LMFDB - Embedded newform 8003.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68916 q^{2} +1.31955 q^{3} +5.23156 q^{4} +0.565625 q^{5} -3.54848 q^{6} -3.46548 q^{7} -8.69016 q^{8} -1.25878 q^{9} +O(q^{10})$	\(q-2.68916 q^{2} +1.31955 q^{3} +5.23156 q^{4} +0.565625 q^{5} -3.54848 q^{6} -3.46548 q^{7} -8.69016 q^{8} -1.25878 q^{9} -1.52105 q^{10} -2.91116 q^{11} +6.90331 q^{12} +1.05428 q^{13} +9.31921 q^{14} +0.746372 q^{15} +12.9061 q^{16} -1.17410 q^{17} +3.38506 q^{18} -1.26420 q^{19} +2.95910 q^{20} -4.57288 q^{21} +7.82856 q^{22} -4.14972 q^{23} -11.4671 q^{24} -4.68007 q^{25} -2.83511 q^{26} -5.61969 q^{27} -18.1298 q^{28} -3.89320 q^{29} -2.00711 q^{30} -7.33008 q^{31} -17.3261 q^{32} -3.84143 q^{33} +3.15734 q^{34} -1.96016 q^{35} -6.58538 q^{36} -2.33020 q^{37} +3.39964 q^{38} +1.39117 q^{39} -4.91537 q^{40} -5.06731 q^{41} +12.2972 q^{42} -8.02855 q^{43} -15.2299 q^{44} -0.711998 q^{45} +11.1593 q^{46} +9.10599 q^{47} +17.0302 q^{48} +5.00955 q^{49} +12.5854 q^{50} -1.54929 q^{51} +5.51551 q^{52} +1.00000 q^{53} +15.1122 q^{54} -1.64662 q^{55} +30.1156 q^{56} -1.66818 q^{57} +10.4694 q^{58} +2.01786 q^{59} +3.90469 q^{60} +10.9886 q^{61} +19.7117 q^{62} +4.36228 q^{63} +20.7805 q^{64} +0.596325 q^{65} +10.3302 q^{66} -4.99500 q^{67} -6.14237 q^{68} -5.47578 q^{69} +5.27118 q^{70} -14.8456 q^{71} +10.9390 q^{72} +11.8831 q^{73} +6.26627 q^{74} -6.17560 q^{75} -6.61375 q^{76} +10.0886 q^{77} -3.74108 q^{78} -0.603822 q^{79} +7.29999 q^{80} -3.63913 q^{81} +13.6268 q^{82} -10.0480 q^{83} -23.9233 q^{84} -0.664100 q^{85} +21.5900 q^{86} -5.13728 q^{87} +25.2984 q^{88} +9.58497 q^{89} +1.91467 q^{90} -3.65357 q^{91} -21.7095 q^{92} -9.67242 q^{93} -24.4874 q^{94} -0.715065 q^{95} -22.8627 q^{96} +16.6652 q^{97} -13.4714 q^{98} +3.66451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) $ 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * 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 $

$2$	−2.68916	−1.90152	−0.950760	−	0.309928i	$-0.899695\pi$
$2$	−2.68916	−1.90152	−0.950760	+	0.309928i	$0.899695\pi$
$3$	1.31955	0.761844	0.380922	−	0.924607i	$-0.375607\pi$
$3$	1.31955	0.761844	0.380922	+	0.924607i	$0.375607\pi$
$4$	5.23156	2.61578
$5$	0.565625	0.252955	0.126478	−	0.991969i	$-0.459633\pi$
$5$	0.565625	0.252955	0.126478	+	0.991969i	$0.459633\pi$
$6$	−3.54848	−1.44866
$7$	−3.46548	−1.30983	−0.654914	−	0.755703i	$-0.727295\pi$
$7$	−3.46548	−1.30983	−0.654914	+	0.755703i	$0.727295\pi$
$8$	−8.69016	−3.07243
$9$	−1.25878	−0.419594
$10$	−1.52105	−0.480999
$11$	−2.91116	−0.877747	−0.438874	−	0.898549i	$-0.644622\pi$
$11$	−2.91116	−0.877747	−0.438874	+	0.898549i	$0.644622\pi$
$12$	6.90331	1.99282
$13$	1.05428	0.292404	0.146202	−	0.989255i	$-0.453295\pi$
$13$	1.05428	0.292404	0.146202	+	0.989255i	$0.453295\pi$
$14$	9.31921	2.49066
$15$	0.746372	0.192712
$16$	12.9061	3.22652
$17$	−1.17410	−0.284761	−0.142381	−	0.989812i	$-0.545476\pi$
$17$	−1.17410	−0.284761	−0.142381	+	0.989812i	$0.545476\pi$
$18$	3.38506	0.797865
$19$	−1.26420	−0.290028	−0.145014	−	0.989430i	$-0.546323\pi$
$19$	−1.26420	−0.290028	−0.145014	+	0.989430i	$0.546323\pi$
$20$	2.95910	0.661674
$21$	−4.57288	−0.997885
$22$	7.82856	1.66905
$23$	−4.14972	−0.865277	−0.432639	−	0.901567i	$-0.642417\pi$
$23$	−4.14972	−0.865277	−0.432639	+	0.901567i	$0.642417\pi$
$24$	−11.4671	−2.34072
$25$	−4.68007	−0.936014
$26$	−2.83511	−0.556012
$27$	−5.61969	−1.08151
$28$	−18.1298	−3.42622
$29$	−3.89320	−0.722948	−0.361474	−	0.932382i	$-0.617726\pi$
$29$	−3.89320	−0.722948	−0.361474	+	0.932382i	$0.617726\pi$
$30$	−2.00711	−0.366446
$31$	−7.33008	−1.31652	−0.658260	−	0.752790i	$-0.728707\pi$
$31$	−7.33008	−1.31652	−0.658260	+	0.752790i	$0.728707\pi$
$32$	−17.3261	−3.06285
$33$	−3.84143	−0.668707
$34$	3.15734	0.541479
$35$	−1.96016	−0.331328
$36$	−6.58538	−1.09756
$37$	−2.33020	−0.383082	−0.191541	−	0.981485i	$-0.561349\pi$
$37$	−2.33020	−0.383082	−0.191541	+	0.981485i	$0.561349\pi$
$38$	3.39964	0.551494
$39$	1.39117	0.222766
$40$	−4.91537	−0.777188
$41$	−5.06731	−0.791381	−0.395690	−	0.918384i	$-0.629495\pi$
$41$	−5.06731	−0.791381	−0.395690	+	0.918384i	$0.629495\pi$
$42$	12.2972	1.89750
$43$	−8.02855	−1.22434	−0.612171	−	0.790725i	$-0.709704\pi$
$43$	−8.02855	−1.22434	−0.612171	+	0.790725i	$0.709704\pi$
$44$	−15.2299	−2.29599
$45$	−0.711998	−0.106138
$46$	11.1593	1.64534
$47$	9.10599	1.32824	0.664122	−	0.747624i	$-0.268805\pi$
$47$	9.10599	1.32824	0.664122	+	0.747624i	$0.268805\pi$
$48$	17.0302	2.45810
$49$	5.00955	0.715650
$50$	12.5854	1.77985
$51$	−1.54929	−0.216944
$52$	5.51551	0.764863
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	15.1122	2.05651
$55$	−1.64662	−0.222031
$56$	30.1156	4.02436
$57$	−1.66818	−0.220956
$58$	10.4694	1.37470
$59$	2.01786	0.262703	0.131351	−	0.991336i	$-0.458068\pi$
$59$	2.01786	0.262703	0.131351	+	0.991336i	$0.458068\pi$
$60$	3.90469	0.504093
$61$	10.9886	1.40695	0.703474	−	0.710721i	$-0.251631\pi$
$61$	10.9886	1.40695	0.703474	+	0.710721i	$0.251631\pi$
$62$	19.7117	2.50339
$63$	4.36228	0.549595
$64$	20.7805	2.59756
$65$	0.596325	0.0739650
$66$	10.3302	1.27156
$67$	−4.99500	−0.610237	−0.305118	−	0.952314i	$-0.598696\pi$
$67$	−4.99500	−0.610237	−0.305118	+	0.952314i	$0.598696\pi$
$68$	−6.14237	−0.744872
$69$	−5.47578	−0.659206
$70$	5.27118	0.630026
$71$	−14.8456	−1.76185	−0.880926	−	0.473254i	$-0.843079\pi$
$71$	−14.8456	−1.76185	−0.880926	+	0.473254i	$0.843079\pi$
$72$	10.9390	1.28917
$73$	11.8831	1.39081	0.695405	−	0.718618i	$-0.255225\pi$
