LMFDB - Embedded newform 4003.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, 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("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$1$
Dimension:	$152$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68690 q^{2} +0.420690 q^{3} +5.21946 q^{4} -4.00007 q^{5} -1.13035 q^{6} -1.97783 q^{7} -8.65037 q^{8} -2.82302 q^{9} +O(q^{10})$	\(q-2.68690 q^{2} +0.420690 q^{3} +5.21946 q^{4} -4.00007 q^{5} -1.13035 q^{6} -1.97783 q^{7} -8.65037 q^{8} -2.82302 q^{9} +10.7478 q^{10} +3.47964 q^{11} +2.19577 q^{12} -2.54963 q^{13} +5.31424 q^{14} -1.68279 q^{15} +12.8038 q^{16} -4.33097 q^{17} +7.58519 q^{18} +4.38839 q^{19} -20.8782 q^{20} -0.832053 q^{21} -9.34945 q^{22} +4.51931 q^{23} -3.63912 q^{24} +11.0006 q^{25} +6.85061 q^{26} -2.44969 q^{27} -10.3232 q^{28} -4.29151 q^{29} +4.52149 q^{30} +0.697882 q^{31} -17.1019 q^{32} +1.46385 q^{33} +11.6369 q^{34} +7.91146 q^{35} -14.7346 q^{36} +0.561776 q^{37} -11.7912 q^{38} -1.07260 q^{39} +34.6021 q^{40} -9.09924 q^{41} +2.23565 q^{42} +3.56903 q^{43} +18.1618 q^{44} +11.2923 q^{45} -12.1430 q^{46} +1.73100 q^{47} +5.38643 q^{48} -3.08819 q^{49} -29.5575 q^{50} -1.82200 q^{51} -13.3077 q^{52} +3.98898 q^{53} +6.58207 q^{54} -13.9188 q^{55} +17.1090 q^{56} +1.84615 q^{57} +11.5309 q^{58} +13.7051 q^{59} -8.78325 q^{60} +7.04260 q^{61} -1.87514 q^{62} +5.58345 q^{63} +20.3435 q^{64} +10.1987 q^{65} -3.93322 q^{66} +10.0443 q^{67} -22.6053 q^{68} +1.90123 q^{69} -21.2573 q^{70} -14.2890 q^{71} +24.4202 q^{72} +13.0688 q^{73} -1.50944 q^{74} +4.62783 q^{75} +22.9050 q^{76} -6.88213 q^{77} +2.88198 q^{78} +3.64155 q^{79} -51.2161 q^{80} +7.43850 q^{81} +24.4488 q^{82} +1.94077 q^{83} -4.34286 q^{84} +17.3242 q^{85} -9.58964 q^{86} -1.80540 q^{87} -30.1001 q^{88} +12.2418 q^{89} -30.3413 q^{90} +5.04273 q^{91} +23.5883 q^{92} +0.293592 q^{93} -4.65104 q^{94} -17.5539 q^{95} -7.19458 q^{96} -5.49719 q^{97} +8.29768 q^{98} -9.82308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) $ 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * 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 $

$2$	−2.68690	−1.89993	−0.949964	−	0.312359i	$-0.898881\pi$
$2$	−2.68690	−1.89993	−0.949964	+	0.312359i	$0.898881\pi$
$3$	0.420690	0.242885	0.121443	−	0.992598i	$-0.461248\pi$
$3$	0.420690	0.242885	0.121443	+	0.992598i	$0.461248\pi$
$4$	5.21946	2.60973
$5$	−4.00007	−1.78889	−0.894443	−	0.447182i	$-0.852428\pi$
$5$	−4.00007	−1.78889	−0.894443	+	0.447182i	$0.852428\pi$
$6$	−1.13035	−0.461465
$7$	−1.97783	−0.747549	−0.373775	−	0.927520i	$-0.621937\pi$
$7$	−1.97783	−0.747549	−0.373775	+	0.927520i	$0.621937\pi$
$8$	−8.65037	−3.05837
$9$	−2.82302	−0.941007
$10$	10.7478	3.39876
$11$	3.47964	1.04915	0.524575	−	0.851364i	$-0.324224\pi$
$11$	3.47964	1.04915	0.524575	+	0.851364i	$0.324224\pi$
$12$	2.19577	0.633865
$13$	−2.54963	−0.707140	−0.353570	−	0.935408i	$-0.615032\pi$
$13$	−2.54963	−0.707140	−0.353570	+	0.935408i	$0.615032\pi$
$14$	5.31424	1.42029
$15$	−1.68279	−0.434494
$16$	12.8038	3.20095
$17$	−4.33097	−1.05041	−0.525207	−	0.850974i	$-0.676012\pi$
$17$	−4.33097	−1.05041	−0.525207	+	0.850974i	$0.676012\pi$
$18$	7.58519	1.78785
$19$	4.38839	1.00676	0.503382	−	0.864064i	$-0.332089\pi$
$19$	4.38839	1.00676	0.503382	+	0.864064i	$0.332089\pi$
$20$	−20.8782	−4.66851
$21$	−0.832053	−0.181569
$22$	−9.34945	−1.99331
$23$	4.51931	0.942342	0.471171	−	0.882042i	$-0.343832\pi$
$23$	4.51931	0.942342	0.471171	+	0.882042i	$0.343832\pi$
$24$	−3.63912	−0.742833
$25$	11.0006	2.20011
$26$	6.85061	1.34351
$27$	−2.44969	−0.471442
$28$	−10.3232	−1.95090
$29$	−4.29151	−0.796914	−0.398457	−	0.917187i	$-0.630454\pi$
$29$	−4.29151	−0.796914	−0.398457	+	0.917187i	$0.630454\pi$
$30$	4.52149	0.825508
$31$	0.697882	0.125343	0.0626717	−	0.998034i	$-0.480038\pi$
$31$	0.697882	0.125343	0.0626717	+	0.998034i	$0.480038\pi$
$32$	−17.1019	−3.02321
$33$	1.46385	0.254823
$34$	11.6369	1.99571
$35$	7.91146	1.33728
$36$	−14.7346	−2.45577
$37$	0.561776	0.0923554	0.0461777	−	0.998933i	$-0.485296\pi$
$37$	0.561776	0.0923554	0.0461777	+	0.998933i	$0.485296\pi$
$38$	−11.7912	−1.91278
$39$	−1.07260	−0.171754
$40$	34.6021	5.47107
$41$	−9.09924	−1.42106	−0.710531	−	0.703666i	$-0.751545\pi$
$41$	−9.09924	−1.42106	−0.710531	+	0.703666i	$0.751545\pi$
$42$	2.23565	0.344968
$43$	3.56903	0.544272	0.272136	−	0.962259i	$-0.412270\pi$
$43$	3.56903	0.544272	0.272136	+	0.962259i	$0.412270\pi$
$44$	18.1618	2.73800
$45$	11.2923	1.68335
$46$	−12.1430	−1.79038
$47$	1.73100	0.252493	0.126246	−	0.991999i	$-0.459707\pi$
$47$	1.73100	0.252493	0.126246	+	0.991999i	$0.459707\pi$
$48$	5.38643	0.777465
$49$	−3.08819	−0.441170
$50$	−29.5575	−4.18006
$51$	−1.82200	−0.255130
$52$	−13.3077	−1.84544
$53$	3.98898	0.547928	0.273964	−	0.961740i	$-0.411665\pi$
$53$	3.98898	0.547928	0.273964	+	0.961740i	$0.411665\pi$
$54$	6.58207	0.895707
$55$	−13.9188	−1.87681
$56$	17.1090	2.28628
$57$	1.84615	0.244528
$58$	11.5309	1.51408
$59$	13.7051	1.78426	0.892129	−	0.451781i	$-0.149211\pi$
$59$	13.7051	1.78426	0.892129	+	0.451781i	$0.149211\pi$
$60$	−8.78325	−1.13391
$61$	7.04260	0.901713	0.450856	−	0.892596i	$-0.351119\pi$
$61$	7.04260	0.901713	0.450856	+	0.892596i	$0.351119\pi$
$62$	−1.87514	−0.238143
$63$	5.58345	0.703449
$64$	20.3435	2.54293
$65$	10.1987	1.26499
$66$	−3.93322	−0.484146
$67$	10.0443	1.22711	0.613556	−	0.789651i	$-0.289738\pi$
$67$	10.0443	1.22711	0.613556	+	0.789651i	$0.289738\pi$
$68$	−22.6053	−2.74130
$69$	1.90123	0.228881
$70$	−21.2573	−2.54074
