LMFDB - Embedded newform 1339.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.203882 q^{2} +1.83284 q^{3} -1.95843 q^{4} +3.17177 q^{5} +0.373682 q^{6} +2.89343 q^{7} -0.807052 q^{8} +0.359299 q^{9} +O(q^{10})$	\(q+0.203882 q^{2} +1.83284 q^{3} -1.95843 q^{4} +3.17177 q^{5} +0.373682 q^{6} +2.89343 q^{7} -0.807052 q^{8} +0.359299 q^{9} +0.646665 q^{10} +1.27153 q^{11} -3.58949 q^{12} +1.00000 q^{13} +0.589916 q^{14} +5.81334 q^{15} +3.75232 q^{16} +3.95617 q^{17} +0.0732545 q^{18} -0.566061 q^{19} -6.21169 q^{20} +5.30318 q^{21} +0.259243 q^{22} -4.54324 q^{23} -1.47920 q^{24} +5.06010 q^{25} +0.203882 q^{26} -4.83998 q^{27} -5.66658 q^{28} -0.716338 q^{29} +1.18523 q^{30} -9.21553 q^{31} +2.37913 q^{32} +2.33052 q^{33} +0.806591 q^{34} +9.17727 q^{35} -0.703663 q^{36} +8.78778 q^{37} -0.115409 q^{38} +1.83284 q^{39} -2.55978 q^{40} +2.95326 q^{41} +1.08122 q^{42} +1.51635 q^{43} -2.49022 q^{44} +1.13961 q^{45} -0.926283 q^{46} +2.99290 q^{47} +6.87740 q^{48} +1.37191 q^{49} +1.03166 q^{50} +7.25103 q^{51} -1.95843 q^{52} +1.66640 q^{53} -0.986783 q^{54} +4.03301 q^{55} -2.33514 q^{56} -1.03750 q^{57} -0.146048 q^{58} +5.40172 q^{59} -11.3850 q^{60} +5.58360 q^{61} -1.87888 q^{62} +1.03961 q^{63} -7.01958 q^{64} +3.17177 q^{65} +0.475150 q^{66} -13.6498 q^{67} -7.74790 q^{68} -8.32702 q^{69} +1.87108 q^{70} -9.21250 q^{71} -0.289973 q^{72} +0.0681013 q^{73} +1.79167 q^{74} +9.27435 q^{75} +1.10859 q^{76} +3.67909 q^{77} +0.373682 q^{78} +11.0777 q^{79} +11.9015 q^{80} -9.94880 q^{81} +0.602115 q^{82} -7.03083 q^{83} -10.3859 q^{84} +12.5481 q^{85} +0.309156 q^{86} -1.31293 q^{87} -1.02619 q^{88} -8.78008 q^{89} +0.232346 q^{90} +2.89343 q^{91} +8.89762 q^{92} -16.8906 q^{93} +0.610198 q^{94} -1.79541 q^{95} +4.36057 q^{96} +11.9373 q^{97} +0.279708 q^{98} +0.456861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) $ 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9} + 5 q^{10} + 9 q^{11} + 15 q^{12} + 28 q^{13} + 20 q^{14} + 4 q^{15} + 32 q^{16} - 7 q^{17} + 10 q^{18} - 3 q^{19} + 53 q^{20} + 25 q^{21} - 14 q^{22} - 6 q^{23} + 10 q^{24} + 45 q^{25} + 6 q^{26} + 8 q^{27} - 12 q^{28} + 25 q^{29} - 43 q^{30} + q^{31} + 28 q^{32} + 17 q^{33} + 10 q^{34} + 11 q^{35} + 27 q^{36} + 18 q^{37} + 2 q^{38} + 5 q^{39} + 37 q^{40} + 56 q^{41} - 29 q^{42} - 30 q^{43} + 30 q^{44} + 38 q^{45} - 27 q^{46} + 40 q^{47} + 19 q^{48} + 36 q^{49} + 20 q^{50} - 18 q^{51} + 32 q^{52} + 51 q^{53} - 36 q^{54} - 5 q^{55} - 13 q^{56} + 31 q^{57} - 29 q^{58} + 29 q^{59} + 48 q^{60} + 16 q^{61} - 38 q^{62} - 23 q^{63} - 5 q^{64} + 27 q^{65} + 25 q^{66} - 2 q^{67} - 43 q^{68} + 38 q^{69} + 10 q^{70} + 34 q^{71} - 28 q^{72} + 14 q^{73} + 21 q^{74} + 19 q^{75} + 5 q^{76} + 34 q^{77} + 9 q^{78} + 3 q^{79} + 58 q^{80} + 4 q^{81} - 9 q^{82} + 38 q^{83} - 78 q^{84} - 27 q^{85} + 49 q^{86} + 8 q^{87} - 25 q^{88} + 125 q^{89} - 74 q^{90} + 6 q^{91} - 35 q^{92} + 36 q^{93} - q^{94} - 12 q^{95} + 26 q^{96} - 2 q^{97} + 18 q^{98} + 56 q^{99}+O(q^{100}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9 + 5 * q^10 + 9 * q^11 + 15 * q^12 + 28 * q^13 + 20 * q^14 + 4 * q^15 + 32 * q^16 - 7 * q^17 + 10 * q^18 - 3 * q^19 + 53 * q^20 + 25 * q^21 - 14 * q^22 - 6 * q^23 + 10 * q^24 + 45 * q^25 + 6 * q^26 + 8 * q^27 - 12 * q^28 + 25 * q^29 - 43 * q^30 + q^31 + 28 * q^32 + 17 * q^33 + 10 * q^34 + 11 * q^35 + 27 * q^36 + 18 * q^37 + 2 * q^38 + 5 * q^39 + 37 * q^40 + 56 * q^41 - 29 * q^42 - 30 * q^43 + 30 * q^44 + 38 * q^45 - 27 * q^46 + 40 * q^47 + 19 * q^48 + 36 * q^49 + 20 * q^50 - 18 * q^51 + 32 * q^52 + 51 * q^53 - 36 * q^54 - 5 * q^55 - 13 * q^56 + 31 * q^57 - 29 * q^58 + 29 * q^59 + 48 * q^60 + 16 * q^61 - 38 * q^62 - 23 * q^63 - 5 * q^64 + 27 * q^65 + 25 * q^66 - 2 * q^67 - 43 * q^68 + 38 * q^69 + 10 * q^70 + 34 * q^71 - 28 * q^72 + 14 * q^73 + 21 * q^74 + 19 * q^75 + 5 * q^76 + 34 * q^77 + 9 * q^78 + 3 * q^79 + 58 * q^80 + 4 * q^81 - 9 * q^82 + 38 * q^83 - 78 * q^84 - 27 * q^85 + 49 * q^86 + 8 * q^87 - 25 * q^88 + 125 * q^89 - 74 * q^90 + 6 * q^91 - 35 * q^92 + 36 * q^93 - q^94 - 12 * q^95 + 26 * q^96 - 2 * q^97 + 18 * q^98 + 56 * 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 $

$2$	0.203882	0.144166	0.0720830	−	0.997399i	$-0.477035\pi$
$2$	0.203882	0.144166	0.0720830	+	0.997399i	$0.477035\pi$
$3$	1.83284	1.05819	0.529095	−	0.848563i	$-0.322531\pi$
$3$	1.83284	1.05819	0.529095	+	0.848563i	$0.322531\pi$
$4$	−1.95843	−0.979216
$5$	3.17177	1.41846	0.709228	−	0.704979i	$-0.249044\pi$
$5$	3.17177	1.41846	0.709228	+	0.704979i	$0.249044\pi$
$6$	0.373682	0.152555
$7$	2.89343	1.09361	0.546806	−	0.837259i	$-0.315844\pi$
$7$	2.89343	1.09361	0.546806	+	0.837259i	$0.315844\pi$
$8$	−0.807052	−0.285336
$9$	0.359299	0.119766
$10$	0.646665	0.204493
$11$	1.27153	0.383382	0.191691	−	0.981455i	$-0.438603\pi$
$11$	1.27153	0.383382	0.191691	+	0.981455i	$0.438603\pi$
$12$	−3.58949	−1.03620
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.589916	0.157662
$15$	5.81334	1.50100
$16$	3.75232	0.938080
$17$	3.95617	0.959513	0.479757	−	0.877402i	$-0.340725\pi$
$17$	3.95617	0.959513	0.479757	+	0.877402i	$0.340725\pi$
$18$	0.0732545	0.0172662
$19$	−0.566061	−0.129863	−0.0649316	−	0.997890i	$-0.520683\pi$
$19$	−0.566061	−0.129863	−0.0649316	+	0.997890i	$0.520683\pi$
$20$	−6.21169	−1.38898
$21$	5.30318	1.15725
$22$	0.259243	0.0552707
$23$	−4.54324	−0.947330	−0.473665	−	0.880705i	$-0.657069\pi$
$23$	−4.54324	−0.947330	−0.473665	+	0.880705i	$0.657069\pi$
$24$	−1.47920	−0.301940
$25$	5.06010	1.01202
$26$	0.203882	0.0399845
$27$	−4.83998	−0.931455
$28$	−5.66658	−1.07088
$29$	−0.716338	−0.133021	−0.0665103	−	0.997786i	$-0.521187\pi$
$29$	−0.716338	−0.133021	−0.0665103	+	0.997786i	$0.521187\pi$
$30$	1.18523	0.216393
$31$	−9.21553	−1.65516	−0.827579	−	0.561349i	$-0.810282\pi$
$31$	−9.21553	−1.65516	−0.827579	+	0.561349i	$0.810282\pi$
$32$	2.37913	0.420575
$33$	2.33052	0.405691
$34$	0.806591	0.138329
$35$	9.17727	1.55124
$36$	−0.703663	−0.117277
$37$	8.78778	1.44470	0.722351	−	0.691527i	$-0.243062\pi$
$37$	8.78778	1.44470	0.722351	+	0.691527i	$0.243062\pi$
$38$	−0.115409	−0.0187219
$39$	1.83284	0.293489
