LMFDB - Embedded newform 8023.2.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.46916 q^{2} +1.70167 q^{3} +4.09677 q^{4} -3.39881 q^{5} -4.20171 q^{6} +3.51551 q^{7} -5.17727 q^{8} -0.104305 q^{9} +O(q^{10})$	\(q-2.46916 q^{2} +1.70167 q^{3} +4.09677 q^{4} -3.39881 q^{5} -4.20171 q^{6} +3.51551 q^{7} -5.17727 q^{8} -0.104305 q^{9} +8.39223 q^{10} -3.57759 q^{11} +6.97137 q^{12} +0.490778 q^{13} -8.68038 q^{14} -5.78368 q^{15} +4.58998 q^{16} -0.461597 q^{17} +0.257546 q^{18} +8.11557 q^{19} -13.9242 q^{20} +5.98226 q^{21} +8.83366 q^{22} +0.0685767 q^{23} -8.81002 q^{24} +6.55194 q^{25} -1.21181 q^{26} -5.28252 q^{27} +14.4022 q^{28} +3.39395 q^{29} +14.2808 q^{30} +5.89489 q^{31} -0.978877 q^{32} -6.08789 q^{33} +1.13976 q^{34} -11.9486 q^{35} -0.427313 q^{36} -2.69036 q^{37} -20.0387 q^{38} +0.835144 q^{39} +17.5966 q^{40} -7.92322 q^{41} -14.7712 q^{42} -11.2048 q^{43} -14.6566 q^{44} +0.354513 q^{45} -0.169327 q^{46} -10.5869 q^{47} +7.81065 q^{48} +5.35883 q^{49} -16.1778 q^{50} -0.785488 q^{51} +2.01060 q^{52} -0.289023 q^{53} +13.0434 q^{54} +12.1596 q^{55} -18.2007 q^{56} +13.8101 q^{57} -8.38021 q^{58} +10.1564 q^{59} -23.6944 q^{60} -2.40510 q^{61} -14.5555 q^{62} -0.366685 q^{63} -6.76295 q^{64} -1.66806 q^{65} +15.0320 q^{66} -8.94666 q^{67} -1.89106 q^{68} +0.116695 q^{69} +29.5030 q^{70} +1.00000 q^{71} +0.540015 q^{72} +2.74462 q^{73} +6.64294 q^{74} +11.1493 q^{75} +33.2476 q^{76} -12.5771 q^{77} -2.06211 q^{78} +4.04125 q^{79} -15.6005 q^{80} -8.67621 q^{81} +19.5637 q^{82} +17.4392 q^{83} +24.5079 q^{84} +1.56888 q^{85} +27.6665 q^{86} +5.77539 q^{87} +18.5221 q^{88} +0.0870007 q^{89} -0.875351 q^{90} +1.72534 q^{91} +0.280943 q^{92} +10.0312 q^{93} +26.1408 q^{94} -27.5833 q^{95} -1.66573 q^{96} +1.48231 q^{97} -13.2318 q^{98} +0.373160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.46916	−1.74596	−0.872981	−	0.487754i	$-0.837816\pi$
$2$	−2.46916	−1.74596	−0.872981	+	0.487754i	$0.837816\pi$
$3$	1.70167	0.982462	0.491231	−	0.871029i	$-0.336547\pi$
$3$	1.70167	0.982462	0.491231	+	0.871029i	$0.336547\pi$
$4$	4.09677	2.04838
$5$	−3.39881	−1.52000	−0.759998	−	0.649925i	$-0.774800\pi$
$5$	−3.39881	−1.52000	−0.759998	+	0.649925i	$0.774800\pi$
$6$	−4.20171	−1.71534
$7$	3.51551	1.32874	0.664369	−	0.747404i	$-0.268700\pi$
$7$	3.51551	1.32874	0.664369	+	0.747404i	$0.268700\pi$
$8$	−5.17727	−1.83044
$9$	−0.104305	−0.0347683
$10$	8.39223	2.65386
$11$	−3.57759	−1.07868	−0.539342	−	0.842087i	$-0.681327\pi$
$11$	−3.57759	−1.07868	−0.539342	+	0.842087i	$0.681327\pi$
$12$	6.97137	2.01246
$13$	0.490778	0.136117	0.0680587	−	0.997681i	$-0.478319\pi$
$13$	0.490778	0.136117	0.0680587	+	0.997681i	$0.478319\pi$
$14$	−8.68038	−2.31993
$15$	−5.78368	−1.49334
$16$	4.58998	1.14749
$17$	−0.461597	−0.111954	−0.0559769	−	0.998432i	$-0.517827\pi$
$17$	−0.461597	−0.111954	−0.0559769	+	0.998432i	$0.517827\pi$
$18$	0.257546	0.0607042
$19$	8.11557	1.86184	0.930919	−	0.365225i	$-0.119008\pi$
$19$	8.11557	1.86184	0.930919	+	0.365225i	$0.119008\pi$
$20$	−13.9242	−3.11354
$21$	5.98226	1.30544
$22$	8.83366	1.88334
$23$	0.0685767	0.0142992	0.00714962	−	0.999974i	$-0.497724\pi$
$23$	0.0685767	0.0142992	0.00714962	+	0.999974i	$0.497724\pi$
$24$	−8.81002	−1.79834
$25$	6.55194	1.31039
$26$	−1.21181	−0.237656
$27$	−5.28252	−1.01662
$28$	14.4022	2.72177
$29$	3.39395	0.630240	0.315120	−	0.949052i	$-0.397955\pi$
$29$	3.39395	0.630240	0.315120	+	0.949052i	$0.397955\pi$
$30$	14.2808	2.60731
$31$	5.89489	1.05875	0.529377	−	0.848387i	$-0.322426\pi$
$31$	5.89489	1.05875	0.529377	+	0.848387i	$0.322426\pi$
$32$	−0.978877	−0.173043
$33$	−6.08789	−1.05977
$34$	1.13976	0.195467
$35$	−11.9486	−2.01968
$36$	−0.427313	−0.0712189
$37$	−2.69036	−0.442293	−0.221146	−	0.975241i	$-0.570980\pi$
$37$	−2.69036	−0.442293	−0.221146	+	0.975241i	$0.570980\pi$
$38$	−20.0387	−3.25070
$39$	0.835144	0.133730
$40$	17.5966	2.78226
$41$	−7.92322	−1.23740	−0.618700	−	0.785628i	$-0.712340\pi$
$41$	−7.92322	−1.23740	−0.618700	+	0.785628i	$0.712340\pi$
$42$	−14.7712	−2.27924
$43$	−11.2048	−1.70871	−0.854357	−	0.519686i	$-0.826049\pi$
$43$	−11.2048	−1.70871	−0.854357	+	0.519686i	$0.826049\pi$
$44$	−14.6566	−2.20956
$45$	0.354513	0.0528477
$46$	−0.169327	−0.0249659
$47$	−10.5869	−1.54426	−0.772131	−	0.635464i	$-0.780809\pi$
$47$	−10.5869	−1.54426	−0.772131	+	0.635464i	$0.780809\pi$
$48$	7.81065	1.12737
$49$	5.35883	0.765547
$50$	−16.1778	−2.28789
$51$	−0.785488	−0.109990
$52$	2.01060	0.278821
$53$	−0.289023	−0.0397004	−0.0198502	−	0.999803i	$-0.506319\pi$
$53$	−0.289023	−0.0397004	−0.0198502	+	0.999803i	$0.506319\pi$
$54$	13.0434	1.77498
$55$	12.1596	1.63960
$56$	−18.2007	−2.43218
$57$	13.8101	1.82919
$58$	−8.38021	−1.10038
$59$	10.1564	1.32225	0.661126	−	0.750275i	$-0.270079\pi$
$59$	10.1564	1.32225	0.661126	+	0.750275i	$0.270079\pi$
$60$	−23.6944	−3.05893
$61$	−2.40510	−0.307941	−0.153970	−	0.988075i	$-0.549206\pi$
$61$	−2.40510	−0.307941	−0.153970	+	0.988075i	$0.549206\pi$
$62$	−14.5555	−1.84854
$63$	−0.366685	−0.0461980
$64$	−6.76295	−0.845369
$65$	−1.66806	−0.206898
$66$	15.0320	1.85031
$67$	−8.94666	−1.09301	−0.546504	−	0.837456i	$-0.684042\pi$
$67$	−8.94666	−1.09301	−0.546504	+	0.837456i	$0.684042\pi$
$68$	−1.89106	−0.229324
$69$	0.116695	0.0140485
$70$	29.5030	3.52628
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	0.540015	0.0636413
$73$	2.74462	0.321234	0.160617	−	0.987017i	$-0.448652\pi$
$73$	2.74462	0.321234	0.160617	+	0.987017i	$0.448652\pi$
$74$	6.64294	0.772227
$75$	11.1493	1.28741
