LMFDB - Embedded newform 667.2.a.a.1.9

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 $ x^10 - 3x^9 - 10x^8 + 32x^7 + 32x^6 - 118x^5 - 29x^4 + 182x^3 - 28x^2 - 101*x + 43
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.57663$ 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)

$f(q)$	$=$	$q+1.57663 q^{2} +0.266494 q^{3} +0.485749 q^{4} -1.88241 q^{5} +0.420161 q^{6} -0.868755 q^{7} -2.38741 q^{8} -2.92898 q^{9} +O(q^{10})$	\(q+1.57663 q^{2} +0.266494 q^{3} +0.485749 q^{4} -1.88241 q^{5} +0.420161 q^{6} -0.868755 q^{7} -2.38741 q^{8} -2.92898 q^{9} -2.96785 q^{10} -4.15064 q^{11} +0.129449 q^{12} -1.68508 q^{13} -1.36970 q^{14} -0.501649 q^{15} -4.73555 q^{16} +6.19890 q^{17} -4.61791 q^{18} -0.936729 q^{19} -0.914376 q^{20} -0.231518 q^{21} -6.54400 q^{22} +1.00000 q^{23} -0.636229 q^{24} -1.45655 q^{25} -2.65675 q^{26} -1.58004 q^{27} -0.421997 q^{28} +1.00000 q^{29} -0.790912 q^{30} +5.44674 q^{31} -2.69137 q^{32} -1.10612 q^{33} +9.77334 q^{34} +1.63535 q^{35} -1.42275 q^{36} -9.23764 q^{37} -1.47687 q^{38} -0.449064 q^{39} +4.49407 q^{40} +8.57766 q^{41} -0.365017 q^{42} +8.65313 q^{43} -2.01617 q^{44} +5.51353 q^{45} +1.57663 q^{46} -2.84654 q^{47} -1.26199 q^{48} -6.24526 q^{49} -2.29644 q^{50} +1.65197 q^{51} -0.818527 q^{52} -9.40655 q^{53} -2.49112 q^{54} +7.81318 q^{55} +2.07407 q^{56} -0.249632 q^{57} +1.57663 q^{58} -13.3750 q^{59} -0.243675 q^{60} +0.878868 q^{61} +8.58747 q^{62} +2.54457 q^{63} +5.22781 q^{64} +3.17201 q^{65} -1.74393 q^{66} +5.75008 q^{67} +3.01111 q^{68} +0.266494 q^{69} +2.57833 q^{70} -11.0541 q^{71} +6.99267 q^{72} -8.68524 q^{73} -14.5643 q^{74} -0.388162 q^{75} -0.455015 q^{76} +3.60589 q^{77} -0.708006 q^{78} -6.12127 q^{79} +8.91421 q^{80} +8.36587 q^{81} +13.5238 q^{82} -2.70897 q^{83} -0.112459 q^{84} -11.6688 q^{85} +13.6428 q^{86} +0.266494 q^{87} +9.90926 q^{88} -1.59743 q^{89} +8.69277 q^{90} +1.46393 q^{91} +0.485749 q^{92} +1.45152 q^{93} -4.48792 q^{94} +1.76330 q^{95} -0.717232 q^{96} +19.0596 q^{97} -9.84644 q^{98} +12.1571 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9 - 6 * q^10 - 17 * q^12 - 13 * q^13 - 12 * q^14 + 2 * q^15 - 5 * q^16 - 22 * q^17 + 12 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 3 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 25 * q^26 - 24 * q^27 + 19 * q^28 + 10 * q^29 - 3 * q^30 - 22 * q^31 - 31 * q^32 - 9 * q^33 + 13 * q^34 - 15 * q^35 + 19 * q^36 - 9 * q^37 - 10 * q^38 + 4 * q^39 - 6 * q^40 - 25 * q^41 - 34 * q^42 + 3 * q^43 - 27 * q^44 - 28 * q^45 - 3 * q^46 - 17 * q^47 - 3 * q^48 + 17 * q^49 + 2 * q^50 + 38 * q^51 - 18 * q^52 - 43 * q^53 - 47 * q^54 - 11 * q^55 - 7 * q^56 + 18 * q^57 - 3 * q^58 - 7 * q^59 - 21 * q^60 - 6 * q^61 + 3 * q^62 + 11 * q^63 + 33 * q^64 + 11 * q^65 + 55 * q^66 + 11 * q^67 - 51 * q^68 - 9 * q^69 + 34 * q^70 - 17 * q^71 + 34 * q^72 - 44 * q^73 + 9 * q^74 + q^75 + 24 * q^76 - 71 * q^77 + 38 * q^78 + 5 * q^79 + 38 * q^80 + 18 * q^81 + 33 * q^82 - 32 * q^83 + 14 * q^84 + 16 * q^85 - 9 * q^86 - 9 * q^87 + 18 * q^88 - 10 * q^89 - 9 * q^90 - 3 * q^91 + 9 * q^92 - 8 * q^93 + 47 * q^94 - 8 * q^95 + 60 * q^96 + 6 * q^97 - 73 * q^98 + 26 * 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 $

$2$	1.57663	1.11484	0.557421	−	0.830230i	$-0.311791\pi$
$2$	1.57663	1.11484	0.557421	+	0.830230i	$0.311791\pi$
$3$	0.266494	0.153860	0.0769301	−	0.997036i	$-0.475488\pi$
$3$	0.266494	0.153860	0.0769301	+	0.997036i	$0.475488\pi$
$4$	0.485749	0.242874
$5$	−1.88241	−0.841837	−0.420919	−	0.907098i	$-0.638292\pi$
$5$	−1.88241	−0.841837	−0.420919	+	0.907098i	$0.638292\pi$
$6$	0.420161	0.171530
$7$	−0.868755	−0.328359	−0.164179	−	0.986431i	$-0.552498\pi$
$7$	−0.868755	−0.328359	−0.164179	+	0.986431i	$0.552498\pi$
$8$	−2.38741	−0.844076
$9$	−2.92898	−0.976327
$10$	−2.96785	−0.938516
$11$	−4.15064	−1.25146	−0.625732	−	0.780038i	$-0.715200\pi$
$11$	−4.15064	−1.25146	−0.625732	+	0.780038i	$0.715200\pi$
$12$	0.129449	0.0373687
$13$	−1.68508	−0.467358	−0.233679	−	0.972314i	$-0.575077\pi$
$13$	−1.68508	−0.467358	−0.233679	+	0.972314i	$0.575077\pi$
$14$	−1.36970	−0.366068
$15$	−0.501649	−0.129525
$16$	−4.73555	−1.18389
$17$	6.19890	1.50345	0.751727	−	0.659474i	$-0.229221\pi$
$17$	6.19890	1.50345	0.751727	+	0.659474i	$0.229221\pi$
$18$	−4.61791	−1.08845
$19$	−0.936729	−0.214900	−0.107450	−	0.994210i	$-0.534269\pi$
$19$	−0.936729	−0.214900	−0.107450	+	0.994210i	$0.534269\pi$
$20$	−0.914376	−0.204461
$21$	−0.231518	−0.0505213
$22$	−6.54400	−1.39519
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.636229	−0.129870
$25$	−1.45655	−0.291310
$26$	−2.65675	−0.521031
$27$	−1.58004	−0.304078
$28$	−0.421997	−0.0797499
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.790912	−0.144400
$31$	5.44674	0.978264	0.489132	−	0.872210i	$-0.337314\pi$
$31$	5.44674	0.978264	0.489132	+	0.872210i	$0.337314\pi$
$32$	−2.69137	−0.475771
$33$	−1.10612	−0.192550
$34$	9.77334	1.67611
$35$	1.63535	0.276424
$36$	−1.42275	−0.237125
$37$	−9.23764	−1.51866	−0.759329	−	0.650707i	$-0.774473\pi$
$37$	−9.23764	−1.51866	−0.759329	+	0.650707i	$0.774473\pi$
$38$	−1.47687	−0.239580
$39$	−0.449064	−0.0719078
$40$	4.49407	0.710575
$41$	8.57766	1.33960	0.669802	−	0.742539i	$-0.266379\pi$
$41$	8.57766	1.33960	0.669802	+	0.742539i	$0.266379\pi$
$42$	−0.365017	−0.0563233
$43$	8.65313	1.31959	0.659795	−	0.751446i	$-0.270643\pi$
$43$	8.65313	1.31959	0.659795	+	0.751446i	$0.270643\pi$
$44$	−2.01617	−0.303949
$45$	5.51353	0.821908
$46$	1.57663	0.232461
$47$	−2.84654	−0.415210	−0.207605	−	0.978213i	$-0.566567\pi$
$47$	−2.84654	−0.415210	−0.207605	+	0.978213i	$0.566567\pi$
$48$	−1.26199	−0.182153
$49$	−6.24526	−0.892181
$50$	−2.29644	−0.324765
$51$	1.65197	0.231322
$52$	−0.818527	−0.113509
$53$	−9.40655	−1.29209	−0.646045	−	0.763300i	$-0.723578\pi$
$53$	−9.40655	−1.29209	−0.646045	+	0.763300i	$0.723578\pi$
