LMFDB - Embedded newform 667.2.a.a.1.2

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			1.2
Root			$2.37954$ 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)

$f(q)$	$=$	$q-2.37954 q^{2} +0.653256 q^{3} +3.66223 q^{4} -2.05928 q^{5} -1.55445 q^{6} +5.08987 q^{7} -3.95536 q^{8} -2.57326 q^{9} +O(q^{10})$	\(q-2.37954 q^{2} +0.653256 q^{3} +3.66223 q^{4} -2.05928 q^{5} -1.55445 q^{6} +5.08987 q^{7} -3.95536 q^{8} -2.57326 q^{9} +4.90014 q^{10} -4.57737 q^{11} +2.39237 q^{12} -1.87097 q^{13} -12.1116 q^{14} -1.34523 q^{15} +2.08748 q^{16} -0.272178 q^{17} +6.12318 q^{18} +0.546501 q^{19} -7.54155 q^{20} +3.32499 q^{21} +10.8920 q^{22} +1.00000 q^{23} -2.58386 q^{24} -0.759381 q^{25} +4.45206 q^{26} -3.64076 q^{27} +18.6403 q^{28} +1.00000 q^{29} +3.20104 q^{30} -4.25284 q^{31} +2.94346 q^{32} -2.99019 q^{33} +0.647660 q^{34} -10.4815 q^{35} -9.42386 q^{36} +1.52870 q^{37} -1.30042 q^{38} -1.22222 q^{39} +8.14517 q^{40} -8.02619 q^{41} -7.91196 q^{42} -8.67751 q^{43} -16.7634 q^{44} +5.29905 q^{45} -2.37954 q^{46} +8.58972 q^{47} +1.36366 q^{48} +18.9068 q^{49} +1.80698 q^{50} -0.177802 q^{51} -6.85194 q^{52} +2.34652 q^{53} +8.66336 q^{54} +9.42606 q^{55} -20.1323 q^{56} +0.357005 q^{57} -2.37954 q^{58} -1.14292 q^{59} -4.92656 q^{60} -7.40397 q^{61} +10.1198 q^{62} -13.0976 q^{63} -11.1791 q^{64} +3.85285 q^{65} +7.11529 q^{66} -11.9170 q^{67} -0.996780 q^{68} +0.653256 q^{69} +24.9411 q^{70} -6.20236 q^{71} +10.1781 q^{72} -10.5699 q^{73} -3.63762 q^{74} -0.496070 q^{75} +2.00141 q^{76} -23.2982 q^{77} +2.90834 q^{78} -16.3652 q^{79} -4.29870 q^{80} +5.34142 q^{81} +19.0987 q^{82} -15.9890 q^{83} +12.1769 q^{84} +0.560490 q^{85} +20.6485 q^{86} +0.653256 q^{87} +18.1051 q^{88} +9.38087 q^{89} -12.6093 q^{90} -9.52302 q^{91} +3.66223 q^{92} -2.77819 q^{93} -20.4396 q^{94} -1.12540 q^{95} +1.92283 q^{96} -13.2320 q^{97} -44.9896 q^{98} +11.7787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.37954	−1.68259	−0.841296	−	0.540575i	$-0.818207\pi$
$2$	−2.37954	−1.68259	−0.841296	+	0.540575i	$0.818207\pi$
$3$	0.653256	0.377157	0.188579	−	0.982058i	$-0.439612\pi$
$3$	0.653256	0.377157	0.188579	+	0.982058i	$0.439612\pi$
$4$	3.66223	1.83112
$5$	−2.05928	−0.920936	−0.460468	−	0.887676i	$-0.652318\pi$
$5$	−2.05928	−0.920936	−0.460468	+	0.887676i	$0.652318\pi$
$6$	−1.55445	−0.634602
$7$	5.08987	1.92379	0.961896	−	0.273416i	$-0.0881537\pi$
$7$	5.08987	1.92379	0.961896	+	0.273416i	$0.0881537\pi$
$8$	−3.95536	−1.39843
$9$	−2.57326	−0.857752
$10$	4.90014	1.54956
$11$	−4.57737	−1.38013	−0.690064	−	0.723748i	$-0.742418\pi$
$11$	−4.57737	−1.38013	−0.690064	+	0.723748i	$0.742418\pi$
$12$	2.39237	0.690619
$13$	−1.87097	−0.518915	−0.259457	−	0.965755i	$-0.583544\pi$
$13$	−1.87097	−0.518915	−0.259457	+	0.965755i	$0.583544\pi$
$14$	−12.1116	−3.23696
$15$	−1.34523	−0.347338
$16$	2.08748	0.521870
$17$	−0.272178	−0.0660129	−0.0330065	−	0.999455i	$-0.510508\pi$
$17$	−0.272178	−0.0660129	−0.0330065	+	0.999455i	$0.510508\pi$
$18$	6.12318	1.44325
$19$	0.546501	0.125376	0.0626879	−	0.998033i	$-0.480033\pi$
$19$	0.546501	0.125376	0.0626879	+	0.998033i	$0.480033\pi$
$20$	−7.54155	−1.68634
$21$	3.32499	0.725572
$22$	10.8920	2.32219
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.58386	−0.527428
$25$	−0.759381	−0.151876
$26$	4.45206	0.873122
$27$	−3.64076	−0.700665
$28$	18.6403	3.52269
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.20104	0.584428
$31$	−4.25284	−0.763832	−0.381916	−	0.924197i	$-0.624736\pi$
$31$	−4.25284	−0.763832	−0.381916	+	0.924197i	$0.624736\pi$
$32$	2.94346	0.520335
$33$	−2.99019	−0.520525
$34$	0.647660	0.111073
$35$	−10.4815	−1.77169
$36$	−9.42386	−1.57064
$37$	1.52870	0.251318	0.125659	−	0.992074i	$-0.459896\pi$
$37$	1.52870	0.251318	0.125659	+	0.992074i	$0.459896\pi$
$38$	−1.30042	−0.210956
$39$	−1.22222	−0.195713
$40$	8.14517	1.28786
$41$	−8.02619	−1.25348	−0.626740	−	0.779228i	$-0.715611\pi$
$41$	−8.02619	−1.25348	−0.626740	+	0.779228i	$0.715611\pi$
$42$	−7.91196	−1.22084
$43$	−8.67751	−1.32331	−0.661654	−	0.749809i	$-0.730145\pi$
$43$	−8.67751	−1.32331	−0.661654	+	0.749809i	$0.730145\pi$
$44$	−16.7634	−2.52717
$45$	5.29905	0.789935
$46$	−2.37954	−0.350845
$47$	8.58972	1.25294	0.626470	−	0.779446i	$-0.284499\pi$
$47$	8.58972	1.25294	0.626470	+	0.779446i	$0.284499\pi$
$48$	1.36366	0.196827
$49$	18.9068	2.70097
$50$	1.80698	0.255546
$51$	−0.177802	−0.0248973
$52$	−6.85194	−0.950193
$53$	2.34652	0.322319	0.161160	−	0.986928i	$-0.448477\pi$
$53$	2.34652	0.322319	0.161160	+	0.986928i	$0.448477\pi$
$54$	8.66336	1.17893
$55$	9.42606	1.27101
$56$	−20.1323	−2.69029
$57$	0.357005	0.0472864
$58$	−2.37954	−0.312450
$59$	−1.14292	−0.148795	−0.0743975	−	0.997229i	$-0.523703\pi$
$59$	−1.14292	−0.148795	−0.0743975	+	0.997229i	$0.523703\pi$
$60$	−4.92656	−0.636016
$61$	−7.40397	−0.947981	−0.473990	−	0.880530i	$-0.657187\pi$
$61$	−7.40397	−0.947981	−0.473990	+	0.880530i	$0.657187\pi$
$62$	10.1198	1.28522
$63$	−13.0976	−1.65014
$64$	−11.1791	−1.39738
$65$	3.85285	0.477887
$66$	7.11529	0.875832
$67$	−11.9170	−1.45590	−0.727948	−	0.685632i	$-0.759526\pi$
$67$	−11.9170	−1.45590	−0.727948	+	0.685632i	$0.759526\pi$
$68$	−0.996780	−0.120877
$69$	0.653256	0.0786428
$70$	24.9411	2.98103
$71$	−6.20236	−0.736085	−0.368043	−	0.929809i	$-0.619972\pi$
$71$	−6.20236	−0.736085	−0.368043	+	0.929809i	$0.619972\pi$
$72$	10.1781	1.19951
$73$	−10.5699	−1.23711	−0.618556	−	0.785741i	$-0.712282\pi$
$73$	−10.5699	−1.23711	−0.618556	+	0.785741i	$0.712282\pi$
