LMFDB - Embedded newform 8023.2.a.d.1.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.54
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.988723 q^{2} +1.19363 q^{3} -1.02243 q^{4} -2.47739 q^{5} -1.18017 q^{6} +3.50885 q^{7} +2.98834 q^{8} -1.57524 q^{9} +O(q^{10})$	\(q-0.988723 q^{2} +1.19363 q^{3} -1.02243 q^{4} -2.47739 q^{5} -1.18017 q^{6} +3.50885 q^{7} +2.98834 q^{8} -1.57524 q^{9} +2.44945 q^{10} +3.13199 q^{11} -1.22040 q^{12} -1.72519 q^{13} -3.46928 q^{14} -2.95710 q^{15} -0.909791 q^{16} -6.38932 q^{17} +1.55747 q^{18} -2.22706 q^{19} +2.53295 q^{20} +4.18829 q^{21} -3.09667 q^{22} -2.05827 q^{23} +3.56699 q^{24} +1.13746 q^{25} +1.70574 q^{26} -5.46116 q^{27} -3.58755 q^{28} +0.622400 q^{29} +2.92375 q^{30} -1.15680 q^{31} -5.07715 q^{32} +3.73845 q^{33} +6.31727 q^{34} -8.69280 q^{35} +1.61056 q^{36} +2.31656 q^{37} +2.20194 q^{38} -2.05925 q^{39} -7.40329 q^{40} -5.71985 q^{41} -4.14106 q^{42} +6.33944 q^{43} -3.20223 q^{44} +3.90248 q^{45} +2.03506 q^{46} +1.25097 q^{47} -1.08596 q^{48} +5.31205 q^{49} -1.12464 q^{50} -7.62651 q^{51} +1.76388 q^{52} +12.3530 q^{53} +5.39958 q^{54} -7.75916 q^{55} +10.4857 q^{56} -2.65829 q^{57} -0.615381 q^{58} +8.78461 q^{59} +3.02342 q^{60} +6.33091 q^{61} +1.14375 q^{62} -5.52727 q^{63} +6.83948 q^{64} +4.27397 q^{65} -3.69629 q^{66} -7.33101 q^{67} +6.53261 q^{68} -2.45682 q^{69} +8.59477 q^{70} +1.00000 q^{71} -4.70735 q^{72} -3.47324 q^{73} -2.29044 q^{74} +1.35772 q^{75} +2.27700 q^{76} +10.9897 q^{77} +2.03603 q^{78} -6.72446 q^{79} +2.25391 q^{80} -1.79292 q^{81} +5.65535 q^{82} +0.357658 q^{83} -4.28222 q^{84} +15.8288 q^{85} -6.26795 q^{86} +0.742918 q^{87} +9.35946 q^{88} +12.3564 q^{89} -3.85847 q^{90} -6.05344 q^{91} +2.10443 q^{92} -1.38079 q^{93} -1.23686 q^{94} +5.51729 q^{95} -6.06027 q^{96} -2.85701 q^{97} -5.25215 q^{98} -4.93362 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−0.988723	−0.699133	−0.349566	−	0.936912i	$-0.613671\pi$
$2$	−0.988723	−0.699133	−0.349566	+	0.936912i	$0.613671\pi$
$3$	1.19363	0.689145	0.344573	−	0.938760i	$-0.388024\pi$
$3$	1.19363	0.689145	0.344573	+	0.938760i	$0.388024\pi$
$4$	−1.02243	−0.511213
$5$	−2.47739	−1.10792	−0.553961	−	0.832542i	$-0.686884\pi$
$5$	−2.47739	−1.10792	−0.553961	+	0.832542i	$0.686884\pi$
$6$	−1.18017	−0.481804
$7$	3.50885	1.32622	0.663111	−	0.748521i	$-0.269236\pi$
$7$	3.50885	1.32622	0.663111	+	0.748521i	$0.269236\pi$
$8$	2.98834	1.05654
$9$	−1.57524	−0.525079
$10$	2.44945	0.774585
$11$	3.13199	0.944330	0.472165	−	0.881510i	$-0.343473\pi$
$11$	3.13199	0.944330	0.472165	+	0.881510i	$0.343473\pi$
$12$	−1.22040	−0.352300
$13$	−1.72519	−0.478482	−0.239241	−	0.970960i	$-0.576899\pi$
$13$	−1.72519	−0.478482	−0.239241	+	0.970960i	$0.576899\pi$
$14$	−3.46928	−0.927205
$15$	−2.95710	−0.763520
$16$	−0.909791	−0.227448
$17$	−6.38932	−1.54964	−0.774819	−	0.632183i	$-0.782159\pi$
$17$	−6.38932	−1.54964	−0.774819	+	0.632183i	$0.782159\pi$
$18$	1.55747	0.367100
$19$	−2.22706	−0.510922	−0.255461	−	0.966819i	$-0.582227\pi$
$19$	−2.22706	−0.510922	−0.255461	+	0.966819i	$0.582227\pi$
$20$	2.53295	0.566385
$21$	4.18829	0.913960
$22$	−3.09667	−0.660212
$23$	−2.05827	−0.429179	−0.214590	−	0.976704i	$-0.568841\pi$
$23$	−2.05827	−0.429179	−0.214590	+	0.976704i	$0.568841\pi$
$24$	3.56699	0.728109
$25$	1.13746	0.227493
$26$	1.70574	0.334522
$27$	−5.46116	−1.05100
$28$	−3.58755	−0.677982
$29$	0.622400	0.115577	0.0577884	−	0.998329i	$-0.481595\pi$
$29$	0.622400	0.115577	0.0577884	+	0.998329i	$0.481595\pi$
$30$	2.92375	0.533802
$31$	−1.15680	−0.207767	−0.103883	−	0.994589i	$-0.533127\pi$
$31$	−1.15680	−0.207767	−0.103883	+	0.994589i	$0.533127\pi$
$32$	−5.07715	−0.897523
$33$	3.73845	0.650781
$34$	6.31727	1.08340
$35$	−8.69280	−1.46935
$36$	1.61056	0.268427
$37$	2.31656	0.380840	0.190420	−	0.981703i	$-0.439015\pi$
$37$	2.31656	0.380840	0.190420	+	0.981703i	$0.439015\pi$
$38$	2.20194	0.357202
$39$	−2.05925	−0.329743
$40$	−7.40329	−1.17056
$41$	−5.71985	−0.893290	−0.446645	−	0.894711i	$-0.647381\pi$
$41$	−5.71985	−0.893290	−0.446645	+	0.894711i	$0.647381\pi$
$42$	−4.14106	−0.638979
$43$	6.33944	0.966755	0.483378	−	0.875412i	$-0.339410\pi$
$43$	6.33944	0.966755	0.483378	+	0.875412i	$0.339410\pi$
$44$	−3.20223	−0.482754
$45$	3.90248	0.581747
$46$	2.03506	0.300053
$47$	1.25097	0.182473	0.0912364	−	0.995829i	$-0.470918\pi$
$47$	1.25097	0.182473	0.0912364	+	0.995829i	$0.470918\pi$
$48$	−1.08596	−0.156744
$49$	5.31205	0.758865
$50$	−1.12464	−0.159048
$51$	−7.62651	−1.06793
$52$	1.76388	0.244606
$53$	12.3530	1.69682	0.848408	−	0.529343i	$-0.177561\pi$
$53$	12.3530	1.69682	0.848408	+	0.529343i	$0.177561\pi$
$54$	5.39958	0.734789
$55$	−7.75916	−1.04624
$56$	10.4857	1.40121
$57$	−2.65829	−0.352099
$58$	−0.615381	−0.0808035
$59$	8.78461	1.14366	0.571830	−	0.820372i	$-0.306234\pi$
$59$	8.78461	1.14366	0.571830	+	0.820372i	$0.306234\pi$
$60$	3.02342	0.390321
$61$	6.33091	0.810590	0.405295	−	0.914186i	$-0.367169\pi$
$61$	6.33091	0.810590	0.405295	+	0.914186i	$0.367169\pi$
$62$	1.14375	0.145257
$63$	−5.52727	−0.696371
$64$	6.83948	0.854935
$65$	4.27397	0.530121
$66$	−3.69629	−0.454982
$67$	−7.33101	−0.895625	−0.447813	−	0.894127i	$-0.647797\pi$
$67$	−7.33101	−0.895625	−0.447813	+	0.894127i	$0.647797\pi$
$68$	6.53261	0.792195
$69$	−2.45682	−0.295767
$70$	8.59477	1.02727
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−4.70735	−0.554766
$73$	−3.47324	−0.406512	−0.203256	−	0.979126i	$-0.565152\pi$
$73$	−3.47324	−0.406512	−0.203256	+	0.979126i	$0.565152\pi$
