LMFDB - Embedded newform 1441.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.13757 q^{2} -1.95057 q^{3} -0.705942 q^{4} +1.75766 q^{5} -2.21891 q^{6} +1.09174 q^{7} -3.07819 q^{8} +0.804735 q^{9} +O(q^{10})$	\(q+1.13757 q^{2} -1.95057 q^{3} -0.705942 q^{4} +1.75766 q^{5} -2.21891 q^{6} +1.09174 q^{7} -3.07819 q^{8} +0.804735 q^{9} +1.99945 q^{10} -1.00000 q^{11} +1.37699 q^{12} +2.00061 q^{13} +1.24193 q^{14} -3.42844 q^{15} -2.08976 q^{16} +3.43459 q^{17} +0.915439 q^{18} -2.69464 q^{19} -1.24080 q^{20} -2.12953 q^{21} -1.13757 q^{22} +4.47210 q^{23} +6.00423 q^{24} -1.91065 q^{25} +2.27583 q^{26} +4.28202 q^{27} -0.770709 q^{28} -6.09860 q^{29} -3.90007 q^{30} +6.39697 q^{31} +3.77914 q^{32} +1.95057 q^{33} +3.90708 q^{34} +1.91891 q^{35} -0.568096 q^{36} +9.61513 q^{37} -3.06534 q^{38} -3.90234 q^{39} -5.41040 q^{40} -7.70692 q^{41} -2.42248 q^{42} +5.45427 q^{43} +0.705942 q^{44} +1.41445 q^{45} +5.08731 q^{46} +11.4366 q^{47} +4.07623 q^{48} -5.80809 q^{49} -2.17349 q^{50} -6.69942 q^{51} -1.41232 q^{52} +0.811524 q^{53} +4.87109 q^{54} -1.75766 q^{55} -3.36060 q^{56} +5.25610 q^{57} -6.93756 q^{58} +15.0522 q^{59} +2.42028 q^{60} +5.64667 q^{61} +7.27698 q^{62} +0.878565 q^{63} +8.47854 q^{64} +3.51639 q^{65} +2.21891 q^{66} -11.0074 q^{67} -2.42463 q^{68} -8.72316 q^{69} +2.18289 q^{70} +5.93400 q^{71} -2.47713 q^{72} +8.69955 q^{73} +10.9379 q^{74} +3.72686 q^{75} +1.90226 q^{76} -1.09174 q^{77} -4.43917 q^{78} +1.30616 q^{79} -3.67308 q^{80} -10.7666 q^{81} -8.76713 q^{82} +14.3500 q^{83} +1.50332 q^{84} +6.03683 q^{85} +6.20459 q^{86} +11.8958 q^{87} +3.07819 q^{88} +5.83903 q^{89} +1.60903 q^{90} +2.18416 q^{91} -3.15705 q^{92} -12.4778 q^{93} +13.0099 q^{94} -4.73625 q^{95} -7.37148 q^{96} +7.73029 q^{97} -6.60709 q^{98} -0.804735 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.13757	0.804381	0.402190	−	0.915556i	$-0.368249\pi$
$2$	1.13757	0.804381	0.402190	+	0.915556i	$0.368249\pi$
$3$	−1.95057	−1.12616	−0.563082	−	0.826401i	$-0.690384\pi$
$3$	−1.95057	−1.12616	−0.563082	+	0.826401i	$0.690384\pi$
$4$	−0.705942	−0.352971
$5$	1.75766	0.786047	0.393024	−	0.919528i	$-0.371429\pi$
$5$	1.75766	0.786047	0.393024	+	0.919528i	$0.371429\pi$
$6$	−2.21891	−0.905865
$7$	1.09174	0.412641	0.206320	−	0.978485i	$-0.433851\pi$
$7$	1.09174	0.412641	0.206320	+	0.978485i	$0.433851\pi$
$8$	−3.07819	−1.08830
$9$	0.804735	0.268245
$10$	1.99945	0.632282
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.37699	0.397503
$13$	2.00061	0.554870	0.277435	−	0.960744i	$-0.410516\pi$
$13$	2.00061	0.554870	0.277435	+	0.960744i	$0.410516\pi$
$14$	1.24193	0.331920
$15$	−3.42844	−0.885218
$16$	−2.08976	−0.522440
$17$	3.43459	0.833011	0.416506	−	0.909133i	$-0.363255\pi$
$17$	3.43459	0.833011	0.416506	+	0.909133i	$0.363255\pi$
$18$	0.915439	0.215771
$19$	−2.69464	−0.618194	−0.309097	−	0.951031i	$-0.600027\pi$
$19$	−2.69464	−0.618194	−0.309097	+	0.951031i	$0.600027\pi$
$20$	−1.24080	−0.277452
$21$	−2.12953	−0.464701
$22$	−1.13757	−0.242530
$23$	4.47210	0.932498	0.466249	−	0.884654i	$-0.345605\pi$
$23$	4.47210	0.932498	0.466249	+	0.884654i	$0.345605\pi$
$24$	6.00423	1.22561
$25$	−1.91065	−0.382130
$26$	2.27583	0.446327
$27$	4.28202	0.824076
$28$	−0.770709	−0.145650
$29$	−6.09860	−1.13248	−0.566241	−	0.824240i	$-0.691603\pi$
$29$	−6.09860	−1.13248	−0.566241	+	0.824240i	$0.691603\pi$
$30$	−3.90007	−0.712053
$31$	6.39697	1.14893	0.574465	−	0.818529i	$-0.305210\pi$
$31$	6.39697	1.14893	0.574465	+	0.818529i	$0.305210\pi$
$32$	3.77914	0.668063
$33$	1.95057	0.339551
$34$	3.90708	0.670058
$35$	1.91891	0.324355
$36$	−0.568096	−0.0946827
$37$	9.61513	1.58072	0.790359	−	0.612644i	$-0.209894\pi$
$37$	9.61513	1.58072	0.790359	+	0.612644i	$0.209894\pi$
$38$	−3.06534	−0.497263
$39$	−3.90234	−0.624874
$40$	−5.41040	−0.855459
$41$	−7.70692	−1.20362	−0.601809	−	0.798640i	$-0.705553\pi$
$41$	−7.70692	−1.20362	−0.601809	+	0.798640i	$0.705553\pi$
$42$	−2.42248	−0.373797
$43$	5.45427	0.831768	0.415884	−	0.909418i	$-0.363472\pi$
$43$	5.45427	0.831768	0.415884	+	0.909418i	$0.363472\pi$
$44$	0.705942	0.106425
$45$	1.41445	0.210853
$46$	5.08731	0.750083
$47$	11.4366	1.66820	0.834101	−	0.551611i	$-0.185987\pi$
$47$	11.4366	1.66820	0.834101	+	0.551611i	$0.185987\pi$
$48$	4.07623	0.588353
$49$	−5.80809	−0.829728
$50$	−2.17349	−0.307378
$51$	−6.69942	−0.938107
$52$	−1.41232	−0.195853
$53$	0.811524	0.111471	0.0557357	−	0.998446i	$-0.482250\pi$
$53$	0.811524	0.111471	0.0557357	+	0.998446i	$0.482250\pi$
$54$	4.87109	0.662871
$55$	−1.75766	−0.237002
$56$	−3.36060	−0.449079
$57$	5.25610	0.696187
$58$	−6.93756	−0.910947
$59$	15.0522	1.95962	0.979812	−	0.199923i	$-0.0640694\pi$
$59$	15.0522	1.95962	0.979812	+	0.199923i	$0.0640694\pi$
$60$	2.42028	0.312457
$61$	5.64667	0.722982	0.361491	−	0.932376i	$-0.382268\pi$
$61$	5.64667	0.722982	0.361491	+	0.932376i	$0.382268\pi$
$62$	7.27698	0.924178
$63$	0.878565	0.110689
$64$	8.47854	1.05982
$65$	3.51639	0.436154
$66$	2.21891	0.273128
$67$	−11.0074	−1.34476	−0.672382	−	0.740204i	$-0.734729\pi$
$67$	−11.0074	−1.34476	−0.672382	+	0.740204i	$0.734729\pi$
$68$	−2.42463	−0.294029
$69$	−8.72316	−1.05015
$70$	2.18289	0.260905
$71$	5.93400	0.704236	0.352118	−	0.935956i	$-0.385462\pi$
$71$	5.93400	0.704236	0.352118	+	0.935956i	$0.385462\pi$
$72$	−2.47713	−0.291932
$73$	8.69955	1.01821	0.509103	−	0.860706i	$-0.329977\pi$
$73$	8.69955	1.01821	0.509103	+	0.860706i	$0.329977\pi$
$74$	10.9379	1.27150
$75$	3.72686	0.430340
$76$	1.90226	0.218205
$77$	−1.09174	−0.124416
