LMFDB - Embedded newform 8007.2.a.f.1.3

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:	$1$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.52044 q^{2} -1.00000 q^{3} +4.35263 q^{4} -1.87454 q^{5} +2.52044 q^{6} -3.72156 q^{7} -5.92968 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.52044 q^{2} -1.00000 q^{3} +4.35263 q^{4} -1.87454 q^{5} +2.52044 q^{6} -3.72156 q^{7} -5.92968 q^{8} +1.00000 q^{9} +4.72466 q^{10} -2.94696 q^{11} -4.35263 q^{12} -4.80391 q^{13} +9.37999 q^{14} +1.87454 q^{15} +6.24016 q^{16} -1.00000 q^{17} -2.52044 q^{18} -2.96492 q^{19} -8.15917 q^{20} +3.72156 q^{21} +7.42764 q^{22} -3.55424 q^{23} +5.92968 q^{24} -1.48611 q^{25} +12.1080 q^{26} -1.00000 q^{27} -16.1986 q^{28} -2.12919 q^{29} -4.72466 q^{30} -1.66517 q^{31} -3.86860 q^{32} +2.94696 q^{33} +2.52044 q^{34} +6.97620 q^{35} +4.35263 q^{36} +0.184027 q^{37} +7.47290 q^{38} +4.80391 q^{39} +11.1154 q^{40} +12.0088 q^{41} -9.37999 q^{42} +0.542752 q^{43} -12.8270 q^{44} -1.87454 q^{45} +8.95825 q^{46} +8.00368 q^{47} -6.24016 q^{48} +6.85003 q^{49} +3.74566 q^{50} +1.00000 q^{51} -20.9097 q^{52} +5.77316 q^{53} +2.52044 q^{54} +5.52418 q^{55} +22.0677 q^{56} +2.96492 q^{57} +5.36651 q^{58} -4.76000 q^{59} +8.15917 q^{60} -8.87761 q^{61} +4.19697 q^{62} -3.72156 q^{63} -2.72973 q^{64} +9.00510 q^{65} -7.42764 q^{66} +6.37330 q^{67} -4.35263 q^{68} +3.55424 q^{69} -17.5831 q^{70} +0.652176 q^{71} -5.92968 q^{72} -10.6625 q^{73} -0.463829 q^{74} +1.48611 q^{75} -12.9052 q^{76} +10.9673 q^{77} -12.1080 q^{78} +5.92951 q^{79} -11.6974 q^{80} +1.00000 q^{81} -30.2675 q^{82} +7.36907 q^{83} +16.1986 q^{84} +1.87454 q^{85} -1.36797 q^{86} +2.12919 q^{87} +17.4745 q^{88} +13.2204 q^{89} +4.72466 q^{90} +17.8780 q^{91} -15.4703 q^{92} +1.66517 q^{93} -20.1728 q^{94} +5.55784 q^{95} +3.86860 q^{96} -6.53499 q^{97} -17.2651 q^{98} -2.94696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.52044	−1.78222	−0.891111	−	0.453785i	$-0.850073\pi$
$2$	−2.52044	−1.78222	−0.891111	+	0.453785i	$0.850073\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.35263	2.17632
$5$	−1.87454	−0.838318	−0.419159	−	0.907913i	$-0.637675\pi$
$5$	−1.87454	−0.838318	−0.419159	+	0.907913i	$0.637675\pi$
$6$	2.52044	1.02897
$7$	−3.72156	−1.40662	−0.703309	−	0.710884i	$-0.748295\pi$
$7$	−3.72156	−1.40662	−0.703309	+	0.710884i	$0.748295\pi$
$8$	−5.92968	−2.09646
$9$	1.00000	0.333333
$10$	4.72466	1.49407
$11$	−2.94696	−0.888542	−0.444271	−	0.895893i	$-0.646537\pi$
$11$	−2.94696	−0.888542	−0.444271	+	0.895893i	$0.646537\pi$
$12$	−4.35263	−1.25650
$13$	−4.80391	−1.33236	−0.666182	−	0.745789i	$-0.732073\pi$
$13$	−4.80391	−1.33236	−0.666182	+	0.745789i	$0.732073\pi$
$14$	9.37999	2.50691
$15$	1.87454	0.484003
$16$	6.24016	1.56004
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.52044	−0.594074
$19$	−2.96492	−0.680198	−0.340099	−	0.940390i	$-0.610461\pi$
$19$	−2.96492	−0.680198	−0.340099	+	0.940390i	$0.610461\pi$
$20$	−8.15917	−1.82445
$21$	3.72156	0.812112
$22$	7.42764	1.58358
$23$	−3.55424	−0.741110	−0.370555	−	0.928811i	$-0.620832\pi$
$23$	−3.55424	−0.741110	−0.370555	+	0.928811i	$0.620832\pi$
$24$	5.92968	1.21039
$25$	−1.48611	−0.297223
$26$	12.1080	2.37457
$27$	−1.00000	−0.192450
$28$	−16.1986	−3.06125
$29$	−2.12919	−0.395381	−0.197691	−	0.980264i	$-0.563344\pi$
$29$	−2.12919	−0.395381	−0.197691	+	0.980264i	$0.563344\pi$
$30$	−4.72466	−0.862601
$31$	−1.66517	−0.299074	−0.149537	−	0.988756i	$-0.547778\pi$
$31$	−1.66517	−0.299074	−0.149537	+	0.988756i	$0.547778\pi$
$32$	−3.86860	−0.683878
$33$	2.94696	0.513000
$34$	2.52044	0.432252
$35$	6.97620	1.17919
$36$	4.35263	0.725439
$37$	0.184027	0.0302538	0.0151269	−	0.999886i	$-0.495185\pi$
$37$	0.184027	0.0302538	0.0151269	+	0.999886i	$0.495185\pi$
$38$	7.47290	1.21226
$39$	4.80391	0.769241
$40$	11.1154	1.75750
$41$	12.0088	1.87546	0.937729	−	0.347368i	$-0.112925\pi$
$41$	12.0088	1.87546	0.937729	+	0.347368i	$0.112925\pi$
$42$	−9.37999	−1.44736
$43$	0.542752	0.0827689	0.0413844	−	0.999143i	$-0.486823\pi$
$43$	0.542752	0.0827689	0.0413844	+	0.999143i	$0.486823\pi$
$44$	−12.8270	−1.93375
$45$	−1.87454	−0.279439
$46$	8.95825	1.32082
$47$	8.00368	1.16746	0.583728	−	0.811949i	$-0.301593\pi$
$47$	8.00368	1.16746	0.583728	+	0.811949i	$0.301593\pi$
$48$	−6.24016	−0.900689
$49$	6.85003	0.978575
$50$	3.74566	0.529717
$51$	1.00000	0.140028
$52$	−20.9097	−2.89965
$53$	5.77316	0.793004	0.396502	−	0.918034i	$-0.370224\pi$
$53$	5.77316	0.793004	0.396502	+	0.918034i	$0.370224\pi$
$54$	2.52044	0.342989
$55$	5.52418	0.744881
$56$	22.0677	2.94892
$57$	2.96492	0.392713
$58$	5.36651	0.704658
$59$	−4.76000	−0.619700	−0.309850	−	0.950786i	$-0.600279\pi$
$59$	−4.76000	−0.619700	−0.309850	+	0.950786i	$0.600279\pi$
$60$	8.15917	1.05334
$61$	−8.87761	−1.13666	−0.568330	−	0.822800i	$-0.692410\pi$
$61$	−8.87761	−1.13666	−0.568330	+	0.822800i	$0.692410\pi$
$62$	4.19697	0.533016
$63$	−3.72156	−0.468873
$64$	−2.72973	−0.341216
$65$	9.00510	1.11695
$66$	−7.42764	−0.914280
$67$	6.37330	0.778623	0.389311	−	0.921106i	$-0.372713\pi$
$67$	6.37330	0.778623	0.389311	+	0.921106i	$0.372713\pi$
$68$	−4.35263	−0.527834
$69$	3.55424	0.427880
$70$	−17.5831	−2.10159
$71$	0.652176	0.0773990	0.0386995	−	0.999251i	$-0.487678\pi$
$71$	0.652176	0.0773990	0.0386995	+	0.999251i	$0.487678\pi$
$72$	−5.92968	−0.698820
$73$	−10.6625	−1.24795	−0.623973	−	0.781446i	$-0.714483\pi$
$73$	−10.6625	−1.24795	−0.623973	+	0.781446i	$0.714483\pi$
$74$	−0.463829	−0.0539191
$75$	1.48611	0.171602
$76$	−12.9052	−1.48033
$77$	10.9673	1.24984
$78$	−12.1080	−1.37096
$79$	5.92951	0.667122	0.333561	−	0.942729i	$-0.391750\pi$
$79$	5.92951	0.667122	0.333561	+	0.942729i	$0.391750\pi$
$80$	−11.6974	−1.30781
$81$	1.00000	0.111111
$82$	−30.2675	−3.34248
