LMFDB - Embedded newform 1441.2.a.d.1.14

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:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-0.200388 q^{2} +2.28550 q^{3} -1.95984 q^{4} -0.516505 q^{5} -0.457986 q^{6} -2.27895 q^{7} +0.793506 q^{8} +2.22349 q^{9} +O(q^{10})$	\(q-0.200388 q^{2} +2.28550 q^{3} -1.95984 q^{4} -0.516505 q^{5} -0.457986 q^{6} -2.27895 q^{7} +0.793506 q^{8} +2.22349 q^{9} +0.103502 q^{10} -1.00000 q^{11} -4.47922 q^{12} +2.92146 q^{13} +0.456675 q^{14} -1.18047 q^{15} +3.76068 q^{16} -6.69800 q^{17} -0.445561 q^{18} +6.33139 q^{19} +1.01227 q^{20} -5.20854 q^{21} +0.200388 q^{22} -7.85148 q^{23} +1.81355 q^{24} -4.73322 q^{25} -0.585427 q^{26} -1.77471 q^{27} +4.46640 q^{28} -1.56615 q^{29} +0.236552 q^{30} +7.96858 q^{31} -2.34061 q^{32} -2.28550 q^{33} +1.34220 q^{34} +1.17709 q^{35} -4.35769 q^{36} -5.74931 q^{37} -1.26873 q^{38} +6.67699 q^{39} -0.409850 q^{40} -9.04129 q^{41} +1.04373 q^{42} -9.60515 q^{43} +1.95984 q^{44} -1.14844 q^{45} +1.57334 q^{46} +3.84012 q^{47} +8.59502 q^{48} -1.80637 q^{49} +0.948482 q^{50} -15.3083 q^{51} -5.72562 q^{52} -7.03493 q^{53} +0.355632 q^{54} +0.516505 q^{55} -1.80836 q^{56} +14.4704 q^{57} +0.313837 q^{58} -2.41016 q^{59} +2.31354 q^{60} -6.01720 q^{61} -1.59681 q^{62} -5.06723 q^{63} -7.05233 q^{64} -1.50895 q^{65} +0.457986 q^{66} +13.4208 q^{67} +13.1270 q^{68} -17.9445 q^{69} -0.235875 q^{70} -11.9294 q^{71} +1.76435 q^{72} +4.01271 q^{73} +1.15209 q^{74} -10.8178 q^{75} -12.4085 q^{76} +2.27895 q^{77} -1.33799 q^{78} -0.201845 q^{79} -1.94241 q^{80} -10.7266 q^{81} +1.81177 q^{82} +14.3766 q^{83} +10.2079 q^{84} +3.45955 q^{85} +1.92476 q^{86} -3.57942 q^{87} -0.793506 q^{88} -4.05998 q^{89} +0.230135 q^{90} -6.65788 q^{91} +15.3877 q^{92} +18.2122 q^{93} -0.769514 q^{94} -3.27020 q^{95} -5.34945 q^{96} +6.89957 q^{97} +0.361975 q^{98} -2.22349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.200388	−0.141696	−0.0708479	−	0.997487i	$-0.522570\pi$
$2$	−0.200388	−0.141696	−0.0708479	+	0.997487i	$0.522570\pi$
$3$	2.28550	1.31953	0.659766	−	0.751471i	$-0.270656\pi$
$3$	2.28550	1.31953	0.659766	+	0.751471i	$0.270656\pi$
$4$	−1.95984	−0.979922
$5$	−0.516505	−0.230988	−0.115494	−	0.993308i	$-0.536845\pi$
$5$	−0.516505	−0.230988	−0.115494	+	0.993308i	$0.536845\pi$
$6$	−0.457986	−0.186972
$7$	−2.27895	−0.861364	−0.430682	−	0.902504i	$-0.641727\pi$
$7$	−2.27895	−0.861364	−0.430682	+	0.902504i	$0.641727\pi$
$8$	0.793506	0.280547
$9$	2.22349	0.741163
$10$	0.103502	0.0327301
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.47922	−1.29304
$13$	2.92146	0.810269	0.405134	−	0.914257i	$-0.367225\pi$
$13$	2.92146	0.810269	0.405134	+	0.914257i	$0.367225\pi$
$14$	0.456675	0.122052
$15$	−1.18047	−0.304796
$16$	3.76068	0.940170
$17$	−6.69800	−1.62450	−0.812252	−	0.583307i	$-0.801759\pi$
$17$	−6.69800	−1.62450	−0.812252	+	0.583307i	$0.801759\pi$
$18$	−0.445561	−0.105020
$19$	6.33139	1.45252	0.726260	−	0.687420i	$-0.241257\pi$
$19$	6.33139	1.45252	0.726260	+	0.687420i	$0.241257\pi$
$20$	1.01227	0.226351
$21$	−5.20854	−1.13660
$22$	0.200388	0.0427229
$23$	−7.85148	−1.63715	−0.818573	−	0.574403i	$-0.805234\pi$
$23$	−7.85148	−1.63715	−0.818573	+	0.574403i	$0.805234\pi$
$24$	1.81355	0.370190
$25$	−4.73322	−0.946644
$26$	−0.585427	−0.114812
$27$	−1.77471	−0.341544
$28$	4.46640	0.844069
$29$	−1.56615	−0.290826	−0.145413	−	0.989371i	$-0.546451\pi$
$29$	−1.56615	−0.290826	−0.145413	+	0.989371i	$0.546451\pi$
$30$	0.236552	0.0431883
$31$	7.96858	1.43120	0.715600	−	0.698511i	$-0.246153\pi$
$31$	7.96858	1.43120	0.715600	+	0.698511i	$0.246153\pi$
$32$	−2.34061	−0.413765
$33$	−2.28550	−0.397854
$34$	1.34220	0.230185
$35$	1.17709	0.198965
$36$	−4.35769	−0.726282
$37$	−5.74931	−0.945180	−0.472590	−	0.881282i	$-0.656681\pi$
$37$	−5.74931	−0.945180	−0.472590	+	0.881282i	$0.656681\pi$
$38$	−1.26873	−0.205816
$39$	6.67699	1.06917
$40$	−0.409850	−0.0648030
$41$	−9.04129	−1.41201	−0.706006	−	0.708206i	$-0.749505\pi$
$41$	−9.04129	−1.41201	−0.706006	+	0.708206i	$0.749505\pi$
$42$	1.04373	0.161051
$43$	−9.60515	−1.46477	−0.732386	−	0.680890i	$-0.761593\pi$
$43$	−9.60515	−1.46477	−0.732386	+	0.680890i	$0.761593\pi$
$44$	1.95984	0.295458
$45$	−1.14844	−0.171200
$46$	1.57334	0.231977
$47$	3.84012	0.560139	0.280070	−	0.959980i	$-0.409642\pi$
$47$	3.84012	0.560139	0.280070	+	0.959980i	$0.409642\pi$
$48$	8.59502	1.24058
$49$	−1.80637	−0.258053
$50$	0.948482	0.134136
$51$	−15.3083	−2.14358
$52$	−5.72562	−0.794000
$53$	−7.03493	−0.966322	−0.483161	−	0.875532i	$-0.660511\pi$
$53$	−7.03493	−0.966322	−0.483161	+	0.875532i	$0.660511\pi$
$54$	0.355632	0.0483953
$55$	0.516505	0.0696456
$56$	−1.80836	−0.241653
$57$	14.4704	1.91665
$58$	0.313837	0.0412088
$59$	−2.41016	−0.313777	−0.156888	−	0.987616i	$-0.550146\pi$
$59$	−2.41016	−0.313777	−0.156888	+	0.987616i	$0.550146\pi$
$60$	2.31354	0.298677
$61$	−6.01720	−0.770424	−0.385212	−	0.922828i	$-0.625872\pi$
$61$	−6.01720	−0.770424	−0.385212	+	0.922828i	$0.625872\pi$
$62$	−1.59681	−0.202795
$63$	−5.06723	−0.638411
$64$	−7.05233	−0.881541
$65$	−1.50895	−0.187162
$66$	0.457986	0.0563742
$67$	13.4208	1.63961	0.819804	−	0.572645i	$-0.194082\pi$
$67$	13.4208	1.63961	0.819804	+	0.572645i	$0.194082\pi$
$68$	13.1270	1.59189
$69$	−17.9445	−2.16027
$70$	−0.235875	−0.0281925
$71$	−11.9294	−1.41575	−0.707877	−	0.706336i	$-0.750347\pi$
$71$	−11.9294	−1.41575	−0.707877	+	0.706336i	$0.750347\pi$
$72$	1.76435	0.207931
$73$	4.01271	0.469652	0.234826	−	0.972037i	$-0.424548\pi$
$73$	4.01271	0.469652	0.234826	+	0.972037i	$0.424548\pi$
$74$	1.15209	0.133928
$75$	−10.8178	−1.24913
$76$	−12.4085	−1.42336
$77$	2.27895	0.259711
$78$	−1.33799	−0.151498
$79$	−0.201845	−0.0227093	−0.0113547	−	0.999936i	$-0.503614\pi$
$79$	−0.201845	−0.0227093	−0.0113547	+	0.999936i	$0.503614\pi$
$80$	−1.94241	−0.217168
