LMFDB - Embedded newform 1003.2.a.j.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.324383 q^{2} +2.83368 q^{3} -1.89478 q^{4} +2.69264 q^{5} +0.919198 q^{6} +3.71446 q^{7} -1.26340 q^{8} +5.02975 q^{9} +O(q^{10})$	\(q+0.324383 q^{2} +2.83368 q^{3} -1.89478 q^{4} +2.69264 q^{5} +0.919198 q^{6} +3.71446 q^{7} -1.26340 q^{8} +5.02975 q^{9} +0.873446 q^{10} +0.340753 q^{11} -5.36919 q^{12} -4.32552 q^{13} +1.20491 q^{14} +7.63008 q^{15} +3.37973 q^{16} -1.00000 q^{17} +1.63157 q^{18} +1.00818 q^{19} -5.10195 q^{20} +10.5256 q^{21} +0.110534 q^{22} -5.84377 q^{23} -3.58007 q^{24} +2.25030 q^{25} -1.40313 q^{26} +5.75167 q^{27} -7.03806 q^{28} +7.99356 q^{29} +2.47507 q^{30} -0.280987 q^{31} +3.62312 q^{32} +0.965586 q^{33} -0.324383 q^{34} +10.0017 q^{35} -9.53025 q^{36} -4.98093 q^{37} +0.327035 q^{38} -12.2572 q^{39} -3.40188 q^{40} -9.93857 q^{41} +3.41432 q^{42} -5.47393 q^{43} -0.645650 q^{44} +13.5433 q^{45} -1.89562 q^{46} -7.98708 q^{47} +9.57707 q^{48} +6.79720 q^{49} +0.729959 q^{50} -2.83368 q^{51} +8.19589 q^{52} +8.66658 q^{53} +1.86574 q^{54} +0.917525 q^{55} -4.69284 q^{56} +2.85685 q^{57} +2.59298 q^{58} +1.00000 q^{59} -14.4573 q^{60} -8.26024 q^{61} -0.0911475 q^{62} +18.6828 q^{63} -5.58417 q^{64} -11.6471 q^{65} +0.313219 q^{66} +15.0154 q^{67} +1.89478 q^{68} -16.5594 q^{69} +3.24438 q^{70} +14.0515 q^{71} -6.35458 q^{72} +6.40457 q^{73} -1.61573 q^{74} +6.37664 q^{75} -1.91027 q^{76} +1.26571 q^{77} -3.97601 q^{78} -1.31699 q^{79} +9.10038 q^{80} +1.20915 q^{81} -3.22390 q^{82} -6.78323 q^{83} -19.9436 q^{84} -2.69264 q^{85} -1.77565 q^{86} +22.6512 q^{87} -0.430507 q^{88} +4.00061 q^{89} +4.39322 q^{90} -16.0670 q^{91} +11.0726 q^{92} -0.796229 q^{93} -2.59087 q^{94} +2.71466 q^{95} +10.2668 q^{96} +17.0241 q^{97} +2.20489 q^{98} +1.71390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) $ 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * 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 $

$2$	0.324383	0.229373	0.114687	−	0.993402i	$-0.463414\pi$
$2$	0.324383	0.229373	0.114687	+	0.993402i	$0.463414\pi$
$3$	2.83368	1.63603	0.818013	−	0.575199i	$-0.195075\pi$
$3$	2.83368	1.63603	0.818013	+	0.575199i	$0.195075\pi$
$4$	−1.89478	−0.947388
$5$	2.69264	1.20418	0.602092	−	0.798427i	$-0.294334\pi$
$5$	2.69264	1.20418	0.602092	+	0.798427i	$0.294334\pi$
$6$	0.919198	0.375261
$7$	3.71446	1.40393	0.701967	−	0.712210i	$-0.252306\pi$
$7$	3.71446	1.40393	0.701967	+	0.712210i	$0.252306\pi$
$8$	−1.26340	−0.446679
$9$	5.02975	1.67658
$10$	0.873446	0.276208
$11$	0.340753	0.102741	0.0513704	−	0.998680i	$-0.483641\pi$
$11$	0.340753	0.102741	0.0513704	+	0.998680i	$0.483641\pi$
$12$	−5.36919	−1.54995
$13$	−4.32552	−1.19968	−0.599842	−	0.800118i	$-0.704770\pi$
$13$	−4.32552	−1.19968	−0.599842	+	0.800118i	$0.704770\pi$
$14$	1.20491	0.322025
$15$	7.63008	1.97008
$16$	3.37973	0.844932
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.63157	0.384564
$19$	1.00818	0.231292	0.115646	−	0.993291i	$-0.463106\pi$
$19$	1.00818	0.231292	0.115646	+	0.993291i	$0.463106\pi$
$20$	−5.10195	−1.14083
$21$	10.5256	2.29687
$22$	0.110534	0.0235660
$23$	−5.84377	−1.21851	−0.609255	−	0.792974i	$-0.708532\pi$
$23$	−5.84377	−1.21851	−0.609255	+	0.792974i	$0.708532\pi$
$24$	−3.58007	−0.730779
$25$	2.25030	0.450060
$26$	−1.40313	−0.275176
$27$	5.75167	1.10691
$28$	−7.03806	−1.33007
$29$	7.99356	1.48437	0.742184	−	0.670196i	$-0.233790\pi$
$29$	7.99356	1.48437	0.742184	+	0.670196i	$0.233790\pi$
$30$	2.47507	0.451883
$31$	−0.280987	−0.0504668	−0.0252334	−	0.999682i	$-0.508033\pi$
$31$	−0.280987	−0.0504668	−0.0252334	+	0.999682i	$0.508033\pi$
$32$	3.62312	0.640484
$33$	0.965586	0.168087
$34$	−0.324383	−0.0556312
$35$	10.0017	1.69059
$36$	−9.53025	−1.58838
$37$	−4.98093	−0.818860	−0.409430	−	0.912342i	$-0.634272\pi$
$37$	−4.98093	−0.818860	−0.409430	+	0.912342i	$0.634272\pi$
$38$	0.327035	0.0530521
$39$	−12.2572	−1.96272
$40$	−3.40188	−0.537884
$41$	−9.93857	−1.55214	−0.776072	−	0.630644i	$-0.782791\pi$
$41$	−9.93857	−1.55214	−0.776072	+	0.630644i	$0.782791\pi$
$42$	3.41432	0.526841
$43$	−5.47393	−0.834766	−0.417383	−	0.908731i	$-0.637053\pi$
$43$	−5.47393	−0.834766	−0.417383	+	0.908731i	$0.637053\pi$
$44$	−0.645650	−0.0973355
$45$	13.5433	2.01892
$46$	−1.89562	−0.279494
$47$	−7.98708	−1.16504	−0.582518	−	0.812818i	$-0.697932\pi$
$47$	−7.98708	−1.16504	−0.582518	+	0.812818i	$0.697932\pi$
$48$	9.57707	1.38233
$49$	6.79720	0.971028
$50$	0.729959	0.103232
$51$	−2.83368	−0.396795
$52$	8.19589	1.13657
$53$	8.66658	1.19045	0.595223	−	0.803560i	$-0.297064\pi$
$53$	8.66658	1.19045	0.595223	+	0.803560i	$0.297064\pi$
$54$	1.86574	0.253896
$55$	0.917525	0.123719
$56$	−4.69284	−0.627107
$57$	2.85685	0.378399
$58$	2.59298	0.340474
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−14.4573	−1.86643
$61$	−8.26024	−1.05761	−0.528807	−	0.848742i	$-0.677361\pi$
$61$	−8.26024	−1.05761	−0.528807	+	0.848742i	$0.677361\pi$
$62$	−0.0911475	−0.0115757
$63$	18.6828	2.35381
$64$	−5.58417	−0.698022
$65$	−11.6471	−1.44464
$66$	0.313219	0.0385546
$67$	15.0154	1.83443	0.917213	−	0.398397i	$-0.130433\pi$
$67$	15.0154	1.83443	0.917213	+	0.398397i	$0.130433\pi$
$68$	1.89478	0.229775
$69$	−16.5594	−1.99352
$70$	3.24438	0.387777
$71$	14.0515	1.66761	0.833803	−	0.552062i	$-0.186159\pi$
$71$	14.0515	1.66761	0.833803	+	0.552062i	$0.186159\pi$
$72$	−6.35458	−0.748895
$73$	6.40457	0.749598	0.374799	−	0.927106i	$-0.377712\pi$
$73$	6.40457	0.749598	0.374799	+	0.927106i	$0.377712\pi$
$74$	−1.61573	−0.187825