$76$	33.2476	3.81376
$77$	−12.5771	−1.43329
$78$	−2.06211	−0.233488
$79$	4.04125	0.454676	0.227338	−	0.973816i	$-0.426998\pi$
$79$	4.04125	0.454676	0.227338	+	0.973816i	$0.426998\pi$
$80$	−15.6005	−1.74419
$81$	−8.67621	−0.964023
$82$	19.5637	2.16045
$83$	17.4392	1.91420	0.957099	−	0.289763i	$-0.0935763\pi$
$83$	17.4392	1.91420	0.957099	+	0.289763i	$0.0935763\pi$
$84$	24.5079	2.67403
$85$	1.56888	0.170169
$86$	27.6665	2.98335
$87$	5.77539	0.619187
$88$	18.5221	1.97447
$89$	0.0870007	0.00922206	0.00461103	−	0.999989i	$-0.498532\pi$
$89$	0.0870007	0.00922206	0.00461103	+	0.999989i	$0.498532\pi$
$90$	−0.875351	−0.0922701
$91$	1.72534	0.180864
$92$	0.280943	0.0292903
$93$	10.0312	1.04019
$94$	26.1408	2.69622
$95$	−27.5833	−2.82999
$96$	−1.66573	−0.170008
$97$	1.48231	0.150506	0.0752529	−	0.997164i	$-0.476024\pi$
$97$	1.48231	0.150506	0.0752529	+	0.997164i	$0.476024\pi$
$98$	−13.2318	−1.33662
$99$	0.373160	0.0375040
$100$	26.8418	2.68418
$101$	5.34398	0.531746	0.265873	−	0.964008i	$-0.414340\pi$
$101$	5.34398	0.531746	0.265873	+	0.964008i	$0.414340\pi$
$102$	1.93950	0.192039
$103$	−6.99292	−0.689033	−0.344517	−	0.938780i	$-0.611957\pi$
$103$	−6.99292	−0.689033	−0.344517	+	0.938780i	$0.611957\pi$
$104$	−2.54089	−0.249155
$105$	−20.3326	−1.98426
$106$	0.713646	0.0693155
$107$	−3.38257	−0.327006	−0.163503	−	0.986543i	$-0.552279\pi$
$107$	−3.38257	−0.327006	−0.163503	+	0.986543i	$0.552279\pi$
$108$	−21.6412	−2.08243
$109$	−7.61282	−0.729176	−0.364588	−	0.931169i	$-0.618790\pi$
$109$	−7.61282	−0.729176	−0.364588	+	0.931169i	$0.618790\pi$
$110$	−30.0240	−2.86267
$111$	−4.57812	−0.434536
$112$	16.1361	1.52472
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−34.0993	−3.19369
$115$	−0.233080	−0.0217348
$116$	13.9042	1.29097
$117$	−0.0511906	−0.00473257
$118$	−25.0778	−2.30860
$119$	−1.62275	−0.148757
$120$	29.9436	2.73347
$121$	1.79915	0.163559
$122$	5.93857	0.537653
$123$	−13.4827	−1.21570
$124$	24.1500	2.16874
$125$	−5.27476	−0.471789
$126$	0.905406	0.0806600
$127$	−8.31256	−0.737621	−0.368810	−	0.929505i	$-0.620235\pi$
$127$	−8.31256	−0.737621	−0.368810	+	0.929505i	$0.620235\pi$
$128$	18.6566	1.64902
$129$	−19.0669	−1.67875
$130$	4.11872	0.361236
$131$	5.67845	0.496128	0.248064	−	0.968744i	$-0.420206\pi$
$131$	5.67845	0.496128	0.248064	+	0.968744i	$0.420206\pi$
$132$	−24.9407	−2.17081
$133$	28.5304	2.47390
$134$	22.0908	1.90835
$135$	17.9543	1.54526
$136$	2.38981	0.204925
$137$	−14.0612	−1.20133	−0.600664	−	0.799501i	$-0.705097\pi$
$137$	−14.0612	−1.20133	−0.600664	+	0.799501i	$0.705097\pi$
$138$	−0.288140	−0.0245281
$139$	18.3752	1.55857	0.779284	−	0.626671i	$-0.215583\pi$
$139$	18.3752	1.55857	0.779284	+	0.626671i	$0.215583\pi$
$140$	−48.9506	−4.13708
$141$	−18.0155	−1.51718
$142$	−2.46916	−0.207208
$143$	−1.75580	−0.146828
$144$	−0.478758	−0.0398965
$145$	−11.5354	−0.957963
$146$	−6.77692	−0.560862
$147$	9.11898	0.752121
$148$	−11.0218	−0.905986
$149$	1.19816	0.0981569	0.0490785	−	0.998795i	$-0.484372\pi$
$149$	1.19816	0.0981569	0.0490785	+	0.998795i	$0.484372\pi$
$150$	−27.5294	−2.24776
$151$	12.3289	1.00331	0.501654	−	0.865068i	$-0.332725\pi$
$151$	12.3289	1.00331	0.501654	+	0.865068i	$0.332725\pi$
$152$	−42.0164	−3.40798
$153$	0.0481469	0.00389244
$154$	31.0548	2.50247
$155$	−20.0356	−1.60930
$156$	3.42139	0.273931
$157$	−3.35954	−0.268120	−0.134060	−	0.990973i	$-0.542802\pi$
$157$	−3.35954	−0.268120	−0.134060	+	0.990973i	$0.542802\pi$
$158$	−9.97850	−0.793847
$159$	−0.491824	−0.0390042
$160$	3.32702	0.263024
$161$	0.241082	0.0189999
$162$	21.4230	1.68315
$163$	2.85910	0.223942	0.111971	−	0.993711i	$-0.464284\pi$
$163$	2.85910	0.223942	0.111971	+	0.993711i	$0.464284\pi$
$164$	−32.4596	−2.53467
$165$	20.6916	1.61084
$166$	−43.0602	−3.34212
$167$	3.99913	0.309462	0.154731	−	0.987957i	$-0.450549\pi$
$167$	3.99913	0.309462	0.154731	+	0.987957i	$0.450549\pi$
$168$	−30.9717	−2.38952
$169$	−12.7591	−0.981472
$170$	−3.87383	−0.297109
$171$	−0.846494	−0.0647330
$172$	−45.9034	−3.50010
$173$	4.63463	0.352364	0.176182	−	0.984358i	$-0.443625\pi$
$173$	4.63463	0.352364	0.176182	+	0.984358i	$0.443625\pi$
$174$	−14.2604	−1.08108
$175$	23.0334	1.74116
$176$	−16.4211	−1.23778
$177$	17.2829	1.29906
$178$	−0.214819	−0.0161014
$179$	5.57183	0.416458	0.208229	−	0.978080i	$-0.433230\pi$
$179$	5.57183	0.416458	0.208229	+	0.978080i	$0.433230\pi$
$180$	1.45236	0.108252
$181$	7.88779	0.586295	0.293147	−	0.956067i	$-0.405297\pi$
$181$	7.88779	0.586295	0.293147	+	0.956067i	$0.405297\pi$
$182$	−4.26014	−0.315782
$183$	−4.09269	−0.302540
$184$	−0.355040	−0.0261739
$185$	9.14404	0.672283
$186$	−24.7686	−1.81612
$187$	1.65141	0.120763
$188$	−43.3722	−3.16324
$189$	−18.5707	−1.35082
$190$	68.1077	4.94105
$191$	9.96289	0.720890	0.360445	−	0.932781i	$-0.382625\pi$
$191$	9.96289	0.720890	0.360445	+	0.932781i	$0.382625\pi$
$192$	−11.5083	−0.830543
$193$	11.6533	0.838825	0.419412	−	0.907796i	$-0.362236\pi$
$193$	11.6533	0.838825	0.419412	+	0.907796i	$0.362236\pi$
$194$	−3.66007	−0.262778
$195$	−2.83850	−0.203269
$196$	21.9539	1.56813
$197$	−22.1135	−1.57552	−0.787761	−	0.615981i	$-0.788760\pi$
$197$	−22.1135	−1.57552	−0.787761	+	0.615981i	$0.788760\pi$
$198$	−0.921394	−0.0654806
$199$	−15.4137	−1.09265	−0.546323	−	0.837574i	$-0.683973\pi$
$199$	−15.4137	−1.09265	−0.546323	+	0.837574i	$0.683973\pi$
$200$	−33.9211	−2.39859
$201$	−15.2243	−1.07384
$202$	−13.1952	−0.928409
$203$	11.9315	0.837425
$204$	−3.21796	−0.225302
$205$	26.9296	1.88084
$206$	17.2667	1.20303
$207$	−0.00715289	−0.000497160 0