$81$	−10.7266	−1.19184
$82$	1.81177	0.200076
$83$	14.3766	1.57804	0.789018	−	0.614369i	$-0.210590\pi$
$83$	14.3766	1.57804	0.789018	+	0.614369i	$0.210590\pi$
$84$	10.2079	1.11378
$85$	3.45955	0.375241
$86$	1.92476	0.207552
$87$	−3.57942	−0.383754
$88$	−0.793506	−0.0845880
$89$	−4.05998	−0.430357	−0.215178	−	0.976575i	$-0.569033\pi$
$89$	−4.05998	−0.430357	−0.215178	+	0.976575i	$0.569033\pi$
$90$	0.230135	0.0242583
$91$	−6.65788	−0.697936
$92$	15.3877	1.60428
$93$	18.2122	1.88851
$94$	−0.769514	−0.0793694
$95$	−3.27020	−0.335515
$96$	−5.34945	−0.545976
$97$	6.89957	0.700546	0.350273	−	0.936648i	$-0.386089\pi$
$97$	6.89957	0.700546	0.350273	+	0.936648i	$0.386089\pi$
$98$	0.361975	0.0365650
$99$	−2.22349	−0.223469
$100$	9.27638	0.927638
$101$	−13.7707	−1.37023	−0.685117	−	0.728433i	$-0.740249\pi$
$101$	−13.7707	−1.37023	−0.685117	+	0.728433i	$0.740249\pi$
$102$	3.06759	0.303737
$103$	−16.9893	−1.67400	−0.837002	−	0.547200i	$-0.815694\pi$
$103$	−16.9893	−1.67400	−0.837002	+	0.547200i	$0.815694\pi$
$104$	2.31820	0.227318
$105$	2.69024	0.262540
$106$	1.40972	0.136924
$107$	9.61476	0.929494	0.464747	−	0.885443i	$-0.346145\pi$
$107$	9.61476	0.929494	0.464747	+	0.885443i	$0.346145\pi$
$108$	3.47816	0.334686
$109$	11.7241	1.12297	0.561483	−	0.827488i	$-0.310231\pi$
$109$	11.7241	1.12297	0.561483	+	0.827488i	$0.310231\pi$
$110$	−0.103502	−0.00986849
$111$	−13.1400	−1.24720
$112$	−8.57042	−0.809828
$113$	7.09034	0.667003	0.333501	−	0.942750i	$-0.391770\pi$
$113$	7.09034	0.667003	0.333501	+	0.942750i	$0.391770\pi$
$114$	−2.89969	−0.271581
$115$	4.05533	0.378161
$116$	3.06940	0.284987
$117$	6.49584	0.600541
$118$	0.482968	0.0444609
$119$	15.2644	1.39929
$120$	−0.936710	−0.0855096
$121$	1.00000	0.0909091
$122$	1.20578	0.109166
$123$	−20.6638	−1.86319
$124$	−15.6172	−1.40246
$125$	5.02726	0.449652
$126$	1.01541	0.0904601
$127$	5.39355	0.478600	0.239300	−	0.970946i	$-0.423082\pi$
$127$	5.39355	0.478600	0.239300	+	0.970946i	$0.423082\pi$
$128$	6.09442	0.538676
$129$	−21.9525	−1.93281
$130$	0.302376	0.0265201
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	4.47922	0.389866
$133$	−14.4289	−1.25115
$134$	−2.68936	−0.232326
$135$	0.916649	0.0788926
$136$	−5.31490	−0.455749
$137$	14.7453	1.25978	0.629888	−	0.776686i	$-0.283101\pi$
$137$	14.7453	1.25978	0.629888	+	0.776686i	$0.283101\pi$
$138$	3.59587	0.306101
$139$	9.61220	0.815296	0.407648	−	0.913139i	$-0.366349\pi$
$139$	9.61220	0.815296	0.407648	+	0.913139i	$0.366349\pi$
$140$	−2.30692	−0.194970
$141$	8.77658	0.739121
$142$	2.39050	0.200606
$143$	−2.92146	−0.244305
$144$	8.36183	0.696819
$145$	0.808923	0.0671774
$146$	−0.804100	−0.0665478
$147$	−4.12845	−0.340508
$148$	11.2678	0.926203
$149$	13.9819	1.14544	0.572720	−	0.819751i	$-0.305888\pi$
$149$	13.9819	1.14544	0.572720	+	0.819751i	$0.305888\pi$
$150$	2.16775	0.176996
$151$	5.27027	0.428888	0.214444	−	0.976736i	$-0.431206\pi$
$151$	5.27027	0.428888	0.214444	+	0.976736i	$0.431206\pi$
$152$	5.02399	0.407500
$153$	−14.8929	−1.20402
$154$	−0.456675	−0.0368000
$155$	−4.11582	−0.330590
$156$	−13.0859	−1.04771
$157$	−2.55851	−0.204191	−0.102096	−	0.994775i	$-0.532555\pi$
$157$	−2.55851	−0.204191	−0.102096	+	0.994775i	$0.532555\pi$
$158$	0.0404473	0.00321782
$159$	−16.0783	−1.27509
$160$	1.20894	0.0955748
$161$	17.8932	1.41018
$162$	2.14948	0.168879
$163$	−19.0844	−1.49481	−0.747404	−	0.664369i	$-0.768700\pi$
$163$	−19.0844	−1.49481	−0.747404	+	0.664369i	$0.768700\pi$
$164$	17.7195	1.38366
$165$	1.18047	0.0918995
$166$	−2.88090	−0.223601
$167$	1.50809	0.116700	0.0583498	−	0.998296i	$-0.481416\pi$
$167$	1.50809	0.116700	0.0583498	+	0.998296i	$0.481416\pi$
$168$	−4.13301	−0.318868
$169$	−4.46504	−0.343465
$170$	−0.693254	−0.0531701
$171$	14.0778	1.07655
$172$	18.8246	1.43536
$173$	19.9347	1.51561	0.757804	−	0.652482i	$-0.226272\pi$
$173$	19.9347	1.51561	0.757804	+	0.652482i	$0.226272\pi$
$174$	0.717273	0.0543763
$175$	10.7868	0.815405
$176$	−3.76068	−0.283472
$177$	−5.50842	−0.414038
$178$	0.813571	0.0609797
$179$	7.91444	0.591553	0.295776	−	0.955257i	$-0.404422\pi$
$179$	7.91444	0.591553	0.295776	+	0.955257i	$0.404422\pi$
$180$	2.25077	0.167763
$181$	−9.10379	−0.676679	−0.338340	−	0.941024i	$-0.609865\pi$
$181$	−9.10379	−0.676679	−0.338340	+	0.941024i	$0.609865\pi$
$182$	1.33416	0.0988946
$183$	−13.7523	−1.01660
$184$	−6.23019	−0.459296
$185$	2.96955	0.218326
$186$	−3.64950	−0.267594
$187$	6.69800	0.489806
$188$	−7.52604	−0.548893
$189$	4.04449	0.294193
$190$	0.655308	0.0475411
$191$	−20.5504	−1.48697	−0.743487	−	0.668751i	$-0.766829\pi$
$191$	−20.5504	−1.48697	−0.743487	+	0.668751i	$0.766829\pi$
$192$	−16.1181	−1.16322
$193$	25.8771	1.86267	0.931337	−	0.364159i	$-0.118643\pi$
$193$	25.8771	1.86267	0.931337	+	0.364159i	$0.118643\pi$
$194$	−1.38259	−0.0992644
$195$	−3.44870	−0.246967
$196$	3.54020	0.252871
$197$	3.98209	0.283713	0.141856	−	0.989887i	$-0.454693\pi$
$197$	3.98209	0.283713	0.141856	+	0.989887i	$0.454693\pi$
$198$	0.445561	0.0316646
$199$	27.9422	1.98077	0.990383	−	0.138351i	$-0.0441801\pi$
$199$	27.9422	1.98077	0.990383	+	0.138351i	$0.0441801\pi$
$200$	−3.75584	−0.265578
$201$	30.6731	2.16351
$202$	2.75948	0.194156
$203$	3.56917	0.250507
$204$	30.0018	2.10055
$205$	4.66988	0.326158
$206$	3.40445	0.237199
$207$	−17.4577	−1.21339
$208$	10.9867	0.761790
$209$	−6.33139	−0.437951
$210$	−0.539092	−0.0372009
$211$	−12.0997	−0.832975	−0.416487	−	0.909141i	$-0.636739\pi$
$211$	−12.0997	−0.832975	−0.416487	+	0.909141i	$0.636739\pi$
$212$	13.7874	0.946921
$213$	−27.2645	−1.86813
$214$	−1.92668	−0.131705
$215$	4.96111	0.338345
$216$	−1.40825	−0.0958190
$217$	−18.1600	−1.23278
$218$	−2.34937	−0.159120
$219$	9.17103	0.619721
$220$	−1.01227	−0.0682473
$221$	−19.5680	−1.31628
$222$	2.63310	0.176722
$223$	−23.9842	−1.60610	−0.803052	−	0.595909i	$-0.796792\pi$
