LMFDB - Embedded newform 8007.2.a.i.1.19

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:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-1.05868 q^{2} +1.00000 q^{3} -0.879191 q^{4} -2.81588 q^{5} -1.05868 q^{6} +4.49493 q^{7} +3.04815 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.05868 q^{2} +1.00000 q^{3} -0.879191 q^{4} -2.81588 q^{5} -1.05868 q^{6} +4.49493 q^{7} +3.04815 q^{8} +1.00000 q^{9} +2.98112 q^{10} +0.781229 q^{11} -0.879191 q^{12} -4.55121 q^{13} -4.75870 q^{14} -2.81588 q^{15} -1.46864 q^{16} +1.00000 q^{17} -1.05868 q^{18} +5.30263 q^{19} +2.47570 q^{20} +4.49493 q^{21} -0.827074 q^{22} +8.31304 q^{23} +3.04815 q^{24} +2.92918 q^{25} +4.81829 q^{26} +1.00000 q^{27} -3.95190 q^{28} -4.37379 q^{29} +2.98112 q^{30} -5.95190 q^{31} -4.54147 q^{32} +0.781229 q^{33} -1.05868 q^{34} -12.6572 q^{35} -0.879191 q^{36} -3.72595 q^{37} -5.61380 q^{38} -4.55121 q^{39} -8.58322 q^{40} +11.9167 q^{41} -4.75870 q^{42} +3.46017 q^{43} -0.686849 q^{44} -2.81588 q^{45} -8.80088 q^{46} +1.03581 q^{47} -1.46864 q^{48} +13.2044 q^{49} -3.10107 q^{50} +1.00000 q^{51} +4.00138 q^{52} +4.45568 q^{53} -1.05868 q^{54} -2.19985 q^{55} +13.7012 q^{56} +5.30263 q^{57} +4.63046 q^{58} -4.12416 q^{59} +2.47570 q^{60} +4.35710 q^{61} +6.30118 q^{62} +4.49493 q^{63} +7.74526 q^{64} +12.8157 q^{65} -0.827074 q^{66} -5.60512 q^{67} -0.879191 q^{68} +8.31304 q^{69} +13.3999 q^{70} +9.07228 q^{71} +3.04815 q^{72} +6.35011 q^{73} +3.94460 q^{74} +2.92918 q^{75} -4.66202 q^{76} +3.51157 q^{77} +4.81829 q^{78} +3.54753 q^{79} +4.13552 q^{80} +1.00000 q^{81} -12.6160 q^{82} -8.01576 q^{83} -3.95190 q^{84} -2.81588 q^{85} -3.66322 q^{86} -4.37379 q^{87} +2.38130 q^{88} +12.1645 q^{89} +2.98112 q^{90} -20.4574 q^{91} -7.30875 q^{92} -5.95190 q^{93} -1.09659 q^{94} -14.9316 q^{95} -4.54147 q^{96} +17.6957 q^{97} -13.9792 q^{98} +0.781229 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * 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 $

$2$	−1.05868	−0.748602	−0.374301	−	0.927307i	$-0.622117\pi$
$2$	−1.05868	−0.748602	−0.374301	+	0.927307i	$0.622117\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.879191	−0.439595
$5$	−2.81588	−1.25930	−0.629650	−	0.776879i	$-0.716802\pi$
$5$	−2.81588	−1.25930	−0.629650	+	0.776879i	$0.716802\pi$
$6$	−1.05868	−0.432205
$7$	4.49493	1.69892	0.849461	−	0.527651i	$-0.176927\pi$
$7$	4.49493	1.69892	0.849461	+	0.527651i	$0.176927\pi$
$8$	3.04815	1.07768
$9$	1.00000	0.333333
$10$	2.98112	0.942714
$11$	0.781229	0.235549	0.117775	−	0.993040i	$-0.462424\pi$
$11$	0.781229	0.235549	0.117775	+	0.993040i	$0.462424\pi$
$12$	−0.879191	−0.253801
$13$	−4.55121	−1.26228	−0.631139	−	0.775669i	$-0.717412\pi$
$13$	−4.55121	−1.26228	−0.631139	+	0.775669i	$0.717412\pi$
$14$	−4.75870	−1.27182
$15$	−2.81588	−0.727057
$16$	−1.46864	−0.367160
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.05868	−0.249534
$19$	5.30263	1.21651	0.608253	−	0.793743i	$-0.291870\pi$
$19$	5.30263	1.21651	0.608253	+	0.793743i	$0.291870\pi$
$20$	2.47570	0.553582
$21$	4.49493	0.980873
$22$	−0.827074	−0.176333
$23$	8.31304	1.73339	0.866695	−	0.498839i	$-0.166240\pi$
$23$	8.31304	1.73339	0.866695	+	0.498839i	$0.166240\pi$
$24$	3.04815	0.622201
$25$	2.92918	0.585835
$26$	4.81829	0.944944
$27$	1.00000	0.192450
$28$	−3.95190	−0.746838
$29$	−4.37379	−0.812193	−0.406097	−	0.913830i	$-0.633110\pi$
$29$	−4.37379	−0.812193	−0.406097	+	0.913830i	$0.633110\pi$
$30$	2.98112	0.544276
$31$	−5.95190	−1.06899	−0.534496	−	0.845171i	$-0.679499\pi$
$31$	−5.95190	−1.06899	−0.534496	+	0.845171i	$0.679499\pi$
$32$	−4.54147	−0.802827
$33$	0.781229	0.135995
$34$	−1.05868	−0.181563
$35$	−12.6572	−2.13945
$36$	−0.879191	−0.146532
$37$	−3.72595	−0.612542	−0.306271	−	0.951944i	$-0.599081\pi$
$37$	−3.72595	−0.612542	−0.306271	+	0.951944i	$0.599081\pi$
$38$	−5.61380	−0.910679
$39$	−4.55121	−0.728777
$40$	−8.58322	−1.35713
$41$	11.9167	1.86107	0.930537	−	0.366197i	$-0.119340\pi$
$41$	11.9167	1.86107	0.930537	+	0.366197i	$0.119340\pi$
$42$	−4.75870	−0.734283
$43$	3.46017	0.527670	0.263835	−	0.964568i	$-0.415012\pi$
$43$	3.46017	0.527670	0.263835	+	0.964568i	$0.415012\pi$
$44$	−0.686849	−0.103546
$45$	−2.81588	−0.419767
$46$	−8.80088	−1.29762
$47$	1.03581	0.151089	0.0755443	−	0.997142i	$-0.475931\pi$
$47$	1.03581	0.151089	0.0755443	+	0.997142i	$0.475931\pi$
$48$	−1.46864	−0.211980
$49$	13.2044	1.88634
$50$	−3.10107	−0.438557
$51$	1.00000	0.140028
$52$	4.00138	0.554892
$53$	4.45568	0.612034	0.306017	−	0.952026i	$-0.401003\pi$
$53$	4.45568	0.612034	0.306017	+	0.952026i	$0.401003\pi$
$54$	−1.05868	−0.144068
$55$	−2.19985	−0.296627
$56$	13.7012	1.83090
$57$	5.30263	0.702351
$58$	4.63046	0.608009
$59$	−4.12416	−0.536920	−0.268460	−	0.963291i	$-0.586515\pi$
$59$	−4.12416	−0.536920	−0.268460	+	0.963291i	$0.586515\pi$
$60$	2.47570	0.319611
$61$	4.35710	0.557870	0.278935	−	0.960310i	$-0.410019\pi$
$61$	4.35710	0.557870	0.278935	+	0.960310i	$0.410019\pi$
$62$	6.30118	0.800250
$63$	4.49493	0.566307
$64$	7.74526	0.968158
$65$	12.8157	1.58959
$66$	−0.827074	−0.101806
$67$	−5.60512	−0.684774	−0.342387	−	0.939559i	$-0.611235\pi$
$67$	−5.60512	−0.684774	−0.342387	+	0.939559i	$0.611235\pi$
$68$	−0.879191	−0.106618
$69$	8.31304	1.00077
$70$	13.3999	1.60160
$71$	9.07228	1.07668	0.538341	−	0.842727i	$-0.319051\pi$
$71$	9.07228	1.07668	0.538341	+	0.842727i	$0.319051\pi$
$72$	3.04815	0.359228
$73$	6.35011	0.743224	0.371612	−	0.928388i	$-0.378805\pi$
$73$	6.35011	0.743224	0.371612	+	0.928388i	$0.378805\pi$
$74$	3.94460	0.458550