$208$	2.25266	0.156194
$209$	−29.0342	−2.00834
$210$	50.2045	3.46444
$211$	−12.1021	−0.833144	−0.416572	−	0.909103i	$-0.636769\pi$
$211$	−12.1021	−0.833144	−0.416572	+	0.909103i	$0.636769\pi$
$212$	−1.18406	−0.0813217
$213$	1.70167	0.116597
$214$	8.35213	0.570940
$215$	38.0830	2.59724
$216$	27.3490	1.86086
$217$	20.7236	1.40681
$218$	18.7973	1.27311
$219$	4.67045	0.315600
$220$	49.8149	3.35852
$221$	−0.226542	−0.0152388
$222$	11.3041	0.758683
$223$	−23.3965	−1.56674	−0.783372	−	0.621553i	$-0.786502\pi$
$223$	−23.3965	−1.56674	−0.783372	+	0.621553i	$0.786502\pi$
$224$	−3.44125	−0.229928
$225$	−0.683400	−0.0455600
$226$	−2.46916	−0.164246
$227$	6.77434	0.449629	0.224814	−	0.974402i	$-0.427822\pi$
$227$	6.77434	0.449629	0.224814	+	0.974402i	$0.427822\pi$
$228$	56.5766	3.74688
$229$	−13.7383	−0.907850	−0.453925	−	0.891040i	$-0.649977\pi$
$229$	−13.7383	−0.907850	−0.453925	+	0.891040i	$0.649977\pi$
$230$	0.575512	0.0379481
$231$	−21.4021	−1.40815
$232$	−17.5714	−1.15362
$233$	15.9235	1.04318	0.521590	−	0.853196i	$-0.325339\pi$
$233$	15.9235	1.04318	0.521590	+	0.853196i	$0.325339\pi$
$234$	0.126398	0.00826289
$235$	35.9830	2.34727
$236$	41.6085	2.70848
$237$	6.87688	0.446702
$238$	4.00684	0.259725
$239$	0.805587	0.0521091	0.0260545	−	0.999661i	$-0.491706\pi$
$239$	0.805587	0.0521091	0.0260545	+	0.999661i	$0.491706\pi$
$240$	−26.5469	−1.71360
$241$	−17.5823	−1.13257	−0.566287	−	0.824208i	$-0.691621\pi$
$241$	−17.5823	−1.13257	−0.566287	+	0.824208i	$0.691621\pi$
$242$	−4.44241	−0.285569
$243$	1.08347	0.0695047
$244$	−9.85312	−0.630781
$245$	−18.2137	−1.16363
$246$	33.2911	2.12256
$247$	3.98294	0.253429
$248$	−30.5194	−1.93799
$249$	29.6758	1.88063
$250$	13.0242	0.823726
$251$	−31.0534	−1.96007	−0.980037	−	0.198815i	$-0.936291\pi$
$251$	−31.0534	−1.96007	−0.980037	+	0.198815i	$0.936291\pi$
$252$	−1.50223	−0.0946313
$253$	−0.245339	−0.0154244
$254$	20.5251	1.28786
$255$	2.66973	0.167185
$256$	−32.5403	−2.03377
$257$	12.2349	0.763189	0.381595	−	0.924330i	$-0.375375\pi$
$257$	12.2349	0.763189	0.381595	+	0.924330i	$0.375375\pi$
$258$	47.0793	2.93103
$259$	−9.45800	−0.587692
$260$	−6.83367	−0.423806
$261$	−0.354006	−0.0219124
$262$	−14.0210	−0.866221
$263$	8.79228	0.542155	0.271078	−	0.962557i	$-0.412620\pi$
$263$	8.79228	0.542155	0.271078	+	0.962557i	$0.412620\pi$
$264$	31.5186	1.93984
$265$	0.982337	0.0603445
$266$	−70.4462	−4.31933
$267$	0.148047	0.00906032
$268$	−36.6524	−2.23890
$269$	−1.89315	−0.115427	−0.0577136	−	0.998333i	$-0.518381\pi$
$269$	−1.89315	−0.115427	−0.0577136	+	0.998333i	$0.518381\pi$
$270$	−44.3321	−2.69796
$271$	15.8173	0.960830	0.480415	−	0.877041i	$-0.340486\pi$
$271$	15.8173	0.960830	0.480415	+	0.877041i	$0.340486\pi$
$272$	−2.11872	−0.128466
$273$	2.93596	0.177692
$274$	34.7194	2.09747
$275$	−23.4402	−1.41350
$276$	0.478073	0.0287766
$277$	−14.6586	−0.880750	−0.440375	−	0.897814i	$-0.645154\pi$
$277$	−14.6586	−0.880750	−0.440375	+	0.897814i	$0.645154\pi$
$278$	−45.3715	−2.72120
$279$	−0.614867	−0.0368111
$280$	61.8610	3.69690
$281$	−9.10342	−0.543065	−0.271532	−	0.962429i	$-0.587530\pi$
$281$	−9.10342	−0.543065	−0.271532	+	0.962429i	$0.587530\pi$
$282$	44.4832	2.64894
$283$	−10.9907	−0.653332	−0.326666	−	0.945140i	$-0.605925\pi$
$283$	−10.9907	−0.653332	−0.326666	+	0.945140i	$0.605925\pi$
$284$	4.09677	0.243099
$285$	−46.9378	−2.78036
$286$	4.33536	0.256355
$287$	−27.8542	−1.64418
$288$	0.102102	0.00601640
$289$	−16.7869	−0.987466
$290$	28.4828	1.67257
$291$	2.52241	0.147866
$292$	11.2441	0.658010
$293$	−11.3982	−0.665891	−0.332946	−	0.942946i	$-0.608043\pi$
$293$	−11.3982	−0.665891	−0.332946	+	0.942946i	$0.608043\pi$
$294$	−22.5162	−1.31317
$295$	−34.5198	−2.00982
$296$	13.9287	0.809590
$297$	18.8987	1.09661
$298$	−2.95845	−0.171378
$299$	0.0336560	0.00194637
$300$	45.6760	2.63710
$301$	−39.3906	−2.27044
$302$	−30.4420	−1.75174
$303$	9.09372	0.522421
$304$	37.2503	2.13645
$305$	8.17447	0.468069
$306$	−0.118883	−0.00679606
$307$	−6.26407	−0.357510	−0.178755	−	0.983894i	$-0.557207\pi$
$307$	−6.26407	−0.357510	−0.178755	+	0.983894i	$0.557207\pi$
$308$	−51.5253	−2.93593
$309$	−11.8997	−0.676949
$310$	49.4713	2.80978
$311$	6.96179	0.394767	0.197384	−	0.980326i	$-0.436756\pi$
$311$	6.96179	0.394767	0.197384	+	0.980326i	$0.436756\pi$
$312$	−4.32376	−0.244785
$313$	14.6960	0.830667	0.415333	−	0.909669i	$-0.363665\pi$
$313$	14.6960	0.830667	0.415333	+	0.909669i	$0.363665\pi$
$314$	8.29525	0.468128
$315$	1.24630	0.0702208
$316$	16.5561	0.931351
$317$	−7.07565	−0.397408	−0.198704	−	0.980060i	$-0.563673\pi$
$317$	−7.07565	−0.397408	−0.198704	+	0.980060i	$0.563673\pi$
$318$	1.21439	0.0680998
$319$	−12.1422	−0.679830
$320$	22.9860	1.28496
$321$	−5.75604	−0.321271
$322$	−0.595272	−0.0331732
$323$	−3.74612	−0.208440
$324$	−35.5444	−1.97469
$325$	3.21555	0.178367
$326$	−7.05958	−0.390994
$327$	−12.9545	−0.716388
$328$	41.0206	2.26498
$329$	−37.2185	−2.05192
$330$	−51.0910	−2.81247
$331$	1.68311	0.0925119	0.0462560	−	0.998930i	$-0.485271\pi$
$331$	1.68311	0.0925119	0.0462560	+	0.998930i	$0.485271\pi$
$332$	71.4442	3.92101
$333$	0.280618	0.0153778
$334$	−9.87451	−0.540309
$335$	30.4080	1.66137
$336$	27.4584	1.49798
$337$	27.3493	1.48981	0.744905	−	0.667170i	$-0.232495\pi$
$337$	27.3493	1.48981	0.744905	+	0.667170i	$0.232495\pi$
$338$	31.5044	1.71361
$339$	1.70167	0.0924223
$340$	6.42735	0.348572
$341$	−21.0895	−1.14206
$342$	2.09013	0.113021
$343$	−5.76956	−0.311527
$344$	58.0102	3.12770
$345$	−0.396626	−0.0213536
$346$	−11.4436	−0.615214