$223$	−23.9842	−1.60610	−0.803052	+	0.595909i	$0.796792\pi$
$224$	5.33414	0.356402
$225$	−10.5243	−0.701618
$226$	−1.42082	−0.0945115
$227$	−23.0880	−1.53241	−0.766203	−	0.642599i	$-0.777856\pi$
$227$	−23.0880	−1.53241	−0.766203	+	0.642599i	$0.777856\pi$
$228$	−28.3596	−1.87816
$229$	−6.85492	−0.452986	−0.226493	−	0.974013i	$-0.572726\pi$
$229$	−6.85492	−0.452986	−0.226493	+	0.974013i	$0.572726\pi$
$230$	−0.812640	−0.0535839
$231$	5.20854	0.342697
$232$	−1.24275	−0.0815903
$233$	−2.83557	−0.185764	−0.0928820	−	0.995677i	$-0.529608\pi$
$233$	−2.83557	−0.185764	−0.0928820	+	0.995677i	$0.529608\pi$
$234$	−1.30169	−0.0850941
$235$	−1.98344	−0.129386
$236$	4.72355	0.307477
$237$	−0.461316	−0.0299657
$238$	−3.05881	−0.198273
$239$	−15.1332	−0.978883	−0.489441	−	0.872036i	$-0.662799\pi$
$239$	−15.1332	−0.978883	−0.489441	+	0.872036i	$0.662799\pi$
$240$	−4.43937	−0.286560
$241$	−16.8372	−1.08458	−0.542290	−	0.840191i	$-0.682443\pi$
$241$	−16.8372	−1.08458	−0.542290	+	0.840191i	$0.682443\pi$
$242$	−0.200388	−0.0128814
$243$	−19.1914	−1.23113
$244$	11.7928	0.754955
$245$	0.932999	0.0596071
$246$	4.14079	0.264007
$247$	18.4969	1.17693
$248$	6.32312	0.401518
$249$	32.8577	2.08227
$250$	−1.00740	−0.0637138
$251$	−11.7411	−0.741092	−0.370546	−	0.928814i	$-0.620829\pi$
$251$	−11.7411	−0.741092	−0.370546	+	0.928814i	$0.620829\pi$
$252$	9.93098	0.625593
$253$	7.85148	0.493618
$254$	−1.08080	−0.0678156
$255$	7.90679	0.495143
$256$	12.8834	0.805213
$257$	−18.9084	−1.17947	−0.589735	−	0.807597i	$-0.700768\pi$
$257$	−18.9084	−1.17947	−0.589735	+	0.807597i	$0.700768\pi$
$258$	4.39903	0.273871
$259$	13.1024	0.814144
$260$	2.95731	0.183405
$261$	−3.48231	−0.215549
$262$	0.200388	0.0123800
$263$	11.2215	0.691945	0.345972	−	0.938245i	$-0.387549\pi$
$263$	11.2215	0.691945	0.345972	+	0.938245i	$0.387549\pi$
$264$	−1.81355	−0.111617
$265$	3.63358	0.223209
$266$	2.89139	0.177282
$267$	−9.27905	−0.567869
$268$	−26.3026	−1.60669
$269$	−18.0238	−1.09893	−0.549464	−	0.835517i	$-0.685168\pi$
$269$	−18.0238	−1.09893	−0.549464	+	0.835517i	$0.685168\pi$
$270$	−0.183686	−0.0111787
$271$	−7.70635	−0.468128	−0.234064	−	0.972221i	$-0.575202\pi$
$271$	−7.70635	−0.468128	−0.234064	+	0.972221i	$0.575202\pi$
$272$	−25.1890	−1.52731
$273$	−15.2166	−0.920948
$274$	−2.95478	−0.178505
$275$	4.73322	0.285424
$276$	35.1685	2.11689
$277$	1.31423	0.0789646	0.0394823	−	0.999220i	$-0.487429\pi$
$277$	1.31423	0.0789646	0.0394823	+	0.999220i	$0.487429\pi$
$278$	−1.92617	−0.115524
$279$	17.7180	1.06075
$280$	0.934030	0.0558189
$281$	−19.8176	−1.18222	−0.591108	−	0.806592i	$-0.701309\pi$
$281$	−19.8176	−1.18222	−0.591108	+	0.806592i	$0.701309\pi$
$282$	−1.75872	−0.104730
$283$	−16.3894	−0.974247	−0.487123	−	0.873333i	$-0.661954\pi$
$283$	−16.3894	−0.974247	−0.487123	+	0.873333i	$0.661954\pi$
$284$	23.3797	1.38733
$285$	−7.47402	−0.442722
$286$	0.585427	0.0346170
$287$	20.6047	1.21626
$288$	−5.20431	−0.306667
$289$	27.8632	1.63901
$290$	−0.162099	−0.00951875
$291$	15.7689	0.924392
$292$	−7.86429	−0.460223
$293$	19.3284	1.12918	0.564589	−	0.825372i	$-0.309035\pi$
$293$	19.3284	1.12918	0.564589	+	0.825372i	$0.309035\pi$
$294$	0.827292	0.0482486
$295$	1.24486	0.0724787
$296$	−4.56211	−0.265167
$297$	1.77471	0.102979
$298$	−2.80180	−0.162304
$299$	−22.9378	−1.32653
$300$	21.2011	1.22405
$301$	21.8897	1.26170
$302$	−1.05610	−0.0607717
$303$	−31.4728	−1.80807
$304$	23.8103	1.36562
$305$	3.10792	0.177959
$306$	2.98437	0.170605
$307$	23.6489	1.34972	0.674858	−	0.737948i	$-0.264205\pi$
$307$	23.6489	1.34972	0.674858	+	0.737948i	$0.264205\pi$
$308$	−4.46640	−0.254497
$309$	−38.8289	−2.20890
$310$	0.824761	0.0468433
$311$	4.11465	0.233320	0.116660	−	0.993172i	$-0.462781\pi$
$311$	4.11465	0.233320	0.116660	+	0.993172i	$0.462781\pi$
$312$	5.29823	0.299953
$313$	32.7321	1.85013	0.925063	−	0.379814i	$-0.124012\pi$
$313$	32.7321	1.85013	0.925063	+	0.379814i	$0.124012\pi$
$314$	0.512694	0.0289330
$315$	2.61725	0.147465
$316$	0.395585	0.0222534
$317$	−13.4062	−0.752968	−0.376484	−	0.926423i	$-0.622867\pi$
$317$	−13.4062	−0.752968	−0.376484	+	0.926423i	$0.622867\pi$
$318$	3.22190	0.180675
$319$	1.56615	0.0876873
$320$	3.64257	0.203626
$321$	21.9745	1.22650
$322$	−3.58558	−0.199816
$323$	−42.4076	−2.35962
$324$	21.0224	1.16791
$325$	−13.8279	−0.767036
$326$	3.82430	0.211808
$327$	26.7954	1.48179
$328$	−7.17432	−0.396135
$329$	−8.75146	−0.482483
$330$	−0.236552	−0.0130218
$331$	7.17686	0.394476	0.197238	−	0.980356i	$-0.436803\pi$
$331$	7.17686	0.394476	0.197238	+	0.980356i	$0.436803\pi$
$332$	−28.1759	−1.54635
$333$	−12.7835	−0.700533
$334$	−0.302204	−0.0165358
$335$	−6.93190	−0.378730
$336$	−19.5876	−1.06859
$337$	6.29285	0.342793	0.171397	−	0.985202i	$-0.445172\pi$
$337$	6.29285	0.342793	0.171397	+	0.985202i	$0.445172\pi$
$338$	0.894742	0.0486675
$339$	16.2049	0.880131
$340$	−6.78019	−0.367707
$341$	−7.96858	−0.431523
$342$	−2.82102	−0.152543
$343$	20.0693	1.08364
$344$	−7.62174	−0.410937
$345$	9.26844	0.498996
$346$	−3.99468	−0.214755
$347$	29.5978	1.58889	0.794447	−	0.607333i	$-0.207761\pi$
$347$	29.5978	1.58889	0.794447	+	0.607333i	$0.207761\pi$
$348$	7.01511	0.376049
$349$	−16.4421	−0.880124	−0.440062	−	0.897967i	$-0.645044\pi$
$349$	−16.4421	−0.880124	−0.440062	+	0.897967i	$0.645044\pi$
$350$	−2.16155	−0.115540
$351$	−5.18476	−0.276742
$352$	2.34061	0.124755
$353$	13.5492	0.721149	0.360575	−	0.932730i	$-0.382581\pi$
$353$	13.5492	0.721149	0.360575	+	0.932730i	$0.382581\pi$
$354$	1.10382	0.0586675
$355$	6.16158	0.327022
$356$	7.95692	0.421716
$357$	34.8868	1.84641
$358$	−1.58596	−0.0838206
$359$	0.246722	0.0130215	0.00651075	−	0.999979i	$-0.497928\pi$
$359$	0.246722	0.0130215	0.00651075	+	0.999979i	$0.497928\pi$
$360$	−0.911297	−0.0480296
$361$	21.0865	1.10981
$362$	1.82429	0.0958826
$363$	2.28550	0.119957
$364$	13.0484	0.683923