$75$	6.37664	0.736311
$76$	−1.91027	−0.219123
$77$	1.26571	0.144241
$78$	−3.97601	−0.450195
$79$	−1.31699	−0.148173	−0.0740866	−	0.997252i	$-0.523604\pi$
$79$	−1.31699	−0.148173	−0.0740866	+	0.997252i	$0.523604\pi$
$80$	9.10038	1.01745
$81$	1.20915	0.134350
$82$	−3.22390	−0.356021
$83$	−6.78323	−0.744556	−0.372278	−	0.928121i	$-0.621423\pi$
$83$	−6.78323	−0.744556	−0.372278	+	0.928121i	$0.621423\pi$
$84$	−19.9436	−2.17603
$85$	−2.69264	−0.292058
$86$	−1.77565	−0.191473
$87$	22.6512	2.42847
$88$	−0.430507	−0.0458922
$89$	4.00061	0.424064	0.212032	−	0.977263i	$-0.431992\pi$
$89$	4.00061	0.424064	0.212032	+	0.977263i	$0.431992\pi$
$90$	4.39322	0.463086
$91$	−16.0670	−1.68428
$92$	11.0726	1.15440
$93$	−0.796229	−0.0825651
$94$	−2.59087	−0.267228
$95$	2.71466	0.278518
$96$	10.2668	1.04785
$97$	17.0241	1.72854	0.864269	−	0.503029i	$-0.167781\pi$
$97$	17.0241	1.72854	0.864269	+	0.503029i	$0.167781\pi$
$98$	2.20489	0.222728
$99$	1.71390	0.172254
$100$	−4.26382	−0.426382
$101$	−3.60432	−0.358644	−0.179322	−	0.983790i	$-0.557390\pi$
$101$	−3.60432	−0.358644	−0.179322	+	0.983790i	$0.557390\pi$
$102$	−0.919198	−0.0910142
$103$	13.4008	1.32042	0.660211	−	0.751080i	$-0.270467\pi$
$103$	13.4008	1.32042	0.660211	+	0.751080i	$0.270467\pi$
$104$	5.46486	0.535874
$105$	28.3416	2.76586
$106$	2.81129	0.273057
$107$	−11.0600	−1.06921	−0.534605	−	0.845102i	$-0.679539\pi$
$107$	−11.0600	−1.06921	−0.534605	+	0.845102i	$0.679539\pi$
$108$	−10.8981	−1.04867
$109$	−11.1909	−1.07190	−0.535949	−	0.844250i	$-0.680046\pi$
$109$	−11.1909	−1.07190	−0.535949	+	0.844250i	$0.680046\pi$
$110$	0.297629	0.0283778
$111$	−14.1144	−1.33968
$112$	12.5539	1.18623
$113$	−5.88789	−0.553886	−0.276943	−	0.960886i	$-0.589321\pi$
$113$	−5.88789	−0.553886	−0.276943	+	0.960886i	$0.589321\pi$
$114$	0.926714	0.0867947
$115$	−15.7352	−1.46731
$116$	−15.1460	−1.40627
$117$	−21.7563	−2.01137
$118$	0.324383	0.0298619
$119$	−3.71446	−0.340504
$120$	−9.63983	−0.879992
$121$	−10.8839	−0.989444
$122$	−2.67948	−0.242589
$123$	−28.1628	−2.53935
$124$	0.532408	0.0478117
$125$	−7.40394	−0.662229
$126$	6.06038	0.539902
$127$	2.04909	0.181827	0.0909135	−	0.995859i	$-0.471021\pi$
$127$	2.04909	0.181827	0.0909135	+	0.995859i	$0.471021\pi$
$128$	−9.05766	−0.800591
$129$	−15.5114	−1.36570
$130$	−3.77811	−0.331362
$131$	7.65668	0.668967	0.334483	−	0.942402i	$-0.391438\pi$
$131$	7.65668	0.668967	0.334483	+	0.942402i	$0.391438\pi$
$132$	−1.82957	−0.159243
$133$	3.74483	0.324718
$134$	4.87075	0.420768
$135$	15.4872	1.33292
$136$	1.26340	0.108336
$137$	−16.6434	−1.42195	−0.710973	−	0.703220i	$-0.751745\pi$
$137$	−16.6434	−1.42195	−0.710973	+	0.703220i	$0.751745\pi$
$138$	−5.37158	−0.457260
$139$	13.6228	1.15547	0.577736	−	0.816224i	$-0.303936\pi$
$139$	13.6228	1.15547	0.577736	+	0.816224i	$0.303936\pi$
$140$	−18.9510	−1.60165
$141$	−22.6328	−1.90603
$142$	4.55807	0.382504
$143$	−1.47393	−0.123257
$144$	16.9992	1.41660
$145$	21.5238	1.78745
$146$	2.07753	0.171938
$147$	19.2611	1.58863
$148$	9.43775	0.775778
$149$	0.149712	0.0122649	0.00613244	−	0.999981i	$-0.498048\pi$
$149$	0.149712	0.0122649	0.00613244	+	0.999981i	$0.498048\pi$
$150$	2.06847	0.168890
$151$	−8.79076	−0.715382	−0.357691	−	0.933840i	$-0.616436\pi$
$151$	−8.79076	−0.715382	−0.357691	+	0.933840i	$0.616436\pi$
$152$	−1.27373	−0.103313
$153$	−5.02975	−0.406631
$154$	0.410576	0.0330851
$155$	−0.756598	−0.0607714
$156$	23.2246	1.85945
$157$	−21.9254	−1.74984	−0.874918	−	0.484270i	$-0.839085\pi$
$157$	−21.9254	−1.74984	−0.874918	+	0.484270i	$0.839085\pi$
$158$	−0.427210	−0.0339870
$159$	24.5583	1.94760
$160$	9.75576	0.771261
$161$	−21.7064	−1.71071
$162$	0.392228	0.0308163
$163$	−11.2648	−0.882325	−0.441163	−	0.897427i	$-0.645434\pi$
$163$	−11.2648	−0.882325	−0.441163	+	0.897427i	$0.645434\pi$
$164$	18.8314	1.47048
$165$	2.59997	0.202408
$166$	−2.20036	−0.170781
$167$	3.61398	0.279658	0.139829	−	0.990176i	$-0.455345\pi$
$167$	3.61398	0.279658	0.139829	+	0.990176i	$0.455345\pi$
$168$	−13.2980	−1.02596
$169$	5.71014	0.439242
$170$	−0.873446	−0.0669902
$171$	5.07088	0.387780
$172$	10.3719	0.790847
$173$	21.3964	1.62674	0.813371	−	0.581745i	$-0.197630\pi$
$173$	21.3964	1.62674	0.813371	+	0.581745i	$0.197630\pi$
$174$	7.34767	0.557025
$175$	8.35865	0.631854
$176$	1.15165	0.0868090
$177$	2.83368	0.212993
$178$	1.29773	0.0972690
$179$	−12.7113	−0.950085	−0.475042	−	0.879963i	$-0.657567\pi$
$179$	−12.7113	−0.950085	−0.475042	+	0.879963i	$0.657567\pi$
$180$	−25.6615	−1.91270
$181$	3.46762	0.257747	0.128873	−	0.991661i	$-0.458864\pi$
$181$	3.46762	0.257747	0.128873	+	0.991661i	$0.458864\pi$
$182$	−5.21185	−0.386328
$183$	−23.4069	−1.73029
$184$	7.38301	0.544283
$185$	−13.4118	−0.986058
$186$	−0.258283	−0.0189382
$187$	−0.340753	−0.0249183
$188$	15.1337	1.10374
$189$	21.3643	1.55403
$190$	0.880588	0.0638846
$191$	15.0324	1.08771	0.543853	−	0.839180i	$-0.316965\pi$
$191$	15.0324	1.08771	0.543853	+	0.839180i	$0.316965\pi$
$192$	−15.8238	−1.14198
$193$	16.9863	1.22270	0.611350	−	0.791360i	$-0.290627\pi$
$193$	16.9863	1.22270	0.611350	+	0.791360i	$0.290627\pi$
$194$	5.52234	0.396481
$195$	−33.0041	−2.36347
$196$	−12.8792	−0.919940
$197$	7.15928	0.510078	0.255039	−	0.966931i	$-0.417912\pi$
$197$	7.15928	0.510078	0.255039	+	0.966931i	$0.417912\pi$
$198$	0.555961	0.0395104
$199$	−7.11426	−0.504317	−0.252158	−	0.967686i	$-0.581140\pi$
$199$	−7.11426	−0.504317	−0.252158	+	0.967686i	$0.581140\pi$
$200$	−2.84303	−0.201032
$201$	42.5489	3.00117
$202$	−1.16918	−0.0822633
$203$	29.6918	2.08395
$204$	5.36919	0.375919
