LMFDB - Embedded newform 2001.4.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,4,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2001.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:	$118.062821921$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.166273 q^{2} -3.00000 q^{3} -7.97235 q^{4} -4.23027 q^{5} -0.498819 q^{6} -0.0898903 q^{7} -2.65577 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.166273 q^{2} -3.00000 q^{3} -7.97235 q^{4} -4.23027 q^{5} -0.498819 q^{6} -0.0898903 q^{7} -2.65577 q^{8} +9.00000 q^{9} -0.703379 q^{10} -19.2581 q^{11} +23.9171 q^{12} +32.8656 q^{13} -0.0149463 q^{14} +12.6908 q^{15} +63.3372 q^{16} +68.3900 q^{17} +1.49646 q^{18} +116.002 q^{19} +33.7252 q^{20} +0.269671 q^{21} -3.20211 q^{22} -23.0000 q^{23} +7.96731 q^{24} -107.105 q^{25} +5.46466 q^{26} -27.0000 q^{27} +0.716637 q^{28} -29.0000 q^{29} +2.11014 q^{30} -83.5866 q^{31} +31.7774 q^{32} +57.7744 q^{33} +11.3714 q^{34} +0.380260 q^{35} -71.7512 q^{36} +73.9793 q^{37} +19.2880 q^{38} -98.5969 q^{39} +11.2346 q^{40} -418.281 q^{41} +0.0448390 q^{42} -412.595 q^{43} +153.533 q^{44} -38.0724 q^{45} -3.82428 q^{46} +160.936 q^{47} -190.012 q^{48} -342.992 q^{49} -17.8086 q^{50} -205.170 q^{51} -262.016 q^{52} +510.257 q^{53} -4.48937 q^{54} +81.4671 q^{55} +0.238728 q^{56} -348.007 q^{57} -4.82191 q^{58} -330.059 q^{59} -101.176 q^{60} -396.328 q^{61} -13.8982 q^{62} -0.809013 q^{63} -501.414 q^{64} -139.030 q^{65} +9.60632 q^{66} +49.9098 q^{67} -545.229 q^{68} +69.0000 q^{69} +0.0632269 q^{70} +321.535 q^{71} -23.9019 q^{72} +404.214 q^{73} +12.3007 q^{74} +321.315 q^{75} -924.810 q^{76} +1.73112 q^{77} -16.3940 q^{78} +91.8836 q^{79} -267.934 q^{80} +81.0000 q^{81} -69.5489 q^{82} +29.0774 q^{83} -2.14991 q^{84} -289.308 q^{85} -68.6034 q^{86} +87.0000 q^{87} +51.1452 q^{88} +210.458 q^{89} -6.33041 q^{90} -2.95430 q^{91} +183.364 q^{92} +250.760 q^{93} +26.7593 q^{94} -490.720 q^{95} -95.3323 q^{96} +1769.23 q^{97} -57.0303 q^{98} -173.323 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9} - 136 q^{10} + 109 q^{11} - 438 q^{12} - 269 q^{13} + 121 q^{14} - 45 q^{15} + 390 q^{16} + 180 q^{17} + 36 q^{18} + 117 q^{19} + 287 q^{20} - 24 q^{21} - 128 q^{22} - 851 q^{23} - 9 q^{24} + 490 q^{25} + 677 q^{26} - 999 q^{27} + 775 q^{28} - 1073 q^{29} + 408 q^{30} - 194 q^{31} + 668 q^{32} - 327 q^{33} + 972 q^{34} - 309 q^{35} + 1314 q^{36} - 565 q^{37} + 725 q^{38} + 807 q^{39} + 263 q^{40} + 521 q^{41} - 363 q^{42} - 61 q^{43} + 2242 q^{44} + 135 q^{45} - 92 q^{46} + 1142 q^{47} - 1170 q^{48} + 919 q^{49} + 1833 q^{50} - 540 q^{51} - 10 q^{52} - 120 q^{53} - 108 q^{54} - 996 q^{55} + 1707 q^{56} - 351 q^{57} - 116 q^{58} + 1073 q^{59} - 861 q^{60} - 428 q^{61} + 174 q^{62} + 72 q^{63} + 1479 q^{64} + 1410 q^{65} + 384 q^{66} + 175 q^{67} + 1483 q^{68} + 2553 q^{69} + 675 q^{70} + 2236 q^{71} + 27 q^{72} - 1058 q^{73} - 695 q^{74} - 1470 q^{75} + 1345 q^{76} - 1547 q^{77} - 2031 q^{78} + 1972 q^{79} - 2017 q^{80} + 2997 q^{81} + 2429 q^{82} - 832 q^{83} - 2325 q^{84} + 2299 q^{85} + 1527 q^{86} + 3219 q^{87} + 2579 q^{88} + 2817 q^{89} - 1224 q^{90} + 3175 q^{91} - 3358 q^{92} + 582 q^{93} + 1900 q^{94} + 8017 q^{95} - 2004 q^{96} + 912 q^{97} - 2565 q^{98} + 981 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9 - 136 * q^10 + 109 * q^11 - 438 * q^12 - 269 * q^13 + 121 * q^14 - 45 * q^15 + 390 * q^16 + 180 * q^17 + 36 * q^18 + 117 * q^19 + 287 * q^20 - 24 * q^21 - 128 * q^22 - 851 * q^23 - 9 * q^24 + 490 * q^25 + 677 * q^26 - 999 * q^27 + 775 * q^28 - 1073 * q^29 + 408 * q^30 - 194 * q^31 + 668 * q^32 - 327 * q^33 + 972 * q^34 - 309 * q^35 + 1314 * q^36 - 565 * q^37 + 725 * q^38 + 807 * q^39 + 263 * q^40 + 521 * q^41 - 363 * q^42 - 61 * q^43 + 2242 * q^44 + 135 * q^45 - 92 * q^46 + 1142 * q^47 - 1170 * q^48 + 919 * q^49 + 1833 * q^50 - 540 * q^51 - 10 * q^52 - 120 * q^53 - 108 * q^54 - 996 * q^55 + 1707 * q^56 - 351 * q^57 - 116 * q^58 + 1073 * q^59 - 861 * q^60 - 428 * q^61 + 174 * q^62 + 72 * q^63 + 1479 * q^64 + 1410 * q^65 + 384 * q^66 + 175 * q^67 + 1483 * q^68 + 2553 * q^69 + 675 * q^70 + 2236 * q^71 + 27 * q^72 - 1058 * q^73 - 695 * q^74 - 1470 * q^75 + 1345 * q^76 - 1547 * q^77 - 2031 * q^78 + 1972 * q^79 - 2017 * q^80 + 2997 * q^81 + 2429 * q^82 - 832 * q^83 - 2325 * q^84 + 2299 * q^85 + 1527 * q^86 + 3219 * q^87 + 2579 * q^88 + 2817 * q^89 - 1224 * q^90 + 3175 * q^91 - 3358 * q^92 + 582 * q^93 + 1900 * q^94 + 8017 * q^95 - 2004 * q^96 + 912 * q^97 - 2565 * q^98 + 981 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.166273	0.0587863	0.0293932	−	0.999568i	$-0.490643\pi$
$2$	0.166273	0.0587863	0.0293932	+	0.999568i	$0.490643\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.97235	−0.996544
$5$	−4.23027	−0.378367	−0.189183	−	0.981942i	$-0.560584\pi$
$5$	−4.23027	−0.378367	−0.189183	+	0.981942i	$0.560584\pi$
$6$	−0.498819	−0.0339403
$7$	−0.0898903	−0.00485362	−0.00242681	−	0.999997i	$-0.500772\pi$
$7$	−0.0898903	−0.00485362	−0.00242681	+	0.999997i	$0.500772\pi$
$8$	−2.65577	−0.117370
$9$	9.00000	0.333333
$10$	−0.703379	−0.0222428
$11$	−19.2581	−0.527868	−0.263934	−	0.964541i	$-0.585020\pi$
$11$	−19.2581	−0.527868	−0.263934	+	0.964541i	$0.585020\pi$
$12$	23.9171	0.575355
$13$	32.8656	0.701176	0.350588	−	0.936530i	$-0.385982\pi$
$13$	32.8656	0.701176	0.350588	+	0.936530i	$0.385982\pi$
$14$	−0.0149463	−0.000285327 0
$15$	12.6908	0.218450
$16$	63.3372	0.989644
$17$	68.3900	0.975706	0.487853	−	0.872926i	$-0.337780\pi$
$17$	68.3900	0.975706	0.487853	+	0.872926i	$0.337780\pi$
$18$	1.49646	0.0195954
$19$	116.002	1.40067	0.700335	−	0.713814i	$-0.253034\pi$
$19$	116.002	1.40067	0.700335	+	0.713814i	$0.253034\pi$
$20$	33.7252	0.377059
$21$	0.269671	0.00280224
$22$	−3.20211	−0.0310314
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	7.96731	0.0677633
$25$	−107.105	−0.856839
$26$	5.46466	0.0412196
$27$	−27.0000	−0.192450
$28$	0.716637	0.00483685
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	2.11014	0.0128419
$31$	−83.5866	−0.484277	−0.242139	−	0.970242i	$-0.577849\pi$
$31$	−83.5866	−0.484277	−0.242139	+	0.970242i	$0.577849\pi$
$32$	31.7774	0.175547
$33$	57.7744	0.304765
$34$	11.3714	0.0573582
$35$	0.380260	0.00183645
$36$	−71.7512	−0.332181
