LMFDB - Embedded newform 2013.4.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, 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("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.01355 q^{2} +3.00000 q^{3} -6.97272 q^{4} +12.1717 q^{5} -3.04064 q^{6} +28.0678 q^{7} +15.1756 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.01355 q^{2} +3.00000 q^{3} -6.97272 q^{4} +12.1717 q^{5} -3.04064 q^{6} +28.0678 q^{7} +15.1756 q^{8} +9.00000 q^{9} -12.3366 q^{10} -11.0000 q^{11} -20.9182 q^{12} -44.9062 q^{13} -28.4480 q^{14} +36.5150 q^{15} +40.4007 q^{16} -112.229 q^{17} -9.12192 q^{18} -46.9155 q^{19} -84.8697 q^{20} +84.2034 q^{21} +11.1490 q^{22} +46.4507 q^{23} +45.5267 q^{24} +23.1496 q^{25} +45.5145 q^{26} +27.0000 q^{27} -195.709 q^{28} +59.0940 q^{29} -37.0097 q^{30} +68.7667 q^{31} -162.352 q^{32} -33.0000 q^{33} +113.749 q^{34} +341.632 q^{35} -62.7545 q^{36} +205.412 q^{37} +47.5510 q^{38} -134.718 q^{39} +184.712 q^{40} +263.333 q^{41} -85.3441 q^{42} -233.359 q^{43} +76.7000 q^{44} +109.545 q^{45} -47.0800 q^{46} +457.622 q^{47} +121.202 q^{48} +444.802 q^{49} -23.4632 q^{50} -336.687 q^{51} +313.118 q^{52} -247.625 q^{53} -27.3658 q^{54} -133.888 q^{55} +425.945 q^{56} -140.746 q^{57} -59.8945 q^{58} +564.067 q^{59} -254.609 q^{60} +61.0000 q^{61} -69.6982 q^{62} +252.610 q^{63} -158.654 q^{64} -546.583 q^{65} +33.4470 q^{66} +915.055 q^{67} +782.542 q^{68} +139.352 q^{69} -346.260 q^{70} +368.092 q^{71} +136.580 q^{72} +519.085 q^{73} -208.194 q^{74} +69.4488 q^{75} +327.129 q^{76} -308.746 q^{77} +136.543 q^{78} +363.667 q^{79} +491.744 q^{80} +81.0000 q^{81} -266.900 q^{82} -1246.87 q^{83} -587.127 q^{84} -1366.02 q^{85} +236.520 q^{86} +177.282 q^{87} -166.931 q^{88} +1480.09 q^{89} -111.029 q^{90} -1260.42 q^{91} -323.888 q^{92} +206.300 q^{93} -463.821 q^{94} -571.040 q^{95} -487.057 q^{96} +1638.27 q^{97} -450.828 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.01355	−0.358343	−0.179171	−	0.983818i	$-0.557342\pi$
$2$	−1.01355	−0.358343	−0.179171	+	0.983818i	$0.557342\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−6.97272	−0.871590
$5$	12.1717	1.08867	0.544334	−	0.838869i	$-0.316783\pi$
$5$	12.1717	1.08867	0.544334	+	0.838869i	$0.316783\pi$
$6$	−3.04064	−0.206889
$7$	28.0678	1.51552	0.757760	−	0.652534i	$-0.226294\pi$
$7$	28.0678	1.51552	0.757760	+	0.652534i	$0.226294\pi$
$8$	15.1756	0.670671
$9$	9.00000	0.333333
$10$	−12.3366	−0.390116
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−20.9182	−0.503213
$13$	−44.9062	−0.958056	−0.479028	−	0.877800i	$-0.659011\pi$
$13$	−44.9062	−0.958056	−0.479028	+	0.877800i	$0.659011\pi$
$14$	−28.4480	−0.543076
$15$	36.5150	0.628542
$16$	40.4007	0.631260
$17$	−112.229	−1.60115	−0.800575	−	0.599232i	$-0.795473\pi$
$17$	−112.229	−1.60115	−0.800575	+	0.599232i	$0.795473\pi$
$18$	−9.12192	−0.119448
$19$	−46.9155	−0.566482	−0.283241	−	0.959049i	$-0.591410\pi$
$19$	−46.9155	−0.566482	−0.283241	+	0.959049i	$0.591410\pi$
$20$	−84.8697	−0.948872
$21$	84.2034	0.874986
$22$	11.1490	0.108044
$23$	46.4507	0.421115	0.210558	−	0.977581i	$-0.432472\pi$
$23$	46.4507	0.421115	0.210558	+	0.977581i	$0.432472\pi$
$24$	45.5267	0.387212
$25$	23.1496	0.185197
$26$	45.5145	0.343312
$27$	27.0000	0.192450
$28$	−195.709	−1.32091
$29$	59.0940	0.378396	0.189198	−	0.981939i	$-0.439411\pi$
$29$	59.0940	0.378396	0.189198	+	0.981939i	$0.439411\pi$
$30$	−37.0097	−0.225234
$31$	68.7667	0.398415	0.199207	−	0.979957i	$-0.436163\pi$
$31$	68.7667	0.398415	0.199207	+	0.979957i	$0.436163\pi$
$32$	−162.352	−0.896879
$33$	−33.0000	−0.174078
$34$	113.749	0.573761
$35$	341.632	1.64990
$36$	−62.7545	−0.290530
$37$	205.412	0.912688	0.456344	−	0.889803i	$-0.349159\pi$
$37$	205.412	0.912688	0.456344	+	0.889803i	$0.349159\pi$
$38$	47.5510	0.202995
$39$	−134.718	−0.553134
$40$	184.712	0.730138
$41$	263.333	1.00307	0.501533	−	0.865139i	$-0.332770\pi$
$41$	263.333	1.00307	0.501533	+	0.865139i	$0.332770\pi$
$42$	−85.3441	−0.313545
$43$	−233.359	−0.827602	−0.413801	−	0.910367i	$-0.635799\pi$
$43$	−233.359	−0.827602	−0.413801	+	0.910367i	$0.635799\pi$
$44$	76.7000	0.262794
$45$	109.545	0.362889
$46$	−47.0800	−0.150904
$47$	457.622	1.42023	0.710117	−	0.704084i	$-0.248642\pi$
$47$	457.622	1.42023	0.710117	+	0.704084i	$0.248642\pi$
$48$	121.202	0.364458
$49$	444.802	1.29680
$50$	−23.4632	−0.0663639
$51$	−336.687	−0.924425
$52$	313.118	0.835033
$53$	−247.625	−0.641773	−0.320886	−	0.947118i	$-0.603981\pi$
$53$	−247.625	−0.641773	−0.320886	+	0.947118i	$0.603981\pi$
$54$	−27.3658	−0.0689631
$55$	−133.888	−0.328246
$56$	425.945	1.01641
$57$	−140.746	−0.327058
$58$	−59.8945	−0.135595
$59$	564.067	1.24467	0.622333	−	0.782752i	$-0.286185\pi$
$59$	564.067	1.24467	0.622333	+	0.782752i	$0.286185\pi$
$60$	−254.609	−0.547832
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−69.6982	−0.142769
$63$	252.610	0.505173
$64$	−158.654	−0.309870
$65$	−546.583	−1.04300
$66$	33.4470	0.0623795
$67$	915.055	1.66853	0.834267	−	0.551361i	$-0.185891\pi$
$67$	915.055	1.66853	0.834267	+	0.551361i	$0.185891\pi$
$68$	782.542	1.39555
$69$	139.352	0.243131
$70$	−346.260	−0.591229
$71$	368.092	0.615275	0.307637	−	0.951504i	$-0.400462\pi$
$71$	368.092	0.615275	0.307637	+	0.951504i	$0.400462\pi$
$72$	136.580	0.223557
$73$	519.085	0.832251	0.416125	−	0.909307i	$-0.363388\pi$
$73$	519.085	0.832251	0.416125	+	0.909307i	$0.363388\pi$
$74$	−208.194	−0.327055
$75$	69.4488	0.106923
$76$	327.129	0.493740
$77$	−308.746	−0.456946
$78$	136.543	0.198212
$79$	363.667	0.517920	0.258960	−	0.965888i	$-0.416620\pi$
$79$	363.667	0.517920	0.258960	+	0.965888i	$0.416620\pi$
$80$	491.744	0.687233
$81$	81.0000	0.111111
$82$	−266.900	−0.359441
