LMFDB - Embedded newform 8018.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.56521 q^{3} +1.00000 q^{4} +3.62382 q^{5} +2.56521 q^{6} +4.81473 q^{7} -1.00000 q^{8} +3.58031 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.56521 q^{3} +1.00000 q^{4} +3.62382 q^{5} +2.56521 q^{6} +4.81473 q^{7} -1.00000 q^{8} +3.58031 q^{9} -3.62382 q^{10} +0.483333 q^{11} -2.56521 q^{12} -5.40690 q^{13} -4.81473 q^{14} -9.29586 q^{15} +1.00000 q^{16} -5.64515 q^{17} -3.58031 q^{18} -1.00000 q^{19} +3.62382 q^{20} -12.3508 q^{21} -0.483333 q^{22} -3.29287 q^{23} +2.56521 q^{24} +8.13206 q^{25} +5.40690 q^{26} -1.48862 q^{27} +4.81473 q^{28} +7.39723 q^{29} +9.29586 q^{30} -3.65660 q^{31} -1.00000 q^{32} -1.23985 q^{33} +5.64515 q^{34} +17.4477 q^{35} +3.58031 q^{36} -4.09678 q^{37} +1.00000 q^{38} +13.8698 q^{39} -3.62382 q^{40} +3.25360 q^{41} +12.3508 q^{42} -9.51322 q^{43} +0.483333 q^{44} +12.9744 q^{45} +3.29287 q^{46} -1.74149 q^{47} -2.56521 q^{48} +16.1816 q^{49} -8.13206 q^{50} +14.4810 q^{51} -5.40690 q^{52} -10.5836 q^{53} +1.48862 q^{54} +1.75151 q^{55} -4.81473 q^{56} +2.56521 q^{57} -7.39723 q^{58} +3.36884 q^{59} -9.29586 q^{60} +0.239416 q^{61} +3.65660 q^{62} +17.2382 q^{63} +1.00000 q^{64} -19.5936 q^{65} +1.23985 q^{66} -2.95102 q^{67} -5.64515 q^{68} +8.44691 q^{69} -17.4477 q^{70} +0.0139607 q^{71} -3.58031 q^{72} +8.52837 q^{73} +4.09678 q^{74} -20.8605 q^{75} -1.00000 q^{76} +2.32711 q^{77} -13.8698 q^{78} +4.43438 q^{79} +3.62382 q^{80} -6.92230 q^{81} -3.25360 q^{82} -3.63352 q^{83} -12.3508 q^{84} -20.4570 q^{85} +9.51322 q^{86} -18.9755 q^{87} -0.483333 q^{88} -13.1060 q^{89} -12.9744 q^{90} -26.0327 q^{91} -3.29287 q^{92} +9.37996 q^{93} +1.74149 q^{94} -3.62382 q^{95} +2.56521 q^{96} -7.06235 q^{97} -16.1816 q^{98} +1.73048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.56521	−1.48103	−0.740513	−	0.672042i	$-0.765417\pi$
$3$	−2.56521	−1.48103	−0.740513	+	0.672042i	$0.765417\pi$
$4$	1.00000	0.500000
$5$	3.62382	1.62062	0.810311	−	0.586001i	$-0.199298\pi$
$5$	3.62382	1.62062	0.810311	+	0.586001i	$0.199298\pi$
$6$	2.56521	1.04724
$7$	4.81473	1.81980	0.909898	−	0.414833i	$-0.136160\pi$
$7$	4.81473	1.81980	0.909898	+	0.414833i	$0.136160\pi$
$8$	−1.00000	−0.353553
$9$	3.58031	1.19344
$10$	−3.62382	−1.14595
$11$	0.483333	0.145730	0.0728651	−	0.997342i	$-0.476786\pi$
$11$	0.483333	0.145730	0.0728651	+	0.997342i	$0.476786\pi$
$12$	−2.56521	−0.740513
$13$	−5.40690	−1.49960	−0.749802	−	0.661662i	$-0.769851\pi$
$13$	−5.40690	−1.49960	−0.749802	+	0.661662i	$0.769851\pi$
$14$	−4.81473	−1.28679
$15$	−9.29586	−2.40018
$16$	1.00000	0.250000
$17$	−5.64515	−1.36915	−0.684575	−	0.728943i	$-0.740012\pi$
$17$	−5.64515	−1.36915	−0.684575	+	0.728943i	$0.740012\pi$
$18$	−3.58031	−0.843888
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.62382	0.810311
$21$	−12.3508	−2.69516
$22$	−0.483333	−0.103047
$23$	−3.29287	−0.686611	−0.343306	−	0.939224i	$-0.611547\pi$
$23$	−3.29287	−0.686611	−0.343306	+	0.939224i	$0.611547\pi$
$24$	2.56521	0.523622
$25$	8.13206	1.62641
$26$	5.40690	1.06038
$27$	−1.48862	−0.286486
$28$	4.81473	0.909898
$29$	7.39723	1.37363	0.686816	−	0.726832i	$-0.259008\pi$
$29$	7.39723	1.37363	0.686816	+	0.726832i	$0.259008\pi$
$30$	9.29586	1.69718
$31$	−3.65660	−0.656745	−0.328373	−	0.944548i	$-0.606500\pi$
$31$	−3.65660	−0.656745	−0.328373	+	0.944548i	$0.606500\pi$
$32$	−1.00000	−0.176777
$33$	−1.23985	−0.215830
$34$	5.64515	0.968135
$35$	17.4477	2.94920
$36$	3.58031	0.596719
$37$	−4.09678	−0.673507	−0.336754	−	0.941593i	$-0.609329\pi$
$37$	−4.09678	−0.673507	−0.336754	+	0.941593i	$0.609329\pi$
$38$	1.00000	0.162221
$39$	13.8698	2.22095
$40$	−3.62382	−0.572976
$41$	3.25360	0.508126	0.254063	−	0.967188i	$-0.418233\pi$
$41$	3.25360	0.508126	0.254063	+	0.967188i	$0.418233\pi$
$42$	12.3508	1.90577
$43$	−9.51322	−1.45075	−0.725376	−	0.688353i	$-0.758334\pi$
$43$	−9.51322	−1.45075	−0.725376	+	0.688353i	$0.758334\pi$
$44$	0.483333	0.0728651
$45$	12.9744	1.93411
$46$	3.29287	0.485508
$47$	−1.74149	−0.254023	−0.127012	−	0.991901i	$-0.540539\pi$
$47$	−1.74149	−0.254023	−0.127012	+	0.991901i	$0.540539\pi$
$48$	−2.56521	−0.370256
$49$	16.1816	2.31165
$50$	−8.13206	−1.15005
$51$	14.4810	2.02775
$52$	−5.40690	−0.749802
$53$	−10.5836	−1.45377	−0.726887	−	0.686757i	$-0.759034\pi$
$53$	−10.5836	−1.45377	−0.726887	+	0.686757i	$0.759034\pi$
$54$	1.48862	0.202576
$55$	1.75151	0.236174
$56$	−4.81473	−0.643395
$57$	2.56521	0.339771
$58$	−7.39723	−0.971304
$59$	3.36884	0.438586	0.219293	−	0.975659i	$-0.429625\pi$
$59$	3.36884	0.438586	0.219293	+	0.975659i	$0.429625\pi$
$60$	−9.29586	−1.20009
$61$	0.239416	0.0306541	0.0153271	−	0.999883i	$-0.495121\pi$
$61$	0.239416	0.0306541	0.0153271	+	0.999883i	$0.495121\pi$
$62$	3.65660	0.464389
$63$	17.2382	2.17181
$64$	1.00000	0.125000
$65$	−19.5936	−2.43029
$66$	1.23985	0.152615
$67$	−2.95102	−0.360525	−0.180262	−	0.983619i	$-0.557695\pi$
$67$	−2.95102	−0.360525	−0.180262	+	0.983619i	$0.557695\pi$
$68$	−5.64515	−0.684575
$69$	8.44691	1.01689
$70$	−17.4477	−2.08540
$71$	0.0139607	0.00165683	0.000828416	−	1.00000i	$-0.499736\pi$
$71$	0.0139607	0.00165683	0.000828416		1.00000i	$0.499736\pi$
$72$	−3.58031	−0.421944
$73$	8.52837	0.998170	0.499085	−	0.866553i	$-0.333669\pi$
$73$	8.52837	0.998170	0.499085	+	0.866553i	$0.333669\pi$
$74$	4.09678	0.476241
$75$	−20.8605	−2.40876
$76$	−1.00000	−0.114708
$77$	2.32711	0.265199
$78$	−13.8698	−1.57045
$79$	4.43438	0.498907	0.249454	−	0.968387i	$-0.419749\pi$
