LMFDB - Embedded newform 731.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + \cdots + 64 $ x^19 - 2x^18 - 30x^17 + 62x^16 + 365x^15 - 786x^14 - 2295x^13 + 5233x^12 + 7816x^11 - 19517x^10 - 13527x^9 + 40173x^8 + 8942x^7 - 41911x^6 + 1140x^5 + 18520x^4 - 1520x^3 - 2640x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.20570$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.20570 q^{2} +2.69039 q^{3} +2.86513 q^{4} +0.920247 q^{5} +5.93420 q^{6} -2.62293 q^{7} +1.90823 q^{8} +4.23819 q^{9} +O(q^{10})$	\(q+2.20570 q^{2} +2.69039 q^{3} +2.86513 q^{4} +0.920247 q^{5} +5.93420 q^{6} -2.62293 q^{7} +1.90823 q^{8} +4.23819 q^{9} +2.02979 q^{10} -3.87012 q^{11} +7.70832 q^{12} +0.665188 q^{13} -5.78540 q^{14} +2.47582 q^{15} -1.52127 q^{16} +1.00000 q^{17} +9.34820 q^{18} +1.11673 q^{19} +2.63663 q^{20} -7.05669 q^{21} -8.53634 q^{22} +9.12196 q^{23} +5.13388 q^{24} -4.15314 q^{25} +1.46721 q^{26} +3.33121 q^{27} -7.51503 q^{28} -3.52319 q^{29} +5.46094 q^{30} +4.39190 q^{31} -7.17194 q^{32} -10.4121 q^{33} +2.20570 q^{34} -2.41374 q^{35} +12.1430 q^{36} -11.2290 q^{37} +2.46318 q^{38} +1.78961 q^{39} +1.75604 q^{40} +7.18302 q^{41} -15.5650 q^{42} -1.00000 q^{43} -11.0884 q^{44} +3.90018 q^{45} +20.1204 q^{46} -4.91183 q^{47} -4.09282 q^{48} -0.120264 q^{49} -9.16061 q^{50} +2.69039 q^{51} +1.90585 q^{52} +2.14763 q^{53} +7.34767 q^{54} -3.56146 q^{55} -5.00515 q^{56} +3.00444 q^{57} -7.77112 q^{58} -12.5846 q^{59} +7.09357 q^{60} +14.3919 q^{61} +9.68723 q^{62} -11.1165 q^{63} -12.7766 q^{64} +0.612138 q^{65} -22.9661 q^{66} +9.51977 q^{67} +2.86513 q^{68} +24.5416 q^{69} -5.32400 q^{70} -6.27249 q^{71} +8.08745 q^{72} +3.62621 q^{73} -24.7680 q^{74} -11.1736 q^{75} +3.19958 q^{76} +10.1510 q^{77} +3.94736 q^{78} -6.08690 q^{79} -1.39995 q^{80} -3.75232 q^{81} +15.8436 q^{82} +5.14989 q^{83} -20.2184 q^{84} +0.920247 q^{85} -2.20570 q^{86} -9.47876 q^{87} -7.38508 q^{88} +2.88153 q^{89} +8.60265 q^{90} -1.74474 q^{91} +26.1356 q^{92} +11.8159 q^{93} -10.8340 q^{94} +1.02767 q^{95} -19.2953 q^{96} +3.05018 q^{97} -0.265268 q^{98} -16.4023 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * 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 $

$2$	2.20570	1.55967	0.779834	−	0.625986i	$-0.215303\pi$
$2$	2.20570	1.55967	0.779834	+	0.625986i	$0.215303\pi$
$3$	2.69039	1.55330	0.776648	−	0.629935i	$-0.216918\pi$
$3$	2.69039	1.55330	0.776648	+	0.629935i	$0.216918\pi$
$4$	2.86513	1.43257
$5$	0.920247	0.411547	0.205774	−	0.978600i	$-0.434029\pi$
$5$	0.920247	0.411547	0.205774	+	0.978600i	$0.434029\pi$
$6$	5.93420	2.42263
$7$	−2.62293	−0.991372	−0.495686	−	0.868502i	$-0.665083\pi$
$7$	−2.62293	−0.991372	−0.495686	+	0.868502i	$0.665083\pi$
$8$	1.90823	0.674662
$9$	4.23819	1.41273
$10$	2.02979	0.641877
$11$	−3.87012	−1.16688	−0.583442	−	0.812155i	$-0.698294\pi$
$11$	−3.87012	−1.16688	−0.583442	+	0.812155i	$0.698294\pi$
$12$	7.70832	2.22520
$13$	0.665188	0.184490	0.0922450	−	0.995736i	$-0.470596\pi$
$13$	0.665188	0.184490	0.0922450	+	0.995736i	$0.470596\pi$
$14$	−5.78540	−1.54621
$15$	2.47582	0.639255
$16$	−1.52127	−0.380318
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	9.34820	2.20339
$19$	1.11673	0.256195	0.128098	−	0.991762i	$-0.459113\pi$
$19$	1.11673	0.256195	0.128098	+	0.991762i	$0.459113\pi$
$20$	2.63663	0.589569
$21$	−7.05669	−1.53990
$22$	−8.53634	−1.81995
$23$	9.12196	1.90206	0.951030	−	0.309098i	$-0.100027\pi$
$23$	9.12196	1.90206	0.951030	+	0.309098i	$0.100027\pi$
$24$	5.13388	1.04795
$25$	−4.15314	−0.830629
$26$	1.46721	0.287743
$27$	3.33121	0.641092
$28$	−7.51503	−1.42021
$29$	−3.52319	−0.654241	−0.327120	−	0.944983i	$-0.606078\pi$
$29$	−3.52319	−0.654241	−0.327120	+	0.944983i	$0.606078\pi$
$30$	5.46094	0.997026
$31$	4.39190	0.788808	0.394404	−	0.918937i	$-0.370951\pi$
$31$	4.39190	0.788808	0.394404	+	0.918937i	$0.370951\pi$
$32$	−7.17194	−1.26783
$33$	−10.4121	−1.81252
$34$	2.20570	0.378275
$35$	−2.41374	−0.407997
$36$	12.1430	2.02383
$37$	−11.2290	−1.84604	−0.923022	−	0.384748i	$-0.874288\pi$
$37$	−11.2290	−1.84604	−0.923022	+	0.384748i	$0.874288\pi$
$38$	2.46318	0.399580
$39$	1.78961	0.286568
$40$	1.75604	0.277655
$41$	7.18302	1.12180	0.560900	−	0.827884i	$-0.310455\pi$
$41$	7.18302	1.12180	0.560900	+	0.827884i	$0.310455\pi$
$42$	−15.5650	−2.40173
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−11.0884	−1.67164
$45$	3.90018	0.581405
$46$	20.1204	2.96658
$47$	−4.91183	−0.716464	−0.358232	−	0.933633i	$-0.616620\pi$
$47$	−4.91183	−0.716464	−0.358232	+	0.933633i	$0.616620\pi$
$48$	−4.09282	−0.590747
$49$	−0.120264	−0.0171806
$50$	−9.16061	−1.29551
$51$	2.69039	0.376730
$52$	1.90585	0.264294
$53$	2.14763	0.294999	0.147500	−	0.989062i	$-0.452877\pi$
$53$	2.14763	0.294999	0.147500	+	0.989062i	$0.452877\pi$
$54$	7.34767	0.999891
$55$	−3.56146	−0.480228
$56$	−5.00515	−0.668841
$57$	3.00444	0.397947
$58$	−7.77112	−1.02040
$59$	−12.5846	−1.63837	−0.819186	−	0.573528i	$-0.805574\pi$
$59$	−12.5846	−1.63837	−0.819186	+	0.573528i	$0.805574\pi$
$60$	7.09357	0.915775
$61$	14.3919	1.84269	0.921346	−	0.388743i	$-0.127091\pi$
$61$	14.3919	1.84269	0.921346	+	0.388743i	$0.127091\pi$
$62$	9.68723	1.23028
$63$	−11.1165	−1.40054
$64$	−12.7766	−1.59708
$65$	0.612138	0.0759264
$66$	−22.9661	−2.82693
$67$	9.51977	1.16302	0.581512	−	0.813538i	$-0.302461\pi$
$67$	9.51977	1.16302	0.581512	+	0.813538i	$0.302461\pi$
$68$	2.86513	0.347449
$69$	24.5416	2.95446
$70$	−5.32400	−0.636340
$71$	−6.27249	−0.744407	−0.372204	−	0.928151i	$-0.621398\pi$