$71$	−14.2890	−1.69579	−0.847894	−	0.530166i	$-0.822130\pi$
$71$	−14.2890	−1.69579	−0.847894	+	0.530166i	$0.822130\pi$
$72$	24.4202	2.87794
$73$	13.0688	1.52958	0.764792	−	0.644277i	$-0.222842\pi$
$73$	13.0688	1.52958	0.764792	+	0.644277i	$0.222842\pi$
$74$	−1.50944	−0.175469
$75$	4.62783	0.534376
$76$	22.9050	2.62738
$77$	−6.88213	−0.784291
$78$	2.88198	0.326320
$79$	3.64155	0.409706	0.204853	−	0.978793i	$-0.434328\pi$
$79$	3.64155	0.409706	0.204853	+	0.978793i	$0.434328\pi$
$80$	−51.2161	−5.72614
$81$	7.43850	0.826500
$82$	24.4488	2.69992
$83$	1.94077	0.213027	0.106514	−	0.994311i	$-0.466031\pi$
$83$	1.94077	0.213027	0.106514	+	0.994311i	$0.466031\pi$
$84$	−4.34286	−0.473845
$85$	17.3242	1.87907
$86$	−9.58964	−1.03408
$87$	−1.80540	−0.193559
$88$	−30.1001	−3.20869
$89$	12.2418	1.29763	0.648813	−	0.760948i	$-0.275266\pi$
$89$	12.2418	1.29763	0.648813	+	0.760948i	$0.275266\pi$
$90$	−30.3413	−3.19825
$91$	5.04273	0.528622
$92$	23.5883	2.45926
$93$	0.293592	0.0304441
$94$	−4.65104	−0.479718
$95$	−17.5539	−1.80099
$96$	−7.19458	−0.734294
$97$	−5.49719	−0.558155	−0.279078	−	0.960269i	$-0.590029\pi$
$97$	−5.49719	−0.558155	−0.279078	+	0.960269i	$0.590029\pi$
$98$	8.29768	0.838192
$99$	−9.82308	−0.987257
$100$	57.4170	5.74170
$101$	14.3475	1.42763	0.713815	−	0.700334i	$-0.246966\pi$
$101$	14.3475	1.42763	0.713815	+	0.700334i	$0.246966\pi$
$102$	4.89553	0.484730
$103$	−15.5032	−1.52757	−0.763787	−	0.645469i	$-0.776662\pi$
$103$	−15.5032	−1.52757	−0.763787	+	0.645469i	$0.776662\pi$
$104$	22.0552	2.16269
$105$	3.32827	0.324806
$106$	−10.7180	−1.04102
$107$	−10.5513	−1.02004	−0.510018	−	0.860164i	$-0.670361\pi$
$107$	−10.5513	−1.02004	−0.510018	+	0.860164i	$0.670361\pi$
$108$	−12.7860	−1.23034
$109$	13.8055	1.32233	0.661164	−	0.750242i	$-0.270063\pi$
$109$	13.8055	1.32233	0.661164	+	0.750242i	$0.270063\pi$
$110$	37.3985	3.56580
$111$	0.236334	0.0224318
$112$	−25.3237	−2.39287
$113$	−16.9137	−1.59111	−0.795553	−	0.605884i	$-0.792819\pi$
$113$	−16.9137	−1.59111	−0.795553	+	0.605884i	$0.792819\pi$
$114$	−4.96043	−0.464587
$115$	−18.0776	−1.68574
$116$	−22.3994	−2.07973
$117$	7.19765	0.665423
$118$	−36.8244	−3.38996
$119$	8.56592	0.785237
$120$	14.5568	1.32884
$121$	1.10787	0.100715
$122$	−18.9228	−1.71319
$123$	−3.82796	−0.345155
$124$	3.64257	0.327112
$125$	−24.0027	−2.14687
$126$	−15.0022	−1.33650
$127$	11.7162	1.03965	0.519823	−	0.854274i	$-0.325998\pi$
$127$	11.7162	1.03965	0.519823	+	0.854274i	$0.325998\pi$
$128$	−20.4572	−1.80818
$129$	1.50145	0.132196
$130$	−27.4029	−2.40339
$131$	6.01570	0.525594	0.262797	−	0.964851i	$-0.415355\pi$
$131$	6.01570	0.525594	0.262797	+	0.964851i	$0.415355\pi$
$132$	7.64049	0.665019
$133$	−8.67948	−0.752606
$134$	−26.9882	−2.33143
$135$	9.79892	0.843357
$136$	37.4645	3.21255
$137$	−17.6505	−1.50798	−0.753991	−	0.656884i	$-0.771874\pi$
$137$	−17.6505	−1.50798	−0.753991	+	0.656884i	$0.771874\pi$
$138$	−5.10842	−0.434858
$139$	12.6521	1.07314	0.536570	−	0.843856i	$-0.319720\pi$
$139$	12.6521	1.07314	0.536570	+	0.843856i	$0.319720\pi$
$140$	41.2935	3.48994
$141$	0.728216	0.0613269
$142$	38.3931	3.22188
$143$	−8.87178	−0.741895
$144$	−36.1454	−3.01212
$145$	17.1664	1.42559
$146$	−35.1145	−2.90610
$147$	−1.29917	−0.107154
$148$	2.93217	0.241023
$149$	12.6293	1.03463	0.517317	−	0.855794i	$-0.326931\pi$
$149$	12.6293	1.03463	0.517317	+	0.855794i	$0.326931\pi$
$150$	−12.4345	−1.01528
$151$	−12.7417	−1.03691	−0.518453	−	0.855106i	$-0.673492\pi$
$151$	−12.7417	−1.03691	−0.518453	+	0.855106i	$0.673492\pi$
$152$	−37.9612	−3.07906
$153$	12.2264	0.988447
$154$	18.4916	1.49010
$155$	−2.79158	−0.224225
$156$	−5.59840	−0.448231
$157$	−15.4884	−1.23611	−0.618053	−	0.786136i	$-0.712078\pi$
$157$	−15.4884	−1.23611	−0.618053	+	0.786136i	$0.712078\pi$
$158$	−9.78449	−0.778412
$159$	1.67812	0.133084
$160$	68.4087	5.40818
$161$	−8.93843	−0.704447
$162$	−19.9865	−1.57029
$163$	−17.4478	−1.36662	−0.683310	−	0.730129i	$-0.739460\pi$
$163$	−17.4478	−1.36662	−0.683310	+	0.730129i	$0.739460\pi$
$164$	−47.4931	−3.70859
$165$	−5.85550	−0.455850
$166$	−5.21467	−0.404737
$167$	4.31610	0.333990	0.166995	−	0.985958i	$-0.446594\pi$
$167$	4.31610	0.333990	0.166995	+	0.985958i	$0.446594\pi$
$168$	7.19757	0.555304
$169$	−6.49939	−0.499953
$170$	−46.5484	−3.57010
$171$	−12.3885	−0.947372
$172$	18.6284	1.42040
$173$	−24.6294	−1.87254	−0.936270	−	0.351282i	$-0.885746\pi$
$173$	−24.6294	−1.87254	−0.936270	+	0.351282i	$0.885746\pi$
$174$	4.85093	0.367748
$175$	−21.7572	−1.64469
$176$	44.5526	3.35828
$177$	5.76562	0.433370
$178$	−32.8925	−2.46540
$179$	−2.56185	−0.191481	−0.0957407	−	0.995406i	$-0.530522\pi$
$179$	−2.56185	−0.191481	−0.0957407	+	0.995406i	$0.530522\pi$
$180$	58.9396	4.39309
$181$	17.8424	1.32621	0.663106	−	0.748525i	$-0.269238\pi$
$181$	17.8424	1.32621	0.663106	+	0.748525i	$0.269238\pi$
$182$	−13.5493	−1.00434
$183$	2.96275	0.219013
$184$	−39.0937	−2.88203
$185$	−2.24714	−0.165213
$186$	−0.788854	−0.0578416
$187$	−15.0702	−1.10204
$188$	9.03490	0.658938
$189$	4.84506	0.352426
$190$	47.1655	3.42175
$191$	1.31894	0.0954349	0.0477174	−	0.998861i	$-0.484805\pi$
$191$	1.31894	0.0954349	0.0477174	+	0.998861i	$0.484805\pi$
$192$	8.55829	0.617641
$193$	19.4965	1.40339	0.701694	−	0.712479i	$-0.252427\pi$
$193$	19.4965	1.40339	0.701694	+	0.712479i	$0.252427\pi$
$194$	14.7704	1.06045
$195$	4.29049	0.307248
$196$	−16.1187	−1.15133
$197$	−0.523930	−0.0373285	−0.0186642	−	0.999826i	$-0.505941\pi$
$197$	−0.523930	−0.0373285	−0.0186642	+	0.999826i	$0.505941\pi$
$198$	26.3937	1.87572
