LMFDB - Embedded newform 2011.2.a.b.1.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$0$
Dimension:	$90$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.47
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.343020 q^{2} +0.822211 q^{3} -1.88234 q^{4} -4.21312 q^{5} +0.282035 q^{6} -4.01438 q^{7} -1.33172 q^{8} -2.32397 q^{9} +O(q^{10})$	\(q+0.343020 q^{2} +0.822211 q^{3} -1.88234 q^{4} -4.21312 q^{5} +0.282035 q^{6} -4.01438 q^{7} -1.33172 q^{8} -2.32397 q^{9} -1.44519 q^{10} -4.53167 q^{11} -1.54768 q^{12} -0.661917 q^{13} -1.37701 q^{14} -3.46408 q^{15} +3.30787 q^{16} -1.48385 q^{17} -0.797169 q^{18} -3.78206 q^{19} +7.93052 q^{20} -3.30067 q^{21} -1.55446 q^{22} -2.04985 q^{23} -1.09496 q^{24} +12.7504 q^{25} -0.227051 q^{26} -4.37743 q^{27} +7.55641 q^{28} +6.69236 q^{29} -1.18825 q^{30} -0.231986 q^{31} +3.79811 q^{32} -3.72599 q^{33} -0.508989 q^{34} +16.9131 q^{35} +4.37449 q^{36} -4.90454 q^{37} -1.29732 q^{38} -0.544236 q^{39} +5.61071 q^{40} +4.20628 q^{41} -1.13220 q^{42} -9.31744 q^{43} +8.53014 q^{44} +9.79117 q^{45} -0.703142 q^{46} -9.98310 q^{47} +2.71976 q^{48} +9.11522 q^{49} +4.37365 q^{50} -1.22003 q^{51} +1.24595 q^{52} -2.59411 q^{53} -1.50155 q^{54} +19.0925 q^{55} +5.34603 q^{56} -3.10965 q^{57} +2.29562 q^{58} -2.01133 q^{59} +6.52056 q^{60} +7.16946 q^{61} -0.0795758 q^{62} +9.32929 q^{63} -5.31290 q^{64} +2.78874 q^{65} -1.27809 q^{66} -11.0825 q^{67} +2.79310 q^{68} -1.68541 q^{69} +5.80153 q^{70} -7.59784 q^{71} +3.09488 q^{72} -11.5795 q^{73} -1.68236 q^{74} +10.4835 q^{75} +7.11910 q^{76} +18.1918 q^{77} -0.186684 q^{78} -12.7286 q^{79} -13.9365 q^{80} +3.37274 q^{81} +1.44284 q^{82} -17.6753 q^{83} +6.21297 q^{84} +6.25163 q^{85} -3.19607 q^{86} +5.50254 q^{87} +6.03493 q^{88} +7.43770 q^{89} +3.35857 q^{90} +2.65719 q^{91} +3.85851 q^{92} -0.190741 q^{93} -3.42441 q^{94} +15.9343 q^{95} +3.12285 q^{96} -16.5198 q^{97} +3.12671 q^{98} +10.5315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) $ 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * 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 $

$2$	0.343020	0.242552	0.121276	−	0.992619i	$-0.461301\pi$
$2$	0.343020	0.242552	0.121276	+	0.992619i	$0.461301\pi$
$3$	0.822211	0.474704	0.237352	−	0.971424i	$-0.423721\pi$
$3$	0.822211	0.474704	0.237352	+	0.971424i	$0.423721\pi$
$4$	−1.88234	−0.941168
$5$	−4.21312	−1.88417	−0.942083	−	0.335379i	$-0.891136\pi$
$5$	−4.21312	−1.88417	−0.942083	+	0.335379i	$0.891136\pi$
$6$	0.282035	0.115140
$7$	−4.01438	−1.51729	−0.758646	−	0.651503i	$-0.774139\pi$
$7$	−4.01438	−1.51729	−0.758646	+	0.651503i	$0.774139\pi$
$8$	−1.33172	−0.470834
$9$	−2.32397	−0.774656
$10$	−1.44519	−0.457009
$11$	−4.53167	−1.36635	−0.683176	−	0.730254i	$-0.739402\pi$
$11$	−4.53167	−1.36635	−0.683176	+	0.730254i	$0.739402\pi$
$12$	−1.54768	−0.446776
$13$	−0.661917	−0.183583	−0.0917914	−	0.995778i	$-0.529259\pi$
$13$	−0.661917	−0.183583	−0.0917914	+	0.995778i	$0.529259\pi$
$14$	−1.37701	−0.368022
$15$	−3.46408	−0.894421
$16$	3.30787	0.826967
$17$	−1.48385	−0.359885	−0.179943	−	0.983677i	$-0.557591\pi$
$17$	−1.48385	−0.359885	−0.179943	+	0.983677i	$0.557591\pi$
$18$	−0.797169	−0.187894
$19$	−3.78206	−0.867663	−0.433832	−	0.900994i	$-0.642839\pi$
$19$	−3.78206	−0.867663	−0.433832	+	0.900994i	$0.642839\pi$
$20$	7.93052	1.77332
$21$	−3.30067	−0.720264
$22$	−1.55446	−0.331411
$23$	−2.04985	−0.427424	−0.213712	−	0.976897i	$-0.568555\pi$
$23$	−2.04985	−0.427424	−0.213712	+	0.976897i	$0.568555\pi$
$24$	−1.09496	−0.223507
$25$	12.7504	2.55008
$26$	−0.227051	−0.0445284
$27$	−4.37743	−0.842436
$28$	7.55641	1.42803
$29$	6.69236	1.24274	0.621370	−	0.783517i	$-0.286576\pi$
$29$	6.69236	1.24274	0.621370	+	0.783517i	$0.286576\pi$
$30$	−1.18825	−0.216944
$31$	−0.231986	−0.0416658	−0.0208329	−	0.999783i	$-0.506632\pi$
$31$	−0.231986	−0.0416658	−0.0208329	+	0.999783i	$0.506632\pi$
$32$	3.79811	0.671417
$33$	−3.72599	−0.648612
$34$	−0.508989	−0.0872910
$35$	16.9131	2.85883
$36$	4.37449	0.729082
$37$	−4.90454	−0.806302	−0.403151	−	0.915134i	$-0.632085\pi$
$37$	−4.90454	−0.806302	−0.403151	+	0.915134i	$0.632085\pi$
$38$	−1.29732	−0.210454
$39$	−0.544236	−0.0871475
$40$	5.61071	0.887131
$41$	4.20628	0.656910	0.328455	−	0.944520i	$-0.393472\pi$
$41$	4.20628	0.656910	0.328455	+	0.944520i	$0.393472\pi$
$42$	−1.13220	−0.174702
$43$	−9.31744	−1.42090	−0.710448	−	0.703750i	$-0.751508\pi$
$43$	−9.31744	−1.42090	−0.710448	+	0.703750i	$0.751508\pi$
$44$	8.53014	1.28597
$45$	9.79117	1.45958
$46$	−0.703142	−0.103673
$47$	−9.98310	−1.45618	−0.728092	−	0.685479i	$-0.759593\pi$
$47$	−9.98310	−1.45618	−0.728092	+	0.685479i	$0.759593\pi$
$48$	2.71976	0.392564
$49$	9.11522	1.30217
$50$	4.37365	0.618528
$51$	−1.22003	−0.170839
$52$	1.24595	0.172782
$53$	−2.59411	−0.356329	−0.178164	−	0.984001i	$-0.557016\pi$
$53$	−2.59411	−0.356329	−0.178164	+	0.984001i	$0.557016\pi$
$54$	−1.50155	−0.204335
$55$	19.0925	2.57443
$56$	5.34603	0.714393
$57$	−3.10965	−0.411883
$58$	2.29562	0.301429
$59$	−2.01133	−0.261854	−0.130927	−	0.991392i	$-0.541795\pi$
$59$	−2.01133	−0.261854	−0.130927	+	0.991392i	$0.541795\pi$
$60$	6.52056	0.841801
$61$	7.16946	0.917955	0.458978	−	0.888448i	$-0.348216\pi$
$61$	7.16946	0.917955	0.458978	+	0.888448i	$0.348216\pi$
$62$	−0.0795758	−0.0101061
$63$	9.32929	1.17538
$64$	−5.31290	−0.664113
$65$	2.78874	0.345901
$66$	−1.27809	−0.157322
$67$	−11.0825	−1.35395	−0.676974	−	0.736007i	$-0.736709\pi$
$67$	−11.0825	−1.35395	−0.676974	+	0.736007i	$0.736709\pi$
$68$	2.79310	0.338713
$69$	−1.68541	−0.202900
$70$	5.80153	0.693415
