LMFDB - Embedded newform 667.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 $ x^16 - 3x^15 - 22x^14 + 68x^13 + 187x^12 - 597x^11 - 795x^10 + 2592x^9 + 1860x^8 - 5877x^7 - 2496x^6 + 6612x^5 + 1842x^4 - 3011x^3 - 505x^2 + 336*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.03000$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.03000 q^{2} -0.920112 q^{3} -0.939097 q^{4} +3.95819 q^{5} +0.947716 q^{6} +4.48231 q^{7} +3.02727 q^{8} -2.15339 q^{9} +O(q^{10})$	\(q-1.03000 q^{2} -0.920112 q^{3} -0.939097 q^{4} +3.95819 q^{5} +0.947716 q^{6} +4.48231 q^{7} +3.02727 q^{8} -2.15339 q^{9} -4.07695 q^{10} +5.58245 q^{11} +0.864074 q^{12} +1.54285 q^{13} -4.61678 q^{14} -3.64198 q^{15} -1.23990 q^{16} -7.55730 q^{17} +2.21800 q^{18} -3.20558 q^{19} -3.71713 q^{20} -4.12423 q^{21} -5.74993 q^{22} +1.00000 q^{23} -2.78543 q^{24} +10.6673 q^{25} -1.58914 q^{26} +4.74170 q^{27} -4.20932 q^{28} -1.00000 q^{29} +3.75125 q^{30} +4.20583 q^{31} -4.77745 q^{32} -5.13648 q^{33} +7.78403 q^{34} +17.7419 q^{35} +2.02225 q^{36} +4.87699 q^{37} +3.30176 q^{38} -1.41960 q^{39} +11.9825 q^{40} -1.92475 q^{41} +4.24796 q^{42} -11.4855 q^{43} -5.24246 q^{44} -8.52355 q^{45} -1.03000 q^{46} -1.70768 q^{47} +1.14085 q^{48} +13.0911 q^{49} -10.9873 q^{50} +6.95356 q^{51} -1.44889 q^{52} +9.65100 q^{53} -4.88396 q^{54} +22.0964 q^{55} +13.5692 q^{56} +2.94950 q^{57} +1.03000 q^{58} -5.68257 q^{59} +3.42017 q^{60} +0.740179 q^{61} -4.33201 q^{62} -9.65218 q^{63} +7.40058 q^{64} +6.10691 q^{65} +5.29058 q^{66} -10.1138 q^{67} +7.09704 q^{68} -0.920112 q^{69} -18.2741 q^{70} +6.76766 q^{71} -6.51892 q^{72} +6.55560 q^{73} -5.02331 q^{74} -9.81511 q^{75} +3.01036 q^{76} +25.0223 q^{77} +1.46219 q^{78} -10.6027 q^{79} -4.90777 q^{80} +2.09729 q^{81} +1.98249 q^{82} -3.13550 q^{83} +3.87305 q^{84} -29.9132 q^{85} +11.8301 q^{86} +0.920112 q^{87} +16.8996 q^{88} +10.3943 q^{89} +8.77927 q^{90} +6.91554 q^{91} -0.939097 q^{92} -3.86984 q^{93} +1.75892 q^{94} -12.6883 q^{95} +4.39579 q^{96} -8.85845 q^{97} -13.4838 q^{98} -12.0212 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * 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 $

$2$	−1.03000	−0.728321	−0.364160	−	0.931336i	$-0.618644\pi$
$2$	−1.03000	−0.728321	−0.364160	+	0.931336i	$0.618644\pi$
$3$	−0.920112	−0.531227	−0.265613	−	0.964080i	$-0.585574\pi$
$3$	−0.920112	−0.531227	−0.265613	+	0.964080i	$0.585574\pi$
$4$	−0.939097	−0.469549
$5$	3.95819	1.77016	0.885079	−	0.465441i	$-0.154104\pi$
$5$	3.95819	1.77016	0.885079	+	0.465441i	$0.154104\pi$
$6$	0.947716	0.386904
$7$	4.48231	1.69415	0.847077	−	0.531471i	$-0.178360\pi$
$7$	4.48231	1.69415	0.847077	+	0.531471i	$0.178360\pi$
$8$	3.02727	1.07030
$9$	−2.15339	−0.717798
$10$	−4.07695	−1.28924
$11$	5.58245	1.68317	0.841586	−	0.540124i	$-0.181623\pi$
$11$	5.58245	1.68317	0.841586	+	0.540124i	$0.181623\pi$
$12$	0.864074	0.249437
$13$	1.54285	0.427910	0.213955	−	0.976844i	$-0.431365\pi$
$13$	1.54285	0.427910	0.213955	+	0.976844i	$0.431365\pi$
$14$	−4.61678	−1.23389
$15$	−3.64198	−0.940355
$16$	−1.23990	−0.309976
$17$	−7.55730	−1.83291	−0.916457	−	0.400134i	$-0.868964\pi$
$17$	−7.55730	−1.83291	−0.916457	+	0.400134i	$0.868964\pi$
$18$	2.21800	0.522787
$19$	−3.20558	−0.735412	−0.367706	−	0.929942i	$-0.619857\pi$
$19$	−3.20558	−0.735412	−0.367706	+	0.929942i	$0.619857\pi$
$20$	−3.71713	−0.831175
$21$	−4.12423	−0.899980
$22$	−5.74993	−1.22589
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.78543	−0.568574
$25$	10.6673	2.13346
$26$	−1.58914	−0.311656
$27$	4.74170	0.912540
$28$	−4.20932	−0.795487
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.75125	0.684881
$31$	4.20583	0.755390	0.377695	−	0.925930i	$-0.376717\pi$
$31$	4.20583	0.755390	0.377695	+	0.925930i	$0.376717\pi$
$32$	−4.77745	−0.844541
$33$	−5.13648	−0.894146
$34$	7.78403	1.33495
$35$	17.7419	2.99892
$36$	2.02225	0.337041
$37$	4.87699	0.801773	0.400886	−	0.916128i	$-0.368702\pi$
$37$	4.87699	0.801773	0.400886	+	0.916128i	$0.368702\pi$
$38$	3.30176	0.535616
$39$	−1.41960	−0.227317
$40$	11.9825	1.89461
$41$	−1.92475	−0.300595	−0.150298	−	0.988641i	$-0.548023\pi$
$41$	−1.92475	−0.300595	−0.150298	+	0.988641i	$0.548023\pi$
$42$	4.24796	0.655474
$43$	−11.4855	−1.75152	−0.875760	−	0.482747i	$-0.839639\pi$
$43$	−11.4855	−1.75152	−0.875760	+	0.482747i	$0.839639\pi$
$44$	−5.24246	−0.790331
$45$	−8.52355	−1.27062
$46$	−1.03000	−0.151865
$47$	−1.70768	−0.249091	−0.124546	−	0.992214i	$-0.539747\pi$
$47$	−1.70768	−0.249091	−0.124546	+	0.992214i	$0.539747\pi$
$48$	1.14085	0.164667
$49$	13.0911	1.87016
$50$	−10.9873	−1.55384
$51$	6.95356	0.973693
$52$	−1.44889	−0.200925
$53$	9.65100	1.32567	0.662833	−	0.748767i	$-0.269354\pi$
$53$	9.65100	1.32567	0.662833	+	0.748767i	$0.269354\pi$
$54$	−4.88396	−0.664622
$55$	22.0964	2.97948
$56$	13.5692	1.81326
$57$	2.94950	0.390670
$58$	1.03000	0.135246
$59$	−5.68257	−0.739808	−0.369904	−	0.929070i	$-0.620609\pi$
$59$	−5.68257	−0.739808	−0.369904	+	0.929070i	$0.620609\pi$
$60$	3.42017	0.441543
$61$	0.740179	0.0947701	0.0473851	−	0.998877i	$-0.484911\pi$
$61$	0.740179	0.0947701	0.0473851	+	0.998877i	$0.484911\pi$
$62$	−4.33201	−0.550166
$63$	−9.65218	−1.21606
$64$	7.40058	0.925073
$65$	6.10691	0.757469
$66$	5.29058	0.651225
$67$	−10.1138	−1.23559	−0.617796	−	0.786339i	$-0.711974\pi$
$67$	−10.1138	−1.23559	−0.617796	+	0.786339i	$0.711974\pi$
$68$	7.09704	0.860642
$69$	−0.920112	−0.110768
$70$	−18.2741	−2.18418
$71$	6.76766	0.803174	0.401587	−	0.915821i	$-0.368459\pi$
$71$	6.76766	0.803174	0.401587	+	0.915821i	$0.368459\pi$