$79$	4.43438	0.498907	0.249454	+	0.968387i	$0.419749\pi$
$80$	3.62382	0.405155
$81$	−6.92230	−0.769145
$82$	−3.25360	−0.359299
$83$	−3.63352	−0.398831	−0.199415	−	0.979915i	$-0.563904\pi$
$83$	−3.63352	−0.398831	−0.199415	+	0.979915i	$0.563904\pi$
$84$	−12.3508	−1.34758
$85$	−20.4570	−2.21887
$86$	9.51322	1.02584
$87$	−18.9755	−2.03438
$88$	−0.483333	−0.0515234
$89$	−13.1060	−1.38924	−0.694618	−	0.719378i	$-0.744427\pi$
$89$	−13.1060	−1.38924	−0.694618	+	0.719378i	$0.744427\pi$
$90$	−12.9744	−1.36762
$91$	−26.0327	−2.72897
$92$	−3.29287	−0.343306
$93$	9.37996	0.972657
$94$	1.74149	0.179621
$95$	−3.62382	−0.371796
$96$	2.56521	0.261811
$97$	−7.06235	−0.717073	−0.358536	−	0.933516i	$-0.616724\pi$
$97$	−7.06235	−0.717073	−0.358536	+	0.933516i	$0.616724\pi$
$98$	−16.1816	−1.63459
$99$	1.73048	0.173920
$100$	8.13206	0.813206
$101$	17.3847	1.72984	0.864921	−	0.501907i	$-0.167368\pi$
$101$	17.3847	1.72984	0.864921	+	0.501907i	$0.167368\pi$
$102$	−14.4810	−1.43383
$103$	1.16071	0.114368	0.0571839	−	0.998364i	$-0.481788\pi$
$103$	1.16071	0.114368	0.0571839	+	0.998364i	$0.481788\pi$
$104$	5.40690	0.530190
$105$	−44.7570	−4.36784
$106$	10.5836	1.02797
$107$	−1.98841	−0.192227	−0.0961135	−	0.995370i	$-0.530641\pi$
$107$	−1.98841	−0.192227	−0.0961135	+	0.995370i	$0.530641\pi$
$108$	−1.48862	−0.143243
$109$	6.13451	0.587580	0.293790	−	0.955870i	$-0.405083\pi$
$109$	6.13451	0.587580	0.293790	+	0.955870i	$0.405083\pi$
$110$	−1.75151	−0.167000
$111$	10.5091	0.997481
$112$	4.81473	0.454949
$113$	−14.2125	−1.33700	−0.668500	−	0.743712i	$-0.733063\pi$
$113$	−14.2125	−1.33700	−0.668500	+	0.743712i	$0.733063\pi$
$114$	−2.56521	−0.240254
$115$	−11.9328	−1.11274
$116$	7.39723	0.686816
$117$	−19.3584	−1.78968
$118$	−3.36884	−0.310127
$119$	−27.1798	−2.49157
$120$	9.29586	0.848592
$121$	−10.7664	−0.978763
$122$	−0.239416	−0.0216757
$123$	−8.34616	−0.752548
$124$	−3.65660	−0.328373
$125$	11.3500	1.01518
$126$	−17.2382	−1.53570
$127$	−0.471433	−0.0418329	−0.0209165	−	0.999781i	$-0.506658\pi$
$127$	−0.471433	−0.0418329	−0.0209165	+	0.999781i	$0.506658\pi$
$128$	−1.00000	−0.0883883
$129$	24.4034	2.14860
$130$	19.5936	1.71847
$131$	−19.0185	−1.66165	−0.830825	−	0.556533i	$-0.812131\pi$
$131$	−19.0185	−1.66165	−0.830825	+	0.556533i	$0.812131\pi$
$132$	−1.23985	−0.107915
$133$	−4.81473	−0.417490
$134$	2.95102	0.254929
$135$	−5.39450	−0.464285
$136$	5.64515	0.484067
$137$	−3.39468	−0.290027	−0.145013	−	0.989430i	$-0.546323\pi$
$137$	−3.39468	−0.290027	−0.145013	+	0.989430i	$0.546323\pi$
$138$	−8.44691	−0.719049
$139$	4.92798	0.417986	0.208993	−	0.977917i	$-0.432981\pi$
$139$	4.92798	0.417986	0.208993	+	0.977917i	$0.432981\pi$
$140$	17.4477	1.47460
$141$	4.46730	0.376215
$142$	−0.0139607	−0.00117156
$143$	−2.61333	−0.218538
$144$	3.58031	0.298359
$145$	26.8062	2.22614
$146$	−8.52837	−0.705813
$147$	−41.5092	−3.42362
$148$	−4.09678	−0.336754
$149$	−12.9917	−1.06432	−0.532160	−	0.846644i	$-0.678620\pi$
$149$	−12.9917	−1.06432	−0.532160	+	0.846644i	$0.678620\pi$
$150$	20.8605	1.70325
$151$	−18.6205	−1.51532	−0.757659	−	0.652651i	$-0.773657\pi$
$151$	−18.6205	−1.51532	−0.757659	+	0.652651i	$0.773657\pi$
$152$	1.00000	0.0811107
$153$	−20.2114	−1.63399
$154$	−2.32711	−0.187524
$155$	−13.2509	−1.06434
$156$	13.8698	1.11048
$157$	4.81982	0.384664	0.192332	−	0.981330i	$-0.438395\pi$
$157$	4.81982	0.384664	0.192332	+	0.981330i	$0.438395\pi$
$158$	−4.43438	−0.352781
$159$	27.1493	2.15308
$160$	−3.62382	−0.286488
$161$	−15.8543	−1.24949
$162$	6.92230	0.543867
$163$	10.5352	0.825179	0.412590	−	0.910917i	$-0.364624\pi$
$163$	10.5352	0.825179	0.412590	+	0.910917i	$0.364624\pi$
$164$	3.25360	0.254063
$165$	−4.49299	−0.349779
$166$	3.63352	0.282016
$167$	−9.47281	−0.733028	−0.366514	−	0.930413i	$-0.619449\pi$
$167$	−9.47281	−0.733028	−0.366514	+	0.930413i	$0.619449\pi$
$168$	12.3508	0.952884
$169$	16.2346	1.24881
$170$	20.4570	1.56898
$171$	−3.58031	−0.273793
$172$	−9.51322	−0.725376
$173$	−17.6072	−1.33865	−0.669326	−	0.742969i	$-0.733417\pi$
$173$	−17.6072	−1.33865	−0.669326	+	0.742969i	$0.733417\pi$
$174$	18.9755	1.43853
$175$	39.1536	2.95974
$176$	0.483333	0.0364326
$177$	−8.64179	−0.649557
$178$	13.1060	0.982339
$179$	16.1982	1.21071	0.605355	−	0.795956i	$-0.293031\pi$
$179$	16.1982	1.21071	0.605355	+	0.795956i	$0.293031\pi$
$180$	12.9744	0.967055
$181$	−14.9491	−1.11116	−0.555578	−	0.831464i	$-0.687503\pi$
$181$	−14.9491	−1.11116	−0.555578	+	0.831464i	$0.687503\pi$
$182$	26.0327	1.92967
$183$	−0.614154	−0.0453996
$184$	3.29287	0.242754
$185$	−14.8460	−1.09150
$186$	−9.37996	−0.687772
$187$	−2.72848	−0.199526
$188$	−1.74149	−0.127012
$189$	−7.16731	−0.521345
$190$	3.62382	0.262899
$191$	16.5906	1.20045	0.600226	−	0.799831i	$-0.295077\pi$
$191$	16.5906	1.20045	0.600226	+	0.799831i	$0.295077\pi$
$192$	−2.56521	−0.185128
$193$	−19.7455	−1.42131	−0.710656	−	0.703540i	$-0.751602\pi$
$193$	−19.7455	−1.42131	−0.710656	+	0.703540i	$0.751602\pi$
$194$	7.06235	0.507047
$195$	50.2618	3.59932
$196$	16.1816	1.15583
$197$	18.8208	1.34093	0.670465	−	0.741941i	$-0.266095\pi$
$197$	18.8208	1.34093	0.670465	+	0.741941i	$0.266095\pi$
$198$	−1.73048	−0.122980
$199$	−11.5459	−0.818464	−0.409232	−	0.912430i	$-0.634203\pi$
$199$	−11.5459	−0.818464	−0.409232	+	0.912430i	$0.634203\pi$
$200$	−8.13206	−0.575024
$201$	7.57000	0.533946
$202$	−17.3847	−1.22318
$203$	35.6156	2.49973
$204$	14.4810	1.01387
$205$	11.7904	0.823480
$206$	−1.16071	−0.0808702
$207$	−11.7895	−0.819428
