LMFDB - Embedded newform 1003.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 $ x^16 - 6x^15 - 5x^14 + 90x^13 - 82x^12 - 456x^11 + 723x^10 + 951x^9 - 2105x^8 - 695x^7 + 2641x^6 - 151x^5 - 1323x^4 + 301x^3 + 179x^2 - 50*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.98811$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98811 q^{2} +1.88888 q^{3} +1.95260 q^{4} +1.43913 q^{5} -3.75530 q^{6} -4.79587 q^{7} +0.0942457 q^{8} +0.567851 q^{9} +O(q^{10})$	\(q-1.98811 q^{2} +1.88888 q^{3} +1.95260 q^{4} +1.43913 q^{5} -3.75530 q^{6} -4.79587 q^{7} +0.0942457 q^{8} +0.567851 q^{9} -2.86115 q^{10} +0.616539 q^{11} +3.68821 q^{12} -2.69731 q^{13} +9.53473 q^{14} +2.71833 q^{15} -4.09256 q^{16} +1.00000 q^{17} -1.12895 q^{18} +4.27135 q^{19} +2.81003 q^{20} -9.05880 q^{21} -1.22575 q^{22} -0.964048 q^{23} +0.178018 q^{24} -2.92892 q^{25} +5.36256 q^{26} -4.59403 q^{27} -9.36439 q^{28} -3.34631 q^{29} -5.40435 q^{30} -3.96607 q^{31} +7.94799 q^{32} +1.16457 q^{33} -1.98811 q^{34} -6.90186 q^{35} +1.10878 q^{36} -10.0049 q^{37} -8.49193 q^{38} -5.09488 q^{39} +0.135631 q^{40} +1.91860 q^{41} +18.0099 q^{42} +2.22681 q^{43} +1.20385 q^{44} +0.817209 q^{45} +1.91664 q^{46} -8.17657 q^{47} -7.73034 q^{48} +16.0004 q^{49} +5.82302 q^{50} +1.88888 q^{51} -5.26675 q^{52} -6.81923 q^{53} +9.13345 q^{54} +0.887277 q^{55} -0.451990 q^{56} +8.06805 q^{57} +6.65285 q^{58} +1.00000 q^{59} +5.30780 q^{60} -5.18894 q^{61} +7.88500 q^{62} -2.72334 q^{63} -7.61638 q^{64} -3.88177 q^{65} -2.31529 q^{66} +0.536878 q^{67} +1.95260 q^{68} -1.82097 q^{69} +13.7217 q^{70} -10.1444 q^{71} +0.0535175 q^{72} +16.9154 q^{73} +19.8909 q^{74} -5.53236 q^{75} +8.34022 q^{76} -2.95684 q^{77} +10.1292 q^{78} +3.14207 q^{79} -5.88971 q^{80} -10.3811 q^{81} -3.81439 q^{82} -3.85508 q^{83} -17.6882 q^{84} +1.43913 q^{85} -4.42715 q^{86} -6.32077 q^{87} +0.0581061 q^{88} +18.6091 q^{89} -1.62470 q^{90} +12.9359 q^{91} -1.88240 q^{92} -7.49142 q^{93} +16.2559 q^{94} +6.14701 q^{95} +15.0128 q^{96} -11.1707 q^{97} -31.8106 q^{98} +0.350102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * 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 $

$2$	−1.98811	−1.40581	−0.702904	−	0.711284i	$-0.748114\pi$
$2$	−1.98811	−1.40581	−0.702904	+	0.711284i	$0.748114\pi$
$3$	1.88888	1.09054	0.545271	−	0.838260i	$-0.316427\pi$
$3$	1.88888	1.09054	0.545271	+	0.838260i	$0.316427\pi$
$4$	1.95260	0.976298
$5$	1.43913	0.643597	0.321798	−	0.946808i	$-0.395713\pi$
$5$	1.43913	0.643597	0.321798	+	0.946808i	$0.395713\pi$
$6$	−3.75530	−1.53309
$7$	−4.79587	−1.81267	−0.906334	−	0.422561i	$-0.861131\pi$
$7$	−4.79587	−1.81267	−0.906334	+	0.422561i	$0.861131\pi$
$8$	0.0942457	0.0333209
$9$	0.567851	0.189284
$10$	−2.86115	−0.904774
$11$	0.616539	0.185893	0.0929467	−	0.995671i	$-0.470371\pi$
$11$	0.616539	0.185893	0.0929467	+	0.995671i	$0.470371\pi$
$12$	3.68821	1.06469
$13$	−2.69731	−0.748099	−0.374050	−	0.927409i	$-0.622031\pi$
$13$	−2.69731	−0.748099	−0.374050	+	0.927409i	$0.622031\pi$
$14$	9.53473	2.54826
$15$	2.71833	0.701870
$16$	−4.09256	−1.02314
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.12895	−0.266097
$19$	4.27135	0.979915	0.489958	−	0.871746i	$-0.337012\pi$
$19$	4.27135	0.979915	0.489958	+	0.871746i	$0.337012\pi$
$20$	2.81003	0.628342
$21$	−9.05880	−1.97679
$22$	−1.22575	−0.261331
$23$	−0.964048	−0.201018	−0.100509	−	0.994936i	$-0.532047\pi$
$23$	−0.964048	−0.201018	−0.100509	+	0.994936i	$0.532047\pi$
$24$	0.178018	0.0363378
$25$	−2.92892	−0.585783
$26$	5.36256	1.05168
$27$	−4.59403	−0.884121
$28$	−9.36439	−1.76970
$29$	−3.34631	−0.621395	−0.310697	−	0.950509i	$-0.600563\pi$
$29$	−3.34631	−0.621395	−0.310697	+	0.950509i	$0.600563\pi$
$30$	−5.40435	−0.986695
$31$	−3.96607	−0.712328	−0.356164	−	0.934424i	$-0.615915\pi$
$31$	−3.96607	−0.712328	−0.356164	+	0.934424i	$0.615915\pi$
$32$	7.94799	1.40502
$33$	1.16457	0.202725
$34$	−1.98811	−0.340959
$35$	−6.90186	−1.16663
$36$	1.10878	0.184797
$37$	−10.0049	−1.64480	−0.822401	−	0.568909i	$-0.807366\pi$
$37$	−10.0049	−1.64480	−0.822401	+	0.568909i	$0.807366\pi$
$38$	−8.49193	−1.37757
$39$	−5.09488	−0.815834
$40$	0.135631	0.0214452
$41$	1.91860	0.299635	0.149817	−	0.988714i	$-0.452131\pi$
$41$	1.91860	0.299635	0.149817	+	0.988714i	$0.452131\pi$
$42$	18.0099	2.77899
$43$	2.22681	0.339585	0.169793	−	0.985480i	$-0.445690\pi$
$43$	2.22681	0.339585	0.169793	+	0.985480i	$0.445690\pi$
$44$	1.20385	0.181487
$45$	0.817209	0.121822
$46$	1.91664	0.282593
$47$	−8.17657	−1.19267	−0.596337	−	0.802734i	$-0.703378\pi$
$47$	−8.17657	−1.19267	−0.596337	+	0.802734i	$0.703378\pi$
$48$	−7.73034	−1.11578
$49$	16.0004	2.28577
$50$	5.82302	0.823499
$51$	1.88888	0.264495
$52$	−5.26675	−0.730367
$53$	−6.81923	−0.936694	−0.468347	−	0.883545i	$-0.655150\pi$
$53$	−6.81923	−0.936694	−0.468347	+	0.883545i	$0.655150\pi$
$54$	9.13345	1.24290
$55$	0.887277	0.119640
$56$	−0.451990	−0.0603997
$57$	8.06805	1.06864
$58$	6.65285	0.873562
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	5.30780	0.685234
$61$	−5.18894	−0.664376	−0.332188	−	0.943213i	$-0.607787\pi$
$61$	−5.18894	−0.664376	−0.332188	+	0.943213i	$0.607787\pi$
$62$	7.88500	1.00140
$63$	−2.72334	−0.343109
$64$	−7.61638	−0.952047
$65$	−3.88177	−0.481474
$66$	−2.31529	−0.284992
$67$	0.536878	0.0655900	0.0327950	−	0.999462i	$-0.489559\pi$
$67$	0.536878	0.0655900	0.0327950	+	0.999462i	$0.489559\pi$
$68$	1.95260	0.236787
$69$	−1.82097	−0.219219
$70$	13.7217	1.64005
$71$	−10.1444	−1.20392	−0.601960	−	0.798526i	$-0.705614\pi$
$71$	−10.1444	−1.20392	−0.601960	+	0.798526i	$0.705614\pi$
