LMFDB - Embedded newform 6033.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$97$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72505 q^{2} +1.00000 q^{3} +5.42589 q^{4} -0.505520 q^{5} -2.72505 q^{6} -2.64822 q^{7} -9.33570 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.72505 q^{2} +1.00000 q^{3} +5.42589 q^{4} -0.505520 q^{5} -2.72505 q^{6} -2.64822 q^{7} -9.33570 q^{8} +1.00000 q^{9} +1.37757 q^{10} -2.44519 q^{11} +5.42589 q^{12} -0.975121 q^{13} +7.21652 q^{14} -0.505520 q^{15} +14.5885 q^{16} +1.72242 q^{17} -2.72505 q^{18} -3.34760 q^{19} -2.74289 q^{20} -2.64822 q^{21} +6.66325 q^{22} -7.22339 q^{23} -9.33570 q^{24} -4.74445 q^{25} +2.65725 q^{26} +1.00000 q^{27} -14.3689 q^{28} +3.08386 q^{29} +1.37757 q^{30} +3.17836 q^{31} -21.0829 q^{32} -2.44519 q^{33} -4.69367 q^{34} +1.33873 q^{35} +5.42589 q^{36} -0.657503 q^{37} +9.12237 q^{38} -0.975121 q^{39} +4.71938 q^{40} -8.10024 q^{41} +7.21652 q^{42} +8.77621 q^{43} -13.2673 q^{44} -0.505520 q^{45} +19.6841 q^{46} -5.22244 q^{47} +14.5885 q^{48} +0.0130612 q^{49} +12.9289 q^{50} +1.72242 q^{51} -5.29090 q^{52} +12.0999 q^{53} -2.72505 q^{54} +1.23609 q^{55} +24.7230 q^{56} -3.34760 q^{57} -8.40365 q^{58} -9.74677 q^{59} -2.74289 q^{60} +3.79030 q^{61} -8.66117 q^{62} -2.64822 q^{63} +28.2749 q^{64} +0.492943 q^{65} +6.66325 q^{66} +9.82477 q^{67} +9.34563 q^{68} -7.22339 q^{69} -3.64809 q^{70} -16.3849 q^{71} -9.33570 q^{72} -1.15260 q^{73} +1.79173 q^{74} -4.74445 q^{75} -18.1637 q^{76} +6.47539 q^{77} +2.65725 q^{78} +9.79151 q^{79} -7.37476 q^{80} +1.00000 q^{81} +22.0736 q^{82} -0.336529 q^{83} -14.3689 q^{84} -0.870716 q^{85} -23.9156 q^{86} +3.08386 q^{87} +22.8275 q^{88} -17.5242 q^{89} +1.37757 q^{90} +2.58233 q^{91} -39.1933 q^{92} +3.17836 q^{93} +14.2314 q^{94} +1.69228 q^{95} -21.0829 q^{96} -5.36977 q^{97} -0.0355925 q^{98} -2.44519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) $ 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.72505	−1.92690	−0.963450	−	0.267889i	$-0.913674\pi$
$2$	−2.72505	−1.92690	−0.963450	+	0.267889i	$0.913674\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.42589	2.71294
$5$	−0.505520	−0.226075	−0.113038	−	0.993591i	$-0.536058\pi$
$5$	−0.505520	−0.226075	−0.113038	+	0.993591i	$0.536058\pi$
$6$	−2.72505	−1.11250
$7$	−2.64822	−1.00093	−0.500466	−	0.865756i	$-0.666838\pi$
$7$	−2.64822	−1.00093	−0.500466	+	0.865756i	$0.666838\pi$
$8$	−9.33570	−3.30067
$9$	1.00000	0.333333
$10$	1.37757	0.435625
$11$	−2.44519	−0.737251	−0.368626	−	0.929578i	$-0.620172\pi$
$11$	−2.44519	−0.737251	−0.368626	+	0.929578i	$0.620172\pi$
$12$	5.42589	1.56632
$13$	−0.975121	−0.270450	−0.135225	−	0.990815i	$-0.543176\pi$
$13$	−0.975121	−0.270450	−0.135225	+	0.990815i	$0.543176\pi$
$14$	7.21652	1.92870
$15$	−0.505520	−0.130525
$16$	14.5885	3.64712
$17$	1.72242	0.417747	0.208874	−	0.977943i	$-0.433020\pi$
$17$	1.72242	0.417747	0.208874	+	0.977943i	$0.433020\pi$
$18$	−2.72505	−0.642300
$19$	−3.34760	−0.767992	−0.383996	−	0.923335i	$-0.625452\pi$
$19$	−3.34760	−0.767992	−0.383996	+	0.923335i	$0.625452\pi$
$20$	−2.74289	−0.613329
$21$	−2.64822	−0.577889
$22$	6.66325	1.42061
$23$	−7.22339	−1.50618	−0.753090	−	0.657918i	$-0.771438\pi$
$23$	−7.22339	−1.50618	−0.753090	+	0.657918i	$0.771438\pi$
$24$	−9.33570	−1.90564
$25$	−4.74445	−0.948890
$26$	2.65725	0.521130
$27$	1.00000	0.192450
$28$	−14.3689	−2.71547
$29$	3.08386	0.572658	0.286329	−	0.958131i	$-0.407565\pi$
$29$	3.08386	0.572658	0.286329	+	0.958131i	$0.407565\pi$
$30$	1.37757	0.251508
$31$	3.17836	0.570850	0.285425	−	0.958401i	$-0.407865\pi$
$31$	3.17836	0.570850	0.285425	+	0.958401i	$0.407865\pi$
$32$	−21.0829	−3.72696
$33$	−2.44519	−0.425652
$34$	−4.69367	−0.804957
$35$	1.33873	0.226286
$36$	5.42589	0.904314
$37$	−0.657503	−0.108093	−0.0540464	−	0.998538i	$-0.517212\pi$
$37$	−0.657503	−0.108093	−0.0540464	+	0.998538i	$0.517212\pi$
$38$	9.12237	1.47984
$39$	−0.975121	−0.156144
$40$	4.71938	0.746200
$41$	−8.10024	−1.26505	−0.632523	−	0.774542i	$-0.717981\pi$
$41$	−8.10024	−1.26505	−0.632523	+	0.774542i	$0.717981\pi$
$42$	7.21652	1.11353
$43$	8.77621	1.33836	0.669180	−	0.743101i	$-0.266646\pi$
$43$	8.77621	1.33836	0.669180	+	0.743101i	$0.266646\pi$
$44$	−13.2673	−2.00012
$45$	−0.505520	−0.0753584
$46$	19.6841	2.90226
$47$	−5.22244	−0.761771	−0.380885	−	0.924622i	$-0.624381\pi$
$47$	−5.22244	−0.761771	−0.380885	+	0.924622i	$0.624381\pi$
$48$	14.5885	2.10566
$49$	0.0130612	0.00186589
$50$	12.9289	1.82842
$51$	1.72242	0.241187
$52$	−5.29090	−0.733715
$53$	12.0999	1.66204	0.831021	−	0.556241i	$-0.187757\pi$
$53$	12.0999	1.66204	0.831021	+	0.556241i	$0.187757\pi$
$54$	−2.72505	−0.370832
$55$	1.23609	0.166674
$56$	24.7230	3.30375
$57$	−3.34760	−0.443401
$58$	−8.40365	−1.10345
$59$	−9.74677	−1.26892	−0.634461	−	0.772955i	$-0.718778\pi$
$59$	−9.74677	−1.26892	−0.634461	+	0.772955i	$0.718778\pi$
$60$	−2.74289	−0.354106
$61$	3.79030	0.485298	0.242649	−	0.970114i	$-0.421984\pi$
$61$	3.79030	0.485298	0.242649	+	0.970114i	$0.421984\pi$
$62$	−8.66117	−1.09997
$63$	−2.64822	−0.333644
$64$	28.2749	3.53436
$65$	0.492943	0.0611421
$66$	6.66325	0.820189
$67$	9.82477	1.20029	0.600143	−	0.799893i	$-0.295110\pi$
$67$	9.82477	1.20029	0.600143	+	0.799893i	$0.295110\pi$
$68$	9.34563	1.13332
$69$	−7.22339	−0.869593
$70$	−3.64809	−0.436031
$71$	−16.3849	−1.94453	−0.972265	−	0.233884i	$-0.924856\pi$
$71$	−16.3849	−1.94453	−0.972265	+	0.233884i	$0.924856\pi$
$72$	−9.33570	−1.10022
$73$	−1.15260	−0.134901	−0.0674507	−	0.997723i	$-0.521487\pi$
$73$	−1.15260	−0.134901	−0.0674507	+	0.997723i	$0.521487\pi$
$74$	1.79173	0.208284
$75$	−4.74445	−0.547842
$76$	−18.1637	−2.08352
$77$	6.47539	0.737939
$78$	2.65725	0.300875
$79$	9.79151	1.10163	0.550816	−	0.834627i	$-0.314317\pi$
$79$	9.79151	1.10163	0.550816	+	0.834627i	$0.314317\pi$