$37$	73.9793	0.328706	0.164353	−	0.986402i	$-0.447446\pi$
$37$	73.9793	0.328706	0.164353	+	0.986402i	$0.447446\pi$
$38$	19.2880	0.0823403
$39$	−98.5969	−0.404824
$40$	11.2346	0.0444087
$41$	−418.281	−1.59328	−0.796641	−	0.604452i	$-0.793392\pi$
$41$	−418.281	−1.59328	−0.796641	+	0.604452i	$0.793392\pi$
$42$	0.0448390	0.000164733 0
$43$	−412.595	−1.46326	−0.731630	−	0.681702i	$-0.761240\pi$
$43$	−412.595	−1.46326	−0.731630	+	0.681702i	$0.761240\pi$
$44$	153.533	0.526044
$45$	−38.0724	−0.126122
$46$	−3.82428	−0.0122578
$47$	160.936	0.499467	0.249733	−	0.968315i	$-0.419657\pi$
$47$	160.936	0.499467	0.249733	+	0.968315i	$0.419657\pi$
$48$	−190.012	−0.571371
$49$	−342.992	−0.999976
$50$	−17.8086	−0.0503704
$51$	−205.170	−0.563324
$52$	−262.016	−0.698753
$53$	510.257	1.32244	0.661219	−	0.750193i	$-0.270039\pi$
$53$	510.257	1.32244	0.661219	+	0.750193i	$0.270039\pi$
$54$	−4.48937	−0.0113134
$55$	81.4671	0.199728
$56$	0.238728	0.000569667 0
$57$	−348.007	−0.808677
$58$	−4.82191	−0.0109163
$59$	−330.059	−0.728306	−0.364153	−	0.931339i	$-0.618642\pi$
$59$	−330.059	−0.728306	−0.364153	+	0.931339i	$0.618642\pi$
$60$	−101.176	−0.217695
$61$	−396.328	−0.831878	−0.415939	−	0.909392i	$-0.636547\pi$
$61$	−396.328	−0.831878	−0.415939	+	0.909392i	$0.636547\pi$
$62$	−13.8982	−0.0284689
$63$	−0.809013	−0.00161787
$64$	−501.414	−0.979325
$65$	−139.030	−0.265302
$66$	9.60632	0.0179160
$67$	49.9098	0.0910068	0.0455034	−	0.998964i	$-0.485511\pi$
$67$	49.9098	0.0910068	0.0455034	+	0.998964i	$0.485511\pi$
$68$	−545.229	−0.972334
$69$	69.0000	0.120386
$70$	0.0632269	0.000107958 0
$71$	321.535	0.537453	0.268726	−	0.963217i	$-0.413397\pi$
$71$	321.535	0.537453	0.268726	+	0.963217i	$0.413397\pi$
$72$	−23.9019	−0.0391232
$73$	404.214	0.648078	0.324039	−	0.946044i	$-0.394959\pi$
$73$	404.214	0.648078	0.324039	+	0.946044i	$0.394959\pi$
$74$	12.3007	0.0193234
$75$	321.315	0.494696
$76$	−924.810	−1.39583
$77$	1.73112	0.00256207
$78$	−16.3940	−0.0237981
$79$	91.8836	0.130857	0.0654285	−	0.997857i	$-0.479159\pi$
$79$	91.8836	0.130857	0.0654285	+	0.997857i	$0.479159\pi$
$80$	−267.934	−0.374448
$81$	81.0000	0.111111
$82$	−69.5489	−0.0936633
$83$	29.0774	0.0384537	0.0192269	−	0.999815i	$-0.493880\pi$
$83$	29.0774	0.0384537	0.0192269	+	0.999815i	$0.493880\pi$
$84$	−2.14991	−0.00279255
$85$	−289.308	−0.369175
$86$	−68.6034	−0.0860197
$87$	87.0000	0.107211
$88$	51.1452	0.0619556
$89$	210.458	0.250657	0.125329	−	0.992115i	$-0.460001\pi$
$89$	210.458	0.250657	0.125329	+	0.992115i	$0.460001\pi$
$90$	−6.33041	−0.00741426
$91$	−2.95430	−0.00340324
$92$	183.364	0.207794
$93$	250.760	0.279598
$94$	26.7593	0.0293618
$95$	−490.720	−0.529967
$96$	−95.3323	−0.101352
$97$	1769.23	1.85193	0.925967	−	0.377604i	$-0.123252\pi$
$97$	1769.23	1.85193	0.925967	+	0.377604i	$0.123252\pi$
$98$	−57.0303	−0.0587850
$99$	−173.323	−0.175956
$100$	853.878	0.853878
$101$	163.293	0.160874	0.0804372	−	0.996760i	$-0.474368\pi$
$101$	163.293	0.160874	0.0804372	+	0.996760i	$0.474368\pi$
$102$	−34.1142	−0.0331158
$103$	−929.682	−0.889362	−0.444681	−	0.895689i	$-0.646683\pi$
$103$	−929.682	−0.889362	−0.444681	+	0.895689i	$0.646683\pi$
$104$	−87.2835	−0.0822967
$105$	−1.14078	−0.00106027
$106$	84.8420	0.0777413
$107$	1235.60	1.11636	0.558178	−	0.829721i	$-0.311501\pi$
$107$	1235.60	1.11636	0.558178	+	0.829721i	$0.311501\pi$
$108$	215.254	0.191785
$109$	−206.960	−0.181864	−0.0909321	−	0.995857i	$-0.528985\pi$
$109$	−206.960	−0.181864	−0.0909321	+	0.995857i	$0.528985\pi$
$110$	13.5458	0.0117413
$111$	−221.938	−0.189778
$112$	−5.69340	−0.00480336
$113$	−947.426	−0.788729	−0.394364	−	0.918954i	$-0.629035\pi$
$113$	−947.426	−0.788729	−0.394364	+	0.918954i	$0.629035\pi$
$114$	−57.8641	−0.0475392
$115$	97.2962	0.0788949
$116$	231.198	0.185054
$117$	295.791	0.233725
$118$	−54.8799	−0.0428145
$119$	−6.14760	−0.00473571
$120$	−33.7038	−0.0256394
$121$	−960.124	−0.721355
$122$	−65.8986	−0.0489031
$123$	1254.84	0.919882
$124$	666.382	0.482603
$125$	981.866	0.702566
$126$	−0.134517	−9.51088e−5 0
$127$	1428.07	0.997803	0.498902	−	0.866659i	$-0.333737\pi$
$127$	1428.07	0.997803	0.498902	+	0.866659i	$0.333737\pi$
$128$	−337.591	−0.233118
$129$	1237.79	0.844814
$130$	−23.1170	−0.0155961
$131$	1018.15	0.679057	0.339528	−	0.940596i	$-0.389733\pi$
$131$	1018.15	0.679057	0.339528	+	0.940596i	$0.389733\pi$
$132$	−460.598	−0.303712
$133$	−10.4275	−0.00679832
$134$	8.29865	0.00534996
$135$	114.217	0.0728167
$136$	−181.628	−0.114518
$137$	−812.135	−0.506463	−0.253231	−	0.967406i	$-0.581493\pi$
$137$	−812.135	−0.506463	−0.253231	+	0.967406i	$0.581493\pi$
$138$	11.4728	0.00707704
$139$	−464.130	−0.283216	−0.141608	−	0.989923i	$-0.545227\pi$
$139$	−464.130	−0.283216	−0.141608	+	0.989923i	$0.545227\pi$
$140$	−3.03157	−0.00183010
$141$	−482.808	−0.288367
$142$	53.4625	0.0315949
$143$	−632.931	−0.370128
$144$	570.035	0.329881
$145$	122.678	0.0702609
$146$	67.2099	0.0380981
$147$	1028.98	0.577337
$148$	−589.789	−0.327570
$149$	−2204.00	−1.21181	−0.605903	−	0.795539i	$-0.707188\pi$
$149$	−2204.00	−1.21181	−0.605903	+	0.795539i	$0.707188\pi$
$150$	53.4259	0.0290814
$151$	2769.11	1.49237	0.746183	−	0.665741i	$-0.231884\pi$
$151$	2769.11	1.49237	0.746183	+	0.665741i	$0.231884\pi$
$152$	−308.075	−0.164396
$153$	615.510	0.325235
$154$	0.287838	0.000150615 0
$155$	353.594	0.183234
$156$	786.049	0.403425
$157$	−1234.53	−0.627555	−0.313777	−	0.949497i	$-0.601595\pi$
$157$	−1234.53	−0.627555	−0.313777	+	0.949497i	$0.601595\pi$
$158$	15.2777	0.00769261
$159$	−1530.77	−0.763510
$160$	−134.427	−0.0664212
$161$	2.06748	0.00101205
$162$	13.4681	0.00653182
$163$	−2709.06	−1.30178	−0.650889	−	0.759173i	$-0.725604\pi$
$163$	−2709.06	−1.30178	−0.650889	+	0.759173i	$0.725604\pi$
$164$	3334.69	1.58778
$165$	−244.401	−0.115313
$166$	4.83478	0.00226055
$167$	−1936.05	−0.897101	−0.448551	−	0.893757i	$-0.648060\pi$
$167$	−1936.05	−0.897101	−0.448551	+	0.893757i	$0.648060\pi$
$168$	−0.716184	−0.000328897 0
$169$	−1116.85	−0.508353
$170$	−48.1041	−0.0217024
$171$	1044.02	0.466890
$172$	3289.36	1.45820
$173$	2238.93	0.983945	0.491973	−	0.870611i	$-0.336276\pi$
$173$	2238.93	0.983945	0.491973	+	0.870611i	$0.336276\pi$
$174$	14.4657	0.00630256
$175$	9.62768	0.00415877
$176$	−1219.76	−0.522402
$177$	990.178	0.420488
$178$	34.9935	0.0147352
