LMFDB - Embedded newform 8002.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.76808 q^{3} +1.00000 q^{4} +4.07666 q^{5} -2.76808 q^{6} +2.61903 q^{7} +1.00000 q^{8} +4.66227 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.76808 q^{3} +1.00000 q^{4} +4.07666 q^{5} -2.76808 q^{6} +2.61903 q^{7} +1.00000 q^{8} +4.66227 q^{9} +4.07666 q^{10} -4.42706 q^{11} -2.76808 q^{12} -6.42164 q^{13} +2.61903 q^{14} -11.2845 q^{15} +1.00000 q^{16} -4.31227 q^{17} +4.66227 q^{18} -3.26346 q^{19} +4.07666 q^{20} -7.24969 q^{21} -4.42706 q^{22} +3.62139 q^{23} -2.76808 q^{24} +11.6192 q^{25} -6.42164 q^{26} -4.60130 q^{27} +2.61903 q^{28} -1.10363 q^{29} -11.2845 q^{30} +10.0846 q^{31} +1.00000 q^{32} +12.2544 q^{33} -4.31227 q^{34} +10.6769 q^{35} +4.66227 q^{36} -1.48795 q^{37} -3.26346 q^{38} +17.7756 q^{39} +4.07666 q^{40} -2.84887 q^{41} -7.24969 q^{42} -9.08959 q^{43} -4.42706 q^{44} +19.0065 q^{45} +3.62139 q^{46} -5.38514 q^{47} -2.76808 q^{48} -0.140671 q^{49} +11.6192 q^{50} +11.9367 q^{51} -6.42164 q^{52} -8.55357 q^{53} -4.60130 q^{54} -18.0476 q^{55} +2.61903 q^{56} +9.03353 q^{57} -1.10363 q^{58} +12.1824 q^{59} -11.2845 q^{60} -6.07490 q^{61} +10.0846 q^{62} +12.2106 q^{63} +1.00000 q^{64} -26.1788 q^{65} +12.2544 q^{66} -7.23324 q^{67} -4.31227 q^{68} -10.0243 q^{69} +10.6769 q^{70} +3.42135 q^{71} +4.66227 q^{72} -16.3826 q^{73} -1.48795 q^{74} -32.1627 q^{75} -3.26346 q^{76} -11.5946 q^{77} +17.7756 q^{78} +0.250564 q^{79} +4.07666 q^{80} -1.25004 q^{81} -2.84887 q^{82} +12.3640 q^{83} -7.24969 q^{84} -17.5796 q^{85} -9.08959 q^{86} +3.05494 q^{87} -4.42706 q^{88} -6.26669 q^{89} +19.0065 q^{90} -16.8185 q^{91} +3.62139 q^{92} -27.9149 q^{93} -5.38514 q^{94} -13.3040 q^{95} -2.76808 q^{96} +11.0161 q^{97} -0.140671 q^{98} -20.6401 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.76808	−1.59815	−0.799076	−	0.601230i	$-0.794678\pi$
$3$	−2.76808	−1.59815	−0.799076	+	0.601230i	$0.794678\pi$
$4$	1.00000	0.500000
$5$	4.07666	1.82314	0.911569	−	0.411148i	$-0.134872\pi$
$5$	4.07666	1.82314	0.911569	+	0.411148i	$0.134872\pi$
$6$	−2.76808	−1.13006
$7$	2.61903	0.989901	0.494951	−	0.868921i	$-0.335186\pi$
$7$	2.61903	0.989901	0.494951	+	0.868921i	$0.335186\pi$
$8$	1.00000	0.353553
$9$	4.66227	1.55409
$10$	4.07666	1.28915
$11$	−4.42706	−1.33481	−0.667404	−	0.744696i	$-0.732594\pi$
$11$	−4.42706	−1.33481	−0.667404	+	0.744696i	$0.732594\pi$
$12$	−2.76808	−0.799076
$13$	−6.42164	−1.78104	−0.890522	−	0.454941i	$-0.849660\pi$
$13$	−6.42164	−1.78104	−0.890522	+	0.454941i	$0.849660\pi$
$14$	2.61903	0.699966
$15$	−11.2845	−2.91365
$16$	1.00000	0.250000
$17$	−4.31227	−1.04588	−0.522939	−	0.852370i	$-0.675165\pi$
$17$	−4.31227	−1.04588	−0.522939	+	0.852370i	$0.675165\pi$
$18$	4.66227	1.09891
$19$	−3.26346	−0.748690	−0.374345	−	0.927289i	$-0.622132\pi$
$19$	−3.26346	−0.748690	−0.374345	+	0.927289i	$0.622132\pi$
$20$	4.07666	0.911569
$21$	−7.24969	−1.58201
$22$	−4.42706	−0.943851
$23$	3.62139	0.755113	0.377557	−	0.925987i	$-0.376764\pi$
$23$	3.62139	0.755113	0.377557	+	0.925987i	$0.376764\pi$
$24$	−2.76808	−0.565032
$25$	11.6192	2.32383
$26$	−6.42164	−1.25939
$27$	−4.60130	−0.885521
$28$	2.61903	0.494951
$29$	−1.10363	−0.204939	−0.102470	−	0.994736i	$-0.532674\pi$
$29$	−1.10363	−0.204939	−0.102470	+	0.994736i	$0.532674\pi$
$30$	−11.2845	−2.06026
$31$	10.0846	1.81124	0.905620	−	0.424091i	$-0.139406\pi$
$31$	10.0846	1.81124	0.905620	+	0.424091i	$0.139406\pi$
$32$	1.00000	0.176777
$33$	12.2544	2.13323
$34$	−4.31227	−0.739548
$35$	10.6769	1.80473
$36$	4.66227	0.777045
$37$	−1.48795	−0.244617	−0.122309	−	0.992492i	$-0.539030\pi$
$37$	−1.48795	−0.244617	−0.122309	+	0.992492i	$0.539030\pi$
$38$	−3.26346	−0.529404
$39$	17.7756	2.84638
$40$	4.07666	0.644576
$41$	−2.84887	−0.444919	−0.222459	−	0.974942i	$-0.571409\pi$
$41$	−2.84887	−0.444919	−0.222459	+	0.974942i	$0.571409\pi$
$42$	−7.24969	−1.11865
$43$	−9.08959	−1.38615	−0.693075	−	0.720866i	$-0.743744\pi$
$43$	−9.08959	−1.38615	−0.693075	+	0.720866i	$0.743744\pi$
$44$	−4.42706	−0.667404
$45$	19.0065	2.83332
$46$	3.62139	0.533946
$47$	−5.38514	−0.785504	−0.392752	−	0.919644i	$-0.628477\pi$
$47$	−5.38514	−0.785504	−0.392752	+	0.919644i	$0.628477\pi$
$48$	−2.76808	−0.399538
$49$	−0.140671	−0.0200958
$50$	11.6192	1.64320
$51$	11.9367	1.67147
$52$	−6.42164	−0.890522
$53$	−8.55357	−1.17492	−0.587461	−	0.809252i	$-0.699873\pi$
$53$	−8.55357	−1.17492	−0.587461	+	0.809252i	$0.699873\pi$
$54$	−4.60130	−0.626158
$55$	−18.0476	−2.43354
$56$	2.61903	0.349983
$57$	9.03353	1.19652
$58$	−1.10363	−0.144914
$59$	12.1824	1.58601	0.793006	−	0.609214i	$-0.208515\pi$
$59$	12.1824	1.58601	0.793006	+	0.609214i	$0.208515\pi$
$60$	−11.2845	−1.45683
$61$	−6.07490	−0.777811	−0.388906	−	0.921278i	$-0.627147\pi$
$61$	−6.07490	−0.777811	−0.388906	+	0.921278i	$0.627147\pi$
$62$	10.0846	1.28074
$63$	12.2106	1.53840
$64$	1.00000	0.125000
$65$	−26.1788	−3.24709
$66$	12.2544	1.50842
$67$	−7.23324	−0.883681	−0.441841	−	0.897094i	$-0.645674\pi$
$67$	−7.23324	−0.883681	−0.441841	+	0.897094i	$0.645674\pi$
$68$	−4.31227	−0.522939
$69$	−10.0243	−1.20679
$70$	10.6769	1.27613
$71$	3.42135	0.406040	0.203020	−	0.979175i	$-0.434924\pi$
$71$	3.42135	0.406040	0.203020	+	0.979175i	$0.434924\pi$
$72$	4.66227	0.549454
$73$	−16.3826	−1.91743	−0.958717	−	0.284362i	$-0.908218\pi$
$73$	−16.3826	−1.91743	−0.958717	+	0.284362i	$0.908218\pi$
$74$	−1.48795	−0.172970
$75$	−32.1627	−3.71383
$76$	−3.26346	−0.374345
$77$	−11.5946	−1.32133
$78$	17.7756	2.01269