$40$	−2.55978	−0.404737
$41$	2.95326	0.461221	0.230611	−	0.973046i	$-0.425928\pi$
$41$	2.95326	0.461221	0.230611	+	0.973046i	$0.425928\pi$
$42$	1.08122	0.166836
$43$	1.51635	0.231241	0.115621	−	0.993293i	$-0.463114\pi$
$43$	1.51635	0.231241	0.115621	+	0.993293i	$0.463114\pi$
$44$	−2.49022	−0.375414
$45$	1.13961	0.169883
$46$	−0.926283	−0.136573
$47$	2.99290	0.436560	0.218280	−	0.975886i	$-0.429955\pi$
$47$	2.99290	0.436560	0.218280	+	0.975886i	$0.429955\pi$
$48$	6.87740	0.992667
$49$	1.37191	0.195987
$50$	1.03166	0.145899
$51$	7.25103	1.01535
$52$	−1.95843	−0.271586
$53$	1.66640	0.228897	0.114449	−	0.993429i	$-0.463490\pi$
$53$	1.66640	0.228897	0.114449	+	0.993429i	$0.463490\pi$
$54$	−0.986783	−0.134284
$55$	4.03301	0.543811
$56$	−2.33514	−0.312047
$57$	−1.03750	−0.137420
$58$	−0.146048	−0.0191771
$59$	5.40172	0.703244	0.351622	−	0.936142i	$-0.385630\pi$
$59$	5.40172	0.703244	0.351622	+	0.936142i	$0.385630\pi$
$60$	−11.3850	−1.46980
$61$	5.58360	0.714906	0.357453	−	0.933931i	$-0.383645\pi$
$61$	5.58360	0.714906	0.357453	+	0.933931i	$0.383645\pi$
$62$	−1.87888	−0.238618
$63$	1.03961	0.130978
$64$	−7.01958	−0.877448
$65$	3.17177	0.393409
$66$	0.475150	0.0584869
$67$	−13.6498	−1.66758	−0.833792	−	0.552078i	$-0.813835\pi$
$67$	−13.6498	−1.66758	−0.833792	+	0.552078i	$0.813835\pi$
$68$	−7.74790	−0.939571
$69$	−8.32702	−1.00246
$70$	1.87108	0.223636
$71$	−9.21250	−1.09332	−0.546661	−	0.837354i	$-0.684101\pi$
$71$	−9.21250	−1.09332	−0.546661	+	0.837354i	$0.684101\pi$
$72$	−0.289973	−0.0341736
$73$	0.0681013	0.00797066	0.00398533	−	0.999992i	$-0.498731\pi$
$73$	0.0681013	0.00797066	0.00398533	+	0.999992i	$0.498731\pi$
$74$	1.79167	0.208277
$75$	9.27435	1.07091
$76$	1.10859	0.127164
$77$	3.67909	0.419271
$78$	0.373682	0.0423112
$79$	11.0777	1.24634	0.623170	−	0.782087i	$-0.285845\pi$
$79$	11.0777	1.24634	0.623170	+	0.782087i	$0.285845\pi$
$80$	11.9015	1.33063
$81$	−9.94880	−1.10542
$82$	0.602115	0.0664925
$83$	−7.03083	−0.771734	−0.385867	−	0.922554i	$-0.626098\pi$
$83$	−7.03083	−0.771734	−0.385867	+	0.922554i	$0.626098\pi$
$84$	−10.3859	−1.13320
$85$	12.5481	1.36103
$86$	0.309156	0.0333372
$87$	−1.31293	−0.140761
$88$	−1.02619	−0.109393
$89$	−8.78008	−0.930686	−0.465343	−	0.885130i	$-0.654069\pi$
$89$	−8.78008	−0.930686	−0.465343	+	0.885130i	$0.654069\pi$
$90$	0.232346	0.0244914
$91$	2.89343	0.303313
$92$	8.89762	0.927641
$93$	−16.8906	−1.75147
$94$	0.610198	0.0629371
$95$	−1.79541	−0.184205
$96$	4.36057	0.445049
$97$	11.9373	1.21205	0.606023	−	0.795447i	$-0.292764\pi$
$97$	11.9373	1.21205	0.606023	+	0.795447i	$0.292764\pi$
$98$	0.279708	0.0282547
$99$	0.456861	0.0459163
$100$	−9.90986	−0.990986
$101$	7.15048	0.711499	0.355749	−	0.934581i	$-0.384226\pi$
$101$	7.15048	0.711499	0.355749	+	0.934581i	$0.384226\pi$
$102$	1.47835	0.146379
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−0.807052	−0.0791379
$105$	16.8205	1.64151
$106$	0.339748	0.0329992
$107$	−10.9054	−1.05426	−0.527130	−	0.849784i	$-0.676732\pi$
$107$	−10.9054	−1.05426	−0.527130	+	0.849784i	$0.676732\pi$
$108$	9.47877	0.912095
$109$	−12.2849	−1.17668	−0.588342	−	0.808612i	$-0.700219\pi$
$109$	−12.2849	−1.17668	−0.588342	+	0.808612i	$0.700219\pi$
$110$	0.822257	0.0783991
$111$	16.1066	1.52877
$112$	10.8571	1.02590
$113$	8.89649	0.836911	0.418456	−	0.908237i	$-0.362572\pi$
$113$	8.89649	0.836911	0.418456	+	0.908237i	$0.362572\pi$
$114$	−0.211527	−0.0198113
$115$	−14.4101	−1.34375
$116$	1.40290	0.130256
$117$	0.359299	0.0332172
$118$	1.10131	0.101384
$119$	11.4469	1.04934
$120$	−4.69166	−0.428288
$121$	−9.38320	−0.853018
$122$	1.13839	0.103065
$123$	5.41284	0.488060
$124$	18.0480	1.62076
$125$	0.190617	0.0170493
$126$	0.211956	0.0188826
$127$	19.4469	1.72564	0.862818	−	0.505516i	$-0.168698\pi$
$127$	19.4469	1.72564	0.862818	+	0.505516i	$0.168698\pi$
$128$	−6.18943	−0.547073
$129$	2.77923	0.244697
$130$	0.646665	0.0567163
$131$	17.6056	1.53821	0.769105	−	0.639122i	$-0.220702\pi$
$131$	17.6056	1.53821	0.769105	+	0.639122i	$0.220702\pi$
$132$	−4.56416	−0.397259
$133$	−1.63785	−0.142020
$134$	−2.78294	−0.240409
$135$	−15.3513	−1.32123
$136$	−3.19284	−0.273783
$137$	−1.05798	−0.0903894	−0.0451947	−	0.998978i	$-0.514391\pi$
$137$	−1.05798	−0.0903894	−0.0451947	+	0.998978i	$0.514391\pi$
$138$	−1.69773	−0.144520
$139$	8.74298	0.741570	0.370785	−	0.928719i	$-0.379089\pi$
$139$	8.74298	0.741570	0.370785	+	0.928719i	$0.379089\pi$
$140$	−17.9731	−1.51900
$141$	5.48551	0.461963
$142$	−1.87826	−0.157620
$143$	1.27153	0.106331
$144$	1.34821	0.112350
$145$	−2.27206	−0.188684
$146$	0.0138846	0.00114910
$147$	2.51449	0.207392
$148$	−17.2103	−1.41468
$149$	−17.1244	−1.40289	−0.701444	−	0.712725i	$-0.747461\pi$
$149$	−17.1244	−1.40289	−0.701444	+	0.712725i	$0.747461\pi$
$150$	1.89087	0.154389
$151$	8.66774	0.705371	0.352685	−	0.935742i	$-0.385269\pi$
$151$	8.66774	0.705371	0.352685	+	0.935742i	$0.385269\pi$
$152$	0.456840	0.0370546
$153$	1.42145	0.114917
$154$	0.750099	0.0604447
$155$	−29.2295	−2.34777
$156$	−3.58949	−0.287389
$157$	−6.36005	−0.507587	−0.253794	−	0.967258i	$-0.581678\pi$
$157$	−6.36005	−0.507587	−0.253794	+	0.967258i	$0.581678\pi$
$158$	2.25854	0.179680
$159$	3.05424	0.242217
$160$	7.54605	0.596568
$161$	−13.1455	−1.03601
$162$	−2.02838	−0.159364
$163$	11.1359	0.872228	0.436114	−	0.899891i	$-0.356354\pi$
$163$	11.1359	0.872228	0.436114	+	0.899891i	$0.356354\pi$
$164$	−5.78375	−0.451635
$165$	7.39186	0.575456
$166$	−1.43346	−0.111258
$167$	−9.77177	−0.756163	−0.378081	−	0.925772i	$-0.623416\pi$
$167$	−9.77177	−0.756163	−0.378081	+	0.925772i	$0.623416\pi$
$168$	−4.27994	−0.330205
$169$	1.00000	0.0769231
$170$	2.55832	0.196214
$171$	−0.203385	−0.0155532
$172$	−2.96967	−0.226435
$173$	−17.1014	−1.30019	−0.650096	−	0.759852i	$-0.725271\pi$
$173$	−17.1014	−1.30019	−0.650096	+	0.759852i	$0.725271\pi$
$174$	−0.267683	−0.0202930
$175$	14.6410	1.10676
$176$	4.77121	0.359643
$177$	9.90048	0.744166
$178$	−1.79010	−0.134173
$179$	−14.2463	−1.06482	−0.532409	−	0.846487i	$-0.678713\pi$
$179$	−14.2463	−1.06482	−0.532409	+	0.846487i	$0.678713\pi$
$180$	−2.23185	−0.166353
$181$	4.42945	0.329238	0.164619	−	0.986357i	$-0.447360\pi$
