LMFDB - Embedded newform 6038.2.a.b.1.16

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:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.93892 q^{3} +1.00000 q^{4} +0.524165 q^{5} -1.93892 q^{6} -1.38269 q^{7} +1.00000 q^{8} +0.759396 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.93892 q^{3} +1.00000 q^{4} +0.524165 q^{5} -1.93892 q^{6} -1.38269 q^{7} +1.00000 q^{8} +0.759396 q^{9} +0.524165 q^{10} -0.659434 q^{11} -1.93892 q^{12} -4.40931 q^{13} -1.38269 q^{14} -1.01631 q^{15} +1.00000 q^{16} +5.35018 q^{17} +0.759396 q^{18} +2.38957 q^{19} +0.524165 q^{20} +2.68092 q^{21} -0.659434 q^{22} -4.23237 q^{23} -1.93892 q^{24} -4.72525 q^{25} -4.40931 q^{26} +4.34434 q^{27} -1.38269 q^{28} +8.87765 q^{29} -1.01631 q^{30} +4.72098 q^{31} +1.00000 q^{32} +1.27859 q^{33} +5.35018 q^{34} -0.724757 q^{35} +0.759396 q^{36} -5.82942 q^{37} +2.38957 q^{38} +8.54928 q^{39} +0.524165 q^{40} +4.05372 q^{41} +2.68092 q^{42} +8.81055 q^{43} -0.659434 q^{44} +0.398049 q^{45} -4.23237 q^{46} +3.48184 q^{47} -1.93892 q^{48} -5.08817 q^{49} -4.72525 q^{50} -10.3736 q^{51} -4.40931 q^{52} -9.89575 q^{53} +4.34434 q^{54} -0.345652 q^{55} -1.38269 q^{56} -4.63318 q^{57} +8.87765 q^{58} -12.7991 q^{59} -1.01631 q^{60} +11.6348 q^{61} +4.72098 q^{62} -1.05001 q^{63} +1.00000 q^{64} -2.31120 q^{65} +1.27859 q^{66} -14.9257 q^{67} +5.35018 q^{68} +8.20621 q^{69} -0.724757 q^{70} +0.201145 q^{71} +0.759396 q^{72} -0.975239 q^{73} -5.82942 q^{74} +9.16187 q^{75} +2.38957 q^{76} +0.911792 q^{77} +8.54928 q^{78} -1.73274 q^{79} +0.524165 q^{80} -10.7015 q^{81} +4.05372 q^{82} -4.06537 q^{83} +2.68092 q^{84} +2.80438 q^{85} +8.81055 q^{86} -17.2130 q^{87} -0.659434 q^{88} -11.1963 q^{89} +0.398049 q^{90} +6.09670 q^{91} -4.23237 q^{92} -9.15358 q^{93} +3.48184 q^{94} +1.25253 q^{95} -1.93892 q^{96} +8.33655 q^{97} -5.08817 q^{98} -0.500772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9} - 14 q^{10} - 31 q^{11} - 21 q^{12} - 34 q^{13} - 44 q^{14} - 22 q^{15} + 54 q^{16} - 40 q^{17} + 39 q^{18} - 44 q^{19} - 14 q^{20} - 3 q^{21} - 31 q^{22} - 33 q^{23} - 21 q^{24} + 14 q^{25} - 34 q^{26} - 66 q^{27} - 44 q^{28} - 22 q^{30} - 65 q^{31} + 54 q^{32} - 43 q^{33} - 40 q^{34} - 46 q^{35} + 39 q^{36} - 58 q^{37} - 44 q^{38} - 36 q^{39} - 14 q^{40} - 49 q^{41} - 3 q^{42} - 47 q^{43} - 31 q^{44} - 45 q^{45} - 33 q^{46} - 66 q^{47} - 21 q^{48} + 16 q^{49} + 14 q^{50} - 33 q^{51} - 34 q^{52} - 16 q^{53} - 66 q^{54} - 50 q^{55} - 44 q^{56} - 33 q^{57} - 70 q^{59} - 22 q^{60} - 40 q^{61} - 65 q^{62} - 117 q^{63} + 54 q^{64} - 33 q^{65} - 43 q^{66} - 82 q^{67} - 40 q^{68} - q^{69} - 46 q^{70} - 60 q^{71} + 39 q^{72} - 92 q^{73} - 58 q^{74} - 68 q^{75} - 44 q^{76} + 13 q^{77} - 36 q^{78} - 57 q^{79} - 14 q^{80} + 26 q^{81} - 49 q^{82} - 77 q^{83} - 3 q^{84} - 24 q^{85} - 47 q^{86} - 61 q^{87} - 31 q^{88} - 54 q^{89} - 45 q^{90} - 46 q^{91} - 33 q^{92} - 24 q^{93} - 66 q^{94} - 66 q^{95} - 21 q^{96} - 137 q^{97} + 16 q^{98} - 71 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9 - 14 * q^10 - 31 * q^11 - 21 * q^12 - 34 * q^13 - 44 * q^14 - 22 * q^15 + 54 * q^16 - 40 * q^17 + 39 * q^18 - 44 * q^19 - 14 * q^20 - 3 * q^21 - 31 * q^22 - 33 * q^23 - 21 * q^24 + 14 * q^25 - 34 * q^26 - 66 * q^27 - 44 * q^28 - 22 * q^30 - 65 * q^31 + 54 * q^32 - 43 * q^33 - 40 * q^34 - 46 * q^35 + 39 * q^36 - 58 * q^37 - 44 * q^38 - 36 * q^39 - 14 * q^40 - 49 * q^41 - 3 * q^42 - 47 * q^43 - 31 * q^44 - 45 * q^45 - 33 * q^46 - 66 * q^47 - 21 * q^48 + 16 * q^49 + 14 * q^50 - 33 * q^51 - 34 * q^52 - 16 * q^53 - 66 * q^54 - 50 * q^55 - 44 * q^56 - 33 * q^57 - 70 * q^59 - 22 * q^60 - 40 * q^61 - 65 * q^62 - 117 * q^63 + 54 * q^64 - 33 * q^65 - 43 * q^66 - 82 * q^67 - 40 * q^68 - q^69 - 46 * q^70 - 60 * q^71 + 39 * q^72 - 92 * q^73 - 58 * q^74 - 68 * q^75 - 44 * q^76 + 13 * q^77 - 36 * q^78 - 57 * q^79 - 14 * q^80 + 26 * q^81 - 49 * q^82 - 77 * q^83 - 3 * q^84 - 24 * q^85 - 47 * q^86 - 61 * q^87 - 31 * q^88 - 54 * q^89 - 45 * q^90 - 46 * q^91 - 33 * q^92 - 24 * q^93 - 66 * q^94 - 66 * q^95 - 21 * q^96 - 137 * q^97 + 16 * q^98 - 71 * 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
$3$	−1.93892	−1.11943	−0.559717	−	0.828684i	$-0.689090\pi$
$3$	−1.93892	−1.11943	−0.559717	+	0.828684i	$0.689090\pi$
$4$	1.00000	0.500000
$5$	0.524165	0.234414	0.117207	−	0.993108i	$-0.462606\pi$
$5$	0.524165	0.234414	0.117207	+	0.993108i	$0.462606\pi$
$6$	−1.93892	−0.791559
$7$	−1.38269	−0.522607	−0.261304	−	0.965257i	$-0.584152\pi$
$7$	−1.38269	−0.522607	−0.261304	+	0.965257i	$0.584152\pi$
$8$	1.00000	0.353553
$9$	0.759396	0.253132
$10$	0.524165	0.165755
$11$	−0.659434	−0.198827	−0.0994134	−	0.995046i	$-0.531697\pi$
$11$	−0.659434	−0.198827	−0.0994134	+	0.995046i	$0.531697\pi$
$12$	−1.93892	−0.559717
$13$	−4.40931	−1.22292	−0.611461	−	0.791275i	$-0.709418\pi$
$13$	−4.40931	−1.22292	−0.611461	+	0.791275i	$0.709418\pi$
$14$	−1.38269	−0.369539
$15$	−1.01631	−0.262410
$16$	1.00000	0.250000
$17$	5.35018	1.29761	0.648805	−	0.760955i	$-0.275269\pi$
$17$	5.35018	1.29761	0.648805	+	0.760955i	$0.275269\pi$
$18$	0.759396	0.178991
$19$	2.38957	0.548205	0.274103	−	0.961700i	$-0.411619\pi$
$19$	2.38957	0.548205	0.274103	+	0.961700i	$0.411619\pi$
$20$	0.524165	0.117207
$21$	2.68092	0.585024
$22$	−0.659434	−0.140592
$23$	−4.23237	−0.882510	−0.441255	−	0.897382i	$-0.645467\pi$
$23$	−4.23237	−0.882510	−0.441255	+	0.897382i	$0.645467\pi$
$24$	−1.93892	−0.395780
$25$	−4.72525	−0.945050
$26$	−4.40931	−0.864736
$27$	4.34434	0.836069
$28$	−1.38269	−0.261304
$29$	8.87765	1.64854	0.824269	−	0.566198i	$-0.191586\pi$
$29$	8.87765	1.64854	0.824269	+	0.566198i	$0.191586\pi$
$30$	−1.01631	−0.185552
$31$	4.72098	0.847913	0.423956	−	0.905683i	$-0.360641\pi$
$31$	4.72098	0.847913	0.423956	+	0.905683i	$0.360641\pi$
$32$	1.00000	0.176777
$33$	1.27859	0.222573
$34$	5.35018	0.917549
$35$	−0.724757	−0.122506
$36$	0.759396	0.126566
$37$	−5.82942	−0.958351	−0.479175	−	0.877719i	$-0.659064\pi$
$37$	−5.82942	−0.958351	−0.479175	+	0.877719i	$0.659064\pi$
$38$	2.38957	0.387640
$39$	8.54928	1.36898
$40$	0.524165	0.0828777