$347$	7.98332	0.428567	0.214284	−	0.976771i	$-0.431258\pi$
$347$	7.98332	0.428567	0.214284	+	0.976771i	$0.431258\pi$
$348$	23.6605	1.26833
$349$	−16.9612	−0.907912	−0.453956	−	0.891024i	$-0.649988\pi$
$349$	−16.9612	−0.907912	−0.453956	+	0.891024i	$0.649988\pi$
$350$	−56.8733	−3.04001
$351$	−2.59254	−0.138380
$352$	3.50202	0.186658
$353$	−11.6268	−0.618834	−0.309417	−	0.950926i	$-0.600134\pi$
$353$	−11.6268	−0.618834	−0.309417	+	0.950926i	$0.600134\pi$
$354$	−42.6743	−2.26811
$355$	−3.39881	−0.180390
$356$	0.356422	0.0188903
$357$	−2.76139	−0.146148
$358$	−13.7578	−0.727120
$359$	−2.08963	−0.110286	−0.0551432	−	0.998478i	$-0.517562\pi$
$359$	−2.08963	−0.110286	−0.0551432	+	0.998478i	$0.517562\pi$
$360$	−1.83541	−0.0967346
$361$	46.8624	2.46644
$362$	−19.4762	−1.02365
$363$	3.06157	0.160691
$364$	7.06830	0.370480
$365$	−9.32846	−0.488274
$366$	10.1055	0.528224
$367$	−29.9820	−1.56505	−0.782525	−	0.622620i	$-0.786068\pi$
$367$	−29.9820	−1.56505	−0.782525	+	0.622620i	$0.786068\pi$
$368$	0.314766	0.0164083
$369$	0.826431	0.0430223
$370$	−22.5781	−1.17378
$371$	−1.01607	−0.0527515
$372$	41.0955	2.13070
$373$	14.9761	0.775433	0.387717	−	0.921779i	$-0.373264\pi$
$373$	14.9761	0.775433	0.387717	+	0.921779i	$0.373264\pi$
$374$	−4.07759	−0.210847
$375$	−8.97592	−0.463515
$376$	54.8113	2.82668
$377$	1.66568	0.0857867
$378$	45.8542	2.35849
$379$	−34.4280	−1.76845	−0.884225	−	0.467061i	$-0.845313\pi$
$379$	−34.4280	−1.76845	−0.884225	+	0.467061i	$0.845313\pi$
$380$	−113.002	−5.79690
$381$	−14.1453	−0.724684
$382$	−24.6000	−1.25865
$383$	−4.67404	−0.238833	−0.119416	−	0.992844i	$-0.538102\pi$
$383$	−4.67404	−0.238833	−0.119416	+	0.992844i	$0.538102\pi$
$384$	31.7474	1.62010
$385$	42.7471	2.17859
$386$	−28.7740	−1.46456
$387$	1.16872	0.0594091
$388$	6.07268	0.308294
$389$	−14.1379	−0.716819	−0.358409	−	0.933565i	$-0.616681\pi$
$389$	−14.1379	−0.716819	−0.358409	+	0.933565i	$0.616681\pi$
$390$	7.00872	0.354900
$391$	−0.0316548	−0.00160085
$392$	−27.7441	−1.40129
$393$	9.66287	0.487427
$394$	54.6019	2.75080
$395$	−13.7354	−0.691105
$396$	1.52875	0.0768227
$397$	−32.9406	−1.65324	−0.826621	−	0.562759i	$-0.809740\pi$
$397$	−32.9406	−1.65324	−0.826621	+	0.562759i	$0.809740\pi$
$398$	38.0589	1.90772
$399$	48.5494	2.43051
$400$	30.0733	1.50366
$401$	−10.2844	−0.513577	−0.256788	−	0.966468i	$-0.582664\pi$
$401$	−10.2844	−0.513577	−0.256788	+	0.966468i	$0.582664\pi$
$402$	37.5913	1.87488
$403$	2.89308	0.144115
$404$	21.8931	1.08922
$405$	29.4888	1.46531
$406$	−29.4607	−1.46211
$407$	9.62501	0.477094
$408$	4.06668	0.201331
$409$	−21.1836	−1.04746	−0.523730	−	0.851884i	$-0.675460\pi$
$409$	−21.1836	−1.04746	−0.523730	+	0.851884i	$0.675460\pi$
$410$	−66.4935	−3.28388
$411$	−23.9276	−1.18026
$412$	−28.6484	−1.41141
$413$	35.7050	1.75693
$414$	0.0176617	0.000868023 0
$415$	−59.2725	−2.90957
$416$	−0.480411	−0.0235541
$417$	31.2687	1.53123
$418$	71.6901	3.50648
$419$	37.3302	1.82370	0.911851	−	0.410522i	$-0.134654\pi$
$419$	37.3302	1.82370	0.911851	+	0.410522i	$0.134654\pi$
$420$	−83.2979	−4.06452
$421$	−24.6139	−1.19961	−0.599803	−	0.800147i	$-0.704755\pi$
$421$	−24.6139	−1.19961	−0.599803	+	0.800147i	$0.704755\pi$
$422$	29.8821	1.45464
$423$	1.10427	0.0536914
$424$	1.49635	0.0726692
$425$	−3.02436	−0.146703
$426$	−4.20171	−0.203574
$427$	−8.45514	−0.409173
$428$	−13.8576	−0.669834
$429$	−2.98780	−0.144253
$430$	−94.0332	−4.53468
$431$	17.7323	0.854137	0.427068	−	0.904219i	$-0.359546\pi$
$431$	17.7323	0.854137	0.427068	+	0.904219i	$0.359546\pi$
$432$	−24.2466	−1.16657
$433$	10.5684	0.507885	0.253943	−	0.967219i	$-0.418273\pi$
$433$	10.5684	0.507885	0.253943	+	0.967219i	$0.418273\pi$
$434$	−51.1699	−2.45623
$435$	−19.6295	−0.941162
$436$	−31.1880	−1.49363
$437$	0.556539	0.0266229
$438$	−11.5321	−0.551026
$439$	21.3758	1.02021	0.510105	−	0.860112i	$-0.329607\pi$
$439$	21.3758	1.02021	0.510105	+	0.860112i	$0.329607\pi$
$440$	−62.9533	−3.00118
$441$	−0.558952	−0.0266168
$442$	0.559369	0.0266065
$443$	−30.6566	−1.45654	−0.728270	−	0.685290i	$-0.759675\pi$
$443$	−30.6566	−1.45654	−0.728270	+	0.685290i	$0.759675\pi$
$444$	−18.7555	−0.890097
$445$	−0.295699	−0.0140175
$446$	57.7697	2.73548
$447$	2.03887	0.0964355
$448$	−23.7752	−1.12327
$449$	−15.6227	−0.737280	−0.368640	−	0.929572i	$-0.620176\pi$
$449$	−15.6227	−0.737280	−0.368640	+	0.929572i	$0.620176\pi$
$450$	1.68743	0.0795460
$451$	28.3460	1.33476
$452$	4.09677	0.192696
$453$	20.9797	0.985712
$454$	−16.7270	−0.785035
$455$	−5.86410	−0.274913
$456$	−71.4983	−3.34822
$457$	3.77966	0.176805	0.0884025	−	0.996085i	$-0.471824\pi$
$457$	3.77966	0.176805	0.0884025	+	0.996085i	$0.471824\pi$
$458$	33.9220	1.58507
$459$	2.43839	0.113814
$460$	−0.954873	−0.0445212
$461$	10.4461	0.486524	0.243262	−	0.969961i	$-0.421782\pi$
$461$	10.4461	0.486524	0.243262	+	0.969961i	$0.421782\pi$
$462$	52.8452	2.45858
$463$	−28.2527	−1.31301	−0.656507	−	0.754320i	$-0.727967\pi$
$463$	−28.2527	−1.31301	−0.656507	+	0.754320i	$0.727967\pi$
$464$	15.5782	0.723198
$465$	−34.0941	−1.58108
$466$	−39.3176	−1.82135
$467$	−29.3042	−1.35604	−0.678019	−	0.735045i	$-0.737161\pi$
$467$	−29.3042	−1.35604	−0.678019	+	0.735045i	$0.737161\pi$
$468$	−0.209716	−0.00969413
$469$	−31.4521	−1.45232
$470$	−88.8479	−4.09825
$471$	−5.71684	−0.263418
$472$	−52.5824	−2.42030
$473$	40.0862	1.84316
$474$	−16.9802	−0.779924
$475$	53.1727	2.43973
$476$	−6.64803	−0.304712
$477$	0.0301466	0.00138032
$478$	−1.98913	−0.0909805
$479$	−1.53263	−0.0700275	−0.0350137	−	0.999387i	$-0.511148\pi$