$79$	0.250564	0.0281906	0.0140953	−	0.999901i	$-0.495513\pi$
$79$	0.250564	0.0281906	0.0140953	+	0.999901i	$0.495513\pi$
$80$	4.07666	0.455784
$81$	−1.25004	−0.138894
$82$	−2.84887	−0.314605
$83$	12.3640	1.35713	0.678565	−	0.734541i	$-0.262602\pi$
$83$	12.3640	1.35713	0.678565	+	0.734541i	$0.262602\pi$
$84$	−7.24969	−0.791006
$85$	−17.5796	−1.90678
$86$	−9.08959	−0.980155
$87$	3.05494	0.327524
$88$	−4.42706	−0.471926
$89$	−6.26669	−0.664268	−0.332134	−	0.943232i	$-0.607769\pi$
$89$	−6.26669	−0.664268	−0.332134	+	0.943232i	$0.607769\pi$
$90$	19.0065	2.00346
$91$	−16.8185	−1.76306
$92$	3.62139	0.377557
$93$	−27.9149	−2.89464
$94$	−5.38514	−0.555435
$95$	−13.3040	−1.36497
$96$	−2.76808	−0.282516
$97$	11.0161	1.11852	0.559259	−	0.828993i	$-0.311086\pi$
$97$	11.0161	1.11852	0.559259	+	0.828993i	$0.311086\pi$
$98$	−0.140671	−0.0142099
$99$	−20.6401	−2.07441
$100$	11.6192	1.16192
$101$	12.9098	1.28457	0.642285	−	0.766466i	$-0.277987\pi$
$101$	12.9098	1.28457	0.642285	+	0.766466i	$0.277987\pi$
$102$	11.9367	1.18191
$103$	1.88415	0.185651	0.0928253	−	0.995682i	$-0.470410\pi$
$103$	1.88415	0.185651	0.0928253	+	0.995682i	$0.470410\pi$
$104$	−6.42164	−0.629694
$105$	−29.5545	−2.88423
$106$	−8.55357	−0.830796
$107$	−16.7897	−1.62312	−0.811559	−	0.584271i	$-0.801381\pi$
$107$	−16.7897	−1.62312	−0.811559	+	0.584271i	$0.801381\pi$
$108$	−4.60130	−0.442760
$109$	8.89079	0.851583	0.425792	−	0.904821i	$-0.359996\pi$
$109$	8.89079	0.851583	0.425792	+	0.904821i	$0.359996\pi$
$110$	−18.0476	−1.72077
$111$	4.11876	0.390935
$112$	2.61903	0.247475
$113$	−3.81909	−0.359270	−0.179635	−	0.983733i	$-0.557492\pi$
$113$	−3.81909	−0.359270	−0.179635	+	0.983733i	$0.557492\pi$
$114$	9.03353	0.846068
$115$	14.7632	1.37667
$116$	−1.10363	−0.102470
$117$	−29.9394	−2.76790
$118$	12.1824	1.12148
$119$	−11.2940	−1.03532
$120$	−11.2845	−1.03013
$121$	8.59882	0.781711
$122$	−6.07490	−0.549996
$123$	7.88591	0.711048
$124$	10.0846	0.905620
$125$	26.9840	2.41352
$126$	12.2106	1.08781
$127$	−14.8373	−1.31660	−0.658299	−	0.752756i	$-0.728724\pi$
$127$	−14.8373	−1.31660	−0.658299	+	0.752756i	$0.728724\pi$
$128$	1.00000	0.0883883
$129$	25.1607	2.21528
$130$	−26.1788	−2.29604
$131$	−12.5690	−1.09816	−0.549081	−	0.835769i	$-0.685022\pi$
$131$	−12.5690	−1.09816	−0.549081	+	0.835769i	$0.685022\pi$
$132$	12.2544	1.06661
$133$	−8.54712	−0.741129
$134$	−7.23324	−0.624857
$135$	−18.7579	−1.61443
$136$	−4.31227	−0.369774
$137$	−10.5628	−0.902442	−0.451221	−	0.892412i	$-0.649011\pi$
$137$	−10.5628	−0.902442	−0.451221	+	0.892412i	$0.649011\pi$
$138$	−10.0243	−0.853326
$139$	−1.94959	−0.165362	−0.0826812	−	0.996576i	$-0.526348\pi$
$139$	−1.94959	−0.165362	−0.0826812	+	0.996576i	$0.526348\pi$
$140$	10.6769	0.902363
$141$	14.9065	1.25535
$142$	3.42135	0.287114
$143$	28.4290	2.37735
$144$	4.66227	0.388523
$145$	−4.49913	−0.373632
$146$	−16.3826	−1.35583
$147$	0.389388	0.0321162
$148$	−1.48795	−0.122309
$149$	−4.53225	−0.371296	−0.185648	−	0.982616i	$-0.559438\pi$
$149$	−4.53225	−0.371296	−0.185648	+	0.982616i	$0.559438\pi$
$150$	−32.1627	−2.62608
$151$	8.66262	0.704954	0.352477	−	0.935820i	$-0.385339\pi$
$151$	8.66262	0.704954	0.352477	+	0.935820i	$0.385339\pi$
$152$	−3.26346	−0.264702
$153$	−20.1050	−1.62539
$154$	−11.5946	−0.934319
$155$	41.1113	3.30214
$156$	17.7756	1.42319
$157$	−23.2800	−1.85794	−0.928972	−	0.370150i	$-0.879306\pi$
$157$	−23.2800	−1.85794	−0.928972	+	0.370150i	$0.879306\pi$
$158$	0.250564	0.0199338
$159$	23.6770	1.87771
$160$	4.07666	0.322288
$161$	9.48455	0.747487
$162$	−1.25004	−0.0982126
$163$	−2.91089	−0.227999	−0.113999	−	0.993481i	$-0.536366\pi$
$163$	−2.91089	−0.227999	−0.113999	+	0.993481i	$0.536366\pi$
$164$	−2.84887	−0.222459
$165$	49.9572	3.88916
$166$	12.3640	0.959635
$167$	−18.5603	−1.43624	−0.718118	−	0.695921i	$-0.754996\pi$
$167$	−18.5603	−1.43624	−0.718118	+	0.695921i	$0.754996\pi$
$168$	−7.24969	−0.559326
$169$	28.2375	2.17211
$170$	−17.5796	−1.34830
$171$	−15.2152	−1.16353
$172$	−9.08959	−0.693075
$173$	−9.08924	−0.691042	−0.345521	−	0.938411i	$-0.612298\pi$
$173$	−9.08924	−0.691042	−0.345521	+	0.938411i	$0.612298\pi$
$174$	3.05494	0.231594
$175$	30.4309	2.30036
$176$	−4.42706	−0.333702
$177$	−33.7218	−2.53469
$178$	−6.26669	−0.469708
$179$	12.1436	0.907659	0.453829	−	0.891089i	$-0.350058\pi$
$179$	12.1436	0.907659	0.453829	+	0.891089i	$0.350058\pi$
$180$	19.0065	1.41666
$181$	−6.12127	−0.454990	−0.227495	−	0.973779i	$-0.573054\pi$
$181$	−6.12127	−0.454990	−0.227495	+	0.973779i	$0.573054\pi$
$182$	−16.8185	−1.24667
$183$	16.8158	1.24306
$184$	3.62139	0.266973
$185$	−6.06586	−0.445971
$186$	−27.9149	−2.04682
$187$	19.0906	1.39605
$188$	−5.38514	−0.392752
$189$	−12.0510	−0.876578
$190$	−13.3040	−0.965176
$191$	−13.8874	−1.00486	−0.502428	−	0.864619i	$-0.667560\pi$
$191$	−13.8874	−1.00486	−0.502428	+	0.864619i	$0.667560\pi$
$192$	−2.76808	−0.199769
$193$	−8.86002	−0.637758	−0.318879	−	0.947795i	$-0.603306\pi$
$193$	−8.86002	−0.637758	−0.318879	+	0.947795i	$0.603306\pi$
$194$	11.0161	0.790912
$195$	72.4652	5.18934
$196$	−0.140671	−0.0100479
$197$	−0.0391097	−0.00278645	−0.00139323	−	0.999999i	$-0.500443\pi$
$197$	−0.0391097	−0.00278645	−0.00139323	+	0.999999i	$0.500443\pi$
$198$	−20.6401	−1.46683
$199$	14.8184	1.05045	0.525224	−	0.850964i	$-0.323981\pi$
$199$	14.8184	1.05045	0.525224	+	0.850964i	$0.323981\pi$
$200$	11.6192	0.821598
$201$	20.0222	1.41226
$202$	12.9098	0.908328
$203$	−2.89044	−0.202869
$204$	11.9367	0.835736
$205$	−11.6139	−0.811148