$71$	−6.27249	−0.744407	−0.372204	+	0.928151i	$0.621398\pi$
$72$	8.08745	0.953115
$73$	3.62621	0.424416	0.212208	−	0.977225i	$-0.431935\pi$
$73$	3.62621	0.424416	0.212208	+	0.977225i	$0.431935\pi$
$74$	−24.7680	−2.87922
$75$	−11.1736	−1.29021
$76$	3.19958	0.367017
$77$	10.1510	1.15682
$78$	3.94736	0.446951
$79$	−6.08690	−0.684830	−0.342415	−	0.939549i	$-0.611245\pi$
$79$	−6.08690	−0.684830	−0.342415	+	0.939549i	$0.611245\pi$
$80$	−1.39995	−0.156519
$81$	−3.75232	−0.416924
$82$	15.8436	1.74964
$83$	5.14989	0.565274	0.282637	−	0.959227i	$-0.408791\pi$
$83$	5.14989	0.565274	0.282637	+	0.959227i	$0.408791\pi$
$84$	−20.2184	−2.20600
$85$	0.920247	0.0998149
$86$	−2.20570	−0.237847
$87$	−9.47876	−1.01623
$88$	−7.38508	−0.787252
$89$	2.88153	0.305442	0.152721	−	0.988269i	$-0.451196\pi$
$89$	2.88153	0.305442	0.152721	+	0.988269i	$0.451196\pi$
$90$	8.60265	0.906799
$91$	−1.74474	−0.182898
$92$	26.1356	2.72483
$93$	11.8159	1.22525
$94$	−10.8340	−1.11745
$95$	1.02767	0.105436
$96$	−19.2953	−1.96932
$97$	3.05018	0.309699	0.154850	−	0.987938i	$-0.450511\pi$
$97$	3.05018	0.309699	0.154850	+	0.987938i	$0.450511\pi$
$98$	−0.265268	−0.0267961
$99$	−16.4023	−1.64849
$100$	−11.8993	−1.18993
$101$	8.59071	0.854808	0.427404	−	0.904061i	$-0.359428\pi$
$101$	8.59071	0.854808	0.427404	+	0.904061i	$0.359428\pi$
$102$	5.93420	0.587574
$103$	9.75040	0.960736	0.480368	−	0.877067i	$-0.340503\pi$
$103$	9.75040	0.960736	0.480368	+	0.877067i	$0.340503\pi$
$104$	1.26933	0.124468
$105$	−6.49390	−0.633740
$106$	4.73703	0.460101
$107$	11.9559	1.15582	0.577911	−	0.816100i	$-0.303868\pi$
$107$	11.9559	1.15582	0.577911	+	0.816100i	$0.303868\pi$
$108$	9.54437	0.918407
$109$	6.80297	0.651606	0.325803	−	0.945438i	$-0.394365\pi$
$109$	6.80297	0.651606	0.325803	+	0.945438i	$0.394365\pi$
$110$	−7.85554	−0.748996
$111$	−30.2105	−2.86745
$112$	3.99019	0.377037
$113$	12.4861	1.17459	0.587297	−	0.809371i	$-0.300192\pi$
$113$	12.4861	1.17459	0.587297	+	0.809371i	$0.300192\pi$
$114$	6.62690	0.620666
$115$	8.39446	0.782788
$116$	−10.0944	−0.937244
$117$	2.81919	0.260635
$118$	−27.7578	−2.55532
$119$	−2.62293	−0.240443
$120$	4.72444	0.431281
$121$	3.97780	0.361618
$122$	31.7443	2.87399
$123$	19.3251	1.74249
$124$	12.5834	1.13002
$125$	−8.42316	−0.753390
$126$	−24.5196	−2.18438
$127$	−16.1511	−1.43318	−0.716590	−	0.697494i	$-0.754298\pi$
$127$	−16.1511	−1.43318	−0.716590	+	0.697494i	$0.754298\pi$
$128$	−13.8376	−1.22308
$129$	−2.69039	−0.236875
$130$	1.35020	0.118420
$131$	5.46851	0.477786	0.238893	−	0.971046i	$-0.423216\pi$
$131$	5.46851	0.477786	0.238893	+	0.971046i	$0.423216\pi$
$132$	−29.8321	−2.59655
$133$	−2.92910	−0.253985
$134$	20.9978	1.81393
$135$	3.06554	0.263840
$136$	1.90823	0.163629
$137$	0.469355	0.0400997	0.0200499	−	0.999799i	$-0.493618\pi$
$137$	0.469355	0.0400997	0.0200499	+	0.999799i	$0.493618\pi$
$138$	54.1316	4.60799
$139$	3.89763	0.330593	0.165296	−	0.986244i	$-0.447142\pi$
$139$	3.89763	0.330593	0.165296	+	0.986244i	$0.447142\pi$
$140$	−6.91569	−0.584482
$141$	−13.2147	−1.11288
$142$	−13.8353	−1.16103
$143$	−2.57436	−0.215278
$144$	−6.44745	−0.537287
$145$	−3.24221	−0.269251
$146$	7.99835	0.661948
$147$	−0.323558	−0.0266866
$148$	−32.1727	−2.64458
$149$	20.1938	1.65434	0.827171	−	0.561950i	$-0.189949\pi$
$149$	20.1938	1.65434	0.827171	+	0.561950i	$0.189949\pi$
$150$	−24.6456	−2.01231
$151$	3.94323	0.320895	0.160448	−	0.987044i	$-0.448706\pi$
$151$	3.94323	0.320895	0.160448	+	0.987044i	$0.448706\pi$
$152$	2.13098	0.172845
$153$	4.23819	0.342637
$154$	22.3902	1.80425
$155$	4.04163	0.324632
$156$	5.12749	0.410528
$157$	−1.25951	−0.100520	−0.0502601	−	0.998736i	$-0.516005\pi$
$157$	−1.25951	−0.100520	−0.0502601	+	0.998736i	$0.516005\pi$
$158$	−13.4259	−1.06811
$159$	5.77795	0.458221
$160$	−6.59996	−0.521773
$161$	−23.9262	−1.88565
$162$	−8.27650	−0.650263
$163$	−10.5658	−0.827574	−0.413787	−	0.910374i	$-0.635794\pi$
$163$	−10.5658	−0.827574	−0.413787	+	0.910374i	$0.635794\pi$
$164$	20.5803	1.60705
$165$	−9.58172	−0.745936
$166$	11.3591	0.881640
$167$	−5.63840	−0.436312	−0.218156	−	0.975914i	$-0.570004\pi$
$167$	−5.63840	−0.436312	−0.218156	+	0.975914i	$0.570004\pi$
$168$	−13.4658	−1.03891
$169$	−12.5575	−0.965963
$170$	2.02979	0.155678
$171$	4.73291	0.361935
$172$	−2.86513	−0.218464
$173$	−3.08770	−0.234753	−0.117377	−	0.993087i	$-0.537448\pi$
$173$	−3.08770	−0.234753	−0.117377	+	0.993087i	$0.537448\pi$
$174$	−20.9073	−1.58498
$175$	10.8934	0.823463
$176$	5.88751	0.443788
$177$	−33.8574	−2.54488
$178$	6.35581	0.476388
$179$	−1.89167	−0.141390	−0.0706951	−	0.997498i	$-0.522522\pi$
$179$	−1.89167	−0.141390	−0.0706951	+	0.997498i	$0.522522\pi$
$180$	11.1745	0.832902
$181$	18.8259	1.39932	0.699660	−	0.714476i	$-0.253335\pi$
$181$	18.8259	1.39932	0.699660	+	0.714476i	$0.253335\pi$
$182$	−3.84838	−0.285261
$183$	38.7198	2.86225
$184$	17.4068	1.28325
$185$	−10.3335	−0.759734
$186$	26.0624	1.91099
$187$	−3.87012	−0.283011
$188$	−14.0730	−1.02638
$189$	−8.73752	−0.635561
$190$	2.26673	0.164446
$191$	6.01866	0.435495	0.217748	−	0.976005i	$-0.430129\pi$
$191$	6.01866	0.435495	0.217748	+	0.976005i	$0.430129\pi$
$192$	−34.3741	−2.48074
$193$	−5.08719	−0.366184	−0.183092	−	0.983096i	$-0.558611\pi$
$193$	−5.08719	−0.366184	−0.183092	+	0.983096i	$0.558611\pi$
$194$	6.72781	0.483028
$195$	1.64689	0.117936
$196$	−0.344574	−0.0246124
$197$	6.36293	0.453340	0.226670	−	0.973972i	$-0.427216\pi$
$197$	6.36293	0.453340	0.226670	+	0.973972i	$0.427216\pi$
$198$	−36.1786	−2.57110
$199$	14.3178	1.01496	0.507482	−	0.861662i	$-0.330576\pi$
