LMFDB - Embedded newform 8047.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, 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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$0$
Dimension:	$168$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55763 q^{2} +0.266085 q^{3} +4.54145 q^{4} -4.02410 q^{5} -0.680547 q^{6} -2.52095 q^{7} -6.50007 q^{8} -2.92920 q^{9} +O(q^{10})$	\(q-2.55763 q^{2} +0.266085 q^{3} +4.54145 q^{4} -4.02410 q^{5} -0.680547 q^{6} -2.52095 q^{7} -6.50007 q^{8} -2.92920 q^{9} +10.2921 q^{10} +2.28121 q^{11} +1.20841 q^{12} +1.00000 q^{13} +6.44765 q^{14} -1.07075 q^{15} +7.54184 q^{16} +4.49092 q^{17} +7.49179 q^{18} +5.35408 q^{19} -18.2752 q^{20} -0.670789 q^{21} -5.83448 q^{22} +8.63447 q^{23} -1.72957 q^{24} +11.1934 q^{25} -2.55763 q^{26} -1.57767 q^{27} -11.4488 q^{28} +7.41547 q^{29} +2.73859 q^{30} -1.79464 q^{31} -6.28907 q^{32} +0.606997 q^{33} -11.4861 q^{34} +10.1446 q^{35} -13.3028 q^{36} -1.06017 q^{37} -13.6937 q^{38} +0.266085 q^{39} +26.1569 q^{40} -1.00498 q^{41} +1.71563 q^{42} +10.3188 q^{43} +10.3600 q^{44} +11.7874 q^{45} -22.0837 q^{46} -3.77897 q^{47} +2.00677 q^{48} -0.644800 q^{49} -28.6284 q^{50} +1.19497 q^{51} +4.54145 q^{52} +8.30978 q^{53} +4.03510 q^{54} -9.17980 q^{55} +16.3864 q^{56} +1.42464 q^{57} -18.9660 q^{58} +12.7760 q^{59} -4.86277 q^{60} -5.51723 q^{61} +4.59002 q^{62} +7.38437 q^{63} +1.00140 q^{64} -4.02410 q^{65} -1.55247 q^{66} -4.95147 q^{67} +20.3953 q^{68} +2.29751 q^{69} -25.9460 q^{70} -13.1681 q^{71} +19.0400 q^{72} +5.21950 q^{73} +2.71152 q^{74} +2.97839 q^{75} +24.3153 q^{76} -5.75082 q^{77} -0.680547 q^{78} -0.640913 q^{79} -30.3491 q^{80} +8.36780 q^{81} +2.57035 q^{82} +13.8435 q^{83} -3.04635 q^{84} -18.0719 q^{85} -26.3917 q^{86} +1.97315 q^{87} -14.8280 q^{88} -0.150292 q^{89} -30.1477 q^{90} -2.52095 q^{91} +39.2130 q^{92} -0.477528 q^{93} +9.66519 q^{94} -21.5453 q^{95} -1.67343 q^{96} -15.3689 q^{97} +1.64916 q^{98} -6.68211 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q + 11 q^{2} + 26 q^{3} + 181 q^{4} + 41 q^{5} + 11 q^{6} + 12 q^{7} + 27 q^{8} + 220 q^{9}+O(q^{10}) $ 168 * q + 11 * q^2 + 26 * q^3 + 181 * q^4 + 41 * q^5 + 11 * q^6 + 12 * q^7 + 27 * q^8 + 220 * q^9	\( 168 q + 11 q^{2} + 26 q^{3} + 181 q^{4} + 41 q^{5} + 11 q^{6} + 12 q^{7} + 27 q^{8} + 220 q^{9} + 11 q^{10} + 23 q^{11} + 78 q^{12} + 168 q^{13} + 47 q^{14} + 10 q^{15} + 203 q^{16} + 147 q^{17} + 13 q^{18} + 17 q^{19} + 81 q^{20} + 13 q^{21} + 20 q^{22} + 85 q^{23} + 14 q^{24} + 225 q^{25} + 11 q^{26} + 89 q^{27} + 12 q^{28} + 137 q^{29} + 26 q^{30} + 13 q^{31} + 60 q^{32} + 78 q^{33} - 2 q^{34} + 77 q^{35} + 278 q^{36} + 41 q^{37} + 68 q^{38} + 26 q^{39} + 11 q^{40} + 107 q^{41} + 43 q^{42} + 27 q^{43} + 39 q^{44} + 88 q^{45} - 23 q^{46} + 112 q^{47} + 127 q^{48} + 236 q^{49} + 14 q^{50} + 55 q^{51} + 181 q^{52} + 149 q^{53} + 3 q^{54} + 40 q^{55} + 134 q^{56} + 55 q^{57} - q^{58} + 44 q^{59} - 13 q^{60} + 81 q^{61} + 106 q^{62} + 34 q^{63} + 197 q^{64} + 41 q^{65} - 20 q^{66} - q^{67} + 278 q^{68} + 75 q^{69} - 42 q^{70} + 48 q^{71} - 34 q^{72} + 107 q^{73} + 74 q^{74} + 93 q^{75} + 20 q^{76} + 206 q^{77} + 11 q^{78} + 14 q^{79} + 115 q^{80} + 328 q^{81} + 48 q^{82} + 62 q^{83} - 11 q^{84} + 6 q^{85} + 27 q^{86} + 51 q^{87} + 31 q^{88} + 173 q^{89} - 21 q^{90} + 12 q^{91} + 179 q^{92} + 73 q^{93} + 17 q^{94} + 90 q^{95} - 33 q^{96} + 110 q^{97} - 13 q^{98} + 24 q^{99}+O(q^{100}) \) 168 * q + 11 * q^2 + 26 * q^3 + 181 * q^4 + 41 * q^5 + 11 * q^6 + 12 * q^7 + 27 * q^8 + 220 * q^9 + 11 * q^10 + 23 * q^11 + 78 * q^12 + 168 * q^13 + 47 * q^14 + 10 * q^15 + 203 * q^16 + 147 * q^17 + 13 * q^18 + 17 * q^19 + 81 * q^20 + 13 * q^21 + 20 * q^22 + 85 * q^23 + 14 * q^24 + 225 * q^25 + 11 * q^26 + 89 * q^27 + 12 * q^28 + 137 * q^29 + 26 * q^30 + 13 * q^31 + 60 * q^32 + 78 * q^33 - 2 * q^34 + 77 * q^35 + 278 * q^36 + 41 * q^37 + 68 * q^38 + 26 * q^39 + 11 * q^40 + 107 * q^41 + 43 * q^42 + 27 * q^43 + 39 * q^44 + 88 * q^45 - 23 * q^46 + 112 * q^47 + 127 * q^48 + 236 * q^49 + 14 * q^50 + 55 * q^51 + 181 * q^52 + 149 * q^53 + 3 * q^54 + 40 * q^55 + 134 * q^56 + 55 * q^57 - q^58 + 44 * q^59 - 13 * q^60 + 81 * q^61 + 106 * q^62 + 34 * q^63 + 197 * q^64 + 41 * q^65 - 20 * q^66 - q^67 + 278 * q^68 + 75 * q^69 - 42 * q^70 + 48 * q^71 - 34 * q^72 + 107 * q^73 + 74 * q^74 + 93 * q^75 + 20 * q^76 + 206 * q^77 + 11 * q^78 + 14 * q^79 + 115 * q^80 + 328 * q^81 + 48 * q^82 + 62 * q^83 - 11 * q^84 + 6 * q^85 + 27 * q^86 + 51 * q^87 + 31 * q^88 + 173 * q^89 - 21 * q^90 + 12 * q^91 + 179 * q^92 + 73 * q^93 + 17 * q^94 + 90 * q^95 - 33 * q^96 + 110 * q^97 - 13 * q^98 + 24 * 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 $

$2$	−2.55763	−1.80851	−0.904257	−	0.426989i	$-0.859574\pi$
$2$	−2.55763	−1.80851	−0.904257	+	0.426989i	$0.859574\pi$
$3$	0.266085	0.153625	0.0768123	−	0.997046i	$-0.475526\pi$
$3$	0.266085	0.153625	0.0768123	+	0.997046i	$0.475526\pi$
$4$	4.54145	2.27072
$5$	−4.02410	−1.79963	−0.899815	−	0.436271i	$-0.856299\pi$
$5$	−4.02410	−1.79963	−0.899815	+	0.436271i	$0.856299\pi$
$6$	−0.680547	−0.277832
$7$	−2.52095	−0.952830	−0.476415	−	0.879220i	$-0.658064\pi$
$7$	−2.52095	−0.952830	−0.476415	+	0.879220i	$0.658064\pi$
$8$	−6.50007	−2.29812
$9$	−2.92920	−0.976400
$10$	10.2921	3.25466
$11$	2.28121	0.687810	0.343905	−	0.939004i	$-0.388250\pi$
$11$	2.28121	0.687810	0.343905	+	0.939004i	$0.388250\pi$
$12$	1.20841	0.348839
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	6.44765	1.72321
$15$	−1.07075	−0.276467
$16$	7.54184	1.88546
$17$	4.49092	1.08921	0.544603	−	0.838694i	$-0.316680\pi$
$17$	4.49092	1.08921	0.544603	+	0.838694i	$0.316680\pi$
$18$	7.49179	1.76583
$19$	5.35408	1.22831	0.614155	−	0.789186i	$-0.289497\pi$
$19$	5.35408	1.22831	0.614155	+	0.789186i	$0.289497\pi$
$20$	−18.2752	−4.08646
$21$	−0.670789	−0.146378
$22$	−5.83448	−1.24391
$23$	8.63447	1.80041	0.900206	−	0.435465i	$-0.143416\pi$
$23$	8.63447	1.80041	0.900206	+	0.435465i	$0.143416\pi$
$24$	−1.72957	−0.353048
$25$	11.1934	2.23867
$26$	−2.55763	−0.501592
$27$	−1.57767	−0.303623
$28$	−11.4488	−2.16361
$29$	7.41547	1.37702	0.688509	−	0.725227i	$-0.258265\pi$
