LMFDB - Embedded newform 1441.2.a.f.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.67025 q^{2} -2.19223 q^{3} +5.13021 q^{4} +1.01111 q^{5} +5.85378 q^{6} -2.59765 q^{7} -8.35844 q^{8} +1.80585 q^{9} +O(q^{10})$	\(q-2.67025 q^{2} -2.19223 q^{3} +5.13021 q^{4} +1.01111 q^{5} +5.85378 q^{6} -2.59765 q^{7} -8.35844 q^{8} +1.80585 q^{9} -2.69992 q^{10} -1.00000 q^{11} -11.2466 q^{12} -5.69020 q^{13} +6.93635 q^{14} -2.21658 q^{15} +12.0587 q^{16} -6.20161 q^{17} -4.82207 q^{18} -1.88109 q^{19} +5.18722 q^{20} +5.69462 q^{21} +2.67025 q^{22} +0.355291 q^{23} +18.3236 q^{24} -3.97765 q^{25} +15.1942 q^{26} +2.61784 q^{27} -13.3265 q^{28} +8.05170 q^{29} +5.91882 q^{30} -4.59167 q^{31} -15.4827 q^{32} +2.19223 q^{33} +16.5598 q^{34} -2.62651 q^{35} +9.26440 q^{36} +1.46826 q^{37} +5.02297 q^{38} +12.4742 q^{39} -8.45131 q^{40} -10.0585 q^{41} -15.2060 q^{42} -3.47722 q^{43} -5.13021 q^{44} +1.82592 q^{45} -0.948714 q^{46} +6.40718 q^{47} -26.4353 q^{48} -0.252238 q^{49} +10.6213 q^{50} +13.5953 q^{51} -29.1919 q^{52} -6.52058 q^{53} -6.99028 q^{54} -1.01111 q^{55} +21.7123 q^{56} +4.12377 q^{57} -21.5000 q^{58} +2.56531 q^{59} -11.3715 q^{60} -14.2883 q^{61} +12.2609 q^{62} -4.69096 q^{63} +17.2253 q^{64} -5.75342 q^{65} -5.85378 q^{66} -6.19571 q^{67} -31.8156 q^{68} -0.778878 q^{69} +7.01342 q^{70} +12.2869 q^{71} -15.0941 q^{72} +13.3347 q^{73} -3.92062 q^{74} +8.71991 q^{75} -9.65038 q^{76} +2.59765 q^{77} -33.3092 q^{78} -2.33151 q^{79} +12.1927 q^{80} -11.1565 q^{81} +26.8587 q^{82} -3.85634 q^{83} +29.2146 q^{84} -6.27052 q^{85} +9.28502 q^{86} -17.6511 q^{87} +8.35844 q^{88} -12.7313 q^{89} -4.87565 q^{90} +14.7811 q^{91} +1.82272 q^{92} +10.0660 q^{93} -17.1088 q^{94} -1.90199 q^{95} +33.9416 q^{96} -5.58988 q^{97} +0.673538 q^{98} -1.80585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67025	−1.88815	−0.944075	−	0.329732i	$-0.893042\pi$
$2$	−2.67025	−1.88815	−0.944075	+	0.329732i	$0.893042\pi$
$3$	−2.19223	−1.26568	−0.632841	−	0.774282i	$-0.718111\pi$
$3$	−2.19223	−1.26568	−0.632841	+	0.774282i	$0.718111\pi$
$4$	5.13021	2.56511
$5$	1.01111	0.452183	0.226091	−	0.974106i	$-0.427405\pi$
$5$	1.01111	0.452183	0.226091	+	0.974106i	$0.427405\pi$
$6$	5.85378	2.38980
$7$	−2.59765	−0.981818	−0.490909	−	0.871211i	$-0.663335\pi$
$7$	−2.59765	−0.981818	−0.490909	+	0.871211i	$0.663335\pi$
$8$	−8.35844	−2.95516
$9$	1.80585	0.601951
$10$	−2.69992	−0.853788
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−11.2466	−3.24661
$13$	−5.69020	−1.57818	−0.789088	−	0.614280i	$-0.789447\pi$
$13$	−5.69020	−1.57818	−0.789088	+	0.614280i	$0.789447\pi$
$14$	6.93635	1.85382
$15$	−2.21658	−0.572319
$16$	12.0587	3.01467
$17$	−6.20161	−1.50411	−0.752056	−	0.659099i	$-0.770938\pi$
$17$	−6.20161	−1.50411	−0.752056	+	0.659099i	$0.770938\pi$
$18$	−4.82207	−1.13657
$19$	−1.88109	−0.431551	−0.215776	−	0.976443i	$-0.569228\pi$
$19$	−1.88109	−0.431551	−0.215776	+	0.976443i	$0.569228\pi$
$20$	5.18722	1.15990
$21$	5.69462	1.24267
$22$	2.67025	0.569298
$23$	0.355291	0.0740833	0.0370416	−	0.999314i	$-0.488207\pi$
$23$	0.355291	0.0740833	0.0370416	+	0.999314i	$0.488207\pi$
$24$	18.3236	3.74029
$25$	−3.97765	−0.795531
$26$	15.1942	2.97983
$27$	2.61784	0.503804
$28$	−13.3265	−2.51847
$29$	8.05170	1.49516	0.747581	−	0.664170i	$-0.231215\pi$
$29$	8.05170	1.49516	0.747581	+	0.664170i	$0.231215\pi$
$30$	5.91882	1.08062
$31$	−4.59167	−0.824688	−0.412344	−	0.911028i	$-0.635290\pi$
$31$	−4.59167	−0.824688	−0.412344	+	0.911028i	$0.635290\pi$
$32$	−15.4827	−2.73698
$33$	2.19223	0.381617
$34$	16.5598	2.83999
$35$	−2.62651	−0.443961
$36$	9.26440	1.54407
$37$	1.46826	0.241381	0.120690	−	0.992690i	$-0.461489\pi$
$37$	1.46826	0.241381	0.120690	+	0.992690i	$0.461489\pi$
$38$	5.02297	0.814833
$39$	12.4742	1.99747
$40$	−8.45131	−1.33627
$41$	−10.0585	−1.57088	−0.785438	−	0.618941i	$-0.787562\pi$
$41$	−10.0585	−1.57088	−0.785438	+	0.618941i	$0.787562\pi$
$42$	−15.2060	−2.34634
$43$	−3.47722	−0.530270	−0.265135	−	0.964211i	$-0.585417\pi$
$43$	−3.47722	−0.530270	−0.265135	+	0.964211i	$0.585417\pi$
$44$	−5.13021	−0.773409
$45$	1.82592	0.272192
$46$	−0.948714	−0.139880
$47$	6.40718	0.934584	0.467292	−	0.884103i	$-0.345230\pi$
$47$	6.40718	0.934584	0.467292	+	0.884103i	$0.345230\pi$
$48$	−26.4353	−3.81561
$49$	−0.252238	−0.0360340
$50$	10.6213	1.50208
$51$	13.5953	1.90373
$52$	−29.1919	−4.04819
$53$	−6.52058	−0.895670	−0.447835	−	0.894116i	$-0.647805\pi$
$53$	−6.52058	−0.895670	−0.447835	+	0.894116i	$0.647805\pi$
$54$	−6.99028	−0.951257
$55$	−1.01111	−0.136338
$56$	21.7123	2.90142
$57$	4.12377	0.546207
$58$	−21.5000	−2.82309
$59$	2.56531	0.333975	0.166988	−	0.985959i	$-0.446596\pi$
$59$	2.56531	0.333975	0.166988	+	0.985959i	$0.446596\pi$
$60$	−11.3715	−1.46806
$61$	−14.2883	−1.82943	−0.914716	−	0.404098i	$-0.867585\pi$
$61$	−14.2883	−1.82943	−0.914716	+	0.404098i	$0.867585\pi$
$62$	12.2609	1.55713
$63$	−4.69096	−0.591006
$64$	17.2253	2.15317
$65$	−5.75342	−0.713624
$66$	−5.85378	−0.720551
$67$	−6.19571	−0.756927	−0.378463	−	0.925616i	$-0.623547\pi$
$67$	−6.19571	−0.756927	−0.378463	+	0.925616i	$0.623547\pi$
$68$	−31.8156	−3.85821
$69$	−0.778878	−0.0937659
$70$	7.01342	0.838265
$71$	12.2869	1.45818	0.729092	−	0.684416i	$-0.239943\pi$
$71$	12.2869	1.45818	0.729092	+	0.684416i	$0.239943\pi$
$72$	−15.0941	−1.77886
$73$	13.3347	1.56071	0.780356	−	0.625335i	$-0.215038\pi$
$73$	13.3347	1.56071	0.780356	+	0.625335i	$0.215038\pi$
$74$	−3.92062	−0.455762