$74$	−2.29044	−0.266258
$75$	1.35772	0.156776
$76$	2.27700	0.261190
$77$	10.9897	1.25239
$78$	2.03603	0.230534
$79$	−6.72446	−0.756561	−0.378280	−	0.925691i	$-0.623484\pi$
$79$	−6.72446	−0.756561	−0.378280	+	0.925691i	$0.623484\pi$
$80$	2.25391	0.251994
$81$	−1.79292	−0.199213
$82$	5.65535	0.624529
$83$	0.357658	0.0392581	0.0196290	−	0.999807i	$-0.493751\pi$
$83$	0.357658	0.0392581	0.0196290	+	0.999807i	$0.493751\pi$
$84$	−4.28222	−0.467228
$85$	15.8288	1.71688
$86$	−6.26795	−0.675890
$87$	0.742918	0.0796492
$88$	9.35946	0.997721
$89$	12.3564	1.30978	0.654890	−	0.755725i	$-0.272715\pi$
$89$	12.3564	1.30978	0.654890	+	0.755725i	$0.272715\pi$
$90$	−3.85847	−0.406718
$91$	−6.05344	−0.634573
$92$	2.10443	0.219402
$93$	−1.38079	−0.143182
$94$	−1.23686	−0.127573
$95$	5.51729	0.566062
$96$	−6.06027	−0.618524
$97$	−2.85701	−0.290086	−0.145043	−	0.989425i	$-0.546332\pi$
$97$	−2.85701	−0.290086	−0.145043	+	0.989425i	$0.546332\pi$
$98$	−5.25215	−0.530547
$99$	−4.93362	−0.495848
$100$	−1.16297	−0.116297
$101$	8.22512	0.818430	0.409215	−	0.912438i	$-0.365803\pi$
$101$	8.22512	0.818430	0.409215	+	0.912438i	$0.365803\pi$
$102$	7.54051	0.746622
$103$	1.22749	0.120949	0.0604743	−	0.998170i	$-0.480739\pi$
$103$	1.22749	0.120949	0.0604743	+	0.998170i	$0.480739\pi$
$104$	−5.15546	−0.505535
$105$	−10.3760	−1.01260
$106$	−12.2137	−1.18630
$107$	−12.1575	−1.17531	−0.587654	−	0.809112i	$-0.699948\pi$
$107$	−12.1575	−1.17531	−0.587654	+	0.809112i	$0.699948\pi$
$108$	5.58364	0.537286
$109$	−4.96284	−0.475354	−0.237677	−	0.971344i	$-0.576386\pi$
$109$	−4.96284	−0.475354	−0.237677	+	0.971344i	$0.576386\pi$
$110$	7.67166	0.731464
$111$	2.76513	0.262454
$112$	−3.19232	−0.301646
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	2.62832	0.246164
$115$	5.09914	0.475497
$116$	−0.636358	−0.0590844
$117$	2.71758	0.251241
$118$	−8.68555	−0.799570
$119$	−22.4192	−2.05516
$120$	−8.83683	−0.806688
$121$	−1.19065	−0.108241
$122$	−6.25951	−0.566710
$123$	−6.82741	−0.615607
$124$	1.18274	0.106213
$125$	9.56901	0.855878
$126$	5.46494	0.486856
$127$	−20.1832	−1.79097	−0.895485	−	0.445092i	$-0.853171\pi$
$127$	−20.1832	−1.79097	−0.895485	+	0.445092i	$0.853171\pi$
$128$	3.39196	0.299809
$129$	7.56697	0.666235
$130$	−4.22577	−0.370625
$131$	9.88350	0.863526	0.431763	−	0.901987i	$-0.357892\pi$
$131$	9.88350	0.863526	0.431763	+	0.901987i	$0.357892\pi$
$132$	−3.82229	−0.332688
$133$	−7.81442	−0.677596
$134$	7.24834	0.626161
$135$	13.5294	1.16443
$136$	−19.0935	−1.63725
$137$	6.84632	0.584921	0.292460	−	0.956278i	$-0.405526\pi$
$137$	6.84632	0.584921	0.292460	+	0.956278i	$0.405526\pi$
$138$	2.42912	0.206780
$139$	3.12859	0.265364	0.132682	−	0.991159i	$-0.457641\pi$
$139$	3.12859	0.265364	0.132682	+	0.991159i	$0.457641\pi$
$140$	8.88775	0.751152
$141$	1.49320	0.125750
$142$	−0.988723	−0.0829718
$143$	−5.40328	−0.451845
$144$	1.43314	0.119428
$145$	−1.54193	−0.128050
$146$	3.43407	0.284206
$147$	6.34065	0.522968
$148$	−2.36851	−0.194691
$149$	9.37056	0.767666	0.383833	−	0.923403i	$-0.374604\pi$
$149$	9.37056	0.767666	0.383833	+	0.923403i	$0.374604\pi$
$150$	−1.34240	−0.109607
$151$	2.83951	0.231076	0.115538	−	0.993303i	$-0.463141\pi$
$151$	2.83951	0.231076	0.115538	+	0.993303i	$0.463141\pi$
$152$	−6.65521	−0.539809
$153$	10.0647	0.813682
$154$	−10.8658	−0.875588
$155$	2.86584	0.230190
$156$	2.10543	0.168569
$157$	15.6373	1.24799	0.623997	−	0.781427i	$-0.285508\pi$
$157$	15.6373	1.24799	0.623997	+	0.781427i	$0.285508\pi$
$158$	6.64863	0.528936
$159$	14.7450	1.16935
$160$	12.5781	0.994386
$161$	−7.22217	−0.569187
$162$	1.77270	0.139277
$163$	21.9292	1.71763	0.858815	−	0.512286i	$-0.171201\pi$
$163$	21.9292	1.71763	0.858815	+	0.512286i	$0.171201\pi$
$164$	5.84813	0.456662
$165$	−9.26160	−0.721015
$166$	−0.353625	−0.0274466
$167$	13.6078	1.05300	0.526502	−	0.850174i	$-0.323503\pi$
$167$	13.6078	1.05300	0.526502	+	0.850174i	$0.323503\pi$
$168$	12.5160	0.965634
$169$	−10.0237	−0.771055
$170$	−15.6503	−1.20033
$171$	3.50814	0.268274
$172$	−6.48161	−0.494218
$173$	−1.94776	−0.148086	−0.0740429	−	0.997255i	$-0.523590\pi$
$173$	−1.94776	−0.148086	−0.0740429	+	0.997255i	$0.523590\pi$
$174$	−0.734540	−0.0556854
$175$	3.99119	0.301706
$176$	−2.84945	−0.214786
$177$	10.4856	0.788147
$178$	−12.2171	−0.915710
$179$	11.1471	0.833174	0.416587	−	0.909096i	$-0.363226\pi$
$179$	11.1471	0.833174	0.416587	+	0.909096i	$0.363226\pi$
$180$	−3.98999	−0.297397
$181$	−16.5949	−1.23349	−0.616745	−	0.787163i	$-0.711549\pi$
$181$	−16.5949	−1.23349	−0.616745	+	0.787163i	$0.711549\pi$
$182$	5.98518	0.443651
$183$	7.55679	0.558614
$184$	−6.15082	−0.453444
$185$	−5.73903	−0.421942
$186$	1.36522	0.100103
$187$	−20.0113	−1.46337
$188$	−1.27903	−0.0932826
$189$	−19.1624	−1.39386
$190$	−5.45507	−0.395753
$191$	−21.1672	−1.53160	−0.765802	−	0.643076i	$-0.777658\pi$
$191$	−21.1672	−1.53160	−0.765802	+	0.643076i	$0.777658\pi$
$192$	8.16384	0.589175
$193$	−15.4450	−1.11175	−0.555876	−	0.831265i	$-0.687617\pi$
$193$	−15.4450	−1.11175	−0.555876	+	0.831265i	$0.687617\pi$
$194$	2.82480	0.202809
$195$	5.10156	0.365330
$196$	−5.43119	−0.387942
$197$	14.5746	1.03840	0.519200	−	0.854653i	$-0.326230\pi$
$197$	14.5746	1.03840	0.519200	+	0.854653i	$0.326230\pi$
$198$	4.87799	0.346663
$199$	−5.85375	−0.414961	−0.207481	−	0.978239i	$-0.566526\pi$
$199$	−5.85375	−0.414961	−0.207481	+	0.978239i	$0.566526\pi$
$200$	3.39913	0.240355
$201$	−8.75054	−0.617216
$202$	−8.13236	−0.572191
$203$	2.18391	0.153280
$204$	7.79755	0.545938
$205$	14.1703	0.989697