$181$	4.42945	0.329238	0.164619	+	0.986357i	$0.447360\pi$
$182$	0.589916	0.0437275
$183$	10.2338	0.756507
$184$	3.66663	0.270307
$185$	27.8728	2.04925
$186$	−3.44368	−0.252503
$187$	5.03041	0.367860
$188$	−5.86140	−0.427487
$189$	−14.0041	−1.01865
$190$	−0.366051	−0.0265562
$191$	−5.09624	−0.368751	−0.184375	−	0.982856i	$-0.559026\pi$
$191$	−5.09624	−0.368751	−0.184375	+	0.982856i	$0.559026\pi$
$192$	−12.8658	−0.928507
$193$	−16.9715	−1.22163	−0.610817	−	0.791772i	$-0.709159\pi$
$193$	−16.9715	−1.22163	−0.610817	+	0.791772i	$0.709159\pi$
$194$	2.43379	0.174736
$195$	5.81334	0.416302
$196$	−2.68680	−0.191914
$197$	11.2750	0.803309	0.401654	−	0.915791i	$-0.368435\pi$
$197$	11.2750	0.803309	0.401654	+	0.915791i	$0.368435\pi$
$198$	0.0931456	0.00661957
$199$	−5.07482	−0.359744	−0.179872	−	0.983690i	$-0.557568\pi$
$199$	−5.07482	−0.359744	−0.179872	+	0.983690i	$0.557568\pi$
$200$	−4.08376	−0.288765
$201$	−25.0178	−1.76462
$202$	1.45785	0.102574
$203$	−2.07267	−0.145473
$204$	−14.2006	−0.994244
$205$	9.36704	0.654222
$206$	−0.203882	−0.0142051
$207$	−1.63238	−0.113458
$208$	3.75232	0.260177
$209$	−0.719766	−0.0497872
$210$	3.42938	0.236650
$211$	−13.6245	−0.937950	−0.468975	−	0.883211i	$-0.655377\pi$
$211$	−13.6245	−0.937950	−0.468975	+	0.883211i	$0.655377\pi$
$212$	−3.26352	−0.224140
$213$	−16.8850	−1.15694
$214$	−2.22340	−0.151989
$215$	4.80951	0.328006
$216$	3.90611	0.265777
$217$	−26.6644	−1.81010
$218$	−2.50467	−0.169638
$219$	0.124819	0.00843447
$220$	−7.89838	−0.532509
$221$	3.95617	0.266121
$222$	3.28384	0.220397
$223$	−19.9272	−1.33442	−0.667212	−	0.744868i	$-0.732513\pi$
$223$	−19.9272	−1.33442	−0.667212	+	0.744868i	$0.732513\pi$
$224$	6.88384	0.459946
$225$	1.81809	0.121206
$226$	1.81383	0.120654
$227$	29.7027	1.97143	0.985717	−	0.168408i	$-0.0538626\pi$
$227$	29.7027	1.97143	0.985717	+	0.168408i	$0.0538626\pi$
$228$	2.03187	0.134564
$229$	−28.2775	−1.86863	−0.934314	−	0.356451i	$-0.883987\pi$
$229$	−28.2775	−1.86863	−0.934314	+	0.356451i	$0.883987\pi$
$230$	−2.93795	−0.193723
$231$	6.74318	0.443669
$232$	0.578122	0.0379555
$233$	−0.850903	−0.0557445	−0.0278722	−	0.999611i	$-0.508873\pi$
$233$	−0.850903	−0.0557445	−0.0278722	+	0.999611i	$0.508873\pi$
$234$	0.0732545	0.00478879
$235$	9.49279	0.619241
$236$	−10.5789	−0.688628
$237$	20.3037	1.31886
$238$	2.33381	0.151279
$239$	3.15963	0.204380	0.102190	−	0.994765i	$-0.467415\pi$
$239$	3.15963	0.204380	0.102190	+	0.994765i	$0.467415\pi$
$240$	21.8135	1.40806
$241$	12.4611	0.802690	0.401345	−	0.915927i	$-0.368543\pi$
$241$	12.4611	0.802690	0.401345	+	0.915927i	$0.368543\pi$
$242$	−1.91306	−0.122976
$243$	−3.71461	−0.238292
$244$	−10.9351	−0.700048
$245$	4.35138	0.278000
$246$	1.10358	0.0703617
$247$	−0.566061	−0.0360176
$248$	7.43741	0.472276
$249$	−12.8864	−0.816641
$250$	0.0388634	0.00245794
$251$	−26.0480	−1.64414	−0.822068	−	0.569389i	$-0.807180\pi$
$251$	−26.0480	−1.64414	−0.822068	+	0.569389i	$0.807180\pi$
$252$	−2.03600	−0.128256
$253$	−5.77688	−0.363190
$254$	3.96487	0.248778
$255$	22.9986	1.44023
$256$	12.7773	0.798578
$257$	8.75076	0.545857	0.272929	−	0.962034i	$-0.412008\pi$
$257$	8.75076	0.545857	0.272929	+	0.962034i	$0.412008\pi$
$258$	0.566633	0.0352771
$259$	25.4268	1.57994
$260$	−6.21169	−0.385233
$261$	−0.257379	−0.0159314
$262$	3.58946	0.221758
$263$	−27.6856	−1.70717	−0.853583	−	0.520956i	$-0.825575\pi$
$263$	−27.6856	−1.70717	−0.853583	+	0.520956i	$0.825575\pi$
$264$	−1.88085	−0.115758
$265$	5.28542	0.324681
$266$	−0.333928	−0.0204745
$267$	−16.0925	−0.984843
$268$	26.7321	1.63293
$269$	0.815835	0.0497424	0.0248712	−	0.999691i	$-0.492082\pi$
$269$	0.815835	0.0497424	0.0248712	+	0.999691i	$0.492082\pi$
$270$	−3.12984	−0.190476
$271$	−28.0368	−1.70312	−0.851558	−	0.524261i	$-0.824342\pi$
$271$	−28.0368	−1.70312	−0.851558	+	0.524261i	$0.824342\pi$
$272$	14.8448	0.900100
$273$	5.30318	0.320963
$274$	−0.215703	−0.0130311
$275$	6.43409	0.387990
$276$	16.3079	0.981621
$277$	1.85614	0.111524	0.0557622	−	0.998444i	$-0.482241\pi$
$277$	1.85614	0.111524	0.0557622	+	0.998444i	$0.482241\pi$
$278$	1.78253	0.106909
$279$	−3.31113	−0.198232
$280$	−7.40653	−0.442625
$281$	−4.06042	−0.242224	−0.121112	−	0.992639i	$-0.538646\pi$
$281$	−4.06042	−0.242224	−0.121112	+	0.992639i	$0.538646\pi$
$282$	1.11839	0.0665995
$283$	−14.4484	−0.858866	−0.429433	−	0.903099i	$-0.641287\pi$
$283$	−14.4484	−0.858866	−0.429433	+	0.903099i	$0.641287\pi$
$284$	18.0421	1.07060
$285$	−3.29070	−0.194924
$286$	0.259243	0.0153293
$287$	8.54503	0.504397
$288$	0.854820	0.0503708
$289$	−1.34869	−0.0793348
$290$	−0.463230	−0.0272018
$291$	21.8791	1.28257
$292$	−0.133372	−0.00780500
$293$	10.5482	0.616233	0.308116	−	0.951349i	$-0.400301\pi$
$293$	10.5482	0.616233	0.308116	+	0.951349i	$0.400301\pi$
$294$	0.512659	0.0298989
$295$	17.1330	0.997521
$296$	−7.09219	−0.412225
$297$	−6.15420	−0.357103
$298$	−3.49136	−0.202249
$299$	−4.54324	−0.262742
$300$	−18.1632	−1.04865
$301$	4.38745	0.252888
$302$	1.76719	0.101691
$303$	13.1057	0.752901
$304$	−2.12404	−0.121822
$305$	17.7099	1.01406
$306$	0.289807	0.0165672
$307$	7.64449	0.436294	0.218147	−	0.975916i	$-0.429999\pi$
$307$	7.64449	0.436294	0.218147	+	0.975916i	$0.429999\pi$
$308$	−7.20525	−0.410557
$309$	−1.83284	−0.104267
$310$	−5.95936	−0.338469
$311$	−28.2564	−1.60227	−0.801136	−	0.598482i	$-0.795771\pi$
$311$	−28.2564	−1.60227	−0.801136	+	0.598482i	$0.795771\pi$
$312$	−1.47920	−0.0837430
$313$	1.41758	0.0801262	0.0400631	−	0.999197i	$-0.487244\pi$
$313$	1.41758	0.0801262	0.0400631	+	0.999197i	$0.487244\pi$
$314$	−1.29670	−0.0731769
$315$	3.29738	0.185787
$316$	−21.6949	−1.22044
$317$	0.806309	0.0452868	0.0226434	−	0.999744i	$-0.492792\pi$
$317$	0.806309	0.0452868	0.0226434	+	0.999744i	$0.492792\pi$
$318$	0.622703	0.0349194
$319$	−0.910849	−0.0509977
$320$	−22.2645	−1.24462
$321$	−19.9878	−1.11561
$322$	−2.68013	−0.149358
$323$	−2.23943	−0.124605
$324$	19.4841	1.08245
$325$	5.06010	0.280684
$326$	2.27040	0.125746
$327$	−22.5163	−1.24516
$328$	−2.38343	−0.131603
$329$	8.65975	0.477427
$330$	1.50706	0.0829612
$331$	−26.2833	−1.44466	−0.722332	−	0.691547i	$-0.756930\pi$
