LMFDB - Embedded newform 8021.2.a.b.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.61802 q^{2} -0.518785 q^{3} +4.85402 q^{4} -1.93655 q^{5} +1.35819 q^{6} +1.44000 q^{7} -7.47189 q^{8} -2.73086 q^{9} +O(q^{10})$	\(q-2.61802 q^{2} -0.518785 q^{3} +4.85402 q^{4} -1.93655 q^{5} +1.35819 q^{6} +1.44000 q^{7} -7.47189 q^{8} -2.73086 q^{9} +5.06994 q^{10} +5.60978 q^{11} -2.51819 q^{12} -1.00000 q^{13} -3.76995 q^{14} +1.00466 q^{15} +9.85349 q^{16} +7.03709 q^{17} +7.14945 q^{18} +1.32146 q^{19} -9.40008 q^{20} -0.747051 q^{21} -14.6865 q^{22} +0.827876 q^{23} +3.87630 q^{24} -1.24976 q^{25} +2.61802 q^{26} +2.97309 q^{27} +6.98980 q^{28} +1.45316 q^{29} -2.63021 q^{30} -4.03781 q^{31} -10.8529 q^{32} -2.91027 q^{33} -18.4232 q^{34} -2.78864 q^{35} -13.2557 q^{36} +9.63276 q^{37} -3.45961 q^{38} +0.518785 q^{39} +14.4697 q^{40} -9.07481 q^{41} +1.95579 q^{42} -1.95814 q^{43} +27.2300 q^{44} +5.28846 q^{45} -2.16740 q^{46} -8.46485 q^{47} -5.11184 q^{48} -4.92640 q^{49} +3.27188 q^{50} -3.65074 q^{51} -4.85402 q^{52} -6.95672 q^{53} -7.78359 q^{54} -10.8636 q^{55} -10.7595 q^{56} -0.685554 q^{57} -3.80440 q^{58} +5.09150 q^{59} +4.87662 q^{60} +0.892700 q^{61} +10.5711 q^{62} -3.93244 q^{63} +8.70601 q^{64} +1.93655 q^{65} +7.61914 q^{66} -7.37255 q^{67} +34.1582 q^{68} -0.429490 q^{69} +7.30071 q^{70} +2.46425 q^{71} +20.4047 q^{72} -11.5885 q^{73} -25.2188 q^{74} +0.648355 q^{75} +6.41440 q^{76} +8.07809 q^{77} -1.35819 q^{78} -12.1375 q^{79} -19.0818 q^{80} +6.65019 q^{81} +23.7580 q^{82} -8.13313 q^{83} -3.62620 q^{84} -13.6277 q^{85} +5.12644 q^{86} -0.753878 q^{87} -41.9156 q^{88} +2.25566 q^{89} -13.8453 q^{90} -1.44000 q^{91} +4.01853 q^{92} +2.09475 q^{93} +22.1611 q^{94} -2.55908 q^{95} +5.63030 q^{96} -1.71192 q^{97} +12.8974 q^{98} -15.3195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.61802	−1.85122	−0.925609	−	0.378480i	$-0.876447\pi$
$2$	−2.61802	−1.85122	−0.925609	+	0.378480i	$0.876447\pi$
$3$	−0.518785	−0.299521	−0.149760	−	0.988722i	$-0.547850\pi$
$3$	−0.518785	−0.299521	−0.149760	+	0.988722i	$0.547850\pi$
$4$	4.85402	2.42701
$5$	−1.93655	−0.866054	−0.433027	−	0.901381i	$-0.642554\pi$
$5$	−1.93655	−0.866054	−0.433027	+	0.901381i	$0.642554\pi$
$6$	1.35819	0.554478
$7$	1.44000	0.544269	0.272135	−	0.962259i	$-0.412270\pi$
$7$	1.44000	0.544269	0.272135	+	0.962259i	$0.412270\pi$
$8$	−7.47189	−2.64171
$9$	−2.73086	−0.910287
$10$	5.06994	1.60325
$11$	5.60978	1.69141	0.845706	−	0.533649i	$-0.179180\pi$
$11$	5.60978	1.69141	0.845706	+	0.533649i	$0.179180\pi$
$12$	−2.51819	−0.726940
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.76995	−1.00756
$15$	1.00466	0.259401
$16$	9.85349	2.46337
$17$	7.03709	1.70675	0.853373	−	0.521301i	$-0.174553\pi$
$17$	7.03709	1.70675	0.853373	+	0.521301i	$0.174553\pi$
$18$	7.14945	1.68514
$19$	1.32146	0.303164	0.151582	−	0.988445i	$-0.451563\pi$
$19$	1.32146	0.303164	0.151582	+	0.988445i	$0.451563\pi$
$20$	−9.40008	−2.10192
$21$	−0.747051	−0.163020
$22$	−14.6865	−3.13117
$23$	0.827876	0.172624	0.0863121	−	0.996268i	$-0.472492\pi$
$23$	0.827876	0.172624	0.0863121	+	0.996268i	$0.472492\pi$
$24$	3.87630	0.791247
$25$	−1.24976	−0.249951
$26$	2.61802	0.513436
$27$	2.97309	0.572171
$28$	6.98980	1.32095
$29$	1.45316	0.269845	0.134923	−	0.990856i	$-0.456921\pi$
$29$	1.45316	0.269845	0.134923	+	0.990856i	$0.456921\pi$
$30$	−2.63021	−0.480208
$31$	−4.03781	−0.725212	−0.362606	−	0.931943i	$-0.618113\pi$
$31$	−4.03781	−0.725212	−0.362606	+	0.931943i	$0.618113\pi$
$32$	−10.8529	−1.91853
$33$	−2.91027	−0.506613
$34$	−18.4232	−3.15956
$35$	−2.78864	−0.471366
$36$	−13.2557	−2.20928
$37$	9.63276	1.58362	0.791808	−	0.610770i	$-0.209140\pi$
$37$	9.63276	1.58362	0.791808	+	0.610770i	$0.209140\pi$
$38$	−3.45961	−0.561223
$39$	0.518785	0.0830721
$40$	14.4697	2.28786
$41$	−9.07481	−1.41725	−0.708624	−	0.705587i	$-0.750684\pi$
$41$	−9.07481	−1.41725	−0.708624	+	0.705587i	$0.750684\pi$
$42$	1.95579	0.301785
$43$	−1.95814	−0.298613	−0.149307	−	0.988791i	$-0.547704\pi$
$43$	−1.95814	−0.298613	−0.149307	+	0.988791i	$0.547704\pi$
$44$	27.2300	4.10508
$45$	5.28846	0.788358
$46$	−2.16740	−0.319565
$47$	−8.46485	−1.23472	−0.617362	−	0.786679i	$-0.711799\pi$
$47$	−8.46485	−1.23472	−0.617362	+	0.786679i	$0.711799\pi$
$48$	−5.11184	−0.737831
$49$	−4.92640	−0.703771
$50$	3.27188	0.462714
$51$	−3.65074	−0.511206
$52$	−4.85402	−0.673132
$53$	−6.95672	−0.955580	−0.477790	−	0.878474i	$-0.658562\pi$
$53$	−6.95672	−0.955580	−0.477790	+	0.878474i	$0.658562\pi$
$54$	−7.78359	−1.05921
$55$	−10.8636	−1.46485
$56$	−10.7595	−1.43780
$57$	−0.685554	−0.0908038
$58$	−3.80440	−0.499543
$59$	5.09150	0.662857	0.331428	−	0.943480i	$-0.392469\pi$
$59$	5.09150	0.662857	0.331428	+	0.943480i	$0.392469\pi$
$60$	4.87662	0.629569
$61$	0.892700	0.114299	0.0571493	−	0.998366i	$-0.481799\pi$
$61$	0.892700	0.114299	0.0571493	+	0.998366i	$0.481799\pi$
$62$	10.5711	1.34253
$63$	−3.93244	−0.495441
$64$	8.70601	1.08825
$65$	1.93655	0.240200
$66$	7.61914	0.937851
$67$	−7.37255	−0.900700	−0.450350	−	0.892852i	$-0.648701\pi$
$67$	−7.37255	−0.900700	−0.450350	+	0.892852i	$0.648701\pi$
$68$	34.1582	4.14229
$69$	−0.429490	−0.0517045
$70$	7.30071	0.872602
$71$	2.46425	0.292453	0.146226	−	0.989251i	$-0.453287\pi$
$71$	2.46425	0.292453	0.146226	+	0.989251i	$0.453287\pi$
$72$	20.4047	2.40472
$73$	−11.5885	−1.35633	−0.678167	−	0.734908i	$-0.737225\pi$
$73$	−11.5885	−1.35633	−0.678167	+	0.734908i	$0.737225\pi$
$74$	−25.2188	−2.93162
$75$	0.648355	0.0748655
