LMFDB - Embedded newform 6015.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46180 q^{2} +1.00000 q^{3} +4.06045 q^{4} +1.00000 q^{5} -2.46180 q^{6} -1.67554 q^{7} -5.07240 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.46180 q^{2} +1.00000 q^{3} +4.06045 q^{4} +1.00000 q^{5} -2.46180 q^{6} -1.67554 q^{7} -5.07240 q^{8} +1.00000 q^{9} -2.46180 q^{10} -2.07892 q^{11} +4.06045 q^{12} -2.05266 q^{13} +4.12484 q^{14} +1.00000 q^{15} +4.36633 q^{16} +1.84172 q^{17} -2.46180 q^{18} +3.33873 q^{19} +4.06045 q^{20} -1.67554 q^{21} +5.11787 q^{22} +2.96151 q^{23} -5.07240 q^{24} +1.00000 q^{25} +5.05323 q^{26} +1.00000 q^{27} -6.80344 q^{28} -3.38465 q^{29} -2.46180 q^{30} -8.85736 q^{31} -0.604223 q^{32} -2.07892 q^{33} -4.53394 q^{34} -1.67554 q^{35} +4.06045 q^{36} +2.84227 q^{37} -8.21927 q^{38} -2.05266 q^{39} -5.07240 q^{40} -3.86445 q^{41} +4.12484 q^{42} +0.694921 q^{43} -8.44133 q^{44} +1.00000 q^{45} -7.29065 q^{46} +3.22764 q^{47} +4.36633 q^{48} -4.19256 q^{49} -2.46180 q^{50} +1.84172 q^{51} -8.33471 q^{52} -2.43888 q^{53} -2.46180 q^{54} -2.07892 q^{55} +8.49901 q^{56} +3.33873 q^{57} +8.33233 q^{58} +7.98528 q^{59} +4.06045 q^{60} +7.06027 q^{61} +21.8050 q^{62} -1.67554 q^{63} -7.24519 q^{64} -2.05266 q^{65} +5.11787 q^{66} -12.3084 q^{67} +7.47820 q^{68} +2.96151 q^{69} +4.12484 q^{70} +7.38657 q^{71} -5.07240 q^{72} +5.59936 q^{73} -6.99709 q^{74} +1.00000 q^{75} +13.5567 q^{76} +3.48331 q^{77} +5.05323 q^{78} -7.04800 q^{79} +4.36633 q^{80} +1.00000 q^{81} +9.51350 q^{82} +10.4398 q^{83} -6.80344 q^{84} +1.84172 q^{85} -1.71075 q^{86} -3.38465 q^{87} +10.5451 q^{88} -11.1419 q^{89} -2.46180 q^{90} +3.43931 q^{91} +12.0251 q^{92} -8.85736 q^{93} -7.94579 q^{94} +3.33873 q^{95} -0.604223 q^{96} +10.7018 q^{97} +10.3212 q^{98} -2.07892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.46180	−1.74075	−0.870377	−	0.492386i	$-0.836125\pi$
$2$	−2.46180	−1.74075	−0.870377	+	0.492386i	$0.836125\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.06045	2.03022
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.46180	−1.00502
$7$	−1.67554	−0.633295	−0.316647	−	0.948543i	$-0.602557\pi$
$7$	−1.67554	−0.633295	−0.316647	+	0.948543i	$0.602557\pi$
$8$	−5.07240	−1.79336
$9$	1.00000	0.333333
$10$	−2.46180	−0.778489
$11$	−2.07892	−0.626817	−0.313408	−	0.949618i	$-0.601471\pi$
$11$	−2.07892	−0.626817	−0.313408	+	0.949618i	$0.601471\pi$
$12$	4.06045	1.17215
$13$	−2.05266	−0.569305	−0.284653	−	0.958631i	$-0.591878\pi$
$13$	−2.05266	−0.569305	−0.284653	+	0.958631i	$0.591878\pi$
$14$	4.12484	1.10241
$15$	1.00000	0.258199
$16$	4.36633	1.09158
$17$	1.84172	0.446682	0.223341	−	0.974740i	$-0.428304\pi$
$17$	1.84172	0.446682	0.223341	+	0.974740i	$0.428304\pi$
$18$	−2.46180	−0.580251
$19$	3.33873	0.765957	0.382978	−	0.923757i	$-0.374898\pi$
$19$	3.33873	0.765957	0.382978	+	0.923757i	$0.374898\pi$
$20$	4.06045	0.907943
$21$	−1.67554	−0.365633
$22$	5.11787	1.09113
$23$	2.96151	0.617518	0.308759	−	0.951140i	$-0.400086\pi$
$23$	2.96151	0.617518	0.308759	+	0.951140i	$0.400086\pi$
$24$	−5.07240	−1.03540
$25$	1.00000	0.200000
$26$	5.05323	0.991020
$27$	1.00000	0.192450
$28$	−6.80344	−1.28573
$29$	−3.38465	−0.628514	−0.314257	−	0.949338i	$-0.601755\pi$
$29$	−3.38465	−0.628514	−0.314257	+	0.949338i	$0.601755\pi$
$30$	−2.46180	−0.449461
$31$	−8.85736	−1.59083	−0.795415	−	0.606066i	$-0.792747\pi$
$31$	−8.85736	−1.59083	−0.795415	+	0.606066i	$0.792747\pi$
$32$	−0.604223	−0.106813
$33$	−2.07892	−0.361893
$34$	−4.53394	−0.777564
$35$	−1.67554	−0.283218
$36$	4.06045	0.676741
$37$	2.84227	0.467266	0.233633	−	0.972325i	$-0.424939\pi$
$37$	2.84227	0.467266	0.233633	+	0.972325i	$0.424939\pi$
$38$	−8.21927	−1.33334
$39$	−2.05266	−0.328688
$40$	−5.07240	−0.802017
$41$	−3.86445	−0.603526	−0.301763	−	0.953383i	$-0.597575\pi$
$41$	−3.86445	−0.603526	−0.301763	+	0.953383i	$0.597575\pi$
$42$	4.12484	0.636477
$43$	0.694921	0.105974	0.0529872	−	0.998595i	$-0.483126\pi$
$43$	0.694921	0.105974	0.0529872	+	0.998595i	$0.483126\pi$
$44$	−8.44133	−1.27258
$45$	1.00000	0.149071
$46$	−7.29065	−1.07495
$47$	3.22764	0.470799	0.235400	−	0.971899i	$-0.424360\pi$
$47$	3.22764	0.470799	0.235400	+	0.971899i	$0.424360\pi$
$48$	4.36633	0.630226
$49$	−4.19256	−0.598938
$50$	−2.46180	−0.348151
$51$	1.84172	0.257892
$52$	−8.33471	−1.15582
$53$	−2.43888	−0.335006	−0.167503	−	0.985872i	$-0.553570\pi$
$53$	−2.43888	−0.335006	−0.167503	+	0.985872i	$0.553570\pi$
$54$	−2.46180	−0.335008
$55$	−2.07892	−0.280321
$56$	8.49901	1.13573
$57$	3.33873	0.442225
$58$	8.33233	1.09409
$59$	7.98528	1.03959	0.519797	−	0.854290i	$-0.326008\pi$
$59$	7.98528	1.03959	0.519797	+	0.854290i	$0.326008\pi$
$60$	4.06045	0.524201
$61$	7.06027	0.903976	0.451988	−	0.892024i	$-0.350715\pi$
$61$	7.06027	0.903976	0.451988	+	0.892024i	$0.350715\pi$
$62$	21.8050	2.76924
$63$	−1.67554	−0.211098
$64$	−7.24519	−0.905649
$65$	−2.05266	−0.254601
$66$	5.11787	0.629966
$67$	−12.3084	−1.50370	−0.751852	−	0.659331i	$-0.770839\pi$
$67$	−12.3084	−1.50370	−0.751852	+	0.659331i	$0.770839\pi$
$68$	7.47820	0.906865
$69$	2.96151	0.356524
$70$	4.12484	0.493013
$71$	7.38657	0.876624	0.438312	−	0.898823i	$-0.355577\pi$
$71$	7.38657	0.876624	0.438312	+	0.898823i	$0.355577\pi$
$72$	−5.07240	−0.597788
$73$	5.59936	0.655356	0.327678	−	0.944789i	$-0.393734\pi$
$73$	5.59936	0.655356	0.327678	+	0.944789i	$0.393734\pi$
$74$	−6.99709	−0.813395
$75$	1.00000	0.115470
$76$	13.5567	1.55506
$77$	3.48331	0.396960
$78$	5.05323	0.572166