$72$	−6.51892	−0.768262
$73$	6.55560	0.767275	0.383637	−	0.923484i	$-0.374671\pi$
$73$	6.55560	0.767275	0.383637	+	0.923484i	$0.374671\pi$
$74$	−5.02331	−0.583948
$75$	−9.81511	−1.13335
$76$	3.01036	0.345311
$77$	25.0223	2.85155
$78$	1.46219	0.165560
$79$	−10.6027	−1.19290	−0.596451	−	0.802650i	$-0.703423\pi$
$79$	−10.6027	−1.19290	−0.596451	+	0.802650i	$0.703423\pi$
$80$	−4.90777	−0.548706
$81$	2.09729	0.233032
$82$	1.98249	0.218930
$83$	−3.13550	−0.344165	−0.172083	−	0.985083i	$-0.555050\pi$
$83$	−3.13550	−0.344165	−0.172083	+	0.985083i	$0.555050\pi$
$84$	3.87305	0.422584
$85$	−29.9132	−3.24455
$86$	11.8301	1.27567
$87$	0.920112	0.0986463
$88$	16.8996	1.80150
$89$	10.3943	1.10180	0.550899	−	0.834572i	$-0.314285\pi$
$89$	10.3943	1.10180	0.550899	+	0.834572i	$0.314285\pi$
$90$	8.77927	0.925417
$91$	6.91554	0.724945
$92$	−0.939097	−0.0979076
$93$	−3.86984	−0.401283
$94$	1.75892	0.181418
$95$	−12.6883	−1.30179
$96$	4.39579	0.448643
$97$	−8.85845	−0.899439	−0.449720	−	0.893170i	$-0.648476\pi$
$97$	−8.85845	−0.899439	−0.449720	+	0.893170i	$0.648476\pi$
$98$	−13.4838	−1.36207
$99$	−12.0212	−1.20818
$100$	−10.0176	−1.00176
$101$	3.50214	0.348476	0.174238	−	0.984704i	$-0.444254\pi$
$101$	3.50214	0.348476	0.174238	+	0.984704i	$0.444254\pi$
$102$	−7.16217	−0.709161
$103$	10.2397	1.00895	0.504475	−	0.863426i	$-0.331686\pi$
$103$	10.2397	1.00895	0.504475	+	0.863426i	$0.331686\pi$
$104$	4.67064	0.457994
$105$	−16.3245	−1.59311
$106$	−9.94054	−0.965511
$107$	−4.66882	−0.451352	−0.225676	−	0.974202i	$-0.572459\pi$
$107$	−4.66882	−0.451352	−0.225676	+	0.974202i	$0.572459\pi$
$108$	−4.45292	−0.428482
$109$	−8.37166	−0.801859	−0.400930	−	0.916109i	$-0.631313\pi$
$109$	−8.37166	−0.801859	−0.400930	+	0.916109i	$0.631313\pi$
$110$	−22.7593	−2.17002
$111$	−4.48738	−0.425923
$112$	−5.55763	−0.525146
$113$	−7.49063	−0.704659	−0.352330	−	0.935876i	$-0.614610\pi$
$113$	−7.49063	−0.704659	−0.352330	+	0.935876i	$0.614610\pi$
$114$	−3.03798	−0.284533
$115$	3.95819	0.369104
$116$	0.939097	0.0871930
$117$	−3.32237	−0.307153
$118$	5.85306	0.538818
$119$	−33.8741	−3.10524
$120$	−11.0253	−1.00647
$121$	20.1637	1.83307
$122$	−0.762385	−0.0690231
$123$	1.77098	0.159684
$124$	−3.94969	−0.354692
$125$	22.4323	2.00640
$126$	9.94176	0.885682
$127$	−3.18394	−0.282529	−0.141265	−	0.989972i	$-0.545117\pi$
$127$	−3.18394	−0.282529	−0.141265	+	0.989972i	$0.545117\pi$
$128$	1.93228	0.170791
$129$	10.5679	0.930454
$130$	−6.29012	−0.551680
$131$	1.43514	0.125388	0.0626942	−	0.998033i	$-0.480031\pi$
$131$	1.43514	0.125388	0.0626942	+	0.998033i	$0.480031\pi$
$132$	4.82365	0.419845
$133$	−14.3684	−1.24590
$134$	10.4172	0.899907
$135$	18.7686	1.61534
$136$	−22.8780	−1.96177
$137$	17.9076	1.52995	0.764973	−	0.644062i	$-0.222752\pi$
$137$	17.9076	1.52995	0.764973	+	0.644062i	$0.222752\pi$
$138$	0.947716	0.0806750
$139$	5.42185	0.459875	0.229938	−	0.973205i	$-0.426148\pi$
$139$	5.42185	0.459875	0.229938	+	0.973205i	$0.426148\pi$
$140$	−16.6613	−1.40814
$141$	1.57126	0.132324
$142$	−6.97070	−0.584968
$143$	8.61289	0.720246
$144$	2.67000	0.222500
$145$	−3.95819	−0.328710
$146$	−6.75228	−0.558822
$147$	−12.0453	−0.993477
$148$	−4.57997	−0.376471
$149$	5.07035	0.415380	0.207690	−	0.978195i	$-0.433406\pi$
$149$	5.07035	0.415380	0.207690	+	0.978195i	$0.433406\pi$
$150$	10.1096	0.825444
$151$	−16.4660	−1.33998	−0.669992	−	0.742368i	$-0.733703\pi$
$151$	−16.4660	−1.33998	−0.669992	+	0.742368i	$0.733703\pi$
$152$	−9.70418	−0.787113
$153$	16.2738	1.31566
$154$	−25.7730	−2.07684
$155$	16.6475	1.33716
$156$	1.33314	0.106737
$157$	−4.55430	−0.363472	−0.181736	−	0.983347i	$-0.558172\pi$
$157$	−4.55430	−0.363472	−0.181736	+	0.983347i	$0.558172\pi$
$158$	10.9208	0.868815
$159$	−8.88000	−0.704229
$160$	−18.9101	−1.49497
$161$	4.48231	0.353255
$162$	−2.16021	−0.169722
$163$	7.06221	0.553155	0.276578	−	0.960992i	$-0.410800\pi$
$163$	7.06221	0.553155	0.276578	+	0.960992i	$0.410800\pi$
$164$	1.80753	0.141144
$165$	−20.3312	−1.58278
$166$	3.22956	0.250663
$167$	6.45941	0.499844	0.249922	−	0.968266i	$-0.419595\pi$
$167$	6.45941	0.499844	0.249922	+	0.968266i	$0.419595\pi$
$168$	−12.4852	−0.963251
$169$	−10.6196	−0.816893
$170$	30.8107	2.36307
$171$	6.90289	0.527877
$172$	10.7860	0.822423
$173$	11.4908	0.873628	0.436814	−	0.899552i	$-0.356107\pi$
$173$	11.4908	0.873628	0.436814	+	0.899552i	$0.356107\pi$
$174$	−0.947716	−0.0718462
$175$	47.8141	3.61441
$176$	−6.92169	−0.521742
$177$	5.22860	0.393006
$178$	−10.7062	−0.802463
$179$	−9.25784	−0.691964	−0.345982	−	0.938241i	$-0.612454\pi$
$179$	−9.25784	−0.691964	−0.345982	+	0.938241i	$0.612454\pi$
$180$	8.00444	0.596616
$181$	−23.0828	−1.71573	−0.857865	−	0.513874i	$-0.828210\pi$
$181$	−23.0828	−1.71573	−0.857865	+	0.513874i	$0.828210\pi$
$182$	−7.12301	−0.527993
$183$	−0.681047	−0.0503444
$184$	3.02727	0.223174
$185$	19.3041	1.41926
$186$	3.98594	0.292263
$187$	−42.1882	−3.08511
$188$	1.60368	0.116960
$189$	21.2538	1.54598
$190$	13.0690	0.948124
$191$	−4.08324	−0.295453	−0.147727	−	0.989028i	$-0.547196\pi$
$191$	−4.08324	−0.295453	−0.147727	+	0.989028i	$0.547196\pi$
$192$	−6.80936	−0.491423
$193$	−13.0498	−0.939347	−0.469674	−	0.882840i	$-0.655628\pi$
$193$	−13.0498	−0.939347	−0.469674	+	0.882840i	$0.655628\pi$
$194$	9.12421	0.655080
$195$	−5.61904	−0.402388
$196$	−12.2938	−0.878129
$197$	0.745096	0.0530859	0.0265430	−	0.999648i	$-0.491550\pi$
$197$	0.745096	0.0530859	0.0265430	+	0.999648i	$0.491550\pi$
$198$	12.3819	0.879941
$199$	3.65472	0.259076	0.129538	−	0.991574i	$-0.458651\pi$