$331$	−26.2833	−1.44466	−0.722332	+	0.691547i	$0.756930\pi$
$332$	13.7694	0.755694
$333$	3.15744	0.173027
$334$	−1.99229	−0.109013
$335$	−43.2939	−2.36540
$336$	19.8992	1.08559
$337$	0.514682	0.0280365	0.0140183	−	0.999902i	$-0.495538\pi$
$337$	0.514682	0.0280365	0.0140183	+	0.999902i	$0.495538\pi$
$338$	0.203882	0.0110897
$339$	16.3058	0.885611
$340$	−24.5745	−1.33274
$341$	−11.7179	−0.634558
$342$	−0.0414665	−0.00224225
$343$	−16.2845	−0.879278
$344$	−1.22377	−0.0659815
$345$	−26.4114	−1.42194
$346$	−3.48665	−0.187444
$347$	7.64919	0.410630	0.205315	−	0.978696i	$-0.434178\pi$
$347$	7.64919	0.410630	0.205315	+	0.978696i	$0.434178\pi$
$348$	2.57129	0.137836
$349$	−7.10549	−0.380348	−0.190174	−	0.981750i	$-0.560905\pi$
$349$	−7.10549	−0.380348	−0.190174	+	0.981750i	$0.560905\pi$
$350$	2.98503	0.159557
$351$	−4.83998	−0.258339
$352$	3.02515	0.161241
$353$	16.1365	0.858858	0.429429	−	0.903101i	$-0.358715\pi$
$353$	16.1365	0.858858	0.429429	+	0.903101i	$0.358715\pi$
$354$	2.01853	0.107283
$355$	−29.2199	−1.55083
$356$	17.1952	0.911343
$357$	20.9803	1.11040
$358$	−2.90456	−0.153511
$359$	7.42388	0.391817	0.195909	−	0.980622i	$-0.437234\pi$
$359$	7.42388	0.391817	0.195909	+	0.980622i	$0.437234\pi$
$360$	−0.919726	−0.0484738
$361$	−18.6796	−0.983136
$362$	0.903083	0.0474650
$363$	−17.1979	−0.902655
$364$	−5.66658	−0.297009
$365$	0.216001	0.0113060
$366$	2.08649	0.109063
$367$	−19.6201	−1.02416	−0.512080	−	0.858938i	$-0.671125\pi$
$367$	−19.6201	−1.02416	−0.512080	+	0.858938i	$0.671125\pi$
$368$	−17.0477	−0.888672
$369$	1.06110	0.0552388
$370$	5.68275	0.295432
$371$	4.82159	0.250325
$372$	33.0791	1.71507
$373$	4.64708	0.240617	0.120308	−	0.992737i	$-0.461612\pi$
$373$	4.64708	0.240617	0.120308	+	0.992737i	$0.461612\pi$
$374$	1.02561	0.0530330
$375$	0.349371	0.0180414
$376$	−2.41543	−0.124566
$377$	−0.716338	−0.0368933
$378$	−2.85518	−0.146855
$379$	13.6197	0.699596	0.349798	−	0.936825i	$-0.386250\pi$
$379$	13.6197	0.699596	0.349798	+	0.936825i	$0.386250\pi$
$380$	3.51619	0.180377
$381$	35.6431	1.82605
$382$	−1.03903	−0.0531614
$383$	35.4148	1.80961	0.904806	−	0.425824i	$-0.140016\pi$
$383$	35.4148	1.80961	0.904806	+	0.425824i	$0.140016\pi$
$384$	−11.3442	−0.578908
$385$	11.6692	0.594718
$386$	−3.46017	−0.176118
$387$	0.544824	0.0276949
$388$	−23.3783	−1.18685
$389$	9.98918	0.506471	0.253236	−	0.967405i	$-0.418505\pi$
$389$	9.98918	0.506471	0.253236	+	0.967405i	$0.418505\pi$
$390$	1.18523	0.0600166
$391$	−17.9738	−0.908976
$392$	−1.10720	−0.0559222
$393$	32.2683	1.62772
$394$	2.29876	0.115810
$395$	35.1359	1.76788
$396$	−0.894732	−0.0449620
$397$	36.8534	1.84962	0.924809	−	0.380431i	$-0.124224\pi$
$397$	36.8534	1.84962	0.924809	+	0.380431i	$0.124224\pi$
$398$	−1.03466	−0.0518629
$399$	−3.00192	−0.150284
$400$	18.9871	0.949356
$401$	12.8638	0.642390	0.321195	−	0.947013i	$-0.395916\pi$
$401$	12.8638	0.642390	0.321195	+	0.947013i	$0.395916\pi$
$402$	−5.10068	−0.254399
$403$	−9.21553	−0.459058
$404$	−14.0037	−0.696711
$405$	−31.5553	−1.56799
$406$	−0.422579	−0.0209723
$407$	11.1740	0.553873
$408$	−5.85195	−0.289715
$409$	2.77003	0.136969	0.0684845	−	0.997652i	$-0.478184\pi$
$409$	2.77003	0.136969	0.0684845	+	0.997652i	$0.478184\pi$
$410$	1.90977	0.0943167
$411$	−1.93911	−0.0956491
$412$	1.95843	0.0964850
$413$	15.6295	0.769076
$414$	−0.332812	−0.0163568
$415$	−22.3001	−1.09467
$416$	2.37913	0.116647
$417$	16.0245	0.784722
$418$	−0.146747	−0.00717763
$419$	−27.8291	−1.35954	−0.679770	−	0.733425i	$-0.737920\pi$
$419$	−27.8291	−1.35954	−0.679770	+	0.733425i	$0.737920\pi$
$420$	−32.9417	−1.60739
$421$	7.81150	0.380709	0.190355	−	0.981715i	$-0.439036\pi$
$421$	7.81150	0.380709	0.190355	+	0.981715i	$0.439036\pi$
$422$	−2.77779	−0.135221
$423$	1.07535	0.0522852
$424$	−1.34487	−0.0653126
$425$	20.0186	0.971046
$426$	−3.44255	−0.166792
$427$	16.1557	0.781830
$428$	21.3574	1.03235
$429$	2.33052	0.112519
$430$	0.980571	0.0472873
$431$	−12.4516	−0.599771	−0.299886	−	0.953975i	$-0.596949\pi$
$431$	−12.4516	−0.599771	−0.299886	+	0.953975i	$0.596949\pi$
$432$	−18.1612	−0.873779
$433$	−1.04354	−0.0501491	−0.0250746	−	0.999686i	$-0.507982\pi$
$433$	−1.04354	−0.0501491	−0.0250746	+	0.999686i	$0.507982\pi$
$434$	−5.43639	−0.260955
$435$	−4.16431	−0.199663
$436$	24.0592	1.15223
$437$	2.57175	0.123023
$438$	0.0254483	0.00121596
$439$	−11.5587	−0.551665	−0.275833	−	0.961206i	$-0.588954\pi$
$439$	−11.5587	−0.551665	−0.275833	+	0.961206i	$0.588954\pi$
$440$	−3.25485	−0.155169
$441$	0.492927	0.0234727
$442$	0.806591	0.0383656
$443$	4.87669	0.231698	0.115849	−	0.993267i	$-0.463041\pi$
$443$	4.87669	0.231698	0.115849	+	0.993267i	$0.463041\pi$
$444$	−31.5437	−1.49700
$445$	−27.8483	−1.32014
$446$	−4.06279	−0.192379
$447$	−31.3863	−1.48452
$448$	−20.3106	−0.959587
$449$	7.21944	0.340706	0.170353	−	0.985383i	$-0.445509\pi$
$449$	7.21944	0.340706	0.170353	+	0.985383i	$0.445509\pi$
$450$	0.370675	0.0174738
$451$	3.75517	0.176824
$452$	−17.4232	−0.819517
$453$	15.8866	0.746416
$454$	6.05583	0.284214
$455$	9.17727	0.430237
$456$	0.837314	0.0392108
$457$	18.3555	0.858636	0.429318	−	0.903153i	$-0.358754\pi$
$457$	18.3555	0.858636	0.429318	+	0.903153i	$0.358754\pi$
$458$	−5.76526	−0.269393
$459$	−19.1478	−0.893743
$460$	28.2212	1.31582
$461$	−11.3646	−0.529302	−0.264651	−	0.964344i	$-0.585257\pi$
$461$	−11.3646	−0.529302	−0.264651	+	0.964344i	$0.585257\pi$
$462$	1.37481	0.0639620
$463$	22.9784	1.06790	0.533948	−	0.845517i	$-0.320708\pi$
$463$	22.9784	1.06790	0.533948	+	0.845517i	$0.320708\pi$
$464$	−2.68793	−0.124784
$465$	−53.5730	−2.48439
$466$	−0.173483	−0.00803646
$467$	33.4647	1.54856	0.774280	−	0.632843i	$-0.218112\pi$
$467$	33.4647	1.54856	0.774280	+	0.632843i	$0.218112\pi$
$468$	−0.703663	−0.0325268
$469$	−39.4946	−1.82369
$470$	1.93541	0.0892736
$471$	−11.6570	−0.537124
$472$	−4.35947	−0.200661
$473$	1.92809	0.0886538
$474$	4.13954	0.190136
$475$	−2.86432	−0.131424
$476$	−22.4180	−1.02753
$477$	0.598735	0.0274142
$478$	0.644191	0.0294646
$479$	28.4266	1.29885	0.649423	−	0.760427i	$-0.275010\pi$
$479$	28.4266	1.29885	0.649423	+	0.760427i	$0.275010\pi$
$480$	13.8307	0.631282
