LMFDB - Embedded newform 8007.2.a.j.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28460 q^{2} -1.00000 q^{3} -0.349799 q^{4} -0.580730 q^{5} +1.28460 q^{6} -1.93204 q^{7} +3.01856 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.28460 q^{2} -1.00000 q^{3} -0.349799 q^{4} -0.580730 q^{5} +1.28460 q^{6} -1.93204 q^{7} +3.01856 q^{8} +1.00000 q^{9} +0.746007 q^{10} +1.58316 q^{11} +0.349799 q^{12} -0.419632 q^{13} +2.48191 q^{14} +0.580730 q^{15} -3.17804 q^{16} +1.00000 q^{17} -1.28460 q^{18} -2.91658 q^{19} +0.203139 q^{20} +1.93204 q^{21} -2.03372 q^{22} +8.95631 q^{23} -3.01856 q^{24} -4.66275 q^{25} +0.539060 q^{26} -1.00000 q^{27} +0.675827 q^{28} +4.63895 q^{29} -0.746007 q^{30} +1.94626 q^{31} -1.95459 q^{32} -1.58316 q^{33} -1.28460 q^{34} +1.12200 q^{35} -0.349799 q^{36} +8.65463 q^{37} +3.74664 q^{38} +0.419632 q^{39} -1.75297 q^{40} +10.2986 q^{41} -2.48191 q^{42} -1.03555 q^{43} -0.553786 q^{44} -0.580730 q^{45} -11.5053 q^{46} +7.92894 q^{47} +3.17804 q^{48} -3.26721 q^{49} +5.98978 q^{50} -1.00000 q^{51} +0.146787 q^{52} -10.1848 q^{53} +1.28460 q^{54} -0.919386 q^{55} -5.83198 q^{56} +2.91658 q^{57} -5.95921 q^{58} -11.7856 q^{59} -0.203139 q^{60} -3.15724 q^{61} -2.50016 q^{62} -1.93204 q^{63} +8.86696 q^{64} +0.243693 q^{65} +2.03372 q^{66} -5.25076 q^{67} -0.349799 q^{68} -8.95631 q^{69} -1.44132 q^{70} +10.2391 q^{71} +3.01856 q^{72} -0.696030 q^{73} -11.1177 q^{74} +4.66275 q^{75} +1.02022 q^{76} -3.05873 q^{77} -0.539060 q^{78} -4.38503 q^{79} +1.84559 q^{80} +1.00000 q^{81} -13.2296 q^{82} -0.402925 q^{83} -0.675827 q^{84} -0.580730 q^{85} +1.33027 q^{86} -4.63895 q^{87} +4.77884 q^{88} +3.07805 q^{89} +0.746007 q^{90} +0.810747 q^{91} -3.13291 q^{92} -1.94626 q^{93} -10.1855 q^{94} +1.69375 q^{95} +1.95459 q^{96} +18.6258 q^{97} +4.19706 q^{98} +1.58316 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−1.28460	−0.908350	−0.454175	−	0.890912i	$-0.650066\pi$
$2$	−1.28460	−0.908350	−0.454175	+	0.890912i	$0.650066\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.349799	−0.174899
$5$	−0.580730	−0.259710	−0.129855	−	0.991533i	$-0.541451\pi$
$5$	−0.580730	−0.259710	−0.129855	+	0.991533i	$0.541451\pi$
$6$	1.28460	0.524436
$7$	−1.93204	−0.730244	−0.365122	−	0.930960i	$-0.618973\pi$
$7$	−1.93204	−0.730244	−0.365122	+	0.930960i	$0.618973\pi$
$8$	3.01856	1.06722
$9$	1.00000	0.333333
$10$	0.746007	0.235908
$11$	1.58316	0.477340	0.238670	−	0.971101i	$-0.423289\pi$
$11$	1.58316	0.477340	0.238670	+	0.971101i	$0.423289\pi$
$12$	0.349799	0.100978
$13$	−0.419632	−0.116385	−0.0581925	−	0.998305i	$-0.518534\pi$
$13$	−0.419632	−0.116385	−0.0581925	+	0.998305i	$0.518534\pi$
$14$	2.48191	0.663317
$15$	0.580730	0.149944
$16$	−3.17804	−0.794511
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.28460	−0.302783
$19$	−2.91658	−0.669109	−0.334555	−	0.942376i	$-0.608586\pi$
$19$	−2.91658	−0.669109	−0.334555	+	0.942376i	$0.608586\pi$
$20$	0.203139	0.0454232
$21$	1.93204	0.421607
$22$	−2.03372	−0.433592
$23$	8.95631	1.86752	0.933760	−	0.357901i	$-0.116507\pi$
$23$	8.95631	1.86752	0.933760	+	0.357901i	$0.116507\pi$
$24$	−3.01856	−0.616160
$25$	−4.66275	−0.932551
$26$	0.539060	0.105718
$27$	−1.00000	−0.192450
$28$	0.675827	0.127719
$29$	4.63895	0.861432	0.430716	−	0.902488i	$-0.358261\pi$
$29$	4.63895	0.861432	0.430716	+	0.902488i	$0.358261\pi$
$30$	−0.746007	−0.136202
$31$	1.94626	0.349558	0.174779	−	0.984608i	$-0.444079\pi$
$31$	1.94626	0.349558	0.174779	+	0.984608i	$0.444079\pi$
$32$	−1.95459	−0.345526
$33$	−1.58316	−0.275592
$34$	−1.28460	−0.220307
$35$	1.12200	0.189652
$36$	−0.349799	−0.0582998
$37$	8.65463	1.42281	0.711406	−	0.702781i	$-0.248059\pi$
$37$	8.65463	1.42281	0.711406	+	0.702781i	$0.248059\pi$
$38$	3.74664	0.607786
$39$	0.419632	0.0671949
$40$	−1.75297	−0.277168
$41$	10.2986	1.60837	0.804187	−	0.594376i	$-0.202601\pi$
$41$	10.2986	1.60837	0.804187	+	0.594376i	$0.202601\pi$
$42$	−2.48191	−0.382967
$43$	−1.03555	−0.157920	−0.0789602	−	0.996878i	$-0.525160\pi$
$43$	−1.03555	−0.157920	−0.0789602	+	0.996878i	$0.525160\pi$
$44$	−0.553786	−0.0834864
$45$	−0.580730	−0.0865701
$46$	−11.5053	−1.69636
$47$	7.92894	1.15656	0.578278	−	0.815840i	$-0.303725\pi$
$47$	7.92894	1.15656	0.578278	+	0.815840i	$0.303725\pi$
$48$	3.17804	0.458711
$49$	−3.26721	−0.466744
$50$	5.98978	0.847083
$51$	−1.00000	−0.140028
$52$	0.146787	0.0203557
$53$	−10.1848	−1.39898	−0.699492	−	0.714641i	$-0.746590\pi$
$53$	−10.1848	−1.39898	−0.699492	+	0.714641i	$0.746590\pi$
$54$	1.28460	0.174812
$55$	−0.919386	−0.123970
$56$	−5.83198	−0.779331
$57$	2.91658	0.386310
$58$	−5.95921	−0.782482
$59$	−11.7856	−1.53436	−0.767179	−	0.641433i	$-0.778340\pi$
$59$	−11.7856	−1.53436	−0.767179	+	0.641433i	$0.778340\pi$
$60$	−0.203139	−0.0262251
$61$	−3.15724	−0.404243	−0.202121	−	0.979360i	$-0.564784\pi$
$61$	−3.15724	−0.404243	−0.202121	+	0.979360i	$0.564784\pi$
$62$	−2.50016	−0.317521
$63$	−1.93204	−0.243415
$64$	8.86696	1.10837
$65$	0.243693	0.0302264
$66$	2.03372	0.250334
$67$	−5.25076	−0.641482	−0.320741	−	0.947167i	$-0.603932\pi$
$67$	−5.25076	−0.641482	−0.320741	+	0.947167i	$0.603932\pi$
$68$	−0.349799	−0.0424193
$69$	−8.95631	−1.07821
$70$	−1.44132	−0.172270
$71$	10.2391	1.21515	0.607577	−	0.794260i	$-0.292141\pi$
$71$	10.2391	1.21515	0.607577	+	0.794260i	$0.292141\pi$
$72$	3.01856	0.355740
$73$	−0.696030	−0.0814641	−0.0407321	−	0.999170i	$-0.512969\pi$
$73$	−0.696030	−0.0814641	−0.0407321	+	0.999170i	$0.512969\pi$
$74$	−11.1177	−1.29241
$75$	4.66275	0.538408
$76$	1.02022	0.117027
$77$	−3.05873	−0.348574