$179$	−1837.26	−0.767169	−0.383585	−	0.923506i	$-0.625311\pi$
$179$	−1837.26	−0.767169	−0.383585	+	0.923506i	$0.625311\pi$
$180$	303.527	0.125686
$181$	−4290.36	−1.76188	−0.880940	−	0.473228i	$-0.843089\pi$
$181$	−4290.36	−1.76188	−0.880940	+	0.473228i	$0.843089\pi$
$182$	−0.491220	−0.000200064 0
$183$	1188.98	0.480285
$184$	61.0827	0.0244732
$185$	−312.952	−0.124371
$186$	41.6945	0.0164365
$187$	−1317.06	−0.515044
$188$	−1283.04	−0.497741
$189$	2.42704	0.000934080 0
$190$	−81.5935	−0.0311548
$191$	−2892.59	−1.09581	−0.547907	−	0.836539i	$-0.684575\pi$
$191$	−2892.59	−1.09581	−0.547907	+	0.836539i	$0.684575\pi$
$192$	1504.24	0.565413
$193$	4752.84	1.77263	0.886313	−	0.463086i	$-0.153258\pi$
$193$	4752.84	1.77263	0.886313	+	0.463086i	$0.153258\pi$
$194$	294.174	0.108868
$195$	417.091	0.153172
$196$	2734.45	0.996521
$197$	5326.02	1.92621	0.963105	−	0.269125i	$-0.0867346\pi$
$197$	5326.02	1.92621	0.963105	+	0.269125i	$0.0867346\pi$
$198$	−28.8190	−0.0103438
$199$	−241.949	−0.0861876	−0.0430938	−	0.999071i	$-0.513721\pi$
$199$	−241.949	−0.0861876	−0.0430938	+	0.999071i	$0.513721\pi$
$200$	284.446	0.100567
$201$	−149.729	−0.0525428
$202$	27.1513	0.00945721
$203$	2.60682	0.000901295 0
$204$	1635.69	0.561378
$205$	1769.44	0.602845
$206$	−154.581	−0.0522824
$207$	−207.000	−0.0695048
$208$	2081.62	0.693915
$209$	−2233.99	−0.739369
$210$	−0.189681	−6.23296e−5 0
$211$	2098.25	0.684595	0.342297	−	0.939592i	$-0.388795\pi$
$211$	2098.25	0.684595	0.342297	+	0.939592i	$0.388795\pi$
$212$	−4067.95	−1.31787
$213$	−964.604	−0.310299
$214$	205.447	0.0656265
$215$	1745.39	0.553649
$216$	71.7058	0.0225878
$217$	7.51362	0.00235050
$218$	−34.4119	−0.0106911
$219$	−1212.64	−0.374168
$220$	−649.485	−0.199037
$221$	2247.68	0.684142
$222$	−36.9022	−0.0111564
$223$	5476.05	1.64441	0.822204	−	0.569192i	$-0.192744\pi$
$223$	5476.05	1.64441	0.822204	+	0.569192i	$0.192744\pi$
$224$	−2.85648	−0.000852039 0
$225$	−963.944	−0.285613
$226$	−157.531	−0.0463665
$227$	4064.44	1.18840	0.594199	−	0.804318i	$-0.297469\pi$
$227$	4064.44	1.18840	0.594199	+	0.804318i	$0.297469\pi$
$228$	2774.43	0.805882
$229$	1955.62	0.564326	0.282163	−	0.959366i	$-0.408948\pi$
$229$	1955.62	0.564326	0.282163	+	0.959366i	$0.408948\pi$
$230$	16.1777	0.00463794
$231$	−5.19336	−0.00147921
$232$	77.0173	0.0217950
$233$	−476.626	−0.134012	−0.0670061	−	0.997753i	$-0.521345\pi$
$233$	−476.626	−0.134012	−0.0670061	+	0.997753i	$0.521345\pi$
$234$	49.1820	0.0137399
$235$	−680.803	−0.188982
$236$	2631.35	0.725789
$237$	−275.651	−0.0755504
$238$	−1.02218	−0.000278395 0
$239$	5716.49	1.54715	0.773576	−	0.633704i	$-0.218466\pi$
$239$	5716.49	1.54715	0.773576	+	0.633704i	$0.218466\pi$
$240$	803.801	0.216188
$241$	6219.60	1.66240	0.831202	−	0.555970i	$-0.187653\pi$
$241$	6219.60	1.66240	0.831202	+	0.555970i	$0.187653\pi$
$242$	−159.643	−0.0424058
$243$	−243.000	−0.0641500
$244$	3159.67	0.829004
$245$	1450.95	0.378358
$246$	208.647	0.0540765
$247$	3812.48	0.982116
$248$	221.987	0.0568394
$249$	−87.2322	−0.0222013
$250$	163.258	0.0413013
$251$	5645.83	1.41977	0.709884	−	0.704319i	$-0.248748\pi$
$251$	5645.83	1.41977	0.709884	+	0.704319i	$0.248748\pi$
$252$	6.44973	0.00161228
$253$	442.937	0.110068
$254$	237.450	0.0586572
$255$	867.924	0.213143
$256$	3955.18	0.965621
$257$	486.025	0.117967	0.0589833	−	0.998259i	$-0.481214\pi$
$257$	486.025	0.117967	0.0589833	+	0.998259i	$0.481214\pi$
$258$	205.810	0.0496635
$259$	−6.65002	−0.00159541
$260$	1108.40	0.264385
$261$	−261.000	−0.0618984
$262$	169.291	0.0399193
$263$	−7272.83	−1.70518	−0.852590	−	0.522581i	$-0.824969\pi$
$263$	−7272.83	−1.70518	−0.852590	+	0.522581i	$0.824969\pi$
$264$	−153.436	−0.0357701
$265$	−2158.52	−0.500367
$266$	−1.73381	−0.000399648 0
$267$	−631.374	−0.144717
$268$	−397.899	−0.0906923
$269$	−519.622	−0.117777	−0.0588884	−	0.998265i	$-0.518756\pi$
$269$	−519.622	−0.117777	−0.0588884	+	0.998265i	$0.518756\pi$
$270$	18.9912	0.00428063
$271$	−4591.49	−1.02920	−0.514600	−	0.857430i	$-0.672060\pi$
$271$	−4591.49	−1.02920	−0.514600	+	0.857430i	$0.672060\pi$
$272$	4331.63	0.965602
$273$	8.86290	0.00196486
$274$	−135.036	−0.0297731
$275$	2062.64	0.452298
$276$	−550.092	−0.119970
$277$	1758.40	0.381416	0.190708	−	0.981647i	$-0.438922\pi$
$277$	1758.40	0.381416	0.190708	+	0.981647i	$0.438922\pi$
$278$	−77.1723	−0.0166492
$279$	−752.279	−0.161426
$280$	−1.00988	−0.000215543 0
$281$	−375.430	−0.0797020	−0.0398510	−	0.999206i	$-0.512688\pi$
$281$	−375.430	−0.0797020	−0.0398510	+	0.999206i	$0.512688\pi$
$282$	−80.2779	−0.0169521
$283$	−597.839	−0.125575	−0.0627877	−	0.998027i	$-0.519999\pi$
$283$	−597.839	−0.125575	−0.0627877	+	0.998027i	$0.519999\pi$
$284$	−2563.39	−0.535596
$285$	1472.16	0.305976
$286$	−105.239	−0.0217585
$287$	37.5994	0.00773319
$288$	285.997	0.0585157
$289$	−235.811	−0.0479973
$290$	20.3980	0.00413038
$291$	−5307.68	−1.06921
$292$	−3222.54	−0.645838
$293$	−3990.09	−0.795576	−0.397788	−	0.917477i	$-0.630222\pi$
$293$	−3990.09	−0.795576	−0.397788	+	0.917477i	$0.630222\pi$
$294$	171.091	0.0339395
$295$	1396.24	0.275567
$296$	−196.472	−0.0385800
$297$	519.970	0.101588
$298$	−366.466	−0.0712376
$299$	−755.909	−0.146205
$300$	−2561.63	−0.492986
$301$	37.0883	0.00710211
$302$	460.429	0.0877308
$303$	−489.880	−0.0928808
$304$	7347.26	1.38616
$305$	1676.57	0.314755
$306$	102.343	0.0191194
$307$	8415.49	1.56449	0.782243	−	0.622973i	$-0.214076\pi$
$307$	8415.49	1.56449	0.782243	+	0.622973i	$0.214076\pi$
$308$	−13.8011	−0.00255322
$309$	2789.05	0.513474
$310$	58.7930	0.0107717
$311$	4062.82	0.740776	0.370388	−	0.928877i	$-0.379225\pi$
$311$	4062.82	0.740776	0.370388	+	0.928877i	$0.379225\pi$
$312$	261.851	0.0475140
$313$	−2188.49	−0.395209	−0.197605	−	0.980282i	$-0.563316\pi$
$313$	−2188.49	−0.395209	−0.197605	+	0.980282i	$0.563316\pi$
$314$	−205.269	−0.0368917
$315$	3.42234	0.000612149 0
$316$	−732.528	−0.130405
$317$	−925.633	−0.164002	−0.0820012	−	0.996632i	$-0.526131\pi$
$317$	−925.633	−0.164002	−0.0820012	+	0.996632i	$0.526131\pi$
$318$	−254.526	−0.0448840
$319$	558.486	0.0980226
$320$	2121.12	0.370544
$321$	−3706.80	−0.644529
$322$	0.343765	5.94947e−5 0
$323$	7933.39	1.36664
$324$	−645.761	−0.110727
$325$	−3520.07	−0.600794
$326$	−450.443	−0.0765268
$327$	620.881	0.104999
$328$	1110.86	0.187003