$365$	−2.07259	−0.108484
$366$	2.75579	0.144048
$367$	6.41564	0.334894	0.167447	−	0.985881i	$-0.446448\pi$
$367$	6.41564	0.334894	0.167447	+	0.985881i	$0.446448\pi$
$368$	−29.5269	−1.53920
$369$	−20.1032	−1.04653
$370$	−0.595062	−0.0309358
$371$	16.0323	0.832355
$372$	−35.6930	−1.85060
$373$	−6.75611	−0.349818	−0.174909	−	0.984585i	$-0.555963\pi$
$373$	−6.75611	−0.349818	−0.174909	+	0.984585i	$0.555963\pi$
$374$	−1.34220	−0.0694035
$375$	11.4898	0.593330
$376$	3.04716	0.157145
$377$	−4.57544	−0.235647
$378$	−0.810468	−0.0416860
$379$	−12.3897	−0.636416	−0.318208	−	0.948021i	$-0.603081\pi$
$379$	−12.3897	−0.636416	−0.318208	+	0.948021i	$0.603081\pi$
$380$	6.40907	0.328779
$381$	12.3269	0.631528
$382$	4.11805	0.210698
$383$	16.1970	0.827626	0.413813	−	0.910362i	$-0.364197\pi$
$383$	16.1970	0.827626	0.413813	+	0.910362i	$0.364197\pi$
$384$	13.9288	0.710799
$385$	−1.17709	−0.0599902
$386$	−5.18546	−0.263933
$387$	−21.3569	−1.08563
$388$	−13.5221	−0.686480
$389$	−0.443539	−0.0224883	−0.0112442	−	0.999937i	$-0.503579\pi$
$389$	−0.443539	−0.0224883	−0.0112442	+	0.999937i	$0.503579\pi$
$390$	0.691079	0.0349942
$391$	52.5892	2.65955
$392$	−1.43336	−0.0723958
$393$	−2.28550	−0.115288
$394$	−0.797965	−0.0402009
$395$	0.104254	0.00524559
$396$	4.35769	0.218982
$397$	12.9537	0.650129	0.325065	−	0.945692i	$-0.394614\pi$
$397$	12.9537	0.650129	0.325065	+	0.945692i	$0.394614\pi$
$398$	−5.59928	−0.280666
$399$	−32.9773	−1.65093
$400$	−17.8001	−0.890007
$401$	7.41448	0.370261	0.185131	−	0.982714i	$-0.440729\pi$
$401$	7.41448	0.370261	0.185131	+	0.982714i	$0.440729\pi$
$402$	−6.14653	−0.306561
$403$	23.2799	1.15966
$404$	26.9884	1.34272
$405$	5.54033	0.275301
$406$	−0.715220	−0.0354958
$407$	5.74931	0.284983
$408$	−12.1472	−0.601375
$409$	37.3768	1.84816	0.924081	−	0.382196i	$-0.124832\pi$
$409$	37.3768	1.84816	0.924081	+	0.382196i	$0.124832\pi$
$410$	−0.935788	−0.0462153
$411$	33.7003	1.66231
$412$	33.2964	1.64039
$413$	5.49266	0.270276
$414$	3.49831	0.171933
$415$	−7.42559	−0.364508
$416$	−6.83800	−0.335261
$417$	21.9686	1.07581
$418$	1.26873	0.0620558
$419$	−22.9200	−1.11972	−0.559858	−	0.828589i	$-0.689144\pi$
$419$	−22.9200	−1.11972	−0.559858	+	0.828589i	$0.689144\pi$
$420$	−5.27245	−0.257269
$421$	−33.4073	−1.62817	−0.814087	−	0.580743i	$-0.802762\pi$
$421$	−33.4073	−1.62817	−0.814087	+	0.580743i	$0.802762\pi$
$422$	2.42463	0.118029
$423$	8.53846	0.415154
$424$	−5.58226	−0.271098
$425$	31.7031	1.53783
$426$	5.46348	0.264706
$427$	13.7129	0.663615
$428$	−18.8434	−0.910832
$429$	−6.67699	−0.322368
$430$	−0.994148	−0.0479421
$431$	−7.60191	−0.366171	−0.183085	−	0.983097i	$-0.558609\pi$
$431$	−7.60191	−0.366171	−0.183085	+	0.983097i	$0.558609\pi$
$432$	−6.67413	−0.321109
$433$	−11.4602	−0.550744	−0.275372	−	0.961338i	$-0.588801\pi$
$433$	−11.4602	−0.550744	−0.275372	+	0.961338i	$0.588801\pi$
$434$	3.63906	0.174680
$435$	1.84879	0.0886427
$436$	−22.9774	−1.10042
$437$	−49.7107	−2.37799
$438$	−1.83777	−0.0878119
$439$	−6.23460	−0.297561	−0.148781	−	0.988870i	$-0.547535\pi$
$439$	−6.23460	−0.297561	−0.148781	+	0.988870i	$0.547535\pi$
$440$	0.409850	0.0195388
$441$	−4.01644	−0.191259
$442$	3.92119	0.186512
$443$	−1.18834	−0.0564596	−0.0282298	−	0.999601i	$-0.508987\pi$
$443$	−1.18834	−0.0564596	−0.0282298	+	0.999601i	$0.508987\pi$
$444$	25.7524	1.22215
$445$	2.09700	0.0994073
$446$	4.80616	0.227578
$447$	31.9555	1.51144
$448$	16.0719	0.759328
$449$	3.97317	0.187506	0.0937529	−	0.995596i	$-0.470114\pi$
$449$	3.97317	0.187506	0.0937529	+	0.995596i	$0.470114\pi$
$450$	2.10894	0.0994163
$451$	9.04129	0.425738
$452$	−13.8960	−0.653611
$453$	12.0452	0.565931
$454$	4.62657	0.217135
$455$	3.43883	0.161215
$456$	11.4823	0.537709
$457$	22.1846	1.03775	0.518876	−	0.854849i	$-0.326351\pi$
$457$	22.1846	1.03775	0.518876	+	0.854849i	$0.326351\pi$
$458$	1.37365	0.0641862
$459$	11.8870	0.554839
$460$	−7.94782	−0.370569
$461$	−14.1199	−0.657631	−0.328815	−	0.944394i	$-0.606649\pi$
$461$	−14.1199	−0.657631	−0.328815	+	0.944394i	$0.606649\pi$
$462$	−1.04373	−0.0485587
$463$	37.1907	1.72840	0.864198	−	0.503152i	$-0.167826\pi$
$463$	37.1907	1.72840	0.864198	+	0.503152i	$0.167826\pi$
$464$	−5.88977	−0.273426
$465$	−9.40668	−0.436224
$466$	0.568214	0.0263220
$467$	13.0976	0.606085	0.303043	−	0.952977i	$-0.401998\pi$
$467$	13.0976	0.606085	0.303043	+	0.952977i	$0.401998\pi$
$468$	−12.7308	−0.588483
$469$	−30.5853	−1.41230
$470$	0.397458	0.0183334
$471$	−5.84746	−0.269437
$472$	−1.91248	−0.0880290
$473$	9.60515	0.441645
$474$	0.0924422	0.00424601
$475$	−29.9679	−1.37502
$476$	−29.9159	−1.37119
$477$	−15.6421	−0.716202
$478$	3.03251	0.138704
$479$	−3.65501	−0.167002	−0.0835008	−	0.996508i	$-0.526610\pi$
$479$	−3.65501	−0.167002	−0.0835008	+	0.996508i	$0.526610\pi$
$480$	2.76302	0.126114
$481$	−16.7964	−0.765850
$482$	3.37398	0.153680
$483$	40.8947	1.86077
$484$	−1.95984	−0.0890838
$485$	−3.56367	−0.161818
$486$	3.84572	0.174446
$487$	−8.79680	−0.398621	−0.199311	−	0.979936i	$-0.563870\pi$
$487$	−8.79680	−0.398621	−0.199311	+	0.979936i	$0.563870\pi$
$488$	−4.77468	−0.216140
$489$	−43.6174	−1.97245
$490$	−0.186962	−0.00844608
$491$	19.4225	0.876523	0.438262	−	0.898847i	$-0.355594\pi$
$491$	19.4225	0.876523	0.438262	+	0.898847i	$0.355594\pi$
$492$	40.4979	1.82579
$493$	10.4900	0.472448
$494$	−3.70656	−0.166766
$495$	1.14844	0.0516187
$496$	29.9673	1.34557
$497$	27.1864	1.21948
$498$	−6.58428	−0.295049
$499$	−10.1650	−0.455047	−0.227523	−	0.973773i	$-0.573063\pi$
$499$	−10.1650	−0.455047	−0.227523	+	0.973773i	$0.573063\pi$
$500$	−9.85265	−0.440624
$501$	3.44674	0.153989
$502$	2.35278	0.105010
$503$	22.5975	1.00757	0.503786	−	0.863828i	$-0.331940\pi$
$503$	22.5975	1.00757	0.503786	+	0.863828i	$0.331940\pi$
$504$	−4.02088	−0.179104
$505$	7.11263	0.316508
$506$	−1.57334	−0.0699436
$507$	−10.2048	−0.453213