$208$	−5.40690	−0.374901
$209$	−0.483333	−0.0334328
$210$	44.7570	3.08853
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−10.5836	−0.726887
$213$	−0.0358122	−0.00245381
$214$	1.98841	0.135925
$215$	−34.4742	−2.35112
$216$	1.48862	0.101288
$217$	−17.6055	−1.19514
$218$	−6.13451	−0.415482
$219$	−21.8771	−1.47832
$220$	1.75151	0.118087
$221$	30.5227	2.05318
$222$	−10.5091	−0.705326
$223$	−23.0712	−1.54496	−0.772479	−	0.635040i	$-0.780984\pi$
$223$	−23.0712	−1.54496	−0.772479	+	0.635040i	$0.780984\pi$
$224$	−4.81473	−0.321697
$225$	29.1153	1.94102
$226$	14.2125	0.945402
$227$	16.5721	1.09993	0.549963	−	0.835189i	$-0.314642\pi$
$227$	16.5721	1.09993	0.549963	+	0.835189i	$0.314642\pi$
$228$	2.56521	0.169885
$229$	3.42397	0.226263	0.113131	−	0.993580i	$-0.463912\pi$
$229$	3.42397	0.226263	0.113131	+	0.993580i	$0.463912\pi$
$230$	11.9328	0.786824
$231$	−5.96954	−0.392767
$232$	−7.39723	−0.485652
$233$	5.79695	0.379770	0.189885	−	0.981806i	$-0.439188\pi$
$233$	5.79695	0.379770	0.189885	+	0.981806i	$0.439188\pi$
$234$	19.3584	1.26550
$235$	−6.31086	−0.411675
$236$	3.36884	0.219293
$237$	−11.3751	−0.738894
$238$	27.1798	1.76181
$239$	−0.233983	−0.0151351	−0.00756755	−	0.999971i	$-0.502409\pi$
$239$	−0.233983	−0.0151351	−0.00756755	+	0.999971i	$0.502409\pi$
$240$	−9.29586	−0.600045
$241$	9.45390	0.608980	0.304490	−	0.952516i	$-0.401514\pi$
$241$	9.45390	0.608980	0.304490	+	0.952516i	$0.401514\pi$
$242$	10.7664	0.692090
$243$	22.2230	1.42561
$244$	0.239416	0.0153271
$245$	58.6391	3.74631
$246$	8.34616	0.532132
$247$	5.40690	0.344033
$248$	3.65660	0.232195
$249$	9.32075	0.590679
$250$	−11.3500	−0.717839
$251$	−14.1920	−0.895788	−0.447894	−	0.894087i	$-0.647826\pi$
$251$	−14.1920	−0.895788	−0.447894	+	0.894087i	$0.647826\pi$
$252$	17.2382	1.08591
$253$	−1.59155	−0.100060
$254$	0.471433	0.0295803
$255$	52.4765	3.28621
$256$	1.00000	0.0625000
$257$	25.7696	1.60746	0.803731	−	0.594992i	$-0.202845\pi$
$257$	25.7696	1.60746	0.803731	+	0.594992i	$0.202845\pi$
$258$	−24.4034	−1.51929
$259$	−19.7249	−1.22564
$260$	−19.5936	−1.21515
$261$	26.4844	1.63934
$262$	19.0185	1.17496
$263$	−26.3234	−1.62317	−0.811586	−	0.584233i	$-0.801395\pi$
$263$	−26.3234	−1.62317	−0.811586	+	0.584233i	$0.801395\pi$
$264$	1.23985	0.0763075
$265$	−38.3532	−2.35602
$266$	4.81473	0.295210
$267$	33.6197	2.05750
$268$	−2.95102	−0.180262
$269$	24.6133	1.50070	0.750349	−	0.661042i	$-0.229886\pi$
$269$	24.6133	1.50070	0.750349	+	0.661042i	$0.229886\pi$
$270$	5.39450	0.328299
$271$	−14.8630	−0.902862	−0.451431	−	0.892306i	$-0.649086\pi$
$271$	−14.8630	−0.902862	−0.451431	+	0.892306i	$0.649086\pi$
$272$	−5.64515	−0.342287
$273$	66.7795	4.04168
$274$	3.39468	0.205080
$275$	3.93049	0.237018
$276$	8.44691	0.508445
$277$	3.58959	0.215678	0.107839	−	0.994168i	$-0.465607\pi$
$277$	3.58959	0.215678	0.107839	+	0.994168i	$0.465607\pi$
$278$	−4.92798	−0.295560
$279$	−13.0918	−0.783785
$280$	−17.4477	−1.04270
$281$	26.4608	1.57852	0.789261	−	0.614059i	$-0.210464\pi$
$281$	26.4608	1.57852	0.789261	+	0.614059i	$0.210464\pi$
$282$	−4.46730	−0.266024
$283$	14.6346	0.869937	0.434969	−	0.900446i	$-0.356759\pi$
$283$	14.6346	0.869937	0.434969	+	0.900446i	$0.356759\pi$
$284$	0.0139607	0.000828416 0
$285$	9.29586	0.550639
$286$	2.61333	0.154530
$287$	15.6652	0.924686
$288$	−3.58031	−0.210972
$289$	14.8677	0.874570
$290$	−26.8062	−1.57412
$291$	18.1164	1.06200
$292$	8.52837	0.499085
$293$	19.7157	1.15180	0.575901	−	0.817520i	$-0.304652\pi$
$293$	19.7157	1.15180	0.575901	+	0.817520i	$0.304652\pi$
$294$	41.5092	2.42086
$295$	12.2081	0.710782
$296$	4.09678	0.238121
$297$	−0.719500	−0.0417496
$298$	12.9917	0.752588
$299$	17.8042	1.02965
$300$	−20.8605	−1.20438
$301$	−45.8035	−2.64007
$302$	18.6205	1.07149
$303$	−44.5955	−2.56194
$304$	−1.00000	−0.0573539
$305$	0.867602	0.0496787
$306$	20.2114	1.15541
$307$	−30.0320	−1.71402	−0.857008	−	0.515303i	$-0.827679\pi$
$307$	−30.0320	−1.71402	−0.857008	+	0.515303i	$0.827679\pi$
$308$	2.32711	0.132600
$309$	−2.97746	−0.169382
$310$	13.2509	0.752599
$311$	−33.1178	−1.87794	−0.938968	−	0.344003i	$-0.888217\pi$
$311$	−33.1178	−1.87794	−0.938968	+	0.344003i	$0.888217\pi$
$312$	−13.8698	−0.785225
$313$	0.709517	0.0401043	0.0200521	−	0.999799i	$-0.493617\pi$
$313$	0.709517	0.0401043	0.0200521	+	0.999799i	$0.493617\pi$
$314$	−4.81982	−0.271998
$315$	62.4682	3.51968
$316$	4.43438	0.249454
$317$	2.38483	0.133946	0.0669728	−	0.997755i	$-0.478666\pi$
$317$	2.38483	0.133946	0.0669728	+	0.997755i	$0.478666\pi$
$318$	−27.1493	−1.52246
$319$	3.57532	0.200180
$320$	3.62382	0.202578
$321$	5.10070	0.284693
$322$	15.8543	0.883524
$323$	5.64515	0.314104
$324$	−6.92230	−0.384572
$325$	−43.9692	−2.43897
$326$	−10.5352	−0.583490
$327$	−15.7363	−0.870221
$328$	−3.25360	−0.179650
$329$	−8.38482	−0.462270
$330$	4.49299	0.247331
$331$	−29.5601	−1.62477	−0.812386	−	0.583120i	$-0.801832\pi$
$331$	−29.5601	−1.62477	−0.812386	+	0.583120i	$0.801832\pi$
$332$	−3.63352	−0.199415
$333$	−14.6678	−0.803789
$334$	9.47281	0.518329
$335$	−10.6940	−0.584274
$336$	−12.3508	−0.673791
$337$	−11.6149	−0.632705	−0.316352	−	0.948642i	$-0.602458\pi$
$337$	−11.6149	−0.632705	−0.316352	+	0.948642i	$0.602458\pi$
$338$	−16.2346	−0.883044
$339$	36.4581	1.98013
$340$	−20.4570	−1.10944
$341$	−1.76736	−0.0957077
$342$	3.58031	0.193601
$343$	44.2068	2.38694
$344$	9.51322	0.512918
$345$	30.6101	1.64799
$346$	17.6072	0.946570
$347$	1.42388	0.0764377	0.0382189	−	0.999269i	$-0.487832\pi$
$347$	1.42388	0.0764377	0.0382189	+	0.999269i	$0.487832\pi$