$73$	11.8831	1.39081	0.695405	+	0.718618i	$0.255225\pi$
$74$	6.26627	0.728439
$75$	−6.17560	−0.713097
$76$	−6.61375	−0.758649
$77$	10.0886	1.14970
$78$	−3.74108	−0.423594
$79$	−0.603822	−0.0679353	−0.0339676	−	0.999423i	$-0.510814\pi$
$79$	−0.603822	−0.0679353	−0.0339676	+	0.999423i	$0.510814\pi$
$80$	7.29999	0.816164
$81$	−3.63913	−0.404348
$82$	13.6268	1.50483
$83$	−10.0480	−1.10291	−0.551457	−	0.834203i	$-0.685928\pi$
$83$	−10.0480	−1.10291	−0.551457	+	0.834203i	$0.685928\pi$
$84$	−23.9233	−2.61025
$85$	−0.664100	−0.0720318
$86$	21.5900	2.32811
$87$	−5.13728	−0.550774
$88$	25.2984	2.69682
$89$	9.58497	1.01601	0.508003	−	0.861356i	$-0.330384\pi$
$89$	9.58497	1.01601	0.508003	+	0.861356i	$0.330384\pi$
$90$	1.91467	0.201824
$91$	−3.65357	−0.382999
$92$	−21.7095	−2.26337
$93$	−9.67242	−1.00298
$94$	−24.4874	−2.52568
$95$	−0.715065	−0.0733641
$96$	−22.8627	−2.33342
$97$	16.6652	1.69210	0.846048	−	0.533107i	$-0.178976\pi$
$97$	16.6652	1.69210	0.846048	+	0.533107i	$0.178976\pi$
$98$	−13.4714	−1.36082
$99$	3.66451	0.368297
$100$	−24.4840	−2.44840
$101$	−3.31064	−0.329421	−0.164711	−	0.986342i	$-0.552669\pi$
$101$	−3.31064	−0.329421	−0.164711	+	0.986342i	$0.552669\pi$
$102$	4.16627	0.412522
$103$	9.21305	0.907789	0.453894	−	0.891055i	$-0.350034\pi$
$103$	9.21305	0.907789	0.453894	+	0.891055i	$0.350034\pi$
$104$	−9.16183	−0.898391
$105$	−2.58654	−0.252420
$106$	−2.68916	−0.261194
$107$	−17.4600	−1.68792	−0.843961	−	0.536405i	$-0.819782\pi$
$107$	−17.4600	−1.68792	−0.843961	+	0.536405i	$0.819782\pi$
$108$	−29.3997	−2.82899
$109$	19.0399	1.82369	0.911846	−	0.410532i	$-0.134657\pi$
$109$	19.0399	1.82369	0.911846	+	0.410532i	$0.134657\pi$
$110$	4.42803	0.422196
$111$	−3.07482	−0.291849
$112$	−44.7257	−4.22618
$113$	11.7805	1.10822	0.554109	−	0.832444i	$-0.313059\pi$
$113$	11.7805	1.10822	0.554109	+	0.832444i	$0.313059\pi$
$114$	4.48600	0.420153
$115$	−2.34719	−0.218876
$116$	−20.3675	−1.89107
$117$	−1.32710	−0.122691
$118$	−5.42634	−0.499535
$119$	4.06882	0.372988
$120$	−6.48609	−0.592096
$121$	−2.52516	−0.229560
$122$	−29.5501	−2.67534
$123$	−6.68658	−0.602909
$124$	−38.3477	−3.44373
$125$	−5.47529	−0.489725
$126$	−11.7308	−1.04507
$127$	−16.1711	−1.43495	−0.717476	−	0.696583i	$-0.754703\pi$
$127$	−16.1711	−1.43495	−0.717476	+	0.696583i	$0.754703\pi$
$128$	−21.2297	−1.87645
$129$	−10.5941	−0.932758
$130$	−1.60361	−0.140646
$131$	−5.72055	−0.499807	−0.249903	−	0.968271i	$-0.580399\pi$
$131$	−5.72055	−0.499807	−0.249903	+	0.968271i	$0.580399\pi$
$132$	−20.0966	−1.74919
$133$	4.38107	0.379887
$134$	13.4323	1.16038
$135$	−3.17863	−0.273573
$136$	10.2031	0.874909
$137$	1.83264	0.156573	0.0782867	−	0.996931i	$-0.475055\pi$
$137$	1.83264	0.156573	0.0782867	+	0.996931i	$0.475055\pi$
$138$	14.7252	1.25349
$139$	10.1126	0.857740	0.428870	−	0.903366i	$-0.358912\pi$
$139$	10.1126	0.857740	0.428870	+	0.903366i	$0.358912\pi$
$140$	−10.2547	−0.866680
$141$	12.0158	1.01192
$142$	39.9222	3.35020
$143$	−3.06917	−0.256657
$144$	−16.2459	−1.35383
$145$	−2.20209	−0.182873
$146$	−31.9555	−2.64465
$147$	6.61036	0.545213
$148$	−12.1906	−1.00206
$149$	−8.37909	−0.686442	−0.343221	−	0.939255i	$-0.611518\pi$
$149$	−8.37909	−0.686442	−0.343221	+	0.939255i	$0.611518\pi$
$150$	16.6071	1.35597
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	10.9861	0.891092
$153$	1.47793	0.119484
$154$	−27.1297	−2.18617
$155$	−4.14607	−0.333021
$156$	7.27800	0.582707
$157$	15.3851	1.22787	0.613933	−	0.789358i	$-0.289587\pi$
$157$	15.3851	1.22787	0.613933	+	0.789358i	$0.289587\pi$
$158$	1.62377	0.129180
$159$	1.31955	0.104647
$160$	−9.80007	−0.774764
$161$	14.3808	1.13336
$162$	9.78618	0.768875
$163$	20.7023	1.62153	0.810763	−	0.585375i	$-0.199053\pi$
$163$	20.7023	1.62153	0.810763	+	0.585375i	$0.199053\pi$
$164$	−26.5099	−2.07008
$165$	−2.17281	−0.169153
$166$	27.0207	2.09721
$167$	11.4444	0.885591	0.442795	−	0.896623i	$-0.353987\pi$
$167$	11.4444	0.885591	0.442795	+	0.896623i	$0.353987\pi$
$168$	39.7391	3.06594
$169$	−11.8885	−0.914500
$170$	1.78587	0.136970
$171$	1.59135	0.121694
$172$	−42.0018	−3.20261
$173$	−10.1882	−0.774598	−0.387299	−	0.921954i	$-0.626592\pi$
$173$	−10.1882	−0.774598	−0.387299	+	0.921954i	$0.626592\pi$
$174$	13.8149	1.04731
$175$	16.2187	1.22602
$176$	−37.5716	−2.83207
$177$	2.66267	0.200139
$178$	−25.7755	−1.93195
$179$	−1.82271	−0.136236	−0.0681180	−	0.997677i	$-0.521699\pi$
$179$	−1.82271	−0.136236	−0.0681180	+	0.997677i	$0.521699\pi$
$180$	−3.72485	−0.277634
$181$	−2.96374	−0.220293	−0.110147	−	0.993915i	$-0.535132\pi$
$181$	−2.96374	−0.220293	−0.110147	+	0.993915i	$0.535132\pi$
$182$	9.82503	0.728279
$183$	14.5001	1.07188
$184$	36.0617	2.65851
$185$	−1.31802	−0.0969026
$186$	26.0106	1.90719
$187$	3.41799	0.249948
$188$	47.6385	3.47439
$189$	19.4749	1.41659
$190$	1.92292	0.139503
$191$	−1.93166	−0.139770	−0.0698849	−	0.997555i	$-0.522263\pi$
$191$	−1.93166	−0.139770	−0.0698849	+	0.997555i	$0.522263\pi$
$192$	27.4209	1.97893
$193$	−1.97429	−0.142113	−0.0710564	−	0.997472i	$-0.522637\pi$
$193$	−1.97429	−0.142113	−0.0710564	+	0.997472i	$0.522637\pi$
$194$	−44.8153	−3.21755
$195$	0.786882	0.0563498
$196$	26.2077	1.87198
$197$	7.25162	0.516656	0.258328	−	0.966057i	$-0.416828\pi$
$197$	7.25162	0.516656	0.258328	+	0.966057i	$0.416828\pi$
$198$	−9.85444	−0.700324
$199$	0.150021	0.0106347	0.00531734	−	0.999986i	$-0.498307\pi$
$199$	0.150021	0.0106347	0.00531734	+	0.999986i	$0.498307\pi$
$200$	40.6705	2.87584
$201$	−6.59117	−0.464905