$75$	8.71991	1.00689
$76$	−9.65038	−1.10697
$77$	2.59765	0.296029
$78$	−33.3092	−3.77152
$79$	−2.33151	−0.262316	−0.131158	−	0.991361i	$-0.541870\pi$
$79$	−2.33151	−0.262316	−0.131158	+	0.991361i	$0.541870\pi$
$80$	12.1927	1.36318
$81$	−11.1565	−1.23961
$82$	26.8587	2.96605
$83$	−3.85634	−0.423288	−0.211644	−	0.977347i	$-0.567882\pi$
$83$	−3.85634	−0.423288	−0.211644	+	0.977347i	$0.567882\pi$
$84$	29.2146	3.18758
$85$	−6.27052	−0.680133
$86$	9.28502	1.00123
$87$	−17.6511	−1.89240
$88$	8.35844	0.891013
$89$	−12.7313	−1.34952	−0.674759	−	0.738038i	$-0.735752\pi$
$89$	−12.7313	−1.34952	−0.674759	+	0.738038i	$0.735752\pi$
$90$	−4.87565	−0.513938
$91$	14.7811	1.54948
$92$	1.82272	0.190032
$93$	10.0660	1.04379
$94$	−17.1088	−1.76463
$95$	−1.90199	−0.195140
$96$	33.9416	3.46415
$97$	−5.58988	−0.567566	−0.283783	−	0.958889i	$-0.591590\pi$
$97$	−5.58988	−0.567566	−0.283783	+	0.958889i	$0.591590\pi$
$98$	0.673538	0.0680376
$99$	−1.80585	−0.181495
$100$	−20.4062	−2.04062
$101$	−0.558899	−0.0556126	−0.0278063	−	0.999613i	$-0.508852\pi$
$101$	−0.558899	−0.0556126	−0.0278063	+	0.999613i	$0.508852\pi$
$102$	−36.3029	−3.59452
$103$	−4.34564	−0.428189	−0.214094	−	0.976813i	$-0.568680\pi$
$103$	−4.34564	−0.428189	−0.214094	+	0.976813i	$0.568680\pi$
$104$	47.5612	4.66376
$105$	5.75790	0.561913
$106$	17.4115	1.69116
$107$	18.6389	1.80189	0.900947	−	0.433928i	$-0.142873\pi$
$107$	18.6389	1.80189	0.900947	+	0.433928i	$0.142873\pi$
$108$	13.4301	1.29231
$109$	−2.46155	−0.235774	−0.117887	−	0.993027i	$-0.537612\pi$
$109$	−2.46155	−0.235774	−0.117887	+	0.993027i	$0.537612\pi$
$110$	2.69992	0.257427
$111$	−3.21876	−0.305511
$112$	−31.3241	−2.95985
$113$	15.1379	1.42405	0.712027	−	0.702152i	$-0.247778\pi$
$113$	15.1379	1.42405	0.712027	+	0.702152i	$0.247778\pi$
$114$	−11.0115	−1.03132
$115$	0.359239	0.0334992
$116$	41.3069	3.83525
$117$	−10.2756	−0.949984
$118$	−6.85002	−0.630595
$119$	16.1096	1.47676
$120$	18.5272	1.69129
$121$	1.00000	0.0909091
$122$	38.1533	3.45424
$123$	22.0505	1.98823
$124$	−23.5562	−2.11541
$125$	−9.07741	−0.811908
$126$	12.5260	1.11591
$127$	−10.2104	−0.906022	−0.453011	−	0.891505i	$-0.649650\pi$
$127$	−10.2104	−0.906022	−0.453011	+	0.891505i	$0.649650\pi$
$128$	−15.0305	−1.32852
$129$	7.62284	0.671154
$130$	15.3631	1.34743
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	11.2466	0.978889
$133$	4.88640	0.423705
$134$	16.5441	1.42919
$135$	2.64693	0.227811
$136$	51.8358	4.44488
$137$	−11.4676	−0.979742	−0.489871	−	0.871795i	$-0.662956\pi$
$137$	−11.4676	−0.979742	−0.489871	+	0.871795i	$0.662956\pi$
$138$	2.07979	0.177044
$139$	7.94704	0.674059	0.337030	−	0.941494i	$-0.390578\pi$
$139$	7.94704	0.674059	0.337030	+	0.941494i	$0.390578\pi$
$140$	−13.4746	−1.13881
$141$	−14.0460	−1.18289
$142$	−32.8090	−2.75327
$143$	5.69020	0.475838
$144$	21.7762	1.81468
$145$	8.14116	0.676087
$146$	−35.6070	−2.94686
$147$	0.552963	0.0456076
$148$	7.53249	0.619167
$149$	15.4791	1.26810	0.634049	−	0.773293i	$-0.281392\pi$
$149$	15.4791	1.26810	0.634049	+	0.773293i	$0.281392\pi$
$150$	−23.2843	−1.90116
$151$	3.41784	0.278140	0.139070	−	0.990283i	$-0.455589\pi$
$151$	3.41784	0.278140	0.139070	+	0.990283i	$0.455589\pi$
$152$	15.7230	1.27530
$153$	−11.1992	−0.905401
$154$	−6.93635	−0.558947
$155$	−4.64269	−0.372910
$156$	63.9953	5.12372
$157$	3.85172	0.307401	0.153700	−	0.988118i	$-0.450881\pi$
$157$	3.85172	0.307401	0.153700	+	0.988118i	$0.450881\pi$
$158$	6.22572	0.495291
$159$	14.2946	1.13363
$160$	−15.6548	−1.23762
$161$	−0.922920	−0.0727363
$162$	29.7905	2.34056
$163$	9.77191	0.765395	0.382698	−	0.923874i	$-0.374995\pi$
$163$	9.77191	0.765395	0.382698	+	0.923874i	$0.374995\pi$
$164$	−51.6023	−4.02946
$165$	2.21658	0.172561
$166$	10.2974	0.799231
$167$	15.0290	1.16298	0.581488	−	0.813555i	$-0.302471\pi$
$167$	15.0290	1.16298	0.581488	+	0.813555i	$0.302471\pi$
$168$	−47.5982	−3.67228
$169$	19.3783	1.49064
$170$	16.7438	1.28419
$171$	−3.39697	−0.259772
$172$	−17.8389	−1.36020
$173$	6.86551	0.521975	0.260988	−	0.965342i	$-0.415952\pi$
$173$	6.86551	0.521975	0.260988	+	0.965342i	$0.415952\pi$
$174$	47.1329	3.57313
$175$	10.3325	0.781066
$176$	−12.0587	−0.908956
$177$	−5.62374	−0.422706
$178$	33.9958	2.54809
$179$	18.5989	1.39015	0.695073	−	0.718939i	$-0.255372\pi$
$179$	18.5989	1.39015	0.695073	+	0.718939i	$0.255372\pi$
$180$	9.36734	0.698201
$181$	−4.92300	−0.365924	−0.182962	−	0.983120i	$-0.558568\pi$
$181$	−4.92300	−0.365924	−0.182962	+	0.983120i	$0.558568\pi$
$182$	−39.4692	−2.92565
$183$	31.3232	2.31548
$184$	−2.96968	−0.218928
$185$	1.48457	0.109148
$186$	−26.8786	−1.97084
$187$	6.20161	0.453507
$188$	32.8702	2.39731
$189$	−6.80023	−0.494644
$190$	5.07878	0.368453
$191$	−17.2545	−1.24849	−0.624247	−	0.781227i	$-0.714594\pi$
$191$	−17.2545	−1.24849	−0.624247	+	0.781227i	$0.714594\pi$
$192$	−37.7618	−2.72523
$193$	16.9899	1.22296	0.611481	−	0.791259i	$-0.290574\pi$
$193$	16.9899	1.22296	0.611481	+	0.791259i	$0.290574\pi$
$194$	14.9263	1.07165
$195$	12.6128	0.903221
$196$	−1.29404	−0.0924312
$197$	−1.65174	−0.117682	−0.0588409	−	0.998267i	$-0.518740\pi$
$197$	−1.65174	−0.117682	−0.0588409	+	0.998267i	$0.518740\pi$
$198$	4.82207	0.342689
$199$	−14.9863	−1.06235	−0.531176	−	0.847261i	$-0.678250\pi$
$199$	−14.9863	−1.06235	−0.531176	+	0.847261i	$0.678250\pi$
$200$	33.2470	2.35092
$201$	13.5824	0.958028
$202$	1.49240	0.105005
$203$	−20.9155	−1.46798
$204$	69.7469	4.88326
$205$	−10.1703	−0.710323
$206$	11.6039	0.808484