$83$	7.36907	0.808861	0.404430	−	0.914569i	$-0.367470\pi$
$83$	7.36907	0.808861	0.404430	+	0.914569i	$0.367470\pi$
$84$	16.1986	1.76741
$85$	1.87454	0.203322
$86$	−1.36797	−0.147513
$87$	2.12919	0.228274
$88$	17.4745	1.86279
$89$	13.2204	1.40136	0.700679	−	0.713477i	$-0.252880\pi$
$89$	13.2204	1.40136	0.700679	+	0.713477i	$0.252880\pi$
$90$	4.72466	0.498023
$91$	17.8780	1.87413
$92$	−15.4703	−1.61289
$93$	1.66517	0.172670
$94$	−20.1728	−2.08067
$95$	5.55784	0.570223
$96$	3.86860	0.394837
$97$	−6.53499	−0.663528	−0.331764	−	0.943362i	$-0.607644\pi$
$97$	−6.53499	−0.663528	−0.331764	+	0.943362i	$0.607644\pi$
$98$	−17.2651	−1.74404
$99$	−2.94696	−0.296181
$100$	−6.46851	−0.646851
$101$	3.06380	0.304860	0.152430	−	0.988314i	$-0.451290\pi$
$101$	3.06380	0.304860	0.152430	+	0.988314i	$0.451290\pi$
$102$	−2.52044	−0.249561
$103$	−1.87708	−0.184954	−0.0924769	−	0.995715i	$-0.529478\pi$
$103$	−1.87708	−0.184954	−0.0924769	+	0.995715i	$0.529478\pi$
$104$	28.4856	2.79325
$105$	−6.97620	−0.680808
$106$	−14.5509	−1.41331
$107$	3.64074	0.351964	0.175982	−	0.984393i	$-0.443690\pi$
$107$	3.64074	0.351964	0.175982	+	0.984393i	$0.443690\pi$
$108$	−4.35263	−0.418832
$109$	19.4663	1.86454	0.932269	−	0.361766i	$-0.117826\pi$
$109$	19.4663	1.86454	0.932269	+	0.361766i	$0.117826\pi$
$110$	−13.9234	−1.32754
$111$	−0.184027	−0.0174671
$112$	−23.2231	−2.19438
$113$	−13.1276	−1.23494	−0.617471	−	0.786594i	$-0.711843\pi$
$113$	−13.1276	−1.23494	−0.617471	+	0.786594i	$0.711843\pi$
$114$	−7.47290	−0.699901
$115$	6.66255	0.621286
$116$	−9.26760	−0.860475
$117$	−4.80391	−0.444122
$118$	11.9973	1.10444
$119$	3.72156	0.341155
$120$	−11.1154	−1.01469
$121$	−2.31543	−0.210494
$122$	22.3755	2.02578
$123$	−12.0088	−1.08280
$124$	−7.24788	−0.650879
$125$	12.1585	1.08749
$126$	9.37999	0.835636
$127$	16.0950	1.42820	0.714102	−	0.700042i	$-0.246835\pi$
$127$	16.0950	1.42820	0.714102	+	0.700042i	$0.246835\pi$
$128$	14.6173	1.29200
$129$	−0.542752	−0.0477866
$130$	−22.6969	−1.99065
$131$	9.54456	0.833912	0.416956	−	0.908927i	$-0.363097\pi$
$131$	9.54456	0.833912	0.416956	+	0.908927i	$0.363097\pi$
$132$	12.8270	1.11645
$133$	11.0341	0.956779
$134$	−16.0635	−1.38768
$135$	1.87454	0.161334
$136$	5.92968	0.508466
$137$	−4.90688	−0.419223	−0.209612	−	0.977785i	$-0.567220\pi$
$137$	−4.90688	−0.419223	−0.209612	+	0.977785i	$0.567220\pi$
$138$	−8.95825	−0.762577
$139$	14.5218	1.23172	0.615862	−	0.787854i	$-0.288808\pi$
$139$	14.5218	1.23172	0.615862	+	0.787854i	$0.288808\pi$
$140$	30.3649	2.56630
$141$	−8.00368	−0.674031
$142$	−1.64377	−0.137942
$143$	14.1569	1.18386
$144$	6.24016	0.520013
$145$	3.99125	0.331455
$146$	26.8741	2.22412
$147$	−6.85003	−0.564981
$148$	0.801002	0.0658419
$149$	4.60363	0.377144	0.188572	−	0.982059i	$-0.439614\pi$
$149$	4.60363	0.377144	0.188572	+	0.982059i	$0.439614\pi$
$150$	−3.74566	−0.305832
$151$	−18.6599	−1.51852	−0.759260	−	0.650788i	$-0.774439\pi$
$151$	−18.6599	−1.51852	−0.759260	+	0.650788i	$0.774439\pi$
$152$	17.5810	1.42601
$153$	−1.00000	−0.0808452
$154$	−27.6424	−2.22749
$155$	3.12142	0.250719
$156$	20.9097	1.67411
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−14.9450	−1.18896
$159$	−5.77316	−0.457841
$160$	7.25183	0.573307
$161$	13.2273	1.04246
$162$	−2.52044	−0.198025
$163$	−9.35777	−0.732957	−0.366479	−	0.930426i	$-0.619437\pi$
$163$	−9.35777	−0.732957	−0.366479	+	0.930426i	$0.619437\pi$
$164$	52.2699	4.08159
$165$	−5.52418	−0.430057
$166$	−18.5733	−1.44157
$167$	−9.19729	−0.711708	−0.355854	−	0.934542i	$-0.615810\pi$
$167$	−9.19729	−0.711708	−0.355854	+	0.934542i	$0.615810\pi$
$168$	−22.0677	−1.70256
$169$	10.0775	0.775195
$170$	−4.72466	−0.362365
$171$	−2.96492	−0.226733
$172$	2.36240	0.180131
$173$	−17.9279	−1.36304	−0.681518	−	0.731801i	$-0.738680\pi$
$173$	−17.9279	−1.36304	−0.681518	+	0.731801i	$0.738680\pi$
$174$	−5.36651	−0.406834
$175$	5.53066	0.418079
$176$	−18.3895	−1.38616
$177$	4.76000	0.357784
$178$	−33.3212	−2.49753
$179$	−7.01235	−0.524128	−0.262064	−	0.965050i	$-0.584403\pi$
$179$	−7.01235	−0.524128	−0.262064	+	0.965050i	$0.584403\pi$
$180$	−8.15917	−0.608149
$181$	−15.9778	−1.18762	−0.593811	−	0.804605i	$-0.702377\pi$
$181$	−15.9778	−1.18762	−0.593811	+	0.804605i	$0.702377\pi$
$182$	−45.0606	−3.34011
$183$	8.87761	0.656251
$184$	21.0755	1.55371
$185$	−0.344965	−0.0253623
$186$	−4.19697	−0.307737
$187$	2.94696	0.215503
$188$	34.8371	2.54076
$189$	3.72156	0.270704
$190$	−14.0082	−1.01626
$191$	5.28229	0.382213	0.191107	−	0.981569i	$-0.438792\pi$
$191$	5.28229	0.382213	0.191107	+	0.981569i	$0.438792\pi$
$192$	2.72973	0.197001
$193$	−2.97462	−0.214118	−0.107059	−	0.994253i	$-0.534143\pi$
$193$	−2.97462	−0.214118	−0.107059	+	0.994253i	$0.534143\pi$
$194$	16.4711	1.18255
$195$	−9.00510	−0.644869
$196$	29.8157	2.12969
$197$	−24.3458	−1.73457	−0.867283	−	0.497815i	$-0.834136\pi$
$197$	−24.3458	−1.73457	−0.867283	+	0.497815i	$0.834136\pi$
$198$	7.42764	0.527860
$199$	17.3592	1.23056	0.615282	−	0.788307i	$-0.289042\pi$
$199$	17.3592	1.23056	0.615282	+	0.788307i	$0.289042\pi$
$200$	8.81218	0.623115
$201$	−6.37330	−0.449538
$202$	−7.72213	−0.543328
$203$	7.92393	0.556151
$204$	4.35263	0.304745
$205$	−22.5109	−1.57223
$206$	4.73106	0.329629
$207$	−3.55424	−0.247037
$208$	−29.9771	−2.07854
$209$	8.73748	0.604384
$210$	17.5831	1.21335
$211$	9.45719	0.651060	0.325530	−	0.945532i	$-0.394457\pi$
$211$	9.45719	0.651060	0.325530	+	0.945532i	$0.394457\pi$
$212$	25.1284	1.72583
$213$	−0.652176	−0.0446863
$214$	−9.17628	−0.627278
$215$	−1.01741	−0.0693866
$216$	5.92968	0.403464
$217$	6.19704	0.420682
$218$	−49.0638	−3.32302
$219$	10.6625	0.720502
$220$	24.0447	1.62110
$221$	4.80391	0.323146
$222$	0.463829	0.0311302
$223$	−28.9506	−1.93868	−0.969338	−	0.245732i	$-0.920972\pi$
$223$	−28.9506	−1.93868	−0.969338	+	0.245732i	$0.920972\pi$