$199$	−10.3754	−0.735496	−0.367748	−	0.929926i	$-0.619871\pi$
$199$	−10.3754	−0.735496	−0.367748	+	0.929926i	$0.619871\pi$
$200$	−95.1590	−6.72876
$201$	4.22556	0.298048
$202$	−38.5504	−2.71240
$203$	8.48788	0.595732
$204$	−9.50983	−0.665821
$205$	36.3976	2.54212
$206$	41.6555	2.90228
$207$	−12.7581	−0.886750
$208$	−32.6449	−2.26352
$209$	15.2700	1.05625
$210$	−8.94274	−0.617108
$211$	−14.6778	−1.01046	−0.505230	−	0.862985i	$-0.668592\pi$
$211$	−14.6778	−1.01046	−0.505230	+	0.862985i	$0.668592\pi$
$212$	20.8203	1.42994
$213$	−6.01122	−0.411882
$214$	28.3504	1.93800
$215$	−14.2764	−0.973640
$216$	21.1907	1.44184
$217$	−1.38029	−0.0937003
$218$	−37.0941	−2.51233
$219$	5.49790	0.371514
$220$	−72.6485	−4.89796
$221$	11.0424	0.742790
$222$	−0.635006	−0.0426188
$223$	8.12228	0.543908	0.271954	−	0.962310i	$-0.412330\pi$
$223$	8.12228	0.543908	0.271954	+	0.962310i	$0.412330\pi$
$224$	33.8246	2.26000
$225$	−31.0548	−2.07032
$226$	45.4454	3.02299
$227$	21.9164	1.45464	0.727320	−	0.686298i	$-0.240766\pi$
$227$	21.9164	1.45464	0.727320	+	0.686298i	$0.240766\pi$
$228$	9.63590	0.638153
$229$	9.19255	0.607461	0.303730	−	0.952758i	$-0.401768\pi$
$229$	9.19255	0.607461	0.303730	+	0.952758i	$0.401768\pi$
$230$	48.5727	3.20279
$231$	−2.89524	−0.190493
$232$	37.1232	2.43726
$233$	−0.413316	−0.0270772	−0.0135386	−	0.999908i	$-0.504310\pi$
$233$	−0.413316	−0.0270772	−0.0135386	+	0.999908i	$0.504310\pi$
$234$	−19.3394	−1.26426
$235$	−6.92414	−0.451681
$236$	71.5334	4.65643
$237$	1.53196	0.0995117
$238$	−23.0158	−1.49189
$239$	−17.5334	−1.13414	−0.567071	−	0.823669i	$-0.691924\pi$
$239$	−17.5334	−1.13414	−0.567071	+	0.823669i	$0.691924\pi$
$240$	−21.5461	−1.39080
$241$	29.4233	1.89532	0.947662	−	0.319276i	$-0.103440\pi$
$241$	29.4233	1.89532	0.947662	+	0.319276i	$0.103440\pi$
$242$	−2.97673	−0.191351
$243$	10.4784	0.672187
$244$	36.7586	2.35323
$245$	12.3530	0.789203
$246$	10.2854	0.655770
$247$	−11.1888	−0.711923
$248$	−6.03694	−0.383346
$249$	0.816463	0.0517412
$250$	64.4929	4.07889
$251$	−10.6770	−0.673925	−0.336963	−	0.941518i	$-0.609400\pi$
$251$	−10.6770	−0.673925	−0.336963	+	0.941518i	$0.609400\pi$
$252$	29.1426	1.83581
$253$	15.7256	0.988657
$254$	−31.4804	−1.97525
$255$	7.28811	0.456399
$256$	14.2797	0.892479
$257$	−6.46137	−0.403049	−0.201524	−	0.979483i	$-0.564590\pi$
$257$	−6.46137	−0.403049	−0.201524	+	0.979483i	$0.564590\pi$
$258$	−4.03426	−0.251162
$259$	−1.11110	−0.0690402
$260$	53.2316	3.30129
$261$	12.1150	0.749901
$262$	−16.1636	−0.998592
$263$	−3.32295	−0.204902	−0.102451	−	0.994738i	$-0.532668\pi$
$263$	−3.32295	−0.204902	−0.102451	+	0.994738i	$0.532668\pi$
$264$	−12.6628	−0.779343
$265$	−15.9562	−0.980181
$266$	23.3209	1.42990
$267$	5.14999	0.315174
$268$	52.4260	3.20243
$269$	16.8635	1.02819	0.514094	−	0.857734i	$-0.328128\pi$
$269$	16.8635	1.02819	0.514094	+	0.857734i	$0.328128\pi$
$270$	−26.3288	−1.60232
$271$	−14.6528	−0.890096	−0.445048	−	0.895507i	$-0.646813\pi$
$271$	−14.6528	−0.890096	−0.445048	+	0.895507i	$0.646813\pi$
$272$	−55.4529	−3.36233
$273$	2.12143	0.128395
$274$	47.4252	2.86506
$275$	38.2780	2.30825
$276$	9.92338	0.597317
$277$	−26.2976	−1.58007	−0.790034	−	0.613062i	$-0.789937\pi$
$277$	−26.2976	−1.58007	−0.790034	+	0.613062i	$0.789937\pi$
$278$	−33.9951	−2.03889
$279$	−1.97014	−0.117949
$280$	−68.4370	−4.08989
$281$	19.9818	1.19202	0.596009	−	0.802978i	$-0.296752\pi$
$281$	19.9818	1.19202	0.596009	+	0.802978i	$0.296752\pi$
$282$	−1.95665	−0.116517
$283$	−16.4821	−0.979762	−0.489881	−	0.871789i	$-0.662960\pi$
$283$	−16.4821	−0.979762	−0.489881	+	0.871789i	$0.662960\pi$
$284$	−74.5806	−4.42555
$285$	−7.38473	−0.437434
$286$	23.8376	1.40955
$287$	17.9967	1.06231
$288$	48.2789	2.84486
$289$	1.75731	0.103371
$290$	−46.1243	−2.70851
$291$	−2.31261	−0.135568
$292$	68.2119	3.99180
$293$	−19.3464	−1.13023	−0.565113	−	0.825013i	$-0.691168\pi$
$293$	−19.3464	−1.13023	−0.565113	+	0.825013i	$0.691168\pi$
$294$	3.49075	0.203585
$295$	−54.8216	−3.19183
$296$	−4.85957	−0.282457
$297$	−8.52402	−0.494614
$298$	−33.9338	−1.96573
$299$	−11.5226	−0.666367
$300$	24.1547	1.39457
$301$	−7.05893	−0.406870
$302$	34.2357	1.97005
$303$	6.03585	0.346751
$304$	56.1880	3.22260
$305$	−28.1709	−1.61306
$306$	−32.8512	−1.87798
$307$	−6.32371	−0.360913	−0.180457	−	0.983583i	$-0.557758\pi$
$307$	−6.32371	−0.360913	−0.180457	+	0.983583i	$0.557758\pi$
$308$	−35.9209	−2.04679
$309$	−6.52203	−0.371025
$310$	7.50071	0.426011
$311$	1.59636	0.0905212	0.0452606	−	0.998975i	$-0.485588\pi$
$311$	1.59636	0.0905212	0.0452606	+	0.998975i	$0.485588\pi$
$312$	9.27841	0.525287
$313$	−13.6077	−0.769154	−0.384577	−	0.923093i	$-0.625653\pi$
$313$	−13.6077	−0.769154	−0.384577	+	0.923093i	$0.625653\pi$
$314$	41.6158	2.34851
$315$	−22.3342	−1.25839
$316$	19.0069	1.06922
$317$	−21.6683	−1.21701	−0.608505	−	0.793550i	$-0.708231\pi$
$317$	−21.6683	−1.21701	−0.608505	+	0.793550i	$0.708231\pi$
$318$	−4.50895	−0.252850
$319$	−14.9329	−0.836082
$320$	−81.3753	−4.54902
$321$	−4.43884	−0.247752
$322$	24.0167	1.33840
$323$	−19.0060	−1.05752
$324$	38.8249	2.15694
$325$	−28.0474	−1.55579
$326$	46.8806	2.59648
$327$	5.80784	0.321174
$328$	78.7118	4.34613
$329$	−3.42363	−0.188751
$330$	15.7332	0.866082
$331$	8.74663	0.480758	0.240379	−	0.970679i	$-0.422728\pi$
$331$	8.74663	0.480758	0.240379	+	0.970679i	$0.422728\pi$
$332$	10.1298	0.555943
$333$	−1.58591	−0.0869071
$334$	−11.5970	−0.634557
$335$	−40.1781	−2.19516
$336$	−10.6534	−0.581193
$337$	17.9330	0.976873	0.488437	−	0.872599i	$-0.337567\pi$