$207$	0.641603	0.0445945
$208$	−68.6162	−4.75768
$209$	1.88109	0.130118
$210$	−15.3750	−1.06098
$211$	18.4626	1.27101	0.635507	−	0.772095i	$-0.280791\pi$
$211$	18.4626	1.27101	0.635507	+	0.772095i	$0.280791\pi$
$212$	−33.4520	−2.29749
$213$	−26.9356	−1.84560
$214$	−49.7706	−3.40225
$215$	−3.51585	−0.239779
$216$	−21.8811	−1.48882
$217$	11.9275	0.809693
$218$	6.57296	0.445177
$219$	−29.2327	−1.97537
$220$	−5.18722	−0.349722
$221$	35.2884	2.37375
$222$	8.59487	0.576850
$223$	−20.0994	−1.34596	−0.672979	−	0.739661i	$-0.734986\pi$
$223$	−20.0994	−1.34596	−0.672979	+	0.739661i	$0.734986\pi$
$224$	40.2186	2.68722
$225$	−7.18305	−0.478870
$226$	−40.4219	−2.68882
$227$	10.3511	0.687025	0.343513	−	0.939148i	$-0.388383\pi$
$227$	10.3511	0.687025	0.343513	+	0.939148i	$0.388383\pi$
$228$	21.1558	1.40108
$229$	2.12289	0.140284	0.0701422	−	0.997537i	$-0.477655\pi$
$229$	2.12289	0.140284	0.0701422	+	0.997537i	$0.477655\pi$
$230$	−0.959256	−0.0632514
$231$	−5.69462	−0.374679
$232$	−67.2996	−4.41844
$233$	−20.8223	−1.36411	−0.682056	−	0.731300i	$-0.738914\pi$
$233$	−20.8223	−1.36411	−0.682056	+	0.731300i	$0.738914\pi$
$234$	27.4385	1.79371
$235$	6.47837	0.422603
$236$	13.1606	0.856682
$237$	5.11121	0.332008
$238$	−43.0166	−2.78835
$239$	−15.2541	−0.986707	−0.493353	−	0.869829i	$-0.664229\pi$
$239$	−15.2541	−0.986707	−0.493353	+	0.869829i	$0.664229\pi$
$240$	−26.7290	−1.72535
$241$	−7.70168	−0.496109	−0.248054	−	0.968746i	$-0.579791\pi$
$241$	−7.70168	−0.496109	−0.248054	+	0.968746i	$0.579791\pi$
$242$	−2.67025	−0.171650
$243$	16.6039	1.06514
$244$	−73.3021	−4.69269
$245$	−0.255041	−0.0162940
$246$	−58.8803	−3.75407
$247$	10.7038	0.681064
$248$	38.3792	2.43708
$249$	8.45396	0.535748
$250$	24.2389	1.53300
$251$	−11.1536	−0.704008	−0.352004	−	0.935999i	$-0.614500\pi$
$251$	−11.1536	−0.704008	−0.352004	+	0.935999i	$0.614500\pi$
$252$	−24.0656	−1.51599
$253$	−0.355291	−0.0223369
$254$	27.2641	1.71070
$255$	13.7464	0.860832
$256$	5.68435	0.355272
$257$	31.2823	1.95134	0.975669	−	0.219248i	$-0.0703604\pi$
$257$	31.2823	1.95134	0.975669	+	0.219248i	$0.0703604\pi$
$258$	−20.3549	−1.26724
$259$	−3.81402	−0.236992
$260$	−29.5163	−1.83052
$261$	14.5402	0.900014
$262$	−2.67025	−0.164968
$263$	12.4351	0.766782	0.383391	−	0.923586i	$-0.374756\pi$
$263$	12.4351	0.766782	0.383391	+	0.923586i	$0.374756\pi$
$264$	−18.3236	−1.12774
$265$	−6.59303	−0.405007
$266$	−13.0479	−0.800017
$267$	27.9099	1.70806
$268$	−31.7853	−1.94160
$269$	−30.4709	−1.85784	−0.928922	−	0.370274i	$-0.879264\pi$
$269$	−30.4709	−1.85784	−0.928922	+	0.370274i	$0.879264\pi$
$270$	−7.06795	−0.430142
$271$	−1.04010	−0.0631819	−0.0315909	−	0.999501i	$-0.510057\pi$
$271$	−1.04010	−0.0631819	−0.0315909	+	0.999501i	$0.510057\pi$
$272$	−74.7831	−4.53439
$273$	−32.4035	−1.96115
$274$	30.6213	1.84990
$275$	3.97765	0.239862
$276$	−3.99581	−0.240519
$277$	−13.0862	−0.786272	−0.393136	−	0.919480i	$-0.628610\pi$
$277$	−13.0862	−0.786272	−0.393136	+	0.919480i	$0.628610\pi$
$278$	−21.2206	−1.27272
$279$	−8.29187	−0.496421
$280$	21.9535	1.31197
$281$	22.5188	1.34336	0.671679	−	0.740842i	$-0.265573\pi$
$281$	22.5188	1.34336	0.671679	+	0.740842i	$0.265573\pi$
$282$	37.5062	2.23346
$283$	−4.84857	−0.288217	−0.144109	−	0.989562i	$-0.546031\pi$
$283$	−4.84857	−0.288217	−0.144109	+	0.989562i	$0.546031\pi$
$284$	63.0343	3.74040
$285$	4.16959	0.246985
$286$	−15.1942	−0.898453
$287$	26.1284	1.54231
$288$	−27.9595	−1.64753
$289$	21.4600	1.26235
$290$	−21.7389	−1.27655
$291$	12.2543	0.718358
$292$	68.4100	4.00340
$293$	−26.2962	−1.53624	−0.768121	−	0.640305i	$-0.778808\pi$
$293$	−26.2962	−1.53624	−0.768121	+	0.640305i	$0.778808\pi$
$294$	−1.47655	−0.0861140
$295$	2.59382	0.151018
$296$	−12.2724	−0.713317
$297$	−2.61784	−0.151903
$298$	−41.3330	−2.39436
$299$	−2.02167	−0.116916
$300$	44.7350	2.58278
$301$	9.03257	0.520629
$302$	−9.12646	−0.525169
$303$	1.22523	0.0703878
$304$	−22.6834	−1.30098
$305$	−14.4471	−0.827237
$306$	29.9046	1.70953
$307$	12.0046	0.685137	0.342569	−	0.939493i	$-0.388703\pi$
$307$	12.0046	0.685137	0.342569	+	0.939493i	$0.388703\pi$
$308$	13.3265	0.759346
$309$	9.52663	0.541951
$310$	12.3971	0.704109
$311$	19.1855	1.08791	0.543956	−	0.839114i	$-0.316926\pi$
$311$	19.1855	1.08791	0.543956	+	0.839114i	$0.316926\pi$
$312$	−104.265	−5.90283
$313$	27.9606	1.58043	0.790213	−	0.612833i	$-0.209970\pi$
$313$	27.9606	1.58043	0.790213	+	0.612833i	$0.209970\pi$
$314$	−10.2850	−0.580418
$315$	−4.74308	−0.267243
$316$	−11.9612	−0.672868
$317$	−10.5214	−0.590943	−0.295472	−	0.955352i	$-0.595477\pi$
$317$	−10.5214	−0.590943	−0.295472	+	0.955352i	$0.595477\pi$
$318$	−38.1700	−2.14047
$319$	−8.05170	−0.450808
$320$	17.4167	0.973625
$321$	−40.8608	−2.28063
$322$	2.46442	0.137337
$323$	11.6658	0.649101
$324$	−57.2350	−3.17972
$325$	22.6336	1.25549
$326$	−26.0934	−1.44518
$327$	5.39628	0.298415
$328$	84.0735	4.64218
$329$	−16.6436	−0.917591
$330$	−5.91882	−0.325821
$331$	4.37452	0.240445	0.120223	−	0.992747i	$-0.461639\pi$
$331$	4.37452	0.240445	0.120223	+	0.992747i	$0.461639\pi$
$332$	−19.7838	−1.08578
$333$	2.65146	0.145299
$334$	−40.1310	−2.19587
$335$	−6.26455	−0.342269
$336$	68.6696	3.74623
$337$	−29.5644	−1.61047	−0.805237	−	0.592954i	$-0.797962\pi$
$337$	−29.5644	−1.61047	−0.805237	+	0.592954i	$0.797962\pi$
$338$	−51.7449	−2.81455
$339$	−33.1857	−1.80240
$340$	−32.1691	−1.74461
$341$	4.59167	0.248653
$342$	9.07073	0.490489
$343$	18.8387	1.01720
$344$	29.0641	1.56703
$345$	−0.787532	−0.0423993