$224$	14.3972	0.961955
$225$	−1.48611	−0.0990742
$226$	33.0874	2.20094
$227$	7.60202	0.504563	0.252282	−	0.967654i	$-0.418819\pi$
$227$	7.60202	0.504563	0.252282	+	0.967654i	$0.418819\pi$
$228$	12.9052	0.854667
$229$	13.6198	0.900019	0.450010	−	0.893024i	$-0.351421\pi$
$229$	13.6198	0.900019	0.450010	+	0.893024i	$0.351421\pi$
$230$	−16.7926	−1.10727
$231$	−10.9673	−0.721595
$232$	12.6254	0.828901
$233$	−4.67412	−0.306212	−0.153106	−	0.988210i	$-0.548928\pi$
$233$	−4.67412	−0.306212	−0.153106	+	0.988210i	$0.548928\pi$
$234$	12.1080	0.791523
$235$	−15.0032	−0.978700
$236$	−20.7186	−1.34866
$237$	−5.92951	−0.385163
$238$	−9.37999	−0.608014
$239$	25.2415	1.63274	0.816369	−	0.577530i	$-0.195983\pi$
$239$	25.2415	1.63274	0.816369	+	0.577530i	$0.195983\pi$
$240$	11.6974	0.755064
$241$	−9.47592	−0.610398	−0.305199	−	0.952289i	$-0.598723\pi$
$241$	−9.47592	−0.610398	−0.305199	+	0.952289i	$0.598723\pi$
$242$	5.83591	0.375147
$243$	−1.00000	−0.0641500
$244$	−38.6410	−2.47373
$245$	−12.8406	−0.820358
$246$	30.2675	1.92978
$247$	14.2432	0.906272
$248$	9.87393	0.626995
$249$	−7.36907	−0.466996
$250$	−30.6447	−1.93814
$251$	−11.4885	−0.725148	−0.362574	−	0.931955i	$-0.618102\pi$
$251$	−11.4885	−0.725148	−0.362574	+	0.931955i	$0.618102\pi$
$252$	−16.1986	−1.02042
$253$	10.4742	0.658507
$254$	−40.5666	−2.54538
$255$	−1.87454	−0.117388
$256$	−31.3827	−1.96142
$257$	−7.47709	−0.466408	−0.233204	−	0.972428i	$-0.574921\pi$
$257$	−7.47709	−0.466408	−0.233204	+	0.972428i	$0.574921\pi$
$258$	1.36797	0.0851664
$259$	−0.684868	−0.0425556
$260$	39.1959	2.43083
$261$	−2.12919	−0.131794
$262$	−24.0565	−1.48622
$263$	1.86511	0.115007	0.0575037	−	0.998345i	$-0.481686\pi$
$263$	1.86511	0.115007	0.0575037	+	0.998345i	$0.481686\pi$
$264$	−17.4745	−1.07548
$265$	−10.8220	−0.664790
$266$	−27.8109	−1.70519
$267$	−13.2204	−0.809075
$268$	27.7406	1.69453
$269$	29.4837	1.79765	0.898827	−	0.438303i	$-0.144420\pi$
$269$	29.4837	1.79765	0.898827	+	0.438303i	$0.144420\pi$
$270$	−4.72466	−0.287534
$271$	18.5631	1.12763	0.563813	−	0.825902i	$-0.309334\pi$
$271$	18.5631	1.12763	0.563813	+	0.825902i	$0.309334\pi$
$272$	−6.24016	−0.378365
$273$	−17.8780	−1.08203
$274$	12.3675	0.747149
$275$	4.37951	0.264095
$276$	15.4703	0.931202
$277$	19.9779	1.20036	0.600178	−	0.799866i	$-0.295096\pi$
$277$	19.9779	1.20036	0.600178	+	0.799866i	$0.295096\pi$
$278$	−36.6014	−2.19520
$279$	−1.66517	−0.0996912
$280$	−41.3667	−2.47213
$281$	−19.7369	−1.17740	−0.588702	−	0.808350i	$-0.700361\pi$
$281$	−19.7369	−1.17740	−0.588702	+	0.808350i	$0.700361\pi$
$282$	20.1728	1.20127
$283$	−15.7621	−0.936957	−0.468478	−	0.883475i	$-0.655198\pi$
$283$	−15.7621	−0.936957	−0.468478	+	0.883475i	$0.655198\pi$
$284$	2.83868	0.168445
$285$	−5.55784	−0.329218
$286$	−35.6817	−2.10990
$287$	−44.6915	−2.63805
$288$	−3.86860	−0.227959
$289$	1.00000	0.0588235
$290$	−10.0597	−0.590727
$291$	6.53499	0.383088
$292$	−46.4098	−2.71593
$293$	16.1592	0.944028	0.472014	−	0.881591i	$-0.343527\pi$
$293$	16.1592	0.944028	0.472014	+	0.881591i	$0.343527\pi$
$294$	17.2651	1.00692
$295$	8.92280	0.519505
$296$	−1.09122	−0.0634259
$297$	2.94696	0.171000
$298$	−11.6032	−0.672154
$299$	17.0742	0.987428
$300$	6.46851	0.373459
$301$	−2.01988	−0.116424
$302$	47.0312	2.70634
$303$	−3.06380	−0.176011
$304$	−18.5015	−1.06114
$305$	16.6414	0.952883
$306$	2.52044	0.144084
$307$	22.9476	1.30969	0.654846	−	0.755763i	$-0.272734\pi$
$307$	22.9476	1.30969	0.654846	+	0.755763i	$0.272734\pi$
$308$	47.7366	2.72005
$309$	1.87708	0.106783
$310$	−7.86737	−0.446837
$311$	28.3295	1.60642	0.803210	−	0.595696i	$-0.203124\pi$
$311$	28.3295	1.60642	0.803210	+	0.595696i	$0.203124\pi$
$312$	−28.4856	−1.61268
$313$	−12.2451	−0.692134	−0.346067	−	0.938210i	$-0.612483\pi$
$313$	−12.2451	−0.692134	−0.346067	+	0.938210i	$0.612483\pi$
$314$	2.52044	0.142237
$315$	6.97620	0.393065
$316$	25.8090	1.45187
$317$	8.74468	0.491150	0.245575	−	0.969378i	$-0.421023\pi$
$317$	8.74468	0.491150	0.245575	+	0.969378i	$0.421023\pi$
$318$	14.5509	0.815975
$319$	6.27465	0.351313
$320$	5.11698	0.286048
$321$	−3.64074	−0.203206
$322$	−33.3387	−1.85789
$323$	2.96492	0.164972
$324$	4.35263	0.241813
$325$	7.13915	0.396009
$326$	23.5857	1.30629
$327$	−19.4663	−1.07649
$328$	−71.2083	−3.93182
$329$	−29.7862	−1.64217
$330$	13.9234	0.766457
$331$	−7.30026	−0.401259	−0.200629	−	0.979667i	$-0.564299\pi$
$331$	−7.30026	−0.401259	−0.200629	+	0.979667i	$0.564299\pi$
$332$	32.0749	1.76034
$333$	0.184027	0.0100846
$334$	23.1812	1.26842
$335$	−11.9470	−0.652733
$336$	23.2231	1.26693
$337$	−29.7260	−1.61928	−0.809639	−	0.586929i	$-0.800337\pi$
$337$	−29.7260	−1.61928	−0.809639	+	0.586929i	$0.800337\pi$
$338$	−25.3999	−1.38157
$339$	13.1276	0.712994
$340$	8.15917	0.442493
$341$	4.90719	0.265739
$342$	7.47290	0.404088
$343$	0.558131	0.0301363
$344$	−3.21834	−0.173522
$345$	−6.66255	−0.358699
$346$	45.1864	2.42923
$347$	12.8598	0.690352	0.345176	−	0.938538i	$-0.387819\pi$
$347$	12.8598	0.690352	0.345176	+	0.938538i	$0.387819\pi$
$348$	9.26760	0.496796
$349$	17.3968	0.931231	0.465616	−	0.884987i	$-0.345833\pi$
$349$	17.3968	0.931231	0.465616	+	0.884987i	$0.345833\pi$
$350$	−13.9397	−0.745109
$351$	4.80391	0.256414
$352$	11.4006	0.607654
$353$	15.2555	0.811969	0.405984	−	0.913880i	$-0.366929\pi$
$353$	15.2555	0.811969	0.405984	+	0.913880i	$0.366929\pi$
$354$	−11.9973	−0.637650
$355$	−1.22253	−0.0648850
$356$	57.5435	3.04980
$357$	−3.72156	−0.196966
$358$	17.6742	0.934113
$359$	22.1169	1.16729	0.583643	−	0.812011i	$-0.301627\pi$
$359$	22.1169	1.16729	0.583643	+	0.812011i	$0.301627\pi$
$360$	11.1154	0.585833
$361$	−10.2093	−0.537330
$362$	40.2712	2.11661
$363$	2.31543	0.121529
$364$	77.8166	4.07870
$365$	19.9872	1.04618
$366$	−22.3755	−1.16959
$367$	−28.8081	−1.50377	−0.751886	−	0.659293i	$-0.770856\pi$