$54$	−2.49112	−0.338999
$55$	7.81318	1.05353
$56$	2.07407	0.277160
$57$	−0.249632	−0.0330646
$58$	1.57663	0.207021
$59$	−13.3750	−1.74128	−0.870640	−	0.491921i	$-0.836295\pi$
$59$	−13.3750	−1.74128	−0.870640	+	0.491921i	$0.836295\pi$
$60$	−0.243675	−0.0314583
$61$	0.878868	0.112528	0.0562638	−	0.998416i	$-0.482081\pi$
$61$	0.878868	0.112528	0.0562638	+	0.998416i	$0.482081\pi$
$62$	8.58747	1.09061
$63$	2.54457	0.320585
$64$	5.22781	0.653476
$65$	3.17201	0.393439
$66$	−1.74393	−0.214663
$67$	5.75008	0.702484	0.351242	−	0.936285i	$-0.385760\pi$
$67$	5.75008	0.702484	0.351242	+	0.936285i	$0.385760\pi$
$68$	3.01111	0.365150
$69$	0.266494	0.0320821
$70$	2.57833	0.308170
$71$	−11.0541	−1.31188	−0.655938	−	0.754815i	$-0.727727\pi$
$71$	−11.0541	−1.31188	−0.655938	+	0.754815i	$0.727727\pi$
$72$	6.99267	0.824094
$73$	−8.68524	−1.01653	−0.508265	−	0.861201i	$-0.669713\pi$
$73$	−8.68524	−1.01653	−0.508265	+	0.861201i	$0.669713\pi$
$74$	−14.5643	−1.69307
$75$	−0.388162	−0.0448210
$76$	−0.455015	−0.0521938
$77$	3.60589	0.410929
$78$	−0.708006	−0.0801659
$79$	−6.12127	−0.688697	−0.344349	−	0.938842i	$-0.611900\pi$
$79$	−6.12127	−0.688697	−0.344349	+	0.938842i	$0.611900\pi$
$80$	8.91421	0.996640
$81$	8.36587	0.929542
$82$	13.5238	1.49345
$83$	−2.70897	−0.297348	−0.148674	−	0.988886i	$-0.547501\pi$
$83$	−2.70897	−0.297348	−0.148674	+	0.988886i	$0.547501\pi$
$84$	−0.112459	−0.0122703
$85$	−11.6688	−1.26566
$86$	13.6428	1.47114
$87$	0.266494	0.0285711
$88$	9.90926	1.05633
$89$	−1.59743	−0.169327	−0.0846635	−	0.996410i	$-0.526982\pi$
$89$	−1.59743	−0.169327	−0.0846635	+	0.996410i	$0.526982\pi$
$90$	8.69277	0.916299
$91$	1.46393	0.153461
$92$	0.485749	0.0506428
$93$	1.45152	0.150516
$94$	−4.48792	−0.462894
$95$	1.76330	0.180911
$96$	−0.717232	−0.0732022
$97$	19.0596	1.93521	0.967603	−	0.252478i	$-0.0812455\pi$
$97$	19.0596	1.93521	0.967603	+	0.252478i	$0.0812455\pi$
$98$	−9.84644	−0.994641
$99$	12.1571	1.22184
$100$	−0.707518	−0.0707518
$101$	−4.74458	−0.472103	−0.236051	−	0.971741i	$-0.575853\pi$
$101$	−4.74458	−0.472103	−0.236051	+	0.971741i	$0.575853\pi$
$102$	2.60453	0.257887
$103$	11.1015	1.09387	0.546933	−	0.837176i	$-0.315795\pi$
$103$	11.1015	1.09387	0.546933	+	0.837176i	$0.315795\pi$
$104$	4.02298	0.394486
$105$	0.435810	0.0425307
$106$	−14.8306	−1.44048
$107$	−6.99846	−0.676566	−0.338283	−	0.941044i	$-0.609846\pi$
$107$	−6.99846	−0.676566	−0.338283	+	0.941044i	$0.609846\pi$
$108$	−0.767500	−0.0738527
$109$	−6.42111	−0.615030	−0.307515	−	0.951543i	$-0.599498\pi$
$109$	−6.42111	−0.615030	−0.307515	+	0.951543i	$0.599498\pi$
$110$	12.3185	1.17452
$111$	−2.46177	−0.233661
$112$	4.11403	0.388739
$113$	−14.6385	−1.37708	−0.688538	−	0.725200i	$-0.741747\pi$
$113$	−14.6385	−1.37708	−0.688538	+	0.725200i	$0.741747\pi$
$114$	−0.393577	−0.0368618
$115$	−1.88241	−0.175535
$116$	0.485749	0.0451006
$117$	4.93558	0.456294
$118$	−21.0874	−1.94125
$119$	−5.38533	−0.493672
$120$	1.19764	0.109329
$121$	6.22778	0.566162
$122$	1.38565	0.125451
$123$	2.28589	0.206112
$124$	2.64575	0.237595
$125$	12.1538	1.08707
$126$	4.01183	0.357402
$127$	12.0445	1.06878	0.534389	−	0.845239i	$-0.320542\pi$
$127$	12.0445	1.06878	0.534389	+	0.845239i	$0.320542\pi$
$128$	13.6250	1.20429
$129$	2.30600	0.203032
$130$	5.00107	0.438623
$131$	−16.5949	−1.44990	−0.724951	−	0.688801i	$-0.758138\pi$
$131$	−16.5949	−1.44990	−0.724951	+	0.688801i	$0.758138\pi$
$132$	−0.537295	−0.0467656
$133$	0.813788	0.0705644
$134$	9.06572	0.783159
$135$	2.97427	0.255984
$136$	−14.7993	−1.26903
$137$	16.3451	1.39646	0.698230	−	0.715874i	$-0.253971\pi$
$137$	16.3451	1.39646	0.698230	+	0.715874i	$0.253971\pi$
$138$	0.420161	0.0357664
$139$	−20.7245	−1.75783	−0.878915	−	0.476979i	$-0.841732\pi$
$139$	−20.7245	−1.75783	−0.878915	+	0.476979i	$0.841732\pi$
$140$	0.794369	0.0671364
$141$	−0.758584	−0.0638843
$142$	−17.4281	−1.46254
$143$	6.99417	0.584882
$144$	13.8703	1.15586
$145$	−1.88241	−0.156325
$146$	−13.6934	−1.13327
$147$	−1.66432	−0.137271
$148$	−4.48717	−0.368843
$149$	15.1727	1.24300	0.621500	−	0.783414i	$-0.286524\pi$
$149$	15.1727	1.24300	0.621500	+	0.783414i	$0.286524\pi$
$150$	−0.611986	−0.0499684
$151$	−7.21297	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$151$	−7.21297	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$152$	2.23635	0.181392
$153$	−18.1565	−1.46786
$154$	5.68514	0.458121
$155$	−10.2530	−0.823539
$156$	−0.218132	−0.0174646
$157$	2.55512	0.203921	0.101961	−	0.994788i	$-0.467488\pi$
$157$	2.55512	0.203921	0.101961	+	0.994788i	$0.467488\pi$
$158$	−9.65096	−0.767789
$159$	−2.50679	−0.198801
$160$	5.06624	0.400522
$161$	−0.868755	−0.0684675
$162$	13.1899	1.03629
$163$	22.4906	1.76160	0.880798	−	0.473491i	$-0.157006\pi$
$163$	22.4906	1.76160	0.880798	+	0.473491i	$0.157006\pi$
$164$	4.16659	0.325356
$165$	2.08216	0.162096
$166$	−4.27104	−0.331497
$167$	−7.59344	−0.587598	−0.293799	−	0.955867i	$-0.594920\pi$
$167$	−7.59344	−0.587598	−0.293799	+	0.955867i	$0.594920\pi$
$168$	0.552727	0.0426438
$169$	−10.1605	−0.781576
$170$	−18.3974	−1.41102
$171$	2.74366	0.209813
$172$	4.20325	0.320495
$173$	−22.9798	−1.74712	−0.873561	−	0.486715i	$-0.838195\pi$
$173$	−22.9798	−1.74712	−0.873561	+	0.486715i	$0.838195\pi$
$174$	0.420161	0.0318523
$175$	1.26539	0.0956543
$176$	19.6555	1.48159
$177$	−3.56436	−0.267913
$178$	−2.51854	−0.188773
$179$	0.974697	0.0728523	0.0364262	−	0.999336i	$-0.488403\pi$
$179$	0.974697	0.0728523	0.0364262	+	0.999336i	$0.488403\pi$
$180$	2.67819	0.199620
$181$	11.6037	0.862494	0.431247	−	0.902234i	$-0.358074\pi$
$181$	11.6037	0.862494	0.431247	+	0.902234i	$0.358074\pi$
$182$	2.30806	0.171085
$183$	0.234213	0.0173135
$184$	−2.38741	−0.176002
$185$	17.3890	1.27846
$186$	2.28851	0.167801
$187$	−25.7294	−1.88152
$188$	−1.38270	−0.100844
$189$	1.37266	0.0998466
$190$	2.78007	0.201687
$191$	5.08587	0.368001	0.184000	−	0.982926i	$-0.441095\pi$
