LMFDB - Embedded newform 8041.2.a.g.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45687 q^{2} -0.886506 q^{3} +4.03623 q^{4} -0.806805 q^{5} +2.17803 q^{6} -3.77933 q^{7} -5.00275 q^{8} -2.21411 q^{9} +O(q^{10})$	\(q-2.45687 q^{2} -0.886506 q^{3} +4.03623 q^{4} -0.806805 q^{5} +2.17803 q^{6} -3.77933 q^{7} -5.00275 q^{8} -2.21411 q^{9} +1.98222 q^{10} -1.00000 q^{11} -3.57814 q^{12} -4.65728 q^{13} +9.28533 q^{14} +0.715238 q^{15} +4.21868 q^{16} +1.00000 q^{17} +5.43978 q^{18} -0.862138 q^{19} -3.25645 q^{20} +3.35040 q^{21} +2.45687 q^{22} +6.34147 q^{23} +4.43497 q^{24} -4.34906 q^{25} +11.4424 q^{26} +4.62234 q^{27} -15.2542 q^{28} +2.76760 q^{29} -1.75725 q^{30} -1.65984 q^{31} -0.359255 q^{32} +0.886506 q^{33} -2.45687 q^{34} +3.04918 q^{35} -8.93664 q^{36} -8.36983 q^{37} +2.11816 q^{38} +4.12871 q^{39} +4.03625 q^{40} -11.1901 q^{41} -8.23150 q^{42} +1.00000 q^{43} -4.03623 q^{44} +1.78635 q^{45} -15.5802 q^{46} -2.05804 q^{47} -3.73988 q^{48} +7.28332 q^{49} +10.6851 q^{50} -0.886506 q^{51} -18.7978 q^{52} +11.3753 q^{53} -11.3565 q^{54} +0.806805 q^{55} +18.9071 q^{56} +0.764290 q^{57} -6.79963 q^{58} -6.13074 q^{59} +2.88686 q^{60} +13.9893 q^{61} +4.07802 q^{62} +8.36784 q^{63} -7.55472 q^{64} +3.75752 q^{65} -2.17803 q^{66} +2.02853 q^{67} +4.03623 q^{68} -5.62175 q^{69} -7.49146 q^{70} +5.35238 q^{71} +11.0766 q^{72} -6.65044 q^{73} +20.5636 q^{74} +3.85547 q^{75} -3.47978 q^{76} +3.77933 q^{77} -10.1437 q^{78} -2.71492 q^{79} -3.40365 q^{80} +2.54460 q^{81} +27.4927 q^{82} +13.0548 q^{83} +13.5230 q^{84} -0.806805 q^{85} -2.45687 q^{86} -2.45349 q^{87} +5.00275 q^{88} -4.76136 q^{89} -4.38885 q^{90} +17.6014 q^{91} +25.5956 q^{92} +1.47146 q^{93} +5.05635 q^{94} +0.695577 q^{95} +0.318482 q^{96} +14.4975 q^{97} -17.8942 q^{98} +2.21411 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−2.45687	−1.73727	−0.868636	−	0.495451i	$-0.835003\pi$
$2$	−2.45687	−1.73727	−0.868636	+	0.495451i	$0.835003\pi$
$3$	−0.886506	−0.511824	−0.255912	−	0.966700i	$-0.582376\pi$
$3$	−0.886506	−0.511824	−0.255912	+	0.966700i	$0.582376\pi$
$4$	4.03623	2.01811
$5$	−0.806805	−0.360814	−0.180407	−	0.983592i	$-0.557742\pi$
$5$	−0.806805	−0.360814	−0.180407	+	0.983592i	$0.557742\pi$
$6$	2.17803	0.889178
$7$	−3.77933	−1.42845	−0.714226	−	0.699915i	$-0.753221\pi$
$7$	−3.77933	−1.42845	−0.714226	+	0.699915i	$0.753221\pi$
$8$	−5.00275	−1.76874
$9$	−2.21411	−0.738036
$10$	1.98222	0.626833
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.57814	−1.03292
$13$	−4.65728	−1.29170	−0.645849	−	0.763465i	$-0.723496\pi$
$13$	−4.65728	−1.29170	−0.645849	+	0.763465i	$0.723496\pi$
$14$	9.28533	2.48161
$15$	0.715238	0.184674
$16$	4.21868	1.05467
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.43978	1.28217
$19$	−0.862138	−0.197788	−0.0988940	−	0.995098i	$-0.531530\pi$
$19$	−0.862138	−0.197788	−0.0988940	+	0.995098i	$0.531530\pi$
$20$	−3.25645	−0.728165
$21$	3.35040	0.731116
$22$	2.45687	0.523807
$23$	6.34147	1.32229	0.661144	−	0.750259i	$-0.270071\pi$
$23$	6.34147	1.32229	0.661144	+	0.750259i	$0.270071\pi$
$24$	4.43497	0.905285
$25$	−4.34906	−0.869813
$26$	11.4424	2.24403
$27$	4.62234	0.889569
$28$	−15.2542	−2.88278
$29$	2.76760	0.513930	0.256965	−	0.966421i	$-0.417278\pi$
$29$	2.76760	0.513930	0.256965	+	0.966421i	$0.417278\pi$
$30$	−1.75725	−0.320828
$31$	−1.65984	−0.298116	−0.149058	−	0.988828i	$-0.547624\pi$
$31$	−1.65984	−0.298116	−0.149058	+	0.988828i	$0.547624\pi$
$32$	−0.359255	−0.0635079
$33$	0.886506	0.154321
$34$	−2.45687	−0.421350
$35$	3.04918	0.515406
$36$	−8.93664	−1.48944
$37$	−8.36983	−1.37599	−0.687996	−	0.725715i	$-0.741509\pi$
$37$	−8.36983	−1.37599	−0.687996	+	0.725715i	$0.741509\pi$
$38$	2.11816	0.343611
$39$	4.12871	0.661122
$40$	4.03625	0.638187
$41$	−11.1901	−1.74760	−0.873801	−	0.486284i	$-0.838352\pi$
$41$	−11.1901	−1.74760	−0.873801	+	0.486284i	$0.838352\pi$
$42$	−8.23150	−1.27015
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−4.03623	−0.608484
$45$	1.78635	0.266294
$46$	−15.5802	−2.29717
$47$	−2.05804	−0.300196	−0.150098	−	0.988671i	$-0.547959\pi$
$47$	−2.05804	−0.300196	−0.150098	+	0.988671i	$0.547959\pi$
$48$	−3.73988	−0.539806
$49$	7.28332	1.04047
$50$	10.6851	1.51110
$51$	−0.886506	−0.124136
$52$	−18.7978	−2.60679
$53$	11.3753	1.56252	0.781258	−	0.624208i	$-0.214578\pi$
$53$	11.3753	1.56252	0.781258	+	0.624208i	$0.214578\pi$
$54$	−11.3565	−1.54542
$55$	0.806805	0.108790
$56$	18.9071	2.52656
$57$	0.764290	0.101233
$58$	−6.79963	−0.892836
$59$	−6.13074	−0.798154	−0.399077	−	0.916917i	$-0.630669\pi$
$59$	−6.13074	−0.798154	−0.399077	+	0.916917i	$0.630669\pi$
$60$	2.88686	0.372692
$61$	13.9893	1.79114	0.895571	−	0.444919i	$-0.146767\pi$
$61$	13.9893	1.79114	0.895571	+	0.444919i	$0.146767\pi$
$62$	4.07802	0.517909
$63$	8.36784	1.05425
$64$	−7.55472	−0.944340
$65$	3.75752	0.466063
$66$	−2.17803	−0.268097
$67$	2.02853	0.247824	0.123912	−	0.992293i	$-0.460456\pi$
$67$	2.02853	0.247824	0.123912	+	0.992293i	$0.460456\pi$
$68$	4.03623	0.489465
$69$	−5.62175	−0.676779
$70$	−7.49146	−0.895400
$71$	5.35238	0.635211	0.317605	−	0.948223i	$-0.397121\pi$
$71$	5.35238	0.635211	0.317605	+	0.948223i	$0.397121\pi$
$72$	11.0766	1.30539
$73$	−6.65044	−0.778375	−0.389187	−	0.921159i	$-0.627244\pi$
$73$	−6.65044	−0.778375	−0.389187	+	0.921159i	$0.627244\pi$
$74$	20.5636	2.39047
$75$	3.85547	0.445191
$76$	−3.47978	−0.399159
$77$	3.77933	0.430694
$78$	−10.1437	−1.14855
$79$	−2.71492	−0.305453	−0.152726	−	0.988269i	$-0.548805\pi$