$199$	14.3178	1.01496	0.507482	+	0.861662i	$0.330576\pi$
$200$	−7.92516	−0.560393
$201$	25.6119	1.80652
$202$	18.9486	1.33322
$203$	9.24107	0.648596
$204$	7.70832	0.539691
$205$	6.61016	0.461673
$206$	21.5065	1.49843
$207$	38.6606	2.68710
$208$	−1.01193	−0.0701650
$209$	−4.32187	−0.298950
$210$	−14.3236	−0.988424
$211$	−22.9693	−1.58127	−0.790637	−	0.612286i	$-0.790250\pi$
$211$	−22.9693	−1.58127	−0.790637	+	0.612286i	$0.790250\pi$
$212$	6.15324	0.422606
$213$	−16.8754	−1.15629
$214$	26.3712	1.80270
$215$	−0.920247	−0.0627604
$216$	6.35672	0.432520
$217$	−11.5196	−0.782003
$218$	15.0053	1.01629
$219$	9.75591	0.659243
$220$	−10.2041	−0.687959
$221$	0.665188	0.0447454
$222$	−66.6354	−4.47228
$223$	19.8451	1.32893	0.664463	−	0.747321i	$-0.268660\pi$
$223$	19.8451	1.32893	0.664463	+	0.747321i	$0.268660\pi$
$224$	18.8115	1.25689
$225$	−17.6018	−1.17345
$226$	27.5407	1.83198
$227$	−24.1209	−1.60096	−0.800480	−	0.599359i	$-0.795422\pi$
$227$	−24.1209	−1.60096	−0.800480	+	0.599359i	$0.795422\pi$
$228$	8.60812	0.570086
$229$	−2.64852	−0.175019	−0.0875095	−	0.996164i	$-0.527891\pi$
$229$	−2.64852	−0.175019	−0.0875095	+	0.996164i	$0.527891\pi$
$230$	18.5157	1.22089
$231$	27.3102	1.79688
$232$	−6.72307	−0.441391
$233$	−3.68977	−0.241725	−0.120863	−	0.992669i	$-0.538566\pi$
$233$	−3.68977	−0.241725	−0.120863	+	0.992669i	$0.538566\pi$
$234$	6.21831	0.406504
$235$	−4.52010	−0.294859
$236$	−36.0565	−2.34708
$237$	−16.3761	−1.06374
$238$	−5.78540	−0.375012
$239$	−26.3265	−1.70292	−0.851458	−	0.524422i	$-0.824281\pi$
$239$	−26.3265	−1.70292	−0.851458	+	0.524422i	$0.824281\pi$
$240$	−3.76641	−0.243120
$241$	−2.58610	−0.166586	−0.0832928	−	0.996525i	$-0.526544\pi$
$241$	−2.58610	−0.166586	−0.0832928	+	0.996525i	$0.526544\pi$
$242$	8.77386	0.564005
$243$	−20.0888	−1.28870
$244$	41.2347	2.63978
$245$	−0.110673	−0.00707064
$246$	42.6255	2.71770
$247$	0.742836	0.0472655
$248$	8.38076	0.532179
$249$	13.8552	0.878038
$250$	−18.5790	−1.17504
$251$	−26.3097	−1.66065	−0.830327	−	0.557276i	$-0.811846\pi$
$251$	−26.3097	−1.66065	−0.830327	+	0.557276i	$0.811846\pi$
$252$	−31.8501	−2.00637
$253$	−35.3031	−2.21948
$254$	−35.6246	−2.23529
$255$	2.47582	0.155042
$256$	−4.96842	−0.310526
$257$	−5.25622	−0.327874	−0.163937	−	0.986471i	$-0.552419\pi$
$257$	−5.25622	−0.327874	−0.163937	+	0.986471i	$0.552419\pi$
$258$	−5.93420	−0.369447
$259$	29.4529	1.83012
$260$	1.75386	0.108770
$261$	−14.9320	−0.924265
$262$	12.0619	0.745188
$263$	−7.95710	−0.490656	−0.245328	−	0.969440i	$-0.578896\pi$
$263$	−7.95710	−0.490656	−0.245328	+	0.969440i	$0.578896\pi$
$264$	−19.8687	−1.22284
$265$	1.97635	0.121406
$266$	−6.46073	−0.396133
$267$	7.75244	0.474442
$268$	27.2754	1.66611
$269$	−2.10690	−0.128460	−0.0642298	−	0.997935i	$-0.520459\pi$
$269$	−2.10690	−0.128460	−0.0642298	+	0.997935i	$0.520459\pi$
$270$	6.76168	0.411502
$271$	−11.4165	−0.693503	−0.346752	−	0.937957i	$-0.612715\pi$
$271$	−11.4165	−0.693503	−0.346752	+	0.937957i	$0.612715\pi$
$272$	−1.52127	−0.0922408
$273$	−4.69403	−0.284095
$274$	1.03526	0.0625423
$275$	16.0732	0.969248
$276$	70.3150	4.23247
$277$	18.1380	1.08981	0.544903	−	0.838499i	$-0.316567\pi$
$277$	18.1380	1.08981	0.544903	+	0.838499i	$0.316567\pi$
$278$	8.59703	0.515615
$279$	18.6137	1.11437
$280$	−4.60597	−0.275260
$281$	−26.4036	−1.57511	−0.787553	−	0.616246i	$-0.788653\pi$
$281$	−26.4036	−1.57511	−0.787553	+	0.616246i	$0.788653\pi$
$282$	−29.1478	−1.73572
$283$	9.36567	0.556731	0.278366	−	0.960475i	$-0.410207\pi$
$283$	9.36567	0.556731	0.278366	+	0.960475i	$0.410207\pi$
$284$	−17.9715	−1.06641
$285$	2.76483	0.163774
$286$	−5.67827	−0.335763
$287$	−18.8405	−1.11212
$288$	−30.3961	−1.79110
$289$	1.00000	0.0588235
$290$	−7.15136	−0.419942
$291$	8.20618	0.481055
$292$	10.3896	0.608004
$293$	18.8704	1.10242	0.551209	−	0.834367i	$-0.314167\pi$
$293$	18.8704	1.10242	0.551209	+	0.834367i	$0.314167\pi$
$294$	−0.713674	−0.0416223
$295$	−11.5809	−0.674267
$296$	−21.4276	−1.24545
$297$	−12.8922	−0.748080
$298$	44.5416	2.58023
$299$	6.06782	0.350911
$300$	−32.0138	−1.84832
$301$	2.62293	0.151183
$302$	8.69759	0.500490
$303$	23.1124	1.32777
$304$	−1.69885	−0.0974358
$305$	13.2441	0.758355
$306$	9.34820	0.534401
$307$	−30.0834	−1.71695	−0.858475	−	0.512856i	$-0.828588\pi$
$307$	−30.0834	−1.71695	−0.858475	+	0.512856i	$0.828588\pi$
$308$	29.0841	1.65722
$309$	26.2324	1.49231
$310$	8.91465	0.506318
$311$	8.85245	0.501976	0.250988	−	0.967990i	$-0.419244\pi$
$311$	8.85245	0.501976	0.250988	+	0.967990i	$0.419244\pi$
$312$	3.41500	0.193336
$313$	19.7562	1.11669	0.558343	−	0.829610i	$-0.311437\pi$
$313$	19.7562	1.11669	0.558343	+	0.829610i	$0.311437\pi$
$314$	−2.77812	−0.156778
$315$	−10.2299	−0.576389
$316$	−17.4398	−0.981065
$317$	8.72386	0.489981	0.244991	−	0.969525i	$-0.421215\pi$
$317$	8.72386	0.489981	0.244991	+	0.969525i	$0.421215\pi$
$318$	12.7445	0.714674
$319$	13.6352	0.763423
$320$	−11.7577	−0.657274
$321$	32.1661	1.79533
$322$	−52.7742	−2.94099
$323$	1.11673	0.0621365
$324$	−10.7509	−0.597272
$325$	−2.76262	−0.153243
$326$	−23.3049	−1.29074
$327$	18.3026	1.01214
$328$	13.7069	0.756835
$329$	12.8834	0.710282
$330$	−21.1345	−1.16341
$331$	−18.4410	−1.01361	−0.506804	−	0.862061i	$-0.669173\pi$
$331$	−18.4410	−1.01361	−0.506804	+	0.862061i	$0.669173\pi$
$332$	14.7551	0.809793
$333$	−47.5908	−2.60796
$334$	−12.4366	−0.680503
$335$	8.76054	0.478639
$336$	10.7352	0.585651
$337$	−4.89341	−0.266561	−0.133281	−	0.991078i	$-0.542551\pi$
$337$	−4.89341	−0.266561	−0.133281	+	0.991078i	$0.542551\pi$
$338$	−27.6982	−1.50658