$41$	4.05372	0.633084	0.316542	−	0.948578i	$-0.397478\pi$
$41$	4.05372	0.633084	0.316542	+	0.948578i	$0.397478\pi$
$42$	2.68092	0.413675
$43$	8.81055	1.34360	0.671798	−	0.740734i	$-0.265522\pi$
$43$	8.81055	1.34360	0.671798	+	0.740734i	$0.265522\pi$
$44$	−0.659434	−0.0994134
$45$	0.398049	0.0593376
$46$	−4.23237	−0.624029
$47$	3.48184	0.507879	0.253940	−	0.967220i	$-0.418274\pi$
$47$	3.48184	0.507879	0.253940	+	0.967220i	$0.418274\pi$
$48$	−1.93892	−0.279858
$49$	−5.08817	−0.726882
$50$	−4.72525	−0.668251
$51$	−10.3736	−1.45259
$52$	−4.40931	−0.611461
$53$	−9.89575	−1.35929	−0.679643	−	0.733543i	$-0.737865\pi$
$53$	−9.89575	−1.35929	−0.679643	+	0.733543i	$0.737865\pi$
$54$	4.34434	0.591190
$55$	−0.345652	−0.0466077
$56$	−1.38269	−0.184770
$57$	−4.63318	−0.613679
$58$	8.87765	1.16569
$59$	−12.7991	−1.66630	−0.833148	−	0.553050i	$-0.813464\pi$
$59$	−12.7991	−1.66630	−0.833148	+	0.553050i	$0.813464\pi$
$60$	−1.01631	−0.131205
$61$	11.6348	1.48968	0.744841	−	0.667242i	$-0.232525\pi$
$61$	11.6348	1.48968	0.744841	+	0.667242i	$0.232525\pi$
$62$	4.72098	0.599565
$63$	−1.05001	−0.132289
$64$	1.00000	0.125000
$65$	−2.31120	−0.286669
$66$	1.27859	0.157383
$67$	−14.9257	−1.82346	−0.911731	−	0.410787i	$-0.865254\pi$
$67$	−14.9257	−1.82346	−0.911731	+	0.410787i	$0.865254\pi$
$68$	5.35018	0.648805
$69$	8.20621	0.987912
$70$	−0.724757	−0.0866250
$71$	0.201145	0.0238716	0.0119358	−	0.999929i	$-0.496201\pi$
$71$	0.201145	0.0238716	0.0119358	+	0.999929i	$0.496201\pi$
$72$	0.759396	0.0894957
$73$	−0.975239	−0.114143	−0.0570716	−	0.998370i	$-0.518176\pi$
$73$	−0.975239	−0.114143	−0.0570716	+	0.998370i	$0.518176\pi$
$74$	−5.82942	−0.677656
$75$	9.16187	1.05792
$76$	2.38957	0.274103
$77$	0.911792	0.103908
$78$	8.54928	0.968015
$79$	−1.73274	−0.194949	−0.0974744	−	0.995238i	$-0.531076\pi$
$79$	−1.73274	−0.194949	−0.0974744	+	0.995238i	$0.531076\pi$
$80$	0.524165	0.0586034
$81$	−10.7015	−1.18906
$82$	4.05372	0.447658
$83$	−4.06537	−0.446232	−0.223116	−	0.974792i	$-0.571623\pi$
$83$	−4.06537	−0.446232	−0.223116	+	0.974792i	$0.571623\pi$
$84$	2.68092	0.292512
$85$	2.80438	0.304177
$86$	8.81055	0.950067
$87$	−17.2130	−1.84543
$88$	−0.659434	−0.0702959
$89$	−11.1963	−1.18680	−0.593401	−	0.804907i	$-0.702215\pi$
$89$	−11.1963	−1.18680	−0.593401	+	0.804907i	$0.702215\pi$
$90$	0.398049	0.0419580
$91$	6.09670	0.639108
$92$	−4.23237	−0.441255
$93$	−9.15358	−0.949182
$94$	3.48184	0.359125
$95$	1.25253	0.128507
$96$	−1.93892	−0.197890
$97$	8.33655	0.846449	0.423224	−	0.906025i	$-0.360898\pi$
$97$	8.33655	0.846449	0.423224	+	0.906025i	$0.360898\pi$
$98$	−5.08817	−0.513983
$99$	−0.500772	−0.0503294
$100$	−4.72525	−0.472525
$101$	−11.6583	−1.16004	−0.580020	−	0.814602i	$-0.696955\pi$
$101$	−11.6583	−1.16004	−0.580020	+	0.814602i	$0.696955\pi$
$102$	−10.3736	−1.02714
$103$	−11.0528	−1.08906	−0.544532	−	0.838740i	$-0.683293\pi$
$103$	−11.0528	−1.08906	−0.544532	+	0.838740i	$0.683293\pi$
$104$	−4.40931	−0.432368
$105$	1.40524	0.137138
$106$	−9.89575	−0.961160
$107$	−6.13445	−0.593040	−0.296520	−	0.955027i	$-0.595826\pi$
$107$	−6.13445	−0.593040	−0.296520	+	0.955027i	$0.595826\pi$
$108$	4.34434	0.418035
$109$	2.15682	0.206586	0.103293	−	0.994651i	$-0.467062\pi$
$109$	2.15682	0.206586	0.103293	+	0.994651i	$0.467062\pi$
$110$	−0.345652	−0.0329566
$111$	11.3028	1.07281
$112$	−1.38269	−0.130652
$113$	14.8485	1.39683	0.698414	−	0.715694i	$-0.253889\pi$
$113$	14.8485	1.39683	0.698414	+	0.715694i	$0.253889\pi$
$114$	−4.63318	−0.433937
$115$	−2.21846	−0.206872
$116$	8.87765	0.824269
$117$	−3.34841	−0.309561
$118$	−12.7991	−1.17825
$119$	−7.39764	−0.678141
$120$	−1.01631	−0.0927761
$121$	−10.5651	−0.960468
$122$	11.6348	1.05336
$123$	−7.85982	−0.708696
$124$	4.72098	0.423956
$125$	−5.09763	−0.455946
$126$	−1.05001	−0.0935422
$127$	−9.42740	−0.836547	−0.418273	−	0.908321i	$-0.637365\pi$
$127$	−9.42740	−0.836547	−0.418273	+	0.908321i	$0.637365\pi$
$128$	1.00000	0.0883883
$129$	−17.0829	−1.50407
$130$	−2.31120	−0.202706
$131$	−4.70830	−0.411366	−0.205683	−	0.978619i	$-0.565942\pi$
$131$	−4.70830	−0.411366	−0.205683	+	0.978619i	$0.565942\pi$
$132$	1.27859	0.111287
$133$	−3.30403	−0.286496
$134$	−14.9257	−1.28938
$135$	2.27715	0.195986
$136$	5.35018	0.458774
$137$	−2.32970	−0.199040	−0.0995200	−	0.995036i	$-0.531731\pi$
$137$	−2.32970	−0.199040	−0.0995200	+	0.995036i	$0.531731\pi$
$138$	8.20621	0.698559
$139$	5.22862	0.443486	0.221743	−	0.975105i	$-0.428825\pi$
$139$	5.22862	0.443486	0.221743	+	0.975105i	$0.428825\pi$
$140$	−0.724757	−0.0612531
$141$	−6.75100	−0.568537
$142$	0.201145	0.0168797
$143$	2.90765	0.243150
$144$	0.759396	0.0632830
$145$	4.65335	0.386440
$146$	−0.975239	−0.0807114
$147$	9.86554	0.813696
$148$	−5.82942	−0.479175
$149$	16.8621	1.38139	0.690697	−	0.723144i	$-0.257304\pi$
$149$	16.8621	1.38139	0.690697	+	0.723144i	$0.257304\pi$
$150$	9.16187	0.748063
$151$	−21.3167	−1.73472	−0.867362	−	0.497677i	$-0.834186\pi$
$151$	−21.3167	−1.73472	−0.867362	+	0.497677i	$0.834186\pi$
$152$	2.38957	0.193820
$153$	4.06291	0.328467
$154$	0.911792	0.0734743
$155$	2.47457	0.198762
$156$	8.54928	0.684490
$157$	16.0784	1.28319	0.641597	−	0.767042i	$-0.278272\pi$
$157$	16.0784	1.28319	0.641597	+	0.767042i	$0.278272\pi$
$158$	−1.73274	−0.137850
$159$	19.1870	1.52163
$160$	0.524165	0.0414389
$161$	5.85205	0.461206
$162$	−10.7015	−0.840790
$163$	7.93083	0.621190	0.310595	−	0.950542i	$-0.399472\pi$
$163$	7.93083	0.621190	0.310595	+	0.950542i	$0.399472\pi$
$164$	4.05372	0.316542
$165$	0.670190	0.0521742
$166$	−4.06537	−0.315534
$167$	−7.79251	−0.603003	−0.301501	−	0.953466i	$-0.597488\pi$
$167$	−7.79251	−0.603003	−0.301501	+	0.953466i	$0.597488\pi$
$168$	2.68092	0.206837
$169$	6.44198	0.495537
$170$	2.80438	0.215086
$171$	1.81463	0.138768
$172$	8.81055	0.671798
$173$	−24.9494	−1.89687	−0.948433	−	0.316979i	$-0.897332\pi$
$173$	−24.9494	−1.89687	−0.948433	+	0.316979i	$0.897332\pi$
$174$	−17.2130	−1.30492
$175$	6.53355	0.493890
$176$	−0.659434	−0.0497067
$177$	24.8163	1.86531
$178$	−11.1963	−0.839196
$179$	−1.82751	−0.136594	−0.0682972	−	0.997665i	$-0.521757\pi$
$179$	−1.82751	−0.136594	−0.0682972	+	0.997665i	$0.521757\pi$
