LMFDB - Embedded newform 6038.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2136727404$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.60124 q^{3} +1.00000 q^{4} -1.76472 q^{5} -1.60124 q^{6} -0.621570 q^{7} +1.00000 q^{8} -0.436015 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.60124 q^{3} +1.00000 q^{4} -1.76472 q^{5} -1.60124 q^{6} -0.621570 q^{7} +1.00000 q^{8} -0.436015 q^{9} -1.76472 q^{10} +5.06537 q^{11} -1.60124 q^{12} +6.63999 q^{13} -0.621570 q^{14} +2.82575 q^{15} +1.00000 q^{16} +6.40137 q^{17} -0.436015 q^{18} -6.97194 q^{19} -1.76472 q^{20} +0.995285 q^{21} +5.06537 q^{22} +1.76018 q^{23} -1.60124 q^{24} -1.88577 q^{25} +6.63999 q^{26} +5.50190 q^{27} -0.621570 q^{28} +4.65630 q^{29} +2.82575 q^{30} +0.133190 q^{31} +1.00000 q^{32} -8.11090 q^{33} +6.40137 q^{34} +1.09690 q^{35} -0.436015 q^{36} -10.8631 q^{37} -6.97194 q^{38} -10.6322 q^{39} -1.76472 q^{40} +2.39707 q^{41} +0.995285 q^{42} -3.33590 q^{43} +5.06537 q^{44} +0.769444 q^{45} +1.76018 q^{46} +2.14590 q^{47} -1.60124 q^{48} -6.61365 q^{49} -1.88577 q^{50} -10.2502 q^{51} +6.63999 q^{52} +0.508866 q^{53} +5.50190 q^{54} -8.93896 q^{55} -0.621570 q^{56} +11.1638 q^{57} +4.65630 q^{58} -7.92618 q^{59} +2.82575 q^{60} +2.52919 q^{61} +0.133190 q^{62} +0.271014 q^{63} +1.00000 q^{64} -11.7177 q^{65} -8.11090 q^{66} +11.0205 q^{67} +6.40137 q^{68} -2.81848 q^{69} +1.09690 q^{70} +13.9984 q^{71} -0.436015 q^{72} -15.1106 q^{73} -10.8631 q^{74} +3.01958 q^{75} -6.97194 q^{76} -3.14848 q^{77} -10.6322 q^{78} +2.75304 q^{79} -1.76472 q^{80} -7.50184 q^{81} +2.39707 q^{82} +12.4989 q^{83} +0.995285 q^{84} -11.2966 q^{85} -3.33590 q^{86} -7.45588 q^{87} +5.06537 q^{88} +9.15235 q^{89} +0.769444 q^{90} -4.12721 q^{91} +1.76018 q^{92} -0.213270 q^{93} +2.14590 q^{94} +12.3035 q^{95} -1.60124 q^{96} -1.95909 q^{97} -6.61365 q^{98} -2.20858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) $ 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.60124	−0.924479	−0.462240	−	0.886755i	$-0.652954\pi$
$3$	−1.60124	−0.924479	−0.462240	+	0.886755i	$0.652954\pi$
$4$	1.00000	0.500000
$5$	−1.76472	−0.789206	−0.394603	−	0.918852i	$-0.629118\pi$
$5$	−1.76472	−0.789206	−0.394603	+	0.918852i	$0.629118\pi$
$6$	−1.60124	−0.653705
$7$	−0.621570	−0.234931	−0.117466	−	0.993077i	$-0.537477\pi$
$7$	−0.621570	−0.234931	−0.117466	+	0.993077i	$0.537477\pi$
$8$	1.00000	0.353553
$9$	−0.436015	−0.145338
$10$	−1.76472	−0.558053
$11$	5.06537	1.52727	0.763634	−	0.645650i	$-0.223413\pi$
$11$	5.06537	1.52727	0.763634	+	0.645650i	$0.223413\pi$
$12$	−1.60124	−0.462240
$13$	6.63999	1.84160	0.920801	−	0.390033i	$-0.127537\pi$
$13$	6.63999	1.84160	0.920801	+	0.390033i	$0.127537\pi$
$14$	−0.621570	−0.166121
$15$	2.82575	0.729605
$16$	1.00000	0.250000
$17$	6.40137	1.55256	0.776280	−	0.630388i	$-0.217104\pi$
$17$	6.40137	1.55256	0.776280	+	0.630388i	$0.217104\pi$
$18$	−0.436015	−0.102770
$19$	−6.97194	−1.59947	−0.799736	−	0.600351i	$-0.795027\pi$
$19$	−6.97194	−1.59947	−0.799736	+	0.600351i	$0.795027\pi$
$20$	−1.76472	−0.394603
$21$	0.995285	0.217189
$22$	5.06537	1.07994
$23$	1.76018	0.367023	0.183512	−	0.983018i	$-0.441254\pi$
$23$	1.76018	0.367023	0.183512	+	0.983018i	$0.441254\pi$
$24$	−1.60124	−0.326853
$25$	−1.88577	−0.377154
$26$	6.63999	1.30221
$27$	5.50190	1.05884
$28$	−0.621570	−0.117466
$29$	4.65630	0.864653	0.432327	−	0.901717i	$-0.357693\pi$
$29$	4.65630	0.864653	0.432327	+	0.901717i	$0.357693\pi$
$30$	2.82575	0.515908
$31$	0.133190	0.0239216	0.0119608	−	0.999928i	$-0.496193\pi$
$31$	0.133190	0.0239216	0.0119608	+	0.999928i	$0.496193\pi$
$32$	1.00000	0.176777
$33$	−8.11090	−1.41193
$34$	6.40137	1.09783
$35$	1.09690	0.185409
$36$	−0.436015	−0.0726692
$37$	−10.8631	−1.78587	−0.892937	−	0.450181i	$-0.851359\pi$
$37$	−10.8631	−1.78587	−0.892937	+	0.450181i	$0.851359\pi$
$38$	−6.97194	−1.13100
$39$	−10.6322	−1.70252
$40$	−1.76472	−0.279026
$41$	2.39707	0.374359	0.187180	−	0.982326i	$-0.440065\pi$
$41$	2.39707	0.374359	0.187180	+	0.982326i	$0.440065\pi$
$42$	0.995285	0.153576
$43$	−3.33590	−0.508720	−0.254360	−	0.967110i	$-0.581865\pi$
$43$	−3.33590	−0.508720	−0.254360	+	0.967110i	$0.581865\pi$
$44$	5.06537	0.763634
$45$	0.769444	0.114702
$46$	1.76018	0.259524
$47$	2.14590	0.313012	0.156506	−	0.987677i	$-0.449977\pi$
$47$	2.14590	0.313012	0.156506	+	0.987677i	$0.449977\pi$
$48$	−1.60124	−0.231120
$49$	−6.61365	−0.944807
$50$	−1.88577	−0.266688
$51$	−10.2502	−1.43531
$52$	6.63999	0.920801
$53$	0.508866	0.0698981	0.0349491	−	0.999389i	$-0.488873\pi$
$53$	0.508866	0.0698981	0.0349491	+	0.999389i	$0.488873\pi$
$54$	5.50190	0.748714
$55$	−8.93896	−1.20533
$56$	−0.621570	−0.0830607
$57$	11.1638	1.47868
$58$	4.65630	0.611402
$59$	−7.92618	−1.03190	−0.515950	−	0.856618i	$-0.672561\pi$
$59$	−7.92618	−1.03190	−0.515950	+	0.856618i	$0.672561\pi$
$60$	2.82575	0.364802
$61$	2.52919	0.323830	0.161915	−	0.986805i	$-0.448233\pi$
$61$	2.52919	0.323830	0.161915	+	0.986805i	$0.448233\pi$
$62$	0.133190	0.0169151
$63$	0.271014	0.0341445
$64$	1.00000	0.125000
$65$	−11.7177	−1.45340
$66$	−8.11090	−0.998383
$67$	11.0205	1.34637	0.673183	−	0.739475i	$-0.264926\pi$
$67$	11.0205	1.34637	0.673183	+	0.739475i	$0.264926\pi$
$68$	6.40137	0.776280
$69$	−2.81848	−0.339305
$70$	1.09690	0.131104
$71$	13.9984	1.66130	0.830652	−	0.556792i	$-0.187968\pi$
$71$	13.9984	1.66130	0.830652	+	0.556792i	$0.187968\pi$
$72$	−0.436015	−0.0513849
$73$	−15.1106	−1.76856	−0.884279	−	0.466959i	$-0.845349\pi$
$73$	−15.1106	−1.76856	−0.884279	+	0.466959i	$0.845349\pi$
