LMFDB - Embedded newform 1003.2.a.j.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.29289 q^{2} -0.141514 q^{3} +3.25733 q^{4} +2.10475 q^{5} -0.324476 q^{6} +3.17762 q^{7} +2.88291 q^{8} -2.97997 q^{9} +O(q^{10})$	\(q+2.29289 q^{2} -0.141514 q^{3} +3.25733 q^{4} +2.10475 q^{5} -0.324476 q^{6} +3.17762 q^{7} +2.88291 q^{8} -2.97997 q^{9} +4.82596 q^{10} +3.76407 q^{11} -0.460958 q^{12} -2.55696 q^{13} +7.28593 q^{14} -0.297852 q^{15} +0.0955312 q^{16} -1.00000 q^{17} -6.83274 q^{18} -3.88868 q^{19} +6.85587 q^{20} -0.449678 q^{21} +8.63059 q^{22} +5.00150 q^{23} -0.407972 q^{24} -0.570022 q^{25} -5.86281 q^{26} +0.846250 q^{27} +10.3506 q^{28} -2.31795 q^{29} -0.682940 q^{30} +9.70842 q^{31} -5.54678 q^{32} -0.532669 q^{33} -2.29289 q^{34} +6.68811 q^{35} -9.70675 q^{36} -11.7229 q^{37} -8.91629 q^{38} +0.361845 q^{39} +6.06781 q^{40} -10.3899 q^{41} -1.03106 q^{42} +5.52501 q^{43} +12.2608 q^{44} -6.27210 q^{45} +11.4679 q^{46} -1.04633 q^{47} -0.0135190 q^{48} +3.09729 q^{49} -1.30700 q^{50} +0.141514 q^{51} -8.32885 q^{52} +1.97756 q^{53} +1.94036 q^{54} +7.92244 q^{55} +9.16081 q^{56} +0.550302 q^{57} -5.31479 q^{58} +1.00000 q^{59} -0.970201 q^{60} +11.2931 q^{61} +22.2603 q^{62} -9.46923 q^{63} -12.9092 q^{64} -5.38176 q^{65} -1.22135 q^{66} +6.08003 q^{67} -3.25733 q^{68} -0.707783 q^{69} +15.3351 q^{70} -8.89112 q^{71} -8.59100 q^{72} +14.2368 q^{73} -26.8794 q^{74} +0.0806661 q^{75} -12.6667 q^{76} +11.9608 q^{77} +0.829670 q^{78} -3.41409 q^{79} +0.201069 q^{80} +8.82017 q^{81} -23.8229 q^{82} -11.7416 q^{83} -1.46475 q^{84} -2.10475 q^{85} +12.6682 q^{86} +0.328022 q^{87} +10.8515 q^{88} +1.04259 q^{89} -14.3812 q^{90} -8.12505 q^{91} +16.2915 q^{92} -1.37388 q^{93} -2.39912 q^{94} -8.18470 q^{95} +0.784947 q^{96} -0.00580143 q^{97} +7.10174 q^{98} -11.2168 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) $ 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.29289	1.62132	0.810658	−	0.585520i	$-0.199110\pi$
$2$	2.29289	1.62132	0.810658	+	0.585520i	$0.199110\pi$
$3$	−0.141514	−0.0817032	−0.0408516	−	0.999165i	$-0.513007\pi$
$3$	−0.141514	−0.0817032	−0.0408516	+	0.999165i	$0.513007\pi$
$4$	3.25733	1.62866
$5$	2.10475	0.941273	0.470637	−	0.882327i	$-0.344024\pi$
$5$	2.10475	0.941273	0.470637	+	0.882327i	$0.344024\pi$
$6$	−0.324476	−0.132467
$7$	3.17762	1.20103	0.600514	−	0.799614i	$-0.294963\pi$
$7$	3.17762	1.20103	0.600514	+	0.799614i	$0.294963\pi$
$8$	2.88291	1.01926
$9$	−2.97997	−0.993325
$10$	4.82596	1.52610
$11$	3.76407	1.13491	0.567455	−	0.823404i	$-0.307928\pi$
$11$	3.76407	1.13491	0.567455	+	0.823404i	$0.307928\pi$
$12$	−0.460958	−0.133067
$13$	−2.55696	−0.709172	−0.354586	−	0.935023i	$-0.615378\pi$
$13$	−2.55696	−0.709172	−0.354586	+	0.935023i	$0.615378\pi$
$14$	7.28593	1.94725
$15$	−0.297852	−0.0769050
$16$	0.0955312	0.0238828
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−6.83274	−1.61049
$19$	−3.88868	−0.892124	−0.446062	−	0.895002i	$-0.647174\pi$
$19$	−3.88868	−0.892124	−0.446062	+	0.895002i	$0.647174\pi$
$20$	6.85587	1.53302
$21$	−0.449678	−0.0981278
$22$	8.63059	1.84005
$23$	5.00150	1.04289	0.521443	−	0.853286i	$-0.325394\pi$
$23$	5.00150	1.04289	0.521443	+	0.853286i	$0.325394\pi$
$24$	−0.407972	−0.0832770
$25$	−0.570022	−0.114004
$26$	−5.86281	−1.14979
$27$	0.846250	0.162861
$28$	10.3506	1.95607
$29$	−2.31795	−0.430432	−0.215216	−	0.976566i	$-0.569046\pi$
$29$	−2.31795	−0.430432	−0.215216	+	0.976566i	$0.569046\pi$
$30$	−0.682940	−0.124687
$31$	9.70842	1.74368	0.871842	−	0.489788i	$-0.162926\pi$
$31$	9.70842	1.74368	0.871842	+	0.489788i	$0.162926\pi$
$32$	−5.54678	−0.980541
$33$	−0.532669	−0.0927258
$34$	−2.29289	−0.393227
$35$	6.68811	1.13050
$36$	−9.70675	−1.61779
$37$	−11.7229	−1.92724	−0.963620	−	0.267277i	$-0.913876\pi$
$37$	−11.7229	−1.92724	−0.963620	+	0.267277i	$0.913876\pi$
$38$	−8.91629	−1.44641
$39$	0.361845	0.0579416
$40$	6.06781	0.959405
$41$	−10.3899	−1.62263	−0.811317	−	0.584606i	$-0.801249\pi$
$41$	−10.3899	−1.62263	−0.811317	+	0.584606i	$0.801249\pi$
$42$	−1.03106	−0.159096
$43$	5.52501	0.842556	0.421278	−	0.906932i	$-0.361582\pi$
$43$	5.52501	0.842556	0.421278	+	0.906932i	$0.361582\pi$
$44$	12.2608	1.84839
$45$	−6.27210	−0.934990
$46$	11.4679	1.69085
$47$	−1.04633	−0.152623	−0.0763115	−	0.997084i	$-0.524314\pi$
$47$	−1.04633	−0.152623	−0.0763115	+	0.997084i	$0.524314\pi$
$48$	−0.0135190	−0.00195130
$49$	3.09729	0.442470
$50$	−1.30700	−0.184837
$51$	0.141514	0.0198159
$52$	−8.32885	−1.15500
$53$	1.97756	0.271638	0.135819	−	0.990734i	$-0.456633\pi$
$53$	1.97756	0.271638	0.135819	+	0.990734i	$0.456633\pi$
$54$	1.94036	0.264049
$55$	7.92244	1.06826
$56$	9.16081	1.22416
$57$	0.550302	0.0728893
$58$	−5.31479	−0.697866
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−0.970201	−0.125252
$61$	11.2931	1.44593	0.722967	−	0.690883i	$-0.242778\pi$
$61$	11.2931	1.44593	0.722967	+	0.690883i	$0.242778\pi$
$62$	22.2603	2.82706
$63$	−9.46923	−1.19301
$64$	−12.9092	−1.61365
$65$	−5.38176	−0.667525
$66$	−1.22135	−0.150338
$67$	6.08003	0.742793	0.371397	−	0.928474i	$-0.378879\pi$
$67$	6.08003	0.742793	0.371397	+	0.928474i	$0.378879\pi$
$68$	−3.25733	−0.395009
$69$	−0.707783	−0.0852070
$70$	15.3351	1.83289
$71$	−8.89112	−1.05518	−0.527591	−	0.849498i	$-0.676905\pi$
$71$	−8.89112	−1.05518	−0.527591	+	0.849498i	$0.676905\pi$
$72$	−8.59100	−1.01246
$73$	14.2368	1.66629	0.833145	−	0.553054i	$-0.186538\pi$
$73$	14.2368	1.66629	0.833145	+	0.553054i	$0.186538\pi$
$74$	−26.8794	−3.12466
$75$	0.0806661	0.00931452
$76$	−12.6667	−1.45297
$77$	11.9608	1.36306