$348$	−18.9755	−1.01719
$349$	−6.02755	−0.322647	−0.161324	−	0.986902i	$-0.551576\pi$
$349$	−6.02755	−0.322647	−0.161324	+	0.986902i	$0.551576\pi$
$350$	−39.1536	−2.09285
$351$	8.04883	0.429615
$352$	−0.483333	−0.0257617
$353$	−1.61861	−0.0861499	−0.0430750	−	0.999072i	$-0.513715\pi$
$353$	−1.61861	−0.0861499	−0.0430750	+	0.999072i	$0.513715\pi$
$354$	8.64179	0.459306
$355$	0.0505911	0.00268510
$356$	−13.1060	−0.694618
$357$	69.7220	3.69008
$358$	−16.1982	−0.856101
$359$	−20.7395	−1.09459	−0.547294	−	0.836940i	$-0.684342\pi$
$359$	−20.7395	−1.09459	−0.547294	+	0.836940i	$0.684342\pi$
$360$	−12.9744	−0.683811
$361$	1.00000	0.0526316
$362$	14.9491	0.785706
$363$	27.6181	1.44957
$364$	−26.0327	−1.36449
$365$	30.9053	1.61766
$366$	0.614154	0.0321023
$367$	−7.59985	−0.396709	−0.198355	−	0.980130i	$-0.563560\pi$
$367$	−7.59985	−0.396709	−0.198355	+	0.980130i	$0.563560\pi$
$368$	−3.29287	−0.171653
$369$	11.6489	0.606417
$370$	14.8460	0.771807
$371$	−50.9573	−2.64557
$372$	9.37996	0.486328
$373$	24.5031	1.26872	0.634362	−	0.773036i	$-0.281263\pi$
$373$	24.5031	1.26872	0.634362	+	0.773036i	$0.281263\pi$
$374$	2.72848	0.141087
$375$	−29.1152	−1.50350
$376$	1.74149	0.0898107
$377$	−39.9961	−2.05990
$378$	7.16731	0.368647
$379$	−8.53571	−0.438450	−0.219225	−	0.975674i	$-0.570353\pi$
$379$	−8.53571	−0.438450	−0.219225	+	0.975674i	$0.570353\pi$
$380$	−3.62382	−0.185898
$381$	1.20933	0.0619556
$382$	−16.5906	−0.848848
$383$	−11.7009	−0.597889	−0.298945	−	0.954270i	$-0.596635\pi$
$383$	−11.7009	−0.597889	−0.298945	+	0.954270i	$0.596635\pi$
$384$	2.56521	0.130905
$385$	8.43304	0.429787
$386$	19.7455	1.00502
$387$	−34.0603	−1.73138
$388$	−7.06235	−0.358536
$389$	24.3028	1.23220	0.616100	−	0.787668i	$-0.288712\pi$
$389$	24.3028	1.23220	0.616100	+	0.787668i	$0.288712\pi$
$390$	−50.2618	−2.54511
$391$	18.5887	0.940073
$392$	−16.1816	−0.817293
$393$	48.7864	2.46095
$394$	−18.8208	−0.948180
$395$	16.0694	0.808540
$396$	1.73048	0.0869600
$397$	−27.2367	−1.36697	−0.683486	−	0.729964i	$-0.739537\pi$
$397$	−27.2367	−1.36697	−0.683486	+	0.729964i	$0.739537\pi$
$398$	11.5459	0.578741
$399$	12.3508	0.618313
$400$	8.13206	0.406603
$401$	−18.5289	−0.925287	−0.462643	−	0.886544i	$-0.653099\pi$
$401$	−18.5289	−0.925287	−0.462643	+	0.886544i	$0.653099\pi$
$402$	−7.57000	−0.377557
$403$	19.7709	0.984858
$404$	17.3847	0.864921
$405$	−25.0852	−1.24649
$406$	−35.6156	−1.76757
$407$	−1.98011	−0.0981504
$408$	−14.4810	−0.716916
$409$	−14.8965	−0.736584	−0.368292	−	0.929710i	$-0.620057\pi$
$409$	−14.8965	−0.736584	−0.368292	+	0.929710i	$0.620057\pi$
$410$	−11.7904	−0.582288
$411$	8.70806	0.429537
$412$	1.16071	0.0571839
$413$	16.2201	0.798137
$414$	11.7895	0.579423
$415$	−13.1672	−0.646354
$416$	5.40690	0.265095
$417$	−12.6413	−0.619047
$418$	0.483333	0.0236406
$419$	0.854101	0.0417256	0.0208628	−	0.999782i	$-0.493359\pi$
$419$	0.854101	0.0417256	0.0208628	+	0.999782i	$0.493359\pi$
$420$	−44.7570	−2.18392
$421$	−17.8339	−0.869171	−0.434585	−	0.900631i	$-0.643105\pi$
$421$	−17.8339	−0.869171	−0.434585	+	0.900631i	$0.643105\pi$
$422$	1.00000	0.0486792
$423$	−6.23509	−0.303161
$424$	10.5836	0.513987
$425$	−45.9067	−2.22680
$426$	0.0358122	0.00173511
$427$	1.15272	0.0557842
$428$	−1.98841	−0.0961135
$429$	6.70375	0.323660
$430$	34.4742	1.66249
$431$	−28.9693	−1.39540	−0.697701	−	0.716389i	$-0.745794\pi$
$431$	−28.9693	−1.39540	−0.697701	+	0.716389i	$0.745794\pi$
$432$	−1.48862	−0.0716214
$433$	24.0138	1.15403	0.577015	−	0.816734i	$-0.304217\pi$
$433$	24.0138	1.15403	0.577015	+	0.816734i	$0.304217\pi$
$434$	17.6055	0.845093
$435$	−68.7636	−3.29696
$436$	6.13451	0.293790
$437$	3.29287	0.157519
$438$	21.8771	1.04533
$439$	13.1530	0.627758	0.313879	−	0.949463i	$-0.398371\pi$
$439$	13.1530	0.627758	0.313879	+	0.949463i	$0.398371\pi$
$440$	−1.75151	−0.0835000
$441$	57.9351	2.75881
$442$	−30.5227	−1.45182
$443$	−8.78113	−0.417204	−0.208602	−	0.978001i	$-0.566891\pi$
$443$	−8.78113	−0.417204	−0.208602	+	0.978001i	$0.566891\pi$
$444$	10.5091	0.498741
$445$	−47.4939	−2.25143
$446$	23.0712	1.09245
$447$	33.3264	1.57629
$448$	4.81473	0.227474
$449$	17.6450	0.832719	0.416359	−	0.909200i	$-0.363306\pi$
$449$	17.6450	0.832719	0.416359	+	0.909200i	$0.363306\pi$
$450$	−29.1153	−1.37251
$451$	1.57257	0.0740494
$452$	−14.2125	−0.668500
$453$	47.7656	2.24422
$454$	−16.5721	−0.777765
$455$	−94.3379	−4.42263
$456$	−2.56521	−0.120127
$457$	−21.8845	−1.02371	−0.511856	−	0.859071i	$-0.671042\pi$
$457$	−21.8845	−1.02371	−0.511856	+	0.859071i	$0.671042\pi$
$458$	−3.42397	−0.159992
$459$	8.40350	0.392242
$460$	−11.9328	−0.556368
$461$	−4.83115	−0.225009	−0.112505	−	0.993651i	$-0.535887\pi$
$461$	−4.83115	−0.225009	−0.112505	+	0.993651i	$0.535887\pi$
$462$	5.96954	0.277728
$463$	5.95116	0.276574	0.138287	−	0.990392i	$-0.455840\pi$
$463$	5.95116	0.276574	0.138287	+	0.990392i	$0.455840\pi$
$464$	7.39723	0.343408
$465$	33.9913	1.57631
$466$	−5.79695	−0.268538
$467$	−0.943463	−0.0436583	−0.0218291	−	0.999762i	$-0.506949\pi$
$467$	−0.943463	−0.0436583	−0.0218291	+	0.999762i	$0.506949\pi$
$468$	−19.3584	−0.894842
$469$	−14.2084	−0.656081
$470$	6.31086	0.291098
$471$	−12.3639	−0.569697
$472$	−3.36884	−0.155064
$473$	−4.59805	−0.211418
$474$	11.3751	0.522477
$475$	−8.13206	−0.373125
$476$	−27.1798	−1.24579
$477$	−37.8927	−1.73499
$478$	0.233983	0.0107021
$479$	−28.7216	−1.31232	−0.656162	−	0.754620i	$-0.727821\pi$
$479$	−28.7216	−1.31232	−0.656162	+	0.754620i	$0.727821\pi$