$79$	−2.71492	−0.305453	−0.152726	+	0.988269i	$0.548805\pi$
$80$	−3.40365	−0.380540
$81$	2.54460	0.282733
$82$	27.4927	3.03606
$83$	13.0548	1.43295	0.716477	−	0.697611i	$-0.245753\pi$
$83$	13.0548	1.43295	0.716477	+	0.697611i	$0.245753\pi$
$84$	13.5230	1.47548
$85$	−0.806805	−0.0875103
$86$	−2.45687	−0.264931
$87$	−2.45349	−0.263042
$88$	5.00275	0.533295
$89$	−4.76136	−0.504703	−0.252351	−	0.967636i	$-0.581204\pi$
$89$	−4.76136	−0.504703	−0.252351	+	0.967636i	$0.581204\pi$
$90$	−4.38885	−0.462625
$91$	17.6014	1.84513
$92$	25.5956	2.66853
$93$	1.47146	0.152583
$94$	5.05635	0.521522
$95$	0.695577	0.0713647
$96$	0.318482	0.0325049
$97$	14.4975	1.47200	0.736001	−	0.676981i	$-0.236712\pi$
$97$	14.4975	1.47200	0.736001	+	0.676981i	$0.236712\pi$
$98$	−17.8942	−1.80759
$99$	2.21411	0.222526
$100$	−17.5538	−1.75538
$101$	−8.11803	−0.807774	−0.403887	−	0.914809i	$-0.632341\pi$
$101$	−8.11803	−0.807774	−0.403887	+	0.914809i	$0.632341\pi$
$102$	2.17803	0.215657
$103$	13.9564	1.37517	0.687583	−	0.726106i	$-0.258672\pi$
$103$	13.9564	1.37517	0.687583	+	0.726106i	$0.258672\pi$
$104$	23.2992	2.28468
$105$	−2.70312	−0.263797
$106$	−27.9476	−2.71452
$107$	−3.66100	−0.353922	−0.176961	−	0.984218i	$-0.556627\pi$
$107$	−3.66100	−0.353922	−0.176961	+	0.984218i	$0.556627\pi$
$108$	18.6568	1.79525
$109$	−1.17742	−0.112777	−0.0563883	−	0.998409i	$-0.517958\pi$
$109$	−1.17742	−0.112777	−0.0563883	+	0.998409i	$0.517958\pi$
$110$	−1.98222	−0.188997
$111$	7.41990	0.704266
$112$	−15.9438	−1.50655
$113$	1.98154	0.186408	0.0932038	−	0.995647i	$-0.470289\pi$
$113$	1.98154	0.186408	0.0932038	+	0.995647i	$0.470289\pi$
$114$	−1.87776	−0.175869
$115$	−5.11633	−0.477101
$116$	11.1706	1.03717
$117$	10.3117	0.953319
$118$	15.0625	1.38661
$119$	−3.77933	−0.346450
$120$	−3.57816	−0.326640
$121$	1.00000	0.0909091
$122$	−34.3699	−3.11170
$123$	9.92010	0.894465
$124$	−6.69950	−0.601632
$125$	7.54288	0.674655
$126$	−20.5587	−1.83152
$127$	15.4418	1.37023	0.685117	−	0.728433i	$-0.259751\pi$
$127$	15.4418	1.37023	0.685117	+	0.728433i	$0.259751\pi$
$128$	19.2795	1.70408
$129$	−0.886506	−0.0780525
$130$	−9.23175	−0.809678
$131$	−4.91099	−0.429075	−0.214538	−	0.976716i	$-0.568824\pi$
$131$	−4.91099	−0.429075	−0.214538	+	0.976716i	$0.568824\pi$
$132$	3.57814	0.311437
$133$	3.25830	0.282531
$134$	−4.98384	−0.430538
$135$	−3.72933	−0.320969
$136$	−5.00275	−0.428983
$137$	−1.29999	−0.111066	−0.0555328	−	0.998457i	$-0.517686\pi$
$137$	−1.29999	−0.111066	−0.0555328	+	0.998457i	$0.517686\pi$
$138$	13.8119	1.17575
$139$	6.85794	0.581683	0.290841	−	0.956771i	$-0.406065\pi$
$139$	6.85794	0.581683	0.290841	+	0.956771i	$0.406065\pi$
$140$	12.3072	1.04015
$141$	1.82446	0.153648
$142$	−13.1501	−1.10353
$143$	4.65728	0.389461
$144$	−9.34061	−0.778384
$145$	−2.23291	−0.185433
$146$	16.3393	1.35225
$147$	−6.45671	−0.532540
$148$	−33.7825	−2.77691
$149$	−8.93399	−0.731901	−0.365950	−	0.930634i	$-0.619256\pi$
$149$	−8.93399	−0.731901	−0.365950	+	0.930634i	$0.619256\pi$
$150$	−9.47240	−0.773419
$151$	−0.0761129	−0.00619398	−0.00309699	−	0.999995i	$-0.500986\pi$
$151$	−0.0761129	−0.00619398	−0.00309699	+	0.999995i	$0.500986\pi$
$152$	4.31306	0.349836
$153$	−2.21411	−0.179000
$154$	−9.28533	−0.748233
$155$	1.33917	0.107565
$156$	16.6644	1.33422
$157$	18.1493	1.44848	0.724238	−	0.689551i	$-0.242192\pi$
$157$	18.1493	1.44848	0.724238	+	0.689551i	$0.242192\pi$
$158$	6.67022	0.530654
$159$	−10.0843	−0.799734
$160$	0.289849	0.0229146
$161$	−23.9665	−1.88883
$162$	−6.25175	−0.491184
$163$	−7.64318	−0.598660	−0.299330	−	0.954150i	$-0.596763\pi$
$163$	−7.64318	−0.598660	−0.299330	+	0.954150i	$0.596763\pi$
$164$	−45.1658	−3.52686
$165$	−0.715238	−0.0556812
$166$	−32.0741	−2.48943
$167$	5.18148	0.400955	0.200477	−	0.979698i	$-0.435751\pi$
$167$	5.18148	0.400955	0.200477	+	0.979698i	$0.435751\pi$
$168$	−16.7612	−1.29316
$169$	8.69027	0.668482
$170$	1.98222	0.152029
$171$	1.90887	0.145975
$172$	4.03623	0.307759
$173$	−19.9666	−1.51803	−0.759015	−	0.651073i	$-0.774319\pi$
$173$	−19.9666	−1.51803	−0.759015	+	0.651073i	$0.774319\pi$
$174$	6.02791	0.456975
$175$	16.4365	1.24249
$176$	−4.21868	−0.317995
$177$	5.43494	0.408515
$178$	11.6981	0.876806
$179$	12.3915	0.926185	0.463093	−	0.886310i	$-0.346740\pi$
$179$	12.3915	0.926185	0.463093	+	0.886310i	$0.346740\pi$
$180$	7.21013	0.537412
$181$	21.9532	1.63177	0.815884	−	0.578216i	$-0.196251\pi$
$181$	21.9532	1.63177	0.815884	+	0.578216i	$0.196251\pi$
$182$	−43.2444	−3.20549
$183$	−12.4016	−0.916750
$184$	−31.7248	−2.33879
$185$	6.75283	0.496478
$186$	−3.61519	−0.265078
$187$	−1.00000	−0.0731272
$188$	−8.30672	−0.605830
$189$	−17.4693	−1.27071
$190$	−1.70895	−0.123980
$191$	−2.75524	−0.199362	−0.0996810	−	0.995019i	$-0.531782\pi$
$191$	−2.75524	−0.199362	−0.0996810	+	0.995019i	$0.531782\pi$
$192$	6.69730	0.483336
$193$	−9.65803	−0.695200	−0.347600	−	0.937643i	$-0.613003\pi$
$193$	−9.65803	−0.695200	−0.347600	+	0.937643i	$0.613003\pi$
$194$	−35.6186	−2.55727
$195$	−3.33106	−0.238542
$196$	29.3971	2.09980
$197$	−11.6721	−0.831604	−0.415802	−	0.909455i	$-0.636499\pi$
$197$	−11.6721	−0.831604	−0.415802	+	0.909455i	$0.636499\pi$
$198$	−5.43978	−0.386589
$199$	−1.42085	−0.100722	−0.0503608	−	0.998731i	$-0.516037\pi$
$199$	−1.42085	−0.100722	−0.0503608	+	0.998731i	$0.516037\pi$
$200$	21.7573	1.53847
$201$	−1.79830	−0.126842
$202$	19.9450	1.40332
$203$	−10.4597	−0.734124
$204$	−3.57814	−0.250520
$205$	9.02824	0.630560
$206$	−34.2891	−2.38904
$207$	−14.0407	−0.975896