$72$	0.0535175	0.00630710
$73$	16.9154	1.97980	0.989900	−	0.141764i	$-0.0452774\pi$
$73$	16.9154	1.97980	0.989900	+	0.141764i	$0.0452774\pi$
$74$	19.8909	2.31228
$75$	−5.53236	−0.638822
$76$	8.34022	0.956689
$77$	−2.95684	−0.336963
$78$	10.1292	1.14691
$79$	3.14207	0.353510	0.176755	−	0.984255i	$-0.443440\pi$
$79$	3.14207	0.353510	0.176755	+	0.984255i	$0.443440\pi$
$80$	−5.88971	−0.658490
$81$	−10.3811	−1.15346
$82$	−3.81439	−0.421229
$83$	−3.85508	−0.423150	−0.211575	−	0.977362i	$-0.567859\pi$
$83$	−3.85508	−0.423150	−0.211575	+	0.977362i	$0.567859\pi$
$84$	−17.6882	−1.92994
$85$	1.43913	0.156095
$86$	−4.42715	−0.477392
$87$	−6.32077	−0.677658
$88$	0.0581061	0.00619413
$89$	18.6091	1.97256	0.986280	−	0.165083i	$-0.0527892\pi$
$89$	18.6091	1.97256	0.986280	+	0.165083i	$0.0527892\pi$
$90$	−1.62470	−0.171259
$91$	12.9359	1.35606
$92$	−1.88240	−0.196253
$93$	−7.49142	−0.776824
$94$	16.2559	1.67667
$95$	6.14701	0.630670
$96$	15.0128	1.53223
$97$	−11.1707	−1.13421	−0.567107	−	0.823644i	$-0.691937\pi$
$97$	−11.1707	−1.13421	−0.567107	+	0.823644i	$0.691937\pi$
$98$	−31.8106	−3.21335
$99$	0.350102	0.0351866
$100$	−5.71899	−0.571899
$101$	−14.5272	−1.44551	−0.722756	−	0.691104i	$-0.757125\pi$
$101$	−14.5272	−1.44551	−0.722756	+	0.691104i	$0.757125\pi$
$102$	−3.75530	−0.371830
$103$	−0.413878	−0.0407806	−0.0203903	−	0.999792i	$-0.506491\pi$
$103$	−0.413878	−0.0407806	−0.0203903	+	0.999792i	$0.506491\pi$
$104$	−0.254210	−0.0249273
$105$	−13.0368	−1.27226
$106$	13.5574	1.31681
$107$	−7.84446	−0.758352	−0.379176	−	0.925325i	$-0.623793\pi$
$107$	−7.84446	−0.758352	−0.379176	+	0.925325i	$0.623793\pi$
$108$	−8.97028	−0.863165
$109$	−6.76738	−0.648198	−0.324099	−	0.946023i	$-0.605061\pi$
$109$	−6.76738	−0.648198	−0.324099	+	0.946023i	$0.605061\pi$
$110$	−1.76401	−0.168192
$111$	−18.8981	−1.79373
$112$	19.6274	1.85461
$113$	−4.86011	−0.457201	−0.228601	−	0.973520i	$-0.573415\pi$
$113$	−4.86011	−0.457201	−0.228601	+	0.973520i	$0.573415\pi$
$114$	−16.0402	−1.50230
$115$	−1.38739	−0.129374
$116$	−6.53400	−0.606666
$117$	−1.53167	−0.141603
$118$	−1.98811	−0.183021
$119$	−4.79587	−0.439637
$120$	0.256191	0.0233869
$121$	−10.6199	−0.965444
$122$	10.3162	0.933986
$123$	3.62399	0.326764
$124$	−7.74413	−0.695444
$125$	−11.4107	−1.02060
$126$	5.41431	0.482345
$127$	14.8498	1.31771	0.658853	−	0.752272i	$-0.271042\pi$
$127$	14.8498	1.31771	0.658853	+	0.752272i	$0.271042\pi$
$128$	−0.753753	−0.0666230
$129$	4.20616	0.370332
$130$	7.71740	0.676860
$131$	12.0686	1.05444	0.527220	−	0.849729i	$-0.323235\pi$
$131$	12.0686	1.05444	0.527220	+	0.849729i	$0.323235\pi$
$132$	2.27392	0.197920
$133$	−20.4848	−1.77626
$134$	−1.06737	−0.0922070
$135$	−6.61138	−0.569017
$136$	0.0942457	0.00808150
$137$	−18.4549	−1.57670	−0.788352	−	0.615224i	$-0.789066\pi$
$137$	−18.4549	−1.57670	−0.788352	+	0.615224i	$0.789066\pi$
$138$	3.62029	0.308179
$139$	−7.98386	−0.677182	−0.338591	−	0.940934i	$-0.609950\pi$
$139$	−7.98386	−0.677182	−0.338591	+	0.940934i	$0.609950\pi$
$140$	−13.4765	−1.13898
$141$	−15.4445	−1.30066
$142$	20.1683	1.69248
$143$	−1.66300	−0.139067
$144$	−2.32397	−0.193664
$145$	−4.81577	−0.399928
$146$	−33.6298	−2.78322
$147$	30.2227	2.49273
$148$	−19.5356	−1.60582
$149$	−3.21403	−0.263304	−0.131652	−	0.991296i	$-0.542028\pi$
$149$	−3.21403	−0.263304	−0.131652	+	0.991296i	$0.542028\pi$
$150$	10.9990	0.898061
$151$	18.7373	1.52482	0.762409	−	0.647096i	$-0.224017\pi$
$151$	18.7373	1.52482	0.762409	+	0.647096i	$0.224017\pi$
$152$	0.402556	0.0326516
$153$	0.567851	0.0459080
$154$	5.87853	0.473706
$155$	−5.70768	−0.458452
$156$	−9.94824	−0.796497
$157$	15.0824	1.20370	0.601852	−	0.798607i	$-0.294430\pi$
$157$	15.0824	1.20370	0.601852	+	0.798607i	$0.294430\pi$
$158$	−6.24679	−0.496968
$159$	−12.8807	−1.02150
$160$	11.4382	0.904265
$161$	4.62345	0.364379
$162$	20.6388	1.62154
$163$	−16.4789	−1.29073	−0.645365	−	0.763874i	$-0.723295\pi$
$163$	−16.4789	−1.29073	−0.645365	+	0.763874i	$0.723295\pi$
$164$	3.74625	0.292533
$165$	1.67596	0.130473
$166$	7.66433	0.594867
$167$	1.08579	0.0840207	0.0420103	−	0.999117i	$-0.486624\pi$
$167$	1.08579	0.0840207	0.0420103	+	0.999117i	$0.486624\pi$
$168$	−0.853753	−0.0658685
$169$	−5.72452	−0.440348
$170$	−2.86115	−0.219440
$171$	2.42549	0.185482
$172$	4.34806	0.331536
$173$	10.1936	0.775006	0.387503	−	0.921868i	$-0.373338\pi$
$173$	10.1936	0.775006	0.387503	+	0.921868i	$0.373338\pi$
$174$	12.5664	0.952657
$175$	14.0467	1.06183
$176$	−2.52322	−0.190195
$177$	1.88888	0.141977
$178$	−36.9970	−2.77304
$179$	12.3009	0.919413	0.459706	−	0.888071i	$-0.347955\pi$
$179$	12.3009	0.919413	0.459706	+	0.888071i	$0.347955\pi$
$180$	1.59568	0.118935
$181$	24.4594	1.81805	0.909025	−	0.416741i	$-0.136828\pi$
$181$	24.4594	1.81805	0.909025	+	0.416741i	$0.136828\pi$
$182$	−25.7181	−1.90635
$183$	−9.80127	−0.724531
$184$	−0.0908573	−0.00669809
$185$	−14.3984	−1.05859
$186$	14.8938	1.09207
$187$	0.616539	0.0450858
$188$	−15.9655	−1.16441
$189$	22.0324	1.60262
$190$	−12.2210	−0.886602
$191$	23.3243	1.68769	0.843844	−	0.536589i	$-0.180288\pi$
$191$	23.3243	1.68769	0.843844	+	0.536589i	$0.180288\pi$
$192$	−14.3864	−1.03825
$193$	−20.6343	−1.48529	−0.742646	−	0.669684i	$-0.766430\pi$
$193$	−20.6343	−1.48529	−0.742646	+	0.669684i	$0.766430\pi$
$194$	22.2086	1.59449
$195$	−7.33218	−0.525068
$196$	31.2422	2.23159
$197$	−6.70508	−0.477717	−0.238858	−	0.971054i	$-0.576773\pi$
$197$	−6.70508	−0.477717	−0.238858	+	0.971054i	$0.576773\pi$
$198$	−0.696043	−0.0494656
$199$	0.724937	0.0513894	0.0256947	−	0.999670i	$-0.491820\pi$