$202$	8.90283	0.626401
$203$	13.4918	0.946938
$204$	−8.10518	−0.567476
$205$	−2.86620	−0.200184
$206$	−24.7753	−1.72618
$207$	5.22359	0.363065
$208$	13.6066	0.943445
$209$	3.68030	0.254571
$210$	6.95560	0.479982
$211$	3.93670	0.271013	0.135507	−	0.990776i	$-0.456734\pi$
$211$	3.93670	0.271013	0.135507	+	0.990776i	$0.456734\pi$
$212$	5.23156	0.359305
$213$	−19.5896	−1.34226
$214$	46.9526	3.20962
$215$	−4.54115	−0.309704
$216$	48.8359	3.32287
$217$	25.4022	1.72442
$218$	−51.2013	−3.46779
$219$	15.6804	1.05958
$220$	−8.61440	−0.580783
$221$	−1.23783	−0.0832652
$222$	8.26867	0.554957
$223$	−14.8459	−0.994154	−0.497077	−	0.867706i	$-0.665593\pi$
$223$	−14.8459	−0.994154	−0.497077	+	0.867706i	$0.665593\pi$
$224$	60.0433	4.01181
$225$	5.89118	0.392745
$226$	−31.6797	−2.10730
$227$	15.9899	1.06129	0.530643	−	0.847595i	$-0.321951\pi$
$227$	15.9899	1.06129	0.530643	+	0.847595i	$0.321951\pi$
$228$	−8.72719	−0.577972
$229$	−7.34706	−0.485507	−0.242754	−	0.970088i	$-0.578051\pi$
$229$	−7.34706	−0.485507	−0.242754	+	0.970088i	$0.578051\pi$
$230$	6.31195	0.416198
$231$	13.3124	0.875891
$232$	33.8325	2.22121
$233$	−2.43036	−0.159218	−0.0796092	−	0.996826i	$-0.525367\pi$
$233$	−2.43036	−0.159218	−0.0796092	+	0.996826i	$0.525367\pi$
$234$	3.56879	0.233299
$235$	5.15057	0.335986
$236$	10.5565	0.687172
$237$	−0.796775	−0.0517561
$238$	−10.9417	−0.709244
$239$	−12.2677	−0.793535	−0.396767	−	0.917919i	$-0.629868\pi$
$239$	−12.2677	−0.793535	−0.396767	+	0.917919i	$0.629868\pi$
$240$	9.63272	0.621790
$241$	22.3956	1.44262	0.721312	−	0.692610i	$-0.243539\pi$
$241$	22.3956	1.44262	0.721312	+	0.692610i	$0.243539\pi$
$242$	6.79054	0.436512
$243$	12.0570	0.773459
$244$	57.4876	3.68026
$245$	2.83352	0.181027
$246$	17.9813	1.14644
$247$	−1.33282	−0.0848053
$248$	63.6995	4.04492
$249$	−13.2589	−0.840248
$250$	14.7239	0.931221
$251$	27.3250	1.72474	0.862371	−	0.506277i	$-0.168979\pi$
$251$	27.3250	1.72474	0.862371	+	0.506277i	$0.168979\pi$
$252$	22.8215	1.43762
$253$	12.0805	0.759495
$254$	43.4866	2.72859
$255$	−0.876315	−0.0548770
$256$	15.5289	0.970558
$257$	−9.88504	−0.616612	−0.308306	−	0.951287i	$-0.599762\pi$
$257$	−9.88504	−0.616612	−0.308306	+	0.951287i	$0.599762\pi$
$258$	28.4892	1.77366
$259$	8.07525	0.501772
$260$	3.11971	0.193476
$261$	4.90068	0.303344
$262$	15.3834	0.950392
$263$	−5.09478	−0.314157	−0.157079	−	0.987586i	$-0.550208\pi$
$263$	−5.09478	−0.314157	−0.157079	+	0.987586i	$0.550208\pi$
$264$	33.3826	2.05456
$265$	0.565625	0.0347461
$266$	−11.7814	−0.722363
$267$	12.6479	0.774038
$268$	−26.1316	−1.59624
$269$	−17.1839	−1.04772	−0.523859	−	0.851805i	$-0.675508\pi$
$269$	−17.1839	−1.04772	−0.523859	+	0.851805i	$0.675508\pi$
$270$	8.54784	0.520205
$271$	−15.2049	−0.923631	−0.461815	−	0.886976i	$-0.652802\pi$
$271$	−15.2049	−0.923631	−0.461815	+	0.886976i	$0.652802\pi$
$272$	−15.1530	−0.918786
$273$	−4.82108	−0.291785
$274$	−4.92826	−0.297727
$275$	13.6244	0.821583
$276$	−28.6468	−1.72434
$277$	7.04405	0.423236	0.211618	−	0.977352i	$-0.432127\pi$
$277$	7.04405	0.423236	0.211618	+	0.977352i	$0.432127\pi$
$278$	−27.1944	−1.63101
$279$	9.22696	0.552404
$280$	17.0341	1.01798
$281$	3.86543	0.230592	0.115296	−	0.993331i	$-0.463218\pi$
$281$	3.86543	0.230592	0.115296	+	0.993331i	$0.463218\pi$
$282$	−32.3124	−1.92418
$283$	−8.57062	−0.509471	−0.254735	−	0.967011i	$-0.581988\pi$
$283$	−8.57062	−0.509471	−0.254735	+	0.967011i	$0.581988\pi$
$284$	−77.6657	−4.60861
$285$	−0.943566	−0.0558920
$286$	8.25346	0.488038
$287$	17.5607	1.03657
$288$	21.8098	1.28515
$289$	−15.6215	−0.918911
$290$	5.92176	0.347738
$291$	21.9906	1.28911
$292$	62.1670	3.63805
$293$	−19.4660	−1.13722	−0.568608	−	0.822609i	$-0.692518\pi$
$293$	−19.4660	−1.13722	−0.568608	+	0.822609i	$0.692518\pi$
$294$	−17.7763	−1.03673
$295$	1.14135	0.0664520
$296$	20.2498	1.17700
$297$	16.3598	0.949292
$298$	22.5327	1.30528
$299$	−4.37496	−0.253010
$300$	−32.3080	−1.86530
$301$	27.8228	1.60368
$302$	2.68916	0.154743
$303$	−4.36857	−0.250968
$304$	−16.3159	−0.935781
$305$	6.21543	0.355895
$306$	−3.97439	−0.227201
$307$	−5.27760	−0.301208	−0.150604	−	0.988594i	$-0.548122\pi$
$307$	−5.27760	−0.301208	−0.150604	+	0.988594i	$0.548122\pi$
$308$	52.7789	3.00735
$309$	12.1571	0.691594
$310$	11.1494	0.633245
$311$	−28.4347	−1.61239	−0.806193	−	0.591652i	$-0.798476\pi$
$311$	−28.4347	−1.61239	−0.806193	+	0.591652i	$0.798476\pi$
$312$	−12.0895	−0.684434
$313$	10.2023	0.576670	0.288335	−	0.957530i	$-0.406898\pi$
$313$	10.2023	0.576670	0.288335	+	0.957530i	$0.406898\pi$
$314$	−41.3730	−2.33481
$315$	2.46741	0.139023
$316$	−3.15893	−0.177704
$317$	14.5372	0.816491	0.408246	−	0.912872i	$-0.366141\pi$
$317$	14.5372	0.816491	0.408246	+	0.912872i	$0.366141\pi$
$318$	−3.54848	−0.198989
$319$	11.3337	0.634566
$320$	11.7539	0.657065
$321$	−23.0394	−1.28593
$322$	−38.6722	−2.15511
$323$	1.48430	0.0825887
$324$	−19.0383	−1.05768
$325$	−4.93409	−0.273694
$326$	−55.6716	−3.08336
$327$	25.1242	1.38937
$328$	44.0357	2.43147
$329$	−31.5566	−1.73977
$330$	5.84301	0.321647
$331$	26.6981	1.46746	0.733730	−	0.679441i	$-0.237777\pi$
$331$	26.6981	1.46746	0.733730	+	0.679441i	$0.237777\pi$
$332$	−52.5668	−2.88498
$333$	2.93321	0.160739
$334$	−30.7757	−1.68397
$335$	−2.82530	−0.154362
$336$	−59.0179	−3.21969
$337$	−16.3333	−0.889734	−0.444867	−	0.895597i	$-0.646749\pi$
$337$	−16.3333	−0.889734	−0.444867	+	0.895597i	$0.646749\pi$
$338$	31.9700	1.73894
$339$	15.5450	0.844290
$340$	−3.47428	−0.188419
$341$	21.3390	1.15557
$342$	−4.27940	−0.231403