$78$	−0.539060	−0.0610365
$79$	−4.38503	−0.493354	−0.246677	−	0.969098i	$-0.579339\pi$
$79$	−4.38503	−0.493354	−0.246677	+	0.969098i	$0.579339\pi$
$80$	1.84559	0.206343
$81$	1.00000	0.111111
$82$	−13.2296	−1.46097
$83$	−0.402925	−0.0442268	−0.0221134	−	0.999755i	$-0.507039\pi$
$83$	−0.402925	−0.0442268	−0.0221134	+	0.999755i	$0.507039\pi$
$84$	−0.675827	−0.0737387
$85$	−0.580730	−0.0629890
$86$	1.33027	0.143447
$87$	−4.63895	−0.497348
$88$	4.77884	0.509426
$89$	3.07805	0.326273	0.163137	−	0.986603i	$-0.447839\pi$
$89$	3.07805	0.326273	0.163137	+	0.986603i	$0.447839\pi$
$90$	0.746007	0.0786360
$91$	0.810747	0.0849894
$92$	−3.13291	−0.326628
$93$	−1.94626	−0.201817
$94$	−10.1855	−1.05056
$95$	1.69375	0.173775
$96$	1.95459	0.199490
$97$	18.6258	1.89117	0.945583	−	0.325382i	$-0.105493\pi$
$97$	18.6258	1.89117	0.945583	+	0.325382i	$0.105493\pi$
$98$	4.19706	0.423967
$99$	1.58316	0.159113
$100$	1.63103	0.163103
$101$	17.5565	1.74694	0.873469	−	0.486880i	$-0.161865\pi$
$101$	17.5565	1.74694	0.873469	+	0.486880i	$0.161865\pi$
$102$	1.28460	0.127195
$103$	−4.39526	−0.433078	−0.216539	−	0.976274i	$-0.569477\pi$
$103$	−4.39526	−0.433078	−0.216539	+	0.976274i	$0.569477\pi$
$104$	−1.26668	−0.124208
$105$	−1.12200	−0.109496
$106$	13.0833	1.27077
$107$	2.56618	0.248082	0.124041	−	0.992277i	$-0.460415\pi$
$107$	2.56618	0.248082	0.124041	+	0.992277i	$0.460415\pi$
$108$	0.349799	0.0336594
$109$	5.05854	0.484520	0.242260	−	0.970211i	$-0.422111\pi$
$109$	5.05854	0.484520	0.242260	+	0.970211i	$0.422111\pi$
$110$	1.18105	0.112608
$111$	−8.65463	−0.821461
$112$	6.14012	0.580187
$113$	0.902607	0.0849102	0.0424551	−	0.999098i	$-0.486482\pi$
$113$	0.902607	0.0849102	0.0424551	+	0.999098i	$0.486482\pi$
$114$	−3.74664	−0.350905
$115$	−5.20120	−0.485014
$116$	−1.62270	−0.150664
$117$	−0.419632	−0.0387950
$118$	15.1398	1.39374
$119$	−1.93204	−0.177110
$120$	1.75297	0.160023
$121$	−8.49362	−0.772147
$122$	4.05579	0.367194
$123$	−10.2986	−0.928596
$124$	−0.680798	−0.0611375
$125$	5.61145	0.501903
$126$	2.48191	0.221106
$127$	−8.31090	−0.737473	−0.368736	−	0.929534i	$-0.620210\pi$
$127$	−8.31090	−0.737473	−0.368736	+	0.929534i	$0.620210\pi$
$128$	−7.48132	−0.661262
$129$	1.03555	0.0911754
$130$	−0.313048	−0.0274561
$131$	−0.701360	−0.0612781	−0.0306391	−	0.999531i	$-0.509754\pi$
$131$	−0.701360	−0.0612781	−0.0306391	+	0.999531i	$0.509754\pi$
$132$	0.553786	0.0482009
$133$	5.63496	0.488613
$134$	6.74513	0.582690
$135$	0.580730	0.0499813
$136$	3.01856	0.258839
$137$	−17.9637	−1.53474	−0.767370	−	0.641205i	$-0.778435\pi$
$137$	−17.9637	−1.53474	−0.767370	+	0.641205i	$0.778435\pi$
$138$	11.5053	0.979395
$139$	−6.77443	−0.574600	−0.287300	−	0.957841i	$-0.592758\pi$
$139$	−6.77443	−0.574600	−0.287300	+	0.957841i	$0.592758\pi$
$140$	−0.392473	−0.0331700
$141$	−7.92894	−0.667738
$142$	−13.1531	−1.10379
$143$	−0.664343	−0.0555551
$144$	−3.17804	−0.264837
$145$	−2.69398	−0.223723
$146$	0.894121	0.0739980
$147$	3.26721	0.269475
$148$	−3.02738	−0.248849
$149$	12.3459	1.01141	0.505707	−	0.862706i	$-0.331232\pi$
$149$	12.3459	1.01141	0.505707	+	0.862706i	$0.331232\pi$
$150$	−5.98978	−0.489063
$151$	19.9042	1.61978	0.809890	−	0.586582i	$-0.199527\pi$
$151$	19.9042	1.61978	0.809890	+	0.586582i	$0.199527\pi$
$152$	−8.80386	−0.714087
$153$	1.00000	0.0808452
$154$	3.92925	0.316628
$155$	−1.13025	−0.0907838
$156$	−0.146787	−0.0117523
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	5.63301	0.448138
$159$	10.1848	0.807703
$160$	1.13509	0.0897367
$161$	−17.3040	−1.36374
$162$	−1.28460	−0.100928
$163$	−22.4318	−1.75699	−0.878496	−	0.477749i	$-0.841453\pi$
$163$	−22.4318	−1.75699	−0.878496	+	0.477749i	$0.841453\pi$
$164$	−3.60245	−0.281304
$165$	0.919386	0.0715741
$166$	0.517598	0.0401734
$167$	3.34538	0.258873	0.129436	−	0.991588i	$-0.458683\pi$
$167$	3.34538	0.258873	0.129436	+	0.991588i	$0.458683\pi$
$168$	5.83198	0.449947
$169$	−12.8239	−0.986455
$170$	0.746007	0.0572161
$171$	−2.91658	−0.223036
$172$	0.362235	0.0276202
$173$	−14.7573	−1.12197	−0.560987	−	0.827824i	$-0.689578\pi$
$173$	−14.7573	−1.12197	−0.560987	+	0.827824i	$0.689578\pi$
$174$	5.95921	0.451766
$175$	9.00864	0.680989
$176$	−5.03134	−0.379251
$177$	11.7856	0.885862
$178$	−3.95407	−0.296370
$179$	−16.7116	−1.24909	−0.624543	−	0.780991i	$-0.714715\pi$
$179$	−16.7116	−1.24909	−0.624543	+	0.780991i	$0.714715\pi$
$180$	0.203139	0.0151411
$181$	−0.391152	−0.0290741	−0.0145371	−	0.999894i	$-0.504627\pi$
$181$	−0.391152	−0.0290741	−0.0145371	+	0.999894i	$0.504627\pi$
$182$	−1.04149	−0.0772002
$183$	3.15724	0.233390
$184$	27.0351	1.99305
$185$	−5.02600	−0.369519
$186$	2.50016	0.183321
$187$	1.58316	0.115772
$188$	−2.77354	−0.202281
$189$	1.93204	0.140536
$190$	−2.17579	−0.157848
$191$	−23.7512	−1.71857	−0.859287	−	0.511495i	$-0.829092\pi$
$191$	−23.7512	−1.71857	−0.859287	+	0.511495i	$0.829092\pi$
$192$	−8.86696	−0.639918
$193$	−15.1485	−1.09041	−0.545206	−	0.838302i	$-0.683548\pi$
$193$	−15.1485	−1.09041	−0.545206	+	0.838302i	$0.683548\pi$
$194$	−23.9268	−1.71784
$195$	−0.243693	−0.0174512
$196$	1.14286	0.0816332
$197$	−10.6745	−0.760528	−0.380264	−	0.924878i	$-0.624167\pi$
$197$	−10.6745	−0.760528	−0.380264	+	0.924878i	$0.624167\pi$
$198$	−2.03372	−0.144531
$199$	9.56418	0.677987	0.338993	−	0.940789i	$-0.389914\pi$
$199$	9.56418	0.677987	0.338993	+	0.940789i	$0.389914\pi$
$200$	−14.0748	−0.995237
$201$	5.25076	0.370360
$202$	−22.5531	−1.58683
$203$	−8.96266	−0.629055
$204$	0.349799	0.0244908
$205$	−5.98072	−0.417712
$206$	5.64616	0.393387
$207$	8.95631	0.622506
