LMFDB - Embedded newform 8023.2.a.b.1.1

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:	$1$
Dimension:	$155$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.80015 q^{2} +0.646146 q^{3} +5.84081 q^{4} +1.34449 q^{5} -1.80930 q^{6} +3.74304 q^{7} -10.7548 q^{8} -2.58250 q^{9} +O(q^{10})$	\(q-2.80015 q^{2} +0.646146 q^{3} +5.84081 q^{4} +1.34449 q^{5} -1.80930 q^{6} +3.74304 q^{7} -10.7548 q^{8} -2.58250 q^{9} -3.76478 q^{10} -1.15108 q^{11} +3.77402 q^{12} -0.0402384 q^{13} -10.4810 q^{14} +0.868739 q^{15} +18.4335 q^{16} -2.62332 q^{17} +7.23136 q^{18} +6.82350 q^{19} +7.85294 q^{20} +2.41855 q^{21} +3.22318 q^{22} +1.41994 q^{23} -6.94919 q^{24} -3.19233 q^{25} +0.112673 q^{26} -3.60710 q^{27} +21.8624 q^{28} -5.19278 q^{29} -2.43260 q^{30} +0.612083 q^{31} -30.1067 q^{32} -0.743763 q^{33} +7.34567 q^{34} +5.03249 q^{35} -15.0839 q^{36} -6.12740 q^{37} -19.1068 q^{38} -0.0259999 q^{39} -14.4598 q^{40} +5.00727 q^{41} -6.77228 q^{42} +7.14329 q^{43} -6.72322 q^{44} -3.47215 q^{45} -3.97604 q^{46} -10.3857 q^{47} +11.9107 q^{48} +7.01033 q^{49} +8.93900 q^{50} -1.69504 q^{51} -0.235025 q^{52} -10.3820 q^{53} +10.1004 q^{54} -1.54762 q^{55} -40.2558 q^{56} +4.40898 q^{57} +14.5405 q^{58} -8.23962 q^{59} +5.07414 q^{60} -3.48909 q^{61} -1.71392 q^{62} -9.66638 q^{63} +47.4363 q^{64} -0.0541003 q^{65} +2.08264 q^{66} -6.73723 q^{67} -15.3223 q^{68} +0.917489 q^{69} -14.0917 q^{70} +1.00000 q^{71} +27.7743 q^{72} -5.65598 q^{73} +17.1576 q^{74} -2.06271 q^{75} +39.8548 q^{76} -4.30852 q^{77} +0.0728034 q^{78} -4.90042 q^{79} +24.7837 q^{80} +5.41677 q^{81} -14.0211 q^{82} +2.68722 q^{83} +14.1263 q^{84} -3.52703 q^{85} -20.0022 q^{86} -3.35529 q^{87} +12.3796 q^{88} +9.48268 q^{89} +9.72253 q^{90} -0.150614 q^{91} +8.29362 q^{92} +0.395495 q^{93} +29.0813 q^{94} +9.17416 q^{95} -19.4533 q^{96} -14.4334 q^{97} -19.6299 q^{98} +2.97265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) $ 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * 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 $

$2$	−2.80015	−1.98000	−0.990001	−	0.141061i	$-0.954949\pi$
$2$	−2.80015	−1.98000	−0.990001	+	0.141061i	$0.954949\pi$
$3$	0.646146	0.373052	0.186526	−	0.982450i	$-0.440277\pi$
$3$	0.646146	0.373052	0.186526	+	0.982450i	$0.440277\pi$
$4$	5.84081	2.92041
$5$	1.34449	0.601276	0.300638	−	0.953738i	$-0.402800\pi$
$5$	1.34449	0.601276	0.300638	+	0.953738i	$0.402800\pi$
$6$	−1.80930	−0.738644
$7$	3.74304	1.41474	0.707368	−	0.706846i	$-0.249883\pi$
$7$	3.74304	1.41474	0.707368	+	0.706846i	$0.249883\pi$
$8$	−10.7548	−3.80241
$9$	−2.58250	−0.860832
$10$	−3.76478	−1.19053
$11$	−1.15108	−0.347062	−0.173531	−	0.984828i	$-0.555518\pi$
$11$	−1.15108	−0.347062	−0.173531	+	0.984828i	$0.555518\pi$
$12$	3.77402	1.08946
$13$	−0.0402384	−0.0111601	−0.00558007	−	0.999984i	$-0.501776\pi$
$13$	−0.0402384	−0.0111601	−0.00558007	+	0.999984i	$0.501776\pi$
$14$	−10.4810	−2.80118
$15$	0.868739	0.224307
$16$	18.4335	4.60837
$17$	−2.62332	−0.636248	−0.318124	−	0.948049i	$-0.603053\pi$
$17$	−2.62332	−0.636248	−0.318124	+	0.948049i	$0.603053\pi$
$18$	7.23136	1.70445
$19$	6.82350	1.56542	0.782709	−	0.622387i	$-0.213837\pi$
$19$	6.82350	1.56542	0.782709	+	0.622387i	$0.213837\pi$
$20$	7.85294	1.75597
$21$	2.41855	0.527770
$22$	3.22318	0.687184
$23$	1.41994	0.296078	0.148039	−	0.988981i	$-0.452704\pi$
$23$	1.41994	0.296078	0.148039	+	0.988981i	$0.452704\pi$
$24$	−6.94919	−1.41850
$25$	−3.19233	−0.638467
$26$	0.112673	0.0220971
$27$	−3.60710	−0.694188
$28$	21.8624	4.13160
$29$	−5.19278	−0.964276	−0.482138	−	0.876095i	$-0.660140\pi$
$29$	−5.19278	−0.964276	−0.482138	+	0.876095i	$0.660140\pi$
$30$	−2.43260	−0.444129
$31$	0.612083	0.109933	0.0549667	−	0.998488i	$-0.482495\pi$
$31$	0.612083	0.109933	0.0549667	+	0.998488i	$0.482495\pi$
$32$	−30.1067	−5.32217
$33$	−0.743763	−0.129472
$34$	7.34567	1.25977
$35$	5.03249	0.850647
$36$	−15.0839	−2.51398
$37$	−6.12740	−1.00734	−0.503669	−	0.863897i	$-0.668017\pi$
$37$	−6.12740	−1.00734	−0.503669	+	0.863897i	$0.668017\pi$
$38$	−19.1068	−3.09953
$39$	−0.0259999	−0.00416331
$40$	−14.4598	−2.28630
$41$	5.00727	0.782004	0.391002	−	0.920390i	$-0.372129\pi$
$41$	5.00727	0.782004	0.391002	+	0.920390i	$0.372129\pi$
$42$	−6.77228	−1.04499
$43$	7.14329	1.08934	0.544671	−	0.838650i	$-0.316655\pi$
$43$	7.14329	1.08934	0.544671	+	0.838650i	$0.316655\pi$
$44$	−6.72322	−1.01356
$45$	−3.47215	−0.517598
$46$	−3.97604	−0.586236
$47$	−10.3857	−1.51490	−0.757451	−	0.652891i	$-0.773556\pi$
$47$	−10.3857	−1.51490	−0.757451	+	0.652891i	$0.773556\pi$
$48$	11.9107	1.71916
$49$	7.01033	1.00148
$50$	8.93900	1.26417
$51$	−1.69504	−0.237354
$52$	−0.235025	−0.0325921
$53$	−10.3820	−1.42608	−0.713041	−	0.701123i	$-0.752682\pi$
$53$	−10.3820	−1.42608	−0.713041	+	0.701123i	$0.752682\pi$
$54$	10.1004	1.37449
$55$	−1.54762	−0.208680
$56$	−40.2558	−5.37940
$57$	4.40898	0.583983
$58$	14.5405	1.90927
$59$	−8.23962	−1.07271	−0.536353	−	0.843994i	$-0.680199\pi$
$59$	−8.23962	−1.07271	−0.536353	+	0.843994i	$0.680199\pi$
$60$	5.07414	0.655069
$61$	−3.48909	−0.446733	−0.223366	−	0.974735i	$-0.571705\pi$
$61$	−3.48909	−0.446733	−0.223366	+	0.974735i	$0.571705\pi$
$62$	−1.71392	−0.217668
$63$	−9.66638	−1.21785
$64$	47.4363	5.92954
$65$	−0.0541003	−0.00671032
$66$	2.08264	0.256356
$67$	−6.73723	−0.823084	−0.411542	−	0.911391i	$-0.635010\pi$
$67$	−6.73723	−0.823084	−0.411542	+	0.911391i	$0.635010\pi$
$68$	−15.3223	−1.85810
$69$	0.917489	0.110453
$70$	−14.0917	−1.68428
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	27.7743	3.27323
$73$	−5.65598	−0.661983	−0.330991	−	0.943634i	$-0.607383\pi$
$73$	−5.65598	−0.661983	−0.330991	+	0.943634i	$0.607383\pi$