$29$	7.41547	1.37702	0.688509	+	0.725227i	$0.258265\pi$
$30$	2.73859	0.499995
$31$	−1.79464	−0.322327	−0.161164	−	0.986928i	$-0.551525\pi$
$31$	−1.79464	−0.322327	−0.161164	+	0.986928i	$0.551525\pi$
$32$	−6.28907	−1.11176
$33$	0.606997	0.105665
$34$	−11.4861	−1.96985
$35$	10.1446	1.71474
$36$	−13.3028	−2.21713
$37$	−1.06017	−0.174291	−0.0871457	−	0.996196i	$-0.527775\pi$
$37$	−1.06017	−0.174291	−0.0871457	+	0.996196i	$0.527775\pi$
$38$	−13.6937	−2.22142
$39$	0.266085	0.0426078
$40$	26.1569	4.13577
$41$	−1.00498	−0.156951	−0.0784754	−	0.996916i	$-0.525005\pi$
$41$	−1.00498	−0.156951	−0.0784754	+	0.996916i	$0.525005\pi$
$42$	1.71563	0.264727
$43$	10.3188	1.57361	0.786804	−	0.617203i	$-0.211734\pi$
$43$	10.3188	1.57361	0.786804	+	0.617203i	$0.211734\pi$
$44$	10.3600	1.56183
$45$	11.7874	1.75716
$46$	−22.0837	−3.25607
$47$	−3.77897	−0.551219	−0.275610	−	0.961270i	$-0.588880\pi$
$47$	−3.77897	−0.551219	−0.275610	+	0.961270i	$0.588880\pi$
$48$	2.00677	0.289653
$49$	−0.644800	−0.0921143
$50$	−28.6284	−4.04867
$51$	1.19497	0.167329
$52$	4.54145	0.629785
$53$	8.30978	1.14144	0.570718	−	0.821146i	$-0.306665\pi$
$53$	8.30978	1.14144	0.570718	+	0.821146i	$0.306665\pi$
$54$	4.03510	0.549107
$55$	−9.17980	−1.23780
$56$	16.3864	2.18972
$57$	1.42464	0.188699
$58$	−18.9660	−2.49036
$59$	12.7760	1.66330	0.831648	−	0.555303i	$-0.187398\pi$
$59$	12.7760	1.66330	0.831648	+	0.555303i	$0.187398\pi$
$60$	−4.86277	−0.627781
$61$	−5.51723	−0.706409	−0.353205	−	0.935546i	$-0.614908\pi$
$61$	−5.51723	−0.706409	−0.353205	+	0.935546i	$0.614908\pi$
$62$	4.59002	0.582933
$63$	7.38437	0.930343
$64$	1.00140	0.125175
$65$	−4.02410	−0.499128
$66$	−1.55247	−0.191096
$67$	−4.95147	−0.604919	−0.302459	−	0.953162i	$-0.597808\pi$
$67$	−4.95147	−0.604919	−0.302459	+	0.953162i	$0.597808\pi$
$68$	20.3953	2.47329
$69$	2.29751	0.276587
$70$	−25.9460	−3.10114
$71$	−13.1681	−1.56277	−0.781386	−	0.624048i	$-0.785487\pi$
$71$	−13.1681	−1.56277	−0.781386	+	0.624048i	$0.785487\pi$
$72$	19.0400	2.24388
$73$	5.21950	0.610896	0.305448	−	0.952209i	$-0.401194\pi$
$73$	5.21950	0.610896	0.305448	+	0.952209i	$0.401194\pi$
$74$	2.71152	0.315208
$75$	2.97839	0.343915
$76$	24.3153	2.78915
$77$	−5.75082	−0.655367
$78$	−0.680547	−0.0770568
$79$	−0.640913	−0.0721083	−0.0360542	−	0.999350i	$-0.511479\pi$
$79$	−0.640913	−0.0721083	−0.0360542	+	0.999350i	$0.511479\pi$
$80$	−30.3491	−3.39313
$81$	8.36780	0.929755
$82$	2.57035	0.283848
$83$	13.8435	1.51952	0.759758	−	0.650205i	$-0.225317\pi$
$83$	13.8435	1.51952	0.759758	+	0.650205i	$0.225317\pi$
$84$	−3.04635	−0.332384
$85$	−18.0719	−1.96017
$86$	−26.3917	−2.84589
$87$	1.97315	0.211544
$88$	−14.8280	−1.58067
$89$	−0.150292	−0.0159309	−0.00796546	−	0.999968i	$-0.502536\pi$
$89$	−0.150292	−0.0159309	−0.00796546	+	0.999968i	$0.502536\pi$
$90$	−30.1477	−3.17785
$91$	−2.52095	−0.264268
$92$	39.2130	4.08824
$93$	−0.477528	−0.0495173
$94$	9.66519	0.996888
$95$	−21.5453	−2.21050
$96$	−1.67343	−0.170794
$97$	−15.3689	−1.56047	−0.780237	−	0.625484i	$-0.784902\pi$
$97$	−15.3689	−1.56047	−0.780237	+	0.625484i	$0.784902\pi$
$98$	1.64916	0.166590
$99$	−6.68211	−0.671578
$100$	50.8340	5.08340
$101$	2.19079	0.217992	0.108996	−	0.994042i	$-0.465236\pi$
$101$	2.19079	0.217992	0.108996	+	0.994042i	$0.465236\pi$
$102$	−3.05628	−0.302617
$103$	−20.0797	−1.97852	−0.989258	−	0.146182i	$-0.953301\pi$
$103$	−20.0797	−1.97852	−0.989258	+	0.146182i	$0.953301\pi$
$104$	−6.50007	−0.637384
$105$	2.69932	0.263427
$106$	−21.2533	−2.06430
$107$	6.07611	0.587400	0.293700	−	0.955898i	$-0.405113\pi$
$107$	6.07611	0.587400	0.293700	+	0.955898i	$0.405113\pi$
$108$	−7.16492	−0.689445
$109$	6.20903	0.594717	0.297359	−	0.954766i	$-0.403894\pi$
$109$	6.20903	0.594717	0.297359	+	0.954766i	$0.403894\pi$
$110$	23.4785	2.23859
$111$	−0.282097	−0.0267754
$112$	−19.0126	−1.79652
$113$	3.75317	0.353068	0.176534	−	0.984295i	$-0.443511\pi$
$113$	3.75317	0.353068	0.176534	+	0.984295i	$0.443511\pi$
$114$	−3.64370	−0.341264
$115$	−34.7459	−3.24008
$116$	33.6770	3.12683
$117$	−2.92920	−0.270804
$118$	−32.6763	−3.00809
$119$	−11.3214	−1.03783
$120$	6.95997	0.635356
$121$	−5.79609	−0.526917
$122$	14.1110	1.27755
$123$	−0.267410	−0.0241115
$124$	−8.15027	−0.731916
$125$	−24.9226	−2.22915
$126$	−18.8864	−1.68254
$127$	−21.5283	−1.91033	−0.955163	−	0.296080i	$-0.904321\pi$
$127$	−21.5283	−1.91033	−0.955163	+	0.296080i	$0.904321\pi$
$128$	10.0169	0.885380
$129$	2.74569	0.241745
$130$	10.2921	0.902680
$131$	10.4219	0.910564	0.455282	−	0.890347i	$-0.349538\pi$
$131$	10.4219	0.910564	0.455282	+	0.890347i	$0.349538\pi$
$132$	2.75664	0.239935
$133$	−13.4974	−1.17037
$134$	12.6640	1.09400
$135$	6.34871	0.546410
$136$	−29.1913	−2.50313
$137$	5.37675	0.459367	0.229683	−	0.973265i	$-0.426231\pi$
$137$	5.37675	0.459367	0.229683	+	0.973265i	$0.426231\pi$
$138$	−5.87616	−0.500212
$139$	1.79741	0.152455	0.0762273	−	0.997090i	$-0.475713\pi$
$139$	1.79741	0.152455	0.0762273	+	0.997090i	$0.475713\pi$
$140$	46.0710	3.89371
$141$	−1.00553	−0.0846808
$142$	33.6792	2.82629
$143$	2.28121	0.190764
$144$	−22.0916	−1.84096
$145$	−29.8406	−2.47812
$146$	−13.3495	−1.10481
$147$	−0.171572	−0.0141510
$148$	−4.81472	−0.395767
$149$	15.1373	1.24009	0.620047	−	0.784565i	$-0.287114\pi$
$149$	15.1373	1.24009	0.620047	+	0.784565i	$0.287114\pi$
$150$	−7.61760	−0.621975
$151$	14.8631	1.20954	0.604771	−	0.796399i	$-0.293264\pi$
$151$	14.8631	1.20954	0.604771	+	0.796399i	$0.293264\pi$
$152$	−34.8019	−2.82280
$153$	−13.1548	−1.06350
$154$	14.7084	1.18524
$155$	7.22181	0.580070
$156$	1.20841	0.0967505
$157$	−8.91164	−0.711227	−0.355613	−	0.934633i	$-0.615728\pi$
$157$	−8.91164	−0.711227	−0.355613	+	0.934633i	$0.615728\pi$
$158$	1.63922	0.130409
$159$	2.21111	0.175352
$160$	25.3078	2.00076
$161$	−21.7671	−1.71549
$162$	−21.4017	−1.68148
$163$	23.1045	1.80968	0.904841	−	0.425750i	$-0.139990\pi$
$163$	23.1045	1.80968	0.904841	+	0.425750i	$0.139990\pi$
$164$	−4.56404	−0.356392
$165$	−2.44261	−0.190157
$166$	−35.4064	−2.74807
$167$	−11.6608	−0.902340	−0.451170	−	0.892438i	$-0.648993\pi$
$167$	−11.6608	−0.902340	−0.451170	+	0.892438i	$0.648993\pi$
$168$	4.36017	0.336395
$169$	1.00000	0.0769231