$75$	2.92918	0.338232
$76$	−4.66202	−0.534771
$77$	3.51157	0.400180
$78$	4.81829	0.545564
$79$	3.54753	0.399129	0.199564	−	0.979885i	$-0.436047\pi$
$79$	3.54753	0.399129	0.199564	+	0.979885i	$0.436047\pi$
$80$	4.13552	0.462365
$81$	1.00000	0.111111
$82$	−12.6160	−1.39320
$83$	−8.01576	−0.879844	−0.439922	−	0.898036i	$-0.644994\pi$
$83$	−8.01576	−0.879844	−0.439922	+	0.898036i	$0.644994\pi$
$84$	−3.95190	−0.431187
$85$	−2.81588	−0.305425
$86$	−3.66322	−0.395015
$87$	−4.37379	−0.468920
$88$	2.38130	0.253848
$89$	12.1645	1.28944	0.644719	−	0.764419i	$-0.276974\pi$
$89$	12.1645	1.28944	0.644719	+	0.764419i	$0.276974\pi$
$90$	2.98112	0.314238
$91$	−20.4574	−2.14451
$92$	−7.30875	−0.761990
$93$	−5.95190	−0.617183
$94$	−1.09659	−0.113105
$95$	−14.9316	−1.53195
$96$	−4.54147	−0.463512
$97$	17.6957	1.79673	0.898363	−	0.439253i	$-0.144757\pi$
$97$	17.6957	1.79673	0.898363	+	0.439253i	$0.144757\pi$
$98$	−13.9792	−1.41211
$99$	0.781229	0.0785165
$100$	−2.57531	−0.257531
$101$	−13.8362	−1.37675	−0.688374	−	0.725356i	$-0.741675\pi$
$101$	−13.8362	−1.37675	−0.688374	+	0.725356i	$0.741675\pi$
$102$	−1.05868	−0.104825
$103$	−18.4145	−1.81443	−0.907216	−	0.420665i	$-0.861797\pi$
$103$	−18.4145	−1.81443	−0.907216	+	0.420665i	$0.861797\pi$
$104$	−13.8728	−1.36034
$105$	−12.6572	−1.23521
$106$	−4.71715	−0.458170
$107$	6.30435	0.609465	0.304732	−	0.952438i	$-0.401433\pi$
$107$	6.30435	0.609465	0.304732	+	0.952438i	$0.401433\pi$
$108$	−0.879191	−0.0846002
$109$	−18.0938	−1.73308	−0.866538	−	0.499111i	$-0.833660\pi$
$109$	−18.0938	−1.73308	−0.866538	+	0.499111i	$0.833660\pi$
$110$	2.32894	0.222056
$111$	−3.72595	−0.353651
$112$	−6.60144	−0.623777
$113$	3.70976	0.348985	0.174492	−	0.984659i	$-0.444172\pi$
$113$	3.70976	0.348985	0.174492	+	0.984659i	$0.444172\pi$
$114$	−5.61380	−0.525781
$115$	−23.4085	−2.18286
$116$	3.84540	0.357036
$117$	−4.55121	−0.420760
$118$	4.36618	0.401940
$119$	4.49493	0.412049
$120$	−8.58322	−0.783537
$121$	−10.3897	−0.944516
$122$	−4.61279	−0.417622
$123$	11.9167	1.07449
$124$	5.23286	0.469924
$125$	5.83119	0.521557
$126$	−4.75870	−0.423939
$127$	−0.0877691	−0.00778824	−0.00389412	−	0.999992i	$-0.501240\pi$
$127$	−0.0877691	−0.00778824	−0.00389412	+	0.999992i	$0.501240\pi$
$128$	0.883170	0.0780619
$129$	3.46017	0.304651
$130$	−13.5677	−1.18997
$131$	0.495117	0.0432585	0.0216293	−	0.999766i	$-0.493115\pi$
$131$	0.495117	0.0432585	0.0216293	+	0.999766i	$0.493115\pi$
$132$	−0.686849	−0.0597826
$133$	23.8349	2.06675
$134$	5.93404	0.512623
$135$	−2.81588	−0.242352
$136$	3.04815	0.261377
$137$	0.0598484	0.00511320	0.00255660	−	0.999997i	$-0.499186\pi$
$137$	0.0598484	0.00511320	0.00255660	+	0.999997i	$0.499186\pi$
$138$	−8.80088	−0.749180
$139$	−6.13138	−0.520057	−0.260028	−	0.965601i	$-0.583732\pi$
$139$	−6.13138	−0.520057	−0.260028	+	0.965601i	$0.583732\pi$
$140$	11.1281	0.940493
$141$	1.03581	0.0872310
$142$	−9.60466	−0.806005
$143$	−3.55554	−0.297329
$144$	−1.46864	−0.122387
$145$	12.3161	1.02279
$146$	−6.72275	−0.556379
$147$	13.2044	1.08908
$148$	3.27582	0.269271
$149$	−17.7352	−1.45293	−0.726463	−	0.687206i	$-0.758837\pi$
$149$	−17.7352	−1.45293	−0.726463	+	0.687206i	$0.758837\pi$
$150$	−3.10107	−0.253201
$151$	−13.1465	−1.06985	−0.534925	−	0.844900i	$-0.679660\pi$
$151$	−13.1465	−1.06985	−0.534925	+	0.844900i	$0.679660\pi$
$152$	16.1632	1.31101
$153$	1.00000	0.0808452
$154$	−3.71763	−0.299576
$155$	16.7598	1.34618
$156$	4.00138	0.320367
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−3.75571	−0.298789
$159$	4.45568	0.353358
$160$	12.7882	1.01100
$161$	37.3665	2.94489
$162$	−1.05868	−0.0831780
$163$	−0.951821	−0.0745524	−0.0372762	−	0.999305i	$-0.511868\pi$
$163$	−0.951821	−0.0745524	−0.0372762	+	0.999305i	$0.511868\pi$
$164$	−10.4770	−0.818120
$165$	−2.19985	−0.171258
$166$	8.48615	0.658653
$167$	11.6990	0.905292	0.452646	−	0.891690i	$-0.350480\pi$
$167$	11.6990	0.905292	0.452646	+	0.891690i	$0.350480\pi$
$168$	13.7012	1.05707
$169$	7.71352	0.593348
$170$	2.98112	0.228642
$171$	5.30263	0.405502
$172$	−3.04215	−0.231962
$173$	−11.4757	−0.872479	−0.436239	−	0.899831i	$-0.643690\pi$
$173$	−11.4757	−0.872479	−0.436239	+	0.899831i	$0.643690\pi$
$174$	4.63046	0.351034
$175$	13.1664	0.995289
$176$	−1.14735	−0.0864844
$177$	−4.12416	−0.309991
$178$	−12.8784	−0.965276
$179$	7.51938	0.562025	0.281012	−	0.959704i	$-0.409330\pi$
$179$	7.51938	0.562025	0.281012	+	0.959704i	$0.409330\pi$
$180$	2.47570	0.184527
$181$	−15.1410	−1.12542	−0.562709	−	0.826655i	$-0.690241\pi$
$181$	−15.1410	−1.12542	−0.562709	+	0.826655i	$0.690241\pi$
$182$	21.6578	1.60539
$183$	4.35710	0.322086
$184$	25.3394	1.86805
$185$	10.4918	0.771374
$186$	6.30118	0.462025
$187$	0.781229	0.0571291
$188$	−0.910675	−0.0664178
$189$	4.49493	0.326958
$190$	15.8078	1.14682
$191$	19.7762	1.43096	0.715478	−	0.698635i	$-0.246209\pi$
$191$	19.7762	1.43096	0.715478	+	0.698635i	$0.246209\pi$
$192$	7.74526	0.558966
$193$	−9.14336	−0.658154	−0.329077	−	0.944303i	$-0.606738\pi$
$193$	−9.14336	−0.658154	−0.329077	+	0.944303i	$0.606738\pi$
$194$	−18.7341	−1.34503
$195$	12.8157	0.917749
$196$	−11.6091	−0.829225
$197$	15.3963	1.09694	0.548469	−	0.836171i	$-0.315211\pi$
$197$	15.3963	1.09694	0.548469	+	0.836171i	$0.315211\pi$
$198$	−0.827074	−0.0587776
$199$	24.4126	1.73057	0.865283	−	0.501284i	$-0.167139\pi$
$199$	24.4126	1.73057	0.865283	+	0.501284i	$0.167139\pi$
$200$	8.92857	0.631345
$201$	−5.60512	−0.395355
$202$	14.6481	1.03064
$203$	−19.6599	−1.37985
$204$	−0.879191	−0.0615557
$205$	−33.5560	−2.34365