$80$	−7.37476	−0.824523
$81$	1.00000	0.111111
$82$	22.0736	2.43762
$83$	−0.336529	−0.0369389	−0.0184695	−	0.999829i	$-0.505879\pi$
$83$	−0.336529	−0.0369389	−0.0184695	+	0.999829i	$0.505879\pi$
$84$	−14.3689	−1.56778
$85$	−0.870716	−0.0944424
$86$	−23.9156	−2.57888
$87$	3.08386	0.330624
$88$	22.8275	2.43342
$89$	−17.5242	−1.85756	−0.928779	−	0.370634i	$-0.879140\pi$
$89$	−17.5242	−1.85756	−0.928779	+	0.370634i	$0.879140\pi$
$90$	1.37757	0.145208
$91$	2.58233	0.270702
$92$	−39.1933	−4.08618
$93$	3.17836	0.329580
$94$	14.2314	1.46786
$95$	1.69228	0.173624
$96$	−21.0829	−2.15176
$97$	−5.36977	−0.545218	−0.272609	−	0.962125i	$-0.587886\pi$
$97$	−5.36977	−0.545218	−0.272609	+	0.962125i	$0.587886\pi$
$98$	−0.0355925	−0.00359538
$99$	−2.44519	−0.245750
$100$	−25.7428	−2.57428
$101$	−16.5335	−1.64515	−0.822574	−	0.568658i	$-0.807463\pi$
$101$	−16.5335	−1.64515	−0.822574	+	0.568658i	$0.807463\pi$
$102$	−4.69367	−0.464742
$103$	1.60119	0.157770	0.0788849	−	0.996884i	$-0.474864\pi$
$103$	1.60119	0.157770	0.0788849	+	0.996884i	$0.474864\pi$
$104$	9.10344	0.892666
$105$	1.33873	0.130646
$106$	−32.9727	−3.20259
$107$	6.45804	0.624322	0.312161	−	0.950029i	$-0.398947\pi$
$107$	6.45804	0.624322	0.312161	+	0.950029i	$0.398947\pi$
$108$	5.42589	0.522106
$109$	−3.23097	−0.309471	−0.154736	−	0.987956i	$-0.549453\pi$
$109$	−3.23097	−0.309471	−0.154736	+	0.987956i	$0.549453\pi$
$110$	−3.36840	−0.321165
$111$	−0.657503	−0.0624074
$112$	−38.6334	−3.65052
$113$	8.50429	0.800016	0.400008	−	0.916512i	$-0.369007\pi$
$113$	8.50429	0.800016	0.400008	+	0.916512i	$0.369007\pi$
$114$	9.12237	0.854389
$115$	3.65156	0.340510
$116$	16.7326	1.55359
$117$	−0.975121	−0.0901500
$118$	26.5604	2.44509
$119$	−4.56134	−0.418137
$120$	4.71938	0.430819
$121$	−5.02106	−0.456460
$122$	−10.3287	−0.935121
$123$	−8.10024	−0.730374
$124$	17.2454	1.54868
$125$	4.92601	0.440596
$126$	7.21652	0.642899
$127$	17.7703	1.57686	0.788429	−	0.615126i	$-0.210895\pi$
$127$	17.7703	1.57686	0.788429	+	0.615126i	$0.210895\pi$
$128$	−34.8847	−3.08340
$129$	8.77621	0.772702
$130$	−1.34329	−0.117815
$131$	−9.00889	−0.787110	−0.393555	−	0.919301i	$-0.628755\pi$
$131$	−9.00889	−0.787110	−0.393555	+	0.919301i	$0.628755\pi$
$132$	−13.2673	−1.15477
$133$	8.86518	0.768709
$134$	−26.7730	−2.31283
$135$	−0.505520	−0.0435082
$136$	−16.0800	−1.37885
$137$	14.6349	1.25035	0.625173	−	0.780486i	$-0.285029\pi$
$137$	14.6349	1.25035	0.625173	+	0.780486i	$0.285029\pi$
$138$	19.6841	1.67562
$139$	16.9697	1.43935	0.719674	−	0.694312i	$-0.244291\pi$
$139$	16.9697	1.43935	0.719674	+	0.694312i	$0.244291\pi$
$140$	7.26378	0.613901
$141$	−5.22244	−0.439809
$142$	44.6496	3.74691
$143$	2.38435	0.199390
$144$	14.5885	1.21571
$145$	−1.55895	−0.129464
$146$	3.14089	0.259942
$147$	0.0130612	0.00107727
$148$	−3.56754	−0.293250
$149$	7.49220	0.613785	0.306892	−	0.951744i	$-0.400711\pi$
$149$	7.49220	0.613785	0.306892	+	0.951744i	$0.400711\pi$
$150$	12.9289	1.05564
$151$	4.68208	0.381022	0.190511	−	0.981685i	$-0.438986\pi$
$151$	4.68208	0.381022	0.190511	+	0.981685i	$0.438986\pi$
$152$	31.2522	2.53489
$153$	1.72242	0.139249
$154$	−17.6457	−1.42193
$155$	−1.60672	−0.129055
$156$	−5.29090	−0.423611
$157$	−6.45903	−0.515486	−0.257743	−	0.966213i	$-0.582979\pi$
$157$	−6.45903	−0.515486	−0.257743	+	0.966213i	$0.582979\pi$
$158$	−26.6823	−2.12273
$159$	12.0999	0.959581
$160$	10.6578	0.842573
$161$	19.1291	1.50758
$162$	−2.72505	−0.214100
$163$	7.99164	0.625953	0.312977	−	0.949761i	$-0.398674\pi$
$163$	7.99164	0.625953	0.312977	+	0.949761i	$0.398674\pi$
$164$	−43.9510	−3.43200
$165$	1.23609	0.0962295
$166$	0.917059	0.0711776
$167$	1.81977	0.140818	0.0704091	−	0.997518i	$-0.477570\pi$
$167$	1.81977	0.140818	0.0704091	+	0.997518i	$0.477570\pi$
$168$	24.7230	1.90742
$169$	−12.0491	−0.926857
$170$	2.37274	0.181981
$171$	−3.34760	−0.255997
$172$	47.6187	3.63089
$173$	−1.37943	−0.104876	−0.0524382	−	0.998624i	$-0.516699\pi$
$173$	−1.37943	−0.104876	−0.0524382	+	0.998624i	$0.516699\pi$
$174$	−8.40365	−0.637079
$175$	12.5643	0.949775
$176$	−35.6715	−2.68884
$177$	−9.74677	−0.732612
$178$	47.7542	3.57933
$179$	23.4277	1.75107	0.875536	−	0.483154i	$-0.160509\pi$
$179$	23.4277	1.75107	0.875536	+	0.483154i	$0.160509\pi$
$180$	−2.74289	−0.204443
$181$	0.144271	0.0107236	0.00536178	−	0.999986i	$-0.498293\pi$
$181$	0.144271	0.0107236	0.00536178	+	0.999986i	$0.498293\pi$
$182$	−7.03698	−0.521616
$183$	3.79030	0.280187
$184$	67.4354	4.97140
$185$	0.332381	0.0244371
$186$	−8.66117	−0.635068
$187$	−4.21163	−0.307985
$188$	−28.3364	−2.06664
$189$	−2.64822	−0.192630
$190$	−4.61154	−0.334556
$191$	−9.69864	−0.701769	−0.350884	−	0.936419i	$-0.614119\pi$
$191$	−9.69864	−0.701769	−0.350884	+	0.936419i	$0.614119\pi$
$192$	28.2749	2.04056
$193$	−10.5351	−0.758332	−0.379166	−	0.925329i	$-0.623789\pi$
$193$	−10.5351	−0.758332	−0.379166	+	0.925329i	$0.623789\pi$
$194$	14.6329	1.05058
$195$	0.492943	0.0353004
$196$	0.0708688	0.00506206
$197$	21.8307	1.55537	0.777685	−	0.628654i	$-0.216394\pi$
$197$	21.8307	1.55537	0.777685	+	0.628654i	$0.216394\pi$
$198$	6.66325	0.473537
$199$	−26.7210	−1.89420	−0.947101	−	0.320934i	$-0.896003\pi$
$199$	−26.7210	−1.89420	−0.947101	+	0.320934i	$0.896003\pi$
$200$	44.2928	3.13197
$201$	9.82477	0.692986
$202$	45.0547	3.17004
$203$	−8.16672	−0.573192
$204$	9.34563	0.654325
$205$	4.09483	0.285996
$206$	−4.36331	−0.304007
$207$	−7.22339	−0.502060
$208$	−14.2255	−0.986362
$209$	8.18551	0.566204
$210$	−3.64809	−0.251742
$211$	−4.85626	−0.334319	−0.167159	−	0.985930i	$-0.553459\pi$
$211$	−4.85626	−0.334319	−0.167159	+	0.985930i	$0.553459\pi$
$212$	65.6524	4.50903
$213$	−16.3849	−1.12267
$214$	−17.5985	−1.20301
$215$	−4.43655	−0.302570
$216$	−9.33570	−0.635214
$217$	−8.41698	−0.571382
$218$	8.80456	0.596320
$219$	−1.15260	−0.0778854
$220$	6.70688	0.452178