$508$	−10.5705	−0.468991
$509$	−29.9602	−1.32796	−0.663980	−	0.747750i	$-0.731134\pi$
$509$	−29.9602	−1.32796	−0.663980	+	0.747750i	$0.731134\pi$
$510$	−1.58443	−0.0701596
$511$	−9.14479	−0.404541
$512$	−14.7705	−0.652771
$513$	−11.2364	−0.496099
$514$	3.78901	0.167126
$515$	8.77506	0.386675
$516$	43.0235	1.89401
$517$	−3.84012	−0.168888
$518$	−2.62557	−0.115361
$519$	45.5607	1.99989
$520$	−1.19736	−0.0525078
$521$	−37.3197	−1.63501	−0.817503	−	0.575925i	$-0.804642\pi$
$521$	−37.3197	−1.63501	−0.817503	+	0.575925i	$0.804642\pi$
$522$	0.697813	0.0305425
$523$	−35.7788	−1.56450	−0.782249	−	0.622965i	$-0.785928\pi$
$523$	−35.7788	−1.56450	−0.782249	+	0.622965i	$0.785928\pi$
$524$	1.95984	0.0856162
$525$	24.6532	1.07595
$526$	−2.24865	−0.0980457
$527$	−53.3736	−2.32499
$528$	−8.59502	−0.374050
$529$	38.6457	1.68025
$530$	−0.728126	−0.0316278
$531$	−5.35897	−0.232560
$532$	28.2785	1.22603
$533$	−26.4138	−1.14411
$534$	1.85941	0.0804647
$535$	−4.96608	−0.214702
$536$	10.6495	0.459986
$537$	18.0884	0.780573
$538$	3.61175	0.155713
$539$	1.80637	0.0778058
$540$	−1.79649	−0.0773086
$541$	−8.44817	−0.363215	−0.181608	−	0.983371i	$-0.558130\pi$
$541$	−8.44817	−0.363215	−0.181608	+	0.983371i	$0.558130\pi$
$542$	1.54426	0.0663317
$543$	−20.8067	−0.892899
$544$	15.6774	0.672163
$545$	−6.05556	−0.259392
$546$	3.04922	0.130495
$547$	−33.1804	−1.41869	−0.709346	−	0.704861i	$-0.751009\pi$
$547$	−33.1804	−1.41869	−0.709346	+	0.704861i	$0.751009\pi$
$548$	−28.8985	−1.23448
$549$	−13.3792	−0.571009
$550$	−0.948482	−0.0404434
$551$	−9.91588	−0.422430
$552$	−14.2391	−0.606055
$553$	0.459995	0.0195610
$554$	−0.263357	−0.0111889
$555$	6.78689	0.288087
$556$	−18.8384	−0.798927
$557$	4.10135	0.173780	0.0868898	−	0.996218i	$-0.472307\pi$
$557$	4.10135	0.173780	0.0868898	+	0.996218i	$0.472307\pi$
$558$	−3.55049	−0.150304
$559$	−28.0611	−1.18686
$560$	4.42667	0.187061
$561$	15.3083	0.646315
$562$	3.97120	0.167515
$563$	−0.318330	−0.0134160	−0.00670800	−	0.999978i	$-0.502135\pi$
$563$	−0.318330	−0.0134160	−0.00670800	+	0.999978i	$0.502135\pi$
$564$	−17.2007	−0.724281
$565$	−3.66220	−0.154070
$566$	3.28424	0.138047
$567$	24.4453	1.02661
$568$	−9.46601	−0.397185
$569$	−20.1596	−0.845136	−0.422568	−	0.906331i	$-0.638871\pi$
$569$	−20.1596	−0.845136	−0.422568	+	0.906331i	$0.638871\pi$
$570$	1.49770	0.0627319
$571$	28.4941	1.19244	0.596221	−	0.802820i	$-0.296668\pi$
$571$	28.4941	1.19244	0.596221	+	0.802820i	$0.296668\pi$
$572$	5.72562	0.239400
$573$	−46.9678	−1.96211
$574$	−4.12893	−0.172338
$575$	37.1628	1.54980
$576$	−15.6808	−0.653366
$577$	−18.3796	−0.765153	−0.382576	−	0.923924i	$-0.624963\pi$
$577$	−18.3796	−0.765153	−0.382576	+	0.923924i	$0.624963\pi$
$578$	−5.58346	−0.232241
$579$	59.1420	2.45786
$580$	−1.58536	−0.0658286
$581$	−32.7636	−1.35926
$582$	−3.15991	−0.130982
$583$	7.03493	0.291357
$584$	3.18411	0.131759
$585$	−3.35514	−0.138718
$586$	−3.87318	−0.160000
$587$	−37.8746	−1.56325	−0.781627	−	0.623747i	$-0.785610\pi$
$587$	−37.8746	−1.56325	−0.781627	+	0.623747i	$0.785610\pi$
$588$	8.09111	0.333672
$589$	50.4522	2.07885
$590$	−0.249456	−0.0102699
$591$	9.10106	0.374368
$592$	−21.6213	−0.888630
$593$	47.6798	1.95797	0.978987	−	0.203924i	$-0.0653697\pi$
$593$	47.6798	1.95797	0.978987	+	0.203924i	$0.0653697\pi$
$594$	−0.355632	−0.0145917
$595$	−7.88417	−0.323219
$596$	−27.4023	−1.12244
$597$	63.8617	2.61368
$598$	4.59647	0.187963
$599$	−28.2355	−1.15367	−0.576835	−	0.816860i	$-0.695713\pi$
$599$	−28.2355	−1.15367	−0.576835	+	0.816860i	$0.695713\pi$
$600$	−8.58395	−0.350438
$601$	7.80513	0.318378	0.159189	−	0.987248i	$-0.449112\pi$
$601$	7.80513	0.318378	0.159189	+	0.987248i	$0.449112\pi$
$602$	−4.38644	−0.178778
$603$	29.8409	1.21522
$604$	−10.3289	−0.420277
$605$	−0.516505	−0.0209989
$606$	6.30678	0.256195
$607$	−33.0592	−1.34183	−0.670917	−	0.741533i	$-0.734099\pi$
$607$	−33.0592	−1.34183	−0.670917	+	0.741533i	$0.734099\pi$
$608$	−14.8193	−0.601002
$609$	8.15733	0.330552
$610$	−0.622790	−0.0252160
$611$	11.2188	0.453863
$612$	29.1878	1.17985
$613$	−32.2894	−1.30416	−0.652079	−	0.758151i	$-0.726103\pi$
$613$	−32.2894	−1.30416	−0.652079	+	0.758151i	$0.726103\pi$
$614$	−4.73896	−0.191249
$615$	10.6730	0.430376
$616$	1.80836	0.0728610
$617$	41.0622	1.65310	0.826551	−	0.562862i	$-0.190300\pi$
$617$	41.0622	1.65310	0.826551	+	0.562862i	$0.190300\pi$
$618$	7.78086	0.312992
$619$	27.5013	1.10537	0.552685	−	0.833390i	$-0.313603\pi$
$619$	27.5013	1.10537	0.552685	+	0.833390i	$0.313603\pi$
$620$	8.06636	0.323953
$621$	13.9341	0.559157
$622$	−0.824527	−0.0330605
$623$	9.25250	0.370693
$624$	25.1100	1.00521
$625$	21.0695	0.842780
$626$	−6.55912	−0.262155
$627$	−14.4704	−0.577890
$628$	5.01428	0.200091
$629$	38.5089	1.53545
$630$	−0.524466	−0.0208952
$631$	−17.2665	−0.687369	−0.343685	−	0.939085i	$-0.611675\pi$
$631$	−17.2665	−0.687369	−0.343685	+	0.939085i	$0.611675\pi$
$632$	−0.160165	−0.00637103
$633$	−27.6537	−1.09914
$634$	2.68645	0.106692
$635$	−2.78580	−0.110551
$636$	31.5110	1.24949
$637$	−5.27724	−0.209092
$638$	−0.313837	−0.0124249
$639$	−26.5248	−1.04930
$640$	−3.14780	−0.124428
$641$	38.9537	1.53858	0.769290	−	0.638900i	$-0.220610\pi$
$641$	38.9537	1.53858	0.769290	+	0.638900i	$0.220610\pi$
$642$	−4.40343	−0.173789
$643$	40.7551	1.60722	0.803612	−	0.595153i	$-0.202909\pi$
$643$	40.7551	1.60722	0.803612	+	0.595153i	$0.202909\pi$
$644$	−35.0678	−1.38186
$645$	11.3386	0.446457
$646$	8.49799	0.334349
$647$	−22.8739	−0.899264	−0.449632	−	0.893214i	$-0.648445\pi$
$647$	−22.8739	−0.899264	−0.449632	+	0.893214i	$0.648445\pi$
$648$	−8.51159	−0.334367
$649$	2.41016	0.0946072
$650$	2.77096	0.108686
$651$	−41.5047	−1.62670
$652$	37.4025	1.46480
$653$	−6.45348	−0.252544	−0.126272	−	0.991996i	$-0.540301\pi$
$653$	−6.45348	−0.252544	−0.126272	+	0.991996i	$0.540301\pi$
$654$	−5.36948	−0.209963