$78$	0.829670	0.0939416
$79$	−3.41409	−0.384115	−0.192057	−	0.981384i	$-0.561516\pi$
$79$	−3.41409	−0.384115	−0.192057	+	0.981384i	$0.561516\pi$
$80$	0.201069	0.0224802
$81$	8.82017	0.980018
$82$	−23.8229	−2.63080
$83$	−11.7416	−1.28881	−0.644407	−	0.764683i	$-0.722896\pi$
$83$	−11.7416	−1.28881	−0.644407	+	0.764683i	$0.722896\pi$
$84$	−1.46475	−0.159817
$85$	−2.10475	−0.228292
$86$	12.6682	1.36605
$87$	0.328022	0.0351676
$88$	10.8515	1.15677
$89$	1.04259	0.110514	0.0552571	−	0.998472i	$-0.482402\pi$
$89$	1.04259	0.110514	0.0552571	+	0.998472i	$0.482402\pi$
$90$	−14.3812	−1.51591
$91$	−8.12505	−0.851736
$92$	16.2915	1.69851
$93$	−1.37388	−0.142464
$94$	−2.39912	−0.247450
$95$	−8.18470	−0.839732
$96$	0.784947	0.0801133
$97$	−0.00580143	−0.000589046 0	−0.000294523	−	1.00000i	$-0.500094\pi$
$97$	−0.00580143	−0.000589046 0	−0.000294523		1.00000i	$0.500094\pi$
$98$	7.10174	0.717384
$99$	−11.2168	−1.12733
$100$	−1.85675	−0.185675
$101$	7.53134	0.749396	0.374698	−	0.927147i	$-0.377746\pi$
$101$	7.53134	0.749396	0.374698	+	0.927147i	$0.377746\pi$
$102$	0.324476	0.0321279
$103$	−12.0240	−1.18476	−0.592382	−	0.805657i	$-0.701813\pi$
$103$	−12.0240	−1.18476	−0.592382	+	0.805657i	$0.701813\pi$
$104$	−7.37148	−0.722833
$105$	−0.946461	−0.0923651
$106$	4.53432	0.440412
$107$	2.18133	0.210878	0.105439	−	0.994426i	$-0.466375\pi$
$107$	2.18133	0.210878	0.105439	+	0.994426i	$0.466375\pi$
$108$	2.75651	0.265246
$109$	6.06237	0.580670	0.290335	−	0.956925i	$-0.406233\pi$
$109$	6.06237	0.580670	0.290335	+	0.956925i	$0.406233\pi$
$110$	18.1653	1.73199
$111$	1.65896	0.157462
$112$	0.303562	0.0286839
$113$	−13.5644	−1.27603	−0.638015	−	0.770024i	$-0.720244\pi$
$113$	−13.5644	−1.27603	−0.638015	+	0.770024i	$0.720244\pi$
$114$	1.26178	0.118177
$115$	10.5269	0.981640
$116$	−7.55031	−0.701029
$117$	7.61966	0.704438
$118$	2.29289	0.211077
$119$	−3.17762	−0.291292
$120$	−0.858680	−0.0783864
$121$	3.16825	0.288023
$122$	25.8938	2.34432
$123$	1.47032	0.132574
$124$	31.6235	2.83988
$125$	−11.7235	−1.04858
$126$	−21.7119	−1.93425
$127$	−14.9806	−1.32932	−0.664658	−	0.747147i	$-0.731423\pi$
$127$	−14.9806	−1.32932	−0.664658	+	0.747147i	$0.731423\pi$
$128$	−18.5058	−1.63569
$129$	−0.781866	−0.0688395
$130$	−12.3398	−1.08227
$131$	4.08628	0.357020	0.178510	−	0.983938i	$-0.442872\pi$
$131$	4.08628	0.357020	0.178510	+	0.983938i	$0.442872\pi$
$132$	−1.73508	−0.151019
$133$	−12.3568	−1.07147
$134$	13.9408	1.20430
$135$	1.78115	0.153297
$136$	−2.88291	−0.247208
$137$	8.62411	0.736807	0.368404	−	0.929666i	$-0.379904\pi$
$137$	8.62411	0.736807	0.368404	+	0.929666i	$0.379904\pi$
$138$	−1.62287	−0.138147
$139$	−15.7010	−1.33174	−0.665872	−	0.746066i	$-0.731940\pi$
$139$	−15.7010	−1.33174	−0.665872	+	0.746066i	$0.731940\pi$
$140$	21.7854	1.84120
$141$	0.148070	0.0124698
$142$	−20.3863	−1.71078
$143$	−9.62457	−0.804847
$144$	−0.284681	−0.0237234
$145$	−4.87870	−0.405154
$146$	32.6434	2.70158
$147$	−0.438310	−0.0361512
$148$	−38.1855	−3.13883
$149$	−0.360441	−0.0295285	−0.0147642	−	0.999891i	$-0.504700\pi$
$149$	−0.360441	−0.0295285	−0.0147642	+	0.999891i	$0.504700\pi$
$150$	0.184958	0.0151018
$151$	−14.1341	−1.15022	−0.575110	−	0.818076i	$-0.695041\pi$
$151$	−14.1341	−1.15022	−0.575110	+	0.818076i	$0.695041\pi$
$152$	−11.2107	−0.909309
$153$	2.97997	0.240917
$154$	27.4248	2.20995
$155$	20.4338	1.64128
$156$	1.17865	0.0943674
$157$	2.80579	0.223926	0.111963	−	0.993712i	$-0.464286\pi$
$157$	2.80579	0.223926	0.111963	+	0.993712i	$0.464286\pi$
$158$	−7.82811	−0.622771
$159$	−0.279852	−0.0221937
$160$	−11.6746	−0.922958
$161$	15.8929	1.25254
$162$	20.2236	1.58892
$163$	22.7186	1.77946	0.889729	−	0.456490i	$-0.150893\pi$
$163$	22.7186	1.77946	0.889729	+	0.456490i	$0.150893\pi$
$164$	−33.8434	−2.64273
$165$	−1.12114	−0.0872803
$166$	−26.9223	−2.08957
$167$	−15.4401	−1.19479	−0.597396	−	0.801946i	$-0.703798\pi$
$167$	−15.4401	−1.19479	−0.597396	+	0.801946i	$0.703798\pi$
$168$	−1.29638	−0.100018
$169$	−6.46197	−0.497075
$170$	−4.82596	−0.370134
$171$	11.5882	0.886168
$172$	17.9968	1.37224
$173$	13.0780	0.994301	0.497151	−	0.867664i	$-0.334380\pi$
$173$	13.0780	0.994301	0.497151	+	0.867664i	$0.334380\pi$
$174$	0.752117	0.0570178
$175$	−1.81132	−0.136923
$176$	0.359587	0.0271049
$177$	−0.141514	−0.0106368
$178$	2.39054	0.179178
$179$	−11.6442	−0.870332	−0.435166	−	0.900350i	$-0.643310\pi$
$179$	−11.6442	−0.870332	−0.435166	+	0.900350i	$0.643310\pi$
$180$	−20.4303	−1.52278
$181$	−4.82023	−0.358285	−0.179142	−	0.983823i	$-0.557332\pi$
$181$	−4.82023	−0.358285	−0.179142	+	0.983823i	$0.557332\pi$
$182$	−18.6298	−1.38093
$183$	−1.59813	−0.118137
$184$	14.4189	1.06297
$185$	−24.6739	−1.81406
$186$	−3.15014	−0.230980
$187$	−3.76407	−0.275256
$188$	−3.40824	−0.248572
$189$	2.68906	0.195601
$190$	−18.7666	−1.36147
$191$	23.2529	1.68252	0.841261	−	0.540630i	$-0.181814\pi$
$191$	23.2529	1.68252	0.841261	+	0.540630i	$0.181814\pi$
$192$	1.82683	0.131840
$193$	−15.6808	−1.12873	−0.564363	−	0.825527i	$-0.690878\pi$
$193$	−15.6808	−1.12873	−0.564363	+	0.825527i	$0.690878\pi$
$194$	−0.0133020	−0.000955030 0
$195$	0.761594	0.0545389
$196$	10.0889	0.720635
$197$	8.27691	0.589705	0.294853	−	0.955543i	$-0.404729\pi$
$197$	8.27691	0.589705	0.294853	+	0.955543i	$0.404729\pi$
$198$	−25.7189	−1.82777
$199$	25.9853	1.84205	0.921025	−	0.389504i	$-0.127353\pi$
$199$	25.9853	1.84205	0.921025	+	0.389504i	$0.127353\pi$
$200$	−1.64332	−0.116200
$201$	−0.860409	−0.0606886
$202$	17.2685	1.21501
$203$	−7.36556	−0.516961
$204$	0.460958	0.0322735
$205$	−21.8682	−1.52734