$329$	−14.4666	−0.00242422
$330$	−40.6373	−0.00677882
$331$	−1988.51	−0.330206	−0.165103	−	0.986276i	$-0.552796\pi$
$331$	−1988.51	−0.330206	−0.165103	+	0.986276i	$0.552796\pi$
$332$	−231.815	−0.0383208
$333$	665.813	0.109569
$334$	−321.912	−0.0527373
$335$	−211.132	−0.0344339
$336$	17.0802	0.00277322
$337$	−7348.02	−1.18775	−0.593875	−	0.804557i	$-0.702403\pi$
$337$	−7348.02	−1.18775	−0.593875	+	0.804557i	$0.702403\pi$
$338$	−185.702	−0.0298842
$339$	2842.28	0.455373
$340$	2306.46	0.367899
$341$	1609.72	0.255634
$342$	173.592	0.0274468
$343$	61.6640	0.00970712
$344$	1095.76	0.171742
$345$	−291.888	−0.0455500
$346$	372.273	0.0578425
$347$	9259.79	1.43254	0.716271	−	0.697823i	$-0.245848\pi$
$347$	9259.79	1.43254	0.716271	+	0.697823i	$0.245848\pi$
$348$	−693.595	−0.106841
$349$	−4646.19	−0.712621	−0.356310	−	0.934368i	$-0.615965\pi$
$349$	−4646.19	−0.712621	−0.356310	+	0.934368i	$0.615965\pi$
$350$	1.60082	0.000244479 0
$351$	−887.372	−0.134941
$352$	−611.974	−0.0926657
$353$	10041.5	1.51404	0.757018	−	0.653394i	$-0.226656\pi$
$353$	10041.5	1.51404	0.757018	+	0.653394i	$0.226656\pi$
$354$	164.640	0.0247189
$355$	−1360.18	−0.203354
$356$	−1677.85	−0.249791
$357$	18.4428	0.00273416
$358$	−305.487	−0.0450991
$359$	1167.65	0.171661	0.0858305	−	0.996310i	$-0.472646\pi$
$359$	1167.65	0.171661	0.0858305	+	0.996310i	$0.472646\pi$
$360$	101.112	0.0148029
$361$	6597.50	0.961876
$362$	−713.371	−0.103574
$363$	2880.37	0.416475
$364$	23.5527	0.00339148
$365$	−1709.93	−0.245211
$366$	197.696	0.0282342
$367$	−1415.04	−0.201266	−0.100633	−	0.994924i	$-0.532087\pi$
$367$	−1415.04	−0.201266	−0.100633	+	0.994924i	$0.532087\pi$
$368$	−1456.76	−0.206355
$369$	−3764.53	−0.531094
$370$	−52.0354	−0.00731133
$371$	−45.8672	−0.00641861
$372$	−1999.14	−0.278631
$373$	−9334.40	−1.29576	−0.647878	−	0.761744i	$-0.724343\pi$
$373$	−9334.40	−1.29576	−0.647878	+	0.761744i	$0.724343\pi$
$374$	−218.992	−0.0302776
$375$	−2945.60	−0.405627
$376$	−427.409	−0.0586222
$377$	−953.103	−0.130205
$378$	0.403551	5.49111e−5 0
$379$	10050.3	1.36214	0.681069	−	0.732219i	$-0.261515\pi$
$379$	10050.3	1.36214	0.681069	+	0.732219i	$0.261515\pi$
$380$	3912.20	0.528135
$381$	−4284.22	−0.576082
$382$	−480.960	−0.0644189
$383$	−2362.72	−0.315220	−0.157610	−	0.987501i	$-0.550379\pi$
$383$	−2362.72	−0.315220	−0.157610	+	0.987501i	$0.550379\pi$
$384$	1012.77	0.134591
$385$	−7.32310	−0.000969402 0
$386$	790.269	0.104206
$387$	−3713.36	−0.487753
$388$	−14104.9	−1.84553
$389$	13135.4	1.71206	0.856031	−	0.516925i	$-0.172923\pi$
$389$	13135.4	1.71206	0.856031	+	0.516925i	$0.172923\pi$
$390$	69.3510	0.00900442
$391$	−1572.97	−0.203449
$392$	910.907	0.117367
$393$	−3054.46	−0.392053
$394$	885.573	0.113235
$395$	−388.692	−0.0495120
$396$	1381.79	0.175348
$397$	5922.87	0.748767	0.374383	−	0.927274i	$-0.377854\pi$
$397$	5922.87	0.748767	0.374383	+	0.927274i	$0.377854\pi$
$398$	−40.2296	−0.00506665
$399$	31.2824	0.00392501
$400$	−6783.73	−0.847966
$401$	3655.29	0.455204	0.227602	−	0.973754i	$-0.426912\pi$
$401$	3655.29	0.455204	0.227602	+	0.973754i	$0.426912\pi$
$402$	−24.8960	−0.00308880
$403$	−2747.12	−0.339563
$404$	−1301.83	−0.160318
$405$	−342.652	−0.0420407
$406$	0.433443	5.29838e−5 0
$407$	−1424.70	−0.173513
$408$	544.884	0.0661171
$409$	10692.5	1.29269	0.646344	−	0.763046i	$-0.276297\pi$
$409$	10692.5	1.29269	0.646344	+	0.763046i	$0.276297\pi$
$410$	294.210	0.0354391
$411$	2436.41	0.292406
$412$	7411.76	0.886289
$413$	29.6691	0.00353492
$414$	−34.4185	−0.00408593
$415$	−123.005	−0.0145496
$416$	1044.38	0.123089
$417$	1392.39	0.163515
$418$	−371.451	−0.0434648
$419$	7929.02	0.924482	0.462241	−	0.886754i	$-0.347046\pi$
$419$	7929.02	0.924482	0.462241	+	0.886754i	$0.347046\pi$
$420$	9.09470	0.00105661
$421$	−7135.44	−0.826034	−0.413017	−	0.910723i	$-0.635525\pi$
$421$	−7135.44	−0.826034	−0.413017	+	0.910723i	$0.635525\pi$
$422$	348.882	0.0402448
$423$	1448.42	0.166489
$424$	−1355.13	−0.155214
$425$	−7324.90	−0.836023
$426$	−160.388	−0.0182413
$427$	35.6260	0.00403762
$428$	−9850.65	−1.11250
$429$	1898.79	0.213694
$430$	290.211	0.0325470
$431$	−10355.4	−1.15732	−0.578658	−	0.815570i	$-0.696423\pi$
$431$	−10355.4	−1.15732	−0.578658	+	0.815570i	$0.696423\pi$
$432$	−1710.11	−0.190457
$433$	15920.2	1.76692	0.883459	−	0.468508i	$-0.155208\pi$
$433$	15920.2	1.76692	0.883459	+	0.468508i	$0.155208\pi$
$434$	1.24931	0.000138177 0
$435$	−368.033	−0.0405652
$436$	1649.96	0.181236
$437$	−2668.05	−0.292060
$438$	−201.630	−0.0219960
$439$	−6840.83	−0.743724	−0.371862	−	0.928288i	$-0.621281\pi$
$439$	−6840.83	−0.743724	−0.371862	+	0.928288i	$0.621281\pi$
$440$	−216.358	−0.0234419
$441$	−3086.93	−0.333325
$442$	373.728	0.0402182
$443$	840.371	0.0901292	0.0450646	−	0.998984i	$-0.485651\pi$
$443$	840.371	0.0901292	0.0450646	+	0.998984i	$0.485651\pi$
$444$	1769.37	0.189123
$445$	−890.294	−0.0948404
$446$	910.518	0.0966688
$447$	6612.01	0.699636
$448$	45.0723	0.00475327
$449$	−11480.9	−1.20672	−0.603362	−	0.797467i	$-0.706173\pi$
$449$	−11480.9	−1.20672	−0.603362	+	0.797467i	$0.706173\pi$
$450$	−160.278	−0.0167901
$451$	8055.32	0.841043
$452$	7553.22	0.786003
$453$	−8307.34	−0.861618
$454$	675.806	0.0698616
$455$	12.4975	0.00128767
$456$	924.225	0.0949140
$457$	−625.481	−0.0640236	−0.0320118	−	0.999487i	$-0.510191\pi$
$457$	−625.481	−0.0640236	−0.0320118	+	0.999487i	$0.510191\pi$
$458$	325.166	0.0331747
$459$	−1846.53	−0.187775
$460$	−775.679	−0.0786223
$461$	1042.16	0.105289	0.0526445	−	0.998613i	$-0.483235\pi$
$461$	1042.16	0.105289	0.0526445	+	0.998613i	$0.483235\pi$
$462$	−0.863515	−8.69575e−5 0
$463$	2965.03	0.297617	0.148809	−	0.988866i	$-0.452456\pi$
$463$	2965.03	0.297617	0.148809	+	0.988866i	$0.452456\pi$
$464$	−1836.78	−0.183772
$465$	−1060.78	−0.105790
$466$	−79.2500	−0.00787808
$467$	−260.276	−0.0257904	−0.0128952	−	0.999917i	$-0.504105\pi$
$467$	−260.276	−0.0257904	−0.0128952	+	0.999917i	$0.504105\pi$
$468$	−2358.15	−0.232918
$469$	−4.48641	−0.000441712 0
$470$	−113.199	−0.0111095
$471$	3703.59	0.362319
$472$	876.562	0.0854810
$473$	7945.82	0.772408
$474$	−45.8332	−0.00444133
$475$	−12424.4	−1.20015
$476$	49.0108	0.00471934
$477$	4592.32	0.440813
$478$	950.498	0.0909514
$479$	3400.47	0.324366	0.162183	−	0.986761i	$-0.448146\pi$