$71$	−7.59784	−0.901698	−0.450849	−	0.892600i	$-0.648879\pi$
$71$	−7.59784	−0.901698	−0.450849	+	0.892600i	$0.648879\pi$
$72$	3.09488	0.364735
$73$	−11.5795	−1.35528	−0.677641	−	0.735393i	$-0.736998\pi$
$73$	−11.5795	−1.35528	−0.677641	+	0.735393i	$0.736998\pi$
$74$	−1.68236	−0.195570
$75$	10.4835	1.21053
$76$	7.11910	0.816617
$77$	18.1918	2.07315
$78$	−0.186684	−0.0211378
$79$	−12.7286	−1.43208	−0.716038	−	0.698061i	$-0.754046\pi$
$79$	−12.7286	−1.43208	−0.716038	+	0.698061i	$0.754046\pi$
$80$	−13.9365	−1.55814
$81$	3.37274	0.374749
$82$	1.44284	0.159335
$83$	−17.6753	−1.94011	−0.970057	−	0.242879i	$-0.921908\pi$
$83$	−17.6753	−1.94011	−0.970057	+	0.242879i	$0.921908\pi$
$84$	6.21297	0.677890
$85$	6.25163	0.678084
$86$	−3.19607	−0.344641
$87$	5.50254	0.589934
$88$	6.03493	0.643325
$89$	7.43770	0.788394	0.394197	−	0.919026i	$-0.371023\pi$
$89$	7.43770	0.788394	0.394197	+	0.919026i	$0.371023\pi$
$90$	3.35857	0.354025
$91$	2.65719	0.278549
$92$	3.85851	0.402278
$93$	−0.190741	−0.0197789
$94$	−3.42441	−0.353201
$95$	15.9343	1.63482
$96$	3.12285	0.318724
$97$	−16.5198	−1.67733	−0.838665	−	0.544647i	$-0.816663\pi$
$97$	−16.5198	−1.67733	−0.838665	+	0.544647i	$0.816663\pi$
$98$	3.12671	0.315845
$99$	10.5315	1.05845
$100$	−24.0006	−2.40006
$101$	10.3756	1.03241	0.516204	−	0.856466i	$-0.327345\pi$
$101$	10.3756	1.03241	0.516204	+	0.856466i	$0.327345\pi$
$102$	−0.418497	−0.0414374
$103$	7.68244	0.756974	0.378487	−	0.925607i	$-0.376445\pi$
$103$	7.68244	0.756974	0.378487	+	0.925607i	$0.376445\pi$
$104$	0.881489	0.0864371
$105$	13.9061	1.35710
$106$	−0.889833	−0.0864282
$107$	4.81365	0.465353	0.232677	−	0.972554i	$-0.425252\pi$
$107$	4.81365	0.465353	0.232677	+	0.972554i	$0.425252\pi$
$108$	8.23979	0.792874
$109$	3.50464	0.335683	0.167842	−	0.985814i	$-0.446320\pi$
$109$	3.50464	0.335683	0.167842	+	0.985814i	$0.446320\pi$
$110$	6.54912	0.624434
$111$	−4.03257	−0.382755
$112$	−13.2790	−1.25475
$113$	−3.88328	−0.365308	−0.182654	−	0.983177i	$-0.558469\pi$
$113$	−3.88328	−0.365308	−0.182654	+	0.983177i	$0.558469\pi$
$114$	−1.06667	−0.0999031
$115$	8.63629	0.805338
$116$	−12.5973	−1.16963
$117$	1.53828	0.142214
$118$	−0.689929	−0.0635131
$119$	5.95672	0.546051
$120$	4.61319	0.421124
$121$	9.53607	0.866915
$122$	2.45927	0.222652
$123$	3.45845	0.311838
$124$	0.436675	0.0392146
$125$	−32.6535	−2.92062
$126$	3.20014	0.285091
$127$	−19.2994	−1.71254	−0.856272	−	0.516525i	$-0.827225\pi$
$127$	−19.2994	−1.71254	−0.856272	+	0.516525i	$0.827225\pi$
$128$	−9.41865	−0.832499
$129$	−7.66090	−0.674505
$130$	0.956595	0.0838989
$131$	13.8928	1.21382	0.606911	−	0.794770i	$-0.292408\pi$
$131$	13.8928	1.21382	0.606911	+	0.794770i	$0.292408\pi$
$132$	7.01357	0.610453
$133$	15.1826	1.31650
$134$	−3.80154	−0.328403
$135$	18.4426	1.58729
$136$	1.97607	0.169446
$137$	16.7136	1.42794	0.713971	−	0.700176i	$-0.246895\pi$
$137$	16.7136	1.42794	0.713971	+	0.700176i	$0.246895\pi$
$138$	−0.578131	−0.0492138
$139$	−12.0008	−1.01790	−0.508948	−	0.860797i	$-0.669966\pi$
$139$	−12.0008	−1.01790	−0.508948	+	0.860797i	$0.669966\pi$
$140$	−31.8361	−2.69064
$141$	−8.20821	−0.691256
$142$	−2.60621	−0.218709
$143$	2.99959	0.250839
$144$	−7.68738	−0.640615
$145$	−28.1958	−2.34153
$146$	−3.97202	−0.328726
$147$	7.49464	0.618147
$148$	9.23200	0.758866
$149$	−11.7171	−0.959899	−0.479950	−	0.877296i	$-0.659345\pi$
$149$	−11.7171	−0.959899	−0.479950	+	0.877296i	$0.659345\pi$
$150$	3.59607	0.293618
$151$	12.6806	1.03193	0.515965	−	0.856610i	$-0.327433\pi$
$151$	12.6806	1.03193	0.515965	+	0.856610i	$0.327433\pi$
$152$	5.03664	0.408526
$153$	3.44841	0.278787
$154$	6.24018	0.502848
$155$	0.977384	0.0785054
$156$	1.02444	0.0820205
$157$	−3.71684	−0.296636	−0.148318	−	0.988940i	$-0.547386\pi$
$157$	−3.71684	−0.296636	−0.148318	+	0.988940i	$0.547386\pi$
$158$	−4.36616	−0.347353
$159$	−2.13291	−0.169151
$160$	−16.0019	−1.26506
$161$	8.22888	0.648527
$162$	1.15692	0.0908960
$163$	23.6788	1.85467	0.927333	−	0.374237i	$-0.122095\pi$
$163$	23.6788	1.85467	0.927333	+	0.374237i	$0.122095\pi$
$164$	−7.91763	−0.618263
$165$	15.6981	1.22209
$166$	−6.06298	−0.470578
$167$	−16.2516	−1.25759	−0.628794	−	0.777572i	$-0.716451\pi$
$167$	−16.2516	−1.25759	−0.628794	+	0.777572i	$0.716451\pi$
$168$	4.39557	0.339125
$169$	−12.5619	−0.966297
$170$	2.14444	0.164471
$171$	8.78938	0.672141
$172$	17.5386	1.33730
$173$	23.5196	1.78817	0.894083	−	0.447902i	$-0.147829\pi$
$173$	23.5196	1.78817	0.894083	+	0.447902i	$0.147829\pi$
$174$	1.88748	0.143090
$175$	−51.1850	−3.86922
$176$	−14.9902	−1.12993
$177$	−1.65374	−0.124303
$178$	2.55128	0.191227
$179$	0.703591	0.0525889	0.0262944	−	0.999654i	$-0.491629\pi$
$179$	0.703591	0.0525889	0.0262944	+	0.999654i	$0.491629\pi$
$180$	−18.4303	−1.37371
$181$	−7.83182	−0.582134	−0.291067	−	0.956703i	$-0.594010\pi$
$181$	−7.83182	−0.582134	−0.291067	+	0.956703i	$0.594010\pi$
$182$	0.911469	0.0675626
$183$	5.89481	0.435757
$184$	2.72983	0.201246
$185$	20.6634	1.51921
$186$	−0.0654281	−0.00479742
$187$	6.72430	0.491730
$188$	18.7916	1.37051
$189$	17.5726	1.27822
$190$	5.46578	0.396529
$191$	0.263128	0.0190393	0.00951965	−	0.999955i	$-0.496970\pi$
$191$	0.263128	0.0190393	0.00951965	+	0.999955i	$0.496970\pi$
$192$	−4.36833	−0.315257
$193$	−5.18754	−0.373407	−0.186704	−	0.982416i	$-0.559780\pi$
$193$	−5.18754	−0.373407	−0.186704	+	0.982416i	$0.559780\pi$
$194$	−5.66662	−0.406840
$195$	2.29293	0.164200
$196$	−17.1579	−1.22557
$197$	5.36761	0.382426	0.191213	−	0.981549i	$-0.438758\pi$
$197$	5.36761	0.382426	0.191213	+	0.981549i	$0.438758\pi$
$198$	3.61251	0.256730