$208$	−19.6476	−1.36231
$209$	0.862138	0.0596353
$210$	6.64122	0.458288
$211$	−2.19054	−0.150803	−0.0754015	−	0.997153i	$-0.524024\pi$
$211$	−2.19054	−0.150803	−0.0754015	+	0.997153i	$0.524024\pi$
$212$	45.9133	3.15334
$213$	−4.74492	−0.325116
$214$	8.99460	0.614858
$215$	−0.806805	−0.0550237
$216$	−23.1244	−1.57342
$217$	6.27308	0.425845
$218$	2.89278	0.195924
$219$	5.89565	0.398391
$220$	3.25645	0.219550
$221$	−4.65728	−0.313283
$222$	−18.2298	−1.22350
$223$	7.37189	0.493659	0.246829	−	0.969059i	$-0.420611\pi$
$223$	7.37189	0.493659	0.246829	+	0.969059i	$0.420611\pi$
$224$	1.35774	0.0907180
$225$	9.62930	0.641953
$226$	−4.86840	−0.323841
$227$	−11.5953	−0.769604	−0.384802	−	0.922999i	$-0.625730\pi$
$227$	−11.5953	−0.769604	−0.384802	+	0.922999i	$0.625730\pi$
$228$	3.08485	0.204299
$229$	13.8873	0.917698	0.458849	−	0.888514i	$-0.348262\pi$
$229$	13.8873	0.917698	0.458849	+	0.888514i	$0.348262\pi$
$230$	12.5702	0.828854
$231$	−3.35040	−0.220440
$232$	−13.8456	−0.909008
$233$	26.1512	1.71322	0.856612	−	0.515961i	$-0.172565\pi$
$233$	26.1512	1.71322	0.856612	+	0.515961i	$0.172565\pi$
$234$	−25.3346	−1.65617
$235$	1.66044	0.108315
$236$	−24.7451	−1.61077
$237$	2.40679	0.156338
$238$	9.28533	0.601879
$239$	−10.7883	−0.697839	−0.348919	−	0.937153i	$-0.613451\pi$
$239$	−10.7883	−0.697839	−0.348919	+	0.937153i	$0.613451\pi$
$240$	3.01736	0.194770
$241$	9.11748	0.587309	0.293654	−	0.955912i	$-0.405129\pi$
$241$	9.11748	0.587309	0.293654	+	0.955912i	$0.405129\pi$
$242$	−2.45687	−0.157934
$243$	−16.1228	−1.03428
$244$	56.4639	3.61473
$245$	−5.87622	−0.375418
$246$	−24.3724	−1.55393
$247$	4.01522	0.255482
$248$	8.30378	0.527290
$249$	−11.5732	−0.733421
$250$	−18.5319	−1.17206
$251$	−28.6068	−1.80564	−0.902822	−	0.430014i	$-0.858509\pi$
$251$	−28.6068	−1.80564	−0.902822	+	0.430014i	$0.858509\pi$
$252$	33.7745	2.12759
$253$	−6.34147	−0.398685
$254$	−37.9385	−2.38047
$255$	0.715238	0.0447899
$256$	−32.2578	−2.01612
$257$	20.2935	1.26587	0.632937	−	0.774204i	$-0.281849\pi$
$257$	20.2935	1.26587	0.632937	+	0.774204i	$0.281849\pi$
$258$	2.17803	0.135598
$259$	31.6323	1.96554
$260$	15.1662	0.940568
$261$	−6.12775	−0.379299
$262$	12.0657	0.745421
$263$	21.9631	1.35430	0.677152	−	0.735843i	$-0.263214\pi$
$263$	21.9631	1.35430	0.677152	+	0.735843i	$0.263214\pi$
$264$	−4.43497	−0.272954
$265$	−9.17765	−0.563778
$266$	−8.00523	−0.490832
$267$	4.22097	0.258319
$268$	8.18761	0.500138
$269$	11.0199	0.671894	0.335947	−	0.941881i	$-0.390944\pi$
$269$	11.0199	0.671894	0.335947	+	0.941881i	$0.390944\pi$
$270$	9.16248	0.557611
$271$	2.67016	0.162200	0.0811002	−	0.996706i	$-0.474157\pi$
$271$	2.67016	0.162200	0.0811002	+	0.996706i	$0.474157\pi$
$272$	4.21868	0.255795
$273$	−15.6037	−0.944381
$274$	3.19391	0.192951
$275$	4.34906	0.262258
$276$	−22.6907	−1.36582
$277$	−6.73935	−0.404928	−0.202464	−	0.979290i	$-0.564895\pi$
$277$	−6.73935	−0.404928	−0.202464	+	0.979290i	$0.564895\pi$
$278$	−16.8491	−1.01054
$279$	3.67507	0.220020
$280$	−15.2543	−0.911620
$281$	−32.0838	−1.91396	−0.956978	−	0.290159i	$-0.906292\pi$
$281$	−32.0838	−1.91396	−0.956978	+	0.290159i	$0.906292\pi$
$282$	−4.48248	−0.266928
$283$	15.3570	0.912878	0.456439	−	0.889755i	$-0.349125\pi$
$283$	15.3570	0.912878	0.456439	+	0.889755i	$0.349125\pi$
$284$	21.6034	1.28193
$285$	−0.616633	−0.0365262
$286$	−11.4424	−0.676600
$287$	42.2911	2.49637
$288$	0.795429	0.0468711
$289$	1.00000	0.0588235
$290$	5.48598	0.322148
$291$	−12.8521	−0.753406
$292$	−26.8427	−1.57085
$293$	−32.7665	−1.91424	−0.957121	−	0.289689i	$-0.906448\pi$
$293$	−32.7665	−1.91424	−0.957121	+	0.289689i	$0.906448\pi$
$294$	15.8633	0.925167
$295$	4.94631	0.287986
$296$	41.8722	2.43377
$297$	−4.62234	−0.268215
$298$	21.9497	1.27151
$299$	−29.5340	−1.70800
$300$	15.5616	0.898447
$301$	−3.77933	−0.217837
$302$	0.187000	0.0107606
$303$	7.19668	0.413438
$304$	−3.63708	−0.208601
$305$	−11.2866	−0.646270
$306$	5.43978	0.310972
$307$	−8.07639	−0.460944	−0.230472	−	0.973079i	$-0.574027\pi$
$307$	−8.07639	−0.460944	−0.230472	+	0.973079i	$0.574027\pi$
$308$	15.2542	0.869190
$309$	−12.3724	−0.703843
$310$	−3.29017	−0.186869
$311$	−10.3457	−0.586649	−0.293325	−	0.956013i	$-0.594762\pi$
$311$	−10.3457	−0.586649	−0.293325	+	0.956013i	$0.594762\pi$
$312$	−20.6549	−1.16935
$313$	24.2793	1.37235	0.686174	−	0.727438i	$-0.259289\pi$
$313$	24.2793	1.37235	0.686174	+	0.727438i	$0.259289\pi$
$314$	−44.5906	−2.51640
$315$	−6.75122	−0.380388
$316$	−10.9580	−0.616438
$317$	6.98517	0.392326	0.196163	−	0.980571i	$-0.437152\pi$
$317$	6.98517	0.392326	0.196163	+	0.980571i	$0.437152\pi$
$318$	24.7757	1.38936
$319$	−2.76760	−0.154956
$320$	6.09519	0.340731
$321$	3.24549	0.181146
$322$	58.8827	3.28140
$323$	−0.862138	−0.0479706
$324$	10.2706	0.570587
$325$	20.2548	1.12354
$326$	18.7783	1.04004
$327$	1.04379	0.0577218
$328$	55.9814	3.09105
$329$	7.77801	0.428816
$330$	1.75725	0.0967334
$331$	2.19206	0.120486	0.0602432	−	0.998184i	$-0.480812\pi$
$331$	2.19206	0.120486	0.0602432	+	0.998184i	$0.480812\pi$
$332$	52.6923	2.89186
$333$	18.5317	1.01553
$334$	−12.7302	−0.696568
$335$	−1.63663	−0.0894186
$336$	14.1343	0.771087
$337$	−20.3694	−1.10959	−0.554796	−	0.831986i	$-0.687204\pi$
$337$	−20.3694	−1.10959	−0.554796	+	0.831986i	$0.687204\pi$
$338$	−21.3509	−1.16134
$339$	−1.75665	−0.0954080
$340$	−3.25645	−0.176606
$341$	1.65984	0.0898854
$342$	−4.68984	−0.253598
$343$	−1.07077	−0.0578159
$344$	−5.00275	−0.269730
$345$	4.53566	0.244192
$346$	49.0553	2.63723