$170$	46.2211	3.54500
$171$	−15.6832	−1.19932
$172$	46.8624	3.57323
$173$	15.2159	1.15685	0.578423	−	0.815737i	$-0.303668\pi$
$173$	15.2159	1.15685	0.578423	+	0.815737i	$0.303668\pi$
$174$	−5.04658	−0.382580
$175$	−28.2179	−2.13307
$176$	17.2045	1.29684
$177$	3.39951	0.255523
$178$	0.384391	0.0288113
$179$	−5.47936	−0.409546	−0.204773	−	0.978809i	$-0.565646\pi$
$179$	−5.47936	−0.409546	−0.204773	+	0.978809i	$0.565646\pi$
$180$	53.5317	3.99002
$181$	−7.01481	−0.521407	−0.260703	−	0.965419i	$-0.583954\pi$
$181$	−7.01481	−0.521407	−0.260703	+	0.965419i	$0.583954\pi$
$182$	6.44765	0.477932
$183$	−1.46806	−0.108522
$184$	−56.1246	−4.13756
$185$	4.26624	0.313660
$186$	1.22134	0.0895528
$187$	10.2447	0.749168
$188$	−17.1620	−1.25167
$189$	3.97724	0.289302
$190$	55.1049	3.99773
$191$	−20.5463	−1.48668	−0.743338	−	0.668915i	$-0.766759\pi$
$191$	−20.5463	−1.48668	−0.743338	+	0.668915i	$0.766759\pi$
$192$	0.266459	0.0192300
$193$	−10.2990	−0.741338	−0.370669	−	0.928765i	$-0.620872\pi$
$193$	−10.2990	−0.741338	−0.370669	+	0.928765i	$0.620872\pi$
$194$	39.3079	2.82214
$195$	−1.07075	−0.0766783
$196$	−2.92833	−0.209166
$197$	−16.6521	−1.18641	−0.593205	−	0.805051i	$-0.702138\pi$
$197$	−16.6521	−1.18641	−0.593205	+	0.805051i	$0.702138\pi$
$198$	17.0903	1.21456
$199$	9.89169	0.701203	0.350602	−	0.936525i	$-0.385977\pi$
$199$	9.89169	0.701203	0.350602	+	0.936525i	$0.385977\pi$
$200$	−72.7575	−5.14474
$201$	−1.31751	−0.0929303
$202$	−5.60322	−0.394241
$203$	−18.6941	−1.31207
$204$	5.42688	0.379958
$205$	4.04412	0.282454
$206$	51.3564	3.57817
$207$	−25.2921	−1.75792
$208$	7.54184	0.522933
$209$	12.2138	0.844844
$210$	−6.90385	−0.476411
$211$	22.7076	1.56326	0.781628	−	0.623744i	$-0.214389\pi$
$211$	22.7076	1.56326	0.781628	+	0.623744i	$0.214389\pi$
$212$	37.7384	2.59188
$213$	−3.50385	−0.240080
$214$	−15.5404	−1.06232
$215$	−41.5240	−2.83191
$216$	10.2550	0.697763
$217$	4.52420	0.307123
$218$	−15.8804	−1.07555
$219$	1.38883	0.0938486
$220$	−41.6896	−2.81071
$221$	4.49092	0.302092
$222$	0.721497	0.0484237
$223$	8.54960	0.572524	0.286262	−	0.958151i	$-0.407587\pi$
$223$	8.54960	0.572524	0.286262	+	0.958151i	$0.407587\pi$
$224$	15.8545	1.05932
$225$	−32.7875	−2.18584
$226$	−9.59920	−0.638529
$227$	20.2997	1.34734	0.673670	−	0.739032i	$-0.264717\pi$
$227$	20.2997	1.34734	0.673670	+	0.739032i	$0.264717\pi$
$228$	6.46994	0.428482
$229$	16.2989	1.07706	0.538530	−	0.842606i	$-0.318980\pi$
$229$	16.2989	1.07706	0.538530	+	0.842606i	$0.318980\pi$
$230$	88.8671	5.85972
$231$	−1.53021	−0.100680
$232$	−48.2011	−3.16456
$233$	−17.3509	−1.13669	−0.568347	−	0.822789i	$-0.692417\pi$
$233$	−17.3509	−1.13669	−0.568347	+	0.822789i	$0.692417\pi$
$234$	7.49179	0.489754
$235$	15.2069	0.991991
$236$	58.0216	3.77689
$237$	−0.170538	−0.0110776
$238$	28.9559	1.87693
$239$	−15.1867	−0.982343	−0.491172	−	0.871063i	$-0.663431\pi$
$239$	−15.1867	−0.982343	−0.491172	+	0.871063i	$0.663431\pi$
$240$	−8.07546	−0.521268
$241$	2.57605	0.165938	0.0829691	−	0.996552i	$-0.473560\pi$
$241$	2.57605	0.165938	0.0829691	+	0.996552i	$0.473560\pi$
$242$	14.8242	0.952937
$243$	6.95957	0.446457
$244$	−25.0562	−1.60406
$245$	2.59474	0.165772
$246$	0.683933	0.0436060
$247$	5.35408	0.340672
$248$	11.6653	0.740747
$249$	3.68354	0.233435
$250$	63.7428	4.03145
$251$	3.50846	0.221452	0.110726	−	0.993851i	$-0.464682\pi$
$251$	3.50846	0.221452	0.110726	+	0.993851i	$0.464682\pi$
$252$	33.5357	2.11255
$253$	19.6970	1.23834
$254$	55.0613	3.45485
$255$	−4.80866	−0.301130
$256$	−27.6224	−1.72640
$257$	15.1432	0.944607	0.472304	−	0.881436i	$-0.343423\pi$
$257$	15.1432	0.944607	0.472304	+	0.881436i	$0.343423\pi$
$258$	−7.02245	−0.437199
$259$	2.67265	0.166070
$260$	−18.2752	−1.13338
$261$	−21.7214	−1.34452
$262$	−26.6553	−1.64677
$263$	15.3517	0.946629	0.473315	−	0.880893i	$-0.343057\pi$
$263$	15.3517	0.946629	0.473315	+	0.880893i	$0.343057\pi$
$264$	−3.94552	−0.242830
$265$	−33.4393	−2.05416
$266$	34.5212	2.11663
$267$	−0.0399905	−0.00244738
$268$	−22.4868	−1.37360
$269$	16.9326	1.03240	0.516200	−	0.856468i	$-0.327346\pi$
$269$	16.9326	1.03240	0.516200	+	0.856468i	$0.327346\pi$
$270$	−16.2376	−0.988190
$271$	18.2278	1.10726	0.553631	−	0.832762i	$-0.313242\pi$
$271$	18.2278	1.10726	0.553631	+	0.832762i	$0.313242\pi$
$272$	33.8698	2.05366
$273$	−0.670789	−0.0405980
$274$	−13.7517	−0.830772
$275$	25.5344	1.53978
$276$	10.4340	0.628053
$277$	29.7357	1.78665	0.893324	−	0.449414i	$-0.148367\pi$
$277$	29.7357	1.78665	0.893324	+	0.449414i	$0.148367\pi$
$278$	−4.59711	−0.275716
$279$	5.25686	0.314720
$280$	−65.9403	−3.94069
$281$	−27.4795	−1.63929	−0.819645	−	0.572872i	$-0.805829\pi$
$281$	−27.4795	−1.63929	−0.819645	+	0.572872i	$0.805829\pi$
$282$	2.57177	0.153146
$283$	−12.3040	−0.731399	−0.365700	−	0.930733i	$-0.619170\pi$
$283$	−12.3040	−0.731399	−0.365700	+	0.930733i	$0.619170\pi$
$284$	−59.8024	−3.54862
$285$	−5.73290	−0.339588
$286$	−5.83448	−0.345000
$287$	2.53350	0.149548
$288$	18.4219	1.08552
$289$	3.16832	0.186372
$290$	76.3210	4.48172
$291$	−4.08944	−0.239727
$292$	23.7041	1.38718
$293$	14.7468	0.861518	0.430759	−	0.902467i	$-0.358246\pi$
$293$	14.7468	0.861518	0.430759	+	0.902467i	$0.358246\pi$
$294$	0.438817	0.0255923
$295$	−51.4119	−2.99332
$296$	6.89120	0.400543
$297$	−3.59900	−0.208835
$298$	−38.7155	−2.24273
$299$	8.63447	0.499344
$300$	13.5262	0.780935
$301$	−26.0133	−1.49938
$302$	−38.0143	−2.18748
$303$	0.582937	0.0334889
$304$	40.3796	2.31593
$305$	22.2019	1.27128
$306$	33.6450	1.92336
$307$	25.4259	1.45113	0.725567	−	0.688151i	$-0.241577\pi$
$307$	25.4259	1.45113	0.725567	+	0.688151i	$0.241577\pi$
$308$	−26.1170	−1.48816
$309$	−5.34293	−0.303948
$310$	−18.4707	−1.04906
$311$	19.4762	1.10439	0.552196	−	0.833714i	$-0.313790\pi$
$311$	19.4762	1.10439	0.552196	+	0.833714i	$0.313790\pi$
$312$	−1.72957	−0.0979178
$313$	25.1499	1.42155	0.710777	−	0.703417i	$-0.248343\pi$
$313$	25.1499	1.42155	0.710777	+	0.703417i	$0.248343\pi$
$314$	22.7926	1.28626
$315$	−29.7154	−1.67427
$316$	−2.91067	−0.163738
$317$	−11.8151	−0.663600	−0.331800	−	0.943350i	$-0.607656\pi$
$317$	−11.8151	−0.663600	−0.331800	+	0.943350i	$0.607656\pi$
$318$	−5.65519	−0.317127
$319$	16.9162	0.947128