$199$	−7.72473	−0.547591	−0.273796	−	0.961788i	$-0.588279\pi$
$199$	−7.72473	−0.547591	−0.273796	+	0.961788i	$0.588279\pi$
$200$	−16.9800	−1.20067
$201$	−9.11219	−0.642724
$202$	3.55903	0.250413
$203$	−26.8657	−1.88560
$204$	2.29652	0.160788
$205$	−17.7216	−1.23773
$206$	2.63524	0.183606
$207$	4.76379	0.331107
$208$	−2.18953	−0.151817
$209$	17.1390	1.18553
$210$	4.77008	0.329167
$211$	−7.50717	−0.516815	−0.258408	−	0.966036i	$-0.583198\pi$
$211$	−7.50717	−0.516815	−0.258408	+	0.966036i	$0.583198\pi$
$212$	4.88299	0.335365
$213$	−6.24703	−0.428039
$214$	1.65118	0.112872
$215$	39.2555	2.67720
$216$	5.82951	0.396648
$217$	0.931278	0.0632192
$218$	1.20216	0.0814207
$219$	−9.52082	−0.643357
$220$	−35.9385	−2.42298
$221$	0.982183	0.0660688
$222$	−1.38325	−0.0928379
$223$	−1.71510	−0.114852	−0.0574259	−	0.998350i	$-0.518289\pi$
$223$	−1.71510	−0.114852	−0.0574259	+	0.998350i	$0.518289\pi$
$224$	−15.2470	−1.01874
$225$	−29.6316	−1.97544
$226$	−1.33204	−0.0886062
$227$	−27.2132	−1.80621	−0.903103	−	0.429424i	$-0.858717\pi$
$227$	−27.2132	−1.80621	−0.903103	+	0.429424i	$0.858717\pi$
$228$	5.85341	0.387651
$229$	27.3411	1.80675	0.903375	−	0.428852i	$-0.141082\pi$
$229$	27.3411	1.80675	0.903375	+	0.428852i	$0.141082\pi$
$230$	2.96242	0.195336
$231$	14.9575	0.984134
$232$	−8.91236	−0.585125
$233$	−5.98848	−0.392318	−0.196159	−	0.980572i	$-0.562847\pi$
$233$	−5.98848	−0.392318	−0.196159	+	0.980572i	$0.562847\pi$
$234$	0.527660	0.0344942
$235$	42.0600	2.74369
$236$	3.78601	0.246448
$237$	−10.4656	−0.679812
$238$	2.04328	0.132446
$239$	6.97676	0.451289	0.225644	−	0.974210i	$-0.427551\pi$
$239$	6.97676	0.451289	0.225644	+	0.974210i	$0.427551\pi$
$240$	−11.4587	−0.739656
$241$	8.23992	0.530780	0.265390	−	0.964141i	$-0.414499\pi$
$241$	8.23992	0.530780	0.265390	+	0.964141i	$0.414499\pi$
$242$	3.27107	0.210272
$243$	15.9054	1.02033
$244$	−13.4953	−0.863951
$245$	−38.4036	−2.45351
$246$	1.18632	0.0756369
$247$	2.50341	0.159288
$248$	0.308940	0.0196177
$249$	−14.5328	−0.920979
$250$	−11.2008	−0.708401
$251$	−12.0485	−0.760497	−0.380249	−	0.924884i	$-0.624162\pi$
$251$	−12.0485	−0.760497	−0.380249	+	0.924884i	$0.624162\pi$
$252$	−17.5609	−1.10623
$253$	9.28927	0.584011
$254$	−6.62009	−0.415381
$255$	5.14016	0.321889
$256$	7.39502	0.462189
$257$	−4.32421	−0.269737	−0.134869	−	0.990863i	$-0.543061\pi$
$257$	−4.32421	−0.269737	−0.134869	+	0.990863i	$0.543061\pi$
$258$	−2.62785	−0.163603
$259$	19.6887	1.22340
$260$	−5.24935	−0.325551
$261$	−15.5528	−0.962697
$262$	4.76553	0.294415
$263$	7.83414	0.483074	0.241537	−	0.970392i	$-0.422349\pi$
$263$	7.83414	0.483074	0.241537	+	0.970392i	$0.422349\pi$
$264$	4.96198	0.305389
$265$	10.9293	0.671382
$266$	5.20794	0.319319
$267$	6.11536	0.374254
$268$	20.8611	1.27429
$269$	12.1882	0.743129	0.371565	−	0.928407i	$-0.378821\pi$
$269$	12.1882	0.743129	0.371565	+	0.928407i	$0.378821\pi$
$270$	6.32620	0.385001
$271$	−21.8337	−1.32630	−0.663151	−	0.748486i	$-0.730781\pi$
$271$	−21.8337	−1.32630	−0.663151	+	0.748486i	$0.730781\pi$
$272$	−4.90836	−0.297613
$273$	2.18477	0.132228
$274$	5.73311	0.346350
$275$	−57.7807	−3.48431
$276$	3.17251	0.190963
$277$	12.6682	0.761157	0.380578	−	0.924749i	$-0.375725\pi$
$277$	12.6682	0.761157	0.380578	+	0.924749i	$0.375725\pi$
$278$	−4.11653	−0.246893
$279$	0.539127	0.0322767
$280$	−22.5235	−1.34604
$281$	−19.1535	−1.14260	−0.571300	−	0.820741i	$-0.693561\pi$
$281$	−19.1535	−1.14260	−0.571300	+	0.820741i	$0.693561\pi$
$282$	−2.81559	−0.167666
$283$	30.0470	1.78611	0.893055	−	0.449948i	$-0.148557\pi$
$283$	30.0470	1.78611	0.893055	+	0.449948i	$0.148557\pi$
$284$	14.3017	0.848649
$285$	13.1013	0.776056
$286$	1.02892	0.0608414
$287$	−16.8856	−0.996724
$288$	−8.82668	−0.520117
$289$	−14.7982	−0.870482
$290$	−9.67172	−0.567943
$291$	−13.5828	−0.796235
$292$	21.7966	1.27555
$293$	13.9898	0.817291	0.408645	−	0.912693i	$-0.366001\pi$
$293$	13.9898	0.817291	0.408645	+	0.912693i	$0.366001\pi$
$294$	2.57081	0.149933
$295$	8.47400	0.493376
$296$	6.53148	0.379635
$297$	19.8371	1.15106
$298$	−4.01919	−0.232826
$299$	1.35683	0.0784677
$300$	−19.7335	−1.13932
$301$	37.4037	2.15591
$302$	4.34969	0.250297
$303$	8.53091	0.490088
$304$	−12.5105	−0.717528
$305$	−30.2058	−1.72958
$306$	1.18288	0.0676205
$307$	−17.8203	−1.01706	−0.508529	−	0.861045i	$-0.669811\pi$
$307$	−17.8203	−1.01706	−0.508529	+	0.861045i	$0.669811\pi$
$308$	−34.2432	−1.95119
$309$	6.31659	0.359338
$310$	0.335263	0.0190416
$311$	−2.55549	−0.144909	−0.0724544	−	0.997372i	$-0.523083\pi$
$311$	−2.55549	−0.144909	−0.0724544	+	0.997372i	$0.523083\pi$
$312$	0.724770	0.0410320
$313$	1.28891	0.0728534	0.0364267	−	0.999336i	$-0.488402\pi$
$313$	1.28891	0.0728534	0.0364267	+	0.999336i	$0.488402\pi$
$314$	−1.27495	−0.0719498
$315$	−39.3054	−2.21461
$316$	23.9595	1.34783
$317$	−23.9102	−1.34293	−0.671464	−	0.741037i	$-0.734334\pi$
$317$	−23.9102	−1.34293	−0.671464	+	0.741037i	$0.734334\pi$
$318$	−0.731631	−0.0410278
$319$	−30.3276	−1.69802
$320$	22.3839	1.25130
$321$	3.95784	0.220905
$322$	2.82268	0.157302
$323$	5.61199	0.312259
$324$	−6.34863	−0.352701
$325$	−8.43972	−0.468152
$326$	8.12231	0.449853
$327$	2.88155	0.159350
$328$	−5.60159	−0.309296
$329$	40.0759	2.20946
$330$	5.38476	0.296421
$331$	−16.8199	−0.924505	−0.462252	−	0.886748i	$-0.652959\pi$
$331$	−16.8199	−0.924505	−0.462252	+	0.886748i	$0.652959\pi$
$332$	33.2708	1.82597
$333$	11.3980	0.624607
$334$	−5.57464	−0.305031
$335$	46.6921	2.55106
$336$	−10.9182	−0.595635
$337$	−29.0214	−1.58090	−0.790448	−	0.612530i	$-0.790152\pi$
$337$	−29.0214	−1.58090	−0.790448	+	0.612530i	$0.790152\pi$