$74$	−10.8631	−1.26280
$75$	3.01958	0.348671
$76$	−6.97194	−0.799736
$77$	−3.14848	−0.358803
$78$	−10.6322	−1.20386
$79$	2.75304	0.309741	0.154871	−	0.987935i	$-0.450504\pi$
$79$	2.75304	0.309741	0.154871	+	0.987935i	$0.450504\pi$
$80$	−1.76472	−0.197302
$81$	−7.50184	−0.833538
$82$	2.39707	0.264712
$83$	12.4989	1.37194	0.685968	−	0.727632i	$-0.259379\pi$
$83$	12.4989	1.37194	0.685968	+	0.727632i	$0.259379\pi$
$84$	0.995285	0.108594
$85$	−11.2966	−1.22529
$86$	−3.33590	−0.359720
$87$	−7.45588	−0.799354
$88$	5.06537	0.539971
$89$	9.15235	0.970147	0.485074	−	0.874473i	$-0.338793\pi$
$89$	9.15235	0.970147	0.485074	+	0.874473i	$0.338793\pi$
$90$	0.769444	0.0811065
$91$	−4.12721	−0.432650
$92$	1.76018	0.183512
$93$	−0.213270	−0.0221150
$94$	2.14590	0.221333
$95$	12.3035	1.26231
$96$	−1.60124	−0.163426
$97$	−1.95909	−0.198916	−0.0994578	−	0.995042i	$-0.531711\pi$
$97$	−1.95909	−0.198916	−0.0994578	+	0.995042i	$0.531711\pi$
$98$	−6.61365	−0.668080
$99$	−2.20858	−0.221971
$100$	−1.88577	−0.188577
$101$	−5.28451	−0.525829	−0.262914	−	0.964819i	$-0.584684\pi$
$101$	−5.28451	−0.525829	−0.262914	+	0.964819i	$0.584684\pi$
$102$	−10.2502	−1.01492
$103$	−4.12665	−0.406610	−0.203305	−	0.979115i	$-0.565168\pi$
$103$	−4.12665	−0.406610	−0.203305	+	0.979115i	$0.565168\pi$
$104$	6.63999	0.651104
$105$	−1.75640	−0.171407
$106$	0.508866	0.0494254
$107$	−5.67949	−0.549057	−0.274529	−	0.961579i	$-0.588522\pi$
$107$	−5.67949	−0.549057	−0.274529	+	0.961579i	$0.588522\pi$
$108$	5.50190	0.529421
$109$	10.9481	1.04864	0.524319	−	0.851522i	$-0.324320\pi$
$109$	10.9481	1.04864	0.524319	+	0.851522i	$0.324320\pi$
$110$	−8.93896	−0.852296
$111$	17.3944	1.65100
$112$	−0.621570	−0.0587328
$113$	−7.87392	−0.740716	−0.370358	−	0.928889i	$-0.620765\pi$
$113$	−7.87392	−0.740716	−0.370358	+	0.928889i	$0.620765\pi$
$114$	11.1638	1.04558
$115$	−3.10622	−0.289657
$116$	4.65630	0.432327
$117$	−2.89514	−0.267655
$118$	−7.92618	−0.729664
$119$	−3.97890	−0.364745
$120$	2.82575	0.257954
$121$	14.6580	1.33255
$122$	2.52919	0.228982
$123$	−3.83830	−0.346087
$124$	0.133190	0.0119608
$125$	12.1514	1.08686
$126$	0.271014	0.0241438
$127$	1.10370	0.0979374	0.0489687	−	0.998800i	$-0.484407\pi$
$127$	1.10370	0.0979374	0.0489687	+	0.998800i	$0.484407\pi$
$128$	1.00000	0.0883883
$129$	5.34159	0.470301
$130$	−11.7177	−1.02771
$131$	15.1456	1.32327	0.661637	−	0.749825i	$-0.269862\pi$
$131$	15.1456	1.32327	0.661637	+	0.749825i	$0.269862\pi$
$132$	−8.11090	−0.705963
$133$	4.33355	0.375766
$134$	11.0205	0.952025
$135$	−9.70931	−0.835644
$136$	6.40137	0.548913
$137$	9.22289	0.787965	0.393982	−	0.919118i	$-0.371097\pi$
$137$	9.22289	0.787965	0.393982	+	0.919118i	$0.371097\pi$
$138$	−2.81848	−0.239925
$139$	3.07593	0.260897	0.130448	−	0.991455i	$-0.458358\pi$
$139$	3.07593	0.260897	0.130448	+	0.991455i	$0.458358\pi$
$140$	1.09690	0.0927046
$141$	−3.43611	−0.289373
$142$	13.9984	1.17472
$143$	33.6340	2.81262
$144$	−0.436015	−0.0363346
$145$	−8.21706	−0.682390
$146$	−15.1106	−1.25056
$147$	10.5901	0.873455
$148$	−10.8631	−0.892937
$149$	12.2189	1.00101	0.500506	−	0.865733i	$-0.333147\pi$
$149$	12.2189	1.00101	0.500506	+	0.865733i	$0.333147\pi$
$150$	3.01958	0.246547
$151$	3.99928	0.325457	0.162728	−	0.986671i	$-0.447971\pi$
$151$	3.99928	0.325457	0.162728	+	0.986671i	$0.447971\pi$
$152$	−6.97194	−0.565499
$153$	−2.79110	−0.225647
$154$	−3.14848	−0.253712
$155$	−0.235043	−0.0188791
$156$	−10.6322	−0.851261
$157$	19.4489	1.55219	0.776097	−	0.630614i	$-0.217197\pi$
$157$	19.4489	1.55219	0.776097	+	0.630614i	$0.217197\pi$
$158$	2.75304	0.219020
$159$	−0.814819	−0.0646193
$160$	−1.76472	−0.139513
$161$	−1.09407	−0.0862252
$162$	−7.50184	−0.589401
$163$	−5.89458	−0.461699	−0.230849	−	0.972989i	$-0.574151\pi$
$163$	−5.89458	−0.461699	−0.230849	+	0.972989i	$0.574151\pi$
$164$	2.39707	0.187180
$165$	14.3135	1.11430
$166$	12.4989	0.970105
$167$	9.40998	0.728166	0.364083	−	0.931366i	$-0.381382\pi$
$167$	9.40998	0.728166	0.364083	+	0.931366i	$0.381382\pi$
$168$	0.995285	0.0767879
$169$	31.0894	2.39150
$170$	−11.2966	−0.866411
$171$	3.03987	0.232465
$172$	−3.33590	−0.254360
$173$	−16.7541	−1.27379	−0.636896	−	0.770950i	$-0.719782\pi$
$173$	−16.7541	−1.27379	−0.636896	+	0.770950i	$0.719782\pi$
$174$	−7.45588	−0.565228
$175$	1.17214	0.0886052
$176$	5.06537	0.381817
$177$	12.6918	0.953971
$178$	9.15235	0.685998
$179$	0.972666	0.0727004	0.0363502	−	0.999339i	$-0.488427\pi$
$179$	0.972666	0.0727004	0.0363502	+	0.999339i	$0.488427\pi$
$180$	0.769444	0.0573510
$181$	−5.77940	−0.429579	−0.214790	−	0.976660i	$-0.568907\pi$
$181$	−5.77940	−0.429579	−0.214790	+	0.976660i	$0.568907\pi$
$182$	−4.12721	−0.305930
$183$	−4.04985	−0.299374
$184$	1.76018	0.129762
$185$	19.1702	1.40942
$186$	−0.213270	−0.0156377
$187$	32.4253	2.37117
$188$	2.14590	0.156506
$189$	−3.41981	−0.248755
$190$	12.3035	0.892590
$191$	1.58524	0.114704	0.0573520	−	0.998354i	$-0.481734\pi$
$191$	1.58524	0.114704	0.0573520	+	0.998354i	$0.481734\pi$
$192$	−1.60124	−0.115560
$193$	0.0430842	0.00310127	0.00155063	−	0.999999i	$-0.499506\pi$
$193$	0.0430842	0.00310127	0.00155063	+	0.999999i	$0.499506\pi$
$194$	−1.95909	−0.140655
$195$	18.7629	1.34364
$196$	−6.61365	−0.472404
$197$	−17.4781	−1.24526	−0.622631	−	0.782516i	$-0.713936\pi$
$197$	−17.4781	−1.24526	−0.622631	+	0.782516i	$0.713936\pi$
$198$	−2.20858	−0.156957
$199$	8.54461	0.605711	0.302856	−	0.953036i	$-0.402060\pi$
$199$	8.54461	0.605711	0.302856	+	0.953036i	$0.402060\pi$
$200$	−1.88577	−0.133344
$201$	−17.6465	−1.24469
$202$	−5.28451	−0.371817
$203$	−2.89421	−0.203134