$320$	−4.02975	−0.225270
$321$	1.61677	0.0902391
$322$	55.6720	3.10248
$323$	24.0447	1.33788
$324$	38.0019	2.11122
$325$	11.1934	0.620895
$326$	−59.0926	−3.27283
$327$	1.65213	0.0913631
$328$	6.53241	0.360692
$329$	9.52660	0.525218
$330$	6.24729	0.343902
$331$	−12.3924	−0.681146	−0.340573	−	0.940218i	$-0.610621\pi$
$331$	−12.3924	−0.681146	−0.340573	+	0.940218i	$0.610621\pi$
$332$	62.8693	3.45040
$333$	3.10546	0.170178
$334$	29.8240	1.63190
$335$	19.9252	1.08863
$336$	−5.05898	−0.275990
$337$	17.5220	0.954485	0.477243	−	0.878772i	$-0.341636\pi$
$337$	17.5220	0.954485	0.477243	+	0.878772i	$0.341636\pi$
$338$	−2.55763	−0.139116
$339$	0.998664	0.0542400
$340$	−82.0725	−4.45100
$341$	−4.09395	−0.221700
$342$	40.1116	2.16899
$343$	19.2722	1.04060
$344$	−67.0731	−3.61634
$345$	−9.24539	−0.497755
$346$	−38.9166	−2.09217
$347$	35.9705	1.93100	0.965500	−	0.260404i	$-0.0838558\pi$
$347$	35.9705	1.93100	0.965500	+	0.260404i	$0.0838558\pi$
$348$	8.96095	0.480358
$349$	20.3382	1.08868	0.544339	−	0.838865i	$-0.316780\pi$
$349$	20.3382	1.08868	0.544339	+	0.838865i	$0.316780\pi$
$350$	72.1708	3.85769
$351$	−1.57767	−0.0842100
$352$	−14.3467	−0.764681
$353$	12.1268	0.645443	0.322722	−	0.946494i	$-0.395402\pi$
$353$	12.1268	0.645443	0.322722	+	0.946494i	$0.395402\pi$
$354$	−8.69468	−0.462117
$355$	52.9899	2.81241
$356$	−0.682543	−0.0361747
$357$	−3.01246	−0.159436
$358$	14.0141	0.740670
$359$	−8.27675	−0.436830	−0.218415	−	0.975856i	$-0.570089\pi$
$359$	−8.27675	−0.436830	−0.218415	+	0.975856i	$0.570089\pi$
$360$	−76.6187	−4.03816
$361$	9.66615	0.508745
$362$	17.9413	0.942972
$363$	−1.54225	−0.0809474
$364$	−11.4488	−0.600079
$365$	−21.0038	−1.09939
$366$	3.75474	0.196263
$367$	−1.94131	−0.101336	−0.0506678	−	0.998716i	$-0.516135\pi$
$367$	−1.94131	−0.101336	−0.0506678	+	0.998716i	$0.516135\pi$
$368$	65.1198	3.39461
$369$	2.94377	0.153247
$370$	−10.9114	−0.567259
$371$	−20.9485	−1.08759
$372$	−2.16867	−0.112440
$373$	19.7336	1.02177	0.510884	−	0.859650i	$-0.329318\pi$
$373$	19.7336	1.02177	0.510884	+	0.859650i	$0.329318\pi$
$374$	−26.2021	−1.35488
$375$	−6.63155	−0.342452
$376$	24.5636	1.26677
$377$	7.41547	0.381916
$378$	−10.1723	−0.523206
$379$	−9.73649	−0.500130	−0.250065	−	0.968229i	$-0.580452\pi$
$379$	−9.73649	−0.500130	−0.250065	+	0.968229i	$0.580452\pi$
$380$	−97.8469	−5.01944
$381$	−5.72836	−0.293473
$382$	52.5497	2.68868
$383$	9.88724	0.505215	0.252607	−	0.967569i	$-0.418712\pi$
$383$	9.88724	0.505215	0.252607	+	0.967569i	$0.418712\pi$
$384$	2.66536	0.136016
$385$	23.1418	1.17942
$386$	26.3410	1.34072
$387$	−30.2259	−1.53647
$388$	−69.7970	−3.54340
$389$	−39.1825	−1.98663	−0.993315	−	0.115432i	$-0.963175\pi$
$389$	−39.1825	−1.98663	−0.993315	+	0.115432i	$0.963175\pi$
$390$	2.73859	0.138674
$391$	38.7767	1.96102
$392$	4.19125	0.211690
$393$	2.77311	0.139885
$394$	42.5897	2.14564
$395$	2.57910	0.129768
$396$	−30.3465	−1.52497
$397$	−25.8305	−1.29640	−0.648198	−	0.761471i	$-0.724477\pi$
$397$	−25.8305	−1.29640	−0.648198	+	0.761471i	$0.724477\pi$
$398$	−25.2992	−1.26814
$399$	−3.59146	−0.179798
$400$	84.4185	4.22093
$401$	−15.3318	−0.765635	−0.382818	−	0.923824i	$-0.625046\pi$
$401$	−15.3318	−0.765635	−0.382818	+	0.923824i	$0.625046\pi$
$402$	3.36971	0.168066
$403$	−1.79464	−0.0893974
$404$	9.94935	0.494999
$405$	−33.6728	−1.67322
$406$	47.8124	2.37289
$407$	−2.41848	−0.119879
$408$	−7.76737	−0.384542
$409$	−21.1271	−1.04467	−0.522334	−	0.852741i	$-0.674939\pi$
$409$	−21.1271	−1.04467	−0.522334	+	0.852741i	$0.674939\pi$
$410$	−10.3433	−0.510821
$411$	1.43068	0.0705700
$412$	−91.1911	−4.49266
$413$	−32.2077	−1.58484
$414$	64.6877	3.17922
$415$	−55.7074	−2.73457
$416$	−6.28907	−0.308347
$417$	0.478266	0.0234208
$418$	−31.2382	−1.52791
$419$	−15.7076	−0.767365	−0.383682	−	0.923465i	$-0.625344\pi$
$419$	−15.7076	−0.767365	−0.383682	+	0.923465i	$0.625344\pi$
$420$	12.2588	0.598169
$421$	−31.0808	−1.51479	−0.757393	−	0.652959i	$-0.773527\pi$
$421$	−31.0808	−1.51479	−0.757393	+	0.652959i	$0.773527\pi$
$422$	−58.0776	−2.82717
$423$	11.0693	0.538210
$424$	−54.0141	−2.62316
$425$	50.2684	2.43838
$426$	8.96154	0.434188
$427$	13.9087	0.673088
$428$	27.5943	1.33382
$429$	0.606997	0.0293061
$430$	106.203	5.12155
$431$	−9.03692	−0.435293	−0.217647	−	0.976028i	$-0.569838\pi$
$431$	−9.03692	−0.435293	−0.217647	+	0.976028i	$0.569838\pi$
$432$	−11.8986	−0.572470
$433$	−1.45195	−0.0697765	−0.0348882	−	0.999391i	$-0.511108\pi$
$433$	−1.45195	−0.0697765	−0.0348882	+	0.999391i	$0.511108\pi$
$434$	−11.5712	−0.555436
$435$	−7.94014	−0.380701
$436$	28.1980	1.35044
$437$	46.2296	2.21146
$438$	−3.55211	−0.169727
$439$	−39.2042	−1.87112	−0.935558	−	0.353173i	$-0.885103\pi$
$439$	−39.2042	−1.87112	−0.935558	+	0.353173i	$0.885103\pi$
$440$	59.6693	2.84462
$441$	1.88875	0.0899404
$442$	−11.4861	−0.546337
$443$	4.68591	0.222634	0.111317	−	0.993785i	$-0.464493\pi$
$443$	4.68591	0.222634	0.111317	+	0.993785i	$0.464493\pi$
$444$	−1.28113	−0.0607996
$445$	0.604790	0.0286698
$446$	−21.8667	−1.03542
$447$	4.02781	0.190509
$448$	−2.52449	−0.119271
$449$	−13.3488	−0.629971	−0.314985	−	0.949097i	$-0.602000\pi$
$449$	−13.3488	−0.629971	−0.314985	+	0.949097i	$0.602000\pi$
$450$	83.8583	3.95312
$451$	−2.29256	−0.107952
$452$	17.0448	0.801721
$453$	3.95486	0.185815
$454$	−51.9191	−2.43668
$455$	10.1446	0.475584
$456$	−9.26027	−0.433652
$457$	2.42800	0.113577	0.0567884	−	0.998386i	$-0.481914\pi$
$457$	2.42800	0.113577	0.0567884	+	0.998386i	$0.481914\pi$
$458$	−41.6864	−1.94788
$459$	−7.08520	−0.330709
$460$	−157.797	−7.35732
$461$	−16.4918	−0.768101	−0.384050	−	0.923312i	$-0.625471\pi$
$461$	−16.4918	−0.768101	−0.384050	+	0.923312i	$0.625471\pi$
$462$	3.91370	0.182082
$463$	26.8299	1.24689	0.623445	−	0.781867i	$-0.285733\pi$
$463$	26.8299	1.24689	0.623445	+	0.781867i	$0.285733\pi$
$464$	55.9263	2.59631
$465$	1.92162	0.0891129
$466$	44.3770	2.05573
$467$	−41.1761	−1.90540	−0.952702	−	0.303906i	$-0.901709\pi$
$467$	−41.1761	−1.90540	−0.952702	+	0.303906i	$0.901709\pi$
$468$	−13.3028	−0.614922
$469$	12.4824	0.576385
$470$	−38.8936	−1.79403
$471$	−2.37126	−0.109262
$472$	−83.0450	−3.82246
$473$	23.5394	1.08234
$474$	0.436171	0.0200340