$79$	−7.04800	−0.792962	−0.396481	−	0.918043i	$-0.629769\pi$
$79$	−7.04800	−0.792962	−0.396481	+	0.918043i	$0.629769\pi$
$80$	4.36633	0.488171
$81$	1.00000	0.111111
$82$	9.51350	1.05059
$83$	10.4398	1.14591	0.572957	−	0.819586i	$-0.305796\pi$
$83$	10.4398	1.14591	0.572957	+	0.819586i	$0.305796\pi$
$84$	−6.80344	−0.742316
$85$	1.84172	0.199762
$86$	−1.71075	−0.184475
$87$	−3.38465	−0.362873
$88$	10.5451	1.12411
$89$	−11.1419	−1.18104	−0.590519	−	0.807023i	$-0.701077\pi$
$89$	−11.1419	−1.18104	−0.590519	+	0.807023i	$0.701077\pi$
$90$	−2.46180	−0.259496
$91$	3.43931	0.360538
$92$	12.0251	1.25370
$93$	−8.85736	−0.918466
$94$	−7.94579	−0.819545
$95$	3.33873	0.342546
$96$	−0.604223	−0.0616683
$97$	10.7018	1.08661	0.543304	−	0.839536i	$-0.317173\pi$
$97$	10.7018	1.08661	0.543304	+	0.839536i	$0.317173\pi$
$98$	10.3212	1.04260
$99$	−2.07892	−0.208939
$100$	4.06045	0.406045
$101$	−0.0490941	−0.00488504	−0.00244252	−	0.999997i	$-0.500777\pi$
$101$	−0.0490941	−0.00488504	−0.00244252	+	0.999997i	$0.500777\pi$
$102$	−4.53394	−0.448927
$103$	−8.37216	−0.824933	−0.412467	−	0.910973i	$-0.635333\pi$
$103$	−8.37216	−0.824933	−0.412467	+	0.910973i	$0.635333\pi$
$104$	10.4119	1.02097
$105$	−1.67554	−0.163516
$106$	6.00402	0.583162
$107$	−3.02238	−0.292185	−0.146092	−	0.989271i	$-0.546670\pi$
$107$	−3.02238	−0.292185	−0.146092	+	0.989271i	$0.546670\pi$
$108$	4.06045	0.390717
$109$	−10.8630	−1.04049	−0.520245	−	0.854017i	$-0.674159\pi$
$109$	−10.8630	−1.04049	−0.520245	+	0.854017i	$0.674159\pi$
$110$	5.11787	0.487970
$111$	2.84227	0.269776
$112$	−7.31597	−0.691294
$113$	−8.11404	−0.763304	−0.381652	−	0.924306i	$-0.624645\pi$
$113$	−8.11404	−0.763304	−0.381652	+	0.924306i	$0.624645\pi$
$114$	−8.21927	−0.769805
$115$	2.96151	0.276163
$116$	−13.7432	−1.27602
$117$	−2.05266	−0.189768
$118$	−19.6581	−1.80968
$119$	−3.08587	−0.282882
$120$	−5.07240	−0.463045
$121$	−6.67811	−0.607101
$122$	−17.3810	−1.57360
$123$	−3.86445	−0.348446
$124$	−35.9649	−3.22974
$125$	1.00000	0.0894427
$126$	4.12484	0.367470
$127$	4.37092	0.387856	0.193928	−	0.981016i	$-0.437877\pi$
$127$	4.37092	0.387856	0.193928	+	0.981016i	$0.437877\pi$
$128$	19.0446	1.68332
$129$	0.694921	0.0611844
$130$	5.05323	0.443198
$131$	14.5339	1.26983	0.634917	−	0.772580i	$-0.281034\pi$
$131$	14.5339	1.26983	0.634917	+	0.772580i	$0.281034\pi$
$132$	−8.44133	−0.734723
$133$	−5.59417	−0.485076
$134$	30.3007	2.61758
$135$	1.00000	0.0860663
$136$	−9.34194	−0.801065
$137$	9.51600	0.813007	0.406504	−	0.913649i	$-0.366748\pi$
$137$	9.51600	0.813007	0.406504	+	0.913649i	$0.366748\pi$
$138$	−7.29065	−0.620621
$139$	−20.5087	−1.73952	−0.869762	−	0.493472i	$-0.835728\pi$
$139$	−20.5087	−1.73952	−0.869762	+	0.493472i	$0.835728\pi$
$140$	−6.80344	−0.574996
$141$	3.22764	0.271816
$142$	−18.1842	−1.52599
$143$	4.26731	0.356850
$144$	4.36633	0.363861
$145$	−3.38465	−0.281080
$146$	−13.7845	−1.14081
$147$	−4.19256	−0.345797
$148$	11.5409	0.948655
$149$	−12.0832	−0.989891	−0.494945	−	0.868924i	$-0.664812\pi$
$149$	−12.0832	−0.989891	−0.494945	+	0.868924i	$0.664812\pi$
$150$	−2.46180	−0.201005
$151$	−24.0976	−1.96104	−0.980519	−	0.196424i	$-0.937067\pi$
$151$	−24.0976	−1.96104	−0.980519	+	0.196424i	$0.937067\pi$
$152$	−16.9354	−1.37364
$153$	1.84172	0.148894
$154$	−8.57520	−0.691009
$155$	−8.85736	−0.711441
$156$	−8.33471	−0.667311
$157$	14.7190	1.17470	0.587351	−	0.809332i	$-0.300171\pi$
$157$	14.7190	1.17470	0.587351	+	0.809332i	$0.300171\pi$
$158$	17.3508	1.38035
$159$	−2.43888	−0.193416
$160$	−0.604223	−0.0477681
$161$	−4.96213	−0.391071
$162$	−2.46180	−0.193417
$163$	−4.06094	−0.318077	−0.159039	−	0.987272i	$-0.550839\pi$
$163$	−4.06094	−0.318077	−0.159039	+	0.987272i	$0.550839\pi$
$164$	−15.6914	−1.22529
$165$	−2.07892	−0.161843
$166$	−25.7006	−1.99475
$167$	23.0755	1.78564	0.892818	−	0.450417i	$-0.148725\pi$
$167$	23.0755	1.78564	0.892818	+	0.450417i	$0.148725\pi$
$168$	8.49901	0.655713
$169$	−8.78659	−0.675892
$170$	−4.53394	−0.347737
$171$	3.33873	0.255319
$172$	2.82169	0.215152
$173$	−18.2527	−1.38773	−0.693864	−	0.720106i	$-0.744093\pi$
$173$	−18.2527	−1.38773	−0.693864	+	0.720106i	$0.744093\pi$
$174$	8.33233	0.631672
$175$	−1.67554	−0.126659
$176$	−9.07724	−0.684223
$177$	7.98528	0.600210
$178$	27.4291	2.05590
$179$	−0.560658	−0.0419056	−0.0209528	−	0.999780i	$-0.506670\pi$
$179$	−0.560658	−0.0419056	−0.0209528	+	0.999780i	$0.506670\pi$
$180$	4.06045	0.302648
$181$	15.9714	1.18715	0.593573	−	0.804780i	$-0.297717\pi$
$181$	15.9714	1.18715	0.593573	+	0.804780i	$0.297717\pi$
$182$	−8.46689	−0.627608
$183$	7.06027	0.521911
$184$	−15.0220	−1.10744
$185$	2.84227	0.208968
$186$	21.8050	1.59882
$187$	−3.82878	−0.279988
$188$	13.1056	0.955827
$189$	−1.67554	−0.121878
$190$	−8.21927	−0.596288
$191$	−16.7296	−1.21051	−0.605256	−	0.796031i	$-0.706929\pi$
$191$	−16.7296	−1.21051	−0.605256	+	0.796031i	$0.706929\pi$
$192$	−7.24519	−0.522877
$193$	−22.7313	−1.63624	−0.818119	−	0.575050i	$-0.804983\pi$
$193$	−22.7313	−1.63624	−0.818119	+	0.575050i	$0.804983\pi$
$194$	−26.3458	−1.89152
$195$	−2.05266	−0.146994
$196$	−17.0237	−1.21598
$197$	−5.80425	−0.413535	−0.206768	−	0.978390i	$-0.566294\pi$
$197$	−5.80425	−0.413535	−0.206768	+	0.978390i	$0.566294\pi$
$198$	5.11787	0.363711
$199$	−16.7758	−1.18921	−0.594604	−	0.804019i	$-0.702691\pi$
$199$	−16.7758	−1.18921	−0.594604	+	0.804019i	$0.702691\pi$
$200$	−5.07240	−0.358673
$201$	−12.3084	−0.868164
$202$	0.120860	0.00850366
$203$	5.67112	0.398035
$204$	7.47820	0.523579
$205$	−3.86445	−0.269905
$206$	20.6106	1.43601