$204$	−10.2502	−0.717655
$205$	−4.23015	−0.295447
$206$	−4.12665	−0.287517
$207$	−0.767466	−0.0533425
$208$	6.63999	0.460400
$209$	−35.3155	−2.44282
$210$	−1.75640	−0.121203
$211$	−18.6544	−1.28422	−0.642111	−	0.766611i	$-0.721941\pi$
$211$	−18.6544	−1.28422	−0.642111	+	0.766611i	$0.721941\pi$
$212$	0.508866	0.0349491
$213$	−22.4149	−1.53584
$214$	−5.67949	−0.388242
$215$	5.88693	0.401485
$216$	5.50190	0.374357
$217$	−0.0827869	−0.00561994
$218$	10.9481	0.741500
$219$	24.1957	1.63499
$220$	−8.93896	−0.602664
$221$	42.5050	2.85920
$222$	17.3944	1.16744
$223$	3.67846	0.246328	0.123164	−	0.992386i	$-0.460696\pi$
$223$	3.67846	0.246328	0.123164	+	0.992386i	$0.460696\pi$
$224$	−0.621570	−0.0415304
$225$	0.822224	0.0548149
$226$	−7.87392	−0.523765
$227$	26.8687	1.78334	0.891669	−	0.452688i	$-0.149535\pi$
$227$	26.8687	1.78334	0.891669	+	0.452688i	$0.149535\pi$
$228$	11.1638	0.739340
$229$	22.1552	1.46406	0.732028	−	0.681275i	$-0.238574\pi$
$229$	22.1552	1.46406	0.732028	+	0.681275i	$0.238574\pi$
$230$	−3.10622	−0.204818
$231$	5.04149	0.331706
$232$	4.65630	0.305701
$233$	−20.3534	−1.33340	−0.666699	−	0.745327i	$-0.732293\pi$
$233$	−20.3534	−1.33340	−0.666699	+	0.745327i	$0.732293\pi$
$234$	−2.89514	−0.189261
$235$	−3.78691	−0.247031
$236$	−7.92618	−0.515950
$237$	−4.40829	−0.286350
$238$	−3.97890	−0.257914
$239$	8.88108	0.574469	0.287235	−	0.957860i	$-0.407264\pi$
$239$	8.88108	0.574469	0.287235	+	0.957860i	$0.407264\pi$
$240$	2.82575	0.182401
$241$	−16.1837	−1.04249	−0.521243	−	0.853408i	$-0.674531\pi$
$241$	−16.1837	−1.04249	−0.521243	+	0.853408i	$0.674531\pi$
$242$	14.6580	0.942252
$243$	−4.49341	−0.288253
$244$	2.52919	0.161915
$245$	11.6712	0.745648
$246$	−3.83830	−0.244721
$247$	−46.2936	−2.94559
$248$	0.133190	0.00845757
$249$	−20.0138	−1.26833
$250$	12.1514	0.768525
$251$	5.97544	0.377167	0.188583	−	0.982057i	$-0.439610\pi$
$251$	5.97544	0.377167	0.188583	+	0.982057i	$0.439610\pi$
$252$	0.271014	0.0170723
$253$	8.91597	0.560542
$254$	1.10370	0.0692522
$255$	18.0886	1.13276
$256$	1.00000	0.0625000
$257$	31.0748	1.93839	0.969197	−	0.246287i	$-0.0792106\pi$
$257$	31.0748	1.93839	0.969197	+	0.246287i	$0.0792106\pi$
$258$	5.34159	0.332553
$259$	6.75214	0.419558
$260$	−11.7177	−0.726702
$261$	−2.03022	−0.125667
$262$	15.1456	0.935696
$263$	2.00933	0.123900	0.0619502	−	0.998079i	$-0.480268\pi$
$263$	2.00933	0.123900	0.0619502	+	0.998079i	$0.480268\pi$
$264$	−8.11090	−0.499192
$265$	−0.898005	−0.0551640
$266$	4.33355	0.265707
$267$	−14.6552	−0.896881
$268$	11.0205	0.673183
$269$	9.97751	0.608340	0.304170	−	0.952618i	$-0.401621\pi$
$269$	9.97751	0.608340	0.304170	+	0.952618i	$0.401621\pi$
$270$	−9.70931	−0.590890
$271$	−7.83092	−0.475695	−0.237847	−	0.971303i	$-0.576442\pi$
$271$	−7.83092	−0.475695	−0.237847	+	0.971303i	$0.576442\pi$
$272$	6.40137	0.388140
$273$	6.60868	0.399976
$274$	9.22289	0.557175
$275$	−9.55212	−0.576015
$276$	−2.81848	−0.169653
$277$	12.7629	0.766847	0.383424	−	0.923573i	$-0.374745\pi$
$277$	12.7629	0.766847	0.383424	+	0.923573i	$0.374745\pi$
$278$	3.07593	0.184482
$279$	−0.0580729	−0.00347673
$280$	1.09690	0.0655520
$281$	11.3868	0.679281	0.339641	−	0.940555i	$-0.389695\pi$
$281$	11.3868	0.679281	0.339641	+	0.940555i	$0.389695\pi$
$282$	−3.43611	−0.204618
$283$	−12.5864	−0.748184	−0.374092	−	0.927392i	$-0.622046\pi$
$283$	−12.5864	−0.748184	−0.374092	+	0.927392i	$0.622046\pi$
$284$	13.9984	0.830652
$285$	−19.7009	−1.16698
$286$	33.6340	1.98882
$287$	−1.48995	−0.0879487
$288$	−0.436015	−0.0256924
$289$	23.9775	1.41044
$290$	−8.21706	−0.482522
$291$	3.13698	0.183893
$292$	−15.1106	−0.884279
$293$	−1.48790	−0.0869243	−0.0434621	−	0.999055i	$-0.513839\pi$
$293$	−1.48790	−0.0869243	−0.0434621	+	0.999055i	$0.513839\pi$
$294$	10.5901	0.617626
$295$	13.9875	0.814382
$296$	−10.8631	−0.631402
$297$	27.8692	1.61713
$298$	12.2189	0.707823
$299$	11.6876	0.675910
$300$	3.01958	0.174335
$301$	2.07349	0.119514
$302$	3.99928	0.230133
$303$	8.46180	0.486118
$304$	−6.97194	−0.399868
$305$	−4.46331	−0.255568
$306$	−2.79110	−0.159556
$307$	9.31032	0.531368	0.265684	−	0.964060i	$-0.414402\pi$
$307$	9.31032	0.531368	0.265684	+	0.964060i	$0.414402\pi$
$308$	−3.14848	−0.179401
$309$	6.60777	0.375903
$310$	−0.235043	−0.0133495
$311$	26.9137	1.52613	0.763067	−	0.646319i	$-0.223692\pi$
$311$	26.9137	1.52613	0.763067	+	0.646319i	$0.223692\pi$
$312$	−10.6322	−0.601932
$313$	0.219569	0.0124108	0.00620539	−	0.999981i	$-0.498025\pi$
$313$	0.219569	0.0124108	0.00620539	+	0.999981i	$0.498025\pi$
$314$	19.4489	1.09757
$315$	−0.478263	−0.0269471
$316$	2.75304	0.154871
$317$	−6.49747	−0.364934	−0.182467	−	0.983212i	$-0.558408\pi$
$317$	−6.49747	−0.364934	−0.182467	+	0.983212i	$0.558408\pi$
$318$	−0.814819	−0.0456928
$319$	23.5859	1.32056
$320$	−1.76472	−0.0986508
$321$	9.09425	0.507592
$322$	−1.09407	−0.0609704
$323$	−44.6300	−2.48328
$324$	−7.50184	−0.416769
$325$	−12.5215	−0.694567
$326$	−5.89458	−0.326470
$327$	−17.5306	−0.969445
$328$	2.39707	0.132356
$329$	−1.33383	−0.0735362
$330$	14.3135	0.787930
$331$	−21.9318	−1.20548	−0.602741	−	0.797937i	$-0.705925\pi$
$331$	−21.9318	−1.20548	−0.602741	+	0.797937i	$0.705925\pi$
$332$	12.4989	0.685968
$333$	4.73646	0.259556
$334$	9.40998	0.514891
$335$	−19.4481	−1.06256
$336$	0.995285	0.0542972
$337$	22.1544	1.20682	0.603412	−	0.797429i	$-0.293807\pi$
$337$	22.1544	1.20682	0.603412	+	0.797429i	$0.293807\pi$
$338$	31.0894	1.69104
$339$	12.6081	0.684776
$340$	−11.2966	−0.612645
$341$	0.674657	0.0365347
$342$	3.03987	0.164377
$343$	8.46183	0.456896