$76$	6.41440	0.735782
$77$	8.07809	0.920583
$78$	−1.35819	−0.153785
$79$	−12.1375	−1.36558	−0.682790	−	0.730615i	$-0.739233\pi$
$79$	−12.1375	−1.36558	−0.682790	+	0.730615i	$0.739233\pi$
$80$	−19.0818	−2.13341
$81$	6.65019	0.738911
$82$	23.7580	2.62363
$83$	−8.13313	−0.892727	−0.446363	−	0.894852i	$-0.647281\pi$
$83$	−8.13313	−0.892727	−0.446363	+	0.894852i	$0.647281\pi$
$84$	−3.62620	−0.395651
$85$	−13.6277	−1.47813
$86$	5.12644	0.552798
$87$	−0.753878	−0.0808243
$88$	−41.9156	−4.46822
$89$	2.25566	0.239099	0.119550	−	0.992828i	$-0.461855\pi$
$89$	2.25566	0.239099	0.119550	+	0.992828i	$0.461855\pi$
$90$	−13.8453	−1.45942
$91$	−1.44000	−0.150953
$92$	4.01853	0.418961
$93$	2.09475	0.217216
$94$	22.1611	2.28575
$95$	−2.55908	−0.262556
$96$	5.63030	0.574640
$97$	−1.71192	−0.173819	−0.0869097	−	0.996216i	$-0.527699\pi$
$97$	−1.71192	−0.173819	−0.0869097	+	0.996216i	$0.527699\pi$
$98$	12.8974	1.30283
$99$	−15.3195	−1.53967
$100$	−6.06634	−0.606634
$101$	12.5649	1.25025	0.625125	−	0.780524i	$-0.285048\pi$
$101$	12.5649	1.25025	0.625125	+	0.780524i	$0.285048\pi$
$102$	9.55770	0.946354
$103$	9.49574	0.935643	0.467822	−	0.883823i	$-0.345039\pi$
$103$	9.49574	0.935643	0.467822	+	0.883823i	$0.345039\pi$
$104$	7.47189	0.732679
$105$	1.44670	0.141184
$106$	18.2128	1.76899
$107$	18.7121	1.80897	0.904486	−	0.426504i	$-0.140255\pi$
$107$	18.7121	1.80897	0.904486	+	0.426504i	$0.140255\pi$
$108$	14.4314	1.38866
$109$	−13.3069	−1.27457	−0.637287	−	0.770626i	$-0.719943\pi$
$109$	−13.3069	−1.27457	−0.637287	+	0.770626i	$0.719943\pi$
$110$	28.4412	2.71176
$111$	−4.99733	−0.474326
$112$	14.1890	1.34074
$113$	−19.1247	−1.79910	−0.899549	−	0.436821i	$-0.856104\pi$
$113$	−19.1247	−1.79910	−0.899549	+	0.436821i	$0.856104\pi$
$114$	1.79479	0.168098
$115$	−1.60323	−0.149502
$116$	7.05368	0.654918
$117$	2.73086	0.252468
$118$	−13.3296	−1.22709
$119$	10.1334	0.928929
$120$	−7.50667	−0.685262
$121$	20.4696	1.86087
$122$	−2.33711	−0.211592
$123$	4.70787	0.424495
$124$	−19.5996	−1.76010
$125$	12.1030	1.08252
$126$	10.2952	0.917170
$127$	5.70605	0.506330	0.253165	−	0.967423i	$-0.418528\pi$
$127$	5.70605	0.506330	0.253165	+	0.967423i	$0.418528\pi$
$128$	−1.08677	−0.0960581
$129$	1.01585	0.0894408
$130$	−5.06994	−0.444663
$131$	−15.4235	−1.34756	−0.673779	−	0.738933i	$-0.735330\pi$
$131$	−15.4235	−1.34756	−0.673779	+	0.738933i	$0.735330\pi$
$132$	−14.1265	−1.22956
$133$	1.90290	0.165003
$134$	19.3015	1.66739
$135$	−5.75754	−0.495530
$136$	−52.5804	−4.50873
$137$	10.7193	0.915813	0.457907	−	0.889000i	$-0.348599\pi$
$137$	10.7193	0.915813	0.457907	+	0.889000i	$0.348599\pi$
$138$	1.12441	0.0957163
$139$	7.60641	0.645167	0.322584	−	0.946541i	$-0.395449\pi$
$139$	7.60641	0.645167	0.322584	+	0.946541i	$0.395449\pi$
$140$	−13.5361	−1.14401
$141$	4.39144	0.369826
$142$	−6.45145	−0.541394
$143$	−5.60978	−0.469113
$144$	−26.9085	−2.24238
$145$	−2.81413	−0.233701
$146$	30.3390	2.51087
$147$	2.55574	0.210794
$148$	46.7577	3.84346
$149$	1.49231	0.122255	0.0611276	−	0.998130i	$-0.480530\pi$
$149$	1.49231	0.122255	0.0611276	+	0.998130i	$0.480530\pi$
$150$	−1.69740	−0.138592
$151$	18.7219	1.52357	0.761783	−	0.647833i	$-0.224324\pi$
$151$	18.7219	1.52357	0.761783	+	0.647833i	$0.224324\pi$
$152$	−9.87380	−0.800871
$153$	−19.2173	−1.55363
$154$	−21.1486	−1.70420
$155$	7.81944	0.628072
$156$	2.51819	0.201617
$157$	−22.5360	−1.79857	−0.899284	−	0.437365i	$-0.855912\pi$
$157$	−22.5360	−1.79857	−0.899284	+	0.437365i	$0.855912\pi$
$158$	31.7763	2.52799
$159$	3.60904	0.286216
$160$	21.0172	1.66155
$161$	1.19214	0.0939540
$162$	−17.4103	−1.36789
$163$	−16.4985	−1.29227	−0.646133	−	0.763225i	$-0.723615\pi$
$163$	−16.4985	−1.29227	−0.646133	+	0.763225i	$0.723615\pi$
$164$	−44.0493	−3.43968
$165$	5.63589	0.438754
$166$	21.2927	1.65263
$167$	−4.79044	−0.370695	−0.185347	−	0.982673i	$-0.559341\pi$
$167$	−4.79044	−0.370695	−0.185347	+	0.982673i	$0.559341\pi$
$168$	5.58188	0.430651
$169$	1.00000	0.0769231
$170$	35.6776	2.73635
$171$	−3.60873	−0.275966
$172$	−9.50484	−0.724737
$173$	19.6063	1.49064	0.745319	−	0.666708i	$-0.232297\pi$
$173$	19.6063	1.49064	0.745319	+	0.666708i	$0.232297\pi$
$174$	1.97367	0.149623
$175$	−1.79965	−0.136041
$176$	55.2759	4.16658
$177$	−2.64139	−0.198539
$178$	−5.90535	−0.442625
$179$	23.2513	1.73789	0.868943	−	0.494912i	$-0.164800\pi$
$179$	23.2513	1.73789	0.868943	+	0.494912i	$0.164800\pi$
$180$	25.6703	1.91335
$181$	−14.0830	−1.04678	−0.523390	−	0.852093i	$-0.675333\pi$
$181$	−14.0830	−1.04678	−0.523390	+	0.852093i	$0.675333\pi$
$182$	3.76995	0.279447
$183$	−0.463120	−0.0342348
$184$	−6.18580	−0.456023
$185$	−18.6544	−1.37150
$186$	−5.48411	−0.402114
$187$	39.4765	2.88681
$188$	−41.0886	−2.99669
$189$	4.28124	0.311415
$190$	6.69972	0.486049
$191$	−13.9316	−1.00806	−0.504028	−	0.863687i	$-0.668149\pi$
$191$	−13.9316	−1.00806	−0.504028	+	0.863687i	$0.668149\pi$
$192$	−4.51655	−0.325954
$193$	−17.3665	−1.25007	−0.625034	−	0.780597i	$-0.714915\pi$
$193$	−17.3665	−1.25007	−0.625034	+	0.780597i	$0.714915\pi$
$194$	4.48185	0.321778
$195$	−1.00466	−0.0719449
$196$	−23.9128	−1.70806
$197$	−11.1934	−0.797496	−0.398748	−	0.917061i	$-0.630555\pi$
$197$	−11.1934	−0.797496	−0.398748	+	0.917061i	$0.630555\pi$
$198$	40.1068	2.85027
$199$	−17.1733	−1.21738	−0.608692	−	0.793407i	$-0.708305\pi$
$199$	−17.1733	−1.21738	−0.608692	+	0.793407i	$0.708305\pi$
$200$	9.33803	0.660299
$201$	3.82477	0.269778
$202$	−32.8951	−2.31449
$203$	2.09255	0.146869
$204$	−17.7208	−1.24070
$205$	17.5739	1.22741