$475$	59.9301	2.74978
$476$	−51.4155	−2.35662
$477$	−24.3410	−1.11450
$478$	38.8418	1.77658
$479$	5.48083	0.250426	0.125213	−	0.992130i	$-0.460039\pi$
$479$	5.48083	0.250426	0.125213	+	0.992130i	$0.460039\pi$
$480$	6.73405	0.307366
$481$	−1.06017	−0.0483397
$482$	−6.58858	−0.300101
$483$	−5.79191	−0.263541
$484$	−26.3226	−1.19648
$485$	61.8459	2.80828
$486$	−17.8000	−0.807423
$487$	−0.986537	−0.0447043	−0.0223521	−	0.999750i	$-0.507115\pi$
$487$	−0.986537	−0.0447043	−0.0223521	+	0.999750i	$0.507115\pi$
$488$	35.8624	1.62341
$489$	6.14776	0.278011
$490$	−6.63637	−0.299801
$491$	12.3631	0.557937	0.278969	−	0.960300i	$-0.410007\pi$
$491$	12.3631	0.557937	0.278969	+	0.960300i	$0.410007\pi$
$492$	−1.21443	−0.0547506
$493$	33.3023	1.49986
$494$	−13.6937	−0.616110
$495$	26.8895	1.20859
$496$	−13.5349	−0.607735
$497$	33.1963	1.48906
$498$	−9.42112	−0.422171
$499$	−41.4866	−1.85719	−0.928597	−	0.371089i	$-0.878985\pi$
$499$	−41.4866	−1.85719	−0.928597	+	0.371089i	$0.878985\pi$
$500$	−113.185	−5.06178
$501$	−3.10277	−0.138622
$502$	−8.97334	−0.400500
$503$	4.72903	0.210857	0.105429	−	0.994427i	$-0.466379\pi$
$503$	4.72903	0.210857	0.105429	+	0.994427i	$0.466379\pi$
$504$	−47.9989	−2.13804
$505$	−8.81595	−0.392304
$506$	−50.3776	−2.23956
$507$	0.266085	0.0118173
$508$	−97.7695	−4.33782
$509$	−10.1935	−0.451819	−0.225909	−	0.974148i	$-0.572535\pi$
$509$	−10.1935	−0.451819	−0.225909	+	0.974148i	$0.572535\pi$
$510$	12.2988	0.544598
$511$	−13.1581	−0.582080
$512$	50.6138	2.23683
$513$	−8.44699	−0.372944
$514$	−38.7306	−1.70834
$515$	80.8028	3.56060
$516$	12.4694	0.548935
$517$	−8.62062	−0.379134
$518$	−6.83562	−0.300340
$519$	4.04874	0.177720
$520$	26.1569	1.14706
$521$	−26.0572	−1.14159	−0.570793	−	0.821094i	$-0.693364\pi$
$521$	−26.0572	−1.14159	−0.570793	+	0.821094i	$0.693364\pi$
$522$	55.5552	2.43158
$523$	−21.5477	−0.942214	−0.471107	−	0.882076i	$-0.656145\pi$
$523$	−21.5477	−0.942214	−0.471107	+	0.882076i	$0.656145\pi$
$524$	47.3304	2.06764
$525$	−7.50838	−0.327692
$526$	−39.2640	−1.71199
$527$	−8.05958	−0.351081
$528$	4.57787	0.199226
$529$	51.5541	2.24148
$530$	85.5253	3.71498
$531$	−37.4235	−1.62404
$532$	−61.2976	−2.65759
$533$	−1.00498	−0.0435303
$534$	0.102281	0.00442612
$535$	−24.4509	−1.05710
$536$	32.1849	1.39018
$537$	−1.45798	−0.0629164
$538$	−43.3073	−1.86711
$539$	−1.47092	−0.0633572
$540$	28.8323	1.24075
$541$	−20.4469	−0.879081	−0.439541	−	0.898223i	$-0.644859\pi$
$541$	−20.4469	−0.879081	−0.439541	+	0.898223i	$0.644859\pi$
$542$	−46.6199	−2.00250
$543$	−1.86654	−0.0801009
$544$	−28.2437	−1.21094
$545$	−24.9857	−1.07027
$546$	1.71563	0.0734220
$547$	−13.1893	−0.563934	−0.281967	−	0.959424i	$-0.590987\pi$
$547$	−13.1893	−0.563934	−0.281967	+	0.959424i	$0.590987\pi$
$548$	24.4182	1.04310
$549$	16.1611	0.689738
$550$	−65.3073	−2.78471
$551$	39.7030	1.69141
$552$	−14.9340	−0.635631
$553$	1.61571	0.0687070
$554$	−76.0529	−3.23118
$555$	1.13518	0.0481859
$556$	8.16286	0.346182
$557$	−0.340784	−0.0144395	−0.00721973	−	0.999974i	$-0.502298\pi$
$557$	−0.340784	−0.0144395	−0.00721973	+	0.999974i	$0.502298\pi$
$558$	−13.4451	−0.569176
$559$	10.3188	0.436440
$560$	76.5086	3.23308
$561$	2.72597	0.115091
$562$	70.2823	2.96468
$563$	−29.5482	−1.24531	−0.622655	−	0.782497i	$-0.713946\pi$
$563$	−29.5482	−1.24531	−0.622655	+	0.782497i	$0.713946\pi$
$564$	−4.56655	−0.192287
$565$	−15.1031	−0.635393
$566$	31.4691	1.32275
$567$	−21.0948	−0.885899
$568$	85.5938	3.59144
$569$	−20.1675	−0.845465	−0.422732	−	0.906255i	$-0.638929\pi$
$569$	−20.1675	−0.845465	−0.422732	+	0.906255i	$0.638929\pi$
$570$	14.6626	0.614149
$571$	−1.64690	−0.0689208	−0.0344604	−	0.999406i	$-0.510971\pi$
$571$	−1.64690	−0.0689208	−0.0344604	+	0.999406i	$0.510971\pi$
$572$	10.3600	0.433173
$573$	−5.46707	−0.228390
$574$	−6.47973	−0.270459
$575$	96.6487	4.03053
$576$	−2.93331	−0.122221
$577$	11.0877	0.461589	0.230794	−	0.973003i	$-0.425868\pi$
$577$	11.0877	0.461589	0.230794	+	0.973003i	$0.425868\pi$
$578$	−8.10337	−0.337056
$579$	−2.74041	−0.113888
$580$	−135.519	−5.62714
$581$	−34.8987	−1.44784
$582$	10.4592	0.433550
$583$	18.9563	0.785091
$584$	−33.9271	−1.40391
$585$	11.7874	0.487348
$586$	−37.7168	−1.55807
$587$	43.5315	1.79674	0.898369	−	0.439242i	$-0.144753\pi$
$587$	43.5315	1.79674	0.898369	+	0.439242i	$0.144753\pi$
$588$	−0.779185	−0.0321331
$589$	−9.60865	−0.395918
$590$	131.492	5.41346
$591$	−4.43087	−0.182262
$592$	−7.99566	−0.328619
$593$	32.1229	1.31913	0.659564	−	0.751649i	$-0.270741\pi$
$593$	32.1229	1.31913	0.659564	+	0.751649i	$0.270741\pi$
$594$	9.20490	0.377682
$595$	45.5583	1.86771
$596$	68.7451	2.81591
$597$	2.63204	0.107722
$598$	−22.0837	−0.903071
$599$	−44.2800	−1.80923	−0.904615	−	0.426229i	$-0.859842\pi$
$599$	−44.2800	−1.80923	−0.904615	+	0.426229i	$0.859842\pi$
$600$	−19.3597	−0.790358
$601$	−21.6567	−0.883396	−0.441698	−	0.897164i	$-0.645624\pi$
$601$	−21.6567	−0.883396	−0.441698	+	0.897164i	$0.645624\pi$
$602$	66.5322	2.71165
$603$	14.5038	0.590642
$604$	67.5000	2.74654
$605$	23.3240	0.948256
$606$	−1.49093	−0.0605651
$607$	23.0092	0.933916	0.466958	−	0.884279i	$-0.345350\pi$
$607$	23.0092	0.933916	0.466958	+	0.884279i	$0.345350\pi$
$608$	−33.6722	−1.36559
$609$	−4.97422	−0.201565
$610$	−56.7841	−2.29912
$611$	−3.77897	−0.152881
$612$	−59.7417	−2.41492
$613$	−10.0794	−0.407105	−0.203552	−	0.979064i	$-0.565249\pi$
$613$	−10.0794	−0.407105	−0.203552	+	0.979064i	$0.565249\pi$
$614$	−65.0300	−2.62440
$615$	1.07608	0.0433918
$616$	37.3807	1.50611
$617$	18.3084	0.737070	0.368535	−	0.929614i	$-0.379860\pi$
$617$	18.3084	0.737070	0.368535	+	0.929614i	$0.379860\pi$
$618$	13.6652	0.549695
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	32.7975	1.31718
$621$	−13.6224	−0.546647
$622$	−49.8127	−1.99731
$623$	0.378879	0.0151795
$624$	2.00677	0.0803353
$625$	44.3244	1.77297
$626$	−64.3239	−2.57090
$627$	3.24991	0.129789
$628$	−40.4717	−1.61500
$629$	−4.76115	−0.189839
$630$	76.0009	3.02795
$631$	−48.4123	−1.92726	−0.963632	−	0.267234i	$-0.913890\pi$
$631$	−48.4123	−1.92726	−0.963632	+	0.267234i	$0.913890\pi$
$632$	4.16598	0.165714
$633$	6.04217	0.240155
$634$	30.2185	1.20013
$635$	86.6319	3.43788