$339$	33.5925	1.82449
$340$	2.63663	0.142991
$341$	−16.9972	−0.920448
$342$	10.4394	0.564499
$343$	18.6759	1.00840
$344$	−1.90823	−0.102885
$345$	22.5844	1.21590
$346$	−6.81055	−0.366138
$347$	28.5259	1.53135	0.765675	−	0.643227i	$-0.222405\pi$
$347$	28.5259	1.53135	0.765675	+	0.643227i	$0.222405\pi$
$348$	−27.1579	−1.45582
$349$	20.3227	1.08785	0.543924	−	0.839135i	$-0.316938\pi$
$349$	20.3227	1.08785	0.543924	+	0.839135i	$0.316938\pi$
$350$	24.0276	1.28433
$351$	2.21588	0.118275
$352$	27.7563	1.47941
$353$	−22.7960	−1.21331	−0.606654	−	0.794966i	$-0.707489\pi$
$353$	−22.7960	−1.21331	−0.606654	+	0.794966i	$0.707489\pi$
$354$	−74.6794	−3.96917
$355$	−5.77224	−0.306359
$356$	8.25598	0.437566
$357$	−7.05669	−0.373479
$358$	−4.17247	−0.220522
$359$	−3.85171	−0.203286	−0.101643	−	0.994821i	$-0.532410\pi$
$359$	−3.85171	−0.203286	−0.101643	+	0.994821i	$0.532410\pi$
$360$	7.44245	0.392252
$361$	−17.7529	−0.934364
$362$	41.5244	2.18248
$363$	10.7018	0.561700
$364$	−4.99891	−0.262014
$365$	3.33701	0.174667
$366$	85.4044	4.46416
$367$	−35.9372	−1.87591	−0.937954	−	0.346760i	$-0.887282\pi$
$367$	−35.9372	−1.87591	−0.937954	+	0.346760i	$0.887282\pi$
$368$	−13.8770	−0.723389
$369$	30.4430	1.58480
$370$	−22.7926	−1.18493
$371$	−5.63307	−0.292454
$372$	33.8542	1.75526
$373$	19.3152	1.00010	0.500051	−	0.865996i	$-0.333315\pi$
$373$	19.3152	1.00010	0.500051	+	0.865996i	$0.333315\pi$
$374$	−8.53634	−0.441403
$375$	−22.6616	−1.17024
$376$	−9.37290	−0.483370
$377$	−2.34359	−0.120701
$378$	−19.2724	−0.991265
$379$	−34.4922	−1.77174	−0.885872	−	0.463931i	$-0.846439\pi$
$379$	−34.4922	−1.77174	−0.885872	+	0.463931i	$0.846439\pi$
$380$	2.94441	0.151045
$381$	−43.4528	−2.22615
$382$	13.2754	0.679228
$383$	−32.7330	−1.67258	−0.836289	−	0.548289i	$-0.815279\pi$
$383$	−32.7330	−1.67258	−0.836289	+	0.548289i	$0.815279\pi$
$384$	−37.2286	−1.89981
$385$	9.34146	0.476085
$386$	−11.2209	−0.571126
$387$	−4.23819	−0.215439
$388$	8.73919	0.443665
$389$	−25.6485	−1.30043	−0.650216	−	0.759749i	$-0.725322\pi$
$389$	−25.6485	−1.30043	−0.650216	+	0.759749i	$0.725322\pi$
$390$	3.63255	0.183941
$391$	9.12196	0.461317
$392$	−0.229492	−0.0115911
$393$	14.7124	0.742143
$394$	14.0347	0.707060
$395$	−5.60145	−0.281840
$396$	−46.9948	−2.36158
$397$	17.0057	0.853493	0.426746	−	0.904371i	$-0.359660\pi$
$397$	17.0057	0.853493	0.426746	+	0.904371i	$0.359660\pi$
$398$	31.5809	1.58301
$399$	−7.88041	−0.394514
$400$	6.31807	0.315904
$401$	9.39552	0.469190	0.234595	−	0.972093i	$-0.424624\pi$
$401$	9.39552	0.469190	0.234595	+	0.972093i	$0.424624\pi$
$402$	56.4922	2.81758
$403$	2.92144	0.145527
$404$	24.6135	1.22457
$405$	−3.45306	−0.171584
$406$	20.3831	1.01160
$407$	43.4577	2.15412
$408$	5.13388	0.254165
$409$	23.4574	1.15989	0.579946	−	0.814655i	$-0.303074\pi$
$409$	23.4574	1.15989	0.579946	+	0.814655i	$0.303074\pi$
$410$	14.5801	0.720058
$411$	1.26275	0.0622868
$412$	27.9362	1.37632
$413$	33.0084	1.62424
$414$	85.2739	4.19098
$415$	4.73917	0.232637
$416$	−4.77069	−0.233902
$417$	10.4861	0.513509
$418$	−9.53278	−0.466264
$419$	35.5123	1.73489	0.867444	−	0.497535i	$-0.165761\pi$
$419$	35.5123	1.73489	0.867444	+	0.497535i	$0.165761\pi$
$420$	−18.6059	−0.907875
$421$	36.8845	1.79764	0.898821	−	0.438316i	$-0.144425\pi$
$421$	36.8845	1.79764	0.898821	+	0.438316i	$0.144425\pi$
$422$	−50.6636	−2.46626
$423$	−20.8173	−1.01217
$424$	4.09817	0.199025
$425$	−4.15314	−0.201457
$426$	−37.2222	−1.80342
$427$	−37.7488	−1.82679
$428$	34.2553	1.65579
$429$	−6.92602	−0.334391
$430$	−2.02979	−0.0978854
$431$	26.3057	1.26710	0.633549	−	0.773702i	$-0.281597\pi$
$431$	26.3057	1.26710	0.633549	+	0.773702i	$0.281597\pi$
$432$	−5.06769	−0.243819
$433$	−25.0317	−1.20295	−0.601473	−	0.798893i	$-0.705419\pi$
$433$	−25.0317	−1.20295	−0.601473	+	0.798893i	$0.705419\pi$
$434$	−25.4089	−1.21967
$435$	−8.72280	−0.418226
$436$	19.4914	0.933470
$437$	10.1868	0.487299
$438$	21.5187	1.02820
$439$	15.8247	0.755271	0.377636	−	0.925954i	$-0.376737\pi$
$439$	15.8247	0.755271	0.377636	+	0.925954i	$0.376737\pi$
$440$	−6.79610	−0.323991
$441$	−0.509704	−0.0242716
$442$	1.46721	0.0697880
$443$	−16.1474	−0.767186	−0.383593	−	0.923502i	$-0.625313\pi$
$443$	−16.1474	−0.767186	−0.383593	+	0.923502i	$0.625313\pi$
$444$	−86.5571	−4.10782
$445$	2.65172	0.125704
$446$	43.7725	2.07269
$447$	54.3292	2.56968
$448$	33.5122	1.58330
$449$	−3.81476	−0.180029	−0.0900147	−	0.995940i	$-0.528691\pi$
$449$	−3.81476	−0.180029	−0.0900147	+	0.995940i	$0.528691\pi$
$450$	−38.8244	−1.83020
$451$	−27.7991	−1.30901
$452$	35.7744	1.68269
$453$	10.6088	0.498445
$454$	−53.2036	−2.49697
$455$	−1.60559	−0.0752713
$456$	5.73316	0.268480
$457$	7.27840	0.340469	0.170235	−	0.985404i	$-0.445547\pi$
$457$	7.27840	0.340469	0.170235	+	0.985404i	$0.445547\pi$
$458$	−5.84185	−0.272972
$459$	3.33121	0.155488
$460$	24.0513	1.12140
$461$	−12.9411	−0.602725	−0.301362	−	0.953510i	$-0.597441\pi$
$461$	−12.9411	−0.602725	−0.301362	+	0.953510i	$0.597441\pi$
$462$	60.2382	2.80254
$463$	20.6852	0.961321	0.480661	−	0.876907i	$-0.340397\pi$
$463$	20.6852	0.961321	0.480661	+	0.876907i	$0.340397\pi$
$464$	5.35974	0.248820
$465$	10.8736	0.504249
$466$	−8.13855	−0.377011
$467$	−15.5468	−0.719419	−0.359710	−	0.933064i	$-0.617124\pi$
$467$	−15.5468	−0.719419	−0.359710	+	0.933064i	$0.617124\pi$
$468$	8.07737	0.373377
$469$	−24.9696	−1.15299
$470$	−9.97000	−0.459882
$471$	−3.38858	−0.156138
$472$	−24.0143	−1.10535
$473$	3.87012	0.177948
$474$	−36.1209	−1.65909
$475$	−4.63794	−0.212803
$476$	−7.51503	−0.344451
$477$	9.10205	0.416754