$78$	−4.43917	−0.502637
$79$	1.30616	0.146954	0.0734771	−	0.997297i	$-0.476590\pi$
$79$	1.30616	0.146954	0.0734771	+	0.997297i	$0.476590\pi$
$80$	−3.67308	−0.410663
$81$	−10.7666	−1.19629
$82$	−8.76713	−0.968168
$83$	14.3500	1.57511	0.787557	−	0.616242i	$-0.211346\pi$
$83$	14.3500	1.57511	0.787557	+	0.616242i	$0.211346\pi$
$84$	1.50332	0.164026
$85$	6.03683	0.654786
$86$	6.20459	0.669058
$87$	11.8958	1.27536
$88$	3.07819	0.328136
$89$	5.83903	0.618936	0.309468	−	0.950910i	$-0.399849\pi$
$89$	5.83903	0.618936	0.309468	+	0.950910i	$0.399849\pi$
$90$	1.60903	0.169606
$91$	2.18416	0.228962
$92$	−3.15705	−0.329145
$93$	−12.4778	−1.29388
$94$	13.0099	1.34187
$95$	−4.73625	−0.485929
$96$	−7.37148	−0.752349
$97$	7.73029	0.784892	0.392446	−	0.919775i	$-0.371629\pi$
$97$	7.73029	0.784892	0.392446	+	0.919775i	$0.371629\pi$
$98$	−6.60709	−0.667417
$99$	−0.804735	−0.0808789
$100$	1.34881	0.134881
$101$	−11.7973	−1.17387	−0.586937	−	0.809632i	$-0.699667\pi$
$101$	−11.7973	−1.17387	−0.586937	+	0.809632i	$0.699667\pi$
$102$	−7.62104	−0.754596
$103$	4.45932	0.439390	0.219695	−	0.975569i	$-0.429494\pi$
$103$	4.45932	0.439390	0.219695	+	0.975569i	$0.429494\pi$
$104$	−6.15826	−0.603867
$105$	−3.74297	−0.365277
$106$	0.923163	0.0896655
$107$	−3.65710	−0.353545	−0.176773	−	0.984252i	$-0.556566\pi$
$107$	−3.65710	−0.353545	−0.176773	+	0.984252i	$0.556566\pi$
$108$	−3.02286	−0.290875
$109$	1.87716	0.179799	0.0898996	−	0.995951i	$-0.471345\pi$
$109$	1.87716	0.179799	0.0898996	+	0.995951i	$0.471345\pi$
$110$	−1.99945	−0.190640
$111$	−18.7550	−1.78015
$112$	−2.28148	−0.215580
$113$	−8.95939	−0.842829	−0.421414	−	0.906868i	$-0.638466\pi$
$113$	−8.95939	−0.842829	−0.421414	+	0.906868i	$0.638466\pi$
$114$	5.97916	0.560000
$115$	7.86041	0.732987
$116$	4.30526	0.399734
$117$	1.60996	0.148841
$118$	17.1228	1.57628
$119$	3.74970	0.343734
$120$	10.5534	0.963387
$121$	1.00000	0.0909091
$122$	6.42346	0.581553
$123$	15.0329	1.35547
$124$	−4.51590	−0.405539
$125$	−12.1465	−1.08642
$126$	0.999426	0.0890359
$127$	9.18504	0.815040	0.407520	−	0.913196i	$-0.366394\pi$
$127$	9.18504	0.815040	0.407520	+	0.913196i	$0.366394\pi$
$128$	2.08663	0.184434
$129$	−10.6389	−0.936707
$130$	4.00012	0.350834
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−1.37699	−0.119852
$133$	−2.94186	−0.255092
$134$	−12.5216	−1.08170
$135$	7.52632	0.647763
$136$	−10.5723	−0.906570
$137$	15.8488	1.35405	0.677025	−	0.735960i	$-0.263269\pi$
$137$	15.8488	1.35405	0.677025	+	0.735960i	$0.263269\pi$
$138$	−9.92318	−0.844717
$139$	−17.8990	−1.51818	−0.759088	−	0.650988i	$-0.774355\pi$
$139$	−17.8990	−1.51818	−0.759088	+	0.650988i	$0.774355\pi$
$140$	−1.35464	−0.114488
$141$	−22.3080	−1.87867
$142$	6.75031	0.566474
$143$	−2.00061	−0.167300
$144$	−1.68170	−0.140142
$145$	−10.7192	−0.890184
$146$	9.89632	0.819025
$147$	11.3291	0.934409
$148$	−6.78773	−0.557948
$149$	−5.65189	−0.463021	−0.231510	−	0.972832i	$-0.574367\pi$
$149$	−5.65189	−0.463021	−0.231510	+	0.972832i	$0.574367\pi$
$150$	4.23955	0.346158
$151$	−22.8834	−1.86222	−0.931112	−	0.364734i	$-0.881160\pi$
$151$	−22.8834	−1.86222	−0.931112	+	0.364734i	$0.881160\pi$
$152$	8.29462	0.672783
$153$	2.76394	0.223451
$154$	−1.24193	−0.100078
$155$	11.2437	0.903114
$156$	2.75483	0.220563
$157$	4.45835	0.355815	0.177908	−	0.984047i	$-0.443067\pi$
$157$	4.45835	0.355815	0.177908	+	0.984047i	$0.443067\pi$
$158$	1.48584	0.118207
$159$	−1.58294	−0.125535
$160$	6.64242	0.525130
$161$	4.88239	0.384786
$162$	−12.2477	−0.962273
$163$	0.308265	0.0241452	0.0120726	−	0.999927i	$-0.496157\pi$
$163$	0.308265	0.0241452	0.0120726	+	0.999927i	$0.496157\pi$
$164$	5.44064	0.424843
$165$	3.42844	0.266903
$166$	16.3240	1.26699
$167$	18.4166	1.42512	0.712561	−	0.701610i	$-0.247535\pi$
$167$	18.4166	1.42512	0.712561	+	0.701610i	$0.247535\pi$
$168$	6.55509	0.505736
$169$	−8.99755	−0.692120
$170$	6.86730	0.526698
$171$	−2.16847	−0.165827
$172$	−3.85040	−0.293590
$173$	−13.8103	−1.04998	−0.524989	−	0.851109i	$-0.675931\pi$
$173$	−13.8103	−1.04998	−0.524989	+	0.851109i	$0.675931\pi$
$174$	13.5322	1.02588
$175$	−2.08594	−0.157682
$176$	2.08976	0.157522
$177$	−29.3603	−2.20686
$178$	6.64229	0.497861
$179$	15.6504	1.16977	0.584884	−	0.811117i	$-0.301140\pi$
$179$	15.6504	1.16977	0.584884	+	0.811117i	$0.301140\pi$
$180$	−0.998518	−0.0744251
$181$	−7.04581	−0.523711	−0.261855	−	0.965107i	$-0.584334\pi$
$181$	−7.04581	−0.523711	−0.261855	+	0.965107i	$0.584334\pi$
$182$	2.48462	0.184172
$183$	−11.0142	−0.814196
$184$	−13.7660	−1.01484
$185$	16.9001	1.24252
$186$	−14.1943	−1.04078
$187$	−3.43459	−0.251162
$188$	−8.07360	−0.588828
$189$	4.67488	0.340047
$190$	−5.38780	−0.390872
$191$	−8.39998	−0.607801	−0.303901	−	0.952704i	$-0.598289\pi$
$191$	−8.39998	−0.607801	−0.303901	+	0.952704i	$0.598289\pi$
$192$	−16.5380	−1.19353
$193$	−3.92772	−0.282724	−0.141362	−	0.989958i	$-0.545148\pi$
$193$	−3.92772	−0.282724	−0.141362	+	0.989958i	$0.545148\pi$
$194$	8.79372	0.631353
$195$	−6.85897	−0.491181
$196$	4.10018	0.292870
$197$	−15.4093	−1.09787	−0.548934	−	0.835866i	$-0.684966\pi$
$197$	−15.4093	−1.09787	−0.548934	+	0.835866i	$0.684966\pi$
$198$	−0.915439	−0.0650574
$199$	21.9965	1.55929	0.779647	−	0.626220i	$-0.215399\pi$
$199$	21.9965	1.55929	0.779647	+	0.626220i	$0.215399\pi$
$200$	5.88134	0.415873
$201$	21.4707	1.51443
$202$	−13.4202	−0.944242
$203$	−6.65811	−0.467308
$204$	4.72941	0.331125
$205$	−13.5461	−0.946101
$206$	5.07278	0.353437
$207$	3.59886	0.250138
$208$	−4.18080	−0.289886