$199$	0.724937	0.0513894	0.0256947	+	0.999670i	$0.491820\pi$
$200$	−0.276038	−0.0195188
$201$	1.01410	0.0715287
$202$	28.8817	2.03211
$203$	16.0485	1.12638
$204$	3.68821	0.258226
$205$	2.76110	0.192844
$206$	0.822837	0.0573297
$207$	−0.547436	−0.0380494
$208$	11.0389	0.765411
$209$	2.63345	0.182160
$210$	25.9186	1.78855
$211$	1.08289	0.0745490	0.0372745	−	0.999305i	$-0.488132\pi$
$211$	1.08289	0.0745490	0.0372745	+	0.999305i	$0.488132\pi$
$212$	−13.3152	−0.914492
$213$	−19.1615	−1.31293
$214$	15.5957	1.06610
$215$	3.20466	0.218556
$216$	−0.432967	−0.0294597
$217$	19.0208	1.29121
$218$	13.4543	0.911242
$219$	31.9511	2.15906
$220$	1.73249	0.116805
$221$	−2.69731	−0.181441
$222$	37.5715	2.52164
$223$	9.32015	0.624123	0.312062	−	0.950062i	$-0.398980\pi$
$223$	9.32015	0.624123	0.312062	+	0.950062i	$0.398980\pi$
$224$	−38.1175	−2.54683
$225$	−1.66319	−0.110879
$226$	9.66246	0.642737
$227$	−10.0724	−0.668526	−0.334263	−	0.942480i	$-0.608487\pi$
$227$	−10.0724	−0.668526	−0.334263	+	0.942480i	$0.608487\pi$
$228$	15.7536	1.04331
$229$	−12.6542	−0.836214	−0.418107	−	0.908398i	$-0.637306\pi$
$229$	−12.6542	−0.836214	−0.418107	+	0.908398i	$0.637306\pi$
$230$	2.75828	0.181876
$231$	−5.58510	−0.367473
$232$	−0.315376	−0.0207054
$233$	−2.64425	−0.173230	−0.0866151	−	0.996242i	$-0.527605\pi$
$233$	−2.64425	−0.173230	−0.0866151	+	0.996242i	$0.527605\pi$
$234$	3.04513	0.199067
$235$	−11.7671	−0.767602
$236$	1.95260	0.127103
$237$	5.93498	0.385518
$238$	9.53473	0.618045
$239$	−10.9108	−0.705762	−0.352881	−	0.935668i	$-0.614798\pi$
$239$	−10.9108	−0.705762	−0.352881	+	0.935668i	$0.614798\pi$
$240$	−11.1249	−0.718111
$241$	4.02169	0.259060	0.129530	−	0.991576i	$-0.458653\pi$
$241$	4.02169	0.259060	0.129530	+	0.991576i	$0.458653\pi$
$242$	21.1135	1.35723
$243$	−5.82652	−0.373772
$244$	−10.1319	−0.648629
$245$	23.0265	1.47111
$246$	−7.20491	−0.459368
$247$	−11.5212	−0.733074
$248$	−0.373785	−0.0237354
$249$	−7.28176	−0.461463
$250$	22.6858	1.43478
$251$	−16.2079	−1.02303	−0.511516	−	0.859274i	$-0.670916\pi$
$251$	−16.2079	−1.02303	−0.511516	+	0.859274i	$0.670916\pi$
$252$	−5.31758	−0.334976
$253$	−0.594373	−0.0373679
$254$	−29.5231	−1.85244
$255$	2.71833	0.170228
$256$	16.7313	1.04571
$257$	22.5441	1.40626	0.703132	−	0.711060i	$-0.251784\pi$
$257$	22.5441	1.40626	0.703132	+	0.711060i	$0.251784\pi$
$258$	−8.36233	−0.520616
$259$	47.9824	2.98148
$260$	−7.57952	−0.470062
$261$	−1.90021	−0.117620
$262$	−23.9938	−1.48234
$263$	23.4520	1.44611	0.723055	−	0.690791i	$-0.242737\pi$
$263$	23.4520	1.44611	0.723055	+	0.690791i	$0.242737\pi$
$264$	0.109755	0.00675497
$265$	−9.81373	−0.602853
$266$	40.7262	2.49708
$267$	35.1503	2.15116
$268$	1.04830	0.0640354
$269$	4.83241	0.294637	0.147319	−	0.989089i	$-0.452936\pi$
$269$	4.83241	0.294637	0.147319	+	0.989089i	$0.452936\pi$
$270$	13.1442	0.799929
$271$	20.1013	1.22106	0.610532	−	0.791991i	$-0.290956\pi$
$271$	20.1013	1.22106	0.610532	+	0.791991i	$0.290956\pi$
$272$	−4.09256	−0.248148
$273$	24.4344	1.47884
$274$	36.6903	2.21654
$275$	−1.80579	−0.108893
$276$	−3.55561	−0.214023
$277$	17.0412	1.02391	0.511953	−	0.859013i	$-0.328922\pi$
$277$	17.0412	1.02391	0.511953	+	0.859013i	$0.328922\pi$
$278$	15.8728	0.951988
$279$	−2.25214	−0.134832
$280$	−0.650470	−0.0388730
$281$	−22.7052	−1.35448	−0.677238	−	0.735764i	$-0.736823\pi$
$281$	−22.7052	−1.35448	−0.677238	+	0.735764i	$0.736823\pi$
$282$	30.7055	1.82848
$283$	23.2197	1.38027	0.690135	−	0.723680i	$-0.257551\pi$
$283$	23.2197	1.38027	0.690135	+	0.723680i	$0.257551\pi$
$284$	−19.8079	−1.17539
$285$	11.6109	0.687773
$286$	3.30622	0.195501
$287$	−9.20135	−0.543138
$288$	4.51327	0.265947
$289$	1.00000	0.0588235
$290$	9.57429	0.562222
$291$	−21.1001	−1.23691
$292$	33.0290	1.93288
$293$	5.68701	0.332239	0.166119	−	0.986106i	$-0.446876\pi$
$293$	5.68701	0.332239	0.166119	+	0.986106i	$0.446876\pi$
$294$	−60.0862	−3.50430
$295$	1.43913	0.0837892
$296$	−0.942922	−0.0548062
$297$	−2.83240	−0.164352
$298$	6.38986	0.370155
$299$	2.60034	0.150381
$300$	−10.8025	−0.623680
$301$	−10.6795	−0.615555
$302$	−37.2518	−2.14360
$303$	−27.4401	−1.57639
$304$	−17.4808	−1.00259
$305$	−7.46754	−0.427590
$306$	−1.12895	−0.0645379
$307$	5.67184	0.323709	0.161855	−	0.986815i	$-0.448252\pi$
$307$	5.67184	0.323709	0.161855	+	0.986815i	$0.448252\pi$
$308$	−5.77351	−0.328976
$309$	−0.781764	−0.0444730
$310$	11.3475	0.644495
$311$	2.72892	0.154743	0.0773714	−	0.997002i	$-0.475347\pi$
$311$	2.72892	0.154743	0.0773714	+	0.997002i	$0.475347\pi$
$312$	−0.480171	−0.0271843
$313$	−4.17601	−0.236042	−0.118021	−	0.993011i	$-0.537655\pi$
$313$	−4.17601	−0.236042	−0.118021	+	0.993011i	$0.537655\pi$
$314$	−29.9855	−1.69218
$315$	−3.91923	−0.220824
$316$	6.13519	0.345131
$317$	−16.2752	−0.914104	−0.457052	−	0.889440i	$-0.651095\pi$
$317$	−16.2752	−0.914104	−0.457052	+	0.889440i	$0.651095\pi$
$318$	25.6083	1.43604
$319$	−2.06313	−0.115513
$320$	−10.9609	−0.612734
$321$	−14.8172	−0.827015
$322$	−9.19194	−0.512247
$323$	4.27135	0.237664
$324$	−20.2701	−1.12612
$325$	7.90019	0.438224
$326$	32.7620	1.81452
$327$	−12.7827	−0.706887
$328$	0.180819	0.00998409
$329$	39.2138	2.16192
$330$	−3.33199	−0.183420
$331$	19.3748	1.06493	0.532467	−	0.846451i	$-0.321265\pi$
$331$	19.3748	1.06493	0.532467	+	0.846451i	$0.321265\pi$
$332$	−7.52741	−0.413120
$333$	−5.68131	−0.311334
$334$	−2.15867	−0.118117
$335$	0.772635	0.0422135
$336$	37.0737	2.02254
$337$	3.84646	0.209530	0.104765	−	0.994497i	$-0.466591\pi$
$337$	3.84646	0.209530	0.104765	+	0.994497i	$0.466591\pi$
$338$	11.3810	0.619045
$339$	−9.18015	−0.498597