$338$	−4.30898	−0.234377
$339$	−3.19287	−0.173413
$340$	−11.7677	−0.638191
$341$	1.05128	0.0569302
$342$	3.01494	0.163029
$343$	−8.49130	−0.458487
$344$	12.4082	0.669007
$345$	7.10085	0.382297
$346$	8.06772	0.433723
$347$	21.8679	1.17393	0.586964	−	0.809613i	$-0.300323\pi$
$347$	21.8679	1.17393	0.586964	+	0.809613i	$0.300323\pi$
$348$	−10.3576	−0.555227
$349$	8.57466	0.458991	0.229495	−	0.973310i	$-0.426292\pi$
$349$	8.57466	0.458991	0.229495	+	0.973310i	$0.426292\pi$
$350$	−17.5575	−0.938488
$351$	2.89750	0.154657
$352$	−17.2118	−0.917391
$353$	−17.6426	−0.939023	−0.469512	−	0.882926i	$-0.655570\pi$
$353$	−17.6426	−0.939023	−0.469512	+	0.882926i	$0.655570\pi$
$354$	−0.567267	−0.0301499
$355$	32.0106	1.69895
$356$	−14.0002	−0.742012
$357$	4.89768	0.259213
$358$	0.241346	0.0127555
$359$	14.4915	0.764831	0.382416	−	0.923990i	$-0.375092\pi$
$359$	14.4915	0.764831	0.382416	+	0.923990i	$0.375092\pi$
$360$	−13.0391	−0.687221
$361$	−4.69605	−0.247161
$362$	−2.68647	−0.141198
$363$	7.84066	0.411528
$364$	−5.00172	−0.262161
$365$	48.7860	2.55358
$366$	2.02204	0.105694
$367$	34.1997	1.78521	0.892606	−	0.450838i	$-0.148875\pi$
$367$	34.1997	1.78521	0.892606	+	0.450838i	$0.148875\pi$
$368$	−6.78064	−0.353465
$369$	−9.77525	−0.508879
$370$	7.08799	0.368487
$371$	10.4137	0.540654
$372$	0.359039	0.0186153
$373$	−16.4479	−0.851640	−0.425820	−	0.904808i	$-0.640014\pi$
$373$	−16.4479	−0.851640	−0.425820	+	0.904808i	$0.640014\pi$
$374$	2.30657	0.119270
$375$	−26.8481	−1.38643
$376$	13.2947	0.685622
$377$	−4.42979	−0.228146
$378$	6.02778	0.310035
$379$	−8.43111	−0.433077	−0.216539	−	0.976274i	$-0.569477\pi$
$379$	−8.43111	−0.433077	−0.216539	+	0.976274i	$0.569477\pi$
$380$	−29.9937	−1.53864
$381$	−15.8682	−0.812951
$382$	0.0902584	0.00461802
$383$	26.9363	1.37638	0.688190	−	0.725530i	$-0.258406\pi$
$383$	26.9363	1.37638	0.688190	+	0.725530i	$0.258406\pi$
$384$	−7.74412	−0.395190
$385$	−76.6445	−3.90617
$386$	−1.77943	−0.0905707
$387$	21.6534	1.10071
$388$	31.0958	1.57865
$389$	−13.4142	−0.680125	−0.340063	−	0.940403i	$-0.610448\pi$
$389$	−13.4142	−0.680125	−0.340063	+	0.940403i	$0.610448\pi$
$390$	0.786523	0.0398272
$391$	3.04167	0.153824
$392$	−12.1389	−0.613109
$393$	11.4228	0.576206
$394$	1.84120	0.0927583
$395$	53.6271	2.69827
$396$	−19.8238	−0.996182
$397$	−8.24661	−0.413886	−0.206943	−	0.978353i	$-0.566351\pi$
$397$	−8.24661	−0.413886	−0.206943	+	0.978353i	$0.566351\pi$
$398$	−2.64974	−0.132819
$399$	12.4833	0.624947
$400$	42.1767	2.10883
$401$	14.6213	0.730151	0.365075	−	0.930978i	$-0.381043\pi$
$401$	14.6213	0.730151	0.365075	+	0.930978i	$0.381043\pi$
$402$	−3.12567	−0.155894
$403$	0.153555	0.00764913
$404$	−19.5303	−0.971669
$405$	−14.2098	−0.706089
$406$	−9.21548	−0.457356
$407$	22.2258	1.10169
$408$	1.62475	0.0804369
$409$	4.18824	0.207095	0.103548	−	0.994624i	$-0.466981\pi$
$409$	4.18824	0.207095	0.103548	+	0.994624i	$0.466981\pi$
$410$	−6.07886	−0.300213
$411$	13.7421	0.677849
$412$	−14.4609	−0.712440
$413$	8.07426	0.397308
$414$	1.63408	0.0803106
$415$	74.4681	3.65550
$416$	−2.51403	−0.123261
$417$	−9.86721	−0.483199
$418$	5.87904	0.287553
$419$	14.5003	0.708385	0.354193	−	0.935172i	$-0.384756\pi$
$419$	14.5003	0.708385	0.354193	+	0.935172i	$0.384756\pi$
$420$	−26.1760	−1.27726
$421$	−18.5525	−0.904194	−0.452097	−	0.891969i	$-0.649324\pi$
$421$	−18.5525	−0.904194	−0.452097	+	0.891969i	$0.649324\pi$
$422$	−2.57511	−0.125355
$423$	23.2004	1.12804
$424$	3.45463	0.167772
$425$	−18.9196	−0.917738
$426$	−2.14286	−0.103822
$427$	−28.7809	−1.39281
$428$	−9.06091	−0.437976
$429$	2.46630	0.119074
$430$	13.4654	0.649362
$431$	17.2189	0.829407	0.414703	−	0.909957i	$-0.363885\pi$
$431$	17.2189	0.829407	0.414703	+	0.909957i	$0.363885\pi$
$432$	−14.4799	−0.696667
$433$	−0.716876	−0.0344509	−0.0172254	−	0.999852i	$-0.505483\pi$
$433$	−0.716876	−0.0344509	−0.0172254	+	0.999852i	$0.505483\pi$
$434$	0.319447	0.0153340
$435$	−23.1829	−1.11153
$436$	−6.59691	−0.315935
$437$	7.75266	0.370860
$438$	−3.26584	−0.156048
$439$	−1.84340	−0.0879809	−0.0439905	−	0.999032i	$-0.514007\pi$
$439$	−1.84340	−0.0879809	−0.0439905	+	0.999032i	$0.514007\pi$
$440$	−25.4259	−1.21213
$441$	−21.1835	−1.00874
$442$	0.336909	0.0160251
$443$	−5.87394	−0.279079	−0.139540	−	0.990216i	$-0.544562\pi$
$443$	−5.87394	−0.279079	−0.139540	+	0.990216i	$0.544562\pi$
$444$	7.59066	0.360237
$445$	−31.3359	−1.48547
$446$	−0.588315	−0.0278575
$447$	−9.63390	−0.455668
$448$	21.3280	1.00765
$449$	38.4105	1.81270	0.906352	−	0.422523i	$-0.138855\pi$
$449$	38.4105	1.81270	0.906352	+	0.422523i	$0.138855\pi$
$450$	−10.1642	−0.479147
$451$	−19.0615	−0.897570
$452$	7.30963	0.343816
$453$	10.4261	0.489861
$454$	−9.33470	−0.438099
$455$	−11.1951	−0.524832
$456$	4.14118	0.193929
$457$	−42.1059	−1.96963	−0.984815	−	0.173606i	$-0.944458\pi$
$457$	−42.1059	−1.96963	−0.984815	+	0.173606i	$0.944458\pi$
$458$	9.37855	0.438231
$459$	6.49543	0.303180
$460$	−16.2564	−0.757959
$461$	−5.48229	−0.255336	−0.127668	−	0.991817i	$-0.540749\pi$
$461$	−5.48229	−0.255336	−0.127668	+	0.991817i	$0.540749\pi$
$462$	5.13074	0.238704
$463$	−1.55683	−0.0723518	−0.0361759	−	0.999345i	$-0.511518\pi$
$463$	−1.55683	−0.0723518	−0.0361759	+	0.999345i	$0.511518\pi$
$464$	22.1374	1.02771
$465$	0.803616	0.0372668
$466$	−2.05417	−0.0951576
$467$	−26.4278	−1.22293	−0.611467	−	0.791270i	$-0.709420\pi$
$467$	−26.4278	−1.22293	−0.611467	+	0.791270i	$0.709420\pi$
$468$	−2.89555	−0.133847
$469$	44.4895	2.05433
$470$	14.4274	0.665489
$471$	−3.05603	−0.140814
$472$	2.67854	0.123290
$473$	42.2236	1.94144
$474$	−3.58991	−0.164890