$191$	5.08587	0.368001	0.184000	+	0.982926i	$0.441095\pi$
$192$	1.39318	0.100544
$193$	3.36825	0.242452	0.121226	−	0.992625i	$-0.461317\pi$
$193$	3.36825	0.242452	0.121226	+	0.992625i	$0.461317\pi$
$194$	30.0498	2.15745
$195$	0.845320	0.0605346
$196$	−3.03363	−0.216688
$197$	−16.4811	−1.17423	−0.587114	−	0.809504i	$-0.699736\pi$
$197$	−16.4811	−1.17423	−0.587114	+	0.809504i	$0.699736\pi$
$198$	19.1673	1.36216
$199$	2.15553	0.152801	0.0764007	−	0.997077i	$-0.475657\pi$
$199$	2.15553	0.152801	0.0764007	+	0.997077i	$0.475657\pi$
$200$	3.47738	0.245888
$201$	1.53236	0.108084
$202$	−7.48042	−0.526321
$203$	−0.868755	−0.0609747
$204$	0.802441	0.0561821
$205$	−16.1466	−1.12773
$206$	17.5030	1.21949
$207$	−2.92898	−0.203578
$208$	7.97979	0.553299
$209$	3.88802	0.268940
$210$	0.687109	0.0474151
$211$	−2.06623	−0.142245	−0.0711227	−	0.997468i	$-0.522658\pi$
$211$	−2.06623	−0.142245	−0.0711227	+	0.997468i	$0.522658\pi$
$212$	−4.56922	−0.313815
$213$	−2.94584	−0.201845
$214$	−11.0339	−0.754265
$215$	−16.2887	−1.11088
$216$	3.77219	0.256665
$217$	−4.73189	−0.321221
$218$	−10.1237	−0.685662
$219$	−2.31456	−0.156403
$220$	3.79524	0.255875
$221$	−10.4457	−0.702652
$222$	−3.88129	−0.260495
$223$	17.2570	1.15561	0.577806	−	0.816174i	$-0.303909\pi$
$223$	17.2570	1.15561	0.577806	+	0.816174i	$0.303909\pi$
$224$	2.33814	0.156224
$225$	4.26621	0.284414
$226$	−23.0795	−1.53522
$227$	26.9508	1.78879	0.894393	−	0.447282i	$-0.147608\pi$
$227$	26.9508	1.78879	0.894393	+	0.447282i	$0.147608\pi$
$228$	−0.121259	−0.00803054
$229$	2.02341	0.133711	0.0668554	−	0.997763i	$-0.478703\pi$
$229$	2.02341	0.133711	0.0668554	+	0.997763i	$0.478703\pi$
$230$	−2.96785	−0.195694
$231$	0.960946	0.0632256
$232$	−2.38741	−0.156741
$233$	−15.6722	−1.02672	−0.513360	−	0.858173i	$-0.671599\pi$
$233$	−15.6722	−1.02672	−0.513360	+	0.858173i	$0.671599\pi$
$234$	7.78156	0.508697
$235$	5.35833	0.349539
$236$	−6.49690	−0.422912
$237$	−1.63128	−0.105963
$238$	−8.49065	−0.550367
$239$	23.4791	1.51873	0.759367	−	0.650662i	$-0.225509\pi$
$239$	23.4791	1.51873	0.759367	+	0.650662i	$0.225509\pi$
$240$	2.37558	0.153343
$241$	−4.20812	−0.271069	−0.135534	−	0.990773i	$-0.543275\pi$
$241$	−4.20812	−0.271069	−0.135534	+	0.990773i	$0.543275\pi$
$242$	9.81888	0.631182
$243$	6.96956	0.447097
$244$	0.426909	0.0273301
$245$	11.7561	0.751071
$246$	3.60399	0.229782
$247$	1.57847	0.100435
$248$	−13.0036	−0.825729
$249$	−0.721924	−0.0457501
$250$	19.1621	1.21192
$251$	1.80549	0.113961	0.0569807	−	0.998375i	$-0.481853\pi$
$251$	1.80549	0.113961	0.0569807	+	0.998375i	$0.481853\pi$
$252$	1.23602	0.0778620
$253$	−4.15064	−0.260948
$254$	18.9897	1.19152
$255$	−3.10967	−0.194735
$256$	11.0260	0.689123
$257$	−22.1239	−1.38005	−0.690026	−	0.723784i	$-0.742401\pi$
$257$	−22.1239	−1.38005	−0.690026	+	0.723784i	$0.742401\pi$
$258$	3.63571	0.226349
$259$	8.02525	0.498665
$260$	1.54080	0.0955564
$261$	−2.92898	−0.181299
$262$	−26.1639	−1.61641
$263$	−15.9265	−0.982070	−0.491035	−	0.871140i	$-0.663381\pi$
$263$	−15.9265	−0.982070	−0.491035	+	0.871140i	$0.663381\pi$
$264$	2.64075	0.162527
$265$	17.7069	1.08773
$266$	1.28304	0.0786682
$267$	−0.425704	−0.0260527
$268$	2.79309	0.170615
$269$	−22.6614	−1.38169	−0.690844	−	0.723004i	$-0.742761\pi$
$269$	−22.6614	−1.38169	−0.690844	+	0.723004i	$0.742761\pi$
$270$	4.68930	0.285382
$271$	−10.8087	−0.656580	−0.328290	−	0.944577i	$-0.606472\pi$
$271$	−10.8087	−0.656580	−0.328290	+	0.944577i	$0.606472\pi$
$272$	−29.3552	−1.77992
$273$	0.390127	0.0236115
$274$	25.7702	1.55683
$275$	6.04562	0.364564
$276$	0.129449	0.00779191
$277$	−21.3226	−1.28115	−0.640574	−	0.767896i	$-0.721304\pi$
$277$	−21.3226	−1.28115	−0.640574	+	0.767896i	$0.721304\pi$
$278$	−32.6748	−1.95970
$279$	−15.9534	−0.955105
$280$	−3.90425	−0.233323
$281$	−25.2749	−1.50777	−0.753887	−	0.657004i	$-0.771823\pi$
$281$	−25.2749	−1.50777	−0.753887	+	0.657004i	$0.771823\pi$
$282$	−1.19600	−0.0712209
$283$	−13.3764	−0.795143	−0.397572	−	0.917571i	$-0.630147\pi$
$283$	−13.3764	−0.795143	−0.397572	+	0.917571i	$0.630147\pi$
$284$	−5.36950	−0.318621
$285$	0.469909	0.0278350
$286$	11.0272	0.652051
$287$	−7.45188	−0.439871
$288$	7.88297	0.464508
$289$	21.4264	1.26037
$290$	−2.96785	−0.174278
$291$	5.07925	0.297751
$292$	−4.21884	−0.246889
$293$	−8.93925	−0.522237	−0.261118	−	0.965307i	$-0.584091\pi$
$293$	−8.93925	−0.522237	−0.261118	+	0.965307i	$0.584091\pi$
$294$	−2.62401	−0.153036
$295$	25.1772	1.46587
$296$	22.0540	1.28186
$297$	6.55815	0.380543
$298$	23.9217	1.38575
$299$	−1.68508	−0.0974509
$300$	−0.188549	−0.0108859
$301$	−7.51745	−0.433299
$302$	−11.3722	−0.654394
$303$	−1.26440	−0.0726378
$304$	4.43592	0.254418
$305$	−1.65439	−0.0947299
$306$	−28.6259	−1.63644
$307$	12.3674	0.705845	0.352923	−	0.935652i	$-0.385188\pi$
$307$	12.3674	0.705845	0.352923	+	0.935652i	$0.385188\pi$
$308$	1.75156	0.0998041
$309$	2.95849	0.168302
$310$	−16.1651	−0.918116
$311$	17.0409	0.966299	0.483150	−	0.875538i	$-0.339493\pi$
$311$	17.0409	0.966299	0.483150	+	0.875538i	$0.339493\pi$
$312$	1.07210	0.0606956
$313$	−2.71567	−0.153499	−0.0767494	−	0.997050i	$-0.524454\pi$
$313$	−2.71567	−0.153499	−0.0767494	+	0.997050i	$0.524454\pi$
$314$	4.02847	0.227340
$315$	−4.78991	−0.269881
$316$	−2.97340	−0.167267
$317$	10.2522	0.575823	0.287912	−	0.957657i	$-0.407039\pi$
$317$	10.2522	0.575823	0.287912	+	0.957657i	$0.407039\pi$
$318$	−3.95226	−0.221632
$319$	−4.15064	−0.232391
$320$	−9.84086	−0.550121
$321$	−1.86504	−0.104097
$322$	−1.36970	−0.0763305
$323$	−5.80669	−0.323093
$324$	4.06371	0.225762
$325$	2.45441	0.136146
$326$	35.4592	1.96390
$327$	−1.71118	−0.0946287
$328$	−20.4784	−1.13073
$329$	2.47294	0.136338
$330$	3.28279	0.180712
$331$	15.7397	0.865130	0.432565	−	0.901603i	$-0.357609\pi$
$331$	15.7397	0.865130	0.432565	+	0.901603i	$0.357609\pi$
$332$	−1.31588	−0.0722183