$343$	6.89787	0.372450
$344$	69.7694	3.76171
$345$	−3.09724	−0.166750
$346$	27.3978	1.47291
$347$	−19.4956	−1.04658	−0.523289	−	0.852155i	$-0.675295\pi$
$347$	−19.4956	−1.04658	−0.523289	+	0.852155i	$0.675295\pi$
$348$	−26.8760	−1.44070
$349$	−19.9714	−1.06905	−0.534523	−	0.845154i	$-0.679509\pi$
$349$	−19.9714	−1.06905	−0.534523	+	0.845154i	$0.679509\pi$
$350$	−43.6146	−2.33130
$351$	−5.92470	−0.316237
$352$	50.4390	2.68841
$353$	−13.7828	−0.733584	−0.366792	−	0.930303i	$-0.619544\pi$
$353$	−13.7828	−0.733584	−0.366792	+	0.930303i	$0.619544\pi$
$354$	−7.16034	−0.380568
$355$	−8.39705	−0.445669
$356$	50.1443	2.65764
$357$	5.36902	0.284159
$358$	4.90156	0.259056
$359$	−12.4690	−0.658089	−0.329044	−	0.944314i	$-0.606727\pi$
$359$	−12.4690	−0.658089	−0.329044	+	0.944314i	$0.606727\pi$
$360$	6.18737	0.326103
$361$	−17.4018	−0.915884
$362$	7.96996	0.418892
$363$	−3.33208	−0.174889
$364$	−19.1139	−1.00184
$365$	6.72137	0.351812
$366$	−38.9929	−2.03819
$367$	22.1180	1.15455	0.577276	−	0.816549i	$-0.304116\pi$
$367$	22.1180	1.15455	0.577276	+	0.816549i	$0.304116\pi$
$368$	−53.5566	−2.79183
$369$	6.37863	0.332058
$370$	3.54436	0.184262
$371$	−3.46548	−0.179919
$372$	−50.6018	−2.62358
$373$	−17.6315	−0.912927	−0.456463	−	0.889742i	$-0.650884\pi$
$373$	−17.6315	−0.912927	−0.456463	+	0.889742i	$0.650884\pi$
$374$	−9.19151	−0.475282
$375$	−7.22493	−0.373094
$376$	−79.1324	−4.08094
$377$	−4.10451	−0.211393
$378$	−52.3710	−2.69368
$379$	5.19604	0.266903	0.133451	−	0.991055i	$-0.457394\pi$
$379$	5.19604	0.266903	0.133451	+	0.991055i	$0.457394\pi$
$380$	−3.74090	−0.191904
$381$	−21.3386	−1.09321
$382$	5.19453	0.265775
$383$	12.4970	0.638566	0.319283	−	0.947659i	$-0.396558\pi$
$383$	12.4970	0.638566	0.319283	+	0.947659i	$0.396558\pi$
$384$	−28.0136	−1.42957
$385$	5.70634	0.290822
$386$	5.30919	0.270230
$387$	10.1062	0.513726
$388$	87.1850	4.42615
$389$	33.7667	1.71204	0.856020	−	0.516943i	$-0.172930\pi$
$389$	33.7667	1.71204	0.856020	+	0.516943i	$0.172930\pi$
$390$	−2.11605	−0.107150
$391$	4.87219	0.246397
$392$	−43.5337	−2.19879
$393$	−7.54856	−0.380775
$394$	−19.5007	−0.982433
$395$	−0.341537	−0.0171846
$396$	19.1711	0.963383
$397$	23.8057	1.19477	0.597386	−	0.801954i	$-0.296206\pi$
$397$	23.8057	1.19477	0.597386	+	0.801954i	$0.296206\pi$
$398$	−0.403429	−0.0202220
$399$	5.78105	0.289415
$400$	−60.4013	−3.02006
$401$	−6.09550	−0.304395	−0.152197	−	0.988350i	$-0.548635\pi$
$401$	−6.09550	−0.304395	−0.152197	+	0.988350i	$0.548635\pi$
$402$	17.7247	0.884027
$403$	−7.72793	−0.384956
$404$	−17.3198	−0.861693
$405$	−2.05838	−0.102282
$406$	−36.2815	−1.80062
$407$	6.78358	0.336249
$408$	13.4635	0.666545
$409$	10.9568	0.541781	0.270891	−	0.962610i	$-0.412682\pi$
$409$	10.9568	0.541781	0.270891	+	0.962610i	$0.412682\pi$
$410$	7.70765	0.380654
$411$	2.41827	0.119284
$412$	48.1986	2.37457
$413$	−6.99285	−0.344096
$414$	−14.0470	−0.690375
$415$	−5.68341	−0.278988
$416$	−18.2665	−0.895589
$417$	13.3441	0.653465
$418$	−9.89689	−0.484073
$419$	−18.2646	−0.892283	−0.446142	−	0.894962i	$-0.647202\pi$
$419$	−18.2646	−0.892283	−0.446142	+	0.894962i	$0.647202\pi$
$420$	−13.5316	−0.660275
$421$	38.5552	1.87907	0.939533	−	0.342458i	$-0.111259\pi$
$421$	38.5552	1.87907	0.939533	+	0.342458i	$0.111259\pi$
$422$	−10.5864	−0.515337
$423$	−11.4624	−0.557323
$424$	−8.69016	−0.422031
$425$	5.49487	0.266540
$426$	52.6794	2.55233
$427$	−38.0808	−1.84286
$428$	−91.3430	−4.41523
$429$	−4.04993	−0.195532
$430$	12.2119	0.588908
$431$	28.9869	1.39625	0.698125	−	0.715975i	$-0.254018\pi$
$431$	28.9869	1.39625	0.698125	+	0.715975i	$0.254018\pi$
$432$	−72.5280	−3.48951
$433$	19.5923	0.941545	0.470773	−	0.882255i	$-0.343975\pi$
$433$	19.5923	0.941545	0.470773	+	0.882255i	$0.343975\pi$
$434$	−68.3105	−3.27901
$435$	−2.90577	−0.139321
$436$	99.6083	4.77037
$437$	5.24609	0.250955
$438$	−42.1669	−2.01481
$439$	−25.4855	−1.21636	−0.608179	−	0.793800i	$-0.708100\pi$
$439$	−25.4855	−1.21636	−0.608179	+	0.793800i	$0.708100\pi$
$440$	14.3094	0.682174
$441$	−6.30592	−0.300282
$442$	3.32871	0.158330
$443$	2.32594	0.110509	0.0552543	−	0.998472i	$-0.482403\pi$
$443$	2.32594	0.110509	0.0552543	+	0.998472i	$0.482403\pi$
$444$	−16.0861	−0.763412
$445$	5.42150	0.257004
$446$	39.9229	1.89040
$447$	−11.0567	−0.522962
$448$	−72.0142	−3.40235
$449$	−14.7734	−0.697199	−0.348599	−	0.937272i	$-0.613343\pi$
$449$	−14.7734	−0.697199	−0.348599	+	0.937272i	$0.613343\pi$
$450$	−15.8423	−0.746813
$451$	14.7517	0.694632
$452$	61.6305	2.89885
$453$	−1.31955	−0.0619980
$454$	−42.9993	−2.01806
$455$	−2.06655	−0.0968814
$456$	14.4968	0.678873
$457$	−11.1688	−0.522456	−0.261228	−	0.965277i	$-0.584127\pi$
$457$	−11.1688	−0.522456	−0.261228	+	0.965277i	$0.584127\pi$
$458$	19.7574	0.923202
$459$	6.59807	0.307972
$460$	−12.2794	−0.572532
$461$	−31.3727	−1.46117	−0.730587	−	0.682819i	$-0.760754\pi$
$461$	−31.3727	−1.46117	−0.730587	+	0.682819i	$0.760754\pi$
$462$	−35.7991	−1.66552
$463$	12.5983	0.585493	0.292747	−	0.956190i	$-0.405431\pi$
$463$	12.5983	0.585493	0.292747	+	0.956190i	$0.405431\pi$
$464$	−50.2458	−2.33260
$465$	−5.47096	−0.253710
$466$	6.53563	0.302757
$467$	40.8801	1.89170	0.945852	−	0.324597i	$-0.105229\pi$
$467$	40.8801	1.89170	0.945852	+	0.324597i	$0.105229\pi$
$468$	−6.94281	−0.320932
$469$	17.3101	0.799305
$470$	−13.8507	−0.638884
$471$	20.3015	0.935442
$472$	−17.5355	−0.807137
$473$	23.3724	1.07466
$474$	2.14265	0.0984153
$475$	5.91656	0.271470
$476$	21.2863	0.975654
$477$	−1.25878	−0.0576356