$206$	−24.8600	−1.73208
$207$	−2.26082	−0.157138
$208$	−9.85349	−0.683217
$209$	7.41310	0.512775
$210$	−3.78750	−0.261362
$211$	−27.8250	−1.91555	−0.957777	−	0.287512i	$-0.907172\pi$
$211$	−27.8250	−1.91555	−0.957777	+	0.287512i	$0.907172\pi$
$212$	−33.7681	−2.31920
$213$	−1.27842	−0.0875956
$214$	−48.9888	−3.34880
$215$	3.79204	0.258615
$216$	−22.2146	−1.51151
$217$	−5.81445	−0.394710
$218$	34.8378	2.35952
$219$	6.01195	0.406250
$220$	−52.7324	−3.55522
$221$	−7.03709	−0.473366
$222$	13.0831	0.878081
$223$	1.73864	0.116428	0.0582141	−	0.998304i	$-0.481459\pi$
$223$	1.73864	0.116428	0.0582141	+	0.998304i	$0.481459\pi$
$224$	−15.6281	−1.04420
$225$	3.41291	0.227527
$226$	50.0687	3.33052
$227$	23.8147	1.58064	0.790319	−	0.612696i	$-0.209915\pi$
$227$	23.8147	1.58064	0.790319	+	0.612696i	$0.209915\pi$
$228$	−3.32769	−0.220382
$229$	20.8044	1.37479	0.687397	−	0.726282i	$-0.258753\pi$
$229$	20.8044	1.37479	0.687397	+	0.726282i	$0.258753\pi$
$230$	4.19728	0.276760
$231$	−4.19079	−0.275734
$232$	−10.8579	−0.712853
$233$	−17.7932	−1.16567	−0.582836	−	0.812590i	$-0.698057\pi$
$233$	−17.7932	−1.16567	−0.582836	+	0.812590i	$0.698057\pi$
$234$	−7.14945	−0.467374
$235$	16.3926	1.06934
$236$	24.7143	1.60876
$237$	6.29677	0.409019
$238$	−26.5295	−1.71965
$239$	−21.5256	−1.39238	−0.696189	−	0.717859i	$-0.745122\pi$
$239$	−21.5256	−1.39238	−0.696189	+	0.717859i	$0.745122\pi$
$240$	9.89937	0.639001
$241$	−17.2683	−1.11235	−0.556174	−	0.831066i	$-0.687731\pi$
$241$	−17.2683	−1.11235	−0.556174	+	0.831066i	$0.687731\pi$
$242$	−53.5898	−3.44489
$243$	−12.3693	−0.793489
$244$	4.33319	0.277404
$245$	9.54024	0.609503
$246$	−12.3253	−0.785833
$247$	−1.32146	−0.0840825
$248$	30.1700	1.91580
$249$	4.21934	0.267390
$250$	−31.6859	−2.00399
$251$	−9.12169	−0.575756	−0.287878	−	0.957667i	$-0.592950\pi$
$251$	−9.12169	−0.575756	−0.287878	+	0.957667i	$0.592950\pi$
$252$	−19.0882	−1.20244
$253$	4.64420	0.291978
$254$	−14.9385	−0.937328
$255$	7.06985	0.442731
$256$	−14.5668	−0.910427
$257$	22.5251	1.40508	0.702539	−	0.711645i	$-0.252050\pi$
$257$	22.5251	1.40508	0.702539	+	0.711645i	$0.252050\pi$
$258$	−2.65952	−0.165574
$259$	13.8712	0.861914
$260$	9.40008	0.582968
$261$	−3.96838	−0.245637
$262$	40.3790	2.49462
$263$	28.0045	1.72683	0.863415	−	0.504494i	$-0.168321\pi$
$263$	28.0045	1.72683	0.863415	+	0.504494i	$0.168321\pi$
$264$	21.7452	1.33832
$265$	13.4721	0.827583
$266$	−4.98184	−0.305456
$267$	−1.17020	−0.0716152
$268$	−35.7865	−2.18601
$269$	15.8383	0.965681	0.482840	−	0.875708i	$-0.339605\pi$
$269$	15.8383	0.965681	0.482840	+	0.875708i	$0.339605\pi$
$270$	15.0734	0.917335
$271$	−0.236759	−0.0143821	−0.00719105	−	0.999974i	$-0.502289\pi$
$271$	−0.236759	−0.0143821	−0.00719105	+	0.999974i	$0.502289\pi$
$272$	69.3400	4.20435
$273$	0.747051	0.0452136
$274$	−28.0634	−1.69537
$275$	−7.01085	−0.422770
$276$	−2.08475	−0.125487
$277$	−3.14485	−0.188955	−0.0944777	−	0.995527i	$-0.530118\pi$
$277$	−3.14485	−0.188955	−0.0944777	+	0.995527i	$0.530118\pi$
$278$	−19.9137	−1.19435
$279$	11.0267	0.660151
$280$	20.8364	1.24521
$281$	−5.33119	−0.318032	−0.159016	−	0.987276i	$-0.550832\pi$
$281$	−5.33119	−0.318032	−0.159016	+	0.987276i	$0.550832\pi$
$282$	−11.4969	−0.684628
$283$	17.3031	1.02856	0.514280	−	0.857622i	$-0.328059\pi$
$283$	17.3031	1.02856	0.514280	+	0.857622i	$0.328059\pi$
$284$	11.9615	0.709786
$285$	1.32761	0.0786410
$286$	14.6865	0.868431
$287$	−13.0677	−0.771364
$288$	29.6377	1.74642
$289$	32.5207	1.91298
$290$	7.36744	0.432631
$291$	0.888120	0.0520625
$292$	−56.2510	−3.29184
$293$	10.6274	0.620860	0.310430	−	0.950596i	$-0.399527\pi$
$293$	10.6274	0.620860	0.310430	+	0.950596i	$0.399527\pi$
$294$	−6.69098	−0.390226
$295$	−9.85997	−0.574069
$296$	−71.9749	−4.18346
$297$	16.6783	0.967776
$298$	−3.90691	−0.226321
$299$	−0.827876	−0.0478773
$300$	3.14713	0.181700
$301$	−2.81972	−0.162526
$302$	−49.0143	−2.82045
$303$	−6.51846	−0.374476
$304$	13.0210	0.746806
$305$	−1.72876	−0.0989887
$306$	50.3113	2.87611
$307$	−1.96349	−0.112062	−0.0560312	−	0.998429i	$-0.517845\pi$
$307$	−1.96349	−0.112062	−0.0560312	+	0.998429i	$0.517845\pi$
$308$	39.2112	2.23427
$309$	−4.92625	−0.280244
$310$	−20.4714	−1.16270
$311$	1.31152	0.0743694	0.0371847	−	0.999308i	$-0.488161\pi$
$311$	1.31152	0.0743694	0.0371847	+	0.999308i	$0.488161\pi$
$312$	−3.87630	−0.219452
$313$	1.90003	0.107396	0.0536981	−	0.998557i	$-0.482899\pi$
$313$	1.90003	0.107396	0.0536981	+	0.998557i	$0.482899\pi$
$314$	58.9996	3.32954
$315$	7.61539	0.429079
$316$	−58.9159	−3.31428
$317$	3.87893	0.217863	0.108931	−	0.994049i	$-0.465257\pi$
$317$	3.87893	0.217863	0.108931	+	0.994049i	$0.465257\pi$
$318$	−9.44855	−0.529848
$319$	8.15192	0.456420
$320$	−16.8597	−0.942484
$321$	−9.70758	−0.541824
$322$	−3.12105	−0.173929
$323$	9.29924	0.517424
$324$	32.2802	1.79334
$325$	1.24976	0.0693240
$326$	43.1935	2.39227
$327$	6.90344	0.381761
$328$	67.8059	3.74396
$329$	−12.1894	−0.672023
$330$	−14.7549	−0.812229
$331$	−2.58442	−0.142053	−0.0710263	−	0.997474i	$-0.522627\pi$
$331$	−2.58442	−0.142053	−0.0710263	+	0.997474i	$0.522627\pi$
$332$	−39.4784	−2.16666
$333$	−26.3057	−1.44155
$334$	12.5414	0.686238
$335$	14.2773	0.780055
$336$	−7.36106	−0.401579
$337$	−9.17640	−0.499870	−0.249935	−	0.968263i	$-0.580409\pi$
$337$	−9.17640	−0.499870	−0.249935	+	0.968263i	$0.580409\pi$
$338$	−2.61802	−0.142401
$339$	9.92159	0.538867
$340$	−66.1493	−3.58745
$341$	−22.6512	−1.22663
$342$	9.44771	0.510874
$343$	−17.1740	−0.927310
$344$	14.6310	0.788849