$206$	19.4951	1.35829
$207$	8.31304	0.577797
$208$	6.68410	0.463459
$209$	4.14257	0.286547
$210$	13.3999	0.924683
$211$	9.63903	0.663578	0.331789	−	0.943354i	$-0.392348\pi$
$211$	9.63903	0.663578	0.331789	+	0.943354i	$0.392348\pi$
$212$	−3.91739	−0.269047
$213$	9.07228	0.621622
$214$	−6.67431	−0.456246
$215$	−9.74341	−0.664495
$216$	3.04815	0.207400
$217$	−26.7534	−1.81614
$218$	19.1556	1.29738
$219$	6.35011	0.429101
$220$	1.93409	0.130396
$221$	−4.55121	−0.306148
$222$	3.94460	0.264744
$223$	−20.4049	−1.36641	−0.683205	−	0.730227i	$-0.739415\pi$
$223$	−20.4049	−1.36641	−0.683205	+	0.730227i	$0.739415\pi$
$224$	−20.4136	−1.36394
$225$	2.92918	0.195278
$226$	−3.92746	−0.261251
$227$	0.494853	0.0328445	0.0164223	−	0.999865i	$-0.494772\pi$
$227$	0.494853	0.0328445	0.0164223	+	0.999865i	$0.494772\pi$
$228$	−4.66202	−0.308750
$229$	10.4968	0.693649	0.346825	−	0.937930i	$-0.387260\pi$
$229$	10.4968	0.693649	0.346825	+	0.937930i	$0.387260\pi$
$230$	24.7822	1.63409
$231$	3.51157	0.231044
$232$	−13.3320	−0.875287
$233$	4.04033	0.264691	0.132345	−	0.991204i	$-0.457749\pi$
$233$	4.04033	0.264691	0.132345	+	0.991204i	$0.457749\pi$
$234$	4.81829	0.314981
$235$	−2.91672	−0.190266
$236$	3.62593	0.236028
$237$	3.54753	0.230437
$238$	−4.75870	−0.308461
$239$	−7.92988	−0.512941	−0.256471	−	0.966552i	$-0.582560\pi$
$239$	−7.92988	−0.512941	−0.256471	+	0.966552i	$0.582560\pi$
$240$	4.13552	0.266947
$241$	−9.27038	−0.597158	−0.298579	−	0.954385i	$-0.596513\pi$
$241$	−9.27038	−0.597158	−0.298579	+	0.954385i	$0.596513\pi$
$242$	10.9994	0.707067
$243$	1.00000	0.0641500
$244$	−3.83072	−0.245237
$245$	−37.1819	−2.37546
$246$	−12.6160	−0.804367
$247$	−24.1334	−1.53557
$248$	−18.1423	−1.15204
$249$	−8.01576	−0.507978
$250$	−6.17338	−0.390439
$251$	−1.01763	−0.0642325	−0.0321162	−	0.999484i	$-0.510225\pi$
$251$	−1.01763	−0.0642325	−0.0321162	+	0.999484i	$0.510225\pi$
$252$	−3.95190	−0.248946
$253$	6.49439	0.408299
$254$	0.0929196	0.00583029
$255$	−2.81588	−0.176337
$256$	−16.4255	−1.02660
$257$	−12.1258	−0.756389	−0.378195	−	0.925726i	$-0.623455\pi$
$257$	−12.1258	−0.756389	−0.378195	+	0.925726i	$0.623455\pi$
$258$	−3.66322	−0.228062
$259$	−16.7479	−1.04066
$260$	−11.2674	−0.698775
$261$	−4.37379	−0.270731
$262$	−0.524171	−0.0323834
$263$	23.8976	1.47359	0.736794	−	0.676117i	$-0.236339\pi$
$263$	23.8976	1.47359	0.736794	+	0.676117i	$0.236339\pi$
$264$	2.38130	0.146559
$265$	−12.5467	−0.770735
$266$	−25.2336	−1.54717
$267$	12.1645	0.744458
$268$	4.92797	0.301024
$269$	7.27034	0.443280	0.221640	−	0.975129i	$-0.428859\pi$
$269$	7.27034	0.443280	0.221640	+	0.975129i	$0.428859\pi$
$270$	2.98112	0.181425
$271$	10.7344	0.652065	0.326033	−	0.945358i	$-0.394288\pi$
$271$	10.7344	0.652065	0.326033	+	0.945358i	$0.394288\pi$
$272$	−1.46864	−0.0890495
$273$	−20.4574	−1.23814
$274$	−0.0633605	−0.00382775
$275$	2.28836	0.137993
$276$	−7.30875	−0.439935
$277$	0.909966	0.0546746	0.0273373	−	0.999626i	$-0.491297\pi$
$277$	0.909966	0.0546746	0.0273373	+	0.999626i	$0.491297\pi$
$278$	6.49118	0.389315
$279$	−5.95190	−0.356331
$280$	−38.5809	−2.30565
$281$	30.0391	1.79198	0.895990	−	0.444073i	$-0.146467\pi$
$281$	30.0391	1.79198	0.895990	+	0.444073i	$0.146467\pi$
$282$	−1.09659	−0.0653013
$283$	17.3808	1.03318	0.516590	−	0.856233i	$-0.327201\pi$
$283$	17.3808	1.03318	0.516590	+	0.856233i	$0.327201\pi$
$284$	−7.97626	−0.473304
$285$	−14.9316	−0.884470
$286$	3.76419	0.222581
$287$	53.5647	3.16182
$288$	−4.54147	−0.267609
$289$	1.00000	0.0588235
$290$	−13.0388	−0.765666
$291$	17.6957	1.03734
$292$	−5.58296	−0.326718
$293$	−8.62299	−0.503761	−0.251880	−	0.967758i	$-0.581049\pi$
$293$	−8.62299	−0.503761	−0.251880	+	0.967758i	$0.581049\pi$
$294$	−13.9792	−0.815285
$295$	11.6131	0.676144
$296$	−11.3572	−0.660127
$297$	0.781229	0.0453315
$298$	18.7760	1.08766
$299$	−37.8344	−2.18802
$300$	−2.57531	−0.148685
$301$	15.5532	0.896471
$302$	13.9180	0.800892
$303$	−13.8362	−0.794866
$304$	−7.78766	−0.446653
$305$	−12.2691	−0.702525
$306$	−1.05868	−0.0605209
$307$	6.17813	0.352605	0.176302	−	0.984336i	$-0.443586\pi$
$307$	6.17813	0.352605	0.176302	+	0.984336i	$0.443586\pi$
$308$	−3.08734	−0.175917
$309$	−18.4145	−1.04756
$310$	−17.7433	−1.00775
$311$	10.4524	0.592702	0.296351	−	0.955079i	$-0.404230\pi$
$311$	10.4524	0.592702	0.296351	+	0.955079i	$0.404230\pi$
$312$	−13.8728	−0.785391
$313$	32.2855	1.82488	0.912442	−	0.409205i	$-0.134194\pi$
$313$	32.2855	1.82488	0.912442	+	0.409205i	$0.134194\pi$
$314$	−1.05868	−0.0597449
$315$	−12.6572	−0.713151
$316$	−3.11896	−0.175455
$317$	14.2323	0.799364	0.399682	−	0.916654i	$-0.369121\pi$
$317$	14.2323	0.799364	0.399682	+	0.916654i	$0.369121\pi$
$318$	−4.71715	−0.264525
$319$	−3.41694	−0.191312
$320$	−21.8097	−1.21920
$321$	6.30435	0.351875
$322$	−39.5593	−2.20455
$323$	5.30263	0.295046
$324$	−0.879191	−0.0488439
$325$	−13.3313	−0.739488
$326$	1.00768	0.0558100
$327$	−18.0938	−1.00059
$328$	36.3239	2.00565
$329$	4.65589	0.256688
$330$	2.32894	0.128204
$331$	23.5695	1.29550	0.647748	−	0.761855i	$-0.275711\pi$
$331$	23.5695	1.29550	0.647748	+	0.761855i	$0.275711\pi$
$332$	7.04739	0.386776
$333$	−3.72595	−0.204181
$334$	−12.3855	−0.677703
$335$	15.7833	0.862336
$336$	−6.60144	−0.360138
$337$	−24.8476	−1.35354	−0.676768	−	0.736196i	$-0.736620\pi$
$337$	−24.8476	−1.35354	−0.676768	+	0.736196i	$0.736620\pi$
$338$	−8.16617	−0.444181
$339$	3.70976	0.201486
$340$	2.47570	0.134263
$341$	−4.64980	−0.251801
$342$	−5.61380	−0.303560
$343$	27.8881	1.50582
$344$	10.5471	0.568662
$345$	−23.4085	−1.26027