$655$	0.516505	0.0201815
$656$	−34.0014	−1.32753
$657$	8.92222	0.348089
$658$	1.75369	0.0683659
$659$	5.57572	0.217199	0.108600	−	0.994086i	$-0.465363\pi$
$659$	5.57572	0.217199	0.108600	+	0.994086i	$0.465363\pi$
$660$	−2.31354	−0.0900544
$661$	−18.5634	−0.722034	−0.361017	−	0.932559i	$-0.617570\pi$
$661$	−18.5634	−0.722034	−0.361017	+	0.932559i	$0.617570\pi$
$662$	−1.43816	−0.0558956
$663$	−44.7225	−1.73688
$664$	11.4079	0.442713
$665$	7.45263	0.289000
$666$	2.56167	0.0992625
$667$	12.2966	0.476125
$668$	−2.95563	−0.114357
$669$	−54.8159	−2.11930
$670$	1.38907	0.0536645
$671$	6.01720	0.232291
$672$	12.1911	0.470284
$673$	28.8431	1.11182	0.555909	−	0.831243i	$-0.312370\pi$
$673$	28.8431	1.11182	0.555909	+	0.831243i	$0.312370\pi$
$674$	−1.26101	−0.0485724
$675$	8.40011	0.323320
$676$	8.75079	0.336569
$677$	−44.0154	−1.69165	−0.845824	−	0.533463i	$-0.820891\pi$
$677$	−44.0154	−1.69165	−0.845824	+	0.533463i	$0.820891\pi$
$678$	−3.24728	−0.124711
$679$	−15.7238	−0.603425
$680$	2.74518	0.105273
$681$	−52.7676	−2.02206
$682$	1.59681	0.0611450
$683$	−7.16435	−0.274136	−0.137068	−	0.990562i	$-0.543768\pi$
$683$	−7.16435	−0.274136	−0.137068	+	0.990562i	$0.543768\pi$
$684$	−27.5902	−1.05494
$685$	−7.61602	−0.290993
$686$	−4.02165	−0.153547
$687$	−15.6669	−0.597729
$688$	−36.1219	−1.37713
$689$	−20.5523	−0.782980
$690$	−1.85728	−0.0707056
$691$	−25.8084	−0.981796	−0.490898	−	0.871217i	$-0.663331\pi$
$691$	−25.8084	−0.981796	−0.490898	+	0.871217i	$0.663331\pi$
$692$	−39.0689	−1.48518
$693$	5.06723	0.192488
$694$	−5.93105	−0.225140
$695$	−4.96475	−0.188324
$696$	−2.84029	−0.107661
$697$	60.5586	2.29382
$698$	3.29480	0.124710
$699$	−6.48067	−0.245122
$700$	−21.1404	−0.799034
$701$	18.4057	0.695175	0.347587	−	0.937648i	$-0.387001\pi$
$701$	18.4057	0.695175	0.347587	+	0.937648i	$0.387001\pi$
$702$	1.03896	0.0392132
$703$	−36.4011	−1.37289
$704$	7.05233	0.265795
$705$	−4.53315	−0.170728
$706$	−2.71509	−0.102184
$707$	31.3827	1.18027
$708$	10.7956	0.405725
$709$	−42.8777	−1.61031	−0.805153	−	0.593068i	$-0.797917\pi$
$709$	−42.8777	−1.61031	−0.805153	+	0.593068i	$0.797917\pi$
$710$	−1.23471	−0.0463377
$711$	−0.448800	−0.0168313
$712$	−3.22161	−0.120735
$713$	−62.5651	−2.34308
$714$	−6.99090	−0.261628
$715$	1.50895	0.0564316
$716$	−15.5111	−0.579676
$717$	−34.5868	−1.29167
$718$	−0.0494402	−0.00184509
$719$	−40.6971	−1.51775	−0.758873	−	0.651239i	$-0.774250\pi$
$719$	−40.6971	−1.51775	−0.758873	+	0.651239i	$0.774250\pi$
$720$	−4.31893	−0.160957
$721$	38.7178	1.44193
$722$	−4.22548	−0.157256
$723$	−38.4814	−1.43114
$724$	17.8420	0.663093
$725$	7.41292	0.275309
$726$	−0.457986	−0.0169975
$727$	14.1749	0.525718	0.262859	−	0.964834i	$-0.415335\pi$
$727$	14.1749	0.525718	0.262859	+	0.964834i	$0.415335\pi$
$728$	−5.28307	−0.195804
$729$	−11.6821	−0.432670
$730$	0.415322	0.0153718
$731$	64.3353	2.37953
$732$	26.9523	0.996187
$733$	−10.4841	−0.387240	−0.193620	−	0.981077i	$-0.562023\pi$
$733$	−10.4841	−0.387240	−0.193620	+	0.981077i	$0.562023\pi$
$734$	−1.28562	−0.0474531
$735$	2.13236	0.0786534
$736$	18.3772	0.677393
$737$	−13.4208	−0.494360
$738$	4.02844	0.148289
$739$	−18.3045	−0.673341	−0.336671	−	0.941622i	$-0.609301\pi$
$739$	−18.3045	−0.673341	−0.336671	+	0.941622i	$0.609301\pi$
$740$	−5.81985	−0.213942
$741$	42.2746	1.55300
$742$	−3.21268	−0.117941
$743$	−38.7742	−1.42249	−0.711243	−	0.702946i	$-0.751868\pi$
$743$	−38.7742	−1.42249	−0.711243	+	0.702946i	$0.751868\pi$
$744$	14.4515	0.529816
$745$	−7.22172	−0.264583
$746$	1.35385	0.0495678
$747$	31.9662	1.16958
$748$	−13.1270	−0.479972
$749$	−21.9116	−0.800633
$750$	−2.30242	−0.0840724
$751$	−11.5155	−0.420207	−0.210104	−	0.977679i	$-0.567380\pi$
$751$	−11.5155	−0.420207	−0.210104	+	0.977679i	$0.567380\pi$
$752$	14.4415	0.526626
$753$	−26.8342	−0.977894
$754$	0.916864	0.0333902
$755$	−2.72212	−0.0990681
$756$	−7.92657	−0.288287
$757$	−48.1844	−1.75129	−0.875645	−	0.482955i	$-0.839564\pi$
$757$	−48.1844	−1.75129	−0.875645	+	0.482955i	$0.839564\pi$
$758$	2.48275	0.0901775
$759$	17.9445	0.651344
$760$	−2.59492	−0.0941276
$761$	8.54908	0.309904	0.154952	−	0.987922i	$-0.450478\pi$
$761$	8.54908	0.309904	0.154952	+	0.987922i	$0.450478\pi$
$762$	−2.47017	−0.0894849
$763$	−26.7187	−0.967282
$764$	40.2756	1.45712
$765$	7.69228	0.278115
$766$	−3.24568	−0.117271
$767$	−7.04121	−0.254243
$768$	29.4450	1.06250
$769$	22.9916	0.829098	0.414549	−	0.910027i	$-0.363939\pi$
$769$	22.9916	0.829098	0.414549	+	0.910027i	$0.363939\pi$
$770$	0.235875	0.00850036
$771$	−43.2150	−1.55635
$772$	−50.7151	−1.82528
$773$	5.99302	0.215554	0.107777	−	0.994175i	$-0.465627\pi$
$773$	5.99302	0.215554	0.107777	+	0.994175i	$0.465627\pi$
$774$	4.27968	0.153830
$775$	−37.7171	−1.35484
$776$	5.47485	0.196536
$777$	29.9455	1.07429
$778$	0.0888799	0.00318650
$779$	−57.2439	−2.05098
$780$	6.75892	0.242008
$781$	11.9294	0.426866
$782$	−10.5383	−0.376847
$783$	2.77946	0.0993298
$784$	−6.79317	−0.242613
$785$	1.32148	0.0471657
$786$	0.457986	0.0163358
$787$	−4.03270	−0.143750	−0.0718751	−	0.997414i	$-0.522898\pi$
$787$	−4.03270	−0.143750	−0.0718751	+	0.997414i	$0.522898\pi$
$788$	−7.80429	−0.278016
$789$	25.6466	0.913043
$790$	−0.0208913	−0.000743278 0
$791$	−16.1586	−0.574532
$792$	−1.76435	−0.0626935
$793$	−17.5790	−0.624250
$794$	−2.59578	−0.0921206
$795$	8.30453	0.294531
$796$	−54.7623	−1.94100
$797$	−3.02176	−0.107036	−0.0535181	−	0.998567i	$-0.517043\pi$
$797$	−3.02176	−0.107036	−0.0535181	+	0.998567i	$0.517043\pi$
$798$	6.60825	0.233930
$799$	−25.7211	−0.909948
$800$	11.0786	0.391688
$801$	−9.02731	−0.318964
$802$	−1.48577	−0.0524645
$803$	−4.01271	−0.141606
$804$	−60.1145	−2.12008
$805$	−9.24191	−0.325735
$806$	−4.66502	−0.164318
$807$	−41.1932	−1.45007
$808$	−10.9271	−0.384415
$809$	11.7504	0.413122	0.206561	−	0.978434i	$-0.433773\pi$