$479$	−1.53263	−0.0700275	−0.0350137	+	0.999387i	$0.511148\pi$
$480$	5.66151	0.258411
$481$	−1.32037	−0.0602037
$482$	43.4136	1.97743
$483$	0.410244	0.0186667
$484$	7.37072	0.335033
$485$	−5.03810	−0.228768
$486$	−2.67527	−0.121353
$487$	−33.3681	−1.51205	−0.756027	−	0.654541i	$-0.772862\pi$
$487$	−33.3681	−1.51205	−0.756027	+	0.654541i	$0.772862\pi$
$488$	12.4518	0.563667
$489$	4.86525	0.220014
$490$	44.9725	2.03165
$491$	−15.5028	−0.699634	−0.349817	−	0.936818i	$-0.613756\pi$
$491$	−15.5028	−0.699634	−0.349817	+	0.936818i	$0.613756\pi$
$492$	−55.2357	−2.49022
$493$	−1.56664	−0.0705578
$494$	−9.83454	−0.442477
$495$	−1.26830	−0.0570060
$496$	27.0574	1.21491
$497$	3.51551	0.157692
$498$	−73.2744	−3.28350
$499$	37.7203	1.68859	0.844295	−	0.535878i	$-0.180019\pi$
$499$	37.7203	1.68859	0.844295	+	0.535878i	$0.180019\pi$
$500$	−21.6095	−0.966405
$501$	6.80522	0.304035
$502$	76.6760	3.42222
$503$	−11.2004	−0.499400	−0.249700	−	0.968323i	$-0.580332\pi$
$503$	−11.2004	−0.499400	−0.249700	+	0.968323i	$0.580332\pi$
$504$	1.89843	0.0845627
$505$	−18.1632	−0.808252
$506$	0.605783	0.0269304
$507$	−21.7119	−0.964259
$508$	−34.0547	−1.51093
$509$	5.47118	0.242506	0.121253	−	0.992622i	$-0.461309\pi$
$509$	5.47118	0.242506	0.121253	+	0.992622i	$0.461309\pi$
$510$	−6.59200	−0.291898
$511$	9.64875	0.426836
$512$	43.0341	1.90185
$513$	−42.8706	−1.89278
$514$	−30.2099	−1.33250
$515$	23.7677	1.04733
$516$	−78.1127	−3.43872
$517$	37.8757	1.66577
$518$	23.3534	1.02609
$519$	7.88662	0.346184
$520$	8.63601	0.378714
$521$	−1.96130	−0.0859261	−0.0429630	−	0.999077i	$-0.513680\pi$
$521$	−1.96130	−0.0859261	−0.0429630	+	0.999077i	$0.513680\pi$
$522$	0.874098	0.0382582
$523$	41.0263	1.79395	0.896977	−	0.442077i	$-0.145758\pi$
$523$	41.0263	1.79395	0.896977	+	0.442077i	$0.145758\pi$
$524$	23.2633	1.01626
$525$	39.1954	1.71063
$526$	−21.7096	−0.946583
$527$	−2.72107	−0.118531
$528$	−27.9433	−1.21608
$529$	−22.9953	−0.999796
$530$	−2.42555	−0.105359
$531$	−1.05936	−0.0459725
$532$	116.882	5.06749
$533$	−3.88854	−0.168431
$534$	−0.365552	−0.0158190
$535$	11.4967	0.497047
$536$	46.3192	2.00069
$537$	9.48144	0.409154
$538$	4.67449	0.201531
$539$	−19.1717	−0.825783
$540$	73.5546	3.16529
$541$	−27.4174	−1.17877	−0.589383	−	0.807854i	$-0.700629\pi$
$541$	−27.4174	−1.17877	−0.589383	+	0.807854i	$0.700629\pi$
$542$	−39.0554	−1.67757
$543$	13.4224	0.576012
$544$	0.451847	0.0193728
$545$	25.8746	1.10834
$546$	−7.24937	−0.310244
$547$	−17.7774	−0.760109	−0.380054	−	0.924964i	$-0.624095\pi$
$547$	−17.7774	−0.760109	−0.380054	+	0.924964i	$0.624095\pi$
$548$	−57.6055	−2.46078
$549$	0.250863	0.0107066
$550$	57.8776	2.46791
$551$	27.5438	1.17341
$552$	−0.604162	−0.0257149
$553$	14.2071	0.604145
$554$	36.1945	1.53776
$555$	15.5602	0.660493
$556$	75.2791	3.19255
$557$	−22.0337	−0.933598	−0.466799	−	0.884363i	$-0.654593\pi$
$557$	−22.0337	−0.933598	−0.466799	+	0.884363i	$0.654593\pi$
$558$	1.51821	0.0642708
$559$	−5.49907	−0.232586
$560$	−54.8437	−2.31757
$561$	2.81015	0.118645
$562$	22.4778	0.948171
$563$	1.33304	0.0561809	0.0280905	−	0.999605i	$-0.491057\pi$
$563$	1.33304	0.0561809	0.0280905	+	0.999605i	$0.491057\pi$
$564$	−73.8053	−3.10776
$565$	−3.39881	−0.142989
$566$	27.1379	1.14069
$567$	−30.5013	−1.28093
$568$	−5.17727	−0.217233
$569$	−6.00351	−0.251680	−0.125840	−	0.992051i	$-0.540163\pi$
$569$	−6.00351	−0.251680	−0.125840	+	0.992051i	$0.540163\pi$
$570$	115.897	4.85440
$571$	1.41852	0.0593633	0.0296817	−	0.999559i	$-0.490551\pi$
$571$	1.41852	0.0593633	0.0296817	+	0.999559i	$0.490551\pi$
$572$	−7.19312	−0.300759
$573$	16.9536	0.708247
$574$	68.7765	2.87068
$575$	0.449311	0.0187376
$576$	0.705409	0.0293921
$577$	−13.3805	−0.557037	−0.278519	−	0.960431i	$-0.589843\pi$
$577$	−13.3805	−0.557037	−0.278519	+	0.960431i	$0.589843\pi$
$578$	41.4497	1.72408
$579$	19.8302	0.824114
$580$	−47.2579	−1.96228
$581$	61.3076	2.54347
$582$	−6.22824	−0.258169
$583$	1.03401	0.0428242
$584$	−14.2096	−0.587999
$585$	0.173987	0.00719349
$586$	28.1441	1.16262
$587$	−29.6018	−1.22180	−0.610898	−	0.791709i	$-0.709192\pi$
$587$	−29.6018	−1.22180	−0.610898	+	0.791709i	$0.709192\pi$
$588$	37.3583	1.54063
$589$	47.8404	1.97123
$590$	85.2349	3.50907
$591$	−37.6300	−1.54789
$592$	−12.3487	−0.507529
$593$	43.1336	1.77128	0.885642	−	0.464368i	$-0.153718\pi$
$593$	43.1336	1.77128	0.885642	+	0.464368i	$0.153718\pi$
$594$	−46.6639	−1.91464
$595$	5.51543	0.226111
$596$	4.90858	0.201063
$597$	−26.2291	−1.07348
$598$	−0.0831021	−0.00339830
$599$	−10.7793	−0.440430	−0.220215	−	0.975451i	$-0.570676\pi$
$599$	−10.7793	−0.440430	−0.220215	+	0.975451i	$0.570676\pi$
$600$	−57.7227	−2.35652
$601$	24.6860	1.00696	0.503482	−	0.864006i	$-0.332052\pi$
$601$	24.6860	1.00696	0.503482	+	0.864006i	$0.332052\pi$
$602$	97.2618	3.96410
$603$	0.933181	0.0380021
$604$	50.5085	2.05516
$605$	−6.11499	−0.248610
$606$	−22.4539	−0.912127
$607$	6.97105	0.282946	0.141473	−	0.989942i	$-0.454816\pi$
$607$	6.97105	0.282946	0.141473	+	0.989942i	$0.454816\pi$
$608$	−7.94414	−0.322177
$609$	20.3035	0.822738
$610$	−20.1841	−0.817231
$611$	−5.19583	−0.210201
$612$	0.197247	0.00797322
$613$	28.4450	1.14888	0.574441	−	0.818546i	$-0.305219\pi$
$613$	28.4450	1.14888	0.574441	+	0.818546i	$0.305219\pi$
$614$	15.4670	0.624198
$615$	45.8253	1.84786
$616$	65.1148	2.62355
$617$	−12.1449	−0.488936	−0.244468	−	0.969657i	$-0.578613\pi$
$617$	−12.1449	−0.488936	−0.244468	+	0.969657i	$0.578613\pi$
$618$	29.3823	1.18193
$619$	16.4274	0.660274	0.330137	−	0.943933i	$-0.392905\pi$