$475$	−48.2228	−2.21261
$476$	−11.2125	−0.513926
$477$	6.02863	0.276032
$478$	2.39317	0.109461
$479$	−36.2129	−1.65461	−0.827304	−	0.561754i	$-0.810127\pi$
$479$	−36.2129	−1.65461	−0.827304	+	0.561754i	$0.810127\pi$
$480$	−13.1569	−0.600530
$481$	3.24640	0.148023
$482$	2.82646	0.128742
$483$	6.76588	0.307858
$484$	−17.9501	−0.815913
$485$	69.5999	3.16037
$486$	5.45587	0.247483
$487$	27.0605	1.22623	0.613114	−	0.789994i	$-0.289917\pi$
$487$	27.0605	1.22623	0.613114	+	0.789994i	$0.289917\pi$
$488$	−9.54772	−0.432205
$489$	19.4690	0.880417
$490$	−13.1732	−0.595105
$491$	−5.37774	−0.242694	−0.121347	−	0.992610i	$-0.538721\pi$
$491$	−5.37774	−0.242694	−0.121347	+	0.992610i	$0.538721\pi$
$492$	−6.50996	−0.293492
$493$	−9.93044	−0.447244
$494$	0.858720	0.0386357
$495$	−44.3704	−1.99430
$496$	−0.767377	−0.0344563
$497$	30.5006	1.36814
$498$	−4.98505	−0.223385
$499$	−5.28099	−0.236410	−0.118205	−	0.992989i	$-0.537714\pi$
$499$	−5.28099	−0.236410	−0.118205	+	0.992989i	$0.537714\pi$
$500$	61.4648	2.74879
$501$	−13.3623	−0.596982
$502$	−4.13290	−0.184460
$503$	−35.8274	−1.59747	−0.798733	−	0.601686i	$-0.794496\pi$
$503$	−35.8274	−1.59747	−0.798733	+	0.601686i	$0.794496\pi$
$504$	−12.4240	−0.553409
$505$	−43.7135	−1.94523
$506$	3.18641	0.141653
$507$	−10.3285	−0.458705
$508$	36.3280	1.61179
$509$	9.12953	0.404659	0.202330	−	0.979317i	$-0.435149\pi$
$509$	9.12953	0.404659	0.202330	+	0.979317i	$0.435149\pi$
$510$	1.76318	0.0780749
$511$	46.4846	2.05636
$512$	21.3739	0.944604
$513$	16.5557	0.730951
$514$	−1.48329	−0.0654253
$515$	−32.3671	−1.42626
$516$	14.4204	0.634823
$517$	45.2401	1.98966
$518$	6.75362	0.296737
$519$	19.3381	0.848849
$520$	−3.71382	−0.162862
$521$	−39.7209	−1.74020	−0.870102	−	0.492872i	$-0.835947\pi$
$521$	−39.7209	−1.74020	−0.870102	+	0.492872i	$0.835947\pi$
$522$	−5.33494	−0.233504
$523$	−0.327917	−0.0143388	−0.00716941	−	0.999974i	$-0.502282\pi$
$523$	−0.327917	−0.0143388	−0.00716941	+	0.999974i	$0.502282\pi$
$524$	−26.1510	−1.14241
$525$	−42.0849	−1.83673
$526$	2.68727	0.117171
$527$	0.344231	0.0149949
$528$	−12.3251	−0.536381
$529$	−18.7981	−0.817309
$530$	3.74898	0.162845
$531$	4.67428	0.202846
$532$	−28.5788	−1.23905
$533$	−2.78421	−0.120597
$534$	2.09769	0.0907760
$535$	−20.2805	−0.876803
$536$	14.7588	0.637485
$537$	0.578501	0.0249641
$538$	4.18081	0.180248
$539$	−41.3072	−1.77923
$540$	−34.7153	−1.49391
$541$	8.19387	0.352282	0.176141	−	0.984365i	$-0.443639\pi$
$541$	8.19387	0.352282	0.176141	+	0.984365i	$0.443639\pi$
$542$	−7.48940	−0.321697
$543$	−6.43941	−0.276341
$544$	−5.63581	−0.241633
$545$	−14.7655	−0.632484
$546$	0.749420	0.0320722
$547$	−37.9404	−1.62221	−0.811107	−	0.584898i	$-0.801134\pi$
$547$	−37.9404	−1.62221	−0.811107	+	0.584898i	$0.801134\pi$
$548$	−31.4607	−1.34393
$549$	−16.6616	−0.711100
$550$	−19.8200	−0.845126
$551$	−25.3109	−1.07828
$552$	2.24450	0.0955322
$553$	51.0973	2.17288
$554$	4.34544	0.184620
$555$	16.9897	0.721173
$556$	22.5896	0.958012
$557$	−22.8577	−0.968513	−0.484257	−	0.874926i	$-0.660910\pi$
$557$	−22.8577	−0.968513	−0.484257	+	0.874926i	$0.660910\pi$
$558$	0.184932	0.00782878
$559$	6.16737	0.260852
$560$	55.9462	2.36416
$561$	5.52880	0.233426
$562$	−6.57004	−0.277140
$563$	−3.28831	−0.138586	−0.0692928	−	0.997596i	$-0.522074\pi$
$563$	−3.28831	−0.138586	−0.0692928	+	0.997596i	$0.522074\pi$
$564$	15.4506	0.650589
$565$	16.3607	0.688301
$566$	10.3067	0.433225
$567$	−13.5394	−0.568603
$568$	10.1182	0.424550
$569$	−12.3170	−0.516354	−0.258177	−	0.966098i	$-0.583122\pi$
$569$	−12.3170	−0.516354	−0.258177	+	0.966098i	$0.583122\pi$
$570$	4.49403	0.188234
$571$	28.8673	1.20806	0.604030	−	0.796962i	$-0.293561\pi$
$571$	28.8673	1.20806	0.604030	+	0.796962i	$0.293561\pi$
$572$	−5.64625	−0.236081
$573$	0.216347	0.00903803
$574$	−5.79210	−0.241758
$575$	−26.1365	−1.08997
$576$	12.3470	0.514459
$577$	−18.1006	−0.753536	−0.376768	−	0.926308i	$-0.622965\pi$
$577$	−18.1006	−0.753536	−0.376768	+	0.926308i	$0.622965\pi$
$578$	−5.07609	−0.211137
$579$	−4.26525	−0.177258
$580$	53.0739	2.20377
$581$	70.9552	2.94372
$582$	−4.65916	−0.193129
$583$	11.7557	0.486870
$584$	15.4207	0.638113
$585$	−6.48095	−0.267954
$586$	4.79877	0.198236
$587$	27.9101	1.15197	0.575987	−	0.817459i	$-0.304618\pi$
$587$	27.9101	1.15197	0.575987	+	0.817459i	$0.304618\pi$
$588$	−14.1074	−0.581781
$589$	0.877382	0.0361519
$590$	2.90676	0.119669
$591$	4.41331	0.181539
$592$	−16.2236	−0.666785
$593$	2.24696	0.0922715	0.0461357	−	0.998935i	$-0.485309\pi$
$593$	2.24696	0.0922715	0.0461357	+	0.998935i	$0.485309\pi$
$594$	6.80452	0.279193
$595$	−25.0964	−1.02885
$596$	22.0555	0.903427
$597$	−6.35136	−0.259944
$598$	0.465422	0.0190325
$599$	29.2537	1.19527	0.597636	−	0.801768i	$-0.296107\pi$
$599$	29.2537	1.19527	0.597636	+	0.801768i	$0.296107\pi$
$600$	−13.9611	−0.569961
$601$	−40.9212	−1.66921	−0.834606	−	0.550848i	$-0.814305\pi$
$601$	−40.9212	−1.66921	−0.834606	+	0.550848i	$0.814305\pi$
$602$	12.8302	0.522921
$603$	25.7555	1.04884
$604$	−23.8691	−0.971220
$605$	−40.1766	−1.63341
$606$	2.92628	0.118872
$607$	−29.7237	−1.20645	−0.603225	−	0.797571i	$-0.706118\pi$
$607$	−29.7237	−1.20645	−0.603225	+	0.797571i	$0.706118\pi$
$608$	−14.3647	−0.582564
$609$	−22.0893	−0.895102
$610$	−10.3612	−0.419513
$611$	6.60799	0.267330
$612$	−6.49107	−0.262386
$613$	−43.6351	−1.76241	−0.881203	−	0.472738i	$-0.843266\pi$
$613$	−43.6351	−1.76241	−0.881203	+	0.472738i	$0.843266\pi$
$614$	−6.11273	−0.246690
$615$	−14.5709	−0.587554
$616$	−24.2265	−0.976112
$617$	−27.9109	−1.12365	−0.561825	−	0.827256i	$-0.689901\pi$