$206$	1.88415	0.131275
$207$	16.8839	1.17351
$208$	−6.42164	−0.445261
$209$	14.4475	0.999357
$210$	−29.5545	−2.03946
$211$	−13.3946	−0.922125	−0.461062	−	0.887368i	$-0.652532\pi$
$211$	−13.3946	−0.922125	−0.461062	+	0.887368i	$0.652532\pi$
$212$	−8.55357	−0.587461
$213$	−9.47058	−0.648914
$214$	−16.7897	−1.14772
$215$	−37.0552	−2.52714
$216$	−4.60130	−0.313079
$217$	26.4118	1.79295
$218$	8.89079	0.602160
$219$	45.3483	3.06435
$220$	−18.0476	−1.21677
$221$	27.6918	1.86275
$222$	4.11876	0.276433
$223$	20.0938	1.34558	0.672789	−	0.739834i	$-0.265096\pi$
$223$	20.0938	1.34558	0.672789	+	0.739834i	$0.265096\pi$
$224$	2.61903	0.174991
$225$	54.1716	3.61144
$226$	−3.81909	−0.254042
$227$	−13.8976	−0.922416	−0.461208	−	0.887292i	$-0.652584\pi$
$227$	−13.8976	−0.922416	−0.461208	+	0.887292i	$0.652584\pi$
$228$	9.03353	0.598260
$229$	−18.1092	−1.19669	−0.598345	−	0.801239i	$-0.704175\pi$
$229$	−18.1092	−1.19669	−0.598345	+	0.801239i	$0.704175\pi$
$230$	14.7632	0.973456
$231$	32.0948	2.11168
$232$	−1.10363	−0.0724569
$233$	−0.852296	−0.0558358	−0.0279179	−	0.999610i	$-0.508888\pi$
$233$	−0.852296	−0.0558358	−0.0279179	+	0.999610i	$0.508888\pi$
$234$	−29.9394	−1.95720
$235$	−21.9534	−1.43208
$236$	12.1824	0.793006
$237$	−0.693581	−0.0450529
$238$	−11.2940	−0.732079
$239$	12.4646	0.806271	0.403135	−	0.915140i	$-0.367920\pi$
$239$	12.4646	0.806271	0.403135	+	0.915140i	$0.367920\pi$
$240$	−11.2845	−0.728413
$241$	1.75884	0.113297	0.0566484	−	0.998394i	$-0.481959\pi$
$241$	1.75884	0.113297	0.0566484	+	0.998394i	$0.481959\pi$
$242$	8.59882	0.552753
$243$	17.2641	1.10749
$244$	−6.07490	−0.388906
$245$	−0.573466	−0.0366374
$246$	7.88591	0.502787
$247$	20.9568	1.33345
$248$	10.0846	0.640370
$249$	−34.2246	−2.16890
$250$	26.9840	1.70662
$251$	−17.6318	−1.11291	−0.556454	−	0.830879i	$-0.687838\pi$
$251$	−17.6318	−1.11291	−0.556454	+	0.830879i	$0.687838\pi$
$252$	12.2106	0.769198
$253$	−16.0321	−1.00793
$254$	−14.8373	−0.930976
$255$	48.6619	3.04732
$256$	1.00000	0.0625000
$257$	−11.5580	−0.720970	−0.360485	−	0.932765i	$-0.617389\pi$
$257$	−11.5580	−0.720970	−0.360485	+	0.932765i	$0.617389\pi$
$258$	25.1607	1.56644
$259$	−3.89698	−0.242147
$260$	−26.1788	−1.62354
$261$	−5.14543	−0.318494
$262$	−12.5690	−0.776518
$263$	24.5521	1.51395	0.756975	−	0.653444i	$-0.226677\pi$
$263$	24.5521	1.51395	0.756975	+	0.653444i	$0.226677\pi$
$264$	12.2544	0.754209
$265$	−34.8700	−2.14205
$266$	−8.54712	−0.524057
$267$	17.3467	1.06160
$268$	−7.23324	−0.441841
$269$	−16.4425	−1.00252	−0.501258	−	0.865298i	$-0.667129\pi$
$269$	−16.4425	−1.00252	−0.501258	+	0.865298i	$0.667129\pi$
$270$	−18.7579	−1.14157
$271$	−27.0026	−1.64029	−0.820146	−	0.572155i	$-0.806108\pi$
$271$	−27.0026	−1.64029	−0.820146	+	0.572155i	$0.806108\pi$
$272$	−4.31227	−0.261470
$273$	46.5549	2.81763
$274$	−10.5628	−0.638123
$275$	−51.4386	−3.10187
$276$	−10.0243	−0.603393
$277$	20.4994	1.23169	0.615843	−	0.787869i	$-0.288815\pi$
$277$	20.4994	1.23169	0.615843	+	0.787869i	$0.288815\pi$
$278$	−1.94959	−0.116929
$279$	47.0169	2.81483
$280$	10.6769	0.638067
$281$	−11.4124	−0.680807	−0.340404	−	0.940279i	$-0.610564\pi$
$281$	−11.4124	−0.680807	−0.340404	+	0.940279i	$0.610564\pi$
$282$	14.9065	0.887670
$283$	27.2109	1.61752	0.808760	−	0.588139i	$-0.200139\pi$
$283$	27.2109	1.61752	0.808760	+	0.588139i	$0.200139\pi$
$284$	3.42135	0.203020
$285$	36.8266	2.18142
$286$	28.4290	1.68104
$287$	−7.46129	−0.440426
$288$	4.66227	0.274727
$289$	1.59565	0.0938618
$290$	−4.49913	−0.264198
$291$	−30.4935	−1.78756
$292$	−16.3826	−0.958717
$293$	−17.6980	−1.03393	−0.516964	−	0.856007i	$-0.672938\pi$
$293$	−17.6980	−1.03393	−0.516964	+	0.856007i	$0.672938\pi$
$294$	0.389388	0.0227096
$295$	49.6634	2.89152
$296$	−1.48795	−0.0864852
$297$	20.3702	1.18200
$298$	−4.53225	−0.262546
$299$	−23.2553	−1.34489
$300$	−32.1627	−1.85692
$301$	−23.8059	−1.37215
$302$	8.66262	0.498478
$303$	−35.7353	−2.05294
$304$	−3.26346	−0.187173
$305$	−24.7653	−1.41806
$306$	−20.1050	−1.14932
$307$	1.99344	0.113772	0.0568858	−	0.998381i	$-0.481883\pi$
$307$	1.99344	0.113772	0.0568858	+	0.998381i	$0.481883\pi$
$308$	−11.5946	−0.660664
$309$	−5.21547	−0.296698
$310$	41.1113	2.33496
$311$	8.59382	0.487311	0.243655	−	0.969862i	$-0.421653\pi$
$311$	8.59382	0.487311	0.243655	+	0.969862i	$0.421653\pi$
$312$	17.7756	1.00635
$313$	−6.30633	−0.356455	−0.178228	−	0.983989i	$-0.557036\pi$
$313$	−6.30633	−0.356455	−0.178228	+	0.983989i	$0.557036\pi$
$314$	−23.2800	−1.31376
$315$	49.7786	2.80471
$316$	0.250564	0.0140953
$317$	21.9281	1.23160	0.615802	−	0.787901i	$-0.288832\pi$
$317$	21.9281	1.23160	0.615802	+	0.787901i	$0.288832\pi$
$318$	23.6770	1.32774
$319$	4.88583	0.273554
$320$	4.07666	0.227892
$321$	46.4751	2.59399
$322$	9.48455	0.528553
$323$	14.0729	0.783039
$324$	−1.25004	−0.0694468
$325$	−74.6140	−4.13884
$326$	−2.91089	−0.161219
$327$	−24.6104	−1.36096
$328$	−2.84887	−0.157303
$329$	−14.1039	−0.777571
$330$	49.9572	2.75005
$331$	16.8527	0.926308	0.463154	−	0.886278i	$-0.346718\pi$
$331$	16.8527	0.926308	0.463154	+	0.886278i	$0.346718\pi$
$332$	12.3640	0.678565
$333$	−6.93721	−0.380157
$334$	−18.5603	−1.01557
$335$	−29.4875	−1.61107
$336$	−7.24969	−0.395503
$337$	0.979731	0.0533693	0.0266847	−	0.999644i	$-0.491505\pi$
$337$	0.979731	0.0533693	0.0266847	+	0.999644i	$0.491505\pi$
$338$	28.2375	1.53592
$339$	10.5716	0.574168
$340$	−17.5796	−0.953390
$341$	−44.6449	−2.41766
$342$	−15.2152	−0.822741
$343$	−18.7016	−1.00979
$344$	−9.08959	−0.490078