$337$	17.9330	0.976873	0.488437	+	0.872599i	$0.337567\pi$
$338$	17.4633	0.949876
$339$	−7.11542	−0.386456
$340$	90.4228	4.90387
$341$	2.42838	0.131504
$342$	33.2867	1.79994
$343$	19.9527	1.07735
$344$	−30.8734	−1.66458
$345$	−7.60505	−0.409442
$346$	66.1769	3.55769
$347$	15.7807	0.847155	0.423577	−	0.905860i	$-0.360774\pi$
$347$	15.7807	0.847155	0.423577	+	0.905860i	$0.360774\pi$
$348$	−9.42318	−0.505136
$349$	16.4879	0.882578	0.441289	−	0.897365i	$-0.354521\pi$
$349$	16.4879	0.882578	0.441289	+	0.897365i	$0.354521\pi$
$350$	58.4596	3.12480
$351$	6.24579	0.333376
$352$	−59.5083	−3.17180
$353$	11.4594	0.609925	0.304962	−	0.952364i	$-0.401356\pi$
$353$	11.4594	0.609925	0.304962	+	0.952364i	$0.401356\pi$
$354$	−15.4917	−0.823373
$355$	57.1569	3.03357
$356$	63.8954	3.38645
$357$	3.60360	0.190723
$358$	6.88344	0.363801
$359$	−1.34046	−0.0707467	−0.0353733	−	0.999374i	$-0.511262\pi$
$359$	−1.34046	−0.0707467	−0.0353733	+	0.999374i	$0.511262\pi$
$360$	−97.6824	−5.14831
$361$	0.257925	0.0135750
$362$	−47.9407	−2.51971
$363$	0.466068	0.0244622
$364$	26.3203	1.37956
$365$	−52.2760	−2.73625
$366$	−7.96063	−0.416109
$367$	−35.7717	−1.86727	−0.933633	−	0.358230i	$-0.883380\pi$
$367$	−35.7717	−1.86727	−0.933633	+	0.358230i	$0.883380\pi$
$368$	57.8644	3.01639
$369$	25.6873	1.33723
$370$	6.03786	0.313894
$371$	−7.88951	−0.409603
$372$	1.53239	0.0794508
$373$	−14.5299	−0.752327	−0.376164	−	0.926553i	$-0.622757\pi$
$373$	−14.5299	−0.752327	−0.376164	+	0.926553i	$0.622757\pi$
$374$	40.4922	2.09380
$375$	−10.0977	−0.521443
$376$	−14.9738	−0.772216
$377$	10.9418	0.563529
$378$	−13.0182	−0.669585
$379$	12.6017	0.647306	0.323653	−	0.946176i	$-0.395089\pi$
$379$	12.6017	0.647306	0.323653	+	0.946176i	$0.395089\pi$
$380$	−91.6216	−4.70009
$381$	4.92890	0.252515
$382$	−3.54386	−0.181319
$383$	−16.7551	−0.856145	−0.428072	−	0.903744i	$-0.640807\pi$
$383$	−16.7551	−0.856145	−0.428072	+	0.903744i	$0.640807\pi$
$384$	−8.60615	−0.439181
$385$	27.5290	1.40301
$386$	−52.3852	−2.66634
$387$	−10.0754	−0.512163
$388$	−28.6923	−1.45663
$389$	−29.5687	−1.49919	−0.749596	−	0.661896i	$-0.769752\pi$
$389$	−29.5687	−1.49919	−0.749596	+	0.661896i	$0.769752\pi$
$390$	−11.5281	−0.583750
$391$	−19.5730	−0.989849
$392$	26.7140	1.34926
$393$	2.53075	0.127659
$394$	1.40775	0.0709215
$395$	−14.5665	−0.732918
$396$	−51.2711	−2.57647
$397$	−0.796357	−0.0399680	−0.0199840	−	0.999800i	$-0.506362\pi$
$397$	−0.796357	−0.0399680	−0.0199840	+	0.999800i	$0.506362\pi$
$398$	27.8778	1.39739
$399$	−3.65137	−0.182797
$400$	140.849	7.04246
$401$	−10.5550	−0.527090	−0.263545	−	0.964647i	$-0.584892\pi$
$401$	−10.5550	−0.527090	−0.263545	+	0.964647i	$0.584892\pi$
$402$	−11.3537	−0.566269
$403$	−1.77934	−0.0886353
$404$	74.8862	3.72573
$405$	−29.7545	−1.47851
$406$	−22.8061	−1.13185
$407$	1.95478	0.0968947
$408$	15.7609	0.780283
$409$	−13.9027	−0.687444	−0.343722	−	0.939071i	$-0.611688\pi$
$409$	−13.9027	−0.687444	−0.343722	+	0.939071i	$0.611688\pi$
$410$	−97.7968	−4.82984
$411$	−7.42538	−0.366267
$412$	−80.9181	−3.98655
$413$	−27.1064	−1.33382
$414$	34.2798	1.68476
$415$	−7.76322	−0.381081
$416$	43.6034	2.13783
$417$	5.32262	0.260650
$418$	−41.0290	−2.00679
$419$	17.8500	0.872031	0.436015	−	0.899939i	$-0.356389\pi$
$419$	17.8500	0.872031	0.436015	+	0.899939i	$0.356389\pi$
$420$	17.3718	0.847655
$421$	−26.1225	−1.27313	−0.636566	−	0.771222i	$-0.719646\pi$
$421$	−26.1225	−1.27313	−0.636566	+	0.771222i	$0.719646\pi$
$422$	39.4378	1.91980
$423$	−4.88666	−0.237598
$424$	−34.5061	−1.67576
$425$	−47.6431	−2.31103
$426$	16.1516	0.782547
$427$	−13.9291	−0.674075
$428$	−55.0722	−2.66202
$429$	−3.73227	−0.180196
$430$	38.3592	1.84985
$431$	−4.43438	−0.213597	−0.106798	−	0.994281i	$-0.534060\pi$
$431$	−4.43438	−0.213597	−0.106798	+	0.994281i	$0.534060\pi$
$432$	−31.3653	−1.50906
$433$	−31.1666	−1.49777	−0.748886	−	0.662699i	$-0.769411\pi$
$433$	−31.1666	−1.49777	−0.748886	+	0.662699i	$0.769411\pi$
$434$	3.70871	0.178024
$435$	7.22171	0.346255
$436$	72.0572	3.45091
$437$	19.8325	0.948716
$438$	−14.7723	−0.705850
$439$	−10.6341	−0.507536	−0.253768	−	0.967265i	$-0.581670\pi$
$439$	−10.6341	−0.507536	−0.253768	+	0.967265i	$0.581670\pi$
$440$	120.403	5.73997
$441$	8.71803	0.415144
$442$	−29.6698	−1.41125
$443$	21.3500	1.01437	0.507185	−	0.861837i	$-0.330686\pi$
$443$	21.3500	1.01437	0.507185	+	0.861837i	$0.330686\pi$
$444$	1.23353	0.0585409
$445$	−48.9680	−2.32130
$446$	−21.8238	−1.03339
$447$	5.31302	0.251297
$448$	−40.2359	−1.90097
$449$	16.6929	0.787787	0.393894	−	0.919156i	$-0.371128\pi$
$449$	16.6929	0.787787	0.393894	+	0.919156i	$0.371128\pi$
$450$	83.4413	3.93346
$451$	−31.6620	−1.49091
$452$	−88.2802	−4.15235
$453$	−5.36031	−0.251849
$454$	−58.8872	−2.76371
$455$	−20.1713	−0.945644
$456$	−15.9699	−0.747858
$457$	−0.525670	−0.0245898	−0.0122949	−	0.999924i	$-0.503914\pi$
$457$	−0.525670	−0.0245898	−0.0122949	+	0.999924i	$0.503914\pi$
$458$	−24.6995	−1.15413
$459$	10.6095	0.495210
$460$	−94.3551	−4.39933
$461$	6.21088	0.289270	0.144635	−	0.989485i	$-0.453799\pi$
$461$	6.21088	0.289270	0.144635	+	0.989485i	$0.453799\pi$
$462$	7.77924	0.361923
$463$	8.57996	0.398745	0.199372	−	0.979924i	$-0.436110\pi$
$463$	8.57996	0.398745	0.199372	+	0.979924i	$0.436110\pi$
$464$	−54.9477	−2.55088
$465$	−1.17439	−0.0544610
$466$	1.11054	0.0514448
$467$	25.3373	1.17247	0.586235	−	0.810141i	$-0.300610\pi$
$467$	25.3373	1.17247	0.586235	+	0.810141i	$0.300610\pi$
$468$	37.5678	1.73657
$469$	−19.8660	−0.917327
$470$	18.6045	0.858162
$471$	−6.51580	−0.300232
$472$	−118.555	−5.45692