$346$	12.1491	0.653139
$347$	3.57294	0.191806	0.0959029	−	0.995391i	$-0.469426\pi$
$347$	3.57294	0.191806	0.0959029	+	0.995391i	$0.469426\pi$
$348$	3.84540	0.206135
$349$	−20.1561	−1.07893	−0.539467	−	0.842007i	$-0.681374\pi$
$349$	−20.1561	−1.07893	−0.539467	+	0.842007i	$0.681374\pi$
$350$	−13.9391	−0.745075
$351$	−4.55121	−0.242926
$352$	−3.54793	−0.189105
$353$	14.9684	0.796687	0.398344	−	0.917236i	$-0.369585\pi$
$353$	14.9684	0.796687	0.398344	+	0.917236i	$0.369585\pi$
$354$	4.36618	0.232060
$355$	−25.5464	−1.35586
$356$	−10.6950	−0.566831
$357$	4.49493	0.237897
$358$	−7.96064	−0.420733
$359$	31.9267	1.68503	0.842513	−	0.538677i	$-0.181076\pi$
$359$	31.9267	1.68503	0.842513	+	0.538677i	$0.181076\pi$
$360$	−8.58322	−0.452376
$361$	9.11789	0.479889
$362$	16.0295	0.842490
$363$	−10.3897	−0.545317
$364$	17.9859	0.942718
$365$	−17.8811	−0.935942
$366$	−4.61279	−0.241114
$367$	0.971444	0.0507090	0.0253545	−	0.999679i	$-0.491929\pi$
$367$	0.971444	0.0507090	0.0253545	+	0.999679i	$0.491929\pi$
$368$	−12.2089	−0.636432
$369$	11.9167	0.620358
$370$	−11.1075	−0.577452
$371$	20.0279	1.03980
$372$	5.23286	0.271311
$373$	−2.35260	−0.121813	−0.0609065	−	0.998143i	$-0.519399\pi$
$373$	−2.35260	−0.121813	−0.0609065	+	0.998143i	$0.519399\pi$
$374$	−0.827074	−0.0427670
$375$	5.83119	0.301121
$376$	3.15731	0.162826
$377$	19.9061	1.02521
$378$	−4.75870	−0.244761
$379$	−2.57765	−0.132405	−0.0662026	−	0.997806i	$-0.521088\pi$
$379$	−2.57765	−0.132405	−0.0662026	+	0.997806i	$0.521088\pi$
$380$	13.1277	0.673437
$381$	−0.0877691	−0.00449654
$382$	−20.9367	−1.07122
$383$	11.9045	0.608291	0.304145	−	0.952626i	$-0.401629\pi$
$383$	11.9045	0.608291	0.304145	+	0.952626i	$0.401629\pi$
$384$	0.883170	0.0450691
$385$	−9.88815	−0.503947
$386$	9.67992	0.492695
$387$	3.46017	0.175890
$388$	−15.5579	−0.789833
$389$	−12.8559	−0.651819	−0.325909	−	0.945401i	$-0.605670\pi$
$389$	−12.8559	−0.651819	−0.325909	+	0.945401i	$0.605670\pi$
$390$	−13.5677	−0.687028
$391$	8.31304	0.420409
$392$	40.2489	2.03287
$393$	0.495117	0.0249753
$394$	−16.2998	−0.821170
$395$	−9.98943	−0.502623
$396$	−0.686849	−0.0345155
$397$	−9.03812	−0.453610	−0.226805	−	0.973940i	$-0.572828\pi$
$397$	−9.03812	−0.453610	−0.226805	+	0.973940i	$0.572828\pi$
$398$	−25.8452	−1.29550
$399$	23.8349	1.19324
$400$	−4.30191	−0.215096
$401$	−29.3033	−1.46334	−0.731670	−	0.681659i	$-0.761259\pi$
$401$	−29.3033	−1.46334	−0.731670	+	0.681659i	$0.761259\pi$
$402$	5.93404	0.295963
$403$	27.0884	1.34937
$404$	12.1646	0.605212
$405$	−2.81588	−0.139922
$406$	20.8136	1.03296
$407$	−2.91082	−0.144284
$408$	3.04815	0.150906
$409$	−5.45302	−0.269634	−0.134817	−	0.990870i	$-0.543045\pi$
$409$	−5.45302	−0.269634	−0.134817	+	0.990870i	$0.543045\pi$
$410$	35.5251	1.75446
$411$	0.0598484	0.00295210
$412$	16.1898	0.797616
$413$	−18.5378	−0.912186
$414$	−8.80088	−0.432540
$415$	22.5714	1.10799
$416$	20.6692	1.01339
$417$	−6.13138	−0.300255
$418$	−4.38567	−0.214510
$419$	1.01313	0.0494944	0.0247472	−	0.999694i	$-0.492122\pi$
$419$	1.01313	0.0494944	0.0247472	+	0.999694i	$0.492122\pi$
$420$	11.1281	0.542994
$421$	13.6192	0.663759	0.331879	−	0.943322i	$-0.392317\pi$
$421$	13.6192	0.663759	0.331879	+	0.943322i	$0.392317\pi$
$422$	−10.2047	−0.496756
$423$	1.03581	0.0503628
$424$	13.5816	0.659579
$425$	2.92918	0.142086
$426$	−9.60466	−0.465347
$427$	19.5848	0.947777
$428$	−5.54273	−0.267918
$429$	−3.55554	−0.171663
$430$	10.3152	0.497442
$431$	−18.0067	−0.867353	−0.433676	−	0.901069i	$-0.642784\pi$
$431$	−18.0067	−0.867353	−0.433676	+	0.901069i	$0.642784\pi$
$432$	−1.46864	−0.0706601
$433$	−16.4497	−0.790520	−0.395260	−	0.918569i	$-0.629346\pi$
$433$	−16.4497	−0.790520	−0.395260	+	0.918569i	$0.629346\pi$
$434$	28.3233	1.35956
$435$	12.3161	0.590511
$436$	15.9079	0.761852
$437$	44.0810	2.10868
$438$	−6.72275	−0.321225
$439$	−7.17905	−0.342638	−0.171319	−	0.985216i	$-0.554803\pi$
$439$	−7.17905	−0.342638	−0.171319	+	0.985216i	$0.554803\pi$
$440$	−6.70546	−0.319670
$441$	13.2044	0.628779
$442$	4.81829	0.229183
$443$	40.8238	1.93959	0.969797	−	0.243911i	$-0.0784306\pi$
$443$	40.8238	1.93959	0.969797	+	0.243911i	$0.0784306\pi$
$444$	3.27582	0.155464
$445$	−34.2539	−1.62379
$446$	21.6023	1.02290
$447$	−17.7352	−0.838847
$448$	34.8144	1.64482
$449$	3.97562	0.187621	0.0938105	−	0.995590i	$-0.470095\pi$
$449$	3.97562	0.187621	0.0938105	+	0.995590i	$0.470095\pi$
$450$	−3.10107	−0.146186
$451$	9.30967	0.438375
$452$	−3.26159	−0.153412
$453$	−13.1465	−0.617678
$454$	−0.523892	−0.0245875
$455$	57.6054	2.70058
$456$	16.1632	0.756912
$457$	−2.35989	−0.110391	−0.0551956	−	0.998476i	$-0.517578\pi$
$457$	−2.35989	−0.110391	−0.0551956	+	0.998476i	$0.517578\pi$
$458$	−11.1128	−0.519267
$459$	1.00000	0.0466760
$460$	20.5806	0.959574
$461$	3.54713	0.165206	0.0826032	−	0.996583i	$-0.473677\pi$
$461$	3.54713	0.165206	0.0826032	+	0.996583i	$0.473677\pi$
$462$	−3.71763	−0.172960
$463$	2.72669	0.126720	0.0633601	−	0.997991i	$-0.479818\pi$
$463$	2.72669	0.126720	0.0633601	+	0.997991i	$0.479818\pi$
$464$	6.42354	0.298205
$465$	16.7598	0.777219
$466$	−4.27743	−0.198148
$467$	−39.6869	−1.83649	−0.918246	−	0.396011i	$-0.870394\pi$
$467$	−39.6869	−1.83649	−0.918246	+	0.396011i	$0.870394\pi$
$468$	4.00138	0.184964
$469$	−25.1946	−1.16338
$470$	3.08788	0.142433
$471$	1.00000	0.0460776
$472$	−12.5711	−0.578630
$473$	2.70318	0.124292
$474$	−3.75571	−0.172506
$475$	15.5323	0.712673
$476$	−3.95190	−0.181135
$477$	4.45568	0.204011
$478$	8.39522	0.383989
$479$	−0.601187	−0.0274689	−0.0137345	−	0.999906i	$-0.504372\pi$