$180$	0.398049	0.0296688
$181$	11.2651	0.837326	0.418663	−	0.908142i	$-0.362499\pi$
$181$	11.2651	0.837326	0.418663	+	0.908142i	$0.362499\pi$
$182$	6.09670	0.451917
$183$	−22.5589	−1.66760
$184$	−4.23237	−0.312015
$185$	−3.05558	−0.224650
$186$	−9.15358	−0.671173
$187$	−3.52809	−0.258000
$188$	3.48184	0.253940
$189$	−6.00688	−0.436936
$190$	1.25253	0.0908680
$191$	−17.7826	−1.28670	−0.643351	−	0.765571i	$-0.722456\pi$
$191$	−17.7826	−1.28670	−0.643351	+	0.765571i	$0.722456\pi$
$192$	−1.93892	−0.139929
$193$	8.63621	0.621648	0.310824	−	0.950468i	$-0.399395\pi$
$193$	8.63621	0.621648	0.310824	+	0.950468i	$0.399395\pi$
$194$	8.33655	0.598530
$195$	4.48123	0.320907
$196$	−5.08817	−0.363441
$197$	−10.1340	−0.722019	−0.361010	−	0.932562i	$-0.617568\pi$
$197$	−10.1340	−0.722019	−0.361010	+	0.932562i	$0.617568\pi$
$198$	−0.500772	−0.0355883
$199$	5.55223	0.393587	0.196794	−	0.980445i	$-0.436947\pi$
$199$	5.55223	0.393587	0.196794	+	0.980445i	$0.436947\pi$
$200$	−4.72525	−0.334126
$201$	28.9397	2.04125
$202$	−11.6583	−0.820272
$203$	−12.2750	−0.861539
$204$	−10.3736	−0.726294
$205$	2.12482	0.148404
$206$	−11.0528	−0.770085
$207$	−3.21405	−0.223392
$208$	−4.40931	−0.305730
$209$	−1.57576	−0.108998
$210$	1.40524	0.0969710
$211$	1.77688	0.122326	0.0611628	−	0.998128i	$-0.480519\pi$
$211$	1.77688	0.122326	0.0611628	+	0.998128i	$0.480519\pi$
$212$	−9.89575	−0.679643
$213$	−0.390004	−0.0267226
$214$	−6.13445	−0.419342
$215$	4.61818	0.314957
$216$	4.34434	0.295595
$217$	−6.52764	−0.443125
$218$	2.15682	0.146078
$219$	1.89091	0.127776
$220$	−0.345652	−0.0233038
$221$	−23.5906	−1.58688
$222$	11.3028	0.758591
$223$	−8.70832	−0.583153	−0.291576	−	0.956548i	$-0.594180\pi$
$223$	−8.70832	−0.583153	−0.291576	+	0.956548i	$0.594180\pi$
$224$	−1.38269	−0.0923848
$225$	−3.58834	−0.239223
$226$	14.8485	0.987707
$227$	−4.21453	−0.279728	−0.139864	−	0.990171i	$-0.544667\pi$
$227$	−4.21453	−0.279728	−0.139864	+	0.990171i	$0.544667\pi$
$228$	−4.63318	−0.306840
$229$	3.12115	0.206251	0.103126	−	0.994668i	$-0.467116\pi$
$229$	3.12115	0.206251	0.103126	+	0.994668i	$0.467116\pi$
$230$	−2.21846	−0.146281
$231$	−1.76789	−0.116319
$232$	8.87765	0.582847
$233$	−17.8429	−1.16892	−0.584462	−	0.811421i	$-0.698694\pi$
$233$	−17.8429	−1.16892	−0.584462	+	0.811421i	$0.698694\pi$
$234$	−3.34841	−0.218892
$235$	1.82506	0.119054
$236$	−12.7991	−0.833148
$237$	3.35964	0.218232
$238$	−7.39764	−0.479518
$239$	6.10657	0.395001	0.197501	−	0.980303i	$-0.436718\pi$
$239$	6.10657	0.395001	0.197501	+	0.980303i	$0.436718\pi$
$240$	−1.01631	−0.0656026
$241$	25.5336	1.64476	0.822381	−	0.568937i	$-0.192645\pi$
$241$	25.5336	1.64476	0.822381	+	0.568937i	$0.192645\pi$
$242$	−10.5651	−0.679153
$243$	7.71629	0.495001
$244$	11.6348	0.744841
$245$	−2.66704	−0.170391
$246$	−7.85982	−0.501124
$247$	−10.5364	−0.670412
$248$	4.72098	0.299782
$249$	7.88240	0.499527
$250$	−5.09763	−0.322403
$251$	−23.3214	−1.47204	−0.736018	−	0.676962i	$-0.763296\pi$
$251$	−23.3214	−1.47204	−0.736018	+	0.676962i	$0.763296\pi$
$252$	−1.05001	−0.0661443
$253$	2.79097	0.175467
$254$	−9.42740	−0.591528
$255$	−5.43745	−0.340506
$256$	1.00000	0.0625000
$257$	−9.69904	−0.605009	−0.302505	−	0.953148i	$-0.597823\pi$
$257$	−9.69904	−0.605009	−0.302505	+	0.953148i	$0.597823\pi$
$258$	−17.0829	−1.06354
$259$	8.06028	0.500841
$260$	−2.31120	−0.143335
$261$	6.74166	0.417298
$262$	−4.70830	−0.290880
$263$	−12.0644	−0.743920	−0.371960	−	0.928249i	$-0.621314\pi$
$263$	−12.0644	−0.743920	−0.371960	+	0.928249i	$0.621314\pi$
$264$	1.27859	0.0786916
$265$	−5.18700	−0.318635
$266$	−3.30403	−0.202583
$267$	21.7086	1.32855
$268$	−14.9257	−0.911731
$269$	−11.9102	−0.726176	−0.363088	−	0.931755i	$-0.618277\pi$
$269$	−11.9102	−0.726176	−0.363088	+	0.931755i	$0.618277\pi$
$270$	2.27715	0.138583
$271$	−30.4602	−1.85033	−0.925164	−	0.379569i	$-0.876072\pi$
$271$	−30.4602	−1.85033	−0.925164	+	0.379569i	$0.876072\pi$
$272$	5.35018	0.324402
$273$	−11.8210	−0.715439
$274$	−2.32970	−0.140743
$275$	3.11599	0.187901
$276$	8.20621	0.493956
$277$	−28.5275	−1.71405	−0.857027	−	0.515272i	$-0.827691\pi$
$277$	−28.5275	−1.71405	−0.857027	+	0.515272i	$0.827691\pi$
$278$	5.22862	0.313592
$279$	3.58509	0.214634
$280$	−0.724757	−0.0433125
$281$	13.9676	0.833237	0.416618	−	0.909081i	$-0.363215\pi$
$281$	13.9676	0.833237	0.416618	+	0.909081i	$0.363215\pi$
$282$	−6.75100	−0.402016
$283$	−21.2078	−1.26067	−0.630337	−	0.776322i	$-0.717083\pi$
$283$	−21.2078	−1.26067	−0.630337	+	0.776322i	$0.717083\pi$
$284$	0.201145	0.0119358
$285$	−2.42855	−0.143855
$286$	2.90765	0.171933
$287$	−5.60503	−0.330855
$288$	0.759396	0.0447479
$289$	11.6245	0.683792
$290$	4.65335	0.273254
$291$	−16.1639	−0.947543
$292$	−0.975239	−0.0570716
$293$	4.29044	0.250650	0.125325	−	0.992116i	$-0.460003\pi$
$293$	4.29044	0.250650	0.125325	+	0.992116i	$0.460003\pi$
$294$	9.86554	0.575370
$295$	−6.70882	−0.390602
$296$	−5.82942	−0.338828
$297$	−2.86481	−0.166233
$298$	16.8621	0.976794
$299$	18.6618	1.07924
$300$	9.16187	0.528961
$301$	−12.1823	−0.702174
$302$	−21.3167	−1.22664
$303$	22.6044	1.29859
$304$	2.38957	0.137051
$305$	6.09854	0.349202
$306$	4.06291	0.232261
$307$	−27.2825	−1.55709	−0.778546	−	0.627588i	$-0.784042\pi$
$307$	−27.2825	−1.55709	−0.778546	+	0.627588i	$0.784042\pi$
$308$	0.911792	0.0519542
$309$	21.4304	1.21914
$310$	2.47457	0.140546
$311$	5.10415	0.289430	0.144715	−	0.989473i	$-0.453774\pi$
$311$	5.10415	0.289430	0.144715	+	0.989473i	$0.453774\pi$
$312$	8.54928	0.484007
$313$	−2.67764	−0.151349	−0.0756744	−	0.997133i	$-0.524111\pi$
$313$	−2.67764	−0.151349	−0.0756744	+	0.997133i	$0.524111\pi$
$314$	16.0784	0.907355
$315$	−0.550378	−0.0310103
$316$	−1.73274	−0.0974744
$317$	25.7060	1.44379	0.721895	−	0.692002i	$-0.243271\pi$
$317$	25.7060	1.44379	0.721895	+	0.692002i	$0.243271\pi$
$318$	19.1870	1.07596
$319$	−5.85423	−0.327774
$320$	0.524165	0.0293017
$321$	11.8942	0.663869
$322$	5.85205	0.326122
$323$	12.7846	0.711357
$324$	−10.7015	−0.594528
$325$	20.8351	1.15572
$326$	7.93083	0.439248
$327$	−4.18189	−0.231259
$328$	4.05372	0.223829
$329$	−4.81431	−0.265421
$330$	0.670190	0.0368927