$208$	1.33361	0.0924691
$209$	−4.61740	−0.319392
$210$	1.44132	0.0994604
$211$	21.5889	1.48624	0.743122	−	0.669156i	$-0.233344\pi$
$211$	21.5889	1.48624	0.743122	+	0.669156i	$0.233344\pi$
$212$	3.56261	0.244681
$213$	−10.2391	−0.701570
$214$	−3.29652	−0.225346
$215$	0.601377	0.0410136
$216$	−3.01856	−0.205387
$217$	−3.76025	−0.255262
$218$	−6.49821	−0.440114
$219$	0.696030	0.0470333
$220$	0.321600	0.0216823
$221$	−0.419632	−0.0282275
$222$	11.1177	0.746175
$223$	29.2522	1.95887	0.979436	−	0.201757i	$-0.0646653\pi$
$223$	29.2522	1.95887	0.979436	+	0.201757i	$0.0646653\pi$
$224$	3.77636	0.252318
$225$	−4.66275	−0.310850
$226$	−1.15949	−0.0771282
$227$	−18.6000	−1.23452	−0.617262	−	0.786758i	$-0.711758\pi$
$227$	−18.6000	−1.23452	−0.617262	+	0.786758i	$0.711758\pi$
$228$	−1.02022	−0.0675655
$229$	−17.4519	−1.15326	−0.576628	−	0.817007i	$-0.695632\pi$
$229$	−17.4519	−1.15326	−0.576628	+	0.817007i	$0.695632\pi$
$230$	6.68147	0.440563
$231$	3.05873	0.201249
$232$	14.0029	0.919338
$233$	16.3122	1.06865	0.534325	−	0.845279i	$-0.320566\pi$
$233$	16.3122	1.06865	0.534325	+	0.845279i	$0.320566\pi$
$234$	0.539060	0.0352394
$235$	−4.60458	−0.300369
$236$	4.12260	0.268358
$237$	4.38503	0.284838
$238$	2.48191	0.160878
$239$	−10.4899	−0.678534	−0.339267	−	0.940690i	$-0.610179\pi$
$239$	−10.4899	−0.678534	−0.339267	+	0.940690i	$0.610179\pi$
$240$	−1.84559	−0.119132
$241$	3.20071	0.206176	0.103088	−	0.994672i	$-0.467128\pi$
$241$	3.20071	0.206176	0.103088	+	0.994672i	$0.467128\pi$
$242$	10.9109	0.701380
$243$	−1.00000	−0.0641500
$244$	1.10440	0.0707018
$245$	1.89737	0.121218
$246$	13.2296	0.843490
$247$	1.22389	0.0778742
$248$	5.87488	0.373055
$249$	0.402925	0.0255343
$250$	−7.20848	−0.455904
$251$	−9.17030	−0.578824	−0.289412	−	0.957205i	$-0.593460\pi$
$251$	−9.17030	−0.578824	−0.289412	+	0.957205i	$0.593460\pi$
$252$	0.675827	0.0425731
$253$	14.1792	0.891441
$254$	10.6762	0.669884
$255$	0.580730	0.0363667
$256$	−8.12339	−0.507712
$257$	17.5100	1.09224	0.546122	−	0.837706i	$-0.316104\pi$
$257$	17.5100	1.09224	0.546122	+	0.837706i	$0.316104\pi$
$258$	−1.33027	−0.0828192
$259$	−16.7211	−1.03900
$260$	−0.0852435	−0.00528658
$261$	4.63895	0.287144
$262$	0.900969	0.0556620
$263$	14.3398	0.884228	0.442114	−	0.896959i	$-0.354229\pi$
$263$	14.3398	0.884228	0.442114	+	0.896959i	$0.354229\pi$
$264$	−4.77884	−0.294118
$265$	5.91459	0.363331
$266$	−7.23868	−0.443832
$267$	−3.07805	−0.188374
$268$	1.83671	0.112195
$269$	5.81592	0.354603	0.177301	−	0.984157i	$-0.443263\pi$
$269$	5.81592	0.354603	0.177301	+	0.984157i	$0.443263\pi$
$270$	−0.746007	−0.0454005
$271$	4.72990	0.287321	0.143661	−	0.989627i	$-0.454113\pi$
$271$	4.72990	0.287321	0.143661	+	0.989627i	$0.454113\pi$
$272$	−3.17804	−0.192697
$273$	−0.810747	−0.0490687
$274$	23.0762	1.39408
$275$	−7.38186	−0.445143
$276$	3.13291	0.188579
$277$	−9.62977	−0.578597	−0.289298	−	0.957239i	$-0.593422\pi$
$277$	−9.62977	−0.578597	−0.289298	+	0.957239i	$0.593422\pi$
$278$	8.70245	0.521938
$279$	1.94626	0.116519
$280$	3.38681	0.202400
$281$	−23.3377	−1.39221	−0.696105	−	0.717940i	$-0.745085\pi$
$281$	−23.3377	−1.39221	−0.696105	+	0.717940i	$0.745085\pi$
$282$	10.1855	0.606540
$283$	10.3845	0.617292	0.308646	−	0.951177i	$-0.400124\pi$
$283$	10.3845	0.617292	0.308646	+	0.951177i	$0.400124\pi$
$284$	−3.58162	−0.212530
$285$	−1.69375	−0.100329
$286$	0.853416	0.0504635
$287$	−19.8974	−1.17451
$288$	−1.95459	−0.115175
$289$	1.00000	0.0588235
$290$	3.46069	0.203219
$291$	−18.6258	−1.09186
$292$	0.243470	0.0142480
$293$	6.43263	0.375798	0.187899	−	0.982188i	$-0.439832\pi$
$293$	6.43263	0.375798	0.187899	+	0.982188i	$0.439832\pi$
$294$	−4.19706	−0.244777
$295$	6.84427	0.398489
$296$	26.1245	1.51845
$297$	−1.58316	−0.0918640
$298$	−15.8595	−0.918718
$299$	−3.75835	−0.217351
$300$	−1.63103	−0.0941673
$301$	2.00074	0.115320
$302$	−25.5690	−1.47133
$303$	−17.5565	−1.00859
$304$	9.26902	0.531615
$305$	1.83350	0.104986
$306$	−1.28460	−0.0734358
$307$	18.5904	1.06101	0.530504	−	0.847682i	$-0.322003\pi$
$307$	18.5904	1.06101	0.530504	+	0.847682i	$0.322003\pi$
$308$	1.06994	0.0609654
$309$	4.39526	0.250038
$310$	1.45192	0.0824635
$311$	−10.0164	−0.567979	−0.283989	−	0.958827i	$-0.591658\pi$
$311$	−10.0164	−0.567979	−0.283989	+	0.958827i	$0.591658\pi$
$312$	1.26668	0.0717118
$313$	−30.8487	−1.74367	−0.871835	−	0.489799i	$-0.837070\pi$
$313$	−30.8487	−1.74367	−0.871835	+	0.489799i	$0.837070\pi$
$314$	1.28460	0.0724943
$315$	1.12200	0.0632173
$316$	1.53388	0.0862873
$317$	30.7099	1.72484	0.862421	−	0.506192i	$-0.168947\pi$
$317$	30.7099	1.72484	0.862421	+	0.506192i	$0.168947\pi$
$318$	−13.0833	−0.733678
$319$	7.34419	0.411195
$320$	−5.14931	−0.287855
$321$	−2.56618	−0.143230
$322$	22.2287	1.23876
$323$	−2.91658	−0.162283
$324$	−0.349799	−0.0194333
$325$	1.95664	0.108535
$326$	28.8159	1.59597
$327$	−5.05854	−0.279738
$328$	31.0870	1.71649
$329$	−15.3191	−0.844568
$330$	−1.18105	−0.0650144
$331$	7.37770	0.405515	0.202758	−	0.979229i	$-0.435010\pi$
$331$	7.37770	0.405515	0.202758	+	0.979229i	$0.435010\pi$
$332$	0.140943	0.00773524
$333$	8.65463	0.474271
$334$	−4.29748	−0.235147
$335$	3.04927	0.166600
$336$	−6.14012	−0.334971
$337$	23.5861	1.28482	0.642408	−	0.766363i	$-0.277936\pi$
$337$	23.5861	1.28482	0.642408	+	0.766363i	$0.277936\pi$
$338$	16.4736	0.896046
$339$	−0.902607	−0.0490229
$340$	0.203139	0.0110167
$341$	3.08123	0.166858
$342$	3.74664	0.202595
$343$	19.8367	1.07108
$344$	−3.12588	−0.168536
$345$	5.20120	0.280023
$346$	18.9572	1.01915
$347$	−7.99274	−0.429073	−0.214536	−	0.976716i	$-0.568824\pi$