$636$	10.0416	0.398177
$637$	−0.644800	−0.0255479
$638$	−43.2654	−1.71289
$639$	38.5721	1.52589
$640$	−40.3091	−1.59336
$641$	−25.9018	−1.02306	−0.511530	−	0.859266i	$-0.670921\pi$
$641$	−25.9018	−1.02306	−0.511530	+	0.859266i	$0.670921\pi$
$642$	−4.13508	−0.163199
$643$	27.8735	1.09922	0.549612	−	0.835420i	$-0.314776\pi$
$643$	27.8735	1.09922	0.549612	+	0.835420i	$0.314776\pi$
$644$	−98.8541	−3.89540
$645$	−11.0489	−0.435051
$646$	−61.4974	−2.41958
$647$	9.94037	0.390796	0.195398	−	0.980724i	$-0.437400\pi$
$647$	9.94037	0.390796	0.195398	+	0.980724i	$0.437400\pi$
$648$	−54.3913	−2.13669
$649$	29.1448	1.14403
$650$	−28.6284	−1.12290
$651$	1.20383	0.0471816
$652$	104.928	4.10929
$653$	−5.41663	−0.211969	−0.105985	−	0.994368i	$-0.533799\pi$
$653$	−5.41663	−0.211969	−0.105985	+	0.994368i	$0.533799\pi$
$654$	−4.22554	−0.165232
$655$	−41.9386	−1.63868
$656$	−7.57937	−0.295925
$657$	−15.2889	−0.596479
$658$	−24.3655	−0.949865
$659$	36.6363	1.42715	0.713574	−	0.700580i	$-0.247075\pi$
$659$	36.6363	1.42715	0.713574	+	0.700580i	$0.247075\pi$
$660$	−11.0930	−0.431794
$661$	−11.5434	−0.448985	−0.224492	−	0.974476i	$-0.572072\pi$
$661$	−11.5434	−0.448985	−0.224492	+	0.974476i	$0.572072\pi$
$662$	31.6950	1.23186
$663$	1.19497	0.0464087
$664$	−89.9834	−3.49203
$665$	54.3147	2.10624
$666$	−7.94259	−0.307769
$667$	64.0287	2.47920
$668$	−52.9569	−2.04897
$669$	2.27492	0.0879537
$670$	−50.9612	−1.96880
$671$	−12.5860	−0.485876
$672$	4.21864	0.162738
$673$	−26.0385	−1.00371	−0.501855	−	0.864952i	$-0.667349\pi$
$673$	−26.0385	−1.00371	−0.501855	+	0.864952i	$0.667349\pi$
$674$	−44.8148	−1.72620
$675$	−17.6595	−0.679713
$676$	4.54145	0.174671
$677$	−3.42917	−0.131794	−0.0658969	−	0.997826i	$-0.520991\pi$
$677$	−3.42917	−0.131794	−0.0658969	+	0.997826i	$0.520991\pi$
$678$	−2.55421	−0.0980938
$679$	38.7442	1.48687
$680$	117.468	4.50471
$681$	5.40147	0.206985
$682$	10.4708	0.400947
$683$	−39.2518	−1.50193	−0.750964	−	0.660343i	$-0.770411\pi$
$683$	−39.2518	−1.50193	−0.750964	+	0.660343i	$0.770411\pi$
$684$	−71.2242	−2.72333
$685$	−21.6366	−0.826691
$686$	−49.2910	−1.88194
$687$	4.33690	0.165463
$688$	77.8230	2.96697
$689$	8.30978	0.316577
$690$	23.6462	0.900197
$691$	8.00874	0.304667	0.152333	−	0.988329i	$-0.451321\pi$
$691$	8.00874	0.304667	0.152333	+	0.988329i	$0.451321\pi$
$692$	69.1023	2.62688
$693$	16.8453	0.639900
$694$	−91.9991	−3.49224
$695$	−7.23297	−0.274362
$696$	−12.8256	−0.486153
$697$	−4.51326	−0.170952
$698$	−52.0175	−1.96889
$699$	−4.61681	−0.174624
$700$	−128.150	−4.84362
$701$	37.9665	1.43397	0.716987	−	0.697087i	$-0.245521\pi$
$701$	37.9665	1.43397	0.716987	+	0.697087i	$0.245521\pi$
$702$	4.03510	0.152295
$703$	−5.67625	−0.214084
$704$	2.28441	0.0860970
$705$	4.04634	0.152394
$706$	−31.0157	−1.16729
$707$	−5.52287	−0.207709
$708$	15.4387	0.580222
$709$	−23.6182	−0.887000	−0.443500	−	0.896274i	$-0.646263\pi$
$709$	−23.6182	−0.887000	−0.443500	+	0.896274i	$0.646263\pi$
$710$	−135.528	−5.08629
$711$	1.87736	0.0704065
$712$	0.976909	0.0366112
$713$	−15.4958	−0.580321
$714$	7.70473	0.288342
$715$	−9.17980	−0.343305
$716$	−24.8842	−0.929966
$717$	−4.04095	−0.150912
$718$	21.1688	0.790014
$719$	18.5552	0.691993	0.345997	−	0.938236i	$-0.387541\pi$
$719$	18.5552	0.691993	0.345997	+	0.938236i	$0.387541\pi$
$720$	88.8985	3.31305
$721$	50.6201	1.88519
$722$	−24.7224	−0.920072
$723$	0.685450	0.0254922
$724$	−31.8574	−1.18397
$725$	83.0040	3.08269
$726$	3.94451	0.146394
$727$	−0.721221	−0.0267486	−0.0133743	−	0.999911i	$-0.504257\pi$
$727$	−0.721221	−0.0267486	−0.0133743	+	0.999911i	$0.504257\pi$
$728$	16.3864	0.607319
$729$	−23.2516	−0.861169
$730$	53.7198	1.98826
$731$	46.3410	1.71398
$732$	−6.66710	−0.246423
$733$	13.2914	0.490931	0.245465	−	0.969405i	$-0.421059\pi$
$733$	13.2914	0.490931	0.245465	+	0.969405i	$0.421059\pi$
$734$	4.96514	0.183267
$735$	0.690422	0.0254666
$736$	−54.3028	−2.00163
$737$	−11.2953	−0.416069
$738$	−7.52907	−0.277149
$739$	−40.2925	−1.48218	−0.741092	−	0.671403i	$-0.765692\pi$
$739$	−40.2925	−1.48218	−0.741092	+	0.671403i	$0.765692\pi$
$740$	19.3749	0.712235
$741$	1.42464	0.0523356
$742$	53.5785	1.96693
$743$	47.6208	1.74704	0.873518	−	0.486791i	$-0.161833\pi$
$743$	47.6208	1.74704	0.873518	+	0.486791i	$0.161833\pi$
$744$	3.10396	0.113797
$745$	−60.9138	−2.23171
$746$	−50.4712	−1.84788
$747$	−40.5502	−1.48366
$748$	46.5258	1.70115
$749$	−15.3176	−0.559693
$750$	16.9610	0.619329
$751$	25.2975	0.923118	0.461559	−	0.887109i	$-0.347290\pi$
$751$	25.2975	0.923118	0.461559	+	0.887109i	$0.347290\pi$
$752$	−28.5004	−1.03930
$753$	0.933551	0.0340205
$754$	−18.9660	−0.690701
$755$	−59.8106	−2.17673
$756$	18.0624	0.656924
$757$	−11.7081	−0.425537	−0.212768	−	0.977103i	$-0.568248\pi$
$757$	−11.7081	−0.425537	−0.212768	+	0.977103i	$0.568248\pi$
$758$	24.9023	0.904492
$759$	5.24109	0.190240
$760$	140.046	5.08001
$761$	10.8203	0.392234	0.196117	−	0.980580i	$-0.437167\pi$
$761$	10.8203	0.392234	0.196117	+	0.980580i	$0.437167\pi$
$762$	14.6510	0.530750
$763$	−15.6527	−0.566665
$764$	−93.3098	−3.37583
$765$	52.9361	1.91391
$766$	−25.2879	−0.913688
$767$	12.7760	0.461315
$768$	−7.34991	−0.265217
$769$	16.1176	0.581215	0.290607	−	0.956842i	$-0.406143\pi$
$769$	16.1176	0.581215	0.290607	+	0.956842i	$0.406143\pi$
$770$	−59.1882	−2.13299
$771$	4.02939	0.145115
$772$	−46.7724	−1.68337
$773$	−17.0042	−0.611598	−0.305799	−	0.952096i	$-0.598924\pi$
$773$	−17.0042	−0.611598	−0.305799	+	0.952096i	$0.598924\pi$
$774$	77.3065	2.77873
$775$	−20.0881	−0.721584
$776$	99.8988	3.58616
$777$	0.711152	0.0255124
$778$	100.214	3.59285
$779$	−5.38072	−0.192784
$780$	−4.86277	−0.174115
$781$	−30.0393	−1.07489
$782$	−99.1762	−3.54653
$783$	−11.6992	−0.418095
$784$	−4.86298	−0.173678
$785$	35.8613	1.27995
$786$	−7.09258	−0.252984
$787$	−47.0114	−1.67577	−0.837887	−	0.545843i	$-0.816209\pi$
$787$	−47.0114	−1.67577	−0.837887	+	0.545843i	$0.816209\pi$
$788$	−75.6244	−2.69401
$789$	4.08488	0.145426
$790$	−6.59636	−0.234688
$791$	−9.46156	−0.336414
$792$	43.4342	1.54337
$793$	−5.51723	−0.195923
$794$	66.0648	2.34455
$795$	−8.89772	−0.315570
$796$	44.9226	1.59224
$797$	−38.6601	−1.36941	−0.684705	−	0.728820i	$-0.740069\pi$