$221$	−1.67956	−0.112980
$222$	1.79173	0.120253
$223$	8.64646	0.579010	0.289505	−	0.957177i	$-0.406509\pi$
$223$	8.64646	0.579010	0.289505	+	0.957177i	$0.406509\pi$
$224$	55.8320	3.73043
$225$	−4.74445	−0.316297
$226$	−23.1746	−1.54155
$227$	27.4386	1.82116	0.910582	−	0.413328i	$-0.135634\pi$
$227$	27.4386	1.82116	0.910582	+	0.413328i	$0.135634\pi$
$228$	−18.1637	−1.20292
$229$	24.4558	1.61608	0.808041	−	0.589126i	$-0.200528\pi$
$229$	24.4558	1.61608	0.808041	+	0.589126i	$0.200528\pi$
$230$	−9.95069	−0.656129
$231$	6.47539	0.426049
$232$	−28.7900	−1.89015
$233$	13.0075	0.852152	0.426076	−	0.904687i	$-0.359896\pi$
$233$	13.0075	0.852152	0.426076	+	0.904687i	$0.359896\pi$
$234$	2.65725	0.173710
$235$	2.64005	0.172218
$236$	−52.8849	−3.44251
$237$	9.79151	0.636027
$238$	12.4299	0.805708
$239$	16.0375	1.03738	0.518691	−	0.854962i	$-0.326419\pi$
$239$	16.0375	1.03738	0.518691	+	0.854962i	$0.326419\pi$
$240$	−7.37476	−0.476039
$241$	15.3044	0.985843	0.492922	−	0.870074i	$-0.335929\pi$
$241$	15.3044	0.985843	0.492922	+	0.870074i	$0.335929\pi$
$242$	13.6826	0.879553
$243$	1.00000	0.0641500
$244$	20.5657	1.31659
$245$	−0.00660271	−0.000421832 0
$246$	22.0736	1.40736
$247$	3.26432	0.207704
$248$	−29.6722	−1.88419
$249$	−0.336529	−0.0213267
$250$	−13.4236	−0.848984
$251$	16.2364	1.02483	0.512417	−	0.858736i	$-0.328750\pi$
$251$	16.2364	1.02483	0.512417	+	0.858736i	$0.328750\pi$
$252$	−14.3689	−0.905158
$253$	17.6625	1.11043
$254$	−48.4249	−3.03845
$255$	−0.870716	−0.0545263
$256$	38.5126	2.40704
$257$	−20.5154	−1.27971	−0.639857	−	0.768494i	$-0.721006\pi$
$257$	−20.5154	−1.27971	−0.639857	+	0.768494i	$0.721006\pi$
$258$	−23.9156	−1.48892
$259$	1.74121	0.108194
$260$	2.67465	0.165875
$261$	3.08386	0.190886
$262$	24.5496	1.51668
$263$	8.15848	0.503074	0.251537	−	0.967848i	$-0.419064\pi$
$263$	8.15848	0.503074	0.251537	+	0.967848i	$0.419064\pi$
$264$	22.8275	1.40494
$265$	−6.11671	−0.375747
$266$	−24.1580	−1.48122
$267$	−17.5242	−1.07246
$268$	53.3081	3.25631
$269$	3.62101	0.220777	0.110389	−	0.993889i	$-0.464790\pi$
$269$	3.62101	0.220777	0.110389	+	0.993889i	$0.464790\pi$
$270$	1.37757	0.0838360
$271$	−3.51037	−0.213240	−0.106620	−	0.994300i	$-0.534003\pi$
$271$	−3.51037	−0.213240	−0.106620	+	0.994300i	$0.534003\pi$
$272$	25.1274	1.52357
$273$	2.58233	0.156290
$274$	−39.8809	−2.40929
$275$	11.6011	0.699570
$276$	−39.1933	−2.35916
$277$	−21.0667	−1.26578	−0.632888	−	0.774243i	$-0.718131\pi$
$277$	−21.0667	−1.26578	−0.632888	+	0.774243i	$0.718131\pi$
$278$	−46.2432	−2.77348
$279$	3.17836	0.190283
$280$	−12.4980	−0.746896
$281$	4.38256	0.261442	0.130721	−	0.991419i	$-0.458271\pi$
$281$	4.38256	0.261442	0.130721	+	0.991419i	$0.458271\pi$
$282$	14.2314	0.847467
$283$	25.0579	1.48954	0.744768	−	0.667324i	$-0.232560\pi$
$283$	25.0579	1.48954	0.744768	+	0.667324i	$0.232560\pi$
$284$	−88.9026	−5.27540
$285$	1.69228	0.100242
$286$	−6.49748	−0.384204
$287$	21.4512	1.26623
$288$	−21.0829	−1.24232
$289$	−14.0333	−0.825487
$290$	4.24821	0.249464
$291$	−5.36977	−0.314782
$292$	−6.25387	−0.365980
$293$	−17.2607	−1.00838	−0.504191	−	0.863592i	$-0.668209\pi$
$293$	−17.2607	−1.00838	−0.504191	+	0.863592i	$0.668209\pi$
$294$	−0.0355925	−0.00207580
$295$	4.92719	0.286872
$296$	6.13825	0.356779
$297$	−2.44519	−0.141884
$298$	−20.4166	−1.18270
$299$	7.04368	0.407346
$300$	−25.7428	−1.48626
$301$	−23.2413	−1.33961
$302$	−12.7589	−0.734191
$303$	−16.5335	−0.949827
$304$	−48.8364	−2.80096
$305$	−1.91607	−0.109714
$306$	−4.69367	−0.268319
$307$	22.6254	1.29130	0.645650	−	0.763634i	$-0.276587\pi$
$307$	22.6254	1.29130	0.645650	+	0.763634i	$0.276587\pi$
$308$	35.1347	2.00199
$309$	1.60119	0.0910884
$310$	4.37839	0.248676
$311$	−21.4525	−1.21646	−0.608231	−	0.793760i	$-0.708121\pi$
$311$	−21.4525	−1.21646	−0.608231	+	0.793760i	$0.708121\pi$
$312$	9.10344	0.515381
$313$	−24.0637	−1.36016	−0.680080	−	0.733138i	$-0.738055\pi$
$313$	−24.0637	−1.36016	−0.680080	+	0.733138i	$0.738055\pi$
$314$	17.6012	0.993290
$315$	1.33873	0.0754287
$316$	53.1276	2.98866
$317$	5.09272	0.286036	0.143018	−	0.989720i	$-0.454319\pi$
$317$	5.09272	0.286036	0.143018	+	0.989720i	$0.454319\pi$
$318$	−32.9727	−1.84902
$319$	−7.54060	−0.422193
$320$	−14.2935	−0.799031
$321$	6.45804	0.360453
$322$	−52.1277	−2.90496
$323$	−5.76596	−0.320827
$324$	5.42589	0.301438
$325$	4.62641	0.256627
$326$	−21.7776	−1.20615
$327$	−3.23097	−0.178673
$328$	75.6215	4.17550
$329$	13.8302	0.762481
$330$	−3.36840	−0.185425
$331$	8.11417	0.445995	0.222998	−	0.974819i	$-0.428416\pi$
$331$	8.11417	0.445995	0.222998	+	0.974819i	$0.428416\pi$
$332$	−1.82597	−0.100213
$333$	−0.657503	−0.0360309
$334$	−4.95897	−0.271343
$335$	−4.96661	−0.271355
$336$	−38.6334	−2.10763
$337$	20.9890	1.14334	0.571671	−	0.820483i	$-0.306295\pi$
$337$	20.9890	1.14334	0.571671	+	0.820483i	$0.306295\pi$
$338$	32.8345	1.78596
$339$	8.50429	0.461890
$340$	−4.72440	−0.256217
$341$	−7.77167	−0.420860
$342$	9.12237	0.493282
$343$	18.5029	0.999065
$344$	−81.9321	−4.41748
$345$	3.65156	0.196594
$346$	3.75902	0.202086
$347$	18.2807	0.981361	0.490680	−	0.871340i	$-0.336748\pi$
$347$	18.2807	0.981361	0.490680	+	0.871340i	$0.336748\pi$
$348$	16.7326	0.896964
$349$	−17.5351	−0.938630	−0.469315	−	0.883031i	$-0.655499\pi$
$349$	−17.5351	−0.938630	−0.469315	+	0.883031i	$0.655499\pi$
$350$	−34.2384	−1.83012
$351$	−0.975121	−0.0520481
$352$	51.5515	2.74771
$353$	−35.5940	−1.89448	−0.947239	−	0.320527i	$-0.896140\pi$
$353$	−35.5940	−1.89448	−0.947239	+	0.320527i	$0.896140\pi$
$354$	26.5604	1.41167
$355$	8.28289	0.439610
$356$	−95.0841	−5.03945
$357$	−4.56134	−0.241411
$358$	−63.8417	−3.37414
$359$	−16.5917	−0.875675	−0.437838	−	0.899054i	$-0.644256\pi$
$359$	−16.5917	−0.875675	−0.437838	+	0.899054i	$0.644256\pi$
$360$	4.71938	0.248733
$361$	−7.79356	−0.410188
$362$	−0.393145	−0.0206632
$363$	−5.02106	−0.263538