$481$	8.78778	0.400688
$482$	2.54059	0.115721
$483$	−24.0936	−1.09630
$484$	18.3764	0.835289
$485$	37.8622	1.71923
$486$	−0.757341	−0.0343537
$487$	9.44125	0.427824	0.213912	−	0.976853i	$-0.431379\pi$
$487$	9.44125	0.427824	0.213912	+	0.976853i	$0.431379\pi$
$488$	−4.50625	−0.203988
$489$	20.4102	0.922983
$490$	0.887167	0.0400781
$491$	8.76827	0.395706	0.197853	−	0.980232i	$-0.436603\pi$
$491$	8.76827	0.395706	0.197853	+	0.980232i	$0.436603\pi$
$492$	−10.6007	−0.477916
$493$	−2.83396	−0.127635
$494$	−0.115409	−0.00519251
$495$	1.44906	0.0651303
$496$	−34.5796	−1.55267
$497$	−26.6557	−1.19567
$498$	−2.62730	−0.117732
$499$	−20.0686	−0.898394	−0.449197	−	0.893433i	$-0.648290\pi$
$499$	−20.0686	−0.898394	−0.449197	+	0.893433i	$0.648290\pi$
$500$	−0.373311	−0.0166950
$501$	−17.9101	−0.800164
$502$	−5.31071	−0.237029
$503$	12.7817	0.569909	0.284955	−	0.958541i	$-0.408021\pi$
$503$	12.7817	0.569909	0.284955	+	0.958541i	$0.408021\pi$
$504$	−0.839015	−0.0373727
$505$	22.6796	1.00923
$506$	−1.17780	−0.0523596
$507$	1.83284	0.0813992
$508$	−38.0855	−1.68977
$509$	−37.6479	−1.66871	−0.834356	−	0.551225i	$-0.814160\pi$
$509$	−37.6479	−1.66871	−0.834356	+	0.551225i	$0.814160\pi$
$510$	4.68899	0.207632
$511$	0.197046	0.00871681
$512$	14.9839	0.662201
$513$	2.73972	0.120962
$514$	1.78412	0.0786941
$515$	−3.17177	−0.139765
$516$	−5.44293	−0.239612
$517$	3.80558	0.167369
$518$	5.18405	0.227774
$519$	−31.3440	−1.37585
$520$	−2.55978	−0.112254
$521$	8.70308	0.381289	0.190644	−	0.981659i	$-0.438942\pi$
$521$	8.70308	0.381289	0.190644	+	0.981659i	$0.438942\pi$
$522$	−0.0524749	−0.00229677
$523$	−4.77041	−0.208595	−0.104298	−	0.994546i	$-0.533259\pi$
$523$	−4.77041	−0.208595	−0.104298	+	0.994546i	$0.533259\pi$
$524$	−34.4794	−1.50624
$525$	26.8346	1.17116
$526$	−5.64458	−0.246116
$527$	−36.4582	−1.58815
$528$	8.74486	0.380571
$529$	−2.35900	−0.102565
$530$	1.07760	0.0468079
$531$	1.94083	0.0842250
$532$	3.20763	0.139068
$533$	2.95326	0.127920
$534$	−3.28096	−0.141981
$535$	−34.5892	−1.49542
$536$	11.0161	0.475822
$537$	−26.1112	−1.12678
$538$	0.166334	0.00717116
$539$	1.74443	0.0751381
$540$	30.0644	1.29377
$541$	11.9657	0.514444	0.257222	−	0.966352i	$-0.417193\pi$
$541$	11.9657	0.514444	0.257222	+	0.966352i	$0.417193\pi$
$542$	−5.71619	−0.245531
$543$	8.11847	0.348397
$544$	9.41226	0.403547
$545$	−38.9650	−1.66908
$546$	1.08122	0.0462720
$547$	−6.05784	−0.259015	−0.129507	−	0.991578i	$-0.541340\pi$
$547$	−6.05784	−0.259015	−0.129507	+	0.991578i	$0.541340\pi$
$548$	2.07198	0.0885107
$549$	2.00618	0.0856217
$550$	1.31179	0.0559350
$551$	0.405491	0.0172745
$552$	6.72034	0.286037
$553$	32.0525	1.36301
$554$	0.378432	0.0160780
$555$	51.0863	2.16849
$556$	−17.1225	−0.726157
$557$	19.5149	0.826871	0.413436	−	0.910533i	$-0.364329\pi$
$557$	19.5149	0.826871	0.413436	+	0.910533i	$0.364329\pi$
$558$	−0.675079	−0.0285784
$559$	1.51635	0.0641348
$560$	34.4361	1.45519
$561$	9.21994	0.389266
$562$	−0.827844	−0.0349205
$563$	8.59800	0.362363	0.181181	−	0.983450i	$-0.442008\pi$
$563$	8.59800	0.362363	0.181181	+	0.983450i	$0.442008\pi$
$564$	−10.7430	−0.452362
$565$	28.2176	1.18712
$566$	−2.94576	−0.123819
$567$	−28.7861	−1.20890
$568$	7.43496	0.311964
$569$	28.4424	1.19237	0.596184	−	0.802848i	$-0.296683\pi$
$569$	28.4424	1.19237	0.596184	+	0.802848i	$0.296683\pi$
$570$	−0.670913	−0.0281015
$571$	−41.5433	−1.73853	−0.869266	−	0.494345i	$-0.835408\pi$
$571$	−41.5433	−1.73853	−0.869266	+	0.494345i	$0.835408\pi$
$572$	−2.49022	−0.104121
$573$	−9.34058	−0.390208
$574$	1.74217	0.0727169
$575$	−22.9892	−0.958717
$576$	−2.52213	−0.105089
$577$	26.4983	1.10314	0.551570	−	0.834129i	$-0.314029\pi$
$577$	26.4983	1.10314	0.551570	+	0.834129i	$0.314029\pi$
$578$	−0.274973	−0.0114374
$579$	−31.1060	−1.29272
$580$	4.44967	0.184762
$581$	−20.3432	−0.843977
$582$	4.46074	0.184904
$583$	2.11888	0.0877551
$584$	−0.0549613	−0.00227431
$585$	1.13961	0.0471172
$586$	2.15058	0.0888398
$587$	15.8740	0.655189	0.327595	−	0.944818i	$-0.393762\pi$
$587$	15.8740	0.655189	0.327595	+	0.944818i	$0.393762\pi$
$588$	−4.92446	−0.203082
$589$	5.21655	0.214944
$590$	3.49310	0.143809
$591$	20.6652	0.850053
$592$	32.9746	1.35525
$593$	−8.69217	−0.356944	−0.178472	−	0.983945i	$-0.557115\pi$
$593$	−8.69217	−0.356944	−0.178472	+	0.983945i	$0.557115\pi$
$594$	−1.25473	−0.0514822
$595$	36.3069	1.48844
$596$	33.5370	1.37373
$597$	−9.30132	−0.380678
$598$	−0.926283	−0.0378785
$599$	−14.8573	−0.607054	−0.303527	−	0.952823i	$-0.598164\pi$
$599$	−14.8573	−0.607054	−0.303527	+	0.952823i	$0.598164\pi$
$600$	−7.48488	−0.305569
$601$	−0.154515	−0.00630281	−0.00315140	−	0.999995i	$-0.501003\pi$
$601$	−0.154515	−0.00630281	−0.00315140	+	0.999995i	$0.501003\pi$
$602$	0.894520	0.0364579
$603$	−4.90435	−0.199721
$604$	−16.9752	−0.690711
$605$	−29.7613	−1.20997
$606$	2.67201	0.108543
$607$	34.1133	1.38462	0.692309	−	0.721601i	$-0.256594\pi$
$607$	34.1133	1.38462	0.692309	+	0.721601i	$0.256594\pi$
$608$	−1.34673	−0.0546172
$609$	−3.79887	−0.153938
$610$	3.61071	0.146194
$611$	2.99290	0.121080
$612$	−2.78381	−0.112529
$613$	−0.948408	−0.0383058	−0.0191529	−	0.999817i	$-0.506097\pi$
$613$	−0.948408	−0.0383058	−0.0191529	+	0.999817i	$0.506097\pi$
$614$	1.55857	0.0628988
$615$	17.1683	0.692292
$616$	−2.96922	−0.119633
$617$	27.9661	1.12587	0.562936	−	0.826501i	$-0.309672\pi$
$617$	27.9661	1.12587	0.562936	+	0.826501i	$0.309672\pi$
$618$	−0.373682	−0.0150317
$619$	−18.4934	−0.743313	−0.371657	−	0.928370i	$-0.621210\pi$
$619$	−18.4934	−0.743313	−0.371657	+	0.928370i	$0.621210\pi$
$620$	57.2440	2.29897
$621$	21.9892	0.882395
$622$	−5.76096	−0.230993
$623$	−25.4045	−1.01781
$624$	6.87740	0.275316
$625$	−24.6959	−0.987836
$626$	0.289018	0.0115515
$627$	−1.31921	−0.0526844
$628$	12.4557	0.497038
$629$	34.7660	1.38621
$630$	0.672276	0.0267841
$631$	39.2730	1.56343	0.781716	−	0.623634i	$-0.214344\pi$
$631$	39.2730	1.56343	0.781716	+	0.623634i	$0.214344\pi$
$632$	−8.94028	−0.355625
$633$	−24.9715	−0.992530
$634$	0.164392	0.00652883
$635$	61.6811	2.44774
$636$	−5.98152	−0.237183
$637$	1.37191	0.0543571
$638$	−0.185705	−0.00735214