$207$	2.96151	0.205839
$208$	−8.96259	−0.621444
$209$	−6.94093	−0.480115
$210$	4.12484	0.284641
$211$	−20.5508	−1.41478	−0.707389	−	0.706825i	$-0.750127\pi$
$211$	−20.5508	−1.41478	−0.707389	+	0.706825i	$0.750127\pi$
$212$	−9.90293	−0.680136
$213$	7.38657	0.506119
$214$	7.44049	0.508622
$215$	0.694921	0.0473932
$216$	−5.07240	−0.345133
$217$	14.8409	1.00746
$218$	26.7426	1.81124
$219$	5.59936	0.378370
$220$	−8.44133	−0.569114
$221$	−3.78042	−0.254299
$222$	−6.99709	−0.469614
$223$	6.92411	0.463673	0.231837	−	0.972755i	$-0.425527\pi$
$223$	6.92411	0.463673	0.231837	+	0.972755i	$0.425527\pi$
$224$	1.01240	0.0676439
$225$	1.00000	0.0666667
$226$	19.9751	1.32872
$227$	−15.7520	−1.04550	−0.522750	−	0.852486i	$-0.675094\pi$
$227$	−15.7520	−1.04550	−0.522750	+	0.852486i	$0.675094\pi$
$228$	13.5567	0.897816
$229$	16.1398	1.06655	0.533273	−	0.845943i	$-0.320962\pi$
$229$	16.1398	1.06655	0.533273	+	0.845943i	$0.320962\pi$
$230$	−7.29065	−0.480731
$231$	3.48331	0.229185
$232$	17.1683	1.12716
$233$	−2.79060	−0.182818	−0.0914092	−	0.995813i	$-0.529137\pi$
$233$	−2.79060	−0.182818	−0.0914092	+	0.995813i	$0.529137\pi$
$234$	5.05323	0.330340
$235$	3.22764	0.210548
$236$	32.4238	2.11061
$237$	−7.04800	−0.457817
$238$	7.59680	0.492427
$239$	16.4186	1.06203	0.531016	−	0.847362i	$-0.321810\pi$
$239$	16.4186	1.06203	0.531016	+	0.847362i	$0.321810\pi$
$240$	4.36633	0.281846
$241$	−9.12961	−0.588090	−0.294045	−	0.955792i	$-0.595001\pi$
$241$	−9.12961	−0.588090	−0.294045	+	0.955792i	$0.595001\pi$
$242$	16.4401	1.05681
$243$	1.00000	0.0641500
$244$	28.6679	1.83527
$245$	−4.19256	−0.267853
$246$	9.51350	0.606558
$247$	−6.85327	−0.436063
$248$	44.9281	2.85294
$249$	10.4398	0.661593
$250$	−2.46180	−0.155698
$251$	−16.7933	−1.05998	−0.529992	−	0.848003i	$-0.677805\pi$
$251$	−16.7933	−1.05998	−0.529992	+	0.848003i	$0.677805\pi$
$252$	−6.80344	−0.428577
$253$	−6.15674	−0.387071
$254$	−10.7603	−0.675162
$255$	1.84172	0.115333
$256$	−32.3937	−2.02460
$257$	−5.26440	−0.328385	−0.164192	−	0.986428i	$-0.552502\pi$
$257$	−5.26440	−0.328385	−0.164192	+	0.986428i	$0.552502\pi$
$258$	−1.71075	−0.106507
$259$	−4.76234	−0.295917
$260$	−8.33471	−0.516897
$261$	−3.38465	−0.209505
$262$	−35.7796	−2.21047
$263$	9.22654	0.568933	0.284466	−	0.958686i	$-0.408184\pi$
$263$	9.22654	0.568933	0.284466	+	0.958686i	$0.408184\pi$
$264$	10.5451	0.649006
$265$	−2.43888	−0.149819
$266$	13.7717	0.844398
$267$	−11.1419	−0.681873
$268$	−49.9774	−3.05286
$269$	7.99991	0.487763	0.243881	−	0.969805i	$-0.421579\pi$
$269$	7.99991	0.487763	0.243881	+	0.969805i	$0.421579\pi$
$270$	−2.46180	−0.149820
$271$	16.7541	1.01774	0.508870	−	0.860843i	$-0.330063\pi$
$271$	16.7541	1.01774	0.508870	+	0.860843i	$0.330063\pi$
$272$	8.04156	0.487591
$273$	3.43931	0.208157
$274$	−23.4265	−1.41525
$275$	−2.07892	−0.125363
$276$	12.0251	0.723824
$277$	−27.7273	−1.66597	−0.832985	−	0.553296i	$-0.813370\pi$
$277$	−27.7273	−1.66597	−0.832985	+	0.553296i	$0.813370\pi$
$278$	50.4882	3.02808
$279$	−8.85736	−0.530276
$280$	8.49901	0.507913
$281$	5.73117	0.341893	0.170946	−	0.985280i	$-0.445317\pi$
$281$	5.73117	0.341893	0.170946	+	0.985280i	$0.445317\pi$
$282$	−7.94579	−0.473165
$283$	−1.59781	−0.0949802	−0.0474901	−	0.998872i	$-0.515122\pi$
$283$	−1.59781	−0.0949802	−0.0474901	+	0.998872i	$0.515122\pi$
$284$	29.9928	1.77974
$285$	3.33873	0.197769
$286$	−10.5052	−0.621188
$287$	6.47504	0.382210
$288$	−0.604223	−0.0356042
$289$	−13.6081	−0.800475
$290$	8.33233	0.489291
$291$	10.7018	0.627353
$292$	22.7359	1.33052
$293$	−29.3216	−1.71299	−0.856493	−	0.516158i	$-0.827362\pi$
$293$	−29.3216	−1.71299	−0.856493	+	0.516158i	$0.827362\pi$
$294$	10.3212	0.601947
$295$	7.98528	0.464921
$296$	−14.4171	−0.837979
$297$	−2.07892	−0.120631
$298$	29.7463	1.72316
$299$	−6.07898	−0.351556
$300$	4.06045	0.234430
$301$	−1.16437	−0.0671130
$302$	59.3235	3.41368
$303$	−0.0490941	−0.00282038
$304$	14.5780	0.836105
$305$	7.06027	0.404270
$306$	−4.53394	−0.259188
$307$	−10.8632	−0.619997	−0.309999	−	0.950737i	$-0.600329\pi$
$307$	−10.8632	−0.619997	−0.309999	+	0.950737i	$0.600329\pi$
$308$	14.1438	0.805917
$309$	−8.37216	−0.476275
$310$	21.8050	1.23844
$311$	33.1390	1.87914	0.939569	−	0.342358i	$-0.111226\pi$
$311$	33.1390	1.87914	0.939569	+	0.342358i	$0.111226\pi$
$312$	10.4119	0.589458
$313$	23.2121	1.31203	0.656013	−	0.754750i	$-0.272242\pi$
$313$	23.2121	1.31203	0.656013	+	0.754750i	$0.272242\pi$
$314$	−36.2351	−2.04487
$315$	−1.67554	−0.0944060
$316$	−28.6180	−1.60989
$317$	2.47190	0.138836	0.0694178	−	0.997588i	$-0.477886\pi$
$317$	2.47190	0.138836	0.0694178	+	0.997588i	$0.477886\pi$
$318$	6.00402	0.336689
$319$	7.03641	0.393963
$320$	−7.24519	−0.405018
$321$	−3.02238	−0.168693
$322$	12.2158	0.680758
$323$	6.14900	0.342139
$324$	4.06045	0.225580
$325$	−2.05266	−0.113861
$326$	9.99721	0.553694
$327$	−10.8630	−0.600727
$328$	19.6020	1.08234
$329$	−5.40803	−0.298155
$330$	5.11787	0.281730
$331$	−12.0937	−0.664729	−0.332365	−	0.943151i	$-0.607846\pi$
$331$	−12.0937	−0.664729	−0.332365	+	0.943151i	$0.607846\pi$
$332$	42.3901	2.32646
$333$	2.84227	0.155755
$334$	−56.8072	−3.10835
$335$	−12.3084	−0.672477
$336$	−7.31597	−0.399119
$337$	−36.0244	−1.96237	−0.981187	−	0.193057i	$-0.938160\pi$
$337$	−36.0244	−1.96237	−0.981187	+	0.193057i	$0.938160\pi$
$338$	21.6308	1.17656
$339$	−8.11404	−0.440694
$340$	7.47820	0.405562
$341$	18.4137	0.997159
$342$	−8.21927	−0.444447
$343$	18.7536	1.01260
$344$	−3.52492	−0.190051
$345$	2.96151	0.159443
$346$	44.9345	2.41569