$199$	3.65472	0.259076	0.129538	+	0.991574i	$0.458651\pi$
$200$	32.2928	2.28345
$201$	9.30578	0.656379
$202$	−3.60721	−0.253802
$203$	−4.48231	−0.314596
$204$	−6.53007	−0.457196
$205$	−7.61853	−0.532101
$206$	−10.5469	−0.734839
$207$	−2.15339	−0.149671
$208$	−1.91299	−0.132642
$209$	−17.8950	−1.23782
$210$	16.8142	1.16029
$211$	−25.1728	−1.73297	−0.866483	−	0.499206i	$-0.833625\pi$
$211$	−25.1728	−1.73297	−0.866483	+	0.499206i	$0.833625\pi$
$212$	−9.06322	−0.622465
$213$	−6.22701	−0.426668
$214$	4.80890	0.328729
$215$	−45.4618	−3.10047
$216$	14.3544	0.976695
$217$	18.8518	1.27975
$218$	8.62282	0.584011
$219$	−6.03188	−0.407597
$220$	−20.7507	−1.39901
$221$	−11.6598	−0.784322
$222$	4.62201	0.310209
$223$	7.72283	0.517159	0.258579	−	0.965990i	$-0.416746\pi$
$223$	7.72283	0.517159	0.258579	+	0.965990i	$0.416746\pi$
$224$	−21.4140	−1.43078
$225$	−22.9709	−1.53139
$226$	7.71536	0.513218
$227$	−1.94258	−0.128934	−0.0644669	−	0.997920i	$-0.520535\pi$
$227$	−1.94258	−0.128934	−0.0644669	+	0.997920i	$0.520535\pi$
$228$	−2.76986	−0.183439
$229$	15.9480	1.05388	0.526938	−	0.849904i	$-0.323340\pi$
$229$	15.9480	1.05388	0.526938	+	0.849904i	$0.323340\pi$
$230$	−4.07695	−0.268826
$231$	−23.0233	−1.51482
$232$	−3.02727	−0.198750
$233$	19.4550	1.27454	0.637268	−	0.770642i	$-0.280064\pi$
$233$	19.4550	1.27454	0.637268	+	0.770642i	$0.280064\pi$
$234$	3.42204	0.223706
$235$	−6.75934	−0.440931
$236$	5.33649	0.347376
$237$	9.75571	0.633701
$238$	34.8904	2.26161
$239$	−15.6778	−1.01412	−0.507058	−	0.861912i	$-0.669267\pi$
$239$	−15.6778	−1.01412	−0.507058	+	0.861912i	$0.669267\pi$
$240$	4.51570	0.291487
$241$	−7.42619	−0.478363	−0.239181	−	0.970975i	$-0.576879\pi$
$241$	−7.42619	−0.478363	−0.239181	+	0.970975i	$0.576879\pi$
$242$	−20.7687	−1.33506
$243$	−16.1548	−1.03633
$244$	−0.695099	−0.0444992
$245$	51.8171	3.31047
$246$	−1.82412	−0.116301
$247$	−4.94574	−0.314690
$248$	12.7322	0.808496
$249$	2.88501	0.182830
$250$	−23.1053	−1.46131
$251$	−10.3226	−0.651554	−0.325777	−	0.945447i	$-0.605626\pi$
$251$	−10.3226	−0.651554	−0.325777	+	0.945447i	$0.605626\pi$
$252$	9.06433	0.570999
$253$	5.58245	0.350965
$254$	3.27946	0.205772
$255$	27.5235	1.72359
$256$	−16.7914	−1.04946
$257$	29.9267	1.86678	0.933389	−	0.358866i	$-0.116836\pi$
$257$	29.9267	1.86678	0.933389	+	0.358866i	$0.116836\pi$
$258$	−10.8850	−0.677669
$259$	21.8602	1.35833
$260$	−5.73498	−0.355668
$261$	2.15339	0.133292
$262$	−1.47819	−0.0913230
$263$	3.49282	0.215377	0.107688	−	0.994185i	$-0.465655\pi$
$263$	3.49282	0.215377	0.107688	+	0.994185i	$0.465655\pi$
$264$	−15.5495	−0.957007
$265$	38.2005	2.34664
$266$	14.7995	0.907415
$267$	−9.56396	−0.585305
$268$	9.49779	0.580170
$269$	1.54881	0.0944327	0.0472164	−	0.998885i	$-0.484965\pi$
$269$	1.54881	0.0944327	0.0472164	+	0.998885i	$0.484965\pi$
$270$	−19.3316	−1.17649
$271$	−10.7318	−0.651912	−0.325956	−	0.945385i	$-0.605686\pi$
$271$	−10.7318	−0.651912	−0.325956	+	0.945385i	$0.605686\pi$
$272$	9.37031	0.568159
$273$	−6.36307	−0.385110
$274$	−18.4448	−1.11429
$275$	59.5497	3.59098
$276$	0.864074	0.0520112
$277$	−14.4071	−0.865637	−0.432818	−	0.901481i	$-0.642481\pi$
$277$	−14.4071	−0.865637	−0.432818	+	0.901481i	$0.642481\pi$
$278$	−5.58451	−0.334937
$279$	−9.05682	−0.542218
$280$	53.7094	3.20975
$281$	13.9764	0.833762	0.416881	−	0.908961i	$-0.363123\pi$
$281$	13.9764	0.833762	0.416881	+	0.908961i	$0.363123\pi$
$282$	−1.61840	−0.0963743
$283$	21.1862	1.25939	0.629693	−	0.776844i	$-0.283181\pi$
$283$	21.1862	1.25939	0.629693	+	0.776844i	$0.283181\pi$
$284$	−6.35549	−0.377129
$285$	11.6747	0.691548
$286$	−8.87129	−0.524570
$287$	−8.62731	−0.509254
$288$	10.2877	0.606210
$289$	40.1127	2.35957
$290$	4.07695	0.239406
$291$	8.15076	0.477806
$292$	−6.15634	−0.360273
$293$	−27.1475	−1.58597	−0.792987	−	0.609238i	$-0.791475\pi$
$293$	−27.1475	−1.58597	−0.792987	+	0.609238i	$0.791475\pi$
$294$	12.4066	0.723570
$295$	−22.4927	−1.30958
$296$	14.7640	0.858140
$297$	26.4703	1.53596
$298$	−5.22247	−0.302530
$299$	1.54285	0.0892254
$300$	9.21734	0.532163
$301$	−51.4815	−2.96734
$302$	16.9600	0.975939
$303$	−3.22236	−0.185120
$304$	3.97461	0.227960
$305$	2.92977	0.167758
$306$	−16.7621	−0.958224
$307$	8.36373	0.477343	0.238672	−	0.971100i	$-0.423288\pi$
$307$	8.36373	0.477343	0.238672	+	0.971100i	$0.423288\pi$
$308$	−23.4983	−1.33894
$309$	−9.42168	−0.535981
$310$	−17.1470	−0.973882
$311$	−27.9312	−1.58383	−0.791916	−	0.610630i	$-0.790916\pi$
$311$	−27.9312	−1.58383	−0.791916	+	0.610630i	$0.790916\pi$
$312$	−4.29751	−0.243298
$313$	−4.19166	−0.236927	−0.118463	−	0.992958i	$-0.537797\pi$
$313$	−4.19166	−0.236927	−0.118463	+	0.992958i	$0.537797\pi$
$314$	4.69093	0.264725
$315$	−38.2052	−2.15262
$316$	9.95701	0.560125
$317$	−3.35364	−0.188359	−0.0941796	−	0.995555i	$-0.530023\pi$
$317$	−3.35364	−0.188359	−0.0941796	+	0.995555i	$0.530023\pi$
$318$	9.14641	0.512905
$319$	−5.58245	−0.312557
$320$	29.2929	1.63753
$321$	4.29584	0.239770
$322$	−4.61678	−0.257283
$323$	24.2256	1.34795
$324$	−1.96956	−0.109420
$325$	16.4581	0.912929
$326$	−7.27409	−0.402875
$327$	7.70286	0.425969
$328$	−5.82674	−0.321728
$329$	−7.65436	−0.421999
$330$	20.9411	1.15277
$331$	26.3713	1.44950	0.724748	−	0.689014i	$-0.241956\pi$
$331$	26.3713	1.44950	0.724748	+	0.689014i	$0.241956\pi$
$332$	2.94453	0.161602
$333$	−10.5021	−0.575511
$334$	−6.65320	−0.364047
$335$	−40.0322	−2.18719
$336$	5.11364	0.278972
$337$	−29.2668	−1.59426	−0.797132	−	0.603806i	$-0.793650\pi$
$337$	−29.2668	−1.59426	−0.797132	+	0.603806i	$0.793650\pi$
$338$	10.9382	0.594960