$83$	−1246.87	−1.64894	−0.824469	−	0.565907i	$-0.808526\pi$
$83$	−1246.87	−1.64894	−0.824469	+	0.565907i	$0.808526\pi$
$84$	−587.127	−0.762629
$85$	−1366.02	−1.74312
$86$	236.520	0.296565
$87$	177.282	0.218467
$88$	−166.931	−0.202215
$89$	1480.09	1.76280	0.881401	−	0.472368i	$-0.156601\pi$
$89$	1480.09	1.76280	0.881401	+	0.472368i	$0.156601\pi$
$90$	−111.029	−0.130039
$91$	−1260.42	−1.45195
$92$	−323.888	−0.367040
$93$	206.300	0.230025
$94$	−463.821	−0.508930
$95$	−571.040	−0.616710
$96$	−487.057	−0.517813
$97$	1638.27	1.71486	0.857430	−	0.514600i	$-0.172060\pi$
$97$	1638.27	1.71486	0.857430	+	0.514600i	$0.172060\pi$
$98$	−450.828	−0.464699
$99$	−99.0000	−0.100504
$100$	−161.416	−0.161416
$101$	92.7199	0.0913463	0.0456731	−	0.998956i	$-0.485457\pi$
$101$	92.7199	0.0913463	0.0456731	+	0.998956i	$0.485457\pi$
$102$	341.248	0.331261
$103$	−548.088	−0.524318	−0.262159	−	0.965025i	$-0.584434\pi$
$103$	−548.088	−0.524318	−0.262159	+	0.965025i	$0.584434\pi$
$104$	−681.476	−0.642540
$105$	1024.90	0.952568
$106$	250.980	0.229975
$107$	890.176	0.804267	0.402133	−	0.915581i	$-0.368269\pi$
$107$	890.176	0.804267	0.402133	+	0.915581i	$0.368269\pi$
$108$	−188.264	−0.167738
$109$	−165.548	−0.145473	−0.0727367	−	0.997351i	$-0.523173\pi$
$109$	−165.548	−0.145473	−0.0727367	+	0.997351i	$0.523173\pi$
$110$	135.702	0.117624
$111$	616.235	0.526941
$112$	1133.96	0.956687
$113$	668.369	0.556414	0.278207	−	0.960521i	$-0.410260\pi$
$113$	668.369	0.556414	0.278207	+	0.960521i	$0.410260\pi$
$114$	142.653	0.117199
$115$	565.383	0.458454
$116$	−412.046	−0.329806
$117$	−404.155	−0.319352
$118$	−571.709	−0.446017
$119$	−3150.03	−2.42657
$120$	554.136	0.421545
$121$	121.000	0.0909091
$122$	−61.8263	−0.0458811
$123$	789.999	0.579120
$124$	−479.491	−0.347255
$125$	−1239.69	−0.887050
$126$	−256.032	−0.181025
$127$	−1208.69	−0.844520	−0.422260	−	0.906475i	$-0.638763\pi$
$127$	−1208.69	−0.844520	−0.422260	+	0.906475i	$0.638763\pi$
$128$	1459.62	1.00792
$129$	−700.076	−0.477816
$130$	553.987	0.373753
$131$	−1475.55	−0.984116	−0.492058	−	0.870563i	$-0.663755\pi$
$131$	−1475.55	−0.984116	−0.492058	+	0.870563i	$0.663755\pi$
$132$	230.100	0.151724
$133$	−1316.82	−0.858514
$134$	−927.451	−0.597907
$135$	328.635	0.209514
$136$	−1703.14	−1.07384
$137$	−3081.77	−1.92185	−0.960924	−	0.276812i	$-0.910722\pi$
$137$	−3081.77	−1.92185	−0.960924	+	0.276812i	$0.910722\pi$
$138$	−141.240	−0.0871242
$139$	716.666	0.437315	0.218658	−	0.975802i	$-0.429832\pi$
$139$	716.666	0.437315	0.218658	+	0.975802i	$0.429832\pi$
$140$	−2382.11	−1.43803
$141$	1372.86	0.819972
$142$	−373.079	−0.220479
$143$	493.968	0.288865
$144$	363.606	0.210420
$145$	719.273	0.411947
$146$	−526.117	−0.298231
$147$	1334.41	0.748708
$148$	−1432.28	−0.795490
$149$	570.925	0.313906	0.156953	−	0.987606i	$-0.449833\pi$
$149$	570.925	0.313906	0.156953	+	0.987606i	$0.449833\pi$
$150$	−70.3896	−0.0383152
$151$	1874.00	1.00996	0.504980	−	0.863131i	$-0.331500\pi$
$151$	1874.00	1.00996	0.504980	+	0.863131i	$0.331500\pi$
$152$	−711.968	−0.379923
$153$	−1010.06	−0.533717
$154$	312.928	0.163743
$155$	837.005	0.433741
$156$	939.355	0.482106
$157$	−517.590	−0.263110	−0.131555	−	0.991309i	$-0.541997\pi$
$157$	−517.590	−0.263110	−0.131555	+	0.991309i	$0.541997\pi$
$158$	−368.593	−0.185593
$159$	−742.876	−0.370528
$160$	−1976.10	−0.976402
$161$	1303.77	0.638208
$162$	−82.0973	−0.0398159
$163$	3631.61	1.74509	0.872546	−	0.488532i	$-0.162467\pi$
$163$	3631.61	1.74509	0.872546	+	0.488532i	$0.162467\pi$
$164$	−1836.15	−0.874262
$165$	−401.665	−0.189513
$166$	1263.76	0.590885
$167$	−20.8364	−0.00965489	−0.00482744	−	0.999988i	$-0.501537\pi$
$167$	−20.8364	−0.00965489	−0.00482744	+	0.999988i	$0.501537\pi$
$168$	1277.83	0.586827
$169$	−180.436	−0.0821286
$170$	1384.52	0.624635
$171$	−422.239	−0.188827
$172$	1627.15	0.721330
$173$	1212.96	0.533059	0.266530	−	0.963827i	$-0.414123\pi$
$173$	1212.96	0.533059	0.266530	+	0.963827i	$0.414123\pi$
$174$	−179.684	−0.0782861
$175$	649.759	0.280669
$176$	−444.407	−0.190332
$177$	1692.20	0.718609
$178$	−1500.14	−0.631688
$179$	1708.91	0.713573	0.356787	−	0.934186i	$-0.383872\pi$
$179$	1708.91	0.713573	0.356787	+	0.934186i	$0.383872\pi$
$180$	−763.827	−0.316291
$181$	2006.87	0.824142	0.412071	−	0.911152i	$-0.364805\pi$
$181$	2006.87	0.824142	0.412071	+	0.911152i	$0.364805\pi$
$182$	1277.49	0.520297
$183$	183.000	0.0739221
$184$	704.915	0.282430
$185$	2500.20	0.993614
$186$	−209.095	−0.0824278
$187$	1234.52	0.482765
$188$	−3190.87	−1.23786
$189$	757.831	0.291662
$190$	578.775	0.220994
$191$	−2906.16	−1.10096	−0.550478	−	0.834850i	$-0.685554\pi$
$191$	−2906.16	−1.10096	−0.550478	+	0.834850i	$0.685554\pi$
$192$	−475.961	−0.178904
$193$	435.069	0.162264	0.0811319	−	0.996703i	$-0.474146\pi$
$193$	435.069	0.162264	0.0811319	+	0.996703i	$0.474146\pi$
$194$	−1660.47	−0.614508
$195$	−1639.75	−0.602179
$196$	−3101.48	−1.13028
$197$	2950.61	1.06712	0.533559	−	0.845763i	$-0.320854\pi$
$197$	2950.61	1.06712	0.533559	+	0.845763i	$0.320854\pi$
$198$	100.341	0.0360148
$199$	−896.691	−0.319421	−0.159710	−	0.987164i	$-0.551056\pi$
$199$	−896.691	−0.319421	−0.159710	+	0.987164i	$0.551056\pi$
$200$	351.308	0.124206
$201$	2745.16	0.963328
$202$	−93.9759	−0.0327333
$203$	1658.64	0.573466
$204$	2347.63	0.805720
$205$	3205.20	1.09200
$206$	555.513	0.187886
$207$	418.057	0.140372
$208$	−1814.24	−0.604783
$209$	516.070	0.170801
$210$	−1038.78	−0.341346
$211$	−1010.95	−0.329844	−0.164922	−	0.986307i	$-0.552737\pi$
$211$	−1010.95	−0.329844	−0.164922	+	0.986307i	$0.552737\pi$
$212$	1726.62	0.559363
$213$	1104.28	0.355229
$214$	−902.235	−0.288203
$215$	−2840.37	−0.900983
$216$	409.740	0.129071
$217$	1930.13	0.603805
$218$	167.790	0.0521293