$479$	3400.47	0.324366	0.162183	+	0.986761i	$0.448146\pi$
$480$	403.281	0.0383483
$481$	2431.37	0.230481
$482$	1034.15	0.0977267
$483$	−6.20243	−0.000584307 0
$484$	7654.45	0.718862
$485$	−7484.30	−0.700710
$486$	−40.4043	−0.00377115
$487$	−8023.50	−0.746570	−0.373285	−	0.927717i	$-0.621769\pi$
$487$	−8023.50	−0.746570	−0.373285	+	0.927717i	$0.621769\pi$
$488$	1052.56	0.0976372
$489$	8127.17	0.751582
$490$	241.253	0.0222423
$491$	1432.88	0.131700	0.0658501	−	0.997830i	$-0.479024\pi$
$491$	1432.88	0.131700	0.0658501	+	0.997830i	$0.479024\pi$
$492$	−10004.1	−0.916703
$493$	−1983.31	−0.181184
$494$	633.913	0.0577350
$495$	733.204	0.0665759
$496$	−5294.14	−0.479262
$497$	−28.9029	−0.00260859
$498$	−14.5043	−0.00130513
$499$	−6151.80	−0.551889	−0.275944	−	0.961174i	$-0.588991\pi$
$499$	−6151.80	−0.551889	−0.275944	+	0.961174i	$0.588991\pi$
$500$	−7827.78	−0.700138
$501$	5808.14	0.517942
$502$	938.748	0.0834629
$503$	9318.92	0.826064	0.413032	−	0.910717i	$-0.364470\pi$
$503$	9318.92	0.826064	0.413032	+	0.910717i	$0.364470\pi$
$504$	2.14855	0.000189889 0
$505$	−690.775	−0.0608695
$506$	73.6485	0.00647050
$507$	3350.55	0.293498
$508$	−11385.1	−0.994355
$509$	7059.43	0.614743	0.307371	−	0.951590i	$-0.400551\pi$
$509$	7059.43	0.614743	0.307371	+	0.951590i	$0.400551\pi$
$510$	144.312	0.0125299
$511$	−36.3349	−0.00314552
$512$	3358.37	0.289883
$513$	−3132.06	−0.269559
$514$	80.8129	0.00693483
$515$	3932.80	0.336505
$516$	−9868.07	−0.841894
$517$	−3099.33	−0.263653
$518$	−1.10572	−9.37885e−5 0
$519$	−6716.78	−0.568081
$520$	369.233	0.0311383
$521$	−10154.7	−0.853905	−0.426953	−	0.904274i	$-0.640413\pi$
$521$	−10154.7	−0.853905	−0.426953	+	0.904274i	$0.640413\pi$
$522$	−43.3972	−0.00363878
$523$	7101.07	0.593706	0.296853	−	0.954923i	$-0.404063\pi$
$523$	7101.07	0.593706	0.296853	+	0.954923i	$0.404063\pi$
$524$	−8117.07	−0.676710
$525$	−28.8831	−0.00240107
$526$	−1209.28	−0.100241
$527$	−5716.48	−0.472512
$528$	3659.27	0.301609
$529$	529.000	0.0434783
$530$	−358.904	−0.0294147
$531$	−2970.53	−0.242769
$532$	83.1315	0.00677482
$533$	−13747.1	−1.11717
$534$	−104.980	−0.00850739
$535$	−5226.93	−0.422392
$536$	−132.549	−0.0106814
$537$	5511.78	0.442925
$538$	−86.3991	−0.00692366
$539$	6605.39	0.527856
$540$	−910.580	−0.0725651
$541$	1375.62	0.109321	0.0546605	−	0.998505i	$-0.482592\pi$
$541$	1375.62	0.109321	0.0546605	+	0.998505i	$0.482592\pi$
$542$	−763.441	−0.0605029
$543$	12871.1	1.01722
$544$	2173.26	0.171282
$545$	875.497	0.0688113
$546$	1.47366	0.000115507 0
$547$	−24370.2	−1.90492	−0.952462	−	0.304658i	$-0.901458\pi$
$547$	−24370.2	−1.90492	−0.952462	+	0.304658i	$0.901458\pi$
$548$	6474.63	0.504713
$549$	−3566.95	−0.277293
$550$	342.961	0.0265889
$551$	−3364.06	−0.260098
$552$	−183.248	−0.0141296
$553$	−8.25944	−0.000635131 0
$554$	292.375	0.0224220
$555$	938.856	0.0718058
$556$	3700.21	0.282237
$557$	9430.12	0.717355	0.358678	−	0.933461i	$-0.383228\pi$
$557$	9430.12	0.717355	0.358678	+	0.933461i	$0.383228\pi$
$558$	−125.084	−0.00948963
$559$	−13560.2	−1.02600
$560$	24.0846	0.00181743
$561$	3951.19	0.297361
$562$	−62.4238	−0.00468539
$563$	25209.6	1.88714	0.943569	−	0.331175i	$-0.107445\pi$
$563$	25209.6	1.88714	0.943569	+	0.331175i	$0.107445\pi$
$564$	3849.12	0.287371
$565$	4007.87	0.298429
$566$	−99.4044	−0.00738212
$567$	−7.28111	−0.000539291 0
$568$	−853.922	−0.0630806
$569$	10572.1	0.778920	0.389460	−	0.921043i	$-0.372662\pi$
$569$	10572.1	0.778920	0.389460	+	0.921043i	$0.372662\pi$
$570$	244.780	0.0179872
$571$	12579.1	0.921927	0.460963	−	0.887419i	$-0.347504\pi$
$571$	12579.1	0.921927	0.460963	+	0.887419i	$0.347504\pi$
$572$	5045.95	0.368849
$573$	8677.78	0.632669
$574$	6.25177	0.000454606 0
$575$	2463.41	0.178663
$576$	−4512.73	−0.326442
$577$	17962.0	1.29596	0.647980	−	0.761658i	$-0.275614\pi$
$577$	17962.0	1.29596	0.647980	+	0.761658i	$0.275614\pi$
$578$	−39.2089	−0.00282159
$579$	−14258.5	−1.02343
$580$	−978.030	−0.0700181
$581$	−2.61378	−0.000186640 0
$582$	−882.523	−0.0628552
$583$	−9826.61	−0.698073
$584$	−1073.50	−0.0760646
$585$	−1251.27	−0.0884338
$586$	−663.445	−0.0467690
$587$	10829.2	0.761448	0.380724	−	0.924689i	$-0.375675\pi$
$587$	10829.2	0.761448	0.380724	+	0.924689i	$0.375675\pi$
$588$	−8203.36	−0.575341
$589$	−9696.22	−0.678312
$590$	232.157	0.0161996
$591$	−15978.1	−1.11210
$592$	4685.64	0.325302
$593$	261.377	0.0181003	0.00905014	−	0.999959i	$-0.497119\pi$
$593$	261.377	0.0181003	0.00905014	+	0.999959i	$0.497119\pi$
$594$	86.4569	0.00597200
$595$	26.0060	0.00179183
$596$	17571.1	1.20762
$597$	725.848	0.0497604
$598$	−125.687	−0.00859487
$599$	−14118.2	−0.963026	−0.481513	−	0.876439i	$-0.659913\pi$
$599$	−14118.2	−0.963026	−0.481513	+	0.876439i	$0.659913\pi$
$600$	−853.337	−0.0580622
$601$	−14123.6	−0.958590	−0.479295	−	0.877654i	$-0.659108\pi$
$601$	−14123.6	−0.958590	−0.479295	+	0.877654i	$0.659108\pi$
$602$	6.16678	0.000417507 0
$603$	449.188	0.0303356
$604$	−22076.4	−1.48721
$605$	4061.58	0.272937
$606$	−81.4538	−0.00546012
$607$	−13663.6	−0.913652	−0.456826	−	0.889556i	$-0.651014\pi$
$607$	−13663.6	−0.913652	−0.456826	+	0.889556i	$0.651014\pi$
$608$	3686.25	0.245884
$609$	−7.82046	−0.000520363 0
$610$	278.769	0.0185033
$611$	5289.26	0.350214
$612$	−4907.06	−0.324111
$613$	−27175.5	−1.79055	−0.895277	−	0.445509i	$-0.853023\pi$
$613$	−27175.5	−1.79055	−0.895277	+	0.445509i	$0.853023\pi$
$614$	1399.27	0.0919704
$615$	−5308.33	−0.348053
$616$	−4.59746	−0.000300709 0
$617$	−16631.4	−1.08518	−0.542590	−	0.839998i	$-0.682556\pi$
$617$	−16631.4	−1.08518	−0.542590	+	0.839998i	$0.682556\pi$
$618$	463.743	0.0301852
$619$	−6280.20	−0.407791	−0.203895	−	0.978993i	$-0.565360\pi$
$619$	−6280.20	−0.407791	−0.203895	+	0.978993i	$0.565360\pi$
$620$	−2818.97	−0.182601
$621$	621.000	0.0401286
$622$	675.537	0.0435475
$623$	−18.9181	−0.00121660
$624$	−6244.85	−0.400632
$625$	9234.55	0.591011
$626$	−363.886	−0.0232329
$627$	6701.96	0.426875
$628$	9842.10	0.625386
$629$	5059.44	0.320720
$630$	0.569042	3.59860e−5 0
$631$	27516.0	1.73597	0.867983	−	0.496595i	$-0.165416\pi$
$631$	27516.0	1.73597	0.867983	+	0.496595i	$0.165416\pi$
$632$	−244.022	−0.0153586
$633$	−6294.75	−0.395251
$634$	−153.908	−0.00964110
$635$	−6041.13	−0.377536
$636$	12203.9	0.760872
$637$	−11272.6	−0.701159
$638$	92.8611	0.00576239