$367$	−28.8081	−1.50377	−0.751886	+	0.659293i	$0.770856\pi$
$368$	−22.1790	−1.15616
$369$	12.0088	0.625152
$370$	0.869465	0.0452013
$371$	−21.4852	−1.11545
$372$	7.24788	0.375785
$373$	−12.7252	−0.658887	−0.329443	−	0.944175i	$-0.606861\pi$
$373$	−12.7252	−0.658887	−0.329443	+	0.944175i	$0.606861\pi$
$374$	−7.42764	−0.384074
$375$	−12.1585	−0.627860
$376$	−47.4593	−2.44752
$377$	10.2285	0.526792
$378$	−9.37999	−0.482454
$379$	26.1581	1.34365	0.671825	−	0.740710i	$-0.265511\pi$
$379$	26.1581	1.34365	0.671825	+	0.740710i	$0.265511\pi$
$380$	24.1913	1.24099
$381$	−16.0950	−0.824574
$382$	−13.3137	−0.681189
$383$	−17.3823	−0.888195	−0.444098	−	0.895978i	$-0.646476\pi$
$383$	−17.3823	−0.888195	−0.444098	+	0.895978i	$0.646476\pi$
$384$	−14.6173	−0.745937
$385$	−20.5586	−1.04776
$386$	7.49737	0.381606
$387$	0.542752	0.0275896
$388$	−28.4444	−1.44405
$389$	−10.2237	−0.518362	−0.259181	−	0.965829i	$-0.583453\pi$
$389$	−10.2237	−0.518362	−0.259181	+	0.965829i	$0.583453\pi$
$390$	22.6969	1.14930
$391$	3.55424	0.179745
$392$	−40.6185	−2.05154
$393$	−9.54456	−0.481459
$394$	61.3622	3.09138
$395$	−11.1151	−0.559260
$396$	−12.8270	−0.644583
$397$	−18.2914	−0.918018	−0.459009	−	0.888432i	$-0.651795\pi$
$397$	−18.2914	−0.918018	−0.459009	+	0.888432i	$0.651795\pi$
$398$	−43.7530	−2.19314
$399$	−11.0341	−0.552397
$400$	−9.27358	−0.463679
$401$	22.9681	1.14697	0.573486	−	0.819215i	$-0.305591\pi$
$401$	22.9681	1.14697	0.573486	+	0.819215i	$0.305591\pi$
$402$	16.0635	0.801177
$403$	7.99933	0.398475
$404$	13.3356	0.663471
$405$	−1.87454	−0.0931465
$406$	−19.9718	−0.991184
$407$	−0.542320	−0.0268818
$408$	−5.92968	−0.293563
$409$	3.02331	0.149493	0.0747466	−	0.997203i	$-0.476185\pi$
$409$	3.02331	0.149493	0.0747466	+	0.997203i	$0.476185\pi$
$410$	56.7375	2.80206
$411$	4.90688	0.242039
$412$	−8.17022	−0.402518
$413$	17.7146	0.871681
$414$	8.95825	0.440274
$415$	−13.8136	−0.678083
$416$	18.5844	0.911175
$417$	−14.5218	−0.711136
$418$	−22.0223	−1.07715
$419$	−0.892352	−0.0435942	−0.0217971	−	0.999762i	$-0.506939\pi$
$419$	−0.892352	−0.0435942	−0.0217971	+	0.999762i	$0.506939\pi$
$420$	−30.3649	−1.48165
$421$	24.3328	1.18591	0.592954	−	0.805236i	$-0.297961\pi$
$421$	24.3328	1.18591	0.592954	+	0.805236i	$0.297961\pi$
$422$	−23.8363	−1.16033
$423$	8.00368	0.389152
$424$	−34.2330	−1.66250
$425$	1.48611	0.0720871
$426$	1.64377	0.0796410
$427$	33.0386	1.59885
$428$	15.8468	0.765985
$429$	−14.1569	−0.683503
$430$	2.56432	0.123662
$431$	9.42564	0.454017	0.227009	−	0.973893i	$-0.427105\pi$
$431$	9.42564	0.454017	0.227009	+	0.973893i	$0.427105\pi$
$432$	−6.24016	−0.300230
$433$	−7.29466	−0.350559	−0.175279	−	0.984519i	$-0.556083\pi$
$433$	−7.29466	−0.350559	−0.175279	+	0.984519i	$0.556083\pi$
$434$	−15.6193	−0.749750
$435$	−3.99125	−0.191366
$436$	84.7299	4.05783
$437$	10.5380	0.504101
$438$	−26.8741	−1.28410
$439$	13.7761	0.657498	0.328749	−	0.944417i	$-0.393373\pi$
$439$	13.7761	0.657498	0.328749	+	0.944417i	$0.393373\pi$
$440$	−32.7566	−1.56161
$441$	6.85003	0.326192
$442$	−12.1080	−0.575918
$443$	−3.46706	−0.164725	−0.0823625	−	0.996602i	$-0.526247\pi$
$443$	−3.46706	−0.164725	−0.0823625	+	0.996602i	$0.526247\pi$
$444$	−0.801002	−0.0380139
$445$	−24.7821	−1.17478
$446$	72.9683	3.45515
$447$	−4.60363	−0.217744
$448$	10.1589	0.479961
$449$	−10.4236	−0.491921	−0.245961	−	0.969280i	$-0.579103\pi$
$449$	−10.4236	−0.491921	−0.245961	+	0.969280i	$0.579103\pi$
$450$	3.74566	0.176572
$451$	−35.3894	−1.66642
$452$	−57.1397	−2.68762
$453$	18.6599	0.876718
$454$	−19.1604	−0.899244
$455$	−33.5131	−1.57112
$456$	−17.5810	−0.823306
$457$	26.5846	1.24357	0.621787	−	0.783186i	$-0.286407\pi$
$457$	26.5846	1.24357	0.621787	+	0.783186i	$0.286407\pi$
$458$	−34.3278	−1.60403
$459$	1.00000	0.0466760
$460$	28.9996	1.35211
$461$	32.9053	1.53255	0.766275	−	0.642513i	$-0.222108\pi$
$461$	32.9053	1.53255	0.766275	+	0.642513i	$0.222108\pi$
$462$	27.6424	1.28604
$463$	23.5261	1.09335	0.546675	−	0.837345i	$-0.315893\pi$
$463$	23.5261	1.09335	0.546675	+	0.837345i	$0.315893\pi$
$464$	−13.2865	−0.616810
$465$	−3.12142	−0.144753
$466$	11.7809	0.545738
$467$	3.00725	0.139159	0.0695795	−	0.997576i	$-0.477834\pi$
$467$	3.00725	0.139159	0.0695795	+	0.997576i	$0.477834\pi$
$468$	−20.9097	−0.966549
$469$	−23.7186	−1.09522
$470$	37.8147	1.74426
$471$	1.00000	0.0460776
$472$	28.2253	1.29917
$473$	−1.59947	−0.0735436
$474$	14.9450	0.686446
$475$	4.40620	0.202170
$476$	16.1986	0.742462
$477$	5.77316	0.264335
$478$	−63.6198	−2.90990
$479$	3.88205	0.177375	0.0886876	−	0.996059i	$-0.471733\pi$
$479$	3.88205	0.177375	0.0886876	+	0.996059i	$0.471733\pi$
$480$	−7.25183	−0.330999
$481$	−0.884048	−0.0403091
$482$	23.8835	1.08786
$483$	−13.2273	−0.601864
$484$	−10.0782	−0.458101
$485$	12.2501	0.556247
$486$	2.52044	0.114330
$487$	−24.2239	−1.09769	−0.548844	−	0.835925i	$-0.684932\pi$
$487$	−24.2239	−1.09769	−0.548844	+	0.835925i	$0.684932\pi$
$488$	52.6414	2.38296
$489$	9.35777	0.423173
$490$	32.3641	1.46206
$491$	9.01271	0.406738	0.203369	−	0.979102i	$-0.434811\pi$
$491$	9.01271	0.406738	0.203369	+	0.979102i	$0.434811\pi$
$492$	−52.2699	−2.35651
$493$	2.12919	0.0958941
$494$	−35.8991	−1.61518
$495$	5.52418	0.248294
$496$	−10.3909	−0.466566
$497$	−2.42711	−0.108871
$498$	18.5733	0.832291
$499$	1.66247	0.0744223	0.0372112	−	0.999307i	$-0.488153\pi$
$499$	1.66247	0.0744223	0.0372112	+	0.999307i	$0.488153\pi$
$500$	52.9213	2.36671
$501$	9.19729	0.410905
$502$	28.9561	1.29237
$503$	−0.185198	−0.00825757	−0.00412878	−	0.999991i	$-0.501314\pi$
$503$	−0.185198	−0.00825757	−0.00412878	+	0.999991i	$0.501314\pi$
$504$	22.0677	0.982973
$505$	−5.74321	−0.255569
$506$	−26.3996	−1.17361
$507$	−10.0775	−0.447559
$508$	70.0558	3.10822
$509$	−19.1100	−0.847036	−0.423518	−	0.905888i	$-0.639205\pi$