$345$	−40.8657	−2.20014
$346$	−9.08924	−0.488640
$347$	31.1263	1.67095	0.835474	−	0.549530i	$-0.185193\pi$
$347$	31.1263	1.67095	0.835474	+	0.549530i	$0.185193\pi$
$348$	3.05494	0.163762
$349$	−15.6169	−0.835953	−0.417977	−	0.908458i	$-0.637261\pi$
$349$	−15.6169	−0.835953	−0.417977	+	0.908458i	$0.637261\pi$
$350$	30.4309	1.62660
$351$	29.5479	1.57715
$352$	−4.42706	−0.235963
$353$	0.904647	0.0481495	0.0240748	−	0.999710i	$-0.492336\pi$
$353$	0.904647	0.0481495	0.0240748	+	0.999710i	$0.492336\pi$
$354$	−33.7218	−1.79230
$355$	13.9477	0.740267
$356$	−6.26669	−0.332134
$357$	31.2626	1.65459
$358$	12.1436	0.641812
$359$	14.0762	0.742914	0.371457	−	0.928450i	$-0.378858\pi$
$359$	14.0762	0.742914	0.371457	+	0.928450i	$0.378858\pi$
$360$	19.0065	1.00173
$361$	−8.34980	−0.439463
$362$	−6.12127	−0.321727
$363$	−23.8022	−1.24929
$364$	−16.8185	−0.881528
$365$	−66.7861	−3.49575
$366$	16.8158	0.878977
$367$	24.3904	1.27317	0.636584	−	0.771208i	$-0.280347\pi$
$367$	24.3904	1.27317	0.636584	+	0.771208i	$0.280347\pi$
$368$	3.62139	0.188778
$369$	−13.2822	−0.691444
$370$	−6.06586	−0.315349
$371$	−22.4021	−1.16306
$372$	−27.9149	−1.44732
$373$	17.3071	0.896130	0.448065	−	0.894001i	$-0.352113\pi$
$373$	17.3071	0.896130	0.448065	+	0.894001i	$0.352113\pi$
$374$	19.0906	0.987154
$375$	−74.6939	−3.85718
$376$	−5.38514	−0.277717
$377$	7.08712	0.365005
$378$	−12.0510	−0.619834
$379$	−1.53442	−0.0788181	−0.0394090	−	0.999223i	$-0.512548\pi$
$379$	−1.53442	−0.0788181	−0.0394090	+	0.999223i	$0.512548\pi$
$380$	−13.3040	−0.682483
$381$	41.0709	2.10412
$382$	−13.8874	−0.710540
$383$	15.2502	0.779250	0.389625	−	0.920974i	$-0.372605\pi$
$383$	15.2502	0.779250	0.389625	+	0.920974i	$0.372605\pi$
$384$	−2.76808	−0.141258
$385$	−47.2672	−2.40896
$386$	−8.86002	−0.450963
$387$	−42.3781	−2.15420
$388$	11.0161	0.559259
$389$	9.01331	0.456993	0.228497	−	0.973545i	$-0.426619\pi$
$389$	9.01331	0.456993	0.228497	+	0.973545i	$0.426619\pi$
$390$	72.4652	3.66942
$391$	−15.6164	−0.789756
$392$	−0.140671	−0.00710494
$393$	34.7921	1.75503
$394$	−0.0391097	−0.00197032
$395$	1.02146	0.0513954
$396$	−20.6401	−1.03721
$397$	13.3055	0.667786	0.333893	−	0.942611i	$-0.391638\pi$
$397$	13.3055	0.667786	0.333893	+	0.942611i	$0.391638\pi$
$398$	14.8184	0.742779
$399$	23.6591	1.18444
$400$	11.6192	0.580958
$401$	21.7260	1.08495	0.542473	−	0.840073i	$-0.317488\pi$
$401$	21.7260	1.08495	0.542473	+	0.840073i	$0.317488\pi$
$402$	20.0222	0.998616
$403$	−64.7594	−3.22589
$404$	12.9098	0.642285
$405$	−5.09600	−0.253222
$406$	−2.89044	−0.143450
$407$	6.58723	0.326517
$408$	11.9367	0.590955
$409$	−18.7793	−0.928576	−0.464288	−	0.885684i	$-0.653690\pi$
$409$	−18.7793	−0.928576	−0.464288	+	0.885684i	$0.653690\pi$
$410$	−11.6139	−0.573569
$411$	29.2387	1.44224
$412$	1.88415	0.0928253
$413$	31.9061	1.56999
$414$	16.8839	0.829800
$415$	50.4040	2.47423
$416$	−6.42164	−0.314847
$417$	5.39663	0.264274
$418$	14.4475	0.706652
$419$	−31.9674	−1.56171	−0.780855	−	0.624712i	$-0.785216\pi$
$419$	−31.9674	−1.56171	−0.780855	+	0.624712i	$0.785216\pi$
$420$	−29.5545	−1.44211
$421$	−0.152108	−0.00741329	−0.00370664	−	0.999993i	$-0.501180\pi$
$421$	−0.152108	−0.00741329	−0.00370664	+	0.999993i	$0.501180\pi$
$422$	−13.3946	−0.652040
$423$	−25.1070	−1.22074
$424$	−8.55357	−0.415398
$425$	−50.1049	−2.43044
$426$	−9.47058	−0.458851
$427$	−15.9104	−0.769956
$428$	−16.7897	−0.811559
$429$	−78.6937	−3.79937
$430$	−37.0552	−1.78696
$431$	20.7945	1.00164	0.500819	−	0.865552i	$-0.333032\pi$
$431$	20.7945	1.00164	0.500819	+	0.865552i	$0.333032\pi$
$432$	−4.60130	−0.221380
$433$	16.8286	0.808731	0.404365	−	0.914598i	$-0.367492\pi$
$433$	16.8286	0.808731	0.404365	+	0.914598i	$0.367492\pi$
$434$	26.4118	1.26781
$435$	12.4539	0.597121
$436$	8.89079	0.425792
$437$	−11.8183	−0.565346
$438$	45.3483	2.16682
$439$	9.79890	0.467676	0.233838	−	0.972276i	$-0.424871\pi$
$439$	9.79890	0.467676	0.233838	+	0.972276i	$0.424871\pi$
$440$	−18.0476	−0.860385
$441$	−0.655845	−0.0312307
$442$	27.6918	1.31717
$443$	−14.8303	−0.704610	−0.352305	−	0.935885i	$-0.614602\pi$
$443$	−14.8303	−0.704610	−0.352305	+	0.935885i	$0.614602\pi$
$444$	4.11876	0.195468
$445$	−25.5472	−1.21105
$446$	20.0938	0.951467
$447$	12.5456	0.593388
$448$	2.61903	0.123738
$449$	16.6571	0.786098	0.393049	−	0.919518i	$-0.371420\pi$
$449$	16.6571	0.786098	0.393049	+	0.919518i	$0.371420\pi$
$450$	54.1716	2.55368
$451$	12.6121	0.593881
$452$	−3.81909	−0.179635
$453$	−23.9788	−1.12662
$454$	−13.8976	−0.652247
$455$	−68.5632	−3.21429
$456$	9.03353	0.423034
$457$	−4.84273	−0.226533	−0.113267	−	0.993565i	$-0.536131\pi$
$457$	−4.84273	−0.226533	−0.113267	+	0.993565i	$0.536131\pi$
$458$	−18.1092	−0.846187
$459$	19.8420	0.926147
$460$	14.7632	0.688337
$461$	−12.0470	−0.561083	−0.280541	−	0.959842i	$-0.590514\pi$
$461$	−12.0470	−0.561083	−0.280541	+	0.959842i	$0.590514\pi$
$462$	32.0948	1.49318
$463$	29.5573	1.37364	0.686821	−	0.726827i	$-0.259006\pi$
$463$	29.5573	1.37364	0.686821	+	0.726827i	$0.259006\pi$
$464$	−1.10363	−0.0512348
$465$	−113.799	−5.27732
$466$	−0.852296	−0.0394819
$467$	−26.9216	−1.24578	−0.622891	−	0.782309i	$-0.714042\pi$
$467$	−26.9216	−1.24578	−0.622891	+	0.782309i	$0.714042\pi$
$468$	−29.9394	−1.38395
$469$	−18.9441	−0.874757
$470$	−21.9534	−1.01263
$471$	64.4408	2.96928
$472$	12.1824	0.560740
$473$	40.2401	1.85024
$474$	−0.693581	−0.0318572
$475$	−37.9187	−1.73983
$476$	−11.2940	−0.517658
$477$	−39.8790	−1.82594
$478$	12.4646	0.570120
