-0.420044\pi$
$773$	13.8212	0.497114	0.248557	+	0.968617i	$0.420044\pi$
$774$	−1.29909	−0.0466949
$775$	−1.31875	−0.0473710
$776$	7.01190	0.251713
$777$	−38.0146	−1.36377
$778$	5.06859	0.181718
$779$	1.21343	0.0434758
$780$	−7.61789	−0.272764
$781$	−48.1654	−1.72349
$782$	−6.68555	−0.239075
$783$	48.2864	1.72562
$784$	−0.825241	−0.0294729
$785$	4.99724	0.178359
$786$	20.4804	0.730513
$787$	−3.94197	−0.140516	−0.0702581	−	0.997529i	$-0.522382\pi$
$787$	−3.94197	−0.140516	−0.0702581	+	0.997529i	$0.522382\pi$
$788$	−71.5722	−2.54965
$789$	15.0352	0.535267
$790$	−1.23594	−0.0439728
$791$	−39.8191	−1.41580
$792$	−1.16667	−0.0414557
$793$	6.04817	0.214777
$794$	−61.4790	−2.18181
$795$	−12.5991	−0.446843
$796$	11.7801	0.417534
$797$	−9.23564	−0.327143	−0.163572	−	0.986531i	$-0.552301\pi$
$797$	−9.23564	−0.327143	−0.163572	+	0.986531i	$0.552301\pi$
$798$	9.29944	0.329197
$799$	−10.7408	−0.379983
$800$	−17.6889	−0.625397
$801$	−0.807103	−0.0285176
$802$	43.1108	1.52230
$803$	−42.8550	−1.51232
$804$	29.6006	1.04393
$805$	−10.4952	−0.369906
$806$	1.25342	0.0441497
$807$	−22.2541	−0.783382
$808$	−14.1432	−0.497557
$809$	−39.1009	−1.37472	−0.687358	−	0.726319i	$-0.741230\pi$
$809$	−39.1009	−1.37472	−0.687358	+	0.726319i	$0.741230\pi$
$810$	34.0542	1.19654
$811$	−46.7332	−1.64102	−0.820512	−	0.571630i	$-0.806311\pi$
$811$	−46.7332	−1.64102	−0.820512	+	0.571630i	$0.806311\pi$
$812$	67.0014	2.35129
$813$	−24.8625	−0.871966
$814$	−74.3256	−2.60511
$815$	−12.3263	−0.431773
$816$	−6.18295	−0.216447
$817$	2.47937	0.0867422
$818$	62.9912	2.20244
$819$	0.595692	0.0208152
$820$	5.74212	0.200523
$821$	−41.1920	−1.43761	−0.718805	−	0.695212i	$-0.755311\pi$
$821$	−41.1920	−1.43761	−0.718805	+	0.695212i	$0.755311\pi$
$822$	57.3834	2.00148
$823$	16.0257	0.558621	0.279311	−	0.960201i	$-0.409894\pi$
$823$	16.0257	0.558621	0.279311	+	0.960201i	$0.409894\pi$
$824$	0.688025	0.0239685
$825$	−17.9231	−0.624004
$826$	−44.6306	−1.55290
$827$	−53.3859	−1.85641	−0.928204	−	0.372071i	$-0.878648\pi$
$827$	−53.3859	−1.85641	−0.928204	+	0.372071i	$0.878648\pi$
$828$	1.31652	0.0457521
$829$	−12.9287	−0.449033	−0.224517	−	0.974470i	$-0.572080\pi$
$829$	−12.9287	−0.449033	−0.224517	+	0.974470i	$0.572080\pi$
$830$	48.5663	1.68576
$831$	59.1972	2.05353
$832$	11.6686	0.404534
$833$	0.429838	0.0148930
$834$	−0.579010	−0.0200495
$835$	−18.2186	−0.630480
$836$	10.2044	0.352925
$837$	−2.92858	−0.101226
$838$	3.92595	0.135620
$839$	−23.1655	−0.799760	−0.399880	−	0.916567i	$-0.630948\pi$
$839$	−23.1655	−0.799760	−0.399880	+	0.916567i	$0.630948\pi$
$840$	9.60231	0.331311
$841$	64.6985	2.23098
$842$	23.5909	0.812997