$333$	27.0569	1.48271
$334$	−11.9720	−0.655079
$335$	−10.8240	−0.591377
$336$	1.09636	0.0598115
$337$	34.4880	1.87868	0.939341	−	0.342984i	$-0.111438\pi$
$337$	34.4880	1.87868	0.939341	+	0.342984i	$0.111438\pi$
$338$	−16.0193	−0.871335
$339$	−3.90107	−0.211877
$340$	−5.66812	−0.307397
$341$	−22.6074	−1.22426
$342$	4.32573	0.233908
$343$	11.5069	0.621314
$344$	−20.6586	−1.11383
$345$	−0.501649	−0.0270079
$346$	−36.2305	−1.94777
$347$	16.0013	0.858996	0.429498	−	0.903068i	$-0.358691\pi$
$347$	16.0013	0.858996	0.429498	+	0.903068i	$0.358691\pi$
$348$	0.129449	0.00693919
$349$	−18.5463	−0.992759	−0.496380	−	0.868106i	$-0.665338\pi$
$349$	−18.5463	−0.992759	−0.496380	+	0.868106i	$0.665338\pi$
$350$	1.99504	0.106639
$351$	2.66249	0.142113
$352$	11.1709	0.595410
$353$	−7.33444	−0.390373	−0.195186	−	0.980766i	$-0.562531\pi$
$353$	−7.33444	−0.390373	−0.195186	+	0.980766i	$0.562531\pi$
$354$	−5.61966	−0.298681
$355$	20.8082	1.10439
$356$	−0.775948	−0.0411252
$357$	−1.43515	−0.0759565
$358$	1.53673	0.0812189
$359$	7.37549	0.389263	0.194632	−	0.980876i	$-0.437649\pi$
$359$	7.37549	0.389263	0.194632	+	0.980876i	$0.437649\pi$
$360$	−13.1630	−0.693753
$361$	−18.1225	−0.953818
$362$	18.2947	0.961546
$363$	1.65966	0.0871098
$364$	0.711100	0.0372718
$365$	16.3491	0.855753
$366$	0.369266	0.0193018
$367$	−4.13238	−0.215708	−0.107854	−	0.994167i	$-0.534398\pi$
$367$	−4.13238	−0.215708	−0.107854	+	0.994167i	$0.534398\pi$
$368$	−4.73555	−0.246857
$369$	−25.1238	−1.30789
$370$	27.4159	1.42529
$371$	8.17199	0.424269
$372$	0.705075	0.0365564
$373$	10.2899	0.532791	0.266396	−	0.963864i	$-0.414167\pi$
$373$	10.2899	0.532791	0.266396	+	0.963864i	$0.414167\pi$
$374$	−40.5656	−2.09760
$375$	3.23892	0.167257
$376$	6.79584	0.350469
$377$	−1.68508	−0.0867862
$378$	2.16418	0.111313
$379$	27.5989	1.41766	0.708830	−	0.705379i	$-0.249223\pi$
$379$	27.5989	1.41766	0.708830	+	0.705379i	$0.249223\pi$
$380$	0.856522	0.0439387
$381$	3.20979	0.164442
$382$	8.01852	0.410263
$383$	−17.7391	−0.906425	−0.453212	−	0.891403i	$-0.649722\pi$
$383$	−17.7391	−0.906425	−0.453212	+	0.891403i	$0.649722\pi$
$384$	3.63098	0.185293
$385$	−6.78774	−0.345935
$386$	5.31046	0.270295
$387$	−25.3449	−1.28835
$388$	9.25816	0.470012
$389$	−19.9988	−1.01398	−0.506990	−	0.861952i	$-0.669242\pi$
$389$	−19.9988	−1.01398	−0.506990	+	0.861952i	$0.669242\pi$
$390$	1.33275	0.0674866
$391$	6.19890	0.313492
$392$	14.9100	0.753068
$393$	−4.42243	−0.223082
$394$	−25.9845	−1.30908
$395$	11.5227	0.579771
$396$	5.90531	0.296753
$397$	−18.0445	−0.905627	−0.452814	−	0.891605i	$-0.649580\pi$
$397$	−18.0445	−0.905627	−0.452814	+	0.891605i	$0.649580\pi$
$398$	3.39846	0.170350
$399$	0.216869	0.0108570
$400$	6.89757	0.344878
$401$	−23.2227	−1.15969	−0.579843	−	0.814728i	$-0.696886\pi$
$401$	−23.2227	−1.15969	−0.579843	+	0.814728i	$0.696886\pi$
$402$	2.41596	0.120497
$403$	−9.17822	−0.457199
$404$	−2.30467	−0.114662
$405$	−15.7480	−0.782523
$406$	−1.36970	−0.0679772
$407$	38.3421	1.90055
$408$	−3.94392	−0.195253
$409$	27.6607	1.36773	0.683866	−	0.729608i	$-0.260297\pi$
$409$	27.6607	1.36773	0.683866	+	0.729608i	$0.260297\pi$
$410$	−25.4572	−1.25724
$411$	4.35587	0.214859
$412$	5.39255	0.265672
$413$	11.6196	0.571764
$414$	−4.61791	−0.226958
$415$	5.09938	0.250319
$416$	4.53518	0.222356
$417$	−5.52295	−0.270460
$418$	6.12995	0.299826
$419$	23.6562	1.15568	0.577840	−	0.816150i	$-0.303896\pi$
$419$	23.6562	1.15568	0.577840	+	0.816150i	$0.303896\pi$
$420$	0.211694	0.0103296
$421$	−29.0298	−1.41483	−0.707414	−	0.706800i	$-0.750138\pi$
$421$	−29.0298	−1.41483	−0.707414	+	0.706800i	$0.750138\pi$
$422$	−3.25768	−0.158581
$423$	8.33745	0.405381
$424$	22.4573	1.09062
$425$	−9.02902	−0.437972
$426$	−4.64448	−0.225026
$427$	−0.763522	−0.0369494
$428$	−3.39949	−0.164321
$429$	1.86390	0.0899900
$430$	−25.6812	−1.23846
$431$	3.64444	0.175547	0.0877733	−	0.996140i	$-0.472025\pi$
$431$	3.64444	0.175547	0.0877733	+	0.996140i	$0.472025\pi$
$432$	7.48233	0.359994
$433$	−34.4447	−1.65530	−0.827652	−	0.561241i	$-0.810324\pi$
$433$	−34.4447	−1.65530	−0.827652	+	0.561241i	$0.810324\pi$
$434$	−7.46041	−0.358111
$435$	−0.501649	−0.0240522
$436$	−3.11904	−0.149375
$437$	−0.936729	−0.0448098
$438$	−3.64920	−0.174365
$439$	−3.96062	−0.189030	−0.0945149	−	0.995523i	$-0.530130\pi$
$439$	−3.96062	−0.189030	−0.0945149	+	0.995523i	$0.530130\pi$
$440$	−18.6532	−0.889258
$441$	18.2923	0.871060
$442$	−16.4689	−0.783346
$443$	9.13741	0.434132	0.217066	−	0.976157i	$-0.430351\pi$
$443$	9.13741	0.434132	0.217066	+	0.976157i	$0.430351\pi$
$444$	−1.19580	−0.0567503
$445$	3.00700	0.142546
$446$	27.2078	1.28833
$447$	4.04344	0.191248
$448$	−4.54169	−0.214575
$449$	8.12020	0.383216	0.191608	−	0.981472i	$-0.438630\pi$
$449$	8.12020	0.383216	0.191608	+	0.981472i	$0.438630\pi$
$450$	6.72622	0.317077
$451$	−35.6027	−1.67647
$452$	−7.11065	−0.334457
$453$	−1.92221	−0.0903133
$454$	42.4913	1.99421
$455$	−2.75570	−0.129189
$456$	0.595974	0.0279090
$457$	−7.38780	−0.345587	−0.172793	−	0.984958i	$-0.555279\pi$
$457$	−7.38780	−0.345587	−0.172793	+	0.984958i	$0.555279\pi$
$458$	3.19016	0.149067
$459$	−9.79448	−0.457167
$460$	−0.914376	−0.0426330
$461$	18.1761	0.846548	0.423274	−	0.906002i	$-0.360881\pi$
$461$	18.1761	0.846548	0.423274	+	0.906002i	$0.360881\pi$
$462$	1.51505	0.0704866
$463$	−30.1544	−1.40140	−0.700698	−	0.713458i	$-0.747128\pi$
$463$	−30.1544	−1.40140	−0.700698	+	0.713458i	$0.747128\pi$
$464$	−4.73555	−0.219842
$465$	−2.73235	−0.126710
$466$	−24.7092	−1.14463
$467$	−2.22092	−0.102772	−0.0513859	−	0.998679i	$-0.516364\pi$
$467$	−2.22092	−0.102772	−0.0513859	+	0.998679i	$0.516364\pi$
$468$	2.39745	0.110822
$469$	−4.99541	−0.230667
$470$	8.44809	0.389681
$471$	0.680924	0.0313753
$472$	31.9316	1.46977
$473$	−35.9160	−1.65142
$474$	−2.57192	−0.118132
$475$	1.36439	0.0626027
$476$	−2.61592	−0.119900