$509$	−19.1100	−0.847036	−0.423518	+	0.905888i	$0.639205\pi$
$510$	4.72466	0.209212
$511$	39.6810	1.75538
$512$	49.8636	2.20368
$513$	2.96492	0.130904
$514$	18.8456	0.831243
$515$	3.51865	0.155050
$516$	−2.36240	−0.103999
$517$	−23.5865	−1.03733
$518$	1.72617	0.0758436
$519$	17.9279	0.786949
$520$	−53.3974	−2.34163
$521$	−21.5567	−0.944415	−0.472207	−	0.881487i	$-0.656543\pi$
$521$	−21.5567	−0.944415	−0.472207	+	0.881487i	$0.656543\pi$
$522$	5.36651	0.234886
$523$	9.44195	0.412868	0.206434	−	0.978461i	$-0.433814\pi$
$523$	9.44195	0.412868	0.206434	+	0.978461i	$0.433814\pi$
$524$	41.5440	1.81486
$525$	−5.53066	−0.241378
$526$	−4.70089	−0.204969
$527$	1.66517	0.0725360
$528$	18.3895	0.800300
$529$	−10.3674	−0.450757
$530$	27.2762	1.18480
$531$	−4.76000	−0.206567
$532$	48.0275	2.08226
$533$	−57.6891	−2.49879
$534$	33.3212	1.44195
$535$	−6.82470	−0.295058
$536$	−37.7916	−1.63235
$537$	7.01235	0.302605
$538$	−74.3121	−3.20382
$539$	−20.1868	−0.869505
$540$	8.15917	0.351115
$541$	−23.7931	−1.02294	−0.511472	−	0.859300i	$-0.670900\pi$
$541$	−23.7931	−1.02294	−0.511472	+	0.859300i	$0.670900\pi$
$542$	−46.7872	−2.00968
$543$	15.9778	0.685674
$544$	3.86860	0.165865
$545$	−36.4904	−1.56308
$546$	45.0606	1.92842
$547$	15.3382	0.655814	0.327907	−	0.944710i	$-0.393657\pi$
$547$	15.3382	0.655814	0.327907	+	0.944710i	$0.393657\pi$
$548$	−21.3579	−0.912362
$549$	−8.87761	−0.378887
$550$	−11.0383	−0.470675
$551$	6.31288	0.268938
$552$	−21.0755	−0.897032
$553$	−22.0670	−0.938386
$554$	−50.3532	−2.13930
$555$	0.344965	0.0146430
$556$	63.2081	2.68062
$557$	0.0226634	0.000960279 0	0.000480139	−	1.00000i	$-0.499847\pi$
$557$	0.0226634	0.000960279 0	0.000480139		1.00000i	$0.499847\pi$
$558$	4.19697	0.177672
$559$	−2.60733	−0.110278
$560$	43.5326	1.83959
$561$	−2.94696	−0.124421
$562$	49.7457	2.09839
$563$	−2.00033	−0.0843038	−0.0421519	−	0.999111i	$-0.513421\pi$
$563$	−2.00033	−0.0843038	−0.0421519	+	0.999111i	$0.513421\pi$
$564$	−34.8371	−1.46691
$565$	24.6082	1.03527
$566$	39.7274	1.66987
$567$	−3.72156	−0.156291
$568$	−3.86719	−0.162264
$569$	−25.6981	−1.07732	−0.538660	−	0.842523i	$-0.681069\pi$
$569$	−25.6981	−1.07732	−0.538660	+	0.842523i	$0.681069\pi$
$570$	14.0082	0.586740
$571$	−22.2678	−0.931879	−0.465939	−	0.884817i	$-0.654284\pi$
$571$	−22.2678	−0.931879	−0.465939	+	0.884817i	$0.654284\pi$
$572$	61.6199	2.57646
$573$	−5.28229	−0.220671
$574$	112.642	4.70160
$575$	5.28200	0.220275
$576$	−2.72973	−0.113739
$577$	−26.7484	−1.11355	−0.556775	−	0.830663i	$-0.687962\pi$
$577$	−26.7484	−1.11355	−0.556775	+	0.830663i	$0.687962\pi$
$578$	−2.52044	−0.104837
$579$	2.97462	0.123621
$580$	17.3725	0.721352
$581$	−27.4245	−1.13776
$582$	−16.4711	−0.682748
$583$	−17.0133	−0.704617
$584$	63.2250	2.61627
$585$	9.00510	0.372315
$586$	−40.7282	−1.68247
$587$	5.45070	0.224974	0.112487	−	0.993653i	$-0.464118\pi$
$587$	5.45070	0.224974	0.112487	+	0.993653i	$0.464118\pi$
$588$	−29.8157	−1.22958
$589$	4.93709	0.203429
$590$	−22.4894	−0.925874
$591$	24.3458	1.00145
$592$	1.14836	0.0471972
$593$	23.5888	0.968675	0.484337	−	0.874881i	$-0.339061\pi$
$593$	23.5888	0.968675	0.484337	+	0.874881i	$0.339061\pi$
$594$	−7.42764	−0.304760
$595$	−6.97620	−0.285997
$596$	20.0379	0.820785
$597$	−17.3592	−0.710466
$598$	−43.0346	−1.75982
$599$	−5.20121	−0.212516	−0.106258	−	0.994339i	$-0.533887\pi$
$599$	−5.20121	−0.212516	−0.106258	+	0.994339i	$0.533887\pi$
$600$	−8.81218	−0.359756
$601$	29.5637	1.20593	0.602964	−	0.797768i	$-0.293986\pi$
$601$	29.5637	1.20593	0.602964	+	0.797768i	$0.293986\pi$
$602$	5.09100	0.207494
$603$	6.37330	0.259541
$604$	−81.2196	−3.30478
$605$	4.34036	0.176461
$606$	7.72213	0.313690
$607$	−15.6165	−0.633854	−0.316927	−	0.948450i	$-0.602651\pi$
$607$	−15.6165	−0.633854	−0.316927	+	0.948450i	$0.602651\pi$
$608$	11.4701	0.465173
$609$	−7.92393	−0.321094
$610$	−41.9437	−1.69825
$611$	−38.4489	−1.55548
$612$	−4.35263	−0.175945
$613$	33.6331	1.35843	0.679214	−	0.733940i	$-0.262321\pi$
$613$	33.6331	1.35843	0.679214	+	0.733940i	$0.262321\pi$
$614$	−57.8382	−2.33416
$615$	22.5109	0.907727
$616$	−65.0325	−2.62024
$617$	10.8403	0.436414	0.218207	−	0.975902i	$-0.429979\pi$
$617$	10.8403	0.436414	0.218207	+	0.975902i	$0.429979\pi$
$618$	−4.73106	−0.190311
$619$	−29.4100	−1.18209	−0.591044	−	0.806640i	$-0.701284\pi$
$619$	−29.4100	−1.18209	−0.591044	+	0.806640i	$0.701284\pi$
$620$	13.5864	0.545644
$621$	3.55424	0.142627
$622$	−71.4030	−2.86300
$623$	−49.2005	−1.97118
$624$	29.9771	1.20005
$625$	−15.3609	−0.614436
$626$	30.8631	1.23354
$627$	−8.73748	−0.348942
$628$	−4.35263	−0.173689
$629$	−0.184027	−0.00733763
$630$	−17.5831	−0.700529
$631$	−39.4954	−1.57229	−0.786143	−	0.618045i	$-0.787925\pi$
$631$	−39.4954	−1.57229	−0.786143	+	0.618045i	$0.787925\pi$
$632$	−35.1601	−1.39859
$633$	−9.45719	−0.375890
$634$	−22.0405	−0.875339
$635$	−30.1707	−1.19729
$636$	−25.1284	−0.996408
$637$	−32.9069	−1.30382
$638$	−15.8149	−0.626118
$639$	0.652176	0.0257997
$640$	−27.4007	−1.08311
$641$	−14.3591	−0.567151	−0.283576	−	0.958950i	$-0.591521\pi$
$641$	−14.3591	−0.567151	−0.283576	+	0.958950i	$0.591521\pi$
$642$	9.17628	0.362159
$643$	45.3534	1.78856	0.894282	−	0.447503i	$-0.147687\pi$
$643$	45.3534	1.78856	0.894282	+	0.447503i	$0.147687\pi$
$644$	57.5737	2.26872
$645$	1.01741	0.0400604
$646$	−7.47290	−0.294017
$647$	6.48076	0.254785	0.127392	−	0.991852i	$-0.459339\pi$
$647$	6.48076	0.254785	0.127392	+	0.991852i	$0.459339\pi$
$648$	−5.92968	−0.232940
$649$	14.0275	0.550629
$650$	−17.9938	−0.705776
$651$	−6.19704	−0.242881
$652$	−40.7310	−1.59515
$653$	−3.05164	−0.119420	−0.0597099	−	0.998216i	$-0.519018\pi$
$653$	−3.05164	−0.119420	−0.0597099	+	0.998216i	$0.519018\pi$
$654$	49.0638	1.91855
$655$	−17.8916	−0.699084
$656$	74.9367	2.92579