$843$	23.5487	0.811061
$844$	−4.01809	−0.138308
$845$	1.65943	0.0570862
$846$	3.76865	0.129569
$847$	−23.7307	−0.815396
$848$	10.8820	0.373688
$849$	45.8695	1.57424
$850$	6.42470	0.220365
$851$	18.3012	0.627358
$852$	−49.7279	−1.70365
$853$	−28.7940	−0.985889	−0.492945	−	0.870061i	$-0.664079\pi$
$853$	−28.7940	−0.985889	−0.492945	+	0.870061i	$0.664079\pi$
$854$	−34.9383	−1.19556
$855$	0.327748	0.0112087
$856$	−9.34134	−0.319281
$857$	39.0198	1.33289	0.666445	−	0.745554i	$-0.267815\pi$
$857$	39.0198	1.33289	0.666445	+	0.745554i	$0.267815\pi$
$858$	17.0352	0.581570
$859$	−27.7613	−0.947203	−0.473602	−	0.880739i	$-0.657046\pi$
$859$	−27.7613	−0.947203	−0.473602	+	0.880739i	$0.657046\pi$
$860$	11.7327	0.400081
$861$	−6.56744	−0.223818
$862$	32.6987	1.11372
$863$	−49.9508	−1.70035	−0.850173	−	0.526504i	$-0.823503\pi$
$863$	−49.9508	−1.70035	−0.850173	+	0.526504i	$0.823503\pi$
$864$	−39.2820	−1.33640
$865$	18.4791	0.628307
$866$	44.8869	1.52532
$867$	−27.2857	−0.926671
$868$	−4.06364	−0.137929
$869$	1.55114	0.0526188
$870$	61.5406	2.08642
$871$	−6.44800	−0.218482
$872$	−23.8323	−0.807064
$873$	−1.29533	−0.0438402
$874$	−4.47699	−0.151436
$875$	32.5354	1.09990
$876$	−44.2453	−1.49491
$877$	−30.5454	−1.03145	−0.515723	−	0.856756i	$-0.672476\pi$
$877$	−30.5454	−1.03145	−0.515723	+	0.856756i	$0.672476\pi$
$878$	−52.0661	−1.75714
$879$	15.2201	0.513362
$880$	−18.9774	−0.639727
$881$	−39.8320	−1.34197	−0.670987	−	0.741469i	$-0.734129\pi$
$881$	−39.8320	−1.34197	−0.670987	+	0.741469i	$0.734129\pi$
$882$	−0.150818	−0.00507829
$883$	42.8591	1.44232	0.721162	−	0.692767i	$-0.243608\pi$
$883$	42.8591	1.44232	0.721162	+	0.692767i	$0.243608\pi$
$884$	−3.42710	−0.115266
$885$	−23.0066	−0.773358
$886$	61.7398	2.07419
$887$	13.8141	0.463831	0.231916	−	0.972736i	$-0.425501\pi$
$887$	13.8141	0.463831	0.231916	+	0.972736i	$0.425501\pi$
$888$	−16.7443	−0.561901
$889$	27.1423	0.910323
$890$	12.9881	0.435361
$891$	−42.7390	−1.43181
$892$	−33.2775	−1.11421
$893$	−7.19262	−0.240692
$894$	−48.3566	−1.61729
$895$	28.5720	0.955058
$896$	−24.7921	−0.828246
$897$	−4.19458	−0.140053
$898$	−31.1563	−1.03970
$899$	−5.68283	−0.189533
$900$	−1.26515	−0.0421717
$901$	−5.66802	−0.188829
$902$	−12.8405	−0.427543
$903$	−13.4190	−0.446558
$904$	−17.5391	−0.583341
$905$	−39.1051	−1.29990
$906$	−49.6733	−1.65028
$907$	−12.1769	−0.404327	−0.202163	−	0.979352i	$-0.564797\pi$
$907$	−12.1769	−0.404327	−0.202163	+	0.979352i	$0.564797\pi$
$908$	−46.7496	−1.55144
$909$	2.61272	0.0866584
$910$	−9.58600	−0.317773
$911$	12.8211	0.424783	0.212392	−	0.977185i	$-0.431875\pi$
$911$	12.8211	0.424783	0.212392	+	0.977185i	$0.431875\pi$