$206$	−1.21365	−0.0845591
$207$	3.24226	0.225353
$208$	1.56956	0.108830
$209$	−6.97512	−0.482479
$210$	10.2590	0.707940
$211$	−15.8868	−1.09369	−0.546847	−	0.837232i	$-0.684172\pi$
$211$	−15.8868	−1.09369	−0.546847	+	0.837232i	$0.684172\pi$
$212$	−12.6300	−0.867435
$213$	1.19363	0.0817865
$214$	12.0204	0.821697
$215$	−15.7053	−1.07109
$216$	−16.3198	−1.11042
$217$	−4.05903	−0.275545
$218$	4.90688	0.332336
$219$	−4.14578	−0.280146
$220$	7.93317	0.534854
$221$	11.0228	0.741473
$222$	−2.73395	−0.183490
$223$	3.07149	0.205682	0.102841	−	0.994698i	$-0.467207\pi$
$223$	3.07149	0.205682	0.102841	+	0.994698i	$0.467207\pi$
$224$	−17.8150	−1.19031
$225$	−1.79177	−0.119452
$226$	0.988723	0.0657689
$227$	−1.33163	−0.0883832	−0.0441916	−	0.999023i	$-0.514071\pi$
$227$	−1.33163	−0.0883832	−0.0441916	+	0.999023i	$0.514071\pi$
$228$	2.71791	0.179998
$229$	8.01423	0.529595	0.264798	−	0.964304i	$-0.414695\pi$
$229$	8.01423	0.529595	0.264798	+	0.964304i	$0.414695\pi$
$230$	−5.04164	−0.332436
$231$	13.1177	0.863080
$232$	1.85994	0.122111
$233$	7.16859	0.469630	0.234815	−	0.972040i	$-0.424552\pi$
$233$	7.16859	0.469630	0.234815	+	0.972040i	$0.424552\pi$
$234$	−2.68694	−0.175651
$235$	−3.09914	−0.202166
$236$	−8.98162	−0.584654
$237$	−8.02655	−0.521380
$238$	22.1664	1.43683
$239$	14.0689	0.910045	0.455022	−	0.890480i	$-0.349631\pi$
$239$	14.0689	0.910045	0.455022	+	0.890480i	$0.349631\pi$
$240$	2.69034	0.173661
$241$	16.1695	1.04157	0.520785	−	0.853688i	$-0.325639\pi$
$241$	16.1695	1.04157	0.520785	+	0.853688i	$0.325639\pi$
$242$	1.17722	0.0756745
$243$	14.2434	0.913714
$244$	−6.47289	−0.414384
$245$	−13.1600	−0.840764
$246$	6.75042	0.430391
$247$	3.84210	0.244467
$248$	−3.45691	−0.219514
$249$	0.426913	0.0270545
$250$	−9.46110	−0.598373
$251$	−29.1225	−1.83820	−0.919099	−	0.394026i	$-0.871082\pi$
$251$	−29.1225	−1.83820	−0.919099	+	0.394026i	$0.871082\pi$
$252$	5.65123	0.355994
$253$	−6.44648	−0.405287
$254$	19.9556	1.25213
$255$	18.8938	1.18318
$256$	−17.0327	−1.06454
$257$	−5.25219	−0.327622	−0.163811	−	0.986492i	$-0.552379\pi$
$257$	−5.25219	−0.327622	−0.163811	+	0.986492i	$0.552379\pi$
$258$	−7.48164	−0.465787
$259$	8.12847	0.505079
$260$	−4.36982	−0.271005
$261$	−0.980427	−0.0606869
$262$	−9.77205	−0.603719
$263$	15.7472	0.971015	0.485507	−	0.874233i	$-0.338635\pi$
$263$	15.7472	0.971015	0.485507	+	0.874233i	$0.338635\pi$
$264$	11.1718	0.687575
$265$	−30.6032	−1.87994
$266$	7.72630	0.473730
$267$	14.7491	0.902628
$268$	7.49542	0.457855
$269$	−4.03561	−0.246055	−0.123028	−	0.992403i	$-0.539260\pi$
$269$	−4.03561	−0.246055	−0.123028	+	0.992403i	$0.539260\pi$
$270$	−13.3769	−0.814090
$271$	12.2835	0.746172	0.373086	−	0.927797i	$-0.378300\pi$
$271$	12.2835	0.746172	0.373086	+	0.927797i	$0.378300\pi$
$272$	5.81294	0.352461
$273$	−7.22560	−0.437313
$274$	−6.76911	−0.408937
$275$	3.56252	0.214828
$276$	2.51192	0.151200
$277$	11.7585	0.706503	0.353251	−	0.935528i	$-0.385076\pi$
$277$	11.7585	0.706503	0.353251	+	0.935528i	$0.385076\pi$
$278$	−3.09331	−0.185525
$279$	1.82223	0.109094
$280$	−25.9771	−1.55243
$281$	6.49541	0.387484	0.193742	−	0.981053i	$-0.437938\pi$
$281$	6.49541	0.387484	0.193742	+	0.981053i	$0.437938\pi$
$282$	−1.47636	−0.0879162
$283$	31.3865	1.86573	0.932867	−	0.360221i	$-0.117299\pi$
$283$	31.3865	1.86573	0.932867	+	0.360221i	$0.117299\pi$
$284$	−1.02243	−0.0606699
$285$	6.58563	0.390099
$286$	5.34235	0.315900
$287$	−20.0701	−1.18470
$288$	7.99772	0.471270
$289$	23.8234	1.40138
$290$	1.52454	0.0895240
$291$	−3.41023	−0.199911
$292$	3.55113	0.207814
$293$	−3.77116	−0.220313	−0.110157	−	0.993914i	$-0.535135\pi$
$293$	−3.77116	−0.220313	−0.110157	+	0.993914i	$0.535135\pi$
$294$	−6.26915	−0.365624
$295$	−21.7629	−1.26709
$296$	6.92268	0.402372
$297$	−17.1043	−0.992492
$298$	−9.26488	−0.536700
$299$	3.55091	0.205354
$300$	−1.38816	−0.0801457
$301$	22.2442	1.28213
$302$	−2.80749	−0.161553
$303$	9.81778	0.564017
$304$	2.02616	0.116208
$305$	−15.6841	−0.898071
$306$	−9.95119	−0.568872
$307$	−9.36081	−0.534250	−0.267125	−	0.963662i	$-0.586074\pi$
$307$	−9.36081	−0.534250	−0.267125	+	0.963662i	$0.586074\pi$
$308$	−11.2362	−0.640239
$309$	1.46518	0.0833511
$310$	−2.83352	−0.160933
$311$	−0.436665	−0.0247610	−0.0123805	−	0.999923i	$-0.503941\pi$
$311$	−0.436665	−0.0247610	−0.0123805	+	0.999923i	$0.503941\pi$
$312$	−6.15374	−0.348387
$313$	2.68947	0.152018	0.0760089	−	0.997107i	$-0.475782\pi$
$313$	2.68947	0.152018	0.0760089	+	0.997107i	$0.475782\pi$
$314$	−15.4610	−0.872514
$315$	13.6932	0.771525
$316$	6.87527	0.386764
$317$	3.57486	0.200784	0.100392	−	0.994948i	$-0.467990\pi$
$317$	3.57486	0.200784	0.100392	+	0.994948i	$0.467990\pi$
$318$	−14.5787	−0.817533
$319$	1.94935	0.109143
$320$	−16.9441	−0.947202
$321$	−14.5116	−0.809958
$322$	7.14073	0.397937
$323$	14.2294	0.791744
$324$	1.83313	0.101841
$325$	−1.96234	−0.108851
$326$	−21.6819	−1.20085
$327$	−5.92382	−0.327588
$328$	−17.0929	−0.943796
$329$	4.38947	0.242000
$330$	9.15716	0.504085
$331$	−1.41093	−0.0775516	−0.0387758	−	0.999248i	$-0.512346\pi$
$331$	−1.41093	−0.0775516	−0.0387758	+	0.999248i	$0.512346\pi$
$332$	−0.365679	−0.0200692
$333$	−3.64913	−0.199971
$334$	−13.4544	−0.736190
$335$	18.1618	0.992283
$336$	−3.81047	−0.207878
$337$	14.2515	0.776329	0.388164	−	0.921590i	$-0.373109\pi$
$337$	14.2515	0.776329	0.388164	+	0.921590i	$0.373109\pi$
$338$	9.91068	0.539070
$339$	−1.19363	−0.0648293
$340$	−16.1838	−0.877691
$341$	−3.62307	−0.196200
$342$	−3.46858	−0.187559
$343$	−5.92275	−0.319799
$344$	18.9444	1.02141