$345$	0.831730	0.0447789
$346$	−51.3296	−2.75950
$347$	11.2861	0.605871	0.302935	−	0.953011i	$-0.402033\pi$
$347$	11.2861	0.605871	0.302935	+	0.953011i	$0.402033\pi$
$348$	−3.65934	−0.196161
$349$	−32.8671	−1.75934	−0.879668	−	0.475588i	$-0.842235\pi$
$349$	−32.8671	−1.75934	−0.879668	+	0.475588i	$0.842235\pi$
$350$	4.71152	0.251841
$351$	−2.97309	−0.158692
$352$	−60.8822	−3.24503
$353$	−23.5869	−1.25541	−0.627703	−	0.778453i	$-0.716005\pi$
$353$	−23.5869	−1.25541	−0.627703	+	0.778453i	$0.716005\pi$
$354$	6.91522	0.367540
$355$	−4.77215	−0.253280
$356$	10.9490	0.580297
$357$	−5.25707	−0.278233
$358$	−60.8724	−3.21721
$359$	−30.5391	−1.61179	−0.805896	−	0.592057i	$-0.798316\pi$
$359$	−30.5391	−1.61179	−0.805896	+	0.592057i	$0.798316\pi$
$360$	−39.5148	−2.08261
$361$	−17.2537	−0.908092
$362$	36.8695	1.93782
$363$	−10.6193	−0.557370
$364$	−6.98980	−0.366365
$365$	22.4418	1.17466
$366$	1.21246	0.0633761
$367$	19.0729	0.995595	0.497797	−	0.867293i	$-0.334142\pi$
$367$	19.0729	0.995595	0.497797	+	0.867293i	$0.334142\pi$
$368$	8.15747	0.425238
$369$	24.7821	1.29010
$370$	48.8375	2.53894
$371$	−10.0177	−0.520093
$372$	10.1680	0.527185
$373$	10.3245	0.534582	0.267291	−	0.963616i	$-0.413871\pi$
$373$	10.3245	0.534582	0.267291	+	0.963616i	$0.413871\pi$
$374$	−103.350	−5.34412
$375$	−6.27885	−0.324238
$376$	63.2484	3.26179
$377$	−1.45316	−0.0748416
$378$	−11.2084	−0.576497
$379$	21.9247	1.12620	0.563098	−	0.826390i	$-0.309609\pi$
$379$	21.9247	1.12620	0.563098	+	0.826390i	$0.309609\pi$
$380$	−12.4218	−0.637227
$381$	−2.96021	−0.151656
$382$	36.4732	1.86613
$383$	−15.2651	−0.780011	−0.390006	−	0.920813i	$-0.627527\pi$
$383$	−15.2651	−0.780011	−0.390006	+	0.920813i	$0.627527\pi$
$384$	0.563802	0.0287714
$385$	−15.6437	−0.797274
$386$	45.4659	2.31415
$387$	5.34740	0.271824
$388$	−8.30971	−0.421862
$389$	5.22782	0.265061	0.132530	−	0.991179i	$-0.457690\pi$
$389$	5.22782	0.265061	0.132530	+	0.991179i	$0.457690\pi$
$390$	2.63021	0.133186
$391$	5.82584	0.294626
$392$	36.8095	1.85916
$393$	8.00148	0.403621
$394$	29.3045	1.47634
$395$	23.5050	1.18266
$396$	−74.3614	−3.73680
$397$	−20.1210	−1.00985	−0.504923	−	0.863164i	$-0.668479\pi$
$397$	−20.1210	−1.00985	−0.504923	+	0.863164i	$0.668479\pi$
$398$	44.9600	2.25364
$399$	−0.987198	−0.0494217
$400$	−12.3145	−0.615723
$401$	−13.8889	−0.693577	−0.346788	−	0.937943i	$-0.612728\pi$
$401$	−13.8889	−0.693577	−0.346788	+	0.937943i	$0.612728\pi$
$402$	−10.0133	−0.499419
$403$	4.03781	0.201138
$404$	60.9902	3.03437
$405$	−12.8785	−0.639936
$406$	−5.47835	−0.271886
$407$	54.0377	2.67855
$408$	27.2779	1.35046
$409$	5.33213	0.263657	0.131828	−	0.991273i	$-0.457915\pi$
$409$	5.33213	0.263657	0.131828	+	0.991273i	$0.457915\pi$
$410$	−46.0087	−2.27221
$411$	−5.56102	−0.274305
$412$	46.0925	2.27082
$413$	7.33176	0.360772
$414$	5.91886	0.290896
$415$	15.7502	0.773149
$416$	10.8529	0.532105
$417$	−3.94609	−0.193241
$418$	−19.4076	−0.949259
$419$	7.74808	0.378519	0.189259	−	0.981927i	$-0.439391\pi$
$419$	7.74808	0.378519	0.189259	+	0.981927i	$0.439391\pi$
$420$	7.02234	0.342655
$421$	−29.8768	−1.45611	−0.728053	−	0.685520i	$-0.759575\pi$
$421$	−29.8768	−1.45611	−0.728053	+	0.685520i	$0.759575\pi$
$422$	72.8465	3.54611
$423$	23.1163	1.12395
$424$	51.9799	2.52437
$425$	−8.79465	−0.426603
$426$	3.34692	0.162159
$427$	1.28549	0.0622092
$428$	90.8292	4.39039
$429$	2.91027	0.140509
$430$	−9.92763	−0.478753
$431$	−15.7100	−0.756722	−0.378361	−	0.925658i	$-0.623512\pi$
$431$	−15.7100	−0.756722	−0.378361	+	0.925658i	$0.623512\pi$
$432$	29.2953	1.40947
$433$	15.1567	0.728387	0.364193	−	0.931323i	$-0.381345\pi$
$433$	15.1567	0.728387	0.364193	+	0.931323i	$0.381345\pi$
$434$	15.2223	0.730695
$435$	1.45993	0.0699981
$436$	−64.5922	−3.09341
$437$	1.09401	0.0523334
$438$	−15.7394	−0.752058
$439$	0.245368	0.0117108	0.00585538	−	0.999983i	$-0.498136\pi$
$439$	0.245368	0.0117108	0.00585538	+	0.999983i	$0.498136\pi$
$440$	81.1719	3.86972
$441$	13.4533	0.640634
$442$	18.4232	0.876304
$443$	41.2186	1.95835	0.979176	−	0.203012i	$-0.0650730\pi$
$443$	41.2186	1.95835	0.979176	+	0.203012i	$0.0650730\pi$
$444$	−24.2572	−1.15119
$445$	−4.36820	−0.207073
$446$	−4.55180	−0.215534
$447$	−0.774190	−0.0366179
$448$	12.5367	0.592302
$449$	−31.1727	−1.47113	−0.735566	−	0.677453i	$-0.763084\pi$
$449$	−31.1727	−1.47113	−0.735566	+	0.677453i	$0.763084\pi$
$450$	−8.93507	−0.421203
$451$	−50.9077	−2.39715
$452$	−92.8316	−4.36643
$453$	−9.71263	−0.456339
$454$	−62.3473	−2.92611
$455$	2.78864	0.130733
$456$	5.12238	0.239877
$457$	33.3802	1.56146	0.780731	−	0.624867i	$-0.214847\pi$
$457$	33.3802	1.56146	0.780731	+	0.624867i	$0.214847\pi$
$458$	−54.4663	−2.54504
$459$	20.9219	0.976550
$460$	−7.78210	−0.362842
$461$	9.41690	0.438589	0.219294	−	0.975659i	$-0.429624\pi$
$461$	9.41690	0.438589	0.219294	+	0.975659i	$0.429624\pi$
$462$	10.9716	0.510443
$463$	30.5838	1.42135	0.710675	−	0.703520i	$-0.248390\pi$
$463$	30.5838	1.42135	0.710675	+	0.703520i	$0.248390\pi$
$464$	14.3187	0.664730
$465$	−4.05661	−0.188121
$466$	46.5829	2.15791
$467$	34.7477	1.60793	0.803965	−	0.594677i	$-0.202720\pi$
$467$	34.7477	1.60793	0.803965	+	0.594677i	$0.202720\pi$
$468$	13.2557	0.612743
$469$	−10.6165	−0.490223
$470$	−42.9162	−1.97958
$471$	11.6913	0.538708
$472$	−38.0431	−1.75108
$473$	−10.9847	−0.505078
$474$	−16.4851	−0.757184
$475$	−1.65150	−0.0757762
$476$	49.1879	2.25452
$477$	18.9979	0.869852
$478$	56.3545	2.57760
$479$	−15.0110	−0.685871	−0.342935	−	0.939359i	$-0.611421\pi$