$209$	2.69464	0.186392
$210$	−4.25788	−0.293822
$211$	19.0523	1.31162	0.655808	−	0.754928i	$-0.272328\pi$
$211$	19.0523	1.31162	0.655808	+	0.754928i	$0.272328\pi$
$212$	−0.572889	−0.0393462
$213$	−11.5747	−0.793085
$214$	−4.16020	−0.284385
$215$	9.58672	0.653809
$216$	−13.1809	−0.896846
$217$	6.98386	0.474095
$218$	2.13539	0.144627
$219$	−16.9691	−1.14667
$220$	1.24080	0.0836550
$221$	6.87129	0.462213
$222$	−21.3351	−1.43192
$223$	−24.2701	−1.62525	−0.812624	−	0.582788i	$-0.801962\pi$
$223$	−24.2701	−1.62525	−0.812624	+	0.582788i	$0.801962\pi$
$224$	4.12585	0.275670
$225$	−1.53756	−0.102504
$226$	−10.1919	−0.677956
$227$	14.5859	0.968102	0.484051	−	0.875040i	$-0.339165\pi$
$227$	14.5859	0.968102	0.484051	+	0.875040i	$0.339165\pi$
$228$	−3.71050	−0.245734
$229$	−6.10368	−0.403343	−0.201671	−	0.979453i	$-0.564637\pi$
$229$	−6.10368	−0.403343	−0.201671	+	0.979453i	$0.564637\pi$
$230$	8.94174	0.589601
$231$	2.12953	0.140113
$232$	18.7727	1.23248
$233$	−28.0101	−1.83500	−0.917501	−	0.397734i	$-0.869797\pi$
$233$	−28.0101	−1.83500	−0.917501	+	0.397734i	$0.869797\pi$
$234$	1.83144	0.119725
$235$	20.1016	1.31129
$236$	−10.6260	−0.691691
$237$	−2.54775	−0.165494
$238$	4.26553	0.276493
$239$	−7.23726	−0.468139	−0.234070	−	0.972220i	$-0.575204\pi$
$239$	−7.23726	−0.468139	−0.234070	+	0.972220i	$0.575204\pi$
$240$	7.16461	0.462473
$241$	14.0898	0.907606	0.453803	−	0.891102i	$-0.350067\pi$
$241$	14.0898	0.907606	0.453803	+	0.891102i	$0.350067\pi$
$242$	1.13757	0.0731255
$243$	8.15498	0.523142
$244$	−3.98622	−0.255192
$245$	−10.2086	−0.652205
$246$	17.1009	1.09032
$247$	−5.39093	−0.343017
$248$	−19.6911	−1.25039
$249$	−27.9907	−1.77384
$250$	−13.8175	−0.873895
$251$	−26.7069	−1.68572	−0.842861	−	0.538131i	$-0.819131\pi$
$251$	−26.7069	−1.68572	−0.842861	+	0.538131i	$0.819131\pi$
$252$	−0.620216	−0.0390699
$253$	−4.47210	−0.281159
$254$	10.4486	0.655603
$255$	−11.7753	−0.737397
$256$	−14.5834	−0.911463
$257$	−19.9317	−1.24330	−0.621652	−	0.783294i	$-0.713538\pi$
$257$	−19.9317	−1.24330	−0.621652	+	0.783294i	$0.713538\pi$
$258$	−12.1025	−0.753469
$259$	10.4973	0.652269
$260$	−2.48237	−0.153950
$261$	−4.90776	−0.303783
$262$	1.13757	0.0702791
$263$	−8.57035	−0.528470	−0.264235	−	0.964458i	$-0.585120\pi$
$263$	−8.57035	−0.528470	−0.264235	+	0.964458i	$0.585120\pi$
$264$	−6.00423	−0.369535
$265$	1.42638	0.0876218
$266$	−3.34656	−0.205191
$267$	−11.3895	−0.697024
$268$	7.77057	0.474663
$269$	0.525731	0.0320544	0.0160272	−	0.999872i	$-0.494898\pi$
$269$	0.525731	0.0320544	0.0160272	+	0.999872i	$0.494898\pi$
$270$	8.56169	0.521048
$271$	23.0570	1.40061	0.700307	−	0.713842i	$-0.253047\pi$
$271$	23.0570	1.40061	0.700307	+	0.713842i	$0.253047\pi$
$272$	−7.17748	−0.435198
$273$	−4.26036	−0.257848
$274$	18.0290	1.08917
$275$	1.91065	0.115216
$276$	6.15805	0.370671
$277$	27.3092	1.64085	0.820426	−	0.571752i	$-0.193736\pi$
$277$	27.3092	1.64085	0.820426	+	0.571752i	$0.193736\pi$
$278$	−20.3613	−1.22119
$279$	5.14787	0.308195
$280$	−5.90677	−0.352997
$281$	3.75780	0.224172	0.112086	−	0.993699i	$-0.464247\pi$
$281$	3.75780	0.224172	0.112086	+	0.993699i	$0.464247\pi$
$282$	−25.3768	−1.51117
$283$	−30.2194	−1.79636	−0.898178	−	0.439631i	$-0.855109\pi$
$283$	−30.2194	−1.79636	−0.898178	+	0.439631i	$0.855109\pi$
$284$	−4.18906	−0.248575
$285$	9.23841	0.547236
$286$	−2.27583	−0.134573
$287$	−8.41399	−0.496662
$288$	3.04120	0.179205
$289$	−5.20357	−0.306092
$290$	−12.1938	−0.716047
$291$	−15.0785	−0.883917
$292$	−6.14138	−0.359397
$293$	−5.98282	−0.349520	−0.174760	−	0.984611i	$-0.555915\pi$
$293$	−5.98282	−0.349520	−0.174760	+	0.984611i	$0.555915\pi$
$294$	12.8876	0.751621
$295$	26.4565	1.54036
$296$	−29.5972	−1.72030
$297$	−4.28202	−0.248468
$298$	−6.42940	−0.372445
$299$	8.94694	0.517415
$300$	−2.63095	−0.151898
$301$	5.95467	0.343221
$302$	−26.0314	−1.49794
$303$	23.0115	1.32198
$304$	5.63116	0.322969
$305$	9.92489	0.568298
$306$	3.14416	0.179740
$307$	−22.6542	−1.29294	−0.646472	−	0.762938i	$-0.723756\pi$
$307$	−22.6542	−1.29294	−0.646472	+	0.762938i	$0.723756\pi$
$308$	0.770709	0.0439152
$309$	−8.69823	−0.494825
$310$	12.7904	0.726448
$311$	19.4225	1.10135	0.550675	−	0.834720i	$-0.314370\pi$
$311$	19.4225	1.10135	0.550675	+	0.834720i	$0.314370\pi$
$312$	12.0121	0.680053
$313$	10.8276	0.612009	0.306005	−	0.952030i	$-0.401008\pi$
$313$	10.8276	0.612009	0.306005	+	0.952030i	$0.401008\pi$
$314$	5.07167	0.286211
$315$	1.54421	0.0870066
$316$	−0.922072	−0.0518706
$317$	12.1650	0.683253	0.341627	−	0.939836i	$-0.389022\pi$
$317$	12.1650	0.683253	0.341627	+	0.939836i	$0.389022\pi$
$318$	−1.80070	−0.100978
$319$	6.09860	0.341456
$320$	14.9024	0.833067
$321$	7.13344	0.398150
$322$	5.55405	0.309515
$323$	−9.25500	−0.514962
$324$	7.60060	0.422256
$325$	−3.82246	−0.212032
$326$	0.350672	0.0194219
$327$	−3.66153	−0.202483
$328$	23.7234	1.30990
$329$	12.4859	0.688368
$330$	3.90007	0.214692
$331$	−24.6957	−1.35740	−0.678700	−	0.734416i	$-0.737456\pi$
$331$	−24.6957	−1.35740	−0.678700	+	0.734416i	$0.737456\pi$
$332$	−10.1303	−0.555970
$333$	7.73763	0.424020
$334$	20.9502	1.14634
$335$	−19.3472	−1.05705
$336$	4.45020	0.242778
$337$	15.9721	0.870054	0.435027	−	0.900417i	$-0.356739\pi$
$337$	15.9721	0.870054	0.435027	+	0.900417i	$0.356739\pi$
$338$	−10.2353	−0.556728
$339$	17.4760	0.949163
$340$	−4.26166	−0.231121
$341$	−6.39697	−0.346416
$342$	−2.46678	−0.133388
$343$	−13.9832	−0.755020
$344$	−16.7893	−0.905217
$345$	−15.3323	−0.825464
$346$	−15.7101	−0.844583
$347$	35.1138	1.88501	0.942503	−	0.334199i	$-0.108466\pi$