$74$	17.1576	1.99453
$75$	−2.06271	−0.238182
$76$	39.8548	4.57166
$77$	−4.30852	−0.491001
$78$	0.0728034	0.00824337
$79$	−4.90042	−0.551340	−0.275670	−	0.961252i	$-0.588900\pi$
$79$	−4.90042	−0.551340	−0.275670	+	0.961252i	$0.588900\pi$
$80$	24.7837	2.77090
$81$	5.41677	0.601864
$82$	−14.0211	−1.54837
$83$	2.68722	0.294961	0.147480	−	0.989065i	$-0.452884\pi$
$83$	2.68722	0.294961	0.147480	+	0.989065i	$0.452884\pi$
$84$	14.1263	1.54130
$85$	−3.52703	−0.382561
$86$	−20.0022	−2.15690
$87$	−3.35529	−0.359725
$88$	12.3796	1.31967
$89$	9.48268	1.00516	0.502581	−	0.864530i	$-0.332384\pi$
$89$	9.48268	1.00516	0.502581	+	0.864530i	$0.332384\pi$
$90$	9.72253	1.02484
$91$	−0.150614	−0.0157886
$92$	8.29362	0.864669
$93$	0.395495	0.0410109
$94$	29.0813	2.99951
$95$	9.17416	0.941249
$96$	−19.4533	−1.98545
$97$	−14.4334	−1.46549	−0.732743	−	0.680505i	$-0.761760\pi$
$97$	−14.4334	−1.46549	−0.732743	+	0.680505i	$0.761760\pi$
$98$	−19.6299	−1.98292
$99$	2.97265	0.298762
$100$	−18.6458	−1.86458
$101$	3.87357	0.385435	0.192717	−	0.981254i	$-0.438270\pi$
$101$	3.87357	0.385435	0.192717	+	0.981254i	$0.438270\pi$
$102$	4.74637	0.469961
$103$	1.78358	0.175742	0.0878709	−	0.996132i	$-0.471994\pi$
$103$	1.78358	0.175742	0.0878709	+	0.996132i	$0.471994\pi$
$104$	0.432758	0.0424354
$105$	3.25172	0.317336
$106$	29.0712	2.82364
$107$	0.904308	0.0874227	0.0437114	−	0.999044i	$-0.486082\pi$
$107$	0.904308	0.0874227	0.0437114	+	0.999044i	$0.486082\pi$
$108$	−21.0684	−2.02731
$109$	19.4971	1.86748	0.933740	−	0.357952i	$-0.116525\pi$
$109$	19.4971	1.86748	0.933740	+	0.357952i	$0.116525\pi$
$110$	4.33355	0.413187
$111$	−3.95919	−0.375790
$112$	68.9972	6.51962
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−12.3458	−1.15629
$115$	1.90910	0.178025
$116$	−30.3301	−2.81608
$117$	0.103916	0.00960700
$118$	23.0721	2.12396
$119$	−9.81917	−0.900122
$120$	−9.34315	−0.852909
$121$	−9.67502	−0.879548
$122$	9.76997	0.884531
$123$	3.23542	0.291728
$124$	3.57506	0.321050
$125$	−11.0145	−0.985171
$126$	27.0673	2.41134
$127$	2.78602	0.247220	0.123610	−	0.992331i	$-0.460553\pi$
$127$	2.78602	0.247220	0.123610	+	0.992331i	$0.460553\pi$
$128$	−72.6150	−6.41832
$129$	4.61560	0.406381
$130$	0.151489	0.0132864
$131$	−8.27309	−0.722824	−0.361412	−	0.932406i	$-0.617705\pi$
$131$	−8.27309	−0.722824	−0.361412	+	0.932406i	$0.617705\pi$
$132$	−4.34418	−0.378112
$133$	25.5406	2.21465
$134$	18.8652	1.62971
$135$	−4.84973	−0.417399
$136$	28.2133	2.41927
$137$	7.11386	0.607778	0.303889	−	0.952707i	$-0.401715\pi$
$137$	7.11386	0.607778	0.303889	+	0.952707i	$0.401715\pi$
$138$	−2.56910	−0.218697
$139$	−17.0789	−1.44861	−0.724305	−	0.689480i	$-0.757839\pi$
$139$	−17.0789	−1.44861	−0.724305	+	0.689480i	$0.757839\pi$
$140$	29.3939	2.48423
$141$	−6.71064	−0.565138
$142$	−2.80015	−0.234983
$143$	0.0463175	0.00387326
$144$	−47.6044	−3.96703
$145$	−6.98167	−0.579796
$146$	15.8376	1.31073
$147$	4.52969	0.373603
$148$	−35.7890	−2.94184
$149$	3.34160	0.273754	0.136877	−	0.990588i	$-0.456293\pi$
$149$	3.34160	0.273754	0.136877	+	0.990588i	$0.456293\pi$
$150$	5.77590	0.471600
$151$	−22.6505	−1.84327	−0.921634	−	0.388059i	$-0.873146\pi$
$151$	−22.6505	−1.84327	−0.921634	+	0.388059i	$0.873146\pi$
$152$	−73.3857	−5.95236
$153$	6.77470	0.547702
$154$	12.0645	0.972184
$155$	0.822942	0.0661003
$156$	−0.151860	−0.0121586
$157$	18.4333	1.47113	0.735567	−	0.677452i	$-0.236916\pi$
$157$	18.4333	1.47113	0.735567	+	0.677452i	$0.236916\pi$
$158$	13.7219	1.09165
$159$	−6.70830	−0.532003
$160$	−40.4783	−3.20009
$161$	5.31490	0.418873
$162$	−15.1678	−1.19169
$163$	−0.623093	−0.0488044	−0.0244022	−	0.999702i	$-0.507768\pi$
$163$	−0.623093	−0.0488044	−0.0244022	+	0.999702i	$0.507768\pi$
$164$	29.2465	2.28377
$165$	−0.999985	−0.0778487
$166$	−7.52460	−0.584022
$167$	13.9057	1.07606	0.538029	−	0.842926i	$-0.319169\pi$
$167$	13.9057	1.07606	0.538029	+	0.842926i	$0.319169\pi$
$168$	−26.0111	−2.00680
$169$	−12.9984	−0.999875
$170$	9.87621	0.757471
$171$	−17.6217	−1.34756
$172$	41.7226	3.18132
$173$	−5.93248	−0.451038	−0.225519	−	0.974239i	$-0.572408\pi$
$173$	−5.93248	−0.451038	−0.225519	+	0.974239i	$0.572408\pi$
$174$	9.39531	0.712257
$175$	−11.9490	−0.903262
$176$	−21.2183	−1.59939
$177$	−5.32399	−0.400176
$178$	−26.5529	−1.99022
$179$	1.67728	0.125365	0.0626827	−	0.998034i	$-0.480034\pi$
$179$	1.67728	0.125365	0.0626827	+	0.998034i	$0.480034\pi$
$180$	−20.2802	−1.51160
$181$	−18.9667	−1.40979	−0.704893	−	0.709314i	$-0.749005\pi$
$181$	−18.9667	−1.40979	−0.704893	+	0.709314i	$0.749005\pi$
$182$	0.421741	0.0312615
$183$	−2.25446	−0.166655
$184$	−15.2712	−1.12581
$185$	−8.23825	−0.605688
$186$	−1.10744	−0.0812016
$187$	3.01964	0.220818
$188$	−60.6607	−4.42413
$189$	−13.5015	−0.982092
$190$	−25.6890	−1.86367
$191$	−20.1992	−1.46156	−0.730781	−	0.682612i	$-0.760844\pi$
$191$	−20.1992	−1.46156	−0.730781	+	0.682612i	$0.760844\pi$
$192$	30.6507	2.21203
$193$	−10.6009	−0.763073	−0.381536	−	0.924354i	$-0.624605\pi$
$193$	−10.6009	−0.763073	−0.381536	+	0.924354i	$0.624605\pi$
$194$	40.4155	2.90167
$195$	−0.0349567	−0.00250330
$196$	40.9460	2.92472
$197$	−8.90308	−0.634318	−0.317159	−	0.948372i	$-0.602729\pi$
$197$	−8.90308	−0.634318	−0.317159	+	0.948372i	$0.602729\pi$
$198$	−8.32385	−0.591550
$199$	6.55299	0.464529	0.232265	−	0.972653i	$-0.425386\pi$
$199$	6.55299	0.464529	0.232265	+	0.972653i	$0.425386\pi$
$200$	34.3330	2.42771
$201$	−4.35323	−0.307053
$202$	−10.8466	−0.763162
$203$	−19.4368	−1.36419
$204$	−9.90044	−0.693169
$205$	6.73224	0.470200
$206$	−4.99430	−0.347969
$207$	−3.66699	−0.254874
$208$	−0.741734	−0.0514300
$209$	−7.85437	−0.543298
$210$	−9.10530	−0.628325
$211$	−24.9573	−1.71813	−0.859066	−	0.511864i	$-0.828955\pi$