$619$	16.4274	0.660274	0.330137	+	0.943933i	$0.392905\pi$
$620$	−82.0814	−3.29647
$621$	−0.362258	−0.0145369
$622$	−17.1898	−0.689248
$623$	0.305852	0.0122537
$624$	3.83329	0.153455
$625$	−14.8318	−0.593271
$626$	−36.2868	−1.45031
$627$	−49.4067	−1.97311
$628$	−13.7632	−0.549213
$629$	1.24186	0.0495163
$630$	−3.07731	−0.122603
$631$	14.0771	0.560400	0.280200	−	0.959942i	$-0.409599\pi$
$631$	14.0771	0.560400	0.280200	+	0.959942i	$0.409599\pi$
$632$	−20.9226	−0.832257
$633$	−20.5938	−0.818532
$634$	17.4709	0.693860
$635$	28.2529	1.12118
$636$	−2.01489	−0.0798955
$637$	2.62999	0.104204
$638$	29.9810	1.18696
$639$	−0.104305	−0.00412624
$640$	−63.4103	−2.50651
$641$	−34.6618	−1.36906	−0.684529	−	0.728986i	$-0.739992\pi$
$641$	−34.6618	−1.36906	−0.684529	+	0.728986i	$0.739992\pi$
$642$	14.2126	0.560927
$643$	16.6663	0.657256	0.328628	−	0.944459i	$-0.393414\pi$
$643$	16.6663	0.657256	0.328628	+	0.944459i	$0.393414\pi$
$644$	0.987659	0.0389192
$645$	64.8049	2.55169
$646$	9.24979	0.363928
$647$	3.94773	0.155201	0.0776006	−	0.996985i	$-0.475274\pi$
$647$	3.94773	0.155201	0.0776006	+	0.996985i	$0.475274\pi$
$648$	44.9190	1.76459
$649$	−36.3355	−1.42629
$650$	−7.93972	−0.311421
$651$	35.2648	1.38213
$652$	11.7131	0.458719
$653$	−20.0346	−0.784015	−0.392008	−	0.919962i	$-0.628219\pi$
$653$	−20.0346	−0.784015	−0.392008	+	0.919962i	$0.628219\pi$
$654$	31.9869	1.25079
$655$	−19.3000	−0.754113
$656$	−36.3674	−1.41991
$657$	−0.286278	−0.0111688
$658$	91.8985	3.58257
$659$	−13.6681	−0.532432	−0.266216	−	0.963913i	$-0.585774\pi$
$659$	−13.6681	−0.532432	−0.266216	+	0.963913i	$0.585774\pi$
$660$	84.7688	3.29962
$661$	−36.7122	−1.42794	−0.713970	−	0.700177i	$-0.753105\pi$
$661$	−36.7122	−1.42794	−0.713970	+	0.700177i	$0.753105\pi$
$662$	−4.15587	−0.161522
$663$	−0.385500	−0.0149716
$664$	−90.2872	−3.50382
$665$	−96.9695	−3.76031
$666$	−0.692892	−0.0268490
$667$	0.232746	0.00901196
$668$	16.3835	0.633897
$669$	−39.8132	−1.53927
$670$	−75.0824	−2.90069
$671$	8.60445	0.332171
$672$	−5.85589	−0.225896
$673$	11.5497	0.445210	0.222605	−	0.974909i	$-0.428544\pi$
$673$	11.5497	0.445210	0.222605	+	0.974909i	$0.428544\pi$
$674$	−67.5299	−2.60115
$675$	−34.6107	−1.33217
$676$	−52.2712	−2.01043
$677$	30.3911	1.16803	0.584013	−	0.811745i	$-0.301482\pi$
$677$	30.3911	1.16803	0.584013	+	0.811745i	$0.301482\pi$
$678$	−4.20171	−0.161366
$679$	5.21108	0.199983
$680$	−8.12253	−0.311485
$681$	11.5277	0.441743
$682$	52.0735	1.99400
$683$	−18.8076	−0.719651	−0.359826	−	0.933020i	$-0.617164\pi$
$683$	−18.8076	−0.719651	−0.359826	+	0.933020i	$0.617164\pi$
$684$	−3.46789	−0.132598
$685$	47.7914	1.82602
$686$	14.2460	0.543915
$687$	−23.3780	−0.891928
$688$	−51.4298	−1.96074
$689$	−0.141846	−0.00540392
$690$	0.979333	0.0372826
$691$	−44.6913	−1.70014	−0.850068	−	0.526673i	$-0.823439\pi$
$691$	−44.6913	−1.70014	−0.850068	+	0.526673i	$0.823439\pi$
$692$	18.9870	0.721777
$693$	1.31185	0.0498331
$694$	−19.7121	−0.748262
$695$	−62.4541	−2.36902
$696$	−29.9008	−1.13339
$697$	3.65734	0.138531
$698$	41.8800	1.58518
$699$	27.0965	1.02489
$700$	94.3626	3.56657
$701$	45.2868	1.71046	0.855229	−	0.518251i	$-0.173417\pi$
$701$	45.2868	1.71046	0.855229	+	0.518251i	$0.173417\pi$
$702$	6.40141	0.241606
$703$	−21.8338	−0.823478
$704$	24.1951	0.911886
$705$	61.2313	2.30610
$706$	28.7086	1.08046
$707$	18.7868	0.706552
$708$	70.8041	2.66098
$709$	23.5695	0.885170	0.442585	−	0.896727i	$-0.354062\pi$
$709$	23.5695	0.885170	0.442585	+	0.896727i	$0.354062\pi$
$710$	8.39223	0.314955
$711$	−0.421522	−0.0158083
$712$	−0.450426	−0.0168804
$713$	0.404252	0.0151394
$714$	6.81833	0.255170
$715$	5.96765	0.223177
$716$	22.8265	0.853066
$717$	1.37085	0.0511952
$718$	5.15964	0.192556
$719$	−39.5703	−1.47572	−0.737861	−	0.674953i	$-0.764164\pi$
$719$	−39.5703	−1.47572	−0.737861	+	0.674953i	$0.764164\pi$
$720$	1.62721	0.0606425
$721$	−24.5837	−0.915545
$722$	−115.711	−4.30632
$723$	−29.9193	−1.11271
$724$	32.3144	1.20096
$725$	22.2370	0.825860
$726$	−7.55953	−0.280560
$727$	26.4246	0.980036	0.490018	−	0.871712i	$-0.336990\pi$
$727$	26.4246	0.980036	0.490018	+	0.871712i	$0.336990\pi$
$728$	−8.93252	−0.331061
$729$	27.8723	1.03231
$730$	23.0335	0.852508
$731$	5.17210	0.191297
$732$	−16.7668	−0.619719
$733$	−18.8915	−0.697772	−0.348886	−	0.937165i	$-0.613440\pi$
$733$	−18.8915	−0.697772	−0.348886	+	0.937165i	$0.613440\pi$
$734$	74.0305	2.73252
$735$	−30.9937	−1.14322
$736$	−0.0671282	−0.00247438
$737$	32.0075	1.17901
$738$	−2.04059	−0.0751153
$739$	−29.0141	−1.06730	−0.533650	−	0.845706i	$-0.679180\pi$
$739$	−29.0141	−1.06730	−0.533650	+	0.845706i	$0.679180\pi$
$740$	37.4610	1.37709
$741$	6.77767	0.248984
$742$	2.50883	0.0921021
$743$	14.2198	0.521672	0.260836	−	0.965383i	$-0.416002\pi$
$743$	14.2198	0.521672	0.260836	+	0.965383i	$0.416002\pi$
$744$	−51.9341	−1.90400
$745$	−4.07232	−0.149198
$746$	−36.9785	−1.35388
$747$	−1.81899	−0.0665534
$748$	6.76543	0.247369
$749$	−11.8915	−0.434505
$750$	22.1630	0.809279
$751$	−28.2924	−1.03241	−0.516203	−	0.856466i	$-0.672655\pi$
$751$	−28.2924	−1.03241	−0.516203	+	0.856466i	$0.672655\pi$
$752$	−48.5938	−1.77203
$753$	−52.8428	−1.92570
$754$	−4.11283	−0.149780
$755$	−41.9035	−1.52502
$756$	−76.0801	−2.76701
$757$	−44.0865	−1.60235	−0.801175	−	0.598430i	$-0.795792\pi$
$757$	−44.0865	−1.60235	−0.801175	+	0.598430i	$0.795792\pi$
$758$	85.0085	3.08765
$759$	−0.417488	−0.0151538
$760$	142.806	5.18012
$761$	−2.31826	−0.0840370	−0.0420185	−	0.999117i	$-0.513379\pi$
$761$	−2.31826	−0.0840370	−0.0420185	+	0.999117i	$0.513379\pi$