$74$	−3.63762	−0.422865
$75$	−0.496070	−0.0572812
$76$	2.00141	0.229578
$77$	−23.2982	−2.65508
$78$	2.90834	0.329304
$79$	−16.3652	−1.84123	−0.920614	−	0.390474i	$-0.872311\pi$
$79$	−16.3652	−1.84123	−0.920614	+	0.390474i	$0.872311\pi$
$80$	−4.29870	−0.480609
$81$	5.34142	0.593491
$82$	19.0987	2.10910
$83$	−15.9890	−1.75502	−0.877509	−	0.479561i	$-0.840796\pi$
$83$	−15.9890	−1.75502	−0.877509	+	0.479561i	$0.840796\pi$
$84$	12.1769	1.32861
$85$	0.560490	0.0607937
$86$	20.6485	2.22659
$87$	0.653256	0.0700364
$88$	18.1051	1.93001
$89$	9.38087	0.994370	0.497185	−	0.867645i	$-0.334367\pi$
$89$	9.38087	0.994370	0.497185	+	0.867645i	$0.334367\pi$
$90$	−12.6093	−1.32914
$91$	−9.52302	−0.998284
$92$	3.66223	0.381814
$93$	−2.77819	−0.288085
$94$	−20.4396	−2.10819
$95$	−1.12540	−0.115463
$96$	1.92283	0.196248
$97$	−13.2320	−1.34350	−0.671751	−	0.740777i	$-0.734458\pi$
$97$	−13.2320	−1.34350	−0.671751	+	0.740777i	$0.734458\pi$
$98$	−44.9896	−4.54464
$99$	11.7787	1.18381
$100$	−2.78103	−0.278103
$101$	6.02178	0.599190	0.299595	−	0.954067i	$-0.403148\pi$
$101$	6.02178	0.599190	0.299595	+	0.954067i	$0.403148\pi$
$102$	0.423088	0.0418920
$103$	15.3180	1.50933	0.754663	−	0.656113i	$-0.227800\pi$
$103$	15.3180	1.50933	0.754663	+	0.656113i	$0.227800\pi$
$104$	7.40036	0.725665
$105$	−6.84707	−0.668206
$106$	−5.58365	−0.542332
$107$	0.735546	0.0711079	0.0355540	−	0.999368i	$-0.488680\pi$
$107$	0.735546	0.0711079	0.0355540	+	0.999368i	$0.488680\pi$
$108$	−13.3333	−1.28300
$109$	8.53593	0.817594	0.408797	−	0.912625i	$-0.365948\pi$
$109$	8.53593	0.817594	0.408797	+	0.912625i	$0.365948\pi$
$110$	−22.4297	−2.13859
$111$	0.998635	0.0947863
$112$	10.6250	1.00397
$113$	−0.738224	−0.0694463	−0.0347231	−	0.999397i	$-0.511055\pi$
$113$	−0.738224	−0.0694463	−0.0347231	+	0.999397i	$0.511055\pi$
$114$	−0.849508	−0.0795638
$115$	−2.05928	−0.192029
$116$	3.66223	0.340030
$117$	4.81450	0.445100
$118$	2.71962	0.250361
$119$	−1.38535	−0.126995
$120$	5.32088	0.485728
$121$	9.95228	0.904753
$122$	17.6181	1.59507
$123$	−5.24316	−0.472760
$124$	−15.5749	−1.39867
$125$	11.8602	1.06080
$126$	31.1662	2.77651
$127$	−6.60130	−0.585771	−0.292885	−	0.956148i	$-0.594615\pi$
$127$	−6.60130	−0.585771	−0.292885	+	0.956148i	$0.594615\pi$
$128$	20.7141	1.83089
$129$	−5.66863	−0.499095
$130$	−9.16803	−0.804090
$131$	−3.35350	−0.292996	−0.146498	−	0.989211i	$-0.546800\pi$
$131$	−3.35350	−0.292996	−0.146498	+	0.989211i	$0.546800\pi$
$132$	−10.9508	−0.953143
$133$	2.78162	0.241197
$134$	28.3571	2.44968
$135$	7.49734	0.645268
$136$	1.07656	0.0923144
$137$	−9.55553	−0.816384	−0.408192	−	0.912896i	$-0.633841\pi$
$137$	−9.55553	−0.816384	−0.408192	+	0.912896i	$0.633841\pi$
$138$	−1.55445	−0.132324
$139$	−6.57246	−0.557469	−0.278734	−	0.960368i	$-0.589915\pi$
$139$	−6.57246	−0.557469	−0.278734	+	0.960368i	$0.589915\pi$
$140$	−38.3855	−3.24417
$141$	5.61128	0.472555
$142$	14.7588	1.23853
$143$	8.56413	0.716169
$144$	−5.37162	−0.447635
$145$	−2.05928	−0.171014
$146$	25.1515	2.08155
$147$	12.3510	1.01869
$148$	5.59847	0.460192
$149$	16.8263	1.37846	0.689232	−	0.724540i	$-0.257948\pi$
$149$	16.8263	1.37846	0.689232	+	0.724540i	$0.257948\pi$
$150$	1.18042	0.0963809
$151$	19.5683	1.59245	0.796223	−	0.605003i	$-0.206828\pi$
$151$	19.5683	1.59245	0.796223	+	0.605003i	$0.206828\pi$
$152$	−2.16160	−0.175329
$153$	0.700385	0.0566228
$154$	55.4391	4.46741
$155$	8.75777	0.703441
$156$	−4.47607	−0.358372
$157$	−12.3661	−0.986922	−0.493461	−	0.869768i	$-0.664268\pi$
$157$	−12.3661	−0.986922	−0.493461	+	0.869768i	$0.664268\pi$
$158$	38.9417	3.09804
$159$	1.53288	0.121565
$160$	−6.06140	−0.479195
$161$	5.08987	0.401138
$162$	−12.7102	−0.998604
$163$	10.0938	0.790611	0.395306	−	0.918550i	$-0.370639\pi$
$163$	10.0938	0.790611	0.395306	+	0.918550i	$0.370639\pi$
$164$	−29.3938	−2.29527
$165$	6.15763	0.479371
$166$	38.0465	2.95298
$167$	1.30505	0.100988	0.0504940	−	0.998724i	$-0.483920\pi$
$167$	1.30505	0.100988	0.0504940	+	0.998724i	$0.483920\pi$
$168$	−13.1515	−1.01466
$169$	−9.49946	−0.730728
$170$	−1.33371	−0.102291
$171$	−1.40629	−0.107541
$172$	−31.7791	−2.42313
$173$	2.20103	0.167342	0.0836708	−	0.996493i	$-0.473336\pi$
$173$	2.20103	0.167342	0.0836708	+	0.996493i	$0.473336\pi$
$174$	−1.55445	−0.117843
$175$	−3.86515	−0.292178
$176$	−9.55516	−0.720247
$177$	−0.746617	−0.0561192
$178$	−22.3222	−1.67312
$179$	−24.6440	−1.84198	−0.920991	−	0.389584i	$-0.872619\pi$
$179$	−24.6440	−1.84198	−0.920991	+	0.389584i	$0.872619\pi$
$180$	19.4063	1.44646
$181$	1.45544	0.108182	0.0540908	−	0.998536i	$-0.482774\pi$
$181$	1.45544	0.108182	0.0540908	+	0.998536i	$0.482774\pi$
$182$	22.6604	1.67970
$183$	−4.83668	−0.357538
$184$	−3.95536	−0.291593
$185$	−3.14803	−0.231447
$186$	6.61083	0.484730
$187$	1.24586	0.0911063
$188$	31.4575	2.29428
$189$	−18.5310	−1.34793
$190$	2.67793	0.194277
$191$	−0.592184	−0.0428489	−0.0214244	−	0.999770i	$-0.506820\pi$
$191$	−0.592184	−0.0428489	−0.0214244	+	0.999770i	$0.506820\pi$
$192$	−7.30278	−0.527033
$193$	24.3728	1.75439	0.877197	−	0.480130i	$-0.159410\pi$
$193$	24.3728	1.75439	0.877197	+	0.480130i	$0.159410\pi$
$194$	31.4861	2.26057
$195$	2.51690	0.180239
$196$	69.2412	4.94580
$197$	−18.2722	−1.30184	−0.650919	−	0.759147i	$-0.725616\pi$
$197$	−18.2722	−1.30184	−0.650919	+	0.759147i	$0.725616\pi$
$198$	−28.0280	−1.99187
$199$	7.74033	0.548697	0.274349	−	0.961630i	$-0.411538\pi$
$199$	7.74033	0.548697	0.274349	+	0.961630i	$0.411538\pi$
$200$	3.00362	0.212388
$201$	−7.78486	−0.549102
$202$	−14.3291	−1.00819