$345$	6.08651	0.327687
$346$	1.92580	0.103532
$347$	18.1106	0.972230	0.486115	−	0.873895i	$-0.338414\pi$
$347$	18.1106	0.972230	0.486115	+	0.873895i	$0.338414\pi$
$348$	−0.759579	−0.0407177
$349$	4.82838	0.258457	0.129229	−	0.991615i	$-0.458750\pi$
$349$	4.82838	0.258457	0.129229	+	0.991615i	$0.458750\pi$
$350$	−3.94618	−0.210932
$351$	9.42154	0.502885
$352$	−15.9016	−0.847558
$353$	−12.9491	−0.689209	−0.344605	−	0.938748i	$-0.611987\pi$
$353$	−12.9491	−0.689209	−0.344605	+	0.938748i	$0.611987\pi$
$354$	−10.3674	−0.551020
$355$	−2.47739	−0.131486
$356$	−12.6335	−0.669577
$357$	−26.7603	−1.41631
$358$	−11.0214	−0.582500
$359$	15.8758	0.837895	0.418948	−	0.908010i	$-0.362399\pi$
$359$	15.8758	0.837895	0.418948	+	0.908010i	$0.362399\pi$
$360$	11.6619	0.614638
$361$	−14.0402	−0.738959
$362$	16.4078	0.862373
$363$	−1.42120	−0.0745934
$364$	6.18920	0.324402
$365$	8.60458	0.450384
$366$	−7.47157	−0.390545
$367$	13.3647	0.697630	0.348815	−	0.937192i	$-0.386584\pi$
$367$	13.3647	0.697630	0.348815	+	0.937192i	$0.386584\pi$
$368$	1.87260	0.0976158
$369$	9.01012	0.469048
$370$	5.67431	0.294993
$371$	43.3449	2.25035
$372$	1.41176	0.0731963
$373$	35.4305	1.83452	0.917261	−	0.398288i	$-0.130395\pi$
$373$	35.4305	1.83452	0.917261	+	0.398288i	$0.130395\pi$
$374$	19.7856	1.02309
$375$	11.4219	0.589825
$376$	3.73833	0.192790
$377$	−1.07376	−0.0553014
$378$	18.9463	0.974494
$379$	20.2367	1.03949	0.519745	−	0.854321i	$-0.326027\pi$
$379$	20.2367	1.03949	0.519745	+	0.854321i	$0.326027\pi$
$380$	−5.64102	−0.289378
$381$	−24.0914	−1.23424
$382$	20.9285	1.07079
$383$	12.9630	0.662376	0.331188	−	0.943565i	$-0.392551\pi$
$383$	12.9630	0.662376	0.331188	+	0.943565i	$0.392551\pi$
$384$	4.04876	0.206612
$385$	−27.2258	−1.38755
$386$	15.2708	0.777262
$387$	−9.98611	−0.507623
$388$	2.92109	0.148296
$389$	−1.33907	−0.0678937	−0.0339468	−	0.999424i	$-0.510808\pi$
$389$	−1.33907	−0.0678937	−0.0339468	+	0.999424i	$0.510808\pi$
$390$	−5.04403	−0.255414
$391$	13.1509	0.665072
$392$	15.8742	0.801770
$393$	11.7973	0.595095
$394$	−14.4103	−0.725980
$395$	16.6591	0.838211
$396$	5.04427	0.253484
$397$	8.47943	0.425571	0.212785	−	0.977099i	$-0.431747\pi$
$397$	8.47943	0.425571	0.212785	+	0.977099i	$0.431747\pi$
$398$	5.78774	0.290113
$399$	−9.32756	−0.466962
$400$	−1.03485	−0.0517427
$401$	−28.2616	−1.41132	−0.705659	−	0.708552i	$-0.749349\pi$
$401$	−28.2616	−1.41132	−0.705659	+	0.708552i	$0.749349\pi$
$402$	8.65187	0.431516
$403$	1.99569	0.0994126
$404$	−8.40958	−0.418392
$405$	4.44177	0.220713
$406$	−2.15928	−0.107163
$407$	7.25544	0.359639
$408$	−22.7906	−1.12830
$409$	−17.2664	−0.853768	−0.426884	−	0.904306i	$-0.640389\pi$
$409$	−17.2664	−0.853768	−0.426884	+	0.904306i	$0.640389\pi$
$410$	−14.0105	−0.691930
$411$	8.17200	0.403095
$412$	−1.25502	−0.0618305
$413$	30.8239	1.51675
$414$	−3.20570	−0.157552
$415$	−0.886058	−0.0434949
$416$	8.75906	0.429448
$417$	3.73440	0.182874
$418$	6.89646	0.337317
$419$	12.4386	0.607664	0.303832	−	0.952726i	$-0.401734\pi$
$419$	12.4386	0.607664	0.303832	+	0.952726i	$0.401734\pi$
$420$	10.6087	0.517653
$421$	9.03172	0.440179	0.220089	−	0.975480i	$-0.429365\pi$
$421$	9.03172	0.440179	0.220089	+	0.975480i	$0.429365\pi$
$422$	15.7077	0.764638
$423$	−1.97058	−0.0958126
$424$	36.9150	1.79275
$425$	−7.26762	−0.352531
$426$	−1.18017	−0.0571796
$427$	22.2142	1.07502
$428$	12.4301	0.600833
$429$	−6.44954	−0.311387
$430$	15.5282	0.748834
$431$	19.1877	0.924238	0.462119	−	0.886818i	$-0.347089\pi$
$431$	19.1877	0.924238	0.462119	+	0.886818i	$0.347089\pi$
$432$	4.96851	0.239048
$433$	34.9889	1.68146	0.840730	−	0.541455i	$-0.182126\pi$
$433$	34.9889	1.68146	0.840730	+	0.541455i	$0.182126\pi$
$434$	4.01326	0.192643
$435$	−1.84050	−0.0882451
$436$	5.07414	0.243007
$437$	4.58389	0.219277
$438$	4.09903	0.195859
$439$	2.74944	0.131224	0.0656118	−	0.997845i	$-0.479100\pi$
$439$	2.74944	0.131224	0.0656118	+	0.997845i	$0.479100\pi$
$440$	−23.1870	−1.10540
$441$	−8.36774	−0.398464
$442$	−10.8985	−0.518388
$443$	−16.9518	−0.805403	−0.402702	−	0.915331i	$-0.631929\pi$
$443$	−16.9518	−0.805403	−0.402702	+	0.915331i	$0.631929\pi$
$444$	−2.82714	−0.134170
$445$	−30.6117	−1.45113
$446$	−3.03685	−0.143799
$447$	11.1850	0.529033
$448$	23.9987	1.13383
$449$	39.3464	1.85687	0.928435	−	0.371495i	$-0.121155\pi$
$449$	39.3464	1.85687	0.928435	+	0.371495i	$0.121155\pi$
$450$	1.77157	0.0835125
$451$	−17.9145	−0.843561
$452$	1.02243	0.0480909
$453$	3.38934	0.159245
$454$	1.31661	0.0617916
$455$	14.9967	0.703058
$456$	−7.94389	−0.372007
$457$	−18.8395	−0.881274	−0.440637	−	0.897685i	$-0.645247\pi$
$457$	−18.8395	−0.881274	−0.440637	+	0.897685i	$0.645247\pi$
$458$	−7.92385	−0.370257
$459$	34.8931	1.62867
$460$	−5.21350	−0.243080
$461$	0.418885	0.0195094	0.00975472	−	0.999952i	$-0.496895\pi$
$461$	0.418885	0.0195094	0.00975472	+	0.999952i	$0.496895\pi$
$462$	−12.9697	−0.603407
$463$	6.95928	0.323425	0.161713	−	0.986838i	$-0.448298\pi$
$463$	6.95928	0.323425	0.161713	+	0.986838i	$0.448298\pi$
$464$	−0.566254	−0.0262877
$465$	3.42076	0.158634
$466$	−7.08775	−0.328333
$467$	16.2322	0.751138	0.375569	−	0.926795i	$-0.377447\pi$
$467$	16.2322	0.751138	0.375569	+	0.926795i	$0.377447\pi$
$468$	−2.77853	−0.128438
$469$	−25.7234	−1.18780
$470$	3.06420	0.141341
$471$	18.6653	0.860050
$472$	26.2514	1.20832
$473$	19.8551	0.912936
$474$	7.93603	0.364514
$475$	−2.53320	−0.116231
$476$	22.9220	1.05063
$477$	−19.4589	−0.890962
$478$	−13.9103	−0.636242
$479$	−12.7735	−0.583635	−0.291817	−	0.956474i	$-0.594260\pi$