$480$	9.29586	0.424296
$481$	22.1509	1.00999
$482$	−9.45390	−0.430614
$483$	40.6696	1.85053
$484$	−10.7664	−0.489381
$485$	−25.5927	−1.16210
$486$	−22.2230	−1.00806
$487$	21.1829	0.959890	0.479945	−	0.877299i	$-0.340657\pi$
$487$	21.1829	0.959890	0.479945	+	0.877299i	$0.340657\pi$
$488$	−0.239416	−0.0108379
$489$	−27.0250	−1.22211
$490$	−58.6391	−2.64904
$491$	−8.36445	−0.377482	−0.188741	−	0.982027i	$-0.560441\pi$
$491$	−8.36445	−0.377482	−0.188741	+	0.982027i	$0.560441\pi$
$492$	−8.34616	−0.376274
$493$	−41.7585	−1.88071
$494$	−5.40690	−0.243268
$495$	6.27095	0.281858
$496$	−3.65660	−0.164186
$497$	0.0672170	0.00301510
$498$	−9.32075	−0.417673
$499$	23.5808	1.05562	0.527810	−	0.849362i	$-0.323013\pi$
$499$	23.5808	1.05562	0.527810	+	0.849362i	$0.323013\pi$
$500$	11.3500	0.507589
$501$	24.2998	1.08563
$502$	14.1920	0.633418
$503$	−21.0962	−0.940635	−0.470318	−	0.882497i	$-0.655861\pi$
$503$	−21.0962	−0.940635	−0.470318	+	0.882497i	$0.655861\pi$
$504$	−17.2382	−0.767851
$505$	62.9990	2.80342
$506$	1.59155	0.0707531
$507$	−41.6451	−1.84952
$508$	−0.471433	−0.0209165
$509$	7.33577	0.325152	0.162576	−	0.986696i	$-0.448020\pi$
$509$	7.33577	0.325152	0.162576	+	0.986696i	$0.448020\pi$
$510$	−52.4765	−2.32370
$511$	41.0618	1.81647
$512$	−1.00000	−0.0441942
$513$	1.48862	0.0657243
$514$	−25.7696	−1.13665
$515$	4.20619	0.185347
$516$	24.4034	1.07430
$517$	−0.841721	−0.0370189
$518$	19.7249	0.866662
$519$	45.1662	1.98258
$520$	19.5936	0.859237
$521$	12.7746	0.559665	0.279833	−	0.960049i	$-0.409721\pi$
$521$	12.7746	0.559665	0.279833	+	0.960049i	$0.409721\pi$
$522$	−26.4844	−1.15919
$523$	−26.6711	−1.16624	−0.583122	−	0.812384i	$-0.698169\pi$
$523$	−26.6711	−1.16624	−0.583122	+	0.812384i	$0.698169\pi$
$524$	−19.0185	−0.830825
$525$	−100.437	−4.38345
$526$	26.3234	1.14776
$527$	20.6421	0.899183
$528$	−1.23985	−0.0539576
$529$	−12.1570	−0.528565
$530$	38.3532	1.66596
$531$	12.0615	0.523425
$532$	−4.81473	−0.208745
$533$	−17.5919	−0.761988
$534$	−33.6197	−1.45487
$535$	−7.20565	−0.311527
$536$	2.95102	0.127465
$537$	−41.5518	−1.79309
$538$	−24.6133	−1.06115
$539$	7.82108	0.336878
$540$	−5.39450	−0.232142
$541$	−7.48518	−0.321813	−0.160907	−	0.986970i	$-0.551442\pi$
$541$	−7.48518	−0.321813	−0.160907	+	0.986970i	$0.551442\pi$
$542$	14.8630	0.638420
$543$	38.3475	1.64565
$544$	5.64515	0.242034
$545$	22.2304	0.952244
$546$	−66.7795	−2.85790
$547$	−25.8450	−1.10505	−0.552526	−	0.833496i	$-0.686336\pi$
$547$	−25.8450	−1.10505	−0.552526	+	0.833496i	$0.686336\pi$
$548$	−3.39468	−0.145013
$549$	0.857185	0.0365838
$550$	−3.93049	−0.167597
$551$	−7.39723	−0.315133
$552$	−8.44691	−0.359525
$553$	21.3503	0.907909
$554$	−3.58959	−0.152507
$555$	38.0831	1.61654
$556$	4.92798	0.208993
$557$	−29.4861	−1.24937	−0.624684	−	0.780878i	$-0.714772\pi$
$557$	−29.4861	−1.24937	−0.624684	+	0.780878i	$0.714772\pi$
$558$	13.0918	0.554219
$559$	51.4370	2.17555
$560$	17.4477	0.737300
$561$	6.99914	0.295504
$562$	−26.4608	−1.11618
$563$	1.73847	0.0732676	0.0366338	−	0.999329i	$-0.488336\pi$
$563$	1.73847	0.0732676	0.0366338	+	0.999329i	$0.488336\pi$
$564$	4.46730	0.188107
$565$	−51.5036	−2.16677
$566$	−14.6346	−0.615138
$567$	−33.3290	−1.39969
$568$	−0.0139607	−0.000585779 0
$569$	36.4497	1.52805	0.764025	−	0.645186i	$-0.223220\pi$
$569$	36.4497	1.52805	0.764025	+	0.645186i	$0.223220\pi$
$570$	−9.29586	−0.389361
$571$	2.10049	0.0879028	0.0439514	−	0.999034i	$-0.486005\pi$
$571$	2.10049	0.0879028	0.0439514	+	0.999034i	$0.486005\pi$
$572$	−2.61333	−0.109269
$573$	−42.5583	−1.77790
$574$	−15.6652	−0.653851
$575$	−26.7778	−1.11671
$576$	3.58031	0.149180
$577$	35.9192	1.49534	0.747668	−	0.664073i	$-0.231174\pi$
$577$	35.9192	1.49534	0.747668	+	0.664073i	$0.231174\pi$
$578$	−14.8677	−0.618414
$579$	50.6514	2.10500
$580$	26.8062	1.11307
$581$	−17.4944	−0.725790
$582$	−18.1164	−0.750949
$583$	−5.11542	−0.211859
$584$	−8.52837	−0.352907
$585$	−70.1513	−2.90040
$586$	−19.7157	−0.814446
$587$	42.6923	1.76210	0.881049	−	0.473025i	$-0.156838\pi$
$587$	42.6923	1.76210	0.881049	+	0.473025i	$0.156838\pi$
$588$	−41.5092	−1.71181
$589$	3.65660	0.150668
$590$	−12.2081	−0.502598
$591$	−48.2794	−1.98595
$592$	−4.09678	−0.168377
$593$	16.6590	0.684105	0.342052	−	0.939681i	$-0.388878\pi$
$593$	16.6590	0.684105	0.342052	+	0.939681i	$0.388878\pi$
$594$	0.719500	0.0295214
$595$	−98.4948	−4.03789
$596$	−12.9917	−0.532160
$597$	29.6176	1.21217
$598$	−17.8042	−0.728069
$599$	−19.6946	−0.804702	−0.402351	−	0.915486i	$-0.631807\pi$
$599$	−19.6946	−0.804702	−0.402351	+	0.915486i	$0.631807\pi$
$600$	20.8605	0.851625
$601$	21.3739	0.871859	0.435930	−	0.899981i	$-0.356420\pi$
$601$	21.3739	0.871859	0.435930	+	0.899981i	$0.356420\pi$
$602$	45.8035	1.86681
$603$	−10.5656	−0.430264
$604$	−18.6205	−0.757659
$605$	−39.0154	−1.58620
$606$	44.5955	1.81157
$607$	16.5595	0.672131	0.336066	−	0.941839i	$-0.390904\pi$
$607$	16.5595	0.672131	0.336066	+	0.941839i	$0.390904\pi$
$608$	1.00000	0.0405554
$609$	−91.3616	−3.70216
$610$	−0.867602	−0.0351282
$611$	9.41609	0.380934
$612$	−20.2114	−0.816997
$613$	−20.0082	−0.808125	−0.404062	−	0.914731i	$-0.632402\pi$
$613$	−20.0082	−0.808125	−0.404062	+	0.914731i	$0.632402\pi$
$614$	30.0320	1.21199
$615$	−30.2450	−1.21960
$616$	−2.32711	−0.0937621
$617$	−1.54570	−0.0622274	−0.0311137	−	0.999516i	$-0.509905\pi$
$617$	−1.54570	−0.0622274	−0.0311137	+	0.999516i	$0.509905\pi$
$618$	2.97746	0.119771
$619$	−28.7093	−1.15392	−0.576962	−	0.816771i	$-0.695762\pi$