$912$	−4.14043	−0.137103
$913$	−60.9521	−2.01722
$914$	70.2487	2.32362
$915$	−18.0103	−0.595403
$916$	−39.0491	−1.29022
$917$	14.4638	0.477638
$918$	14.2674	0.470896
$919$	41.6704	1.37458	0.687289	−	0.726384i	$-0.258800\pi$
$919$	41.6704	1.37458	0.687289	+	0.726384i	$0.258800\pi$
$920$	−4.62280	−0.152409
$921$	−2.75652	−0.0908303
$922$	27.5119	0.906055
$923$	10.8324	0.356553
$924$	−55.2289	−1.81690
$925$	−17.5872	−0.578263
$926$	44.1231	1.44997
$927$	−0.127101	−0.00417454
$928$	−76.2257	−2.50223
$929$	−28.3913	−0.931487	−0.465743	−	0.884920i	$-0.654213\pi$
$929$	−28.3913	−0.931487	−0.465743	+	0.884920i	$0.654213\pi$
$930$	−3.73245	−0.122392
$931$	0.287842	0.00943363
$932$	−38.2845	−1.25405
$933$	−13.1501	−0.430515
$934$	−30.5237	−0.998766
$935$	9.88461	0.323261
$936$	0.262384	0.00857629
$937$	28.3138	0.924973	0.462487	−	0.886626i	$-0.346957\pi$
$937$	28.3138	0.924973	0.462487	+	0.886626i	$0.346957\pi$
$938$	37.2480	1.21619
$939$	37.2902	1.21692
$940$	−34.0364	−1.11014
$941$	30.3607	0.989731	0.494866	−	0.868970i	$-0.335217\pi$
$941$	30.3607	0.989731	0.494866	+	0.868970i	$0.335217\pi$
$942$	−11.5374	−0.375908
$943$	3.16173	0.102960
$944$	19.8711	0.646748
$945$	22.3975	0.728589
$946$	−26.2367	−0.853028
$947$	−20.0283	−0.650831	−0.325416	−	0.945571i	$-0.605504\pi$
$947$	−20.0283	−0.650831	−0.325416	+	0.945571i	$0.605504\pi$
$948$	1.60146	0.0520130
$949$	9.63811	0.312866
$950$	4.30232	0.139586
$951$	44.6982	1.44944
$952$	4.31984	0.140007
$953$	18.9946	0.615294	0.307647	−	0.951501i	$-0.400458\pi$
$953$	18.9946	0.615294	0.307647	+	0.951501i	$0.400458\pi$
$954$	1.98874	0.0643880
$955$	36.8277	1.19172
$956$	−33.5157	−1.08398
$957$	−77.2352	−2.49666
$958$	−76.7629	−2.48010
$959$	40.5258	1.30865
$960$	−34.7468	−1.12145
$961$	−30.6553	−0.988882
$962$	16.7158	0.538941
$963$	1.72565	0.0556084
$964$	50.1262	1.61446
$965$	−35.9161	−1.15618
$966$	24.2307	0.779611
$967$	9.59074	0.308418	0.154209	−	0.988038i	$-0.450717\pi$
$967$	9.59074	0.308418	0.154209	+	0.988038i	$0.450717\pi$
$968$	−10.4526	−0.335960
$969$	2.15660	0.0692799
$970$	20.8447	0.669283
$971$	−57.8925	−1.85786	−0.928929	−	0.370257i	$-0.879269\pi$
$971$	−57.8925	−1.85786	−0.928929	+	0.370257i	$0.879269\pi$
$972$	−5.84160	−0.187369
$973$	−0.408913	−0.0131091
$974$	70.2877	2.25216
$975$	4.03092	0.129093
$976$	15.5557	0.497927
$977$	−22.4687	−0.718836	−0.359418	−	0.933177i	$-0.617025\pi$
$977$	−22.4687	−0.718836	−0.359418	+	0.933177i	$0.617025\pi$
$978$	28.4584	0.910000
$979$	−16.3004	−0.520963
$980$	1.36210	0.0435108
$981$	4.40262	0.140565
$982$	−14.3862	−0.459081
$983$	33.5644	1.07054	0.535269	−	0.844682i	$-0.320210\pi$