$364$	14.0114	0.734400
$365$	0.582662	0.0304979
$366$	−10.3287	−0.539892
$367$	5.60179	0.292411	0.146206	−	0.989254i	$-0.453294\pi$
$367$	5.60179	0.292411	0.146206	+	0.989254i	$0.453294\pi$
$368$	−105.378	−5.49321
$369$	−8.10024	−0.421682
$370$	−0.905753	−0.0470879
$371$	−32.0430	−1.66359
$372$	17.2454	0.894132
$373$	−4.97353	−0.257519	−0.128760	−	0.991676i	$-0.541100\pi$
$373$	−4.97353	−0.257519	−0.128760	+	0.991676i	$0.541100\pi$
$374$	11.4769	0.593456
$375$	4.92601	0.254378
$376$	48.7551	2.51435
$377$	−3.00713	−0.154875
$378$	7.21652	0.371178
$379$	−1.83245	−0.0941268	−0.0470634	−	0.998892i	$-0.514986\pi$
$379$	−1.83245	−0.0941268	−0.0470634	+	0.998892i	$0.514986\pi$
$380$	9.18211	0.471032
$381$	17.7703	0.910399
$382$	26.4292	1.35224
$383$	20.7685	1.06122	0.530609	−	0.847617i	$-0.321963\pi$
$383$	20.7685	1.06122	0.530609	+	0.847617i	$0.321963\pi$
$384$	−34.8847	−1.78020
$385$	−3.27344	−0.166830
$386$	28.7086	1.46123
$387$	8.77621	0.446120
$388$	−29.1358	−1.47914
$389$	29.1321	1.47706	0.738529	−	0.674222i	$-0.235521\pi$
$389$	29.1321	1.47706	0.738529	+	0.674222i	$0.235521\pi$
$390$	−1.34329	−0.0680203
$391$	−12.4417	−0.629203
$392$	−0.121936	−0.00615869
$393$	−9.00889	−0.454438
$394$	−59.4896	−2.99704
$395$	−4.94980	−0.249052
$396$	−13.2673	−0.666707
$397$	−18.2488	−0.915880	−0.457940	−	0.888983i	$-0.651413\pi$
$397$	−18.2488	−0.915880	−0.457940	+	0.888983i	$0.651413\pi$
$398$	72.8161	3.64994
$399$	8.86518	0.443814
$400$	−69.2142	−3.46071
$401$	23.3583	1.16646	0.583230	−	0.812307i	$-0.301789\pi$
$401$	23.3583	1.16646	0.583230	+	0.812307i	$0.301789\pi$
$402$	−26.7730	−1.33531
$403$	−3.09928	−0.154386
$404$	−89.7091	−4.46319
$405$	−0.505520	−0.0251195
$406$	22.2547	1.10448
$407$	1.60772	0.0796916
$408$	−16.0800	−0.796077
$409$	25.1840	1.24527	0.622635	−	0.782513i	$-0.286062\pi$
$409$	25.1840	1.24527	0.622635	+	0.782513i	$0.286062\pi$
$410$	−11.1586	−0.551085
$411$	14.6349	0.721887
$412$	8.68786	0.428020
$413$	25.8116	1.27011
$414$	19.6841	0.967419
$415$	0.170122	0.00835098
$416$	20.5583	1.00796
$417$	16.9697	0.831008
$418$	−22.3059	−1.09102
$419$	−9.48578	−0.463411	−0.231705	−	0.972786i	$-0.574430\pi$
$419$	−9.48578	−0.463411	−0.231705	+	0.972786i	$0.574430\pi$
$420$	7.26378	0.354436
$421$	−7.58603	−0.369721	−0.184860	−	0.982765i	$-0.559183\pi$
$421$	−7.58603	−0.369721	−0.184860	+	0.982765i	$0.559183\pi$
$422$	13.2335	0.644198
$423$	−5.22244	−0.253924
$424$	−112.961	−5.48585
$425$	−8.17192	−0.396396
$426$	44.6496	2.16328
$427$	−10.0375	−0.485751
$428$	35.0406	1.69375
$429$	2.38435	0.115118
$430$	12.0898	0.583022
$431$	26.1792	1.26101	0.630503	−	0.776186i	$-0.282848\pi$
$431$	26.1792	1.26101	0.630503	+	0.776186i	$0.282848\pi$
$432$	14.5885	0.701888
$433$	−0.252538	−0.0121362	−0.00606810	−	0.999982i	$-0.501932\pi$
$433$	−0.252538	−0.0121362	−0.00606810	+	0.999982i	$0.501932\pi$
$434$	22.9367	1.10100
$435$	−1.55895	−0.0747459
$436$	−17.5309	−0.839578
$437$	24.1810	1.15673
$438$	3.14089	0.150077
$439$	−38.7009	−1.84709	−0.923546	−	0.383489i	$-0.874722\pi$
$439$	−38.7009	−1.84709	−0.923546	+	0.383489i	$0.874722\pi$
$440$	−11.5398	−0.550137
$441$	0.0130612	0.000621964 0
$442$	4.57689	0.217701
$443$	−16.2478	−0.771954	−0.385977	−	0.922508i	$-0.626136\pi$
$443$	−16.2478	−0.771954	−0.385977	+	0.922508i	$0.626136\pi$
$444$	−3.56754	−0.169308
$445$	8.85881	0.419948
$446$	−23.5620	−1.11569
$447$	7.49220	0.354369
$448$	−74.8780	−3.53765
$449$	−2.67205	−0.126102	−0.0630509	−	0.998010i	$-0.520083\pi$
$449$	−2.67205	−0.126102	−0.0630509	+	0.998010i	$0.520083\pi$
$450$	12.9289	0.609472
$451$	19.8066	0.932657
$452$	46.1433	2.17040
$453$	4.68208	0.219983
$454$	−74.7715	−3.50920
$455$	−1.30542	−0.0611991
$456$	31.2522	1.46352
$457$	−3.65492	−0.170970	−0.0854849	−	0.996339i	$-0.527244\pi$
$457$	−3.65492	−0.170970	−0.0854849	+	0.996339i	$0.527244\pi$
$458$	−66.6431	−3.11403
$459$	1.72242	0.0803955
$460$	19.8130	0.923785
$461$	2.76199	0.128639	0.0643193	−	0.997929i	$-0.479512\pi$
$461$	2.76199	0.128639	0.0643193	+	0.997929i	$0.479512\pi$
$462$	−17.6457	−0.820954
$463$	−1.20570	−0.0560337	−0.0280169	−	0.999607i	$-0.508919\pi$
$463$	−1.20570	−0.0560337	−0.0280169	+	0.999607i	$0.508919\pi$
$464$	44.9887	2.08855
$465$	−1.60672	−0.0745099
$466$	−35.4462	−1.64201
$467$	6.95982	0.322062	0.161031	−	0.986949i	$-0.448518\pi$
$467$	6.95982	0.322062	0.161031	+	0.986949i	$0.448518\pi$
$468$	−5.29090	−0.244572
$469$	−26.0181	−1.20141
$470$	−7.19425	−0.331846
$471$	−6.45903	−0.297616
$472$	90.9930	4.18829
$473$	−21.4595	−0.986707
$474$	−26.6823	−1.22556
$475$	15.8825	0.728740
$476$	−24.7493	−1.13438
$477$	12.0999	0.554014
$478$	−43.7031	−1.99893
$479$	−18.0820	−0.826188	−0.413094	−	0.910688i	$-0.635552\pi$
$479$	−18.0820	−0.826188	−0.413094	+	0.910688i	$0.635552\pi$
$480$	10.6578	0.486460
$481$	0.641145	0.0292337
$482$	−41.7052	−1.89962
$483$	19.1291	0.870404
$484$	−27.2437	−1.23835
$485$	2.71453	0.123260
$486$	−2.72505	−0.123611
$487$	9.43221	0.427414	0.213707	−	0.976898i	$-0.431446\pi$
$487$	9.43221	0.427414	0.213707	+	0.976898i	$0.431446\pi$
$488$	−35.3851	−1.60181
$489$	7.99164	0.361394
$490$	0.0179927	0.000812828 0
$491$	33.4320	1.50877	0.754383	−	0.656435i	$-0.227936\pi$
$491$	33.4320	1.50877	0.754383	+	0.656435i	$0.227936\pi$
$492$	−43.9510	−1.98146
$493$	5.31168	0.239226
$494$	−8.89542	−0.400224
$495$	1.23609	0.0555581
$496$	46.3673	2.08195
$497$	43.3908	1.94634
$498$	0.917059	0.0410944
$499$	27.1360	1.21477	0.607387	−	0.794406i	$-0.292218\pi$
$499$	27.1360	1.21477	0.607387	+	0.794406i	$0.292218\pi$
$500$	26.7280	1.19531
$501$	1.81977	0.0813014
$502$	−44.2451	−1.97475
$503$	34.7234	1.54824	0.774121	−	0.633038i	$-0.218192\pi$
$503$	34.7234	1.54824	0.774121	+	0.633038i	$0.218192\pi$
$504$	24.7230	1.10125
$505$	8.35803	0.371927
$506$	−48.1312	−2.13969
$507$	−12.0491	−0.535121