$479$	−15.0110	−0.685871	−0.342935	+	0.939359i	$0.611421\pi$
$480$	−10.9034	−0.497669
$481$	−9.63276	−0.439216
$482$	45.2087	2.05920
$483$	−0.618466	−0.0281412
$484$	99.3600	4.51636
$485$	3.31523	0.150537
$486$	32.3830	1.46892
$487$	24.3010	1.10118	0.550591	−	0.834775i	$-0.314402\pi$
$487$	24.3010	1.10118	0.550591	+	0.834775i	$0.314402\pi$
$488$	−6.67016	−0.301944
$489$	8.55919	0.387060
$490$	−24.9765	−1.12832
$491$	24.6672	1.11322	0.556609	−	0.830775i	$-0.312102\pi$
$491$	24.6672	1.11322	0.556609	+	0.830775i	$0.312102\pi$
$492$	22.8521	1.03025
$493$	10.2260	0.460557
$494$	3.45961	0.155655
$495$	29.6671	1.33344
$496$	−39.7865	−1.78647
$497$	3.54852	0.159173
$498$	−11.0463	−0.494998
$499$	−14.3415	−0.642012	−0.321006	−	0.947077i	$-0.604021\pi$
$499$	−14.3415	−0.642012	−0.321006	+	0.947077i	$0.604021\pi$
$500$	58.7482	2.62730
$501$	2.48521	0.111031
$502$	23.8808	1.06585
$503$	33.4281	1.49048	0.745242	−	0.666794i	$-0.232334\pi$
$503$	33.4281	1.49048	0.745242	+	0.666794i	$0.232334\pi$
$504$	29.3828	1.30881
$505$	−24.3326	−1.08278
$506$	−12.1586	−0.540516
$507$	−0.518785	−0.0230400
$508$	27.6973	1.22887
$509$	−19.7584	−0.875776	−0.437888	−	0.899029i	$-0.644273\pi$
$509$	−19.7584	−0.875776	−0.437888	+	0.899029i	$0.644273\pi$
$510$	−18.5090	−0.819593
$511$	−16.6875	−0.738211
$512$	40.3098	1.78146
$513$	3.92881	0.173461
$514$	−58.9712	−2.60111
$515$	−18.3890	−0.810317
$516$	4.93097	0.217074
$517$	−47.4859	−2.08843
$518$	−36.3150	−1.59559
$519$	−10.1714	−0.446477
$520$	−14.4697	−0.634539
$521$	8.94061	0.391695	0.195848	−	0.980634i	$-0.437254\pi$
$521$	8.94061	0.391695	0.195848	+	0.980634i	$0.437254\pi$
$522$	10.3893	0.454728
$523$	23.3969	1.02308	0.511538	−	0.859261i	$-0.329076\pi$
$523$	23.3969	1.02308	0.511538	+	0.859261i	$0.329076\pi$
$524$	−74.8660	−3.27054
$525$	0.933631	0.0407470
$526$	−73.3163	−3.19674
$527$	−28.4144	−1.23775
$528$	−28.6763	−1.24798
$529$	−22.3146	−0.970201
$530$	−35.2702	−1.53204
$531$	−13.9042	−0.603390
$532$	9.23674	0.400464
$533$	9.07481	0.393074
$534$	3.06361	0.132575
$535$	−36.2371	−1.56667
$536$	55.0868	2.37939
$537$	−12.0624	−0.520533
$538$	−41.4651	−1.78769
$539$	−27.6360	−1.19037
$540$	−27.9472	−1.20266
$541$	−18.4716	−0.794158	−0.397079	−	0.917785i	$-0.629976\pi$
$541$	−18.4716	−0.794158	−0.397079	+	0.917785i	$0.629976\pi$
$542$	0.619841	0.0266244
$543$	7.30604	0.313532
$544$	−76.3726	−3.27445
$545$	25.7696	1.10385
$546$	−1.95579	−0.0837002
$547$	29.4265	1.25819	0.629094	−	0.777329i	$-0.283426\pi$
$547$	29.4265	1.25819	0.629094	+	0.777329i	$0.283426\pi$
$548$	52.0318	2.22269
$549$	−2.43784	−0.104045
$550$	18.3545	0.782641
$551$	1.92030	0.0818074
$552$	3.20910	0.136588
$553$	−17.4781	−0.743243
$554$	8.23326	0.349798
$555$	9.67761	0.410792
$556$	36.9217	1.56583
$557$	−3.24202	−0.137369	−0.0686844	−	0.997638i	$-0.521880\pi$
$557$	−3.24202	−0.137369	−0.0686844	+	0.997638i	$0.521880\pi$
$558$	−28.8681	−1.22208
$559$	1.95814	0.0828204
$560$	−27.4779	−1.16115
$561$	−20.4798	−0.864659
$562$	13.9572	0.588747
$563$	−37.0039	−1.55953	−0.779764	−	0.626074i	$-0.784661\pi$
$563$	−37.0039	−1.55953	−0.779764	+	0.626074i	$0.784661\pi$
$564$	21.3161	0.897571
$565$	37.0360	1.55811
$566$	−45.2998	−1.90409
$567$	9.57629	0.402166
$568$	−18.4126	−0.772575
$569$	−5.51539	−0.231217	−0.115609	−	0.993295i	$-0.536882\pi$
$569$	−5.51539	−0.231217	−0.115609	+	0.993295i	$0.536882\pi$
$570$	−3.47571	−0.145582
$571$	−21.5595	−0.902237	−0.451119	−	0.892464i	$-0.648975\pi$
$571$	−21.5595	−0.902237	−0.451119	+	0.892464i	$0.648975\pi$
$572$	−27.2300	−1.13854
$573$	7.22751	0.301934
$574$	34.2116	1.42796
$575$	−1.03464	−0.0431476
$576$	−23.7749	−0.990621
$577$	8.67596	0.361185	0.180592	−	0.983558i	$-0.442198\pi$
$577$	8.67596	0.361185	0.180592	+	0.983558i	$0.442198\pi$
$578$	−85.1398	−3.54135
$579$	9.00948	0.374421
$580$	−13.6598	−0.567194
$581$	−11.7117	−0.485884
$582$	−2.32511	−0.0963791
$583$	−39.0257	−1.61628
$584$	86.5881	3.58304
$585$	−5.28846	−0.218651
$586$	−27.8228	−1.14935
$587$	−11.1145	−0.458743	−0.229372	−	0.973339i	$-0.573667\pi$
$587$	−11.1145	−0.458743	−0.229372	+	0.973339i	$0.573667\pi$
$588$	12.4056	0.511599
$589$	−5.33580	−0.219858
$590$	25.8136	1.06273
$591$	5.80696	0.238867
$592$	94.9164	3.90104
$593$	−21.4264	−0.879877	−0.439939	−	0.898028i	$-0.645000\pi$
$593$	−21.4264	−0.879877	−0.439939	+	0.898028i	$0.645000\pi$
$594$	−43.6642	−1.79157
$595$	−19.6239	−0.804502
$596$	7.24373	0.296715
$597$	8.90925	0.364631
$598$	2.16740	0.0886314
$599$	−35.5692	−1.45332	−0.726658	−	0.686999i	$-0.758928\pi$
$599$	−35.5692	−1.45332	−0.726658	+	0.686999i	$0.758928\pi$
$600$	−4.84443	−0.197773
$601$	−25.7381	−1.04988	−0.524940	−	0.851139i	$-0.675912\pi$
$601$	−25.7381	−1.04988	−0.524940	+	0.851139i	$0.675912\pi$
$602$	7.38208	0.300871
$603$	20.1334	0.819896
$604$	90.8765	3.69771
$605$	−39.6405	−1.61162
$606$	17.0655	0.693237
$607$	4.61478	0.187308	0.0936540	−	0.995605i	$-0.470145\pi$
$607$	4.61478	0.187308	0.0936540	+	0.995605i	$0.470145\pi$
$608$	−14.3416	−0.581630
$609$	−1.08559	−0.0439901
$610$	4.52593	0.183250
$611$	8.46485	0.342451
$612$	−93.2814	−3.77068
$613$	−9.38217	−0.378942	−0.189471	−	0.981886i	$-0.560677\pi$
$613$	−9.38217	−0.378942	−0.189471	+	0.981886i	$0.560677\pi$
$614$	5.14046	0.207452
$615$	−9.11706	−0.367635
$616$	−60.3585	−2.43191
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	12.8970	0.518794
$619$	−23.2434	−0.934233	−0.467116	−	0.884196i	$-0.654707\pi$
$619$	−23.2434	−0.934233	−0.467116	+	0.884196i	$0.654707\pi$