$762$	34.9270	1.26527
$763$	−26.7630	−0.968884
$764$	40.8157	1.47666
$765$	−0.163642	−0.00591650
$766$	11.5410	0.416993
$767$	4.98454	0.179981
$768$	−55.3729	−1.99810
$769$	5.38514	0.194193	0.0970965	−	0.995275i	$-0.469044\pi$
$769$	5.38514	0.194193	0.0970965	+	0.995275i	$0.469044\pi$
$770$	−105.550	−3.80374
$771$	20.8197	0.749804
$772$	47.7410	1.71824
$773$	37.6290	1.35342	0.676710	−	0.736250i	$-0.263405\pi$
$773$	37.6290	1.35342	0.676710	+	0.736250i	$0.263405\pi$
$774$	−2.88575	−0.103726
$775$	38.6230	1.38738
$776$	−7.67432	−0.275492
$777$	−16.0944	−0.577385
$778$	34.9087	1.25154
$779$	−64.3014	−2.30384
$780$	−11.6287	−0.416374
$781$	−3.57759	−0.128016
$782$	0.0781609	0.00279503
$783$	−17.9286	−0.640715
$784$	24.5969	0.878461
$785$	11.4184	0.407542
$786$	−23.8592	−0.851030
$787$	−4.20590	−0.149924	−0.0749621	−	0.997186i	$-0.523884\pi$
$787$	−4.20590	−0.149924	−0.0749621	+	0.997186i	$0.523884\pi$
$788$	−90.5939	−3.22727
$789$	14.9616	0.532647
$790$	33.9151	1.20664
$791$	3.51551	0.124997
$792$	−1.93195	−0.0686489
$793$	−1.18037	−0.0419161
$794$	81.3357	2.88650
$795$	1.67162	0.0592862
$796$	−63.1463	−2.23816
$797$	34.9821	1.23913	0.619565	−	0.784945i	$-0.287309\pi$
$797$	34.9821	1.23913	0.619565	+	0.784945i	$0.287309\pi$
$798$	−119.876	−4.24358
$799$	4.88689	0.172886
$800$	−6.41354	−0.226753
$801$	−0.00907461	−0.000320635 0
$802$	25.3938	0.896686
$803$	−9.81914	−0.346510
$804$	−62.3705	−2.19964
$805$	−0.819394	−0.0288799
$806$	−7.14350	−0.251619
$807$	−3.22152	−0.113403
$808$	−27.6672	−0.973330
$809$	−22.7496	−0.799834	−0.399917	−	0.916551i	$-0.630961\pi$
$809$	−22.7496	−0.799834	−0.399917	+	0.916551i	$0.630961\pi$
$810$	−72.8127	−2.55838
$811$	12.7505	0.447731	0.223865	−	0.974620i	$-0.428132\pi$
$811$	12.7505	0.447731	0.223865	+	0.974620i	$0.428132\pi$
$812$	48.8805	1.71537
$813$	26.9158	0.943979
$814$	−23.7657	−0.832989
$815$	−9.71754	−0.340391
$816$	−3.60537	−0.126213
$817$	−90.9332	−3.18135
$818$	52.3057	1.82883
$819$	−0.179961	−0.00628835
$820$	110.324	3.85269
$821$	46.7648	1.63210	0.816051	−	0.577980i	$-0.196159\pi$
$821$	46.7648	1.63210	0.816051	+	0.577980i	$0.196159\pi$
$822$	59.0811	2.06069
$823$	34.7869	1.21260	0.606298	−	0.795237i	$-0.292654\pi$
$823$	34.7869	1.21260	0.606298	+	0.795237i	$0.292654\pi$
$824$	36.2042	1.26123
$825$	−39.8875	−1.38871
$826$	−88.1615	−3.06753
$827$	−33.1920	−1.15420	−0.577100	−	0.816673i	$-0.695816\pi$
$827$	−33.1920	−1.15420	−0.577100	+	0.816673i	$0.695816\pi$
$828$	−0.0293038	−0.00101838
$829$	22.6467	0.786551	0.393275	−	0.919421i	$-0.371342\pi$
$829$	22.6467	0.786551	0.393275	+	0.919421i	$0.371342\pi$
$830$	146.353	5.08000
$831$	−24.9442	−0.865303
$832$	−3.31911	−0.115069
$833$	−2.47362	−0.0857058
$834$	−77.2075	−2.67348
$835$	−13.5923	−0.470381
$836$	−118.946	−4.11384
$837$	−31.1399	−1.07635
$838$	−92.1745	−3.18411
$839$	−24.9315	−0.860733	−0.430366	−	0.902654i	$-0.641616\pi$
$839$	−24.9315	−0.860733	−0.430366	+	0.902654i	$0.641616\pi$
$840$	105.267	3.63206
$841$	−17.4811	−0.602797
$842$	60.7757	2.09447
$843$	−15.4911	−0.533541
$844$	−49.5795	−1.70660
$845$	43.3659	1.49183
$846$	−2.72662	−0.0937431
$847$	6.32495	0.217328
$848$	−1.32661	−0.0455560
$849$	−18.7027	−0.641874
$850$	7.46763	0.256138
$851$	−0.184496	−0.00632445
$852$	6.97137	0.238835
$853$	−4.08405	−0.139835	−0.0699176	−	0.997553i	$-0.522274\pi$
$853$	−4.08405	−0.139835	−0.0699176	+	0.997553i	$0.522274\pi$
$854$	20.8771	0.714401
$855$	2.87708	0.0983939
$856$	17.5125	0.598564
$857$	−31.3001	−1.06919	−0.534596	−	0.845108i	$-0.679536\pi$
$857$	−31.3001	−1.06919	−0.534596	+	0.845108i	$0.679536\pi$
$858$	7.37738	0.251860
$859$	31.0627	1.05985	0.529923	−	0.848046i	$-0.322221\pi$
$859$	31.0627	1.05985	0.529923	+	0.848046i	$0.322221\pi$
$860$	156.017	5.32015
$861$	−47.3987	−1.61534
$862$	−43.7841	−1.49129
$863$	−48.0917	−1.63706	−0.818530	−	0.574464i	$-0.805211\pi$
$863$	−48.0917	−1.63706	−0.818530	+	0.574464i	$0.805211\pi$
$864$	5.17093	0.175919
$865$	−15.7522	−0.535592
$866$	−26.0951	−0.886749
$867$	−28.5659	−0.970148
$868$	84.8997	2.88168
$869$	−14.4579	−0.490451
$870$	48.4684	1.64323
$871$	−4.39082	−0.148777
$872$	39.4136	1.33471
$873$	−0.154612	−0.00523284
$874$	−1.37419	−0.0464825
$875$	−18.5435	−0.626884
$876$	19.1338	0.646470
$877$	−30.1411	−1.01779	−0.508897	−	0.860828i	$-0.669947\pi$
$877$	−30.1411	−1.01779	−0.508897	+	0.860828i	$0.669947\pi$
$878$	−52.7803	−1.78125
$879$	−19.3961	−0.654213
$880$	55.8122	1.88143
$881$	−5.75922	−0.194033	−0.0970166	−	0.995283i	$-0.530930\pi$
$881$	−5.75922	−0.194033	−0.0970166	+	0.995283i	$0.530930\pi$
$882$	1.38014	0.0464719
$883$	−9.04559	−0.304408	−0.152204	−	0.988349i	$-0.548637\pi$
$883$	−9.04559	−0.304408	−0.152204	+	0.988349i	$0.548637\pi$
$884$	−0.928089	−0.0312150
$885$	−58.7414	−1.97457
$886$	75.6962	2.54307
$887$	−47.4938	−1.59469	−0.797343	−	0.603527i	$-0.793762\pi$
$887$	−47.4938	−1.59469	−0.797343	+	0.603527i	$0.793762\pi$
$888$	23.7021	0.795392
$889$	−29.2229	−0.980105
$890$	0.730130	0.0244740
$891$	31.0399	1.03988
$892$	−95.8499	−3.20929
$893$	−85.9189	−2.87517
$894$	−5.03432	−0.168373
$895$	−18.9376	−0.633015
$896$	65.5875	2.19112
$897$	0.0572715	0.00191224
$898$	38.5750	1.28726
$899$	20.0070	0.667270
$900$	−2.79973	−0.0933244
$901$	0.133412	0.00444461
$902$	−69.9910	−2.33045
$903$	−67.0299	−2.23062
$904$	−5.17727	−0.172193
$905$	−26.8091	−0.891166
$906$	−51.8023	−1.72102
$907$	−15.6712	−0.520353	−0.260176	−	0.965561i	$-0.583781\pi$
$907$	−15.6712	−0.520353	−0.260176	+	0.965561i	$0.583781\pi$