$479$	−12.7735	−0.583635	−0.291817	+	0.956474i	$0.594260\pi$
$480$	15.0136	0.685276
$481$	−3.99651	−0.182225
$482$	−15.9872	−0.728195
$483$	−8.62063	−0.392252
$484$	1.21735	0.0553340
$485$	7.07794	0.321393
$486$	−14.0828	−0.638807
$487$	11.9884	0.543246	0.271623	−	0.962404i	$-0.412440\pi$
$487$	11.9884	0.543246	0.271623	+	0.962404i	$0.412440\pi$
$488$	18.9189	0.856419
$489$	26.1755	1.18370
$490$	13.0116	0.587805
$491$	4.98187	0.224829	0.112414	−	0.993661i	$-0.464142\pi$
$491$	4.98187	0.224829	0.112414	+	0.993661i	$0.464142\pi$
$492$	6.98053	0.314706
$493$	−3.97671	−0.179102
$494$	−3.79877	−0.170915
$495$	12.2225	0.549361
$496$	1.05244	0.0472561
$497$	3.50885	0.157394
$498$	−0.422099	−0.0189147
$499$	18.5951	0.832430	0.416215	−	0.909266i	$-0.363356\pi$
$499$	18.5951	0.832430	0.416215	+	0.909266i	$0.363356\pi$
$500$	−9.78361	−0.437536
$501$	16.2428	0.725673
$502$	28.7941	1.28515
$503$	23.8879	1.06511	0.532555	−	0.846395i	$-0.321232\pi$
$503$	23.8879	1.06511	0.532555	+	0.846395i	$0.321232\pi$
$504$	−16.5174	−0.735743
$505$	−20.3768	−0.906757
$506$	6.37378	0.283349
$507$	−11.9647	−0.531369
$508$	20.6358	0.915567
$509$	38.4146	1.70270	0.851349	−	0.524599i	$-0.175785\pi$
$509$	38.4146	1.70270	0.851349	+	0.524599i	$0.175785\pi$
$510$	−18.6808	−0.827199
$511$	−12.1871	−0.539125
$512$	10.0567	0.444447
$513$	12.1623	0.536979
$514$	5.19296	0.229052
$515$	−3.04098	−0.134002
$516$	−7.73667	−0.340588
$517$	3.91803	0.172315
$518$	−8.03681	−0.353117
$519$	−2.32492	−0.102053
$520$	12.7721	0.560093
$521$	21.5176	0.942702	0.471351	−	0.881946i	$-0.343766\pi$
$521$	21.5176	0.942702	0.471351	+	0.881946i	$0.343766\pi$
$522$	0.969371	0.0424282
$523$	16.7661	0.733129	0.366564	−	0.930393i	$-0.380534\pi$
$523$	16.7661	0.733129	0.366564	+	0.930393i	$0.380534\pi$
$524$	−10.1052	−0.441446
$525$	4.76403	0.207919
$526$	−15.5696	−0.678868
$527$	7.39114	0.321963
$528$	−3.40121	−0.148019
$529$	−18.7635	−0.815805
$530$	30.2581	1.31433
$531$	−13.8378	−0.600511
$532$	7.98967	0.346396
$533$	9.86783	0.427423
$534$	−14.5827	−0.631057
$535$	30.1188	1.30215
$536$	−21.9076	−0.946263
$537$	13.3056	0.574178
$538$	3.99010	0.172025
$539$	16.6373	0.716619
$540$	−13.8328	−0.595271
$541$	20.5806	0.884827	0.442414	−	0.896811i	$-0.354122\pi$
$541$	20.5806	0.884827	0.442414	+	0.896811i	$0.354122\pi$
$542$	−12.1450	−0.521673
$543$	−19.8083	−0.850054
$544$	32.4396	1.39083
$545$	12.2949	0.526655
$546$	7.14412	0.305740
$547$	−8.40402	−0.359330	−0.179665	−	0.983728i	$-0.557501\pi$
$547$	−8.40402	−0.359330	−0.179665	+	0.983728i	$0.557501\pi$
$548$	−6.99986	−0.299019
$549$	−9.97267	−0.425623
$550$	−3.52235	−0.150193
$551$	−1.38612	−0.0590507
$552$	−7.34183	−0.312489
$553$	−23.5951	−1.00337
$554$	−11.6260	−0.493939
$555$	−6.85030	−0.290779
$556$	−3.19876	−0.135658
$557$	−22.4327	−0.950503	−0.475251	−	0.879850i	$-0.657643\pi$
$557$	−22.4327	−0.950503	−0.475251	+	0.879850i	$0.657643\pi$
$558$	−1.80168	−0.0762712
$559$	−10.9367	−0.462575
$560$	7.90863	0.334201
$561$	−23.8862	−1.00847
$562$	−6.42216	−0.270903
$563$	14.9594	0.630464	0.315232	−	0.949015i	$-0.397918\pi$
$563$	14.9594	0.630464	0.315232	+	0.949015i	$0.397918\pi$
$564$	−1.52669	−0.0642852
$565$	2.47739	0.104225
$566$	−31.0326	−1.30440
$567$	−6.29110	−0.264201
$568$	2.98834	0.125388
$569$	−14.3425	−0.601270	−0.300635	−	0.953739i	$-0.597199\pi$
$569$	−14.3425	−0.601270	−0.300635	+	0.953739i	$0.597199\pi$
$570$	−6.51136	−0.272731
$571$	6.88659	0.288195	0.144097	−	0.989564i	$-0.453972\pi$
$571$	6.88659	0.288195	0.144097	+	0.989564i	$0.453972\pi$
$572$	5.52445	0.230989
$573$	−25.2659	−1.05550
$574$	19.8438	0.828264
$575$	−2.34121	−0.0976351
$576$	−10.7738	−0.448908
$577$	7.96884	0.331747	0.165874	−	0.986147i	$-0.446956\pi$
$577$	7.96884	0.331747	0.165874	+	0.986147i	$0.446956\pi$
$578$	−23.5547	−0.979748
$579$	−18.4356	−0.766159
$580$	1.57651	0.0654609
$581$	1.25497	0.0520649
$582$	3.37177	0.139765
$583$	38.6895	1.60235
$584$	−10.3792	−0.429496
$585$	−6.73251	−0.278355
$586$	3.72863	0.154028
$587$	−1.47284	−0.0607906	−0.0303953	−	0.999538i	$-0.509677\pi$
$587$	−1.47284	−0.0607906	−0.0303953	+	0.999538i	$0.509677\pi$
$588$	−6.48285	−0.267348
$589$	2.57625	0.106153
$590$	21.5175	0.885861
$591$	17.3968	0.715609
$592$	−2.10759	−0.0866212
$593$	−15.8033	−0.648962	−0.324481	−	0.945892i	$-0.605190\pi$
$593$	−15.8033	−0.648962	−0.324481	+	0.945892i	$0.605190\pi$
$594$	16.9114	0.693884
$595$	55.5411	2.27696
$596$	−9.58070	−0.392441
$597$	−6.98724	−0.285969
$598$	−3.51087	−0.143570
$599$	40.1772	1.64160	0.820798	−	0.571218i	$-0.193529\pi$
$599$	40.1772	1.64160	0.820798	+	0.571218i	$0.193529\pi$
$600$	4.05732	0.165639
$601$	31.0405	1.26617	0.633084	−	0.774083i	$-0.281789\pi$
$601$	31.0405	1.26617	0.633084	+	0.774083i	$0.281789\pi$
$602$	−21.9933	−0.896381
$603$	11.5481	0.470274
$604$	−2.90319	−0.118129
$605$	2.94969	0.119922
$606$	−9.70707	−0.394323
$607$	−25.2602	−1.02528	−0.512640	−	0.858604i	$-0.671332\pi$
$607$	−25.2602	−1.02528	−0.512640	+	0.858604i	$0.671332\pi$
$608$	11.3071	0.458564
$609$	2.60679	0.105632
$610$	15.5073	0.627871
$611$	−2.15816	−0.0873100
$612$	−10.2904	−0.415965
$613$	−12.9381	−0.522565	−0.261282	−	0.965262i	$-0.584145\pi$
$613$	−12.9381	−0.522565	−0.261282	+	0.965262i	$0.584145\pi$
$614$	9.25525	0.373511
$615$	16.9142	0.682045
$616$	32.8410	1.32320
$617$	−46.8093	−1.88447	−0.942236	−	0.334951i	$-0.891280\pi$
$617$	−46.8093	−1.88447	−0.942236	+	0.334951i	$0.891280\pi$
$618$	−1.44866	−0.0582735
$619$	30.6579	1.23224	0.616122	−	0.787651i	$-0.288703\pi$