$340$	2.81003	0.152395
$341$	−2.44524	−0.132417
$342$	−4.82215	−0.260752
$343$	−43.1646	−2.33067
$344$	0.209867	0.0113153
$345$	−2.62060	−0.141088
$346$	−20.2661	−1.08951
$347$	−14.9851	−0.804440	−0.402220	−	0.915543i	$-0.631761\pi$
$347$	−14.9851	−0.804440	−0.402220	+	0.915543i	$0.631761\pi$
$348$	−12.3419	−0.661596
$349$	3.34388	0.178994	0.0894968	−	0.995987i	$-0.471474\pi$
$349$	3.34388	0.178994	0.0894968	+	0.995987i	$0.471474\pi$
$350$	−27.9264	−1.49273
$351$	12.3915	0.661410
$352$	4.90024	0.261184
$353$	−27.8698	−1.48336	−0.741679	−	0.670755i	$-0.765970\pi$
$353$	−27.8698	−1.48336	−0.741679	+	0.670755i	$0.765970\pi$
$354$	−3.75530	−0.199592
$355$	−14.5991	−0.774840
$356$	36.3360	1.92581
$357$	−9.05880	−0.479443
$358$	−24.4556	−1.29252
$359$	1.00386	0.0529817	0.0264909	−	0.999649i	$-0.491567\pi$
$359$	1.00386	0.0529817	0.0264909	+	0.999649i	$0.491567\pi$
$360$	0.0770184	0.00405923
$361$	−0.755560	−0.0397663
$362$	−48.6280	−2.55583
$363$	−20.0596	−1.05286
$364$	25.2587	1.32391
$365$	24.3434	1.27419
$366$	19.4860	1.01855
$367$	12.9274	0.674804	0.337402	−	0.941361i	$-0.390452\pi$
$367$	12.9274	0.674804	0.337402	+	0.941361i	$0.390452\pi$
$368$	3.94543	0.205670
$369$	1.08948	0.0567159
$370$	28.6256	1.48817
$371$	32.7041	1.69791
$372$	−14.6277	−0.758411
$373$	−3.21910	−0.166679	−0.0833394	−	0.996521i	$-0.526559\pi$
$373$	−3.21910	−0.166679	−0.0833394	+	0.996521i	$0.526559\pi$
$374$	−1.22575	−0.0633820
$375$	−21.5534	−1.11301
$376$	−0.770606	−0.0397410
$377$	9.02605	0.464865
$378$	−43.8028	−2.25297
$379$	−31.6919	−1.62790	−0.813952	−	0.580932i	$-0.802688\pi$
$379$	−31.6919	−1.62790	−0.813952	+	0.580932i	$0.802688\pi$
$380$	12.0026	0.615722
$381$	28.0494	1.43701
$382$	−46.3714	−2.37257
$383$	−14.4770	−0.739739	−0.369870	−	0.929084i	$-0.620598\pi$
$383$	−14.4770	−0.739739	−0.369870	+	0.929084i	$0.620598\pi$
$384$	−1.42375	−0.0726553
$385$	−4.25527	−0.216868
$386$	41.0234	2.08804
$387$	1.26450	0.0642779
$388$	−21.8119	−1.10733
$389$	3.04906	0.154593	0.0772967	−	0.997008i	$-0.475371\pi$
$389$	3.04906	0.154593	0.0772967	+	0.997008i	$0.475371\pi$
$390$	14.5772	0.738145
$391$	−0.964048	−0.0487540
$392$	1.50797	0.0761638
$393$	22.7961	1.14991
$394$	13.3305	0.671579
$395$	4.52183	0.227518
$396$	0.683608	0.0343526
$397$	0.273957	0.0137495	0.00687474	−	0.999976i	$-0.497812\pi$
$397$	0.273957	0.0137495	0.00687474	+	0.999976i	$0.497812\pi$
$398$	−1.44126	−0.0722437
$399$	−38.6933	−1.93709
$400$	11.9868	0.599339
$401$	16.1791	0.807944	0.403972	−	0.914771i	$-0.367629\pi$
$401$	16.1791	0.807944	0.403972	+	0.914771i	$0.367629\pi$
$402$	−2.01614	−0.100556
$403$	10.6977	0.532892
$404$	−28.3658	−1.41125
$405$	−14.9397	−0.742360
$406$	−31.9062	−1.58348
$407$	−6.16843	−0.305758
$408$	0.178018	0.00881322
$409$	17.3294	0.856885	0.428442	−	0.903569i	$-0.359062\pi$
$409$	17.3294	0.856885	0.428442	+	0.903569i	$0.359062\pi$
$410$	−5.48939	−0.271102
$411$	−34.8589	−1.71946
$412$	−0.808136	−0.0398140
$413$	−4.79587	−0.235989
$414$	1.08836	0.0534902
$415$	−5.54794	−0.272338
$416$	−21.4382	−1.05109
$417$	−15.0805	−0.738496
$418$	−5.23560	−0.256082
$419$	3.67232	0.179404	0.0897022	−	0.995969i	$-0.471408\pi$
$419$	3.67232	0.179404	0.0897022	+	0.995969i	$0.471408\pi$
$420$	−25.4555	−1.24210
$421$	−13.5246	−0.659151	−0.329575	−	0.944129i	$-0.606906\pi$
$421$	−13.5246	−0.659151	−0.329575	+	0.944129i	$0.606906\pi$
$422$	−2.15290	−0.104802
$423$	−4.64307	−0.225754
$424$	−0.642683	−0.0312114
$425$	−2.92892	−0.142073
$426$	38.0953	1.84572
$427$	24.8855	1.20429
$428$	−15.3170	−0.740377
$429$	−3.14119	−0.151658
$430$	−6.37122	−0.307248
$431$	24.6732	1.18847	0.594234	−	0.804292i	$-0.297455\pi$
$431$	24.6732	1.18847	0.594234	+	0.804292i	$0.297455\pi$
$432$	18.8013	0.904580
$433$	−26.4329	−1.27028	−0.635142	−	0.772396i	$-0.719058\pi$
$433$	−26.4329	−1.27028	−0.635142	+	0.772396i	$0.719058\pi$
$434$	−37.8154	−1.81520
$435$	−9.09639	−0.436138
$436$	−13.2140	−0.632834
$437$	−4.11779	−0.196981
$438$	−63.5225	−3.03522
$439$	−18.5290	−0.884339	−0.442169	−	0.896932i	$-0.645791\pi$
$439$	−18.5290	−0.884339	−0.442169	+	0.896932i	$0.645791\pi$
$440$	0.0836220	0.00398652
$441$	9.08583	0.432658
$442$	5.36256	0.255071
$443$	14.7144	0.699103	0.349551	−	0.936917i	$-0.386334\pi$
$443$	14.7144	0.699103	0.349551	+	0.936917i	$0.386334\pi$
$444$	−36.9003	−1.75121
$445$	26.7808	1.26953
$446$	−18.5295	−0.877398
$447$	−6.07091	−0.287144
$448$	36.5271	1.72575
$449$	14.6116	0.689563	0.344781	−	0.938683i	$-0.387953\pi$
$449$	14.6116	0.689563	0.344781	+	0.938683i	$0.387953\pi$
$450$	3.30661	0.155875
$451$	1.18289	0.0557001
$452$	−9.48984	−0.446364
$453$	35.3924	1.66288
$454$	20.0250	0.939819
$455$	18.6165	0.872753
$456$	0.760379	0.0356080
$457$	23.9600	1.12080	0.560401	−	0.828222i	$-0.310647\pi$
$457$	23.9600	1.12080	0.560401	+	0.828222i	$0.310647\pi$
$458$	25.1580	1.17556
$459$	−4.59403	−0.214431
$460$	−2.70901	−0.126308
$461$	−18.6170	−0.867079	−0.433540	−	0.901134i	$-0.642736\pi$
$461$	−18.6170	−0.867079	−0.433540	+	0.901134i	$0.642736\pi$
$462$	11.1038	0.516596
$463$	−21.6446	−1.00591	−0.502955	−	0.864313i	$-0.667754\pi$
$463$	−21.6446	−1.00591	−0.502955	+	0.864313i	$0.667754\pi$
$464$	13.6950	0.635774
$465$	−10.7811	−0.499961
$466$	5.25706	0.243529
$467$	41.0313	1.89870	0.949351	−	0.314218i	$-0.101742\pi$
$467$	41.0313	1.89870	0.949351	+	0.314218i	$0.101742\pi$
$468$	−2.99073	−0.138247
$469$	−2.57480	−0.118893
$470$	23.3944	1.07910
$471$	28.4887	1.31269
$472$	0.0942457	0.00433801
$473$	1.37291	0.0631266
$474$	−11.7994	−0.541965
$475$	−12.5104	−0.574018
$476$	−9.36439	−0.429216