$206$	−27.5698	−1.92088
$207$	−14.9043	−1.03592
$208$	−0.244269	−0.0169370
$209$	−14.6373	−1.01248
$210$	−2.17013	−0.149753
$211$	−9.60126	−0.660978	−0.330489	−	0.943810i	$-0.607214\pi$
$211$	−9.60126	−0.660978	−0.330489	+	0.943810i	$0.607214\pi$
$212$	6.44156	0.442408
$213$	1.25822	0.0862117
$214$	5.00155	0.341899
$215$	11.6288	0.793075
$216$	2.43966	0.165998
$217$	30.8497	2.09421
$218$	13.9003	0.941449
$219$	−2.01471	−0.136141
$220$	25.8060	1.73984
$221$	2.55696	0.172000
$222$	3.80381	0.255295
$223$	1.52585	0.102178	0.0510891	−	0.998694i	$-0.483731\pi$
$223$	1.52585	0.102178	0.0510891	+	0.998694i	$0.483731\pi$
$224$	−17.6256	−1.17766
$225$	1.69865	0.113243
$226$	−31.1016	−2.06885
$227$	24.5994	1.63272	0.816359	−	0.577545i	$-0.195989\pi$
$227$	24.5994	1.63272	0.816359	+	0.577545i	$0.195989\pi$
$228$	1.79252	0.118712
$229$	−25.1278	−1.66049	−0.830245	−	0.557399i	$-0.811799\pi$
$229$	−25.1278	−1.66049	−0.830245	+	0.557399i	$0.811799\pi$
$230$	24.1370	1.59155
$231$	−1.69262	−0.111366
$232$	−6.68243	−0.438723
$233$	2.01785	0.132194	0.0660969	−	0.997813i	$-0.478945\pi$
$233$	2.01785	0.132194	0.0660969	+	0.997813i	$0.478945\pi$
$234$	17.4710	1.14212
$235$	−2.20226	−0.143660
$236$	3.25733	0.212034
$237$	0.483141	0.0313834
$238$	−7.28593	−0.472277
$239$	22.3816	1.44775	0.723873	−	0.689934i	$-0.242360\pi$
$239$	22.3816	1.44775	0.723873	+	0.689934i	$0.242360\pi$
$240$	−0.0284541	−0.00183671
$241$	25.5681	1.64698	0.823492	−	0.567328i	$-0.192023\pi$
$241$	25.5681	1.64698	0.823492	+	0.567328i	$0.192023\pi$
$242$	7.26444	0.466976
$243$	−3.78693	−0.242931
$244$	36.7854	2.35494
$245$	6.51903	0.416485
$246$	3.37128	0.214945
$247$	9.94318	0.632669
$248$	27.9885	1.77727
$249$	1.66161	0.105300
$250$	−26.8807	−1.70008
$251$	8.63370	0.544954	0.272477	−	0.962162i	$-0.412157\pi$
$251$	8.63370	0.544954	0.272477	+	0.962162i	$0.412157\pi$
$252$	−30.8444	−1.94302
$253$	18.8260	1.18358
$254$	−34.3489	−2.15524
$255$	0.297852	0.0186522
$256$	−16.6132	−1.03833
$257$	0.330518	0.0206171	0.0103086	−	0.999947i	$-0.496719\pi$
$257$	0.330518	0.0206171	0.0103086	+	0.999947i	$0.496719\pi$
$258$	−1.79273	−0.111610
$259$	−37.2511	−2.31467
$260$	−17.5302	−1.08717
$261$	6.90742	0.427559
$262$	9.36938	0.578842
$263$	−11.4626	−0.706812	−0.353406	−	0.935470i	$-0.614977\pi$
$263$	−11.4626	−0.706812	−0.353406	+	0.935470i	$0.614977\pi$
$264$	−1.53564	−0.0945120
$265$	4.16227	0.255686
$266$	−28.3326	−1.73718
$267$	−0.147541	−0.00902936
$268$	19.8046	1.20976
$269$	−21.5343	−1.31297	−0.656486	−	0.754338i	$-0.727958\pi$
$269$	−21.5343	−1.31297	−0.656486	+	0.754338i	$0.727958\pi$
$270$	4.08397	0.248542
$271$	15.0283	0.912903	0.456451	−	0.889748i	$-0.349120\pi$
$271$	15.0283	0.912903	0.456451	+	0.889748i	$0.349120\pi$
$272$	−0.0955312	−0.00579243
$273$	1.14981	0.0695895
$274$	19.7741	1.19460
$275$	−2.14560	−0.129385
$276$	−2.30548	−0.138774
$277$	−14.0587	−0.844705	−0.422353	−	0.906432i	$-0.638796\pi$
$277$	−14.0587	−0.844705	−0.422353	+	0.906432i	$0.638796\pi$
$278$	−36.0007	−2.15918
$279$	−28.9308	−1.73204
$280$	19.2812	1.15227
$281$	19.9802	1.19192	0.595961	−	0.803014i	$-0.296771\pi$
$281$	19.9802	1.19192	0.595961	+	0.803014i	$0.296771\pi$
$282$	0.339509	0.0202174
$283$	7.80953	0.464228	0.232114	−	0.972689i	$-0.425436\pi$
$283$	7.80953	0.464228	0.232114	+	0.972689i	$0.425436\pi$
$284$	−28.9613	−1.71854
$285$	1.15825	0.0686088
$286$	−22.0681	−1.30491
$287$	−33.0153	−1.94883
$288$	16.5293	0.973996
$289$	1.00000	0.0588235
$290$	−11.1863	−0.656883
$291$	0.000820984 0	4.81269e−5 0
$292$	46.3739	2.71383
$293$	−1.02700	−0.0599979	−0.0299990	−	0.999550i	$-0.509550\pi$
$293$	−1.02700	−0.0599979	−0.0299990	+	0.999550i	$0.509550\pi$
$294$	−1.00500	−0.0586125
$295$	2.10475	0.122543
$296$	−33.7962	−1.96436
$297$	3.18535	0.184833
$298$	−0.826451	−0.0478750
$299$	−12.7886	−0.739585
$300$	0.262756	0.0151702
$301$	17.5564	1.01193
$302$	−32.4080	−1.86487
$303$	−1.06579	−0.0612280
$304$	−0.371490	−0.0213064
$305$	23.7692	1.36102
$306$	6.83274	0.390602
$307$	1.24392	0.0709941	0.0354971	−	0.999370i	$-0.488699\pi$
$307$	1.24392	0.0709941	0.0354971	+	0.999370i	$0.488699\pi$
$308$	38.9603	2.21997
$309$	1.70157	0.0967990
$310$	46.8524	2.66104
$311$	12.6873	0.719428	0.359714	−	0.933063i	$-0.382874\pi$
$311$	12.6873	0.719428	0.359714	+	0.933063i	$0.382874\pi$
$312$	1.04317	0.0590577
$313$	24.8018	1.40188	0.700942	−	0.713219i	$-0.252763\pi$
$313$	24.8018	1.40188	0.700942	+	0.713219i	$0.252763\pi$
$314$	6.43335	0.363055
$315$	−19.9304	−1.12295
$316$	−11.1208	−0.625594
$317$	10.7810	0.605519	0.302760	−	0.953067i	$-0.402092\pi$
$317$	10.7810	0.605519	0.302760	+	0.953067i	$0.402092\pi$
$318$	−0.641669	−0.0359830
$319$	−8.72492	−0.488502
$320$	−27.1707	−1.51889
$321$	−0.308689	−0.0172294
$322$	36.4406	2.03075
$323$	3.88868	0.216372
$324$	28.7302	1.59612
$325$	1.45752	0.0808487
$326$	52.0912	2.88506
$327$	−0.857911	−0.0474426
$328$	−29.9532	−1.65389
$329$	−3.32484	−0.183305
$330$	−2.57064	−0.141509
$331$	21.8133	1.19897	0.599483	−	0.800388i	$-0.295373\pi$
$331$	21.8133	1.19897	0.599483	+	0.800388i	$0.295373\pi$
$332$	−38.2464	−2.09904
$333$	34.9341	1.91437
$334$	−35.4024	−1.93713
$335$	12.7969	0.699172
$336$	−0.0429583	−0.00234357
$337$	−9.90115	−0.539350	−0.269675	−	0.962951i	$-0.586916\pi$
$337$	−9.90115	−0.539350	−0.269675	+	0.962951i	$0.586916\pi$
$338$	−14.8166	−0.805915
$339$	1.91955	0.104256
$340$	−6.85587	−0.371812
$341$	36.5432	1.97893
$342$	26.5703	1.43676
$343$	−12.4013	−0.669609
$344$	15.9281	0.858786
$345$	−1.48971	−0.0802031
$346$	29.9863	1.61208