$478$	−58.0684	−2.65599
$479$	−30.6734	−1.40150	−0.700752	−	0.713405i	$-0.747152\pi$
$479$	−30.6734	−1.40150	−0.700752	+	0.713405i	$0.747152\pi$
$480$	−17.7565	−0.810468
$481$	−7.46943	−0.340577
$482$	−5.70418	−0.259818
$483$	−64.3708	−2.92897
$484$	11.3969	0.518043
$485$	2.80692	0.127456
$486$	−44.3100	−2.00994
$487$	5.78159	0.261989	0.130994	−	0.991383i	$-0.458183\pi$
$487$	5.78159	0.261989	0.130994	+	0.991383i	$0.458183\pi$
$488$	27.4631	1.24319
$489$	−28.4260	−1.28547
$490$	−0.244112	−0.0110279
$491$	10.4145	0.470002	0.235001	−	0.971995i	$-0.424491\pi$
$491$	10.4145	0.470002	0.235001	+	0.971995i	$0.424491\pi$
$492$	55.3691	2.49623
$493$	−3.52319	−0.158677
$494$	1.63848	0.0737185
$495$	−15.0942	−0.678432
$496$	−6.68128	−0.299998
$497$	16.4523	0.737985
$498$	30.5605	1.36945
$499$	5.50618	0.246490	0.123245	−	0.992376i	$-0.460670\pi$
$499$	5.50618	0.246490	0.123245	+	0.992376i	$0.460670\pi$
$500$	−24.1335	−1.07928
$501$	−15.1695	−0.677723
$502$	−58.0315	−2.59007
$503$	21.1804	0.944386	0.472193	−	0.881495i	$-0.343463\pi$
$503$	21.1804	0.944386	0.472193	+	0.881495i	$0.343463\pi$
$504$	−21.2128	−0.944892
$505$	7.90558	0.351794
$506$	−77.8681	−3.46166
$507$	−33.7846	−1.50043
$508$	−46.2751	−2.05313
$509$	19.5342	0.865840	0.432920	−	0.901432i	$-0.357483\pi$
$509$	19.5342	0.865840	0.432920	+	0.901432i	$0.357483\pi$
$510$	5.46094	0.241814
$511$	−9.51127	−0.420754
$512$	16.7164	0.738766
$513$	3.72006	0.164245
$514$	−11.5937	−0.511375
$515$	8.97278	0.395388
$516$	−7.70832	−0.339340
$517$	19.0093	0.836030
$518$	64.9645	2.85438
$519$	−8.30711	−0.364642
$520$	1.16810	0.0512246
$521$	−14.9199	−0.653652	−0.326826	−	0.945084i	$-0.605979\pi$
$521$	−14.9199	−0.653652	−0.326826	+	0.945084i	$0.605979\pi$
$522$	−32.9355	−1.44155
$523$	0.250290	0.0109444	0.00547221	−	0.999985i	$-0.498258\pi$
$523$	0.250290	0.0109444	0.00547221	+	0.999985i	$0.498258\pi$
$524$	15.6680	0.684460
$525$	29.3074	1.27908
$526$	−17.5510	−0.765260
$527$	4.39190	0.191314
$528$	15.8397	0.689334
$529$	60.2102	2.61783
$530$	4.35924	0.189353
$531$	−53.3358	−2.31458
$532$	−8.39226	−0.363851
$533$	4.77806	0.206961
$534$	17.0996	0.739972
$535$	11.0024	0.475675
$536$	18.1659	0.784648
$537$	−5.08933	−0.219621
$538$	−4.64719	−0.200355
$539$	0.465437	0.0200478
$540$	8.78318	0.377968
$541$	10.3525	0.445087	0.222544	−	0.974923i	$-0.428564\pi$
$541$	10.3525	0.445087	0.222544	+	0.974923i	$0.428564\pi$
$542$	−25.1814	−1.08164
$543$	50.6490	2.17356
$544$	−7.17194	−0.307495
$545$	6.26041	0.268167
$546$	−10.3536	−0.443095
$547$	31.6358	1.35265	0.676325	−	0.736604i	$-0.263572\pi$
$547$	31.6358	1.35265	0.676325	+	0.736604i	$0.263572\pi$
$548$	1.34477	0.0574456
$549$	60.9956	2.60323
$550$	35.4526	1.51171
$551$	−3.93445	−0.167613
$552$	46.8311	1.99326
$553$	15.9655	0.678921
$554$	40.0070	1.69974
$555$	−27.8011	−1.18009
$556$	11.1672	0.473597
$557$	14.5434	0.616223	0.308112	−	0.951350i	$-0.400303\pi$
$557$	14.5434	0.616223	0.308112	+	0.951350i	$0.400303\pi$
$558$	41.0563	1.73805
$559$	−0.665188	−0.0281345
$560$	3.67196	0.155169
$561$	−10.4121	−0.439600
$562$	−58.2386	−2.45665
$563$	−2.99155	−0.126079	−0.0630395	−	0.998011i	$-0.520079\pi$
$563$	−2.99155	−0.126079	−0.0630395	+	0.998011i	$0.520079\pi$
$564$	−37.8620	−1.59428
$565$	11.4903	0.483401
$566$	20.6579	0.868317
$567$	9.84204	0.413327
$568$	−11.9694	−0.502223
$569$	0.218643	0.00916599	0.00458300	−	0.999989i	$-0.498541\pi$
$569$	0.218643	0.00916599	0.00458300	+	0.999989i	$0.498541\pi$
$570$	6.09839	0.255433
$571$	−12.1229	−0.507329	−0.253665	−	0.967292i	$-0.581636\pi$
$571$	−12.1229	−0.507329	−0.253665	+	0.967292i	$0.581636\pi$
$572$	−7.37588	−0.308401
$573$	16.1925	0.676453
$574$	−41.5566	−1.73454
$575$	−37.8848	−1.57991
$576$	−54.1498	−2.25624
$577$	−18.3669	−0.764626	−0.382313	−	0.924033i	$-0.624872\pi$
$577$	−18.3669	−0.764626	−0.382313	+	0.924033i	$0.624872\pi$
$578$	2.20570	0.0917452
$579$	−13.6865	−0.568793
$580$	−9.28937	−0.385720
$581$	−13.5078	−0.560397
$582$	18.1004	0.750286
$583$	−8.31157	−0.344230
$584$	6.91964	0.286337
$585$	2.59436	0.107263
$586$	41.6225	1.71941
$587$	−44.1423	−1.82195	−0.910975	−	0.412462i	$-0.864669\pi$
$587$	−44.1423	−1.82195	−0.910975	+	0.412462i	$0.864669\pi$
$588$	−0.927037	−0.0382304
$589$	4.90456	0.202089
$590$	−25.5441	−1.05163
$591$	17.1188	0.704171
$592$	17.0825	0.702084
$593$	−30.2235	−1.24113	−0.620565	−	0.784155i	$-0.713097\pi$
$593$	−30.2235	−1.24113	−0.620565	+	0.784155i	$0.713097\pi$
$594$	−28.4363	−1.16676
$595$	−2.41374	−0.0989537
$596$	57.8580	2.36996
$597$	38.5205	1.57654
$598$	13.3838	0.547305
$599$	−11.2957	−0.461530	−0.230765	−	0.973009i	$-0.574123\pi$
$599$	−11.2957	−0.461530	−0.230765	+	0.973009i	$0.574123\pi$
$600$	−21.3218	−0.870457
$601$	−6.94507	−0.283295	−0.141648	−	0.989917i	$-0.545240\pi$
$601$	−6.94507	−0.283295	−0.141648	+	0.989917i	$0.545240\pi$
$602$	5.78540	0.235795
$603$	40.3466	1.64304
$604$	11.2979	0.459704
$605$	3.66056	0.148823
$606$	50.9790	2.07088
$607$	39.6061	1.60756	0.803781	−	0.594925i	$-0.202818\pi$
$607$	39.6061	1.60756	0.803781	+	0.594925i	$0.202818\pi$
$608$	−8.00912	−0.324813
$609$	24.8621	1.00746
$610$	29.2126	1.18278
$611$	−3.26729	−0.132180
$612$	12.1430	0.490851
$613$	17.7392	0.716478	0.358239	−	0.933630i	$-0.383377\pi$
$613$	17.7392	0.716478	0.358239	+	0.933630i	$0.383377\pi$
$614$	−66.3551	−2.67787
$615$	17.7839	0.717116
$616$	19.3705	0.780460
$617$	−45.2576	−1.82200	−0.911001	−	0.412405i	$-0.864689\pi$
$617$	−45.2576	−1.82200	−0.911001	+	0.412405i	$0.864689\pi$
$618$	57.8609	2.32751