$347$	16.1734	0.868235	0.434117	−	0.900856i	$-0.357060\pi$
$347$	16.1734	0.868235	0.434117	+	0.900856i	$0.357060\pi$
$348$	−9.90284	−0.530848
$349$	−30.7769	−1.64745	−0.823726	−	0.566988i	$-0.808109\pi$
$349$	−30.7769	−1.64745	−0.823726	+	0.566988i	$0.808109\pi$
$350$	−40.3825	−2.15854
$351$	−21.5275	−1.14905
$352$	0.359255	0.0191484
$353$	26.3520	1.40258	0.701288	−	0.712878i	$-0.252609\pi$
$353$	26.3520	1.40258	0.701288	+	0.712878i	$0.252609\pi$
$354$	−13.3529	−0.709701
$355$	−4.31833	−0.229193
$356$	−19.2179	−1.01855
$357$	3.35040	0.177322
$358$	−30.4444	−1.60904
$359$	15.7461	0.831046	0.415523	−	0.909583i	$-0.363599\pi$
$359$	15.7461	0.831046	0.415523	+	0.909583i	$0.363599\pi$
$360$	−8.93669	−0.471005
$361$	−18.2567	−0.960880
$362$	−53.9362	−2.83482
$363$	−0.886506	−0.0465295
$364$	71.0432	3.72368
$365$	5.36561	0.280849
$366$	30.4691	1.59264
$367$	−25.6519	−1.33902	−0.669509	−	0.742804i	$-0.733495\pi$
$367$	−25.6519	−1.33902	−0.669509	+	0.742804i	$0.733495\pi$
$368$	26.7526	1.39458
$369$	24.7761	1.28979
$370$	−16.5908	−0.862517
$371$	−42.9910	−2.23198
$372$	5.93914	0.307930
$373$	37.3390	1.93334	0.966670	−	0.256026i	$-0.0824131\pi$
$373$	37.3390	1.93334	0.966670	+	0.256026i	$0.0824131\pi$
$374$	2.45687	0.127042
$375$	−6.68680	−0.345305
$376$	10.2959	0.530969
$377$	−12.8895	−0.663842
$378$	42.9199	2.20756
$379$	2.83870	0.145814	0.0729072	−	0.997339i	$-0.476772\pi$
$379$	2.83870	0.145814	0.0729072	+	0.997339i	$0.476772\pi$
$380$	2.80751	0.144022
$381$	−13.6892	−0.701319
$382$	6.76927	0.346346
$383$	8.18481	0.418224	0.209112	−	0.977892i	$-0.432943\pi$
$383$	8.18481	0.418224	0.209112	+	0.977892i	$0.432943\pi$
$384$	−17.0914	−0.872191
$385$	−3.04918	−0.155401
$386$	23.7286	1.20775
$387$	−2.21411	−0.112549
$388$	58.5153	2.97067
$389$	12.6477	0.641265	0.320633	−	0.947204i	$-0.396104\pi$
$389$	12.6477	0.641265	0.320633	+	0.947204i	$0.396104\pi$
$390$	8.18400	0.414413
$391$	6.34147	0.320702
$392$	−36.4367	−1.84033
$393$	4.35362	0.219611
$394$	28.6769	1.44472
$395$	2.19041	0.110212
$396$	8.93664	0.449083
$397$	−3.73996	−0.187703	−0.0938517	−	0.995586i	$-0.529918\pi$
$397$	−3.73996	−0.187703	−0.0938517	+	0.995586i	$0.529918\pi$
$398$	3.49086	0.174981
$399$	−2.88850	−0.144606
$400$	−18.3473	−0.917366
$401$	4.81273	0.240336	0.120168	−	0.992754i	$-0.461657\pi$
$401$	4.81273	0.240336	0.120168	+	0.992754i	$0.461657\pi$
$402$	4.41820	0.220360
$403$	7.73034	0.385076
$404$	−32.7662	−1.63018
$405$	−2.05299	−0.102014
$406$	25.6980	1.27537
$407$	8.36983	0.414877
$408$	4.43497	0.219564
$409$	1.22734	0.0606881	0.0303441	−	0.999540i	$-0.490340\pi$
$409$	1.22734	0.0606881	0.0303441	+	0.999540i	$0.490340\pi$
$410$	−22.1813	−1.09545
$411$	1.15245	0.0568461
$412$	56.3312	2.77524
$413$	23.1701	1.14012
$414$	34.4962	1.69540
$415$	−10.5327	−0.517030
$416$	1.67315	0.0820330
$417$	−6.07960	−0.297719
$418$	−2.11816	−0.103603
$419$	−1.27285	−0.0621826	−0.0310913	−	0.999517i	$-0.509898\pi$
$419$	−1.27285	−0.0621826	−0.0310913	+	0.999517i	$0.509898\pi$
$420$	−10.9104	−0.532373
$421$	−36.7832	−1.79270	−0.896352	−	0.443343i	$-0.853792\pi$
$421$	−36.7832	−1.79270	−0.896352	+	0.443343i	$0.853792\pi$
$422$	5.38188	0.261986
$423$	4.55672	0.221555
$424$	−56.9078	−2.76369
$425$	−4.34906	−0.210961
$426$	11.6577	0.564816
$427$	−52.8700	−2.55856
$428$	−14.7766	−0.714255
$429$	−4.12871	−0.199336
$430$	1.98222	0.0955911
$431$	15.5099	0.747085	0.373542	−	0.927613i	$-0.378143\pi$
$431$	15.5099	0.747085	0.373542	+	0.927613i	$0.378143\pi$
$432$	19.5002	0.938202
$433$	−32.1192	−1.54355	−0.771776	−	0.635894i	$-0.780631\pi$
$433$	−32.1192	−1.54355	−0.771776	+	0.635894i	$0.780631\pi$
$434$	−15.4122	−0.739808
$435$	1.97949	0.0949092
$436$	−4.75234	−0.227596
$437$	−5.46722	−0.261533
$438$	−14.4849	−0.692114
$439$	14.4252	0.688477	0.344238	−	0.938882i	$-0.388137\pi$
$439$	14.4252	0.688477	0.344238	+	0.938882i	$0.388137\pi$
$440$	−4.03625	−0.192421
$441$	−16.1261	−0.767908
$442$	11.4424	0.544257
$443$	−20.0106	−0.950730	−0.475365	−	0.879789i	$-0.657684\pi$
$443$	−20.0106	−0.950730	−0.475365	+	0.879789i	$0.657684\pi$
$444$	29.9484	1.42129
$445$	3.84149	0.182104
$446$	−18.1118	−0.857619
$447$	7.92003	0.374605
$448$	28.5518	1.34894
$449$	35.4480	1.67289	0.836447	−	0.548048i	$-0.184629\pi$
$449$	35.4480	1.67289	0.836447	+	0.548048i	$0.184629\pi$
$450$	−23.6580	−1.11525
$451$	11.1901	0.526922
$452$	7.99795	0.376192
$453$	0.0674745	0.00317023
$454$	28.4881	1.33701
$455$	−14.2009	−0.665749
$456$	−3.82356	−0.179054
$457$	−31.3899	−1.46836	−0.734178	−	0.678957i	$-0.762432\pi$
$457$	−31.3899	−1.46836	−0.734178	+	0.678957i	$0.762432\pi$
$458$	−34.1193	−1.59429
$459$	4.62234	0.215752
$460$	−20.6507	−0.962844
$461$	11.0680	0.515489	0.257744	−	0.966213i	$-0.417021\pi$
$461$	11.0680	0.515489	0.257744	+	0.966213i	$0.417021\pi$
$462$	8.23150	0.382964
$463$	−3.90936	−0.181683	−0.0908417	−	0.995865i	$-0.528956\pi$
$463$	−3.90936	−0.181683	−0.0908417	+	0.995865i	$0.528956\pi$
$464$	11.6756	0.542026
$465$	−1.18718	−0.0550542
$466$	−64.2503	−2.97634
$467$	16.3775	0.757859	0.378929	−	0.925426i	$-0.376292\pi$
$467$	16.3775	0.757859	0.378929	+	0.925426i	$0.376292\pi$
$468$	41.6205	1.92391
$469$	−7.66648	−0.354005
$470$	−4.07949	−0.188173
$471$	−16.0895	−0.741365
$472$	30.6706	1.41173
$473$	−1.00000	−0.0459800
$474$	−5.91319	−0.271602
$475$	3.74949	0.172039
$476$	−15.2542	−0.699176
$477$	−25.1861	−1.15319
$478$	26.5056	1.21234
$479$	−11.6699	−0.533213	−0.266607	−	0.963805i	$-0.585902\pi$
$479$	−11.6699	−0.533213	−0.266607	+	0.963805i	$0.585902\pi$