$344$	−3.33590	−0.179860
$345$	4.97382	0.267782
$346$	−16.7541	−0.900707
$347$	12.6767	0.680520	0.340260	−	0.940331i	$-0.389485\pi$
$347$	12.6767	0.680520	0.340260	+	0.940331i	$0.389485\pi$
$348$	−7.45588	−0.399677
$349$	20.0369	1.07255	0.536276	−	0.844043i	$-0.319831\pi$
$349$	20.0369	1.07255	0.536276	+	0.844043i	$0.319831\pi$
$350$	1.17214	0.0626533
$351$	36.5326	1.94996
$352$	5.06537	0.269985
$353$	−4.84896	−0.258084	−0.129042	−	0.991639i	$-0.541190\pi$
$353$	−4.84896	−0.258084	−0.129042	+	0.991639i	$0.541190\pi$
$354$	12.6918	0.674559
$355$	−24.7032	−1.31111
$356$	9.15235	0.485074
$357$	6.37119	0.337199
$358$	0.972666	0.0514070
$359$	−36.0530	−1.90280	−0.951402	−	0.307952i	$-0.900356\pi$
$359$	−36.0530	−1.90280	−0.951402	+	0.307952i	$0.900356\pi$
$360$	0.769444	0.0405533
$361$	29.6079	1.55831
$362$	−5.77940	−0.303758
$363$	−23.4711	−1.23191
$364$	−4.12721	−0.216325
$365$	26.6659	1.39576
$366$	−4.04985	−0.211689
$367$	29.8869	1.56008	0.780041	−	0.625728i	$-0.215198\pi$
$367$	29.8869	1.56008	0.780041	+	0.625728i	$0.215198\pi$
$368$	1.76018	0.0917558
$369$	−1.04516	−0.0544088
$370$	19.1702	0.996613
$371$	−0.316296	−0.0164212
$372$	−0.213270	−0.0110575
$373$	−32.2614	−1.67043	−0.835215	−	0.549924i	$-0.814657\pi$
$373$	−32.2614	−1.67043	−0.835215	+	0.549924i	$0.814657\pi$
$374$	32.4253	1.67667
$375$	−19.4574	−1.00478
$376$	2.14590	0.110666
$377$	30.9178	1.59235
$378$	−3.41981	−0.175896
$379$	14.8202	0.761262	0.380631	−	0.924727i	$-0.375707\pi$
$379$	14.8202	0.761262	0.380631	+	0.924727i	$0.375707\pi$
$380$	12.3035	0.631157
$381$	−1.76729	−0.0905411
$382$	1.58524	0.0811080
$383$	−25.4748	−1.30170	−0.650850	−	0.759206i	$-0.725587\pi$
$383$	−25.4748	−1.30170	−0.650850	+	0.759206i	$0.725587\pi$
$384$	−1.60124	−0.0817132
$385$	5.55618	0.283169
$386$	0.0430842	0.00219293
$387$	1.45450	0.0739366
$388$	−1.95909	−0.0994578
$389$	−19.3733	−0.982267	−0.491134	−	0.871084i	$-0.663417\pi$
$389$	−19.3733	−0.982267	−0.491134	+	0.871084i	$0.663417\pi$
$390$	18.7629	0.950097
$391$	11.2676	0.569825
$392$	−6.61365	−0.334040
$393$	−24.2517	−1.22334
$394$	−17.4781	−0.880533
$395$	−4.85834	−0.244450
$396$	−2.20858	−0.110985
$397$	−5.54040	−0.278065	−0.139032	−	0.990288i	$-0.544399\pi$
$397$	−5.54040	−0.278065	−0.139032	+	0.990288i	$0.544399\pi$
$398$	8.54461	0.428303
$399$	−6.93907	−0.347388
$400$	−1.88577	−0.0942884
$401$	−31.1587	−1.55599	−0.777996	−	0.628270i	$-0.783763\pi$
$401$	−31.1587	−1.55599	−0.777996	+	0.628270i	$0.783763\pi$
$402$	−17.6465	−0.880127
$403$	0.884380	0.0440541
$404$	−5.28451	−0.262914
$405$	13.2386	0.657834
$406$	−2.89421	−0.143637
$407$	−55.0254	−2.72751
$408$	−10.2502	−0.507459
$409$	−25.1936	−1.24574	−0.622871	−	0.782324i	$-0.714034\pi$
$409$	−25.1936	−1.24574	−0.622871	+	0.782324i	$0.714034\pi$
$410$	−4.23015	−0.208912
$411$	−14.7681	−0.728457
$412$	−4.12665	−0.203305
$413$	4.92667	0.242426
$414$	−0.767466	−0.0377189
$415$	−22.0571	−1.08274
$416$	6.63999	0.325552
$417$	−4.92531	−0.241194
$418$	−35.3155	−1.72734
$419$	11.8541	0.579111	0.289555	−	0.957161i	$-0.406493\pi$
$419$	11.8541	0.579111	0.289555	+	0.957161i	$0.406493\pi$
$420$	−1.75640	−0.0857034
$421$	−5.53973	−0.269990	−0.134995	−	0.990846i	$-0.543102\pi$
$421$	−5.53973	−0.269990	−0.134995	+	0.990846i	$0.543102\pi$
$422$	−18.6544	−0.908083
$423$	−0.935646	−0.0454926
$424$	0.508866	0.0247127
$425$	−12.0715	−0.585554
$426$	−22.4149	−1.08600
$427$	−1.57207	−0.0760777
$428$	−5.67949	−0.274529
$429$	−53.8563	−2.60021
$430$	5.88693	0.283893
$431$	6.65772	0.320691	0.160346	−	0.987061i	$-0.448739\pi$
$431$	6.65772	0.320691	0.160346	+	0.987061i	$0.448739\pi$
$432$	5.50190	0.264710
$433$	4.37434	0.210217	0.105109	−	0.994461i	$-0.466481\pi$
$433$	4.37434	0.210217	0.105109	+	0.994461i	$0.466481\pi$
$434$	−0.0827869	−0.00397390
$435$	13.1575	0.630855
$436$	10.9481	0.524319
$437$	−12.2719	−0.587043
$438$	24.1957	1.15612
$439$	26.8853	1.28317	0.641583	−	0.767054i	$-0.278278\pi$
$439$	26.8853	1.28317	0.641583	+	0.767054i	$0.278278\pi$
$440$	−8.93896	−0.426148
$441$	2.88365	0.137317
$442$	42.5050	2.02176
$443$	21.1226	1.00357	0.501783	−	0.864993i	$-0.332678\pi$
$443$	21.1226	1.00357	0.501783	+	0.864993i	$0.332678\pi$
$444$	17.3944	0.825502
$445$	−16.1513	−0.765646
$446$	3.67846	0.174180
$447$	−19.5655	−0.925415
$448$	−0.621570	−0.0293664
$449$	−14.9017	−0.703253	−0.351627	−	0.936140i	$-0.614371\pi$
$449$	−14.9017	−0.703253	−0.351627	+	0.936140i	$0.614371\pi$
$450$	0.822224	0.0387600
$451$	12.1421	0.571747
$452$	−7.87392	−0.370358
$453$	−6.40383	−0.300878
$454$	26.8687	1.26101
$455$	7.28337	0.341450
$456$	11.1638	0.522792
$457$	−6.92826	−0.324091	−0.162045	−	0.986783i	$-0.551809\pi$
$457$	−6.92826	−0.324091	−0.162045	+	0.986783i	$0.551809\pi$
$458$	22.1552	1.03524
$459$	35.2197	1.64392
$460$	−3.10622	−0.144828
$461$	−22.2355	−1.03561	−0.517805	−	0.855499i	$-0.673251\pi$
$461$	−22.2355	−1.03561	−0.517805	+	0.855499i	$0.673251\pi$
$462$	5.04149	0.234551
$463$	32.1789	1.49548	0.747740	−	0.663991i	$-0.231139\pi$
$463$	32.1789	1.49548	0.747740	+	0.663991i	$0.231139\pi$
$464$	4.65630	0.216163
$465$	0.376361	0.0174533
$466$	−20.3534	−0.942855
$467$	−17.7372	−0.820781	−0.410391	−	0.911910i	$-0.634608\pi$
$467$	−17.7372	−0.820781	−0.410391	+	0.911910i	$0.634608\pi$
$468$	−2.89514	−0.133828
$469$	−6.85000	−0.316304
$470$	−3.78691	−0.174677
$471$	−31.1425	−1.43497
$472$	−7.92618	−0.364832
$473$	−16.8976	−0.776952
$474$	−4.40829	−0.202480
$475$	13.1475	0.603247
$476$	−3.97890	−0.182372
$477$	−0.221873	−0.0101589
$478$	8.88108	0.406211