$203$	5.08987	0.357239
$204$	−0.651152	−0.0455898
$205$	16.5281	1.15438
$206$	−36.4498	−2.53958
$207$	−2.57326	−0.178854
$208$	−3.90562	−0.270806
$209$	−2.50153	−0.173035
$210$	16.2929	1.12432
$211$	13.6581	0.940262	0.470131	−	0.882597i	$-0.344207\pi$
$211$	13.6581	0.940262	0.470131	+	0.882597i	$0.344207\pi$
$212$	8.59350	0.590204
$213$	−4.05173	−0.277620
$214$	−1.75027	−0.119646
$215$	17.8694	1.21868
$216$	14.4005	0.979830
$217$	−21.6464	−1.46945
$218$	−20.3116	−1.37568
$219$	−6.90484	−0.466586
$220$	34.5204	2.32737
$221$	0.509238	0.0342551
$222$	−2.37630	−0.159487
$223$	0.497369	0.0333063	0.0166532	−	0.999861i	$-0.494699\pi$
$223$	0.497369	0.0333063	0.0166532	+	0.999861i	$0.494699\pi$
$224$	14.9818	1.00102
$225$	1.95408	0.130272
$226$	1.75664	0.116850
$227$	12.6270	0.838082	0.419041	−	0.907967i	$-0.362366\pi$
$227$	12.6270	0.838082	0.419041	+	0.907967i	$0.362366\pi$
$228$	1.30743	0.0865869
$229$	5.22393	0.345207	0.172603	−	0.984991i	$-0.444782\pi$
$229$	5.22393	0.345207	0.172603	+	0.984991i	$0.444782\pi$
$230$	4.90014	0.323106
$231$	−15.2197	−1.00138
$232$	−3.95536	−0.259682
$233$	14.1679	0.928173	0.464086	−	0.885790i	$-0.346383\pi$
$233$	14.1679	0.928173	0.464086	+	0.885790i	$0.346383\pi$
$234$	−11.4563	−0.748922
$235$	−17.6886	−1.15388
$236$	−4.18563	−0.272461
$237$	−10.6907	−0.694433
$238$	3.29651	0.213681
$239$	15.7660	1.01981	0.509907	−	0.860229i	$-0.329680\pi$
$239$	15.7660	1.01981	0.509907	+	0.860229i	$0.329680\pi$
$240$	−2.80815	−0.181265
$241$	26.7382	1.72236	0.861179	−	0.508302i	$-0.169726\pi$
$241$	26.7382	1.72236	0.861179	+	0.508302i	$0.169726\pi$
$242$	−23.6819	−1.52233
$243$	14.4116	0.924505
$244$	−27.1150	−1.73586
$245$	−38.9344	−2.48743
$246$	12.4763	0.795461
$247$	−1.02249	−0.0650594
$248$	16.8215	1.06817
$249$	−10.4449	−0.661918
$250$	−28.2218	−1.78490
$251$	−6.69588	−0.422640	−0.211320	−	0.977417i	$-0.567776\pi$
$251$	−6.69588	−0.422640	−0.211320	+	0.977417i	$0.567776\pi$
$252$	−47.9663	−3.02159
$253$	−4.57737	−0.287777
$254$	15.7081	0.985613
$255$	0.366144	0.0229288
$256$	−26.9321	−1.68326
$257$	−10.6964	−0.667224	−0.333612	−	0.942711i	$-0.608267\pi$
$257$	−10.6964	−0.667224	−0.333612	+	0.942711i	$0.608267\pi$
$258$	13.4888	0.839774
$259$	7.78092	0.483483
$260$	14.1100	0.875067
$261$	−2.57326	−0.159281
$262$	7.97979	0.492993
$263$	−16.9191	−1.04328	−0.521638	−	0.853167i	$-0.674679\pi$
$263$	−16.9191	−1.04328	−0.521638	+	0.853167i	$0.674679\pi$
$264$	11.8273	0.727918
$265$	−4.83213	−0.296836
$266$	−6.61899	−0.405836
$267$	6.12811	0.375034
$268$	−43.6429	−2.66591
$269$	−6.78462	−0.413666	−0.206833	−	0.978376i	$-0.566316\pi$
$269$	−6.78462	−0.413666	−0.206833	+	0.978376i	$0.566316\pi$
$270$	−17.8402	−1.08572
$271$	20.3901	1.23861	0.619305	−	0.785151i	$-0.287415\pi$
$271$	20.3901	1.23861	0.619305	+	0.785151i	$0.287415\pi$
$272$	−0.568167	−0.0344502
$273$	−6.22097	−0.376510
$274$	22.7378	1.37364
$275$	3.47596	0.209609
$276$	2.39237	0.144004
$277$	−6.68828	−0.401860	−0.200930	−	0.979606i	$-0.564396\pi$
$277$	−6.68828	−0.401860	−0.200930	+	0.979606i	$0.564396\pi$
$278$	15.6395	0.937993
$279$	10.9436	0.655179
$280$	41.4579	2.47758
$281$	6.60817	0.394211	0.197105	−	0.980382i	$-0.436846\pi$
$281$	6.60817	0.394211	0.197105	+	0.980382i	$0.436846\pi$
$282$	−13.3523	−0.795118
$283$	17.0146	1.01141	0.505706	−	0.862706i	$-0.331232\pi$
$283$	17.0146	1.01141	0.505706	+	0.862706i	$0.331232\pi$
$284$	−22.7145	−1.34786
$285$	−0.735171	−0.0435478
$286$	−20.3787	−1.20502
$287$	−40.8523	−2.41144
$288$	−7.57428	−0.446319
$289$	−16.9259	−0.995642
$290$	4.90014	0.287746
$291$	−8.64386	−0.506712
$292$	−38.7094	−2.26530
$293$	−28.2553	−1.65069	−0.825347	−	0.564625i	$-0.809021\pi$
$293$	−28.2553	−1.65069	−0.825347	+	0.564625i	$0.809021\pi$
$294$	−29.3897	−1.71404
$295$	2.35358	0.137031
$296$	−6.04657	−0.351450
$297$	16.6651	0.967007
$298$	−40.0389	−2.31939
$299$	−1.87097	−0.108201
$300$	−1.81672	−0.104889
$301$	−44.1674	−2.54577
$302$	−46.5637	−2.67944
$303$	3.93376	0.225989
$304$	1.14081	0.0654299
$305$	15.2468	0.873030
$306$	−1.66660	−0.0952730
$307$	−7.93383	−0.452808	−0.226404	−	0.974034i	$-0.572697\pi$
$307$	−7.93383	−0.452808	−0.226404	+	0.974034i	$0.572697\pi$
$308$	−85.3235	−4.86176
$309$	10.0066	0.569253
$310$	−20.8395	−1.18360
$311$	−8.99087	−0.509825	−0.254913	−	0.966964i	$-0.582047\pi$
$311$	−8.99087	−0.509825	−0.254913	+	0.966964i	$0.582047\pi$
$312$	4.83433	0.273690
$313$	18.2556	1.03187	0.515934	−	0.856628i	$-0.327445\pi$
$313$	18.2556	1.03187	0.515934	+	0.856628i	$0.327445\pi$
$314$	29.4257	1.66059
$315$	26.9715	1.51967
$316$	−59.9331	−3.37150
$317$	−4.09860	−0.230200	−0.115100	−	0.993354i	$-0.536719\pi$
$317$	−4.09860	−0.230200	−0.115100	+	0.993354i	$0.536719\pi$
$318$	−3.64755	−0.204545
$319$	−4.57737	−0.256283
$320$	23.0208	1.28690
$321$	0.480500	0.0268189
$322$	−12.1116	−0.674952
$323$	−0.148746	−0.00827643
$324$	19.5615	1.08675
$325$	1.42078	0.0788108
$326$	−24.0188	−1.33028
$327$	5.57614	0.308361
$328$	31.7464	1.75290
$329$	43.7206	2.41039
$330$	−14.6524	−0.806586
$331$	−8.00388	−0.439933	−0.219967	−	0.975507i	$-0.570595\pi$
$331$	−8.00388	−0.439933	−0.219967	+	0.975507i	$0.570595\pi$
$332$	−58.5553	−3.21364
$333$	−3.93375	−0.215568
$334$	−3.10543	−0.169922
$335$	24.5404	1.34079
$336$	6.94085	0.378654
$337$	−3.94617	−0.214962	−0.107481	−	0.994207i	$-0.534278\pi$
$337$	−3.94617	−0.214962	−0.107481	+	0.994207i	$0.534278\pi$
$338$	22.6044	1.22952
$339$	−0.482249	−0.0261922
$340$	2.05265	0.111320
$341$	19.4668	1.05419