$477$	−3.87231	−0.177301
$478$	21.6920	0.992167
$479$	1.13109	0.0516806	0.0258403	−	0.999666i	$-0.491774\pi$
$479$	1.13109	0.0516806	0.0258403	+	0.999666i	$0.491774\pi$
$480$	21.6053	0.986140
$481$	26.9864	1.23047
$482$	−7.99558	−0.364189
$483$	8.73312	0.397371
$484$	−20.7363	−0.942560
$485$	−16.0761	−0.729976
$486$	11.5838	0.525451
$487$	−15.7952	−0.715751	−0.357875	−	0.933769i	$-0.616499\pi$
$487$	−15.7952	−0.715751	−0.357875	+	0.933769i	$0.616499\pi$
$488$	−0.489035	−0.0221376
$489$	−31.1267	−1.40760
$490$	−45.7794	−2.06810
$491$	22.8665	1.03195	0.515975	−	0.856604i	$-0.327430\pi$
$491$	22.8665	1.03195	0.515975	+	0.856604i	$0.327430\pi$
$492$	7.07619	0.319019
$493$	−3.34631	−0.150710
$494$	22.9054	1.03056
$495$	0.503841	0.0226460
$496$	16.2314	0.728811
$497$	48.6513	2.18231
$498$	14.4770	0.648728
$499$	23.5485	1.05418	0.527089	−	0.849810i	$-0.323284\pi$
$499$	23.5485	1.05418	0.527089	+	0.849810i	$0.323284\pi$
$500$	−22.2805	−0.996414
$501$	2.05092	0.0916282
$502$	32.2231	1.43819
$503$	−0.000991397 0	−4.42042e−5 0	−2.21021e−5	−	1.00000i	$-0.500007\pi$
$503$	−0.000991397 0	−4.42042e−5 0	−2.21021e−5		1.00000i	$0.500007\pi$
$504$	−0.256663	−0.0114327
$505$	−20.9065	−0.930326
$506$	1.18168	0.0525321
$507$	−10.8129	−0.480218
$508$	28.9956	1.28647
$509$	14.6997	0.651553	0.325776	−	0.945447i	$-0.394374\pi$
$509$	14.6997	0.651553	0.325776	+	0.945447i	$0.394374\pi$
$510$	−5.40435	−0.239309
$511$	−81.1242	−3.58872
$512$	−31.7562	−1.40344
$513$	−19.6227	−0.866363
$514$	−44.8203	−1.97694
$515$	−0.595623	−0.0262463
$516$	8.21294	0.361554
$517$	−5.04117	−0.221710
$518$	−95.3944	−4.19139
$519$	19.2545	0.845177
$520$	−0.365840	−0.0160431
$521$	22.4308	0.982713	0.491357	−	0.870959i	$-0.336501\pi$
$521$	22.4308	0.982713	0.491357	+	0.870959i	$0.336501\pi$
$522$	3.77783	0.165351
$523$	−9.05345	−0.395880	−0.197940	−	0.980214i	$-0.563425\pi$
$523$	−9.05345	−0.395880	−0.197940	+	0.980214i	$0.563425\pi$
$524$	23.5651	1.02945
$525$	26.5325	1.15797
$526$	−46.6251	−2.03295
$527$	−3.96607	−0.172765
$528$	−4.76605	−0.207416
$529$	−22.0706	−0.959592
$530$	19.5108	0.847496
$531$	0.567851	0.0246426
$532$	−39.9986	−1.73416
$533$	−5.17505	−0.224156
$534$	−69.8827	−3.02412
$535$	−11.2892	−0.488073
$536$	0.0505984	0.00218552
$537$	23.2349	1.00266
$538$	−9.60738	−0.414203
$539$	9.86485	0.424909
$540$	−12.9094	−0.555530
$541$	34.1806	1.46954	0.734769	−	0.678317i	$-0.237291\pi$
$541$	34.1806	1.46954	0.734769	+	0.678317i	$0.237291\pi$
$542$	−39.9636	−1.71658
$543$	46.2007	1.98266
$544$	7.94799	0.340767
$545$	−9.73912	−0.417178
$546$	−48.5784	−2.07896
$547$	1.23781	0.0529250	0.0264625	−	0.999650i	$-0.491576\pi$
$547$	1.23781	0.0529250	0.0264625	+	0.999650i	$0.491576\pi$
$548$	−36.0349	−1.53933
$549$	−2.94655	−0.125756
$550$	3.59012	0.153083
$551$	−14.2933	−0.608914
$552$	−0.171618	−0.00730456
$553$	−15.0690	−0.640797
$554$	−33.8798	−1.43942
$555$	−27.1967	−1.15444
$556$	−15.5892	−0.661131
$557$	−36.7382	−1.55665	−0.778324	−	0.627863i	$-0.783930\pi$
$557$	−36.7382	−1.55665	−0.778324	+	0.627863i	$0.783930\pi$
$558$	4.47751	0.189548
$559$	−6.00639	−0.254043
$560$	28.2463	1.19362
$561$	1.16457	0.0491680
$562$	45.1405	1.90414
$563$	−34.3120	−1.44608	−0.723039	−	0.690807i	$-0.757255\pi$
$563$	−34.3120	−1.44608	−0.723039	+	0.690807i	$0.757255\pi$
$564$	−30.1569	−1.26983
$565$	−6.99432	−0.294253
$566$	−46.1635	−1.94040
$567$	49.7864	2.09083
$568$	−0.956067	−0.0401157
$569$	−34.6693	−1.45341	−0.726706	−	0.686948i	$-0.758950\pi$
$569$	−34.6693	−1.45341	−0.726706	+	0.686948i	$0.758950\pi$
$570$	−23.0839	−0.966877
$571$	−17.8247	−0.745939	−0.372970	−	0.927844i	$-0.621660\pi$
$571$	−17.8247	−0.745939	−0.372970	+	0.927844i	$0.621660\pi$
$572$	−3.24716	−0.135771
$573$	44.0567	1.84050
$574$	18.2933	0.763548
$575$	2.82362	0.117753
$576$	−4.32497	−0.180207
$577$	−32.7021	−1.36141	−0.680703	−	0.732559i	$-0.738326\pi$
$577$	−32.7021	−1.36141	−0.680703	+	0.732559i	$0.738326\pi$
$578$	−1.98811	−0.0826946
$579$	−38.9757	−1.61978
$580$	−9.40325	−0.390449
$581$	18.4884	0.767030
$582$	41.9494	1.73886
$583$	−4.20432	−0.174125
$584$	1.59421	0.0659687
$585$	−2.20427	−0.0911352
$586$	−11.3064	−0.467064
$587$	10.2935	0.424860	0.212430	−	0.977176i	$-0.431862\pi$
$587$	10.2935	0.424860	0.212430	+	0.977176i	$0.431862\pi$
$588$	59.0127	2.43364
$589$	−16.9405	−0.698021
$590$	−2.86115	−0.117792
$591$	−12.6651	−0.520971
$592$	40.9458	1.68286
$593$	−8.83917	−0.362981	−0.181491	−	0.983393i	$-0.558092\pi$
$593$	−8.83917	−0.362981	−0.181491	+	0.983393i	$0.558092\pi$
$594$	5.63112	0.231048
$595$	−6.90186	−0.282949
$596$	−6.27571	−0.257063
$597$	1.36932	0.0560424
$598$	−5.16976	−0.211407
$599$	−32.1607	−1.31405	−0.657025	−	0.753869i	$-0.728186\pi$
$599$	−32.1607	−1.31405	−0.657025	+	0.753869i	$0.728186\pi$
$600$	−0.521401	−0.0212861
$601$	−1.94151	−0.0791958	−0.0395979	−	0.999216i	$-0.512608\pi$
$601$	−1.94151	−0.0791958	−0.0395979	+	0.999216i	$0.512608\pi$
$602$	21.2320	0.865353
$603$	0.304867	0.0124151
$604$	36.5863	1.48868
$605$	−15.2833	−0.621356
$606$	54.5540	2.21610
$607$	4.54479	0.184467	0.0922337	−	0.995737i	$-0.470599\pi$
$607$	4.54479	0.184467	0.0922337	+	0.995737i	$0.470599\pi$
$608$	33.9486	1.37680
$609$	30.3136	1.22837
$610$	14.8463	0.601110
$611$	22.0547	0.892239
$612$	1.10878	0.0448199
$613$	14.4639	0.584190	0.292095	−	0.956389i	$-0.405648\pi$
$613$	14.4639	0.584190	0.292095	+	0.956389i	$0.405648\pi$
$614$	−11.2763	−0.455073
$615$	5.21538	0.210304
$616$	−0.278669	−0.0112279
$617$	37.5746	1.51270	0.756348	−	0.654170i	$-0.226982\pi$
$617$	37.5746	1.51270	0.756348	+	0.654170i	$0.226982\pi$