$347$	35.1138	1.88501	0.942503	+	0.334199i	$0.108466\pi$
$348$	−8.39773	−0.450165
$349$	16.1312	0.863481	0.431741	−	0.901998i	$-0.357900\pi$
$349$	16.1312	0.863481	0.431741	+	0.901998i	$0.357900\pi$
$350$	−2.37289	−0.126837
$351$	8.56667	0.457255
$352$	−3.77914	−0.201429
$353$	−3.12868	−0.166523	−0.0832613	−	0.996528i	$-0.526534\pi$
$353$	−3.12868	−0.166523	−0.0832613	+	0.996528i	$0.526534\pi$
$354$	−33.3993	−1.77515
$355$	10.4299	0.553563
$356$	−4.12202	−0.218467
$357$	−7.31406	−0.387101
$358$	17.8034	0.940939
$359$	−0.0215923	−0.00113960	−0.000569800	−	1.00000i	$-0.500181\pi$
$359$	−0.0215923	−0.00113960	−0.000569800		1.00000i	$0.500181\pi$
$360$	−4.35393	−0.229472
$361$	−11.7389	−0.617837
$362$	−8.01508	−0.421263
$363$	−1.95057	−0.102379
$364$	−1.54189	−0.0808169
$365$	15.2908	0.800358
$366$	−12.5294	−0.654924
$367$	18.4828	0.964795	0.482398	−	0.875952i	$-0.339766\pi$
$367$	18.4828	0.964795	0.482398	+	0.875952i	$0.339766\pi$
$368$	−9.34562	−0.487174
$369$	−6.20203	−0.322865
$370$	19.2250	0.999459
$371$	0.885977	0.0459976
$372$	8.80858	0.456704
$373$	−2.87353	−0.148785	−0.0743927	−	0.997229i	$-0.523702\pi$
$373$	−2.87353	−0.148785	−0.0743927	+	0.997229i	$0.523702\pi$
$374$	−3.90708	−0.202030
$375$	23.6927	1.22349
$376$	−35.2041	−1.81551
$377$	−12.2009	−0.628380
$378$	5.31798	0.273528
$379$	−29.2177	−1.50081	−0.750406	−	0.660977i	$-0.770142\pi$
$379$	−29.2177	−1.50081	−0.750406	+	0.660977i	$0.770142\pi$
$380$	3.34352	0.171519
$381$	−17.9161	−0.917869
$382$	−9.55554	−0.488904
$383$	−38.2620	−1.95510	−0.977549	−	0.210709i	$-0.932423\pi$
$383$	−38.2620	−1.95510	−0.977549	+	0.210709i	$0.932423\pi$
$384$	−4.07012	−0.207703
$385$	−1.91891	−0.0977967
$386$	−4.46805	−0.227418
$387$	4.38924	0.223118
$388$	−5.45714	−0.277044
$389$	20.5669	1.04278	0.521392	−	0.853317i	$-0.325413\pi$
$389$	20.5669	1.04278	0.521392	+	0.853317i	$0.325413\pi$
$390$	−7.80253	−0.395096
$391$	15.3599	0.776781
$392$	17.8784	0.902996
$393$	−1.95057	−0.0983934
$394$	−17.5291	−0.883104
$395$	2.29577	0.115513
$396$	0.568096	0.0285479
$397$	−15.8314	−0.794556	−0.397278	−	0.917698i	$-0.630045\pi$
$397$	−15.8314	−0.794556	−0.397278	+	0.917698i	$0.630045\pi$
$398$	25.0225	1.25427
$399$	5.73832	0.287275
$400$	3.99280	0.199640
$401$	19.3481	0.966196	0.483098	−	0.875566i	$-0.339511\pi$
$401$	19.3481	0.966196	0.483098	+	0.875566i	$0.339511\pi$
$402$	24.4243	1.21817
$403$	12.7979	0.637507
$404$	8.32821	0.414344
$405$	−18.9240	−0.940340
$406$	−7.57405	−0.375894
$407$	−9.61513	−0.476605
$408$	20.6221	1.02095
$409$	25.4854	1.26017	0.630086	−	0.776525i	$-0.283020\pi$
$409$	25.4854	1.26017	0.630086	+	0.776525i	$0.283020\pi$
$410$	−15.4096	−0.761026
$411$	−30.9142	−1.52488
$412$	−3.14803	−0.155092
$413$	16.4331	0.808620
$414$	4.09394	0.201206
$415$	25.2223	1.23811
$416$	7.56059	0.370688
$417$	34.9134	1.70971
$418$	3.06534	0.149930
$419$	31.9263	1.55970	0.779851	−	0.625965i	$-0.215295\pi$
$419$	31.9263	1.55970	0.779851	+	0.625965i	$0.215295\pi$
$420$	2.64232	0.128932
$421$	5.41374	0.263849	0.131925	−	0.991260i	$-0.457884\pi$
$421$	5.41374	0.263849	0.131925	+	0.991260i	$0.457884\pi$
$422$	21.6733	1.05504
$423$	9.20345	0.447487
$424$	−2.49803	−0.121315
$425$	−6.56230	−0.318318
$426$	−13.1670	−0.637942
$427$	6.16472	0.298332
$428$	2.58170	0.124791
$429$	3.90234	0.188407
$430$	10.9055	0.525912
$431$	−7.71959	−0.371840	−0.185920	−	0.982565i	$-0.559526\pi$
$431$	−7.71959	−0.371840	−0.185920	+	0.982565i	$0.559526\pi$
$432$	−8.94841	−0.430530
$433$	33.1543	1.59329	0.796647	−	0.604445i	$-0.206605\pi$
$433$	33.1543	1.59329	0.796647	+	0.604445i	$0.206605\pi$
$434$	7.94461	0.381353
$435$	20.9087	1.00249
$436$	−1.32517	−0.0634639
$437$	−12.0507	−0.576464
$438$	−19.3035	−0.922356
$439$	21.7082	1.03607	0.518037	−	0.855358i	$-0.326663\pi$
$439$	21.7082	1.03607	0.518037	+	0.855358i	$0.326663\pi$
$440$	5.41040	0.257931
$441$	−4.67398	−0.222570
$442$	7.81655	0.371795
$443$	19.4593	0.924539	0.462270	−	0.886739i	$-0.347035\pi$
$443$	19.4593	0.924539	0.462270	+	0.886739i	$0.347035\pi$
$444$	13.2400	0.628341
$445$	10.2630	0.486513
$446$	−27.6089	−1.30732
$447$	11.0244	0.521437
$448$	9.25640	0.437324
$449$	23.6281	1.11508	0.557540	−	0.830150i	$-0.311745\pi$
$449$	23.6281	1.11508	0.557540	+	0.830150i	$0.311745\pi$
$450$	−1.74908	−0.0824525
$451$	7.70692	0.362905
$452$	6.32482	0.297494
$453$	44.6357	2.09717
$454$	16.5925	0.778723
$455$	3.83899	0.179975
$456$	−16.1793	−0.757664
$457$	39.2363	1.83540	0.917698	−	0.397279i	$-0.130045\pi$
$457$	39.2363	1.83540	0.917698	+	0.397279i	$0.130045\pi$
$458$	−6.94335	−0.324441
$459$	14.7070	0.686465
$460$	−5.54900	−0.258723
$461$	−15.3999	−0.717244	−0.358622	−	0.933483i	$-0.616753\pi$
$461$	−15.3999	−0.717244	−0.358622	+	0.933483i	$0.616753\pi$
$462$	2.42248	0.112704
$463$	13.9125	0.646569	0.323284	−	0.946302i	$-0.395213\pi$
$463$	13.9125	0.646569	0.323284	+	0.946302i	$0.395213\pi$
$464$	12.7446	0.591654
$465$	−21.9316	−1.01705
$466$	−31.8633	−1.47604
$467$	−10.2319	−0.473477	−0.236738	−	0.971573i	$-0.576078\pi$
$467$	−10.2319	−0.473477	−0.236738	+	0.971573i	$0.576078\pi$
$468$	−1.13654	−0.0525366
$469$	−12.0172	−0.554904
$470$	22.8670	1.05477
$471$	−8.69634	−0.400706
$472$	−46.3334	−2.13267
$473$	−5.45427	−0.250788
$474$	−2.89824	−0.133121
$475$	5.14851	0.236230
$476$	−2.64707	−0.121328
$477$	0.653062	0.0299016
$478$	−8.23287	−0.376563
$479$	−40.0909	−1.83180	−0.915900	−	0.401407i	$-0.868521\pi$
$479$	−40.0909	−1.83180	−0.915900	+	0.401407i	$0.868521\pi$