$346$	−18.3326	−0.985567
$347$	−22.5644	−1.21132	−0.605660	−	0.795723i	$-0.707091\pi$
$347$	−22.5644	−1.21132	−0.605660	+	0.795723i	$0.707091\pi$
$348$	−90.5541	−4.85421
$349$	−4.40177	−0.235622	−0.117811	−	0.993036i	$-0.537588\pi$
$349$	−4.40177	−0.235622	−0.117811	+	0.993036i	$0.537588\pi$
$350$	−27.5904	−1.47477
$351$	−14.8960	−0.795092
$352$	15.4827	0.825232
$353$	27.9833	1.48940	0.744699	−	0.667400i	$-0.232593\pi$
$353$	27.9833	1.48940	0.744699	+	0.667400i	$0.232593\pi$
$354$	15.0168	0.798133
$355$	12.4234	0.659365
$356$	−65.3144	−3.46166
$357$	−35.3158	−1.86911
$358$	−49.6636	−2.62480
$359$	13.7925	0.727938	0.363969	−	0.931411i	$-0.381421\pi$
$359$	13.7925	0.727938	0.363969	+	0.931411i	$0.381421\pi$
$360$	−15.2618	−0.804368
$361$	−15.4615	−0.813764
$362$	13.1456	0.690919
$363$	−2.19223	−0.115062
$364$	75.8303	3.97459
$365$	13.4829	0.705727
$366$	−83.6407	−4.37197
$367$	24.4024	1.27379	0.636897	−	0.770949i	$-0.280218\pi$
$367$	24.4024	1.27379	0.636897	+	0.770949i	$0.280218\pi$
$368$	4.28433	0.223336
$369$	−18.1642	−0.945589
$370$	−3.96418	−0.206088
$371$	16.9381	0.879385
$372$	51.6406	2.67744
$373$	−20.4255	−1.05759	−0.528795	−	0.848749i	$-0.677356\pi$
$373$	−20.4255	−1.05759	−0.528795	+	0.848749i	$0.677356\pi$
$374$	−16.5598	−0.856288
$375$	19.8997	1.02762
$376$	−53.5541	−2.76184
$377$	−45.8157	−2.35963
$378$	18.1583	0.933961
$379$	23.3378	1.19878	0.599391	−	0.800456i	$-0.295409\pi$
$379$	23.3378	1.19878	0.599391	+	0.800456i	$0.295409\pi$
$380$	−9.75761	−0.500555
$381$	22.3834	1.14674
$382$	46.0739	2.35734
$383$	36.1426	1.84680	0.923401	−	0.383837i	$-0.125397\pi$
$383$	36.1426	1.84680	0.923401	+	0.383837i	$0.125397\pi$
$384$	32.9502	1.68148
$385$	2.62651	0.133859
$386$	−45.3673	−2.30913
$387$	−6.27934	−0.319197
$388$	−28.6773	−1.45587
$389$	0.507358	0.0257241	0.0128620	−	0.999917i	$-0.495906\pi$
$389$	0.507358	0.0257241	0.0128620	+	0.999917i	$0.495906\pi$
$390$	−33.6793	−1.70542
$391$	−2.20338	−0.111430
$392$	2.10832	0.106486
$393$	−2.19223	−0.110583
$394$	4.41056	0.222201
$395$	−2.35742	−0.118615
$396$	−9.26440	−0.465554
$397$	21.1668	1.06233	0.531166	−	0.847267i	$-0.321754\pi$
$397$	21.1668	1.06233	0.531166	+	0.847267i	$0.321754\pi$
$398$	40.0172	2.00588
$399$	−10.7121	−0.536275
$400$	−47.9652	−2.39826
$401$	20.6738	1.03240	0.516201	−	0.856467i	$-0.327346\pi$
$401$	20.6738	1.03240	0.516201	+	0.856467i	$0.327346\pi$
$402$	−36.2683	−1.80890
$403$	26.1275	1.30150
$404$	−2.86727	−0.142652
$405$	−11.2804	−0.560528
$406$	55.8494	2.77176
$407$	−1.46826	−0.0727790
$408$	−113.636	−5.62581
$409$	26.4629	1.30850	0.654252	−	0.756276i	$-0.272984\pi$
$409$	26.4629	1.30850	0.654252	+	0.756276i	$0.272984\pi$
$410$	27.1571	1.34120
$411$	25.1395	1.24004
$412$	−22.2941	−1.09835
$413$	−6.66377	−0.327903
$414$	−1.71324	−0.0842010
$415$	−3.89919	−0.191404
$416$	88.0997	4.31944
$417$	−17.4217	−0.853144
$418$	−5.02297	−0.245681
$419$	−18.1371	−0.886057	−0.443028	−	0.896508i	$-0.646096\pi$
$419$	−18.1371	−0.886057	−0.443028	+	0.896508i	$0.646096\pi$
$420$	29.5392	1.44137
$421$	30.4878	1.48589	0.742943	−	0.669355i	$-0.233430\pi$
$421$	30.4878	1.48589	0.742943	+	0.669355i	$0.233430\pi$
$422$	−49.2996	−2.39987
$423$	11.5704	0.562573
$424$	54.5019	2.64684
$425$	24.6679	1.19657
$426$	71.9246	3.48476
$427$	37.1160	1.79617
$428$	95.6218	4.62205
$429$	−12.4742	−0.602260
$430$	9.38819	0.452739
$431$	21.8919	1.05450	0.527248	−	0.849711i	$-0.323224\pi$
$431$	21.8919	1.05450	0.527248	+	0.849711i	$0.323224\pi$
$432$	31.5677	1.51880
$433$	5.79397	0.278440	0.139220	−	0.990261i	$-0.455540\pi$
$433$	5.79397	0.278440	0.139220	+	0.990261i	$0.455540\pi$
$434$	−31.8494	−1.52882
$435$	−17.8473	−0.855710
$436$	−12.6283	−0.604786
$437$	−0.668333	−0.0319707
$438$	78.0586	3.72979
$439$	8.00230	0.381929	0.190964	−	0.981597i	$-0.438839\pi$
$439$	8.00230	0.381929	0.190964	+	0.981597i	$0.438839\pi$
$440$	8.45131	0.402901
$441$	−0.455505	−0.0216907
$442$	−94.2287	−4.48200
$443$	−1.19314	−0.0566878	−0.0283439	−	0.999598i	$-0.509023\pi$
$443$	−1.19314	−0.0566878	−0.0283439	+	0.999598i	$0.509023\pi$
$444$	−16.5129	−0.783668
$445$	−12.8728	−0.610229
$446$	53.6705	2.54137
$447$	−33.9337	−1.60501
$448$	−44.7453	−2.11402
$449$	−17.5784	−0.829576	−0.414788	−	0.909918i	$-0.636144\pi$
$449$	−17.5784	−0.829576	−0.414788	+	0.909918i	$0.636144\pi$
$450$	19.1805	0.904178
$451$	10.0585	0.473637
$452$	77.6606	3.65285
$453$	−7.49267	−0.352036
$454$	−27.6399	−1.29721
$455$	14.9453	0.700649
$456$	−34.4683	−1.61412
$457$	−16.2702	−0.761087	−0.380543	−	0.924763i	$-0.624263\pi$
$457$	−16.2702	−0.761087	−0.380543	+	0.924763i	$0.624263\pi$
$458$	−5.66863	−0.264878
$459$	−16.2348	−0.757777
$460$	1.84297	0.0859290
$461$	−25.9797	−1.20999	−0.604997	−	0.796228i	$-0.706826\pi$
$461$	−25.9797	−1.20999	−0.604997	+	0.796228i	$0.706826\pi$
$462$	15.2060	0.707449
$463$	−36.0241	−1.67418	−0.837091	−	0.547063i	$-0.815746\pi$
$463$	−36.0241	−1.67418	−0.837091	+	0.547063i	$0.815746\pi$
$464$	97.0927	4.50742
$465$	10.1778	0.471985
$466$	55.6006	2.57565
$467$	−16.0370	−0.742102	−0.371051	−	0.928613i	$-0.621002\pi$
$467$	−16.0370	−0.742102	−0.371051	+	0.928613i	$0.621002\pi$
$468$	−52.7163	−2.43681
$469$	16.0943	0.743164
$470$	−17.2989	−0.797937
$471$	−8.44383	−0.389071
$472$	−21.4420	−0.986949
$473$	3.47722	0.159883
$474$	−13.6482	−0.626881
$475$	7.48232	0.343312
$476$	82.6456	3.78806
$477$	−11.7752	−0.539149
$478$	40.7322	1.86305
$479$	−10.1227	−0.462516	−0.231258	−	0.972892i	$-0.574284\pi$