$619$	5.45494	0.219253	0.109626	−	0.993973i	$-0.465035\pi$
$619$	5.45494	0.219253	0.109626	+	0.993973i	$0.465035\pi$
$620$	11.5798	0.465057
$621$	30.3872	1.21940
$622$	19.5259	0.782917
$623$	−7.55804	−0.302807
$624$	−2.72249	−0.108987
$625$	13.0143	0.520573
$626$	43.5763	1.74166
$627$	−11.6275	−0.464358
$628$	−3.60868	−0.144002
$629$	−11.2290	−0.447731
$630$	−22.5641	−0.898976
$631$	29.9888	1.19384	0.596918	−	0.802302i	$-0.296392\pi$
$631$	29.9888	1.19384	0.596918	+	0.802302i	$0.296392\pi$
$632$	−11.6152	−0.462028
$633$	−61.7964	−2.45619
$634$	19.2423	0.764208
$635$	−14.8630	−0.589821
$636$	16.5546	0.656433
$637$	−0.0799985	−0.00316966
$638$	30.0752	1.19069
$639$	−26.5840	−1.05165
$640$	−12.7340	−0.503357
$641$	−19.0311	−0.751682	−0.375841	−	0.926684i	$-0.622646\pi$
$641$	−19.0311	−0.751682	−0.375841	+	0.926684i	$0.622646\pi$
$642$	70.9488	2.80013
$643$	23.8762	0.941586	0.470793	−	0.882244i	$-0.343968\pi$
$643$	23.8762	0.941586	0.470793	+	0.882244i	$0.343968\pi$
$644$	−68.5518	−2.70132
$645$	−2.47582	−0.0974854
$646$	2.46318	0.0969124
$647$	−13.0899	−0.514617	−0.257308	−	0.966329i	$-0.582836\pi$
$647$	−13.0899	−0.514617	−0.257308	+	0.966329i	$0.582836\pi$
$648$	−7.16029	−0.281283
$649$	48.7038	1.91179
$650$	−6.09353	−0.239008
$651$	−30.9923	−1.21468
$652$	−30.2723	−1.18555
$653$	−17.2251	−0.674071	−0.337035	−	0.941492i	$-0.609424\pi$
$653$	−17.2251	−0.674071	−0.337035	+	0.941492i	$0.609424\pi$
$654$	40.3702	1.57860
$655$	5.03238	0.196631
$656$	−10.9273	−0.426641
$657$	15.3686	0.599585
$658$	28.4169	1.10781
$659$	−17.3539	−0.676011	−0.338006	−	0.941144i	$-0.609752\pi$
$659$	−17.3539	−0.676011	−0.338006	+	0.941144i	$0.609752\pi$
$660$	−27.4529	−1.06860
$661$	−16.2079	−0.630416	−0.315208	−	0.949023i	$-0.602074\pi$
$661$	−16.2079	−0.630416	−0.315208	+	0.949023i	$0.602074\pi$
$662$	−40.6754	−1.58089
$663$	1.78961	0.0695029
$664$	9.82718	0.381369
$665$	−2.69550	−0.104527
$666$	−104.971	−4.06756
$667$	−32.1384	−1.24441
$668$	−16.1548	−0.625047
$669$	53.3911	2.06422
$670$	19.3232	0.746519
$671$	−55.6983	−2.15021
$672$	50.6102	1.95233
$673$	34.9640	1.34776	0.673882	−	0.738839i	$-0.264626\pi$
$673$	34.9640	1.34776	0.673882	+	0.738839i	$0.264626\pi$
$674$	−10.7934	−0.415747
$675$	−13.8350	−0.532510
$676$	−35.9790	−1.38381
$677$	−31.8809	−1.22528	−0.612642	−	0.790360i	$-0.709893\pi$
$677$	−31.8809	−1.22528	−0.612642	+	0.790360i	$0.709893\pi$
$678$	74.0951	2.84560
$679$	−8.00041	−0.307027
$680$	1.75604	0.0673412
$681$	−64.8946	−2.48677
$682$	−37.4907	−1.43559
$683$	−23.1722	−0.886661	−0.443330	−	0.896358i	$-0.646203\pi$
$683$	−23.1722	−0.886661	−0.443330	+	0.896358i	$0.646203\pi$
$684$	13.5604	0.518496
$685$	0.431923	0.0165029
$686$	41.1936	1.57278
$687$	−7.12554	−0.271856
$688$	1.52127	0.0579980
$689$	1.42858	0.0544244
$690$	49.8144	1.89640
$691$	−2.50611	−0.0953369	−0.0476684	−	0.998863i	$-0.515179\pi$
$691$	−2.50611	−0.0953369	−0.0476684	+	0.998863i	$0.515179\pi$
$692$	−8.84667	−0.336300
$693$	43.0220	1.63427
$694$	62.9197	2.38840
$695$	3.58679	0.136055
$696$	−18.0877	−0.685611
$697$	7.18302	0.272076
$698$	44.8258	1.69668
$699$	−9.92693	−0.375471
$700$	31.2110	1.17967
$701$	−7.68515	−0.290264	−0.145132	−	0.989412i	$-0.546361\pi$
$701$	−7.68515	−0.290264	−0.145132	+	0.989412i	$0.546361\pi$
$702$	4.88758	0.184470
$703$	−12.5398	−0.472948
$704$	49.4471	1.86361
$705$	−12.1608	−0.458003
$706$	−50.2812	−1.89236
$707$	−22.5328	−0.847433
$708$	−97.0060	−3.64571
$709$	−36.5025	−1.37088	−0.685439	−	0.728130i	$-0.740390\pi$
$709$	−36.5025	−1.37088	−0.685439	+	0.728130i	$0.740390\pi$
$710$	−12.7319	−0.477818
$711$	−25.7974	−0.967480
$712$	5.49863	0.206070
$713$	40.0627	1.50036
$714$	−15.5650	−0.582504
$715$	−2.36904	−0.0885972
$716$	−5.41990	−0.202551
$717$	−70.8284	−2.64513
$718$	−8.49575	−0.317058
$719$	−29.9901	−1.11844	−0.559220	−	0.829019i	$-0.688899\pi$
$719$	−29.9901	−1.11844	−0.559220	+	0.829019i	$0.688899\pi$
$720$	−5.93325	−0.221119
$721$	−25.5746	−0.952447
$722$	−39.1577	−1.45730
$723$	−6.95763	−0.258757
$724$	53.9388	2.00462
$725$	14.6323	0.543431
$726$	23.6051	0.876067
$727$	17.6561	0.654828	0.327414	−	0.944881i	$-0.393823\pi$
$727$	17.6561	0.654828	0.327414	+	0.944881i	$0.393823\pi$
$728$	−3.32937	−0.123394
$729$	−42.7898	−1.58481
$730$	7.36046	0.272423
$731$	−1.00000	−0.0369863
$732$	110.937	4.10036
$733$	−28.1333	−1.03913	−0.519564	−	0.854432i	$-0.673905\pi$
$733$	−28.1333	−1.03913	−0.519564	+	0.854432i	$0.673905\pi$
$734$	−79.2669	−2.92579
$735$	−0.297753	−0.0109828
$736$	−65.4222	−2.41149
$737$	−36.8426	−1.35711
$738$	67.1483	2.47176
$739$	47.1715	1.73523	0.867616	−	0.497235i	$-0.165651\pi$
$739$	47.1715	1.73523	0.867616	+	0.497235i	$0.165651\pi$
$740$	−29.6069	−1.08837
$741$	1.99852	0.0734173
$742$	−12.4249	−0.456132
$743$	−47.9183	−1.75795	−0.878976	−	0.476866i	$-0.841773\pi$
$743$	−47.9183	−1.75795	−0.878976	+	0.476866i	$0.841773\pi$
$744$	22.5475	0.826631
$745$	18.5833	0.680840
$746$	42.6036	1.55983
$747$	21.8262	0.798579
$748$	−11.0884	−0.405432
$749$	−31.3595	−1.14585
$750$	−49.9847	−1.82518
$751$	−21.7802	−0.794771	−0.397385	−	0.917652i	$-0.630082\pi$
$751$	−21.7802	−0.794771	−0.397385	+	0.917652i	$0.630082\pi$
$752$	7.47223	0.272484
$753$	−70.7833	−2.57949
$754$	−5.16926	−0.188253
$755$	3.62874	0.132064
$756$	−25.0342	−0.910484
$757$	14.4250	0.524287	0.262144	−	0.965029i	$-0.415571\pi$
$757$	14.4250	0.524287	0.262144	+	0.965029i	$0.415571\pi$
$758$	−76.0795	−2.76333
$759$	−94.9789	−3.44752
$760$	1.96103	0.0711339
$761$	−25.7229	−0.932455	−0.466227	−	0.884665i	$-0.654387\pi$