$657$	−10.6625	−0.415982
$658$	75.0744	2.92671
$659$	−10.9964	−0.428357	−0.214179	−	0.976794i	$-0.568708\pi$
$659$	−10.9964	−0.428357	−0.214179	+	0.976794i	$0.568708\pi$
$660$	−24.0447	−0.935940
$661$	43.6844	1.69913	0.849563	−	0.527487i	$-0.176865\pi$
$661$	43.6844	1.69913	0.849563	+	0.527487i	$0.176865\pi$
$662$	18.3999	0.715132
$663$	−4.80391	−0.186568
$664$	−43.6963	−1.69574
$665$	−20.6839	−0.802086
$666$	−0.463829	−0.0179730
$667$	7.56766	0.293021
$668$	−40.0324	−1.54890
$669$	28.9506	1.11929
$670$	30.1117	1.16332
$671$	26.1619	1.00997
$672$	−14.3972	−0.555385
$673$	−16.5922	−0.639584	−0.319792	−	0.947488i	$-0.603613\pi$
$673$	−16.5922	−0.639584	−0.319792	+	0.947488i	$0.603613\pi$
$674$	74.9226	2.88591
$675$	1.48611	0.0572005
$676$	43.8639	1.68707
$677$	7.05970	0.271326	0.135663	−	0.990755i	$-0.456683\pi$
$677$	7.05970	0.271326	0.135663	+	0.990755i	$0.456683\pi$
$678$	−33.0874	−1.27071
$679$	24.3204	0.933330
$680$	−11.1154	−0.426256
$681$	−7.60202	−0.291310
$682$	−12.3683	−0.473607
$683$	15.2706	0.584315	0.292157	−	0.956370i	$-0.405627\pi$
$683$	15.2706	0.584315	0.292157	+	0.956370i	$0.405627\pi$
$684$	−12.9052	−0.493442
$685$	9.19813	0.351442
$686$	−1.40674	−0.0537095
$687$	−13.6198	−0.519626
$688$	3.38686	0.129123
$689$	−27.7337	−1.05657
$690$	16.7926	0.639282
$691$	−10.6766	−0.406155	−0.203078	−	0.979163i	$-0.565094\pi$
$691$	−10.6766	−0.406155	−0.203078	+	0.979163i	$0.565094\pi$
$692$	−78.0338	−2.96640
$693$	10.9673	0.416613
$694$	−32.4125	−1.23036
$695$	−27.2216	−1.03258
$696$	−12.6254	−0.478566
$697$	−12.0088	−0.454865
$698$	−43.8477	−1.65966
$699$	4.67412	0.176792
$700$	24.0730	0.909872
$701$	25.0522	0.946210	0.473105	−	0.881006i	$-0.343133\pi$
$701$	25.0522	0.946210	0.473105	+	0.881006i	$0.343133\pi$
$702$	−12.1080	−0.456986
$703$	−0.545624	−0.0205786
$704$	8.04441	0.303185
$705$	15.0032	0.565053
$706$	−38.4507	−1.44711
$707$	−11.4021	−0.428821
$708$	20.7186	0.778651
$709$	−41.8013	−1.56988	−0.784941	−	0.619571i	$-0.787307\pi$
$709$	−41.8013	−1.56988	−0.784941	+	0.619571i	$0.787307\pi$
$710$	3.08131	0.115640
$711$	5.92951	0.222374
$712$	−78.3927	−2.93789
$713$	5.91841	0.221646
$714$	9.37999	0.351037
$715$	−26.5377	−0.992453
$716$	−30.5222	−1.14067
$717$	−25.2415	−0.942662
$718$	−55.7444	−2.08036
$719$	−1.31995	−0.0492257	−0.0246129	−	0.999697i	$-0.507835\pi$
$719$	−1.31995	−0.0492257	−0.0246129	+	0.999697i	$0.507835\pi$
$720$	−11.6974	−0.435936
$721$	6.98565	0.260159
$722$	25.7319	0.957642
$723$	9.47592	0.352413
$724$	−69.5456	−2.58464
$725$	3.16422	0.117516
$726$	−5.83591	−0.216591
$727$	7.40415	0.274605	0.137302	−	0.990529i	$-0.456157\pi$
$727$	7.40415	0.274605	0.137302	+	0.990529i	$0.456157\pi$
$728$	−106.011	−3.92903
$729$	1.00000	0.0370370
$730$	−50.3765	−1.86452
$731$	−0.542752	−0.0200744
$732$	38.6410	1.42821
$733$	17.4941	0.646160	0.323080	−	0.946372i	$-0.395282\pi$
$733$	17.4941	0.646160	0.323080	+	0.946372i	$0.395282\pi$
$734$	72.6093	2.68006
$735$	12.8406	0.473634
$736$	13.7499	0.506828
$737$	−18.7819	−0.691839
$738$	−30.2675	−1.11416
$739$	−0.456404	−0.0167891	−0.00839455	−	0.999965i	$-0.502672\pi$
$739$	−0.456404	−0.0167891	−0.00839455	+	0.999965i	$0.502672\pi$
$740$	−1.50151	−0.0551965
$741$	−14.2432	−0.523236
$742$	54.1521	1.98799
$743$	−42.8477	−1.57193	−0.785965	−	0.618271i	$-0.787833\pi$
$743$	−42.8477	−1.57193	−0.785965	+	0.618271i	$0.787833\pi$
$744$	−9.87393	−0.361996
$745$	−8.62967	−0.316167
$746$	32.0732	1.17428
$747$	7.36907	0.269620
$748$	12.8270	0.469003
$749$	−13.5492	−0.495079
$750$	30.6447	1.11899
$751$	−10.3788	−0.378729	−0.189365	−	0.981907i	$-0.560643\pi$
$751$	−10.3788	−0.378729	−0.189365	+	0.981907i	$0.560643\pi$
$752$	49.9442	1.82128
$753$	11.4885	0.418664
$754$	−25.7802	−0.938861
$755$	34.9786	1.27300
$756$	16.1986	0.589137
$757$	50.9710	1.85257	0.926286	−	0.376821i	$-0.122983\pi$
$757$	50.9710	1.85257	0.926286	+	0.376821i	$0.122983\pi$
$758$	−65.9299	−2.39468
$759$	−10.4742	−0.380189
$760$	−32.9562	−1.19545
$761$	16.7766	0.608151	0.304075	−	0.952648i	$-0.401653\pi$
$761$	16.7766	0.608151	0.304075	+	0.952648i	$0.401653\pi$
$762$	40.5666	1.46957
$763$	−72.4452	−2.62269
$764$	22.9919	0.831818
$765$	1.87454	0.0677740
$766$	43.8112	1.58296
$767$	22.8666	0.825666
$768$	31.3827	1.13243
$769$	12.7734	0.460619	0.230310	−	0.973117i	$-0.426026\pi$
$769$	12.7734	0.460619	0.230310	+	0.973117i	$0.426026\pi$
$770$	51.8168	1.86735
$771$	7.47709	0.269281
$772$	−12.9474	−0.465989
$773$	−26.7526	−0.962224	−0.481112	−	0.876659i	$-0.659767\pi$
$773$	−26.7526	−0.962224	−0.481112	+	0.876659i	$0.659767\pi$
$774$	−1.36797	−0.0491708
$775$	2.47463	0.0888914
$776$	38.7504	1.39106
$777$	0.684868	0.0245695
$778$	25.7683	0.923837
$779$	−35.6050	−1.27568
$780$	−39.1959	−1.40344
$781$	−1.92194	−0.0687723
$782$	−8.95825	−0.320346
$783$	2.12919	0.0760912
$784$	42.7452	1.52662
$785$	1.87454	0.0669051
$786$	24.0565	0.858068
$787$	30.0905	1.07261	0.536305	−	0.844024i	$-0.319820\pi$
$787$	30.0905	1.07261	0.536305	+	0.844024i	$0.319820\pi$
$788$	−105.968	−3.77497
$789$	−1.86511	−0.0663995
$790$	28.0149	0.996727
$791$	48.8552	1.73709
$792$	17.4745	0.620930
$793$	42.6472	1.51445
$794$	46.1024	1.63611
$795$	10.8220	0.383817
$796$	75.5584	2.67810
$797$	27.2747	0.966120	0.483060	−	0.875587i	$-0.339525\pi$
$797$	27.2747	0.966120	0.483060	+	0.875587i	$0.339525\pi$
$798$	27.8109	0.984494
$799$	−8.00368	−0.283150
$800$	5.74917	0.203264
$801$	13.2204	0.467119
$802$	−57.8898	−2.04416
$803$	31.4218	1.10885
$804$	−27.7406	−0.978337
$805$	−24.7951	−0.873912
$806$	−20.1619	−0.710171
$807$	−29.4837	−1.03788
$808$	−18.1674	−0.639125
$809$	−11.4849	−0.403789	−0.201894	−	0.979407i	$-0.564710\pi$
$809$	−11.4849	−0.403789	−0.201894	+	0.979407i	$0.564710\pi$
$810$	4.72466	0.166008