$479$	−10.1227	−0.462516	−0.231258	+	0.972892i	$0.574284\pi$
$480$	34.3187	1.56643
$481$	−8.35469	−0.380941
$482$	20.5654	0.936727
$483$	2.02325	0.0920610
$484$	5.13021	0.233192
$485$	−5.65199	−0.256644
$486$	−44.3366	−2.01115
$487$	19.4892	0.883140	0.441570	−	0.897227i	$-0.354422\pi$
$487$	19.4892	0.883140	0.441570	+	0.897227i	$0.354422\pi$
$488$	119.428	5.40625
$489$	−21.4222	−0.968747
$490$	0.681022	0.0307654
$491$	19.1786	0.865518	0.432759	−	0.901510i	$-0.357540\pi$
$491$	19.1786	0.865518	0.432759	+	0.901510i	$0.357540\pi$
$492$	113.124	5.10002
$493$	−49.9335	−2.24889
$494$	−28.5817	−1.28595
$495$	−1.82592	−0.0820689
$496$	−55.3694	−2.48616
$497$	−31.9169	−1.43167
$498$	−22.5742	−1.01157
$499$	11.9432	0.534652	0.267326	−	0.963606i	$-0.413860\pi$
$499$	11.9432	0.534652	0.267326	+	0.963606i	$0.413860\pi$
$500$	−46.5690	−2.08263
$501$	−32.9468	−1.47196
$502$	29.7828	1.32927
$503$	18.5068	0.825177	0.412588	−	0.910918i	$-0.364625\pi$
$503$	18.5068	0.825177	0.412588	+	0.910918i	$0.364625\pi$
$504$	39.2091	1.74651
$505$	−0.565110	−0.0251470
$506$	0.948714	0.0421755
$507$	−42.4817	−1.88668
$508$	−52.3813	−2.32404
$509$	18.7095	0.829282	0.414641	−	0.909985i	$-0.363907\pi$
$509$	18.7095	0.829282	0.414641	+	0.909985i	$0.363907\pi$
$510$	−36.7062	−1.62538
$511$	−34.6389	−1.53234
$512$	14.8823	0.657712
$513$	−4.92439	−0.217417
$514$	−83.5315	−3.68442
$515$	−4.39393	−0.193620
$516$	39.1068	1.72158
$517$	−6.40718	−0.281788
$518$	10.1844	0.447476
$519$	−15.0507	−0.660655
$520$	48.0896	2.10887
$521$	−3.29510	−0.144361	−0.0721806	−	0.997392i	$-0.522996\pi$
$521$	−3.29510	−0.144361	−0.0721806	+	0.997392i	$0.522996\pi$
$522$	−38.8258	−1.69936
$523$	−11.2143	−0.490366	−0.245183	−	0.969477i	$-0.578848\pi$
$523$	−11.2143	−0.490366	−0.245183	+	0.969477i	$0.578848\pi$
$524$	5.13021	0.224114
$525$	−22.6512	−0.988581
$526$	−33.2048	−1.44780
$527$	28.4757	1.24042
$528$	26.4353	1.15045
$529$	−22.8738	−0.994512
$530$	17.6050	0.764713
$531$	4.63257	0.201037
$532$	25.0683	1.08685
$533$	57.2349	2.47912
$534$	−74.5264	−3.22507
$535$	18.8460	0.814786
$536$	51.7865	2.23684
$537$	−40.7730	−1.75948
$538$	81.3649	3.50789
$539$	0.252238	0.0108647
$540$	13.5793	0.584361
$541$	5.24236	0.225387	0.112693	−	0.993630i	$-0.464052\pi$
$541$	5.24236	0.225387	0.112693	+	0.993630i	$0.464052\pi$
$542$	2.77734	0.119297
$543$	10.7923	0.463143
$544$	96.0178	4.11673
$545$	−2.48891	−0.106613
$546$	86.5254	3.70294
$547$	17.8146	0.761697	0.380848	−	0.924637i	$-0.375632\pi$
$547$	17.8146	0.761697	0.380848	+	0.924637i	$0.375632\pi$
$548$	−58.8312	−2.51314
$549$	−25.8026	−1.10123
$550$	−10.6213	−0.452894
$551$	−15.1459	−0.645239
$552$	6.51020	0.277093
$553$	6.05645	0.257546
$554$	34.9433	1.48460
$555$	−3.25452	−0.138147
$556$	40.7700	1.72903
$557$	7.02886	0.297822	0.148911	−	0.988851i	$-0.452423\pi$
$557$	7.02886	0.297822	0.148911	+	0.988851i	$0.452423\pi$
$558$	22.1413	0.937317
$559$	19.7860	0.836860
$560$	−31.6722	−1.33839
$561$	−13.5953	−0.573995
$562$	−60.1307	−2.53646
$563$	−41.9471	−1.76786	−0.883930	−	0.467619i	$-0.845112\pi$
$563$	−41.9471	−1.76786	−0.883930	+	0.467619i	$0.845112\pi$
$564$	−72.0589	−3.03423
$565$	15.3061	0.643932
$566$	12.9469	0.544197
$567$	28.9805	1.21707
$568$	−102.699	−4.30916
$569$	14.1132	0.591655	0.295827	−	0.955241i	$-0.404405\pi$
$569$	14.1132	0.591655	0.295827	+	0.955241i	$0.404405\pi$
$570$	−11.1338	−0.466345
$571$	11.3943	0.476836	0.238418	−	0.971163i	$-0.423371\pi$
$571$	11.3943	0.476836	0.238418	+	0.971163i	$0.423371\pi$
$572$	29.1919	1.22058
$573$	37.8258	1.58020
$574$	−69.7694	−2.91212
$575$	−1.41322	−0.0589355
$576$	31.1064	1.29610
$577$	−32.0233	−1.33315	−0.666574	−	0.745439i	$-0.732240\pi$
$577$	−32.0233	−1.33315	−0.666574	+	0.745439i	$0.732240\pi$
$578$	−57.3034	−2.38351
$579$	−37.2457	−1.54788
$580$	41.7659	1.73423
$581$	10.0174	0.415592
$582$	−32.7219	−1.35637
$583$	6.52058	0.270055
$584$	−111.458	−4.61215
$585$	−10.3898	−0.429566
$586$	70.2174	2.90065
$587$	−46.1562	−1.90507	−0.952536	−	0.304426i	$-0.901535\pi$
$587$	−46.1562	−1.90507	−0.952536	+	0.304426i	$0.901535\pi$
$588$	2.83682	0.116988
$589$	8.63733	0.355895
$590$	−6.92613	−0.285144
$591$	3.62099	0.148948
$592$	17.7053	0.727682
$593$	−47.0499	−1.93211	−0.966055	−	0.258337i	$-0.916826\pi$
$593$	−47.0499	−1.93211	−0.966055	+	0.258337i	$0.916826\pi$
$594$	6.99028	0.286815
$595$	16.2886	0.667767
$596$	79.4111	3.25280
$597$	32.8534	1.34460
$598$	5.39837	0.220756
$599$	−23.9118	−0.977009	−0.488505	−	0.872561i	$-0.662457\pi$
$599$	−23.9118	−0.977009	−0.488505	+	0.872561i	$0.662457\pi$
$600$	−72.8849	−2.97551
$601$	−4.84243	−0.197527	−0.0987634	−	0.995111i	$-0.531489\pi$
$601$	−4.84243	−0.197527	−0.0987634	+	0.995111i	$0.531489\pi$
$602$	−24.1192	−0.983025
$603$	−11.1885	−0.455632
$604$	17.5342	0.713458
$605$	1.01111	0.0411075
$606$	−3.27168	−0.132903
$607$	28.1144	1.14113	0.570565	−	0.821252i	$-0.306724\pi$
$607$	28.1144	1.14113	0.570565	+	0.821252i	$0.306724\pi$
$608$	29.1244	1.18115
$609$	45.8514	1.85799
$610$	38.5772	1.56195
$611$	−36.4581	−1.47494
$612$	−57.4542	−2.32245
$613$	−19.6370	−0.793132	−0.396566	−	0.918006i	$-0.629798\pi$
$613$	−19.6370	−0.793132	−0.396566	+	0.918006i	$0.629798\pi$
$614$	−32.0552	−1.29364
$615$	22.2955	0.899042
$616$	−21.7123	−0.874812
$617$	22.1087	0.890063	0.445032	−	0.895515i	$-0.353192\pi$
$617$	22.1087	0.890063	0.445032	+	0.895515i	$0.353192\pi$
$618$	−25.4384	−1.02328