$478$	32.9899	1.50892
$479$	25.7196	1.17516	0.587578	−	0.809167i	$-0.300081\pi$
$479$	25.7196	1.17516	0.587578	+	0.809167i	$0.300081\pi$
$480$	−12.9317	−0.590249
$481$	−2.45667	−0.112015
$482$	−60.2251	−2.74318
$483$	18.9762	0.863447
$484$	−13.2105	−0.600477
$485$	9.42626	0.428024
$486$	−32.4232	−1.47075
$487$	32.7151	1.48246	0.741231	−	0.671250i	$-0.234242\pi$
$487$	32.7151	1.48246	0.741231	+	0.671250i	$0.234242\pi$
$488$	−95.4928	−4.32276
$489$	27.3177	1.23535
$490$	−7.61979	−0.344227
$491$	−36.5991	−1.65169	−0.825847	−	0.563894i	$-0.809303\pi$
$491$	−36.5991	−1.65169	−0.825847	+	0.563894i	$0.809303\pi$
$492$	−34.9812	−1.57708
$493$	4.57100	0.205868
$494$	3.58416	0.161259
$495$	2.07274	0.0931626
$496$	−94.6024	−4.24778
$497$	51.4472	2.30772
$498$	35.6552	1.59775
$499$	3.99870	0.179006	0.0895032	−	0.995987i	$-0.471472\pi$
$499$	3.99870	0.179006	0.0895032	+	0.995987i	$0.471472\pi$
$500$	−28.6443	−1.28101
$501$	15.1014	0.674682
$502$	−73.4813	−3.27963
$503$	−32.2027	−1.43585	−0.717923	−	0.696122i	$-0.754907\pi$
$503$	−32.2027	−1.43585	−0.717923	+	0.696122i	$0.754907\pi$
$504$	−37.9089	−1.68860
$505$	−1.87258	−0.0833288
$506$	−32.4863	−1.44419
$507$	−15.6875	−0.696706
$508$	−84.5999	−3.75352
$509$	15.6702	0.694569	0.347284	−	0.937760i	$-0.387104\pi$
$509$	15.6702	0.694569	0.347284	+	0.937760i	$0.387104\pi$
$510$	2.35655	0.104350
$511$	−41.1806	−1.82172
$512$	0.699605	0.0309185
$513$	7.10443	0.313668
$514$	26.5824	1.17250
$515$	5.21113	0.229630
$516$	−55.4236	−2.43989
$517$	−26.5090	−1.16586
$518$	−21.7156	−0.954129
$519$	−13.4439	−0.590123
$520$	−5.18216	−0.227253
$521$	−33.2317	−1.45591	−0.727953	−	0.685627i	$-0.759528\pi$
$521$	−33.2317	−1.45591	−0.727953	+	0.685627i	$0.759528\pi$
$522$	−13.1787	−0.576816
$523$	9.84781	0.430615	0.215307	−	0.976546i	$-0.430925\pi$
$523$	9.84781	0.430615	0.215307	+	0.976546i	$0.430925\pi$
$524$	−29.9274	−1.30738
$525$	21.4014	0.934034
$526$	13.7006	0.597376
$527$	8.60624	0.374894
$528$	−49.5777	−2.15759
$529$	−5.77979	−0.251295
$530$	−1.52105	−0.0660703
$531$	−2.54004	−0.110228
$532$	22.9198	0.993700
$533$	−5.34235	−0.231403
$534$	−34.0121	−1.47185
$535$	−9.87581	−0.426968
$536$	43.4074	1.87491
$537$	−2.40517	−0.103791
$538$	46.2101	1.99226
$539$	−14.5836	−0.628159
$540$	−16.6292	−0.715607
$541$	−33.0088	−1.41916	−0.709579	−	0.704626i	$-0.751115\pi$
$541$	−33.0088	−1.41916	−0.709579	+	0.704626i	$0.751115\pi$
$542$	40.8883	1.75630
$543$	−3.91081	−0.167829
$544$	20.3426	0.872181
$545$	10.7694	0.461312
$546$	12.9646	0.554835
$547$	23.4601	1.00308	0.501540	−	0.865135i	$-0.332767\pi$
$547$	23.4601	1.00308	0.501540	+	0.865135i	$0.332767\pi$
$548$	9.58758	0.409561
$549$	−13.8323	−0.590346
$550$	−36.6382	−1.56226
$551$	4.92179	0.209675
$552$	47.5854	2.02537
$553$	2.09253	0.0889835
$554$	−18.9426	−0.804792
$555$	−1.73919	−0.0738247
$556$	52.9047	2.24366
$557$	−11.3159	−0.479470	−0.239735	−	0.970838i	$-0.577061\pi$
$557$	−11.3159	−0.479470	−0.239735	+	0.970838i	$0.577061\pi$
$558$	−24.8127	−1.05041
$559$	−8.46432	−0.358002
$560$	−25.2980	−1.06903
$561$	4.51022	0.190422
$562$	−10.3947	−0.438476
$563$	−23.2902	−0.981566	−0.490783	−	0.871282i	$-0.663289\pi$
$563$	−23.2902	−0.981566	−0.490783	+	0.871282i	$0.663289\pi$
$564$	62.8615	2.64695
$565$	6.66336	0.280330
$566$	23.0477	0.968769
$567$	12.6113	0.529626
$568$	129.011	5.41317
$569$	18.4730	0.774430	0.387215	−	0.921989i	$-0.373437\pi$
$569$	18.4730	0.774430	0.387215	+	0.921989i	$0.373437\pi$
$570$	2.53739	0.106280
$571$	10.4126	0.435755	0.217878	−	0.975976i	$-0.430087\pi$
$571$	10.4126	0.435755	0.217878	+	0.975976i	$0.430087\pi$
$572$	−16.0565	−0.671357
$573$	−2.54893	−0.106483
$574$	−47.2233	−1.97106
$575$	19.4210	0.809911
$576$	−26.1580	−1.08992
$577$	37.8056	1.57387	0.786934	−	0.617037i	$-0.211667\pi$
$577$	37.8056	1.57387	0.786934	+	0.617037i	$0.211667\pi$
$578$	42.0086	1.74733
$579$	−2.60519	−0.108268
$580$	−11.5203	−0.478356
$581$	34.8212	1.44463
$582$	−59.1362	−2.45127
$583$	−2.91116	−0.120568
$584$	−103.266	−4.27317
$585$	−0.750642	−0.0310352
$586$	52.3471	2.16244
$587$	13.5147	0.557812	0.278906	−	0.960318i	$-0.410028\pi$
$587$	13.5147	0.557812	0.278906	+	0.960318i	$0.410028\pi$
$588$	34.5825	1.42616
$589$	9.26671	0.381828
$590$	−3.06927	−0.126360
$591$	9.56889	0.393612
$592$	−30.0737	−1.23602
$593$	−12.8177	−0.526360	−0.263180	−	0.964747i	$-0.584771\pi$
$593$	−12.8177	−0.526360	−0.263180	+	0.964747i	$0.584771\pi$
$594$	−43.9940	−1.80510
$595$	2.30142	0.0943492
$596$	−43.8357	−1.79558
$597$	0.197960	0.00810197
$598$	11.7649	0.481104
$599$	−44.5328	−1.81956	−0.909781	−	0.415089i	$-0.863750\pi$
$599$	−44.5328	−1.81956	−0.909781	+	0.415089i	$0.863750\pi$
$600$	53.6669	2.19094
$601$	20.3575	0.830401	0.415201	−	0.909730i	$-0.363711\pi$
$601$	20.3575	0.830401	0.415201	+	0.909730i	$0.363711\pi$
$602$	−74.8198	−3.04943
$603$	6.28761	0.256051
$604$	−5.23156	−0.212869
$605$	−1.42829	−0.0580683
$606$	11.7478	0.477220
$607$	−7.57190	−0.307334	−0.153667	−	0.988123i	$-0.549108\pi$
$607$	−7.57190	−0.307334	−0.153667	+	0.988123i	$0.549108\pi$
$608$	21.9037	0.888313
$609$	17.8031	0.721419
$610$	−16.7143	−0.676741
$611$	9.60023	0.388384
$612$	7.73189	0.312543
$613$	−24.9390	−1.00728	−0.503639	−	0.863914i	$-0.668006\pi$
$613$	−24.9390	−1.00728	−0.503639	+	0.863914i	$0.668006\pi$
$614$	14.1923	0.572754
$615$	−3.78210	−0.152509
$616$	−87.6711	−3.53237
$617$	24.4297	0.983504	0.491752	−	0.870735i	$-0.336357\pi$
$617$	24.4297	0.983504	0.491752	+	0.870735i	$0.336357\pi$