$617$	−27.9109	−1.12365	−0.561825	+	0.827256i	$0.689901\pi$
$618$	2.16672	0.0871583
$619$	6.59801	0.265196	0.132598	−	0.991170i	$-0.457668\pi$
$619$	6.59801	0.265196	0.132598	+	0.991170i	$0.457668\pi$
$620$	−1.83977	−0.0738868
$621$	8.97308	0.360077
$622$	−0.876587	−0.0351479
$623$	−29.8577	−1.19622
$624$	−1.80026	−0.0720681
$625$	73.8211	2.95284
$626$	0.442122	0.0176708
$627$	14.0919	0.562777
$628$	6.99635	0.279185
$629$	7.27758	0.290176
$630$	−13.4826	−0.537159
$631$	20.1139	0.800721	0.400361	−	0.916358i	$-0.368885\pi$
$631$	20.1139	0.800721	0.400361	+	0.916358i	$0.368885\pi$
$632$	16.9509	0.674271
$633$	−6.17248	−0.245334
$634$	−8.20167	−0.325730
$635$	81.3108	3.22672
$636$	4.01485	0.159199
$637$	−6.03353	−0.239057
$638$	−10.4030	−0.411858
$639$	17.6571	0.698506
$640$	39.6819	1.56857
$641$	−7.59126	−0.299837	−0.149918	−	0.988698i	$-0.547901\pi$
$641$	−7.59126	−0.299837	−0.149918	+	0.988698i	$0.547901\pi$
$642$	1.35762	0.0535810
$643$	−7.22214	−0.284814	−0.142407	−	0.989808i	$-0.545484\pi$
$643$	−7.22214	−0.284814	−0.142407	+	0.989808i	$0.545484\pi$
$644$	−15.4895	−0.610373
$645$	32.2763	1.27088
$646$	1.92503	0.0757391
$647$	−12.6200	−0.496142	−0.248071	−	0.968742i	$-0.579797\pi$
$647$	−12.6200	−0.496142	−0.248071	+	0.968742i	$0.579797\pi$
$648$	−4.49154	−0.176445
$649$	9.11471	0.357784
$650$	−2.89500	−0.113551
$651$	0.765707	0.0300104
$652$	−44.5715	−1.74555
$653$	−26.1928	−1.02500	−0.512502	−	0.858686i	$-0.671281\pi$
$653$	−26.1928	−1.02500	−0.512502	+	0.858686i	$0.671281\pi$
$654$	0.988432	0.0386507
$655$	−58.5322	−2.28704
$656$	13.9138	0.543243
$657$	26.9105	1.04988
$658$	13.7469	0.535908
$659$	−10.8249	−0.421679	−0.210839	−	0.977521i	$-0.567620\pi$
$659$	−10.8249	−0.421679	−0.210839	+	0.977521i	$0.567620\pi$
$660$	−29.5491	−1.15020
$661$	−37.3195	−1.45156	−0.725780	−	0.687927i	$-0.758521\pi$
$661$	−37.3195	−1.45156	−0.725780	+	0.687927i	$0.758521\pi$
$662$	−5.76957	−0.224241
$663$	0.807562	0.0313631
$664$	23.5385	0.913472
$665$	−63.9662	−2.48050
$666$	3.90975	0.151500
$667$	−13.7184	−0.531177
$668$	30.5910	1.18360
$669$	−1.41018	−0.0545206
$670$	16.0163	0.618765
$671$	−32.4897	−1.25425
$672$	−12.5363	−0.483598
$673$	−18.3240	−0.706337	−0.353169	−	0.935560i	$-0.614896\pi$
$673$	−18.3240	−0.706337	−0.353169	+	0.935560i	$0.614896\pi$
$674$	−9.95493	−0.383449
$675$	−55.8140	−2.14828
$676$	23.6457	0.909449
$677$	1.90170	0.0730885	0.0365442	−	0.999332i	$-0.488365\pi$
$677$	1.90170	0.0730885	0.0365442	+	0.999332i	$0.488365\pi$
$678$	−1.09522	−0.0420617
$679$	66.3167	2.54500
$680$	−8.32542	−0.319265
$681$	−22.3750	−0.857413
$682$	0.360612	0.0138085
$683$	−44.4690	−1.70156	−0.850779	−	0.525523i	$-0.823870\pi$
$683$	−44.4690	−1.70156	−0.850779	+	0.525523i	$0.823870\pi$
$684$	−16.5446	−0.632598
$685$	−70.4166	−2.69048
$686$	−2.91269	−0.111207
$687$	22.4801	0.857671
$688$	−30.8208	−1.17503
$689$	1.71709	0.0654158
$690$	2.43574	0.0927269
$691$	−20.0062	−0.761071	−0.380535	−	0.924766i	$-0.624260\pi$
$691$	−20.0062	−0.761071	−0.380535	+	0.924766i	$0.624260\pi$
$692$	−44.2719	−1.68297
$693$	−42.2773	−1.60598
$694$	7.50113	0.284739
$695$	50.5610	1.91789
$696$	−7.32784	−0.277761
$697$	−6.24146	−0.236412
$698$	2.94128	0.111329
$699$	−4.92379	−0.186235
$700$	96.3474	3.64159
$701$	22.9606	0.867210	0.433605	−	0.901103i	$-0.357241\pi$
$701$	22.9606	0.867210	0.433605	+	0.901103i	$0.357241\pi$
$702$	0.993900	0.0375123
$703$	18.5493	0.699598
$704$	24.0763	0.907411
$705$	34.5822	1.30244
$706$	−6.05179	−0.227762
$707$	−41.6514	−1.56646
$708$	3.11290	0.116990
$709$	−0.752581	−0.0282638	−0.0141319	−	0.999900i	$-0.504498\pi$
$709$	−0.752581	−0.0282638	−0.0141319	+	0.999900i	$0.504498\pi$
$710$	10.9803	0.412084
$711$	29.5808	1.10937
$712$	−9.90494	−0.371203
$713$	0.475536	0.0178090
$714$	1.68000	0.0628726
$715$	−12.6377	−0.472622
$716$	−1.32440	−0.0494950
$717$	5.73637	0.214229
$718$	4.97087	0.185511
$719$	−31.0750	−1.15890	−0.579451	−	0.815007i	$-0.696733\pi$
$719$	−31.0750	−1.15890	−0.579451	+	0.815007i	$0.696733\pi$
$720$	32.3879	1.20703
$721$	−30.8402	−1.14855
$722$	−1.61084	−0.0599493
$723$	6.77495	0.251963
$724$	14.7421	0.547887
$725$	85.3304	3.16909
$726$	2.68951	0.0998170
$727$	−28.1896	−1.04549	−0.522747	−	0.852488i	$-0.675093\pi$
$727$	−28.1896	−1.04549	−0.522747	+	0.852488i	$0.675093\pi$
$728$	−3.53863	−0.131150
$729$	2.95937	0.109606
$730$	16.7346	0.619375
$731$	13.8256	0.511360
$732$	−11.0960	−0.410121
$733$	−5.16617	−0.190817	−0.0954084	−	0.995438i	$-0.530416\pi$
$733$	−5.16617	−0.190817	−0.0954084	+	0.995438i	$0.530416\pi$
$734$	11.7312	0.433007
$735$	−31.5758	−1.16469
$736$	−7.78556	−0.286980
$737$	50.2224	1.84997
$738$	−3.35311	−0.123430
$739$	18.5108	0.680931	0.340466	−	0.940257i	$-0.389415\pi$
$739$	18.5108	0.680931	0.340466	+	0.940257i	$0.389415\pi$
$740$	−38.8956	−1.42983
$741$	2.05833	0.0756147
$742$	3.57213	0.131137
$743$	39.5645	1.45148	0.725740	−	0.687969i	$-0.241498\pi$
$743$	39.5645	1.45148	0.725740	+	0.687969i	$0.241498\pi$
$744$	0.254014	0.00931260
$745$	49.3654	1.80861
$746$	−5.64197	−0.206567
$747$	41.0768	1.50292
$748$	−12.6574	−0.462801
$749$	−19.3238	−0.706077
$750$	−9.20943	−0.336281
$751$	−13.6103	−0.496649	−0.248324	−	0.968677i	$-0.579880\pi$
$751$	−13.6103	−0.496649	−0.248324	+	0.968677i	$0.579880\pi$
$752$	−33.0227	−1.20422
$753$	−9.90645	−0.361011
$754$	−1.51951	−0.0553373
$755$	−53.4248	−1.94433
$756$	−33.0776	−1.20302
$757$	29.1207	1.05841	0.529204	−	0.848494i	$-0.322490\pi$
$757$	29.1207	1.05841	0.529204	+	0.848494i	$0.322490\pi$
$758$	−2.89204	−0.105044
$759$	7.63774	0.277232
$760$	−21.2200	−0.769730