$342$	3.34632	0.180948
$343$	60.6042	3.27232
$344$	34.3226	1.85055
$345$	−1.34523	−0.0724250
$346$	−5.23746	−0.281568
$347$	−24.9359	−1.33863	−0.669315	−	0.742979i	$-0.733412\pi$
$347$	−24.9359	−1.33863	−0.669315	+	0.742979i	$0.733412\pi$
$348$	2.39237	0.128245
$349$	−8.80474	−0.471307	−0.235653	−	0.971837i	$-0.575723\pi$
$349$	−8.80474	−0.471307	−0.235653	+	0.971837i	$0.575723\pi$
$350$	9.19730	0.491616
$351$	6.81177	0.363585
$352$	−13.4733	−0.718129
$353$	−8.66021	−0.460937	−0.230468	−	0.973080i	$-0.574026\pi$
$353$	−8.66021	−0.460937	−0.230468	+	0.973080i	$0.574026\pi$
$354$	1.77661	0.0944257
$355$	12.7724	0.677887
$356$	34.3549	1.82081
$357$	−0.904990	−0.0478972
$358$	58.6416	3.09930
$359$	22.8271	1.20477	0.602385	−	0.798205i	$-0.294217\pi$
$359$	22.8271	1.20477	0.602385	+	0.798205i	$0.294217\pi$
$360$	−20.9596	−1.10467
$361$	−18.7013	−0.984281
$362$	−3.46327	−0.182026
$363$	6.50139	0.341234
$364$	−34.8755	−1.82797
$365$	21.7663	1.13930
$366$	11.5091	0.601591
$367$	31.3609	1.63702	0.818512	−	0.574489i	$-0.194799\pi$
$367$	31.3609	1.63702	0.818512	+	0.574489i	$0.194799\pi$
$368$	2.08748	0.108817
$369$	20.6535	1.07518
$370$	7.49087	0.389432
$371$	11.9435	0.620075
$372$	−10.1744	−0.527517
$373$	−23.9416	−1.23965	−0.619825	−	0.784740i	$-0.712796\pi$
$373$	−23.9416	−1.23965	−0.619825	+	0.784740i	$0.712796\pi$
$374$	−2.96458	−0.153295
$375$	7.74772	0.400090
$376$	−33.9754	−1.75215
$377$	−1.87097	−0.0963600
$378$	44.0954	2.26802
$379$	10.9308	0.561478	0.280739	−	0.959784i	$-0.409420\pi$
$379$	10.9308	0.561478	0.280739	+	0.959784i	$0.409420\pi$
$380$	−4.12146	−0.211426
$381$	−4.31234	−0.220928
$382$	1.40913	0.0720972
$383$	−15.2443	−0.778946	−0.389473	−	0.921038i	$-0.627343\pi$
$383$	−15.2443	−0.778946	−0.389473	+	0.921038i	$0.627343\pi$
$384$	13.5316	0.690533
$385$	47.9775	2.44516
$386$	−57.9962	−2.95193
$387$	22.3295	1.13507
$388$	−48.4585	−2.46011
$389$	−28.9315	−1.46688	−0.733441	−	0.679753i	$-0.762087\pi$
$389$	−28.9315	−1.46688	−0.733441	+	0.679753i	$0.762087\pi$
$390$	−5.98907	−0.303268
$391$	−0.272178	−0.0137647
$392$	−74.7832	−3.77712
$393$	−2.19069	−0.110506
$394$	43.4794	2.19046
$395$	33.7005	1.69565
$396$	43.1365	2.16769
$397$	19.3878	0.973048	0.486524	−	0.873667i	$-0.338265\pi$
$397$	19.3878	0.973048	0.486524	+	0.873667i	$0.338265\pi$
$398$	−18.4185	−0.923234
$399$	1.81711	0.0909692
$400$	−1.58519	−0.0792596
$401$	5.19885	0.259618	0.129809	−	0.991539i	$-0.458564\pi$
$401$	5.19885	0.259618	0.129809	+	0.991539i	$0.458564\pi$
$402$	18.5244	0.923915
$403$	7.95695	0.396364
$404$	22.0532	1.09719
$405$	−10.9995	−0.546568
$406$	−12.1116	−0.601088
$407$	−6.99744	−0.346850
$408$	0.703270	0.0348171
$409$	−25.6121	−1.26644	−0.633219	−	0.773972i	$-0.718267\pi$
$409$	−25.6121	−1.26644	−0.633219	+	0.773972i	$0.718267\pi$
$410$	−39.3295	−1.94234
$411$	−6.24220	−0.307905
$412$	56.0980	2.76375
$413$	−5.81730	−0.286251
$414$	6.12318	0.300938
$415$	32.9257	1.61626
$416$	−5.50713	−0.270009
$417$	−4.29350	−0.210254
$418$	5.95251	0.291147
$419$	10.3556	0.505907	0.252953	−	0.967478i	$-0.418598\pi$
$419$	10.3556	0.505907	0.252953	+	0.967478i	$0.418598\pi$
$420$	−25.0756	−1.22356
$421$	12.1491	0.592111	0.296055	−	0.955171i	$-0.404329\pi$
$421$	12.1491	0.592111	0.296055	+	0.955171i	$0.404329\pi$
$422$	−32.5000	−1.58208
$423$	−22.1036	−1.07471
$424$	−9.28132	−0.450741
$425$	0.206687	0.0100258
$426$	9.64127	0.467121
$427$	−37.6853	−1.82372
$428$	2.69374	0.130207
$429$	5.59457	0.270108
$430$	−42.5210	−2.05055
$431$	28.2807	1.36223	0.681116	−	0.732175i	$-0.261495\pi$
$431$	28.2807	1.36223	0.681116	+	0.732175i	$0.261495\pi$
$432$	−7.60002	−0.365656
$433$	−4.15742	−0.199793	−0.0998964	−	0.994998i	$-0.531851\pi$
$433$	−4.15742	−0.199793	−0.0998964	+	0.994998i	$0.531851\pi$
$434$	51.5086	2.47249
$435$	−1.34523	−0.0644990
$436$	31.2605	1.49711
$437$	0.546501	0.0261427
$438$	16.4304	0.785074
$439$	18.6089	0.888153	0.444076	−	0.895989i	$-0.353532\pi$
$439$	18.6089	0.888153	0.444076	+	0.895989i	$0.353532\pi$
$440$	−37.2834	−1.77742
$441$	−48.6521	−2.31677
$442$	−1.21176	−0.0576373
$443$	−7.39743	−0.351462	−0.175731	−	0.984438i	$-0.556229\pi$
$443$	−7.39743	−0.351462	−0.175731	+	0.984438i	$0.556229\pi$
$444$	3.65723	0.173565
$445$	−19.3178	−0.915751
$446$	−1.18351	−0.0560409
$447$	10.9919	0.519898
$448$	−56.9000	−2.68827
$449$	23.3610	1.10247	0.551236	−	0.834349i	$-0.314156\pi$
$449$	23.3610	1.10247	0.551236	+	0.834349i	$0.314156\pi$
$450$	−4.64982	−0.219195
$451$	36.7388	1.72996
$452$	−2.70355	−0.127164
$453$	12.7831	0.600603
$454$	−30.0465	−1.41015
$455$	19.6105	0.919356
$456$	−1.41208	−0.0661267
$457$	−6.43183	−0.300868	−0.150434	−	0.988620i	$-0.548067\pi$
$457$	−6.43183	−0.300868	−0.150434	+	0.988620i	$0.548067\pi$
$458$	−12.4306	−0.580842
$459$	0.990937	0.0462530
$460$	−7.54155	−0.351626
$461$	−28.5832	−1.33125	−0.665627	−	0.746285i	$-0.731836\pi$
$461$	−28.5832	−1.33125	−0.665627	+	0.746285i	$0.731836\pi$
$462$	36.2159	1.68492
$463$	31.8120	1.47843	0.739214	−	0.673470i	$-0.235197\pi$
$463$	31.8120	1.47843	0.739214	+	0.673470i	$0.235197\pi$
$464$	2.08748	0.0969088
$465$	5.72106	0.265308
$466$	−33.7133	−1.56174
$467$	34.9300	1.61637	0.808183	−	0.588931i	$-0.200451\pi$
$467$	34.9300	1.61637	0.808183	+	0.588931i	$0.200451\pi$
$468$	17.6318	0.815030
$469$	−60.6561	−2.80084
$470$	42.0908	1.94151
$471$	−8.07823	−0.372225
$472$	4.52064	0.208079
$473$	39.7201	1.82633
$474$	25.4389	1.16845
$475$	−0.415002	−0.0190416
$476$	−5.07349	−0.232543
$477$	−6.03820	−0.276470