$339$	6.89222	0.374334
$340$	28.0914	1.52347
$341$	23.4788	1.27145
$342$	−7.10998	−0.384464
$343$	27.3022	1.47418
$344$	−34.7697	−1.87466
$345$	−3.64198	−0.196078
$346$	−11.8355	−0.636281
$347$	28.4110	1.52518	0.762592	−	0.646880i	$-0.223926\pi$
$347$	28.4110	1.52518	0.762592	+	0.646880i	$0.223926\pi$
$348$	−0.864074	−0.0463192
$349$	−9.09625	−0.486911	−0.243456	−	0.969912i	$-0.578281\pi$
$349$	−9.09625	−0.486911	−0.243456	+	0.969912i	$0.578281\pi$
$350$	−49.2486	−2.63245
$351$	7.31574	0.390485
$352$	−26.6698	−1.42151
$353$	−13.8729	−0.738379	−0.369190	−	0.929354i	$-0.620365\pi$
$353$	−13.8729	−0.738379	−0.369190	+	0.929354i	$0.620365\pi$
$354$	−5.38547	−0.286234
$355$	26.7877	1.42175
$356$	−9.76130	−0.517348
$357$	31.1680	1.64959
$358$	9.53559	0.503972
$359$	−8.10850	−0.427950	−0.213975	−	0.976839i	$-0.568641\pi$
$359$	−8.10850	−0.427950	−0.213975	+	0.976839i	$0.568641\pi$
$360$	−25.8031	−1.35994
$361$	−8.72423	−0.459170
$362$	23.7753	1.24960
$363$	−18.5529	−0.973773
$364$	−6.49436	−0.340397
$365$	25.9483	1.35820
$366$	0.701479	0.0366669
$367$	−26.5897	−1.38797	−0.693987	−	0.719988i	$-0.744147\pi$
$367$	−26.5897	−1.38797	−0.693987	+	0.719988i	$0.744147\pi$
$368$	−1.23990	−0.0646344
$369$	4.14474	0.215767
$370$	−19.8832	−1.03368
$371$	43.2587	2.24588
$372$	3.63415	0.188422
$373$	−16.3583	−0.846999	−0.423500	−	0.905896i	$-0.639199\pi$
$373$	−16.3583	−0.846999	−0.423500	+	0.905896i	$0.639199\pi$
$374$	43.4539	2.24695
$375$	−20.6402	−1.06586
$376$	−5.16963	−0.266603
$377$	−1.54285	−0.0794609
$378$	−21.8914	−1.12597
$379$	−10.4643	−0.537513	−0.268756	−	0.963208i	$-0.586613\pi$
$379$	−10.4643	−0.537513	−0.268756	+	0.963208i	$0.586613\pi$
$380$	11.9156	0.611256
$381$	2.92958	0.150087
$382$	4.20575	0.215185
$383$	7.07450	0.361490	0.180745	−	0.983530i	$-0.442149\pi$
$383$	7.07450	0.361490	0.180745	+	0.983530i	$0.442149\pi$
$384$	−1.77792	−0.0907290
$385$	99.0430	5.04770
$386$	13.4413	0.684146
$387$	24.7328	1.25724
$388$	8.31894	0.422330
$389$	−2.37583	−0.120459	−0.0602297	−	0.998185i	$-0.519183\pi$
$389$	−2.37583	−0.120459	−0.0602297	+	0.998185i	$0.519183\pi$
$390$	5.78762	0.293067
$391$	−7.55730	−0.382189
$392$	39.6303	2.00163
$393$	−1.32049	−0.0666097
$394$	−0.767450	−0.0386636
$395$	−41.9677	−2.11163
$396$	11.2891	0.567298
$397$	32.4735	1.62980	0.814899	−	0.579603i	$-0.196792\pi$
$397$	32.4735	1.62980	0.814899	+	0.579603i	$0.196792\pi$
$398$	−3.76437	−0.188691
$399$	13.2206	0.661855
$400$	−13.2264	−0.661321
$401$	9.72352	0.485569	0.242785	−	0.970080i	$-0.421939\pi$
$401$	9.72352	0.485569	0.242785	+	0.970080i	$0.421939\pi$
$402$	−9.58497	−0.478055
$403$	6.48898	0.323239
$404$	−3.28885	−0.163626
$405$	8.30148	0.412504
$406$	4.61678	0.229127
$407$	27.2256	1.34952
$408$	21.0503	1.04215
$409$	−26.8132	−1.32583	−0.662915	−	0.748695i	$-0.730681\pi$
$409$	−26.8132	−1.32583	−0.662915	+	0.748695i	$0.730681\pi$
$410$	7.84709	0.387540
$411$	−16.4770	−0.812749
$412$	−9.61609	−0.473751
$413$	−25.4710	−1.25335
$414$	2.21800	0.109009
$415$	−12.4109	−0.609227
$416$	−7.37089	−0.361388
$417$	−4.98871	−0.244298
$418$	18.4319	0.901533
$419$	−28.6227	−1.39831	−0.699156	−	0.714969i	$-0.746441\pi$
$419$	−28.6227	−1.39831	−0.699156	+	0.714969i	$0.746441\pi$
$420$	15.3303	0.748041
$421$	−12.4491	−0.606732	−0.303366	−	0.952874i	$-0.598110\pi$
$421$	−12.4491	−0.606732	−0.303366	+	0.952874i	$0.598110\pi$
$422$	25.9280	1.26216
$423$	3.67732	0.178797
$424$	29.2162	1.41886
$425$	−80.6160	−3.91045
$426$	6.41383	0.310751
$427$	3.31771	0.160555
$428$	4.38448	0.211932
$429$	−7.92482	−0.382614
$430$	46.8257	2.25813
$431$	−23.2274	−1.11883	−0.559413	−	0.828889i	$-0.688973\pi$
$431$	−23.2274	−1.11883	−0.559413	+	0.828889i	$0.688973\pi$
$432$	−5.87924	−0.282865
$433$	−12.9335	−0.621544	−0.310772	−	0.950484i	$-0.600588\pi$
$433$	−12.9335	−0.621544	−0.310772	+	0.950484i	$0.600588\pi$
$434$	−19.4174	−0.932066
$435$	3.64198	0.174620
$436$	7.86180	0.376512
$437$	−3.20558	−0.153344
$438$	6.21285	0.296861
$439$	−15.4117	−0.735560	−0.367780	−	0.929913i	$-0.619882\pi$
$439$	−15.4117	−0.735560	−0.367780	+	0.929913i	$0.619882\pi$
$440$	66.8919	3.18895
$441$	−28.1903	−1.34239
$442$	12.0096	0.571238
$443$	20.3157	0.965226	0.482613	−	0.875834i	$-0.339688\pi$
$443$	20.3157	0.965226	0.482613	+	0.875834i	$0.339688\pi$
$444$	4.21409	0.199992
$445$	41.1428	1.95036
$446$	−7.95453	−0.376658
$447$	−4.66529	−0.220661
$448$	33.1717	1.56722
$449$	−6.05351	−0.285683	−0.142841	−	0.989746i	$-0.545624\pi$
$449$	−6.05351	−0.285683	−0.142841	+	0.989746i	$0.545624\pi$
$450$	23.6601	1.11535
$451$	−10.7448	−0.505953
$452$	7.03443	0.330872
$453$	15.1506	0.711836
$454$	2.00086	0.0939052
$455$	27.3730	1.28327
$456$	8.92893	0.418136
$457$	28.1224	1.31551	0.657754	−	0.753233i	$-0.271507\pi$
$457$	28.1224	1.31551	0.657754	+	0.753233i	$0.271507\pi$
$458$	−16.4265	−0.767560
$459$	−35.8344	−1.67261
$460$	−3.71713	−0.173312
$461$	16.8087	0.782857	0.391429	−	0.920208i	$-0.371981\pi$
$461$	16.8087	0.782857	0.391429	+	0.920208i	$0.371981\pi$
$462$	23.7140	1.10328
$463$	−21.4247	−0.995691	−0.497845	−	0.867266i	$-0.665875\pi$
$463$	−21.4247	−0.995691	−0.497845	+	0.867266i	$0.665875\pi$
$464$	1.23990	0.0575610
$465$	−15.3176	−0.710335
$466$	−20.0386	−0.928271
$467$	−11.7990	−0.545993	−0.272997	−	0.962015i	$-0.588015\pi$
$467$	−11.7990	−0.545993	−0.272997	+	0.962015i	$0.588015\pi$
$468$	3.12003	0.144223
$469$	−45.3330	−2.09328
$470$	6.96213	0.321139
$471$	4.19046	0.193086
$472$	−17.2027	−0.791819
$473$	−64.1171	−2.94811
$474$	−10.0484	−0.461538