$479$	−4.54626	−0.207724	−0.103862	−	0.994592i	$-0.533120\pi$
$479$	−4.54626	−0.207724	−0.103862	+	0.994592i	$0.533120\pi$
$480$	−11.2845	−0.515066
$481$	9.55507	0.435674
$482$	1.75884	0.0801129
$483$	−26.2540	−1.19460
$484$	8.59882	0.390855
$485$	44.9090	2.03921
$486$	17.2641	0.783116
$487$	−18.4525	−0.836165	−0.418082	−	0.908409i	$-0.637298\pi$
$487$	−18.4525	−0.836165	−0.418082	+	0.908409i	$0.637298\pi$
$488$	−6.07490	−0.274998
$489$	8.05759	0.364377
$490$	−0.573466	−0.0259066
$491$	24.6500	1.11244	0.556220	−	0.831035i	$-0.312251\pi$
$491$	24.6500	1.11244	0.556220	+	0.831035i	$0.312251\pi$
$492$	7.88591	0.355524
$493$	4.75915	0.214341
$494$	20.9568	0.942891
$495$	−84.1428	−3.78194
$496$	10.0846	0.452810
$497$	8.96063	0.401939
$498$	−34.2246	−1.53364
$499$	−40.5470	−1.81513	−0.907566	−	0.419910i	$-0.862062\pi$
$499$	−40.5470	−1.81513	−0.907566	+	0.419910i	$0.862062\pi$
$500$	26.9840	1.20676
$501$	51.3763	2.29532
$502$	−17.6318	−0.786945
$503$	5.55903	0.247865	0.123932	−	0.992291i	$-0.460449\pi$
$503$	5.55903	0.247865	0.123932	+	0.992291i	$0.460449\pi$
$504$	12.2106	0.543905
$505$	52.6287	2.34195
$506$	−16.0321	−0.712714
$507$	−78.1636	−3.47137
$508$	−14.8373	−0.658299
$509$	−42.5344	−1.88530	−0.942651	−	0.333779i	$-0.891676\pi$
$509$	−42.5344	−1.88530	−0.942651	+	0.333779i	$0.891676\pi$
$510$	48.6619	2.15478
$511$	−42.9065	−1.89807
$512$	1.00000	0.0441942
$513$	15.0162	0.662981
$514$	−11.5580	−0.509803
$515$	7.68103	0.338467
$516$	25.1607	1.10764
$517$	23.8403	1.04850
$518$	−3.89698	−0.171224
$519$	25.1597	1.10439
$520$	−26.1788	−1.14802
$521$	6.56873	0.287781	0.143891	−	0.989594i	$-0.454039\pi$
$521$	6.56873	0.287781	0.143891	+	0.989594i	$0.454039\pi$
$522$	−5.14543	−0.225209
$523$	5.40387	0.236295	0.118147	−	0.992996i	$-0.462304\pi$
$523$	5.40387	0.236295	0.118147	+	0.992996i	$0.462304\pi$
$524$	−12.5690	−0.549081
$525$	−84.2353	−3.67633
$526$	24.5521	1.07052
$527$	−43.4873	−1.89434
$528$	12.2544	0.533306
$529$	−9.88550	−0.429804
$530$	−34.8700	−1.51465
$531$	56.7976	2.46481
$532$	−8.54712	−0.370565
$533$	18.2944	0.792420
$534$	17.3467	0.750665
$535$	−68.4457	−2.95917
$536$	−7.23324	−0.312428
$537$	−33.6146	−1.45058
$538$	−16.4425	−0.708886
$539$	0.622757	0.0268240
$540$	−18.7579	−0.807213
$541$	−2.60376	−0.111944	−0.0559721	−	0.998432i	$-0.517826\pi$
$541$	−2.60376	−0.111944	−0.0559721	+	0.998432i	$0.517826\pi$
$542$	−27.0026	−1.15986
$543$	16.9442	0.727144
$544$	−4.31227	−0.184887
$545$	36.2447	1.55255
$546$	46.5549	1.99237
$547$	−19.5946	−0.837807	−0.418903	−	0.908031i	$-0.637585\pi$
$547$	−19.5946	−0.837807	−0.418903	+	0.908031i	$0.637585\pi$
$548$	−10.5628	−0.451221
$549$	−28.3228	−1.20879
$550$	−51.4386	−2.19335
$551$	3.60166	0.153436
$552$	−10.0243	−0.426663
$553$	0.656235	0.0279059
$554$	20.4994	0.870934
$555$	16.7908	0.712729
$556$	−1.94959	−0.0826812
$557$	−13.7897	−0.584289	−0.292144	−	0.956374i	$-0.594369\pi$
$557$	−13.7897	−0.584289	−0.292144	+	0.956374i	$0.594369\pi$
$558$	47.0169	1.99038
$559$	58.3701	2.46879
$560$	10.6769	0.451181
$561$	−52.8444	−2.23109
$562$	−11.4124	−0.481404
$563$	−28.1674	−1.18712	−0.593558	−	0.804791i	$-0.702277\pi$
$563$	−28.1674	−1.18712	−0.593558	+	0.804791i	$0.702277\pi$
$564$	14.9065	0.627677
$565$	−15.5691	−0.654998
$566$	27.2109	1.14376
$567$	−3.27390	−0.137491
$568$	3.42135	0.143557
$569$	26.6749	1.11827	0.559135	−	0.829077i	$-0.311133\pi$
$569$	26.6749	1.11827	0.559135	+	0.829077i	$0.311133\pi$
$570$	36.8266	1.54250
$571$	−21.2917	−0.891031	−0.445516	−	0.895274i	$-0.646980\pi$
$571$	−21.2917	−0.891031	−0.445516	+	0.895274i	$0.646980\pi$
$572$	28.4290	1.18867
$573$	38.4414	1.60591
$574$	−7.46129	−0.311428
$575$	42.0775	1.75475
$576$	4.66227	0.194261
$577$	−28.7089	−1.19517	−0.597584	−	0.801806i	$-0.703873\pi$
$577$	−28.7089	−1.19517	−0.597584	+	0.801806i	$0.703873\pi$
$578$	1.59565	0.0663703
$579$	24.5252	1.01923
$580$	−4.49913	−0.186816
$581$	32.3818	1.34342
$582$	−30.4935	−1.26400
$583$	37.8671	1.56830
$584$	−16.3826	−0.677915
$585$	−122.053	−5.04627
$586$	−17.6980	−0.731098
$587$	−4.92944	−0.203460	−0.101730	−	0.994812i	$-0.532438\pi$
$587$	−4.92944	−0.203460	−0.101730	+	0.994812i	$0.532438\pi$
$588$	0.389388	0.0160581
$589$	−32.9106	−1.35606
$590$	49.6634	2.04461
$591$	0.108259	0.00445317
$592$	−1.48795	−0.0611543
$593$	−8.14147	−0.334330	−0.167165	−	0.985929i	$-0.553461\pi$
$593$	−8.14147	−0.334330	−0.167165	+	0.985929i	$0.553461\pi$
$594$	20.3702	0.835800
$595$	−46.0417	−1.88752
$596$	−4.53225	−0.185648
$597$	−41.0185	−1.67878
$598$	−23.2553	−0.950980
$599$	−5.47770	−0.223813	−0.111906	−	0.993719i	$-0.535696\pi$
$599$	−5.47770	−0.223813	−0.111906	+	0.993719i	$0.535696\pi$
$600$	−32.1627	−1.31304
$601$	−11.2020	−0.456938	−0.228469	−	0.973551i	$-0.573372\pi$
$601$	−11.2020	−0.456938	−0.228469	+	0.973551i	$0.573372\pi$
$602$	−23.8059	−0.970257
$603$	−33.7233	−1.37332
$604$	8.66262	0.352477
$605$	35.0544	1.42517
$606$	−35.7353	−1.45165
$607$	44.3486	1.80005	0.900027	−	0.435834i	$-0.143547\pi$
$607$	44.3486	1.80005	0.900027	+	0.435834i	$0.143547\pi$
$608$	−3.26346	−0.132351
$609$	8.00098	0.324216
$610$	−24.7653	−1.00272
$611$	34.5815	1.39902
$612$	−20.1050	−0.812695
$613$	5.82769	0.235378	0.117689	−	0.993050i	$-0.462451\pi$
$613$	5.82769	0.235378	0.117689	+	0.993050i	$0.462451\pi$
$614$	1.99344	0.0804487
$615$	32.1481	1.29634
$616$	−11.5946	−0.467160
$617$	−9.86089	−0.396985	−0.198492	−	0.980102i	$-0.563604\pi$
$617$	−9.86089	−0.396985	−0.198492	+	0.980102i	$0.563604\pi$
$618$	−5.21547	−0.209797