$809$	11.7504	0.413122	0.206561	+	0.978434i	$0.433773\pi$
$810$	−1.11022	−0.0390090
$811$	31.5974	1.10954	0.554768	−	0.832005i	$-0.312807\pi$
$811$	31.5974	1.10954	0.554768	+	0.832005i	$0.312807\pi$
$812$	−6.99503	−0.245477
$813$	−17.6128	−0.617709
$814$	−1.15209	−0.0403808
$815$	9.85722	0.345283
$816$	−57.5694	−2.01533
$817$	−60.8139	−2.12761
$818$	−7.48986	−0.261877
$819$	−14.8037	−0.517284
$820$	−9.15223	−0.319610
$821$	8.90643	0.310837	0.155418	−	0.987849i	$-0.450327\pi$
$821$	8.90643	0.310837	0.155418	+	0.987849i	$0.450327\pi$
$822$	−6.75314	−0.235543
$823$	−47.8969	−1.66958	−0.834790	−	0.550569i	$-0.814411\pi$
$823$	−47.8969	−1.66958	−0.834790	+	0.550569i	$0.814411\pi$
$824$	−13.4811	−0.469636
$825$	10.8178	0.376626
$826$	−1.10066	−0.0382970
$827$	35.0594	1.21913	0.609567	−	0.792734i	$-0.291343\pi$
$827$	35.0594	1.21913	0.609567	+	0.792734i	$0.291343\pi$
$828$	34.2143	1.18903
$829$	−35.1394	−1.22044	−0.610221	−	0.792231i	$-0.708919\pi$
$829$	−35.1394	−1.22044	−0.610221	+	0.792231i	$0.708919\pi$
$830$	1.48800	0.0516493
$831$	3.00367	0.104196
$832$	−20.6031	−0.714285
$833$	12.0991	0.419207
$834$	−4.40226	−0.152438
$835$	−0.778937	−0.0269562
$836$	12.4085	0.429158
$837$	−14.1419	−0.488817
$838$	4.59290	0.158659
$839$	22.4812	0.776138	0.388069	−	0.921630i	$-0.373142\pi$
$839$	22.4812	0.776138	0.388069	+	0.921630i	$0.373142\pi$
$840$	2.13472	0.0736548
$841$	−26.5472	−0.915420
$842$	6.69443	0.230705
$843$	−45.2929	−1.55997
$844$	23.7134	0.816251
$845$	2.30622	0.0793364
$846$	−1.71101	−0.0588256
$847$	−2.27895	−0.0783058
$848$	−26.4561	−0.908507
$849$	−37.4578	−1.28555
$850$	−6.35293	−0.217904
$851$	45.1406	1.54740
$852$	53.4341	1.83062
$853$	−16.5056	−0.565142	−0.282571	−	0.959246i	$-0.591187\pi$
$853$	−16.5056	−0.565142	−0.282571	+	0.959246i	$0.591187\pi$
$854$	−2.74791	−0.0940314
$855$	−7.27124	−0.248671
$856$	7.62937	0.260767
$857$	−19.8418	−0.677783	−0.338891	−	0.940826i	$-0.610052\pi$
$857$	−19.8418	−0.677783	−0.338891	+	0.940826i	$0.610052\pi$
$858$	1.33799	0.0456782
$859$	−1.17783	−0.0401869	−0.0200935	−	0.999798i	$-0.506396\pi$
$859$	−1.17783	−0.0401869	−0.0200935	+	0.999798i	$0.506396\pi$
$860$	−9.72301	−0.331552
$861$	47.0919	1.60489
$862$	1.52333	0.0518849
$863$	−25.8529	−0.880044	−0.440022	−	0.897987i	$-0.645029\pi$
$863$	−25.8529	−0.880044	−0.440022	+	0.897987i	$0.645029\pi$
$864$	4.15391	0.141319
$865$	−10.2964	−0.350088
$866$	2.29649	0.0780381
$867$	63.6813	2.16273
$868$	35.5908	1.20803
$869$	0.201845	0.00684712
$870$	−0.370475	−0.0125603
$871$	39.2083	1.32852
$872$	9.30315	0.315044
$873$	15.3411	0.519218
$874$	9.96144	0.336951
$875$	−11.4569	−0.387314
$876$	−17.9738	−0.607278
$877$	12.8547	0.434071	0.217035	−	0.976164i	$-0.430361\pi$
$877$	12.8547	0.434071	0.217035	+	0.976164i	$0.430361\pi$
$878$	1.24934	0.0421632
$879$	44.1750	1.48999
$880$	1.94241	0.0654787
$881$	−37.7074	−1.27039	−0.635197	−	0.772350i	$-0.719081\pi$
$881$	−37.7074	−1.27039	−0.635197	+	0.772350i	$0.719081\pi$
$882$	0.804847	0.0271006
$883$	22.6923	0.763658	0.381829	−	0.924233i	$-0.375294\pi$
$883$	22.6923	0.763658	0.381829	+	0.924233i	$0.375294\pi$
$884$	38.3502	1.28986
$885$	2.84513	0.0956380
$886$	0.238129	0.00800008
$887$	−10.8016	−0.362682	−0.181341	−	0.983420i	$-0.558044\pi$
$887$	−10.8016	−0.362682	−0.181341	+	0.983420i	$0.558044\pi$
$888$	−10.4267	−0.349897
$889$	−12.2917	−0.412249
$890$	−0.420214	−0.0140856
$891$	10.7266	0.359353
$892$	47.0054	1.57386
$893$	24.3133	0.813613
$894$	−6.40351	−0.214165
$895$	−4.08785	−0.136642
$896$	−13.8889	−0.463996
$897$	−52.4243	−1.75039
$898$	−0.796177	−0.0265688
$899$	−12.4800	−0.416230
$900$	20.6259	0.687531
$901$	47.1200	1.56979
$902$	−1.81177	−0.0603253
$903$	50.0288	1.66485
$904$	5.62622	0.187125
$905$	4.70216	0.156305
$906$	−2.41371	−0.0801901
$907$	26.5574	0.881825	0.440913	−	0.897550i	$-0.354655\pi$
$907$	26.5574	0.881825	0.440913	+	0.897550i	$0.354655\pi$
$908$	45.2489	1.50164
$909$	−30.6190	−1.01557
$910$	−0.689101	−0.0228435
$911$	10.8717	0.360196	0.180098	−	0.983649i	$-0.442358\pi$
$911$	10.8717	0.360196	0.180098	+	0.983649i	$0.442358\pi$
$912$	54.4184	1.80197
$913$	−14.3766	−0.475796
$914$	−4.44553	−0.147045
$915$	7.10313	0.234822
$916$	13.4346	0.443891
$917$	2.27895	0.0752577
$918$	−2.38202	−0.0786184
$919$	−24.4453	−0.806376	−0.403188	−	0.915117i	$-0.632098\pi$
$919$	−24.4453	−0.806376	−0.403188	+	0.915117i	$0.632098\pi$
$920$	3.21793	0.106092
$921$	54.0495	1.78099
$922$	2.82947	0.0931836
$923$	−34.8512	−1.14714
$924$	−10.2079	−0.335816
$925$	27.2128	0.894750
$926$	−7.45257	−0.244907
$927$	−37.7755	−1.24071
$928$	3.66573	0.120334
$929$	−49.0101	−1.60797	−0.803985	−	0.594649i	$-0.797291\pi$
$929$	−49.0101	−1.60797	−0.803985	+	0.594649i	$0.797291\pi$
$930$	1.88499	0.0618111
$931$	−11.4368	−0.374826
$932$	5.55727	0.182034
$933$	9.40402	0.307874
$934$	−2.62461	−0.0858797
$935$	−3.45955	−0.113140
$936$	5.15449	0.168480
$937$	42.4239	1.38593	0.692964	−	0.720972i	$-0.256304\pi$
$937$	42.4239	1.38593	0.692964	+	0.720972i	$0.256304\pi$
$938$	6.12893	0.200117
$939$	74.8090	2.44130
$940$	3.88724	0.126788
$941$	−3.07199	−0.100144	−0.0500720	−	0.998746i	$-0.515945\pi$
$941$	−3.07199	−0.100144	−0.0500720	+	0.998746i	$0.515945\pi$
$942$	1.17176	0.0381780
$943$	70.9875	2.31167
$944$	−9.06386	−0.295003
$945$	−2.08900	−0.0679552
$946$	−1.92476	−0.0625793
$947$	−18.1001	−0.588174	−0.294087	−	0.955779i	$-0.595016\pi$
$947$	−18.1001	−0.588174	−0.294087	+	0.955779i	$0.595016\pi$
$948$	0.904107	0.0293640
$949$	11.7230	0.380545
$950$	6.00520	0.194835
$951$	−30.6398	−0.993565
$952$	12.1124	0.392566
$953$	35.3751	1.14591	0.572957	−	0.819586i	$-0.305796\pi$
$953$	35.3751	1.14591	0.572957	+	0.819586i	$0.305796\pi$
$954$	3.13449	0.101483
$955$	10.6144	0.343473
$956$	29.6586	0.959229
$957$	3.57942	0.115706
$958$	0.732421	0.0236634
$959$	−33.6038	−1.08512