$639$	2893.81	0.179151
$640$	1428.10	0.0882041
$641$	1912.07	0.117820	0.0589098	−	0.998263i	$-0.481238\pi$
$641$	1912.07	0.117820	0.0589098	+	0.998263i	$0.481238\pi$
$642$	−616.341	−0.0378895
$643$	24301.2	1.49043	0.745214	−	0.666826i	$-0.232347\pi$
$643$	24301.2	1.49043	0.745214	+	0.666826i	$0.232347\pi$
$644$	−16.4827	−0.00100855
$645$	−5236.17	−0.319649
$646$	1319.11	0.0803399
$647$	28704.9	1.74421	0.872106	−	0.489316i	$-0.162754\pi$
$647$	28704.9	1.74421	0.872106	+	0.489316i	$0.162754\pi$
$648$	−215.117	−0.0130411
$649$	6356.33	0.384450
$650$	−585.292	−0.0353185
$651$	−22.5409	−0.00135706
$652$	21597.6	1.29728
$653$	12197.2	0.730954	0.365477	−	0.930820i	$-0.380906\pi$
$653$	12197.2	0.730954	0.365477	+	0.930820i	$0.380906\pi$
$654$	103.236	0.00617253
$655$	−4307.06	−0.256932
$656$	−26492.8	−1.57678
$657$	3637.93	0.216026
$658$	−2.40540	−0.000142511 0
$659$	20846.6	1.23228	0.616138	−	0.787638i	$-0.288696\pi$
$659$	20846.6	1.23228	0.616138	+	0.787638i	$0.288696\pi$
$660$	1948.45	0.114914
$661$	−20419.2	−1.20154	−0.600769	−	0.799423i	$-0.705139\pi$
$661$	−20419.2	−1.20154	−0.600769	+	0.799423i	$0.705139\pi$
$662$	−330.635	−0.0194116
$663$	−6743.04	−0.394989
$664$	−77.2228	−0.00451329
$665$	44.1110	0.00257226
$666$	110.707	0.00644114
$667$	667.000	0.0387202
$668$	15434.9	0.894001
$669$	−16428.1	−0.949400
$670$	−35.1055	−0.00202425
$671$	7632.54	0.439122
$672$	8.56945	0.000491925 0
$673$	−21743.8	−1.24541	−0.622707	−	0.782455i	$-0.713967\pi$
$673$	−21743.8	−1.24541	−0.622707	+	0.782455i	$0.713967\pi$
$674$	−1221.78	−0.0698235
$675$	2891.83	0.164899
$676$	8903.93	0.506596
$677$	−24462.1	−1.38871	−0.694354	−	0.719633i	$-0.744310\pi$
$677$	−24462.1	−1.38871	−0.694354	+	0.719633i	$0.744310\pi$
$678$	472.594	0.0267697
$679$	−159.036	−0.00898858
$680$	768.335	0.0433299
$681$	−12193.3	−0.686122
$682$	267.653	0.0150278
$683$	23002.8	1.28869	0.644347	−	0.764733i	$-0.277129\pi$
$683$	23002.8	1.28869	0.644347	+	0.764733i	$0.277129\pi$
$684$	−8323.29	−0.465276
$685$	3435.55	0.191629
$686$	10.2531	0.000570646 0
$687$	−5866.85	−0.325814
$688$	−26132.6	−1.44811
$689$	16769.9	0.927262
$690$	−48.5331	−0.00267772
$691$	15811.3	0.870463	0.435232	−	0.900319i	$-0.356666\pi$
$691$	15811.3	0.870463	0.435232	+	0.900319i	$0.356666\pi$
$692$	−17849.5	−0.980545
$693$	15.5801	0.000854024 0
$694$	1539.65	0.0842138
$695$	1963.39	0.107159
$696$	−231.052	−0.0125833
$697$	−28606.3	−1.55458
$698$	−772.535	−0.0418924
$699$	1429.88	0.0773719
$700$	−76.7553	−0.00414440
$701$	−9567.66	−0.515500	−0.257750	−	0.966212i	$-0.582981\pi$
$701$	−9567.66	−0.515500	−0.257750	+	0.966212i	$0.582981\pi$
$702$	−147.546	−0.00793271
$703$	8581.75	0.460408
$704$	9656.31	0.516954
$705$	2042.41	0.109109
$706$	1669.63	0.0890046
$707$	−14.6785	−0.000780823 0
$708$	−7894.05	−0.419035
$709$	12891.5	0.682865	0.341432	−	0.939906i	$-0.389088\pi$
$709$	12891.5	0.682865	0.341432	+	0.939906i	$0.389088\pi$
$710$	−226.161	−0.0119545
$711$	826.952	0.0436190
$712$	−558.928	−0.0294195
$713$	1922.49	0.100979
$714$	3.06654	0.000160731 0
$715$	2677.47	0.140044
$716$	14647.3	0.764518
$717$	−17149.5	−0.893248
$718$	194.149	0.0100913
$719$	28920.6	1.50008	0.750040	−	0.661392i	$-0.230034\pi$
$719$	28920.6	1.50008	0.750040	+	0.661392i	$0.230034\pi$
$720$	−2411.40	−0.124816
$721$	83.5694	0.00431663
$722$	1096.99	0.0565452
$723$	−18658.8	−0.959790
$724$	34204.3	1.75579
$725$	3106.04	0.159111
$726$	478.928	0.0244830
$727$	20038.4	1.02226	0.511130	−	0.859504i	$-0.329227\pi$
$727$	20038.4	1.02226	0.511130	+	0.859504i	$0.329227\pi$
$728$	7.84594	0.000399437 0
$729$	729.000	0.0370370
$730$	−284.316	−0.0144151
$731$	−28217.4	−1.42771
$732$	−9479.00	−0.478625
$733$	7393.75	0.372571	0.186285	−	0.982496i	$-0.440355\pi$
$733$	7393.75	0.372571	0.186285	+	0.982496i	$0.440355\pi$
$734$	−235.283	−0.0118317
$735$	−4352.84	−0.218445
$736$	−730.881	−0.0366041
$737$	−961.171	−0.0480396
$738$	−625.940	−0.0312211
$739$	−33714.0	−1.67820	−0.839101	−	0.543976i	$-0.816918\pi$
$739$	−33714.0	−1.67820	−0.839101	+	0.543976i	$0.816918\pi$
$740$	2494.96	0.123942
$741$	−11437.5	−0.567025
$742$	−7.62647	−0.000377327 0
$743$	36485.0	1.80148	0.900742	−	0.434354i	$-0.143023\pi$
$743$	36485.0	1.80148	0.900742	+	0.434354i	$0.143023\pi$
$744$	−665.960	−0.0328162
$745$	9323.53	0.458507
$746$	−1552.06	−0.0761727
$747$	261.697	0.0128179
$748$	10500.1	0.513264
$749$	−111.069	−0.00541837
$750$	−489.773	−0.0238453
$751$	−12033.6	−0.584705	−0.292353	−	0.956311i	$-0.594438\pi$
$751$	−12033.6	−0.584705	−0.292353	+	0.956311i	$0.594438\pi$
$752$	10193.2	0.494295
$753$	−16937.5	−0.819703
$754$	−158.475	−0.00765428
$755$	−11714.1	−0.564662
$756$	−19.3492	−0.000930852 0
$757$	−26142.5	−1.25517	−0.627586	−	0.778547i	$-0.715957\pi$
$757$	−26142.5	−1.25517	−0.627586	+	0.778547i	$0.715957\pi$
$758$	1671.10	0.0800751
$759$	−1328.81	−0.0635478
$760$	1303.24	0.0622019
$761$	−18558.6	−0.884032	−0.442016	−	0.897007i	$-0.645737\pi$
$761$	−18558.6	−0.884032	−0.442016	+	0.897007i	$0.645737\pi$
$762$	−712.350	−0.0338658
$763$	18.6037	0.000882699 0
$764$	23060.8	1.09203
$765$	−2603.77	−0.123058
$766$	−392.855	−0.0185306
$767$	−10847.6	−0.510671
$768$	−11865.5	−0.557501
$769$	18676.1	0.875782	0.437891	−	0.899028i	$-0.355726\pi$
$769$	18676.1	0.875782	0.437891	+	0.899028i	$0.355726\pi$
$770$	−1.21763	−5.69876e−5 0
$771$	−1458.08	−0.0681081
$772$	−37891.3	−1.76650
$773$	18784.1	0.874022	0.437011	−	0.899456i	$-0.356037\pi$
$773$	18784.1	0.874022	0.437011	+	0.899456i	$0.356037\pi$
$774$	−617.431	−0.0286732
$775$	8952.52	0.414947
$776$	−4698.65	−0.217361
$777$	19.9501	0.000921112 0
$778$	2184.06	0.100646
$779$	−48521.6	−2.23166
$780$	−3325.20	−0.152643
$781$	−6192.16	−0.283704
$782$	−261.542	−0.0119600
$783$	783.000	0.0357371
$784$	−21724.2	−0.989621
$785$	5222.39	0.237446
$786$	−507.874	−0.0230474
$787$	−9473.34	−0.429083	−0.214541	−	0.976715i	$-0.568826\pi$
$787$	−9473.34	−0.429083	−0.214541	+	0.976715i	$0.568826\pi$
$788$	−42460.9	−1.91955
$789$	21818.5	0.984486
$790$	−64.6290	−0.00291063
$791$	85.1644	0.00382819
$792$	460.307	0.0206519
$793$	−13025.6	−0.583293
$794$	984.813	0.0440173
$795$	6475.57	0.288887
$796$	1928.90	0.0858897
$797$	40371.2	1.79426	0.897128	−	0.441770i	$-0.145649\pi$
$797$	40371.2	1.79426	0.897128	+	0.441770i	$0.145649\pi$