$347$	−26.2860	−1.41111	−0.705554	−	0.708657i	$-0.749302\pi$
$347$	−26.2860	−1.41111	−0.705554	+	0.708657i	$0.749302\pi$
$348$	−13.7432	−0.736713
$349$	27.8809	1.49243	0.746216	−	0.665704i	$-0.231869\pi$
$349$	27.8809	1.49243	0.746216	+	0.665704i	$0.231869\pi$
$350$	4.12484	0.220482
$351$	−2.05266	−0.109563
$352$	1.25613	0.0669520
$353$	25.3483	1.34915	0.674577	−	0.738205i	$-0.264326\pi$
$353$	25.3483	1.34915	0.674577	+	0.738205i	$0.264326\pi$
$354$	−19.6581	−1.04482
$355$	7.38657	0.392038
$356$	−45.2411	−2.39777
$357$	−3.08587	−0.163322
$358$	1.38023	0.0729473
$359$	13.8388	0.730385	0.365193	−	0.930932i	$-0.381003\pi$
$359$	13.8388	0.730385	0.365193	+	0.930932i	$0.381003\pi$
$360$	−5.07240	−0.267339
$361$	−7.85290	−0.413311
$362$	−39.3184	−2.06653
$363$	−6.67811	−0.350510
$364$	13.9651	0.731973
$365$	5.59936	0.293084
$366$	−17.3810	−0.908518
$367$	13.6265	0.711298	0.355649	−	0.934620i	$-0.384260\pi$
$367$	13.6265	0.711298	0.355649	+	0.934620i	$0.384260\pi$
$368$	12.9310	0.674072
$369$	−3.86445	−0.201175
$370$	−6.99709	−0.363762
$371$	4.08644	0.212157
$372$	−35.9649	−1.86469
$373$	−25.6003	−1.32553	−0.662767	−	0.748825i	$-0.730618\pi$
$373$	−25.6003	−1.32553	−0.662767	+	0.748825i	$0.730618\pi$
$374$	9.42568	0.487390
$375$	1.00000	0.0516398
$376$	−16.3719	−0.844315
$377$	6.94754	0.357816
$378$	4.12484	0.212159
$379$	2.88242	0.148060	0.0740300	−	0.997256i	$-0.476414\pi$
$379$	2.88242	0.148060	0.0740300	+	0.997256i	$0.476414\pi$
$380$	13.5567	0.695445
$381$	4.37092	0.223929
$382$	41.1849	2.10720
$383$	4.28532	0.218970	0.109485	−	0.993988i	$-0.465080\pi$
$383$	4.28532	0.218970	0.109485	+	0.993988i	$0.465080\pi$
$384$	19.0446	0.971868
$385$	3.48331	0.177526
$386$	55.9599	2.84829
$387$	0.694921	0.0353248
$388$	43.4543	2.20606
$389$	−2.15079	−0.109050	−0.0545248	−	0.998512i	$-0.517364\pi$
$389$	−2.15079	−0.109050	−0.0545248	+	0.998512i	$0.517364\pi$
$390$	5.05323	0.255880
$391$	5.45427	0.275834
$392$	21.2664	1.07411
$393$	14.5339	0.733140
$394$	14.2889	0.719863
$395$	−7.04800	−0.354624
$396$	−8.44133	−0.424193
$397$	13.8728	0.696256	0.348128	−	0.937447i	$-0.386818\pi$
$397$	13.8728	0.696256	0.348128	+	0.937447i	$0.386818\pi$
$398$	41.2987	2.07012
$399$	−5.59417	−0.280059
$400$	4.36633	0.218317
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	30.3007	1.51126
$403$	18.1811	0.905667
$404$	−0.199344	−0.00991773
$405$	1.00000	0.0496904
$406$	−13.9611	−0.692880
$407$	−5.90884	−0.292890
$408$	−9.34194	−0.462495
$409$	−11.3775	−0.562579	−0.281289	−	0.959623i	$-0.590762\pi$
$409$	−11.3775	−0.562579	−0.281289	+	0.959623i	$0.590762\pi$
$410$	9.51350	0.469838
$411$	9.51600	0.469390
$412$	−33.9947	−1.67480
$413$	−13.3797	−0.658370
$414$	−7.29065	−0.358316
$415$	10.4398	0.512468
$416$	1.24026	0.0608090
$417$	−20.5087	−1.00431
$418$	17.0872	0.835761
$419$	16.5078	0.806458	0.403229	−	0.915099i	$-0.367888\pi$
$419$	16.5078	0.806458	0.403229	+	0.915099i	$0.367888\pi$
$420$	−6.80344	−0.331974
$421$	−0.0670012	−0.00326544	−0.00163272	−	0.999999i	$-0.500520\pi$
$421$	−0.0670012	−0.00326544	−0.00163272	+	0.999999i	$0.500520\pi$
$422$	50.5920	2.46278
$423$	3.22764	0.156933
$424$	12.3710	0.600787
$425$	1.84172	0.0893365
$426$	−18.1842	−0.881029
$427$	−11.8298	−0.572483
$428$	−12.2722	−0.593200
$429$	4.26731	0.206028
$430$	−1.71075	−0.0824999
$431$	−8.01742	−0.386185	−0.193093	−	0.981181i	$-0.561852\pi$
$431$	−8.01742	−0.386185	−0.193093	+	0.981181i	$0.561852\pi$
$432$	4.36633	0.210075
$433$	15.7623	0.757489	0.378744	−	0.925501i	$-0.376356\pi$
$433$	15.7623	0.757489	0.378744	+	0.925501i	$0.376356\pi$
$434$	−36.5352	−1.75375
$435$	−3.38465	−0.162282
$436$	−44.1088	−2.11243
$437$	9.88768	0.472992
$438$	−13.7845	−0.658649
$439$	−30.8501	−1.47240	−0.736198	−	0.676766i	$-0.763381\pi$
$439$	−30.8501	−1.47240	−0.736198	+	0.676766i	$0.763381\pi$
$440$	10.5451	0.502718
$441$	−4.19256	−0.199646
$442$	9.30663	0.442671
$443$	−12.5340	−0.595508	−0.297754	−	0.954643i	$-0.596238\pi$
$443$	−12.5340	−0.595508	−0.297754	+	0.954643i	$0.596238\pi$
$444$	11.5409	0.547706
$445$	−11.1419	−0.528177
$446$	−17.0458	−0.807140
$447$	−12.0832	−0.571514
$448$	12.1396	0.573543
$449$	−10.3347	−0.487724	−0.243862	−	0.969810i	$-0.578414\pi$
$449$	−10.3347	−0.487724	−0.243862	+	0.969810i	$0.578414\pi$
$450$	−2.46180	−0.116050
$451$	8.03387	0.378300
$452$	−32.9466	−1.54968
$453$	−24.0976	−1.13221
$454$	38.7783	1.81996
$455$	3.43931	0.161237
$456$	−16.9354	−0.793071
$457$	−1.68835	−0.0789776	−0.0394888	−	0.999220i	$-0.512573\pi$
$457$	−1.68835	−0.0789776	−0.0394888	+	0.999220i	$0.512573\pi$
$458$	−39.7328	−1.85659
$459$	1.84172	0.0859641
$460$	12.0251	0.560672
$461$	1.61531	0.0752324	0.0376162	−	0.999292i	$-0.488024\pi$
$461$	1.61531	0.0752324	0.0376162	+	0.999292i	$0.488024\pi$
$462$	−8.57520	−0.398954
$463$	30.8273	1.43267	0.716334	−	0.697757i	$-0.245819\pi$
$463$	30.8273	1.43267	0.716334	+	0.697757i	$0.245819\pi$
$464$	−14.7785	−0.686075
$465$	−8.85736	−0.410750
$466$	6.86989	0.318242
$467$	−15.5086	−0.717654	−0.358827	−	0.933404i	$-0.616823\pi$
$467$	−15.5086	−0.717654	−0.358827	+	0.933404i	$0.616823\pi$
$468$	−8.33471	−0.385272
$469$	20.6231	0.952288
$470$	−7.94579	−0.366512
$471$	14.7190	0.678215
$472$	−40.5045	−1.86437
$473$	−1.44468	−0.0664266
$474$	17.3508	0.796947
$475$	3.33873	0.153191
$476$	−12.5300	−0.574313
$477$	−2.43888	−0.111669
$478$	−40.4193	−1.84874
$479$	−27.8285	−1.27152	−0.635759	−	0.771887i	$-0.719313\pi$
$479$	−27.8285	−1.27152	−0.635759	+	0.771887i	$0.719313\pi$