$618$	−32.6923	−1.31508
$619$	−23.8486	−0.958558	−0.479279	−	0.877663i	$-0.659102\pi$
$619$	−23.8486	−0.958558	−0.479279	+	0.877663i	$0.659102\pi$
$620$	−21.6904	−0.871108
$621$	23.3201	0.935805
$622$	76.4655	3.06599
$623$	−33.2165	−1.33079
$624$	17.9546	0.718758
$625$	20.3034	0.812135
$626$	−27.4357	−1.09655
$627$	4.85634	0.193944
$628$	80.4881	3.21182
$629$	2.73589	0.109087
$630$	−6.63526	−0.264355
$631$	−38.9186	−1.54933	−0.774663	−	0.632375i	$-0.782080\pi$
$631$	−38.9186	−1.54933	−0.774663	+	0.632375i	$0.782080\pi$
$632$	5.24731	0.208727
$633$	5.19468	0.206470
$634$	−39.0928	−1.55257
$635$	−9.14677	−0.362978
$636$	6.90331	0.273734
$637$	5.28145	0.209259
$638$	−30.4781	−1.20664
$639$	18.6874	0.739262
$640$	−12.0080	−0.474659
$641$	−18.8969	−0.746384	−0.373192	−	0.927754i	$-0.621737\pi$
$641$	−18.8969	−0.746384	−0.373192	+	0.927754i	$0.621737\pi$
$642$	61.9565	2.44523
$643$	−29.6373	−1.16878	−0.584390	−	0.811473i	$-0.698666\pi$
$643$	−29.6373	−1.16878	−0.584390	+	0.811473i	$0.698666\pi$
$644$	75.2339	2.96463
$645$	−5.99229	−0.235946
$646$	−3.99152	−0.157044
$647$	−20.0704	−0.789049	−0.394524	−	0.918885i	$-0.629091\pi$
$647$	−20.0704	−0.789049	−0.394524	+	0.918885i	$0.629091\pi$
$648$	31.6246	1.24233
$649$	−5.87431	−0.230587
$650$	13.2685	0.520434
$651$	33.5196	1.31374
$652$	108.305	4.24155
$653$	−25.7011	−1.00576	−0.502881	−	0.864355i	$-0.667727\pi$
$653$	−25.7011	−1.00576	−0.502881	+	0.864355i	$0.667727\pi$
$654$	−67.5628	−2.64191
$655$	−3.23568	−0.126429
$656$	−65.3990	−2.55340
$657$	−14.9582	−0.583575
$658$	84.8606	3.30821
$659$	29.5051	1.14936	0.574678	−	0.818379i	$-0.305127\pi$
$659$	29.5051	1.14936	0.574678	+	0.818379i	$0.305127\pi$
$660$	−11.3672	−0.442466
$661$	−40.1415	−1.56132	−0.780662	−	0.624953i	$-0.785118\pi$
$661$	−40.1415	−1.56132	−0.780662	+	0.624953i	$0.785118\pi$
$662$	−71.7954	−2.79041
$663$	−1.63338	−0.0634351
$664$	87.3189	3.38863
$665$	2.47804	0.0960944
$666$	−7.88785	−0.305648
$667$	16.1557	0.625551
$668$	59.8718	2.31651
$669$	−19.5899	−0.757390
$670$	7.59766	0.293523
$671$	−31.9896	−1.23495
$672$	79.2302	3.05637
$673$	7.99188	0.308064	0.154032	−	0.988066i	$-0.450774\pi$
$673$	7.99188	0.308064	0.154032	+	0.988066i	$0.450774\pi$
$674$	43.9229	1.69185
$675$	26.3005	1.01231
$676$	−62.1954	−2.39213
$677$	−5.62040	−0.216010	−0.108005	−	0.994150i	$-0.534446\pi$
$677$	−5.62040	−0.216010	−0.108005	+	0.994150i	$0.534446\pi$
$678$	−41.8030	−1.60543
$679$	−57.7529	−2.21635
$680$	5.77113	0.221313
$681$	21.0995	0.808534
$682$	−57.3839	−2.19734
$683$	34.1226	1.30567	0.652833	−	0.757502i	$-0.273580\pi$
$683$	34.1226	1.30567	0.652833	+	0.757502i	$0.273580\pi$
$684$	8.32526	0.318324
$685$	1.03659	0.0396060
$686$	−18.5495	−0.708221
$687$	−9.69483	−0.369881
$688$	−103.617	−3.95036
$689$	1.05428	0.0401647
$690$	8.32895	0.317078
$691$	2.60719	0.0991820	0.0495910	−	0.998770i	$-0.484208\pi$
$691$	2.60719	0.0991820	0.0495910	+	0.998770i	$0.484208\pi$
$692$	−53.3004	−2.02618
$693$	−12.6993	−0.482406
$694$	52.4267	1.99009
$695$	5.71994	0.216970
$696$	44.6437	1.69222
$697$	5.94953	0.225354
$698$	53.7063	2.03281
$699$	−3.20699	−0.121300
$700$	84.8489	3.20699
$701$	7.75790	0.293012	0.146506	−	0.989210i	$-0.453197\pi$
$701$	7.75790	0.293012	0.146506	+	0.989210i	$0.453197\pi$
$702$	15.9324	0.601331
$703$	2.94584	0.111105
$704$	−60.4952	−2.28000
$705$	6.79645	0.255969
$706$	37.0641	1.39492
$707$	11.4730	0.431485
$708$	13.9299	0.523518
$709$	43.9106	1.64910	0.824549	−	0.565791i	$-0.191429\pi$
$709$	43.9106	1.64910	0.824549	+	0.565791i	$0.191429\pi$
$710$	22.5810	0.847449
$711$	0.760080	0.0285052
$712$	−83.2949	−3.12161
$713$	30.4178	1.13916
$714$	−14.4381	−0.540333
$715$	−1.73600	−0.0649226
$716$	−9.53563	−0.356363
$717$	−16.1879	−0.604550
$718$	33.5311	1.25137
$719$	−6.85413	−0.255616	−0.127808	−	0.991799i	$-0.540794\pi$
$719$	−6.85413	−0.255616	−0.127808	+	0.991799i	$0.540794\pi$
$720$	−9.18909	−0.342457
$721$	−31.9276	−1.18905
$722$	46.7961	1.74157
$723$	29.5521	1.09905
$724$	−15.5050	−0.576238
$725$	18.2204	0.676690
$726$	8.96048	0.332554
$727$	16.8928	0.626520	0.313260	−	0.949667i	$-0.398579\pi$
$727$	16.8928	0.626520	0.313260	+	0.949667i	$0.398579\pi$
$728$	31.7501	1.17674
$729$	26.8273	0.993603
$730$	−18.0748	−0.668978
$731$	9.42632	0.348645
$732$	75.8579	2.80379
$733$	24.7538	0.914302	0.457151	−	0.889389i	$-0.348870\pi$
$733$	24.7538	0.914302	0.457151	+	0.889389i	$0.348870\pi$
$734$	−59.4789	−2.19540
$735$	3.73898	0.137915
$736$	71.8985	2.65022
$737$	14.5412	0.535634
$738$	−17.1531	−0.631415
$739$	1.25442	0.0461446	0.0230723	−	0.999734i	$-0.492655\pi$
$739$	1.25442	0.0461446	0.0230723	+	0.999734i	$0.492655\pi$
$740$	−6.89529	−0.253476
$741$	−1.75873	−0.0646084
$742$	9.31921	0.342119
$743$	15.9234	0.584172	0.292086	−	0.956392i	$-0.405651\pi$
$743$	15.9234	0.584172	0.292086	+	0.956392i	$0.405651\pi$
$744$	84.0549	3.08160
$745$	−4.73942	−0.173639
$746$	47.4140	1.73595
$747$	12.6483	0.462775
$748$	17.8814	0.653809
$749$	60.5073	2.21089
$750$	19.4290	0.709445
$751$	14.2476	0.519903	0.259951	−	0.965622i	$-0.416293\pi$
$751$	14.2476	0.519903	0.259951	+	0.965622i	$0.416293\pi$
$752$	117.522	4.28560
$753$	36.0568	1.31398
$754$	11.0377	0.401968
$755$	−0.565625	−0.0205852
$756$	101.884	3.70549
$757$	28.4461	1.03389	0.516945	−	0.856019i	$-0.327069\pi$
$757$	28.4461	1.03389	0.516945	+	0.856019i	$0.327069\pi$
$758$	−13.9730	−0.507521
$759$	15.9409	0.578617
$760$	6.21402	0.225406
$761$	−25.0579	−0.908349	−0.454175	−	0.890913i	$-0.650066\pi$