$761$	−25.7229	−0.932455	−0.466227	+	0.884665i	$0.654387\pi$
$762$	−95.8440	−3.47206
$763$	−17.8437	−0.645984
$764$	17.2443	0.623876
$765$	3.90018	0.141011
$766$	−72.1993	−2.60867
$767$	−8.37111	−0.302263
$768$	−13.3670	−0.482339
$769$	20.4614	0.737856	0.368928	−	0.929458i	$-0.379725\pi$
$769$	20.4614	0.737856	0.368928	+	0.929458i	$0.379725\pi$
$770$	20.6045	0.742534
$771$	−14.1413	−0.509285
$772$	−14.5755	−0.524584
$773$	−20.0731	−0.721979	−0.360989	−	0.932570i	$-0.617561\pi$
$773$	−20.0731	−0.721979	−0.360989	+	0.932570i	$0.617561\pi$
$774$	−9.34820	−0.336014
$775$	−18.2402	−0.655207
$776$	5.82046	0.208942
$777$	79.2398	2.84271
$778$	−56.5731	−2.02824
$779$	8.02150	0.287400
$780$	4.71856	0.168951
$781$	24.2753	0.868637
$782$	20.1204	0.719502
$783$	−11.7365	−0.419428
$784$	0.182955	0.00653411
$785$	−1.15906	−0.0413688
$786$	32.4512	1.15750
$787$	−27.0946	−0.965817	−0.482909	−	0.875671i	$-0.660420\pi$
$787$	−27.0946	−0.965817	−0.482909	+	0.875671i	$0.660420\pi$
$788$	18.2306	0.649440
$789$	−21.4077	−0.762134
$790$	−12.3552	−0.439577
$791$	−32.7501	−1.16446
$792$	−31.2994	−1.11217
$793$	9.57332	0.339958
$794$	37.5096	1.33117
$795$	5.31715	0.188580
$796$	41.0225	1.45400
$797$	−15.2943	−0.541751	−0.270875	−	0.962614i	$-0.587313\pi$
$797$	−15.2943	−0.541751	−0.270875	+	0.962614i	$0.587313\pi$
$798$	−17.3819	−0.615311
$799$	−4.91183	−0.173768
$800$	29.7861	1.05310
$801$	12.2125	0.431507
$802$	20.7238	0.731781
$803$	−14.0339	−0.495244
$804$	73.3814	2.58796
$805$	−22.0180	−0.776034
$806$	6.44383	0.226974
$807$	−5.66837	−0.199536
$808$	16.3931	0.576706
$809$	28.6362	1.00679	0.503397	−	0.864055i	$-0.332083\pi$
$809$	28.6362	1.00679	0.503397	+	0.864055i	$0.332083\pi$
$810$	−7.61643	−0.267614
$811$	−40.0253	−1.40548	−0.702739	−	0.711447i	$-0.748040\pi$
$811$	−40.0253	−1.40548	−0.702739	+	0.711447i	$0.748040\pi$
$812$	26.4769	0.929157
$813$	−30.7148	−1.07722
$814$	95.8549	3.35971
$815$	−9.72311	−0.340586
$816$	−4.09282	−0.143277
$817$	−1.11673	−0.0390694
$818$	51.7400	1.80905
$819$	−7.39454	−0.258386
$820$	18.9390	0.661378
$821$	−3.11087	−0.108570	−0.0542850	−	0.998525i	$-0.517288\pi$
$821$	−3.11087	−0.108570	−0.0542850	+	0.998525i	$0.517288\pi$
$822$	2.78525	0.0971468
$823$	−55.5170	−1.93520	−0.967600	−	0.252487i	$-0.918751\pi$
$823$	−55.5170	−1.93520	−0.967600	+	0.252487i	$0.918751\pi$
$824$	18.6060	0.648172
$825$	43.2430	1.50553
$826$	72.8068	2.53327
$827$	47.0013	1.63439	0.817197	−	0.576358i	$-0.195527\pi$
$827$	47.0013	1.63439	0.817197	+	0.576358i	$0.195527\pi$
$828$	110.768	3.84945
$829$	−2.32418	−0.0807220	−0.0403610	−	0.999185i	$-0.512851\pi$
$829$	−2.32418	−0.0807220	−0.0403610	+	0.999185i	$0.512851\pi$
$830$	10.4532	0.362837
$831$	48.7982	1.69279
$832$	−8.49887	−0.294645
$833$	−0.120264	−0.00416692
$834$	23.1293	0.800904
$835$	−5.18872	−0.179563
$836$	−12.3828	−0.428266
$837$	14.6303	0.505699
$838$	78.3296	2.70585
$839$	2.33261	0.0805308	0.0402654	−	0.999189i	$-0.487180\pi$
$839$	2.33261	0.0805308	0.0402654	+	0.999189i	$0.487180\pi$
$840$	−12.3919	−0.427560
$841$	−16.5871	−0.571969
$842$	81.3564	2.80373
$843$	−71.0359	−2.44661
$844$	−65.8102	−2.26528
$845$	−11.5560	−0.397540
$846$	−45.9167	−1.57865
$847$	−10.4335	−0.358498
$848$	−3.26713	−0.112194
$849$	25.1973	0.864769
$850$	−9.16061	−0.314206
$851$	−102.431	−3.51129
$852$	−48.3504	−1.65646
$853$	7.17197	0.245564	0.122782	−	0.992434i	$-0.460818\pi$
$853$	7.17197	0.245564	0.122782	+	0.992434i	$0.460818\pi$
$854$	−83.2628	−2.84919
$855$	4.35545	0.148953
$856$	22.8147	0.779789
$857$	25.5332	0.872196	0.436098	−	0.899899i	$-0.356360\pi$
$857$	25.5332	0.872196	0.436098	+	0.899899i	$0.356360\pi$
$858$	−15.2768	−0.521540
$859$	−40.5562	−1.38376	−0.691880	−	0.722012i	$-0.743217\pi$
$859$	−40.5562	−1.38376	−0.691880	+	0.722012i	$0.743217\pi$
$860$	−2.63663	−0.0899084
$861$	−50.6883	−1.72745
$862$	58.0225	1.97625
$863$	45.0964	1.53510	0.767550	−	0.640989i	$-0.221476\pi$
$863$	45.0964	1.53510	0.767550	+	0.640989i	$0.221476\pi$
$864$	−23.8913	−0.812797
$865$	−2.84145	−0.0966121
$866$	−55.2125	−1.87620
$867$	2.69039	0.0913704
$868$	−33.0053	−1.12027
$869$	23.5570	0.799117
$870$	−19.2399	−0.652295
$871$	6.33244	0.214566
$872$	12.9816	0.439614
$873$	12.9273	0.437522
$874$	22.4690	0.760025
$875$	22.0933	0.746890
$876$	27.9520	0.944410
$877$	44.1168	1.48972	0.744859	−	0.667222i	$-0.232517\pi$
$877$	44.1168	1.48972	0.744859	+	0.667222i	$0.232517\pi$
$878$	34.9046	1.17797
$879$	50.7686	1.71238
$880$	5.41796	0.182640
$881$	9.45587	0.318576	0.159288	−	0.987232i	$-0.449080\pi$
$881$	9.45587	0.318576	0.159288	+	0.987232i	$0.449080\pi$
$882$	−1.12426	−0.0378557
$883$	−23.3188	−0.784739	−0.392370	−	0.919808i	$-0.628345\pi$
$883$	−23.3188	−0.784739	−0.392370	+	0.919808i	$0.628345\pi$
$884$	1.90585	0.0641008
$885$	−31.1572	−1.04734
$886$	−35.6164	−1.19656
$887$	8.85527	0.297331	0.148665	−	0.988888i	$-0.452502\pi$
$887$	8.85527	0.297331	0.148665	+	0.988888i	$0.452502\pi$
$888$	−57.6486	−1.93456
$889$	42.3632	1.42082
$890$	5.84892	0.196056
$891$	14.5219	0.486502
$892$	56.8589	1.90378
$893$	−5.48518	−0.183555
$894$	119.834	4.00786
$895$	−1.74081	−0.0581888
$896$	36.2950	1.21253
$897$	16.3248	0.545069
$898$	−8.41422	−0.280786
$899$	−15.4735	−0.516070
$900$	−50.4316	−1.68105
$901$	2.14763	0.0715478
$902$	−61.3167	−2.04162
$903$	7.05669	0.234832
$904$	23.8264	0.792454
$905$	17.3245	0.575886
$906$	23.3999	0.777410
$907$	−48.6045	−1.61388	−0.806942	−	0.590630i	$-0.798879\pi$
$907$	−48.6045	−1.61388	−0.806942	+	0.590630i	$0.798879\pi$