$639$	−3.31004	−0.130943
$640$	−19.6314	−0.776000
$641$	45.0128	1.77790	0.888950	−	0.458005i	$-0.151436\pi$
$641$	45.0128	1.77790	0.888950	+	0.458005i	$0.151436\pi$
$642$	−4.07514	−0.160833
$643$	−27.9118	−1.10073	−0.550367	−	0.834923i	$-0.685512\pi$
$643$	−27.9118	−1.10073	−0.550367	+	0.834923i	$0.685512\pi$
$644$	25.7446	1.01448
$645$	8.81506	0.347093
$646$	−0.456579	−0.0179639
$647$	−10.9830	−0.431788	−0.215894	−	0.976417i	$-0.569267\pi$
$647$	−10.9830	−0.431788	−0.215894	+	0.976417i	$0.569267\pi$
$648$	8.02920	0.315417
$649$	6.86848	0.269611
$650$	1.03166	0.0404651
$651$	−48.8716	−1.91543
$652$	−21.8088	−0.854100
$653$	−1.72033	−0.0673216	−0.0336608	−	0.999433i	$-0.510717\pi$
$653$	−1.72033	−0.0673216	−0.0336608	+	0.999433i	$0.510717\pi$
$654$	−4.59066	−0.179509
$655$	55.8409	2.18189
$656$	11.0816	0.432663
$657$	0.0244687	0.000954617 0
$658$	1.76556	0.0688288
$659$	40.6986	1.58539	0.792697	−	0.609616i	$-0.208676\pi$
$659$	40.6986	1.58539	0.792697	+	0.609616i	$0.208676\pi$
$660$	−14.4765	−0.563495
$661$	−15.1825	−0.590531	−0.295266	−	0.955415i	$-0.595408\pi$
$661$	−15.1825	−0.590531	−0.295266	+	0.955415i	$0.595408\pi$
$662$	−5.35869	−0.208271
$663$	7.25103	0.281607
$664$	5.67424	0.220203
$665$	−5.19489	−0.201449
$666$	0.643744	0.0249446
$667$	3.25449	0.126014
$668$	19.1374	0.740447
$669$	−36.5234	−1.41208
$670$	−8.82682	−0.341010
$671$	7.09974	0.274082
$672$	12.6170	0.486710
$673$	14.3206	0.552018	0.276009	−	0.961155i	$-0.410988\pi$
$673$	14.3206	0.552018	0.276009	+	0.961155i	$0.410988\pi$
$674$	0.104934	0.00404192
$675$	−24.4908	−0.942650
$676$	−1.95843	−0.0753243
$677$	35.2519	1.35484	0.677419	−	0.735597i	$-0.263098\pi$
$677$	35.2519	1.35484	0.677419	+	0.735597i	$0.263098\pi$
$678$	3.32446	0.127675
$679$	34.5396	1.32551
$680$	−10.1269	−0.388350
$681$	54.4402	2.08615
$682$	−2.38906	−0.0914818
$683$	46.8127	1.79124	0.895620	−	0.444821i	$-0.146733\pi$
$683$	46.8127	1.79124	0.895620	+	0.444821i	$0.146733\pi$
$684$	0.398316	0.0152300
$685$	−3.35567	−0.128213
$686$	−3.32010	−0.126762
$687$	−51.8281	−1.97736
$688$	5.68984	0.216923
$689$	1.66640	0.0634847
$690$	−5.38479	−0.204996
$691$	−4.93276	−0.187651	−0.0938255	−	0.995589i	$-0.529910\pi$
$691$	−4.93276	−0.187651	−0.0938255	+	0.995589i	$0.529910\pi$
$692$	33.4918	1.27317
$693$	1.32189	0.0502146
$694$	1.55953	0.0591989
$695$	27.7307	1.05189
$696$	1.05960	0.0401642
$697$	11.6836	0.442548
$698$	−1.44868	−0.0548333
$699$	−1.55957	−0.0589883
$700$	−28.6734	−1.08375
$701$	1.00904	0.0381109	0.0190554	−	0.999818i	$-0.493934\pi$
$701$	1.00904	0.0381109	0.0190554	+	0.999818i	$0.493934\pi$
$702$	−0.986783	−0.0372437
$703$	−4.97441	−0.187614
$704$	−8.92564	−0.336398
$705$	17.3988	0.655275
$706$	3.28993	0.123818
$707$	20.6894	0.778104
$708$	−19.3894	−0.728699
$709$	29.0877	1.09241	0.546206	−	0.837651i	$-0.316071\pi$
$709$	29.0877	1.09241	0.546206	+	0.837651i	$0.316071\pi$
$710$	−5.95740	−0.223577
$711$	3.98021	0.149270
$712$	7.08597	0.265558
$713$	41.8683	1.56798
$714$	4.27750	0.160081
$715$	4.03301	0.150826
$716$	27.9004	1.04269
$717$	5.79110	0.216272
$718$	1.51359	0.0564867
$719$	40.9624	1.52764	0.763821	−	0.645429i	$-0.223321\pi$
$719$	40.9624	1.52764	0.763821	+	0.645429i	$0.223321\pi$
$720$	4.27619	0.159364
$721$	−2.89343	−0.107757
$722$	−3.80842	−0.141735
$723$	22.8392	0.849399
$724$	−8.67478	−0.322396
$725$	−3.62474	−0.134619
$726$	−3.50633	−0.130132
$727$	−18.5444	−0.687775	−0.343888	−	0.939011i	$-0.611744\pi$
$727$	−18.5444	−0.687775	−0.343888	+	0.939011i	$0.611744\pi$
$728$	−2.33514	−0.0865462
$729$	23.0381	0.853264
$730$	0.0440387	0.00162995
$731$	5.99895	0.221879
$732$	−20.0423	−0.740783
$733$	−47.8412	−1.76706	−0.883528	−	0.468379i	$-0.844838\pi$
$733$	−47.8412	−1.76706	−0.883528	+	0.468379i	$0.844838\pi$
$734$	−4.00018	−0.147649
$735$	7.97538	0.294176
$736$	−10.8090	−0.398424
$737$	−17.3562	−0.639322
$738$	0.216339	0.00796356
$739$	16.2687	0.598453	0.299227	−	0.954182i	$-0.403271\pi$
$739$	16.2687	0.598453	0.299227	+	0.954182i	$0.403271\pi$
$740$	−54.5869	−2.00666
$741$	−1.03750	−0.0381134
$742$	0.983034	0.0360883
$743$	2.80197	0.102794	0.0513972	−	0.998678i	$-0.483633\pi$
$743$	2.80197	0.102794	0.0513972	+	0.998678i	$0.483633\pi$
$744$	13.6316	0.499758
$745$	−54.3147	−1.98994
$746$	0.947454	0.0346888
$747$	−2.52617	−0.0924277
$748$	−9.85172	−0.360215
$749$	−31.5538	−1.15295
$750$	0.0712303	0.00260096
$751$	52.1742	1.90387	0.951933	−	0.306308i	$-0.0990936\pi$
$751$	52.1742	1.90387	0.951933	+	0.306308i	$0.0990936\pi$
$752$	11.2303	0.409528
$753$	−47.7418	−1.73981
$754$	−0.146048	−0.00531876
$755$	27.4920	1.00054
$756$	27.4261	0.997478
$757$	−6.87828	−0.249995	−0.124998	−	0.992157i	$-0.539892\pi$
$757$	−6.87828	−0.249995	−0.124998	+	0.992157i	$0.539892\pi$
$758$	2.77680	0.100858
$759$	−10.5881	−0.384324
$760$	1.44899	0.0525604
$761$	−32.0246	−1.16089	−0.580445	−	0.814300i	$-0.697121\pi$
$761$	−32.0246	−1.16089	−0.580445	+	0.814300i	$0.697121\pi$
$762$	7.26697	0.263254
$763$	−35.5456	−1.28684
$764$	9.98064	0.361087
$765$	4.50850	0.163005
$766$	7.22043	0.260885
$767$	5.40172	0.195045
$768$	23.4186	0.845048
$769$	26.7495	0.964612	0.482306	−	0.876003i	$-0.339799\pi$
$769$	26.7495	0.964612	0.482306	+	0.876003i	$0.339799\pi$
$770$	2.37914	0.0857382
$771$	16.0387	0.577621
$772$	33.2375	1.19624
$773$	32.8125	1.18018	0.590091	−	0.807336i	$-0.299092\pi$
$773$	32.8125	1.18018	0.590091	+	0.807336i	$0.299092\pi$
$774$	0.111080	0.00399267
$775$	−46.6315	−1.67505
$776$	−9.63399	−0.345840
$777$	46.6032	1.67188
$778$	2.03661	0.0730160
$779$	−1.67172	−0.0598957
$780$	−11.3850	−0.407649
$781$	−11.7140	−0.419160
$782$	−3.66453	−0.131043
$783$	3.46706	0.123903
$784$	5.14785	0.183852
$785$	−20.1726	−0.719991
$786$	6.57891	0.234662
$787$	−8.17426	−0.291381	−0.145690	−	0.989330i	$-0.546540\pi$
$787$	−8.17426	−0.291381	−0.145690	+	0.989330i	$0.546540\pi$
$788$	−22.0813	−0.786613
$789$	−50.7432	−1.80651
$790$	7.16356	0.254868
$791$	25.7413	0.915256
$792$	−0.368711	−0.0131016
$793$	5.58360	0.198279
$794$	7.51373	0.266652
$795$	9.68732	0.343574
$796$	9.93868	0.352267
$797$	−23.8712	−0.845563	−0.422781	−	0.906232i	$-0.638946\pi$