$811$	47.8148	1.67901	0.839503	−	0.543355i	$-0.182846\pi$
$811$	47.8148	1.67901	0.839503	+	0.543355i	$0.182846\pi$
$812$	34.4900	1.21036
$813$	−18.5631	−0.651035
$814$	1.36689	0.0479093
$815$	17.5415	0.614452
$816$	6.24016	0.218449
$817$	−1.60921	−0.0562992
$818$	−7.62009	−0.266430
$819$	17.8780	0.624710
$820$	−97.9818	−3.42167
$821$	−16.3535	−0.570741	−0.285370	−	0.958417i	$-0.592117\pi$
$821$	−16.3535	−0.570741	−0.285370	+	0.958417i	$0.592117\pi$
$822$	−12.3675	−0.431367
$823$	3.95095	0.137721	0.0688607	−	0.997626i	$-0.478064\pi$
$823$	3.95095	0.137721	0.0688607	+	0.997626i	$0.478064\pi$
$824$	11.1305	0.387748
$825$	−4.37951	−0.152475
$826$	−44.6488	−1.55353
$827$	−42.7224	−1.48560	−0.742801	−	0.669512i	$-0.766503\pi$
$827$	−42.7224	−1.48560	−0.742801	+	0.669512i	$0.766503\pi$
$828$	−15.4703	−0.537630
$829$	−3.02966	−0.105225	−0.0526123	−	0.998615i	$-0.516755\pi$
$829$	−3.02966	−0.105225	−0.0526123	+	0.998615i	$0.516755\pi$
$830$	34.8164	1.20849
$831$	−19.9779	−0.693026
$832$	13.1134	0.454625
$833$	−6.85003	−0.237339
$834$	36.6014	1.26740
$835$	17.2407	0.596638
$836$	38.0311	1.31533
$837$	1.66517	0.0575567
$838$	2.24912	0.0776946
$839$	−8.76015	−0.302434	−0.151217	−	0.988501i	$-0.548319\pi$
$839$	−8.76015	−0.302434	−0.151217	+	0.988501i	$0.548319\pi$
$840$	41.3667	1.42729
$841$	−24.4665	−0.843674
$842$	−61.3295	−2.11355
$843$	19.7369	0.679774
$844$	41.1637	1.41691
$845$	−18.8907	−0.649860
$846$	−20.1728	−0.693556
$847$	8.61702	0.296084
$848$	36.0254	1.23712
$849$	15.7621	0.540952
$850$	−3.74566	−0.128475
$851$	−0.654075	−0.0224214
$852$	−2.83868	−0.0972517
$853$	−23.1819	−0.793732	−0.396866	−	0.917877i	$-0.629902\pi$
$853$	−23.1819	−0.793732	−0.396866	+	0.917877i	$0.629902\pi$
$854$	−83.2718	−2.84950
$855$	5.55784	0.190074
$856$	−21.5884	−0.737877
$857$	−49.0605	−1.67587	−0.837937	−	0.545767i	$-0.816239\pi$
$857$	−49.0605	−1.67587	−0.837937	+	0.545767i	$0.816239\pi$
$858$	35.6817	1.21815
$859$	−27.5243	−0.939118	−0.469559	−	0.882901i	$-0.655587\pi$
$859$	−27.5243	−0.939118	−0.469559	+	0.882901i	$0.655587\pi$
$860$	−4.42840	−0.151007
$861$	44.6915	1.52308
$862$	−23.7568	−0.809160
$863$	6.70822	0.228351	0.114175	−	0.993461i	$-0.463577\pi$
$863$	6.70822	0.228351	0.114175	+	0.993461i	$0.463577\pi$
$864$	3.86860	0.131612
$865$	33.6066	1.14266
$866$	18.3858	0.624774
$867$	−1.00000	−0.0339618
$868$	26.9734	0.915538
$869$	−17.4740	−0.592766
$870$	10.0597	0.341057
$871$	−30.6168	−1.03741
$872$	−115.429	−3.90893
$873$	−6.53499	−0.221176
$874$	−26.5605	−0.898421
$875$	−45.2485	−1.52968
$876$	46.4098	1.56804
$877$	24.1639	0.815957	0.407979	−	0.912991i	$-0.366234\pi$
$877$	24.1639	0.815957	0.407979	+	0.912991i	$0.366234\pi$
$878$	−34.7219	−1.17181
$879$	−16.1592	−0.545035
$880$	34.4718	1.16204
$881$	21.3942	0.720790	0.360395	−	0.932800i	$-0.382642\pi$
$881$	21.3942	0.720790	0.360395	+	0.932800i	$0.382642\pi$
$882$	−17.2651	−0.581346
$883$	15.5395	0.522947	0.261474	−	0.965211i	$-0.415792\pi$
$883$	15.5395	0.522947	0.261474	+	0.965211i	$0.415792\pi$
$884$	20.9097	0.703268
$885$	−8.92280	−0.299937
$886$	8.73853	0.293577
$887$	28.3488	0.951858	0.475929	−	0.879484i	$-0.342112\pi$
$887$	28.3488	0.951858	0.475929	+	0.879484i	$0.342112\pi$
$888$	1.09122	0.0366190
$889$	−59.8987	−2.00894
$890$	62.4619	2.09373
$891$	−2.94696	−0.0987268
$892$	−126.011	−4.21917
$893$	−23.7302	−0.794102
$894$	11.6032	0.388069
$895$	13.1449	0.439386
$896$	−54.3993	−1.81735
$897$	−17.0742	−0.570092
$898$	26.2722	0.876713
$899$	3.54547	0.118248
$900$	−6.46851	−0.215617
$901$	−5.77316	−0.192332
$902$	89.1970	2.96993
$903$	2.01988	0.0672175
$904$	77.8425	2.58900
$905$	29.9510	0.995605
$906$	−47.0312	−1.56251
$907$	−47.6943	−1.58366	−0.791832	−	0.610739i	$-0.790873\pi$
$907$	−47.6943	−1.58366	−0.791832	+	0.610739i	$0.790873\pi$
$908$	33.0888	1.09809
$909$	3.06380	0.101620
$910$	84.4677	2.80008
$911$	53.2038	1.76272	0.881360	−	0.472446i	$-0.156629\pi$
$911$	53.2038	1.76272	0.881360	+	0.472446i	$0.156629\pi$
$912$	18.5015	0.612647
$913$	−21.7164	−0.718707
$914$	−67.0049	−2.21633
$915$	−16.6414	−0.550148
$916$	59.2818	1.95873
$917$	−35.5207	−1.17300
$918$	−2.52044	−0.0831870
$919$	−49.1423	−1.62106	−0.810528	−	0.585700i	$-0.800820\pi$
$919$	−49.1423	−1.62106	−0.810528	+	0.585700i	$0.800820\pi$
$920$	−39.5068	−1.30250
$921$	−22.9476	−0.756151
$922$	−82.9358	−2.73135
$923$	−3.13299	−0.103124
$924$	−47.7366	−1.57042
$925$	−0.273485	−0.00899212
$926$	−59.2961	−1.94859
$927$	−1.87708	−0.0616512
$928$	8.23699	0.270393
$929$	−8.68961	−0.285097	−0.142548	−	0.989788i	$-0.545530\pi$
$929$	−8.68961	−0.285097	−0.142548	+	0.989788i	$0.545530\pi$
$930$	7.86737	0.257981
$931$	−20.3098	−0.665625
$932$	−20.3447	−0.666414
$933$	−28.3295	−0.927467
$934$	−7.57960	−0.248012
$935$	−5.52418	−0.180660
$936$	28.4856	0.931083
$937$	−48.0327	−1.56916	−0.784580	−	0.620027i	$-0.787121\pi$
$937$	−48.0327	−1.56916	−0.784580	+	0.620027i	$0.787121\pi$
$938$	59.7815	1.95193
$939$	12.2451	0.399604
$940$	−65.3034	−2.12996
$941$	−51.7791	−1.68795	−0.843975	−	0.536383i	$-0.819790\pi$
$941$	−51.7791	−1.68795	−0.843975	+	0.536383i	$0.819790\pi$
$942$	−2.52044	−0.0821205
$943$	−42.6821	−1.38992
$944$	−29.7032	−0.966756
$945$	−6.97620	−0.226936
$946$	4.03137	0.131071
$947$	18.6060	0.604614	0.302307	−	0.953211i	$-0.402243\pi$
$947$	18.6060	0.604614	0.302307	+	0.953211i	$0.402243\pi$
$948$	−25.8090	−0.838237
$949$	51.2215	1.66272
$950$	−11.1056	−0.360312
$951$	−8.74468	−0.283566
$952$	−22.0677	−0.715218
$953$	3.94458	0.127778	0.0638888	−	0.997957i	$-0.479650\pi$
$953$	3.94458	0.127778	0.0638888	+	0.997957i	$0.479650\pi$
$954$	−14.5509	−0.471103
$955$	−9.90185	−0.320416
$956$	109.867	3.55336
$957$	−6.27465	−0.202831
$958$	−9.78448	−0.316122
$959$	18.2613	0.589687
$960$	−5.11698	−0.165150
$961$	−28.2272	−0.910555