$219$	1557.25	0.480500
$220$	933.567	0.286096
$221$	5039.78	1.53399
$222$	−624.583	−0.188825
$223$	1812.17	0.544180	0.272090	−	0.962272i	$-0.412285\pi$
$223$	1812.17	0.544180	0.272090	+	0.962272i	$0.412285\pi$
$224$	−4556.88	−1.35924
$225$	208.346	0.0617323
$226$	−677.423	−0.199387
$227$	1960.61	0.573262	0.286631	−	0.958041i	$-0.407465\pi$
$227$	1960.61	0.573262	0.286631	+	0.958041i	$0.407465\pi$
$228$	981.386	0.285061
$229$	2907.57	0.839028	0.419514	−	0.907749i	$-0.362200\pi$
$229$	2907.57	0.839028	0.419514	+	0.907749i	$0.362200\pi$
$230$	−573.042	−0.164284
$231$	−926.238	−0.263818
$232$	896.784	0.253779
$233$	2774.70	0.780158	0.390079	−	0.920781i	$-0.372448\pi$
$233$	2774.70	0.780158	0.390079	+	0.920781i	$0.372448\pi$
$234$	409.630	0.114437
$235$	5570.02	1.54616
$236$	−3933.09	−1.08484
$237$	1091.00	0.299021
$238$	3192.70	0.869545
$239$	−1410.99	−0.381881	−0.190941	−	0.981602i	$-0.561154\pi$
$239$	−1410.99	−0.381881	−0.190941	+	0.981602i	$0.561154\pi$
$240$	1475.23	0.396774
$241$	−4890.93	−1.30727	−0.653637	−	0.756809i	$-0.726757\pi$
$241$	−4890.93	−1.30727	−0.653637	+	0.756809i	$0.726757\pi$
$242$	−122.639	−0.0325766
$243$	243.000	0.0641500
$244$	−425.336	−0.111596
$245$	5413.99	1.41178
$246$	−800.700	−0.207524
$247$	2106.79	0.542721
$248$	1043.57	0.267205
$249$	−3740.61	−0.952015
$250$	1256.48	0.317868
$251$	−454.177	−0.114213	−0.0571064	−	0.998368i	$-0.518187\pi$
$251$	−454.177	−0.114213	−0.0571064	+	0.998368i	$0.518187\pi$
$252$	−1761.38	−0.440304
$253$	−510.958	−0.126971
$254$	1225.07	0.302628
$255$	−4098.05	−1.00639
$256$	−210.166	−0.0513099
$257$	2809.31	0.681868	0.340934	−	0.940087i	$-0.389257\pi$
$257$	2809.31	0.681868	0.340934	+	0.940087i	$0.389257\pi$
$258$	709.560	0.171222
$259$	5765.46	1.38320
$260$	3811.17	0.909073
$261$	531.846	0.126132
$262$	1495.54	0.352651
$263$	4945.68	1.15956	0.579778	−	0.814774i	$-0.303139\pi$
$263$	4945.68	1.15956	0.579778	+	0.814774i	$0.303139\pi$
$264$	−500.793	−0.116749
$265$	−3014.01	−0.698677
$266$	1334.65	0.307642
$267$	4440.28	1.01775
$268$	−6380.42	−1.45428
$269$	−2195.95	−0.497729	−0.248865	−	0.968538i	$-0.580057\pi$
$269$	−2195.95	−0.497729	−0.248865	+	0.968538i	$0.580057\pi$
$270$	−333.087	−0.0750779
$271$	−2283.57	−0.511870	−0.255935	−	0.966694i	$-0.582383\pi$
$271$	−2283.57	−0.511870	−0.255935	+	0.966694i	$0.582383\pi$
$272$	−4534.13	−1.01074
$273$	−3781.25	−0.838285
$274$	3123.52	0.688680
$275$	−254.646	−0.0558389
$276$	−971.664	−0.211911
$277$	4347.94	0.943112	0.471556	−	0.881836i	$-0.343692\pi$
$277$	4347.94	0.943112	0.471556	+	0.881836i	$0.343692\pi$
$278$	−726.374	−0.156709
$279$	618.900	0.132805
$280$	5184.46	1.10654
$281$	−334.179	−0.0709447	−0.0354724	−	0.999371i	$-0.511294\pi$
$281$	−334.179	−0.0709447	−0.0354724	+	0.999371i	$0.511294\pi$
$282$	−1391.46	−0.293831
$283$	−1662.62	−0.349231	−0.174615	−	0.984637i	$-0.555868\pi$
$283$	−1662.62	−0.349231	−0.174615	+	0.984637i	$0.555868\pi$
$284$	−2566.60	−0.536268
$285$	−1713.12	−0.356058
$286$	−500.659	−0.103513
$287$	7391.18	1.52017
$288$	−1461.17	−0.298960
$289$	7682.37	1.56368
$290$	−729.017	−0.147618
$291$	4914.82	0.990075
$292$	−3619.44	−0.725382
$293$	6716.06	1.33910	0.669550	−	0.742767i	$-0.266487\pi$
$293$	6716.06	1.33910	0.669550	+	0.742767i	$0.266487\pi$
$294$	−1352.48	−0.268294
$295$	6865.64	1.35503
$296$	3117.24	0.612114
$297$	−297.000	−0.0580259
$298$	−578.659	−0.112486
$299$	−2085.92	−0.403452
$300$	−484.247	−0.0931934
$301$	−6549.87	−1.25425
$302$	−1899.39	−0.361912
$303$	278.160	0.0527388
$304$	−1895.42	−0.357597
$305$	742.472	0.139390
$306$	1023.74	0.191254
$307$	−2459.00	−0.457143	−0.228571	−	0.973527i	$-0.573405\pi$
$307$	−2459.00	−0.457143	−0.228571	+	0.973527i	$0.573405\pi$
$308$	2152.80	0.398270
$309$	−1644.27	−0.302715
$310$	−848.344	−0.155428
$311$	−3423.46	−0.624202	−0.312101	−	0.950049i	$-0.601033\pi$
$311$	−3423.46	−0.624202	−0.312101	+	0.950049i	$0.601033\pi$
$312$	−2044.43	−0.370971
$313$	−445.102	−0.0803791	−0.0401896	−	0.999192i	$-0.512796\pi$
$313$	−445.102	−0.0803791	−0.0401896	+	0.999192i	$0.512796\pi$
$314$	524.602	0.0942834
$315$	3074.69	0.549966
$316$	−2535.75	−0.451414
$317$	2509.28	0.444591	0.222296	−	0.974979i	$-0.428645\pi$
$317$	2509.28	0.444591	0.222296	+	0.974979i	$0.428645\pi$
$318$	752.939	0.132776
$319$	−650.034	−0.114091
$320$	−1931.08	−0.337346
$321$	2670.53	0.464344
$322$	−1321.43	−0.228697
$323$	5265.28	0.907022
$324$	−564.791	−0.0968434
$325$	−1039.56	−0.177429
$326$	−3680.81	−0.625341
$327$	−496.643	−0.0839891
$328$	3996.22	0.672727
$329$	12844.4	2.15239
$330$	407.106	0.0679105
$331$	−4564.91	−0.758037	−0.379018	−	0.925389i	$-0.623738\pi$
$331$	−4564.91	−0.758037	−0.379018	+	0.925389i	$0.623738\pi$
$332$	8694.08	1.43720
$333$	1848.70	0.304229
$334$	21.1186	0.00345976
$335$	11137.7	1.81648
$336$	3401.87	0.552344
$337$	−10152.8	−1.64112	−0.820560	−	0.571560i	$-0.806338\pi$
$337$	−10152.8	−1.64112	−0.820560	+	0.571560i	$0.806338\pi$
$338$	182.881	0.0294302
$339$	2005.11	0.321246
$340$	9524.85	1.51929
$341$	−756.433	−0.120127
$342$	427.959	0.0676649
$343$	2857.37	0.449805
$344$	−3541.35	−0.555049
$345$	1696.15	0.264689
$346$	−1229.39	−0.191018
$347$	−961.928	−0.148816	−0.0744078	−	0.997228i	$-0.523707\pi$
$347$	−961.928	−0.148816	−0.0744078	+	0.997228i	$0.523707\pi$
$348$	−1236.14	−0.190414
$349$	−441.666	−0.0677417	−0.0338708	−	0.999426i	$-0.510783\pi$
$349$	−441.666	−0.0677417	−0.0338708	+	0.999426i	$0.510783\pi$
$350$	−658.561	−0.100576
$351$	−1212.47	−0.184378
$352$	1785.88	0.270419
$353$	6016.28	0.907123	0.453561	−	0.891225i	$-0.350153\pi$
$353$	6016.28	0.907123	0.453561	+	0.891225i	$0.350153\pi$
$354$	−1715.13	−0.257508
$355$	4480.30	0.669830
$356$	−10320.3	−1.53644