$211$	−24.9573	−1.71813	−0.859066	+	0.511864i	$0.828955\pi$
$212$	−60.6395	−4.16474
$213$	0.646146	0.0442732
$214$	−2.53219	−0.173097
$215$	9.60411	0.654995
$216$	38.7938	2.63959
$217$	2.29105	0.155527
$218$	−54.5946	−3.69761
$219$	−3.65459	−0.246954
$220$	−9.03933	−0.609432
$221$	0.105558	0.00710061
$222$	11.0863	0.744064
$223$	−15.8977	−1.06459	−0.532294	−	0.846560i	$-0.678670\pi$
$223$	−15.8977	−1.06459	−0.532294	+	0.846560i	$0.678670\pi$
$224$	−112.691	−7.52946
$225$	8.24419	0.549613
$226$	−2.80015	−0.186263
$227$	3.44736	0.228809	0.114405	−	0.993434i	$-0.463504\pi$
$227$	3.44736	0.228809	0.114405	+	0.993434i	$0.463504\pi$
$228$	25.7520	1.70547
$229$	25.6674	1.69615	0.848074	−	0.529878i	$-0.177762\pi$
$229$	25.6674	1.69615	0.848074	+	0.529878i	$0.177762\pi$
$230$	−5.34577	−0.352490
$231$	−2.78393	−0.183169
$232$	55.8475	3.66657
$233$	2.33494	0.152967	0.0764836	−	0.997071i	$-0.475631\pi$
$233$	2.33494	0.152967	0.0764836	+	0.997071i	$0.475631\pi$
$234$	−0.290979	−0.0190219
$235$	−13.9635	−0.910875
$236$	−48.1261	−3.13274
$237$	−3.16638	−0.205679
$238$	27.4951	1.78224
$239$	16.5133	1.06815	0.534077	−	0.845436i	$-0.320659\pi$
$239$	16.5133	1.06815	0.534077	+	0.845436i	$0.320659\pi$
$240$	16.0139	1.03369
$241$	21.2476	1.36868	0.684338	−	0.729165i	$-0.260092\pi$
$241$	21.2476	1.36868	0.684338	+	0.729165i	$0.260092\pi$
$242$	27.0915	1.74151
$243$	14.3213	0.918714
$244$	−20.3791	−1.30464
$245$	9.42535	0.602164
$246$	−9.05965	−0.577622
$247$	−0.274567	−0.0174703
$248$	−6.58285	−0.418012
$249$	1.73633	0.110036
$250$	30.8423	1.95064
$251$	−11.8363	−0.747099	−0.373550	−	0.927610i	$-0.621859\pi$
$251$	−11.8363	−0.747099	−0.373550	+	0.927610i	$0.621859\pi$
$252$	−56.4595	−3.55662
$253$	−1.63446	−0.102758
$254$	−7.80127	−0.489495
$255$	−2.27898	−0.142715
$256$	108.460	6.77875
$257$	12.1118	0.755514	0.377757	−	0.925905i	$-0.376696\pi$
$257$	12.1118	0.755514	0.377757	+	0.925905i	$0.376696\pi$
$258$	−12.9244	−0.804635
$259$	−22.9351	−1.42512
$260$	−0.315990	−0.0195969
$261$	13.4103	0.830079
$262$	23.1659	1.43119
$263$	−11.0476	−0.681223	−0.340612	−	0.940204i	$-0.610634\pi$
$263$	−11.0476	−0.681223	−0.340612	+	0.940204i	$0.610634\pi$
$264$	7.99904	0.492307
$265$	−13.9586	−0.857469
$266$	−71.5175	−4.38502
$267$	6.12719	0.374978
$268$	−39.3509	−2.40374
$269$	−12.1461	−0.740563	−0.370281	−	0.928920i	$-0.620739\pi$
$269$	−12.1461	−0.740563	−0.370281	+	0.928920i	$0.620739\pi$
$270$	13.5800	0.826450
$271$	−4.01378	−0.243820	−0.121910	−	0.992541i	$-0.538902\pi$
$271$	−4.01378	−0.243820	−0.121910	+	0.992541i	$0.538902\pi$
$272$	−48.3568	−2.93206
$273$	−0.0973185	−0.00588999
$274$	−19.9199	−1.20340
$275$	3.67462	0.221588
$276$	5.35888	0.322567
$277$	−21.8895	−1.31521	−0.657607	−	0.753361i	$-0.728431\pi$
$277$	−21.8895	−1.31521	−0.657607	+	0.753361i	$0.728431\pi$
$278$	47.8233	2.86825
$279$	−1.58070	−0.0946342
$280$	−54.1236	−3.23451
$281$	16.7586	0.999736	0.499868	−	0.866102i	$-0.333382\pi$
$281$	16.7586	0.999736	0.499868	+	0.866102i	$0.333382\pi$
$282$	18.7908	1.11897
$283$	11.4103	0.678273	0.339136	−	0.940737i	$-0.389865\pi$
$283$	11.4103	0.678273	0.339136	+	0.940737i	$0.389865\pi$
$284$	5.84081	0.346589
$285$	5.92784	0.351135
$286$	−0.129696	−0.00766907
$287$	18.7424	1.10633
$288$	77.7505	4.58149
$289$	−10.1182	−0.595189
$290$	19.5497	1.14800
$291$	−9.32606	−0.546703
$292$	−33.0355	−1.93326
$293$	1.13122	0.0660865	0.0330432	−	0.999454i	$-0.489480\pi$
$293$	1.13122	0.0660865	0.0330432	+	0.999454i	$0.489480\pi$
$294$	−12.6838	−0.739734
$295$	−11.0781	−0.644993
$296$	65.8992	3.83031
$297$	4.15205	0.240926
$298$	−9.35695	−0.542034
$299$	−0.0571362	−0.00330427
$300$	−12.0479	−0.695587
$301$	26.7376	1.54113
$302$	63.4246	3.64968
$303$	2.50289	0.143787
$304$	125.781	7.21403
$305$	−4.69107	−0.268610
$306$	−18.9702	−1.08445
$307$	−7.95356	−0.453934	−0.226967	−	0.973902i	$-0.572881\pi$
$307$	−7.95356	−0.453934	−0.226967	+	0.973902i	$0.572881\pi$
$308$	−25.1653	−1.43392
$309$	1.15246	0.0655609
$310$	−2.30436	−0.130879
$311$	20.9872	1.19007	0.595036	−	0.803699i	$-0.297138\pi$
$311$	20.9872	1.19007	0.595036	+	0.803699i	$0.297138\pi$
$312$	0.279624	0.0158306
$313$	4.32979	0.244734	0.122367	−	0.992485i	$-0.460951\pi$
$313$	4.32979	0.244734	0.122367	+	0.992485i	$0.460951\pi$
$314$	−51.6158	−2.91285
$315$	−12.9964	−0.732264
$316$	−28.6224	−1.61014
$317$	−17.3106	−0.972262	−0.486131	−	0.873886i	$-0.661592\pi$
$317$	−17.3106	−0.972262	−0.486131	+	0.873886i	$0.661592\pi$
$318$	18.7842	1.05337
$319$	5.97729	0.334664
$320$	63.7778	3.56529
$321$	0.584314	0.0326132
$322$	−14.8825	−0.829368
$323$	−17.9002	−0.995994
$324$	31.6384	1.75769
$325$	0.128455	0.00712537
$326$	1.74475	0.0966328
$327$	12.5979	0.696668
$328$	−53.8523	−2.97350
$329$	−38.8739	−2.14319
$330$	2.80010	0.154141
$331$	−8.60483	−0.472964	−0.236482	−	0.971636i	$-0.575994\pi$
$331$	−8.60483	−0.472964	−0.236482	+	0.971636i	$0.575994\pi$
$332$	15.6955	0.861405
$333$	15.8240	0.867149
$334$	−38.9381	−2.13060
$335$	−9.05817	−0.494901
$336$	44.5822	2.43216
$337$	−35.3628	−1.92633	−0.963166	−	0.268907i	$-0.913338\pi$
$337$	−35.3628	−1.92633	−0.963166	+	0.268907i	$0.913338\pi$
$338$	36.3974	1.97976
$339$	0.646146	0.0350938
$340$	−20.6008	−1.11723
$341$	−0.704554	−0.0381537
$342$	49.3432	2.66818
$343$	0.0386739	0.00208819
$344$	−76.8249	−4.14212
$345$	1.23356	0.0664126
$346$	16.6118	0.893055
$347$	−7.56089	−0.405890	−0.202945	−	0.979190i	$-0.565051\pi$
$347$	−7.56089	−0.405890	−0.202945	+	0.979190i	$0.565051\pi$
$348$	−19.5976	−1.05054
$349$	11.7228	0.627507	0.313754	−	0.949504i	$-0.398413\pi$
$349$	11.7228	0.627507	0.313754	+	0.949504i	$0.398413\pi$
$350$	33.4590	1.78846