$475$	−34.1949	−1.56897
$476$	31.8111	1.45806
$477$	−20.7824	−0.951561
$478$	16.1482	0.738602
$479$	30.3535	1.38689	0.693444	−	0.720510i	$-0.256092\pi$
$479$	30.3535	1.38689	0.693444	+	0.720510i	$0.256092\pi$
$480$	17.3994	0.794169
$481$	7.52448	0.343087
$482$	7.64898	0.348402
$483$	−4.12423	−0.187659
$484$	−18.9357	−0.860713
$485$	−35.0635	−1.59215
$486$	16.6395	0.754783
$487$	8.43053	0.382024	0.191012	−	0.981588i	$-0.438823\pi$
$487$	8.43053	0.382024	0.191012	+	0.981588i	$0.438823\pi$
$488$	2.24072	0.101433
$489$	−6.49803	−0.293851
$490$	−53.3717	−2.41109
$491$	36.0960	1.62899	0.814495	−	0.580170i	$-0.197014\pi$
$491$	36.0960	1.62899	0.814495	+	0.580170i	$0.197014\pi$
$492$	−1.66313	−0.0749795
$493$	7.55730	0.340364
$494$	5.09412	0.229195
$495$	−47.5823	−2.13866
$496$	−5.21482	−0.234152
$497$	30.3348	1.36070
$498$	−2.97156	−0.133159
$499$	−22.1018	−0.989413	−0.494707	−	0.869060i	$-0.664724\pi$
$499$	−22.1018	−0.989413	−0.494707	+	0.869060i	$0.664724\pi$
$500$	−21.0661	−0.942104
$501$	−5.94338	−0.265531
$502$	10.6323	0.474541
$503$	−9.65157	−0.430342	−0.215171	−	0.976576i	$-0.569031\pi$
$503$	−9.65157	−0.430342	−0.215171	+	0.976576i	$0.569031\pi$
$504$	−29.2198	−1.30155
$505$	13.8621	0.616858
$506$	−5.74993	−0.255616
$507$	9.77123	0.433955
$508$	2.99003	0.132661
$509$	−28.3884	−1.25829	−0.629146	−	0.777287i	$-0.716595\pi$
$509$	−28.3884	−1.25829	−0.629146	+	0.777287i	$0.716595\pi$
$510$	−28.3493	−1.25533
$511$	29.3842	1.29988
$512$	13.4306	0.593555
$513$	−15.1999	−0.671093
$514$	−30.8246	−1.35961
$515$	40.5308	1.78600
$516$	−9.92431	−0.436893
$517$	−9.53305	−0.419263
$518$	−22.5160	−0.989298
$519$	−10.5728	−0.464094
$520$	18.4873	0.810721
$521$	2.27334	0.0995970	0.0497985	−	0.998759i	$-0.484142\pi$
$521$	2.27334	0.0995970	0.0497985	+	0.998759i	$0.484142\pi$
$522$	−2.21800	−0.0970792
$523$	−10.3759	−0.453705	−0.226853	−	0.973929i	$-0.572844\pi$
$523$	−10.3759	−0.453705	−0.226853	+	0.973929i	$0.572844\pi$
$524$	−1.34773	−0.0588759
$525$	−43.9944	−1.92007
$526$	−3.59761	−0.156863
$527$	−31.7847	−1.38456
$528$	6.36873	0.277163
$529$	1.00000	0.0434783
$530$	−39.3466	−1.70911
$531$	12.2368	0.531033
$532$	13.4933	0.585011
$533$	−2.96960	−0.128628
$534$	9.85089	0.426290
$535$	−18.4801	−0.798965
$536$	−30.6171	−1.32246
$537$	8.51825	0.367590
$538$	−1.59528	−0.0687773
$539$	73.0804	3.14779
$540$	−17.6255	−0.758481
$541$	−23.0163	−0.989546	−0.494773	−	0.869022i	$-0.664749\pi$
$541$	−23.0163	−0.989546	−0.494773	+	0.869022i	$0.664749\pi$
$542$	11.0538	0.474801
$543$	21.2388	0.911442
$544$	36.1046	1.54797
$545$	−33.1366	−1.41942
$546$	6.55397	0.280484
$547$	28.0291	1.19844	0.599219	−	0.800585i	$-0.295478\pi$
$547$	28.0291	1.19844	0.599219	+	0.800585i	$0.295478\pi$
$548$	−16.8169	−0.718384
$549$	−1.59390	−0.0680258
$550$	−61.3362	−2.61539
$551$	3.20558	0.136562
$552$	−2.78543	−0.118556
$553$	−47.5248	−2.02096
$554$	14.8393	0.630462
$555$	−17.7619	−0.753952
$556$	−5.09164	−0.215934
$557$	−4.79213	−0.203049	−0.101525	−	0.994833i	$-0.532372\pi$
$557$	−4.79213	−0.203049	−0.101525	+	0.994833i	$0.532372\pi$
$558$	9.32854	0.394908
$559$	−17.7204	−0.749493
$560$	−21.9982	−0.929592
$561$	38.8179	1.63889
$562$	−14.3957	−0.607246
$563$	−4.03874	−0.170213	−0.0851063	−	0.996372i	$-0.527123\pi$
$563$	−4.03874	−0.170213	−0.0851063	+	0.996372i	$0.527123\pi$
$564$	−1.47557	−0.0621325
$565$	−29.6494	−1.24736
$566$	−21.8218	−0.917237
$567$	9.40071	0.394793
$568$	20.4876	0.859640
$569$	−5.07151	−0.212609	−0.106304	−	0.994334i	$-0.533902\pi$
$569$	−5.07151	−0.212609	−0.106304	+	0.994334i	$0.533902\pi$
$570$	−12.0249	−0.503669
$571$	−18.6566	−0.780755	−0.390377	−	0.920655i	$-0.627655\pi$
$571$	−18.6566	−0.780755	−0.390377	+	0.920655i	$0.627655\pi$
$572$	−8.08834	−0.338190
$573$	3.75704	0.156953
$574$	8.88615	0.370901
$575$	10.6673	0.444857
$576$	−15.9364	−0.664016
$577$	−5.09852	−0.212254	−0.106127	−	0.994353i	$-0.533845\pi$
$577$	−5.09852	−0.212254	−0.106127	+	0.994353i	$0.533845\pi$
$578$	−41.3162	−1.71853
$579$	12.0073	0.499006
$580$	3.71713	0.154345
$581$	−14.0543	−0.583069
$582$	−8.39530	−0.347996
$583$	53.8762	2.23132
$584$	19.8456	0.821217
$585$	−13.1506	−0.543710
$586$	27.9620	1.15510
$587$	−16.7995	−0.693392	−0.346696	−	0.937978i	$-0.612696\pi$
$587$	−16.7995	−0.693392	−0.346696	+	0.937978i	$0.612696\pi$
$588$	11.3117	0.466486
$589$	−13.4822	−0.555523
$590$	23.1675	0.953793
$591$	−0.685572	−0.0282007
$592$	−6.04700	−0.248530
$593$	17.8837	0.734395	0.367197	−	0.930143i	$-0.380317\pi$
$593$	17.8837	0.734395	0.367197	+	0.930143i	$0.380317\pi$
$594$	−27.2644	−1.11867
$595$	−134.080	−5.49676
$596$	−4.76155	−0.195041
$597$	−3.36275	−0.137628
$598$	−1.58914	−0.0649848
$599$	−7.25904	−0.296596	−0.148298	−	0.988943i	$-0.547380\pi$
$599$	−7.25904	−0.296596	−0.148298	+	0.988943i	$0.547380\pi$
$600$	−29.7130	−1.21303
$601$	−1.93195	−0.0788059	−0.0394030	−	0.999223i	$-0.512546\pi$
$601$	−1.93195	−0.0788059	−0.0394030	+	0.999223i	$0.512546\pi$
$602$	53.0260	2.16118
$603$	21.7789	0.886905
$604$	15.4632	0.629188
$605$	79.8119	3.24482
$606$	3.31904	0.134827
$607$	28.8068	1.16923	0.584615	−	0.811311i	$-0.301246\pi$
$607$	28.8068	1.16923	0.584615	+	0.811311i	$0.301246\pi$
$608$	15.3145	0.621085
$609$	4.12423	0.167122
$610$	−3.01767	−0.122182
$611$	−2.63470	−0.106589
$612$	−15.2827	−0.617767
$613$	13.6370	0.550794	0.275397	−	0.961331i	$-0.411191\pi$
$613$	13.6370	0.550794	0.275397	+	0.961331i	$0.411191\pi$
$614$	−8.61465	−0.347659
$615$	7.00990	0.282666
$616$	75.7492	3.05202
$617$	5.82175	0.234375	0.117187	−	0.993110i	$-0.462612\pi$