$478$	−37.5158	−1.71593
$479$	−4.20878	−0.192304	−0.0961521	−	0.995367i	$-0.530654\pi$
$479$	−4.20878	−0.192304	−0.0961521	+	0.995367i	$0.530654\pi$
$480$	−3.95964	−0.180732
$481$	−2.86017	−0.130412
$482$	−63.6247	−2.89803
$483$	3.32499	0.151292
$484$	36.4476	1.65671
$485$	27.2483	1.23728
$486$	−34.2930	−1.55556
$487$	−11.1540	−0.505437	−0.252719	−	0.967540i	$-0.581325\pi$
$487$	−11.1540	−0.505437	−0.252719	+	0.967540i	$0.581325\pi$
$488$	29.2853	1.32568
$489$	6.59386	0.298185
$490$	92.6461	4.18532
$491$	0.298683	0.0134794	0.00673969	−	0.999977i	$-0.497855\pi$
$491$	0.298683	0.0134794	0.00673969	+	0.999977i	$0.497855\pi$
$492$	−19.2017	−0.865678
$493$	−0.272178	−0.0122583
$494$	2.43306	0.109468
$495$	−24.2557	−1.09021
$496$	−8.87771	−0.398621
$497$	−31.5692	−1.41607
$498$	24.8541	1.11374
$499$	−19.6615	−0.880168	−0.440084	−	0.897957i	$-0.645051\pi$
$499$	−19.6615	−0.880168	−0.440084	+	0.897957i	$0.645051\pi$
$500$	43.4346	1.94246
$501$	0.852534	0.0380884
$502$	15.9331	0.711131
$503$	−0.660795	−0.0294634	−0.0147317	−	0.999891i	$-0.504689\pi$
$503$	−0.660795	−0.0294634	−0.0147317	+	0.999891i	$0.504689\pi$
$504$	51.8055	2.30760
$505$	−12.4005	−0.551816
$506$	10.8920	0.484211
$507$	−6.20558	−0.275599
$508$	−24.1755	−1.07261
$509$	34.5373	1.53084	0.765420	−	0.643531i	$-0.222531\pi$
$509$	34.5373	1.53084	0.765420	+	0.643531i	$0.222531\pi$
$510$	−0.871255	−0.0385798
$511$	−53.7994	−2.37995
$512$	22.6579	1.00135
$513$	−1.98968	−0.0878465
$514$	25.4526	1.12267
$515$	−31.5440	−1.38999
$516$	−20.7599	−0.913902
$517$	−39.3183	−1.72922
$518$	−18.5150	−0.813504
$519$	1.43784	0.0631141
$520$	−15.2394	−0.668292
$521$	2.47755	0.108543	0.0542717	−	0.998526i	$-0.482716\pi$
$521$	2.47755	0.108543	0.0542717	+	0.998526i	$0.482716\pi$
$522$	6.12318	0.268004
$523$	21.1107	0.923108	0.461554	−	0.887112i	$-0.347292\pi$
$523$	21.1107	0.923108	0.461554	+	0.887112i	$0.347292\pi$
$524$	−12.2813	−0.536510
$525$	−2.52493	−0.110197
$526$	40.2597	1.75541
$527$	1.15753	0.0504228
$528$	−6.24196	−0.271647
$529$	1.00000	0.0434783
$530$	11.4983	0.499453
$531$	2.94102	0.127629
$532$	10.1869	0.441660
$533$	15.0168	0.650449
$534$	−14.5821	−0.631029
$535$	−1.51469	−0.0654859
$536$	47.1361	2.03597
$537$	−16.0989	−0.694717
$538$	16.1443	0.696030
$539$	−86.5434	−3.72769
$540$	27.4570	1.18156
$541$	27.0220	1.16177	0.580884	−	0.813986i	$-0.302707\pi$
$541$	27.0220	1.16177	0.580884	+	0.813986i	$0.302707\pi$
$542$	−48.5191	−2.08407
$543$	0.950772	0.0408015
$544$	−0.801146	−0.0343488
$545$	−17.5778	−0.752952
$546$	14.8031	0.633513
$547$	−40.1096	−1.71496	−0.857481	−	0.514516i	$-0.827972\pi$
$547$	−40.1096	−1.71496	−0.857481	+	0.514516i	$0.827972\pi$
$548$	−34.9946	−1.49489
$549$	19.0523	0.813133
$550$	−8.27121	−0.352686
$551$	0.546501	0.0232817
$552$	−2.58386	−0.109976
$553$	−83.2968	−3.54214
$554$	15.9151	0.676166
$555$	−2.05647	−0.0872921
$556$	−24.0699	−1.02079
$557$	12.7652	0.540880	0.270440	−	0.962737i	$-0.412831\pi$
$557$	12.7652	0.540880	0.270440	+	0.962737i	$0.412831\pi$
$558$	−26.0409	−1.10240
$559$	16.2354	0.686684
$560$	−21.8798	−0.924592
$561$	0.813865	0.0343614
$562$	−15.7244	−0.663296
$563$	1.70334	0.0717873	0.0358937	−	0.999356i	$-0.488572\pi$
$563$	1.70334	0.0717873	0.0358937	+	0.999356i	$0.488572\pi$
$564$	20.5498	0.865304
$565$	1.52021	0.0639556
$566$	−40.4870	−1.70179
$567$	27.1872	1.14175
$568$	24.5325	1.02936
$569$	11.6091	0.486678	0.243339	−	0.969941i	$-0.421757\pi$
$569$	11.6091	0.486678	0.243339	+	0.969941i	$0.421757\pi$
$570$	1.74937	0.0732732
$571$	33.4149	1.39837	0.699185	−	0.714941i	$-0.253546\pi$
$571$	33.4149	1.39837	0.699185	+	0.714941i	$0.253546\pi$
$572$	31.3638	1.31139
$573$	−0.386847	−0.0161608
$574$	97.2099	4.05746
$575$	−0.759381	−0.0316684
$576$	28.7666	1.19861
$577$	40.6873	1.69384	0.846918	−	0.531723i	$-0.178455\pi$
$577$	40.6873	1.69384	0.846918	+	0.531723i	$0.178455\pi$
$578$	40.2760	1.67526
$579$	15.9217	0.661683
$580$	−7.54155	−0.313146
$581$	−81.3818	−3.37629
$582$	20.5684	0.852590
$583$	−10.7409	−0.444842
$584$	41.8077	1.73001
$585$	−9.91438	−0.409909
$586$	67.2349	2.77745
$587$	−13.3233	−0.549910	−0.274955	−	0.961457i	$-0.588663\pi$
$587$	−13.3233	−0.549910	−0.274955	+	0.961457i	$0.588663\pi$
$588$	45.2322	1.86534
$589$	−2.32418	−0.0957661
$590$	−5.60045	−0.230567
$591$	−11.9364	−0.490998
$592$	3.19114	0.131155
$593$	4.89062	0.200834	0.100417	−	0.994945i	$-0.467982\pi$
$593$	4.89062	0.200834	0.100417	+	0.994945i	$0.467982\pi$
$594$	−39.6554	−1.62708
$595$	2.85283	0.116954
$596$	61.6218	2.52413
$597$	5.05641	0.206945
$598$	4.45206	0.182058
$599$	40.1284	1.63960	0.819800	−	0.572650i	$-0.194085\pi$
$599$	40.1284	1.63960	0.819800	+	0.572650i	$0.194085\pi$
$600$	1.96213	0.0801037
$601$	−37.1812	−1.51665	−0.758326	−	0.651876i	$-0.773982\pi$
$601$	−37.1812	−1.51665	−0.758326	+	0.651876i	$0.773982\pi$
$602$	105.098	4.28349
$603$	30.6656	1.24880
$604$	71.6637	2.91595
$605$	−20.4945	−0.833220
$606$	−9.36057	−0.380247
$607$	−11.2868	−0.458117	−0.229058	−	0.973413i	$-0.573565\pi$
$607$	−11.2868	−0.458117	−0.229058	+	0.973413i	$0.573565\pi$
$608$	1.60860	0.0652374
$609$	3.32499	0.134735
$610$	−36.2805	−1.46895
$611$	−16.0711	−0.650169
$612$	2.56497	0.103683
$613$	44.5301	1.79855	0.899277	−	0.437380i	$-0.144093\pi$
$613$	44.5301	1.79855	0.899277	+	0.437380i	$0.144093\pi$
$614$	18.8789	0.761891
$615$	10.7971	0.435381
$616$	92.1527	3.71294
$617$	22.2432	0.895477	0.447739	−	0.894164i	$-0.352229\pi$
$617$	22.2432	0.895477	0.447739	+	0.894164i	$0.352229\pi$