$347$	−7.99274	−0.429073	−0.214536	+	0.976716i	$0.568824\pi$
$348$	1.62270	0.0869859
$349$	2.28026	0.122060	0.0610298	−	0.998136i	$-0.480562\pi$
$349$	2.28026	0.122060	0.0610298	+	0.998136i	$0.480562\pi$
$350$	−11.5725	−0.618577
$351$	0.419632	0.0223983
$352$	−3.09442	−0.164933
$353$	15.6438	0.832633	0.416317	−	0.909220i	$-0.363321\pi$
$353$	15.6438	0.832633	0.416317	+	0.909220i	$0.363321\pi$
$354$	−15.1398	−0.804673
$355$	−5.94614	−0.315588
$356$	−1.07670	−0.0570650
$357$	1.93204	0.102255
$358$	21.4678	1.13461
$359$	37.0267	1.95420	0.977098	−	0.212791i	$-0.0682554\pi$
$359$	37.0267	1.95420	0.977098	+	0.212791i	$0.0682554\pi$
$360$	−1.75297	−0.0923894
$361$	−10.4936	−0.552293
$362$	0.502475	0.0264095
$363$	8.49362	0.445799
$364$	−0.283598	−0.0148646
$365$	0.404205	0.0211571
$366$	−4.05579	−0.212000
$367$	6.04369	0.315478	0.157739	−	0.987481i	$-0.449580\pi$
$367$	6.04369	0.315478	0.157739	+	0.987481i	$0.449580\pi$
$368$	−28.4635	−1.48376
$369$	10.2986	0.536125
$370$	6.45641	0.335653
$371$	19.6774	1.02160
$372$	0.680798	0.0352977
$373$	−33.3692	−1.72779	−0.863896	−	0.503670i	$-0.831983\pi$
$373$	−33.3692	−1.72779	−0.863896	+	0.503670i	$0.831983\pi$
$374$	−2.03372	−0.105161
$375$	−5.61145	−0.289774
$376$	23.9340	1.23430
$377$	−1.94665	−0.100258
$378$	−2.48191	−0.127656
$379$	4.49054	0.230663	0.115332	−	0.993327i	$-0.463207\pi$
$379$	4.49054	0.230663	0.115332	+	0.993327i	$0.463207\pi$
$380$	−0.592470	−0.0303931
$381$	8.31090	0.425780
$382$	30.5108	1.56107
$383$	−31.6450	−1.61698	−0.808492	−	0.588507i	$-0.799716\pi$
$383$	−31.6450	−1.61698	−0.808492	+	0.588507i	$0.799716\pi$
$384$	7.48132	0.381780
$385$	1.77629	0.0905284
$386$	19.4598	0.990476
$387$	−1.03555	−0.0526402
$388$	−6.51529	−0.330764
$389$	−21.8230	−1.10647	−0.553234	−	0.833026i	$-0.686606\pi$
$389$	−21.8230	−1.10647	−0.553234	+	0.833026i	$0.686606\pi$
$390$	0.313048	0.0158518
$391$	8.95631	0.452940
$392$	−9.86224	−0.498118
$393$	0.701360	0.0353789
$394$	13.7125	0.690826
$395$	2.54652	0.128129
$396$	−0.553786	−0.0278288
$397$	3.00144	0.150638	0.0753191	−	0.997159i	$-0.476002\pi$
$397$	3.00144	0.150638	0.0753191	+	0.997159i	$0.476002\pi$
$398$	−12.2862	−0.615849
$399$	−5.63496	−0.282101
$400$	14.8184	0.740921
$401$	8.96913	0.447897	0.223949	−	0.974601i	$-0.428105\pi$
$401$	8.96913	0.447897	0.223949	+	0.974601i	$0.428105\pi$
$402$	−6.74513	−0.336416
$403$	−0.816711	−0.0406833
$404$	−6.14125	−0.305538
$405$	−0.580730	−0.0288567
$406$	11.5134	0.571403
$407$	13.7016	0.679164
$408$	−3.01856	−0.149441
$409$	−5.88355	−0.290923	−0.145461	−	0.989364i	$-0.546467\pi$
$409$	−5.88355	−0.290923	−0.145461	+	0.989364i	$0.546467\pi$
$410$	7.68284	0.379429
$411$	17.9637	0.886082
$412$	1.53746	0.0757451
$413$	22.7704	1.12046
$414$	−11.5053	−0.565454
$415$	0.233991	0.0114862
$416$	0.820209	0.0402140
$417$	6.77443	0.331745
$418$	5.93152	0.290120
$419$	15.5704	0.760663	0.380332	−	0.924850i	$-0.375810\pi$
$419$	15.5704	0.760663	0.380332	+	0.924850i	$0.375810\pi$
$420$	0.392473	0.0191507
$421$	7.58791	0.369812	0.184906	−	0.982756i	$-0.440802\pi$
$421$	7.58791	0.369812	0.184906	+	0.982756i	$0.440802\pi$
$422$	−27.7332	−1.35003
$423$	7.92894	0.385518
$424$	−30.7432	−1.49302
$425$	−4.66275	−0.226177
$426$	13.1531	0.637271
$427$	6.09992	0.295196
$428$	−0.897647	−0.0433894
$429$	0.664343	0.0320748
$430$	−0.772530	−0.0372547
$431$	17.4846	0.842204	0.421102	−	0.907013i	$-0.361643\pi$
$431$	17.4846	0.842204	0.421102	+	0.907013i	$0.361643\pi$
$432$	3.17804	0.152904
$433$	7.59170	0.364834	0.182417	−	0.983221i	$-0.441608\pi$
$433$	7.59170	0.364834	0.182417	+	0.983221i	$0.441608\pi$
$434$	4.83042	0.231868
$435$	2.69398	0.129166
$436$	−1.76947	−0.0847423
$437$	−26.1218	−1.24957
$438$	−0.894121	−0.0427227
$439$	8.08953	0.386092	0.193046	−	0.981190i	$-0.438163\pi$
$439$	8.08953	0.386092	0.193046	+	0.981190i	$0.438163\pi$
$440$	−2.77522	−0.132303
$441$	−3.26721	−0.155581
$442$	0.539060	0.0256405
$443$	−15.9530	−0.757951	−0.378975	−	0.925407i	$-0.623723\pi$
$443$	−15.9530	−0.757951	−0.378975	+	0.925407i	$0.623723\pi$
$444$	3.02738	0.143673
$445$	−1.78752	−0.0847365
$446$	−37.5774	−1.77934
$447$	−12.3459	−0.583940
$448$	−17.1314	−0.809380
$449$	38.0474	1.79557	0.897784	−	0.440435i	$-0.145176\pi$
$449$	38.0474	1.79557	0.897784	+	0.440435i	$0.145176\pi$
$450$	5.98978	0.282361
$451$	16.3043	0.767741
$452$	−0.315731	−0.0148507
$453$	−19.9042	−0.935180
$454$	23.8936	1.12138
$455$	−0.470825	−0.0220726
$456$	8.80386	0.412278
$457$	23.3400	1.09180	0.545899	−	0.837851i	$-0.316188\pi$
$457$	23.3400	1.09180	0.545899	+	0.837851i	$0.316188\pi$
$458$	22.4188	1.04756
$459$	−1.00000	−0.0466760
$460$	1.81937	0.0848287
$461$	−19.1263	−0.890800	−0.445400	−	0.895332i	$-0.646939\pi$
$461$	−19.1263	−0.890800	−0.445400	+	0.895332i	$0.646939\pi$
$462$	−3.92925	−0.182805
$463$	−19.7251	−0.916703	−0.458351	−	0.888771i	$-0.651560\pi$
$463$	−19.7251	−0.916703	−0.458351	+	0.888771i	$0.651560\pi$
$464$	−14.7428	−0.684417
$465$	1.13025	0.0524141
$466$	−20.9547	−0.970708
$467$	22.4299	1.03793	0.518966	−	0.854795i	$-0.326317\pi$
$467$	22.4299	1.03793	0.518966	+	0.854795i	$0.326317\pi$
$468$	0.146787	0.00678522
$469$	10.1447	0.468438
$470$	5.91505	0.272841
$471$	1.00000	0.0460776
$472$	−35.5756	−1.63750
$473$	−1.63944	−0.0753817
$474$	−5.63301	−0.258733
$475$	13.5993	0.623978
$476$	0.675827	0.0309765
$477$	−10.1848	−0.466328
$478$	13.4753	0.616347
$479$	0.871785	0.0398329	0.0199164	−	0.999802i	$-0.493660\pi$
$479$	0.871785	0.0398329	0.0199164	+	0.999802i	$0.493660\pi$
$480$	−1.13509	−0.0518095