$508$	96.4195	4.27792
$509$	15.4563	0.685088	0.342544	−	0.939502i	$-0.388711\pi$
$509$	15.4563	0.685088	0.342544	+	0.939502i	$0.388711\pi$
$510$	2.37274	0.105067
$511$	3.05233	0.135027
$512$	−35.1794	−1.55473
$513$	−3.34760	−0.147800
$514$	55.9053	2.46588
$515$	−0.809432	−0.0356678
$516$	47.6187	2.09630
$517$	12.7698	0.561617
$518$	−4.74488	−0.208478
$519$	−1.37943	−0.0605504
$520$	−4.60197	−0.201810
$521$	−15.3148	−0.670953	−0.335477	−	0.942049i	$-0.608897\pi$
$521$	−15.3148	−0.670953	−0.335477	+	0.942049i	$0.608897\pi$
$522$	−8.40365	−0.367818
$523$	−16.8276	−0.735820	−0.367910	−	0.929861i	$-0.619927\pi$
$523$	−16.8276	−0.735820	−0.367910	+	0.929861i	$0.619927\pi$
$524$	−48.8812	−2.13538
$525$	12.5643	0.548353
$526$	−22.2323	−0.969372
$527$	5.47445	0.238471
$528$	−35.6715	−1.55240
$529$	29.1773	1.26858
$530$	16.6683	0.724026
$531$	−9.74677	−0.422974
$532$	48.1015	2.08546
$533$	7.89872	0.342132
$534$	47.7542	2.06653
$535$	−3.26467	−0.141144
$536$	−91.7211	−3.96175
$537$	23.4277	1.01098
$538$	−9.86743	−0.425415
$539$	−0.0319372	−0.00137563
$540$	−2.74289	−0.118035
$541$	26.5966	1.14348	0.571739	−	0.820436i	$-0.306269\pi$
$541$	26.5966	1.14348	0.571739	+	0.820436i	$0.306269\pi$
$542$	9.56592	0.410891
$543$	0.144271	0.00619125
$544$	−36.3135	−1.55693
$545$	1.63332	0.0699638
$546$	−7.03698	−0.301155
$547$	15.4277	0.659642	0.329821	−	0.944043i	$-0.393012\pi$
$547$	15.4277	0.659642	0.329821	+	0.944043i	$0.393012\pi$
$548$	79.4074	3.39212
$549$	3.79030	0.161766
$550$	−31.6135	−1.34800
$551$	−10.3235	−0.439797
$552$	67.4354	2.87024
$553$	−25.9301	−1.10266
$554$	57.4078	2.43902
$555$	0.332381	0.0141088
$556$	92.0755	3.90487
$557$	9.06544	0.384115	0.192058	−	0.981384i	$-0.438484\pi$
$557$	9.06544	0.384115	0.192058	+	0.981384i	$0.438484\pi$
$558$	−8.66117	−0.366657
$559$	−8.55787	−0.361959
$560$	19.5300	0.825292
$561$	−4.21163	−0.177815
$562$	−11.9427	−0.503772
$563$	−25.9562	−1.09392	−0.546962	−	0.837157i	$-0.684216\pi$
$563$	−25.9562	−1.09392	−0.546962	+	0.837157i	$0.684216\pi$
$564$	−28.3364	−1.19318
$565$	−4.29909	−0.180864
$566$	−68.2839	−2.87019
$567$	−2.64822	−0.111215
$568$	152.964	6.41825
$569$	−36.7300	−1.53980	−0.769900	−	0.638164i	$-0.779694\pi$
$569$	−36.7300	−1.53980	−0.769900	+	0.638164i	$0.779694\pi$
$570$	−4.61154	−0.193156
$571$	27.6419	1.15678	0.578388	−	0.815762i	$-0.303682\pi$
$571$	27.6419	1.15678	0.578388	+	0.815762i	$0.303682\pi$
$572$	12.9372	0.540933
$573$	−9.69864	−0.405166
$574$	−58.4556	−2.43989
$575$	34.2710	1.42920
$576$	28.2749	1.17812
$577$	−25.3865	−1.05686	−0.528428	−	0.848978i	$-0.677218\pi$
$577$	−25.3865	−1.05686	−0.528428	+	0.848978i	$0.677218\pi$
$578$	38.2414	1.59063
$579$	−10.5351	−0.437823
$580$	−8.45869	−0.351228
$581$	0.891204	0.0369734
$582$	14.6329	0.606552
$583$	−29.5864	−1.22534
$584$	10.7603	0.445265
$585$	0.492943	0.0203807
$586$	47.0363	1.94305
$587$	−13.9641	−0.576360	−0.288180	−	0.957576i	$-0.593050\pi$
$587$	−13.9641	−0.576360	−0.288180	+	0.957576i	$0.593050\pi$
$588$	0.0708688	0.00292258
$589$	−10.6399	−0.438408
$590$	−13.4268	−0.552773
$591$	21.8307	0.897993
$592$	−9.59196	−0.394227
$593$	−34.8352	−1.43051	−0.715255	−	0.698863i	$-0.753689\pi$
$593$	−34.8352	−1.43051	−0.715255	+	0.698863i	$0.753689\pi$
$594$	6.66325	0.273396
$595$	2.30585	0.0945304
$596$	40.6518	1.66516
$597$	−26.7210	−1.09362
$598$	−19.1944	−0.784916
$599$	33.6207	1.37370	0.686852	−	0.726798i	$-0.258992\pi$
$599$	33.6207	1.37370	0.686852	+	0.726798i	$0.258992\pi$
$600$	44.2928	1.80824
$601$	−1.36541	−0.0556961	−0.0278480	−	0.999612i	$-0.508865\pi$
$601$	−1.36541	−0.0556961	−0.0278480	+	0.999612i	$0.508865\pi$
$602$	63.3337	2.58129
$603$	9.82477	0.400095
$604$	25.4044	1.03369
$605$	2.53825	0.103194
$606$	45.0547	1.83022
$607$	−36.2477	−1.47125	−0.735624	−	0.677390i	$-0.763111\pi$
$607$	−36.2477	−1.47125	−0.735624	+	0.677390i	$0.763111\pi$
$608$	70.5770	2.86228
$609$	−8.16672	−0.330932
$610$	5.22139	0.211408
$611$	5.09251	0.206021
$612$	9.34563	0.377775
$613$	9.46139	0.382142	0.191071	−	0.981576i	$-0.438804\pi$
$613$	9.46139	0.382142	0.191071	+	0.981576i	$0.438804\pi$
$614$	−61.6553	−2.48820
$615$	4.09483	0.165120
$616$	−60.4523	−2.43569
$617$	−15.1886	−0.611471	−0.305735	−	0.952117i	$-0.598902\pi$
$617$	−15.1886	−0.611471	−0.305735	+	0.952117i	$0.598902\pi$
$618$	−4.36331	−0.175518
$619$	−17.2948	−0.695137	−0.347569	−	0.937655i	$-0.612993\pi$
$619$	−17.2948	−0.695137	−0.347569	+	0.937655i	$0.612993\pi$
$620$	−8.71789	−0.350119
$621$	−7.22339	−0.289864
$622$	58.4592	2.34400
$623$	46.4078	1.85929
$624$	−14.2255	−0.569477
$625$	21.2321	0.849282
$626$	65.5747	2.62089
$627$	8.18551	0.326898
$628$	−35.0459	−1.39848
$629$	−1.13249	−0.0451555
$630$	−3.64809	−0.145344
$631$	41.8553	1.66623	0.833117	−	0.553097i	$-0.186554\pi$
$631$	41.8553	1.66623	0.833117	+	0.553097i	$0.186554\pi$
$632$	−91.4107	−3.63612
$633$	−4.85626	−0.193019
$634$	−13.8779	−0.551162
$635$	−8.98323	−0.356489
$636$	65.6524	2.60329
$637$	−0.0127363	−0.000504630 0
$638$	20.5485	0.813523
$639$	−16.3849	−0.648176
$640$	17.6349	0.697080
$641$	4.15374	0.164063	0.0820314	−	0.996630i	$-0.473859\pi$
$641$	4.15374	0.164063	0.0820314	+	0.996630i	$0.473859\pi$
$642$	−17.5985	−0.694556
$643$	12.0031	0.473357	0.236678	−	0.971588i	$-0.423941\pi$
$643$	12.0031	0.473357	0.236678	+	0.971588i	$0.423941\pi$
$644$	103.792	4.08999
$645$	−4.43655	−0.174689
$646$	15.7125	0.618201
$647$	14.6870	0.577404	0.288702	−	0.957419i	$-0.406776\pi$
$647$	14.6870	0.577404	0.288702	+	0.957419i	$0.406776\pi$
$648$	−9.33570	−0.366741
$649$	23.8327	0.935514
$650$	−12.6072	−0.494495
$651$	−8.41698	−0.329888
$652$	43.3617	1.69818
$653$	0.836166	0.0327217	0.0163608	−	0.999866i	$-0.494792\pi$
$653$	0.836166	0.0327217	0.0163608	+	0.999866i	$0.494792\pi$
$654$	8.80456	0.344286
$655$	4.55417	0.177946