$619$	−28.7093	−1.15392	−0.576962	+	0.816771i	$0.695762\pi$
$620$	−13.2509	−0.532168
$621$	4.90184	0.196704
$622$	33.1178	1.32790
$623$	−63.1019	−2.52813
$624$	13.8698	0.555238
$625$	0.470126	0.0188050
$626$	−0.709517	−0.0283580
$627$	1.23985	0.0495149
$628$	4.81982	0.192332
$629$	23.1269	0.922132
$630$	−62.4682	−2.48879
$631$	−32.6313	−1.29903	−0.649516	−	0.760348i	$-0.725028\pi$
$631$	−32.6313	−1.29903	−0.649516	+	0.760348i	$0.725028\pi$
$632$	−4.43438	−0.176390
$633$	2.56521	0.101958
$634$	−2.38483	−0.0947139
$635$	−1.70839	−0.0677953
$636$	27.1493	1.07654
$637$	−87.4922	−3.46657
$638$	−3.57532	−0.141548
$639$	0.0499837	0.00197733
$640$	−3.62382	−0.143244
$641$	29.4825	1.16449	0.582245	−	0.813014i	$-0.302175\pi$
$641$	29.4825	1.16449	0.582245	+	0.813014i	$0.302175\pi$
$642$	−5.10070	−0.201309
$643$	26.1111	1.02972	0.514861	−	0.857274i	$-0.327844\pi$
$643$	26.1111	1.02972	0.514861	+	0.857274i	$0.327844\pi$
$644$	−15.8543	−0.624746
$645$	88.4335	3.48207
$646$	−5.64515	−0.222105
$647$	34.3605	1.35085	0.675425	−	0.737428i	$-0.263960\pi$
$647$	34.3605	1.35085	0.675425	+	0.737428i	$0.263960\pi$
$648$	6.92230	0.271934
$649$	1.62827	0.0639152
$650$	43.9692	1.72462
$651$	45.1619	1.77004
$652$	10.5352	0.412590
$653$	−40.3342	−1.57840	−0.789200	−	0.614137i	$-0.789504\pi$
$653$	−40.3342	−1.57840	−0.789200	+	0.614137i	$0.789504\pi$
$654$	15.7363	0.615339
$655$	−68.9195	−2.69291
$656$	3.25360	0.127032
$657$	30.5342	1.19125
$658$	8.38482	0.326874
$659$	17.7621	0.691915	0.345957	−	0.938250i	$-0.387554\pi$
$659$	17.7621	0.691915	0.345957	+	0.938250i	$0.387554\pi$
$660$	−4.49299	−0.174890
$661$	37.7222	1.46722	0.733612	−	0.679568i	$-0.237833\pi$
$661$	37.7222	1.46722	0.733612	+	0.679568i	$0.237833\pi$
$662$	29.5601	1.14889
$663$	−78.2973	−3.04082
$664$	3.63352	0.141008
$665$	−17.4477	−0.676592
$666$	14.6678	0.568364
$667$	−24.3581	−0.943151
$668$	−9.47281	−0.366514
$669$	59.1824	2.28812
$670$	10.6940	0.413144
$671$	0.115718	0.00446723
$672$	12.3508	0.476442
$673$	34.8916	1.34497	0.672486	−	0.740109i	$-0.265226\pi$
$673$	34.8916	1.34497	0.672486	+	0.740109i	$0.265226\pi$
$674$	11.6149	0.447390
$675$	−12.1056	−0.465944
$676$	16.2346	0.624406
$677$	−30.7839	−1.18312	−0.591560	−	0.806261i	$-0.701488\pi$
$677$	−30.7839	−1.18312	−0.591560	+	0.806261i	$0.701488\pi$
$678$	−36.4581	−1.40016
$679$	−34.0033	−1.30493
$680$	20.4570	0.784490
$681$	−42.5108	−1.62902
$682$	1.76736	0.0676756
$683$	29.6790	1.13564	0.567819	−	0.823154i	$-0.307788\pi$
$683$	29.6790	1.13564	0.567819	+	0.823154i	$0.307788\pi$
$684$	−3.58031	−0.136897
$685$	−12.3017	−0.470023
$686$	−44.2068	−1.68782
$687$	−8.78322	−0.335101
$688$	−9.51322	−0.362688
$689$	57.2247	2.18009
$690$	−30.6101	−1.16531
$691$	5.38223	0.204750	0.102375	−	0.994746i	$-0.467356\pi$
$691$	5.38223	0.204750	0.102375	+	0.994746i	$0.467356\pi$
$692$	−17.6072	−0.669326
$693$	8.33179	0.316499
$694$	−1.42388	−0.0540496
$695$	17.8581	0.677396
$696$	18.9755	0.719263
$697$	−18.3670	−0.695701
$698$	6.02755	0.228146
$699$	−14.8704	−0.562450
$700$	39.1536	1.47987
$701$	−0.881147	−0.0332805	−0.0166402	−	0.999862i	$-0.505297\pi$
$701$	−0.881147	−0.0332805	−0.0166402	+	0.999862i	$0.505297\pi$
$702$	−8.04883	−0.303784
$703$	4.09678	0.154513
$704$	0.483333	0.0182163
$705$	16.1887	0.609702
$706$	1.61861	0.0609172
$707$	83.7026	3.14796
$708$	−8.64179	−0.324779
$709$	35.1686	1.32078	0.660391	−	0.750922i	$-0.270390\pi$
$709$	35.1686	1.32078	0.660391	+	0.750922i	$0.270390\pi$
$710$	−0.0505911	−0.00189865
$711$	15.8765	0.595415
$712$	13.1060	0.491169
$713$	12.0407	0.450929
$714$	−69.7220	−2.60928
$715$	−9.47024	−0.354167
$716$	16.1982	0.605355
$717$	0.600216	0.0224155
$718$	20.7395	0.773991
$719$	−23.4978	−0.876320	−0.438160	−	0.898897i	$-0.644370\pi$
$719$	−23.4978	−0.876320	−0.438160	+	0.898897i	$0.644370\pi$
$720$	12.9744	0.483527
$721$	5.58848	0.208126
$722$	−1.00000	−0.0372161
$723$	−24.2513	−0.901914
$724$	−14.9491	−0.555578
$725$	60.1547	2.23409
$726$	−27.6181	−1.02500
$727$	31.7852	1.17885	0.589423	−	0.807824i	$-0.299355\pi$
$727$	31.7852	1.17885	0.589423	+	0.807824i	$0.299355\pi$
$728$	26.0327	0.964837
$729$	−36.2399	−1.34222
$730$	−30.9053	−1.14386
$731$	53.7035	1.98630
$732$	−0.614154	−0.0226998
$733$	47.8357	1.76685	0.883425	−	0.468572i	$-0.155231\pi$
$733$	47.8357	1.76685	0.883425	+	0.468572i	$0.155231\pi$
$734$	7.59985	0.280516
$735$	−150.422	−5.54839
$736$	3.29287	0.121377
$737$	−1.42633	−0.0525394
$738$	−11.6489	−0.428801
$739$	−51.1768	−1.88257	−0.941284	−	0.337615i	$-0.890380\pi$
$739$	−51.1768	−1.88257	−0.941284	+	0.337615i	$0.890380\pi$
$740$	−14.8460	−0.545750
$741$	−13.8698	−0.509521
$742$	50.9573	1.87070
$743$	−16.8041	−0.616484	−0.308242	−	0.951308i	$-0.599741\pi$
$743$	−16.8041	−0.616484	−0.308242	+	0.951308i	$0.599741\pi$
$744$	−9.37996	−0.343886
$745$	−47.0795	−1.72486
$746$	−24.5031	−0.897123
$747$	−13.0091	−0.475980
$748$	−2.72848	−0.0997632
$749$	−9.57366	−0.349814
$750$	29.1152	1.06314
$751$	−23.7296	−0.865905	−0.432953	−	0.901417i	$-0.642528\pi$
$751$	−23.7296	−0.865905	−0.432953	+	0.901417i	$0.642528\pi$
$752$	−1.74149	−0.0635058
$753$	36.4054	1.32669
$754$	39.9961	1.45657
$755$	−67.4775	−2.45576
$756$	−7.16731	−0.260673
$757$	−5.90532	−0.214632	−0.107316	−	0.994225i	$-0.534226\pi$
$757$	−5.90532	−0.214632	−0.107316	+	0.994225i	$0.534226\pi$
$758$	8.53571	0.310031
$759$	4.08267	0.148192
$760$	3.62382	0.131450
$761$	47.0067	1.70399	0.851997	−	0.523547i	$-0.175392\pi$
$761$	47.0067	1.70399	0.851997	+	0.523547i	$0.175392\pi$