$617$	5.82175	0.234375	0.117187	+	0.993110i	$0.462612\pi$
$618$	9.70435	0.390366
$619$	28.8940	1.16135	0.580674	−	0.814136i	$-0.302789\pi$
$619$	28.8940	1.16135	0.580674	+	0.814136i	$0.302789\pi$
$620$	−15.6336	−0.627862
$621$	4.74170	0.190278
$622$	28.7692	1.15354
$623$	46.5907	1.86662
$624$	1.76016	0.0704628
$625$	35.4548	1.41819
$626$	4.31742	0.172559
$627$	16.4654	0.657565
$628$	4.27693	0.170668
$629$	−36.8569	−1.46958
$630$	39.3514	1.56780
$631$	−33.9972	−1.35341	−0.676703	−	0.736256i	$-0.736592\pi$
$631$	−33.9972	−1.35341	−0.676703	+	0.736256i	$0.736592\pi$
$632$	−32.0974	−1.27677
$633$	23.1618	0.920598
$634$	3.45425	0.137186
$635$	−12.6027	−0.500121
$636$	8.33918	0.330670
$637$	20.1976	0.800259
$638$	5.74993	0.227642
$639$	−14.5735	−0.576517
$640$	7.64836	0.302328
$641$	−5.20966	−0.205769	−0.102885	−	0.994693i	$-0.532807\pi$
$641$	−5.20966	−0.205769	−0.102885	+	0.994693i	$0.532807\pi$
$642$	−4.42472	−0.174630
$643$	−9.97538	−0.393391	−0.196695	−	0.980465i	$-0.563021\pi$
$643$	−9.97538	−0.393391	−0.196695	+	0.980465i	$0.563021\pi$
$644$	−4.20932	−0.165871
$645$	41.8299	1.64705
$646$	−24.9524	−0.981737
$647$	−9.14442	−0.359504	−0.179752	−	0.983712i	$-0.557530\pi$
$647$	−9.14442	−0.359504	−0.179752	+	0.983712i	$0.557530\pi$
$648$	6.34907	0.249415
$649$	−31.7227	−1.24522
$650$	−16.9518	−0.664906
$651$	−17.3458	−0.679836
$652$	−6.63210	−0.259733
$653$	−2.87403	−0.112470	−0.0562348	−	0.998418i	$-0.517910\pi$
$653$	−2.87403	−0.112470	−0.0562348	+	0.998418i	$0.517910\pi$
$654$	−7.93396	−0.310242
$655$	5.68055	0.221957
$656$	2.38650	0.0931772
$657$	−14.1168	−0.550748
$658$	7.88401	0.307351
$659$	11.8713	0.462439	0.231219	−	0.972902i	$-0.425729\pi$
$659$	11.8713	0.462439	0.231219	+	0.972902i	$0.425729\pi$
$660$	19.0929	0.743192
$661$	−9.74878	−0.379184	−0.189592	−	0.981863i	$-0.560716\pi$
$661$	−9.74878	−0.379184	−0.189592	+	0.981863i	$0.560716\pi$
$662$	−27.1625	−1.05570
$663$	10.7283	0.416653
$664$	−9.49200	−0.368361
$665$	−56.8730	−2.20544
$666$	10.8172	0.419157
$667$	−1.00000	−0.0387202
$668$	−6.06602	−0.234701
$669$	−7.10587	−0.274729
$670$	41.2332	1.59298
$671$	4.13201	0.159514
$672$	19.7033	0.760070
$673$	−17.7848	−0.685554	−0.342777	−	0.939417i	$-0.611368\pi$
$673$	−17.7848	−0.685554	−0.342777	+	0.939417i	$0.611368\pi$
$674$	30.1448	1.16114
$675$	50.5811	1.94687
$676$	9.97284	0.383571
$677$	7.08914	0.272458	0.136229	−	0.990677i	$-0.456502\pi$
$677$	7.08914	0.272458	0.136229	+	0.990677i	$0.456502\pi$
$678$	−7.09900	−0.272635
$679$	−39.7063	−1.52379
$680$	−90.5556	−3.47265
$681$	1.78739	0.0684931
$682$	−24.1832	−0.926024
$683$	2.72661	0.104331	0.0521654	−	0.998638i	$-0.483388\pi$
$683$	2.72661	0.104331	0.0521654	+	0.998638i	$0.483388\pi$
$684$	−6.48248	−0.247864
$685$	70.8816	2.70825
$686$	−28.1213	−1.07368
$687$	−14.6740	−0.559847
$688$	14.2409	0.542928
$689$	14.8901	0.567266
$690$	3.75125	0.142807
$691$	−36.0905	−1.37295	−0.686473	−	0.727155i	$-0.740842\pi$
$691$	−36.0905	−1.37295	−0.686473	+	0.727155i	$0.740842\pi$
$692$	−10.7910	−0.410211
$693$	−53.8828	−2.04684
$694$	−29.2634	−1.11082
$695$	21.4607	0.814052
$696$	2.78543	0.105581
$697$	14.5459	0.550965
$698$	9.36915	0.354628
$699$	−17.9007	−0.677068
$700$	−44.9021	−1.69714
$701$	9.17628	0.346583	0.173292	−	0.984871i	$-0.444560\pi$
$701$	9.17628	0.346583	0.173292	+	0.984871i	$0.444560\pi$
$702$	−7.53522	−0.284399
$703$	−15.6336	−0.589633
$704$	41.3134	1.55706
$705$	6.21935	0.234234
$706$	14.2891	0.537777
$707$	15.6977	0.590372
$708$	−4.91017	−0.184535
$709$	−11.9213	−0.447713	−0.223856	−	0.974622i	$-0.571865\pi$
$709$	−11.9213	−0.447713	−0.223856	+	0.974622i	$0.571865\pi$
$710$	−27.5914	−1.03549
$711$	22.8319	0.856263
$712$	31.4665	1.17926
$713$	4.20583	0.157510
$714$	−32.1031	−1.20143
$715$	34.0915	1.27495
$716$	8.69401	0.324911
$717$	14.4254	0.538725
$718$	8.35177	0.311685
$719$	−46.8342	−1.74662	−0.873310	−	0.487166i	$-0.838031\pi$
$719$	−46.8342	−1.74662	−0.873310	+	0.487166i	$0.838031\pi$
$720$	10.5684	0.393860
$721$	45.8976	1.70932
$722$	8.98597	0.334423
$723$	6.83292	0.254119
$724$	21.6770	0.805619
$725$	−10.6673	−0.396174
$726$	19.1095	0.709220
$727$	0.568609	0.0210886	0.0105443	−	0.999944i	$-0.496644\pi$
$727$	0.568609	0.0210886	0.0105443	+	0.999944i	$0.496644\pi$
$728$	20.9352	0.775911
$729$	8.57238	0.317496
$730$	−26.7268	−0.989204
$731$	86.7992	3.21038
$732$	0.639569	0.0236392
$733$	43.9920	1.62488	0.812441	−	0.583043i	$-0.198138\pi$
$733$	43.9920	1.62488	0.812441	+	0.583043i	$0.198138\pi$
$734$	27.3875	1.01089
$735$	−47.6775	−1.75861
$736$	−4.77745	−0.176099
$737$	−56.4595	−2.07971
$738$	−4.26909	−0.157147
$739$	30.8281	1.13403	0.567015	−	0.823708i	$-0.308098\pi$
$739$	30.8281	1.13403	0.567015	+	0.823708i	$0.308098\pi$
$740$	−18.1284	−0.666414
$741$	4.55064	0.167172
$742$	−44.5566	−1.63572
$743$	−21.2479	−0.779510	−0.389755	−	0.920919i	$-0.627440\pi$
$743$	−21.2479	−0.779510	−0.389755	+	0.920919i	$0.627440\pi$
$744$	−11.7151	−0.429495
$745$	20.0694	0.735288
$746$	16.8490	0.616887
$747$	6.75196	0.247041
$748$	39.6188	1.44861
$749$	−20.9271	−0.764660
$750$	21.2594	0.776285
$751$	3.75923	0.137176	0.0685882	−	0.997645i	$-0.478151\pi$
$751$	3.75923	0.137176	0.0685882	+	0.997645i	$0.478151\pi$
$752$	2.11736	0.0772122
$753$	9.49791	0.346123
$754$	1.58914	0.0578731
$755$	−65.1757	−2.37198
$756$	−19.9593	−0.725914
$757$	17.0669	0.620307	0.310154	−	0.950686i	$-0.399619\pi$
$757$	17.0669	0.620307	0.310154	+	0.950686i	$0.399619\pi$
$758$	10.7782	0.391482
$759$	−5.13648	−0.186442
$760$	−38.4110	−1.39331