$618$	−23.8111	−0.957821
$619$	−19.3967	−0.779621	−0.389811	−	0.920895i	$-0.627460\pi$
$619$	−19.3967	−0.779621	−0.389811	+	0.920895i	$0.627460\pi$
$620$	32.0730	1.28808
$621$	−3.64076	−0.146099
$622$	21.3942	0.857828
$623$	47.7474	1.91296
$624$	−2.55137	−0.102136
$625$	−20.6264	−0.825057
$626$	−43.4401	−1.73621
$627$	−1.63414	−0.0652613
$628$	−45.2875	−1.80717
$629$	−0.416080	−0.0165902
$630$	−64.1798	−2.55699
$631$	−34.9451	−1.39114	−0.695572	−	0.718456i	$-0.744849\pi$
$631$	−34.9451	−1.39114	−0.695572	+	0.718456i	$0.744849\pi$
$632$	64.7302	2.57483
$633$	8.92222	0.354627
$634$	9.75280	0.387333
$635$	13.5939	0.539458
$636$	5.61376	0.222600
$637$	−35.3742	−1.40158
$638$	10.8920	0.431220
$639$	15.9603	0.631379
$640$	−42.6561	−1.68613
$641$	−26.1304	−1.03209	−0.516044	−	0.856562i	$-0.672596\pi$
$641$	−26.1304	−1.03209	−0.516044	+	0.856562i	$0.672596\pi$
$642$	−1.14337	−0.0451252
$643$	33.8053	1.33315	0.666576	−	0.745437i	$-0.267759\pi$
$643$	33.8053	1.33315	0.666576	+	0.745437i	$0.267759\pi$
$644$	18.6403	0.734531
$645$	11.6733	0.459635
$646$	0.353947	0.0139259
$647$	−41.8834	−1.64660	−0.823302	−	0.567603i	$-0.807871\pi$
$647$	−41.8834	−1.64660	−0.823302	+	0.567603i	$0.807871\pi$
$648$	−21.1272	−0.829956
$649$	5.23155	0.205356
$650$	−3.38081	−0.132606
$651$	−14.1406	−0.554216
$652$	36.9660	1.44770
$653$	−17.5154	−0.685432	−0.342716	−	0.939439i	$-0.611347\pi$
$653$	−17.5154	−0.685432	−0.342716	+	0.939439i	$0.611347\pi$
$654$	−13.2687	−0.518847
$655$	6.90578	0.269831
$656$	−16.7545	−0.654154
$657$	27.1990	1.06114
$658$	−104.035	−4.05571
$659$	14.8699	0.579247	0.289624	−	0.957141i	$-0.406470\pi$
$659$	14.8699	0.579247	0.289624	+	0.957141i	$0.406470\pi$
$660$	22.5507	0.877784
$661$	−27.7449	−1.07915	−0.539577	−	0.841936i	$-0.681416\pi$
$661$	−27.7449	−1.07915	−0.539577	+	0.841936i	$0.681416\pi$
$662$	19.0456	0.740228
$663$	0.332663	0.0129196
$664$	63.2421	2.45427
$665$	−5.72812	−0.222127
$666$	9.36053	0.362713
$667$	1.00000	0.0387202
$668$	4.77941	0.184921
$669$	0.324909	0.0125617
$670$	−58.3951	−2.25600
$671$	33.8907	1.30833
$672$	9.78697	0.377541
$673$	16.8217	0.648427	0.324214	−	0.945984i	$-0.394900\pi$
$673$	16.8217	0.648427	0.324214	+	0.945984i	$0.394900\pi$
$674$	9.39010	0.361693
$675$	2.76472	0.106414
$676$	−34.7892	−1.33805
$677$	−28.3544	−1.08975	−0.544874	−	0.838518i	$-0.683422\pi$
$677$	−28.3544	−1.08975	−0.544874	+	0.838518i	$0.683422\pi$
$678$	1.14753	0.0440707
$679$	−67.3491	−2.58462
$680$	−2.21694	−0.0850157
$681$	8.24865	0.316089
$682$	−46.3221	−1.77377
$683$	18.3962	0.703912	0.351956	−	0.936017i	$-0.385517\pi$
$683$	18.3962	0.703912	0.351956	+	0.936017i	$0.385517\pi$
$684$	−5.15015	−0.196921
$685$	19.6775	0.751837
$686$	−144.210	−5.50598
$687$	3.41256	0.130197
$688$	−18.1141	−0.690595
$689$	−4.39028	−0.167256
$690$	3.20104	0.121862
$691$	−48.7956	−1.85627	−0.928136	−	0.372240i	$-0.878590\pi$
$691$	−48.7956	−1.85627	−0.928136	+	0.372240i	$0.878590\pi$
$692$	8.06070	0.306422
$693$	59.9523	2.27740
$694$	59.3361	2.25237
$695$	13.5345	0.513393
$696$	−2.58386	−0.0979409
$697$	2.18456	0.0827460
$698$	20.9513	0.793017
$699$	9.25529	0.350067
$700$	−14.1551	−0.535012
$701$	−11.8246	−0.446610	−0.223305	−	0.974749i	$-0.571685\pi$
$701$	−11.8246	−0.446610	−0.223305	+	0.974749i	$0.571685\pi$
$702$	−16.2089	−0.611766
$703$	0.835438	0.0315091
$704$	51.1706	1.92857
$705$	−11.5552	−0.435193
$706$	20.6074	0.775568
$707$	30.6501	1.15272
$708$	−2.73428	−0.102761
$709$	18.6243	0.699448	0.349724	−	0.936853i	$-0.386275\pi$
$709$	18.6243	0.699448	0.349724	+	0.936853i	$0.386275\pi$
$710$	−30.3924	−1.14061
$711$	42.1118	1.57932
$712$	−37.1047	−1.39056
$713$	−4.25284	−0.159270
$714$	2.15346	0.0805914
$715$	−17.6359	−0.659546
$716$	−90.2522	−3.37288
$717$	10.2992	0.384631
$718$	−54.3182	−2.02714
$719$	−46.0282	−1.71656	−0.858282	−	0.513178i	$-0.828468\pi$
$719$	−46.0282	−1.71656	−0.858282	+	0.513178i	$0.828468\pi$
$720$	11.0617	0.412244
$721$	77.9666	2.90363
$722$	44.5007	1.65614
$723$	17.4669	0.649600
$724$	5.33014	0.198093
$725$	−0.759381	−0.0282027
$726$	−15.4703	−0.574158
$727$	−9.43522	−0.349933	−0.174966	−	0.984574i	$-0.555982\pi$
$727$	−9.43522	−0.349933	−0.174966	+	0.984574i	$0.555982\pi$
$728$	37.6669	1.39603
$729$	−6.60980	−0.244808
$730$	−51.7939	−1.91698
$731$	2.36183	0.0873555
$732$	−17.7131	−0.654694
$733$	−35.1930	−1.29988	−0.649941	−	0.759985i	$-0.725206\pi$
$733$	−35.1930	−1.29988	−0.649941	+	0.759985i	$0.725206\pi$
$734$	−74.6246	−2.75444
$735$	−25.4341	−0.938151
$736$	2.94346	0.108497
$737$	54.5486	2.00932
$738$	−49.1458	−1.80908
$739$	−20.3793	−0.749666	−0.374833	−	0.927092i	$-0.622300\pi$
$739$	−20.3793	−0.749666	−0.374833	+	0.927092i	$0.622300\pi$
$740$	−11.5288	−0.423807
$741$	−0.667946	−0.0245376
$742$	−28.4201	−1.04333
$743$	−44.2871	−1.62474	−0.812368	−	0.583146i	$-0.801822\pi$
$743$	−44.2871	−1.62474	−0.812368	+	0.583146i	$0.801822\pi$
$744$	10.9887	0.402867
$745$	−34.6500	−1.26948
$746$	56.9701	2.08583
$747$	41.1437	1.50537
$748$	4.56263	0.166826
$749$	3.74384	0.136797
$750$	−18.4360	−0.673189
$751$	−31.1048	−1.13503	−0.567514	−	0.823363i	$-0.692095\pi$
$751$	−31.1048	−1.13503	−0.567514	+	0.823363i	$0.692095\pi$
$752$	17.9309	0.653871
$753$	−4.37412	−0.159402
$754$	4.45206	0.162135
$755$	−40.2966	−1.46654
$756$	−67.8649	−2.46822
$757$	−40.6495	−1.47743	−0.738715	−	0.674018i	$-0.764567\pi$
$757$	−40.6495	−1.47743	−0.738715	+	0.674018i	$0.764567\pi$
$758$	−26.0104	−0.944739
$759$	−2.99019	−0.108537
$760$	4.45134	0.161467