$331$	18.2922	1.00543	0.502714	−	0.864453i	$-0.332335\pi$
$331$	18.2922	1.00543	0.502714	+	0.864453i	$0.332335\pi$
$332$	−4.06537	−0.223116
$333$	−4.42684	−0.242589
$334$	−7.79251	−0.426387
$335$	−7.82352	−0.427444
$336$	2.68092	0.146256
$337$	23.0178	1.25386	0.626930	−	0.779075i	$-0.284311\pi$
$337$	23.0178	1.25386	0.626930	+	0.779075i	$0.284311\pi$
$338$	6.44198	0.350398
$339$	−28.7900	−1.56366
$340$	2.80438	0.152089
$341$	−3.11317	−0.168588
$342$	1.81463	0.0981240
$343$	16.7142	0.902481
$344$	8.81055	0.475033
$345$	4.30141	0.231580
$346$	−24.9494	−1.34129
$347$	−33.7568	−1.81216	−0.906080	−	0.423107i	$-0.860940\pi$
$347$	−33.7568	−1.81216	−0.906080	+	0.423107i	$0.860940\pi$
$348$	−17.2130	−0.922715
$349$	28.2784	1.51371	0.756855	−	0.653583i	$-0.226735\pi$
$349$	28.2784	1.51371	0.756855	+	0.653583i	$0.226735\pi$
$350$	6.53355	0.349233
$351$	−19.1555	−1.02245
$352$	−0.659434	−0.0351479
$353$	13.8657	0.737994	0.368997	−	0.929431i	$-0.379701\pi$
$353$	13.8657	0.737994	0.368997	+	0.929431i	$0.379701\pi$
$354$	24.8163	1.31897
$355$	0.105433	0.00559582
$356$	−11.1963	−0.593401
$357$	14.3434	0.759133
$358$	−1.82751	−0.0965868
$359$	30.6349	1.61685	0.808424	−	0.588601i	$-0.200321\pi$
$359$	30.6349	1.61685	0.808424	+	0.588601i	$0.200321\pi$
$360$	0.398049	0.0209790
$361$	−13.2899	−0.699471
$362$	11.2651	0.592079
$363$	20.4849	1.07518
$364$	6.09670	0.319554
$365$	−0.511186	−0.0267567
$366$	−22.5589	−1.17917
$367$	−29.1527	−1.52176	−0.760880	−	0.648893i	$-0.775232\pi$
$367$	−29.1527	−1.52176	−0.760880	+	0.648893i	$0.775232\pi$
$368$	−4.23237	−0.220628
$369$	3.07838	0.160254
$370$	−3.05558	−0.158852
$371$	13.6827	0.710373
$372$	−9.15358	−0.474591
$373$	13.8421	0.716716	0.358358	−	0.933584i	$-0.383337\pi$
$373$	13.8421	0.716716	0.358358	+	0.933584i	$0.383337\pi$
$374$	−3.52809	−0.182433
$375$	9.88388	0.510402
$376$	3.48184	0.179562
$377$	−39.1443	−2.01603
$378$	−6.00688	−0.308960
$379$	2.13666	0.109753	0.0548764	−	0.998493i	$-0.482524\pi$
$379$	2.13666	0.109753	0.0548764	+	0.998493i	$0.482524\pi$
$380$	1.25253	0.0642534
$381$	18.2789	0.936459
$382$	−17.7826	−0.909836
$383$	3.00447	0.153521	0.0767606	−	0.997050i	$-0.475542\pi$
$383$	3.00447	0.153521	0.0767606	+	0.997050i	$0.475542\pi$
$384$	−1.93892	−0.0989449
$385$	0.477929	0.0243575
$386$	8.63621	0.439571
$387$	6.69070	0.340108
$388$	8.33655	0.423224
$389$	14.4250	0.731376	0.365688	−	0.930738i	$-0.380834\pi$
$389$	14.4250	0.731376	0.365688	+	0.930738i	$0.380834\pi$
$390$	4.48123	0.226916
$391$	−22.6440	−1.14515
$392$	−5.08817	−0.256991
$393$	9.12900	0.460497
$394$	−10.1340	−0.510545
$395$	−0.908243	−0.0456987
$396$	−0.500772	−0.0251647
$397$	−13.5678	−0.680947	−0.340473	−	0.940254i	$-0.610587\pi$
$397$	−13.5678	−0.680947	−0.340473	+	0.940254i	$0.610587\pi$
$398$	5.55223	0.278308
$399$	6.40625	0.320713
$400$	−4.72525	−0.236263
$401$	4.88537	0.243964	0.121982	−	0.992532i	$-0.461075\pi$
$401$	4.88537	0.243964	0.121982	+	0.992532i	$0.461075\pi$
$402$	28.9397	1.44338
$403$	−20.8162	−1.03693
$404$	−11.6583	−0.580020
$405$	−5.60935	−0.278731
$406$	−12.2750	−0.609200
$407$	3.84412	0.190546
$408$	−10.3736	−0.513568
$409$	−26.5853	−1.31456	−0.657280	−	0.753646i	$-0.728293\pi$
$409$	−26.5853	−1.31456	−0.657280	+	0.753646i	$0.728293\pi$
$410$	2.12482	0.104937
$411$	4.51710	0.222812
$412$	−11.0528	−0.544532
$413$	17.6971	0.870819
$414$	−3.21405	−0.157962
$415$	−2.13092	−0.104603
$416$	−4.40931	−0.216184
$417$	−10.1379	−0.496453
$418$	−1.57576	−0.0770731
$419$	−36.9371	−1.80450	−0.902248	−	0.431217i	$-0.858084\pi$
$419$	−36.9371	−1.80450	−0.902248	+	0.431217i	$0.858084\pi$
$420$	1.40524	0.0685688
$421$	8.09591	0.394571	0.197285	−	0.980346i	$-0.436787\pi$
$421$	8.09591	0.394571	0.197285	+	0.980346i	$0.436787\pi$
$422$	1.77688	0.0864973
$423$	2.64410	0.128560
$424$	−9.89575	−0.480580
$425$	−25.2810	−1.22631
$426$	−0.390004	−0.0188958
$427$	−16.0873	−0.778519
$428$	−6.13445	−0.296520
$429$	−5.63768	−0.272190
$430$	4.61818	0.222708
$431$	−2.02576	−0.0975772	−0.0487886	−	0.998809i	$-0.515536\pi$
$431$	−2.02576	−0.0975772	−0.0487886	+	0.998809i	$0.515536\pi$
$432$	4.34434	0.209017
$433$	−20.7167	−0.995581	−0.497790	−	0.867297i	$-0.665855\pi$
$433$	−20.7167	−0.995581	−0.497790	+	0.867297i	$0.665855\pi$
$434$	−6.52764	−0.313337
$435$	−9.02246	−0.432594
$436$	2.15682	0.103293
$437$	−10.1136	−0.483797
$438$	1.89091	0.0903510
$439$	24.4272	1.16584	0.582922	−	0.812528i	$-0.301909\pi$
$439$	24.4272	1.16584	0.582922	+	0.812528i	$0.301909\pi$
$440$	−0.345652	−0.0164783
$441$	−3.86394	−0.183997
$442$	−23.5906	−1.12209
$443$	−22.2088	−1.05517	−0.527586	−	0.849502i	$-0.676903\pi$
$443$	−22.2088	−1.05517	−0.527586	+	0.849502i	$0.676903\pi$
$444$	11.3028	0.536405
$445$	−5.86869	−0.278203
$446$	−8.70832	−0.412351
$447$	−32.6941	−1.54638
$448$	−1.38269	−0.0653259
$449$	24.5501	1.15859	0.579295	−	0.815118i	$-0.303328\pi$
$449$	24.5501	1.15859	0.579295	+	0.815118i	$0.303328\pi$
$450$	−3.58834	−0.169156
$451$	−2.67316	−0.125874
$452$	14.8485	0.698414
$453$	41.3312	1.94191
$454$	−4.21453	−0.197798
$455$	3.19567	0.149816
$456$	−4.63318	−0.216968
$457$	−13.8625	−0.648462	−0.324231	−	0.945978i	$-0.605105\pi$
$457$	−13.8625	−0.648462	−0.324231	+	0.945978i	$0.605105\pi$
$458$	3.12115	0.145842
$459$	23.2430	1.08489
$460$	−2.21846	−0.103436
$461$	−2.21865	−0.103333	−0.0516665	−	0.998664i	$-0.516453\pi$
$461$	−2.21865	−0.103333	−0.0516665	+	0.998664i	$0.516453\pi$
$462$	−1.76789	−0.0822496
$463$	−8.59172	−0.399291	−0.199646	−	0.979868i	$-0.563979\pi$
$463$	−8.59172	−0.399291	−0.199646	+	0.979868i	$0.563979\pi$
$464$	8.87765	0.412135
$465$	−4.79798	−0.222501
$466$	−17.8429	−0.826554
$467$	26.4574	1.22430	0.612150	−	0.790742i	$-0.290305\pi$
$467$	26.4574	1.22430	0.612150	+	0.790742i	$0.290305\pi$
$468$	−3.34841	−0.154780
$469$	20.6376	0.952955
$470$	1.82506	0.0841837
$471$	−31.1746	−1.43645
$472$	−12.7991	−0.589125
$473$	−5.80998	−0.267143
$474$	3.35964	0.154314
$475$	−11.2913	−0.518082
$476$	−7.39764	−0.339070
$477$	−7.51480	−0.344079
$478$	6.10657	0.279308
$479$	12.3196	0.562899	0.281449	−	0.959576i	$-0.409185\pi$
$479$	12.3196	0.562899	0.281449	+	0.959576i	$0.409185\pi$