$473$	12.4189	0.571022
$474$	−4.11624	−0.189065
$475$	48.2747	2.21500
$476$	44.7094	2.04925
$477$	−11.2610	−0.515604
$478$	47.1106	2.15479
$479$	−18.2777	−0.835130	−0.417565	−	0.908647i	$-0.637116\pi$
$479$	−18.2777	−0.835130	−0.417565	+	0.908647i	$0.637116\pi$
$480$	28.7788	1.31357
$481$	−1.43232	−0.0653082
$482$	−79.0577	−3.60098
$483$	−3.76031	−0.171100
$484$	5.78246	0.262839
$485$	21.9892	0.998476
$486$	−28.1544	−1.27711
$487$	−12.6657	−0.573939	−0.286970	−	0.957940i	$-0.592648\pi$
$487$	−12.6657	−0.573939	−0.286970	+	0.957940i	$0.592648\pi$
$488$	−60.9211	−2.75777
$489$	−7.34012	−0.331932
$490$	−33.1913	−1.49943
$491$	−41.4093	−1.86878	−0.934389	−	0.356255i	$-0.884053\pi$
$491$	−41.4093	−1.86878	−0.934389	+	0.356255i	$0.884053\pi$
$492$	−19.9799	−0.900761
$493$	18.5864	0.837090
$494$	30.0631	1.35260
$495$	39.2930	1.76609
$496$	8.93555	0.401218
$497$	28.2611	1.26769
$498$	−2.19376	−0.0983046
$499$	−18.7842	−0.840894	−0.420447	−	0.907317i	$-0.638127\pi$
$499$	−18.7842	−0.840894	−0.420447	+	0.907317i	$0.638127\pi$
$500$	−125.281	−5.60274
$501$	1.81574	0.0811213
$502$	28.6880	1.28041
$503$	−7.51792	−0.335207	−0.167604	−	0.985854i	$-0.553603\pi$
$503$	−7.51792	−0.335207	−0.167604	+	0.985854i	$0.553603\pi$
$504$	−48.2989	−2.15140
$505$	−57.3910	−2.55387
$506$	−42.2531	−1.87838
$507$	−2.73423	−0.121431
$508$	61.1523	2.71319
$509$	−20.8304	−0.923292	−0.461646	−	0.887064i	$-0.652741\pi$
$509$	−20.8304	−0.923292	−0.461646	+	0.887064i	$0.652741\pi$
$510$	−19.5825	−0.867126
$511$	−25.8478	−1.14344
$512$	2.54635	0.112534
$513$	−10.7502	−0.474631
$514$	17.3611	0.765764
$515$	62.0138	2.73265
$516$	7.83677	0.344995
$517$	6.02326	0.264903
$518$	2.98541	0.131172
$519$	−10.3613	−0.454813
$520$	−88.2225	−3.86881
$521$	−1.95775	−0.0857706	−0.0428853	−	0.999080i	$-0.513655\pi$
$521$	−1.95775	−0.0857706	−0.0428853	+	0.999080i	$0.513655\pi$
$522$	−32.5519	−1.42476
$523$	2.70844	0.118432	0.0592159	−	0.998245i	$-0.481140\pi$
$523$	2.70844	0.118432	0.0592159	+	0.998245i	$0.481140\pi$
$524$	31.3987	1.37166
$525$	−9.15305	−0.399472
$526$	8.92845	0.389299
$527$	−3.02251	−0.131663
$528$	18.7428	0.815677
$529$	−2.57582	−0.111992
$530$	42.8727	1.86227
$531$	−38.6899	−1.67900
$532$	−45.3021	−1.96410
$533$	23.1997	1.00489
$534$	−13.8375	−0.598809
$535$	42.2061	1.82473
$536$	−86.8873	−3.75296
$537$	−1.07774	−0.0465081
$538$	−45.3107	−1.95348
$539$	−10.7458	−0.462854
$540$	51.1450	2.20093
$541$	12.4835	0.536706	0.268353	−	0.963321i	$-0.413521\pi$
$541$	12.4835	0.536706	0.268353	+	0.963321i	$0.413521\pi$
$542$	39.3707	1.69112
$543$	7.50610	0.322118
$544$	74.0677	3.17563
$545$	−55.2230	−2.36549
$546$	−5.70007	−0.243940
$547$	35.3280	1.51052	0.755259	−	0.655427i	$-0.227511\pi$
$547$	35.3280	1.51052	0.755259	+	0.655427i	$0.227511\pi$
$548$	−92.1259	−3.93542
$549$	−19.8814	−0.848518
$550$	−102.849	−4.38551
$551$	−18.8328	−0.802305
$552$	−16.4463	−0.700002
$553$	−7.20236	−0.306276
$554$	70.6591	3.00202
$555$	−0.945351	−0.0401279
$556$	66.0372	2.80060
$557$	6.71952	0.284715	0.142358	−	0.989815i	$-0.454532\pi$
$557$	6.71952	0.284715	0.142358	+	0.989815i	$0.454532\pi$
$558$	5.29357	0.224095
$559$	−9.09970	−0.384876
$560$	101.297	4.28057
$561$	−6.33988	−0.267670
$562$	−53.6893	−2.26475
$563$	−2.26789	−0.0955800	−0.0477900	−	0.998857i	$-0.515218\pi$
$563$	−2.26789	−0.0955800	−0.0477900	+	0.998857i	$0.515218\pi$
$564$	3.80089	0.160046
$565$	67.6559	2.84631
$566$	44.2859	1.86148
$567$	−14.7121	−0.617850
$568$	123.605	5.18634
$569$	43.5035	1.82376	0.911880	−	0.410456i	$-0.134630\pi$
$569$	43.5035	1.82376	0.911880	+	0.410456i	$0.134630\pi$
$570$	19.8421	0.831092
$571$	−43.3433	−1.81386	−0.906931	−	0.421279i	$-0.861581\pi$
$571$	−43.3433	−1.81386	−0.906931	+	0.421279i	$0.861581\pi$
$572$	−46.3059	−1.93615
$573$	0.554863	0.0231797
$574$	−48.3555	−2.01832
$575$	49.7150	2.07326
$576$	−57.4300	−2.39292
$577$	−3.99964	−0.166507	−0.0832536	−	0.996528i	$-0.526531\pi$
$577$	−3.99964	−0.166507	−0.0832536	+	0.996528i	$0.526531\pi$
$578$	−4.72172	−0.196398
$579$	8.20198	0.340862
$580$	89.5990	3.72040
$581$	−3.83851	−0.159248
$582$	6.21377	0.257569
$583$	13.8802	0.574858
$584$	−113.050	−4.67803
$585$	−28.7911	−1.19037
$586$	51.9818	2.14735
$587$	−36.4316	−1.50369	−0.751846	−	0.659339i	$-0.770836\pi$
$587$	−36.4316	−1.50369	−0.751846	+	0.659339i	$0.770836\pi$
$588$	−6.78097	−0.279642
$589$	3.06258	0.126191
$590$	147.300	6.06426
$591$	−0.220412	−0.00906655
$592$	7.19287	0.295625
$593$	−11.1919	−0.459594	−0.229797	−	0.973239i	$-0.573806\pi$
$593$	−11.1919	−0.459594	−0.229797	+	0.973239i	$0.573806\pi$
$594$	22.9032	0.939730
$595$	−34.2643	−1.40470
$596$	65.9181	2.70011
$597$	−4.36484	−0.178641
$598$	30.9600	1.26605
$599$	18.1366	0.741041	0.370521	−	0.928824i	$-0.379179\pi$
$599$	18.1366	0.741041	0.370521	+	0.928824i	$0.379179\pi$
$600$	−40.0324	−1.63432
$601$	30.7298	1.25350	0.626748	−	0.779222i	$-0.284386\pi$
$601$	30.7298	1.25350	0.626748	+	0.779222i	$0.284386\pi$
$602$	18.9667	0.773024
$603$	−28.3554	−1.15472
$604$	−66.5048	−2.70604
$605$	−4.43154	−0.180168
$606$	−16.2178	−0.658801
$607$	−39.8347	−1.61684	−0.808421	−	0.588605i	$-0.799677\pi$
$607$	−39.8347	−1.61684	−0.808421	+	0.588605i	$0.799677\pi$
$608$	−75.0496	−3.04366
$609$	3.57076	0.144695
$610$	75.6926	3.06470
$611$	−4.41342	−0.178548
$612$	63.8152	2.57958
$613$	−4.08131	−0.164842	−0.0824212	−	0.996598i	$-0.526265\pi$
$613$	−4.08131	−0.164842	−0.0824212	+	0.996598i	$0.526265\pi$
$614$	16.9912	0.685710
$615$	15.3121	0.617443
$616$	59.5329	2.39865