$761$	−25.0579	−0.908349	−0.454175	+	0.890913i	$0.650066\pi$
$762$	57.3828	2.07876
$763$	−65.9824	−2.38872
$764$	−10.1056	−0.365607
$765$	0.835956	0.0302241
$766$	−33.6063	−1.21425
$767$	2.12738	0.0768153
$768$	20.4912	0.739414
$769$	16.4513	0.593250	0.296625	−	0.954994i	$-0.404139\pi$
$769$	16.4513	0.593250	0.296625	+	0.954994i	$0.404139\pi$
$770$	−15.3452	−0.553004
$771$	−13.0438	−0.469762
$772$	−10.3286	−0.371736
$773$	−22.4996	−0.809253	−0.404626	−	0.914482i	$-0.632598\pi$
$773$	−22.4996	−0.809253	−0.404626	+	0.914482i	$0.632598\pi$
$774$	−27.1771	−0.976861
$775$	34.3053	1.23228
$776$	−144.823	−5.19885
$777$	10.6557	0.382272
$778$	−90.8039	−3.25548
$779$	6.40611	0.229523
$780$	4.11662	0.147399
$781$	43.2180	1.54646
$782$	−13.1021	−0.468529
$783$	21.8785	0.781875
$784$	64.6535	2.30906
$785$	8.70220	0.310595
$786$	20.2993	0.724051
$787$	−50.9935	−1.81772	−0.908861	−	0.417098i	$-0.863047\pi$
$787$	−50.9935	−1.81772	−0.908861	+	0.417098i	$0.863047\pi$
$788$	37.9373	1.35146
$789$	−6.72282	−0.239339
$790$	0.918445	0.0326768
$791$	−40.8252	−1.45158
$792$	−31.8452	−1.13157
$793$	11.5850	0.411397
$794$	−64.0172	−2.27188
$795$	0.746372	0.0264711
$796$	0.784841	0.0278180
$797$	12.2642	0.434420	0.217210	−	0.976125i	$-0.430304\pi$
$797$	12.2642	0.434420	0.217210	+	0.976125i	$0.430304\pi$
$798$	−15.5462	−0.550328
$799$	−10.6913	−0.378232
$800$	81.0874	2.86687
$801$	−12.0654	−0.426309
$802$	16.3917	0.578813
$803$	−34.5935	−1.22078
$804$	−34.4821	−1.21609
$805$	8.13413	0.286690
$806$	20.7816	0.732001
$807$	−22.6750	−0.798198
$808$	28.7700	1.01212
$809$	−13.2469	−0.465737	−0.232869	−	0.972508i	$-0.574811\pi$
$809$	−13.2469	−0.465737	−0.232869	+	0.972508i	$0.574811\pi$
$810$	5.53531	0.194491
$811$	−28.7757	−1.01045	−0.505225	−	0.862987i	$-0.668591\pi$
$811$	−28.7757	−1.01045	−0.505225	+	0.862987i	$0.668591\pi$
$812$	70.5831	2.47698
$813$	−20.0636	−0.703663
$814$	−18.2421	−0.639385
$815$	11.7097	0.410173
$816$	−19.9952	−0.699972
$817$	10.1497	0.355094
$818$	−29.4647	−1.03021
$819$	4.59905	0.160704
$820$	−14.9947	−0.523636
$821$	35.5182	1.23959	0.619797	−	0.784762i	$-0.287215\pi$
$821$	35.5182	1.23959	0.619797	+	0.784762i	$0.287215\pi$
$822$	−6.50310	−0.226822
$823$	−4.97221	−0.173320	−0.0866601	−	0.996238i	$-0.527619\pi$
$823$	−4.97221	−0.173320	−0.0866601	+	0.996238i	$0.527619\pi$
$824$	−80.0629	−2.78912
$825$	17.9781	0.625919
$826$	18.8049	0.654305
$827$	−24.5133	−0.852412	−0.426206	−	0.904626i	$-0.640150\pi$
$827$	−24.5133	−0.852412	−0.426206	+	0.904626i	$0.640150\pi$
$828$	27.3275	0.949697
$829$	−0.851452	−0.0295722	−0.0147861	−	0.999891i	$-0.504707\pi$
$829$	−0.851452	−0.0295722	−0.0147861	+	0.999891i	$0.504707\pi$
$830$	15.2836	0.530501
$831$	9.29500	0.322440
$832$	21.9083	0.759535
$833$	−5.88171	−0.203789
$834$	−35.8844	−1.24258
$835$	6.47321	0.224015
$836$	19.2537	0.665902
$837$	41.1927	1.42383
$838$	49.1163	1.69669
$839$	−12.0468	−0.415903	−0.207951	−	0.978139i	$-0.566680\pi$
$839$	−12.0468	−0.415903	−0.207951	+	0.978139i	$0.566680\pi$
$840$	22.4774	0.775544
$841$	−13.8430	−0.477346
$842$	−103.681	−3.57308
$843$	5.10064	0.175675
$844$	20.5950	0.708911
$845$	−6.72443	−0.231327
$846$	30.8243	1.05976
$847$	8.75088	0.300684
$848$	12.9061	0.443196
$849$	−11.3094	−0.388137
$850$	−14.7766	−0.506832
$851$	9.66968	0.331472
$852$	−102.484	−3.51104
$853$	−13.0946	−0.448349	−0.224175	−	0.974549i	$-0.571969\pi$
$853$	−13.0946	−0.448349	−0.224175	+	0.974549i	$0.571969\pi$
$854$	102.405	3.50424
$855$	0.900110	0.0307831
$856$	151.730	5.18603
$857$	−39.6468	−1.35431	−0.677154	−	0.735841i	$-0.736787\pi$
$857$	−39.6468	−1.35431	−0.677154	+	0.735841i	$0.736787\pi$
$858$	10.8909	0.371809
$859$	−11.9562	−0.407940	−0.203970	−	0.978977i	$-0.565385\pi$
$859$	−11.9562	−0.407940	−0.203970	+	0.978977i	$0.565385\pi$
$860$	−23.7573	−0.810116
$861$	23.1722	0.789707
$862$	−77.9503	−2.65500
$863$	37.7833	1.28616	0.643079	−	0.765800i	$-0.277657\pi$
$863$	37.7833	1.28616	0.643079	+	0.765800i	$0.277657\pi$
$864$	97.3673	3.31250
$865$	−5.76272	−0.195939
$866$	−52.6867	−1.79037
$867$	−20.6134	−0.700067
$868$	132.893	4.51069
$869$	1.75782	0.0596300
$870$	7.81407	0.264922
$871$	−5.26611	−0.178435
$872$	−165.460	−5.60317
$873$	−20.9778	−0.709992
$874$	−14.1076	−0.477195
$875$	18.9745	0.641455
$876$	82.0326	2.77163
$877$	−1.71144	−0.0577913	−0.0288957	−	0.999582i	$-0.509199\pi$
$877$	−1.71144	−0.0577913	−0.0288957	+	0.999582i	$0.509199\pi$
$878$	68.5345	2.31293
$879$	−25.6864	−0.866381
$880$	−21.2514	−0.716386
$881$	40.3361	1.35896	0.679478	−	0.733696i	$-0.262206\pi$
$881$	40.3361	1.35896	0.679478	+	0.733696i	$0.262206\pi$
$882$	16.9576	0.570992
$883$	41.7500	1.40500	0.702500	−	0.711684i	$-0.252067\pi$
$883$	41.7500	1.40500	0.702500	+	0.711684i	$0.252067\pi$
$884$	−6.47576	−0.217803
$885$	1.50607	0.0506261
$886$	−6.25481	−0.210134
$887$	37.0845	1.24517	0.622587	−	0.782551i	$-0.286082\pi$
$887$	37.0845	1.24517	0.622587	+	0.782551i	$0.286082\pi$
$888$	26.7207	0.896687
$889$	56.0406	1.87954
$890$	−14.5793	−0.488698
$891$	10.5941	0.354915
$892$	−77.6671	−2.60049
$893$	−11.5118	−0.385228
$894$	29.7331	0.994423
$895$	−1.03097	−0.0344616
$896$	73.5709	2.45783
$897$	−5.77299	−0.192754
$898$	39.7279	1.32574
$899$	28.5374	0.951776
$900$	30.8200	1.02733
$901$	−1.17410	−0.0391149
$902$	−39.6697	−1.32086
$903$	36.7136	1.22175
$904$	−102.375	−3.40493
$905$	−1.67637	−0.0557243
$906$	3.54848	0.117890
$907$	−36.2642	−1.20413	−0.602067	−	0.798446i	$-0.705656\pi$