$357$	−9450.08	−1.40098
$358$	−1732.06	−0.255704
$359$	−26.8129	−0.00394186	−0.00197093	−	0.999998i	$-0.500627\pi$
$359$	−26.8129	−0.00394186	−0.00197093	+	0.999998i	$0.500627\pi$
$360$	1662.41	0.243379
$361$	−4657.94	−0.679099
$362$	−2034.06	−0.295326
$363$	363.000	0.0524864
$364$	8788.55	1.26551
$365$	6318.13	0.906044
$366$	−185.479	−0.0264895
$367$	−3950.51	−0.561894	−0.280947	−	0.959723i	$-0.590649\pi$
$367$	−3950.51	−0.561894	−0.280947	+	0.959723i	$0.590649\pi$
$368$	1876.64	0.265833
$369$	2370.00	0.334355
$370$	−2534.07	−0.356054
$371$	−6950.30	−0.972619
$372$	−1438.47	−0.200488
$373$	1250.07	0.173528	0.0867642	−	0.996229i	$-0.472347\pi$
$373$	1250.07	0.173528	0.0867642	+	0.996229i	$0.472347\pi$
$374$	−1251.24	−0.172995
$375$	−3719.07	−0.512138
$376$	6944.66	0.952509
$377$	−2653.69	−0.362525
$378$	−768.097	−0.104515
$379$	−702.129	−0.0951608	−0.0475804	−	0.998867i	$-0.515151\pi$
$379$	−702.129	−0.0951608	−0.0475804	+	0.998867i	$0.515151\pi$
$380$	3981.70	0.537519
$381$	−3626.08	−0.487584
$382$	2945.53	0.394520
$383$	−14190.6	−1.89323	−0.946614	−	0.322369i	$-0.895521\pi$
$383$	−14190.6	−1.89323	−0.946614	+	0.322369i	$0.895521\pi$
$384$	4378.87	0.581922
$385$	−3757.95	−0.497463
$386$	−440.962	−0.0581461
$387$	−2100.23	−0.275867
$388$	−11423.2	−1.49466
$389$	−2413.80	−0.314613	−0.157307	−	0.987550i	$-0.550281\pi$
$389$	−2413.80	−0.314613	−0.157307	+	0.987550i	$0.550281\pi$
$390$	1661.96	0.215786
$391$	−5213.12	−0.674268
$392$	6750.12	0.869726
$393$	−4426.64	−0.568179
$394$	−2990.58	−0.382394
$395$	4426.43	0.563843
$396$	690.300	0.0875981
$397$	14585.2	1.84385	0.921926	−	0.387366i	$-0.126615\pi$
$397$	14585.2	1.84385	0.921926	+	0.387366i	$0.126615\pi$
$398$	908.838	0.114462
$399$	−3950.45	−0.495663
$400$	935.259	0.116907
$401$	324.181	0.0403711	0.0201856	−	0.999796i	$-0.493574\pi$
$401$	324.181	0.0403711	0.0201856	+	0.999796i	$0.493574\pi$
$402$	−2782.35	−0.345202
$403$	−3088.05	−0.381704
$404$	−646.510	−0.0796165
$405$	985.905	0.120963
$406$	−1681.11	−0.205498
$407$	−2259.53	−0.275186
$408$	−5109.42	−0.619985
$409$	−10748.8	−1.29950	−0.649750	−	0.760148i	$-0.725127\pi$
$409$	−10748.8	−1.29950	−0.649750	+	0.760148i	$0.725127\pi$
$410$	−3248.62	−0.391312
$411$	−9245.30	−1.10958
$412$	3821.67	0.456991
$413$	15832.1	1.88632
$414$	−423.720	−0.0503012
$415$	−15176.5	−1.79514
$416$	7290.62	0.859260
$417$	2150.00	0.252484
$418$	−523.061	−0.0612052
$419$	−14612.2	−1.70371	−0.851853	−	0.523781i	$-0.824521\pi$
$419$	−14612.2	−1.70371	−0.851853	+	0.523781i	$0.824521\pi$
$420$	−7146.32	−0.830249
$421$	4265.36	0.493779	0.246889	−	0.969044i	$-0.420592\pi$
$421$	4265.36	0.493779	0.246889	+	0.969044i	$0.420592\pi$
$422$	1024.65	0.118197
$423$	4118.59	0.473411
$424$	−3757.85	−0.430418
$425$	−2598.06	−0.296528
$426$	−1119.24	−0.127294
$427$	1712.14	0.194042
$428$	−6206.95	−0.700991
$429$	1481.90	0.166776
$430$	2878.84	0.322861
$431$	7513.96	0.839756	0.419878	−	0.907581i	$-0.362073\pi$
$431$	7513.96	0.839756	0.419878	+	0.907581i	$0.362073\pi$
$432$	1090.82	0.121486
$433$	−3840.09	−0.426196	−0.213098	−	0.977031i	$-0.568355\pi$
$433$	−3840.09	−0.426196	−0.213098	+	0.977031i	$0.568355\pi$
$434$	−1956.28	−0.216369
$435$	2157.82	0.237838
$436$	1154.32	0.126793
$437$	−2179.26	−0.238554
$438$	−1578.35	−0.172184
$439$	8081.19	0.878574	0.439287	−	0.898347i	$-0.355231\pi$
$439$	8081.19	0.878574	0.439287	+	0.898347i	$0.355231\pi$
$440$	−2031.83	−0.220145
$441$	4003.22	0.432266
$442$	−5108.05	−0.549695
$443$	−1293.24	−0.138699	−0.0693494	−	0.997592i	$-0.522092\pi$
$443$	−1293.24	−0.138699	−0.0693494	+	0.997592i	$0.522092\pi$
$444$	−4296.84	−0.459277
$445$	18015.2	1.91911
$446$	−1836.72	−0.195003
$447$	1712.77	0.181234
$448$	−4453.06	−0.469615
$449$	9429.93	0.991149	0.495574	−	0.868566i	$-0.334958\pi$
$449$	9429.93	0.991149	0.495574	+	0.868566i	$0.334958\pi$
$450$	−211.169	−0.0221213
$451$	−2896.66	−0.302436
$452$	−4660.35	−0.484965
$453$	5622.01	0.583101
$454$	−1987.17	−0.205424
$455$	−15341.4	−1.58069
$456$	−2135.91	−0.219349
$457$	7397.12	0.757162	0.378581	−	0.925568i	$-0.376412\pi$
$457$	7397.12	0.757162	0.378581	+	0.925568i	$0.376412\pi$
$458$	−2946.96	−0.300660
$459$	−3030.19	−0.308142
$460$	−3942.26	−0.399584
$461$	−4763.00	−0.481204	−0.240602	−	0.970624i	$-0.577345\pi$
$461$	−4763.00	−0.481204	−0.240602	+	0.970624i	$0.577345\pi$
$462$	938.785	0.0945373
$463$	−7482.76	−0.751087	−0.375544	−	0.926805i	$-0.622544\pi$
$463$	−7482.76	−0.751087	−0.375544	+	0.926805i	$0.622544\pi$
$464$	2387.44	0.238866
$465$	2511.02	0.250421
$466$	−2812.29	−0.279564
$467$	−5552.04	−0.550145	−0.275072	−	0.961424i	$-0.588702\pi$
$467$	−5552.04	−0.550145	−0.275072	+	0.961424i	$0.588702\pi$
$468$	2818.06	0.278344
$469$	25683.6	2.52869
$470$	−5645.47	−0.554056
$471$	−1552.77	−0.151906
$472$	8560.04	0.834762
$473$	2566.95	0.249531
$474$	−1105.78	−0.107152
$475$	−1086.07	−0.104911
$476$	21964.3	2.11498
$477$	−2228.63	−0.213924
$478$	1430.11	0.136844
$479$	19778.6	1.88666	0.943328	−	0.331862i	$-0.107677\pi$
$479$	19778.6	1.88666	0.943328	+	0.331862i	$0.107677\pi$
$480$	−5928.30	−0.563726
$481$	−9224.25	−0.874407
$482$	4957.19	0.468452
$483$	3911.31	0.368470
$484$	−843.700	−0.0792355
$485$	19940.5	1.86691
$486$	−246.292	−0.0229877
$487$	−698.501	−0.0649940	−0.0324970	−	0.999472i	$-0.510346\pi$
$487$	−698.501	−0.0649940	−0.0324970	+	0.999472i	$0.510346\pi$
$488$	925.709	0.0858706
$489$	10894.8	1.00753
$490$	−5487.33	−0.505902
$491$	−5974.69	−0.549153	−0.274576	−	0.961565i	$-0.588538\pi$
$491$	−5974.69	−0.549153	−0.274576	+	0.961565i	$0.588538\pi$
$492$	−5508.44	−0.504756
$493$	−6632.07	−0.605869
$494$	−2135.33	−0.194480
$495$	−1205.00	−0.109415
$496$	2778.22	0.251503