$619$	−11.7007	−0.470289	−0.235144	−	0.971960i	$-0.575556\pi$
$619$	−11.7007	−0.470289	−0.235144	+	0.971960i	$0.575556\pi$
$620$	41.1113	1.65107
$621$	−16.6631	−0.668668
$622$	8.59382	0.344581
$623$	−16.4127	−0.657560
$624$	17.7756	0.711594
$625$	51.9089	2.07636
$626$	−6.30633	−0.252052
$627$	−39.9920	−1.59712
$628$	−23.2800	−0.928972
$629$	6.41643	0.255840
$630$	49.7786	1.98323
$631$	28.9703	1.15329	0.576644	−	0.816996i	$-0.304362\pi$
$631$	28.9703	1.15329	0.576644	+	0.816996i	$0.304362\pi$
$632$	0.250564	0.00996689
$633$	37.0774	1.47370
$634$	21.9281	0.870875
$635$	−60.4866	−2.40034
$636$	23.6770	0.938853
$637$	0.903337	0.0357915
$638$	4.88583	0.193432
$639$	15.9513	0.631023
$640$	4.07666	0.161144
$641$	0.106120	0.00419148	0.00209574	−	0.999998i	$-0.499333\pi$
$641$	0.106120	0.00419148	0.00209574	+	0.999998i	$0.499333\pi$
$642$	46.4751	1.83423
$643$	−1.78669	−0.0704604	−0.0352302	−	0.999379i	$-0.511216\pi$
$643$	−1.78669	−0.0704604	−0.0352302	+	0.999379i	$0.511216\pi$
$644$	9.48455	0.373744
$645$	102.572	4.03875
$646$	14.0729	0.553692
$647$	−19.6340	−0.771892	−0.385946	−	0.922521i	$-0.626125\pi$
$647$	−19.6340	−0.771892	−0.385946	+	0.922521i	$0.626125\pi$
$648$	−1.25004	−0.0491063
$649$	−53.9321	−2.11702
$650$	−74.6140	−2.92660
$651$	−73.1099	−2.86540
$652$	−2.91089	−0.113999
$653$	−6.77993	−0.265319	−0.132660	−	0.991162i	$-0.542352\pi$
$653$	−6.77993	−0.265319	−0.132660	+	0.991162i	$0.542352\pi$
$654$	−24.6104	−0.962344
$655$	−51.2397	−2.00210
$656$	−2.84887	−0.111230
$657$	−76.3799	−2.97987
$658$	−14.1039	−0.549826
$659$	−21.2496	−0.827767	−0.413884	−	0.910330i	$-0.635828\pi$
$659$	−21.2496	−0.827767	−0.413884	+	0.910330i	$0.635828\pi$
$660$	49.9572	1.94458
$661$	−21.5810	−0.839402	−0.419701	−	0.907662i	$-0.637865\pi$
$661$	−21.5810	−0.839402	−0.419701	+	0.907662i	$0.637865\pi$
$662$	16.8527	0.654999
$663$	−76.6532	−2.97697
$664$	12.3640	0.479818
$665$	−34.8437	−1.35118
$666$	−6.93721	−0.268812
$667$	−3.99668	−0.154752
$668$	−18.5603	−0.718118
$669$	−55.6212	−2.15044
$670$	−29.4875	−1.13920
$671$	26.8939	1.03823
$672$	−7.24969	−0.279663
$673$	−41.7443	−1.60912	−0.804562	−	0.593869i	$-0.797600\pi$
$673$	−41.7443	−1.60912	−0.804562	+	0.593869i	$0.797600\pi$
$674$	0.979731	0.0377378
$675$	−53.4632	−2.05780
$676$	28.2375	1.08606
$677$	1.35759	0.0521765	0.0260882	−	0.999660i	$-0.491695\pi$
$677$	1.35759	0.0521765	0.0260882	+	0.999660i	$0.491695\pi$
$678$	10.5716	0.405998
$679$	28.8516	1.10722
$680$	−17.5796	−0.674149
$681$	38.4697	1.47416
$682$	−44.6449	−1.70954
$683$	12.0638	0.461607	0.230803	−	0.973000i	$-0.425865\pi$
$683$	12.0638	0.461607	0.230803	+	0.973000i	$0.425865\pi$
$684$	−15.2152	−0.581766
$685$	−43.0610	−1.64528
$686$	−18.7016	−0.714032
$687$	50.1277	1.91249
$688$	−9.08959	−0.346537
$689$	54.9279	2.09259
$690$	−40.8657	−1.55573
$691$	47.8693	1.82103	0.910517	−	0.413472i	$-0.135684\pi$
$691$	47.8693	1.82103	0.910517	+	0.413472i	$0.135684\pi$
$692$	−9.08924	−0.345521
$693$	−54.0572	−2.05346
$694$	31.1263	1.18154
$695$	−7.94783	−0.301478
$696$	3.05494	0.115797
$697$	12.2851	0.465331
$698$	−15.6169	−0.591108
$699$	2.35923	0.0892341
$700$	30.4309	1.15018
$701$	14.1512	0.534485	0.267242	−	0.963629i	$-0.413888\pi$
$701$	14.1512	0.534485	0.267242	+	0.963629i	$0.413888\pi$
$702$	29.5479	1.11521
$703$	4.85586	0.183142
$704$	−4.42706	−0.166851
$705$	60.7688	2.28868
$706$	0.904647	0.0340469
$707$	33.8111	1.27160
$708$	−33.7218	−1.26734
$709$	−17.5721	−0.659934	−0.329967	−	0.943992i	$-0.607038\pi$
$709$	−17.5721	−0.659934	−0.329967	+	0.943992i	$0.607038\pi$
$710$	13.9477	0.523447
$711$	1.16820	0.0438108
$712$	−6.26669	−0.234854
$713$	36.5201	1.36769
$714$	31.2626	1.16997
$715$	115.895	4.33423
$716$	12.1436	0.453829
$717$	−34.5031	−1.28854
$718$	14.0762	0.525320
$719$	48.9097	1.82402	0.912012	−	0.410164i	$-0.134529\pi$
$719$	48.9097	1.82402	0.912012	+	0.410164i	$0.134529\pi$
$720$	19.0065	0.708330
$721$	4.93464	0.183776
$722$	−8.34980	−0.310747
$723$	−4.86861	−0.181065
$724$	−6.12127	−0.227495
$725$	−12.8233	−0.476244
$726$	−23.8022	−0.883383
$727$	−48.5496	−1.80060	−0.900302	−	0.435266i	$-0.856654\pi$
$727$	−48.5496	−1.80060	−0.900302	+	0.435266i	$0.856654\pi$
$728$	−16.8185	−0.623335
$729$	−44.0383	−1.63105
$730$	−66.7861	−2.47187
$731$	39.1967	1.44974
$732$	16.8158	0.621530
$733$	35.8106	1.32270	0.661348	−	0.750079i	$-0.269985\pi$
$733$	35.8106	1.32270	0.661348	+	0.750079i	$0.269985\pi$
$734$	24.3904	0.900265
$735$	1.58740	0.0585522
$736$	3.62139	0.133486
$737$	32.0220	1.17954
$738$	−13.2822	−0.488925
$739$	−17.7784	−0.653989	−0.326995	−	0.945026i	$-0.606036\pi$
$739$	−17.7784	−0.653989	−0.326995	+	0.945026i	$0.606036\pi$
$740$	−6.06586	−0.222985
$741$	−58.0101	−2.13105
$742$	−22.4021	−0.822406
$743$	−43.6704	−1.60211	−0.801056	−	0.598589i	$-0.795728\pi$
$743$	−43.6704	−1.60211	−0.801056	+	0.598589i	$0.795728\pi$
$744$	−27.9149	−1.02341
$745$	−18.4764	−0.676924
$746$	17.3071	0.633659
$747$	57.6445	2.10910
$748$	19.0906	0.698023
$749$	−43.9727	−1.60673
$750$	−74.6939	−2.72744
$751$	25.9057	0.945312	0.472656	−	0.881247i	$-0.343295\pi$
$751$	25.9057	0.945312	0.472656	+	0.881247i	$0.343295\pi$
$752$	−5.38514	−0.196376
$753$	48.8062	1.77860
$754$	7.08712	0.258098
$755$	35.3145	1.28523
$756$	−12.0510	−0.438289
$757$	23.7023	0.861476	0.430738	−	0.902477i	$-0.358253\pi$
$757$	23.7023	0.861476	0.430738	+	0.902477i	$0.358253\pi$
$758$	−1.53442	−0.0557328
$759$	44.3782	1.61083
$760$	−13.3040	−0.482588