$479$	−0.601187	−0.0274689	−0.0137345	+	0.999906i	$0.504372\pi$
$480$	12.7882	0.583701
$481$	16.9576	0.773199
$482$	9.81439	0.447033
$483$	37.3665	1.70024
$484$	9.13451	0.415205
$485$	−49.8290	−2.26262
$486$	−1.05868	−0.0480228
$487$	−7.29816	−0.330711	−0.165356	−	0.986234i	$-0.552877\pi$
$487$	−7.29816	−0.330711	−0.165356	+	0.986234i	$0.552877\pi$
$488$	13.2811	0.601207
$489$	−0.951821	−0.0430428
$490$	39.3638	1.77828
$491$	28.3222	1.27816	0.639081	−	0.769140i	$-0.279315\pi$
$491$	28.3222	1.27816	0.639081	+	0.769140i	$0.279315\pi$
$492$	−10.4770	−0.472342
$493$	−4.37379	−0.196986
$494$	25.5496	1.14953
$495$	−2.19985	−0.0988758
$496$	8.74121	0.392492
$497$	40.7792	1.82920
$498$	8.48615	0.380273
$499$	20.7994	0.931110	0.465555	−	0.885019i	$-0.345855\pi$
$499$	20.7994	0.931110	0.465555	+	0.885019i	$0.345855\pi$
$500$	−5.12673	−0.229274
$501$	11.6990	0.522671
$502$	1.07735	0.0480845
$503$	1.25702	0.0560479	0.0280240	−	0.999607i	$-0.491079\pi$
$503$	1.25702	0.0560479	0.0280240	+	0.999607i	$0.491079\pi$
$504$	13.7012	0.610300
$505$	38.9609	1.73374
$506$	−6.87550	−0.305653
$507$	7.71352	0.342569
$508$	0.0771657	0.00342368
$509$	25.7187	1.13996	0.569981	−	0.821658i	$-0.306951\pi$
$509$	25.7187	1.13996	0.569981	+	0.821658i	$0.306951\pi$
$510$	2.98112	0.132006
$511$	28.5433	1.26268
$512$	15.6231	0.690449
$513$	5.30263	0.234117
$514$	12.8374	0.566234
$515$	51.8529	2.28491
$516$	−3.04215	−0.133923
$517$	0.809205	0.0355888
$518$	17.7307	0.779041
$519$	−11.4757	−0.503726
$520$	39.0641	1.71307
$521$	19.1874	0.840615	0.420307	−	0.907382i	$-0.361922\pi$
$521$	19.1874	0.840615	0.420307	+	0.907382i	$0.361922\pi$
$522$	4.63046	0.202670
$523$	37.4851	1.63911	0.819556	−	0.573000i	$-0.194220\pi$
$523$	37.4851	1.63911	0.819556	+	0.573000i	$0.194220\pi$
$524$	−0.435302	−0.0190163
$525$	13.1664	0.574630
$526$	−25.3000	−1.10313
$527$	−5.95190	−0.259269
$528$	−1.14735	−0.0499318
$529$	46.1067	2.00464
$530$	13.2829	0.576973
$531$	−4.12416	−0.178973
$532$	−20.9554	−0.908534
$533$	−54.2354	−2.34920
$534$	−12.8784	−0.557302
$535$	−17.7523	−0.767499
$536$	−17.0852	−0.737970
$537$	7.51938	0.324485
$538$	−7.69698	−0.331840
$539$	10.3156	0.444325
$540$	2.47570	0.106537
$541$	−31.6988	−1.36284	−0.681418	−	0.731894i	$-0.738637\pi$
$541$	−31.6988	−1.36284	−0.681418	+	0.731894i	$0.738637\pi$
$542$	−11.3643	−0.488137
$543$	−15.1410	−0.649761
$544$	−4.54147	−0.194714
$545$	50.9501	2.18246
$546$	21.6578	0.926870
$547$	37.2802	1.59399	0.796993	−	0.603988i	$-0.206423\pi$
$547$	37.2802	1.59399	0.796993	+	0.603988i	$0.206423\pi$
$548$	−0.0526182	−0.00224774
$549$	4.35710	0.185957
$550$	−2.42265	−0.103302
$551$	−23.1926	−0.988039
$552$	25.3394	1.07852
$553$	15.9459	0.678089
$554$	−0.963366	−0.0409295
$555$	10.4918	0.445353
$556$	5.39065	0.228615
$557$	−41.5530	−1.76066	−0.880328	−	0.474366i	$-0.842677\pi$
$557$	−41.5530	−1.76066	−0.880328	+	0.474366i	$0.842677\pi$
$558$	6.30118	0.266750
$559$	−15.7479	−0.666067
$560$	18.5888	0.785522
$561$	0.781229	0.0329835
$562$	−31.8018	−1.34148
$563$	−35.2849	−1.48708	−0.743540	−	0.668692i	$-0.766855\pi$
$563$	−35.2849	−1.48708	−0.743540	+	0.668692i	$0.766855\pi$
$564$	−0.910675	−0.0383463
$565$	−10.4462	−0.439476
$566$	−18.4007	−0.773440
$567$	4.49493	0.188769
$568$	27.6537	1.16032
$569$	−15.0975	−0.632919	−0.316460	−	0.948606i	$-0.602494\pi$
$569$	−15.0975	−0.632919	−0.316460	+	0.948606i	$0.602494\pi$
$570$	15.8078	0.662116
$571$	27.3176	1.14321	0.571604	−	0.820530i	$-0.306321\pi$
$571$	27.3176	1.14321	0.571604	+	0.820530i	$0.306321\pi$
$572$	3.12600	0.130704
$573$	19.7762	0.826163
$574$	−56.7080	−2.36695
$575$	24.3504	1.01548
$576$	7.74526	0.322719
$577$	−11.2533	−0.468482	−0.234241	−	0.972179i	$-0.575261\pi$
$577$	−11.2533	−0.468482	−0.234241	+	0.972179i	$0.575261\pi$
$578$	−1.05868	−0.0440354
$579$	−9.14336	−0.379985
$580$	−10.8282	−0.449616
$581$	−36.0303	−1.49479
$582$	−18.7341	−0.776555
$583$	3.48090	0.144164
$584$	19.3561	0.800960
$585$	12.8157	0.529862
$586$	9.12901	0.377116
$587$	24.4021	1.00718	0.503591	−	0.863942i	$-0.332012\pi$
$587$	24.4021	1.00718	0.503591	+	0.863942i	$0.332012\pi$
$588$	−11.6091	−0.478753
$589$	−31.5607	−1.30044
$590$	−12.2946	−0.506162
$591$	15.3963	0.633318
$592$	5.47208	0.224901
$593$	43.2917	1.77778	0.888888	−	0.458125i	$-0.151479\pi$
$593$	43.2917	1.77778	0.888888	+	0.458125i	$0.151479\pi$
$594$	−0.827074	−0.0339352
$595$	−12.6572	−0.518893
$596$	15.5926	0.638699
$597$	24.4126	0.999142
$598$	40.0546	1.63796
$599$	5.88109	0.240295	0.120147	−	0.992756i	$-0.461663\pi$
$599$	5.88109	0.240295	0.120147	+	0.992756i	$0.461663\pi$
$600$	8.92857	0.364507
$601$	15.7409	0.642084	0.321042	−	0.947065i	$-0.395967\pi$
$601$	15.7409	0.642084	0.321042	+	0.947065i	$0.395967\pi$
$602$	−16.4659	−0.671100
$603$	−5.60512	−0.228258
$604$	11.5583	0.470301
$605$	29.2561	1.18943
$606$	14.6481	0.595038
$607$	29.9357	1.21505	0.607527	−	0.794299i	$-0.292162\pi$
$607$	29.9357	1.21505	0.607527	+	0.794299i	$0.292162\pi$
$608$	−24.0818	−0.976644
$609$	−19.6599	−0.796659
$610$	12.9891	0.525912
$611$	−4.71419	−0.190716
$612$	−0.879191	−0.0355392
$613$	2.81953	0.113880	0.0569398	−	0.998378i	$-0.481866\pi$
$613$	2.81953	0.113880	0.0569398	+	0.998378i	$0.481866\pi$
$614$	−6.54068	−0.263960
$615$	−33.5560	−1.35311
$616$	10.7038	0.431268
$617$	34.4732	1.38784	0.693920	−	0.720052i	$-0.255882\pi$
$617$	34.4732	1.38784	0.693920	+	0.720052i	$0.255882\pi$
$618$	19.4951	0.784207
$619$	44.2438	1.77831	0.889155	−	0.457607i	$-0.151293\pi$