$617$	−25.1471	−1.01238	−0.506192	−	0.862421i	$-0.668947\pi$
$617$	−25.1471	−1.01238	−0.506192	+	0.862421i	$0.668947\pi$
$618$	17.5241	0.704922
$619$	40.9642	1.64649	0.823246	−	0.567685i	$-0.192161\pi$
$619$	40.9642	1.64649	0.823246	+	0.567685i	$0.192161\pi$
$620$	−14.5705	−0.585166
$621$	−11.0709	−0.444260
$622$	−4.28926	−0.171984
$623$	−24.2121	−0.970039
$624$	−13.7334	−0.549776
$625$	41.0096	1.64039
$626$	36.5626	1.46134
$627$	6.42393	0.256547
$628$	−80.8409	−3.22590
$629$	−2.43304	−0.0970115
$630$	60.0099	2.39085
$631$	−10.3066	−0.410299	−0.205149	−	0.978731i	$-0.565768\pi$
$631$	−10.3066	−0.410299	−0.205149	+	0.978731i	$0.565768\pi$
$632$	−31.5007	−1.25303
$633$	−6.17479	−0.245426
$634$	58.2206	2.31223
$635$	−46.8657	−1.85981
$636$	8.75888	0.347312
$637$	7.87374	0.311969
$638$	40.1233	1.58850
$639$	40.3380	1.59575
$640$	81.8303	3.23463
$641$	21.1114	0.833851	0.416925	−	0.908941i	$-0.363108\pi$
$641$	21.1114	0.833851	0.416925	+	0.908941i	$0.363108\pi$
$642$	11.9267	0.470711
$643$	15.2860	0.602821	0.301410	−	0.953494i	$-0.402543\pi$
$643$	15.2860	0.602821	0.301410	+	0.953494i	$0.402543\pi$
$644$	−46.6537	−1.83841
$645$	−6.00592	−0.236483
$646$	51.0672	2.00921
$647$	−7.47418	−0.293840	−0.146920	−	0.989148i	$-0.546936\pi$
$647$	−7.47418	−0.293840	−0.146920	+	0.989148i	$0.546936\pi$
$648$	−64.3458	−2.52774
$649$	47.6889	1.87195
$650$	75.3606	2.95588
$651$	−0.580675	−0.0227584
$652$	−91.0682	−3.56650
$653$	13.0449	0.510486	0.255243	−	0.966877i	$-0.417844\pi$
$653$	13.0449	0.510486	0.255243	+	0.966877i	$0.417844\pi$
$654$	−15.6051	−0.610208
$655$	−24.0632	−0.940228
$656$	−116.505	−4.54875
$657$	−36.8934	−1.43935
$658$	9.19897	0.358613
$659$	−31.6772	−1.23397	−0.616984	−	0.786975i	$-0.711646\pi$
$659$	−31.6772	−1.23397	−0.616984	+	0.786975i	$0.711646\pi$
$660$	−30.5625	−1.18964
$661$	−6.71929	−0.261350	−0.130675	−	0.991425i	$-0.541714\pi$
$661$	−6.71929	−0.261350	−0.130675	+	0.991425i	$0.541714\pi$
$662$	−23.5013	−0.913406
$663$	4.64541	0.180413
$664$	−16.7884	−0.651516
$665$	34.7185	1.34633
$666$	4.26118	0.165117
$667$	−19.3947	−0.750965
$668$	22.5277	0.871623
$669$	3.41696	0.132107
$670$	107.955	4.17065
$671$	24.5057	0.946032
$672$	14.2297	0.548921
$673$	−17.9538	−0.692069	−0.346034	−	0.938222i	$-0.612472\pi$
$673$	−17.9538	−0.692069	−0.346034	+	0.938222i	$0.612472\pi$
$674$	−48.1843	−1.85599
$675$	−26.9479	−1.03723
$676$	−33.9233	−1.30474
$677$	36.6598	1.40895	0.704475	−	0.709729i	$-0.251183\pi$
$677$	36.6598	1.40895	0.704475	+	0.709729i	$0.251183\pi$
$678$	19.1184	0.734239
$679$	10.8725	0.417248
$680$	−149.861	−5.74689
$681$	9.22000	0.353311
$682$	−6.52482	−0.249848
$683$	32.0078	1.22474	0.612372	−	0.790570i	$-0.290216\pi$
$683$	32.0078	1.22474	0.612372	+	0.790570i	$0.290216\pi$
$684$	−64.6612	−2.47238
$685$	70.6032	2.69761
$686$	−53.6111	−2.04688
$687$	3.86721	0.147543
$688$	45.6971	1.74219
$689$	−10.1704	−0.387462
$690$	20.4340	0.777911
$691$	−14.5176	−0.552275	−0.276138	−	0.961118i	$-0.589055\pi$
$691$	−14.5176	−0.552275	−0.276138	+	0.961118i	$0.589055\pi$
$692$	−128.552	−4.88682
$693$	19.4284	0.738023
$694$	−42.4013	−1.60953
$695$	−50.6094	−1.91972
$696$	15.6173	0.591974
$697$	39.4085	1.49270
$698$	−44.3015	−1.67684
$699$	−0.173878	−0.00657666
$700$	−113.561	−4.29220
$701$	4.45492	0.168260	0.0841301	−	0.996455i	$-0.473189\pi$
$701$	4.45492	0.168260	0.0841301	+	0.996455i	$0.473189\pi$
$702$	−16.7818	−0.633390
$703$	2.46529	0.0929802
$704$	70.7879	2.66792
$705$	−2.91292	−0.109707
$706$	−30.7904	−1.15881
$707$	−28.3769	−1.06722
$708$	30.0934	1.13098
$709$	−27.1358	−1.01911	−0.509554	−	0.860439i	$-0.670189\pi$
$709$	−27.1358	−1.01911	−0.509554	+	0.860439i	$0.670189\pi$
$710$	−153.575	−5.76357
$711$	−10.2802	−0.385536
$712$	−105.896	−3.96862
$713$	3.15395	0.118116
$714$	−9.68252	−0.362359
$715$	35.4877	1.32717
$716$	−13.3714	−0.499714
$717$	−7.37613	−0.275467
$718$	3.60168	0.134414
$719$	−19.4840	−0.726632	−0.363316	−	0.931666i	$-0.618355\pi$
$719$	−19.4840	−0.726632	−0.363316	+	0.931666i	$0.618355\pi$
$720$	144.584	5.38833
$721$	30.6626	1.14194
$722$	−0.693019	−0.0257915
$723$	12.3781	0.460347
$724$	93.1274	3.46105
$725$	−47.2091	−1.75330
$726$	−1.25228	−0.0464765
$727$	41.8194	1.55099	0.775497	−	0.631351i	$-0.217499\pi$
$727$	41.8194	1.55099	0.775497	+	0.631351i	$0.217499\pi$
$728$	−43.6215	−1.61672
$729$	−17.9074	−0.663236
$730$	140.461	5.19868
$731$	−15.4574	−0.571711
$732$	15.4640	0.571564
$733$	11.8062	0.436072	0.218036	−	0.975941i	$-0.430035\pi$
$733$	11.8062	0.436072	0.218036	+	0.975941i	$0.430035\pi$
$734$	96.1151	3.54767
$735$	5.19678	0.191686
$736$	−77.2887	−2.84890
$737$	34.9507	1.28742
$738$	−69.0194	−2.54064
$739$	36.9572	1.35949	0.679746	−	0.733447i	$-0.262090\pi$
$739$	36.9572	1.35949	0.679746	+	0.733447i	$0.262090\pi$
$740$	−11.7289	−0.431162
$741$	−4.70700	−0.172916
$742$	21.1984	0.778216
$743$	−1.71315	−0.0628495	−0.0314248	−	0.999506i	$-0.510004\pi$
$743$	−1.71315	−0.0628495	−0.0314248	+	0.999506i	$0.510004\pi$
$744$	−2.53968	−0.0931092
$745$	−50.5181	−1.85084
$746$	39.0403	1.42937
$747$	−5.47883	−0.200460
$748$	−78.6582	−2.87603
$749$	20.8687	0.762527
$750$	27.1315	0.990703
$751$	−13.0401	−0.475841	−0.237920	−	0.971285i	$-0.576466\pi$
$751$	−13.0401	−0.475841	−0.237920	+	0.971285i	$0.576466\pi$
$752$	22.1634	0.808218
$753$	−4.49170	−0.163687
$754$	−29.3995	−1.07067
$755$	50.9677	1.85491
$756$	25.2886	0.919737
$757$	−9.32396	−0.338885	−0.169443	−	0.985540i	$-0.554197\pi$
$757$	−9.32396	−0.338885	−0.169443	+	0.985540i	$0.554197\pi$
$758$	−33.8596	−1.22984