$480$	−1.01631	−0.0463881
$481$	25.7037	1.17199
$482$	25.5336	1.16302
$483$	−11.3466	−0.516290
$484$	−10.5651	−0.480234
$485$	4.36973	0.198419
$486$	7.71629	0.350018
$487$	−14.6109	−0.662083	−0.331042	−	0.943616i	$-0.607400\pi$
$487$	−14.6109	−0.662083	−0.331042	+	0.943616i	$0.607400\pi$
$488$	11.6348	0.526682
$489$	−15.3772	−0.695381
$490$	−2.66704	−0.120485
$491$	−31.4895	−1.42110	−0.710550	−	0.703647i	$-0.751554\pi$
$491$	−31.4895	−1.42110	−0.710550	+	0.703647i	$0.751554\pi$
$492$	−7.85982	−0.354348
$493$	47.4971	2.13916
$494$	−10.5364	−0.474053
$495$	−0.262487	−0.0117979
$496$	4.72098	0.211978
$497$	−0.278122	−0.0124755
$498$	7.88240	0.353219
$499$	−2.33685	−0.104612	−0.0523059	−	0.998631i	$-0.516657\pi$
$499$	−2.33685	−0.104612	−0.0523059	+	0.998631i	$0.516657\pi$
$500$	−5.09763	−0.227973
$501$	15.1090	0.675021
$502$	−23.3214	−1.04089
$503$	−0.956995	−0.0426703	−0.0213351	−	0.999772i	$-0.506792\pi$
$503$	−0.956995	−0.0426703	−0.0213351	+	0.999772i	$0.506792\pi$
$504$	−1.05001	−0.0467711
$505$	−6.11084	−0.271929
$506$	2.79097	0.124074
$507$	−12.4905	−0.554721
$508$	−9.42740	−0.418273
$509$	−12.4510	−0.551881	−0.275941	−	0.961175i	$-0.588989\pi$
$509$	−12.4510	−0.551881	−0.275941	+	0.961175i	$0.588989\pi$
$510$	−5.43745	−0.240774
$511$	1.34845	0.0596520
$512$	1.00000	0.0441942
$513$	10.3811	0.458338
$514$	−9.69904	−0.427806
$515$	−5.79348	−0.255291
$516$	−17.0829	−0.752034
$517$	−2.29605	−0.100980
$518$	8.06028	0.354148
$519$	48.3747	2.12342
$520$	−2.31120	−0.101353
$521$	−32.8852	−1.44073	−0.720363	−	0.693597i	$-0.756025\pi$
$521$	−32.8852	−1.44073	−0.720363	+	0.693597i	$0.756025\pi$
$522$	6.74166	0.295074
$523$	−14.4623	−0.632391	−0.316196	−	0.948694i	$-0.602406\pi$
$523$	−14.4623	−0.632391	−0.316196	+	0.948694i	$0.602406\pi$
$524$	−4.70830	−0.205683
$525$	−12.6680	−0.552877
$526$	−12.0644	−0.526031
$527$	25.2581	1.10026
$528$	1.27859	0.0556434
$529$	−5.08703	−0.221175
$530$	−5.18700	−0.225309
$531$	−9.71956	−0.421793
$532$	−3.30403	−0.143248
$533$	−17.8741	−0.774212
$534$	21.7086	0.939425
$535$	−3.21546	−0.139017
$536$	−14.9257	−0.644691
$537$	3.54339	0.152908
$538$	−11.9102	−0.513484
$539$	3.35531	0.144524
$540$	2.27715	0.0979930
$541$	12.9196	0.555455	0.277728	−	0.960660i	$-0.410419\pi$
$541$	12.9196	0.555455	0.277728	+	0.960660i	$0.410419\pi$
$542$	−30.4602	−1.30838
$543$	−21.8420	−0.937331
$544$	5.35018	0.229387
$545$	1.13053	0.0484264
$546$	−11.8210	−0.505892
$547$	27.2190	1.16380	0.581900	−	0.813261i	$-0.302310\pi$
$547$	27.2190	1.16380	0.581900	+	0.813261i	$0.302310\pi$
$548$	−2.32970	−0.0995200
$549$	8.83541	0.377086
$550$	3.11599	0.132866
$551$	21.2138	0.903738
$552$	8.20621	0.349280
$553$	2.39585	0.101882
$554$	−28.5275	−1.21202
$555$	5.92450	0.251481
$556$	5.22862	0.221743
$557$	−19.7753	−0.837907	−0.418954	−	0.908008i	$-0.637603\pi$
$557$	−19.7753	−0.837907	−0.418954	+	0.908008i	$0.637603\pi$
$558$	3.58509	0.151769
$559$	−38.8484	−1.64311
$560$	−0.724757	−0.0306266
$561$	6.84067	0.288813
$562$	13.9676	0.589187
$563$	−7.91747	−0.333682	−0.166841	−	0.985984i	$-0.553357\pi$
$563$	−7.91747	−0.333682	−0.166841	+	0.985984i	$0.553357\pi$
$564$	−6.75100	−0.284269
$565$	7.78305	0.327435
$566$	−21.2078	−0.891431
$567$	14.7969	0.621410
$568$	0.201145	0.00843987
$569$	−27.5288	−1.15407	−0.577033	−	0.816721i	$-0.695790\pi$
$569$	−27.5288	−1.15407	−0.577033	+	0.816721i	$0.695790\pi$
$570$	−2.42855	−0.101721
$571$	43.8730	1.83603	0.918014	−	0.396549i	$-0.129792\pi$
$571$	43.8730	1.83603	0.918014	+	0.396549i	$0.129792\pi$
$572$	2.90765	0.121575
$573$	34.4789	1.44038
$574$	−5.60503	−0.233949
$575$	19.9990	0.834017
$576$	0.759396	0.0316415
$577$	−14.5133	−0.604198	−0.302099	−	0.953277i	$-0.597687\pi$
$577$	−14.5133	−0.604198	−0.302099	+	0.953277i	$0.597687\pi$
$578$	11.6245	0.483514
$579$	−16.7449	−0.695894
$580$	4.65335	0.193220
$581$	5.62114	0.233204
$582$	−16.1639	−0.670014
$583$	6.52559	0.270262
$584$	−0.975239	−0.0403557
$585$	−1.75512	−0.0725652
$586$	4.29044	0.177236
$587$	16.4110	0.677354	0.338677	−	0.940903i	$-0.390021\pi$
$587$	16.4110	0.677354	0.338677	+	0.940903i	$0.390021\pi$
$588$	9.86554	0.406848
$589$	11.2811	0.464830
$590$	−6.70882	−0.276198
$591$	19.6490	0.808253
$592$	−5.82942	−0.239588
$593$	−34.4663	−1.41536	−0.707680	−	0.706533i	$-0.750258\pi$
$593$	−34.4663	−1.41536	−0.707680	+	0.706533i	$0.750258\pi$
$594$	−2.86481	−0.117544
$595$	−3.87758	−0.158965
$596$	16.8621	0.690697
$597$	−10.7653	−0.440595
$598$	18.6618	0.763139
$599$	39.0404	1.59515	0.797574	−	0.603221i	$-0.206116\pi$
$599$	39.0404	1.59515	0.797574	+	0.603221i	$0.206116\pi$
$600$	9.16187	0.374032
$601$	−13.7010	−0.558875	−0.279437	−	0.960164i	$-0.590148\pi$
$601$	−13.7010	−0.558875	−0.279437	+	0.960164i	$0.590148\pi$
$602$	−12.1823	−0.496512
$603$	−11.3345	−0.461577
$604$	−21.3167	−0.867362
$605$	−5.53788	−0.225147
$606$	22.6044	0.918240
$607$	21.7568	0.883081	0.441541	−	0.897241i	$-0.354432\pi$
$607$	21.7568	0.883081	0.441541	+	0.897241i	$0.354432\pi$
$608$	2.38957	0.0969099
$609$	23.8003	0.964436
$610$	6.09854	0.246923
$611$	−15.3525	−0.621096
$612$	4.06291	0.164233
$613$	4.73348	0.191184	0.0955918	−	0.995421i	$-0.469526\pi$
$613$	4.73348	0.191184	0.0955918	+	0.995421i	$0.469526\pi$
$614$	−27.2825	−1.10103
$615$	−4.11984	−0.166128
$616$	0.911792	0.0367371
$617$	28.4339	1.14471	0.572354	−	0.820007i	$-0.306030\pi$
$617$	28.4339	1.14471	0.572354	+	0.820007i	$0.306030\pi$
$618$	21.4304	0.862059
$619$	39.6408	1.59330	0.796649	−	0.604442i	$-0.206604\pi$
$619$	39.6408	1.59330	0.796649	+	0.604442i	$0.206604\pi$
$620$	2.47457	0.0993811
$621$	−18.3869	−0.737840
$622$	5.10415	0.204658
$623$	15.4810	0.620232
$624$	8.54928	0.342245
$625$	20.9543	0.838170
$626$	−2.67764	−0.107020
$627$	3.05527	0.122016
$628$	16.0784	0.641597
$629$	−31.1885	−1.24357
$630$	−0.550378	−0.0219276
$631$	−23.2754	−0.926578	−0.463289	−	0.886207i	$-0.653331\pi$
$631$	−23.2754	−0.926578	−0.463289	+	0.886207i	$0.653331\pi$
$632$	−1.73274	−0.0689248
$633$	−3.44523	−0.136935
$634$	25.7060	1.02091
$635$	−4.94151	−0.196098
$636$	19.1870	0.760815
$637$	22.4353	0.888919