$797$	−38.6601	−1.36941	−0.684705	+	0.728820i	$0.740069\pi$
$798$	9.18560	0.325167
$799$	−16.9710	−0.600392
$800$	−70.3958	−2.48887
$801$	0.440235	0.0155549
$802$	39.2131	1.38466
$803$	11.9068	0.420181
$804$	−5.98342	−0.211019
$805$	87.5929	3.08724
$806$	4.59002	0.161677
$807$	4.50552	0.158602
$808$	−14.2403	−0.500971
$809$	32.4630	1.14134	0.570669	−	0.821180i	$-0.306684\pi$
$809$	32.4630	1.14134	0.570669	+	0.821180i	$0.306684\pi$
$810$	86.1225	3.02604
$811$	14.1573	0.497130	0.248565	−	0.968615i	$-0.420041\pi$
$811$	14.1573	0.497130	0.248565	+	0.968615i	$0.420041\pi$
$812$	−84.8980	−2.97934
$813$	4.85016	0.170103
$814$	6.18555	0.216804
$815$	−92.9746	−3.25676
$816$	9.01226	0.315492
$817$	55.2478	1.93288
$818$	54.0352	1.88930
$819$	7.38437	0.258031
$820$	18.3662	0.641374
$821$	0.219262	0.00765229	0.00382614	−	0.999993i	$-0.498782\pi$
$821$	0.219262	0.00765229	0.00382614	+	0.999993i	$0.498782\pi$
$822$	−3.65913	−0.127627
$823$	18.5249	0.645737	0.322869	−	0.946444i	$-0.395353\pi$
$823$	18.5249	0.645737	0.322869	+	0.946444i	$0.395353\pi$
$824$	130.520	4.54687
$825$	6.79433	0.236548
$826$	82.3753	2.86620
$827$	33.9353	1.18005	0.590023	−	0.807386i	$-0.299119\pi$
$827$	33.9353	1.18005	0.590023	+	0.807386i	$0.299119\pi$
$828$	−114.863	−3.99175
$829$	1.68445	0.0585034	0.0292517	−	0.999572i	$-0.490688\pi$
$829$	1.68445	0.0585034	0.0292517	+	0.999572i	$0.490688\pi$
$830$	142.479	4.94551
$831$	7.91225	0.274473
$832$	1.00140	0.0347174
$833$	−2.89574	−0.100332
$834$	−1.22322	−0.0423568
$835$	46.9242	1.62388
$836$	55.4682	1.91841
$837$	2.83136	0.0978661
$838$	40.1740	1.38779
$839$	−19.6768	−0.679318	−0.339659	−	0.940549i	$-0.610312\pi$
$839$	−19.6768	−0.679318	−0.339659	+	0.940549i	$0.610312\pi$
$840$	−17.5458	−0.605386
$841$	25.9892	0.896180
$842$	79.4931	2.73951
$843$	−7.31190	−0.251835
$844$	103.125	3.54972
$845$	−4.02410	−0.138433
$846$	−28.3112	−0.973361
$847$	14.6117	0.502063
$848$	62.6710	2.15213
$849$	−3.27393	−0.112361
$850$	−128.568	−4.40984
$851$	−9.15403	−0.313796
$852$	−15.9126	−0.545155
$853$	40.7629	1.39570	0.697848	−	0.716246i	$-0.254141\pi$
$853$	40.7629	1.39570	0.697848	+	0.716246i	$0.254141\pi$
$854$	−35.5732	−1.21729
$855$	63.1105	2.15833
$856$	−39.4951	−1.34992
$857$	18.0132	0.615320	0.307660	−	0.951496i	$-0.400454\pi$
$857$	18.0132	0.615320	0.307660	+	0.951496i	$0.400454\pi$
$858$	−1.55247	−0.0530004
$859$	41.0093	1.39922	0.699610	−	0.714525i	$-0.253357\pi$
$859$	41.0093	1.39922	0.699610	+	0.714525i	$0.253357\pi$
$860$	−188.579	−6.43049
$861$	0.674127	0.0229742
$862$	23.1130	0.787234
$863$	31.9463	1.08746	0.543732	−	0.839259i	$-0.317011\pi$
$863$	31.9463	1.08746	0.543732	+	0.839259i	$0.317011\pi$
$864$	9.92210	0.337557
$865$	−61.2304	−2.08190
$866$	3.71355	0.126192
$867$	0.843044	0.0286313
$868$	20.5464	0.697391
$869$	−1.46206	−0.0495969
$870$	20.3079	0.688503
$871$	−4.95147	−0.167774
$872$	−40.3591	−1.36673
$873$	45.0185	1.52365
$874$	−118.238	−3.99946
$875$	62.8288	2.12400
$876$	6.30731	0.213104
$877$	−33.0542	−1.11616	−0.558080	−	0.829787i	$-0.688462\pi$
$877$	−33.0542	−1.11616	−0.558080	+	0.829787i	$0.688462\pi$
$878$	100.270	3.38394
$879$	3.92391	0.132350
$880$	−69.2326	−2.33383
$881$	5.97788	0.201400	0.100700	−	0.994917i	$-0.467892\pi$
$881$	5.97788	0.201400	0.100700	+	0.994917i	$0.467892\pi$
$882$	−4.83071	−0.162658
$883$	−0.0447044	−0.00150442	−0.000752211	−	1.00000i	$-0.500239\pi$
$883$	−0.0447044	−0.00150442	−0.000752211		1.00000i	$0.500239\pi$
$884$	20.3953	0.685967
$885$	−13.6800	−0.459847
$886$	−11.9848	−0.402637
$887$	2.10994	0.0708448	0.0354224	−	0.999372i	$-0.488722\pi$
$887$	2.10994	0.0708448	0.0354224	+	0.999372i	$0.488722\pi$
$888$	1.83365	0.0615332
$889$	54.2718	1.82022
$890$	−1.54683	−0.0518497
$891$	19.0887	0.639495
$892$	38.8276	1.30004
$893$	−20.2329	−0.677068
$894$	−10.3016	−0.344538
$895$	22.0495	0.737032
$896$	−25.2522	−0.843617
$897$	2.29751	0.0767115
$898$	34.1413	1.13931
$899$	−13.3081	−0.443850
$900$	−148.903	−4.96343
$901$	37.3185	1.24326
$902$	5.86351	0.195233
$903$	−6.92176	−0.230342
$904$	−24.3959	−0.811394
$905$	28.2283	0.938340
$906$	−10.1150	−0.336050
$907$	−25.5518	−0.848435	−0.424218	−	0.905560i	$-0.639451\pi$
$907$	−25.5518	−0.848435	−0.424218	+	0.905560i	$0.639451\pi$
$908$	92.1902	3.05944
$909$	−6.41726	−0.212847
$910$	−25.9460	−0.860100
$911$	12.6204	0.418133	0.209067	−	0.977901i	$-0.432957\pi$
$911$	12.6204	0.418133	0.209067	+	0.977901i	$0.432957\pi$
$912$	10.7444	0.355784
$913$	31.5798	1.04514
$914$	−6.20990	−0.205405
$915$	5.90760	0.195299
$916$	74.0205	2.44571
$917$	−26.2731	−0.867613
$918$	18.1213	0.598091
$919$	48.7531	1.60821	0.804107	−	0.594484i	$-0.202644\pi$
$919$	48.7531	1.60821	0.804107	+	0.594484i	$0.202644\pi$
$920$	225.851	7.44609
$921$	6.76547	0.222930
$922$	42.1799	1.38912
$923$	−13.1681	−0.433435
$924$	−6.94936	−0.228617
$925$	−11.8669	−0.390181
$926$	−68.6207	−2.25502
$927$	58.8175	1.93182
$928$	−46.6364	−1.53092
$929$	31.8227	1.04407	0.522035	−	0.852924i	$-0.325173\pi$
$929$	31.8227	1.04407	0.522035	+	0.852924i	$0.325173\pi$
$930$	−4.91478	−0.161162
$931$	−3.45231	−0.113145
$932$	−78.7980	−2.58112
$933$	5.18233	0.169662
$934$	105.313	3.44595
$935$	−41.2257	−1.34823
$936$	19.0400	0.622341
$937$	−21.4837	−0.701841	−0.350921	−	0.936405i	$-0.614131\pi$
$937$	−21.4837	−0.701841	−0.350921	+	0.936405i	$0.614131\pi$
$938$	−31.9254	−1.04240
$939$	6.69202	0.218386
$940$	69.0615	2.25254
$941$	38.4808	1.25444	0.627219	−	0.778843i	$-0.284193\pi$
$941$	38.4808	1.25444	0.627219	+	0.778843i	$0.284193\pi$
$942$	6.06479	0.197602
$943$	−8.67743	−0.282576
$944$	96.3547	3.13608
$945$	−16.0048	−0.520636
$946$	−60.2050	−1.95743
$947$	−9.56403	−0.310789	−0.155395	−	0.987852i	$-0.549665\pi$
$947$	−9.56403	−0.310789	−0.155395	+	0.987852i	$0.549665\pi$
$948$	−0.774488	−0.0251542
$949$	5.21950	0.169432
$950$	−153.279	−4.97302
$951$	−3.14382	−0.101945
$952$	73.5897	2.38506
$953$	−35.5380	−1.15119	−0.575595	−	0.817735i	$-0.695229\pi$
$953$	−35.5380	−1.15119	−0.575595	+	0.817735i	$0.695229\pi$
$954$	62.2551	2.01558
$955$	82.6802	2.67547
$956$	−68.9694	−2.23063
$957$	4.50117	0.145502
$958$	−14.0179	−0.452898
$959$	−13.5545	−0.437699