$205$	−26.7610	−1.86907
$206$	4.34700	0.302870
$207$	−29.3927	−2.04294
$208$	−14.6191	−1.01365
$209$	0.343539	0.0237631
$210$	9.19353	0.634414
$211$	−2.29312	−0.157865	−0.0789325	−	0.996880i	$-0.525151\pi$
$211$	−2.29312	−0.157865	−0.0789325	+	0.996880i	$0.525151\pi$
$212$	−16.4212	−1.12781
$213$	39.8175	2.72825
$214$	−3.58767	−0.245248
$215$	−14.7393	−1.00521
$216$	−7.26665	−0.494433
$217$	−1.04372	−0.0708521
$218$	−3.63015	−0.245865
$219$	18.1485	1.22636
$220$	−1.73850	−0.117210
$221$	4.32552	0.290966
$222$	−4.57846	−0.307286
$223$	−16.5770	−1.11007	−0.555037	−	0.831825i	$-0.687296\pi$
$223$	−16.5770	−1.11007	−0.555037	+	0.831825i	$0.687296\pi$
$224$	13.4579	0.899196
$225$	11.3185	0.754564
$226$	−1.90993	−0.127047
$227$	1.96949	0.130720	0.0653599	−	0.997862i	$-0.479180\pi$
$227$	1.96949	0.130720	0.0653599	+	0.997862i	$0.479180\pi$
$228$	−5.41309	−0.358491
$229$	13.3234	0.880434	0.440217	−	0.897891i	$-0.354901\pi$
$229$	13.3234	0.880434	0.440217	+	0.897891i	$0.354901\pi$
$230$	−5.10422	−0.336562
$231$	3.58663	0.235983
$232$	−10.0991	−0.663036
$233$	0.274657	0.0179933	0.00899667	−	0.999960i	$-0.497136\pi$
$233$	0.274657	0.0179933	0.00899667	+	0.999960i	$0.497136\pi$
$234$	−7.05737	−0.461355
$235$	−21.5063	−1.40292
$236$	−1.89478	−0.123339
$237$	−3.73194	−0.242415
$238$	−1.20491	−0.0781025
$239$	1.86106	0.120382	0.0601910	−	0.998187i	$-0.480829\pi$
$239$	1.86106	0.120382	0.0601910	+	0.998187i	$0.480829\pi$
$240$	25.7876	1.66458
$241$	−23.7306	−1.52862	−0.764311	−	0.644848i	$-0.776921\pi$
$241$	−23.7306	−1.52862	−0.764311	+	0.644848i	$0.776921\pi$
$242$	−3.53055	−0.226952
$243$	−13.8287	−0.887110
$244$	15.6513	1.00197
$245$	18.3024	1.16930
$246$	−9.13552	−0.582459
$247$	−4.36089	−0.277477
$248$	0.354999	0.0225425
$249$	−19.2215	−1.21811
$250$	−2.40171	−0.151898
$251$	−25.1732	−1.58892	−0.794459	−	0.607318i	$-0.792246\pi$
$251$	−25.1732	−1.58892	−0.794459	+	0.607318i	$0.792246\pi$
$252$	−35.3997	−2.22997
$253$	−1.99128	−0.125191
$254$	0.664688	0.0417063
$255$	−7.63008	−0.477814
$256$	8.23020	0.514387
$257$	14.1936	0.885373	0.442687	−	0.896676i	$-0.354025\pi$
$257$	14.1936	0.885373	0.442687	+	0.896676i	$0.354025\pi$
$258$	−5.03162	−0.313255
$259$	−18.5015	−1.14962
$260$	22.0686	1.36864
$261$	40.2056	2.48867
$262$	2.48369	0.153443
$263$	10.6949	0.659475	0.329737	−	0.944073i	$-0.393040\pi$
$263$	10.6949	0.659475	0.329737	+	0.944073i	$0.393040\pi$
$264$	−1.21992	−0.0750809
$265$	23.3360	1.43352
$266$	1.21476	0.0744816
$267$	11.3365	0.693780
$268$	−28.4509	−1.73791
$269$	−13.8804	−0.846304	−0.423152	−	0.906059i	$-0.639076\pi$
$269$	−13.8804	−0.846304	−0.423152	+	0.906059i	$0.639076\pi$
$270$	5.02377	0.305737
$271$	−25.0411	−1.52114	−0.760568	−	0.649258i	$-0.775079\pi$
$271$	−25.0411	−1.52114	−0.760568	+	0.649258i	$0.775079\pi$
$272$	−3.37973	−0.204926
$273$	−45.5287	−2.75552
$274$	−5.39885	−0.326156
$275$	0.766797	0.0462396
$276$	31.3763	1.88863
$277$	−25.8759	−1.55473	−0.777366	−	0.629049i	$-0.783445\pi$
$277$	−25.8759	−1.55473	−0.777366	+	0.629049i	$0.783445\pi$
$278$	4.41901	0.265034
$279$	−1.41330	−0.0846119
$280$	−12.6361	−0.755153
$281$	−10.3732	−0.618815	−0.309407	−	0.950930i	$-0.600131\pi$
$281$	−10.3732	−0.618815	−0.309407	+	0.950930i	$0.600131\pi$
$282$	−7.34171	−0.437192
$283$	16.3279	0.970591	0.485295	−	0.874350i	$-0.338712\pi$
$283$	16.3279	0.970591	0.485295	+	0.874350i	$0.338712\pi$
$284$	−26.6244	−1.57987
$285$	7.69247	0.455663
$286$	−0.478119	−0.0282718
$287$	−36.9164	−2.17911
$288$	18.2234	1.07382
$289$	1.00000	0.0588235
$290$	6.98195	0.409994
$291$	48.2410	2.82794
$292$	−12.1352	−0.710160
$293$	17.6430	1.03072	0.515358	−	0.856975i	$-0.327659\pi$
$293$	17.6430	1.03072	0.515358	+	0.856975i	$0.327659\pi$
$294$	6.24797	0.364389
$295$	2.69264	0.156771
$296$	6.29290	0.365767
$297$	1.95990	0.113725
$298$	0.0485640	0.00281324
$299$	25.2774	1.46183
$300$	−12.0823	−0.697572
$301$	−20.3327	−1.17196
$302$	−2.85157	−0.164089
$303$	−10.2135	−0.586750
$304$	3.40736	0.195426
$305$	−22.2418	−1.27356
$306$	−1.63157	−0.0932704
$307$	−9.29328	−0.530395	−0.265198	−	0.964194i	$-0.585437\pi$
$307$	−9.29328	−0.530395	−0.265198	+	0.964194i	$0.585437\pi$
$308$	−2.39824	−0.136652
$309$	37.9737	2.16025
$310$	−0.245427	−0.0139393
$311$	18.8085	1.06653	0.533267	−	0.845947i	$-0.320964\pi$
$311$	18.8085	1.06653	0.533267	+	0.845947i	$0.320964\pi$
$312$	15.4857	0.876703
$313$	21.3975	1.20946	0.604730	−	0.796431i	$-0.293281\pi$
$313$	21.3975	1.20946	0.604730	+	0.796431i	$0.293281\pi$
$314$	−7.11222	−0.401366
$315$	50.3060	2.83442
$316$	2.49540	0.140377
$317$	0.847612	0.0476066	0.0238033	−	0.999717i	$-0.492422\pi$
$317$	0.847612	0.0476066	0.0238033	+	0.999717i	$0.492422\pi$
$318$	7.96630	0.446728
$319$	2.72383	0.152505
$320$	−15.0362	−0.840547
$321$	−31.3405	−1.74925
$322$	−7.04120	−0.392391
$323$	−1.00818	−0.0560965
$324$	−2.29107	−0.127282
$325$	−9.73373	−0.539930
$326$	−3.65410	−0.202382
$327$	−31.7116	−1.75365
$328$	12.5564	0.693310
$329$	−29.6677	−1.63563
$330$	0.843387	0.0464269
$331$	2.95458	0.162398	0.0811991	−	0.996698i	$-0.474125\pi$
$331$	2.95458	0.162398	0.0811991	+	0.996698i	$0.474125\pi$
$332$	12.8527	0.705383
$333$	−25.0528	−1.37289
$334$	1.17231	0.0641461
$335$	40.4311	2.20899
$336$	35.5736	1.94070
$337$	16.8977	0.920474	0.460237	−	0.887796i	$-0.347764\pi$
$337$	16.8977	0.920474	0.460237	+	0.887796i	$0.347764\pi$
$338$	1.85227	0.100750
$339$	−16.6844	−0.906172
$340$	5.10195	0.276692
$341$	−0.0957473	−0.00518501
$342$	1.64491	0.0889464
$343$	−0.753309	−0.0406749
$344$	6.91575	0.372872