$477$	27.5516	1.26150
$478$	37.0177	1.69315
$479$	−15.6547	−0.715281	−0.357641	−	0.933859i	$-0.616419\pi$
$479$	−15.6547	−0.715281	−0.357641	+	0.933859i	$0.616419\pi$
$480$	1.35012	0.0616243
$481$	15.5662	0.709757
$482$	−6.63463	−0.302199
$483$	−0.231518	−0.0105344
$484$	3.02514	0.137506
$485$	−35.8778	−1.62913
$486$	10.9884	0.498443
$487$	24.6539	1.11718	0.558588	−	0.829445i	$-0.311343\pi$
$487$	24.6539	1.11718	0.558588	+	0.829445i	$0.311343\pi$
$488$	−2.09822	−0.0949818
$489$	5.99359	0.271040
$490$	18.5350	0.837326
$491$	−9.69323	−0.437449	−0.218725	−	0.975787i	$-0.570190\pi$
$491$	−9.69323	−0.437449	−0.218725	+	0.975787i	$0.570190\pi$
$492$	1.11037	0.0500593
$493$	6.19890	0.279184
$494$	2.48865	0.111970
$495$	−22.8847	−1.02859
$496$	−25.7933	−1.15815
$497$	9.60328	0.430766
$498$	−1.13820	−0.0510041
$499$	3.36493	0.150635	0.0753174	−	0.997160i	$-0.476003\pi$
$499$	3.36493	0.150635	0.0753174	+	0.997160i	$0.476003\pi$
$500$	5.90371	0.264022
$501$	−2.02360	−0.0904079
$502$	2.84658	0.127049
$503$	−19.9130	−0.887876	−0.443938	−	0.896058i	$-0.646419\pi$
$503$	−19.9130	−0.887876	−0.443938	+	0.896058i	$0.646419\pi$
$504$	−6.07492	−0.270598
$505$	8.93121	0.397434
$506$	−6.54400	−0.290916
$507$	−2.70771	−0.120253
$508$	5.85061	0.259579
$509$	−14.8402	−0.657779	−0.328890	−	0.944368i	$-0.606674\pi$
$509$	−14.8402	−0.657779	−0.328890	+	0.944368i	$0.606674\pi$
$510$	−4.90279	−0.217099
$511$	7.54535	0.333787
$512$	−9.86626	−0.436031
$513$	1.48006	0.0653464
$514$	−34.8811	−1.53854
$515$	−20.8976	−0.920857
$516$	1.12014	0.0493113
$517$	11.8149	0.519620
$518$	12.6528	0.555933
$519$	−6.12397	−0.268812
$520$	−7.57288	−0.332093
$521$	−14.5329	−0.636699	−0.318350	−	0.947973i	$-0.603129\pi$
$521$	−14.5329	−0.636699	−0.318350	+	0.947973i	$0.603129\pi$
$522$	−4.61791	−0.202120
$523$	−38.9988	−1.70530	−0.852649	−	0.522485i	$-0.825005\pi$
$523$	−38.9988	−1.70530	−0.852649	+	0.522485i	$0.825005\pi$
$524$	−8.06094	−0.352144
$525$	0.337217	0.0147174
$526$	−25.1101	−1.09485
$527$	33.7638	1.47077
$528$	5.23807	0.227958
$529$	1.00000	0.0434783
$530$	27.9172	1.21265
$531$	39.1752	1.70006
$532$	0.395297	0.0171383
$533$	−14.4541	−0.626075
$534$	−0.671176	−0.0290446
$535$	13.1739	0.569559
$536$	−13.7278	−0.592950
$537$	0.259751	0.0112091
$538$	−35.7285	−1.54036
$539$	25.9218	1.11653
$540$	1.44475	0.0621720
$541$	26.3591	1.13327	0.566634	−	0.823970i	$-0.308245\pi$
$541$	26.3591	1.13327	0.566634	+	0.823970i	$0.308245\pi$
$542$	−17.0412	−0.731983
$543$	3.09230	0.132703
$544$	−16.6835	−0.715300
$545$	12.0871	0.517755
$546$	0.615084	0.0263232
$547$	24.9433	1.06650	0.533250	−	0.845958i	$-0.320970\pi$
$547$	24.9433	1.06650	0.533250	+	0.845958i	$0.320970\pi$
$548$	7.93963	0.339164
$549$	−2.57419	−0.109864
$550$	9.53167	0.406432
$551$	−0.936729	−0.0399060
$552$	−0.636229	−0.0270797
$553$	5.31789	0.226140
$554$	−33.6177	−1.42828
$555$	4.63405	0.196704
$556$	−10.0669	−0.426932
$557$	−44.6582	−1.89223	−0.946114	−	0.323833i	$-0.895029\pi$
$557$	−44.6582	−1.89223	−0.946114	+	0.323833i	$0.895029\pi$
$558$	−25.1525	−1.06479
$559$	−14.5813	−0.616721
$560$	−7.74427	−0.327255
$561$	−6.85671	−0.289491
$562$	−39.8490	−1.68093
$563$	1.37744	0.0580524	0.0290262	−	0.999579i	$-0.490759\pi$
$563$	1.37744	0.0580524	0.0290262	+	0.999579i	$0.490759\pi$
$564$	−0.368481	−0.0155158
$565$	27.5556	1.15927
$566$	−21.0895	−0.886460
$567$	−7.26790	−0.305223
$568$	26.3906	1.10732
$569$	35.8858	1.50441	0.752206	−	0.658928i	$-0.228990\pi$
$569$	35.8858	1.50441	0.752206	+	0.658928i	$0.228990\pi$
$570$	0.740870	0.0310316
$571$	6.82971	0.285814	0.142907	−	0.989736i	$-0.454355\pi$
$571$	6.82971	0.285814	0.142907	+	0.989736i	$0.454355\pi$
$572$	3.39741	0.142053
$573$	1.35535	0.0566207
$574$	−11.7488	−0.490387
$575$	−1.45655	−0.0607424
$576$	−15.3122	−0.638007
$577$	41.7976	1.74006	0.870029	−	0.493000i	$-0.164100\pi$
$577$	41.7976	1.74006	0.870029	+	0.493000i	$0.164100\pi$
$578$	33.7813	1.40512
$579$	0.897616	0.0373036
$580$	−0.914376	−0.0379674
$581$	2.35343	0.0976369
$582$	8.00808	0.331945
$583$	39.0432	1.61700
$584$	20.7352	0.858029
$585$	−9.29076	−0.384126
$586$	−14.0939	−0.582212
$587$	36.6226	1.51158	0.755788	−	0.654816i	$-0.227254\pi$
$587$	36.6226	1.51158	0.755788	+	0.654816i	$0.227254\pi$
$588$	−0.808443	−0.0333396
$589$	−5.10212	−0.210229
$590$	39.6950	1.63422
$591$	−4.39210	−0.180667
$592$	43.7453	1.79792
$593$	−20.1074	−0.825711	−0.412856	−	0.910796i	$-0.635469\pi$
$593$	−20.1074	−0.825711	−0.412856	+	0.910796i	$0.635469\pi$
$594$	10.3398	0.424245
$595$	10.1374	0.415592
$596$	7.37014	0.301893
$597$	0.574435	0.0235100
$598$	−2.65675	−0.108642
$599$	12.2148	0.499083	0.249542	−	0.968364i	$-0.419720\pi$
$599$	12.2148	0.499083	0.249542	+	0.968364i	$0.419720\pi$
$600$	0.926700	0.0378324
$601$	3.18128	0.129767	0.0648835	−	0.997893i	$-0.479332\pi$
$601$	3.18128	0.129767	0.0648835	+	0.997893i	$0.479332\pi$
$602$	−11.8522	−0.483060
$603$	−16.8419	−0.685854
$604$	−3.50369	−0.142563
$605$	−11.7232	−0.476616
$606$	−1.99348	−0.0809798
$607$	−24.9014	−1.01072	−0.505358	−	0.862910i	$-0.668639\pi$
$607$	−24.9014	−1.01072	−0.505358	+	0.862910i	$0.668639\pi$
$608$	2.52108	0.102243
$609$	−0.231518	−0.00938157
$610$	−2.60835	−0.105609
$611$	4.79665	0.194052
$612$	−8.81948	−0.356506
$613$	31.6868	1.27982	0.639910	−	0.768450i	$-0.278972\pi$
$613$	31.6868	1.27982	0.639910	+	0.768450i	$0.278972\pi$
$614$	19.4988	0.786907
$615$	−4.30297	−0.173513
$616$	−8.60872	−0.346855
$617$	−13.6332	−0.548853	−0.274427	−	0.961608i	$-0.588488\pi$
$617$	−13.6332	−0.548853	−0.274427	+	0.961608i	$0.588488\pi$
$618$	4.66442	0.187631
$619$	34.9084	1.40309	0.701544	−	0.712626i	$-0.252494\pi$
$619$	34.9084	1.40309	0.701544	+	0.712626i	$0.252494\pi$
$620$	−4.98037	−0.200016
$621$	−1.58004	−0.0634046
$622$	26.8671	1.07727
$623$	1.38777	0.0556000
$624$	2.12656	0.0851307
$625$	−15.5957	−0.623828