$798$	5.20142	0.000230737 0
$799$	11006.4	0.487333
$800$	−3403.52	−0.150416
$801$	1894.12	0.0835525
$802$	607.776	0.0267598
$803$	−7784.42	−0.342100
$804$	1193.70	0.0523612
$805$	−8.74598	−0.000382926 0
$806$	−456.772	−0.0199617
$807$	1558.87	0.0679984
$808$	−433.670	−0.0188817
$809$	−29659.5	−1.28896	−0.644482	−	0.764620i	$-0.722927\pi$
$809$	−29659.5	−1.28896	−0.644482	+	0.764620i	$0.722927\pi$
$810$	−56.9737	−0.00247142
$811$	30213.4	1.30818	0.654091	−	0.756416i	$-0.273051\pi$
$811$	30213.4	1.30818	0.654091	+	0.756416i	$0.273051\pi$
$812$	−20.7825	−0.000898180 0
$813$	13774.5	0.594209
$814$	−236.889	−0.0102002
$815$	11460.0	0.492549
$816$	−12994.9	−0.557491
$817$	−47861.9	−2.04954
$818$	1777.87	0.0759924
$819$	−26.5887	−0.00113441
$820$	−14106.6	−0.600762
$821$	40447.6	1.71940	0.859702	−	0.510796i	$-0.170649\pi$
$821$	40447.6	1.71940	0.859702	+	0.510796i	$0.170649\pi$
$822$	405.108	0.0171895
$823$	−40716.3	−1.72452	−0.862260	−	0.506466i	$-0.830951\pi$
$823$	−40716.3	−1.72452	−0.862260	+	0.506466i	$0.830951\pi$
$824$	2469.02	0.104384
$825$	−6187.92	−0.261134
$826$	4.93317	0.000207805 0
$827$	26897.9	1.13099	0.565497	−	0.824750i	$-0.308684\pi$
$827$	26897.9	1.13099	0.565497	+	0.824750i	$0.308684\pi$
$828$	1650.28	0.0692646
$829$	4300.15	0.180157	0.0900786	−	0.995935i	$-0.471288\pi$
$829$	4300.15	0.180157	0.0900786	+	0.995935i	$0.471288\pi$
$830$	−20.4524	−0.000855318 0
$831$	−5275.21	−0.220210
$832$	−16479.3	−0.686679
$833$	−23457.2	−0.975683
$834$	231.517	0.00961243
$835$	8190.00	0.339433
$836$	17810.1	0.736814
$837$	2256.84	0.0931992
$838$	1318.38	0.0543469
$839$	−23913.0	−0.983993	−0.491996	−	0.870597i	$-0.663733\pi$
$839$	−23913.0	−0.983993	−0.491996	+	0.870597i	$0.663733\pi$
$840$	3.02965	0.000124444 0
$841$	841.000	0.0344828
$842$	−1186.43	−0.0485595
$843$	1126.29	0.0460160
$844$	−16728.0	−0.682229
$845$	4724.58	0.192344
$846$	240.834	0.00978728
$847$	86.3058	0.00350118
$848$	32318.3	1.30874
$849$	1793.52	0.0725010
$850$	−1217.93	−0.0491467
$851$	−1701.52	−0.0685399
$852$	7690.17	0.309226
$853$	42542.5	1.70765	0.853826	−	0.520558i	$-0.174276\pi$
$853$	42542.5	1.70765	0.853826	+	0.520558i	$0.174276\pi$
$854$	5.92364	0.000237357 0
$855$	−4416.48	−0.176656
$856$	−3281.47	−0.131026
$857$	13409.1	0.534475	0.267238	−	0.963631i	$-0.413889\pi$
$857$	13409.1	0.534475	0.267238	+	0.963631i	$0.413889\pi$
$858$	315.718	0.0125623
$859$	−7444.19	−0.295684	−0.147842	−	0.989011i	$-0.547233\pi$
$859$	−7444.19	−0.295684	−0.147842	+	0.989011i	$0.547233\pi$
$860$	−13914.9	−0.551736
$861$	−112.798	−0.00446476
$862$	−1721.83	−0.0680344
$863$	−22450.0	−0.885526	−0.442763	−	0.896639i	$-0.646002\pi$
$863$	−22450.0	−0.885526	−0.442763	+	0.896639i	$0.646002\pi$
$864$	−857.990	−0.0337841
$865$	−9471.26	−0.372292
$866$	2647.10	0.103871
$867$	707.432	0.0277113
$868$	−59.9012	−0.00234237
$869$	−1769.51	−0.0690753
$870$	−61.1940	−0.00238468
$871$	1640.32	0.0638118
$872$	549.639	0.0213453
$873$	15923.0	0.617311
$874$	−443.624	−0.0171691
$875$	−88.2602	−0.00340999
$876$	9667.62	0.372875
$877$	14257.1	0.548950	0.274475	−	0.961594i	$-0.411496\pi$
$877$	14257.1	0.548950	0.274475	+	0.961594i	$0.411496\pi$
$878$	−1137.44	−0.0437208
$879$	11970.3	0.459326
$880$	5159.90	0.197659
$881$	−6140.94	−0.234839	−0.117420	−	0.993082i	$-0.537462\pi$
$881$	−6140.94	−0.234839	−0.117420	+	0.993082i	$0.537462\pi$
$882$	−513.272	−0.0195950
$883$	24488.2	0.933287	0.466644	−	0.884445i	$-0.345463\pi$
$883$	24488.2	0.933287	0.466644	+	0.884445i	$0.345463\pi$
$884$	−17919.3	−0.681777
$885$	−4188.72	−0.159099
$886$	139.731	0.00529837
$887$	12917.0	0.488965	0.244482	−	0.969654i	$-0.421382\pi$
$887$	12917.0	0.488965	0.244482	+	0.969654i	$0.421382\pi$
$888$	589.416	0.0222742
$889$	−128.370	−0.00484296
$890$	−148.032	−0.00557532
$891$	−1559.91	−0.0586520
$892$	−43657.0	−1.63873
$893$	18668.9	0.699588
$894$	1099.40	0.0411291
$895$	7772.10	0.290271
$896$	30.3462	0.00113147
$897$	2267.73	0.0844116
$898$	−1908.97	−0.0709389
$899$	2424.01	0.0899280
$900$	7684.90	0.284626
$901$	34896.5	1.29031
$902$	1339.38	0.0494418
$903$	−111.265	−0.00410040
$904$	2516.15	0.0925727
$905$	18149.4	0.666637
$906$	−1381.29	−0.0506514
$907$	−16919.4	−0.619403	−0.309701	−	0.950834i	$-0.600229\pi$
$907$	−16919.4	−0.619403	−0.309701	+	0.950834i	$0.600229\pi$
$908$	−32403.2	−1.18429
$909$	1469.64	0.0536248
$910$	2.07799	7.56976e−5 0
$911$	6227.03	0.226466	0.113233	−	0.993568i	$-0.463879\pi$
$911$	6227.03	0.226466	0.113233	+	0.993568i	$0.463879\pi$
$912$	−22041.8	−0.800303
$913$	−559.977	−0.0202985
$914$	−104.001	−0.00376371
$915$	−5029.72	−0.181724
$916$	−15590.9	−0.562376
$917$	−91.5220	−0.00329588
$918$	−307.028	−0.0110386
$919$	−21469.9	−0.770650	−0.385325	−	0.922781i	$-0.625911\pi$
$919$	−21469.9	−0.770650	−0.385325	+	0.922781i	$0.625911\pi$
$920$	−258.396	−0.00925986
$921$	−25246.5	−0.903256
$922$	173.283	0.00618956
$923$	10567.4	0.376849
$924$	41.4033	0.00147410
$925$	−7923.54	−0.281648
$926$	493.005	0.0174958
$927$	−8367.14	−0.296454
$928$	−921.545	−0.0325983
$929$	46300.5	1.63517	0.817583	−	0.575811i	$-0.195314\pi$
$929$	46300.5	1.63517	0.817583	+	0.575811i	$0.195314\pi$
$930$	−176.379	−0.00621903
$931$	−39787.8	−1.40064
$932$	3799.83	0.133549
$933$	−12188.5	−0.427687
$934$	−43.2768	−0.00151612
$935$	5571.53	0.194876
$936$	−785.552	−0.0274322
$937$	32599.9	1.13660	0.568300	−	0.822822i	$-0.307601\pi$
$937$	32599.9	1.13660	0.568300	+	0.822822i	$0.307601\pi$
$938$	−0.745968	−2.59667e−5 0
$939$	6565.46	0.228174
$940$	5427.60	0.188328
$941$	−9562.39	−0.331270	−0.165635	−	0.986187i	$-0.552967\pi$
$941$	−9562.39	−0.331270	−0.165635	+	0.986187i	$0.552967\pi$
$942$	615.806	0.0212994
$943$	9620.47	0.332222
$944$	−20905.1	−0.720764
$945$	−10.2670	−0.000353425 0
$946$	1321.17	0.0454071
$947$	37911.3	1.30090	0.650450	−	0.759549i	$-0.274580\pi$
$947$	37911.3	1.30090	0.650450	+	0.759549i	$0.274580\pi$
$948$	2197.59	0.0752893
$949$	13284.8	0.454417
$950$	−2065.84	−0.0705523
$951$	2776.90	0.0946868
$952$	16.3266	0.000555828 0
$953$	26765.9	0.909793	0.454896	−	0.890544i	$-0.349676\pi$
$953$	26765.9	0.909793	0.454896	+	0.890544i	$0.349676\pi$
$954$	763.578	0.0259138
$955$	12236.4	0.414620
$956$	−45573.9	−1.54180
$957$	−1675.46	−0.0565934
$958$	565.406	0.0190683