$907$	−36.2642	−1.20413	−0.602067	+	0.798446i	$0.705656\pi$
$908$	83.6520	2.77609
$909$	4.16737	0.138223
$910$	5.55728	0.184222
$911$	15.6671	0.519073	0.259536	−	0.965733i	$-0.416430\pi$
$911$	15.6671	0.519073	0.259536	+	0.965733i	$0.416430\pi$
$912$	−21.5297	−0.712919
$913$	29.2514	0.968079
$914$	30.0347	0.993460
$915$	8.20159	0.271136
$916$	−38.4365	−1.26998
$917$	19.8244	0.654661
$918$	−17.7432	−0.585614
$919$	−24.9704	−0.823699	−0.411850	−	0.911252i	$-0.635117\pi$
$919$	−24.9704	−0.823699	−0.411850	+	0.911252i	$0.635117\pi$
$920$	20.3974	0.672483
$921$	−6.96407	−0.229474
$922$	84.3662	2.77845
$923$	−15.6514	−0.515172
$924$	69.6445	2.29114
$925$	10.9055	0.358570
$926$	−33.8788	−1.11333
$927$	−11.5972	−0.380902
$928$	67.4539	2.21428
$929$	14.2199	0.466539	0.233269	−	0.972412i	$-0.425058\pi$
$929$	14.2199	0.466539	0.233269	+	0.972412i	$0.425058\pi$
$930$	14.7123	0.482434
$931$	−6.33309	−0.207559
$932$	−12.7146	−0.416480
$933$	−37.5211	−1.22839
$934$	−109.933	−3.59711
$935$	1.93330	0.0632257
$936$	11.5327	0.376959
$937$	54.9710	1.79582	0.897912	−	0.440175i	$-0.145083\pi$
$937$	54.9710	1.79582	0.897912	+	0.440175i	$0.145083\pi$
$938$	−46.5495	−1.51989
$939$	13.4625	0.439333
$940$	26.9455	0.878865
$941$	−56.8135	−1.85207	−0.926034	−	0.377439i	$-0.876805\pi$
$941$	−56.8135	−1.85207	−0.926034	+	0.377439i	$0.876805\pi$
$942$	−54.5938	−1.77876
$943$	21.0279	0.684764
$944$	26.0426	0.847615
$945$	11.0155	0.358334
$946$	−62.8520	−2.04349
$947$	26.5392	0.862407	0.431203	−	0.902255i	$-0.358089\pi$
$947$	26.5392	0.862407	0.431203	+	0.902255i	$0.358089\pi$
$948$	−4.16837	−0.135382
$949$	12.5281	0.406678
$950$	−15.9105	−0.516206
$951$	19.1826	0.622039
$952$	−35.3587	−1.14598
$953$	−47.5427	−1.54006	−0.770030	−	0.638008i	$-0.779759\pi$
$953$	−47.5427	−1.54006	−0.770030	+	0.638008i	$0.779759\pi$
$954$	3.38506	0.109595
$955$	−1.09259	−0.0353555
$956$	−64.1794	−2.07571
$957$	14.9554	0.483440
$958$	−69.1639	−2.23458
$959$	−6.35099	−0.205084
$960$	15.5099	0.500581
$961$	22.7300	0.733226
$962$	6.60638	0.212998
$963$	21.9783	0.708241
$964$	117.164	3.77359
$965$	−1.11671	−0.0359482
$966$	−51.0299	−1.64186
$967$	5.14660	0.165503	0.0827517	−	0.996570i	$-0.473629\pi$
$967$	5.14660	0.165503	0.0827517	+	0.996570i	$0.473629\pi$
$968$	21.9440	0.705307
$969$	1.95861	0.0629197
$970$	−25.3487	−0.813897
$971$	21.0051	0.674087	0.337043	−	0.941489i	$-0.390573\pi$
$971$	21.0051	0.674087	0.337043	+	0.941489i	$0.390573\pi$
$972$	63.0770	2.02320
$973$	−35.0450	−1.12349
$974$	−87.9759	−2.81893
$975$	−6.51079	−0.208512
$976$	141.820	4.53954
$977$	9.20440	0.294475	0.147237	−	0.989101i	$-0.452962\pi$
$977$	9.20440	0.294475	0.147237	+	0.989101i	$0.452962\pi$
$978$	−73.4616	−2.34904
$979$	−27.9034	−0.891796
$980$	14.8237	0.473527
$981$	−23.9671	−0.765210
$982$	98.4207	3.14073
$983$	6.42053	0.204783	0.102392	−	0.994744i	$-0.467351\pi$
$983$	6.42053	0.204783	0.102392	+	0.994744i	$0.467351\pi$
$984$	58.1074	1.85240
$985$	4.10170	0.130691
$986$	−12.2921	−0.391461
$987$	−41.6406	−1.32544
$988$	−6.97272	−0.221832
$989$	33.3163	1.05940
$990$	−5.57391	−0.177151
$991$	26.7759	0.850566	0.425283	−	0.905060i	$-0.360175\pi$
$991$	26.7759	0.850566	0.425283	+	0.905060i	$0.360175\pi$
$992$	127.002	4.03231
$993$	35.2296	1.11798
$994$	−138.350	−4.38818
$995$	0.0848554	0.00269010
$996$	−69.3646	−2.19790
$997$	−29.5865	−0.937013	−0.468507	−	0.883460i	$-0.655208\pi$
$997$	−29.5865	−0.937013	−0.468507	+	0.883460i	$0.655208\pi$
$998$	−10.7531	−0.340384
$999$	13.0950	0.414307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.d.1.7	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.7	✓	179	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68916 q^{2} +1.31955 q^{3} +5.23156 q^{4} +0.565625 q^{5} -3.54848 q^{6} -3.46548 q^{7} -8.69016 q^{8} -1.25878 q^{9} +O(q^{10})\)	\(q-2.68916 q^{2} +1.31955 q^{3} +5.23156 q^{4} +0.565625 q^{5} -3.54848 q^{6} -3.46548 q^{7} -8.69016 q^{8} -1.25878 q^{9} -1.52105 q^{10} -2.91116 q^{11} +6.90331 q^{12} +1.05428 q^{13} +9.31921 q^{14} +0.746372 q^{15} +12.9061 q^{16} -1.17410 q^{17} +3.38506 q^{18} -1.26420 q^{19} +2.95910 q^{20} -4.57288 q^{21} +7.82856 q^{22} -4.14972 q^{23} -11.4671 q^{24} -4.68007 q^{25} -2.83511 q^{26} -5.61969 q^{27} -18.1298 q^{28} -3.89320 q^{29} -2.00711 q^{30} -7.33008 q^{31} -17.3261 q^{32} -3.84143 q^{33} +3.15734 q^{34} -1.96016 q^{35} -6.58538 q^{36} -2.33020 q^{37} +3.39964 q^{38} +1.39117 q^{39} -4.91537 q^{40} -5.06731 q^{41} +12.2972 q^{42} -8.02855 q^{43} -15.2299 q^{44} -0.711998 q^{45} +11.1593 q^{46} +9.10599 q^{47} +17.0302 q^{48} +5.00955 q^{49} +12.5854 q^{50} -1.54929 q^{51} +5.51551 q^{52} +1.00000 q^{53} +15.1122 q^{54} -1.64662 q^{55} +30.1156 q^{56} -1.66818 q^{57} +10.4694 q^{58} +2.01786 q^{59} +3.90469 q^{60} +10.9886 q^{61} +19.7117 q^{62} +4.36228 q^{63} +20.7805 q^{64} +0.596325 q^{65} +10.3302 q^{66} -4.99500 q^{67} -6.14237 q^{68} -5.47578 q^{69} +5.27118 q^{70} -14.8456 q^{71} +10.9390 q^{72} +11.8831 q^{73} +6.26627 q^{74} -6.17560 q^{75} -6.61375 q^{76} +10.0886 q^{77} -3.74108 q^{78} -0.603822 q^{79} +7.29999 q^{80} -3.63913 q^{81} +13.6268 q^{82} -10.0480 q^{83} -23.9233 q^{84} -0.664100 q^{85} +21.5900 q^{86} -5.13728 q^{87} +25.2984 q^{88} +9.58497 q^{89} +1.91467 q^{90} -3.65357 q^{91} -21.7095 q^{92} -9.67242 q^{93} -24.4874 q^{94} -0.715065 q^{95} -22.8627 q^{96} +16.6652 q^{97} -13.4714 q^{98} +3.66451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * q^99

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