$761$	11.1752	0.405101	0.202551	−	0.979272i	$-0.435077\pi$
$761$	11.1752	0.405101	0.202551	+	0.979272i	$0.435077\pi$
$762$	−3.01747	−0.109312
$763$	−37.5243	−1.35847
$764$	3.83456	0.138730
$765$	64.4150	2.32893
$766$	−7.28675	−0.263281
$767$	−8.76737	−0.316571
$768$	15.4500	0.557503
$769$	−46.6242	−1.68131	−0.840656	−	0.541569i	$-0.817831\pi$
$769$	−46.6242	−1.68131	−0.840656	+	0.541569i	$0.817831\pi$
$770$	−102.014	−3.67634
$771$	−27.5359	−0.991683
$772$	12.2551	0.441069
$773$	37.9835	1.36617	0.683086	−	0.730338i	$-0.260638\pi$
$773$	37.9835	1.36617	0.683086	+	0.730338i	$0.260638\pi$
$774$	−25.4748	−0.915672
$775$	44.8649	1.61159
$776$	−26.8170	−0.962672
$777$	−20.1138	−0.721579
$778$	2.44711	0.0877332
$779$	6.16994	0.221061
$780$	5.27682	0.188941
$781$	37.7801	1.35188
$782$	7.78403	0.278356
$783$	−4.74170	−0.169454
$784$	−16.2317	−0.579703
$785$	−18.0268	−0.643404
$786$	1.36010	0.0485132
$787$	28.3953	1.01218	0.506092	−	0.862480i	$-0.331090\pi$
$787$	28.3953	1.01218	0.506092	+	0.862480i	$0.331090\pi$
$788$	−0.699718	−0.0249264
$789$	−3.21379	−0.114414
$790$	43.2268	1.53794
$791$	−33.5753	−1.19380
$792$	−36.3915	−1.29312
$793$	1.14199	0.0405531
$794$	−33.4477	−1.18702
$795$	−35.1487	−1.24660
$796$	−3.43214	−0.121649
$797$	29.7031	1.05214	0.526068	−	0.850442i	$-0.323666\pi$
$797$	29.7031	1.05214	0.526068	+	0.850442i	$0.323666\pi$
$798$	−13.6172	−0.482043
$799$	12.9055	0.456563
$800$	−50.9625	−1.80180
$801$	−22.3831	−0.790869
$802$	−10.0152	−0.353650
$803$	36.5963	1.29146
$804$	−8.73903	−0.308202
$805$	17.7419	0.625318
$806$	−6.68366	−0.235422
$807$	−1.42508	−0.0501652
$808$	10.6019	0.372975
$809$	30.6595	1.07793	0.538965	−	0.842328i	$-0.318816\pi$
$809$	30.6595	1.07793	0.538965	+	0.842328i	$0.318816\pi$
$810$	−8.55054	−0.300435
$811$	18.4219	0.646881	0.323441	−	0.946248i	$-0.395160\pi$
$811$	18.4219	0.646881	0.323441	+	0.946248i	$0.395160\pi$
$812$	4.20932	0.147718
$813$	9.87447	0.346313
$814$	−28.0424	−0.982885
$815$	27.9536	0.979172
$816$	−8.62173	−0.301821
$817$	36.8177	1.28809
$818$	27.6177	0.965629
$819$	−14.8919	−0.520365
$820$	7.15454	0.249847
$821$	−46.7160	−1.63040	−0.815199	−	0.579181i	$-0.803373\pi$
$821$	−46.7160	−1.63040	−0.815199	+	0.579181i	$0.803373\pi$
$822$	16.9713	0.591942
$823$	9.15823	0.319236	0.159618	−	0.987179i	$-0.448974\pi$
$823$	9.15823	0.319236	0.159618	+	0.987179i	$0.448974\pi$
$824$	30.9984	1.07988
$825$	−54.7923	−1.90762
$826$	26.2352	0.912840
$827$	−56.5427	−1.96618	−0.983090	−	0.183121i	$-0.941380\pi$
$827$	−56.5427	−1.96618	−0.983090	+	0.183121i	$0.941380\pi$
$828$	2.02225	0.0702779
$829$	−3.31793	−0.115236	−0.0576182	−	0.998339i	$-0.518351\pi$
$829$	−3.31793	−0.115236	−0.0576182	+	0.998339i	$0.518351\pi$
$830$	12.7832	0.443713
$831$	13.2561	0.459849
$832$	11.4180	0.395848
$833$	−98.9333	−3.42784
$834$	5.13838	0.177927
$835$	25.5676	0.884804
$836$	16.8051	0.581218
$837$	19.9428	0.689324
$838$	29.4815	1.01842
$839$	39.7713	1.37306	0.686530	−	0.727102i	$-0.259133\pi$
$839$	39.7713	1.37306	0.686530	+	0.727102i	$0.259133\pi$
$840$	−49.4187	−1.70511
$841$	1.00000	0.0344828
$842$	12.8226	0.441896
$843$	−12.8598	−0.442916
$844$	23.6397	0.813712
$845$	−42.0345	−1.44603
$846$	−3.78764	−0.130222
$847$	90.3800	3.10549
$848$	−11.9663	−0.410924
$849$	−19.4936	−0.669019
$850$	83.0346	2.84806
$851$	4.87699	0.167181
$852$	5.84776	0.200341
$853$	20.8747	0.714737	0.357369	−	0.933963i	$-0.383674\pi$
$853$	20.8747	0.714737	0.357369	+	0.933963i	$0.383674\pi$
$854$	−3.41724	−0.116936
$855$	27.3230	0.934426
$856$	−14.1338	−0.483084
$857$	−43.5186	−1.48657	−0.743283	−	0.668977i	$-0.766732\pi$
$857$	−43.5186	−1.48657	−0.743283	+	0.668977i	$0.766732\pi$
$858$	8.16258	0.278666
$859$	−21.7817	−0.743181	−0.371591	−	0.928397i	$-0.621187\pi$
$859$	−21.7817	−0.743181	−0.371591	+	0.928397i	$0.621187\pi$
$860$	42.6930	1.45582
$861$	7.93809	0.270530
$862$	23.9243	0.814864
$863$	−40.8871	−1.39181	−0.695906	−	0.718133i	$-0.744997\pi$
$863$	−40.8871	−1.39181	−0.695906	+	0.718133i	$0.744997\pi$
$864$	−22.6532	−0.770678
$865$	45.4827	1.54646
$866$	13.3215	0.452684
$867$	−36.9082	−1.25347
$868$	−17.7037	−0.600903
$869$	−59.1893	−2.00786
$870$	−3.75125	−0.127179
$871$	−15.6040	−0.528722
$872$	−25.3433	−0.858232
$873$	19.0757	0.645616
$874$	3.30176	0.111684
$875$	100.548	3.39916
$876$	5.66452	0.191387
$877$	31.0562	1.04869	0.524347	−	0.851505i	$-0.324309\pi$
$877$	31.0562	1.04869	0.524347	+	0.851505i	$0.324309\pi$
$878$	15.8741	0.535724
$879$	24.9787	0.842512
$880$	−27.3974	−0.923566
$881$	49.5220	1.66844	0.834219	−	0.551433i	$-0.185919\pi$
$881$	49.5220	1.66844	0.834219	+	0.551433i	$0.185919\pi$
$882$	29.0360	0.977694
$883$	15.7559	0.530229	0.265114	−	0.964217i	$-0.414590\pi$
$883$	15.7559	0.530229	0.265114	+	0.964217i	$0.414590\pi$
$884$	10.9497	0.368277
$885$	20.6958	0.695683
$886$	−20.9252	−0.702994
$887$	−12.3349	−0.414165	−0.207082	−	0.978323i	$-0.566397\pi$
$887$	−12.3349	−0.414165	−0.207082	+	0.978323i	$0.566397\pi$
$888$	−13.5845	−0.455867
$889$	−14.2714	−0.478648
$890$	−42.3772	−1.42049
$891$	11.7080	0.392233
$892$	−7.25249	−0.242831
$893$	5.47412	0.183185
$894$	4.80526	0.160712
$895$	−36.6443	−1.22489
$896$	8.66109	0.289347
$897$	−1.41960	−0.0473989
$898$	6.23513	0.208069
$899$	−4.20583	−0.140272
$900$	21.5719	0.719064
$901$	−72.9354	−2.42983
$902$	11.0672	0.368496
$903$	47.3687	1.57633
$904$	−22.6762	−0.754199
$905$	−91.3662	−3.03712
$906$	−15.6051	−0.518445
$907$	−12.4717	−0.414117	−0.207058	−	0.978329i	$-0.566389\pi$
$907$	−12.4717	−0.414117	−0.207058	+	0.978329i	$0.566389\pi$