$626$	−4.28159	−0.171127
$627$	1.03613	0.0413791
$628$	1.24115	0.0495272
$629$	−57.2632	−2.28323
$630$	−7.55189	−0.300875
$631$	19.7464	0.786092	0.393046	−	0.919519i	$-0.371421\pi$
$631$	19.7464	0.786092	0.393046	+	0.919519i	$0.371421\pi$
$632$	14.6140	0.581313
$633$	−0.550638	−0.0218859
$634$	16.1640	0.641952
$635$	−22.6727	−0.899737
$636$	−1.21767	−0.0482837
$637$	10.5238	0.416968
$638$	−6.54400	−0.259079
$639$	32.3772	1.28082
$640$	−25.6478	−1.01382
$641$	40.0441	1.58165	0.790823	−	0.612044i	$-0.209653\pi$
$641$	40.0441	1.58165	0.790823	+	0.612044i	$0.209653\pi$
$642$	−2.94048	−0.116051
$643$	34.5243	1.36151	0.680753	−	0.732513i	$-0.261653\pi$
$643$	34.5243	1.36151	0.680753	+	0.732513i	$0.261653\pi$
$644$	−0.421997	−0.0166290
$645$	−4.34083	−0.170920
$646$	−9.15497	−0.360198
$647$	−44.7524	−1.75940	−0.879700	−	0.475529i	$-0.842257\pi$
$647$	−44.7524	−1.75940	−0.879700	+	0.475529i	$0.842257\pi$
$648$	−19.9728	−0.784604
$649$	55.5149	2.17915
$650$	3.86969	0.151782
$651$	−1.26102	−0.0494232
$652$	10.9248	0.427847
$653$	−1.70807	−0.0668421	−0.0334210	−	0.999441i	$-0.510640\pi$
$653$	−1.70807	−0.0668421	−0.0334210	+	0.999441i	$0.510640\pi$
$654$	−2.69790	−0.105496
$655$	31.2383	1.22058
$656$	−40.6199	−1.58594
$657$	25.4389	0.992466
$658$	3.89891	0.151995
$659$	−15.3246	−0.596963	−0.298482	−	0.954415i	$-0.596480\pi$
$659$	−15.3246	−0.596963	−0.298482	+	0.954415i	$0.596480\pi$
$660$	1.01141	0.0393690
$661$	25.7316	1.00084	0.500422	−	0.865781i	$-0.333178\pi$
$661$	25.7316	1.00084	0.500422	+	0.865781i	$0.333178\pi$
$662$	24.8156	0.964484
$663$	−2.78370	−0.108110
$664$	6.46742	0.250985
$665$	−1.53188	−0.0594037
$666$	42.6586	1.65299
$667$	1.00000	0.0387202
$668$	−3.68850	−0.142712
$669$	4.59887	0.177803
$670$	−17.0654	−0.659292
$671$	−3.64786	−0.140824
$672$	0.623099	0.0240366
$673$	42.3052	1.63075	0.815373	−	0.578935i	$-0.196532\pi$
$673$	42.3052	1.63075	0.815373	+	0.578935i	$0.196532\pi$
$674$	54.3747	2.09444
$675$	2.30140	0.0885810
$676$	−4.93545	−0.189825
$677$	43.5902	1.67531	0.837653	−	0.546202i	$-0.183927\pi$
$677$	43.5902	1.67531	0.837653	+	0.546202i	$0.183927\pi$
$678$	−6.15053	−0.236210
$679$	−16.5581	−0.635441
$680$	27.8583	1.06832
$681$	7.18221	0.275223
$682$	−35.6435	−1.36486
$683$	18.3291	0.701343	0.350672	−	0.936499i	$-0.385953\pi$
$683$	18.3291	0.701343	0.350672	+	0.936499i	$0.385953\pi$
$684$	1.33273	0.0509582
$685$	−30.7682	−1.17559
$686$	18.1421	0.692667
$687$	0.539226	0.0205728
$688$	−40.9773	−1.56224
$689$	15.8508	0.603869
$690$	−0.790912	−0.0301095
$691$	45.0053	1.71208	0.856041	−	0.516908i	$-0.172917\pi$
$691$	45.0053	1.71208	0.856041	+	0.516908i	$0.172917\pi$
$692$	−11.1624	−0.424331
$693$	−10.5616	−0.401201
$694$	25.2281	0.957646
$695$	39.0119	1.47981
$696$	−0.636229	−0.0241162
$697$	53.1720	2.01403
$698$	−29.2405	−1.10677
$699$	−4.17654	−0.157971
$700$	0.614660	0.0232320
$701$	−38.7789	−1.46466	−0.732329	−	0.680951i	$-0.761566\pi$
$701$	−38.7789	−1.46466	−0.732329	+	0.680951i	$0.761566\pi$
$702$	4.19775	0.158434
$703$	8.65316	0.326360
$704$	−21.6987	−0.817802
$705$	1.42796	0.0537801
$706$	−11.5637	−0.435204
$707$	4.12188	0.155019
$708$	−1.73138	−0.0650693
$709$	−4.71179	−0.176955	−0.0884776	−	0.996078i	$-0.528200\pi$
$709$	−4.71179	−0.176955	−0.0884776	+	0.996078i	$0.528200\pi$
$710$	32.8068	1.23122
$711$	17.9291	0.672394
$712$	3.81371	0.142925
$713$	5.44674	0.203982
$714$	−2.26270	−0.0846795
$715$	−13.1659	−0.492375
$716$	0.473458	0.0176940
$717$	6.25702	0.233673
$718$	11.6284	0.433967
$719$	−37.5908	−1.40190	−0.700950	−	0.713211i	$-0.747240\pi$
$719$	−37.5908	−1.40190	−0.700950	+	0.713211i	$0.747240\pi$
$720$	−26.1096	−0.973046
$721$	−9.64451	−0.359180
$722$	−28.5725	−1.06336
$723$	−1.12144	−0.0417067
$724$	5.63647	0.209478
$725$	−1.45655	−0.0540950
$726$	2.61667	0.0971137
$727$	15.6317	0.579747	0.289874	−	0.957065i	$-0.406387\pi$
$727$	15.6317	0.579747	0.289874	+	0.957065i	$0.406387\pi$
$728$	−3.49499	−0.129533
$729$	−23.2403	−0.860751
$730$	25.7765	0.954030
$731$	53.6399	1.98394
$732$	0.113769	0.00420501
$733$	−40.0865	−1.48063	−0.740315	−	0.672260i	$-0.765324\pi$
$733$	−40.0865	−1.48063	−0.740315	+	0.672260i	$0.765324\pi$
$734$	−6.51521	−0.240481
$735$	3.13293	0.115560
$736$	−2.69137	−0.0992051
$737$	−23.8665	−0.879133
$738$	−39.6108	−1.45809
$739$	−15.5471	−0.571911	−0.285955	−	0.958243i	$-0.592311\pi$
$739$	−15.5471	−0.571911	−0.285955	+	0.958243i	$0.592311\pi$
$740$	8.44667	0.310506
$741$	0.420651	0.0154530
$742$	12.8842	0.472993
$743$	9.14826	0.335617	0.167809	−	0.985820i	$-0.446331\pi$
$743$	9.14826	0.335617	0.167809	+	0.985820i	$0.446331\pi$
$744$	−3.46537	−0.127047
$745$	−28.5613	−1.04640
$746$	16.2233	0.593979
$747$	7.93453	0.290309
$748$	−12.4980	−0.456973
$749$	6.07995	0.222156
$750$	5.10657	0.186465
$751$	−25.0186	−0.912942	−0.456471	−	0.889738i	$-0.650887\pi$
$751$	−25.0186	−0.912942	−0.456471	+	0.889738i	$0.650887\pi$
$752$	13.4799	0.491561
$753$	0.481151	0.0175341
$754$	−2.65675	−0.0967530
$755$	13.5777	0.494144
$756$	0.666770	0.0242502
$757$	−6.91937	−0.251489	−0.125744	−	0.992063i	$-0.540132\pi$
$757$	−6.91937	−0.251489	−0.125744	+	0.992063i	$0.540132\pi$
$758$	43.5131	1.58047
$759$	−1.10612	−0.0401495
$760$	−4.20972	−0.152703
$761$	8.82260	0.319819	0.159909	−	0.987132i	$-0.448880\pi$
$761$	8.82260	0.319819	0.159909	+	0.987132i	$0.448880\pi$
$762$	5.06063	0.183327
$763$	5.57837	0.201951
$764$	2.47046	0.0893780
$765$	34.1778	1.23570
$766$	−27.9679	−1.01052
$767$	22.5380	0.813801
$768$	2.93835	0.106029
$769$	1.32325	0.0477176	0.0238588	−	0.999715i	$-0.492405\pi$
$769$	1.32325	0.0477176	0.0238588	+	0.999715i	$0.492405\pi$
$770$	−10.7017	−0.385663
$771$	−5.89588	−0.212335
$772$	1.63612	0.0588853
$773$	−5.40626	−0.194450	−0.0972249	−	0.995262i	$-0.530997\pi$
$773$	−5.40626	−0.194450	−0.0972249	+	0.995262i	$0.530997\pi$
$774$	−39.9594	−1.43631