$480$	−0.256953	−0.0117282
$481$	38.9807	1.77736
$482$	−22.4005	−1.02031
$483$	21.2464	0.966747
$484$	4.03623	0.183465
$485$	−11.6967	−0.531119
$486$	39.6117	1.79682
$487$	28.1759	1.27677	0.638386	−	0.769717i	$-0.279603\pi$
$487$	28.1759	1.27677	0.638386	+	0.769717i	$0.279603\pi$
$488$	−69.9849	−3.16807
$489$	6.77572	0.306409
$490$	14.4371	0.652203
$491$	−8.00194	−0.361123	−0.180561	−	0.983564i	$-0.557791\pi$
$491$	−8.00194	−0.361123	−0.180561	+	0.983564i	$0.557791\pi$
$492$	40.0398	1.80513
$493$	2.76760	0.124646
$494$	−9.86488	−0.443842
$495$	−1.78635	−0.0802907
$496$	−7.00234	−0.314414
$497$	−20.2284	−0.907368
$498$	28.4338	1.27415
$499$	26.2471	1.17498	0.587490	−	0.809231i	$-0.300116\pi$
$499$	26.2471	1.17498	0.587490	+	0.809231i	$0.300116\pi$
$500$	30.4448	1.36153
$501$	−4.59341	−0.205218
$502$	70.2833	3.13690
$503$	−31.2721	−1.39436	−0.697178	−	0.716898i	$-0.745561\pi$
$503$	−31.2721	−1.39436	−0.697178	+	0.716898i	$0.745561\pi$
$504$	−41.8622	−1.86469
$505$	6.54967	0.291456
$506$	15.5802	0.692624
$507$	−7.70397	−0.342145
$508$	62.3265	2.76529
$509$	−37.6877	−1.67048	−0.835238	−	0.549888i	$-0.814670\pi$
$509$	−37.6877	−1.67048	−0.835238	+	0.549888i	$0.814670\pi$
$510$	−1.75725	−0.0778123
$511$	25.1342	1.11187
$512$	40.6945	1.79846
$513$	−3.98509	−0.175946
$514$	−49.8585	−2.19917
$515$	−11.2601	−0.496179
$516$	−3.57814	−0.157519
$517$	2.05804	0.0905125
$518$	−77.7166	−3.41467
$519$	17.7005	0.776965
$520$	−18.7980	−0.824345
$521$	29.6520	1.29908	0.649539	−	0.760328i	$-0.274962\pi$
$521$	29.6520	1.29908	0.649539	+	0.760328i	$0.274962\pi$
$522$	15.0551	0.658945
$523$	37.2857	1.63039	0.815196	−	0.579186i	$-0.196629\pi$
$523$	37.2857	1.63039	0.815196	+	0.579186i	$0.196629\pi$
$524$	−19.8219	−0.865923
$525$	−14.5711	−0.635934
$526$	−53.9606	−2.35279
$527$	−1.65984	−0.0723038
$528$	3.73988	0.162758
$529$	17.2143	0.748447
$530$	22.5483	0.979436
$531$	13.5741	0.589066
$532$	13.1512	0.570179
$533$	52.1155	2.25737
$534$	−10.3704	−0.448771
$535$	2.95371	0.127700
$536$	−10.1482	−0.438337
$537$	−10.9851	−0.474044
$538$	−27.0745	−1.16726
$539$	−7.28332	−0.313715
$540$	−15.0524	−0.647753
$541$	37.5255	1.61335	0.806673	−	0.590998i	$-0.201266\pi$
$541$	37.5255	1.61335	0.806673	+	0.590998i	$0.201266\pi$
$542$	−6.56024	−0.281786
$543$	−19.4616	−0.835178
$544$	−0.359255	−0.0154029
$545$	0.949950	0.0406914
$546$	38.3364	1.64065
$547$	−13.4283	−0.574151	−0.287075	−	0.957908i	$-0.592683\pi$
$547$	−13.4283	−0.574151	−0.287075	+	0.957908i	$0.592683\pi$
$548$	−5.24706	−0.224143
$549$	−30.9737	−1.32193
$550$	−10.6851	−0.455614
$551$	−2.38605	−0.101649
$552$	28.1242	1.19705
$553$	10.2606	0.436324
$554$	16.5577	0.703470
$555$	−5.98642	−0.254109
$556$	27.6802	1.17390
$557$	9.20104	0.389860	0.194930	−	0.980817i	$-0.437552\pi$
$557$	9.20104	0.389860	0.194930	+	0.980817i	$0.437552\pi$
$558$	−9.02917	−0.382235
$559$	−4.65728	−0.196982
$560$	12.8635	0.543583
$561$	0.886506	0.0374283
$562$	78.8258	3.32506
$563$	−28.0597	−1.18257	−0.591287	−	0.806461i	$-0.701380\pi$
$563$	−28.0597	−1.18257	−0.591287	+	0.806461i	$0.701380\pi$
$564$	7.36396	0.310078
$565$	−1.59872	−0.0672586
$566$	−37.7302	−1.58592
$567$	−9.61686	−0.403870
$568$	−26.7767	−1.12352
$569$	−8.93769	−0.374688	−0.187344	−	0.982294i	$-0.559988\pi$
$569$	−8.93769	−0.374688	−0.187344	+	0.982294i	$0.559988\pi$
$570$	1.51499	0.0634560
$571$	12.7777	0.534732	0.267366	−	0.963595i	$-0.413847\pi$
$571$	12.7777	0.534732	0.267366	+	0.963595i	$0.413847\pi$
$572$	18.7978	0.785978
$573$	2.44253	0.102038
$574$	−103.904	−4.33687
$575$	−27.5795	−1.15014
$576$	16.7270	0.696956
$577$	−22.3765	−0.931546	−0.465773	−	0.884904i	$-0.654224\pi$
$577$	−22.3765	−0.931546	−0.465773	+	0.884904i	$0.654224\pi$
$578$	−2.45687	−0.102192
$579$	8.56190	0.355820
$580$	−9.01254	−0.374225
$581$	−49.3385	−2.04691
$582$	31.5761	1.30887
$583$	−11.3753	−0.471116
$584$	33.2705	1.37674
$585$	−8.31955	−0.343971
$586$	80.5032	3.32556
$587$	19.5857	0.808390	0.404195	−	0.914673i	$-0.367552\pi$
$587$	19.5857	0.808390	0.404195	+	0.914673i	$0.367552\pi$
$588$	−26.0607	−1.07473
$589$	1.43101	0.0589638
$590$	−12.1525	−0.500309
$591$	10.3474	0.425635
$592$	−35.3096	−1.45122
$593$	39.4378	1.61952	0.809759	−	0.586762i	$-0.199598\pi$
$593$	39.4378	1.61952	0.809759	+	0.586762i	$0.199598\pi$
$594$	11.3565	0.465963
$595$	3.04918	0.125004
$596$	−36.0596	−1.47706
$597$	1.25959	0.0515518
$598$	72.5614	2.96725
$599$	−27.8142	−1.13646	−0.568230	−	0.822870i	$-0.692371\pi$
$599$	−27.8142	−1.13646	−0.568230	+	0.822870i	$0.692371\pi$
$600$	−19.2880	−0.787428
$601$	−14.8850	−0.607171	−0.303586	−	0.952804i	$-0.598184\pi$
$601$	−14.8850	−0.607171	−0.303586	+	0.952804i	$0.598184\pi$
$602$	9.28533	0.378442
$603$	−4.49138	−0.182903
$604$	−0.307209	−0.0125002
$605$	−0.806805	−0.0328013
$606$	−17.6813	−0.718255
$607$	−45.5701	−1.84963	−0.924816	−	0.380415i	$-0.875781\pi$
$607$	−45.5701	−1.84963	−0.924816	+	0.380415i	$0.875781\pi$
$608$	0.309727	0.0125611
$609$	9.27254	0.375742
$610$	27.7298	1.12275
$611$	9.58487	0.387762
$612$	−8.93664	−0.361242
$613$	2.70182	0.109125	0.0545627	−	0.998510i	$-0.482624\pi$
$613$	2.70182	0.109125	0.0545627	+	0.998510i	$0.482624\pi$
$614$	19.8427	0.800785
$615$	−8.00359	−0.322736
$616$	−18.9071	−0.761787
$617$	20.2650	0.815837	0.407919	−	0.913018i	$-0.366255\pi$
$617$	20.2650	0.815837	0.407919	+	0.913018i	$0.366255\pi$
$618$	30.3975	1.22277
$619$	−26.8529	−1.07931	−0.539654	−	0.841887i	$-0.681445\pi$