$479$	−3.33404	−0.152336	−0.0761682	−	0.997095i	$-0.524269\pi$
$479$	−3.33404	−0.152336	−0.0761682	+	0.997095i	$0.524269\pi$
$480$	2.82575	0.128977
$481$	−72.1305	−3.28887
$482$	−16.1837	−0.737148
$483$	1.75188	0.0797134
$484$	14.6580	0.666273
$485$	3.45724	0.156985
$486$	−4.49341	−0.203825
$487$	−20.0111	−0.906789	−0.453395	−	0.891310i	$-0.649787\pi$
$487$	−20.0111	−0.906789	−0.453395	+	0.891310i	$0.649787\pi$
$488$	2.52919	0.114491
$489$	9.43866	0.426831
$490$	11.6712	0.527253
$491$	14.2488	0.643039	0.321519	−	0.946903i	$-0.395807\pi$
$491$	14.2488	0.643039	0.321519	+	0.946903i	$0.395807\pi$
$492$	−3.83830	−0.173044
$493$	29.8067	1.34243
$494$	−46.2936	−2.08285
$495$	3.89752	0.175181
$496$	0.133190	0.00598041
$497$	−8.70097	−0.390292
$498$	−20.0138	−0.896841
$499$	11.6922	0.523417	0.261708	−	0.965147i	$-0.415714\pi$
$499$	11.6922	0.523417	0.261708	+	0.965147i	$0.415714\pi$
$500$	12.1514	0.543429
$501$	−15.0677	−0.673174
$502$	5.97544	0.266697
$503$	−38.1739	−1.70209	−0.851045	−	0.525092i	$-0.824031\pi$
$503$	−38.1739	−1.70209	−0.851045	+	0.525092i	$0.824031\pi$
$504$	0.271014	0.0120719
$505$	9.32568	0.414987
$506$	8.91597	0.396363
$507$	−49.7818	−2.21089
$508$	1.10370	0.0489687
$509$	−11.1241	−0.493068	−0.246534	−	0.969134i	$-0.579292\pi$
$509$	−11.1241	−0.493068	−0.246534	+	0.969134i	$0.579292\pi$
$510$	18.0886	0.800979
$511$	9.39227	0.415489
$512$	1.00000	0.0441942
$513$	−38.3589	−1.69359
$514$	31.0748	1.37065
$515$	7.28237	0.320899
$516$	5.34159	0.235151
$517$	10.8698	0.478053
$518$	6.75214	0.296672
$519$	26.8274	1.17759
$520$	−11.7177	−0.513856
$521$	−20.8774	−0.914657	−0.457329	−	0.889298i	$-0.651194\pi$
$521$	−20.8774	−0.914657	−0.457329	+	0.889298i	$0.651194\pi$
$522$	−2.03022	−0.0888602
$523$	23.9217	1.04602	0.523011	−	0.852326i	$-0.324809\pi$
$523$	23.9217	1.04602	0.523011	+	0.852326i	$0.324809\pi$
$524$	15.1456	0.661637
$525$	−1.87688	−0.0819137
$526$	2.00933	0.0876108
$527$	0.852599	0.0371398
$528$	−8.11090	−0.352982
$529$	−19.9018	−0.865294
$530$	−0.898005	−0.0390068
$531$	3.45594	0.149975
$532$	4.33355	0.187883
$533$	15.9165	0.689421
$534$	−14.6552	−0.634190
$535$	10.0227	0.433319
$536$	11.0205	0.476013
$537$	−1.55748	−0.0672100
$538$	9.97751	0.430161
$539$	−33.5006	−1.44297
$540$	−9.70931	−0.417822
$541$	32.3775	1.39202	0.696008	−	0.718034i	$-0.254958\pi$
$541$	32.3775	1.39202	0.696008	+	0.718034i	$0.254958\pi$
$542$	−7.83092	−0.336367
$543$	9.25423	0.397137
$544$	6.40137	0.274456
$545$	−19.3203	−0.827592
$546$	6.60868	0.282825
$547$	−24.7664	−1.05894	−0.529468	−	0.848330i	$-0.677608\pi$
$547$	−24.7664	−1.05894	−0.529468	+	0.848330i	$0.677608\pi$
$548$	9.22289	0.393982
$549$	−1.10277	−0.0470649
$550$	−9.55212	−0.407304
$551$	−32.4634	−1.38299
$552$	−2.81848	−0.119962
$553$	−1.71121	−0.0727679
$554$	12.7629	0.542243
$555$	−30.6962	−1.30298
$556$	3.07593	0.130448
$557$	26.6189	1.12788	0.563939	−	0.825816i	$-0.309285\pi$
$557$	26.6189	1.12788	0.563939	+	0.825816i	$0.309285\pi$
$558$	−0.0580729	−0.00245842
$559$	−22.1503	−0.936860
$560$	1.09690	0.0463523
$561$	−51.9209	−2.19210
$562$	11.3868	0.480324
$563$	−27.0949	−1.14191	−0.570957	−	0.820980i	$-0.693428\pi$
$563$	−27.0949	−1.14191	−0.570957	+	0.820980i	$0.693428\pi$
$564$	−3.43611	−0.144686
$565$	13.8952	0.584577
$566$	−12.5864	−0.529046
$567$	4.66292	0.195824
$568$	13.9984	0.587359
$569$	−8.84650	−0.370865	−0.185432	−	0.982657i	$-0.559369\pi$
$569$	−8.84650	−0.370865	−0.185432	+	0.982657i	$0.559369\pi$
$570$	−19.7009	−0.825181
$571$	−19.1770	−0.802531	−0.401266	−	0.915962i	$-0.631430\pi$
$571$	−19.1770	−0.802531	−0.401266	+	0.915962i	$0.631430\pi$
$572$	33.6340	1.40631
$573$	−2.53836	−0.106041
$574$	−1.48995	−0.0621891
$575$	−3.31929	−0.138424
$576$	−0.436015	−0.0181673
$577$	26.4040	1.09921	0.549606	−	0.835424i	$-0.314778\pi$
$577$	26.4040	1.09921	0.549606	+	0.835424i	$0.314778\pi$
$578$	23.9775	0.997334
$579$	−0.0689883	−0.00286706
$580$	−8.21706	−0.341195
$581$	−7.76895	−0.322310
$582$	3.13698	0.130032
$583$	2.57760	0.106753
$584$	−15.1106	−0.625280
$585$	5.10910	0.211235
$586$	−1.48790	−0.0614648
$587$	30.7244	1.26813	0.634065	−	0.773280i	$-0.281385\pi$
$587$	30.7244	1.26813	0.634065	+	0.773280i	$0.281385\pi$
$588$	10.5901	0.436727
$589$	−0.928593	−0.0382620
$590$	13.9875	0.575855
$591$	27.9867	1.15122
$592$	−10.8631	−0.446469
$593$	35.2302	1.44673	0.723366	−	0.690465i	$-0.242594\pi$
$593$	35.2302	1.44673	0.723366	+	0.690465i	$0.242594\pi$
$594$	27.8692	1.14349
$595$	7.02163	0.287859
$596$	12.2189	0.500506
$597$	−13.6820	−0.559967
$598$	11.6876	0.477941
$599$	13.4083	0.547848	0.273924	−	0.961751i	$-0.411678\pi$
$599$	13.4083	0.547848	0.273924	+	0.961751i	$0.411678\pi$
$600$	3.01958	0.123274
$601$	8.39104	0.342277	0.171139	−	0.985247i	$-0.445255\pi$
$601$	8.39104	0.342277	0.171139	+	0.985247i	$0.445255\pi$
$602$	2.07349	0.0845093
$603$	−4.80510	−0.195679
$604$	3.99928	0.162728
$605$	−25.8672	−1.05165
$606$	8.46180	0.343737
$607$	24.6884	1.00207	0.501036	−	0.865427i	$-0.332953\pi$
$607$	24.6884	1.00207	0.501036	+	0.865427i	$0.332953\pi$
$608$	−6.97194	−0.282750
$609$	4.63435	0.187793
$610$	−4.46331	−0.180714
$611$	14.2488	0.576443
$612$	−2.79110	−0.112823
$613$	−34.1999	−1.38132	−0.690660	−	0.723180i	$-0.742680\pi$
$613$	−34.1999	−1.38132	−0.690660	+	0.723180i	$0.742680\pi$
$614$	9.31032	0.375734
$615$	6.77351	0.273134
$616$	−3.14848	−0.126856
$617$	31.3489	1.26206	0.631030	−	0.775758i	$-0.282632\pi$
$617$	31.3489	1.26206	0.631030	+	0.775758i	$0.282632\pi$
$618$	6.60777	0.265803
$619$	−5.07822	−0.204111	−0.102056	−	0.994779i	$-0.532542\pi$