$480$	−12.9565	−0.591382
$481$	19.2361	0.877093
$482$	16.0281	0.730061
$483$	−9.52346	−0.433332
$484$	−0.705942	−0.0320883
$485$	13.5872	0.616963
$486$	9.27683	0.420805
$487$	−26.1046	−1.18291	−0.591456	−	0.806337i	$-0.701447\pi$
$487$	−26.1046	−1.18291	−0.591456	+	0.806337i	$0.701447\pi$
$488$	−17.3815	−0.786824
$489$	−0.601293	−0.0271914
$490$	−11.6130	−0.524622
$491$	−18.8564	−0.850975	−0.425488	−	0.904964i	$-0.639897\pi$
$491$	−18.8564	−0.850975	−0.425488	+	0.904964i	$0.639897\pi$
$492$	−10.6124	−0.478443
$493$	−20.9462	−0.943370
$494$	−6.13255	−0.275916
$495$	−1.41445	−0.0635746
$496$	−13.3681	−0.600247
$497$	6.47841	0.290596
$498$	−31.8412	−1.42684
$499$	3.48327	0.155933	0.0779663	−	0.996956i	$-0.475157\pi$
$499$	3.48327	0.155933	0.0779663	+	0.996956i	$0.475157\pi$
$500$	8.57476	0.383475
$501$	−35.9230	−1.60492
$502$	−30.3808	−1.35596
$503$	39.6260	1.76684	0.883418	−	0.468586i	$-0.155237\pi$
$503$	39.6260	1.76684	0.883418	+	0.468586i	$0.155237\pi$
$504$	−2.70439	−0.120463
$505$	−20.7356	−0.922721
$506$	−5.08731	−0.226159
$507$	17.5504	0.779440
$508$	−6.48411	−0.287686
$509$	37.4963	1.66200	0.830998	−	0.556276i	$-0.187770\pi$
$509$	37.4963	1.66200	0.830998	+	0.556276i	$0.187770\pi$
$510$	−13.3952	−0.593148
$511$	9.49768	0.420153
$512$	−20.7628	−0.917597
$513$	−11.5385	−0.509439
$514$	−22.6736	−1.00009
$515$	7.83795	0.345381
$516$	7.51048	0.330631
$517$	−11.4366	−0.502982
$518$	11.9413	0.524672
$519$	26.9380	1.18245
$520$	−10.8241	−0.474668
$521$	34.6407	1.51764	0.758818	−	0.651302i	$-0.225777\pi$
$521$	34.6407	1.51764	0.758818	+	0.651302i	$0.225777\pi$
$522$	−5.58290	−0.244357
$523$	−4.87646	−0.213233	−0.106616	−	0.994300i	$-0.534002\pi$
$523$	−4.87646	−0.213233	−0.106616	+	0.994300i	$0.534002\pi$
$524$	−0.705942	−0.0308392
$525$	4.06878	0.177576
$526$	−9.74934	−0.425092
$527$	21.9710	0.957072
$528$	−4.07623	−0.177395
$529$	−3.00031	−0.130448
$530$	1.62260	0.0704813
$531$	12.1130	0.525659
$532$	2.07678	0.0900400
$533$	−15.4186	−0.667852
$534$	−12.9563	−0.560673
$535$	−6.42792	−0.277903
$536$	33.8828	1.46351
$537$	−30.5273	−1.31735
$538$	0.598054	0.0257840
$539$	5.80809	0.250172
$540$	−5.31315	−0.228642
$541$	10.5127	0.451978	0.225989	−	0.974130i	$-0.427439\pi$
$541$	10.5127	0.451978	0.225989	+	0.974130i	$0.427439\pi$
$542$	26.2289	1.12663
$543$	13.7434	0.589784
$544$	12.9798	0.556504
$545$	3.29940	0.141331
$546$	−4.84644	−0.207408
$547$	18.1230	0.774884	0.387442	−	0.921894i	$-0.373359\pi$
$547$	18.1230	0.774884	0.387442	+	0.921894i	$0.373359\pi$
$548$	−11.1883	−0.477941
$549$	4.54407	0.193936
$550$	2.17349	0.0926779
$551$	16.4336	0.700093
$552$	26.8515	1.14288
$553$	1.42599	0.0606392
$554$	31.0661	1.31987
$555$	−32.9649	−1.39928
$556$	12.6357	0.535872
$557$	2.00993	0.0851634	0.0425817	−	0.999093i	$-0.486442\pi$
$557$	2.00993	0.0851634	0.0425817	+	0.999093i	$0.486442\pi$
$558$	5.85604	0.247906
$559$	10.9119	0.461523
$560$	−4.01006	−0.169456
$561$	6.69942	0.282850
$562$	4.27475	0.180319
$563$	13.6203	0.574027	0.287013	−	0.957927i	$-0.407338\pi$
$563$	13.6203	0.574027	0.287013	+	0.957927i	$0.407338\pi$
$564$	15.7481	0.663116
$565$	−15.7475	−0.662503
$566$	−34.3766	−1.44496
$567$	−11.7544	−0.493638
$568$	−18.2660	−0.766423
$569$	13.2879	0.557059	0.278529	−	0.960428i	$-0.410153\pi$
$569$	13.2879	0.557059	0.278529	+	0.960428i	$0.410153\pi$
$570$	10.5093	0.440186
$571$	−4.46627	−0.186908	−0.0934538	−	0.995624i	$-0.529791\pi$
$571$	−4.46627	−0.186908	−0.0934538	+	0.995624i	$0.529791\pi$
$572$	1.41232	0.0590519
$573$	16.3848	0.684484
$574$	−9.57147	−0.399505
$575$	−8.54461	−0.356335
$576$	6.82298	0.284291
$577$	−33.7833	−1.40642	−0.703208	−	0.710985i	$-0.748250\pi$
$577$	−33.7833	−1.40642	−0.703208	+	0.710985i	$0.748250\pi$
$578$	−5.91940	−0.246215
$579$	7.66131	0.318393
$580$	7.56717	0.314209
$581$	15.6665	0.649956
$582$	−17.1528	−0.711006
$583$	−0.811524	−0.0336099
$584$	−26.7789	−1.10812
$585$	2.82976	0.116996
$586$	−6.80585	−0.281147
$587$	−8.60283	−0.355077	−0.177538	−	0.984114i	$-0.556813\pi$
$587$	−8.60283	−0.355077	−0.177538	+	0.984114i	$0.556813\pi$
$588$	−7.99770	−0.329820
$589$	−17.2376	−0.710261
$590$	30.0960	1.23903
$591$	30.0570	1.23638
$592$	−20.0933	−0.825831
$593$	7.82861	0.321482	0.160741	−	0.986997i	$-0.448612\pi$
$593$	7.82861	0.321482	0.160741	+	0.986997i	$0.448612\pi$
$594$	−4.87109	−0.199863
$595$	6.59068	0.270191
$596$	3.98991	0.163433
$597$	−42.9059	−1.75602
$598$	10.1777	0.416199
$599$	−11.8346	−0.483550	−0.241775	−	0.970332i	$-0.577730\pi$
$599$	−11.8346	−0.483550	−0.241775	+	0.970332i	$0.577730\pi$
$600$	−11.4720	−0.468341
$601$	−17.9521	−0.732279	−0.366140	−	0.930560i	$-0.619321\pi$
$601$	−17.9521	−0.732279	−0.366140	+	0.930560i	$0.619321\pi$
$602$	6.77383	0.276081
$603$	−8.85802	−0.360726
$604$	16.1544	0.657311
$605$	1.75766	0.0714589
$606$	26.1771	1.06337
$607$	−12.6055	−0.511640	−0.255820	−	0.966724i	$-0.582345\pi$
$607$	−12.6055	−0.511640	−0.255820	+	0.966724i	$0.582345\pi$
$608$	−10.1834	−0.412993
$609$	12.9871	0.526265
$610$	11.2902	0.457128
$611$	22.8802	0.925635
$612$	−1.95118	−0.0788718
$613$	−27.4558	−1.10893	−0.554465	−	0.832207i	$-0.687077\pi$
$613$	−27.4558	−1.10893	−0.554465	+	0.832207i	$0.687077\pi$
$614$	−25.7707	−1.04002
$615$	26.4227	1.06547
$616$	3.36060	0.135402
$617$	−3.30308	−0.132977	−0.0664884	−	0.997787i	$-0.521180\pi$
$617$	−3.30308	−0.132977	−0.0664884	+	0.997787i	$0.521180\pi$
$618$	−9.89482	−0.398028
$619$	−24.0139	−0.965201	−0.482601	−	0.875841i	$-0.660308\pi$