$351$	0.145144	0.00774723
$352$	34.6551	1.84713
$353$	12.4116	0.660604	0.330302	−	0.943875i	$-0.392849\pi$
$353$	12.4116	0.660604	0.330302	+	0.943875i	$0.392849\pi$
$354$	14.9079	0.792349
$355$	1.34449	0.0713584
$356$	55.3866	2.93548
$357$	−6.34462	−0.335793
$358$	−4.69661	−0.248224
$359$	6.39889	0.337721	0.168860	−	0.985640i	$-0.445991\pi$
$359$	6.39889	0.337721	0.168860	+	0.985640i	$0.445991\pi$
$360$	37.3424	1.96812
$361$	27.5602	1.45054
$362$	53.1096	2.79138
$363$	−6.25147	−0.328117
$364$	−0.879708	−0.0461092
$365$	−7.60444	−0.398034
$366$	6.31282	0.329977
$367$	19.6085	1.02356	0.511778	−	0.859118i	$-0.328987\pi$
$367$	19.6085	1.02356	0.511778	+	0.859118i	$0.328987\pi$
$368$	26.1745	1.36444
$369$	−12.9312	−0.673174
$370$	23.0683	1.19926
$371$	−38.8603	−2.01753
$372$	2.31001	0.119768
$373$	18.6405	0.965168	0.482584	−	0.875850i	$-0.339698\pi$
$373$	18.6405	0.965168	0.482584	+	0.875850i	$0.339698\pi$
$374$	−8.45542	−0.437219
$375$	−7.11700	−0.367520
$376$	111.696	5.76028
$377$	0.208949	0.0107614
$378$	37.8062	1.94454
$379$	10.6636	0.547751	0.273875	−	0.961765i	$-0.411694\pi$
$379$	10.6636	0.547751	0.273875	+	0.961765i	$0.411694\pi$
$380$	53.5846	2.74883
$381$	1.80018	0.0922259
$382$	56.5607	2.89389
$383$	−28.3672	−1.44950	−0.724749	−	0.689013i	$-0.758044\pi$
$383$	−28.3672	−1.44950	−0.724749	+	0.689013i	$0.758044\pi$
$384$	−46.9199	−2.39437
$385$	−5.79278	−0.295227
$386$	29.6842	1.51088
$387$	−18.4475	−0.937740
$388$	−84.3026	−4.27982
$389$	27.4866	1.39363	0.696813	−	0.717253i	$-0.254601\pi$
$389$	27.4866	1.39363	0.696813	+	0.717253i	$0.254601\pi$
$390$	0.0978838	0.00495654
$391$	−3.72496	−0.188379
$392$	−75.3950	−3.80802
$393$	−5.34562	−0.269651
$394$	24.9299	1.25595
$395$	−6.58859	−0.331508
$396$	17.3627	0.872508
$397$	25.1822	1.26386	0.631929	−	0.775026i	$-0.282263\pi$
$397$	25.1822	1.26386	0.631929	+	0.775026i	$0.282263\pi$
$398$	−18.3493	−0.919769
$399$	16.5030	0.826182
$400$	−58.8458	−2.94229
$401$	−8.44405	−0.421676	−0.210838	−	0.977521i	$-0.567619\pi$
$401$	−8.44405	−0.421676	−0.210838	+	0.977521i	$0.567619\pi$
$402$	12.1897	0.607966
$403$	−0.0246293	−0.00122687
$404$	22.6248	1.12563
$405$	7.28282	0.361886
$406$	54.4258	2.70111
$407$	7.05310	0.349609
$408$	18.2299	0.902516
$409$	−7.07459	−0.349816	−0.174908	−	0.984585i	$-0.555963\pi$
$409$	−7.07459	−0.349816	−0.174908	+	0.984585i	$0.555963\pi$
$410$	−18.8513	−0.930997
$411$	4.59659	0.226733
$412$	10.4176	0.513238
$413$	−30.8412	−1.51760
$414$	10.2681	0.504650
$415$	3.61295	0.177353
$416$	1.21145	0.0593961
$417$	−11.0354	−0.540407
$418$	21.9934	1.07573
$419$	−21.6045	−1.05545	−0.527725	−	0.849416i	$-0.676955\pi$
$419$	−21.6045	−1.05545	−0.527725	+	0.849416i	$0.676955\pi$
$420$	18.9927	0.926749
$421$	31.5077	1.53559	0.767795	−	0.640696i	$-0.221354\pi$
$421$	31.5077	1.53559	0.767795	+	0.640696i	$0.221354\pi$
$422$	69.8841	3.40191
$423$	26.8209	1.30408
$424$	111.657	5.42254
$425$	8.37450	0.406223
$426$	−1.80930	−0.0876609
$427$	−13.0598	−0.632009
$428$	5.28189	0.255310
$429$	0.0299278	0.00144493
$430$	−26.8929	−1.29689
$431$	8.69560	0.418852	0.209426	−	0.977824i	$-0.432840\pi$
$431$	8.69560	0.418852	0.209426	+	0.977824i	$0.432840\pi$
$432$	−66.4915	−3.19907
$433$	−15.1372	−0.727446	−0.363723	−	0.931507i	$-0.618494\pi$
$433$	−15.1372	−0.727446	−0.363723	+	0.931507i	$0.618494\pi$
$434$	−6.41527	−0.307943
$435$	−4.51117	−0.216294
$436$	113.879	5.45380
$437$	9.68898	0.463487
$438$	10.2334	0.488970
$439$	−31.9762	−1.52614	−0.763072	−	0.646314i	$-0.776310\pi$
$439$	−31.9762	−1.52614	−0.763072	+	0.646314i	$0.776310\pi$
$440$	16.6443	0.793488
$441$	−18.1042	−0.862103
$442$	−0.295578	−0.0140592
$443$	9.29808	0.441765	0.220883	−	0.975300i	$-0.429106\pi$
$443$	9.29808	0.441765	0.220883	+	0.975300i	$0.429106\pi$
$444$	−23.1249	−1.09746
$445$	12.7494	0.604380
$446$	44.5158	2.10789
$447$	2.15916	0.102125
$448$	177.556	8.38872
$449$	22.8922	1.08035	0.540174	−	0.841553i	$-0.318358\pi$
$449$	22.8922	1.08035	0.540174	+	0.841553i	$0.318358\pi$
$450$	−23.0849	−1.08823
$451$	−5.76374	−0.271404
$452$	5.84081	0.274729
$453$	−14.6355	−0.687636
$454$	−9.65310	−0.453042
$455$	−0.202500	−0.00949333
$456$	−47.4178	−2.22054
$457$	−10.2900	−0.481347	−0.240673	−	0.970606i	$-0.577368\pi$
$457$	−10.2900	−0.481347	−0.240673	+	0.970606i	$0.577368\pi$
$458$	−71.8724	−3.35838
$459$	9.46258	0.441675
$460$	11.1507	0.519905
$461$	3.26574	0.152101	0.0760503	−	0.997104i	$-0.475769\pi$
$461$	3.26574	0.152101	0.0760503	+	0.997104i	$0.475769\pi$
$462$	7.79541	0.362675
$463$	6.16662	0.286587	0.143293	−	0.989680i	$-0.454231\pi$
$463$	6.16662	0.286587	0.143293	+	0.989680i	$0.454231\pi$
$464$	−95.7211	−4.44374
$465$	0.531740	0.0246589
$466$	−6.53818	−0.302875
$467$	15.7318	0.727982	0.363991	−	0.931402i	$-0.381414\pi$
$467$	15.7318	0.727982	0.363991	+	0.931402i	$0.381414\pi$
$468$	0.606951	0.0280563
$469$	−25.2177	−1.16445
$470$	39.0997	1.80353
$471$	11.9106	0.548810
$472$	88.6157	4.07887
$473$	−8.22246	−0.378069
$474$	8.86634	0.407244
$475$	−21.7829	−0.999468
$476$	−57.3520	−2.62872
$477$	26.8115	1.22762
$478$	−46.2396	−2.11495
$479$	−17.5532	−0.802028	−0.401014	−	0.916072i	$-0.631342\pi$
$479$	−17.5532	−0.802028	−0.401014	+	0.916072i	$0.631342\pi$
$480$	−26.1549	−1.19380
$481$	0.246557	0.0112420
$482$	−59.4962	−2.70998
$483$	3.43420	0.156261
$484$	−56.5100	−2.56864
$485$	−19.4056	−0.881162
$486$	−40.1018	−1.81906
$487$	9.79987	0.444075	0.222037	−	0.975038i	$-0.428729\pi$
$487$	9.79987	0.444075	0.222037	+	0.975038i	$0.428729\pi$
$488$	37.5246	1.69866
$489$	−0.402609	−0.0182066
$490$	−26.3924	−1.19229
$491$	−31.7710	−1.43381	−0.716903	−	0.697173i	$-0.754441\pi$
$491$	−31.7710	−1.43381	−0.716903	+	0.697173i	$0.754441\pi$