$618$	1.55424	0.0625205
$619$	−15.4064	−0.619234	−0.309617	−	0.950861i	$-0.600201\pi$
$619$	−15.4064	−0.619234	−0.309617	+	0.950861i	$0.600201\pi$
$620$	−11.1448	−0.447585
$621$	4.42886	0.177724
$622$	−5.42540	−0.217539
$623$	−89.2468	−3.57560
$624$	20.8511	0.834713
$625$	−1.77687	−0.0710747
$626$	8.30237	0.331830
$627$	4.97427	0.198653
$628$	29.4498	1.17517
$629$	−10.0049	−0.398923
$630$	7.79187	0.310436
$631$	40.2633	1.60286	0.801428	−	0.598091i	$-0.204074\pi$
$631$	40.2633	1.60286	0.801428	+	0.598091i	$0.204074\pi$
$632$	0.296126	0.0117793
$633$	2.04544	0.0812989
$634$	32.3569	1.28506
$635$	21.3707	0.848071
$636$	−25.1508	−0.997292
$637$	−43.1580	−1.70998
$638$	4.10174	0.162390
$639$	−5.76052	−0.227883
$640$	−1.08475	−0.0428784
$641$	−23.8006	−0.940066	−0.470033	−	0.882649i	$-0.655758\pi$
$641$	−23.8006	−0.940066	−0.470033	+	0.882649i	$0.655758\pi$
$642$	29.4583	1.16263
$643$	26.3566	1.03940	0.519701	−	0.854348i	$-0.326043\pi$
$643$	26.3566	1.03940	0.519701	+	0.854348i	$0.326043\pi$
$644$	9.02773	0.355742
$645$	6.05320	0.238345
$646$	−8.49193	−0.334111
$647$	−28.9902	−1.13972	−0.569861	−	0.821741i	$-0.693003\pi$
$647$	−28.9902	−1.13972	−0.569861	+	0.821741i	$0.693003\pi$
$648$	−0.978373	−0.0384341
$649$	0.616539	0.0242013
$650$	−15.7065	−0.616059
$651$	35.9279	1.40812
$652$	−32.1767	−1.26014
$653$	−2.69243	−0.105363	−0.0526815	−	0.998611i	$-0.516777\pi$
$653$	−2.69243	−0.105363	−0.0526815	+	0.998611i	$0.516777\pi$
$654$	25.4135	0.993748
$655$	17.3682	0.678634
$656$	−7.85198	−0.306568
$657$	9.60544	0.374744
$658$	−77.9614	−3.03925
$659$	44.9095	1.74942	0.874712	−	0.484643i	$-0.161050\pi$
$659$	44.9095	1.74942	0.874712	+	0.484643i	$0.161050\pi$
$660$	3.27246	0.127380
$661$	−21.3071	−0.828751	−0.414376	−	0.910106i	$-0.636000\pi$
$661$	−21.3071	−0.828751	−0.414376	+	0.910106i	$0.636000\pi$
$662$	−38.5193	−1.49709
$663$	−5.09488	−0.197869
$664$	−0.363324	−0.0140997
$665$	−29.4803	−1.14320
$666$	11.2951	0.437676
$667$	3.22601	0.124912
$668$	2.12010	0.0820292
$669$	17.6046	0.680633
$670$	−1.53609	−0.0593441
$671$	−3.19918	−0.123503
$672$	−71.9992	−2.77743
$673$	17.1824	0.662334	0.331167	−	0.943572i	$-0.392558\pi$
$673$	17.1824	0.662334	0.331167	+	0.943572i	$0.392558\pi$
$674$	−7.64721	−0.294559
$675$	13.4555	0.517903
$676$	−11.1777	−0.429910
$677$	3.59804	0.138284	0.0691420	−	0.997607i	$-0.477974\pi$
$677$	3.59804	0.138284	0.0691420	+	0.997607i	$0.477974\pi$
$678$	18.2512	0.700932
$679$	53.5733	2.05595
$680$	0.135631	0.00520123
$681$	−19.0254	−0.729056
$682$	4.86141	0.186153
$683$	−17.3152	−0.662548	−0.331274	−	0.943535i	$-0.607478\pi$
$683$	−17.3152	−0.662548	−0.331274	+	0.943535i	$0.607478\pi$
$684$	4.73600	0.181086
$685$	−26.5589	−1.01476
$686$	85.8161	3.27648
$687$	−23.9022	−0.911927
$688$	−9.11335	−0.347443
$689$	18.3936	0.700740
$690$	5.21005	0.198343
$691$	18.2275	0.693408	0.346704	−	0.937975i	$-0.387301\pi$
$691$	18.2275	0.693408	0.346704	+	0.937975i	$0.387301\pi$
$692$	19.9040	0.756636
$693$	−1.67904	−0.0637816
$694$	29.7920	1.13089
$695$	−11.4898	−0.435832
$696$	−0.595705	−0.0225801
$697$	1.91860	0.0726721
$698$	−6.64800	−0.251631
$699$	−4.99465	−0.188915
$700$	27.4275	1.03666
$701$	−28.7074	−1.08426	−0.542132	−	0.840293i	$-0.682383\pi$
$701$	−28.7074	−1.08426	−0.542132	+	0.840293i	$0.682383\pi$
$702$	−24.6357	−0.929816
$703$	−42.7346	−1.61177
$704$	−4.69579	−0.176979
$705$	−22.2266	−0.837102
$706$	55.4082	2.08532
$707$	69.6706	2.62023
$708$	3.68821	0.138611
$709$	−29.7765	−1.11828	−0.559139	−	0.829074i	$-0.688868\pi$
$709$	−29.7765	−1.11828	−0.559139	+	0.829074i	$0.688868\pi$
$710$	29.0247	1.08928
$711$	1.78423	0.0669137
$712$	1.75383	0.0657274
$713$	3.82348	0.143191
$714$	18.0099	0.674005
$715$	−2.39326	−0.0895029
$716$	24.0187	0.897621
$717$	−20.6092	−0.769664
$718$	−1.99579	−0.0744821
$719$	23.7333	0.885101	0.442551	−	0.896744i	$-0.354074\pi$
$719$	23.7333	0.885101	0.442551	+	0.896744i	$0.354074\pi$
$720$	−3.34448	−0.124641
$721$	1.98491	0.0739217
$722$	1.50214	0.0559038
$723$	7.59648	0.282516
$724$	47.7592	1.77496
$725$	9.80107	0.364003
$726$	39.8808	1.48012
$727$	−1.98021	−0.0734419	−0.0367209	−	0.999326i	$-0.511691\pi$
$727$	−1.98021	−0.0734419	−0.0367209	+	0.999326i	$0.511691\pi$
$728$	1.21916	0.0451850
$729$	20.1377	0.745841
$730$	−48.3975	−1.79127
$731$	2.22681	0.0823615
$732$	−19.1379	−0.707358
$733$	18.5812	0.686313	0.343156	−	0.939278i	$-0.388504\pi$
$733$	18.5812	0.686313	0.343156	+	0.939278i	$0.388504\pi$
$734$	−25.7011	−0.948645
$735$	43.4943	1.60431
$736$	−7.66224	−0.282434
$737$	0.331006	0.0121928
$738$	−2.16601	−0.0797318
$739$	37.6736	1.38585	0.692923	−	0.721012i	$-0.256323\pi$
$739$	37.6736	1.38585	0.692923	+	0.721012i	$0.256323\pi$
$740$	−28.1142	−1.03350
$741$	−21.7620	−0.799448
$742$	−65.0196	−2.38694
$743$	−51.0091	−1.87134	−0.935670	−	0.352875i	$-0.885204\pi$
$743$	−51.0091	−1.87134	−0.935670	+	0.352875i	$0.885204\pi$
$744$	−0.706033	−0.0258844
$745$	−4.62540	−0.169462
$746$	6.39994	0.234318
$747$	−2.18911	−0.0800953
$748$	1.20385	0.0440171
$749$	37.6210	1.37464
$750$	42.8506	1.56468
$751$	20.6563	0.753759	0.376879	−	0.926262i	$-0.376997\pi$
$751$	20.6563	0.753759	0.376879	+	0.926262i	$0.376997\pi$
$752$	33.4631	1.22027
$753$	−30.6147	−1.11566
$754$	−17.9448	−0.653511
$755$	26.9653	0.981367
$756$	43.0203	1.56463
$757$	−42.0625	−1.52879	−0.764394	−	0.644749i	$-0.776962\pi$
$757$	−42.0625	−1.52879	−0.764394	+	0.644749i	$0.776962\pi$
$758$	63.0071	2.28852
$759$	−1.12270	−0.0407513
$760$	0.579329	0.0210145
$761$	−10.5534	−0.382561	−0.191280	−	0.981535i	$-0.561264\pi$