$619$	−24.0139	−0.965201	−0.482601	+	0.875841i	$0.660308\pi$
$620$	−7.93739	−0.318773
$621$	19.1497	0.768449
$622$	22.0944	0.885906
$623$	6.37473	0.255398
$624$	8.15495	0.326459
$625$	−11.7962	−0.471848
$626$	12.3171	0.492289
$627$	−5.25610	−0.209908
$628$	−3.14734	−0.125593
$629$	33.0241	1.31676
$630$	1.75665	0.0699864
$631$	−17.9033	−0.712717	−0.356359	−	0.934349i	$-0.615982\pi$
$631$	−17.9033	−0.712717	−0.356359	+	0.934349i	$0.615982\pi$
$632$	−4.02060	−0.159931
$633$	−37.1629	−1.47709
$634$	13.8385	0.549596
$635$	16.1441	0.640660
$636$	1.11746	0.0443103
$637$	−11.6197	−0.460391
$638$	6.93756	0.274661
$639$	4.77529	0.188908
$640$	3.66757	0.144974
$641$	34.7303	1.37177	0.685883	−	0.727712i	$-0.259416\pi$
$641$	34.7303	1.37177	0.685883	+	0.727712i	$0.259416\pi$
$642$	8.11476	0.320264
$643$	15.2374	0.600905	0.300453	−	0.953797i	$-0.402862\pi$
$643$	15.2374	0.600905	0.300453	+	0.953797i	$0.402862\pi$
$644$	−3.44669	−0.135819
$645$	−18.6996	−0.736296
$646$	−10.5282	−0.414226
$647$	31.7613	1.24867	0.624333	−	0.781159i	$-0.285371\pi$
$647$	31.7613	1.24867	0.624333	+	0.781159i	$0.285371\pi$
$648$	33.1417	1.30193
$649$	−15.0522	−0.590849
$650$	−4.34831	−0.170555
$651$	−13.6225	−0.533909
$652$	−0.217617	−0.00852255
$653$	8.28279	0.324131	0.162065	−	0.986780i	$-0.448184\pi$
$653$	8.28279	0.324131	0.162065	+	0.986780i	$0.448184\pi$
$654$	−4.16524	−0.162874
$655$	1.75766	0.0686773
$656$	16.1056	0.628819
$657$	7.00083	0.273128
$658$	14.2035	0.553710
$659$	−2.57352	−0.100250	−0.0501250	−	0.998743i	$-0.515962\pi$
$659$	−2.57352	−0.100250	−0.0501250	+	0.998743i	$0.515962\pi$
$660$	−2.42028	−0.0942092
$661$	−39.8325	−1.54930	−0.774652	−	0.632388i	$-0.782075\pi$
$661$	−39.8325	−1.54930	−0.774652	+	0.632388i	$0.782075\pi$
$662$	−28.0930	−1.09187
$663$	−13.4029	−0.520527
$664$	−44.1719	−1.71420
$665$	−5.17078	−0.200514
$666$	8.80207	0.341073
$667$	−27.2736	−1.05604
$668$	−13.0011	−0.503027
$669$	47.3407	1.83030
$670$	−22.0087	−0.850270
$671$	−5.64667	−0.217987
$672$	−8.04778	−0.310450
$673$	−1.57525	−0.0607213	−0.0303607	−	0.999539i	$-0.509666\pi$
$673$	−1.57525	−0.0607213	−0.0303607	+	0.999539i	$0.509666\pi$
$674$	18.1693	0.699855
$675$	−8.18144	−0.314904
$676$	6.35176	0.244298
$677$	−47.2379	−1.81550	−0.907750	−	0.419511i	$-0.862202\pi$
$677$	−47.2379	−1.81550	−0.907750	+	0.419511i	$0.862202\pi$
$678$	19.8801	0.763489
$679$	8.43950	0.323878
$680$	−18.5825	−0.712607
$681$	−28.4509	−1.09024
$682$	−7.27698	−0.278650
$683$	14.3977	0.550912	0.275456	−	0.961314i	$-0.411171\pi$
$683$	14.3977	0.550912	0.275456	+	0.961314i	$0.411171\pi$
$684$	1.53082	0.0585323
$685$	27.8567	1.06435
$686$	−15.9068	−0.607324
$687$	11.9057	0.454230
$688$	−11.3981	−0.434549
$689$	1.62354	0.0618521
$690$	−17.4415	−0.663987
$691$	−17.9227	−0.681810	−0.340905	−	0.940098i	$-0.610734\pi$
$691$	−17.9227	−0.681810	−0.340905	+	0.940098i	$0.610734\pi$
$692$	9.74928	0.370612
$693$	−0.878565	−0.0333739
$694$	39.9442	1.51626
$695$	−31.4603	−1.19336
$696$	−36.6174	−1.38798
$697$	−26.4701	−1.00263
$698$	18.3503	0.694568
$699$	54.6357	2.06651
$700$	1.47255	0.0556573
$701$	−43.4718	−1.64191	−0.820953	−	0.570995i	$-0.806557\pi$
$701$	−43.4718	−1.64191	−0.820953	+	0.570995i	$0.806557\pi$
$702$	9.74515	0.367807
$703$	−25.9094	−0.977190
$704$	−8.47854	−0.319547
$705$	−39.2097	−1.47672
$706$	−3.55908	−0.133948
$707$	−12.8796	−0.484388
$708$	20.7267	0.778957
$709$	−37.1979	−1.39700	−0.698499	−	0.715611i	$-0.746148\pi$
$709$	−37.1979	−1.39700	−0.698499	+	0.715611i	$0.746148\pi$
$710$	11.8647	0.445275
$711$	1.05111	0.0394197
$712$	−17.9737	−0.673591
$713$	28.6079	1.07138
$714$	−8.32023	−0.311377
$715$	−3.51639	−0.131505
$716$	−11.0483	−0.412894
$717$	14.1168	0.527202
$718$	−0.0245627	−0.000916672 0
$719$	−26.3528	−0.982793	−0.491397	−	0.870936i	$-0.663513\pi$
$719$	−26.3528	−0.982793	−0.491397	+	0.870936i	$0.663513\pi$
$720$	−2.95585	−0.110158
$721$	4.86844	0.181310
$722$	−13.3538	−0.496976
$723$	−27.4833	−1.02211
$724$	4.97394	0.184855
$725$	11.6523	0.432755
$726$	−2.21891	−0.0823513
$727$	49.5107	1.83625	0.918126	−	0.396289i	$-0.129702\pi$
$727$	49.5107	1.83625	0.918126	+	0.396289i	$0.129702\pi$
$728$	−6.72325	−0.249180
$729$	16.3929	0.607146
$730$	17.3943	0.643792
$731$	18.7332	0.692872
$732$	7.77542	0.287388
$733$	−20.2404	−0.747596	−0.373798	−	0.927510i	$-0.621945\pi$
$733$	−20.2404	−0.747596	−0.373798	+	0.927510i	$0.621945\pi$
$734$	21.0254	0.776063
$735$	19.9127	0.734490
$736$	16.9007	0.622968
$737$	11.0074	0.405462
$738$	−7.05522	−0.259706
$739$	16.5128	0.607434	0.303717	−	0.952762i	$-0.401772\pi$
$739$	16.5128	0.607434	0.303717	+	0.952762i	$0.401772\pi$
$740$	−11.9305	−0.438574
$741$	10.5154	0.386293
$742$	1.00786	0.0369996
$743$	48.0271	1.76194	0.880972	−	0.473169i	$-0.156890\pi$
$743$	48.0271	1.76194	0.880972	+	0.473169i	$0.156890\pi$
$744$	38.4089	1.40814
$745$	−9.93407	−0.363956
$746$	−3.26883	−0.119680
$747$	11.5479	0.422516
$748$	2.42463	0.0886531
$749$	−3.99262	−0.145887
$750$	26.9520	0.984149
$751$	−22.2433	−0.811668	−0.405834	−	0.913947i	$-0.633019\pi$
$751$	−22.2433	−0.811668	−0.405834	+	0.913947i	$0.633019\pi$
$752$	−23.8998	−0.871536
$753$	52.0937	1.89840
$754$	−13.8794	−0.505457
$755$	−40.2211	−1.46380
$756$	−3.30019	−0.120027
$757$	−27.5235	−1.00036	−0.500180	−	0.865921i	$-0.666733\pi$
$757$	−27.5235	−1.00036	−0.500180	+	0.865921i	$0.666733\pi$
$758$	−33.2371	−1.20722
$759$	8.72316	0.316631
$760$	14.5791	0.528839
$761$	−10.9265	−0.396084	−0.198042	−	0.980194i	$-0.563458\pi$
$761$	−10.9265	−0.396084	−0.198042	+	0.980194i	$0.563458\pi$