$497$	10331.5	0.932461
$498$	3791.28	0.341148
$499$	7396.94	0.663592	0.331796	−	0.943351i	$-0.392345\pi$
$499$	7396.94	0.663592	0.331796	+	0.943351i	$0.392345\pi$
$500$	8644.01	0.773144
$501$	−62.5091	−0.00557425
$502$	460.330	0.0409274
$503$	1097.63	0.0972982	0.0486491	−	0.998816i	$-0.484508\pi$
$503$	1097.63	0.0972982	0.0486491	+	0.998816i	$0.484508\pi$
$504$	3833.50	0.338805
$505$	1128.56	0.0994457
$506$	517.880	0.0454991
$507$	−541.309	−0.0474170
$508$	8427.88	0.736076
$509$	1860.10	0.161979	0.0809897	−	0.996715i	$-0.474192\pi$
$509$	1860.10	0.161979	0.0809897	+	0.996715i	$0.474192\pi$
$510$	4153.56	0.360633
$511$	14569.6	1.26129
$512$	−11464.0	−0.989532
$513$	−1266.72	−0.109019
$514$	−2847.37	−0.244342
$515$	−6671.15	−0.570808
$516$	4881.44	0.416460
$517$	−5033.84	−0.428217
$518$	−5843.56	−0.495659
$519$	3638.87	0.307762
$520$	−8294.70	−0.699513
$521$	18146.6	1.52594	0.762971	−	0.646433i	$-0.223740\pi$
$521$	18146.6	1.52594	0.762971	+	0.646433i	$0.223740\pi$
$522$	−539.051	−0.0451985
$523$	−15101.5	−1.26261	−0.631304	−	0.775536i	$-0.717480\pi$
$523$	−15101.5	−1.26261	−0.631304	+	0.775536i	$0.717480\pi$
$524$	10288.6	0.857746
$525$	1949.28	0.162045
$526$	−5012.67	−0.415519
$527$	−7717.62	−0.637922
$528$	−1333.22	−0.109888
$529$	−10009.3	−0.822662
$530$	3054.84	0.250366
$531$	5076.61	0.414889
$532$	9181.79	0.748273
$533$	−11825.3	−0.960993
$534$	−4500.43	−0.364705
$535$	10834.9	0.875579
$536$	13886.5	1.11904
$537$	5126.72	0.411982
$538$	2225.69	0.178358
$539$	−4892.82	−0.391000
$540$	−2291.48	−0.182611
$541$	−5110.27	−0.406114	−0.203057	−	0.979167i	$-0.565088\pi$
$541$	−5110.27	−0.406114	−0.203057	+	0.979167i	$0.565088\pi$
$542$	2314.50	0.183425
$543$	6020.62	0.475819
$544$	18220.7	1.43604
$545$	−2014.99	−0.158372
$546$	3832.48	0.300393
$547$	−6481.98	−0.506672	−0.253336	−	0.967378i	$-0.581528\pi$
$547$	−6481.98	−0.506672	−0.253336	+	0.967378i	$0.581528\pi$
$548$	21488.3	1.67506
$549$	549.000	0.0426790
$550$	258.095	0.0200095
$551$	−2772.42	−0.214354
$552$	2114.75	0.163061
$553$	10207.3	0.784918
$554$	−4406.83	−0.337957
$555$	7500.61	0.573663
$556$	−4997.11	−0.381160
$557$	15004.3	1.14139	0.570694	−	0.821163i	$-0.306674\pi$
$557$	15004.3	1.14139	0.570694	+	0.821163i	$0.306674\pi$
$558$	−627.284	−0.0475897
$559$	10479.2	0.792889
$560$	13802.2	1.04151
$561$	3703.56	0.278724
$562$	338.706	0.0254225
$563$	10077.7	0.754396	0.377198	−	0.926133i	$-0.376888\pi$
$563$	10077.7	0.754396	0.377198	+	0.926133i	$0.376888\pi$
$564$	−9572.61	−0.714680
$565$	8135.16	0.605750
$566$	1685.14	0.125144
$567$	2273.49	0.168391
$568$	5586.00	0.412647
$569$	−11528.4	−0.849381	−0.424690	−	0.905339i	$-0.639617\pi$
$569$	−11528.4	−0.849381	−0.424690	+	0.905339i	$0.639617\pi$
$570$	1736.33	0.127591
$571$	−2984.22	−0.218714	−0.109357	−	0.994003i	$-0.534879\pi$
$571$	−2984.22	−0.218714	−0.109357	+	0.994003i	$0.534879\pi$
$572$	−3444.30	−0.251772
$573$	−8718.49	−0.635637
$574$	−7491.30	−0.544740
$575$	1075.32	0.0779892
$576$	−1427.88	−0.103290
$577$	−12263.8	−0.884830	−0.442415	−	0.896810i	$-0.645878\pi$
$577$	−12263.8	−0.884830	−0.442415	+	0.896810i	$0.645878\pi$
$578$	−7786.44	−0.560334
$579$	1305.21	0.0936831
$580$	−5015.29	−0.359049
$581$	−34996.9	−2.49900
$582$	−4981.40	−0.354786
$583$	2723.88	0.193502
$584$	7877.40	0.558166
$585$	−4919.25	−0.347668
$586$	−6807.04	−0.479857
$587$	−15161.5	−1.06607	−0.533036	−	0.846093i	$-0.678949\pi$
$587$	−15161.5	−1.06607	−0.533036	+	0.846093i	$0.678949\pi$
$588$	−9304.45	−0.652566
$589$	−3226.22	−0.225695
$590$	−6958.65	−0.485565
$591$	8851.83	0.616101
$592$	8298.77	0.576144
$593$	−1299.14	−0.0899652	−0.0449826	−	0.998988i	$-0.514323\pi$
$593$	−1299.14	−0.0899652	−0.0449826	+	0.998988i	$0.514323\pi$
$594$	301.023	0.0207932
$595$	−38341.1	−2.64173
$596$	−3980.90	−0.273597
$597$	−2690.07	−0.184418
$598$	2114.18	0.144574
$599$	7654.57	0.522132	0.261066	−	0.965321i	$-0.415926\pi$
$599$	7654.57	0.522132	0.261066	+	0.965321i	$0.415926\pi$
$600$	1053.92	0.0717104
$601$	5679.62	0.385485	0.192743	−	0.981249i	$-0.438262\pi$
$601$	5679.62	0.385485	0.192743	+	0.981249i	$0.438262\pi$
$602$	6638.60	0.449450
$603$	8235.49	0.556178
$604$	−13066.9	−0.880272
$605$	1472.77	0.0989698
$606$	−281.928	−0.0188986
$607$	15924.4	1.06483	0.532415	−	0.846484i	$-0.321285\pi$
$607$	15924.4	1.06483	0.532415	+	0.846484i	$0.321285\pi$
$608$	7616.84	0.508065
$609$	4975.92	0.331091
$610$	−752.530	−0.0499493
$611$	−20550.0	−1.36066
$612$	7042.88	0.465182
$613$	−12014.6	−0.791622	−0.395811	−	0.918332i	$-0.629537\pi$
$613$	−12014.6	−0.791622	−0.395811	+	0.918332i	$0.629537\pi$
$614$	2492.31	0.163814
$615$	9615.60	0.630469
$616$	−4685.39	−0.306461
$617$	−12051.5	−0.786343	−0.393171	−	0.919465i	$-0.628622\pi$
$617$	−12051.5	−0.786343	−0.393171	+	0.919465i	$0.628622\pi$
$618$	1666.54	0.108476
$619$	−12790.3	−0.830510	−0.415255	−	0.909705i	$-0.636308\pi$
$619$	−12790.3	−0.830510	−0.415255	+	0.909705i	$0.636308\pi$
$620$	−5836.21	−0.378045
$621$	1254.17	0.0810436
$622$	3469.84	0.223678
$623$	41542.9	2.67156
$624$	−5442.72	−0.349171
$625$	−17982.8	−1.15090
$626$	451.132	0.0288033
$627$	1548.21	0.0986118
$628$	3609.01	0.229324
$629$	−23053.2	−1.46135
$630$	−3116.34	−0.197076
$631$	−18661.2	−1.17732	−0.588660	−	0.808381i	$-0.700344\pi$
$631$	−18661.2	−1.17732	−0.588660	+	0.808381i	$0.700344\pi$
$632$	5518.84	0.347354
$633$	−3032.86	−0.190435
$634$	−2543.28	−0.159316
$635$	−14711.8	−0.919402
$636$	5179.87	0.322948
$637$	−19974.4	−1.24241
$638$	658.840	0.0408836
$639$	3312.83	0.205092
$640$	17766.0	1.09729
$641$	17491.6	1.07781	0.538904	−	0.842367i	$-0.318838\pi$
$641$	17491.6	1.07781	0.538904	+	0.842367i	$0.318838\pi$
$642$	−2706.70	−0.166394