$347$	21.8889	1.17506	0.587528	−	0.809204i	$-0.300101\pi$
$347$	21.8889	1.17506	0.587528	+	0.809204i	$0.300101\pi$
$348$	1.06848	0.0572763
$349$	33.6095	1.79908	0.899539	−	0.436841i	$-0.143903\pi$
$349$	33.6095	1.79908	0.899539	+	0.436841i	$0.143903\pi$
$350$	−4.15314	−0.221995
$351$	−2.16382	−0.115496
$352$	−20.8785	−1.11283
$353$	24.0639	1.28079	0.640396	−	0.768045i	$-0.278770\pi$
$353$	24.0639	1.28079	0.640396	+	0.768045i	$0.278770\pi$
$354$	−0.324476	−0.0172457
$355$	−18.7136	−0.993215
$356$	3.39605	0.179990
$357$	0.449678	0.0237995
$358$	−26.6989	−1.41108
$359$	−20.7211	−1.09362	−0.546810	−	0.837257i	$-0.684158\pi$
$359$	−20.7211	−1.09362	−0.546810	+	0.837257i	$0.684158\pi$
$360$	−18.0819	−0.953001
$361$	−3.87819	−0.204115
$362$	−11.0522	−0.580893
$363$	−0.448352	−0.0235324
$364$	−26.4659	−1.38719
$365$	29.9649	1.56844
$366$	−3.66434	−0.191538
$367$	27.1027	1.41475	0.707376	−	0.706838i	$-0.249879\pi$
$367$	27.1027	1.41475	0.707376	+	0.706838i	$0.249879\pi$
$368$	0.477800	0.0249070
$369$	30.9617	1.61180
$370$	−56.5744	−2.94116
$371$	6.28393	0.326246
$372$	−4.47517	−0.232027
$373$	−7.79840	−0.403786	−0.201893	−	0.979408i	$-0.564709\pi$
$373$	−7.79840	−0.403786	−0.201893	+	0.979408i	$0.564709\pi$
$374$	−8.63059	−0.446277
$375$	1.65904	0.0856725
$376$	−3.01648	−0.155563
$377$	5.92689	0.305250
$378$	6.16572	0.317130
$379$	29.3650	1.50838	0.754188	−	0.656658i	$-0.228030\pi$
$379$	29.3650	1.50838	0.754188	+	0.656658i	$0.228030\pi$
$380$	−26.6602	−1.36764
$381$	2.11997	0.108609
$382$	53.3163	2.72790
$383$	18.7756	0.959386	0.479693	−	0.877436i	$-0.340748\pi$
$383$	18.7756	0.959386	0.479693	+	0.877436i	$0.340748\pi$
$384$	2.61883	0.133641
$385$	25.1745	1.28301
$386$	−35.9542	−1.83002
$387$	−16.4644	−0.836931
$388$	−0.0188972	−0.000959358 0
$389$	−11.4717	−0.581641	−0.290820	−	0.956778i	$-0.593928\pi$
$389$	−11.4717	−0.581641	−0.290820	+	0.956778i	$0.593928\pi$
$390$	1.74625	0.0884247
$391$	−5.00150	−0.252937
$392$	8.92922	0.450994
$393$	−0.578266	−0.0291697
$394$	18.9780	0.956098
$395$	−7.18580	−0.361557
$396$	−36.5369	−1.83605
$397$	−36.9709	−1.85552	−0.927758	−	0.373183i	$-0.878266\pi$
$397$	−36.9709	−1.85552	−0.927758	+	0.373183i	$0.878266\pi$
$398$	59.5814	2.98654
$399$	1.74865	0.0875422
$400$	−0.0544549	−0.00272274
$401$	24.9427	1.24558	0.622788	−	0.782390i	$-0.286000\pi$
$401$	24.9427	1.24558	0.622788	+	0.782390i	$0.286000\pi$
$402$	−1.97282	−0.0983953
$403$	−24.8240	−1.23657
$404$	24.5320	1.22051
$405$	18.5643	0.922465
$406$	−16.8884	−0.838157
$407$	−44.1260	−2.18725
$408$	0.407972	0.0201976
$409$	−18.8220	−0.930689	−0.465345	−	0.885130i	$-0.654070\pi$
$409$	−18.8220	−0.930689	−0.465345	+	0.885130i	$0.654070\pi$
$410$	−50.1413	−2.47630
$411$	−1.22043	−0.0601995
$412$	−39.1663	−1.92958
$413$	3.17762	0.156361
$414$	−34.1740	−1.67956
$415$	−24.7133	−1.21313
$416$	14.1829	0.695373
$417$	2.22192	0.108808
$418$	−33.5616	−1.64155
$419$	33.5598	1.63950	0.819752	−	0.572719i	$-0.194111\pi$
$419$	33.5598	1.63950	0.819752	+	0.572719i	$0.194111\pi$
$420$	−3.08293	−0.150432
$421$	−12.5897	−0.613586	−0.306793	−	0.951776i	$-0.599256\pi$
$421$	−12.5897	−0.613586	−0.306793	+	0.951776i	$0.599256\pi$
$422$	−22.0146	−1.07165
$423$	3.11804	0.151604
$424$	5.70112	0.276871
$425$	0.570022	0.0276501
$426$	2.88495	0.139776
$427$	35.8852	1.73661
$428$	7.10532	0.343449
$429$	1.36201	0.0657586
$430$	26.6634	1.28583
$431$	25.6211	1.23412	0.617062	−	0.786914i	$-0.288323\pi$
$431$	25.6211	1.23412	0.617062	+	0.786914i	$0.288323\pi$
$432$	0.0808433	0.00388957
$433$	28.1616	1.35336	0.676680	−	0.736277i	$-0.263418\pi$
$433$	28.1616	1.35336	0.676680	+	0.736277i	$0.263418\pi$
$434$	70.7349	3.39538
$435$	0.690405	0.0331024
$436$	19.7471	0.945716
$437$	−19.4492	−0.930383
$438$	−4.61949	−0.220728
$439$	−15.5272	−0.741075	−0.370538	−	0.928817i	$-0.620827\pi$
$439$	−15.5272	−0.741075	−0.370538	+	0.928817i	$0.620827\pi$
$440$	22.8397	1.08884
$441$	−9.22985	−0.439517
$442$	5.86281	0.278865
$443$	−34.1142	−1.62081	−0.810407	−	0.585867i	$-0.800754\pi$
$443$	−34.1142	−1.62081	−0.810407	+	0.585867i	$0.800754\pi$
$444$	5.40378	0.256452
$445$	2.19439	0.104024
$446$	3.49859	0.165663
$447$	0.0510075	0.00241257
$448$	−41.0206	−1.93804
$449$	−16.1408	−0.761730	−0.380865	−	0.924631i	$-0.624374\pi$
$449$	−16.1408	−0.761730	−0.380865	+	0.924631i	$0.624374\pi$
$450$	3.89481	0.183603
$451$	−39.1085	−1.84155
$452$	−44.1836	−2.07822
$453$	2.00018	0.0939767
$454$	56.4036	2.64715
$455$	−17.1012	−0.801717
$456$	1.58647	0.0742934
$457$	−7.90782	−0.369912	−0.184956	−	0.982747i	$-0.559214\pi$
$457$	−7.90782	−0.369912	−0.184956	+	0.982747i	$0.559214\pi$
$458$	−57.6151	−2.69218
$459$	−0.846250	−0.0394996
$460$	34.2896	1.59876
$461$	−2.06056	−0.0959697	−0.0479849	−	0.998848i	$-0.515280\pi$
$461$	−2.06056	−0.0959697	−0.0479849	+	0.998848i	$0.515280\pi$
$462$	−3.88099	−0.180560
$463$	−34.9888	−1.62607	−0.813034	−	0.582217i	$-0.802185\pi$
$463$	−34.9888	−1.62607	−0.813034	+	0.582217i	$0.802185\pi$
$464$	−0.221436	−0.0102799
$465$	−2.89167	−0.134098
$466$	4.62671	0.214328
$467$	−0.518573	−0.0239967	−0.0119983	−	0.999928i	$-0.503819\pi$
$467$	−0.518573	−0.0239967	−0.0119983	+	0.999928i	$0.503819\pi$
$468$	24.8197	1.14729
$469$	19.3200	0.892116
$470$	−5.04954	−0.232918
$471$	−0.397058	−0.0182955
$472$	2.88291	0.132697
$473$	20.7965	0.956226
$474$	1.10779	0.0508824
$475$	2.21663	0.101706
$476$	−10.3506	−0.474417
$477$	−5.89307	−0.269825
$478$	51.3185	2.34725
$479$	1.44879	0.0661971	0.0330985	−	0.999452i	$-0.489462\pi$
$479$	1.44879	0.0661971	0.0330985	+	0.999452i	$0.489462\pi$