$619$	44.2438	1.77831	0.889155	+	0.457607i	$0.151293\pi$
$620$	−14.7351	−0.591776
$621$	8.31304	0.333591
$622$	−11.0658	−0.443698
$623$	54.6787	2.19066
$624$	6.68410	0.267578
$625$	−31.0658	−1.24263
$626$	−34.1801	−1.36611
$627$	4.14257	0.165438
$628$	−0.879191	−0.0350835
$629$	−3.72595	−0.148563
$630$	13.3999	0.533866
$631$	18.0561	0.718801	0.359401	−	0.933183i	$-0.382981\pi$
$631$	18.0561	0.718801	0.359401	+	0.933183i	$0.382981\pi$
$632$	10.8134	0.430135
$633$	9.63903	0.383117
$634$	−15.0675	−0.598405
$635$	0.247147	0.00980773
$636$	−3.91739	−0.155335
$637$	−60.0958	−2.38108
$638$	3.61745	0.143216
$639$	9.07228	0.358894
$640$	−2.48690	−0.0983034
$641$	44.8487	1.77142	0.885709	−	0.464240i	$-0.153672\pi$
$641$	44.8487	1.77142	0.885709	+	0.464240i	$0.153672\pi$
$642$	−6.67431	−0.263414
$643$	−37.4685	−1.47761	−0.738807	−	0.673917i	$-0.764611\pi$
$643$	−37.4685	−1.47761	−0.738807	+	0.673917i	$0.764611\pi$
$644$	−32.8523	−1.29456
$645$	−9.74341	−0.383646
$646$	−5.61380	−0.220872
$647$	−32.7155	−1.28618	−0.643089	−	0.765792i	$-0.722347\pi$
$647$	−32.7155	−1.28618	−0.643089	+	0.765792i	$0.722347\pi$
$648$	3.04815	0.119743
$649$	−3.22192	−0.126471
$650$	14.1136	0.553582
$651$	−26.7534	−1.04855
$652$	0.836832	0.0327729
$653$	42.7031	1.67110	0.835552	−	0.549412i	$-0.185148\pi$
$653$	42.7031	1.67110	0.835552	+	0.549412i	$0.185148\pi$
$654$	19.1556	0.749045
$655$	−1.39419	−0.0544755
$656$	−17.5014	−0.683313
$657$	6.35011	0.247741
$658$	−4.92911	−0.192157
$659$	−35.5477	−1.38474	−0.692370	−	0.721542i	$-0.743434\pi$
$659$	−35.5477	−1.38474	−0.692370	+	0.721542i	$0.743434\pi$
$660$	1.93409	0.0752842
$661$	39.0029	1.51704	0.758518	−	0.651652i	$-0.225924\pi$
$661$	39.0029	1.51704	0.758518	+	0.651652i	$0.225924\pi$
$662$	−24.9526	−0.969811
$663$	−4.55121	−0.176754
$664$	−24.4332	−0.948194
$665$	−67.1163	−2.60266
$666$	3.94460	0.152850
$667$	−36.3595	−1.40785
$668$	−10.2856	−0.397962
$669$	−20.4049	−0.788897
$670$	−16.7095	−0.645546
$671$	3.40389	0.131406
$672$	−20.4136	−0.787471
$673$	−6.52485	−0.251515	−0.125757	−	0.992061i	$-0.540136\pi$
$673$	−6.52485	−0.251515	−0.125757	+	0.992061i	$0.540136\pi$
$674$	26.3058	1.01326
$675$	2.92918	0.112744
$676$	−6.78166	−0.260833
$677$	10.1381	0.389639	0.194819	−	0.980839i	$-0.437588\pi$
$677$	10.1381	0.389639	0.194819	+	0.980839i	$0.437588\pi$
$678$	−3.92746	−0.150833
$679$	79.5409	3.05250
$680$	−8.58322	−0.329152
$681$	0.494853	0.0189628
$682$	4.92266	0.188498
$683$	14.5587	0.557073	0.278537	−	0.960426i	$-0.410151\pi$
$683$	14.5587	0.557073	0.278537	+	0.960426i	$0.410151\pi$
$684$	−4.66202	−0.178257
$685$	−0.168526	−0.00643904
$686$	−29.5247	−1.12726
$687$	10.4968	0.400479
$688$	−5.08175	−0.193740
$689$	−20.2787	−0.772558
$690$	24.7822	0.943443
$691$	−13.7567	−0.523331	−0.261665	−	0.965159i	$-0.584272\pi$
$691$	−13.7567	−0.523331	−0.261665	+	0.965159i	$0.584272\pi$
$692$	10.0893	0.383538
$693$	3.51157	0.133393
$694$	−3.78262	−0.143586
$695$	17.2652	0.654907
$696$	−13.3320	−0.505347
$697$	11.9167	0.451377
$698$	21.3390	0.807691
$699$	4.04033	0.152819
$700$	−11.5758	−0.437524
$701$	15.2854	0.577321	0.288660	−	0.957432i	$-0.406790\pi$
$701$	15.2854	0.577321	0.288660	+	0.957432i	$0.406790\pi$
$702$	4.81829	0.181855
$703$	−19.7573	−0.745162
$704$	6.05083	0.228049
$705$	−2.91672	−0.109850
$706$	−15.8468	−0.596402
$707$	−62.1925	−2.33899
$708$	3.62593	0.136271
$709$	42.0701	1.57998	0.789988	−	0.613122i	$-0.210087\pi$
$709$	42.0701	1.57998	0.789988	+	0.613122i	$0.210087\pi$
$710$	27.0456	1.01500
$711$	3.54753	0.133043
$712$	37.0793	1.38961
$713$	−49.4784	−1.85298
$714$	−4.75870	−0.178090
$715$	10.0120	0.374426
$716$	−6.61097	−0.247064
$717$	−7.92988	−0.296147
$718$	−33.8002	−1.26141
$719$	−17.2932	−0.644926	−0.322463	−	0.946582i	$-0.604511\pi$
$719$	−17.2932	−0.644926	−0.322463	+	0.946582i	$0.604511\pi$
$720$	4.13552	0.154122
$721$	−82.7717	−3.08258
$722$	−9.65295	−0.359246
$723$	−9.27038	−0.344769
$724$	13.3118	0.494729
$725$	−12.8116	−0.475812
$726$	10.9994	0.408225
$727$	−2.60955	−0.0967827	−0.0483913	−	0.998828i	$-0.515409\pi$
$727$	−2.60955	−0.0967827	−0.0483913	+	0.998828i	$0.515409\pi$
$728$	−62.3571	−2.31111
$729$	1.00000	0.0370370
$730$	18.9305	0.700648
$731$	3.46017	0.127979
$732$	−3.83072	−0.141588
$733$	14.3408	0.529689	0.264844	−	0.964291i	$-0.414679\pi$
$733$	14.3408	0.529689	0.264844	+	0.964291i	$0.414679\pi$
$734$	−1.02845	−0.0379608
$735$	−37.1819	−1.37147
$736$	−37.7535	−1.39161
$737$	−4.37888	−0.161298
$738$	−12.6160	−0.464401
$739$	−21.3772	−0.786371	−0.393186	−	0.919459i	$-0.628627\pi$
$739$	−21.3772	−0.786371	−0.393186	+	0.919459i	$0.628627\pi$
$740$	−9.22431	−0.339093
$741$	−24.1334	−0.886562
$742$	−21.2032	−0.778395
$743$	−15.5474	−0.570379	−0.285189	−	0.958471i	$-0.592057\pi$
$743$	−15.5474	−0.570379	−0.285189	+	0.958471i	$0.592057\pi$
$744$	−18.1423	−0.665128
$745$	49.9402	1.82967
$746$	2.49066	0.0911895
$747$	−8.01576	−0.293281
$748$	−0.686849	−0.0251137
$749$	28.3376	1.03543
$750$	−6.17338	−0.225420
$751$	22.9848	0.838728	0.419364	−	0.907818i	$-0.362253\pi$
$751$	22.9848	0.838728	0.419364	+	0.907818i	$0.362253\pi$
$752$	−1.52123	−0.0554737
$753$	−1.01763	−0.0370846
$754$	−21.0742	−0.767477
$755$	37.0191	1.34726
$756$	−3.95190	−0.143729
$757$	−11.1436	−0.405020	−0.202510	−	0.979280i	$-0.564910\pi$
$757$	−11.1436	−0.405020	−0.202510	+	0.979280i	$0.564910\pi$
$758$	2.72892	0.0991188
$759$	6.49439	0.235732
$760$	−45.5137	−1.65095
$761$	−26.8793	−0.974375	−0.487187	−	0.873298i	$-0.661977\pi$
$761$	−26.8793	−0.974375	−0.487187	+	0.873298i	$0.661977\pi$