$656$	−118.170	−4.61377
$657$	−1.15260	−0.0449672
$658$	−37.6878	−1.46922
$659$	48.1581	1.87597	0.937986	−	0.346673i	$-0.112689\pi$
$659$	48.1581	1.87597	0.937986	+	0.346673i	$0.112689\pi$
$660$	6.70688	0.261065
$661$	45.9891	1.78877	0.894385	−	0.447298i	$-0.147614\pi$
$661$	45.9891	1.78877	0.894385	+	0.447298i	$0.147614\pi$
$662$	−22.1115	−0.859388
$663$	−1.67956	−0.0652289
$664$	3.14174	0.121923
$665$	−4.48152	−0.173786
$666$	1.79173	0.0694280
$667$	−22.2759	−0.862525
$668$	9.87387	0.382032
$669$	8.64646	0.334292
$670$	13.5343	0.522874
$671$	−9.26799	−0.357787
$672$	55.8320	2.15377
$673$	−14.7496	−0.568554	−0.284277	−	0.958742i	$-0.591754\pi$
$673$	−14.7496	−0.568554	−0.284277	+	0.958742i	$0.591754\pi$
$674$	−57.1960	−2.20311
$675$	−4.74445	−0.182614
$676$	−65.3772	−2.51451
$677$	−15.6496	−0.601462	−0.300731	−	0.953709i	$-0.597231\pi$
$677$	−15.6496	−0.601462	−0.300731	+	0.953709i	$0.597231\pi$
$678$	−23.1746	−0.890015
$679$	14.2203	0.545726
$680$	8.12874	0.311723
$681$	27.4386	1.05145
$682$	21.1782	0.810954
$683$	−7.45886	−0.285405	−0.142703	−	0.989766i	$-0.545579\pi$
$683$	−7.45886	−0.285405	−0.142703	+	0.989766i	$0.545579\pi$
$684$	−18.1637	−0.694507
$685$	−7.39824	−0.282672
$686$	−50.4214	−1.92510
$687$	24.4558	0.933046
$688$	128.031	4.88115
$689$	−11.7988	−0.449499
$690$	−9.95069	−0.378816
$691$	39.2949	1.49485	0.747425	−	0.664346i	$-0.231290\pi$
$691$	39.2949	1.49485	0.747425	+	0.664346i	$0.231290\pi$
$692$	−7.48465	−0.284524
$693$	6.47539	0.245980
$694$	−49.8158	−1.89098
$695$	−8.57850	−0.325401
$696$	−28.7900	−1.09128
$697$	−13.9520	−0.528469
$698$	47.7839	1.80865
$699$	13.0075	0.491990
$700$	68.1727	2.57668
$701$	17.8170	0.672940	0.336470	−	0.941694i	$-0.390767\pi$
$701$	17.8170	0.672940	0.336470	+	0.941694i	$0.390767\pi$
$702$	2.65725	0.100292
$703$	2.20106	0.0830145
$704$	−69.1373	−2.60571
$705$	2.64005	0.0994299
$706$	96.9954	3.65047
$707$	43.7844	1.64668
$708$	−52.8849	−1.98754
$709$	0.134921	0.00506707	0.00253354	−	0.999997i	$-0.499194\pi$
$709$	0.134921	0.00506707	0.00253354	+	0.999997i	$0.499194\pi$
$710$	−22.5713	−0.847085
$711$	9.79151	0.367210
$712$	163.600	6.13118
$713$	−22.9585	−0.859802
$714$	12.4299	0.465176
$715$	−1.20534	−0.0450771
$716$	127.116	4.75056
$717$	16.0375	0.598933
$718$	45.2131	1.68734
$719$	14.4474	0.538796	0.269398	−	0.963029i	$-0.413175\pi$
$719$	14.4474	0.538796	0.269398	+	0.963029i	$0.413175\pi$
$720$	−7.37476	−0.274841
$721$	−4.24030	−0.157917
$722$	21.2378	0.790390
$723$	15.3044	0.569177
$724$	0.782796	0.0290924
$725$	−14.6312	−0.543389
$726$	13.6826	0.507810
$727$	−39.5043	−1.46513	−0.732567	−	0.680695i	$-0.761678\pi$
$727$	−39.5043	−1.46513	−0.732567	+	0.680695i	$0.761678\pi$
$728$	−24.1079	−0.893498
$729$	1.00000	0.0370370
$730$	−1.58778	−0.0587664
$731$	15.1163	0.559096
$732$	20.5657	0.760131
$733$	33.5803	1.24032	0.620159	−	0.784476i	$-0.287068\pi$
$733$	33.5803	1.24032	0.620159	+	0.784476i	$0.287068\pi$
$734$	−15.2652	−0.563447
$735$	−0.00660271	−0.000243545 0
$736$	152.290	5.61347
$737$	−24.0234	−0.884913
$738$	22.0736	0.812539
$739$	18.5056	0.680738	0.340369	−	0.940292i	$-0.389448\pi$
$739$	18.5056	0.680738	0.340369	+	0.940292i	$0.389448\pi$
$740$	1.80346	0.0662965
$741$	3.26432	0.119918
$742$	87.3188	3.20558
$743$	32.4736	1.19134	0.595670	−	0.803229i	$-0.296886\pi$
$743$	32.4736	1.19134	0.595670	+	0.803229i	$0.296886\pi$
$744$	−29.6722	−1.08784
$745$	−3.78745	−0.138762
$746$	13.5531	0.496214
$747$	−0.336529	−0.0123130
$748$	−22.8518	−0.835545
$749$	−17.1023	−0.624904
$750$	−13.4236	−0.490161
$751$	12.4164	0.453080	0.226540	−	0.974002i	$-0.427259\pi$
$751$	12.4164	0.453080	0.226540	+	0.974002i	$0.427259\pi$
$752$	−76.1874	−2.77827
$753$	16.2364	0.591689
$754$	8.19458	0.298429
$755$	−2.36688	−0.0861397
$756$	−14.3689	−0.522593
$757$	−26.9787	−0.980556	−0.490278	−	0.871566i	$-0.663105\pi$
$757$	−26.9787	−0.980556	−0.490278	+	0.871566i	$0.663105\pi$
$758$	4.99352	0.181373
$759$	17.6625	0.641109
$760$	−15.7986	−0.573076
$761$	−2.99931	−0.108725	−0.0543624	−	0.998521i	$-0.517313\pi$
$761$	−2.99931	−0.108725	−0.0543624	+	0.998521i	$0.517313\pi$
$762$	−48.4249	−1.75425
$763$	8.55633	0.309760
$764$	−52.6237	−1.90386
$765$	−0.870716	−0.0314808
$766$	−56.5950	−2.04486
$767$	9.50429	0.343180
$768$	38.5126	1.38970
$769$	19.5261	0.704130	0.352065	−	0.935976i	$-0.385480\pi$
$769$	19.5261	0.704130	0.352065	+	0.935976i	$0.385480\pi$
$770$	8.92027	0.321464
$771$	−20.5154	−0.738843
$772$	−57.1622	−2.05731
$773$	35.2270	1.26703	0.633513	−	0.773732i	$-0.281612\pi$
$773$	35.2270	1.26703	0.633513	+	0.773732i	$0.281612\pi$
$774$	−23.9156	−0.859628
$775$	−15.0796	−0.541673
$776$	50.1306	1.79958
$777$	1.74121	0.0624656
$778$	−79.3864	−2.84614
$779$	27.1164	0.971545
$780$	2.67465	0.0957679
$781$	40.0641	1.43361
$782$	33.9042	1.21241
$783$	3.08386	0.110208
$784$	0.190543	0.00680512
$785$	3.26517	0.116539
$786$	24.5496	0.875657
$787$	−42.0191	−1.49782	−0.748910	−	0.662672i	$-0.769423\pi$
$787$	−42.0191	−1.49782	−0.748910	+	0.662672i	$0.769423\pi$
$788$	118.451	4.21963
$789$	8.15848	0.290450
$790$	13.4885	0.479898
$791$	−22.5212	−0.800763
$792$	22.8275	0.811141
$793$	−3.69600	−0.131249
$794$	49.7288	1.76481
$795$	−6.11671	−0.216937
$796$	−144.985	−5.13886
$797$	32.4384	1.14903	0.574513	−	0.818495i	$-0.305191\pi$
$797$	32.4384	1.14903	0.574513	+	0.818495i	$0.305191\pi$
$798$	−24.1580	−0.855185
$799$	−8.99521	−0.318228
$800$	100.027	3.53647
$801$	−17.5242	−0.619186
$802$	−63.6526	−2.24765
$803$	2.81832	0.0994563
$804$	53.3081	1.88003
$805$	−9.67014	−0.340828
$806$	8.44569	0.297487
$807$	3.62101	0.127466
$808$	154.352	5.43009
$809$	−10.8128	−0.380158	−0.190079	−	0.981769i	$-0.560874\pi$
$809$	−10.8128	−0.380158	−0.190079	+	0.981769i	$0.560874\pi$
$810$	1.37757	0.0484027
$811$	−12.1320	−0.426011	−0.213006	−	0.977051i	$-0.568325\pi$