$345$	−44.5885	−2.40056
$346$	6.94064	0.373131
$347$	11.1544	0.598800	0.299400	−	0.954128i	$-0.403213\pi$
$347$	11.1544	0.598800	0.299400	+	0.954128i	$0.403213\pi$
$348$	−42.9190	−2.30070
$349$	20.0511	1.07331	0.536655	−	0.843802i	$-0.319688\pi$
$349$	20.0511	1.07331	0.536655	+	0.843802i	$0.319688\pi$
$350$	2.71140	0.144931
$351$	−24.8790	−1.32794
$352$	1.23459	0.0658039
$353$	17.3350	0.922648	0.461324	−	0.887232i	$-0.347375\pi$
$353$	17.3350	0.922648	0.461324	+	0.887232i	$0.347375\pi$
$354$	0.919198	0.0488548
$355$	37.8356	2.00811
$356$	−7.58026	−0.401753
$357$	−10.5256	−0.557073
$358$	−4.12332	−0.217924
$359$	33.3891	1.76221	0.881104	−	0.472922i	$-0.156801\pi$
$359$	33.3891	1.76221	0.881104	+	0.472922i	$0.156801\pi$
$360$	−17.1106	−0.901807
$361$	−17.9836	−0.946504
$362$	1.12484	0.0591202
$363$	−30.8415	−1.61876
$364$	30.4433	1.59566
$365$	17.2452	0.902654
$366$	−7.59279	−0.396882
$367$	9.01784	0.470728	0.235364	−	0.971907i	$-0.424372\pi$
$367$	9.01784	0.470728	0.235364	+	0.971907i	$0.424372\pi$
$368$	−19.7504	−1.02956
$369$	−49.9886	−2.60230
$370$	−4.35057	−0.226176
$371$	32.1916	1.67131
$372$	1.50868	0.0782212
$373$	−11.4194	−0.591273	−0.295636	−	0.955301i	$-0.595532\pi$
$373$	−11.4194	−0.591273	−0.295636	+	0.955301i	$0.595532\pi$
$374$	−0.110534	−0.00571560
$375$	−20.9804	−1.08342
$376$	10.0909	0.520397
$377$	−34.5763	−1.78077
$378$	6.93023	0.356452
$379$	−4.64312	−0.238501	−0.119251	−	0.992864i	$-0.538049\pi$
$379$	−4.64312	−0.238501	−0.119251	+	0.992864i	$0.538049\pi$
$380$	−5.14366	−0.263864
$381$	5.80646	0.297474
$382$	4.87626	0.249491
$383$	−25.0826	−1.28166	−0.640829	−	0.767683i	$-0.721409\pi$
$383$	−25.0826	−1.28166	−0.640829	+	0.767683i	$0.721409\pi$
$384$	−25.6665	−1.30979
$385$	3.40811	0.173693
$386$	5.51006	0.280455
$387$	−27.5325	−1.39956
$388$	−32.2569	−1.63760
$389$	18.4933	0.937646	0.468823	−	0.883292i	$-0.344678\pi$
$389$	18.4933	0.937646	0.468823	+	0.883292i	$0.344678\pi$
$390$	−10.7060	−0.542117
$391$	5.84377	0.295532
$392$	−8.58757	−0.433738
$393$	21.6966	1.09445
$394$	2.32235	0.116998
$395$	−3.54618	−0.178428
$396$	−3.24746	−0.163191
$397$	24.0474	1.20691	0.603453	−	0.797399i	$-0.293791\pi$
$397$	24.0474	1.20691	0.603453	+	0.797399i	$0.293791\pi$
$398$	−2.30775	−0.115677
$399$	10.6117	0.531247
$400$	7.60540	0.380270
$401$	−10.6009	−0.529382	−0.264691	−	0.964333i	$-0.585270\pi$
$401$	−10.6009	−0.529382	−0.264691	+	0.964333i	$0.585270\pi$
$402$	13.8021	0.688389
$403$	1.21542	0.0605443
$404$	6.82938	0.339775
$405$	3.25580	0.161782
$406$	9.63150	0.478003
$407$	−1.69727	−0.0841304
$408$	3.58007	0.177240
$409$	29.5517	1.46124	0.730618	−	0.682787i	$-0.239232\pi$
$409$	29.5517	1.46124	0.730618	+	0.682787i	$0.239232\pi$
$410$	−8.68081	−0.428715
$411$	−47.1622	−2.32634
$412$	−25.3916	−1.25095
$413$	3.71446	0.182777
$414$	−9.53450	−0.468595
$415$	−18.2648	−0.896583
$416$	−15.6719	−0.768378
$417$	38.6027	1.89038
$418$	0.111438	0.00545062
$419$	28.1781	1.37659	0.688295	−	0.725431i	$-0.258360\pi$
$419$	28.1781	1.37659	0.688295	+	0.725431i	$0.258360\pi$
$420$	−53.7010	−2.62034
$421$	−1.21620	−0.0592739	−0.0296370	−	0.999561i	$-0.509435\pi$
$421$	−1.21620	−0.0592739	−0.0296370	+	0.999561i	$0.509435\pi$
$422$	−0.743849	−0.0362100
$423$	−40.1730	−1.95328
$424$	−10.9493	−0.531747
$425$	−2.25030	−0.109156
$426$	12.9161	0.625787
$427$	−30.6823	−1.48482
$428$	20.9562	1.01296
$429$	−4.17666	−0.201651
$430$	−4.78118	−0.230569
$431$	−6.53740	−0.314895	−0.157448	−	0.987527i	$-0.550327\pi$
$431$	−6.53740	−0.314895	−0.157448	+	0.987527i	$0.550327\pi$
$432$	19.4391	0.935263
$433$	−5.56036	−0.267214	−0.133607	−	0.991034i	$-0.542656\pi$
$433$	−5.56036	−0.267214	−0.133607	+	0.991034i	$0.542656\pi$
$434$	−0.338564	−0.0162516
$435$	60.9915	2.92432
$436$	21.2043	1.01550
$437$	−5.89156	−0.281831
$438$	5.88706	0.281295
$439$	−9.56202	−0.456371	−0.228185	−	0.973618i	$-0.573279\pi$
$439$	−9.56202	−0.456371	−0.228185	+	0.973618i	$0.573279\pi$
$440$	−1.15920	−0.0552627
$441$	34.1882	1.62801
$442$	1.40313	0.0667399
$443$	14.2173	0.675485	0.337743	−	0.941238i	$-0.390337\pi$
$443$	14.2173	0.675485	0.337743	+	0.941238i	$0.390337\pi$
$444$	26.7436	1.26919
$445$	10.7722	0.510651
$446$	−5.37728	−0.254622
$447$	0.424236	0.0200657
$448$	−20.7422	−0.979976
$449$	−2.65776	−0.125428	−0.0627138	−	0.998032i	$-0.519976\pi$
$449$	−2.65776	−0.125428	−0.0627138	+	0.998032i	$0.519976\pi$
$450$	3.67151	0.173077
$451$	−3.38660	−0.159469
$452$	11.1562	0.524745
$453$	−24.9102	−1.17038
$454$	0.638870	0.0299837
$455$	−43.2625	−2.02818
$456$	−3.60934	−0.169023
$457$	−21.0820	−0.986175	−0.493087	−	0.869980i	$-0.664132\pi$
$457$	−21.0820	−0.986175	−0.493087	+	0.869980i	$0.664132\pi$
$458$	4.32188	0.201948
$459$	−5.75167	−0.268465
$460$	29.8146	1.39011
$461$	−24.4159	−1.13716	−0.568580	−	0.822628i	$-0.692507\pi$
$461$	−24.4159	−1.13716	−0.568580	+	0.822628i	$0.692507\pi$
$462$	1.16344	0.0541281
$463$	1.67157	0.0776845	0.0388423	−	0.999245i	$-0.487633\pi$
$463$	1.67157	0.0776845	0.0388423	+	0.999245i	$0.487633\pi$
$464$	27.0161	1.25419
$465$	−2.14396	−0.0994236
$466$	0.0890939	0.00412719
$467$	30.6978	1.42052	0.710261	−	0.703938i	$-0.248577\pi$
$467$	30.6978	1.42052	0.710261	+	0.703938i	$0.248577\pi$
$468$	41.2233	1.90555
$469$	55.7742	2.57541
$470$	−6.97628	−0.321792
$471$	−62.1296	−2.86278
$472$	−1.26340	−0.0581526
$473$	−1.86526	−0.0857646
$474$	−1.21058	−0.0556036
$475$	2.26870	0.104095
$476$	7.03806	0.322589
$477$	43.5907	1.99588
$478$	0.603696	0.0276124
$479$	17.3431	0.792425	0.396212	−	0.918159i	$-0.370324\pi$