$480$	−0.604223	−0.0275789
$481$	−5.83421	−0.266017
$482$	22.4752	1.02372
$483$	−4.96213	−0.225785
$484$	−27.1161	−1.23255
$485$	10.7018	0.485946
$486$	−2.46180	−0.111669
$487$	−16.0485	−0.727226	−0.363613	−	0.931550i	$-0.618457\pi$
$487$	−16.0485	−0.727226	−0.363613	+	0.931550i	$0.618457\pi$
$488$	−35.8125	−1.62116
$489$	−4.06094	−0.183642
$490$	10.3212	0.466266
$491$	−10.4806	−0.472984	−0.236492	−	0.971633i	$-0.575998\pi$
$491$	−10.4806	−0.472984	−0.236492	+	0.971633i	$0.575998\pi$
$492$	−15.6914	−0.707423
$493$	−6.23358	−0.280746
$494$	16.8714	0.759078
$495$	−2.07892	−0.0934403
$496$	−38.6742	−1.73652
$497$	−12.3765	−0.555161
$498$	−25.7006	−1.15167
$499$	4.22555	0.189162	0.0945809	−	0.995517i	$-0.469849\pi$
$499$	4.22555	0.189162	0.0945809	+	0.995517i	$0.469849\pi$
$500$	4.06045	0.181589
$501$	23.0755	1.03094
$502$	41.3417	1.84517
$503$	−28.5774	−1.27421	−0.637103	−	0.770779i	$-0.719867\pi$
$503$	−28.5774	−1.27421	−0.637103	+	0.770779i	$0.719867\pi$
$504$	8.49901	0.378576
$505$	−0.0490941	−0.00218466
$506$	15.1566	0.673795
$507$	−8.78659	−0.390226
$508$	17.7479	0.787435
$509$	14.9879	0.664328	0.332164	−	0.943222i	$-0.392221\pi$
$509$	14.9879	0.664328	0.332164	+	0.943222i	$0.392221\pi$
$510$	−4.53394	−0.200766
$511$	−9.38196	−0.415033
$512$	41.6574	1.84101
$513$	3.33873	0.147408
$514$	12.9599	0.571637
$515$	−8.37216	−0.368921
$516$	2.82169	0.124218
$517$	−6.70999	−0.295105
$518$	11.7239	0.515119
$519$	−18.2527	−0.801205
$520$	10.4119	0.456593
$521$	6.15310	0.269572	0.134786	−	0.990875i	$-0.456965\pi$
$521$	6.15310	0.269572	0.134786	+	0.990875i	$0.456965\pi$
$522$	8.33233	0.364696
$523$	10.4356	0.456317	0.228158	−	0.973624i	$-0.426730\pi$
$523$	10.4356	0.456317	0.228158	+	0.973624i	$0.426730\pi$
$524$	59.0142	2.57805
$525$	−1.67554	−0.0731266
$526$	−22.7139	−0.990372
$527$	−16.3128	−0.710595
$528$	−9.07724	−0.395036
$529$	−14.2294	−0.618671
$530$	6.00402	0.260798
$531$	7.98528	0.346531
$532$	−22.7148	−0.984813
$533$	7.93240	0.343590
$534$	27.4291	1.18697
$535$	−3.02238	−0.130669
$536$	62.4329	2.69669
$537$	−0.560658	−0.0241942
$538$	−19.6942	−0.849075
$539$	8.71599	0.375424
$540$	4.06045	0.174734
$541$	−3.49313	−0.150181	−0.0750907	−	0.997177i	$-0.523925\pi$
$541$	−3.49313	−0.150181	−0.0750907	+	0.997177i	$0.523925\pi$
$542$	−41.2453	−1.77164
$543$	15.9714	0.685399
$544$	−1.11281	−0.0477113
$545$	−10.8630	−0.465321
$546$	−8.46689	−0.362350
$547$	5.11418	0.218667	0.109333	−	0.994005i	$-0.465128\pi$
$547$	5.11418	0.218667	0.109333	+	0.994005i	$0.465128\pi$
$548$	38.6392	1.65059
$549$	7.06027	0.301325
$550$	5.11787	0.218227
$551$	−11.3004	−0.481414
$552$	−15.0220	−0.639378
$553$	11.8092	0.502179
$554$	68.2589	2.90004
$555$	2.84227	0.120648
$556$	−83.2744	−3.53162
$557$	−21.4946	−0.910756	−0.455378	−	0.890298i	$-0.650496\pi$
$557$	−21.4946	−0.910756	−0.455378	+	0.890298i	$0.650496\pi$
$558$	21.8050	0.923081
$559$	−1.42644	−0.0603318
$560$	−7.31597	−0.309156
$561$	−3.82878	−0.161651
$562$	−14.1090	−0.595151
$563$	39.2305	1.65337	0.826684	−	0.562667i	$-0.190225\pi$
$563$	39.2305	1.65337	0.826684	+	0.562667i	$0.190225\pi$
$564$	13.1056	0.551847
$565$	−8.11404	−0.341360
$566$	3.93349	0.165337
$567$	−1.67554	−0.0703661
$568$	−37.4676	−1.57211
$569$	−23.3160	−0.977458	−0.488729	−	0.872436i	$-0.662539\pi$
$569$	−23.3160	−0.977458	−0.488729	+	0.872436i	$0.662539\pi$
$570$	−8.21927	−0.344267
$571$	−18.4361	−0.771526	−0.385763	−	0.922598i	$-0.626062\pi$
$571$	−18.4361	−0.771526	−0.385763	+	0.922598i	$0.626062\pi$
$572$	17.3272	0.724485
$573$	−16.7296	−0.698889
$574$	−15.9402	−0.665333
$575$	2.96151	0.123504
$576$	−7.24519	−0.301883
$577$	19.2393	0.800943	0.400471	−	0.916309i	$-0.368846\pi$
$577$	19.2393	0.800943	0.400471	+	0.916309i	$0.368846\pi$
$578$	33.5003	1.39343
$579$	−22.7313	−0.944682
$580$	−13.7432	−0.570655
$581$	−17.4923	−0.725701
$582$	−26.3458	−1.09207
$583$	5.07022	0.209987
$584$	−28.4022	−1.17529
$585$	−2.05266	−0.0848670
$586$	72.1839	2.98189
$587$	−20.6533	−0.852453	−0.426226	−	0.904616i	$-0.640157\pi$
$587$	−20.6533	−0.852453	−0.426226	+	0.904616i	$0.640157\pi$
$588$	−17.0237	−0.702045
$589$	−29.5723	−1.21851
$590$	−19.6581	−0.809312
$591$	−5.80425	−0.238755
$592$	12.4103	0.510060
$593$	25.6345	1.05268	0.526342	−	0.850273i	$-0.323563\pi$
$593$	25.6345	1.05268	0.526342	+	0.850273i	$0.323563\pi$
$594$	5.11787	0.209989
$595$	−3.08587	−0.126508
$596$	−49.0630	−2.00970
$597$	−16.7758	−0.686589
$598$	14.9652	0.611973
$599$	17.1361	0.700163	0.350082	−	0.936719i	$-0.386154\pi$
$599$	17.1361	0.700163	0.350082	+	0.936719i	$0.386154\pi$
$600$	−5.07240	−0.207080
$601$	−19.1030	−0.779227	−0.389614	−	0.920978i	$-0.627391\pi$
$601$	−19.1030	−0.779227	−0.389614	+	0.920978i	$0.627391\pi$
$602$	2.86644	0.116827
$603$	−12.3084	−0.501235
$604$	−97.8472	−3.98134
$605$	−6.67811	−0.271504
$606$	0.120860	0.00490959
$607$	39.7672	1.61410	0.807051	−	0.590482i	$-0.201062\pi$
$607$	39.7672	1.61410	0.807051	+	0.590482i	$0.201062\pi$
$608$	−2.01734	−0.0818138
$609$	5.67112	0.229805
$610$	−17.3810	−0.703735
$611$	−6.62524	−0.268028
$612$	7.47820	0.302288
$613$	20.2273	0.816971	0.408486	−	0.912765i	$-0.366057\pi$
$613$	20.2273	0.816971	0.408486	+	0.912765i	$0.366057\pi$
$614$	26.7431	1.07926
$615$	−3.86445	−0.155830
$616$	−17.6687	−0.711894
$617$	−24.2241	−0.975224	−0.487612	−	0.873060i	$-0.662132\pi$
$617$	−24.2241	−0.975224	−0.487612	+	0.873060i	$0.662132\pi$
$618$	20.6106	0.829078
$619$	17.9593	0.721846	0.360923	−	0.932596i	$-0.382462\pi$
$619$	17.9593	0.721846	0.360923	+	0.932596i	$0.382462\pi$