$761$	31.1496	1.12917	0.564587	−	0.825374i	$-0.309036\pi$
$761$	31.1496	1.12917	0.564587	+	0.825374i	$0.309036\pi$
$762$	−5.44311	−0.197183
$763$	−14.0689	−0.509330
$764$	−0.495296	−0.0179192
$765$	−14.5286	−0.525282
$766$	9.23970	0.333844
$767$	1.33134	0.0480718
$768$	6.08027	0.219403
$769$	−23.4666	−0.846228	−0.423114	−	0.906076i	$-0.639063\pi$
$769$	−23.4666	−0.846228	−0.423114	+	0.906076i	$0.639063\pi$
$770$	−26.2906	−0.947449
$771$	−3.55542	−0.128045
$772$	9.76469	0.351439
$773$	10.9382	0.393418	0.196709	−	0.980462i	$-0.436975\pi$
$773$	10.9382	0.393418	0.196709	+	0.980462i	$0.436975\pi$
$774$	7.42757	0.266979
$775$	−2.95791	−0.106251
$776$	21.9997	0.789745
$777$	16.1883	0.580750
$778$	−4.60133	−0.164966
$779$	−15.9084	−0.569977
$780$	−4.31607	−0.154540
$781$	34.4309	1.23204
$782$	1.04335	0.0373102
$783$	−29.2953	−1.04693
$784$	30.1519	1.07685
$785$	15.6595	0.558912
$786$	3.91827	0.139760
$787$	22.9622	0.818516	0.409258	−	0.912419i	$-0.365788\pi$
$787$	22.9622	0.818516	0.409258	+	0.912419i	$0.365788\pi$
$788$	−10.1036	−0.359927
$789$	6.44132	0.229317
$790$	18.3952	0.654471
$791$	15.5889	0.554279
$792$	−14.0250	−0.498356
$793$	−4.74559	−0.168521
$794$	−2.82876	−0.100389
$795$	8.98620	0.318708
$796$	14.5405	0.515376
$797$	9.89557	0.350519	0.175260	−	0.984522i	$-0.443924\pi$
$797$	9.89557	0.350519	0.175260	+	0.984522i	$0.443924\pi$
$798$	4.28203	0.151582
$799$	14.8134	0.524059
$800$	48.4275	1.71217
$801$	−17.2850	−0.610734
$802$	5.01539	0.177100
$803$	52.4747	1.85179
$804$	17.1522	0.604912
$805$	−34.6693	−1.22193
$806$	0.0526726	0.00185531
$807$	10.0213	0.352766
$808$	−13.8174	−0.486093
$809$	−11.4253	−0.401692	−0.200846	−	0.979623i	$-0.564369\pi$
$809$	−11.4253	−0.401692	−0.200846	+	0.979623i	$0.564369\pi$
$810$	−4.87424	−0.171263
$811$	−18.0372	−0.633372	−0.316686	−	0.948530i	$-0.602570\pi$
$811$	−18.0372	−0.633372	−0.316686	+	0.948530i	$0.602570\pi$
$812$	50.5703	1.77467
$813$	−17.9519	−0.629600
$814$	7.62390	0.267218
$815$	−99.7617	−3.49450
$816$	−4.03571	−0.141278
$817$	35.2391	1.23286
$818$	1.43665	0.0502314
$819$	−6.17522	−0.215780
$820$	33.3580	1.16491
$821$	10.0129	0.349452	0.174726	−	0.984617i	$-0.444096\pi$
$821$	10.0129	0.349452	0.174726	+	0.984617i	$0.444096\pi$
$822$	4.71383	0.164414
$823$	−42.1087	−1.46782	−0.733908	−	0.679249i	$-0.762306\pi$
$823$	−42.1087	−1.46782	−0.733908	+	0.679249i	$0.762306\pi$
$824$	−10.2309	−0.356409
$825$	−47.5080	−1.65402
$826$	2.76964	0.0963679
$827$	6.66190	0.231657	0.115828	−	0.993269i	$-0.463048\pi$
$827$	6.66190	0.231657	0.115828	+	0.993269i	$0.463048\pi$
$828$	−8.96707	−0.311627
$829$	−32.8907	−1.14234	−0.571170	−	0.820832i	$-0.693510\pi$
$829$	−32.8907	−1.14234	−0.571170	+	0.820832i	$0.693510\pi$
$830$	25.5441	0.886648
$831$	10.4159	0.361324
$832$	3.51670	0.121920
$833$	−13.5256	−0.468634
$834$	−3.38466	−0.117201
$835$	68.4701	2.36951
$836$	−32.2615	−1.11579
$837$	1.01550	0.0351008
$838$	4.97389	0.171820
$839$	−2.47167	−0.0853314	−0.0426657	−	0.999089i	$-0.513585\pi$
$839$	−2.47167	−0.0853314	−0.0426657	+	0.999089i	$0.513585\pi$
$840$	−18.5191	−0.638968
$841$	15.7877	0.544405
$842$	−6.36389	−0.219314
$843$	−15.7482	−0.542397
$844$	14.1310	0.486410
$845$	52.9247	1.82067
$846$	7.95821	0.273609
$847$	−38.2814	−1.31536
$848$	−8.58097	−0.294672
$849$	24.7050	0.847873
$850$	−6.48983	−0.222599
$851$	10.0536	0.344633
$852$	11.7590	0.402857
$853$	27.3423	0.936183	0.468092	−	0.883680i	$-0.344942\pi$
$853$	27.3423	0.936183	0.468092	+	0.883680i	$0.344942\pi$
$854$	−9.87245	−0.337828
$855$	−37.0308	−1.26642
$856$	−6.41044	−0.219104
$857$	−15.8790	−0.542418	−0.271209	−	0.962520i	$-0.587423\pi$
$857$	−15.8790	−0.542418	−0.271209	+	0.962520i	$0.587423\pi$
$858$	0.845991	0.0288817
$859$	12.6504	0.431625	0.215813	−	0.976435i	$-0.430760\pi$
$859$	12.6504	0.431625	0.215813	+	0.976435i	$0.430760\pi$
$860$	−73.8921	−2.51970
$861$	−13.8835	−0.473149
$862$	5.90645	0.201174
$863$	−27.2858	−0.928821	−0.464411	−	0.885620i	$-0.653734\pi$
$863$	−27.2858	−0.928821	−0.464411	+	0.885620i	$0.653734\pi$
$864$	−16.6259	−0.565626
$865$	−99.0912	−3.36920
$866$	−0.245903	−0.00835613
$867$	−12.1672	−0.413221
$868$	−1.75298	−0.0595000
$869$	57.6817	1.95672
$870$	−7.95220	−0.269605
$871$	7.33572	0.248562
$872$	−4.66720	−0.158051
$873$	38.3915	1.29935
$874$	2.65932	0.0899529
$875$	131.083	4.43143
$876$	17.9214	0.605508
$877$	8.41503	0.284155	0.142078	−	0.989856i	$-0.454622\pi$
$877$	8.41503	0.284155	0.142078	+	0.989856i	$0.454622\pi$
$878$	−0.632326	−0.0213400
$879$	11.5025	0.387971
$880$	63.1555	2.12897
$881$	−7.74301	−0.260869	−0.130434	−	0.991457i	$-0.541637\pi$
$881$	−7.74301	−0.260869	−0.130434	+	0.991457i	$0.541637\pi$
$882$	−7.26637	−0.244671
$883$	1.03049	0.0346787	0.0173393	−	0.999850i	$-0.494480\pi$
$883$	1.03049	0.0346787	0.0173393	+	0.999850i	$0.494480\pi$
$884$	−1.84880	−0.0621819
$885$	6.96742	0.234207
$886$	−2.01488	−0.0676913
$887$	37.1251	1.24654	0.623270	−	0.782007i	$-0.285804\pi$
$887$	37.1251	1.24654	0.623270	+	0.782007i	$0.285804\pi$
$888$	5.37026	0.180214
$889$	77.4751	2.59843
$890$	−10.7489	−0.360303
$891$	−15.2841	−0.512038
$892$	3.22840	0.108095
$893$	37.7566	1.26348
$894$	−3.30463	−0.110523
$895$	−2.96432	−0.0990862
$896$	37.8100	1.26314
$897$	1.11560	0.0372489
$898$	13.1756	0.439675
$899$	−1.55253	−0.0517798
$900$	55.7766	1.85922
$901$	3.84926	0.128237
$902$	−6.53847	−0.217707
$903$	30.7537	1.02342
$904$	5.17144	0.172000
$905$	32.9964	1.09684
$906$	3.57637	0.118817
$907$	−0.413457	−0.0137286	−0.00686430	−	0.999976i	$-0.502185\pi$
$907$	−0.413457	−0.0137286	−0.00686430	+	0.999976i	$0.502185\pi$