$479$	17.3431	0.792425	0.396212	+	0.918159i	$0.370324\pi$
$480$	27.6447	1.26180
$481$	21.5451	0.982373
$482$	−7.69780	−0.350625
$483$	−61.5092	−2.79876
$484$	20.6225	0.937388
$485$	45.8398	2.08148
$486$	−4.48578	−0.203479
$487$	30.2579	1.37111	0.685557	−	0.728019i	$-0.259559\pi$
$487$	30.2579	1.37111	0.685557	+	0.728019i	$0.259559\pi$
$488$	10.4360	0.472414
$489$	−31.9208	−1.44351
$490$	5.93698	0.268206
$491$	15.1445	0.683463	0.341732	−	0.939798i	$-0.388987\pi$
$491$	15.1445	0.683463	0.341732	+	0.939798i	$0.388987\pi$
$492$	53.3621	2.40575
$493$	−7.99356	−0.360012
$494$	−1.41460	−0.0636458
$495$	4.61492	0.207425
$496$	−0.949661	−0.0426410
$497$	52.1937	2.34121
$498$	−6.23513	−0.279403
$499$	8.04045	0.359940	0.179970	−	0.983672i	$-0.442400\pi$
$499$	8.04045	0.359940	0.179970	+	0.983672i	$0.442400\pi$
$500$	14.0288	0.627388
$501$	10.2409	0.457528
$502$	−8.16576	−0.364456
$503$	16.4864	0.735090	0.367545	−	0.930006i	$-0.380198\pi$
$503$	16.4864	0.735090	0.367545	+	0.930006i	$0.380198\pi$
$504$	−23.6038	−1.05140
$505$	−9.70514	−0.431873
$506$	−0.645938	−0.0287155
$507$	16.1807	0.718611
$508$	−3.88256	−0.172261
$509$	38.9626	1.72698	0.863492	−	0.504362i	$-0.168272\pi$
$509$	38.9626	1.72698	0.863492	+	0.504362i	$0.168272\pi$
$510$	−2.47507	−0.109598
$511$	23.7895	1.05239
$512$	20.7850	0.918578
$513$	5.79870	0.256019
$514$	4.60417	0.203081
$515$	36.0836	1.59003
$516$	29.3906	1.29385
$517$	−2.72162	−0.119697
$518$	−6.00156	−0.263693
$519$	60.6307	2.66139
$520$	14.7149	0.645291
$521$	28.0112	1.22719	0.613596	−	0.789620i	$-0.289723\pi$
$521$	28.0112	1.22719	0.613596	+	0.789620i	$0.289723\pi$
$522$	13.0420	0.570834
$523$	−18.0870	−0.790891	−0.395445	−	0.918490i	$-0.629410\pi$
$523$	−18.0870	−0.790891	−0.395445	+	0.918490i	$0.629410\pi$
$524$	−14.5077	−0.633771
$525$	23.6858	1.03373
$526$	3.46924	0.151266
$527$	0.280987	0.0122400
$528$	3.26341	0.142022
$529$	11.1497	0.484769
$530$	7.56979	0.328811
$531$	5.02975	0.218273
$532$	−7.09561	−0.307634
$533$	42.9895	1.86208
$534$	3.67735	0.159135
$535$	−29.7805	−1.28753
$536$	−18.9705	−0.819399
$537$	−36.0197	−1.55436
$538$	−4.50257	−0.194120
$539$	2.31616	0.0997643
$540$	−29.3447	−1.26280
$541$	−7.69199	−0.330704	−0.165352	−	0.986235i	$-0.552876\pi$
$541$	−7.69199	−0.330704	−0.165352	+	0.986235i	$0.552876\pi$
$542$	−8.12289	−0.348908
$543$	9.82614	0.421680
$544$	−3.62312	−0.155340
$545$	−30.1332	−1.29076
$546$	−14.7687	−0.632043
$547$	13.5959	0.581317	0.290658	−	0.956827i	$-0.406126\pi$
$547$	13.5959	0.581317	0.290658	+	0.956827i	$0.406126\pi$
$548$	31.5356	1.34713
$549$	−41.5469	−1.77318
$550$	0.248736	0.0106061
$551$	8.05893	0.343322
$552$	20.9211	0.890462
$553$	−4.89191	−0.208025
$554$	−8.39370	−0.356614
$555$	−38.0049	−1.61322
$556$	−25.8122	−1.09468
$557$	−6.30537	−0.267167	−0.133583	−	0.991038i	$-0.542648\pi$
$557$	−6.30537	−0.267167	−0.133583	+	0.991038i	$0.542648\pi$
$558$	−0.458450	−0.0194077
$559$	23.6776	1.00146
$560$	33.8030	1.42844
$561$	−0.965586	−0.0407671
$562$	−3.36490	−0.141940
$563$	−16.6334	−0.701016	−0.350508	−	0.936560i	$-0.613991\pi$
$563$	−16.6334	−0.701016	−0.350508	+	0.936560i	$0.613991\pi$
$564$	42.8842	1.80575
$565$	−15.8540	−0.666981
$566$	5.29648	0.222628
$567$	4.49134	0.188618
$568$	−17.7526	−0.744884
$569$	17.4058	0.729690	0.364845	−	0.931068i	$-0.381122\pi$
$569$	17.4058	0.729690	0.364845	+	0.931068i	$0.381122\pi$
$570$	2.49531	0.104517
$571$	−28.1380	−1.17754	−0.588769	−	0.808301i	$-0.700387\pi$
$571$	−28.1380	−1.17754	−0.588769	+	0.808301i	$0.700387\pi$
$572$	2.79278	0.116772
$573$	42.5971	1.77952
$574$	−11.9751	−0.499829
$575$	−13.1503	−0.548403
$576$	−28.0870	−1.17029
$577$	16.6512	0.693198	0.346599	−	0.938013i	$-0.387337\pi$
$577$	16.6512	0.693198	0.346599	+	0.938013i	$0.387337\pi$
$578$	0.324383	0.0134926
$579$	48.1337	2.00037
$580$	−40.7827	−1.69341
$581$	−25.1960	−1.04531
$582$	15.6485	0.648653
$583$	2.95316	0.122308
$584$	−8.09152	−0.334829
$585$	−58.5819	−2.42206
$586$	5.72309	0.236419
$587$	−45.9933	−1.89835	−0.949173	−	0.314756i	$-0.898077\pi$
$587$	−45.9933	−1.89835	−0.949173	+	0.314756i	$0.898077\pi$
$588$	−36.4954	−1.50505
$589$	−0.283285	−0.0116726
$590$	0.873446	0.0359592
$591$	20.2871	0.834501
$592$	−16.8342	−0.691881
$593$	41.4656	1.70279	0.851395	−	0.524526i	$-0.175757\pi$
$593$	41.4656	1.70279	0.851395	+	0.524526i	$0.175757\pi$
$594$	0.635758	0.0260855
$595$	−10.0017	−0.410029
$596$	−0.283670	−0.0116196
$597$	−20.1596	−0.825076
$598$	8.19955	0.335304
$599$	26.1886	1.07004	0.535019	−	0.844840i	$-0.320305\pi$
$599$	26.1886	1.07004	0.535019	+	0.844840i	$0.320305\pi$
$600$	−8.05624	−0.328894
$601$	−32.4970	−1.32558	−0.662789	−	0.748806i	$-0.730628\pi$
$601$	−32.4970	−1.32558	−0.662789	+	0.748806i	$0.730628\pi$
$602$	−6.59557	−0.268815
$603$	75.5239	3.07557
$604$	16.6565	0.677744
$605$	−29.3064	−1.19147
$606$	−3.31309	−0.134585
$607$	−15.0232	−0.609773	−0.304886	−	0.952389i	$-0.598618\pi$
$607$	−15.0232	−0.609773	−0.304886	+	0.952389i	$0.598618\pi$
$608$	3.65275	0.148139
$609$	84.1370	3.40940
$610$	−7.21487	−0.292121
$611$	34.5483	1.39767
$612$	9.53025	0.385238
$613$	−18.0533	−0.729166	−0.364583	−	0.931171i	$-0.618788\pi$
$613$	−18.0533	−0.729166	−0.364583	+	0.931171i	$0.618788\pi$
$614$	−3.01458	−0.121659
$615$	−75.8321	−3.05785
$616$	−1.59910	−0.0644296
$617$	21.5165	0.866223	0.433112	−	0.901340i	$-0.357416\pi$
$617$	21.5165	0.866223	0.433112	+	0.901340i	$0.357416\pi$
$618$	12.3180	0.495503
$619$	−47.1688	−1.89587	−0.947937	−	0.318458i	$-0.896835\pi$