$492$	18.8975	0.851965
$493$	13.6223	0.613518
$494$	0.768828	0.0345912
$495$	3.99671	0.179639
$496$	11.2828	0.506613
$497$	3.74304	0.167898
$498$	−4.86199	−0.217871
$499$	−14.9023	−0.667118	−0.333559	−	0.942729i	$-0.608250\pi$
$499$	−14.9023	−0.667118	−0.333559	+	0.942729i	$0.608250\pi$
$500$	−64.3339	−2.87710
$501$	8.98513	0.401426
$502$	33.1433	1.47926
$503$	19.8613	0.885572	0.442786	−	0.896627i	$-0.353990\pi$
$503$	19.8613	0.885572	0.442786	+	0.896627i	$0.353990\pi$
$504$	103.960	4.63076
$505$	5.20800	0.231753
$506$	4.57673	0.203460
$507$	−8.39885	−0.373006
$508$	16.2726	0.721982
$509$	3.94985	0.175074	0.0875370	−	0.996161i	$-0.472100\pi$
$509$	3.94985	0.175074	0.0875370	+	0.996161i	$0.472100\pi$
$510$	6.38147	0.282576
$511$	−21.1706	−0.936530
$512$	−158.474	−7.00362
$513$	−24.6131	−1.08669
$514$	−33.9148	−1.49592
$515$	2.39802	0.105669
$516$	26.9589	1.18680
$517$	11.9547	0.525766
$518$	64.2216	2.82173
$519$	−3.83324	−0.168261
$520$	0.581840	0.0255154
$521$	−11.2550	−0.493091	−0.246546	−	0.969131i	$-0.579296\pi$
$521$	−11.2550	−0.493091	−0.246546	+	0.969131i	$0.579296\pi$
$522$	−37.5509	−1.64356
$523$	−5.29924	−0.231719	−0.115860	−	0.993266i	$-0.536962\pi$
$523$	−5.29924	−0.231719	−0.115860	+	0.993266i	$0.536962\pi$
$524$	−48.3216	−2.11094
$525$	−7.72081	−0.336964
$526$	30.9348	1.34882
$527$	−1.60569	−0.0699449
$528$	−13.7101	−0.596657
$529$	−20.9838	−0.912338
$530$	39.0860	1.69779
$531$	21.2788	0.923420
$532$	149.178	6.46769
$533$	−0.201485	−0.00872726
$534$	−17.1570	−0.742457
$535$	1.21584	0.0525652
$536$	72.4578	3.12970
$537$	1.08376	0.0467679
$538$	34.0109	1.46632
$539$	−8.06942	−0.347575
$540$	−28.3264	−1.21897
$541$	−33.0659	−1.42161	−0.710807	−	0.703387i	$-0.751670\pi$
$541$	−33.0659	−1.42161	−0.710807	+	0.703387i	$0.751670\pi$
$542$	11.2392	0.482764
$543$	−12.2553	−0.525924
$544$	78.9795	3.38622
$545$	26.2137	1.12287
$546$	0.272506	0.0116622
$547$	10.2251	0.437194	0.218597	−	0.975815i	$-0.429852\pi$
$547$	10.2251	0.437194	0.218597	+	0.975815i	$0.429852\pi$
$548$	41.5508	1.77496
$549$	9.01057	0.384562
$550$	−10.2895	−0.438744
$551$	−35.4330	−1.50950
$552$	−9.86745	−0.419986
$553$	−18.3425	−0.780001
$554$	61.2939	2.60413
$555$	−5.32311	−0.225953
$556$	−99.7544	−4.23053
$557$	−45.1579	−1.91340	−0.956701	−	0.291073i	$-0.905988\pi$
$557$	−45.1579	−1.91340	−0.956701	+	0.291073i	$0.905988\pi$
$558$	4.42620	0.187376
$559$	−0.287435	−0.0121572
$560$	92.7663	3.92009
$561$	1.95112	0.0823765
$562$	−46.9266	−1.97948
$563$	−27.3342	−1.15200	−0.575999	−	0.817451i	$-0.695387\pi$
$563$	−27.3342	−1.15200	−0.575999	+	0.817451i	$0.695387\pi$
$564$	−39.1956	−1.65043
$565$	1.34449	0.0565633
$566$	−31.9505	−1.34298
$567$	20.2752	0.851478
$568$	−10.7548	−0.451263
$569$	25.2175	1.05717	0.528587	−	0.848879i	$-0.322722\pi$
$569$	25.2175	1.05717	0.528587	+	0.848879i	$0.322722\pi$
$570$	−16.5988	−0.695248
$571$	41.7391	1.74673	0.873364	−	0.487068i	$-0.161934\pi$
$571$	41.7391	1.74673	0.873364	+	0.487068i	$0.161934\pi$
$572$	0.270532	0.0113115
$573$	−13.0516	−0.545239
$574$	−52.4814	−2.19053
$575$	−4.53293	−0.189036
$576$	−122.504	−5.10433
$577$	−21.3828	−0.890178	−0.445089	−	0.895486i	$-0.646828\pi$
$577$	−21.3828	−0.890178	−0.445089	+	0.895486i	$0.646828\pi$
$578$	28.3325	1.17847
$579$	−6.84975	−0.284666
$580$	−40.7786	−1.69324
$581$	10.0584	0.417291
$582$	26.1143	1.08247
$583$	11.9505	0.494939
$584$	60.8292	2.51713
$585$	0.139714	0.00577646
$586$	−3.16758	−0.130851
$587$	22.7809	0.940267	0.470133	−	0.882595i	$-0.344206\pi$
$587$	22.7809	0.940267	0.470133	+	0.882595i	$0.344206\pi$
$588$	26.4571	1.09107
$589$	4.17655	0.172092
$590$	31.0203	1.27709
$591$	−5.75268	−0.236634
$592$	−112.949	−4.64218
$593$	29.0521	1.19303	0.596514	−	0.802603i	$-0.296552\pi$
$593$	29.0521	1.19303	0.596514	+	0.802603i	$0.296552\pi$
$594$	−11.6263	−0.477035
$595$	−13.2018	−0.541222
$596$	19.5176	0.799474
$597$	4.23419	0.173294
$598$	0.159990	0.00654247
$599$	−30.1320	−1.23116	−0.615580	−	0.788074i	$-0.711078\pi$
$599$	−30.1320	−1.23116	−0.615580	+	0.788074i	$0.711078\pi$
$600$	22.1841	0.905664
$601$	−0.999210	−0.0407586	−0.0203793	−	0.999792i	$-0.506487\pi$
$601$	−0.999210	−0.0407586	−0.0203793	+	0.999792i	$0.506487\pi$
$602$	−74.8691	−3.05144
$603$	17.3989	0.708537
$604$	−132.297	−5.38310
$605$	−13.0080	−0.528851
$606$	−7.00846	−0.284699
$607$	−13.5100	−0.548354	−0.274177	−	0.961679i	$-0.588405\pi$
$607$	−13.5100	−0.548354	−0.274177	+	0.961679i	$0.588405\pi$
$608$	−205.433	−8.33143
$609$	−12.5590	−0.508916
$610$	13.1357	0.531848
$611$	0.417902	0.0169065
$612$	39.5698	1.59951
$613$	8.42170	0.340149	0.170075	−	0.985431i	$-0.445599\pi$
$613$	8.42170	0.340149	0.170075	+	0.985431i	$0.445599\pi$
$614$	22.2711	0.898790
$615$	4.35001	0.175409
$616$	46.3374	1.86699
$617$	45.3141	1.82428	0.912138	−	0.409883i	$-0.134430\pi$
$617$	45.3141	1.82428	0.912138	+	0.409883i	$0.134430\pi$
$618$	−3.22704	−0.129811
$619$	24.2338	0.974040	0.487020	−	0.873391i	$-0.338084\pi$
$619$	24.2338	0.974040	0.487020	+	0.873391i	$0.338084\pi$
$620$	4.80665	0.193040
$621$	−5.12188	−0.205534
$622$	−58.7671	−2.35635
$623$	35.4940	1.42204
$624$	−0.479268	−0.0191861
$625$	1.15267	0.0461069
$626$	−12.1240	−0.484574
$627$	−5.07507	−0.202679
$628$	107.665	4.29631
$629$	16.0741	0.640916
$630$	36.3918	1.44988
$631$	47.5046	1.89113	0.945565	−	0.325434i	$-0.105510\pi$
$631$	47.5046	1.89113	0.945565	+	0.325434i	$0.105510\pi$
$632$	52.7032	2.09642
$633$	−16.1261	−0.640953
$634$	48.4723	1.92508
$635$	3.74579	0.148647
$636$	−39.1819	−1.55366
$637$	−0.282085	−0.0111766
$638$	−16.7373	−0.662635
$639$	−2.58250	−0.102162
$640$	−97.6305	−3.85918
$641$	31.3205	1.23709	0.618543	−	0.785751i	$-0.287723\pi$