$811$	−12.1320	−0.426011	−0.213006	+	0.977051i	$0.568325\pi$
$812$	−44.3117	−1.55504
$813$	−3.51037	−0.123114
$814$	−4.38111	−0.153558
$815$	−4.03993	−0.141513
$816$	25.1274	0.879635
$817$	−29.3793	−1.02785
$818$	−68.6277	−2.39951
$819$	2.58233	0.0902341
$820$	22.2181	0.775890
$821$	−47.7803	−1.66754	−0.833772	−	0.552109i	$-0.813823\pi$
$821$	−47.7803	−1.66754	−0.833772	+	0.552109i	$0.813823\pi$
$822$	−39.8809	−1.39100
$823$	−5.12348	−0.178593	−0.0892967	−	0.996005i	$-0.528462\pi$
$823$	−5.12348	−0.178593	−0.0892967	+	0.996005i	$0.528462\pi$
$824$	−14.9482	−0.520746
$825$	11.6011	0.403897
$826$	−70.3378	−2.44737
$827$	−20.0151	−0.695994	−0.347997	−	0.937496i	$-0.613138\pi$
$827$	−20.0151	−0.695994	−0.347997	+	0.937496i	$0.613138\pi$
$828$	−39.1933	−1.36206
$829$	−0.693336	−0.0240806	−0.0120403	−	0.999928i	$-0.503833\pi$
$829$	−0.693336	−0.0240806	−0.0120403	+	0.999928i	$0.503833\pi$
$830$	−0.463591	−0.0160915
$831$	−21.0667	−0.730796
$832$	−27.5714	−0.955867
$833$	0.0224969	0.000779471 0
$834$	−46.2432	−1.60127
$835$	−0.919931	−0.0318355
$836$	44.4136	1.53608
$837$	3.17836	0.109860
$838$	25.8492	0.892946
$839$	20.4884	0.707339	0.353670	−	0.935370i	$-0.384934\pi$
$839$	20.4884	0.707339	0.353670	+	0.935370i	$0.384934\pi$
$840$	−12.4980	−0.431220
$841$	−19.4898	−0.672063
$842$	20.6723	0.712414
$843$	4.38256	0.150943
$844$	−26.3495	−0.906987
$845$	6.09108	0.209539
$846$	14.2314	0.489285
$847$	13.2969	0.456886
$848$	176.518	6.06166
$849$	25.0579	0.859984
$850$	22.2689	0.763816
$851$	4.74940	0.162807
$852$	−88.9026	−3.04575
$853$	−34.3335	−1.17556	−0.587778	−	0.809022i	$-0.699997\pi$
$853$	−34.3335	−1.17556	−0.587778	+	0.809022i	$0.699997\pi$
$854$	27.3528	0.935993
$855$	1.69228	0.0578747
$856$	−60.2903	−2.06068
$857$	5.06237	0.172927	0.0864636	−	0.996255i	$-0.472443\pi$
$857$	5.06237	0.172927	0.0864636	+	0.996255i	$0.472443\pi$
$858$	−6.49748	−0.221820
$859$	30.1225	1.02777	0.513883	−	0.857860i	$-0.328206\pi$
$859$	30.1225	1.02777	0.513883	+	0.857860i	$0.328206\pi$
$860$	−24.0722	−0.820855
$861$	21.4512	0.731055
$862$	−71.3395	−2.42983
$863$	31.2254	1.06293	0.531463	−	0.847081i	$-0.321642\pi$
$863$	31.2254	1.06293	0.531463	+	0.847081i	$0.321642\pi$
$864$	−21.0829	−0.717253
$865$	0.697331	0.0237100
$866$	0.688178	0.0233852
$867$	−14.0333	−0.476595
$868$	−45.6696	−1.55013
$869$	−23.9421	−0.812179
$870$	4.24821	0.144028
$871$	−9.58034	−0.324617
$872$	30.1634	1.02146
$873$	−5.36977	−0.181739
$874$	−65.8944	−2.22891
$875$	−13.0452	−0.441007
$876$	−6.25387	−0.211299
$877$	−10.1796	−0.343739	−0.171870	−	0.985120i	$-0.554981\pi$
$877$	−10.1796	−0.343739	−0.171870	+	0.985120i	$0.554981\pi$
$878$	105.462	3.55916
$879$	−17.2607	−0.582190
$880$	18.0327	0.607881
$881$	33.4081	1.12555	0.562773	−	0.826611i	$-0.309734\pi$
$881$	33.4081	1.12555	0.562773	+	0.826611i	$0.309734\pi$
$882$	−0.0355925	−0.00119846
$883$	−39.3853	−1.32542	−0.662710	−	0.748876i	$-0.730594\pi$
$883$	−39.3853	−1.32542	−0.662710	+	0.748876i	$0.730594\pi$
$884$	−9.11313	−0.306508
$885$	4.92719	0.165626
$886$	44.2759	1.48748
$887$	−41.2378	−1.38463	−0.692315	−	0.721595i	$-0.743409\pi$
$887$	−41.2378	−1.38463	−0.692315	+	0.721595i	$0.743409\pi$
$888$	6.13825	0.205986
$889$	−47.0596	−1.57833
$890$	−24.1407	−0.809198
$891$	−2.44519	−0.0819168
$892$	46.9147	1.57082
$893$	17.4826	0.585034
$894$	−20.4166	−0.682833
$895$	−11.8432	−0.395874
$896$	92.3822	3.08627
$897$	7.04368	0.235182
$898$	7.28146	0.242986
$899$	9.80159	0.326901
$900$	−25.7428	−0.858095
$901$	20.8410	0.694314
$902$	−53.9739	−1.79714
$903$	−23.2413	−0.773423
$904$	−79.3935	−2.64059
$905$	−0.0729317	−0.00242433
$906$	−12.7589	−0.423885
$907$	35.5469	1.18032	0.590158	−	0.807288i	$-0.299065\pi$
$907$	35.5469	1.18032	0.590158	+	0.807288i	$0.299065\pi$
$908$	148.879	4.94072
$909$	−16.5335	−0.548383
$910$	3.55733	0.117924
$911$	6.83240	0.226367	0.113184	−	0.993574i	$-0.463895\pi$
$911$	6.83240	0.226367	0.113184	+	0.993574i	$0.463895\pi$
$912$	−48.8364	−1.61713
$913$	0.822877	0.0272333
$914$	9.95983	0.329442
$915$	−1.91607	−0.0633434
$916$	132.694	4.38434
$917$	23.8575	0.787844
$918$	−4.69367	−0.154914
$919$	−1.95229	−0.0644001	−0.0322000	−	0.999481i	$-0.510251\pi$
$919$	−1.95229	−0.0644001	−0.0322000	+	0.999481i	$0.510251\pi$
$920$	−34.0899	−1.12391
$921$	22.6254	0.745532
$922$	−7.52655	−0.247874
$923$	15.9773	0.525898
$924$	35.1347	1.15585
$925$	3.11949	0.102568
$926$	3.28560	0.107971
$927$	1.60119	0.0525899
$928$	−65.0165	−2.13427
$929$	−24.7953	−0.813507	−0.406754	−	0.913538i	$-0.633339\pi$
$929$	−24.7953	−0.813507	−0.406754	+	0.913538i	$0.633339\pi$
$930$	4.37839	0.143573
$931$	−0.0437238	−0.00143299
$932$	70.5774	2.31184
$933$	−21.4525	−0.702325
$934$	−18.9658	−0.620581
$935$	2.12906	0.0696278
$936$	9.10344	0.297555
$937$	−30.8489	−1.00779	−0.503895	−	0.863765i	$-0.668100\pi$
$937$	−30.8489	−1.00779	−0.503895	+	0.863765i	$0.668100\pi$
$938$	70.9006	2.31499
$939$	−24.0637	−0.785288
$940$	14.3246	0.467217
$941$	−30.0625	−0.980010	−0.490005	−	0.871720i	$-0.663005\pi$
$941$	−30.0625	−0.980010	−0.490005	+	0.871720i	$0.663005\pi$
$942$	17.6012	0.573477
$943$	58.5112	1.90539
$944$	−142.190	−4.62791
$945$	1.33873	0.0435488
$946$	58.4781	1.90129
$947$	−7.95347	−0.258453	−0.129227	−	0.991615i	$-0.541249\pi$
$947$	−7.95347	−0.258453	−0.129227	+	0.991615i	$0.541249\pi$
$948$	53.1276	1.72551
$949$	1.12392	0.0364841
$950$	−43.2806	−1.40421
$951$	5.09272	0.165143
$952$	42.5833	1.38013
$953$	35.1977	1.14016	0.570082	−	0.821588i	$-0.306911\pi$
$953$	35.1977	1.14016	0.570082	+	0.821588i	$0.306911\pi$
$954$	−32.9727	−1.06753
$955$	4.90285	0.158653
$956$	87.0179	2.81436
$957$	−7.54060	−0.243753
$958$	49.2743	1.59198
$959$	−38.7565	−1.25151
$960$	−14.2935	−0.461321
$961$	−20.8981	−0.674131
$962$	−1.74715	−0.0563304
$963$	6.45804	0.208107
$964$	83.0399	2.67454