$619$	−26.8529	−1.07931	−0.539654	+	0.841887i	$0.681445\pi$
$620$	5.40519	0.217078
$621$	29.3124	1.17627
$622$	25.4180	1.01917
$623$	17.9947	0.720944
$624$	17.4177	0.697266
$625$	15.6597	0.626388
$626$	−59.6512	−2.38414
$627$	−0.764290	−0.0305228
$628$	73.2549	2.92319
$629$	−8.36983	−0.333727
$630$	16.5869	0.660838
$631$	34.6381	1.37892	0.689461	−	0.724323i	$-0.257848\pi$
$631$	34.6381	1.37892	0.689461	+	0.724323i	$0.257848\pi$
$632$	13.5821	0.540266
$633$	1.94193	0.0771846
$634$	−17.1617	−0.681578
$635$	−12.4585	−0.494400
$636$	−40.7024	−1.61395
$637$	−33.9205	−1.34398
$638$	6.79963	0.269200
$639$	−11.8508	−0.468808
$640$	−15.5548	−0.614858
$641$	−12.5892	−0.497242	−0.248621	−	0.968601i	$-0.579977\pi$
$641$	−12.5892	−0.497242	−0.248621	+	0.968601i	$0.579977\pi$
$642$	−7.97377	−0.314700
$643$	40.8840	1.61231	0.806154	−	0.591706i	$-0.201545\pi$
$643$	40.8840	1.61231	0.806154	+	0.591706i	$0.201545\pi$
$644$	−96.7343	−3.81186
$645$	0.715238	0.0281625
$646$	2.11816	0.0833380
$647$	23.1544	0.910293	0.455146	−	0.890417i	$-0.349587\pi$
$647$	23.1544	0.910293	0.455146	+	0.890417i	$0.349587\pi$
$648$	−12.7300	−0.500081
$649$	6.13074	0.240653
$650$	−49.7635	−1.95189
$651$	−5.56112	−0.217958
$652$	−30.8496	−1.20816
$653$	−28.3555	−1.10964	−0.554819	−	0.831971i	$-0.687212\pi$
$653$	−28.3555	−1.10964	−0.554819	+	0.831971i	$0.687212\pi$
$654$	−2.56446	−0.100278
$655$	3.96222	0.154817
$656$	−47.2075	−1.84314
$657$	14.7248	0.574468
$658$	−19.1096	−0.744969
$659$	−8.72016	−0.339689	−0.169845	−	0.985471i	$-0.554327\pi$
$659$	−8.72016	−0.339689	−0.169845	+	0.985471i	$0.554327\pi$
$660$	−2.88686	−0.112371
$661$	−14.6667	−0.570470	−0.285235	−	0.958458i	$-0.592072\pi$
$661$	−14.6667	−0.570470	−0.285235	+	0.958458i	$0.592072\pi$
$662$	−5.38561	−0.209317
$663$	4.12871	0.160346
$664$	−65.3101	−2.53452
$665$	−2.62882	−0.101941
$666$	−45.5301	−1.76425
$667$	17.5506	0.679563
$668$	20.9136	0.809173
$669$	−6.53523	−0.252666
$670$	4.02099	0.155344
$671$	−13.9893	−0.540050
$672$	−1.20365	−0.0464317
$673$	−30.9797	−1.19418	−0.597089	−	0.802175i	$-0.703676\pi$
$673$	−30.9797	−1.19418	−0.597089	+	0.802175i	$0.703676\pi$
$674$	50.0451	1.92766
$675$	−20.1028	−0.773759
$676$	35.0759	1.34907
$677$	2.40270	0.0923434	0.0461717	−	0.998934i	$-0.485298\pi$
$677$	2.40270	0.0923434	0.0461717	+	0.998934i	$0.485298\pi$
$678$	4.31586	0.165750
$679$	−54.7909	−2.10268
$680$	4.03625	0.154783
$681$	10.2793	0.393902
$682$	−4.07802	−0.156155
$683$	−26.8448	−1.02719	−0.513594	−	0.858033i	$-0.671686\pi$
$683$	−26.8448	−1.02719	−0.513594	+	0.858033i	$0.671686\pi$
$684$	7.70462	0.294593
$685$	1.04884	0.0400741
$686$	2.63074	0.100442
$687$	−12.3112	−0.469700
$688$	4.21868	0.160836
$689$	−52.9779	−2.01830
$690$	−11.1435	−0.424227
$691$	34.2946	1.30463	0.652314	−	0.757948i	$-0.273798\pi$
$691$	34.2946	1.30463	0.652314	+	0.757948i	$0.273798\pi$
$692$	−80.5896	−3.06356
$693$	−8.36784	−0.317868
$694$	−39.7361	−1.50836
$695$	−5.53302	−0.209879
$696$	12.2742	0.465253
$697$	−11.1901	−0.423856
$698$	75.6151	2.86207
$699$	−23.1832	−0.876870
$700$	66.3416	2.50748
$701$	−40.4732	−1.52865	−0.764326	−	0.644829i	$-0.776928\pi$
$701$	−40.4732	−1.52865	−0.764326	+	0.644829i	$0.776928\pi$
$702$	52.8904	1.99622
$703$	7.21595	0.272155
$704$	7.55472	0.284729
$705$	−1.47199	−0.0554383
$706$	−64.7436	−2.43666
$707$	30.6807	1.15387
$708$	21.9366	0.824429
$709$	−33.1652	−1.24554	−0.622772	−	0.782403i	$-0.713994\pi$
$709$	−33.1652	−1.24554	−0.622772	+	0.782403i	$0.713994\pi$
$710$	10.6096	0.398171
$711$	6.01113	0.225435
$712$	23.8199	0.892689
$713$	−10.5258	−0.394196
$714$	−8.23150	−0.308056
$715$	−3.75752	−0.140523
$716$	50.0150	1.86915
$717$	9.56391	0.357171
$718$	−38.6861	−1.44375
$719$	−23.1103	−0.861869	−0.430934	−	0.902383i	$-0.641816\pi$
$719$	−23.1103	−0.861869	−0.430934	+	0.902383i	$0.641816\pi$
$720$	7.53606	0.280852
$721$	−52.7458	−1.96436
$722$	44.8545	1.66931
$723$	−8.08270	−0.300599
$724$	88.6081	3.29309
$725$	−12.0365	−0.447023
$726$	2.17803	0.0808344
$727$	−29.4737	−1.09312	−0.546560	−	0.837420i	$-0.684063\pi$
$727$	−29.4737	−1.09312	−0.546560	+	0.837420i	$0.684063\pi$
$728$	−88.0555	−3.26355
$729$	6.65917	0.246636
$730$	−13.1826	−0.487911
$731$	1.00000	0.0369863
$732$	−50.0555	−1.85011
$733$	50.0111	1.84720	0.923601	−	0.383356i	$-0.125232\pi$
$733$	50.0111	1.84720	0.923601	+	0.383356i	$0.125232\pi$
$734$	63.0234	2.32624
$735$	5.20931	0.192148
$736$	−2.27821	−0.0839758
$737$	−2.02853	−0.0747218
$738$	−60.8718	−2.24072
$739$	−37.3021	−1.37218	−0.686090	−	0.727516i	$-0.740675\pi$
$739$	−37.3021	−1.37218	−0.686090	+	0.727516i	$0.740675\pi$
$740$	27.2559	1.00195
$741$	−3.55951	−0.130762
$742$	105.623	3.87755
$743$	19.3397	0.709506	0.354753	−	0.934960i	$-0.384565\pi$
$743$	19.3397	0.709506	0.354753	+	0.934960i	$0.384565\pi$
$744$	−7.36134	−0.269880
$745$	7.20799	0.264080
$746$	−91.7372	−3.35874
$747$	−28.9048	−1.05757
$748$	−4.03623	−0.147579
$749$	13.8361	0.505560
$750$	16.4286	0.599889
$751$	−2.40462	−0.0877457	−0.0438729	−	0.999037i	$-0.513970\pi$
$751$	−2.40462	−0.0877457	−0.0438729	+	0.999037i	$0.513970\pi$
$752$	−8.68222	−0.316608
$753$	25.3601	0.924173
$754$	31.6678	1.15327
$755$	0.0614083	0.00223488
$756$	−70.5102	−2.56443
$757$	10.1310	0.368216	0.184108	−	0.982906i	$-0.441060\pi$
$757$	10.1310	0.368216	0.184108	+	0.982906i	$0.441060\pi$
$758$	−6.97433	−0.253319
$759$	5.62175	0.204057
$760$	−3.47980	−0.126226
$761$	27.0771	0.981545	0.490772	−	0.871288i	$-0.336715\pi$
$761$	27.0771	0.981545	0.490772	+	0.871288i	$0.336715\pi$