$619$	30.6579	1.23224	0.616122	+	0.787651i	$0.288703\pi$
$620$	−2.93011	−0.117676
$621$	11.2405	0.451068
$622$	0.431741	0.0173112
$623$	43.3569	1.73706
$624$	1.87348	0.0749994
$625$	−29.3935	−1.17574
$626$	−2.65914	−0.106281
$627$	−8.32574	−0.332498
$628$	−15.9880	−0.637991
$629$	−14.8012	−0.590164
$630$	−13.5388	−0.539399
$631$	−41.4286	−1.64925	−0.824623	−	0.565683i	$-0.808613\pi$
$631$	−41.4286	−1.64925	−0.824623	+	0.565683i	$0.808613\pi$
$632$	−20.0950	−0.799336
$633$	−18.9631	−0.753714
$634$	−3.53455	−0.140375
$635$	50.0017	1.98426
$636$	−15.0757	−0.597789
$637$	−9.16431	−0.363103
$638$	−1.92737	−0.0763052
$639$	−1.57524	−0.0623154
$640$	−8.40320	−0.332166
$641$	−16.4013	−0.647811	−0.323905	−	0.946089i	$-0.604996\pi$
$641$	−16.4013	−0.647811	−0.323905	+	0.946089i	$0.604996\pi$
$642$	14.3479	0.566268
$643$	−38.3101	−1.51080	−0.755401	−	0.655262i	$-0.772558\pi$
$643$	−38.3101	−1.51080	−0.755401	+	0.655262i	$0.772558\pi$
$644$	7.38414	0.290976
$645$	−18.7463	−0.738137
$646$	−14.0689	−0.553534
$647$	5.42976	0.213466	0.106733	−	0.994288i	$-0.465961\pi$
$647$	5.42976	0.213466	0.106733	+	0.994288i	$0.465961\pi$
$648$	−5.35786	−0.210477
$649$	27.5133	1.07999
$650$	1.94021	0.0761014
$651$	−4.84500	−0.189890
$652$	−22.4210	−0.878075
$653$	22.9083	0.896471	0.448236	−	0.893915i	$-0.352053\pi$
$653$	22.9083	0.896471	0.448236	+	0.893915i	$0.352053\pi$
$654$	5.85702	0.229027
$655$	−24.4853	−0.956720
$656$	5.20387	0.203177
$657$	5.47118	0.213451
$658$	−4.33998	−0.169190
$659$	19.0715	0.742918	0.371459	−	0.928449i	$-0.378858\pi$
$659$	19.0715	0.742918	0.371459	+	0.928449i	$0.378858\pi$
$660$	9.46931	0.368592
$661$	46.3726	1.80368	0.901842	−	0.432067i	$-0.142216\pi$
$661$	46.3726	1.80368	0.901842	+	0.432067i	$0.142216\pi$
$662$	1.39502	0.0542189
$663$	13.1572	0.510983
$664$	1.06880	0.0414777
$665$	19.3594	0.750724
$666$	3.60798	0.139806
$667$	−1.28107	−0.0496031
$668$	−13.9130	−0.538310
$669$	3.66624	0.141745
$670$	−17.9570	−0.693738
$671$	19.8283	0.765464
$672$	−21.2646	−0.820300
$673$	−29.3900	−1.13290	−0.566450	−	0.824096i	$-0.691683\pi$
$673$	−29.3900	−1.13290	−0.566450	+	0.824096i	$0.691683\pi$
$674$	−14.0908	−0.542757
$675$	−6.21187	−0.239095
$676$	10.2485	0.394174
$677$	20.1203	0.773286	0.386643	−	0.922229i	$-0.373635\pi$
$677$	20.1203	0.773286	0.386643	+	0.922229i	$0.373635\pi$
$678$	1.18017	0.0453243
$679$	−10.0248	−0.384718
$680$	47.3020	1.81395
$681$	−1.58948	−0.0609089
$682$	3.58222	0.137170
$683$	−15.2723	−0.584379	−0.292190	−	0.956360i	$-0.594384\pi$
$683$	−15.2723	−0.584379	−0.292190	+	0.956360i	$0.594384\pi$
$684$	−3.58682	−0.137145
$685$	−16.9610	−0.648047
$686$	5.85596	0.223582
$687$	9.56606	0.364968
$688$	−5.76756	−0.219886
$689$	−21.3113	−0.811896
$690$	−6.01787	−0.229096
$691$	−46.0899	−1.75334	−0.876672	−	0.481089i	$-0.840241\pi$
$691$	−46.0899	−1.75334	−0.876672	+	0.481089i	$0.840241\pi$
$692$	1.99145	0.0757034
$693$	−17.3114	−0.657604
$694$	−17.9064	−0.679718
$695$	−7.75075	−0.294003
$696$	2.22009	0.0841525
$697$	36.5459	1.38428
$698$	−4.77393	−0.180696
$699$	8.55667	0.323643
$700$	−4.08070	−0.154236
$701$	12.4739	0.471132	0.235566	−	0.971858i	$-0.424306\pi$
$701$	12.4739	0.471132	0.235566	+	0.971858i	$0.424306\pi$
$702$	−9.31530	−0.351583
$703$	−5.15911	−0.194580
$704$	21.4212	0.807341
$705$	−3.69925	−0.139322
$706$	12.8030	0.481849
$707$	28.8607	1.08542
$708$	−10.7208	−0.402911
$709$	−2.55898	−0.0961045	−0.0480522	−	0.998845i	$-0.515301\pi$
$709$	−2.55898	−0.0961045	−0.0480522	+	0.998845i	$0.515301\pi$
$710$	2.44945	0.0919263
$711$	10.5926	0.397254
$712$	36.9253	1.38383
$713$	2.38100	0.0891692
$714$	26.4585	0.990186
$715$	13.3860	0.500609
$716$	−11.3971	−0.425930
$717$	16.7932	0.627153
$718$	−15.6968	−0.585800
$719$	18.5667	0.692422	0.346211	−	0.938157i	$-0.387468\pi$
$719$	18.5667	0.692422	0.346211	+	0.938157i	$0.387468\pi$
$720$	−3.55044	−0.132317
$721$	4.30710	0.160405
$722$	13.8819	0.516630
$723$	19.3005	0.717793
$724$	16.9671	0.630576
$725$	0.707957	0.0262929
$726$	1.40517	0.0521507
$727$	3.19334	0.118435	0.0592173	−	0.998245i	$-0.481140\pi$
$727$	3.19334	0.118435	0.0592173	+	0.998245i	$0.481140\pi$
$728$	−18.0898	−0.670451
$729$	22.3802	0.828895
$730$	−8.50754	−0.314878
$731$	−40.5047	−1.49812
$732$	−7.72626	−0.285571
$733$	22.8933	0.845582	0.422791	−	0.906227i	$-0.361050\pi$
$733$	22.8933	0.845582	0.422791	+	0.906227i	$0.361050\pi$
$734$	−13.2140	−0.487736
$735$	−15.7083	−0.579408
$736$	10.4502	0.385198
$737$	−22.9606	−0.845766
$738$	−8.90851	−0.327927
$739$	−44.6533	−1.64260	−0.821300	−	0.570497i	$-0.806751\pi$
$739$	−44.6533	−1.64260	−0.821300	+	0.570497i	$0.806751\pi$
$740$	5.86773	0.215702
$741$	4.58606	0.168473
$742$	−42.8561	−1.57330
$743$	−8.41303	−0.308644	−0.154322	−	0.988021i	$-0.549319\pi$
$743$	−8.41303	−0.308644	−0.154322	+	0.988021i	$0.549319\pi$
$744$	−4.12628	−0.151277
$745$	−23.2145	−0.850514
$746$	−35.0309	−1.28257
$747$	−0.563396	−0.0206136
$748$	20.4601	0.748094
$749$	−42.6588	−1.55872
$750$	−11.2931	−0.412366
$751$	26.0427	0.950312	0.475156	−	0.879902i	$-0.342392\pi$
$751$	26.0427	0.950312	0.475156	+	0.879902i	$0.342392\pi$
$752$	−1.13812	−0.0415030
$753$	−34.7617	−1.26679
$754$	1.06165	0.0386630
$755$	−7.03458	−0.256015
$756$	19.5922	0.712560
$757$	−29.3436	−1.06651	−0.533255	−	0.845955i	$-0.679031\pi$
$757$	−29.3436	−1.06651	−0.533255	+	0.845955i	$0.679031\pi$
$758$	−20.0085	−0.726742
$759$	−7.69474	−0.279301
$760$	16.4876	0.598066
$761$	45.0882	1.63445	0.817223	−	0.576322i	$-0.195513\pi$
$761$	45.0882	1.63445	0.817223	+	0.576322i	$0.195513\pi$