$960$	−1.07226	−0.0346069
$961$	−27.7793	−0.896105
$962$	2.71152	0.0874231
$963$	−17.7981	−0.573537
$964$	11.6990	0.376800
$965$	41.4442	1.33414
$966$	14.8135	0.476617
$967$	−38.5954	−1.24114	−0.620572	−	0.784149i	$-0.713100\pi$
$967$	−38.5954	−1.24114	−0.620572	+	0.784149i	$0.713100\pi$
$968$	37.6750	1.21092
$969$	6.39795	0.205532
$970$	−158.179	−5.07881
$971$	6.37150	0.204471	0.102236	−	0.994760i	$-0.467400\pi$
$971$	6.37150	0.204471	0.102236	+	0.994760i	$0.467400\pi$
$972$	31.6065	1.01378
$973$	−4.53119	−0.145263
$974$	2.52319	0.0808483
$975$	2.97839	0.0953848
$976$	−41.6101	−1.33191
$977$	−35.6946	−1.14197	−0.570986	−	0.820960i	$-0.693439\pi$
$977$	−35.6946	−1.14197	−0.570986	+	0.820960i	$0.693439\pi$
$978$	−15.7237	−0.502788
$979$	−0.342848	−0.0109575
$980$	11.7839	0.376422
$981$	−18.1875	−0.580682
$982$	−31.6201	−1.00904
$983$	47.7839	1.52407	0.762035	−	0.647536i	$-0.224201\pi$
$983$	47.7839	1.52407	0.762035	+	0.647536i	$0.224201\pi$
$984$	1.73818	0.0554111
$985$	67.0095	2.13510
$986$	−85.1747	−2.71251
$987$	2.53489	0.0806864
$988$	24.3153	0.773571
$989$	89.0977	2.83314
$990$	−68.7732	−2.18576
$991$	−31.6332	−1.00486	−0.502430	−	0.864618i	$-0.667561\pi$
$991$	−31.6332	−1.00486	−0.502430	+	0.864618i	$0.667561\pi$
$992$	11.2866	0.358351
$993$	−3.29743	−0.104641
$994$	−84.9036	−2.69298
$995$	−39.8051	−1.26191
$996$	16.7286	0.530066
$997$	13.6424	0.432058	0.216029	−	0.976387i	$-0.430689\pi$
$997$	13.6424	0.432058	0.216029	+	0.976387i	$0.430689\pi$
$998$	106.107	3.35876
$999$	1.67261	0.0529189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.e.1.10	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.e.1.10	✓	168	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55763 q^{2} +0.266085 q^{3} +4.54145 q^{4} -4.02410 q^{5} -0.680547 q^{6} -2.52095 q^{7} -6.50007 q^{8} -2.92920 q^{9} +O(q^{10})\)	\(q-2.55763 q^{2} +0.266085 q^{3} +4.54145 q^{4} -4.02410 q^{5} -0.680547 q^{6} -2.52095 q^{7} -6.50007 q^{8} -2.92920 q^{9} +10.2921 q^{10} +2.28121 q^{11} +1.20841 q^{12} +1.00000 q^{13} +6.44765 q^{14} -1.07075 q^{15} +7.54184 q^{16} +4.49092 q^{17} +7.49179 q^{18} +5.35408 q^{19} -18.2752 q^{20} -0.670789 q^{21} -5.83448 q^{22} +8.63447 q^{23} -1.72957 q^{24} +11.1934 q^{25} -2.55763 q^{26} -1.57767 q^{27} -11.4488 q^{28} +7.41547 q^{29} +2.73859 q^{30} -1.79464 q^{31} -6.28907 q^{32} +0.606997 q^{33} -11.4861 q^{34} +10.1446 q^{35} -13.3028 q^{36} -1.06017 q^{37} -13.6937 q^{38} +0.266085 q^{39} +26.1569 q^{40} -1.00498 q^{41} +1.71563 q^{42} +10.3188 q^{43} +10.3600 q^{44} +11.7874 q^{45} -22.0837 q^{46} -3.77897 q^{47} +2.00677 q^{48} -0.644800 q^{49} -28.6284 q^{50} +1.19497 q^{51} +4.54145 q^{52} +8.30978 q^{53} +4.03510 q^{54} -9.17980 q^{55} +16.3864 q^{56} +1.42464 q^{57} -18.9660 q^{58} +12.7760 q^{59} -4.86277 q^{60} -5.51723 q^{61} +4.59002 q^{62} +7.38437 q^{63} +1.00140 q^{64} -4.02410 q^{65} -1.55247 q^{66} -4.95147 q^{67} +20.3953 q^{68} +2.29751 q^{69} -25.9460 q^{70} -13.1681 q^{71} +19.0400 q^{72} +5.21950 q^{73} +2.71152 q^{74} +2.97839 q^{75} +24.3153 q^{76} -5.75082 q^{77} -0.680547 q^{78} -0.640913 q^{79} -30.3491 q^{80} +8.36780 q^{81} +2.57035 q^{82} +13.8435 q^{83} -3.04635 q^{84} -18.0719 q^{85} -26.3917 q^{86} +1.97315 q^{87} -14.8280 q^{88} -0.150292 q^{89} -30.1477 q^{90} -2.52095 q^{91} +39.2130 q^{92} -0.477528 q^{93} +9.66519 q^{94} -21.5453 q^{95} -1.67343 q^{96} -15.3689 q^{97} +1.64916 q^{98} -6.68211 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q + 11 q^{2} + 26 q^{3} + 181 q^{4} + 41 q^{5} + 11 q^{6} + 12 q^{7} + 27 q^{8} + 220 q^{9}+O(q^{10}) \) 168 * q + 11 * q^2 + 26 * q^3 + 181 * q^4 + 41 * q^5 + 11 * q^6 + 12 * q^7 + 27 * q^8 + 220 * q^9	\( 168 q + 11 q^{2} + 26 q^{3} + 181 q^{4} + 41 q^{5} + 11 q^{6} + 12 q^{7} + 27 q^{8} + 220 q^{9} + 11 q^{10} + 23 q^{11} + 78 q^{12} + 168 q^{13} + 47 q^{14} + 10 q^{15} + 203 q^{16} + 147 q^{17} + 13 q^{18} + 17 q^{19} + 81 q^{20} + 13 q^{21} + 20 q^{22} + 85 q^{23} + 14 q^{24} + 225 q^{25} + 11 q^{26} + 89 q^{27} + 12 q^{28} + 137 q^{29} + 26 q^{30} + 13 q^{31} + 60 q^{32} + 78 q^{33} - 2 q^{34} + 77 q^{35} + 278 q^{36} + 41 q^{37} + 68 q^{38} + 26 q^{39} + 11 q^{40} + 107 q^{41} + 43 q^{42} + 27 q^{43} + 39 q^{44} + 88 q^{45} - 23 q^{46} + 112 q^{47} + 127 q^{48} + 236 q^{49} + 14 q^{50} + 55 q^{51} + 181 q^{52} + 149 q^{53} + 3 q^{54} + 40 q^{55} + 134 q^{56} + 55 q^{57} - q^{58} + 44 q^{59} - 13 q^{60} + 81 q^{61} + 106 q^{62} + 34 q^{63} + 197 q^{64} + 41 q^{65} - 20 q^{66} - q^{67} + 278 q^{68} + 75 q^{69} - 42 q^{70} + 48 q^{71} - 34 q^{72} + 107 q^{73} + 74 q^{74} + 93 q^{75} + 20 q^{76} + 206 q^{77} + 11 q^{78} + 14 q^{79} + 115 q^{80} + 328 q^{81} + 48 q^{82} + 62 q^{83} - 11 q^{84} + 6 q^{85} + 27 q^{86} + 51 q^{87} + 31 q^{88} + 173 q^{89} - 21 q^{90} + 12 q^{91} + 179 q^{92} + 73 q^{93} + 17 q^{94} + 90 q^{95} - 33 q^{96} + 110 q^{97} - 13 q^{98} + 24 q^{99}+O(q^{100}) \) 168 * q + 11 * q^2 + 26 * q^3 + 181 * q^4 + 41 * q^5 + 11 * q^6 + 12 * q^7 + 27 * q^8 + 220 * q^9 + 11 * q^10 + 23 * q^11 + 78 * q^12 + 168 * q^13 + 47 * q^14 + 10 * q^15 + 203 * q^16 + 147 * q^17 + 13 * q^18 + 17 * q^19 + 81 * q^20 + 13 * q^21 + 20 * q^22 + 85 * q^23 + 14 * q^24 + 225 * q^25 + 11 * q^26 + 89 * q^27 + 12 * q^28 + 137 * q^29 + 26 * q^30 + 13 * q^31 + 60 * q^32 + 78 * q^33 - 2 * q^34 + 77 * q^35 + 278 * q^36 + 41 * q^37 + 68 * q^38 + 26 * q^39 + 11 * q^40 + 107 * q^41 + 43 * q^42 + 27 * q^43 + 39 * q^44 + 88 * q^45 - 23 * q^46 + 112 * q^47 + 127 * q^48 + 236 * q^49 + 14 * q^50 + 55 * q^51 + 181 * q^52 + 149 * q^53 + 3 * q^54 + 40 * q^55 + 134 * q^56 + 55 * q^57 - q^58 + 44 * q^59 - 13 * q^60 + 81 * q^61 + 106 * q^62 + 34 * q^63 + 197 * q^64 + 41 * q^65 - 20 * q^66 - q^67 + 278 * q^68 + 75 * q^69 - 42 * q^70 + 48 * q^71 - 34 * q^72 + 107 * q^73 + 74 * q^74 + 93 * q^75 + 20 * q^76 + 206 * q^77 + 11 * q^78 + 14 * q^79 + 115 * q^80 + 328 * q^81 + 48 * q^82 + 62 * q^83 - 11 * q^84 + 6 * q^85 + 27 * q^86 + 51 * q^87 + 31 * q^88 + 173 * q^89 - 21 * q^90 + 12 * q^91 + 179 * q^92 + 73 * q^93 + 17 * q^94 + 90 * q^95 - 33 * q^96 + 110 * q^97 - 13 * q^98 + 24 * q^99

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