$481$	−3.63176	−0.165594
$482$	−4.11164	−0.187280
$483$	17.3040	0.787358
$484$	2.97106	0.135048
$485$	−10.8166	−0.491155
$486$	1.28460	0.0582707
$487$	14.2150	0.644144	0.322072	−	0.946715i	$-0.395621\pi$
$487$	14.2150	0.644144	0.322072	+	0.946715i	$0.395621\pi$
$488$	−9.53029	−0.431416
$489$	22.4318	1.01440
$490$	−2.43736	−0.110109
$491$	1.41434	0.0638284	0.0319142	−	0.999491i	$-0.489840\pi$
$491$	1.41434	0.0638284	0.0319142	+	0.999491i	$0.489840\pi$
$492$	3.60245	0.162411
$493$	4.63895	0.208928
$494$	−1.57221	−0.0707371
$495$	−0.919386	−0.0413233
$496$	−6.18528	−0.277727
$497$	−19.7823	−0.887359
$498$	−0.517598	−0.0231941
$499$	−11.3148	−0.506519	−0.253259	−	0.967398i	$-0.581503\pi$
$499$	−11.3148	−0.506519	−0.253259	+	0.967398i	$0.581503\pi$
$500$	−1.96288	−0.0877826
$501$	−3.34538	−0.149460
$502$	11.7802	0.525775
$503$	7.36129	0.328224	0.164112	−	0.986442i	$-0.447524\pi$
$503$	7.36129	0.328224	0.164112	+	0.986442i	$0.447524\pi$
$504$	−5.83198	−0.259777
$505$	−10.1956	−0.453698
$506$	−18.2147	−0.809741
$507$	12.8239	0.569530
$508$	2.90714	0.128984
$509$	39.5981	1.75515	0.877577	−	0.479436i	$-0.159159\pi$
$509$	39.5981	1.75515	0.877577	+	0.479436i	$0.159159\pi$
$510$	−0.746007	−0.0330337
$511$	1.34476	0.0594887
$512$	25.3980	1.12244
$513$	2.91658	0.128770
$514$	−22.4934	−0.992140
$515$	2.55246	0.112475
$516$	−0.362235	−0.0159465
$517$	12.5528	0.552070
$518$	21.4800	0.943776
$519$	14.7573	0.647772
$520$	0.735600	0.0322582
$521$	36.4594	1.59732	0.798658	−	0.601785i	$-0.205543\pi$
$521$	36.4594	1.59732	0.798658	+	0.601785i	$0.205543\pi$
$522$	−5.95921	−0.260827
$523$	−0.196520	−0.00859323	−0.00429661	−	0.999991i	$-0.501368\pi$
$523$	−0.196520	−0.00859323	−0.00429661	+	0.999991i	$0.501368\pi$
$524$	0.245335	0.0107175
$525$	−9.00864	−0.393169
$526$	−18.4209	−0.803189
$527$	1.94626	0.0847802
$528$	5.03134	0.218961
$529$	57.2154	2.48763
$530$	−7.59790	−0.330031
$531$	−11.7856	−0.511453
$532$	−1.97110	−0.0854581
$533$	−4.32163	−0.187191
$534$	3.95407	0.171110
$535$	−1.49026	−0.0644295
$536$	−15.8497	−0.684603
$537$	16.7116	0.721160
$538$	−7.47113	−0.322103
$539$	−5.17250	−0.222795
$540$	−0.203139	−0.00874170
$541$	21.9594	0.944110	0.472055	−	0.881569i	$-0.343512\pi$
$541$	21.9594	0.944110	0.472055	+	0.881569i	$0.343512\pi$
$542$	−6.07604	−0.260988
$543$	0.391152	0.0167859
$544$	−1.95459	−0.0838024
$545$	−2.93765	−0.125835
$546$	1.04149	0.0445715
$547$	42.7422	1.82753	0.913763	−	0.406248i	$-0.133163\pi$
$547$	42.7422	1.82753	0.913763	+	0.406248i	$0.133163\pi$
$548$	6.28367	0.268425
$549$	−3.15724	−0.134748
$550$	9.48276	0.404346
$551$	−13.5299	−0.576392
$552$	−27.0351	−1.15069
$553$	8.47206	0.360269
$554$	12.3704	0.525569
$555$	5.02600	0.213342
$556$	2.36969	0.100497
$557$	30.0082	1.27149	0.635745	−	0.771900i	$-0.280693\pi$
$557$	30.0082	1.27149	0.635745	+	0.771900i	$0.280693\pi$
$558$	−2.50016	−0.105840
$559$	0.434551	0.0183796
$560$	−3.56575	−0.150681
$561$	−1.58316	−0.0668409
$562$	29.9797	1.26462
$563$	−46.6016	−1.96402	−0.982012	−	0.188819i	$-0.939534\pi$
$563$	−46.6016	−1.96402	−0.982012	+	0.188819i	$0.939534\pi$
$564$	2.77354	0.116787
$565$	−0.524171	−0.0220521
$566$	−13.3399	−0.560717
$567$	−1.93204	−0.0811382
$568$	30.9072	1.29684
$569$	28.5846	1.19833	0.599164	−	0.800626i	$-0.295500\pi$
$569$	28.5846	1.19833	0.599164	+	0.800626i	$0.295500\pi$
$570$	2.17579	0.0911337
$571$	−27.9481	−1.16959	−0.584797	−	0.811180i	$-0.698826\pi$
$571$	−27.9481	−1.16959	−0.584797	+	0.811180i	$0.698826\pi$
$572$	0.232386	0.00971656
$573$	23.7512	0.992219
$574$	25.5602	1.06686
$575$	−41.7610	−1.74156
$576$	8.86696	0.369457
$577$	32.3210	1.34554	0.672770	−	0.739852i	$-0.265104\pi$
$577$	32.3210	1.34554	0.672770	+	0.739852i	$0.265104\pi$
$578$	−1.28460	−0.0534324
$579$	15.1485	0.629549
$580$	0.942351	0.0391290
$581$	0.778469	0.0322963
$582$	23.9268	0.991796
$583$	−16.1241	−0.667790
$584$	−2.10100	−0.0869402
$585$	0.243693	0.0100755
$586$	−8.26336	−0.341356
$587$	11.0951	0.457945	0.228972	−	0.973433i	$-0.426463\pi$
$587$	11.0951	0.457945	0.228972	+	0.973433i	$0.426463\pi$
$588$	−1.14286	−0.0471310
$589$	−5.67641	−0.233892
$590$	−8.79216	−0.361968
$591$	10.6745	0.439091
$592$	−27.5048	−1.13044
$593$	−18.8893	−0.775692	−0.387846	−	0.921724i	$-0.626781\pi$
$593$	−18.8893	−0.775692	−0.387846	+	0.921724i	$0.626781\pi$
$594$	2.03372	0.0834447
$595$	1.12200	0.0459974
$596$	−4.31857	−0.176896
$597$	−9.56418	−0.391436
$598$	4.82798	0.197431
$599$	−36.1983	−1.47902	−0.739510	−	0.673145i	$-0.764943\pi$
$599$	−36.1983	−1.47902	−0.739510	+	0.673145i	$0.764943\pi$
$600$	14.0748	0.574600
$601$	−0.160125	−0.00653163	−0.00326582	−	0.999995i	$-0.501040\pi$
$601$	−0.160125	−0.00653163	−0.00326582	+	0.999995i	$0.501040\pi$
$602$	−2.57015	−0.104751
$603$	−5.25076	−0.213827
$604$	−6.96246	−0.283299
$605$	4.93250	0.200535
$606$	22.5531	0.916158
$607$	43.5689	1.76841	0.884204	−	0.467102i	$-0.154702\pi$
$607$	43.5689	1.76841	0.884204	+	0.467102i	$0.154702\pi$
$608$	5.70072	0.231195
$609$	8.96266	0.363185
$610$	−2.35532	−0.0953641
$611$	−3.32724	−0.134606
$612$	−0.349799	−0.0141398
$613$	39.9136	1.61209	0.806047	−	0.591851i	$-0.201603\pi$
$613$	39.9136	1.61209	0.806047	+	0.591851i	$0.201603\pi$
$614$	−23.8812	−0.963768
$615$	5.98072	0.241166
$616$	−9.23294	−0.372006
$617$	22.0134	0.886224	0.443112	−	0.896466i	$-0.353874\pi$
$617$	22.0134	0.886224	0.443112	+	0.896466i	$0.353874\pi$
$618$	−5.64616	−0.227122
$619$	0.629398	0.0252976	0.0126488	−	0.999920i	$-0.495974\pi$
$619$	0.629398	0.0252976	0.0126488	+	0.999920i	$0.495974\pi$