$619$	−5.07822	−0.204111	−0.102056	+	0.994779i	$0.532542\pi$
$620$	−0.235043	−0.00943955
$621$	9.68434	0.388619
$622$	26.9137	1.07914
$623$	−5.68882	−0.227918
$624$	−10.6322	−0.425631
$625$	−12.0150	−0.480601
$626$	0.219569	0.00877575
$627$	56.5487	2.25834
$628$	19.4489	0.776097
$629$	−69.5384	−2.77268
$630$	−0.478263	−0.0190545
$631$	−5.34702	−0.212862	−0.106431	−	0.994320i	$-0.533942\pi$
$631$	−5.34702	−0.212862	−0.106431	+	0.994320i	$0.533942\pi$
$632$	2.75304	0.109510
$633$	29.8703	1.18724
$634$	−6.49747	−0.258048
$635$	−1.94772	−0.0772928
$636$	−0.814819	−0.0323097
$637$	−43.9146	−1.73996
$638$	23.5859	0.933775
$639$	−6.10351	−0.241451
$640$	−1.76472	−0.0697566
$641$	33.2927	1.31498	0.657492	−	0.753461i	$-0.271617\pi$
$641$	33.2927	1.31498	0.657492	+	0.753461i	$0.271617\pi$
$642$	9.09425	0.358922
$643$	37.9617	1.49706	0.748531	−	0.663100i	$-0.230759\pi$
$643$	37.9617	1.49706	0.748531	+	0.663100i	$0.230759\pi$
$644$	−1.09407	−0.0431126
$645$	−9.42641	−0.371165
$646$	−44.6300	−1.75594
$647$	39.2568	1.54334	0.771672	−	0.636021i	$-0.219421\pi$
$647$	39.2568	1.54334	0.771672	+	0.636021i	$0.219421\pi$
$648$	−7.50184	−0.294700
$649$	−40.1491	−1.57599
$650$	−12.5215	−0.491133
$651$	0.132562	0.00519552
$652$	−5.89458	−0.230849
$653$	4.50493	0.176291	0.0881457	−	0.996108i	$-0.471906\pi$
$653$	4.50493	0.176291	0.0881457	+	0.996108i	$0.471906\pi$
$654$	−17.5306	−0.685501
$655$	−26.7276	−1.04434
$656$	2.39707	0.0935899
$657$	6.58844	0.257039
$658$	−1.33383	−0.0519980
$659$	24.1479	0.940667	0.470334	−	0.882489i	$-0.344134\pi$
$659$	24.1479	0.940667	0.470334	+	0.882489i	$0.344134\pi$
$660$	14.3135	0.557151
$661$	18.4012	0.715725	0.357863	−	0.933774i	$-0.383506\pi$
$661$	18.4012	0.715725	0.357863	+	0.933774i	$0.383506\pi$
$662$	−21.9318	−0.852404
$663$	−68.0610	−2.64327
$664$	12.4989	0.485052
$665$	−7.64749	−0.296557
$666$	4.73646	0.183534
$667$	8.19593	0.317348
$668$	9.40998	0.364083
$669$	−5.89011	−0.227725
$670$	−19.4481	−0.751344
$671$	12.8113	0.494575
$672$	0.995285	0.0383940
$673$	14.1860	0.546830	0.273415	−	0.961896i	$-0.411847\pi$
$673$	14.1860	0.546830	0.273415	+	0.961896i	$0.411847\pi$
$674$	22.1544	0.853354
$675$	−10.3753	−0.399346
$676$	31.0894	1.19575
$677$	21.1850	0.814205	0.407103	−	0.913382i	$-0.366539\pi$
$677$	21.1850	0.814205	0.407103	+	0.913382i	$0.366539\pi$
$678$	12.6081	0.484210
$679$	1.21771	0.0467315
$680$	−11.2966	−0.433205
$681$	−43.0234	−1.64866
$682$	0.674657	0.0258340
$683$	−6.84692	−0.261990	−0.130995	−	0.991383i	$-0.541817\pi$
$683$	−6.84692	−0.261990	−0.130995	+	0.991383i	$0.541817\pi$
$684$	3.03987	0.116232
$685$	−16.2758	−0.621866
$686$	8.46183	0.323074
$687$	−35.4759	−1.35349
$688$	−3.33590	−0.127180
$689$	3.37886	0.128724
$690$	4.97382	0.189350
$691$	33.5569	1.27657	0.638283	−	0.769802i	$-0.279645\pi$
$691$	33.5569	1.27657	0.638283	+	0.769802i	$0.279645\pi$
$692$	−16.7541	−0.636896
$693$	1.37279	0.0521478
$694$	12.6767	0.481200
$695$	−5.42815	−0.205901
$696$	−7.45588	−0.282614
$697$	15.3445	0.581216
$698$	20.0369	0.758408
$699$	32.5909	1.23270
$700$	1.17214	0.0443026
$701$	−15.0027	−0.566645	−0.283322	−	0.959025i	$-0.591437\pi$
$701$	−15.0027	−0.566645	−0.283322	+	0.959025i	$0.591437\pi$
$702$	36.5326	1.37883
$703$	75.7365	2.85646
$704$	5.06537	0.190908
$705$	6.06377	0.228375
$706$	−4.84896	−0.182493
$707$	3.28469	0.123534
$708$	12.6918	0.476985
$709$	47.9431	1.80054	0.900271	−	0.435331i	$-0.143369\pi$
$709$	47.9431	1.80054	0.900271	+	0.435331i	$0.143369\pi$
$710$	−24.7032	−0.927095
$711$	−1.20037	−0.0450173
$712$	9.15235	0.342999
$713$	0.234438	0.00877979
$714$	6.37119	0.238436
$715$	−59.3546	−2.21974
$716$	0.972666	0.0363502
$717$	−14.2208	−0.531085
$718$	−36.0530	−1.34549
$719$	25.6164	0.955331	0.477665	−	0.878542i	$-0.341483\pi$
$719$	25.6164	0.955331	0.477665	+	0.878542i	$0.341483\pi$
$720$	0.769444	0.0286755
$721$	2.56500	0.0955255
$722$	29.6079	1.10189
$723$	25.9141	0.963756
$724$	−5.77940	−0.214790
$725$	−8.78071	−0.326107
$726$	−23.4711	−0.871092
$727$	−49.9733	−1.85341	−0.926704	−	0.375791i	$-0.877371\pi$
$727$	−49.9733	−1.85341	−0.926704	+	0.375791i	$0.877371\pi$
$728$	−4.12721	−0.152965
$729$	29.7006	1.10002
$730$	26.6659	0.986949
$731$	−21.3543	−0.789819
$732$	−4.04985	−0.149687
$733$	−18.5797	−0.686258	−0.343129	−	0.939288i	$-0.611487\pi$
$733$	−18.5797	−0.686258	−0.343129	+	0.939288i	$0.611487\pi$
$734$	29.8869	1.10314
$735$	−18.6885	−0.689336
$736$	1.76018	0.0648811
$737$	55.8229	2.05626
$738$	−1.04516	−0.0384728
$739$	−43.6065	−1.60409	−0.802045	−	0.597264i	$-0.796254\pi$
$739$	−43.6065	−1.60409	−0.802045	+	0.597264i	$0.796254\pi$
$740$	19.1702	0.704712
$741$	74.1274	2.72314
$742$	−0.316296	−0.0116116
$743$	3.19454	0.117196	0.0585982	−	0.998282i	$-0.481337\pi$
$743$	3.19454	0.117196	0.0585982	+	0.998282i	$0.481337\pi$
$744$	−0.213270	−0.00781885
$745$	−21.5629	−0.790005
$746$	−32.2614	−1.18117
$747$	−5.44972	−0.199395
$748$	32.4253	1.18559
$749$	3.53020	0.128991
$750$	−19.4574	−0.710485
$751$	−7.24686	−0.264442	−0.132221	−	0.991220i	$-0.542211\pi$
$751$	−7.24686	−0.264442	−0.132221	+	0.991220i	$0.542211\pi$
$752$	2.14590	0.0782530
$753$	−9.56815	−0.348683
$754$	30.9178	1.12596
$755$	−7.05760	−0.256852
$756$	−3.41981	−0.124377
$757$	−35.3421	−1.28453	−0.642265	−	0.766482i	$-0.722005\pi$
$757$	−35.3421	−1.28453	−0.642265	+	0.766482i	$0.722005\pi$
$758$	14.8202	0.538293
$759$	−14.2767	−0.518210
$760$	12.3035	0.446295
$761$	−11.9919	−0.434705	−0.217353	−	0.976093i	$-0.569742\pi$
$761$	−11.9919	−0.434705	−0.217353	+	0.976093i	$0.569742\pi$