$797$	−23.8712	−0.845563	−0.422781	+	0.906232i	$0.638946\pi$
$798$	−0.612037	−0.0216659
$799$	11.8404	0.418885
$800$	12.0386	0.425630
$801$	−3.15467	−0.111465
$802$	2.62270	0.0926108
$803$	0.0865932	0.00305581
$804$	48.9957	1.72795
$805$	−41.6945	−1.46954
$806$	−1.87888	−0.0661806
$807$	1.49529	0.0526369
$808$	−5.77080	−0.203016
$809$	41.5827	1.46197	0.730985	−	0.682394i	$-0.239061\pi$
$809$	41.5827	1.46197	0.730985	+	0.682394i	$0.239061\pi$
$810$	−6.43354	−0.226052
$811$	−45.5385	−1.59907	−0.799536	−	0.600619i	$-0.794921\pi$
$811$	−45.5385	−1.59907	−0.799536	+	0.600619i	$0.794921\pi$
$812$	4.05918	0.142449
$813$	−51.3870	−1.80222
$814$	2.27817	0.0798497
$815$	35.3203	1.23722
$816$	27.2082	0.952477
$817$	−0.858347	−0.0300297
$818$	0.564758	0.0197463
$819$	1.03961	0.0363267
$820$	−18.3447	−0.640625
$821$	30.2964	1.05735	0.528676	−	0.848824i	$-0.322689\pi$
$821$	30.2964	1.05735	0.528676	+	0.848824i	$0.322689\pi$
$822$	−0.395348	−0.0137894
$823$	−4.83035	−0.168375	−0.0841877	−	0.996450i	$-0.526830\pi$
$823$	−4.83035	−0.168375	−0.0841877	+	0.996450i	$0.526830\pi$
$824$	0.807052	0.0281150
$825$	11.7927	0.410568
$826$	3.18656	0.110875
$827$	45.9604	1.59820	0.799100	−	0.601198i	$-0.205310\pi$
$827$	45.9604	1.59820	0.799100	+	0.601198i	$0.205310\pi$
$828$	3.19691	0.111100
$829$	19.6514	0.682521	0.341260	−	0.939969i	$-0.389146\pi$
$829$	19.6514	0.682521	0.341260	+	0.939969i	$0.389146\pi$
$830$	−4.54659	−0.157814
$831$	3.40200	0.118014
$832$	−7.01958	−0.243360
$833$	5.42752	0.188052
$834$	3.26710	0.113130
$835$	−30.9938	−1.07258
$836$	1.40961	0.0487525
$837$	44.6030	1.54170
$838$	−5.67384	−0.196000
$839$	−14.6655	−0.506308	−0.253154	−	0.967426i	$-0.581468\pi$
$839$	−14.6655	−0.506308	−0.253154	+	0.967426i	$0.581468\pi$
$840$	−13.5750	−0.468381
$841$	−28.4869	−0.982306
$842$	1.59262	0.0548853
$843$	−7.44209	−0.256319
$844$	26.6827	0.918456
$845$	3.17177	0.109112
$846$	0.219244	0.00753775
$847$	−27.1496	−0.932871
$848$	6.25286	0.214724
$849$	−26.4815	−0.908843
$850$	4.08143	0.139992
$851$	−39.9250	−1.36861
$852$	33.0682	1.13290
$853$	−47.9496	−1.64176	−0.820881	−	0.571099i	$-0.806517\pi$
$853$	−47.9496	−1.64176	−0.820881	+	0.571099i	$0.806517\pi$
$854$	3.29385	0.112713
$855$	−0.645090	−0.0220616
$856$	8.80119	0.300818
$857$	−24.5821	−0.839709	−0.419855	−	0.907591i	$-0.637919\pi$
$857$	−24.5821	−0.839709	−0.419855	+	0.907591i	$0.637919\pi$
$858$	0.475150	0.0162214
$859$	7.34189	0.250502	0.125251	−	0.992125i	$-0.460026\pi$
$859$	7.34189	0.250502	0.125251	+	0.992125i	$0.460026\pi$
$860$	−9.41910	−0.321189
$861$	15.6617	0.533748
$862$	−2.53865	−0.0864667
$863$	26.6227	0.906246	0.453123	−	0.891448i	$-0.350310\pi$
$863$	26.6227	0.906246	0.453123	+	0.891448i	$0.350310\pi$
$864$	−11.5150	−0.391747
$865$	−54.2415	−1.84427
$866$	−0.212758	−0.00722981
$867$	−2.47193	−0.0839513
$868$	52.2205	1.77248
$869$	14.0857	0.477824
$870$	−0.849027	−0.0287847
$871$	−13.6498	−0.462505
$872$	9.91458	0.335750
$873$	4.28905	0.145162
$874$	0.524332	0.0177358
$875$	0.551537	0.0186454
$876$	−0.244449	−0.00825917
$877$	29.0254	0.980117	0.490058	−	0.871690i	$-0.336975\pi$
$877$	29.0254	0.980117	0.490058	+	0.871690i	$0.336975\pi$
$878$	−2.35660	−0.0795314
$879$	19.3332	0.652091
$880$	15.1332	0.510139
$881$	−26.0652	−0.878158	−0.439079	−	0.898448i	$-0.644695\pi$
$881$	−26.0652	−0.878158	−0.439079	+	0.898448i	$0.644695\pi$
$882$	0.100499	0.00338397
$883$	−48.1731	−1.62115	−0.810577	−	0.585632i	$-0.800847\pi$
$883$	−48.1731	−1.62115	−0.810577	+	0.585632i	$0.800847\pi$
$884$	−7.74790	−0.260590
$885$	31.4020	1.05557
$886$	0.994267	0.0334031
$887$	24.9993	0.839396	0.419698	−	0.907664i	$-0.362136\pi$
$887$	24.9993	0.839396	0.419698	+	0.907664i	$0.362136\pi$
$888$	−12.9988	−0.436213
$889$	56.2682	1.88718
$890$	−5.67777	−0.190319
$891$	−12.6502	−0.423799
$892$	39.0261	1.30669
$893$	−1.69417	−0.0566931
$894$	−6.39909	−0.214018
$895$	−45.1859	−1.51040
$896$	−17.9087	−0.598286
$897$	−8.32702	−0.278031
$898$	1.47191	0.0491183
$899$	6.60143	0.220170
$900$	−3.56060	−0.118687
$901$	6.59255	0.219630
$902$	0.765610	0.0254920
$903$	8.04149	0.267604
$904$	−7.17993	−0.238801
$905$	14.0492	0.467010
$906$	3.23898	0.107608
$907$	−25.4370	−0.844621	−0.422310	−	0.906451i	$-0.638781\pi$
$907$	−25.4370	−0.844621	−0.422310	+	0.906451i	$0.638781\pi$
$908$	−58.1706	−1.93046
$909$	2.56916	0.0852136
$910$	1.87108	0.0620256
$911$	22.2980	0.738767	0.369384	−	0.929277i	$-0.379569\pi$
$911$	22.2980	0.738767	0.369384	+	0.929277i	$0.379569\pi$
$912$	−3.89303	−0.128911
$913$	−8.93995	−0.295869
$914$	3.74236	0.123786
$915$	32.4593	1.07307
$916$	55.3795	1.82979
$917$	50.9406	1.68221
$918$	−3.90388	−0.128847
$919$	−48.4598	−1.59854	−0.799271	−	0.600971i	$-0.794781\pi$
$919$	−48.4598	−1.59854	−0.799271	+	0.600971i	$0.794781\pi$
$920$	11.6297	0.383419
$921$	14.0111	0.461682
$922$	−2.31703	−0.0763073
$923$	−9.21250	−0.303233
$924$	−13.2061	−0.434448
$925$	44.4670	1.46207
$926$	4.68487	0.153954
$927$	−0.359299	−0.0118009
$928$	−1.70426	−0.0559452
$929$	36.5640	1.19963	0.599813	−	0.800140i	$-0.295242\pi$
$929$	36.5640	1.19963	0.599813	+	0.800140i	$0.295242\pi$
$930$	−10.9225	−0.358164
$931$	−0.776585	−0.0254516
$932$	1.66644	0.0545859
$933$	−51.7894	−1.69551
$934$	6.82283	0.223250
$935$	15.9553	0.521794
$936$	−0.289973	−0.00947806
$937$	−23.9591	−0.782709	−0.391355	−	0.920240i	$-0.627993\pi$
$937$	−23.9591	−0.782709	−0.391355	+	0.920240i	$0.627993\pi$
$938$	−8.05222	−0.262914
$939$	2.59819	0.0847887
$940$	−18.5910	−0.606371
$941$	3.78953	0.123535	0.0617676	−	0.998091i	$-0.480326\pi$
$941$	3.78953	0.123535	0.0617676	+	0.998091i	$0.480326\pi$
$942$	−2.37664	−0.0774350
$943$	−13.4173	−0.436929
$944$	20.2690	0.659699
$945$	−44.4178	−1.44491
$946$	0.393103	0.0127809
$947$	6.08257	0.197657	0.0988285	−	0.995104i	$-0.468490\pi$
$947$	6.08257	0.197657	0.0988285	+	0.995104i	$0.468490\pi$
$948$	−39.7633	−1.29145
$949$	0.0681013	0.00221066
$950$	−0.583983	−0.0189469
$951$	1.47784	0.0479221
$952$	−9.23823	−0.299413
$953$	−40.7073	−1.31864	−0.659320	−	0.751863i	$-0.729156\pi$
$953$	−40.7073	−1.31864	−0.659320	+	0.751863i	$0.729156\pi$
$954$	0.122071	0.00395219