$480$	1.65212	0.0754085
$481$	29.9751	1.36674
$482$	58.6246	2.67028
$483$	−2.24907	−0.102336
$484$	10.3200	0.469092
$485$	−0.0122106	−0.000554454 0
$486$	−8.68299	−0.393869
$487$	−13.2334	−0.599661	−0.299830	−	0.953992i	$-0.596930\pi$
$487$	−13.2334	−0.599661	−0.299830	+	0.953992i	$0.596930\pi$
$488$	32.5570	1.47379
$489$	−3.21500	−0.145387
$490$	14.9474	0.675254
$491$	−6.56932	−0.296469	−0.148235	−	0.988952i	$-0.547359\pi$
$491$	−6.56932	−0.296469	−0.148235	+	0.988952i	$0.547359\pi$
$492$	4.78932	0.215919
$493$	2.31795	0.104395
$494$	22.7986	1.02576
$495$	−23.6087	−1.06113
$496$	0.927457	0.0416441
$497$	−28.2526	−1.26730
$498$	3.80988	0.170725
$499$	−7.02311	−0.314398	−0.157199	−	0.987567i	$-0.550246\pi$
$499$	−7.02311	−0.314398	−0.157199	+	0.987567i	$0.550246\pi$
$500$	−38.1873	−1.70779
$501$	2.18499	0.0976183
$502$	19.7961	0.883543
$503$	10.8587	0.484164	0.242082	−	0.970256i	$-0.422170\pi$
$503$	10.8587	0.484164	0.242082	+	0.970256i	$0.422170\pi$
$504$	−27.2990	−1.21599
$505$	15.8516	0.705387
$506$	43.1659	1.91896
$507$	0.914460	0.0406126
$508$	−48.7969	−2.16501
$509$	11.5384	0.511430	0.255715	−	0.966752i	$-0.417689\pi$
$509$	11.5384	0.511430	0.255715	+	0.966752i	$0.417689\pi$
$510$	0.682940	0.0302411
$511$	45.2392	2.00126
$512$	−1.08071	−0.0477609
$513$	−3.29079	−0.145292
$514$	0.757839	0.0334269
$515$	−25.3076	−1.11519
$516$	−2.54679	−0.112116
$517$	−3.93846	−0.173213
$518$	−85.4125	−3.75281
$519$	−1.85072	−0.0812375
$520$	−15.5151	−0.680383
$521$	−15.9910	−0.700578	−0.350289	−	0.936642i	$-0.613917\pi$
$521$	−15.9910	−0.700578	−0.350289	+	0.936642i	$0.613917\pi$
$522$	15.8379	0.693207
$523$	−22.9452	−1.00332	−0.501661	−	0.865064i	$-0.667277\pi$
$523$	−22.9452	−1.00332	−0.501661	+	0.865064i	$0.667277\pi$
$524$	13.3104	0.581466
$525$	0.256327	0.0111870
$526$	−26.2824	−1.14597
$527$	−9.70842	−0.422905
$528$	−0.0508865	−0.00221455
$529$	2.01502	0.0876096
$530$	9.54361	0.414548
$531$	−2.97997	−0.129320
$532$	−40.2500	−1.74506
$533$	26.5666	1.15073
$534$	−0.338295	−0.0146394
$535$	4.59117	0.198493
$536$	17.5282	0.757102
$537$	1.64782	0.0711089
$538$	−49.3758	−2.12874
$539$	11.6584	0.502164
$540$	5.80178	0.249669
$541$	−14.3269	−0.615964	−0.307982	−	0.951392i	$-0.599654\pi$
$541$	−14.3269	−0.615964	−0.307982	+	0.951392i	$0.599654\pi$
$542$	34.4581	1.48010
$543$	0.682130	0.0292730
$544$	5.54678	0.237816
$545$	12.7598	0.546569
$546$	2.63638	0.112827
$547$	10.4174	0.445417	0.222709	−	0.974885i	$-0.428510\pi$
$547$	10.4174	0.445417	0.222709	+	0.974885i	$0.428510\pi$
$548$	28.0916	1.20001
$549$	−33.6532	−1.43628
$550$	−4.91963	−0.209774
$551$	9.01374	0.383998
$552$	−2.04047	−0.0868484
$553$	−10.8487	−0.461333
$554$	−32.2350	−1.36953
$555$	3.49170	0.148214
$556$	−51.1434	−2.16896
$557$	19.6454	0.832402	0.416201	−	0.909273i	$-0.363361\pi$
$557$	19.6454	0.832402	0.416201	+	0.909273i	$0.363361\pi$
$558$	−66.3351	−2.80819
$559$	−14.1272	−0.597517
$560$	0.638923	0.0269994
$561$	0.532669	0.0224893
$562$	45.8124	1.93248
$563$	6.28228	0.264767	0.132383	−	0.991199i	$-0.457737\pi$
$563$	6.28228	0.264767	0.132383	+	0.991199i	$0.457737\pi$
$564$	0.482314	0.0203091
$565$	−28.5496	−1.20109
$566$	17.9064	0.752660
$567$	28.0272	1.17703
$568$	−25.6323	−1.07551
$569$	21.0300	0.881625	0.440813	−	0.897599i	$-0.354690\pi$
$569$	21.0300	0.881625	0.440813	+	0.897599i	$0.354690\pi$
$570$	2.65573	0.111236
$571$	−34.8408	−1.45804	−0.729021	−	0.684491i	$-0.760024\pi$
$571$	−34.8408	−1.45804	−0.729021	+	0.684491i	$0.760024\pi$
$572$	−31.3504	−1.31083
$573$	−3.29061	−0.137467
$574$	−75.7003	−3.15967
$575$	−2.85097	−0.118894
$576$	38.4691	1.60288
$577$	19.2606	0.801828	0.400914	−	0.916116i	$-0.368693\pi$
$577$	19.2606	0.801828	0.400914	+	0.916116i	$0.368693\pi$
$578$	2.29289	0.0953715
$579$	2.21905	0.0922205
$580$	−15.8915	−0.659860
$581$	−37.3105	−1.54790
$582$	0.00188242	7.80289e−5 0
$583$	7.44367	0.308285
$584$	41.0434	1.69839
$585$	16.0375	0.663069
$586$	−2.35479	−0.0972756
$587$	−4.19787	−0.173265	−0.0866324	−	0.996240i	$-0.527611\pi$
$587$	−4.19787	−0.173265	−0.0866324	+	0.996240i	$0.527611\pi$
$588$	−1.42772	−0.0588782
$589$	−37.7529	−1.55558
$590$	4.82596	0.198681
$591$	−1.17130	−0.0481808
$592$	−1.11991	−0.0460279
$593$	−14.6638	−0.602169	−0.301084	−	0.953597i	$-0.597349\pi$
$593$	−14.6638	−0.602169	−0.301084	+	0.953597i	$0.597349\pi$
$594$	7.30364	0.299672
$595$	−6.68811	−0.274186
$596$	−1.17408	−0.0480920
$597$	−3.67729	−0.150501
$598$	−29.3229	−1.19910
$599$	−30.9476	−1.26448	−0.632241	−	0.774771i	$-0.717865\pi$
$599$	−30.9476	−1.26448	−0.632241	+	0.774771i	$0.717865\pi$
$600$	0.232553	0.00949394
$601$	36.9151	1.50580	0.752900	−	0.658135i	$-0.228654\pi$
$601$	36.9151	1.50580	0.752900	+	0.658135i	$0.228654\pi$
$602$	40.2548	1.64066
$603$	−18.1183	−0.737835
$604$	−46.0396	−1.87332
$605$	6.66838	0.271108
$606$	−2.44374	−0.0992700
$607$	−13.3283	−0.540978	−0.270489	−	0.962723i	$-0.587185\pi$
$607$	−13.3283	−0.540978	−0.270489	+	0.962723i	$0.587185\pi$
$608$	21.5696	0.874764
$609$	1.04233	0.0422373
$610$	54.5000	2.20664
$611$	2.67542	0.108236
$612$	9.70675	0.392372
$613$	−9.10033	−0.367559	−0.183780	−	0.982967i	$-0.558833\pi$
$613$	−9.10033	−0.367559	−0.183780	+	0.982967i	$0.558833\pi$
$614$	2.85216	0.115104
$615$	3.09466	0.124789
$616$	34.4820	1.38932
$617$	−8.23353	−0.331469	−0.165735	−	0.986170i	$-0.553000\pi$
$617$	−8.23353	−0.331469	−0.165735	+	0.986170i	$0.553000\pi$
$618$	3.90151	0.156942
$619$	−15.6390	−0.628584	−0.314292	−	0.949326i	$-0.601767\pi$
$619$	−15.6390	−0.628584	−0.314292	+	0.949326i	$0.601767\pi$