$775$	−7.93346	−0.284978
$776$	−45.5029	−1.63346
$777$	2.13868	0.0767246
$778$	−31.5307	−1.13043
$779$	−8.03494	−0.287881
$780$	0.410613	0.0147023
$781$	45.8814	1.64177
$782$	9.77334	0.349494
$783$	−1.58004	−0.0564659
$784$	29.5747	1.05624
$785$	−4.80978	−0.171668
$786$	−6.97252	−0.248701
$787$	41.8981	1.49351	0.746753	−	0.665102i	$-0.231612\pi$
$787$	41.8981	1.49351	0.746753	+	0.665102i	$0.231612\pi$
$788$	−8.00566	−0.285190
$789$	−4.24431	−0.151101
$790$	18.1670	0.646353
$791$	12.7173	0.452175
$792$	−29.0240	−1.03132
$793$	−1.48097	−0.0525907
$794$	−28.4494	−1.00963
$795$	4.71879	0.167358
$796$	1.04705	0.0371115
$797$	−5.09257	−0.180388	−0.0901940	−	0.995924i	$-0.528749\pi$
$797$	−5.09257	−0.180388	−0.0901940	+	0.995924i	$0.528749\pi$
$798$	0.341922	0.0121039
$799$	−17.6454	−0.624249
$800$	3.92012	0.138597
$801$	4.67883	0.165318
$802$	−36.6135	−1.29287
$803$	36.0493	1.27215
$804$	0.744341	0.0262509
$805$	1.63535	0.0576385
$806$	−14.4706	−0.509706
$807$	−6.03911	−0.212587
$808$	11.3272	0.398491
$809$	29.1875	1.02618	0.513089	−	0.858335i	$-0.328501\pi$
$809$	29.1875	1.02618	0.513089	+	0.858335i	$0.328501\pi$
$810$	−24.8286	−0.872390
$811$	22.9329	0.805283	0.402641	−	0.915358i	$-0.368092\pi$
$811$	22.9329	0.805283	0.402641	+	0.915358i	$0.368092\pi$
$812$	−0.421997	−0.0148092
$813$	−2.88044	−0.101021
$814$	60.4511	2.11881
$815$	−42.3364	−1.48298
$816$	−7.82296	−0.273859
$817$	−8.10564	−0.283580
$818$	43.6105	1.52481
$819$	−4.28781	−0.149828
$820$	−7.84320	−0.273896
$821$	7.21749	0.251892	0.125946	−	0.992037i	$-0.459803\pi$
$821$	7.21749	0.251892	0.125946	+	0.992037i	$0.459803\pi$
$822$	6.86758	0.239535
$823$	35.6266	1.24186	0.620932	−	0.783865i	$-0.286754\pi$
$823$	35.6266	1.24186	0.620932	+	0.783865i	$0.286754\pi$
$824$	−26.5039	−0.923306
$825$	1.61112	0.0560919
$826$	18.3198	0.637427
$827$	−36.4344	−1.26695	−0.633473	−	0.773765i	$-0.718371\pi$
$827$	−36.4344	−1.26695	−0.633473	+	0.773765i	$0.718371\pi$
$828$	−1.42275	−0.0494439
$829$	−25.5740	−0.888223	−0.444112	−	0.895972i	$-0.646481\pi$
$829$	−25.5740	−0.888223	−0.444112	+	0.895972i	$0.646481\pi$
$830$	8.03982	0.279066
$831$	−5.68232	−0.197118
$832$	−8.80930	−0.305408
$833$	−38.7138	−1.34135
$834$	−8.70762	−0.301520
$835$	14.2939	0.494662
$836$	1.88860	0.0653186
$837$	−8.60604	−0.297468
$838$	37.2969	1.28840
$839$	40.2505	1.38960	0.694801	−	0.719202i	$-0.255492\pi$
$839$	40.2505	1.38960	0.694801	+	0.719202i	$0.255492\pi$
$840$	−1.04046	−0.0358992
$841$	1.00000	0.0344828
$842$	−45.7692	−1.57731
$843$	−6.73560	−0.231986
$844$	−1.00367	−0.0345478
$845$	19.1262	0.657960
$846$	13.1450	0.451936
$847$	−5.41042	−0.185904
$848$	44.5452	1.52969
$849$	−3.56472	−0.122341
$850$	−14.2354	−0.488269
$851$	−9.23764	−0.316662
$852$	−1.43094	−0.0490231
$853$	−41.6762	−1.42697	−0.713484	−	0.700672i	$-0.752884\pi$
$853$	−41.6762	−1.42697	−0.713484	+	0.700672i	$0.752884\pi$
$854$	−1.20379	−0.0411928
$855$	−5.16468	−0.176628
$856$	16.7082	0.571073
$857$	−12.9088	−0.440955	−0.220477	−	0.975392i	$-0.570761\pi$
$857$	−12.9088	−0.440955	−0.220477	+	0.975392i	$0.570761\pi$
$858$	2.93867	0.100325
$859$	−16.0206	−0.546614	−0.273307	−	0.961927i	$-0.588118\pi$
$859$	−16.0206	−0.546614	−0.273307	+	0.961927i	$0.588118\pi$
$860$	−7.91221	−0.269804
$861$	−1.98588	−0.0676786
$862$	5.74592	0.195707
$863$	−51.2650	−1.74508	−0.872541	−	0.488541i	$-0.837529\pi$
$863$	−51.2650	−1.74508	−0.872541	+	0.488541i	$0.837529\pi$
$864$	4.25246	0.144672
$865$	43.2573	1.47079
$866$	−54.3063	−1.84540
$867$	5.70999	0.193921
$868$	−2.29851	−0.0780164
$869$	25.4072	0.861880
$870$	−0.790912	−0.0268144
$871$	−9.68936	−0.328311
$872$	15.3298	0.519132
$873$	−55.8251	−1.88939
$874$	−1.47687	−0.0499559
$875$	−10.5587	−0.356950
$876$	−1.12429	−0.0379864
$877$	−35.0554	−1.18374	−0.591868	−	0.806035i	$-0.701610\pi$
$877$	−35.0554	−1.18374	−0.591868	+	0.806035i	$0.701610\pi$
$878$	−6.24441	−0.210739
$879$	−2.38225	−0.0803514
$880$	−36.9997	−1.24726
$881$	7.68816	0.259021	0.129510	−	0.991578i	$-0.458659\pi$
$881$	7.68816	0.259021	0.129510	+	0.991578i	$0.458659\pi$
$882$	28.8400	0.971095
$883$	−21.6048	−0.727058	−0.363529	−	0.931583i	$-0.618428\pi$
$883$	−21.6048	−0.727058	−0.363529	+	0.931583i	$0.618428\pi$
$884$	−5.07397	−0.170656
$885$	6.70956	0.225540
$886$	14.4063	0.483989
$887$	−13.9394	−0.468040	−0.234020	−	0.972232i	$-0.575188\pi$
$887$	−13.9394	−0.468040	−0.234020	+	0.972232i	$0.575188\pi$
$888$	5.87725	0.197228
$889$	−10.4637	−0.350942
$890$	4.74092	0.158916
$891$	−34.7237	−1.16329
$892$	8.38256	0.280669
$893$	2.66643	0.0892288
$894$	6.37499	0.213212
$895$	−1.83478	−0.0613298
$896$	−11.8368	−0.395441
$897$	−0.449064	−0.0149938
$898$	12.8025	0.427226
$899$	5.44674	0.181659
$900$	2.07231	0.0690769
$901$	−58.3103	−1.94260
$902$	−56.1322	−1.86900
$903$	−2.00335	−0.0666674
$904$	34.9481	1.16236
$905$	−21.8428	−0.726080
$906$	−3.03061	−0.100685
$907$	−52.9629	−1.75860	−0.879302	−	0.476264i	$-0.841991\pi$
$907$	−52.9629	−1.75860	−0.879302	+	0.476264i	$0.841991\pi$
$908$	13.0913	0.434450
$909$	13.8968	0.460927
$910$	−4.34471	−0.144026
$911$	45.0081	1.49118	0.745592	−	0.666403i	$-0.232167\pi$
$911$	45.0081	1.49118	0.745592	+	0.666403i	$0.232167\pi$
$912$	1.18214	0.0391447
$913$	11.2440	0.372121
$914$	−11.6478	−0.385275
$915$	−0.440883	−0.0145752
$916$	0.982870	0.0324749
$917$	14.4169	0.476088
$918$	−15.4422	−0.509669
$919$	−4.73468	−0.156183	−0.0780913	−	0.996946i	$-0.524883\pi$
$919$	−4.73468	−0.156183	−0.0780913	+	0.996946i	$0.524883\pi$
$920$	4.49407	0.148165
$921$	3.29583	0.108601
$922$	28.6570	0.943768
$923$	18.6270	0.613116
$924$	0.466778	0.0153559
$925$	13.4551	0.442401
$926$	−47.5423	−1.56234
$927$	−32.5162	−1.06797
$928$	−2.69137	−0.0883485
$929$	−11.8684	−0.389391	−0.194695	−	0.980864i	$-0.562372\pi$
$929$	−11.8684	−0.389391	−0.194695	+	0.980864i	$0.562372\pi$
$930$	−4.30790	−0.141261