$762$	−1.76729	−0.0640222
$763$	−6.80501	−0.246358
$764$	1.58524	0.0573520
$765$	4.92550	0.178082
$766$	−25.4748	−0.920441
$767$	−52.6298	−1.90035
$768$	−1.60124	−0.0577799
$769$	14.6182	0.527145	0.263572	−	0.964640i	$-0.415099\pi$
$769$	14.6182	0.527145	0.263572	+	0.964640i	$0.415099\pi$
$770$	5.55618	0.200231
$771$	−49.7584	−1.79200
$772$	0.0430842	0.00155063
$773$	12.3160	0.442977	0.221488	−	0.975163i	$-0.428908\pi$
$773$	12.3160	0.442977	0.221488	+	0.975163i	$0.428908\pi$
$774$	1.45450	0.0522811
$775$	−0.251166	−0.00902213
$776$	−1.95909	−0.0703273
$777$	−10.8118	−0.387872
$778$	−19.3733	−0.694568
$779$	−16.7122	−0.598778
$780$	18.7629	0.671820
$781$	70.9071	2.53725
$782$	11.2676	0.402927
$783$	25.6185	0.915531
$784$	−6.61365	−0.236202
$785$	−34.3219	−1.22500
$786$	−24.2517	−0.865031
$787$	−13.3223	−0.474890	−0.237445	−	0.971401i	$-0.576310\pi$
$787$	−13.3223	−0.474890	−0.237445	+	0.971401i	$0.576310\pi$
$788$	−17.4781	−0.622631
$789$	−3.21742	−0.114543
$790$	−4.85834	−0.172852
$791$	4.89419	0.174017
$792$	−2.20858	−0.0784785
$793$	16.7938	0.596365
$794$	−5.54040	−0.196621
$795$	1.43793	0.0509980
$796$	8.54461	0.302856
$797$	−13.2565	−0.469570	−0.234785	−	0.972047i	$-0.575439\pi$
$797$	−13.2565	−0.469570	−0.234785	+	0.972047i	$0.575439\pi$
$798$	−6.93907	−0.245640
$799$	13.7367	0.485970
$800$	−1.88577	−0.0666720
$801$	−3.99056	−0.141000
$802$	−31.1587	−1.10025
$803$	−76.5406	−2.70106
$804$	−17.6465	−0.622344
$805$	1.93073	0.0680494
$806$	0.884380	0.0311510
$807$	−15.9764	−0.562397
$808$	−5.28451	−0.185909
$809$	26.8234	0.943061	0.471530	−	0.881850i	$-0.343702\pi$
$809$	26.8234	0.943061	0.471530	+	0.881850i	$0.343702\pi$
$810$	13.2386	0.465159
$811$	−35.5783	−1.24932	−0.624662	−	0.780895i	$-0.714763\pi$
$811$	−35.5783	−1.24932	−0.624662	+	0.780895i	$0.714763\pi$
$812$	−2.89421	−0.101567
$813$	12.5392	0.439770
$814$	−55.0254	−1.92864
$815$	10.4023	0.364376
$816$	−10.2502	−0.358827
$817$	23.2577	0.813684
$818$	−25.1936	−0.880873
$819$	1.79953	0.0628806
$820$	−4.23015	−0.147723
$821$	−56.4710	−1.97085	−0.985426	−	0.170103i	$-0.945590\pi$
$821$	−56.4710	−1.97085	−0.985426	+	0.170103i	$0.945590\pi$
$822$	−14.7681	−0.515097
$823$	40.3372	1.40607	0.703033	−	0.711157i	$-0.251829\pi$
$823$	40.3372	1.40607	0.703033	+	0.711157i	$0.251829\pi$
$824$	−4.12665	−0.143759
$825$	15.2953	0.532514
$826$	4.92667	0.171421
$827$	18.0591	0.627978	0.313989	−	0.949427i	$-0.398335\pi$
$827$	18.0591	0.627978	0.313989	+	0.949427i	$0.398335\pi$
$828$	−0.767466	−0.0266713
$829$	−23.6738	−0.822224	−0.411112	−	0.911585i	$-0.634860\pi$
$829$	−23.6738	−0.822224	−0.411112	+	0.911585i	$0.634860\pi$
$830$	−22.0571	−0.765612
$831$	−20.4365	−0.708934
$832$	6.63999	0.230200
$833$	−42.3364	−1.46687
$834$	−4.92531	−0.170550
$835$	−16.6060	−0.574673
$836$	−35.3155	−1.22141
$837$	0.732798	0.0253292
$838$	11.8541	0.409493
$839$	12.1657	0.420006	0.210003	−	0.977701i	$-0.432653\pi$
$839$	12.1657	0.420006	0.210003	+	0.977701i	$0.432653\pi$
$840$	−1.75640	−0.0606015
$841$	−7.31887	−0.252375
$842$	−5.53973	−0.190912
$843$	−18.2331	−0.627981
$844$	−18.6544	−0.642111
$845$	−54.8641	−1.88738
$846$	−0.935646	−0.0321682
$847$	−9.11097	−0.313057
$848$	0.508866	0.0174745
$849$	20.1539	0.691681
$850$	−12.0715	−0.414049
$851$	−19.1209	−0.655457
$852$	−22.4149	−0.767920
$853$	−15.0463	−0.515175	−0.257587	−	0.966255i	$-0.582928\pi$
$853$	−15.0463	−0.515175	−0.257587	+	0.966255i	$0.582928\pi$
$854$	−1.57207	−0.0537951
$855$	−5.36452	−0.183463
$856$	−5.67949	−0.194121
$857$	22.0795	0.754221	0.377110	−	0.926168i	$-0.376918\pi$
$857$	22.0795	0.754221	0.377110	+	0.926168i	$0.376918\pi$
$858$	−53.8563	−1.83862
$859$	23.8955	0.815303	0.407651	−	0.913138i	$-0.366348\pi$
$859$	23.8955	0.815303	0.407651	+	0.913138i	$0.366348\pi$
$860$	5.88693	0.200743
$861$	2.38577	0.0813068
$862$	6.65772	0.226763
$863$	32.3288	1.10048	0.550242	−	0.835005i	$-0.314535\pi$
$863$	32.3288	1.10048	0.550242	+	0.835005i	$0.314535\pi$
$864$	5.50190	0.187178
$865$	29.5663	1.00528
$866$	4.37434	0.148646
$867$	−38.3939	−1.30393
$868$	−0.0827869	−0.00280997
$869$	13.9452	0.473058
$870$	13.1575	0.446082
$871$	73.1759	2.47947
$872$	10.9481	0.370750
$873$	0.854194	0.0289101
$874$	−12.2719	−0.415102
$875$	−7.55297	−0.255337
$876$	24.1957	0.817497
$877$	−6.78925	−0.229257	−0.114628	−	0.993408i	$-0.536568\pi$
$877$	−6.78925	−0.229257	−0.114628	+	0.993408i	$0.536568\pi$
$878$	26.8853	0.907336
$879$	2.38250	0.0803597
$880$	−8.93896	−0.301332
$881$	−43.4738	−1.46467	−0.732334	−	0.680945i	$-0.761569\pi$
$881$	−43.4738	−1.46467	−0.732334	+	0.680945i	$0.761569\pi$
$882$	2.88365	0.0970976
$883$	−1.34012	−0.0450986	−0.0225493	−	0.999746i	$-0.507178\pi$
$883$	−1.34012	−0.0450986	−0.0225493	+	0.999746i	$0.507178\pi$
$884$	42.5050	1.42960
$885$	−22.3974	−0.752880
$886$	21.1226	0.709628
$887$	−22.2649	−0.747582	−0.373791	−	0.927513i	$-0.621942\pi$
$887$	−22.2649	−0.747582	−0.373791	+	0.927513i	$0.621942\pi$
$888$	17.3944	0.583718
$889$	−0.686025	−0.0230086
$890$	−16.1513	−0.541393
$891$	−37.9996	−1.27304
$892$	3.67846	0.123164
$893$	−14.9611	−0.500654
$894$	−19.5655	−0.654367
$895$	−1.71648	−0.0573756
$896$	−0.621570	−0.0207652
$897$	−18.7147	−0.624865
$898$	−14.9017	−0.497275
$899$	0.620173	0.0206839
$900$	0.822224	0.0274075
$901$	3.25744	0.108521
$902$	12.1421	0.404286
$903$	−3.32017	−0.110488
$904$	−7.87392	−0.261883
$905$	10.1990	0.339026
$906$	−6.40383	−0.212753
$907$	−16.9993	−0.564453	−0.282226	−	0.959348i	$-0.591073\pi$
$907$	−16.9993	−0.564453	−0.282226	+	0.959348i	$0.591073\pi$