$908$	27.7529	0.921013
$909$	−0.557404	−0.0184879
$910$	14.4794	0.479988
$911$	−17.3647	−0.575318	−0.287659	−	0.957733i	$-0.592877\pi$
$911$	−17.3647	−0.575318	−0.287659	+	0.957733i	$0.592877\pi$
$912$	63.3878	2.09898
$913$	−62.3902	−2.06481
$914$	−9.33259	−0.308695
$915$	13.9103	0.459860
$916$	−56.2825	−1.85963
$917$	19.9627	0.659225
$918$	−6.02079	−0.198716
$919$	29.6598	0.978388	0.489194	−	0.872175i	$-0.337291\pi$
$919$	29.6598	0.978388	0.489194	+	0.872175i	$0.337291\pi$
$920$	1.20672	0.0397842
$921$	−10.6594	−0.351240
$922$	−25.7932	−0.849453
$923$	0.490778	0.0161542
$924$	−87.6793	−2.88444
$925$	−17.6271	−0.579575
$926$	69.7605	2.29247
$927$	0.729397	0.0239565
$928$	−3.32226	−0.109058
$929$	−25.1087	−0.823789	−0.411894	−	0.911232i	$-0.635133\pi$
$929$	−25.1087	−0.823789	−0.411894	+	0.911232i	$0.635133\pi$
$930$	84.1840	2.76050
$931$	43.4899	1.42532
$932$	65.2347	2.13684
$933$	11.8467	0.387844
$934$	72.3569	2.36759
$935$	−5.61282	−0.183559
$936$	0.265027	0.00866269
$937$	1.88918	0.0617169	0.0308584	−	0.999524i	$-0.490176\pi$
$937$	1.88918	0.0617169	0.0308584	+	0.999524i	$0.490176\pi$
$938$	77.6604	2.53570
$939$	25.0078	0.816099
$940$	147.414	4.80811
$941$	16.4125	0.535034	0.267517	−	0.963553i	$-0.413797\pi$
$941$	16.4125	0.535034	0.267517	+	0.963553i	$0.413797\pi$
$942$	14.1158	0.459918
$943$	−0.543349	−0.0176939
$944$	46.6177	1.51728
$945$	63.1185	2.05325
$946$	−98.9793	−3.21809
$947$	−61.3906	−1.99493	−0.997464	−	0.0711780i	$-0.977324\pi$
$947$	−61.3906	−1.99493	−0.997464	+	0.0711780i	$0.977324\pi$
$948$	28.1730	0.915017
$949$	1.34700	0.0437255
$950$	−131.292	−4.25968
$951$	−12.0405	−0.390438
$952$	8.40141	0.272291
$953$	−14.6806	−0.475552	−0.237776	−	0.971320i	$-0.576418\pi$
$953$	−14.6806	−0.475552	−0.237776	+	0.971320i	$0.576418\pi$
$954$	−0.0744368	−0.00240998
$955$	−33.8620	−1.09575
$956$	3.30030	0.106739
$957$	−20.6620	−0.667908
$958$	3.78431	0.122265
$959$	−49.4323	−1.59625
$960$	39.1147	1.26242
$961$	3.74976	0.120960
$962$	3.26021	0.105113
$963$	0.352819	0.0113694
$964$	−72.0306	−2.31995
$965$	−39.6075	−1.27501
$966$	−1.01296	−0.0325914
$967$	−51.0041	−1.64018	−0.820091	−	0.572234i	$-0.806077\pi$
$967$	−51.0041	−1.64018	−0.820091	+	0.572234i	$0.806077\pi$
$968$	−9.31470	−0.299386
$969$	−6.37468	−0.204784
$970$	12.4399	0.399421
$971$	−35.4012	−1.13608	−0.568039	−	0.823002i	$-0.692298\pi$
$971$	−35.4012	−1.13608	−0.568039	+	0.823002i	$0.692298\pi$
$972$	4.43873	0.142372
$973$	64.5984	2.07093
$974$	82.3913	2.63999
$975$	5.47182	0.175238
$976$	−11.0393	−0.353361
$977$	−50.5701	−1.61788	−0.808941	−	0.587890i	$-0.799959\pi$
$977$	−50.5701	−1.61788	−0.808941	+	0.587890i	$0.799959\pi$
$978$	−12.0131	−0.384137
$979$	−0.311253	−0.00994769
$980$	−74.6172	−2.38356
$981$	0.794055	0.0253522
$982$	38.2791	1.22153
$983$	50.2499	1.60272	0.801361	−	0.598181i	$-0.204110\pi$
$983$	50.2499	1.60272	0.801361	+	0.598181i	$0.204110\pi$
$984$	69.8037	2.22526
$985$	75.1597	2.39479
$986$	3.86828	0.123191
$987$	−63.3337	−2.01593
$988$	16.3172	0.519119
$989$	−0.768388	−0.0244333
$990$	3.13165	0.0995303
$991$	−34.8894	−1.10830	−0.554149	−	0.832418i	$-0.686956\pi$
$991$	−34.8894	−1.10830	−0.554149	+	0.832418i	$0.686956\pi$
$992$	−5.77037	−0.183210
$993$	2.86410	0.0908895
$994$	−8.68038	−0.275325
$995$	52.3882	1.66082
$996$	121.575	3.85225
$997$	20.6784	0.654890	0.327445	−	0.944870i	$-0.393812\pi$
$997$	20.6784	0.654890	0.327445	+	0.944870i	$0.393812\pi$
$998$	−93.1375	−2.94822
$999$	14.2119	0.449644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.b.1.16	✓	155

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.46916 q^{2} +1.70167 q^{3} +4.09677 q^{4} -3.39881 q^{5} -4.20171 q^{6} +3.51551 q^{7} -5.17727 q^{8} -0.104305 q^{9} +O(q^{10})\)	\(q-2.46916 q^{2} +1.70167 q^{3} +4.09677 q^{4} -3.39881 q^{5} -4.20171 q^{6} +3.51551 q^{7} -5.17727 q^{8} -0.104305 q^{9} +8.39223 q^{10} -3.57759 q^{11} +6.97137 q^{12} +0.490778 q^{13} -8.68038 q^{14} -5.78368 q^{15} +4.58998 q^{16} -0.461597 q^{17} +0.257546 q^{18} +8.11557 q^{19} -13.9242 q^{20} +5.98226 q^{21} +8.83366 q^{22} +0.0685767 q^{23} -8.81002 q^{24} +6.55194 q^{25} -1.21181 q^{26} -5.28252 q^{27} +14.4022 q^{28} +3.39395 q^{29} +14.2808 q^{30} +5.89489 q^{31} -0.978877 q^{32} -6.08789 q^{33} +1.13976 q^{34} -11.9486 q^{35} -0.427313 q^{36} -2.69036 q^{37} -20.0387 q^{38} +0.835144 q^{39} +17.5966 q^{40} -7.92322 q^{41} -14.7712 q^{42} -11.2048 q^{43} -14.6566 q^{44} +0.354513 q^{45} -0.169327 q^{46} -10.5869 q^{47} +7.81065 q^{48} +5.35883 q^{49} -16.1778 q^{50} -0.785488 q^{51} +2.01060 q^{52} -0.289023 q^{53} +13.0434 q^{54} +12.1596 q^{55} -18.2007 q^{56} +13.8101 q^{57} -8.38021 q^{58} +10.1564 q^{59} -23.6944 q^{60} -2.40510 q^{61} -14.5555 q^{62} -0.366685 q^{63} -6.76295 q^{64} -1.66806 q^{65} +15.0320 q^{66} -8.94666 q^{67} -1.89106 q^{68} +0.116695 q^{69} +29.5030 q^{70} +1.00000 q^{71} +0.540015 q^{72} +2.74462 q^{73} +6.64294 q^{74} +11.1493 q^{75} +33.2476 q^{76} -12.5771 q^{77} -2.06211 q^{78} +4.04125 q^{79} -15.6005 q^{80} -8.67621 q^{81} +19.5637 q^{82} +17.4392 q^{83} +24.5079 q^{84} +1.56888 q^{85} +27.6665 q^{86} +5.77539 q^{87} +18.5221 q^{88} +0.0870007 q^{89} -0.875351 q^{90} +1.72534 q^{91} +0.280943 q^{92} +10.0312 q^{93} +26.1408 q^{94} -27.5833 q^{95} -1.66573 q^{96} +1.48231 q^{97} -13.2318 q^{98} +0.373160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) 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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