$761$	−10.5534	−0.382561	−0.191280	+	0.981535i	$0.561264\pi$
$762$	−55.7654	−2.02017
$763$	32.4555	1.17497
$764$	45.5429	1.64769
$765$	0.817209	0.0295463
$766$	28.7819	1.03993
$767$	−2.69731	−0.0973942
$768$	31.6033	1.14039
$769$	1.51065	0.0544754	0.0272377	−	0.999629i	$-0.491329\pi$
$769$	1.51065	0.0544754	0.0272377	+	0.999629i	$0.491329\pi$
$770$	8.45995	0.304875
$771$	42.5830	1.53359
$772$	−40.2905	−1.45009
$773$	−27.5981	−0.992633	−0.496317	−	0.868142i	$-0.665314\pi$
$773$	−27.5981	−0.992633	−0.496317	+	0.868142i	$0.665314\pi$
$774$	−2.51396	−0.0903625
$775$	11.6163	0.417270
$776$	−1.05279	−0.0377930
$777$	90.6327	3.25143
$778$	−6.06188	−0.217329
$779$	8.19500	0.293617
$780$	−14.3168	−0.512623
$781$	−6.25443	−0.223801
$782$	1.91664	0.0685388
$783$	15.3731	0.549388
$784$	−65.4825	−2.33866
$785$	21.7054	0.774700
$786$	−45.3212	−1.61656
$787$	−52.6882	−1.87813	−0.939066	−	0.343738i	$-0.888307\pi$
$787$	−52.6882	−1.87813	−0.939066	+	0.343738i	$0.888307\pi$
$788$	−13.0923	−0.466394
$789$	44.2978	1.57704
$790$	−8.98992	−0.319847
$791$	23.3085	0.828754
$792$	0.0329956	0.00117245
$793$	13.9962	0.497019
$794$	−0.544657	−0.0193291
$795$	−18.5369	−0.657437
$796$	1.41551	0.0501714
$797$	28.4765	1.00869	0.504344	−	0.863503i	$-0.331734\pi$
$797$	28.4765	1.00869	0.504344	+	0.863503i	$0.331734\pi$
$798$	76.9267	2.72318
$799$	−8.17657	−0.289266
$800$	−23.2790	−0.823036
$801$	10.5672	0.373373
$802$	−32.1658	−1.13581
$803$	10.4290	0.368032
$804$	1.98012	0.0698334
$805$	6.65373	0.234513
$806$	−21.2683	−0.749144
$807$	9.12782	0.321314
$808$	−1.36913	−0.0481657
$809$	10.3372	0.363435	0.181718	−	0.983351i	$-0.441834\pi$
$809$	10.3372	0.363435	0.181718	+	0.983351i	$0.441834\pi$
$810$	29.7018	1.04362
$811$	−38.2352	−1.34262	−0.671310	−	0.741177i	$-0.734268\pi$
$811$	−38.2352	−1.34262	−0.671310	+	0.741177i	$0.734268\pi$
$812$	31.3362	1.09969
$813$	37.9688	1.33162
$814$	12.2635	0.429837
$815$	−23.7153	−0.830710
$816$	−7.73034	−0.270616
$817$	9.51148	0.332765
$818$	−34.4529	−1.20462
$819$	7.34569	0.256679
$820$	5.39132	0.188273
$821$	−39.6871	−1.38509	−0.692544	−	0.721376i	$-0.743510\pi$
$821$	−39.6871	−1.38509	−0.692544	+	0.721376i	$0.743510\pi$
$822$	69.3035	2.41724
$823$	7.53447	0.262635	0.131318	−	0.991340i	$-0.458079\pi$
$823$	7.53447	0.262635	0.131318	+	0.991340i	$0.458079\pi$
$824$	−0.0390062	−0.00135885
$825$	−3.41091	−0.118753
$826$	9.53473	0.331756
$827$	0.866384	0.0301271	0.0150636	−	0.999887i	$-0.495205\pi$
$827$	0.866384	0.0301271	0.0150636	+	0.999887i	$0.495205\pi$
$828$	−1.06892	−0.0371476
$829$	54.3944	1.88919	0.944597	−	0.328231i	$-0.106453\pi$
$829$	54.3944	1.88919	0.944597	+	0.328231i	$0.106453\pi$
$830$	11.0299	0.382855
$831$	32.1887	1.11661
$832$	20.5437	0.712225
$833$	16.0004	0.554380
$834$	29.9818	1.03818
$835$	1.56258	0.0540754
$836$	5.14207	0.177842
$837$	18.2202	0.629784
$838$	−7.30098	−0.252208
$839$	17.8614	0.616646	0.308323	−	0.951282i	$-0.400232\pi$
$839$	17.8614	0.616646	0.308323	+	0.951282i	$0.400232\pi$
$840$	−1.22866	−0.0423927
$841$	−17.8022	−0.613868
$842$	26.8885	0.926640
$843$	−42.8872	−1.47712
$844$	2.11444	0.0727820
$845$	−8.23831	−0.283406
$846$	9.23095	0.317367
$847$	50.9316	1.75003
$848$	27.9081	0.958369
$849$	43.8592	1.50524
$850$	5.82302	0.199728
$851$	9.64524	0.330635
$852$	−37.4147	−1.28181
$853$	20.6634	0.707500	0.353750	−	0.935340i	$-0.384906\pi$
$853$	20.6634	0.707500	0.353750	+	0.935340i	$0.384906\pi$
$854$	−49.4752	−1.69301
$855$	3.49059	0.119376
$856$	−0.739306	−0.0252690
$857$	−49.2216	−1.68138	−0.840689	−	0.541518i	$-0.817850\pi$
$857$	−49.2216	−1.68138	−0.840689	+	0.541518i	$0.817850\pi$
$858$	6.24505	0.213202
$859$	21.8166	0.744373	0.372186	−	0.928158i	$-0.378608\pi$
$859$	21.8166	0.744373	0.372186	+	0.928158i	$0.378608\pi$
$860$	6.25740	0.213376
$861$	−17.3802	−0.592316
$862$	−49.0532	−1.67076
$863$	−57.2336	−1.94825	−0.974127	−	0.226001i	$-0.927435\pi$
$863$	−57.2336	−1.94825	−0.974127	+	0.226001i	$0.927435\pi$
$864$	−36.5133	−1.24221
$865$	14.6699	0.498791
$866$	52.5516	1.78578
$867$	1.88888	0.0641496
$868$	37.1399	1.26061
$869$	1.93721	0.0657153
$870$	18.0847	0.613127
$871$	−1.44813	−0.0490679
$872$	−0.637796	−0.0215985
$873$	−6.34330	−0.214688
$874$	8.18663	0.276917
$875$	54.7243	1.85002
$876$	62.3876	2.10788
$877$	−13.2974	−0.449021	−0.224510	−	0.974472i	$-0.572078\pi$
$877$	−13.2974	−0.449021	−0.224510	+	0.974472i	$0.572078\pi$
$878$	36.8377	1.24321
$879$	10.7421	0.362320
$880$	−3.63124	−0.122409
$881$	3.70709	0.124895	0.0624475	−	0.998048i	$-0.480109\pi$
$881$	3.70709	0.124895	0.0624475	+	0.998048i	$0.480109\pi$
$882$	−18.0637	−0.608235
$883$	−42.4839	−1.42970	−0.714848	−	0.699280i	$-0.753504\pi$
$883$	−42.4839	−1.42970	−0.714848	+	0.699280i	$0.753504\pi$
$884$	−5.26675	−0.177140
$885$	2.71833	0.0913757
$886$	−29.2539	−0.982805
$887$	49.1125	1.64904	0.824518	−	0.565836i	$-0.191447\pi$
$887$	49.1125	1.64904	0.824518	+	0.565836i	$0.191447\pi$
$888$	−1.78106	−0.0597685
$889$	−71.2177	−2.38856
$890$	−53.2433	−1.78472
$891$	−6.40035	−0.214420
$892$	18.1985	0.609330
$893$	−34.9250	−1.16872
$894$	12.0697	0.403670
$895$	17.7026	0.591731
$896$	3.61490	0.120765
$897$	4.91171	0.163997
$898$	−29.0495	−0.969393
$899$	13.2717	0.442637
$900$	−3.24753	−0.108251
$901$	−6.81923	−0.227182
$902$	−2.35172	−0.0783037
$903$	−20.1722	−0.671289
$904$	−0.458045	−0.0152343
$905$	35.2001	1.17009
$906$	−70.3641	−2.33769
$907$	−17.2643	−0.573250	−0.286625	−	0.958043i	$-0.592533\pi$
$907$	−17.2643	−0.573250	−0.286625	+	0.958043i	$0.592533\pi$
$908$	−19.6672	−0.652680