$620$	0.395360	0.0158780
$621$	−8.95631	−0.359404
$622$	12.8671	0.515924
$623$	−5.94694	−0.238259
$624$	−1.33361	−0.0533871
$625$	20.0550	0.802201
$626$	39.6283	1.58386
$627$	4.61740	0.184401
$628$	0.349799	0.0139585
$629$	8.65463	0.345083
$630$	−1.44132	−0.0574235
$631$	30.9936	1.23384	0.616919	−	0.787027i	$-0.288381\pi$
$631$	30.9936	1.23384	0.616919	+	0.787027i	$0.288381\pi$
$632$	−13.2364	−0.526517
$633$	−21.5889	−0.858083
$634$	−39.4500	−1.56676
$635$	4.82639	0.191529
$636$	−3.56261	−0.141267
$637$	1.37102	0.0543219
$638$	−9.43435	−0.373510
$639$	10.2391	0.405052
$640$	4.34463	0.171737
$641$	−1.27589	−0.0503946	−0.0251973	−	0.999682i	$-0.508021\pi$
$641$	−1.27589	−0.0503946	−0.0251973	+	0.999682i	$0.508021\pi$
$642$	3.29652	0.130103
$643$	−17.5334	−0.691451	−0.345725	−	0.938336i	$-0.612367\pi$
$643$	−17.5334	−0.691451	−0.345725	+	0.938336i	$0.612367\pi$
$644$	6.05291	0.238518
$645$	−0.601377	−0.0236792
$646$	3.74664	0.147410
$647$	40.3844	1.58767	0.793837	−	0.608131i	$-0.208080\pi$
$647$	40.3844	1.58767	0.793837	+	0.608131i	$0.208080\pi$
$648$	3.01856	0.118580
$649$	−18.6585	−0.732410
$650$	−2.51350	−0.0985877
$651$	3.76025	0.147376
$652$	7.84661	0.307297
$653$	−2.29700	−0.0898887	−0.0449444	−	0.998989i	$-0.514311\pi$
$653$	−2.29700	−0.0898887	−0.0449444	+	0.998989i	$0.514311\pi$
$654$	6.49821	0.254100
$655$	0.407301	0.0159146
$656$	−32.7295	−1.27787
$657$	−0.696030	−0.0271547
$658$	19.6789	0.767163
$659$	−10.5022	−0.409108	−0.204554	−	0.978855i	$-0.565574\pi$
$659$	−10.5022	−0.409108	−0.204554	+	0.978855i	$0.565574\pi$
$660$	−0.321600	−0.0125183
$661$	−22.8718	−0.889611	−0.444805	−	0.895627i	$-0.646727\pi$
$661$	−22.8718	−0.889611	−0.444805	+	0.895627i	$0.646727\pi$
$662$	−9.47741	−0.368350
$663$	0.419632	0.0162972
$664$	−1.21625	−0.0471997
$665$	−3.27239	−0.126898
$666$	−11.1177	−0.430804
$667$	41.5479	1.60874
$668$	−1.17021	−0.0452767
$669$	−29.2522	−1.13095
$670$	−3.91710	−0.151331
$671$	−4.99840	−0.192961
$672$	−3.77636	−0.145676
$673$	21.1862	0.816667	0.408333	−	0.912833i	$-0.366110\pi$
$673$	21.1862	0.816667	0.408333	+	0.912833i	$0.366110\pi$
$674$	−30.2987	−1.16706
$675$	4.66275	0.179469
$676$	4.48579	0.172530
$677$	32.2338	1.23885	0.619423	−	0.785057i	$-0.287367\pi$
$677$	32.2338	1.23885	0.619423	+	0.785057i	$0.287367\pi$
$678$	1.15949	0.0445300
$679$	−35.9859	−1.38101
$680$	−1.75297	−0.0672232
$681$	18.6000	0.712753
$682$	−3.95815	−0.151565
$683$	−1.30901	−0.0500878	−0.0250439	−	0.999686i	$-0.507973\pi$
$683$	−1.30901	−0.0500878	−0.0250439	+	0.999686i	$0.507973\pi$
$684$	1.02022	0.0390089
$685$	10.4320	0.398588
$686$	−25.4822	−0.972917
$687$	17.4519	0.665832
$688$	3.29103	0.125470
$689$	4.27385	0.162821
$690$	−6.68147	−0.254359
$691$	−16.2990	−0.620044	−0.310022	−	0.950729i	$-0.600336\pi$
$691$	−16.2990	−0.620044	−0.310022	+	0.950729i	$0.600336\pi$
$692$	5.16208	0.196233
$693$	−3.05873	−0.116191
$694$	10.2675	0.389748
$695$	3.93412	0.149230
$696$	−14.0029	−0.530780
$697$	10.2986	0.390088
$698$	−2.92923	−0.110873
$699$	−16.3122	−0.616985
$700$	−3.15121	−0.119105
$701$	−27.0494	−1.02164	−0.510822	−	0.859687i	$-0.670659\pi$
$701$	−27.0494	−1.02164	−0.510822	+	0.859687i	$0.670659\pi$
$702$	−0.539060	−0.0203455
$703$	−25.2419	−0.952017
$704$	14.0378	0.529069
$705$	4.60458	0.173418
$706$	−20.0960	−0.756323
$707$	−33.9199	−1.27569
$708$	−4.12260	−0.154937
$709$	35.3361	1.32708	0.663538	−	0.748143i	$-0.269054\pi$
$709$	35.3361	1.32708	0.663538	+	0.748143i	$0.269054\pi$
$710$	7.63842	0.286665
$711$	−4.38503	−0.164451
$712$	9.29128	0.348205
$713$	17.4313	0.652806
$714$	−2.48191	−0.0928830
$715$	0.385804	0.0144282
$716$	5.84571	0.218464
$717$	10.4899	0.391752
$718$	−47.5646	−1.77509
$719$	−12.0611	−0.449802	−0.224901	−	0.974382i	$-0.572206\pi$
$719$	−12.0611	−0.449802	−0.224901	+	0.974382i	$0.572206\pi$
$720$	1.84559	0.0687809
$721$	8.49184	0.316253
$722$	13.4800	0.501675
$723$	−3.20071	−0.119036
$724$	0.136825	0.00508505
$725$	−21.6303	−0.803329
$726$	−10.9109	−0.404942
$727$	−30.9749	−1.14880	−0.574399	−	0.818576i	$-0.694764\pi$
$727$	−30.9749	−1.14880	−0.574399	+	0.818576i	$0.694764\pi$
$728$	2.44729	0.0907024
$729$	1.00000	0.0370370
$730$	−0.519243	−0.0192180
$731$	−1.03555	−0.0383013
$732$	−1.10440	−0.0408197
$733$	−11.5014	−0.424814	−0.212407	−	0.977181i	$-0.568130\pi$
$733$	−11.5014	−0.424814	−0.212407	+	0.977181i	$0.568130\pi$
$734$	−7.76373	−0.286565
$735$	−1.89737	−0.0699854
$736$	−17.5059	−0.645277
$737$	−8.31277	−0.306205
$738$	−13.2296	−0.486989
$739$	−44.0418	−1.62010	−0.810052	−	0.586358i	$-0.800561\pi$
$739$	−44.0418	−1.62010	−0.810052	+	0.586358i	$0.800561\pi$
$740$	1.75809	0.0646287
$741$	−1.22389	−0.0449607
$742$	−25.2776	−0.927970
$743$	42.9094	1.57419	0.787096	−	0.616830i	$-0.211583\pi$
$743$	42.9094	1.57419	0.787096	+	0.616830i	$0.211583\pi$
$744$	−5.87488	−0.215384
$745$	−7.16962	−0.262675
$746$	42.8661	1.56944
$747$	−0.402925	−0.0147423
$748$	−0.553786	−0.0202484
$749$	−4.95798	−0.181160
$750$	7.20848	0.263216
$751$	−2.33818	−0.0853215	−0.0426607	−	0.999090i	$-0.513583\pi$
$751$	−2.33818	−0.0853215	−0.0426607	+	0.999090i	$0.513583\pi$
$752$	−25.1985	−0.918896
$753$	9.17030	0.334184
$754$	2.50067	0.0910691
$755$	−11.5590	−0.420674
$756$	−0.675827	−0.0245796
$757$	31.0994	1.13033	0.565164	−	0.824979i	$-0.308813\pi$
$757$	31.0994	1.13033	0.565164	+	0.824979i	$0.308813\pi$
$758$	−5.76855	−0.209523
$759$	−14.1792	−0.514673
$760$	5.11267	0.185456
$761$	−3.11941	−0.113079	−0.0565393	−	0.998400i	$-0.518007\pi$
$761$	−3.11941	−0.113079	−0.0565393	+	0.998400i	$0.518007\pi$