$762$	−1.20933	−0.0438093
$763$	29.5360	1.06927
$764$	16.5906	0.600226
$765$	−73.2424	−2.64808
$766$	11.7009	0.422771
$767$	−18.2150	−0.657705
$768$	−2.56521	−0.0925641
$769$	−23.1141	−0.833517	−0.416758	−	0.909017i	$-0.636834\pi$
$769$	−23.1141	−0.833517	−0.416758	+	0.909017i	$0.636834\pi$
$770$	−8.43304	−0.303906
$771$	−66.1044	−2.38069
$772$	−19.7455	−0.710656
$773$	24.5982	0.884734	0.442367	−	0.896834i	$-0.354139\pi$
$773$	24.5982	0.884734	0.442367	+	0.896834i	$0.354139\pi$
$774$	34.0603	1.22427
$775$	−29.7357	−1.06814
$776$	7.06235	0.253523
$777$	50.5985	1.81521
$778$	−24.3028	−0.871298
$779$	−3.25360	−0.116572
$780$	50.2618	1.79966
$781$	0.00674767	0.000241451 0
$782$	−18.5887	−0.664732
$783$	−11.0117	−0.393526
$784$	16.1816	0.577913
$785$	17.4662	0.623394
$786$	−48.7864	−1.74015
$787$	−13.4320	−0.478799	−0.239400	−	0.970921i	$-0.576951\pi$
$787$	−13.4320	−0.478799	−0.239400	+	0.970921i	$0.576951\pi$
$788$	18.8208	0.670465
$789$	67.5252	2.40396
$790$	−16.0694	−0.571724
$791$	−68.4293	−2.43307
$792$	−1.73048	−0.0614900
$793$	−1.29450	−0.0459691
$794$	27.2367	0.966595
$795$	98.3841	3.48932
$796$	−11.5459	−0.409232
$797$	22.9776	0.813908	0.406954	−	0.913449i	$-0.366591\pi$
$797$	22.9776	0.813908	0.406954	+	0.913449i	$0.366591\pi$
$798$	−12.3508	−0.437213
$799$	9.83099	0.347796
$800$	−8.13206	−0.287512
$801$	−46.9237	−1.65797
$802$	18.5289	0.654277
$803$	4.12204	0.145464
$804$	7.57000	0.266973
$805$	−57.4530	−2.02495
$806$	−19.7709	−0.696400
$807$	−63.1382	−2.22257
$808$	−17.3847	−0.611592
$809$	−39.7478	−1.39746	−0.698729	−	0.715386i	$-0.746251\pi$
$809$	−39.7478	−1.39746	−0.698729	+	0.715386i	$0.746251\pi$
$810$	25.0852	0.881403
$811$	21.6945	0.761797	0.380898	−	0.924617i	$-0.375615\pi$
$811$	21.6945	0.761797	0.380898	+	0.924617i	$0.375615\pi$
$812$	35.6156	1.24986
$813$	38.1267	1.33716
$814$	1.98011	0.0694028
$815$	38.1776	1.33730
$816$	14.4810	0.506936
$817$	9.51322	0.332825
$818$	14.8965	0.520844
$819$	−93.2053	−3.25686
$820$	11.7904	0.411740
$821$	0.906308	0.0316304	0.0158152	−	0.999875i	$-0.494966\pi$
$821$	0.906308	0.0316304	0.0158152	+	0.999875i	$0.494966\pi$
$822$	−8.70806	−0.303729
$823$	−33.4016	−1.16431	−0.582154	−	0.813079i	$-0.697790\pi$
$823$	−33.4016	−1.16431	−0.582154	+	0.813079i	$0.697790\pi$
$824$	−1.16071	−0.0404351
$825$	−10.0825	−0.351029
$826$	−16.2201	−0.564368
$827$	−48.4821	−1.68589	−0.842944	−	0.538002i	$-0.819179\pi$
$827$	−48.4821	−1.68589	−0.842944	+	0.538002i	$0.819179\pi$
$828$	−11.7895	−0.409714
$829$	21.1802	0.735619	0.367810	−	0.929901i	$-0.380108\pi$
$829$	21.1802	0.735619	0.367810	+	0.929901i	$0.380108\pi$
$830$	13.1672	0.457041
$831$	−9.20806	−0.319424
$832$	−5.40690	−0.187451
$833$	−91.3474	−3.16500
$834$	12.6413	0.437733
$835$	−34.3277	−1.18796
$836$	−0.483333	−0.0167164
$837$	5.44330	0.188148
$838$	−0.854101	−0.0295044
$839$	55.3200	1.90986	0.954930	−	0.296831i	$-0.0959299\pi$
$839$	55.3200	1.90986	0.954930	+	0.296831i	$0.0959299\pi$
$840$	44.7570	1.54426
$841$	25.7190	0.886863
$842$	17.8339	0.614597
$843$	−67.8776	−2.33783
$844$	−1.00000	−0.0344214
$845$	58.8311	2.02385
$846$	6.23509	0.214367
$847$	−51.8372	−1.78115
$848$	−10.5836	−0.363444
$849$	−37.5409	−1.28840
$850$	45.9067	1.57459
$851$	13.4902	0.462438
$852$	−0.0358122	−0.00122691
$853$	46.8225	1.60317	0.801585	−	0.597880i	$-0.203990\pi$
$853$	46.8225	1.60317	0.801585	+	0.597880i	$0.203990\pi$
$854$	−1.15272	−0.0394454
$855$	−12.9744	−0.443715
$856$	1.98841	0.0679625
$857$	−3.25186	−0.111082	−0.0555408	−	0.998456i	$-0.517688\pi$
$857$	−3.25186	−0.111082	−0.0555408	+	0.998456i	$0.517688\pi$
$858$	−6.70375	−0.228862
$859$	−14.1103	−0.481438	−0.240719	−	0.970595i	$-0.577383\pi$
$859$	−14.1103	−0.481438	−0.240719	+	0.970595i	$0.577383\pi$
$860$	−34.4742	−1.17556
$861$	−40.1845	−1.36948
$862$	28.9693	0.986698
$863$	2.88423	0.0981804	0.0490902	−	0.998794i	$-0.484368\pi$
$863$	2.88423	0.0981804	0.0490902	+	0.998794i	$0.484368\pi$
$864$	1.48862	0.0506440
$865$	−63.8054	−2.16945
$866$	−24.0138	−0.816022
$867$	−38.1388	−1.29526
$868$	−17.6055	−0.597571
$869$	2.14328	0.0727059
$870$	68.7636	2.33131
$871$	15.9559	0.540644
$872$	−6.13451	−0.207741
$873$	−25.2854	−0.855781
$874$	−3.29287	−0.111383
$875$	54.6473	1.84741
$876$	−21.8771	−0.739158
$877$	52.5613	1.77487	0.887435	−	0.460933i	$-0.152485\pi$
$877$	52.5613	1.77487	0.887435	+	0.460933i	$0.152485\pi$
$878$	−13.1530	−0.443892
$879$	−50.5748	−1.70585
$880$	1.75151	0.0590434
$881$	−2.76352	−0.0931054	−0.0465527	−	0.998916i	$-0.514824\pi$
$881$	−2.76352	−0.0931054	−0.0465527	+	0.998916i	$0.514824\pi$
$882$	−57.9351	−1.95078
$883$	−18.1987	−0.612434	−0.306217	−	0.951962i	$-0.599063\pi$
$883$	−18.1987	−0.612434	−0.306217	+	0.951962i	$0.599063\pi$
$884$	30.5227	1.02659
$885$	−31.3163	−1.05269
$886$	8.78113	0.295008
$887$	−31.3928	−1.05407	−0.527034	−	0.849844i	$-0.676696\pi$
$887$	−31.3928	−1.05407	−0.527034	+	0.849844i	$0.676696\pi$
$888$	−10.5091	−0.352663
$889$	−2.26982	−0.0761273
$890$	47.4939	1.59200
$891$	−3.34577	−0.112088
$892$	−23.0712	−0.772479
$893$	1.74149	0.0582769
$894$	−33.3264	−1.11460
$895$	58.6993	1.96210
$896$	−4.81473	−0.160849
$897$	−45.6716	−1.52493
$898$	−17.6450	−0.588821
$899$	−27.0487	−0.902126
$900$	29.1153	0.970511
$901$	59.7462	1.99043
$902$	−1.57257	−0.0523608
$903$	117.496	3.91001
$904$	14.2125	0.472701
$905$	−54.1727	−1.80076
$906$	−47.7656	−1.58691
$907$	−0.694013	−0.0230443	−0.0115222	−	0.999934i	$-0.503668\pi$