$619$	−42.9568	−1.72658	−0.863289	−	0.504710i	$-0.831599\pi$
$619$	−42.9568	−1.72658	−0.863289	+	0.504710i	$0.831599\pi$
$620$	−23.8180	−0.956553
$621$	0.930096	0.0373234
$622$	−51.2301	−2.05414
$623$	33.0715	1.32498
$624$	150.422	6.02170
$625$	10.7100	0.428400
$626$	−74.6616	−2.98408
$627$	−4.12377	−0.164687
$628$	19.7601	0.788515
$629$	−9.10558	−0.363063
$630$	12.6652	0.504594
$631$	−21.1137	−0.840523	−0.420262	−	0.907403i	$-0.638062\pi$
$631$	−21.1137	−0.840523	−0.420262	+	0.907403i	$0.638062\pi$
$632$	19.4878	0.775184
$633$	−40.4741	−1.60870
$634$	28.0948	1.11579
$635$	−10.3238	−0.409688
$636$	73.3342	2.90789
$637$	1.43529	0.0568681
$638$	21.5000	0.851193
$639$	22.1883	0.877754
$640$	−15.1975	−0.600733
$641$	−1.36832	−0.0540453	−0.0270226	−	0.999635i	$-0.508603\pi$
$641$	−1.36832	−0.0540453	−0.0270226	+	0.999635i	$0.508603\pi$
$642$	109.108	4.30616
$643$	−27.1646	−1.07127	−0.535634	−	0.844450i	$-0.679927\pi$
$643$	−27.1646	−1.07127	−0.535634	+	0.844450i	$0.679927\pi$
$644$	−4.73478	−0.186576
$645$	7.70754	0.303484
$646$	−31.1505	−1.22560
$647$	−16.9012	−0.664456	−0.332228	−	0.943199i	$-0.607800\pi$
$647$	−16.9012	−0.664456	−0.332228	+	0.943199i	$0.607800\pi$
$648$	93.2506	3.66323
$649$	−2.56531	−0.100697
$650$	−60.4374	−2.37055
$651$	−26.1478	−1.02481
$652$	50.1320	1.96332
$653$	15.0668	0.589609	0.294805	−	0.955558i	$-0.404745\pi$
$653$	15.0668	0.589609	0.294805	+	0.955558i	$0.404745\pi$
$654$	−14.4094	−0.563452
$655$	1.01111	0.0395074
$656$	−121.292	−4.73566
$657$	24.0806	0.939472
$658$	44.4425	1.73255
$659$	−46.4117	−1.80794	−0.903972	−	0.427592i	$-0.859362\pi$
$659$	−46.4117	−1.80794	−0.903972	+	0.427592i	$0.859362\pi$
$660$	11.3715	0.442637
$661$	−1.85549	−0.0721702	−0.0360851	−	0.999349i	$-0.511489\pi$
$661$	−1.85549	−0.0721702	−0.0360851	+	0.999349i	$0.511489\pi$
$662$	−11.6810	−0.453996
$663$	−77.3601	−3.00442
$664$	32.2330	1.25088
$665$	4.94069	0.191592
$666$	−7.08005	−0.274346
$667$	2.86069	0.110767
$668$	77.1017	2.98316
$669$	44.0625	1.70356
$670$	16.7279	0.646255
$671$	14.2883	0.551594
$672$	−88.1683	−3.40117
$673$	−46.5856	−1.79574	−0.897872	−	0.440257i	$-0.854887\pi$
$673$	−46.5856	−1.79574	−0.897872	+	0.440257i	$0.854887\pi$
$674$	78.9441	3.04081
$675$	−10.4129	−0.400792
$676$	99.4150	3.82365
$677$	−18.8608	−0.724879	−0.362439	−	0.932007i	$-0.618056\pi$
$677$	−18.8608	−0.724879	−0.362439	+	0.932007i	$0.618056\pi$
$678$	88.6139	3.40320
$679$	14.5205	0.557246
$680$	52.4118	2.00990
$681$	−22.6919	−0.869555
$682$	−12.2609	−0.469493
$683$	21.2367	0.812598	0.406299	−	0.913740i	$-0.366819\pi$
$683$	21.2367	0.812598	0.406299	+	0.913740i	$0.366819\pi$
$684$	−17.4272	−0.666344
$685$	−11.5950	−0.443022
$686$	−50.3041	−1.92062
$687$	−4.65385	−0.177555
$688$	−41.9306	−1.59859
$689$	37.1034	1.41353
$690$	2.10290	0.0800562
$691$	−9.81529	−0.373391	−0.186696	−	0.982418i	$-0.559778\pi$
$691$	−9.81529	−0.373391	−0.186696	+	0.982418i	$0.559778\pi$
$692$	35.2215	1.33892
$693$	4.69096	0.178195
$694$	60.2525	2.28715
$695$	8.03534	0.304798
$696$	147.536	5.59233
$697$	62.3790	2.36277
$698$	11.7538	0.444889
$699$	45.6471	1.72653
$700$	53.0081	2.00352
$701$	−10.0840	−0.380869	−0.190434	−	0.981700i	$-0.560990\pi$
$701$	−10.0840	−0.380869	−0.190434	+	0.981700i	$0.560990\pi$
$702$	39.7761	1.50125
$703$	−2.76193	−0.104168
$704$	−17.2253	−0.649205
$705$	−14.2021	−0.534880
$706$	−74.7222	−2.81221
$707$	1.45182	0.0546014
$708$	−28.8510	−1.08429
$709$	−13.8238	−0.519163	−0.259582	−	0.965721i	$-0.583585\pi$
$709$	−13.8238	−0.519163	−0.259582	+	0.965721i	$0.583585\pi$
$710$	−33.1735	−1.24498
$711$	−4.21037	−0.157901
$712$	106.414	3.98803
$713$	−1.63138	−0.0610956
$714$	94.3020	3.52916
$715$	5.75342	0.215166
$716$	95.4163	3.56587
$717$	33.4405	1.24886
$718$	−36.8292	−1.37446
$719$	−6.98670	−0.260560	−0.130280	−	0.991477i	$-0.541588\pi$
$719$	−6.98670	−0.260560	−0.130280	+	0.991477i	$0.541588\pi$
$720$	22.0181	0.820567
$721$	11.2884	0.420403
$722$	41.2860	1.53651
$723$	16.8838	0.627916
$724$	−25.2560	−0.938634
$725$	−32.0269	−1.18945
$726$	5.85378	0.217254
$727$	−9.98035	−0.370151	−0.185075	−	0.982724i	$-0.559253\pi$
$727$	−9.98035	−0.370151	−0.185075	+	0.982724i	$0.559253\pi$
$728$	−123.547	−4.57896
$729$	−2.93020	−0.108526
$730$	−36.0027	−1.33252
$731$	21.5643	0.797586
$732$	160.695	5.93945
$733$	−16.6970	−0.616717	−0.308358	−	0.951270i	$-0.599780\pi$
$733$	−16.6970	−0.616717	−0.308358	+	0.951270i	$0.599780\pi$
$734$	−65.1604	−2.40511
$735$	0.559107	0.0206230
$736$	−5.50087	−0.202765
$737$	6.19571	0.228222
$738$	48.5028	1.78541
$739$	8.49641	0.312545	0.156273	−	0.987714i	$-0.450052\pi$
$739$	8.49641	0.312545	0.156273	+	0.987714i	$0.450052\pi$
$740$	7.61619	0.279977
$741$	−23.4651	−0.862010
$742$	−45.2290	−1.66041
$743$	1.19162	0.0437163	0.0218582	−	0.999761i	$-0.493042\pi$
$743$	1.19162	0.0437163	0.0218582	+	0.999761i	$0.493042\pi$
$744$	−84.1358	−3.08457
$745$	15.6511	0.573412
$746$	54.5410	1.99689
$747$	−6.96398	−0.254799
$748$	31.8156	1.16329
$749$	−48.4174	−1.76913
$750$	−53.1372	−1.94029
$751$	29.3870	1.07235	0.536174	−	0.844108i	$-0.319869\pi$
$751$	29.3870	1.07235	0.536174	+	0.844108i	$0.319869\pi$
$752$	77.2621	2.81746
$753$	24.4512	0.891050
$754$	122.339	4.45533
$755$	3.45581	0.125770
$756$	−34.8866	−1.26881
$757$	35.0455	1.27375	0.636876	−	0.770966i	$-0.280226\pi$
$757$	35.0455	1.27375	0.636876	+	0.770966i	$0.280226\pi$
$758$	−62.3177	−2.26348
$759$	0.778878	0.0282715
$760$	15.8977	0.576669
$761$	11.5602	0.419056	0.209528	−	0.977803i	$-0.432807\pi$