$638$	−5.85423	−0.231771
$639$	0.152749	0.00604266
$640$	0.524165	0.0207194
$641$	−5.92931	−0.234194	−0.117097	−	0.993121i	$-0.537359\pi$
$641$	−5.92931	−0.234194	−0.117097	+	0.993121i	$0.537359\pi$
$642$	11.8942	0.469426
$643$	−4.17741	−0.164741	−0.0823704	−	0.996602i	$-0.526249\pi$
$643$	−4.17741	−0.164741	−0.0823704	+	0.996602i	$0.526249\pi$
$644$	5.85205	0.230603
$645$	−8.95427	−0.352574
$646$	12.7846	0.503005
$647$	6.32200	0.248543	0.124272	−	0.992248i	$-0.460341\pi$
$647$	6.32200	0.248543	0.124272	+	0.992248i	$0.460341\pi$
$648$	−10.7015	−0.420395
$649$	8.44014	0.331304
$650$	20.8351	0.817219
$651$	12.6566	0.496050
$652$	7.93083	0.310595
$653$	19.1767	0.750441	0.375221	−	0.926936i	$-0.377567\pi$
$653$	19.1767	0.750441	0.375221	+	0.926936i	$0.377567\pi$
$654$	−4.18189	−0.163525
$655$	−2.46792	−0.0964298
$656$	4.05372	0.158271
$657$	−0.740593	−0.0288933
$658$	−4.81431	−0.187681
$659$	24.7513	0.964176	0.482088	−	0.876123i	$-0.339879\pi$
$659$	24.7513	0.964176	0.482088	+	0.876123i	$0.339879\pi$
$660$	0.670190	0.0260871
$661$	−14.9331	−0.580831	−0.290416	−	0.956901i	$-0.593794\pi$
$661$	−14.9331	−0.580831	−0.290416	+	0.956901i	$0.593794\pi$
$662$	18.2922	0.710945
$663$	45.7402	1.77640
$664$	−4.06537	−0.157767
$665$	−1.73186	−0.0671586
$666$	−4.42684	−0.171537
$667$	−37.5735	−1.45485
$668$	−7.79251	−0.301501
$669$	16.8847	0.652801
$670$	−7.82352	−0.302249
$671$	−7.67237	−0.296189
$672$	2.68092	0.103419
$673$	−28.9123	−1.11449	−0.557244	−	0.830348i	$-0.688141\pi$
$673$	−28.9123	−1.11449	−0.557244	+	0.830348i	$0.688141\pi$
$674$	23.0178	0.886613
$675$	−20.5281	−0.790127
$676$	6.44198	0.247769
$677$	−3.50035	−0.134530	−0.0672648	−	0.997735i	$-0.521427\pi$
$677$	−3.50035	−0.134530	−0.0672648	+	0.997735i	$0.521427\pi$
$678$	−28.7900	−1.10567
$679$	−11.5269	−0.442360
$680$	2.80438	0.107543
$681$	8.17163	0.313137
$682$	−3.11317	−0.119210
$683$	5.31232	0.203270	0.101635	−	0.994822i	$-0.467593\pi$
$683$	5.31232	0.203270	0.101635	+	0.994822i	$0.467593\pi$
$684$	1.81463	0.0693842
$685$	−1.22115	−0.0466577
$686$	16.7142	0.638150
$687$	−6.05165	−0.230885
$688$	8.81055	0.335899
$689$	43.6334	1.66230
$690$	4.30141	0.163752
$691$	−22.0738	−0.839727	−0.419864	−	0.907587i	$-0.637922\pi$
$691$	−22.0738	−0.839727	−0.419864	+	0.907587i	$0.637922\pi$
$692$	−24.9494	−0.948433
$693$	0.692411	0.0263025
$694$	−33.7568	−1.28139
$695$	2.74066	0.103959
$696$	−17.2130	−0.652458
$697$	21.6881	0.821497
$698$	28.2784	1.07035
$699$	34.5958	1.30853
$700$	6.53355	0.246945
$701$	17.4839	0.660357	0.330178	−	0.943919i	$-0.392891\pi$
$701$	17.4839	0.660357	0.330178	+	0.943919i	$0.392891\pi$
$702$	−19.1555	−0.722979
$703$	−13.9298	−0.525373
$704$	−0.659434	−0.0248533
$705$	−3.53864	−0.133273
$706$	13.8657	0.521841
$707$	16.1197	0.606245
$708$	24.8163	0.932654
$709$	11.0096	0.413473	0.206736	−	0.978397i	$-0.433716\pi$
$709$	11.0096	0.413473	0.206736	+	0.978397i	$0.433716\pi$
$710$	0.105433	0.00395684
$711$	−1.31584	−0.0493478
$712$	−11.1963	−0.419598
$713$	−19.9809	−0.748292
$714$	14.3434	0.536788
$715$	1.52409	0.0569975
$716$	−1.82751	−0.0682972
$717$	−11.8401	−0.442178
$718$	30.6349	1.14328
$719$	−25.2385	−0.941238	−0.470619	−	0.882337i	$-0.655969\pi$
$719$	−25.2385	−0.941238	−0.470619	+	0.882337i	$0.655969\pi$
$720$	0.398049	0.0148344
$721$	15.2826	0.569153
$722$	−13.2899	−0.494601
$723$	−49.5075	−1.84120
$724$	11.2651	0.418663
$725$	−41.9491	−1.55795
$726$	20.4849	0.760267
$727$	−15.8324	−0.587191	−0.293596	−	0.955930i	$-0.594852\pi$
$727$	−15.8324	−0.587191	−0.293596	+	0.955930i	$0.594852\pi$
$728$	6.09670	0.225959
$729$	17.1433	0.634936
$730$	−0.511186	−0.0189198
$731$	47.1381	1.74346
$732$	−22.5589	−0.833800
$733$	6.36538	0.235111	0.117555	−	0.993066i	$-0.462494\pi$
$733$	6.36538	0.235111	0.117555	+	0.993066i	$0.462494\pi$
$734$	−29.1527	−1.07605
$735$	5.17117	0.190741
$736$	−4.23237	−0.156007
$737$	9.84250	0.362553
$738$	3.07838	0.113317
$739$	−11.3091	−0.416013	−0.208007	−	0.978127i	$-0.566698\pi$
$739$	−11.3091	−0.416013	−0.208007	+	0.978127i	$0.566698\pi$
$740$	−3.05558	−0.112325
$741$	20.4291	0.750482
$742$	13.6827	0.502310
$743$	−22.0400	−0.808570	−0.404285	−	0.914633i	$-0.632480\pi$
$743$	−22.0400	−0.808570	−0.404285	+	0.914633i	$0.632480\pi$
$744$	−9.15358	−0.335587
$745$	8.83850	0.323818
$746$	13.8421	0.506795
$747$	−3.08722	−0.112956
$748$	−3.52809	−0.129000
$749$	8.48204	0.309927
$750$	9.88388	0.360908
$751$	−5.21529	−0.190309	−0.0951543	−	0.995463i	$-0.530334\pi$
$751$	−5.21529	−0.190309	−0.0951543	+	0.995463i	$0.530334\pi$
$752$	3.48184	0.126970
$753$	45.2183	1.64785
$754$	−39.1443	−1.42555
$755$	−11.1734	−0.406643
$756$	−6.00688	−0.218468
$757$	2.11739	0.0769579	0.0384789	−	0.999259i	$-0.487749\pi$
$757$	2.11739	0.0769579	0.0384789	+	0.999259i	$0.487749\pi$
$758$	2.13666	0.0776069
$759$	−5.41146	−0.196423
$760$	1.25253	0.0454340
$761$	5.02287	0.182079	0.0910395	−	0.995847i	$-0.470981\pi$
$761$	5.02287	0.182079	0.0910395	+	0.995847i	$0.470981\pi$
$762$	18.2789	0.662176
$763$	−2.98221	−0.107963
$764$	−17.7826	−0.643351
$765$	2.12963	0.0769970
$766$	3.00447	0.108556
$767$	56.4350	2.03775
$768$	−1.93892	−0.0699646
$769$	−0.681462	−0.0245741	−0.0122871	−	0.999925i	$-0.503911\pi$
$769$	−0.681462	−0.0245741	−0.0122871	+	0.999925i	$0.503911\pi$
$770$	0.477929	0.0172234
$771$	18.8056	0.677268
$772$	8.63621	0.310824
$773$	39.4139	1.41762	0.708810	−	0.705399i	$-0.249232\pi$
$773$	39.4139	1.41762	0.708810	+	0.705399i	$0.249232\pi$
$774$	6.69070	0.240492
$775$	−22.3078	−0.801320
$776$	8.33655	0.299265
$777$	−15.6282	−0.560659
$778$	14.4250	0.517161
$779$	9.68665	0.347060
$780$	4.48123	0.160454
$781$	−0.132642	−0.00474631
$782$	−22.6440	−0.809746
$783$	38.5676	1.37829
$784$	−5.08817	−0.181720
$785$	8.42772	0.300798
$786$	9.12900	0.325621
$787$	−5.78337	−0.206155	−0.103078	−	0.994673i	$-0.532869\pi$
$787$	−5.78337	−0.206155	−0.103078	+	0.994673i	$0.532869\pi$
$788$	−10.1340	−0.361010
$789$	23.3918	0.832770
$790$	−0.908243	−0.0323138
$791$	−20.5308	−0.729993
$792$	−0.500772	−0.0177941
$793$	−51.3013	−1.82176
$794$	−13.5678	−0.481502
$795$	10.0572	0.356691
$796$	5.55223	0.196794