$762$	23.8197	0.862896
$763$	−17.4139	−0.630425
$764$	21.6419	0.782976
$765$	−24.9342	−0.901496
$766$	−12.8168	−0.463089
$767$	−15.1551	−0.547220
$768$	−20.3308	−0.733624
$769$	11.6317	0.419450	0.209725	−	0.977760i	$-0.432743\pi$
$769$	11.6317	0.419450	0.209725	+	0.977760i	$0.432743\pi$
$770$	26.9187	0.970084
$771$	−6.26919	−0.225779
$772$	15.7913	0.568342
$773$	−44.9987	−1.61849	−0.809245	−	0.587471i	$-0.800124\pi$
$773$	−44.9987	−1.61849	−0.809245	+	0.587471i	$0.800124\pi$
$774$	9.87350	0.354896
$775$	−1.31581	−0.0472654
$776$	−8.53774	−0.306487
$777$	9.70243	0.348073
$778$	1.32397	0.0474667
$779$	12.7384	0.456402
$780$	−5.21597	−0.186762
$781$	3.13199	0.112071
$782$	−13.0026	−0.464974
$783$	−3.39903	−0.121471
$784$	−4.83286	−0.172602
$785$	−38.7398	−1.38268
$786$	−11.6643	−0.416050
$787$	−11.0143	−0.392617	−0.196308	−	0.980542i	$-0.562895\pi$
$787$	−11.0143	−0.392617	−0.196308	+	0.980542i	$0.562895\pi$
$788$	−14.9015	−0.530844
$789$	18.7964	0.669170
$790$	−16.4712	−0.586021
$791$	−3.50885	−0.124760
$792$	−14.7434	−0.523882
$793$	−10.9220	−0.387852
$794$	−8.38381	−0.297530
$795$	−36.5291	−1.29555
$796$	5.98503	0.212134
$797$	51.4007	1.82071	0.910353	−	0.413833i	$-0.135810\pi$
$797$	51.4007	1.82071	0.910353	+	0.413833i	$0.135810\pi$
$798$	9.22237	0.326468
$799$	−7.99285	−0.282767
$800$	−5.77508	−0.204180
$801$	−19.4643	−0.687737
$802$	27.9429	0.986699
$803$	−10.8782	−0.383882
$804$	8.94679	0.315529
$805$	17.8921	0.630615
$806$	−1.97319	−0.0695026
$807$	−4.81704	−0.169568
$808$	24.5795	0.864703
$809$	16.4132	0.577059	0.288529	−	0.957471i	$-0.406834\pi$
$809$	16.4132	0.577059	0.288529	+	0.957471i	$0.406834\pi$
$810$	−4.39168	−0.154308
$811$	−4.95974	−0.174160	−0.0870800	−	0.996201i	$-0.527754\pi$
$811$	−4.95974	−0.174160	−0.0870800	+	0.996201i	$0.527754\pi$
$812$	−2.23289	−0.0783590
$813$	14.6621	0.514221
$814$	−7.17362	−0.251435
$815$	−54.3273	−1.90300
$816$	6.93853	0.242897
$817$	−14.1183	−0.493936
$818$	17.0717	0.596897
$819$	9.53560	0.333201
$820$	−14.4881	−0.505946
$821$	−14.8743	−0.519117	−0.259559	−	0.965727i	$-0.583577\pi$
$821$	−14.8743	−0.519117	−0.259559	+	0.965727i	$0.583577\pi$
$822$	−8.07985	−0.281817
$823$	6.18228	0.215501	0.107750	−	0.994178i	$-0.465635\pi$
$823$	6.18228	0.215501	0.107750	+	0.994178i	$0.465635\pi$
$824$	3.66817	0.127787
$825$	4.25235	0.148048
$826$	−30.4763	−1.06041
$827$	5.85093	0.203457	0.101728	−	0.994812i	$-0.467563\pi$
$827$	5.85093	0.203457	0.101728	+	0.994812i	$0.467563\pi$
$828$	−3.31498	−0.115203
$829$	−35.1444	−1.22062	−0.610308	−	0.792164i	$-0.708954\pi$
$829$	−35.1444	−1.22062	−0.610308	+	0.792164i	$0.708954\pi$
$830$	0.876066	0.0304087
$831$	14.0354	0.486883
$832$	−11.7994	−0.409071
$833$	−33.9404	−1.17597
$834$	−3.69229	−0.127853
$835$	−33.7119	−1.16665
$836$	7.13155	0.246650
$837$	6.31745	0.218363
$838$	−12.2983	−0.424838
$839$	−24.2239	−0.836302	−0.418151	−	0.908377i	$-0.637322\pi$
$839$	−24.2239	−0.836302	−0.418151	+	0.908377i	$0.637322\pi$
$840$	−31.0071	−1.06985
$841$	−28.6126	−0.986642
$842$	−8.92987	−0.307744
$843$	7.75315	0.267033
$844$	16.2431	0.559111
$845$	24.8327	0.854270
$846$	1.94835	0.0669858
$847$	−4.17780	−0.143551
$848$	−11.2387	−0.385937
$849$	37.4640	1.28576
$850$	7.18566	0.246466
$851$	−4.76811	−0.163449
$852$	−1.22040	−0.0418103
$853$	−23.0652	−0.789738	−0.394869	−	0.918737i	$-0.629210\pi$
$853$	−23.0652	−0.789738	−0.394869	+	0.918737i	$0.629210\pi$
$854$	−21.9637	−0.751583
$855$	−8.69104	−0.297227
$856$	−36.3307	−1.24176
$857$	10.5357	0.359894	0.179947	−	0.983676i	$-0.442407\pi$
$857$	10.5357	0.359894	0.179947	+	0.983676i	$0.442407\pi$
$858$	6.37681	0.217701
$859$	49.0554	1.67375	0.836874	−	0.547395i	$-0.184381\pi$
$859$	49.0554	1.67375	0.836874	+	0.547395i	$0.184381\pi$
$860$	16.0575	0.547556
$861$	−23.9564	−0.816431
$862$	−18.9713	−0.646165
$863$	−5.42817	−0.184777	−0.0923885	−	0.995723i	$-0.529450\pi$
$863$	−5.42817	−0.184777	−0.0923885	+	0.995723i	$0.529450\pi$
$864$	27.7272	0.943297
$865$	4.82537	0.164068
$866$	−34.5943	−1.17556
$867$	28.4364	0.965752
$868$	4.15006	0.140862
$869$	−21.0609	−0.714443
$870$	1.81974	0.0616951
$871$	12.6474	0.428540
$872$	−14.8307	−0.502230
$873$	4.50047	0.152318
$874$	−4.53219	−0.153304
$875$	33.5763	1.13508
$876$	4.23876	0.143214
$877$	20.3603	0.687517	0.343759	−	0.939058i	$-0.388300\pi$
$877$	20.3603	0.687517	0.343759	+	0.939058i	$0.388300\pi$
$878$	−2.71843	−0.0917427
$879$	−4.50138	−0.151828
$880$	7.05921	0.237966
$881$	−27.5526	−0.928271	−0.464135	−	0.885764i	$-0.653635\pi$
$881$	−27.5526	−0.928271	−0.464135	+	0.885764i	$0.653635\pi$
$882$	8.27338	0.278579
$883$	0.631731	0.0212594	0.0106297	−	0.999944i	$-0.496616\pi$
$883$	0.631731	0.0212594	0.0106297	+	0.999944i	$0.496616\pi$
$884$	−11.2700	−0.379051
$885$	−25.9770	−0.873206
$886$	16.7606	0.563084
$887$	12.8233	0.430563	0.215281	−	0.976552i	$-0.430933\pi$
$887$	12.8233	0.430563	0.215281	+	0.976552i	$0.430933\pi$
$888$	8.26315	0.277293
$889$	−70.8199	−2.37522
$890$	30.2665	1.01454
$891$	−5.61541	−0.188123
$892$	−3.14037	−0.105148
$893$	−2.78598	−0.0932294
$894$	−11.0589	−0.369865
$895$	−27.6158	−0.923093
$896$	11.9019	0.397614
$897$	4.23849	0.141519
$898$	−38.9027	−1.29820
$899$	−0.719990	−0.0240130
$900$	1.83196	0.0610652
$901$	−78.9273	−2.62945
$902$	17.7125	0.589761
$903$	26.5514	0.883575
$904$	−2.98834	−0.0993908
$905$	41.1121	1.36661
$906$	−3.35112	−0.111334
$907$	34.8631	1.15761	0.578805	−	0.815466i	$-0.303519\pi$
$907$	34.8631	1.15761	0.578805	+	0.815466i	$0.303519\pi$