$641$	31.3205	1.23709	0.618543	+	0.785751i	$0.287723\pi$
$642$	−1.63617	−0.0645743
$643$	12.3143	0.485628	0.242814	−	0.970073i	$-0.421930\pi$
$643$	12.3143	0.485628	0.242814	+	0.970073i	$0.421930\pi$
$644$	31.0433	1.22328
$645$	6.20565	0.244347
$646$	50.1232	1.97207
$647$	−35.5055	−1.39587	−0.697933	−	0.716163i	$-0.745897\pi$
$647$	−35.5055	−1.39587	−0.697933	+	0.716163i	$0.745897\pi$
$648$	−58.2565	−2.28853
$649$	9.48442	0.372296
$650$	−0.359691	−0.0141083
$651$	1.48035	0.0580196
$652$	−3.63937	−0.142529
$653$	−11.7839	−0.461139	−0.230569	−	0.973056i	$-0.574059\pi$
$653$	−11.7839	−0.461139	−0.230569	+	0.973056i	$0.574059\pi$
$654$	−35.2761	−1.37940
$655$	−11.1231	−0.434617
$656$	92.3013	3.60376
$657$	14.6066	0.569856
$658$	108.853	4.24351
$659$	47.5019	1.85041	0.925205	−	0.379467i	$-0.123893\pi$
$659$	47.5019	1.85041	0.925205	+	0.379467i	$0.123893\pi$
$660$	−5.84072	−0.227350
$661$	7.72503	0.300469	0.150234	−	0.988650i	$-0.451997\pi$
$661$	7.72503	0.300469	0.150234	+	0.988650i	$0.451997\pi$
$662$	24.0948	0.936469
$663$	0.0682059	0.00264890
$664$	−28.9006	−1.12156
$665$	34.3392	1.33162
$666$	−44.3094	−1.71696
$667$	−7.37345	−0.285501
$668$	81.2208	3.14253
$669$	−10.2722	−0.397147
$670$	25.3642	0.979904
$671$	4.01621	0.155044
$672$	−72.8146	−2.80888
$673$	−6.59923	−0.254381	−0.127191	−	0.991878i	$-0.540596\pi$
$673$	−6.59923	−0.254381	−0.127191	+	0.991878i	$0.540596\pi$
$674$	99.0209	3.81414
$675$	11.5151	0.443216
$676$	−75.9211	−2.92004
$677$	−25.8679	−0.994183	−0.497091	−	0.867698i	$-0.665599\pi$
$677$	−25.8679	−0.994183	−0.497091	+	0.867698i	$0.665599\pi$
$678$	−1.80930	−0.0694858
$679$	−54.0247	−2.07328
$680$	37.9327	1.45465
$681$	2.22749	0.0853578
$682$	1.97285	0.0755445
$683$	−31.1754	−1.19289	−0.596447	−	0.802653i	$-0.703421\pi$
$683$	−31.1754	−1.19289	−0.596447	+	0.802653i	$0.703421\pi$
$684$	−102.925	−3.93543
$685$	9.56455	0.365443
$686$	−0.108293	−0.00413463
$687$	16.5849	0.632752
$688$	131.676	5.02009
$689$	0.417756	0.0159153
$690$	−3.45414	−0.131497
$691$	−11.9785	−0.455683	−0.227842	−	0.973698i	$-0.573167\pi$
$691$	−11.9785	−0.455683	−0.227842	+	0.973698i	$0.573167\pi$
$692$	−34.6505	−1.31721
$693$	11.1267	0.422670
$694$	21.1716	0.803663
$695$	−22.9624	−0.871014
$696$	36.0856	1.36782
$697$	−13.1356	−0.497548
$698$	−32.8255	−1.24247
$699$	1.50871	0.0570648
$700$	−69.7921	−2.63789
$701$	30.4384	1.14964	0.574822	−	0.818279i	$-0.305071\pi$
$701$	30.4384	1.14964	0.574822	+	0.818279i	$0.305071\pi$
$702$	−0.406425	−0.0153395
$703$	−41.8103	−1.57691
$704$	−54.6028	−2.05792
$705$	−9.02242	−0.339804
$706$	−34.7544	−1.30800
$707$	14.4989	0.545288
$708$	−31.0964	−1.16868
$709$	−6.02388	−0.226231	−0.113116	−	0.993582i	$-0.536083\pi$
$709$	−6.02388	−0.226231	−0.113116	+	0.993582i	$0.536083\pi$
$710$	−3.76478	−0.141290
$711$	12.6553	0.474611
$712$	−101.985	−3.82204
$713$	0.869122	0.0325489
$714$	17.7658	0.664870
$715$	0.0622736	0.00232890
$716$	9.79665	0.366118
$717$	10.6700	0.398478
$718$	−17.9178	−0.668688
$719$	20.4605	0.763048	0.381524	−	0.924359i	$-0.375399\pi$
$719$	20.4605	0.763048	0.381524	+	0.924359i	$0.375399\pi$
$720$	−64.0038	−2.38528
$721$	6.67602	0.248628
$722$	−77.1725	−2.87206
$723$	13.7290	0.510587
$724$	−110.781	−4.11715
$725$	16.5771	0.615658
$726$	17.5050	0.649673
$727$	−34.9702	−1.29697	−0.648486	−	0.761226i	$-0.724598\pi$
$727$	−34.9702	−1.29697	−0.648486	+	0.761226i	$0.724598\pi$
$728$	1.61983	0.0600348
$729$	−6.99665	−0.259135
$730$	21.2935	0.788109
$731$	−18.7391	−0.693091
$732$	−13.1679	−0.486699
$733$	−44.3025	−1.63635	−0.818176	−	0.574968i	$-0.805014\pi$
$733$	−44.3025	−1.63635	−0.818176	+	0.574968i	$0.805014\pi$
$734$	−54.9067	−2.02664
$735$	6.09015	0.224639
$736$	−42.7498	−1.57578
$737$	7.75506	0.285661
$738$	36.2094	1.33289
$739$	18.5287	0.681589	0.340795	−	0.940138i	$-0.389304\pi$
$739$	18.5287	0.681589	0.340795	+	0.940138i	$0.389304\pi$
$740$	−48.1181	−1.76886
$741$	−0.177410	−0.00651733
$742$	108.815	3.99471
$743$	−21.8024	−0.799853	−0.399927	−	0.916547i	$-0.630964\pi$
$743$	−21.8024	−0.799853	−0.399927	+	0.916547i	$0.630964\pi$
$744$	−4.25348	−0.155940
$745$	4.49276	0.164602
$746$	−52.1961	−1.91103
$747$	−6.93973	−0.253911
$748$	17.6371	0.644877
$749$	3.38486	0.123680
$750$	19.9286	0.727691
$751$	−18.5334	−0.676292	−0.338146	−	0.941094i	$-0.609800\pi$
$751$	−18.5334	−0.676292	−0.338146	+	0.941094i	$0.609800\pi$
$752$	−191.444	−6.98123
$753$	−7.64796	−0.278707
$754$	−0.585089	−0.0213077
$755$	−30.4534	−1.10831
$756$	−78.8599	−2.86811
$757$	51.1983	1.86083	0.930416	−	0.366505i	$-0.119446\pi$
$757$	51.1983	1.86083	0.930416	+	0.366505i	$0.119446\pi$
$758$	−29.8595	−1.08455
$759$	−1.05610	−0.0383340
$760$	−98.6666	−3.57901
$761$	−29.7047	−1.07679	−0.538397	−	0.842691i	$-0.680970\pi$
$761$	−29.7047	−1.07679	−0.538397	+	0.842691i	$0.680970\pi$
$762$	−5.04076	−0.182607
$763$	72.9782	2.64199
$764$	−117.980	−4.26835
$765$	9.10855	0.329320
$766$	79.4324	2.87001
$767$	0.331549	0.0119715
$768$	70.0810	2.52883
$769$	−36.4867	−1.31574	−0.657872	−	0.753130i	$-0.728543\pi$
$769$	−36.4867	−1.31574	−0.657872	+	0.753130i	$0.728543\pi$
$770$	16.2206	0.584551
$771$	7.82599	0.281846
$772$	−61.9181	−2.22848
$773$	4.64563	0.167092	0.0835459	−	0.996504i	$-0.473375\pi$
$773$	4.64563	0.167092	0.0835459	+	0.996504i	$0.473375\pi$
$774$	51.6557	1.85673
$775$	−1.95397	−0.0701888
$776$	155.229	5.57238
$777$	−14.8194	−0.531643
$778$	−76.9665	−2.75938
$779$	34.1671	1.22416
$780$	−0.204176	−0.00731066
$781$	−1.15108	−0.0411887
$782$	10.4304	0.372991
$783$	18.7309	0.669388
$784$	129.225	4.61517
$785$	24.7834	0.884558
$786$	14.9685	0.533909
$787$	−19.7795	−0.705064	−0.352532	−	0.935800i	$-0.614679\pi$