$643$	18321.4	1.12368	0.561839	−	0.827247i	$-0.310094\pi$
$643$	18321.4	1.12368	0.561839	+	0.827247i	$0.310094\pi$
$644$	−9090.83	−0.556256
$645$	−8521.10	−0.520183
$646$	−5336.61	−0.325025
$647$	32546.9	1.97766	0.988832	−	0.149033i	$-0.0476161\pi$
$647$	32546.9	1.97766	0.988832	+	0.149033i	$0.0476161\pi$
$648$	1229.22	0.0745190
$649$	−6204.74	−0.375281
$650$	1053.64	0.0635804
$651$	5790.39	0.348607
$652$	−25322.2	−1.52101
$653$	7792.33	0.466979	0.233490	−	0.972359i	$-0.424985\pi$
$653$	7792.33	0.466979	0.233490	+	0.972359i	$0.424985\pi$
$654$	503.371	0.0300969
$655$	−17959.9	−1.07137
$656$	10638.8	0.633195
$657$	4671.76	0.277417
$658$	−13018.4	−0.771294
$659$	32558.4	1.92457	0.962287	−	0.272035i	$-0.0876965\pi$
$659$	32558.4	1.92457	0.962287	+	0.272035i	$0.0876965\pi$
$660$	2800.70	0.165177
$661$	11278.4	0.663661	0.331831	−	0.943339i	$-0.392334\pi$
$661$	11278.4	0.663661	0.331831	+	0.943339i	$0.392334\pi$
$662$	4626.75	0.271637
$663$	15119.3	0.885651
$664$	−18922.0	−1.10589
$665$	−16027.8	−0.934636
$666$	−1873.75	−0.109018
$667$	2744.96	0.159348
$668$	145.286	0.00841511
$669$	5436.52	0.314182
$670$	−11288.6	−0.650922
$671$	−671.000	−0.0386046
$672$	−13670.6	−0.784756
$673$	−14944.4	−0.855964	−0.427982	−	0.903787i	$-0.640775\pi$
$673$	−14944.4	−0.855964	−0.427982	+	0.903787i	$0.640775\pi$
$674$	10290.3	0.588084
$675$	625.039	0.0356411
$676$	1258.13	0.0715825
$677$	11372.6	0.645617	0.322809	−	0.946464i	$-0.395373\pi$
$677$	11372.6	0.645617	0.322809	+	0.946464i	$0.395373\pi$
$678$	−2032.27	−0.115116
$679$	45982.8	2.59890
$680$	−20730.0	−1.16906
$681$	5881.84	0.330973
$682$	766.680	0.0430465
$683$	23559.0	1.31986	0.659928	−	0.751329i	$-0.270587\pi$
$683$	23559.0	1.31986	0.659928	+	0.751329i	$0.270587\pi$
$684$	2944.16	0.164580
$685$	−37510.3	−2.09225
$686$	−2896.07	−0.161185
$687$	8722.70	0.484413
$688$	−9427.85	−0.522432
$689$	11119.9	0.614854
$690$	−1719.13	−0.0948493
$691$	−30864.1	−1.69917	−0.849584	−	0.527454i	$-0.823147\pi$
$691$	−30864.1	−1.69917	−0.849584	+	0.527454i	$0.823147\pi$
$692$	−8457.60	−0.464609
$693$	−2778.71	−0.152315
$694$	974.959	0.0533270
$695$	8723.02	0.476091
$696$	2690.35	0.146519
$697$	−29553.6	−1.60606
$698$	447.649	0.0242747
$699$	8324.11	0.450424
$700$	−4530.59	−0.244629
$701$	28567.4	1.53919	0.769597	−	0.638530i	$-0.220457\pi$
$701$	28567.4	1.53919	0.769597	+	0.638530i	$0.220457\pi$
$702$	1228.89	0.0660705
$703$	−9636.99	−0.517021
$704$	1745.19	0.0934294
$705$	16710.1	0.892677
$706$	−6097.78	−0.325061
$707$	2602.44	0.138437
$708$	−11799.3	−0.626332
$709$	19611.2	1.03880	0.519402	−	0.854530i	$-0.326155\pi$
$709$	19611.2	1.03880	0.519402	+	0.854530i	$0.326155\pi$
$710$	−4540.99	−0.240029
$711$	3273.00	0.172640
$712$	22461.2	1.18226
$713$	3194.26	0.167778
$714$	9578.09	0.502032
$715$	6012.41	0.314478
$716$	−11915.7	−0.621944
$717$	−4232.98	−0.220479
$718$	27.1761	0.00141254
$719$	−30350.1	−1.57423	−0.787113	−	0.616809i	$-0.788425\pi$
$719$	−30350.1	−1.57423	−0.787113	+	0.616809i	$0.788425\pi$
$720$	4425.69	0.229078
$721$	−15383.6	−0.794614
$722$	4721.04	0.243350
$723$	−14672.8	−0.754754
$724$	−13993.4	−0.718315
$725$	1368.00	0.0700777
$726$	−367.917	−0.0188081
$727$	−16657.4	−0.849778	−0.424889	−	0.905246i	$-0.639687\pi$
$727$	−16657.4	−0.849778	−0.424889	+	0.905246i	$0.639687\pi$
$728$	−19127.5	−0.973783
$729$	729.000	0.0370370
$730$	−6403.72	−0.324674
$731$	26189.7	1.32512
$732$	−1276.01	−0.0644298
$733$	−36065.1	−1.81732	−0.908659	−	0.417539i	$-0.862893\pi$
$733$	−36065.1	−1.81732	−0.908659	+	0.417539i	$0.862893\pi$
$734$	4004.03	0.201351
$735$	16242.0	0.815093
$736$	−7541.39	−0.377689
$737$	−10065.6	−0.503082
$738$	−2402.10	−0.119814
$739$	−9417.73	−0.468791	−0.234396	−	0.972141i	$-0.575311\pi$
$739$	−9417.73	−0.468791	−0.234396	+	0.972141i	$0.575311\pi$
$740$	−17433.2	−0.866024
$741$	6320.38	0.313340
$742$	7044.45	0.348531
$743$	27325.6	1.34923	0.674616	−	0.738169i	$-0.264309\pi$
$743$	27325.6	1.34923	0.674616	+	0.738169i	$0.264309\pi$
$744$	3130.72	0.154271
$745$	6949.11	0.341739
$746$	−1267.00	−0.0621826
$747$	−11221.8	−0.549646
$748$	−8607.97	−0.420773
$749$	24985.3	1.21888
$750$	3769.45	0.183521
$751$	−38528.7	−1.87208	−0.936041	−	0.351892i	$-0.885539\pi$
$751$	−38528.7	−1.87208	−0.936041	+	0.351892i	$0.885539\pi$
$752$	18488.2	0.896537
$753$	−1362.53	−0.0659408
$754$	2689.63	0.129908
$755$	22809.7	1.09951
$756$	−5284.15	−0.254210
$757$	−37566.1	−1.80365	−0.901826	−	0.432100i	$-0.857773\pi$
$757$	−37566.1	−1.80365	−0.901826	+	0.432100i	$0.857773\pi$
$758$	711.640	0.0341002
$759$	−1532.87	−0.0733067
$760$	−8665.85	−0.413610
$761$	−6685.58	−0.318465	−0.159233	−	0.987241i	$-0.550902\pi$
$761$	−6685.58	−0.318465	−0.159233	+	0.987241i	$0.550902\pi$
$762$	3675.20	0.174722
$763$	−4646.56	−0.220468
$764$	20263.9	0.959583
$765$	−12294.1	−0.581040
$766$	14382.8	0.678425
$767$	−25330.1	−1.19246
$768$	−630.497	−0.0296238
$769$	27369.0	1.28342	0.641711	−	0.766947i	$-0.278225\pi$
$769$	27369.0	1.28342	0.641711	+	0.766947i	$0.278225\pi$
$770$	3808.86	0.178262
$771$	8427.93	0.393677
$772$	−3033.61	−0.141428
$773$	15991.4	0.744074	0.372037	−	0.928218i	$-0.378659\pi$
$773$	15991.4	0.744074	0.372037	+	0.928218i	$0.378659\pi$
$774$	2128.68	0.0988551
$775$	1591.92	0.0737851
$776$	24861.7	1.15011
$777$	17296.4	0.798589
$778$	2446.50	0.112739
$779$	−12354.4	−0.568218
$780$	11433.5	0.524853
$781$	−4049.01	−0.185512
$782$	5283.74	0.241619
$783$	1595.54	0.0728223
$784$	17970.3	0.818618
$785$	−6299.94	−0.286439
$786$	4486.61	0.203603
$787$	4826.31	0.218602	0.109301	−	0.994009i	$-0.465139\pi$
$787$	4826.31	0.218602	0.109301	+	0.994009i	$0.465139\pi$
$788$	−20573.8	−0.930089
$789$	14837.0	0.669471
$790$	−4486.39	−0.202049
$791$	18759.6	0.843257