$797$	38.7364	1.37211	0.686056	−	0.727549i	$-0.259340\pi$
$797$	38.7364	1.37211	0.686056	+	0.727549i	$0.259340\pi$
$798$	6.40625	0.226779
$799$	18.6285	0.659029
$800$	−4.72525	−0.167063
$801$	−8.50241	−0.300418
$802$	4.88537	0.172508
$803$	0.643106	0.0226947
$804$	28.9397	1.02062
$805$	3.06744	0.108113
$806$	−20.8162	−0.733221
$807$	23.0928	0.812906
$808$	−11.6583	−0.410136
$809$	−2.63717	−0.0927181	−0.0463590	−	0.998925i	$-0.514762\pi$
$809$	−2.63717	−0.0927181	−0.0463590	+	0.998925i	$0.514762\pi$
$810$	−5.60935	−0.197092
$811$	−22.6421	−0.795073	−0.397536	−	0.917586i	$-0.630135\pi$
$811$	−22.6421	−0.795073	−0.397536	+	0.917586i	$0.630135\pi$
$812$	−12.2750	−0.430769
$813$	59.0598	2.07132
$814$	3.84412	0.134736
$815$	4.15706	0.145615
$816$	−10.3736	−0.363147
$817$	21.0534	0.736567
$818$	−26.5853	−0.929535
$819$	4.62981	0.161779
$820$	2.12482	0.0742018
$821$	−21.0096	−0.733240	−0.366620	−	0.930371i	$-0.619485\pi$
$821$	−21.0096	−0.733240	−0.366620	+	0.930371i	$0.619485\pi$
$822$	4.51710	0.157552
$823$	−6.53514	−0.227801	−0.113900	−	0.993492i	$-0.536334\pi$
$823$	−6.53514	−0.227801	−0.113900	+	0.993492i	$0.536334\pi$
$824$	−11.0528	−0.385042
$825$	−6.04165	−0.210343
$826$	17.6971	0.615762
$827$	31.0010	1.07801	0.539005	−	0.842302i	$-0.318800\pi$
$827$	31.0010	1.07801	0.539005	+	0.842302i	$0.318800\pi$
$828$	−3.21405	−0.111696
$829$	29.3719	1.02013	0.510065	−	0.860136i	$-0.329621\pi$
$829$	29.3719	1.02013	0.510065	+	0.860136i	$0.329621\pi$
$830$	−2.13092	−0.0739654
$831$	55.3125	1.91877
$832$	−4.40931	−0.152865
$833$	−27.2226	−0.943209
$834$	−10.1379	−0.351045
$835$	−4.08456	−0.141352
$836$	−1.57576	−0.0544989
$837$	20.5095	0.708914
$838$	−36.9371	−1.27597
$839$	19.9224	0.687796	0.343898	−	0.939007i	$-0.388252\pi$
$839$	19.9224	0.687796	0.343898	+	0.939007i	$0.388252\pi$
$840$	1.40524	0.0484855
$841$	49.8127	1.71768
$842$	8.09591	0.279004
$843$	−27.0820	−0.932754
$844$	1.77688	0.0611628
$845$	3.37666	0.116161
$846$	2.64410	0.0909060
$847$	14.6083	0.501948
$848$	−9.89575	−0.339822
$849$	41.1202	1.41124
$850$	−25.2810	−0.867130
$851$	24.6723	0.845754
$852$	−0.390004	−0.0133613
$853$	35.5283	1.21647	0.608233	−	0.793759i	$-0.291879\pi$
$853$	35.5283	1.21647	0.608233	+	0.793759i	$0.291879\pi$
$854$	−16.0873	−0.550496
$855$	0.951166	0.0325292
$856$	−6.13445	−0.209671
$857$	21.0296	0.718356	0.359178	−	0.933269i	$-0.383057\pi$
$857$	21.0296	0.718356	0.359178	+	0.933269i	$0.383057\pi$
$858$	−5.63768	−0.192467
$859$	−35.6398	−1.21601	−0.608007	−	0.793932i	$-0.708031\pi$
$859$	−35.6398	−1.21601	−0.608007	+	0.793932i	$0.708031\pi$
$860$	4.61818	0.157479
$861$	10.8677	0.370370
$862$	−2.02576	−0.0689975
$863$	33.1980	1.13007	0.565036	−	0.825066i	$-0.308862\pi$
$863$	33.1980	1.13007	0.565036	+	0.825066i	$0.308862\pi$
$864$	4.34434	0.147798
$865$	−13.0776	−0.444651
$866$	−20.7167	−0.703982
$867$	−22.5388	−0.765459
$868$	−6.52764	−0.221563
$869$	1.14263	0.0387611
$870$	−9.02246	−0.305890
$871$	65.8119	2.22995
$872$	2.15682	0.0730390
$873$	6.33075	0.214263
$874$	−10.1136	−0.342096
$875$	7.04844	0.238281
$876$	1.89091	0.0638878
$877$	−30.5403	−1.03127	−0.515637	−	0.856807i	$-0.672445\pi$
$877$	−30.5403	−1.03127	−0.515637	+	0.856807i	$0.672445\pi$
$878$	24.4272	0.824377
$879$	−8.31881	−0.280586
$880$	−0.345652	−0.0116519
$881$	−22.0999	−0.744565	−0.372283	−	0.928119i	$-0.621425\pi$
$881$	−22.0999	−0.744565	−0.372283	+	0.928119i	$0.621425\pi$
$882$	−3.86394	−0.130106
$883$	1.84327	0.0620310	0.0310155	−	0.999519i	$-0.490126\pi$
$883$	1.84327	0.0620310	0.0310155	+	0.999519i	$0.490126\pi$
$884$	−23.5906	−0.793438
$885$	13.0078	0.437254
$886$	−22.2088	−0.746119
$887$	−22.4885	−0.755090	−0.377545	−	0.925991i	$-0.623232\pi$
$887$	−22.4885	−0.755090	−0.377545	+	0.925991i	$0.623232\pi$
$888$	11.3028	0.379296
$889$	13.0352	0.437185
$890$	−5.86869	−0.196719
$891$	7.05694	0.236416
$892$	−8.70832	−0.291576
$893$	8.32011	0.278422
$894$	−32.6941	−1.09346
$895$	−0.957915	−0.0320196
$896$	−1.38269	−0.0461924
$897$	−36.1837	−1.20814
$898$	24.5501	0.819247
$899$	41.9112	1.39782
$900$	−3.58834	−0.119611
$901$	−52.9441	−1.76382
$902$	−2.67316	−0.0890064
$903$	23.6204	0.786037
$904$	14.8485	0.493853
$905$	5.90475	0.196281
$906$	41.3312	1.37314
$907$	5.13642	0.170552	0.0852761	−	0.996357i	$-0.472823\pi$
$907$	5.13642	0.170552	0.0852761	+	0.996357i	$0.472823\pi$
$908$	−4.21453	−0.139864
$909$	−8.85323	−0.293643
$910$	3.19567	0.105936
$911$	−54.6488	−1.81060	−0.905298	−	0.424778i	$-0.860352\pi$
$911$	−54.6488	−1.81060	−0.905298	+	0.424778i	$0.860352\pi$
$912$	−4.63318	−0.153420
$913$	2.68084	0.0887229
$914$	−13.8625	−0.458532
$915$	−11.8246	−0.390908
$916$	3.12115	0.103126
$917$	6.51011	0.214983
$918$	23.2430	0.767134
$919$	−22.5747	−0.744671	−0.372336	−	0.928098i	$-0.621443\pi$
$919$	−22.5747	−0.744671	−0.372336	+	0.928098i	$0.621443\pi$
$920$	−2.21846	−0.0731404
$921$	52.8984	1.74306
$922$	−2.21865	−0.0730675
$923$	−0.886911	−0.0291930
$924$	−1.76789	−0.0581593
$925$	27.5455	0.905690
$926$	−8.59172	−0.282342
$927$	−8.39345	−0.275677
$928$	8.87765	0.291423
$929$	21.4335	0.703211	0.351606	−	0.936148i	$-0.385636\pi$
$929$	21.4335	0.703211	0.351606	+	0.936148i	$0.385636\pi$
$930$	−4.79798	−0.157332
$931$	−12.1585	−0.398480
$932$	−17.8429	−0.584462
$933$	−9.89652	−0.323997
$934$	26.4574	0.865711
$935$	−1.84930	−0.0604786
$936$	−3.34841	−0.109446
$937$	−37.0618	−1.21076	−0.605378	−	0.795938i	$-0.706978\pi$
$937$	−37.0618	−1.21076	−0.605378	+	0.795938i	$0.706978\pi$
$938$	20.6376	0.673841
$939$	5.19171	0.169425
$940$	1.82506	0.0595269
$941$	−15.5731	−0.507670	−0.253835	−	0.967248i	$-0.581692\pi$
$941$	−15.5731	−0.507670	−0.253835	+	0.967248i	$0.581692\pi$
$942$	−31.1746	−1.01572
$943$	−17.1568	−0.558704
$944$	−12.7991	−0.416574
$945$	−3.14859	−0.102424
$946$	−5.80998	−0.188899
$947$	−35.5973	−1.15676	−0.578378	−	0.815769i	$-0.696314\pi$
$947$	−35.5973	−1.15676	−0.578378	+	0.815769i	$0.696314\pi$
$948$	3.35964	0.109116
$949$	4.30013	0.139588
$950$	−11.2913	−0.366339
$951$	−49.8417	−1.61623
$952$	−7.39764	−0.239759
$953$	2.31981	0.0751461	0.0375730	−	0.999294i	$-0.488037\pi$