$761$	−11.5547	−0.418858	−0.209429	−	0.977824i	$-0.567160\pi$
$761$	−11.5547	−0.418858	−0.209429	+	0.977824i	$0.567160\pi$
$762$	41.0709	1.48784
$763$	23.2853	0.842983
$764$	−13.8874	−0.502428
$765$	−81.9611	−2.96331
$766$	15.2502	0.551013
$767$	−78.2309	−2.82476
$768$	−2.76808	−0.0998845
$769$	−32.2203	−1.16189	−0.580946	−	0.813942i	$-0.697317\pi$
$769$	−32.2203	−1.16189	−0.580946	+	0.813942i	$0.697317\pi$
$770$	−47.2672	−1.70339
$771$	31.9936	1.15222
$772$	−8.86002	−0.318879
$773$	43.7149	1.57231	0.786157	−	0.618026i	$-0.212068\pi$
$773$	43.7149	1.57231	0.786157	+	0.618026i	$0.212068\pi$
$774$	−42.3781	−1.52325
$775$	117.174	4.20901
$776$	11.0161	0.395456
$777$	10.7872	0.386987
$778$	9.01331	0.323143
$779$	9.29719	0.333106
$780$	72.4652	2.59467
$781$	−15.1465	−0.541985
$782$	−15.6164	−0.558442
$783$	5.07814	0.181478
$784$	−0.140671	−0.00502395
$785$	−94.9045	−3.38729
$786$	34.7921	1.24099
$787$	20.3664	0.725984	0.362992	−	0.931792i	$-0.381755\pi$
$787$	20.3664	0.725984	0.362992	+	0.931792i	$0.381755\pi$
$788$	−0.0391097	−0.00139323
$789$	−67.9623	−2.41952
$790$	1.02146	0.0363420
$791$	−10.0023	−0.355642
$792$	−20.6401	−0.733415
$793$	39.0108	1.38532
$794$	13.3055	0.472196
$795$	96.5229	3.42331
$796$	14.8184	0.525224
$797$	21.6137	0.765597	0.382798	−	0.923832i	$-0.374960\pi$
$797$	21.6137	0.765597	0.382798	+	0.923832i	$0.374960\pi$
$798$	23.6591	0.837524
$799$	23.2222	0.821541
$800$	11.6192	0.410799
$801$	−29.2170	−1.03233
$802$	21.7260	0.767173
$803$	72.5265	2.55940
$804$	20.0222	0.706128
$805$	38.6653	1.36277
$806$	−64.7594	−2.28105
$807$	45.5141	1.60217
$808$	12.9098	0.454164
$809$	3.17882	0.111761	0.0558806	−	0.998437i	$-0.482203\pi$
$809$	3.17882	0.111761	0.0558806	+	0.998437i	$0.482203\pi$
$810$	−5.09600	−0.179055
$811$	15.0015	0.526775	0.263388	−	0.964690i	$-0.415160\pi$
$811$	15.0015	0.526775	0.263388	+	0.964690i	$0.415160\pi$
$812$	−2.89044	−0.101435
$813$	74.7454	2.62144
$814$	6.58723	0.230882
$815$	−11.8667	−0.415673
$816$	11.9367	0.417868
$817$	29.6635	1.03780
$818$	−18.7793	−0.656602
$819$	−78.4123	−2.73995
$820$	−11.6139	−0.405574
$821$	42.0632	1.46802	0.734008	−	0.679141i	$-0.237648\pi$
$821$	42.0632	1.46802	0.734008	+	0.679141i	$0.237648\pi$
$822$	29.2387	1.01982
$823$	25.1776	0.877636	0.438818	−	0.898576i	$-0.355397\pi$
$823$	25.1776	0.877636	0.438818	+	0.898576i	$0.355397\pi$
$824$	1.88415	0.0656374
$825$	142.386	4.95725
$826$	31.9061	1.11015
$827$	25.7884	0.896751	0.448375	−	0.893845i	$-0.352003\pi$
$827$	25.7884	0.896751	0.448375	+	0.893845i	$0.352003\pi$
$828$	16.8839	0.586757
$829$	−46.5701	−1.61745	−0.808723	−	0.588190i	$-0.799841\pi$
$829$	−46.5701	−1.61745	−0.808723	+	0.588190i	$0.799841\pi$
$830$	50.4040	1.74955
$831$	−56.7439	−1.96842
$832$	−6.42164	−0.222630
$833$	0.606609	0.0210178
$834$	5.39663	0.186870
$835$	−75.6638	−2.61846
$836$	14.4475	0.499679
$837$	−46.4021	−1.60389
$838$	−31.9674	−1.10430
$839$	27.1817	0.938417	0.469208	−	0.883088i	$-0.344539\pi$
$839$	27.1817	0.938417	0.469208	+	0.883088i	$0.344539\pi$
$840$	−29.5545	−1.01973
$841$	−27.7820	−0.958000
$842$	−0.152108	−0.00524199
$843$	31.5905	1.08803
$844$	−13.3946	−0.461062
$845$	115.115	3.96006
$846$	−25.1070	−0.863196
$847$	22.5206	0.773816
$848$	−8.55357	−0.293731
$849$	−75.3220	−2.58504
$850$	−50.1049	−1.71858
$851$	−5.38845	−0.184714
$852$	−9.47058	−0.324457
$853$	43.4306	1.48704	0.743518	−	0.668716i	$-0.233156\pi$
$853$	43.4306	1.48704	0.743518	+	0.668716i	$0.233156\pi$
$854$	−15.9104	−0.544441
$855$	−62.0270	−2.12128
$856$	−16.7897	−0.573859
$857$	13.6322	0.465667	0.232833	−	0.972517i	$-0.425200\pi$
$857$	13.6322	0.465667	0.232833	+	0.972517i	$0.425200\pi$
$858$	−78.6937	−2.68656
$859$	2.83685	0.0967921	0.0483960	−	0.998828i	$-0.484589\pi$
$859$	2.83685	0.0967921	0.0483960	+	0.998828i	$0.484589\pi$
$860$	−37.0552	−1.26357
$861$	20.6534	0.703867
$862$	20.7945	0.708264
$863$	2.18430	0.0743546	0.0371773	−	0.999309i	$-0.488163\pi$
$863$	2.18430	0.0743546	0.0371773	+	0.999309i	$0.488163\pi$
$864$	−4.60130	−0.156539
$865$	−37.0537	−1.25986
$866$	16.8286	0.571859
$867$	−4.41689	−0.150005
$868$	26.4118	0.896474
$869$	−1.10926	−0.0376291
$870$	12.4539	0.422228
$871$	46.4493	1.57387
$872$	8.89079	0.301080
$873$	51.3602	1.73828
$874$	−11.8183	−0.399760
$875$	70.6720	2.38915
$876$	45.3483	1.53218
$877$	56.1083	1.89464	0.947321	−	0.320285i	$-0.103779\pi$
$877$	56.1083	1.89464	0.947321	+	0.320285i	$0.103779\pi$
$878$	9.79890	0.330697
$879$	48.9895	1.65237
$880$	−18.0476	−0.608384
$881$	23.8877	0.804798	0.402399	−	0.915464i	$-0.368177\pi$
$881$	23.8877	0.804798	0.402399	+	0.915464i	$0.368177\pi$
$882$	−0.655845	−0.0220834
$883$	−58.3397	−1.96329	−0.981644	−	0.190721i	$-0.938917\pi$
$883$	−58.3397	−1.96329	−0.981644	+	0.190721i	$0.938917\pi$
$884$	27.6918	0.931377
$885$	−137.472	−4.62108
$886$	−14.8303	−0.498234
$887$	−40.1668	−1.34867	−0.674334	−	0.738426i	$-0.735569\pi$
$887$	−40.1668	−1.34867	−0.674334	+	0.738426i	$0.735569\pi$
$888$	4.11876	0.138217
$889$	−38.8594	−1.30330
$890$	−25.5472	−0.856343
$891$	5.53401	0.185396
$892$	20.0938	0.672789
$893$	17.5742	0.588099
$894$	12.5456	0.419589
$895$	49.5055	1.65479
$896$	2.61903	0.0874957
$897$	64.3725	2.14934
$898$	16.6571	0.555855
$899$	−11.1296	−0.371194
$900$	54.1716	1.80572
$901$	36.8853	1.22883
$902$	12.6121	0.419937
$903$	65.8967	2.19291
$904$	−3.81909	−0.127021
$905$	−24.9543	−0.829510
$906$	−23.9788	−0.796643
$907$	43.4544	1.44288	0.721439	−	0.692478i	$-0.243481\pi$
$907$	43.4544	1.44288	0.721439	+	0.692478i	$0.243481\pi$