$960$	8.32507	0.268690
$961$	32.4983	1.04833
$962$	3.36580	0.108518
$963$	21.3783	0.688907
$964$	32.9983	1.06280
$965$	−13.3657	−0.430256
$966$	−8.19482	−0.263664
$967$	29.9526	0.963212	0.481606	−	0.876388i	$-0.340054\pi$
$967$	29.9526	0.963212	0.481606	+	0.876388i	$0.340054\pi$
$968$	0.793506	0.0255042
$969$	−96.9225	−3.11360
$970$	0.714117	0.0229289
$971$	−8.91327	−0.286041	−0.143020	−	0.989720i	$-0.545681\pi$
$971$	−8.91327	−0.286041	−0.143020	+	0.989720i	$0.545681\pi$
$972$	37.6121	1.20641
$973$	−21.9058	−0.702267
$974$	1.76278	0.0564830
$975$	−31.6037	−1.01213
$976$	−22.6288	−0.724329
$977$	23.6905	0.757925	0.378962	−	0.925412i	$-0.376281\pi$
$977$	23.6905	0.757925	0.378962	+	0.925412i	$0.376281\pi$
$978$	8.74041	0.279488
$979$	4.05998	0.129757
$980$	−1.82853	−0.0584103
$981$	26.0684	0.832300
$982$	−3.89203	−0.124200
$983$	−20.7030	−0.660323	−0.330161	−	0.943925i	$-0.607103\pi$
$983$	−20.7030	−0.660323	−0.330161	+	0.943925i	$0.607103\pi$
$984$	−16.3969	−0.522713
$985$	−2.05677	−0.0655343
$986$	−2.10208	−0.0669439
$987$	−20.0014	−0.636652
$988$	−36.2511	−1.15330
$989$	75.4146	2.39804
$990$	−0.230135	−0.00731416
$991$	−20.4886	−0.650842	−0.325421	−	0.945569i	$-0.605506\pi$
$991$	−20.4886	−0.650842	−0.325421	+	0.945569i	$0.605506\pi$
$992$	−18.6513	−0.592180
$993$	16.4027	0.520523
$994$	−5.44784	−0.172795
$995$	−14.4323	−0.457534
$996$	−64.3959	−2.04046
$997$	34.8915	1.10502	0.552512	−	0.833505i	$-0.313669\pi$
$997$	34.8915	1.10502	0.552512	+	0.833505i	$0.313669\pi$
$998$	2.03694	0.0644782
$999$	10.2034	0.322820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.d.1.14	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.d.1.14	✓	23	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)

\(f(q)\)	\(=\)	\(q-0.200388 q^{2} +2.28550 q^{3} -1.95984 q^{4} -0.516505 q^{5} -0.457986 q^{6} -2.27895 q^{7} +0.793506 q^{8} +2.22349 q^{9} +O(q^{10})\)	\(q-0.200388 q^{2} +2.28550 q^{3} -1.95984 q^{4} -0.516505 q^{5} -0.457986 q^{6} -2.27895 q^{7} +0.793506 q^{8} +2.22349 q^{9} +0.103502 q^{10} -1.00000 q^{11} -4.47922 q^{12} +2.92146 q^{13} +0.456675 q^{14} -1.18047 q^{15} +3.76068 q^{16} -6.69800 q^{17} -0.445561 q^{18} +6.33139 q^{19} +1.01227 q^{20} -5.20854 q^{21} +0.200388 q^{22} -7.85148 q^{23} +1.81355 q^{24} -4.73322 q^{25} -0.585427 q^{26} -1.77471 q^{27} +4.46640 q^{28} -1.56615 q^{29} +0.236552 q^{30} +7.96858 q^{31} -2.34061 q^{32} -2.28550 q^{33} +1.34220 q^{34} +1.17709 q^{35} -4.35769 q^{36} -5.74931 q^{37} -1.26873 q^{38} +6.67699 q^{39} -0.409850 q^{40} -9.04129 q^{41} +1.04373 q^{42} -9.60515 q^{43} +1.95984 q^{44} -1.14844 q^{45} +1.57334 q^{46} +3.84012 q^{47} +8.59502 q^{48} -1.80637 q^{49} +0.948482 q^{50} -15.3083 q^{51} -5.72562 q^{52} -7.03493 q^{53} +0.355632 q^{54} +0.516505 q^{55} -1.80836 q^{56} +14.4704 q^{57} +0.313837 q^{58} -2.41016 q^{59} +2.31354 q^{60} -6.01720 q^{61} -1.59681 q^{62} -5.06723 q^{63} -7.05233 q^{64} -1.50895 q^{65} +0.457986 q^{66} +13.4208 q^{67} +13.1270 q^{68} -17.9445 q^{69} -0.235875 q^{70} -11.9294 q^{71} +1.76435 q^{72} +4.01271 q^{73} +1.15209 q^{74} -10.8178 q^{75} -12.4085 q^{76} +2.27895 q^{77} -1.33799 q^{78} -0.201845 q^{79} -1.94241 q^{80} -10.7266 q^{81} +1.81177 q^{82} +14.3766 q^{83} +10.2079 q^{84} +3.45955 q^{85} +1.92476 q^{86} -3.57942 q^{87} -0.793506 q^{88} -4.05998 q^{89} +0.230135 q^{90} -6.65788 q^{91} +15.3877 q^{92} +18.2122 q^{93} -0.769514 q^{94} -3.27020 q^{95} -5.34945 q^{96} +6.89957 q^{97} +0.361975 q^{98} -2.22349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 19 q^{4} - 9 q^{5} - 5 q^{6} - 8 q^{7} - 15 q^{8} + 12 q^{9} - 2 q^{10} - 23 q^{11} - 12 q^{12} + 6 q^{13} - 13 q^{14} - 27 q^{15} - q^{16} - 11 q^{17} - 16 q^{19} - 24 q^{20} - 7 q^{21} + 7 q^{22} - 30 q^{23} - 20 q^{24} + 10 q^{25} - 22 q^{26} - 15 q^{27} + 11 q^{28} - 15 q^{29} + 17 q^{30} - 31 q^{31} - 22 q^{32} + 3 q^{33} - 18 q^{34} - 34 q^{35} - 18 q^{36} - 26 q^{37} - 32 q^{39} + 16 q^{40} - 21 q^{41} - 37 q^{42} - 2 q^{43} - 19 q^{44} - 18 q^{45} - 6 q^{46} - 25 q^{47} + 14 q^{48} + 7 q^{49} - 27 q^{50} - 7 q^{51} + 23 q^{52} - 34 q^{53} + 26 q^{54} + 9 q^{55} - 42 q^{56} + 6 q^{57} - 5 q^{58} - 31 q^{59} - 7 q^{60} + 19 q^{61} + 24 q^{62} - 34 q^{63} - 17 q^{64} - 13 q^{65} + 5 q^{66} - 39 q^{67} - 59 q^{68} - 12 q^{69} + 17 q^{70} - 103 q^{71} + 19 q^{72} + q^{73} - 9 q^{74} - 19 q^{75} + 10 q^{76} + 8 q^{77} - 43 q^{78} - 14 q^{79} - q^{80} - 29 q^{81} + 20 q^{82} - 14 q^{83} + 57 q^{84} + 20 q^{85} - 54 q^{86} - 23 q^{87} + 15 q^{88} - 71 q^{89} - 52 q^{90} - 18 q^{91} - 24 q^{92} - q^{93} + q^{94} - 38 q^{95} - 31 q^{96} - 26 q^{97} + 19 q^{98} - 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 19 * q^4 - 9 * q^5 - 5 * q^6 - 8 * q^7 - 15 * q^8 + 12 * q^9 - 2 * q^10 - 23 * q^11 - 12 * q^12 + 6 * q^13 - 13 * q^14 - 27 * q^15 - q^16 - 11 * q^17 - 16 * q^19 - 24 * q^20 - 7 * q^21 + 7 * q^22 - 30 * q^23 - 20 * q^24 + 10 * q^25 - 22 * q^26 - 15 * q^27 + 11 * q^28 - 15 * q^29 + 17 * q^30 - 31 * q^31 - 22 * q^32 + 3 * q^33 - 18 * q^34 - 34 * q^35 - 18 * q^36 - 26 * q^37 - 32 * q^39 + 16 * q^40 - 21 * q^41 - 37 * q^42 - 2 * q^43 - 19 * q^44 - 18 * q^45 - 6 * q^46 - 25 * q^47 + 14 * q^48 + 7 * q^49 - 27 * q^50 - 7 * q^51 + 23 * q^52 - 34 * q^53 + 26 * q^54 + 9 * q^55 - 42 * q^56 + 6 * q^57 - 5 * q^58 - 31 * q^59 - 7 * q^60 + 19 * q^61 + 24 * q^62 - 34 * q^63 - 17 * q^64 - 13 * q^65 + 5 * q^66 - 39 * q^67 - 59 * q^68 - 12 * q^69 + 17 * q^70 - 103 * q^71 + 19 * q^72 + q^73 - 9 * q^74 - 19 * q^75 + 10 * q^76 + 8 * q^77 - 43 * q^78 - 14 * q^79 - q^80 - 29 * q^81 + 20 * q^82 - 14 * q^83 + 57 * q^84 + 20 * q^85 - 54 * q^86 - 23 * q^87 + 15 * q^88 - 71 * q^89 - 52 * q^90 - 18 * q^91 - 24 * q^92 - q^93 + q^94 - 38 * q^95 - 31 * q^96 - 26 * q^97 + 19 * q^98 - 12 * q^99

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