$908$	51.2245	1.69994
$909$	−24.1125	−0.799761
$910$	−3.84013	−0.127299
$911$	−23.3397	−0.773277	−0.386639	−	0.922231i	$-0.626364\pi$
$911$	−23.3397	−0.773277	−0.386639	+	0.922231i	$0.626364\pi$
$912$	−10.2863	−0.340614
$913$	80.0986	2.65088
$914$	−14.4432	−0.477738
$915$	−24.8356	−0.821039
$916$	−51.4651	−1.70046
$917$	−55.7711	−1.84172
$918$	2.22806	0.0735371
$919$	−48.2962	−1.59315	−0.796573	−	0.604543i	$-0.793356\pi$
$919$	−48.2962	−1.59315	−0.796573	+	0.604543i	$0.793356\pi$
$920$	−11.5011	−0.379181
$921$	−14.6521	−0.482802
$922$	−1.88054	−0.0619322
$923$	5.02914	0.165536
$924$	−28.1551	−0.926236
$925$	−62.5350	−2.05614
$926$	−0.534023	−0.0175491
$927$	−17.8538	−0.586394
$928$	25.4183	0.834397
$929$	−9.25447	−0.303629	−0.151815	−	0.988409i	$-0.548512\pi$
$929$	−9.25447	−0.303629	−0.151815	+	0.988409i	$0.548512\pi$
$930$	0.275657	0.00903914
$931$	−34.4743	−1.12985
$932$	11.2723	0.369238
$933$	−2.10116	−0.0687888
$934$	−9.06528	−0.296625
$935$	−28.3303	−0.926501
$936$	−2.04855	−0.0669591
$937$	28.1657	0.920135	0.460067	−	0.887884i	$-0.347825\pi$
$937$	28.1657	0.920135	0.460067	+	0.887884i	$0.347825\pi$
$938$	15.2608	0.498283
$939$	1.05976	0.0345838
$940$	−79.1711	−2.58228
$941$	10.3013	0.335813	0.167907	−	0.985803i	$-0.446299\pi$
$941$	10.3013	0.335813	0.167907	+	0.985803i	$0.446299\pi$
$942$	−1.04828	−0.0341548
$943$	−8.62225	−0.280779
$944$	−6.65323	−0.216544
$945$	−74.0357	−2.40838
$946$	14.4836	0.470901
$947$	18.5189	0.601783	0.300892	−	0.953658i	$-0.402716\pi$
$947$	18.5189	0.601783	0.300892	+	0.953658i	$0.402716\pi$
$948$	19.6997	0.639818
$949$	7.66469	0.248807
$950$	−16.5414	−0.536674
$951$	−19.6592	−0.637493
$952$	−7.93268	−0.257100
$953$	51.3451	1.66323	0.831616	−	0.555352i	$-0.187416\pi$
$953$	51.3451	1.66323	0.831616	+	0.555352i	$0.187416\pi$
$954$	2.06794	0.0669522
$955$	−1.10859	−0.0358732
$956$	−13.1326	−0.424739
$957$	−24.9357	−0.806057
$958$	−12.4218	−0.401329
$959$	−67.0948	−2.16660
$960$	18.4043	0.593997
$961$	−30.9462	−0.998264
$962$	1.11358	0.0359033
$963$	−11.1868	−0.360489
$964$	−15.5103	−0.499553
$965$	21.8557	0.703561
$966$	2.32084	0.0746717
$967$	27.7490	0.892347	0.446174	−	0.894946i	$-0.352786\pi$
$967$	27.7490	0.892347	0.446174	+	0.894946i	$0.352786\pi$
$968$	−12.6994	−0.408174
$969$	4.61424	0.148231
$970$	23.8742	0.766554
$971$	−26.3385	−0.845241	−0.422621	−	0.906307i	$-0.638890\pi$
$971$	−26.3385	−0.845241	−0.422621	+	0.906307i	$0.638890\pi$
$972$	−29.9393	−0.960303
$973$	48.1758	1.54445
$974$	9.28230	0.297424
$975$	−6.93924	−0.222233
$976$	23.7156	0.759119
$977$	51.9173	1.66098	0.830490	−	0.557033i	$-0.188060\pi$
$977$	51.9173	1.66098	0.830490	+	0.557033i	$0.188060\pi$
$978$	6.67826	0.213547
$979$	−33.7052	−1.07722
$980$	72.2885	2.30917
$981$	−8.14467	−0.260039
$982$	−1.84467	−0.0588659
$983$	57.5114	1.83433	0.917165	−	0.398508i	$-0.130472\pi$
$983$	57.5114	1.83433	0.917165	+	0.398508i	$0.130472\pi$
$984$	−4.60569	−0.146824
$985$	−22.6144	−0.720554
$986$	−3.40634	−0.108480
$987$	32.9509	1.04884
$988$	−4.71226	−0.149917
$989$	19.0994	0.607325
$990$	−15.2199	−0.483722
$991$	42.6511	1.35486	0.677429	−	0.735588i	$-0.263094\pi$
$991$	42.6511	1.35486	0.677429	+	0.735588i	$0.263094\pi$
$992$	−0.881106	−0.0279752
$993$	−13.8295	−0.438866
$994$	10.4623	0.331845
$995$	32.5452	1.03175
$996$	27.3556	0.866797
$997$	30.2531	0.958125	0.479063	−	0.877781i	$-0.340977\pi$
$997$	30.2531	0.958125	0.479063	+	0.877781i	$0.340977\pi$
$998$	−1.81149	−0.0573416
$999$	21.4693	0.679258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.b.1.47	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.b.1.47	✓	90	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:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q+0.343020 q^{2} +0.822211 q^{3} -1.88234 q^{4} -4.21312 q^{5} +0.282035 q^{6} -4.01438 q^{7} -1.33172 q^{8} -2.32397 q^{9} +O(q^{10})\)	\(q+0.343020 q^{2} +0.822211 q^{3} -1.88234 q^{4} -4.21312 q^{5} +0.282035 q^{6} -4.01438 q^{7} -1.33172 q^{8} -2.32397 q^{9} -1.44519 q^{10} -4.53167 q^{11} -1.54768 q^{12} -0.661917 q^{13} -1.37701 q^{14} -3.46408 q^{15} +3.30787 q^{16} -1.48385 q^{17} -0.797169 q^{18} -3.78206 q^{19} +7.93052 q^{20} -3.30067 q^{21} -1.55446 q^{22} -2.04985 q^{23} -1.09496 q^{24} +12.7504 q^{25} -0.227051 q^{26} -4.37743 q^{27} +7.55641 q^{28} +6.69236 q^{29} -1.18825 q^{30} -0.231986 q^{31} +3.79811 q^{32} -3.72599 q^{33} -0.508989 q^{34} +16.9131 q^{35} +4.37449 q^{36} -4.90454 q^{37} -1.29732 q^{38} -0.544236 q^{39} +5.61071 q^{40} +4.20628 q^{41} -1.13220 q^{42} -9.31744 q^{43} +8.53014 q^{44} +9.79117 q^{45} -0.703142 q^{46} -9.98310 q^{47} +2.71976 q^{48} +9.11522 q^{49} +4.37365 q^{50} -1.22003 q^{51} +1.24595 q^{52} -2.59411 q^{53} -1.50155 q^{54} +19.0925 q^{55} +5.34603 q^{56} -3.10965 q^{57} +2.29562 q^{58} -2.01133 q^{59} +6.52056 q^{60} +7.16946 q^{61} -0.0795758 q^{62} +9.32929 q^{63} -5.31290 q^{64} +2.78874 q^{65} -1.27809 q^{66} -11.0825 q^{67} +2.79310 q^{68} -1.68541 q^{69} +5.80153 q^{70} -7.59784 q^{71} +3.09488 q^{72} -11.5795 q^{73} -1.68236 q^{74} +10.4835 q^{75} +7.11910 q^{76} +18.1918 q^{77} -0.186684 q^{78} -12.7286 q^{79} -13.9365 q^{80} +3.37274 q^{81} +1.44284 q^{82} -17.6753 q^{83} +6.21297 q^{84} +6.25163 q^{85} -3.19607 q^{86} +5.50254 q^{87} +6.03493 q^{88} +7.43770 q^{89} +3.35857 q^{90} +2.65719 q^{91} +3.85851 q^{92} -0.190741 q^{93} -3.42441 q^{94} +15.9343 q^{95} +3.12285 q^{96} -16.5198 q^{97} +3.12671 q^{98} +10.5315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * q^99

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