$759$	6.61558	0.240131
$760$	151.847	5.50808
$761$	−34.5995	−1.25423	−0.627115	−	0.778927i	$-0.715764\pi$
$761$	−34.5995	−1.25423	−0.627115	+	0.778927i	$0.715764\pi$
$762$	−13.2435	−0.479761
$763$	−27.3049	−0.988505
$764$	6.88413	0.249059
$765$	−48.9065	−1.76822
$766$	45.0193	1.62661
$767$	−34.9430	−1.26172
$768$	6.00731	0.216770
$769$	42.3784	1.52820	0.764102	−	0.645096i	$-0.223183\pi$
$769$	42.3784	1.52820	0.764102	+	0.645096i	$0.223183\pi$
$770$	−73.9678	−2.66561
$771$	−2.71823	−0.0978947
$772$	101.761	3.66246
$773$	17.8026	0.640316	0.320158	−	0.947364i	$-0.396264\pi$
$773$	17.8026	0.640316	0.320158	+	0.947364i	$0.396264\pi$
$774$	27.0717	0.973074
$775$	7.67710	0.275770
$776$	47.5527	1.70704
$777$	−0.467428	−0.0167689
$778$	79.4482	2.84836
$779$	−39.9310	−1.43067
$780$	22.3940	0.801834
$781$	−49.7204	−1.77914
$782$	52.5908	1.88064
$783$	10.5129	0.375699
$784$	−39.5406	−1.41216
$785$	61.9546	2.21125
$786$	−6.79987	−0.242543
$787$	−7.07032	−0.252030	−0.126015	−	0.992028i	$-0.540219\pi$
$787$	−7.07032	−0.252030	−0.126015	+	0.992028i	$0.540219\pi$
$788$	−2.73463	−0.0974172
$789$	−1.39793	−0.0497677
$790$	39.1387	1.39249
$791$	33.4524	1.18943
$792$	84.9733	3.01939
$793$	−17.9560	−0.637637
$794$	2.13974	0.0759364
$795$	−6.71261	−0.238072
$796$	−54.1542	−1.91944
$797$	31.6135	1.11981	0.559904	−	0.828558i	$-0.310838\pi$
$797$	31.6135	1.11981	0.559904	+	0.828558i	$0.310838\pi$
$798$	9.81088	0.347301
$799$	−7.49693	−0.265222
$800$	−188.130	−6.65141
$801$	−34.5588	−1.22107
$802$	28.3602	1.00143
$803$	45.4746	1.60476
$804$	22.0551	0.777823
$805$	35.7543	1.26017
$806$	4.78092	0.168401
$807$	7.09432	0.249732
$808$	−124.111	−4.36622
$809$	−27.0891	−0.952403	−0.476201	−	0.879336i	$-0.657987\pi$
$809$	−27.0891	−0.952403	−0.476201	+	0.879336i	$0.657987\pi$
$810$	79.9476	2.80907
$811$	29.0111	1.01872	0.509359	−	0.860554i	$-0.329883\pi$
$811$	29.0111	1.01872	0.509359	+	0.860554i	$0.329883\pi$
$812$	44.3021	1.55470
$813$	−6.16430	−0.216191
$814$	−5.25230	−0.184093
$815$	69.7925	2.44473
$816$	−23.3285	−0.816660
$817$	15.6623	0.547953
$818$	37.3552	1.30609
$819$	−14.2357	−0.497437
$820$	189.976	6.63424
$821$	−39.0357	−1.36236	−0.681178	−	0.732118i	$-0.738532\pi$
$821$	−39.0357	−1.36236	−0.681178	+	0.732118i	$0.738532\pi$
$822$	19.9513	0.695881
$823$	25.0475	0.873102	0.436551	−	0.899679i	$-0.356200\pi$
$823$	25.0475	0.873102	0.436551	+	0.899679i	$0.356200\pi$
$824$	134.108	4.67188
$825$	16.1032	0.560640
$826$	72.8324	2.53416
$827$	−13.1012	−0.455573	−0.227787	−	0.973711i	$-0.573149\pi$
$827$	−13.1012	−0.455573	−0.227787	+	0.973711i	$0.573149\pi$
$828$	−66.5904	−2.31418
$829$	−38.1379	−1.32458	−0.662292	−	0.749246i	$-0.730416\pi$
$829$	−38.1379	−1.32458	−0.662292	+	0.749246i	$0.730416\pi$
$830$	20.8590	0.724028
$831$	−11.0631	−0.383776
$832$	−51.8683	−1.79821
$833$	13.3749	0.463412
$834$	−14.3014	−0.495216
$835$	−17.2647	−0.597470
$836$	79.7010	2.75652
$837$	−1.70959	−0.0590922
$838$	−47.9613	−1.65680
$839$	−0.849033	−0.0293119	−0.0146559	−	0.999893i	$-0.504665\pi$
$839$	−0.849033	−0.0293119	−0.0146559	+	0.999893i	$0.504665\pi$
$840$	−28.7908	−0.993376
$841$	−10.5829	−0.364929
$842$	70.1886	2.41886
$843$	8.40616	0.289524
$844$	−76.6099	−2.63702
$845$	25.9980	0.894360
$846$	13.1300	0.451418
$847$	−2.19117	−0.0752895
$848$	51.0741	1.75389
$849$	−6.93387	−0.237970
$850$	128.013	4.39079
$851$	2.53884	0.0870304
$852$	−31.3753	−1.07490
$853$	45.4746	1.55702	0.778510	−	0.627632i	$-0.215976\pi$
$853$	45.4746	1.55702	0.778510	+	0.627632i	$0.215976\pi$
$854$	37.4261	1.28069
$855$	49.5549	1.69474
$856$	91.2730	3.11965
$857$	45.9337	1.56907	0.784533	−	0.620087i	$-0.212903\pi$
$857$	45.9337	1.56907	0.784533	+	0.620087i	$0.212903\pi$
$858$	10.0282	0.342359
$859$	−11.1390	−0.380058	−0.190029	−	0.981778i	$-0.560858\pi$
$859$	−11.1390	−0.380058	−0.190029	+	0.981778i	$0.560858\pi$
$860$	−74.5149	−2.54094
$861$	7.57105	0.258021
$862$	11.9148	0.405818
$863$	−26.3734	−0.897761	−0.448880	−	0.893592i	$-0.648177\pi$
$863$	−26.3734	−0.897761	−0.448880	+	0.893592i	$0.648177\pi$
$864$	41.8942	1.42527
$865$	98.5194	3.34976
$866$	83.7417	2.84566
$867$	0.739281	0.0251073
$868$	−7.20437	−0.244532
$869$	12.6713	0.429843
$870$	−19.4040	−0.657859
$871$	−25.6093	−0.867740
$872$	−119.423	−4.04416
$873$	15.5187	0.525228
$874$	−53.2880	−1.80249
$875$	47.4732	1.60489
$876$	28.6961	0.969550
$877$	−0.968243	−0.0326952	−0.0163476	−	0.999866i	$-0.505204\pi$
$877$	−0.968243	−0.0326952	−0.0163476	+	0.999866i	$0.505204\pi$
$878$	28.5727	0.964283
$879$	−8.13882	−0.274516
$880$	−178.213	−6.00758
$881$	−9.66838	−0.325736	−0.162868	−	0.986648i	$-0.552074\pi$
$881$	−9.66838	−0.325736	−0.162868	+	0.986648i	$0.552074\pi$
$882$	−23.4245	−0.788744
$883$	−18.6754	−0.628477	−0.314239	−	0.949344i	$-0.601749\pi$
$883$	−18.6754	−0.628477	−0.314239	+	0.949344i	$0.601749\pi$
$884$	57.6351	1.93848
$885$	−23.0629	−0.775250
$886$	−57.3655	−1.92723
$887$	1.42565	0.0478685	0.0239343	−	0.999714i	$-0.492381\pi$
$887$	1.42565	0.0478685	0.0239343	+	0.999714i	$0.492381\pi$
$888$	−2.04437	−0.0686047
$889$	−23.1727	−0.777187
$890$	131.572	4.41031
$891$	25.8833	0.867122
$892$	42.3939	1.41945
$893$	7.59631	0.254201
$894$	−14.2756	−0.477447
$895$	10.2476	0.342538
$896$	40.4609	1.35170
$897$	−4.84743	−0.161851
$898$	−44.8523	−1.49674
$899$	−2.99497	−0.0998878
$900$	−162.089	−5.40297
$901$	−17.2761	−0.575552
$902$	85.0728	2.83262
$903$	−2.96962	−0.0988228
$904$	146.310	4.86619
$905$	−71.3707	−2.37244
$906$	14.4026	0.478495
$907$	−19.2206	−0.638210	−0.319105	−	0.947719i	$-0.603382\pi$