$762$	−10.6762	−0.386758
$763$	−9.77332	−0.353818
$764$	8.30812	0.300577
$765$	−0.580730	−0.0209963
$766$	40.6512	1.46879
$767$	4.94563	0.178576
$768$	8.12339	0.293128
$769$	−3.95661	−0.142679	−0.0713396	−	0.997452i	$-0.522727\pi$
$769$	−3.95661	−0.142679	−0.0713396	+	0.997452i	$0.522727\pi$
$770$	−2.28183	−0.0822315
$771$	−17.5100	−0.630607
$772$	5.29892	0.190712
$773$	11.8318	0.425560	0.212780	−	0.977100i	$-0.431748\pi$
$773$	11.8318	0.425560	0.212780	+	0.977100i	$0.431748\pi$
$774$	1.33027	0.0478157
$775$	−9.07491	−0.325980
$776$	56.2231	2.01829
$777$	16.7211	0.599867
$778$	28.0338	1.00506
$779$	−30.0368	−1.07618
$780$	0.0852435	0.00305221
$781$	16.2101	0.580041
$782$	−11.5053	−0.411428
$783$	−4.63895	−0.165783
$784$	10.3833	0.370833
$785$	0.580730	0.0207271
$786$	−0.900969	−0.0321365
$787$	31.3642	1.11801	0.559007	−	0.829163i	$-0.311183\pi$
$787$	31.3642	1.11801	0.559007	+	0.829163i	$0.311183\pi$
$788$	3.73393	0.133016
$789$	−14.3398	−0.510509
$790$	−3.27126	−0.116386
$791$	−1.74388	−0.0620051
$792$	4.77884	0.169809
$793$	1.32488	0.0470478
$794$	−3.85566	−0.136832
$795$	−5.91459	−0.209769
$796$	−3.34554	−0.118579
$797$	24.4835	0.867250	0.433625	−	0.901093i	$-0.357234\pi$
$797$	24.4835	0.867250	0.433625	+	0.901093i	$0.357234\pi$
$798$	7.23868	0.256246
$799$	7.92894	0.280506
$800$	9.11378	0.322221
$801$	3.07805	0.108758
$802$	−11.5218	−0.406848
$803$	−1.10192	−0.0388860
$804$	−1.83671	−0.0647757
$805$	10.0489	0.354179
$806$	1.04915	0.0369547
$807$	−5.81592	−0.204730
$808$	52.9953	1.86437
$809$	−18.3096	−0.643731	−0.321866	−	0.946785i	$-0.604310\pi$
$809$	−18.3096	−0.643731	−0.321866	+	0.946785i	$0.604310\pi$
$810$	0.746007	0.0262120
$811$	−38.1005	−1.33789	−0.668945	−	0.743312i	$-0.733254\pi$
$811$	−38.1005	−1.33789	−0.668945	+	0.743312i	$0.733254\pi$
$812$	3.13513	0.110021
$813$	−4.72990	−0.165885
$814$	−17.6011	−0.616919
$815$	13.0268	0.456309
$816$	3.17804	0.111254
$817$	3.02027	0.105666
$818$	7.55801	0.264260
$819$	0.810747	0.0283298
$820$	2.09205	0.0730575
$821$	16.7676	0.585195	0.292597	−	0.956236i	$-0.405480\pi$
$821$	16.7676	0.585195	0.292597	+	0.956236i	$0.405480\pi$
$822$	−23.0762	−0.804873
$823$	−2.29394	−0.0799617	−0.0399809	−	0.999200i	$-0.512730\pi$
$823$	−2.29394	−0.0799617	−0.0399809	+	0.999200i	$0.512730\pi$
$824$	−13.2673	−0.462190
$825$	7.38186	0.257004
$826$	−29.2508	−1.01777
$827$	20.3470	0.707534	0.353767	−	0.935334i	$-0.384901\pi$
$827$	20.3470	0.707534	0.353767	+	0.935334i	$0.384901\pi$
$828$	−3.13291	−0.108876
$829$	11.8751	0.412439	0.206220	−	0.978506i	$-0.433884\pi$
$829$	11.8751	0.412439	0.206220	+	0.978506i	$0.433884\pi$
$830$	−0.300585	−0.0104335
$831$	9.62977	0.334053
$832$	−3.72086	−0.128998
$833$	−3.26721	−0.113202
$834$	−8.70245	−0.301341
$835$	−1.94276	−0.0672320
$836$	1.61516	0.0558615
$837$	−1.94626	−0.0672724
$838$	−20.0017	−0.690949
$839$	−35.7098	−1.23284	−0.616420	−	0.787418i	$-0.711417\pi$
$839$	−35.7098	−1.23284	−0.616420	+	0.787418i	$0.711417\pi$
$840$	−3.38681	−0.116856
$841$	−7.48012	−0.257935
$842$	−9.74744	−0.335919
$843$	23.3377	0.803793
$844$	−7.55178	−0.259943
$845$	7.44723	0.256193
$846$	−10.1855	−0.350186
$847$	16.4100	0.563856
$848$	32.3676	1.11151
$849$	−10.3845	−0.356393
$850$	5.98978	0.205448
$851$	77.5135	2.65713
$852$	3.58162	0.122704
$853$	1.39229	0.0476712	0.0238356	−	0.999716i	$-0.492412\pi$
$853$	1.39229	0.0476712	0.0238356	+	0.999716i	$0.492412\pi$
$854$	−7.83597	−0.268141
$855$	1.69375	0.0579249
$856$	7.74616	0.264758
$857$	−36.6477	−1.25186	−0.625932	−	0.779878i	$-0.715281\pi$
$857$	−36.6477	−1.25186	−0.625932	+	0.779878i	$0.715281\pi$
$858$	−0.853416	−0.0291351
$859$	−2.53062	−0.0863436	−0.0431718	−	0.999068i	$-0.513746\pi$
$859$	−2.53062	−0.0863436	−0.0431718	+	0.999068i	$0.513746\pi$
$860$	−0.210361	−0.00717325
$861$	19.8974	0.678101
$862$	−22.4607	−0.765016
$863$	1.06128	0.0361264	0.0180632	−	0.999837i	$-0.494250\pi$
$863$	1.06128	0.0361264	0.0180632	+	0.999837i	$0.494250\pi$
$864$	1.95459	0.0664965
$865$	8.56999	0.291389
$866$	−9.75231	−0.331397
$867$	−1.00000	−0.0339618
$868$	1.31533	0.0446453
$869$	−6.94218	−0.235497
$870$	−3.46069	−0.117328
$871$	2.20338	0.0746588
$872$	15.2695	0.517090
$873$	18.6258	0.630388
$874$	33.5561	1.13505
$875$	−10.8416	−0.366512
$876$	−0.243470	−0.00822610
$877$	25.1578	0.849517	0.424759	−	0.905307i	$-0.360359\pi$
$877$	25.1578	0.849517	0.424759	+	0.905307i	$0.360359\pi$
$878$	−10.3918	−0.350707
$879$	−6.43263	−0.216967
$880$	2.92185	0.0984955
$881$	−15.5299	−0.523216	−0.261608	−	0.965174i	$-0.584253\pi$
$881$	−15.5299	−0.523216	−0.261608	+	0.965174i	$0.584253\pi$
$882$	4.19706	0.141322
$883$	−22.0705	−0.742730	−0.371365	−	0.928487i	$-0.621110\pi$
$883$	−22.0705	−0.742730	−0.371365	+	0.928487i	$0.621110\pi$
$884$	0.146787	0.00493697
$885$	−6.84427	−0.230068
$886$	20.4933	0.688485
$887$	−35.8404	−1.20340	−0.601701	−	0.798721i	$-0.705510\pi$
$887$	−35.8404	−1.20340	−0.601701	+	0.798721i	$0.705510\pi$
$888$	−26.1245	−0.876680
$889$	16.0570	0.538535
$890$	2.29625	0.0769705
$891$	1.58316	0.0530377
$892$	−10.2324	−0.342605
$893$	−23.1254	−0.773862
$894$	15.8595	0.530422
$895$	9.70494	0.324400
$896$	14.4542	0.482883
$897$	3.75835	0.125488
$898$	−48.8758	−1.63101
$899$	9.02859	0.301120
$900$	1.63103	0.0543675
$901$	−10.1848	−0.339303
$902$	−20.9446	−0.697378
$903$	−2.00074	−0.0665803
$904$	2.72457	0.0906179
$905$	0.227154	0.00755085
$906$	25.5690	0.849472
$907$	48.3005	1.60379	0.801896	−	0.597464i	$-0.203825\pi$
$907$	48.3005	1.60379	0.801896	+	0.597464i	$0.203825\pi$
$908$	6.50625	0.215917