$620$	66.5596	2.67310
$621$	4.23252	0.169845
$622$	29.0904	1.16642
$623$	3.31295	0.132731
$624$	0.0345675	0.00138381
$625$	−21.8250	−0.872999
$626$	56.8678	2.27290
$627$	2.07138	0.0827229
$628$	9.13937	0.364701
$629$	11.7229	0.467424
$630$	−45.6981	−1.82066
$631$	30.2995	1.20620	0.603102	−	0.797664i	$-0.293931\pi$
$631$	30.2995	1.20620	0.603102	+	0.797664i	$0.293931\pi$
$632$	−9.84251	−0.391514
$633$	1.35871	0.0540040
$634$	24.7195	0.981738
$635$	−31.5305	−1.25125
$636$	−0.911570	−0.0361461
$637$	−7.91964	−0.313788
$638$	−20.0053	−0.792016
$639$	26.4953	1.04814
$640$	−38.9500	−1.53964
$641$	−38.0817	−1.50414	−0.752069	−	0.659085i	$-0.770944\pi$
$641$	−38.0817	−1.50414	−0.752069	+	0.659085i	$0.770944\pi$
$642$	−0.707790	−0.0279342
$643$	27.1076	1.06902	0.534510	−	0.845162i	$-0.320496\pi$
$643$	27.1076	1.06902	0.534510	+	0.845162i	$0.320496\pi$
$644$	51.7684	2.03996
$645$	−1.64563	−0.0647968
$646$	8.91629	0.350807
$647$	30.2973	1.19111	0.595556	−	0.803314i	$-0.296932\pi$
$647$	30.2973	1.19111	0.595556	+	0.803314i	$0.296932\pi$
$648$	25.4278	0.998896
$649$	3.76407	0.147753
$650$	3.34193	0.131081
$651$	−4.36567	−0.171104
$652$	74.0019	2.89814
$653$	16.4677	0.644432	0.322216	−	0.946666i	$-0.395572\pi$
$653$	16.4677	0.644432	0.322216	+	0.946666i	$0.395572\pi$
$654$	−1.96709	−0.0769194
$655$	8.60060	0.336053
$656$	−0.992562	−0.0387531
$657$	−42.4253	−1.65517
$658$	−7.62349	−0.297195
$659$	40.0411	1.55978	0.779890	−	0.625916i	$-0.215275\pi$
$659$	40.0411	1.55978	0.779890	+	0.625916i	$0.215275\pi$
$660$	−3.65191	−0.142150
$661$	25.2907	0.983693	0.491846	−	0.870682i	$-0.336322\pi$
$661$	25.2907	0.983693	0.491846	+	0.870682i	$0.336322\pi$
$662$	50.0154	1.94390
$663$	−0.361845	−0.0140529
$664$	−33.8501	−1.31364
$665$	−26.0079	−1.00854
$666$	80.0998	3.10381
$667$	−11.5932	−0.448891
$668$	−50.2935	−1.94591
$669$	−0.215929	−0.00834828
$670$	29.3419	1.13358
$671$	42.5081	1.64101
$672$	2.49427	0.0962184
$673$	3.17962	0.122565	0.0612826	−	0.998120i	$-0.480481\pi$
$673$	3.17962	0.122565	0.0612826	+	0.998120i	$0.480481\pi$
$674$	−22.7022	−0.874457
$675$	−0.482381	−0.0185669
$676$	−21.0488	−0.809568
$677$	−1.25818	−0.0483557	−0.0241779	−	0.999708i	$-0.507697\pi$
$677$	−1.25818	−0.0483557	−0.0241779	+	0.999708i	$0.507697\pi$
$678$	4.40131	0.169031
$679$	−0.0184348	−0.000707461 0
$680$	−6.06781	−0.232690
$681$	−3.48116	−0.133398
$682$	83.7894	3.20846
$683$	1.11448	0.0426445	0.0213222	−	0.999773i	$-0.493212\pi$
$683$	1.11448	0.0426445	0.0213222	+	0.999773i	$0.493212\pi$
$684$	37.7464	1.44327
$685$	18.1516	0.693537
$686$	−28.4349	−1.08565
$687$	3.55593	0.135667
$688$	0.527811	0.0201226
$689$	−5.05653	−0.192638
$690$	−3.41573	−0.130035
$691$	−14.3826	−0.547141	−0.273570	−	0.961852i	$-0.588205\pi$
$691$	−14.3826	−0.547141	−0.273570	+	0.961852i	$0.588205\pi$
$692$	42.5993	1.61938
$693$	−35.6429	−1.35396
$694$	50.1887	1.90514
$695$	−33.0468	−1.25354
$696$	0.945658	0.0358451
$697$	10.3899	0.393547
$698$	77.0628	2.91687
$699$	−0.285554	−0.0108007
$700$	−5.90005	−0.223001
$701$	−0.0861316	−0.00325315	−0.00162657	−	0.999999i	$-0.500518\pi$
$701$	−0.0861316	−0.00325315	−0.00162657	+	0.999999i	$0.500518\pi$
$702$	−4.96140	−0.187256
$703$	45.5867	1.71934
$704$	−48.5912	−1.83135
$705$	0.311651	0.0117375
$706$	55.1758	2.07657
$707$	23.9318	0.900047
$708$	−0.460958	−0.0173238
$709$	18.6007	0.698566	0.349283	−	0.937017i	$-0.386425\pi$
$709$	18.6007	0.698566	0.349283	+	0.937017i	$0.386425\pi$
$710$	−42.9082	−1.61032
$711$	10.1739	0.381551
$712$	3.00569	0.112643
$713$	48.5567	1.81846
$714$	1.03106	0.0385865
$715$	−20.2573	−0.757581
$716$	−37.9291	−1.41748
$717$	−3.16731	−0.118285
$718$	−47.5112	−1.77310
$719$	20.9366	0.780803	0.390401	−	0.920645i	$-0.372336\pi$
$719$	20.9366	0.780803	0.390401	+	0.920645i	$0.372336\pi$
$720$	−0.599182	−0.0223302
$721$	−38.2079	−1.42294
$722$	−8.89225	−0.330935
$723$	−3.61824	−0.134564
$724$	−15.7011	−0.583526
$725$	1.32128	0.0490711
$726$	−1.02802	−0.0381534
$727$	41.0022	1.52069	0.760344	−	0.649521i	$-0.225030\pi$
$727$	41.0022	1.52069	0.760344	+	0.649521i	$0.225030\pi$
$728$	−23.4238	−0.868143
$729$	−25.9246	−0.960170
$730$	68.7061	2.54293
$731$	−5.52501	−0.204350
$732$	−5.20564	−0.192406
$733$	10.3603	0.382668	0.191334	−	0.981525i	$-0.438719\pi$
$733$	10.3603	0.382668	0.191334	+	0.981525i	$0.438719\pi$
$734$	62.1435	2.29376
$735$	−0.922534	−0.0340282
$736$	−27.7422	−1.02259
$737$	22.8857	0.843004
$738$	70.9917	2.61324
$739$	−28.7907	−1.05908	−0.529542	−	0.848284i	$-0.677636\pi$
$739$	−28.7907	−1.05908	−0.529542	+	0.848284i	$0.677636\pi$
$740$	−80.3709	−2.95449
$741$	−1.40710	−0.0516911
$742$	14.4083	0.528947
$743$	−43.1251	−1.58211	−0.791054	−	0.611746i	$-0.790467\pi$
$743$	−43.1251	−1.58211	−0.791054	+	0.611746i	$0.790467\pi$
$744$	−3.96077	−0.145209
$745$	−0.758639	−0.0277944
$746$	−17.8808	−0.654664
$747$	34.9898	1.28021
$748$	−12.2608	−0.448300
$749$	6.93146	0.253270
$750$	3.80399	0.138902
$751$	−23.7642	−0.867167	−0.433584	−	0.901113i	$-0.642751\pi$
$751$	−23.7642	−0.867167	−0.433584	+	0.901113i	$0.642751\pi$
$752$	−0.0999572	−0.00364506
$753$	−1.22179	−0.0445245
$754$	13.5897	0.494907
$755$	−29.7489	−1.08267
$756$	8.75917	0.318568
$757$	5.69363	0.206939	0.103469	−	0.994633i	$-0.467006\pi$
$757$	5.69363	0.206939	0.103469	+	0.994633i	$0.467006\pi$
$758$	67.3305	2.44556
$759$	−2.66415	−0.0967024
$760$	−23.5958	−0.855908
$761$	−17.9821	−0.651850	−0.325925	−	0.945396i	$-0.605676\pi$
$761$	−17.9821	−0.651850	−0.325925	+	0.945396i	$0.605676\pi$
$762$	4.86085	0.176090