$908$	1.82427	0.0605407
$909$	−7.54149	−0.250135
$910$	−28.1943	−0.934631
$911$	34.3809	1.13909	0.569545	−	0.821960i	$-0.307119\pi$
$911$	34.3809	1.13909	0.569545	+	0.821960i	$0.307119\pi$
$912$	−3.65709	−0.121098
$913$	−17.5037	−0.579289
$914$	−28.9661	−0.958112
$915$	−2.69572	−0.0891176
$916$	−14.9768	−0.494846
$917$	6.43272	0.212427
$918$	36.9095	1.21820
$919$	−15.5788	−0.513898	−0.256949	−	0.966425i	$-0.582717\pi$
$919$	−15.5788	−0.513898	−0.256949	+	0.966425i	$0.582717\pi$
$920$	11.9825	0.395053
$921$	−7.69556	−0.253577
$922$	−17.3129	−0.570171
$923$	10.4415	0.343686
$924$	21.6211	0.711282
$925$	52.0244	1.71055
$926$	22.0675	0.725182
$927$	−22.0502	−0.724222
$928$	4.77745	0.156827
$929$	43.9844	1.44308	0.721541	−	0.692371i	$-0.243434\pi$
$929$	43.9844	1.44308	0.721541	+	0.692371i	$0.243434\pi$
$930$	15.7771	0.517352
$931$	−41.9646	−1.37533
$932$	−18.2701	−0.598457
$933$	25.6998	0.841374
$934$	12.1530	0.397658
$935$	−166.989	−5.46113
$936$	−10.0577	−0.328747
$937$	56.3144	1.83971	0.919855	−	0.392259i	$-0.128306\pi$
$937$	56.3144	1.83971	0.919855	+	0.392259i	$0.128306\pi$
$938$	46.6930	1.52458
$939$	3.85680	0.125862
$940$	6.34768	0.207038
$941$	−16.2465	−0.529622	−0.264811	−	0.964300i	$-0.585310\pi$
$941$	−16.2465	−0.529622	−0.264811	+	0.964300i	$0.585310\pi$
$942$	−4.31618	−0.140629
$943$	−1.92475	−0.0626784
$944$	7.04584	0.229322
$945$	84.1265	2.73664
$946$	66.0407	2.14717
$947$	36.2464	1.17785	0.588926	−	0.808187i	$-0.299551\pi$
$947$	36.2464	1.17785	0.588926	+	0.808187i	$0.299551\pi$
$948$	−9.16156	−0.297554
$949$	10.1143	0.328325
$950$	35.2208	1.14271
$951$	3.08572	0.100061
$952$	−102.546	−3.32354
$953$	−53.9400	−1.74729	−0.873643	−	0.486567i	$-0.838249\pi$
$953$	−53.9400	−1.74729	−0.873643	+	0.486567i	$0.838249\pi$
$954$	21.4059	0.693042
$955$	−16.1623	−0.522999
$956$	14.7230	0.476177
$957$	5.13648	0.166039
$958$	−31.2642	−1.01010
$959$	80.2672	2.59196
$960$	−26.9528	−0.869897
$961$	−13.3110	−0.429386
$962$	−7.75022	−0.249877
$963$	10.0538	0.323980
$964$	6.97391	0.224614
$965$	−51.6538	−1.66279
$966$	4.24796	0.136676
$967$	62.0485	1.99535	0.997673	−	0.0681872i	$-0.0217215\pi$
$967$	62.0485	1.99535	0.997673	+	0.0681872i	$0.0217215\pi$
$968$	61.0411	1.96194
$969$	−22.2902	−0.716065
$970$	36.1154	1.15960
$971$	−24.3236	−0.780583	−0.390291	−	0.920691i	$-0.627626\pi$
$971$	−24.3236	−0.780583	−0.390291	+	0.920691i	$0.627626\pi$
$972$	15.1710	0.486609
$973$	24.3024	0.779100
$974$	−8.68345	−0.278236
$975$	−15.1433	−0.484972
$976$	−0.917749	−0.0293764
$977$	34.3435	1.09875	0.549373	−	0.835577i	$-0.314867\pi$
$977$	34.3435	1.09875	0.549373	+	0.835577i	$0.314867\pi$
$978$	6.69298	0.214018
$979$	58.0259	1.85452
$980$	−48.6613	−1.55443
$981$	18.0275	0.575573
$982$	−37.1790	−1.18643
$983$	−52.1361	−1.66288	−0.831442	−	0.555612i	$-0.812484\pi$
$983$	−52.1361	−1.66288	−0.831442	+	0.555612i	$0.812484\pi$
$984$	5.36125	0.170910
$985$	2.94924	0.0939705
$986$	−7.78403	−0.247894
$987$	7.04287	0.224177
$988$	4.64453	0.147762
$989$	−11.4855	−0.365217
$990$	49.0098	1.55763
$991$	21.4342	0.680880	0.340440	−	0.940266i	$-0.389424\pi$
$991$	21.4342	0.680880	0.340440	+	0.940266i	$0.389424\pi$
$992$	−20.0931	−0.637958
$993$	−24.2645	−0.770011
$994$	−31.2449	−0.991026
$995$	14.4661	0.458606
$996$	−2.70930	−0.0858475
$997$	−20.0157	−0.633904	−0.316952	−	0.948442i	$-0.602659\pi$
$997$	−20.0157	−0.633904	−0.316952	+	0.948442i	$0.602659\pi$
$998$	22.7649	0.720610
$999$	23.1252	0.731650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.6	✓	16
3.2	odd	2		6003.2.a.q.1.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.6	✓	16	1.1	even	1	trivial
6003.2.a.q.1.11		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-1.03000 q^{2} -0.920112 q^{3} -0.939097 q^{4} +3.95819 q^{5} +0.947716 q^{6} +4.48231 q^{7} +3.02727 q^{8} -2.15339 q^{9} +O(q^{10})\)	\(q-1.03000 q^{2} -0.920112 q^{3} -0.939097 q^{4} +3.95819 q^{5} +0.947716 q^{6} +4.48231 q^{7} +3.02727 q^{8} -2.15339 q^{9} -4.07695 q^{10} +5.58245 q^{11} +0.864074 q^{12} +1.54285 q^{13} -4.61678 q^{14} -3.64198 q^{15} -1.23990 q^{16} -7.55730 q^{17} +2.21800 q^{18} -3.20558 q^{19} -3.71713 q^{20} -4.12423 q^{21} -5.74993 q^{22} +1.00000 q^{23} -2.78543 q^{24} +10.6673 q^{25} -1.58914 q^{26} +4.74170 q^{27} -4.20932 q^{28} -1.00000 q^{29} +3.75125 q^{30} +4.20583 q^{31} -4.77745 q^{32} -5.13648 q^{33} +7.78403 q^{34} +17.7419 q^{35} +2.02225 q^{36} +4.87699 q^{37} +3.30176 q^{38} -1.41960 q^{39} +11.9825 q^{40} -1.92475 q^{41} +4.24796 q^{42} -11.4855 q^{43} -5.24246 q^{44} -8.52355 q^{45} -1.03000 q^{46} -1.70768 q^{47} +1.14085 q^{48} +13.0911 q^{49} -10.9873 q^{50} +6.95356 q^{51} -1.44889 q^{52} +9.65100 q^{53} -4.88396 q^{54} +22.0964 q^{55} +13.5692 q^{56} +2.94950 q^{57} +1.03000 q^{58} -5.68257 q^{59} +3.42017 q^{60} +0.740179 q^{61} -4.33201 q^{62} -9.65218 q^{63} +7.40058 q^{64} +6.10691 q^{65} +5.29058 q^{66} -10.1138 q^{67} +7.09704 q^{68} -0.920112 q^{69} -18.2741 q^{70} +6.76766 q^{71} -6.51892 q^{72} +6.55560 q^{73} -5.02331 q^{74} -9.81511 q^{75} +3.01036 q^{76} +25.0223 q^{77} +1.46219 q^{78} -10.6027 q^{79} -4.90777 q^{80} +2.09729 q^{81} +1.98249 q^{82} -3.13550 q^{83} +3.87305 q^{84} -29.9132 q^{85} +11.8301 q^{86} +0.920112 q^{87} +16.8996 q^{88} +10.3943 q^{89} +8.77927 q^{90} +6.91554 q^{91} -0.939097 q^{92} -3.86984 q^{93} +1.75892 q^{94} -12.6883 q^{95} +4.39579 q^{96} -8.85845 q^{97} -13.4838 q^{98} -12.0212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

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