$909$	17.5565	0.582313
$910$	0.604823	0.0200497
$911$	16.5488	0.548287	0.274144	−	0.961689i	$-0.411606\pi$
$911$	16.5488	0.548287	0.274144	+	0.961689i	$0.411606\pi$
$912$	−9.26902	−0.306928
$913$	−0.637893	−0.0211112
$914$	−29.9826	−0.991736
$915$	−1.83350	−0.0606137
$916$	6.10466	0.201704
$917$	1.35506	0.0447480
$918$	1.28460	0.0423982
$919$	−18.0335	−0.594870	−0.297435	−	0.954742i	$-0.596131\pi$
$919$	−18.0335	−0.594870	−0.297435	+	0.954742i	$0.596131\pi$
$920$	−15.7001	−0.517617
$921$	−18.5904	−0.612574
$922$	24.5697	0.809159
$923$	−4.29664	−0.141426
$924$	−1.06994	−0.0351984
$925$	−40.3544	−1.32684
$926$	25.3389	0.832688
$927$	−4.39526	−0.144359
$928$	−9.06726	−0.297647
$929$	−51.8467	−1.70104	−0.850518	−	0.525946i	$-0.823711\pi$
$929$	−51.8467	−1.70104	−0.850518	+	0.525946i	$0.823711\pi$
$930$	−1.45192	−0.0476103
$931$	9.52907	0.312303
$932$	−5.70600	−0.186906
$933$	10.0164	0.327923
$934$	−28.8135	−0.942807
$935$	−0.919386	−0.0300672
$936$	−1.26668	−0.0414028
$937$	−11.6436	−0.380381	−0.190190	−	0.981747i	$-0.560911\pi$
$937$	−11.6436	−0.380381	−0.190190	+	0.981747i	$0.560911\pi$
$938$	−13.0319	−0.425506
$939$	30.8487	1.00671
$940$	1.61068	0.0525344
$941$	−12.3134	−0.401406	−0.200703	−	0.979652i	$-0.564323\pi$
$941$	−12.3134	−0.401406	−0.200703	+	0.979652i	$0.564323\pi$
$942$	−1.28460	−0.0418546
$943$	92.2376	3.00367
$944$	37.4552	1.21906
$945$	−1.12200	−0.0364985
$946$	2.10603	0.0684730
$947$	20.8079	0.676166	0.338083	−	0.941116i	$-0.390222\pi$
$947$	20.8079	0.676166	0.338083	+	0.941116i	$0.390222\pi$
$948$	−1.53388	−0.0498180
$949$	0.292076	0.00948120
$950$	−17.4697	−0.566791
$951$	−30.7099	−0.995838
$952$	−5.83198	−0.189016
$953$	−12.1442	−0.393389	−0.196694	−	0.980465i	$-0.563021\pi$
$953$	−12.1442	−0.393389	−0.196694	+	0.980465i	$0.563021\pi$
$954$	13.0833	0.423589
$955$	13.7930	0.446331
$956$	3.66935	0.118675
$957$	−7.34419	−0.237404
$958$	−1.11990	−0.0361822
$959$	34.7066	1.12073
$960$	5.14931	0.166193
$961$	−27.2121	−0.877809
$962$	4.66536	0.150417
$963$	2.56618	0.0826940
$964$	−1.11960	−0.0360600
$965$	8.79718	0.283191
$966$	−22.2287	−0.715197
$967$	44.4464	1.42930	0.714649	−	0.699483i	$-0.246586\pi$
$967$	44.4464	1.42930	0.714649	+	0.699483i	$0.246586\pi$
$968$	−25.6385	−0.824051
$969$	2.91658	0.0936940
$970$	13.8950	0.446141
$971$	−26.0163	−0.834904	−0.417452	−	0.908699i	$-0.637077\pi$
$971$	−26.0163	−0.834904	−0.417452	+	0.908699i	$0.637077\pi$
$972$	0.349799	0.0112198
$973$	13.0885	0.419598
$974$	−18.2606	−0.585109
$975$	−1.95664	−0.0626626
$976$	10.0338	0.321175
$977$	−1.97570	−0.0632084	−0.0316042	−	0.999500i	$-0.510062\pi$
$977$	−1.97570	−0.0632084	−0.0316042	+	0.999500i	$0.510062\pi$
$978$	−28.8159	−0.921431
$979$	4.87304	0.155743
$980$	−0.663696	−0.0212010
$981$	5.05854	0.161507
$982$	−1.81687	−0.0579785
$983$	−12.8906	−0.411148	−0.205574	−	0.978642i	$-0.565906\pi$
$983$	−12.8906	−0.411148	−0.205574	+	0.978642i	$0.565906\pi$
$984$	−31.0870	−0.991016
$985$	6.19902	0.197517
$986$	−5.95921	−0.189780
$987$	15.3191	0.487611
$988$	−0.428115	−0.0136202
$989$	−9.27474	−0.294919
$990$	1.18105	0.0375361
$991$	12.7498	0.405011	0.202506	−	0.979281i	$-0.435092\pi$
$991$	12.7498	0.405011	0.202506	+	0.979281i	$0.435092\pi$
$992$	−3.80413	−0.120781
$993$	−7.37770	−0.234124
$994$	25.4124	0.806033
$995$	−5.55421	−0.176080
$996$	−0.140943	−0.00446594
$997$	33.3101	1.05494	0.527470	−	0.849573i	$-0.323141\pi$
$997$	33.3101	1.05494	0.527470	+	0.849573i	$0.323141\pi$
$998$	14.5350	0.460097
$999$	−8.65463	−0.273820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.20	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.20	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.28460 q^{2} -1.00000 q^{3} -0.349799 q^{4} -0.580730 q^{5} +1.28460 q^{6} -1.93204 q^{7} +3.01856 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.28460 q^{2} -1.00000 q^{3} -0.349799 q^{4} -0.580730 q^{5} +1.28460 q^{6} -1.93204 q^{7} +3.01856 q^{8} +1.00000 q^{9} +0.746007 q^{10} +1.58316 q^{11} +0.349799 q^{12} -0.419632 q^{13} +2.48191 q^{14} +0.580730 q^{15} -3.17804 q^{16} +1.00000 q^{17} -1.28460 q^{18} -2.91658 q^{19} +0.203139 q^{20} +1.93204 q^{21} -2.03372 q^{22} +8.95631 q^{23} -3.01856 q^{24} -4.66275 q^{25} +0.539060 q^{26} -1.00000 q^{27} +0.675827 q^{28} +4.63895 q^{29} -0.746007 q^{30} +1.94626 q^{31} -1.95459 q^{32} -1.58316 q^{33} -1.28460 q^{34} +1.12200 q^{35} -0.349799 q^{36} +8.65463 q^{37} +3.74664 q^{38} +0.419632 q^{39} -1.75297 q^{40} +10.2986 q^{41} -2.48191 q^{42} -1.03555 q^{43} -0.553786 q^{44} -0.580730 q^{45} -11.5053 q^{46} +7.92894 q^{47} +3.17804 q^{48} -3.26721 q^{49} +5.98978 q^{50} -1.00000 q^{51} +0.146787 q^{52} -10.1848 q^{53} +1.28460 q^{54} -0.919386 q^{55} -5.83198 q^{56} +2.91658 q^{57} -5.95921 q^{58} -11.7856 q^{59} -0.203139 q^{60} -3.15724 q^{61} -2.50016 q^{62} -1.93204 q^{63} +8.86696 q^{64} +0.243693 q^{65} +2.03372 q^{66} -5.25076 q^{67} -0.349799 q^{68} -8.95631 q^{69} -1.44132 q^{70} +10.2391 q^{71} +3.01856 q^{72} -0.696030 q^{73} -11.1177 q^{74} +4.66275 q^{75} +1.02022 q^{76} -3.05873 q^{77} -0.539060 q^{78} -4.38503 q^{79} +1.84559 q^{80} +1.00000 q^{81} -13.2296 q^{82} -0.402925 q^{83} -0.675827 q^{84} -0.580730 q^{85} +1.33027 q^{86} -4.63895 q^{87} +4.77884 q^{88} +3.07805 q^{89} +0.746007 q^{90} +0.810747 q^{91} -3.13291 q^{92} -1.94626 q^{93} -10.1855 q^{94} +1.69375 q^{95} +1.95459 q^{96} +18.6258 q^{97} +4.19706 q^{98} +1.58316 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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