$931$	5.85012	0.191730
$932$	−7.61275	−0.249364
$933$	4.54128	0.148675
$934$	−3.50156	−0.114574
$935$	48.4331	1.58393
$936$	−11.7832	−0.385147
$937$	−4.23328	−0.138295	−0.0691476	−	0.997606i	$-0.522028\pi$
$937$	−4.23328	−0.138295	−0.0691476	+	0.997606i	$0.522028\pi$
$938$	−7.87589	−0.257157
$939$	−0.723708	−0.0236173
$940$	2.60280	0.0848941
$941$	23.5729	0.768454	0.384227	−	0.923239i	$-0.374468\pi$
$941$	23.5729	0.768454	0.384227	+	0.923239i	$0.374468\pi$
$942$	1.07356	0.0349786
$943$	8.57766	0.279327
$944$	63.3380	2.06148
$945$	−2.58391	−0.0840546
$946$	−56.6261	−1.84107
$947$	0.731434	0.0237684	0.0118842	−	0.999929i	$-0.496217\pi$
$947$	0.731434	0.0237684	0.0118842	+	0.999929i	$0.496217\pi$
$948$	−0.792392	−0.0257357
$949$	14.6354	0.475084
$950$	2.15114	0.0697921
$951$	2.73216	0.0885963
$952$	12.8570	0.416697
$953$	−51.8022	−1.67804	−0.839020	−	0.544101i	$-0.816871\pi$
$953$	−51.8022	−1.67804	−0.839020	+	0.544101i	$0.816871\pi$
$954$	43.4386	1.40638
$955$	−9.57367	−0.309797
$956$	11.4049	0.368862
$957$	−1.10612	−0.0357557
$958$	−24.6816	−0.797426
$959$	−14.1999	−0.458540
$960$	−2.62253	−0.0846416
$961$	−1.33301	−0.0430004
$962$	24.5421	0.791268
$963$	20.4983	0.660550
$964$	−2.04409	−0.0658357
$965$	−6.34040	−0.204105
$966$	−0.365017	−0.0117442
$967$	15.9898	0.514198	0.257099	−	0.966385i	$-0.417233\pi$
$967$	15.9898	0.514198	0.257099	+	0.966385i	$0.417233\pi$
$968$	−14.8683	−0.477884
$969$	−1.54744	−0.0497111
$970$	−56.5659	−1.81622
$971$	−33.5583	−1.07694	−0.538469	−	0.842645i	$-0.680997\pi$
$971$	−33.5583	−1.07694	−0.538469	+	0.842645i	$0.680997\pi$
$972$	3.38545	0.108588
$973$	18.0045	0.577198
$974$	38.8700	1.24547
$975$	0.654085	0.0209475
$976$	−4.16192	−0.133220
$977$	44.1508	1.41251	0.706255	−	0.707958i	$-0.250383\pi$
$977$	44.1508	1.41251	0.706255	+	0.707958i	$0.250383\pi$
$978$	9.44965	0.302166
$979$	6.63034	0.211907
$980$	5.71052	0.182416
$981$	18.8073	0.600471
$982$	−15.2826	−0.487687
$983$	−24.0011	−0.765518	−0.382759	−	0.923848i	$-0.625026\pi$
$983$	−24.0011	−0.765518	−0.382759	+	0.923848i	$0.625026\pi$
$984$	−5.45735	−0.173974
$985$	31.0241	0.988508
$986$	9.77334	0.311247
$987$	0.659024	0.0209769
$988$	0.766738	0.0243932
$989$	8.65313	0.275154
$990$	−36.0805	−1.14671
$991$	−46.4921	−1.47687	−0.738436	−	0.674324i	$-0.764435\pi$
$991$	−46.4921	−1.47687	−0.738436	+	0.674324i	$0.764435\pi$
$992$	−14.6592	−0.465430
$993$	4.19452	0.133109
$994$	15.1408	0.480236
$995$	−4.05758	−0.128634
$996$	−0.350673	−0.0111115
$997$	−19.7245	−0.624680	−0.312340	−	0.949970i	$-0.601113\pi$
$997$	−19.7245	−0.624680	−0.312340	+	0.949970i	$0.601113\pi$
$998$	5.30523	0.167934
$999$	14.5958	0.461790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.a.1.9	✓	10
3.2	odd	2		6003.2.a.l.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.a.1.9	✓	10	1.1	even	1	trivial
6003.2.a.l.1.2		10	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)

\(f(q)\)	\(=\)	\(q+1.57663 q^{2} +0.266494 q^{3} +0.485749 q^{4} -1.88241 q^{5} +0.420161 q^{6} -0.868755 q^{7} -2.38741 q^{8} -2.92898 q^{9} +O(q^{10})\)	\(q+1.57663 q^{2} +0.266494 q^{3} +0.485749 q^{4} -1.88241 q^{5} +0.420161 q^{6} -0.868755 q^{7} -2.38741 q^{8} -2.92898 q^{9} -2.96785 q^{10} -4.15064 q^{11} +0.129449 q^{12} -1.68508 q^{13} -1.36970 q^{14} -0.501649 q^{15} -4.73555 q^{16} +6.19890 q^{17} -4.61791 q^{18} -0.936729 q^{19} -0.914376 q^{20} -0.231518 q^{21} -6.54400 q^{22} +1.00000 q^{23} -0.636229 q^{24} -1.45655 q^{25} -2.65675 q^{26} -1.58004 q^{27} -0.421997 q^{28} +1.00000 q^{29} -0.790912 q^{30} +5.44674 q^{31} -2.69137 q^{32} -1.10612 q^{33} +9.77334 q^{34} +1.63535 q^{35} -1.42275 q^{36} -9.23764 q^{37} -1.47687 q^{38} -0.449064 q^{39} +4.49407 q^{40} +8.57766 q^{41} -0.365017 q^{42} +8.65313 q^{43} -2.01617 q^{44} +5.51353 q^{45} +1.57663 q^{46} -2.84654 q^{47} -1.26199 q^{48} -6.24526 q^{49} -2.29644 q^{50} +1.65197 q^{51} -0.818527 q^{52} -9.40655 q^{53} -2.49112 q^{54} +7.81318 q^{55} +2.07407 q^{56} -0.249632 q^{57} +1.57663 q^{58} -13.3750 q^{59} -0.243675 q^{60} +0.878868 q^{61} +8.58747 q^{62} +2.54457 q^{63} +5.22781 q^{64} +3.17201 q^{65} -1.74393 q^{66} +5.75008 q^{67} +3.01111 q^{68} +0.266494 q^{69} +2.57833 q^{70} -11.0541 q^{71} +6.99267 q^{72} -8.68524 q^{73} -14.5643 q^{74} -0.388162 q^{75} -0.455015 q^{76} +3.60589 q^{77} -0.708006 q^{78} -6.12127 q^{79} +8.91421 q^{80} +8.36587 q^{81} +13.5238 q^{82} -2.70897 q^{83} -0.112459 q^{84} -11.6688 q^{85} +13.6428 q^{86} +0.266494 q^{87} +9.90926 q^{88} -1.59743 q^{89} +8.69277 q^{90} +1.46393 q^{91} +0.485749 q^{92} +1.45152 q^{93} -4.48792 q^{94} +1.76330 q^{95} -0.717232 q^{96} +19.0596 q^{97} -9.84644 q^{98} +12.1571 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9 - 6 * q^10 - 17 * q^12 - 13 * q^13 - 12 * q^14 + 2 * q^15 - 5 * q^16 - 22 * q^17 + 12 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 3 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 25 * q^26 - 24 * q^27 + 19 * q^28 + 10 * q^29 - 3 * q^30 - 22 * q^31 - 31 * q^32 - 9 * q^33 + 13 * q^34 - 15 * q^35 + 19 * q^36 - 9 * q^37 - 10 * q^38 + 4 * q^39 - 6 * q^40 - 25 * q^41 - 34 * q^42 + 3 * q^43 - 27 * q^44 - 28 * q^45 - 3 * q^46 - 17 * q^47 - 3 * q^48 + 17 * q^49 + 2 * q^50 + 38 * q^51 - 18 * q^52 - 43 * q^53 - 47 * q^54 - 11 * q^55 - 7 * q^56 + 18 * q^57 - 3 * q^58 - 7 * q^59 - 21 * q^60 - 6 * q^61 + 3 * q^62 + 11 * q^63 + 33 * q^64 + 11 * q^65 + 55 * q^66 + 11 * q^67 - 51 * q^68 - 9 * q^69 + 34 * q^70 - 17 * q^71 + 34 * q^72 - 44 * q^73 + 9 * q^74 + q^75 + 24 * q^76 - 71 * q^77 + 38 * q^78 + 5 * q^79 + 38 * q^80 + 18 * q^81 + 33 * q^82 - 32 * q^83 + 14 * q^84 + 16 * q^85 - 9 * q^86 - 9 * q^87 + 18 * q^88 - 10 * q^89 - 9 * q^90 - 3 * q^91 + 9 * q^92 - 8 * q^93 + 47 * q^94 - 8 * q^95 + 60 * q^96 + 6 * q^97 - 73 * q^98 + 26 * q^99

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