$761$	18.6533	0.676180	0.338090	−	0.941114i	$-0.390219\pi$
$761$	18.6533	0.676180	0.338090	+	0.941114i	$0.390219\pi$
$762$	10.2614	0.371731
$763$	43.4468	1.57288
$764$	−2.16871	−0.0784613
$765$	−1.44229	−0.0521460
$766$	36.2744	1.31065
$767$	2.13837	0.0772119
$768$	−17.5935	−0.634853
$769$	17.4326	0.628637	0.314318	−	0.949318i	$-0.398224\pi$
$769$	17.4326	0.628637	0.314318	+	0.949318i	$0.398224\pi$
$770$	−114.165	−4.11420
$771$	−6.98749	−0.251648
$772$	89.2590	3.21250
$773$	46.9728	1.68949	0.844747	−	0.535166i	$-0.179751\pi$
$773$	46.9728	1.68949	0.844747	+	0.535166i	$0.179751\pi$
$774$	−53.1340	−1.90986
$775$	3.22952	0.116008
$776$	52.3371	1.87879
$777$	5.08293	0.182349
$778$	68.8437	2.46817
$779$	−4.38632	−0.157156
$780$	9.21746	0.330038
$781$	28.3905	1.01589
$782$	0.647660	0.0231603
$783$	−3.64076	−0.130110
$784$	39.4676	1.40956
$785$	25.4652	0.908893
$786$	5.21285	0.185936
$787$	−48.1005	−1.71460	−0.857300	−	0.514818i	$-0.827860\pi$
$787$	−48.1005	−1.71460	−0.857300	+	0.514818i	$0.827860\pi$
$788$	−66.9169	−2.38382
$789$	−11.0525	−0.393479
$790$	−80.1917	−2.85309
$791$	−3.75747	−0.133600
$792$	−46.5891	−1.65547
$793$	13.8526	0.491921
$794$	−46.1342	−1.63724
$795$	−3.15662	−0.111954
$796$	28.3469	1.00473
$797$	−6.84219	−0.242363	−0.121181	−	0.992630i	$-0.538668\pi$
$797$	−6.84219	−0.242363	−0.121181	+	0.992630i	$0.538668\pi$
$798$	−4.32389	−0.153064
$799$	−2.33794	−0.0827102
$800$	−2.23521	−0.0790265
$801$	−24.1394	−0.852923
$802$	−12.3709	−0.436832
$803$	48.3823	1.70737
$804$	−28.5100	−1.00547
$805$	−10.4815	−0.369423
$806$	−18.9339	−0.666919
$807$	−4.43209	−0.156017
$808$	−23.8183	−0.837924
$809$	2.15661	0.0758223	0.0379112	−	0.999281i	$-0.487930\pi$
$809$	2.15661	0.0758223	0.0379112	+	0.999281i	$0.487930\pi$
$810$	26.1737	0.919651
$811$	30.0010	1.05348	0.526739	−	0.850027i	$-0.323414\pi$
$811$	30.0010	1.05348	0.526739	+	0.850027i	$0.323414\pi$
$812$	18.6403	0.654146
$813$	13.3199	0.467151
$814$	16.6507	0.583608
$815$	−20.7860	−0.728102
$816$	−0.371158	−0.0129931
$817$	−4.74226	−0.165911
$818$	60.9452	2.13090
$819$	24.5052	0.856280
$820$	60.5299	2.11380
$821$	−35.2369	−1.22977	−0.614887	−	0.788615i	$-0.710799\pi$
$821$	−35.2369	−1.22977	−0.614887	+	0.788615i	$0.710799\pi$
$822$	14.8536	0.518079
$823$	−36.9231	−1.28706	−0.643530	−	0.765421i	$-0.722531\pi$
$823$	−36.9231	−1.28706	−0.643530	+	0.765421i	$0.722531\pi$
$824$	−60.5881	−2.11069
$825$	2.27069	0.0790554
$826$	13.8425	0.481643
$827$	45.8002	1.59263	0.796314	−	0.604884i	$-0.206780\pi$
$827$	45.8002	1.59263	0.796314	+	0.604884i	$0.206780\pi$
$828$	−9.42386	−0.327502
$829$	13.3071	0.462176	0.231088	−	0.972933i	$-0.425771\pi$
$829$	13.3071	0.462176	0.231088	+	0.972933i	$0.425771\pi$
$830$	−78.3482	−2.71951
$831$	−4.36916	−0.151564
$832$	20.9157	0.725122
$833$	−5.14603	−0.178299
$834$	10.2166	0.353771
$835$	−2.68747	−0.0930036
$836$	−9.16120	−0.316847
$837$	15.4836	0.535191
$838$	−24.6417	−0.851234
$839$	5.43546	0.187653	0.0938264	−	0.995589i	$-0.470090\pi$
$839$	5.43546	0.187653	0.0938264	+	0.995589i	$0.470090\pi$
$840$	27.0826	0.934439
$841$	1.00000	0.0344828
$842$	−28.9093	−0.996281
$843$	4.31683	0.148679
$844$	50.0191	1.72173
$845$	19.5620	0.672954
$846$	52.5964	1.80830
$847$	50.6559	1.74056
$848$	4.89831	0.168209
$849$	11.1149	0.381462
$850$	−0.491821	−0.0168693
$851$	1.52870	0.0524033
$852$	−14.8384	−0.508354
$853$	4.95255	0.169572	0.0847861	−	0.996399i	$-0.472979\pi$
$853$	4.95255	0.169572	0.0847861	+	0.996399i	$0.472979\pi$
$854$	89.6738	3.06857
$855$	2.89593	0.0990388
$856$	−2.90935	−0.0994394
$857$	13.5239	0.461967	0.230983	−	0.972958i	$-0.425806\pi$
$857$	13.5239	0.461967	0.230983	+	0.972958i	$0.425806\pi$
$858$	−13.3125	−0.454482
$859$	−34.5149	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$859$	−34.5149	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$860$	65.4419	2.23155
$861$	−26.6870	−0.909491
$862$	−67.2951	−2.29208
$863$	2.25993	0.0769289	0.0384645	−	0.999260i	$-0.487753\pi$
$863$	2.25993	0.0769289	0.0384645	+	0.999260i	$0.487753\pi$
$864$	−10.7164	−0.364581
$865$	−4.53254	−0.154111
$866$	9.89276	0.336170
$867$	−11.0570	−0.375514
$868$	−79.2742	−2.69074
$869$	74.9095	2.54113
$870$	3.20104	0.108526
$871$	22.2964	0.755486
$872$	−33.7626	−1.14335
$873$	34.0493	1.15239
$874$	−1.30042	−0.0439874
$875$	60.3667	2.04077
$876$	−25.2871	−0.854373
$877$	−37.1470	−1.25436	−0.627182	−	0.778873i	$-0.715792\pi$
$877$	−37.1470	−1.25436	−0.627182	+	0.778873i	$0.715792\pi$
$878$	−44.2806	−1.49440
$879$	−18.4580	−0.622572
$880$	19.6767	0.663302
$881$	3.76794	0.126945	0.0634726	−	0.997984i	$-0.479782\pi$
$881$	3.76794	0.126945	0.0634726	+	0.997984i	$0.479782\pi$
$882$	115.770	3.89817
$883$	31.1564	1.04850	0.524248	−	0.851566i	$-0.324347\pi$
$883$	31.1564	1.04850	0.524248	+	0.851566i	$0.324347\pi$
$884$	1.86495	0.0627250
$885$	1.53749	0.0516822
$886$	17.6025	0.591368
$887$	−49.0264	−1.64614	−0.823072	−	0.567937i	$-0.807742\pi$
$887$	−49.0264	−1.64614	−0.823072	+	0.567937i	$0.807742\pi$
$888$	−3.94996	−0.132552
$889$	−33.5998	−1.12690
$890$	45.9676	1.54084
$891$	−24.4496	−0.819094
$892$	1.82148	0.0609877
$893$	4.69429	0.157088
$894$	−26.1557	−0.874776
$895$	50.7489	1.69635
$896$	105.432	3.52225
$897$	−1.22222	−0.0408089
$898$	−55.5885	−1.85501
$899$	−4.25284	−0.141840
$900$	7.15630	0.238543
$901$	−0.638672	−0.0212773
$902$	−87.4217	−2.91082
$903$	−28.8526	−0.960156
$904$	2.91994	0.0971157
$905$	−2.99714	−0.0996284
$906$	−30.4180	−1.01057
$907$	9.47164	0.314501	0.157250	−	0.987559i	$-0.449737\pi$