$763$	19.2639	0.697401
$764$	75.7423	2.74026
$765$	6.27210	0.226768
$766$	43.0502	1.55547
$767$	−2.55696	−0.0923264
$768$	2.35100	0.0848346
$769$	−12.8906	−0.464848	−0.232424	−	0.972615i	$-0.574666\pi$
$769$	−12.8906	−0.464848	−0.232424	+	0.972615i	$0.574666\pi$
$770$	57.7223	2.08017
$771$	−0.0467729	−0.00168448
$772$	−51.0774	−1.83832
$773$	−11.2110	−0.403232	−0.201616	−	0.979465i	$-0.564619\pi$
$773$	−11.2110	−0.403232	−0.201616	+	0.979465i	$0.564619\pi$
$774$	−37.7509	−1.35693
$775$	−5.53401	−0.198788
$776$	−0.0167250	−0.000600393 0
$777$	5.27155	0.189116
$778$	−26.3034	−0.943023
$779$	40.4031	1.44759
$780$	2.48076	0.0888255
$781$	−33.4668	−1.19754
$782$	−11.4679	−0.410090
$783$	−1.96156	−0.0701005
$784$	0.295888	0.0105674
$785$	5.90549	0.210776
$786$	−1.32590	−0.0472932
$787$	−1.83100	−0.0652682	−0.0326341	−	0.999467i	$-0.510390\pi$
$787$	−1.83100	−0.0652682	−0.0326341	+	0.999467i	$0.510390\pi$
$788$	26.9606	0.960432
$789$	1.62211	0.0577488
$790$	−16.4762	−0.586198
$791$	−43.1025	−1.53255
$792$	−32.3372	−1.14905
$793$	−28.8760	−1.02542
$794$	−84.7700	−3.00838
$795$	−0.589019	−0.0208904
$796$	84.6427	3.00008
$797$	53.9508	1.91104	0.955518	−	0.294931i	$-0.0952968\pi$
$797$	53.9508	1.91104	0.955518	+	0.294931i	$0.0952968\pi$
$798$	4.00946	0.141933
$799$	1.04633	0.0370165
$800$	3.16179	0.111786
$801$	−3.10689	−0.109776
$802$	57.1907	2.01947
$803$	53.5883	1.89109
$804$	−2.80263	−0.0988413
$805$	33.4506	1.17898
$806$	−56.9186	−2.00487
$807$	3.04741	0.107274
$808$	21.7122	0.763832
$809$	−45.5292	−1.60072	−0.800361	−	0.599518i	$-0.795359\pi$
$809$	−45.5292	−1.60072	−0.800361	+	0.599518i	$0.795359\pi$
$810$	42.5657	1.49561
$811$	−19.2011	−0.674243	−0.337122	−	0.941461i	$-0.609453\pi$
$811$	−19.2011	−0.674243	−0.337122	+	0.941461i	$0.609453\pi$
$812$	−23.9921	−0.841956
$813$	−2.12671	−0.0745870
$814$	−101.176	−3.54621
$815$	47.8170	1.67496
$816$	0.0135190	0.000473260 0
$817$	−21.4850	−0.751664
$818$	−43.1568	−1.50894
$819$	24.2124	0.846051
$820$	−71.2320	−2.48753
$821$	−14.2253	−0.496466	−0.248233	−	0.968700i	$-0.579850\pi$
$821$	−14.2253	−0.496466	−0.248233	+	0.968700i	$0.579850\pi$
$822$	−2.79831	−0.0976024
$823$	−50.9435	−1.77578	−0.887890	−	0.460056i	$-0.847829\pi$
$823$	−50.9435	−1.77578	−0.887890	+	0.460056i	$0.847829\pi$
$824$	−34.6643	−1.20759
$825$	0.303633	0.0105711
$826$	7.28593	0.253510
$827$	24.8413	0.863818	0.431909	−	0.901917i	$-0.357840\pi$
$827$	24.8413	0.863818	0.431909	+	0.901917i	$0.357840\pi$
$828$	−48.5483	−1.68717
$829$	22.2218	0.771796	0.385898	−	0.922542i	$-0.373892\pi$
$829$	22.2218	0.771796	0.385898	+	0.922542i	$0.373892\pi$
$830$	−56.6647	−1.96686
$831$	1.98950	0.0690151
$832$	33.0083	1.14436
$833$	−3.09729	−0.107315
$834$	5.09460	0.176412
$835$	−32.4976	−1.12463
$836$	−47.6784	−1.64899
$837$	8.21575	0.283978
$838$	76.9488	2.65815
$839$	−33.7292	−1.16446	−0.582230	−	0.813024i	$-0.697820\pi$
$839$	−33.7292	−1.16446	−0.582230	+	0.813024i	$0.697820\pi$
$840$	−2.72856	−0.0941444
$841$	−23.6271	−0.814728
$842$	−28.8668	−0.994817
$843$	−2.82748	−0.0973838
$844$	−31.2745	−1.07651
$845$	−13.6008	−0.467883
$846$	7.14930	0.245798
$847$	10.0675	0.345924
$848$	0.188919	0.00648749
$849$	−1.10516	−0.0379289
$850$	1.30700	0.0448296
$851$	−58.6323	−2.00989
$852$	4.09843	0.140410
$853$	−25.9067	−0.887027	−0.443513	−	0.896268i	$-0.646268\pi$
$853$	−25.9067	−0.887027	−0.443513	+	0.896268i	$0.646268\pi$
$854$	82.2808	2.81559
$855$	24.3902	0.834127
$856$	6.28859	0.214940
$857$	2.55304	0.0872100	0.0436050	−	0.999049i	$-0.486116\pi$
$857$	2.55304	0.0872100	0.0436050	+	0.999049i	$0.486116\pi$
$858$	3.12294	0.106615
$859$	−1.53907	−0.0525125	−0.0262562	−	0.999655i	$-0.508359\pi$
$859$	−1.53907	−0.0525125	−0.0262562	+	0.999655i	$0.508359\pi$
$860$	37.8787	1.29165
$861$	4.67212	0.159226
$862$	58.7463	2.00091
$863$	−14.8200	−0.504477	−0.252238	−	0.967665i	$-0.581167\pi$
$863$	−14.8200	−0.504477	−0.252238	+	0.967665i	$0.581167\pi$
$864$	−4.69396	−0.159692
$865$	27.5259	0.935909
$866$	64.5714	2.19422
$867$	−0.141514	−0.00480607
$868$	100.488	3.41077
$869$	−12.8509	−0.435936
$870$	1.58302	0.0536694
$871$	−15.5464	−0.526768
$872$	17.4773	0.591855
$873$	0.0172881	0.000585114 0
$874$	−44.5949	−1.50844
$875$	−37.2529	−1.25938
$876$	−6.56256	−0.221728
$877$	−53.0194	−1.79034	−0.895169	−	0.445727i	$-0.852945\pi$
$877$	−53.0194	−1.79034	−0.895169	+	0.445727i	$0.852945\pi$
$878$	−35.6022	−1.20152
$879$	0.145335	0.00490202
$880$	0.756840	0.0255131
$881$	6.96854	0.234776	0.117388	−	0.993086i	$-0.462548\pi$
$881$	6.96854	0.234776	0.117388	+	0.993086i	$0.462548\pi$
$882$	−21.1630	−0.712595
$883$	28.7588	0.967810	0.483905	−	0.875120i	$-0.339218\pi$
$883$	28.7588	0.967810	0.483905	+	0.875120i	$0.339218\pi$
$884$	8.32885	0.280129
$885$	−0.297852	−0.0100122
$886$	−78.2200	−2.62785
$887$	−42.4593	−1.42564	−0.712822	−	0.701345i	$-0.752583\pi$
$887$	−42.4593	−1.42564	−0.712822	+	0.701345i	$0.752583\pi$
$888$	4.78264	0.160495
$889$	−47.6028	−1.59655
$890$	5.03149	0.168656
$891$	33.1998	1.11223
$892$	4.97018	0.166414
$893$	4.06884	0.136159
$894$	0.116954	0.00391154
$895$	−24.5082	−0.819220
$896$	−58.8044	−1.96452
$897$	1.80977	0.0604264
$898$	−37.0090	−1.23500
$899$	−22.5036	−0.750537
$900$	5.53306	0.184435
$901$	−1.97756	−0.0658820
$902$	−89.6712	−2.98573
$903$	−2.48448	−0.0826782
$904$	−39.1049	−1.30061
$905$	−10.1454	−0.337244
$906$	4.58619	0.152366
$907$	−26.5710	−0.882274	−0.441137	−	0.897440i	$-0.645425\pi$
$907$	−26.5710	−0.882274	−0.441137	+	0.897440i	$0.645425\pi$
$908$	80.1282	2.65915
$909$	−22.4432	−0.744394