$965$	5.32570	0.171440
$966$	−52.1277	−1.67718
$967$	58.9678	1.89628	0.948138	−	0.317858i	$-0.102964\pi$
$967$	58.9678	1.89628	0.948138	+	0.317858i	$0.102964\pi$
$968$	46.8752	1.50662
$969$	−5.76596	−0.185229
$970$	−7.39721	−0.237510
$971$	−21.9670	−0.704955	−0.352478	−	0.935820i	$-0.614661\pi$
$971$	−21.9670	−0.704955	−0.352478	+	0.935820i	$0.614661\pi$
$972$	5.42589	0.174035
$973$	−44.9394	−1.44069
$974$	−25.7032	−0.823584
$975$	4.62641	0.148164
$976$	55.2946	1.76994
$977$	48.7047	1.55820	0.779101	−	0.626898i	$-0.215676\pi$
$977$	48.7047	1.55820	0.779101	+	0.626898i	$0.215676\pi$
$978$	−21.7776	−0.696371
$979$	42.8499	1.36949
$980$	−0.0358256	−0.00114441
$981$	−3.23097	−0.103157
$982$	−91.1038	−2.90724
$983$	−51.9550	−1.65711	−0.828553	−	0.559910i	$-0.810836\pi$
$983$	−51.9550	−1.65711	−0.828553	+	0.559910i	$0.810836\pi$
$984$	75.6215	2.41072
$985$	−11.0358	−0.351631
$986$	−14.4746	−0.460965
$987$	13.8302	0.440219
$988$	17.7118	0.563488
$989$	−63.3939	−2.01581
$990$	−3.36840	−0.107055
$991$	24.3795	0.774440	0.387220	−	0.921987i	$-0.373435\pi$
$991$	24.3795	0.774440	0.387220	+	0.921987i	$0.373435\pi$
$992$	−67.0088	−2.12753
$993$	8.11417	0.257495
$994$	−118.242	−3.75041
$995$	13.5080	0.428233
$996$	−1.82597	−0.0578581
$997$	43.1396	1.36625	0.683123	−	0.730304i	$-0.260621\pi$
$997$	43.1396	1.36625	0.683123	+	0.730304i	$0.260621\pi$
$998$	−73.9469	−2.34075
$999$	−0.657503	−0.0208025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.e.1.3	✓	97

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.e.1.3	✓	97	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72505 q^{2} +1.00000 q^{3} +5.42589 q^{4} -0.505520 q^{5} -2.72505 q^{6} -2.64822 q^{7} -9.33570 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.72505 q^{2} +1.00000 q^{3} +5.42589 q^{4} -0.505520 q^{5} -2.72505 q^{6} -2.64822 q^{7} -9.33570 q^{8} +1.00000 q^{9} +1.37757 q^{10} -2.44519 q^{11} +5.42589 q^{12} -0.975121 q^{13} +7.21652 q^{14} -0.505520 q^{15} +14.5885 q^{16} +1.72242 q^{17} -2.72505 q^{18} -3.34760 q^{19} -2.74289 q^{20} -2.64822 q^{21} +6.66325 q^{22} -7.22339 q^{23} -9.33570 q^{24} -4.74445 q^{25} +2.65725 q^{26} +1.00000 q^{27} -14.3689 q^{28} +3.08386 q^{29} +1.37757 q^{30} +3.17836 q^{31} -21.0829 q^{32} -2.44519 q^{33} -4.69367 q^{34} +1.33873 q^{35} +5.42589 q^{36} -0.657503 q^{37} +9.12237 q^{38} -0.975121 q^{39} +4.71938 q^{40} -8.10024 q^{41} +7.21652 q^{42} +8.77621 q^{43} -13.2673 q^{44} -0.505520 q^{45} +19.6841 q^{46} -5.22244 q^{47} +14.5885 q^{48} +0.0130612 q^{49} +12.9289 q^{50} +1.72242 q^{51} -5.29090 q^{52} +12.0999 q^{53} -2.72505 q^{54} +1.23609 q^{55} +24.7230 q^{56} -3.34760 q^{57} -8.40365 q^{58} -9.74677 q^{59} -2.74289 q^{60} +3.79030 q^{61} -8.66117 q^{62} -2.64822 q^{63} +28.2749 q^{64} +0.492943 q^{65} +6.66325 q^{66} +9.82477 q^{67} +9.34563 q^{68} -7.22339 q^{69} -3.64809 q^{70} -16.3849 q^{71} -9.33570 q^{72} -1.15260 q^{73} +1.79173 q^{74} -4.74445 q^{75} -18.1637 q^{76} +6.47539 q^{77} +2.65725 q^{78} +9.79151 q^{79} -7.37476 q^{80} +1.00000 q^{81} +22.0736 q^{82} -0.336529 q^{83} -14.3689 q^{84} -0.870716 q^{85} -23.9156 q^{86} +3.08386 q^{87} +22.8275 q^{88} -17.5242 q^{89} +1.37757 q^{90} +2.58233 q^{91} -39.1933 q^{92} +3.17836 q^{93} +14.2314 q^{94} +1.69228 q^{95} -21.0829 q^{96} -5.36977 q^{97} -0.0355925 q^{98} -2.44519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9}+O(q^{10}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9	\( 97 q + 12 q^{2} + 97 q^{3} + 120 q^{4} + 6 q^{5} + 12 q^{6} + 50 q^{7} + 30 q^{8} + 97 q^{9} + 35 q^{10} + 18 q^{11} + 120 q^{12} + 67 q^{13} - q^{14} + 6 q^{15} + 158 q^{16} + 25 q^{17} + 12 q^{18} + 51 q^{19} + 10 q^{20} + 50 q^{21} + 39 q^{22} + 87 q^{23} + 30 q^{24} + 149 q^{25} + 14 q^{26} + 97 q^{27} + 83 q^{28} + 23 q^{29} + 35 q^{30} + 72 q^{31} + 57 q^{32} + 18 q^{33} + 28 q^{34} + 45 q^{35} + 120 q^{36} + 72 q^{37} + 3 q^{38} + 67 q^{39} + 90 q^{40} + 5 q^{41} - q^{42} + 122 q^{43} + 11 q^{44} + 6 q^{45} + 56 q^{46} + 49 q^{47} + 158 q^{48} + 167 q^{49} + 13 q^{50} + 25 q^{51} + 128 q^{52} + 30 q^{53} + 12 q^{54} + 120 q^{55} - 21 q^{56} + 51 q^{57} + 37 q^{58} + 2 q^{59} + 10 q^{60} + 158 q^{61} + 17 q^{62} + 50 q^{63} + 212 q^{64} + q^{65} + 39 q^{66} + 77 q^{67} + 56 q^{68} + 87 q^{69} + 9 q^{70} + 38 q^{71} + 30 q^{72} + 82 q^{73} - 6 q^{74} + 149 q^{75} + 93 q^{76} + 49 q^{77} + 14 q^{78} + 134 q^{79} - 25 q^{80} + 97 q^{81} + 53 q^{82} + 69 q^{83} + 83 q^{84} + 72 q^{85} + 23 q^{87} + 107 q^{88} + 35 q^{90} + 84 q^{91} + 108 q^{92} + 72 q^{93} + 65 q^{94} + 89 q^{95} + 57 q^{96} + 65 q^{97} + 18 q^{99}+O(q^{100}) \) 97 * q + 12 * q^2 + 97 * q^3 + 120 * q^4 + 6 * q^5 + 12 * q^6 + 50 * q^7 + 30 * q^8 + 97 * q^9 + 35 * q^10 + 18 * q^11 + 120 * q^12 + 67 * q^13 - q^14 + 6 * q^15 + 158 * q^16 + 25 * q^17 + 12 * q^18 + 51 * q^19 + 10 * q^20 + 50 * q^21 + 39 * q^22 + 87 * q^23 + 30 * q^24 + 149 * q^25 + 14 * q^26 + 97 * q^27 + 83 * q^28 + 23 * q^29 + 35 * q^30 + 72 * q^31 + 57 * q^32 + 18 * q^33 + 28 * q^34 + 45 * q^35 + 120 * q^36 + 72 * q^37 + 3 * q^38 + 67 * q^39 + 90 * q^40 + 5 * q^41 - q^42 + 122 * q^43 + 11 * q^44 + 6 * q^45 + 56 * q^46 + 49 * q^47 + 158 * q^48 + 167 * q^49 + 13 * q^50 + 25 * q^51 + 128 * q^52 + 30 * q^53 + 12 * q^54 + 120 * q^55 - 21 * q^56 + 51 * q^57 + 37 * q^58 + 2 * q^59 + 10 * q^60 + 158 * q^61 + 17 * q^62 + 50 * q^63 + 212 * q^64 + q^65 + 39 * q^66 + 77 * q^67 + 56 * q^68 + 87 * q^69 + 9 * q^70 + 38 * q^71 + 30 * q^72 + 82 * q^73 - 6 * q^74 + 149 * q^75 + 93 * q^76 + 49 * q^77 + 14 * q^78 + 134 * q^79 - 25 * q^80 + 97 * q^81 + 53 * q^82 + 69 * q^83 + 83 * q^84 + 72 * q^85 + 23 * q^87 + 107 * q^88 + 35 * q^90 + 84 * q^91 + 108 * q^92 + 72 * q^93 + 65 * q^94 + 89 * q^95 + 57 * q^96 + 65 * q^97 + 18 * q^99

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