$619$	−47.1688	−1.89587	−0.947937	+	0.318458i	$0.896835\pi$
$620$	1.43358	0.0575741
$621$	−33.6115	−1.34878
$622$	6.10116	0.244634
$623$	14.8601	0.595357
$624$	−41.4258	−1.65836
$625$	−31.1877	−1.24751
$626$	6.94099	0.277418
$627$	0.973481	0.0388771
$628$	41.5437	1.65777
$629$	4.98093	0.198603
$630$	16.3184	0.650141
$631$	−28.4672	−1.13326	−0.566631	−	0.823972i	$-0.691753\pi$
$631$	−28.4672	−1.13326	−0.566631	+	0.823972i	$0.691753\pi$
$632$	1.66389	0.0661858
$633$	−6.49798	−0.258271
$634$	0.274951	0.0109197
$635$	5.51745	0.218953
$636$	−46.5325	−1.84513
$637$	−29.4014	−1.16493
$638$	0.883564	0.0349806
$639$	70.6755	2.79588
$640$	−24.3890	−0.964060
$641$	27.2666	1.07697	0.538483	−	0.842637i	$-0.318998\pi$
$641$	27.2666	1.07697	0.538483	+	0.842637i	$0.318998\pi$
$642$	−10.1663	−0.401232
$643$	−7.94836	−0.313453	−0.156726	−	0.987642i	$-0.550094\pi$
$643$	−7.94836	−0.313453	−0.156726	+	0.987642i	$0.550094\pi$
$644$	41.1288	1.62070
$645$	−41.7665	−1.64455
$646$	−0.327035	−0.0128670
$647$	36.6730	1.44176	0.720882	−	0.693058i	$-0.243737\pi$
$647$	36.6730	1.44176	0.720882	+	0.693058i	$0.243737\pi$
$648$	−1.52764	−0.0600113
$649$	0.340753	0.0133757
$650$	−3.15746	−0.123846
$651$	−2.95756	−0.115916
$652$	21.3442	0.835904
$653$	13.3146	0.521039	0.260519	−	0.965469i	$-0.416106\pi$
$653$	13.3146	0.521039	0.260519	+	0.965469i	$0.416106\pi$
$654$	−10.2867	−0.402242
$655$	20.6167	0.805559
$656$	−33.5897	−1.31146
$657$	32.2134	1.25676
$658$	−9.62369	−0.375170
$659$	30.8061	1.20004	0.600018	−	0.799987i	$-0.295160\pi$
$659$	30.8061	1.20004	0.600018	+	0.799987i	$0.295160\pi$
$660$	−4.92637	−0.191758
$661$	−9.85051	−0.383140	−0.191570	−	0.981479i	$-0.561358\pi$
$661$	−9.85051	−0.383140	−0.191570	+	0.981479i	$0.561358\pi$
$662$	0.958414	0.0372498
$663$	12.2572	0.476028
$664$	8.56992	0.332578
$665$	10.0835	0.391020
$666$	−8.12671	−0.314904
$667$	−46.7126	−1.80872
$668$	−6.84768	−0.264945
$669$	−46.9738	−1.81611
$670$	13.1152	0.506683
$671$	−2.81470	−0.108660
$672$	38.1355	1.47111
$673$	0.0399067	0.00153829	0.000769146	−	1.00000i	$-0.499755\pi$
$673$	0.0399067	0.00153829	0.000769146		1.00000i	$0.499755\pi$
$674$	5.48131	0.211132
$675$	12.9430	0.498176
$676$	−10.8194	−0.416132
$677$	−6.37188	−0.244891	−0.122446	−	0.992475i	$-0.539074\pi$
$677$	−6.37188	−0.244891	−0.122446	+	0.992475i	$0.539074\pi$
$678$	−5.41213	−0.207852
$679$	63.2354	2.42675
$680$	3.40188	0.130456
$681$	5.58092	0.213861
$682$	−0.0310588	−0.00118930
$683$	40.8317	1.56238	0.781191	−	0.624292i	$-0.214613\pi$
$683$	40.8317	1.56238	0.781191	+	0.624292i	$0.214613\pi$
$684$	−9.60818	−0.367378
$685$	−44.8148	−1.71228
$686$	−0.244361	−0.00932973
$687$	37.7542	1.44041
$688$	−18.5004	−0.705320
$689$	−37.4875	−1.42816
$690$	−14.4637	−0.550625
$691$	−41.0861	−1.56299	−0.781495	−	0.623912i	$-0.785542\pi$
$691$	−41.0861	−1.56299	−0.781495	+	0.623912i	$0.785542\pi$
$692$	−40.5415	−1.54116
$693$	6.36622	0.241833
$694$	3.61830	0.137349
$695$	36.6813	1.39140
$696$	−28.6175	−1.08474
$697$	9.93857	0.376450
$698$	6.50423	0.246189
$699$	0.778289	0.0294376
$700$	−15.8378	−0.598611
$701$	25.7427	0.972287	0.486143	−	0.873879i	$-0.338403\pi$
$701$	25.7427	0.972287	0.486143	+	0.873879i	$0.338403\pi$
$702$	−8.07032	−0.304594
$703$	−5.02166	−0.189395
$704$	−1.90282	−0.0717154
$705$	−60.9421	−2.29521
$706$	5.62317	0.211631
$707$	−13.3881	−0.503512
$708$	−5.36919	−0.201787
$709$	44.0074	1.65273	0.826366	−	0.563134i	$-0.190404\pi$
$709$	44.0074	1.65273	0.826366	+	0.563134i	$0.190404\pi$
$710$	12.2732	0.460606
$711$	−6.62414	−0.248425
$712$	−5.05437	−0.189420
$713$	1.64203	0.0614944
$714$	−3.41432	−0.127778
$715$	−3.96877	−0.148424
$716$	24.0850	0.900099
$717$	5.27365	0.196948
$718$	10.8308	0.404204
$719$	−28.7713	−1.07299	−0.536493	−	0.843905i	$-0.680251\pi$
$719$	−28.7713	−1.07299	−0.536493	+	0.843905i	$0.680251\pi$
$720$	45.7727	1.70585
$721$	49.7768	1.85378
$722$	−5.83357	−0.217103
$723$	−67.2449	−2.50087
$724$	−6.57037	−0.244186
$725$	17.9879	0.668055
$726$	−10.0044	−0.371300
$727$	−41.9981	−1.55763	−0.778813	−	0.627257i	$-0.784178\pi$
$727$	−41.9981	−1.55763	−0.778813	+	0.627257i	$0.784178\pi$
$728$	20.2990	0.752331
$729$	−42.8135	−1.58568
$730$	5.59404	0.207045
$731$	5.47393	0.202461
$732$	44.3508	1.63925
$733$	11.3137	0.417882	0.208941	−	0.977928i	$-0.432998\pi$
$733$	11.3137	0.417882	0.208941	+	0.977928i	$0.432998\pi$
$734$	2.92523	0.107972
$735$	51.8631	1.91300
$736$	−21.1727	−0.780436
$737$	5.11655	0.188471
$738$	−16.2154	−0.596898
$739$	0.0209287	0.000769873 0	0.000384937	−	1.00000i	$-0.499877\pi$
$739$	0.0209287	0.000769873 0	0.000384937		1.00000i	$0.499877\pi$
$740$	25.4124	0.934180
$741$	−12.3574	−0.453960
$742$	10.4424	0.383353
$743$	−0.781000	−0.0286521	−0.0143261	−	0.999897i	$-0.504560\pi$
$743$	−0.781000	−0.0286521	−0.0143261	+	0.999897i	$0.504560\pi$
$744$	1.00595	0.0368801
$745$	0.403120	0.0147692
$746$	−3.70425	−0.135622
$747$	−34.1180	−1.24831
$748$	0.645650	0.0236073
$749$	−41.0818	−1.50110
$750$	−6.80569	−0.248509
$751$	36.3856	1.32773	0.663865	−	0.747852i	$-0.268915\pi$
$751$	36.3856	1.32773	0.663865	+	0.747852i	$0.268915\pi$
$752$	−26.9941	−0.984375
$753$	−71.3328	−2.59951
$754$	−11.2160	−0.408462
$755$	−23.6703	−0.861451
$756$	−40.4806	−1.47227
$757$	46.5387	1.69148	0.845739	−	0.533596i	$-0.179160\pi$
$757$	46.5387	1.69148	0.845739	+	0.533596i	$0.179160\pi$
$758$	−1.50615	−0.0547058
$759$	−5.64266	−0.204816
$760$	−3.42969	−0.124408
$761$	−38.5091	−1.39595	−0.697977	−	0.716120i	$-0.745916\pi$
$761$	−38.5091	−1.39595	−0.697977	+	0.716120i	$0.745916\pi$