$909$	−8.24929	−0.273612
$910$	−37.0116	−1.22692
$911$	−38.2954	−1.26878	−0.634392	−	0.773012i	$-0.718749\pi$
$911$	−38.2954	−1.26878	−0.634392	+	0.773012i	$0.718749\pi$
$912$	−33.0190	−1.09337
$913$	−2.37680	−0.0786607
$914$	−47.6352	−1.57563
$915$	−14.1053	−0.466305
$916$	−24.7086	−0.816394
$917$	−57.8795	−1.91135
$918$	9.13345	0.301449
$919$	17.5743	0.579723	0.289861	−	0.957069i	$-0.406391\pi$
$919$	17.5743	0.579723	0.289861	+	0.957069i	$0.406391\pi$
$920$	−0.130755	−0.00431087
$921$	10.7134	0.353019
$922$	37.0127	1.21895
$923$	27.3626	0.900652
$924$	−10.9054	−0.358763
$925$	29.3036	0.963497
$926$	43.0319	1.41412
$927$	−0.235021	−0.00771911
$928$	−26.5965	−0.873072
$929$	−42.9783	−1.41007	−0.705036	−	0.709172i	$-0.749069\pi$
$929$	−42.9783	−1.41007	−0.705036	+	0.709172i	$0.749069\pi$
$930$	21.4340	0.702850
$931$	68.3432	2.23986
$932$	−5.16314	−0.169124
$933$	5.15459	0.168754
$934$	−81.5749	−2.66921
$935$	0.887277	0.0290171
$936$	−0.144353	−0.00471833
$937$	−2.10600	−0.0687999	−0.0343999	−	0.999408i	$-0.510952\pi$
$937$	−2.10600	−0.0687999	−0.0343999	+	0.999408i	$0.510952\pi$
$938$	5.11899	0.167141
$939$	−7.88795	−0.257414
$940$	−22.9764	−0.749408
$941$	40.5350	1.32140	0.660702	−	0.750648i	$-0.270259\pi$
$941$	40.5350	1.32140	0.660702	+	0.750648i	$0.270259\pi$
$942$	−56.6388	−1.84539
$943$	−1.84962	−0.0602319
$944$	−4.09256	−0.133202
$945$	31.7073	1.03144
$946$	−2.72951	−0.0887440
$947$	11.4590	0.372366	0.186183	−	0.982515i	$-0.440388\pi$
$947$	11.4590	0.372366	0.186183	+	0.982515i	$0.440388\pi$
$948$	11.5886	0.376381
$949$	−45.6261	−1.48109
$950$	24.8722	0.806959
$951$	−30.7417	−0.996869
$952$	−0.451990	−0.0146491
$953$	−49.4467	−1.60174	−0.800868	−	0.598841i	$-0.795628\pi$
$953$	−49.4467	−1.60174	−0.800868	+	0.598841i	$0.795628\pi$
$954$	7.69859	0.249251
$955$	33.5666	1.08619
$956$	−21.3044	−0.689034
$957$	−3.89700	−0.125972
$958$	−2.24873	−0.0726530
$959$	88.5071	2.85804
$960$	−20.7038	−0.668213
$961$	−15.2703	−0.492589
$962$	−53.6520	−1.72981
$963$	−4.45448	−0.143544
$964$	7.85274	0.252920
$965$	−29.6954	−0.955930
$966$	−17.3624	−0.558627
$967$	−24.8793	−0.800066	−0.400033	−	0.916501i	$-0.631001\pi$
$967$	−24.8793	−0.800066	−0.400033	+	0.916501i	$0.631001\pi$
$968$	−1.00088	−0.0321694
$969$	8.06805	0.259183
$970$	31.9610	1.02621
$971$	42.8922	1.37648	0.688238	−	0.725485i	$-0.258385\pi$
$971$	42.8922	1.37648	0.688238	+	0.725485i	$0.258385\pi$
$972$	−11.3768	−0.364912
$973$	38.2895	1.22751
$974$	31.4027	1.00621
$975$	14.9225	0.477902
$976$	21.2361	0.679750
$977$	−53.3919	−1.70816	−0.854080	−	0.520142i	$-0.825879\pi$
$977$	−53.3919	−1.70816	−0.854080	+	0.520142i	$0.825879\pi$
$978$	61.8834	1.97881
$979$	11.4732	0.366686
$980$	44.9615	1.43624
$981$	−3.84287	−0.122693
$982$	−45.4612	−1.45072
$983$	−26.5097	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$983$	−26.5097	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$984$	0.341546	0.0108881
$985$	−9.64945	−0.307457
$986$	6.65285	0.211870
$987$	74.0699	2.35767
$988$	−22.4962	−0.715698
$989$	−2.14675	−0.0682627
$990$	−1.00169	−0.0318359
$991$	−55.9775	−1.77818	−0.889092	−	0.457729i	$-0.848663\pi$
$991$	−55.9775	−1.77818	−0.889092	+	0.457729i	$0.848663\pi$
$992$	−31.5223	−1.00083
$993$	36.5965	1.16136
$994$	−96.7243	−3.06791
$995$	1.04328	0.0330741
$996$	−14.2183	−0.450525
$997$	−21.1577	−0.670072	−0.335036	−	0.942205i	$-0.608749\pi$
$997$	−21.1577	−0.670072	−0.335036	+	0.942205i	$0.608749\pi$
$998$	−46.8172	−1.48197
$999$	45.9629	1.45420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.4	✓	16
3.2	odd	2		9027.2.a.n.1.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.4	✓	16	1.1	even	1	trivial
9027.2.a.n.1.13		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-1.98811 q^{2} +1.88888 q^{3} +1.95260 q^{4} +1.43913 q^{5} -3.75530 q^{6} -4.79587 q^{7} +0.0942457 q^{8} +0.567851 q^{9} +O(q^{10})\)	\(q-1.98811 q^{2} +1.88888 q^{3} +1.95260 q^{4} +1.43913 q^{5} -3.75530 q^{6} -4.79587 q^{7} +0.0942457 q^{8} +0.567851 q^{9} -2.86115 q^{10} +0.616539 q^{11} +3.68821 q^{12} -2.69731 q^{13} +9.53473 q^{14} +2.71833 q^{15} -4.09256 q^{16} +1.00000 q^{17} -1.12895 q^{18} +4.27135 q^{19} +2.81003 q^{20} -9.05880 q^{21} -1.22575 q^{22} -0.964048 q^{23} +0.178018 q^{24} -2.92892 q^{25} +5.36256 q^{26} -4.59403 q^{27} -9.36439 q^{28} -3.34631 q^{29} -5.40435 q^{30} -3.96607 q^{31} +7.94799 q^{32} +1.16457 q^{33} -1.98811 q^{34} -6.90186 q^{35} +1.10878 q^{36} -10.0049 q^{37} -8.49193 q^{38} -5.09488 q^{39} +0.135631 q^{40} +1.91860 q^{41} +18.0099 q^{42} +2.22681 q^{43} +1.20385 q^{44} +0.817209 q^{45} +1.91664 q^{46} -8.17657 q^{47} -7.73034 q^{48} +16.0004 q^{49} +5.82302 q^{50} +1.88888 q^{51} -5.26675 q^{52} -6.81923 q^{53} +9.13345 q^{54} +0.887277 q^{55} -0.451990 q^{56} +8.06805 q^{57} +6.65285 q^{58} +1.00000 q^{59} +5.30780 q^{60} -5.18894 q^{61} +7.88500 q^{62} -2.72334 q^{63} -7.61638 q^{64} -3.88177 q^{65} -2.31529 q^{66} +0.536878 q^{67} +1.95260 q^{68} -1.82097 q^{69} +13.7217 q^{70} -10.1444 q^{71} +0.0535175 q^{72} +16.9154 q^{73} +19.8909 q^{74} -5.53236 q^{75} +8.34022 q^{76} -2.95684 q^{77} +10.1292 q^{78} +3.14207 q^{79} -5.88971 q^{80} -10.3811 q^{81} -3.81439 q^{82} -3.85508 q^{83} -17.6882 q^{84} +1.43913 q^{85} -4.42715 q^{86} -6.32077 q^{87} +0.0581061 q^{88} +18.6091 q^{89} -1.62470 q^{90} +12.9359 q^{91} -1.88240 q^{92} -7.49142 q^{93} +16.2559 q^{94} +6.14701 q^{95} +15.0128 q^{96} -11.1707 q^{97} -31.8106 q^{98} +0.350102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

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