$620$	−35.9649	−1.44438
$621$	2.96151	0.118841
$622$	−81.5814	−3.27112
$623$	18.6687	0.747946
$624$	−8.96259	−0.358791
$625$	1.00000	0.0400000
$626$	−57.1435	−2.28391
$627$	−6.94093	−0.277194
$628$	59.7656	2.38491
$629$	5.23466	0.208720
$630$	4.12484	0.164338
$631$	3.47163	0.138203	0.0691016	−	0.997610i	$-0.477987\pi$
$631$	3.47163	0.138203	0.0691016	+	0.997610i	$0.477987\pi$
$632$	35.7503	1.42207
$633$	−20.5508	−0.816822
$634$	−6.08531	−0.241679
$635$	4.37092	0.173455
$636$	−9.90293	−0.392677
$637$	8.60591	0.340978
$638$	−17.3222	−0.685793
$639$	7.38657	0.292208
$640$	19.0446	0.752805
$641$	10.4417	0.412421	0.206210	−	0.978508i	$-0.433887\pi$
$641$	10.4417	0.412421	0.206210	+	0.978508i	$0.433887\pi$
$642$	7.44049	0.293653
$643$	−11.3435	−0.447342	−0.223671	−	0.974665i	$-0.571804\pi$
$643$	−11.3435	−0.447342	−0.223671	+	0.974665i	$0.571804\pi$
$644$	−20.1485	−0.793961
$645$	0.694921	0.0273625
$646$	−15.1376	−0.595580
$647$	14.5017	0.570120	0.285060	−	0.958510i	$-0.407987\pi$
$647$	14.5017	0.570120	0.285060	+	0.958510i	$0.407987\pi$
$648$	−5.07240	−0.199263
$649$	−16.6007	−0.651635
$650$	5.05323	0.198204
$651$	14.8409	0.581660
$652$	−16.4892	−0.645768
$653$	−31.1458	−1.21883	−0.609415	−	0.792852i	$-0.708596\pi$
$653$	−31.1458	−1.21883	−0.609415	+	0.792852i	$0.708596\pi$
$654$	26.7426	1.04572
$655$	14.5339	0.567887
$656$	−16.8735	−0.658799
$657$	5.59936	0.218452
$658$	13.3135	0.519014
$659$	−3.63198	−0.141482	−0.0707409	−	0.997495i	$-0.522536\pi$
$659$	−3.63198	−0.141482	−0.0707409	+	0.997495i	$0.522536\pi$
$660$	−8.44133	−0.328578
$661$	−10.3786	−0.403679	−0.201840	−	0.979419i	$-0.564692\pi$
$661$	−10.3786	−0.403679	−0.201840	+	0.979419i	$0.564692\pi$
$662$	29.7722	1.15713
$663$	−3.78042	−0.146819
$664$	−52.9547	−2.05504
$665$	−5.59417	−0.216933
$666$	−6.99709	−0.271132
$667$	−10.0237	−0.388119
$668$	93.6969	3.62524
$669$	6.92411	0.267702
$670$	30.3007	1.17062
$671$	−14.6777	−0.566627
$672$	1.01240	0.0390542
$673$	−36.4431	−1.40478	−0.702388	−	0.711794i	$-0.747883\pi$
$673$	−36.4431	−1.40478	−0.702388	+	0.711794i	$0.747883\pi$
$674$	88.6848	3.41601
$675$	1.00000	0.0384900
$676$	−35.6775	−1.37221
$677$	−43.1290	−1.65758	−0.828791	−	0.559558i	$-0.810971\pi$
$677$	−43.1290	−1.65758	−0.828791	+	0.559558i	$0.810971\pi$
$678$	19.9751	0.767140
$679$	−17.9314	−0.688143
$680$	−9.34194	−0.358247
$681$	−15.7520	−0.603619
$682$	−45.3308	−1.73581
$683$	3.81436	0.145953	0.0729763	−	0.997334i	$-0.476750\pi$
$683$	3.81436	0.145953	0.0729763	+	0.997334i	$0.476750\pi$
$684$	13.5567	0.518354
$685$	9.51600	0.363588
$686$	−46.1675	−1.76269
$687$	16.1398	0.615770
$688$	3.03426	0.115680
$689$	5.00618	0.190720
$690$	−7.29065	−0.277550
$691$	−26.4342	−1.00560	−0.502802	−	0.864402i	$-0.667697\pi$
$691$	−26.4342	−1.00560	−0.502802	+	0.864402i	$0.667697\pi$
$692$	−74.1141	−2.81740
$693$	3.48331	0.132320
$694$	64.7108	2.45639
$695$	−20.5087	−0.777939
$696$	17.1683	0.650763
$697$	−7.11723	−0.269584
$698$	−68.6372	−2.59796
$699$	−2.79060	−0.105550
$700$	−6.80344	−0.257146
$701$	−36.5055	−1.37879	−0.689396	−	0.724384i	$-0.742124\pi$
$701$	−36.5055	−1.37879	−0.689396	+	0.724384i	$0.742124\pi$
$702$	5.05323	0.190722
$703$	9.48956	0.357906
$704$	15.0621	0.567676
$705$	3.22764	0.121560
$706$	−62.4024	−2.34854
$707$	0.0822591	0.00309367
$708$	32.4238	1.21856
$709$	−48.9509	−1.83839	−0.919195	−	0.393803i	$-0.871159\pi$
$709$	−48.9509	−1.83839	−0.919195	+	0.393803i	$0.871159\pi$
$710$	−18.1842	−0.682442
$711$	−7.04800	−0.264321
$712$	56.5162	2.11803
$713$	−26.2312	−0.982366
$714$	7.59680	0.284303
$715$	4.26731	0.159588
$716$	−2.27652	−0.0850776
$717$	16.4186	0.613165
$718$	−34.0684	−1.27142
$719$	−25.3476	−0.945307	−0.472653	−	0.881248i	$-0.656704\pi$
$719$	−25.3476	−0.945307	−0.472653	+	0.881248i	$0.656704\pi$
$720$	4.36633	0.162724
$721$	14.0279	0.522426
$722$	19.3323	0.719472
$723$	−9.12961	−0.339534
$724$	64.8511	2.41017
$725$	−3.38465	−0.125703
$726$	16.4401	0.610151
$727$	−27.2274	−1.00981	−0.504905	−	0.863175i	$-0.668472\pi$
$727$	−27.2274	−1.00981	−0.504905	+	0.863175i	$0.668472\pi$
$728$	−17.4456	−0.646576
$729$	1.00000	0.0370370
$730$	−13.7845	−0.510187
$731$	1.27985	0.0473369
$732$	28.6679	1.05959
$733$	32.4675	1.19922	0.599608	−	0.800294i	$-0.295323\pi$
$733$	32.4675	1.19922	0.599608	+	0.800294i	$0.295323\pi$
$734$	−33.5457	−1.23820
$735$	−4.19256	−0.154645
$736$	−1.78942	−0.0659587
$737$	25.5880	0.942548
$738$	9.51350	0.350197
$739$	−16.6720	−0.613289	−0.306645	−	0.951824i	$-0.599206\pi$
$739$	−16.6720	−0.613289	−0.306645	+	0.951824i	$0.599206\pi$
$740$	11.5409	0.424251
$741$	−6.85327	−0.251761
$742$	−10.0600	−0.369314
$743$	−7.78907	−0.285753	−0.142877	−	0.989741i	$-0.545635\pi$
$743$	−7.78907	−0.285753	−0.142877	+	0.989741i	$0.545635\pi$
$744$	44.9281	1.64714
$745$	−12.0832	−0.442693
$746$	63.0228	2.30743
$747$	10.4398	0.381971
$748$	−15.5466	−0.568438
$749$	5.06412	0.185039
$750$	−2.46180	−0.0898921
$751$	−8.32185	−0.303669	−0.151834	−	0.988406i	$-0.548518\pi$
$751$	−8.32185	−0.303669	−0.151834	+	0.988406i	$0.548518\pi$
$752$	14.0929	0.513916
$753$	−16.7933	−0.611982
$754$	−17.1034	−0.622870
$755$	−24.0976	−0.877003
$756$	−6.80344	−0.247439
$757$	42.8747	1.55831	0.779154	−	0.626832i	$-0.215649\pi$
$757$	42.8747	1.55831	0.779154	+	0.626832i	$0.215649\pi$
$758$	−7.09594	−0.257736
$759$	−6.15674	−0.223475
$760$	−16.9354	−0.614310
$761$	−45.0881	−1.63444	−0.817221	−	0.576325i	$-0.804486\pi$
$761$	−45.0881	−1.63444	−0.817221	+	0.576325i	$0.804486\pi$