$762$	−20.3807	−0.738316
$763$	2.04938	0.0741924
$764$	5.92990	0.214536
$765$	4.85805	0.175643
$766$	−43.5256	−1.57264
$767$	30.1135	1.08734
$768$	28.4460	1.02646
$769$	−44.5038	−1.60485	−0.802424	−	0.596755i	$-0.796457\pi$
$769$	−44.5038	−1.60485	−0.802424	+	0.596755i	$0.796457\pi$
$770$	−2.18289	−0.0786658
$771$	38.8782	1.40016
$772$	2.77275	0.0997933
$773$	36.0813	1.29775	0.648876	−	0.760894i	$-0.275239\pi$
$773$	36.0813	1.29775	0.648876	+	0.760894i	$0.275239\pi$
$774$	4.99305	0.179472
$775$	−12.2224	−0.439040
$776$	−23.7953	−0.854202
$777$	−20.4757	−0.734561
$778$	23.3963	0.838796
$779$	20.7674	0.744069
$780$	4.84204	0.173373
$781$	−5.93400	−0.212335
$782$	17.4729	0.624828
$783$	−26.1144	−0.933251
$784$	12.1375	0.433483
$785$	7.83625	0.279688
$786$	−2.21891	−0.0791458
$787$	−38.4177	−1.36944	−0.684722	−	0.728804i	$-0.740077\pi$
$787$	−38.4177	−1.36944	−0.684722	+	0.728804i	$0.740077\pi$
$788$	10.8781	0.387516
$789$	16.7171	0.595144
$790$	2.61160	0.0929164
$791$	−9.78137	−0.347785
$792$	2.47713	0.0880208
$793$	11.2968	0.401161
$794$	−18.0093	−0.639126
$795$	−2.78226	−0.0986765
$796$	−15.5283	−0.550386
$797$	−40.8412	−1.44667	−0.723335	−	0.690497i	$-0.757392\pi$
$797$	−40.8412	−1.44667	−0.723335	+	0.690497i	$0.757392\pi$
$798$	6.52772	0.231079
$799$	39.2802	1.38963
$800$	−7.22060	−0.255287
$801$	4.69887	0.166027
$802$	22.0097	0.777190
$803$	−8.69955	−0.307000
$804$	−15.1571	−0.534549
$805$	8.58156	0.302460
$806$	14.5584	0.512798
$807$	−1.02548	−0.0360985
$808$	36.3143	1.27753
$809$	−21.8674	−0.768815	−0.384408	−	0.923163i	$-0.625594\pi$
$809$	−21.8674	−0.768815	−0.384408	+	0.923163i	$0.625594\pi$
$810$	−21.5273	−0.756392
$811$	−0.0669815	−0.00235204	−0.00117602	−	0.999999i	$-0.500374\pi$
$811$	−0.0669815	−0.00235204	−0.00117602	+	0.999999i	$0.500374\pi$
$812$	4.70025	0.164946
$813$	−44.9744	−1.57732
$814$	−10.9379	−0.383372
$815$	0.541824	0.0189793
$816$	14.0002	0.490105
$817$	−14.6973	−0.514194
$818$	28.9913	1.01366
$819$	1.75767	0.0614178
$820$	9.56277	0.333947
$821$	16.2689	0.567787	0.283894	−	0.958856i	$-0.408374\pi$
$821$	16.2689	0.567787	0.283894	+	0.958856i	$0.408374\pi$
$822$	−35.1669	−1.22659
$823$	−16.7175	−0.582736	−0.291368	−	0.956611i	$-0.594110\pi$
$823$	−16.7175	−0.582736	−0.291368	+	0.956611i	$0.594110\pi$
$824$	−13.7266	−0.478190
$825$	−3.72686	−0.129753
$826$	18.6937	0.650439
$827$	49.7206	1.72896	0.864478	−	0.502671i	$-0.167649\pi$
$827$	49.7206	1.72896	0.864478	+	0.502671i	$0.167649\pi$
$828$	−2.54058	−0.0882914
$829$	−6.97007	−0.242081	−0.121040	−	0.992648i	$-0.538623\pi$
$829$	−6.97007	−0.242081	−0.121040	+	0.992648i	$0.538623\pi$
$830$	28.6920	0.995915
$831$	−53.2687	−1.84787
$832$	16.9623	0.588061
$833$	−19.9484	−0.691173
$834$	39.7163	1.37526
$835$	32.3701	1.12021
$836$	−1.90226	−0.0657911
$837$	27.3920	0.946806
$838$	36.3183	1.25459
$839$	21.0361	0.726246	0.363123	−	0.931741i	$-0.381711\pi$
$839$	21.0361	0.726246	0.363123	+	0.931741i	$0.381711\pi$
$840$	11.5216	0.397532
$841$	8.19294	0.282515
$842$	6.15849	0.212235
$843$	−7.32986	−0.252454
$844$	−13.4498	−0.462962
$845$	−15.8146	−0.544039
$846$	10.4695	0.359950
$847$	1.09174	0.0375128
$848$	−1.69589	−0.0582371
$849$	58.9451	2.02299
$850$	−7.46505	−0.256049
$851$	42.9999	1.47402
$852$	8.17107	0.279936
$853$	−35.9630	−1.23135	−0.615674	−	0.788001i	$-0.711116\pi$
$853$	−35.9630	−1.23135	−0.615674	+	0.788001i	$0.711116\pi$
$854$	7.01277	0.239972
$855$	−3.81143	−0.130348
$856$	11.2572	0.384765
$857$	18.6464	0.636949	0.318475	−	0.947931i	$-0.396829\pi$
$857$	18.6464	0.636949	0.318475	+	0.947931i	$0.396829\pi$
$858$	4.43917	0.151551
$859$	−48.0131	−1.63819	−0.819093	−	0.573661i	$-0.805523\pi$
$859$	−48.0131	−1.63819	−0.819093	+	0.573661i	$0.805523\pi$
$860$	−6.76768	−0.230776
$861$	16.4121	0.559323
$862$	−8.78155	−0.299101
$863$	14.8925	0.506945	0.253473	−	0.967343i	$-0.418427\pi$
$863$	14.8925	0.506945	0.253473	+	0.967343i	$0.418427\pi$
$864$	16.1824	0.550535
$865$	−24.2738	−0.825333
$866$	37.7152	1.28162
$867$	10.1499	0.344710
$868$	−4.93020	−0.167342
$869$	−1.30616	−0.0443083
$870$	23.7850	0.806387
$871$	−22.0215	−0.746169
$872$	−5.77825	−0.195676
$873$	6.22084	0.210543
$874$	−13.7085	−0.463697
$875$	−13.2609	−0.448301
$876$	11.9792	0.404740
$877$	−14.3643	−0.485047	−0.242523	−	0.970146i	$-0.577975\pi$
$877$	−14.3643	−0.485047	−0.242523	+	0.970146i	$0.577975\pi$
$878$	24.6945	0.833398
$879$	11.6699	0.393617
$880$	3.67308	0.123819
$881$	40.9924	1.38107	0.690534	−	0.723300i	$-0.257376\pi$
$881$	40.9924	1.38107	0.690534	+	0.723300i	$0.257376\pi$
$882$	−5.31696	−0.179031
$883$	45.6966	1.53781	0.768907	−	0.639361i	$-0.220801\pi$
$883$	45.6966	1.53781	0.768907	+	0.639361i	$0.220801\pi$
$884$	−4.85073	−0.163148
$885$	−51.6053	−1.73469
$886$	22.1362	0.743682
$887$	−52.8359	−1.77406	−0.887029	−	0.461714i	$-0.847235\pi$
$887$	−52.8359	−1.77406	−0.887029	+	0.461714i	$0.847235\pi$
$888$	57.7315	1.93734
$889$	10.0277	0.336319
$890$	11.6749	0.391342
$891$	10.7666	0.360695
$892$	17.1333	0.573666
$893$	−30.8176	−1.03127
$894$	12.5410	0.419434
$895$	27.5080	0.919493
$896$	2.27807	0.0761048
$897$	−17.4517	−0.582694
$898$	26.8785	0.896949
$899$	−39.0126	−1.30114
$900$	1.08543	0.0361811
$901$	2.78726	0.0928570
$902$	8.76713	0.291914
$903$	−11.6150	−0.386523
$904$	27.5787	0.917254
$905$	−12.3841	−0.411662
$906$	50.7761	1.68692
$907$	16.6522	0.552927	0.276463	−	0.961024i	$-0.410838\pi$
$907$	16.6522	0.552927	0.276463	+	0.961024i	$0.410838\pi$
$908$	−10.2968	−0.341712