$953$	2.31981	0.0751461	0.0375730	+	0.999294i	$0.488037\pi$
$954$	−7.51480	−0.243301
$955$	−9.32100	−0.301620
$956$	6.10657	0.197501
$957$	11.3509	0.366921
$958$	12.3196	0.398030
$959$	3.22126	0.104020
$960$	−1.01631	−0.0328013
$961$	−8.71237	−0.281044
$962$	25.7037	0.828720
$963$	−4.65848	−0.150117
$964$	25.5336	0.822381
$965$	4.52679	0.145723
$966$	−11.3466	−0.365072
$967$	26.0252	0.836915	0.418457	−	0.908236i	$-0.362571\pi$
$967$	26.0252	0.836915	0.418457	+	0.908236i	$0.362571\pi$
$968$	−10.5651	−0.339577
$969$	−24.7884	−0.796317
$970$	4.36973	0.140303
$971$	32.9198	1.05645	0.528223	−	0.849106i	$-0.322858\pi$
$971$	32.9198	1.05645	0.528223	+	0.849106i	$0.322858\pi$
$972$	7.71629	0.247500
$973$	−7.22956	−0.231769
$974$	−14.6109	−0.468163
$975$	−40.3975	−1.29375
$976$	11.6348	0.372420
$977$	22.3861	0.716193	0.358097	−	0.933685i	$-0.383426\pi$
$977$	22.3861	0.716193	0.358097	+	0.933685i	$0.383426\pi$
$978$	−15.3772	−0.491709
$979$	7.38320	0.235968
$980$	−2.66704	−0.0851954
$981$	1.63788	0.0522934
$982$	−31.4895	−1.00487
$983$	−22.5436	−0.719030	−0.359515	−	0.933139i	$-0.617058\pi$
$983$	−22.5436	−0.719030	−0.359515	+	0.933139i	$0.617058\pi$
$984$	−7.85982	−0.250562
$985$	−5.31190	−0.169251
$986$	47.4971	1.51261
$987$	9.33454	0.297122
$988$	−10.5364	−0.335206
$989$	−37.2895	−1.18574
$990$	−0.262487	−0.00834238
$991$	−3.50833	−0.111446	−0.0557229	−	0.998446i	$-0.517746\pi$
$991$	−3.50833	−0.111446	−0.0557229	+	0.998446i	$0.517746\pi$
$992$	4.72098	0.149891
$993$	−35.4670	−1.12551
$994$	−0.278122	−0.00882148
$995$	2.91028	0.0922622
$996$	7.88240	0.249764
$997$	−50.7663	−1.60779	−0.803893	−	0.594774i	$-0.797242\pi$
$997$	−50.7663	−1.60779	−0.803893	+	0.594774i	$0.797242\pi$
$998$	−2.33685	−0.0739717
$999$	−25.3250	−0.801247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.b.1.16	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.b.1.16	✓	54	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.93892 q^{3} +1.00000 q^{4} +0.524165 q^{5} -1.93892 q^{6} -1.38269 q^{7} +1.00000 q^{8} +0.759396 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.93892 q^{3} +1.00000 q^{4} +0.524165 q^{5} -1.93892 q^{6} -1.38269 q^{7} +1.00000 q^{8} +0.759396 q^{9} +0.524165 q^{10} -0.659434 q^{11} -1.93892 q^{12} -4.40931 q^{13} -1.38269 q^{14} -1.01631 q^{15} +1.00000 q^{16} +5.35018 q^{17} +0.759396 q^{18} +2.38957 q^{19} +0.524165 q^{20} +2.68092 q^{21} -0.659434 q^{22} -4.23237 q^{23} -1.93892 q^{24} -4.72525 q^{25} -4.40931 q^{26} +4.34434 q^{27} -1.38269 q^{28} +8.87765 q^{29} -1.01631 q^{30} +4.72098 q^{31} +1.00000 q^{32} +1.27859 q^{33} +5.35018 q^{34} -0.724757 q^{35} +0.759396 q^{36} -5.82942 q^{37} +2.38957 q^{38} +8.54928 q^{39} +0.524165 q^{40} +4.05372 q^{41} +2.68092 q^{42} +8.81055 q^{43} -0.659434 q^{44} +0.398049 q^{45} -4.23237 q^{46} +3.48184 q^{47} -1.93892 q^{48} -5.08817 q^{49} -4.72525 q^{50} -10.3736 q^{51} -4.40931 q^{52} -9.89575 q^{53} +4.34434 q^{54} -0.345652 q^{55} -1.38269 q^{56} -4.63318 q^{57} +8.87765 q^{58} -12.7991 q^{59} -1.01631 q^{60} +11.6348 q^{61} +4.72098 q^{62} -1.05001 q^{63} +1.00000 q^{64} -2.31120 q^{65} +1.27859 q^{66} -14.9257 q^{67} +5.35018 q^{68} +8.20621 q^{69} -0.724757 q^{70} +0.201145 q^{71} +0.759396 q^{72} -0.975239 q^{73} -5.82942 q^{74} +9.16187 q^{75} +2.38957 q^{76} +0.911792 q^{77} +8.54928 q^{78} -1.73274 q^{79} +0.524165 q^{80} -10.7015 q^{81} +4.05372 q^{82} -4.06537 q^{83} +2.68092 q^{84} +2.80438 q^{85} +8.81055 q^{86} -17.2130 q^{87} -0.659434 q^{88} -11.1963 q^{89} +0.398049 q^{90} +6.09670 q^{91} -4.23237 q^{92} -9.15358 q^{93} +3.48184 q^{94} +1.25253 q^{95} -1.93892 q^{96} +8.33655 q^{97} -5.08817 q^{98} -0.500772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9	\( 54 q + 54 q^{2} - 21 q^{3} + 54 q^{4} - 14 q^{5} - 21 q^{6} - 44 q^{7} + 54 q^{8} + 39 q^{9} - 14 q^{10} - 31 q^{11} - 21 q^{12} - 34 q^{13} - 44 q^{14} - 22 q^{15} + 54 q^{16} - 40 q^{17} + 39 q^{18} - 44 q^{19} - 14 q^{20} - 3 q^{21} - 31 q^{22} - 33 q^{23} - 21 q^{24} + 14 q^{25} - 34 q^{26} - 66 q^{27} - 44 q^{28} - 22 q^{30} - 65 q^{31} + 54 q^{32} - 43 q^{33} - 40 q^{34} - 46 q^{35} + 39 q^{36} - 58 q^{37} - 44 q^{38} - 36 q^{39} - 14 q^{40} - 49 q^{41} - 3 q^{42} - 47 q^{43} - 31 q^{44} - 45 q^{45} - 33 q^{46} - 66 q^{47} - 21 q^{48} + 16 q^{49} + 14 q^{50} - 33 q^{51} - 34 q^{52} - 16 q^{53} - 66 q^{54} - 50 q^{55} - 44 q^{56} - 33 q^{57} - 70 q^{59} - 22 q^{60} - 40 q^{61} - 65 q^{62} - 117 q^{63} + 54 q^{64} - 33 q^{65} - 43 q^{66} - 82 q^{67} - 40 q^{68} - q^{69} - 46 q^{70} - 60 q^{71} + 39 q^{72} - 92 q^{73} - 58 q^{74} - 68 q^{75} - 44 q^{76} + 13 q^{77} - 36 q^{78} - 57 q^{79} - 14 q^{80} + 26 q^{81} - 49 q^{82} - 77 q^{83} - 3 q^{84} - 24 q^{85} - 47 q^{86} - 61 q^{87} - 31 q^{88} - 54 q^{89} - 45 q^{90} - 46 q^{91} - 33 q^{92} - 24 q^{93} - 66 q^{94} - 66 q^{95} - 21 q^{96} - 137 q^{97} + 16 q^{98} - 71 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 21 * q^3 + 54 * q^4 - 14 * q^5 - 21 * q^6 - 44 * q^7 + 54 * q^8 + 39 * q^9 - 14 * q^10 - 31 * q^11 - 21 * q^12 - 34 * q^13 - 44 * q^14 - 22 * q^15 + 54 * q^16 - 40 * q^17 + 39 * q^18 - 44 * q^19 - 14 * q^20 - 3 * q^21 - 31 * q^22 - 33 * q^23 - 21 * q^24 + 14 * q^25 - 34 * q^26 - 66 * q^27 - 44 * q^28 - 22 * q^30 - 65 * q^31 + 54 * q^32 - 43 * q^33 - 40 * q^34 - 46 * q^35 + 39 * q^36 - 58 * q^37 - 44 * q^38 - 36 * q^39 - 14 * q^40 - 49 * q^41 - 3 * q^42 - 47 * q^43 - 31 * q^44 - 45 * q^45 - 33 * q^46 - 66 * q^47 - 21 * q^48 + 16 * q^49 + 14 * q^50 - 33 * q^51 - 34 * q^52 - 16 * q^53 - 66 * q^54 - 50 * q^55 - 44 * q^56 - 33 * q^57 - 70 * q^59 - 22 * q^60 - 40 * q^61 - 65 * q^62 - 117 * q^63 + 54 * q^64 - 33 * q^65 - 43 * q^66 - 82 * q^67 - 40 * q^68 - q^69 - 46 * q^70 - 60 * q^71 + 39 * q^72 - 92 * q^73 - 58 * q^74 - 68 * q^75 - 44 * q^76 + 13 * q^77 - 36 * q^78 - 57 * q^79 - 14 * q^80 + 26 * q^81 - 49 * q^82 - 77 * q^83 - 3 * q^84 - 24 * q^85 - 47 * q^86 - 61 * q^87 - 31 * q^88 - 54 * q^89 - 45 * q^90 - 46 * q^91 - 33 * q^92 - 24 * q^93 - 66 * q^94 - 66 * q^95 - 21 * q^96 - 137 * q^97 + 16 * q^98 - 71 * q^99

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