$620$	37.9557	1.52434
$621$	2.46135	0.0987704
$622$	−3.43358	−0.137674
$623$	3.24815	0.130134
$624$	5.11184	0.204638
$625$	−17.1893	−0.687573
$626$	−4.97432	−0.198814
$627$	−3.84581	−0.153587
$628$	−109.390	−4.36514
$629$	67.7867	2.70283
$630$	−19.9372	−0.794319
$631$	8.26396	0.328983	0.164492	−	0.986378i	$-0.447402\pi$
$631$	8.26396	0.328983	0.164492	+	0.986378i	$0.447402\pi$
$632$	90.6903	3.60747
$633$	14.4352	0.573748
$634$	−10.1551	−0.403311
$635$	−11.0501	−0.438509
$636$	17.5184	0.694649
$637$	4.92640	0.195191
$638$	−21.3419	−0.844933
$639$	−6.72952	−0.266216
$640$	2.10460	0.0831915
$641$	28.7756	1.13657	0.568284	−	0.822833i	$-0.307608\pi$
$641$	28.7756	1.13657	0.568284	+	0.822833i	$0.307608\pi$
$642$	25.4146	1.00304
$643$	−33.0826	−1.30465	−0.652325	−	0.757939i	$-0.726206\pi$
$643$	−33.0826	−1.30465	−0.652325	+	0.757939i	$0.726206\pi$
$644$	5.78669	0.228027
$645$	−1.96725	−0.0774605
$646$	−24.3456	−0.957864
$647$	23.2947	0.915811	0.457905	−	0.889001i	$-0.348600\pi$
$647$	23.2947	0.915811	0.457905	+	0.889001i	$0.348600\pi$
$648$	−49.6895	−1.95199
$649$	28.5622	1.12116
$650$	−3.27188	−0.128334
$651$	3.01645	0.118224
$652$	−80.0843	−3.13634
$653$	−37.7066	−1.47557	−0.737787	−	0.675034i	$-0.764129\pi$
$653$	−37.7066	−1.47557	−0.737787	+	0.675034i	$0.764129\pi$
$654$	−18.0733	−0.706724
$655$	29.8684	1.16706
$656$	−89.4186	−3.49121
$657$	31.6467	1.23465
$658$	31.9120	1.24406
$659$	30.6307	1.19320	0.596600	−	0.802538i	$-0.296518\pi$
$659$	30.6307	1.19320	0.596600	+	0.802538i	$0.296518\pi$
$660$	27.3568	1.06486
$661$	5.09646	0.198229	0.0991147	−	0.995076i	$-0.468399\pi$
$661$	5.09646	0.198229	0.0991147	+	0.995076i	$0.468399\pi$
$662$	6.76606	0.262971
$663$	3.65074	0.141783
$664$	60.7698	2.35833
$665$	−3.68508	−0.142901
$666$	68.8689	2.66862
$667$	1.20304	0.0465818
$668$	−23.2529	−0.899681
$669$	−0.901982	−0.0348727
$670$	−37.3784	−1.44405
$671$	5.00785	0.193326
$672$	8.10764	0.312759
$673$	−25.2875	−0.974763	−0.487381	−	0.873189i	$-0.662048\pi$
$673$	−25.2875	−0.974763	−0.487381	+	0.873189i	$0.662048\pi$
$674$	24.0240	0.925369
$675$	−3.71563	−0.143015
$676$	4.85402	0.186693
$677$	−39.3656	−1.51294	−0.756471	−	0.654028i	$-0.773078\pi$
$677$	−39.3656	−1.51294	−0.756471	+	0.654028i	$0.773078\pi$
$678$	−25.9749	−0.997560
$679$	−2.46517	−0.0946045
$680$	101.825	3.90480
$681$	−12.3547	−0.473433
$682$	59.3013	2.27076
$683$	37.4592	1.43334	0.716669	−	0.697414i	$-0.245666\pi$
$683$	37.4592	1.43334	0.716669	+	0.697414i	$0.245666\pi$
$684$	−17.5168	−0.669773
$685$	−20.7585	−0.793143
$686$	44.9619	1.71665
$687$	−10.7930	−0.411779
$688$	−19.2945	−0.735596
$689$	6.95672	0.265030
$690$	−2.17749	−0.0828955
$691$	−40.4287	−1.53798	−0.768990	−	0.639261i	$-0.779240\pi$
$691$	−40.4287	−1.53798	−0.768990	+	0.639261i	$0.779240\pi$
$692$	95.1694	3.61780
$693$	−22.0601	−0.837995
$694$	−29.5473	−1.12160
$695$	−14.7302	−0.558749
$696$	5.63289	0.213514
$697$	−63.8603	−2.41888
$698$	86.0467	3.25692
$699$	9.23085	0.349143
$700$	−8.73554	−0.330172
$701$	−9.19569	−0.347316	−0.173658	−	0.984806i	$-0.555559\pi$
$701$	−9.19569	−0.347316	−0.173658	+	0.984806i	$0.555559\pi$
$702$	7.78359	0.293773
$703$	12.7293	0.480095
$704$	48.8388	1.84068
$705$	−8.50426	−0.320289
$706$	61.7510	2.32403
$707$	18.0934	0.680473
$708$	−12.8214	−0.481857
$709$	2.28517	0.0858214	0.0429107	−	0.999079i	$-0.486337\pi$
$709$	2.28517	0.0858214	0.0429107	+	0.999079i	$0.486337\pi$
$710$	12.4936	0.468876
$711$	33.1459	1.24307
$712$	−16.8540	−0.631631
$713$	−3.34281	−0.125189
$714$	13.7631	0.515071
$715$	10.8636	0.406277
$716$	112.862	4.21787
$717$	11.1672	0.417046
$718$	79.9520	2.98378
$719$	−44.4537	−1.65784	−0.828922	−	0.559364i	$-0.811045\pi$
$719$	−44.4537	−1.65784	−0.828922	+	0.559364i	$0.811045\pi$
$720$	52.1099	1.94202
$721$	13.6739	0.509242
$722$	45.1706	1.68108
$723$	8.95853	0.333171
$724$	−68.3591	−2.54055
$725$	−1.81610	−0.0674482
$726$	27.8016	1.03181
$727$	17.3055	0.641827	0.320914	−	0.947108i	$-0.396010\pi$
$727$	17.3055	0.641827	0.320914	+	0.947108i	$0.396010\pi$
$728$	10.7595	0.398774
$729$	−13.5336	−0.501244
$730$	−58.7531	−2.17455
$731$	−13.7796	−0.509657
$732$	−2.24799	−0.0830882
$733$	7.23674	0.267295	0.133647	−	0.991029i	$-0.457331\pi$
$733$	7.23674	0.267295	0.133647	+	0.991029i	$0.457331\pi$
$734$	−49.9331	−1.84306
$735$	−4.94933	−0.182559
$736$	−8.98483	−0.331185
$737$	−41.3584	−1.52345
$738$	−64.8799	−2.38826
$739$	−44.4543	−1.63528	−0.817639	−	0.575731i	$-0.804718\pi$
$739$	−44.4543	−1.63528	−0.817639	+	0.575731i	$0.804718\pi$
$740$	−90.5487	−3.32864
$741$	0.685554	0.0251844
$742$	26.2265	0.962805
$743$	2.38494	0.0874948	0.0437474	−	0.999043i	$-0.486070\pi$
$743$	2.38494	0.0874948	0.0437474	+	0.999043i	$0.486070\pi$
$744$	−15.6518	−0.573822
$745$	−2.88995	−0.105880
$746$	−27.0297	−0.989629
$747$	22.2105	0.812638
$748$	191.620	7.00632
$749$	26.9455	0.984567
$750$	16.4382	0.600236
$751$	0.559162	0.0204041	0.0102021	−	0.999948i	$-0.496753\pi$
$751$	0.559162	0.0204041	0.0102021	+	0.999948i	$0.496753\pi$
$752$	−83.4083	−3.04159
$753$	4.73220	0.172451
$754$	3.80440	0.138548
$755$	−36.2560	−1.31949
$756$	20.7813	0.755807
$757$	25.7851	0.937175	0.468587	−	0.883417i	$-0.344763\pi$
$757$	25.7851	0.937175	0.468587	+	0.883417i	$0.344763\pi$
$758$	−57.3993	−2.08484
$759$	−2.40934	−0.0874536
$760$	19.1212	0.693597
$761$	−22.5612	−0.817842	−0.408921	−	0.912570i	$-0.634095\pi$
$761$	−22.5612	−0.817842	−0.408921	+	0.912570i	$0.634095\pi$
$762$	7.74989	0.280749
$763$	−19.1620	−0.693711