$762$	−10.7603	−0.389805
$763$	18.2015	0.658937
$764$	−67.9297	−2.45761
$765$	1.84172	0.0665875
$766$	−10.5496	−0.381172
$767$	−16.3910	−0.591846
$768$	−32.3937	−1.16891
$769$	−42.6032	−1.53631	−0.768155	−	0.640263i	$-0.778825\pi$
$769$	−42.6032	−1.53631	−0.768155	+	0.640263i	$0.778825\pi$
$770$	−8.57520	−0.309029
$771$	−5.26440	−0.189593
$772$	−92.2994	−3.32193
$773$	30.7257	1.10513	0.552563	−	0.833471i	$-0.313650\pi$
$773$	30.7257	1.10513	0.552563	+	0.833471i	$0.313650\pi$
$774$	−1.71075	−0.0614918
$775$	−8.85736	−0.318166
$776$	−54.2840	−1.94868
$777$	−4.76234	−0.170848
$778$	5.29482	0.189828
$779$	−12.9023	−0.462275
$780$	−8.33471	−0.298431
$781$	−15.3561	−0.549483
$782$	−13.4273	−0.480160
$783$	−3.38465	−0.120958
$784$	−18.3061	−0.653790
$785$	14.7190	0.525343
$786$	−35.7796	−1.27622
$787$	−47.8391	−1.70528	−0.852641	−	0.522498i	$-0.825000\pi$
$787$	−47.8391	−1.70528	−0.852641	+	0.522498i	$0.825000\pi$
$788$	−23.5678	−0.839569
$789$	9.22654	0.328473
$790$	17.3508	0.617312
$791$	13.5954	0.483397
$792$	10.5451	0.374704
$793$	−14.4923	−0.514638
$794$	−34.1520	−1.21201
$795$	−2.43888	−0.0864981
$796$	−68.1174	−2.41436
$797$	−18.6243	−0.659706	−0.329853	−	0.944032i	$-0.606999\pi$
$797$	−18.6243	−0.659706	−0.329853	+	0.944032i	$0.606999\pi$
$798$	13.7717	0.487514
$799$	5.94440	0.210298
$800$	−0.604223	−0.0213625
$801$	−11.1419	−0.393680
$802$	2.46180	0.0869291
$803$	−11.6406	−0.410788
$804$	−49.9774	−1.76257
$805$	−4.96213	−0.174892
$806$	−44.7583	−1.57654
$807$	7.99991	0.281610
$808$	0.249025	0.00876066
$809$	19.9437	0.701184	0.350592	−	0.936528i	$-0.385980\pi$
$809$	19.9437	0.701184	0.350592	+	0.936528i	$0.385980\pi$
$810$	−2.46180	−0.0864987
$811$	51.0341	1.79205	0.896024	−	0.444006i	$-0.146443\pi$
$811$	51.0341	1.79205	0.896024	+	0.444006i	$0.146443\pi$
$812$	23.0273	0.808099
$813$	16.7541	0.587593
$814$	14.5464	0.509850
$815$	−4.06094	−0.142248
$816$	8.04156	0.281511
$817$	2.32015	0.0811718
$818$	28.0090	0.979311
$819$	3.43931	0.120179
$820$	−15.6914	−0.547967
$821$	−28.8039	−1.00526	−0.502632	−	0.864500i	$-0.667635\pi$
$821$	−28.8039	−1.00526	−0.502632	+	0.864500i	$0.667635\pi$
$822$	−23.4265	−0.817092
$823$	−29.6108	−1.03217	−0.516084	−	0.856538i	$-0.672611\pi$
$823$	−29.6108	−1.03217	−0.516084	+	0.856538i	$0.672611\pi$
$824$	42.4669	1.47941
$825$	−2.07892	−0.0723786
$826$	32.9380	1.14606
$827$	44.9863	1.56433	0.782164	−	0.623073i	$-0.214116\pi$
$827$	44.9863	1.56433	0.782164	+	0.623073i	$0.214116\pi$
$828$	12.0251	0.417900
$829$	−7.34751	−0.255190	−0.127595	−	0.991826i	$-0.540726\pi$
$829$	−7.34751	−0.255190	−0.127595	+	0.991826i	$0.540726\pi$
$830$	−25.7006	−0.892081
$831$	−27.7273	−0.961848
$832$	14.8719	0.515591
$833$	−7.72152	−0.267535
$834$	50.4882	1.74826
$835$	23.0755	0.798561
$836$	−28.1833	−0.974740
$837$	−8.85736	−0.306155
$838$	−40.6388	−1.40384
$839$	10.4510	0.360809	0.180405	−	0.983592i	$-0.442259\pi$
$839$	10.4510	0.360809	0.180405	+	0.983592i	$0.442259\pi$
$840$	8.49901	0.293244
$841$	−17.5441	−0.604970
$842$	0.164943	0.00568433
$843$	5.73117	0.197392
$844$	−83.4455	−2.87231
$845$	−8.78659	−0.302268
$846$	−7.94579	−0.273182
$847$	11.1894	0.384474
$848$	−10.6490	−0.365687
$849$	−1.59781	−0.0548368
$850$	−4.53394	−0.155513
$851$	8.41742	0.288545
$852$	29.9928	1.02753
$853$	−21.5046	−0.736302	−0.368151	−	0.929766i	$-0.620009\pi$
$853$	−21.5046	−0.736302	−0.368151	+	0.929766i	$0.620009\pi$
$854$	29.1225	0.996552
$855$	3.33873	0.114182
$856$	15.3307	0.523994
$857$	−38.3031	−1.30841	−0.654204	−	0.756318i	$-0.726996\pi$
$857$	−38.3031	−1.30841	−0.654204	+	0.756318i	$0.726996\pi$
$858$	−10.5052	−0.358643
$859$	−1.65423	−0.0564416	−0.0282208	−	0.999602i	$-0.508984\pi$
$859$	−1.65423	−0.0564416	−0.0282208	+	0.999602i	$0.508984\pi$
$860$	2.82169	0.0962188
$861$	6.47504	0.220669
$862$	19.7373	0.672254
$863$	14.2813	0.486141	0.243071	−	0.970009i	$-0.421845\pi$
$863$	14.2813	0.486141	0.243071	+	0.970009i	$0.421845\pi$
$864$	−0.604223	−0.0205561
$865$	−18.2527	−0.620611
$866$	−38.8036	−1.31860
$867$	−13.6081	−0.462154
$868$	60.2606	2.04538
$869$	14.6522	0.497042
$870$	8.33233	0.282492
$871$	25.2649	0.856067
$872$	55.1017	1.86598
$873$	10.7018	0.362202
$874$	−24.3415	−0.823363
$875$	−1.67554	−0.0566436
$876$	22.7359	0.768175
$877$	−5.63561	−0.190301	−0.0951505	−	0.995463i	$-0.530333\pi$
$877$	−5.63561	−0.190301	−0.0951505	+	0.995463i	$0.530333\pi$
$878$	75.9467	2.56308
$879$	−29.3216	−0.988993
$880$	−9.07724	−0.305994
$881$	10.7565	0.362395	0.181198	−	0.983447i	$-0.442003\pi$
$881$	10.7565	0.362395	0.181198	+	0.983447i	$0.442003\pi$
$882$	10.3212	0.347534
$883$	48.2577	1.62400	0.812001	−	0.583656i	$-0.198378\pi$
$883$	48.2577	1.62400	0.812001	+	0.583656i	$0.198378\pi$
$884$	−15.3502	−0.516283
$885$	7.98528	0.268422
$886$	30.8562	1.03663
$887$	−28.3038	−0.950348	−0.475174	−	0.879892i	$-0.657615\pi$
$887$	−28.3038	−0.950348	−0.475174	+	0.879892i	$0.657615\pi$
$888$	−14.4171	−0.483807
$889$	−7.32365	−0.245627
$890$	27.4291	0.919425
$891$	−2.07892	−0.0696463
$892$	28.1150	0.941360
$893$	10.7762	0.360612
$894$	29.7463	0.994864
$895$	−0.560658	−0.0187407
$896$	−31.9101	−1.06604
$897$	−6.07898	−0.202971
$898$	25.4419	0.849008
$899$	29.9791	0.999859
$900$	4.06045	0.135348
$901$	−4.49173	−0.149641
$902$	−19.7778	−0.658527
$903$	−1.16437	−0.0387477
$904$	41.1577	1.36888
$905$	15.9714	0.530908
$906$	59.3235	1.97089
$907$	34.1376	1.13352	0.566759	−	0.823883i	$-0.308197\pi$
$907$	34.1376	1.13352	0.566759	+	0.823883i	$0.308197\pi$