$762$	33.6327	1.21838
$763$	4.44986	0.161096
$764$	−11.1208	−0.402335
$765$	1.78635	0.0645858
$766$	−20.1091	−0.726570
$767$	28.5526	1.03097
$768$	28.5968	1.03190
$769$	40.4282	1.45788	0.728939	−	0.684579i	$-0.240014\pi$
$769$	40.4282	1.45788	0.728939	+	0.684579i	$0.240014\pi$
$770$	7.49146	0.269973
$771$	−17.9903	−0.647905
$772$	−38.9820	−1.40299
$773$	29.8571	1.07389	0.536943	−	0.843618i	$-0.319579\pi$
$773$	29.8571	1.07389	0.536943	+	0.843618i	$0.319579\pi$
$774$	5.43978	0.195529
$775$	7.21875	0.259305
$776$	−72.5276	−2.60359
$777$	−28.0422	−1.00601
$778$	−31.0739	−1.11405
$779$	9.64742	0.345655
$780$	−13.4449	−0.481406
$781$	−5.35238	−0.191523
$782$	−15.5802	−0.557147
$783$	12.7928	0.457176
$784$	30.7260	1.09736
$785$	−14.6430	−0.522631
$786$	−10.6963	−0.381524
$787$	−47.0094	−1.67571	−0.837853	−	0.545896i	$-0.816189\pi$
$787$	−47.0094	−1.67571	−0.837853	+	0.545896i	$0.816189\pi$
$788$	−47.1113	−1.67827
$789$	−19.4704	−0.693166
$790$	−5.38157	−0.191468
$791$	−7.48889	−0.266274
$792$	−11.0766	−0.393591
$793$	−65.1519	−2.31361
$794$	9.18862	0.326092
$795$	8.13604	0.288555
$796$	−5.73489	−0.203268
$797$	10.8342	0.383768	0.191884	−	0.981418i	$-0.438540\pi$
$797$	10.8342	0.383768	0.191884	+	0.981418i	$0.438540\pi$
$798$	7.09669	0.251220
$799$	−2.05804	−0.0728082
$800$	1.56242	0.0552400
$801$	10.5422	0.372489
$802$	−11.8243	−0.417529
$803$	6.65044	0.234689
$804$	−7.25836	−0.255983
$805$	19.3363	0.681515
$806$	−18.9925	−0.668982
$807$	−9.76919	−0.343892
$808$	40.6125	1.42874
$809$	−40.9838	−1.44091	−0.720457	−	0.693499i	$-0.756068\pi$
$809$	−40.9838	−1.44091	−0.720457	+	0.693499i	$0.756068\pi$
$810$	5.04395	0.177226
$811$	−22.1634	−0.778261	−0.389131	−	0.921183i	$-0.627225\pi$
$811$	−22.1634	−0.778261	−0.389131	+	0.921183i	$0.627225\pi$
$812$	−42.2175	−1.48155
$813$	−2.36711	−0.0830181
$814$	−20.5636	−0.720754
$815$	6.16656	0.216005
$816$	−3.73988	−0.130922
$817$	−0.862138	−0.0301624
$818$	−3.01542	−0.105432
$819$	−38.9714	−1.36177
$820$	36.4401	1.27254
$821$	−18.0694	−0.630625	−0.315312	−	0.948988i	$-0.602109\pi$
$821$	−18.0694	−0.630625	−0.315312	+	0.948988i	$0.602109\pi$
$822$	−2.83142	−0.0987571
$823$	29.2263	1.01876	0.509382	−	0.860541i	$-0.329874\pi$
$823$	29.2263	1.01876	0.509382	+	0.860541i	$0.329874\pi$
$824$	−69.8205	−2.43231
$825$	−3.85547	−0.134230
$826$	−56.9259	−1.98071
$827$	−54.5303	−1.89621	−0.948103	−	0.317965i	$-0.897001\pi$
$827$	−54.5303	−1.89621	−0.948103	+	0.317965i	$0.897001\pi$
$828$	−56.6715	−1.96947
$829$	48.5058	1.68468	0.842338	−	0.538950i	$-0.181179\pi$
$829$	48.5058	1.68468	0.842338	+	0.538950i	$0.181179\pi$
$830$	25.8775	0.898222
$831$	5.97447	0.207252
$832$	35.1844	1.21980
$833$	7.28332	0.252352
$834$	14.9368	0.517219
$835$	−4.18045	−0.144670
$836$	3.47978	0.120351
$837$	−7.67234	−0.265195
$838$	3.12722	0.108028
$839$	−6.60532	−0.228041	−0.114020	−	0.993478i	$-0.536373\pi$
$839$	−6.60532	−0.228041	−0.114020	+	0.993478i	$0.536373\pi$
$840$	13.5230	0.466589
$841$	−21.3404	−0.735876
$842$	90.3717	3.11441
$843$	28.4424	0.979610
$844$	−8.84152	−0.304338
$845$	−7.01136	−0.241198
$846$	−11.1953	−0.384902
$847$	−3.77933	−0.129859
$848$	47.9887	1.64794
$849$	−13.6141	−0.467233
$850$	10.6851	0.366496
$851$	−53.0770	−1.81946
$852$	−19.1516	−0.656122
$853$	−16.4219	−0.562277	−0.281138	−	0.959667i	$-0.590712\pi$
$853$	−16.4219	−0.562277	−0.281138	+	0.959667i	$0.590712\pi$
$854$	129.895	4.44491
$855$	−1.54008	−0.0526697
$856$	18.3151	0.625996
$857$	26.0854	0.891060	0.445530	−	0.895267i	$-0.353015\pi$
$857$	26.0854	0.891060	0.445530	+	0.895267i	$0.353015\pi$
$858$	10.1437	0.346301
$859$	−50.5524	−1.72483	−0.862413	−	0.506206i	$-0.831048\pi$
$859$	−50.5524	−1.72483	−0.862413	+	0.506206i	$0.831048\pi$
$860$	−3.25645	−0.111044
$861$	−37.4913	−1.27770
$862$	−38.1058	−1.29789
$863$	10.8897	0.370688	0.185344	−	0.982674i	$-0.440660\pi$
$863$	10.8897	0.370688	0.185344	+	0.982674i	$0.440660\pi$
$864$	−1.66060	−0.0564947
$865$	16.1091	0.547727
$866$	78.9129	2.68157
$867$	−0.886506	−0.0301073
$868$	25.3196	0.859403
$869$	2.71492	0.0920974
$870$	−4.86335	−0.164883
$871$	−9.44743	−0.320114
$872$	5.89035	0.199472
$873$	−32.0991	−1.08639
$874$	13.4323	0.454353
$875$	−28.5070	−0.963713
$876$	23.7962	0.803999
$877$	−36.9488	−1.24767	−0.623836	−	0.781555i	$-0.714427\pi$
$877$	−36.9488	−1.24767	−0.623836	+	0.781555i	$0.714427\pi$
$878$	−35.4409	−1.19607
$879$	29.0477	0.979755
$880$	3.40365	0.114737
$881$	−13.3098	−0.448419	−0.224209	−	0.974541i	$-0.571980\pi$
$881$	−13.3098	−0.448419	−0.224209	+	0.974541i	$0.571980\pi$
$882$	39.6197	1.33406
$883$	−35.4485	−1.19294	−0.596469	−	0.802636i	$-0.703430\pi$
$883$	−35.4485	−1.19294	−0.596469	+	0.802636i	$0.703430\pi$
$884$	−18.7978	−0.632240
$885$	−4.38494	−0.147398
$886$	49.1634	1.65168
$887$	17.4160	0.584773	0.292386	−	0.956300i	$-0.405551\pi$
$887$	17.4160	0.584773	0.292386	+	0.956300i	$0.405551\pi$
$888$	−37.1200	−1.24566
$889$	−58.3595	−1.95731
$890$	−9.43805	−0.316364
$891$	−2.54460	−0.0852472
$892$	29.7546	0.996259
$893$	1.77431	0.0593752
$894$	−19.4585	−0.650790
$895$	−9.99754	−0.334181
$896$	−72.8635	−2.43420
$897$	26.1821	0.874194
$898$	−87.0912	−2.90627
$899$	−4.59377	−0.153211
$900$	38.8660	1.29553
$901$	11.3753	0.378966
$902$	−27.4927	−0.915406
$903$	3.35040	0.111494
$904$	−9.91316	−0.329707
$905$	−17.7120	−0.588765
$906$	−0.165776	−0.00550755
$907$	4.05748	0.134726	0.0673632	−	0.997729i	$-0.478541\pi$
$907$	4.05748	0.134726	0.0673632	+	0.997729i	$0.478541\pi$