$787$	−19.7795	−0.705064	−0.352532	+	0.935800i	$0.614679\pi$
$788$	−52.0012	−1.85247
$789$	−7.13835	−0.254132
$790$	18.4490	0.656386
$791$	3.74304	0.133087
$792$	−31.9703	−1.13602
$793$	0.140396	0.00498560
$794$	−70.5138	−2.50244
$795$	−9.01927	−0.319881
$796$	38.2748	1.35662
$797$	−48.7292	−1.72608	−0.863038	−	0.505139i	$-0.831441\pi$
$797$	−48.7292	−1.72608	−0.863038	+	0.505139i	$0.831441\pi$
$798$	−46.2107	−1.63584
$799$	27.2449	0.963854
$800$	96.1108	3.39803
$801$	−24.4890	−0.865276
$802$	23.6446	0.834919
$803$	6.51047	0.229749
$804$	−25.4264	−0.896721
$805$	7.14585	0.251858
$806$	0.0689655	0.00242921
$807$	−7.84817	−0.276269
$808$	−41.6596	−1.46558
$809$	−39.7618	−1.39795	−0.698975	−	0.715146i	$-0.746360\pi$
$809$	−39.7618	−1.39795	−0.698975	+	0.715146i	$0.746360\pi$
$810$	−20.3930	−0.716536
$811$	22.4089	0.786883	0.393441	−	0.919350i	$-0.371284\pi$
$811$	22.4089	0.786883	0.393441	+	0.919350i	$0.371284\pi$
$812$	−113.527	−3.98400
$813$	−2.59349	−0.0909576
$814$	−19.7497	−0.692227
$815$	−0.837745	−0.0293449
$816$	−31.2456	−1.09381
$817$	48.7422	1.70528
$818$	19.8099	0.692636
$819$	0.388960	0.0135914
$820$	39.3218	1.37318
$821$	16.8185	0.586969	0.293485	−	0.955964i	$-0.405185\pi$
$821$	16.8185	0.586969	0.293485	+	0.955964i	$0.405185\pi$
$822$	−12.8711	−0.448932
$823$	30.9461	1.07871	0.539356	−	0.842078i	$-0.318668\pi$
$823$	30.9461	1.07871	0.539356	+	0.842078i	$0.318668\pi$
$824$	−19.1822	−0.668242
$825$	2.37434	0.0826639
$826$	86.3598	3.00484
$827$	41.7438	1.45157	0.725787	−	0.687920i	$-0.241476\pi$
$827$	41.7438	1.45157	0.725787	+	0.687920i	$0.241476\pi$
$828$	−21.4182	−0.744335
$829$	46.1736	1.60367	0.801837	−	0.597543i	$-0.203856\pi$
$829$	46.1736	1.60367	0.801837	+	0.597543i	$0.203856\pi$
$830$	−10.1168	−0.351159
$831$	−14.1438	−0.490644
$832$	−1.90876	−0.0661744
$833$	−18.3903	−0.637187
$834$	30.9008	1.07001
$835$	18.6962	0.647008
$836$	−45.8759	−1.58665
$837$	−2.20785	−0.0763144
$838$	60.4958	2.08979
$839$	32.6098	1.12582	0.562908	−	0.826520i	$-0.309683\pi$
$839$	32.6098	1.12582	0.562908	+	0.826520i	$0.309683\pi$
$840$	−34.9718	−1.20664
$841$	−2.03500	−0.0701723
$842$	−88.2260	−3.04047
$843$	10.8285	0.372954
$844$	−145.771	−5.01765
$845$	−17.4763	−0.601201
$846$	−75.1024	−2.58207
$847$	−36.2140	−1.24433
$848$	−191.377	−6.57191
$849$	7.37272	0.253031
$850$	−23.4498	−0.804323
$851$	−8.70055	−0.298251
$852$	3.77402	0.129296
$853$	−23.1123	−0.791349	−0.395674	−	0.918391i	$-0.629489\pi$
$853$	−23.1123	−0.791349	−0.395674	+	0.918391i	$0.629489\pi$
$854$	36.5694	1.25138
$855$	−23.6922	−0.810257
$856$	−9.72568	−0.332417
$857$	22.0162	0.752060	0.376030	−	0.926608i	$-0.377289\pi$
$857$	22.0162	0.752060	0.376030	+	0.926608i	$0.377289\pi$
$858$	−0.0838023	−0.00286096
$859$	−40.6280	−1.38621	−0.693104	−	0.720837i	$-0.743758\pi$
$859$	−40.6280	−1.38621	−0.693104	+	0.720837i	$0.743758\pi$
$860$	56.0958	1.91285
$861$	12.1103	0.412718
$862$	−24.3489	−0.829328
$863$	6.09422	0.207450	0.103725	−	0.994606i	$-0.466924\pi$
$863$	6.09422	0.207450	0.103725	+	0.994606i	$0.466924\pi$
$864$	108.598	3.69458
$865$	−7.97618	−0.271198
$866$	42.3863	1.44034
$867$	−6.53784	−0.222037
$868$	13.3816	0.454201
$869$	5.64076	0.191350
$870$	12.6319	0.428263
$871$	0.271096	0.00918572
$872$	−209.688	−7.10092
$873$	37.2741	1.26154
$874$	−27.1305	−0.917704
$875$	−41.2279	−1.39376
$876$	−21.3458	−0.721207
$877$	−43.1239	−1.45619	−0.728095	−	0.685476i	$-0.759594\pi$
$877$	−43.1239	−1.45619	−0.728095	+	0.685476i	$0.759594\pi$
$878$	89.5381	3.02177
$879$	0.730932	0.0246537
$880$	−28.5279	−0.961676
$881$	50.1898	1.69094	0.845469	−	0.534025i	$-0.179321\pi$
$881$	50.1898	1.69094	0.845469	+	0.534025i	$0.179321\pi$
$882$	50.6943	1.70696
$883$	17.6742	0.594784	0.297392	−	0.954756i	$-0.403883\pi$
$883$	17.6742	0.594784	0.297392	+	0.954756i	$0.403883\pi$
$884$	0.616545	0.0207367
$885$	−7.15808	−0.240616
$886$	−26.0360	−0.874696
$887$	−4.68428	−0.157283	−0.0786414	−	0.996903i	$-0.525058\pi$
$887$	−4.68428	−0.157283	−0.0786414	+	0.996903i	$0.525058\pi$
$888$	42.5804	1.42891
$889$	10.4282	0.349750
$890$	−35.7002	−1.19667
$891$	−6.23512	−0.208884
$892$	−92.8554	−3.10903
$893$	−70.8665	−2.37146
$894$	−6.04595	−0.202207
$895$	2.25509	0.0753792
$896$	−271.801	−9.08023
$897$	−0.0369183	−0.00123267
$898$	−64.1014	−2.13909
$899$	−3.17841	−0.106006
$900$	48.1528	1.60509
$901$	27.2353	0.907341
$902$	16.1393	0.537381
$903$	17.2764	0.574922
$904$	−10.7548	−0.357701
$905$	−25.5007	−0.847670
$906$	40.9815	1.36152
$907$	−27.1752	−0.902336	−0.451168	−	0.892439i	$-0.648992\pi$
$907$	−27.1752	−0.902336	−0.451168	+	0.892439i	$0.648992\pi$
$908$	20.1354	0.668216
$909$	−10.0035	−0.331795
$910$	0.567028	0.0187968
$911$	−25.7954	−0.854639	−0.427319	−	0.904101i	$-0.640542\pi$
$911$	−25.7954	−0.854639	−0.427319	+	0.904101i	$0.640542\pi$
$912$	81.2728	2.69121
$913$	−3.09319	−0.102370
$914$	28.8136	0.953068
$915$	−3.03111	−0.100205
$916$	149.918	4.95344
$917$	−30.9665	−1.02260
$918$	−26.4966	−0.874518
$919$	40.0818	1.32218	0.661089	−	0.750308i	$-0.270095\pi$
$919$	40.0818	1.32218	0.661089	+	0.750308i	$0.270095\pi$
$920$	−20.5321	−0.676923
$921$	−5.13916	−0.169341
$922$	−9.14454	−0.301159
$923$	−0.0402384	−0.00132446
$924$	−16.2604	−0.534929
$925$	19.5607	0.643152
$926$	−17.2674	−0.567443
$927$	−4.60610	−0.151284
$928$	156.338	5.13204
$929$	24.9152	0.817441	0.408721	−	0.912660i	$-0.365975\pi$
$929$	24.9152	0.817441	0.408721	+	0.912660i	$0.365975\pi$
$930$	−1.48895	−0.0488246
$931$	47.8350	1.56773
$932$	13.6380	0.446726
$933$	13.5608	0.443959
$934$	−44.0514	−1.44141
$935$	4.05988	0.132772
$936$	−1.11759	−0.0365297
$937$	−0.489975	−0.0160068	−0.00800340	−	0.999968i	$-0.502548\pi$