$762$	0.0929196	0.00336612
$763$	−81.3305	−2.94436
$764$	−17.3871	−0.629042
$765$	−2.81588	−0.101808
$766$	−12.6031	−0.455368
$767$	18.7699	0.677743
$768$	−16.4255	−0.592705
$769$	−17.1316	−0.617783	−0.308891	−	0.951097i	$-0.599958\pi$
$769$	−17.1316	−0.617783	−0.308891	+	0.951097i	$0.599958\pi$
$770$	10.4684	0.377255
$771$	−12.1258	−0.436702
$772$	8.03876	0.289321
$773$	23.1577	0.832924	0.416462	−	0.909153i	$-0.363270\pi$
$773$	23.1577	0.832924	0.416462	+	0.909153i	$0.363270\pi$
$774$	−3.66322	−0.131672
$775$	−17.4342	−0.626254
$776$	53.9392	1.93630
$777$	−16.7479	−0.600826
$778$	13.6103	0.487953
$779$	63.1898	2.26401
$780$	−11.2674	−0.403438
$781$	7.08753	0.253612
$782$	−8.80088	−0.314719
$783$	−4.37379	−0.156307
$784$	−19.3925	−0.692588
$785$	−2.81588	−0.100503
$786$	−0.524171	−0.0186966
$787$	23.6023	0.841329	0.420665	−	0.907216i	$-0.361797\pi$
$787$	23.6023	0.841329	0.420665	+	0.907216i	$0.361797\pi$
$788$	−13.5363	−0.482209
$789$	23.8976	0.850776
$790$	10.5756	0.376264
$791$	16.6751	0.592898
$792$	2.38130	0.0846159
$793$	−19.8301	−0.704187
$794$	9.56850	0.339574
$795$	−12.5467	−0.444984
$796$	−21.4634	−0.760749
$797$	−39.8831	−1.41273	−0.706367	−	0.707846i	$-0.749667\pi$
$797$	−39.8831	−1.41273	−0.706367	+	0.707846i	$0.749667\pi$
$798$	−25.2336	−0.893261
$799$	1.03581	0.0366443
$800$	−13.3028	−0.470324
$801$	12.1645	0.429813
$802$	31.0230	1.09546
$803$	4.96089	0.175066
$804$	4.92797	0.173796
$805$	−105.220	−3.70850
$806$	−28.6780	−1.01014
$807$	7.27034	0.255928
$808$	−42.1747	−1.48370
$809$	−21.9613	−0.772118	−0.386059	−	0.922474i	$-0.626164\pi$
$809$	−21.9613	−0.772118	−0.386059	+	0.922474i	$0.626164\pi$
$810$	2.98112	0.104746
$811$	10.1507	0.356438	0.178219	−	0.983991i	$-0.442966\pi$
$811$	10.1507	0.356438	0.178219	+	0.983991i	$0.442966\pi$
$812$	17.2848	0.606577
$813$	10.7344	0.376470
$814$	3.08163	0.108011
$815$	2.68021	0.0938838
$816$	−1.46864	−0.0514127
$817$	18.3480	0.641915
$818$	5.77302	0.201849
$819$	−20.4574	−0.714838
$820$	29.5021	1.03026
$821$	−2.53877	−0.0886038	−0.0443019	−	0.999018i	$-0.514106\pi$
$821$	−2.53877	−0.0886038	−0.0443019	+	0.999018i	$0.514106\pi$
$822$	−0.0633605	−0.00220995
$823$	46.2265	1.61136	0.805678	−	0.592354i	$-0.201801\pi$
$823$	46.2265	1.61136	0.805678	+	0.592354i	$0.201801\pi$
$824$	−56.1301	−1.95538
$825$	2.28836	0.0796704
$826$	19.6257	0.682864
$827$	21.1299	0.734760	0.367380	−	0.930071i	$-0.380255\pi$
$827$	21.1299	0.734760	0.367380	+	0.930071i	$0.380255\pi$
$828$	−7.30875	−0.253997
$829$	11.5189	0.400067	0.200034	−	0.979789i	$-0.435895\pi$
$829$	11.5189	0.400067	0.200034	+	0.979789i	$0.435895\pi$
$830$	−23.8960	−0.829441
$831$	0.909966	0.0315664
$832$	−35.2503	−1.22209
$833$	13.2044	0.457504
$834$	6.49118	0.224771
$835$	−32.9428	−1.14003
$836$	−3.64211	−0.125965
$837$	−5.95190	−0.205728
$838$	−1.07258	−0.0370516
$839$	18.0705	0.623864	0.311932	−	0.950104i	$-0.399024\pi$
$839$	18.0705	0.623864	0.311932	+	0.950104i	$0.399024\pi$
$840$	−38.5809	−1.33117
$841$	−9.86992	−0.340342
$842$	−14.4184	−0.496891
$843$	30.0391	1.03460
$844$	−8.47455	−0.291706
$845$	−21.7203	−0.747202
$846$	−1.09659	−0.0377017
$847$	−46.7008	−1.60466
$848$	−6.54379	−0.224715
$849$	17.3808	0.596507
$850$	−3.10107	−0.106366
$851$	−30.9740	−1.06177
$852$	−7.97626	−0.273262
$853$	−15.6468	−0.535735	−0.267868	−	0.963456i	$-0.586319\pi$
$853$	−15.6468	−0.535735	−0.267868	+	0.963456i	$0.586319\pi$
$854$	−20.7341	−0.709508
$855$	−14.9316	−0.510649
$856$	19.2166	0.656810
$857$	−21.1853	−0.723676	−0.361838	−	0.932241i	$-0.617851\pi$
$857$	−21.1853	−0.723676	−0.361838	+	0.932241i	$0.617851\pi$
$858$	3.76419	0.128507
$859$	−4.53711	−0.154804	−0.0774021	−	0.997000i	$-0.524663\pi$
$859$	−4.53711	−0.154804	−0.0774021	+	0.997000i	$0.524663\pi$
$860$	8.56632	0.292109
$861$	53.5647	1.82548
$862$	19.0634	0.649302
$863$	−11.8046	−0.401833	−0.200916	−	0.979608i	$-0.564392\pi$
$863$	−11.8046	−0.401833	−0.200916	+	0.979608i	$0.564392\pi$
$864$	−4.54147	−0.154504
$865$	32.3141	1.09871
$866$	17.4150	0.591785
$867$	1.00000	0.0339618
$868$	23.5213	0.798365
$869$	2.77144	0.0940146
$870$	−13.0388	−0.442057
$871$	25.5101	0.864376
$872$	−55.1527	−1.86771
$873$	17.6957	0.598909
$874$	−46.6678	−1.57856
$875$	26.2108	0.886085
$876$	−5.58296	−0.188631
$877$	−23.4130	−0.790602	−0.395301	−	0.918552i	$-0.629360\pi$
$877$	−23.4130	−0.790602	−0.395301	+	0.918552i	$0.629360\pi$
$878$	7.60034	0.256499
$879$	−8.62299	−0.290846
$880$	3.23079	0.108910
$881$	−4.17329	−0.140602	−0.0703009	−	0.997526i	$-0.522396\pi$
$881$	−4.17329	−0.140602	−0.0703009	+	0.997526i	$0.522396\pi$
$882$	−13.9792	−0.470705
$883$	−16.1797	−0.544489	−0.272245	−	0.962228i	$-0.587766\pi$
$883$	−16.1797	−0.544489	−0.272245	+	0.962228i	$0.587766\pi$
$884$	4.00138	0.134581
$885$	11.6131	0.390372
$886$	−43.2194	−1.45198
$887$	−13.6259	−0.457515	−0.228757	−	0.973483i	$-0.573466\pi$
$887$	−13.6259	−0.457515	−0.228757	+	0.973483i	$0.573466\pi$
$888$	−11.3572	−0.381124
$889$	−0.394515	−0.0132316
$890$	36.2640	1.21557
$891$	0.781229	0.0261722
$892$	17.9398	0.600668
$893$	5.49252	0.183800
$894$	18.7760	0.627962
$895$	−21.1737	−0.707758
$896$	3.96978	0.132621
$897$	−37.8344	−1.26325
$898$	−4.20892	−0.140453
$899$	26.0324	0.868229
$900$	−2.57531	−0.0858435
$901$	4.45568	0.148440
$902$	−9.85598	−0.328168
$903$	15.5532	0.517578
$904$	11.3079	0.376095
$905$	42.6351	1.41724
$906$	13.9180	0.462395
$907$	37.4352	1.24302	0.621508	−	0.783408i	$-0.286520\pi$
$907$	37.4352	1.24302	0.621508	+	0.783408i	$0.286520\pi$