$761$	11.5602	0.419056	0.209528	+	0.977803i	$0.432807\pi$
$762$	−59.7692	−2.16521
$763$	6.39425	0.231487
$764$	−88.5194	−3.20252
$765$	−11.3236	−0.409407
$766$	−96.5097	−3.48704
$767$	−14.5971	−0.527072
$768$	−12.4614	−0.449661
$769$	23.5415	0.848927	0.424463	−	0.905445i	$-0.360463\pi$
$769$	23.5415	0.848927	0.424463	+	0.905445i	$0.360463\pi$
$770$	−7.01342	−0.252746
$771$	−68.5779	−2.46977
$772$	87.1619	3.13703
$773$	−27.0638	−0.973418	−0.486709	−	0.873564i	$-0.661803\pi$
$773$	−27.0638	−0.973418	−0.486709	+	0.873564i	$0.661803\pi$
$774$	16.7674	0.602691
$775$	18.2641	0.656065
$776$	46.7226	1.67725
$777$	8.36119	0.299956
$778$	−1.35477	−0.0485709
$779$	18.9209	0.677913
$780$	64.7063	2.31686
$781$	−12.2869	−0.439659
$782$	5.88356	0.210396
$783$	21.0781	0.753269
$784$	−3.04166	−0.108631
$785$	3.89452	0.139001
$786$	5.85378	0.208797
$787$	−9.62665	−0.343153	−0.171577	−	0.985171i	$-0.554886\pi$
$787$	−9.62665	−0.343153	−0.171577	+	0.985171i	$0.554886\pi$
$788$	−8.47379	−0.301866
$789$	−27.2606	−0.970502
$790$	6.29489	0.223962
$791$	−39.3229	−1.39816
$792$	15.0941	0.536346
$793$	81.3033	2.88717
$794$	−56.5207	−2.00584
$795$	14.4534	0.512609
$796$	−76.8831	−2.72505
$797$	−54.2238	−1.92071	−0.960353	−	0.278788i	$-0.910067\pi$
$797$	−54.2238	−1.92071	−0.960353	+	0.278788i	$0.910067\pi$
$798$	28.6039	1.01257
$799$	−39.7349	−1.40572
$800$	61.5849	2.17736
$801$	−22.9909	−0.812343
$802$	−55.2042	−1.94933
$803$	−13.3347	−0.470573
$804$	69.6806	2.45744
$805$	−0.933175	−0.0328901
$806$	−69.7668	−2.45743
$807$	66.7991	2.35144
$808$	4.67153	0.164344
$809$	−4.39708	−0.154593	−0.0772966	−	0.997008i	$-0.524629\pi$
$809$	−4.39708	−0.154593	−0.0772966	+	0.997008i	$0.524629\pi$
$810$	30.1215	1.05836
$811$	−3.89507	−0.136774	−0.0683871	−	0.997659i	$-0.521785\pi$
$811$	−3.89507	−0.136774	−0.0683871	+	0.997659i	$0.521785\pi$
$812$	−107.301	−3.76552
$813$	2.28014	0.0799681
$814$	3.92062	0.137418
$815$	9.88049	0.346098
$816$	163.942	5.73910
$817$	6.54095	0.228839
$818$	−70.6623	−2.47065
$819$	26.6925	0.932711
$820$	−52.1757	−1.82205
$821$	35.3423	1.23345	0.616727	−	0.787177i	$-0.288458\pi$
$821$	35.3423	1.23345	0.616727	+	0.787177i	$0.288458\pi$
$822$	−67.1287	−2.34138
$823$	−24.8088	−0.864780	−0.432390	−	0.901687i	$-0.642330\pi$
$823$	−24.8088	−0.864780	−0.432390	+	0.901687i	$0.642330\pi$
$824$	36.3228	1.26536
$825$	−8.71991	−0.303588
$826$	17.7939	0.619129
$827$	−9.39083	−0.326551	−0.163276	−	0.986581i	$-0.552206\pi$
$827$	−9.39083	−0.326551	−0.163276	+	0.986581i	$0.552206\pi$
$828$	3.29156	0.114390
$829$	8.08603	0.280840	0.140420	−	0.990092i	$-0.455155\pi$
$829$	8.08603	0.280840	0.140420	+	0.990092i	$0.455155\pi$
$830$	10.4118	0.361399
$831$	28.6878	0.995170
$832$	−98.0156	−3.39808
$833$	1.56428	0.0541992
$834$	46.5202	1.61086
$835$	15.1959	0.525877
$836$	9.65038	0.333765
$837$	−12.0203	−0.415481
$838$	48.4306	1.67301
$839$	−55.1420	−1.90371	−0.951856	−	0.306544i	$-0.900827\pi$
$839$	−55.1420	−1.90371	−0.951856	+	0.306544i	$0.900827\pi$
$840$	−48.1271	−1.66054
$841$	35.8298	1.23551
$842$	−81.4100	−2.80557
$843$	−49.3663	−1.70026
$844$	94.7169	3.26029
$845$	19.5937	0.674042
$846$	−30.8959	−1.06222
$847$	−2.59765	−0.0892562
$848$	−78.6295	−2.70015
$849$	10.6291	0.364791
$850$	−65.8693	−2.25930
$851$	0.521660	0.0178823
$852$	−138.185	−4.73415
$853$	44.7391	1.53184	0.765919	−	0.642937i	$-0.222284\pi$
$853$	44.7391	1.53184	0.765919	+	0.642937i	$0.222284\pi$
$854$	−99.1088	−3.39143
$855$	−3.43471	−0.117465
$856$	−155.793	−5.32488
$857$	20.2111	0.690399	0.345199	−	0.938529i	$-0.387811\pi$
$857$	20.2111	0.690399	0.345199	+	0.938529i	$0.387811\pi$
$858$	33.3092	1.13716
$859$	1.84371	0.0629065	0.0314533	−	0.999505i	$-0.489986\pi$
$859$	1.84371	0.0629065	0.0314533	+	0.999505i	$0.489986\pi$
$860$	−18.0371	−0.615059
$861$	−57.2794	−1.95208
$862$	−58.4568	−1.99105
$863$	23.5864	0.802892	0.401446	−	0.915883i	$-0.368508\pi$
$863$	23.5864	0.802892	0.401446	+	0.915883i	$0.368508\pi$
$864$	−40.5313	−1.37890
$865$	6.94180	0.236028
$866$	−15.4713	−0.525737
$867$	−47.0451	−1.59774
$868$	61.1907	2.07695
$869$	2.33151	0.0790912
$870$	47.6566	1.61571
$871$	35.2548	1.19456
$872$	20.5748	0.696749
$873$	−10.0945	−0.341647
$874$	1.78461	0.0603655
$875$	23.5799	0.797146
$876$	−149.970	−5.06702
$877$	2.95495	0.0997814	0.0498907	−	0.998755i	$-0.484113\pi$
$877$	2.95495	0.0997814	0.0498907	+	0.998755i	$0.484113\pi$
$878$	−21.3681	−0.721138
$879$	57.6473	1.94439
$880$	−12.1927	−0.411014
$881$	13.9673	0.470571	0.235285	−	0.971926i	$-0.424397\pi$
$881$	13.9673	0.470571	0.235285	+	0.971926i	$0.424397\pi$
$882$	1.21631	0.0409553
$883$	−10.8733	−0.365917	−0.182959	−	0.983121i	$-0.558567\pi$
$883$	−10.8733	−0.365917	−0.182959	+	0.983121i	$0.558567\pi$
$884$	181.037	6.08893
$885$	−5.68623	−0.191141
$886$	3.18598	0.107035
$887$	2.21780	0.0744663	0.0372331	−	0.999307i	$-0.488146\pi$
$887$	2.21780	0.0744663	0.0372331	+	0.999307i	$0.488146\pi$
$888$	26.9038	0.902832
$889$	26.5229	0.889549
$890$	34.3735	1.15220
$891$	11.1565	0.373755
$892$	−103.114	−3.45253
$893$	−12.0525	−0.403321
$894$	90.6113	3.03049
$895$	18.8056	0.628600
$896$	39.0438	1.30436
$897$	4.43197	0.147979
$898$	46.9387	1.56636
$899$	−36.9707	−1.23304
$900$	−36.8506	−1.22835
$901$	40.4381	1.34719
$902$	−26.8587	−0.894297
$903$	−19.8014	−0.658951
$904$	−126.529	−4.20830
$905$	−4.97770	−0.165464
$906$	20.0073	0.664697
$907$	−13.8012	−0.458263	−0.229131	−	0.973396i	$-0.573589\pi$