$909$	−9.49369	−0.314886
$910$	4.36711	0.144768
$911$	−10.8575	−0.359724	−0.179862	−	0.983692i	$-0.557565\pi$
$911$	−10.8575	−0.359724	−0.179862	+	0.983692i	$0.557565\pi$
$912$	−10.9840	−0.363716
$913$	−14.3500	−0.474915
$914$	44.6339	1.47636
$915$	−19.3592	−0.639996
$916$	4.30885	0.142368
$917$	1.09174	0.0360526
$918$	16.7302	0.552179
$919$	16.5230	0.545043	0.272522	−	0.962150i	$-0.412142\pi$
$919$	16.5230	0.545043	0.272522	+	0.962150i	$0.412142\pi$
$920$	−24.1958	−0.797713
$921$	44.1887	1.45607
$922$	−17.5184	−0.576937
$923$	11.8716	0.390759
$924$	−1.50332	−0.0494557
$925$	−18.3711	−0.604039
$926$	15.8264	0.520088
$927$	3.58857	0.117864
$928$	−23.0475	−0.756570
$929$	−0.831142	−0.0272689	−0.0136344	−	0.999907i	$-0.504340\pi$
$929$	−0.831142	−0.0272689	−0.0136344	+	0.999907i	$0.504340\pi$
$930$	−24.9487	−0.818099
$931$	15.6507	0.512932
$932$	19.7735	0.647703
$933$	−37.8851	−1.24030
$934$	−11.6395	−0.380856
$935$	−6.03683	−0.197426
$936$	−4.95577	−0.161984
$937$	−49.4188	−1.61444	−0.807221	−	0.590250i	$-0.799029\pi$
$937$	−49.4188	−1.61444	−0.807221	+	0.590250i	$0.799029\pi$
$938$	−13.6704	−0.446355
$939$	−21.1199	−0.689223
$940$	−14.1906	−0.462846
$941$	2.08939	0.0681120	0.0340560	−	0.999420i	$-0.489158\pi$
$941$	2.08939	0.0681120	0.0340560	+	0.999420i	$0.489158\pi$
$942$	−9.89267	−0.322320
$943$	−34.4661	−1.12237
$944$	−31.4554	−1.02379
$945$	8.21682	0.267293
$946$	−6.20459	−0.201729
$947$	37.7122	1.22548	0.612741	−	0.790284i	$-0.290067\pi$
$947$	37.7122	1.22548	0.612741	+	0.790284i	$0.290067\pi$
$948$	1.79857	0.0584148
$949$	17.4044	0.564971
$950$	5.85678	0.190019
$951$	−23.7287	−0.769455
$952$	−11.5423	−0.374087
$953$	−6.84925	−0.221869	−0.110935	−	0.993828i	$-0.535384\pi$
$953$	−6.84925	−0.221869	−0.110935	+	0.993828i	$0.535384\pi$
$954$	0.742901	0.0240523
$955$	−14.7643	−0.477761
$956$	5.10909	0.165240
$957$	−11.8958	−0.384536
$958$	−45.6061	−1.47346
$959$	17.3028	0.558736
$960$	−29.0681	−0.938170
$961$	9.92129	0.320041
$962$	21.8824	0.705517
$963$	−2.94300	−0.0948367
$964$	−9.94662	−0.320359
$965$	−6.90358	−0.222234
$966$	−10.8336	−0.348564
$967$	−5.21500	−0.167703	−0.0838516	−	0.996478i	$-0.526722\pi$
$967$	−5.21500	−0.167703	−0.0838516	+	0.996478i	$0.526722\pi$
$968$	−3.07819	−0.0989368
$969$	18.0526	0.579932
$970$	15.4563	0.496273
$971$	31.2824	1.00390	0.501949	−	0.864897i	$-0.332616\pi$
$971$	31.2824	1.00390	0.501949	+	0.864897i	$0.332616\pi$
$972$	−5.75694	−0.184654
$973$	−19.5412	−0.626461
$974$	−29.6957	−0.951513
$975$	7.45599	0.238783
$976$	−11.8002	−0.377715
$977$	35.1493	1.12453	0.562263	−	0.826959i	$-0.309931\pi$
$977$	35.1493	1.12453	0.562263	+	0.826959i	$0.309931\pi$
$978$	−0.684011	−0.0218723
$979$	−5.83903	−0.186616
$980$	7.20670	0.230210
$981$	1.51061	0.0482302
$982$	−21.4504	−0.684508
$983$	−25.3641	−0.808989	−0.404495	−	0.914540i	$-0.632553\pi$
$983$	−25.3641	−0.808989	−0.404495	+	0.914540i	$0.632553\pi$
$984$	−46.2741	−1.47517
$985$	−27.0843	−0.862976
$986$	−23.8277	−0.758829
$987$	−24.3546	−0.775215
$988$	3.80569	0.121075
$989$	24.3920	0.775622
$990$	−1.60903	−0.0511382
$991$	−1.31764	−0.0418562	−0.0209281	−	0.999781i	$-0.506662\pi$
$991$	−1.31764	−0.0418562	−0.0209281	+	0.999781i	$0.506662\pi$
$992$	24.1750	0.767559
$993$	48.1708	1.52865
$994$	7.36962	0.233750
$995$	38.6623	1.22568
$996$	19.7598	0.626113
$997$	13.5819	0.430143	0.215072	−	0.976598i	$-0.431001\pi$
$997$	13.5819	0.430143	0.215072	+	0.976598i	$0.431001\pi$
$998$	3.96245	0.125429
$999$	41.1722	1.30263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.20	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.20	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q+1.13757 q^{2} -1.95057 q^{3} -0.705942 q^{4} +1.75766 q^{5} -2.21891 q^{6} +1.09174 q^{7} -3.07819 q^{8} +0.804735 q^{9} +O(q^{10})\)	\(q+1.13757 q^{2} -1.95057 q^{3} -0.705942 q^{4} +1.75766 q^{5} -2.21891 q^{6} +1.09174 q^{7} -3.07819 q^{8} +0.804735 q^{9} +1.99945 q^{10} -1.00000 q^{11} +1.37699 q^{12} +2.00061 q^{13} +1.24193 q^{14} -3.42844 q^{15} -2.08976 q^{16} +3.43459 q^{17} +0.915439 q^{18} -2.69464 q^{19} -1.24080 q^{20} -2.12953 q^{21} -1.13757 q^{22} +4.47210 q^{23} +6.00423 q^{24} -1.91065 q^{25} +2.27583 q^{26} +4.28202 q^{27} -0.770709 q^{28} -6.09860 q^{29} -3.90007 q^{30} +6.39697 q^{31} +3.77914 q^{32} +1.95057 q^{33} +3.90708 q^{34} +1.91891 q^{35} -0.568096 q^{36} +9.61513 q^{37} -3.06534 q^{38} -3.90234 q^{39} -5.41040 q^{40} -7.70692 q^{41} -2.42248 q^{42} +5.45427 q^{43} +0.705942 q^{44} +1.41445 q^{45} +5.08731 q^{46} +11.4366 q^{47} +4.07623 q^{48} -5.80809 q^{49} -2.17349 q^{50} -6.69942 q^{51} -1.41232 q^{52} +0.811524 q^{53} +4.87109 q^{54} -1.75766 q^{55} -3.36060 q^{56} +5.25610 q^{57} -6.93756 q^{58} +15.0522 q^{59} +2.42028 q^{60} +5.64667 q^{61} +7.27698 q^{62} +0.878565 q^{63} +8.47854 q^{64} +3.51639 q^{65} +2.21891 q^{66} -11.0074 q^{67} -2.42463 q^{68} -8.72316 q^{69} +2.18289 q^{70} +5.93400 q^{71} -2.47713 q^{72} +8.69955 q^{73} +10.9379 q^{74} +3.72686 q^{75} +1.90226 q^{76} -1.09174 q^{77} -4.43917 q^{78} +1.30616 q^{79} -3.67308 q^{80} -10.7666 q^{81} -8.76713 q^{82} +14.3500 q^{83} +1.50332 q^{84} +6.03683 q^{85} +6.20459 q^{86} +11.8958 q^{87} +3.07819 q^{88} +5.83903 q^{89} +1.60903 q^{90} +2.18416 q^{91} -3.15705 q^{92} -12.4778 q^{93} +13.0099 q^{94} -4.73625 q^{95} -7.37148 q^{96} +7.73029 q^{97} -6.60709 q^{98} -0.804735 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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