$907$	9.47164	0.314501	0.157250	+	0.987559i	$0.449737\pi$
$908$	46.2429	1.53463
$909$	−15.4956	−0.513956
$910$	−46.6641	−1.54690
$911$	19.2798	0.638769	0.319385	−	0.947625i	$-0.396524\pi$
$911$	19.2798	0.638769	0.319385	+	0.947625i	$0.396524\pi$
$912$	0.745240	0.0246774
$913$	73.1874	2.42215
$914$	15.3048	0.506239
$915$	9.96007	0.329270
$916$	19.1312	0.632114
$917$	−17.0689	−0.563664
$918$	−2.35798	−0.0778249
$919$	−17.8590	−0.589115	−0.294558	−	0.955634i	$-0.595172\pi$
$919$	−17.8590	−0.589115	−0.294558	+	0.955634i	$0.595172\pi$
$920$	8.14517	0.268538
$921$	−5.18282	−0.170780
$922$	68.0150	2.23996
$923$	11.6045	0.381965
$924$	−55.7381	−1.83365
$925$	−1.16087	−0.0381691
$926$	−75.6980	−2.48759
$927$	−39.4171	−1.29463
$928$	2.94346	0.0966238
$929$	−39.6211	−1.29993	−0.649963	−	0.759966i	$-0.725216\pi$
$929$	−39.6211	−1.29993	−0.649963	+	0.759966i	$0.725216\pi$
$930$	−13.6135	−0.446405
$931$	10.3326	0.338637
$932$	51.8863	1.69959
$933$	−5.87334	−0.192284
$934$	−83.1174	−2.71968
$935$	−2.56557	−0.0839031
$936$	−19.0430	−0.622441
$937$	−37.4465	−1.22332	−0.611662	−	0.791119i	$-0.709499\pi$
$937$	−37.4465	−1.22332	−0.611662	+	0.791119i	$0.709499\pi$
$938$	144.334	4.71267
$939$	11.9256	0.389177
$940$	−64.7798	−2.11288
$941$	−15.4626	−0.504068	−0.252034	−	0.967718i	$-0.581099\pi$
$941$	−15.4626	−0.504068	−0.252034	+	0.967718i	$0.581099\pi$
$942$	19.2225	0.626303
$943$	−8.02619	−0.261369
$944$	−2.38582	−0.0776517
$945$	38.1605	1.24136
$946$	−94.5159	−3.07298
$947$	−32.7987	−1.06581	−0.532907	−	0.846174i	$-0.678900\pi$
$947$	−32.7987	−1.06581	−0.532907	+	0.846174i	$0.678900\pi$
$948$	−39.1517	−1.27159
$949$	19.7760	0.641955
$950$	0.987516	0.0320392
$951$	−2.67743	−0.0868217
$952$	5.47957	0.177594
$953$	−16.0845	−0.521027	−0.260513	−	0.965470i	$-0.583892\pi$
$953$	−16.0845	−0.521027	−0.260513	+	0.965470i	$0.583892\pi$
$954$	14.3682	0.465187
$955$	1.21947	0.0394611
$956$	57.7386	1.86740
$957$	−2.99019	−0.0966591
$958$	10.0150	0.323570
$959$	−48.6364	−1.57055
$960$	15.0384	0.485364
$961$	−12.9134	−0.416560
$962$	6.80589	0.219431
$963$	−1.89275	−0.0609930
$964$	97.9215	3.15384
$965$	−50.1904	−1.61569
$966$	−7.91196	−0.254563
$967$	24.9701	0.802986	0.401493	−	0.915862i	$-0.368491\pi$
$967$	24.9701	0.802986	0.401493	+	0.915862i	$0.368491\pi$
$968$	−39.3648	−1.26523
$969$	−0.0971689	−0.00312152
$970$	−64.8385	−2.08184
$971$	1.43669	0.0461056	0.0230528	−	0.999734i	$-0.492661\pi$
$971$	1.43669	0.0461056	0.0230528	+	0.999734i	$0.492661\pi$
$972$	52.7786	1.69288
$973$	−33.4530	−1.07245
$974$	26.5415	0.850445
$975$	0.928133	0.0297241
$976$	−15.4556	−0.494723
$977$	45.3505	1.45089	0.725446	−	0.688279i	$-0.241634\pi$
$977$	45.3505	1.45089	0.725446	+	0.688279i	$0.241634\pi$
$978$	−15.6904	−0.501723
$979$	−42.9397	−1.37236
$980$	−142.587	−4.55476
$981$	−21.9651	−0.701293
$982$	−0.710729	−0.0226803
$983$	−60.0472	−1.91521	−0.957604	−	0.288086i	$-0.906981\pi$
$983$	−60.0472	−1.91521	−0.957604	+	0.288086i	$0.906981\pi$
$984$	20.7385	0.661121
$985$	37.6274	1.19891
$986$	0.647660	0.0206257
$987$	28.5607	0.909098
$988$	−3.74459	−0.119131
$989$	−8.67751	−0.275929
$990$	57.7175	1.83438
$991$	11.5981	0.368425	0.184212	−	0.982886i	$-0.441027\pi$
$991$	11.5981	0.368425	0.184212	+	0.982886i	$0.441027\pi$
$992$	−12.5181	−0.397449
$993$	−5.22858	−0.165924
$994$	75.1204	2.38268
$995$	−15.9395	−0.505315
$996$	−38.2516	−1.21205
$997$	22.6532	0.717433	0.358717	−	0.933446i	$-0.383214\pi$
$997$	22.6532	0.717433	0.358717	+	0.933446i	$0.383214\pi$
$998$	46.7853	1.48096
$999$	−5.56565	−0.176089

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.37954 q^{2} +0.653256 q^{3} +3.66223 q^{4} -2.05928 q^{5} -1.55445 q^{6} +5.08987 q^{7} -3.95536 q^{8} -2.57326 q^{9} +O(q^{10})\)	\(q-2.37954 q^{2} +0.653256 q^{3} +3.66223 q^{4} -2.05928 q^{5} -1.55445 q^{6} +5.08987 q^{7} -3.95536 q^{8} -2.57326 q^{9} +4.90014 q^{10} -4.57737 q^{11} +2.39237 q^{12} -1.87097 q^{13} -12.1116 q^{14} -1.34523 q^{15} +2.08748 q^{16} -0.272178 q^{17} +6.12318 q^{18} +0.546501 q^{19} -7.54155 q^{20} +3.32499 q^{21} +10.8920 q^{22} +1.00000 q^{23} -2.58386 q^{24} -0.759381 q^{25} +4.45206 q^{26} -3.64076 q^{27} +18.6403 q^{28} +1.00000 q^{29} +3.20104 q^{30} -4.25284 q^{31} +2.94346 q^{32} -2.99019 q^{33} +0.647660 q^{34} -10.4815 q^{35} -9.42386 q^{36} +1.52870 q^{37} -1.30042 q^{38} -1.22222 q^{39} +8.14517 q^{40} -8.02619 q^{41} -7.91196 q^{42} -8.67751 q^{43} -16.7634 q^{44} +5.29905 q^{45} -2.37954 q^{46} +8.58972 q^{47} +1.36366 q^{48} +18.9068 q^{49} +1.80698 q^{50} -0.177802 q^{51} -6.85194 q^{52} +2.34652 q^{53} +8.66336 q^{54} +9.42606 q^{55} -20.1323 q^{56} +0.357005 q^{57} -2.37954 q^{58} -1.14292 q^{59} -4.92656 q^{60} -7.40397 q^{61} +10.1198 q^{62} -13.0976 q^{63} -11.1791 q^{64} +3.85285 q^{65} +7.11529 q^{66} -11.9170 q^{67} -0.996780 q^{68} +0.653256 q^{69} +24.9411 q^{70} -6.20236 q^{71} +10.1781 q^{72} -10.5699 q^{73} -3.63762 q^{74} -0.496070 q^{75} +2.00141 q^{76} -23.2982 q^{77} +2.90834 q^{78} -16.3652 q^{79} -4.29870 q^{80} +5.34142 q^{81} +19.0987 q^{82} -15.9890 q^{83} +12.1769 q^{84} +0.560490 q^{85} +20.6485 q^{86} +0.653256 q^{87} +18.1051 q^{88} +9.38087 q^{89} -12.6093 q^{90} -9.52302 q^{91} +3.66223 q^{92} -2.77819 q^{93} -20.4396 q^{94} -1.12540 q^{95} +1.92283 q^{96} -13.2320 q^{97} -44.9896 q^{98} +11.7787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 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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