$959$	73.0031	0.00245818
$960$	−6363.35	−0.213934
$961$	−22804.3	−0.765476
$962$	404.272	0.0135491
$963$	11120.4	0.372119
$964$	−49584.8	−1.65666
$965$	−20105.8	−0.670703
$966$	−1.03130	−3.43493e−5 0
$967$	3008.04	0.100033	0.0500166	−	0.998748i	$-0.484073\pi$
$967$	3008.04	0.100033	0.0500166	+	0.998748i	$0.484073\pi$
$968$	2549.87	0.0846651
$969$	−23800.2	−0.789031
$970$	−1244.44	−0.0411922
$971$	−25034.3	−0.827382	−0.413691	−	0.910417i	$-0.635761\pi$
$971$	−25034.3	−0.827382	−0.413691	+	0.910417i	$0.635761\pi$
$972$	1937.28	0.0639283
$973$	41.7208	0.00137462
$974$	−1334.09	−0.0438881
$975$	10560.2	0.346869
$976$	−25102.3	−0.823264
$977$	482.587	0.0158028	0.00790140	−	0.999969i	$-0.497485\pi$
$977$	482.587	0.0158028	0.00790140	+	0.999969i	$0.497485\pi$
$978$	1351.33	0.0441827
$979$	−4053.03	−0.132314
$980$	−11567.5	−0.377050
$981$	−1862.64	−0.0606214
$982$	238.248	0.00774217
$983$	43929.7	1.42537	0.712686	−	0.701484i	$-0.247479\pi$
$983$	43929.7	1.42537	0.712686	+	0.701484i	$0.247479\pi$
$984$	−3332.58	−0.107966
$985$	−22530.5	−0.728814
$986$	−329.771	−0.0106512
$987$	43.3998	0.00139963
$988$	−30394.5	−0.978722
$989$	9489.69	0.305111
$990$	121.912	0.00391375
$991$	−59379.4	−1.90338	−0.951689	−	0.307062i	$-0.900654\pi$
$991$	−59379.4	−1.90338	−0.951689	+	0.307062i	$0.900654\pi$
$992$	−2656.17	−0.0850134
$993$	5965.53	0.190645
$994$	−4.80576	−0.000153350 0
$995$	1023.51	0.0326105
$996$	695.446	0.0221245
$997$	28674.1	0.910850	0.455425	−	0.890274i	$-0.349487\pi$
$997$	28674.1	0.910850	0.455425	+	0.890274i	$0.349487\pi$
$998$	−1022.88	−0.0324435
$999$	−1997.44	−0.0632595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.4.a.d.1.19	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.4.a.d.1.19	✓	37	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+0.166273 q^{2} -3.00000 q^{3} -7.97235 q^{4} -4.23027 q^{5} -0.498819 q^{6} -0.0898903 q^{7} -2.65577 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.166273 q^{2} -3.00000 q^{3} -7.97235 q^{4} -4.23027 q^{5} -0.498819 q^{6} -0.0898903 q^{7} -2.65577 q^{8} +9.00000 q^{9} -0.703379 q^{10} -19.2581 q^{11} +23.9171 q^{12} +32.8656 q^{13} -0.0149463 q^{14} +12.6908 q^{15} +63.3372 q^{16} +68.3900 q^{17} +1.49646 q^{18} +116.002 q^{19} +33.7252 q^{20} +0.269671 q^{21} -3.20211 q^{22} -23.0000 q^{23} +7.96731 q^{24} -107.105 q^{25} +5.46466 q^{26} -27.0000 q^{27} +0.716637 q^{28} -29.0000 q^{29} +2.11014 q^{30} -83.5866 q^{31} +31.7774 q^{32} +57.7744 q^{33} +11.3714 q^{34} +0.380260 q^{35} -71.7512 q^{36} +73.9793 q^{37} +19.2880 q^{38} -98.5969 q^{39} +11.2346 q^{40} -418.281 q^{41} +0.0448390 q^{42} -412.595 q^{43} +153.533 q^{44} -38.0724 q^{45} -3.82428 q^{46} +160.936 q^{47} -190.012 q^{48} -342.992 q^{49} -17.8086 q^{50} -205.170 q^{51} -262.016 q^{52} +510.257 q^{53} -4.48937 q^{54} +81.4671 q^{55} +0.238728 q^{56} -348.007 q^{57} -4.82191 q^{58} -330.059 q^{59} -101.176 q^{60} -396.328 q^{61} -13.8982 q^{62} -0.809013 q^{63} -501.414 q^{64} -139.030 q^{65} +9.60632 q^{66} +49.9098 q^{67} -545.229 q^{68} +69.0000 q^{69} +0.0632269 q^{70} +321.535 q^{71} -23.9019 q^{72} +404.214 q^{73} +12.3007 q^{74} +321.315 q^{75} -924.810 q^{76} +1.73112 q^{77} -16.3940 q^{78} +91.8836 q^{79} -267.934 q^{80} +81.0000 q^{81} -69.5489 q^{82} +29.0774 q^{83} -2.14991 q^{84} -289.308 q^{85} -68.6034 q^{86} +87.0000 q^{87} +51.1452 q^{88} +210.458 q^{89} -6.33041 q^{90} -2.95430 q^{91} +183.364 q^{92} +250.760 q^{93} +26.7593 q^{94} -490.720 q^{95} -95.3323 q^{96} +1769.23 q^{97} -57.0303 q^{98} -173.323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9	\( 37 q + 4 q^{2} - 111 q^{3} + 146 q^{4} + 15 q^{5} - 12 q^{6} + 8 q^{7} + 3 q^{8} + 333 q^{9} - 136 q^{10} + 109 q^{11} - 438 q^{12} - 269 q^{13} + 121 q^{14} - 45 q^{15} + 390 q^{16} + 180 q^{17} + 36 q^{18} + 117 q^{19} + 287 q^{20} - 24 q^{21} - 128 q^{22} - 851 q^{23} - 9 q^{24} + 490 q^{25} + 677 q^{26} - 999 q^{27} + 775 q^{28} - 1073 q^{29} + 408 q^{30} - 194 q^{31} + 668 q^{32} - 327 q^{33} + 972 q^{34} - 309 q^{35} + 1314 q^{36} - 565 q^{37} + 725 q^{38} + 807 q^{39} + 263 q^{40} + 521 q^{41} - 363 q^{42} - 61 q^{43} + 2242 q^{44} + 135 q^{45} - 92 q^{46} + 1142 q^{47} - 1170 q^{48} + 919 q^{49} + 1833 q^{50} - 540 q^{51} - 10 q^{52} - 120 q^{53} - 108 q^{54} - 996 q^{55} + 1707 q^{56} - 351 q^{57} - 116 q^{58} + 1073 q^{59} - 861 q^{60} - 428 q^{61} + 174 q^{62} + 72 q^{63} + 1479 q^{64} + 1410 q^{65} + 384 q^{66} + 175 q^{67} + 1483 q^{68} + 2553 q^{69} + 675 q^{70} + 2236 q^{71} + 27 q^{72} - 1058 q^{73} - 695 q^{74} - 1470 q^{75} + 1345 q^{76} - 1547 q^{77} - 2031 q^{78} + 1972 q^{79} - 2017 q^{80} + 2997 q^{81} + 2429 q^{82} - 832 q^{83} - 2325 q^{84} + 2299 q^{85} + 1527 q^{86} + 3219 q^{87} + 2579 q^{88} + 2817 q^{89} - 1224 q^{90} + 3175 q^{91} - 3358 q^{92} + 582 q^{93} + 1900 q^{94} + 8017 q^{95} - 2004 q^{96} + 912 q^{97} - 2565 q^{98} + 981 q^{99}+O(q^{100}) \) 37 * q + 4 * q^2 - 111 * q^3 + 146 * q^4 + 15 * q^5 - 12 * q^6 + 8 * q^7 + 3 * q^8 + 333 * q^9 - 136 * q^10 + 109 * q^11 - 438 * q^12 - 269 * q^13 + 121 * q^14 - 45 * q^15 + 390 * q^16 + 180 * q^17 + 36 * q^18 + 117 * q^19 + 287 * q^20 - 24 * q^21 - 128 * q^22 - 851 * q^23 - 9 * q^24 + 490 * q^25 + 677 * q^26 - 999 * q^27 + 775 * q^28 - 1073 * q^29 + 408 * q^30 - 194 * q^31 + 668 * q^32 - 327 * q^33 + 972 * q^34 - 309 * q^35 + 1314 * q^36 - 565 * q^37 + 725 * q^38 + 807 * q^39 + 263 * q^40 + 521 * q^41 - 363 * q^42 - 61 * q^43 + 2242 * q^44 + 135 * q^45 - 92 * q^46 + 1142 * q^47 - 1170 * q^48 + 919 * q^49 + 1833 * q^50 - 540 * q^51 - 10 * q^52 - 120 * q^53 - 108 * q^54 - 996 * q^55 + 1707 * q^56 - 351 * q^57 - 116 * q^58 + 1073 * q^59 - 861 * q^60 - 428 * q^61 + 174 * q^62 + 72 * q^63 + 1479 * q^64 + 1410 * q^65 + 384 * q^66 + 175 * q^67 + 1483 * q^68 + 2553 * q^69 + 675 * q^70 + 2236 * q^71 + 27 * q^72 - 1058 * q^73 - 695 * q^74 - 1470 * q^75 + 1345 * q^76 - 1547 * q^77 - 2031 * q^78 + 1972 * q^79 - 2017 * q^80 + 2997 * q^81 + 2429 * q^82 - 832 * q^83 - 2325 * q^84 + 2299 * q^85 + 1527 * q^86 + 3219 * q^87 + 2579 * q^88 + 2817 * q^89 - 1224 * q^90 + 3175 * q^91 - 3358 * q^92 + 582 * q^93 + 1900 * q^94 + 8017 * q^95 - 2004 * q^96 + 912 * q^97 - 2565 * q^98 + 981 * q^99

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