$908$	−0.435070	−0.0144383
$909$	−13.8362	−0.458916
$910$	−60.9859	−2.02166
$911$	49.3950	1.63653	0.818264	−	0.574842i	$-0.194936\pi$
$911$	49.3950	1.63653	0.818264	+	0.574842i	$0.194936\pi$
$912$	−7.78766	−0.257875
$913$	−6.26215	−0.207247
$914$	2.49838	0.0826390
$915$	−12.2691	−0.405603
$916$	−9.22871	−0.304925
$917$	2.22551	0.0734929
$918$	−1.05868	−0.0349417
$919$	3.51029	0.115794	0.0578969	−	0.998323i	$-0.481561\pi$
$919$	3.51029	0.115794	0.0578969	+	0.998323i	$0.481561\pi$
$920$	−71.3527	−2.35243
$921$	6.17813	0.203576
$922$	−3.75529	−0.123674
$923$	−41.2898	−1.35907
$924$	−3.08734	−0.101566
$925$	−10.9140	−0.358849
$926$	−2.88670	−0.0948629
$927$	−18.4145	−0.604811
$928$	19.8635	0.652050
$929$	−23.2602	−0.763142	−0.381571	−	0.924340i	$-0.624617\pi$
$929$	−23.2602	−0.763142	−0.381571	+	0.924340i	$0.624617\pi$
$930$	−17.7433	−0.581827
$931$	70.0178	2.29474
$932$	−3.55222	−0.116357
$933$	10.4524	0.342197
$934$	42.0159	1.37480
$935$	−2.19985	−0.0719427
$936$	−13.8728	−0.453446
$937$	−20.7788	−0.678814	−0.339407	−	0.940640i	$-0.610226\pi$
$937$	−20.7788	−0.678814	−0.339407	+	0.940640i	$0.610226\pi$
$938$	26.6731	0.870907
$939$	32.2855	1.05360
$940$	2.56435	0.0836399
$941$	16.7953	0.547510	0.273755	−	0.961799i	$-0.411734\pi$
$941$	16.7953	0.547510	0.273755	+	0.961799i	$0.411734\pi$
$942$	−1.05868	−0.0344937
$943$	99.0640	3.22597
$944$	6.05692	0.197136
$945$	−12.6572	−0.411738
$946$	−2.86181	−0.0930456
$947$	6.30008	0.204725	0.102363	−	0.994747i	$-0.467360\pi$
$947$	6.30008	0.204725	0.102363	+	0.994747i	$0.467360\pi$
$948$	−3.11896	−0.101299
$949$	−28.9007	−0.938156
$950$	−16.4438	−0.533508
$951$	14.2323	0.461513
$952$	13.7012	0.444059
$953$	−39.4091	−1.27659	−0.638293	−	0.769794i	$-0.720359\pi$
$953$	−39.4091	−1.27659	−0.638293	+	0.769794i	$0.720359\pi$
$954$	−4.71715	−0.152723
$955$	−55.6874	−1.80200
$956$	6.97187	0.225487
$957$	−3.41694	−0.110454
$958$	0.636466	0.0205633
$959$	0.269014	0.00868692
$960$	−21.8097	−0.703906
$961$	4.42513	0.142746
$962$	−17.9527	−0.578818
$963$	6.30435	0.203155
$964$	8.15043	0.262508
$965$	25.7466	0.828813
$966$	−39.5593	−1.27280
$967$	−49.5630	−1.59384	−0.796920	−	0.604085i	$-0.793539\pi$
$967$	−49.5630	−1.59384	−0.796920	+	0.604085i	$0.793539\pi$
$968$	−31.6693	−1.01789
$969$	5.30263	0.170345
$970$	52.7531	1.69380
$971$	9.74906	0.312862	0.156431	−	0.987689i	$-0.450001\pi$
$971$	9.74906	0.312862	0.156431	+	0.987689i	$0.450001\pi$
$972$	−0.879191	−0.0282001
$973$	−27.5601	−0.883536
$974$	7.72643	0.247571
$975$	−13.3313	−0.426943
$976$	−6.39902	−0.204828
$977$	55.3393	1.77046	0.885231	−	0.465152i	$-0.154000\pi$
$977$	55.3393	1.77046	0.885231	+	0.465152i	$0.154000\pi$
$978$	1.00768	0.0322219
$979$	9.50329	0.303727
$980$	32.6900	1.04424
$981$	−18.0938	−0.577692
$982$	−29.9842	−0.956834
$983$	−22.5665	−0.719759	−0.359879	−	0.932999i	$-0.617182\pi$
$983$	−22.5665	−0.719759	−0.359879	+	0.932999i	$0.617182\pi$
$984$	36.3239	1.15796
$985$	−43.3540	−1.38137
$986$	4.63046	0.147464
$987$	4.65589	0.148199
$988$	21.2179	0.675030
$989$	28.7645	0.914659
$990$	2.32894	0.0740186
$991$	−38.8669	−1.23465	−0.617324	−	0.786709i	$-0.711783\pi$
$991$	−38.8669	−1.23465	−0.617324	+	0.786709i	$0.711783\pi$
$992$	27.0304	0.858216
$993$	23.5695	0.747955
$994$	−43.1722	−1.36934
$995$	−68.7430	−2.17930
$996$	7.04739	0.223305
$997$	40.9831	1.29795	0.648974	−	0.760811i	$-0.275198\pi$
$997$	40.9831	1.29795	0.648974	+	0.760811i	$0.275198\pi$
$998$	−22.0200	−0.697031
$999$	−3.72595	−0.117884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.19	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.19	✓	63	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)

\(f(q)\)	\(=\)	\(q-1.05868 q^{2} +1.00000 q^{3} -0.879191 q^{4} -2.81588 q^{5} -1.05868 q^{6} +4.49493 q^{7} +3.04815 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.05868 q^{2} +1.00000 q^{3} -0.879191 q^{4} -2.81588 q^{5} -1.05868 q^{6} +4.49493 q^{7} +3.04815 q^{8} +1.00000 q^{9} +2.98112 q^{10} +0.781229 q^{11} -0.879191 q^{12} -4.55121 q^{13} -4.75870 q^{14} -2.81588 q^{15} -1.46864 q^{16} +1.00000 q^{17} -1.05868 q^{18} +5.30263 q^{19} +2.47570 q^{20} +4.49493 q^{21} -0.827074 q^{22} +8.31304 q^{23} +3.04815 q^{24} +2.92918 q^{25} +4.81829 q^{26} +1.00000 q^{27} -3.95190 q^{28} -4.37379 q^{29} +2.98112 q^{30} -5.95190 q^{31} -4.54147 q^{32} +0.781229 q^{33} -1.05868 q^{34} -12.6572 q^{35} -0.879191 q^{36} -3.72595 q^{37} -5.61380 q^{38} -4.55121 q^{39} -8.58322 q^{40} +11.9167 q^{41} -4.75870 q^{42} +3.46017 q^{43} -0.686849 q^{44} -2.81588 q^{45} -8.80088 q^{46} +1.03581 q^{47} -1.46864 q^{48} +13.2044 q^{49} -3.10107 q^{50} +1.00000 q^{51} +4.00138 q^{52} +4.45568 q^{53} -1.05868 q^{54} -2.19985 q^{55} +13.7012 q^{56} +5.30263 q^{57} +4.63046 q^{58} -4.12416 q^{59} +2.47570 q^{60} +4.35710 q^{61} +6.30118 q^{62} +4.49493 q^{63} +7.74526 q^{64} +12.8157 q^{65} -0.827074 q^{66} -5.60512 q^{67} -0.879191 q^{68} +8.31304 q^{69} +13.3999 q^{70} +9.07228 q^{71} +3.04815 q^{72} +6.35011 q^{73} +3.94460 q^{74} +2.92918 q^{75} -4.66202 q^{76} +3.51157 q^{77} +4.81829 q^{78} +3.54753 q^{79} +4.13552 q^{80} +1.00000 q^{81} -12.6160 q^{82} -8.01576 q^{83} -3.95190 q^{84} -2.81588 q^{85} -3.66322 q^{86} -4.37379 q^{87} +2.38130 q^{88} +12.1645 q^{89} +2.98112 q^{90} -20.4574 q^{91} -7.30875 q^{92} -5.95190 q^{93} -1.09659 q^{94} -14.9316 q^{95} -4.54147 q^{96} +17.6957 q^{97} -13.9792 q^{98} +0.781229 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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