$762$	1.88351	0.0682325
$763$	−41.5683	−1.50487
$764$	−28.4830	−1.03048
$765$	−13.5433	−0.489659
$766$	−8.13635	−0.293978
$767$	−4.32552	−0.156186
$768$	23.3218	0.841552
$769$	−23.0954	−0.832841	−0.416421	−	0.909172i	$-0.636716\pi$
$769$	−23.0954	−0.832841	−0.416421	+	0.909172i	$0.636716\pi$
$770$	1.10553	0.0398406
$771$	40.2202	1.44849
$772$	−32.1852	−1.15837
$773$	−5.46314	−0.196495	−0.0982477	−	0.995162i	$-0.531324\pi$
$773$	−5.46314	−0.196495	−0.0982477	+	0.995162i	$0.531324\pi$
$774$	−8.93107	−0.321021
$775$	−0.632307	−0.0227131
$776$	−21.5083	−0.772102
$777$	−52.4272	−1.88082
$778$	5.99890	0.215071
$779$	−10.0198	−0.358998
$780$	62.5353	2.23912
$781$	4.78809	0.171331
$782$	1.89562	0.0677872
$783$	45.9764	1.64306
$784$	22.9727	0.820452
$785$	−59.0372	−2.10713
$786$	7.03800	0.251037
$787$	36.6575	1.30670	0.653350	−	0.757056i	$-0.273363\pi$
$787$	36.6575	1.30670	0.653350	+	0.757056i	$0.273363\pi$
$788$	−13.5652	−0.483242
$789$	30.3059	1.07892
$790$	−1.15032	−0.0409266
$791$	−21.8703	−0.777619
$792$	−2.16534	−0.0769421
$793$	35.7298	1.26880
$794$	7.80057	0.276832
$795$	66.1267	2.34527
$796$	13.4799	0.477784
$797$	37.6009	1.33189	0.665947	−	0.745999i	$-0.268028\pi$
$797$	37.6009	1.33189	0.665947	+	0.745999i	$0.268028\pi$
$798$	3.44224	0.121854
$799$	7.98708	0.282563
$800$	8.15312	0.288256
$801$	20.1221	0.710979
$802$	−3.43874	−0.121426
$803$	2.18237	0.0770143
$804$	−80.6207	−2.84327
$805$	−58.4476	−2.06001
$806$	0.394261	0.0138872
$807$	−39.3327	−1.38458
$808$	4.55370	0.160199
$809$	−28.8514	−1.01436	−0.507181	−	0.861839i	$-0.669313\pi$
$809$	−28.8514	−1.01436	−0.507181	+	0.861839i	$0.669313\pi$
$810$	1.05613	0.0371085
$811$	−24.7172	−0.867937	−0.433969	−	0.900928i	$-0.642887\pi$
$811$	−24.7172	−0.867937	−0.433969	+	0.900928i	$0.642887\pi$
$812$	−56.2592	−1.97431
$813$	−70.9584	−2.48862
$814$	−0.550564	−0.0192973
$815$	−30.3320	−1.06248
$816$	−9.57707	−0.335264
$817$	−5.51869	−0.193074
$818$	9.58605	0.335169
$819$	−80.8129	−2.82383
$820$	50.7061	1.77073
$821$	35.7840	1.24887	0.624436	−	0.781076i	$-0.285329\pi$
$821$	35.7840	1.24887	0.624436	+	0.781076i	$0.285329\pi$
$822$	−15.2986	−0.533601
$823$	34.8782	1.21578	0.607888	−	0.794023i	$-0.292017\pi$
$823$	34.8782	1.21578	0.607888	+	0.794023i	$0.292017\pi$
$824$	−16.9306	−0.589805
$825$	2.17286	0.0756492
$826$	1.20491	0.0419241
$827$	−37.2888	−1.29666	−0.648329	−	0.761360i	$-0.724532\pi$
$827$	−37.2888	−1.29666	−0.648329	+	0.761360i	$0.724532\pi$
$828$	55.6926	1.93545
$829$	23.4580	0.814730	0.407365	−	0.913265i	$-0.366448\pi$
$829$	23.4580	0.814730	0.407365	+	0.913265i	$0.366448\pi$
$830$	−5.92478	−0.205652
$831$	−73.3241	−2.54358
$832$	24.1545	0.837405
$833$	−6.79720	−0.235509
$834$	12.5221	0.433603
$835$	9.73114	0.336760
$836$	−0.650930	−0.0225129
$837$	−1.61615	−0.0558622
$838$	9.14049	0.315753
$839$	51.0098	1.76106	0.880528	−	0.473995i	$-0.157189\pi$
$839$	51.0098	1.76106	0.880528	+	0.473995i	$0.157189\pi$
$840$	−35.8068	−1.23545
$841$	34.8971	1.20335
$842$	−0.394514	−0.0135959
$843$	−29.3944	−1.01240
$844$	4.34495	0.149559
$845$	15.3753	0.528928
$846$	−13.0314	−0.448030
$847$	−40.4277	−1.38911
$848$	29.2907	1.00585
$849$	46.2680	1.58791
$850$	−0.729959	−0.0250374
$851$	29.1074	0.997790
$852$	−75.4452	−2.58471
$853$	41.8867	1.43417	0.717086	−	0.696984i	$-0.245475\pi$
$853$	41.8867	1.43417	0.717086	+	0.696984i	$0.245475\pi$
$854$	−9.95281	−0.340578
$855$	13.6540	0.466958
$856$	13.9732	0.477593
$857$	6.00351	0.205076	0.102538	−	0.994729i	$-0.467304\pi$
$857$	6.00351	0.205076	0.102538	+	0.994729i	$0.467304\pi$
$858$	−1.35484	−0.0462534
$859$	−41.1486	−1.40397	−0.701987	−	0.712190i	$-0.747703\pi$
$859$	−41.1486	−1.40397	−0.701987	+	0.712190i	$0.747703\pi$
$860$	27.9277	0.952326
$861$	−104.609	−3.56508
$862$	−2.12062	−0.0722286
$863$	−5.57578	−0.189802	−0.0949009	−	0.995487i	$-0.530253\pi$
$863$	−5.57578	−0.189802	−0.0949009	+	0.995487i	$0.530253\pi$
$864$	20.8390	0.708958
$865$	57.6129	1.95890
$866$	−1.80369	−0.0612918
$867$	2.83368	0.0962369
$868$	1.97761	0.0671244
$869$	−0.448769	−0.0152234
$870$	19.7846	0.670761
$871$	−64.9495	−2.20073
$872$	14.1386	0.478794
$873$	85.6272	2.89804
$874$	−1.91112	−0.0646446
$875$	−27.5016	−0.929725
$876$	−34.3873	−1.16184
$877$	16.1609	0.545713	0.272857	−	0.962055i	$-0.412032\pi$
$877$	16.1609	0.545713	0.272857	+	0.962055i	$0.412032\pi$
$878$	−3.10176	−0.104679
$879$	49.9947	1.68628
$880$	3.10098	0.104534
$881$	55.5155	1.87037	0.935183	−	0.354165i	$-0.115235\pi$
$881$	55.5155	1.87037	0.935183	+	0.354165i	$0.115235\pi$
$882$	11.0901	0.373422
$883$	−50.9371	−1.71417	−0.857085	−	0.515175i	$-0.827727\pi$
$883$	−50.9371	−1.71417	−0.857085	+	0.515175i	$0.827727\pi$
$884$	−8.19589	−0.275658
$885$	7.63008	0.256482
$886$	4.61186	0.154938
$887$	−8.42184	−0.282778	−0.141389	−	0.989954i	$-0.545157\pi$
$887$	−8.42184	−0.282778	−0.141389	+	0.989954i	$0.545157\pi$
$888$	17.8321	0.598405
$889$	7.61124	0.255273
$890$	3.49432	0.117130
$891$	0.412021	0.0138032
$892$	31.4096	1.05167
$893$	−8.05239	−0.269463
$894$	0.137615	0.00460253
$895$	−34.2269	−1.14408
$896$	−33.6443	−1.12398
$897$	71.6280	2.39159
$898$	−0.862133	−0.0287698
$899$	−2.24609	−0.0749113
$900$	−21.4459	−0.714865
$901$	−8.66658	−0.288726
$902$	−1.09855	−0.0365779
$903$	−57.6163	−1.91735
$904$	7.43875	0.247409
$905$	9.33706	0.310374
$906$	−8.08044	−0.268455
$907$	−11.0169	−0.365810	−0.182905	−	0.983131i	$-0.558550\pi$
$907$	−11.0169	−0.365810	−0.182905	+	0.983131i	$0.558550\pi$
$908$	−3.73175	−0.123842
$909$	−18.1289	−0.601296