$907$	−0.694013	−0.0230443	−0.0115222	+	0.999934i	$0.503668\pi$
$908$	16.5721	0.549963
$909$	62.2427	2.06446
$910$	94.3379	3.12727
$911$	49.4228	1.63745	0.818726	−	0.574185i	$-0.194681\pi$
$911$	49.4228	1.63745	0.818726	+	0.574185i	$0.194681\pi$
$912$	2.56521	0.0849427
$913$	−1.75620	−0.0581217
$914$	21.8845	0.723874
$915$	−2.22558	−0.0735755
$916$	3.42397	0.113131
$917$	−91.5687	−3.02386
$918$	−8.40350	−0.277357
$919$	−35.4504	−1.16940	−0.584700	−	0.811249i	$-0.698788\pi$
$919$	−35.4504	−1.16940	−0.584700	+	0.811249i	$0.698788\pi$
$920$	11.9328	0.393412
$921$	77.0384	2.53850
$922$	4.83115	0.159105
$923$	−0.0754842	−0.00248459
$924$	−5.96954	−0.196383
$925$	−33.3153	−1.09540
$926$	−5.95116	−0.195567
$927$	4.15569	0.136491
$928$	−7.39723	−0.242826
$929$	−42.7113	−1.40131	−0.700657	−	0.713498i	$-0.747110\pi$
$929$	−42.7113	−1.40131	−0.700657	+	0.713498i	$0.747110\pi$
$930$	−33.9913	−1.11462
$931$	−16.1816	−0.530330
$932$	5.79695	0.189885
$933$	84.9541	2.78127
$934$	0.943463	0.0308710
$935$	−9.88753	−0.323357
$936$	19.3584	0.632749
$937$	−37.5728	−1.22745	−0.613725	−	0.789520i	$-0.710330\pi$
$937$	−37.5728	−1.22745	−0.613725	+	0.789520i	$0.710330\pi$
$938$	14.2084	0.463919
$939$	−1.82006	−0.0593955
$940$	−6.31086	−0.205838
$941$	−49.3760	−1.60961	−0.804805	−	0.593539i	$-0.797730\pi$
$941$	−49.3760	−1.60961	−0.804805	+	0.593539i	$0.797730\pi$
$942$	12.3639	0.402836
$943$	−10.7137	−0.348885
$944$	3.36884	0.109646
$945$	−25.9730	−0.844903
$946$	4.59805	0.149495
$947$	20.2355	0.657566	0.328783	−	0.944405i	$-0.393361\pi$
$947$	20.2355	0.657566	0.328783	+	0.944405i	$0.393361\pi$
$948$	−11.3751	−0.369447
$949$	−46.1121	−1.49686
$950$	8.13206	0.263839
$951$	−6.11760	−0.198377
$952$	27.1798	0.880903
$953$	37.6841	1.22071	0.610355	−	0.792128i	$-0.291027\pi$
$953$	37.6841	1.22071	0.610355	+	0.792128i	$0.291027\pi$
$954$	37.8927	1.22682
$955$	60.1212	1.94548
$956$	−0.233983	−0.00756755
$957$	−9.17146	−0.296471
$958$	28.7216	0.927953
$959$	−16.3444	−0.527789
$960$	−9.29586	−0.300023
$961$	−17.6292	−0.568685
$962$	−22.1509	−0.714174
$963$	−7.11914	−0.229411
$964$	9.45390	0.304490
$965$	−71.5541	−2.30341
$966$	−40.6696	−1.30852
$967$	25.1088	0.807445	0.403722	−	0.914882i	$-0.367716\pi$
$967$	25.1088	0.807445	0.403722	+	0.914882i	$0.367716\pi$
$968$	10.7664	0.346045
$969$	−14.4810	−0.465197
$970$	25.5927	0.821731
$971$	9.66498	0.310164	0.155082	−	0.987902i	$-0.450436\pi$
$971$	9.66498	0.310164	0.155082	+	0.987902i	$0.450436\pi$
$972$	22.2230	0.712804
$973$	23.7269	0.760648
$974$	−21.1829	−0.678745
$975$	112.790	3.61218
$976$	0.239416	0.00766353
$977$	41.3547	1.32305	0.661527	−	0.749921i	$-0.269909\pi$
$977$	41.3547	1.32305	0.661527	+	0.749921i	$0.269909\pi$
$978$	27.0250	0.864164
$979$	−6.33457	−0.202454
$980$	58.6391	1.87316
$981$	21.9635	0.701240
$982$	8.36445	0.266920
$983$	36.1878	1.15421	0.577105	−	0.816670i	$-0.304182\pi$
$983$	36.1878	1.15421	0.577105	+	0.816670i	$0.304182\pi$
$984$	8.34616	0.266066
$985$	68.2033	2.17314
$986$	41.7585	1.32986
$987$	21.5088	0.684634
$988$	5.40690	0.172016
$989$	31.3258	0.996103
$990$	−6.27095	−0.199304
$991$	−50.1090	−1.59176	−0.795882	−	0.605452i	$-0.792992\pi$
$991$	−50.1090	−1.59176	−0.795882	+	0.605452i	$0.792992\pi$
$992$	3.65660	0.116097
$993$	75.8280	2.40633
$994$	−0.0672170	−0.00213199
$995$	−41.8401	−1.32642
$996$	9.32075	0.295339
$997$	−46.9996	−1.48849	−0.744247	−	0.667905i	$-0.767191\pi$
$997$	−46.9996	−1.48849	−0.744247	+	0.667905i	$0.767191\pi$
$998$	−23.5808	−0.746436
$999$	6.09857	0.192950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.5	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.5	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.56521 q^{3} +1.00000 q^{4} +3.62382 q^{5} +2.56521 q^{6} +4.81473 q^{7} -1.00000 q^{8} +3.58031 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.56521 q^{3} +1.00000 q^{4} +3.62382 q^{5} +2.56521 q^{6} +4.81473 q^{7} -1.00000 q^{8} +3.58031 q^{9} -3.62382 q^{10} +0.483333 q^{11} -2.56521 q^{12} -5.40690 q^{13} -4.81473 q^{14} -9.29586 q^{15} +1.00000 q^{16} -5.64515 q^{17} -3.58031 q^{18} -1.00000 q^{19} +3.62382 q^{20} -12.3508 q^{21} -0.483333 q^{22} -3.29287 q^{23} +2.56521 q^{24} +8.13206 q^{25} +5.40690 q^{26} -1.48862 q^{27} +4.81473 q^{28} +7.39723 q^{29} +9.29586 q^{30} -3.65660 q^{31} -1.00000 q^{32} -1.23985 q^{33} +5.64515 q^{34} +17.4477 q^{35} +3.58031 q^{36} -4.09678 q^{37} +1.00000 q^{38} +13.8698 q^{39} -3.62382 q^{40} +3.25360 q^{41} +12.3508 q^{42} -9.51322 q^{43} +0.483333 q^{44} +12.9744 q^{45} +3.29287 q^{46} -1.74149 q^{47} -2.56521 q^{48} +16.1816 q^{49} -8.13206 q^{50} +14.4810 q^{51} -5.40690 q^{52} -10.5836 q^{53} +1.48862 q^{54} +1.75151 q^{55} -4.81473 q^{56} +2.56521 q^{57} -7.39723 q^{58} +3.36884 q^{59} -9.29586 q^{60} +0.239416 q^{61} +3.65660 q^{62} +17.2382 q^{63} +1.00000 q^{64} -19.5936 q^{65} +1.23985 q^{66} -2.95102 q^{67} -5.64515 q^{68} +8.44691 q^{69} -17.4477 q^{70} +0.0139607 q^{71} -3.58031 q^{72} +8.52837 q^{73} +4.09678 q^{74} -20.8605 q^{75} -1.00000 q^{76} +2.32711 q^{77} -13.8698 q^{78} +4.43438 q^{79} +3.62382 q^{80} -6.92230 q^{81} -3.25360 q^{82} -3.63352 q^{83} -12.3508 q^{84} -20.4570 q^{85} +9.51322 q^{86} -18.9755 q^{87} -0.483333 q^{88} -13.1060 q^{89} -12.9744 q^{90} -26.0327 q^{91} -3.29287 q^{92} +9.37996 q^{93} +1.74149 q^{94} -3.62382 q^{95} +2.56521 q^{96} -7.06235 q^{97} -16.1816 q^{98} +1.73048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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