$764$	−67.6244	−2.44656
$765$	37.2154	1.34553
$766$	39.9644	1.44397
$767$	−5.09150	−0.183843
$768$	7.55705	0.272692
$769$	42.1598	1.52032	0.760161	−	0.649735i	$-0.225120\pi$
$769$	42.1598	1.52032	0.760161	+	0.649735i	$0.225120\pi$
$770$	40.9554	1.47593
$771$	−11.6857	−0.420850
$772$	−84.2974	−3.03393
$773$	14.4752	0.520638	0.260319	−	0.965523i	$-0.416172\pi$
$773$	14.4752	0.520638	0.260319	+	0.965523i	$0.416172\pi$
$774$	−13.9996	−0.503205
$775$	5.04627	0.181268
$776$	12.7913	0.459181
$777$	−7.19616	−0.258161
$778$	−13.6865	−0.490686
$779$	−11.9920	−0.429658
$780$	−4.87662	−0.174611
$781$	13.8239	0.494658
$782$	−15.2522	−0.545416
$783$	4.32037	0.154398
$784$	−48.5422	−1.73365
$785$	43.6422	1.55766
$786$	−20.9480	−0.747191
$787$	−32.0056	−1.14088	−0.570439	−	0.821340i	$-0.693227\pi$
$787$	−32.0056	−1.14088	−0.570439	+	0.821340i	$0.693227\pi$
$788$	−54.3330	−1.93553
$789$	−14.5283	−0.517221
$790$	−61.5365	−2.18937
$791$	−27.5395	−0.979193
$792$	114.466	4.06737
$793$	−0.892700	−0.0317007
$794$	52.6773	1.86945
$795$	−6.98911	−0.247878
$796$	−83.3596	−2.95460
$797$	31.7176	1.12349	0.561747	−	0.827309i	$-0.310130\pi$
$797$	31.7176	1.12349	0.561747	+	0.827309i	$0.310130\pi$
$798$	2.58450	0.0914904
$799$	−59.5679	−2.10736
$800$	13.5634	0.479540
$801$	−6.15989	−0.217649
$802$	36.3613	1.28396
$803$	−65.0091	−2.29412
$804$	18.5655	0.654755
$805$	−2.30865	−0.0813692
$806$	−10.5711	−0.372350
$807$	−8.21669	−0.289241
$808$	−93.8833	−3.30280
$809$	−45.6974	−1.60663	−0.803317	−	0.595552i	$-0.796934\pi$
$809$	−45.6974	−1.60663	−0.803317	+	0.595552i	$0.796934\pi$
$810$	33.7161	1.18466
$811$	−27.6208	−0.969898	−0.484949	−	0.874542i	$-0.661162\pi$
$811$	−27.6208	−0.969898	−0.484949	+	0.874542i	$0.661162\pi$
$812$	10.1573	0.356452
$813$	0.122827	0.00430774
$814$	−141.472	−4.95858
$815$	31.9503	1.11917
$816$	−35.9725	−1.25929
$817$	−2.58760	−0.0905287
$818$	−13.9596	−0.488086
$819$	3.93244	0.137411
$820$	85.3039	2.97894
$821$	−13.8738	−0.484199	−0.242099	−	0.970251i	$-0.577836\pi$
$821$	−13.8738	−0.484199	−0.242099	+	0.970251i	$0.577836\pi$
$822$	14.5589	0.507798
$823$	−32.3256	−1.12680	−0.563400	−	0.826185i	$-0.690507\pi$
$823$	−32.3256	−1.12680	−0.563400	+	0.826185i	$0.690507\pi$
$824$	−70.9511	−2.47170
$825$	3.63713	0.126628
$826$	−19.1947	−0.667869
$827$	−9.18327	−0.319334	−0.159667	−	0.987171i	$-0.551042\pi$
$827$	−9.18327	−0.319334	−0.159667	+	0.987171i	$0.551042\pi$
$828$	−10.9741	−0.381375
$829$	8.41228	0.292171	0.146085	−	0.989272i	$-0.453333\pi$
$829$	8.41228	0.292171	0.146085	+	0.989272i	$0.453333\pi$
$830$	−41.2344	−1.43127
$831$	1.63150	0.0565961
$832$	−8.70601	−0.301827
$833$	−34.6675	−1.20116
$834$	10.3309	0.357731
$835$	9.27694	0.321042
$836$	35.9834	1.24451
$837$	−12.0047	−0.414945
$838$	−20.2846	−0.700721
$839$	11.4572	0.395546	0.197773	−	0.980248i	$-0.436629\pi$
$839$	11.4572	0.395546	0.197773	+	0.980248i	$0.436629\pi$
$840$	−10.8096	−0.372967
$841$	−26.8883	−0.927183
$842$	78.2181	2.69557
$843$	2.76574	0.0952571
$844$	−135.063	−4.64907
$845$	−1.93655	−0.0666195
$846$	−60.5190	−2.08069
$847$	29.4763	1.01282
$848$	−68.5481	−2.35395
$849$	−8.97657	−0.308075
$850$	23.0246	0.789736
$851$	7.97473	0.273370
$852$	−6.20546	−0.212595
$853$	16.9321	0.579744	0.289872	−	0.957065i	$-0.406387\pi$
$853$	16.9321	0.579744	0.289872	+	0.957065i	$0.406387\pi$
$854$	−3.36544	−0.115163
$855$	6.98850	0.239002
$856$	−139.815	−4.77878
$857$	−44.8062	−1.53055	−0.765275	−	0.643704i	$-0.777397\pi$
$857$	−44.8062	−1.53055	−0.765275	+	0.643704i	$0.777397\pi$
$858$	−7.61914	−0.260113
$859$	−15.5376	−0.530135	−0.265067	−	0.964230i	$-0.585394\pi$
$859$	−15.5376	−0.530135	−0.265067	+	0.964230i	$0.585394\pi$
$860$	18.4066	0.627661
$861$	6.77934	0.231039
$862$	41.1290	1.40086
$863$	2.88653	0.0982586	0.0491293	−	0.998792i	$-0.484355\pi$
$863$	2.88653	0.0982586	0.0491293	+	0.998792i	$0.484355\pi$
$864$	−32.2665	−1.09773
$865$	−37.9687	−1.29097
$866$	−39.6807	−1.34840
$867$	−16.8712	−0.572978
$868$	−28.2235	−0.957967
$869$	−68.0889	−2.30976
$870$	−3.82212	−0.129582
$871$	7.37255	0.249809
$872$	99.4280	3.36706
$873$	4.67502	0.158226
$874$	−2.86413	−0.0968806
$875$	17.4283	0.589185
$876$	29.1822	0.985974
$877$	1.73359	0.0585391	0.0292696	−	0.999572i	$-0.490682\pi$
$877$	1.73359	0.0585391	0.0292696	+	0.999572i	$0.490682\pi$
$878$	−0.642378	−0.0216792
$879$	−5.51334	−0.185960
$880$	−107.045	−3.60848
$881$	35.7224	1.20352	0.601759	−	0.798678i	$-0.294467\pi$
$881$	35.7224	1.20352	0.601759	+	0.798678i	$0.294467\pi$
$882$	−35.2210	−1.18595
$883$	36.6797	1.23437	0.617185	−	0.786818i	$-0.288273\pi$
$883$	36.6797	1.23437	0.617185	+	0.786818i	$0.288273\pi$
$884$	−34.1582	−1.14887
$885$	5.11520	0.171946
$886$	−107.911	−3.62534
$887$	−39.9327	−1.34081	−0.670404	−	0.741996i	$-0.733879\pi$
$887$	−39.9327	−1.34081	−0.670404	+	0.741996i	$0.733879\pi$
$888$	37.3395	1.25303
$889$	8.21672	0.275580
$890$	11.4360	0.383337
$891$	37.3061	1.24980
$892$	8.43942	0.282573
$893$	−11.1860	−0.374324
$894$	2.02684	0.0677878
$895$	−45.0275	−1.50510
$896$	−1.56495	−0.0522815
$897$	0.429490	0.0143402
$898$	81.6108	2.72339
$899$	−5.86759	−0.195695
$900$	16.5663	0.552212
$901$	−48.9551	−1.63093
$902$	133.277	4.43765
$903$	1.46283	0.0486799
$904$	142.897	4.75269
$905$	27.2725	0.906567
$906$	25.4279	0.844784
$907$	19.9342	0.661903	0.330951	−	0.943648i	$-0.392630\pi$
$907$	19.9342	0.661903	0.330951	+	0.943648i	$0.392630\pi$
$908$	115.597	3.83622
$909$	−34.3129	−1.13809
$910$	−7.30071	−0.242016