$910$	−14.0336	−0.465210
$911$	25.3825	0.840960	0.420480	−	0.907302i	$-0.361862\pi$
$911$	25.3825	0.840960	0.420480	+	0.907302i	$0.361862\pi$
$912$	9.65538	0.319722
$913$	−2.31141	−0.0764964
$914$	−6.83864	−0.226202
$915$	−63.0263	−2.08358
$916$	−25.2448	−0.834113
$917$	28.4404	0.939185
$918$	−1.86574	−0.0615787
$919$	−49.2733	−1.62537	−0.812687	−	0.582700i	$-0.801996\pi$
$919$	−49.2733	−1.62537	−0.812687	+	0.582700i	$0.801996\pi$
$920$	19.8798	0.655417
$921$	−26.3342	−0.867741
$922$	−7.92009	−0.260834
$923$	−60.7801	−2.00060
$924$	−6.79585	−0.223567
$925$	−11.2086	−0.368536
$926$	0.542229	0.0178188
$927$	67.4028	2.21380
$928$	28.9617	0.950713
$929$	−4.63013	−0.151910	−0.0759549	−	0.997111i	$-0.524200\pi$
$929$	−4.63013	−0.151910	−0.0759549	+	0.997111i	$0.524200\pi$
$930$	−0.695463	−0.0228051
$931$	6.85277	0.224591
$932$	−0.520413	−0.0170467
$933$	53.2974	1.74488
$934$	9.95783	0.325830
$935$	−0.917525	−0.0300063
$936$	27.4869	0.898437
$937$	50.9529	1.66456	0.832280	−	0.554356i	$-0.187035\pi$
$937$	50.9529	1.66456	0.832280	+	0.554356i	$0.187035\pi$
$938$	18.0922	0.590731
$939$	60.6338	1.97871
$940$	40.7497	1.32911
$941$	−3.45039	−0.112479	−0.0562397	−	0.998417i	$-0.517911\pi$
$941$	−3.45039	−0.112479	−0.0562397	+	0.998417i	$0.517911\pi$
$942$	−20.1538	−0.656646
$943$	58.0788	1.89131
$944$	3.37973	0.110001
$945$	57.5264	1.87134
$946$	−0.605058	−0.0196721
$947$	−32.1461	−1.04461	−0.522304	−	0.852760i	$-0.674927\pi$
$947$	−32.1461	−1.04461	−0.522304	+	0.852760i	$0.674927\pi$
$948$	7.07118	0.229661
$949$	−27.7031	−0.899280
$950$	0.735928	0.0238767
$951$	2.40186	0.0778857
$952$	4.69284	0.152096
$953$	−40.5840	−1.31464	−0.657322	−	0.753610i	$-0.728311\pi$
$953$	−40.5840	−1.31464	−0.657322	+	0.753610i	$0.728311\pi$
$954$	14.1401	0.457802
$955$	40.4768	1.30980
$956$	−3.52629	−0.114048
$957$	7.71847	0.249503
$958$	5.62579	0.181761
$959$	−61.8214	−1.99632
$960$	−42.6077	−1.37516
$961$	−30.9210	−0.997453
$962$	6.98887	0.225330
$963$	−55.6290	−1.79262
$964$	44.9641	1.44820
$965$	45.7379	1.47236
$966$	−19.9525	−0.641962
$967$	−19.8832	−0.639401	−0.319701	−	0.947519i	$-0.603582\pi$
$967$	−19.8832	−0.639401	−0.319701	+	0.947519i	$0.603582\pi$
$968$	13.7507	0.441964
$969$	−2.85685	−0.0917753
$970$	14.8697	0.477436
$971$	−43.3977	−1.39270	−0.696350	−	0.717702i	$-0.745194\pi$
$971$	−43.3977	−1.39270	−0.696350	+	0.717702i	$0.745194\pi$
$972$	26.2022	0.840437
$973$	50.6013	1.62220
$974$	9.81513	0.314497
$975$	−27.5823	−0.883340
$976$	−27.9173	−0.893612
$977$	−24.0306	−0.768808	−0.384404	−	0.923165i	$-0.625593\pi$
$977$	−24.0306	−0.768808	−0.384404	+	0.923165i	$0.625593\pi$
$978$	−10.3546	−0.331102
$979$	1.36322	0.0435687
$980$	−34.6789	−1.10778
$981$	−56.2877	−1.79713
$982$	4.91263	0.156768
$983$	−20.6654	−0.659123	−0.329561	−	0.944134i	$-0.606901\pi$
$983$	−20.6654	−0.659123	−0.329561	+	0.944134i	$0.606901\pi$
$984$	35.5808	1.13427
$985$	19.2774	0.614228
$986$	−2.59298	−0.0825772
$987$	−84.0687	−2.67594
$988$	8.26291	0.262878
$989$	31.9884	1.01717
$990$	1.49700	0.0475778
$991$	−33.6959	−1.07039	−0.535193	−	0.844730i	$-0.679761\pi$
$991$	−33.6959	−1.07039	−0.535193	+	0.844730i	$0.679761\pi$
$992$	−1.01805	−0.0323232
$993$	8.37233	0.265688
$994$	16.9307	0.537011
$995$	−19.1561	−0.607290
$996$	36.4205	1.15403
$997$	26.4670	0.838217	0.419108	−	0.907936i	$-0.362343\pi$
$997$	26.4670	0.838217	0.419108	+	0.907936i	$0.362343\pi$
$998$	2.60819	0.0825607
$999$	−28.6487	−0.906404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.12	✓	22
3.2	odd	2		9027.2.a.s.1.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.12	✓	22	1.1	even	1	trivial
9027.2.a.s.1.11		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+0.324383 q^{2} +2.83368 q^{3} -1.89478 q^{4} +2.69264 q^{5} +0.919198 q^{6} +3.71446 q^{7} -1.26340 q^{8} +5.02975 q^{9} +O(q^{10})\)	\(q+0.324383 q^{2} +2.83368 q^{3} -1.89478 q^{4} +2.69264 q^{5} +0.919198 q^{6} +3.71446 q^{7} -1.26340 q^{8} +5.02975 q^{9} +0.873446 q^{10} +0.340753 q^{11} -5.36919 q^{12} -4.32552 q^{13} +1.20491 q^{14} +7.63008 q^{15} +3.37973 q^{16} -1.00000 q^{17} +1.63157 q^{18} +1.00818 q^{19} -5.10195 q^{20} +10.5256 q^{21} +0.110534 q^{22} -5.84377 q^{23} -3.58007 q^{24} +2.25030 q^{25} -1.40313 q^{26} +5.75167 q^{27} -7.03806 q^{28} +7.99356 q^{29} +2.47507 q^{30} -0.280987 q^{31} +3.62312 q^{32} +0.965586 q^{33} -0.324383 q^{34} +10.0017 q^{35} -9.53025 q^{36} -4.98093 q^{37} +0.327035 q^{38} -12.2572 q^{39} -3.40188 q^{40} -9.93857 q^{41} +3.41432 q^{42} -5.47393 q^{43} -0.645650 q^{44} +13.5433 q^{45} -1.89562 q^{46} -7.98708 q^{47} +9.57707 q^{48} +6.79720 q^{49} +0.729959 q^{50} -2.83368 q^{51} +8.19589 q^{52} +8.66658 q^{53} +1.86574 q^{54} +0.917525 q^{55} -4.69284 q^{56} +2.85685 q^{57} +2.59298 q^{58} +1.00000 q^{59} -14.4573 q^{60} -8.26024 q^{61} -0.0911475 q^{62} +18.6828 q^{63} -5.58417 q^{64} -11.6471 q^{65} +0.313219 q^{66} +15.0154 q^{67} +1.89478 q^{68} -16.5594 q^{69} +3.24438 q^{70} +14.0515 q^{71} -6.35458 q^{72} +6.40457 q^{73} -1.61573 q^{74} +6.37664 q^{75} -1.91027 q^{76} +1.26571 q^{77} -3.97601 q^{78} -1.31699 q^{79} +9.10038 q^{80} +1.20915 q^{81} -3.22390 q^{82} -6.78323 q^{83} -19.9436 q^{84} -2.69264 q^{85} -1.77565 q^{86} +22.6512 q^{87} -0.430507 q^{88} +4.00061 q^{89} +4.39322 q^{90} -16.0670 q^{91} +11.0726 q^{92} -0.796229 q^{93} -2.59087 q^{94} +2.71466 q^{95} +10.2668 q^{96} +17.0241 q^{97} +2.20489 q^{98} +1.71390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

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