$910$	−39.2111	−1.29984
$911$	24.6041	0.815171	0.407585	−	0.913167i	$-0.366371\pi$
$911$	24.6041	0.815171	0.407585	+	0.913167i	$0.366371\pi$
$912$	0.0525710	0.00174080
$913$	−44.1964	−1.46269
$914$	−18.1317	−0.599745
$915$	−3.36367	−0.111200
$916$	−81.8494	−2.70438
$917$	12.9847	0.428791
$918$	−1.94036	−0.0640413
$919$	−21.6020	−0.712585	−0.356293	−	0.934374i	$-0.615959\pi$
$919$	−21.6020	−0.712585	−0.356293	+	0.934374i	$0.615959\pi$
$920$	30.3482	1.00055
$921$	−0.176032	−0.00580045
$922$	−4.72462	−0.155597
$923$	22.7342	0.748306
$924$	−5.51343	−0.181378
$925$	6.68233	0.219714
$926$	−80.2253	−2.63637
$927$	35.8313	1.17686
$928$	12.8571	0.422056
$929$	38.5202	1.26381	0.631903	−	0.775047i	$-0.282274\pi$
$929$	38.5202	1.26381	0.631903	+	0.775047i	$0.282274\pi$
$930$	−6.63027	−0.217415
$931$	−12.0444	−0.394738
$932$	6.57281	0.215299
$933$	−1.79542	−0.0587795
$934$	−1.18903	−0.0389062
$935$	−7.92244	−0.259091
$936$	21.9668	0.718008
$937$	−8.11940	−0.265249	−0.132625	−	0.991166i	$-0.542340\pi$
$937$	−8.11940	−0.265249	−0.132625	+	0.991166i	$0.542340\pi$
$938$	44.2986	1.44640
$939$	−3.50981	−0.114538
$940$	−7.17350	−0.233974
$941$	50.0284	1.63088	0.815440	−	0.578841i	$-0.196495\pi$
$941$	50.0284	1.63088	0.815440	+	0.578841i	$0.196495\pi$
$942$	−0.910410	−0.0296628
$943$	−51.9652	−1.69222
$944$	0.0955312	0.00310928
$945$	5.65981	0.184114
$946$	47.6841	1.55034
$947$	39.8060	1.29352	0.646760	−	0.762694i	$-0.276124\pi$
$947$	39.8060	1.29352	0.646760	+	0.762694i	$0.276124\pi$
$948$	1.57375	0.0511130
$949$	−36.4029	−1.18169
$950$	5.08248	0.164898
$951$	−1.52566	−0.0494728
$952$	−9.16081	−0.296903
$953$	2.64703	0.0857459	0.0428729	−	0.999081i	$-0.486349\pi$
$953$	2.64703	0.0857459	0.0428729	+	0.999081i	$0.486349\pi$
$954$	−13.5121	−0.437472
$955$	48.9416	1.58371
$956$	72.9042	2.35789
$957$	1.23470	0.0399121
$958$	3.32192	0.107326
$959$	27.4042	0.884927
$960$	3.84503	0.124098
$961$	63.2534	2.04043
$962$	68.7294	2.21592
$963$	−6.50032	−0.209470
$964$	83.2835	2.68238
$965$	−33.0041	−1.06244
$966$	−5.15685	−0.165919
$967$	−35.9064	−1.15467	−0.577337	−	0.816506i	$-0.695908\pi$
$967$	−35.9064	−1.15467	−0.577337	+	0.816506i	$0.695908\pi$
$968$	9.13379	0.293571
$969$	−0.550302	−0.0176783
$970$	−0.0279975	−0.000898944 0
$971$	5.76525	0.185016	0.0925079	−	0.995712i	$-0.470512\pi$
$971$	5.76525	0.185016	0.0925079	+	0.995712i	$0.470512\pi$
$972$	−12.3353	−0.395654
$973$	−49.8920	−1.59946
$974$	−30.3426	−0.972240
$975$	−0.206260	−0.00660560
$976$	1.07884	0.0345330
$977$	54.1964	1.73390	0.866949	−	0.498397i	$-0.166078\pi$
$977$	54.1964	1.73390	0.866949	+	0.498397i	$0.166078\pi$
$978$	−7.37163	−0.235719
$979$	3.92438	0.125424
$980$	21.2346	0.678315
$981$	−18.0657	−0.576794
$982$	−15.0627	−0.480670
$983$	−8.77885	−0.280002	−0.140001	−	0.990151i	$-0.544711\pi$
$983$	−8.77885	−0.280002	−0.140001	+	0.990151i	$0.544711\pi$
$984$	4.23880	0.135128
$985$	17.4208	0.555074
$986$	5.31479	0.169257
$987$	0.470512	0.0149766
$988$	32.3882	1.03041
$989$	27.6333	0.878689
$990$	−54.1320	−1.72043
$991$	−12.9953	−0.412808	−0.206404	−	0.978467i	$-0.566176\pi$
$991$	−12.9953	−0.412808	−0.206404	+	0.978467i	$0.566176\pi$
$992$	−53.8505	−1.70975
$993$	−3.08688	−0.0979593
$994$	−64.7801	−2.05470
$995$	54.6926	1.73387
$996$	5.41240	0.171499
$997$	−0.204148	−0.00646542	−0.00323271	−	0.999995i	$-0.501029\pi$
$997$	−0.204148	−0.00646542	−0.00323271	+	0.999995i	$0.501029\pi$
$998$	−16.1032	−0.509738
$999$	−9.92054	−0.313872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.19	✓	22
3.2	odd	2		9027.2.a.s.1.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.19	✓	22	1.1	even	1	trivial
9027.2.a.s.1.4		22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.29289 q^{2} -0.141514 q^{3} +3.25733 q^{4} +2.10475 q^{5} -0.324476 q^{6} +3.17762 q^{7} +2.88291 q^{8} -2.97997 q^{9} +O(q^{10})\)	\(q+2.29289 q^{2} -0.141514 q^{3} +3.25733 q^{4} +2.10475 q^{5} -0.324476 q^{6} +3.17762 q^{7} +2.88291 q^{8} -2.97997 q^{9} +4.82596 q^{10} +3.76407 q^{11} -0.460958 q^{12} -2.55696 q^{13} +7.28593 q^{14} -0.297852 q^{15} +0.0955312 q^{16} -1.00000 q^{17} -6.83274 q^{18} -3.88868 q^{19} +6.85587 q^{20} -0.449678 q^{21} +8.63059 q^{22} +5.00150 q^{23} -0.407972 q^{24} -0.570022 q^{25} -5.86281 q^{26} +0.846250 q^{27} +10.3506 q^{28} -2.31795 q^{29} -0.682940 q^{30} +9.70842 q^{31} -5.54678 q^{32} -0.532669 q^{33} -2.29289 q^{34} +6.68811 q^{35} -9.70675 q^{36} -11.7229 q^{37} -8.91629 q^{38} +0.361845 q^{39} +6.06781 q^{40} -10.3899 q^{41} -1.03106 q^{42} +5.52501 q^{43} +12.2608 q^{44} -6.27210 q^{45} +11.4679 q^{46} -1.04633 q^{47} -0.0135190 q^{48} +3.09729 q^{49} -1.30700 q^{50} +0.141514 q^{51} -8.32885 q^{52} +1.97756 q^{53} +1.94036 q^{54} +7.92244 q^{55} +9.16081 q^{56} +0.550302 q^{57} -5.31479 q^{58} +1.00000 q^{59} -0.970201 q^{60} +11.2931 q^{61} +22.2603 q^{62} -9.46923 q^{63} -12.9092 q^{64} -5.38176 q^{65} -1.22135 q^{66} +6.08003 q^{67} -3.25733 q^{68} -0.707783 q^{69} +15.3351 q^{70} -8.89112 q^{71} -8.59100 q^{72} +14.2368 q^{73} -26.8794 q^{74} +0.0806661 q^{75} -12.6667 q^{76} +11.9608 q^{77} +0.829670 q^{78} -3.41409 q^{79} +0.201069 q^{80} +8.82017 q^{81} -23.8229 q^{82} -11.7416 q^{83} -1.46475 q^{84} -2.10475 q^{85} +12.6682 q^{86} +0.328022 q^{87} +10.8515 q^{88} +1.04259 q^{89} -14.3812 q^{90} -8.12505 q^{91} +16.2915 q^{92} -1.37388 q^{93} -2.39912 q^{94} -8.18470 q^{95} +0.784947 q^{96} -0.00580143 q^{97} +7.10174 q^{98} -11.2168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

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