$792$	−1502.38	−0.0674050
$793$	−2739.28	−0.122667
$794$	−14782.8	−0.660731
$795$	−9042.04	−0.403381
$796$	6252.38	0.278404
$797$	−18730.7	−0.832468	−0.416234	−	0.909258i	$-0.636650\pi$
$797$	−18730.7	−0.832468	−0.416234	+	0.909258i	$0.636650\pi$
$798$	4003.96	0.177617
$799$	−51358.5	−2.27401
$800$	−3758.39	−0.166099
$801$	13320.8	0.587601
$802$	−328.573	−0.0144667
$803$	−5709.93	−0.250933
$804$	−19141.3	−0.839628
$805$	15869.1	0.694796
$806$	3129.88	0.136781
$807$	−6587.84	−0.287364
$808$	1407.08	0.0612633
$809$	−9173.98	−0.398690	−0.199345	−	0.979929i	$-0.563881\pi$
$809$	−9173.98	−0.398690	−0.199345	+	0.979929i	$0.563881\pi$
$810$	−999.261	−0.0433462
$811$	−12409.0	−0.537285	−0.268643	−	0.963240i	$-0.586575\pi$
$811$	−12409.0	−0.537285	−0.268643	+	0.963240i	$0.586575\pi$
$812$	−11565.2	−0.499828
$813$	−6850.70	−0.295528
$814$	2290.14	0.0986109
$815$	44202.8	1.89982
$816$	−13602.4	−0.583553
$817$	10948.1	0.468821
$818$	10894.4	0.465667
$819$	−11343.8	−0.483984
$820$	−22349.0	−0.951781
$821$	−6803.25	−0.289202	−0.144601	−	0.989490i	$-0.546190\pi$
$821$	−6803.25	−0.289202	−0.144601	+	0.989490i	$0.546190\pi$
$822$	9370.55	0.397610
$823$	−5822.58	−0.246613	−0.123306	−	0.992369i	$-0.539350\pi$
$823$	−5822.58	−0.246613	−0.123306	+	0.992369i	$0.539350\pi$
$824$	−8317.54	−0.351645
$825$	−763.937	−0.0322386
$826$	−16046.6	−0.675948
$827$	−30593.2	−1.28637	−0.643187	−	0.765709i	$-0.722388\pi$
$827$	−30593.2	−1.28637	−0.643187	+	0.765709i	$0.722388\pi$
$828$	−2914.99	−0.122347
$829$	19979.8	0.837067	0.418534	−	0.908201i	$-0.362544\pi$
$829$	19979.8	0.837067	0.418534	+	0.908201i	$0.362544\pi$
$830$	15382.1	0.643277
$831$	13043.8	0.544506
$832$	7124.53	0.296873
$833$	−49919.8	−2.07637
$834$	−2179.12	−0.0904758
$835$	−253.613	−0.0105110
$836$	−3598.42	−0.148868
$837$	1856.70	0.0766750
$838$	14810.1	0.610511
$839$	33716.9	1.38741	0.693704	−	0.720260i	$-0.255978\pi$
$839$	33716.9	1.38741	0.693704	+	0.720260i	$0.255978\pi$
$840$	15553.4	0.638860
$841$	−20896.9	−0.856816
$842$	−4323.14	−0.176942
$843$	−1002.54	−0.0409599
$844$	7049.11	0.287489
$845$	−2196.21	−0.0894107
$846$	−4174.39	−0.169643
$847$	3396.21	0.137775
$848$	−10004.2	−0.405126
$849$	−4987.85	−0.201629
$850$	2633.25	0.106259
$851$	9541.52	0.384347
$852$	−7699.81	−0.309614
$853$	14815.2	0.594679	0.297340	−	0.954772i	$-0.403901\pi$
$853$	14815.2	0.594679	0.297340	+	0.954772i	$0.403901\pi$
$854$	−1735.33	−0.0695337
$855$	−5139.36	−0.205570
$856$	13508.9	0.539398
$857$	−30413.4	−1.21225	−0.606127	−	0.795368i	$-0.707277\pi$
$857$	−30413.4	−1.21225	−0.606127	+	0.795368i	$0.707277\pi$
$858$	−1501.98	−0.0597630
$859$	10739.8	0.426586	0.213293	−	0.976988i	$-0.431581\pi$
$859$	10739.8	0.426586	0.213293	+	0.976988i	$0.431581\pi$
$860$	19805.1	0.785288
$861$	22173.5	0.877668
$862$	−7615.75	−0.300921
$863$	−309.446	−0.0122059	−0.00610293	−	0.999981i	$-0.501943\pi$
$863$	−309.446	−0.0122059	−0.00610293	+	0.999981i	$0.501943\pi$
$864$	−4383.51	−0.172604
$865$	14763.7	0.580324
$866$	3892.11	0.152724
$867$	23047.1	0.902792
$868$	−13458.3	−0.526271
$869$	−4000.33	−0.156159
$870$	−2187.05	−0.0852275
$871$	−41091.6	−1.59855
$872$	−2512.28	−0.0975647
$873$	14744.5	0.571620
$874$	2208.78	0.0854841
$875$	−34795.4	−1.34434
$876$	−10858.3	−0.418799
$877$	8288.56	0.319139	0.159569	−	0.987187i	$-0.448989\pi$
$877$	8288.56	0.319139	0.159569	+	0.987187i	$0.448989\pi$
$878$	−8190.66	−0.314831
$879$	20148.2	0.773130
$880$	−5409.18	−0.207208
$881$	38527.7	1.47336	0.736682	−	0.676240i	$-0.236392\pi$
$881$	38527.7	1.47336	0.736682	+	0.676240i	$0.236392\pi$
$882$	−4057.45	−0.154900
$883$	35549.5	1.35485	0.677427	−	0.735590i	$-0.263095\pi$
$883$	35549.5	1.35485	0.677427	+	0.735590i	$0.263095\pi$
$884$	−35141.0	−1.33701
$885$	20596.9	0.782326
$886$	1310.76	0.0497017
$887$	−5635.72	−0.213336	−0.106668	−	0.994295i	$-0.534018\pi$
$887$	−5635.72	−0.213336	−0.106668	+	0.994295i	$0.534018\pi$
$888$	9351.71	0.353404
$889$	−33925.4	−1.27989
$890$	−18259.2	−0.687698
$891$	−891.000	−0.0335013
$892$	−12635.8	−0.474302
$893$	−21469.5	−0.804536
$894$	−1735.98	−0.0649438
$895$	20800.2	0.776844
$896$	40968.4	1.52752
$897$	−6257.77	−0.232933
$898$	−9557.67	−0.355171
$899$	4063.70	0.150759
$900$	−1452.74	−0.0538052
$901$	27790.8	1.02757
$902$	2935.90	0.108376
$903$	−19649.6	−0.724140
$904$	10142.9	0.373171
$905$	24427.0	0.897217
$906$	−5698.16	−0.208950
$907$	−23672.9	−0.866644	−0.433322	−	0.901239i	$-0.642659\pi$
$907$	−23672.9	−0.866644	−0.433322	+	0.901239i	$0.642659\pi$
$908$	−13670.8	−0.499650
$909$	834.479	0.0304488
$910$	15549.2	0.566430
$911$	−26640.2	−0.968857	−0.484429	−	0.874831i	$-0.660972\pi$
$911$	−26640.2	−0.968857	−0.484429	+	0.874831i	$0.660972\pi$
$912$	−5686.25	−0.206459
$913$	13715.6	0.497173
$914$	−7497.33	−0.271323
$915$	2227.42	0.0804766
$916$	−20273.7	−0.731289
$917$	−41415.4	−1.49145
$918$	3071.23	0.110420
$919$	−26567.5	−0.953626	−0.476813	−	0.879005i	$-0.658208\pi$
$919$	−26567.5	−0.953626	−0.476813	+	0.879005i	$0.658208\pi$
$920$	8580.00	0.307472
$921$	−7377.01	−0.263931
$922$	4827.52	0.172436
$923$	−16529.6	−0.589468
$924$	6458.40	0.229941
$925$	4755.20	0.169027
$926$	7584.13	0.269147
$927$	−4932.80	−0.174773
$928$	−9594.05	−0.339375
$929$	−9626.04	−0.339957	−0.169979	−	0.985448i	$-0.554370\pi$
$929$	−9626.04	−0.339957	−0.169979	+	0.985448i	$0.554370\pi$
$930$	−2545.03	−0.0897364
$931$	−20868.1	−0.734613
$932$	−19347.2	−0.679978
$933$	−10270.4	−0.360383
$934$	5627.25	0.197140
$935$	15026.2	0.525570
$936$	−6133.28	−0.214180
$937$	−56320.9	−1.96363	−0.981817	−	0.189829i	$-0.939206\pi$
$937$	−56320.9	−1.96363	−0.981817	+	0.189829i	$0.939206\pi$
$938$	−26031.5	−0.906140
$939$	−1335.31	−0.0464069