$962$	2.22819	0.0718399
$963$	3.64074	0.117321
$964$	−41.2452	−1.32842
$965$	5.57604	0.179499
$966$	33.3387	1.07265
$967$	10.6783	0.343392	0.171696	−	0.985150i	$-0.445075\pi$
$967$	10.6783	0.343392	0.171696	+	0.985150i	$0.445075\pi$
$968$	13.7298	0.441292
$969$	−2.96492	−0.0952468
$970$	−30.8756	−0.991357
$971$	−10.0143	−0.321374	−0.160687	−	0.987005i	$-0.551371\pi$
$971$	−10.0143	−0.321374	−0.160687	+	0.987005i	$0.551371\pi$
$972$	−4.35263	−0.139611
$973$	−54.0438	−1.73256
$974$	61.0548	1.95632
$975$	−7.13915	−0.228636
$976$	−55.3976	−1.77324
$977$	−45.4519	−1.45413	−0.727067	−	0.686566i	$-0.759117\pi$
$977$	−45.4519	−1.45413	−0.727067	+	0.686566i	$0.759117\pi$
$978$	−23.5857	−0.754189
$979$	−38.9599	−1.24517
$980$	−55.8906	−1.78536
$981$	19.4663	0.621513
$982$	−22.7160	−0.724897
$983$	27.0407	0.862465	0.431233	−	0.902241i	$-0.358079\pi$
$983$	27.0407	0.862465	0.431233	+	0.902241i	$0.358079\pi$
$984$	71.2083	2.27004
$985$	45.6371	1.45412
$986$	−5.36651	−0.170905
$987$	29.7862	0.948105
$988$	61.9954	1.97234
$989$	−1.92907	−0.0613408
$990$	−13.9234	−0.442514
$991$	−4.95423	−0.157376	−0.0786881	−	0.996899i	$-0.525073\pi$
$991$	−4.95423	−0.157376	−0.0786881	+	0.996899i	$0.525073\pi$
$992$	6.44188	0.204530
$993$	7.30026	0.231667
$994$	6.11740	0.194032
$995$	−32.5405	−1.03160
$996$	−32.0749	−1.01633
$997$	22.5256	0.713394	0.356697	−	0.934220i	$-0.383903\pi$
$997$	22.5256	0.713394	0.356697	+	0.934220i	$0.383903\pi$
$998$	−4.19016	−0.132637
$999$	−0.184027	−0.00582235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.f.1.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.f.1.3	✓	48	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)

\(f(q)\)	\(=\)	\(q-2.52044 q^{2} -1.00000 q^{3} +4.35263 q^{4} -1.87454 q^{5} +2.52044 q^{6} -3.72156 q^{7} -5.92968 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.52044 q^{2} -1.00000 q^{3} +4.35263 q^{4} -1.87454 q^{5} +2.52044 q^{6} -3.72156 q^{7} -5.92968 q^{8} +1.00000 q^{9} +4.72466 q^{10} -2.94696 q^{11} -4.35263 q^{12} -4.80391 q^{13} +9.37999 q^{14} +1.87454 q^{15} +6.24016 q^{16} -1.00000 q^{17} -2.52044 q^{18} -2.96492 q^{19} -8.15917 q^{20} +3.72156 q^{21} +7.42764 q^{22} -3.55424 q^{23} +5.92968 q^{24} -1.48611 q^{25} +12.1080 q^{26} -1.00000 q^{27} -16.1986 q^{28} -2.12919 q^{29} -4.72466 q^{30} -1.66517 q^{31} -3.86860 q^{32} +2.94696 q^{33} +2.52044 q^{34} +6.97620 q^{35} +4.35263 q^{36} +0.184027 q^{37} +7.47290 q^{38} +4.80391 q^{39} +11.1154 q^{40} +12.0088 q^{41} -9.37999 q^{42} +0.542752 q^{43} -12.8270 q^{44} -1.87454 q^{45} +8.95825 q^{46} +8.00368 q^{47} -6.24016 q^{48} +6.85003 q^{49} +3.74566 q^{50} +1.00000 q^{51} -20.9097 q^{52} +5.77316 q^{53} +2.52044 q^{54} +5.52418 q^{55} +22.0677 q^{56} +2.96492 q^{57} +5.36651 q^{58} -4.76000 q^{59} +8.15917 q^{60} -8.87761 q^{61} +4.19697 q^{62} -3.72156 q^{63} -2.72973 q^{64} +9.00510 q^{65} -7.42764 q^{66} +6.37330 q^{67} -4.35263 q^{68} +3.55424 q^{69} -17.5831 q^{70} +0.652176 q^{71} -5.92968 q^{72} -10.6625 q^{73} -0.463829 q^{74} +1.48611 q^{75} -12.9052 q^{76} +10.9673 q^{77} -12.1080 q^{78} +5.92951 q^{79} -11.6974 q^{80} +1.00000 q^{81} -30.2675 q^{82} +7.36907 q^{83} +16.1986 q^{84} +1.87454 q^{85} -1.36797 q^{86} +2.12919 q^{87} +17.4745 q^{88} +13.2204 q^{89} +4.72466 q^{90} +17.8780 q^{91} -15.4703 q^{92} +1.66517 q^{93} -20.1728 q^{94} +5.55784 q^{95} +3.86860 q^{96} -6.53499 q^{97} -17.2651 q^{98} -2.94696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9	\( 48 q - q^{2} - 48 q^{3} + 45 q^{4} + q^{5} + q^{6} - 13 q^{7} - 6 q^{8} + 48 q^{9} - 20 q^{10} + 5 q^{11} - 45 q^{12} - 8 q^{13} + 4 q^{14} - q^{15} + 39 q^{16} - 48 q^{17} - q^{18} - 6 q^{19} + 6 q^{20} + 13 q^{21} - 35 q^{22} - 8 q^{23} + 6 q^{24} + 13 q^{25} + 17 q^{26} - 48 q^{27} - 38 q^{28} + q^{29} + 20 q^{30} - 21 q^{31} - 3 q^{32} - 5 q^{33} + q^{34} + 19 q^{35} + 45 q^{36} - 58 q^{37} - 14 q^{38} + 8 q^{39} - 54 q^{40} - 3 q^{41} - 4 q^{42} - 33 q^{43} + 2 q^{44} + q^{45} - 26 q^{46} + 9 q^{47} - 39 q^{48} + 11 q^{49} + 4 q^{50} + 48 q^{51} - 31 q^{52} - 33 q^{53} + q^{54} - 21 q^{55} + 6 q^{57} - 55 q^{58} + 77 q^{59} - 6 q^{60} - 29 q^{61} - 46 q^{62} - 13 q^{63} + 24 q^{64} - 49 q^{65} + 35 q^{66} - 44 q^{67} - 45 q^{68} + 8 q^{69} + 4 q^{70} + 22 q^{71} - 6 q^{72} - 63 q^{73} - 16 q^{74} - 13 q^{75} - 46 q^{76} - 30 q^{77} - 17 q^{78} - 46 q^{79} - 14 q^{80} + 48 q^{81} - 75 q^{82} + 11 q^{83} + 38 q^{84} - q^{85} + 8 q^{86} - q^{87} - 116 q^{88} + 10 q^{89} - 20 q^{90} - 67 q^{91} - 64 q^{92} + 21 q^{93} - 16 q^{94} - 8 q^{95} + 3 q^{96} - 96 q^{97} - 46 q^{98} + 5 q^{99}+O(q^{100}) \) 48 * q - q^2 - 48 * q^3 + 45 * q^4 + q^5 + q^6 - 13 * q^7 - 6 * q^8 + 48 * q^9 - 20 * q^10 + 5 * q^11 - 45 * q^12 - 8 * q^13 + 4 * q^14 - q^15 + 39 * q^16 - 48 * q^17 - q^18 - 6 * q^19 + 6 * q^20 + 13 * q^21 - 35 * q^22 - 8 * q^23 + 6 * q^24 + 13 * q^25 + 17 * q^26 - 48 * q^27 - 38 * q^28 + q^29 + 20 * q^30 - 21 * q^31 - 3 * q^32 - 5 * q^33 + q^34 + 19 * q^35 + 45 * q^36 - 58 * q^37 - 14 * q^38 + 8 * q^39 - 54 * q^40 - 3 * q^41 - 4 * q^42 - 33 * q^43 + 2 * q^44 + q^45 - 26 * q^46 + 9 * q^47 - 39 * q^48 + 11 * q^49 + 4 * q^50 + 48 * q^51 - 31 * q^52 - 33 * q^53 + q^54 - 21 * q^55 + 6 * q^57 - 55 * q^58 + 77 * q^59 - 6 * q^60 - 29 * q^61 - 46 * q^62 - 13 * q^63 + 24 * q^64 - 49 * q^65 + 35 * q^66 - 44 * q^67 - 45 * q^68 + 8 * q^69 + 4 * q^70 + 22 * q^71 - 6 * q^72 - 63 * q^73 - 16 * q^74 - 13 * q^75 - 46 * q^76 - 30 * q^77 - 17 * q^78 - 46 * q^79 - 14 * q^80 + 48 * q^81 - 75 * q^82 + 11 * q^83 + 38 * q^84 - q^85 + 8 * q^86 - q^87 - 116 * q^88 + 10 * q^89 - 20 * q^90 - 67 * q^91 - 64 * q^92 + 21 * q^93 - 16 * q^94 - 8 * q^95 + 3 * q^96 - 96 * q^97 - 46 * q^98 + 5 * q^99

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