$911$	40.5252	1.34266	0.671331	−	0.741158i	$-0.265723\pi$
$911$	40.5252	1.34266	0.671331	+	0.741158i	$0.265723\pi$
$912$	−6.75510	−0.223684
$913$	−45.6250	−1.50997
$914$	−87.3901	−2.89061
$915$	0.896856	0.0296492
$916$	100.985	3.33664
$917$	−22.2098	−0.733434
$918$	−54.7739	−1.80781
$919$	28.4591	0.938779	0.469389	−	0.882991i	$-0.344474\pi$
$919$	28.4591	0.938779	0.469389	+	0.882991i	$0.344474\pi$
$920$	11.9791	0.394940
$921$	1.01863	0.0335650
$922$	−24.6536	−0.811924
$923$	−2.46425	−0.0811118
$924$	−20.3422	−0.669209
$925$	−12.0386	−0.395827
$926$	−80.0690	−2.63123
$927$	−25.9316	−0.851704
$928$	−15.7710	−0.517707
$929$	−6.10486	−0.200294	−0.100147	−	0.994973i	$-0.531931\pi$
$929$	−6.10486	−0.200294	−0.100147	+	0.994973i	$0.531931\pi$
$930$	10.6203	0.348252
$931$	−6.51004	−0.213358
$932$	−86.3686	−2.82910
$933$	−0.680396	−0.0222752
$934$	−90.9700	−2.97663
$935$	−76.4485	−2.50013
$936$	−20.4047	−0.666948
$937$	−34.0747	−1.11317	−0.556586	−	0.830790i	$-0.687889\pi$
$937$	−34.0747	−1.11317	−0.556586	+	0.830790i	$0.687889\pi$
$938$	27.7941	0.907511
$939$	−0.985708	−0.0321674
$940$	79.5703	2.59530
$941$	−54.5589	−1.77857	−0.889285	−	0.457354i	$-0.848797\pi$
$941$	−54.5589	−1.77857	−0.889285	+	0.457354i	$0.848797\pi$
$942$	−30.6081	−0.997267
$943$	−7.51282	−0.244651
$944$	50.1691	1.63286
$945$	−8.29087	−0.269702
$946$	28.7582	0.935009
$947$	−33.6539	−1.09360	−0.546802	−	0.837262i	$-0.684155\pi$
$947$	−33.6539	−1.09360	−0.546802	+	0.837262i	$0.684155\pi$
$948$	30.5647	0.992694
$949$	11.5885	0.376179
$950$	4.32367	0.140278
$951$	−2.01233	−0.0652543
$952$	−75.7158	−2.45396
$953$	−7.91582	−0.256418	−0.128209	−	0.991747i	$-0.540923\pi$
$953$	−7.91582	−0.256418	−0.128209	+	0.991747i	$0.540923\pi$
$954$	−49.7367	−1.61029
$955$	26.9793	0.873030
$956$	−104.486	−3.37932
$957$	−4.22909	−0.136707
$958$	39.2991	1.26970
$959$	15.4358	0.498449
$960$	8.74654	0.282293
$961$	−14.6961	−0.474068
$962$	25.2188	0.813085
$963$	−51.1003	−1.64668
$964$	−83.8207	−2.69968
$965$	33.6312	1.08263
$966$	1.61915	0.0520954
$967$	−23.1224	−0.743565	−0.371782	−	0.928320i	$-0.621253\pi$
$967$	−23.1224	−0.743565	−0.371782	+	0.928320i	$0.621253\pi$
$968$	−152.947	−4.91589
$969$	−4.82431	−0.154979
$970$	−8.67934	−0.278677
$971$	26.8298	0.861008	0.430504	−	0.902589i	$-0.358336\pi$
$971$	26.8298	0.861008	0.430504	+	0.902589i	$0.358336\pi$
$972$	−60.0408	−1.92581
$973$	10.9532	0.351145
$974$	−63.6204	−2.03853
$975$	−0.648355	−0.0207640
$976$	8.79622	0.281560
$977$	−39.2824	−1.25676	−0.628378	−	0.777908i	$-0.716281\pi$
$977$	−39.2824	−1.25676	−0.628378	+	0.777908i	$0.716281\pi$
$978$	−22.4081	−0.716533
$979$	12.6537	0.404415
$980$	46.3085	1.47927
$981$	36.3394	1.16023
$982$	−64.5793	−2.06081
$983$	3.52463	0.112418	0.0562091	−	0.998419i	$-0.482099\pi$
$983$	3.52463	0.112418	0.0562091	+	0.998419i	$0.482099\pi$
$984$	−35.1767	−1.12139
$985$	21.6766	0.690674
$986$	−26.7720	−0.852593
$987$	6.32367	0.201285
$988$	−6.41440	−0.204069
$989$	−1.62109	−0.0515478
$990$	−77.6691	−2.46848
$991$	26.3190	0.836050	0.418025	−	0.908436i	$-0.362723\pi$
$991$	26.3190	0.836050	0.418025	+	0.908436i	$0.362723\pi$
$992$	43.8218	1.39134
$993$	1.34076	0.0425477
$994$	−9.29009	−0.294664
$995$	33.2570	1.05432
$996$	20.4808	0.648959
$997$	−39.2677	−1.24362	−0.621810	−	0.783168i	$-0.713602\pi$
$997$	−39.2677	−1.24362	−0.621810	+	0.783168i	$0.713602\pi$
$998$	37.5462	1.18851
$999$	28.6390	0.906099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.b.1.5	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.61802 q^{2} -0.518785 q^{3} +4.85402 q^{4} -1.93655 q^{5} +1.35819 q^{6} +1.44000 q^{7} -7.47189 q^{8} -2.73086 q^{9} +O(q^{10})\)	\(q-2.61802 q^{2} -0.518785 q^{3} +4.85402 q^{4} -1.93655 q^{5} +1.35819 q^{6} +1.44000 q^{7} -7.47189 q^{8} -2.73086 q^{9} +5.06994 q^{10} +5.60978 q^{11} -2.51819 q^{12} -1.00000 q^{13} -3.76995 q^{14} +1.00466 q^{15} +9.85349 q^{16} +7.03709 q^{17} +7.14945 q^{18} +1.32146 q^{19} -9.40008 q^{20} -0.747051 q^{21} -14.6865 q^{22} +0.827876 q^{23} +3.87630 q^{24} -1.24976 q^{25} +2.61802 q^{26} +2.97309 q^{27} +6.98980 q^{28} +1.45316 q^{29} -2.63021 q^{30} -4.03781 q^{31} -10.8529 q^{32} -2.91027 q^{33} -18.4232 q^{34} -2.78864 q^{35} -13.2557 q^{36} +9.63276 q^{37} -3.45961 q^{38} +0.518785 q^{39} +14.4697 q^{40} -9.07481 q^{41} +1.95579 q^{42} -1.95814 q^{43} +27.2300 q^{44} +5.28846 q^{45} -2.16740 q^{46} -8.46485 q^{47} -5.11184 q^{48} -4.92640 q^{49} +3.27188 q^{50} -3.65074 q^{51} -4.85402 q^{52} -6.95672 q^{53} -7.78359 q^{54} -10.8636 q^{55} -10.7595 q^{56} -0.685554 q^{57} -3.80440 q^{58} +5.09150 q^{59} +4.87662 q^{60} +0.892700 q^{61} +10.5711 q^{62} -3.93244 q^{63} +8.70601 q^{64} +1.93655 q^{65} +7.61914 q^{66} -7.37255 q^{67} +34.1582 q^{68} -0.429490 q^{69} +7.30071 q^{70} +2.46425 q^{71} +20.4047 q^{72} -11.5885 q^{73} -25.2188 q^{74} +0.648355 q^{75} +6.41440 q^{76} +8.07809 q^{77} -1.35819 q^{78} -12.1375 q^{79} -19.0818 q^{80} +6.65019 q^{81} +23.7580 q^{82} -8.13313 q^{83} -3.62620 q^{84} -13.6277 q^{85} +5.12644 q^{86} -0.753878 q^{87} -41.9156 q^{88} +2.25566 q^{89} -13.8453 q^{90} -1.44000 q^{91} +4.01853 q^{92} +2.09475 q^{93} +22.1611 q^{94} -2.55908 q^{95} +5.63030 q^{96} -1.71192 q^{97} +12.8974 q^{98} -15.3195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 6 q^{2} - 9 q^{3} + 112 q^{4} - 12 q^{5} - 18 q^{6} - 32 q^{7} - 15 q^{8} + 111 q^{9}+O(q^{10}) \) 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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