$907$	−13.8012	−0.458263	−0.229131	+	0.973396i	$0.573589\pi$
$908$	53.1032	1.76229
$909$	−1.00929	−0.0334760
$910$	−39.9078	−1.32293
$911$	−2.94092	−0.0974371	−0.0487186	−	0.998813i	$-0.515514\pi$
$911$	−2.94092	−0.0974371	−0.0487186	+	0.998813i	$0.515514\pi$
$912$	49.7271	1.64663
$913$	3.85634	0.127626
$914$	43.4454	1.43705
$915$	31.6712	1.04702
$916$	10.8909	0.359845
$917$	−2.59765	−0.0857818
$918$	43.3510	1.43080
$919$	−43.6792	−1.44084	−0.720422	−	0.693536i	$-0.756052\pi$
$919$	−43.6792	−1.44084	−0.720422	+	0.693536i	$0.756052\pi$
$920$	−3.00267	−0.0989953
$921$	−26.3167	−0.867166
$922$	69.3721	2.28465
$923$	−69.9147	−2.30127
$924$	−29.2146	−0.961091
$925$	−5.84023	−0.192026
$926$	96.1932	3.16111
$927$	−7.84758	−0.257749
$928$	−124.662	−4.09224
$929$	19.7100	0.646663	0.323331	−	0.946286i	$-0.395197\pi$
$929$	19.7100	0.646663	0.323331	+	0.946286i	$0.395197\pi$
$930$	−27.1773	−0.891178
$931$	0.474482	0.0155505
$932$	−106.823	−3.49909
$933$	−42.0590	−1.37695
$934$	42.8226	1.40120
$935$	6.27052	0.205068
$936$	85.8884	2.80735
$937$	14.5574	0.475571	0.237786	−	0.971318i	$-0.423578\pi$
$937$	14.5574	0.475571	0.237786	+	0.971318i	$0.423578\pi$
$938$	−42.9756	−1.40320
$939$	−61.2959	−2.00032
$940$	33.2354	1.08402
$941$	18.7698	0.611879	0.305939	−	0.952051i	$-0.401030\pi$
$941$	18.7698	0.611879	0.305939	+	0.952051i	$0.401030\pi$
$942$	22.5471	0.734625
$943$	−3.57370	−0.116376
$944$	30.9343	1.00682
$945$	−6.87579	−0.223669
$946$	−9.28502	−0.301882
$947$	−50.3535	−1.63627	−0.818135	−	0.575027i	$-0.804992\pi$
$947$	−50.3535	−1.63627	−0.818135	+	0.575027i	$0.804992\pi$
$948$	26.2216	0.851637
$949$	−75.8773	−2.46308
$950$	−19.9796	−0.648225
$951$	23.0654	0.747946
$952$	−134.651	−4.36406
$953$	−15.2308	−0.493375	−0.246687	−	0.969095i	$-0.579342\pi$
$953$	−15.2308	−0.493375	−0.246687	+	0.969095i	$0.579342\pi$
$954$	31.4427	1.01799
$955$	−17.4463	−0.564548
$956$	−78.2569	−2.53101
$957$	17.6511	0.570580
$958$	27.0300	0.873300
$959$	29.7887	0.961928
$960$	−38.1814	−1.23230
$961$	−9.91659	−0.319890
$962$	22.3091	0.719274
$963$	33.6592	1.08465
$964$	−39.5113	−1.27257
$965$	17.1787	0.553002
$966$	−5.40257	−0.173825
$967$	15.9115	0.511681	0.255840	−	0.966719i	$-0.417648\pi$
$967$	15.9115	0.511681	0.255840	+	0.966719i	$0.417648\pi$
$968$	−8.35844	−0.268650
$969$	−25.5740	−0.821555
$970$	15.0922	0.484581
$971$	−13.3332	−0.427884	−0.213942	−	0.976846i	$-0.568630\pi$
$971$	−13.3332	−0.427884	−0.213942	+	0.976846i	$0.568630\pi$
$972$	85.1817	2.73221
$973$	−20.6436	−0.661803
$974$	−52.0410	−1.66750
$975$	−49.6180	−1.58905
$976$	−172.298	−5.51512
$977$	−57.5112	−1.83995	−0.919973	−	0.391981i	$-0.871790\pi$
$977$	−57.5112	−1.83995	−0.919973	+	0.391981i	$0.871790\pi$
$978$	57.2026	1.82914
$979$	12.7313	0.406895
$980$	−1.30841	−0.0417958
$981$	−4.44520	−0.141924
$982$	−51.2116	−1.63423
$983$	34.0980	1.08756	0.543779	−	0.839229i	$-0.316993\pi$
$983$	34.0980	1.08756	0.543779	+	0.839229i	$0.316993\pi$
$984$	−184.308	−5.87552
$985$	−1.67010	−0.0532137
$986$	133.335	4.24624
$987$	36.4865	1.16138
$988$	54.9126	1.74700
$989$	−1.23542	−0.0392842
$990$	4.87565	0.154958
$991$	5.88125	0.186824	0.0934121	−	0.995628i	$-0.470223\pi$
$991$	5.88125	0.186824	0.0934121	+	0.995628i	$0.470223\pi$
$992$	71.0915	2.25716
$993$	−9.58993	−0.304327
$994$	85.2261	2.70321
$995$	−15.1528	−0.480378
$996$	43.3706	1.37425
$997$	−18.3412	−0.580871	−0.290435	−	0.956895i	$-0.593800\pi$
$997$	−18.3412	−0.580871	−0.290435	+	0.956895i	$0.593800\pi$
$998$	−31.8913	−1.00950
$999$	3.84367	0.121608

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.67025 q^{2} -2.19223 q^{3} +5.13021 q^{4} +1.01111 q^{5} +5.85378 q^{6} -2.59765 q^{7} -8.35844 q^{8} +1.80585 q^{9} +O(q^{10})\)	\(q-2.67025 q^{2} -2.19223 q^{3} +5.13021 q^{4} +1.01111 q^{5} +5.85378 q^{6} -2.59765 q^{7} -8.35844 q^{8} +1.80585 q^{9} -2.69992 q^{10} -1.00000 q^{11} -11.2466 q^{12} -5.69020 q^{13} +6.93635 q^{14} -2.21658 q^{15} +12.0587 q^{16} -6.20161 q^{17} -4.82207 q^{18} -1.88109 q^{19} +5.18722 q^{20} +5.69462 q^{21} +2.67025 q^{22} +0.355291 q^{23} +18.3236 q^{24} -3.97765 q^{25} +15.1942 q^{26} +2.61784 q^{27} -13.3265 q^{28} +8.05170 q^{29} +5.91882 q^{30} -4.59167 q^{31} -15.4827 q^{32} +2.19223 q^{33} +16.5598 q^{34} -2.62651 q^{35} +9.26440 q^{36} +1.46826 q^{37} +5.02297 q^{38} +12.4742 q^{39} -8.45131 q^{40} -10.0585 q^{41} -15.2060 q^{42} -3.47722 q^{43} -5.13021 q^{44} +1.82592 q^{45} -0.948714 q^{46} +6.40718 q^{47} -26.4353 q^{48} -0.252238 q^{49} +10.6213 q^{50} +13.5953 q^{51} -29.1919 q^{52} -6.52058 q^{53} -6.99028 q^{54} -1.01111 q^{55} +21.7123 q^{56} +4.12377 q^{57} -21.5000 q^{58} +2.56531 q^{59} -11.3715 q^{60} -14.2883 q^{61} +12.2609 q^{62} -4.69096 q^{63} +17.2253 q^{64} -5.75342 q^{65} -5.85378 q^{66} -6.19571 q^{67} -31.8156 q^{68} -0.778878 q^{69} +7.01342 q^{70} +12.2869 q^{71} -15.0941 q^{72} +13.3347 q^{73} -3.92062 q^{74} +8.71991 q^{75} -9.65038 q^{76} +2.59765 q^{77} -33.3092 q^{78} -2.33151 q^{79} +12.1927 q^{80} -11.1565 q^{81} +26.8587 q^{82} -3.85634 q^{83} +29.2146 q^{84} -6.27052 q^{85} +9.28502 q^{86} -17.6511 q^{87} +8.35844 q^{88} -12.7313 q^{89} -4.87565 q^{90} +14.7811 q^{91} +1.82272 q^{92} +10.0660 q^{93} -17.1088 q^{94} -1.90199 q^{95} +33.9416 q^{96} -5.58988 q^{97} +0.673538 q^{98} -1.80585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 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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