$908$	−13.8976	−0.461208
$909$	60.1888	1.99634
$910$	−68.5632	−2.27285
$911$	−7.91301	−0.262170	−0.131085	−	0.991371i	$-0.541846\pi$
$911$	−7.91301	−0.262170	−0.131085	+	0.991371i	$0.541846\pi$
$912$	9.03353	0.299130
$913$	−54.7363	−1.81151
$914$	−4.84273	−0.160183
$915$	68.5524	2.26627
$916$	−18.1092	−0.598345
$917$	−32.9187	−1.08707
$918$	19.8420	0.654885
$919$	−17.1197	−0.564727	−0.282363	−	0.959308i	$-0.591118\pi$
$919$	−17.1197	−0.564727	−0.282363	+	0.959308i	$0.591118\pi$
$920$	14.7632	0.486728
$921$	−5.51800	−0.181824
$922$	−12.0470	−0.396745
$923$	−21.9707	−0.723175
$924$	32.0948	1.05584
$925$	−17.2887	−0.568449
$926$	29.5573	0.971312
$927$	8.78441	0.288518
$928$	−1.10363	−0.0362285
$929$	15.9814	0.524334	0.262167	−	0.965023i	$-0.415563\pi$
$929$	15.9814	0.524334	0.262167	+	0.965023i	$0.415563\pi$
$930$	−113.799	−3.73163
$931$	0.459074	0.0150455
$932$	−0.852296	−0.0279179
$933$	−23.7884	−0.778797
$934$	−26.9216	−0.880901
$935$	77.8261	2.54518
$936$	−29.9394	−0.978601
$937$	1.31248	0.0428770	0.0214385	−	0.999770i	$-0.493175\pi$
$937$	1.31248	0.0428770	0.0214385	+	0.999770i	$0.493175\pi$
$938$	−18.9441	−0.618546
$939$	17.4564	0.569669
$940$	−21.9534	−0.716041
$941$	−13.7344	−0.447728	−0.223864	−	0.974620i	$-0.571867\pi$
$941$	−13.7344	−0.447728	−0.223864	+	0.974620i	$0.571867\pi$
$942$	64.4408	2.09960
$943$	−10.3169	−0.335964
$944$	12.1824	0.396503
$945$	−49.1276	−1.59812
$946$	40.2401	1.30832
$947$	−50.6953	−1.64738	−0.823689	−	0.567042i	$-0.808088\pi$
$947$	−50.6953	−1.64738	−0.823689	+	0.567042i	$0.808088\pi$
$948$	−0.693581	−0.0225265
$949$	105.203	3.41503
$950$	−37.9187	−1.23024
$951$	−60.6987	−1.96829
$952$	−11.2940	−0.366040
$953$	29.9770	0.971051	0.485525	−	0.874223i	$-0.338628\pi$
$953$	29.9770	0.971051	0.485525	+	0.874223i	$0.338628\pi$
$954$	−39.8790	−1.29113
$955$	−56.6141	−1.83199
$956$	12.4646	0.403135
$957$	−13.5244	−0.437181
$958$	−4.54626	−0.146883
$959$	−27.6643	−0.893328
$960$	−11.2845	−0.364206
$961$	70.6982	2.28059
$962$	9.55507	0.308068
$963$	−78.2779	−2.52247
$964$	1.75884	0.0566484
$965$	−36.1193	−1.16272
$966$	−26.2540	−0.844709
$967$	−47.2758	−1.52029	−0.760143	−	0.649756i	$-0.774871\pi$
$967$	−47.2758	−1.52029	−0.760143	+	0.649756i	$0.774871\pi$
$968$	8.59882	0.276376
$969$	−38.9550	−1.25142
$970$	44.9090	1.44194
$971$	57.2167	1.83617	0.918086	−	0.396382i	$-0.129734\pi$
$971$	57.2167	1.83617	0.918086	+	0.396382i	$0.129734\pi$
$972$	17.2641	0.553747
$973$	−5.10605	−0.163692
$974$	−18.4525	−0.591258
$975$	206.538	6.61450
$976$	−6.07490	−0.194453
$977$	−17.2206	−0.550935	−0.275468	−	0.961310i	$-0.588833\pi$
$977$	−17.2206	−0.550935	−0.275468	+	0.961310i	$0.588833\pi$
$978$	8.05759	0.257653
$979$	27.7430	0.886670
$980$	−0.573466	−0.0183187
$981$	41.4513	1.32344
$982$	24.6500	0.786614
$983$	−15.4510	−0.492810	−0.246405	−	0.969167i	$-0.579249\pi$
$983$	−15.4510	−0.492810	−0.246405	+	0.969167i	$0.579249\pi$
$984$	7.88591	0.251393
$985$	−0.159437	−0.00508008
$986$	4.75915	0.151562
$987$	39.0406	1.24268
$988$	20.9568	0.666725
$989$	−32.9170	−1.04670
$990$	−84.1428	−2.67423
$991$	59.2672	1.88269	0.941343	−	0.337452i	$-0.109565\pi$
$991$	59.2672	1.88269	0.941343	+	0.337452i	$0.109565\pi$
$992$	10.0846	0.320185
$993$	−46.6496	−1.48038
$994$	8.96063	0.284214
$995$	60.4096	1.91511
$996$	−34.2246	−1.08445
$997$	−32.8228	−1.03951	−0.519754	−	0.854316i	$-0.673976\pi$
$997$	−32.8228	−1.03951	−0.519754	+	0.854316i	$0.673976\pi$
$998$	−40.5470	−1.28349
$999$	6.84649	0.216613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.9	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.9	✓	69	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.76808 q^{3} +1.00000 q^{4} +4.07666 q^{5} -2.76808 q^{6} +2.61903 q^{7} +1.00000 q^{8} +4.66227 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.76808 q^{3} +1.00000 q^{4} +4.07666 q^{5} -2.76808 q^{6} +2.61903 q^{7} +1.00000 q^{8} +4.66227 q^{9} +4.07666 q^{10} -4.42706 q^{11} -2.76808 q^{12} -6.42164 q^{13} +2.61903 q^{14} -11.2845 q^{15} +1.00000 q^{16} -4.31227 q^{17} +4.66227 q^{18} -3.26346 q^{19} +4.07666 q^{20} -7.24969 q^{21} -4.42706 q^{22} +3.62139 q^{23} -2.76808 q^{24} +11.6192 q^{25} -6.42164 q^{26} -4.60130 q^{27} +2.61903 q^{28} -1.10363 q^{29} -11.2845 q^{30} +10.0846 q^{31} +1.00000 q^{32} +12.2544 q^{33} -4.31227 q^{34} +10.6769 q^{35} +4.66227 q^{36} -1.48795 q^{37} -3.26346 q^{38} +17.7756 q^{39} +4.07666 q^{40} -2.84887 q^{41} -7.24969 q^{42} -9.08959 q^{43} -4.42706 q^{44} +19.0065 q^{45} +3.62139 q^{46} -5.38514 q^{47} -2.76808 q^{48} -0.140671 q^{49} +11.6192 q^{50} +11.9367 q^{51} -6.42164 q^{52} -8.55357 q^{53} -4.60130 q^{54} -18.0476 q^{55} +2.61903 q^{56} +9.03353 q^{57} -1.10363 q^{58} +12.1824 q^{59} -11.2845 q^{60} -6.07490 q^{61} +10.0846 q^{62} +12.2106 q^{63} +1.00000 q^{64} -26.1788 q^{65} +12.2544 q^{66} -7.23324 q^{67} -4.31227 q^{68} -10.0243 q^{69} +10.6769 q^{70} +3.42135 q^{71} +4.66227 q^{72} -16.3826 q^{73} -1.48795 q^{74} -32.1627 q^{75} -3.26346 q^{76} -11.5946 q^{77} +17.7756 q^{78} +0.250564 q^{79} +4.07666 q^{80} -1.25004 q^{81} -2.84887 q^{82} +12.3640 q^{83} -7.24969 q^{84} -17.5796 q^{85} -9.08959 q^{86} +3.05494 q^{87} -4.42706 q^{88} -6.26669 q^{89} +19.0065 q^{90} -16.8185 q^{91} +3.62139 q^{92} -27.9149 q^{93} -5.38514 q^{94} -13.3040 q^{95} -2.76808 q^{96} +11.0161 q^{97} -0.140671 q^{98} -20.6401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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