$908$	−63.9603	−2.12260
$909$	−0.0490941	−0.00162835
$910$	−8.46689	−0.280675
$911$	−12.1659	−0.403076	−0.201538	−	0.979481i	$-0.564594\pi$
$911$	−12.1659	−0.403076	−0.201538	+	0.979481i	$0.564594\pi$
$912$	14.5780	0.482726
$913$	−21.7034	−0.718278
$914$	4.15637	0.137481
$915$	7.06027	0.233405
$916$	65.5346	2.16532
$917$	−24.3522	−0.804180
$918$	−4.53394	−0.149642
$919$	29.0314	0.957658	0.478829	−	0.877908i	$-0.341061\pi$
$919$	29.0314	0.957658	0.478829	+	0.877908i	$0.341061\pi$
$920$	−15.0220	−0.495260
$921$	−10.8632	−0.357956
$922$	−3.97656	−0.130961
$923$	−15.1621	−0.499067
$924$	14.1438	0.465296
$925$	2.84227	0.0934533
$926$	−75.8907	−2.49392
$927$	−8.37216	−0.274978
$928$	2.04509	0.0671332
$929$	−17.4422	−0.572260	−0.286130	−	0.958191i	$-0.592369\pi$
$929$	−17.4422	−0.572260	−0.286130	+	0.958191i	$0.592369\pi$
$930$	21.8050	0.715015
$931$	−13.9978	−0.458760
$932$	−11.3311	−0.371162
$933$	33.1390	1.08492
$934$	38.1791	1.24926
$935$	−3.82878	−0.125214
$936$	10.4119	0.340324
$937$	11.9770	0.391272	0.195636	−	0.980677i	$-0.437323\pi$
$937$	11.9770	0.391272	0.195636	+	0.980677i	$0.437323\pi$
$938$	−50.7700	−1.65770
$939$	23.2121	0.757499
$940$	13.1056	0.427459
$941$	−48.2578	−1.57316	−0.786579	−	0.617489i	$-0.788150\pi$
$941$	−48.2578	−1.57316	−0.786579	+	0.617489i	$0.788150\pi$
$942$	−36.2351	−1.18060
$943$	−11.4446	−0.372688
$944$	34.8664	1.13480
$945$	−1.67554	−0.0545053
$946$	3.55652	0.115632
$947$	−9.62277	−0.312698	−0.156349	−	0.987702i	$-0.549972\pi$
$947$	−9.62277	−0.312698	−0.156349	+	0.987702i	$0.549972\pi$
$948$	−28.6180	−0.929471
$949$	−11.4936	−0.373098
$950$	−8.21927	−0.266668
$951$	2.47190	0.0801568
$952$	15.6528	0.507310
$953$	13.8665	0.449179	0.224590	−	0.974453i	$-0.427896\pi$
$953$	13.8665	0.449179	0.224590	+	0.974453i	$0.427896\pi$
$954$	6.00402	0.194387
$955$	−16.7296	−0.541357
$956$	66.6669	2.15616
$957$	7.03641	0.227455
$958$	68.5082	2.21340
$959$	−15.9444	−0.514873
$960$	−7.24519	−0.233838
$961$	47.4529	1.53074
$962$	14.3626	0.463070
$963$	−3.02238	−0.0973949
$964$	−37.0703	−1.19395
$965$	−22.7313	−0.731747
$966$	12.2158	0.393036
$967$	−4.13020	−0.132818	−0.0664092	−	0.997792i	$-0.521154\pi$
$967$	−4.13020	−0.132818	−0.0664092	+	0.997792i	$0.521154\pi$
$968$	33.8740	1.08875
$969$	6.14900	0.197534
$970$	−26.3458	−0.845912
$971$	13.2681	0.425794	0.212897	−	0.977075i	$-0.431710\pi$
$971$	13.2681	0.425794	0.212897	+	0.977075i	$0.431710\pi$
$972$	4.06045	0.130239
$973$	34.3631	1.10163
$974$	39.5081	1.26592
$975$	−2.05266	−0.0657377
$976$	30.8275	0.986765
$977$	−4.85444	−0.155307	−0.0776537	−	0.996980i	$-0.524743\pi$
$977$	−4.85444	−0.155307	−0.0776537	+	0.996980i	$0.524743\pi$
$978$	9.99721	0.319676
$979$	23.1631	0.740295
$980$	−17.0237	−0.543802
$981$	−10.8630	−0.346830
$982$	25.8012	0.823348
$983$	−7.77901	−0.248112	−0.124056	−	0.992275i	$-0.539590\pi$
$983$	−7.77901	−0.248112	−0.124056	+	0.992275i	$0.539590\pi$
$984$	19.6020	0.624891
$985$	−5.80425	−0.184939
$986$	15.3458	0.488710
$987$	−5.40803	−0.172140
$988$	−27.8273	−0.885305
$989$	2.05802	0.0654411
$990$	5.11787	0.162657
$991$	−2.06248	−0.0655169	−0.0327584	−	0.999463i	$-0.510429\pi$
$991$	−2.06248	−0.0655169	−0.0327584	+	0.999463i	$0.510429\pi$
$992$	5.35183	0.169921
$993$	−12.0937	−0.383782
$994$	30.4684	0.966399
$995$	−16.7758	−0.531830
$996$	42.3901	1.34318
$997$	−48.7809	−1.54491	−0.772453	−	0.635072i	$-0.780971\pi$
$997$	−48.7809	−1.54491	−0.772453	+	0.635072i	$0.780971\pi$
$998$	−10.4025	−0.329284
$999$	2.84227	0.0899254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.2	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.2	✓	23	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46180 q^{2} +1.00000 q^{3} +4.06045 q^{4} +1.00000 q^{5} -2.46180 q^{6} -1.67554 q^{7} -5.07240 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.46180 q^{2} +1.00000 q^{3} +4.06045 q^{4} +1.00000 q^{5} -2.46180 q^{6} -1.67554 q^{7} -5.07240 q^{8} +1.00000 q^{9} -2.46180 q^{10} -2.07892 q^{11} +4.06045 q^{12} -2.05266 q^{13} +4.12484 q^{14} +1.00000 q^{15} +4.36633 q^{16} +1.84172 q^{17} -2.46180 q^{18} +3.33873 q^{19} +4.06045 q^{20} -1.67554 q^{21} +5.11787 q^{22} +2.96151 q^{23} -5.07240 q^{24} +1.00000 q^{25} +5.05323 q^{26} +1.00000 q^{27} -6.80344 q^{28} -3.38465 q^{29} -2.46180 q^{30} -8.85736 q^{31} -0.604223 q^{32} -2.07892 q^{33} -4.53394 q^{34} -1.67554 q^{35} +4.06045 q^{36} +2.84227 q^{37} -8.21927 q^{38} -2.05266 q^{39} -5.07240 q^{40} -3.86445 q^{41} +4.12484 q^{42} +0.694921 q^{43} -8.44133 q^{44} +1.00000 q^{45} -7.29065 q^{46} +3.22764 q^{47} +4.36633 q^{48} -4.19256 q^{49} -2.46180 q^{50} +1.84172 q^{51} -8.33471 q^{52} -2.43888 q^{53} -2.46180 q^{54} -2.07892 q^{55} +8.49901 q^{56} +3.33873 q^{57} +8.33233 q^{58} +7.98528 q^{59} +4.06045 q^{60} +7.06027 q^{61} +21.8050 q^{62} -1.67554 q^{63} -7.24519 q^{64} -2.05266 q^{65} +5.11787 q^{66} -12.3084 q^{67} +7.47820 q^{68} +2.96151 q^{69} +4.12484 q^{70} +7.38657 q^{71} -5.07240 q^{72} +5.59936 q^{73} -6.99709 q^{74} +1.00000 q^{75} +13.5567 q^{76} +3.48331 q^{77} +5.05323 q^{78} -7.04800 q^{79} +4.36633 q^{80} +1.00000 q^{81} +9.51350 q^{82} +10.4398 q^{83} -6.80344 q^{84} +1.84172 q^{85} -1.71075 q^{86} -3.38465 q^{87} +10.5451 q^{88} -11.1419 q^{89} -2.46180 q^{90} +3.43931 q^{91} +12.0251 q^{92} -8.85736 q^{93} -7.94579 q^{94} +3.33873 q^{95} -0.604223 q^{96} +10.7018 q^{97} +10.3212 q^{98} -2.07892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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