$908$	1.36149	0.0451827
$909$	−12.9565	−0.429740
$910$	−14.8276	−0.491531
$911$	−21.3588	−0.707648	−0.353824	−	0.935312i	$-0.615119\pi$
$911$	−21.3588	−0.707648	−0.353824	+	0.935312i	$0.615119\pi$
$912$	2.41849	0.0800842
$913$	1.12018	0.0370726
$914$	18.6270	0.616128
$915$	−18.7211	−0.618901
$916$	−8.19396	−0.270736
$917$	34.6798	1.14523
$918$	−34.4996	−1.13866
$919$	−32.0029	−1.05568	−0.527838	−	0.849345i	$-0.676997\pi$
$919$	−32.0029	−1.05568	−0.527838	+	0.849345i	$0.676997\pi$
$920$	15.2380	0.502381
$921$	−11.1734	−0.368176
$922$	−0.414162	−0.0136397
$923$	−1.72519	−0.0567853
$924$	−13.4119	−0.441218
$925$	2.63500	0.0866384
$926$	−6.88080	−0.226117
$927$	−1.93359	−0.0635075
$928$	−3.16002	−0.103733
$929$	−21.5611	−0.707396	−0.353698	−	0.935360i	$-0.615076\pi$
$929$	−21.5611	−0.707396	−0.353698	+	0.935360i	$0.615076\pi$
$930$	−3.38219	−0.110906
$931$	−11.8302	−0.387721
$932$	−7.32935	−0.240081
$933$	−0.521219	−0.0170639
$934$	−16.0492	−0.525145
$935$	49.5757	1.62130
$936$	8.12107	0.265445
$937$	4.48705	0.146586	0.0732928	−	0.997310i	$-0.476649\pi$
$937$	4.48705	0.146586	0.0732928	+	0.997310i	$0.476649\pi$
$938$	25.4334	0.830428
$939$	3.21024	0.104762
$940$	3.16865	0.103350
$941$	−5.64303	−0.183957	−0.0919787	−	0.995761i	$-0.529319\pi$
$941$	−5.64303	−0.183957	−0.0919787	+	0.995761i	$0.529319\pi$
$942$	−18.4548	−0.601289
$943$	11.7730	0.383382
$944$	−7.99216	−0.260123
$945$	47.4728	1.54429
$946$	−19.6311	−0.638264
$947$	6.40732	0.208210	0.104105	−	0.994566i	$-0.466802\pi$
$947$	6.40732	0.208210	0.104105	+	0.994566i	$0.466802\pi$
$948$	8.20655	0.266536
$949$	5.99200	0.194509
$950$	2.50463	0.0812609
$951$	4.26708	0.138369
$952$	−66.9962	−2.17136
$953$	14.3935	0.466252	0.233126	−	0.972447i	$-0.425105\pi$
$953$	14.3935	0.466252	0.233126	+	0.972447i	$0.425105\pi$
$954$	19.2395	0.622901
$955$	52.4394	1.69690
$956$	−14.3845	−0.465227
$957$	2.32681	0.0752151
$958$	12.6294	0.408038
$959$	24.0227	0.775735
$960$	−20.2250	−0.652760
$961$	−29.6618	−0.956833
$962$	3.95144	0.127400
$963$	19.1509	0.617130
$964$	−16.5321	−0.532464
$965$	38.2632	1.23174
$966$	8.52342	0.274236
$967$	−38.4709	−1.23714	−0.618571	−	0.785729i	$-0.712288\pi$
$967$	−38.4709	−1.23714	−0.618571	+	0.785729i	$0.712288\pi$
$968$	−3.55806	−0.114360
$969$	16.9847	0.545626
$970$	−6.99812	−0.224696
$971$	−27.0749	−0.868874	−0.434437	−	0.900702i	$-0.643053\pi$
$971$	−27.0749	−0.868874	−0.434437	+	0.900702i	$0.643053\pi$
$972$	−14.5628	−0.467103
$973$	10.9778	0.351931
$974$	−11.8532	−0.379801
$975$	−2.34232	−0.0750142
$976$	−5.75980	−0.184367
$977$	53.2078	1.70227	0.851134	−	0.524949i	$-0.175916\pi$
$977$	53.2078	1.70227	0.851134	+	0.524949i	$0.175916\pi$
$978$	−25.8803	−0.827561
$979$	38.7002	1.23686
$980$	13.4552	0.429810
$981$	7.81765	0.249598
$982$	−4.92569	−0.157185
$983$	−30.8877	−0.985165	−0.492582	−	0.870266i	$-0.663947\pi$
$983$	−30.8877	−0.985165	−0.492582	+	0.870266i	$0.663947\pi$
$984$	−20.4026	−0.650413
$985$	−36.1071	−1.15047
$986$	3.93187	0.125216
$987$	5.23943	0.166773
$988$	−3.92826	−0.124975
$989$	−13.0483	−0.414911
$990$	−12.0847	−0.384076
$991$	45.1465	1.43413	0.717064	−	0.697008i	$-0.245486\pi$
$991$	45.1465	1.43413	0.717064	+	0.697008i	$0.245486\pi$
$992$	5.87324	0.186475
$993$	−1.68413	−0.0534443
$994$	−3.46928	−0.110039
$995$	14.5020	0.459745
$996$	−0.436487	−0.0138306
$997$	−32.1171	−1.01716	−0.508579	−	0.861016i	$-0.669829\pi$
$997$	−32.1171	−1.01716	−0.508579	+	0.861016i	$0.669829\pi$
$998$	−18.3854	−0.581979
$999$	−12.6511	−0.400263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.54	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.54	✓	165	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-0.988723 q^{2} +1.19363 q^{3} -1.02243 q^{4} -2.47739 q^{5} -1.18017 q^{6} +3.50885 q^{7} +2.98834 q^{8} -1.57524 q^{9} +O(q^{10})\)	\(q-0.988723 q^{2} +1.19363 q^{3} -1.02243 q^{4} -2.47739 q^{5} -1.18017 q^{6} +3.50885 q^{7} +2.98834 q^{8} -1.57524 q^{9} +2.44945 q^{10} +3.13199 q^{11} -1.22040 q^{12} -1.72519 q^{13} -3.46928 q^{14} -2.95710 q^{15} -0.909791 q^{16} -6.38932 q^{17} +1.55747 q^{18} -2.22706 q^{19} +2.53295 q^{20} +4.18829 q^{21} -3.09667 q^{22} -2.05827 q^{23} +3.56699 q^{24} +1.13746 q^{25} +1.70574 q^{26} -5.46116 q^{27} -3.58755 q^{28} +0.622400 q^{29} +2.92375 q^{30} -1.15680 q^{31} -5.07715 q^{32} +3.73845 q^{33} +6.31727 q^{34} -8.69280 q^{35} +1.61056 q^{36} +2.31656 q^{37} +2.20194 q^{38} -2.05925 q^{39} -7.40329 q^{40} -5.71985 q^{41} -4.14106 q^{42} +6.33944 q^{43} -3.20223 q^{44} +3.90248 q^{45} +2.03506 q^{46} +1.25097 q^{47} -1.08596 q^{48} +5.31205 q^{49} -1.12464 q^{50} -7.62651 q^{51} +1.76388 q^{52} +12.3530 q^{53} +5.39958 q^{54} -7.75916 q^{55} +10.4857 q^{56} -2.65829 q^{57} -0.615381 q^{58} +8.78461 q^{59} +3.02342 q^{60} +6.33091 q^{61} +1.14375 q^{62} -5.52727 q^{63} +6.83948 q^{64} +4.27397 q^{65} -3.69629 q^{66} -7.33101 q^{67} +6.53261 q^{68} -2.45682 q^{69} +8.59477 q^{70} +1.00000 q^{71} -4.70735 q^{72} -3.47324 q^{73} -2.29044 q^{74} +1.35772 q^{75} +2.27700 q^{76} +10.9897 q^{77} +2.03603 q^{78} -6.72446 q^{79} +2.25391 q^{80} -1.79292 q^{81} +5.65535 q^{82} +0.357658 q^{83} -4.28222 q^{84} +15.8288 q^{85} -6.26795 q^{86} +0.742918 q^{87} +9.35946 q^{88} +12.3564 q^{89} -3.85847 q^{90} -6.05344 q^{91} +2.10443 q^{92} -1.38079 q^{93} -1.23686 q^{94} +5.51729 q^{95} -6.06027 q^{96} -2.85701 q^{97} -5.25215 q^{98} -4.93362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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