$908$	26.8687	0.891669
$909$	2.30413	0.0764231
$910$	7.28337	0.241441
$911$	24.1263	0.799340	0.399670	−	0.916659i	$-0.369125\pi$
$911$	24.1263	0.799340	0.399670	+	0.916659i	$0.369125\pi$
$912$	11.1638	0.369670
$913$	63.3117	2.09531
$914$	−6.92826	−0.229167
$915$	7.14685	0.236268
$916$	22.1552	0.732028
$917$	−9.41402	−0.310878
$918$	35.2197	1.16242
$919$	9.64075	0.318019	0.159009	−	0.987277i	$-0.449170\pi$
$919$	9.64075	0.318019	0.159009	+	0.987277i	$0.449170\pi$
$920$	−3.10622	−0.102409
$921$	−14.9081	−0.491239
$922$	−22.2355	−0.732286
$923$	92.9492	3.05946
$924$	5.04149	0.165853
$925$	20.4852	0.673549
$926$	32.1789	1.05746
$927$	1.79928	0.0590961
$928$	4.65630	0.152851
$929$	−53.7635	−1.76392	−0.881962	−	0.471320i	$-0.843778\pi$
$929$	−53.7635	−1.76392	−0.881962	+	0.471320i	$0.843778\pi$
$930$	0.376361	0.0123414
$931$	46.1100	1.51119
$932$	−20.3534	−0.666699
$933$	−43.0954	−1.41088
$934$	−17.7372	−0.580380
$935$	−57.2216	−1.87135
$936$	−2.89514	−0.0946305
$937$	27.6674	0.903853	0.451927	−	0.892055i	$-0.350737\pi$
$937$	27.6674	0.903853	0.451927	+	0.892055i	$0.350737\pi$
$938$	−6.85000	−0.223660
$939$	−0.351584	−0.0114735
$940$	−3.78691	−0.123515
$941$	29.4112	0.958778	0.479389	−	0.877603i	$-0.340858\pi$
$941$	29.4112	0.958778	0.479389	+	0.877603i	$0.340858\pi$
$942$	−31.1425	−1.01468
$943$	4.21928	0.137399
$944$	−7.92618	−0.257975
$945$	6.03501	0.196319
$946$	−16.8976	−0.549388
$947$	−11.6788	−0.379511	−0.189755	−	0.981831i	$-0.560770\pi$
$947$	−11.6788	−0.379511	−0.189755	+	0.981831i	$0.560770\pi$
$948$	−4.40829	−0.143175
$949$	−100.334	−3.25698
$950$	13.1475	0.426560
$951$	10.4040	0.337374
$952$	−3.97890	−0.128957
$953$	−10.5514	−0.341795	−0.170897	−	0.985289i	$-0.554667\pi$
$953$	−10.5514	−0.341795	−0.170897	+	0.985289i	$0.554667\pi$
$954$	−0.221873	−0.00718341
$955$	−2.79750	−0.0905251
$956$	8.88108	0.287235
$957$	−37.7668	−1.22083
$958$	−3.33404	−0.107718
$959$	−5.73267	−0.185117
$960$	2.82575	0.0912006
$961$	−30.9823	−0.999428
$962$	−72.1305	−2.32558
$963$	2.47634	0.0797991
$964$	−16.1837	−0.521243
$965$	−0.0760314	−0.00244754
$966$	1.75188	0.0563659
$967$	−1.56895	−0.0504542	−0.0252271	−	0.999682i	$-0.508031\pi$
$967$	−1.56895	−0.0504542	−0.0252271	+	0.999682i	$0.508031\pi$
$968$	14.6580	0.471126
$969$	71.4635	2.29574
$970$	3.45724	0.111005
$971$	21.0501	0.675529	0.337764	−	0.941231i	$-0.390329\pi$
$971$	21.0501	0.675529	0.337764	+	0.941231i	$0.390329\pi$
$972$	−4.49341	−0.144126
$973$	−1.91190	−0.0612928
$974$	−20.0111	−0.641197
$975$	20.0500	0.642113
$976$	2.52919	0.0809574
$977$	−33.3354	−1.06650	−0.533248	−	0.845959i	$-0.679029\pi$
$977$	−33.3354	−1.06650	−0.533248	+	0.845959i	$0.679029\pi$
$978$	9.43866	0.301815
$979$	46.3601	1.48167
$980$	11.6712	0.372824
$981$	−4.77354	−0.152408
$982$	14.2488	0.454697
$983$	7.69221	0.245344	0.122672	−	0.992447i	$-0.460854\pi$
$983$	7.69221	0.245344	0.122672	+	0.992447i	$0.460854\pi$
$984$	−3.83830	−0.122360
$985$	30.8439	0.982768
$986$	29.8067	0.949239
$987$	2.13578	0.0679827
$988$	−46.2936	−1.47280
$989$	−5.87179	−0.186712
$990$	3.89752	0.123871
$991$	−4.88347	−0.155129	−0.0775643	−	0.996987i	$-0.524714\pi$
$991$	−4.88347	−0.155129	−0.0775643	+	0.996987i	$0.524714\pi$
$992$	0.133190	0.00422879
$993$	35.1182	1.11444
$994$	−8.70097	−0.275978
$995$	−15.0788	−0.478031
$996$	−20.0138	−0.634163
$997$	23.6776	0.749877	0.374939	−	0.927050i	$-0.377664\pi$
$997$	23.6776	0.749877	0.374939	+	0.927050i	$0.377664\pi$
$998$	11.6922	0.370112
$999$	−59.7674	−1.89096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.e.1.15	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.e.1.15	✓	70	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.60124 q^{3} +1.00000 q^{4} -1.76472 q^{5} -1.60124 q^{6} -0.621570 q^{7} +1.00000 q^{8} -0.436015 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.60124 q^{3} +1.00000 q^{4} -1.76472 q^{5} -1.60124 q^{6} -0.621570 q^{7} +1.00000 q^{8} -0.436015 q^{9} -1.76472 q^{10} +5.06537 q^{11} -1.60124 q^{12} +6.63999 q^{13} -0.621570 q^{14} +2.82575 q^{15} +1.00000 q^{16} +6.40137 q^{17} -0.436015 q^{18} -6.97194 q^{19} -1.76472 q^{20} +0.995285 q^{21} +5.06537 q^{22} +1.76018 q^{23} -1.60124 q^{24} -1.88577 q^{25} +6.63999 q^{26} +5.50190 q^{27} -0.621570 q^{28} +4.65630 q^{29} +2.82575 q^{30} +0.133190 q^{31} +1.00000 q^{32} -8.11090 q^{33} +6.40137 q^{34} +1.09690 q^{35} -0.436015 q^{36} -10.8631 q^{37} -6.97194 q^{38} -10.6322 q^{39} -1.76472 q^{40} +2.39707 q^{41} +0.995285 q^{42} -3.33590 q^{43} +5.06537 q^{44} +0.769444 q^{45} +1.76018 q^{46} +2.14590 q^{47} -1.60124 q^{48} -6.61365 q^{49} -1.88577 q^{50} -10.2502 q^{51} +6.63999 q^{52} +0.508866 q^{53} +5.50190 q^{54} -8.93896 q^{55} -0.621570 q^{56} +11.1638 q^{57} +4.65630 q^{58} -7.92618 q^{59} +2.82575 q^{60} +2.52919 q^{61} +0.133190 q^{62} +0.271014 q^{63} +1.00000 q^{64} -11.7177 q^{65} -8.11090 q^{66} +11.0205 q^{67} +6.40137 q^{68} -2.81848 q^{69} +1.09690 q^{70} +13.9984 q^{71} -0.436015 q^{72} -15.1106 q^{73} -10.8631 q^{74} +3.01958 q^{75} -6.97194 q^{76} -3.14848 q^{77} -10.6322 q^{78} +2.75304 q^{79} -1.76472 q^{80} -7.50184 q^{81} +2.39707 q^{82} +12.4989 q^{83} +0.995285 q^{84} -11.2966 q^{85} -3.33590 q^{86} -7.45588 q^{87} +5.06537 q^{88} +9.15235 q^{89} +0.769444 q^{90} -4.12721 q^{91} +1.76018 q^{92} -0.213270 q^{93} +2.14590 q^{94} +12.3035 q^{95} -1.60124 q^{96} -1.95909 q^{97} -6.61365 q^{98} -2.20858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

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