$955$	−16.1641	−0.523057
$956$	−6.18792	−0.200132
$957$	−1.66944	−0.0539653
$958$	5.79567	0.187250
$959$	−3.06119	−0.0988509
$960$	−40.8072	−1.31705
$961$	53.9260	1.73955
$962$	1.79167	0.0577656
$963$	−3.91828	−0.126265
$964$	−24.4042	−0.786007
$965$	−53.8296	−1.73283
$966$	−4.91225	−0.158049
$967$	30.5446	0.982250	0.491125	−	0.871089i	$-0.336586\pi$
$967$	30.5446	0.982250	0.491125	+	0.871089i	$0.336586\pi$
$968$	7.57273	0.243397
$969$	−4.10452	−0.131856
$970$	7.71941	0.247855
$971$	−30.5972	−0.981911	−0.490955	−	0.871185i	$-0.663352\pi$
$971$	−30.5972	−0.981911	−0.490955	+	0.871185i	$0.663352\pi$
$972$	7.27482	0.233340
$973$	25.2972	0.810990
$974$	1.92490	0.0616777
$975$	9.27435	0.297017
$976$	20.9514	0.670639
$977$	−22.8782	−0.731937	−0.365969	−	0.930627i	$-0.619262\pi$
$977$	−22.8782	−0.731937	−0.365969	+	0.930627i	$0.619262\pi$
$978$	4.16127	0.133063
$979$	−11.1642	−0.356809
$980$	−8.52189	−0.272222
$981$	−4.41397	−0.140927
$982$	1.78769	0.0570474
$983$	2.72001	0.0867550	0.0433775	−	0.999059i	$-0.486188\pi$
$983$	2.72001	0.0867550	0.0433775	+	0.999059i	$0.486188\pi$
$984$	−4.36844	−0.139261
$985$	35.7616	1.13946
$986$	−0.577792	−0.0184006
$987$	15.8719	0.505209
$988$	1.10859	0.0352690
$989$	−6.88914	−0.219062
$990$	0.295436	0.00938958
$991$	−12.2565	−0.389340	−0.194670	−	0.980869i	$-0.562364\pi$
$991$	−12.2565	−0.389340	−0.194670	+	0.980869i	$0.562364\pi$
$992$	−21.9250	−0.696118
$993$	−48.1731	−1.52873
$994$	−5.43460	−0.172375
$995$	−16.0961	−0.510281
$996$	25.2371	0.799668
$997$	−38.3618	−1.21493	−0.607466	−	0.794346i	$-0.707814\pi$
$997$	−38.3618	−1.21493	−0.607466	+	0.794346i	$0.707814\pi$
$998$	−4.09162	−0.129518
$999$	−42.5327	−1.34567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.f.1.14	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.f.1.14	✓	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q+0.203882 q^{2} +1.83284 q^{3} -1.95843 q^{4} +3.17177 q^{5} +0.373682 q^{6} +2.89343 q^{7} -0.807052 q^{8} +0.359299 q^{9} +O(q^{10})\)	\(q+0.203882 q^{2} +1.83284 q^{3} -1.95843 q^{4} +3.17177 q^{5} +0.373682 q^{6} +2.89343 q^{7} -0.807052 q^{8} +0.359299 q^{9} +0.646665 q^{10} +1.27153 q^{11} -3.58949 q^{12} +1.00000 q^{13} +0.589916 q^{14} +5.81334 q^{15} +3.75232 q^{16} +3.95617 q^{17} +0.0732545 q^{18} -0.566061 q^{19} -6.21169 q^{20} +5.30318 q^{21} +0.259243 q^{22} -4.54324 q^{23} -1.47920 q^{24} +5.06010 q^{25} +0.203882 q^{26} -4.83998 q^{27} -5.66658 q^{28} -0.716338 q^{29} +1.18523 q^{30} -9.21553 q^{31} +2.37913 q^{32} +2.33052 q^{33} +0.806591 q^{34} +9.17727 q^{35} -0.703663 q^{36} +8.78778 q^{37} -0.115409 q^{38} +1.83284 q^{39} -2.55978 q^{40} +2.95326 q^{41} +1.08122 q^{42} +1.51635 q^{43} -2.49022 q^{44} +1.13961 q^{45} -0.926283 q^{46} +2.99290 q^{47} +6.87740 q^{48} +1.37191 q^{49} +1.03166 q^{50} +7.25103 q^{51} -1.95843 q^{52} +1.66640 q^{53} -0.986783 q^{54} +4.03301 q^{55} -2.33514 q^{56} -1.03750 q^{57} -0.146048 q^{58} +5.40172 q^{59} -11.3850 q^{60} +5.58360 q^{61} -1.87888 q^{62} +1.03961 q^{63} -7.01958 q^{64} +3.17177 q^{65} +0.475150 q^{66} -13.6498 q^{67} -7.74790 q^{68} -8.32702 q^{69} +1.87108 q^{70} -9.21250 q^{71} -0.289973 q^{72} +0.0681013 q^{73} +1.79167 q^{74} +9.27435 q^{75} +1.10859 q^{76} +3.67909 q^{77} +0.373682 q^{78} +11.0777 q^{79} +11.9015 q^{80} -9.94880 q^{81} +0.602115 q^{82} -7.03083 q^{83} -10.3859 q^{84} +12.5481 q^{85} +0.309156 q^{86} -1.31293 q^{87} -1.02619 q^{88} -8.78008 q^{89} +0.232346 q^{90} +2.89343 q^{91} +8.89762 q^{92} -16.8906 q^{93} +0.610198 q^{94} -1.79541 q^{95} +4.36057 q^{96} +11.9373 q^{97} +0.279708 q^{98} +0.456861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9}+O(q^{10}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9	\( 28 q + 6 q^{2} + 5 q^{3} + 32 q^{4} + 27 q^{5} + 9 q^{6} + 6 q^{7} + 21 q^{8} + 39 q^{9} + 5 q^{10} + 9 q^{11} + 15 q^{12} + 28 q^{13} + 20 q^{14} + 4 q^{15} + 32 q^{16} - 7 q^{17} + 10 q^{18} - 3 q^{19} + 53 q^{20} + 25 q^{21} - 14 q^{22} - 6 q^{23} + 10 q^{24} + 45 q^{25} + 6 q^{26} + 8 q^{27} - 12 q^{28} + 25 q^{29} - 43 q^{30} + q^{31} + 28 q^{32} + 17 q^{33} + 10 q^{34} + 11 q^{35} + 27 q^{36} + 18 q^{37} + 2 q^{38} + 5 q^{39} + 37 q^{40} + 56 q^{41} - 29 q^{42} - 30 q^{43} + 30 q^{44} + 38 q^{45} - 27 q^{46} + 40 q^{47} + 19 q^{48} + 36 q^{49} + 20 q^{50} - 18 q^{51} + 32 q^{52} + 51 q^{53} - 36 q^{54} - 5 q^{55} - 13 q^{56} + 31 q^{57} - 29 q^{58} + 29 q^{59} + 48 q^{60} + 16 q^{61} - 38 q^{62} - 23 q^{63} - 5 q^{64} + 27 q^{65} + 25 q^{66} - 2 q^{67} - 43 q^{68} + 38 q^{69} + 10 q^{70} + 34 q^{71} - 28 q^{72} + 14 q^{73} + 21 q^{74} + 19 q^{75} + 5 q^{76} + 34 q^{77} + 9 q^{78} + 3 q^{79} + 58 q^{80} + 4 q^{81} - 9 q^{82} + 38 q^{83} - 78 q^{84} - 27 q^{85} + 49 q^{86} + 8 q^{87} - 25 q^{88} + 125 q^{89} - 74 q^{90} + 6 q^{91} - 35 q^{92} + 36 q^{93} - q^{94} - 12 q^{95} + 26 q^{96} - 2 q^{97} + 18 q^{98} + 56 q^{99}+O(q^{100}) \) 28 * q + 6 * q^2 + 5 * q^3 + 32 * q^4 + 27 * q^5 + 9 * q^6 + 6 * q^7 + 21 * q^8 + 39 * q^9 + 5 * q^10 + 9 * q^11 + 15 * q^12 + 28 * q^13 + 20 * q^14 + 4 * q^15 + 32 * q^16 - 7 * q^17 + 10 * q^18 - 3 * q^19 + 53 * q^20 + 25 * q^21 - 14 * q^22 - 6 * q^23 + 10 * q^24 + 45 * q^25 + 6 * q^26 + 8 * q^27 - 12 * q^28 + 25 * q^29 - 43 * q^30 + q^31 + 28 * q^32 + 17 * q^33 + 10 * q^34 + 11 * q^35 + 27 * q^36 + 18 * q^37 + 2 * q^38 + 5 * q^39 + 37 * q^40 + 56 * q^41 - 29 * q^42 - 30 * q^43 + 30 * q^44 + 38 * q^45 - 27 * q^46 + 40 * q^47 + 19 * q^48 + 36 * q^49 + 20 * q^50 - 18 * q^51 + 32 * q^52 + 51 * q^53 - 36 * q^54 - 5 * q^55 - 13 * q^56 + 31 * q^57 - 29 * q^58 + 29 * q^59 + 48 * q^60 + 16 * q^61 - 38 * q^62 - 23 * q^63 - 5 * q^64 + 27 * q^65 + 25 * q^66 - 2 * q^67 - 43 * q^68 + 38 * q^69 + 10 * q^70 + 34 * q^71 - 28 * q^72 + 14 * q^73 + 21 * q^74 + 19 * q^75 + 5 * q^76 + 34 * q^77 + 9 * q^78 + 3 * q^79 + 58 * q^80 + 4 * q^81 - 9 * q^82 + 38 * q^83 - 78 * q^84 - 27 * q^85 + 49 * q^86 + 8 * q^87 - 25 * q^88 + 125 * q^89 - 74 * q^90 + 6 * q^91 - 35 * q^92 + 36 * q^93 - q^94 - 12 * q^95 + 26 * q^96 - 2 * q^97 + 18 * q^98 + 56 * q^99

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