$908$	−69.1096	−2.29348
$909$	36.4091	1.20761
$910$	−3.54146	−0.117398
$911$	−6.97407	−0.231061	−0.115531	−	0.993304i	$-0.536857\pi$
$911$	−6.97407	−0.231061	−0.115531	+	0.993304i	$0.536857\pi$
$912$	−4.57057	−0.151347
$913$	−19.9307	−0.659609
$914$	16.0540	0.531019
$915$	35.6318	1.17795
$916$	−7.58836	−0.250726
$917$	−14.3435	−0.473664
$918$	7.34767	0.242509
$919$	−3.65724	−0.120641	−0.0603206	−	0.998179i	$-0.519212\pi$
$919$	−3.65724	−0.120641	−0.0603206	+	0.998179i	$0.519212\pi$
$920$	16.0186	0.528117
$921$	−80.9360	−2.66693
$922$	−28.5441	−0.940051
$923$	−4.17239	−0.137336
$924$	78.2474	2.57415
$925$	46.6358	1.53338
$926$	45.6254	1.49934
$927$	41.3241	1.35726
$928$	25.2681	0.829467
$929$	−29.4517	−0.966279	−0.483140	−	0.875543i	$-0.660504\pi$
$929$	−29.4517	−0.966279	−0.483140	+	0.875543i	$0.660504\pi$
$930$	23.9839	0.786462
$931$	−0.134303	−0.00440160
$932$	−10.5717	−0.346287
$933$	23.8165	0.779718
$934$	−34.2916	−1.12206
$935$	−3.56146	−0.116472
$936$	5.37967	0.175840
$937$	11.0449	0.360821	0.180411	−	0.983591i	$-0.442257\pi$
$937$	11.0449	0.360821	0.180411	+	0.983591i	$0.442257\pi$
$938$	−55.0756	−1.79828
$939$	53.1518	1.73454
$940$	−12.9507	−0.422405
$941$	−26.1310	−0.851845	−0.425922	−	0.904760i	$-0.640050\pi$
$941$	−26.1310	−0.851845	−0.425922	+	0.904760i	$0.640050\pi$
$942$	−7.47421	−0.243523
$943$	65.5233	2.13373
$944$	19.1446	0.623103
$945$	−8.04068	−0.261563
$946$	8.53634	0.277540
$947$	18.0073	0.585158	0.292579	−	0.956241i	$-0.405487\pi$
$947$	18.0073	0.585158	0.292579	+	0.956241i	$0.405487\pi$
$948$	−46.9198	−1.52388
$949$	2.41211	0.0783005
$950$	−10.2299	−0.331903
$951$	23.4706	0.761086
$952$	−5.00515	−0.162218
$953$	21.4959	0.696321	0.348161	−	0.937435i	$-0.386806\pi$
$953$	21.4959	0.696321	0.348161	+	0.937435i	$0.386806\pi$
$954$	20.0764	0.649999
$955$	5.53866	0.179227
$956$	−75.4288	−2.43954
$957$	36.6839	1.18582
$958$	−67.6565	−2.18588
$959$	−1.23108	−0.0397538
$960$	−31.6327	−1.02094
$961$	−11.7112	−0.377782
$962$	−16.4754	−0.531187
$963$	50.6714	1.63286
$964$	−7.40954	−0.238645
$965$	−4.68148	−0.150702
$966$	−141.983	−4.56823
$967$	−23.2690	−0.748281	−0.374141	−	0.927372i	$-0.622062\pi$
$967$	−23.2690	−0.748281	−0.374141	+	0.927372i	$0.622062\pi$
$968$	7.59056	0.243970
$969$	3.00444	0.0965164
$970$	6.19125	0.198789
$971$	59.1462	1.89809	0.949046	−	0.315139i	$-0.102051\pi$
$971$	59.1462	1.89809	0.949046	+	0.315139i	$0.102051\pi$
$972$	−57.5572	−1.84615
$973$	−10.2232	−0.327741
$974$	12.7525	0.408616
$975$	−7.43253	−0.238031
$976$	−21.8940	−0.700810
$977$	37.1908	1.18984	0.594919	−	0.803785i	$-0.297184\pi$
$977$	37.1908	1.18984	0.594919	+	0.803785i	$0.297184\pi$
$978$	−62.6993	−2.00490
$979$	−11.1519	−0.356415
$980$	−0.317093	−0.0101292
$981$	28.8323	0.920544
$982$	22.9714	0.733047
$983$	24.1267	0.769523	0.384762	−	0.923016i	$-0.374284\pi$
$983$	24.1267	0.769523	0.384762	+	0.923016i	$0.374284\pi$
$984$	36.8768	1.17559
$985$	5.85547	0.186571
$986$	−7.77112	−0.247483
$987$	34.6612	1.10328
$988$	2.12832	0.0677110
$989$	−9.12196	−0.290062
$990$	−33.2933	−1.05813
$991$	20.4841	0.650697	0.325349	−	0.945594i	$-0.394518\pi$
$991$	20.4841	0.650697	0.325349	+	0.945594i	$0.394518\pi$
$992$	−31.4984	−1.00008
$993$	−49.6134	−1.57443
$994$	36.2888	1.15101
$995$	13.1760	0.417706
$996$	39.6970	1.25785
$997$	44.1896	1.39950	0.699749	−	0.714389i	$-0.253295\pi$
$997$	44.1896	1.39950	0.699749	+	0.714389i	$0.253295\pi$
$998$	12.1450	0.384443
$999$	−37.4063	−1.18348

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.16	✓	19
3.2	odd	2		6579.2.a.t.1.4		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.16	✓	19	1.1	even	1	trivial
6579.2.a.t.1.4		19	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+2.20570 q^{2} +2.69039 q^{3} +2.86513 q^{4} +0.920247 q^{5} +5.93420 q^{6} -2.62293 q^{7} +1.90823 q^{8} +4.23819 q^{9} +O(q^{10})\)	\(q+2.20570 q^{2} +2.69039 q^{3} +2.86513 q^{4} +0.920247 q^{5} +5.93420 q^{6} -2.62293 q^{7} +1.90823 q^{8} +4.23819 q^{9} +2.02979 q^{10} -3.87012 q^{11} +7.70832 q^{12} +0.665188 q^{13} -5.78540 q^{14} +2.47582 q^{15} -1.52127 q^{16} +1.00000 q^{17} +9.34820 q^{18} +1.11673 q^{19} +2.63663 q^{20} -7.05669 q^{21} -8.53634 q^{22} +9.12196 q^{23} +5.13388 q^{24} -4.15314 q^{25} +1.46721 q^{26} +3.33121 q^{27} -7.51503 q^{28} -3.52319 q^{29} +5.46094 q^{30} +4.39190 q^{31} -7.17194 q^{32} -10.4121 q^{33} +2.20570 q^{34} -2.41374 q^{35} +12.1430 q^{36} -11.2290 q^{37} +2.46318 q^{38} +1.78961 q^{39} +1.75604 q^{40} +7.18302 q^{41} -15.5650 q^{42} -1.00000 q^{43} -11.0884 q^{44} +3.90018 q^{45} +20.1204 q^{46} -4.91183 q^{47} -4.09282 q^{48} -0.120264 q^{49} -9.16061 q^{50} +2.69039 q^{51} +1.90585 q^{52} +2.14763 q^{53} +7.34767 q^{54} -3.56146 q^{55} -5.00515 q^{56} +3.00444 q^{57} -7.77112 q^{58} -12.5846 q^{59} +7.09357 q^{60} +14.3919 q^{61} +9.68723 q^{62} -11.1165 q^{63} -12.7766 q^{64} +0.612138 q^{65} -22.9661 q^{66} +9.51977 q^{67} +2.86513 q^{68} +24.5416 q^{69} -5.32400 q^{70} -6.27249 q^{71} +8.08745 q^{72} +3.62621 q^{73} -24.7680 q^{74} -11.1736 q^{75} +3.19958 q^{76} +10.1510 q^{77} +3.94736 q^{78} -6.08690 q^{79} -1.39995 q^{80} -3.75232 q^{81} +15.8436 q^{82} +5.14989 q^{83} -20.2184 q^{84} +0.920247 q^{85} -2.20570 q^{86} -9.47876 q^{87} -7.38508 q^{88} +2.88153 q^{89} +8.60265 q^{90} -1.74474 q^{91} +26.1356 q^{92} +11.8159 q^{93} -10.8340 q^{94} +1.02767 q^{95} -19.2953 q^{96} +3.05018 q^{97} -0.265268 q^{98} -16.4023 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

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