$983$	33.5644	1.07054	0.535269	+	0.844682i	$0.320210\pi$
$984$	−2.89275	−0.0922176
$985$	−46.4266	−1.47928
$986$	27.6856	0.881689
$987$	38.9285	1.23911
$988$	−2.29497	−0.0730126
$989$	6.46027	0.205425
$990$	−3.46823	−0.110227
$991$	−56.4859	−1.79433	−0.897167	−	0.441691i	$-0.854379\pi$
$991$	−56.4859	−1.79433	−0.897167	+	0.441691i	$0.854379\pi$
$992$	4.62310	0.146784
$993$	−8.18241	−0.259661
$994$	−62.5753	−1.98477
$995$	7.64137	0.242248
$996$	−62.9295	−1.99400
$997$	28.6267	0.906617	0.453309	−	0.891354i	$-0.350244\pi$
$997$	28.6267	0.906617	0.453309	+	0.891354i	$0.350244\pi$
$998$	−35.0014	−1.10795
$999$	−39.0562	−1.23568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.19	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-2.13500 q^{2} +1.79448 q^{3} +2.55821 q^{4} +1.65943 q^{5} -3.83121 q^{6} -2.70571 q^{7} -1.19178 q^{8} +0.220161 q^{9} +O(q^{10})\)	\(q-2.13500 q^{2} +1.79448 q^{3} +2.55821 q^{4} +1.65943 q^{5} -3.83121 q^{6} -2.70571 q^{7} -1.19178 q^{8} +0.220161 q^{9} -3.54288 q^{10} +4.44641 q^{11} +4.59066 q^{12} -1.00000 q^{13} +5.77668 q^{14} +2.97782 q^{15} -2.57198 q^{16} +1.33965 q^{17} -0.470044 q^{18} +0.897098 q^{19} +4.24518 q^{20} -4.85534 q^{21} -9.49308 q^{22} +2.33749 q^{23} -2.13863 q^{24} -2.24629 q^{25} +2.13500 q^{26} -4.98837 q^{27} -6.92178 q^{28} -9.67980 q^{29} -6.35763 q^{30} +0.587081 q^{31} +7.87472 q^{32} +7.97901 q^{33} -2.86014 q^{34} -4.48994 q^{35} +0.563219 q^{36} +7.82945 q^{37} -1.91530 q^{38} -1.79448 q^{39} -1.97768 q^{40} +1.35262 q^{41} +10.3661 q^{42} +2.76377 q^{43} +11.3749 q^{44} +0.365342 q^{45} -4.99053 q^{46} -8.01765 q^{47} -4.61536 q^{48} +0.320859 q^{49} +4.79582 q^{50} +2.40397 q^{51} -2.55821 q^{52} -4.23098 q^{53} +10.6501 q^{54} +7.37852 q^{55} +3.22461 q^{56} +1.60982 q^{57} +20.6663 q^{58} -7.72599 q^{59} +7.61789 q^{60} -6.04817 q^{61} -1.25342 q^{62} -0.595692 q^{63} -11.6686 q^{64} -1.65943 q^{65} -17.0352 q^{66} +6.44800 q^{67} +3.42710 q^{68} +4.19458 q^{69} +9.58600 q^{70} -10.8324 q^{71} -0.262384 q^{72} -9.63811 q^{73} -16.7158 q^{74} -4.03092 q^{75} +2.29497 q^{76} -12.0307 q^{77} +3.83121 q^{78} +0.348852 q^{79} -4.26802 q^{80} -9.61201 q^{81} -2.88784 q^{82} -13.7081 q^{83} -12.4210 q^{84} +2.22305 q^{85} -5.90064 q^{86} -17.3702 q^{87} -5.29915 q^{88} -3.66596 q^{89} -0.780005 q^{90} +2.70571 q^{91} +5.97979 q^{92} +1.05351 q^{93} +17.1177 q^{94} +1.48867 q^{95} +14.1310 q^{96} -5.88355 q^{97} -0.685032 q^{98} +0.978928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 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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