$907$	−19.2206	−0.638210	−0.319105	+	0.947719i	$0.603382\pi$
$908$	114.392	3.79622
$909$	−40.5033	−1.34341
$910$	54.1983	1.79666
$911$	16.6522	0.551711	0.275856	−	0.961199i	$-0.411039\pi$
$911$	16.6522	0.551711	0.275856	+	0.961199i	$0.411039\pi$
$912$	23.6377	0.782724
$913$	6.75318	0.223497
$914$	1.41242	0.0467188
$915$	−11.8512	−0.391789
$916$	47.9801	1.58531
$917$	−11.8980	−0.392908
$918$	−28.5068	−0.940863
$919$	−51.3896	−1.69519	−0.847593	−	0.530647i	$-0.821949\pi$
$919$	−51.3896	−1.69519	−0.847593	+	0.530647i	$0.821949\pi$
$920$	156.378	5.15562
$921$	−2.66032	−0.0876606
$922$	−16.6880	−0.549591
$923$	36.4316	1.19916
$924$	−15.1116	−0.497135
$925$	6.17986	0.203192
$926$	−23.0535	−0.757586
$927$	43.7658	1.43746
$928$	73.3929	2.40924
$929$	9.49538	0.311533	0.155767	−	0.987794i	$-0.450215\pi$
$929$	9.49538	0.311533	0.155767	+	0.987794i	$0.450215\pi$
$930$	3.15547	0.103472
$931$	−13.5522	−0.444155
$932$	−2.15728	−0.0706642
$933$	0.671572	0.0219863
$934$	−68.0788	−2.22761
$935$	60.2819	1.97143
$936$	−62.2624	−2.03511
$937$	29.4188	0.961071	0.480536	−	0.876975i	$-0.340442\pi$
$937$	29.4188	0.961071	0.480536	+	0.876975i	$0.340442\pi$
$938$	53.3780	1.74285
$939$	−5.72463	−0.186816
$940$	−36.1402	−1.17876
$941$	−37.5242	−1.22325	−0.611626	−	0.791147i	$-0.709484\pi$
$941$	−37.5242	−1.22325	−0.611626	+	0.791147i	$0.709484\pi$
$942$	17.5073	0.570420
$943$	−41.1223	−1.33913
$944$	175.478	5.71132
$945$	−19.3806	−0.630450
$946$	−33.3684	−1.08490
$947$	3.86902	0.125726	0.0628631	−	0.998022i	$-0.479977\pi$
$947$	3.86902	0.125726	0.0628631	+	0.998022i	$0.479977\pi$
$948$	7.99601	0.259698
$949$	−33.3205	−1.08163
$950$	−129.710	−4.20833
$951$	−9.11562	−0.295594
$952$	−74.0984	−2.40154
$953$	6.14411	0.199027	0.0995136	−	0.995036i	$-0.468271\pi$
$953$	6.14411	0.199027	0.0995136	+	0.995036i	$0.468271\pi$
$954$	30.2571	0.979610
$955$	−5.27584	−0.170722
$956$	−91.5149	−2.95980
$957$	−6.28212	−0.203072
$958$	49.1105	1.58669
$959$	34.9096	1.12729
$960$	−34.2338	−1.10489
$961$	−30.5130	−0.984289
$962$	3.84851	0.124081
$963$	29.7866	0.959861
$964$	153.574	4.94628
$965$	−77.9873	−2.51050
$966$	10.1036	0.325077
$967$	−22.8244	−0.733983	−0.366992	−	0.930224i	$-0.619612\pi$
$967$	−22.8244	−0.733983	−0.366992	+	0.930224i	$0.619612\pi$
$968$	−9.58345	−0.308024
$969$	−7.99562	−0.256856
$970$	−59.0828	−1.89703
$971$	−29.1569	−0.935690	−0.467845	−	0.883811i	$-0.654969\pi$
$971$	−29.1569	−0.935690	−0.467845	+	0.883811i	$0.654969\pi$
$972$	54.6913	1.75423
$973$	−25.0237	−0.802225
$974$	34.0316	1.09044
$975$	−11.7992	−0.377878
$976$	90.1721	2.88634
$977$	50.9835	1.63111	0.815554	−	0.578681i	$-0.196433\pi$
$977$	50.9835	1.63111	0.815554	+	0.578681i	$0.196433\pi$
$978$	19.7222	0.630647
$979$	42.5969	1.36140
$980$	64.4759	2.05961
$981$	−38.9732	−1.24432
$982$	111.263	3.55054
$983$	38.2064	1.21860	0.609298	−	0.792941i	$-0.291451\pi$
$983$	38.2064	1.21860	0.609298	+	0.792941i	$0.291451\pi$
$984$	33.1132	1.05561
$985$	2.09576	0.0667764
$986$	−49.9399	−1.59041
$987$	−1.44029	−0.0458448
$988$	−58.3992	−1.85793
$989$	16.1296	0.512890
$990$	−105.577	−3.35544
$991$	12.1005	0.384384	0.192192	−	0.981357i	$-0.438440\pi$
$991$	12.1005	0.384384	0.192192	+	0.981357i	$0.438440\pi$
$992$	−11.9351	−0.378939
$993$	3.67962	0.116769
$994$	−75.9350	−2.40851
$995$	41.5025	1.31572
$996$	4.26149	0.135031
$997$	7.02131	0.222367	0.111184	−	0.993800i	$-0.464536\pi$
$997$	7.02131	0.222367	0.111184	+	0.993800i	$0.464536\pi$
$998$	50.4712	1.59764
$999$	−1.37618	−0.0435403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.7	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.7	✓	152	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68690 q^{2} +0.420690 q^{3} +5.21946 q^{4} -4.00007 q^{5} -1.13035 q^{6} -1.97783 q^{7} -8.65037 q^{8} -2.82302 q^{9} +O(q^{10})\)	\(q-2.68690 q^{2} +0.420690 q^{3} +5.21946 q^{4} -4.00007 q^{5} -1.13035 q^{6} -1.97783 q^{7} -8.65037 q^{8} -2.82302 q^{9} +10.7478 q^{10} +3.47964 q^{11} +2.19577 q^{12} -2.54963 q^{13} +5.31424 q^{14} -1.68279 q^{15} +12.8038 q^{16} -4.33097 q^{17} +7.58519 q^{18} +4.38839 q^{19} -20.8782 q^{20} -0.832053 q^{21} -9.34945 q^{22} +4.51931 q^{23} -3.63912 q^{24} +11.0006 q^{25} +6.85061 q^{26} -2.44969 q^{27} -10.3232 q^{28} -4.29151 q^{29} +4.52149 q^{30} +0.697882 q^{31} -17.1019 q^{32} +1.46385 q^{33} +11.6369 q^{34} +7.91146 q^{35} -14.7346 q^{36} +0.561776 q^{37} -11.7912 q^{38} -1.07260 q^{39} +34.6021 q^{40} -9.09924 q^{41} +2.23565 q^{42} +3.56903 q^{43} +18.1618 q^{44} +11.2923 q^{45} -12.1430 q^{46} +1.73100 q^{47} +5.38643 q^{48} -3.08819 q^{49} -29.5575 q^{50} -1.82200 q^{51} -13.3077 q^{52} +3.98898 q^{53} +6.58207 q^{54} -13.9188 q^{55} +17.1090 q^{56} +1.84615 q^{57} +11.5309 q^{58} +13.7051 q^{59} -8.78325 q^{60} +7.04260 q^{61} -1.87514 q^{62} +5.58345 q^{63} +20.3435 q^{64} +10.1987 q^{65} -3.93322 q^{66} +10.0443 q^{67} -22.6053 q^{68} +1.90123 q^{69} -21.2573 q^{70} -14.2890 q^{71} +24.4202 q^{72} +13.0688 q^{73} -1.50944 q^{74} +4.62783 q^{75} +22.9050 q^{76} -6.88213 q^{77} +2.88198 q^{78} +3.64155 q^{79} -51.2161 q^{80} +7.43850 q^{81} +24.4488 q^{82} +1.94077 q^{83} -4.34286 q^{84} +17.3242 q^{85} -9.58964 q^{86} -1.80540 q^{87} -30.1001 q^{88} +12.2418 q^{89} -30.3413 q^{90} +5.04273 q^{91} +23.5883 q^{92} +0.293592 q^{93} -4.65104 q^{94} -17.5539 q^{95} -7.19458 q^{96} -5.49719 q^{97} +8.29768 q^{98} -9.82308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

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