$908$	−46.8011	−1.55315
$909$	17.9742	0.596166
$910$	34.8898	1.15659
$911$	−36.4373	−1.20722	−0.603611	−	0.797279i	$-0.706272\pi$
$911$	−36.4373	−1.20722	−0.603611	+	0.797279i	$0.706272\pi$
$912$	3.22430	0.106767
$913$	−13.0548	−0.432052
$914$	77.1210	2.55093
$915$	10.0057	0.330777
$916$	56.0523	1.85202
$917$	18.5602	0.612913
$918$	−11.3565	−0.374820
$919$	−24.5738	−0.810614	−0.405307	−	0.914181i	$-0.632835\pi$
$919$	−24.5738	−0.810614	−0.405307	+	0.914181i	$0.632835\pi$
$920$	25.5958	0.843868
$921$	7.15977	0.235922
$922$	−27.1927	−0.895544
$923$	−24.9276	−0.820500
$924$	−13.5230	−0.444873
$925$	36.4009	1.19686
$926$	9.60480	0.315633
$927$	−30.9010	−1.01492
$928$	−0.994273	−0.0326386
$929$	6.03459	0.197988	0.0989942	−	0.995088i	$-0.468437\pi$
$929$	6.03459	0.197988	0.0989942	+	0.995088i	$0.468437\pi$
$930$	2.91675	0.0956441
$931$	−6.27923	−0.205793
$932$	105.552	3.45748
$933$	9.17150	0.300261
$934$	−40.2374	−1.31661
$935$	0.806805	0.0263854
$936$	−51.5870	−1.68617
$937$	−56.4994	−1.84575	−0.922877	−	0.385094i	$-0.874169\pi$
$937$	−56.4994	−1.84575	−0.922877	+	0.385094i	$0.874169\pi$
$938$	18.8356	0.615003
$939$	−21.5237	−0.702401
$940$	6.70191	0.218592
$941$	−33.1839	−1.08176	−0.540882	−	0.841099i	$-0.681909\pi$
$941$	−33.1839	−1.08176	−0.540882	+	0.841099i	$0.681909\pi$
$942$	39.5299	1.28795
$943$	−70.9618	−2.31083
$944$	−25.8636	−0.841789
$945$	14.0943	0.458489
$946$	2.45687	0.0798799
$947$	−32.6341	−1.06047	−0.530233	−	0.847852i	$-0.677896\pi$
$947$	−32.6341	−1.06047	−0.530233	+	0.847852i	$0.677896\pi$
$948$	9.71437	0.315508
$949$	30.9730	1.00542
$950$	−9.21203	−0.298878
$951$	−6.19239	−0.200802
$952$	18.9071	0.612781
$953$	−15.3278	−0.496515	−0.248258	−	0.968694i	$-0.579858\pi$
$953$	−15.3278	−0.496515	−0.248258	+	0.968694i	$0.579858\pi$
$954$	61.8791	2.00341
$955$	2.22294	0.0719327
$956$	−43.5441	−1.40832
$957$	2.45349	0.0793101
$958$	28.6716	0.926337
$959$	4.91309	0.158652
$960$	−5.40342	−0.174395
$961$	−28.2449	−0.911127
$962$	−95.7705	−3.08777
$963$	8.10584	0.261207
$964$	36.8002	1.18526
$965$	7.79215	0.250838
$966$	−52.1998	−1.67950
$967$	22.9748	0.738820	0.369410	−	0.929267i	$-0.379560\pi$
$967$	22.9748	0.738820	0.369410	+	0.929267i	$0.379560\pi$
$968$	−5.00275	−0.160795
$969$	0.764290	0.0245525
$970$	28.7373	0.922698
$971$	−25.5688	−0.820542	−0.410271	−	0.911964i	$-0.634566\pi$
$971$	−25.5688	−0.820542	−0.410271	+	0.911964i	$0.634566\pi$
$972$	−65.0753	−2.08729
$973$	−25.9184	−0.830905
$974$	−69.2246	−2.21810
$975$	−17.9560	−0.575053
$976$	59.0162	1.88906
$977$	−2.52292	−0.0807153	−0.0403576	−	0.999185i	$-0.512850\pi$
$977$	−2.52292	−0.0807153	−0.0403576	+	0.999185i	$0.512850\pi$
$978$	−16.6471	−0.532315
$979$	4.76136	0.152174
$980$	−23.7178	−0.757637
$981$	2.60694	0.0832331
$982$	19.6598	0.627368
$983$	−55.1314	−1.75842	−0.879210	−	0.476435i	$-0.841929\pi$
$983$	−55.1314	−1.75842	−0.879210	+	0.476435i	$0.841929\pi$
$984$	−49.6278	−1.58208
$985$	9.41713	0.300055
$986$	−6.79963	−0.216544
$987$	−6.89525	−0.219478
$988$	16.2063	0.515592
$989$	6.34147	0.201647
$990$	4.38885	0.139487
$991$	−61.7472	−1.96147	−0.980733	−	0.195354i	$-0.937414\pi$
$991$	−61.7472	−1.96147	−0.980733	+	0.195354i	$0.937414\pi$
$992$	0.596306	0.0189327
$993$	−1.94327	−0.0616678
$994$	49.6987	1.57635
$995$	1.14635	0.0363418
$996$	−46.7120	−1.48013
$997$	26.3416	0.834247	0.417123	−	0.908850i	$-0.363038\pi$
$997$	26.3416	0.834247	0.417123	+	0.908850i	$0.363038\pi$
$998$	−64.4857	−2.04126
$999$	−38.6882	−1.22404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.8	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.8	✓	69	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45687 q^{2} -0.886506 q^{3} +4.03623 q^{4} -0.806805 q^{5} +2.17803 q^{6} -3.77933 q^{7} -5.00275 q^{8} -2.21411 q^{9} +O(q^{10})\)	\(q-2.45687 q^{2} -0.886506 q^{3} +4.03623 q^{4} -0.806805 q^{5} +2.17803 q^{6} -3.77933 q^{7} -5.00275 q^{8} -2.21411 q^{9} +1.98222 q^{10} -1.00000 q^{11} -3.57814 q^{12} -4.65728 q^{13} +9.28533 q^{14} +0.715238 q^{15} +4.21868 q^{16} +1.00000 q^{17} +5.43978 q^{18} -0.862138 q^{19} -3.25645 q^{20} +3.35040 q^{21} +2.45687 q^{22} +6.34147 q^{23} +4.43497 q^{24} -4.34906 q^{25} +11.4424 q^{26} +4.62234 q^{27} -15.2542 q^{28} +2.76760 q^{29} -1.75725 q^{30} -1.65984 q^{31} -0.359255 q^{32} +0.886506 q^{33} -2.45687 q^{34} +3.04918 q^{35} -8.93664 q^{36} -8.36983 q^{37} +2.11816 q^{38} +4.12871 q^{39} +4.03625 q^{40} -11.1901 q^{41} -8.23150 q^{42} +1.00000 q^{43} -4.03623 q^{44} +1.78635 q^{45} -15.5802 q^{46} -2.05804 q^{47} -3.73988 q^{48} +7.28332 q^{49} +10.6851 q^{50} -0.886506 q^{51} -18.7978 q^{52} +11.3753 q^{53} -11.3565 q^{54} +0.806805 q^{55} +18.9071 q^{56} +0.764290 q^{57} -6.79963 q^{58} -6.13074 q^{59} +2.88686 q^{60} +13.9893 q^{61} +4.07802 q^{62} +8.36784 q^{63} -7.55472 q^{64} +3.75752 q^{65} -2.17803 q^{66} +2.02853 q^{67} +4.03623 q^{68} -5.62175 q^{69} -7.49146 q^{70} +5.35238 q^{71} +11.0766 q^{72} -6.65044 q^{73} +20.5636 q^{74} +3.85547 q^{75} -3.47978 q^{76} +3.77933 q^{77} -10.1437 q^{78} -2.71492 q^{79} -3.40365 q^{80} +2.54460 q^{81} +27.4927 q^{82} +13.0548 q^{83} +13.5230 q^{84} -0.806805 q^{85} -2.45687 q^{86} -2.45349 q^{87} +5.00275 q^{88} -4.76136 q^{89} -4.38885 q^{90} +17.6014 q^{91} +25.5956 q^{92} +1.47146 q^{93} +5.05635 q^{94} +0.695577 q^{95} +0.318482 q^{96} +14.4975 q^{97} -17.8942 q^{98} +2.21411 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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