$940$	−38838.2	−1.34762
$941$	15652.4	0.542248	0.271124	−	0.962544i	$-0.412605\pi$
$941$	15652.4	0.542248	0.271124	+	0.962544i	$0.412605\pi$
$942$	1573.81	0.0544346
$943$	12232.0	0.422406
$944$	22788.7	0.785709
$945$	9224.07	0.317523
$946$	−2601.72	−0.0894178
$947$	42959.5	1.47413	0.737063	−	0.675824i	$-0.236212\pi$
$947$	42959.5	1.47413	0.737063	+	0.675824i	$0.236212\pi$
$948$	−7607.24	−0.260624
$949$	−23310.1	−0.797343
$950$	1100.79	0.0375939
$951$	7527.85	0.256685
$952$	−47803.4	−1.62743
$953$	−51456.6	−1.74905	−0.874524	−	0.484983i	$-0.838826\pi$
$953$	−51456.6	−1.74905	−0.874524	+	0.484983i	$0.838826\pi$
$954$	2258.82	0.0766582
$955$	−35372.9	−1.19857
$956$	9838.48	0.332844
$957$	−1950.10	−0.0658703
$958$	−20046.6	−0.676070
$959$	−86498.5	−2.91260
$960$	−5793.24	−0.194767
$961$	−25062.1	−0.841266
$962$	9349.21	0.313337
$963$	8011.58	0.268089
$964$	34103.1	1.13941
$965$	5295.51	0.176651
$966$	−3964.30	−0.132038
$967$	5630.15	0.187232	0.0936160	−	0.995608i	$-0.470157\pi$
$967$	5630.15	0.187232	0.0936160	+	0.995608i	$0.470157\pi$
$968$	1836.24	0.0609701
$969$	15795.8	0.523669
$970$	−20210.6	−0.668995
$971$	36874.9	1.21871	0.609357	−	0.792896i	$-0.291428\pi$
$971$	36874.9	1.21871	0.609357	+	0.792896i	$0.291428\pi$
$972$	−1694.37	−0.0559126
$973$	20115.2	0.662760
$974$	707.963	0.0232901
$975$	−3118.68	−0.102439
$976$	2464.44	0.0808246
$977$	−12376.9	−0.405293	−0.202646	−	0.979252i	$-0.564954\pi$
$977$	−12376.9	−0.405293	−0.202646	+	0.979252i	$0.564954\pi$
$978$	−11042.4	−0.361041
$979$	−16281.0	−0.531505
$980$	−37750.2	−1.23050
$981$	−1489.93	−0.0484911
$982$	6055.62	0.196785
$983$	−48480.0	−1.57301	−0.786507	−	0.617581i	$-0.788113\pi$
$983$	−48480.0	−1.57301	−0.786507	+	0.617581i	$0.788113\pi$
$984$	11988.7	0.388399
$985$	35913.8	1.16174
$986$	6721.91	0.217109
$987$	38533.3	1.24268
$988$	−14690.1	−0.473031
$989$	−10839.7	−0.348516
$990$	1221.32	0.0392081
$991$	46865.6	1.50226	0.751128	−	0.660157i	$-0.229510\pi$
$991$	46865.6	1.50226	0.751128	+	0.660157i	$0.229510\pi$
$992$	−11164.4	−0.357330
$993$	−13694.7	−0.437653
$994$	−10471.5	−0.334141
$995$	−10914.2	−0.347743
$996$	26082.3	0.829767
$997$	4022.29	0.127770	0.0638852	−	0.997957i	$-0.479651\pi$
$997$	4022.29	0.127770	0.0638852	+	0.997957i	$0.479651\pi$
$998$	−7497.15	−0.237794
$999$	5546.11	0.175647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.h.1.16	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.h.1.16	✓	39	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.01355 q^{2} +3.00000 q^{3} -6.97272 q^{4} +12.1717 q^{5} -3.04064 q^{6} +28.0678 q^{7} +15.1756 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.01355 q^{2} +3.00000 q^{3} -6.97272 q^{4} +12.1717 q^{5} -3.04064 q^{6} +28.0678 q^{7} +15.1756 q^{8} +9.00000 q^{9} -12.3366 q^{10} -11.0000 q^{11} -20.9182 q^{12} -44.9062 q^{13} -28.4480 q^{14} +36.5150 q^{15} +40.4007 q^{16} -112.229 q^{17} -9.12192 q^{18} -46.9155 q^{19} -84.8697 q^{20} +84.2034 q^{21} +11.1490 q^{22} +46.4507 q^{23} +45.5267 q^{24} +23.1496 q^{25} +45.5145 q^{26} +27.0000 q^{27} -195.709 q^{28} +59.0940 q^{29} -37.0097 q^{30} +68.7667 q^{31} -162.352 q^{32} -33.0000 q^{33} +113.749 q^{34} +341.632 q^{35} -62.7545 q^{36} +205.412 q^{37} +47.5510 q^{38} -134.718 q^{39} +184.712 q^{40} +263.333 q^{41} -85.3441 q^{42} -233.359 q^{43} +76.7000 q^{44} +109.545 q^{45} -47.0800 q^{46} +457.622 q^{47} +121.202 q^{48} +444.802 q^{49} -23.4632 q^{50} -336.687 q^{51} +313.118 q^{52} -247.625 q^{53} -27.3658 q^{54} -133.888 q^{55} +425.945 q^{56} -140.746 q^{57} -59.8945 q^{58} +564.067 q^{59} -254.609 q^{60} +61.0000 q^{61} -69.6982 q^{62} +252.610 q^{63} -158.654 q^{64} -546.583 q^{65} +33.4470 q^{66} +915.055 q^{67} +782.542 q^{68} +139.352 q^{69} -346.260 q^{70} +368.092 q^{71} +136.580 q^{72} +519.085 q^{73} -208.194 q^{74} +69.4488 q^{75} +327.129 q^{76} -308.746 q^{77} +136.543 q^{78} +363.667 q^{79} +491.744 q^{80} +81.0000 q^{81} -266.900 q^{82} -1246.87 q^{83} -587.127 q^{84} -1366.02 q^{85} +236.520 q^{86} +177.282 q^{87} -166.931 q^{88} +1480.09 q^{89} -111.029 q^{90} -1260.42 q^{91} -323.888 q^{92} +206.300 q^{93} -463.821 q^{94} -571.040 q^{95} -487.057 q^{96} +1638.27 q^{97} -450.828 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9	\( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 39 * q + 8 * q^2 + 117 * q^3 + 154 * q^4 + 65 * q^5 + 24 * q^6 + 35 * q^7 + 75 * q^8 + 351 * q^9 - 21 * q^10 - 429 * q^11 + 462 * q^12 - 27 * q^13 + 164 * q^14 + 195 * q^15 + 686 * q^16 + 170 * q^17 + 72 * q^18 + 139 * q^19 + 1056 * q^20 + 105 * q^21 - 88 * q^22 + 291 * q^23 + 225 * q^24 + 1236 * q^25 + 583 * q^26 + 1053 * q^27 + 976 * q^28 + 374 * q^29 - 63 * q^30 + 232 * q^31 + 933 * q^32 - 1287 * q^33 + 332 * q^34 + 626 * q^35 + 1386 * q^36 + 232 * q^37 + 989 * q^38 - 81 * q^39 - 263 * q^40 + 1014 * q^41 + 492 * q^42 + 515 * q^43 - 1694 * q^44 + 585 * q^45 - 371 * q^46 + 2005 * q^47 + 2058 * q^48 + 2064 * q^49 + 4582 * q^50 + 510 * q^51 + 216 * q^52 + 1485 * q^53 + 216 * q^54 - 715 * q^55 + 2307 * q^56 + 417 * q^57 + 573 * q^58 + 2749 * q^59 + 3168 * q^60 + 2379 * q^61 + 1837 * q^62 + 315 * q^63 + 7295 * q^64 + 3630 * q^65 - 264 * q^66 + 3575 * q^67 + 2630 * q^68 + 873 * q^69 + 4218 * q^70 + 4723 * q^71 + 675 * q^72 + 859 * q^73 + 4232 * q^74 + 3708 * q^75 + 2466 * q^76 - 385 * q^77 + 1749 * q^78 - 1887 * q^79 + 8933 * q^80 + 3159 * q^81 + 6806 * q^82 + 5609 * q^83 + 2928 * q^84 - 565 * q^85 + 5185 * q^86 + 1122 * q^87 - 825 * q^88 + 6725 * q^89 - 189 * q^90 + 2808 * q^91 + 3257 * q^92 + 696 * q^93 + 3184 * q^94 + 3216 * q^95 + 2799 * q^96 + 3512 * q^97 + 4464 * q^98 - 3861 * q^99

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