$937$	−0.489975	−0.0160068	−0.00800340	+	0.999968i	$0.502548\pi$
$938$	70.6133	2.30560
$939$	2.79767	0.0912986
$940$	−81.5579	−2.66013
$941$	5.08530	0.165776	0.0828881	−	0.996559i	$-0.473586\pi$
$941$	5.08530	0.165776	0.0828881	+	0.996559i	$0.473586\pi$
$942$	−33.3513	−1.08664
$943$	7.11003	0.231534
$944$	−151.885	−4.94343
$945$	−18.1527	−0.590508
$946$	23.0241	0.748578
$947$	5.98306	0.194423	0.0972117	−	0.995264i	$-0.469008\pi$
$947$	5.98306	0.194423	0.0972117	+	0.995264i	$0.469008\pi$
$948$	−18.4943	−0.600666
$949$	0.227588	0.00738781
$950$	60.9953	1.97895
$951$	−11.1852	−0.362704
$952$	105.604	3.42263
$953$	−57.4102	−1.85970	−0.929850	−	0.367938i	$-0.880064\pi$
$953$	−57.4102	−1.85970	−0.929850	+	0.367938i	$0.880064\pi$
$954$	−75.0762	−2.43068
$955$	−27.1577	−0.878802
$956$	96.4509	3.11945
$957$	3.86220	0.124847
$958$	49.1516	1.58802
$959$	26.6275	0.859846
$960$	41.2098	1.33004
$961$	−30.6254	−0.987915
$962$	−0.690395	−0.0222592
$963$	−2.33537	−0.0752563
$964$	124.103	3.99709
$965$	−14.2529	−0.458817
$966$	−9.61625	−0.309398
$967$	15.0799	0.484938	0.242469	−	0.970159i	$-0.422043\pi$
$967$	15.0799	0.484938	0.242469	+	0.970159i	$0.422043\pi$
$968$	104.053	3.34440
$969$	−11.5661	−0.371558
$970$	54.3385	1.74470
$971$	−47.6410	−1.52887	−0.764436	−	0.644700i	$-0.776982\pi$
$971$	−47.6410	−1.52887	−0.764436	+	0.644700i	$0.776982\pi$
$972$	83.6483	2.68302
$973$	−63.9268	−2.04940
$974$	−27.4411	−0.879269
$975$	0.0830003	0.00265814
$976$	−64.3161	−2.05871
$977$	−30.5063	−0.975984	−0.487992	−	0.872848i	$-0.662270\pi$
$977$	−30.5063	−0.975984	−0.487992	+	0.872848i	$0.662270\pi$
$978$	1.12736	0.0360491
$979$	−10.9153	−0.348854
$980$	55.0517	1.75856
$981$	−50.3511	−1.60759
$982$	88.9634	2.83894
$983$	−29.6320	−0.945113	−0.472557	−	0.881300i	$-0.656669\pi$
$983$	−29.6320	−0.945113	−0.472557	+	0.881300i	$0.656669\pi$
$984$	−34.7964	−1.10927
$985$	−11.9701	−0.381400
$986$	−38.1445	−1.21477
$987$	−25.1182	−0.799521
$988$	−1.60369	−0.0510203
$989$	10.1431	0.322530
$990$	−11.1914	−0.355685
$991$	52.7021	1.67414	0.837069	−	0.547097i	$-0.184267\pi$
$991$	52.7021	1.67414	0.837069	+	0.547097i	$0.184267\pi$
$992$	−18.4278	−0.585084
$993$	−5.55997	−0.176440
$994$	−10.4810	−0.332439
$995$	8.81047	0.279311
$996$	10.1416	0.321349
$997$	−25.5344	−0.808682	−0.404341	−	0.914608i	$-0.632499\pi$
$997$	−25.5344	−0.808682	−0.404341	+	0.914608i	$0.632499\pi$
$998$	41.7286	1.32089
$999$	22.1022	0.699282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.1	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.1	✓	155	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)

\(f(q)\)	\(=\)	\(q-2.80015 q^{2} +0.646146 q^{3} +5.84081 q^{4} +1.34449 q^{5} -1.80930 q^{6} +3.74304 q^{7} -10.7548 q^{8} -2.58250 q^{9} +O(q^{10})\)	\(q-2.80015 q^{2} +0.646146 q^{3} +5.84081 q^{4} +1.34449 q^{5} -1.80930 q^{6} +3.74304 q^{7} -10.7548 q^{8} -2.58250 q^{9} -3.76478 q^{10} -1.15108 q^{11} +3.77402 q^{12} -0.0402384 q^{13} -10.4810 q^{14} +0.868739 q^{15} +18.4335 q^{16} -2.62332 q^{17} +7.23136 q^{18} +6.82350 q^{19} +7.85294 q^{20} +2.41855 q^{21} +3.22318 q^{22} +1.41994 q^{23} -6.94919 q^{24} -3.19233 q^{25} +0.112673 q^{26} -3.60710 q^{27} +21.8624 q^{28} -5.19278 q^{29} -2.43260 q^{30} +0.612083 q^{31} -30.1067 q^{32} -0.743763 q^{33} +7.34567 q^{34} +5.03249 q^{35} -15.0839 q^{36} -6.12740 q^{37} -19.1068 q^{38} -0.0259999 q^{39} -14.4598 q^{40} +5.00727 q^{41} -6.77228 q^{42} +7.14329 q^{43} -6.72322 q^{44} -3.47215 q^{45} -3.97604 q^{46} -10.3857 q^{47} +11.9107 q^{48} +7.01033 q^{49} +8.93900 q^{50} -1.69504 q^{51} -0.235025 q^{52} -10.3820 q^{53} +10.1004 q^{54} -1.54762 q^{55} -40.2558 q^{56} +4.40898 q^{57} +14.5405 q^{58} -8.23962 q^{59} +5.07414 q^{60} -3.48909 q^{61} -1.71392 q^{62} -9.66638 q^{63} +47.4363 q^{64} -0.0541003 q^{65} +2.08264 q^{66} -6.73723 q^{67} -15.3223 q^{68} +0.917489 q^{69} -14.0917 q^{70} +1.00000 q^{71} +27.7743 q^{72} -5.65598 q^{73} +17.1576 q^{74} -2.06271 q^{75} +39.8548 q^{76} -4.30852 q^{77} +0.0728034 q^{78} -4.90042 q^{79} +24.7837 q^{80} +5.41677 q^{81} -14.0211 q^{82} +2.68722 q^{83} +14.1263 q^{84} -3.52703 q^{85} -20.0022 q^{86} -3.35529 q^{87} +12.3796 q^{88} +9.48268 q^{89} +9.72253 q^{90} -0.150614 q^{91} +8.29362 q^{92} +0.395495 q^{93} +29.0813 q^{94} +9.17416 q^{95} -19.4533 q^{96} -14.4334 q^{97} -19.6299 q^{98} +2.97265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 155 * q - 21 * q^2 - 16 * q^3 + 151 * q^4 - 26 * q^5 - 10 * q^6 - 40 * q^7 - 57 * q^8 + 135 * q^9 - 2 * q^10 - 24 * q^11 - 32 * q^12 - 62 * q^13 - 18 * q^14 - 12 * q^15 + 155 * q^16 - 129 * q^17 - 42 * q^18 - 18 * q^19 - 59 * q^20 - 45 * q^21 - 17 * q^22 - 38 * q^23 - 27 * q^24 + 129 * q^25 - 44 * q^26 - 43 * q^27 - 100 * q^28 - 52 * q^29 - 39 * q^30 - 56 * q^31 - 145 * q^32 - 126 * q^33 - q^34 - 49 * q^35 + 131 * q^36 - 30 * q^37 - 91 * q^38 - 29 * q^39 - 5 * q^40 - 163 * q^41 - 80 * q^42 - 15 * q^43 - 118 * q^44 - 66 * q^45 + 2 * q^46 - 111 * q^47 - 89 * q^48 + 101 * q^49 - 121 * q^50 + 5 * q^51 - 111 * q^52 - 93 * q^53 - 68 * q^54 - 60 * q^55 - 27 * q^56 - 106 * q^57 + 16 * q^58 - 79 * q^59 - 103 * q^60 - 74 * q^61 - 102 * q^62 - 118 * q^63 + 175 * q^64 - 109 * q^65 + 65 * q^66 - 18 * q^67 - 346 * q^68 - 39 * q^69 + 32 * q^70 + 155 * q^71 - 203 * q^72 - 108 * q^73 - 87 * q^74 - 22 * q^75 - 16 * q^76 - 121 * q^77 - 75 * q^78 - 6 * q^79 - 136 * q^80 + 107 * q^81 - 30 * q^82 - 116 * q^83 - 5 * q^84 - 53 * q^85 + 8 * q^86 - 100 * q^87 - 43 * q^88 - 189 * q^89 - 76 * q^90 + 14 * q^91 - 99 * q^92 - 72 * q^93 + 17 * q^94 - 18 * q^95 - 50 * q^96 - 184 * q^97 - 249 * q^98 - 114 * q^99

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